id	sid	tid	token	lemma	pos
ejpam-5857	1	1	european	european	PROPN
ejpam-5857	1	2	journal	journal	PROPN
ejpam-5857	1	3	of	of	ADP
ejpam-5857	1	4	pure	pure	ADJ
ejpam-5857	1	5	and	and	CCONJ
ejpam-5857	1	6	applied	applied	ADJ
ejpam-5857	1	7	mathematics	mathematic	NOUN
ejpam-5857	1	8	2025	2025	NUM
ejpam-5857	1	9	,	,	PUNCT
ejpam-5857	1	10	vol	vol	NOUN
ejpam-5857	1	11	.	.	PROPN
ejpam-5857	1	12	18	18	NUM
ejpam-5857	1	13	,	,	PUNCT
ejpam-5857	1	14	issue	issue	NOUN
ejpam-5857	1	15	2	2	NUM
ejpam-5857	1	16	,	,	PUNCT
ejpam-5857	1	17	article	article	NOUN
ejpam-5857	1	18	number	number	NOUN
ejpam-5857	1	19	5857	5857	NUM
ejpam-5857	1	20	issn	issn	VERB
ejpam-5857	1	21	1307	1307	NUM
ejpam-5857	1	22	-	-	SYM
ejpam-5857	1	23	5543	5543	NUM
ejpam-5857	1	24	–	–	PUNCT
ejpam-5857	1	25	ejpam.com	ejpam.com	X
ejpam-5857	1	26	published	publish	VERB
ejpam-5857	1	27	by	by	ADP
ejpam-5857	1	28	new	new	PROPN
ejpam-5857	1	29	york	york	PROPN
ejpam-5857	1	30	business	business	PROPN
ejpam-5857	1	31	global	global	ADJ
ejpam-5857	1	32	structural	structural	ADJ
ejpam-5857	1	33	insights	insight	NOUN
ejpam-5857	1	34	into	into	ADP
ejpam-5857	1	35	iup	iup	NOUN
ejpam-5857	1	36	-	-	PUNCT
ejpam-5857	1	37	algebras	algebras	PROPN
ejpam-5857	1	38	via	via	ADP
ejpam-5857	1	39	intuitionistic	intuitionistic	ADJ
ejpam-5857	1	40	neutrosophic	neutrosophic	ADJ
ejpam-5857	1	41	set	set	NOUN
ejpam-5857	1	42	theory	theory	NOUN
ejpam-5857	1	43	kannirun	kannirun	VERB
ejpam-5857	1	44	suayngam1	suayngam1	PROPN
ejpam-5857	1	45	,	,	PUNCT
ejpam-5857	1	46	pongpun	pongpun	PROPN
ejpam-5857	1	47	julatha2	julatha2	PROPN
ejpam-5857	1	48	,	,	PUNCT
ejpam-5857	1	49	warud	warud	NOUN
ejpam-5857	1	50	nakkhasen3	nakkhasen3	PROPN
ejpam-5857	1	51	,	,	PUNCT
ejpam-5857	1	52	aiyared	aiyare	VERB
ejpam-5857	1	53	iampan1,∗	iampan1,∗	NOUN
ejpam-5857	1	54	1	1	NUM
ejpam-5857	1	55	department	department	NOUN
ejpam-5857	1	56	of	of	ADP
ejpam-5857	1	57	mathematics	mathematic	NOUN
ejpam-5857	1	58	,	,	PUNCT
ejpam-5857	1	59	school	school	NOUN
ejpam-5857	1	60	of	of	ADP
ejpam-5857	1	61	science	science	NOUN
ejpam-5857	1	62	,	,	PUNCT
ejpam-5857	1	63	university	university	NOUN
ejpam-5857	1	64	of	of	ADP
ejpam-5857	1	65	phayao	phayao	NOUN
ejpam-5857	1	66	,	,	PUNCT
ejpam-5857	1	67	mae	mae	PROPN
ejpam-5857	1	68	ka	ka	PROPN
ejpam-5857	1	69	,	,	PUNCT
ejpam-5857	1	70	mueang	mueang	PROPN
ejpam-5857	1	71	,	,	PUNCT
ejpam-5857	1	72	phayao	phayao	NOUN
ejpam-5857	1	73	56000	56000	NUM
ejpam-5857	1	74	,	,	PUNCT
ejpam-5857	1	75	thailand	thailand	PROPN
ejpam-5857	1	76	2	2	NUM
ejpam-5857	1	77	department	department	NOUN
ejpam-5857	1	78	of	of	ADP
ejpam-5857	1	79	mathematics	mathematic	NOUN
ejpam-5857	1	80	,	,	PUNCT
ejpam-5857	1	81	faculty	faculty	NOUN
ejpam-5857	1	82	of	of	ADP
ejpam-5857	1	83	science	science	NOUN
ejpam-5857	1	84	and	and	CCONJ
ejpam-5857	1	85	technology	technology	NOUN
ejpam-5857	1	86	,	,	PUNCT
ejpam-5857	1	87	pibulsongkram	pibulsongkram	PROPN
ejpam-5857	1	88	rajabhat	rajabhat	PROPN
ejpam-5857	1	89	university	university	NOUN
ejpam-5857	1	90	,	,	PUNCT
ejpam-5857	1	91	phitsanulok	phitsanulok	NOUN
ejpam-5857	1	92	65000	65000	NUM
ejpam-5857	1	93	,	,	PUNCT
ejpam-5857	1	94	thailand	thailand	PROPN
ejpam-5857	1	95	3	3	NUM
ejpam-5857	1	96	department	department	NOUN
ejpam-5857	1	97	of	of	ADP
ejpam-5857	1	98	mathematics	mathematic	NOUN
ejpam-5857	1	99	,	,	PUNCT
ejpam-5857	1	100	faculty	faculty	NOUN
ejpam-5857	1	101	of	of	ADP
ejpam-5857	1	102	science	science	NOUN
ejpam-5857	1	103	,	,	PUNCT
ejpam-5857	1	104	mahasarakham	mahasarakham	PROPN
ejpam-5857	1	105	university	university	PROPN
ejpam-5857	1	106	,	,	PUNCT
ejpam-5857	1	107	khamriang	khamriang	PROPN
ejpam-5857	1	108	,	,	PUNCT
ejpam-5857	1	109	kantarawichai	kantarawichai	PROPN
ejpam-5857	1	110	,	,	PUNCT
ejpam-5857	1	111	maha	maha	PROPN
ejpam-5857	1	112	sarakham	sarakham	PROPN
ejpam-5857	1	113	44150	44150	NUM
ejpam-5857	1	114	,	,	PUNCT
ejpam-5857	1	115	thailand	thailand	PROPN
ejpam-5857	1	116	abstract	abstract	PROPN
ejpam-5857	1	117	.	.	PUNCT
ejpam-5857	2	1	this	this	DET
ejpam-5857	2	2	paper	paper	NOUN
ejpam-5857	2	3	introduces	introduce	NOUN
ejpam-5857	2	4	and	and	CCONJ
ejpam-5857	2	5	explores	explore	VERB
ejpam-5857	2	6	the	the	DET
ejpam-5857	2	7	concepts	concept	NOUN
ejpam-5857	2	8	of	of	ADP
ejpam-5857	2	9	intuitionistic	intuitionistic	ADJ
ejpam-5857	2	10	neutrosophic	neutrosophic	ADJ
ejpam-5857	2	11	iupsubalgebras	iupsubalgebra	NOUN
ejpam-5857	2	12	,	,	PUNCT
ejpam-5857	2	13	iup	iup	NOUN
ejpam-5857	2	14	-	-	PUNCT
ejpam-5857	2	15	ideals	ideal	NOUN
ejpam-5857	2	16	,	,	PUNCT
ejpam-5857	2	17	iup	iup	NOUN
ejpam-5857	2	18	-	-	PUNCT
ejpam-5857	2	19	filters	filter	NOUN
ejpam-5857	2	20	and	and	CCONJ
ejpam-5857	2	21	strong	strong	ADJ
ejpam-5857	2	22	iup	iup	NOUN
ejpam-5857	2	23	-	-	PUNCT
ejpam-5857	2	24	ideals	ideal	NOUN
ejpam-5857	2	25	within	within	ADP
ejpam-5857	2	26	the	the	DET
ejpam-5857	2	27	framework	framework	NOUN
ejpam-5857	2	28	of	of	ADP
ejpam-5857	2	29	iup	iup	NOUN
ejpam-5857	2	30	-	-	PUNCT
ejpam-5857	2	31	algebras	algebras	PROPN
ejpam-5857	2	32	.	.	PUNCT
ejpam-5857	3	1	by	by	ADP
ejpam-5857	3	2	leveraging	leverage	VERB
ejpam-5857	3	3	the	the	DET
ejpam-5857	3	4	principles	principle	NOUN
ejpam-5857	3	5	of	of	ADP
ejpam-5857	3	6	complement	complement	NOUN
ejpam-5857	3	7	,	,	PUNCT
ejpam-5857	3	8	characteristic	characteristic	ADJ
ejpam-5857	3	9	and	and	CCONJ
ejpam-5857	3	10	level	level	NOUN
ejpam-5857	3	11	subsets	subset	NOUN
ejpam-5857	3	12	,	,	PUNCT
ejpam-5857	3	13	we	we	PRON
ejpam-5857	3	14	present	present	VERB
ejpam-5857	3	15	a	a	DET
ejpam-5857	3	16	detailed	detailed	ADJ
ejpam-5857	3	17	analysis	analysis	NOUN
ejpam-5857	3	18	of	of	ADP
ejpam-5857	3	19	their	their	PRON
ejpam-5857	3	20	structural	structural	ADJ
ejpam-5857	3	21	properties	property	NOUN
ejpam-5857	3	22	and	and	CCONJ
ejpam-5857	3	23	interrelationships	interrelationship	NOUN
ejpam-5857	3	24	.	.	PUNCT
ejpam-5857	4	1	these	these	DET
ejpam-5857	4	2	innovative	innovative	ADJ
ejpam-5857	4	3	approaches	approach	NOUN
ejpam-5857	4	4	not	not	PART
ejpam-5857	4	5	only	only	ADV
ejpam-5857	4	6	enhance	enhance	VERB
ejpam-5857	4	7	the	the	DET
ejpam-5857	4	8	theoretical	theoretical	ADJ
ejpam-5857	4	9	foundations	foundation	NOUN
ejpam-5857	4	10	of	of	ADP
ejpam-5857	4	11	intuitionistic	intuitionistic	ADJ
ejpam-5857	4	12	neutrosophic	neutrosophic	ADJ
ejpam-5857	4	13	set	set	NOUN
ejpam-5857	4	14	theory	theory	NOUN
ejpam-5857	4	15	but	but	CCONJ
ejpam-5857	4	16	also	also	ADV
ejpam-5857	4	17	provide	provide	VERB
ejpam-5857	4	18	new	new	ADJ
ejpam-5857	4	19	insights	insight	NOUN
ejpam-5857	4	20	into	into	ADP
ejpam-5857	4	21	managing	manage	VERB
ejpam-5857	4	22	uncertainty	uncertainty	NOUN
ejpam-5857	4	23	in	in	ADP
ejpam-5857	4	24	algebraic	algebraic	ADJ
ejpam-5857	4	25	structures	structure	NOUN
ejpam-5857	4	26	.	.	PUNCT
ejpam-5857	5	1	the	the	DET
ejpam-5857	5	2	findings	finding	NOUN
ejpam-5857	5	3	contribute	contribute	VERB
ejpam-5857	5	4	significantly	significantly	ADV
ejpam-5857	5	5	to	to	ADP
ejpam-5857	5	6	the	the	DET
ejpam-5857	5	7	advancement	advancement	NOUN
ejpam-5857	5	8	of	of	ADP
ejpam-5857	5	9	algebraic	algebraic	ADJ
ejpam-5857	5	10	logic	logic	NOUN
ejpam-5857	5	11	,	,	PUNCT
ejpam-5857	5	12	offering	offer	VERB
ejpam-5857	5	13	novel	novel	ADJ
ejpam-5857	5	14	perspectives	perspective	NOUN
ejpam-5857	5	15	for	for	ADP
ejpam-5857	5	16	handling	handle	VERB
ejpam-5857	5	17	indeterminate	indeterminate	ADJ
ejpam-5857	5	18	,	,	PUNCT
ejpam-5857	5	19	ambiguous	ambiguous	ADJ
ejpam-5857	5	20	and	and	CCONJ
ejpam-5857	5	21	incomplete	incomplete	ADJ
ejpam-5857	5	22	information	information	NOUN
ejpam-5857	5	23	in	in	ADP
ejpam-5857	5	24	mathematical	mathematical	ADJ
ejpam-5857	5	25	systems	system	NOUN
ejpam-5857	5	26	.	.	PUNCT
ejpam-5857	6	1	this	this	DET
ejpam-5857	6	2	study	study	NOUN
ejpam-5857	6	3	lays	lay	VERB
ejpam-5857	6	4	the	the	DET
ejpam-5857	6	5	groundwork	groundwork	NOUN
ejpam-5857	6	6	for	for	ADP
ejpam-5857	6	7	future	future	ADJ
ejpam-5857	6	8	research	research	NOUN
ejpam-5857	6	9	and	and	CCONJ
ejpam-5857	6	10	potential	potential	ADJ
ejpam-5857	6	11	applications	application	NOUN
ejpam-5857	6	12	of	of	ADP
ejpam-5857	6	13	intuitionistic	intuitionistic	ADJ
ejpam-5857	6	14	neutrosophic	neutrosophic	ADJ
ejpam-5857	6	15	iup	iup	NOUN
ejpam-5857	6	16	-	-	PUNCT
ejpam-5857	6	17	algebras	algebras	PROPN
ejpam-5857	6	18	in	in	ADP
ejpam-5857	6	19	areas	area	NOUN
ejpam-5857	6	20	such	such	ADJ
ejpam-5857	6	21	as	as	ADP
ejpam-5857	6	22	decision	decision	NOUN
ejpam-5857	6	23	-	-	PUNCT
ejpam-5857	6	24	making	making	NOUN
ejpam-5857	6	25	,	,	PUNCT
ejpam-5857	6	26	computational	computational	ADJ
ejpam-5857	6	27	intelligence	intelligence	NOUN
ejpam-5857	6	28	and	and	CCONJ
ejpam-5857	6	29	information	information	NOUN
ejpam-5857	6	30	theory	theory	NOUN
ejpam-5857	6	31	.	.	PUNCT
ejpam-5857	7	1	2020	2020	NUM
ejpam-5857	7	2	mathematics	mathematic	NOUN
ejpam-5857	7	3	subject	subject	NOUN
ejpam-5857	7	4	classifications	classification	NOUN
ejpam-5857	7	5	:	:	PUNCT
ejpam-5857	7	6	03g25	03g25	NUM
ejpam-5857	7	7	,	,	PUNCT
ejpam-5857	7	8	03e72	03e72	NUM
ejpam-5857	7	9	,	,	PUNCT
ejpam-5857	7	10	03b60	03b60	NOUN
ejpam-5857	7	11	key	key	ADJ
ejpam-5857	7	12	words	word	NOUN
ejpam-5857	7	13	and	and	CCONJ
ejpam-5857	7	14	phrases	phrase	NOUN
ejpam-5857	7	15	:	:	PUNCT
ejpam-5857	7	16	iup	iup	NOUN
ejpam-5857	7	17	-	-	PUNCT
ejpam-5857	7	18	algebra	algebra	PROPN
ejpam-5857	7	19	,	,	PUNCT
ejpam-5857	7	20	intuitionistic	intuitionistic	ADJ
ejpam-5857	7	21	neutrosophic	neutrosophic	ADJ
ejpam-5857	7	22	set	set	NOUN
ejpam-5857	7	23	,	,	PUNCT
ejpam-5857	7	24	intuitionistic	intuitionistic	ADJ
ejpam-5857	7	25	neutrosophic	neutrosophic	ADJ
ejpam-5857	7	26	iup	iup	NOUN
ejpam-5857	7	27	-	-	PUNCT
ejpam-5857	7	28	subalgebra	subalgebra	PROPN
ejpam-5857	7	29	,	,	PUNCT
ejpam-5857	7	30	intuitionistic	intuitionistic	ADJ
ejpam-5857	7	31	neutrosophic	neutrosophic	ADJ
ejpam-5857	7	32	iup	iup	NOUN
ejpam-5857	7	33	-	-	PUNCT
ejpam-5857	7	34	ideal	ideal	NOUN
ejpam-5857	7	35	,	,	PUNCT
ejpam-5857	7	36	intuitionistic	intuitionistic	ADJ
ejpam-5857	7	37	neutrosophic	neutrosophic	ADJ
ejpam-5857	7	38	iup	iup	NOUN
ejpam-5857	7	39	-	-	PUNCT
ejpam-5857	7	40	filter	filter	NOUN
ejpam-5857	7	41	,	,	PUNCT
ejpam-5857	7	42	intuitionistic	intuitionistic	ADJ
ejpam-5857	7	43	neutrosophic	neutrosophic	ADJ
ejpam-5857	7	44	strong	strong	ADJ
ejpam-5857	7	45	iup	iup	NOUN
ejpam-5857	7	46	-	-	PUNCT
ejpam-5857	7	47	ideal	ideal	NOUN
ejpam-5857	7	48	1	1	NUM
ejpam-5857	7	49	.	.	PUNCT
ejpam-5857	7	50	introduction	introduction	NOUN
ejpam-5857	7	51	in	in	ADP
ejpam-5857	7	52	1965	1965	NUM
ejpam-5857	7	53	,	,	PUNCT
ejpam-5857	7	54	zadeh	zadeh	PROPN
ejpam-5857	8	1	[	[	X
ejpam-5857	8	2	16	16	NUM
ejpam-5857	8	3	]	]	PUNCT
ejpam-5857	8	4	introduced	introduce	VERB
ejpam-5857	8	5	the	the	DET
ejpam-5857	8	6	concept	concept	NOUN
ejpam-5857	8	7	of	of	ADP
ejpam-5857	8	8	fuzzy	fuzzy	ADJ
ejpam-5857	8	9	set	set	NOUN
ejpam-5857	8	10	(	(	PUNCT
ejpam-5857	8	11	fs	fs	NOUN
ejpam-5857	8	12	)	)	PUNCT
ejpam-5857	8	13	theory	theory	NOUN
ejpam-5857	8	14	as	as	ADP
ejpam-5857	8	15	a	a	DET
ejpam-5857	8	16	means	means	NOUN
ejpam-5857	8	17	to	to	PART
ejpam-5857	8	18	manage	manage	VERB
ejpam-5857	8	19	vague	vague	ADJ
ejpam-5857	8	20	and	and	CCONJ
ejpam-5857	8	21	uncertain	uncertain	ADJ
ejpam-5857	8	22	information	information	NOUN
ejpam-5857	8	23	,	,	PUNCT
ejpam-5857	8	24	addressing	address	VERB
ejpam-5857	8	25	limitations	limitation	NOUN
ejpam-5857	8	26	inherent	inherent	ADJ
ejpam-5857	8	27	in	in	ADP
ejpam-5857	8	28	classical	classical	ADJ
ejpam-5857	8	29	set	set	NOUN
ejpam-5857	8	30	theory	theory	NOUN
ejpam-5857	8	31	.	.	PUNCT
ejpam-5857	9	1	this	this	DET
ejpam-5857	9	2	groundbreaking	groundbreake	VERB
ejpam-5857	9	3	framework	framework	NOUN
ejpam-5857	9	4	proved	prove	VERB
ejpam-5857	9	5	to	to	PART
ejpam-5857	9	6	be	be	AUX
ejpam-5857	9	7	both	both	CCONJ
ejpam-5857	9	8	practical	practical	ADJ
ejpam-5857	9	9	and	and	CCONJ
ejpam-5857	9	10	significant	significant	ADJ
ejpam-5857	9	11	,	,	PUNCT
ejpam-5857	9	12	particularly	particularly	ADV
ejpam-5857	9	13	for	for	ADP
ejpam-5857	9	14	scenarios	scenario	NOUN
ejpam-5857	9	15	involving	involve	VERB
ejpam-5857	9	16	incomplete	incomplete	ADJ
ejpam-5857	9	17	or	or	CCONJ
ejpam-5857	9	18	ambiguous	ambiguous	ADJ
ejpam-5857	9	19	data	datum	NOUN
ejpam-5857	9	20	where	where	SCONJ
ejpam-5857	9	21	truth	truth	NOUN
ejpam-5857	9	22	and	and	CCONJ
ejpam-5857	9	23	falsehood	falsehood	NOUN
ejpam-5857	9	24	can	can	AUX
ejpam-5857	9	25	not	not	PART
ejpam-5857	9	26	be	be	AUX
ejpam-5857	9	27	definitively	definitively	ADV
ejpam-5857	9	28	determined	determine	VERB
ejpam-5857	9	29	.	.	PUNCT
ejpam-5857	10	1	fuzzy	fuzzy	ADJ
ejpam-5857	10	2	set	set	PROPN
ejpam-5857	10	3	theory	theory	NOUN
ejpam-5857	10	4	provided	provide	VERB
ejpam-5857	10	5	a	a	DET
ejpam-5857	10	6	more	more	ADV
ejpam-5857	10	7	nuanced	nuanced	ADJ
ejpam-5857	10	8	approach	approach	NOUN
ejpam-5857	10	9	to	to	ADP
ejpam-5857	10	10	representing	represent	VERB
ejpam-5857	10	11	ambiguity	ambiguity	NOUN
ejpam-5857	10	12	,	,	PUNCT
ejpam-5857	10	13	thereby	thereby	ADV
ejpam-5857	10	14	facilitating	facilitate	VERB
ejpam-5857	10	15	more	more	ADV
ejpam-5857	10	16	effective	effective	ADJ
ejpam-5857	10	17	modeling	modeling	NOUN
ejpam-5857	10	18	and	and	CCONJ
ejpam-5857	10	19	analysis	analysis	NOUN
ejpam-5857	10	20	of	of	ADP
ejpam-5857	10	21	∗corresponding	∗corresponde	VERB
ejpam-5857	10	22	author	author	NOUN
ejpam-5857	10	23	.	.	PUNCT
ejpam-5857	11	1	doi	doi	NOUN
ejpam-5857	11	2	:	:	PUNCT
ejpam-5857	11	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5857	https://doi.org/10.29020/nybg.ejpam.v18i2.5857	ADJ
ejpam-5857	11	4	email	email	NOUN
ejpam-5857	11	5	addresses	address	NOUN
ejpam-5857	11	6	:	:	PUNCT
ejpam-5857	12	1	kannirun.s@gmail.com	kannirun.s@gmail.com	X
ejpam-5857	12	2	(	(	PUNCT
ejpam-5857	12	3	k.	k.	NOUN
ejpam-5857	12	4	suayngam	suayngam	PROPN
ejpam-5857	12	5	)	)	PUNCT
ejpam-5857	12	6	,	,	PUNCT
ejpam-5857	12	7	pongpun.j@psru.ac.th	pongpun.j@psru.ac.th	PROPN
ejpam-5857	12	8	(	(	PUNCT
ejpam-5857	12	9	p.	p.	NOUN
ejpam-5857	12	10	julatha	julatha	NOUN
ejpam-5857	12	11	)	)	PUNCT
ejpam-5857	12	12	,	,	PUNCT
ejpam-5857	12	13	warud.n@msu.ac.th	warud.n@msu.ac.th	PRON
ejpam-5857	12	14	(	(	PUNCT
ejpam-5857	12	15	w.	w.	PROPN
ejpam-5857	12	16	nakkhasen	nakkhasen	PROPN
ejpam-5857	12	17	)	)	PUNCT
ejpam-5857	12	18	,	,	PUNCT
ejpam-5857	12	19	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-5857	12	20	(	(	PUNCT
ejpam-5857	12	21	a.	a.	NOUN
ejpam-5857	12	22	iampan	iampan	PROPN
ejpam-5857	12	23	)	)	PUNCT
ejpam-5857	12	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5857	12	25	1	1	NUM
ejpam-5857	12	26	copyright	copyright	NOUN
ejpam-5857	12	27	:	:	PUNCT
ejpam-5857	12	28	©	©	PROPN
ejpam-5857	12	29	2025	2025	NUM
ejpam-5857	12	30	the	the	DET
ejpam-5857	12	31	author(s	author(s	NOUN
ejpam-5857	12	32	)	)	PUNCT
ejpam-5857	12	33	.	.	PUNCT
ejpam-5857	13	1	(	(	PUNCT
ejpam-5857	13	2	cc	cc	NOUN
ejpam-5857	13	3	by	by	ADP
ejpam-5857	13	4	-	-	PUNCT
ejpam-5857	13	5	nc	nc	PROPN
ejpam-5857	13	6	4.0	4.0	NUM
ejpam-5857	13	7	)	)	PUNCT
ejpam-5857	13	8	k.	k.	NOUN
ejpam-5857	13	9	suayngam	suayngam	PROPN
ejpam-5857	13	10	,	,	PUNCT
ejpam-5857	13	11	p.	p.	NOUN
ejpam-5857	13	12	julatha	julatha	PROPN
ejpam-5857	13	13	,	,	PUNCT
ejpam-5857	13	14	w.	w.	PROPN
ejpam-5857	13	15	nakkhasen	nakkhasen	PROPN
ejpam-5857	13	16	,	,	PUNCT
ejpam-5857	13	17	a.	a.	NOUN
ejpam-5857	13	18	iampan	iampan	PROPN
ejpam-5857	13	19	/	/	SYM
ejpam-5857	13	20	eur	eur	PROPN
ejpam-5857	13	21	.	.	PUNCT
ejpam-5857	14	1	j.	j.	PROPN
ejpam-5857	14	2	pure	pure	PROPN
ejpam-5857	14	3	appl	appl	PROPN
ejpam-5857	14	4	.	.	PROPN
ejpam-5857	14	5	math	math	PROPN
ejpam-5857	14	6	,	,	PUNCT
ejpam-5857	14	7	18	18	NUM
ejpam-5857	14	8	(	(	PUNCT
ejpam-5857	14	9	2	2	NUM
ejpam-5857	14	10	)	)	PUNCT
ejpam-5857	14	11	(	(	PUNCT
ejpam-5857	14	12	2025	2025	NUM
ejpam-5857	14	13	)	)	PUNCT
ejpam-5857	14	14	,	,	PUNCT
ejpam-5857	14	15	5857	5857	NUM
ejpam-5857	14	16	2	2	NUM
ejpam-5857	14	17	of	of	ADP
ejpam-5857	14	18	30	30	NUM
ejpam-5857	14	19	uncertainty	uncertainty	NOUN
ejpam-5857	14	20	-	-	PUNCT
ejpam-5857	14	21	laden	laden	ADJ
ejpam-5857	14	22	information	information	NOUN
ejpam-5857	14	23	.	.	PUNCT
ejpam-5857	15	1	building	build	VERB
ejpam-5857	15	2	on	on	ADP
ejpam-5857	15	3	this	this	DET
ejpam-5857	15	4	foundation	foundation	NOUN
ejpam-5857	15	5	,	,	PUNCT
ejpam-5857	15	6	atanassov	atanassov	VERB
ejpam-5857	16	1	[	[	X
ejpam-5857	16	2	1	1	X
ejpam-5857	16	3	]	]	PUNCT
ejpam-5857	16	4	in	in	ADP
ejpam-5857	16	5	1986	1986	NUM
ejpam-5857	16	6	proposed	propose	VERB
ejpam-5857	16	7	the	the	DET
ejpam-5857	16	8	concept	concept	NOUN
ejpam-5857	16	9	of	of	ADP
ejpam-5857	16	10	intuitionistic	intuitionistic	ADJ
ejpam-5857	16	11	fuzzy	fuzzy	ADJ
ejpam-5857	16	12	sets	set	NOUN
ejpam-5857	16	13	(	(	PUNCT
ejpam-5857	16	14	ifss	ifss	NOUN
ejpam-5857	16	15	)	)	PUNCT
ejpam-5857	16	16	,	,	PUNCT
ejpam-5857	16	17	an	an	DET
ejpam-5857	16	18	extension	extension	NOUN
ejpam-5857	16	19	of	of	ADP
ejpam-5857	16	20	fs	fs	ADP
ejpam-5857	16	21	theory	theory	NOUN
ejpam-5857	16	22	that	that	PRON
ejpam-5857	16	23	introduced	introduce	VERB
ejpam-5857	16	24	a	a	DET
ejpam-5857	16	25	non	non	ADJ
ejpam-5857	16	26	-	-	ADJ
ejpam-5857	16	27	membership	membership	ADJ
ejpam-5857	16	28	degree	degree	NOUN
ejpam-5857	16	29	alongside	alongside	ADP
ejpam-5857	16	30	the	the	DET
ejpam-5857	16	31	membership	membership	NOUN
ejpam-5857	16	32	degree	degree	NOUN
ejpam-5857	16	33	.	.	PUNCT
ejpam-5857	17	1	these	these	DET
ejpam-5857	17	2	two	two	NUM
ejpam-5857	17	3	degrees	degree	NOUN
ejpam-5857	17	4	collectively	collectively	ADV
ejpam-5857	17	5	contribute	contribute	VERB
ejpam-5857	17	6	to	to	ADP
ejpam-5857	17	7	the	the	DET
ejpam-5857	17	8	indeterminacy	indeterminacy	NOUN
ejpam-5857	17	9	degree	degree	NOUN
ejpam-5857	17	10	,	,	PUNCT
ejpam-5857	17	11	capturing	capture	VERB
ejpam-5857	17	12	a	a	DET
ejpam-5857	17	13	more	more	ADV
ejpam-5857	17	14	comprehensive	comprehensive	ADJ
ejpam-5857	17	15	measure	measure	NOUN
ejpam-5857	17	16	of	of	ADP
ejpam-5857	17	17	uncertainty	uncertainty	NOUN
ejpam-5857	17	18	.	.	PUNCT
ejpam-5857	18	1	this	this	DET
ejpam-5857	18	2	enhanced	enhance	VERB
ejpam-5857	18	3	framework	framework	NOUN
ejpam-5857	18	4	proved	prove	VERB
ejpam-5857	18	5	especially	especially	ADV
ejpam-5857	18	6	adept	adept	ADJ
ejpam-5857	18	7	at	at	ADP
ejpam-5857	18	8	addressing	address	VERB
ejpam-5857	18	9	decision	decision	NOUN
ejpam-5857	18	10	-	-	PUNCT
ejpam-5857	18	11	making	make	VERB
ejpam-5857	18	12	and	and	CCONJ
ejpam-5857	18	13	analytical	analytical	ADJ
ejpam-5857	18	14	challenges	challenge	NOUN
ejpam-5857	18	15	in	in	ADP
ejpam-5857	18	16	environments	environment	NOUN
ejpam-5857	18	17	characterized	characterize	VERB
ejpam-5857	18	18	by	by	ADP
ejpam-5857	18	19	complex	complex	ADJ
ejpam-5857	18	20	uncertainties	uncertainty	NOUN
ejpam-5857	18	21	or	or	CCONJ
ejpam-5857	18	22	ignorance	ignorance	NOUN
ejpam-5857	18	23	,	,	PUNCT
ejpam-5857	18	24	as	as	SCONJ
ejpam-5857	18	25	it	it	PRON
ejpam-5857	18	26	accounts	account	VERB
ejpam-5857	18	27	for	for	ADP
ejpam-5857	18	28	ambiguity	ambiguity	NOUN
ejpam-5857	18	29	arising	arise	VERB
ejpam-5857	18	30	from	from	ADP
ejpam-5857	18	31	both	both	PRON
ejpam-5857	18	32	membership	membership	NOUN
ejpam-5857	18	33	and	and	CCONJ
ejpam-5857	18	34	non	non	ADJ
ejpam-5857	18	35	-	-	NOUN
ejpam-5857	18	36	membership	membership	NOUN
ejpam-5857	18	37	.	.	PUNCT
ejpam-5857	19	1	later	later	ADV
ejpam-5857	19	2	,	,	PUNCT
ejpam-5857	19	3	in	in	ADP
ejpam-5857	19	4	1995	1995	NUM
ejpam-5857	19	5	,	,	PUNCT
ejpam-5857	19	6	smarandache	smarandache	NOUN
ejpam-5857	20	1	[	[	X
ejpam-5857	20	2	11	11	NUM
ejpam-5857	20	3	]	]	X
ejpam-5857	20	4	advanced	advance	VERB
ejpam-5857	20	5	the	the	DET
ejpam-5857	20	6	field	field	NOUN
ejpam-5857	20	7	further	far	ADV
ejpam-5857	20	8	with	with	ADP
ejpam-5857	20	9	the	the	DET
ejpam-5857	20	10	introduction	introduction	NOUN
ejpam-5857	20	11	of	of	ADP
ejpam-5857	20	12	neutrosophic	neutrosophic	ADJ
ejpam-5857	20	13	sets	set	NOUN
ejpam-5857	20	14	(	(	PUNCT
ejpam-5857	20	15	nss	ns	NOUN
ejpam-5857	20	16	)	)	PUNCT
ejpam-5857	20	17	,	,	PUNCT
ejpam-5857	20	18	a	a	DET
ejpam-5857	20	19	powerful	powerful	ADJ
ejpam-5857	20	20	generalization	generalization	NOUN
ejpam-5857	20	21	of	of	ADP
ejpam-5857	20	22	fuzzy	fuzzy	ADJ
ejpam-5857	20	23	set	set	NOUN
ejpam-5857	20	24	theory	theory	NOUN
ejpam-5857	20	25	.	.	PUNCT
ejpam-5857	21	1	nss	ns	NOUN
ejpam-5857	21	2	incorporate	incorporate	VERB
ejpam-5857	21	3	three	three	NUM
ejpam-5857	21	4	independent	independent	ADJ
ejpam-5857	21	5	components	component	NOUN
ejpam-5857	21	6	:	:	PUNCT
ejpam-5857	21	7	degrees	degree	NOUN
ejpam-5857	21	8	of	of	ADP
ejpam-5857	21	9	truth	truth	NOUN
ejpam-5857	21	10	,	,	PUNCT
ejpam-5857	21	11	degrees	degree	NOUN
ejpam-5857	21	12	of	of	ADP
ejpam-5857	21	13	falsehood	falsehood	NOUN
ejpam-5857	21	14	and	and	CCONJ
ejpam-5857	21	15	degrees	degree	NOUN
ejpam-5857	21	16	of	of	ADP
ejpam-5857	21	17	indeterminacy	indeterminacy	NOUN
ejpam-5857	21	18	,	,	PUNCT
ejpam-5857	21	19	offering	offer	VERB
ejpam-5857	21	20	a	a	DET
ejpam-5857	21	21	flexible	flexible	ADJ
ejpam-5857	21	22	and	and	CCONJ
ejpam-5857	21	23	robust	robust	ADJ
ejpam-5857	21	24	tool	tool	NOUN
ejpam-5857	21	25	for	for	ADP
ejpam-5857	21	26	analyzing	analyze	VERB
ejpam-5857	21	27	and	and	CCONJ
ejpam-5857	21	28	making	make	VERB
ejpam-5857	21	29	decisions	decision	NOUN
ejpam-5857	21	30	under	under	ADP
ejpam-5857	21	31	highly	highly	ADV
ejpam-5857	21	32	uncertain	uncertain	ADJ
ejpam-5857	21	33	conditions	condition	NOUN
ejpam-5857	21	34	.	.	PUNCT
ejpam-5857	22	1	by	by	ADP
ejpam-5857	22	2	explicitly	explicitly	ADV
ejpam-5857	22	3	modeling	model	VERB
ejpam-5857	22	4	these	these	DET
ejpam-5857	22	5	three	three	NUM
ejpam-5857	22	6	dimensions	dimension	NOUN
ejpam-5857	22	7	,	,	PUNCT
ejpam-5857	22	8	the	the	DET
ejpam-5857	22	9	ns	ns	NUM
ejpam-5857	22	10	framework	framework	NOUN
ejpam-5857	22	11	provides	provide	VERB
ejpam-5857	22	12	unparalleled	unparalleled	ADJ
ejpam-5857	22	13	utility	utility	NOUN
ejpam-5857	22	14	in	in	ADP
ejpam-5857	22	15	addressing	address	VERB
ejpam-5857	22	16	complex	complex	ADJ
ejpam-5857	22	17	,	,	PUNCT
ejpam-5857	22	18	ambiguous	ambiguous	ADJ
ejpam-5857	22	19	and	and	CCONJ
ejpam-5857	22	20	incomplete	incomplete	ADJ
ejpam-5857	22	21	data	datum	NOUN
ejpam-5857	22	22	scenarios	scenario	NOUN
ejpam-5857	22	23	.	.	PUNCT
ejpam-5857	23	1	in	in	ADP
ejpam-5857	23	2	2022	2022	NUM
ejpam-5857	23	3	,	,	PUNCT
ejpam-5857	23	4	iampan	iampan	NOUN
ejpam-5857	23	5	[	[	X
ejpam-5857	23	6	9	9	NUM
ejpam-5857	23	7	]	]	PUNCT
ejpam-5857	23	8	introduced	introduce	VERB
ejpam-5857	23	9	a	a	DET
ejpam-5857	23	10	novel	novel	ADJ
ejpam-5857	23	11	algebraic	algebraic	ADJ
ejpam-5857	23	12	framework	framework	NOUN
ejpam-5857	23	13	termed	term	VERB
ejpam-5857	23	14	iup	iup	NOUN
ejpam-5857	23	15	-	-	PUNCT
ejpam-5857	23	16	algebra	algebra	NOUN
ejpam-5857	23	17	,	,	PUNCT
ejpam-5857	23	18	representing	represent	VERB
ejpam-5857	23	19	a	a	DET
ejpam-5857	23	20	sophisticated	sophisticated	ADJ
ejpam-5857	23	21	and	and	CCONJ
ejpam-5857	23	22	abstract	abstract	ADJ
ejpam-5857	23	23	extension	extension	NOUN
ejpam-5857	23	24	of	of	ADP
ejpam-5857	23	25	algebraic	algebraic	ADJ
ejpam-5857	23	26	logic	logic	NOUN
ejpam-5857	23	27	.	.	PUNCT
ejpam-5857	24	1	this	this	DET
ejpam-5857	24	2	framework	framework	NOUN
ejpam-5857	24	3	encompasses	encompass	VERB
ejpam-5857	24	4	four	four	NUM
ejpam-5857	24	5	foundational	foundational	ADJ
ejpam-5857	24	6	subsets	subset	NOUN
ejpam-5857	24	7	:	:	PUNCT
ejpam-5857	24	8	iup	iup	PROPN
ejpam-5857	24	9	-	-	PUNCT
ejpam-5857	24	10	subalgebras	subalgebras	PROPN
ejpam-5857	24	11	,	,	PUNCT
ejpam-5857	24	12	iup	iup	NOUN
ejpam-5857	24	13	-	-	PUNCT
ejpam-5857	24	14	filters	filter	NOUN
ejpam-5857	24	15	,	,	PUNCT
ejpam-5857	24	16	iup	iup	NOUN
ejpam-5857	24	17	-	-	PUNCT
ejpam-5857	24	18	ideals	ideal	NOUN
ejpam-5857	24	19	and	and	CCONJ
ejpam-5857	24	20	strong	strong	ADJ
ejpam-5857	24	21	iup	iup	NOUN
ejpam-5857	24	22	-	-	PUNCT
ejpam-5857	24	23	ideals	ideal	NOUN
ejpam-5857	24	24	,	,	PUNCT
ejpam-5857	24	25	along	along	ADP
ejpam-5857	24	26	with	with	ADP
ejpam-5857	24	27	the	the	DET
ejpam-5857	24	28	concept	concept	NOUN
ejpam-5857	24	29	of	of	ADP
ejpam-5857	24	30	homomorphism	homomorphism	PROPN
ejpam-5857	24	31	in	in	ADP
ejpam-5857	24	32	iup	iup	NOUN
ejpam-5857	24	33	-	-	PUNCT
ejpam-5857	24	34	algebras	algebras	PROPN
ejpam-5857	24	35	.	.	PUNCT
ejpam-5857	25	1	the	the	DET
ejpam-5857	25	2	flexibility	flexibility	NOUN
ejpam-5857	25	3	of	of	ADP
ejpam-5857	25	4	iup	iup	NOUN
ejpam-5857	25	5	-	-	PUNCT
ejpam-5857	25	6	algebras	algebras	PROPN
ejpam-5857	25	7	allows	allow	VERB
ejpam-5857	25	8	for	for	ADP
ejpam-5857	25	9	integration	integration	NOUN
ejpam-5857	25	10	with	with	ADP
ejpam-5857	25	11	diverse	diverse	ADJ
ejpam-5857	25	12	mathematical	mathematical	ADJ
ejpam-5857	25	13	concepts	concept	NOUN
ejpam-5857	25	14	,	,	PUNCT
ejpam-5857	25	15	fostering	foster	VERB
ejpam-5857	25	16	the	the	DET
ejpam-5857	25	17	generation	generation	NOUN
ejpam-5857	25	18	of	of	ADP
ejpam-5857	25	19	new	new	ADJ
ejpam-5857	25	20	theoretical	theoretical	ADJ
ejpam-5857	25	21	insights	insight	NOUN
ejpam-5857	25	22	and	and	CCONJ
ejpam-5857	25	23	practical	practical	ADJ
ejpam-5857	25	24	applications	application	NOUN
ejpam-5857	25	25	.	.	PUNCT
ejpam-5857	26	1	subsequent	subsequent	ADJ
ejpam-5857	26	2	research	research	NOUN
ejpam-5857	26	3	has	have	AUX
ejpam-5857	26	4	significantly	significantly	ADV
ejpam-5857	26	5	expanded	expand	VERB
ejpam-5857	26	6	the	the	DET
ejpam-5857	26	7	theoretical	theoretical	ADJ
ejpam-5857	26	8	underpinnings	underpinning	NOUN
ejpam-5857	26	9	and	and	CCONJ
ejpam-5857	26	10	applications	application	NOUN
ejpam-5857	26	11	of	of	ADP
ejpam-5857	26	12	iup	iup	NOUN
ejpam-5857	26	13	-	-	PUNCT
ejpam-5857	26	14	algebras	algebras	PROPN
ejpam-5857	26	15	.	.	PUNCT
ejpam-5857	27	1	in	in	ADP
ejpam-5857	27	2	2023	2023	NUM
ejpam-5857	27	3	,	,	PUNCT
ejpam-5857	27	4	chanmanee	chanmanee	NOUN
ejpam-5857	27	5	et	et	PROPN
ejpam-5857	27	6	al	al	PROPN
ejpam-5857	27	7	.	.	PUNCT
ejpam-5857	28	1	[	[	X
ejpam-5857	28	2	8	8	NUM
ejpam-5857	28	3	]	]	PUNCT
ejpam-5857	28	4	introduced	introduce	VERB
ejpam-5857	28	5	the	the	DET
ejpam-5857	28	6	concept	concept	NOUN
ejpam-5857	28	7	of	of	ADP
ejpam-5857	28	8	the	the	DET
ejpam-5857	28	9	external	external	ADJ
ejpam-5857	28	10	direct	direct	ADJ
ejpam-5857	28	11	product	product	NOUN
ejpam-5857	28	12	,	,	PUNCT
ejpam-5857	28	13	analyzing	analyze	VERB
ejpam-5857	28	14	its	its	PRON
ejpam-5857	28	15	implications	implication	NOUN
ejpam-5857	28	16	for	for	ADP
ejpam-5857	28	17	special	special	ADJ
ejpam-5857	28	18	subsets	subset	NOUN
ejpam-5857	28	19	of	of	ADP
ejpam-5857	28	20	iup	iup	NOUN
ejpam-5857	28	21	-	-	PUNCT
ejpam-5857	28	22	algebras	algebras	PROPN
ejpam-5857	28	23	.	.	PUNCT
ejpam-5857	29	1	they	they	PRON
ejpam-5857	29	2	further	far	ADV
ejpam-5857	29	3	developed	develop	VERB
ejpam-5857	29	4	the	the	DET
ejpam-5857	29	5	notion	notion	NOUN
ejpam-5857	29	6	of	of	ADP
ejpam-5857	29	7	weak	weak	ADJ
ejpam-5857	29	8	direct	direct	ADJ
ejpam-5857	29	9	products	product	NOUN
ejpam-5857	29	10	and	and	CCONJ
ejpam-5857	29	11	established	establish	VERB
ejpam-5857	29	12	fundamental	fundamental	ADJ
ejpam-5857	29	13	theorems	theorem	NOUN
ejpam-5857	29	14	concerning	concern	VERB
ejpam-5857	29	15	(	(	PUNCT
ejpam-5857	29	16	anti)iup	anti)iup	NOUN
ejpam-5857	29	17	-	-	PUNCT
ejpam-5857	29	18	homomorphisms	homomorphism	NOUN
ejpam-5857	29	19	within	within	ADP
ejpam-5857	29	20	this	this	DET
ejpam-5857	29	21	context	context	NOUN
ejpam-5857	29	22	.	.	PUNCT
ejpam-5857	30	1	later	later	ADV
ejpam-5857	30	2	,	,	PUNCT
ejpam-5857	30	3	chanmanee	chanmanee	PROPN
ejpam-5857	30	4	et	et	PROPN
ejpam-5857	30	5	al	al	PROPN
ejpam-5857	30	6	.	.	PUNCT
ejpam-5857	31	1	[	[	X
ejpam-5857	31	2	7	7	NUM
ejpam-5857	31	3	]	]	PUNCT
ejpam-5857	31	4	extended	extend	VERB
ejpam-5857	31	5	these	these	DET
ejpam-5857	31	6	ideas	idea	NOUN
ejpam-5857	31	7	by	by	ADP
ejpam-5857	31	8	investigating	investigate	VERB
ejpam-5857	31	9	direct	direct	ADJ
ejpam-5857	31	10	products	product	NOUN
ejpam-5857	31	11	for	for	ADP
ejpam-5857	31	12	infinite	infinite	ADJ
ejpam-5857	31	13	families	family	NOUN
ejpam-5857	31	14	of	of	ADP
ejpam-5857	31	15	iup	iup	NOUN
ejpam-5857	31	16	-	-	PUNCT
ejpam-5857	31	17	algebras	algebras	X
ejpam-5857	31	18	,	,	PUNCT
ejpam-5857	31	19	thereby	thereby	ADV
ejpam-5857	31	20	formalizing	formalize	VERB
ejpam-5857	31	21	the	the	DET
ejpam-5857	31	22	concept	concept	NOUN
ejpam-5857	31	23	of	of	ADP
ejpam-5857	31	24	diup	diup	NOUN
ejpam-5857	31	25	-	-	PUNCT
ejpam-5857	31	26	algebras	algebras	PROPN
ejpam-5857	31	27	and	and	CCONJ
ejpam-5857	31	28	proposing	propose	VERB
ejpam-5857	31	29	the	the	DET
ejpam-5857	31	30	innovative	innovative	ADJ
ejpam-5857	31	31	framework	framework	NOUN
ejpam-5857	31	32	of	of	ADP
ejpam-5857	31	33	weak	weak	ADJ
ejpam-5857	31	34	direct	direct	ADJ
ejpam-5857	31	35	product	product	NOUN
ejpam-5857	31	36	diup	diup	NOUN
ejpam-5857	31	37	-	-	PUNCT
ejpam-5857	31	38	algebras	algebras	X
ejpam-5857	31	39	,	,	PUNCT
ejpam-5857	31	40	enhancing	enhance	VERB
ejpam-5857	31	41	the	the	DET
ejpam-5857	31	42	structural	structural	ADJ
ejpam-5857	31	43	depth	depth	NOUN
ejpam-5857	31	44	of	of	ADP
ejpam-5857	31	45	the	the	DET
ejpam-5857	31	46	theory	theory	NOUN
ejpam-5857	31	47	.	.	PUNCT
ejpam-5857	32	1	building	build	VERB
ejpam-5857	32	2	on	on	ADP
ejpam-5857	32	3	these	these	DET
ejpam-5857	32	4	advancements	advancement	NOUN
ejpam-5857	32	5	,	,	PUNCT
ejpam-5857	32	6	kuntama	kuntama	NOUN
ejpam-5857	32	7	et	et	PROPN
ejpam-5857	32	8	al	al	PROPN
ejpam-5857	32	9	.	.	PUNCT
ejpam-5857	33	1	[	[	X
ejpam-5857	33	2	10	10	NUM
ejpam-5857	33	3	]	]	PUNCT
ejpam-5857	33	4	in	in	ADP
ejpam-5857	33	5	2024	2024	NUM
ejpam-5857	33	6	applied	apply	VERB
ejpam-5857	33	7	fs	fs	ADP
ejpam-5857	33	8	theory	theory	NOUN
ejpam-5857	33	9	to	to	PART
ejpam-5857	33	10	iup	iup	VERB
ejpam-5857	33	11	-	-	PUNCT
ejpam-5857	33	12	algebras	algebras	X
ejpam-5857	33	13	,	,	PUNCT
ejpam-5857	33	14	introducing	introduce	VERB
ejpam-5857	33	15	fuzzy	fuzzy	ADJ
ejpam-5857	33	16	iup	iup	NOUN
ejpam-5857	33	17	-	-	PUNCT
ejpam-5857	33	18	subalgebras	subalgebras	PROPN
ejpam-5857	33	19	,	,	PUNCT
ejpam-5857	33	20	fuzzy	fuzzy	ADJ
ejpam-5857	33	21	iup	iup	NOUN
ejpam-5857	33	22	-	-	PUNCT
ejpam-5857	33	23	filters	filter	NOUN
ejpam-5857	33	24	,	,	PUNCT
ejpam-5857	33	25	fuzzy	fuzzy	ADJ
ejpam-5857	33	26	iup	iup	NOUN
ejpam-5857	33	27	-	-	PUNCT
ejpam-5857	33	28	ideals	ideal	NOUN
ejpam-5857	33	29	and	and	CCONJ
ejpam-5857	33	30	fuzzy	fuzzy	ADJ
ejpam-5857	33	31	strong	strong	ADJ
ejpam-5857	33	32	iup	iup	NOUN
ejpam-5857	33	33	-	-	PUNCT
ejpam-5857	33	34	ideals	ideal	NOUN
ejpam-5857	33	35	.	.	PUNCT
ejpam-5857	34	1	they	they	PRON
ejpam-5857	34	2	examined	examine	VERB
ejpam-5857	34	3	the	the	DET
ejpam-5857	34	4	intricate	intricate	ADJ
ejpam-5857	34	5	relationships	relationship	NOUN
ejpam-5857	34	6	between	between	ADP
ejpam-5857	34	7	these	these	DET
ejpam-5857	34	8	subsets	subset	NOUN
ejpam-5857	34	9	and	and	CCONJ
ejpam-5857	34	10	characteristic	characteristic	ADJ
ejpam-5857	34	11	functions	function	NOUN
ejpam-5857	34	12	while	while	SCONJ
ejpam-5857	34	13	also	also	ADV
ejpam-5857	34	14	exploring	explore	VERB
ejpam-5857	34	15	the	the	DET
ejpam-5857	34	16	concepts	concept	NOUN
ejpam-5857	34	17	of	of	ADP
ejpam-5857	34	18	prime	prime	ADJ
ejpam-5857	34	19	subsets	subset	NOUN
ejpam-5857	34	20	and	and	CCONJ
ejpam-5857	34	21	prime	prime	ADJ
ejpam-5857	34	22	fuzzy	fuzzy	ADJ
ejpam-5857	34	23	subsets	subset	NOUN
ejpam-5857	34	24	.	.	PUNCT
ejpam-5857	35	1	their	their	PRON
ejpam-5857	35	2	work	work	NOUN
ejpam-5857	35	3	introduced	introduce	VERB
ejpam-5857	35	4	upper	upper	ADJ
ejpam-5857	35	5	and	and	CCONJ
ejpam-5857	35	6	lower	low	ADJ
ejpam-5857	35	7	t	t	NOUN
ejpam-5857	35	8	-	-	PUNCT
ejpam-5857	35	9	level	level	NOUN
ejpam-5857	35	10	(	(	PUNCT
ejpam-5857	35	11	strong	strong	ADJ
ejpam-5857	35	12	)	)	PUNCT
ejpam-5857	35	13	subsets	subset	NOUN
ejpam-5857	35	14	,	,	PUNCT
ejpam-5857	35	15	providing	provide	VERB
ejpam-5857	35	16	novel	novel	ADJ
ejpam-5857	35	17	tools	tool	NOUN
ejpam-5857	35	18	for	for	ADP
ejpam-5857	35	19	analyzing	analyze	VERB
ejpam-5857	35	20	fss	fss	ADV
ejpam-5857	35	21	in	in	ADP
ejpam-5857	35	22	iup	iup	NOUN
ejpam-5857	35	23	-	-	PUNCT
ejpam-5857	35	24	algebras	algebras	PROPN
ejpam-5857	35	25	.	.	PUNCT
ejpam-5857	36	1	suayngam	suayngam	PROPN
ejpam-5857	36	2	et	et	PROPN
ejpam-5857	36	3	al	al	PROPN
ejpam-5857	36	4	.	.	PUNCT
ejpam-5857	37	1	[	[	X
ejpam-5857	37	2	15	15	NUM
ejpam-5857	37	3	]	]	PUNCT
ejpam-5857	37	4	significantly	significantly	ADV
ejpam-5857	37	5	enriched	enrich	VERB
ejpam-5857	37	6	the	the	DET
ejpam-5857	37	7	theoretical	theoretical	ADJ
ejpam-5857	37	8	framework	framework	NOUN
ejpam-5857	37	9	of	of	ADP
ejpam-5857	37	10	iup	iup	NOUN
ejpam-5857	37	11	-	-	PUNCT
ejpam-5857	37	12	algebras	algebras	PROPN
ejpam-5857	37	13	by	by	ADP
ejpam-5857	37	14	integrating	integrate	VERB
ejpam-5857	37	15	ifss	ifss	NOUN
ejpam-5857	37	16	.	.	PUNCT
ejpam-5857	38	1	their	their	PRON
ejpam-5857	38	2	work	work	NOUN
ejpam-5857	38	3	introduced	introduce	VERB
ejpam-5857	38	4	intuitionistic	intuitionistic	ADJ
ejpam-5857	38	5	fuzzy	fuzzy	ADJ
ejpam-5857	38	6	iup	iup	NOUN
ejpam-5857	38	7	-	-	PUNCT
ejpam-5857	38	8	subalgebras	subalgebras	PROPN
ejpam-5857	38	9	,	,	PUNCT
ejpam-5857	38	10	iup	iup	NOUN
ejpam-5857	38	11	-	-	PUNCT
ejpam-5857	38	12	ideals	ideal	NOUN
ejpam-5857	38	13	,	,	PUNCT
ejpam-5857	38	14	iup	iup	NOUN
ejpam-5857	38	15	-	-	PUNCT
ejpam-5857	38	16	filters	filter	NOUN
ejpam-5857	38	17	and	and	CCONJ
ejpam-5857	38	18	strong	strong	ADJ
ejpam-5857	38	19	iup	iup	NOUN
ejpam-5857	38	20	-	-	PUNCT
ejpam-5857	38	21	ideals	ideal	NOUN
ejpam-5857	38	22	alongside	alongside	ADP
ejpam-5857	38	23	an	an	DET
ejpam-5857	38	24	in	in	ADP
ejpam-5857	38	25	-	-	PUNCT
ejpam-5857	38	26	depth	depth	NOUN
ejpam-5857	38	27	exploration	exploration	NOUN
ejpam-5857	38	28	of	of	ADP
ejpam-5857	38	29	their	their	PRON
ejpam-5857	38	30	fundamental	fundamental	ADJ
ejpam-5857	38	31	properties	property	NOUN
ejpam-5857	38	32	and	and	CCONJ
ejpam-5857	38	33	the	the	DET
ejpam-5857	38	34	intricate	intricate	ADJ
ejpam-5857	38	35	relationships	relationship	NOUN
ejpam-5857	38	36	involving	involve	VERB
ejpam-5857	38	37	upper	upper	ADJ
ejpam-5857	38	38	and	and	CCONJ
ejpam-5857	38	39	lower	low	ADJ
ejpam-5857	38	40	t	t	NOUN
ejpam-5857	38	41	-	-	PUNCT
ejpam-5857	38	42	level	level	NOUN
ejpam-5857	38	43	subsets	subset	NOUN
ejpam-5857	38	44	.	.	PUNCT
ejpam-5857	39	1	building	build	VERB
ejpam-5857	39	2	on	on	ADP
ejpam-5857	39	3	this	this	DET
ejpam-5857	39	4	foundation	foundation	NOUN
ejpam-5857	39	5	,	,	PUNCT
ejpam-5857	39	6	they	they	PRON
ejpam-5857	39	7	[	[	X
ejpam-5857	39	8	12	12	NUM
ejpam-5857	39	9	]	]	PUNCT
ejpam-5857	39	10	further	far	ADV
ejpam-5857	39	11	expanded	expand	VERB
ejpam-5857	39	12	the	the	DET
ejpam-5857	39	13	framework	framework	NOUN
ejpam-5857	39	14	by	by	ADP
ejpam-5857	39	15	incorporating	incorporate	VERB
ejpam-5857	39	16	nss	ns	NOUN
ejpam-5857	39	17	,	,	PUNCT
ejpam-5857	39	18	proposing	propose	VERB
ejpam-5857	39	19	neutrosophic	neutrosophic	ADJ
ejpam-5857	39	20	iup	iup	NOUN
ejpam-5857	39	21	-	-	PUNCT
ejpam-5857	39	22	subalgebras	subalgebras	PROPN
ejpam-5857	39	23	,	,	PUNCT
ejpam-5857	39	24	iup	iup	NOUN
ejpam-5857	39	25	-	-	PUNCT
ejpam-5857	39	26	ideals	ideal	NOUN
ejpam-5857	39	27	,	,	PUNCT
ejpam-5857	39	28	iup	iup	NOUN
ejpam-5857	39	29	-	-	PUNCT
ejpam-5857	39	30	filters	filter	NOUN
ejpam-5857	39	31	and	and	CCONJ
ejpam-5857	39	32	strong	strong	ADJ
ejpam-5857	39	33	iup	iup	NOUN
ejpam-5857	39	34	-	-	PUNCT
ejpam-5857	39	35	ideals	ideal	NOUN
ejpam-5857	39	36	.	.	PUNCT
ejpam-5857	40	1	these	these	DET
ejpam-5857	40	2	advancements	advancement	NOUN
ejpam-5857	40	3	provided	provide	VERB
ejpam-5857	40	4	comprehensive	comprehensive	ADJ
ejpam-5857	40	5	conditions	condition	NOUN
ejpam-5857	40	6	for	for	ADP
ejpam-5857	40	7	nss	nss	NOUN
ejpam-5857	40	8	to	to	PART
ejpam-5857	40	9	conform	conform	VERB
ejpam-5857	40	10	to	to	ADP
ejpam-5857	40	11	these	these	DET
ejpam-5857	40	12	structures	structure	NOUN
ejpam-5857	40	13	,	,	PUNCT
ejpam-5857	40	14	alongside	alongside	ADP
ejpam-5857	40	15	an	an	DET
ejpam-5857	40	16	analysis	analysis	NOUN
ejpam-5857	40	17	of	of	ADP
ejpam-5857	40	18	their	their	PRON
ejpam-5857	40	19	interactions	interaction	NOUN
ejpam-5857	40	20	with	with	ADP
ejpam-5857	40	21	level	level	NOUN
ejpam-5857	40	22	subsets	subset	NOUN
ejpam-5857	40	23	,	,	PUNCT
ejpam-5857	40	24	thereby	thereby	ADV
ejpam-5857	40	25	illustrating	illustrate	VERB
ejpam-5857	40	26	the	the	DET
ejpam-5857	40	27	adaptability	adaptability	NOUN
ejpam-5857	40	28	of	of	ADP
ejpam-5857	40	29	iup	iup	NOUN
ejpam-5857	40	30	-	-	PUNCT
ejpam-5857	40	31	algebras	algebras	PROPN
ejpam-5857	40	32	in	in	ADP
ejpam-5857	40	33	managing	manage	VERB
ejpam-5857	40	34	uncertainty	uncertainty	NOUN
ejpam-5857	40	35	.	.	PUNCT
ejpam-5857	41	1	moreover	moreover	ADV
ejpam-5857	41	2	,	,	PUNCT
ejpam-5857	41	3	they	they	PRON
ejpam-5857	41	4	[	[	X
ejpam-5857	41	5	13	13	NUM
ejpam-5857	41	6	]	]	PUNCT
ejpam-5857	41	7	extended	extend	VERB
ejpam-5857	41	8	their	their	PRON
ejpam-5857	41	9	work	work	NOUN
ejpam-5857	41	10	to	to	PART
ejpam-5857	41	11	include	include	VERB
ejpam-5857	41	12	fermatean	fermatean	ADJ
ejpam-5857	41	13	fuzzy	fuzzy	ADJ
ejpam-5857	41	14	sets	set	NOUN
ejpam-5857	41	15	,	,	PUNCT
ejpam-5857	41	16	introduck	introduck	NOUN
ejpam-5857	41	17	.	.	PUNCT
ejpam-5857	42	1	suayngam	suayngam	PROPN
ejpam-5857	42	2	,	,	PUNCT
ejpam-5857	42	3	p.	p.	NOUN
ejpam-5857	42	4	julatha	julatha	PROPN
ejpam-5857	42	5	,	,	PUNCT
ejpam-5857	43	1	w.	w.	PROPN
ejpam-5857	43	2	nakkhasen	nakkhasen	PROPN
ejpam-5857	43	3	,	,	PUNCT
ejpam-5857	43	4	a.	a.	NOUN
ejpam-5857	43	5	iampan	iampan	PROPN
ejpam-5857	43	6	/	/	SYM
ejpam-5857	43	7	eur	eur	PROPN
ejpam-5857	43	8	.	.	PUNCT
ejpam-5857	44	1	j.	j.	PROPN
ejpam-5857	44	2	pure	pure	PROPN
ejpam-5857	44	3	appl	appl	PROPN
ejpam-5857	44	4	.	.	PROPN
ejpam-5857	44	5	math	math	PROPN
ejpam-5857	44	6	,	,	PUNCT
ejpam-5857	44	7	18	18	NUM
ejpam-5857	44	8	(	(	PUNCT
ejpam-5857	44	9	2	2	NUM
ejpam-5857	44	10	)	)	PUNCT
ejpam-5857	44	11	(	(	PUNCT
ejpam-5857	44	12	2025	2025	NUM
ejpam-5857	44	13	)	)	PUNCT
ejpam-5857	44	14	,	,	PUNCT
ejpam-5857	44	15	5857	5857	NUM
ejpam-5857	44	16	3	3	NUM
ejpam-5857	44	17	of	of	ADP
ejpam-5857	44	18	30	30	NUM
ejpam-5857	44	19	ing	ing	ADJ
ejpam-5857	44	20	fermatean	fermatean	NOUN
ejpam-5857	44	21	fuzzy	fuzzy	ADJ
ejpam-5857	44	22	iup	iup	NOUN
ejpam-5857	44	23	-	-	PUNCT
ejpam-5857	44	24	subalgebras	subalgebras	PROPN
ejpam-5857	44	25	,	,	PUNCT
ejpam-5857	44	26	iup	iup	NOUN
ejpam-5857	44	27	-	-	PUNCT
ejpam-5857	44	28	ideals	ideal	NOUN
ejpam-5857	44	29	,	,	PUNCT
ejpam-5857	44	30	iup	iup	NOUN
ejpam-5857	44	31	-	-	PUNCT
ejpam-5857	44	32	filters	filter	NOUN
ejpam-5857	44	33	and	and	CCONJ
ejpam-5857	44	34	strong	strong	ADJ
ejpam-5857	44	35	iup	iup	NOUN
ejpam-5857	44	36	-	-	PUNCT
ejpam-5857	44	37	ideals	ideal	NOUN
ejpam-5857	44	38	.	.	PUNCT
ejpam-5857	45	1	this	this	DET
ejpam-5857	45	2	study	study	NOUN
ejpam-5857	45	3	advanced	advance	VERB
ejpam-5857	45	4	the	the	DET
ejpam-5857	45	5	algebraic	algebraic	ADJ
ejpam-5857	45	6	understanding	understanding	NOUN
ejpam-5857	45	7	of	of	ADP
ejpam-5857	45	8	fermatean	fermatean	ADJ
ejpam-5857	45	9	fuzzy	fuzzy	ADJ
ejpam-5857	45	10	structures	structure	NOUN
ejpam-5857	45	11	within	within	ADP
ejpam-5857	45	12	the	the	DET
ejpam-5857	45	13	iupalgebra	iupalgebra	NOUN
ejpam-5857	45	14	framework	framework	NOUN
ejpam-5857	45	15	.	.	PUNCT
ejpam-5857	46	1	additionally	additionally	ADV
ejpam-5857	46	2	,	,	PUNCT
ejpam-5857	46	3	they	they	PRON
ejpam-5857	46	4	[	[	X
ejpam-5857	46	5	14	14	NUM
ejpam-5857	46	6	]	]	PUNCT
ejpam-5857	46	7	explored	explore	VERB
ejpam-5857	46	8	the	the	DET
ejpam-5857	46	9	application	application	NOUN
ejpam-5857	46	10	of	of	ADP
ejpam-5857	46	11	pythagorean	pythagorean	PROPN
ejpam-5857	46	12	fuzzy	fuzzy	ADJ
ejpam-5857	46	13	sets	set	NOUN
ejpam-5857	46	14	to	to	PART
ejpam-5857	46	15	iup	iup	VERB
ejpam-5857	46	16	-	-	PUNCT
ejpam-5857	46	17	algebras	algebras	PROPN
ejpam-5857	46	18	,	,	PUNCT
ejpam-5857	46	19	presenting	present	VERB
ejpam-5857	46	20	pythagorean	pythagorean	PROPN
ejpam-5857	46	21	fuzzy	fuzzy	ADJ
ejpam-5857	46	22	iup	iup	PROPN
ejpam-5857	46	23	-	-	PUNCT
ejpam-5857	46	24	subalgebras	subalgebras	PROPN
ejpam-5857	46	25	,	,	PUNCT
ejpam-5857	46	26	iup	iup	NOUN
ejpam-5857	46	27	-	-	PUNCT
ejpam-5857	46	28	ideals	ideal	NOUN
ejpam-5857	46	29	,	,	PUNCT
ejpam-5857	46	30	iupfilters	iupfilter	NOUN
ejpam-5857	46	31	and	and	CCONJ
ejpam-5857	46	32	strong	strong	ADJ
ejpam-5857	46	33	iup	iup	NOUN
ejpam-5857	46	34	-	-	PUNCT
ejpam-5857	46	35	ideals	ideal	NOUN
ejpam-5857	46	36	.	.	PUNCT
ejpam-5857	47	1	the	the	DET
ejpam-5857	47	2	analysis	analysis	NOUN
ejpam-5857	47	3	revealed	reveal	VERB
ejpam-5857	47	4	that	that	SCONJ
ejpam-5857	47	5	pythagorean	pythagorean	PROPN
ejpam-5857	47	6	fuzzy	fuzzy	ADJ
ejpam-5857	47	7	iup	iup	NOUN
ejpam-5857	47	8	-	-	PUNCT
ejpam-5857	47	9	ideals	ideal	NOUN
ejpam-5857	47	10	and	and	CCONJ
ejpam-5857	47	11	subalgebras	subalgebras	PROPN
ejpam-5857	47	12	serve	serve	VERB
ejpam-5857	47	13	as	as	ADP
ejpam-5857	47	14	generalizations	generalization	NOUN
ejpam-5857	47	15	of	of	ADP
ejpam-5857	47	16	pythagorean	pythagorean	PROPN
ejpam-5857	47	17	fuzzy	fuzzy	ADJ
ejpam-5857	47	18	strong	strong	ADJ
ejpam-5857	47	19	iup	iup	NOUN
ejpam-5857	47	20	-	-	PUNCT
ejpam-5857	47	21	ideals	ideal	NOUN
ejpam-5857	47	22	within	within	ADP
ejpam-5857	47	23	iup	iup	NOUN
ejpam-5857	47	24	-	-	PUNCT
ejpam-5857	47	25	algebras	algebra	NOUN
ejpam-5857	47	26	,	,	PUNCT
ejpam-5857	47	27	with	with	ADP
ejpam-5857	47	28	the	the	DET
ejpam-5857	47	29	latter	latter	ADJ
ejpam-5857	47	30	constrained	constrain	VERB
ejpam-5857	47	31	to	to	ADP
ejpam-5857	47	32	constant	constant	ADJ
ejpam-5857	47	33	pythagorean	pythagorean	NOUN
ejpam-5857	47	34	fuzzy	fuzzy	ADJ
ejpam-5857	47	35	sets	set	NOUN
ejpam-5857	47	36	.	.	PUNCT
ejpam-5857	48	1	this	this	DET
ejpam-5857	48	2	body	body	NOUN
ejpam-5857	48	3	of	of	ADP
ejpam-5857	48	4	research	research	NOUN
ejpam-5857	48	5	underscores	underscore	VERB
ejpam-5857	48	6	the	the	DET
ejpam-5857	48	7	progressive	progressive	ADJ
ejpam-5857	48	8	evolution	evolution	NOUN
ejpam-5857	48	9	of	of	ADP
ejpam-5857	48	10	iup	iup	NOUN
ejpam-5857	48	11	-	-	PUNCT
ejpam-5857	48	12	algebras	algebras	PROPN
ejpam-5857	48	13	as	as	ADP
ejpam-5857	48	14	a	a	DET
ejpam-5857	48	15	versatile	versatile	ADJ
ejpam-5857	48	16	mathematical	mathematical	ADJ
ejpam-5857	48	17	framework	framework	NOUN
ejpam-5857	48	18	,	,	PUNCT
ejpam-5857	48	19	capable	capable	ADJ
ejpam-5857	48	20	of	of	ADP
ejpam-5857	48	21	accommodating	accommodate	VERB
ejpam-5857	48	22	and	and	CCONJ
ejpam-5857	48	23	addressing	address	VERB
ejpam-5857	48	24	complex	complex	ADJ
ejpam-5857	48	25	forms	form	NOUN
ejpam-5857	48	26	of	of	ADP
ejpam-5857	48	27	uncertainty	uncertainty	NOUN
ejpam-5857	48	28	through	through	ADP
ejpam-5857	48	29	the	the	DET
ejpam-5857	48	30	integration	integration	NOUN
ejpam-5857	48	31	of	of	ADP
ejpam-5857	48	32	diverse	diverse	ADJ
ejpam-5857	48	33	fuzzy	fuzzy	ADJ
ejpam-5857	48	34	set	set	NOUN
ejpam-5857	48	35	theories	theory	NOUN
ejpam-5857	48	36	.	.	PUNCT
ejpam-5857	49	1	in	in	ADP
ejpam-5857	49	2	2017	2017	NUM
ejpam-5857	49	3	,	,	PUNCT
ejpam-5857	49	4	the	the	DET
ejpam-5857	49	5	concept	concept	NOUN
ejpam-5857	49	6	of	of	ADP
ejpam-5857	49	7	nss	nss	NOUN
ejpam-5857	49	8	was	be	AUX
ejpam-5857	49	9	extended	extend	VERB
ejpam-5857	49	10	through	through	ADP
ejpam-5857	49	11	the	the	DET
ejpam-5857	49	12	integration	integration	NOUN
ejpam-5857	49	13	of	of	ADP
ejpam-5857	49	14	ifs	ifs	PROPN
ejpam-5857	49	15	theory	theory	NOUN
ejpam-5857	49	16	,	,	PUNCT
ejpam-5857	49	17	giving	give	VERB
ejpam-5857	49	18	rise	rise	NOUN
ejpam-5857	49	19	to	to	ADP
ejpam-5857	49	20	the	the	DET
ejpam-5857	49	21	intuitionistic	intuitionistic	ADJ
ejpam-5857	49	22	neutrosophic	neutrosophic	ADJ
ejpam-5857	49	23	set	set	NOUN
ejpam-5857	49	24	(	(	PUNCT
ejpam-5857	49	25	ins	in	NOUN
ejpam-5857	49	26	)	)	PUNCT
ejpam-5857	49	27	,	,	PUNCT
ejpam-5857	49	28	as	as	SCONJ
ejpam-5857	49	29	introduced	introduce	VERB
ejpam-5857	49	30	by	by	ADP
ejpam-5857	49	31	bhowmik	bhowmik	ADJ
ejpam-5857	49	32	and	and	CCONJ
ejpam-5857	49	33	pal	pal	ADJ
ejpam-5857	49	34	[	[	X
ejpam-5857	49	35	2	2	NUM
ejpam-5857	49	36	]	]	PUNCT
ejpam-5857	49	37	.	.	PUNCT
ejpam-5857	50	1	this	this	DET
ejpam-5857	50	2	novel	novel	ADJ
ejpam-5857	50	3	framework	framework	NOUN
ejpam-5857	50	4	combines	combine	VERB
ejpam-5857	50	5	the	the	DET
ejpam-5857	50	6	three	three	NUM
ejpam-5857	50	7	fundamental	fundamental	ADJ
ejpam-5857	50	8	degrees	degree	NOUN
ejpam-5857	50	9	of	of	ADP
ejpam-5857	50	10	truth	truth	NOUN
ejpam-5857	50	11	,	,	PUNCT
ejpam-5857	50	12	falsehood	falsehood	NOUN
ejpam-5857	50	13	and	and	CCONJ
ejpam-5857	50	14	uncertainty	uncertainty	NOUN
ejpam-5857	50	15	from	from	ADP
ejpam-5857	50	16	ns	ns	ADJ
ejpam-5857	50	17	theory	theory	NOUN
ejpam-5857	50	18	with	with	ADP
ejpam-5857	50	19	the	the	DET
ejpam-5857	50	20	ifs	ifs	PROPN
ejpam-5857	50	21	principle	principle	NOUN
ejpam-5857	50	22	,	,	PUNCT
ejpam-5857	50	23	which	which	PRON
ejpam-5857	50	24	restricts	restrict	VERB
ejpam-5857	50	25	the	the	DET
ejpam-5857	50	26	sum	sum	NOUN
ejpam-5857	50	27	of	of	ADP
ejpam-5857	50	28	these	these	DET
ejpam-5857	50	29	degrees	degree	NOUN
ejpam-5857	50	30	to	to	PART
ejpam-5857	50	31	be	be	AUX
ejpam-5857	50	32	less	less	ADJ
ejpam-5857	50	33	than	than	ADP
ejpam-5857	50	34	or	or	CCONJ
ejpam-5857	50	35	equal	equal	ADJ
ejpam-5857	50	36	to	to	ADP
ejpam-5857	50	37	2	2	NUM
ejpam-5857	50	38	.	.	PUNCT
ejpam-5857	50	39	such	such	DET
ejpam-5857	50	40	an	an	DET
ejpam-5857	50	41	approach	approach	NOUN
ejpam-5857	50	42	enhances	enhance	VERB
ejpam-5857	50	43	the	the	DET
ejpam-5857	50	44	ability	ability	NOUN
ejpam-5857	50	45	to	to	PART
ejpam-5857	50	46	model	model	VERB
ejpam-5857	50	47	and	and	CCONJ
ejpam-5857	50	48	analyze	analyze	VERB
ejpam-5857	50	49	high	high	ADJ
ejpam-5857	50	50	degrees	degree	NOUN
ejpam-5857	50	51	of	of	ADP
ejpam-5857	50	52	uncertainty	uncertainty	NOUN
ejpam-5857	50	53	and	and	CCONJ
ejpam-5857	50	54	ambiguity	ambiguity	NOUN
ejpam-5857	50	55	,	,	PUNCT
ejpam-5857	50	56	making	make	VERB
ejpam-5857	50	57	it	it	PRON
ejpam-5857	50	58	particularly	particularly	ADV
ejpam-5857	50	59	valuable	valuable	ADJ
ejpam-5857	50	60	for	for	ADP
ejpam-5857	50	61	complex	complex	ADJ
ejpam-5857	50	62	decision	decision	NOUN
ejpam-5857	50	63	-	-	PUNCT
ejpam-5857	50	64	making	make	VERB
ejpam-5857	50	65	and	and	CCONJ
ejpam-5857	50	66	data	data	VERB
ejpam-5857	51	1	analysis	analysis	NOUN
ejpam-5857	51	2	scenarios	scenario	NOUN
ejpam-5857	51	3	.	.	PUNCT
ejpam-5857	52	1	the	the	DET
ejpam-5857	52	2	significance	significance	NOUN
ejpam-5857	52	3	of	of	ADP
ejpam-5857	52	4	inss	ins	NOUN
ejpam-5857	52	5	has	have	AUX
ejpam-5857	52	6	been	be	AUX
ejpam-5857	52	7	widely	widely	ADV
ejpam-5857	52	8	acknowledged	acknowledge	VERB
ejpam-5857	52	9	,	,	PUNCT
ejpam-5857	52	10	spurring	spur	VERB
ejpam-5857	52	11	further	further	ADJ
ejpam-5857	52	12	exploration	exploration	NOUN
ejpam-5857	52	13	and	and	CCONJ
ejpam-5857	52	14	application	application	NOUN
ejpam-5857	52	15	in	in	ADP
ejpam-5857	52	16	various	various	ADJ
ejpam-5857	52	17	domains	domain	NOUN
ejpam-5857	52	18	.	.	PUNCT
ejpam-5857	53	1	for	for	ADP
ejpam-5857	53	2	instance	instance	NOUN
ejpam-5857	53	3	,	,	PUNCT
ejpam-5857	53	4	in	in	ADP
ejpam-5857	53	5	2010	2010	NUM
ejpam-5857	53	6	,	,	PUNCT
ejpam-5857	53	7	bhowmik	bhowmik	ADJ
ejpam-5857	53	8	and	and	CCONJ
ejpam-5857	53	9	pal	pal	ADJ
ejpam-5857	53	10	[	[	X
ejpam-5857	53	11	3	3	NUM
ejpam-5857	53	12	]	]	PUNCT
ejpam-5857	53	13	introduced	introduce	VERB
ejpam-5857	53	14	refined	refined	ADJ
ejpam-5857	53	15	definitions	definition	NOUN
ejpam-5857	53	16	for	for	ADP
ejpam-5857	53	17	operations	operation	NOUN
ejpam-5857	53	18	such	such	ADJ
ejpam-5857	53	19	as	as	ADP
ejpam-5857	53	20	complement	complement	NOUN
ejpam-5857	53	21	,	,	PUNCT
ejpam-5857	53	22	union	union	NOUN
ejpam-5857	53	23	and	and	CCONJ
ejpam-5857	53	24	intersection	intersection	NOUN
ejpam-5857	53	25	within	within	ADP
ejpam-5857	53	26	inss	ins	NOUN
ejpam-5857	53	27	.	.	PUNCT
ejpam-5857	54	1	they	they	PRON
ejpam-5857	54	2	also	also	ADV
ejpam-5857	54	3	examined	examine	VERB
ejpam-5857	54	4	relationships	relationship	NOUN
ejpam-5857	54	5	between	between	ADP
ejpam-5857	54	6	inss	ins	NOUN
ejpam-5857	54	7	,	,	PUNCT
ejpam-5857	54	8	identifying	identify	VERB
ejpam-5857	54	9	four	four	NUM
ejpam-5857	54	10	specialized	specialized	ADJ
ejpam-5857	54	11	types	type	NOUN
ejpam-5857	54	12	of	of	ADP
ejpam-5857	54	13	relations	relation	NOUN
ejpam-5857	54	14	and	and	CCONJ
ejpam-5857	54	15	studying	study	VERB
ejpam-5857	54	16	their	their	PRON
ejpam-5857	54	17	properties	property	NOUN
ejpam-5857	54	18	.	.	PUNCT
ejpam-5857	55	1	building	build	VERB
ejpam-5857	55	2	on	on	ADP
ejpam-5857	55	3	this	this	DET
ejpam-5857	55	4	foundation	foundation	NOUN
ejpam-5857	55	5	,	,	PUNCT
ejpam-5857	55	6	broumi	broumi	PROPN
ejpam-5857	55	7	et	et	PROPN
ejpam-5857	55	8	al	al	PROPN
ejpam-5857	55	9	.	.	PUNCT
ejpam-5857	56	1	[	[	X
ejpam-5857	56	2	4	4	X
ejpam-5857	56	3	]	]	PUNCT
ejpam-5857	56	4	in	in	ADP
ejpam-5857	56	5	2013	2013	NUM
ejpam-5857	56	6	expanded	expand	VERB
ejpam-5857	56	7	the	the	DET
ejpam-5857	56	8	application	application	NOUN
ejpam-5857	56	9	of	of	ADP
ejpam-5857	56	10	inss	ins	NOUN
ejpam-5857	56	11	by	by	ADP
ejpam-5857	56	12	incorporating	incorporate	VERB
ejpam-5857	56	13	them	they	PRON
ejpam-5857	56	14	into	into	ADP
ejpam-5857	56	15	soft	soft	ADJ
ejpam-5857	56	16	set	set	NOUN
ejpam-5857	56	17	theory	theory	NOUN
ejpam-5857	56	18	,	,	PUNCT
ejpam-5857	56	19	thereby	thereby	ADV
ejpam-5857	56	20	defining	define	VERB
ejpam-5857	56	21	intuitionistic	intuitionistic	ADJ
ejpam-5857	56	22	neutrosophic	neutrosophic	ADJ
ejpam-5857	56	23	soft	soft	ADJ
ejpam-5857	56	24	sets	set	NOUN
ejpam-5857	56	25	(	(	PUNCT
ejpam-5857	56	26	inss	ins	NOUN
ejpam-5857	56	27	)	)	PUNCT
ejpam-5857	56	28	.	.	PUNCT
ejpam-5857	57	1	their	their	PRON
ejpam-5857	57	2	work	work	NOUN
ejpam-5857	57	3	established	establish	VERB
ejpam-5857	57	4	operations	operation	NOUN
ejpam-5857	57	5	and	and	CCONJ
ejpam-5857	57	6	definitions	definition	NOUN
ejpam-5857	57	7	specific	specific	ADJ
ejpam-5857	57	8	to	to	ADP
ejpam-5857	57	9	inss	ins	NOUN
ejpam-5857	57	10	,	,	PUNCT
ejpam-5857	57	11	creating	create	VERB
ejpam-5857	57	12	a	a	DET
ejpam-5857	57	13	basis	basis	NOUN
ejpam-5857	57	14	for	for	ADP
ejpam-5857	57	15	further	further	ADJ
ejpam-5857	57	16	theoretical	theoretical	ADJ
ejpam-5857	57	17	developments	development	NOUN
ejpam-5857	57	18	.	.	PUNCT
ejpam-5857	58	1	later	later	ADV
ejpam-5857	58	2	that	that	DET
ejpam-5857	58	3	year	year	NOUN
ejpam-5857	58	4	,	,	PUNCT
ejpam-5857	58	5	broumi	broumi	PROPN
ejpam-5857	58	6	and	and	CCONJ
ejpam-5857	58	7	smarandache	smarandache	NOUN
ejpam-5857	59	1	[	[	X
ejpam-5857	59	2	5	5	NUM
ejpam-5857	59	3	]	]	PUNCT
ejpam-5857	59	4	proposed	propose	VERB
ejpam-5857	59	5	additional	additional	ADJ
ejpam-5857	59	6	operations	operation	NOUN
ejpam-5857	59	7	on	on	ADP
ejpam-5857	59	8	inss	ins	NOUN
ejpam-5857	59	9	,	,	PUNCT
ejpam-5857	59	10	demonstrating	demonstrate	VERB
ejpam-5857	59	11	key	key	ADJ
ejpam-5857	59	12	interconnections	interconnection	NOUN
ejpam-5857	59	13	and	and	CCONJ
ejpam-5857	59	14	results	result	NOUN
ejpam-5857	59	15	that	that	PRON
ejpam-5857	59	16	elucidate	elucidate	VERB
ejpam-5857	59	17	the	the	DET
ejpam-5857	59	18	properties	property	NOUN
ejpam-5857	59	19	of	of	ADP
ejpam-5857	59	20	these	these	DET
ejpam-5857	59	21	operations	operation	NOUN
ejpam-5857	59	22	.	.	PUNCT
ejpam-5857	60	1	in	in	ADP
ejpam-5857	60	2	2014	2014	NUM
ejpam-5857	60	3	,	,	PUNCT
ejpam-5857	60	4	broumi	broumi	PROPN
ejpam-5857	60	5	et	et	PROPN
ejpam-5857	60	6	al	al	PROPN
ejpam-5857	60	7	.	.	PUNCT
ejpam-5857	61	1	[	[	X
ejpam-5857	61	2	6	6	NUM
ejpam-5857	61	3	]	]	PUNCT
ejpam-5857	61	4	extended	extended	ADJ
ejpam-5857	61	5	ins	in	NOUN
ejpam-5857	61	6	applications	application	NOUN
ejpam-5857	61	7	to	to	PART
ejpam-5857	61	8	ring	ring	NOUN
ejpam-5857	61	9	theory	theory	NOUN
ejpam-5857	61	10	,	,	PUNCT
ejpam-5857	61	11	introducing	introduce	VERB
ejpam-5857	61	12	the	the	DET
ejpam-5857	61	13	notion	notion	NOUN
ejpam-5857	61	14	of	of	ADP
ejpam-5857	61	15	intuitionistic	intuitionistic	ADJ
ejpam-5857	61	16	neutrosophic	neutrosophic	ADJ
ejpam-5857	61	17	soft	soft	ADJ
ejpam-5857	61	18	sets	set	NOUN
ejpam-5857	61	19	over	over	ADP
ejpam-5857	61	20	rings	ring	NOUN
ejpam-5857	61	21	.	.	PUNCT
ejpam-5857	62	1	their	their	PRON
ejpam-5857	62	2	study	study	NOUN
ejpam-5857	62	3	analyzed	analyze	VERB
ejpam-5857	62	4	fundamental	fundamental	ADJ
ejpam-5857	62	5	properties	property	NOUN
ejpam-5857	62	6	and	and	CCONJ
ejpam-5857	62	7	defined	define	VERB
ejpam-5857	62	8	operations	operation	NOUN
ejpam-5857	62	9	such	such	ADJ
ejpam-5857	62	10	as	as	ADP
ejpam-5857	62	11	intersection	intersection	NOUN
ejpam-5857	62	12	,	,	PUNCT
ejpam-5857	62	13	union	union	NOUN
ejpam-5857	62	14	,	,	PUNCT
ejpam-5857	62	15	and	and	CCONJ
ejpam-5857	62	16	and	and	CCONJ
ejpam-5857	62	17	or	or	CCONJ
ejpam-5857	62	18	,	,	PUNCT
ejpam-5857	62	19	as	as	ADV
ejpam-5857	62	20	well	well	ADV
ejpam-5857	62	21	as	as	ADP
ejpam-5857	62	22	the	the	DET
ejpam-5857	62	23	product	product	NOUN
ejpam-5857	62	24	of	of	ADP
ejpam-5857	62	25	two	two	NUM
ejpam-5857	62	26	inss	ins	NOUN
ejpam-5857	62	27	over	over	ADP
ejpam-5857	62	28	rings	ring	NOUN
ejpam-5857	62	29	.	.	PUNCT
ejpam-5857	63	1	this	this	DET
ejpam-5857	63	2	body	body	NOUN
ejpam-5857	63	3	of	of	ADP
ejpam-5857	63	4	work	work	NOUN
ejpam-5857	63	5	highlights	highlight	VERB
ejpam-5857	63	6	the	the	DET
ejpam-5857	63	7	adaptability	adaptability	NOUN
ejpam-5857	63	8	and	and	CCONJ
ejpam-5857	63	9	utility	utility	NOUN
ejpam-5857	63	10	of	of	ADP
ejpam-5857	63	11	inss	ins	NOUN
ejpam-5857	63	12	in	in	ADP
ejpam-5857	63	13	addressing	address	VERB
ejpam-5857	63	14	complex	complex	ADJ
ejpam-5857	63	15	algebraic	algebraic	ADJ
ejpam-5857	63	16	structures	structure	NOUN
ejpam-5857	63	17	and	and	CCONJ
ejpam-5857	63	18	uncertainty	uncertainty	NOUN
ejpam-5857	63	19	-	-	PUNCT
ejpam-5857	63	20	rich	rich	ADJ
ejpam-5857	63	21	environments	environment	NOUN
ejpam-5857	63	22	.	.	PUNCT
ejpam-5857	64	1	2	2	X
ejpam-5857	64	2	.	.	X
ejpam-5857	64	3	preliminaries	preliminary	NOUN
ejpam-5857	64	4	algebraic	algebraic	ADJ
ejpam-5857	64	5	structures	structure	NOUN
ejpam-5857	64	6	have	have	AUX
ejpam-5857	64	7	long	long	ADV
ejpam-5857	64	8	been	be	AUX
ejpam-5857	64	9	a	a	DET
ejpam-5857	64	10	cornerstone	cornerstone	NOUN
ejpam-5857	64	11	of	of	ADP
ejpam-5857	64	12	mathematical	mathematical	ADJ
ejpam-5857	64	13	theory	theory	NOUN
ejpam-5857	64	14	,	,	PUNCT
ejpam-5857	64	15	offering	offer	VERB
ejpam-5857	64	16	robust	robust	ADJ
ejpam-5857	64	17	frameworks	framework	NOUN
ejpam-5857	64	18	for	for	ADP
ejpam-5857	64	19	solving	solve	VERB
ejpam-5857	64	20	complex	complex	ADJ
ejpam-5857	64	21	problems	problem	NOUN
ejpam-5857	64	22	and	and	CCONJ
ejpam-5857	64	23	modeling	model	VERB
ejpam-5857	64	24	abstract	abstract	ADJ
ejpam-5857	64	25	relationships	relationship	NOUN
ejpam-5857	64	26	.	.	PUNCT
ejpam-5857	65	1	among	among	ADP
ejpam-5857	65	2	these	these	PRON
ejpam-5857	65	3	,	,	PUNCT
ejpam-5857	65	4	the	the	DET
ejpam-5857	65	5	iup	iup	NOUN
ejpam-5857	65	6	-	-	PUNCT
ejpam-5857	65	7	algebra	algebra	NOUN
ejpam-5857	65	8	emerges	emerge	VERB
ejpam-5857	65	9	as	as	ADP
ejpam-5857	65	10	a	a	DET
ejpam-5857	65	11	sophisticated	sophisticated	ADJ
ejpam-5857	65	12	and	and	CCONJ
ejpam-5857	65	13	highly	highly	ADV
ejpam-5857	65	14	versatile	versatile	ADJ
ejpam-5857	65	15	system	system	NOUN
ejpam-5857	65	16	,	,	PUNCT
ejpam-5857	65	17	first	first	ADV
ejpam-5857	65	18	introduced	introduce	VERB
ejpam-5857	65	19	as	as	ADP
ejpam-5857	65	20	an	an	DET
ejpam-5857	65	21	extension	extension	NOUN
ejpam-5857	65	22	of	of	ADP
ejpam-5857	65	23	classical	classical	ADJ
ejpam-5857	65	24	algebraic	algebraic	ADJ
ejpam-5857	65	25	logic	logic	NOUN
ejpam-5857	65	26	.	.	PUNCT
ejpam-5857	66	1	this	this	DET
ejpam-5857	66	2	innovative	innovative	ADJ
ejpam-5857	66	3	structure	structure	NOUN
ejpam-5857	66	4	integrates	integrate	VERB
ejpam-5857	66	5	unique	unique	ADJ
ejpam-5857	66	6	axioms	axiom	NOUN
ejpam-5857	66	7	that	that	PRON
ejpam-5857	66	8	enable	enable	VERB
ejpam-5857	66	9	the	the	DET
ejpam-5857	66	10	study	study	NOUN
ejpam-5857	66	11	of	of	ADP
ejpam-5857	66	12	operations	operation	NOUN
ejpam-5857	66	13	and	and	CCONJ
ejpam-5857	66	14	relations	relation	NOUN
ejpam-5857	66	15	under	under	ADP
ejpam-5857	66	16	specific	specific	ADJ
ejpam-5857	66	17	constraints	constraint	NOUN
ejpam-5857	66	18	,	,	PUNCT
ejpam-5857	66	19	making	make	VERB
ejpam-5857	66	20	it	it	PRON
ejpam-5857	66	21	a	a	DET
ejpam-5857	66	22	powerful	powerful	ADJ
ejpam-5857	66	23	tool	tool	NOUN
ejpam-5857	66	24	for	for	ADP
ejpam-5857	66	25	exploring	explore	VERB
ejpam-5857	66	26	uncertainty	uncertainty	NOUN
ejpam-5857	66	27	,	,	PUNCT
ejpam-5857	66	28	symmetry	symmetry	NOUN
ejpam-5857	66	29	and	and	CCONJ
ejpam-5857	66	30	interdependence	interdependence	NOUN
ejpam-5857	66	31	in	in	ADP
ejpam-5857	66	32	algebraic	algebraic	ADJ
ejpam-5857	66	33	contexts	contexts	NOUN
ejpam-5857	66	34	.	.	PUNCT
ejpam-5857	67	1	in	in	ADP
ejpam-5857	67	2	this	this	DET
ejpam-5857	67	3	section	section	NOUN
ejpam-5857	67	4	,	,	PUNCT
ejpam-5857	67	5	we	we	PRON
ejpam-5857	67	6	delve	delve	VERB
ejpam-5857	67	7	into	into	ADP
ejpam-5857	67	8	the	the	DET
ejpam-5857	67	9	concept	concept	NOUN
ejpam-5857	67	10	of	of	ADP
ejpam-5857	67	11	iup	iup	NOUN
ejpam-5857	67	12	-	-	PUNCT
ejpam-5857	67	13	algebra	algebra	NOUN
ejpam-5857	67	14	by	by	ADP
ejpam-5857	67	15	defining	define	VERB
ejpam-5857	67	16	its	its	PRON
ejpam-5857	67	17	fundamental	fundamental	ADJ
ejpam-5857	67	18	k.	k.	PROPN
ejpam-5857	67	19	suayngam	suayngam	PROPN
ejpam-5857	67	20	,	,	PUNCT
ejpam-5857	67	21	p.	p.	NOUN
ejpam-5857	67	22	julatha	julatha	PROPN
ejpam-5857	67	23	,	,	PUNCT
ejpam-5857	67	24	w.	w.	PROPN
ejpam-5857	67	25	nakkhasen	nakkhasen	PROPN
ejpam-5857	67	26	,	,	PUNCT
ejpam-5857	67	27	a.	a.	NOUN
ejpam-5857	67	28	iampan	iampan	PROPN
ejpam-5857	67	29	/	/	SYM
ejpam-5857	67	30	eur	eur	PROPN
ejpam-5857	67	31	.	.	PUNCT
ejpam-5857	68	1	j.	j.	PROPN
ejpam-5857	68	2	pure	pure	PROPN
ejpam-5857	68	3	appl	appl	PROPN
ejpam-5857	68	4	.	.	PROPN
ejpam-5857	68	5	math	math	PROPN
ejpam-5857	68	6	,	,	PUNCT
ejpam-5857	68	7	18	18	NUM
ejpam-5857	68	8	(	(	PUNCT
ejpam-5857	68	9	2	2	NUM
ejpam-5857	68	10	)	)	PUNCT
ejpam-5857	68	11	(	(	PUNCT
ejpam-5857	68	12	2025	2025	NUM
ejpam-5857	68	13	)	)	PUNCT
ejpam-5857	68	14	,	,	PUNCT
ejpam-5857	68	15	5857	5857	NUM
ejpam-5857	68	16	4	4	NUM
ejpam-5857	68	17	of	of	ADP
ejpam-5857	68	18	30	30	NUM
ejpam-5857	68	19	components	component	NOUN
ejpam-5857	68	20	,	,	PUNCT
ejpam-5857	68	21	which	which	PRON
ejpam-5857	68	22	consist	consist	VERB
ejpam-5857	68	23	of	of	ADP
ejpam-5857	68	24	three	three	NUM
ejpam-5857	68	25	primary	primary	ADJ
ejpam-5857	68	26	axioms	axiom	NOUN
ejpam-5857	68	27	that	that	PRON
ejpam-5857	68	28	govern	govern	VERB
ejpam-5857	68	29	its	its	PRON
ejpam-5857	68	30	structure	structure	NOUN
ejpam-5857	68	31	.	.	PUNCT
ejpam-5857	69	1	additionally	additionally	ADV
ejpam-5857	69	2	,	,	PUNCT
ejpam-5857	69	3	we	we	PRON
ejpam-5857	69	4	identify	identify	VERB
ejpam-5857	69	5	and	and	CCONJ
ejpam-5857	69	6	elaborate	elaborate	VERB
ejpam-5857	69	7	on	on	ADP
ejpam-5857	69	8	four	four	NUM
ejpam-5857	69	9	special	special	ADJ
ejpam-5857	69	10	subsets	subset	NOUN
ejpam-5857	69	11	—	—	PUNCT
ejpam-5857	69	12	iup	iup	NOUN
ejpam-5857	69	13	-	-	PUNCT
ejpam-5857	69	14	subalgebra	subalgebra	NOUN
ejpam-5857	69	15	,	,	PUNCT
ejpam-5857	69	16	iup	iup	NOUN
ejpam-5857	69	17	-	-	PUNCT
ejpam-5857	69	18	filter	filter	NOUN
ejpam-5857	69	19	,	,	PUNCT
ejpam-5857	69	20	iupideal	iupideal	ADJ
ejpam-5857	69	21	and	and	CCONJ
ejpam-5857	69	22	strong	strong	ADJ
ejpam-5857	69	23	iup	iup	NOUN
ejpam-5857	69	24	-	-	PUNCT
ejpam-5857	69	25	ideal	ideal	NOUN
ejpam-5857	69	26	—	—	PUNCT
ejpam-5857	69	27	which	which	PRON
ejpam-5857	69	28	form	form	VERB
ejpam-5857	69	29	the	the	DET
ejpam-5857	69	30	backbone	backbone	NOUN
ejpam-5857	69	31	of	of	ADP
ejpam-5857	69	32	further	further	ADJ
ejpam-5857	69	33	theoretical	theoretical	ADJ
ejpam-5857	69	34	developments	development	NOUN
ejpam-5857	69	35	.	.	PUNCT
ejpam-5857	70	1	these	these	DET
ejpam-5857	70	2	subsets	subset	NOUN
ejpam-5857	70	3	serve	serve	VERB
ejpam-5857	70	4	as	as	ADP
ejpam-5857	70	5	critical	critical	ADJ
ejpam-5857	70	6	tools	tool	NOUN
ejpam-5857	70	7	for	for	ADP
ejpam-5857	70	8	analyzing	analyze	VERB
ejpam-5857	70	9	and	and	CCONJ
ejpam-5857	70	10	categorizing	categorize	VERB
ejpam-5857	70	11	the	the	DET
ejpam-5857	70	12	behaviors	behavior	NOUN
ejpam-5857	70	13	and	and	CCONJ
ejpam-5857	70	14	properties	property	NOUN
ejpam-5857	70	15	of	of	ADP
ejpam-5857	70	16	iup	iup	NOUN
ejpam-5857	70	17	-	-	PUNCT
ejpam-5857	70	18	algebraic	algebraic	PROPN
ejpam-5857	70	19	systems	system	NOUN
ejpam-5857	70	20	,	,	PUNCT
ejpam-5857	70	21	setting	set	VERB
ejpam-5857	70	22	the	the	DET
ejpam-5857	70	23	stage	stage	NOUN
ejpam-5857	70	24	for	for	ADP
ejpam-5857	70	25	advanced	advanced	ADJ
ejpam-5857	70	26	research	research	NOUN
ejpam-5857	70	27	and	and	CCONJ
ejpam-5857	70	28	applications	application	NOUN
ejpam-5857	70	29	in	in	ADP
ejpam-5857	70	30	the	the	DET
ejpam-5857	70	31	subsequent	subsequent	ADJ
ejpam-5857	70	32	topics	topic	NOUN
ejpam-5857	70	33	.	.	PUNCT
ejpam-5857	71	1	the	the	DET
ejpam-5857	71	2	detailed	detailed	ADJ
ejpam-5857	71	3	content	content	NOUN
ejpam-5857	71	4	is	be	AUX
ejpam-5857	71	5	organized	organize	VERB
ejpam-5857	71	6	as	as	SCONJ
ejpam-5857	71	7	follows	follow	VERB
ejpam-5857	71	8	:	:	PUNCT
ejpam-5857	71	9	definition	definition	NOUN
ejpam-5857	71	10	1	1	NUM
ejpam-5857	71	11	.	.	PUNCT
ejpam-5857	72	1	[	[	X
ejpam-5857	72	2	9	9	NUM
ejpam-5857	72	3	]	]	PUNCT
ejpam-5857	72	4	an	an	DET
ejpam-5857	72	5	algebra	algebra	NOUN
ejpam-5857	72	6	x	x	X
ejpam-5857	72	7	=	=	SYM
ejpam-5857	72	8	(	(	PUNCT
ejpam-5857	72	9	x	x	NOUN
ejpam-5857	72	10	;	;	PUNCT
ejpam-5857	72	11	·	·	PUNCT
ejpam-5857	72	12	,	,	PUNCT
ejpam-5857	72	13	0	0	NUM
ejpam-5857	72	14	)	)	PUNCT
ejpam-5857	72	15	of	of	ADP
ejpam-5857	72	16	type	type	NOUN
ejpam-5857	72	17	(	(	PUNCT
ejpam-5857	72	18	2	2	NUM
ejpam-5857	72	19	,	,	PUNCT
ejpam-5857	72	20	0	0	NUM
ejpam-5857	72	21	)	)	PUNCT
ejpam-5857	72	22	is	be	AUX
ejpam-5857	72	23	called	call	VERB
ejpam-5857	72	24	an	an	DET
ejpam-5857	72	25	iup	iup	NOUN
ejpam-5857	72	26	-	-	PUNCT
ejpam-5857	72	27	algebra	algebra	NOUN
ejpam-5857	72	28	,	,	PUNCT
ejpam-5857	72	29	where	where	SCONJ
ejpam-5857	72	30	x	x	PRON
ejpam-5857	72	31	is	be	AUX
ejpam-5857	72	32	a	a	DET
ejpam-5857	72	33	nonempty	nonempty	ADJ
ejpam-5857	72	34	set	set	VERB
ejpam-5857	72	35	,	,	PUNCT
ejpam-5857	72	36	·	·	PUNCT
ejpam-5857	72	37	is	be	AUX
ejpam-5857	72	38	a	a	DET
ejpam-5857	72	39	binary	binary	ADJ
ejpam-5857	72	40	operation	operation	NOUN
ejpam-5857	72	41	on	on	ADP
ejpam-5857	72	42	x	x	X
ejpam-5857	72	43	and	and	CCONJ
ejpam-5857	72	44	0	0	NUM
ejpam-5857	72	45	is	be	AUX
ejpam-5857	72	46	a	a	DET
ejpam-5857	72	47	fixed	fix	VERB
ejpam-5857	72	48	element	element	NOUN
ejpam-5857	72	49	of	of	ADP
ejpam-5857	72	50	x	x	PRON
ejpam-5857	72	51	if	if	SCONJ
ejpam-5857	72	52	it	it	PRON
ejpam-5857	72	53	satisfies	satisfy	VERB
ejpam-5857	72	54	the	the	DET
ejpam-5857	72	55	following	follow	VERB
ejpam-5857	72	56	axioms	axiom	NOUN
ejpam-5857	72	57	:	:	PUNCT
ejpam-5857	72	58	(	(	PUNCT
ejpam-5857	72	59	∀x	∀x	X
ejpam-5857	72	60	∈	∈	NOUN
ejpam-5857	72	61	x)(0	x)(0	X
ejpam-5857	72	62	·	·	PUNCT
ejpam-5857	73	1	x	x	PUNCT
ejpam-5857	73	2	=	=	PUNCT
ejpam-5857	73	3	x	x	NOUN
ejpam-5857	73	4	)	)	PUNCT
ejpam-5857	73	5	,	,	PUNCT
ejpam-5857	73	6	(	(	PUNCT
ejpam-5857	73	7	iup-1	iup-1	X
ejpam-5857	73	8	)	)	PUNCT
ejpam-5857	73	9	(	(	PUNCT
ejpam-5857	73	10	∀x	∀x	X
ejpam-5857	73	11	∈	∈	PROPN
ejpam-5857	73	12	x)(x	x)(x	PROPN
ejpam-5857	73	13	·	·	PUNCT
ejpam-5857	73	14	x	x	PUNCT
ejpam-5857	74	1	=	=	PUNCT
ejpam-5857	74	2	0	0	NUM
ejpam-5857	74	3	)	)	PUNCT
ejpam-5857	74	4	,	,	PUNCT
ejpam-5857	74	5	(	(	PUNCT
ejpam-5857	74	6	iup-2	iup-2	X
ejpam-5857	74	7	)	)	PUNCT
ejpam-5857	74	8	(	(	PUNCT
ejpam-5857	74	9	∀x	∀x	X
ejpam-5857	74	10	,	,	PUNCT
ejpam-5857	74	11	y	y	PROPN
ejpam-5857	74	12	,	,	PUNCT
ejpam-5857	74	13	z	z	PROPN
ejpam-5857	74	14	∈	∈	PROPN
ejpam-5857	74	15	x)((x	x)((x	NOUN
ejpam-5857	74	16	·	·	PUNCT
ejpam-5857	74	17	y	y	X
ejpam-5857	74	18	)	)	PUNCT
ejpam-5857	74	19	·	·	PUNCT
ejpam-5857	74	20	(	(	PUNCT
ejpam-5857	74	21	x	x	X
ejpam-5857	74	22	·	·	PUNCT
ejpam-5857	74	23	z	z	X
ejpam-5857	74	24	)	)	PUNCT
ejpam-5857	74	25	=	=	SYM
ejpam-5857	75	1	y	y	PROPN
ejpam-5857	75	2	·	·	PUNCT
ejpam-5857	75	3	z	z	X
ejpam-5857	75	4	)	)	PUNCT
ejpam-5857	75	5	.	.	PUNCT
ejpam-5857	76	1	(	(	PUNCT
ejpam-5857	76	2	iup-3	iup-3	NOUN
ejpam-5857	76	3	)	)	PUNCT
ejpam-5857	76	4	for	for	ADP
ejpam-5857	76	5	the	the	DET
ejpam-5857	76	6	sake	sake	NOUN
ejpam-5857	76	7	of	of	ADP
ejpam-5857	76	8	simplicity	simplicity	NOUN
ejpam-5857	76	9	and	and	CCONJ
ejpam-5857	76	10	clarity	clarity	NOUN
ejpam-5857	76	11	,	,	PUNCT
ejpam-5857	76	12	we	we	PRON
ejpam-5857	76	13	will	will	AUX
ejpam-5857	76	14	denote	denote	VERB
ejpam-5857	76	15	x	x	PUNCT
ejpam-5857	76	16	as	as	ADP
ejpam-5857	76	17	an	an	DET
ejpam-5857	76	18	iup	iup	NOUN
ejpam-5857	76	19	-	-	PUNCT
ejpam-5857	76	20	algebra	algebra	NOUN
ejpam-5857	76	21	,	,	PUNCT
ejpam-5857	76	22	expressed	express	VERB
ejpam-5857	76	23	in	in	ADP
ejpam-5857	76	24	the	the	DET
ejpam-5857	76	25	form	form	NOUN
ejpam-5857	76	26	x	x	PUNCT
ejpam-5857	77	1	=	=	SYM
ejpam-5857	77	2	(	(	PUNCT
ejpam-5857	77	3	x	x	NOUN
ejpam-5857	77	4	;	;	PUNCT
ejpam-5857	77	5	·	·	PUNCT
ejpam-5857	77	6	,	,	PUNCT
ejpam-5857	77	7	0	0	NUM
ejpam-5857	77	8	)	)	PUNCT
ejpam-5857	77	9	,	,	PUNCT
ejpam-5857	77	10	unless	unless	SCONJ
ejpam-5857	77	11	stated	state	VERB
ejpam-5857	77	12	otherwise	otherwise	ADV
ejpam-5857	77	13	.	.	PUNCT
ejpam-5857	78	1	example	example	NOUN
ejpam-5857	79	1	1	1	NUM
ejpam-5857	79	2	.	.	PUNCT
ejpam-5857	79	3	let	let	VERB
ejpam-5857	79	4	x	x	PUNCT
ejpam-5857	79	5	=	=	PUNCT
ejpam-5857	79	6	{	{	PUNCT
ejpam-5857	79	7	0	0	NUM
ejpam-5857	79	8	,	,	PUNCT
ejpam-5857	79	9	1	1	NUM
ejpam-5857	79	10	,	,	PUNCT
ejpam-5857	79	11	2	2	NUM
ejpam-5857	79	12	,	,	PUNCT
ejpam-5857	79	13	3	3	NUM
ejpam-5857	79	14	,	,	PUNCT
ejpam-5857	79	15	4	4	NUM
ejpam-5857	79	16	,	,	PUNCT
ejpam-5857	79	17	5	5	NUM
ejpam-5857	79	18	}	}	PUNCT
ejpam-5857	79	19	be	be	AUX
ejpam-5857	79	20	a	a	DET
ejpam-5857	79	21	set	set	NOUN
ejpam-5857	79	22	with	with	ADP
ejpam-5857	79	23	a	a	DET
ejpam-5857	79	24	binary	binary	ADJ
ejpam-5857	79	25	operation	operation	NOUN
ejpam-5857	79	26	·	·	PUNCT
ejpam-5857	79	27	defined	define	VERB
ejpam-5857	79	28	by	by	ADP
ejpam-5857	79	29	the	the	DET
ejpam-5857	79	30	following	following	ADJ
ejpam-5857	79	31	cayley	cayley	ADJ
ejpam-5857	79	32	table	table	NOUN
ejpam-5857	79	33	:	:	PUNCT
ejpam-5857	79	34	·	·	PUNCT
ejpam-5857	79	35	0	0	NUM
ejpam-5857	79	36	1	1	NUM
ejpam-5857	79	37	2	2	NUM
ejpam-5857	79	38	3	3	NUM
ejpam-5857	79	39	4	4	NUM
ejpam-5857	79	40	5	5	NUM
ejpam-5857	79	41	0	0	NUM
ejpam-5857	79	42	0	0	NUM
ejpam-5857	79	43	1	1	NUM
ejpam-5857	79	44	2	2	NUM
ejpam-5857	79	45	3	3	NUM
ejpam-5857	79	46	4	4	NUM
ejpam-5857	79	47	5	5	NUM
ejpam-5857	79	48	1	1	NUM
ejpam-5857	79	49	3	3	NUM
ejpam-5857	79	50	0	0	NUM
ejpam-5857	79	51	5	5	NUM
ejpam-5857	79	52	1	1	NUM
ejpam-5857	79	53	2	2	NUM
ejpam-5857	79	54	4	4	NUM
ejpam-5857	79	55	2	2	NUM
ejpam-5857	79	56	5	5	NUM
ejpam-5857	79	57	2	2	NUM
ejpam-5857	79	58	0	0	NUM
ejpam-5857	79	59	4	4	NUM
ejpam-5857	79	60	1	1	NUM
ejpam-5857	79	61	3	3	NUM
ejpam-5857	79	62	3	3	NUM
ejpam-5857	79	63	1	1	NUM
ejpam-5857	79	64	3	3	NUM
ejpam-5857	79	65	4	4	NUM
ejpam-5857	79	66	0	0	NUM
ejpam-5857	79	67	5	5	NUM
ejpam-5857	79	68	2	2	NUM
ejpam-5857	79	69	4	4	NUM
ejpam-5857	79	70	4	4	NUM
ejpam-5857	79	71	5	5	NUM
ejpam-5857	79	72	3	3	NUM
ejpam-5857	79	73	2	2	NUM
ejpam-5857	79	74	0	0	NUM
ejpam-5857	79	75	1	1	NUM
ejpam-5857	79	76	5	5	NUM
ejpam-5857	79	77	2	2	NUM
ejpam-5857	79	78	4	4	NUM
ejpam-5857	79	79	1	1	NUM
ejpam-5857	79	80	5	5	NUM
ejpam-5857	79	81	3	3	NUM
ejpam-5857	79	82	0	0	NUM
ejpam-5857	79	83	then	then	ADV
ejpam-5857	79	84	x	x	SYM
ejpam-5857	79	85	=	=	SYM
ejpam-5857	79	86	(	(	PUNCT
ejpam-5857	79	87	x	x	NOUN
ejpam-5857	79	88	;	;	PUNCT
ejpam-5857	79	89	·	·	PUNCT
ejpam-5857	79	90	,	,	PUNCT
ejpam-5857	79	91	0	0	NUM
ejpam-5857	79	92	)	)	PUNCT
ejpam-5857	79	93	is	be	AUX
ejpam-5857	79	94	an	an	DET
ejpam-5857	79	95	iup	iup	NOUN
ejpam-5857	79	96	-	-	PUNCT
ejpam-5857	79	97	algebra	algebra	NOUN
ejpam-5857	79	98	.	.	PUNCT
ejpam-5857	79	99	example	example	NOUN
ejpam-5857	80	1	2	2	NUM
ejpam-5857	80	2	.	.	PUNCT
ejpam-5857	81	1	[	[	X
ejpam-5857	81	2	9	9	NUM
ejpam-5857	81	3	]	]	X
ejpam-5857	81	4	let	let	VERB
ejpam-5857	81	5	(	(	PUNCT
ejpam-5857	81	6	g	g	NOUN
ejpam-5857	81	7	;	;	PUNCT
ejpam-5857	81	8	·	·	PUNCT
ejpam-5857	81	9	,	,	PUNCT
ejpam-5857	81	10	e	e	X
ejpam-5857	81	11	)	)	PUNCT
ejpam-5857	81	12	be	be	AUX
ejpam-5857	81	13	a	a	DET
ejpam-5857	81	14	group	group	NOUN
ejpam-5857	81	15	where	where	SCONJ
ejpam-5857	81	16	every	every	DET
ejpam-5857	81	17	element	element	NOUN
ejpam-5857	81	18	is	be	AUX
ejpam-5857	81	19	self	self	NOUN
ejpam-5857	81	20	-	-	PUNCT
ejpam-5857	81	21	inverse	inverse	ADJ
ejpam-5857	81	22	,	,	PUNCT
ejpam-5857	81	23	meaning	mean	VERB
ejpam-5857	81	24	that	that	SCONJ
ejpam-5857	81	25	for	for	ADP
ejpam-5857	81	26	all	all	DET
ejpam-5857	81	27	x	x	SYM
ejpam-5857	81	28	∈	∈	PROPN
ejpam-5857	81	29	g	g	NOUN
ejpam-5857	81	30	,	,	PUNCT
ejpam-5857	81	31	x	x	X
ejpam-5857	81	32	·	·	PUNCT
ejpam-5857	81	33	x	x	PUNCT
ejpam-5857	81	34	=	=	PUNCT
ejpam-5857	81	35	e.	e.	PROPN
ejpam-5857	81	36	under	under	ADP
ejpam-5857	81	37	this	this	DET
ejpam-5857	81	38	condition	condition	NOUN
ejpam-5857	81	39	,	,	PUNCT
ejpam-5857	81	40	(	(	PUNCT
ejpam-5857	81	41	g	g	NOUN
ejpam-5857	81	42	;	;	PUNCT
ejpam-5857	81	43	·	·	PUNCT
ejpam-5857	81	44	,	,	PUNCT
ejpam-5857	81	45	e	e	X
ejpam-5857	81	46	)	)	PUNCT
ejpam-5857	81	47	satisfies	satisfy	VERB
ejpam-5857	81	48	the	the	DET
ejpam-5857	81	49	axioms	axiom	NOUN
ejpam-5857	81	50	required	require	VERB
ejpam-5857	81	51	for	for	SCONJ
ejpam-5857	81	52	it	it	PRON
ejpam-5857	81	53	to	to	PART
ejpam-5857	81	54	be	be	AUX
ejpam-5857	81	55	classified	classify	VERB
ejpam-5857	81	56	as	as	ADP
ejpam-5857	81	57	an	an	DET
ejpam-5857	81	58	iup	iup	NOUN
ejpam-5857	81	59	-	-	PUNCT
ejpam-5857	81	60	algebra	algebra	NOUN
ejpam-5857	81	61	.	.	PUNCT
ejpam-5857	82	1	this	this	DET
ejpam-5857	82	2	structural	structural	ADJ
ejpam-5857	82	3	property	property	NOUN
ejpam-5857	82	4	highlights	highlight	NOUN
ejpam-5857	82	5	the	the	DET
ejpam-5857	82	6	inherent	inherent	ADJ
ejpam-5857	82	7	symmetry	symmetry	NOUN
ejpam-5857	82	8	and	and	CCONJ
ejpam-5857	82	9	unique	unique	ADJ
ejpam-5857	82	10	characteristics	characteristic	NOUN
ejpam-5857	82	11	of	of	ADP
ejpam-5857	82	12	self	self	NOUN
ejpam-5857	82	13	-	-	PUNCT
ejpam-5857	82	14	inverse	inverse	NOUN
ejpam-5857	82	15	elements	element	NOUN
ejpam-5857	82	16	,	,	PUNCT
ejpam-5857	82	17	which	which	PRON
ejpam-5857	82	18	play	play	VERB
ejpam-5857	82	19	a	a	DET
ejpam-5857	82	20	fundamental	fundamental	ADJ
ejpam-5857	82	21	role	role	NOUN
ejpam-5857	82	22	in	in	ADP
ejpam-5857	82	23	defining	define	VERB
ejpam-5857	82	24	the	the	DET
ejpam-5857	82	25	algebraic	algebraic	ADJ
ejpam-5857	82	26	operations	operation	NOUN
ejpam-5857	82	27	and	and	CCONJ
ejpam-5857	82	28	logical	logical	ADJ
ejpam-5857	82	29	relationships	relationship	NOUN
ejpam-5857	82	30	within	within	ADP
ejpam-5857	82	31	the	the	DET
ejpam-5857	82	32	framework	framework	NOUN
ejpam-5857	82	33	of	of	ADP
ejpam-5857	82	34	iup	iup	NOUN
ejpam-5857	82	35	-	-	PUNCT
ejpam-5857	82	36	algebras	algebras	PROPN
ejpam-5857	82	37	.	.	PUNCT
ejpam-5857	83	1	example	example	NOUN
ejpam-5857	84	1	3	3	NUM
ejpam-5857	84	2	.	.	PUNCT
ejpam-5857	85	1	[	[	X
ejpam-5857	85	2	9	9	NUM
ejpam-5857	85	3	]	]	PUNCT
ejpam-5857	85	4	let	let	VERB
ejpam-5857	85	5	x	x	PRON
ejpam-5857	85	6	be	be	AUX
ejpam-5857	85	7	a	a	DET
ejpam-5857	85	8	set	set	NOUN
ejpam-5857	85	9	and	and	CCONJ
ejpam-5857	85	10	p(x	p(x	PROPN
ejpam-5857	85	11	)	)	PUNCT
ejpam-5857	85	12	means	mean	VERB
ejpam-5857	85	13	the	the	DET
ejpam-5857	85	14	power	power	NOUN
ejpam-5857	85	15	set	set	NOUN
ejpam-5857	85	16	of	of	ADP
ejpam-5857	85	17	x.	x.	NOUN
ejpam-5857	85	18	it	it	PRON
ejpam-5857	85	19	follows	follow	VERB
ejpam-5857	85	20	from	from	ADP
ejpam-5857	85	21	example	example	NOUN
ejpam-5857	85	22	2	2	NUM
ejpam-5857	85	23	that	that	SCONJ
ejpam-5857	85	24	(	(	PUNCT
ejpam-5857	85	25	p(x	p(x	PROPN
ejpam-5857	85	26	)	)	PUNCT
ejpam-5857	85	27	;	;	PUNCT
ejpam-5857	85	28	△	△	X
ejpam-5857	85	29	,	,	PUNCT
ejpam-5857	85	30	∅	∅	NOUN
ejpam-5857	85	31	)	)	PUNCT
ejpam-5857	85	32	is	be	AUX
ejpam-5857	85	33	an	an	DET
ejpam-5857	85	34	iup	iup	NOUN
ejpam-5857	85	35	-	-	PUNCT
ejpam-5857	85	36	algebra	algebra	NOUN
ejpam-5857	85	37	where	where	SCONJ
ejpam-5857	85	38	the	the	DET
ejpam-5857	85	39	binary	binary	PROPN
ejpam-5857	85	40	operation	operation	PROPN
ejpam-5857	85	41	△	△	PROPN
ejpam-5857	85	42	is	be	AUX
ejpam-5857	85	43	defined	define	VERB
ejpam-5857	85	44	as	as	ADP
ejpam-5857	85	45	the	the	DET
ejpam-5857	85	46	symmetric	symmetric	ADJ
ejpam-5857	85	47	difference	difference	NOUN
ejpam-5857	85	48	of	of	ADP
ejpam-5857	85	49	any	any	DET
ejpam-5857	85	50	two	two	NUM
ejpam-5857	85	51	sets	set	NOUN
ejpam-5857	85	52	.	.	PUNCT
ejpam-5857	86	1	example	example	NOUN
ejpam-5857	86	2	4	4	NUM
ejpam-5857	86	3	.	.	PUNCT
ejpam-5857	87	1	[	[	X
ejpam-5857	87	2	9	9	NUM
ejpam-5857	87	3	]	]	X
ejpam-5857	87	4	let	let	VERB
ejpam-5857	87	5	(	(	PUNCT
ejpam-5857	87	6	g	g	NOUN
ejpam-5857	87	7	;	;	PUNCT
ejpam-5857	87	8	·	·	PUNCT
ejpam-5857	87	9	,	,	PUNCT
ejpam-5857	87	10	e	e	X
ejpam-5857	87	11	)	)	PUNCT
ejpam-5857	87	12	be	be	AUX
ejpam-5857	87	13	a	a	DET
ejpam-5857	87	14	group	group	NOUN
ejpam-5857	87	15	with	with	ADP
ejpam-5857	87	16	the	the	DET
ejpam-5857	87	17	identity	identity	NOUN
ejpam-5857	87	18	element	element	NOUN
ejpam-5857	87	19	e.	e.	PROPN
ejpam-5857	87	20	define	define	VERB
ejpam-5857	87	21	a	a	DET
ejpam-5857	87	22	binary	binary	ADJ
ejpam-5857	87	23	operation	operation	NOUN
ejpam-5857	87	24	•	•	NOUN
ejpam-5857	87	25	on	on	ADP
ejpam-5857	87	26	g	g	NOUN
ejpam-5857	87	27	by	by	ADP
ejpam-5857	87	28	:	:	PUNCT
ejpam-5857	87	29	(	(	PUNCT
ejpam-5857	87	30	∀x	∀x	X
ejpam-5857	87	31	,	,	PUNCT
ejpam-5857	87	32	y	y	PROPN
ejpam-5857	87	33	∈	∈	PROPN
ejpam-5857	87	34	g)(x	g)(x	PROPN
ejpam-5857	87	35	•	•	NOUN
ejpam-5857	87	36	y	y	PROPN
ejpam-5857	87	37	=	=	SYM
ejpam-5857	87	38	y	y	PROPN
ejpam-5857	87	39	·	·	PUNCT
ejpam-5857	87	40	x−1	x−1	PROPN
ejpam-5857	87	41	)	)	PUNCT
ejpam-5857	87	42	.	.	PUNCT
ejpam-5857	88	1	(	(	PUNCT
ejpam-5857	88	2	2.1	2.1	NUM
ejpam-5857	88	3	)	)	PUNCT
ejpam-5857	88	4	then	then	ADV
ejpam-5857	88	5	(	(	PUNCT
ejpam-5857	88	6	g	g	NOUN
ejpam-5857	88	7	;	;	PUNCT
ejpam-5857	88	8	•	•	NUM
ejpam-5857	88	9	,	,	PUNCT
ejpam-5857	88	10	e	e	NOUN
ejpam-5857	88	11	)	)	PUNCT
ejpam-5857	88	12	is	be	AUX
ejpam-5857	88	13	an	an	DET
ejpam-5857	88	14	iup	iup	NOUN
ejpam-5857	88	15	-	-	PUNCT
ejpam-5857	88	16	algebra	algebra	NOUN
ejpam-5857	88	17	.	.	PUNCT
ejpam-5857	89	1	k.	k.	PROPN
ejpam-5857	89	2	suayngam	suayngam	PROPN
ejpam-5857	89	3	,	,	PUNCT
ejpam-5857	89	4	p.	p.	NOUN
ejpam-5857	89	5	julatha	julatha	PROPN
ejpam-5857	89	6	,	,	PUNCT
ejpam-5857	90	1	w.	w.	PROPN
ejpam-5857	90	2	nakkhasen	nakkhasen	PROPN
ejpam-5857	90	3	,	,	PUNCT
ejpam-5857	90	4	a.	a.	NOUN
ejpam-5857	90	5	iampan	iampan	PROPN
ejpam-5857	90	6	/	/	SYM
ejpam-5857	90	7	eur	eur	PROPN
ejpam-5857	90	8	.	.	PUNCT
ejpam-5857	91	1	j.	j.	PROPN
ejpam-5857	91	2	pure	pure	PROPN
ejpam-5857	91	3	appl	appl	PROPN
ejpam-5857	91	4	.	.	PROPN
ejpam-5857	91	5	math	math	PROPN
ejpam-5857	91	6	,	,	PUNCT
ejpam-5857	91	7	18	18	NUM
ejpam-5857	91	8	(	(	PUNCT
ejpam-5857	91	9	2	2	NUM
ejpam-5857	91	10	)	)	PUNCT
ejpam-5857	91	11	(	(	PUNCT
ejpam-5857	91	12	2025	2025	NUM
ejpam-5857	91	13	)	)	PUNCT
ejpam-5857	91	14	,	,	PUNCT
ejpam-5857	91	15	5857	5857	NUM
ejpam-5857	91	16	5	5	NUM
ejpam-5857	91	17	of	of	ADP
ejpam-5857	91	18	30	30	NUM
ejpam-5857	91	19	proposition	proposition	NOUN
ejpam-5857	91	20	1	1	NUM
ejpam-5857	91	21	.	.	PUNCT
ejpam-5857	92	1	[	[	X
ejpam-5857	92	2	9	9	NUM
ejpam-5857	92	3	]	]	PUNCT
ejpam-5857	92	4	in	in	ADP
ejpam-5857	92	5	an	an	DET
ejpam-5857	92	6	iup	iup	NOUN
ejpam-5857	92	7	-	-	PUNCT
ejpam-5857	92	8	algebra	algebra	NOUN
ejpam-5857	92	9	x	x	PUNCT
ejpam-5857	92	10	=	=	SYM
ejpam-5857	92	11	(	(	PUNCT
ejpam-5857	92	12	x	x	NOUN
ejpam-5857	92	13	;	;	PUNCT
ejpam-5857	92	14	·	·	PUNCT
ejpam-5857	92	15	,	,	PUNCT
ejpam-5857	92	16	0	0	NUM
ejpam-5857	92	17	)	)	PUNCT
ejpam-5857	92	18	,	,	PUNCT
ejpam-5857	92	19	the	the	DET
ejpam-5857	92	20	following	follow	VERB
ejpam-5857	92	21	assertions	assertion	NOUN
ejpam-5857	92	22	are	be	AUX
ejpam-5857	92	23	valid	valid	ADJ
ejpam-5857	92	24	(	(	PUNCT
ejpam-5857	92	25	see	see	VERB
ejpam-5857	92	26	[	[	X
ejpam-5857	92	27	9	9	NUM
ejpam-5857	92	28	]	]	NUM
ejpam-5857	92	29	)	)	PUNCT
ejpam-5857	92	30	.	.	PUNCT
ejpam-5857	93	1	(	(	PUNCT
ejpam-5857	93	2	∀x	∀x	X
ejpam-5857	93	3	,	,	PUNCT
ejpam-5857	93	4	y	y	PROPN
ejpam-5857	93	5	∈	∈	PROPN
ejpam-5857	93	6	x)((x	x)((x	PROPN
ejpam-5857	93	7	·	·	PUNCT
ejpam-5857	93	8	0	0	NUM
ejpam-5857	93	9	)	)	PUNCT
ejpam-5857	93	10	·	·	PUNCT
ejpam-5857	93	11	(	(	PUNCT
ejpam-5857	93	12	x	x	X
ejpam-5857	93	13	·	·	PUNCT
ejpam-5857	93	14	y	y	X
ejpam-5857	93	15	)	)	PUNCT
ejpam-5857	93	16	=	=	SYM
ejpam-5857	93	17	y	y	PROPN
ejpam-5857	93	18	)	)	PUNCT
ejpam-5857	93	19	,	,	PUNCT
ejpam-5857	93	20	(	(	PUNCT
ejpam-5857	93	21	2.2	2.2	NUM
ejpam-5857	93	22	)	)	PUNCT
ejpam-5857	93	23	(	(	PUNCT
ejpam-5857	93	24	∀x	∀x	X
ejpam-5857	93	25	∈	∈	PROPN
ejpam-5857	93	26	x)((x	x)((x	NOUN
ejpam-5857	93	27	·	·	PUNCT
ejpam-5857	93	28	0	0	NUM
ejpam-5857	93	29	)	)	PUNCT
ejpam-5857	93	30	·	·	PUNCT
ejpam-5857	94	1	(	(	PUNCT
ejpam-5857	94	2	x	x	X
ejpam-5857	94	3	·	·	PUNCT
ejpam-5857	94	4	0	0	NUM
ejpam-5857	94	5	)	)	PUNCT
ejpam-5857	94	6	=	=	SYM
ejpam-5857	94	7	0	0	NUM
ejpam-5857	94	8	)	)	PUNCT
ejpam-5857	94	9	,	,	PUNCT
ejpam-5857	94	10	(	(	PUNCT
ejpam-5857	94	11	2.3	2.3	NUM
ejpam-5857	94	12	)	)	PUNCT
ejpam-5857	94	13	(	(	PUNCT
ejpam-5857	94	14	∀x	∀x	X
ejpam-5857	94	15	,	,	PUNCT
ejpam-5857	94	16	y	y	PROPN
ejpam-5857	94	17	∈	∈	PROPN
ejpam-5857	94	18	x)((x	x)((x	NOUN
ejpam-5857	94	19	·	·	PUNCT
ejpam-5857	94	20	y	y	X
ejpam-5857	94	21	)	)	PUNCT
ejpam-5857	94	22	·	·	PUNCT
ejpam-5857	94	23	0	0	PUNCT
ejpam-5857	95	1	=	=	SYM
ejpam-5857	95	2	y	y	PROPN
ejpam-5857	95	3	·	·	PUNCT
ejpam-5857	95	4	x	x	X
ejpam-5857	95	5	)	)	PUNCT
ejpam-5857	95	6	,	,	PUNCT
ejpam-5857	95	7	(	(	PUNCT
ejpam-5857	95	8	2.4	2.4	NUM
ejpam-5857	95	9	)	)	PUNCT
ejpam-5857	95	10	(	(	PUNCT
ejpam-5857	95	11	∀x	∀x	X
ejpam-5857	95	12	∈	∈	PROPN
ejpam-5857	95	13	x)((x	x)((x	NOUN
ejpam-5857	95	14	·	·	PUNCT
ejpam-5857	95	15	0	0	NUM
ejpam-5857	95	16	)	)	PUNCT
ejpam-5857	95	17	·	·	PUNCT
ejpam-5857	95	18	0	0	PUNCT
ejpam-5857	96	1	=	=	SYM
ejpam-5857	96	2	x	x	X
ejpam-5857	96	3	)	)	PUNCT
ejpam-5857	96	4	,	,	PUNCT
ejpam-5857	96	5	(	(	PUNCT
ejpam-5857	96	6	2.5	2.5	NUM
ejpam-5857	96	7	)	)	PUNCT
ejpam-5857	96	8	(	(	PUNCT
ejpam-5857	96	9	∀x	∀x	X
ejpam-5857	96	10	,	,	PUNCT
ejpam-5857	96	11	y	y	PROPN
ejpam-5857	96	12	∈	∈	PROPN
ejpam-5857	96	13	x)(x	x)(x	PROPN
ejpam-5857	96	14	·	·	PUNCT
ejpam-5857	96	15	(	(	PUNCT
ejpam-5857	96	16	(	(	PUNCT
ejpam-5857	96	17	x	x	X
ejpam-5857	96	18	·	·	PUNCT
ejpam-5857	96	19	0	0	NUM
ejpam-5857	96	20	)	)	PUNCT
ejpam-5857	96	21	·	·	PUNCT
ejpam-5857	97	1	y	y	X
ejpam-5857	97	2	)	)	PUNCT
ejpam-5857	97	3	=	=	SYM
ejpam-5857	97	4	y	y	PROPN
ejpam-5857	97	5	)	)	PUNCT
ejpam-5857	97	6	,	,	PUNCT
ejpam-5857	97	7	(	(	PUNCT
ejpam-5857	97	8	2.6	2.6	NUM
ejpam-5857	97	9	)	)	PUNCT
ejpam-5857	97	10	(	(	PUNCT
ejpam-5857	97	11	∀x	∀x	X
ejpam-5857	97	12	,	,	PUNCT
ejpam-5857	97	13	y	y	PROPN
ejpam-5857	97	14	∈	∈	PROPN
ejpam-5857	97	15	x)(((x	x)(((x	PUNCT
ejpam-5857	97	16	·	·	PUNCT
ejpam-5857	97	17	0	0	NUM
ejpam-5857	97	18	)	)	PUNCT
ejpam-5857	97	19	·	·	PUNCT
ejpam-5857	98	1	y	y	X
ejpam-5857	98	2	)	)	PUNCT
ejpam-5857	98	3	·	·	PUNCT
ejpam-5857	99	1	x	x	PUNCT
ejpam-5857	99	2	=	=	PUNCT
ejpam-5857	99	3	y	y	PROPN
ejpam-5857	99	4	·	·	PUNCT
ejpam-5857	99	5	0	0	NUM
ejpam-5857	99	6	)	)	PUNCT
ejpam-5857	99	7	,	,	PUNCT
ejpam-5857	99	8	(	(	PUNCT
ejpam-5857	99	9	2.7	2.7	NUM
ejpam-5857	99	10	)	)	PUNCT
ejpam-5857	99	11	(	(	PUNCT
ejpam-5857	99	12	∀x	∀x	X
ejpam-5857	99	13	,	,	PUNCT
ejpam-5857	99	14	y	y	PROPN
ejpam-5857	99	15	,	,	PUNCT
ejpam-5857	99	16	z	z	PROPN
ejpam-5857	99	17	∈	∈	PROPN
ejpam-5857	99	18	x)(x	x)(x	PROPN
ejpam-5857	99	19	·	·	PUNCT
ejpam-5857	99	20	y	y	X
ejpam-5857	99	21	=	=	PUNCT
ejpam-5857	99	22	x	x	PUNCT
ejpam-5857	99	23	·	·	PUNCT
ejpam-5857	99	24	z	z	PROPN
ejpam-5857	99	25	⇔	⇔	PROPN
ejpam-5857	99	26	y	y	PROPN
ejpam-5857	99	27	=	=	SYM
ejpam-5857	99	28	z	z	PROPN
ejpam-5857	99	29	)	)	PUNCT
ejpam-5857	99	30	,	,	PUNCT
ejpam-5857	99	31	(	(	PUNCT
ejpam-5857	99	32	2.8	2.8	NUM
ejpam-5857	99	33	)	)	PUNCT
ejpam-5857	99	34	(	(	PUNCT
ejpam-5857	99	35	∀x	∀x	X
ejpam-5857	99	36	,	,	PUNCT
ejpam-5857	99	37	y	y	PROPN
ejpam-5857	99	38	∈	∈	PROPN
ejpam-5857	99	39	x)(x	x)(x	PROPN
ejpam-5857	99	40	·	·	PUNCT
ejpam-5857	100	1	y	y	X
ejpam-5857	100	2	=	=	SYM
ejpam-5857	100	3	0	0	NUM
ejpam-5857	100	4	⇔	⇔	X
ejpam-5857	100	5	x	x	X
ejpam-5857	100	6	=	=	SYM
ejpam-5857	100	7	y	y	PROPN
ejpam-5857	100	8	)	)	PUNCT
ejpam-5857	100	9	,	,	PUNCT
ejpam-5857	100	10	(	(	PUNCT
ejpam-5857	100	11	2.9	2.9	NUM
ejpam-5857	100	12	)	)	PUNCT
ejpam-5857	100	13	(	(	PUNCT
ejpam-5857	100	14	∀x	∀x	X
ejpam-5857	100	15	∈	∈	PROPN
ejpam-5857	100	16	x)(x	x)(x	PROPN
ejpam-5857	100	17	·	·	PUNCT
ejpam-5857	100	18	0	0	PUNCT
ejpam-5857	101	1	=	=	SYM
ejpam-5857	101	2	0	0	NUM
ejpam-5857	101	3	⇔	⇔	X
ejpam-5857	101	4	x	x	PUNCT
ejpam-5857	101	5	=	=	SYM
ejpam-5857	101	6	0	0	NUM
ejpam-5857	101	7	)	)	PUNCT
ejpam-5857	101	8	,	,	PUNCT
ejpam-5857	101	9	(	(	PUNCT
ejpam-5857	101	10	2.10	2.10	NUM
ejpam-5857	101	11	)	)	PUNCT
ejpam-5857	101	12	(	(	PUNCT
ejpam-5857	101	13	∀x	∀x	X
ejpam-5857	101	14	,	,	PUNCT
ejpam-5857	101	15	y	y	PROPN
ejpam-5857	101	16	,	,	PUNCT
ejpam-5857	101	17	z	z	PROPN
ejpam-5857	101	18	∈	∈	PROPN
ejpam-5857	101	19	x)(y	x)(y	PUNCT
ejpam-5857	101	20	·	·	PUNCT
ejpam-5857	101	21	x	x	PUNCT
ejpam-5857	101	22	=	=	PUNCT
ejpam-5857	101	23	z	z	X
ejpam-5857	101	24	·	·	PUNCT
ejpam-5857	101	25	x⇔	x⇔	PROPN
ejpam-5857	101	26	y	y	PROPN
ejpam-5857	101	27	=	=	SYM
ejpam-5857	101	28	z	z	PROPN
ejpam-5857	101	29	)	)	PUNCT
ejpam-5857	101	30	,	,	PUNCT
ejpam-5857	101	31	(	(	PUNCT
ejpam-5857	101	32	2.11	2.11	NUM
ejpam-5857	101	33	)	)	PUNCT
ejpam-5857	101	34	(	(	PUNCT
ejpam-5857	101	35	∀x	∀x	X
ejpam-5857	101	36	,	,	PUNCT
ejpam-5857	101	37	y	y	PROPN
ejpam-5857	101	38	∈	∈	PROPN
ejpam-5857	101	39	x)(x	x)(x	PROPN
ejpam-5857	101	40	·	·	PUNCT
ejpam-5857	101	41	y	y	X
ejpam-5857	101	42	=	=	PUNCT
ejpam-5857	101	43	y	y	PROPN
ejpam-5857	101	44	⇒	⇒	VERB
ejpam-5857	101	45	x	x	PUNCT
ejpam-5857	102	1	=	=	NOUN
ejpam-5857	102	2	0	0	NUM
ejpam-5857	102	3	)	)	PUNCT
ejpam-5857	102	4	,	,	PUNCT
ejpam-5857	102	5	(	(	PUNCT
ejpam-5857	102	6	2.12	2.12	NUM
ejpam-5857	102	7	)	)	PUNCT
ejpam-5857	102	8	(	(	PUNCT
ejpam-5857	102	9	∀x	∀x	X
ejpam-5857	102	10	,	,	PUNCT
ejpam-5857	102	11	y	y	PROPN
ejpam-5857	102	12	,	,	PUNCT
ejpam-5857	102	13	z	z	PROPN
ejpam-5857	102	14	∈	∈	PROPN
ejpam-5857	102	15	x)((x	x)((x	NOUN
ejpam-5857	102	16	·	·	PUNCT
ejpam-5857	102	17	y	y	X
ejpam-5857	102	18	)	)	PUNCT
ejpam-5857	102	19	·	·	PUNCT
ejpam-5857	102	20	0	0	PUNCT
ejpam-5857	103	1	=	=	SYM
ejpam-5857	103	2	(	(	PUNCT
ejpam-5857	103	3	z	z	NOUN
ejpam-5857	103	4	·	·	PUNCT
ejpam-5857	103	5	y	y	X
ejpam-5857	103	6	)	)	PUNCT
ejpam-5857	103	7	·	·	PUNCT
ejpam-5857	104	1	(	(	PUNCT
ejpam-5857	104	2	z	z	NOUN
ejpam-5857	104	3	·	·	PUNCT
ejpam-5857	104	4	x	x	X
ejpam-5857	104	5	)	)	PUNCT
ejpam-5857	104	6	)	)	PUNCT
ejpam-5857	104	7	,	,	PUNCT
ejpam-5857	104	8	(	(	PUNCT
ejpam-5857	104	9	2.13	2.13	NUM
ejpam-5857	104	10	)	)	PUNCT
ejpam-5857	104	11	(	(	PUNCT
ejpam-5857	104	12	∀x	∀x	X
ejpam-5857	104	13	,	,	PUNCT
ejpam-5857	104	14	y	y	PROPN
ejpam-5857	104	15	,	,	PUNCT
ejpam-5857	104	16	z	z	PROPN
ejpam-5857	104	17	∈	∈	PROPN
ejpam-5857	104	18	x)(x	x)(x	PROPN
ejpam-5857	104	19	·	·	PUNCT
ejpam-5857	104	20	y	y	X
ejpam-5857	104	21	=	=	SYM
ejpam-5857	104	22	0	0	PROPN
ejpam-5857	104	23	⇔	⇔	X
ejpam-5857	104	24	(	(	PUNCT
ejpam-5857	104	25	z	z	NOUN
ejpam-5857	104	26	·	·	PUNCT
ejpam-5857	104	27	x	x	X
ejpam-5857	104	28	)	)	PUNCT
ejpam-5857	104	29	·	·	PUNCT
ejpam-5857	104	30	(	(	PUNCT
ejpam-5857	104	31	z	z	X
ejpam-5857	104	32	·	·	PUNCT
ejpam-5857	104	33	y	y	X
ejpam-5857	104	34	)	)	PUNCT
ejpam-5857	104	35	=	=	NOUN
ejpam-5857	104	36	0	0	NUM
ejpam-5857	104	37	)	)	PUNCT
ejpam-5857	104	38	,	,	PUNCT
ejpam-5857	104	39	(	(	PUNCT
ejpam-5857	104	40	2.14	2.14	NUM
ejpam-5857	104	41	)	)	PUNCT
ejpam-5857	104	42	(	(	PUNCT
ejpam-5857	104	43	∀x	∀x	X
ejpam-5857	104	44	,	,	PUNCT
ejpam-5857	104	45	y	y	PROPN
ejpam-5857	104	46	,	,	PUNCT
ejpam-5857	104	47	z	z	PROPN
ejpam-5857	104	48	∈	∈	PROPN
ejpam-5857	104	49	x)(x	x)(x	PROPN
ejpam-5857	104	50	·	·	PUNCT
ejpam-5857	104	51	y	y	X
ejpam-5857	104	52	=	=	SYM
ejpam-5857	104	53	0	0	PROPN
ejpam-5857	104	54	⇔	⇔	X
ejpam-5857	104	55	(	(	PUNCT
ejpam-5857	104	56	x	x	PROPN
ejpam-5857	104	57	·	·	PUNCT
ejpam-5857	104	58	z	z	X
ejpam-5857	104	59	)	)	PUNCT
ejpam-5857	104	60	·	·	PUNCT
ejpam-5857	104	61	(	(	PUNCT
ejpam-5857	104	62	y	y	PROPN
ejpam-5857	104	63	·	·	PUNCT
ejpam-5857	104	64	z	z	X
ejpam-5857	104	65	)	)	PUNCT
ejpam-5857	104	66	=	=	SYM
ejpam-5857	104	67	0	0	NUM
ejpam-5857	104	68	)	)	PUNCT
ejpam-5857	104	69	,	,	PUNCT
ejpam-5857	104	70	(	(	PUNCT
ejpam-5857	104	71	2.15	2.15	NUM
ejpam-5857	104	72	)	)	PUNCT
ejpam-5857	104	73	the	the	DET
ejpam-5857	104	74	right	right	NOUN
ejpam-5857	104	75	and	and	CCONJ
ejpam-5857	104	76	the	the	DET
ejpam-5857	104	77	left	left	ADJ
ejpam-5857	104	78	cancellation	cancellation	NOUN
ejpam-5857	104	79	laws	law	NOUN
ejpam-5857	104	80	hold	hold	VERB
ejpam-5857	104	81	.	.	PUNCT
ejpam-5857	105	1	(	(	PUNCT
ejpam-5857	105	2	2.16	2.16	NUM
ejpam-5857	105	3	)	)	PUNCT
ejpam-5857	105	4	definition	definition	NOUN
ejpam-5857	105	5	2	2	NUM
ejpam-5857	105	6	.	.	PUNCT
ejpam-5857	106	1	[	[	X
ejpam-5857	106	2	9	9	NUM
ejpam-5857	106	3	]	]	PUNCT
ejpam-5857	106	4	a	a	DET
ejpam-5857	106	5	nonempty	nonempty	NOUN
ejpam-5857	106	6	subset	subset	VERB
ejpam-5857	106	7	s	s	NOUN
ejpam-5857	106	8	of	of	ADP
ejpam-5857	106	9	x	x	PRON
ejpam-5857	106	10	is	be	AUX
ejpam-5857	106	11	called	call	VERB
ejpam-5857	106	12	(	(	PUNCT
ejpam-5857	106	13	i	i	NOUN
ejpam-5857	106	14	)	)	PUNCT
ejpam-5857	106	15	an	an	DET
ejpam-5857	106	16	iup	iup	NOUN
ejpam-5857	106	17	-	-	PUNCT
ejpam-5857	106	18	subalgebra	subalgebra	NOUN
ejpam-5857	106	19	of	of	ADP
ejpam-5857	106	20	x	x	PRON
ejpam-5857	106	21	if	if	SCONJ
ejpam-5857	106	22	it	it	PRON
ejpam-5857	106	23	satisfies	satisfy	VERB
ejpam-5857	106	24	the	the	DET
ejpam-5857	106	25	following	follow	VERB
ejpam-5857	106	26	condition	condition	NOUN
ejpam-5857	106	27	:	:	PUNCT
ejpam-5857	106	28	(	(	PUNCT
ejpam-5857	106	29	∀x	∀x	X
ejpam-5857	106	30	,	,	PUNCT
ejpam-5857	106	31	y	y	PROPN
ejpam-5857	106	32	∈	∈	PROPN
ejpam-5857	106	33	s)(x	s)(x	PROPN
ejpam-5857	106	34	·	·	PUNCT
ejpam-5857	107	1	y	y	PROPN
ejpam-5857	107	2	∈	∈	PROPN
ejpam-5857	107	3	s	s	PART
ejpam-5857	107	4	)	)	PUNCT
ejpam-5857	107	5	(	(	PUNCT
ejpam-5857	107	6	2.17	2.17	NUM
ejpam-5857	107	7	)	)	PUNCT
ejpam-5857	107	8	(	(	PUNCT
ejpam-5857	107	9	ii	ii	NOUN
ejpam-5857	107	10	)	)	PUNCT
ejpam-5857	107	11	an	an	DET
ejpam-5857	107	12	iup	iup	NOUN
ejpam-5857	107	13	-	-	PUNCT
ejpam-5857	107	14	filter	filter	NOUN
ejpam-5857	107	15	of	of	ADP
ejpam-5857	107	16	x	x	PRON
ejpam-5857	107	17	if	if	SCONJ
ejpam-5857	107	18	it	it	PRON
ejpam-5857	107	19	satisfies	satisfy	VERB
ejpam-5857	107	20	the	the	DET
ejpam-5857	107	21	following	follow	VERB
ejpam-5857	107	22	conditions	condition	NOUN
ejpam-5857	107	23	:	:	PUNCT
ejpam-5857	107	24	the	the	DET
ejpam-5857	107	25	constant	constant	ADJ
ejpam-5857	107	26	0	0	NUM
ejpam-5857	107	27	of	of	ADP
ejpam-5857	107	28	x	x	PRON
ejpam-5857	107	29	is	be	AUX
ejpam-5857	107	30	in	in	ADP
ejpam-5857	107	31	s	s	PROPN
ejpam-5857	107	32	,	,	PUNCT
ejpam-5857	107	33	(	(	PUNCT
ejpam-5857	107	34	2.18	2.18	NUM
ejpam-5857	107	35	)	)	PUNCT
ejpam-5857	107	36	(	(	PUNCT
ejpam-5857	107	37	∀x	∀x	X
ejpam-5857	107	38	,	,	PUNCT
ejpam-5857	107	39	y	y	PROPN
ejpam-5857	107	40	∈	∈	PROPN
ejpam-5857	107	41	x)(x	x)(x	PROPN
ejpam-5857	107	42	·	·	PUNCT
ejpam-5857	108	1	y	y	PROPN
ejpam-5857	108	2	∈	∈	PROPN
ejpam-5857	108	3	s	s	PROPN
ejpam-5857	108	4	,	,	PUNCT
ejpam-5857	108	5	x	x	SYM
ejpam-5857	108	6	∈	∈	PROPN
ejpam-5857	108	7	s	s	PART
ejpam-5857	108	8	⇒	⇒	NOUN
ejpam-5857	108	9	y	y	PROPN
ejpam-5857	108	10	∈	∈	PROPN
ejpam-5857	108	11	s	s	PART
ejpam-5857	108	12	)	)	PUNCT
ejpam-5857	108	13	(	(	PUNCT
ejpam-5857	108	14	2.19	2.19	NUM
ejpam-5857	108	15	)	)	PUNCT
ejpam-5857	108	16	(	(	PUNCT
ejpam-5857	108	17	iii	iii	X
ejpam-5857	108	18	)	)	PUNCT
ejpam-5857	108	19	an	an	DET
ejpam-5857	108	20	iup	iup	NOUN
ejpam-5857	108	21	-	-	PUNCT
ejpam-5857	108	22	ideal	ideal	NOUN
ejpam-5857	108	23	of	of	ADP
ejpam-5857	108	24	x	x	PRON
ejpam-5857	108	25	if	if	SCONJ
ejpam-5857	108	26	it	it	PRON
ejpam-5857	108	27	satisfies	satisfy	VERB
ejpam-5857	108	28	the	the	DET
ejpam-5857	108	29	condition	condition	NOUN
ejpam-5857	108	30	(	(	PUNCT
ejpam-5857	108	31	2.18	2.18	NUM
ejpam-5857	108	32	)	)	PUNCT
ejpam-5857	108	33	and	and	CCONJ
ejpam-5857	108	34	the	the	DET
ejpam-5857	108	35	following	follow	VERB
ejpam-5857	108	36	condition	condition	NOUN
ejpam-5857	108	37	:	:	PUNCT
ejpam-5857	108	38	(	(	PUNCT
ejpam-5857	108	39	∀x	∀x	X
ejpam-5857	108	40	,	,	PUNCT
ejpam-5857	108	41	y	y	PROPN
ejpam-5857	108	42	,	,	PUNCT
ejpam-5857	108	43	z	z	PROPN
ejpam-5857	108	44	∈	∈	PROPN
ejpam-5857	108	45	x)(x	x)(x	PROPN
ejpam-5857	108	46	·	·	PUNCT
ejpam-5857	108	47	(	(	PUNCT
ejpam-5857	108	48	y	y	PROPN
ejpam-5857	108	49	·	·	PUNCT
ejpam-5857	108	50	z	z	X
ejpam-5857	108	51	)	)	PUNCT
ejpam-5857	108	52	∈	∈	PROPN
ejpam-5857	108	53	s	s	PROPN
ejpam-5857	108	54	,	,	PUNCT
ejpam-5857	108	55	y	y	PROPN
ejpam-5857	108	56	∈	∈	PROPN
ejpam-5857	108	57	s	s	PART
ejpam-5857	108	58	⇒	⇒	NOUN
ejpam-5857	108	59	x	x	PUNCT
ejpam-5857	108	60	·	·	PUNCT
ejpam-5857	108	61	z	z	PUNCT
ejpam-5857	108	62	∈	∈	PROPN
ejpam-5857	108	63	s	s	PART
ejpam-5857	108	64	)	)	PUNCT
ejpam-5857	108	65	(	(	PUNCT
ejpam-5857	108	66	2.20	2.20	NUM
ejpam-5857	108	67	)	)	PUNCT
ejpam-5857	108	68	(	(	PUNCT
ejpam-5857	108	69	iv	iv	X
ejpam-5857	108	70	)	)	PUNCT
ejpam-5857	108	71	a	a	DET
ejpam-5857	108	72	strong	strong	ADJ
ejpam-5857	108	73	iup	iup	NOUN
ejpam-5857	108	74	-	-	PUNCT
ejpam-5857	108	75	ideal	ideal	NOUN
ejpam-5857	108	76	of	of	ADP
ejpam-5857	108	77	x	x	PRON
ejpam-5857	108	78	if	if	SCONJ
ejpam-5857	108	79	it	it	PRON
ejpam-5857	108	80	satisfies	satisfy	VERB
ejpam-5857	108	81	the	the	DET
ejpam-5857	108	82	following	follow	VERB
ejpam-5857	108	83	condition	condition	NOUN
ejpam-5857	108	84	:	:	PUNCT
ejpam-5857	108	85	(	(	PUNCT
ejpam-5857	108	86	∀x	∀x	X
ejpam-5857	108	87	,	,	PUNCT
ejpam-5857	108	88	y	y	PROPN
ejpam-5857	108	89	∈	∈	PROPN
ejpam-5857	108	90	x)(y	x)(y	PUNCT
ejpam-5857	109	1	∈	∈	PROPN
ejpam-5857	109	2	s	s	PART
ejpam-5857	109	3	⇒	⇒	NOUN
ejpam-5857	109	4	x	x	X
ejpam-5857	109	5	·	·	PUNCT
ejpam-5857	109	6	y	y	X
ejpam-5857	109	7	∈	∈	PROPN
ejpam-5857	109	8	s	s	PART
ejpam-5857	109	9	)	)	PUNCT
ejpam-5857	109	10	(	(	PUNCT
ejpam-5857	109	11	2.21	2.21	NUM
ejpam-5857	109	12	)	)	PUNCT
ejpam-5857	109	13	according	accord	VERB
ejpam-5857	109	14	to	to	ADP
ejpam-5857	109	15	[	[	X
ejpam-5857	109	16	9	9	NUM
ejpam-5857	109	17	]	]	PUNCT
ejpam-5857	109	18	,	,	PUNCT
ejpam-5857	109	19	the	the	DET
ejpam-5857	109	20	concept	concept	NOUN
ejpam-5857	109	21	of	of	ADP
ejpam-5857	109	22	iup	iup	NOUN
ejpam-5857	109	23	-	-	PUNCT
ejpam-5857	109	24	filters	filter	NOUN
ejpam-5857	109	25	extends	extend	VERB
ejpam-5857	109	26	and	and	CCONJ
ejpam-5857	109	27	generalizes	generalize	VERB
ejpam-5857	109	28	the	the	DET
ejpam-5857	109	29	notions	notion	NOUN
ejpam-5857	109	30	of	of	ADP
ejpam-5857	109	31	both	both	DET
ejpam-5857	109	32	iup	iup	NOUN
ejpam-5857	109	33	-	-	PUNCT
ejpam-5857	109	34	ideals	ideal	NOUN
ejpam-5857	109	35	and	and	CCONJ
ejpam-5857	109	36	iup	iup	NOUN
ejpam-5857	109	37	-	-	PUNCT
ejpam-5857	109	38	subalgebras	subalgebras	PROPN
ejpam-5857	109	39	,	,	PUNCT
ejpam-5857	109	40	while	while	SCONJ
ejpam-5857	109	41	iup	iup	NOUN
ejpam-5857	109	42	-	-	PUNCT
ejpam-5857	109	43	ideals	ideal	NOUN
ejpam-5857	109	44	and	and	CCONJ
ejpam-5857	109	45	iup	iup	NOUN
ejpam-5857	109	46	-	-	PUNCT
ejpam-5857	109	47	subalgebras	subalgebras	PROPN
ejpam-5857	109	48	themselves	themselves	PRON
ejpam-5857	109	49	serve	serve	VERB
ejpam-5857	109	50	as	as	ADP
ejpam-5857	109	51	generalizations	generalization	NOUN
ejpam-5857	109	52	of	of	ADP
ejpam-5857	109	53	strong	strong	ADJ
ejpam-5857	109	54	iup	iup	NOUN
ejpam-5857	109	55	-	-	PUNCT
ejpam-5857	109	56	ideals	ideal	NOUN
ejpam-5857	109	57	.	.	PUNCT
ejpam-5857	110	1	in	in	ADP
ejpam-5857	110	2	an	an	DET
ejpam-5857	110	3	iup	iup	NOUN
ejpam-5857	110	4	-	-	PUNCT
ejpam-5857	110	5	algebra	algebra	NOUN
ejpam-5857	110	6	x	x	NOUN
ejpam-5857	110	7	,	,	PUNCT
ejpam-5857	110	8	it	it	PRON
ejpam-5857	110	9	is	be	AUX
ejpam-5857	110	10	observed	observe	VERB
ejpam-5857	110	11	that	that	SCONJ
ejpam-5857	110	12	strong	strong	ADJ
ejpam-5857	110	13	iup	iup	NOUN
ejpam-5857	110	14	-	-	PUNCT
ejpam-5857	110	15	ideals	ideal	NOUN
ejpam-5857	110	16	coincide	coincide	VERB
ejpam-5857	110	17	with	with	ADP
ejpam-5857	110	18	x	x	X
ejpam-5857	110	19	itself	itself	PRON
ejpam-5857	110	20	.	.	PUNCT
ejpam-5857	111	1	a	a	DET
ejpam-5857	111	2	visual	visual	ADJ
ejpam-5857	111	3	representation	representation	NOUN
ejpam-5857	111	4	of	of	ADP
ejpam-5857	111	5	these	these	DET
ejpam-5857	111	6	special	special	ADJ
ejpam-5857	111	7	subsets	subset	NOUN
ejpam-5857	111	8	and	and	CCONJ
ejpam-5857	111	9	their	their	PRON
ejpam-5857	111	10	interrelationships	interrelationship	NOUN
ejpam-5857	111	11	is	be	AUX
ejpam-5857	111	12	provided	provide	VERB
ejpam-5857	111	13	in	in	ADP
ejpam-5857	111	14	figure	figure	NOUN
ejpam-5857	111	15	1	1	NUM
ejpam-5857	111	16	,	,	PUNCT
ejpam-5857	111	17	offering	offer	VERB
ejpam-5857	111	18	a	a	DET
ejpam-5857	111	19	clear	clear	ADJ
ejpam-5857	111	20	and	and	CCONJ
ejpam-5857	111	21	intuitive	intuitive	ADJ
ejpam-5857	111	22	understanding	understanding	NOUN
ejpam-5857	111	23	of	of	ADP
ejpam-5857	111	24	the	the	DET
ejpam-5857	111	25	subset	subset	NOUN
ejpam-5857	111	26	hierarchy	hierarchy	NOUN
ejpam-5857	111	27	within	within	ADP
ejpam-5857	111	28	the	the	DET
ejpam-5857	111	29	framework	framework	NOUN
ejpam-5857	111	30	of	of	ADP
ejpam-5857	111	31	iup	iup	NOUN
ejpam-5857	111	32	-	-	PUNCT
ejpam-5857	111	33	algebras	algebras	PROPN
ejpam-5857	111	34	.	.	PUNCT
ejpam-5857	112	1	k.	k.	PROPN
ejpam-5857	112	2	suayngam	suayngam	PROPN
ejpam-5857	112	3	,	,	PUNCT
ejpam-5857	112	4	p.	p.	NOUN
ejpam-5857	112	5	julatha	julatha	PROPN
ejpam-5857	112	6	,	,	PUNCT
ejpam-5857	112	7	w.	w.	PROPN
ejpam-5857	112	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	112	9	,	,	PUNCT
ejpam-5857	112	10	a.	a.	NOUN
ejpam-5857	112	11	iampan	iampan	PROPN
ejpam-5857	112	12	/	/	SYM
ejpam-5857	112	13	eur	eur	PROPN
ejpam-5857	112	14	.	.	PUNCT
ejpam-5857	113	1	j.	j.	PROPN
ejpam-5857	113	2	pure	pure	PROPN
ejpam-5857	113	3	appl	appl	PROPN
ejpam-5857	113	4	.	.	PROPN
ejpam-5857	113	5	math	math	PROPN
ejpam-5857	113	6	,	,	PUNCT
ejpam-5857	113	7	18	18	NUM
ejpam-5857	113	8	(	(	PUNCT
ejpam-5857	113	9	2	2	NUM
ejpam-5857	113	10	)	)	PUNCT
ejpam-5857	113	11	(	(	PUNCT
ejpam-5857	113	12	2025	2025	NUM
ejpam-5857	113	13	)	)	PUNCT
ejpam-5857	113	14	,	,	PUNCT
ejpam-5857	113	15	5857	5857	NUM
ejpam-5857	113	16	6	6	NUM
ejpam-5857	113	17	of	of	ADP
ejpam-5857	113	18	30	30	NUM
ejpam-5857	113	19	iup	iup	ADJ
ejpam-5857	113	20	-	-	PUNCT
ejpam-5857	113	21	filter	filter	NOUN
ejpam-5857	113	22	iup	iup	NOUN
ejpam-5857	113	23	-	-	PUNCT
ejpam-5857	113	24	ideal	ideal	NOUN
ejpam-5857	113	25	iup	iup	NOUN
ejpam-5857	113	26	-	-	PUNCT
ejpam-5857	113	27	subalgebra	subalgebra	NOUN
ejpam-5857	113	28	strong	strong	ADJ
ejpam-5857	113	29	iup	iup	NOUN
ejpam-5857	113	30	-	-	PUNCT
ejpam-5857	113	31	ideal	ideal	NOUN
ejpam-5857	113	32	an	an	DET
ejpam-5857	113	33	iup	iup	NOUN
ejpam-5857	113	34	-	-	PUNCT
ejpam-5857	113	35	algebra	algebra	NOUN
ejpam-5857	113	36	x	x	VERB
ejpam-5857	113	37	figure	figure	NOUN
ejpam-5857	113	38	1	1	NUM
ejpam-5857	113	39	:	:	PUNCT
ejpam-5857	113	40	special	special	ADJ
ejpam-5857	113	41	subsets	subset	NOUN
ejpam-5857	113	42	of	of	ADP
ejpam-5857	113	43	iup	iup	NOUN
ejpam-5857	113	44	-	-	PUNCT
ejpam-5857	113	45	algebras	algebras	PROPN
ejpam-5857	113	46	3	3	NUM
ejpam-5857	113	47	.	.	NOUN
ejpam-5857	113	48	main	main	ADJ
ejpam-5857	113	49	results	result	NOUN
ejpam-5857	113	50	in	in	ADP
ejpam-5857	113	51	this	this	DET
ejpam-5857	113	52	section	section	NOUN
ejpam-5857	114	1	,	,	PUNCT
ejpam-5857	114	2	we	we	PRON
ejpam-5857	114	3	will	will	AUX
ejpam-5857	114	4	apply	apply	VERB
ejpam-5857	114	5	the	the	DET
ejpam-5857	114	6	concept	concept	NOUN
ejpam-5857	114	7	of	of	ADP
ejpam-5857	114	8	inss	ins	NOUN
ejpam-5857	114	9	to	to	PART
ejpam-5857	114	10	iup	iup	VERB
ejpam-5857	114	11	-	-	PUNCT
ejpam-5857	114	12	algebras	algebra	NOUN
ejpam-5857	114	13	,	,	PUNCT
ejpam-5857	114	14	which	which	PRON
ejpam-5857	114	15	will	will	AUX
ejpam-5857	114	16	result	result	VERB
ejpam-5857	114	17	in	in	ADP
ejpam-5857	114	18	the	the	DET
ejpam-5857	114	19	creation	creation	NOUN
ejpam-5857	114	20	of	of	ADP
ejpam-5857	114	21	four	four	NUM
ejpam-5857	114	22	special	special	ADJ
ejpam-5857	114	23	subsets	subset	NOUN
ejpam-5857	114	24	.	.	PUNCT
ejpam-5857	115	1	additionally	additionally	ADV
ejpam-5857	115	2	,	,	PUNCT
ejpam-5857	115	3	we	we	PRON
ejpam-5857	115	4	will	will	AUX
ejpam-5857	115	5	explore	explore	VERB
ejpam-5857	115	6	the	the	DET
ejpam-5857	115	7	various	various	ADJ
ejpam-5857	115	8	properties	property	NOUN
ejpam-5857	115	9	of	of	ADP
ejpam-5857	115	10	these	these	DET
ejpam-5857	115	11	special	special	ADJ
ejpam-5857	115	12	subsets	subset	NOUN
ejpam-5857	115	13	,	,	PUNCT
ejpam-5857	115	14	which	which	PRON
ejpam-5857	115	15	will	will	AUX
ejpam-5857	115	16	be	be	AUX
ejpam-5857	115	17	further	far	ADV
ejpam-5857	115	18	elaborated	elaborate	VERB
ejpam-5857	115	19	upon	upon	SCONJ
ejpam-5857	115	20	in	in	ADP
ejpam-5857	115	21	this	this	DET
ejpam-5857	115	22	section	section	NOUN
ejpam-5857	115	23	.	.	PUNCT
ejpam-5857	116	1	before	before	SCONJ
ejpam-5857	116	2	we	we	PRON
ejpam-5857	116	3	begin	begin	VERB
ejpam-5857	116	4	,	,	PUNCT
ejpam-5857	116	5	for	for	ADP
ejpam-5857	116	6	all	all	DET
ejpam-5857	116	7	a	a	PRON
ejpam-5857	116	8	,	,	PUNCT
ejpam-5857	116	9	b	b	X
ejpam-5857	116	10	∈	∈	NOUN
ejpam-5857	116	11	r	r	NOUN
ejpam-5857	116	12	we	we	PRON
ejpam-5857	116	13	will	will	AUX
ejpam-5857	116	14	define	define	VERB
ejpam-5857	116	15	a	a	DET
ejpam-5857	116	16	∧	∧	PROPN
ejpam-5857	116	17	b	b	NOUN
ejpam-5857	116	18	=	=	SYM
ejpam-5857	116	19	min{a	min{a	PROPN
ejpam-5857	116	20	,	,	PUNCT
ejpam-5857	116	21	b	b	NOUN
ejpam-5857	116	22	}	}	PUNCT
ejpam-5857	116	23	and	and	CCONJ
ejpam-5857	116	24	a	a	DET
ejpam-5857	116	25	∨	∨	NUM
ejpam-5857	116	26	b	b	NOUN
ejpam-5857	116	27	=	=	SYM
ejpam-5857	116	28	max{a	max{a	PROPN
ejpam-5857	116	29	,	,	PUNCT
ejpam-5857	116	30	b	b	NOUN
ejpam-5857	116	31	}	}	PUNCT
ejpam-5857	116	32	for	for	ADP
ejpam-5857	116	33	the	the	DET
ejpam-5857	116	34	sake	sake	NOUN
ejpam-5857	116	35	of	of	ADP
ejpam-5857	116	36	ease	ease	NOUN
ejpam-5857	116	37	in	in	ADP
ejpam-5857	116	38	reading	reading	NOUN
ejpam-5857	116	39	.	.	PUNCT
ejpam-5857	117	1	definition	definition	NOUN
ejpam-5857	117	2	3	3	NUM
ejpam-5857	117	3	.	.	PUNCT
ejpam-5857	118	1	[	[	X
ejpam-5857	118	2	2	2	X
ejpam-5857	118	3	]	]	PUNCT
ejpam-5857	118	4	an	an	DET
ejpam-5857	118	5	element	element	NOUN
ejpam-5857	118	6	x	x	PUNCT
ejpam-5857	118	7	of	of	ADP
ejpam-5857	118	8	x	x	PROPN
ejpam-5857	118	9	is	be	AUX
ejpam-5857	118	10	called	call	VERB
ejpam-5857	118	11	significant	significant	ADJ
ejpam-5857	118	12	with	with	ADP
ejpam-5857	118	13	respect	respect	NOUN
ejpam-5857	118	14	to	to	ADP
ejpam-5857	118	15	a	a	DET
ejpam-5857	118	16	neutrosophic	neutrosophic	ADJ
ejpam-5857	118	17	set	set	NOUN
ejpam-5857	118	18	(	(	PUNCT
ejpam-5857	118	19	ns	ns	PROPN
ejpam-5857	118	20	)	)	PUNCT
ejpam-5857	118	21	a	a	PRON
ejpam-5857	118	22	of	of	ADP
ejpam-5857	118	23	x	x	PRON
ejpam-5857	118	24	if	if	SCONJ
ejpam-5857	118	25	the	the	DET
ejpam-5857	118	26	degree	degree	NOUN
ejpam-5857	118	27	of	of	ADP
ejpam-5857	118	28	truth	truth	NOUN
ejpam-5857	118	29	-	-	PUNCT
ejpam-5857	118	30	membership	membership	NOUN
ejpam-5857	118	31	or	or	CCONJ
ejpam-5857	118	32	falsity	falsity	NOUN
ejpam-5857	118	33	-	-	PUNCT
ejpam-5857	118	34	membership	membership	NOUN
ejpam-5857	118	35	or	or	CCONJ
ejpam-5857	118	36	indeterminancymembership	indeterminancymembership	NOUN
ejpam-5857	118	37	value	value	NOUN
ejpam-5857	118	38	,	,	PUNCT
ejpam-5857	118	39	i.e.	i.e.	X
ejpam-5857	118	40	,	,	PUNCT
ejpam-5857	118	41	at	at	ADP
ejpam-5857	118	42	or	or	CCONJ
ejpam-5857	118	43	ai	ai	VERB
ejpam-5857	118	44	or	or	CCONJ
ejpam-5857	118	45	af	af	PROPN
ejpam-5857	118	46	≥	≥	NOUN
ejpam-5857	118	47	0.5	0.5	NUM
ejpam-5857	118	48	.	.	PUNCT
ejpam-5857	119	1	otherwise	otherwise	ADV
ejpam-5857	119	2	,	,	PUNCT
ejpam-5857	119	3	we	we	PRON
ejpam-5857	119	4	call	call	VERB
ejpam-5857	119	5	it	it	PRON
ejpam-5857	119	6	insignificant	insignificant	ADJ
ejpam-5857	119	7	.	.	PUNCT
ejpam-5857	120	1	also	also	ADV
ejpam-5857	120	2	,	,	PUNCT
ejpam-5857	120	3	for	for	ADP
ejpam-5857	120	4	the	the	DET
ejpam-5857	120	5	ns	ns	ADJ
ejpam-5857	120	6	,	,	PUNCT
ejpam-5857	120	7	the	the	DET
ejpam-5857	120	8	truth	truth	NOUN
ejpam-5857	120	9	-	-	PUNCT
ejpam-5857	120	10	membership	membership	NOUN
ejpam-5857	120	11	,	,	PUNCT
ejpam-5857	120	12	indeterminacy	indeterminacy	NOUN
ejpam-5857	120	13	-	-	PUNCT
ejpam-5857	120	14	membership	membership	NOUN
ejpam-5857	120	15	and	and	CCONJ
ejpam-5857	120	16	falsity	falsity	NOUN
ejpam-5857	120	17	-	-	PUNCT
ejpam-5857	120	18	membership	membership	NOUN
ejpam-5857	120	19	can	can	AUX
ejpam-5857	120	20	not	not	PART
ejpam-5857	120	21	be	be	AUX
ejpam-5857	120	22	significant	significant	ADJ
ejpam-5857	120	23	.	.	PUNCT
ejpam-5857	121	1	we	we	PRON
ejpam-5857	121	2	define	define	VERB
ejpam-5857	121	3	an	an	DET
ejpam-5857	121	4	intuitionistic	intuitionistic	ADJ
ejpam-5857	121	5	neutrosophic	neutrosophic	ADJ
ejpam-5857	121	6	set	set	NOUN
ejpam-5857	121	7	(	(	PUNCT
ejpam-5857	121	8	ins	in	NOUN
ejpam-5857	121	9	)	)	PUNCT
ejpam-5857	121	10	by	by	ADP
ejpam-5857	121	11	ψ	ψ	X
ejpam-5857	121	12	=	=	X
ejpam-5857	121	13	{	{	PUNCT
ejpam-5857	121	14	(	(	PUNCT
ejpam-5857	121	15	x	x	NOUN
ejpam-5857	121	16	,	,	PUNCT
ejpam-5857	121	17	ψt	ψt	NUM
ejpam-5857	121	18	(	(	PUNCT
ejpam-5857	121	19	x	x	NOUN
ejpam-5857	121	20	)	)	PUNCT
ejpam-5857	121	21	,	,	PUNCT
ejpam-5857	121	22	ψi(x	ψi(x	NUM
ejpam-5857	121	23	)	)	PUNCT
ejpam-5857	121	24	,	,	PUNCT
ejpam-5857	121	25	ψf	ψf	X
ejpam-5857	121	26	(	(	PUNCT
ejpam-5857	121	27	x	x	NOUN
ejpam-5857	121	28	)	)	PUNCT
ejpam-5857	121	29	)	)	PUNCT
ejpam-5857	122	1	|	|	ADV
ejpam-5857	122	2	x	x	SYM
ejpam-5857	122	3	∈	∈	NOUN
ejpam-5857	122	4	x	x	X
ejpam-5857	122	5	}	}	PUNCT
ejpam-5857	122	6	,	,	PUNCT
ejpam-5857	122	7	(	(	PUNCT
ejpam-5857	122	8	3.1	3.1	NUM
ejpam-5857	122	9	)	)	PUNCT
ejpam-5857	122	10	where	where	SCONJ
ejpam-5857	122	11	ψt	ψt	NOUN
ejpam-5857	122	12	(	(	PUNCT
ejpam-5857	122	13	x)∧ψf	x)∧ψf	PROPN
ejpam-5857	122	14	(	(	PUNCT
ejpam-5857	122	15	x	x	NOUN
ejpam-5857	122	16	)	)	PUNCT
ejpam-5857	122	17	≤	≤	NUM
ejpam-5857	122	18	0.5	0.5	NUM
ejpam-5857	122	19	,	,	PUNCT
ejpam-5857	122	20	ψt	ψt	VERB
ejpam-5857	122	21	(	(	PUNCT
ejpam-5857	122	22	x)∧ψi(x	x)∧ψi(x	X
ejpam-5857	122	23	)	)	PUNCT
ejpam-5857	122	24	≤	≤	NUM
ejpam-5857	122	25	0.5	0.5	NUM
ejpam-5857	122	26	and	and	CCONJ
ejpam-5857	122	27	ψf	ψf	X
ejpam-5857	122	28	(	(	PUNCT
ejpam-5857	122	29	x)∧ψi(x	x)∧ψi(x	X
ejpam-5857	122	30	)	)	PUNCT
ejpam-5857	122	31	≤	≤	NUM
ejpam-5857	122	32	0.5	0.5	NUM
ejpam-5857	122	33	with	with	ADP
ejpam-5857	122	34	the	the	DET
ejpam-5857	122	35	condition	condition	NOUN
ejpam-5857	122	36	0	0	NUM
ejpam-5857	122	37	≤	≤	NUM
ejpam-5857	122	38	ψt	ψt	VERB
ejpam-5857	122	39	(	(	PUNCT
ejpam-5857	122	40	x	x	X
ejpam-5857	122	41	)	)	PUNCT
ejpam-5857	122	42	+	+	CCONJ
ejpam-5857	122	43	ψi(x	ψi(x	NUM
ejpam-5857	122	44	)	)	PUNCT
ejpam-5857	123	1	+	+	CCONJ
ejpam-5857	123	2	ψf	ψf	X
ejpam-5857	123	3	(	(	PUNCT
ejpam-5857	123	4	x	x	NOUN
ejpam-5857	123	5	)	)	PUNCT
ejpam-5857	123	6	≤	≤	NOUN
ejpam-5857	123	7	2	2	NUM
ejpam-5857	123	8	.	.	PUNCT
ejpam-5857	123	9	before	before	SCONJ
ejpam-5857	123	10	we	we	PRON
ejpam-5857	123	11	delve	delve	VERB
ejpam-5857	123	12	into	into	ADP
ejpam-5857	123	13	the	the	DET
ejpam-5857	123	14	study	study	NOUN
ejpam-5857	123	15	complement	complement	NOUN
ejpam-5857	123	16	of	of	ADP
ejpam-5857	123	17	an	an	DET
ejpam-5857	123	18	fs	fs	X
ejpam-5857	123	19	f	f	PROPN
ejpam-5857	123	20	,	,	PUNCT
ejpam-5857	123	21	we	we	PRON
ejpam-5857	123	22	will	will	AUX
ejpam-5857	123	23	introduce	introduce	VERB
ejpam-5857	123	24	the	the	DET
ejpam-5857	123	25	fundamental	fundamental	ADJ
ejpam-5857	123	26	symbols	symbol	NOUN
ejpam-5857	123	27	used	use	VERB
ejpam-5857	123	28	in	in	ADP
ejpam-5857	123	29	the	the	DET
ejpam-5857	123	30	study	study	NOUN
ejpam-5857	123	31	complement	complement	NOUN
ejpam-5857	123	32	of	of	ADP
ejpam-5857	123	33	f	f	PROPN
ejpam-5857	123	34	as	as	SCONJ
ejpam-5857	123	35	follows	follow	VERB
ejpam-5857	123	36	:	:	PUNCT
ejpam-5857	123	37	f(x	f(x	PROPN
ejpam-5857	123	38	)	)	PUNCT
ejpam-5857	123	39	=	=	SYM
ejpam-5857	124	1	1−	1−	NUM
ejpam-5857	124	2	f(x	f(x	PROPN
ejpam-5857	124	3	)	)	PUNCT
ejpam-5857	124	4	.	.	PUNCT
ejpam-5857	125	1	definition	definition	NOUN
ejpam-5857	125	2	4	4	NUM
ejpam-5857	125	3	.	.	PUNCT
ejpam-5857	126	1	let	let	VERB
ejpam-5857	126	2	ψ	ψ	PART
ejpam-5857	126	3	be	be	AUX
ejpam-5857	126	4	an	an	DET
ejpam-5857	126	5	ins	in	NOUN
ejpam-5857	126	6	in	in	ADP
ejpam-5857	126	7	a	a	DET
ejpam-5857	126	8	nonempty	nonempty	ADV
ejpam-5857	126	9	set	set	VERB
ejpam-5857	126	10	x.	x.	NOUN
ejpam-5857	127	1	the	the	DET
ejpam-5857	127	2	ins	ins	PROPN
ejpam-5857	127	3	ψ	ψ	X
ejpam-5857	127	4	is	be	AUX
ejpam-5857	127	5	defined	define	VERB
ejpam-5857	127	6	by	by	ADP
ejpam-5857	127	7	(	(	PUNCT
ejpam-5857	127	8	∀x	∀x	X
ejpam-5857	127	9	∈	∈	PROPN
ejpam-5857	127	10	x)(ψt	x)(ψt	X
ejpam-5857	127	11	(	(	PUNCT
ejpam-5857	127	12	x	x	X
ejpam-5857	127	13	)	)	PUNCT
ejpam-5857	127	14	=	=	SYM
ejpam-5857	128	1	ψi(x	ψi(x	X
ejpam-5857	128	2	)	)	PUNCT
ejpam-5857	129	1	∧	∧	NOUN
ejpam-5857	129	2	ψt	ψt	NOUN
ejpam-5857	129	3	(	(	PUNCT
ejpam-5857	129	4	x	x	NOUN
ejpam-5857	129	5	)	)	PUNCT
ejpam-5857	129	6	)	)	PUNCT
ejpam-5857	129	7	,	,	PUNCT
ejpam-5857	129	8	(	(	PUNCT
ejpam-5857	129	9	3.2	3.2	NUM
ejpam-5857	129	10	)	)	PUNCT
ejpam-5857	129	11	(	(	PUNCT
ejpam-5857	129	12	∀x	∀x	X
ejpam-5857	129	13	∈	∈	PROPN
ejpam-5857	129	14	x)(ψi(x	x)(ψi(x	NOUN
ejpam-5857	129	15	)	)	PUNCT
ejpam-5857	129	16	=	=	SYM
ejpam-5857	129	17	ψi(x	ψi(x	NUM
ejpam-5857	129	18	)	)	PUNCT
ejpam-5857	129	19	)	)	PUNCT
ejpam-5857	129	20	,	,	PUNCT
ejpam-5857	129	21	(	(	PUNCT
ejpam-5857	129	22	3.3	3.3	NUM
ejpam-5857	129	23	)	)	PUNCT
ejpam-5857	129	24	(	(	PUNCT
ejpam-5857	129	25	∀x	∀x	X
ejpam-5857	129	26	∈	∈	PROPN
ejpam-5857	129	27	x)(ψf	x)(ψf	X
ejpam-5857	130	1	(	(	PUNCT
ejpam-5857	130	2	x	x	X
ejpam-5857	130	3	)	)	PUNCT
ejpam-5857	130	4	=	=	SYM
ejpam-5857	130	5	ψi(x	ψi(x	X
ejpam-5857	130	6	)	)	PUNCT
ejpam-5857	131	1	∧	∧	NOUN
ejpam-5857	131	2	ψf	ψf	X
ejpam-5857	131	3	(	(	PUNCT
ejpam-5857	131	4	x	x	NOUN
ejpam-5857	131	5	)	)	PUNCT
ejpam-5857	131	6	)	)	PUNCT
ejpam-5857	131	7	(	(	PUNCT
ejpam-5857	131	8	3.4	3.4	NUM
ejpam-5857	131	9	)	)	PUNCT
ejpam-5857	131	10	is	be	AUX
ejpam-5857	131	11	called	call	VERB
ejpam-5857	131	12	the	the	DET
ejpam-5857	131	13	complement	complement	NOUN
ejpam-5857	131	14	of	of	ADP
ejpam-5857	131	15	ψ	ψ	PRON
ejpam-5857	131	16	in	in	ADP
ejpam-5857	131	17	x.	x.	NOUN
ejpam-5857	131	18	definition	definition	NOUN
ejpam-5857	131	19	5	5	NUM
ejpam-5857	131	20	.	.	PUNCT
ejpam-5857	132	1	an	an	DET
ejpam-5857	132	2	ins	ins	PROPN
ejpam-5857	132	3	ψ	ψ	X
ejpam-5857	132	4	in	in	ADP
ejpam-5857	132	5	x	x	PROPN
ejpam-5857	132	6	is	be	AUX
ejpam-5857	132	7	called	call	VERB
ejpam-5857	132	8	an	an	DET
ejpam-5857	132	9	intuitionistic	intuitionistic	ADJ
ejpam-5857	132	10	neutrosophic	neutrosophic	ADJ
ejpam-5857	132	11	iup	iup	NOUN
ejpam-5857	132	12	-	-	PUNCT
ejpam-5857	132	13	subalgebra	subalgebra	NOUN
ejpam-5857	132	14	(	(	PUNCT
ejpam-5857	132	15	iniup	iniup	VERB
ejpam-5857	132	16	-	-	PUNCT
ejpam-5857	132	17	subalgebra	subalgebra	NOUN
ejpam-5857	132	18	)	)	PUNCT
ejpam-5857	132	19	of	of	ADP
ejpam-5857	132	20	x	x	PRON
ejpam-5857	132	21	if	if	SCONJ
ejpam-5857	132	22	it	it	PRON
ejpam-5857	132	23	satisfies	satisfy	VERB
ejpam-5857	132	24	the	the	DET
ejpam-5857	132	25	following	follow	VERB
ejpam-5857	132	26	conditions	condition	NOUN
ejpam-5857	132	27	:	:	PUNCT
ejpam-5857	132	28	(	(	PUNCT
ejpam-5857	132	29	∀x	∀x	X
ejpam-5857	132	30	,	,	PUNCT
ejpam-5857	132	31	y	y	PROPN
ejpam-5857	132	32	∈	∈	PROPN
ejpam-5857	132	33	x)(ψt	x)(ψt	X
ejpam-5857	133	1	(	(	PUNCT
ejpam-5857	133	2	x	x	X
ejpam-5857	133	3	·	·	PUNCT
ejpam-5857	133	4	y	y	X
ejpam-5857	133	5	)	)	PUNCT
ejpam-5857	133	6	≥	≥	NOUN
ejpam-5857	133	7	(	(	PUNCT
ejpam-5857	133	8	ψt	ψt	VERB
ejpam-5857	133	9	(	(	PUNCT
ejpam-5857	133	10	x	x	NOUN
ejpam-5857	133	11	)	)	PUNCT
ejpam-5857	133	12	∧	∧	NOUN
ejpam-5857	133	13	ψt	ψt	NOUN
ejpam-5857	133	14	(	(	PUNCT
ejpam-5857	133	15	y	y	NOUN
ejpam-5857	133	16	)	)	PUNCT
ejpam-5857	133	17	)	)	PUNCT
ejpam-5857	134	1	∨	∨	NUM
ejpam-5857	134	2	0.5	0.5	NUM
ejpam-5857	134	3	)	)	PUNCT
ejpam-5857	134	4	,	,	PUNCT
ejpam-5857	134	5	(	(	PUNCT
ejpam-5857	134	6	3.5	3.5	NUM
ejpam-5857	134	7	)	)	PUNCT
ejpam-5857	134	8	k.	k.	NOUN
ejpam-5857	134	9	suayngam	suayngam	PROPN
ejpam-5857	134	10	,	,	PUNCT
ejpam-5857	134	11	p.	p.	NOUN
ejpam-5857	134	12	julatha	julatha	PROPN
ejpam-5857	134	13	,	,	PUNCT
ejpam-5857	134	14	w.	w.	PROPN
ejpam-5857	134	15	nakkhasen	nakkhasen	PROPN
ejpam-5857	134	16	,	,	PUNCT
ejpam-5857	134	17	a.	a.	NOUN
ejpam-5857	134	18	iampan	iampan	PROPN
ejpam-5857	134	19	/	/	SYM
ejpam-5857	134	20	eur	eur	PROPN
ejpam-5857	134	21	.	.	PUNCT
ejpam-5857	135	1	j.	j.	PROPN
ejpam-5857	135	2	pure	pure	PROPN
ejpam-5857	135	3	appl	appl	PROPN
ejpam-5857	135	4	.	.	PROPN
ejpam-5857	135	5	math	math	PROPN
ejpam-5857	135	6	,	,	PUNCT
ejpam-5857	135	7	18	18	NUM
ejpam-5857	135	8	(	(	PUNCT
ejpam-5857	135	9	2	2	NUM
ejpam-5857	135	10	)	)	PUNCT
ejpam-5857	135	11	(	(	PUNCT
ejpam-5857	135	12	2025	2025	NUM
ejpam-5857	135	13	)	)	PUNCT
ejpam-5857	135	14	,	,	PUNCT
ejpam-5857	135	15	5857	5857	NUM
ejpam-5857	135	16	7	7	NUM
ejpam-5857	135	17	of	of	ADP
ejpam-5857	135	18	30	30	NUM
ejpam-5857	135	19	(	(	PUNCT
ejpam-5857	135	20	∀x	∀x	NUM
ejpam-5857	135	21	,	,	PUNCT
ejpam-5857	135	22	y	y	PROPN
ejpam-5857	135	23	∈	∈	PROPN
ejpam-5857	135	24	x)(ψi(x	x)(ψi(x	PROPN
ejpam-5857	136	1	·	·	PUNCT
ejpam-5857	136	2	y	y	X
ejpam-5857	136	3	)	)	PUNCT
ejpam-5857	136	4	≤	≤	NOUN
ejpam-5857	136	5	(	(	PUNCT
ejpam-5857	136	6	ψi(x	ψi(x	NUM
ejpam-5857	136	7	)	)	PUNCT
ejpam-5857	136	8	∨	∨	NUM
ejpam-5857	136	9	ψi(y	ψi(y	NUM
ejpam-5857	136	10	)	)	PUNCT
ejpam-5857	136	11	)	)	PUNCT
ejpam-5857	137	1	∧	∧	NOUN
ejpam-5857	137	2	0.5	0.5	NUM
ejpam-5857	137	3	)	)	PUNCT
ejpam-5857	137	4	,	,	PUNCT
ejpam-5857	137	5	(	(	PUNCT
ejpam-5857	137	6	3.6	3.6	NUM
ejpam-5857	137	7	)	)	PUNCT
ejpam-5857	137	8	(	(	PUNCT
ejpam-5857	137	9	∀x	∀x	X
ejpam-5857	137	10	,	,	PUNCT
ejpam-5857	137	11	y	y	PROPN
ejpam-5857	137	12	∈	∈	PROPN
ejpam-5857	137	13	x)(ψf	x)(ψf	PUNCT
ejpam-5857	138	1	(	(	PUNCT
ejpam-5857	138	2	x	x	X
ejpam-5857	138	3	·	·	PUNCT
ejpam-5857	138	4	y	y	X
ejpam-5857	138	5	)	)	PUNCT
ejpam-5857	138	6	≥	≥	NOUN
ejpam-5857	138	7	(	(	PUNCT
ejpam-5857	138	8	ψf	ψf	X
ejpam-5857	138	9	(	(	PUNCT
ejpam-5857	138	10	x	x	NOUN
ejpam-5857	138	11	)	)	PUNCT
ejpam-5857	138	12	∧	∧	NOUN
ejpam-5857	138	13	ψf	ψf	X
ejpam-5857	138	14	(	(	PUNCT
ejpam-5857	138	15	y	y	NOUN
ejpam-5857	138	16	)	)	PUNCT
ejpam-5857	138	17	)	)	PUNCT
ejpam-5857	139	1	∨	∨	NUM
ejpam-5857	139	2	0.5	0.5	NUM
ejpam-5857	139	3	)	)	PUNCT
ejpam-5857	139	4	.	.	PUNCT
ejpam-5857	140	1	(	(	PUNCT
ejpam-5857	140	2	3.7	3.7	NUM
ejpam-5857	140	3	)	)	PUNCT
ejpam-5857	140	4	definition	definition	NOUN
ejpam-5857	140	5	6	6	NUM
ejpam-5857	140	6	.	.	PUNCT
ejpam-5857	141	1	an	an	DET
ejpam-5857	141	2	ins	ins	PROPN
ejpam-5857	141	3	ψ	ψ	X
ejpam-5857	141	4	in	in	ADP
ejpam-5857	141	5	x	x	PROPN
ejpam-5857	141	6	is	be	AUX
ejpam-5857	141	7	called	call	VERB
ejpam-5857	141	8	an	an	DET
ejpam-5857	141	9	intuitionistic	intuitionistic	ADJ
ejpam-5857	141	10	neutrosophic	neutrosophic	ADJ
ejpam-5857	141	11	iup	iup	NOUN
ejpam-5857	141	12	-	-	PUNCT
ejpam-5857	141	13	ideal	ideal	NOUN
ejpam-5857	141	14	(	(	PUNCT
ejpam-5857	141	15	iniupideal	iniupideal	NOUN
ejpam-5857	141	16	)	)	PUNCT
ejpam-5857	141	17	of	of	ADP
ejpam-5857	141	18	x	x	PRON
ejpam-5857	141	19	if	if	SCONJ
ejpam-5857	141	20	it	it	PRON
ejpam-5857	141	21	satisfies	satisfy	VERB
ejpam-5857	141	22	the	the	DET
ejpam-5857	141	23	following	follow	VERB
ejpam-5857	141	24	conditions	condition	NOUN
ejpam-5857	141	25	:	:	PUNCT
ejpam-5857	141	26	(	(	PUNCT
ejpam-5857	141	27	∀x	∀x	X
ejpam-5857	141	28	∈	∈	NOUN
ejpam-5857	141	29	x)(ψt	x)(ψt	X
ejpam-5857	141	30	(	(	PUNCT
ejpam-5857	141	31	0	0	NUM
ejpam-5857	141	32	)	)	PUNCT
ejpam-5857	141	33	≥	≥	PRON
ejpam-5857	142	1	ψt	ψt	VERB
ejpam-5857	142	2	(	(	PUNCT
ejpam-5857	142	3	x	x	NOUN
ejpam-5857	142	4	)	)	PUNCT
ejpam-5857	142	5	)	)	PUNCT
ejpam-5857	142	6	,	,	PUNCT
ejpam-5857	142	7	(	(	PUNCT
ejpam-5857	142	8	3.8	3.8	NUM
ejpam-5857	142	9	)	)	PUNCT
ejpam-5857	142	10	(	(	PUNCT
ejpam-5857	142	11	∀x	∀x	X
ejpam-5857	142	12	∈	∈	PROPN
ejpam-5857	142	13	x)(ψi(0	x)(ψi(0	PROPN
ejpam-5857	142	14	)	)	PUNCT
ejpam-5857	142	15	≤	≤	NUM
ejpam-5857	142	16	ψi(x	ψi(x	NUM
ejpam-5857	142	17	)	)	PUNCT
ejpam-5857	142	18	)	)	PUNCT
ejpam-5857	142	19	,	,	PUNCT
ejpam-5857	142	20	(	(	PUNCT
ejpam-5857	142	21	3.9	3.9	NUM
ejpam-5857	142	22	)	)	PUNCT
ejpam-5857	142	23	(	(	PUNCT
ejpam-5857	142	24	∀x	∀x	X
ejpam-5857	142	25	∈	∈	PROPN
ejpam-5857	142	26	x)(ψf	x)(ψf	X
ejpam-5857	143	1	(	(	PUNCT
ejpam-5857	143	2	0	0	NUM
ejpam-5857	143	3	)	)	PUNCT
ejpam-5857	143	4	≥	≥	NOUN
ejpam-5857	143	5	ψf	ψf	X
ejpam-5857	143	6	(	(	PUNCT
ejpam-5857	143	7	x	x	NOUN
ejpam-5857	143	8	)	)	PUNCT
ejpam-5857	143	9	)	)	PUNCT
ejpam-5857	144	1	,	,	PUNCT
ejpam-5857	144	2	(	(	PUNCT
ejpam-5857	144	3	3.10	3.10	NUM
ejpam-5857	144	4	)	)	PUNCT
ejpam-5857	144	5	(	(	PUNCT
ejpam-5857	144	6	∀x	∀x	X
ejpam-5857	144	7	,	,	PUNCT
ejpam-5857	144	8	y	y	PROPN
ejpam-5857	144	9	,	,	PUNCT
ejpam-5857	144	10	z	z	PROPN
ejpam-5857	144	11	∈	∈	PROPN
ejpam-5857	144	12	x)(ψt	x)(ψt	X
ejpam-5857	145	1	(	(	PUNCT
ejpam-5857	145	2	x	x	X
ejpam-5857	145	3	·	·	PUNCT
ejpam-5857	145	4	z	z	X
ejpam-5857	145	5	)	)	PUNCT
ejpam-5857	145	6	≥	≥	NOUN
ejpam-5857	145	7	(	(	PUNCT
ejpam-5857	145	8	ψt	ψt	VERB
ejpam-5857	145	9	(	(	PUNCT
ejpam-5857	145	10	x	x	X
ejpam-5857	145	11	·	·	PUNCT
ejpam-5857	145	12	(	(	PUNCT
ejpam-5857	145	13	y	y	PROPN
ejpam-5857	145	14	·	·	PUNCT
ejpam-5857	145	15	z	z	NOUN
ejpam-5857	145	16	)	)	PUNCT
ejpam-5857	145	17	)	)	PUNCT
ejpam-5857	146	1	∧	∧	NOUN
ejpam-5857	146	2	ψt	ψt	NOUN
ejpam-5857	146	3	(	(	PUNCT
ejpam-5857	146	4	y	y	NOUN
ejpam-5857	146	5	)	)	PUNCT
ejpam-5857	146	6	)	)	PUNCT
ejpam-5857	146	7	∨	∨	NUM
ejpam-5857	146	8	0.5	0.5	NUM
ejpam-5857	146	9	)	)	PUNCT
ejpam-5857	146	10	,	,	PUNCT
ejpam-5857	146	11	(	(	PUNCT
ejpam-5857	146	12	3.11	3.11	NUM
ejpam-5857	146	13	)	)	PUNCT
ejpam-5857	146	14	(	(	PUNCT
ejpam-5857	146	15	∀x	∀x	X
ejpam-5857	146	16	,	,	PUNCT
ejpam-5857	146	17	y	y	PROPN
ejpam-5857	146	18	,	,	PUNCT
ejpam-5857	146	19	z	z	PROPN
ejpam-5857	146	20	∈	∈	PROPN
ejpam-5857	146	21	x)(ψi(x	x)(ψi(x	NOUN
ejpam-5857	147	1	·	·	PUNCT
ejpam-5857	147	2	z	z	X
ejpam-5857	147	3	)	)	PUNCT
ejpam-5857	147	4	≤	≤	NOUN
ejpam-5857	147	5	(	(	PUNCT
ejpam-5857	147	6	ψi(x	ψi(x	X
ejpam-5857	147	7	·	·	PUNCT
ejpam-5857	147	8	(	(	PUNCT
ejpam-5857	147	9	y	y	PROPN
ejpam-5857	147	10	·	·	PUNCT
ejpam-5857	147	11	z	z	NOUN
ejpam-5857	147	12	)	)	PUNCT
ejpam-5857	147	13	)	)	PUNCT
ejpam-5857	148	1	∨	∨	NUM
ejpam-5857	148	2	ψi(y	ψi(y	NUM
ejpam-5857	148	3	)	)	PUNCT
ejpam-5857	148	4	)	)	PUNCT
ejpam-5857	149	1	∧	∧	NOUN
ejpam-5857	149	2	0.5	0.5	NUM
ejpam-5857	149	3	)	)	PUNCT
ejpam-5857	149	4	,	,	PUNCT
ejpam-5857	149	5	(	(	PUNCT
ejpam-5857	149	6	3.12	3.12	NUM
ejpam-5857	149	7	)	)	PUNCT
ejpam-5857	149	8	(	(	PUNCT
ejpam-5857	149	9	∀x	∀x	X
ejpam-5857	149	10	,	,	PUNCT
ejpam-5857	149	11	y	y	PROPN
ejpam-5857	149	12	,	,	PUNCT
ejpam-5857	149	13	z	z	PROPN
ejpam-5857	149	14	∈	∈	PROPN
ejpam-5857	149	15	x)(ψf	x)(ψf	PUNCT
ejpam-5857	150	1	(	(	PUNCT
ejpam-5857	150	2	x	x	X
ejpam-5857	150	3	·	·	PUNCT
ejpam-5857	150	4	z	z	X
ejpam-5857	150	5	)	)	PUNCT
ejpam-5857	150	6	≥	≥	NOUN
ejpam-5857	150	7	(	(	PUNCT
ejpam-5857	150	8	ψf	ψf	X
ejpam-5857	150	9	(	(	PUNCT
ejpam-5857	150	10	x	x	X
ejpam-5857	150	11	·	·	PUNCT
ejpam-5857	150	12	(	(	PUNCT
ejpam-5857	150	13	y	y	PROPN
ejpam-5857	150	14	·	·	PUNCT
ejpam-5857	150	15	z	z	NOUN
ejpam-5857	150	16	)	)	PUNCT
ejpam-5857	150	17	)	)	PUNCT
ejpam-5857	151	1	∧	∧	NOUN
ejpam-5857	151	2	ψf	ψf	X
ejpam-5857	151	3	(	(	PUNCT
ejpam-5857	151	4	y	y	NOUN
ejpam-5857	151	5	)	)	PUNCT
ejpam-5857	151	6	)	)	PUNCT
ejpam-5857	151	7	∨	∨	NUM
ejpam-5857	151	8	0.5	0.5	NUM
ejpam-5857	151	9	)	)	PUNCT
ejpam-5857	151	10	.	.	PUNCT
ejpam-5857	152	1	(	(	PUNCT
ejpam-5857	152	2	3.13	3.13	NUM
ejpam-5857	152	3	)	)	PUNCT
ejpam-5857	152	4	definition	definition	NOUN
ejpam-5857	152	5	7	7	NUM
ejpam-5857	152	6	.	.	PUNCT
ejpam-5857	153	1	an	an	DET
ejpam-5857	153	2	ins	ins	PROPN
ejpam-5857	153	3	ψ	ψ	X
ejpam-5857	153	4	in	in	ADP
ejpam-5857	153	5	x	x	PROPN
ejpam-5857	153	6	is	be	AUX
ejpam-5857	153	7	called	call	VERB
ejpam-5857	153	8	an	an	DET
ejpam-5857	153	9	intuitionistic	intuitionistic	ADJ
ejpam-5857	153	10	neutrosophic	neutrosophic	ADJ
ejpam-5857	153	11	iup	iup	NOUN
ejpam-5857	153	12	-	-	PUNCT
ejpam-5857	153	13	filter	filter	NOUN
ejpam-5857	153	14	(	(	PUNCT
ejpam-5857	153	15	iniupfilter	iniupfilter	NOUN
ejpam-5857	153	16	)	)	PUNCT
ejpam-5857	153	17	of	of	ADP
ejpam-5857	153	18	x	x	PRON
ejpam-5857	153	19	if	if	SCONJ
ejpam-5857	153	20	it	it	PRON
ejpam-5857	153	21	satisfies	satisfy	VERB
ejpam-5857	153	22	the	the	DET
ejpam-5857	153	23	conditions	condition	NOUN
ejpam-5857	153	24	(	(	PUNCT
ejpam-5857	153	25	3.8	3.8	NUM
ejpam-5857	153	26	)	)	PUNCT
ejpam-5857	153	27	,	,	PUNCT
ejpam-5857	153	28	(	(	PUNCT
ejpam-5857	153	29	3.9	3.9	NUM
ejpam-5857	153	30	)	)	PUNCT
ejpam-5857	153	31	and	and	CCONJ
ejpam-5857	153	32	(	(	PUNCT
ejpam-5857	153	33	3.10	3.10	NUM
ejpam-5857	153	34	)	)	PUNCT
ejpam-5857	153	35	and	and	CCONJ
ejpam-5857	153	36	the	the	DET
ejpam-5857	153	37	following	follow	VERB
ejpam-5857	153	38	conditions	condition	NOUN
ejpam-5857	153	39	:	:	PUNCT
ejpam-5857	153	40	(	(	PUNCT
ejpam-5857	153	41	∀x	∀x	X
ejpam-5857	153	42	,	,	PUNCT
ejpam-5857	153	43	y	y	PROPN
ejpam-5857	153	44	∈	∈	PROPN
ejpam-5857	153	45	x)(ψt	x)(ψt	X
ejpam-5857	154	1	(	(	PUNCT
ejpam-5857	154	2	y	y	NOUN
ejpam-5857	154	3	)	)	PUNCT
ejpam-5857	154	4	≥	≥	NOUN
ejpam-5857	154	5	(	(	PUNCT
ejpam-5857	154	6	ψt	ψt	VERB
ejpam-5857	154	7	(	(	PUNCT
ejpam-5857	154	8	x	x	PROPN
ejpam-5857	154	9	·	·	PUNCT
ejpam-5857	154	10	y	y	X
ejpam-5857	154	11	)	)	PUNCT
ejpam-5857	154	12	∧	∧	NOUN
ejpam-5857	154	13	ψt	ψt	NOUN
ejpam-5857	154	14	(	(	PUNCT
ejpam-5857	154	15	x	x	NOUN
ejpam-5857	154	16	)	)	PUNCT
ejpam-5857	154	17	)	)	PUNCT
ejpam-5857	155	1	∨	∨	NUM
ejpam-5857	155	2	0.5	0.5	NUM
ejpam-5857	155	3	)	)	PUNCT
ejpam-5857	155	4	,	,	PUNCT
ejpam-5857	155	5	(	(	PUNCT
ejpam-5857	155	6	3.14	3.14	NUM
ejpam-5857	155	7	)	)	PUNCT
ejpam-5857	155	8	(	(	PUNCT
ejpam-5857	155	9	∀x	∀x	X
ejpam-5857	155	10	,	,	PUNCT
ejpam-5857	155	11	y	y	PROPN
ejpam-5857	155	12	∈	∈	PROPN
ejpam-5857	155	13	x)(ψi(y	x)(ψi(y	VERB
ejpam-5857	155	14	)	)	PUNCT
ejpam-5857	155	15	≤	≤	NOUN
ejpam-5857	155	16	(	(	PUNCT
ejpam-5857	155	17	ψi(x	ψi(x	X
ejpam-5857	155	18	·	·	PUNCT
ejpam-5857	155	19	y	y	X
ejpam-5857	155	20	)	)	PUNCT
ejpam-5857	155	21	∨	∨	NUM
ejpam-5857	155	22	ψi(x	ψi(x	NUM
ejpam-5857	155	23	)	)	PUNCT
ejpam-5857	155	24	)	)	PUNCT
ejpam-5857	156	1	∧	∧	NOUN
ejpam-5857	156	2	0.5	0.5	NUM
ejpam-5857	156	3	)	)	PUNCT
ejpam-5857	156	4	,	,	PUNCT
ejpam-5857	156	5	(	(	PUNCT
ejpam-5857	156	6	3.15	3.15	NUM
ejpam-5857	156	7	)	)	PUNCT
ejpam-5857	156	8	(	(	PUNCT
ejpam-5857	156	9	∀x	∀x	X
ejpam-5857	156	10	,	,	PUNCT
ejpam-5857	156	11	y	y	PROPN
ejpam-5857	156	12	∈	∈	PROPN
ejpam-5857	156	13	x)(ψf	x)(ψf	PUNCT
ejpam-5857	157	1	(	(	PUNCT
ejpam-5857	157	2	y	y	NOUN
ejpam-5857	157	3	)	)	PUNCT
ejpam-5857	157	4	≥	≥	NOUN
ejpam-5857	157	5	(	(	PUNCT
ejpam-5857	157	6	ψf	ψf	X
ejpam-5857	157	7	(	(	PUNCT
ejpam-5857	157	8	x	x	PROPN
ejpam-5857	157	9	·	·	PUNCT
ejpam-5857	157	10	y	y	X
ejpam-5857	157	11	)	)	PUNCT
ejpam-5857	157	12	∧	∧	NOUN
ejpam-5857	157	13	ψf	ψf	X
ejpam-5857	157	14	(	(	PUNCT
ejpam-5857	157	15	x	x	NOUN
ejpam-5857	157	16	)	)	PUNCT
ejpam-5857	157	17	)	)	PUNCT
ejpam-5857	157	18	∨	∨	NUM
ejpam-5857	157	19	0.5	0.5	NUM
ejpam-5857	157	20	)	)	PUNCT
ejpam-5857	157	21	.	.	PUNCT
ejpam-5857	158	1	(	(	PUNCT
ejpam-5857	158	2	3.16	3.16	NUM
ejpam-5857	158	3	)	)	PUNCT
ejpam-5857	158	4	definition	definition	NOUN
ejpam-5857	158	5	8	8	NUM
ejpam-5857	158	6	.	.	PUNCT
ejpam-5857	159	1	an	an	DET
ejpam-5857	159	2	ins	ins	PROPN
ejpam-5857	159	3	ψ	ψ	X
ejpam-5857	159	4	in	in	ADP
ejpam-5857	159	5	x	x	PROPN
ejpam-5857	159	6	is	be	AUX
ejpam-5857	159	7	called	call	VERB
ejpam-5857	159	8	an	an	DET
ejpam-5857	159	9	intuitionistic	intuitionistic	ADJ
ejpam-5857	159	10	neutrosophic	neutrosophic	ADJ
ejpam-5857	159	11	strong	strong	ADJ
ejpam-5857	159	12	iup	iup	NOUN
ejpam-5857	159	13	-	-	PUNCT
ejpam-5857	159	14	ideal	ideal	NOUN
ejpam-5857	159	15	(	(	PUNCT
ejpam-5857	159	16	insiup	insiup	NOUN
ejpam-5857	159	17	-	-	PUNCT
ejpam-5857	159	18	ideal	ideal	NOUN
ejpam-5857	159	19	)	)	PUNCT
ejpam-5857	159	20	of	of	ADP
ejpam-5857	159	21	x	x	PRON
ejpam-5857	159	22	if	if	SCONJ
ejpam-5857	159	23	it	it	PRON
ejpam-5857	159	24	satisfies	satisfy	VERB
ejpam-5857	159	25	the	the	DET
ejpam-5857	159	26	following	follow	VERB
ejpam-5857	159	27	conditions	condition	NOUN
ejpam-5857	159	28	:	:	PUNCT
ejpam-5857	159	29	(	(	PUNCT
ejpam-5857	159	30	∀x	∀x	X
ejpam-5857	159	31	,	,	PUNCT
ejpam-5857	159	32	y	y	PROPN
ejpam-5857	159	33	∈	∈	PROPN
ejpam-5857	159	34	x)(ψt	x)(ψt	X
ejpam-5857	160	1	(	(	PUNCT
ejpam-5857	160	2	x	x	X
ejpam-5857	160	3	·	·	PUNCT
ejpam-5857	160	4	y	y	X
ejpam-5857	160	5	)	)	PUNCT
ejpam-5857	160	6	≥	≥	NOUN
ejpam-5857	160	7	ψt	ψt	NOUN
ejpam-5857	160	8	(	(	PUNCT
ejpam-5857	160	9	y	y	NOUN
ejpam-5857	160	10	)	)	PUNCT
ejpam-5857	160	11	)	)	PUNCT
ejpam-5857	160	12	,	,	PUNCT
ejpam-5857	160	13	(	(	PUNCT
ejpam-5857	160	14	3.17	3.17	NUM
ejpam-5857	160	15	)	)	PUNCT
ejpam-5857	160	16	(	(	PUNCT
ejpam-5857	160	17	∀x	∀x	X
ejpam-5857	160	18	,	,	PUNCT
ejpam-5857	160	19	y	y	PROPN
ejpam-5857	160	20	∈	∈	PROPN
ejpam-5857	160	21	x)(ψi(x	x)(ψi(x	PROPN
ejpam-5857	161	1	·	·	PUNCT
ejpam-5857	161	2	y	y	X
ejpam-5857	161	3	)	)	PUNCT
ejpam-5857	161	4	≤	≤	NOUN
ejpam-5857	161	5	ψi(y	ψi(y	NOUN
ejpam-5857	161	6	)	)	PUNCT
ejpam-5857	161	7	)	)	PUNCT
ejpam-5857	161	8	,	,	PUNCT
ejpam-5857	161	9	(	(	PUNCT
ejpam-5857	161	10	3.18	3.18	NUM
ejpam-5857	161	11	)	)	PUNCT
ejpam-5857	161	12	(	(	PUNCT
ejpam-5857	161	13	∀x	∀x	X
ejpam-5857	161	14	,	,	PUNCT
ejpam-5857	161	15	y	y	PROPN
ejpam-5857	161	16	∈	∈	PROPN
ejpam-5857	161	17	x)(ψf	x)(ψf	PUNCT
ejpam-5857	162	1	(	(	PUNCT
ejpam-5857	162	2	x	x	X
ejpam-5857	162	3	·	·	PUNCT
ejpam-5857	162	4	y	y	X
ejpam-5857	162	5	)	)	PUNCT
ejpam-5857	162	6	≥	≥	NOUN
ejpam-5857	162	7	ψf	ψf	X
ejpam-5857	163	1	(	(	PUNCT
ejpam-5857	163	2	y	y	NOUN
ejpam-5857	163	3	)	)	PUNCT
ejpam-5857	163	4	)	)	PUNCT
ejpam-5857	163	5	.	.	PUNCT
ejpam-5857	164	1	(	(	PUNCT
ejpam-5857	164	2	3.19	3.19	NUM
ejpam-5857	164	3	)	)	PUNCT
ejpam-5857	164	4	lemma	lemma	PROPN
ejpam-5857	164	5	1	1	NUM
ejpam-5857	164	6	.	.	PUNCT
ejpam-5857	165	1	every	every	DET
ejpam-5857	165	2	intuitionistic	intuitionistic	ADJ
ejpam-5857	165	3	neutrosophic	neutrosophic	ADJ
ejpam-5857	165	4	iup	iup	NOUN
ejpam-5857	165	5	-	-	PUNCT
ejpam-5857	165	6	subalgebra	subalgebra	NOUN
ejpam-5857	165	7	of	of	ADP
ejpam-5857	165	8	x	x	PRON
ejpam-5857	165	9	satisfies	satisfy	VERB
ejpam-5857	165	10	the	the	DET
ejpam-5857	165	11	conditions	condition	NOUN
ejpam-5857	165	12	(	(	PUNCT
ejpam-5857	165	13	3.8	3.8	NUM
ejpam-5857	165	14	)	)	PUNCT
ejpam-5857	165	15	,	,	PUNCT
ejpam-5857	165	16	(	(	PUNCT
ejpam-5857	165	17	3.9	3.9	NUM
ejpam-5857	165	18	)	)	PUNCT
ejpam-5857	165	19	and	and	CCONJ
ejpam-5857	165	20	(	(	PUNCT
ejpam-5857	165	21	3.10	3.10	NUM
ejpam-5857	165	22	)	)	PUNCT
ejpam-5857	165	23	.	.	PUNCT
ejpam-5857	166	1	proof	proof	NOUN
ejpam-5857	166	2	.	.	PUNCT
ejpam-5857	167	1	assume	assume	VERB
ejpam-5857	167	2	that	that	SCONJ
ejpam-5857	167	3	ψ	ψ	NOUN
ejpam-5857	167	4	is	be	AUX
ejpam-5857	167	5	an	an	DET
ejpam-5857	167	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	167	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	167	8	iup	iup	NOUN
ejpam-5857	167	9	-	-	PUNCT
ejpam-5857	167	10	subalgebra	subalgebra	NOUN
ejpam-5857	167	11	of	of	ADP
ejpam-5857	167	12	x.	x.	NOUN
ejpam-5857	167	13	let	let	VERB
ejpam-5857	167	14	x	x	SYM
ejpam-5857	167	15	∈	∈	PROPN
ejpam-5857	167	16	x.	x.	NOUN
ejpam-5857	167	17	then	then	ADV
ejpam-5857	167	18	ψt	ψt	VERB
ejpam-5857	167	19	(	(	PUNCT
ejpam-5857	167	20	0	0	NUM
ejpam-5857	167	21	)	)	PUNCT
ejpam-5857	167	22	=	=	VERB
ejpam-5857	168	1	ψt	ψt	ADJ
ejpam-5857	168	2	(	(	PUNCT
ejpam-5857	168	3	x	x	X
ejpam-5857	168	4	·	·	PUNCT
ejpam-5857	168	5	x	x	X
ejpam-5857	168	6	)	)	PUNCT
ejpam-5857	168	7	(	(	PUNCT
ejpam-5857	168	8	by	by	ADP
ejpam-5857	168	9	(	(	PUNCT
ejpam-5857	168	10	iup-2	iup-2	NUM
ejpam-5857	168	11	)	)	PUNCT
ejpam-5857	168	12	)	)	PUNCT
ejpam-5857	168	13	≥	≥	NOUN
ejpam-5857	168	14	(	(	PUNCT
ejpam-5857	168	15	ψt	ψt	VERB
ejpam-5857	168	16	(	(	PUNCT
ejpam-5857	168	17	x	x	NOUN
ejpam-5857	168	18	)	)	PUNCT
ejpam-5857	168	19	∧	∧	NOUN
ejpam-5857	168	20	ψt	ψt	NUM
ejpam-5857	168	21	(	(	PUNCT
ejpam-5857	168	22	x	x	NOUN
ejpam-5857	168	23	)	)	PUNCT
ejpam-5857	168	24	)	)	PUNCT
ejpam-5857	169	1	∨	∨	NUM
ejpam-5857	169	2	0.5	0.5	NUM
ejpam-5857	169	3	(	(	PUNCT
ejpam-5857	169	4	by	by	ADP
ejpam-5857	169	5	(	(	PUNCT
ejpam-5857	169	6	3.5	3.5	NUM
ejpam-5857	169	7	)	)	PUNCT
ejpam-5857	169	8	)	)	PUNCT
ejpam-5857	170	1	=	=	PRON
ejpam-5857	170	2	ψt	ψt	X
ejpam-5857	170	3	(	(	PUNCT
ejpam-5857	170	4	x	x	NOUN
ejpam-5857	170	5	)	)	PUNCT
ejpam-5857	170	6	∨	∨	NUM
ejpam-5857	170	7	0.5	0.5	NUM
ejpam-5857	170	8	≥	≥	NOUN
ejpam-5857	170	9	ψt	ψt	NUM
ejpam-5857	170	10	(	(	PUNCT
ejpam-5857	170	11	x	x	NOUN
ejpam-5857	170	12	)	)	PUNCT
ejpam-5857	170	13	,	,	PUNCT
ejpam-5857	170	14	ψi(0	ψi(0	PROPN
ejpam-5857	170	15	)	)	PUNCT
ejpam-5857	170	16	=	=	X
ejpam-5857	170	17	ψi(x	ψi(x	X
ejpam-5857	170	18	·	·	PUNCT
ejpam-5857	171	1	x	x	X
ejpam-5857	171	2	)	)	PUNCT
ejpam-5857	171	3	(	(	PUNCT
ejpam-5857	171	4	by	by	ADP
ejpam-5857	171	5	(	(	PUNCT
ejpam-5857	171	6	iup-2	iup-2	NUM
ejpam-5857	171	7	)	)	PUNCT
ejpam-5857	171	8	)	)	PUNCT
ejpam-5857	171	9	≤	≤	NOUN
ejpam-5857	171	10	(	(	PUNCT
ejpam-5857	171	11	ψi(x	ψi(x	NUM
ejpam-5857	171	12	)	)	PUNCT
ejpam-5857	171	13	∨	∨	NUM
ejpam-5857	171	14	ψi(x	ψi(x	NUM
ejpam-5857	171	15	)	)	PUNCT
ejpam-5857	171	16	)	)	PUNCT
ejpam-5857	172	1	∧	∧	NOUN
ejpam-5857	172	2	0.5	0.5	NUM
ejpam-5857	172	3	(	(	PUNCT
ejpam-5857	172	4	by	by	ADP
ejpam-5857	172	5	(	(	PUNCT
ejpam-5857	172	6	3.6	3.6	NUM
ejpam-5857	172	7	)	)	PUNCT
ejpam-5857	172	8	)	)	PUNCT
ejpam-5857	173	1	=	=	SYM
ejpam-5857	173	2	ψi(x	ψi(x	X
ejpam-5857	173	3	)	)	PUNCT
ejpam-5857	173	4	∧	∧	PROPN
ejpam-5857	173	5	0.5	0.5	NUM
ejpam-5857	173	6	k.	k.	NOUN
ejpam-5857	173	7	suayngam	suayngam	PROPN
ejpam-5857	173	8	,	,	PUNCT
ejpam-5857	173	9	p.	p.	NOUN
ejpam-5857	173	10	julatha	julatha	PROPN
ejpam-5857	173	11	,	,	PUNCT
ejpam-5857	173	12	w.	w.	PROPN
ejpam-5857	173	13	nakkhasen	nakkhasen	PROPN
ejpam-5857	173	14	,	,	PUNCT
ejpam-5857	173	15	a.	a.	NOUN
ejpam-5857	173	16	iampan	iampan	PROPN
ejpam-5857	173	17	/	/	SYM
ejpam-5857	173	18	eur	eur	PROPN
ejpam-5857	173	19	.	.	PUNCT
ejpam-5857	174	1	j.	j.	PROPN
ejpam-5857	174	2	pure	pure	PROPN
ejpam-5857	174	3	appl	appl	PROPN
ejpam-5857	174	4	.	.	PROPN
ejpam-5857	174	5	math	math	PROPN
ejpam-5857	174	6	,	,	PUNCT
ejpam-5857	174	7	18	18	NUM
ejpam-5857	174	8	(	(	PUNCT
ejpam-5857	174	9	2	2	NUM
ejpam-5857	174	10	)	)	PUNCT
ejpam-5857	174	11	(	(	PUNCT
ejpam-5857	174	12	2025	2025	NUM
ejpam-5857	174	13	)	)	PUNCT
ejpam-5857	174	14	,	,	PUNCT
ejpam-5857	174	15	5857	5857	NUM
ejpam-5857	174	16	8	8	NUM
ejpam-5857	174	17	of	of	ADP
ejpam-5857	174	18	30	30	NUM
ejpam-5857	174	19	≤	≤	NUM
ejpam-5857	174	20	ψi(x	ψi(x	NUM
ejpam-5857	174	21	)	)	PUNCT
ejpam-5857	174	22	,	,	PUNCT
ejpam-5857	174	23	ψf	ψf	X
ejpam-5857	174	24	(	(	PUNCT
ejpam-5857	174	25	0	0	NUM
ejpam-5857	174	26	)	)	PUNCT
ejpam-5857	174	27	=	=	PRON
ejpam-5857	175	1	ψf	ψf	X
ejpam-5857	175	2	(	(	PUNCT
ejpam-5857	175	3	x	x	X
ejpam-5857	175	4	·	·	PUNCT
ejpam-5857	175	5	x	x	X
ejpam-5857	175	6	)	)	PUNCT
ejpam-5857	175	7	(	(	PUNCT
ejpam-5857	175	8	by	by	ADP
ejpam-5857	175	9	(	(	PUNCT
ejpam-5857	175	10	iup-2	iup-2	NUM
ejpam-5857	175	11	)	)	PUNCT
ejpam-5857	175	12	)	)	PUNCT
ejpam-5857	175	13	≥	≥	NOUN
ejpam-5857	175	14	(	(	PUNCT
ejpam-5857	175	15	ψf	ψf	X
ejpam-5857	175	16	(	(	PUNCT
ejpam-5857	175	17	x	x	NOUN
ejpam-5857	175	18	)	)	PUNCT
ejpam-5857	175	19	∧	∧	NOUN
ejpam-5857	175	20	ψf	ψf	X
ejpam-5857	175	21	(	(	PUNCT
ejpam-5857	175	22	x	x	NOUN
ejpam-5857	175	23	)	)	PUNCT
ejpam-5857	175	24	)	)	PUNCT
ejpam-5857	176	1	∨	∨	NUM
ejpam-5857	176	2	0.5	0.5	NUM
ejpam-5857	176	3	(	(	PUNCT
ejpam-5857	176	4	by	by	ADP
ejpam-5857	176	5	(	(	PUNCT
ejpam-5857	176	6	3.5	3.5	NUM
ejpam-5857	176	7	)	)	PUNCT
ejpam-5857	176	8	)	)	PUNCT
ejpam-5857	177	1	=	=	PRON
ejpam-5857	177	2	ψf	ψf	X
ejpam-5857	177	3	(	(	PUNCT
ejpam-5857	177	4	x	x	X
ejpam-5857	177	5	)	)	PUNCT
ejpam-5857	177	6	∨	∨	NUM
ejpam-5857	177	7	0.5	0.5	NUM
ejpam-5857	177	8	≥	≥	NOUN
ejpam-5857	177	9	ψf	ψf	X
ejpam-5857	177	10	(	(	PUNCT
ejpam-5857	177	11	x	x	NOUN
ejpam-5857	177	12	)	)	PUNCT
ejpam-5857	177	13	.	.	PUNCT
ejpam-5857	178	1	hence	hence	ADV
ejpam-5857	178	2	,	,	PUNCT
ejpam-5857	178	3	it	it	PRON
ejpam-5857	178	4	satisfies	satisfy	VERB
ejpam-5857	178	5	the	the	DET
ejpam-5857	178	6	conditions	condition	NOUN
ejpam-5857	178	7	(	(	PUNCT
ejpam-5857	178	8	3.8	3.8	NUM
ejpam-5857	178	9	)	)	PUNCT
ejpam-5857	178	10	,	,	PUNCT
ejpam-5857	178	11	(	(	PUNCT
ejpam-5857	178	12	3.9	3.9	NUM
ejpam-5857	178	13	)	)	PUNCT
ejpam-5857	178	14	and	and	CCONJ
ejpam-5857	178	15	(	(	PUNCT
ejpam-5857	178	16	3.10	3.10	NUM
ejpam-5857	178	17	)	)	PUNCT
ejpam-5857	178	18	.	.	PUNCT
ejpam-5857	179	1	lemma	lemma	PROPN
ejpam-5857	179	2	2	2	NUM
ejpam-5857	179	3	.	.	PUNCT
ejpam-5857	180	1	every	every	DET
ejpam-5857	180	2	intuitionistic	intuitionistic	ADJ
ejpam-5857	180	3	neutrosophic	neutrosophic	ADJ
ejpam-5857	180	4	strong	strong	ADJ
ejpam-5857	180	5	iup	iup	NOUN
ejpam-5857	180	6	-	-	PUNCT
ejpam-5857	180	7	ideal	ideal	NOUN
ejpam-5857	180	8	of	of	ADP
ejpam-5857	180	9	x	x	PUNCT
ejpam-5857	180	10	satisfies	satisfy	VERB
ejpam-5857	180	11	the	the	DET
ejpam-5857	180	12	conditions	condition	NOUN
ejpam-5857	180	13	(	(	PUNCT
ejpam-5857	180	14	3.8	3.8	NUM
ejpam-5857	180	15	)	)	PUNCT
ejpam-5857	180	16	,	,	PUNCT
ejpam-5857	180	17	(	(	PUNCT
ejpam-5857	180	18	3.9	3.9	NUM
ejpam-5857	180	19	)	)	PUNCT
ejpam-5857	180	20	and	and	CCONJ
ejpam-5857	180	21	(	(	PUNCT
ejpam-5857	180	22	3.10	3.10	NUM
ejpam-5857	180	23	)	)	PUNCT
ejpam-5857	180	24	.	.	PUNCT
ejpam-5857	181	1	proof	proof	NOUN
ejpam-5857	181	2	.	.	PUNCT
ejpam-5857	182	1	assume	assume	VERB
ejpam-5857	182	2	that	that	SCONJ
ejpam-5857	182	3	ψ	ψ	NOUN
ejpam-5857	182	4	is	be	AUX
ejpam-5857	182	5	an	an	DET
ejpam-5857	182	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	182	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	182	8	strong	strong	ADJ
ejpam-5857	182	9	iup	iup	NOUN
ejpam-5857	182	10	-	-	PUNCT
ejpam-5857	182	11	ideal	ideal	NOUN
ejpam-5857	182	12	of	of	ADP
ejpam-5857	182	13	x.	x.	NOUN
ejpam-5857	182	14	let	let	VERB
ejpam-5857	182	15	x	x	SYM
ejpam-5857	182	16	∈	∈	PROPN
ejpam-5857	182	17	x.	x.	NOUN
ejpam-5857	182	18	then	then	ADV
ejpam-5857	182	19	ψt	ψt	VERB
ejpam-5857	182	20	(	(	PUNCT
ejpam-5857	182	21	0	0	NUM
ejpam-5857	182	22	)	)	PUNCT
ejpam-5857	182	23	=	=	VERB
ejpam-5857	183	1	ψt	ψt	ADJ
ejpam-5857	183	2	(	(	PUNCT
ejpam-5857	183	3	x	x	X
ejpam-5857	183	4	·	·	PUNCT
ejpam-5857	183	5	x	x	X
ejpam-5857	183	6	)	)	PUNCT
ejpam-5857	183	7	(	(	PUNCT
ejpam-5857	183	8	by	by	ADP
ejpam-5857	183	9	(	(	PUNCT
ejpam-5857	183	10	iup-2	iup-2	NUM
ejpam-5857	183	11	)	)	PUNCT
ejpam-5857	183	12	)	)	PUNCT
ejpam-5857	183	13	≥	≥	PRON
ejpam-5857	183	14	ψt	ψt	VERB
ejpam-5857	183	15	(	(	PUNCT
ejpam-5857	183	16	x	x	NOUN
ejpam-5857	183	17	)	)	PUNCT
ejpam-5857	183	18	,	,	PUNCT
ejpam-5857	183	19	(	(	PUNCT
ejpam-5857	183	20	by	by	ADP
ejpam-5857	183	21	(	(	PUNCT
ejpam-5857	183	22	3.17	3.17	NUM
ejpam-5857	183	23	)	)	PUNCT
ejpam-5857	183	24	)	)	PUNCT
ejpam-5857	183	25	ψi(0	ψi(0	PROPN
ejpam-5857	183	26	)	)	PUNCT
ejpam-5857	183	27	=	=	X
ejpam-5857	183	28	ψi(x	ψi(x	X
ejpam-5857	183	29	·	·	PUNCT
ejpam-5857	184	1	x	x	X
ejpam-5857	184	2	)	)	PUNCT
ejpam-5857	184	3	(	(	PUNCT
ejpam-5857	184	4	by	by	ADP
ejpam-5857	184	5	(	(	PUNCT
ejpam-5857	184	6	iup-2	iup-2	NUM
ejpam-5857	184	7	)	)	PUNCT
ejpam-5857	184	8	)	)	PUNCT
ejpam-5857	184	9	≤	≤	NUM
ejpam-5857	184	10	ψi(x	ψi(x	NUM
ejpam-5857	184	11	)	)	PUNCT
ejpam-5857	184	12	,	,	PUNCT
ejpam-5857	184	13	(	(	PUNCT
ejpam-5857	184	14	by	by	ADP
ejpam-5857	184	15	(	(	PUNCT
ejpam-5857	184	16	3.18	3.18	NUM
ejpam-5857	184	17	)	)	PUNCT
ejpam-5857	184	18	)	)	PUNCT
ejpam-5857	184	19	ψf	ψf	X
ejpam-5857	184	20	(	(	PUNCT
ejpam-5857	184	21	0	0	NUM
ejpam-5857	184	22	)	)	PUNCT
ejpam-5857	184	23	=	=	PRON
ejpam-5857	184	24	ψf	ψf	X
ejpam-5857	184	25	(	(	PUNCT
ejpam-5857	184	26	x	x	X
ejpam-5857	184	27	·	·	PUNCT
ejpam-5857	184	28	x	x	X
ejpam-5857	184	29	)	)	PUNCT
ejpam-5857	184	30	(	(	PUNCT
ejpam-5857	184	31	by	by	ADP
ejpam-5857	184	32	(	(	PUNCT
ejpam-5857	184	33	iup-2	iup-2	NUM
ejpam-5857	184	34	)	)	PUNCT
ejpam-5857	184	35	)	)	PUNCT
ejpam-5857	184	36	≥	≥	NOUN
ejpam-5857	184	37	ψf	ψf	X
ejpam-5857	184	38	(	(	PUNCT
ejpam-5857	184	39	x	x	NOUN
ejpam-5857	184	40	)	)	PUNCT
ejpam-5857	184	41	.	.	PUNCT
ejpam-5857	185	1	(	(	PUNCT
ejpam-5857	185	2	by	by	ADP
ejpam-5857	185	3	(	(	PUNCT
ejpam-5857	185	4	3.19	3.19	NUM
ejpam-5857	185	5	)	)	PUNCT
ejpam-5857	185	6	)	)	PUNCT
ejpam-5857	185	7	hence	hence	ADV
ejpam-5857	185	8	,	,	PUNCT
ejpam-5857	185	9	it	it	PRON
ejpam-5857	185	10	satisfies	satisfy	VERB
ejpam-5857	185	11	the	the	DET
ejpam-5857	185	12	conditions	condition	NOUN
ejpam-5857	185	13	(	(	PUNCT
ejpam-5857	185	14	3.8	3.8	NUM
ejpam-5857	185	15	)	)	PUNCT
ejpam-5857	185	16	,	,	PUNCT
ejpam-5857	185	17	(	(	PUNCT
ejpam-5857	185	18	3.9	3.9	NUM
ejpam-5857	185	19	)	)	PUNCT
ejpam-5857	185	20	and	and	CCONJ
ejpam-5857	185	21	(	(	PUNCT
ejpam-5857	185	22	3.10	3.10	NUM
ejpam-5857	185	23	)	)	PUNCT
ejpam-5857	185	24	.	.	PUNCT
ejpam-5857	186	1	theorem	theorem	NOUN
ejpam-5857	186	2	1	1	NUM
ejpam-5857	186	3	.	.	PUNCT
ejpam-5857	187	1	an	an	DET
ejpam-5857	187	2	intuitionistic	intuitionistic	ADJ
ejpam-5857	187	3	neutrosophic	neutrosophic	ADJ
ejpam-5857	187	4	strong	strong	ADJ
ejpam-5857	187	5	iup	iup	NOUN
ejpam-5857	187	6	-	-	PUNCT
ejpam-5857	187	7	ideal	ideal	ADJ
ejpam-5857	187	8	and	and	CCONJ
ejpam-5857	187	9	constant	constant	ADJ
ejpam-5857	187	10	ins	in	NOUN
ejpam-5857	187	11	coincide	coincide	NOUN
ejpam-5857	187	12	.	.	PUNCT
ejpam-5857	188	1	proof	proof	NOUN
ejpam-5857	188	2	.	.	PUNCT
ejpam-5857	189	1	assume	assume	VERB
ejpam-5857	189	2	that	that	SCONJ
ejpam-5857	189	3	ψ	ψ	NOUN
ejpam-5857	189	4	is	be	AUX
ejpam-5857	189	5	an	an	DET
ejpam-5857	189	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	189	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	189	8	strong	strong	ADJ
ejpam-5857	189	9	iup	iup	NOUN
ejpam-5857	189	10	-	-	PUNCT
ejpam-5857	189	11	ideal	ideal	NOUN
ejpam-5857	189	12	of	of	ADP
ejpam-5857	189	13	x.	x.	NOUN
ejpam-5857	189	14	let	let	VERB
ejpam-5857	189	15	x	x	SYM
ejpam-5857	189	16	∈	∈	PROPN
ejpam-5857	189	17	x.	x.	NOUN
ejpam-5857	189	18	then	then	ADV
ejpam-5857	189	19	ψt	ψt	VERB
ejpam-5857	189	20	(	(	PUNCT
ejpam-5857	189	21	x	x	X
ejpam-5857	189	22	)	)	PUNCT
ejpam-5857	189	23	=	=	SYM
ejpam-5857	190	1	ψt	ψt	X
ejpam-5857	190	2	(	(	PUNCT
ejpam-5857	190	3	(	(	PUNCT
ejpam-5857	190	4	x	x	X
ejpam-5857	190	5	·	·	PUNCT
ejpam-5857	190	6	0	0	NUM
ejpam-5857	190	7	)	)	PUNCT
ejpam-5857	190	8	·	·	PUNCT
ejpam-5857	190	9	0	0	X
ejpam-5857	190	10	)	)	PUNCT
ejpam-5857	190	11	(	(	PUNCT
ejpam-5857	190	12	by	by	ADP
ejpam-5857	190	13	(	(	PUNCT
ejpam-5857	190	14	2.5	2.5	NUM
ejpam-5857	190	15	)	)	PUNCT
ejpam-5857	190	16	)	)	PUNCT
ejpam-5857	190	17	≥	≥	PRON
ejpam-5857	190	18	ψt	ψt	VERB
ejpam-5857	190	19	(	(	PUNCT
ejpam-5857	190	20	0	0	NUM
ejpam-5857	190	21	)	)	PUNCT
ejpam-5857	190	22	,	,	PUNCT
ejpam-5857	190	23	(	(	PUNCT
ejpam-5857	190	24	by	by	ADP
ejpam-5857	190	25	(	(	PUNCT
ejpam-5857	190	26	3.17	3.17	NUM
ejpam-5857	190	27	)	)	PUNCT
ejpam-5857	190	28	)	)	PUNCT
ejpam-5857	190	29	ψi(x	ψi(x	NUM
ejpam-5857	190	30	)	)	PUNCT
ejpam-5857	191	1	=	=	NOUN
ejpam-5857	191	2	ψi((x	ψi((x	NOUN
ejpam-5857	191	3	·	·	PUNCT
ejpam-5857	191	4	0	0	X
ejpam-5857	191	5	)	)	PUNCT
ejpam-5857	191	6	·	·	PUNCT
ejpam-5857	192	1	0	0	X
ejpam-5857	192	2	)	)	PUNCT
ejpam-5857	192	3	(	(	PUNCT
ejpam-5857	192	4	by	by	ADP
ejpam-5857	192	5	(	(	PUNCT
ejpam-5857	192	6	2.5	2.5	NUM
ejpam-5857	192	7	)	)	PUNCT
ejpam-5857	192	8	)	)	PUNCT
ejpam-5857	192	9	≤	≤	PROPN
ejpam-5857	192	10	ψi(0	ψi(0	PROPN
ejpam-5857	192	11	)	)	PUNCT
ejpam-5857	192	12	,	,	PUNCT
ejpam-5857	192	13	(	(	PUNCT
ejpam-5857	192	14	by	by	ADP
ejpam-5857	192	15	(	(	PUNCT
ejpam-5857	192	16	3.18	3.18	NUM
ejpam-5857	192	17	)	)	PUNCT
ejpam-5857	192	18	)	)	PUNCT
ejpam-5857	192	19	ψf	ψf	X
ejpam-5857	192	20	(	(	PUNCT
ejpam-5857	192	21	x	x	X
ejpam-5857	192	22	)	)	PUNCT
ejpam-5857	192	23	=	=	SYM
ejpam-5857	192	24	ψf	ψf	X
ejpam-5857	192	25	(	(	PUNCT
ejpam-5857	192	26	(	(	PUNCT
ejpam-5857	192	27	x	x	X
ejpam-5857	192	28	·	·	PUNCT
ejpam-5857	192	29	0	0	NUM
ejpam-5857	192	30	)	)	PUNCT
ejpam-5857	192	31	·	·	PUNCT
ejpam-5857	192	32	0	0	X
ejpam-5857	192	33	)	)	PUNCT
ejpam-5857	192	34	(	(	PUNCT
ejpam-5857	192	35	by	by	ADP
ejpam-5857	192	36	(	(	PUNCT
ejpam-5857	192	37	2.5	2.5	NUM
ejpam-5857	192	38	)	)	PUNCT
ejpam-5857	192	39	)	)	PUNCT
ejpam-5857	192	40	≥	≥	NOUN
ejpam-5857	192	41	ψf	ψf	X
ejpam-5857	192	42	(	(	PUNCT
ejpam-5857	192	43	0	0	NUM
ejpam-5857	192	44	)	)	PUNCT
ejpam-5857	192	45	.	.	PUNCT
ejpam-5857	193	1	(	(	PUNCT
ejpam-5857	193	2	by	by	ADP
ejpam-5857	193	3	(	(	PUNCT
ejpam-5857	193	4	3.19	3.19	NUM
ejpam-5857	193	5	)	)	PUNCT
ejpam-5857	193	6	)	)	PUNCT
ejpam-5857	193	7	hence	hence	ADV
ejpam-5857	193	8	,	,	PUNCT
ejpam-5857	193	9	ψ	ψ	X
ejpam-5857	193	10	is	be	AUX
ejpam-5857	193	11	a	a	DET
ejpam-5857	193	12	constant	constant	ADJ
ejpam-5857	193	13	ins	in	NOUN
ejpam-5857	193	14	of	of	ADP
ejpam-5857	193	15	x.	x.	NOUN
ejpam-5857	193	16	conversely	conversely	ADV
ejpam-5857	193	17	,	,	PUNCT
ejpam-5857	193	18	it	it	PRON
ejpam-5857	193	19	is	be	AUX
ejpam-5857	193	20	obvious	obvious	ADJ
ejpam-5857	193	21	that	that	SCONJ
ejpam-5857	193	22	every	every	DET
ejpam-5857	193	23	constant	constant	ADJ
ejpam-5857	193	24	ins	in	NOUN
ejpam-5857	193	25	of	of	ADP
ejpam-5857	193	26	x	x	X
ejpam-5857	193	27	is	be	AUX
ejpam-5857	193	28	an	an	DET
ejpam-5857	193	29	intuitionistic	intuitionistic	ADJ
ejpam-5857	193	30	neutrosophic	neutrosophic	ADJ
ejpam-5857	193	31	strong	strong	ADJ
ejpam-5857	193	32	iup	iup	NOUN
ejpam-5857	193	33	-	-	PUNCT
ejpam-5857	193	34	ideal	ideal	NOUN
ejpam-5857	193	35	.	.	PUNCT
ejpam-5857	194	1	k.	k.	PROPN
ejpam-5857	194	2	suayngam	suayngam	PROPN
ejpam-5857	194	3	,	,	PUNCT
ejpam-5857	194	4	p.	p.	NOUN
ejpam-5857	194	5	julatha	julatha	PROPN
ejpam-5857	194	6	,	,	PUNCT
ejpam-5857	194	7	w.	w.	PROPN
ejpam-5857	194	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	194	9	,	,	PUNCT
ejpam-5857	194	10	a.	a.	NOUN
ejpam-5857	194	11	iampan	iampan	PROPN
ejpam-5857	194	12	/	/	SYM
ejpam-5857	194	13	eur	eur	PROPN
ejpam-5857	194	14	.	.	PUNCT
ejpam-5857	195	1	j.	j.	PROPN
ejpam-5857	195	2	pure	pure	PROPN
ejpam-5857	195	3	appl	appl	PROPN
ejpam-5857	195	4	.	.	PROPN
ejpam-5857	195	5	math	math	PROPN
ejpam-5857	195	6	,	,	PUNCT
ejpam-5857	195	7	18	18	NUM
ejpam-5857	195	8	(	(	PUNCT
ejpam-5857	195	9	2	2	NUM
ejpam-5857	195	10	)	)	PUNCT
ejpam-5857	195	11	(	(	PUNCT
ejpam-5857	195	12	2025	2025	NUM
ejpam-5857	195	13	)	)	PUNCT
ejpam-5857	195	14	,	,	PUNCT
ejpam-5857	195	15	5857	5857	NUM
ejpam-5857	195	16	9	9	NUM
ejpam-5857	195	17	of	of	ADP
ejpam-5857	195	18	30	30	NUM
ejpam-5857	195	19	example	example	NOUN
ejpam-5857	195	20	5	5	NUM
ejpam-5857	195	21	.	.	PUNCT
ejpam-5857	196	1	let	let	VERB
ejpam-5857	196	2	x	x	PUNCT
ejpam-5857	196	3	=	=	PUNCT
ejpam-5857	196	4	{	{	PUNCT
ejpam-5857	196	5	0	0	NUM
ejpam-5857	196	6	,	,	PUNCT
ejpam-5857	196	7	1	1	NUM
ejpam-5857	196	8	,	,	PUNCT
ejpam-5857	196	9	2	2	NUM
ejpam-5857	196	10	,	,	PUNCT
ejpam-5857	196	11	3	3	NUM
ejpam-5857	196	12	,	,	PUNCT
ejpam-5857	196	13	4	4	NUM
ejpam-5857	196	14	,	,	PUNCT
ejpam-5857	196	15	5	5	NUM
ejpam-5857	196	16	}	}	PUNCT
ejpam-5857	196	17	with	with	ADP
ejpam-5857	196	18	the	the	DET
ejpam-5857	196	19	following	follow	VERB
ejpam-5857	196	20	cayley	cayley	ADJ
ejpam-5857	196	21	table	table	NOUN
ejpam-5857	196	22	:	:	PUNCT
ejpam-5857	196	23	·	·	PUNCT
ejpam-5857	196	24	0	0	NUM
ejpam-5857	196	25	1	1	NUM
ejpam-5857	196	26	2	2	NUM
ejpam-5857	196	27	3	3	NUM
ejpam-5857	196	28	4	4	NUM
ejpam-5857	196	29	5	5	NUM
ejpam-5857	196	30	0	0	NUM
ejpam-5857	196	31	0	0	NUM
ejpam-5857	196	32	1	1	NUM
ejpam-5857	196	33	2	2	NUM
ejpam-5857	196	34	3	3	NUM
ejpam-5857	196	35	4	4	NUM
ejpam-5857	196	36	5	5	NUM
ejpam-5857	196	37	1	1	NUM
ejpam-5857	196	38	5	5	NUM
ejpam-5857	196	39	0	0	NUM
ejpam-5857	196	40	3	3	NUM
ejpam-5857	196	41	4	4	NUM
ejpam-5857	196	42	2	2	NUM
ejpam-5857	196	43	1	1	NUM
ejpam-5857	196	44	2	2	NUM
ejpam-5857	196	45	3	3	NUM
ejpam-5857	196	46	2	2	NUM
ejpam-5857	196	47	0	0	NUM
ejpam-5857	196	48	5	5	NUM
ejpam-5857	196	49	1	1	NUM
ejpam-5857	196	50	4	4	NUM
ejpam-5857	196	51	3	3	NUM
ejpam-5857	196	52	2	2	NUM
ejpam-5857	196	53	4	4	NUM
ejpam-5857	196	54	1	1	NUM
ejpam-5857	196	55	0	0	NUM
ejpam-5857	196	56	5	5	NUM
ejpam-5857	196	57	3	3	NUM
ejpam-5857	196	58	4	4	NUM
ejpam-5857	196	59	4	4	NUM
ejpam-5857	196	60	3	3	NUM
ejpam-5857	196	61	5	5	NUM
ejpam-5857	196	62	1	1	NUM
ejpam-5857	196	63	0	0	NUM
ejpam-5857	196	64	2	2	NUM
ejpam-5857	196	65	5	5	NUM
ejpam-5857	196	66	1	1	NUM
ejpam-5857	196	67	5	5	NUM
ejpam-5857	196	68	4	4	NUM
ejpam-5857	196	69	2	2	NUM
ejpam-5857	196	70	3	3	NUM
ejpam-5857	196	71	0	0	NUM
ejpam-5857	196	72	then	then	ADV
ejpam-5857	196	73	x	x	PUNCT
ejpam-5857	196	74	is	be	AUX
ejpam-5857	196	75	an	an	DET
ejpam-5857	196	76	iup	iup	NOUN
ejpam-5857	196	77	-	-	PUNCT
ejpam-5857	196	78	algebra	algebra	NOUN
ejpam-5857	196	79	.	.	PUNCT
ejpam-5857	197	1	we	we	PRON
ejpam-5857	197	2	define	define	VERB
ejpam-5857	197	3	an	an	DET
ejpam-5857	197	4	ins	in	NOUN
ejpam-5857	197	5	ψ	ψ	X
ejpam-5857	197	6	on	on	ADP
ejpam-5857	197	7	x	x	PUNCT
ejpam-5857	197	8	as	as	SCONJ
ejpam-5857	197	9	follows	follow	VERB
ejpam-5857	197	10	:	:	PUNCT
ejpam-5857	197	11	ψt	ψt	NOUN
ejpam-5857	197	12	=	=	PUNCT
ejpam-5857	197	13	(	(	PUNCT
ejpam-5857	197	14	0	0	NUM
ejpam-5857	197	15	0.6	0.6	NUM
ejpam-5857	197	16	1	1	NUM
ejpam-5857	197	17	0.6	0.6	NUM
ejpam-5857	197	18	2	2	NUM
ejpam-5857	197	19	0.6	0.6	NUM
ejpam-5857	197	20	3	3	NUM
ejpam-5857	197	21	0.6	0.6	NUM
ejpam-5857	197	22	4	4	NUM
ejpam-5857	197	23	0.6	0.6	NUM
ejpam-5857	197	24	5	5	NUM
ejpam-5857	197	25	0.6	0.6	NUM
ejpam-5857	197	26	)	)	PUNCT
ejpam-5857	197	27	ψi	ψi	ADP
ejpam-5857	198	1	=	=	PUNCT
ejpam-5857	198	2	(	(	PUNCT
ejpam-5857	198	3	0	0	NUM
ejpam-5857	198	4	0.4	0.4	NUM
ejpam-5857	198	5	1	1	NUM
ejpam-5857	198	6	0.4	0.4	NUM
ejpam-5857	198	7	2	2	NUM
ejpam-5857	198	8	0.4	0.4	NUM
ejpam-5857	198	9	3	3	NUM
ejpam-5857	198	10	0.4	0.4	NUM
ejpam-5857	198	11	4	4	NUM
ejpam-5857	198	12	0.4	0.4	NUM
ejpam-5857	198	13	5	5	NUM
ejpam-5857	198	14	0.4	0.4	NUM
ejpam-5857	198	15	)	)	PUNCT
ejpam-5857	198	16	ψf	ψf	X
ejpam-5857	198	17	=	=	PUNCT
ejpam-5857	198	18	(	(	PUNCT
ejpam-5857	198	19	0	0	NUM
ejpam-5857	198	20	0.3	0.3	NUM
ejpam-5857	198	21	1	1	NUM
ejpam-5857	198	22	0.3	0.3	NUM
ejpam-5857	198	23	2	2	NUM
ejpam-5857	198	24	0.3	0.3	NUM
ejpam-5857	198	25	3	3	NUM
ejpam-5857	198	26	0.3	0.3	NUM
ejpam-5857	198	27	4	4	NUM
ejpam-5857	198	28	0.3	0.3	NUM
ejpam-5857	198	29	5	5	NUM
ejpam-5857	198	30	0.3	0.3	NUM
ejpam-5857	198	31	)	)	PUNCT
ejpam-5857	198	32	then	then	ADV
ejpam-5857	198	33	ψ	ψ	X
ejpam-5857	198	34	is	be	AUX
ejpam-5857	198	35	an	an	DET
ejpam-5857	198	36	intuitionistic	intuitionistic	ADJ
ejpam-5857	198	37	neutrosophic	neutrosophic	ADJ
ejpam-5857	198	38	strong	strong	ADJ
ejpam-5857	198	39	iup	iup	NOUN
ejpam-5857	198	40	-	-	PUNCT
ejpam-5857	198	41	ideal	ideal	NOUN
ejpam-5857	198	42	of	of	ADP
ejpam-5857	198	43	x.	x.	NOUN
ejpam-5857	198	44	since	since	SCONJ
ejpam-5857	198	45	ψf	ψf	X
ejpam-5857	198	46	(	(	PUNCT
ejpam-5857	198	47	0	0	NUM
ejpam-5857	198	48	·	·	SYM
ejpam-5857	198	49	2	2	NUM
ejpam-5857	198	50	)	)	PUNCT
ejpam-5857	198	51	=	=	PRON
ejpam-5857	198	52	ψf	ψf	X
ejpam-5857	198	53	(	(	PUNCT
ejpam-5857	198	54	2	2	NUM
ejpam-5857	198	55	)	)	PUNCT
ejpam-5857	198	56	=	=	PUNCT
ejpam-5857	198	57	0.3	0.3	NUM
ejpam-5857	198	58	≱	≱	PROPN
ejpam-5857	198	59	0.5	0.5	NUM
ejpam-5857	198	60	=	=	SYM
ejpam-5857	198	61	0.3	0.3	NUM
ejpam-5857	198	62	∨	∨	NUM
ejpam-5857	198	63	0.5	0.5	NUM
ejpam-5857	198	64	=	=	SYM
ejpam-5857	198	65	(	(	PUNCT
ejpam-5857	198	66	0.3	0.3	NUM
ejpam-5857	198	67	∧	∧	PROPN
ejpam-5857	198	68	0.3	0.3	NUM
ejpam-5857	198	69	)	)	PUNCT
ejpam-5857	198	70	∨	∨	NUM
ejpam-5857	198	71	0.5	0.5	NUM
ejpam-5857	198	72	=	=	SYM
ejpam-5857	198	73	(	(	PUNCT
ejpam-5857	198	74	ψf	ψf	X
ejpam-5857	198	75	(	(	PUNCT
ejpam-5857	198	76	0	0	NUM
ejpam-5857	198	77	)	)	PUNCT
ejpam-5857	198	78	∧	∧	NOUN
ejpam-5857	198	79	ψf	ψf	X
ejpam-5857	198	80	(	(	PUNCT
ejpam-5857	198	81	2	2	NUM
ejpam-5857	198	82	)	)	PUNCT
ejpam-5857	198	83	)	)	PUNCT
ejpam-5857	198	84	∨	∨	NUM
ejpam-5857	198	85	0.5	0.5	NUM
ejpam-5857	198	86	.	.	PUNCT
ejpam-5857	199	1	hence	hence	ADV
ejpam-5857	199	2	,	,	PUNCT
ejpam-5857	199	3	ψ	ψ	X
ejpam-5857	199	4	is	be	AUX
ejpam-5857	199	5	not	not	PART
ejpam-5857	199	6	an	an	DET
ejpam-5857	199	7	intuitionistic	intuitionistic	ADJ
ejpam-5857	199	8	neutrosophic	neutrosophic	ADJ
ejpam-5857	199	9	iup	iup	NOUN
ejpam-5857	199	10	-	-	PUNCT
ejpam-5857	199	11	subalgebra	subalgebra	NOUN
ejpam-5857	199	12	of	of	ADP
ejpam-5857	199	13	x.	x.	NOUN
ejpam-5857	199	14	example	example	NOUN
ejpam-5857	199	15	6	6	NUM
ejpam-5857	199	16	.	.	PUNCT
ejpam-5857	200	1	let	let	VERB
ejpam-5857	200	2	x	x	PUNCT
ejpam-5857	200	3	=	=	PUNCT
ejpam-5857	200	4	{	{	PUNCT
ejpam-5857	200	5	0	0	NUM
ejpam-5857	200	6	,	,	PUNCT
ejpam-5857	200	7	1	1	NUM
ejpam-5857	200	8	,	,	PUNCT
ejpam-5857	200	9	2	2	NUM
ejpam-5857	200	10	,	,	PUNCT
ejpam-5857	200	11	3	3	NUM
ejpam-5857	200	12	,	,	PUNCT
ejpam-5857	200	13	4	4	NUM
ejpam-5857	200	14	,	,	PUNCT
ejpam-5857	200	15	5	5	NUM
ejpam-5857	200	16	}	}	PUNCT
ejpam-5857	200	17	with	with	ADP
ejpam-5857	200	18	the	the	DET
ejpam-5857	200	19	following	follow	VERB
ejpam-5857	200	20	cayley	cayley	ADJ
ejpam-5857	200	21	table	table	NOUN
ejpam-5857	200	22	:	:	PUNCT
ejpam-5857	200	23	·	·	PUNCT
ejpam-5857	200	24	0	0	NUM
ejpam-5857	200	25	1	1	NUM
ejpam-5857	200	26	2	2	NUM
ejpam-5857	200	27	3	3	NUM
ejpam-5857	200	28	4	4	NUM
ejpam-5857	200	29	5	5	NUM
ejpam-5857	200	30	0	0	NUM
ejpam-5857	200	31	0	0	NUM
ejpam-5857	200	32	1	1	NUM
ejpam-5857	200	33	2	2	NUM
ejpam-5857	200	34	3	3	NUM
ejpam-5857	200	35	4	4	NUM
ejpam-5857	200	36	5	5	NUM
ejpam-5857	200	37	1	1	NUM
ejpam-5857	200	38	5	5	NUM
ejpam-5857	200	39	0	0	NUM
ejpam-5857	200	40	4	4	NUM
ejpam-5857	200	41	2	2	NUM
ejpam-5857	200	42	1	1	NUM
ejpam-5857	200	43	3	3	NUM
ejpam-5857	200	44	2	2	NUM
ejpam-5857	200	45	2	2	NUM
ejpam-5857	200	46	3	3	NUM
ejpam-5857	200	47	0	0	NUM
ejpam-5857	200	48	1	1	NUM
ejpam-5857	200	49	5	5	NUM
ejpam-5857	200	50	4	4	NUM
ejpam-5857	200	51	3	3	NUM
ejpam-5857	200	52	4	4	NUM
ejpam-5857	200	53	2	2	NUM
ejpam-5857	200	54	5	5	NUM
ejpam-5857	200	55	0	0	NUM
ejpam-5857	200	56	3	3	NUM
ejpam-5857	200	57	1	1	NUM
ejpam-5857	200	58	4	4	NUM
ejpam-5857	200	59	3	3	NUM
ejpam-5857	200	60	5	5	NUM
ejpam-5857	200	61	1	1	NUM
ejpam-5857	200	62	4	4	NUM
ejpam-5857	200	63	0	0	NUM
ejpam-5857	200	64	2	2	NUM
ejpam-5857	200	65	5	5	NUM
ejpam-5857	200	66	1	1	NUM
ejpam-5857	200	67	4	4	NUM
ejpam-5857	200	68	3	3	NUM
ejpam-5857	200	69	5	5	NUM
ejpam-5857	200	70	2	2	NUM
ejpam-5857	200	71	0	0	NUM
ejpam-5857	200	72	then	then	ADV
ejpam-5857	200	73	x	x	PUNCT
ejpam-5857	200	74	is	be	AUX
ejpam-5857	200	75	an	an	DET
ejpam-5857	200	76	iup	iup	NOUN
ejpam-5857	200	77	-	-	PUNCT
ejpam-5857	200	78	algebra	algebra	NOUN
ejpam-5857	200	79	.	.	PUNCT
ejpam-5857	201	1	we	we	PRON
ejpam-5857	201	2	define	define	VERB
ejpam-5857	201	3	an	an	DET
ejpam-5857	201	4	ins	in	NOUN
ejpam-5857	201	5	ψ	ψ	X
ejpam-5857	201	6	on	on	ADP
ejpam-5857	201	7	x	x	PUNCT
ejpam-5857	201	8	as	as	SCONJ
ejpam-5857	201	9	follows	follow	VERB
ejpam-5857	201	10	:	:	PUNCT
ejpam-5857	201	11	ψt	ψt	NOUN
ejpam-5857	201	12	=	=	PUNCT
ejpam-5857	201	13	(	(	PUNCT
ejpam-5857	201	14	0	0	NUM
ejpam-5857	201	15	0.9	0.9	NUM
ejpam-5857	201	16	1	1	NUM
ejpam-5857	201	17	0.6	0.6	NUM
ejpam-5857	201	18	2	2	NUM
ejpam-5857	201	19	0.6	0.6	NUM
ejpam-5857	201	20	3	3	NUM
ejpam-5857	201	21	0.7	0.7	NUM
ejpam-5857	201	22	4	4	NUM
ejpam-5857	201	23	0.7	0.7	NUM
ejpam-5857	201	24	5	5	NUM
ejpam-5857	201	25	0.6	0.6	NUM
ejpam-5857	201	26	)	)	PUNCT
ejpam-5857	201	27	ψi	ψi	ADP
ejpam-5857	202	1	=	=	PUNCT
ejpam-5857	202	2	(	(	PUNCT
ejpam-5857	202	3	0	0	NUM
ejpam-5857	202	4	0.1	0.1	NUM
ejpam-5857	202	5	1	1	NUM
ejpam-5857	202	6	0.4	0.4	NUM
ejpam-5857	202	7	2	2	NUM
ejpam-5857	202	8	0.4	0.4	NUM
ejpam-5857	202	9	3	3	NUM
ejpam-5857	202	10	0.3	0.3	NUM
ejpam-5857	202	11	4	4	NUM
ejpam-5857	202	12	0.3	0.3	NUM
ejpam-5857	202	13	5	5	NUM
ejpam-5857	202	14	0.4	0.4	NUM
ejpam-5857	202	15	)	)	PUNCT
ejpam-5857	202	16	ψf	ψf	X
ejpam-5857	202	17	=	=	PUNCT
ejpam-5857	202	18	(	(	PUNCT
ejpam-5857	202	19	0	0	NUM
ejpam-5857	202	20	0.5	0.5	NUM
ejpam-5857	202	21	1	1	NUM
ejpam-5857	202	22	0.5	0.5	NUM
ejpam-5857	202	23	2	2	NUM
ejpam-5857	202	24	0.5	0.5	NUM
ejpam-5857	202	25	3	3	NUM
ejpam-5857	202	26	0.5	0.5	NUM
ejpam-5857	202	27	4	4	NUM
ejpam-5857	202	28	0.5	0.5	NUM
ejpam-5857	202	29	5	5	NUM
ejpam-5857	202	30	0.5	0.5	NUM
ejpam-5857	202	31	)	)	PUNCT
ejpam-5857	202	32	then	then	ADV
ejpam-5857	202	33	ψ	ψ	X
ejpam-5857	202	34	is	be	AUX
ejpam-5857	202	35	an	an	DET
ejpam-5857	202	36	intuitionistic	intuitionistic	ADJ
ejpam-5857	202	37	neutrosophic	neutrosophic	ADJ
ejpam-5857	202	38	iup	iup	NOUN
ejpam-5857	202	39	-	-	PUNCT
ejpam-5857	202	40	subalgebra	subalgebra	NOUN
ejpam-5857	202	41	of	of	ADP
ejpam-5857	202	42	x.	x.	NOUN
ejpam-5857	202	43	since	since	SCONJ
ejpam-5857	202	44	ψt	ψt	VERB
ejpam-5857	202	45	(	(	PUNCT
ejpam-5857	202	46	5	5	NUM
ejpam-5857	202	47	·	·	SYM
ejpam-5857	202	48	3	3	NUM
ejpam-5857	202	49	)	)	PUNCT
ejpam-5857	202	50	=	=	PRON
ejpam-5857	203	1	ψt	ψt	NOUN
ejpam-5857	203	2	(	(	PUNCT
ejpam-5857	203	3	5	5	NUM
ejpam-5857	203	4	)	)	PUNCT
ejpam-5857	203	5	=	=	SYM
ejpam-5857	203	6	0.6	0.6	NUM
ejpam-5857	203	7	≱	≱	PROPN
ejpam-5857	203	8	0.7	0.7	NUM
ejpam-5857	203	9	=	=	SYM
ejpam-5857	203	10	ψt	ψt	NUM
ejpam-5857	203	11	(	(	PUNCT
ejpam-5857	203	12	3	3	NUM
ejpam-5857	203	13	)	)	PUNCT
ejpam-5857	203	14	and	and	CCONJ
ejpam-5857	203	15	ψi(5	ψi(5	PROPN
ejpam-5857	203	16	·	·	PUNCT
ejpam-5857	203	17	4	4	X
ejpam-5857	203	18	)	)	PUNCT
ejpam-5857	203	19	=	=	SYM
ejpam-5857	203	20	ψi(2	ψi(2	PROPN
ejpam-5857	203	21	)	)	PUNCT
ejpam-5857	203	22	=	=	PUNCT
ejpam-5857	204	1	0.4	0.4	NUM
ejpam-5857	204	2	≰	≰	PROPN
ejpam-5857	204	3	0.3	0.3	NUM
ejpam-5857	204	4	=	=	SYM
ejpam-5857	204	5	ψi(4	ψi(4	NOUN
ejpam-5857	204	6	)	)	PUNCT
ejpam-5857	204	7	.	.	PUNCT
ejpam-5857	205	1	hence	hence	ADV
ejpam-5857	205	2	,	,	PUNCT
ejpam-5857	205	3	ψ	ψ	X
ejpam-5857	205	4	is	be	AUX
ejpam-5857	205	5	not	not	PART
ejpam-5857	205	6	an	an	DET
ejpam-5857	205	7	intuitionistic	intuitionistic	ADJ
ejpam-5857	205	8	neutrosophic	neutrosophic	ADJ
ejpam-5857	205	9	strong	strong	ADJ
ejpam-5857	205	10	iup	iup	NOUN
ejpam-5857	205	11	-	-	PUNCT
ejpam-5857	205	12	ideal	ideal	NOUN
ejpam-5857	205	13	of	of	ADP
ejpam-5857	205	14	x.	x.	PROPN
ejpam-5857	205	15	k.	k.	PROPN
ejpam-5857	205	16	suayngam	suayngam	PROPN
ejpam-5857	205	17	,	,	PUNCT
ejpam-5857	205	18	p.	p.	NOUN
ejpam-5857	205	19	julatha	julatha	PROPN
ejpam-5857	205	20	,	,	PUNCT
ejpam-5857	205	21	w.	w.	PROPN
ejpam-5857	205	22	nakkhasen	nakkhasen	PROPN
ejpam-5857	205	23	,	,	PUNCT
ejpam-5857	205	24	a.	a.	NOUN
ejpam-5857	205	25	iampan	iampan	PROPN
ejpam-5857	205	26	/	/	SYM
ejpam-5857	205	27	eur	eur	PROPN
ejpam-5857	205	28	.	.	PUNCT
ejpam-5857	206	1	j.	j.	PROPN
ejpam-5857	206	2	pure	pure	PROPN
ejpam-5857	206	3	appl	appl	PROPN
ejpam-5857	206	4	.	.	PROPN
ejpam-5857	206	5	math	math	PROPN
ejpam-5857	206	6	,	,	PUNCT
ejpam-5857	206	7	18	18	NUM
ejpam-5857	206	8	(	(	PUNCT
ejpam-5857	206	9	2	2	NUM
ejpam-5857	206	10	)	)	PUNCT
ejpam-5857	206	11	(	(	PUNCT
ejpam-5857	206	12	2025	2025	NUM
ejpam-5857	206	13	)	)	PUNCT
ejpam-5857	206	14	,	,	PUNCT
ejpam-5857	206	15	5857	5857	NUM
ejpam-5857	206	16	10	10	NUM
ejpam-5857	206	17	of	of	ADP
ejpam-5857	206	18	30	30	NUM
ejpam-5857	206	19	example	example	NOUN
ejpam-5857	206	20	7	7	NUM
ejpam-5857	206	21	.	.	PUNCT
ejpam-5857	207	1	let	let	VERB
ejpam-5857	207	2	x	x	PUNCT
ejpam-5857	207	3	=	=	PUNCT
ejpam-5857	207	4	{	{	PUNCT
ejpam-5857	207	5	0	0	NUM
ejpam-5857	207	6	,	,	PUNCT
ejpam-5857	207	7	1	1	NUM
ejpam-5857	207	8	,	,	PUNCT
ejpam-5857	207	9	2	2	NUM
ejpam-5857	207	10	,	,	PUNCT
ejpam-5857	207	11	3	3	NUM
ejpam-5857	207	12	,	,	PUNCT
ejpam-5857	207	13	4	4	NUM
ejpam-5857	207	14	,	,	PUNCT
ejpam-5857	207	15	5	5	NUM
ejpam-5857	207	16	}	}	PUNCT
ejpam-5857	207	17	with	with	ADP
ejpam-5857	207	18	the	the	DET
ejpam-5857	207	19	following	follow	VERB
ejpam-5857	207	20	cayley	cayley	ADJ
ejpam-5857	207	21	table	table	NOUN
ejpam-5857	207	22	:	:	PUNCT
ejpam-5857	207	23	·	·	PUNCT
ejpam-5857	207	24	0	0	NUM
ejpam-5857	208	1	1	1	NUM
ejpam-5857	208	2	2	2	NUM
ejpam-5857	208	3	3	3	NUM
ejpam-5857	208	4	4	4	NUM
ejpam-5857	208	5	5	5	NUM
ejpam-5857	208	6	0	0	NUM
ejpam-5857	208	7	0	0	NUM
ejpam-5857	208	8	1	1	NUM
ejpam-5857	208	9	2	2	NUM
ejpam-5857	208	10	3	3	NUM
ejpam-5857	208	11	4	4	NUM
ejpam-5857	208	12	5	5	NUM
ejpam-5857	208	13	1	1	NUM
ejpam-5857	208	14	1	1	NUM
ejpam-5857	208	15	0	0	NUM
ejpam-5857	208	16	4	4	NUM
ejpam-5857	208	17	5	5	NUM
ejpam-5857	208	18	2	2	NUM
ejpam-5857	208	19	3	3	NUM
ejpam-5857	208	20	2	2	NUM
ejpam-5857	208	21	5	5	NUM
ejpam-5857	208	22	3	3	NUM
ejpam-5857	208	23	0	0	NUM
ejpam-5857	208	24	2	2	NUM
ejpam-5857	208	25	1	1	NUM
ejpam-5857	208	26	4	4	NUM
ejpam-5857	208	27	3	3	NUM
ejpam-5857	208	28	4	4	NUM
ejpam-5857	208	29	2	2	NUM
ejpam-5857	208	30	5	5	NUM
ejpam-5857	208	31	0	0	NUM
ejpam-5857	208	32	3	3	NUM
ejpam-5857	208	33	1	1	NUM
ejpam-5857	208	34	4	4	NUM
ejpam-5857	208	35	3	3	NUM
ejpam-5857	208	36	5	5	NUM
ejpam-5857	208	37	1	1	NUM
ejpam-5857	208	38	4	4	NUM
ejpam-5857	208	39	0	0	NUM
ejpam-5857	208	40	2	2	NUM
ejpam-5857	208	41	5	5	NUM
ejpam-5857	208	42	2	2	NUM
ejpam-5857	208	43	4	4	NUM
ejpam-5857	208	44	3	3	NUM
ejpam-5857	208	45	1	1	NUM
ejpam-5857	208	46	5	5	NUM
ejpam-5857	208	47	0	0	NUM
ejpam-5857	208	48	then	then	ADV
ejpam-5857	208	49	x	x	PUNCT
ejpam-5857	208	50	is	be	AUX
ejpam-5857	208	51	an	an	DET
ejpam-5857	208	52	iup	iup	NOUN
ejpam-5857	208	53	-	-	PUNCT
ejpam-5857	208	54	algebra	algebra	NOUN
ejpam-5857	208	55	.	.	PUNCT
ejpam-5857	209	1	we	we	PRON
ejpam-5857	209	2	define	define	VERB
ejpam-5857	209	3	an	an	DET
ejpam-5857	209	4	ins	in	NOUN
ejpam-5857	209	5	ψ	ψ	X
ejpam-5857	209	6	on	on	ADP
ejpam-5857	209	7	x	x	PUNCT
ejpam-5857	209	8	as	as	SCONJ
ejpam-5857	209	9	follows	follow	VERB
ejpam-5857	209	10	:	:	PUNCT
ejpam-5857	209	11	ψt	ψt	NOUN
ejpam-5857	209	12	=	=	PUNCT
ejpam-5857	209	13	(	(	PUNCT
ejpam-5857	209	14	0	0	NUM
ejpam-5857	209	15	0.5	0.5	NUM
ejpam-5857	209	16	1	1	NUM
ejpam-5857	209	17	0.5	0.5	NUM
ejpam-5857	209	18	2	2	NUM
ejpam-5857	209	19	0.5	0.5	NUM
ejpam-5857	209	20	3	3	NUM
ejpam-5857	209	21	0.5	0.5	NUM
ejpam-5857	209	22	4	4	NUM
ejpam-5857	209	23	0.5	0.5	NUM
ejpam-5857	209	24	5	5	NUM
ejpam-5857	209	25	0.5	0.5	NUM
ejpam-5857	209	26	)	)	PUNCT
ejpam-5857	209	27	ψi	ψi	ADP
ejpam-5857	209	28	=	=	PUNCT
ejpam-5857	209	29	(	(	PUNCT
ejpam-5857	209	30	0	0	NUM
ejpam-5857	209	31	0.7	0.7	NUM
ejpam-5857	209	32	1	1	NUM
ejpam-5857	209	33	0.7	0.7	NUM
ejpam-5857	209	34	2	2	NUM
ejpam-5857	209	35	0.7	0.7	NUM
ejpam-5857	209	36	3	3	NUM
ejpam-5857	209	37	0.7	0.7	NUM
ejpam-5857	209	38	4	4	NUM
ejpam-5857	209	39	0.7	0.7	NUM
ejpam-5857	209	40	5	5	NUM
ejpam-5857	209	41	0.7	0.7	NUM
ejpam-5857	209	42	)	)	PUNCT
ejpam-5857	209	43	ψf	ψf	NOUN
ejpam-5857	210	1	=	=	PUNCT
ejpam-5857	210	2	(	(	PUNCT
ejpam-5857	210	3	0	0	NUM
ejpam-5857	210	4	0.3	0.3	NUM
ejpam-5857	210	5	1	1	NUM
ejpam-5857	210	6	0.3	0.3	NUM
ejpam-5857	210	7	2	2	NUM
ejpam-5857	210	8	0.3	0.3	NUM
ejpam-5857	210	9	3	3	NUM
ejpam-5857	210	10	0.3	0.3	NUM
ejpam-5857	210	11	4	4	NUM
ejpam-5857	210	12	0.3	0.3	NUM
ejpam-5857	210	13	5	5	NUM
ejpam-5857	210	14	0.3	0.3	NUM
ejpam-5857	210	15	)	)	PUNCT
ejpam-5857	210	16	then	then	ADV
ejpam-5857	210	17	ψ	ψ	X
ejpam-5857	210	18	is	be	AUX
ejpam-5857	210	19	an	an	DET
ejpam-5857	210	20	intuitionistic	intuitionistic	ADJ
ejpam-5857	210	21	neutrosophic	neutrosophic	ADJ
ejpam-5857	210	22	strong	strong	ADJ
ejpam-5857	210	23	iup	iup	NOUN
ejpam-5857	210	24	-	-	PUNCT
ejpam-5857	210	25	ideal	ideal	NOUN
ejpam-5857	210	26	of	of	ADP
ejpam-5857	210	27	x.	x.	NOUN
ejpam-5857	210	28	since	since	SCONJ
ejpam-5857	210	29	ψi(4	ψi(4	PROPN
ejpam-5857	210	30	·	·	PUNCT
ejpam-5857	210	31	3	3	X
ejpam-5857	210	32	)	)	PUNCT
ejpam-5857	210	33	=	=	SYM
ejpam-5857	210	34	ψi(4	ψi(4	NOUN
ejpam-5857	210	35	)	)	PUNCT
ejpam-5857	210	36	=	=	PUNCT
ejpam-5857	210	37	0.7	0.7	NUM
ejpam-5857	210	38	≰	≰	PROPN
ejpam-5857	210	39	0.5	0.5	NUM
ejpam-5857	210	40	=	=	SYM
ejpam-5857	210	41	0.7∧	0.7∧	NOUN
ejpam-5857	210	42	0.5	0.5	NUM
ejpam-5857	210	43	=	=	SYM
ejpam-5857	210	44	(	(	PUNCT
ejpam-5857	210	45	0.7∨	0.7∨	NOUN
ejpam-5857	210	46	0.7)∧	0.7)∧	NUM
ejpam-5857	210	47	0.5	0.5	NUM
ejpam-5857	210	48	=	=	SYM
ejpam-5857	210	49	(	(	PUNCT
ejpam-5857	210	50	ψi(0)∨ψi(4))∧	ψi(0)∨ψi(4))∧	NOUN
ejpam-5857	210	51	0.5	0.5	NUM
ejpam-5857	210	52	=	=	SYM
ejpam-5857	210	53	(	(	PUNCT
ejpam-5857	210	54	ψi(4	ψi(4	PROPN
ejpam-5857	210	55	·	·	PUNCT
ejpam-5857	210	56	4)∨ψi(4))∧	4)∨ψi(4))∧	PROPN
ejpam-5857	210	57	0.5	0.5	NUM
ejpam-5857	210	58	=	=	SYM
ejpam-5857	210	59	ψi(4	ψi(4	NOUN
ejpam-5857	210	60	·	·	PUNCT
ejpam-5857	210	61	(	(	PUNCT
ejpam-5857	210	62	4	4	NUM
ejpam-5857	210	63	·	·	SYM
ejpam-5857	210	64	3))∨ψi(4))∧0.5	3))∨ψi(4))∧0.5	NUM
ejpam-5857	210	65	and	and	CCONJ
ejpam-5857	210	66	ψf	ψf	X
ejpam-5857	210	67	(	(	PUNCT
ejpam-5857	210	68	0	0	NUM
ejpam-5857	210	69	·	·	SYM
ejpam-5857	210	70	5	5	NUM
ejpam-5857	210	71	)	)	PUNCT
ejpam-5857	210	72	=	=	PRON
ejpam-5857	210	73	ψf	ψf	X
ejpam-5857	210	74	(	(	PUNCT
ejpam-5857	210	75	5	5	NUM
ejpam-5857	210	76	)	)	PUNCT
ejpam-5857	210	77	=	=	PUNCT
ejpam-5857	210	78	0.3	0.3	NUM
ejpam-5857	210	79	≱	≱	PROPN
ejpam-5857	210	80	0.5	0.5	NUM
ejpam-5857	210	81	=	=	SYM
ejpam-5857	210	82	0.3∨0.5	0.3∨0.5	SYM
ejpam-5857	211	1	=	=	SYM
ejpam-5857	211	2	(	(	PUNCT
ejpam-5857	211	3	0.3∧0.3)∨0.5	0.3∧0.3)∨0.5	NUM
ejpam-5857	211	4	=	=	SYM
ejpam-5857	211	5	(	(	PUNCT
ejpam-5857	211	6	ψf	ψf	X
ejpam-5857	211	7	(	(	PUNCT
ejpam-5857	211	8	0	0	NUM
ejpam-5857	211	9	)	)	PUNCT
ejpam-5857	211	10	∧	∧	NOUN
ejpam-5857	211	11	ψf	ψf	X
ejpam-5857	211	12	(	(	PUNCT
ejpam-5857	211	13	5	5	NUM
ejpam-5857	211	14	)	)	PUNCT
ejpam-5857	211	15	)	)	PUNCT
ejpam-5857	211	16	∨	∨	NOUN
ejpam-5857	211	17	0.5	0.5	NUM
ejpam-5857	211	18	=	=	SYM
ejpam-5857	211	19	(	(	PUNCT
ejpam-5857	211	20	ψf	ψf	X
ejpam-5857	211	21	(	(	PUNCT
ejpam-5857	211	22	0	0	NUM
ejpam-5857	211	23	·	·	SYM
ejpam-5857	211	24	0	0	X
ejpam-5857	211	25	)	)	PUNCT
ejpam-5857	211	26	∧	∧	NOUN
ejpam-5857	211	27	ψf	ψf	X
ejpam-5857	211	28	(	(	PUNCT
ejpam-5857	211	29	5	5	NUM
ejpam-5857	211	30	)	)	PUNCT
ejpam-5857	211	31	)	)	PUNCT
ejpam-5857	211	32	∨	∨	NOUN
ejpam-5857	211	33	0.5	0.5	NUM
ejpam-5857	211	34	=	=	SYM
ejpam-5857	211	35	ψf	ψf	X
ejpam-5857	211	36	(	(	PUNCT
ejpam-5857	211	37	0	0	NUM
ejpam-5857	211	38	·	·	PUNCT
ejpam-5857	211	39	(	(	PUNCT
ejpam-5857	211	40	5	5	NUM
ejpam-5857	211	41	·	·	SYM
ejpam-5857	211	42	5	5	NUM
ejpam-5857	211	43	)	)	PUNCT
ejpam-5857	211	44	)	)	PUNCT
ejpam-5857	211	45	∧	∧	NOUN
ejpam-5857	211	46	ψf	ψf	X
ejpam-5857	211	47	(	(	PUNCT
ejpam-5857	211	48	5	5	NUM
ejpam-5857	211	49	)	)	PUNCT
ejpam-5857	211	50	)	)	PUNCT
ejpam-5857	211	51	∨	∨	NUM
ejpam-5857	211	52	0.5	0.5	NUM
ejpam-5857	211	53	.	.	PUNCT
ejpam-5857	212	1	hence	hence	ADV
ejpam-5857	212	2	,	,	PUNCT
ejpam-5857	212	3	ψ	ψ	X
ejpam-5857	212	4	is	be	AUX
ejpam-5857	212	5	not	not	PART
ejpam-5857	212	6	an	an	DET
ejpam-5857	212	7	intuitionistic	intuitionistic	ADJ
ejpam-5857	212	8	neutrosophic	neutrosophic	ADJ
ejpam-5857	212	9	iup	iup	NOUN
ejpam-5857	212	10	-	-	PUNCT
ejpam-5857	212	11	ideal	ideal	NOUN
ejpam-5857	212	12	of	of	ADP
ejpam-5857	212	13	x.	x.	PROPN
ejpam-5857	212	14	example	example	NOUN
ejpam-5857	212	15	8	8	NUM
ejpam-5857	212	16	.	.	PUNCT
ejpam-5857	213	1	let	let	VERB
ejpam-5857	213	2	x	x	PUNCT
ejpam-5857	213	3	=	=	PUNCT
ejpam-5857	213	4	{	{	PUNCT
ejpam-5857	213	5	0	0	NUM
ejpam-5857	213	6	,	,	PUNCT
ejpam-5857	213	7	1	1	NUM
ejpam-5857	213	8	,	,	PUNCT
ejpam-5857	213	9	2	2	NUM
ejpam-5857	213	10	,	,	PUNCT
ejpam-5857	213	11	3	3	NUM
ejpam-5857	213	12	,	,	PUNCT
ejpam-5857	213	13	4	4	NUM
ejpam-5857	213	14	,	,	PUNCT
ejpam-5857	213	15	5	5	NUM
ejpam-5857	213	16	}	}	PUNCT
ejpam-5857	213	17	with	with	ADP
ejpam-5857	213	18	the	the	DET
ejpam-5857	213	19	following	follow	VERB
ejpam-5857	213	20	cayley	cayley	ADJ
ejpam-5857	213	21	table	table	NOUN
ejpam-5857	213	22	:	:	PUNCT
ejpam-5857	213	23	·	·	PUNCT
ejpam-5857	213	24	0	0	NUM
ejpam-5857	213	25	1	1	NUM
ejpam-5857	213	26	2	2	NUM
ejpam-5857	213	27	3	3	NUM
ejpam-5857	213	28	4	4	NUM
ejpam-5857	213	29	5	5	NUM
ejpam-5857	213	30	0	0	NUM
ejpam-5857	213	31	0	0	NUM
ejpam-5857	213	32	1	1	NUM
ejpam-5857	213	33	2	2	NUM
ejpam-5857	213	34	3	3	NUM
ejpam-5857	213	35	4	4	NUM
ejpam-5857	213	36	5	5	NUM
ejpam-5857	213	37	1	1	NUM
ejpam-5857	213	38	2	2	NUM
ejpam-5857	213	39	0	0	NUM
ejpam-5857	213	40	1	1	NUM
ejpam-5857	213	41	4	4	NUM
ejpam-5857	213	42	5	5	NUM
ejpam-5857	213	43	3	3	NUM
ejpam-5857	213	44	2	2	NUM
ejpam-5857	213	45	1	1	NUM
ejpam-5857	213	46	2	2	NUM
ejpam-5857	213	47	0	0	NUM
ejpam-5857	213	48	5	5	NUM
ejpam-5857	213	49	3	3	NUM
ejpam-5857	213	50	4	4	NUM
ejpam-5857	213	51	3	3	NUM
ejpam-5857	213	52	3	3	NUM
ejpam-5857	213	53	5	5	NUM
ejpam-5857	213	54	4	4	NUM
ejpam-5857	213	55	0	0	NUM
ejpam-5857	213	56	2	2	NUM
ejpam-5857	213	57	1	1	NUM
ejpam-5857	213	58	4	4	NUM
ejpam-5857	213	59	5	5	NUM
ejpam-5857	213	60	4	4	NUM
ejpam-5857	213	61	3	3	NUM
ejpam-5857	213	62	1	1	NUM
ejpam-5857	213	63	0	0	NUM
ejpam-5857	213	64	2	2	NUM
ejpam-5857	213	65	5	5	NUM
ejpam-5857	213	66	4	4	NUM
ejpam-5857	213	67	3	3	NUM
ejpam-5857	213	68	5	5	NUM
ejpam-5857	213	69	2	2	NUM
ejpam-5857	213	70	1	1	NUM
ejpam-5857	213	71	0	0	NUM
ejpam-5857	213	72	then	then	ADV
ejpam-5857	213	73	x	x	PUNCT
ejpam-5857	213	74	is	be	AUX
ejpam-5857	213	75	an	an	DET
ejpam-5857	213	76	iup	iup	NOUN
ejpam-5857	213	77	-	-	PUNCT
ejpam-5857	213	78	algebra	algebra	NOUN
ejpam-5857	213	79	.	.	PUNCT
ejpam-5857	214	1	we	we	PRON
ejpam-5857	214	2	define	define	VERB
ejpam-5857	214	3	an	an	DET
ejpam-5857	214	4	ins	in	NOUN
ejpam-5857	214	5	ψ	ψ	X
ejpam-5857	214	6	on	on	ADP
ejpam-5857	214	7	x	x	PUNCT
ejpam-5857	214	8	as	as	SCONJ
ejpam-5857	214	9	follows	follow	VERB
ejpam-5857	214	10	:	:	PUNCT
ejpam-5857	214	11	ψt	ψt	NOUN
ejpam-5857	214	12	=	=	PUNCT
ejpam-5857	214	13	(	(	PUNCT
ejpam-5857	214	14	0	0	NUM
ejpam-5857	214	15	0.5	0.5	NUM
ejpam-5857	214	16	1	1	NUM
ejpam-5857	214	17	0.5	0.5	NUM
ejpam-5857	214	18	2	2	NUM
ejpam-5857	214	19	0.5	0.5	NUM
ejpam-5857	214	20	3	3	NUM
ejpam-5857	214	21	0.5	0.5	NUM
ejpam-5857	214	22	4	4	NUM
ejpam-5857	214	23	0.5	0.5	NUM
ejpam-5857	214	24	5	5	NUM
ejpam-5857	214	25	0.5	0.5	NUM
ejpam-5857	214	26	)	)	PUNCT
ejpam-5857	214	27	ψi	ψi	ADP
ejpam-5857	214	28	=	=	PUNCT
ejpam-5857	214	29	(	(	PUNCT
ejpam-5857	214	30	0	0	NUM
ejpam-5857	214	31	0	0	NUM
ejpam-5857	214	32	1	1	NUM
ejpam-5857	214	33	0.21	0.21	NUM
ejpam-5857	214	34	2	2	NUM
ejpam-5857	214	35	0.21	0.21	NUM
ejpam-5857	214	36	3	3	NUM
ejpam-5857	214	37	0.4	0.4	NUM
ejpam-5857	214	38	4	4	NUM
ejpam-5857	214	39	0.4	0.4	NUM
ejpam-5857	214	40	5	5	NUM
ejpam-5857	214	41	0.4	0.4	NUM
ejpam-5857	214	42	)	)	PUNCT
ejpam-5857	214	43	ψf	ψf	X
ejpam-5857	215	1	=	=	PUNCT
ejpam-5857	215	2	(	(	PUNCT
ejpam-5857	215	3	0	0	NUM
ejpam-5857	215	4	1	1	NUM
ejpam-5857	215	5	1	1	NUM
ejpam-5857	215	6	0.8	0.8	NUM
ejpam-5857	215	7	2	2	NUM
ejpam-5857	215	8	0.8	0.8	NUM
ejpam-5857	215	9	3	3	NUM
ejpam-5857	215	10	0.55	0.55	NUM
ejpam-5857	215	11	4	4	NUM
ejpam-5857	215	12	0.55	0.55	NUM
ejpam-5857	215	13	5	5	NUM
ejpam-5857	215	14	0.55	0.55	NUM
ejpam-5857	215	15	)	)	PUNCT
ejpam-5857	216	1	then	then	ADV
ejpam-5857	216	2	ψ	ψ	X
ejpam-5857	216	3	is	be	AUX
ejpam-5857	216	4	an	an	DET
ejpam-5857	216	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	216	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	216	7	iup	iup	NOUN
ejpam-5857	216	8	-	-	PUNCT
ejpam-5857	216	9	ideal	ideal	NOUN
ejpam-5857	216	10	of	of	ADP
ejpam-5857	216	11	x.	x.	NOUN
ejpam-5857	216	12	since	since	SCONJ
ejpam-5857	216	13	ψi(3	ψi(3	PROPN
ejpam-5857	216	14	·	·	SYM
ejpam-5857	216	15	1	1	X
ejpam-5857	216	16	)	)	PUNCT
ejpam-5857	216	17	=	=	SYM
ejpam-5857	216	18	ψi(5	ψi(5	PROPN
ejpam-5857	216	19	)	)	PUNCT
ejpam-5857	216	20	=	=	NOUN
ejpam-5857	216	21	0.4	0.4	NUM
ejpam-5857	216	22	≰	≰	PROPN
ejpam-5857	216	23	0.21	0.21	NUM
ejpam-5857	216	24	=	=	SYM
ejpam-5857	216	25	ψi(1	ψi(1	PROPN
ejpam-5857	216	26	)	)	PUNCT
ejpam-5857	216	27	and	and	CCONJ
ejpam-5857	216	28	ψf	ψf	X
ejpam-5857	216	29	(	(	PUNCT
ejpam-5857	216	30	5·0	5·0	NUM
ejpam-5857	216	31	)	)	PUNCT
ejpam-5857	217	1	=	=	PRON
ejpam-5857	217	2	ψf	ψf	X
ejpam-5857	217	3	(	(	PUNCT
ejpam-5857	217	4	4	4	NUM
ejpam-5857	217	5	)	)	PUNCT
ejpam-5857	217	6	=	=	NUM
ejpam-5857	218	1	0.55	0.55	NUM
ejpam-5857	218	2	≱	≱	PROPN
ejpam-5857	218	3	0.1	0.1	NUM
ejpam-5857	218	4	=	=	SYM
ejpam-5857	218	5	ψf	ψf	X
ejpam-5857	218	6	(	(	PUNCT
ejpam-5857	218	7	0	0	NUM
ejpam-5857	218	8	)	)	PUNCT
ejpam-5857	218	9	.	.	PUNCT
ejpam-5857	219	1	hence	hence	ADV
ejpam-5857	219	2	,	,	PUNCT
ejpam-5857	219	3	ψ	ψ	X
ejpam-5857	219	4	is	be	AUX
ejpam-5857	219	5	not	not	PART
ejpam-5857	219	6	an	an	DET
ejpam-5857	219	7	intuitionistic	intuitionistic	ADJ
ejpam-5857	219	8	neutrosophic	neutrosophic	ADJ
ejpam-5857	219	9	strong	strong	ADJ
ejpam-5857	219	10	iup	iup	NOUN
ejpam-5857	219	11	-	-	PUNCT
ejpam-5857	219	12	ideal	ideal	NOUN
ejpam-5857	219	13	of	of	ADP
ejpam-5857	219	14	x.	x.	PROPN
ejpam-5857	219	15	k.	k.	PROPN
ejpam-5857	219	16	suayngam	suayngam	PROPN
ejpam-5857	219	17	,	,	PUNCT
ejpam-5857	219	18	p.	p.	NOUN
ejpam-5857	219	19	julatha	julatha	PROPN
ejpam-5857	219	20	,	,	PUNCT
ejpam-5857	219	21	w.	w.	PROPN
ejpam-5857	219	22	nakkhasen	nakkhasen	PROPN
ejpam-5857	219	23	,	,	PUNCT
ejpam-5857	219	24	a.	a.	NOUN
ejpam-5857	219	25	iampan	iampan	PROPN
ejpam-5857	219	26	/	/	SYM
ejpam-5857	219	27	eur	eur	PROPN
ejpam-5857	219	28	.	.	PUNCT
ejpam-5857	220	1	j.	j.	PROPN
ejpam-5857	220	2	pure	pure	PROPN
ejpam-5857	220	3	appl	appl	PROPN
ejpam-5857	220	4	.	.	PROPN
ejpam-5857	220	5	math	math	PROPN
ejpam-5857	220	6	,	,	PUNCT
ejpam-5857	220	7	18	18	NUM
ejpam-5857	220	8	(	(	PUNCT
ejpam-5857	220	9	2	2	NUM
ejpam-5857	220	10	)	)	PUNCT
ejpam-5857	220	11	(	(	PUNCT
ejpam-5857	220	12	2025	2025	NUM
ejpam-5857	220	13	)	)	PUNCT
ejpam-5857	220	14	,	,	PUNCT
ejpam-5857	220	15	5857	5857	NUM
ejpam-5857	220	16	11	11	NUM
ejpam-5857	220	17	of	of	ADP
ejpam-5857	220	18	30	30	NUM
ejpam-5857	220	19	theorem	theorem	NOUN
ejpam-5857	220	20	2	2	NUM
ejpam-5857	220	21	.	.	PUNCT
ejpam-5857	221	1	every	every	DET
ejpam-5857	221	2	intuitionistic	intuitionistic	ADJ
ejpam-5857	221	3	neutrosophic	neutrosophic	ADJ
ejpam-5857	221	4	iup	iup	NOUN
ejpam-5857	221	5	-	-	PUNCT
ejpam-5857	221	6	ideal	ideal	NOUN
ejpam-5857	221	7	of	of	ADP
ejpam-5857	221	8	x	x	PUNCT
ejpam-5857	221	9	is	be	AUX
ejpam-5857	221	10	an	an	DET
ejpam-5857	221	11	intuitionistic	intuitionistic	ADJ
ejpam-5857	221	12	neutrosophic	neutrosophic	ADJ
ejpam-5857	221	13	iup	iup	NOUN
ejpam-5857	221	14	-	-	PUNCT
ejpam-5857	221	15	filter	filter	NOUN
ejpam-5857	221	16	of	of	ADP
ejpam-5857	221	17	x.	x.	NOUN
ejpam-5857	221	18	proof	proof	PROPN
ejpam-5857	221	19	.	.	PUNCT
ejpam-5857	222	1	assume	assume	VERB
ejpam-5857	222	2	that	that	SCONJ
ejpam-5857	222	3	ψ	ψ	NOUN
ejpam-5857	222	4	is	be	AUX
ejpam-5857	222	5	an	an	DET
ejpam-5857	222	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	222	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	222	8	iup	iup	NOUN
ejpam-5857	222	9	-	-	PUNCT
ejpam-5857	222	10	ideal	ideal	NOUN
ejpam-5857	222	11	of	of	ADP
ejpam-5857	222	12	x.	x.	NOUN
ejpam-5857	222	13	by	by	ADP
ejpam-5857	222	14	assumption	assumption	NOUN
ejpam-5857	222	15	,	,	PUNCT
ejpam-5857	222	16	it	it	PRON
ejpam-5857	222	17	satisfies	satisfy	VERB
ejpam-5857	222	18	the	the	DET
ejpam-5857	222	19	conditions	condition	NOUN
ejpam-5857	222	20	(	(	PUNCT
ejpam-5857	222	21	3.8	3.8	NUM
ejpam-5857	222	22	)	)	PUNCT
ejpam-5857	222	23	,	,	PUNCT
ejpam-5857	222	24	(	(	PUNCT
ejpam-5857	222	25	3.9	3.9	NUM
ejpam-5857	222	26	)	)	PUNCT
ejpam-5857	222	27	and	and	CCONJ
ejpam-5857	222	28	(	(	PUNCT
ejpam-5857	222	29	3.10	3.10	NUM
ejpam-5857	222	30	)	)	PUNCT
ejpam-5857	222	31	.	.	PUNCT
ejpam-5857	223	1	let	let	VERB
ejpam-5857	223	2	x	x	PRON
ejpam-5857	223	3	,	,	PUNCT
ejpam-5857	223	4	y	y	PROPN
ejpam-5857	223	5	∈	∈	PROPN
ejpam-5857	223	6	x.	x.	NOUN
ejpam-5857	224	1	then	then	ADV
ejpam-5857	224	2	ψt	ψt	VERB
ejpam-5857	224	3	(	(	PUNCT
ejpam-5857	224	4	y	y	NOUN
ejpam-5857	224	5	)	)	PUNCT
ejpam-5857	224	6	=	=	PRON
ejpam-5857	225	1	ψt	ψt	NUM
ejpam-5857	225	2	(	(	PUNCT
ejpam-5857	225	3	0	0	NUM
ejpam-5857	225	4	·	·	PUNCT
ejpam-5857	225	5	y	y	X
ejpam-5857	225	6	)	)	PUNCT
ejpam-5857	225	7	(	(	PUNCT
ejpam-5857	225	8	by	by	ADP
ejpam-5857	225	9	(	(	PUNCT
ejpam-5857	225	10	iup-1	iup-1	NOUN
ejpam-5857	225	11	)	)	PUNCT
ejpam-5857	225	12	)	)	PUNCT
ejpam-5857	225	13	≥	≥	NOUN
ejpam-5857	225	14	(	(	PUNCT
ejpam-5857	225	15	ψt	ψt	VERB
ejpam-5857	225	16	(	(	PUNCT
ejpam-5857	225	17	0	0	NUM
ejpam-5857	225	18	·	·	PUNCT
ejpam-5857	225	19	(	(	PUNCT
ejpam-5857	225	20	x	x	X
ejpam-5857	225	21	·	·	PUNCT
ejpam-5857	225	22	y	y	NOUN
ejpam-5857	225	23	)	)	PUNCT
ejpam-5857	225	24	)	)	PUNCT
ejpam-5857	226	1	∧	∧	NOUN
ejpam-5857	226	2	ψt	ψt	NOUN
ejpam-5857	226	3	(	(	PUNCT
ejpam-5857	226	4	x	x	NOUN
ejpam-5857	226	5	)	)	PUNCT
ejpam-5857	226	6	)	)	PUNCT
ejpam-5857	227	1	∨	∨	NUM
ejpam-5857	227	2	0.5	0.5	NUM
ejpam-5857	227	3	(	(	PUNCT
ejpam-5857	227	4	by	by	ADP
ejpam-5857	227	5	(	(	PUNCT
ejpam-5857	227	6	3.11	3.11	NUM
ejpam-5857	227	7	)	)	PUNCT
ejpam-5857	227	8	)	)	PUNCT
ejpam-5857	228	1	=	=	PUNCT
ejpam-5857	228	2	(	(	PUNCT
ejpam-5857	228	3	ψt	ψt	NOUN
ejpam-5857	228	4	(	(	PUNCT
ejpam-5857	228	5	x	x	PROPN
ejpam-5857	228	6	·	·	PUNCT
ejpam-5857	228	7	y	y	X
ejpam-5857	228	8	)	)	PUNCT
ejpam-5857	228	9	∧	∧	NOUN
ejpam-5857	228	10	ψt	ψt	NOUN
ejpam-5857	228	11	(	(	PUNCT
ejpam-5857	228	12	x	x	NOUN
ejpam-5857	228	13	)	)	PUNCT
ejpam-5857	228	14	)	)	PUNCT
ejpam-5857	228	15	∨	∨	NUM
ejpam-5857	228	16	0.5	0.5	NUM
ejpam-5857	228	17	,	,	PUNCT
ejpam-5857	228	18	(	(	PUNCT
ejpam-5857	228	19	by	by	ADP
ejpam-5857	228	20	(	(	PUNCT
ejpam-5857	228	21	iup-1	iup-1	NOUN
ejpam-5857	228	22	)	)	PUNCT
ejpam-5857	228	23	)	)	PUNCT
ejpam-5857	228	24	ψi(y	ψi(y	PUNCT
ejpam-5857	228	25	)	)	PUNCT
ejpam-5857	229	1	=	=	SYM
ejpam-5857	229	2	ψi(0	ψi(0	PROPN
ejpam-5857	229	3	·	·	PUNCT
ejpam-5857	229	4	y	y	X
ejpam-5857	229	5	)	)	PUNCT
ejpam-5857	229	6	(	(	PUNCT
ejpam-5857	229	7	by	by	ADP
ejpam-5857	229	8	(	(	PUNCT
ejpam-5857	229	9	iup-1	iup-1	NOUN
ejpam-5857	229	10	)	)	PUNCT
ejpam-5857	229	11	)	)	PUNCT
ejpam-5857	229	12	≤	≤	NOUN
ejpam-5857	229	13	(	(	PUNCT
ejpam-5857	229	14	ψi(0	ψi(0	PROPN
ejpam-5857	229	15	·	·	PUNCT
ejpam-5857	229	16	(	(	PUNCT
ejpam-5857	229	17	x	x	X
ejpam-5857	229	18	·	·	PUNCT
ejpam-5857	229	19	y	y	NOUN
ejpam-5857	229	20	)	)	PUNCT
ejpam-5857	229	21	)	)	PUNCT
ejpam-5857	229	22	∨	∨	NUM
ejpam-5857	229	23	ψi(x	ψi(x	NUM
ejpam-5857	229	24	)	)	PUNCT
ejpam-5857	229	25	)	)	PUNCT
ejpam-5857	230	1	∧	∧	NOUN
ejpam-5857	230	2	0.5	0.5	NUM
ejpam-5857	230	3	(	(	PUNCT
ejpam-5857	230	4	by	by	ADP
ejpam-5857	230	5	(	(	PUNCT
ejpam-5857	230	6	3.12	3.12	NUM
ejpam-5857	230	7	)	)	PUNCT
ejpam-5857	230	8	)	)	PUNCT
ejpam-5857	230	9	=	=	SYM
ejpam-5857	230	10	(	(	PUNCT
ejpam-5857	230	11	ψi(x	ψi(x	X
ejpam-5857	230	12	·	·	PUNCT
ejpam-5857	230	13	y	y	X
ejpam-5857	230	14	)	)	PUNCT
ejpam-5857	230	15	∨	∨	NUM
ejpam-5857	230	16	ψi(x	ψi(x	NUM
ejpam-5857	230	17	)	)	PUNCT
ejpam-5857	230	18	)	)	PUNCT
ejpam-5857	231	1	∧	∧	NOUN
ejpam-5857	231	2	0.5	0.5	NUM
ejpam-5857	231	3	,	,	PUNCT
ejpam-5857	231	4	(	(	PUNCT
ejpam-5857	231	5	by	by	ADP
ejpam-5857	231	6	(	(	PUNCT
ejpam-5857	231	7	iup-1	iup-1	NOUN
ejpam-5857	231	8	)	)	PUNCT
ejpam-5857	231	9	)	)	PUNCT
ejpam-5857	231	10	ψf	ψf	X
ejpam-5857	232	1	(	(	PUNCT
ejpam-5857	232	2	y	y	NOUN
ejpam-5857	232	3	)	)	PUNCT
ejpam-5857	232	4	=	=	PRON
ejpam-5857	232	5	ψf	ψf	X
ejpam-5857	232	6	(	(	PUNCT
ejpam-5857	232	7	0	0	NUM
ejpam-5857	232	8	·	·	SYM
ejpam-5857	232	9	y	y	X
ejpam-5857	232	10	)	)	PUNCT
ejpam-5857	232	11	(	(	PUNCT
ejpam-5857	232	12	by	by	ADP
ejpam-5857	232	13	(	(	PUNCT
ejpam-5857	232	14	iup-1	iup-1	NOUN
ejpam-5857	232	15	)	)	PUNCT
ejpam-5857	232	16	)	)	PUNCT
ejpam-5857	232	17	≥	≥	NOUN
ejpam-5857	232	18	(	(	PUNCT
ejpam-5857	232	19	ψf	ψf	X
ejpam-5857	232	20	(	(	PUNCT
ejpam-5857	232	21	0	0	NUM
ejpam-5857	232	22	·	·	PUNCT
ejpam-5857	232	23	(	(	PUNCT
ejpam-5857	232	24	x	x	X
ejpam-5857	232	25	·	·	PUNCT
ejpam-5857	232	26	y	y	NOUN
ejpam-5857	232	27	)	)	PUNCT
ejpam-5857	232	28	)	)	PUNCT
ejpam-5857	233	1	∧	∧	NOUN
ejpam-5857	233	2	ψf	ψf	X
ejpam-5857	233	3	(	(	PUNCT
ejpam-5857	233	4	x	x	NOUN
ejpam-5857	233	5	)	)	PUNCT
ejpam-5857	233	6	)	)	PUNCT
ejpam-5857	234	1	∨	∨	NUM
ejpam-5857	234	2	0.5	0.5	NUM
ejpam-5857	234	3	(	(	PUNCT
ejpam-5857	234	4	by	by	ADP
ejpam-5857	234	5	(	(	PUNCT
ejpam-5857	234	6	3.13	3.13	NUM
ejpam-5857	234	7	)	)	PUNCT
ejpam-5857	234	8	)	)	PUNCT
ejpam-5857	235	1	=	=	PUNCT
ejpam-5857	235	2	(	(	PUNCT
ejpam-5857	235	3	ψf	ψf	X
ejpam-5857	235	4	(	(	PUNCT
ejpam-5857	235	5	x	x	PROPN
ejpam-5857	235	6	·	·	PUNCT
ejpam-5857	235	7	y	y	X
ejpam-5857	235	8	)	)	PUNCT
ejpam-5857	235	9	∧	∧	NOUN
ejpam-5857	235	10	ψf	ψf	X
ejpam-5857	235	11	(	(	PUNCT
ejpam-5857	235	12	x	x	NOUN
ejpam-5857	235	13	)	)	PUNCT
ejpam-5857	235	14	)	)	PUNCT
ejpam-5857	235	15	∨	∨	NUM
ejpam-5857	235	16	0.5	0.5	NUM
ejpam-5857	235	17	.	.	PUNCT
ejpam-5857	236	1	(	(	PUNCT
ejpam-5857	236	2	by	by	ADP
ejpam-5857	236	3	(	(	PUNCT
ejpam-5857	236	4	iup-1	iup-1	NOUN
ejpam-5857	236	5	)	)	PUNCT
ejpam-5857	236	6	)	)	PUNCT
ejpam-5857	236	7	hence	hence	ADV
ejpam-5857	236	8	,	,	PUNCT
ejpam-5857	236	9	ψ	ψ	X
ejpam-5857	236	10	is	be	AUX
ejpam-5857	236	11	an	an	DET
ejpam-5857	236	12	intuitionistic	intuitionistic	ADJ
ejpam-5857	236	13	neutrosophic	neutrosophic	ADJ
ejpam-5857	236	14	iup	iup	NOUN
ejpam-5857	236	15	-	-	PUNCT
ejpam-5857	236	16	filter	filter	NOUN
ejpam-5857	236	17	of	of	ADP
ejpam-5857	236	18	x.	x.	NOUN
ejpam-5857	236	19	example	example	NOUN
ejpam-5857	237	1	9	9	NUM
ejpam-5857	237	2	.	.	PUNCT
ejpam-5857	238	1	let	let	VERB
ejpam-5857	238	2	x	x	PUNCT
ejpam-5857	238	3	=	=	PUNCT
ejpam-5857	238	4	{	{	PUNCT
ejpam-5857	238	5	0	0	NUM
ejpam-5857	238	6	,	,	PUNCT
ejpam-5857	238	7	1	1	NUM
ejpam-5857	238	8	,	,	PUNCT
ejpam-5857	238	9	2	2	NUM
ejpam-5857	238	10	,	,	PUNCT
ejpam-5857	238	11	3	3	NUM
ejpam-5857	238	12	,	,	PUNCT
ejpam-5857	238	13	4	4	NUM
ejpam-5857	238	14	,	,	PUNCT
ejpam-5857	238	15	5	5	NUM
ejpam-5857	238	16	}	}	PUNCT
ejpam-5857	238	17	with	with	ADP
ejpam-5857	238	18	the	the	DET
ejpam-5857	238	19	following	follow	VERB
ejpam-5857	238	20	cayley	cayley	ADJ
ejpam-5857	238	21	table	table	NOUN
ejpam-5857	238	22	:	:	PUNCT
ejpam-5857	238	23	·	·	PUNCT
ejpam-5857	238	24	0	0	NUM
ejpam-5857	238	25	1	1	NUM
ejpam-5857	238	26	2	2	NUM
ejpam-5857	238	27	3	3	NUM
ejpam-5857	238	28	4	4	NUM
ejpam-5857	238	29	5	5	NUM
ejpam-5857	238	30	0	0	NUM
ejpam-5857	238	31	0	0	NUM
ejpam-5857	238	32	1	1	NUM
ejpam-5857	238	33	2	2	NUM
ejpam-5857	238	34	3	3	NUM
ejpam-5857	238	35	4	4	NUM
ejpam-5857	238	36	5	5	NUM
ejpam-5857	238	37	1	1	NUM
ejpam-5857	238	38	1	1	NUM
ejpam-5857	238	39	0	0	NUM
ejpam-5857	238	40	5	5	NUM
ejpam-5857	238	41	4	4	NUM
ejpam-5857	238	42	3	3	NUM
ejpam-5857	238	43	2	2	NUM
ejpam-5857	238	44	2	2	NUM
ejpam-5857	238	45	2	2	NUM
ejpam-5857	238	46	4	4	NUM
ejpam-5857	238	47	0	0	NUM
ejpam-5857	238	48	5	5	NUM
ejpam-5857	238	49	1	1	NUM
ejpam-5857	238	50	3	3	NUM
ejpam-5857	238	51	3	3	NUM
ejpam-5857	238	52	3	3	NUM
ejpam-5857	238	53	5	5	NUM
ejpam-5857	238	54	4	4	NUM
ejpam-5857	238	55	0	0	NUM
ejpam-5857	238	56	2	2	NUM
ejpam-5857	238	57	1	1	NUM
ejpam-5857	238	58	4	4	NUM
ejpam-5857	238	59	5	5	NUM
ejpam-5857	238	60	3	3	NUM
ejpam-5857	238	61	1	1	NUM
ejpam-5857	238	62	2	2	NUM
ejpam-5857	238	63	0	0	NUM
ejpam-5857	238	64	4	4	NUM
ejpam-5857	238	65	5	5	NUM
ejpam-5857	238	66	4	4	NUM
ejpam-5857	238	67	2	2	NUM
ejpam-5857	238	68	3	3	NUM
ejpam-5857	238	69	1	1	NUM
ejpam-5857	238	70	5	5	NUM
ejpam-5857	238	71	0	0	NUM
ejpam-5857	238	72	then	then	ADV
ejpam-5857	238	73	x	x	PUNCT
ejpam-5857	238	74	is	be	AUX
ejpam-5857	238	75	an	an	DET
ejpam-5857	238	76	iup	iup	NOUN
ejpam-5857	238	77	-	-	PUNCT
ejpam-5857	238	78	algebra	algebra	NOUN
ejpam-5857	238	79	.	.	PUNCT
ejpam-5857	239	1	we	we	PRON
ejpam-5857	239	2	define	define	VERB
ejpam-5857	239	3	an	an	DET
ejpam-5857	239	4	ins	in	NOUN
ejpam-5857	239	5	ψ	ψ	X
ejpam-5857	239	6	on	on	ADP
ejpam-5857	239	7	x	x	PUNCT
ejpam-5857	239	8	as	as	SCONJ
ejpam-5857	239	9	follows	follow	VERB
ejpam-5857	239	10	:	:	PUNCT
ejpam-5857	239	11	ψt	ψt	NOUN
ejpam-5857	239	12	=	=	PUNCT
ejpam-5857	239	13	(	(	PUNCT
ejpam-5857	239	14	0	0	NUM
ejpam-5857	239	15	0.5	0.5	NUM
ejpam-5857	239	16	1	1	NUM
ejpam-5857	239	17	0.5	0.5	NUM
ejpam-5857	239	18	2	2	NUM
ejpam-5857	239	19	0.5	0.5	NUM
ejpam-5857	239	20	3	3	NUM
ejpam-5857	239	21	0.5	0.5	NUM
ejpam-5857	239	22	4	4	NUM
ejpam-5857	239	23	0.5	0.5	NUM
ejpam-5857	239	24	5	5	NUM
ejpam-5857	239	25	0.5	0.5	NUM
ejpam-5857	239	26	)	)	PUNCT
ejpam-5857	239	27	ψi	ψi	ADP
ejpam-5857	239	28	=	=	PUNCT
ejpam-5857	239	29	(	(	PUNCT
ejpam-5857	239	30	0	0	NUM
ejpam-5857	239	31	0.1	0.1	NUM
ejpam-5857	239	32	1	1	NUM
ejpam-5857	239	33	0.4	0.4	NUM
ejpam-5857	239	34	2	2	NUM
ejpam-5857	239	35	0.4	0.4	NUM
ejpam-5857	239	36	3	3	NUM
ejpam-5857	239	37	0.3	0.3	NUM
ejpam-5857	239	38	4	4	NUM
ejpam-5857	239	39	0.4	0.4	NUM
ejpam-5857	239	40	5	5	NUM
ejpam-5857	239	41	0.4	0.4	NUM
ejpam-5857	239	42	)	)	PUNCT
ejpam-5857	239	43	ψf	ψf	X
ejpam-5857	240	1	=	=	PUNCT
ejpam-5857	240	2	(	(	PUNCT
ejpam-5857	240	3	0	0	NUM
ejpam-5857	240	4	0.8	0.8	NUM
ejpam-5857	240	5	1	1	NUM
ejpam-5857	240	6	0.5	0.5	NUM
ejpam-5857	240	7	2	2	NUM
ejpam-5857	240	8	0.5	0.5	NUM
ejpam-5857	240	9	3	3	NUM
ejpam-5857	240	10	0.6	0.6	NUM
ejpam-5857	240	11	4	4	NUM
ejpam-5857	240	12	0.5	0.5	NUM
ejpam-5857	240	13	5	5	NUM
ejpam-5857	240	14	0.5	0.5	NUM
ejpam-5857	240	15	)	)	PUNCT
ejpam-5857	240	16	then	then	ADV
ejpam-5857	240	17	ψ	ψ	X
ejpam-5857	240	18	is	be	AUX
ejpam-5857	240	19	an	an	DET
ejpam-5857	240	20	intuitionistic	intuitionistic	ADJ
ejpam-5857	240	21	neutrosophic	neutrosophic	ADJ
ejpam-5857	240	22	iup	iup	NOUN
ejpam-5857	240	23	-	-	PUNCT
ejpam-5857	240	24	filter	filter	NOUN
ejpam-5857	240	25	of	of	ADP
ejpam-5857	240	26	x.	x.	NOUN
ejpam-5857	240	27	since	since	SCONJ
ejpam-5857	240	28	ψi(4	ψi(4	PROPN
ejpam-5857	240	29	·	·	PUNCT
ejpam-5857	240	30	5	5	X
ejpam-5857	240	31	)	)	PUNCT
ejpam-5857	240	32	=	=	SYM
ejpam-5857	240	33	ψi(4	ψi(4	NOUN
ejpam-5857	240	34	)	)	PUNCT
ejpam-5857	240	35	=	=	PUNCT
ejpam-5857	241	1	0.4	0.4	NUM
ejpam-5857	241	2	≰	≰	PROPN
ejpam-5857	241	3	0.3	0.3	NUM
ejpam-5857	241	4	=	=	SYM
ejpam-5857	241	5	(	(	PUNCT
ejpam-5857	241	6	0.3	0.3	NUM
ejpam-5857	241	7	∨	∨	NUM
ejpam-5857	241	8	0.3	0.3	NUM
ejpam-5857	241	9	)	)	PUNCT
ejpam-5857	241	10	∧	∧	NOUN
ejpam-5857	241	11	0.5	0.5	NUM
ejpam-5857	241	12	=	=	SYM
ejpam-5857	241	13	(	(	PUNCT
ejpam-5857	241	14	ψi(3	ψi(3	ADJ
ejpam-5857	241	15	)	)	PUNCT
ejpam-5857	241	16	∨	∨	NUM
ejpam-5857	241	17	ψt	ψt	NOUN
ejpam-5857	241	18	(	(	PUNCT
ejpam-5857	241	19	3	3	NUM
ejpam-5857	241	20	)	)	PUNCT
ejpam-5857	241	21	)	)	PUNCT
ejpam-5857	242	1	∧	∧	NOUN
ejpam-5857	242	2	0.5	0.5	NUM
ejpam-5857	242	3	=	=	SYM
ejpam-5857	242	4	(	(	PUNCT
ejpam-5857	242	5	ψi(4	ψi(4	PROPN
ejpam-5857	242	6	·	·	PUNCT
ejpam-5857	242	7	1	1	X
ejpam-5857	242	8	)	)	PUNCT
ejpam-5857	242	9	∨	∨	NUM
ejpam-5857	242	10	ψi(3	ψi(3	ADJ
ejpam-5857	242	11	)	)	PUNCT
ejpam-5857	242	12	)	)	PUNCT
ejpam-5857	243	1	∧	∧	NOUN
ejpam-5857	243	2	0.5	0.5	NUM
ejpam-5857	243	3	=	=	SYM
ejpam-5857	243	4	(	(	PUNCT
ejpam-5857	243	5	ψi(4	ψi(4	PROPN
ejpam-5857	243	6	·	·	PUNCT
ejpam-5857	243	7	(	(	PUNCT
ejpam-5857	243	8	3	3	NUM
ejpam-5857	243	9	·	·	SYM
ejpam-5857	243	10	5	5	NUM
ejpam-5857	243	11	)	)	PUNCT
ejpam-5857	243	12	)	)	PUNCT
ejpam-5857	244	1	∨	∨	NUM
ejpam-5857	244	2	ψi(3	ψi(3	ADJ
ejpam-5857	244	3	)	)	PUNCT
ejpam-5857	244	4	)	)	PUNCT
ejpam-5857	245	1	∧	∧	NOUN
ejpam-5857	245	2	0.5	0.5	NUM
ejpam-5857	245	3	and	and	CCONJ
ejpam-5857	245	4	ψf	ψf	X
ejpam-5857	245	5	(	(	PUNCT
ejpam-5857	245	6	4	4	NUM
ejpam-5857	245	7	·	·	SYM
ejpam-5857	245	8	5	5	NUM
ejpam-5857	245	9	)	)	PUNCT
ejpam-5857	245	10	=	=	PRON
ejpam-5857	245	11	ψf	ψf	X
ejpam-5857	245	12	(	(	PUNCT
ejpam-5857	245	13	4	4	NUM
ejpam-5857	245	14	)	)	PUNCT
ejpam-5857	245	15	=	=	SYM
ejpam-5857	245	16	0.5	0.5	NUM
ejpam-5857	245	17	≱	≱	PROPN
ejpam-5857	245	18	0.6	0.6	NUM
ejpam-5857	245	19	=	=	SYM
ejpam-5857	245	20	(	(	PUNCT
ejpam-5857	245	21	0.6	0.6	NUM
ejpam-5857	245	22	∧	∧	PROPN
ejpam-5857	245	23	0.6	0.6	NUM
ejpam-5857	245	24	)	)	PUNCT
ejpam-5857	245	25	∨	∨	NUM
ejpam-5857	245	26	0.5	0.5	NUM
ejpam-5857	245	27	=	=	SYM
ejpam-5857	245	28	(	(	PUNCT
ejpam-5857	245	29	ψf	ψf	X
ejpam-5857	245	30	(	(	PUNCT
ejpam-5857	245	31	3	3	X
ejpam-5857	245	32	)	)	PUNCT
ejpam-5857	245	33	∧	∧	NOUN
ejpam-5857	245	34	ψf	ψf	X
ejpam-5857	245	35	(	(	PUNCT
ejpam-5857	245	36	3	3	NUM
ejpam-5857	245	37	)	)	PUNCT
ejpam-5857	245	38	)	)	PUNCT
ejpam-5857	245	39	∨	∨	NOUN
ejpam-5857	245	40	0.5	0.5	NUM
ejpam-5857	245	41	=	=	SYM
ejpam-5857	245	42	(	(	PUNCT
ejpam-5857	245	43	ψf	ψf	X
ejpam-5857	245	44	(	(	PUNCT
ejpam-5857	245	45	4	4	NUM
ejpam-5857	245	46	·	·	SYM
ejpam-5857	245	47	1	1	X
ejpam-5857	245	48	)	)	PUNCT
ejpam-5857	245	49	∧	∧	NOUN
ejpam-5857	245	50	ψf	ψf	X
ejpam-5857	245	51	(	(	PUNCT
ejpam-5857	245	52	3	3	NUM
ejpam-5857	245	53	)	)	PUNCT
ejpam-5857	245	54	)	)	PUNCT
ejpam-5857	245	55	∨	∨	NOUN
ejpam-5857	245	56	0.5	0.5	NUM
ejpam-5857	245	57	=	=	SYM
ejpam-5857	245	58	(	(	PUNCT
ejpam-5857	245	59	ψf	ψf	X
ejpam-5857	245	60	(	(	PUNCT
ejpam-5857	245	61	4	4	NUM
ejpam-5857	245	62	·	·	PUNCT
ejpam-5857	245	63	(	(	PUNCT
ejpam-5857	245	64	3	3	NUM
ejpam-5857	245	65	·	·	SYM
ejpam-5857	245	66	5	5	NUM
ejpam-5857	245	67	)	)	PUNCT
ejpam-5857	245	68	)	)	PUNCT
ejpam-5857	246	1	∧	∧	NOUN
ejpam-5857	246	2	ψf	ψf	X
ejpam-5857	246	3	(	(	PUNCT
ejpam-5857	246	4	3	3	NUM
ejpam-5857	246	5	)	)	PUNCT
ejpam-5857	246	6	)	)	PUNCT
ejpam-5857	246	7	∨	∨	NUM
ejpam-5857	246	8	0.5	0.5	NUM
ejpam-5857	246	9	.	.	PUNCT
ejpam-5857	247	1	hence	hence	ADV
ejpam-5857	247	2	,	,	PUNCT
ejpam-5857	247	3	ψ	ψ	X
ejpam-5857	247	4	is	be	AUX
ejpam-5857	247	5	not	not	PART
ejpam-5857	247	6	an	an	DET
ejpam-5857	247	7	intuitionistic	intuitionistic	ADJ
ejpam-5857	247	8	neutrosophic	neutrosophic	ADJ
ejpam-5857	247	9	iup	iup	NOUN
ejpam-5857	247	10	-	-	PUNCT
ejpam-5857	247	11	ideal	ideal	NOUN
ejpam-5857	247	12	of	of	ADP
ejpam-5857	247	13	x.	x.	PROPN
ejpam-5857	247	14	k.	k.	PROPN
ejpam-5857	247	15	suayngam	suayngam	PROPN
ejpam-5857	247	16	,	,	PUNCT
ejpam-5857	247	17	p.	p.	NOUN
ejpam-5857	247	18	julatha	julatha	PROPN
ejpam-5857	247	19	,	,	PUNCT
ejpam-5857	247	20	w.	w.	PROPN
ejpam-5857	247	21	nakkhasen	nakkhasen	PROPN
ejpam-5857	247	22	,	,	PUNCT
ejpam-5857	247	23	a.	a.	NOUN
ejpam-5857	247	24	iampan	iampan	PROPN
ejpam-5857	247	25	/	/	SYM
ejpam-5857	247	26	eur	eur	PROPN
ejpam-5857	247	27	.	.	PUNCT
ejpam-5857	248	1	j.	j.	PROPN
ejpam-5857	248	2	pure	pure	PROPN
ejpam-5857	248	3	appl	appl	PROPN
ejpam-5857	248	4	.	.	PROPN
ejpam-5857	248	5	math	math	PROPN
ejpam-5857	248	6	,	,	PUNCT
ejpam-5857	248	7	18	18	NUM
ejpam-5857	248	8	(	(	PUNCT
ejpam-5857	248	9	2	2	NUM
ejpam-5857	248	10	)	)	PUNCT
ejpam-5857	248	11	(	(	PUNCT
ejpam-5857	248	12	2025	2025	NUM
ejpam-5857	248	13	)	)	PUNCT
ejpam-5857	248	14	,	,	PUNCT
ejpam-5857	248	15	5857	5857	NUM
ejpam-5857	248	16	12	12	NUM
ejpam-5857	248	17	of	of	ADP
ejpam-5857	248	18	30	30	NUM
ejpam-5857	248	19	theorem	theorem	NOUN
ejpam-5857	248	20	3	3	NUM
ejpam-5857	248	21	.	.	PUNCT
ejpam-5857	249	1	every	every	DET
ejpam-5857	249	2	intuitionistic	intuitionistic	ADJ
ejpam-5857	249	3	neutrosophic	neutrosophic	ADJ
ejpam-5857	249	4	iup	iup	NOUN
ejpam-5857	249	5	-	-	PUNCT
ejpam-5857	249	6	subalgebra	subalgebra	NOUN
ejpam-5857	249	7	of	of	ADP
ejpam-5857	249	8	x	x	PUNCT
ejpam-5857	249	9	is	be	AUX
ejpam-5857	249	10	an	an	DET
ejpam-5857	249	11	intuitionistic	intuitionistic	ADJ
ejpam-5857	249	12	neutrosophic	neutrosophic	ADJ
ejpam-5857	249	13	iup	iup	NOUN
ejpam-5857	249	14	-	-	PUNCT
ejpam-5857	249	15	filter	filter	NOUN
ejpam-5857	249	16	of	of	ADP
ejpam-5857	249	17	x.	x.	NOUN
ejpam-5857	249	18	proof	proof	PROPN
ejpam-5857	249	19	.	.	PUNCT
ejpam-5857	250	1	assume	assume	VERB
ejpam-5857	250	2	that	that	SCONJ
ejpam-5857	250	3	ψ	ψ	NOUN
ejpam-5857	250	4	is	be	AUX
ejpam-5857	250	5	an	an	DET
ejpam-5857	250	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	250	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	250	8	iup	iup	NOUN
ejpam-5857	250	9	-	-	PUNCT
ejpam-5857	250	10	subalgebra	subalgebra	NOUN
ejpam-5857	250	11	of	of	ADP
ejpam-5857	250	12	x.	x.	NOUN
ejpam-5857	250	13	by	by	ADP
ejpam-5857	250	14	lemma	lemma	PROPN
ejpam-5857	250	15	1	1	NUM
ejpam-5857	250	16	,	,	PUNCT
ejpam-5857	250	17	it	it	PRON
ejpam-5857	250	18	satisfies	satisfy	VERB
ejpam-5857	250	19	the	the	DET
ejpam-5857	250	20	conditions	condition	NOUN
ejpam-5857	250	21	(	(	PUNCT
ejpam-5857	250	22	3.8	3.8	NUM
ejpam-5857	250	23	)	)	PUNCT
ejpam-5857	250	24	,	,	PUNCT
ejpam-5857	250	25	(	(	PUNCT
ejpam-5857	250	26	3.9	3.9	NUM
ejpam-5857	250	27	)	)	PUNCT
ejpam-5857	250	28	and	and	CCONJ
ejpam-5857	250	29	(	(	PUNCT
ejpam-5857	250	30	3.10	3.10	NUM
ejpam-5857	250	31	)	)	PUNCT
ejpam-5857	250	32	.	.	PUNCT
ejpam-5857	251	1	let	let	VERB
ejpam-5857	251	2	x	x	PRON
ejpam-5857	251	3	,	,	PUNCT
ejpam-5857	251	4	y	y	PROPN
ejpam-5857	251	5	∈	∈	PROPN
ejpam-5857	251	6	x.	x.	NOUN
ejpam-5857	252	1	then	then	ADV
ejpam-5857	252	2	ψt	ψt	VERB
ejpam-5857	252	3	(	(	PUNCT
ejpam-5857	252	4	y	y	NOUN
ejpam-5857	252	5	)	)	PUNCT
ejpam-5857	252	6	=	=	PRON
ejpam-5857	253	1	ψt	ψt	NUM
ejpam-5857	253	2	(	(	PUNCT
ejpam-5857	253	3	0	0	NUM
ejpam-5857	253	4	·	·	PUNCT
ejpam-5857	253	5	y	y	X
ejpam-5857	253	6	)	)	PUNCT
ejpam-5857	253	7	(	(	PUNCT
ejpam-5857	253	8	by	by	ADP
ejpam-5857	253	9	(	(	PUNCT
ejpam-5857	253	10	iup-1	iup-1	NOUN
ejpam-5857	253	11	)	)	PUNCT
ejpam-5857	253	12	)	)	PUNCT
ejpam-5857	254	1	=	=	PRON
ejpam-5857	254	2	ψt	ψt	X
ejpam-5857	254	3	(	(	PUNCT
ejpam-5857	254	4	(	(	PUNCT
ejpam-5857	254	5	x	x	X
ejpam-5857	254	6	·	·	PUNCT
ejpam-5857	254	7	0	0	NUM
ejpam-5857	254	8	)	)	PUNCT
ejpam-5857	254	9	·	·	PUNCT
ejpam-5857	254	10	(	(	PUNCT
ejpam-5857	254	11	x	x	X
ejpam-5857	254	12	·	·	PUNCT
ejpam-5857	254	13	y	y	NOUN
ejpam-5857	254	14	)	)	PUNCT
ejpam-5857	254	15	)	)	PUNCT
ejpam-5857	254	16	(	(	PUNCT
ejpam-5857	254	17	by	by	ADP
ejpam-5857	254	18	(	(	PUNCT
ejpam-5857	254	19	iup-3	iup-3	NUM
ejpam-5857	254	20	)	)	PUNCT
ejpam-5857	254	21	)	)	PUNCT
ejpam-5857	254	22	≥	≥	NOUN
ejpam-5857	254	23	(	(	PUNCT
ejpam-5857	254	24	ψt	ψt	VERB
ejpam-5857	254	25	(	(	PUNCT
ejpam-5857	254	26	x	x	X
ejpam-5857	254	27	·	·	PUNCT
ejpam-5857	254	28	0	0	X
ejpam-5857	254	29	)	)	PUNCT
ejpam-5857	254	30	∧	∧	NOUN
ejpam-5857	254	31	ψt	ψt	NOUN
ejpam-5857	254	32	(	(	PUNCT
ejpam-5857	254	33	x	x	PROPN
ejpam-5857	254	34	·	·	PUNCT
ejpam-5857	254	35	y	y	NOUN
ejpam-5857	254	36	)	)	PUNCT
ejpam-5857	254	37	)	)	PUNCT
ejpam-5857	254	38	∨	∨	NUM
ejpam-5857	254	39	0.5	0.5	NUM
ejpam-5857	254	40	(	(	PUNCT
ejpam-5857	254	41	by	by	ADP
ejpam-5857	254	42	(	(	PUNCT
ejpam-5857	254	43	3.5	3.5	NUM
ejpam-5857	254	44	)	)	PUNCT
ejpam-5857	254	45	)	)	PUNCT
ejpam-5857	254	46	≥	≥	X
ejpam-5857	254	47	(	(	PUNCT
ejpam-5857	254	48	(	(	PUNCT
ejpam-5857	254	49	(	(	PUNCT
ejpam-5857	254	50	ψt	ψt	VERB
ejpam-5857	254	51	(	(	PUNCT
ejpam-5857	254	52	x	x	NOUN
ejpam-5857	254	53	)	)	PUNCT
ejpam-5857	254	54	∧	∧	NOUN
ejpam-5857	254	55	ψt	ψt	NUM
ejpam-5857	254	56	(	(	PUNCT
ejpam-5857	254	57	0	0	NUM
ejpam-5857	254	58	)	)	PUNCT
ejpam-5857	254	59	)	)	PUNCT
ejpam-5857	254	60	∨	∨	NUM
ejpam-5857	254	61	0.5	0.5	NUM
ejpam-5857	254	62	)	)	PUNCT
ejpam-5857	254	63	∧	∧	NOUN
ejpam-5857	254	64	ψt	ψt	NOUN
ejpam-5857	254	65	(	(	PUNCT
ejpam-5857	254	66	x	x	PROPN
ejpam-5857	254	67	·	·	PUNCT
ejpam-5857	254	68	y	y	NOUN
ejpam-5857	254	69	)	)	PUNCT
ejpam-5857	254	70	)	)	PUNCT
ejpam-5857	255	1	∨	∨	NUM
ejpam-5857	255	2	0.5	0.5	NUM
ejpam-5857	255	3	(	(	PUNCT
ejpam-5857	255	4	by	by	ADP
ejpam-5857	255	5	(	(	PUNCT
ejpam-5857	255	6	3.5	3.5	NUM
ejpam-5857	255	7	)	)	PUNCT
ejpam-5857	255	8	)	)	PUNCT
ejpam-5857	256	1	=	=	PUNCT
ejpam-5857	256	2	(	(	PUNCT
ejpam-5857	256	3	(	(	PUNCT
ejpam-5857	256	4	ψt	ψt	NOUN
ejpam-5857	256	5	(	(	PUNCT
ejpam-5857	256	6	x	x	NOUN
ejpam-5857	256	7	)	)	PUNCT
ejpam-5857	256	8	∨	∨	NUM
ejpam-5857	256	9	0.5	0.5	NUM
ejpam-5857	256	10	)	)	PUNCT
ejpam-5857	256	11	∧	∧	NOUN
ejpam-5857	256	12	ψt	ψt	NOUN
ejpam-5857	256	13	(	(	PUNCT
ejpam-5857	256	14	x	x	PROPN
ejpam-5857	256	15	·	·	PUNCT
ejpam-5857	256	16	y	y	NOUN
ejpam-5857	256	17	)	)	PUNCT
ejpam-5857	256	18	)	)	PUNCT
ejpam-5857	257	1	∨	∨	NUM
ejpam-5857	257	2	0.5	0.5	NUM
ejpam-5857	257	3	(	(	PUNCT
ejpam-5857	257	4	by	by	ADP
ejpam-5857	257	5	(	(	PUNCT
ejpam-5857	257	6	3.8	3.8	NUM
ejpam-5857	257	7	)	)	PUNCT
ejpam-5857	257	8	)	)	PUNCT
ejpam-5857	257	9	≥	≥	X
ejpam-5857	257	10	(	(	PUNCT
ejpam-5857	257	11	ψt	ψt	VERB
ejpam-5857	257	12	(	(	PUNCT
ejpam-5857	257	13	x	x	NOUN
ejpam-5857	257	14	)	)	PUNCT
ejpam-5857	257	15	∧	∧	NOUN
ejpam-5857	257	16	ψt	ψt	NUM
ejpam-5857	257	17	(	(	PUNCT
ejpam-5857	257	18	x	x	PROPN
ejpam-5857	257	19	·	·	PUNCT
ejpam-5857	257	20	y	y	NOUN
ejpam-5857	257	21	)	)	PUNCT
ejpam-5857	257	22	)	)	PUNCT
ejpam-5857	258	1	∨	∨	NUM
ejpam-5857	258	2	0.5	0.5	NUM
ejpam-5857	258	3	,	,	PUNCT
ejpam-5857	258	4	ψi(y	ψi(y	NUM
ejpam-5857	258	5	)	)	PUNCT
ejpam-5857	259	1	=	=	SYM
ejpam-5857	259	2	ψi(0	ψi(0	PROPN
ejpam-5857	259	3	·	·	PUNCT
ejpam-5857	259	4	y	y	X
ejpam-5857	259	5	)	)	PUNCT
ejpam-5857	259	6	(	(	PUNCT
ejpam-5857	259	7	by	by	ADP
ejpam-5857	259	8	(	(	PUNCT
ejpam-5857	259	9	iup-1	iup-1	NOUN
ejpam-5857	259	10	)	)	PUNCT
ejpam-5857	259	11	)	)	PUNCT
ejpam-5857	260	1	=	=	NOUN
ejpam-5857	260	2	ψi((x	ψi((x	NOUN
ejpam-5857	260	3	·	·	PUNCT
ejpam-5857	260	4	0	0	X
ejpam-5857	260	5	)	)	PUNCT
ejpam-5857	260	6	·	·	PUNCT
ejpam-5857	260	7	(	(	PUNCT
ejpam-5857	260	8	x	x	X
ejpam-5857	260	9	·	·	PUNCT
ejpam-5857	260	10	y	y	NOUN
ejpam-5857	260	11	)	)	PUNCT
ejpam-5857	260	12	)	)	PUNCT
ejpam-5857	260	13	(	(	PUNCT
ejpam-5857	260	14	by	by	ADP
ejpam-5857	260	15	(	(	PUNCT
ejpam-5857	260	16	iup-3	iup-3	NUM
ejpam-5857	260	17	)	)	PUNCT
ejpam-5857	260	18	)	)	PUNCT
ejpam-5857	260	19	≤	≤	NOUN
ejpam-5857	260	20	(	(	PUNCT
ejpam-5857	260	21	ψi(x	ψi(x	X
ejpam-5857	260	22	·	·	PUNCT
ejpam-5857	260	23	0	0	X
ejpam-5857	260	24	)	)	PUNCT
ejpam-5857	260	25	∨	∨	NUM
ejpam-5857	260	26	ψi(x	ψi(x	NUM
ejpam-5857	260	27	·	·	PUNCT
ejpam-5857	260	28	y	y	X
ejpam-5857	260	29	)	)	PUNCT
ejpam-5857	260	30	)	)	PUNCT
ejpam-5857	261	1	∧	∧	NOUN
ejpam-5857	261	2	0.5	0.5	NUM
ejpam-5857	261	3	(	(	PUNCT
ejpam-5857	261	4	by	by	ADP
ejpam-5857	261	5	(	(	PUNCT
ejpam-5857	261	6	3.6	3.6	NUM
ejpam-5857	261	7	)	)	PUNCT
ejpam-5857	261	8	)	)	PUNCT
ejpam-5857	261	9	≤	≤	NOUN
ejpam-5857	261	10	(	(	PUNCT
ejpam-5857	261	11	(	(	PUNCT
ejpam-5857	261	12	(	(	PUNCT
ejpam-5857	261	13	ψi(x	ψi(x	NUM
ejpam-5857	261	14	)	)	PUNCT
ejpam-5857	261	15	∨	∨	NUM
ejpam-5857	261	16	ψi(x	ψi(x	NUM
ejpam-5857	261	17	)	)	PUNCT
ejpam-5857	261	18	)	)	PUNCT
ejpam-5857	262	1	∧	∧	NOUN
ejpam-5857	262	2	0.5	0.5	NUM
ejpam-5857	262	3	)	)	PUNCT
ejpam-5857	262	4	∨	∨	NUM
ejpam-5857	262	5	ψi(x	ψi(x	NUM
ejpam-5857	262	6	·	·	PUNCT
ejpam-5857	262	7	y	y	X
ejpam-5857	262	8	)	)	PUNCT
ejpam-5857	262	9	)	)	PUNCT
ejpam-5857	263	1	∧	∧	NOUN
ejpam-5857	263	2	0.5	0.5	NUM
ejpam-5857	263	3	(	(	PUNCT
ejpam-5857	263	4	by	by	ADP
ejpam-5857	263	5	(	(	PUNCT
ejpam-5857	263	6	3.6	3.6	NUM
ejpam-5857	263	7	)	)	PUNCT
ejpam-5857	263	8	)	)	PUNCT
ejpam-5857	264	1	=	=	SYM
ejpam-5857	264	2	(	(	PUNCT
ejpam-5857	264	3	(	(	PUNCT
ejpam-5857	264	4	ψi(x	ψi(x	NUM
ejpam-5857	264	5	)	)	PUNCT
ejpam-5857	264	6	∧	∧	NOUN
ejpam-5857	264	7	0.5	0.5	NUM
ejpam-5857	264	8	)	)	PUNCT
ejpam-5857	264	9	∨	∨	NUM
ejpam-5857	264	10	ψi(x	ψi(x	NUM
ejpam-5857	264	11	·	·	PUNCT
ejpam-5857	264	12	y	y	X
ejpam-5857	264	13	)	)	PUNCT
ejpam-5857	264	14	)	)	PUNCT
ejpam-5857	265	1	∧	∧	NOUN
ejpam-5857	265	2	0.5	0.5	NUM
ejpam-5857	265	3	(	(	PUNCT
ejpam-5857	265	4	by	by	ADP
ejpam-5857	265	5	(	(	PUNCT
ejpam-5857	265	6	3.9	3.9	NUM
ejpam-5857	265	7	)	)	PUNCT
ejpam-5857	265	8	)	)	PUNCT
ejpam-5857	265	9	≤	≤	NOUN
ejpam-5857	265	10	(	(	PUNCT
ejpam-5857	265	11	ψi(x	ψi(x	NUM
ejpam-5857	265	12	)	)	PUNCT
ejpam-5857	265	13	∨	∨	NUM
ejpam-5857	265	14	ψi(x	ψi(x	NUM
ejpam-5857	265	15	·	·	PUNCT
ejpam-5857	265	16	y	y	X
ejpam-5857	265	17	)	)	PUNCT
ejpam-5857	265	18	)	)	PUNCT
ejpam-5857	266	1	∧	∧	NOUN
ejpam-5857	266	2	0.5	0.5	NUM
ejpam-5857	266	3	,	,	PUNCT
ejpam-5857	266	4	ψf	ψf	X
ejpam-5857	266	5	(	(	PUNCT
ejpam-5857	266	6	y	y	NOUN
ejpam-5857	266	7	)	)	PUNCT
ejpam-5857	266	8	=	=	PRON
ejpam-5857	266	9	ψf	ψf	X
ejpam-5857	266	10	(	(	PUNCT
ejpam-5857	266	11	0	0	NUM
ejpam-5857	266	12	·	·	SYM
ejpam-5857	266	13	y	y	X
ejpam-5857	266	14	)	)	PUNCT
ejpam-5857	266	15	(	(	PUNCT
ejpam-5857	266	16	by	by	ADP
ejpam-5857	266	17	(	(	PUNCT
ejpam-5857	266	18	iup-1	iup-1	NOUN
ejpam-5857	266	19	)	)	PUNCT
ejpam-5857	266	20	)	)	PUNCT
ejpam-5857	267	1	=	=	PRON
ejpam-5857	267	2	ψf	ψf	X
ejpam-5857	267	3	(	(	PUNCT
ejpam-5857	267	4	(	(	PUNCT
ejpam-5857	267	5	x	x	X
ejpam-5857	267	6	·	·	PUNCT
ejpam-5857	267	7	0	0	NUM
ejpam-5857	267	8	)	)	PUNCT
ejpam-5857	267	9	·	·	PUNCT
ejpam-5857	268	1	(	(	PUNCT
ejpam-5857	268	2	x	x	X
ejpam-5857	268	3	·	·	PUNCT
ejpam-5857	268	4	y	y	NOUN
ejpam-5857	268	5	)	)	PUNCT
ejpam-5857	268	6	)	)	PUNCT
ejpam-5857	268	7	(	(	PUNCT
ejpam-5857	268	8	by	by	ADP
ejpam-5857	268	9	(	(	PUNCT
ejpam-5857	268	10	iup-3	iup-3	NUM
ejpam-5857	268	11	)	)	PUNCT
ejpam-5857	268	12	)	)	PUNCT
ejpam-5857	268	13	≥	≥	NOUN
ejpam-5857	268	14	(	(	PUNCT
ejpam-5857	268	15	ψf	ψf	X
ejpam-5857	268	16	(	(	PUNCT
ejpam-5857	268	17	x	x	X
ejpam-5857	268	18	·	·	PUNCT
ejpam-5857	268	19	0	0	X
ejpam-5857	268	20	)	)	PUNCT
ejpam-5857	268	21	∧	∧	NOUN
ejpam-5857	268	22	ψf	ψf	X
ejpam-5857	268	23	(	(	PUNCT
ejpam-5857	268	24	x	x	PROPN
ejpam-5857	268	25	·	·	PUNCT
ejpam-5857	268	26	y	y	NOUN
ejpam-5857	268	27	)	)	PUNCT
ejpam-5857	268	28	)	)	PUNCT
ejpam-5857	269	1	∨	∨	NUM
ejpam-5857	269	2	0.5	0.5	NUM
ejpam-5857	269	3	(	(	PUNCT
ejpam-5857	269	4	by	by	ADP
ejpam-5857	269	5	(	(	PUNCT
ejpam-5857	269	6	3.7	3.7	NUM
ejpam-5857	269	7	)	)	PUNCT
ejpam-5857	269	8	)	)	PUNCT
ejpam-5857	269	9	≥	≥	X
ejpam-5857	269	10	(	(	PUNCT
ejpam-5857	269	11	(	(	PUNCT
ejpam-5857	269	12	(	(	PUNCT
ejpam-5857	269	13	ψf	ψf	X
ejpam-5857	269	14	(	(	PUNCT
ejpam-5857	269	15	x	x	NOUN
ejpam-5857	269	16	)	)	PUNCT
ejpam-5857	269	17	∧	∧	NOUN
ejpam-5857	269	18	ψf	ψf	X
ejpam-5857	269	19	(	(	PUNCT
ejpam-5857	269	20	0	0	NUM
ejpam-5857	269	21	)	)	PUNCT
ejpam-5857	269	22	)	)	PUNCT
ejpam-5857	270	1	∨	∨	NUM
ejpam-5857	270	2	0.5	0.5	NUM
ejpam-5857	270	3	)	)	PUNCT
ejpam-5857	270	4	∧	∧	NOUN
ejpam-5857	270	5	ψf	ψf	X
ejpam-5857	270	6	(	(	PUNCT
ejpam-5857	270	7	x	x	PROPN
ejpam-5857	270	8	·	·	PUNCT
ejpam-5857	270	9	y	y	NOUN
ejpam-5857	270	10	)	)	PUNCT
ejpam-5857	270	11	)	)	PUNCT
ejpam-5857	270	12	∨	∨	NUM
ejpam-5857	270	13	0.5	0.5	NUM
ejpam-5857	270	14	(	(	PUNCT
ejpam-5857	270	15	by	by	ADP
ejpam-5857	270	16	(	(	PUNCT
ejpam-5857	270	17	3.7	3.7	NUM
ejpam-5857	270	18	)	)	PUNCT
ejpam-5857	270	19	)	)	PUNCT
ejpam-5857	271	1	=	=	PUNCT
ejpam-5857	271	2	(	(	PUNCT
ejpam-5857	271	3	(	(	PUNCT
ejpam-5857	271	4	ψf	ψf	X
ejpam-5857	271	5	(	(	PUNCT
ejpam-5857	271	6	x	x	NOUN
ejpam-5857	271	7	)	)	PUNCT
ejpam-5857	271	8	∨	∨	NUM
ejpam-5857	271	9	0.5	0.5	NUM
ejpam-5857	271	10	)	)	PUNCT
ejpam-5857	271	11	∧	∧	NOUN
ejpam-5857	271	12	ψf	ψf	X
ejpam-5857	271	13	(	(	PUNCT
ejpam-5857	271	14	x	x	PROPN
ejpam-5857	271	15	·	·	PUNCT
ejpam-5857	271	16	y	y	NOUN
ejpam-5857	271	17	)	)	PUNCT
ejpam-5857	271	18	)	)	PUNCT
ejpam-5857	271	19	∨	∨	NUM
ejpam-5857	271	20	0.5	0.5	NUM
ejpam-5857	271	21	(	(	PUNCT
ejpam-5857	271	22	by	by	ADP
ejpam-5857	271	23	(	(	PUNCT
ejpam-5857	271	24	3.10	3.10	NUM
ejpam-5857	271	25	)	)	PUNCT
ejpam-5857	271	26	)	)	PUNCT
ejpam-5857	271	27	≥	≥	X
ejpam-5857	271	28	(	(	PUNCT
ejpam-5857	271	29	ψf	ψf	X
ejpam-5857	271	30	(	(	PUNCT
ejpam-5857	271	31	x	x	NOUN
ejpam-5857	271	32	)	)	PUNCT
ejpam-5857	271	33	∧	∧	NOUN
ejpam-5857	271	34	ψf	ψf	X
ejpam-5857	271	35	(	(	PUNCT
ejpam-5857	271	36	x	x	PROPN
ejpam-5857	271	37	·	·	PUNCT
ejpam-5857	271	38	y	y	NOUN
ejpam-5857	271	39	)	)	PUNCT
ejpam-5857	271	40	)	)	PUNCT
ejpam-5857	272	1	∨	∨	NUM
ejpam-5857	272	2	0.5	0.5	NUM
ejpam-5857	272	3	.	.	PUNCT
ejpam-5857	273	1	hence	hence	ADV
ejpam-5857	273	2	,	,	PUNCT
ejpam-5857	273	3	ψ	ψ	X
ejpam-5857	273	4	is	be	AUX
ejpam-5857	273	5	an	an	DET
ejpam-5857	273	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	273	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	273	8	iup	iup	NOUN
ejpam-5857	273	9	-	-	PUNCT
ejpam-5857	273	10	filter	filter	NOUN
ejpam-5857	273	11	of	of	ADP
ejpam-5857	273	12	x.	x.	PROPN
ejpam-5857	273	13	example	example	NOUN
ejpam-5857	273	14	10	10	NUM
ejpam-5857	273	15	.	.	PUNCT
ejpam-5857	274	1	[	[	X
ejpam-5857	274	2	9	9	NUM
ejpam-5857	274	3	]	]	PUNCT
ejpam-5857	274	4	let	let	VERB
ejpam-5857	274	5	r∗	r∗	PROPN
ejpam-5857	274	6	be	be	AUX
ejpam-5857	274	7	the	the	DET
ejpam-5857	274	8	set	set	NOUN
ejpam-5857	274	9	of	of	ADP
ejpam-5857	274	10	all	all	DET
ejpam-5857	274	11	nonzero	nonzero	ADJ
ejpam-5857	274	12	real	real	ADJ
ejpam-5857	274	13	numbers	number	NOUN
ejpam-5857	274	14	.	.	PUNCT
ejpam-5857	275	1	define	define	VERB
ejpam-5857	275	2	a	a	DET
ejpam-5857	275	3	binary	binary	ADJ
ejpam-5857	275	4	operation	operation	NOUN
ejpam-5857	275	5	·	·	PUNCT
ejpam-5857	275	6	on	on	ADP
ejpam-5857	275	7	r∗	r∗	VERB
ejpam-5857	275	8	by	by	ADP
ejpam-5857	275	9	(	(	PUNCT
ejpam-5857	275	10	∀x	∀x	NUM
ejpam-5857	275	11	,	,	PUNCT
ejpam-5857	275	12	y	y	PROPN
ejpam-5857	275	13	∈	∈	PROPN
ejpam-5857	275	14	r∗)(x	r∗)(x	NOUN
ejpam-5857	275	15	·	·	PUNCT
ejpam-5857	275	16	y	y	X
ejpam-5857	275	17	=	=	SYM
ejpam-5857	275	18	y	y	PROPN
ejpam-5857	275	19	x	x	PROPN
ejpam-5857	275	20	)	)	PUNCT
ejpam-5857	275	21	.	.	PUNCT
ejpam-5857	276	1	then	then	ADV
ejpam-5857	276	2	(	(	PUNCT
ejpam-5857	276	3	r∗	r∗	PROPN
ejpam-5857	276	4	;	;	PUNCT
ejpam-5857	276	5	·	·	PUNCT
ejpam-5857	276	6	,	,	PUNCT
ejpam-5857	276	7	1	1	NUM
ejpam-5857	276	8	)	)	PUNCT
ejpam-5857	276	9	is	be	AUX
ejpam-5857	276	10	an	an	DET
ejpam-5857	276	11	iup	iup	NOUN
ejpam-5857	276	12	-	-	PUNCT
ejpam-5857	276	13	algebra	algebra	NOUN
ejpam-5857	276	14	.	.	PUNCT
ejpam-5857	276	15	example	example	NOUN
ejpam-5857	277	1	11	11	NUM
ejpam-5857	277	2	.	.	PUNCT
ejpam-5857	278	1	from	from	ADP
ejpam-5857	278	2	example	example	NOUN
ejpam-5857	278	3	10	10	NUM
ejpam-5857	278	4	,	,	PUNCT
ejpam-5857	278	5	let	let	VERB
ejpam-5857	278	6	p	p	NOUN
ejpam-5857	278	7	=	=	PRON
ejpam-5857	278	8	{	{	PUNCT
ejpam-5857	278	9	x	x	PUNCT
ejpam-5857	278	10	∈	∈	PROPN
ejpam-5857	278	11	r∗	r∗	NOUN
ejpam-5857	278	12	|	|	ADV
ejpam-5857	278	13	x	x	NOUN
ejpam-5857	278	14	≥	≥	NOUN
ejpam-5857	278	15	1	1	NUM
ejpam-5857	278	16	}	}	PUNCT
ejpam-5857	278	17	.	.	PUNCT
ejpam-5857	279	1	then	then	ADV
ejpam-5857	279	2	1	1	NUM
ejpam-5857	279	3	∈	∈	PROPN
ejpam-5857	279	4	p	p	NOUN
ejpam-5857	279	5	.	.	PUNCT
ejpam-5857	280	1	next	next	ADV
ejpam-5857	280	2	,	,	PUNCT
ejpam-5857	280	3	let	let	VERB
ejpam-5857	280	4	x	x	PRON
ejpam-5857	280	5	,	,	PUNCT
ejpam-5857	280	6	y	y	PROPN
ejpam-5857	280	7	,	,	PUNCT
ejpam-5857	280	8	z	z	PROPN
ejpam-5857	280	9	∈	∈	PROPN
ejpam-5857	280	10	r∗	r∗	NOUN
ejpam-5857	280	11	be	be	VERB
ejpam-5857	280	12	such	such	ADJ
ejpam-5857	280	13	that	that	SCONJ
ejpam-5857	280	14	x·(y	x·(y	PUNCT
ejpam-5857	281	1	·	·	PUNCT
ejpam-5857	281	2	z	z	X
ejpam-5857	281	3	)	)	PUNCT
ejpam-5857	281	4	≥	≥	NOUN
ejpam-5857	281	5	1	1	NUM
ejpam-5857	281	6	and	and	CCONJ
ejpam-5857	281	7	y	y	PROPN
ejpam-5857	281	8	≥	≥	NUM
ejpam-5857	281	9	1	1	NUM
ejpam-5857	281	10	.	.	PUNCT
ejpam-5857	282	1	then	then	ADV
ejpam-5857	282	2	z	z	PROPN
ejpam-5857	282	3	yx	yx	PROPN
ejpam-5857	282	4	≥	≥	NUM
ejpam-5857	282	5	1	1	NUM
ejpam-5857	282	6	.	.	PUNCT
ejpam-5857	283	1	thus	thus	ADV
ejpam-5857	283	2	,	,	PUNCT
ejpam-5857	283	3	x·z	x·z	PROPN
ejpam-5857	283	4	=	=	PUNCT
ejpam-5857	284	1	z	z	NOUN
ejpam-5857	284	2	x	x	SYM
ejpam-5857	284	3	=	=	PUNCT
ejpam-5857	284	4	(	(	PUNCT
ejpam-5857	284	5	z	z	PROPN
ejpam-5857	284	6	yx)y	yx)y	PROPN
ejpam-5857	284	7	≥	≥	NUM
ejpam-5857	284	8	1	1	NUM
ejpam-5857	284	9	,	,	PUNCT
ejpam-5857	284	10	that	that	ADV
ejpam-5857	284	11	is	is	ADV
ejpam-5857	284	12	,	,	PUNCT
ejpam-5857	284	13	x	x	X
ejpam-5857	284	14	·	·	PUNCT
ejpam-5857	284	15	z	z	X
ejpam-5857	284	16	∈	∈	PROPN
ejpam-5857	284	17	p	p	NOUN
ejpam-5857	284	18	.	.	PUNCT
ejpam-5857	285	1	hence	hence	ADV
ejpam-5857	285	2	,	,	PUNCT
ejpam-5857	285	3	p	p	PROPN
ejpam-5857	285	4	is	be	AUX
ejpam-5857	285	5	an	an	DET
ejpam-5857	285	6	iup	iup	NOUN
ejpam-5857	285	7	-	-	PUNCT
ejpam-5857	285	8	ideal	ideal	NOUN
ejpam-5857	285	9	of	of	ADP
ejpam-5857	285	10	r∗.	r∗.	NOUN
ejpam-5857	285	11	then	then	ADV
ejpam-5857	285	12	p	p	NOUN
ejpam-5857	285	13	is	be	AUX
ejpam-5857	285	14	an	an	DET
ejpam-5857	285	15	iup	iup	NOUN
ejpam-5857	285	16	-	-	PUNCT
ejpam-5857	285	17	filter	filter	NOUN
ejpam-5857	285	18	of	of	ADP
ejpam-5857	285	19	r∗.	r∗.	NOUN
ejpam-5857	285	20	from	from	ADP
ejpam-5857	285	21	theorems	theorem	NOUN
ejpam-5857	285	22	7	7	NUM
ejpam-5857	285	23	and	and	CCONJ
ejpam-5857	285	24	8	8	NUM
ejpam-5857	285	25	,	,	PUNCT
ejpam-5857	285	26	ψg[α	ψg[α	PROPN
ejpam-5857	285	27	+	+	PROPN
ejpam-5857	285	28	,	,	PUNCT
ejpam-5857	285	29	β−	β−	PROPN
ejpam-5857	285	30	α−,β+	α−,β+	NUM
ejpam-5857	285	31	,	,	PUNCT
ejpam-5857	285	32	0.5	0.5	NUM
ejpam-5857	285	33	]	]	PUNCT
ejpam-5857	285	34	is	be	AUX
ejpam-5857	285	35	an	an	DET
ejpam-5857	285	36	intuitionistic	intuitionistic	ADJ
ejpam-5857	285	37	neutrosophic	neutrosophic	ADJ
ejpam-5857	285	38	iup	iup	NOUN
ejpam-5857	285	39	-	-	PUNCT
ejpam-5857	285	40	ideal	ideal	NOUN
ejpam-5857	285	41	and	and	CCONJ
ejpam-5857	285	42	an	an	DET
ejpam-5857	285	43	k.	k.	PROPN
ejpam-5857	285	44	suayngam	suayngam	PROPN
ejpam-5857	285	45	,	,	PUNCT
ejpam-5857	285	46	p.	p.	NOUN
ejpam-5857	285	47	julatha	julatha	PROPN
ejpam-5857	285	48	,	,	PUNCT
ejpam-5857	285	49	w.	w.	PROPN
ejpam-5857	285	50	nakkhasen	nakkhasen	PROPN
ejpam-5857	285	51	,	,	PUNCT
ejpam-5857	285	52	a.	a.	NOUN
ejpam-5857	285	53	iampan	iampan	PROPN
ejpam-5857	285	54	/	/	SYM
ejpam-5857	285	55	eur	eur	PROPN
ejpam-5857	285	56	.	.	PUNCT
ejpam-5857	286	1	j.	j.	PROPN
ejpam-5857	286	2	pure	pure	PROPN
ejpam-5857	286	3	appl	appl	PROPN
ejpam-5857	286	4	.	.	PROPN
ejpam-5857	286	5	math	math	PROPN
ejpam-5857	286	6	,	,	PUNCT
ejpam-5857	286	7	18	18	NUM
ejpam-5857	286	8	(	(	PUNCT
ejpam-5857	286	9	2	2	NUM
ejpam-5857	286	10	)	)	PUNCT
ejpam-5857	286	11	(	(	PUNCT
ejpam-5857	286	12	2025	2025	NUM
ejpam-5857	286	13	)	)	PUNCT
ejpam-5857	286	14	,	,	PUNCT
ejpam-5857	286	15	5857	5857	NUM
ejpam-5857	286	16	13	13	NUM
ejpam-5857	286	17	of	of	ADP
ejpam-5857	286	18	30	30	NUM
ejpam-5857	286	19	intuitionistic	intuitionistic	ADJ
ejpam-5857	286	20	neutrosophic	neutrosophic	ADJ
ejpam-5857	286	21	iup	iup	NOUN
ejpam-5857	286	22	-	-	PUNCT
ejpam-5857	286	23	filter	filter	NOUN
ejpam-5857	286	24	of	of	ADP
ejpam-5857	286	25	r∗.	r∗.	NOUN
ejpam-5857	286	26	thus	thus	ADV
ejpam-5857	286	27	,	,	PUNCT
ejpam-5857	286	28	ψ	ψ	X
ejpam-5857	286	29	is	be	AUX
ejpam-5857	286	30	an	an	DET
ejpam-5857	286	31	intuitionistic	intuitionistic	ADJ
ejpam-5857	286	32	neutrosophic	neutrosophic	ADJ
ejpam-5857	286	33	iupideal	iupideal	NOUN
ejpam-5857	286	34	and	and	CCONJ
ejpam-5857	286	35	an	an	DET
ejpam-5857	286	36	intuitionistic	intuitionistic	ADJ
ejpam-5857	286	37	neutrosophic	neutrosophic	ADJ
ejpam-5857	286	38	iup	iup	NOUN
ejpam-5857	286	39	-	-	PUNCT
ejpam-5857	286	40	filter	filter	NOUN
ejpam-5857	286	41	of	of	ADP
ejpam-5857	286	42	r∗.	r∗.	NOUN
ejpam-5857	286	43	since	since	SCONJ
ejpam-5857	286	44	1	1	NUM
ejpam-5857	286	45	,	,	PUNCT
ejpam-5857	286	46	3	3	NUM
ejpam-5857	286	47	∈	∈	NOUN
ejpam-5857	286	48	p	p	NOUN
ejpam-5857	286	49	but	but	CCONJ
ejpam-5857	286	50	3	3	NUM
ejpam-5857	286	51	·	·	SYM
ejpam-5857	286	52	1	1	NUM
ejpam-5857	286	53	=	=	SYM
ejpam-5857	286	54	1	1	NUM
ejpam-5857	286	55	3	3	NUM
ejpam-5857	286	56	∈	∈	NOUN
ejpam-5857	286	57	p	p	NOUN
ejpam-5857	286	58	,	,	PUNCT
ejpam-5857	286	59	we	we	PRON
ejpam-5857	286	60	have	have	VERB
ejpam-5857	286	61	p	p	NOUN
ejpam-5857	286	62	is	be	AUX
ejpam-5857	286	63	not	not	PART
ejpam-5857	286	64	an	an	DET
ejpam-5857	286	65	iup	iup	NOUN
ejpam-5857	286	66	-	-	PUNCT
ejpam-5857	286	67	subalgebra	subalgebra	NOUN
ejpam-5857	286	68	of	of	ADP
ejpam-5857	286	69	r∗.	r∗.	NOUN
ejpam-5857	286	70	from	from	ADP
ejpam-5857	286	71	theorem	theorem	ADJ
ejpam-5857	286	72	6	6	NUM
ejpam-5857	286	73	,	,	PUNCT
ejpam-5857	286	74	we	we	PRON
ejpam-5857	286	75	have	have	VERB
ejpam-5857	286	76	ψg[α	ψg[α	NOUN
ejpam-5857	286	77	+	+	PROPN
ejpam-5857	286	78	,	,	PUNCT
ejpam-5857	286	79	β−	β−	PROPN
ejpam-5857	286	80	α−,β+	α−,β+	NUM
ejpam-5857	286	81	,	,	PUNCT
ejpam-5857	286	82	0.5	0.5	NUM
ejpam-5857	286	83	]	]	PUNCT
ejpam-5857	286	84	is	be	AUX
ejpam-5857	286	85	not	not	PART
ejpam-5857	286	86	an	an	DET
ejpam-5857	286	87	intuitionistic	intuitionistic	ADJ
ejpam-5857	286	88	neutrosophic	neutrosophic	ADJ
ejpam-5857	286	89	iup	iup	NOUN
ejpam-5857	286	90	-	-	PUNCT
ejpam-5857	286	91	subalgebra	subalgebra	NOUN
ejpam-5857	286	92	of	of	ADP
ejpam-5857	286	93	r∗.	r∗.	NOUN
ejpam-5857	286	94	hence	hence	ADV
ejpam-5857	286	95	,	,	PUNCT
ejpam-5857	286	96	ψ	ψ	X
ejpam-5857	286	97	is	be	AUX
ejpam-5857	286	98	not	not	PART
ejpam-5857	286	99	an	an	DET
ejpam-5857	286	100	intuitionistic	intuitionistic	ADJ
ejpam-5857	286	101	neutrosophic	neutrosophic	ADJ
ejpam-5857	286	102	iup	iup	NOUN
ejpam-5857	286	103	-	-	PUNCT
ejpam-5857	286	104	subalgebra	subalgebra	NOUN
ejpam-5857	286	105	of	of	ADP
ejpam-5857	286	106	r∗.	r∗.	NOUN
ejpam-5857	286	107	example	example	NOUN
ejpam-5857	286	108	12	12	NUM
ejpam-5857	286	109	.	.	PUNCT
ejpam-5857	287	1	let	let	VERB
ejpam-5857	287	2	x	x	PUNCT
ejpam-5857	287	3	=	=	PUNCT
ejpam-5857	287	4	{	{	PUNCT
ejpam-5857	287	5	0	0	NUM
ejpam-5857	287	6	,	,	PUNCT
ejpam-5857	287	7	1	1	NUM
ejpam-5857	287	8	,	,	PUNCT
ejpam-5857	287	9	2	2	NUM
ejpam-5857	287	10	,	,	PUNCT
ejpam-5857	287	11	3	3	NUM
ejpam-5857	287	12	,	,	PUNCT
ejpam-5857	287	13	4	4	NUM
ejpam-5857	287	14	,	,	PUNCT
ejpam-5857	287	15	5	5	NUM
ejpam-5857	287	16	}	}	PUNCT
ejpam-5857	287	17	with	with	ADP
ejpam-5857	287	18	the	the	DET
ejpam-5857	287	19	following	follow	VERB
ejpam-5857	287	20	cayley	cayley	ADJ
ejpam-5857	287	21	table	table	NOUN
ejpam-5857	287	22	:	:	PUNCT
ejpam-5857	287	23	·	·	PUNCT
ejpam-5857	287	24	0	0	NUM
ejpam-5857	287	25	1	1	NUM
ejpam-5857	287	26	2	2	NUM
ejpam-5857	287	27	3	3	NUM
ejpam-5857	287	28	4	4	NUM
ejpam-5857	287	29	5	5	NUM
ejpam-5857	287	30	0	0	NUM
ejpam-5857	287	31	0	0	NUM
ejpam-5857	287	32	1	1	NUM
ejpam-5857	287	33	2	2	NUM
ejpam-5857	287	34	3	3	NUM
ejpam-5857	287	35	4	4	NUM
ejpam-5857	287	36	5	5	NUM
ejpam-5857	287	37	1	1	NUM
ejpam-5857	287	38	2	2	NUM
ejpam-5857	287	39	0	0	NUM
ejpam-5857	287	40	1	1	NUM
ejpam-5857	287	41	4	4	NUM
ejpam-5857	287	42	5	5	NUM
ejpam-5857	287	43	3	3	NUM
ejpam-5857	287	44	2	2	NUM
ejpam-5857	287	45	1	1	NUM
ejpam-5857	287	46	2	2	NUM
ejpam-5857	287	47	0	0	NUM
ejpam-5857	287	48	5	5	NUM
ejpam-5857	287	49	3	3	NUM
ejpam-5857	287	50	4	4	NUM
ejpam-5857	287	51	3	3	NUM
ejpam-5857	287	52	3	3	NUM
ejpam-5857	287	53	4	4	NUM
ejpam-5857	287	54	5	5	NUM
ejpam-5857	287	55	0	0	NUM
ejpam-5857	287	56	1	1	NUM
ejpam-5857	287	57	2	2	NUM
ejpam-5857	287	58	4	4	NUM
ejpam-5857	287	59	4	4	NUM
ejpam-5857	287	60	5	5	NUM
ejpam-5857	287	61	3	3	NUM
ejpam-5857	287	62	2	2	NUM
ejpam-5857	287	63	0	0	NUM
ejpam-5857	287	64	1	1	NUM
ejpam-5857	287	65	5	5	NUM
ejpam-5857	287	66	5	5	NUM
ejpam-5857	287	67	3	3	NUM
ejpam-5857	287	68	4	4	NUM
ejpam-5857	287	69	1	1	NUM
ejpam-5857	287	70	2	2	NUM
ejpam-5857	287	71	0	0	NUM
ejpam-5857	287	72	then	then	ADV
ejpam-5857	287	73	x	x	PUNCT
ejpam-5857	287	74	is	be	AUX
ejpam-5857	287	75	an	an	DET
ejpam-5857	287	76	iup	iup	NOUN
ejpam-5857	287	77	-	-	PUNCT
ejpam-5857	287	78	algebra	algebra	NOUN
ejpam-5857	287	79	.	.	PUNCT
ejpam-5857	288	1	we	we	PRON
ejpam-5857	288	2	define	define	VERB
ejpam-5857	288	3	an	an	DET
ejpam-5857	288	4	ins	in	NOUN
ejpam-5857	288	5	ψ	ψ	X
ejpam-5857	288	6	on	on	ADP
ejpam-5857	288	7	x	x	PUNCT
ejpam-5857	288	8	as	as	SCONJ
ejpam-5857	288	9	follows	follow	VERB
ejpam-5857	288	10	:	:	PUNCT
ejpam-5857	288	11	ψt	ψt	NOUN
ejpam-5857	288	12	=	=	PUNCT
ejpam-5857	288	13	(	(	PUNCT
ejpam-5857	288	14	0	0	NUM
ejpam-5857	288	15	0.9	0.9	NUM
ejpam-5857	288	16	1	1	NUM
ejpam-5857	288	17	0.5	0.5	NUM
ejpam-5857	288	18	2	2	NUM
ejpam-5857	288	19	0.5	0.5	NUM
ejpam-5857	288	20	3	3	NUM
ejpam-5857	288	21	0.5	0.5	NUM
ejpam-5857	288	22	4	4	NUM
ejpam-5857	288	23	0.5	0.5	NUM
ejpam-5857	288	24	5	5	NUM
ejpam-5857	288	25	0.8	0.8	NUM
ejpam-5857	288	26	)	)	PUNCT
ejpam-5857	288	27	ψi	ψi	ADP
ejpam-5857	288	28	=	=	PUNCT
ejpam-5857	288	29	(	(	PUNCT
ejpam-5857	288	30	0	0	NUM
ejpam-5857	288	31	0	0	NUM
ejpam-5857	288	32	1	1	NUM
ejpam-5857	288	33	0.4	0.4	NUM
ejpam-5857	288	34	2	2	NUM
ejpam-5857	288	35	0.4	0.4	NUM
ejpam-5857	288	36	3	3	NUM
ejpam-5857	288	37	0.4	0.4	NUM
ejpam-5857	288	38	4	4	NUM
ejpam-5857	288	39	0.4	0.4	NUM
ejpam-5857	288	40	5	5	NUM
ejpam-5857	288	41	0.2	0.2	NUM
ejpam-5857	288	42	)	)	PUNCT
ejpam-5857	288	43	ψf	ψf	X
ejpam-5857	289	1	=	=	PUNCT
ejpam-5857	289	2	(	(	PUNCT
ejpam-5857	289	3	0	0	NUM
ejpam-5857	289	4	0.5	0.5	NUM
ejpam-5857	289	5	1	1	NUM
ejpam-5857	289	6	0.5	0.5	NUM
ejpam-5857	289	7	2	2	NUM
ejpam-5857	289	8	0.5	0.5	NUM
ejpam-5857	289	9	3	3	NUM
ejpam-5857	289	10	0.5	0.5	NUM
ejpam-5857	289	11	4	4	NUM
ejpam-5857	289	12	0.5	0.5	NUM
ejpam-5857	289	13	5	5	NUM
ejpam-5857	289	14	0.5	0.5	NUM
ejpam-5857	289	15	)	)	PUNCT
ejpam-5857	289	16	then	then	ADV
ejpam-5857	289	17	ψ	ψ	X
ejpam-5857	289	18	is	be	AUX
ejpam-5857	289	19	an	an	DET
ejpam-5857	289	20	intuitionistic	intuitionistic	ADJ
ejpam-5857	289	21	neutrosophic	neutrosophic	ADJ
ejpam-5857	289	22	iup	iup	NOUN
ejpam-5857	289	23	-	-	PUNCT
ejpam-5857	289	24	subalgebra	subalgebra	NOUN
ejpam-5857	289	25	of	of	ADP
ejpam-5857	289	26	x.	x.	NOUN
ejpam-5857	289	27	since	since	SCONJ
ejpam-5857	289	28	ψt	ψt	VERB
ejpam-5857	289	29	(	(	PUNCT
ejpam-5857	289	30	2	2	NUM
ejpam-5857	289	31	·	·	SYM
ejpam-5857	289	32	4	4	NUM
ejpam-5857	289	33	)	)	PUNCT
ejpam-5857	289	34	=	=	VERB
ejpam-5857	290	1	ψt	ψt	NOUN
ejpam-5857	290	2	(	(	PUNCT
ejpam-5857	290	3	3	3	NUM
ejpam-5857	290	4	)	)	PUNCT
ejpam-5857	290	5	=	=	SYM
ejpam-5857	290	6	0.5	0.5	NUM
ejpam-5857	290	7	≱	≱	PROPN
ejpam-5857	290	8	0.8	0.8	NUM
ejpam-5857	290	9	=	=	SYM
ejpam-5857	290	10	0.8∨0.5	0.8∨0.5	NUM
ejpam-5857	290	11	=	=	SYM
ejpam-5857	290	12	(	(	PUNCT
ejpam-5857	290	13	0.9∧0.8)∨0.5	0.9∧0.8)∨0.5	NUM
ejpam-5857	290	14	=	=	SYM
ejpam-5857	290	15	(	(	PUNCT
ejpam-5857	290	16	ψt	ψt	NUM
ejpam-5857	290	17	(	(	PUNCT
ejpam-5857	290	18	0)∧ψt	0)∧ψt	NUM
ejpam-5857	290	19	(	(	PUNCT
ejpam-5857	290	20	5))∨0.5	5))∨0.5	NUM
ejpam-5857	290	21	=	=	SYM
ejpam-5857	290	22	(	(	PUNCT
ejpam-5857	290	23	ψt	ψt	NUM
ejpam-5857	290	24	(	(	PUNCT
ejpam-5857	290	25	2·(5·4))∧ψt	2·(5·4))∧ψt	NUM
ejpam-5857	290	26	(	(	PUNCT
ejpam-5857	290	27	5))∨0.5	5))∨0.5	NUM
ejpam-5857	290	28	and	and	CCONJ
ejpam-5857	290	29	ψi(2	ψi(2	PROPN
ejpam-5857	290	30	·	·	PUNCT
ejpam-5857	290	31	4	4	X
ejpam-5857	290	32	)	)	PUNCT
ejpam-5857	290	33	=	=	SYM
ejpam-5857	290	34	ψi(3	ψi(3	ADJ
ejpam-5857	290	35	)	)	PUNCT
ejpam-5857	290	36	=	=	SYM
ejpam-5857	291	1	0.4	0.4	NUM
ejpam-5857	291	2	≰	≰	PROPN
ejpam-5857	291	3	0.2	0.2	NUM
ejpam-5857	291	4	=	=	SYM
ejpam-5857	291	5	0.2	0.2	NUM
ejpam-5857	291	6	∧	∧	PROPN
ejpam-5857	291	7	0.5	0.5	NUM
ejpam-5857	291	8	=	=	SYM
ejpam-5857	291	9	(	(	PUNCT
ejpam-5857	291	10	0	0	NUM
ejpam-5857	291	11	∨	∨	NUM
ejpam-5857	291	12	0.2	0.2	NUM
ejpam-5857	291	13	)	)	PUNCT
ejpam-5857	291	14	∧	∧	NOUN
ejpam-5857	291	15	0.5	0.5	NUM
ejpam-5857	291	16	=	=	SYM
ejpam-5857	291	17	(	(	PUNCT
ejpam-5857	291	18	ψi(0	ψi(0	PROPN
ejpam-5857	291	19	)	)	PUNCT
ejpam-5857	291	20	∨	∨	NUM
ejpam-5857	291	21	ψi(5	ψi(5	PROPN
ejpam-5857	291	22	)	)	PUNCT
ejpam-5857	291	23	)	)	PUNCT
ejpam-5857	292	1	∧	∧	NOUN
ejpam-5857	292	2	0.5	0.5	NUM
ejpam-5857	292	3	=	=	SYM
ejpam-5857	292	4	(	(	PUNCT
ejpam-5857	292	5	ψi(2	ψi(2	PROPN
ejpam-5857	292	6	·	·	PUNCT
ejpam-5857	292	7	(	(	PUNCT
ejpam-5857	292	8	5	5	NUM
ejpam-5857	292	9	·	·	SYM
ejpam-5857	292	10	4	4	NUM
ejpam-5857	292	11	)	)	PUNCT
ejpam-5857	292	12	)	)	PUNCT
ejpam-5857	292	13	∨	∨	NUM
ejpam-5857	292	14	ψi(5	ψi(5	NOUN
ejpam-5857	292	15	)	)	PUNCT
ejpam-5857	292	16	)	)	PUNCT
ejpam-5857	293	1	∧	∧	NOUN
ejpam-5857	293	2	0.5	0.5	NUM
ejpam-5857	293	3	.	.	PUNCT
ejpam-5857	294	1	hence	hence	ADV
ejpam-5857	294	2	,	,	PUNCT
ejpam-5857	294	3	ψ	ψ	X
ejpam-5857	294	4	is	be	AUX
ejpam-5857	294	5	not	not	PART
ejpam-5857	294	6	an	an	DET
ejpam-5857	294	7	intuitionistic	intuitionistic	ADJ
ejpam-5857	294	8	neutrosophic	neutrosophic	ADJ
ejpam-5857	294	9	iup	iup	NOUN
ejpam-5857	294	10	-	-	PUNCT
ejpam-5857	294	11	ideal	ideal	NOUN
ejpam-5857	294	12	of	of	ADP
ejpam-5857	294	13	x.	x.	PROPN
ejpam-5857	294	14	theorem	theorem	VERB
ejpam-5857	294	15	4	4	NUM
ejpam-5857	294	16	.	.	PUNCT
ejpam-5857	295	1	if	if	SCONJ
ejpam-5857	295	2	ψ	ψ	NOUN
ejpam-5857	295	3	is	be	AUX
ejpam-5857	295	4	an	an	DET
ejpam-5857	295	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	295	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	295	7	iup	iup	NOUN
ejpam-5857	295	8	-	-	PUNCT
ejpam-5857	295	9	subalgebra	subalgebra	NOUN
ejpam-5857	295	10	of	of	ADP
ejpam-5857	295	11	x	x	PUNCT
ejpam-5857	295	12	satisfying	satisfy	VERB
ejpam-5857	295	13	the	the	DET
ejpam-5857	295	14	following	follow	VERB
ejpam-5857	295	15	condition	condition	NOUN
ejpam-5857	295	16	:	:	PUNCT
ejpam-5857	295	17	(	(	PUNCT
ejpam-5857	295	18	∀x	∀x	X
ejpam-5857	295	19	,	,	PUNCT
ejpam-5857	295	20	y	y	PROPN
ejpam-5857	295	21	∈	∈	PROPN
ejpam-5857	295	22	x	x	X
ejpam-5857	295	23	)	)	PUNCT
ejpam-5857	295	24	x	x	NOUN
ejpam-5857	295	25	·	·	PUNCT
ejpam-5857	295	26	y	y	SYM
ejpam-5857	295	27	̸=	̸=	PROPN
ejpam-5857	295	28	0	0	NUM
ejpam-5857	295	29	⇒	⇒	NOUN
ejpam-5857	295	30			PRON
ejpam-5857	295	31	ψt	ψt	VERB
ejpam-5857	295	32	(	(	PUNCT
ejpam-5857	295	33	x	x	NOUN
ejpam-5857	295	34	)	)	PUNCT
ejpam-5857	295	35	≥	≥	PRON
ejpam-5857	295	36	ψt	ψt	NOUN
ejpam-5857	295	37	(	(	PUNCT
ejpam-5857	295	38	y	y	NOUN
ejpam-5857	295	39	)	)	PUNCT
ejpam-5857	295	40	ψi(x	ψi(x	NUM
ejpam-5857	295	41	)	)	PUNCT
ejpam-5857	295	42	≤	≤	NOUN
ejpam-5857	295	43	ψi(y	ψi(y	VERB
ejpam-5857	295	44	)	)	PUNCT
ejpam-5857	295	45	ψf	ψf	X
ejpam-5857	296	1	(	(	PUNCT
ejpam-5857	296	2	x	x	X
ejpam-5857	296	3	)	)	PUNCT
ejpam-5857	296	4	≥	≥	NOUN
ejpam-5857	296	5	ψf	ψf	X
ejpam-5857	296	6	(	(	PUNCT
ejpam-5857	296	7	y	y	NOUN
ejpam-5857	296	8	)	)	PUNCT
ejpam-5857	296	9			NOUN
ejpam-5857	296	10	,	,	PUNCT
ejpam-5857	296	11	(	(	PUNCT
ejpam-5857	296	12	3.20	3.20	NUM
ejpam-5857	296	13	)	)	PUNCT
ejpam-5857	296	14	then	then	ADV
ejpam-5857	296	15	ψ	ψ	X
ejpam-5857	296	16	is	be	AUX
ejpam-5857	296	17	an	an	DET
ejpam-5857	296	18	intuitionistic	intuitionistic	ADJ
ejpam-5857	296	19	neutrosophic	neutrosophic	ADJ
ejpam-5857	296	20	strong	strong	ADJ
ejpam-5857	296	21	iup	iup	NOUN
ejpam-5857	296	22	-	-	PUNCT
ejpam-5857	296	23	ideal	ideal	NOUN
ejpam-5857	296	24	of	of	ADP
ejpam-5857	296	25	x.	x.	NOUN
ejpam-5857	296	26	proof	proof	PROPN
ejpam-5857	296	27	.	.	PUNCT
ejpam-5857	297	1	assume	assume	VERB
ejpam-5857	297	2	that	that	SCONJ
ejpam-5857	297	3	ψ	ψ	NOUN
ejpam-5857	297	4	is	be	AUX
ejpam-5857	297	5	an	an	DET
ejpam-5857	297	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	297	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	297	8	iup	iup	NOUN
ejpam-5857	297	9	-	-	PUNCT
ejpam-5857	297	10	subalgebra	subalgebra	NOUN
ejpam-5857	297	11	of	of	ADP
ejpam-5857	297	12	x	x	PUNCT
ejpam-5857	297	13	satisfying	satisfy	VERB
ejpam-5857	297	14	the	the	DET
ejpam-5857	297	15	condition	condition	NOUN
ejpam-5857	297	16	(	(	PUNCT
ejpam-5857	297	17	3.20	3.20	NUM
ejpam-5857	297	18	)	)	PUNCT
ejpam-5857	297	19	.	.	PUNCT
ejpam-5857	298	1	let	let	VERB
ejpam-5857	298	2	x	x	PRON
ejpam-5857	298	3	,	,	PUNCT
ejpam-5857	298	4	y	y	PROPN
ejpam-5857	298	5	∈	∈	PROPN
ejpam-5857	298	6	x.	x.	NOUN
ejpam-5857	298	7	case	case	NOUN
ejpam-5857	298	8	1	1	NUM
ejpam-5857	298	9	:	:	PUNCT
ejpam-5857	298	10	suppose	suppose	VERB
ejpam-5857	298	11	x	x	X
ejpam-5857	298	12	·	·	PUNCT
ejpam-5857	298	13	y	y	SYM
ejpam-5857	298	14	=	=	PUNCT
ejpam-5857	298	15	0	0	PROPN
ejpam-5857	298	16	.	.	PUNCT
ejpam-5857	299	1	then	then	ADV
ejpam-5857	299	2	ψt	ψt	VERB
ejpam-5857	299	3	(	(	PUNCT
ejpam-5857	299	4	x	x	PROPN
ejpam-5857	299	5	·	·	PUNCT
ejpam-5857	299	6	y	y	X
ejpam-5857	299	7	)	)	PUNCT
ejpam-5857	299	8	=	=	PRON
ejpam-5857	300	1	ψt	ψt	NOUN
ejpam-5857	300	2	(	(	PUNCT
ejpam-5857	300	3	0	0	NUM
ejpam-5857	300	4	)	)	PUNCT
ejpam-5857	300	5	k.	k.	NOUN
ejpam-5857	300	6	suayngam	suayngam	PROPN
ejpam-5857	300	7	,	,	PUNCT
ejpam-5857	300	8	p.	p.	NOUN
ejpam-5857	300	9	julatha	julatha	PROPN
ejpam-5857	300	10	,	,	PUNCT
ejpam-5857	301	1	w.	w.	PROPN
ejpam-5857	301	2	nakkhasen	nakkhasen	PROPN
ejpam-5857	301	3	,	,	PUNCT
ejpam-5857	301	4	a.	a.	NOUN
ejpam-5857	301	5	iampan	iampan	PROPN
ejpam-5857	301	6	/	/	SYM
ejpam-5857	301	7	eur	eur	PROPN
ejpam-5857	301	8	.	.	PUNCT
ejpam-5857	302	1	j.	j.	PROPN
ejpam-5857	302	2	pure	pure	PROPN
ejpam-5857	302	3	appl	appl	PROPN
ejpam-5857	302	4	.	.	PROPN
ejpam-5857	302	5	math	math	PROPN
ejpam-5857	302	6	,	,	PUNCT
ejpam-5857	302	7	18	18	NUM
ejpam-5857	302	8	(	(	PUNCT
ejpam-5857	302	9	2	2	NUM
ejpam-5857	302	10	)	)	PUNCT
ejpam-5857	302	11	(	(	PUNCT
ejpam-5857	302	12	2025	2025	NUM
ejpam-5857	302	13	)	)	PUNCT
ejpam-5857	302	14	,	,	PUNCT
ejpam-5857	302	15	5857	5857	NUM
ejpam-5857	302	16	14	14	NUM
ejpam-5857	302	17	of	of	ADP
ejpam-5857	302	18	30	30	NUM
ejpam-5857	302	19	≥	≥	NOUN
ejpam-5857	302	20	ψt	ψt	NOUN
ejpam-5857	302	21	(	(	PUNCT
ejpam-5857	302	22	y	y	NOUN
ejpam-5857	302	23	)	)	PUNCT
ejpam-5857	302	24	,	,	PUNCT
ejpam-5857	302	25	(	(	PUNCT
ejpam-5857	302	26	by	by	ADP
ejpam-5857	302	27	(	(	PUNCT
ejpam-5857	302	28	3.8	3.8	NUM
ejpam-5857	302	29	)	)	PUNCT
ejpam-5857	302	30	)	)	PUNCT
ejpam-5857	302	31	ψi(x	ψi(x	X
ejpam-5857	302	32	·	·	PUNCT
ejpam-5857	303	1	y	y	X
ejpam-5857	303	2	)	)	PUNCT
ejpam-5857	303	3	=	=	SYM
ejpam-5857	303	4	ψi(0	ψi(0	PROPN
ejpam-5857	303	5	)	)	PUNCT
ejpam-5857	303	6	≤	≤	NOUN
ejpam-5857	303	7	ψi(y	ψi(y	VERB
ejpam-5857	303	8	)	)	PUNCT
ejpam-5857	303	9	,	,	PUNCT
ejpam-5857	303	10	(	(	PUNCT
ejpam-5857	303	11	by	by	ADP
ejpam-5857	303	12	(	(	PUNCT
ejpam-5857	303	13	3.9	3.9	NUM
ejpam-5857	303	14	)	)	PUNCT
ejpam-5857	303	15	)	)	PUNCT
ejpam-5857	303	16	ψf	ψf	X
ejpam-5857	304	1	(	(	PUNCT
ejpam-5857	304	2	x	x	X
ejpam-5857	304	3	·	·	PUNCT
ejpam-5857	304	4	y	y	X
ejpam-5857	304	5	)	)	PUNCT
ejpam-5857	304	6	=	=	PRON
ejpam-5857	304	7	ψf	ψf	X
ejpam-5857	304	8	(	(	PUNCT
ejpam-5857	304	9	0	0	NUM
ejpam-5857	304	10	)	)	PUNCT
ejpam-5857	304	11	≥	≥	NOUN
ejpam-5857	304	12	ψf	ψf	X
ejpam-5857	304	13	(	(	PUNCT
ejpam-5857	304	14	y	y	NOUN
ejpam-5857	304	15	)	)	PUNCT
ejpam-5857	304	16	.	.	PUNCT
ejpam-5857	305	1	(	(	PUNCT
ejpam-5857	305	2	by	by	ADP
ejpam-5857	305	3	(	(	PUNCT
ejpam-5857	305	4	3.10	3.10	NUM
ejpam-5857	305	5	)	)	PUNCT
ejpam-5857	305	6	)	)	PUNCT
ejpam-5857	305	7	case	case	NOUN
ejpam-5857	305	8	2	2	NUM
ejpam-5857	305	9	:	:	PUNCT
ejpam-5857	305	10	suppose	suppose	VERB
ejpam-5857	305	11	x	x	X
ejpam-5857	305	12	·	·	PUNCT
ejpam-5857	305	13	y	y	PROPN
ejpam-5857	305	14	̸=	̸=	PROPN
ejpam-5857	305	15	0	0	NUM
ejpam-5857	305	16	.	.	PUNCT
ejpam-5857	306	1	then	then	ADV
ejpam-5857	306	2	ψt	ψt	VERB
ejpam-5857	306	3	(	(	PUNCT
ejpam-5857	306	4	x	x	PROPN
ejpam-5857	306	5	·	·	PUNCT
ejpam-5857	306	6	y	y	X
ejpam-5857	306	7	)	)	PUNCT
ejpam-5857	306	8	≥	≥	NOUN
ejpam-5857	306	9	ψt	ψt	NOUN
ejpam-5857	306	10	(	(	PUNCT
ejpam-5857	306	11	x	x	X
ejpam-5857	306	12	)	)	PUNCT
ejpam-5857	306	13	∧	∧	NOUN
ejpam-5857	306	14	ψt	ψt	NOUN
ejpam-5857	306	15	(	(	PUNCT
ejpam-5857	306	16	y	y	NOUN
ejpam-5857	306	17	)	)	PUNCT
ejpam-5857	306	18	(	(	PUNCT
ejpam-5857	306	19	by	by	ADP
ejpam-5857	306	20	(	(	PUNCT
ejpam-5857	306	21	3.5	3.5	NUM
ejpam-5857	306	22	)	)	PUNCT
ejpam-5857	306	23	)	)	PUNCT
ejpam-5857	307	1	=	=	PRON
ejpam-5857	307	2	ψt	ψt	NOUN
ejpam-5857	307	3	(	(	PUNCT
ejpam-5857	307	4	y	y	NOUN
ejpam-5857	307	5	)	)	PUNCT
ejpam-5857	307	6	,	,	PUNCT
ejpam-5857	307	7	ψi(x	ψi(x	X
ejpam-5857	307	8	·	·	PUNCT
ejpam-5857	307	9	y	y	X
ejpam-5857	307	10	)	)	PUNCT
ejpam-5857	307	11	≤	≤	NOUN
ejpam-5857	307	12	ψi(x	ψi(x	NUM
ejpam-5857	307	13	)	)	PUNCT
ejpam-5857	307	14	∨	∨	NUM
ejpam-5857	307	15	ψi(y	ψi(y	NUM
ejpam-5857	307	16	)	)	PUNCT
ejpam-5857	307	17	(	(	PUNCT
ejpam-5857	307	18	by	by	ADP
ejpam-5857	307	19	(	(	PUNCT
ejpam-5857	307	20	3.9	3.9	NUM
ejpam-5857	307	21	)	)	PUNCT
ejpam-5857	307	22	)	)	PUNCT
ejpam-5857	308	1	=	=	PRON
ejpam-5857	308	2	ψi(y	ψi(y	NUM
ejpam-5857	308	3	)	)	PUNCT
ejpam-5857	308	4	,	,	PUNCT
ejpam-5857	308	5	ψf	ψf	X
ejpam-5857	308	6	(	(	PUNCT
ejpam-5857	308	7	x	x	X
ejpam-5857	308	8	·	·	PUNCT
ejpam-5857	308	9	y	y	X
ejpam-5857	308	10	)	)	PUNCT
ejpam-5857	308	11	≥	≥	NOUN
ejpam-5857	308	12	ψf	ψf	X
ejpam-5857	308	13	(	(	PUNCT
ejpam-5857	308	14	x	x	X
ejpam-5857	308	15	)	)	PUNCT
ejpam-5857	308	16	∧	∧	NOUN
ejpam-5857	308	17	ψf	ψf	X
ejpam-5857	308	18	(	(	PUNCT
ejpam-5857	308	19	y	y	NOUN
ejpam-5857	308	20	)	)	PUNCT
ejpam-5857	308	21	(	(	PUNCT
ejpam-5857	308	22	by	by	ADP
ejpam-5857	308	23	(	(	PUNCT
ejpam-5857	308	24	3.10	3.10	NUM
ejpam-5857	308	25	)	)	PUNCT
ejpam-5857	308	26	)	)	PUNCT
ejpam-5857	309	1	=	=	PRON
ejpam-5857	309	2	ψf	ψf	X
ejpam-5857	309	3	(	(	PUNCT
ejpam-5857	309	4	y	y	NOUN
ejpam-5857	309	5	)	)	PUNCT
ejpam-5857	309	6	.	.	PUNCT
ejpam-5857	310	1	hence	hence	ADV
ejpam-5857	310	2	,	,	PUNCT
ejpam-5857	310	3	ψ	ψ	X
ejpam-5857	310	4	is	be	AUX
ejpam-5857	310	5	an	an	DET
ejpam-5857	310	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	310	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	310	8	strong	strong	ADJ
ejpam-5857	310	9	iup	iup	NOUN
ejpam-5857	310	10	-	-	PUNCT
ejpam-5857	310	11	ideal	ideal	NOUN
ejpam-5857	310	12	of	of	ADP
ejpam-5857	310	13	x.	x.	PROPN
ejpam-5857	310	14	theorem	theorem	VERB
ejpam-5857	310	15	5	5	NUM
ejpam-5857	310	16	.	.	PUNCT
ejpam-5857	311	1	if	if	SCONJ
ejpam-5857	311	2	ψ	ψ	NOUN
ejpam-5857	311	3	is	be	AUX
ejpam-5857	311	4	an	an	DET
ejpam-5857	311	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	311	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	311	7	iup	iup	NOUN
ejpam-5857	311	8	-	-	PUNCT
ejpam-5857	311	9	filter	filter	NOUN
ejpam-5857	311	10	of	of	ADP
ejpam-5857	311	11	x	x	PUNCT
ejpam-5857	311	12	satisfying	satisfy	VERB
ejpam-5857	311	13	the	the	DET
ejpam-5857	311	14	following	follow	VERB
ejpam-5857	311	15	condition	condition	NOUN
ejpam-5857	311	16	:	:	PUNCT
ejpam-5857	311	17	(	(	PUNCT
ejpam-5857	311	18	∀x	∀x	X
ejpam-5857	311	19	,	,	PUNCT
ejpam-5857	311	20	y	y	PROPN
ejpam-5857	311	21	,	,	PUNCT
ejpam-5857	311	22	z	z	NOUN
ejpam-5857	311	23	∈	∈	PROPN
ejpam-5857	311	24	x	x	NOUN
ejpam-5857	311	25	)	)	PUNCT
ejpam-5857	311	26	ψt	ψt	ADV
ejpam-5857	311	27	(	(	PUNCT
ejpam-5857	311	28	y	y	NOUN
ejpam-5857	311	29	·	·	PUNCT
ejpam-5857	311	30	(	(	PUNCT
ejpam-5857	311	31	x	x	X
ejpam-5857	311	32	·	·	PUNCT
ejpam-5857	311	33	z	z	NOUN
ejpam-5857	311	34	)	)	PUNCT
ejpam-5857	311	35	)	)	PUNCT
ejpam-5857	312	1	=	=	PRON
ejpam-5857	312	2	ψt	ψt	X
ejpam-5857	312	3	(	(	PUNCT
ejpam-5857	312	4	x	x	X
ejpam-5857	312	5	·	·	PUNCT
ejpam-5857	312	6	(	(	PUNCT
ejpam-5857	312	7	y	y	PROPN
ejpam-5857	312	8	·	·	PUNCT
ejpam-5857	312	9	z	z	NOUN
ejpam-5857	312	10	)	)	PUNCT
ejpam-5857	312	11	)	)	PUNCT
ejpam-5857	312	12	ψi(y	ψi(y	PUNCT
ejpam-5857	312	13	·	·	PUNCT
ejpam-5857	312	14	(	(	PUNCT
ejpam-5857	312	15	x	x	X
ejpam-5857	312	16	·	·	PUNCT
ejpam-5857	312	17	z	z	NOUN
ejpam-5857	312	18	)	)	PUNCT
ejpam-5857	312	19	)	)	PUNCT
ejpam-5857	313	1	=	=	SYM
ejpam-5857	313	2	ψi(x	ψi(x	X
ejpam-5857	313	3	·	·	PUNCT
ejpam-5857	313	4	(	(	PUNCT
ejpam-5857	313	5	y	y	PROPN
ejpam-5857	313	6	·	·	PUNCT
ejpam-5857	313	7	z	z	NOUN
ejpam-5857	313	8	)	)	PUNCT
ejpam-5857	313	9	)	)	PUNCT
ejpam-5857	313	10	ψf	ψf	PUNCT
ejpam-5857	314	1	(	(	PUNCT
ejpam-5857	314	2	y	y	PROPN
ejpam-5857	314	3	·	·	PUNCT
ejpam-5857	314	4	(	(	PUNCT
ejpam-5857	314	5	x	x	X
ejpam-5857	314	6	·	·	PUNCT
ejpam-5857	314	7	z	z	NOUN
ejpam-5857	314	8	)	)	PUNCT
ejpam-5857	314	9	)	)	PUNCT
ejpam-5857	315	1	=	=	PRON
ejpam-5857	315	2	ψf	ψf	X
ejpam-5857	315	3	(	(	PUNCT
ejpam-5857	315	4	x	x	X
ejpam-5857	315	5	·	·	PUNCT
ejpam-5857	315	6	(	(	PUNCT
ejpam-5857	315	7	y	y	PROPN
ejpam-5857	315	8	·	·	PUNCT
ejpam-5857	315	9	z	z	NOUN
ejpam-5857	315	10	)	)	PUNCT
ejpam-5857	315	11	)	)	PUNCT
ejpam-5857	316	1			PROPN
ejpam-5857	316	2	,	,	PUNCT
ejpam-5857	316	3	(	(	PUNCT
ejpam-5857	316	4	3.21	3.21	NUM
ejpam-5857	316	5	)	)	PUNCT
ejpam-5857	316	6	then	then	ADV
ejpam-5857	316	7	ψ	ψ	X
ejpam-5857	316	8	is	be	AUX
ejpam-5857	316	9	an	an	DET
ejpam-5857	316	10	intuitionistic	intuitionistic	ADJ
ejpam-5857	316	11	neutrosophic	neutrosophic	ADJ
ejpam-5857	316	12	iup	iup	NOUN
ejpam-5857	316	13	-	-	PUNCT
ejpam-5857	316	14	ideal	ideal	NOUN
ejpam-5857	316	15	of	of	ADP
ejpam-5857	316	16	x.	x.	NOUN
ejpam-5857	316	17	proof	proof	PROPN
ejpam-5857	316	18	.	.	PUNCT
ejpam-5857	317	1	assume	assume	VERB
ejpam-5857	317	2	that	that	SCONJ
ejpam-5857	317	3	ψ	ψ	NOUN
ejpam-5857	317	4	is	be	AUX
ejpam-5857	317	5	an	an	DET
ejpam-5857	317	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	317	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	317	8	iup	iup	NOUN
ejpam-5857	317	9	-	-	PUNCT
ejpam-5857	317	10	filter	filter	NOUN
ejpam-5857	317	11	of	of	ADP
ejpam-5857	317	12	x	x	PUNCT
ejpam-5857	317	13	satisfying	satisfy	VERB
ejpam-5857	317	14	the	the	DET
ejpam-5857	317	15	condition	condition	NOUN
ejpam-5857	317	16	(	(	PUNCT
ejpam-5857	317	17	3.21	3.21	NUM
ejpam-5857	317	18	)	)	PUNCT
ejpam-5857	317	19	.	.	PUNCT
ejpam-5857	318	1	by	by	ADP
ejpam-5857	318	2	assumption	assumption	NOUN
ejpam-5857	318	3	,	,	PUNCT
ejpam-5857	318	4	it	it	PRON
ejpam-5857	318	5	satisfies	satisfy	VERB
ejpam-5857	318	6	the	the	DET
ejpam-5857	318	7	conditions	condition	NOUN
ejpam-5857	318	8	(	(	PUNCT
ejpam-5857	318	9	3.8	3.8	NUM
ejpam-5857	318	10	)	)	PUNCT
ejpam-5857	318	11	,	,	PUNCT
ejpam-5857	318	12	(	(	PUNCT
ejpam-5857	318	13	3.9	3.9	NUM
ejpam-5857	318	14	)	)	PUNCT
ejpam-5857	318	15	and	and	CCONJ
ejpam-5857	318	16	(	(	PUNCT
ejpam-5857	318	17	3.10	3.10	NUM
ejpam-5857	318	18	)	)	PUNCT
ejpam-5857	318	19	.	.	PUNCT
ejpam-5857	319	1	let	let	VERB
ejpam-5857	319	2	x	x	PRON
ejpam-5857	319	3	,	,	PUNCT
ejpam-5857	319	4	y	y	PROPN
ejpam-5857	319	5	∈	∈	PROPN
ejpam-5857	319	6	x.	x.	NOUN
ejpam-5857	320	1	then	then	ADV
ejpam-5857	320	2	ψt	ψt	VERB
ejpam-5857	320	3	(	(	PUNCT
ejpam-5857	320	4	x	x	X
ejpam-5857	320	5	·	·	PUNCT
ejpam-5857	320	6	z	z	X
ejpam-5857	320	7	)	)	PUNCT
ejpam-5857	320	8	≥	≥	NOUN
ejpam-5857	320	9	(	(	PUNCT
ejpam-5857	320	10	ψt	ψt	VERB
ejpam-5857	320	11	(	(	PUNCT
ejpam-5857	320	12	y	y	NOUN
ejpam-5857	320	13	·	·	PUNCT
ejpam-5857	320	14	(	(	PUNCT
ejpam-5857	320	15	x	x	X
ejpam-5857	320	16	·	·	PUNCT
ejpam-5857	320	17	z	z	NOUN
ejpam-5857	320	18	)	)	PUNCT
ejpam-5857	320	19	)	)	PUNCT
ejpam-5857	321	1	∧	∧	NOUN
ejpam-5857	321	2	ψt	ψt	NOUN
ejpam-5857	321	3	(	(	PUNCT
ejpam-5857	321	4	y	y	NOUN
ejpam-5857	321	5	)	)	PUNCT
ejpam-5857	321	6	)	)	PUNCT
ejpam-5857	322	1	∨	∨	NUM
ejpam-5857	322	2	0.5	0.5	NUM
ejpam-5857	322	3	(	(	PUNCT
ejpam-5857	322	4	by	by	ADP
ejpam-5857	322	5	(	(	PUNCT
ejpam-5857	322	6	3.14	3.14	NUM
ejpam-5857	322	7	)	)	PUNCT
ejpam-5857	322	8	)	)	PUNCT
ejpam-5857	323	1	=	=	PUNCT
ejpam-5857	323	2	(	(	PUNCT
ejpam-5857	323	3	ψt	ψt	NOUN
ejpam-5857	323	4	(	(	PUNCT
ejpam-5857	323	5	x	x	X
ejpam-5857	323	6	·	·	PUNCT
ejpam-5857	323	7	(	(	PUNCT
ejpam-5857	323	8	y	y	PROPN
ejpam-5857	323	9	·	·	PUNCT
ejpam-5857	323	10	z	z	NOUN
ejpam-5857	323	11	)	)	PUNCT
ejpam-5857	323	12	)	)	PUNCT
ejpam-5857	324	1	∧	∧	NOUN
ejpam-5857	324	2	ψt	ψt	NOUN
ejpam-5857	324	3	(	(	PUNCT
ejpam-5857	324	4	y	y	NOUN
ejpam-5857	324	5	)	)	PUNCT
ejpam-5857	324	6	)	)	PUNCT
ejpam-5857	325	1	∨	∨	NUM
ejpam-5857	325	2	0.5	0.5	NUM
ejpam-5857	325	3	,	,	PUNCT
ejpam-5857	325	4	ψi(x	ψi(x	AUX
ejpam-5857	325	5	·	·	PUNCT
ejpam-5857	325	6	z	z	X
ejpam-5857	325	7	)	)	PUNCT
ejpam-5857	325	8	≤	≤	NOUN
ejpam-5857	325	9	(	(	PUNCT
ejpam-5857	325	10	ψi(y	ψi(y	NUM
ejpam-5857	325	11	·	·	PUNCT
ejpam-5857	325	12	(	(	PUNCT
ejpam-5857	325	13	x	x	X
ejpam-5857	325	14	·	·	PUNCT
ejpam-5857	325	15	z	z	NOUN
ejpam-5857	325	16	)	)	PUNCT
ejpam-5857	325	17	)	)	PUNCT
ejpam-5857	325	18	∨	∨	NUM
ejpam-5857	325	19	ψi(y	ψi(y	NUM
ejpam-5857	325	20	)	)	PUNCT
ejpam-5857	325	21	)	)	PUNCT
ejpam-5857	326	1	∧	∧	NOUN
ejpam-5857	326	2	0.5	0.5	NUM
ejpam-5857	326	3	(	(	PUNCT
ejpam-5857	326	4	by	by	ADP
ejpam-5857	326	5	(	(	PUNCT
ejpam-5857	326	6	3.15	3.15	NUM
ejpam-5857	326	7	)	)	PUNCT
ejpam-5857	326	8	)	)	PUNCT
ejpam-5857	327	1	=	=	SYM
ejpam-5857	327	2	(	(	PUNCT
ejpam-5857	327	3	ψi(x	ψi(x	X
ejpam-5857	327	4	·	·	PUNCT
ejpam-5857	327	5	(	(	PUNCT
ejpam-5857	327	6	y	y	PROPN
ejpam-5857	327	7	·	·	PUNCT
ejpam-5857	327	8	z	z	NOUN
ejpam-5857	327	9	)	)	PUNCT
ejpam-5857	327	10	)	)	PUNCT
ejpam-5857	328	1	∨	∨	NUM
ejpam-5857	328	2	ψi(y	ψi(y	NUM
ejpam-5857	328	3	)	)	PUNCT
ejpam-5857	328	4	)	)	PUNCT
ejpam-5857	329	1	∧	∧	NOUN
ejpam-5857	329	2	0.5	0.5	NUM
ejpam-5857	329	3	,	,	PUNCT
ejpam-5857	329	4	ψf	ψf	X
ejpam-5857	329	5	(	(	PUNCT
ejpam-5857	329	6	x	x	X
ejpam-5857	329	7	·	·	PUNCT
ejpam-5857	329	8	z	z	X
ejpam-5857	329	9	)	)	PUNCT
ejpam-5857	329	10	≥	≥	NOUN
ejpam-5857	329	11	(	(	PUNCT
ejpam-5857	329	12	ψf	ψf	X
ejpam-5857	329	13	(	(	PUNCT
ejpam-5857	329	14	y	y	PROPN
ejpam-5857	329	15	·	·	PUNCT
ejpam-5857	329	16	(	(	PUNCT
ejpam-5857	329	17	x	x	X
ejpam-5857	329	18	·	·	PUNCT
ejpam-5857	329	19	z	z	NOUN
ejpam-5857	329	20	)	)	PUNCT
ejpam-5857	329	21	)	)	PUNCT
ejpam-5857	330	1	∧	∧	NOUN
ejpam-5857	330	2	ψf	ψf	X
ejpam-5857	330	3	(	(	PUNCT
ejpam-5857	330	4	y	y	NOUN
ejpam-5857	330	5	)	)	PUNCT
ejpam-5857	330	6	)	)	PUNCT
ejpam-5857	331	1	∨	∨	NUM
ejpam-5857	331	2	0.5	0.5	NUM
ejpam-5857	331	3	(	(	PUNCT
ejpam-5857	331	4	by	by	ADP
ejpam-5857	331	5	(	(	PUNCT
ejpam-5857	331	6	3.16	3.16	NUM
ejpam-5857	331	7	)	)	PUNCT
ejpam-5857	331	8	)	)	PUNCT
ejpam-5857	332	1	k.	k.	PROPN
ejpam-5857	332	2	suayngam	suayngam	PROPN
ejpam-5857	332	3	,	,	PUNCT
ejpam-5857	332	4	p.	p.	NOUN
ejpam-5857	332	5	julatha	julatha	PROPN
ejpam-5857	332	6	,	,	PUNCT
ejpam-5857	332	7	w.	w.	PROPN
ejpam-5857	332	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	332	9	,	,	PUNCT
ejpam-5857	332	10	a.	a.	NOUN
ejpam-5857	332	11	iampan	iampan	PROPN
ejpam-5857	332	12	/	/	SYM
ejpam-5857	332	13	eur	eur	PROPN
ejpam-5857	332	14	.	.	PUNCT
ejpam-5857	333	1	j.	j.	PROPN
ejpam-5857	333	2	pure	pure	PROPN
ejpam-5857	333	3	appl	appl	PROPN
ejpam-5857	333	4	.	.	PROPN
ejpam-5857	333	5	math	math	PROPN
ejpam-5857	333	6	,	,	PUNCT
ejpam-5857	333	7	18	18	NUM
ejpam-5857	333	8	(	(	PUNCT
ejpam-5857	333	9	2	2	NUM
ejpam-5857	333	10	)	)	PUNCT
ejpam-5857	333	11	(	(	PUNCT
ejpam-5857	333	12	2025	2025	NUM
ejpam-5857	333	13	)	)	PUNCT
ejpam-5857	333	14	,	,	PUNCT
ejpam-5857	333	15	5857	5857	NUM
ejpam-5857	333	16	15	15	NUM
ejpam-5857	333	17	of	of	ADP
ejpam-5857	333	18	30	30	NUM
ejpam-5857	333	19	=	=	SYM
ejpam-5857	333	20	(	(	PUNCT
ejpam-5857	333	21	ψf	ψf	X
ejpam-5857	333	22	(	(	PUNCT
ejpam-5857	333	23	x	x	X
ejpam-5857	333	24	·	·	PUNCT
ejpam-5857	333	25	(	(	PUNCT
ejpam-5857	333	26	y	y	PROPN
ejpam-5857	333	27	·	·	PUNCT
ejpam-5857	333	28	z	z	NOUN
ejpam-5857	333	29	)	)	PUNCT
ejpam-5857	333	30	)	)	PUNCT
ejpam-5857	334	1	∧	∧	NOUN
ejpam-5857	334	2	ψf	ψf	X
ejpam-5857	334	3	(	(	PUNCT
ejpam-5857	334	4	y	y	NOUN
ejpam-5857	334	5	)	)	PUNCT
ejpam-5857	334	6	)	)	PUNCT
ejpam-5857	335	1	∨	∨	NUM
ejpam-5857	335	2	0.5	0.5	NUM
ejpam-5857	335	3	.	.	PUNCT
ejpam-5857	336	1	hence	hence	ADV
ejpam-5857	336	2	,	,	PUNCT
ejpam-5857	336	3	ψ	ψ	X
ejpam-5857	336	4	is	be	AUX
ejpam-5857	336	5	an	an	DET
ejpam-5857	336	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	336	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	336	8	iup	iup	NOUN
ejpam-5857	336	9	-	-	PUNCT
ejpam-5857	336	10	ideal	ideal	NOUN
ejpam-5857	336	11	of	of	ADP
ejpam-5857	336	12	x.	x.	NOUN
ejpam-5857	336	13	for	for	ADP
ejpam-5857	336	14	any	any	DET
ejpam-5857	336	15	fixed	fix	VERB
ejpam-5857	336	16	numbers	number	NOUN
ejpam-5857	336	17	α+	α+	ADP
ejpam-5857	336	18	,	,	PUNCT
ejpam-5857	336	19	α−	α−	ADP
ejpam-5857	336	20	∈	∈	PROPN
ejpam-5857	337	1	[	[	X
ejpam-5857	337	2	0.5	0.5	NUM
ejpam-5857	337	3	,	,	PUNCT
ejpam-5857	337	4	1	1	NUM
ejpam-5857	337	5	]	]	PUNCT
ejpam-5857	337	6	and	and	CCONJ
ejpam-5857	337	7	β+	β+	NUM
ejpam-5857	337	8	,	,	PUNCT
ejpam-5857	337	9	β−	β−	PRON
ejpam-5857	337	10	∈	∈	PROPN
ejpam-5857	338	1	[	[	X
ejpam-5857	338	2	0	0	NUM
ejpam-5857	338	3	,	,	PUNCT
ejpam-5857	338	4	0.5	0.5	NUM
ejpam-5857	338	5	)	)	PUNCT
ejpam-5857	338	6	such	such	ADJ
ejpam-5857	338	7	that	that	SCONJ
ejpam-5857	338	8	α+	α+	X
ejpam-5857	338	9	>	>	X
ejpam-5857	338	10	α−	α−	PROPN
ejpam-5857	338	11	,	,	PUNCT
ejpam-5857	338	12	β+	β+	PUNCT
ejpam-5857	338	13	>	>	X
ejpam-5857	338	14	β−	β−	PUNCT
ejpam-5857	338	15	and	and	CCONJ
ejpam-5857	338	16	a	a	DET
ejpam-5857	338	17	nonempty	nonempty	NOUN
ejpam-5857	338	18	subset	subset	VERB
ejpam-5857	338	19	g	g	NOUN
ejpam-5857	338	20	of	of	ADP
ejpam-5857	338	21	x	x	PROPN
ejpam-5857	338	22	,	,	PUNCT
ejpam-5857	338	23	an	an	DET
ejpam-5857	338	24	ins	in	NOUN
ejpam-5857	338	25	ψg	ψg	NOUN
ejpam-5857	338	26	=	=	SYM
ejpam-5857	338	27	(	(	PUNCT
ejpam-5857	338	28	x	x	X
ejpam-5857	338	29	,	,	PUNCT
ejpam-5857	338	30	ψg	ψg	PROPN
ejpam-5857	338	31	t	t	PROPN
ejpam-5857	338	32	[	[	PUNCT
ejpam-5857	338	33	α+	α+	X
ejpam-5857	338	34	α−	α−	ADP
ejpam-5857	338	35	]	]	PUNCT
ejpam-5857	338	36	,	,	PUNCT
ejpam-5857	338	37	ψ	ψ	X
ejpam-5857	338	38	g	g	NOUN
ejpam-5857	338	39	i	i	PRON
ejpam-5857	338	40	[	[	PUNCT
ejpam-5857	338	41	β−	β−	PROPN
ejpam-5857	338	42	β+	β+	NUM
ejpam-5857	338	43	]	]	X
ejpam-5857	338	44	,	,	PUNCT
ejpam-5857	338	45	ψ	ψ	X
ejpam-5857	338	46	g	g	PROPN
ejpam-5857	338	47	f	f	PROPN
ejpam-5857	339	1	[	[	X
ejpam-5857	339	2	0.5	0.5	NUM
ejpam-5857	339	3	]	]	PUNCT
ejpam-5857	339	4	)	)	PUNCT
ejpam-5857	339	5	in	in	ADP
ejpam-5857	339	6	x	x	SYM
ejpam-5857	339	7	where	where	SCONJ
ejpam-5857	339	8	ψg	ψg	NOUN
ejpam-5857	339	9	t	t	PROPN
ejpam-5857	339	10	[	[	PUNCT
ejpam-5857	339	11	α+	α+	X
ejpam-5857	339	12	α−	α−	ADP
ejpam-5857	339	13	]	]	PUNCT
ejpam-5857	339	14	,	,	PUNCT
ejpam-5857	339	15	ψ	ψ	X
ejpam-5857	339	16	g	g	NOUN
ejpam-5857	339	17	i	i	PRON
ejpam-5857	339	18	[	[	PUNCT
ejpam-5857	339	19	β−	β−	PROPN
ejpam-5857	339	20	β+	β+	PUNCT
ejpam-5857	339	21	]	]	PUNCT
ejpam-5857	339	22	and	and	CCONJ
ejpam-5857	339	23	ψ	ψ	X
ejpam-5857	339	24	g	g	PROPN
ejpam-5857	339	25	f	f	PROPN
ejpam-5857	339	26	[	[	X
ejpam-5857	339	27	0.5	0.5	NUM
ejpam-5857	339	28	]	]	PUNCT
ejpam-5857	339	29	are	be	AUX
ejpam-5857	339	30	function	function	NOUN
ejpam-5857	339	31	on	on	ADP
ejpam-5857	339	32	x	x	PUNCT
ejpam-5857	339	33	which	which	PRON
ejpam-5857	339	34	are	be	AUX
ejpam-5857	339	35	given	give	VERB
ejpam-5857	339	36	as	as	SCONJ
ejpam-5857	339	37	follows	follow	VERB
ejpam-5857	339	38	:	:	PUNCT
ejpam-5857	340	1	ψg	ψg	PROPN
ejpam-5857	340	2	t	t	PROPN
ejpam-5857	340	3	[	[	PUNCT
ejpam-5857	340	4	α+	α+	X
ejpam-5857	340	5	α−	α−	ADP
ejpam-5857	340	6	]	]	PUNCT
ejpam-5857	340	7	(	(	PUNCT
ejpam-5857	340	8	x	x	X
ejpam-5857	340	9	)	)	PUNCT
ejpam-5857	340	10	=	=	PRON
ejpam-5857	340	11	{	{	PUNCT
ejpam-5857	340	12	α+	α+	X
ejpam-5857	341	1	if	if	SCONJ
ejpam-5857	341	2	x	x	SYM
ejpam-5857	341	3	∈	∈	PROPN
ejpam-5857	341	4	g	g	NOUN
ejpam-5857	341	5	α−	α−	ADP
ejpam-5857	341	6	otherwise	otherwise	ADV
ejpam-5857	341	7	,	,	PUNCT
ejpam-5857	341	8	ψg	ψg	PROPN
ejpam-5857	342	1	i	i	PRON
ejpam-5857	342	2	[	[	PUNCT
ejpam-5857	342	3	β−	β−	PUNCT
ejpam-5857	342	4	β+	β+	PUNCT
ejpam-5857	342	5	]	]	X
ejpam-5857	342	6	(	(	PUNCT
ejpam-5857	342	7	x	x	X
ejpam-5857	342	8	)	)	PUNCT
ejpam-5857	342	9	=	=	NOUN
ejpam-5857	342	10	{	{	PUNCT
ejpam-5857	342	11	β−	β−	INTJ
ejpam-5857	343	1	if	if	SCONJ
ejpam-5857	343	2	x	x	SYM
ejpam-5857	343	3	∈	∈	PROPN
ejpam-5857	343	4	g	g	NOUN
ejpam-5857	343	5	β+	β+	PUNCT
ejpam-5857	343	6	otherwise	otherwise	ADV
ejpam-5857	343	7	,	,	PUNCT
ejpam-5857	343	8	ψg	ψg	PROPN
ejpam-5857	343	9	f	f	PROPN
ejpam-5857	344	1	[	[	X
ejpam-5857	344	2	0.5](x	0.5](x	NUM
ejpam-5857	344	3	)	)	PUNCT
ejpam-5857	344	4	=	=	SYM
ejpam-5857	344	5	0.5	0.5	NUM
ejpam-5857	344	6	for	for	ADP
ejpam-5857	344	7	all	all	DET
ejpam-5857	344	8	x	x	SYM
ejpam-5857	344	9	∈	∈	PROPN
ejpam-5857	344	10	x.	x.	NOUN
ejpam-5857	344	11	lemma	lemma	PROPN
ejpam-5857	344	12	3	3	X
ejpam-5857	344	13	.	.	PUNCT
ejpam-5857	345	1	let	let	VERB
ejpam-5857	345	2	g	g	PRON
ejpam-5857	345	3	be	be	AUX
ejpam-5857	345	4	a	a	DET
ejpam-5857	345	5	nonempty	nonempty	ADJ
ejpam-5857	345	6	subset	subset	NOUN
ejpam-5857	345	7	of	of	ADP
ejpam-5857	345	8	x.	x.	NOUN
ejpam-5857	345	9	then	then	ADV
ejpam-5857	345	10	the	the	DET
ejpam-5857	345	11	constant	constant	ADJ
ejpam-5857	345	12	0	0	NUM
ejpam-5857	345	13	of	of	ADP
ejpam-5857	345	14	x	x	PRON
ejpam-5857	345	15	is	be	AUX
ejpam-5857	345	16	in	in	ADP
ejpam-5857	345	17	g	g	PROPN
ejpam-5857	345	18	if	if	SCONJ
ejpam-5857	346	1	and	and	CCONJ
ejpam-5857	346	2	only	only	ADV
ejpam-5857	346	3	if	if	SCONJ
ejpam-5857	346	4	the	the	DET
ejpam-5857	346	5	characteristic	characteristic	ADJ
ejpam-5857	346	6	ins	in	NOUN
ejpam-5857	346	7	ψg	ψg	PROPN
ejpam-5857	346	8	satisfies	satisfy	VERB
ejpam-5857	346	9	the	the	DET
ejpam-5857	346	10	conditions	condition	NOUN
ejpam-5857	346	11	(	(	PUNCT
ejpam-5857	346	12	3.8	3.8	NUM
ejpam-5857	346	13	)	)	PUNCT
ejpam-5857	346	14	,	,	PUNCT
ejpam-5857	346	15	(	(	PUNCT
ejpam-5857	346	16	3.9	3.9	NUM
ejpam-5857	346	17	)	)	PUNCT
ejpam-5857	346	18	and	and	CCONJ
ejpam-5857	346	19	(	(	PUNCT
ejpam-5857	346	20	3.10	3.10	NUM
ejpam-5857	346	21	)	)	PUNCT
ejpam-5857	346	22	.	.	PUNCT
ejpam-5857	347	1	proof	proof	NOUN
ejpam-5857	347	2	.	.	PUNCT
ejpam-5857	348	1	assume	assume	VERB
ejpam-5857	348	2	that	that	SCONJ
ejpam-5857	348	3	0	0	NUM
ejpam-5857	348	4	∈	∈	PROPN
ejpam-5857	348	5	g.	g.	NOUN
ejpam-5857	348	6	then	then	ADV
ejpam-5857	348	7	ψg	ψg	PROPN
ejpam-5857	348	8	t	t	PROPN
ejpam-5857	348	9	[	[	PUNCT
ejpam-5857	348	10	α+	α+	X
ejpam-5857	348	11	α−	α−	ADP
ejpam-5857	348	12	]	]	X
ejpam-5857	348	13	(	(	PUNCT
ejpam-5857	348	14	0	0	NUM
ejpam-5857	348	15	)	)	PUNCT
ejpam-5857	348	16	=	=	SYM
ejpam-5857	348	17	α+	α+	X
ejpam-5857	348	18	,	,	PUNCT
ejpam-5857	348	19	ψg	ψg	NOUN
ejpam-5857	349	1	i	i	PRON
ejpam-5857	349	2	[	[	PUNCT
ejpam-5857	349	3	β−	β−	PUNCT
ejpam-5857	349	4	β+	β+	PUNCT
ejpam-5857	349	5	]	]	X
ejpam-5857	349	6	(	(	PUNCT
ejpam-5857	349	7	0	0	NUM
ejpam-5857	349	8	)	)	PUNCT
ejpam-5857	349	9	=	=	SYM
ejpam-5857	349	10	β−	β−	PROPN
ejpam-5857	349	11	and	and	CCONJ
ejpam-5857	349	12	ψg	ψg	X
ejpam-5857	349	13	f	f	PROPN
ejpam-5857	350	1	[	[	X
ejpam-5857	350	2	0.5](0	0.5](0	X
ejpam-5857	350	3	)	)	PUNCT
ejpam-5857	350	4	=	=	SYM
ejpam-5857	350	5	0.5	0.5	NUM
ejpam-5857	350	6	.	.	PUNCT
ejpam-5857	351	1	thus	thus	ADV
ejpam-5857	351	2	,	,	PUNCT
ejpam-5857	351	3	ψg	ψg	PROPN
ejpam-5857	351	4	t	t	PROPN
ejpam-5857	351	5	[	[	PUNCT
ejpam-5857	351	6	α+	α+	X
ejpam-5857	351	7	α−	α−	ADP
ejpam-5857	351	8	]	]	X
ejpam-5857	351	9	(	(	PUNCT
ejpam-5857	351	10	0	0	NUM
ejpam-5857	351	11	)	)	PUNCT
ejpam-5857	351	12	=	=	SYM
ejpam-5857	351	13	α+	α+	PUNCT
ejpam-5857	351	14	≥	≥	NUM
ejpam-5857	351	15	ψg	ψg	X
ejpam-5857	351	16	t	t	PROPN
ejpam-5857	351	17	[	[	PUNCT
ejpam-5857	351	18	α+	α+	X
ejpam-5857	351	19	α−	α−	ADP
ejpam-5857	351	20	]	]	PUNCT
ejpam-5857	351	21	(	(	PUNCT
ejpam-5857	351	22	x	x	NOUN
ejpam-5857	351	23	)	)	PUNCT
ejpam-5857	351	24	,	,	PUNCT
ejpam-5857	351	25	ψ	ψ	X
ejpam-5857	351	26	g	g	NOUN
ejpam-5857	351	27	i	i	PRON
ejpam-5857	351	28	[	[	PUNCT
ejpam-5857	351	29	β−	β−	PUNCT
ejpam-5857	351	30	β+	β+	PUNCT
ejpam-5857	351	31	]	]	X
ejpam-5857	351	32	(	(	PUNCT
ejpam-5857	351	33	0	0	NUM
ejpam-5857	351	34	)	)	PUNCT
ejpam-5857	351	35	=	=	SYM
ejpam-5857	352	1	β−	β−	PUNCT
ejpam-5857	352	2	≤	≤	NUM
ejpam-5857	352	3	ψg	ψg	NOUN
ejpam-5857	353	1	i	i	PRON
ejpam-5857	353	2	[	[	PUNCT
ejpam-5857	353	3	β−	β−	PUNCT
ejpam-5857	353	4	β+	β+	PUNCT
ejpam-5857	353	5	]	]	X
ejpam-5857	353	6	(	(	PUNCT
ejpam-5857	353	7	x	x	X
ejpam-5857	353	8	)	)	PUNCT
ejpam-5857	353	9	and	and	CCONJ
ejpam-5857	353	10	ψ	ψ	X
ejpam-5857	353	11	g	g	PROPN
ejpam-5857	353	12	f	f	PROPN
ejpam-5857	354	1	[	[	X
ejpam-5857	354	2	0.5](0	0.5](0	X
ejpam-5857	354	3	)	)	PUNCT
ejpam-5857	354	4	=	=	SYM
ejpam-5857	354	5	0.5	0.5	NUM
ejpam-5857	354	6	≥	≥	NOUN
ejpam-5857	354	7	ψg	ψg	X
ejpam-5857	354	8	f	f	PROPN
ejpam-5857	355	1	[	[	X
ejpam-5857	355	2	0.5](x	0.5](x	NUM
ejpam-5857	355	3	)	)	PUNCT
ejpam-5857	355	4	for	for	ADP
ejpam-5857	355	5	all	all	PRON
ejpam-5857	355	6	x	x	SYM
ejpam-5857	355	7	∈	∈	PROPN
ejpam-5857	355	8	x	x	NOUN
ejpam-5857	355	9	,	,	PUNCT
ejpam-5857	355	10	that	that	ADV
ejpam-5857	355	11	is	is	ADV
ejpam-5857	355	12	,	,	PUNCT
ejpam-5857	355	13	ψg	ψg	PROPN
ejpam-5857	355	14	satisfies	satisfy	VERB
ejpam-5857	355	15	the	the	DET
ejpam-5857	355	16	conditions	condition	NOUN
ejpam-5857	355	17	(	(	PUNCT
ejpam-5857	355	18	3.8	3.8	NUM
ejpam-5857	355	19	)	)	PUNCT
ejpam-5857	355	20	,	,	PUNCT
ejpam-5857	355	21	(	(	PUNCT
ejpam-5857	355	22	3.9	3.9	NUM
ejpam-5857	355	23	)	)	PUNCT
ejpam-5857	355	24	and	and	CCONJ
ejpam-5857	355	25	(	(	PUNCT
ejpam-5857	355	26	3.10	3.10	NUM
ejpam-5857	355	27	)	)	PUNCT
ejpam-5857	355	28	.	.	PUNCT
ejpam-5857	356	1	conversely	conversely	ADV
ejpam-5857	356	2	,	,	PUNCT
ejpam-5857	356	3	assume	assume	VERB
ejpam-5857	356	4	that	that	SCONJ
ejpam-5857	356	5	ψg	ψg	PROPN
ejpam-5857	356	6	satisfies	satisfy	VERB
ejpam-5857	356	7	the	the	DET
ejpam-5857	356	8	conditions	condition	NOUN
ejpam-5857	356	9	(	(	PUNCT
ejpam-5857	356	10	3.8	3.8	NUM
ejpam-5857	356	11	)	)	PUNCT
ejpam-5857	356	12	,	,	PUNCT
ejpam-5857	356	13	(	(	PUNCT
ejpam-5857	356	14	3.9	3.9	NUM
ejpam-5857	356	15	)	)	PUNCT
ejpam-5857	356	16	and	and	CCONJ
ejpam-5857	356	17	(	(	PUNCT
ejpam-5857	356	18	3.10	3.10	NUM
ejpam-5857	356	19	)	)	PUNCT
ejpam-5857	356	20	.	.	PUNCT
ejpam-5857	357	1	then	then	ADV
ejpam-5857	357	2	ψg	ψg	X
ejpam-5857	357	3	t	t	PROPN
ejpam-5857	357	4	[	[	PUNCT
ejpam-5857	357	5	α+	α+	X
ejpam-5857	357	6	α−	α−	ADP
ejpam-5857	357	7	]	]	X
ejpam-5857	357	8	(	(	PUNCT
ejpam-5857	357	9	0	0	NUM
ejpam-5857	357	10	)	)	PUNCT
ejpam-5857	357	11	≥	≥	NOUN
ejpam-5857	357	12	ψg	ψg	PROPN
ejpam-5857	357	13	t	t	PROPN
ejpam-5857	357	14	[	[	PUNCT
ejpam-5857	357	15	α+	α+	X
ejpam-5857	357	16	α−	α−	ADP
ejpam-5857	357	17	]	]	PUNCT
ejpam-5857	357	18	(	(	PUNCT
ejpam-5857	357	19	x	x	X
ejpam-5857	357	20	)	)	PUNCT
ejpam-5857	357	21	for	for	ADP
ejpam-5857	357	22	all	all	DET
ejpam-5857	357	23	x	x	SYM
ejpam-5857	357	24	∈	∈	PROPN
ejpam-5857	357	25	x.	x.	NOUN
ejpam-5857	357	26	since	since	SCONJ
ejpam-5857	357	27	g	g	PROPN
ejpam-5857	357	28	is	be	AUX
ejpam-5857	357	29	a	a	DET
ejpam-5857	357	30	nonempty	nonempty	ADJ
ejpam-5857	357	31	subset	subset	NOUN
ejpam-5857	357	32	of	of	ADP
ejpam-5857	357	33	x	x	PRON
ejpam-5857	357	34	,	,	PUNCT
ejpam-5857	357	35	we	we	PRON
ejpam-5857	357	36	let	let	VERB
ejpam-5857	357	37	a	a	DET
ejpam-5857	357	38	∈	∈	PROPN
ejpam-5857	357	39	g.	g.	NOUN
ejpam-5857	357	40	then	then	ADV
ejpam-5857	357	41	ψg	ψg	PROPN
ejpam-5857	357	42	t	t	PROPN
ejpam-5857	357	43	[	[	PUNCT
ejpam-5857	358	1	α+	α+	X
ejpam-5857	358	2	α−	α−	ADP
ejpam-5857	358	3	]	]	X
ejpam-5857	358	4	(	(	PUNCT
ejpam-5857	358	5	0	0	NUM
ejpam-5857	358	6	)	)	PUNCT
ejpam-5857	358	7	≥	≥	NOUN
ejpam-5857	358	8	ψg	ψg	PROPN
ejpam-5857	358	9	t	t	PROPN
ejpam-5857	358	10	[	[	PUNCT
ejpam-5857	358	11	α+	α+	X
ejpam-5857	358	12	α−	α−	ADP
ejpam-5857	358	13	]	]	X
ejpam-5857	358	14	(	(	PUNCT
ejpam-5857	358	15	a	a	X
ejpam-5857	358	16	)	)	PUNCT
ejpam-5857	358	17	=	=	SYM
ejpam-5857	358	18	α+	α+	NOUN
ejpam-5857	358	19	,	,	PUNCT
ejpam-5857	358	20	so	so	SCONJ
ejpam-5857	358	21	ψg	ψg	PROPN
ejpam-5857	358	22	t	t	PROPN
ejpam-5857	358	23	[	[	PUNCT
ejpam-5857	358	24	α+	α+	X
ejpam-5857	358	25	α−	α−	ADP
ejpam-5857	358	26	]	]	X
ejpam-5857	358	27	(	(	PUNCT
ejpam-5857	358	28	0	0	NUM
ejpam-5857	358	29	)	)	PUNCT
ejpam-5857	358	30	=	=	SYM
ejpam-5857	359	1	α+	α+	NOUN
ejpam-5857	359	2	.	.	PUNCT
ejpam-5857	360	1	hence	hence	ADV
ejpam-5857	360	2	,	,	PUNCT
ejpam-5857	360	3	0	0	NUM
ejpam-5857	360	4	∈	∈	PROPN
ejpam-5857	360	5	g.	g.	NOUN
ejpam-5857	360	6	theorem	theorem	VERB
ejpam-5857	360	7	6	6	NUM
ejpam-5857	360	8	.	.	PUNCT
ejpam-5857	361	1	a	a	DET
ejpam-5857	361	2	nonempty	nonempty	NOUN
ejpam-5857	361	3	subset	subset	VERB
ejpam-5857	361	4	g	g	NOUN
ejpam-5857	361	5	is	be	AUX
ejpam-5857	361	6	an	an	DET
ejpam-5857	361	7	iup	iup	NOUN
ejpam-5857	361	8	-	-	PUNCT
ejpam-5857	361	9	subalgebra	subalgebra	NOUN
ejpam-5857	361	10	of	of	ADP
ejpam-5857	361	11	x	x	PRON
ejpam-5857	361	12	if	if	SCONJ
ejpam-5857	361	13	and	and	CCONJ
ejpam-5857	361	14	only	only	ADV
ejpam-5857	361	15	if	if	SCONJ
ejpam-5857	361	16	the	the	DET
ejpam-5857	361	17	characteristic	characteristic	ADJ
ejpam-5857	361	18	ins	ins	PROPN
ejpam-5857	361	19	ψg	ψg	PROPN
ejpam-5857	361	20	is	be	AUX
ejpam-5857	361	21	an	an	DET
ejpam-5857	361	22	intuitionistic	intuitionistic	ADJ
ejpam-5857	361	23	neutrosophic	neutrosophic	ADJ
ejpam-5857	361	24	iup	iup	NOUN
ejpam-5857	361	25	-	-	PUNCT
ejpam-5857	361	26	subalgebra	subalgebra	NOUN
ejpam-5857	361	27	of	of	ADP
ejpam-5857	361	28	x.	x.	NOUN
ejpam-5857	361	29	proof	proof	PROPN
ejpam-5857	361	30	.	.	PUNCT
ejpam-5857	362	1	assume	assume	VERB
ejpam-5857	362	2	that	that	SCONJ
ejpam-5857	362	3	g	g	PROPN
ejpam-5857	362	4	is	be	AUX
ejpam-5857	362	5	an	an	DET
ejpam-5857	362	6	iup	iup	NOUN
ejpam-5857	362	7	-	-	PUNCT
ejpam-5857	362	8	subalgebra	subalgebra	NOUN
ejpam-5857	362	9	of	of	ADP
ejpam-5857	362	10	x.	x.	NOUN
ejpam-5857	362	11	let	let	VERB
ejpam-5857	362	12	x	x	PRON
ejpam-5857	362	13	,	,	PUNCT
ejpam-5857	362	14	y	y	PROPN
ejpam-5857	362	15	∈	∈	PROPN
ejpam-5857	362	16	x.	x.	NOUN
ejpam-5857	362	17	then	then	ADV
ejpam-5857	362	18	case	case	NOUN
ejpam-5857	362	19	1	1	NUM
ejpam-5857	362	20	:	:	PUNCT
ejpam-5857	362	21	suppose	suppose	VERB
ejpam-5857	362	22	x	x	PRON
ejpam-5857	362	23	,	,	PUNCT
ejpam-5857	362	24	y	y	PROPN
ejpam-5857	362	25	∈	∈	PROPN
ejpam-5857	362	26	g.	g.	NOUN
ejpam-5857	362	27	then	then	ADV
ejpam-5857	362	28	ψg	ψg	PROPN
ejpam-5857	362	29	t	t	PROPN
ejpam-5857	362	30	[	[	PUNCT
ejpam-5857	362	31	α+	α+	X
ejpam-5857	362	32	α−	α−	ADP
ejpam-5857	362	33	]	]	PUNCT
ejpam-5857	362	34	(	(	PUNCT
ejpam-5857	362	35	x	x	X
ejpam-5857	362	36	)	)	PUNCT
ejpam-5857	362	37	=	=	SYM
ejpam-5857	362	38	α+	α+	PUNCT
ejpam-5857	362	39	and	and	CCONJ
ejpam-5857	362	40	ψg	ψg	X
ejpam-5857	362	41	t	t	PROPN
ejpam-5857	362	42	[	[	PUNCT
ejpam-5857	362	43	α+	α+	X
ejpam-5857	362	44	α−	α−	ADP
ejpam-5857	362	45	]	]	X
ejpam-5857	362	46	(	(	PUNCT
ejpam-5857	362	47	y	y	NOUN
ejpam-5857	362	48	)	)	PUNCT
ejpam-5857	362	49	=	=	SYM
ejpam-5857	362	50	α+	α+	NOUN
ejpam-5857	362	51	.	.	PUNCT
ejpam-5857	363	1	since	since	SCONJ
ejpam-5857	363	2	g	g	PROPN
ejpam-5857	363	3	be	be	AUX
ejpam-5857	363	4	an	an	DET
ejpam-5857	363	5	iup	iup	NOUN
ejpam-5857	363	6	-	-	PUNCT
ejpam-5857	363	7	subalgebra	subalgebra	NOUN
ejpam-5857	363	8	of	of	ADP
ejpam-5857	363	9	x	x	PRON
ejpam-5857	363	10	,	,	PUNCT
ejpam-5857	363	11	we	we	PRON
ejpam-5857	363	12	have	have	VERB
ejpam-5857	363	13	x	x	X
ejpam-5857	363	14	·	·	PUNCT
ejpam-5857	363	15	y	y	PROPN
ejpam-5857	363	16	∈	∈	PROPN
ejpam-5857	363	17	g.	g.	PROPN
ejpam-5857	364	1	thus	thus	ADV
ejpam-5857	364	2	,	,	PUNCT
ejpam-5857	364	3	ψg	ψg	PROPN
ejpam-5857	364	4	t	t	PROPN
ejpam-5857	364	5	[	[	PUNCT
ejpam-5857	364	6	α+	α+	X
ejpam-5857	364	7	α−	α−	ADP
ejpam-5857	364	8	]	]	PUNCT
ejpam-5857	364	9	(	(	PUNCT
ejpam-5857	364	10	x	x	SYM
ejpam-5857	364	11	·	·	PUNCT
ejpam-5857	364	12	y	y	X
ejpam-5857	364	13	)	)	PUNCT
ejpam-5857	364	14	=	=	PRON
ejpam-5857	364	15	α+	α+	PUNCT
ejpam-5857	364	16	≥	≥	X
ejpam-5857	364	17	α+	α+	PUNCT
ejpam-5857	364	18	∨	∨	X
ejpam-5857	364	19	0.5	0.5	NUM
ejpam-5857	364	20	=	=	SYM
ejpam-5857	364	21	(	(	PUNCT
ejpam-5857	364	22	α+	α+	X
ejpam-5857	364	23	∧	∧	PROPN
ejpam-5857	364	24	α+	α+	PRON
ejpam-5857	364	25	)	)	PUNCT
ejpam-5857	364	26	∨	∨	NOUN
ejpam-5857	364	27	0.5	0.5	NUM
ejpam-5857	364	28	=	=	SYM
ejpam-5857	364	29	(	(	PUNCT
ejpam-5857	364	30	ψg	ψg	NOUN
ejpam-5857	364	31	t	t	PROPN
ejpam-5857	364	32	[	[	PUNCT
ejpam-5857	364	33	α+	α+	X
ejpam-5857	364	34	α−	α−	ADP
ejpam-5857	364	35	]	]	PUNCT
ejpam-5857	364	36	(	(	PUNCT
ejpam-5857	364	37	x	x	X
ejpam-5857	364	38	)	)	PUNCT
ejpam-5857	364	39	∧	∧	PROPN
ejpam-5857	364	40	ψg	ψg	PROPN
ejpam-5857	364	41	t	t	PROPN
ejpam-5857	364	42	[	[	PUNCT
ejpam-5857	364	43	α+	α+	X
ejpam-5857	364	44	α−	α−	ADP
ejpam-5857	364	45	]	]	X
ejpam-5857	364	46	(	(	PUNCT
ejpam-5857	364	47	y	y	NOUN
ejpam-5857	364	48	)	)	PUNCT
ejpam-5857	364	49	)	)	PUNCT
ejpam-5857	364	50	∨	∨	NUM
ejpam-5857	364	51	0.5	0.5	NUM
ejpam-5857	364	52	.	.	PUNCT
ejpam-5857	364	53	case	case	NOUN
ejpam-5857	364	54	2	2	NUM
ejpam-5857	364	55	:	:	PUNCT
ejpam-5857	364	56	suppose	suppose	VERB
ejpam-5857	364	57	x	x	X
ejpam-5857	364	58	/∈	/∈	PUNCT
ejpam-5857	364	59	g	g	NOUN
ejpam-5857	364	60	or	or	CCONJ
ejpam-5857	364	61	y	y	PROPN
ejpam-5857	364	62	/∈	/∈	PUNCT
ejpam-5857	365	1	g.	g.	PROPN
ejpam-5857	366	1	then	then	ADV
ejpam-5857	366	2	ψg	ψg	PROPN
ejpam-5857	366	3	t	t	PROPN
ejpam-5857	366	4	[	[	PUNCT
ejpam-5857	366	5	α+	α+	X
ejpam-5857	366	6	α−	α−	ADP
ejpam-5857	366	7	]	]	PUNCT
ejpam-5857	366	8	(	(	PUNCT
ejpam-5857	366	9	x	x	X
ejpam-5857	366	10	)	)	PUNCT
ejpam-5857	366	11	=	=	SYM
ejpam-5857	367	1	α−	α−	ADP
ejpam-5857	367	2	or	or	CCONJ
ejpam-5857	367	3	ψg	ψg	X
ejpam-5857	367	4	t	t	PROPN
ejpam-5857	367	5	[	[	PUNCT
ejpam-5857	367	6	α+	α+	X
ejpam-5857	367	7	α−	α−	ADP
ejpam-5857	367	8	]	]	X
ejpam-5857	367	9	(	(	PUNCT
ejpam-5857	367	10	y	y	NOUN
ejpam-5857	367	11	)	)	PUNCT
ejpam-5857	367	12	=	=	SYM
ejpam-5857	367	13	α−.	α−.	NOUN
ejpam-5857	367	14	thus	thus	ADV
ejpam-5857	367	15	,	,	PUNCT
ejpam-5857	367	16	ψg	ψg	PROPN
ejpam-5857	367	17	t	t	PROPN
ejpam-5857	367	18	[	[	PUNCT
ejpam-5857	367	19	α+	α+	X
ejpam-5857	367	20	α−	α−	ADP
ejpam-5857	367	21	]	]	PUNCT
ejpam-5857	367	22	(	(	PUNCT
ejpam-5857	367	23	x	x	SYM
ejpam-5857	367	24	·	·	PUNCT
ejpam-5857	367	25	y	y	X
ejpam-5857	367	26	)	)	PUNCT
ejpam-5857	367	27	≥	≥	NOUN
ejpam-5857	367	28	α−	α−	ADP
ejpam-5857	367	29	≥	≥	NOUN
ejpam-5857	367	30	α−	α−	ADP
ejpam-5857	367	31	∨	∨	NUM
ejpam-5857	367	32	0.5	0.5	NUM
ejpam-5857	367	33	=	=	SYM
ejpam-5857	367	34	(	(	PUNCT
ejpam-5857	367	35	ψg	ψg	NOUN
ejpam-5857	367	36	t	t	PROPN
ejpam-5857	367	37	[	[	PUNCT
ejpam-5857	367	38	α+	α+	X
ejpam-5857	367	39	α−	α−	ADP
ejpam-5857	367	40	]	]	PUNCT
ejpam-5857	367	41	(	(	PUNCT
ejpam-5857	367	42	x	x	X
ejpam-5857	367	43	)	)	PUNCT
ejpam-5857	367	44	∧	∧	PROPN
ejpam-5857	367	45	ψg	ψg	PROPN
ejpam-5857	367	46	t	t	PROPN
ejpam-5857	367	47	[	[	PUNCT
ejpam-5857	367	48	α+	α+	X
ejpam-5857	367	49	α−	α−	ADP
ejpam-5857	367	50	]	]	X
ejpam-5857	367	51	(	(	PUNCT
ejpam-5857	367	52	y	y	NOUN
ejpam-5857	367	53	)	)	PUNCT
ejpam-5857	367	54	)	)	PUNCT
ejpam-5857	367	55	∨	∨	NUM
ejpam-5857	367	56	0.5	0.5	NUM
ejpam-5857	367	57	.	.	PUNCT
ejpam-5857	367	58	case	case	NOUN
ejpam-5857	367	59	1	1	NUM
ejpam-5857	367	60	’	'	PUNCT
ejpam-5857	367	61	:	:	PUNCT
ejpam-5857	367	62	suppose	suppose	VERB
ejpam-5857	367	63	x	x	PRON
ejpam-5857	367	64	,	,	PUNCT
ejpam-5857	367	65	y	y	PROPN
ejpam-5857	367	66	∈	∈	PROPN
ejpam-5857	367	67	g.	g.	NOUN
ejpam-5857	367	68	then	then	ADV
ejpam-5857	367	69	ψg	ψg	PROPN
ejpam-5857	368	1	i	i	PRON
ejpam-5857	368	2	[	[	PUNCT
ejpam-5857	368	3	β−	β−	PUNCT
ejpam-5857	368	4	β+	β+	PUNCT
ejpam-5857	368	5	]	]	X
ejpam-5857	368	6	(	(	PUNCT
ejpam-5857	368	7	x	x	X
ejpam-5857	368	8	)	)	PUNCT
ejpam-5857	368	9	=	=	SYM
ejpam-5857	368	10	β−	β−	PROPN
ejpam-5857	368	11	and	and	CCONJ
ejpam-5857	368	12	ψg	ψg	INTJ
ejpam-5857	369	1	i	i	PRON
ejpam-5857	369	2	[	[	PUNCT
ejpam-5857	369	3	β−	β−	PUNCT
ejpam-5857	369	4	β+	β+	PUNCT
ejpam-5857	369	5	]	]	X
ejpam-5857	369	6	(	(	PUNCT
ejpam-5857	369	7	y	y	NOUN
ejpam-5857	369	8	)	)	PUNCT
ejpam-5857	369	9	=	=	SYM
ejpam-5857	369	10	β−.	β−.	NOUN
ejpam-5857	369	11	since	since	SCONJ
ejpam-5857	369	12	g	g	PROPN
ejpam-5857	369	13	be	be	AUX
ejpam-5857	369	14	an	an	DET
ejpam-5857	369	15	iup	iup	NOUN
ejpam-5857	369	16	-	-	PUNCT
ejpam-5857	369	17	subalgebra	subalgebra	NOUN
ejpam-5857	369	18	of	of	ADP
ejpam-5857	369	19	x	x	PRON
ejpam-5857	369	20	,	,	PUNCT
ejpam-5857	369	21	we	we	PRON
ejpam-5857	369	22	have	have	VERB
ejpam-5857	369	23	x	x	X
ejpam-5857	369	24	·	·	PUNCT
ejpam-5857	369	25	y	y	PROPN
ejpam-5857	369	26	∈	∈	PROPN
ejpam-5857	369	27	g.	g.	PROPN
ejpam-5857	370	1	thus	thus	ADV
ejpam-5857	370	2	,	,	PUNCT
ejpam-5857	370	3	ψg	ψg	PROPN
ejpam-5857	371	1	i	i	PRON
ejpam-5857	371	2	[	[	PUNCT
ejpam-5857	371	3	β−	β−	PUNCT
ejpam-5857	371	4	β+	β+	PUNCT
ejpam-5857	371	5	]	]	X
ejpam-5857	371	6	(	(	PUNCT
ejpam-5857	371	7	x	x	SYM
ejpam-5857	371	8	·	·	PUNCT
ejpam-5857	371	9	y	y	X
ejpam-5857	371	10	)	)	PUNCT
ejpam-5857	371	11	=	=	PUNCT
ejpam-5857	372	1	β−	β−	PUNCT
ejpam-5857	372	2	≤	≤	NUM
ejpam-5857	372	3	β−	β−	PUNCT
ejpam-5857	373	1	∧	∧	NOUN
ejpam-5857	373	2	0.5	0.5	NUM
ejpam-5857	373	3	=	=	SYM
ejpam-5857	373	4	(	(	PUNCT
ejpam-5857	373	5	β−	β−	PROPN
ejpam-5857	373	6	∨	∨	NUM
ejpam-5857	373	7	β−	β−	NUM
ejpam-5857	373	8	)	)	PUNCT
ejpam-5857	373	9	∧	∧	NOUN
ejpam-5857	373	10	0.5	0.5	NUM
ejpam-5857	373	11	=	=	SYM
ejpam-5857	373	12	(	(	PUNCT
ejpam-5857	373	13	ψg	ψg	NOUN
ejpam-5857	373	14	i	i	PRON
ejpam-5857	373	15	[	[	PUNCT
ejpam-5857	373	16	β−	β−	PUNCT
ejpam-5857	373	17	β+	β+	PUNCT
ejpam-5857	373	18	]	]	X
ejpam-5857	373	19	(	(	PUNCT
ejpam-5857	373	20	x	x	X
ejpam-5857	373	21	)	)	PUNCT
ejpam-5857	373	22	∨	∨	NUM
ejpam-5857	373	23	ψg	ψg	NOUN
ejpam-5857	374	1	i	i	PRON
ejpam-5857	374	2	[	[	PUNCT
ejpam-5857	374	3	β−	β−	PUNCT
ejpam-5857	374	4	β+	β+	PUNCT
ejpam-5857	374	5	]	]	X
ejpam-5857	374	6	(	(	PUNCT
ejpam-5857	374	7	y	y	NOUN
ejpam-5857	374	8	)	)	PUNCT
ejpam-5857	374	9	)	)	PUNCT
ejpam-5857	375	1	∧	∧	NOUN
ejpam-5857	375	2	0.5	0.5	NUM
ejpam-5857	375	3	.	.	PUNCT
ejpam-5857	375	4	case	case	NOUN
ejpam-5857	375	5	2	2	NUM
ejpam-5857	375	6	’	'	PUNCT
ejpam-5857	375	7	:	:	PUNCT
ejpam-5857	375	8	suppose	suppose	VERB
ejpam-5857	375	9	x	x	X
ejpam-5857	375	10	/∈	/∈	PUNCT
ejpam-5857	375	11	g	g	NOUN
ejpam-5857	375	12	or	or	CCONJ
ejpam-5857	375	13	y	y	PROPN
ejpam-5857	375	14	/∈	/∈	PUNCT
ejpam-5857	376	1	g.	g.	PROPN
ejpam-5857	377	1	then	then	ADV
ejpam-5857	377	2	ψg	ψg	PROPN
ejpam-5857	378	1	i	i	PRON
ejpam-5857	378	2	[	[	PUNCT
ejpam-5857	378	3	β−	β−	PUNCT
ejpam-5857	378	4	β+	β+	PUNCT
ejpam-5857	378	5	]	]	X
ejpam-5857	378	6	(	(	PUNCT
ejpam-5857	378	7	x	x	X
ejpam-5857	378	8	)	)	PUNCT
ejpam-5857	378	9	=	=	SYM
ejpam-5857	378	10	β+	β+	PUNCT
ejpam-5857	378	11	or	or	CCONJ
ejpam-5857	378	12	ψg	ψg	INTJ
ejpam-5857	378	13	i	i	PRON
ejpam-5857	378	14	[	[	PUNCT
ejpam-5857	378	15	β−	β−	PUNCT
ejpam-5857	378	16	β+	β+	PUNCT
ejpam-5857	378	17	]	]	X
ejpam-5857	378	18	(	(	PUNCT
ejpam-5857	378	19	y	y	NOUN
ejpam-5857	378	20	)	)	PUNCT
ejpam-5857	378	21	=	=	PUNCT
ejpam-5857	378	22	β+	β+	X
ejpam-5857	378	23	.	.	PUNCT
ejpam-5857	379	1	thus	thus	ADV
ejpam-5857	379	2	,	,	PUNCT
ejpam-5857	379	3	ψg	ψg	PROPN
ejpam-5857	380	1	i	i	PRON
ejpam-5857	380	2	[	[	PUNCT
ejpam-5857	380	3	β−	β−	PUNCT
ejpam-5857	380	4	β+	β+	PUNCT
ejpam-5857	380	5	]	]	X
ejpam-5857	380	6	(	(	PUNCT
ejpam-5857	380	7	x	x	SYM
ejpam-5857	380	8	·	·	PUNCT
ejpam-5857	380	9	y	y	X
ejpam-5857	380	10	)	)	PUNCT
ejpam-5857	380	11	≤	≤	NOUN
ejpam-5857	380	12	β+	β+	PUNCT
ejpam-5857	380	13	≤	≤	NUM
ejpam-5857	380	14	β+	β+	PUNCT
ejpam-5857	380	15	∧	∧	NOUN
ejpam-5857	380	16	0.5	0.5	NUM
ejpam-5857	380	17	=	=	SYM
ejpam-5857	380	18	(	(	PUNCT
ejpam-5857	380	19	ψg	ψg	NOUN
ejpam-5857	380	20	i	i	PRON
ejpam-5857	380	21	[	[	PUNCT
ejpam-5857	380	22	β−	β−	PUNCT
ejpam-5857	380	23	β+	β+	PUNCT
ejpam-5857	380	24	]	]	X
ejpam-5857	380	25	(	(	PUNCT
ejpam-5857	380	26	x	x	X
ejpam-5857	380	27	)	)	PUNCT
ejpam-5857	380	28	∨	∨	NUM
ejpam-5857	380	29	ψg	ψg	NOUN
ejpam-5857	381	1	i	i	PRON
ejpam-5857	381	2	[	[	PUNCT
ejpam-5857	381	3	β−	β−	PUNCT
ejpam-5857	381	4	β+	β+	PUNCT
ejpam-5857	381	5	]	]	X
ejpam-5857	381	6	(	(	PUNCT
ejpam-5857	381	7	y	y	NOUN
ejpam-5857	381	8	)	)	PUNCT
ejpam-5857	381	9	)	)	PUNCT
ejpam-5857	382	1	∧	∧	NOUN
ejpam-5857	382	2	0.5	0.5	NUM
ejpam-5857	382	3	.	.	PUNCT
ejpam-5857	383	1	it	it	PRON
ejpam-5857	383	2	is	be	AUX
ejpam-5857	383	3	obvious	obvious	ADJ
ejpam-5857	383	4	to	to	PART
ejpam-5857	383	5	prove	prove	VERB
ejpam-5857	383	6	that	that	SCONJ
ejpam-5857	383	7	ψg	ψg	PROPN
ejpam-5857	383	8	f	f	PROPN
ejpam-5857	384	1	[	[	X
ejpam-5857	384	2	0.5	0.5	NUM
ejpam-5857	384	3	]	]	PUNCT
ejpam-5857	384	4	satisfied	satisfy	VERB
ejpam-5857	384	5	the	the	DET
ejpam-5857	384	6	condition	condition	NOUN
ejpam-5857	384	7	(	(	PUNCT
ejpam-5857	384	8	3.7	3.7	NUM
ejpam-5857	384	9	)	)	PUNCT
ejpam-5857	384	10	.	.	PUNCT
ejpam-5857	385	1	k.	k.	PROPN
ejpam-5857	385	2	suayngam	suayngam	PROPN
ejpam-5857	385	3	,	,	PUNCT
ejpam-5857	385	4	p.	p.	NOUN
ejpam-5857	385	5	julatha	julatha	PROPN
ejpam-5857	385	6	,	,	PUNCT
ejpam-5857	385	7	w.	w.	PROPN
ejpam-5857	385	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	385	9	,	,	PUNCT
ejpam-5857	385	10	a.	a.	NOUN
ejpam-5857	385	11	iampan	iampan	PROPN
ejpam-5857	385	12	/	/	SYM
ejpam-5857	385	13	eur	eur	PROPN
ejpam-5857	385	14	.	.	PUNCT
ejpam-5857	386	1	j.	j.	PROPN
ejpam-5857	386	2	pure	pure	PROPN
ejpam-5857	386	3	appl	appl	PROPN
ejpam-5857	386	4	.	.	PROPN
ejpam-5857	386	5	math	math	PROPN
ejpam-5857	386	6	,	,	PUNCT
ejpam-5857	386	7	18	18	NUM
ejpam-5857	386	8	(	(	PUNCT
ejpam-5857	386	9	2	2	NUM
ejpam-5857	386	10	)	)	PUNCT
ejpam-5857	386	11	(	(	PUNCT
ejpam-5857	386	12	2025	2025	NUM
ejpam-5857	386	13	)	)	PUNCT
ejpam-5857	386	14	,	,	PUNCT
ejpam-5857	386	15	5857	5857	NUM
ejpam-5857	386	16	16	16	NUM
ejpam-5857	386	17	of	of	ADP
ejpam-5857	386	18	30	30	NUM
ejpam-5857	386	19	hence	hence	ADV
ejpam-5857	386	20	,	,	PUNCT
ejpam-5857	386	21	the	the	DET
ejpam-5857	386	22	characteristic	characteristic	ADJ
ejpam-5857	386	23	ins	in	NOUN
ejpam-5857	386	24	ψg	ψg	PROPN
ejpam-5857	386	25	is	be	AUX
ejpam-5857	386	26	an	an	DET
ejpam-5857	386	27	intuitionistic	intuitionistic	ADJ
ejpam-5857	386	28	neutrosophic	neutrosophic	ADJ
ejpam-5857	386	29	iup	iup	NOUN
ejpam-5857	386	30	-	-	PUNCT
ejpam-5857	386	31	subalgebra	subalgebra	NOUN
ejpam-5857	386	32	of	of	ADP
ejpam-5857	386	33	x.	x.	NOUN
ejpam-5857	386	34	conversely	conversely	ADV
ejpam-5857	386	35	,	,	PUNCT
ejpam-5857	386	36	assume	assume	VERB
ejpam-5857	386	37	that	that	SCONJ
ejpam-5857	386	38	the	the	DET
ejpam-5857	386	39	characteristic	characteristic	ADJ
ejpam-5857	386	40	ins	ins	PROPN
ejpam-5857	386	41	ψg	ψg	PROPN
ejpam-5857	386	42	is	be	AUX
ejpam-5857	386	43	an	an	DET
ejpam-5857	386	44	intuitionistic	intuitionistic	ADJ
ejpam-5857	386	45	neutrosophic	neutrosophic	ADJ
ejpam-5857	386	46	iup	iup	NOUN
ejpam-5857	386	47	-	-	PUNCT
ejpam-5857	386	48	subalgebra	subalgebra	NOUN
ejpam-5857	386	49	of	of	ADP
ejpam-5857	386	50	x.	x.	NOUN
ejpam-5857	386	51	let	let	VERB
ejpam-5857	386	52	x	x	PRON
ejpam-5857	386	53	,	,	PUNCT
ejpam-5857	387	1	y	y	PROPN
ejpam-5857	387	2	∈	∈	PROPN
ejpam-5857	387	3	g.	g.	NOUN
ejpam-5857	387	4	then	then	ADV
ejpam-5857	387	5	ψg	ψg	PROPN
ejpam-5857	387	6	t	t	PROPN
ejpam-5857	387	7	[	[	PUNCT
ejpam-5857	387	8	α+	α+	X
ejpam-5857	387	9	α−	α−	ADP
ejpam-5857	387	10	]	]	PUNCT
ejpam-5857	387	11	(	(	PUNCT
ejpam-5857	387	12	x	x	X
ejpam-5857	387	13	)	)	PUNCT
ejpam-5857	387	14	=	=	SYM
ejpam-5857	387	15	α+	α+	PUNCT
ejpam-5857	387	16	and	and	CCONJ
ejpam-5857	387	17	ψg	ψg	X
ejpam-5857	387	18	t	t	PROPN
ejpam-5857	387	19	[	[	PUNCT
ejpam-5857	387	20	α+	α+	X
ejpam-5857	387	21	α−	α−	ADP
ejpam-5857	387	22	]	]	X
ejpam-5857	387	23	(	(	PUNCT
ejpam-5857	387	24	y	y	NOUN
ejpam-5857	387	25	)	)	PUNCT
ejpam-5857	387	26	=	=	SYM
ejpam-5857	387	27	α+	α+	NOUN
ejpam-5857	387	28	.	.	PUNCT
ejpam-5857	388	1	by	by	ADP
ejpam-5857	388	2	the	the	DET
ejpam-5857	388	3	condition	condition	NOUN
ejpam-5857	388	4	(	(	PUNCT
ejpam-5857	388	5	3.5	3.5	NUM
ejpam-5857	388	6	)	)	PUNCT
ejpam-5857	388	7	,	,	PUNCT
ejpam-5857	388	8	we	we	PRON
ejpam-5857	388	9	have	have	VERB
ejpam-5857	388	10	ψg	ψg	PROPN
ejpam-5857	388	11	t	t	PROPN
ejpam-5857	388	12	[	[	PUNCT
ejpam-5857	388	13	α+	α+	X
ejpam-5857	388	14	α−	α−	ADP
ejpam-5857	388	15	]	]	PUNCT
ejpam-5857	388	16	(	(	PUNCT
ejpam-5857	388	17	x	x	X
ejpam-5857	388	18	·	·	PUNCT
ejpam-5857	388	19	y	y	NOUN
ejpam-5857	388	20	)	)	PUNCT
ejpam-5857	388	21	≥	≥	PROPN
ejpam-5857	388	22	(	(	PUNCT
ejpam-5857	388	23	ψg	ψg	NOUN
ejpam-5857	388	24	t	t	PROPN
ejpam-5857	388	25	[	[	PUNCT
ejpam-5857	388	26	α+	α+	X
ejpam-5857	388	27	α−	α−	ADP
ejpam-5857	388	28	]	]	PUNCT
ejpam-5857	388	29	(	(	PUNCT
ejpam-5857	388	30	x)∧ψg	x)∧ψg	PROPN
ejpam-5857	388	31	t	t	PROPN
ejpam-5857	388	32	[	[	PUNCT
ejpam-5857	388	33	α+	α+	X
ejpam-5857	388	34	α−	α−	ADP
ejpam-5857	388	35	]	]	X
ejpam-5857	388	36	(	(	PUNCT
ejpam-5857	388	37	y))∨0.5	y))∨0.5	NOUN
ejpam-5857	388	38	=	=	SYM
ejpam-5857	388	39	(	(	PUNCT
ejpam-5857	388	40	α+∧α+)∨0.5	α+∧α+)∨0.5	NUM
ejpam-5857	388	41	=	=	NUM
ejpam-5857	388	42	α+∨0.5	α+∨0.5	NUM
ejpam-5857	388	43	≥	≥	NOUN
ejpam-5857	388	44	α+	α+	NOUN
ejpam-5857	388	45	.	.	PUNCT
ejpam-5857	389	1	thus	thus	ADV
ejpam-5857	389	2	,	,	PUNCT
ejpam-5857	389	3	ψg	ψg	PROPN
ejpam-5857	389	4	t	t	PROPN
ejpam-5857	389	5	[	[	PUNCT
ejpam-5857	389	6	α+	α+	X
ejpam-5857	389	7	α−	α−	ADP
ejpam-5857	389	8	]	]	PUNCT
ejpam-5857	389	9	(	(	PUNCT
ejpam-5857	389	10	x	x	X
ejpam-5857	389	11	·	·	PUNCT
ejpam-5857	389	12	y	y	NOUN
ejpam-5857	389	13	)	)	PUNCT
ejpam-5857	389	14	=	=	SYM
ejpam-5857	389	15	α+	α+	NOUN
ejpam-5857	389	16	,	,	PUNCT
ejpam-5857	389	17	that	that	ADV
ejpam-5857	389	18	is	is	ADV
ejpam-5857	389	19	,	,	PUNCT
ejpam-5857	389	20	x	x	X
ejpam-5857	389	21	·	·	PUNCT
ejpam-5857	389	22	y	y	PROPN
ejpam-5857	389	23	∈	∈	PROPN
ejpam-5857	389	24	g.	g.	NOUN
ejpam-5857	389	25	hence	hence	ADV
ejpam-5857	389	26	,	,	PUNCT
ejpam-5857	389	27	g	g	PROPN
ejpam-5857	389	28	is	be	AUX
ejpam-5857	389	29	an	an	DET
ejpam-5857	389	30	iup	iup	NOUN
ejpam-5857	389	31	-	-	PUNCT
ejpam-5857	389	32	subalgebra	subalgebra	NOUN
ejpam-5857	389	33	of	of	ADP
ejpam-5857	389	34	x.	x.	NOUN
ejpam-5857	389	35	theorem	theorem	VERB
ejpam-5857	389	36	7	7	NUM
ejpam-5857	389	37	.	.	PUNCT
ejpam-5857	390	1	a	a	DET
ejpam-5857	390	2	nonempty	nonempty	NOUN
ejpam-5857	390	3	subset	subset	VERB
ejpam-5857	390	4	g	g	NOUN
ejpam-5857	390	5	is	be	AUX
ejpam-5857	390	6	an	an	DET
ejpam-5857	390	7	iup	iup	NOUN
ejpam-5857	390	8	-	-	PUNCT
ejpam-5857	390	9	ideal	ideal	NOUN
ejpam-5857	390	10	of	of	ADP
ejpam-5857	390	11	x	x	SYM
ejpam-5857	390	12	if	if	SCONJ
ejpam-5857	390	13	and	and	CCONJ
ejpam-5857	390	14	only	only	ADV
ejpam-5857	390	15	if	if	SCONJ
ejpam-5857	390	16	the	the	DET
ejpam-5857	390	17	characteristic	characteristic	ADJ
ejpam-5857	390	18	ins	ins	PROPN
ejpam-5857	390	19	ψg	ψg	PROPN
ejpam-5857	390	20	is	be	AUX
ejpam-5857	390	21	an	an	DET
ejpam-5857	390	22	intuitionistic	intuitionistic	ADJ
ejpam-5857	390	23	neutrosophic	neutrosophic	ADJ
ejpam-5857	390	24	iup	iup	NOUN
ejpam-5857	390	25	-	-	PUNCT
ejpam-5857	390	26	ideal	ideal	NOUN
ejpam-5857	390	27	of	of	ADP
ejpam-5857	390	28	x.	x.	NOUN
ejpam-5857	390	29	proof	proof	PROPN
ejpam-5857	390	30	.	.	PUNCT
ejpam-5857	391	1	assume	assume	VERB
ejpam-5857	391	2	that	that	SCONJ
ejpam-5857	391	3	g	g	PROPN
ejpam-5857	391	4	is	be	AUX
ejpam-5857	391	5	an	an	DET
ejpam-5857	391	6	iup	iup	NOUN
ejpam-5857	391	7	-	-	PUNCT
ejpam-5857	391	8	ideal	ideal	NOUN
ejpam-5857	391	9	of	of	ADP
ejpam-5857	391	10	x.	x.	NOUN
ejpam-5857	391	11	since	since	SCONJ
ejpam-5857	391	12	0	0	NUM
ejpam-5857	391	13	∈	∈	PROPN
ejpam-5857	391	14	g	g	NOUN
ejpam-5857	391	15	,	,	PUNCT
ejpam-5857	391	16	it	it	PRON
ejpam-5857	391	17	follows	follow	VERB
ejpam-5857	391	18	from	from	ADP
ejpam-5857	391	19	lemma	lemma	PROPN
ejpam-5857	391	20	3	3	NUM
ejpam-5857	391	21	that	that	PRON
ejpam-5857	391	22	ψg	ψg	PROPN
ejpam-5857	391	23	t	t	PROPN
ejpam-5857	391	24	[	[	PUNCT
ejpam-5857	391	25	α+	α+	X
ejpam-5857	391	26	α−	α−	ADP
ejpam-5857	391	27	]	]	PUNCT
ejpam-5857	391	28	,	,	PUNCT
ejpam-5857	391	29	ψ	ψ	X
ejpam-5857	391	30	g	g	NOUN
ejpam-5857	391	31	i	i	PRON
ejpam-5857	391	32	[	[	PUNCT
ejpam-5857	391	33	β−	β−	PROPN
ejpam-5857	391	34	β+	β+	PUNCT
ejpam-5857	391	35	]	]	PUNCT
ejpam-5857	391	36	and	and	CCONJ
ejpam-5857	391	37	ψ	ψ	X
ejpam-5857	391	38	g	g	PROPN
ejpam-5857	391	39	f	f	PROPN
ejpam-5857	392	1	[	[	X
ejpam-5857	392	2	0.5	0.5	NUM
ejpam-5857	392	3	]	]	PUNCT
ejpam-5857	392	4	satisfy	satisfy	NOUN
ejpam-5857	392	5	the	the	DET
ejpam-5857	392	6	conditions	condition	NOUN
ejpam-5857	392	7	(	(	PUNCT
ejpam-5857	392	8	3.8	3.8	NUM
ejpam-5857	392	9	)	)	PUNCT
ejpam-5857	392	10	,	,	PUNCT
ejpam-5857	392	11	(	(	PUNCT
ejpam-5857	392	12	3.9	3.9	NUM
ejpam-5857	392	13	)	)	PUNCT
ejpam-5857	392	14	and	and	CCONJ
ejpam-5857	392	15	(	(	PUNCT
ejpam-5857	392	16	3.10	3.10	NUM
ejpam-5857	392	17	)	)	PUNCT
ejpam-5857	392	18	,	,	PUNCT
ejpam-5857	392	19	respectively	respectively	ADV
ejpam-5857	392	20	.	.	PUNCT
ejpam-5857	393	1	next	next	ADV
ejpam-5857	393	2	,	,	PUNCT
ejpam-5857	393	3	let	let	VERB
ejpam-5857	393	4	x	x	PRON
ejpam-5857	393	5	,	,	PUNCT
ejpam-5857	393	6	y	y	PROPN
ejpam-5857	393	7	,	,	PUNCT
ejpam-5857	393	8	z	z	PROPN
ejpam-5857	393	9	∈	∈	NOUN
ejpam-5857	393	10	x.	x.	NOUN
ejpam-5857	393	11	case	case	NOUN
ejpam-5857	393	12	1	1	NUM
ejpam-5857	393	13	:	:	PUNCT
ejpam-5857	393	14	suppose	suppose	VERB
ejpam-5857	393	15	x·(y·z	x·(y·z	NUM
ejpam-5857	393	16	)	)	PUNCT
ejpam-5857	393	17	∈	∈	PROPN
ejpam-5857	393	18	g	g	PROPN
ejpam-5857	393	19	and	and	CCONJ
ejpam-5857	393	20	y	y	PROPN
ejpam-5857	393	21	∈	∈	PROPN
ejpam-5857	393	22	g.	g.	PROPN
ejpam-5857	393	23	sinceg	sinceg	PROPN
ejpam-5857	393	24	is	be	AUX
ejpam-5857	393	25	an	an	DET
ejpam-5857	393	26	iup	iup	ADJ
ejpam-5857	393	27	-	-	PUNCT
ejpam-5857	393	28	ideal	ideal	NOUN
ejpam-5857	393	29	ofx	ofx	NOUN
ejpam-5857	393	30	,	,	PUNCT
ejpam-5857	393	31	we	we	PRON
ejpam-5857	393	32	have	have	VERB
ejpam-5857	393	33	x·z	x·z	PROPN
ejpam-5857	393	34	∈	∈	PROPN
ejpam-5857	393	35	g.	g.	PROPN
ejpam-5857	394	1	thus	thus	ADV
ejpam-5857	394	2	,	,	PUNCT
ejpam-5857	394	3	ψg	ψg	PROPN
ejpam-5857	394	4	t	t	PROPN
ejpam-5857	394	5	[	[	PUNCT
ejpam-5857	394	6	α+	α+	X
ejpam-5857	394	7	α−	α−	ADP
ejpam-5857	394	8	]	]	PUNCT
ejpam-5857	394	9	(	(	PUNCT
ejpam-5857	394	10	x·z	x·z	PROPN
ejpam-5857	394	11	)	)	PUNCT
ejpam-5857	394	12	=	=	SYM
ejpam-5857	394	13	α+	α+	PUNCT
ejpam-5857	394	14	≥	≥	NOUN
ejpam-5857	395	1	α+∨0.5	α+∨0.5	NUM
ejpam-5857	395	2	=	=	SYM
ejpam-5857	395	3	(	(	PUNCT
ejpam-5857	395	4	α+∧α+)∨0.5	α+∧α+)∨0.5	NUM
ejpam-5857	395	5	=	=	SYM
ejpam-5857	395	6	(	(	PUNCT
ejpam-5857	395	7	ψg	ψg	NOUN
ejpam-5857	395	8	t	t	PROPN
ejpam-5857	395	9	[	[	PUNCT
ejpam-5857	395	10	α+	α+	X
ejpam-5857	395	11	α−	α−	ADP
ejpam-5857	395	12	]	]	PUNCT
ejpam-5857	395	13	(	(	PUNCT
ejpam-5857	395	14	x·(y·z))∧ψg	x·(y·z))∧ψg	PROPN
ejpam-5857	395	15	t	t	PROPN
ejpam-5857	395	16	[	[	PUNCT
ejpam-5857	395	17	α+	α+	X
ejpam-5857	395	18	α−	α−	ADP
ejpam-5857	395	19	]	]	X
ejpam-5857	395	20	(	(	PUNCT
ejpam-5857	395	21	y))∨0.5	y))∨0.5	PROPN
ejpam-5857	395	22	.	.	NOUN
ejpam-5857	395	23	case	case	NOUN
ejpam-5857	395	24	2	2	NUM
ejpam-5857	395	25	:	:	PUNCT
ejpam-5857	395	26	suppose	suppose	VERB
ejpam-5857	395	27	x·(y·z	x·(y·z	PROPN
ejpam-5857	395	28	)	)	PUNCT
ejpam-5857	395	29	/∈	/∈	PUNCT
ejpam-5857	396	1	g	g	NOUN
ejpam-5857	396	2	or	or	CCONJ
ejpam-5857	396	3	y	y	PROPN
ejpam-5857	396	4	/∈	/∈	PUNCT
ejpam-5857	397	1	g.	g.	PROPN
ejpam-5857	398	1	then	then	ADV
ejpam-5857	398	2	ψg	ψg	PROPN
ejpam-5857	398	3	t	t	PROPN
ejpam-5857	398	4	[	[	PUNCT
ejpam-5857	398	5	α+	α+	X
ejpam-5857	398	6	α−	α−	ADP
ejpam-5857	398	7	]	]	X
ejpam-5857	398	8	(	(	PUNCT
ejpam-5857	398	9	x·(y·z	x·(y·z	NUM
ejpam-5857	398	10	)	)	PUNCT
ejpam-5857	398	11	)	)	PUNCT
ejpam-5857	399	1	=	=	PUNCT
ejpam-5857	400	1	α−	α−	ADP
ejpam-5857	400	2	or	or	CCONJ
ejpam-5857	400	3	ψg	ψg	X
ejpam-5857	400	4	t	t	PROPN
ejpam-5857	400	5	[	[	PUNCT
ejpam-5857	400	6	α+	α+	X
ejpam-5857	400	7	α−	α−	ADP
ejpam-5857	400	8	]	]	X
ejpam-5857	400	9	(	(	PUNCT
ejpam-5857	400	10	y	y	NOUN
ejpam-5857	400	11	)	)	PUNCT
ejpam-5857	400	12	=	=	SYM
ejpam-5857	400	13	α−.	α−.	NOUN
ejpam-5857	400	14	thus	thus	ADV
ejpam-5857	400	15	,	,	PUNCT
ejpam-5857	400	16	ψg	ψg	PROPN
ejpam-5857	400	17	t	t	PROPN
ejpam-5857	400	18	[	[	PUNCT
ejpam-5857	400	19	α+	α+	X
ejpam-5857	400	20	α−	α−	ADP
ejpam-5857	400	21	]	]	PUNCT
ejpam-5857	400	22	(	(	PUNCT
ejpam-5857	400	23	x	x	SYM
ejpam-5857	400	24	·	·	PUNCT
ejpam-5857	400	25	z	z	X
ejpam-5857	400	26	)	)	PUNCT
ejpam-5857	400	27	≥	≥	NOUN
ejpam-5857	400	28	α−	α−	ADP
ejpam-5857	400	29	≥	≥	NOUN
ejpam-5857	400	30	α−	α−	ADP
ejpam-5857	400	31	∨	∨	NUM
ejpam-5857	400	32	0.5	0.5	NUM
ejpam-5857	400	33	=	=	SYM
ejpam-5857	400	34	(	(	PUNCT
ejpam-5857	400	35	ψg	ψg	NOUN
ejpam-5857	400	36	t	t	PROPN
ejpam-5857	400	37	[	[	PUNCT
ejpam-5857	400	38	α+	α+	X
ejpam-5857	400	39	α−	α−	ADP
ejpam-5857	400	40	]	]	PUNCT
ejpam-5857	400	41	(	(	PUNCT
ejpam-5857	400	42	x	x	X
ejpam-5857	400	43	·	·	PUNCT
ejpam-5857	400	44	(	(	PUNCT
ejpam-5857	400	45	y	y	PROPN
ejpam-5857	400	46	·	·	PUNCT
ejpam-5857	400	47	z	z	NOUN
ejpam-5857	400	48	)	)	PUNCT
ejpam-5857	400	49	)	)	PUNCT
ejpam-5857	401	1	∧	∧	PROPN
ejpam-5857	401	2	ψg	ψg	PROPN
ejpam-5857	401	3	t	t	PROPN
ejpam-5857	401	4	[	[	PUNCT
ejpam-5857	401	5	α+	α+	X
ejpam-5857	401	6	α−	α−	ADP
ejpam-5857	401	7	]	]	X
ejpam-5857	401	8	(	(	PUNCT
ejpam-5857	401	9	y	y	NOUN
ejpam-5857	401	10	)	)	PUNCT
ejpam-5857	401	11	)	)	PUNCT
ejpam-5857	401	12	∨	∨	NUM
ejpam-5857	401	13	0.5	0.5	NUM
ejpam-5857	401	14	.	.	PUNCT
ejpam-5857	401	15	case	case	NOUN
ejpam-5857	401	16	1	1	NUM
ejpam-5857	401	17	’	'	PUNCT
ejpam-5857	401	18	:	:	PUNCT
ejpam-5857	401	19	suppose	suppose	VERB
ejpam-5857	401	20	x	x	X
ejpam-5857	401	21	·	·	PUNCT
ejpam-5857	401	22	(	(	PUNCT
ejpam-5857	401	23	y	y	PROPN
ejpam-5857	401	24	·	·	PUNCT
ejpam-5857	401	25	z	z	X
ejpam-5857	401	26	)	)	PUNCT
ejpam-5857	401	27	∈	∈	PROPN
ejpam-5857	401	28	g	g	PROPN
ejpam-5857	401	29	and	and	CCONJ
ejpam-5857	401	30	y	y	PROPN
ejpam-5857	401	31	∈	∈	PROPN
ejpam-5857	401	32	g.	g.	NOUN
ejpam-5857	401	33	since	since	SCONJ
ejpam-5857	401	34	g	g	PROPN
ejpam-5857	401	35	is	be	AUX
ejpam-5857	401	36	an	an	DET
ejpam-5857	401	37	iup	iup	NOUN
ejpam-5857	401	38	-	-	PUNCT
ejpam-5857	401	39	ideal	ideal	NOUN
ejpam-5857	401	40	of	of	ADP
ejpam-5857	401	41	x	x	SYM
ejpam-5857	401	42	,	,	PUNCT
ejpam-5857	401	43	we	we	PRON
ejpam-5857	401	44	have	have	VERB
ejpam-5857	401	45	x	x	X
ejpam-5857	401	46	·	·	PUNCT
ejpam-5857	401	47	z	z	SYM
ejpam-5857	401	48	∈	∈	PROPN
ejpam-5857	401	49	g.	g.	PROPN
ejpam-5857	401	50	thus	thus	ADV
ejpam-5857	401	51	,	,	PUNCT
ejpam-5857	401	52	ψg	ψg	PROPN
ejpam-5857	402	1	i	i	PRON
ejpam-5857	402	2	[	[	PUNCT
ejpam-5857	402	3	β−	β−	PUNCT
ejpam-5857	402	4	β+	β+	PUNCT
ejpam-5857	402	5	]	]	X
ejpam-5857	402	6	(	(	PUNCT
ejpam-5857	402	7	x	x	SYM
ejpam-5857	402	8	·	·	PUNCT
ejpam-5857	402	9	z	z	X
ejpam-5857	402	10	)	)	PUNCT
ejpam-5857	402	11	=	=	PUNCT
ejpam-5857	402	12	β−	β−	PUNCT
ejpam-5857	403	1	≤	≤	NUM
ejpam-5857	403	2	β−	β−	PUNCT
ejpam-5857	404	1	∧	∧	NOUN
ejpam-5857	404	2	0.5	0.5	NUM
ejpam-5857	404	3	=	=	SYM
ejpam-5857	404	4	(	(	PUNCT
ejpam-5857	404	5	β−	β−	PROPN
ejpam-5857	404	6	∨	∨	NUM
ejpam-5857	404	7	β−	β−	NUM
ejpam-5857	404	8	)	)	PUNCT
ejpam-5857	404	9	∧	∧	NOUN
ejpam-5857	404	10	0.5	0.5	NUM
ejpam-5857	404	11	=	=	SYM
ejpam-5857	404	12	(	(	PUNCT
ejpam-5857	404	13	ψg	ψg	NOUN
ejpam-5857	404	14	i	i	PRON
ejpam-5857	404	15	[	[	PUNCT
ejpam-5857	404	16	β−	β−	PUNCT
ejpam-5857	404	17	β+	β+	PUNCT
ejpam-5857	404	18	]	]	X
ejpam-5857	404	19	(	(	PUNCT
ejpam-5857	404	20	x	x	X
ejpam-5857	404	21	·	·	PUNCT
ejpam-5857	404	22	(	(	PUNCT
ejpam-5857	404	23	y	y	PROPN
ejpam-5857	404	24	·	·	PUNCT
ejpam-5857	404	25	z	z	NOUN
ejpam-5857	404	26	)	)	PUNCT
ejpam-5857	404	27	)	)	PUNCT
ejpam-5857	405	1	∨	∨	NUM
ejpam-5857	405	2	ψg	ψg	INTJ
ejpam-5857	406	1	i	i	PRON
ejpam-5857	406	2	[	[	PUNCT
ejpam-5857	406	3	β−	β−	PUNCT
ejpam-5857	406	4	β+	β+	PUNCT
ejpam-5857	406	5	]	]	X
ejpam-5857	406	6	(	(	PUNCT
ejpam-5857	406	7	y	y	NOUN
ejpam-5857	406	8	)	)	PUNCT
ejpam-5857	406	9	)	)	PUNCT
ejpam-5857	407	1	∧	∧	NOUN
ejpam-5857	407	2	0.5	0.5	NUM
ejpam-5857	407	3	.	.	PUNCT
ejpam-5857	407	4	case	case	NOUN
ejpam-5857	407	5	2	2	NUM
ejpam-5857	407	6	’	'	PUNCT
ejpam-5857	407	7	:	:	PUNCT
ejpam-5857	407	8	suppose	suppose	VERB
ejpam-5857	407	9	x·(y·z	x·(y·z	PROPN
ejpam-5857	407	10	)	)	PUNCT
ejpam-5857	407	11	/∈	/∈	PUNCT
ejpam-5857	408	1	g	g	NOUN
ejpam-5857	408	2	or	or	CCONJ
ejpam-5857	408	3	y	y	PROPN
ejpam-5857	408	4	/∈	/∈	PUNCT
ejpam-5857	409	1	g.	g.	PROPN
ejpam-5857	410	1	then	then	ADV
ejpam-5857	410	2	ψg	ψg	PROPN
ejpam-5857	411	1	i	i	PRON
ejpam-5857	411	2	[	[	PUNCT
ejpam-5857	411	3	β−	β−	PUNCT
ejpam-5857	411	4	β+	β+	PUNCT
ejpam-5857	411	5	]	]	X
ejpam-5857	411	6	(	(	PUNCT
ejpam-5857	411	7	x·(y·z	x·(y·z	NUM
ejpam-5857	411	8	)	)	PUNCT
ejpam-5857	411	9	)	)	PUNCT
ejpam-5857	412	1	=	=	PRON
ejpam-5857	412	2	β+	β+	PUNCT
ejpam-5857	412	3	or	or	CCONJ
ejpam-5857	412	4	ψg	ψg	INTJ
ejpam-5857	413	1	i	i	PRON
ejpam-5857	413	2	[	[	PUNCT
ejpam-5857	413	3	β−	β−	PUNCT
ejpam-5857	413	4	β+	β+	PUNCT
ejpam-5857	413	5	]	]	X
ejpam-5857	413	6	(	(	PUNCT
ejpam-5857	413	7	y	y	NOUN
ejpam-5857	413	8	)	)	PUNCT
ejpam-5857	413	9	=	=	PUNCT
ejpam-5857	414	1	β+	β+	X
ejpam-5857	414	2	.	.	PUNCT
ejpam-5857	415	1	thus	thus	ADV
ejpam-5857	415	2	,	,	PUNCT
ejpam-5857	415	3	ψg	ψg	PROPN
ejpam-5857	416	1	i	i	PRON
ejpam-5857	416	2	[	[	PUNCT
ejpam-5857	416	3	β−	β−	PUNCT
ejpam-5857	416	4	β+	β+	PUNCT
ejpam-5857	416	5	]	]	X
ejpam-5857	416	6	(	(	PUNCT
ejpam-5857	416	7	x	x	SYM
ejpam-5857	416	8	·	·	PUNCT
ejpam-5857	416	9	z	z	X
ejpam-5857	416	10	)	)	PUNCT
ejpam-5857	416	11	≤	≤	NOUN
ejpam-5857	416	12	β+	β+	PUNCT
ejpam-5857	416	13	≤	≤	NUM
ejpam-5857	416	14	β+	β+	PUNCT
ejpam-5857	416	15	∧	∧	NOUN
ejpam-5857	416	16	0.5	0.5	NUM
ejpam-5857	416	17	=	=	SYM
ejpam-5857	416	18	(	(	PUNCT
ejpam-5857	416	19	ψg	ψg	NOUN
ejpam-5857	416	20	i	i	PRON
ejpam-5857	416	21	[	[	PUNCT
ejpam-5857	416	22	β−	β−	PUNCT
ejpam-5857	416	23	β+	β+	PUNCT
ejpam-5857	416	24	]	]	X
ejpam-5857	416	25	(	(	PUNCT
ejpam-5857	416	26	x	x	X
ejpam-5857	416	27	·	·	PUNCT
ejpam-5857	416	28	(	(	PUNCT
ejpam-5857	416	29	y	y	PROPN
ejpam-5857	416	30	·	·	PUNCT
ejpam-5857	416	31	z	z	NOUN
ejpam-5857	416	32	)	)	PUNCT
ejpam-5857	416	33	)	)	PUNCT
ejpam-5857	417	1	∨	∨	NUM
ejpam-5857	417	2	ψg	ψg	INTJ
ejpam-5857	418	1	i	i	PRON
ejpam-5857	418	2	[	[	PUNCT
ejpam-5857	418	3	β−	β−	PUNCT
ejpam-5857	418	4	β+	β+	PUNCT
ejpam-5857	418	5	]	]	X
ejpam-5857	418	6	(	(	PUNCT
ejpam-5857	418	7	y	y	NOUN
ejpam-5857	418	8	)	)	PUNCT
ejpam-5857	418	9	)	)	PUNCT
ejpam-5857	419	1	∧	∧	NOUN
ejpam-5857	419	2	0.5	0.5	NUM
ejpam-5857	419	3	.	.	PUNCT
ejpam-5857	420	1	it	it	PRON
ejpam-5857	420	2	is	be	AUX
ejpam-5857	420	3	obvious	obvious	ADJ
ejpam-5857	420	4	to	to	PART
ejpam-5857	420	5	prove	prove	VERB
ejpam-5857	420	6	that	that	SCONJ
ejpam-5857	420	7	ψg	ψg	PROPN
ejpam-5857	420	8	f	f	PROPN
ejpam-5857	421	1	[	[	X
ejpam-5857	421	2	0.5	0.5	NUM
ejpam-5857	421	3	]	]	PUNCT
ejpam-5857	421	4	satisfied	satisfy	VERB
ejpam-5857	421	5	the	the	DET
ejpam-5857	421	6	condition	condition	NOUN
ejpam-5857	421	7	(	(	PUNCT
ejpam-5857	421	8	3.13	3.13	NUM
ejpam-5857	421	9	)	)	PUNCT
ejpam-5857	421	10	.	.	PUNCT
ejpam-5857	422	1	hence	hence	ADV
ejpam-5857	422	2	,	,	PUNCT
ejpam-5857	422	3	ψg	ψg	PROPN
ejpam-5857	422	4	is	be	AUX
ejpam-5857	422	5	an	an	DET
ejpam-5857	422	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	422	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	422	8	iup	iup	NOUN
ejpam-5857	422	9	-	-	PUNCT
ejpam-5857	422	10	ideal	ideal	NOUN
ejpam-5857	422	11	of	of	ADP
ejpam-5857	422	12	x.	x.	NOUN
ejpam-5857	422	13	conversely	conversely	ADV
ejpam-5857	422	14	,	,	PUNCT
ejpam-5857	422	15	assume	assume	VERB
ejpam-5857	422	16	that	that	SCONJ
ejpam-5857	422	17	the	the	DET
ejpam-5857	422	18	characteristic	characteristic	ADJ
ejpam-5857	422	19	ins	ins	PROPN
ejpam-5857	422	20	ψg	ψg	PROPN
ejpam-5857	422	21	is	be	AUX
ejpam-5857	422	22	an	an	DET
ejpam-5857	422	23	intuitionistic	intuitionistic	ADJ
ejpam-5857	422	24	neutrosophic	neutrosophic	ADJ
ejpam-5857	422	25	iup	iup	NOUN
ejpam-5857	422	26	-	-	PUNCT
ejpam-5857	422	27	ideal	ideal	NOUN
ejpam-5857	422	28	of	of	ADP
ejpam-5857	422	29	x.	x.	NOUN
ejpam-5857	422	30	since	since	SCONJ
ejpam-5857	422	31	ψg	ψg	PROPN
ejpam-5857	422	32	t	t	PROPN
ejpam-5857	422	33	[	[	PUNCT
ejpam-5857	422	34	α+	α+	X
ejpam-5857	422	35	α−	α−	X
ejpam-5857	422	36	]	]	PUNCT
ejpam-5857	422	37	satisfies	satisfie	NOUN
ejpam-5857	422	38	the	the	DET
ejpam-5857	422	39	condition	condition	NOUN
ejpam-5857	422	40	(	(	PUNCT
ejpam-5857	422	41	3.8	3.8	NUM
ejpam-5857	422	42	)	)	PUNCT
ejpam-5857	422	43	,	,	PUNCT
ejpam-5857	422	44	it	it	PRON
ejpam-5857	422	45	follows	follow	VERB
ejpam-5857	422	46	from	from	ADP
ejpam-5857	422	47	lemma	lemma	PROPN
ejpam-5857	422	48	3	3	NUM
ejpam-5857	422	49	that	that	SCONJ
ejpam-5857	422	50	0	0	NUM
ejpam-5857	422	51	∈	∈	PROPN
ejpam-5857	422	52	g.	g.	NOUN
ejpam-5857	422	53	next	next	ADV
ejpam-5857	422	54	,	,	PUNCT
ejpam-5857	422	55	let	let	VERB
ejpam-5857	422	56	x	x	PRON
ejpam-5857	422	57	,	,	PUNCT
ejpam-5857	422	58	y	y	PROPN
ejpam-5857	422	59	,	,	PUNCT
ejpam-5857	422	60	z	z	NOUN
ejpam-5857	422	61	∈	∈	PROPN
ejpam-5857	422	62	x	x	AUX
ejpam-5857	422	63	be	be	AUX
ejpam-5857	422	64	such	such	ADJ
ejpam-5857	422	65	that	that	SCONJ
ejpam-5857	422	66	x·(y	x·(y	PUNCT
ejpam-5857	423	1	·	·	PUNCT
ejpam-5857	423	2	z	z	X
ejpam-5857	423	3	)	)	PUNCT
ejpam-5857	423	4	∈	∈	PROPN
ejpam-5857	423	5	g	g	PROPN
ejpam-5857	423	6	and	and	CCONJ
ejpam-5857	423	7	y	y	PROPN
ejpam-5857	423	8	∈	∈	PROPN
ejpam-5857	424	1	g.	g.	NOUN
ejpam-5857	424	2	then	then	ADV
ejpam-5857	424	3	ψg	ψg	PROPN
ejpam-5857	424	4	t	t	PROPN
ejpam-5857	424	5	[	[	PUNCT
ejpam-5857	424	6	α+	α+	X
ejpam-5857	424	7	α−	α−	ADP
ejpam-5857	424	8	]	]	PUNCT
ejpam-5857	424	9	(	(	PUNCT
ejpam-5857	424	10	x·(y	x·(y	NOUN
ejpam-5857	424	11	·	·	SYM
ejpam-5857	424	12	z	z	NOUN
ejpam-5857	424	13	)	)	PUNCT
ejpam-5857	424	14	)	)	PUNCT
ejpam-5857	425	1	=	=	SYM
ejpam-5857	425	2	α+	α+	PUNCT
ejpam-5857	425	3	and	and	CCONJ
ejpam-5857	425	4	ψg	ψg	X
ejpam-5857	425	5	t	t	PROPN
ejpam-5857	425	6	[	[	PUNCT
ejpam-5857	425	7	α+	α+	X
ejpam-5857	425	8	α−	α−	ADP
ejpam-5857	425	9	]	]	X
ejpam-5857	425	10	(	(	PUNCT
ejpam-5857	425	11	y	y	NOUN
ejpam-5857	425	12	)	)	PUNCT
ejpam-5857	425	13	=	=	SYM
ejpam-5857	425	14	α+	α+	PROPN
ejpam-5857	425	15	.	.	PUNCT
ejpam-5857	426	1	thus	thus	ADV
ejpam-5857	426	2	,	,	PUNCT
ejpam-5857	426	3	min{ψg	min{ψg	NOUN
ejpam-5857	426	4	t	t	X
ejpam-5857	426	5	[	[	PUNCT
ejpam-5857	426	6	α+	α+	X
ejpam-5857	426	7	α−	α−	ADP
ejpam-5857	426	8	]	]	PUNCT
ejpam-5857	426	9	(	(	PUNCT
ejpam-5857	426	10	x	x	X
ejpam-5857	426	11	·	·	PUNCT
ejpam-5857	426	12	(	(	PUNCT
ejpam-5857	426	13	y	y	PROPN
ejpam-5857	426	14	·	·	PROPN
ejpam-5857	426	15	z	z	NOUN
ejpam-5857	426	16	)	)	PUNCT
ejpam-5857	426	17	)	)	PUNCT
ejpam-5857	426	18	,	,	PUNCT
ejpam-5857	426	19	ψg	ψg	PROPN
ejpam-5857	426	20	t	t	PROPN
ejpam-5857	426	21	[	[	PUNCT
ejpam-5857	426	22	α+	α+	X
ejpam-5857	426	23	α−	α−	ADP
ejpam-5857	426	24	]	]	X
ejpam-5857	426	25	(	(	PUNCT
ejpam-5857	426	26	y	y	NOUN
ejpam-5857	426	27	)	)	PUNCT
ejpam-5857	426	28	}	}	PUNCT
ejpam-5857	426	29	=	=	SYM
ejpam-5857	426	30	α+	α+	NOUN
ejpam-5857	426	31	.	.	PUNCT
ejpam-5857	427	1	by	by	ADP
ejpam-5857	427	2	the	the	DET
ejpam-5857	427	3	condition	condition	NOUN
ejpam-5857	427	4	(	(	PUNCT
ejpam-5857	427	5	3.11	3.11	NUM
ejpam-5857	427	6	)	)	PUNCT
ejpam-5857	427	7	,	,	PUNCT
ejpam-5857	427	8	we	we	PRON
ejpam-5857	427	9	have	have	VERB
ejpam-5857	427	10	ψg	ψg	PROPN
ejpam-5857	427	11	t	t	PROPN
ejpam-5857	427	12	[	[	PUNCT
ejpam-5857	427	13	α+	α+	X
ejpam-5857	427	14	α−	α−	ADP
ejpam-5857	427	15	]	]	PUNCT
ejpam-5857	427	16	(	(	PUNCT
ejpam-5857	427	17	x	x	SYM
ejpam-5857	427	18	·	·	PUNCT
ejpam-5857	427	19	z	z	X
ejpam-5857	427	20	)	)	PUNCT
ejpam-5857	427	21	≥	≥	PROPN
ejpam-5857	427	22	(	(	PUNCT
ejpam-5857	427	23	ψg	ψg	NOUN
ejpam-5857	427	24	t	t	PROPN
ejpam-5857	427	25	[	[	PUNCT
ejpam-5857	427	26	α+	α+	X
ejpam-5857	427	27	α−	α−	ADP
ejpam-5857	427	28	]	]	PUNCT
ejpam-5857	427	29	(	(	PUNCT
ejpam-5857	427	30	x	x	X
ejpam-5857	427	31	·	·	PUNCT
ejpam-5857	427	32	(	(	PUNCT
ejpam-5857	427	33	y	y	PROPN
ejpam-5857	427	34	·	·	PUNCT
ejpam-5857	427	35	z))∧	z))∧	NUM
ejpam-5857	427	36	ψg	ψg	PROPN
ejpam-5857	427	37	t	t	PROPN
ejpam-5857	427	38	[	[	PUNCT
ejpam-5857	427	39	α+	α+	X
ejpam-5857	427	40	α−	α−	ADP
ejpam-5857	427	41	]	]	PUNCT
ejpam-5857	427	42	(	(	PUNCT
ejpam-5857	427	43	y))∨	y))∨	NOUN
ejpam-5857	427	44	0.5	0.5	NUM
ejpam-5857	427	45	=	=	SYM
ejpam-5857	427	46	(	(	PUNCT
ejpam-5857	427	47	α+	α+	X
ejpam-5857	427	48	∧	∧	PROPN
ejpam-5857	427	49	α+)∨	α+)∨	X
ejpam-5857	427	50	0.5	0.5	NUM
ejpam-5857	427	51	=	=	SYM
ejpam-5857	427	52	α+	α+	PROPN
ejpam-5857	427	53	∨	∨	NUM
ejpam-5857	427	54	0.5	0.5	NUM
ejpam-5857	427	55	≥	≥	NOUN
ejpam-5857	427	56	α+	α+	NOUN
ejpam-5857	427	57	,	,	PUNCT
ejpam-5857	427	58	that	that	ADV
ejpam-5857	427	59	is	is	ADV
ejpam-5857	427	60	,	,	PUNCT
ejpam-5857	427	61	ψg	ψg	PROPN
ejpam-5857	427	62	t	t	PROPN
ejpam-5857	427	63	[	[	PUNCT
ejpam-5857	427	64	α+	α+	X
ejpam-5857	427	65	α−	α−	ADP
ejpam-5857	427	66	]	]	PUNCT
ejpam-5857	427	67	(	(	PUNCT
ejpam-5857	427	68	x	x	X
ejpam-5857	427	69	·	·	PUNCT
ejpam-5857	427	70	z	z	X
ejpam-5857	427	71	)	)	PUNCT
ejpam-5857	427	72	=	=	SYM
ejpam-5857	427	73	α+	α+	NOUN
ejpam-5857	427	74	.	.	PUNCT
ejpam-5857	428	1	hence	hence	ADV
ejpam-5857	428	2	,	,	PUNCT
ejpam-5857	428	3	x	x	X
ejpam-5857	428	4	·	·	PUNCT
ejpam-5857	428	5	z	z	X
ejpam-5857	428	6	∈	∈	PROPN
ejpam-5857	428	7	g	g	NOUN
ejpam-5857	428	8	,	,	PUNCT
ejpam-5857	428	9	so	so	SCONJ
ejpam-5857	428	10	g	g	PROPN
ejpam-5857	428	11	is	be	AUX
ejpam-5857	428	12	an	an	DET
ejpam-5857	428	13	iup	iup	NOUN
ejpam-5857	428	14	-	-	PUNCT
ejpam-5857	428	15	ideal	ideal	NOUN
ejpam-5857	428	16	of	of	ADP
ejpam-5857	428	17	x.	x.	PROPN
ejpam-5857	428	18	theorem	theorem	VERB
ejpam-5857	428	19	8	8	NUM
ejpam-5857	428	20	.	.	PUNCT
ejpam-5857	429	1	a	a	DET
ejpam-5857	429	2	nonempty	nonempty	NOUN
ejpam-5857	429	3	subset	subset	VERB
ejpam-5857	429	4	g	g	NOUN
ejpam-5857	429	5	is	be	AUX
ejpam-5857	429	6	an	an	DET
ejpam-5857	429	7	iup	iup	NOUN
ejpam-5857	429	8	-	-	PUNCT
ejpam-5857	429	9	filter	filter	NOUN
ejpam-5857	429	10	of	of	ADP
ejpam-5857	429	11	x	x	SYM
ejpam-5857	429	12	if	if	SCONJ
ejpam-5857	429	13	and	and	CCONJ
ejpam-5857	429	14	only	only	ADV
ejpam-5857	429	15	if	if	SCONJ
ejpam-5857	429	16	the	the	DET
ejpam-5857	429	17	characteristic	characteristic	ADJ
ejpam-5857	429	18	ins	ins	PROPN
ejpam-5857	429	19	ψg	ψg	PROPN
ejpam-5857	429	20	is	be	AUX
ejpam-5857	429	21	an	an	DET
ejpam-5857	429	22	intuitionistic	intuitionistic	ADJ
ejpam-5857	429	23	neutrosophic	neutrosophic	ADJ
ejpam-5857	429	24	iup	iup	NOUN
ejpam-5857	429	25	-	-	PUNCT
ejpam-5857	429	26	filter	filter	NOUN
ejpam-5857	429	27	of	of	ADP
ejpam-5857	429	28	x.	x.	NOUN
ejpam-5857	429	29	proof	proof	PROPN
ejpam-5857	429	30	.	.	PUNCT
ejpam-5857	430	1	assume	assume	VERB
ejpam-5857	430	2	that	that	SCONJ
ejpam-5857	430	3	g	g	PROPN
ejpam-5857	430	4	is	be	AUX
ejpam-5857	430	5	an	an	DET
ejpam-5857	430	6	iup	iup	NOUN
ejpam-5857	430	7	-	-	PUNCT
ejpam-5857	430	8	filter	filter	NOUN
ejpam-5857	430	9	of	of	ADP
ejpam-5857	430	10	x.	x.	NOUN
ejpam-5857	430	11	since	since	SCONJ
ejpam-5857	430	12	0	0	NUM
ejpam-5857	430	13	∈	∈	PROPN
ejpam-5857	430	14	g	g	NOUN
ejpam-5857	430	15	,	,	PUNCT
ejpam-5857	430	16	it	it	PRON
ejpam-5857	430	17	follows	follow	VERB
ejpam-5857	430	18	from	from	ADP
ejpam-5857	430	19	lemma	lemma	PROPN
ejpam-5857	430	20	3	3	NUM
ejpam-5857	430	21	that	that	PRON
ejpam-5857	430	22	ψg	ψg	PROPN
ejpam-5857	430	23	t	t	PROPN
ejpam-5857	430	24	[	[	PUNCT
ejpam-5857	430	25	α+	α+	X
ejpam-5857	430	26	α−	α−	ADP
ejpam-5857	430	27	]	]	PUNCT
ejpam-5857	430	28	,	,	PUNCT
ejpam-5857	430	29	ψ	ψ	X
ejpam-5857	430	30	g	g	NOUN
ejpam-5857	430	31	i	i	PRON
ejpam-5857	430	32	[	[	PUNCT
ejpam-5857	430	33	β−	β−	PROPN
ejpam-5857	430	34	β+	β+	PUNCT
ejpam-5857	430	35	]	]	PUNCT
ejpam-5857	430	36	and	and	CCONJ
ejpam-5857	430	37	ψ	ψ	X
ejpam-5857	430	38	g	g	PROPN
ejpam-5857	430	39	f	f	PROPN
ejpam-5857	431	1	[	[	X
ejpam-5857	431	2	0.5	0.5	NUM
ejpam-5857	431	3	]	]	PUNCT
ejpam-5857	431	4	satisfy	satisfy	NOUN
ejpam-5857	431	5	the	the	DET
ejpam-5857	431	6	conditions	condition	NOUN
ejpam-5857	431	7	(	(	PUNCT
ejpam-5857	431	8	3.8	3.8	NUM
ejpam-5857	431	9	)	)	PUNCT
ejpam-5857	431	10	,	,	PUNCT
ejpam-5857	431	11	(	(	PUNCT
ejpam-5857	431	12	3.9	3.9	NUM
ejpam-5857	431	13	)	)	PUNCT
ejpam-5857	431	14	and	and	CCONJ
ejpam-5857	431	15	(	(	PUNCT
ejpam-5857	431	16	3.10	3.10	NUM
ejpam-5857	431	17	)	)	PUNCT
ejpam-5857	431	18	,	,	PUNCT
ejpam-5857	431	19	respectively	respectively	ADV
ejpam-5857	431	20	.	.	PUNCT
ejpam-5857	432	1	next	next	ADV
ejpam-5857	432	2	,	,	PUNCT
ejpam-5857	432	3	let	let	VERB
ejpam-5857	432	4	x	x	PRON
ejpam-5857	432	5	,	,	PUNCT
ejpam-5857	432	6	y	y	PROPN
ejpam-5857	432	7	∈	∈	PROPN
ejpam-5857	432	8	x.	x.	NOUN
ejpam-5857	432	9	case	case	NOUN
ejpam-5857	432	10	1	1	NUM
ejpam-5857	432	11	:	:	PUNCT
ejpam-5857	432	12	suppose	suppose	VERB
ejpam-5857	432	13	x	x	X
ejpam-5857	432	14	·	·	PUNCT
ejpam-5857	432	15	y	y	PROPN
ejpam-5857	432	16	∈	∈	PROPN
ejpam-5857	432	17	g	g	PROPN
ejpam-5857	432	18	and	and	CCONJ
ejpam-5857	432	19	x	x	PROPN
ejpam-5857	432	20	∈	∈	PROPN
ejpam-5857	432	21	g.	g.	NOUN
ejpam-5857	432	22	since	since	SCONJ
ejpam-5857	432	23	g	g	PROPN
ejpam-5857	432	24	is	be	AUX
ejpam-5857	432	25	an	an	DET
ejpam-5857	432	26	iup	iup	NOUN
ejpam-5857	432	27	-	-	PUNCT
ejpam-5857	432	28	filter	filter	NOUN
ejpam-5857	432	29	of	of	ADP
ejpam-5857	432	30	x	x	PRON
ejpam-5857	432	31	,	,	PUNCT
ejpam-5857	432	32	we	we	PRON
ejpam-5857	432	33	have	have	VERB
ejpam-5857	432	34	y	y	PROPN
ejpam-5857	432	35	∈	∈	PROPN
ejpam-5857	432	36	g.	g.	PROPN
ejpam-5857	433	1	thus	thus	ADV
ejpam-5857	433	2	,	,	PUNCT
ejpam-5857	433	3	ψg	ψg	PROPN
ejpam-5857	433	4	t	t	PROPN
ejpam-5857	433	5	[	[	PUNCT
ejpam-5857	433	6	α+	α+	X
ejpam-5857	433	7	α−	α−	ADP
ejpam-5857	433	8	]	]	X
ejpam-5857	433	9	(	(	PUNCT
ejpam-5857	433	10	y	y	NOUN
ejpam-5857	433	11	)	)	PUNCT
ejpam-5857	433	12	=	=	SYM
ejpam-5857	433	13	α+	α+	PUNCT
ejpam-5857	433	14	≥	≥	X
ejpam-5857	433	15	α+	α+	PUNCT
ejpam-5857	433	16	∨	∨	X
ejpam-5857	433	17	0.5	0.5	NUM
ejpam-5857	433	18	=	=	SYM
ejpam-5857	433	19	(	(	PUNCT
ejpam-5857	433	20	α+	α+	X
ejpam-5857	433	21	∧	∧	PROPN
ejpam-5857	433	22	α+	α+	PRON
ejpam-5857	433	23	)	)	PUNCT
ejpam-5857	433	24	∨	∨	NOUN
ejpam-5857	433	25	0.5	0.5	NUM
ejpam-5857	433	26	=	=	SYM
ejpam-5857	433	27	(	(	PUNCT
ejpam-5857	433	28	ψg	ψg	NOUN
ejpam-5857	433	29	t	t	PROPN
ejpam-5857	433	30	[	[	PUNCT
ejpam-5857	433	31	α+	α+	X
ejpam-5857	433	32	α−	α−	ADP
ejpam-5857	433	33	]	]	PUNCT
ejpam-5857	433	34	(	(	PUNCT
ejpam-5857	433	35	x	x	SYM
ejpam-5857	433	36	·	·	PUNCT
ejpam-5857	433	37	y	y	X
ejpam-5857	433	38	)	)	PUNCT
ejpam-5857	433	39	∧	∧	PROPN
ejpam-5857	433	40	ψg	ψg	PROPN
ejpam-5857	433	41	t	t	PROPN
ejpam-5857	433	42	[	[	PUNCT
ejpam-5857	433	43	α+	α+	X
ejpam-5857	433	44	α−	α−	ADP
ejpam-5857	433	45	]	]	PUNCT
ejpam-5857	433	46	(	(	PUNCT
ejpam-5857	433	47	x	x	NOUN
ejpam-5857	433	48	)	)	PUNCT
ejpam-5857	433	49	)	)	PUNCT
ejpam-5857	433	50	∨	∨	NUM
ejpam-5857	433	51	0.5	0.5	NUM
ejpam-5857	433	52	.	.	PUNCT
ejpam-5857	434	1	k.	k.	PROPN
ejpam-5857	434	2	suayngam	suayngam	PROPN
ejpam-5857	434	3	,	,	PUNCT
ejpam-5857	434	4	p.	p.	NOUN
ejpam-5857	434	5	julatha	julatha	PROPN
ejpam-5857	434	6	,	,	PUNCT
ejpam-5857	434	7	w.	w.	PROPN
ejpam-5857	434	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	434	9	,	,	PUNCT
ejpam-5857	434	10	a.	a.	NOUN
ejpam-5857	434	11	iampan	iampan	PROPN
ejpam-5857	434	12	/	/	SYM
ejpam-5857	434	13	eur	eur	PROPN
ejpam-5857	434	14	.	.	PUNCT
ejpam-5857	435	1	j.	j.	PROPN
ejpam-5857	435	2	pure	pure	PROPN
ejpam-5857	435	3	appl	appl	PROPN
ejpam-5857	435	4	.	.	PROPN
ejpam-5857	435	5	math	math	PROPN
ejpam-5857	435	6	,	,	PUNCT
ejpam-5857	435	7	18	18	NUM
ejpam-5857	435	8	(	(	PUNCT
ejpam-5857	435	9	2	2	NUM
ejpam-5857	435	10	)	)	PUNCT
ejpam-5857	435	11	(	(	PUNCT
ejpam-5857	435	12	2025	2025	NUM
ejpam-5857	435	13	)	)	PUNCT
ejpam-5857	435	14	,	,	PUNCT
ejpam-5857	435	15	5857	5857	NUM
ejpam-5857	435	16	17	17	NUM
ejpam-5857	435	17	of	of	ADP
ejpam-5857	435	18	30	30	NUM
ejpam-5857	435	19	case	case	NOUN
ejpam-5857	435	20	2	2	NUM
ejpam-5857	435	21	:	:	PUNCT
ejpam-5857	435	22	suppose	suppose	VERB
ejpam-5857	435	23	x	x	X
ejpam-5857	435	24	·	·	PUNCT
ejpam-5857	435	25	y	y	X
ejpam-5857	435	26	/∈	/∈	PUNCT
ejpam-5857	436	1	g	g	NOUN
ejpam-5857	436	2	or	or	CCONJ
ejpam-5857	436	3	x	x	PROPN
ejpam-5857	436	4	/∈	/∈	PROPN
ejpam-5857	437	1	g.	g.	PROPN
ejpam-5857	438	1	then	then	ADV
ejpam-5857	438	2	ψg	ψg	PROPN
ejpam-5857	438	3	t	t	PROPN
ejpam-5857	438	4	[	[	PUNCT
ejpam-5857	438	5	α+	α+	X
ejpam-5857	438	6	α−	α−	ADP
ejpam-5857	438	7	]	]	PUNCT
ejpam-5857	438	8	(	(	PUNCT
ejpam-5857	438	9	x	x	SYM
ejpam-5857	438	10	·	·	PUNCT
ejpam-5857	438	11	y	y	X
ejpam-5857	438	12	)	)	PUNCT
ejpam-5857	438	13	=	=	PUNCT
ejpam-5857	439	1	α−	α−	ADP
ejpam-5857	439	2	or	or	CCONJ
ejpam-5857	439	3	ψg	ψg	X
ejpam-5857	439	4	t	t	PROPN
ejpam-5857	439	5	[	[	PUNCT
ejpam-5857	439	6	α+	α+	X
ejpam-5857	439	7	α−	α−	ADP
ejpam-5857	439	8	]	]	PUNCT
ejpam-5857	439	9	(	(	PUNCT
ejpam-5857	439	10	x	x	X
ejpam-5857	439	11	)	)	PUNCT
ejpam-5857	439	12	=	=	SYM
ejpam-5857	439	13	α−.	α−.	NOUN
ejpam-5857	439	14	thus	thus	ADV
ejpam-5857	439	15	,	,	PUNCT
ejpam-5857	439	16	ψg	ψg	PROPN
ejpam-5857	439	17	t	t	PROPN
ejpam-5857	439	18	[	[	PUNCT
ejpam-5857	439	19	α+	α+	X
ejpam-5857	439	20	α−	α−	ADP
ejpam-5857	439	21	]	]	X
ejpam-5857	439	22	(	(	PUNCT
ejpam-5857	439	23	y	y	NOUN
ejpam-5857	439	24	)	)	PUNCT
ejpam-5857	439	25	≥	≥	NOUN
ejpam-5857	439	26	α−	α−	ADP
ejpam-5857	439	27	≥	≥	NOUN
ejpam-5857	439	28	α−	α−	ADP
ejpam-5857	439	29	∨	∨	NUM
ejpam-5857	439	30	0.5	0.5	NUM
ejpam-5857	439	31	=	=	SYM
ejpam-5857	439	32	(	(	PUNCT
ejpam-5857	439	33	ψg	ψg	NOUN
ejpam-5857	439	34	t	t	PROPN
ejpam-5857	439	35	[	[	PUNCT
ejpam-5857	439	36	α+	α+	X
ejpam-5857	439	37	α−	α−	ADP
ejpam-5857	439	38	]	]	PUNCT
ejpam-5857	439	39	(	(	PUNCT
ejpam-5857	439	40	x	x	SYM
ejpam-5857	439	41	·	·	PUNCT
ejpam-5857	439	42	y	y	X
ejpam-5857	439	43	)	)	PUNCT
ejpam-5857	439	44	∧	∧	PROPN
ejpam-5857	439	45	ψg	ψg	PROPN
ejpam-5857	439	46	t	t	PROPN
ejpam-5857	439	47	[	[	PUNCT
ejpam-5857	439	48	α+	α+	X
ejpam-5857	439	49	α−	α−	ADP
ejpam-5857	439	50	]	]	PUNCT
ejpam-5857	439	51	(	(	PUNCT
ejpam-5857	439	52	x	x	NOUN
ejpam-5857	439	53	)	)	PUNCT
ejpam-5857	439	54	)	)	PUNCT
ejpam-5857	439	55	∨	∨	NUM
ejpam-5857	439	56	0.5	0.5	NUM
ejpam-5857	439	57	.	.	PUNCT
ejpam-5857	439	58	case	case	NOUN
ejpam-5857	439	59	1	1	NUM
ejpam-5857	439	60	’	'	PUNCT
ejpam-5857	439	61	:	:	PUNCT
ejpam-5857	439	62	suppose	suppose	VERB
ejpam-5857	439	63	x	x	X
ejpam-5857	439	64	·	·	PUNCT
ejpam-5857	439	65	y	y	PROPN
ejpam-5857	439	66	∈	∈	PROPN
ejpam-5857	439	67	g	g	PROPN
ejpam-5857	439	68	and	and	CCONJ
ejpam-5857	439	69	x	x	PROPN
ejpam-5857	439	70	∈	∈	PROPN
ejpam-5857	439	71	g.	g.	NOUN
ejpam-5857	439	72	since	since	SCONJ
ejpam-5857	439	73	g	g	PROPN
ejpam-5857	439	74	is	be	AUX
ejpam-5857	439	75	an	an	DET
ejpam-5857	439	76	iup	iup	NOUN
ejpam-5857	439	77	-	-	PUNCT
ejpam-5857	439	78	filter	filter	NOUN
ejpam-5857	439	79	of	of	ADP
ejpam-5857	439	80	x	x	PRON
ejpam-5857	439	81	,	,	PUNCT
ejpam-5857	439	82	we	we	PRON
ejpam-5857	439	83	have	have	VERB
ejpam-5857	439	84	y	y	PROPN
ejpam-5857	439	85	∈	∈	PROPN
ejpam-5857	439	86	g.	g.	PROPN
ejpam-5857	440	1	thus	thus	ADV
ejpam-5857	440	2	,	,	PUNCT
ejpam-5857	440	3	ψg	ψg	PROPN
ejpam-5857	441	1	i	i	PRON
ejpam-5857	441	2	[	[	PUNCT
ejpam-5857	441	3	β−	β−	PUNCT
ejpam-5857	441	4	β+	β+	PUNCT
ejpam-5857	441	5	]	]	X
ejpam-5857	441	6	(	(	PUNCT
ejpam-5857	441	7	y	y	NOUN
ejpam-5857	441	8	)	)	PUNCT
ejpam-5857	441	9	=	=	PUNCT
ejpam-5857	442	1	β−	β−	PUNCT
ejpam-5857	442	2	≤	≤	NUM
ejpam-5857	442	3	β−	β−	PUNCT
ejpam-5857	443	1	∧	∧	NOUN
ejpam-5857	443	2	0.5	0.5	NUM
ejpam-5857	443	3	=	=	SYM
ejpam-5857	443	4	(	(	PUNCT
ejpam-5857	443	5	β−	β−	PROPN
ejpam-5857	443	6	∨	∨	NUM
ejpam-5857	443	7	β−	β−	NUM
ejpam-5857	443	8	)	)	PUNCT
ejpam-5857	443	9	∧	∧	NOUN
ejpam-5857	443	10	0.5	0.5	NUM
ejpam-5857	443	11	=	=	SYM
ejpam-5857	443	12	(	(	PUNCT
ejpam-5857	443	13	ψg	ψg	NOUN
ejpam-5857	443	14	i	i	PRON
ejpam-5857	443	15	[	[	PUNCT
ejpam-5857	443	16	β−	β−	PUNCT
ejpam-5857	443	17	β+	β+	PUNCT
ejpam-5857	443	18	]	]	X
ejpam-5857	443	19	(	(	PUNCT
ejpam-5857	443	20	x	x	SYM
ejpam-5857	443	21	·	·	PUNCT
ejpam-5857	443	22	y	y	X
ejpam-5857	443	23	)	)	PUNCT
ejpam-5857	443	24	∨	∨	NUM
ejpam-5857	443	25	ψg	ψg	NOUN
ejpam-5857	444	1	i	i	PRON
ejpam-5857	444	2	[	[	PUNCT
ejpam-5857	444	3	β−	β−	PUNCT
ejpam-5857	444	4	β+	β+	PUNCT
ejpam-5857	444	5	]	]	X
ejpam-5857	444	6	(	(	PUNCT
ejpam-5857	444	7	x	x	NOUN
ejpam-5857	444	8	)	)	PUNCT
ejpam-5857	444	9	)	)	PUNCT
ejpam-5857	445	1	∧	∧	NOUN
ejpam-5857	445	2	0.5	0.5	NUM
ejpam-5857	445	3	.	.	PUNCT
ejpam-5857	445	4	case	case	NOUN
ejpam-5857	445	5	2	2	NUM
ejpam-5857	445	6	’	'	PUNCT
ejpam-5857	445	7	:	:	PUNCT
ejpam-5857	445	8	suppose	suppose	VERB
ejpam-5857	445	9	x	x	X
ejpam-5857	445	10	·	·	PUNCT
ejpam-5857	445	11	y	y	X
ejpam-5857	445	12	/∈	/∈	PUNCT
ejpam-5857	445	13	g	g	NOUN
ejpam-5857	445	14	or	or	CCONJ
ejpam-5857	445	15	x	x	PROPN
ejpam-5857	445	16	/∈	/∈	PROPN
ejpam-5857	446	1	g.	g.	PROPN
ejpam-5857	447	1	then	then	ADV
ejpam-5857	447	2	ψg	ψg	PROPN
ejpam-5857	448	1	i	i	PRON
ejpam-5857	448	2	[	[	PUNCT
ejpam-5857	448	3	β−	β−	PUNCT
ejpam-5857	448	4	β+	β+	PUNCT
ejpam-5857	448	5	]	]	X
ejpam-5857	448	6	(	(	PUNCT
ejpam-5857	448	7	x	x	SYM
ejpam-5857	448	8	·	·	PUNCT
ejpam-5857	448	9	y	y	X
ejpam-5857	448	10	)	)	PUNCT
ejpam-5857	448	11	=	=	SYM
ejpam-5857	448	12	β+	β+	PUNCT
ejpam-5857	448	13	or	or	CCONJ
ejpam-5857	448	14	ψg	ψg	INTJ
ejpam-5857	448	15	i	i	PRON
ejpam-5857	448	16	[	[	PUNCT
ejpam-5857	448	17	β−	β−	PUNCT
ejpam-5857	448	18	β+	β+	PUNCT
ejpam-5857	448	19	]	]	X
ejpam-5857	448	20	(	(	PUNCT
ejpam-5857	448	21	x	x	X
ejpam-5857	448	22	)	)	PUNCT
ejpam-5857	448	23	=	=	SYM
ejpam-5857	448	24	β+	β+	X
ejpam-5857	448	25	.	.	PUNCT
ejpam-5857	449	1	thus	thus	ADV
ejpam-5857	449	2	,	,	PUNCT
ejpam-5857	449	3	ψg	ψg	PROPN
ejpam-5857	450	1	i	i	PRON
ejpam-5857	450	2	[	[	PUNCT
ejpam-5857	450	3	β−	β−	PUNCT
ejpam-5857	450	4	β+	β+	PUNCT
ejpam-5857	450	5	]	]	X
ejpam-5857	450	6	(	(	PUNCT
ejpam-5857	450	7	y	y	NOUN
ejpam-5857	450	8	)	)	PUNCT
ejpam-5857	450	9	≤	≤	NOUN
ejpam-5857	450	10	β+	β+	PUNCT
ejpam-5857	450	11	≤	≤	NUM
ejpam-5857	450	12	β+	β+	PUNCT
ejpam-5857	450	13	∧	∧	NOUN
ejpam-5857	450	14	0.5	0.5	NUM
ejpam-5857	450	15	=	=	SYM
ejpam-5857	450	16	(	(	PUNCT
ejpam-5857	450	17	ψg	ψg	NOUN
ejpam-5857	450	18	i	i	PRON
ejpam-5857	450	19	[	[	PUNCT
ejpam-5857	450	20	β−	β−	PUNCT
ejpam-5857	450	21	β+	β+	PUNCT
ejpam-5857	450	22	]	]	X
ejpam-5857	450	23	(	(	PUNCT
ejpam-5857	450	24	x	x	SYM
ejpam-5857	450	25	·	·	PUNCT
ejpam-5857	450	26	y	y	X
ejpam-5857	450	27	)	)	PUNCT
ejpam-5857	450	28	∨	∨	NUM
ejpam-5857	450	29	ψg	ψg	NOUN
ejpam-5857	451	1	i	i	PRON
ejpam-5857	451	2	[	[	PUNCT
ejpam-5857	451	3	β−	β−	PUNCT
ejpam-5857	451	4	β+	β+	PUNCT
ejpam-5857	451	5	]	]	X
ejpam-5857	451	6	(	(	PUNCT
ejpam-5857	451	7	x	x	NOUN
ejpam-5857	451	8	)	)	PUNCT
ejpam-5857	451	9	)	)	PUNCT
ejpam-5857	451	10	∧	∧	NOUN
ejpam-5857	451	11	0.5	0.5	NUM
ejpam-5857	451	12	.	.	PUNCT
ejpam-5857	452	1	it	it	PRON
ejpam-5857	452	2	is	be	AUX
ejpam-5857	452	3	obvious	obvious	ADJ
ejpam-5857	452	4	to	to	PART
ejpam-5857	452	5	prove	prove	VERB
ejpam-5857	452	6	that	that	SCONJ
ejpam-5857	452	7	ψg	ψg	PROPN
ejpam-5857	452	8	f	f	PROPN
ejpam-5857	453	1	[	[	X
ejpam-5857	453	2	0.5	0.5	NUM
ejpam-5857	453	3	]	]	PUNCT
ejpam-5857	453	4	satisfied	satisfy	VERB
ejpam-5857	453	5	the	the	DET
ejpam-5857	453	6	condition	condition	NOUN
ejpam-5857	453	7	(	(	PUNCT
ejpam-5857	453	8	3.16	3.16	NUM
ejpam-5857	453	9	)	)	PUNCT
ejpam-5857	453	10	.	.	PUNCT
ejpam-5857	454	1	hence	hence	ADV
ejpam-5857	454	2	,	,	PUNCT
ejpam-5857	454	3	ψg	ψg	PROPN
ejpam-5857	454	4	is	be	AUX
ejpam-5857	454	5	an	an	DET
ejpam-5857	454	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	454	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	454	8	iup	iup	NOUN
ejpam-5857	454	9	-	-	PUNCT
ejpam-5857	454	10	filter	filter	NOUN
ejpam-5857	454	11	of	of	ADP
ejpam-5857	454	12	x.	x.	NOUN
ejpam-5857	454	13	conversely	conversely	ADV
ejpam-5857	454	14	,	,	PUNCT
ejpam-5857	454	15	assume	assume	VERB
ejpam-5857	454	16	that	that	SCONJ
ejpam-5857	454	17	the	the	DET
ejpam-5857	454	18	characteristic	characteristic	ADJ
ejpam-5857	454	19	ins	ins	PROPN
ejpam-5857	454	20	ψg	ψg	PROPN
ejpam-5857	454	21	is	be	AUX
ejpam-5857	454	22	an	an	DET
ejpam-5857	454	23	intuitionistic	intuitionistic	ADJ
ejpam-5857	454	24	neutrosophic	neutrosophic	ADJ
ejpam-5857	454	25	iup	iup	NOUN
ejpam-5857	454	26	-	-	PUNCT
ejpam-5857	454	27	filter	filter	NOUN
ejpam-5857	454	28	of	of	ADP
ejpam-5857	454	29	x.	x.	NOUN
ejpam-5857	454	30	since	since	SCONJ
ejpam-5857	454	31	ψg	ψg	PROPN
ejpam-5857	454	32	t	t	PROPN
ejpam-5857	454	33	[	[	PUNCT
ejpam-5857	454	34	α+	α+	X
ejpam-5857	454	35	α−	α−	X
ejpam-5857	454	36	]	]	PUNCT
ejpam-5857	454	37	satisfies	satisfie	NOUN
ejpam-5857	454	38	the	the	DET
ejpam-5857	454	39	condition	condition	NOUN
ejpam-5857	454	40	(	(	PUNCT
ejpam-5857	454	41	3.8	3.8	NUM
ejpam-5857	454	42	)	)	PUNCT
ejpam-5857	454	43	,	,	PUNCT
ejpam-5857	454	44	it	it	PRON
ejpam-5857	454	45	follows	follow	VERB
ejpam-5857	454	46	from	from	ADP
ejpam-5857	454	47	lemma	lemma	PROPN
ejpam-5857	454	48	3	3	NUM
ejpam-5857	454	49	that	that	SCONJ
ejpam-5857	454	50	0	0	NUM
ejpam-5857	454	51	∈	∈	PROPN
ejpam-5857	454	52	g.	g.	NOUN
ejpam-5857	454	53	next	next	ADV
ejpam-5857	454	54	,	,	PUNCT
ejpam-5857	454	55	let	let	VERB
ejpam-5857	454	56	x	x	PRON
ejpam-5857	454	57	,	,	PUNCT
ejpam-5857	454	58	y	y	PROPN
ejpam-5857	454	59	∈	∈	PROPN
ejpam-5857	454	60	g	g	PROPN
ejpam-5857	454	61	be	be	AUX
ejpam-5857	454	62	such	such	ADJ
ejpam-5857	454	63	that	that	SCONJ
ejpam-5857	454	64	x	x	X
ejpam-5857	454	65	·	·	PUNCT
ejpam-5857	454	66	y	y	PROPN
ejpam-5857	454	67	∈	∈	PROPN
ejpam-5857	454	68	g	g	PROPN
ejpam-5857	454	69	and	and	CCONJ
ejpam-5857	454	70	x	x	PROPN
ejpam-5857	454	71	∈	∈	PROPN
ejpam-5857	454	72	g.	g.	NOUN
ejpam-5857	455	1	then	then	ADV
ejpam-5857	455	2	ψg	ψg	PROPN
ejpam-5857	455	3	t	t	PROPN
ejpam-5857	455	4	[	[	PUNCT
ejpam-5857	455	5	α+	α+	X
ejpam-5857	455	6	α−	α−	ADP
ejpam-5857	455	7	]	]	PUNCT
ejpam-5857	455	8	(	(	PUNCT
ejpam-5857	455	9	x	x	SYM
ejpam-5857	455	10	·	·	PUNCT
ejpam-5857	455	11	y	y	X
ejpam-5857	455	12	)	)	PUNCT
ejpam-5857	455	13	=	=	SYM
ejpam-5857	455	14	α+	α+	PUNCT
ejpam-5857	455	15	and	and	CCONJ
ejpam-5857	455	16	ψg	ψg	X
ejpam-5857	455	17	t	t	PROPN
ejpam-5857	455	18	[	[	PUNCT
ejpam-5857	455	19	α+	α+	X
ejpam-5857	455	20	α−	α−	ADP
ejpam-5857	455	21	]	]	PUNCT
ejpam-5857	455	22	(	(	PUNCT
ejpam-5857	455	23	x	x	X
ejpam-5857	455	24	)	)	PUNCT
ejpam-5857	455	25	=	=	SYM
ejpam-5857	455	26	α+	α+	NOUN
ejpam-5857	455	27	.	.	PUNCT
ejpam-5857	456	1	thus	thus	ADV
ejpam-5857	456	2	,	,	PUNCT
ejpam-5857	456	3	ψg	ψg	PROPN
ejpam-5857	456	4	t	t	PROPN
ejpam-5857	456	5	[	[	PUNCT
ejpam-5857	456	6	α+	α+	X
ejpam-5857	456	7	α−	α−	ADP
ejpam-5857	456	8	]	]	PUNCT
ejpam-5857	456	9	(	(	PUNCT
ejpam-5857	456	10	x	x	X
ejpam-5857	456	11	·	·	PUNCT
ejpam-5857	456	12	y)∧ψg	y)∧ψg	NOUN
ejpam-5857	456	13	t	t	NOUN
ejpam-5857	456	14	[	[	PUNCT
ejpam-5857	456	15	α+	α+	X
ejpam-5857	456	16	α−	α−	ADP
ejpam-5857	456	17	]	]	PUNCT
ejpam-5857	456	18	(	(	PUNCT
ejpam-5857	456	19	x	x	X
ejpam-5857	456	20	)	)	PUNCT
ejpam-5857	456	21	=	=	SYM
ejpam-5857	456	22	α+	α+	NOUN
ejpam-5857	456	23	.	.	PUNCT
ejpam-5857	456	24	by	by	ADP
ejpam-5857	456	25	the	the	DET
ejpam-5857	456	26	condition	condition	NOUN
ejpam-5857	456	27	(	(	PUNCT
ejpam-5857	456	28	3.14	3.14	NUM
ejpam-5857	456	29	)	)	PUNCT
ejpam-5857	456	30	,	,	PUNCT
ejpam-5857	456	31	we	we	PRON
ejpam-5857	456	32	have	have	VERB
ejpam-5857	456	33	ψg	ψg	PROPN
ejpam-5857	456	34	t	t	PROPN
ejpam-5857	456	35	[	[	PUNCT
ejpam-5857	456	36	α+	α+	X
ejpam-5857	456	37	α−	α−	ADP
ejpam-5857	456	38	]	]	X
ejpam-5857	456	39	(	(	PUNCT
ejpam-5857	456	40	y	y	NOUN
ejpam-5857	456	41	)	)	PUNCT
ejpam-5857	456	42	=	=	SYM
ejpam-5857	457	1	(	(	PUNCT
ejpam-5857	457	2	ψg	ψg	NOUN
ejpam-5857	457	3	t	t	PROPN
ejpam-5857	457	4	[	[	PUNCT
ejpam-5857	457	5	α+	α+	X
ejpam-5857	457	6	α−	α−	ADP
ejpam-5857	457	7	]	]	PUNCT
ejpam-5857	457	8	(	(	PUNCT
ejpam-5857	457	9	x	x	SYM
ejpam-5857	457	10	·	·	PUNCT
ejpam-5857	457	11	y	y	X
ejpam-5857	457	12	)	)	PUNCT
ejpam-5857	457	13	∧	∧	PROPN
ejpam-5857	457	14	ψg	ψg	PROPN
ejpam-5857	457	15	t	t	PROPN
ejpam-5857	457	16	[	[	PUNCT
ejpam-5857	457	17	α+	α+	X
ejpam-5857	457	18	α−	α−	ADP
ejpam-5857	457	19	]	]	PUNCT
ejpam-5857	457	20	(	(	PUNCT
ejpam-5857	457	21	x	x	NOUN
ejpam-5857	457	22	)	)	PUNCT
ejpam-5857	457	23	)	)	PUNCT
ejpam-5857	458	1	∨	∨	NOUN
ejpam-5857	458	2	0.5	0.5	NUM
ejpam-5857	458	3	=	=	SYM
ejpam-5857	458	4	α+	α+	PUNCT
ejpam-5857	458	5	∨	∨	NUM
ejpam-5857	458	6	0.5	0.5	NUM
ejpam-5857	458	7	≥	≥	NOUN
ejpam-5857	458	8	α+	α+	NOUN
ejpam-5857	458	9	,	,	PUNCT
ejpam-5857	458	10	that	that	ADV
ejpam-5857	458	11	is	is	ADV
ejpam-5857	458	12	,	,	PUNCT
ejpam-5857	458	13	ψg	ψg	PROPN
ejpam-5857	458	14	t	t	PROPN
ejpam-5857	458	15	[	[	PUNCT
ejpam-5857	458	16	α+	α+	X
ejpam-5857	458	17	α−	α−	ADP
ejpam-5857	458	18	]	]	X
ejpam-5857	458	19	(	(	PUNCT
ejpam-5857	458	20	y	y	NOUN
ejpam-5857	458	21	)	)	PUNCT
ejpam-5857	458	22	=	=	SYM
ejpam-5857	458	23	α+	α+	NOUN
ejpam-5857	458	24	.	.	PUNCT
ejpam-5857	459	1	hence	hence	ADV
ejpam-5857	459	2	,	,	PUNCT
ejpam-5857	459	3	y	y	PROPN
ejpam-5857	459	4	∈	∈	PROPN
ejpam-5857	459	5	g	g	PROPN
ejpam-5857	459	6	,	,	PUNCT
ejpam-5857	459	7	so	so	SCONJ
ejpam-5857	459	8	g	g	PROPN
ejpam-5857	459	9	is	be	AUX
ejpam-5857	459	10	an	an	DET
ejpam-5857	459	11	iup	iup	NOUN
ejpam-5857	459	12	-	-	PUNCT
ejpam-5857	459	13	filter	filter	NOUN
ejpam-5857	459	14	of	of	ADP
ejpam-5857	459	15	x.	x.	NOUN
ejpam-5857	459	16	theorem	theorem	VERB
ejpam-5857	459	17	9	9	NUM
ejpam-5857	459	18	.	.	PUNCT
ejpam-5857	460	1	a	a	DET
ejpam-5857	460	2	nonempty	nonempty	NOUN
ejpam-5857	460	3	subset	subset	VERB
ejpam-5857	460	4	g	g	NOUN
ejpam-5857	460	5	is	be	AUX
ejpam-5857	460	6	a	a	DET
ejpam-5857	460	7	strong	strong	ADJ
ejpam-5857	460	8	iup	iup	NOUN
ejpam-5857	460	9	-	-	PUNCT
ejpam-5857	460	10	ideal	ideal	NOUN
ejpam-5857	460	11	of	of	ADP
ejpam-5857	460	12	x	x	SYM
ejpam-5857	460	13	if	if	SCONJ
ejpam-5857	460	14	and	and	CCONJ
ejpam-5857	460	15	only	only	ADV
ejpam-5857	460	16	if	if	SCONJ
ejpam-5857	460	17	the	the	DET
ejpam-5857	460	18	characteristic	characteristic	ADJ
ejpam-5857	460	19	ins	ins	PROPN
ejpam-5857	460	20	ψg	ψg	PROPN
ejpam-5857	460	21	is	be	AUX
ejpam-5857	460	22	an	an	DET
ejpam-5857	460	23	intuitionistic	intuitionistic	ADJ
ejpam-5857	460	24	neutrosophic	neutrosophic	ADJ
ejpam-5857	460	25	strong	strong	ADJ
ejpam-5857	460	26	iup	iup	NOUN
ejpam-5857	460	27	-	-	PUNCT
ejpam-5857	460	28	ideal	ideal	NOUN
ejpam-5857	460	29	of	of	ADP
ejpam-5857	460	30	x.	x.	NOUN
ejpam-5857	460	31	proof	proof	NOUN
ejpam-5857	460	32	.	.	PUNCT
ejpam-5857	461	1	it	it	PRON
ejpam-5857	461	2	is	be	AUX
ejpam-5857	461	3	straightforward	straightforward	ADJ
ejpam-5857	461	4	by	by	ADP
ejpam-5857	461	5	theorem	theorem	NOUN
ejpam-5857	461	6	1	1	NUM
ejpam-5857	461	7	.	.	PUNCT
ejpam-5857	462	1	lemma	lemma	PROPN
ejpam-5857	462	2	4	4	X
ejpam-5857	462	3	.	.	PUNCT
ejpam-5857	463	1	let	let	VERB
ejpam-5857	463	2	f	f	PRON
ejpam-5857	463	3	be	be	AUX
ejpam-5857	463	4	an	an	DET
ejpam-5857	463	5	fs	fs	NOUN
ejpam-5857	463	6	in	in	ADP
ejpam-5857	463	7	x.	x.	PROPN
ejpam-5857	463	8	then	then	ADV
ejpam-5857	463	9	the	the	DET
ejpam-5857	463	10	following	follow	VERB
ejpam-5857	463	11	statements	statement	NOUN
ejpam-5857	463	12	hold	hold	VERB
ejpam-5857	463	13	:	:	PUNCT
ejpam-5857	463	14	(	(	PUNCT
ejpam-5857	463	15	∀x	∀x	X
ejpam-5857	463	16	,	,	PUNCT
ejpam-5857	463	17	y	y	PROPN
ejpam-5857	463	18	∈	∈	PROPN
ejpam-5857	463	19	x)(1−	x)(1−	PROPN
ejpam-5857	463	20	(	(	PUNCT
ejpam-5857	463	21	f(x	f(x	PROPN
ejpam-5857	463	22	)	)	PUNCT
ejpam-5857	463	23	∨	∨	NUM
ejpam-5857	463	24	f(y	f(y	NOUN
ejpam-5857	463	25	)	)	PUNCT
ejpam-5857	463	26	)	)	PUNCT
ejpam-5857	464	1	=	=	SYM
ejpam-5857	464	2	(	(	PUNCT
ejpam-5857	464	3	1−	1−	NUM
ejpam-5857	464	4	f(x	f(x	PROPN
ejpam-5857	464	5	)	)	PUNCT
ejpam-5857	464	6	)	)	PUNCT
ejpam-5857	465	1	∧	∧	PROPN
ejpam-5857	465	2	(	(	PUNCT
ejpam-5857	465	3	1−	1−	NUM
ejpam-5857	465	4	f(y	f(y	NOUN
ejpam-5857	465	5	)	)	PUNCT
ejpam-5857	465	6	)	)	PUNCT
ejpam-5857	465	7	)	)	PUNCT
ejpam-5857	465	8	,	,	PUNCT
ejpam-5857	465	9	(	(	PUNCT
ejpam-5857	465	10	3.22	3.22	NUM
ejpam-5857	465	11	)	)	PUNCT
ejpam-5857	465	12	(	(	PUNCT
ejpam-5857	465	13	∀x	∀x	X
ejpam-5857	465	14	,	,	PUNCT
ejpam-5857	465	15	y	y	PROPN
ejpam-5857	465	16	∈	∈	PROPN
ejpam-5857	465	17	x)(1−	x)(1−	PROPN
ejpam-5857	465	18	(	(	PUNCT
ejpam-5857	465	19	f(x	f(x	PROPN
ejpam-5857	465	20	)	)	PUNCT
ejpam-5857	465	21	∧	∧	PROPN
ejpam-5857	465	22	f(y	f(y	NOUN
ejpam-5857	465	23	)	)	PUNCT
ejpam-5857	465	24	)	)	PUNCT
ejpam-5857	465	25	=	=	SYM
ejpam-5857	465	26	(	(	PUNCT
ejpam-5857	465	27	1−	1−	NUM
ejpam-5857	465	28	f(x	f(x	PROPN
ejpam-5857	465	29	)	)	PUNCT
ejpam-5857	465	30	)	)	PUNCT
ejpam-5857	465	31	∨	∨	NUM
ejpam-5857	465	32	(	(	PUNCT
ejpam-5857	465	33	1−	1−	NUM
ejpam-5857	465	34	f(y	f(y	NOUN
ejpam-5857	465	35	)	)	PUNCT
ejpam-5857	465	36	)	)	PUNCT
ejpam-5857	465	37	)	)	PUNCT
ejpam-5857	465	38	.	.	PUNCT
ejpam-5857	466	1	(	(	PUNCT
ejpam-5857	466	2	3.23	3.23	NUM
ejpam-5857	466	3	)	)	PUNCT
ejpam-5857	466	4	proof	proof	NOUN
ejpam-5857	466	5	.	.	PUNCT
ejpam-5857	467	1	let	let	VERB
ejpam-5857	467	2	x	x	PRON
ejpam-5857	467	3	,	,	PUNCT
ejpam-5857	467	4	y	y	PROPN
ejpam-5857	467	5	∈	∈	PROPN
ejpam-5857	467	6	x.	x.	NOUN
ejpam-5857	467	7	suppose	suppose	VERB
ejpam-5857	467	8	f(x	f(x	PROPN
ejpam-5857	467	9	)	)	PUNCT
ejpam-5857	467	10	∨	∨	NUM
ejpam-5857	467	11	f(y	f(y	NOUN
ejpam-5857	467	12	)	)	PUNCT
ejpam-5857	467	13	=	=	SYM
ejpam-5857	467	14	f(x	f(x	PROPN
ejpam-5857	467	15	)	)	PUNCT
ejpam-5857	467	16	.	.	PUNCT
ejpam-5857	468	1	then	then	ADV
ejpam-5857	468	2	f(y	f(y	NOUN
ejpam-5857	468	3	)	)	PUNCT
ejpam-5857	468	4	≤	≤	NOUN
ejpam-5857	468	5	f(x	f(x	PROPN
ejpam-5857	468	6	)	)	PUNCT
ejpam-5857	468	7	,	,	PUNCT
ejpam-5857	468	8	that	that	ADV
ejpam-5857	468	9	is	is	ADV
ejpam-5857	468	10	,	,	PUNCT
ejpam-5857	468	11	1−f(y	1−f(y	NUM
ejpam-5857	468	12	)	)	PUNCT
ejpam-5857	468	13	≥	≥	NOUN
ejpam-5857	468	14	1−f(x	1−f(x	NUM
ejpam-5857	468	15	)	)	PUNCT
ejpam-5857	468	16	.	.	PUNCT
ejpam-5857	469	1	thus	thus	ADV
ejpam-5857	469	2	,	,	PUNCT
ejpam-5857	469	3	1−(f(x)∨f(y	1−(f(x)∨f(y	NUM
ejpam-5857	469	4	)	)	PUNCT
ejpam-5857	469	5	)	)	PUNCT
ejpam-5857	470	1	=	=	SYM
ejpam-5857	470	2	1−f(x	1−f(x	NUM
ejpam-5857	470	3	)	)	PUNCT
ejpam-5857	470	4	=	=	PRON
ejpam-5857	470	5	(	(	PUNCT
ejpam-5857	470	6	1−f(x))∧(1−f(y	1−f(x))∧(1−f(y	NUM
ejpam-5857	470	7	)	)	PUNCT
ejpam-5857	470	8	)	)	PUNCT
ejpam-5857	470	9	.	.	PUNCT
ejpam-5857	471	1	similarly	similarly	ADV
ejpam-5857	471	2	,	,	PUNCT
ejpam-5857	471	3	suppose	suppose	VERB
ejpam-5857	471	4	f(x	f(x	PROPN
ejpam-5857	471	5	)	)	PUNCT
ejpam-5857	471	6	∨	∨	NUM
ejpam-5857	471	7	f(y	f(y	NOUN
ejpam-5857	471	8	)	)	PUNCT
ejpam-5857	471	9	=	=	SYM
ejpam-5857	471	10	f(y	f(y	NOUN
ejpam-5857	471	11	)	)	PUNCT
ejpam-5857	471	12	.	.	PUNCT
ejpam-5857	472	1	then	then	ADV
ejpam-5857	472	2	f(x	f(x	PROPN
ejpam-5857	472	3	)	)	PUNCT
ejpam-5857	472	4	≤	≤	NUM
ejpam-5857	472	5	f(y	f(y	NOUN
ejpam-5857	472	6	)	)	PUNCT
ejpam-5857	472	7	,	,	PUNCT
ejpam-5857	472	8	that	that	ADV
ejpam-5857	472	9	is	is	ADV
ejpam-5857	472	10	,	,	PUNCT
ejpam-5857	472	11	1	1	NUM
ejpam-5857	472	12	−	−	PROPN
ejpam-5857	472	13	f(x	f(x	PROPN
ejpam-5857	472	14	)	)	PUNCT
ejpam-5857	472	15	≥	≥	NOUN
ejpam-5857	472	16	1	1	NUM
ejpam-5857	472	17	−	−	PROPN
ejpam-5857	472	18	f(y	f(y	NOUN
ejpam-5857	472	19	)	)	PUNCT
ejpam-5857	472	20	.	.	PUNCT
ejpam-5857	473	1	thus	thus	ADV
ejpam-5857	473	2	,	,	PUNCT
ejpam-5857	473	3	1−	1−	NUM
ejpam-5857	473	4	(	(	PUNCT
ejpam-5857	473	5	f(x	f(x	PROPN
ejpam-5857	473	6	)	)	PUNCT
ejpam-5857	473	7	∨	∨	NUM
ejpam-5857	473	8	f(y	f(y	NOUN
ejpam-5857	473	9	)	)	PUNCT
ejpam-5857	473	10	)	)	PUNCT
ejpam-5857	474	1	=	=	SYM
ejpam-5857	474	2	1−	1−	NUM
ejpam-5857	474	3	f(y	f(y	NOUN
ejpam-5857	474	4	)	)	PUNCT
ejpam-5857	474	5	=	=	PUNCT
ejpam-5857	474	6	(	(	PUNCT
ejpam-5857	474	7	1−	1−	NUM
ejpam-5857	474	8	f(x	f(x	PROPN
ejpam-5857	474	9	)	)	PUNCT
ejpam-5857	474	10	)	)	PUNCT
ejpam-5857	475	1	∧	∧	PROPN
ejpam-5857	475	2	(	(	PUNCT
ejpam-5857	475	3	1−	1−	NUM
ejpam-5857	475	4	f(y	f(y	NOUN
ejpam-5857	475	5	)	)	PUNCT
ejpam-5857	475	6	)	)	PUNCT
ejpam-5857	475	7	.	.	PUNCT
ejpam-5857	476	1	let	let	VERB
ejpam-5857	476	2	x	x	PRON
ejpam-5857	476	3	,	,	PUNCT
ejpam-5857	476	4	y	y	PROPN
ejpam-5857	476	5	∈	∈	PROPN
ejpam-5857	476	6	x.	x.	NOUN
ejpam-5857	476	7	suppose	suppose	VERB
ejpam-5857	476	8	f(x	f(x	NOUN
ejpam-5857	476	9	)	)	PUNCT
ejpam-5857	476	10	∧	∧	PROPN
ejpam-5857	476	11	f(y	f(y	NOUN
ejpam-5857	476	12	)	)	PUNCT
ejpam-5857	476	13	=	=	SYM
ejpam-5857	476	14	f(x	f(x	PROPN
ejpam-5857	476	15	)	)	PUNCT
ejpam-5857	476	16	.	.	PUNCT
ejpam-5857	477	1	then	then	ADV
ejpam-5857	477	2	f(x	f(x	PROPN
ejpam-5857	477	3	)	)	PUNCT
ejpam-5857	477	4	≤	≤	NUM
ejpam-5857	477	5	f(y	f(y	NOUN
ejpam-5857	477	6	)	)	PUNCT
ejpam-5857	477	7	,	,	PUNCT
ejpam-5857	477	8	that	that	ADV
ejpam-5857	477	9	is	is	ADV
ejpam-5857	477	10	,	,	PUNCT
ejpam-5857	477	11	1	1	NUM
ejpam-5857	477	12	−	−	PROPN
ejpam-5857	477	13	f(x	f(x	PROPN
ejpam-5857	477	14	)	)	PUNCT
ejpam-5857	477	15	≥	≥	NOUN
ejpam-5857	477	16	1	1	NUM
ejpam-5857	477	17	−	−	PROPN
ejpam-5857	477	18	f(y	f(y	NOUN
ejpam-5857	477	19	)	)	PUNCT
ejpam-5857	477	20	.	.	PUNCT
ejpam-5857	478	1	thus	thus	ADV
ejpam-5857	478	2	,	,	PUNCT
ejpam-5857	478	3	1	1	NUM
ejpam-5857	478	4	−	−	PROPN
ejpam-5857	478	5	(	(	PUNCT
ejpam-5857	478	6	f(x	f(x	PROPN
ejpam-5857	478	7	)	)	PUNCT
ejpam-5857	478	8	∧	∧	PROPN
ejpam-5857	478	9	f(y	f(y	NOUN
ejpam-5857	478	10	)	)	PUNCT
ejpam-5857	478	11	)	)	PUNCT
ejpam-5857	479	1	=	=	SYM
ejpam-5857	480	1	1	1	NUM
ejpam-5857	480	2	−	−	PROPN
ejpam-5857	480	3	f(x	f(x	PROPN
ejpam-5857	480	4	)	)	PUNCT
ejpam-5857	480	5	=	=	PUNCT
ejpam-5857	480	6	(	(	PUNCT
ejpam-5857	480	7	1	1	NUM
ejpam-5857	480	8	−	−	PROPN
ejpam-5857	480	9	f(x	f(x	PROPN
ejpam-5857	480	10	)	)	PUNCT
ejpam-5857	480	11	)	)	PUNCT
ejpam-5857	481	1	∨	∨	NUM
ejpam-5857	482	1	(	(	PUNCT
ejpam-5857	482	2	1	1	NUM
ejpam-5857	482	3	−	−	PROPN
ejpam-5857	482	4	f(y	f(y	NOUN
ejpam-5857	482	5	)	)	PUNCT
ejpam-5857	482	6	)	)	PUNCT
ejpam-5857	482	7	.	.	PUNCT
ejpam-5857	483	1	similarly	similarly	ADV
ejpam-5857	483	2	,	,	PUNCT
ejpam-5857	483	3	suppose	suppose	VERB
ejpam-5857	483	4	f(x	f(x	NOUN
ejpam-5857	483	5	)	)	PUNCT
ejpam-5857	483	6	∧	∧	PROPN
ejpam-5857	483	7	f(y	f(y	NOUN
ejpam-5857	483	8	)	)	PUNCT
ejpam-5857	483	9	=	=	SYM
ejpam-5857	483	10	f(y	f(y	NOUN
ejpam-5857	483	11	)	)	PUNCT
ejpam-5857	483	12	.	.	PUNCT
ejpam-5857	484	1	then	then	ADV
ejpam-5857	484	2	f(y	f(y	NOUN
ejpam-5857	484	3	)	)	PUNCT
ejpam-5857	484	4	≤	≤	NOUN
ejpam-5857	484	5	f(x	f(x	PROPN
ejpam-5857	484	6	)	)	PUNCT
ejpam-5857	484	7	,	,	PUNCT
ejpam-5857	484	8	that	that	ADV
ejpam-5857	484	9	is	is	ADV
ejpam-5857	484	10	,	,	PUNCT
ejpam-5857	484	11	1	1	NUM
ejpam-5857	484	12	−	−	PROPN
ejpam-5857	484	13	f(y	f(y	NOUN
ejpam-5857	484	14	)	)	PUNCT
ejpam-5857	484	15	≥	≥	NOUN
ejpam-5857	484	16	1	1	NUM
ejpam-5857	484	17	−	−	PROPN
ejpam-5857	484	18	f(x	f(x	PROPN
ejpam-5857	484	19	)	)	PUNCT
ejpam-5857	484	20	.	.	PUNCT
ejpam-5857	485	1	thus	thus	ADV
ejpam-5857	485	2	,	,	PUNCT
ejpam-5857	485	3	1−	1−	NUM
ejpam-5857	485	4	(	(	PUNCT
ejpam-5857	485	5	f(x	f(x	PROPN
ejpam-5857	485	6	)	)	PUNCT
ejpam-5857	485	7	∧	∧	PROPN
ejpam-5857	485	8	f(y	f(y	NOUN
ejpam-5857	485	9	)	)	PUNCT
ejpam-5857	485	10	)	)	PUNCT
ejpam-5857	486	1	=	=	SYM
ejpam-5857	486	2	1−	1−	NUM
ejpam-5857	486	3	f(y	f(y	NOUN
ejpam-5857	486	4	)	)	PUNCT
ejpam-5857	486	5	=	=	PUNCT
ejpam-5857	486	6	(	(	PUNCT
ejpam-5857	486	7	1−	1−	NUM
ejpam-5857	486	8	f(x	f(x	PROPN
ejpam-5857	486	9	)	)	PUNCT
ejpam-5857	486	10	)	)	PUNCT
ejpam-5857	487	1	∨	∨	NUM
ejpam-5857	487	2	(	(	PUNCT
ejpam-5857	487	3	1−	1−	NUM
ejpam-5857	487	4	f(y	f(y	NOUN
ejpam-5857	487	5	)	)	PUNCT
ejpam-5857	487	6	)	)	PUNCT
ejpam-5857	487	7	.	.	PUNCT
ejpam-5857	488	1	lemma	lemma	PROPN
ejpam-5857	488	2	5	5	X
ejpam-5857	488	3	.	.	PUNCT
ejpam-5857	489	1	let	let	VERB
ejpam-5857	489	2	f	f	PRON
ejpam-5857	489	3	be	be	AUX
ejpam-5857	489	4	an	an	DET
ejpam-5857	489	5	fs	fs	NOUN
ejpam-5857	489	6	in	in	ADP
ejpam-5857	489	7	x.	x.	PROPN
ejpam-5857	489	8	then	then	ADV
ejpam-5857	489	9	the	the	DET
ejpam-5857	489	10	following	follow	VERB
ejpam-5857	489	11	statements	statement	NOUN
ejpam-5857	489	12	hold	hold	VERB
ejpam-5857	489	13	:	:	PUNCT
ejpam-5857	489	14	(	(	PUNCT
ejpam-5857	489	15	∀x	∀x	X
ejpam-5857	489	16	,	,	PUNCT
ejpam-5857	489	17	y	y	PROPN
ejpam-5857	489	18	,	,	PUNCT
ejpam-5857	489	19	z	z	PROPN
ejpam-5857	489	20	∈	∈	PROPN
ejpam-5857	489	21	x)(f(z	x)(f(z	PROPN
ejpam-5857	489	22	)	)	PUNCT
ejpam-5857	489	23	≥	≥	PROPN
ejpam-5857	489	24	(	(	PUNCT
ejpam-5857	489	25	f(x	f(x	PROPN
ejpam-5857	489	26	)	)	PUNCT
ejpam-5857	489	27	∧	∧	PROPN
ejpam-5857	489	28	f(y	f(y	NOUN
ejpam-5857	489	29	)	)	PUNCT
ejpam-5857	489	30	)	)	PUNCT
ejpam-5857	490	1	∨	∨	NUM
ejpam-5857	490	2	0.5	0.5	NUM
ejpam-5857	490	3	⇔	⇔	PROPN
ejpam-5857	490	4	f(z	f(z	PROPN
ejpam-5857	490	5	)	)	PUNCT
ejpam-5857	490	6	≤	≤	NOUN
ejpam-5857	490	7	(	(	PUNCT
ejpam-5857	490	8	f(x	f(x	PROPN
ejpam-5857	490	9	)	)	PUNCT
ejpam-5857	490	10	∨	∨	NUM
ejpam-5857	490	11	f(y	f(y	NOUN
ejpam-5857	490	12	)	)	PUNCT
ejpam-5857	490	13	)	)	PUNCT
ejpam-5857	491	1	∧	∧	NOUN
ejpam-5857	491	2	0.5	0.5	NUM
ejpam-5857	491	3	)	)	PUNCT
ejpam-5857	491	4	,	,	PUNCT
ejpam-5857	491	5	(	(	PUNCT
ejpam-5857	491	6	3.24	3.24	NUM
ejpam-5857	491	7	)	)	PUNCT
ejpam-5857	491	8	(	(	PUNCT
ejpam-5857	491	9	∀x	∀x	X
ejpam-5857	491	10	,	,	PUNCT
ejpam-5857	491	11	y	y	PROPN
ejpam-5857	491	12	,	,	PUNCT
ejpam-5857	491	13	z	z	PROPN
ejpam-5857	491	14	∈	∈	PROPN
ejpam-5857	491	15	x)(f(z	x)(f(z	PROPN
ejpam-5857	491	16	)	)	PUNCT
ejpam-5857	491	17	≤	≤	NOUN
ejpam-5857	491	18	(	(	PUNCT
ejpam-5857	491	19	f(x	f(x	PROPN
ejpam-5857	491	20	)	)	PUNCT
ejpam-5857	491	21	∨	∨	NUM
ejpam-5857	491	22	f(y	f(y	NOUN
ejpam-5857	491	23	)	)	PUNCT
ejpam-5857	491	24	)	)	PUNCT
ejpam-5857	492	1	∧	∧	NOUN
ejpam-5857	492	2	0.5	0.5	NUM
ejpam-5857	492	3	⇔	⇔	PROPN
ejpam-5857	492	4	f(z	f(z	PROPN
ejpam-5857	492	5	)	)	PUNCT
ejpam-5857	492	6	≥	≥	NOUN
ejpam-5857	492	7	(	(	PUNCT
ejpam-5857	492	8	f(x	f(x	PROPN
ejpam-5857	492	9	)	)	PUNCT
ejpam-5857	492	10	∧	∧	PROPN
ejpam-5857	492	11	f(y	f(y	NOUN
ejpam-5857	492	12	)	)	PUNCT
ejpam-5857	492	13	)	)	PUNCT
ejpam-5857	492	14	)	)	PUNCT
ejpam-5857	493	1	∨	∨	NUM
ejpam-5857	493	2	0.5	0.5	NUM
ejpam-5857	493	3	)	)	PUNCT
ejpam-5857	493	4	.	.	PUNCT
ejpam-5857	494	1	(	(	PUNCT
ejpam-5857	494	2	3.25	3.25	NUM
ejpam-5857	494	3	)	)	PUNCT
ejpam-5857	494	4	proof	proof	NOUN
ejpam-5857	494	5	.	.	PUNCT
ejpam-5857	495	1	let	let	VERB
ejpam-5857	495	2	x	x	PRON
ejpam-5857	495	3	,	,	PUNCT
ejpam-5857	495	4	y	y	PROPN
ejpam-5857	495	5	,	,	PUNCT
ejpam-5857	495	6	z	z	PROPN
ejpam-5857	495	7	∈	∈	PROPN
ejpam-5857	495	8	x.	x.	NOUN
ejpam-5857	495	9	then	then	ADV
ejpam-5857	495	10	f(z	f(z	PROPN
ejpam-5857	495	11	)	)	PUNCT
ejpam-5857	495	12	≥	≥	NOUN
ejpam-5857	495	13	(	(	PUNCT
ejpam-5857	495	14	f(x	f(x	PROPN
ejpam-5857	495	15	)	)	PUNCT
ejpam-5857	495	16	∧	∧	PROPN
ejpam-5857	495	17	f(y	f(y	NOUN
ejpam-5857	495	18	)	)	PUNCT
ejpam-5857	495	19	)	)	PUNCT
ejpam-5857	496	1	∨	∨	NUM
ejpam-5857	496	2	0.5	0.5	NUM
ejpam-5857	496	3	⇔	⇔	X
ejpam-5857	496	4	1−	1−	NUM
ejpam-5857	496	5	f(z	f(z	PROPN
ejpam-5857	496	6	)	)	PUNCT
ejpam-5857	496	7	≤	≤	NOUN
ejpam-5857	496	8	1−	1−	NUM
ejpam-5857	497	1	(	(	PUNCT
ejpam-5857	497	2	(	(	PUNCT
ejpam-5857	497	3	f(x	f(x	PROPN
ejpam-5857	497	4	)	)	PUNCT
ejpam-5857	497	5	∧	∧	PROPN
ejpam-5857	497	6	f(y	f(y	NOUN
ejpam-5857	497	7	)	)	PUNCT
ejpam-5857	497	8	)	)	PUNCT
ejpam-5857	498	1	∨	∨	NUM
ejpam-5857	498	2	0.5	0.5	NUM
ejpam-5857	498	3	)	)	PUNCT
ejpam-5857	498	4	k.	k.	NOUN
ejpam-5857	498	5	suayngam	suayngam	PROPN
ejpam-5857	498	6	,	,	PUNCT
ejpam-5857	498	7	p.	p.	NOUN
ejpam-5857	498	8	julatha	julatha	PROPN
ejpam-5857	498	9	,	,	PUNCT
ejpam-5857	498	10	w.	w.	PROPN
ejpam-5857	498	11	nakkhasen	nakkhasen	PROPN
ejpam-5857	498	12	,	,	PUNCT
ejpam-5857	498	13	a.	a.	NOUN
ejpam-5857	498	14	iampan	iampan	PROPN
ejpam-5857	498	15	/	/	SYM
ejpam-5857	498	16	eur	eur	PROPN
ejpam-5857	498	17	.	.	PUNCT
ejpam-5857	499	1	j.	j.	PROPN
ejpam-5857	499	2	pure	pure	PROPN
ejpam-5857	499	3	appl	appl	PROPN
ejpam-5857	499	4	.	.	PROPN
ejpam-5857	499	5	math	math	PROPN
ejpam-5857	499	6	,	,	PUNCT
ejpam-5857	499	7	18	18	NUM
ejpam-5857	499	8	(	(	PUNCT
ejpam-5857	499	9	2	2	NUM
ejpam-5857	499	10	)	)	PUNCT
ejpam-5857	499	11	(	(	PUNCT
ejpam-5857	499	12	2025	2025	NUM
ejpam-5857	499	13	)	)	PUNCT
ejpam-5857	499	14	,	,	PUNCT
ejpam-5857	499	15	5857	5857	NUM
ejpam-5857	499	16	18	18	NUM
ejpam-5857	499	17	of	of	ADP
ejpam-5857	499	18	30	30	NUM
ejpam-5857	499	19	⇔	⇔	NUM
ejpam-5857	499	20	f(z	f(z	PROPN
ejpam-5857	499	21	)	)	PUNCT
ejpam-5857	499	22	≤	≤	NOUN
ejpam-5857	499	23	(	(	PUNCT
ejpam-5857	499	24	1−	1−	NUM
ejpam-5857	499	25	(	(	PUNCT
ejpam-5857	499	26	f(x	f(x	PROPN
ejpam-5857	499	27	)	)	PUNCT
ejpam-5857	499	28	∧	∧	PROPN
ejpam-5857	499	29	f(y	f(y	NOUN
ejpam-5857	499	30	)	)	PUNCT
ejpam-5857	499	31	)	)	PUNCT
ejpam-5857	500	1	∧	∧	NOUN
ejpam-5857	500	2	(	(	PUNCT
ejpam-5857	500	3	1−	1−	NUM
ejpam-5857	500	4	0.5	0.5	NUM
ejpam-5857	500	5	)	)	PUNCT
ejpam-5857	500	6	(	(	PUNCT
ejpam-5857	500	7	by	by	ADP
ejpam-5857	500	8	(	(	PUNCT
ejpam-5857	500	9	3.22	3.22	NUM
ejpam-5857	500	10	)	)	PUNCT
ejpam-5857	500	11	)	)	PUNCT
ejpam-5857	500	12	⇔	⇔	PROPN
ejpam-5857	500	13	f(z	f(z	PROPN
ejpam-5857	500	14	)	)	PUNCT
ejpam-5857	500	15	≤	≤	NOUN
ejpam-5857	500	16	(	(	PUNCT
ejpam-5857	500	17	(	(	PUNCT
ejpam-5857	500	18	1−	1−	NUM
ejpam-5857	500	19	f(x	f(x	PROPN
ejpam-5857	500	20	)	)	PUNCT
ejpam-5857	500	21	)	)	PUNCT
ejpam-5857	500	22	∨	∨	NUM
ejpam-5857	500	23	(	(	PUNCT
ejpam-5857	500	24	1−	1−	NUM
ejpam-5857	500	25	f(y	f(y	NOUN
ejpam-5857	500	26	)	)	PUNCT
ejpam-5857	500	27	)	)	PUNCT
ejpam-5857	500	28	)	)	PUNCT
ejpam-5857	501	1	∧	∧	NOUN
ejpam-5857	501	2	0.5	0.5	NUM
ejpam-5857	501	3	(	(	PUNCT
ejpam-5857	501	4	by	by	ADP
ejpam-5857	501	5	(	(	PUNCT
ejpam-5857	501	6	3.23	3.23	NUM
ejpam-5857	501	7	)	)	PUNCT
ejpam-5857	501	8	)	)	PUNCT
ejpam-5857	501	9	⇔	⇔	PROPN
ejpam-5857	501	10	f(z	f(z	PROPN
ejpam-5857	501	11	)	)	PUNCT
ejpam-5857	501	12	≤	≤	NOUN
ejpam-5857	501	13	(	(	PUNCT
ejpam-5857	501	14	f(x	f(x	PROPN
ejpam-5857	501	15	)	)	PUNCT
ejpam-5857	501	16	∨	∨	NUM
ejpam-5857	501	17	f(y	f(y	NOUN
ejpam-5857	501	18	)	)	PUNCT
ejpam-5857	501	19	)	)	PUNCT
ejpam-5857	502	1	∧	∧	NOUN
ejpam-5857	502	2	0.5	0.5	NUM
ejpam-5857	502	3	,	,	PUNCT
ejpam-5857	502	4	f(z	f(z	NUM
ejpam-5857	502	5	)	)	PUNCT
ejpam-5857	502	6	≤	≤	NOUN
ejpam-5857	502	7	(	(	PUNCT
ejpam-5857	502	8	(	(	PUNCT
ejpam-5857	502	9	f(x	f(x	PROPN
ejpam-5857	502	10	)	)	PUNCT
ejpam-5857	502	11	∨	∨	NUM
ejpam-5857	502	12	f(y	f(y	NOUN
ejpam-5857	502	13	)	)	PUNCT
ejpam-5857	502	14	)	)	PUNCT
ejpam-5857	503	1	∧	∧	NOUN
ejpam-5857	503	2	0.5	0.5	NUM
ejpam-5857	503	3	)	)	PUNCT
ejpam-5857	503	4	⇔	⇔	PROPN
ejpam-5857	503	5	1−	1−	NUM
ejpam-5857	503	6	f(z	f(z	PROPN
ejpam-5857	503	7	)	)	PUNCT
ejpam-5857	503	8	≥	≥	NOUN
ejpam-5857	503	9	1−	1−	NUM
ejpam-5857	503	10	(	(	PUNCT
ejpam-5857	503	11	(	(	PUNCT
ejpam-5857	503	12	f(x	f(x	PROPN
ejpam-5857	503	13	)	)	PUNCT
ejpam-5857	503	14	∨	∨	NUM
ejpam-5857	503	15	f(y	f(y	NOUN
ejpam-5857	503	16	)	)	PUNCT
ejpam-5857	503	17	)	)	PUNCT
ejpam-5857	504	1	∧	∧	NOUN
ejpam-5857	504	2	0.5	0.5	NUM
ejpam-5857	504	3	)	)	PUNCT
ejpam-5857	504	4	⇔	⇔	PROPN
ejpam-5857	504	5	f(z	f(z	PROPN
ejpam-5857	504	6	)	)	PUNCT
ejpam-5857	504	7	≥	≥	NUM
ejpam-5857	504	8	(	(	PUNCT
ejpam-5857	504	9	1−	1−	NUM
ejpam-5857	504	10	(	(	PUNCT
ejpam-5857	504	11	f(x	f(x	PROPN
ejpam-5857	504	12	)	)	PUNCT
ejpam-5857	504	13	∨	∨	NUM
ejpam-5857	504	14	f(y	f(y	NOUN
ejpam-5857	504	15	)	)	PUNCT
ejpam-5857	504	16	)	)	PUNCT
ejpam-5857	504	17	)	)	PUNCT
ejpam-5857	505	1	∨	∨	NUM
ejpam-5857	505	2	(	(	PUNCT
ejpam-5857	505	3	1−	1−	NUM
ejpam-5857	505	4	0.5	0.5	NUM
ejpam-5857	505	5	)	)	PUNCT
ejpam-5857	505	6	(	(	PUNCT
ejpam-5857	505	7	by	by	ADP
ejpam-5857	505	8	(	(	PUNCT
ejpam-5857	505	9	3.23	3.23	NUM
ejpam-5857	505	10	)	)	PUNCT
ejpam-5857	505	11	)	)	PUNCT
ejpam-5857	505	12	⇔	⇔	PROPN
ejpam-5857	505	13	f(z	f(z	PROPN
ejpam-5857	505	14	)	)	PUNCT
ejpam-5857	505	15	≥	≥	NOUN
ejpam-5857	505	16	(	(	PUNCT
ejpam-5857	505	17	(	(	PUNCT
ejpam-5857	505	18	1−	1−	NUM
ejpam-5857	505	19	f(x	f(x	PROPN
ejpam-5857	505	20	)	)	PUNCT
ejpam-5857	505	21	)	)	PUNCT
ejpam-5857	506	1	∧	∧	PROPN
ejpam-5857	506	2	(	(	PUNCT
ejpam-5857	506	3	1−	1−	NUM
ejpam-5857	506	4	f(y	f(y	NOUN
ejpam-5857	506	5	)	)	PUNCT
ejpam-5857	506	6	)	)	PUNCT
ejpam-5857	506	7	)	)	PUNCT
ejpam-5857	507	1	∨	∨	NUM
ejpam-5857	507	2	0.5	0.5	NUM
ejpam-5857	507	3	(	(	PUNCT
ejpam-5857	507	4	by	by	ADP
ejpam-5857	507	5	(	(	PUNCT
ejpam-5857	507	6	3.22	3.22	NUM
ejpam-5857	507	7	)	)	PUNCT
ejpam-5857	507	8	)	)	PUNCT
ejpam-5857	507	9	⇔	⇔	PROPN
ejpam-5857	507	10	f(z	f(z	PROPN
ejpam-5857	507	11	)	)	PUNCT
ejpam-5857	507	12	≥	≥	NOUN
ejpam-5857	507	13	(	(	PUNCT
ejpam-5857	507	14	f(x	f(x	PROPN
ejpam-5857	507	15	)	)	PUNCT
ejpam-5857	507	16	∧	∧	PROPN
ejpam-5857	507	17	f(y	f(y	NOUN
ejpam-5857	507	18	)	)	PUNCT
ejpam-5857	507	19	)	)	PUNCT
ejpam-5857	507	20	∨	∨	NUM
ejpam-5857	507	21	0.5	0.5	NUM
ejpam-5857	507	22	.	.	PUNCT
ejpam-5857	508	1	theorem	theorem	VERB
ejpam-5857	508	2	10	10	NUM
ejpam-5857	508	3	.	.	PUNCT
ejpam-5857	509	1	if	if	SCONJ
ejpam-5857	509	2	ψ	ψ	NOUN
ejpam-5857	509	3	is	be	AUX
ejpam-5857	509	4	an	an	DET
ejpam-5857	509	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	509	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	509	7	iup	iup	NOUN
ejpam-5857	509	8	-	-	PUNCT
ejpam-5857	509	9	subalgebra	subalgebra	NOUN
ejpam-5857	509	10	of	of	ADP
ejpam-5857	509	11	x	x	PRON
ejpam-5857	509	12	,	,	PUNCT
ejpam-5857	509	13	then	then	ADV
ejpam-5857	509	14	the	the	DET
ejpam-5857	509	15	fss	fss	NOUN
ejpam-5857	509	16	ψt	ψt	VERB
ejpam-5857	509	17	and	and	CCONJ
ejpam-5857	509	18	ψf	ψf	AUX
ejpam-5857	509	19	satisfy	satisfy	VERB
ejpam-5857	509	20	the	the	DET
ejpam-5857	509	21	condition	condition	NOUN
ejpam-5857	509	22	(	(	PUNCT
ejpam-5857	509	23	3.5	3.5	NUM
ejpam-5857	509	24	)	)	PUNCT
ejpam-5857	509	25	and	and	CCONJ
ejpam-5857	509	26	the	the	DET
ejpam-5857	509	27	fs	f	NOUN
ejpam-5857	509	28	ψi	ψi	ADJ
ejpam-5857	509	29	satisfies	satisfie	NOUN
ejpam-5857	509	30	the	the	DET
ejpam-5857	509	31	condition	condition	NOUN
ejpam-5857	509	32	(	(	PUNCT
ejpam-5857	509	33	3.6	3.6	NUM
ejpam-5857	509	34	)	)	PUNCT
ejpam-5857	509	35	.	.	PUNCT
ejpam-5857	510	1	proof	proof	NOUN
ejpam-5857	510	2	.	.	PUNCT
ejpam-5857	511	1	assume	assume	VERB
ejpam-5857	511	2	that	that	SCONJ
ejpam-5857	511	3	ψ	ψ	NOUN
ejpam-5857	511	4	is	be	AUX
ejpam-5857	511	5	an	an	DET
ejpam-5857	511	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	511	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	511	8	iup	iup	NOUN
ejpam-5857	511	9	-	-	PUNCT
ejpam-5857	511	10	subalgebra	subalgebra	NOUN
ejpam-5857	511	11	of	of	ADP
ejpam-5857	511	12	x.	x.	NOUN
ejpam-5857	511	13	let	let	VERB
ejpam-5857	511	14	x	x	PRON
ejpam-5857	511	15	,	,	PUNCT
ejpam-5857	511	16	y	y	PROPN
ejpam-5857	511	17	∈	∈	PROPN
ejpam-5857	511	18	x.	x.	NOUN
ejpam-5857	511	19	then	then	ADV
ejpam-5857	511	20	ψt	ψt	VERB
ejpam-5857	511	21	(	(	PUNCT
ejpam-5857	511	22	x	x	PROPN
ejpam-5857	511	23	·	·	PUNCT
ejpam-5857	511	24	y	y	X
ejpam-5857	511	25	)	)	PUNCT
ejpam-5857	511	26	=	=	SYM
ejpam-5857	511	27	ψi(x	ψi(x	X
ejpam-5857	511	28	·	·	PUNCT
ejpam-5857	511	29	y	y	X
ejpam-5857	511	30	)	)	PUNCT
ejpam-5857	511	31	∧	∧	NOUN
ejpam-5857	511	32	ψt	ψt	NOUN
ejpam-5857	511	33	(	(	PUNCT
ejpam-5857	511	34	x	x	PROPN
ejpam-5857	511	35	·	·	PUNCT
ejpam-5857	511	36	y	y	X
ejpam-5857	511	37	)	)	PUNCT
ejpam-5857	511	38	≥	≥	NOUN
ejpam-5857	511	39	(	(	PUNCT
ejpam-5857	511	40	(	(	PUNCT
ejpam-5857	511	41	ψi(x	ψi(x	NUM
ejpam-5857	511	42	)	)	PUNCT
ejpam-5857	511	43	∧	∧	NOUN
ejpam-5857	511	44	ψi(y	ψi(y	NOUN
ejpam-5857	511	45	)	)	PUNCT
ejpam-5857	511	46	)	)	PUNCT
ejpam-5857	511	47	∨	∨	NUM
ejpam-5857	511	48	0.5	0.5	NUM
ejpam-5857	511	49	)	)	PUNCT
ejpam-5857	511	50	∧	∧	NOUN
ejpam-5857	511	51	(	(	PUNCT
ejpam-5857	511	52	(	(	PUNCT
ejpam-5857	511	53	ψt	ψt	ADJ
ejpam-5857	511	54	(	(	PUNCT
ejpam-5857	511	55	x	x	NOUN
ejpam-5857	511	56	)	)	PUNCT
ejpam-5857	511	57	∧	∧	NOUN
ejpam-5857	511	58	ψt	ψt	NOUN
ejpam-5857	511	59	(	(	PUNCT
ejpam-5857	511	60	y	y	NOUN
ejpam-5857	511	61	)	)	PUNCT
ejpam-5857	511	62	)	)	PUNCT
ejpam-5857	511	63	∨	∨	NUM
ejpam-5857	511	64	0.5	0.5	NUM
ejpam-5857	511	65	)	)	PUNCT
ejpam-5857	511	66	=	=	SYM
ejpam-5857	511	67	(	(	PUNCT
ejpam-5857	511	68	(	(	PUNCT
ejpam-5857	511	69	ψi(x	ψi(x	NUM
ejpam-5857	511	70	)	)	PUNCT
ejpam-5857	511	71	∧	∧	NOUN
ejpam-5857	511	72	ψi(y	ψi(y	NOUN
ejpam-5857	511	73	)	)	PUNCT
ejpam-5857	511	74	)	)	PUNCT
ejpam-5857	512	1	∧	∧	NOUN
ejpam-5857	512	2	(	(	PUNCT
ejpam-5857	512	3	ψt	ψt	NOUN
ejpam-5857	512	4	(	(	PUNCT
ejpam-5857	512	5	x	x	NOUN
ejpam-5857	512	6	)	)	PUNCT
ejpam-5857	512	7	∧	∧	NOUN
ejpam-5857	512	8	ψt	ψt	NOUN
ejpam-5857	512	9	(	(	PUNCT
ejpam-5857	512	10	y	y	NOUN
ejpam-5857	512	11	)	)	PUNCT
ejpam-5857	512	12	)	)	PUNCT
ejpam-5857	512	13	)	)	PUNCT
ejpam-5857	513	1	∨	∨	NUM
ejpam-5857	513	2	0.5	0.5	NUM
ejpam-5857	513	3	=	=	SYM
ejpam-5857	513	4	(	(	PUNCT
ejpam-5857	513	5	(	(	PUNCT
ejpam-5857	513	6	ψi(x	ψi(x	NUM
ejpam-5857	513	7	)	)	PUNCT
ejpam-5857	513	8	∧	∧	NOUN
ejpam-5857	513	9	ψt	ψt	NOUN
ejpam-5857	513	10	(	(	PUNCT
ejpam-5857	513	11	x	x	NOUN
ejpam-5857	513	12	)	)	PUNCT
ejpam-5857	513	13	)	)	PUNCT
ejpam-5857	513	14	∧	∧	PROPN
ejpam-5857	513	15	(	(	PUNCT
ejpam-5857	513	16	ψi(y	ψi(y	NUM
ejpam-5857	513	17	)	)	PUNCT
ejpam-5857	513	18	∧	∧	NOUN
ejpam-5857	513	19	ψt	ψt	NOUN
ejpam-5857	513	20	(	(	PUNCT
ejpam-5857	513	21	y	y	NOUN
ejpam-5857	513	22	)	)	PUNCT
ejpam-5857	513	23	)	)	PUNCT
ejpam-5857	513	24	)	)	PUNCT
ejpam-5857	514	1	∨	∨	NUM
ejpam-5857	514	2	0.5	0.5	NUM
ejpam-5857	514	3	=	=	SYM
ejpam-5857	514	4	(	(	PUNCT
ejpam-5857	514	5	ψi(x	ψi(x	NUM
ejpam-5857	514	6	)	)	PUNCT
ejpam-5857	514	7	∧	∧	NOUN
ejpam-5857	514	8	ψi(y	ψi(y	NOUN
ejpam-5857	514	9	)	)	PUNCT
ejpam-5857	514	10	)	)	PUNCT
ejpam-5857	515	1	∨	∨	NUM
ejpam-5857	515	2	0.5	0.5	NUM
ejpam-5857	515	3	,	,	PUNCT
ejpam-5857	515	4	ψi(x	ψi(x	AUX
ejpam-5857	515	5	·	·	PUNCT
ejpam-5857	515	6	y	y	X
ejpam-5857	515	7	)	)	PUNCT
ejpam-5857	515	8	=	=	SYM
ejpam-5857	515	9	ψi(x	ψi(x	X
ejpam-5857	515	10	·	·	PUNCT
ejpam-5857	515	11	y	y	X
ejpam-5857	515	12	)	)	PUNCT
ejpam-5857	515	13	≤	≤	NOUN
ejpam-5857	515	14	(	(	PUNCT
ejpam-5857	515	15	ψi(x	ψi(x	NUM
ejpam-5857	515	16	)	)	PUNCT
ejpam-5857	515	17	∨	∨	NUM
ejpam-5857	515	18	ψi(y	ψi(y	NUM
ejpam-5857	515	19	)	)	PUNCT
ejpam-5857	515	20	)	)	PUNCT
ejpam-5857	516	1	∧	∧	NOUN
ejpam-5857	516	2	0.5	0.5	NUM
ejpam-5857	516	3	=	=	SYM
ejpam-5857	516	4	(	(	PUNCT
ejpam-5857	516	5	ψi(x	ψi(x	NUM
ejpam-5857	516	6	)	)	PUNCT
ejpam-5857	516	7	∨	∨	NUM
ejpam-5857	516	8	ψi(y	ψi(y	NUM
ejpam-5857	516	9	)	)	PUNCT
ejpam-5857	516	10	)	)	PUNCT
ejpam-5857	517	1	∧	∧	NOUN
ejpam-5857	517	2	0.5	0.5	NUM
ejpam-5857	517	3	,	,	PUNCT
ejpam-5857	517	4	ψf	ψf	X
ejpam-5857	517	5	(	(	PUNCT
ejpam-5857	517	6	x	x	X
ejpam-5857	517	7	·	·	PUNCT
ejpam-5857	517	8	y	y	X
ejpam-5857	517	9	)	)	PUNCT
ejpam-5857	517	10	=	=	SYM
ejpam-5857	517	11	ψi(x	ψi(x	X
ejpam-5857	517	12	·	·	PUNCT
ejpam-5857	517	13	y	y	X
ejpam-5857	517	14	)	)	PUNCT
ejpam-5857	517	15	∧	∧	NOUN
ejpam-5857	517	16	ψf	ψf	X
ejpam-5857	517	17	(	(	PUNCT
ejpam-5857	517	18	x	x	PROPN
ejpam-5857	517	19	·	·	PUNCT
ejpam-5857	517	20	y	y	X
ejpam-5857	517	21	)	)	PUNCT
ejpam-5857	517	22	≥	≥	NOUN
ejpam-5857	517	23	(	(	PUNCT
ejpam-5857	517	24	(	(	PUNCT
ejpam-5857	517	25	ψi(x	ψi(x	NUM
ejpam-5857	517	26	)	)	PUNCT
ejpam-5857	517	27	∧	∧	NOUN
ejpam-5857	517	28	ψi(y	ψi(y	NOUN
ejpam-5857	517	29	)	)	PUNCT
ejpam-5857	517	30	)	)	PUNCT
ejpam-5857	517	31	∨	∨	NUM
ejpam-5857	517	32	0.5	0.5	NUM
ejpam-5857	517	33	)	)	PUNCT
ejpam-5857	517	34	∧	∧	NOUN
ejpam-5857	517	35	(	(	PUNCT
ejpam-5857	517	36	(	(	PUNCT
ejpam-5857	517	37	ψf	ψf	X
ejpam-5857	517	38	(	(	PUNCT
ejpam-5857	517	39	x	x	NOUN
ejpam-5857	517	40	)	)	PUNCT
ejpam-5857	517	41	∧	∧	NOUN
ejpam-5857	517	42	ψf	ψf	X
ejpam-5857	517	43	(	(	PUNCT
ejpam-5857	517	44	y	y	NOUN
ejpam-5857	517	45	)	)	PUNCT
ejpam-5857	517	46	)	)	PUNCT
ejpam-5857	517	47	∨	∨	NUM
ejpam-5857	517	48	0.5	0.5	NUM
ejpam-5857	517	49	)	)	PUNCT
ejpam-5857	517	50	=	=	SYM
ejpam-5857	517	51	(	(	PUNCT
ejpam-5857	517	52	(	(	PUNCT
ejpam-5857	517	53	ψi(x	ψi(x	NUM
ejpam-5857	517	54	)	)	PUNCT
ejpam-5857	517	55	∧	∧	NOUN
ejpam-5857	517	56	ψi(y	ψi(y	NOUN
ejpam-5857	517	57	)	)	PUNCT
ejpam-5857	517	58	)	)	PUNCT
ejpam-5857	518	1	∧	∧	NOUN
ejpam-5857	518	2	(	(	PUNCT
ejpam-5857	518	3	ψf	ψf	X
ejpam-5857	518	4	(	(	PUNCT
ejpam-5857	518	5	x	x	NOUN
ejpam-5857	518	6	)	)	PUNCT
ejpam-5857	518	7	∧	∧	NOUN
ejpam-5857	518	8	ψf	ψf	X
ejpam-5857	518	9	(	(	PUNCT
ejpam-5857	518	10	y	y	NOUN
ejpam-5857	518	11	)	)	PUNCT
ejpam-5857	518	12	)	)	PUNCT
ejpam-5857	518	13	)	)	PUNCT
ejpam-5857	519	1	∨	∨	NUM
ejpam-5857	519	2	0.5	0.5	NUM
ejpam-5857	519	3	=	=	SYM
ejpam-5857	519	4	(	(	PUNCT
ejpam-5857	519	5	(	(	PUNCT
ejpam-5857	519	6	ψi(x	ψi(x	NUM
ejpam-5857	519	7	)	)	PUNCT
ejpam-5857	519	8	∧	∧	NOUN
ejpam-5857	519	9	ψf	ψf	X
ejpam-5857	519	10	(	(	PUNCT
ejpam-5857	519	11	x	x	NOUN
ejpam-5857	519	12	)	)	PUNCT
ejpam-5857	519	13	)	)	PUNCT
ejpam-5857	520	1	∧	∧	PROPN
ejpam-5857	520	2	(	(	PUNCT
ejpam-5857	520	3	ψi(y	ψi(y	NUM
ejpam-5857	520	4	)	)	PUNCT
ejpam-5857	520	5	∧	∧	NOUN
ejpam-5857	520	6	ψf	ψf	X
ejpam-5857	520	7	(	(	PUNCT
ejpam-5857	520	8	y	y	NOUN
ejpam-5857	520	9	)	)	PUNCT
ejpam-5857	520	10	)	)	PUNCT
ejpam-5857	520	11	)	)	PUNCT
ejpam-5857	521	1	∨	∨	NUM
ejpam-5857	521	2	0.5	0.5	NUM
ejpam-5857	521	3	=	=	SYM
ejpam-5857	521	4	(	(	PUNCT
ejpam-5857	521	5	ψf	ψf	X
ejpam-5857	521	6	(	(	PUNCT
ejpam-5857	521	7	x	x	NOUN
ejpam-5857	521	8	)	)	PUNCT
ejpam-5857	521	9	∧	∧	NOUN
ejpam-5857	521	10	ψf	ψf	X
ejpam-5857	521	11	(	(	PUNCT
ejpam-5857	521	12	y	y	NOUN
ejpam-5857	521	13	)	)	PUNCT
ejpam-5857	521	14	)	)	PUNCT
ejpam-5857	521	15	∨	∨	NUM
ejpam-5857	521	16	0.5	0.5	NUM
ejpam-5857	521	17	.	.	PUNCT
ejpam-5857	522	1	hence	hence	ADV
ejpam-5857	522	2	,	,	PUNCT
ejpam-5857	522	3	the	the	DET
ejpam-5857	522	4	fss	fss	NOUN
ejpam-5857	522	5	ψt	ψt	VERB
ejpam-5857	522	6	and	and	CCONJ
ejpam-5857	522	7	ψf	ψf	AUX
ejpam-5857	522	8	satisfy	satisfy	VERB
ejpam-5857	522	9	the	the	DET
ejpam-5857	522	10	condition	condition	NOUN
ejpam-5857	522	11	(	(	PUNCT
ejpam-5857	522	12	3.5	3.5	NUM
ejpam-5857	522	13	)	)	PUNCT
ejpam-5857	522	14	and	and	CCONJ
ejpam-5857	522	15	the	the	DET
ejpam-5857	522	16	fs	f	NOUN
ejpam-5857	522	17	ψi	ψi	ADJ
ejpam-5857	522	18	satisfies	satisfie	NOUN
ejpam-5857	522	19	the	the	DET
ejpam-5857	522	20	condition	condition	NOUN
ejpam-5857	522	21	(	(	PUNCT
ejpam-5857	522	22	3.6	3.6	NUM
ejpam-5857	522	23	)	)	PUNCT
ejpam-5857	522	24	.	.	PUNCT
ejpam-5857	523	1	theorem	theorem	VERB
ejpam-5857	523	2	11	11	NUM
ejpam-5857	523	3	.	.	PUNCT
ejpam-5857	524	1	if	if	SCONJ
ejpam-5857	524	2	ψ	ψ	NOUN
ejpam-5857	524	3	is	be	AUX
ejpam-5857	524	4	an	an	DET
ejpam-5857	524	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	524	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	524	7	iup	iup	NOUN
ejpam-5857	524	8	-	-	PUNCT
ejpam-5857	524	9	ideal	ideal	NOUN
ejpam-5857	524	10	of	of	ADP
ejpam-5857	524	11	x	x	PRON
ejpam-5857	524	12	,	,	PUNCT
ejpam-5857	524	13	then	then	ADV
ejpam-5857	524	14	the	the	DET
ejpam-5857	524	15	fss	fss	NOUN
ejpam-5857	524	16	ψt	ψt	VERB
ejpam-5857	524	17	and	and	CCONJ
ejpam-5857	524	18	ψf	ψf	AUX
ejpam-5857	524	19	satisfy	satisfy	VERB
ejpam-5857	524	20	the	the	DET
ejpam-5857	524	21	conditions	condition	NOUN
ejpam-5857	524	22	(	(	PUNCT
ejpam-5857	524	23	3.8	3.8	NUM
ejpam-5857	524	24	)	)	PUNCT
ejpam-5857	524	25	and	and	CCONJ
ejpam-5857	524	26	(	(	PUNCT
ejpam-5857	524	27	3.11	3.11	NUM
ejpam-5857	524	28	)	)	PUNCT
ejpam-5857	524	29	and	and	CCONJ
ejpam-5857	524	30	the	the	DET
ejpam-5857	524	31	fs	f	NOUN
ejpam-5857	524	32	ψi	ψi	ADJ
ejpam-5857	524	33	satisfies	satisfie	NOUN
ejpam-5857	524	34	the	the	DET
ejpam-5857	524	35	conditions	condition	NOUN
ejpam-5857	524	36	(	(	PUNCT
ejpam-5857	524	37	3.9	3.9	NUM
ejpam-5857	524	38	)	)	PUNCT
ejpam-5857	524	39	and	and	CCONJ
ejpam-5857	524	40	(	(	PUNCT
ejpam-5857	524	41	3.12	3.12	NUM
ejpam-5857	524	42	)	)	PUNCT
ejpam-5857	524	43	.	.	PUNCT
ejpam-5857	525	1	k.	k.	PROPN
ejpam-5857	525	2	suayngam	suayngam	PROPN
ejpam-5857	525	3	,	,	PUNCT
ejpam-5857	525	4	p.	p.	NOUN
ejpam-5857	525	5	julatha	julatha	PROPN
ejpam-5857	525	6	,	,	PUNCT
ejpam-5857	525	7	w.	w.	PROPN
ejpam-5857	525	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	525	9	,	,	PUNCT
ejpam-5857	525	10	a.	a.	NOUN
ejpam-5857	525	11	iampan	iampan	PROPN
ejpam-5857	525	12	/	/	SYM
ejpam-5857	525	13	eur	eur	PROPN
ejpam-5857	525	14	.	.	PUNCT
ejpam-5857	526	1	j.	j.	PROPN
ejpam-5857	526	2	pure	pure	PROPN
ejpam-5857	526	3	appl	appl	PROPN
ejpam-5857	526	4	.	.	PROPN
ejpam-5857	526	5	math	math	PROPN
ejpam-5857	526	6	,	,	PUNCT
ejpam-5857	526	7	18	18	NUM
ejpam-5857	526	8	(	(	PUNCT
ejpam-5857	526	9	2	2	NUM
ejpam-5857	526	10	)	)	PUNCT
ejpam-5857	526	11	(	(	PUNCT
ejpam-5857	526	12	2025	2025	NUM
ejpam-5857	526	13	)	)	PUNCT
ejpam-5857	526	14	,	,	PUNCT
ejpam-5857	526	15	5857	5857	NUM
ejpam-5857	526	16	19	19	NUM
ejpam-5857	526	17	of	of	ADP
ejpam-5857	526	18	30	30	NUM
ejpam-5857	526	19	proof	proof	NOUN
ejpam-5857	526	20	.	.	PUNCT
ejpam-5857	527	1	assume	assume	VERB
ejpam-5857	527	2	that	that	SCONJ
ejpam-5857	527	3	ψ	ψ	NOUN
ejpam-5857	527	4	is	be	AUX
ejpam-5857	527	5	an	an	DET
ejpam-5857	527	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	527	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	527	8	iup	iup	NOUN
ejpam-5857	527	9	-	-	PUNCT
ejpam-5857	527	10	ideal	ideal	NOUN
ejpam-5857	527	11	of	of	ADP
ejpam-5857	527	12	x.	x.	NOUN
ejpam-5857	527	13	let	let	VERB
ejpam-5857	527	14	x	x	PRON
ejpam-5857	527	15	,	,	PUNCT
ejpam-5857	527	16	y	y	PROPN
ejpam-5857	527	17	,	,	PUNCT
ejpam-5857	527	18	z	z	PROPN
ejpam-5857	527	19	∈	∈	PROPN
ejpam-5857	527	20	x.	x.	NOUN
ejpam-5857	527	21	then	then	ADV
ejpam-5857	527	22	ψt	ψt	VERB
ejpam-5857	527	23	(	(	PUNCT
ejpam-5857	527	24	0	0	NUM
ejpam-5857	527	25	)	)	PUNCT
ejpam-5857	527	26	=	=	SYM
ejpam-5857	527	27	ψi(0	ψi(0	PROPN
ejpam-5857	527	28	)	)	PUNCT
ejpam-5857	527	29	∧	∧	NOUN
ejpam-5857	527	30	ψt	ψt	NUM
ejpam-5857	527	31	(	(	PUNCT
ejpam-5857	527	32	0	0	NUM
ejpam-5857	527	33	)	)	PUNCT
ejpam-5857	527	34	≥	≥	NOUN
ejpam-5857	527	35	ψi(x	ψi(x	NUM
ejpam-5857	527	36	)	)	PUNCT
ejpam-5857	528	1	∧	∧	NOUN
ejpam-5857	528	2	ψt	ψt	NOUN
ejpam-5857	528	3	(	(	PUNCT
ejpam-5857	528	4	x	x	NOUN
ejpam-5857	528	5	)	)	PUNCT
ejpam-5857	528	6	=	=	SYM
ejpam-5857	528	7	ψt	ψt	ADJ
ejpam-5857	528	8	(	(	PUNCT
ejpam-5857	528	9	x	x	NOUN
ejpam-5857	528	10	)	)	PUNCT
ejpam-5857	528	11	,	,	PUNCT
ejpam-5857	528	12	ψi(0	ψi(0	PROPN
ejpam-5857	528	13	)	)	PUNCT
ejpam-5857	528	14	=	=	SYM
ejpam-5857	528	15	ψi(0	ψi(0	PROPN
ejpam-5857	528	16	)	)	PUNCT
ejpam-5857	528	17	≤	≤	NOUN
ejpam-5857	528	18	ψi(x	ψi(x	NUM
ejpam-5857	528	19	)	)	PUNCT
ejpam-5857	528	20	=	=	SYM
ejpam-5857	528	21	ψi(x	ψi(x	NUM
ejpam-5857	528	22	)	)	PUNCT
ejpam-5857	528	23	,	,	PUNCT
ejpam-5857	528	24	ψf	ψf	X
ejpam-5857	528	25	(	(	PUNCT
ejpam-5857	528	26	0	0	NUM
ejpam-5857	528	27	)	)	PUNCT
ejpam-5857	528	28	=	=	SYM
ejpam-5857	528	29	ψi(0	ψi(0	PROPN
ejpam-5857	528	30	)	)	PUNCT
ejpam-5857	528	31	∧	∧	NOUN
ejpam-5857	528	32	ψf	ψf	X
ejpam-5857	528	33	(	(	PUNCT
ejpam-5857	528	34	0	0	NUM
ejpam-5857	528	35	)	)	PUNCT
ejpam-5857	528	36	≥	≥	NOUN
ejpam-5857	528	37	ψi(x	ψi(x	NUM
ejpam-5857	528	38	)	)	PUNCT
ejpam-5857	529	1	∧	∧	NOUN
ejpam-5857	529	2	ψf	ψf	X
ejpam-5857	529	3	(	(	PUNCT
ejpam-5857	529	4	x	x	X
ejpam-5857	529	5	)	)	PUNCT
ejpam-5857	529	6	=	=	SYM
ejpam-5857	529	7	ψf	ψf	X
ejpam-5857	529	8	(	(	PUNCT
ejpam-5857	529	9	x	x	NOUN
ejpam-5857	529	10	)	)	PUNCT
ejpam-5857	529	11	,	,	PUNCT
ejpam-5857	529	12	ψt	ψt	VERB
ejpam-5857	529	13	(	(	PUNCT
ejpam-5857	529	14	x	x	X
ejpam-5857	529	15	·	·	PUNCT
ejpam-5857	529	16	z	z	X
ejpam-5857	529	17	)	)	PUNCT
ejpam-5857	529	18	=	=	SYM
ejpam-5857	529	19	ψi(x	ψi(x	NOUN
ejpam-5857	529	20	·	·	PUNCT
ejpam-5857	529	21	z	z	X
ejpam-5857	529	22	)	)	PUNCT
ejpam-5857	529	23	∧	∧	NOUN
ejpam-5857	529	24	ψt	ψt	NOUN
ejpam-5857	529	25	(	(	PUNCT
ejpam-5857	529	26	x	x	X
ejpam-5857	529	27	·	·	PUNCT
ejpam-5857	529	28	z	z	X
ejpam-5857	529	29	)	)	PUNCT
ejpam-5857	529	30	≥	≥	NOUN
ejpam-5857	529	31	(	(	PUNCT
ejpam-5857	529	32	(	(	PUNCT
ejpam-5857	529	33	ψi(x	ψi(x	X
ejpam-5857	529	34	·	·	PUNCT
ejpam-5857	529	35	(	(	PUNCT
ejpam-5857	529	36	y	y	PROPN
ejpam-5857	529	37	·	·	PUNCT
ejpam-5857	529	38	z	z	NOUN
ejpam-5857	529	39	)	)	PUNCT
ejpam-5857	529	40	)	)	PUNCT
ejpam-5857	530	1	∧	∧	NOUN
ejpam-5857	530	2	ψi(y	ψi(y	NOUN
ejpam-5857	530	3	)	)	PUNCT
ejpam-5857	530	4	)	)	PUNCT
ejpam-5857	530	5	∨	∨	NUM
ejpam-5857	530	6	0.5	0.5	NUM
ejpam-5857	530	7	)	)	PUNCT
ejpam-5857	530	8	∧	∧	NOUN
ejpam-5857	530	9	(	(	PUNCT
ejpam-5857	530	10	(	(	PUNCT
ejpam-5857	530	11	ψt	ψt	VERB
ejpam-5857	530	12	(	(	PUNCT
ejpam-5857	530	13	x	x	X
ejpam-5857	530	14	·	·	PUNCT
ejpam-5857	530	15	(	(	PUNCT
ejpam-5857	530	16	y	y	PROPN
ejpam-5857	530	17	·	·	PUNCT
ejpam-5857	530	18	z	z	NOUN
ejpam-5857	530	19	)	)	PUNCT
ejpam-5857	530	20	)	)	PUNCT
ejpam-5857	531	1	∧	∧	NOUN
ejpam-5857	531	2	ψt	ψt	NOUN
ejpam-5857	531	3	(	(	PUNCT
ejpam-5857	531	4	y	y	NOUN
ejpam-5857	531	5	)	)	PUNCT
ejpam-5857	531	6	)	)	PUNCT
ejpam-5857	531	7	∨	∨	NUM
ejpam-5857	531	8	0.5	0.5	NUM
ejpam-5857	531	9	)	)	PUNCT
ejpam-5857	531	10	=	=	SYM
ejpam-5857	531	11	(	(	PUNCT
ejpam-5857	531	12	(	(	PUNCT
ejpam-5857	531	13	ψi(x	ψi(x	X
ejpam-5857	531	14	·	·	PUNCT
ejpam-5857	531	15	(	(	PUNCT
ejpam-5857	531	16	y	y	PROPN
ejpam-5857	531	17	·	·	PUNCT
ejpam-5857	531	18	z	z	NOUN
ejpam-5857	531	19	)	)	PUNCT
ejpam-5857	531	20	)	)	PUNCT
ejpam-5857	532	1	∧	∧	NOUN
ejpam-5857	532	2	ψi(y	ψi(y	NOUN
ejpam-5857	532	3	)	)	PUNCT
ejpam-5857	532	4	)	)	PUNCT
ejpam-5857	533	1	∧	∧	NOUN
ejpam-5857	533	2	(	(	PUNCT
ejpam-5857	533	3	ψt	ψt	NOUN
ejpam-5857	533	4	(	(	PUNCT
ejpam-5857	533	5	x	x	X
ejpam-5857	533	6	·	·	PUNCT
ejpam-5857	533	7	(	(	PUNCT
ejpam-5857	533	8	y	y	PROPN
ejpam-5857	533	9	·	·	PUNCT
ejpam-5857	533	10	z	z	NOUN
ejpam-5857	533	11	)	)	PUNCT
ejpam-5857	533	12	)	)	PUNCT
ejpam-5857	534	1	∧	∧	NOUN
ejpam-5857	534	2	ψt	ψt	NOUN
ejpam-5857	534	3	(	(	PUNCT
ejpam-5857	534	4	y	y	NOUN
ejpam-5857	534	5	)	)	PUNCT
ejpam-5857	534	6	)	)	PUNCT
ejpam-5857	534	7	)	)	PUNCT
ejpam-5857	535	1	∨	∨	NUM
ejpam-5857	535	2	0.5	0.5	NUM
ejpam-5857	535	3	=	=	SYM
ejpam-5857	535	4	(	(	PUNCT
ejpam-5857	535	5	(	(	PUNCT
ejpam-5857	535	6	ψi(x	ψi(x	X
ejpam-5857	535	7	·	·	PUNCT
ejpam-5857	535	8	(	(	PUNCT
ejpam-5857	535	9	y	y	PROPN
ejpam-5857	535	10	·	·	PUNCT
ejpam-5857	535	11	z	z	NOUN
ejpam-5857	535	12	)	)	PUNCT
ejpam-5857	535	13	)	)	PUNCT
ejpam-5857	536	1	∧	∧	NOUN
ejpam-5857	536	2	ψt	ψt	NOUN
ejpam-5857	536	3	(	(	PUNCT
ejpam-5857	536	4	x	x	X
ejpam-5857	536	5	·	·	PUNCT
ejpam-5857	536	6	(	(	PUNCT
ejpam-5857	536	7	y	y	PROPN
ejpam-5857	536	8	·	·	PUNCT
ejpam-5857	536	9	z	z	NOUN
ejpam-5857	536	10	)	)	PUNCT
ejpam-5857	536	11	)	)	PUNCT
ejpam-5857	536	12	)	)	PUNCT
ejpam-5857	537	1	∧	∧	NOUN
ejpam-5857	537	2	(	(	PUNCT
ejpam-5857	537	3	ψi(y	ψi(y	NUM
ejpam-5857	537	4	)	)	PUNCT
ejpam-5857	537	5	∧	∧	NOUN
ejpam-5857	537	6	ψt	ψt	NOUN
ejpam-5857	537	7	(	(	PUNCT
ejpam-5857	537	8	y	y	NOUN
ejpam-5857	537	9	)	)	PUNCT
ejpam-5857	537	10	)	)	PUNCT
ejpam-5857	537	11	)	)	PUNCT
ejpam-5857	538	1	∨	∨	NUM
ejpam-5857	538	2	0.5	0.5	NUM
ejpam-5857	538	3	=	=	SYM
ejpam-5857	538	4	(	(	PUNCT
ejpam-5857	538	5	ψt	ψt	NUM
ejpam-5857	538	6	(	(	PUNCT
ejpam-5857	538	7	x	x	X
ejpam-5857	538	8	·	·	PUNCT
ejpam-5857	538	9	(	(	PUNCT
ejpam-5857	538	10	y	y	PROPN
ejpam-5857	538	11	·	·	PUNCT
ejpam-5857	538	12	z	z	NOUN
ejpam-5857	538	13	)	)	PUNCT
ejpam-5857	538	14	)	)	PUNCT
ejpam-5857	538	15	∧	∧	NOUN
ejpam-5857	538	16	ψt	ψt	NOUN
ejpam-5857	538	17	(	(	PUNCT
ejpam-5857	538	18	y	y	NOUN
ejpam-5857	538	19	)	)	PUNCT
ejpam-5857	538	20	)	)	PUNCT
ejpam-5857	538	21	∨	∨	NUM
ejpam-5857	538	22	0.5	0.5	NUM
ejpam-5857	538	23	,	,	PUNCT
ejpam-5857	538	24	ψi(x	ψi(x	AUX
ejpam-5857	538	25	·	·	PUNCT
ejpam-5857	538	26	z	z	X
ejpam-5857	538	27	)	)	PUNCT
ejpam-5857	538	28	=	=	SYM
ejpam-5857	538	29	ψi(x	ψi(x	NOUN
ejpam-5857	538	30	·	·	PUNCT
ejpam-5857	538	31	z	z	X
ejpam-5857	538	32	)	)	PUNCT
ejpam-5857	538	33	≤	≤	NOUN
ejpam-5857	538	34	(	(	PUNCT
ejpam-5857	538	35	ψi(x	ψi(x	X
ejpam-5857	538	36	·	·	PUNCT
ejpam-5857	538	37	(	(	PUNCT
ejpam-5857	538	38	y	y	PROPN
ejpam-5857	538	39	·	·	PUNCT
ejpam-5857	538	40	z	z	NOUN
ejpam-5857	538	41	)	)	PUNCT
ejpam-5857	538	42	)	)	PUNCT
ejpam-5857	539	1	∨	∨	NUM
ejpam-5857	539	2	ψi(y	ψi(y	NUM
ejpam-5857	539	3	)	)	PUNCT
ejpam-5857	539	4	)	)	PUNCT
ejpam-5857	540	1	∧	∧	NOUN
ejpam-5857	540	2	0.5	0.5	NUM
ejpam-5857	540	3	=	=	SYM
ejpam-5857	540	4	(	(	PUNCT
ejpam-5857	540	5	ψi(x	ψi(x	X
ejpam-5857	540	6	·	·	PUNCT
ejpam-5857	540	7	(	(	PUNCT
ejpam-5857	540	8	y	y	PROPN
ejpam-5857	540	9	·	·	PUNCT
ejpam-5857	540	10	z	z	NOUN
ejpam-5857	540	11	)	)	PUNCT
ejpam-5857	540	12	)	)	PUNCT
ejpam-5857	540	13	∨	∨	NUM
ejpam-5857	540	14	ψi(y	ψi(y	NUM
ejpam-5857	540	15	)	)	PUNCT
ejpam-5857	540	16	)	)	PUNCT
ejpam-5857	541	1	∧	∧	NOUN
ejpam-5857	541	2	0.5	0.5	NUM
ejpam-5857	541	3	,	,	PUNCT
ejpam-5857	541	4	ψf	ψf	X
ejpam-5857	541	5	(	(	PUNCT
ejpam-5857	541	6	x	x	X
ejpam-5857	541	7	·	·	PUNCT
ejpam-5857	541	8	z	z	X
ejpam-5857	541	9	)	)	PUNCT
ejpam-5857	541	10	=	=	SYM
ejpam-5857	541	11	ψi(x	ψi(x	NOUN
ejpam-5857	541	12	·	·	PUNCT
ejpam-5857	541	13	z	z	X
ejpam-5857	541	14	)	)	PUNCT
ejpam-5857	541	15	∧	∧	NOUN
ejpam-5857	541	16	ψf	ψf	X
ejpam-5857	541	17	(	(	PUNCT
ejpam-5857	541	18	x	x	X
ejpam-5857	541	19	·	·	PUNCT
ejpam-5857	541	20	z	z	X
ejpam-5857	541	21	)	)	PUNCT
ejpam-5857	541	22	≥	≥	NOUN
ejpam-5857	541	23	(	(	PUNCT
ejpam-5857	541	24	(	(	PUNCT
ejpam-5857	541	25	ψi(x	ψi(x	X
ejpam-5857	541	26	·	·	PUNCT
ejpam-5857	541	27	(	(	PUNCT
ejpam-5857	541	28	y	y	PROPN
ejpam-5857	541	29	·	·	PUNCT
ejpam-5857	541	30	z	z	NOUN
ejpam-5857	541	31	)	)	PUNCT
ejpam-5857	541	32	)	)	PUNCT
ejpam-5857	542	1	∧	∧	NOUN
ejpam-5857	542	2	ψi(y	ψi(y	NOUN
ejpam-5857	542	3	)	)	PUNCT
ejpam-5857	542	4	)	)	PUNCT
ejpam-5857	542	5	∨	∨	NUM
ejpam-5857	542	6	0.5	0.5	NUM
ejpam-5857	542	7	)	)	PUNCT
ejpam-5857	542	8	∧	∧	NOUN
ejpam-5857	542	9	(	(	PUNCT
ejpam-5857	542	10	(	(	PUNCT
ejpam-5857	542	11	ψf	ψf	X
ejpam-5857	542	12	(	(	PUNCT
ejpam-5857	542	13	x	x	X
ejpam-5857	542	14	·	·	PUNCT
ejpam-5857	542	15	(	(	PUNCT
ejpam-5857	542	16	y	y	PROPN
ejpam-5857	542	17	·	·	PUNCT
ejpam-5857	542	18	z	z	NOUN
ejpam-5857	542	19	)	)	PUNCT
ejpam-5857	542	20	)	)	PUNCT
ejpam-5857	543	1	∧	∧	NOUN
ejpam-5857	543	2	ψf	ψf	X
ejpam-5857	543	3	(	(	PUNCT
ejpam-5857	543	4	y	y	NOUN
ejpam-5857	543	5	)	)	PUNCT
ejpam-5857	543	6	)	)	PUNCT
ejpam-5857	543	7	∨	∨	NUM
ejpam-5857	543	8	0.5	0.5	NUM
ejpam-5857	543	9	)	)	PUNCT
ejpam-5857	543	10	=	=	SYM
ejpam-5857	543	11	(	(	PUNCT
ejpam-5857	543	12	(	(	PUNCT
ejpam-5857	543	13	ψi(x	ψi(x	X
ejpam-5857	543	14	·	·	PUNCT
ejpam-5857	543	15	(	(	PUNCT
ejpam-5857	543	16	y	y	PROPN
ejpam-5857	543	17	·	·	PUNCT
ejpam-5857	543	18	z	z	NOUN
ejpam-5857	543	19	)	)	PUNCT
ejpam-5857	543	20	)	)	PUNCT
ejpam-5857	544	1	∧	∧	NOUN
ejpam-5857	544	2	ψi(y	ψi(y	NOUN
ejpam-5857	544	3	)	)	PUNCT
ejpam-5857	544	4	)	)	PUNCT
ejpam-5857	545	1	∧	∧	NOUN
ejpam-5857	545	2	(	(	PUNCT
ejpam-5857	545	3	ψf	ψf	X
ejpam-5857	545	4	(	(	PUNCT
ejpam-5857	545	5	x	x	X
ejpam-5857	545	6	·	·	PUNCT
ejpam-5857	545	7	(	(	PUNCT
ejpam-5857	545	8	y	y	PROPN
ejpam-5857	545	9	·	·	PUNCT
ejpam-5857	545	10	z	z	NOUN
ejpam-5857	545	11	)	)	PUNCT
ejpam-5857	545	12	)	)	PUNCT
ejpam-5857	546	1	∧	∧	NOUN
ejpam-5857	546	2	ψf	ψf	X
ejpam-5857	546	3	(	(	PUNCT
ejpam-5857	546	4	y	y	NOUN
ejpam-5857	546	5	)	)	PUNCT
ejpam-5857	546	6	)	)	PUNCT
ejpam-5857	546	7	)	)	PUNCT
ejpam-5857	547	1	∨	∨	NUM
ejpam-5857	547	2	0.5	0.5	NUM
ejpam-5857	547	3	=	=	SYM
ejpam-5857	547	4	(	(	PUNCT
ejpam-5857	547	5	(	(	PUNCT
ejpam-5857	547	6	ψi(x	ψi(x	X
ejpam-5857	547	7	·	·	PUNCT
ejpam-5857	547	8	(	(	PUNCT
ejpam-5857	547	9	y	y	PROPN
ejpam-5857	547	10	·	·	PUNCT
ejpam-5857	547	11	z	z	NOUN
ejpam-5857	547	12	)	)	PUNCT
ejpam-5857	547	13	)	)	PUNCT
ejpam-5857	548	1	∧	∧	NOUN
ejpam-5857	548	2	ψf	ψf	X
ejpam-5857	548	3	(	(	PUNCT
ejpam-5857	548	4	x	x	X
ejpam-5857	548	5	·	·	PUNCT
ejpam-5857	548	6	(	(	PUNCT
ejpam-5857	548	7	y	y	PROPN
ejpam-5857	548	8	·	·	PUNCT
ejpam-5857	548	9	z	z	NOUN
ejpam-5857	548	10	)	)	PUNCT
ejpam-5857	548	11	)	)	PUNCT
ejpam-5857	548	12	)	)	PUNCT
ejpam-5857	549	1	∧	∧	NOUN
ejpam-5857	549	2	(	(	PUNCT
ejpam-5857	549	3	ψi(y	ψi(y	NUM
ejpam-5857	549	4	)	)	PUNCT
ejpam-5857	549	5	∧	∧	NOUN
ejpam-5857	549	6	ψf	ψf	X
ejpam-5857	549	7	(	(	PUNCT
ejpam-5857	549	8	y	y	NOUN
ejpam-5857	549	9	)	)	PUNCT
ejpam-5857	549	10	)	)	PUNCT
ejpam-5857	549	11	)	)	PUNCT
ejpam-5857	550	1	∨	∨	NUM
ejpam-5857	550	2	0.5	0.5	NUM
ejpam-5857	550	3	=	=	SYM
ejpam-5857	550	4	(	(	PUNCT
ejpam-5857	550	5	ψf	ψf	X
ejpam-5857	550	6	(	(	PUNCT
ejpam-5857	550	7	x	x	X
ejpam-5857	550	8	·	·	PUNCT
ejpam-5857	550	9	(	(	PUNCT
ejpam-5857	550	10	y	y	PROPN
ejpam-5857	550	11	·	·	PUNCT
ejpam-5857	550	12	z	z	NOUN
ejpam-5857	550	13	)	)	PUNCT
ejpam-5857	550	14	)	)	PUNCT
ejpam-5857	551	1	∧	∧	NOUN
ejpam-5857	551	2	ψf	ψf	X
ejpam-5857	551	3	(	(	PUNCT
ejpam-5857	551	4	y	y	NOUN
ejpam-5857	551	5	)	)	PUNCT
ejpam-5857	551	6	)	)	PUNCT
ejpam-5857	552	1	∨	∨	NUM
ejpam-5857	552	2	0.5	0.5	NUM
ejpam-5857	552	3	.	.	PUNCT
ejpam-5857	553	1	hence	hence	ADV
ejpam-5857	553	2	,	,	PUNCT
ejpam-5857	553	3	the	the	DET
ejpam-5857	553	4	fss	fss	NOUN
ejpam-5857	553	5	ψt	ψt	VERB
ejpam-5857	553	6	and	and	CCONJ
ejpam-5857	553	7	ψf	ψf	AUX
ejpam-5857	553	8	satisfy	satisfy	VERB
ejpam-5857	553	9	the	the	DET
ejpam-5857	553	10	conditions	condition	NOUN
ejpam-5857	553	11	(	(	PUNCT
ejpam-5857	553	12	3.8	3.8	NUM
ejpam-5857	553	13	)	)	PUNCT
ejpam-5857	553	14	and	and	CCONJ
ejpam-5857	553	15	(	(	PUNCT
ejpam-5857	553	16	3.11	3.11	NUM
ejpam-5857	553	17	)	)	PUNCT
ejpam-5857	553	18	and	and	CCONJ
ejpam-5857	553	19	the	the	DET
ejpam-5857	553	20	fs	f	NOUN
ejpam-5857	553	21	ψi	ψi	ADJ
ejpam-5857	553	22	satisfies	satisfie	NOUN
ejpam-5857	553	23	the	the	DET
ejpam-5857	553	24	conditions	condition	NOUN
ejpam-5857	553	25	(	(	PUNCT
ejpam-5857	553	26	3.9	3.9	NUM
ejpam-5857	553	27	)	)	PUNCT
ejpam-5857	553	28	and	and	CCONJ
ejpam-5857	553	29	(	(	PUNCT
ejpam-5857	553	30	3.12	3.12	NUM
ejpam-5857	553	31	)	)	PUNCT
ejpam-5857	553	32	.	.	PUNCT
ejpam-5857	554	1	k.	k.	PROPN
ejpam-5857	554	2	suayngam	suayngam	PROPN
ejpam-5857	554	3	,	,	PUNCT
ejpam-5857	554	4	p.	p.	NOUN
ejpam-5857	554	5	julatha	julatha	PROPN
ejpam-5857	554	6	,	,	PUNCT
ejpam-5857	554	7	w.	w.	PROPN
ejpam-5857	554	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	554	9	,	,	PUNCT
ejpam-5857	554	10	a.	a.	NOUN
ejpam-5857	554	11	iampan	iampan	PROPN
ejpam-5857	554	12	/	/	SYM
ejpam-5857	554	13	eur	eur	PROPN
ejpam-5857	554	14	.	.	PUNCT
ejpam-5857	555	1	j.	j.	PROPN
ejpam-5857	555	2	pure	pure	PROPN
ejpam-5857	555	3	appl	appl	PROPN
ejpam-5857	555	4	.	.	PROPN
ejpam-5857	555	5	math	math	PROPN
ejpam-5857	555	6	,	,	PUNCT
ejpam-5857	555	7	18	18	NUM
ejpam-5857	555	8	(	(	PUNCT
ejpam-5857	555	9	2	2	NUM
ejpam-5857	555	10	)	)	PUNCT
ejpam-5857	555	11	(	(	PUNCT
ejpam-5857	555	12	2025	2025	NUM
ejpam-5857	555	13	)	)	PUNCT
ejpam-5857	555	14	,	,	PUNCT
ejpam-5857	555	15	5857	5857	NUM
ejpam-5857	555	16	20	20	NUM
ejpam-5857	555	17	of	of	ADP
ejpam-5857	555	18	30	30	NUM
ejpam-5857	555	19	theorem	theorem	NOUN
ejpam-5857	555	20	12	12	NUM
ejpam-5857	555	21	.	.	PUNCT
ejpam-5857	556	1	if	if	SCONJ
ejpam-5857	556	2	ψ	ψ	NOUN
ejpam-5857	556	3	is	be	AUX
ejpam-5857	556	4	an	an	DET
ejpam-5857	556	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	556	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	556	7	iup	iup	NOUN
ejpam-5857	556	8	-	-	PUNCT
ejpam-5857	556	9	filter	filter	NOUN
ejpam-5857	556	10	of	of	ADP
ejpam-5857	556	11	x	x	NOUN
ejpam-5857	556	12	,	,	PUNCT
ejpam-5857	556	13	then	then	ADV
ejpam-5857	556	14	the	the	DET
ejpam-5857	556	15	fss	fss	NOUN
ejpam-5857	556	16	ψt	ψt	VERB
ejpam-5857	556	17	and	and	CCONJ
ejpam-5857	556	18	ψf	ψf	AUX
ejpam-5857	556	19	satisfy	satisfy	VERB
ejpam-5857	556	20	the	the	DET
ejpam-5857	556	21	conditions	condition	NOUN
ejpam-5857	556	22	(	(	PUNCT
ejpam-5857	556	23	3.8	3.8	NUM
ejpam-5857	556	24	)	)	PUNCT
ejpam-5857	556	25	and	and	CCONJ
ejpam-5857	556	26	(	(	PUNCT
ejpam-5857	556	27	3.14	3.14	NUM
ejpam-5857	556	28	)	)	PUNCT
ejpam-5857	556	29	and	and	CCONJ
ejpam-5857	556	30	the	the	DET
ejpam-5857	556	31	fs	f	NOUN
ejpam-5857	556	32	ψi	ψi	ADJ
ejpam-5857	556	33	satisfies	satisfie	NOUN
ejpam-5857	556	34	the	the	DET
ejpam-5857	556	35	conditions	condition	NOUN
ejpam-5857	556	36	(	(	PUNCT
ejpam-5857	556	37	3.9	3.9	NUM
ejpam-5857	556	38	)	)	PUNCT
ejpam-5857	556	39	and	and	CCONJ
ejpam-5857	556	40	(	(	PUNCT
ejpam-5857	556	41	3.15	3.15	NUM
ejpam-5857	556	42	)	)	PUNCT
ejpam-5857	556	43	.	.	PUNCT
ejpam-5857	557	1	proof	proof	NOUN
ejpam-5857	557	2	.	.	PUNCT
ejpam-5857	558	1	assume	assume	VERB
ejpam-5857	558	2	that	that	SCONJ
ejpam-5857	558	3	ψ	ψ	NOUN
ejpam-5857	558	4	is	be	AUX
ejpam-5857	558	5	an	an	DET
ejpam-5857	558	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	558	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	558	8	iup	iup	NOUN
ejpam-5857	558	9	-	-	PUNCT
ejpam-5857	558	10	filter	filter	NOUN
ejpam-5857	558	11	of	of	ADP
ejpam-5857	558	12	x.	x.	NOUN
ejpam-5857	558	13	let	let	VERB
ejpam-5857	558	14	x	x	PRON
ejpam-5857	558	15	,	,	PUNCT
ejpam-5857	558	16	y	y	PROPN
ejpam-5857	558	17	∈	∈	PROPN
ejpam-5857	558	18	x.	x.	NOUN
ejpam-5857	558	19	then	then	ADV
ejpam-5857	558	20	ψt	ψt	VERB
ejpam-5857	558	21	(	(	PUNCT
ejpam-5857	558	22	0	0	NUM
ejpam-5857	558	23	)	)	PUNCT
ejpam-5857	558	24	=	=	SYM
ejpam-5857	558	25	ψi(0	ψi(0	PROPN
ejpam-5857	558	26	)	)	PUNCT
ejpam-5857	558	27	∧	∧	NOUN
ejpam-5857	558	28	ψt	ψt	NUM
ejpam-5857	558	29	(	(	PUNCT
ejpam-5857	558	30	0	0	NUM
ejpam-5857	558	31	)	)	PUNCT
ejpam-5857	558	32	≥	≥	NOUN
ejpam-5857	558	33	ψi(x	ψi(x	NUM
ejpam-5857	558	34	)	)	PUNCT
ejpam-5857	559	1	∧	∧	NOUN
ejpam-5857	559	2	ψt	ψt	NOUN
ejpam-5857	559	3	(	(	PUNCT
ejpam-5857	559	4	x	x	NOUN
ejpam-5857	559	5	)	)	PUNCT
ejpam-5857	559	6	=	=	SYM
ejpam-5857	559	7	ψt	ψt	ADJ
ejpam-5857	559	8	(	(	PUNCT
ejpam-5857	559	9	x	x	NOUN
ejpam-5857	559	10	)	)	PUNCT
ejpam-5857	559	11	,	,	PUNCT
ejpam-5857	559	12	ψi(0	ψi(0	PROPN
ejpam-5857	559	13	)	)	PUNCT
ejpam-5857	559	14	=	=	SYM
ejpam-5857	559	15	ψi(0	ψi(0	PROPN
ejpam-5857	559	16	)	)	PUNCT
ejpam-5857	559	17	≤	≤	NOUN
ejpam-5857	559	18	ψi(x	ψi(x	NUM
ejpam-5857	559	19	)	)	PUNCT
ejpam-5857	559	20	=	=	SYM
ejpam-5857	559	21	ψi(x	ψi(x	NUM
ejpam-5857	559	22	)	)	PUNCT
ejpam-5857	559	23	,	,	PUNCT
ejpam-5857	559	24	ψf	ψf	X
ejpam-5857	559	25	(	(	PUNCT
ejpam-5857	559	26	0	0	NUM
ejpam-5857	559	27	)	)	PUNCT
ejpam-5857	559	28	=	=	SYM
ejpam-5857	559	29	ψi(0	ψi(0	PROPN
ejpam-5857	559	30	)	)	PUNCT
ejpam-5857	559	31	∧	∧	NOUN
ejpam-5857	559	32	ψf	ψf	X
ejpam-5857	559	33	(	(	PUNCT
ejpam-5857	559	34	0	0	NUM
ejpam-5857	559	35	)	)	PUNCT
ejpam-5857	559	36	≥	≥	NOUN
ejpam-5857	559	37	ψi(x	ψi(x	NUM
ejpam-5857	559	38	)	)	PUNCT
ejpam-5857	560	1	∧	∧	NOUN
ejpam-5857	560	2	ψf	ψf	X
ejpam-5857	560	3	(	(	PUNCT
ejpam-5857	560	4	x	x	X
ejpam-5857	560	5	)	)	PUNCT
ejpam-5857	560	6	=	=	SYM
ejpam-5857	560	7	ψf	ψf	X
ejpam-5857	560	8	(	(	PUNCT
ejpam-5857	560	9	x	x	NOUN
ejpam-5857	560	10	)	)	PUNCT
ejpam-5857	560	11	,	,	PUNCT
ejpam-5857	560	12	ψt	ψt	VERB
ejpam-5857	560	13	(	(	PUNCT
ejpam-5857	560	14	y	y	NOUN
ejpam-5857	560	15	)	)	PUNCT
ejpam-5857	560	16	=	=	NOUN
ejpam-5857	560	17	ψi(y	ψi(y	X
ejpam-5857	560	18	)	)	PUNCT
ejpam-5857	560	19	∧	∧	NOUN
ejpam-5857	560	20	ψt	ψt	NOUN
ejpam-5857	560	21	(	(	PUNCT
ejpam-5857	560	22	y	y	NOUN
ejpam-5857	560	23	)	)	PUNCT
ejpam-5857	560	24	≥	≥	NOUN
ejpam-5857	560	25	(	(	PUNCT
ejpam-5857	560	26	(	(	PUNCT
ejpam-5857	560	27	ψi(x	ψi(x	X
ejpam-5857	560	28	·	·	PUNCT
ejpam-5857	560	29	y	y	X
ejpam-5857	560	30	)	)	PUNCT
ejpam-5857	560	31	∧	∧	NOUN
ejpam-5857	560	32	ψi(x	ψi(x	NUM
ejpam-5857	560	33	)	)	PUNCT
ejpam-5857	560	34	)	)	PUNCT
ejpam-5857	561	1	∨	∨	NUM
ejpam-5857	561	2	0.5	0.5	NUM
ejpam-5857	561	3	)	)	PUNCT
ejpam-5857	561	4	∧	∧	NOUN
ejpam-5857	561	5	(	(	PUNCT
ejpam-5857	561	6	(	(	PUNCT
ejpam-5857	561	7	ψt	ψt	VERB
ejpam-5857	561	8	(	(	PUNCT
ejpam-5857	561	9	x	x	PROPN
ejpam-5857	561	10	·	·	PUNCT
ejpam-5857	561	11	y	y	X
ejpam-5857	561	12	)	)	PUNCT
ejpam-5857	561	13	∧	∧	NOUN
ejpam-5857	561	14	ψt	ψt	NOUN
ejpam-5857	561	15	(	(	PUNCT
ejpam-5857	561	16	x	x	NOUN
ejpam-5857	561	17	)	)	PUNCT
ejpam-5857	561	18	)	)	PUNCT
ejpam-5857	561	19	∨	∨	NUM
ejpam-5857	561	20	0.5	0.5	NUM
ejpam-5857	561	21	)	)	PUNCT
ejpam-5857	561	22	=	=	SYM
ejpam-5857	561	23	(	(	PUNCT
ejpam-5857	561	24	(	(	PUNCT
ejpam-5857	561	25	ψi(x	ψi(x	X
ejpam-5857	561	26	·	·	PUNCT
ejpam-5857	561	27	y	y	X
ejpam-5857	561	28	)	)	PUNCT
ejpam-5857	561	29	∧	∧	NOUN
ejpam-5857	561	30	ψi(x	ψi(x	NUM
ejpam-5857	561	31	)	)	PUNCT
ejpam-5857	561	32	)	)	PUNCT
ejpam-5857	562	1	∧	∧	NOUN
ejpam-5857	562	2	(	(	PUNCT
ejpam-5857	562	3	ψt	ψt	NOUN
ejpam-5857	562	4	(	(	PUNCT
ejpam-5857	562	5	x	x	PROPN
ejpam-5857	562	6	·	·	PUNCT
ejpam-5857	562	7	y	y	X
ejpam-5857	562	8	)	)	PUNCT
ejpam-5857	562	9	∧	∧	NOUN
ejpam-5857	562	10	ψt	ψt	NOUN
ejpam-5857	562	11	(	(	PUNCT
ejpam-5857	562	12	x	x	NOUN
ejpam-5857	562	13	)	)	PUNCT
ejpam-5857	562	14	)	)	PUNCT
ejpam-5857	562	15	)	)	PUNCT
ejpam-5857	563	1	∨	∨	NUM
ejpam-5857	563	2	0.5	0.5	NUM
ejpam-5857	563	3	=	=	SYM
ejpam-5857	563	4	(	(	PUNCT
ejpam-5857	563	5	(	(	PUNCT
ejpam-5857	563	6	ψi(x	ψi(x	X
ejpam-5857	563	7	·	·	PUNCT
ejpam-5857	563	8	y	y	X
ejpam-5857	563	9	)	)	PUNCT
ejpam-5857	563	10	∧	∧	NOUN
ejpam-5857	563	11	ψt	ψt	NOUN
ejpam-5857	563	12	(	(	PUNCT
ejpam-5857	563	13	x	x	PROPN
ejpam-5857	563	14	·	·	PUNCT
ejpam-5857	563	15	y	y	NOUN
ejpam-5857	563	16	)	)	PUNCT
ejpam-5857	563	17	)	)	PUNCT
ejpam-5857	564	1	∧	∧	NOUN
ejpam-5857	564	2	(	(	PUNCT
ejpam-5857	564	3	ψi(x	ψi(x	NUM
ejpam-5857	564	4	)	)	PUNCT
ejpam-5857	564	5	∧	∧	NOUN
ejpam-5857	564	6	ψt	ψt	NOUN
ejpam-5857	564	7	(	(	PUNCT
ejpam-5857	564	8	x	x	NOUN
ejpam-5857	564	9	)	)	PUNCT
ejpam-5857	564	10	)	)	PUNCT
ejpam-5857	564	11	)	)	PUNCT
ejpam-5857	565	1	∨	∨	NUM
ejpam-5857	565	2	0.5	0.5	NUM
ejpam-5857	565	3	=	=	SYM
ejpam-5857	565	4	(	(	PUNCT
ejpam-5857	565	5	ψt	ψt	NUM
ejpam-5857	565	6	(	(	PUNCT
ejpam-5857	565	7	x	x	PROPN
ejpam-5857	565	8	·	·	PUNCT
ejpam-5857	565	9	y	y	X
ejpam-5857	565	10	)	)	PUNCT
ejpam-5857	565	11	∧	∧	NOUN
ejpam-5857	565	12	ψt	ψt	NOUN
ejpam-5857	565	13	(	(	PUNCT
ejpam-5857	565	14	x	x	NOUN
ejpam-5857	565	15	)	)	PUNCT
ejpam-5857	565	16	)	)	PUNCT
ejpam-5857	565	17	∨	∨	NUM
ejpam-5857	565	18	0.5	0.5	NUM
ejpam-5857	565	19	,	,	PUNCT
ejpam-5857	565	20	ψi(y	ψi(y	NUM
ejpam-5857	565	21	)	)	PUNCT
ejpam-5857	565	22	=	=	PRON
ejpam-5857	565	23	ψi(y	ψi(y	X
ejpam-5857	565	24	)	)	PUNCT
ejpam-5857	565	25	≤	≤	NOUN
ejpam-5857	565	26	(	(	PUNCT
ejpam-5857	565	27	ψi(x	ψi(x	X
ejpam-5857	565	28	·	·	PUNCT
ejpam-5857	565	29	y	y	X
ejpam-5857	565	30	)	)	PUNCT
ejpam-5857	565	31	∨	∨	NUM
ejpam-5857	565	32	ψi(x	ψi(x	NUM
ejpam-5857	565	33	)	)	PUNCT
ejpam-5857	565	34	)	)	PUNCT
ejpam-5857	566	1	∧	∧	NOUN
ejpam-5857	566	2	0.5	0.5	NUM
ejpam-5857	566	3	=	=	SYM
ejpam-5857	566	4	(	(	PUNCT
ejpam-5857	566	5	ψi(x	ψi(x	X
ejpam-5857	566	6	·	·	PUNCT
ejpam-5857	566	7	y	y	X
ejpam-5857	566	8	)	)	PUNCT
ejpam-5857	566	9	∨	∨	NUM
ejpam-5857	566	10	ψi(x	ψi(x	NUM
ejpam-5857	566	11	)	)	PUNCT
ejpam-5857	566	12	)	)	PUNCT
ejpam-5857	567	1	∧	∧	NOUN
ejpam-5857	567	2	0.5	0.5	NUM
ejpam-5857	567	3	,	,	PUNCT
ejpam-5857	567	4	ψf	ψf	X
ejpam-5857	567	5	(	(	PUNCT
ejpam-5857	567	6	y	y	NOUN
ejpam-5857	567	7	)	)	PUNCT
ejpam-5857	567	8	=	=	NOUN
ejpam-5857	567	9	ψi(y	ψi(y	X
ejpam-5857	567	10	)	)	PUNCT
ejpam-5857	567	11	∧	∧	NOUN
ejpam-5857	567	12	ψf	ψf	X
ejpam-5857	567	13	(	(	PUNCT
ejpam-5857	567	14	y	y	NOUN
ejpam-5857	567	15	)	)	PUNCT
ejpam-5857	567	16	≥	≥	NOUN
ejpam-5857	567	17	(	(	PUNCT
ejpam-5857	567	18	(	(	PUNCT
ejpam-5857	567	19	ψi(x	ψi(x	X
ejpam-5857	567	20	·	·	PUNCT
ejpam-5857	567	21	y	y	X
ejpam-5857	567	22	)	)	PUNCT
ejpam-5857	567	23	∧	∧	NOUN
ejpam-5857	567	24	ψi(x	ψi(x	NUM
ejpam-5857	567	25	)	)	PUNCT
ejpam-5857	567	26	)	)	PUNCT
ejpam-5857	568	1	∨	∨	NUM
ejpam-5857	568	2	0.5	0.5	NUM
ejpam-5857	568	3	)	)	PUNCT
ejpam-5857	568	4	∧	∧	NOUN
ejpam-5857	568	5	(	(	PUNCT
ejpam-5857	568	6	(	(	PUNCT
ejpam-5857	568	7	ψf	ψf	X
ejpam-5857	568	8	(	(	PUNCT
ejpam-5857	568	9	x	x	PROPN
ejpam-5857	568	10	·	·	PUNCT
ejpam-5857	568	11	y	y	X
ejpam-5857	568	12	)	)	PUNCT
ejpam-5857	568	13	∧	∧	NOUN
ejpam-5857	568	14	ψf	ψf	X
ejpam-5857	568	15	(	(	PUNCT
ejpam-5857	568	16	x	x	NOUN
ejpam-5857	568	17	)	)	PUNCT
ejpam-5857	568	18	)	)	PUNCT
ejpam-5857	568	19	∨	∨	NUM
ejpam-5857	568	20	0.5	0.5	NUM
ejpam-5857	568	21	)	)	PUNCT
ejpam-5857	568	22	=	=	SYM
ejpam-5857	568	23	(	(	PUNCT
ejpam-5857	568	24	(	(	PUNCT
ejpam-5857	568	25	ψi(x	ψi(x	X
ejpam-5857	568	26	·	·	PUNCT
ejpam-5857	568	27	y	y	X
ejpam-5857	568	28	)	)	PUNCT
ejpam-5857	568	29	∧	∧	NOUN
ejpam-5857	568	30	ψi(x	ψi(x	NUM
ejpam-5857	568	31	)	)	PUNCT
ejpam-5857	568	32	)	)	PUNCT
ejpam-5857	569	1	∧	∧	NOUN
ejpam-5857	569	2	(	(	PUNCT
ejpam-5857	569	3	ψf	ψf	X
ejpam-5857	569	4	(	(	PUNCT
ejpam-5857	569	5	x	x	PROPN
ejpam-5857	569	6	·	·	PUNCT
ejpam-5857	569	7	y	y	X
ejpam-5857	569	8	)	)	PUNCT
ejpam-5857	569	9	∧	∧	NOUN
ejpam-5857	569	10	ψf	ψf	X
ejpam-5857	569	11	(	(	PUNCT
ejpam-5857	569	12	x	x	NOUN
ejpam-5857	569	13	)	)	PUNCT
ejpam-5857	569	14	)	)	PUNCT
ejpam-5857	569	15	)	)	PUNCT
ejpam-5857	570	1	∨	∨	NUM
ejpam-5857	570	2	0.5	0.5	NUM
ejpam-5857	570	3	=	=	SYM
ejpam-5857	570	4	(	(	PUNCT
ejpam-5857	570	5	(	(	PUNCT
ejpam-5857	570	6	ψi(x	ψi(x	X
ejpam-5857	570	7	·	·	PUNCT
ejpam-5857	570	8	y	y	X
ejpam-5857	570	9	)	)	PUNCT
ejpam-5857	570	10	∧	∧	NOUN
ejpam-5857	570	11	ψf	ψf	X
ejpam-5857	570	12	(	(	PUNCT
ejpam-5857	570	13	x	x	PROPN
ejpam-5857	570	14	·	·	PUNCT
ejpam-5857	570	15	y	y	NOUN
ejpam-5857	570	16	)	)	PUNCT
ejpam-5857	570	17	)	)	PUNCT
ejpam-5857	570	18	∧	∧	NOUN
ejpam-5857	570	19	(	(	PUNCT
ejpam-5857	570	20	ψi(x	ψi(x	NUM
ejpam-5857	570	21	)	)	PUNCT
ejpam-5857	570	22	∧	∧	NOUN
ejpam-5857	570	23	ψf	ψf	X
ejpam-5857	570	24	(	(	PUNCT
ejpam-5857	570	25	x	x	NOUN
ejpam-5857	570	26	)	)	PUNCT
ejpam-5857	570	27	)	)	PUNCT
ejpam-5857	570	28	)	)	PUNCT
ejpam-5857	571	1	∨	∨	NUM
ejpam-5857	571	2	0.5	0.5	NUM
ejpam-5857	571	3	=	=	SYM
ejpam-5857	571	4	(	(	PUNCT
ejpam-5857	571	5	ψf	ψf	X
ejpam-5857	571	6	(	(	PUNCT
ejpam-5857	571	7	x	x	PROPN
ejpam-5857	571	8	·	·	PUNCT
ejpam-5857	571	9	y	y	X
ejpam-5857	571	10	)	)	PUNCT
ejpam-5857	571	11	∧	∧	NOUN
ejpam-5857	571	12	ψf	ψf	X
ejpam-5857	571	13	(	(	PUNCT
ejpam-5857	571	14	x	x	NOUN
ejpam-5857	571	15	)	)	PUNCT
ejpam-5857	571	16	)	)	PUNCT
ejpam-5857	571	17	∨	∨	NUM
ejpam-5857	571	18	0.5	0.5	NUM
ejpam-5857	571	19	.	.	PUNCT
ejpam-5857	572	1	hence	hence	ADV
ejpam-5857	572	2	,	,	PUNCT
ejpam-5857	572	3	the	the	DET
ejpam-5857	572	4	fss	fss	NOUN
ejpam-5857	572	5	ψt	ψt	VERB
ejpam-5857	572	6	and	and	CCONJ
ejpam-5857	572	7	ψf	ψf	AUX
ejpam-5857	572	8	satisfy	satisfy	VERB
ejpam-5857	572	9	the	the	DET
ejpam-5857	572	10	conditions	condition	NOUN
ejpam-5857	572	11	(	(	PUNCT
ejpam-5857	572	12	3.8	3.8	NUM
ejpam-5857	572	13	)	)	PUNCT
ejpam-5857	572	14	and	and	CCONJ
ejpam-5857	572	15	(	(	PUNCT
ejpam-5857	572	16	3.14	3.14	NUM
ejpam-5857	572	17	)	)	PUNCT
ejpam-5857	572	18	and	and	CCONJ
ejpam-5857	572	19	the	the	DET
ejpam-5857	572	20	fs	f	NOUN
ejpam-5857	572	21	ψi	ψi	ADJ
ejpam-5857	572	22	satisfies	satisfie	NOUN
ejpam-5857	572	23	the	the	DET
ejpam-5857	572	24	conditions	condition	NOUN
ejpam-5857	572	25	(	(	PUNCT
ejpam-5857	572	26	3.9	3.9	NUM
ejpam-5857	572	27	)	)	PUNCT
ejpam-5857	572	28	and	and	CCONJ
ejpam-5857	572	29	(	(	PUNCT
ejpam-5857	572	30	3.15	3.15	NUM
ejpam-5857	572	31	)	)	PUNCT
ejpam-5857	572	32	.	.	PUNCT
ejpam-5857	573	1	k.	k.	PROPN
ejpam-5857	573	2	suayngam	suayngam	PROPN
ejpam-5857	573	3	,	,	PUNCT
ejpam-5857	573	4	p.	p.	NOUN
ejpam-5857	573	5	julatha	julatha	PROPN
ejpam-5857	573	6	,	,	PUNCT
ejpam-5857	573	7	w.	w.	PROPN
ejpam-5857	573	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	573	9	,	,	PUNCT
ejpam-5857	573	10	a.	a.	NOUN
ejpam-5857	573	11	iampan	iampan	PROPN
ejpam-5857	573	12	/	/	SYM
ejpam-5857	573	13	eur	eur	PROPN
ejpam-5857	573	14	.	.	PUNCT
ejpam-5857	574	1	j.	j.	PROPN
ejpam-5857	574	2	pure	pure	PROPN
ejpam-5857	574	3	appl	appl	PROPN
ejpam-5857	574	4	.	.	PROPN
ejpam-5857	574	5	math	math	PROPN
ejpam-5857	574	6	,	,	PUNCT
ejpam-5857	574	7	18	18	NUM
ejpam-5857	574	8	(	(	PUNCT
ejpam-5857	574	9	2	2	NUM
ejpam-5857	574	10	)	)	PUNCT
ejpam-5857	574	11	(	(	PUNCT
ejpam-5857	574	12	2025	2025	NUM
ejpam-5857	574	13	)	)	PUNCT
ejpam-5857	574	14	,	,	PUNCT
ejpam-5857	574	15	5857	5857	NUM
ejpam-5857	574	16	21	21	NUM
ejpam-5857	574	17	of	of	ADP
ejpam-5857	574	18	30	30	NUM
ejpam-5857	574	19	theorem	theorem	NOUN
ejpam-5857	574	20	13	13	NUM
ejpam-5857	574	21	.	.	PUNCT
ejpam-5857	575	1	if	if	SCONJ
ejpam-5857	575	2	ψ	ψ	NOUN
ejpam-5857	575	3	is	be	AUX
ejpam-5857	575	4	an	an	DET
ejpam-5857	575	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	575	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	575	7	strong	strong	ADJ
ejpam-5857	575	8	iup	iup	NOUN
ejpam-5857	575	9	-	-	PUNCT
ejpam-5857	575	10	ideal	ideal	NOUN
ejpam-5857	575	11	of	of	ADP
ejpam-5857	575	12	x	x	PRON
ejpam-5857	575	13	,	,	PUNCT
ejpam-5857	575	14	then	then	ADV
ejpam-5857	575	15	the	the	DET
ejpam-5857	575	16	fss	fss	NOUN
ejpam-5857	575	17	ψt	ψt	VERB
ejpam-5857	575	18	and	and	CCONJ
ejpam-5857	575	19	ψf	ψf	AUX
ejpam-5857	575	20	satisfy	satisfy	VERB
ejpam-5857	575	21	the	the	DET
ejpam-5857	575	22	condition	condition	NOUN
ejpam-5857	575	23	(	(	PUNCT
ejpam-5857	575	24	3.17	3.17	NUM
ejpam-5857	575	25	)	)	PUNCT
ejpam-5857	575	26	and	and	CCONJ
ejpam-5857	575	27	the	the	DET
ejpam-5857	575	28	fs	f	NOUN
ejpam-5857	575	29	ψi	ψi	ADJ
ejpam-5857	575	30	satisfies	satisfie	NOUN
ejpam-5857	575	31	the	the	DET
ejpam-5857	575	32	condition	condition	NOUN
ejpam-5857	575	33	(	(	PUNCT
ejpam-5857	575	34	3.18	3.18	NUM
ejpam-5857	575	35	)	)	PUNCT
ejpam-5857	575	36	.	.	PUNCT
ejpam-5857	576	1	proof	proof	NOUN
ejpam-5857	576	2	.	.	PUNCT
ejpam-5857	577	1	it	it	PRON
ejpam-5857	577	2	is	be	AUX
ejpam-5857	577	3	straightforward	straightforward	ADJ
ejpam-5857	577	4	by	by	ADP
ejpam-5857	577	5	theorem	theorem	NOUN
ejpam-5857	577	6	1	1	NUM
ejpam-5857	577	7	.	.	PUNCT
ejpam-5857	577	8	theorem	theorem	VERB
ejpam-5857	577	9	14	14	NUM
ejpam-5857	577	10	.	.	PUNCT
ejpam-5857	578	1	an	an	DET
ejpam-5857	578	2	ins	ins	PROPN
ejpam-5857	578	3	ψ	ψ	NOUN
ejpam-5857	578	4	is	be	AUX
ejpam-5857	578	5	an	an	DET
ejpam-5857	578	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	578	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	578	8	iup	iup	NOUN
ejpam-5857	578	9	-	-	PUNCT
ejpam-5857	578	10	subalgebra	subalgebra	NOUN
ejpam-5857	578	11	of	of	ADP
ejpam-5857	578	12	x	x	PRON
ejpam-5857	578	13	if	if	SCONJ
ejpam-5857	578	14	and	and	CCONJ
ejpam-5857	578	15	only	only	ADV
ejpam-5857	578	16	if	if	SCONJ
ejpam-5857	578	17	ins	in	NOUN
ejpam-5857	578	18	□	□	PUNCT
ejpam-5857	578	19	ψ	ψ	X
ejpam-5857	578	20	=	=	X
ejpam-5857	578	21	(	(	PUNCT
ejpam-5857	578	22	ψt	ψt	NOUN
ejpam-5857	578	23	,	,	PUNCT
ejpam-5857	578	24	ψi	ψi	ADV
ejpam-5857	578	25	,	,	PUNCT
ejpam-5857	578	26	ψt	ψt	NOUN
ejpam-5857	578	27	)	)	PUNCT
ejpam-5857	578	28	and	and	CCONJ
ejpam-5857	578	29	♢	♢	PROPN
ejpam-5857	578	30	ψ	ψ	X
ejpam-5857	578	31	=	=	PUNCT
ejpam-5857	578	32	(	(	PUNCT
ejpam-5857	578	33	ψf	ψf	X
ejpam-5857	578	34	,	,	PUNCT
ejpam-5857	578	35	ψi	ψi	ADV
ejpam-5857	578	36	,	,	PUNCT
ejpam-5857	578	37	ψf	ψf	X
ejpam-5857	578	38	)	)	PUNCT
ejpam-5857	578	39	are	be	AUX
ejpam-5857	578	40	intuitionistic	intuitionistic	ADJ
ejpam-5857	578	41	neutrosophic	neutrosophic	ADJ
ejpam-5857	578	42	iup	iup	NOUN
ejpam-5857	578	43	-	-	PUNCT
ejpam-5857	578	44	subalgebras	subalgebras	PROPN
ejpam-5857	578	45	of	of	ADP
ejpam-5857	578	46	x.	x.	NOUN
ejpam-5857	578	47	proof	proof	NOUN
ejpam-5857	578	48	.	.	PUNCT
ejpam-5857	579	1	it	it	PRON
ejpam-5857	579	2	is	be	AUX
ejpam-5857	579	3	obvious	obvious	ADJ
ejpam-5857	579	4	by	by	ADP
ejpam-5857	579	5	theorem	theorem	NOUN
ejpam-5857	579	6	10	10	NUM
ejpam-5857	579	7	.	.	PUNCT
ejpam-5857	580	1	theorem	theorem	VERB
ejpam-5857	580	2	15	15	NUM
ejpam-5857	580	3	.	.	PUNCT
ejpam-5857	581	1	an	an	DET
ejpam-5857	581	2	ins	ins	PROPN
ejpam-5857	581	3	ψ	ψ	NOUN
ejpam-5857	581	4	is	be	AUX
ejpam-5857	581	5	an	an	DET
ejpam-5857	581	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	581	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	581	8	iup	iup	NOUN
ejpam-5857	581	9	-	-	PUNCT
ejpam-5857	581	10	ideal	ideal	NOUN
ejpam-5857	581	11	of	of	ADP
ejpam-5857	581	12	x	x	SYM
ejpam-5857	581	13	if	if	SCONJ
ejpam-5857	581	14	and	and	CCONJ
ejpam-5857	581	15	only	only	ADV
ejpam-5857	581	16	if	if	SCONJ
ejpam-5857	581	17	ins	in	NOUN
ejpam-5857	581	18	□	□	PUNCT
ejpam-5857	581	19	ψ	ψ	X
ejpam-5857	581	20	=	=	X
ejpam-5857	581	21	(	(	PUNCT
ejpam-5857	581	22	ψt	ψt	NOUN
ejpam-5857	581	23	,	,	PUNCT
ejpam-5857	581	24	ψi	ψi	ADV
ejpam-5857	581	25	,	,	PUNCT
ejpam-5857	581	26	ψt	ψt	NOUN
ejpam-5857	581	27	)	)	PUNCT
ejpam-5857	581	28	and	and	CCONJ
ejpam-5857	581	29	♢	♢	PROPN
ejpam-5857	581	30	ψ	ψ	X
ejpam-5857	581	31	=	=	PUNCT
ejpam-5857	581	32	(	(	PUNCT
ejpam-5857	581	33	ψf	ψf	X
ejpam-5857	581	34	,	,	PUNCT
ejpam-5857	581	35	ψi	ψi	ADV
ejpam-5857	581	36	,	,	PUNCT
ejpam-5857	581	37	ψf	ψf	X
ejpam-5857	581	38	)	)	PUNCT
ejpam-5857	581	39	are	be	AUX
ejpam-5857	581	40	intuitionistic	intuitionistic	ADJ
ejpam-5857	581	41	neutrosophic	neutrosophic	ADJ
ejpam-5857	581	42	iup	iup	NOUN
ejpam-5857	581	43	-	-	PUNCT
ejpam-5857	581	44	ideals	ideal	NOUN
ejpam-5857	581	45	of	of	ADP
ejpam-5857	581	46	x.	x.	NOUN
ejpam-5857	581	47	proof	proof	NOUN
ejpam-5857	581	48	.	.	PUNCT
ejpam-5857	582	1	it	it	PRON
ejpam-5857	582	2	is	be	AUX
ejpam-5857	582	3	obvious	obvious	ADJ
ejpam-5857	582	4	by	by	ADP
ejpam-5857	582	5	theorem	theorem	NOUN
ejpam-5857	582	6	11	11	NUM
ejpam-5857	582	7	.	.	PUNCT
ejpam-5857	583	1	theorem	theorem	VERB
ejpam-5857	583	2	16	16	NUM
ejpam-5857	583	3	.	.	PUNCT
ejpam-5857	584	1	an	an	DET
ejpam-5857	584	2	ins	ins	PROPN
ejpam-5857	584	3	ψ	ψ	NOUN
ejpam-5857	584	4	is	be	AUX
ejpam-5857	584	5	an	an	DET
ejpam-5857	584	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	584	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	584	8	iup	iup	NOUN
ejpam-5857	584	9	-	-	PUNCT
ejpam-5857	584	10	filter	filter	NOUN
ejpam-5857	584	11	of	of	ADP
ejpam-5857	584	12	x	x	SYM
ejpam-5857	584	13	if	if	SCONJ
ejpam-5857	584	14	and	and	CCONJ
ejpam-5857	584	15	only	only	ADV
ejpam-5857	584	16	if	if	SCONJ
ejpam-5857	584	17	ins	in	NOUN
ejpam-5857	584	18	□	□	PUNCT
ejpam-5857	584	19	ψ	ψ	X
ejpam-5857	584	20	=	=	X
ejpam-5857	584	21	(	(	PUNCT
ejpam-5857	584	22	ψt	ψt	NOUN
ejpam-5857	584	23	,	,	PUNCT
ejpam-5857	584	24	ψi	ψi	ADV
ejpam-5857	584	25	,	,	PUNCT
ejpam-5857	584	26	ψt	ψt	NOUN
ejpam-5857	584	27	)	)	PUNCT
ejpam-5857	584	28	and	and	CCONJ
ejpam-5857	584	29	♢	♢	PROPN
ejpam-5857	584	30	ψ	ψ	X
ejpam-5857	584	31	=	=	PUNCT
ejpam-5857	584	32	(	(	PUNCT
ejpam-5857	584	33	ψf	ψf	X
ejpam-5857	584	34	,	,	PUNCT
ejpam-5857	584	35	ψi	ψi	ADV
ejpam-5857	584	36	,	,	PUNCT
ejpam-5857	584	37	ψf	ψf	X
ejpam-5857	584	38	)	)	PUNCT
ejpam-5857	584	39	are	be	AUX
ejpam-5857	584	40	intuitionistic	intuitionistic	ADJ
ejpam-5857	584	41	neutrosophic	neutrosophic	ADJ
ejpam-5857	584	42	iup	iup	NOUN
ejpam-5857	584	43	-	-	PUNCT
ejpam-5857	584	44	filters	filter	NOUN
ejpam-5857	584	45	of	of	ADP
ejpam-5857	584	46	x.	x.	NOUN
ejpam-5857	584	47	proof	proof	NOUN
ejpam-5857	584	48	.	.	PUNCT
ejpam-5857	585	1	it	it	PRON
ejpam-5857	585	2	is	be	AUX
ejpam-5857	585	3	obvious	obvious	ADJ
ejpam-5857	585	4	by	by	ADP
ejpam-5857	585	5	theorem	theorem	NOUN
ejpam-5857	585	6	12	12	NUM
ejpam-5857	585	7	.	.	PUNCT
ejpam-5857	586	1	theorem	theorem	VERB
ejpam-5857	586	2	17	17	NUM
ejpam-5857	586	3	.	.	PUNCT
ejpam-5857	587	1	an	an	DET
ejpam-5857	587	2	ins	ins	PROPN
ejpam-5857	587	3	ψ	ψ	NOUN
ejpam-5857	587	4	is	be	AUX
ejpam-5857	587	5	an	an	DET
ejpam-5857	587	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	587	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	587	8	strong	strong	ADJ
ejpam-5857	587	9	iup	iup	NOUN
ejpam-5857	587	10	-	-	PUNCT
ejpam-5857	587	11	ideal	ideal	NOUN
ejpam-5857	587	12	of	of	ADP
ejpam-5857	587	13	x	x	SYM
ejpam-5857	587	14	if	if	SCONJ
ejpam-5857	587	15	and	and	CCONJ
ejpam-5857	587	16	only	only	ADV
ejpam-5857	587	17	if	if	SCONJ
ejpam-5857	587	18	ins	in	NOUN
ejpam-5857	587	19	□	□	PUNCT
ejpam-5857	587	20	ψ	ψ	X
ejpam-5857	587	21	=	=	X
ejpam-5857	587	22	(	(	PUNCT
ejpam-5857	587	23	ψt	ψt	NOUN
ejpam-5857	587	24	,	,	PUNCT
ejpam-5857	587	25	ψi	ψi	ADV
ejpam-5857	587	26	,	,	PUNCT
ejpam-5857	587	27	ψt	ψt	NOUN
ejpam-5857	587	28	)	)	PUNCT
ejpam-5857	587	29	and	and	CCONJ
ejpam-5857	587	30	♢	♢	PROPN
ejpam-5857	587	31	ψ	ψ	X
ejpam-5857	587	32	=	=	PUNCT
ejpam-5857	587	33	(	(	PUNCT
ejpam-5857	587	34	ψf	ψf	X
ejpam-5857	587	35	,	,	PUNCT
ejpam-5857	587	36	ψi	ψi	ADV
ejpam-5857	587	37	,	,	PUNCT
ejpam-5857	587	38	ψf	ψf	X
ejpam-5857	587	39	)	)	PUNCT
ejpam-5857	587	40	are	be	AUX
ejpam-5857	587	41	intuitionistic	intuitionistic	ADJ
ejpam-5857	587	42	neutrosophic	neutrosophic	ADJ
ejpam-5857	587	43	strong	strong	ADJ
ejpam-5857	587	44	iup	iup	NOUN
ejpam-5857	587	45	-	-	PUNCT
ejpam-5857	587	46	ideals	ideal	NOUN
ejpam-5857	587	47	of	of	ADP
ejpam-5857	587	48	x.	x.	NOUN
ejpam-5857	587	49	proof	proof	NOUN
ejpam-5857	587	50	.	.	PUNCT
ejpam-5857	588	1	it	it	PRON
ejpam-5857	588	2	is	be	AUX
ejpam-5857	588	3	obvious	obvious	ADJ
ejpam-5857	588	4	by	by	ADP
ejpam-5857	588	5	theorem	theorem	NOUN
ejpam-5857	588	6	13	13	NUM
ejpam-5857	588	7	.	.	PUNCT
ejpam-5857	589	1	definition	definition	NOUN
ejpam-5857	589	2	9	9	NUM
ejpam-5857	589	3	.	.	PUNCT
ejpam-5857	590	1	let	let	VERB
ejpam-5857	590	2	f	f	PRON
ejpam-5857	590	3	be	be	AUX
ejpam-5857	590	4	an	an	DET
ejpam-5857	590	5	fs	fs	NOUN
ejpam-5857	590	6	in	in	ADP
ejpam-5857	590	7	x.	x.	NOUN
ejpam-5857	590	8	for	for	ADP
ejpam-5857	590	9	any	any	DET
ejpam-5857	590	10	t	t	NOUN
ejpam-5857	590	11	∈	∈	PROPN
ejpam-5857	591	1	[	[	X
ejpam-5857	591	2	0	0	NUM
ejpam-5857	591	3	,	,	PUNCT
ejpam-5857	591	4	1	1	NUM
ejpam-5857	591	5	]	]	PUNCT
ejpam-5857	591	6	,	,	PUNCT
ejpam-5857	591	7	the	the	DET
ejpam-5857	591	8	sets	set	VERB
ejpam-5857	591	9	u(f	u(f	PROPN
ejpam-5857	591	10	;	;	PUNCT
ejpam-5857	591	11	t	t	X
ejpam-5857	591	12	)	)	PUNCT
ejpam-5857	591	13	=	=	PRON
ejpam-5857	592	1	{	{	PUNCT
ejpam-5857	592	2	x	x	PUNCT
ejpam-5857	592	3	∈	∈	PROPN
ejpam-5857	592	4	x	x	X
ejpam-5857	592	5	|	|	ADV
ejpam-5857	592	6	f(x	f(x	PROPN
ejpam-5857	592	7	)	)	PUNCT
ejpam-5857	592	8	≥	≥	NOUN
ejpam-5857	592	9	t	t	PROPN
ejpam-5857	592	10	}	}	PUNCT
ejpam-5857	592	11	,	,	PUNCT
ejpam-5857	592	12	(	(	PUNCT
ejpam-5857	592	13	3.26	3.26	NUM
ejpam-5857	592	14	)	)	PUNCT
ejpam-5857	592	15	l(f	l(f	PROPN
ejpam-5857	592	16	;	;	PUNCT
ejpam-5857	592	17	t	t	X
ejpam-5857	592	18	)	)	PUNCT
ejpam-5857	592	19	=	=	PRON
ejpam-5857	592	20	{	{	PUNCT
ejpam-5857	592	21	x	x	PUNCT
ejpam-5857	592	22	∈	∈	PROPN
ejpam-5857	592	23	x	x	X
ejpam-5857	592	24	|	|	ADV
ejpam-5857	592	25	f(x	f(x	PROPN
ejpam-5857	592	26	)	)	PUNCT
ejpam-5857	592	27	≤	≤	NOUN
ejpam-5857	592	28	t	t	PROPN
ejpam-5857	592	29	}	}	PUNCT
ejpam-5857	592	30	,	,	PUNCT
ejpam-5857	592	31	(	(	PUNCT
ejpam-5857	592	32	3.27	3.27	NUM
ejpam-5857	592	33	)	)	PUNCT
ejpam-5857	592	34	e(f	e(f	PROPN
ejpam-5857	592	35	;	;	PUNCT
ejpam-5857	592	36	t	t	PROPN
ejpam-5857	592	37	)	)	PUNCT
ejpam-5857	592	38	=	=	PRON
ejpam-5857	592	39	{	{	PUNCT
ejpam-5857	592	40	x	x	PUNCT
ejpam-5857	592	41	∈	∈	PROPN
ejpam-5857	592	42	x	x	X
ejpam-5857	592	43	|	|	ADV
ejpam-5857	592	44	f(x	f(x	PROPN
ejpam-5857	592	45	)	)	PUNCT
ejpam-5857	592	46	=	=	SYM
ejpam-5857	592	47	t	t	PROPN
ejpam-5857	592	48	}	}	PUNCT
ejpam-5857	592	49	(	(	PUNCT
ejpam-5857	592	50	3.28	3.28	NUM
ejpam-5857	592	51	)	)	PUNCT
ejpam-5857	592	52	are	be	AUX
ejpam-5857	592	53	called	call	VERB
ejpam-5857	592	54	an	an	DET
ejpam-5857	592	55	upper	upper	ADJ
ejpam-5857	592	56	t	t	NOUN
ejpam-5857	592	57	-	-	PUNCT
ejpam-5857	592	58	level	level	NOUN
ejpam-5857	592	59	subset	subset	NOUN
ejpam-5857	592	60	,	,	PUNCT
ejpam-5857	592	61	a	a	DET
ejpam-5857	592	62	lower	low	ADJ
ejpam-5857	592	63	t	t	NOUN
ejpam-5857	592	64	-	-	PUNCT
ejpam-5857	592	65	level	level	NOUN
ejpam-5857	592	66	subset	subset	NOUN
ejpam-5857	592	67	and	and	CCONJ
ejpam-5857	592	68	an	an	DET
ejpam-5857	592	69	equal	equal	ADJ
ejpam-5857	592	70	t	t	NOUN
ejpam-5857	592	71	-	-	PUNCT
ejpam-5857	592	72	level	level	NOUN
ejpam-5857	592	73	subset	subset	NOUN
ejpam-5857	592	74	of	of	ADP
ejpam-5857	592	75	f	f	PROPN
ejpam-5857	592	76	,	,	PUNCT
ejpam-5857	592	77	respectively	respectively	ADV
ejpam-5857	592	78	.	.	PUNCT
ejpam-5857	593	1	the	the	DET
ejpam-5857	593	2	sets	set	VERB
ejpam-5857	593	3	u	u	NOUN
ejpam-5857	593	4	+	+	X
ejpam-5857	593	5	(	(	PUNCT
ejpam-5857	593	6	f	f	PROPN
ejpam-5857	593	7	;	;	PUNCT
ejpam-5857	593	8	t	t	PROPN
ejpam-5857	593	9	)	)	PUNCT
ejpam-5857	593	10	=	=	PRON
ejpam-5857	594	1	{	{	PUNCT
ejpam-5857	594	2	x	x	PUNCT
ejpam-5857	594	3	∈	∈	PROPN
ejpam-5857	594	4	x	x	X
ejpam-5857	594	5	|	|	ADV
ejpam-5857	594	6	f(x	f(x	PROPN
ejpam-5857	594	7	)	)	PUNCT
ejpam-5857	594	8	>	>	X
ejpam-5857	594	9	t	t	PROPN
ejpam-5857	594	10	}	}	PUNCT
ejpam-5857	594	11	,	,	PUNCT
ejpam-5857	594	12	(	(	PUNCT
ejpam-5857	594	13	3.29	3.29	NUM
ejpam-5857	594	14	)	)	PUNCT
ejpam-5857	594	15	l	l	NOUN
ejpam-5857	594	16	−	−	PROPN
ejpam-5857	594	17	(	(	PUNCT
ejpam-5857	594	18	f	f	PROPN
ejpam-5857	594	19	;	;	PUNCT
ejpam-5857	594	20	t	t	PROPN
ejpam-5857	594	21	)	)	PUNCT
ejpam-5857	594	22	=	=	PRON
ejpam-5857	594	23	{	{	PUNCT
ejpam-5857	594	24	x	x	PUNCT
ejpam-5857	594	25	∈	∈	PROPN
ejpam-5857	594	26	x	x	X
ejpam-5857	594	27	|	|	ADV
ejpam-5857	594	28	f(x	f(x	PROPN
ejpam-5857	594	29	)	)	PUNCT
ejpam-5857	594	30	<	<	X
ejpam-5857	594	31	t	t	PROPN
ejpam-5857	594	32	}	}	PUNCT
ejpam-5857	594	33	(	(	PUNCT
ejpam-5857	594	34	3.30	3.30	NUM
ejpam-5857	594	35	)	)	PUNCT
ejpam-5857	594	36	are	be	AUX
ejpam-5857	594	37	called	call	VERB
ejpam-5857	594	38	an	an	DET
ejpam-5857	594	39	upper	upper	ADJ
ejpam-5857	594	40	t	t	NOUN
ejpam-5857	594	41	-	-	PUNCT
ejpam-5857	594	42	strong	strong	ADJ
ejpam-5857	594	43	level	level	NOUN
ejpam-5857	594	44	subset	subset	NOUN
ejpam-5857	594	45	and	and	CCONJ
ejpam-5857	594	46	a	a	DET
ejpam-5857	594	47	lower	low	ADJ
ejpam-5857	594	48	t	t	NOUN
ejpam-5857	594	49	-	-	PUNCT
ejpam-5857	594	50	strong	strong	ADJ
ejpam-5857	594	51	level	level	NOUN
ejpam-5857	594	52	subset	subset	NOUN
ejpam-5857	594	53	of	of	ADP
ejpam-5857	594	54	f	f	PROPN
ejpam-5857	594	55	,	,	PUNCT
ejpam-5857	594	56	respectively	respectively	ADV
ejpam-5857	594	57	.	.	PUNCT
ejpam-5857	595	1	theorem	theorem	VERB
ejpam-5857	595	2	18	18	NUM
ejpam-5857	595	3	.	.	PUNCT
ejpam-5857	596	1	let	let	VERB
ejpam-5857	596	2	an	an	DET
ejpam-5857	596	3	ins	in	NOUN
ejpam-5857	596	4	ψ	ψ	NOUN
ejpam-5857	596	5	is	be	AUX
ejpam-5857	596	6	an	an	DET
ejpam-5857	596	7	intuitionistic	intuitionistic	ADJ
ejpam-5857	596	8	neutrosophic	neutrosophic	ADJ
ejpam-5857	596	9	iup	iup	NOUN
ejpam-5857	596	10	-	-	PUNCT
ejpam-5857	596	11	subalgebra	subalgebra	NOUN
ejpam-5857	596	12	of	of	ADP
ejpam-5857	596	13	x.	x.	NOUN
ejpam-5857	596	14	then	then	ADV
ejpam-5857	596	15	for	for	ADP
ejpam-5857	596	16	all	all	DET
ejpam-5857	596	17	α	α	NOUN
ejpam-5857	596	18	,	,	PUNCT
ejpam-5857	596	19	γ	γ	PROPN
ejpam-5857	596	20	∈	∈	PROPN
ejpam-5857	597	1	[	[	X
ejpam-5857	597	2	0.5	0.5	NUM
ejpam-5857	597	3	,	,	PUNCT
ejpam-5857	597	4	1	1	NUM
ejpam-5857	597	5	]	]	PUNCT
ejpam-5857	597	6	and	and	CCONJ
ejpam-5857	597	7	β	β	X
ejpam-5857	597	8	∈	∈	PROPN
ejpam-5857	597	9	[	[	X
ejpam-5857	597	10	0	0	NUM
ejpam-5857	597	11	,	,	PUNCT
ejpam-5857	597	12	0.5	0.5	NUM
ejpam-5857	597	13	)	)	PUNCT
ejpam-5857	597	14	,	,	PUNCT
ejpam-5857	597	15	the	the	DET
ejpam-5857	597	16	sets	set	NOUN
ejpam-5857	597	17	u(ψt	u(ψt	PROPN
ejpam-5857	597	18	;	;	PUNCT
ejpam-5857	597	19	α	α	X
ejpam-5857	597	20	)	)	PUNCT
ejpam-5857	597	21	,	,	PUNCT
ejpam-5857	597	22	l(ψi	l(ψi	PROPN
ejpam-5857	597	23	;	;	PUNCT
ejpam-5857	597	24	β	β	X
ejpam-5857	597	25	)	)	PUNCT
ejpam-5857	597	26	and	and	CCONJ
ejpam-5857	597	27	u(ψf	u(ψf	PROPN
ejpam-5857	597	28	;	;	PUNCT
ejpam-5857	597	29	γ	γ	X
ejpam-5857	597	30	)	)	PUNCT
ejpam-5857	597	31	are	be	AUX
ejpam-5857	597	32	either	either	CCONJ
ejpam-5857	597	33	empty	empty	ADJ
ejpam-5857	597	34	or	or	CCONJ
ejpam-5857	597	35	iup	iup	NOUN
ejpam-5857	597	36	-	-	PUNCT
ejpam-5857	597	37	subalgebras	subalgebras	PROPN
ejpam-5857	597	38	of	of	ADP
ejpam-5857	597	39	x.	x.	PROPN
ejpam-5857	597	40	k.	k.	PROPN
ejpam-5857	597	41	suayngam	suayngam	PROPN
ejpam-5857	597	42	,	,	PUNCT
ejpam-5857	597	43	p.	p.	NOUN
ejpam-5857	597	44	julatha	julatha	PROPN
ejpam-5857	597	45	,	,	PUNCT
ejpam-5857	597	46	w.	w.	PROPN
ejpam-5857	597	47	nakkhasen	nakkhasen	PROPN
ejpam-5857	597	48	,	,	PUNCT
ejpam-5857	597	49	a.	a.	NOUN
ejpam-5857	597	50	iampan	iampan	PROPN
ejpam-5857	597	51	/	/	SYM
ejpam-5857	597	52	eur	eur	PROPN
ejpam-5857	597	53	.	.	PUNCT
ejpam-5857	598	1	j.	j.	PROPN
ejpam-5857	598	2	pure	pure	PROPN
ejpam-5857	598	3	appl	appl	PROPN
ejpam-5857	598	4	.	.	PROPN
ejpam-5857	598	5	math	math	PROPN
ejpam-5857	598	6	,	,	PUNCT
ejpam-5857	598	7	18	18	NUM
ejpam-5857	598	8	(	(	PUNCT
ejpam-5857	598	9	2	2	NUM
ejpam-5857	598	10	)	)	PUNCT
ejpam-5857	598	11	(	(	PUNCT
ejpam-5857	598	12	2025	2025	NUM
ejpam-5857	598	13	)	)	PUNCT
ejpam-5857	598	14	,	,	PUNCT
ejpam-5857	598	15	5857	5857	NUM
ejpam-5857	598	16	22	22	NUM
ejpam-5857	598	17	of	of	ADP
ejpam-5857	598	18	30	30	NUM
ejpam-5857	598	19	proof	proof	NOUN
ejpam-5857	598	20	.	.	PUNCT
ejpam-5857	599	1	assume	assume	VERB
ejpam-5857	599	2	that	that	SCONJ
ejpam-5857	599	3	ψ	ψ	NOUN
ejpam-5857	599	4	is	be	AUX
ejpam-5857	599	5	an	an	DET
ejpam-5857	599	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	599	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	599	8	iup	iup	NOUN
ejpam-5857	599	9	-	-	PUNCT
ejpam-5857	599	10	subalgebra	subalgebra	NOUN
ejpam-5857	599	11	of	of	ADP
ejpam-5857	599	12	x.	x.	NOUN
ejpam-5857	599	13	let	let	VERB
ejpam-5857	599	14	α	α	PRON
ejpam-5857	599	15	∈	∈	PROPN
ejpam-5857	600	1	[	[	X
ejpam-5857	600	2	0.5	0.5	NUM
ejpam-5857	600	3	,	,	PUNCT
ejpam-5857	600	4	1	1	NUM
ejpam-5857	600	5	]	]	PUNCT
ejpam-5857	600	6	be	be	AUX
ejpam-5857	600	7	such	such	ADJ
ejpam-5857	600	8	that	that	SCONJ
ejpam-5857	600	9	u(ψt	u(ψt	PROPN
ejpam-5857	600	10	;	;	PUNCT
ejpam-5857	600	11	α	α	X
ejpam-5857	600	12	)	)	PUNCT
ejpam-5857	600	13	̸=	̸=	PROPN
ejpam-5857	600	14	∅.	∅.	ADV
ejpam-5857	600	15	let	let	VERB
ejpam-5857	600	16	x	x	PRON
ejpam-5857	600	17	,	,	PUNCT
ejpam-5857	600	18	y	y	PROPN
ejpam-5857	600	19	∈	∈	PROPN
ejpam-5857	600	20	u(ψt	u(ψt	PROPN
ejpam-5857	600	21	;	;	PUNCT
ejpam-5857	600	22	α	α	X
ejpam-5857	600	23	)	)	PUNCT
ejpam-5857	600	24	.	.	PUNCT
ejpam-5857	601	1	then	then	ADV
ejpam-5857	601	2	ψt	ψt	VERB
ejpam-5857	601	3	(	(	PUNCT
ejpam-5857	601	4	x	x	NOUN
ejpam-5857	601	5	)	)	PUNCT
ejpam-5857	601	6	≥	≥	PROPN
ejpam-5857	601	7	α	α	NOUN
ejpam-5857	601	8	and	and	CCONJ
ejpam-5857	601	9	ψt	ψt	ADJ
ejpam-5857	601	10	(	(	PUNCT
ejpam-5857	601	11	y	y	NOUN
ejpam-5857	601	12	)	)	PUNCT
ejpam-5857	601	13	≥	≥	PROPN
ejpam-5857	601	14	α	α	NOUN
ejpam-5857	601	15	.	.	PUNCT
ejpam-5857	602	1	thus	thus	ADV
ejpam-5857	602	2	,	,	PUNCT
ejpam-5857	602	3	ψt	ψt	VERB
ejpam-5857	602	4	(	(	PUNCT
ejpam-5857	602	5	x	x	X
ejpam-5857	602	6	)	)	PUNCT
ejpam-5857	602	7	∧	∧	NOUN
ejpam-5857	602	8	ψt	ψt	NOUN
ejpam-5857	602	9	(	(	PUNCT
ejpam-5857	602	10	y	y	NOUN
ejpam-5857	602	11	)	)	PUNCT
ejpam-5857	602	12	≥	≥	PROPN
ejpam-5857	602	13	α	α	NOUN
ejpam-5857	602	14	.	.	PUNCT
ejpam-5857	603	1	by	by	ADP
ejpam-5857	603	2	the	the	DET
ejpam-5857	603	3	condition	condition	NOUN
ejpam-5857	603	4	(	(	PUNCT
ejpam-5857	603	5	3.5	3.5	NUM
ejpam-5857	603	6	)	)	PUNCT
ejpam-5857	603	7	,	,	PUNCT
ejpam-5857	603	8	we	we	PRON
ejpam-5857	603	9	have	have	AUX
ejpam-5857	603	10	ψt	ψt	VERB
ejpam-5857	603	11	(	(	PUNCT
ejpam-5857	603	12	x	x	PROPN
ejpam-5857	603	13	·	·	PUNCT
ejpam-5857	603	14	y	y	X
ejpam-5857	603	15	)	)	PUNCT
ejpam-5857	603	16	≥	≥	NOUN
ejpam-5857	603	17	(	(	PUNCT
ejpam-5857	603	18	ψt	ψt	VERB
ejpam-5857	603	19	(	(	PUNCT
ejpam-5857	603	20	x)∧ψt	x)∧ψt	PROPN
ejpam-5857	603	21	(	(	PUNCT
ejpam-5857	603	22	y))∨	y))∨	NOUN
ejpam-5857	603	23	0.5	0.5	NUM
ejpam-5857	603	24	≥	≥	NOUN
ejpam-5857	603	25	α∨	α∨	PROPN
ejpam-5857	603	26	0.5	0.5	NUM
ejpam-5857	603	27	≥	≥	NUM
ejpam-5857	603	28	α	α	NOUN
ejpam-5857	603	29	,	,	PUNCT
ejpam-5857	603	30	that	that	ADV
ejpam-5857	603	31	is	is	ADV
ejpam-5857	603	32	,	,	PUNCT
ejpam-5857	603	33	ψt	ψt	VERB
ejpam-5857	603	34	(	(	PUNCT
ejpam-5857	603	35	x	x	PROPN
ejpam-5857	603	36	·	·	PUNCT
ejpam-5857	603	37	y	y	X
ejpam-5857	603	38	)	)	PUNCT
ejpam-5857	603	39	≥	≥	PROPN
ejpam-5857	603	40	α	α	NOUN
ejpam-5857	603	41	.	.	PUNCT
ejpam-5857	604	1	thus	thus	ADV
ejpam-5857	604	2	,	,	PUNCT
ejpam-5857	604	3	x	x	X
ejpam-5857	604	4	·	·	PUNCT
ejpam-5857	604	5	y	y	PROPN
ejpam-5857	604	6	∈	∈	PROPN
ejpam-5857	604	7	u(ψt	u(ψt	PROPN
ejpam-5857	604	8	;	;	PUNCT
ejpam-5857	604	9	α	α	X
ejpam-5857	604	10	)	)	PUNCT
ejpam-5857	604	11	.	.	PUNCT
ejpam-5857	605	1	hence	hence	ADV
ejpam-5857	605	2	,	,	PUNCT
ejpam-5857	605	3	u(ψt	u(ψt	PROPN
ejpam-5857	605	4	;	;	PUNCT
ejpam-5857	605	5	α	α	X
ejpam-5857	605	6	)	)	PUNCT
ejpam-5857	605	7	is	be	AUX
ejpam-5857	605	8	an	an	DET
ejpam-5857	605	9	iup	iup	NOUN
ejpam-5857	605	10	-	-	PUNCT
ejpam-5857	605	11	subalgebra	subalgebra	NOUN
ejpam-5857	605	12	of	of	ADP
ejpam-5857	605	13	x.	x.	NOUN
ejpam-5857	605	14	let	let	VERB
ejpam-5857	605	15	β	β	X
ejpam-5857	605	16	∈	∈	PROPN
ejpam-5857	606	1	[	[	X
ejpam-5857	606	2	0	0	NUM
ejpam-5857	606	3	,	,	PUNCT
ejpam-5857	606	4	0.5	0.5	NUM
ejpam-5857	606	5	)	)	PUNCT
ejpam-5857	606	6	be	be	VERB
ejpam-5857	606	7	such	such	ADJ
ejpam-5857	606	8	that	that	SCONJ
ejpam-5857	606	9	l(ψi	l(ψi	NOUN
ejpam-5857	606	10	;	;	PUNCT
ejpam-5857	606	11	β	β	X
ejpam-5857	606	12	)	)	PUNCT
ejpam-5857	606	13	̸=	̸=	PROPN
ejpam-5857	606	14	∅.	∅.	ADV
ejpam-5857	606	15	let	let	VERB
ejpam-5857	606	16	x	x	PRON
ejpam-5857	606	17	,	,	PUNCT
ejpam-5857	606	18	y	y	PROPN
ejpam-5857	606	19	∈	∈	PROPN
ejpam-5857	606	20	l(ψi	l(ψi	PROPN
ejpam-5857	606	21	;	;	PUNCT
ejpam-5857	606	22	β	β	X
ejpam-5857	606	23	)	)	PUNCT
ejpam-5857	606	24	.	.	PUNCT
ejpam-5857	607	1	then	then	ADV
ejpam-5857	607	2	ψi(x	ψi(x	NUM
ejpam-5857	607	3	)	)	PUNCT
ejpam-5857	607	4	≤	≤	NUM
ejpam-5857	607	5	β	β	X
ejpam-5857	607	6	and	and	CCONJ
ejpam-5857	607	7	ψi(y	ψi(y	NUM
ejpam-5857	607	8	)	)	PUNCT
ejpam-5857	607	9	≤	≤	NOUN
ejpam-5857	607	10	β	β	X
ejpam-5857	607	11	.	.	PUNCT
ejpam-5857	608	1	thus	thus	ADV
ejpam-5857	608	2	,	,	PUNCT
ejpam-5857	608	3	ψi(x	ψi(x	NUM
ejpam-5857	608	4	)	)	PUNCT
ejpam-5857	608	5	∨	∨	NUM
ejpam-5857	608	6	ψi(y	ψi(y	NUM
ejpam-5857	608	7	)	)	PUNCT
ejpam-5857	608	8	≤	≤	NOUN
ejpam-5857	609	1	β	β	X
ejpam-5857	609	2	.	.	PUNCT
ejpam-5857	610	1	by	by	ADP
ejpam-5857	610	2	the	the	DET
ejpam-5857	610	3	condition	condition	NOUN
ejpam-5857	610	4	(	(	PUNCT
ejpam-5857	610	5	3.6	3.6	NUM
ejpam-5857	610	6	)	)	PUNCT
ejpam-5857	610	7	,	,	PUNCT
ejpam-5857	610	8	we	we	PRON
ejpam-5857	610	9	have	have	VERB
ejpam-5857	610	10	ψi(x	ψi(x	NUM
ejpam-5857	610	11	·	·	PUNCT
ejpam-5857	610	12	y	y	X
ejpam-5857	610	13	)	)	PUNCT
ejpam-5857	610	14	≤	≤	NOUN
ejpam-5857	610	15	(	(	PUNCT
ejpam-5857	610	16	ψi(x	ψi(x	NUM
ejpam-5857	610	17	)	)	PUNCT
ejpam-5857	610	18	∨	∨	NUM
ejpam-5857	610	19	ψi(y	ψi(y	NUM
ejpam-5857	610	20	)	)	PUNCT
ejpam-5857	610	21	)	)	PUNCT
ejpam-5857	611	1	∧	∧	NOUN
ejpam-5857	611	2	0.5	0.5	NUM
ejpam-5857	611	3	≤	≤	NOUN
ejpam-5857	611	4	β	β	X
ejpam-5857	611	5	∧	∧	PROPN
ejpam-5857	611	6	0.5	0.5	NUM
ejpam-5857	611	7	≤	≤	NOUN
ejpam-5857	611	8	β	β	NOUN
ejpam-5857	611	9	,	,	PUNCT
ejpam-5857	611	10	that	that	ADV
ejpam-5857	611	11	is	is	ADV
ejpam-5857	611	12	,	,	PUNCT
ejpam-5857	611	13	ψi(x	ψi(x	X
ejpam-5857	611	14	·	·	PUNCT
ejpam-5857	611	15	y	y	X
ejpam-5857	611	16	)	)	PUNCT
ejpam-5857	611	17	≤	≤	NOUN
ejpam-5857	611	18	β	β	X
ejpam-5857	611	19	.	.	PUNCT
ejpam-5857	612	1	thus	thus	ADV
ejpam-5857	612	2	,	,	PUNCT
ejpam-5857	612	3	x	x	X
ejpam-5857	612	4	·	·	PUNCT
ejpam-5857	612	5	y	y	PROPN
ejpam-5857	612	6	∈	∈	PROPN
ejpam-5857	612	7	l(ψi	l(ψi	PROPN
ejpam-5857	612	8	;	;	PUNCT
ejpam-5857	612	9	β	β	X
ejpam-5857	612	10	)	)	PUNCT
ejpam-5857	612	11	.	.	PUNCT
ejpam-5857	613	1	hence	hence	ADV
ejpam-5857	613	2	,	,	PUNCT
ejpam-5857	613	3	l(ψi	l(ψi	PROPN
ejpam-5857	613	4	;	;	PUNCT
ejpam-5857	613	5	β	β	X
ejpam-5857	613	6	)	)	PUNCT
ejpam-5857	613	7	is	be	AUX
ejpam-5857	613	8	an	an	DET
ejpam-5857	613	9	iup	iup	NOUN
ejpam-5857	613	10	-	-	PUNCT
ejpam-5857	613	11	subalgebra	subalgebra	NOUN
ejpam-5857	613	12	of	of	ADP
ejpam-5857	613	13	x.	x.	NOUN
ejpam-5857	613	14	let	let	VERB
ejpam-5857	613	15	γ	γ	X
ejpam-5857	613	16	∈	∈	PROPN
ejpam-5857	614	1	[	[	X
ejpam-5857	614	2	0.5	0.5	NUM
ejpam-5857	614	3	,	,	PUNCT
ejpam-5857	614	4	1	1	NUM
ejpam-5857	614	5	]	]	PUNCT
ejpam-5857	614	6	be	be	AUX
ejpam-5857	614	7	such	such	ADJ
ejpam-5857	614	8	that	that	SCONJ
ejpam-5857	614	9	u(ψf	u(ψf	PROPN
ejpam-5857	614	10	;	;	PUNCT
ejpam-5857	614	11	γ	γ	X
ejpam-5857	614	12	)	)	PUNCT
ejpam-5857	614	13	̸=	̸=	PROPN
ejpam-5857	614	14	∅.	∅.	ADV
ejpam-5857	614	15	let	let	VERB
ejpam-5857	614	16	x	x	PRON
ejpam-5857	614	17	,	,	PUNCT
ejpam-5857	614	18	y	y	PROPN
ejpam-5857	614	19	∈	∈	PROPN
ejpam-5857	614	20	u(ψf	u(ψf	PROPN
ejpam-5857	614	21	;	;	PUNCT
ejpam-5857	614	22	γ	γ	X
ejpam-5857	614	23	)	)	PUNCT
ejpam-5857	614	24	.	.	PUNCT
ejpam-5857	615	1	then	then	ADV
ejpam-5857	615	2	ψf	ψf	X
ejpam-5857	615	3	(	(	PUNCT
ejpam-5857	615	4	x	x	X
ejpam-5857	615	5	)	)	PUNCT
ejpam-5857	615	6	≥	≥	PROPN
ejpam-5857	615	7	γ	γ	PROPN
ejpam-5857	615	8	and	and	CCONJ
ejpam-5857	615	9	ψf	ψf	X
ejpam-5857	615	10	(	(	PUNCT
ejpam-5857	615	11	y	y	PROPN
ejpam-5857	615	12	)	)	PUNCT
ejpam-5857	615	13	≥	≥	PROPN
ejpam-5857	615	14	γ	γ	PROPN
ejpam-5857	615	15	.	.	PUNCT
ejpam-5857	615	16	thus	thus	ADV
ejpam-5857	615	17	,	,	PUNCT
ejpam-5857	615	18	ψf	ψf	X
ejpam-5857	615	19	(	(	PUNCT
ejpam-5857	615	20	x	x	X
ejpam-5857	615	21	)	)	PUNCT
ejpam-5857	615	22	∧	∧	NOUN
ejpam-5857	615	23	ψf	ψf	X
ejpam-5857	615	24	(	(	PUNCT
ejpam-5857	615	25	y	y	PROPN
ejpam-5857	615	26	)	)	PUNCT
ejpam-5857	615	27	≥	≥	PROPN
ejpam-5857	615	28	γ	γ	X
ejpam-5857	615	29	.	.	PROPN
ejpam-5857	615	30	by	by	ADP
ejpam-5857	615	31	the	the	DET
ejpam-5857	615	32	condition	condition	NOUN
ejpam-5857	615	33	(	(	PUNCT
ejpam-5857	615	34	3.7	3.7	NUM
ejpam-5857	615	35	)	)	PUNCT
ejpam-5857	615	36	,	,	PUNCT
ejpam-5857	615	37	we	we	PRON
ejpam-5857	615	38	have	have	VERB
ejpam-5857	615	39	ψf	ψf	VERB
ejpam-5857	615	40	(	(	PUNCT
ejpam-5857	615	41	x	x	X
ejpam-5857	615	42	·	·	PUNCT
ejpam-5857	615	43	y	y	X
ejpam-5857	615	44	)	)	PUNCT
ejpam-5857	615	45	≥	≥	NOUN
ejpam-5857	615	46	(	(	PUNCT
ejpam-5857	615	47	ψf	ψf	X
ejpam-5857	616	1	(	(	PUNCT
ejpam-5857	616	2	x)∧ψf	x)∧ψf	PROPN
ejpam-5857	616	3	(	(	PUNCT
ejpam-5857	616	4	y))∨	y))∨	NOUN
ejpam-5857	616	5	0.5	0.5	NUM
ejpam-5857	616	6	≥	≥	PROPN
ejpam-5857	616	7	γ	γ	PROPN
ejpam-5857	616	8	∨	∨	NUM
ejpam-5857	616	9	0.5	0.5	NUM
ejpam-5857	616	10	≥	≥	PROPN
ejpam-5857	616	11	γ	γ	PROPN
ejpam-5857	616	12	,	,	PUNCT
ejpam-5857	616	13	that	that	ADV
ejpam-5857	616	14	is	is	ADV
ejpam-5857	616	15	,	,	PUNCT
ejpam-5857	616	16	ψf	ψf	X
ejpam-5857	616	17	(	(	PUNCT
ejpam-5857	616	18	x	x	X
ejpam-5857	616	19	·	·	PUNCT
ejpam-5857	616	20	y	y	X
ejpam-5857	616	21	)	)	PUNCT
ejpam-5857	616	22	≥	≥	PROPN
ejpam-5857	616	23	γ	γ	PROPN
ejpam-5857	616	24	.	.	PUNCT
ejpam-5857	617	1	thus	thus	ADV
ejpam-5857	617	2	,	,	PUNCT
ejpam-5857	617	3	x	x	X
ejpam-5857	617	4	·	·	PUNCT
ejpam-5857	617	5	y	y	X
ejpam-5857	617	6	∈	∈	PROPN
ejpam-5857	617	7	u(ψf	u(ψf	PROPN
ejpam-5857	617	8	;	;	PUNCT
ejpam-5857	617	9	γ	γ	X
ejpam-5857	617	10	)	)	PUNCT
ejpam-5857	617	11	.	.	PUNCT
ejpam-5857	618	1	hence	hence	ADV
ejpam-5857	618	2	,	,	PUNCT
ejpam-5857	618	3	u(ψf	u(ψf	PROPN
ejpam-5857	618	4	;	;	PUNCT
ejpam-5857	618	5	γ	γ	X
ejpam-5857	618	6	)	)	PUNCT
ejpam-5857	618	7	is	be	AUX
ejpam-5857	618	8	an	an	DET
ejpam-5857	618	9	iup	iup	NOUN
ejpam-5857	618	10	-	-	PUNCT
ejpam-5857	618	11	subalgebra	subalgebra	NOUN
ejpam-5857	618	12	of	of	ADP
ejpam-5857	618	13	x.	x.	PROPN
ejpam-5857	618	14	theorem	theorem	VERB
ejpam-5857	618	15	19	19	NUM
ejpam-5857	618	16	.	.	PUNCT
ejpam-5857	619	1	let	let	VERB
ejpam-5857	619	2	an	an	DET
ejpam-5857	619	3	ins	in	NOUN
ejpam-5857	619	4	ψ	ψ	NOUN
ejpam-5857	619	5	is	be	AUX
ejpam-5857	619	6	an	an	DET
ejpam-5857	619	7	intuitionistic	intuitionistic	ADJ
ejpam-5857	619	8	neutrosophic	neutrosophic	ADJ
ejpam-5857	619	9	iup	iup	NOUN
ejpam-5857	619	10	-	-	PUNCT
ejpam-5857	619	11	ideal	ideal	NOUN
ejpam-5857	619	12	of	of	ADP
ejpam-5857	619	13	x.	x.	NOUN
ejpam-5857	619	14	then	then	ADV
ejpam-5857	619	15	for	for	ADP
ejpam-5857	619	16	all	all	DET
ejpam-5857	619	17	α	α	NOUN
ejpam-5857	619	18	,	,	PUNCT
ejpam-5857	619	19	γ	γ	PROPN
ejpam-5857	619	20	∈	∈	PROPN
ejpam-5857	620	1	[	[	X
ejpam-5857	620	2	0.5	0.5	NUM
ejpam-5857	620	3	,	,	PUNCT
ejpam-5857	620	4	1	1	NUM
ejpam-5857	620	5	]	]	PUNCT
ejpam-5857	620	6	and	and	CCONJ
ejpam-5857	620	7	β	β	X
ejpam-5857	620	8	∈	∈	PROPN
ejpam-5857	620	9	[	[	X
ejpam-5857	620	10	0	0	NUM
ejpam-5857	620	11	,	,	PUNCT
ejpam-5857	620	12	0.5	0.5	NUM
ejpam-5857	620	13	)	)	PUNCT
ejpam-5857	620	14	,	,	PUNCT
ejpam-5857	620	15	the	the	DET
ejpam-5857	620	16	sets	set	NOUN
ejpam-5857	620	17	u(ψt	u(ψt	PROPN
ejpam-5857	620	18	;	;	PUNCT
ejpam-5857	620	19	α	α	X
ejpam-5857	620	20	)	)	PUNCT
ejpam-5857	620	21	,	,	PUNCT
ejpam-5857	620	22	l(ψi	l(ψi	PROPN
ejpam-5857	620	23	;	;	PUNCT
ejpam-5857	620	24	β	β	X
ejpam-5857	620	25	)	)	PUNCT
ejpam-5857	620	26	and	and	CCONJ
ejpam-5857	620	27	u(ψf	u(ψf	PROPN
ejpam-5857	620	28	;	;	PUNCT
ejpam-5857	620	29	γ	γ	X
ejpam-5857	620	30	)	)	PUNCT
ejpam-5857	620	31	are	be	AUX
ejpam-5857	620	32	either	either	CCONJ
ejpam-5857	620	33	empty	empty	ADJ
ejpam-5857	620	34	or	or	CCONJ
ejpam-5857	620	35	iup	iup	NOUN
ejpam-5857	620	36	-	-	PUNCT
ejpam-5857	620	37	ideals	ideal	NOUN
ejpam-5857	620	38	of	of	ADP
ejpam-5857	620	39	x.	x.	NOUN
ejpam-5857	620	40	proof	proof	NOUN
ejpam-5857	620	41	.	.	PUNCT
ejpam-5857	621	1	assume	assume	VERB
ejpam-5857	621	2	that	that	SCONJ
ejpam-5857	621	3	ψ	ψ	X
ejpam-5857	621	4	in	in	ADP
ejpam-5857	621	5	x	x	SYM
ejpam-5857	621	6	is	be	AUX
ejpam-5857	621	7	an	an	DET
ejpam-5857	621	8	intuitionistic	intuitionistic	ADJ
ejpam-5857	621	9	neutrosophic	neutrosophic	ADJ
ejpam-5857	621	10	iup	iup	NOUN
ejpam-5857	621	11	-	-	PUNCT
ejpam-5857	621	12	ideal	ideal	NOUN
ejpam-5857	621	13	of	of	ADP
ejpam-5857	621	14	x.	x.	NOUN
ejpam-5857	621	15	let	let	VERB
ejpam-5857	621	16	α	α	PRON
ejpam-5857	621	17	∈	∈	PROPN
ejpam-5857	622	1	[	[	X
ejpam-5857	622	2	0.5	0.5	NUM
ejpam-5857	622	3	,	,	PUNCT
ejpam-5857	622	4	1	1	NUM
ejpam-5857	622	5	]	]	PUNCT
ejpam-5857	622	6	be	be	AUX
ejpam-5857	622	7	such	such	ADJ
ejpam-5857	622	8	that	that	SCONJ
ejpam-5857	622	9	u(ψt	u(ψt	PROPN
ejpam-5857	622	10	;	;	PUNCT
ejpam-5857	622	11	α	α	X
ejpam-5857	622	12	)	)	PUNCT
ejpam-5857	622	13	̸=	̸=	PROPN
ejpam-5857	622	14	∅.	∅.	ADV
ejpam-5857	622	15	let	let	VERB
ejpam-5857	622	16	a	a	DET
ejpam-5857	622	17	∈	∈	PROPN
ejpam-5857	622	18	u(ψt	u(ψt	PROPN
ejpam-5857	622	19	;	;	PUNCT
ejpam-5857	622	20	α	α	X
ejpam-5857	622	21	)	)	PUNCT
ejpam-5857	622	22	.	.	PUNCT
ejpam-5857	623	1	then	then	ADV
ejpam-5857	623	2	ψt	ψt	VERB
ejpam-5857	623	3	(	(	PUNCT
ejpam-5857	623	4	a	a	NOUN
ejpam-5857	623	5	)	)	PUNCT
ejpam-5857	623	6	≥	≥	NOUN
ejpam-5857	623	7	α	α	NOUN
ejpam-5857	623	8	.	.	PUNCT
ejpam-5857	624	1	by	by	ADP
ejpam-5857	624	2	the	the	DET
ejpam-5857	624	3	condition	condition	NOUN
ejpam-5857	624	4	(	(	PUNCT
ejpam-5857	624	5	3.8	3.8	NUM
ejpam-5857	624	6	)	)	PUNCT
ejpam-5857	624	7	,	,	PUNCT
ejpam-5857	624	8	we	we	PRON
ejpam-5857	624	9	have	have	AUX
ejpam-5857	624	10	ψt	ψt	VERB
ejpam-5857	624	11	(	(	PUNCT
ejpam-5857	624	12	0	0	NUM
ejpam-5857	624	13	)	)	PUNCT
ejpam-5857	624	14	≥	≥	PRON
ejpam-5857	624	15	ψt	ψt	NOUN
ejpam-5857	624	16	(	(	PUNCT
ejpam-5857	624	17	a	a	NOUN
ejpam-5857	624	18	)	)	PUNCT
ejpam-5857	624	19	≥	≥	NOUN
ejpam-5857	624	20	α	α	NOUN
ejpam-5857	624	21	.	.	PUNCT
ejpam-5857	625	1	thus	thus	ADV
ejpam-5857	625	2	,	,	PUNCT
ejpam-5857	625	3	0	0	NUM
ejpam-5857	625	4	∈	∈	PROPN
ejpam-5857	625	5	u(ψt	u(ψt	NOUN
ejpam-5857	625	6	;	;	PUNCT
ejpam-5857	625	7	α	α	X
ejpam-5857	625	8	)	)	PUNCT
ejpam-5857	625	9	.	.	PUNCT
ejpam-5857	626	1	let	let	VERB
ejpam-5857	626	2	x	x	PRON
ejpam-5857	626	3	,	,	PUNCT
ejpam-5857	626	4	y	y	PROPN
ejpam-5857	626	5	,	,	PUNCT
ejpam-5857	626	6	z	z	NOUN
ejpam-5857	626	7	∈	∈	PROPN
ejpam-5857	626	8	x	x	AUX
ejpam-5857	626	9	be	be	AUX
ejpam-5857	626	10	such	such	ADJ
ejpam-5857	626	11	that	that	SCONJ
ejpam-5857	626	12	x	x	PART
ejpam-5857	626	13	·	·	PUNCT
ejpam-5857	626	14	(	(	PUNCT
ejpam-5857	626	15	y	y	PROPN
ejpam-5857	626	16	·	·	PUNCT
ejpam-5857	626	17	z	z	X
ejpam-5857	626	18	)	)	PUNCT
ejpam-5857	626	19	∈	∈	PROPN
ejpam-5857	626	20	u(ψt	u(ψt	PROPN
ejpam-5857	626	21	;	;	PUNCT
ejpam-5857	626	22	α	α	X
ejpam-5857	626	23	)	)	PUNCT
ejpam-5857	626	24	and	and	CCONJ
ejpam-5857	626	25	y	y	PROPN
ejpam-5857	626	26	∈	∈	PROPN
ejpam-5857	626	27	u(ψt	u(ψt	PROPN
ejpam-5857	626	28	;	;	PUNCT
ejpam-5857	626	29	α	α	X
ejpam-5857	626	30	)	)	PUNCT
ejpam-5857	626	31	.	.	PUNCT
ejpam-5857	627	1	then	then	ADV
ejpam-5857	627	2	ψt	ψt	VERB
ejpam-5857	627	3	(	(	PUNCT
ejpam-5857	627	4	x	x	X
ejpam-5857	627	5	·	·	PUNCT
ejpam-5857	627	6	(	(	PUNCT
ejpam-5857	627	7	y	y	PROPN
ejpam-5857	627	8	·	·	PUNCT
ejpam-5857	627	9	z	z	NOUN
ejpam-5857	627	10	)	)	PUNCT
ejpam-5857	627	11	)	)	PUNCT
ejpam-5857	627	12	≥	≥	PROPN
ejpam-5857	627	13	α	α	NOUN
ejpam-5857	627	14	and	and	CCONJ
ejpam-5857	627	15	ψt	ψt	ADJ
ejpam-5857	627	16	(	(	PUNCT
ejpam-5857	627	17	y	y	NOUN
ejpam-5857	627	18	)	)	PUNCT
ejpam-5857	627	19	≥	≥	PROPN
ejpam-5857	627	20	α	α	NOUN
ejpam-5857	627	21	.	.	PUNCT
ejpam-5857	628	1	thus	thus	ADV
ejpam-5857	628	2	,	,	PUNCT
ejpam-5857	628	3	ψt	ψt	VERB
ejpam-5857	628	4	(	(	PUNCT
ejpam-5857	628	5	x	x	X
ejpam-5857	628	6	·	·	PUNCT
ejpam-5857	628	7	(	(	PUNCT
ejpam-5857	628	8	y	y	PROPN
ejpam-5857	628	9	·	·	PUNCT
ejpam-5857	628	10	z))∧ψt	z))∧ψt	PROPN
ejpam-5857	628	11	(	(	PUNCT
ejpam-5857	628	12	y	y	NOUN
ejpam-5857	628	13	)	)	PUNCT
ejpam-5857	628	14	≥	≥	PROPN
ejpam-5857	628	15	α	α	NOUN
ejpam-5857	628	16	.	.	PUNCT
ejpam-5857	629	1	by	by	ADP
ejpam-5857	629	2	the	the	DET
ejpam-5857	629	3	condition	condition	NOUN
ejpam-5857	629	4	(	(	PUNCT
ejpam-5857	629	5	3.11	3.11	NUM
ejpam-5857	629	6	)	)	PUNCT
ejpam-5857	629	7	,	,	PUNCT
ejpam-5857	629	8	we	we	PRON
ejpam-5857	629	9	have	have	AUX
ejpam-5857	629	10	ψt	ψt	VERB
ejpam-5857	629	11	(	(	PUNCT
ejpam-5857	629	12	x	x	X
ejpam-5857	629	13	·	·	PUNCT
ejpam-5857	629	14	z	z	X
ejpam-5857	629	15	)	)	PUNCT
ejpam-5857	629	16	≥	≥	NOUN
ejpam-5857	629	17	(	(	PUNCT
ejpam-5857	629	18	ψt	ψt	VERB
ejpam-5857	629	19	(	(	PUNCT
ejpam-5857	629	20	x	x	X
ejpam-5857	629	21	·	·	PUNCT
ejpam-5857	629	22	(	(	PUNCT
ejpam-5857	629	23	y	y	PROPN
ejpam-5857	629	24	·	·	PUNCT
ejpam-5857	629	25	z	z	NOUN
ejpam-5857	629	26	)	)	PUNCT
ejpam-5857	629	27	)	)	PUNCT
ejpam-5857	630	1	∧	∧	NOUN
ejpam-5857	630	2	ψt	ψt	NOUN
ejpam-5857	630	3	(	(	PUNCT
ejpam-5857	630	4	y	y	NOUN
ejpam-5857	630	5	)	)	PUNCT
ejpam-5857	630	6	)	)	PUNCT
ejpam-5857	631	1	∨	∨	NUM
ejpam-5857	631	2	0.5	0.5	NUM
ejpam-5857	631	3	≥	≥	PROPN
ejpam-5857	631	4	α	α	PROPN
ejpam-5857	631	5	∨	∨	NUM
ejpam-5857	631	6	0.5	0.5	NUM
ejpam-5857	631	7	≥	≥	NOUN
ejpam-5857	631	8	α	α	NOUN
ejpam-5857	631	9	.	.	PUNCT
ejpam-5857	632	1	thus	thus	ADV
ejpam-5857	632	2	,	,	PUNCT
ejpam-5857	632	3	x	x	X
ejpam-5857	632	4	·	·	PUNCT
ejpam-5857	632	5	z	z	X
ejpam-5857	632	6	∈	∈	PROPN
ejpam-5857	632	7	u(ψt	u(ψt	PROPN
ejpam-5857	632	8	;	;	PUNCT
ejpam-5857	632	9	α	α	X
ejpam-5857	632	10	)	)	PUNCT
ejpam-5857	632	11	.	.	PUNCT
ejpam-5857	633	1	hence	hence	ADV
ejpam-5857	633	2	,	,	PUNCT
ejpam-5857	633	3	u(ψt	u(ψt	PROPN
ejpam-5857	633	4	;	;	PUNCT
ejpam-5857	633	5	α	α	X
ejpam-5857	633	6	)	)	PUNCT
ejpam-5857	633	7	is	be	AUX
ejpam-5857	633	8	an	an	DET
ejpam-5857	633	9	iup	iup	NOUN
ejpam-5857	633	10	-	-	PUNCT
ejpam-5857	633	11	ideal	ideal	NOUN
ejpam-5857	633	12	of	of	ADP
ejpam-5857	633	13	x.	x.	NOUN
ejpam-5857	633	14	let	let	VERB
ejpam-5857	633	15	β	β	X
ejpam-5857	633	16	∈	∈	PROPN
ejpam-5857	634	1	[	[	X
ejpam-5857	634	2	0	0	NUM
ejpam-5857	634	3	,	,	PUNCT
ejpam-5857	634	4	0.5	0.5	NUM
ejpam-5857	634	5	)	)	PUNCT
ejpam-5857	634	6	be	be	VERB
ejpam-5857	634	7	such	such	ADJ
ejpam-5857	634	8	that	that	SCONJ
ejpam-5857	634	9	l(ψi	l(ψi	NOUN
ejpam-5857	634	10	;	;	PUNCT
ejpam-5857	634	11	β	β	X
ejpam-5857	634	12	)	)	PUNCT
ejpam-5857	634	13	̸=	̸=	PROPN
ejpam-5857	634	14	∅.	∅.	ADV
ejpam-5857	634	15	let	let	VERB
ejpam-5857	634	16	b	b	NOUN
ejpam-5857	634	17	∈	∈	PROPN
ejpam-5857	634	18	l(ψi	l(ψi	PROPN
ejpam-5857	634	19	;	;	PUNCT
ejpam-5857	634	20	β	β	X
ejpam-5857	634	21	)	)	PUNCT
ejpam-5857	634	22	.	.	PUNCT
ejpam-5857	635	1	then	then	ADV
ejpam-5857	635	2	ψi(b	ψi(b	X
ejpam-5857	635	3	)	)	PUNCT
ejpam-5857	635	4	≤	≤	NOUN
ejpam-5857	636	1	β	β	X
ejpam-5857	636	2	.	.	PUNCT
ejpam-5857	637	1	by	by	ADP
ejpam-5857	637	2	the	the	DET
ejpam-5857	637	3	condition	condition	NOUN
ejpam-5857	637	4	(	(	PUNCT
ejpam-5857	637	5	3.9	3.9	NUM
ejpam-5857	637	6	)	)	PUNCT
ejpam-5857	637	7	,	,	PUNCT
ejpam-5857	637	8	we	we	PRON
ejpam-5857	637	9	have	have	VERB
ejpam-5857	637	10	ψi(0	ψi(0	PROPN
ejpam-5857	637	11	)	)	PUNCT
ejpam-5857	637	12	≤	≤	NOUN
ejpam-5857	637	13	ψi(b	ψi(b	PUNCT
ejpam-5857	637	14	)	)	PUNCT
ejpam-5857	637	15	≤	≤	NUM
ejpam-5857	638	1	β	β	X
ejpam-5857	638	2	.	.	PUNCT
ejpam-5857	639	1	thus	thus	ADV
ejpam-5857	639	2	,	,	PUNCT
ejpam-5857	639	3	0	0	NUM
ejpam-5857	639	4	∈	∈	NOUN
ejpam-5857	639	5	l(ψi	l(ψi	NOUN
ejpam-5857	639	6	;	;	PUNCT
ejpam-5857	639	7	β	β	X
ejpam-5857	639	8	)	)	PUNCT
ejpam-5857	639	9	.	.	PUNCT
ejpam-5857	640	1	let	let	VERB
ejpam-5857	640	2	x	x	PRON
ejpam-5857	640	3	,	,	PUNCT
ejpam-5857	640	4	y	y	PROPN
ejpam-5857	640	5	,	,	PUNCT
ejpam-5857	640	6	z	z	NOUN
ejpam-5857	640	7	∈	∈	PROPN
ejpam-5857	640	8	x	x	AUX
ejpam-5857	640	9	be	be	AUX
ejpam-5857	640	10	such	such	ADJ
ejpam-5857	640	11	that	that	SCONJ
ejpam-5857	640	12	x	x	PART
ejpam-5857	640	13	·	·	PUNCT
ejpam-5857	640	14	(	(	PUNCT
ejpam-5857	640	15	y	y	PROPN
ejpam-5857	640	16	·	·	PUNCT
ejpam-5857	640	17	z	z	X
ejpam-5857	640	18	)	)	PUNCT
ejpam-5857	640	19	∈	∈	PROPN
ejpam-5857	640	20	l(ψi	l(ψi	NOUN
ejpam-5857	640	21	;	;	PUNCT
ejpam-5857	640	22	β	β	X
ejpam-5857	640	23	)	)	PUNCT
ejpam-5857	640	24	and	and	CCONJ
ejpam-5857	640	25	y	y	PROPN
ejpam-5857	640	26	∈	∈	PROPN
ejpam-5857	640	27	l(ψi	l(ψi	PROPN
ejpam-5857	640	28	;	;	PUNCT
ejpam-5857	640	29	β	β	X
ejpam-5857	640	30	)	)	PUNCT
ejpam-5857	640	31	.	.	PUNCT
ejpam-5857	641	1	then	then	ADV
ejpam-5857	641	2	ψi(x	ψi(x	NOUN
ejpam-5857	641	3	·	·	PUNCT
ejpam-5857	641	4	(	(	PUNCT
ejpam-5857	641	5	y	y	PROPN
ejpam-5857	641	6	·	·	PUNCT
ejpam-5857	641	7	z	z	NOUN
ejpam-5857	641	8	)	)	PUNCT
ejpam-5857	641	9	)	)	PUNCT
ejpam-5857	641	10	≤	≤	NUM
ejpam-5857	641	11	β	β	X
ejpam-5857	641	12	and	and	CCONJ
ejpam-5857	641	13	ψi(y	ψi(y	NUM
ejpam-5857	641	14	)	)	PUNCT
ejpam-5857	641	15	≤	≤	NOUN
ejpam-5857	641	16	β	β	X
ejpam-5857	641	17	.	.	PUNCT
ejpam-5857	642	1	thus	thus	ADV
ejpam-5857	642	2	,	,	PUNCT
ejpam-5857	642	3	ψi(x	ψi(x	X
ejpam-5857	642	4	·	·	PUNCT
ejpam-5857	642	5	(	(	PUNCT
ejpam-5857	642	6	y	y	PROPN
ejpam-5857	642	7	·	·	PUNCT
ejpam-5857	642	8	z	z	NOUN
ejpam-5857	642	9	)	)	PUNCT
ejpam-5857	642	10	)	)	PUNCT
ejpam-5857	642	11	∨	∨	NUM
ejpam-5857	642	12	ψi(y	ψi(y	NUM
ejpam-5857	642	13	)	)	PUNCT
ejpam-5857	642	14	≤	≤	NOUN
ejpam-5857	642	15	β	β	X
ejpam-5857	642	16	.	.	PUNCT
ejpam-5857	643	1	by	by	ADP
ejpam-5857	643	2	the	the	DET
ejpam-5857	643	3	condition	condition	NOUN
ejpam-5857	643	4	(	(	PUNCT
ejpam-5857	643	5	3.12	3.12	NUM
ejpam-5857	643	6	)	)	PUNCT
ejpam-5857	643	7	,	,	PUNCT
ejpam-5857	643	8	we	we	PRON
ejpam-5857	643	9	have	have	VERB
ejpam-5857	643	10	ψi(x	ψi(x	NUM
ejpam-5857	643	11	·	·	PUNCT
ejpam-5857	644	1	z	z	X
ejpam-5857	644	2	)	)	PUNCT
ejpam-5857	644	3	≤	≤	NOUN
ejpam-5857	644	4	(	(	PUNCT
ejpam-5857	644	5	ψi(x	ψi(x	X
ejpam-5857	644	6	·	·	PUNCT
ejpam-5857	644	7	(	(	PUNCT
ejpam-5857	644	8	y	y	PROPN
ejpam-5857	644	9	·	·	PUNCT
ejpam-5857	644	10	z	z	NOUN
ejpam-5857	644	11	)	)	PUNCT
ejpam-5857	644	12	)	)	PUNCT
ejpam-5857	645	1	∨	∨	NUM
ejpam-5857	645	2	ψi(y	ψi(y	NUM
ejpam-5857	645	3	)	)	PUNCT
ejpam-5857	645	4	)	)	PUNCT
ejpam-5857	646	1	∧	∧	NOUN
ejpam-5857	646	2	0.5	0.5	NUM
ejpam-5857	646	3	≤	≤	NOUN
ejpam-5857	646	4	β	β	X
ejpam-5857	646	5	∨	∨	NUM
ejpam-5857	646	6	0.5	0.5	NUM
ejpam-5857	646	7	≤	≤	NUM
ejpam-5857	646	8	β	β	NOUN
ejpam-5857	646	9	.	.	PUNCT
ejpam-5857	647	1	thus	thus	ADV
ejpam-5857	647	2	,	,	PUNCT
ejpam-5857	647	3	x	x	X
ejpam-5857	647	4	·	·	PUNCT
ejpam-5857	647	5	z	z	SYM
ejpam-5857	647	6	∈	∈	PROPN
ejpam-5857	647	7	l(ψi	l(ψi	PROPN
ejpam-5857	647	8	;	;	PUNCT
ejpam-5857	647	9	β	β	X
ejpam-5857	647	10	)	)	PUNCT
ejpam-5857	647	11	.	.	PUNCT
ejpam-5857	648	1	hence	hence	ADV
ejpam-5857	648	2	,	,	PUNCT
ejpam-5857	648	3	l(ψi	l(ψi	PROPN
ejpam-5857	648	4	;	;	PUNCT
ejpam-5857	648	5	β	β	X
ejpam-5857	648	6	)	)	PUNCT
ejpam-5857	648	7	is	be	AUX
ejpam-5857	648	8	an	an	DET
ejpam-5857	648	9	iup	iup	NOUN
ejpam-5857	648	10	-	-	PUNCT
ejpam-5857	648	11	ideal	ideal	NOUN
ejpam-5857	648	12	of	of	ADP
ejpam-5857	648	13	x.	x.	NOUN
ejpam-5857	648	14	let	let	VERB
ejpam-5857	648	15	γ	γ	X
ejpam-5857	648	16	∈	∈	PROPN
ejpam-5857	649	1	[	[	X
ejpam-5857	649	2	0.5	0.5	NUM
ejpam-5857	649	3	,	,	PUNCT
ejpam-5857	649	4	1	1	NUM
ejpam-5857	649	5	]	]	PUNCT
ejpam-5857	649	6	be	be	AUX
ejpam-5857	649	7	such	such	ADJ
ejpam-5857	649	8	that	that	SCONJ
ejpam-5857	649	9	u(ψf	u(ψf	PROPN
ejpam-5857	649	10	;	;	PUNCT
ejpam-5857	649	11	γ	γ	X
ejpam-5857	649	12	)	)	PUNCT
ejpam-5857	649	13	̸=	̸=	PROPN
ejpam-5857	649	14	∅.	∅.	ADV
ejpam-5857	649	15	let	let	VERB
ejpam-5857	649	16	c	c	PROPN
ejpam-5857	649	17	∈	∈	PROPN
ejpam-5857	649	18	u(ψf	u(ψf	PROPN
ejpam-5857	649	19	;	;	PUNCT
ejpam-5857	649	20	γ	γ	X
ejpam-5857	649	21	)	)	PUNCT
ejpam-5857	649	22	.	.	PUNCT
ejpam-5857	650	1	then	then	ADV
ejpam-5857	650	2	ψf	ψf	X
ejpam-5857	650	3	(	(	PUNCT
ejpam-5857	650	4	c	c	NOUN
ejpam-5857	650	5	)	)	PUNCT
ejpam-5857	650	6	≥	≥	PROPN
ejpam-5857	650	7	γ	γ	X
ejpam-5857	650	8	.	.	PROPN
ejpam-5857	650	9	by	by	ADP
ejpam-5857	650	10	the	the	DET
ejpam-5857	650	11	condition	condition	NOUN
ejpam-5857	650	12	(	(	PUNCT
ejpam-5857	650	13	3.10	3.10	NUM
ejpam-5857	650	14	)	)	PUNCT
ejpam-5857	650	15	,	,	PUNCT
ejpam-5857	650	16	we	we	PRON
ejpam-5857	650	17	have	have	VERB
ejpam-5857	650	18	ψf	ψf	X
ejpam-5857	650	19	(	(	PUNCT
ejpam-5857	650	20	0	0	NUM
ejpam-5857	650	21	)	)	PUNCT
ejpam-5857	650	22	≥	≥	NOUN
ejpam-5857	650	23	ψf	ψf	X
ejpam-5857	650	24	(	(	PUNCT
ejpam-5857	650	25	c	c	NOUN
ejpam-5857	650	26	)	)	PUNCT
ejpam-5857	650	27	≥	≥	PROPN
ejpam-5857	650	28	γ	γ	PROPN
ejpam-5857	650	29	.	.	PROPN
ejpam-5857	650	30	thus	thus	ADV
ejpam-5857	650	31	,	,	PUNCT
ejpam-5857	650	32	0	0	X
ejpam-5857	650	33	∈	∈	PROPN
ejpam-5857	650	34	u(ψf	u(ψf	PROPN
ejpam-5857	650	35	;	;	PUNCT
ejpam-5857	650	36	γ	γ	X
ejpam-5857	650	37	)	)	PUNCT
ejpam-5857	650	38	.	.	PUNCT
ejpam-5857	651	1	let	let	VERB
ejpam-5857	651	2	x	x	PRON
ejpam-5857	651	3	,	,	PUNCT
ejpam-5857	651	4	y	y	PROPN
ejpam-5857	651	5	,	,	PUNCT
ejpam-5857	651	6	z	z	NOUN
ejpam-5857	651	7	∈	∈	PROPN
ejpam-5857	651	8	x	x	AUX
ejpam-5857	651	9	be	be	AUX
ejpam-5857	651	10	such	such	ADJ
ejpam-5857	651	11	that	that	SCONJ
ejpam-5857	651	12	x	x	PART
ejpam-5857	651	13	·	·	PUNCT
ejpam-5857	651	14	(	(	PUNCT
ejpam-5857	651	15	y	y	PROPN
ejpam-5857	651	16	·	·	PUNCT
ejpam-5857	651	17	z	z	X
ejpam-5857	651	18	)	)	PUNCT
ejpam-5857	651	19	∈	∈	PROPN
ejpam-5857	651	20	u(ψf	u(ψf	PROPN
ejpam-5857	651	21	;	;	PUNCT
ejpam-5857	651	22	γ	γ	X
ejpam-5857	651	23	)	)	PUNCT
ejpam-5857	651	24	and	and	CCONJ
ejpam-5857	651	25	y	y	PROPN
ejpam-5857	651	26	∈	∈	PROPN
ejpam-5857	651	27	u(ψf	u(ψf	PROPN
ejpam-5857	651	28	;	;	PUNCT
ejpam-5857	651	29	γ	γ	X
ejpam-5857	651	30	)	)	PUNCT
ejpam-5857	651	31	.	.	PUNCT
ejpam-5857	652	1	then	then	ADV
ejpam-5857	652	2	ψf	ψf	X
ejpam-5857	652	3	(	(	PUNCT
ejpam-5857	652	4	x	x	X
ejpam-5857	652	5	·	·	PUNCT
ejpam-5857	652	6	(	(	PUNCT
ejpam-5857	652	7	y	y	PROPN
ejpam-5857	652	8	·	·	PUNCT
ejpam-5857	652	9	z	z	NOUN
ejpam-5857	652	10	)	)	PUNCT
ejpam-5857	652	11	)	)	PUNCT
ejpam-5857	652	12	≥	≥	PROPN
ejpam-5857	652	13	γ	γ	PROPN
ejpam-5857	652	14	and	and	CCONJ
ejpam-5857	652	15	ψf	ψf	X
ejpam-5857	652	16	(	(	PUNCT
ejpam-5857	652	17	y	y	PROPN
ejpam-5857	652	18	)	)	PUNCT
ejpam-5857	652	19	≥	≥	PROPN
ejpam-5857	652	20	γ	γ	PROPN
ejpam-5857	652	21	.	.	PUNCT
ejpam-5857	652	22	thus	thus	ADV
ejpam-5857	652	23	,	,	PUNCT
ejpam-5857	652	24	ψf	ψf	X
ejpam-5857	652	25	(	(	PUNCT
ejpam-5857	652	26	x	x	X
ejpam-5857	652	27	·	·	PUNCT
ejpam-5857	652	28	(	(	PUNCT
ejpam-5857	652	29	y	y	X
ejpam-5857	652	30	·	·	PUNCT
ejpam-5857	652	31	z))∧ψf	z))∧ψf	X
ejpam-5857	652	32	(	(	PUNCT
ejpam-5857	652	33	y	y	NOUN
ejpam-5857	652	34	)	)	PUNCT
ejpam-5857	652	35	≥	≥	PROPN
ejpam-5857	652	36	γ	γ	X
ejpam-5857	652	37	.	.	PROPN
ejpam-5857	652	38	by	by	ADP
ejpam-5857	652	39	the	the	DET
ejpam-5857	652	40	condition	condition	NOUN
ejpam-5857	652	41	(	(	PUNCT
ejpam-5857	652	42	3.13	3.13	NUM
ejpam-5857	652	43	)	)	PUNCT
ejpam-5857	652	44	,	,	PUNCT
ejpam-5857	652	45	we	we	PRON
ejpam-5857	652	46	have	have	VERB
ejpam-5857	652	47	ψf	ψf	VERB
ejpam-5857	652	48	(	(	PUNCT
ejpam-5857	652	49	x	x	X
ejpam-5857	652	50	·	·	PUNCT
ejpam-5857	652	51	z	z	X
ejpam-5857	652	52	)	)	PUNCT
ejpam-5857	652	53	≥	≥	NOUN
ejpam-5857	652	54	(	(	PUNCT
ejpam-5857	652	55	ψf	ψf	X
ejpam-5857	652	56	(	(	PUNCT
ejpam-5857	652	57	x	x	X
ejpam-5857	652	58	·	·	PUNCT
ejpam-5857	652	59	(	(	PUNCT
ejpam-5857	652	60	y	y	PROPN
ejpam-5857	652	61	·	·	PUNCT
ejpam-5857	652	62	z	z	NOUN
ejpam-5857	652	63	)	)	PUNCT
ejpam-5857	652	64	)	)	PUNCT
ejpam-5857	653	1	∧	∧	NOUN
ejpam-5857	653	2	ψf	ψf	X
ejpam-5857	653	3	(	(	PUNCT
ejpam-5857	653	4	y	y	NOUN
ejpam-5857	653	5	)	)	PUNCT
ejpam-5857	653	6	)	)	PUNCT
ejpam-5857	654	1	∨	∨	NUM
ejpam-5857	654	2	0.5	0.5	NUM
ejpam-5857	654	3	≥	≥	PROPN
ejpam-5857	654	4	γ	γ	PROPN
ejpam-5857	654	5	∨	∨	NUM
ejpam-5857	654	6	0.5	0.5	NUM
ejpam-5857	654	7	≥	≥	PROPN
ejpam-5857	654	8	γ	γ	PROPN
ejpam-5857	654	9	.	.	PROPN
ejpam-5857	654	10	thus	thus	ADV
ejpam-5857	654	11	,	,	PUNCT
ejpam-5857	654	12	x	x	X
ejpam-5857	654	13	·	·	PUNCT
ejpam-5857	654	14	z	z	X
ejpam-5857	654	15	∈	∈	PROPN
ejpam-5857	654	16	u(ψf	u(ψf	PROPN
ejpam-5857	654	17	;	;	PUNCT
ejpam-5857	654	18	γ	γ	X
ejpam-5857	654	19	)	)	PUNCT
ejpam-5857	654	20	.	.	PUNCT
ejpam-5857	655	1	hence	hence	ADV
ejpam-5857	655	2	,	,	PUNCT
ejpam-5857	655	3	u(ψf	u(ψf	PROPN
ejpam-5857	655	4	;	;	PUNCT
ejpam-5857	655	5	γ	γ	X
ejpam-5857	655	6	)	)	PUNCT
ejpam-5857	655	7	is	be	AUX
ejpam-5857	655	8	an	an	DET
ejpam-5857	655	9	iup	iup	NOUN
ejpam-5857	655	10	-	-	PUNCT
ejpam-5857	655	11	ideal	ideal	NOUN
ejpam-5857	655	12	of	of	ADP
ejpam-5857	655	13	x.	x.	PROPN
ejpam-5857	655	14	theorem	theorem	VERB
ejpam-5857	655	15	20	20	NUM
ejpam-5857	655	16	.	.	PUNCT
ejpam-5857	656	1	let	let	VERB
ejpam-5857	656	2	an	an	DET
ejpam-5857	656	3	ins	in	NOUN
ejpam-5857	656	4	ψ	ψ	NOUN
ejpam-5857	656	5	is	be	AUX
ejpam-5857	656	6	an	an	DET
ejpam-5857	656	7	intuitionistic	intuitionistic	ADJ
ejpam-5857	656	8	neutrosophic	neutrosophic	ADJ
ejpam-5857	656	9	iup	iup	NOUN
ejpam-5857	656	10	-	-	PUNCT
ejpam-5857	656	11	filter	filter	NOUN
ejpam-5857	656	12	of	of	ADP
ejpam-5857	656	13	x.	x.	NOUN
ejpam-5857	656	14	then	then	ADV
ejpam-5857	656	15	for	for	ADP
ejpam-5857	656	16	all	all	DET
ejpam-5857	656	17	α	α	NOUN
ejpam-5857	656	18	,	,	PUNCT
ejpam-5857	656	19	γ	γ	PROPN
ejpam-5857	656	20	∈	∈	PROPN
ejpam-5857	657	1	[	[	X
ejpam-5857	657	2	0.5	0.5	NUM
ejpam-5857	657	3	,	,	PUNCT
ejpam-5857	657	4	1	1	NUM
ejpam-5857	657	5	]	]	PUNCT
ejpam-5857	657	6	and	and	CCONJ
ejpam-5857	657	7	β	β	X
ejpam-5857	657	8	∈	∈	PROPN
ejpam-5857	657	9	[	[	X
ejpam-5857	657	10	0	0	NUM
ejpam-5857	657	11	,	,	PUNCT
ejpam-5857	657	12	0.5	0.5	NUM
ejpam-5857	657	13	)	)	PUNCT
ejpam-5857	657	14	,	,	PUNCT
ejpam-5857	657	15	the	the	DET
ejpam-5857	657	16	sets	set	NOUN
ejpam-5857	657	17	u(ψt	u(ψt	PROPN
ejpam-5857	657	18	;	;	PUNCT
ejpam-5857	657	19	α	α	X
ejpam-5857	657	20	)	)	PUNCT
ejpam-5857	657	21	,	,	PUNCT
ejpam-5857	657	22	l(ψi	l(ψi	PROPN
ejpam-5857	657	23	;	;	PUNCT
ejpam-5857	657	24	β	β	X
ejpam-5857	657	25	)	)	PUNCT
ejpam-5857	657	26	and	and	CCONJ
ejpam-5857	657	27	u(ψf	u(ψf	PROPN
ejpam-5857	657	28	;	;	PUNCT
ejpam-5857	657	29	γ	γ	X
ejpam-5857	657	30	)	)	PUNCT
ejpam-5857	657	31	are	be	AUX
ejpam-5857	657	32	either	either	CCONJ
ejpam-5857	657	33	empty	empty	ADJ
ejpam-5857	657	34	or	or	CCONJ
ejpam-5857	657	35	iup	iup	NOUN
ejpam-5857	657	36	-	-	PUNCT
ejpam-5857	657	37	filters	filter	NOUN
ejpam-5857	657	38	of	of	ADP
ejpam-5857	657	39	x.	x.	NOUN
ejpam-5857	657	40	proof	proof	PROPN
ejpam-5857	657	41	.	.	PUNCT
ejpam-5857	658	1	assume	assume	VERB
ejpam-5857	658	2	that	that	SCONJ
ejpam-5857	658	3	ψ	ψ	X
ejpam-5857	658	4	in	in	ADP
ejpam-5857	658	5	x	x	SYM
ejpam-5857	658	6	is	be	AUX
ejpam-5857	658	7	an	an	DET
ejpam-5857	658	8	intuitionistic	intuitionistic	ADJ
ejpam-5857	658	9	neutrosophic	neutrosophic	ADJ
ejpam-5857	658	10	iup	iup	NOUN
ejpam-5857	658	11	-	-	PUNCT
ejpam-5857	658	12	filter	filter	NOUN
ejpam-5857	658	13	of	of	ADP
ejpam-5857	658	14	x.	x.	NOUN
ejpam-5857	658	15	let	let	VERB
ejpam-5857	658	16	α	α	PRON
ejpam-5857	658	17	∈	∈	PROPN
ejpam-5857	659	1	[	[	X
ejpam-5857	659	2	0.5	0.5	NUM
ejpam-5857	659	3	,	,	PUNCT
ejpam-5857	659	4	1	1	NUM
ejpam-5857	659	5	]	]	PUNCT
ejpam-5857	659	6	be	be	AUX
ejpam-5857	659	7	such	such	ADJ
ejpam-5857	659	8	that	that	SCONJ
ejpam-5857	659	9	u(ψt	u(ψt	PROPN
ejpam-5857	659	10	;	;	PUNCT
ejpam-5857	659	11	α	α	X
ejpam-5857	659	12	)	)	PUNCT
ejpam-5857	659	13	̸=	̸=	PROPN
ejpam-5857	659	14	∅.	∅.	ADV
ejpam-5857	659	15	let	let	VERB
ejpam-5857	659	16	a	a	DET
ejpam-5857	659	17	∈	∈	PROPN
ejpam-5857	659	18	u(ψt	u(ψt	PROPN
ejpam-5857	659	19	;	;	PUNCT
ejpam-5857	659	20	α	α	X
ejpam-5857	659	21	)	)	PUNCT
ejpam-5857	659	22	.	.	PUNCT
ejpam-5857	660	1	then	then	ADV
ejpam-5857	660	2	ψt	ψt	VERB
ejpam-5857	660	3	(	(	PUNCT
ejpam-5857	660	4	a	a	NOUN
ejpam-5857	660	5	)	)	PUNCT
ejpam-5857	660	6	≥	≥	NOUN
ejpam-5857	660	7	α	α	NOUN
ejpam-5857	660	8	.	.	PUNCT
ejpam-5857	661	1	by	by	ADP
ejpam-5857	661	2	the	the	DET
ejpam-5857	661	3	k.	k.	PROPN
ejpam-5857	661	4	suayngam	suayngam	PROPN
ejpam-5857	661	5	,	,	PUNCT
ejpam-5857	661	6	p.	p.	NOUN
ejpam-5857	661	7	julatha	julatha	PROPN
ejpam-5857	661	8	,	,	PUNCT
ejpam-5857	661	9	w.	w.	PROPN
ejpam-5857	661	10	nakkhasen	nakkhasen	PROPN
ejpam-5857	661	11	,	,	PUNCT
ejpam-5857	661	12	a.	a.	NOUN
ejpam-5857	661	13	iampan	iampan	PROPN
ejpam-5857	661	14	/	/	SYM
ejpam-5857	661	15	eur	eur	PROPN
ejpam-5857	661	16	.	.	PUNCT
ejpam-5857	662	1	j.	j.	PROPN
ejpam-5857	662	2	pure	pure	PROPN
ejpam-5857	662	3	appl	appl	PROPN
ejpam-5857	662	4	.	.	PROPN
ejpam-5857	662	5	math	math	PROPN
ejpam-5857	662	6	,	,	PUNCT
ejpam-5857	662	7	18	18	NUM
ejpam-5857	662	8	(	(	PUNCT
ejpam-5857	662	9	2	2	NUM
ejpam-5857	662	10	)	)	PUNCT
ejpam-5857	662	11	(	(	PUNCT
ejpam-5857	662	12	2025	2025	NUM
ejpam-5857	662	13	)	)	PUNCT
ejpam-5857	662	14	,	,	PUNCT
ejpam-5857	662	15	5857	5857	NUM
ejpam-5857	662	16	23	23	NUM
ejpam-5857	662	17	of	of	ADP
ejpam-5857	662	18	30	30	NUM
ejpam-5857	662	19	condition	condition	NOUN
ejpam-5857	662	20	(	(	PUNCT
ejpam-5857	662	21	3.8	3.8	NUM
ejpam-5857	662	22	)	)	PUNCT
ejpam-5857	662	23	,	,	PUNCT
ejpam-5857	662	24	we	we	PRON
ejpam-5857	662	25	have	have	AUX
ejpam-5857	662	26	ψt	ψt	VERB
ejpam-5857	662	27	(	(	PUNCT
ejpam-5857	662	28	0	0	NUM
ejpam-5857	662	29	)	)	PUNCT
ejpam-5857	662	30	≥	≥	PRON
ejpam-5857	662	31	ψt	ψt	NOUN
ejpam-5857	662	32	(	(	PUNCT
ejpam-5857	662	33	a	a	NOUN
ejpam-5857	662	34	)	)	PUNCT
ejpam-5857	662	35	≥	≥	NOUN
ejpam-5857	662	36	α	α	NOUN
ejpam-5857	662	37	.	.	PUNCT
ejpam-5857	663	1	thus	thus	ADV
ejpam-5857	663	2	,	,	PUNCT
ejpam-5857	663	3	0	0	NUM
ejpam-5857	663	4	∈	∈	PROPN
ejpam-5857	663	5	u(ψt	u(ψt	NOUN
ejpam-5857	663	6	;	;	PUNCT
ejpam-5857	663	7	α	α	X
ejpam-5857	663	8	)	)	PUNCT
ejpam-5857	663	9	.	.	PUNCT
ejpam-5857	664	1	let	let	VERB
ejpam-5857	664	2	x	x	PRON
ejpam-5857	664	3	,	,	PUNCT
ejpam-5857	664	4	y	y	PROPN
ejpam-5857	664	5	∈	∈	PROPN
ejpam-5857	664	6	x	x	AUX
ejpam-5857	664	7	be	be	AUX
ejpam-5857	664	8	such	such	ADJ
ejpam-5857	664	9	that	that	SCONJ
ejpam-5857	664	10	x	x	X
ejpam-5857	664	11	·	·	PUNCT
ejpam-5857	664	12	y	y	PROPN
ejpam-5857	664	13	∈	∈	PROPN
ejpam-5857	664	14	u(ψt	u(ψt	PROPN
ejpam-5857	664	15	;	;	PUNCT
ejpam-5857	664	16	α	α	X
ejpam-5857	664	17	)	)	PUNCT
ejpam-5857	664	18	and	and	CCONJ
ejpam-5857	664	19	x	x	PUNCT
ejpam-5857	664	20	∈	∈	PROPN
ejpam-5857	664	21	u(ψt	u(ψt	PROPN
ejpam-5857	664	22	;	;	PUNCT
ejpam-5857	664	23	α	α	X
ejpam-5857	664	24	)	)	PUNCT
ejpam-5857	664	25	.	.	PUNCT
ejpam-5857	665	1	then	then	ADV
ejpam-5857	665	2	ψt	ψt	VERB
ejpam-5857	665	3	(	(	PUNCT
ejpam-5857	665	4	x	x	PROPN
ejpam-5857	665	5	·	·	PUNCT
ejpam-5857	665	6	y	y	X
ejpam-5857	665	7	)	)	PUNCT
ejpam-5857	665	8	≥	≥	NOUN
ejpam-5857	665	9	α	α	NOUN
ejpam-5857	665	10	and	and	CCONJ
ejpam-5857	665	11	ψt	ψt	ADJ
ejpam-5857	665	12	(	(	PUNCT
ejpam-5857	665	13	x	x	NOUN
ejpam-5857	665	14	)	)	PUNCT
ejpam-5857	665	15	≥	≥	PROPN
ejpam-5857	665	16	α	α	NOUN
ejpam-5857	665	17	.	.	PUNCT
ejpam-5857	666	1	thus	thus	ADV
ejpam-5857	666	2	,	,	PUNCT
ejpam-5857	666	3	ψt	ψt	VERB
ejpam-5857	666	4	(	(	PUNCT
ejpam-5857	666	5	x	x	X
ejpam-5857	666	6	·	·	PUNCT
ejpam-5857	666	7	y)∧ψt	y)∧ψt	PROPN
ejpam-5857	666	8	(	(	PUNCT
ejpam-5857	666	9	x	x	NOUN
ejpam-5857	666	10	)	)	PUNCT
ejpam-5857	666	11	≥	≥	PROPN
ejpam-5857	666	12	α	α	NOUN
ejpam-5857	666	13	.	.	PUNCT
ejpam-5857	667	1	by	by	ADP
ejpam-5857	667	2	the	the	DET
ejpam-5857	667	3	condition	condition	NOUN
ejpam-5857	667	4	(	(	PUNCT
ejpam-5857	667	5	3.14	3.14	NUM
ejpam-5857	667	6	)	)	PUNCT
ejpam-5857	667	7	,	,	PUNCT
ejpam-5857	667	8	we	we	PRON
ejpam-5857	667	9	have	have	AUX
ejpam-5857	667	10	ψt	ψt	VERB
ejpam-5857	667	11	(	(	PUNCT
ejpam-5857	667	12	y	y	NOUN
ejpam-5857	667	13	)	)	PUNCT
ejpam-5857	667	14	≥	≥	NOUN
ejpam-5857	667	15	(	(	PUNCT
ejpam-5857	667	16	ψt	ψt	VERB
ejpam-5857	667	17	(	(	PUNCT
ejpam-5857	667	18	x	x	X
ejpam-5857	667	19	·	·	PUNCT
ejpam-5857	667	20	y)∧ψt	y)∧ψt	PROPN
ejpam-5857	667	21	(	(	PUNCT
ejpam-5857	667	22	x))∨0.5	x))∨0.5	X
ejpam-5857	667	23	≥	≥	NUM
ejpam-5857	667	24	α	α	PROPN
ejpam-5857	667	25	∨	∨	NUM
ejpam-5857	667	26	0.5	0.5	NUM
ejpam-5857	667	27	≥	≥	NOUN
ejpam-5857	667	28	α	α	NOUN
ejpam-5857	667	29	.	.	PUNCT
ejpam-5857	668	1	thus	thus	ADV
ejpam-5857	668	2	,	,	PUNCT
ejpam-5857	668	3	y	y	PROPN
ejpam-5857	668	4	∈	∈	PROPN
ejpam-5857	668	5	u(ψt	u(ψt	PROPN
ejpam-5857	668	6	;	;	PUNCT
ejpam-5857	668	7	α	α	X
ejpam-5857	668	8	)	)	PUNCT
ejpam-5857	668	9	.	.	PUNCT
ejpam-5857	669	1	hence	hence	ADV
ejpam-5857	669	2	,	,	PUNCT
ejpam-5857	669	3	u(ψt	u(ψt	PROPN
ejpam-5857	669	4	;	;	PUNCT
ejpam-5857	669	5	α	α	X
ejpam-5857	669	6	)	)	PUNCT
ejpam-5857	669	7	is	be	AUX
ejpam-5857	669	8	an	an	DET
ejpam-5857	669	9	iup	iup	NOUN
ejpam-5857	669	10	-	-	PUNCT
ejpam-5857	669	11	filter	filter	NOUN
ejpam-5857	669	12	of	of	ADP
ejpam-5857	669	13	x.	x.	NOUN
ejpam-5857	669	14	let	let	VERB
ejpam-5857	669	15	β	β	X
ejpam-5857	669	16	∈	∈	PROPN
ejpam-5857	670	1	[	[	X
ejpam-5857	670	2	0	0	NUM
ejpam-5857	670	3	,	,	PUNCT
ejpam-5857	670	4	0.5	0.5	NUM
ejpam-5857	670	5	)	)	PUNCT
ejpam-5857	670	6	be	be	VERB
ejpam-5857	670	7	such	such	ADJ
ejpam-5857	670	8	that	that	SCONJ
ejpam-5857	670	9	l(ψi	l(ψi	NOUN
ejpam-5857	670	10	;	;	PUNCT
ejpam-5857	670	11	β	β	X
ejpam-5857	670	12	)	)	PUNCT
ejpam-5857	670	13	̸=	̸=	PROPN
ejpam-5857	670	14	∅.	∅.	ADV
ejpam-5857	670	15	let	let	VERB
ejpam-5857	670	16	b	b	NOUN
ejpam-5857	670	17	∈	∈	PROPN
ejpam-5857	670	18	l(ψi	l(ψi	PROPN
ejpam-5857	670	19	;	;	PUNCT
ejpam-5857	670	20	β	β	X
ejpam-5857	670	21	)	)	PUNCT
ejpam-5857	670	22	.	.	PUNCT
ejpam-5857	671	1	then	then	ADV
ejpam-5857	671	2	ψi(b	ψi(b	X
ejpam-5857	671	3	)	)	PUNCT
ejpam-5857	671	4	≤	≤	NOUN
ejpam-5857	672	1	β	β	X
ejpam-5857	672	2	.	.	PUNCT
ejpam-5857	673	1	by	by	ADP
ejpam-5857	673	2	the	the	DET
ejpam-5857	673	3	condition	condition	NOUN
ejpam-5857	673	4	(	(	PUNCT
ejpam-5857	673	5	3.9	3.9	NUM
ejpam-5857	673	6	)	)	PUNCT
ejpam-5857	673	7	,	,	PUNCT
ejpam-5857	673	8	we	we	PRON
ejpam-5857	673	9	have	have	VERB
ejpam-5857	673	10	ψi(0	ψi(0	PROPN
ejpam-5857	673	11	)	)	PUNCT
ejpam-5857	673	12	≤	≤	NOUN
ejpam-5857	673	13	ψi(b	ψi(b	PUNCT
ejpam-5857	673	14	)	)	PUNCT
ejpam-5857	673	15	≤	≤	NUM
ejpam-5857	674	1	β	β	X
ejpam-5857	674	2	.	.	PUNCT
ejpam-5857	675	1	thus	thus	ADV
ejpam-5857	675	2	,	,	PUNCT
ejpam-5857	675	3	0	0	NUM
ejpam-5857	675	4	∈	∈	NOUN
ejpam-5857	675	5	l(ψi	l(ψi	NOUN
ejpam-5857	675	6	;	;	PUNCT
ejpam-5857	675	7	β	β	X
ejpam-5857	675	8	)	)	PUNCT
ejpam-5857	675	9	.	.	PUNCT
ejpam-5857	676	1	let	let	VERB
ejpam-5857	676	2	x	x	PRON
ejpam-5857	676	3	,	,	PUNCT
ejpam-5857	676	4	y	y	PROPN
ejpam-5857	676	5	∈	∈	PROPN
ejpam-5857	676	6	x	x	AUX
ejpam-5857	676	7	be	be	AUX
ejpam-5857	676	8	such	such	ADJ
ejpam-5857	676	9	that	that	SCONJ
ejpam-5857	676	10	x	x	X
ejpam-5857	676	11	·	·	PUNCT
ejpam-5857	676	12	y	y	PROPN
ejpam-5857	676	13	∈	∈	PROPN
ejpam-5857	676	14	l(ψi	l(ψi	PROPN
ejpam-5857	676	15	;	;	PUNCT
ejpam-5857	676	16	β	β	X
ejpam-5857	676	17	)	)	PUNCT
ejpam-5857	676	18	and	and	CCONJ
ejpam-5857	676	19	x	x	PUNCT
ejpam-5857	676	20	∈	∈	NOUN
ejpam-5857	676	21	l(ψi	l(ψi	NOUN
ejpam-5857	676	22	;	;	PUNCT
ejpam-5857	676	23	β	β	X
ejpam-5857	676	24	)	)	PUNCT
ejpam-5857	676	25	.	.	PUNCT
ejpam-5857	677	1	then	then	ADV
ejpam-5857	677	2	ψi(x	ψi(x	NOUN
ejpam-5857	677	3	·	·	PUNCT
ejpam-5857	677	4	y	y	X
ejpam-5857	677	5	)	)	PUNCT
ejpam-5857	677	6	≤	≤	NOUN
ejpam-5857	677	7	β	β	X
ejpam-5857	677	8	and	and	CCONJ
ejpam-5857	677	9	ψi(x	ψi(x	NUM
ejpam-5857	677	10	)	)	PUNCT
ejpam-5857	677	11	≤	≤	NOUN
ejpam-5857	678	1	β	β	X
ejpam-5857	678	2	.	.	PUNCT
ejpam-5857	679	1	thus	thus	ADV
ejpam-5857	679	2	,	,	PUNCT
ejpam-5857	679	3	ψi(x	ψi(x	X
ejpam-5857	679	4	·	·	PUNCT
ejpam-5857	679	5	y)∨ψi(x	y)∨ψi(x	X
ejpam-5857	679	6	)	)	PUNCT
ejpam-5857	679	7	≤	≤	NOUN
ejpam-5857	679	8	β	β	X
ejpam-5857	679	9	.	.	PUNCT
ejpam-5857	680	1	by	by	ADP
ejpam-5857	680	2	the	the	DET
ejpam-5857	680	3	condition	condition	NOUN
ejpam-5857	680	4	(	(	PUNCT
ejpam-5857	680	5	3.15	3.15	NUM
ejpam-5857	680	6	)	)	PUNCT
ejpam-5857	680	7	,	,	PUNCT
ejpam-5857	680	8	we	we	PRON
ejpam-5857	680	9	have	have	VERB
ejpam-5857	680	10	ψi(y	ψi(y	NOUN
ejpam-5857	680	11	)	)	PUNCT
ejpam-5857	680	12	≤	≤	NOUN
ejpam-5857	680	13	(	(	PUNCT
ejpam-5857	680	14	ψi(x	ψi(x	NUM
ejpam-5857	680	15	·	·	PUNCT
ejpam-5857	680	16	y)∨ψi(x))∧	y)∨ψi(x))∧	NOUN
ejpam-5857	680	17	0.5	0.5	NUM
ejpam-5857	680	18	≤	≤	NOUN
ejpam-5857	680	19	β	β	X
ejpam-5857	680	20	∧	∧	PROPN
ejpam-5857	680	21	0.5	0.5	NUM
ejpam-5857	680	22	≤	≤	NUM
ejpam-5857	680	23	β	β	NOUN
ejpam-5857	680	24	.	.	PUNCT
ejpam-5857	681	1	thus	thus	ADV
ejpam-5857	681	2	,	,	PUNCT
ejpam-5857	681	3	y	y	PROPN
ejpam-5857	681	4	∈	∈	PROPN
ejpam-5857	681	5	l(ψi	l(ψi	PROPN
ejpam-5857	681	6	;	;	PUNCT
ejpam-5857	681	7	β	β	X
ejpam-5857	681	8	)	)	PUNCT
ejpam-5857	681	9	.	.	PUNCT
ejpam-5857	682	1	hence	hence	ADV
ejpam-5857	682	2	,	,	PUNCT
ejpam-5857	682	3	l(ψi	l(ψi	PROPN
ejpam-5857	682	4	;	;	PUNCT
ejpam-5857	682	5	β	β	X
ejpam-5857	682	6	)	)	PUNCT
ejpam-5857	682	7	is	be	AUX
ejpam-5857	682	8	an	an	DET
ejpam-5857	682	9	iup	iup	NOUN
ejpam-5857	682	10	-	-	PUNCT
ejpam-5857	682	11	ideal	ideal	NOUN
ejpam-5857	682	12	of	of	ADP
ejpam-5857	682	13	x.	x.	NOUN
ejpam-5857	682	14	let	let	VERB
ejpam-5857	682	15	γ	γ	X
ejpam-5857	682	16	∈	∈	PROPN
ejpam-5857	683	1	[	[	X
ejpam-5857	683	2	0.5	0.5	NUM
ejpam-5857	683	3	,	,	PUNCT
ejpam-5857	683	4	1	1	NUM
ejpam-5857	683	5	]	]	PUNCT
ejpam-5857	683	6	be	be	AUX
ejpam-5857	683	7	such	such	ADJ
ejpam-5857	683	8	that	that	SCONJ
ejpam-5857	683	9	u(ψf	u(ψf	PROPN
ejpam-5857	683	10	;	;	PUNCT
ejpam-5857	683	11	γ	γ	X
ejpam-5857	683	12	)	)	PUNCT
ejpam-5857	683	13	̸=	̸=	PROPN
ejpam-5857	683	14	∅.	∅.	ADV
ejpam-5857	683	15	let	let	VERB
ejpam-5857	683	16	c	c	PROPN
ejpam-5857	683	17	∈	∈	PROPN
ejpam-5857	683	18	u(ψf	u(ψf	PROPN
ejpam-5857	683	19	;	;	PUNCT
ejpam-5857	683	20	γ	γ	X
ejpam-5857	683	21	)	)	PUNCT
ejpam-5857	683	22	.	.	PUNCT
ejpam-5857	684	1	then	then	ADV
ejpam-5857	684	2	ψf	ψf	X
ejpam-5857	684	3	(	(	PUNCT
ejpam-5857	684	4	c	c	NOUN
ejpam-5857	684	5	)	)	PUNCT
ejpam-5857	684	6	≥	≥	PROPN
ejpam-5857	684	7	γ	γ	X
ejpam-5857	684	8	.	.	PROPN
ejpam-5857	684	9	by	by	ADP
ejpam-5857	684	10	the	the	DET
ejpam-5857	684	11	condition	condition	NOUN
ejpam-5857	684	12	(	(	PUNCT
ejpam-5857	684	13	3.10	3.10	NUM
ejpam-5857	684	14	)	)	PUNCT
ejpam-5857	684	15	,	,	PUNCT
ejpam-5857	684	16	we	we	PRON
ejpam-5857	684	17	have	have	VERB
ejpam-5857	684	18	ψf	ψf	X
ejpam-5857	684	19	(	(	PUNCT
ejpam-5857	684	20	0	0	NUM
ejpam-5857	684	21	)	)	PUNCT
ejpam-5857	684	22	≥	≥	NOUN
ejpam-5857	684	23	ψf	ψf	X
ejpam-5857	684	24	(	(	PUNCT
ejpam-5857	684	25	c	c	NOUN
ejpam-5857	684	26	)	)	PUNCT
ejpam-5857	684	27	≥	≥	PROPN
ejpam-5857	684	28	γ	γ	PROPN
ejpam-5857	684	29	.	.	PROPN
ejpam-5857	684	30	thus	thus	ADV
ejpam-5857	684	31	,	,	PUNCT
ejpam-5857	684	32	0	0	X
ejpam-5857	684	33	∈	∈	PROPN
ejpam-5857	684	34	u(ψf	u(ψf	PROPN
ejpam-5857	684	35	;	;	PUNCT
ejpam-5857	684	36	γ	γ	X
ejpam-5857	684	37	)	)	PUNCT
ejpam-5857	684	38	.	.	PUNCT
ejpam-5857	685	1	let	let	VERB
ejpam-5857	685	2	x	x	PRON
ejpam-5857	685	3	,	,	PUNCT
ejpam-5857	685	4	y	y	PROPN
ejpam-5857	685	5	∈	∈	PROPN
ejpam-5857	685	6	x	x	AUX
ejpam-5857	685	7	be	be	AUX
ejpam-5857	685	8	such	such	ADJ
ejpam-5857	685	9	that	that	SCONJ
ejpam-5857	685	10	x	x	X
ejpam-5857	685	11	·	·	PUNCT
ejpam-5857	685	12	y	y	X
ejpam-5857	685	13	∈	∈	PROPN
ejpam-5857	685	14	u(ψf	u(ψf	PROPN
ejpam-5857	685	15	;	;	PUNCT
ejpam-5857	685	16	γ	γ	X
ejpam-5857	685	17	)	)	PUNCT
ejpam-5857	685	18	and	and	CCONJ
ejpam-5857	685	19	x	x	PUNCT
ejpam-5857	685	20	∈	∈	PROPN
ejpam-5857	685	21	u(ψf	u(ψf	PROPN
ejpam-5857	685	22	;	;	PUNCT
ejpam-5857	685	23	γ	γ	X
ejpam-5857	685	24	)	)	PUNCT
ejpam-5857	685	25	.	.	PUNCT
ejpam-5857	686	1	then	then	ADV
ejpam-5857	686	2	ψf	ψf	X
ejpam-5857	686	3	(	(	PUNCT
ejpam-5857	686	4	x	x	PROPN
ejpam-5857	686	5	·	·	PUNCT
ejpam-5857	686	6	y	y	X
ejpam-5857	686	7	)	)	PUNCT
ejpam-5857	686	8	≥	≥	PROPN
ejpam-5857	686	9	γ	γ	PROPN
ejpam-5857	686	10	and	and	CCONJ
ejpam-5857	686	11	ψf	ψf	X
ejpam-5857	686	12	(	(	PUNCT
ejpam-5857	686	13	x	x	X
ejpam-5857	686	14	)	)	PUNCT
ejpam-5857	686	15	≥	≥	PROPN
ejpam-5857	686	16	γ	γ	PROPN
ejpam-5857	686	17	.	.	PUNCT
ejpam-5857	686	18	thus	thus	ADV
ejpam-5857	686	19	,	,	PUNCT
ejpam-5857	686	20	ψf	ψf	X
ejpam-5857	686	21	(	(	PUNCT
ejpam-5857	686	22	x	x	X
ejpam-5857	686	23	·	·	PUNCT
ejpam-5857	686	24	y)∧ψf	y)∧ψf	NOUN
ejpam-5857	686	25	(	(	PUNCT
ejpam-5857	686	26	x	x	NOUN
ejpam-5857	686	27	)	)	PUNCT
ejpam-5857	686	28	≥	≥	PROPN
ejpam-5857	686	29	γ	γ	X
ejpam-5857	686	30	.	.	PROPN
ejpam-5857	686	31	by	by	ADP
ejpam-5857	686	32	the	the	DET
ejpam-5857	686	33	condition	condition	NOUN
ejpam-5857	686	34	(	(	PUNCT
ejpam-5857	686	35	3.16	3.16	NUM
ejpam-5857	686	36	)	)	PUNCT
ejpam-5857	686	37	,	,	PUNCT
ejpam-5857	686	38	we	we	PRON
ejpam-5857	686	39	have	have	VERB
ejpam-5857	686	40	ψf	ψf	VERB
ejpam-5857	686	41	(	(	PUNCT
ejpam-5857	686	42	y	y	NOUN
ejpam-5857	686	43	)	)	PUNCT
ejpam-5857	686	44	≥	≥	NOUN
ejpam-5857	686	45	(	(	PUNCT
ejpam-5857	686	46	ψf	ψf	X
ejpam-5857	686	47	(	(	PUNCT
ejpam-5857	686	48	x	x	PROPN
ejpam-5857	686	49	·	·	PUNCT
ejpam-5857	686	50	y)∧ψf	y)∧ψf	PROPN
ejpam-5857	686	51	(	(	PUNCT
ejpam-5857	686	52	x))∨0.5	x))∨0.5	PROPN
ejpam-5857	686	53	≥	≥	NUM
ejpam-5857	686	54	γ	γ	PROPN
ejpam-5857	686	55	∨	∨	NUM
ejpam-5857	686	56	0.5	0.5	NUM
ejpam-5857	686	57	≥	≥	PROPN
ejpam-5857	686	58	γ	γ	PROPN
ejpam-5857	686	59	.	.	PUNCT
ejpam-5857	686	60	thus	thus	ADV
ejpam-5857	686	61	,	,	PUNCT
ejpam-5857	686	62	y	y	PROPN
ejpam-5857	686	63	∈	∈	PROPN
ejpam-5857	686	64	u(ψf	u(ψf	PROPN
ejpam-5857	686	65	;	;	PUNCT
ejpam-5857	686	66	γ	γ	X
ejpam-5857	686	67	)	)	PUNCT
ejpam-5857	686	68	.	.	PUNCT
ejpam-5857	687	1	hence	hence	ADV
ejpam-5857	687	2	,	,	PUNCT
ejpam-5857	687	3	u(ψf	u(ψf	PROPN
ejpam-5857	687	4	;	;	PUNCT
ejpam-5857	687	5	γ	γ	X
ejpam-5857	687	6	)	)	PUNCT
ejpam-5857	687	7	is	be	AUX
ejpam-5857	687	8	an	an	DET
ejpam-5857	687	9	iup	iup	NOUN
ejpam-5857	687	10	-	-	PUNCT
ejpam-5857	687	11	filter	filter	NOUN
ejpam-5857	687	12	of	of	ADP
ejpam-5857	687	13	x.	x.	PROPN
ejpam-5857	687	14	theorem	theorem	VERB
ejpam-5857	687	15	21	21	NUM
ejpam-5857	687	16	.	.	PUNCT
ejpam-5857	688	1	let	let	VERB
ejpam-5857	688	2	an	an	DET
ejpam-5857	688	3	ins	in	NOUN
ejpam-5857	688	4	ψ	ψ	PART
ejpam-5857	688	5	be	be	AUX
ejpam-5857	688	6	an	an	DET
ejpam-5857	688	7	intuitionistic	intuitionistic	ADJ
ejpam-5857	688	8	neutrosophic	neutrosophic	ADJ
ejpam-5857	688	9	strong	strong	ADJ
ejpam-5857	688	10	iup	iup	NOUN
ejpam-5857	688	11	-	-	PUNCT
ejpam-5857	688	12	ideal	ideal	NOUN
ejpam-5857	688	13	of	of	ADP
ejpam-5857	688	14	x.	x.	NOUN
ejpam-5857	688	15	then	then	ADV
ejpam-5857	688	16	for	for	ADP
ejpam-5857	688	17	all	all	DET
ejpam-5857	688	18	α	α	NOUN
ejpam-5857	688	19	,	,	PUNCT
ejpam-5857	688	20	γ	γ	PROPN
ejpam-5857	688	21	∈	∈	PROPN
ejpam-5857	689	1	[	[	X
ejpam-5857	689	2	0.5	0.5	NUM
ejpam-5857	689	3	,	,	PUNCT
ejpam-5857	689	4	1	1	NUM
ejpam-5857	689	5	]	]	PUNCT
ejpam-5857	689	6	and	and	CCONJ
ejpam-5857	689	7	β	β	X
ejpam-5857	689	8	∈	∈	PROPN
ejpam-5857	690	1	[	[	X
ejpam-5857	690	2	0	0	NUM
ejpam-5857	690	3	,	,	PUNCT
ejpam-5857	690	4	0.5	0.5	NUM
ejpam-5857	690	5	)	)	PUNCT
ejpam-5857	690	6	,	,	PUNCT
ejpam-5857	690	7	the	the	DET
ejpam-5857	690	8	sets	set	NOUN
ejpam-5857	690	9	u(ψt	u(ψt	PROPN
ejpam-5857	690	10	;	;	PUNCT
ejpam-5857	690	11	α	α	X
ejpam-5857	690	12	)	)	PUNCT
ejpam-5857	690	13	,	,	PUNCT
ejpam-5857	690	14	l(ψi	l(ψi	PROPN
ejpam-5857	690	15	;	;	PUNCT
ejpam-5857	690	16	β	β	X
ejpam-5857	690	17	)	)	PUNCT
ejpam-5857	690	18	and	and	CCONJ
ejpam-5857	690	19	u(ψf	u(ψf	PROPN
ejpam-5857	690	20	;	;	PUNCT
ejpam-5857	690	21	γ	γ	X
ejpam-5857	690	22	)	)	PUNCT
ejpam-5857	690	23	are	be	AUX
ejpam-5857	690	24	either	either	CCONJ
ejpam-5857	690	25	empty	empty	ADJ
ejpam-5857	690	26	or	or	CCONJ
ejpam-5857	690	27	strong	strong	ADJ
ejpam-5857	690	28	iup	iup	NOUN
ejpam-5857	690	29	-	-	PUNCT
ejpam-5857	690	30	ideals	ideal	NOUN
ejpam-5857	690	31	of	of	ADP
ejpam-5857	690	32	x.	x.	NOUN
ejpam-5857	690	33	proof	proof	NOUN
ejpam-5857	690	34	.	.	PUNCT
ejpam-5857	691	1	it	it	PRON
ejpam-5857	691	2	is	be	AUX
ejpam-5857	691	3	straightforward	straightforward	ADJ
ejpam-5857	691	4	by	by	ADP
ejpam-5857	691	5	theorem	theorem	NOUN
ejpam-5857	691	6	1	1	NUM
ejpam-5857	691	7	.	.	PUNCT
ejpam-5857	691	8	theorem	theorem	NOUN
ejpam-5857	691	9	22	22	NUM
ejpam-5857	691	10	.	.	PUNCT
ejpam-5857	692	1	let	let	VERB
ejpam-5857	692	2	for	for	ADP
ejpam-5857	692	3	all	all	DET
ejpam-5857	692	4	α	α	NOUN
ejpam-5857	692	5	,	,	PUNCT
ejpam-5857	692	6	γ	γ	PROPN
ejpam-5857	692	7	∈	∈	PROPN
ejpam-5857	693	1	[	[	X
ejpam-5857	693	2	0.5	0.5	NUM
ejpam-5857	693	3	,	,	PUNCT
ejpam-5857	693	4	1	1	NUM
ejpam-5857	693	5	]	]	PUNCT
ejpam-5857	693	6	and	and	CCONJ
ejpam-5857	693	7	β	β	X
ejpam-5857	693	8	∈	∈	PROPN
ejpam-5857	693	9	[	[	X
ejpam-5857	693	10	0	0	NUM
ejpam-5857	693	11	,	,	PUNCT
ejpam-5857	693	12	0.5	0.5	NUM
ejpam-5857	693	13	)	)	PUNCT
ejpam-5857	693	14	,	,	PUNCT
ejpam-5857	693	15	the	the	DET
ejpam-5857	693	16	sets	set	NOUN
ejpam-5857	693	17	u(ψt	u(ψt	PROPN
ejpam-5857	693	18	;	;	PUNCT
ejpam-5857	693	19	α	α	X
ejpam-5857	693	20	)	)	PUNCT
ejpam-5857	693	21	,	,	PUNCT
ejpam-5857	693	22	l(ψi	l(ψi	PROPN
ejpam-5857	693	23	;	;	PUNCT
ejpam-5857	693	24	β	β	X
ejpam-5857	693	25	)	)	PUNCT
ejpam-5857	693	26	and	and	CCONJ
ejpam-5857	693	27	u(ψf	u(ψf	PROPN
ejpam-5857	693	28	;	;	PUNCT
ejpam-5857	693	29	γ	γ	X
ejpam-5857	693	30	)	)	PUNCT
ejpam-5857	693	31	are	be	AUX
ejpam-5857	693	32	either	either	CCONJ
ejpam-5857	693	33	empty	empty	ADJ
ejpam-5857	693	34	or	or	CCONJ
ejpam-5857	693	35	iup	iup	NOUN
ejpam-5857	693	36	-	-	PUNCT
ejpam-5857	693	37	subalgebras	subalgebras	PROPN
ejpam-5857	693	38	of	of	ADP
ejpam-5857	693	39	x.	x.	NOUN
ejpam-5857	693	40	if	if	SCONJ
ejpam-5857	693	41	ψt	ψt	VERB
ejpam-5857	693	42	(	(	PUNCT
ejpam-5857	693	43	x	x	NOUN
ejpam-5857	693	44	)	)	PUNCT
ejpam-5857	693	45	≥	≥	NOUN
ejpam-5857	693	46	0.5	0.5	NUM
ejpam-5857	693	47	,	,	PUNCT
ejpam-5857	693	48	ψi(x	ψi(x	NUM
ejpam-5857	693	49	)	)	PUNCT
ejpam-5857	693	50	<	<	X
ejpam-5857	693	51	0.5	0.5	NUM
ejpam-5857	693	52	and	and	CCONJ
ejpam-5857	693	53	ψf	ψf	X
ejpam-5857	693	54	(	(	PUNCT
ejpam-5857	693	55	x	x	X
ejpam-5857	693	56	)	)	PUNCT
ejpam-5857	693	57	≥	≥	NOUN
ejpam-5857	693	58	0.5	0.5	NUM
ejpam-5857	693	59	.	.	PUNCT
ejpam-5857	694	1	then	then	ADV
ejpam-5857	694	2	ψ	ψ	X
ejpam-5857	694	3	is	be	AUX
ejpam-5857	694	4	an	an	DET
ejpam-5857	694	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	694	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	694	7	iup	iup	NOUN
ejpam-5857	694	8	-	-	PUNCT
ejpam-5857	694	9	subalgebra	subalgebra	NOUN
ejpam-5857	694	10	of	of	ADP
ejpam-5857	694	11	x.	x.	NOUN
ejpam-5857	694	12	proof	proof	PROPN
ejpam-5857	694	13	.	.	PUNCT
ejpam-5857	695	1	assume	assume	VERB
ejpam-5857	695	2	that	that	SCONJ
ejpam-5857	695	3	for	for	ADP
ejpam-5857	695	4	all	all	DET
ejpam-5857	695	5	α	α	NOUN
ejpam-5857	695	6	,	,	PUNCT
ejpam-5857	695	7	γ	γ	PROPN
ejpam-5857	695	8	∈	∈	PROPN
ejpam-5857	696	1	[	[	X
ejpam-5857	696	2	0.5	0.5	NUM
ejpam-5857	696	3	,	,	PUNCT
ejpam-5857	696	4	1	1	NUM
ejpam-5857	696	5	]	]	PUNCT
ejpam-5857	696	6	and	and	CCONJ
ejpam-5857	696	7	β	β	X
ejpam-5857	696	8	∈	∈	PROPN
ejpam-5857	697	1	[	[	X
ejpam-5857	697	2	0	0	NUM
ejpam-5857	697	3	,	,	PUNCT
ejpam-5857	697	4	0.5	0.5	NUM
ejpam-5857	697	5	)	)	PUNCT
ejpam-5857	697	6	,	,	PUNCT
ejpam-5857	697	7	the	the	DET
ejpam-5857	697	8	sets	set	NOUN
ejpam-5857	697	9	u(ψt	u(ψt	PROPN
ejpam-5857	697	10	;	;	PUNCT
ejpam-5857	697	11	α	α	X
ejpam-5857	697	12	)	)	PUNCT
ejpam-5857	697	13	,	,	PUNCT
ejpam-5857	697	14	l(ψi	l(ψi	PROPN
ejpam-5857	697	15	;	;	PUNCT
ejpam-5857	697	16	β	β	X
ejpam-5857	697	17	)	)	PUNCT
ejpam-5857	697	18	and	and	CCONJ
ejpam-5857	697	19	u(ψf	u(ψf	PROPN
ejpam-5857	697	20	;	;	PUNCT
ejpam-5857	697	21	γ	γ	X
ejpam-5857	697	22	)	)	PUNCT
ejpam-5857	697	23	are	be	AUX
ejpam-5857	697	24	either	either	CCONJ
ejpam-5857	697	25	empty	empty	ADJ
ejpam-5857	697	26	or	or	CCONJ
ejpam-5857	697	27	iup	iup	NOUN
ejpam-5857	697	28	-	-	PUNCT
ejpam-5857	697	29	subalgebras	subalgebras	PROPN
ejpam-5857	697	30	of	of	ADP
ejpam-5857	697	31	x.	x.	PROPN
ejpam-5857	697	32	let	let	VERB
ejpam-5857	697	33	x	x	PRON
ejpam-5857	697	34	,	,	PUNCT
ejpam-5857	697	35	y	y	PROPN
ejpam-5857	697	36	∈	∈	PROPN
ejpam-5857	697	37	x	x	AUX
ejpam-5857	697	38	be	be	AUX
ejpam-5857	697	39	such	such	ADJ
ejpam-5857	697	40	that	that	SCONJ
ejpam-5857	697	41	ψt	ψt	NOUN
ejpam-5857	697	42	(	(	PUNCT
ejpam-5857	697	43	x	x	X
ejpam-5857	697	44	)	)	PUNCT
ejpam-5857	697	45	≥	≥	NOUN
ejpam-5857	697	46	0.5	0.5	NUM
ejpam-5857	697	47	and	and	CCONJ
ejpam-5857	697	48	ψt	ψt	ADJ
ejpam-5857	697	49	(	(	PUNCT
ejpam-5857	697	50	y	y	NOUN
ejpam-5857	697	51	)	)	PUNCT
ejpam-5857	697	52	≥	≥	NOUN
ejpam-5857	697	53	0.5	0.5	NUM
ejpam-5857	697	54	.	.	PUNCT
ejpam-5857	698	1	let	let	VERB
ejpam-5857	698	2	α	α	NOUN
ejpam-5857	698	3	=	=	VERB
ejpam-5857	698	4	ψt	ψt	ADJ
ejpam-5857	698	5	(	(	PUNCT
ejpam-5857	698	6	x	x	NOUN
ejpam-5857	698	7	)	)	PUNCT
ejpam-5857	698	8	∧	∧	NOUN
ejpam-5857	698	9	ψt	ψt	NOUN
ejpam-5857	698	10	(	(	PUNCT
ejpam-5857	698	11	y	y	NOUN
ejpam-5857	698	12	)	)	PUNCT
ejpam-5857	698	13	.	.	PUNCT
ejpam-5857	699	1	then	then	ADV
ejpam-5857	699	2	ψt	ψt	VERB
ejpam-5857	699	3	(	(	PUNCT
ejpam-5857	699	4	x	x	NOUN
ejpam-5857	699	5	)	)	PUNCT
ejpam-5857	699	6	≥	≥	PROPN
ejpam-5857	699	7	α	α	NOUN
ejpam-5857	699	8	and	and	CCONJ
ejpam-5857	699	9	ψt	ψt	ADJ
ejpam-5857	699	10	(	(	PUNCT
ejpam-5857	699	11	y	y	NOUN
ejpam-5857	699	12	)	)	PUNCT
ejpam-5857	699	13	≥	≥	PROPN
ejpam-5857	699	14	α	α	NOUN
ejpam-5857	699	15	.	.	PUNCT
ejpam-5857	700	1	thus	thus	ADV
ejpam-5857	700	2	,	,	PUNCT
ejpam-5857	700	3	x	x	PRON
ejpam-5857	700	4	,	,	PUNCT
ejpam-5857	700	5	y	y	PROPN
ejpam-5857	700	6	∈	∈	PROPN
ejpam-5857	700	7	u(ψt	u(ψt	PROPN
ejpam-5857	700	8	;	;	PUNCT
ejpam-5857	700	9	α	α	X
ejpam-5857	700	10	)	)	PUNCT
ejpam-5857	700	11	̸=	̸=	PROPN
ejpam-5857	700	12	∅.	∅.	NOUN
ejpam-5857	700	13	by	by	ADP
ejpam-5857	700	14	assumption	assumption	NOUN
ejpam-5857	700	15	,	,	PUNCT
ejpam-5857	700	16	we	we	PRON
ejpam-5857	700	17	have	have	VERB
ejpam-5857	700	18	u(ψt	u(ψt	NOUN
ejpam-5857	700	19	;	;	PUNCT
ejpam-5857	700	20	α	α	X
ejpam-5857	700	21	)	)	PUNCT
ejpam-5857	700	22	is	be	AUX
ejpam-5857	700	23	an	an	DET
ejpam-5857	700	24	iup	iup	NOUN
ejpam-5857	700	25	-	-	PUNCT
ejpam-5857	700	26	subalgebra	subalgebra	NOUN
ejpam-5857	700	27	of	of	ADP
ejpam-5857	700	28	x.	x.	NOUN
ejpam-5857	700	29	by	by	ADP
ejpam-5857	700	30	the	the	DET
ejpam-5857	700	31	condition	condition	NOUN
ejpam-5857	700	32	(	(	PUNCT
ejpam-5857	700	33	2.17	2.17	NUM
ejpam-5857	700	34	)	)	PUNCT
ejpam-5857	700	35	,	,	PUNCT
ejpam-5857	700	36	we	we	PRON
ejpam-5857	700	37	have	have	VERB
ejpam-5857	700	38	x	x	X
ejpam-5857	700	39	·	·	PUNCT
ejpam-5857	700	40	y	y	PROPN
ejpam-5857	700	41	∈	∈	PROPN
ejpam-5857	700	42	u(ψt	u(ψt	PROPN
ejpam-5857	700	43	;	;	PUNCT
ejpam-5857	700	44	α	α	X
ejpam-5857	700	45	)	)	PUNCT
ejpam-5857	700	46	.	.	PUNCT
ejpam-5857	701	1	thus	thus	ADV
ejpam-5857	701	2	,	,	PUNCT
ejpam-5857	701	3	ψt	ψt	VERB
ejpam-5857	701	4	(	(	PUNCT
ejpam-5857	701	5	x	x	PROPN
ejpam-5857	701	6	·	·	PUNCT
ejpam-5857	701	7	y	y	X
ejpam-5857	701	8	)	)	PUNCT
ejpam-5857	701	9	≥	≥	NOUN
ejpam-5857	701	10	α	α	NOUN
ejpam-5857	701	11	=	=	X
ejpam-5857	701	12	ψt	ψt	NOUN
ejpam-5857	701	13	(	(	PUNCT
ejpam-5857	701	14	x)∧ψt	x)∧ψt	PROPN
ejpam-5857	701	15	(	(	PUNCT
ejpam-5857	701	16	y	y	PROPN
ejpam-5857	701	17	)	)	PUNCT
ejpam-5857	701	18	≥	≥	NOUN
ejpam-5857	701	19	(	(	PUNCT
ejpam-5857	701	20	ψt	ψt	VERB
ejpam-5857	701	21	(	(	PUNCT
ejpam-5857	701	22	x	x	NOUN
ejpam-5857	701	23	)	)	PUNCT
ejpam-5857	701	24	∧	∧	NOUN
ejpam-5857	701	25	ψt	ψt	NOUN
ejpam-5857	701	26	(	(	PUNCT
ejpam-5857	701	27	y	y	NOUN
ejpam-5857	701	28	)	)	PUNCT
ejpam-5857	701	29	)	)	PUNCT
ejpam-5857	701	30	∨	∨	NUM
ejpam-5857	701	31	0.5	0.5	NUM
ejpam-5857	701	32	.	.	PUNCT
ejpam-5857	702	1	let	let	VERB
ejpam-5857	702	2	x	x	PRON
ejpam-5857	702	3	,	,	PUNCT
ejpam-5857	702	4	y	y	PROPN
ejpam-5857	702	5	∈	∈	PROPN
ejpam-5857	702	6	x	x	AUX
ejpam-5857	702	7	be	be	AUX
ejpam-5857	702	8	such	such	ADJ
ejpam-5857	702	9	that	that	SCONJ
ejpam-5857	702	10	ψi(x	ψi(x	NUM
ejpam-5857	702	11	)	)	PUNCT
ejpam-5857	702	12	<	<	X
ejpam-5857	702	13	0.5	0.5	NUM
ejpam-5857	702	14	and	and	CCONJ
ejpam-5857	702	15	ψi(y	ψi(y	NUM
ejpam-5857	702	16	)	)	PUNCT
ejpam-5857	702	17	<	<	X
ejpam-5857	702	18	0.5	0.5	NUM
ejpam-5857	702	19	.	.	PUNCT
ejpam-5857	703	1	let	let	VERB
ejpam-5857	703	2	β	β	X
ejpam-5857	703	3	=	=	SYM
ejpam-5857	703	4	ψi(x	ψi(x	NUM
ejpam-5857	703	5	)	)	PUNCT
ejpam-5857	703	6	∨	∨	NUM
ejpam-5857	703	7	ψi(y	ψi(y	NUM
ejpam-5857	703	8	)	)	PUNCT
ejpam-5857	703	9	.	.	PUNCT
ejpam-5857	704	1	then	then	ADV
ejpam-5857	704	2	ψi(x	ψi(x	NUM
ejpam-5857	704	3	)	)	PUNCT
ejpam-5857	704	4	≤	≤	NUM
ejpam-5857	704	5	β	β	X
ejpam-5857	704	6	and	and	CCONJ
ejpam-5857	704	7	ψi(y	ψi(y	NUM
ejpam-5857	704	8	)	)	PUNCT
ejpam-5857	704	9	≤	≤	NOUN
ejpam-5857	704	10	β	β	X
ejpam-5857	704	11	.	.	PUNCT
ejpam-5857	705	1	thus	thus	ADV
ejpam-5857	705	2	,	,	PUNCT
ejpam-5857	705	3	x	x	PRON
ejpam-5857	705	4	,	,	PUNCT
ejpam-5857	705	5	y	y	PROPN
ejpam-5857	705	6	∈	∈	PROPN
ejpam-5857	705	7	l(ψi	l(ψi	PROPN
ejpam-5857	705	8	;	;	PUNCT
ejpam-5857	705	9	β	β	X
ejpam-5857	705	10	)	)	PUNCT
ejpam-5857	705	11	̸=	̸=	PROPN
ejpam-5857	705	12	∅.	∅.	VERB
ejpam-5857	705	13	by	by	ADP
ejpam-5857	705	14	assumption	assumption	NOUN
ejpam-5857	705	15	,	,	PUNCT
ejpam-5857	705	16	we	we	PRON
ejpam-5857	705	17	have	have	VERB
ejpam-5857	705	18	l(ψi	l(ψi	NOUN
ejpam-5857	705	19	;	;	PUNCT
ejpam-5857	705	20	β	β	X
ejpam-5857	705	21	)	)	PUNCT
ejpam-5857	705	22	is	be	AUX
ejpam-5857	705	23	an	an	DET
ejpam-5857	705	24	iup	iup	NOUN
ejpam-5857	705	25	-	-	PUNCT
ejpam-5857	705	26	subalgebra	subalgebra	NOUN
ejpam-5857	705	27	of	of	ADP
ejpam-5857	705	28	x.	x.	NOUN
ejpam-5857	705	29	by	by	ADP
ejpam-5857	705	30	the	the	DET
ejpam-5857	705	31	condition	condition	NOUN
ejpam-5857	705	32	(	(	PUNCT
ejpam-5857	705	33	2.17	2.17	NUM
ejpam-5857	705	34	)	)	PUNCT
ejpam-5857	705	35	,	,	PUNCT
ejpam-5857	705	36	we	we	PRON
ejpam-5857	705	37	have	have	VERB
ejpam-5857	705	38	x	x	X
ejpam-5857	705	39	·	·	PUNCT
ejpam-5857	705	40	y	y	PROPN
ejpam-5857	705	41	∈	∈	PROPN
ejpam-5857	705	42	l(ψi	l(ψi	PROPN
ejpam-5857	705	43	;	;	PUNCT
ejpam-5857	705	44	β	β	X
ejpam-5857	705	45	)	)	PUNCT
ejpam-5857	705	46	.	.	PUNCT
ejpam-5857	706	1	thus	thus	ADV
ejpam-5857	706	2	,	,	PUNCT
ejpam-5857	706	3	ψi(x	ψi(x	X
ejpam-5857	706	4	·	·	PUNCT
ejpam-5857	706	5	y	y	X
ejpam-5857	706	6	)	)	PUNCT
ejpam-5857	706	7	≤	≤	NOUN
ejpam-5857	706	8	β	β	X
ejpam-5857	706	9	=	=	SYM
ejpam-5857	706	10	ψi(x	ψi(x	X
ejpam-5857	706	11	)	)	PUNCT
ejpam-5857	706	12	∨	∨	NUM
ejpam-5857	706	13	ψi(y	ψi(y	NUM
ejpam-5857	706	14	)	)	PUNCT
ejpam-5857	706	15	≤	≤	NOUN
ejpam-5857	706	16	(	(	PUNCT
ejpam-5857	706	17	ψi(x	ψi(x	NUM
ejpam-5857	706	18	)	)	PUNCT
ejpam-5857	706	19	∨	∨	NUM
ejpam-5857	706	20	ψi(y	ψi(y	NUM
ejpam-5857	706	21	)	)	PUNCT
ejpam-5857	706	22	)	)	PUNCT
ejpam-5857	706	23	∧	∧	NOUN
ejpam-5857	706	24	0.5	0.5	NUM
ejpam-5857	706	25	.	.	PUNCT
ejpam-5857	707	1	let	let	VERB
ejpam-5857	707	2	x	x	PRON
ejpam-5857	707	3	,	,	PUNCT
ejpam-5857	707	4	y	y	PROPN
ejpam-5857	707	5	∈	∈	PROPN
ejpam-5857	707	6	x	x	AUX
ejpam-5857	707	7	be	be	AUX
ejpam-5857	707	8	such	such	ADJ
ejpam-5857	707	9	that	that	SCONJ
ejpam-5857	707	10	ψf	ψf	X
ejpam-5857	707	11	(	(	PUNCT
ejpam-5857	707	12	x	x	X
ejpam-5857	707	13	)	)	PUNCT
ejpam-5857	707	14	≥	≥	NOUN
ejpam-5857	707	15	0.5	0.5	NUM
ejpam-5857	707	16	and	and	CCONJ
ejpam-5857	707	17	ψf	ψf	X
ejpam-5857	707	18	(	(	PUNCT
ejpam-5857	707	19	y	y	PROPN
ejpam-5857	707	20	)	)	PUNCT
ejpam-5857	707	21	≥	≥	NOUN
ejpam-5857	707	22	0.5	0.5	NUM
ejpam-5857	707	23	.	.	PUNCT
ejpam-5857	708	1	let	let	VERB
ejpam-5857	708	2	γ	γ	X
ejpam-5857	708	3	=	=	PRON
ejpam-5857	708	4	ψf	ψf	X
ejpam-5857	708	5	(	(	PUNCT
ejpam-5857	708	6	x	x	X
ejpam-5857	708	7	)	)	PUNCT
ejpam-5857	708	8	∧	∧	NOUN
ejpam-5857	708	9	ψf	ψf	X
ejpam-5857	708	10	(	(	PUNCT
ejpam-5857	708	11	y	y	NOUN
ejpam-5857	708	12	)	)	PUNCT
ejpam-5857	708	13	.	.	PUNCT
ejpam-5857	709	1	then	then	ADV
ejpam-5857	709	2	ψf	ψf	X
ejpam-5857	709	3	(	(	PUNCT
ejpam-5857	709	4	x	x	X
ejpam-5857	709	5	)	)	PUNCT
ejpam-5857	709	6	≥	≥	PROPN
ejpam-5857	709	7	γ	γ	PROPN
ejpam-5857	709	8	and	and	CCONJ
ejpam-5857	709	9	ψf	ψf	X
ejpam-5857	709	10	(	(	PUNCT
ejpam-5857	709	11	y	y	PROPN
ejpam-5857	709	12	)	)	PUNCT
ejpam-5857	709	13	≥	≥	PROPN
ejpam-5857	709	14	γ	γ	PROPN
ejpam-5857	709	15	.	.	PROPN
ejpam-5857	709	16	thus	thus	ADV
ejpam-5857	709	17	,	,	PUNCT
ejpam-5857	709	18	x	x	PRON
ejpam-5857	709	19	,	,	PUNCT
ejpam-5857	709	20	y	y	PROPN
ejpam-5857	709	21	∈	∈	PROPN
ejpam-5857	709	22	u(ψf	u(ψf	PROPN
ejpam-5857	709	23	;	;	PUNCT
ejpam-5857	709	24	γ	γ	X
ejpam-5857	709	25	)	)	PUNCT
ejpam-5857	709	26	̸=	̸=	PROPN
ejpam-5857	709	27	∅.	∅.	VERB
ejpam-5857	709	28	by	by	ADP
ejpam-5857	709	29	assumption	assumption	NOUN
ejpam-5857	709	30	,	,	PUNCT
ejpam-5857	709	31	we	we	PRON
ejpam-5857	709	32	have	have	VERB
ejpam-5857	709	33	u(ψf	u(ψf	PROPN
ejpam-5857	709	34	;	;	PUNCT
ejpam-5857	709	35	γ	γ	X
ejpam-5857	709	36	)	)	PUNCT
ejpam-5857	709	37	is	be	AUX
ejpam-5857	709	38	an	an	DET
ejpam-5857	709	39	iup	iup	NOUN
ejpam-5857	709	40	-	-	PUNCT
ejpam-5857	709	41	subalgebra	subalgebra	NOUN
ejpam-5857	709	42	of	of	ADP
ejpam-5857	709	43	x.	x.	NOUN
ejpam-5857	709	44	by	by	ADP
ejpam-5857	709	45	the	the	DET
ejpam-5857	709	46	condition	condition	NOUN
ejpam-5857	709	47	(	(	PUNCT
ejpam-5857	709	48	2.17	2.17	NUM
ejpam-5857	709	49	)	)	PUNCT
ejpam-5857	709	50	,	,	PUNCT
ejpam-5857	709	51	we	we	PRON
ejpam-5857	709	52	have	have	VERB
ejpam-5857	709	53	x	x	X
ejpam-5857	709	54	·	·	PUNCT
ejpam-5857	709	55	y	y	X
ejpam-5857	709	56	∈	∈	PROPN
ejpam-5857	709	57	u(ψf	u(ψf	PROPN
ejpam-5857	709	58	;	;	PUNCT
ejpam-5857	709	59	γ	γ	X
ejpam-5857	709	60	)	)	PUNCT
ejpam-5857	709	61	.	.	PUNCT
ejpam-5857	710	1	thus	thus	ADV
ejpam-5857	710	2	,	,	PUNCT
ejpam-5857	710	3	ψf	ψf	X
ejpam-5857	710	4	(	(	PUNCT
ejpam-5857	710	5	x	x	X
ejpam-5857	710	6	·	·	PUNCT
ejpam-5857	710	7	y	y	X
ejpam-5857	710	8	)	)	PUNCT
ejpam-5857	710	9	≥	≥	PROPN
ejpam-5857	710	10	γ	γ	X
ejpam-5857	710	11	=	=	X
ejpam-5857	710	12	ψf	ψf	X
ejpam-5857	710	13	(	(	PUNCT
ejpam-5857	710	14	x	x	X
ejpam-5857	710	15	)	)	PUNCT
ejpam-5857	710	16	∧	∧	NOUN
ejpam-5857	710	17	ψf	ψf	X
ejpam-5857	710	18	(	(	PUNCT
ejpam-5857	710	19	y	y	NOUN
ejpam-5857	710	20	)	)	PUNCT
ejpam-5857	710	21	≥	≥	NOUN
ejpam-5857	710	22	(	(	PUNCT
ejpam-5857	710	23	ψf	ψf	X
ejpam-5857	710	24	(	(	PUNCT
ejpam-5857	710	25	x	x	NOUN
ejpam-5857	710	26	)	)	PUNCT
ejpam-5857	710	27	∧	∧	NOUN
ejpam-5857	710	28	ψf	ψf	X
ejpam-5857	710	29	(	(	PUNCT
ejpam-5857	710	30	y	y	NOUN
ejpam-5857	710	31	)	)	PUNCT
ejpam-5857	710	32	)	)	PUNCT
ejpam-5857	710	33	∨	∨	NUM
ejpam-5857	710	34	0.5	0.5	NUM
ejpam-5857	710	35	.	.	PUNCT
ejpam-5857	711	1	hence	hence	ADV
ejpam-5857	711	2	,	,	PUNCT
ejpam-5857	711	3	ψ	ψ	X
ejpam-5857	711	4	is	be	AUX
ejpam-5857	711	5	an	an	DET
ejpam-5857	711	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	711	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	711	8	iup	iup	NOUN
ejpam-5857	711	9	-	-	PUNCT
ejpam-5857	711	10	subalgebra	subalgebra	NOUN
ejpam-5857	711	11	of	of	ADP
ejpam-5857	711	12	x.	x.	NOUN
ejpam-5857	711	13	theorem	theorem	VERB
ejpam-5857	711	14	23	23	NUM
ejpam-5857	711	15	.	.	PUNCT
ejpam-5857	712	1	let	let	VERB
ejpam-5857	712	2	for	for	ADP
ejpam-5857	712	3	all	all	DET
ejpam-5857	712	4	α	α	NOUN
ejpam-5857	712	5	,	,	PUNCT
ejpam-5857	712	6	γ	γ	PROPN
ejpam-5857	712	7	∈	∈	PROPN
ejpam-5857	713	1	[	[	X
ejpam-5857	713	2	0.5	0.5	NUM
ejpam-5857	713	3	,	,	PUNCT
ejpam-5857	713	4	1	1	NUM
ejpam-5857	713	5	]	]	PUNCT
ejpam-5857	713	6	and	and	CCONJ
ejpam-5857	713	7	β	β	X
ejpam-5857	713	8	∈	∈	PROPN
ejpam-5857	713	9	[	[	X
ejpam-5857	713	10	0	0	NUM
ejpam-5857	713	11	,	,	PUNCT
ejpam-5857	713	12	0.5	0.5	NUM
ejpam-5857	713	13	)	)	PUNCT
ejpam-5857	713	14	,	,	PUNCT
ejpam-5857	713	15	the	the	DET
ejpam-5857	713	16	sets	set	NOUN
ejpam-5857	713	17	u(ψt	u(ψt	PROPN
ejpam-5857	713	18	;	;	PUNCT
ejpam-5857	713	19	α	α	X
ejpam-5857	713	20	)	)	PUNCT
ejpam-5857	713	21	,	,	PUNCT
ejpam-5857	713	22	l(ψi	l(ψi	PROPN
ejpam-5857	713	23	;	;	PUNCT
ejpam-5857	713	24	β	β	X
ejpam-5857	713	25	)	)	PUNCT
ejpam-5857	713	26	and	and	CCONJ
ejpam-5857	713	27	u(ψf	u(ψf	PROPN
ejpam-5857	713	28	;	;	PUNCT
ejpam-5857	713	29	γ	γ	X
ejpam-5857	713	30	)	)	PUNCT
ejpam-5857	713	31	are	be	AUX
ejpam-5857	713	32	either	either	CCONJ
ejpam-5857	713	33	empty	empty	ADJ
ejpam-5857	713	34	or	or	CCONJ
ejpam-5857	713	35	iup	iup	NOUN
ejpam-5857	713	36	-	-	PUNCT
ejpam-5857	713	37	ideals	ideal	NOUN
ejpam-5857	713	38	of	of	ADP
ejpam-5857	713	39	x.	x.	NOUN
ejpam-5857	713	40	if	if	SCONJ
ejpam-5857	713	41	ψt	ψt	VERB
ejpam-5857	713	42	(	(	PUNCT
ejpam-5857	713	43	x	x	NOUN
ejpam-5857	713	44	)	)	PUNCT
ejpam-5857	713	45	≥	≥	NOUN
ejpam-5857	713	46	0.5	0.5	NUM
ejpam-5857	713	47	,	,	PUNCT
ejpam-5857	713	48	ψi(x	ψi(x	NUM
ejpam-5857	713	49	)	)	PUNCT
ejpam-5857	713	50	<	<	X
ejpam-5857	713	51	0.5	0.5	NUM
ejpam-5857	713	52	and	and	CCONJ
ejpam-5857	713	53	ψf	ψf	X
ejpam-5857	713	54	(	(	PUNCT
ejpam-5857	713	55	x	x	X
ejpam-5857	713	56	)	)	PUNCT
ejpam-5857	713	57	≥	≥	NOUN
ejpam-5857	713	58	0.5	0.5	NUM
ejpam-5857	713	59	.	.	PUNCT
ejpam-5857	714	1	then	then	ADV
ejpam-5857	714	2	ψ	ψ	X
ejpam-5857	714	3	is	be	AUX
ejpam-5857	714	4	an	an	DET
ejpam-5857	714	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	714	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	714	7	iup	iup	NOUN
ejpam-5857	714	8	-	-	PUNCT
ejpam-5857	714	9	ideal	ideal	NOUN
ejpam-5857	714	10	of	of	ADP
ejpam-5857	714	11	x.	x.	PROPN
ejpam-5857	714	12	k.	k.	PROPN
ejpam-5857	714	13	suayngam	suayngam	PROPN
ejpam-5857	714	14	,	,	PUNCT
ejpam-5857	714	15	p.	p.	NOUN
ejpam-5857	714	16	julatha	julatha	PROPN
ejpam-5857	714	17	,	,	PUNCT
ejpam-5857	714	18	w.	w.	PROPN
ejpam-5857	714	19	nakkhasen	nakkhasen	PROPN
ejpam-5857	714	20	,	,	PUNCT
ejpam-5857	714	21	a.	a.	NOUN
ejpam-5857	714	22	iampan	iampan	PROPN
ejpam-5857	714	23	/	/	SYM
ejpam-5857	714	24	eur	eur	PROPN
ejpam-5857	714	25	.	.	PUNCT
ejpam-5857	715	1	j.	j.	PROPN
ejpam-5857	715	2	pure	pure	PROPN
ejpam-5857	715	3	appl	appl	PROPN
ejpam-5857	715	4	.	.	PROPN
ejpam-5857	715	5	math	math	PROPN
ejpam-5857	715	6	,	,	PUNCT
ejpam-5857	715	7	18	18	NUM
ejpam-5857	715	8	(	(	PUNCT
ejpam-5857	715	9	2	2	NUM
ejpam-5857	715	10	)	)	PUNCT
ejpam-5857	715	11	(	(	PUNCT
ejpam-5857	715	12	2025	2025	NUM
ejpam-5857	715	13	)	)	PUNCT
ejpam-5857	715	14	,	,	PUNCT
ejpam-5857	715	15	5857	5857	NUM
ejpam-5857	715	16	24	24	NUM
ejpam-5857	715	17	of	of	ADP
ejpam-5857	715	18	30	30	NUM
ejpam-5857	715	19	proof	proof	NOUN
ejpam-5857	715	20	.	.	PUNCT
ejpam-5857	716	1	assume	assume	VERB
ejpam-5857	716	2	that	that	SCONJ
ejpam-5857	716	3	for	for	ADP
ejpam-5857	716	4	all	all	DET
ejpam-5857	716	5	α	α	NOUN
ejpam-5857	716	6	,	,	PUNCT
ejpam-5857	716	7	γ	γ	PROPN
ejpam-5857	716	8	∈	∈	PROPN
ejpam-5857	717	1	[	[	X
ejpam-5857	717	2	0.5	0.5	NUM
ejpam-5857	717	3	,	,	PUNCT
ejpam-5857	717	4	1	1	NUM
ejpam-5857	717	5	]	]	PUNCT
ejpam-5857	717	6	and	and	CCONJ
ejpam-5857	717	7	β	β	X
ejpam-5857	717	8	∈	∈	PROPN
ejpam-5857	718	1	[	[	X
ejpam-5857	718	2	0	0	NUM
ejpam-5857	718	3	,	,	PUNCT
ejpam-5857	718	4	0.5	0.5	NUM
ejpam-5857	718	5	)	)	PUNCT
ejpam-5857	718	6	,	,	PUNCT
ejpam-5857	718	7	the	the	DET
ejpam-5857	718	8	sets	set	NOUN
ejpam-5857	718	9	u(ψt	u(ψt	PROPN
ejpam-5857	718	10	;	;	PUNCT
ejpam-5857	718	11	α	α	X
ejpam-5857	718	12	)	)	PUNCT
ejpam-5857	718	13	,	,	PUNCT
ejpam-5857	718	14	l(ψi	l(ψi	PROPN
ejpam-5857	718	15	;	;	PUNCT
ejpam-5857	718	16	β	β	X
ejpam-5857	718	17	)	)	PUNCT
ejpam-5857	718	18	and	and	CCONJ
ejpam-5857	718	19	u(ψf	u(ψf	PROPN
ejpam-5857	718	20	;	;	PUNCT
ejpam-5857	718	21	γ	γ	X
ejpam-5857	718	22	)	)	PUNCT
ejpam-5857	718	23	are	be	AUX
ejpam-5857	718	24	either	either	CCONJ
ejpam-5857	718	25	empty	empty	ADJ
ejpam-5857	718	26	or	or	CCONJ
ejpam-5857	718	27	iup	iup	NOUN
ejpam-5857	718	28	-	-	PUNCT
ejpam-5857	718	29	ideals	ideal	NOUN
ejpam-5857	718	30	of	of	ADP
ejpam-5857	718	31	x.	x.	NOUN
ejpam-5857	718	32	let	let	VERB
ejpam-5857	718	33	x	x	SYM
ejpam-5857	718	34	∈	∈	PROPN
ejpam-5857	718	35	x.	x.	NOUN
ejpam-5857	718	36	let	let	VERB
ejpam-5857	718	37	α	α	NOUN
ejpam-5857	718	38	=	=	VERB
ejpam-5857	718	39	ψt	ψt	ADJ
ejpam-5857	718	40	(	(	PUNCT
ejpam-5857	718	41	x	x	NOUN
ejpam-5857	718	42	)	)	PUNCT
ejpam-5857	718	43	.	.	PUNCT
ejpam-5857	719	1	then	then	ADV
ejpam-5857	719	2	ψt	ψt	VERB
ejpam-5857	719	3	(	(	PUNCT
ejpam-5857	719	4	x	x	NOUN
ejpam-5857	719	5	)	)	PUNCT
ejpam-5857	719	6	≥	≥	PROPN
ejpam-5857	719	7	α	α	NOUN
ejpam-5857	719	8	.	.	PUNCT
ejpam-5857	720	1	thus	thus	ADV
ejpam-5857	720	2	,	,	PUNCT
ejpam-5857	720	3	x	x	SYM
ejpam-5857	720	4	∈	∈	PROPN
ejpam-5857	720	5	u(ψt	u(ψt	NOUN
ejpam-5857	720	6	;	;	PUNCT
ejpam-5857	720	7	α	α	X
ejpam-5857	720	8	)	)	PUNCT
ejpam-5857	720	9	̸=	̸=	PROPN
ejpam-5857	720	10	∅.	∅.	NOUN
ejpam-5857	720	11	by	by	ADP
ejpam-5857	720	12	assumption	assumption	NOUN
ejpam-5857	720	13	,	,	PUNCT
ejpam-5857	720	14	we	we	PRON
ejpam-5857	720	15	have	have	VERB
ejpam-5857	720	16	u(ψt	u(ψt	NOUN
ejpam-5857	720	17	;	;	PUNCT
ejpam-5857	720	18	α	α	X
ejpam-5857	720	19	)	)	PUNCT
ejpam-5857	720	20	is	be	AUX
ejpam-5857	720	21	an	an	DET
ejpam-5857	720	22	iup	iup	NOUN
ejpam-5857	720	23	-	-	PUNCT
ejpam-5857	720	24	ideal	ideal	NOUN
ejpam-5857	720	25	of	of	ADP
ejpam-5857	720	26	x.	x.	NOUN
ejpam-5857	720	27	by	by	ADP
ejpam-5857	720	28	the	the	DET
ejpam-5857	720	29	condition	condition	NOUN
ejpam-5857	720	30	(	(	PUNCT
ejpam-5857	720	31	2.18	2.18	NUM
ejpam-5857	720	32	)	)	PUNCT
ejpam-5857	720	33	,	,	PUNCT
ejpam-5857	720	34	we	we	PRON
ejpam-5857	720	35	have	have	VERB
ejpam-5857	720	36	0	0	NUM
ejpam-5857	720	37	∈	∈	PROPN
ejpam-5857	720	38	u(ψt	u(ψt	NOUN
ejpam-5857	720	39	;	;	PUNCT
ejpam-5857	720	40	α	α	X
ejpam-5857	720	41	)	)	PUNCT
ejpam-5857	720	42	.	.	PUNCT
ejpam-5857	721	1	then	then	ADV
ejpam-5857	721	2	ψt	ψt	VERB
ejpam-5857	721	3	(	(	PUNCT
ejpam-5857	721	4	0	0	NUM
ejpam-5857	721	5	)	)	PUNCT
ejpam-5857	721	6	≥	≥	NOUN
ejpam-5857	721	7	α	α	NOUN
ejpam-5857	721	8	=	=	X
ejpam-5857	721	9	ψt	ψt	ADJ
ejpam-5857	721	10	(	(	PUNCT
ejpam-5857	721	11	x	x	NOUN
ejpam-5857	721	12	)	)	PUNCT
ejpam-5857	721	13	.	.	PUNCT
ejpam-5857	722	1	let	let	VERB
ejpam-5857	722	2	x	x	PRON
ejpam-5857	722	3	,	,	PUNCT
ejpam-5857	722	4	y	y	PROPN
ejpam-5857	722	5	,	,	PUNCT
ejpam-5857	722	6	z	z	NOUN
ejpam-5857	722	7	∈	∈	PROPN
ejpam-5857	722	8	x	x	AUX
ejpam-5857	722	9	be	be	AUX
ejpam-5857	722	10	such	such	ADJ
ejpam-5857	722	11	that	that	SCONJ
ejpam-5857	722	12	ψt	ψt	NOUN
ejpam-5857	722	13	(	(	PUNCT
ejpam-5857	722	14	x·(y	x·(y	NOUN
ejpam-5857	722	15	·	·	SYM
ejpam-5857	722	16	z	z	NOUN
ejpam-5857	722	17	)	)	PUNCT
ejpam-5857	722	18	)	)	PUNCT
ejpam-5857	722	19	≥	≥	NOUN
ejpam-5857	722	20	0.5	0.5	NUM
ejpam-5857	722	21	and	and	CCONJ
ejpam-5857	722	22	ψt	ψt	ADJ
ejpam-5857	722	23	(	(	PUNCT
ejpam-5857	722	24	y	y	NOUN
ejpam-5857	722	25	)	)	PUNCT
ejpam-5857	722	26	≥	≥	NOUN
ejpam-5857	722	27	0.5	0.5	NUM
ejpam-5857	722	28	.	.	PUNCT
ejpam-5857	723	1	let	let	VERB
ejpam-5857	723	2	α	α	NOUN
ejpam-5857	723	3	=	=	VERB
ejpam-5857	723	4	ψt	ψt	ADJ
ejpam-5857	723	5	(	(	PUNCT
ejpam-5857	723	6	x·(y	x·(y	NOUN
ejpam-5857	723	7	·	·	SYM
ejpam-5857	723	8	z))∧ψt	z))∧ψt	X
ejpam-5857	723	9	(	(	PUNCT
ejpam-5857	723	10	y	y	PROPN
ejpam-5857	723	11	)	)	PUNCT
ejpam-5857	723	12	.	.	PUNCT
ejpam-5857	724	1	then	then	ADV
ejpam-5857	724	2	ψt	ψt	VERB
ejpam-5857	724	3	(	(	PUNCT
ejpam-5857	724	4	x	x	X
ejpam-5857	724	5	·	·	PUNCT
ejpam-5857	724	6	(	(	PUNCT
ejpam-5857	724	7	y	y	PROPN
ejpam-5857	724	8	·	·	PROPN
ejpam-5857	724	9	z	z	NOUN
ejpam-5857	724	10	)	)	PUNCT
ejpam-5857	724	11	)	)	PUNCT
ejpam-5857	724	12	≥	≥	PROPN
ejpam-5857	724	13	α	α	NOUN
ejpam-5857	724	14	and	and	CCONJ
ejpam-5857	724	15	ψt	ψt	ADJ
ejpam-5857	724	16	(	(	PUNCT
ejpam-5857	724	17	y	y	NOUN
ejpam-5857	724	18	)	)	PUNCT
ejpam-5857	724	19	≥	≥	PROPN
ejpam-5857	724	20	α	α	NOUN
ejpam-5857	724	21	.	.	PUNCT
ejpam-5857	725	1	thus	thus	ADV
ejpam-5857	725	2	,	,	PUNCT
ejpam-5857	725	3	x	x	X
ejpam-5857	725	4	·	·	PUNCT
ejpam-5857	725	5	(	(	PUNCT
ejpam-5857	725	6	y	y	PROPN
ejpam-5857	725	7	·	·	PUNCT
ejpam-5857	725	8	z	z	NOUN
ejpam-5857	725	9	)	)	PUNCT
ejpam-5857	725	10	,	,	PUNCT
ejpam-5857	725	11	y	y	PROPN
ejpam-5857	725	12	∈	∈	PROPN
ejpam-5857	725	13	u(ψt	u(ψt	PROPN
ejpam-5857	725	14	;	;	PUNCT
ejpam-5857	725	15	α	α	X
ejpam-5857	725	16	)	)	PUNCT
ejpam-5857	725	17	̸=	̸=	PROPN
ejpam-5857	725	18	∅.	∅.	NOUN
ejpam-5857	725	19	by	by	ADP
ejpam-5857	725	20	assumption	assumption	NOUN
ejpam-5857	725	21	,	,	PUNCT
ejpam-5857	725	22	we	we	PRON
ejpam-5857	725	23	have	have	VERB
ejpam-5857	725	24	u(ψt	u(ψt	NOUN
ejpam-5857	725	25	;	;	PUNCT
ejpam-5857	725	26	α	α	X
ejpam-5857	725	27	)	)	PUNCT
ejpam-5857	725	28	is	be	AUX
ejpam-5857	725	29	an	an	DET
ejpam-5857	725	30	iup	iup	NOUN
ejpam-5857	725	31	-	-	PUNCT
ejpam-5857	725	32	ideal	ideal	NOUN
ejpam-5857	725	33	of	of	ADP
ejpam-5857	725	34	x.	x.	NOUN
ejpam-5857	725	35	by	by	ADP
ejpam-5857	725	36	the	the	DET
ejpam-5857	725	37	condition	condition	NOUN
ejpam-5857	725	38	(	(	PUNCT
ejpam-5857	725	39	2.20	2.20	NUM
ejpam-5857	725	40	)	)	PUNCT
ejpam-5857	725	41	,	,	PUNCT
ejpam-5857	725	42	we	we	PRON
ejpam-5857	725	43	have	have	VERB
ejpam-5857	725	44	x	x	X
ejpam-5857	725	45	·	·	PUNCT
ejpam-5857	725	46	z	z	SYM
ejpam-5857	725	47	∈	∈	PROPN
ejpam-5857	725	48	u(ψt	u(ψt	PROPN
ejpam-5857	725	49	;	;	PUNCT
ejpam-5857	725	50	α	α	X
ejpam-5857	725	51	)	)	PUNCT
ejpam-5857	725	52	.	.	PUNCT
ejpam-5857	726	1	thus	thus	ADV
ejpam-5857	726	2	,	,	PUNCT
ejpam-5857	726	3	ψt	ψt	VERB
ejpam-5857	726	4	(	(	PUNCT
ejpam-5857	726	5	x	x	X
ejpam-5857	726	6	·	·	PUNCT
ejpam-5857	726	7	z	z	X
ejpam-5857	726	8	)	)	PUNCT
ejpam-5857	726	9	≥	≥	NOUN
ejpam-5857	726	10	α	α	NOUN
ejpam-5857	726	11	=	=	X
ejpam-5857	726	12	ψt	ψt	ADJ
ejpam-5857	726	13	(	(	PUNCT
ejpam-5857	726	14	x	x	X
ejpam-5857	726	15	·	·	PUNCT
ejpam-5857	726	16	(	(	PUNCT
ejpam-5857	726	17	y	y	PROPN
ejpam-5857	726	18	·	·	PUNCT
ejpam-5857	726	19	z	z	NOUN
ejpam-5857	726	20	)	)	PUNCT
ejpam-5857	726	21	)	)	PUNCT
ejpam-5857	727	1	∧	∧	NOUN
ejpam-5857	727	2	ψt	ψt	NOUN
ejpam-5857	727	3	(	(	PUNCT
ejpam-5857	727	4	y	y	NOUN
ejpam-5857	727	5	)	)	PUNCT
ejpam-5857	727	6	≥	≥	NOUN
ejpam-5857	727	7	(	(	PUNCT
ejpam-5857	727	8	ψt	ψt	VERB
ejpam-5857	727	9	(	(	PUNCT
ejpam-5857	727	10	x	x	X
ejpam-5857	727	11	·	·	PUNCT
ejpam-5857	727	12	(	(	PUNCT
ejpam-5857	727	13	y	y	PROPN
ejpam-5857	727	14	·	·	PUNCT
ejpam-5857	727	15	z	z	NOUN
ejpam-5857	727	16	)	)	PUNCT
ejpam-5857	727	17	)	)	PUNCT
ejpam-5857	728	1	∧	∧	NOUN
ejpam-5857	728	2	ψt	ψt	NOUN
ejpam-5857	728	3	(	(	PUNCT
ejpam-5857	728	4	y	y	NOUN
ejpam-5857	728	5	)	)	PUNCT
ejpam-5857	728	6	)	)	PUNCT
ejpam-5857	729	1	∨	∨	NUM
ejpam-5857	729	2	0.5	0.5	NUM
ejpam-5857	729	3	.	.	PUNCT
ejpam-5857	730	1	let	let	VERB
ejpam-5857	730	2	x	x	SYM
ejpam-5857	730	3	∈	∈	PROPN
ejpam-5857	730	4	x.	x.	NOUN
ejpam-5857	730	5	let	let	VERB
ejpam-5857	730	6	β	β	X
ejpam-5857	730	7	=	=	SYM
ejpam-5857	730	8	ψi(x	ψi(x	NUM
ejpam-5857	730	9	)	)	PUNCT
ejpam-5857	730	10	.	.	PUNCT
ejpam-5857	731	1	then	then	ADV
ejpam-5857	731	2	ψi(x	ψi(x	NUM
ejpam-5857	731	3	)	)	PUNCT
ejpam-5857	731	4	≤	≤	NOUN
ejpam-5857	732	1	β	β	X
ejpam-5857	732	2	.	.	PUNCT
ejpam-5857	733	1	thus	thus	ADV
ejpam-5857	733	2	,	,	PUNCT
ejpam-5857	733	3	x	x	SYM
ejpam-5857	733	4	∈	∈	NOUN
ejpam-5857	733	5	l(ψi	l(ψi	NOUN
ejpam-5857	733	6	;	;	PUNCT
ejpam-5857	733	7	β	β	X
ejpam-5857	733	8	)	)	PUNCT
ejpam-5857	733	9	̸=	̸=	PROPN
ejpam-5857	733	10	∅.	∅.	VERB
ejpam-5857	733	11	by	by	ADP
ejpam-5857	733	12	assumption	assumption	NOUN
ejpam-5857	733	13	,	,	PUNCT
ejpam-5857	733	14	we	we	PRON
ejpam-5857	733	15	have	have	VERB
ejpam-5857	733	16	l(ψi	l(ψi	NOUN
ejpam-5857	733	17	;	;	PUNCT
ejpam-5857	733	18	β	β	X
ejpam-5857	733	19	)	)	PUNCT
ejpam-5857	733	20	is	be	AUX
ejpam-5857	733	21	an	an	DET
ejpam-5857	733	22	iup	iup	NOUN
ejpam-5857	733	23	-	-	PUNCT
ejpam-5857	733	24	ideal	ideal	NOUN
ejpam-5857	733	25	of	of	ADP
ejpam-5857	733	26	x.	x.	NOUN
ejpam-5857	733	27	by	by	ADP
ejpam-5857	733	28	the	the	DET
ejpam-5857	733	29	condition	condition	NOUN
ejpam-5857	733	30	(	(	PUNCT
ejpam-5857	733	31	2.18	2.18	NUM
ejpam-5857	733	32	)	)	PUNCT
ejpam-5857	733	33	,	,	PUNCT
ejpam-5857	733	34	we	we	PRON
ejpam-5857	733	35	have	have	VERB
ejpam-5857	733	36	0	0	NUM
ejpam-5857	733	37	∈	∈	NOUN
ejpam-5857	733	38	l(ψi	l(ψi	NOUN
ejpam-5857	733	39	;	;	PUNCT
ejpam-5857	733	40	β	β	X
ejpam-5857	733	41	)	)	PUNCT
ejpam-5857	733	42	.	.	PUNCT
ejpam-5857	734	1	then	then	ADV
ejpam-5857	734	2	ψi(0	ψi(0	PROPN
ejpam-5857	734	3	)	)	PUNCT
ejpam-5857	734	4	≤	≤	NOUN
ejpam-5857	734	5	β	β	X
ejpam-5857	734	6	=	=	PUNCT
ejpam-5857	734	7	ψi(x	ψi(x	NUM
ejpam-5857	734	8	)	)	PUNCT
ejpam-5857	734	9	.	.	PUNCT
ejpam-5857	735	1	let	let	VERB
ejpam-5857	735	2	x	x	PRON
ejpam-5857	735	3	,	,	PUNCT
ejpam-5857	735	4	y	y	PROPN
ejpam-5857	735	5	,	,	PUNCT
ejpam-5857	735	6	z	z	NOUN
ejpam-5857	735	7	∈	∈	PROPN
ejpam-5857	735	8	x	x	AUX
ejpam-5857	735	9	be	be	AUX
ejpam-5857	735	10	such	such	ADJ
ejpam-5857	735	11	that	that	SCONJ
ejpam-5857	735	12	ψi(x	ψi(x	NUM
ejpam-5857	735	13	·	·	PUNCT
ejpam-5857	735	14	(	(	PUNCT
ejpam-5857	735	15	y	y	PROPN
ejpam-5857	735	16	·	·	PUNCT
ejpam-5857	735	17	z	z	X
ejpam-5857	735	18	)	)	PUNCT
ejpam-5857	735	19	)	)	PUNCT
ejpam-5857	735	20	<	<	X
ejpam-5857	735	21	0.5	0.5	NUM
ejpam-5857	735	22	and	and	CCONJ
ejpam-5857	735	23	ψi(y	ψi(y	NUM
ejpam-5857	735	24	)	)	PUNCT
ejpam-5857	735	25	<	<	X
ejpam-5857	735	26	0.5	0.5	NUM
ejpam-5857	735	27	.	.	PUNCT
ejpam-5857	736	1	let	let	VERB
ejpam-5857	736	2	β	β	NOUN
ejpam-5857	736	3	=	=	PUNCT
ejpam-5857	736	4	ψi(x	ψi(x	X
ejpam-5857	736	5	·	·	PUNCT
ejpam-5857	736	6	(	(	PUNCT
ejpam-5857	736	7	y	y	PROPN
ejpam-5857	736	8	·	·	PUNCT
ejpam-5857	736	9	z	z	NOUN
ejpam-5857	736	10	)	)	PUNCT
ejpam-5857	736	11	)	)	PUNCT
ejpam-5857	736	12	∨	∨	NUM
ejpam-5857	736	13	ψi(y	ψi(y	NUM
ejpam-5857	736	14	)	)	PUNCT
ejpam-5857	736	15	.	.	PUNCT
ejpam-5857	737	1	then	then	ADV
ejpam-5857	737	2	ψi(x	ψi(x	NOUN
ejpam-5857	737	3	·	·	PUNCT
ejpam-5857	737	4	(	(	PUNCT
ejpam-5857	737	5	y	y	PROPN
ejpam-5857	737	6	·	·	PUNCT
ejpam-5857	737	7	z	z	NOUN
ejpam-5857	737	8	)	)	PUNCT
ejpam-5857	737	9	)	)	PUNCT
ejpam-5857	737	10	≤	≤	NUM
ejpam-5857	737	11	β	β	X
ejpam-5857	737	12	and	and	CCONJ
ejpam-5857	737	13	ψi(y	ψi(y	NUM
ejpam-5857	737	14	)	)	PUNCT
ejpam-5857	737	15	≤	≤	NOUN
ejpam-5857	737	16	β	β	X
ejpam-5857	737	17	.	.	PUNCT
ejpam-5857	738	1	thus	thus	ADV
ejpam-5857	738	2	,	,	PUNCT
ejpam-5857	738	3	x	x	X
ejpam-5857	738	4	·	·	PUNCT
ejpam-5857	738	5	(	(	PUNCT
ejpam-5857	738	6	y	y	PROPN
ejpam-5857	738	7	·	·	PUNCT
ejpam-5857	738	8	z	z	NOUN
ejpam-5857	738	9	)	)	PUNCT
ejpam-5857	738	10	,	,	PUNCT
ejpam-5857	738	11	y	y	PROPN
ejpam-5857	738	12	∈	∈	PROPN
ejpam-5857	738	13	l(ψi	l(ψi	PROPN
ejpam-5857	738	14	;	;	PUNCT
ejpam-5857	738	15	β	β	X
ejpam-5857	738	16	)	)	PUNCT
ejpam-5857	738	17	̸=	̸=	PROPN
ejpam-5857	738	18	∅.	∅.	VERB
ejpam-5857	738	19	by	by	ADP
ejpam-5857	738	20	assumption	assumption	NOUN
ejpam-5857	738	21	,	,	PUNCT
ejpam-5857	738	22	we	we	PRON
ejpam-5857	738	23	have	have	VERB
ejpam-5857	738	24	u(ψi	u(ψi	NOUN
ejpam-5857	738	25	;	;	PUNCT
ejpam-5857	738	26	β	β	X
ejpam-5857	738	27	)	)	PUNCT
ejpam-5857	738	28	is	be	AUX
ejpam-5857	738	29	an	an	DET
ejpam-5857	738	30	iup	iup	NOUN
ejpam-5857	738	31	-	-	PUNCT
ejpam-5857	738	32	ideal	ideal	NOUN
ejpam-5857	738	33	of	of	ADP
ejpam-5857	738	34	x.	x.	NOUN
ejpam-5857	738	35	by	by	ADP
ejpam-5857	738	36	the	the	DET
ejpam-5857	738	37	condition	condition	NOUN
ejpam-5857	738	38	(	(	PUNCT
ejpam-5857	738	39	2.20	2.20	NUM
ejpam-5857	738	40	)	)	PUNCT
ejpam-5857	738	41	,	,	PUNCT
ejpam-5857	738	42	we	we	PRON
ejpam-5857	738	43	have	have	VERB
ejpam-5857	738	44	x	x	X
ejpam-5857	738	45	·	·	PUNCT
ejpam-5857	738	46	z	z	SYM
ejpam-5857	738	47	∈	∈	PROPN
ejpam-5857	738	48	l(ψi	l(ψi	PROPN
ejpam-5857	738	49	;	;	PUNCT
ejpam-5857	738	50	β	β	X
ejpam-5857	738	51	)	)	PUNCT
ejpam-5857	738	52	.	.	PUNCT
ejpam-5857	739	1	thus	thus	ADV
ejpam-5857	739	2	,	,	PUNCT
ejpam-5857	739	3	ψi(x	ψi(x	X
ejpam-5857	739	4	·	·	PUNCT
ejpam-5857	739	5	z	z	X
ejpam-5857	739	6	)	)	PUNCT
ejpam-5857	739	7	≤	≤	NOUN
ejpam-5857	739	8	β	β	X
ejpam-5857	739	9	=	=	SYM
ejpam-5857	739	10	ψi(x	ψi(x	X
ejpam-5857	739	11	·	·	PUNCT
ejpam-5857	739	12	(	(	PUNCT
ejpam-5857	739	13	y	y	PROPN
ejpam-5857	739	14	·	·	PUNCT
ejpam-5857	739	15	z	z	NOUN
ejpam-5857	739	16	)	)	PUNCT
ejpam-5857	739	17	)	)	PUNCT
ejpam-5857	740	1	∨	∨	NUM
ejpam-5857	740	2	ψi(y	ψi(y	NUM
ejpam-5857	740	3	)	)	PUNCT
ejpam-5857	740	4	≤	≤	NOUN
ejpam-5857	740	5	(	(	PUNCT
ejpam-5857	740	6	ψi(x	ψi(x	X
ejpam-5857	740	7	·	·	PUNCT
ejpam-5857	740	8	(	(	PUNCT
ejpam-5857	740	9	y	y	PROPN
ejpam-5857	740	10	·	·	PUNCT
ejpam-5857	740	11	z	z	NOUN
ejpam-5857	740	12	)	)	PUNCT
ejpam-5857	740	13	)	)	PUNCT
ejpam-5857	740	14	∨	∨	NUM
ejpam-5857	740	15	ψi(y	ψi(y	NUM
ejpam-5857	740	16	)	)	PUNCT
ejpam-5857	740	17	)	)	PUNCT
ejpam-5857	741	1	∧	∧	NOUN
ejpam-5857	741	2	0.5	0.5	NUM
ejpam-5857	741	3	.	.	PUNCT
ejpam-5857	742	1	let	let	VERB
ejpam-5857	742	2	x	x	SYM
ejpam-5857	742	3	∈	∈	PROPN
ejpam-5857	742	4	x.	x.	NOUN
ejpam-5857	742	5	let	let	VERB
ejpam-5857	742	6	γ	γ	X
ejpam-5857	742	7	=	=	PRON
ejpam-5857	742	8	ψf	ψf	X
ejpam-5857	742	9	(	(	PUNCT
ejpam-5857	742	10	x	x	NOUN
ejpam-5857	742	11	)	)	PUNCT
ejpam-5857	742	12	.	.	PUNCT
ejpam-5857	743	1	then	then	ADV
ejpam-5857	743	2	ψf	ψf	X
ejpam-5857	743	3	(	(	PUNCT
ejpam-5857	743	4	x	x	X
ejpam-5857	743	5	)	)	PUNCT
ejpam-5857	743	6	≥	≥	PROPN
ejpam-5857	743	7	γ	γ	PROPN
ejpam-5857	743	8	.	.	PUNCT
ejpam-5857	743	9	thus	thus	ADV
ejpam-5857	743	10	,	,	PUNCT
ejpam-5857	743	11	x	x	SYM
ejpam-5857	743	12	∈	∈	PROPN
ejpam-5857	743	13	u(ψf	u(ψf	PROPN
ejpam-5857	743	14	;	;	PUNCT
ejpam-5857	743	15	γ	γ	X
ejpam-5857	743	16	)	)	PUNCT
ejpam-5857	743	17	̸=	̸=	PROPN
ejpam-5857	743	18	∅.	∅.	VERB
ejpam-5857	743	19	by	by	ADP
ejpam-5857	743	20	assumption	assumption	NOUN
ejpam-5857	743	21	,	,	PUNCT
ejpam-5857	743	22	we	we	PRON
ejpam-5857	743	23	have	have	VERB
ejpam-5857	743	24	u(ψf	u(ψf	PROPN
ejpam-5857	743	25	;	;	PUNCT
ejpam-5857	743	26	γ	γ	X
ejpam-5857	743	27	)	)	PUNCT
ejpam-5857	743	28	is	be	AUX
ejpam-5857	743	29	an	an	DET
ejpam-5857	743	30	iup	iup	NOUN
ejpam-5857	743	31	-	-	PUNCT
ejpam-5857	743	32	ideal	ideal	NOUN
ejpam-5857	743	33	of	of	ADP
ejpam-5857	743	34	x.	x.	NOUN
ejpam-5857	743	35	by	by	ADP
ejpam-5857	743	36	the	the	DET
ejpam-5857	743	37	condition	condition	NOUN
ejpam-5857	743	38	(	(	PUNCT
ejpam-5857	743	39	2.18	2.18	NUM
ejpam-5857	743	40	)	)	PUNCT
ejpam-5857	743	41	,	,	PUNCT
ejpam-5857	743	42	we	we	PRON
ejpam-5857	743	43	have	have	VERB
ejpam-5857	743	44	0	0	NUM
ejpam-5857	743	45	∈	∈	PROPN
ejpam-5857	743	46	u(ψf	u(ψf	PROPN
ejpam-5857	743	47	;	;	PUNCT
ejpam-5857	743	48	γ	γ	X
ejpam-5857	743	49	)	)	PUNCT
ejpam-5857	743	50	.	.	PUNCT
ejpam-5857	744	1	then	then	ADV
ejpam-5857	744	2	ψf	ψf	X
ejpam-5857	744	3	(	(	PUNCT
ejpam-5857	744	4	0	0	NUM
ejpam-5857	744	5	)	)	PUNCT
ejpam-5857	744	6	≥	≥	NOUN
ejpam-5857	744	7	γ	γ	X
ejpam-5857	744	8	=	=	X
ejpam-5857	744	9	ψf	ψf	X
ejpam-5857	744	10	(	(	PUNCT
ejpam-5857	744	11	x	x	NOUN
ejpam-5857	744	12	)	)	PUNCT
ejpam-5857	744	13	.	.	PUNCT
ejpam-5857	745	1	let	let	VERB
ejpam-5857	745	2	x	x	PRON
ejpam-5857	745	3	,	,	PUNCT
ejpam-5857	745	4	y	y	PROPN
ejpam-5857	745	5	,	,	PUNCT
ejpam-5857	745	6	z	z	NOUN
ejpam-5857	745	7	∈	∈	PROPN
ejpam-5857	745	8	x	x	AUX
ejpam-5857	745	9	be	be	AUX
ejpam-5857	745	10	such	such	ADJ
ejpam-5857	745	11	that	that	SCONJ
ejpam-5857	745	12	ψf	ψf	X
ejpam-5857	745	13	(	(	PUNCT
ejpam-5857	745	14	x	x	X
ejpam-5857	745	15	·	·	PUNCT
ejpam-5857	745	16	(	(	PUNCT
ejpam-5857	745	17	y	y	PROPN
ejpam-5857	745	18	·	·	PUNCT
ejpam-5857	745	19	z	z	NOUN
ejpam-5857	745	20	)	)	PUNCT
ejpam-5857	745	21	)	)	PUNCT
ejpam-5857	745	22	≥	≥	NOUN
ejpam-5857	745	23	0.5	0.5	NUM
ejpam-5857	745	24	and	and	CCONJ
ejpam-5857	745	25	ψf	ψf	X
ejpam-5857	745	26	(	(	PUNCT
ejpam-5857	745	27	y	y	PROPN
ejpam-5857	745	28	)	)	PUNCT
ejpam-5857	745	29	≥	≥	NOUN
ejpam-5857	745	30	0.5	0.5	NUM
ejpam-5857	745	31	.	.	PUNCT
ejpam-5857	746	1	let	let	VERB
ejpam-5857	746	2	γ	γ	X
ejpam-5857	746	3	=	=	PRON
ejpam-5857	746	4	ψf	ψf	X
ejpam-5857	746	5	(	(	PUNCT
ejpam-5857	746	6	x	x	X
ejpam-5857	746	7	·	·	PUNCT
ejpam-5857	746	8	(	(	PUNCT
ejpam-5857	746	9	y	y	PROPN
ejpam-5857	746	10	·	·	SYM
ejpam-5857	746	11	z))∧ψf	z))∧ψf	X
ejpam-5857	746	12	(	(	PUNCT
ejpam-5857	746	13	y	y	NOUN
ejpam-5857	746	14	)	)	PUNCT
ejpam-5857	746	15	.	.	PUNCT
ejpam-5857	747	1	then	then	ADV
ejpam-5857	747	2	ψf	ψf	X
ejpam-5857	747	3	(	(	PUNCT
ejpam-5857	747	4	x	x	X
ejpam-5857	747	5	·	·	PUNCT
ejpam-5857	747	6	(	(	PUNCT
ejpam-5857	747	7	y	y	PROPN
ejpam-5857	747	8	·	·	PROPN
ejpam-5857	747	9	z	z	NOUN
ejpam-5857	747	10	)	)	PUNCT
ejpam-5857	747	11	)	)	PUNCT
ejpam-5857	747	12	≥	≥	PROPN
ejpam-5857	747	13	γ	γ	PROPN
ejpam-5857	747	14	and	and	CCONJ
ejpam-5857	747	15	ψf	ψf	X
ejpam-5857	747	16	(	(	PUNCT
ejpam-5857	747	17	y	y	PROPN
ejpam-5857	747	18	)	)	PUNCT
ejpam-5857	747	19	≥	≥	PROPN
ejpam-5857	747	20	γ	γ	PROPN
ejpam-5857	747	21	.	.	PUNCT
ejpam-5857	747	22	thus	thus	ADV
ejpam-5857	747	23	,	,	PUNCT
ejpam-5857	747	24	x	x	X
ejpam-5857	747	25	·	·	PUNCT
ejpam-5857	747	26	(	(	PUNCT
ejpam-5857	747	27	y	y	PROPN
ejpam-5857	747	28	·	·	PROPN
ejpam-5857	747	29	z	z	NOUN
ejpam-5857	747	30	)	)	PUNCT
ejpam-5857	747	31	,	,	PUNCT
ejpam-5857	747	32	y	y	PROPN
ejpam-5857	747	33	∈	∈	PROPN
ejpam-5857	747	34	u(ψf	u(ψf	PROPN
ejpam-5857	747	35	;	;	PUNCT
ejpam-5857	747	36	γ	γ	X
ejpam-5857	747	37	)	)	PUNCT
ejpam-5857	747	38	̸=	̸=	PROPN
ejpam-5857	747	39	∅.	∅.	VERB
ejpam-5857	747	40	by	by	ADP
ejpam-5857	747	41	assumption	assumption	NOUN
ejpam-5857	747	42	,	,	PUNCT
ejpam-5857	747	43	we	we	PRON
ejpam-5857	747	44	have	have	VERB
ejpam-5857	747	45	u(ψf	u(ψf	PROPN
ejpam-5857	747	46	;	;	PUNCT
ejpam-5857	747	47	γ	γ	X
ejpam-5857	747	48	)	)	PUNCT
ejpam-5857	747	49	is	be	AUX
ejpam-5857	747	50	an	an	DET
ejpam-5857	747	51	iup	iup	NOUN
ejpam-5857	747	52	-	-	PUNCT
ejpam-5857	747	53	ideal	ideal	NOUN
ejpam-5857	747	54	of	of	ADP
ejpam-5857	747	55	x.	x.	NOUN
ejpam-5857	747	56	by	by	ADP
ejpam-5857	747	57	the	the	DET
ejpam-5857	747	58	condition	condition	NOUN
ejpam-5857	747	59	(	(	PUNCT
ejpam-5857	747	60	2.20	2.20	NUM
ejpam-5857	747	61	)	)	PUNCT
ejpam-5857	747	62	,	,	PUNCT
ejpam-5857	747	63	we	we	PRON
ejpam-5857	747	64	have	have	VERB
ejpam-5857	747	65	x	x	X
ejpam-5857	747	66	·	·	PUNCT
ejpam-5857	747	67	z	z	SYM
ejpam-5857	747	68	∈	∈	PROPN
ejpam-5857	747	69	u(ψf	u(ψf	PROPN
ejpam-5857	747	70	;	;	PUNCT
ejpam-5857	747	71	γ	γ	X
ejpam-5857	747	72	)	)	PUNCT
ejpam-5857	747	73	.	.	PUNCT
ejpam-5857	748	1	thus	thus	ADV
ejpam-5857	748	2	,	,	PUNCT
ejpam-5857	748	3	ψf	ψf	X
ejpam-5857	748	4	(	(	PUNCT
ejpam-5857	748	5	x	x	X
ejpam-5857	748	6	·	·	PUNCT
ejpam-5857	748	7	z	z	X
ejpam-5857	748	8	)	)	PUNCT
ejpam-5857	748	9	≥	≥	PROPN
ejpam-5857	748	10	γ	γ	X
ejpam-5857	748	11	=	=	X
ejpam-5857	748	12	ψf	ψf	X
ejpam-5857	748	13	(	(	PUNCT
ejpam-5857	748	14	x	x	X
ejpam-5857	748	15	·	·	PUNCT
ejpam-5857	748	16	(	(	PUNCT
ejpam-5857	748	17	y	y	X
ejpam-5857	748	18	·	·	PUNCT
ejpam-5857	748	19	z))∧ψf	z))∧ψf	X
ejpam-5857	748	20	(	(	PUNCT
ejpam-5857	748	21	y	y	NOUN
ejpam-5857	748	22	)	)	PUNCT
ejpam-5857	748	23	≥	≥	NOUN
ejpam-5857	748	24	(	(	PUNCT
ejpam-5857	748	25	ψf	ψf	X
ejpam-5857	748	26	(	(	PUNCT
ejpam-5857	748	27	x	x	X
ejpam-5857	748	28	·	·	PUNCT
ejpam-5857	748	29	(	(	PUNCT
ejpam-5857	748	30	y	y	PROPN
ejpam-5857	748	31	·	·	PUNCT
ejpam-5857	748	32	z	z	NOUN
ejpam-5857	748	33	)	)	PUNCT
ejpam-5857	748	34	)	)	PUNCT
ejpam-5857	748	35	∧	∧	NOUN
ejpam-5857	748	36	ψf	ψf	X
ejpam-5857	748	37	(	(	PUNCT
ejpam-5857	748	38	y	y	NOUN
ejpam-5857	748	39	)	)	PUNCT
ejpam-5857	748	40	)	)	PUNCT
ejpam-5857	748	41	∨	∨	NUM
ejpam-5857	748	42	0.5	0.5	NUM
ejpam-5857	748	43	.	.	PUNCT
ejpam-5857	749	1	hence	hence	ADV
ejpam-5857	749	2	,	,	PUNCT
ejpam-5857	749	3	ψ	ψ	X
ejpam-5857	749	4	is	be	AUX
ejpam-5857	749	5	an	an	DET
ejpam-5857	749	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	749	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	749	8	iup	iup	NOUN
ejpam-5857	749	9	-	-	PUNCT
ejpam-5857	749	10	ideal	ideal	NOUN
ejpam-5857	749	11	of	of	ADP
ejpam-5857	749	12	x.	x.	PROPN
ejpam-5857	749	13	theorem	theorem	VERB
ejpam-5857	749	14	24	24	NUM
ejpam-5857	749	15	.	.	PUNCT
ejpam-5857	750	1	let	let	VERB
ejpam-5857	750	2	for	for	ADP
ejpam-5857	750	3	all	all	DET
ejpam-5857	750	4	α	α	NOUN
ejpam-5857	750	5	,	,	PUNCT
ejpam-5857	750	6	γ	γ	PROPN
ejpam-5857	750	7	∈	∈	PROPN
ejpam-5857	751	1	[	[	X
ejpam-5857	751	2	0.5	0.5	NUM
ejpam-5857	751	3	,	,	PUNCT
ejpam-5857	751	4	1	1	NUM
ejpam-5857	751	5	]	]	PUNCT
ejpam-5857	751	6	and	and	CCONJ
ejpam-5857	751	7	β	β	X
ejpam-5857	751	8	∈	∈	PROPN
ejpam-5857	751	9	[	[	X
ejpam-5857	751	10	0	0	NUM
ejpam-5857	751	11	,	,	PUNCT
ejpam-5857	751	12	0.5	0.5	NUM
ejpam-5857	751	13	)	)	PUNCT
ejpam-5857	751	14	,	,	PUNCT
ejpam-5857	751	15	the	the	DET
ejpam-5857	751	16	sets	set	NOUN
ejpam-5857	751	17	u(ψt	u(ψt	PROPN
ejpam-5857	751	18	;	;	PUNCT
ejpam-5857	751	19	α	α	X
ejpam-5857	751	20	)	)	PUNCT
ejpam-5857	751	21	,	,	PUNCT
ejpam-5857	751	22	l(ψi	l(ψi	PROPN
ejpam-5857	751	23	;	;	PUNCT
ejpam-5857	751	24	β	β	X
ejpam-5857	751	25	)	)	PUNCT
ejpam-5857	751	26	and	and	CCONJ
ejpam-5857	751	27	u(ψf	u(ψf	PROPN
ejpam-5857	751	28	;	;	PUNCT
ejpam-5857	751	29	γ	γ	X
ejpam-5857	751	30	)	)	PUNCT
ejpam-5857	751	31	are	be	AUX
ejpam-5857	751	32	either	either	CCONJ
ejpam-5857	751	33	empty	empty	ADJ
ejpam-5857	751	34	or	or	CCONJ
ejpam-5857	751	35	iup	iup	NOUN
ejpam-5857	751	36	-	-	PUNCT
ejpam-5857	751	37	filters	filter	NOUN
ejpam-5857	751	38	of	of	ADP
ejpam-5857	751	39	x.	x.	NOUN
ejpam-5857	751	40	if	if	SCONJ
ejpam-5857	751	41	ψt	ψt	VERB
ejpam-5857	751	42	(	(	PUNCT
ejpam-5857	751	43	x	x	NOUN
ejpam-5857	751	44	)	)	PUNCT
ejpam-5857	751	45	≥	≥	NOUN
ejpam-5857	751	46	0.5	0.5	NUM
ejpam-5857	751	47	,	,	PUNCT
ejpam-5857	751	48	ψi(x	ψi(x	NUM
ejpam-5857	751	49	)	)	PUNCT
ejpam-5857	751	50	<	<	X
ejpam-5857	751	51	0.5	0.5	NUM
ejpam-5857	751	52	and	and	CCONJ
ejpam-5857	751	53	ψf	ψf	X
ejpam-5857	751	54	(	(	PUNCT
ejpam-5857	751	55	x	x	X
ejpam-5857	751	56	)	)	PUNCT
ejpam-5857	751	57	≥	≥	NOUN
ejpam-5857	751	58	0.5	0.5	NUM
ejpam-5857	751	59	.	.	PUNCT
ejpam-5857	752	1	then	then	ADV
ejpam-5857	752	2	ψ	ψ	X
ejpam-5857	752	3	is	be	AUX
ejpam-5857	752	4	an	an	DET
ejpam-5857	752	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	752	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	752	7	iup	iup	NOUN
ejpam-5857	752	8	-	-	PUNCT
ejpam-5857	752	9	filter	filter	NOUN
ejpam-5857	752	10	of	of	ADP
ejpam-5857	752	11	x.	x.	NOUN
ejpam-5857	752	12	proof	proof	PROPN
ejpam-5857	752	13	.	.	PUNCT
ejpam-5857	753	1	assume	assume	VERB
ejpam-5857	753	2	that	that	SCONJ
ejpam-5857	753	3	for	for	ADP
ejpam-5857	753	4	all	all	DET
ejpam-5857	753	5	α	α	NOUN
ejpam-5857	753	6	,	,	PUNCT
ejpam-5857	753	7	γ	γ	PROPN
ejpam-5857	753	8	∈	∈	PROPN
ejpam-5857	754	1	[	[	X
ejpam-5857	754	2	0.5	0.5	NUM
ejpam-5857	754	3	,	,	PUNCT
ejpam-5857	754	4	1	1	NUM
ejpam-5857	754	5	]	]	PUNCT
ejpam-5857	754	6	and	and	CCONJ
ejpam-5857	754	7	β	β	X
ejpam-5857	754	8	∈	∈	PROPN
ejpam-5857	755	1	[	[	X
ejpam-5857	755	2	0	0	NUM
ejpam-5857	755	3	,	,	PUNCT
ejpam-5857	755	4	0.5	0.5	NUM
ejpam-5857	755	5	)	)	PUNCT
ejpam-5857	755	6	,	,	PUNCT
ejpam-5857	755	7	the	the	DET
ejpam-5857	755	8	sets	set	NOUN
ejpam-5857	755	9	u(ψt	u(ψt	PROPN
ejpam-5857	755	10	;	;	PUNCT
ejpam-5857	755	11	α	α	X
ejpam-5857	755	12	)	)	PUNCT
ejpam-5857	755	13	,	,	PUNCT
ejpam-5857	755	14	l(ψi	l(ψi	PROPN
ejpam-5857	755	15	;	;	PUNCT
ejpam-5857	755	16	β	β	X
ejpam-5857	755	17	)	)	PUNCT
ejpam-5857	755	18	and	and	CCONJ
ejpam-5857	755	19	u(ψf	u(ψf	PROPN
ejpam-5857	755	20	;	;	PUNCT
ejpam-5857	755	21	γ	γ	X
ejpam-5857	755	22	)	)	PUNCT
ejpam-5857	755	23	are	be	AUX
ejpam-5857	755	24	either	either	CCONJ
ejpam-5857	755	25	empty	empty	ADJ
ejpam-5857	755	26	or	or	CCONJ
ejpam-5857	755	27	iup	iup	NOUN
ejpam-5857	755	28	-	-	PUNCT
ejpam-5857	755	29	filters	filter	NOUN
ejpam-5857	755	30	of	of	ADP
ejpam-5857	755	31	x.	x.	NOUN
ejpam-5857	755	32	let	let	VERB
ejpam-5857	755	33	x	x	SYM
ejpam-5857	755	34	∈	∈	PROPN
ejpam-5857	755	35	x.	x.	NOUN
ejpam-5857	755	36	let	let	VERB
ejpam-5857	755	37	α	α	NOUN
ejpam-5857	755	38	=	=	VERB
ejpam-5857	755	39	ψt	ψt	ADJ
ejpam-5857	755	40	(	(	PUNCT
ejpam-5857	755	41	x	x	NOUN
ejpam-5857	755	42	)	)	PUNCT
ejpam-5857	755	43	.	.	PUNCT
ejpam-5857	756	1	then	then	ADV
ejpam-5857	756	2	ψt	ψt	VERB
ejpam-5857	756	3	(	(	PUNCT
ejpam-5857	756	4	x	x	NOUN
ejpam-5857	756	5	)	)	PUNCT
ejpam-5857	756	6	≥	≥	PROPN
ejpam-5857	756	7	α	α	NOUN
ejpam-5857	756	8	.	.	PUNCT
ejpam-5857	757	1	thus	thus	ADV
ejpam-5857	757	2	,	,	PUNCT
ejpam-5857	757	3	x	x	SYM
ejpam-5857	757	4	∈	∈	PROPN
ejpam-5857	757	5	u(ψt	u(ψt	NOUN
ejpam-5857	757	6	;	;	PUNCT
ejpam-5857	757	7	α	α	X
ejpam-5857	757	8	)	)	PUNCT
ejpam-5857	757	9	̸=	̸=	PROPN
ejpam-5857	757	10	∅.	∅.	NOUN
ejpam-5857	757	11	by	by	ADP
ejpam-5857	757	12	assumption	assumption	NOUN
ejpam-5857	757	13	,	,	PUNCT
ejpam-5857	757	14	we	we	PRON
ejpam-5857	757	15	have	have	VERB
ejpam-5857	757	16	u(ψt	u(ψt	NOUN
ejpam-5857	757	17	;	;	PUNCT
ejpam-5857	757	18	α	α	X
ejpam-5857	757	19	)	)	PUNCT
ejpam-5857	757	20	is	be	AUX
ejpam-5857	757	21	an	an	DET
ejpam-5857	757	22	iup	iup	NOUN
ejpam-5857	757	23	-	-	PUNCT
ejpam-5857	757	24	filter	filter	NOUN
ejpam-5857	757	25	of	of	ADP
ejpam-5857	757	26	x.	x.	NOUN
ejpam-5857	757	27	by	by	ADP
ejpam-5857	757	28	the	the	DET
ejpam-5857	757	29	condition	condition	NOUN
ejpam-5857	757	30	(	(	PUNCT
ejpam-5857	757	31	2.18	2.18	NUM
ejpam-5857	757	32	)	)	PUNCT
ejpam-5857	757	33	,	,	PUNCT
ejpam-5857	757	34	we	we	PRON
ejpam-5857	757	35	have	have	VERB
ejpam-5857	757	36	0	0	NUM
ejpam-5857	757	37	∈	∈	PROPN
ejpam-5857	757	38	u(ψt	u(ψt	NOUN
ejpam-5857	757	39	;	;	PUNCT
ejpam-5857	757	40	α	α	X
ejpam-5857	757	41	)	)	PUNCT
ejpam-5857	757	42	.	.	PUNCT
ejpam-5857	758	1	then	then	ADV
ejpam-5857	758	2	ψt	ψt	VERB
ejpam-5857	758	3	(	(	PUNCT
ejpam-5857	758	4	0	0	NUM
ejpam-5857	758	5	)	)	PUNCT
ejpam-5857	758	6	≥	≥	NOUN
ejpam-5857	758	7	α	α	NOUN
ejpam-5857	758	8	=	=	X
ejpam-5857	758	9	ψt	ψt	ADJ
ejpam-5857	758	10	(	(	PUNCT
ejpam-5857	758	11	x	x	NOUN
ejpam-5857	758	12	)	)	PUNCT
ejpam-5857	758	13	.	.	PUNCT
ejpam-5857	759	1	let	let	VERB
ejpam-5857	759	2	x	x	PRON
ejpam-5857	759	3	,	,	PUNCT
ejpam-5857	759	4	y	y	PROPN
ejpam-5857	759	5	∈	∈	PROPN
ejpam-5857	759	6	x	x	AUX
ejpam-5857	759	7	be	be	AUX
ejpam-5857	759	8	such	such	ADJ
ejpam-5857	759	9	that	that	SCONJ
ejpam-5857	759	10	ψt	ψt	NOUN
ejpam-5857	759	11	(	(	PUNCT
ejpam-5857	759	12	x	x	PROPN
ejpam-5857	759	13	·	·	PUNCT
ejpam-5857	759	14	y	y	X
ejpam-5857	759	15	)	)	PUNCT
ejpam-5857	759	16	≥	≥	NOUN
ejpam-5857	759	17	0.5	0.5	NUM
ejpam-5857	759	18	and	and	CCONJ
ejpam-5857	759	19	ψt	ψt	ADJ
ejpam-5857	759	20	(	(	PUNCT
ejpam-5857	759	21	x	x	NOUN
ejpam-5857	759	22	)	)	PUNCT
ejpam-5857	759	23	≥	≥	NOUN
ejpam-5857	759	24	0.5	0.5	NUM
ejpam-5857	759	25	.	.	PUNCT
ejpam-5857	760	1	let	let	VERB
ejpam-5857	760	2	α	α	NOUN
ejpam-5857	760	3	=	=	VERB
ejpam-5857	760	4	ψt	ψt	ADJ
ejpam-5857	760	5	(	(	PUNCT
ejpam-5857	760	6	x	x	PROPN
ejpam-5857	760	7	·	·	PUNCT
ejpam-5857	760	8	y	y	X
ejpam-5857	760	9	)	)	PUNCT
ejpam-5857	760	10	∧	∧	NOUN
ejpam-5857	760	11	ψt	ψt	NOUN
ejpam-5857	760	12	(	(	PUNCT
ejpam-5857	760	13	x	x	NOUN
ejpam-5857	760	14	)	)	PUNCT
ejpam-5857	760	15	.	.	PUNCT
ejpam-5857	761	1	then	then	ADV
ejpam-5857	761	2	ψt	ψt	VERB
ejpam-5857	761	3	(	(	PUNCT
ejpam-5857	761	4	x	x	PROPN
ejpam-5857	761	5	·	·	PUNCT
ejpam-5857	761	6	y	y	X
ejpam-5857	761	7	)	)	PUNCT
ejpam-5857	761	8	≥	≥	NOUN
ejpam-5857	761	9	α	α	NOUN
ejpam-5857	761	10	and	and	CCONJ
ejpam-5857	761	11	ψt	ψt	ADJ
ejpam-5857	761	12	(	(	PUNCT
ejpam-5857	761	13	x	x	NOUN
ejpam-5857	761	14	)	)	PUNCT
ejpam-5857	761	15	≥	≥	PROPN
ejpam-5857	761	16	α	α	NOUN
ejpam-5857	761	17	.	.	PUNCT
ejpam-5857	762	1	thus	thus	ADV
ejpam-5857	762	2	,	,	PUNCT
ejpam-5857	762	3	x	x	X
ejpam-5857	762	4	·	·	PUNCT
ejpam-5857	762	5	y	y	X
ejpam-5857	762	6	,	,	PUNCT
ejpam-5857	762	7	x	x	SYM
ejpam-5857	762	8	∈	∈	PROPN
ejpam-5857	762	9	u(ψt	u(ψt	NOUN
ejpam-5857	762	10	;	;	PUNCT
ejpam-5857	762	11	α	α	X
ejpam-5857	762	12	)	)	PUNCT
ejpam-5857	762	13	̸=	̸=	PROPN
ejpam-5857	762	14	∅.	∅.	NOUN
ejpam-5857	762	15	by	by	ADP
ejpam-5857	762	16	assumption	assumption	NOUN
ejpam-5857	762	17	,	,	PUNCT
ejpam-5857	762	18	we	we	PRON
ejpam-5857	762	19	have	have	VERB
ejpam-5857	762	20	u(ψt	u(ψt	NOUN
ejpam-5857	762	21	;	;	PUNCT
ejpam-5857	762	22	α	α	X
ejpam-5857	762	23	)	)	PUNCT
ejpam-5857	762	24	is	be	AUX
ejpam-5857	762	25	an	an	DET
ejpam-5857	762	26	iup	iup	NOUN
ejpam-5857	762	27	-	-	PUNCT
ejpam-5857	762	28	filter	filter	NOUN
ejpam-5857	762	29	of	of	ADP
ejpam-5857	762	30	x.	x.	NOUN
ejpam-5857	762	31	by	by	ADP
ejpam-5857	762	32	the	the	DET
ejpam-5857	762	33	condition	condition	NOUN
ejpam-5857	762	34	(	(	PUNCT
ejpam-5857	762	35	2.19	2.19	NUM
ejpam-5857	762	36	)	)	PUNCT
ejpam-5857	762	37	,	,	PUNCT
ejpam-5857	762	38	we	we	PRON
ejpam-5857	762	39	have	have	VERB
ejpam-5857	762	40	y	y	PROPN
ejpam-5857	762	41	∈	∈	PROPN
ejpam-5857	762	42	u(ψt	u(ψt	PROPN
ejpam-5857	762	43	;	;	PUNCT
ejpam-5857	762	44	α	α	X
ejpam-5857	762	45	)	)	PUNCT
ejpam-5857	762	46	.	.	PUNCT
ejpam-5857	763	1	thus	thus	ADV
ejpam-5857	763	2	,	,	PUNCT
ejpam-5857	763	3	ψt	ψt	NUM
ejpam-5857	763	4	(	(	PUNCT
ejpam-5857	763	5	y	y	NOUN
ejpam-5857	763	6	)	)	PUNCT
ejpam-5857	763	7	≥	≥	NOUN
ejpam-5857	763	8	α	α	NOUN
ejpam-5857	763	9	=	=	X
ejpam-5857	763	10	ψt	ψt	ADJ
ejpam-5857	763	11	(	(	PUNCT
ejpam-5857	763	12	x	x	PROPN
ejpam-5857	763	13	·	·	PUNCT
ejpam-5857	763	14	y	y	X
ejpam-5857	763	15	)	)	PUNCT
ejpam-5857	763	16	∧	∧	NOUN
ejpam-5857	763	17	ψt	ψt	NUM
ejpam-5857	763	18	(	(	PUNCT
ejpam-5857	763	19	x	x	NOUN
ejpam-5857	763	20	)	)	PUNCT
ejpam-5857	763	21	≥	≥	NOUN
ejpam-5857	763	22	(	(	PUNCT
ejpam-5857	763	23	ψt	ψt	VERB
ejpam-5857	763	24	(	(	PUNCT
ejpam-5857	763	25	x	x	PROPN
ejpam-5857	763	26	·	·	PUNCT
ejpam-5857	763	27	y	y	X
ejpam-5857	763	28	)	)	PUNCT
ejpam-5857	763	29	∧	∧	NOUN
ejpam-5857	763	30	ψt	ψt	NOUN
ejpam-5857	763	31	(	(	PUNCT
ejpam-5857	763	32	x	x	NOUN
ejpam-5857	763	33	)	)	PUNCT
ejpam-5857	763	34	)	)	PUNCT
ejpam-5857	763	35	∨	∨	NUM
ejpam-5857	763	36	0.5	0.5	NUM
ejpam-5857	763	37	.	.	PUNCT
ejpam-5857	763	38	let	let	VERB
ejpam-5857	763	39	x	x	SYM
ejpam-5857	763	40	∈	∈	PROPN
ejpam-5857	763	41	x.	x.	NOUN
ejpam-5857	763	42	let	let	VERB
ejpam-5857	763	43	β	β	X
ejpam-5857	763	44	=	=	SYM
ejpam-5857	763	45	ψi(x	ψi(x	NUM
ejpam-5857	763	46	)	)	PUNCT
ejpam-5857	763	47	.	.	PUNCT
ejpam-5857	764	1	then	then	ADV
ejpam-5857	764	2	ψi(x	ψi(x	NUM
ejpam-5857	764	3	)	)	PUNCT
ejpam-5857	764	4	≤	≤	NOUN
ejpam-5857	765	1	β	β	X
ejpam-5857	765	2	.	.	PUNCT
ejpam-5857	766	1	thus	thus	ADV
ejpam-5857	766	2	,	,	PUNCT
ejpam-5857	766	3	x	x	SYM
ejpam-5857	766	4	∈	∈	NOUN
ejpam-5857	766	5	l(ψi	l(ψi	NOUN
ejpam-5857	766	6	;	;	PUNCT
ejpam-5857	766	7	β	β	X
ejpam-5857	766	8	)	)	PUNCT
ejpam-5857	766	9	̸=	̸=	PROPN
ejpam-5857	766	10	∅.	∅.	VERB
ejpam-5857	766	11	by	by	ADP
ejpam-5857	766	12	assumption	assumption	NOUN
ejpam-5857	766	13	,	,	PUNCT
ejpam-5857	766	14	we	we	PRON
ejpam-5857	766	15	have	have	VERB
ejpam-5857	766	16	l(ψi	l(ψi	NOUN
ejpam-5857	766	17	;	;	PUNCT
ejpam-5857	766	18	β	β	X
ejpam-5857	766	19	)	)	PUNCT
ejpam-5857	766	20	is	be	AUX
ejpam-5857	766	21	an	an	DET
ejpam-5857	766	22	iup	iup	NOUN
ejpam-5857	766	23	-	-	PUNCT
ejpam-5857	766	24	filter	filter	NOUN
ejpam-5857	766	25	of	of	ADP
ejpam-5857	766	26	x.	x.	NOUN
ejpam-5857	766	27	by	by	ADP
ejpam-5857	766	28	the	the	DET
ejpam-5857	766	29	condition	condition	NOUN
ejpam-5857	766	30	(	(	PUNCT
ejpam-5857	766	31	2.18	2.18	NUM
ejpam-5857	766	32	)	)	PUNCT
ejpam-5857	766	33	,	,	PUNCT
ejpam-5857	766	34	we	we	PRON
ejpam-5857	766	35	have	have	VERB
ejpam-5857	766	36	0	0	NUM
ejpam-5857	766	37	∈	∈	NOUN
ejpam-5857	766	38	l(ψi	l(ψi	NOUN
ejpam-5857	766	39	;	;	PUNCT
ejpam-5857	766	40	β	β	X
ejpam-5857	766	41	)	)	PUNCT
ejpam-5857	766	42	.	.	PUNCT
ejpam-5857	767	1	then	then	ADV
ejpam-5857	767	2	ψi(0	ψi(0	PROPN
ejpam-5857	767	3	)	)	PUNCT
ejpam-5857	767	4	≤	≤	NOUN
ejpam-5857	767	5	β	β	X
ejpam-5857	767	6	=	=	PUNCT
ejpam-5857	767	7	ψi(x	ψi(x	NUM
ejpam-5857	767	8	)	)	PUNCT
ejpam-5857	767	9	.	.	PUNCT
ejpam-5857	768	1	let	let	VERB
ejpam-5857	768	2	x	x	PRON
ejpam-5857	768	3	,	,	PUNCT
ejpam-5857	768	4	y	y	PROPN
ejpam-5857	768	5	∈	∈	PROPN
ejpam-5857	768	6	x	x	AUX
ejpam-5857	768	7	be	be	AUX
ejpam-5857	768	8	such	such	ADJ
ejpam-5857	768	9	that	that	SCONJ
ejpam-5857	768	10	ψi(x	ψi(x	NUM
ejpam-5857	768	11	·	·	PUNCT
ejpam-5857	768	12	y	y	X
ejpam-5857	768	13	)	)	PUNCT
ejpam-5857	768	14	<	<	X
ejpam-5857	768	15	0.5	0.5	NUM
ejpam-5857	768	16	and	and	CCONJ
ejpam-5857	768	17	ψi(x	ψi(x	NUM
ejpam-5857	768	18	)	)	PUNCT
ejpam-5857	768	19	<	<	X
ejpam-5857	769	1	0.5	0.5	NUM
ejpam-5857	769	2	.	.	PUNCT
ejpam-5857	770	1	let	let	VERB
ejpam-5857	770	2	β	β	NOUN
ejpam-5857	770	3	=	=	PUNCT
ejpam-5857	770	4	ψi(x	ψi(x	X
ejpam-5857	770	5	·	·	PUNCT
ejpam-5857	770	6	y	y	X
ejpam-5857	770	7	)	)	PUNCT
ejpam-5857	770	8	∨	∨	NUM
ejpam-5857	770	9	ψi(x	ψi(x	NUM
ejpam-5857	770	10	)	)	PUNCT
ejpam-5857	770	11	.	.	PUNCT
ejpam-5857	771	1	then	then	ADV
ejpam-5857	771	2	ψi(x	ψi(x	NOUN
ejpam-5857	771	3	·	·	PUNCT
ejpam-5857	771	4	y	y	X
ejpam-5857	771	5	)	)	PUNCT
ejpam-5857	771	6	≤	≤	NOUN
ejpam-5857	771	7	β	β	X
ejpam-5857	771	8	and	and	CCONJ
ejpam-5857	771	9	ψi(x	ψi(x	NUM
ejpam-5857	771	10	)	)	PUNCT
ejpam-5857	771	11	≤	≤	NOUN
ejpam-5857	772	1	β	β	X
ejpam-5857	772	2	.	.	PUNCT
ejpam-5857	773	1	thus	thus	ADV
ejpam-5857	773	2	,	,	PUNCT
ejpam-5857	773	3	x	x	X
ejpam-5857	773	4	·	·	PUNCT
ejpam-5857	773	5	y	y	X
ejpam-5857	773	6	,	,	PUNCT
ejpam-5857	773	7	x	x	SYM
ejpam-5857	773	8	∈	∈	NOUN
ejpam-5857	773	9	l(ψi	l(ψi	NOUN
ejpam-5857	773	10	;	;	PUNCT
ejpam-5857	773	11	β	β	X
ejpam-5857	773	12	)	)	PUNCT
ejpam-5857	773	13	̸=	̸=	PROPN
ejpam-5857	773	14	∅.	∅.	VERB
ejpam-5857	773	15	by	by	ADP
ejpam-5857	773	16	assumption	assumption	NOUN
ejpam-5857	773	17	,	,	PUNCT
ejpam-5857	773	18	we	we	PRON
ejpam-5857	773	19	have	have	VERB
ejpam-5857	773	20	l(ψi	l(ψi	NOUN
ejpam-5857	773	21	;	;	PUNCT
ejpam-5857	773	22	β	β	X
ejpam-5857	773	23	)	)	PUNCT
ejpam-5857	773	24	is	be	AUX
ejpam-5857	773	25	an	an	DET
ejpam-5857	773	26	iup	iup	NOUN
ejpam-5857	773	27	-	-	PUNCT
ejpam-5857	773	28	filter	filter	NOUN
ejpam-5857	773	29	of	of	ADP
ejpam-5857	773	30	x.	x.	NOUN
ejpam-5857	773	31	by	by	ADP
ejpam-5857	773	32	the	the	DET
ejpam-5857	773	33	condition	condition	NOUN
ejpam-5857	773	34	(	(	PUNCT
ejpam-5857	773	35	2.19	2.19	NUM
ejpam-5857	773	36	)	)	PUNCT
ejpam-5857	773	37	,	,	PUNCT
ejpam-5857	773	38	we	we	PRON
ejpam-5857	773	39	have	have	VERB
ejpam-5857	773	40	y	y	PROPN
ejpam-5857	773	41	∈	∈	PROPN
ejpam-5857	773	42	l(ψi	l(ψi	PROPN
ejpam-5857	773	43	;	;	PUNCT
ejpam-5857	773	44	β	β	X
ejpam-5857	773	45	)	)	PUNCT
ejpam-5857	773	46	.	.	PUNCT
ejpam-5857	774	1	thus	thus	ADV
ejpam-5857	774	2	,	,	PUNCT
ejpam-5857	774	3	ψi(y	ψi(y	NOUN
ejpam-5857	774	4	)	)	PUNCT
ejpam-5857	774	5	≤	≤	NOUN
ejpam-5857	775	1	β	β	X
ejpam-5857	775	2	=	=	SYM
ejpam-5857	775	3	ψi(x	ψi(x	X
ejpam-5857	775	4	·	·	PUNCT
ejpam-5857	775	5	y	y	X
ejpam-5857	775	6	)	)	PUNCT
ejpam-5857	775	7	∨	∨	NUM
ejpam-5857	775	8	ψi(x	ψi(x	NUM
ejpam-5857	775	9	)	)	PUNCT
ejpam-5857	775	10	≤	≤	NOUN
ejpam-5857	775	11	(	(	PUNCT
ejpam-5857	775	12	ψi(x	ψi(x	X
ejpam-5857	775	13	·	·	PUNCT
ejpam-5857	775	14	y	y	X
ejpam-5857	775	15	)	)	PUNCT
ejpam-5857	775	16	∨	∨	NUM
ejpam-5857	775	17	ψi(x	ψi(x	NUM
ejpam-5857	775	18	)	)	PUNCT
ejpam-5857	775	19	)	)	PUNCT
ejpam-5857	775	20	∧	∧	NOUN
ejpam-5857	775	21	0.5	0.5	NUM
ejpam-5857	775	22	.	.	PUNCT
ejpam-5857	776	1	let	let	VERB
ejpam-5857	776	2	x	x	SYM
ejpam-5857	776	3	∈	∈	PROPN
ejpam-5857	776	4	x.	x.	NOUN
ejpam-5857	776	5	let	let	VERB
ejpam-5857	776	6	γ	γ	X
ejpam-5857	776	7	=	=	PRON
ejpam-5857	776	8	ψf	ψf	X
ejpam-5857	776	9	(	(	PUNCT
ejpam-5857	776	10	x	x	NOUN
ejpam-5857	776	11	)	)	PUNCT
ejpam-5857	776	12	.	.	PUNCT
ejpam-5857	777	1	then	then	ADV
ejpam-5857	777	2	ψf	ψf	X
ejpam-5857	777	3	(	(	PUNCT
ejpam-5857	777	4	x	x	X
ejpam-5857	777	5	)	)	PUNCT
ejpam-5857	777	6	≥	≥	PROPN
ejpam-5857	777	7	γ	γ	PROPN
ejpam-5857	777	8	.	.	PUNCT
ejpam-5857	777	9	thus	thus	ADV
ejpam-5857	777	10	,	,	PUNCT
ejpam-5857	777	11	x	x	SYM
ejpam-5857	777	12	∈	∈	PROPN
ejpam-5857	777	13	u(ψf	u(ψf	PROPN
ejpam-5857	777	14	;	;	PUNCT
ejpam-5857	777	15	γ	γ	X
ejpam-5857	777	16	)	)	PUNCT
ejpam-5857	777	17	̸=	̸=	PROPN
ejpam-5857	777	18	∅.	∅.	VERB
ejpam-5857	777	19	by	by	ADP
ejpam-5857	777	20	assumption	assumption	NOUN
ejpam-5857	777	21	,	,	PUNCT
ejpam-5857	777	22	we	we	PRON
ejpam-5857	777	23	have	have	VERB
ejpam-5857	777	24	u(ψf	u(ψf	PROPN
ejpam-5857	777	25	;	;	PUNCT
ejpam-5857	777	26	γ	γ	X
ejpam-5857	777	27	)	)	PUNCT
ejpam-5857	777	28	is	be	AUX
ejpam-5857	777	29	an	an	DET
ejpam-5857	777	30	iup	iup	NOUN
ejpam-5857	777	31	-	-	PUNCT
ejpam-5857	777	32	filter	filter	NOUN
ejpam-5857	777	33	of	of	ADP
ejpam-5857	777	34	x.	x.	NOUN
ejpam-5857	777	35	by	by	ADP
ejpam-5857	777	36	the	the	DET
ejpam-5857	777	37	condition	condition	NOUN
ejpam-5857	777	38	(	(	PUNCT
ejpam-5857	777	39	2.18	2.18	NUM
ejpam-5857	777	40	)	)	PUNCT
ejpam-5857	777	41	,	,	PUNCT
ejpam-5857	777	42	we	we	PRON
ejpam-5857	777	43	have	have	VERB
ejpam-5857	777	44	0	0	NUM
ejpam-5857	777	45	∈	∈	PROPN
ejpam-5857	777	46	u(ψf	u(ψf	PROPN
ejpam-5857	777	47	;	;	PUNCT
ejpam-5857	777	48	γ	γ	X
ejpam-5857	777	49	)	)	PUNCT
ejpam-5857	777	50	.	.	PUNCT
ejpam-5857	778	1	k.	k.	PROPN
ejpam-5857	778	2	suayngam	suayngam	PROPN
ejpam-5857	778	3	,	,	PUNCT
ejpam-5857	778	4	p.	p.	NOUN
ejpam-5857	778	5	julatha	julatha	PROPN
ejpam-5857	778	6	,	,	PUNCT
ejpam-5857	778	7	w.	w.	PROPN
ejpam-5857	778	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	778	9	,	,	PUNCT
ejpam-5857	778	10	a.	a.	NOUN
ejpam-5857	778	11	iampan	iampan	PROPN
ejpam-5857	778	12	/	/	SYM
ejpam-5857	778	13	eur	eur	PROPN
ejpam-5857	778	14	.	.	PUNCT
ejpam-5857	779	1	j.	j.	PROPN
ejpam-5857	779	2	pure	pure	PROPN
ejpam-5857	779	3	appl	appl	PROPN
ejpam-5857	779	4	.	.	PROPN
ejpam-5857	779	5	math	math	PROPN
ejpam-5857	779	6	,	,	PUNCT
ejpam-5857	779	7	18	18	NUM
ejpam-5857	779	8	(	(	PUNCT
ejpam-5857	779	9	2	2	NUM
ejpam-5857	779	10	)	)	PUNCT
ejpam-5857	779	11	(	(	PUNCT
ejpam-5857	779	12	2025	2025	NUM
ejpam-5857	779	13	)	)	PUNCT
ejpam-5857	779	14	,	,	PUNCT
ejpam-5857	779	15	5857	5857	NUM
ejpam-5857	779	16	25	25	NUM
ejpam-5857	779	17	of	of	ADP
ejpam-5857	779	18	30	30	NUM
ejpam-5857	779	19	then	then	ADV
ejpam-5857	779	20	ψf	ψf	X
ejpam-5857	780	1	(	(	PUNCT
ejpam-5857	780	2	0	0	NUM
ejpam-5857	780	3	)	)	PUNCT
ejpam-5857	780	4	≥	≥	NOUN
ejpam-5857	780	5	γ	γ	X
ejpam-5857	780	6	=	=	X
ejpam-5857	780	7	ψf	ψf	X
ejpam-5857	780	8	(	(	PUNCT
ejpam-5857	780	9	x	x	NOUN
ejpam-5857	780	10	)	)	PUNCT
ejpam-5857	780	11	.	.	PUNCT
ejpam-5857	781	1	let	let	VERB
ejpam-5857	781	2	x	x	PRON
ejpam-5857	781	3	,	,	PUNCT
ejpam-5857	781	4	y	y	PROPN
ejpam-5857	781	5	∈	∈	PROPN
ejpam-5857	781	6	x	x	AUX
ejpam-5857	781	7	be	be	AUX
ejpam-5857	781	8	such	such	ADJ
ejpam-5857	781	9	that	that	SCONJ
ejpam-5857	781	10	ψf	ψf	X
ejpam-5857	781	11	(	(	PUNCT
ejpam-5857	781	12	x	x	PROPN
ejpam-5857	781	13	·	·	PUNCT
ejpam-5857	781	14	y	y	NOUN
ejpam-5857	781	15	)	)	PUNCT
ejpam-5857	781	16	≥	≥	NOUN
ejpam-5857	781	17	0.5	0.5	NUM
ejpam-5857	781	18	and	and	CCONJ
ejpam-5857	781	19	ψf	ψf	X
ejpam-5857	781	20	(	(	PUNCT
ejpam-5857	781	21	x	x	X
ejpam-5857	781	22	)	)	PUNCT
ejpam-5857	781	23	≥	≥	NOUN
ejpam-5857	781	24	0.5	0.5	NUM
ejpam-5857	781	25	.	.	PUNCT
ejpam-5857	782	1	let	let	VERB
ejpam-5857	782	2	γ	γ	X
ejpam-5857	782	3	=	=	PRON
ejpam-5857	782	4	ψf	ψf	X
ejpam-5857	782	5	(	(	PUNCT
ejpam-5857	782	6	x	x	PROPN
ejpam-5857	782	7	·	·	PUNCT
ejpam-5857	782	8	y	y	X
ejpam-5857	782	9	)	)	PUNCT
ejpam-5857	782	10	∧	∧	NOUN
ejpam-5857	782	11	ψf	ψf	X
ejpam-5857	782	12	(	(	PUNCT
ejpam-5857	782	13	x	x	NOUN
ejpam-5857	782	14	)	)	PUNCT
ejpam-5857	782	15	.	.	PUNCT
ejpam-5857	783	1	then	then	ADV
ejpam-5857	783	2	ψf	ψf	X
ejpam-5857	783	3	(	(	PUNCT
ejpam-5857	783	4	x	x	PROPN
ejpam-5857	783	5	·	·	PUNCT
ejpam-5857	783	6	y	y	X
ejpam-5857	783	7	)	)	PUNCT
ejpam-5857	783	8	≥	≥	PROPN
ejpam-5857	783	9	γ	γ	PROPN
ejpam-5857	783	10	and	and	CCONJ
ejpam-5857	783	11	ψf	ψf	X
ejpam-5857	783	12	(	(	PUNCT
ejpam-5857	783	13	x	x	X
ejpam-5857	783	14	)	)	PUNCT
ejpam-5857	783	15	≥	≥	PROPN
ejpam-5857	783	16	γ	γ	PROPN
ejpam-5857	783	17	.	.	PUNCT
ejpam-5857	783	18	thus	thus	ADV
ejpam-5857	783	19	,	,	PUNCT
ejpam-5857	783	20	x	x	X
ejpam-5857	783	21	·	·	PUNCT
ejpam-5857	783	22	y	y	X
ejpam-5857	783	23	,	,	PUNCT
ejpam-5857	783	24	x	x	SYM
ejpam-5857	783	25	∈	∈	PROPN
ejpam-5857	783	26	u(ψf	u(ψf	PROPN
ejpam-5857	783	27	;	;	PUNCT
ejpam-5857	783	28	γ	γ	X
ejpam-5857	783	29	)	)	PUNCT
ejpam-5857	783	30	̸=	̸=	PROPN
ejpam-5857	783	31	∅.	∅.	VERB
ejpam-5857	783	32	by	by	ADP
ejpam-5857	783	33	assumption	assumption	NOUN
ejpam-5857	783	34	,	,	PUNCT
ejpam-5857	783	35	we	we	PRON
ejpam-5857	783	36	have	have	VERB
ejpam-5857	783	37	u(ψf	u(ψf	PROPN
ejpam-5857	783	38	;	;	PUNCT
ejpam-5857	783	39	γ	γ	X
ejpam-5857	783	40	)	)	PUNCT
ejpam-5857	783	41	is	be	AUX
ejpam-5857	783	42	an	an	DET
ejpam-5857	783	43	iup	iup	NOUN
ejpam-5857	783	44	-	-	PUNCT
ejpam-5857	783	45	filter	filter	NOUN
ejpam-5857	783	46	of	of	ADP
ejpam-5857	783	47	x.	x.	NOUN
ejpam-5857	783	48	by	by	ADP
ejpam-5857	783	49	the	the	DET
ejpam-5857	783	50	condition	condition	NOUN
ejpam-5857	783	51	(	(	PUNCT
ejpam-5857	783	52	2.19	2.19	NUM
ejpam-5857	783	53	)	)	PUNCT
ejpam-5857	783	54	,	,	PUNCT
ejpam-5857	783	55	we	we	PRON
ejpam-5857	783	56	have	have	VERB
ejpam-5857	783	57	y	y	PROPN
ejpam-5857	783	58	∈	∈	PROPN
ejpam-5857	783	59	u(ψf	u(ψf	PROPN
ejpam-5857	783	60	;	;	PUNCT
ejpam-5857	783	61	γ	γ	X
ejpam-5857	783	62	)	)	PUNCT
ejpam-5857	783	63	.	.	PUNCT
ejpam-5857	784	1	thus	thus	ADV
ejpam-5857	784	2	,	,	PUNCT
ejpam-5857	784	3	ψf	ψf	X
ejpam-5857	784	4	(	(	PUNCT
ejpam-5857	784	5	y	y	PROPN
ejpam-5857	784	6	)	)	PUNCT
ejpam-5857	784	7	≥	≥	NOUN
ejpam-5857	784	8	γ	γ	X
ejpam-5857	784	9	=	=	SYM
ejpam-5857	784	10	min{ψf	min{ψf	NOUN
ejpam-5857	784	11	(	(	PUNCT
ejpam-5857	784	12	x	x	X
ejpam-5857	784	13	·	·	PUNCT
ejpam-5857	784	14	y	y	X
ejpam-5857	784	15	)	)	PUNCT
ejpam-5857	784	16	,	,	PUNCT
ejpam-5857	784	17	ψf	ψf	X
ejpam-5857	784	18	(	(	PUNCT
ejpam-5857	784	19	x	x	NOUN
ejpam-5857	784	20	)	)	PUNCT
ejpam-5857	784	21	}	}	PUNCT
ejpam-5857	784	22	≥	≥	NUM
ejpam-5857	784	23	(	(	PUNCT
ejpam-5857	784	24	ψf	ψf	X
ejpam-5857	784	25	(	(	PUNCT
ejpam-5857	784	26	x	x	PROPN
ejpam-5857	784	27	·	·	PUNCT
ejpam-5857	784	28	y	y	X
ejpam-5857	784	29	)	)	PUNCT
ejpam-5857	784	30	∧	∧	NOUN
ejpam-5857	784	31	ψf	ψf	X
ejpam-5857	784	32	(	(	PUNCT
ejpam-5857	784	33	x	x	NOUN
ejpam-5857	784	34	)	)	PUNCT
ejpam-5857	784	35	)	)	PUNCT
ejpam-5857	784	36	∨	∨	NUM
ejpam-5857	784	37	0.5	0.5	NUM
ejpam-5857	784	38	.	.	PUNCT
ejpam-5857	785	1	hence	hence	ADV
ejpam-5857	785	2	,	,	PUNCT
ejpam-5857	785	3	ψ	ψ	X
ejpam-5857	785	4	is	be	AUX
ejpam-5857	785	5	an	an	DET
ejpam-5857	785	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	785	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	785	8	iup	iup	NOUN
ejpam-5857	785	9	-	-	PUNCT
ejpam-5857	785	10	filter	filter	NOUN
ejpam-5857	785	11	of	of	ADP
ejpam-5857	785	12	x.	x.	PROPN
ejpam-5857	785	13	theorem	theorem	VERB
ejpam-5857	785	14	25	25	NUM
ejpam-5857	785	15	.	.	PUNCT
ejpam-5857	786	1	let	let	VERB
ejpam-5857	786	2	for	for	ADP
ejpam-5857	786	3	all	all	DET
ejpam-5857	786	4	α	α	NOUN
ejpam-5857	786	5	,	,	PUNCT
ejpam-5857	786	6	γ	γ	PROPN
ejpam-5857	786	7	∈	∈	PROPN
ejpam-5857	787	1	[	[	X
ejpam-5857	787	2	0.5	0.5	NUM
ejpam-5857	787	3	,	,	PUNCT
ejpam-5857	787	4	1	1	NUM
ejpam-5857	787	5	]	]	PUNCT
ejpam-5857	787	6	and	and	CCONJ
ejpam-5857	787	7	β	β	X
ejpam-5857	787	8	∈	∈	PROPN
ejpam-5857	787	9	[	[	X
ejpam-5857	787	10	0	0	NUM
ejpam-5857	787	11	,	,	PUNCT
ejpam-5857	787	12	0.5	0.5	NUM
ejpam-5857	787	13	)	)	PUNCT
ejpam-5857	787	14	,	,	PUNCT
ejpam-5857	787	15	the	the	DET
ejpam-5857	787	16	sets	set	NOUN
ejpam-5857	787	17	u(ψt	u(ψt	PROPN
ejpam-5857	787	18	;	;	PUNCT
ejpam-5857	787	19	α	α	X
ejpam-5857	787	20	)	)	PUNCT
ejpam-5857	787	21	,	,	PUNCT
ejpam-5857	787	22	l(ψi	l(ψi	PROPN
ejpam-5857	787	23	;	;	PUNCT
ejpam-5857	787	24	β	β	X
ejpam-5857	787	25	)	)	PUNCT
ejpam-5857	787	26	and	and	CCONJ
ejpam-5857	787	27	u(ψf	u(ψf	PROPN
ejpam-5857	787	28	;	;	PUNCT
ejpam-5857	787	29	γ	γ	X
ejpam-5857	787	30	)	)	PUNCT
ejpam-5857	787	31	are	be	AUX
ejpam-5857	787	32	either	either	CCONJ
ejpam-5857	787	33	empty	empty	ADJ
ejpam-5857	787	34	or	or	CCONJ
ejpam-5857	787	35	strong	strong	ADJ
ejpam-5857	787	36	iup	iup	NOUN
ejpam-5857	787	37	-	-	PUNCT
ejpam-5857	787	38	ideals	ideal	NOUN
ejpam-5857	787	39	of	of	ADP
ejpam-5857	787	40	x.	x.	NOUN
ejpam-5857	787	41	if	if	SCONJ
ejpam-5857	787	42	ψt	ψt	VERB
ejpam-5857	787	43	(	(	PUNCT
ejpam-5857	787	44	x	x	NOUN
ejpam-5857	787	45	)	)	PUNCT
ejpam-5857	787	46	≥	≥	NOUN
ejpam-5857	787	47	0.5	0.5	NUM
ejpam-5857	787	48	,	,	PUNCT
ejpam-5857	787	49	ψi(x	ψi(x	NUM
ejpam-5857	787	50	)	)	PUNCT
ejpam-5857	787	51	<	<	X
ejpam-5857	787	52	0.5	0.5	NUM
ejpam-5857	787	53	and	and	CCONJ
ejpam-5857	787	54	ψf	ψf	X
ejpam-5857	787	55	(	(	PUNCT
ejpam-5857	787	56	x	x	X
ejpam-5857	787	57	)	)	PUNCT
ejpam-5857	787	58	≥	≥	NOUN
ejpam-5857	787	59	0.5	0.5	NUM
ejpam-5857	787	60	.	.	PUNCT
ejpam-5857	788	1	then	then	ADV
ejpam-5857	788	2	ψ	ψ	X
ejpam-5857	788	3	is	be	AUX
ejpam-5857	788	4	an	an	DET
ejpam-5857	788	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	788	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	788	7	strong	strong	ADJ
ejpam-5857	788	8	iup	iup	NOUN
ejpam-5857	788	9	-	-	PUNCT
ejpam-5857	788	10	ideal	ideal	NOUN
ejpam-5857	788	11	of	of	ADP
ejpam-5857	788	12	x.	x.	NOUN
ejpam-5857	788	13	proof	proof	NOUN
ejpam-5857	788	14	.	.	PUNCT
ejpam-5857	789	1	it	it	PRON
ejpam-5857	789	2	is	be	AUX
ejpam-5857	789	3	straightforward	straightforward	ADJ
ejpam-5857	789	4	by	by	ADP
ejpam-5857	789	5	theorem	theorem	NOUN
ejpam-5857	789	6	1	1	NUM
ejpam-5857	789	7	.	.	PUNCT
ejpam-5857	789	8	theorem	theorem	NOUN
ejpam-5857	789	9	26	26	NUM
ejpam-5857	789	10	.	.	PUNCT
ejpam-5857	790	1	let	let	VERB
ejpam-5857	790	2	ψ	ψ	PART
ejpam-5857	790	3	be	be	AUX
ejpam-5857	790	4	an	an	DET
ejpam-5857	790	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	790	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	790	7	iup	iup	NOUN
ejpam-5857	790	8	-	-	PUNCT
ejpam-5857	790	9	subalgebra	subalgebra	NOUN
ejpam-5857	790	10	of	of	ADP
ejpam-5857	790	11	x.	x.	NOUN
ejpam-5857	790	12	then	then	ADV
ejpam-5857	790	13	for	for	ADP
ejpam-5857	790	14	all	all	DET
ejpam-5857	790	15	α	α	NOUN
ejpam-5857	790	16	,	,	PUNCT
ejpam-5857	790	17	γ	γ	PROPN
ejpam-5857	790	18	∈	∈	PROPN
ejpam-5857	791	1	[	[	X
ejpam-5857	791	2	0.5	0.5	NUM
ejpam-5857	791	3	,	,	PUNCT
ejpam-5857	791	4	1	1	NUM
ejpam-5857	791	5	]	]	PUNCT
ejpam-5857	791	6	and	and	CCONJ
ejpam-5857	791	7	β	β	X
ejpam-5857	791	8	∈	∈	PROPN
ejpam-5857	791	9	[	[	X
ejpam-5857	791	10	0	0	NUM
ejpam-5857	791	11	,	,	PUNCT
ejpam-5857	791	12	0.5	0.5	NUM
ejpam-5857	791	13	)	)	PUNCT
ejpam-5857	791	14	,	,	PUNCT
ejpam-5857	791	15	the	the	DET
ejpam-5857	791	16	sets	set	NOUN
ejpam-5857	791	17	u	u	NOUN
ejpam-5857	791	18	+	+	X
ejpam-5857	791	19	(	(	PUNCT
ejpam-5857	791	20	ψt	ψt	NUM
ejpam-5857	791	21	;	;	PUNCT
ejpam-5857	791	22	α	α	X
ejpam-5857	791	23	)	)	PUNCT
ejpam-5857	791	24	,	,	PUNCT
ejpam-5857	791	25	l	l	NOUN
ejpam-5857	791	26	−	−	PROPN
ejpam-5857	791	27	(	(	PUNCT
ejpam-5857	791	28	ψi	ψi	ADP
ejpam-5857	791	29	;	;	PUNCT
ejpam-5857	791	30	β	β	X
ejpam-5857	791	31	)	)	PUNCT
ejpam-5857	791	32	and	and	CCONJ
ejpam-5857	791	33	u	u	PRON
ejpam-5857	791	34	+	+	X
ejpam-5857	791	35	(	(	PUNCT
ejpam-5857	791	36	ψf	ψf	X
ejpam-5857	791	37	;	;	PUNCT
ejpam-5857	791	38	γ	γ	X
ejpam-5857	791	39	)	)	PUNCT
ejpam-5857	791	40	are	be	AUX
ejpam-5857	791	41	either	either	CCONJ
ejpam-5857	791	42	empty	empty	ADJ
ejpam-5857	791	43	or	or	CCONJ
ejpam-5857	791	44	iup	iup	NOUN
ejpam-5857	791	45	-	-	PUNCT
ejpam-5857	791	46	subalgebras	subalgebras	PROPN
ejpam-5857	791	47	of	of	ADP
ejpam-5857	791	48	x.	x.	PROPN
ejpam-5857	791	49	proof	proof	PROPN
ejpam-5857	791	50	.	.	PUNCT
ejpam-5857	792	1	assume	assume	VERB
ejpam-5857	792	2	that	that	SCONJ
ejpam-5857	792	3	ψ	ψ	NOUN
ejpam-5857	792	4	is	be	AUX
ejpam-5857	792	5	an	an	DET
ejpam-5857	792	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	792	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	792	8	iup	iup	NOUN
ejpam-5857	792	9	-	-	PUNCT
ejpam-5857	792	10	subalgebra	subalgebra	NOUN
ejpam-5857	792	11	of	of	ADP
ejpam-5857	792	12	x.	x.	NOUN
ejpam-5857	792	13	let	let	VERB
ejpam-5857	792	14	α	α	PRON
ejpam-5857	792	15	∈	∈	PROPN
ejpam-5857	793	1	[	[	X
ejpam-5857	793	2	0.5	0.5	NUM
ejpam-5857	793	3	,	,	PUNCT
ejpam-5857	793	4	1	1	NUM
ejpam-5857	793	5	]	]	PUNCT
ejpam-5857	793	6	be	be	AUX
ejpam-5857	793	7	such	such	ADJ
ejpam-5857	793	8	that	that	SCONJ
ejpam-5857	793	9	u	u	NOUN
ejpam-5857	793	10	+	+	X
ejpam-5857	793	11	(	(	PUNCT
ejpam-5857	793	12	ψt	ψt	NUM
ejpam-5857	793	13	;	;	PUNCT
ejpam-5857	793	14	α	α	X
ejpam-5857	793	15	)	)	PUNCT
ejpam-5857	793	16	̸=	̸=	PROPN
ejpam-5857	793	17	∅.	∅.	ADV
ejpam-5857	793	18	let	let	VERB
ejpam-5857	793	19	x	x	PRON
ejpam-5857	793	20	,	,	PUNCT
ejpam-5857	793	21	y	y	PROPN
ejpam-5857	793	22	∈	∈	PROPN
ejpam-5857	793	23	u	u	PROPN
ejpam-5857	793	24	+	+	X
ejpam-5857	793	25	(	(	PUNCT
ejpam-5857	793	26	ψt	ψt	NUM
ejpam-5857	793	27	;	;	PUNCT
ejpam-5857	793	28	α	α	X
ejpam-5857	793	29	)	)	PUNCT
ejpam-5857	793	30	.	.	PUNCT
ejpam-5857	794	1	then	then	ADV
ejpam-5857	794	2	ψt	ψt	VERB
ejpam-5857	794	3	(	(	PUNCT
ejpam-5857	794	4	x	x	X
ejpam-5857	794	5	)	)	PUNCT
ejpam-5857	794	6	>	>	X
ejpam-5857	795	1	α	α	PROPN
ejpam-5857	795	2	and	and	CCONJ
ejpam-5857	795	3	ψt	ψt	ADJ
ejpam-5857	795	4	(	(	PUNCT
ejpam-5857	795	5	y	y	NOUN
ejpam-5857	795	6	)	)	PUNCT
ejpam-5857	795	7	>	>	X
ejpam-5857	796	1	α	α	X
ejpam-5857	796	2	.	.	PUNCT
ejpam-5857	797	1	thus	thus	ADV
ejpam-5857	797	2	,	,	PUNCT
ejpam-5857	797	3	ψt	ψt	VERB
ejpam-5857	797	4	(	(	PUNCT
ejpam-5857	797	5	x	x	X
ejpam-5857	797	6	)	)	PUNCT
ejpam-5857	797	7	∧	∧	NOUN
ejpam-5857	797	8	ψt	ψt	NOUN
ejpam-5857	797	9	(	(	PUNCT
ejpam-5857	797	10	y	y	NOUN
ejpam-5857	797	11	)	)	PUNCT
ejpam-5857	797	12	>	>	X
ejpam-5857	797	13	α	α	X
ejpam-5857	797	14	.	.	PUNCT
ejpam-5857	798	1	by	by	ADP
ejpam-5857	798	2	the	the	DET
ejpam-5857	798	3	condition	condition	NOUN
ejpam-5857	798	4	(	(	PUNCT
ejpam-5857	798	5	3.5	3.5	NUM
ejpam-5857	798	6	)	)	PUNCT
ejpam-5857	798	7	,	,	PUNCT
ejpam-5857	798	8	we	we	PRON
ejpam-5857	798	9	have	have	AUX
ejpam-5857	798	10	ψt	ψt	VERB
ejpam-5857	798	11	(	(	PUNCT
ejpam-5857	798	12	x	x	PROPN
ejpam-5857	798	13	·	·	PUNCT
ejpam-5857	798	14	y	y	X
ejpam-5857	798	15	)	)	PUNCT
ejpam-5857	798	16	≥	≥	NOUN
ejpam-5857	798	17	(	(	PUNCT
ejpam-5857	798	18	ψt	ψt	VERB
ejpam-5857	798	19	(	(	PUNCT
ejpam-5857	798	20	x	x	NOUN
ejpam-5857	798	21	)	)	PUNCT
ejpam-5857	798	22	∧	∧	NOUN
ejpam-5857	798	23	ψt	ψt	NOUN
ejpam-5857	798	24	(	(	PUNCT
ejpam-5857	798	25	y	y	NOUN
ejpam-5857	798	26	)	)	PUNCT
ejpam-5857	798	27	)	)	PUNCT
ejpam-5857	799	1	∨	∨	NUM
ejpam-5857	799	2	0.5	0.5	NUM
ejpam-5857	799	3	>	>	X
ejpam-5857	799	4	α	α	PROPN
ejpam-5857	799	5	∨	∨	NUM
ejpam-5857	799	6	0.5	0.5	NUM
ejpam-5857	799	7	≥	≥	NOUN
ejpam-5857	799	8	α	α	NOUN
ejpam-5857	799	9	.	.	PUNCT
ejpam-5857	800	1	thus	thus	ADV
ejpam-5857	800	2	,	,	PUNCT
ejpam-5857	800	3	x	x	X
ejpam-5857	800	4	·	·	PUNCT
ejpam-5857	800	5	y	y	PROPN
ejpam-5857	800	6	∈	∈	PROPN
ejpam-5857	800	7	u	u	PROPN
ejpam-5857	800	8	+	+	X
ejpam-5857	800	9	(	(	PUNCT
ejpam-5857	800	10	ψt	ψt	NUM
ejpam-5857	800	11	;	;	PUNCT
ejpam-5857	800	12	α	α	X
ejpam-5857	800	13	)	)	PUNCT
ejpam-5857	800	14	.	.	PUNCT
ejpam-5857	801	1	hence	hence	ADV
ejpam-5857	801	2	,	,	PUNCT
ejpam-5857	801	3	u	u	PROPN
ejpam-5857	801	4	+	+	X
ejpam-5857	801	5	(	(	PUNCT
ejpam-5857	801	6	ψt	ψt	NUM
ejpam-5857	801	7	;	;	PUNCT
ejpam-5857	801	8	α	α	X
ejpam-5857	801	9	)	)	PUNCT
ejpam-5857	801	10	is	be	AUX
ejpam-5857	801	11	an	an	DET
ejpam-5857	801	12	iup	iup	NOUN
ejpam-5857	801	13	-	-	PUNCT
ejpam-5857	801	14	subalgebra	subalgebra	NOUN
ejpam-5857	801	15	of	of	ADP
ejpam-5857	801	16	x.	x.	NOUN
ejpam-5857	801	17	let	let	VERB
ejpam-5857	801	18	β	β	X
ejpam-5857	801	19	∈	∈	PROPN
ejpam-5857	802	1	[	[	X
ejpam-5857	802	2	0	0	NUM
ejpam-5857	802	3	,	,	PUNCT
ejpam-5857	802	4	0.5	0.5	NUM
ejpam-5857	802	5	)	)	PUNCT
ejpam-5857	802	6	be	be	VERB
ejpam-5857	802	7	such	such	ADJ
ejpam-5857	802	8	that	that	SCONJ
ejpam-5857	802	9	l	l	NOUN
ejpam-5857	803	1	−	−	PROPN
ejpam-5857	803	2	(	(	PUNCT
ejpam-5857	803	3	ψi	ψi	ADP
ejpam-5857	803	4	;	;	PUNCT
ejpam-5857	803	5	β	β	X
ejpam-5857	803	6	)	)	PUNCT
ejpam-5857	803	7	̸=	̸=	PROPN
ejpam-5857	803	8	∅.	∅.	ADV
ejpam-5857	803	9	let	let	VERB
ejpam-5857	803	10	x	x	PRON
ejpam-5857	803	11	,	,	PUNCT
ejpam-5857	803	12	y	y	PROPN
ejpam-5857	803	13	∈	∈	PROPN
ejpam-5857	803	14	l	l	NOUN
ejpam-5857	804	1	−	−	PROPN
ejpam-5857	805	1	(	(	PUNCT
ejpam-5857	805	2	ψi	ψi	ADP
ejpam-5857	805	3	;	;	PUNCT
ejpam-5857	805	4	β	β	X
ejpam-5857	805	5	)	)	PUNCT
ejpam-5857	805	6	.	.	PUNCT
ejpam-5857	806	1	then	then	ADV
ejpam-5857	806	2	ψi(x	ψi(x	NUM
ejpam-5857	806	3	)	)	PUNCT
ejpam-5857	806	4	<	<	X
ejpam-5857	806	5	β	β	X
ejpam-5857	806	6	and	and	CCONJ
ejpam-5857	806	7	ψi(y	ψi(y	NUM
ejpam-5857	806	8	)	)	PUNCT
ejpam-5857	806	9	<	<	X
ejpam-5857	806	10	β	β	X
ejpam-5857	806	11	.	.	PUNCT
ejpam-5857	807	1	thus	thus	ADV
ejpam-5857	807	2	,	,	PUNCT
ejpam-5857	807	3	ψi(x	ψi(x	NUM
ejpam-5857	807	4	)	)	PUNCT
ejpam-5857	807	5	∨	∨	NUM
ejpam-5857	807	6	ψi(y	ψi(y	NUM
ejpam-5857	807	7	)	)	PUNCT
ejpam-5857	807	8	<	<	X
ejpam-5857	807	9	β	β	X
ejpam-5857	807	10	.	.	PUNCT
ejpam-5857	808	1	by	by	ADP
ejpam-5857	808	2	the	the	DET
ejpam-5857	808	3	condition	condition	NOUN
ejpam-5857	808	4	(	(	PUNCT
ejpam-5857	808	5	3.6	3.6	NUM
ejpam-5857	808	6	)	)	PUNCT
ejpam-5857	808	7	,	,	PUNCT
ejpam-5857	808	8	we	we	PRON
ejpam-5857	808	9	have	have	VERB
ejpam-5857	808	10	ψi(x	ψi(x	NUM
ejpam-5857	808	11	·	·	PUNCT
ejpam-5857	808	12	y	y	X
ejpam-5857	808	13	)	)	PUNCT
ejpam-5857	808	14	≤	≤	NOUN
ejpam-5857	808	15	(	(	PUNCT
ejpam-5857	808	16	ψi(x	ψi(x	NUM
ejpam-5857	808	17	)	)	PUNCT
ejpam-5857	808	18	∨	∨	NUM
ejpam-5857	808	19	ψi(y	ψi(y	NUM
ejpam-5857	808	20	)	)	PUNCT
ejpam-5857	808	21	)	)	PUNCT
ejpam-5857	809	1	∧	∧	NOUN
ejpam-5857	809	2	0.5	0.5	NUM
ejpam-5857	809	3	<	<	X
ejpam-5857	809	4	β	β	X
ejpam-5857	809	5	∧	∧	PROPN
ejpam-5857	809	6	0.5	0.5	NUM
ejpam-5857	809	7	≤	≤	NUM
ejpam-5857	809	8	β	β	NOUN
ejpam-5857	809	9	.	.	PUNCT
ejpam-5857	810	1	thus	thus	ADV
ejpam-5857	810	2	,	,	PUNCT
ejpam-5857	810	3	x	x	X
ejpam-5857	810	4	·	·	PUNCT
ejpam-5857	810	5	y	y	SYM
ejpam-5857	810	6	∈	∈	PROPN
ejpam-5857	810	7	l	l	NOUN
ejpam-5857	811	1	−	−	PROPN
ejpam-5857	811	2	(	(	PUNCT
ejpam-5857	811	3	ψi	ψi	ADP
ejpam-5857	811	4	;	;	PUNCT
ejpam-5857	811	5	β	β	X
ejpam-5857	811	6	)	)	PUNCT
ejpam-5857	811	7	.	.	PUNCT
ejpam-5857	812	1	hence	hence	ADV
ejpam-5857	812	2	,	,	PUNCT
ejpam-5857	812	3	l	l	NOUN
ejpam-5857	812	4	−	−	PROPN
ejpam-5857	812	5	(	(	PUNCT
ejpam-5857	812	6	ψi	ψi	ADP
ejpam-5857	812	7	;	;	PUNCT
ejpam-5857	812	8	β	β	X
ejpam-5857	812	9	)	)	PUNCT
ejpam-5857	812	10	is	be	AUX
ejpam-5857	812	11	an	an	DET
ejpam-5857	812	12	iup	iup	NOUN
ejpam-5857	812	13	-	-	PUNCT
ejpam-5857	812	14	subalgebra	subalgebra	NOUN
ejpam-5857	812	15	of	of	ADP
ejpam-5857	812	16	x.	x.	NOUN
ejpam-5857	812	17	let	let	VERB
ejpam-5857	812	18	γ	γ	X
ejpam-5857	812	19	∈	∈	PROPN
ejpam-5857	813	1	[	[	X
ejpam-5857	813	2	0.5	0.5	NUM
ejpam-5857	813	3	,	,	PUNCT
ejpam-5857	813	4	1	1	NUM
ejpam-5857	813	5	]	]	PUNCT
ejpam-5857	813	6	be	be	AUX
ejpam-5857	813	7	such	such	ADJ
ejpam-5857	813	8	that	that	SCONJ
ejpam-5857	813	9	u	u	NOUN
ejpam-5857	813	10	+	+	X
ejpam-5857	813	11	(	(	PUNCT
ejpam-5857	813	12	ψf	ψf	X
ejpam-5857	813	13	;	;	PUNCT
ejpam-5857	813	14	γ	γ	X
ejpam-5857	813	15	)	)	PUNCT
ejpam-5857	813	16	̸=	̸=	PROPN
ejpam-5857	813	17	∅.	∅.	ADV
ejpam-5857	813	18	let	let	VERB
ejpam-5857	813	19	x	x	PRON
ejpam-5857	813	20	,	,	PUNCT
ejpam-5857	813	21	y	y	PROPN
ejpam-5857	813	22	∈	∈	PROPN
ejpam-5857	813	23	u	u	PROPN
ejpam-5857	813	24	+	+	X
ejpam-5857	813	25	(	(	PUNCT
ejpam-5857	813	26	ψf	ψf	X
ejpam-5857	813	27	;	;	PUNCT
ejpam-5857	813	28	γ	γ	X
ejpam-5857	813	29	)	)	PUNCT
ejpam-5857	813	30	.	.	PUNCT
ejpam-5857	814	1	then	then	ADV
ejpam-5857	814	2	ψf	ψf	X
ejpam-5857	814	3	(	(	PUNCT
ejpam-5857	814	4	x	x	X
ejpam-5857	814	5	)	)	PUNCT
ejpam-5857	814	6	>	>	X
ejpam-5857	814	7	γ	γ	PROPN
ejpam-5857	814	8	and	and	CCONJ
ejpam-5857	814	9	ψf	ψf	X
ejpam-5857	814	10	(	(	PUNCT
ejpam-5857	814	11	y	y	PROPN
ejpam-5857	814	12	)	)	PUNCT
ejpam-5857	814	13	>	>	X
ejpam-5857	815	1	γ	γ	X
ejpam-5857	815	2	.	.	PUNCT
ejpam-5857	815	3	thus	thus	ADV
ejpam-5857	815	4	,	,	PUNCT
ejpam-5857	815	5	ψf	ψf	X
ejpam-5857	815	6	(	(	PUNCT
ejpam-5857	815	7	x	x	X
ejpam-5857	815	8	)	)	PUNCT
ejpam-5857	815	9	∧	∧	NOUN
ejpam-5857	815	10	ψf	ψf	X
ejpam-5857	815	11	(	(	PUNCT
ejpam-5857	815	12	y	y	NOUN
ejpam-5857	815	13	)	)	PUNCT
ejpam-5857	815	14	>	>	X
ejpam-5857	815	15	γ	γ	X
ejpam-5857	815	16	.	.	PROPN
ejpam-5857	815	17	by	by	ADP
ejpam-5857	815	18	the	the	DET
ejpam-5857	815	19	condition	condition	NOUN
ejpam-5857	815	20	(	(	PUNCT
ejpam-5857	815	21	3.5	3.5	NUM
ejpam-5857	815	22	)	)	PUNCT
ejpam-5857	815	23	,	,	PUNCT
ejpam-5857	815	24	we	we	PRON
ejpam-5857	815	25	have	have	VERB
ejpam-5857	815	26	ψf	ψf	VERB
ejpam-5857	815	27	(	(	PUNCT
ejpam-5857	815	28	x	x	X
ejpam-5857	815	29	·	·	PUNCT
ejpam-5857	815	30	y	y	X
ejpam-5857	815	31	)	)	PUNCT
ejpam-5857	815	32	≥	≥	NOUN
ejpam-5857	815	33	(	(	PUNCT
ejpam-5857	815	34	ψf	ψf	X
ejpam-5857	815	35	(	(	PUNCT
ejpam-5857	815	36	x	x	NOUN
ejpam-5857	815	37	)	)	PUNCT
ejpam-5857	815	38	∧	∧	NOUN
ejpam-5857	815	39	ψf	ψf	X
ejpam-5857	815	40	(	(	PUNCT
ejpam-5857	815	41	y	y	NOUN
ejpam-5857	815	42	)	)	PUNCT
ejpam-5857	815	43	)	)	PUNCT
ejpam-5857	816	1	∨	∨	NUM
ejpam-5857	816	2	0.5	0.5	NUM
ejpam-5857	816	3	>	>	X
ejpam-5857	816	4	γ	γ	PROPN
ejpam-5857	816	5	∨	∨	NUM
ejpam-5857	816	6	0.5	0.5	NUM
ejpam-5857	816	7	≥	≥	PROPN
ejpam-5857	816	8	γ	γ	PROPN
ejpam-5857	816	9	.	.	PROPN
ejpam-5857	816	10	thus	thus	ADV
ejpam-5857	816	11	,	,	PUNCT
ejpam-5857	816	12	x	x	X
ejpam-5857	816	13	·	·	PUNCT
ejpam-5857	816	14	y	y	PROPN
ejpam-5857	816	15	∈	∈	PROPN
ejpam-5857	816	16	u	u	PROPN
ejpam-5857	816	17	+	+	X
ejpam-5857	816	18	(	(	PUNCT
ejpam-5857	816	19	ψf	ψf	X
ejpam-5857	816	20	;	;	PUNCT
ejpam-5857	816	21	γ	γ	X
ejpam-5857	816	22	)	)	PUNCT
ejpam-5857	816	23	.	.	PUNCT
ejpam-5857	817	1	hence	hence	ADV
ejpam-5857	817	2	,	,	PUNCT
ejpam-5857	817	3	u	u	PROPN
ejpam-5857	817	4	+	+	X
ejpam-5857	817	5	(	(	PUNCT
ejpam-5857	817	6	ψf	ψf	X
ejpam-5857	817	7	;	;	PUNCT
ejpam-5857	817	8	γ	γ	X
ejpam-5857	817	9	)	)	PUNCT
ejpam-5857	817	10	is	be	AUX
ejpam-5857	817	11	an	an	DET
ejpam-5857	817	12	iup	iup	NOUN
ejpam-5857	817	13	-	-	PUNCT
ejpam-5857	817	14	subalgebra	subalgebra	NOUN
ejpam-5857	817	15	of	of	ADP
ejpam-5857	817	16	x.	x.	PROPN
ejpam-5857	817	17	theorem	theorem	VERB
ejpam-5857	817	18	27	27	NUM
ejpam-5857	817	19	.	.	PUNCT
ejpam-5857	818	1	let	let	VERB
ejpam-5857	818	2	ψ	ψ	PART
ejpam-5857	818	3	be	be	AUX
ejpam-5857	818	4	an	an	DET
ejpam-5857	818	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	818	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	818	7	iup	iup	NOUN
ejpam-5857	818	8	-	-	PUNCT
ejpam-5857	818	9	ideal	ideal	NOUN
ejpam-5857	818	10	of	of	ADP
ejpam-5857	818	11	x.	x.	NOUN
ejpam-5857	818	12	then	then	ADV
ejpam-5857	818	13	for	for	ADP
ejpam-5857	818	14	all	all	DET
ejpam-5857	818	15	α	α	NOUN
ejpam-5857	818	16	,	,	PUNCT
ejpam-5857	818	17	γ	γ	PROPN
ejpam-5857	818	18	∈	∈	PROPN
ejpam-5857	819	1	[	[	X
ejpam-5857	819	2	0.5	0.5	NUM
ejpam-5857	819	3	,	,	PUNCT
ejpam-5857	819	4	1	1	NUM
ejpam-5857	819	5	]	]	PUNCT
ejpam-5857	819	6	and	and	CCONJ
ejpam-5857	819	7	β	β	X
ejpam-5857	819	8	∈	∈	PROPN
ejpam-5857	819	9	[	[	X
ejpam-5857	819	10	0	0	NUM
ejpam-5857	819	11	,	,	PUNCT
ejpam-5857	819	12	0.5	0.5	NUM
ejpam-5857	819	13	)	)	PUNCT
ejpam-5857	819	14	,	,	PUNCT
ejpam-5857	819	15	the	the	DET
ejpam-5857	819	16	sets	set	NOUN
ejpam-5857	819	17	u	u	NOUN
ejpam-5857	819	18	+	+	X
ejpam-5857	819	19	(	(	PUNCT
ejpam-5857	819	20	ψt	ψt	NUM
ejpam-5857	819	21	;	;	PUNCT
ejpam-5857	819	22	α	α	X
ejpam-5857	819	23	)	)	PUNCT
ejpam-5857	819	24	,	,	PUNCT
ejpam-5857	819	25	l	l	NOUN
ejpam-5857	819	26	−	−	PROPN
ejpam-5857	819	27	(	(	PUNCT
ejpam-5857	819	28	ψi	ψi	ADP
ejpam-5857	819	29	;	;	PUNCT
ejpam-5857	819	30	β	β	X
ejpam-5857	819	31	)	)	PUNCT
ejpam-5857	819	32	and	and	CCONJ
ejpam-5857	819	33	u	u	PRON
ejpam-5857	819	34	+	+	X
ejpam-5857	819	35	(	(	PUNCT
ejpam-5857	819	36	ψf	ψf	X
ejpam-5857	819	37	;	;	PUNCT
ejpam-5857	819	38	γ	γ	X
ejpam-5857	819	39	)	)	PUNCT
ejpam-5857	819	40	are	be	AUX
ejpam-5857	819	41	either	either	CCONJ
ejpam-5857	819	42	empty	empty	ADJ
ejpam-5857	819	43	or	or	CCONJ
ejpam-5857	819	44	iup	iup	NOUN
ejpam-5857	819	45	-	-	PUNCT
ejpam-5857	819	46	ideals	ideal	NOUN
ejpam-5857	819	47	of	of	ADP
ejpam-5857	819	48	x.	x.	NOUN
ejpam-5857	819	49	proof	proof	NOUN
ejpam-5857	819	50	.	.	PUNCT
ejpam-5857	820	1	assume	assume	VERB
ejpam-5857	820	2	that	that	SCONJ
ejpam-5857	820	3	ψ	ψ	NOUN
ejpam-5857	820	4	is	be	AUX
ejpam-5857	820	5	an	an	DET
ejpam-5857	820	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	820	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	820	8	iup	iup	NOUN
ejpam-5857	820	9	-	-	PUNCT
ejpam-5857	820	10	ideal	ideal	NOUN
ejpam-5857	820	11	of	of	ADP
ejpam-5857	820	12	x.	x.	NOUN
ejpam-5857	820	13	let	let	VERB
ejpam-5857	820	14	α	α	PRON
ejpam-5857	820	15	∈	∈	PROPN
ejpam-5857	821	1	[	[	X
ejpam-5857	821	2	0.5	0.5	NUM
ejpam-5857	821	3	,	,	PUNCT
ejpam-5857	821	4	1	1	NUM
ejpam-5857	821	5	]	]	PUNCT
ejpam-5857	821	6	be	be	AUX
ejpam-5857	821	7	such	such	ADJ
ejpam-5857	821	8	that	that	SCONJ
ejpam-5857	821	9	u	u	NOUN
ejpam-5857	821	10	+	+	X
ejpam-5857	821	11	(	(	PUNCT
ejpam-5857	821	12	ψt	ψt	NUM
ejpam-5857	821	13	;	;	PUNCT
ejpam-5857	821	14	α	α	X
ejpam-5857	821	15	)	)	PUNCT
ejpam-5857	821	16	̸=	̸=	PROPN
ejpam-5857	821	17	∅.	∅.	ADV
ejpam-5857	821	18	let	let	VERB
ejpam-5857	821	19	a	a	DET
ejpam-5857	821	20	∈	∈	PROPN
ejpam-5857	821	21	u	u	NOUN
ejpam-5857	821	22	+	+	X
ejpam-5857	821	23	(	(	PUNCT
ejpam-5857	821	24	ψt	ψt	NUM
ejpam-5857	821	25	;	;	PUNCT
ejpam-5857	821	26	α	α	X
ejpam-5857	821	27	)	)	PUNCT
ejpam-5857	821	28	.	.	PUNCT
ejpam-5857	822	1	then	then	ADV
ejpam-5857	822	2	ψt	ψt	VERB
ejpam-5857	822	3	(	(	PUNCT
ejpam-5857	822	4	a	a	NOUN
ejpam-5857	822	5	)	)	PUNCT
ejpam-5857	822	6	>	>	X
ejpam-5857	823	1	α	α	X
ejpam-5857	823	2	.	.	PUNCT
ejpam-5857	824	1	by	by	ADP
ejpam-5857	824	2	the	the	DET
ejpam-5857	824	3	condition	condition	NOUN
ejpam-5857	824	4	(	(	PUNCT
ejpam-5857	824	5	3.8	3.8	NUM
ejpam-5857	824	6	)	)	PUNCT
ejpam-5857	824	7	,	,	PUNCT
ejpam-5857	824	8	we	we	PRON
ejpam-5857	824	9	have	have	AUX
ejpam-5857	824	10	ψt	ψt	VERB
ejpam-5857	824	11	(	(	PUNCT
ejpam-5857	824	12	0	0	NUM
ejpam-5857	824	13	)	)	PUNCT
ejpam-5857	824	14	≥	≥	PRON
ejpam-5857	824	15	ψt	ψt	NOUN
ejpam-5857	824	16	(	(	PUNCT
ejpam-5857	824	17	a	a	NOUN
ejpam-5857	824	18	)	)	PUNCT
ejpam-5857	825	1	>	>	X
ejpam-5857	825	2	α	α	X
ejpam-5857	825	3	.	.	PUNCT
ejpam-5857	826	1	thus	thus	ADV
ejpam-5857	826	2	,	,	PUNCT
ejpam-5857	826	3	0	0	NUM
ejpam-5857	826	4	∈	∈	PROPN
ejpam-5857	826	5	u	u	NOUN
ejpam-5857	826	6	+	+	X
ejpam-5857	826	7	(	(	PUNCT
ejpam-5857	826	8	ψt	ψt	NUM
ejpam-5857	826	9	;	;	PUNCT
ejpam-5857	826	10	α	α	X
ejpam-5857	826	11	)	)	PUNCT
ejpam-5857	826	12	.	.	PUNCT
ejpam-5857	827	1	let	let	VERB
ejpam-5857	827	2	x	x	PRON
ejpam-5857	827	3	,	,	PUNCT
ejpam-5857	827	4	y	y	PROPN
ejpam-5857	827	5	,	,	PUNCT
ejpam-5857	827	6	z	z	PROPN
ejpam-5857	827	7	∈	∈	PROPN
ejpam-5857	827	8	u	u	NOUN
ejpam-5857	827	9	+	+	X
ejpam-5857	827	10	(	(	PUNCT
ejpam-5857	827	11	ψt	ψt	NUM
ejpam-5857	827	12	;	;	PUNCT
ejpam-5857	827	13	α	α	X
ejpam-5857	827	14	)	)	PUNCT
ejpam-5857	827	15	be	be	VERB
ejpam-5857	827	16	such	such	ADJ
ejpam-5857	827	17	that	that	SCONJ
ejpam-5857	827	18	x	x	PART
ejpam-5857	827	19	·	·	PUNCT
ejpam-5857	827	20	(	(	PUNCT
ejpam-5857	827	21	y	y	PROPN
ejpam-5857	827	22	·	·	PUNCT
ejpam-5857	827	23	z	z	X
ejpam-5857	827	24	)	)	PUNCT
ejpam-5857	827	25	,	,	PUNCT
ejpam-5857	827	26	y	y	PROPN
ejpam-5857	827	27	∈	∈	PROPN
ejpam-5857	827	28	u	u	PROPN
ejpam-5857	827	29	+	+	X
ejpam-5857	827	30	(	(	PUNCT
ejpam-5857	827	31	ψt	ψt	NUM
ejpam-5857	827	32	;	;	PUNCT
ejpam-5857	827	33	α	α	X
ejpam-5857	827	34	)	)	PUNCT
ejpam-5857	827	35	.	.	PUNCT
ejpam-5857	828	1	then	then	ADV
ejpam-5857	828	2	ψt	ψt	VERB
ejpam-5857	828	3	(	(	PUNCT
ejpam-5857	828	4	x	x	X
ejpam-5857	828	5	·	·	PUNCT
ejpam-5857	828	6	(	(	PUNCT
ejpam-5857	828	7	y	y	PROPN
ejpam-5857	828	8	·	·	PUNCT
ejpam-5857	828	9	z	z	X
ejpam-5857	828	10	)	)	PUNCT
ejpam-5857	828	11	)	)	PUNCT
ejpam-5857	828	12	>	>	X
ejpam-5857	829	1	α	α	PROPN
ejpam-5857	829	2	and	and	CCONJ
ejpam-5857	829	3	ψt	ψt	ADJ
ejpam-5857	829	4	(	(	PUNCT
ejpam-5857	829	5	y	y	NOUN
ejpam-5857	829	6	)	)	PUNCT
ejpam-5857	829	7	>	>	X
ejpam-5857	830	1	α	α	X
ejpam-5857	830	2	.	.	PUNCT
ejpam-5857	831	1	thus	thus	ADV
ejpam-5857	831	2	,	,	PUNCT
ejpam-5857	831	3	ψt	ψt	VERB
ejpam-5857	831	4	(	(	PUNCT
ejpam-5857	831	5	x	x	X
ejpam-5857	831	6	·	·	PUNCT
ejpam-5857	831	7	(	(	PUNCT
ejpam-5857	831	8	y	y	PROPN
ejpam-5857	831	9	·	·	PUNCT
ejpam-5857	831	10	z	z	NOUN
ejpam-5857	831	11	)	)	PUNCT
ejpam-5857	831	12	)	)	PUNCT
ejpam-5857	832	1	∧	∧	NOUN
ejpam-5857	832	2	ψt	ψt	NOUN
ejpam-5857	832	3	(	(	PUNCT
ejpam-5857	832	4	y	y	NOUN
ejpam-5857	832	5	)	)	PUNCT
ejpam-5857	832	6	>	>	X
ejpam-5857	833	1	α	α	X
ejpam-5857	833	2	.	.	PUNCT
ejpam-5857	834	1	by	by	ADP
ejpam-5857	834	2	the	the	DET
ejpam-5857	834	3	condition	condition	NOUN
ejpam-5857	834	4	(	(	PUNCT
ejpam-5857	834	5	3.11	3.11	NUM
ejpam-5857	834	6	)	)	PUNCT
ejpam-5857	834	7	.	.	PUNCT
ejpam-5857	835	1	we	we	PRON
ejpam-5857	835	2	have	have	AUX
ejpam-5857	835	3	ψt	ψt	VERB
ejpam-5857	835	4	(	(	PUNCT
ejpam-5857	835	5	x	x	X
ejpam-5857	835	6	·	·	PUNCT
ejpam-5857	835	7	z	z	X
ejpam-5857	835	8	)	)	PUNCT
ejpam-5857	835	9	≥	≥	NOUN
ejpam-5857	835	10	(	(	PUNCT
ejpam-5857	835	11	ψt	ψt	VERB
ejpam-5857	835	12	(	(	PUNCT
ejpam-5857	835	13	x	x	X
ejpam-5857	835	14	·	·	PUNCT
ejpam-5857	835	15	(	(	PUNCT
ejpam-5857	835	16	y	y	PROPN
ejpam-5857	835	17	·	·	PUNCT
ejpam-5857	835	18	z	z	NOUN
ejpam-5857	835	19	)	)	PUNCT
ejpam-5857	835	20	)	)	PUNCT
ejpam-5857	836	1	∧	∧	NOUN
ejpam-5857	836	2	ψt	ψt	NOUN
ejpam-5857	836	3	(	(	PUNCT
ejpam-5857	836	4	y))∨	y))∨	NOUN
ejpam-5857	836	5	0.5	0.5	NUM
ejpam-5857	836	6	>	>	X
ejpam-5857	836	7	α∨	α∨	PROPN
ejpam-5857	836	8	0.5	0.5	NUM
ejpam-5857	836	9	≥	≥	NUM
ejpam-5857	836	10	α	α	NOUN
ejpam-5857	836	11	.	.	PUNCT
ejpam-5857	837	1	thus	thus	ADV
ejpam-5857	837	2	,	,	PUNCT
ejpam-5857	837	3	x	x	X
ejpam-5857	837	4	·	·	PUNCT
ejpam-5857	837	5	z	z	X
ejpam-5857	837	6	∈	∈	PROPN
ejpam-5857	837	7	u	u	NOUN
ejpam-5857	837	8	+	+	X
ejpam-5857	837	9	(	(	PUNCT
ejpam-5857	837	10	ψt	ψt	NUM
ejpam-5857	837	11	;	;	PUNCT
ejpam-5857	837	12	α	α	X
ejpam-5857	837	13	)	)	PUNCT
ejpam-5857	837	14	.	.	PUNCT
ejpam-5857	838	1	hence	hence	ADV
ejpam-5857	838	2	,	,	PUNCT
ejpam-5857	838	3	u	u	PROPN
ejpam-5857	838	4	+	+	X
ejpam-5857	838	5	(	(	PUNCT
ejpam-5857	838	6	ψt	ψt	NUM
ejpam-5857	838	7	;	;	PUNCT
ejpam-5857	838	8	α	α	X
ejpam-5857	838	9	)	)	PUNCT
ejpam-5857	838	10	is	be	AUX
ejpam-5857	838	11	an	an	DET
ejpam-5857	838	12	iup	iup	NOUN
ejpam-5857	838	13	-	-	PUNCT
ejpam-5857	838	14	ideal	ideal	NOUN
ejpam-5857	838	15	of	of	ADP
ejpam-5857	838	16	x.	x.	NOUN
ejpam-5857	838	17	let	let	VERB
ejpam-5857	838	18	β	β	X
ejpam-5857	838	19	∈	∈	PROPN
ejpam-5857	839	1	[	[	X
ejpam-5857	839	2	0	0	NUM
ejpam-5857	839	3	,	,	PUNCT
ejpam-5857	839	4	0.5	0.5	NUM
ejpam-5857	839	5	)	)	PUNCT
ejpam-5857	839	6	be	be	VERB
ejpam-5857	839	7	such	such	ADJ
ejpam-5857	839	8	that	that	SCONJ
ejpam-5857	839	9	l	l	NOUN
ejpam-5857	840	1	−	−	PROPN
ejpam-5857	840	2	(	(	PUNCT
ejpam-5857	840	3	ψi	ψi	ADP
ejpam-5857	840	4	;	;	PUNCT
ejpam-5857	840	5	β	β	X
ejpam-5857	840	6	)	)	PUNCT
ejpam-5857	840	7	̸=	̸=	PROPN
ejpam-5857	840	8	∅.	∅.	ADV
ejpam-5857	840	9	let	let	VERB
ejpam-5857	840	10	b	b	NOUN
ejpam-5857	840	11	∈	∈	PROPN
ejpam-5857	840	12	l	l	NOUN
ejpam-5857	840	13	−	−	PROPN
ejpam-5857	841	1	(	(	PUNCT
ejpam-5857	841	2	ψi	ψi	ADP
ejpam-5857	841	3	;	;	PUNCT
ejpam-5857	841	4	β	β	X
ejpam-5857	841	5	)	)	PUNCT
ejpam-5857	841	6	.	.	PUNCT
ejpam-5857	842	1	then	then	ADV
ejpam-5857	842	2	ψi(b	ψi(b	PUNCT
ejpam-5857	842	3	)	)	PUNCT
ejpam-5857	842	4	<	<	X
ejpam-5857	842	5	β	β	X
ejpam-5857	842	6	.	.	PUNCT
ejpam-5857	843	1	by	by	ADP
ejpam-5857	843	2	the	the	DET
ejpam-5857	843	3	condition	condition	NOUN
ejpam-5857	843	4	(	(	PUNCT
ejpam-5857	843	5	3.9	3.9	NUM
ejpam-5857	843	6	)	)	PUNCT
ejpam-5857	843	7	,	,	PUNCT
ejpam-5857	843	8	we	we	PRON
ejpam-5857	843	9	have	have	VERB
ejpam-5857	843	10	ψi(0	ψi(0	PROPN
ejpam-5857	843	11	)	)	PUNCT
ejpam-5857	843	12	≤	≤	NOUN
ejpam-5857	843	13	ψi(b	ψi(b	PUNCT
ejpam-5857	843	14	)	)	PUNCT
ejpam-5857	843	15	<	<	X
ejpam-5857	843	16	β	β	X
ejpam-5857	843	17	.	.	PUNCT
ejpam-5857	844	1	thus	thus	ADV
ejpam-5857	844	2	,	,	PUNCT
ejpam-5857	844	3	0	0	NUM
ejpam-5857	844	4	∈	∈	PROPN
ejpam-5857	844	5	l	l	NOUN
ejpam-5857	844	6	−	−	PROPN
ejpam-5857	844	7	(	(	PUNCT
ejpam-5857	844	8	ψi	ψi	ADP
ejpam-5857	844	9	;	;	PUNCT
ejpam-5857	844	10	β	β	X
ejpam-5857	844	11	)	)	PUNCT
ejpam-5857	844	12	.	.	PUNCT
ejpam-5857	845	1	let	let	VERB
ejpam-5857	845	2	x	x	PRON
ejpam-5857	845	3	,	,	PUNCT
ejpam-5857	845	4	y	y	PROPN
ejpam-5857	845	5	,	,	PUNCT
ejpam-5857	845	6	z	z	NOUN
ejpam-5857	845	7	∈	∈	PROPN
ejpam-5857	845	8	l	l	NOUN
ejpam-5857	845	9	−	−	PROPN
ejpam-5857	845	10	(	(	PUNCT
ejpam-5857	845	11	ψi	ψi	ADP
ejpam-5857	845	12	;	;	PUNCT
ejpam-5857	845	13	β	β	X
ejpam-5857	845	14	)	)	PUNCT
ejpam-5857	845	15	be	be	AUX
ejpam-5857	845	16	such	such	ADJ
ejpam-5857	845	17	that	that	SCONJ
ejpam-5857	846	1	x	x	PART
ejpam-5857	846	2	·	·	PUNCT
ejpam-5857	846	3	(	(	PUNCT
ejpam-5857	846	4	y	y	PROPN
ejpam-5857	846	5	·	·	PUNCT
ejpam-5857	846	6	z	z	X
ejpam-5857	846	7	)	)	PUNCT
ejpam-5857	846	8	,	,	PUNCT
ejpam-5857	846	9	y	y	PROPN
ejpam-5857	846	10	∈	∈	PROPN
ejpam-5857	846	11	l	l	NOUN
ejpam-5857	847	1	−	−	PROPN
ejpam-5857	847	2	(	(	PUNCT
ejpam-5857	847	3	ψi	ψi	ADP
ejpam-5857	847	4	;	;	PUNCT
ejpam-5857	847	5	β	β	X
ejpam-5857	847	6	)	)	PUNCT
ejpam-5857	847	7	.	.	PUNCT
ejpam-5857	848	1	then	then	ADV
ejpam-5857	848	2	ψi(x	ψi(x	NOUN
ejpam-5857	848	3	·	·	PUNCT
ejpam-5857	848	4	(	(	PUNCT
ejpam-5857	848	5	y	y	PROPN
ejpam-5857	848	6	·	·	PUNCT
ejpam-5857	848	7	z	z	X
ejpam-5857	848	8	)	)	PUNCT
ejpam-5857	848	9	)	)	PUNCT
ejpam-5857	849	1	<	<	X
ejpam-5857	849	2	β	β	PROPN
ejpam-5857	849	3	k.	k.	PROPN
ejpam-5857	849	4	suayngam	suayngam	PROPN
ejpam-5857	849	5	,	,	PUNCT
ejpam-5857	849	6	p.	p.	NOUN
ejpam-5857	849	7	julatha	julatha	PROPN
ejpam-5857	849	8	,	,	PUNCT
ejpam-5857	849	9	w.	w.	PROPN
ejpam-5857	849	10	nakkhasen	nakkhasen	PROPN
ejpam-5857	849	11	,	,	PUNCT
ejpam-5857	849	12	a.	a.	NOUN
ejpam-5857	849	13	iampan	iampan	PROPN
ejpam-5857	849	14	/	/	SYM
ejpam-5857	849	15	eur	eur	PROPN
ejpam-5857	849	16	.	.	PUNCT
ejpam-5857	850	1	j.	j.	PROPN
ejpam-5857	850	2	pure	pure	PROPN
ejpam-5857	850	3	appl	appl	PROPN
ejpam-5857	850	4	.	.	PROPN
ejpam-5857	850	5	math	math	PROPN
ejpam-5857	850	6	,	,	PUNCT
ejpam-5857	850	7	18	18	NUM
ejpam-5857	850	8	(	(	PUNCT
ejpam-5857	850	9	2	2	NUM
ejpam-5857	850	10	)	)	PUNCT
ejpam-5857	850	11	(	(	PUNCT
ejpam-5857	850	12	2025	2025	NUM
ejpam-5857	850	13	)	)	PUNCT
ejpam-5857	850	14	,	,	PUNCT
ejpam-5857	850	15	5857	5857	NUM
ejpam-5857	850	16	26	26	NUM
ejpam-5857	850	17	of	of	ADP
ejpam-5857	850	18	30	30	NUM
ejpam-5857	850	19	and	and	CCONJ
ejpam-5857	850	20	ψt	ψt	ADJ
ejpam-5857	850	21	(	(	PUNCT
ejpam-5857	850	22	y	y	NOUN
ejpam-5857	850	23	)	)	PUNCT
ejpam-5857	850	24	<	<	X
ejpam-5857	850	25	β	β	X
ejpam-5857	850	26	.	.	PUNCT
ejpam-5857	851	1	thus	thus	ADV
ejpam-5857	851	2	,	,	PUNCT
ejpam-5857	851	3	ψi(x	ψi(x	X
ejpam-5857	851	4	·	·	PUNCT
ejpam-5857	851	5	(	(	PUNCT
ejpam-5857	851	6	y	y	PROPN
ejpam-5857	851	7	·	·	PUNCT
ejpam-5857	851	8	z	z	NOUN
ejpam-5857	851	9	)	)	PUNCT
ejpam-5857	851	10	)	)	PUNCT
ejpam-5857	851	11	∨	∨	NUM
ejpam-5857	851	12	ψi(y	ψi(y	NUM
ejpam-5857	851	13	)	)	PUNCT
ejpam-5857	851	14	<	<	X
ejpam-5857	851	15	β	β	X
ejpam-5857	851	16	.	.	PUNCT
ejpam-5857	851	17	by	by	ADP
ejpam-5857	851	18	the	the	DET
ejpam-5857	851	19	condition	condition	NOUN
ejpam-5857	851	20	(	(	PUNCT
ejpam-5857	851	21	3.12	3.12	NUM
ejpam-5857	851	22	)	)	PUNCT
ejpam-5857	851	23	.	.	PUNCT
ejpam-5857	852	1	we	we	PRON
ejpam-5857	852	2	have	have	VERB
ejpam-5857	852	3	ψi(x	ψi(x	NUM
ejpam-5857	852	4	·	·	PUNCT
ejpam-5857	853	1	z	z	X
ejpam-5857	853	2	)	)	PUNCT
ejpam-5857	853	3	≤	≤	NOUN
ejpam-5857	853	4	(	(	PUNCT
ejpam-5857	853	5	ψi(x	ψi(x	X
ejpam-5857	853	6	·	·	PUNCT
ejpam-5857	853	7	(	(	PUNCT
ejpam-5857	853	8	y	y	PROPN
ejpam-5857	853	9	·	·	PUNCT
ejpam-5857	853	10	z	z	NOUN
ejpam-5857	853	11	)	)	PUNCT
ejpam-5857	853	12	)	)	PUNCT
ejpam-5857	854	1	∨	∨	NUM
ejpam-5857	854	2	ψi(y	ψi(y	NUM
ejpam-5857	854	3	)	)	PUNCT
ejpam-5857	854	4	)	)	PUNCT
ejpam-5857	855	1	∧	∧	NOUN
ejpam-5857	855	2	0.5	0.5	NUM
ejpam-5857	855	3	<	<	X
ejpam-5857	855	4	β	β	X
ejpam-5857	855	5	∧	∧	PROPN
ejpam-5857	855	6	0.5	0.5	NUM
ejpam-5857	855	7	≤	≤	NUM
ejpam-5857	855	8	β	β	NOUN
ejpam-5857	855	9	.	.	PUNCT
ejpam-5857	856	1	thus	thus	ADV
ejpam-5857	856	2	,	,	PUNCT
ejpam-5857	856	3	x	x	X
ejpam-5857	856	4	·	·	PUNCT
ejpam-5857	856	5	z	z	SYM
ejpam-5857	856	6	∈	∈	PROPN
ejpam-5857	856	7	l	l	NOUN
ejpam-5857	856	8	−	−	PROPN
ejpam-5857	856	9	(	(	PUNCT
ejpam-5857	856	10	ψi	ψi	ADP
ejpam-5857	856	11	;	;	PUNCT
ejpam-5857	856	12	β	β	X
ejpam-5857	856	13	)	)	PUNCT
ejpam-5857	856	14	.	.	PUNCT
ejpam-5857	857	1	hence	hence	ADV
ejpam-5857	857	2	,	,	PUNCT
ejpam-5857	857	3	l	l	NOUN
ejpam-5857	857	4	−	−	PROPN
ejpam-5857	857	5	(	(	PUNCT
ejpam-5857	857	6	ψi	ψi	ADP
ejpam-5857	857	7	;	;	PUNCT
ejpam-5857	857	8	β	β	X
ejpam-5857	857	9	)	)	PUNCT
ejpam-5857	857	10	is	be	AUX
ejpam-5857	857	11	an	an	DET
ejpam-5857	857	12	iup	iup	NOUN
ejpam-5857	857	13	-	-	PUNCT
ejpam-5857	857	14	ideal	ideal	NOUN
ejpam-5857	857	15	of	of	ADP
ejpam-5857	857	16	x.	x.	NOUN
ejpam-5857	857	17	let	let	VERB
ejpam-5857	857	18	γ	γ	X
ejpam-5857	857	19	∈	∈	PROPN
ejpam-5857	857	20	[	[	X
ejpam-5857	857	21	0.5	0.5	NUM
ejpam-5857	857	22	,	,	PUNCT
ejpam-5857	857	23	1	1	NUM
ejpam-5857	857	24	]	]	PUNCT
ejpam-5857	857	25	be	be	AUX
ejpam-5857	857	26	such	such	ADJ
ejpam-5857	857	27	that	that	SCONJ
ejpam-5857	857	28	u	u	NOUN
ejpam-5857	857	29	+	+	X
ejpam-5857	857	30	(	(	PUNCT
ejpam-5857	857	31	ψf	ψf	X
ejpam-5857	857	32	;	;	PUNCT
ejpam-5857	857	33	γ	γ	X
ejpam-5857	857	34	)	)	PUNCT
ejpam-5857	857	35	̸=	̸=	PROPN
ejpam-5857	857	36	∅.	∅.	ADV
ejpam-5857	857	37	let	let	VERB
ejpam-5857	857	38	c	c	NOUN
ejpam-5857	857	39	∈	∈	PROPN
ejpam-5857	857	40	u	u	NOUN
ejpam-5857	857	41	+	+	X
ejpam-5857	857	42	(	(	PUNCT
ejpam-5857	857	43	ψf	ψf	X
ejpam-5857	857	44	;	;	PUNCT
ejpam-5857	857	45	γ	γ	X
ejpam-5857	857	46	)	)	PUNCT
ejpam-5857	857	47	.	.	PUNCT
ejpam-5857	858	1	then	then	ADV
ejpam-5857	858	2	ψf	ψf	X
ejpam-5857	858	3	(	(	PUNCT
ejpam-5857	858	4	c	c	NOUN
ejpam-5857	858	5	)	)	PUNCT
ejpam-5857	858	6	>	>	X
ejpam-5857	859	1	γ	γ	X
ejpam-5857	859	2	.	.	PROPN
ejpam-5857	859	3	by	by	ADP
ejpam-5857	859	4	the	the	DET
ejpam-5857	859	5	condition	condition	NOUN
ejpam-5857	859	6	(	(	PUNCT
ejpam-5857	859	7	3.10	3.10	NUM
ejpam-5857	859	8	)	)	PUNCT
ejpam-5857	859	9	,	,	PUNCT
ejpam-5857	859	10	we	we	PRON
ejpam-5857	859	11	have	have	AUX
ejpam-5857	859	12	ψf	ψf	X
ejpam-5857	859	13	(	(	PUNCT
ejpam-5857	859	14	0	0	NUM
ejpam-5857	859	15	)	)	PUNCT
ejpam-5857	859	16	≥	≥	NOUN
ejpam-5857	859	17	ψf	ψf	X
ejpam-5857	859	18	(	(	PUNCT
ejpam-5857	859	19	c	c	NOUN
ejpam-5857	859	20	)	)	PUNCT
ejpam-5857	859	21	>	>	X
ejpam-5857	860	1	γ	γ	X
ejpam-5857	860	2	.	.	PUNCT
ejpam-5857	860	3	thus	thus	ADV
ejpam-5857	860	4	,	,	PUNCT
ejpam-5857	860	5	0	0	NUM
ejpam-5857	860	6	∈	∈	PROPN
ejpam-5857	860	7	u	u	NOUN
ejpam-5857	860	8	+	+	X
ejpam-5857	860	9	(	(	PUNCT
ejpam-5857	860	10	ψf	ψf	X
ejpam-5857	860	11	;	;	PUNCT
ejpam-5857	860	12	γ	γ	X
ejpam-5857	860	13	)	)	PUNCT
ejpam-5857	860	14	.	.	PUNCT
ejpam-5857	861	1	let	let	VERB
ejpam-5857	861	2	x	x	PRON
ejpam-5857	861	3	,	,	PUNCT
ejpam-5857	861	4	y	y	PROPN
ejpam-5857	861	5	,	,	PUNCT
ejpam-5857	861	6	z	z	PROPN
ejpam-5857	861	7	∈	∈	PROPN
ejpam-5857	861	8	u	u	NOUN
ejpam-5857	861	9	+	+	X
ejpam-5857	861	10	(	(	PUNCT
ejpam-5857	861	11	ψf	ψf	X
ejpam-5857	861	12	;	;	PUNCT
ejpam-5857	861	13	γ	γ	X
ejpam-5857	861	14	)	)	PUNCT
ejpam-5857	861	15	be	be	VERB
ejpam-5857	861	16	such	such	ADJ
ejpam-5857	861	17	that	that	SCONJ
ejpam-5857	861	18	x	x	PART
ejpam-5857	861	19	·	·	PUNCT
ejpam-5857	861	20	(	(	PUNCT
ejpam-5857	861	21	y	y	PROPN
ejpam-5857	861	22	·	·	PUNCT
ejpam-5857	861	23	z	z	X
ejpam-5857	861	24	)	)	PUNCT
ejpam-5857	861	25	,	,	PUNCT
ejpam-5857	861	26	y	y	PROPN
ejpam-5857	861	27	∈	∈	PROPN
ejpam-5857	861	28	u	u	PROPN
ejpam-5857	861	29	+	+	X
ejpam-5857	861	30	(	(	PUNCT
ejpam-5857	861	31	ψf	ψf	X
ejpam-5857	861	32	;	;	PUNCT
ejpam-5857	861	33	γ	γ	X
ejpam-5857	861	34	)	)	PUNCT
ejpam-5857	861	35	.	.	PUNCT
ejpam-5857	862	1	then	then	ADV
ejpam-5857	862	2	ψf	ψf	X
ejpam-5857	862	3	(	(	PUNCT
ejpam-5857	862	4	x	x	X
ejpam-5857	862	5	·	·	PUNCT
ejpam-5857	862	6	(	(	PUNCT
ejpam-5857	862	7	y	y	PROPN
ejpam-5857	862	8	·	·	PUNCT
ejpam-5857	862	9	z	z	X
ejpam-5857	862	10	)	)	PUNCT
ejpam-5857	862	11	)	)	PUNCT
ejpam-5857	862	12	>	>	X
ejpam-5857	862	13	γ	γ	PROPN
ejpam-5857	862	14	and	and	CCONJ
ejpam-5857	862	15	ψf	ψf	X
ejpam-5857	862	16	(	(	PUNCT
ejpam-5857	862	17	y	y	PROPN
ejpam-5857	862	18	)	)	PUNCT
ejpam-5857	862	19	>	>	X
ejpam-5857	862	20	γ	γ	X
ejpam-5857	862	21	.	.	PUNCT
ejpam-5857	862	22	thus	thus	ADV
ejpam-5857	862	23	,	,	PUNCT
ejpam-5857	862	24	ψf	ψf	X
ejpam-5857	862	25	(	(	PUNCT
ejpam-5857	862	26	x	x	X
ejpam-5857	862	27	·	·	PUNCT
ejpam-5857	862	28	(	(	PUNCT
ejpam-5857	862	29	y	y	PROPN
ejpam-5857	862	30	·	·	PUNCT
ejpam-5857	862	31	z	z	NOUN
ejpam-5857	862	32	)	)	PUNCT
ejpam-5857	862	33	)	)	PUNCT
ejpam-5857	862	34	∧	∧	NOUN
ejpam-5857	862	35	ψf	ψf	X
ejpam-5857	862	36	(	(	PUNCT
ejpam-5857	862	37	y	y	NOUN
ejpam-5857	862	38	)	)	PUNCT
ejpam-5857	862	39	>	>	X
ejpam-5857	863	1	γ	γ	X
ejpam-5857	863	2	.	.	PROPN
ejpam-5857	863	3	by	by	ADP
ejpam-5857	863	4	the	the	DET
ejpam-5857	863	5	condition	condition	NOUN
ejpam-5857	863	6	(	(	PUNCT
ejpam-5857	863	7	3.13	3.13	NUM
ejpam-5857	863	8	)	)	PUNCT
ejpam-5857	863	9	.	.	PUNCT
ejpam-5857	864	1	we	we	PRON
ejpam-5857	864	2	have	have	VERB
ejpam-5857	864	3	ψf	ψf	VERB
ejpam-5857	864	4	(	(	PUNCT
ejpam-5857	864	5	x	x	X
ejpam-5857	864	6	·	·	PUNCT
ejpam-5857	864	7	z	z	X
ejpam-5857	864	8	)	)	PUNCT
ejpam-5857	864	9	≥	≥	NOUN
ejpam-5857	864	10	(	(	PUNCT
ejpam-5857	864	11	ψf	ψf	X
ejpam-5857	864	12	(	(	PUNCT
ejpam-5857	864	13	x	x	X
ejpam-5857	864	14	·	·	PUNCT
ejpam-5857	864	15	(	(	PUNCT
ejpam-5857	864	16	y	y	PROPN
ejpam-5857	864	17	·	·	PUNCT
ejpam-5857	864	18	z	z	NOUN
ejpam-5857	864	19	)	)	PUNCT
ejpam-5857	864	20	)	)	PUNCT
ejpam-5857	865	1	∧	∧	NOUN
ejpam-5857	865	2	ψf	ψf	X
ejpam-5857	865	3	(	(	PUNCT
ejpam-5857	865	4	y	y	NOUN
ejpam-5857	865	5	)	)	PUNCT
ejpam-5857	865	6	)	)	PUNCT
ejpam-5857	866	1	∨	∨	NUM
ejpam-5857	866	2	0.5	0.5	NUM
ejpam-5857	866	3	>	>	X
ejpam-5857	866	4	γ	γ	PROPN
ejpam-5857	866	5	∨	∨	NUM
ejpam-5857	866	6	0.5	0.5	NUM
ejpam-5857	866	7	≥	≥	PROPN
ejpam-5857	866	8	γ	γ	PROPN
ejpam-5857	866	9	.	.	PROPN
ejpam-5857	866	10	thus	thus	ADV
ejpam-5857	866	11	,	,	PUNCT
ejpam-5857	866	12	x	x	X
ejpam-5857	866	13	·	·	PUNCT
ejpam-5857	866	14	z	z	X
ejpam-5857	866	15	∈	∈	PROPN
ejpam-5857	866	16	u	u	NOUN
ejpam-5857	866	17	+	+	X
ejpam-5857	866	18	(	(	PUNCT
ejpam-5857	866	19	ψf	ψf	X
ejpam-5857	866	20	;	;	PUNCT
ejpam-5857	866	21	γ	γ	X
ejpam-5857	866	22	)	)	PUNCT
ejpam-5857	866	23	.	.	PUNCT
ejpam-5857	867	1	hence	hence	ADV
ejpam-5857	867	2	,	,	PUNCT
ejpam-5857	867	3	u	u	PROPN
ejpam-5857	867	4	+	+	X
ejpam-5857	867	5	(	(	PUNCT
ejpam-5857	867	6	ψf	ψf	X
ejpam-5857	867	7	;	;	PUNCT
ejpam-5857	867	8	γ	γ	X
ejpam-5857	867	9	)	)	PUNCT
ejpam-5857	867	10	is	be	AUX
ejpam-5857	867	11	an	an	DET
ejpam-5857	867	12	iup	iup	NOUN
ejpam-5857	867	13	-	-	PUNCT
ejpam-5857	867	14	ideal	ideal	NOUN
ejpam-5857	867	15	of	of	ADP
ejpam-5857	867	16	x.	x.	PROPN
ejpam-5857	867	17	theorem	theorem	VERB
ejpam-5857	867	18	28	28	NUM
ejpam-5857	867	19	.	.	PUNCT
ejpam-5857	868	1	let	let	VERB
ejpam-5857	868	2	ψ	ψ	PART
ejpam-5857	868	3	be	be	AUX
ejpam-5857	868	4	an	an	DET
ejpam-5857	868	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	868	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	868	7	iup	iup	NOUN
ejpam-5857	868	8	-	-	PUNCT
ejpam-5857	868	9	filter	filter	NOUN
ejpam-5857	868	10	of	of	ADP
ejpam-5857	868	11	x.	x.	NOUN
ejpam-5857	868	12	then	then	ADV
ejpam-5857	868	13	for	for	ADP
ejpam-5857	868	14	all	all	DET
ejpam-5857	868	15	α	α	NOUN
ejpam-5857	868	16	,	,	PUNCT
ejpam-5857	868	17	γ	γ	PROPN
ejpam-5857	868	18	∈	∈	PROPN
ejpam-5857	869	1	[	[	X
ejpam-5857	869	2	0.5	0.5	NUM
ejpam-5857	869	3	,	,	PUNCT
ejpam-5857	869	4	1	1	NUM
ejpam-5857	869	5	]	]	PUNCT
ejpam-5857	869	6	and	and	CCONJ
ejpam-5857	869	7	β	β	X
ejpam-5857	869	8	∈	∈	PROPN
ejpam-5857	869	9	[	[	X
ejpam-5857	869	10	0	0	NUM
ejpam-5857	869	11	,	,	PUNCT
ejpam-5857	869	12	0.5	0.5	NUM
ejpam-5857	869	13	)	)	PUNCT
ejpam-5857	869	14	,	,	PUNCT
ejpam-5857	869	15	the	the	DET
ejpam-5857	869	16	sets	set	NOUN
ejpam-5857	869	17	u	u	NOUN
ejpam-5857	869	18	+	+	X
ejpam-5857	869	19	(	(	PUNCT
ejpam-5857	869	20	ψt	ψt	NUM
ejpam-5857	869	21	;	;	PUNCT
ejpam-5857	869	22	α	α	X
ejpam-5857	869	23	)	)	PUNCT
ejpam-5857	869	24	,	,	PUNCT
ejpam-5857	869	25	l	l	NOUN
ejpam-5857	869	26	−	−	PROPN
ejpam-5857	869	27	(	(	PUNCT
ejpam-5857	869	28	ψi	ψi	ADP
ejpam-5857	869	29	;	;	PUNCT
ejpam-5857	869	30	β	β	X
ejpam-5857	869	31	)	)	PUNCT
ejpam-5857	869	32	and	and	CCONJ
ejpam-5857	869	33	u	u	PRON
ejpam-5857	869	34	+	+	X
ejpam-5857	869	35	(	(	PUNCT
ejpam-5857	869	36	ψf	ψf	X
ejpam-5857	869	37	;	;	PUNCT
ejpam-5857	869	38	γ	γ	X
ejpam-5857	869	39	)	)	PUNCT
ejpam-5857	869	40	are	be	AUX
ejpam-5857	869	41	either	either	CCONJ
ejpam-5857	869	42	empty	empty	ADJ
ejpam-5857	869	43	or	or	CCONJ
ejpam-5857	869	44	iup	iup	NOUN
ejpam-5857	869	45	-	-	PUNCT
ejpam-5857	869	46	filters	filter	NOUN
ejpam-5857	869	47	of	of	ADP
ejpam-5857	869	48	x.	x.	NOUN
ejpam-5857	869	49	proof	proof	PROPN
ejpam-5857	869	50	.	.	PUNCT
ejpam-5857	870	1	assume	assume	VERB
ejpam-5857	870	2	that	that	SCONJ
ejpam-5857	870	3	ψ	ψ	PART
ejpam-5857	870	4	be	be	AUX
ejpam-5857	870	5	an	an	DET
ejpam-5857	870	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	870	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	870	8	iup	iup	NOUN
ejpam-5857	870	9	-	-	PUNCT
ejpam-5857	870	10	filter	filter	NOUN
ejpam-5857	870	11	of	of	ADP
ejpam-5857	870	12	x.	x.	NOUN
ejpam-5857	870	13	let	let	VERB
ejpam-5857	870	14	α	α	PRON
ejpam-5857	870	15	∈	∈	PROPN
ejpam-5857	871	1	[	[	X
ejpam-5857	871	2	0.5	0.5	NUM
ejpam-5857	871	3	,	,	PUNCT
ejpam-5857	871	4	1	1	NUM
ejpam-5857	871	5	]	]	PUNCT
ejpam-5857	871	6	be	be	AUX
ejpam-5857	871	7	such	such	ADJ
ejpam-5857	871	8	that	that	SCONJ
ejpam-5857	871	9	u	u	NOUN
ejpam-5857	871	10	+	+	X
ejpam-5857	871	11	(	(	PUNCT
ejpam-5857	871	12	ψt	ψt	NUM
ejpam-5857	871	13	;	;	PUNCT
ejpam-5857	871	14	α	α	X
ejpam-5857	871	15	)	)	PUNCT
ejpam-5857	871	16	̸=	̸=	PROPN
ejpam-5857	871	17	∅.	∅.	ADV
ejpam-5857	871	18	let	let	VERB
ejpam-5857	871	19	a	a	DET
ejpam-5857	871	20	∈	∈	PROPN
ejpam-5857	871	21	u	u	NOUN
ejpam-5857	871	22	+	+	X
ejpam-5857	871	23	(	(	PUNCT
ejpam-5857	871	24	ψt	ψt	NUM
ejpam-5857	871	25	;	;	PUNCT
ejpam-5857	871	26	α	α	X
ejpam-5857	871	27	)	)	PUNCT
ejpam-5857	871	28	.	.	PUNCT
ejpam-5857	872	1	then	then	ADV
ejpam-5857	872	2	ψt	ψt	VERB
ejpam-5857	872	3	(	(	PUNCT
ejpam-5857	872	4	a	a	NOUN
ejpam-5857	872	5	)	)	PUNCT
ejpam-5857	872	6	>	>	X
ejpam-5857	873	1	α	α	X
ejpam-5857	873	2	.	.	PUNCT
ejpam-5857	874	1	by	by	ADP
ejpam-5857	874	2	the	the	DET
ejpam-5857	874	3	condition	condition	NOUN
ejpam-5857	874	4	(	(	PUNCT
ejpam-5857	874	5	3.8	3.8	NUM
ejpam-5857	874	6	)	)	PUNCT
ejpam-5857	874	7	,	,	PUNCT
ejpam-5857	874	8	we	we	PRON
ejpam-5857	874	9	have	have	AUX
ejpam-5857	874	10	ψt	ψt	VERB
ejpam-5857	874	11	(	(	PUNCT
ejpam-5857	874	12	0	0	NUM
ejpam-5857	874	13	)	)	PUNCT
ejpam-5857	874	14	≥	≥	PRON
ejpam-5857	874	15	ψt	ψt	NOUN
ejpam-5857	874	16	(	(	PUNCT
ejpam-5857	874	17	a	a	NOUN
ejpam-5857	874	18	)	)	PUNCT
ejpam-5857	875	1	>	>	X
ejpam-5857	875	2	α	α	X
ejpam-5857	875	3	.	.	PUNCT
ejpam-5857	876	1	thus	thus	ADV
ejpam-5857	876	2	,	,	PUNCT
ejpam-5857	876	3	0	0	NUM
ejpam-5857	876	4	∈	∈	PROPN
ejpam-5857	876	5	u	u	NOUN
ejpam-5857	876	6	+	+	X
ejpam-5857	876	7	(	(	PUNCT
ejpam-5857	876	8	ψt	ψt	NUM
ejpam-5857	876	9	;	;	PUNCT
ejpam-5857	876	10	α	α	X
ejpam-5857	876	11	)	)	PUNCT
ejpam-5857	876	12	.	.	PUNCT
ejpam-5857	877	1	let	let	VERB
ejpam-5857	877	2	x	x	PRON
ejpam-5857	877	3	,	,	PUNCT
ejpam-5857	877	4	y	y	PROPN
ejpam-5857	877	5	∈	∈	PROPN
ejpam-5857	877	6	u	u	PROPN
ejpam-5857	877	7	+	+	X
ejpam-5857	877	8	(	(	PUNCT
ejpam-5857	877	9	ψt	ψt	NUM
ejpam-5857	877	10	;	;	PUNCT
ejpam-5857	877	11	α	α	X
ejpam-5857	877	12	)	)	PUNCT
ejpam-5857	877	13	be	be	VERB
ejpam-5857	877	14	such	such	ADJ
ejpam-5857	877	15	that	that	SCONJ
ejpam-5857	877	16	x	x	X
ejpam-5857	877	17	·	·	PUNCT
ejpam-5857	877	18	y	y	X
ejpam-5857	877	19	,	,	PUNCT
ejpam-5857	877	20	x	x	SYM
ejpam-5857	877	21	∈	∈	PROPN
ejpam-5857	877	22	u	u	NOUN
ejpam-5857	877	23	+	+	X
ejpam-5857	877	24	(	(	PUNCT
ejpam-5857	877	25	ψt	ψt	NUM
ejpam-5857	877	26	;	;	PUNCT
ejpam-5857	877	27	α	α	X
ejpam-5857	877	28	)	)	PUNCT
ejpam-5857	877	29	.	.	PUNCT
ejpam-5857	878	1	then	then	ADV
ejpam-5857	878	2	ψt	ψt	VERB
ejpam-5857	878	3	(	(	PUNCT
ejpam-5857	878	4	x	x	PROPN
ejpam-5857	878	5	·	·	PUNCT
ejpam-5857	878	6	y	y	X
ejpam-5857	878	7	)	)	PUNCT
ejpam-5857	878	8	>	>	X
ejpam-5857	879	1	α	α	PROPN
ejpam-5857	879	2	and	and	CCONJ
ejpam-5857	879	3	ψt	ψt	ADJ
ejpam-5857	879	4	(	(	PUNCT
ejpam-5857	879	5	x	x	X
ejpam-5857	879	6	)	)	PUNCT
ejpam-5857	879	7	>	>	X
ejpam-5857	880	1	α	α	X
ejpam-5857	880	2	.	.	PUNCT
ejpam-5857	881	1	thus	thus	ADV
ejpam-5857	881	2	,	,	PUNCT
ejpam-5857	881	3	ψt	ψt	VERB
ejpam-5857	881	4	(	(	PUNCT
ejpam-5857	881	5	x	x	PROPN
ejpam-5857	881	6	·	·	PUNCT
ejpam-5857	881	7	y	y	X
ejpam-5857	881	8	)	)	PUNCT
ejpam-5857	881	9	∧	∧	NOUN
ejpam-5857	881	10	ψt	ψt	NOUN
ejpam-5857	881	11	(	(	PUNCT
ejpam-5857	881	12	x	x	X
ejpam-5857	881	13	)	)	PUNCT
ejpam-5857	881	14	>	>	X
ejpam-5857	881	15	α	α	X
ejpam-5857	881	16	.	.	PUNCT
ejpam-5857	882	1	by	by	ADP
ejpam-5857	882	2	the	the	DET
ejpam-5857	882	3	condition	condition	NOUN
ejpam-5857	882	4	(	(	PUNCT
ejpam-5857	882	5	3.14	3.14	NUM
ejpam-5857	882	6	)	)	PUNCT
ejpam-5857	882	7	.	.	PUNCT
ejpam-5857	883	1	we	we	PRON
ejpam-5857	883	2	have	have	AUX
ejpam-5857	883	3	ψt	ψt	VERB
ejpam-5857	883	4	(	(	PUNCT
ejpam-5857	883	5	y	y	NOUN
ejpam-5857	883	6	)	)	PUNCT
ejpam-5857	883	7	≥	≥	NOUN
ejpam-5857	883	8	(	(	PUNCT
ejpam-5857	883	9	ψt	ψt	VERB
ejpam-5857	883	10	(	(	PUNCT
ejpam-5857	883	11	x	x	PROPN
ejpam-5857	883	12	·	·	PUNCT
ejpam-5857	883	13	y	y	X
ejpam-5857	883	14	)	)	PUNCT
ejpam-5857	883	15	∧	∧	NOUN
ejpam-5857	883	16	ψt	ψt	NOUN
ejpam-5857	883	17	(	(	PUNCT
ejpam-5857	883	18	x	x	NOUN
ejpam-5857	883	19	)	)	PUNCT
ejpam-5857	883	20	)	)	PUNCT
ejpam-5857	883	21	∨	∨	NUM
ejpam-5857	883	22	0.5	0.5	NUM
ejpam-5857	883	23	>	>	X
ejpam-5857	883	24	α	α	PROPN
ejpam-5857	883	25	∨	∨	NUM
ejpam-5857	883	26	0.5	0.5	NUM
ejpam-5857	883	27	≥	≥	NOUN
ejpam-5857	883	28	α	α	NOUN
ejpam-5857	883	29	.	.	PUNCT
ejpam-5857	884	1	thus	thus	ADV
ejpam-5857	884	2	,	,	PUNCT
ejpam-5857	884	3	y	y	PROPN
ejpam-5857	884	4	∈	∈	PROPN
ejpam-5857	884	5	u	u	PROPN
ejpam-5857	884	6	+	+	X
ejpam-5857	884	7	(	(	PUNCT
ejpam-5857	884	8	ψt	ψt	NUM
ejpam-5857	884	9	;	;	PUNCT
ejpam-5857	884	10	α	α	X
ejpam-5857	884	11	)	)	PUNCT
ejpam-5857	884	12	.	.	PUNCT
ejpam-5857	885	1	hence	hence	ADV
ejpam-5857	885	2	,	,	PUNCT
ejpam-5857	885	3	u	u	PROPN
ejpam-5857	885	4	+	+	X
ejpam-5857	885	5	(	(	PUNCT
ejpam-5857	885	6	ψt	ψt	NUM
ejpam-5857	885	7	;	;	PUNCT
ejpam-5857	885	8	α	α	X
ejpam-5857	885	9	)	)	PUNCT
ejpam-5857	885	10	is	be	AUX
ejpam-5857	885	11	an	an	DET
ejpam-5857	885	12	iup	iup	NOUN
ejpam-5857	885	13	-	-	PUNCT
ejpam-5857	885	14	filter	filter	NOUN
ejpam-5857	885	15	of	of	ADP
ejpam-5857	885	16	x.	x.	NOUN
ejpam-5857	885	17	let	let	VERB
ejpam-5857	885	18	β	β	X
ejpam-5857	885	19	∈	∈	PROPN
ejpam-5857	886	1	[	[	X
ejpam-5857	886	2	0	0	NUM
ejpam-5857	886	3	,	,	PUNCT
ejpam-5857	886	4	0.5	0.5	NUM
ejpam-5857	886	5	)	)	PUNCT
ejpam-5857	886	6	be	be	VERB
ejpam-5857	886	7	such	such	ADJ
ejpam-5857	886	8	that	that	SCONJ
ejpam-5857	886	9	l	l	NOUN
ejpam-5857	887	1	−	−	PROPN
ejpam-5857	887	2	(	(	PUNCT
ejpam-5857	887	3	ψi	ψi	ADP
ejpam-5857	887	4	;	;	PUNCT
ejpam-5857	887	5	β	β	X
ejpam-5857	887	6	)	)	PUNCT
ejpam-5857	887	7	̸=	̸=	PROPN
ejpam-5857	887	8	∅.	∅.	ADV
ejpam-5857	887	9	let	let	VERB
ejpam-5857	887	10	b	b	NOUN
ejpam-5857	887	11	∈	∈	PROPN
ejpam-5857	887	12	l	l	NOUN
ejpam-5857	887	13	−	−	PROPN
ejpam-5857	888	1	(	(	PUNCT
ejpam-5857	888	2	ψi	ψi	ADP
ejpam-5857	888	3	;	;	PUNCT
ejpam-5857	888	4	β	β	X
ejpam-5857	888	5	)	)	PUNCT
ejpam-5857	888	6	.	.	PUNCT
ejpam-5857	889	1	then	then	ADV
ejpam-5857	889	2	ψi(b	ψi(b	PUNCT
ejpam-5857	889	3	)	)	PUNCT
ejpam-5857	889	4	<	<	X
ejpam-5857	889	5	β	β	X
ejpam-5857	889	6	.	.	PUNCT
ejpam-5857	890	1	by	by	ADP
ejpam-5857	890	2	the	the	DET
ejpam-5857	890	3	condition	condition	NOUN
ejpam-5857	890	4	(	(	PUNCT
ejpam-5857	890	5	3.9	3.9	NUM
ejpam-5857	890	6	)	)	PUNCT
ejpam-5857	890	7	,	,	PUNCT
ejpam-5857	890	8	we	we	PRON
ejpam-5857	890	9	have	have	VERB
ejpam-5857	890	10	ψi(0	ψi(0	PROPN
ejpam-5857	890	11	)	)	PUNCT
ejpam-5857	890	12	≤	≤	NOUN
ejpam-5857	890	13	ψi(b	ψi(b	PUNCT
ejpam-5857	890	14	)	)	PUNCT
ejpam-5857	890	15	<	<	X
ejpam-5857	890	16	β	β	X
ejpam-5857	890	17	.	.	PUNCT
ejpam-5857	891	1	thus	thus	ADV
ejpam-5857	891	2	,	,	PUNCT
ejpam-5857	891	3	0	0	NUM
ejpam-5857	891	4	∈	∈	PROPN
ejpam-5857	891	5	l	l	NOUN
ejpam-5857	891	6	−	−	PROPN
ejpam-5857	891	7	(	(	PUNCT
ejpam-5857	891	8	ψi	ψi	ADP
ejpam-5857	891	9	;	;	PUNCT
ejpam-5857	891	10	β	β	X
ejpam-5857	891	11	)	)	PUNCT
ejpam-5857	891	12	.	.	PUNCT
ejpam-5857	892	1	let	let	VERB
ejpam-5857	892	2	x	x	PRON
ejpam-5857	892	3	,	,	PUNCT
ejpam-5857	892	4	y	y	PROPN
ejpam-5857	892	5	∈	∈	PROPN
ejpam-5857	892	6	l	l	NOUN
ejpam-5857	893	1	−	−	PROPN
ejpam-5857	894	1	(	(	PUNCT
ejpam-5857	894	2	ψi	ψi	ADP
ejpam-5857	894	3	;	;	PUNCT
ejpam-5857	894	4	β	β	X
ejpam-5857	894	5	)	)	PUNCT
ejpam-5857	894	6	be	be	AUX
ejpam-5857	894	7	such	such	ADJ
ejpam-5857	894	8	that	that	SCONJ
ejpam-5857	894	9	x	x	X
ejpam-5857	894	10	·	·	PUNCT
ejpam-5857	894	11	y	y	NOUN
ejpam-5857	894	12	,	,	PUNCT
ejpam-5857	894	13	x	x	X
ejpam-5857	894	14	∈	∈	NOUN
ejpam-5857	894	15	l	l	NOUN
ejpam-5857	894	16	−	−	PROPN
ejpam-5857	895	1	(	(	PUNCT
ejpam-5857	895	2	ψi	ψi	ADP
ejpam-5857	895	3	;	;	PUNCT
ejpam-5857	895	4	β	β	X
ejpam-5857	895	5	)	)	PUNCT
ejpam-5857	895	6	.	.	PUNCT
ejpam-5857	896	1	then	then	ADV
ejpam-5857	896	2	ψi(x	ψi(x	NOUN
ejpam-5857	896	3	·	·	PUNCT
ejpam-5857	896	4	y	y	X
ejpam-5857	896	5	)	)	PUNCT
ejpam-5857	896	6	<	<	X
ejpam-5857	896	7	β	β	X
ejpam-5857	896	8	and	and	CCONJ
ejpam-5857	896	9	ψt	ψt	ADJ
ejpam-5857	896	10	(	(	PUNCT
ejpam-5857	896	11	x	x	X
ejpam-5857	896	12	)	)	PUNCT
ejpam-5857	896	13	<	<	X
ejpam-5857	896	14	β	β	X
ejpam-5857	896	15	.	.	PUNCT
ejpam-5857	897	1	thus	thus	ADV
ejpam-5857	897	2	,	,	PUNCT
ejpam-5857	897	3	ψi(x	ψi(x	X
ejpam-5857	897	4	·	·	PUNCT
ejpam-5857	897	5	y)∨ψi(x	y)∨ψi(x	NUM
ejpam-5857	897	6	)	)	PUNCT
ejpam-5857	897	7	<	<	X
ejpam-5857	897	8	β	β	X
ejpam-5857	897	9	.	.	PUNCT
ejpam-5857	898	1	by	by	ADP
ejpam-5857	898	2	the	the	DET
ejpam-5857	898	3	condition	condition	NOUN
ejpam-5857	898	4	(	(	PUNCT
ejpam-5857	898	5	3.15	3.15	NUM
ejpam-5857	898	6	)	)	PUNCT
ejpam-5857	898	7	.	.	PUNCT
ejpam-5857	899	1	we	we	PRON
ejpam-5857	899	2	have	have	VERB
ejpam-5857	899	3	ψi(y	ψi(y	NOUN
ejpam-5857	899	4	)	)	PUNCT
ejpam-5857	899	5	≤	≤	NOUN
ejpam-5857	899	6	(	(	PUNCT
ejpam-5857	899	7	ψi(x	ψi(x	NUM
ejpam-5857	899	8	·	·	PUNCT
ejpam-5857	899	9	y)∨ψi(x))∧	y)∨ψi(x))∧	NOUN
ejpam-5857	899	10	0.5	0.5	NUM
ejpam-5857	899	11	<	<	X
ejpam-5857	899	12	β	β	X
ejpam-5857	899	13	∧	∧	PROPN
ejpam-5857	899	14	0.5	0.5	NUM
ejpam-5857	899	15	≤	≤	NUM
ejpam-5857	899	16	β	β	NOUN
ejpam-5857	899	17	.	.	PUNCT
ejpam-5857	900	1	thus	thus	ADV
ejpam-5857	900	2	,	,	PUNCT
ejpam-5857	900	3	y	y	PROPN
ejpam-5857	900	4	∈	∈	PROPN
ejpam-5857	900	5	l	l	NOUN
ejpam-5857	900	6	−	−	PROPN
ejpam-5857	900	7	(	(	PUNCT
ejpam-5857	900	8	ψi	ψi	ADP
ejpam-5857	900	9	;	;	PUNCT
ejpam-5857	900	10	β	β	X
ejpam-5857	900	11	)	)	PUNCT
ejpam-5857	900	12	.	.	PUNCT
ejpam-5857	901	1	hence	hence	ADV
ejpam-5857	901	2	,	,	PUNCT
ejpam-5857	901	3	l	l	NOUN
ejpam-5857	901	4	−	−	PROPN
ejpam-5857	901	5	(	(	PUNCT
ejpam-5857	901	6	ψi	ψi	ADP
ejpam-5857	901	7	;	;	PUNCT
ejpam-5857	901	8	β	β	X
ejpam-5857	901	9	)	)	PUNCT
ejpam-5857	901	10	is	be	AUX
ejpam-5857	901	11	an	an	DET
ejpam-5857	901	12	iup	iup	NOUN
ejpam-5857	901	13	-	-	PUNCT
ejpam-5857	901	14	filter	filter	NOUN
ejpam-5857	901	15	of	of	ADP
ejpam-5857	901	16	x.	x.	NOUN
ejpam-5857	901	17	let	let	VERB
ejpam-5857	901	18	γ	γ	X
ejpam-5857	901	19	∈	∈	PROPN
ejpam-5857	901	20	[	[	X
ejpam-5857	901	21	0.5	0.5	NUM
ejpam-5857	901	22	,	,	PUNCT
ejpam-5857	901	23	1	1	NUM
ejpam-5857	901	24	]	]	PUNCT
ejpam-5857	901	25	be	be	AUX
ejpam-5857	901	26	such	such	ADJ
ejpam-5857	901	27	that	that	SCONJ
ejpam-5857	901	28	u	u	NOUN
ejpam-5857	901	29	+	+	X
ejpam-5857	901	30	(	(	PUNCT
ejpam-5857	901	31	ψf	ψf	X
ejpam-5857	901	32	;	;	PUNCT
ejpam-5857	901	33	γ	γ	X
ejpam-5857	901	34	)	)	PUNCT
ejpam-5857	901	35	̸=	̸=	PROPN
ejpam-5857	901	36	∅.	∅.	ADV
ejpam-5857	901	37	let	let	VERB
ejpam-5857	901	38	c	c	NOUN
ejpam-5857	901	39	∈	∈	PROPN
ejpam-5857	901	40	u	u	NOUN
ejpam-5857	901	41	+	+	X
ejpam-5857	901	42	(	(	PUNCT
ejpam-5857	901	43	ψf	ψf	X
ejpam-5857	901	44	;	;	PUNCT
ejpam-5857	901	45	γ	γ	X
ejpam-5857	901	46	)	)	PUNCT
ejpam-5857	901	47	.	.	PUNCT
ejpam-5857	902	1	then	then	ADV
ejpam-5857	902	2	ψf	ψf	X
ejpam-5857	902	3	(	(	PUNCT
ejpam-5857	902	4	c	c	NOUN
ejpam-5857	902	5	)	)	PUNCT
ejpam-5857	902	6	>	>	X
ejpam-5857	903	1	γ	γ	X
ejpam-5857	903	2	.	.	PROPN
ejpam-5857	903	3	by	by	ADP
ejpam-5857	903	4	the	the	DET
ejpam-5857	903	5	condition	condition	NOUN
ejpam-5857	903	6	(	(	PUNCT
ejpam-5857	903	7	3.10	3.10	NUM
ejpam-5857	903	8	)	)	PUNCT
ejpam-5857	903	9	,	,	PUNCT
ejpam-5857	903	10	we	we	PRON
ejpam-5857	903	11	have	have	AUX
ejpam-5857	903	12	ψf	ψf	X
ejpam-5857	903	13	(	(	PUNCT
ejpam-5857	903	14	0	0	NUM
ejpam-5857	903	15	)	)	PUNCT
ejpam-5857	903	16	≥	≥	NOUN
ejpam-5857	903	17	ψf	ψf	X
ejpam-5857	903	18	(	(	PUNCT
ejpam-5857	903	19	c	c	NOUN
ejpam-5857	903	20	)	)	PUNCT
ejpam-5857	903	21	>	>	X
ejpam-5857	904	1	γ	γ	X
ejpam-5857	904	2	.	.	PUNCT
ejpam-5857	904	3	thus	thus	ADV
ejpam-5857	904	4	,	,	PUNCT
ejpam-5857	904	5	0	0	NUM
ejpam-5857	904	6	∈	∈	PROPN
ejpam-5857	904	7	u	u	NOUN
ejpam-5857	904	8	+	+	X
ejpam-5857	904	9	(	(	PUNCT
ejpam-5857	904	10	ψf	ψf	X
ejpam-5857	904	11	;	;	PUNCT
ejpam-5857	904	12	γ	γ	X
ejpam-5857	904	13	)	)	PUNCT
ejpam-5857	904	14	.	.	PUNCT
ejpam-5857	905	1	let	let	VERB
ejpam-5857	905	2	x	x	PRON
ejpam-5857	905	3	,	,	PUNCT
ejpam-5857	905	4	y	y	PROPN
ejpam-5857	905	5	∈	∈	PROPN
ejpam-5857	905	6	u	u	PROPN
ejpam-5857	905	7	+	+	X
ejpam-5857	905	8	(	(	PUNCT
ejpam-5857	905	9	ψf	ψf	X
ejpam-5857	905	10	;	;	PUNCT
ejpam-5857	905	11	γ	γ	X
ejpam-5857	905	12	)	)	PUNCT
ejpam-5857	905	13	be	be	VERB
ejpam-5857	905	14	such	such	ADJ
ejpam-5857	905	15	that	that	SCONJ
ejpam-5857	905	16	x	x	X
ejpam-5857	905	17	·	·	PUNCT
ejpam-5857	905	18	y	y	X
ejpam-5857	905	19	,	,	PUNCT
ejpam-5857	905	20	x	x	SYM
ejpam-5857	905	21	∈	∈	PROPN
ejpam-5857	905	22	u	u	NOUN
ejpam-5857	905	23	+	+	X
ejpam-5857	905	24	(	(	PUNCT
ejpam-5857	905	25	ψf	ψf	X
ejpam-5857	905	26	;	;	PUNCT
ejpam-5857	905	27	γ	γ	X
ejpam-5857	905	28	)	)	PUNCT
ejpam-5857	905	29	.	.	PUNCT
ejpam-5857	906	1	then	then	ADV
ejpam-5857	906	2	ψf	ψf	X
ejpam-5857	906	3	(	(	PUNCT
ejpam-5857	906	4	x	x	PROPN
ejpam-5857	906	5	·	·	PUNCT
ejpam-5857	906	6	y	y	X
ejpam-5857	906	7	)	)	PUNCT
ejpam-5857	906	8	>	>	X
ejpam-5857	906	9	γ	γ	PROPN
ejpam-5857	906	10	and	and	CCONJ
ejpam-5857	906	11	ψf	ψf	X
ejpam-5857	906	12	(	(	PUNCT
ejpam-5857	906	13	x	x	X
ejpam-5857	906	14	)	)	PUNCT
ejpam-5857	906	15	>	>	X
ejpam-5857	906	16	γ	γ	X
ejpam-5857	906	17	.	.	PUNCT
ejpam-5857	906	18	thus	thus	ADV
ejpam-5857	906	19	,	,	PUNCT
ejpam-5857	906	20	ψf	ψf	X
ejpam-5857	906	21	(	(	PUNCT
ejpam-5857	906	22	x·y)∧ψf	x·y)∧ψf	PROPN
ejpam-5857	906	23	(	(	PUNCT
ejpam-5857	906	24	x	x	X
ejpam-5857	906	25	)	)	PUNCT
ejpam-5857	906	26	>	>	X
ejpam-5857	906	27	γ	γ	X
ejpam-5857	906	28	.	.	PROPN
ejpam-5857	906	29	by	by	ADP
ejpam-5857	906	30	the	the	DET
ejpam-5857	906	31	condition	condition	NOUN
ejpam-5857	906	32	(	(	PUNCT
ejpam-5857	906	33	3.16	3.16	NUM
ejpam-5857	906	34	)	)	PUNCT
ejpam-5857	906	35	.	.	PUNCT
ejpam-5857	907	1	we	we	PRON
ejpam-5857	907	2	have	have	VERB
ejpam-5857	907	3	ψf	ψf	VERB
ejpam-5857	907	4	(	(	PUNCT
ejpam-5857	907	5	y	y	NOUN
ejpam-5857	907	6	)	)	PUNCT
ejpam-5857	907	7	≥	≥	NOUN
ejpam-5857	907	8	(	(	PUNCT
ejpam-5857	907	9	ψf	ψf	X
ejpam-5857	907	10	(	(	PUNCT
ejpam-5857	907	11	x·y)∧ψf	x·y)∧ψf	PROPN
ejpam-5857	907	12	(	(	PUNCT
ejpam-5857	907	13	x))∨0.5	x))∨0.5	X
ejpam-5857	907	14	>	>	X
ejpam-5857	907	15	γ	γ	PROPN
ejpam-5857	907	16	∨	∨	NUM
ejpam-5857	907	17	0.5	0.5	NUM
ejpam-5857	907	18	≥	≥	PROPN
ejpam-5857	907	19	γ	γ	PROPN
ejpam-5857	907	20	.	.	PUNCT
ejpam-5857	908	1	thus	thus	ADV
ejpam-5857	908	2	,	,	PUNCT
ejpam-5857	908	3	y	y	PROPN
ejpam-5857	908	4	∈	∈	PROPN
ejpam-5857	908	5	u	u	PROPN
ejpam-5857	908	6	+	+	X
ejpam-5857	908	7	(	(	PUNCT
ejpam-5857	908	8	ψf	ψf	X
ejpam-5857	908	9	;	;	PUNCT
ejpam-5857	908	10	γ	γ	X
ejpam-5857	908	11	)	)	PUNCT
ejpam-5857	908	12	.	.	PUNCT
ejpam-5857	909	1	hence	hence	ADV
ejpam-5857	909	2	,	,	PUNCT
ejpam-5857	909	3	u	u	PROPN
ejpam-5857	909	4	+	+	X
ejpam-5857	909	5	(	(	PUNCT
ejpam-5857	909	6	ψf	ψf	X
ejpam-5857	909	7	;	;	PUNCT
ejpam-5857	909	8	γ	γ	X
ejpam-5857	909	9	)	)	PUNCT
ejpam-5857	909	10	is	be	AUX
ejpam-5857	909	11	an	an	DET
ejpam-5857	909	12	iup	iup	NOUN
ejpam-5857	909	13	-	-	PUNCT
ejpam-5857	909	14	filter	filter	NOUN
ejpam-5857	909	15	of	of	ADP
ejpam-5857	909	16	x.	x.	PROPN
ejpam-5857	909	17	theorem	theorem	VERB
ejpam-5857	909	18	29	29	NUM
ejpam-5857	909	19	.	.	PUNCT
ejpam-5857	910	1	let	let	VERB
ejpam-5857	910	2	ψ	ψ	PART
ejpam-5857	910	3	be	be	AUX
ejpam-5857	910	4	an	an	DET
ejpam-5857	910	5	intuitionistic	intuitionistic	ADJ
ejpam-5857	910	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	910	7	strong	strong	ADJ
ejpam-5857	910	8	iup	iup	NOUN
ejpam-5857	910	9	-	-	PUNCT
ejpam-5857	910	10	ideal	ideal	NOUN
ejpam-5857	910	11	of	of	ADP
ejpam-5857	910	12	x.	x.	NOUN
ejpam-5857	910	13	then	then	ADV
ejpam-5857	910	14	for	for	ADP
ejpam-5857	910	15	all	all	DET
ejpam-5857	910	16	α	α	NOUN
ejpam-5857	910	17	,	,	PUNCT
ejpam-5857	910	18	γ	γ	PROPN
ejpam-5857	910	19	∈	∈	PROPN
ejpam-5857	911	1	[	[	X
ejpam-5857	911	2	0.5	0.5	NUM
ejpam-5857	911	3	,	,	PUNCT
ejpam-5857	911	4	1	1	NUM
ejpam-5857	911	5	]	]	PUNCT
ejpam-5857	911	6	and	and	CCONJ
ejpam-5857	911	7	β	β	X
ejpam-5857	911	8	∈	∈	PROPN
ejpam-5857	911	9	[	[	X
ejpam-5857	911	10	0	0	NUM
ejpam-5857	911	11	,	,	PUNCT
ejpam-5857	911	12	0.5	0.5	NUM
ejpam-5857	911	13	)	)	PUNCT
ejpam-5857	911	14	,	,	PUNCT
ejpam-5857	911	15	the	the	DET
ejpam-5857	911	16	sets	set	NOUN
ejpam-5857	911	17	u	u	NOUN
ejpam-5857	911	18	+	+	X
ejpam-5857	911	19	(	(	PUNCT
ejpam-5857	911	20	ψt	ψt	NUM
ejpam-5857	911	21	;	;	PUNCT
ejpam-5857	911	22	α	α	X
ejpam-5857	911	23	)	)	PUNCT
ejpam-5857	911	24	,	,	PUNCT
ejpam-5857	911	25	l	l	NOUN
ejpam-5857	911	26	−	−	PROPN
ejpam-5857	911	27	(	(	PUNCT
ejpam-5857	911	28	ψi	ψi	ADP
ejpam-5857	911	29	;	;	PUNCT
ejpam-5857	911	30	β	β	X
ejpam-5857	911	31	)	)	PUNCT
ejpam-5857	911	32	and	and	CCONJ
ejpam-5857	911	33	u	u	PRON
ejpam-5857	911	34	+	+	X
ejpam-5857	911	35	(	(	PUNCT
ejpam-5857	911	36	ψf	ψf	X
ejpam-5857	911	37	;	;	PUNCT
ejpam-5857	911	38	γ	γ	X
ejpam-5857	911	39	)	)	PUNCT
ejpam-5857	911	40	are	be	AUX
ejpam-5857	911	41	either	either	CCONJ
ejpam-5857	911	42	empty	empty	ADJ
ejpam-5857	911	43	or	or	CCONJ
ejpam-5857	911	44	strong	strong	ADJ
ejpam-5857	911	45	iup	iup	NOUN
ejpam-5857	911	46	-	-	PUNCT
ejpam-5857	911	47	ideals	ideal	NOUN
ejpam-5857	911	48	of	of	ADP
ejpam-5857	911	49	x.	x.	NOUN
ejpam-5857	911	50	proof	proof	NOUN
ejpam-5857	911	51	.	.	PUNCT
ejpam-5857	912	1	it	it	PRON
ejpam-5857	912	2	is	be	AUX
ejpam-5857	912	3	straightforward	straightforward	ADJ
ejpam-5857	912	4	by	by	ADP
ejpam-5857	912	5	theorem	theorem	NOUN
ejpam-5857	912	6	1	1	NUM
ejpam-5857	912	7	.	.	PUNCT
ejpam-5857	912	8	theorem	theorem	NOUN
ejpam-5857	912	9	30	30	NUM
ejpam-5857	912	10	.	.	PUNCT
ejpam-5857	913	1	let	let	VERB
ejpam-5857	913	2	for	for	ADP
ejpam-5857	913	3	all	all	DET
ejpam-5857	913	4	α	α	NOUN
ejpam-5857	913	5	,	,	PUNCT
ejpam-5857	913	6	γ	γ	PROPN
ejpam-5857	913	7	∈	∈	PROPN
ejpam-5857	914	1	[	[	X
ejpam-5857	914	2	0.5	0.5	NUM
ejpam-5857	914	3	,	,	PUNCT
ejpam-5857	914	4	1	1	NUM
ejpam-5857	914	5	]	]	PUNCT
ejpam-5857	914	6	and	and	CCONJ
ejpam-5857	914	7	β	β	X
ejpam-5857	914	8	∈	∈	PROPN
ejpam-5857	914	9	[	[	X
ejpam-5857	914	10	0	0	NUM
ejpam-5857	914	11	,	,	PUNCT
ejpam-5857	914	12	0.5	0.5	NUM
ejpam-5857	914	13	)	)	PUNCT
ejpam-5857	914	14	,	,	PUNCT
ejpam-5857	914	15	the	the	DET
ejpam-5857	914	16	sets	set	NOUN
ejpam-5857	914	17	u	u	NOUN
ejpam-5857	914	18	+	+	X
ejpam-5857	914	19	(	(	PUNCT
ejpam-5857	914	20	ψt	ψt	NUM
ejpam-5857	914	21	;	;	PUNCT
ejpam-5857	914	22	α	α	X
ejpam-5857	914	23	)	)	PUNCT
ejpam-5857	914	24	,	,	PUNCT
ejpam-5857	914	25	l	l	NOUN
ejpam-5857	914	26	−	−	PROPN
ejpam-5857	914	27	(	(	PUNCT
ejpam-5857	914	28	ψi	ψi	ADP
ejpam-5857	914	29	;	;	PUNCT
ejpam-5857	914	30	β	β	X
ejpam-5857	914	31	)	)	PUNCT
ejpam-5857	914	32	and	and	CCONJ
ejpam-5857	914	33	u	u	PRON
ejpam-5857	914	34	+	+	X
ejpam-5857	914	35	(	(	PUNCT
ejpam-5857	914	36	ψf	ψf	X
ejpam-5857	914	37	;	;	PUNCT
ejpam-5857	914	38	γ	γ	X
ejpam-5857	914	39	)	)	PUNCT
ejpam-5857	914	40	are	be	AUX
ejpam-5857	914	41	either	either	CCONJ
ejpam-5857	914	42	empty	empty	ADJ
ejpam-5857	914	43	or	or	CCONJ
ejpam-5857	914	44	iup	iup	NOUN
ejpam-5857	914	45	-	-	PUNCT
ejpam-5857	914	46	subalgebras	subalgebras	PROPN
ejpam-5857	914	47	of	of	ADP
ejpam-5857	914	48	x.	x.	NOUN
ejpam-5857	914	49	if	if	SCONJ
ejpam-5857	914	50	ψt	ψt	VERB
ejpam-5857	914	51	(	(	PUNCT
ejpam-5857	914	52	x	x	NOUN
ejpam-5857	914	53	)	)	PUNCT
ejpam-5857	914	54	≥	≥	NOUN
ejpam-5857	914	55	0.5	0.5	NUM
ejpam-5857	914	56	,	,	PUNCT
ejpam-5857	914	57	ψi(x	ψi(x	NUM
ejpam-5857	914	58	)	)	PUNCT
ejpam-5857	914	59	<	<	X
ejpam-5857	914	60	0.5	0.5	NUM
ejpam-5857	914	61	and	and	CCONJ
ejpam-5857	914	62	ψf	ψf	X
ejpam-5857	914	63	(	(	PUNCT
ejpam-5857	914	64	x	x	X
ejpam-5857	914	65	)	)	PUNCT
ejpam-5857	914	66	≥	≥	NOUN
ejpam-5857	914	67	0.5	0.5	NUM
ejpam-5857	914	68	for	for	ADP
ejpam-5857	914	69	all	all	DET
ejpam-5857	914	70	x	x	SYM
ejpam-5857	914	71	∈	∈	NOUN
ejpam-5857	914	72	x	x	NOUN
ejpam-5857	914	73	,	,	PUNCT
ejpam-5857	914	74	then	then	ADV
ejpam-5857	914	75	ψ	ψ	NOUN
ejpam-5857	914	76	is	be	AUX
ejpam-5857	914	77	an	an	DET
ejpam-5857	914	78	intuitionistic	intuitionistic	ADJ
ejpam-5857	914	79	neutrosophic	neutrosophic	ADJ
ejpam-5857	914	80	iup	iup	NOUN
ejpam-5857	914	81	-	-	PUNCT
ejpam-5857	914	82	subalgebra	subalgebra	NOUN
ejpam-5857	914	83	of	of	ADP
ejpam-5857	914	84	x.	x.	NOUN
ejpam-5857	914	85	proof	proof	PROPN
ejpam-5857	914	86	.	.	PUNCT
ejpam-5857	915	1	assume	assume	VERB
ejpam-5857	915	2	that	that	SCONJ
ejpam-5857	915	3	for	for	ADP
ejpam-5857	915	4	all	all	DET
ejpam-5857	915	5	α	α	NOUN
ejpam-5857	915	6	,	,	PUNCT
ejpam-5857	915	7	γ	γ	PROPN
ejpam-5857	915	8	∈	∈	PROPN
ejpam-5857	916	1	[	[	X
ejpam-5857	916	2	0.5	0.5	NUM
ejpam-5857	916	3	,	,	PUNCT
ejpam-5857	916	4	1	1	NUM
ejpam-5857	916	5	]	]	PUNCT
ejpam-5857	916	6	and	and	CCONJ
ejpam-5857	916	7	β	β	X
ejpam-5857	916	8	∈	∈	PROPN
ejpam-5857	917	1	[	[	X
ejpam-5857	917	2	0	0	NUM
ejpam-5857	917	3	,	,	PUNCT
ejpam-5857	917	4	0.5	0.5	NUM
ejpam-5857	917	5	)	)	PUNCT
ejpam-5857	917	6	,	,	PUNCT
ejpam-5857	917	7	the	the	DET
ejpam-5857	917	8	sets	set	NOUN
ejpam-5857	917	9	u	u	NOUN
ejpam-5857	917	10	+	+	X
ejpam-5857	917	11	(	(	PUNCT
ejpam-5857	917	12	ψt	ψt	NUM
ejpam-5857	917	13	;	;	PUNCT
ejpam-5857	917	14	α	α	X
ejpam-5857	917	15	)	)	PUNCT
ejpam-5857	917	16	,	,	PUNCT
ejpam-5857	917	17	l	l	NOUN
ejpam-5857	917	18	−	−	PROPN
ejpam-5857	917	19	(	(	PUNCT
ejpam-5857	917	20	ψi	ψi	ADP
ejpam-5857	917	21	;	;	PUNCT
ejpam-5857	917	22	β	β	X
ejpam-5857	917	23	)	)	PUNCT
ejpam-5857	917	24	and	and	CCONJ
ejpam-5857	917	25	u	u	PRON
ejpam-5857	917	26	+	+	X
ejpam-5857	917	27	(	(	PUNCT
ejpam-5857	917	28	ψf	ψf	X
ejpam-5857	917	29	;	;	PUNCT
ejpam-5857	917	30	γ	γ	X
ejpam-5857	917	31	)	)	PUNCT
ejpam-5857	917	32	are	be	AUX
ejpam-5857	917	33	either	either	CCONJ
ejpam-5857	917	34	empty	empty	ADJ
ejpam-5857	917	35	or	or	CCONJ
ejpam-5857	917	36	iup	iup	NOUN
ejpam-5857	917	37	-	-	PUNCT
ejpam-5857	917	38	subalgebras	subalgebras	PROPN
ejpam-5857	917	39	of	of	ADP
ejpam-5857	917	40	x.	x.	PROPN
ejpam-5857	917	41	let	let	VERB
ejpam-5857	917	42	x	x	PRON
ejpam-5857	917	43	,	,	PUNCT
ejpam-5857	917	44	y	y	PROPN
ejpam-5857	917	45	∈	∈	PROPN
ejpam-5857	917	46	x	x	AUX
ejpam-5857	917	47	be	be	AUX
ejpam-5857	917	48	such	such	ADJ
ejpam-5857	917	49	that	that	SCONJ
ejpam-5857	917	50	ψt	ψt	NOUN
ejpam-5857	917	51	(	(	PUNCT
ejpam-5857	917	52	x	x	X
ejpam-5857	917	53	)	)	PUNCT
ejpam-5857	917	54	≥	≥	NOUN
ejpam-5857	917	55	0.5	0.5	NUM
ejpam-5857	917	56	and	and	CCONJ
ejpam-5857	917	57	ψt	ψt	ADJ
ejpam-5857	917	58	(	(	PUNCT
ejpam-5857	917	59	y	y	NOUN
ejpam-5857	917	60	)	)	PUNCT
ejpam-5857	917	61	≥	≥	NOUN
ejpam-5857	917	62	0.5	0.5	NUM
ejpam-5857	917	63	.	.	PUNCT
ejpam-5857	918	1	assume	assume	VERB
ejpam-5857	918	2	that	that	SCONJ
ejpam-5857	918	3	ψt	ψt	VERB
ejpam-5857	918	4	(	(	PUNCT
ejpam-5857	918	5	x	x	PROPN
ejpam-5857	918	6	·	·	PUNCT
ejpam-5857	918	7	y	y	X
ejpam-5857	918	8	)	)	PUNCT
ejpam-5857	918	9	<	<	X
ejpam-5857	919	1	(	(	PUNCT
ejpam-5857	919	2	ψt	ψt	ADJ
ejpam-5857	919	3	(	(	PUNCT
ejpam-5857	919	4	x	x	NOUN
ejpam-5857	919	5	)	)	PUNCT
ejpam-5857	919	6	∧	∧	NOUN
ejpam-5857	919	7	ψt	ψt	NOUN
ejpam-5857	919	8	(	(	PUNCT
ejpam-5857	919	9	y	y	NOUN
ejpam-5857	919	10	)	)	PUNCT
ejpam-5857	919	11	)	)	PUNCT
ejpam-5857	919	12	∨	∨	NUM
ejpam-5857	919	13	0.5	0.5	NUM
ejpam-5857	919	14	.	.	PUNCT
ejpam-5857	920	1	let	let	VERB
ejpam-5857	920	2	k.	k.	PROPN
ejpam-5857	920	3	suayngam	suayngam	PROPN
ejpam-5857	920	4	,	,	PUNCT
ejpam-5857	920	5	p.	p.	NOUN
ejpam-5857	920	6	julatha	julatha	PROPN
ejpam-5857	920	7	,	,	PUNCT
ejpam-5857	920	8	w.	w.	PROPN
ejpam-5857	920	9	nakkhasen	nakkhasen	PROPN
ejpam-5857	920	10	,	,	PUNCT
ejpam-5857	920	11	a.	a.	NOUN
ejpam-5857	920	12	iampan	iampan	PROPN
ejpam-5857	920	13	/	/	SYM
ejpam-5857	920	14	eur	eur	PROPN
ejpam-5857	920	15	.	.	PUNCT
ejpam-5857	921	1	j.	j.	PROPN
ejpam-5857	921	2	pure	pure	PROPN
ejpam-5857	921	3	appl	appl	PROPN
ejpam-5857	921	4	.	.	PROPN
ejpam-5857	921	5	math	math	PROPN
ejpam-5857	921	6	,	,	PUNCT
ejpam-5857	921	7	18	18	NUM
ejpam-5857	921	8	(	(	PUNCT
ejpam-5857	921	9	2	2	NUM
ejpam-5857	921	10	)	)	PUNCT
ejpam-5857	921	11	(	(	PUNCT
ejpam-5857	921	12	2025	2025	NUM
ejpam-5857	921	13	)	)	PUNCT
ejpam-5857	921	14	,	,	PUNCT
ejpam-5857	921	15	5857	5857	NUM
ejpam-5857	921	16	27	27	NUM
ejpam-5857	921	17	of	of	ADP
ejpam-5857	921	18	30	30	NUM
ejpam-5857	921	19	α	α	NOUN
ejpam-5857	921	20	=	=	NOUN
ejpam-5857	922	1	ψt	ψt	NOUN
ejpam-5857	922	2	(	(	PUNCT
ejpam-5857	922	3	x	x	PROPN
ejpam-5857	922	4	·	·	PUNCT
ejpam-5857	922	5	y	y	X
ejpam-5857	922	6	)	)	PUNCT
ejpam-5857	922	7	.	.	PUNCT
ejpam-5857	923	1	if	if	SCONJ
ejpam-5857	923	2	(	(	PUNCT
ejpam-5857	923	3	ψt	ψt	VERB
ejpam-5857	923	4	(	(	PUNCT
ejpam-5857	923	5	x	x	NOUN
ejpam-5857	923	6	)	)	PUNCT
ejpam-5857	923	7	∧	∧	NOUN
ejpam-5857	923	8	ψt	ψt	NOUN
ejpam-5857	923	9	(	(	PUNCT
ejpam-5857	923	10	y	y	NOUN
ejpam-5857	923	11	)	)	PUNCT
ejpam-5857	923	12	)	)	PUNCT
ejpam-5857	923	13	∨	∨	NUM
ejpam-5857	923	14	0.5	0.5	NUM
ejpam-5857	923	15	=	=	SYM
ejpam-5857	923	16	ψt	ψt	ADJ
ejpam-5857	923	17	(	(	PUNCT
ejpam-5857	923	18	x	x	NOUN
ejpam-5857	923	19	)	)	PUNCT
ejpam-5857	923	20	∧	∧	NOUN
ejpam-5857	923	21	ψt	ψt	NOUN
ejpam-5857	923	22	(	(	PUNCT
ejpam-5857	923	23	y	y	NOUN
ejpam-5857	923	24	)	)	PUNCT
ejpam-5857	923	25	,	,	PUNCT
ejpam-5857	923	26	then	then	ADV
ejpam-5857	923	27	ψt	ψt	VERB
ejpam-5857	923	28	(	(	PUNCT
ejpam-5857	923	29	x	x	X
ejpam-5857	923	30	)	)	PUNCT
ejpam-5857	923	31	>	>	X
ejpam-5857	923	32	α	α	PROPN
ejpam-5857	923	33	and	and	CCONJ
ejpam-5857	923	34	ψt	ψt	ADJ
ejpam-5857	923	35	(	(	PUNCT
ejpam-5857	923	36	y	y	NOUN
ejpam-5857	923	37	)	)	PUNCT
ejpam-5857	923	38	>	>	X
ejpam-5857	924	1	α	α	X
ejpam-5857	924	2	.	.	PUNCT
ejpam-5857	925	1	thus	thus	ADV
ejpam-5857	925	2	,	,	PUNCT
ejpam-5857	925	3	x	x	PRON
ejpam-5857	925	4	,	,	PUNCT
ejpam-5857	925	5	y	y	PROPN
ejpam-5857	925	6	∈	∈	PROPN
ejpam-5857	925	7	u	u	PROPN
ejpam-5857	925	8	+	+	X
ejpam-5857	925	9	(	(	PUNCT
ejpam-5857	925	10	ψt	ψt	NUM
ejpam-5857	925	11	;	;	PUNCT
ejpam-5857	925	12	α	α	X
ejpam-5857	925	13	)	)	PUNCT
ejpam-5857	925	14	.	.	PUNCT
ejpam-5857	926	1	by	by	ADP
ejpam-5857	926	2	assumption	assumption	NOUN
ejpam-5857	926	3	,	,	PUNCT
ejpam-5857	926	4	we	we	PRON
ejpam-5857	926	5	have	have	VERB
ejpam-5857	926	6	u	u	NOUN
ejpam-5857	926	7	+	+	PUNCT
ejpam-5857	926	8	(	(	PUNCT
ejpam-5857	926	9	ψt	ψt	NUM
ejpam-5857	926	10	;	;	PUNCT
ejpam-5857	926	11	α	α	X
ejpam-5857	926	12	)	)	PUNCT
ejpam-5857	926	13	is	be	AUX
ejpam-5857	926	14	an	an	DET
ejpam-5857	926	15	iup	iup	NOUN
ejpam-5857	926	16	-	-	PUNCT
ejpam-5857	926	17	subalgebra	subalgebra	NOUN
ejpam-5857	926	18	of	of	ADP
ejpam-5857	926	19	x.	x.	NOUN
ejpam-5857	926	20	by	by	ADP
ejpam-5857	926	21	the	the	DET
ejpam-5857	926	22	condition	condition	NOUN
ejpam-5857	926	23	(	(	PUNCT
ejpam-5857	926	24	2.17	2.17	NUM
ejpam-5857	926	25	)	)	PUNCT
ejpam-5857	926	26	,	,	PUNCT
ejpam-5857	926	27	we	we	PRON
ejpam-5857	926	28	have	have	VERB
ejpam-5857	926	29	x	x	X
ejpam-5857	926	30	·	·	PUNCT
ejpam-5857	926	31	y	y	PROPN
ejpam-5857	926	32	∈	∈	PROPN
ejpam-5857	926	33	u	u	PROPN
ejpam-5857	926	34	+	+	X
ejpam-5857	926	35	(	(	PUNCT
ejpam-5857	926	36	ψt	ψt	NUM
ejpam-5857	926	37	;	;	PUNCT
ejpam-5857	926	38	α	α	X
ejpam-5857	926	39	)	)	PUNCT
ejpam-5857	926	40	.	.	PUNCT
ejpam-5857	927	1	so	so	ADV
ejpam-5857	927	2	ψt	ψt	VERB
ejpam-5857	927	3	(	(	PUNCT
ejpam-5857	927	4	x	x	PROPN
ejpam-5857	927	5	·	·	PUNCT
ejpam-5857	927	6	y	y	X
ejpam-5857	927	7	)	)	PUNCT
ejpam-5857	927	8	>	>	X
ejpam-5857	928	1	α	α	X
ejpam-5857	928	2	=	=	X
ejpam-5857	928	3	ψt	ψt	ADJ
ejpam-5857	928	4	(	(	PUNCT
ejpam-5857	928	5	x	x	PROPN
ejpam-5857	928	6	·	·	PUNCT
ejpam-5857	928	7	y	y	X
ejpam-5857	928	8	)	)	PUNCT
ejpam-5857	928	9	,	,	PUNCT
ejpam-5857	928	10	which	which	PRON
ejpam-5857	928	11	is	be	AUX
ejpam-5857	928	12	a	a	DET
ejpam-5857	928	13	contradiction	contradiction	NOUN
ejpam-5857	928	14	.	.	PUNCT
ejpam-5857	929	1	if	if	SCONJ
ejpam-5857	929	2	(	(	PUNCT
ejpam-5857	929	3	ψt	ψt	VERB
ejpam-5857	929	4	(	(	PUNCT
ejpam-5857	929	5	x	x	NOUN
ejpam-5857	929	6	)	)	PUNCT
ejpam-5857	929	7	∧	∧	NOUN
ejpam-5857	929	8	ψt	ψt	NOUN
ejpam-5857	929	9	(	(	PUNCT
ejpam-5857	929	10	y	y	NOUN
ejpam-5857	929	11	)	)	PUNCT
ejpam-5857	929	12	)	)	PUNCT
ejpam-5857	929	13	∨	∨	NUM
ejpam-5857	929	14	0.5	0.5	NUM
ejpam-5857	929	15	=	=	SYM
ejpam-5857	929	16	0.5	0.5	NUM
ejpam-5857	929	17	,	,	PUNCT
ejpam-5857	929	18	then	then	ADV
ejpam-5857	929	19	α	α	PROPN
ejpam-5857	929	20	=	=	NOUN
ejpam-5857	929	21	ψt	ψt	ADJ
ejpam-5857	929	22	(	(	PUNCT
ejpam-5857	929	23	x	x	PROPN
ejpam-5857	929	24	·	·	PUNCT
ejpam-5857	929	25	y	y	X
ejpam-5857	929	26	)	)	PUNCT
ejpam-5857	929	27	<	<	X
ejpam-5857	929	28	0.5	0.5	NUM
ejpam-5857	929	29	,	,	PUNCT
ejpam-5857	929	30	which	which	PRON
ejpam-5857	929	31	is	be	AUX
ejpam-5857	929	32	a	a	DET
ejpam-5857	929	33	contradiction	contradiction	NOUN
ejpam-5857	929	34	.	.	PUNCT
ejpam-5857	930	1	thus	thus	ADV
ejpam-5857	930	2	,	,	PUNCT
ejpam-5857	930	3	ψt	ψt	VERB
ejpam-5857	930	4	(	(	PUNCT
ejpam-5857	930	5	x	x	PROPN
ejpam-5857	930	6	·	·	PUNCT
ejpam-5857	930	7	y	y	X
ejpam-5857	930	8	)	)	PUNCT
ejpam-5857	930	9	≥	≥	NOUN
ejpam-5857	930	10	(	(	PUNCT
ejpam-5857	930	11	ψt	ψt	VERB
ejpam-5857	930	12	(	(	PUNCT
ejpam-5857	930	13	x	x	NOUN
ejpam-5857	930	14	)	)	PUNCT
ejpam-5857	930	15	∧	∧	NOUN
ejpam-5857	930	16	ψt	ψt	NOUN
ejpam-5857	930	17	(	(	PUNCT
ejpam-5857	930	18	y	y	NOUN
ejpam-5857	930	19	)	)	PUNCT
ejpam-5857	930	20	)	)	PUNCT
ejpam-5857	930	21	∨	∨	NUM
ejpam-5857	930	22	0.5	0.5	NUM
ejpam-5857	930	23	.	.	PUNCT
ejpam-5857	931	1	let	let	VERB
ejpam-5857	931	2	x	x	PRON
ejpam-5857	931	3	,	,	PUNCT
ejpam-5857	931	4	y	y	PROPN
ejpam-5857	931	5	∈	∈	PROPN
ejpam-5857	931	6	x	x	AUX
ejpam-5857	931	7	be	be	AUX
ejpam-5857	931	8	such	such	ADJ
ejpam-5857	931	9	that	that	SCONJ
ejpam-5857	931	10	ψi(x	ψi(x	NUM
ejpam-5857	931	11	)	)	PUNCT
ejpam-5857	931	12	<	<	X
ejpam-5857	931	13	0.5	0.5	NUM
ejpam-5857	931	14	and	and	CCONJ
ejpam-5857	931	15	ψi(y	ψi(y	NUM
ejpam-5857	931	16	)	)	PUNCT
ejpam-5857	931	17	<	<	X
ejpam-5857	931	18	0.5	0.5	NUM
ejpam-5857	931	19	.	.	PUNCT
ejpam-5857	931	20	assume	assume	VERB
ejpam-5857	931	21	that	that	SCONJ
ejpam-5857	931	22	ψi(x	ψi(x	NUM
ejpam-5857	931	23	·	·	PUNCT
ejpam-5857	931	24	y	y	X
ejpam-5857	931	25	)	)	PUNCT
ejpam-5857	931	26	>	>	X
ejpam-5857	932	1	(	(	PUNCT
ejpam-5857	932	2	ψi(x	ψi(x	NUM
ejpam-5857	932	3	)	)	PUNCT
ejpam-5857	932	4	∨	∨	NUM
ejpam-5857	932	5	ψi(y	ψi(y	NUM
ejpam-5857	932	6	)	)	PUNCT
ejpam-5857	932	7	)	)	PUNCT
ejpam-5857	933	1	∧	∧	NOUN
ejpam-5857	933	2	0.5	0.5	NUM
ejpam-5857	933	3	.	.	PUNCT
ejpam-5857	934	1	let	let	VERB
ejpam-5857	934	2	β	β	NOUN
ejpam-5857	934	3	=	=	PUNCT
ejpam-5857	934	4	ψi(x	ψi(x	X
ejpam-5857	934	5	·	·	PUNCT
ejpam-5857	934	6	y	y	X
ejpam-5857	934	7	)	)	PUNCT
ejpam-5857	934	8	.	.	PUNCT
ejpam-5857	935	1	if	if	SCONJ
ejpam-5857	935	2	(	(	PUNCT
ejpam-5857	935	3	ψi(x	ψi(x	NUM
ejpam-5857	935	4	)	)	PUNCT
ejpam-5857	935	5	∨	∨	NUM
ejpam-5857	935	6	ψi(y	ψi(y	NUM
ejpam-5857	935	7	)	)	PUNCT
ejpam-5857	935	8	)	)	PUNCT
ejpam-5857	936	1	∧	∧	NOUN
ejpam-5857	936	2	0.5	0.5	NUM
ejpam-5857	936	3	=	=	SYM
ejpam-5857	936	4	ψi(x	ψi(x	NUM
ejpam-5857	936	5	)	)	PUNCT
ejpam-5857	936	6	∨	∨	NUM
ejpam-5857	936	7	ψi(y	ψi(y	NUM
ejpam-5857	936	8	)	)	PUNCT
ejpam-5857	936	9	,	,	PUNCT
ejpam-5857	936	10	then	then	ADV
ejpam-5857	936	11	ψi(x	ψi(x	NUM
ejpam-5857	936	12	)	)	PUNCT
ejpam-5857	936	13	<	<	X
ejpam-5857	936	14	β	β	X
ejpam-5857	936	15	and	and	CCONJ
ejpam-5857	936	16	ψi(y	ψi(y	NUM
ejpam-5857	936	17	)	)	PUNCT
ejpam-5857	936	18	<	<	X
ejpam-5857	936	19	β	β	X
ejpam-5857	936	20	.	.	PUNCT
ejpam-5857	937	1	thus	thus	ADV
ejpam-5857	937	2	,	,	PUNCT
ejpam-5857	937	3	x	x	PRON
ejpam-5857	937	4	,	,	PUNCT
ejpam-5857	937	5	y	y	PROPN
ejpam-5857	937	6	∈	∈	PROPN
ejpam-5857	937	7	l	l	NOUN
ejpam-5857	937	8	−	−	PROPN
ejpam-5857	937	9	(	(	PUNCT
ejpam-5857	937	10	ψi	ψi	ADP
ejpam-5857	937	11	;	;	PUNCT
ejpam-5857	937	12	β	β	X
ejpam-5857	937	13	)	)	PUNCT
ejpam-5857	937	14	.	.	PUNCT
ejpam-5857	938	1	by	by	ADP
ejpam-5857	938	2	assumption	assumption	NOUN
ejpam-5857	938	3	,	,	PUNCT
ejpam-5857	938	4	we	we	PRON
ejpam-5857	938	5	have	have	VERB
ejpam-5857	938	6	l	l	NOUN
ejpam-5857	938	7	−	−	PROPN
ejpam-5857	938	8	(	(	PUNCT
ejpam-5857	938	9	ψi	ψi	ADP
ejpam-5857	938	10	;	;	PUNCT
ejpam-5857	938	11	β	β	X
ejpam-5857	938	12	)	)	PUNCT
ejpam-5857	938	13	is	be	AUX
ejpam-5857	938	14	an	an	DET
ejpam-5857	938	15	iup	iup	NOUN
ejpam-5857	938	16	-	-	PUNCT
ejpam-5857	938	17	subalgebra	subalgebra	NOUN
ejpam-5857	938	18	of	of	ADP
ejpam-5857	938	19	x.	x.	NOUN
ejpam-5857	938	20	by	by	ADP
ejpam-5857	938	21	the	the	DET
ejpam-5857	938	22	condition	condition	NOUN
ejpam-5857	938	23	(	(	PUNCT
ejpam-5857	938	24	2.17	2.17	NUM
ejpam-5857	938	25	)	)	PUNCT
ejpam-5857	938	26	,	,	PUNCT
ejpam-5857	938	27	we	we	PRON
ejpam-5857	938	28	have	have	VERB
ejpam-5857	938	29	x	x	X
ejpam-5857	938	30	·	·	PUNCT
ejpam-5857	938	31	y	y	SYM
ejpam-5857	938	32	∈	∈	PROPN
ejpam-5857	938	33	l	l	NOUN
ejpam-5857	939	1	−	−	PROPN
ejpam-5857	939	2	(	(	PUNCT
ejpam-5857	939	3	ψi	ψi	ADP
ejpam-5857	939	4	;	;	PUNCT
ejpam-5857	939	5	β	β	X
ejpam-5857	939	6	)	)	PUNCT
ejpam-5857	939	7	.	.	PUNCT
ejpam-5857	940	1	so	so	ADV
ejpam-5857	940	2	ψi(x	ψi(x	VERB
ejpam-5857	940	3	·	·	PUNCT
ejpam-5857	941	1	y	y	X
ejpam-5857	941	2	)	)	PUNCT
ejpam-5857	941	3	<	<	X
ejpam-5857	941	4	β	β	X
ejpam-5857	941	5	=	=	SYM
ejpam-5857	941	6	ψi(x	ψi(x	X
ejpam-5857	941	7	·	·	PUNCT
ejpam-5857	941	8	y	y	X
ejpam-5857	941	9	)	)	PUNCT
ejpam-5857	941	10	,	,	PUNCT
ejpam-5857	941	11	which	which	PRON
ejpam-5857	941	12	is	be	AUX
ejpam-5857	941	13	a	a	DET
ejpam-5857	941	14	contradiction	contradiction	NOUN
ejpam-5857	941	15	.	.	PUNCT
ejpam-5857	942	1	if	if	SCONJ
ejpam-5857	942	2	(	(	PUNCT
ejpam-5857	942	3	ψi(x	ψi(x	NUM
ejpam-5857	942	4	)	)	PUNCT
ejpam-5857	942	5	∨	∨	NUM
ejpam-5857	942	6	ψi(y	ψi(y	NUM
ejpam-5857	942	7	)	)	PUNCT
ejpam-5857	942	8	)	)	PUNCT
ejpam-5857	943	1	∧	∧	NOUN
ejpam-5857	943	2	0.5	0.5	NUM
ejpam-5857	943	3	=	=	SYM
ejpam-5857	943	4	0.5	0.5	NUM
ejpam-5857	943	5	,	,	PUNCT
ejpam-5857	943	6	then	then	ADV
ejpam-5857	943	7	β	β	X
ejpam-5857	943	8	=	=	SYM
ejpam-5857	943	9	ψi(x	ψi(x	X
ejpam-5857	943	10	·	·	PUNCT
ejpam-5857	943	11	y	y	X
ejpam-5857	943	12	)	)	PUNCT
ejpam-5857	943	13	>	>	X
ejpam-5857	943	14	0.5	0.5	NUM
ejpam-5857	943	15	,	,	PUNCT
ejpam-5857	943	16	which	which	PRON
ejpam-5857	943	17	is	be	AUX
ejpam-5857	943	18	a	a	DET
ejpam-5857	943	19	contradiction	contradiction	NOUN
ejpam-5857	943	20	.	.	PUNCT
ejpam-5857	944	1	thus	thus	ADV
ejpam-5857	944	2	,	,	PUNCT
ejpam-5857	944	3	ψi(x	ψi(x	X
ejpam-5857	944	4	·	·	PUNCT
ejpam-5857	944	5	y	y	X
ejpam-5857	944	6	)	)	PUNCT
ejpam-5857	944	7	≤	≤	NOUN
ejpam-5857	944	8	(	(	PUNCT
ejpam-5857	944	9	ψi(x	ψi(x	NUM
ejpam-5857	944	10	)	)	PUNCT
ejpam-5857	944	11	∨	∨	NUM
ejpam-5857	944	12	ψi(y	ψi(y	NUM
ejpam-5857	944	13	)	)	PUNCT
ejpam-5857	944	14	)	)	PUNCT
ejpam-5857	944	15	∧	∧	NOUN
ejpam-5857	944	16	0.5	0.5	NUM
ejpam-5857	944	17	.	.	PUNCT
ejpam-5857	945	1	let	let	VERB
ejpam-5857	945	2	x	x	PRON
ejpam-5857	945	3	,	,	PUNCT
ejpam-5857	945	4	y	y	PROPN
ejpam-5857	945	5	∈	∈	PROPN
ejpam-5857	945	6	x	x	AUX
ejpam-5857	945	7	be	be	AUX
ejpam-5857	945	8	such	such	ADJ
ejpam-5857	945	9	that	that	SCONJ
ejpam-5857	945	10	ψf	ψf	X
ejpam-5857	945	11	(	(	PUNCT
ejpam-5857	945	12	x	x	X
ejpam-5857	945	13	)	)	PUNCT
ejpam-5857	945	14	≥	≥	NOUN
ejpam-5857	945	15	0.5	0.5	NUM
ejpam-5857	945	16	and	and	CCONJ
ejpam-5857	945	17	ψf	ψf	X
ejpam-5857	945	18	(	(	PUNCT
ejpam-5857	945	19	y	y	PROPN
ejpam-5857	945	20	)	)	PUNCT
ejpam-5857	945	21	≥	≥	NOUN
ejpam-5857	945	22	0.5	0.5	NUM
ejpam-5857	945	23	.	.	PUNCT
ejpam-5857	946	1	assume	assume	VERB
ejpam-5857	946	2	that	that	SCONJ
ejpam-5857	946	3	ψf	ψf	X
ejpam-5857	946	4	(	(	PUNCT
ejpam-5857	946	5	x	x	X
ejpam-5857	946	6	·	·	PUNCT
ejpam-5857	946	7	y	y	X
ejpam-5857	946	8	)	)	PUNCT
ejpam-5857	946	9	<	<	X
ejpam-5857	946	10	(	(	PUNCT
ejpam-5857	946	11	ψf	ψf	X
ejpam-5857	946	12	(	(	PUNCT
ejpam-5857	946	13	x)∧	x)∧	X
ejpam-5857	946	14	ψf	ψf	X
ejpam-5857	946	15	(	(	PUNCT
ejpam-5857	946	16	y))∨	y))∨	NOUN
ejpam-5857	946	17	0.5	0.5	NUM
ejpam-5857	946	18	.	.	PUNCT
ejpam-5857	947	1	let	let	VERB
ejpam-5857	947	2	γ	γ	X
ejpam-5857	947	3	=	=	PRON
ejpam-5857	947	4	ψf	ψf	X
ejpam-5857	947	5	(	(	PUNCT
ejpam-5857	947	6	x	x	PROPN
ejpam-5857	947	7	·	·	PUNCT
ejpam-5857	947	8	y	y	X
ejpam-5857	947	9	)	)	PUNCT
ejpam-5857	947	10	.	.	PUNCT
ejpam-5857	948	1	if	if	SCONJ
ejpam-5857	948	2	(	(	PUNCT
ejpam-5857	948	3	ψf	ψf	X
ejpam-5857	948	4	(	(	PUNCT
ejpam-5857	948	5	x)∧	x)∧	PROPN
ejpam-5857	948	6	ψf	ψf	X
ejpam-5857	948	7	(	(	PUNCT
ejpam-5857	948	8	y))∨	y))∨	NOUN
ejpam-5857	948	9	0.5	0.5	NUM
ejpam-5857	948	10	=	=	NOUN
ejpam-5857	948	11	ψf	ψf	X
ejpam-5857	948	12	(	(	PUNCT
ejpam-5857	948	13	x)∧	x)∧	PROPN
ejpam-5857	948	14	ψf	ψf	X
ejpam-5857	948	15	(	(	PUNCT
ejpam-5857	948	16	y	y	NOUN
ejpam-5857	948	17	)	)	PUNCT
ejpam-5857	948	18	,	,	PUNCT
ejpam-5857	948	19	then	then	ADV
ejpam-5857	948	20	ψf	ψf	X
ejpam-5857	948	21	(	(	PUNCT
ejpam-5857	948	22	x	x	X
ejpam-5857	948	23	)	)	PUNCT
ejpam-5857	948	24	>	>	X
ejpam-5857	948	25	γ	γ	PROPN
ejpam-5857	948	26	and	and	CCONJ
ejpam-5857	948	27	ψf	ψf	X
ejpam-5857	948	28	(	(	PUNCT
ejpam-5857	948	29	y	y	PROPN
ejpam-5857	948	30	)	)	PUNCT
ejpam-5857	948	31	>	>	X
ejpam-5857	948	32	γ	γ	X
ejpam-5857	948	33	.	.	PUNCT
ejpam-5857	948	34	thus	thus	ADV
ejpam-5857	948	35	,	,	PUNCT
ejpam-5857	948	36	x	x	PRON
ejpam-5857	948	37	,	,	PUNCT
ejpam-5857	948	38	y	y	PROPN
ejpam-5857	948	39	∈	∈	PROPN
ejpam-5857	948	40	u	u	PROPN
ejpam-5857	948	41	+	+	X
ejpam-5857	948	42	(	(	PUNCT
ejpam-5857	948	43	ψf	ψf	X
ejpam-5857	948	44	;	;	PUNCT
ejpam-5857	948	45	γ	γ	X
ejpam-5857	948	46	)	)	PUNCT
ejpam-5857	948	47	.	.	PUNCT
ejpam-5857	948	48	by	by	ADP
ejpam-5857	948	49	assumption	assumption	NOUN
ejpam-5857	948	50	,	,	PUNCT
ejpam-5857	948	51	we	we	PRON
ejpam-5857	948	52	have	have	VERB
ejpam-5857	948	53	u	u	NOUN
ejpam-5857	948	54	+	+	CCONJ
ejpam-5857	948	55	(	(	PUNCT
ejpam-5857	948	56	ψf	ψf	X
ejpam-5857	948	57	;	;	PUNCT
ejpam-5857	948	58	γ	γ	X
ejpam-5857	948	59	)	)	PUNCT
ejpam-5857	948	60	is	be	AUX
ejpam-5857	948	61	an	an	DET
ejpam-5857	948	62	iup	iup	NOUN
ejpam-5857	948	63	-	-	PUNCT
ejpam-5857	948	64	subalgebra	subalgebra	NOUN
ejpam-5857	948	65	of	of	ADP
ejpam-5857	948	66	x.	x.	NOUN
ejpam-5857	948	67	by	by	ADP
ejpam-5857	948	68	the	the	DET
ejpam-5857	948	69	condition	condition	NOUN
ejpam-5857	948	70	(	(	PUNCT
ejpam-5857	948	71	2.17	2.17	NUM
ejpam-5857	948	72	)	)	PUNCT
ejpam-5857	948	73	,	,	PUNCT
ejpam-5857	948	74	we	we	PRON
ejpam-5857	948	75	have	have	VERB
ejpam-5857	948	76	x	x	X
ejpam-5857	948	77	·	·	PUNCT
ejpam-5857	948	78	y	y	PROPN
ejpam-5857	948	79	∈	∈	PROPN
ejpam-5857	948	80	u	u	PROPN
ejpam-5857	948	81	+	+	X
ejpam-5857	948	82	(	(	PUNCT
ejpam-5857	948	83	ψf	ψf	X
ejpam-5857	948	84	;	;	PUNCT
ejpam-5857	948	85	γ	γ	X
ejpam-5857	948	86	)	)	PUNCT
ejpam-5857	948	87	.	.	PUNCT
ejpam-5857	949	1	so	so	ADV
ejpam-5857	949	2	ψf	ψf	X
ejpam-5857	949	3	(	(	PUNCT
ejpam-5857	949	4	x	x	X
ejpam-5857	949	5	·	·	PUNCT
ejpam-5857	949	6	y	y	X
ejpam-5857	949	7	)	)	PUNCT
ejpam-5857	949	8	>	>	X
ejpam-5857	949	9	γ	γ	X
ejpam-5857	949	10	=	=	X
ejpam-5857	949	11	ψf	ψf	X
ejpam-5857	949	12	(	(	PUNCT
ejpam-5857	949	13	x	x	X
ejpam-5857	949	14	·	·	PUNCT
ejpam-5857	949	15	y	y	X
ejpam-5857	949	16	)	)	PUNCT
ejpam-5857	949	17	,	,	PUNCT
ejpam-5857	949	18	which	which	PRON
ejpam-5857	949	19	is	be	AUX
ejpam-5857	949	20	a	a	DET
ejpam-5857	949	21	contradiction	contradiction	NOUN
ejpam-5857	949	22	.	.	PUNCT
ejpam-5857	950	1	if	if	SCONJ
ejpam-5857	950	2	(	(	PUNCT
ejpam-5857	950	3	ψf	ψf	X
ejpam-5857	950	4	(	(	PUNCT
ejpam-5857	950	5	x	x	NOUN
ejpam-5857	950	6	)	)	PUNCT
ejpam-5857	950	7	∧	∧	NOUN
ejpam-5857	950	8	ψf	ψf	X
ejpam-5857	950	9	(	(	PUNCT
ejpam-5857	950	10	y	y	NOUN
ejpam-5857	950	11	)	)	PUNCT
ejpam-5857	950	12	)	)	PUNCT
ejpam-5857	950	13	∨	∨	NUM
ejpam-5857	950	14	0.5	0.5	NUM
ejpam-5857	950	15	=	=	SYM
ejpam-5857	950	16	0.5	0.5	NUM
ejpam-5857	950	17	,	,	PUNCT
ejpam-5857	950	18	then	then	ADV
ejpam-5857	950	19	γ	γ	X
ejpam-5857	950	20	=	=	PUNCT
ejpam-5857	950	21	ψf	ψf	X
ejpam-5857	950	22	(	(	PUNCT
ejpam-5857	950	23	x	x	X
ejpam-5857	950	24	·	·	PUNCT
ejpam-5857	950	25	y	y	X
ejpam-5857	950	26	)	)	PUNCT
ejpam-5857	950	27	<	<	X
ejpam-5857	950	28	0.5	0.5	NUM
ejpam-5857	950	29	,	,	PUNCT
ejpam-5857	950	30	which	which	PRON
ejpam-5857	950	31	is	be	AUX
ejpam-5857	950	32	a	a	DET
ejpam-5857	950	33	contradiction	contradiction	NOUN
ejpam-5857	950	34	.	.	PUNCT
ejpam-5857	951	1	thus	thus	ADV
ejpam-5857	951	2	,	,	PUNCT
ejpam-5857	951	3	ψf	ψf	X
ejpam-5857	951	4	(	(	PUNCT
ejpam-5857	951	5	x	x	X
ejpam-5857	951	6	·	·	PUNCT
ejpam-5857	951	7	y	y	X
ejpam-5857	951	8	)	)	PUNCT
ejpam-5857	951	9	≥	≥	NOUN
ejpam-5857	951	10	(	(	PUNCT
ejpam-5857	951	11	ψf	ψf	X
ejpam-5857	951	12	(	(	PUNCT
ejpam-5857	951	13	x	x	NOUN
ejpam-5857	951	14	)	)	PUNCT
ejpam-5857	951	15	∧	∧	NOUN
ejpam-5857	951	16	ψf	ψf	X
ejpam-5857	951	17	(	(	PUNCT
ejpam-5857	951	18	y	y	NOUN
ejpam-5857	951	19	)	)	PUNCT
ejpam-5857	951	20	)	)	PUNCT
ejpam-5857	951	21	∨	∨	NUM
ejpam-5857	951	22	0.5	0.5	NUM
ejpam-5857	951	23	.	.	PUNCT
ejpam-5857	952	1	hence	hence	ADV
ejpam-5857	952	2	,	,	PUNCT
ejpam-5857	952	3	ψ	ψ	X
ejpam-5857	952	4	is	be	AUX
ejpam-5857	952	5	an	an	DET
ejpam-5857	952	6	intuitionistic	intuitionistic	ADJ
ejpam-5857	952	7	neutrosophic	neutrosophic	ADJ
ejpam-5857	952	8	iup	iup	NOUN
ejpam-5857	952	9	-	-	PUNCT
ejpam-5857	952	10	subalgebra	subalgebra	NOUN
ejpam-5857	952	11	of	of	ADP
ejpam-5857	952	12	x.	x.	NOUN
ejpam-5857	952	13	theorem	theorem	VERB
ejpam-5857	952	14	31	31	NUM
ejpam-5857	952	15	.	.	PUNCT
ejpam-5857	953	1	let	let	VERB
ejpam-5857	953	2	for	for	ADP
ejpam-5857	953	3	all	all	DET
ejpam-5857	953	4	α	α	NOUN
ejpam-5857	953	5	,	,	PUNCT
ejpam-5857	953	6	γ	γ	PROPN
ejpam-5857	953	7	∈	∈	PROPN
ejpam-5857	954	1	[	[	X
ejpam-5857	954	2	0.5	0.5	NUM
ejpam-5857	954	3	,	,	PUNCT
ejpam-5857	954	4	1	1	NUM
ejpam-5857	954	5	]	]	PUNCT
ejpam-5857	954	6	and	and	CCONJ
ejpam-5857	954	7	β	β	X
ejpam-5857	954	8	∈	∈	PROPN
ejpam-5857	954	9	[	[	X
ejpam-5857	954	10	0	0	NUM
ejpam-5857	954	11	,	,	PUNCT
ejpam-5857	954	12	0.5	0.5	NUM
ejpam-5857	954	13	)	)	PUNCT
ejpam-5857	954	14	,	,	PUNCT
ejpam-5857	954	15	the	the	DET
ejpam-5857	954	16	sets	set	NOUN
ejpam-5857	954	17	u	u	NOUN
ejpam-5857	954	18	+	+	X
ejpam-5857	954	19	(	(	PUNCT
ejpam-5857	954	20	ψt	ψt	NUM
ejpam-5857	954	21	;	;	PUNCT
ejpam-5857	954	22	α	α	X
ejpam-5857	954	23	)	)	PUNCT
ejpam-5857	954	24	,	,	PUNCT
ejpam-5857	954	25	l	l	NOUN
ejpam-5857	954	26	−	−	PROPN
ejpam-5857	954	27	(	(	PUNCT
ejpam-5857	954	28	ψi	ψi	ADP
ejpam-5857	954	29	;	;	PUNCT
ejpam-5857	954	30	β	β	X
ejpam-5857	954	31	)	)	PUNCT
ejpam-5857	954	32	and	and	CCONJ
ejpam-5857	954	33	u	u	PRON
ejpam-5857	954	34	+	+	X
ejpam-5857	954	35	(	(	PUNCT
ejpam-5857	954	36	ψf	ψf	X
ejpam-5857	954	37	;	;	PUNCT
ejpam-5857	954	38	γ	γ	X
ejpam-5857	954	39	)	)	PUNCT
ejpam-5857	954	40	are	be	AUX
ejpam-5857	954	41	either	either	CCONJ
ejpam-5857	954	42	empty	empty	ADJ
ejpam-5857	954	43	or	or	CCONJ
ejpam-5857	954	44	iup	iup	NOUN
ejpam-5857	954	45	-	-	PUNCT
ejpam-5857	954	46	ideals	ideal	NOUN
ejpam-5857	954	47	of	of	ADP
ejpam-5857	954	48	x.	x.	NOUN
ejpam-5857	954	49	if	if	SCONJ
ejpam-5857	954	50	ψt	ψt	VERB
ejpam-5857	954	51	(	(	PUNCT
ejpam-5857	954	52	x	x	NOUN
ejpam-5857	954	53	)	)	PUNCT
ejpam-5857	954	54	≥	≥	NOUN
ejpam-5857	954	55	0.5	0.5	NUM
ejpam-5857	954	56	,	,	PUNCT
ejpam-5857	954	57	ψi(x	ψi(x	NUM
ejpam-5857	954	58	)	)	PUNCT
ejpam-5857	954	59	<	<	X
ejpam-5857	954	60	0.5	0.5	NUM
ejpam-5857	954	61	and	and	CCONJ
ejpam-5857	954	62	ψf	ψf	X
ejpam-5857	954	63	(	(	PUNCT
ejpam-5857	954	64	x	x	X
ejpam-5857	954	65	)	)	PUNCT
ejpam-5857	954	66	≥	≥	NOUN
ejpam-5857	954	67	0.5	0.5	NUM
ejpam-5857	954	68	for	for	ADP
ejpam-5857	954	69	all	all	DET
ejpam-5857	954	70	x	x	SYM
ejpam-5857	954	71	∈	∈	NOUN
ejpam-5857	954	72	x	x	NOUN
ejpam-5857	954	73	,	,	PUNCT
ejpam-5857	954	74	then	then	ADV
ejpam-5857	954	75	ψ	ψ	NOUN
ejpam-5857	954	76	is	be	AUX
ejpam-5857	954	77	an	an	DET
ejpam-5857	954	78	intuitionistic	intuitionistic	ADJ
ejpam-5857	954	79	neutrosophic	neutrosophic	ADJ
ejpam-5857	954	80	iup	iup	NOUN
ejpam-5857	954	81	-	-	PUNCT
ejpam-5857	954	82	ideal	ideal	NOUN
ejpam-5857	954	83	of	of	ADP
ejpam-5857	954	84	x.	x.	NOUN
ejpam-5857	954	85	proof	proof	PROPN
ejpam-5857	954	86	.	.	PUNCT
ejpam-5857	955	1	assume	assume	VERB
ejpam-5857	955	2	that	that	SCONJ
ejpam-5857	955	3	for	for	ADP
ejpam-5857	955	4	all	all	DET
ejpam-5857	955	5	α	α	NOUN
ejpam-5857	955	6	,	,	PUNCT
ejpam-5857	955	7	γ	γ	PROPN
ejpam-5857	955	8	∈	∈	PROPN
ejpam-5857	956	1	[	[	X
ejpam-5857	956	2	0.5	0.5	NUM
ejpam-5857	956	3	,	,	PUNCT
ejpam-5857	956	4	1	1	NUM
ejpam-5857	956	5	]	]	PUNCT
ejpam-5857	956	6	and	and	CCONJ
ejpam-5857	956	7	β	β	X
ejpam-5857	956	8	∈	∈	PROPN
ejpam-5857	957	1	[	[	X
ejpam-5857	957	2	0	0	NUM
ejpam-5857	957	3	,	,	PUNCT
ejpam-5857	957	4	0.5	0.5	NUM
ejpam-5857	957	5	)	)	PUNCT
ejpam-5857	957	6	,	,	PUNCT
ejpam-5857	957	7	the	the	DET
ejpam-5857	957	8	sets	set	NOUN
ejpam-5857	957	9	u	u	NOUN
ejpam-5857	957	10	+	+	X
ejpam-5857	957	11	(	(	PUNCT
ejpam-5857	957	12	ψt	ψt	NUM
ejpam-5857	957	13	;	;	PUNCT
ejpam-5857	957	14	α	α	X
ejpam-5857	957	15	)	)	PUNCT
ejpam-5857	957	16	,	,	PUNCT
ejpam-5857	957	17	l	l	NOUN
ejpam-5857	957	18	−	−	PROPN
ejpam-5857	957	19	(	(	PUNCT
ejpam-5857	957	20	ψi	ψi	ADP
ejpam-5857	957	21	;	;	PUNCT
ejpam-5857	957	22	β	β	X
ejpam-5857	957	23	)	)	PUNCT
ejpam-5857	957	24	and	and	CCONJ
ejpam-5857	957	25	u	u	PRON
ejpam-5857	957	26	+	+	X
ejpam-5857	957	27	(	(	PUNCT
ejpam-5857	957	28	ψf	ψf	X
ejpam-5857	957	29	;	;	PUNCT
ejpam-5857	957	30	γ	γ	X
ejpam-5857	957	31	)	)	PUNCT
ejpam-5857	957	32	are	be	AUX
ejpam-5857	957	33	either	either	CCONJ
ejpam-5857	957	34	empty	empty	ADJ
ejpam-5857	957	35	or	or	CCONJ
ejpam-5857	957	36	iup	iup	NOUN
ejpam-5857	957	37	-	-	PUNCT
ejpam-5857	957	38	ideals	ideal	NOUN
ejpam-5857	957	39	of	of	ADP
ejpam-5857	957	40	x.	x.	NOUN
ejpam-5857	957	41	let	let	VERB
ejpam-5857	957	42	x	x	SYM
ejpam-5857	957	43	∈	∈	PROPN
ejpam-5857	957	44	x.	x.	NOUN
ejpam-5857	957	45	assume	assume	VERB
ejpam-5857	957	46	that	that	SCONJ
ejpam-5857	957	47	ψt	ψt	VERB
ejpam-5857	957	48	(	(	PUNCT
ejpam-5857	957	49	0	0	NUM
ejpam-5857	957	50	)	)	PUNCT
ejpam-5857	957	51	<	<	X
ejpam-5857	958	1	ψt	ψt	X
ejpam-5857	958	2	(	(	PUNCT
ejpam-5857	958	3	x	x	NOUN
ejpam-5857	958	4	)	)	PUNCT
ejpam-5857	958	5	.	.	PUNCT
ejpam-5857	959	1	let	let	VERB
ejpam-5857	959	2	α	α	NOUN
ejpam-5857	959	3	=	=	VERB
ejpam-5857	959	4	ψt	ψt	ADJ
ejpam-5857	959	5	(	(	PUNCT
ejpam-5857	959	6	0	0	NUM
ejpam-5857	959	7	)	)	PUNCT
ejpam-5857	959	8	.	.	PUNCT
ejpam-5857	960	1	then	then	ADV
ejpam-5857	960	2	x	x	SYM
ejpam-5857	960	3	∈	∈	PROPN
ejpam-5857	960	4	u	u	NOUN
ejpam-5857	960	5	+	+	X
ejpam-5857	960	6	(	(	PUNCT
ejpam-5857	960	7	ψt	ψt	NUM
ejpam-5857	960	8	;	;	PUNCT
ejpam-5857	960	9	α	α	X
ejpam-5857	960	10	)	)	PUNCT
ejpam-5857	960	11	̸=	̸=	PROPN
ejpam-5857	960	12	∅.	∅.	NOUN
ejpam-5857	960	13	by	by	ADP
ejpam-5857	960	14	assumption	assumption	NOUN
ejpam-5857	960	15	,	,	PUNCT
ejpam-5857	960	16	we	we	PRON
ejpam-5857	960	17	have	have	VERB
ejpam-5857	960	18	u	u	NOUN
ejpam-5857	960	19	+	+	PUNCT
ejpam-5857	960	20	(	(	PUNCT
ejpam-5857	960	21	ψt	ψt	NUM
ejpam-5857	960	22	;	;	PUNCT
ejpam-5857	960	23	α	α	X
ejpam-5857	960	24	)	)	PUNCT
ejpam-5857	960	25	is	be	AUX
ejpam-5857	960	26	an	an	DET
ejpam-5857	960	27	iup	iup	NOUN
ejpam-5857	960	28	-	-	PUNCT
ejpam-5857	960	29	ideal	ideal	NOUN
ejpam-5857	960	30	of	of	ADP
ejpam-5857	960	31	x.	x.	NOUN
ejpam-5857	960	32	by	by	ADP
ejpam-5857	960	33	the	the	DET
ejpam-5857	960	34	condition	condition	NOUN
ejpam-5857	960	35	(	(	PUNCT
ejpam-5857	960	36	2.18	2.18	NUM
ejpam-5857	960	37	)	)	PUNCT
ejpam-5857	960	38	,	,	PUNCT
ejpam-5857	960	39	we	we	PRON
ejpam-5857	960	40	have	have	VERB
ejpam-5857	960	41	0	0	NUM
ejpam-5857	960	42	∈	∈	PROPN
ejpam-5857	960	43	u	u	NOUN
ejpam-5857	960	44	+	+	X
ejpam-5857	960	45	(	(	PUNCT
ejpam-5857	960	46	ψt	ψt	NUM
ejpam-5857	960	47	;	;	PUNCT
ejpam-5857	960	48	α	α	X
ejpam-5857	960	49	)	)	PUNCT
ejpam-5857	960	50	.	.	PUNCT
ejpam-5857	961	1	so	so	ADV
ejpam-5857	961	2	ψt	ψt	VERB
ejpam-5857	961	3	(	(	PUNCT
ejpam-5857	961	4	0	0	NUM
ejpam-5857	961	5	)	)	PUNCT
ejpam-5857	961	6	>	>	X
ejpam-5857	962	1	α	α	X
ejpam-5857	962	2	=	=	X
ejpam-5857	962	3	ψt	ψt	NOUN
ejpam-5857	962	4	(	(	PUNCT
ejpam-5857	962	5	0	0	NUM
ejpam-5857	962	6	)	)	PUNCT
ejpam-5857	962	7	,	,	PUNCT
ejpam-5857	962	8	which	which	PRON
ejpam-5857	962	9	is	be	AUX
ejpam-5857	962	10	a	a	DET
ejpam-5857	962	11	contradiction	contradiction	NOUN
ejpam-5857	962	12	.	.	PUNCT
ejpam-5857	963	1	thus	thus	ADV
ejpam-5857	963	2	,	,	PUNCT
ejpam-5857	963	3	ψt	ψt	VERB
ejpam-5857	963	4	(	(	PUNCT
ejpam-5857	963	5	0	0	NUM
ejpam-5857	963	6	)	)	PUNCT
ejpam-5857	963	7	≥	≥	PRON
ejpam-5857	963	8	ψt	ψt	VERB
ejpam-5857	963	9	(	(	PUNCT
ejpam-5857	963	10	x	x	NOUN
ejpam-5857	963	11	)	)	PUNCT
ejpam-5857	963	12	.	.	PUNCT
ejpam-5857	964	1	let	let	VERB
ejpam-5857	964	2	x	x	PRON
ejpam-5857	964	3	,	,	PUNCT
ejpam-5857	964	4	y	y	PROPN
ejpam-5857	964	5	,	,	PUNCT
ejpam-5857	964	6	z	z	NOUN
ejpam-5857	964	7	∈	∈	PROPN
ejpam-5857	964	8	x	x	AUX
ejpam-5857	964	9	be	be	AUX
ejpam-5857	964	10	such	such	ADJ
ejpam-5857	964	11	that	that	SCONJ
ejpam-5857	964	12	ψt	ψt	NOUN
ejpam-5857	964	13	(	(	PUNCT
ejpam-5857	964	14	x	x	X
ejpam-5857	964	15	·	·	PUNCT
ejpam-5857	964	16	(	(	PUNCT
ejpam-5857	964	17	y	y	PROPN
ejpam-5857	964	18	·	·	PROPN
ejpam-5857	964	19	z	z	NOUN
ejpam-5857	964	20	)	)	PUNCT
ejpam-5857	964	21	)	)	PUNCT
ejpam-5857	964	22	≥	≥	NOUN
ejpam-5857	964	23	0.5	0.5	NUM
ejpam-5857	964	24	and	and	CCONJ
ejpam-5857	964	25	ψt	ψt	ADJ
ejpam-5857	964	26	(	(	PUNCT
ejpam-5857	964	27	y	y	NOUN
ejpam-5857	964	28	)	)	PUNCT
ejpam-5857	964	29	≥	≥	NOUN
ejpam-5857	964	30	0.5	0.5	NUM
ejpam-5857	964	31	.	.	PUNCT
ejpam-5857	965	1	assume	assume	VERB
ejpam-5857	965	2	that	that	SCONJ
ejpam-5857	965	3	ψt	ψt	VERB
ejpam-5857	965	4	(	(	PUNCT
ejpam-5857	965	5	x	x	NOUN
ejpam-5857	965	6	·	·	SYM
ejpam-5857	965	7	z	z	X
ejpam-5857	965	8	)	)	PUNCT
ejpam-5857	965	9	<	<	X
ejpam-5857	965	10	(	(	PUNCT
ejpam-5857	965	11	ψt	ψt	ADJ
ejpam-5857	965	12	(	(	PUNCT
ejpam-5857	965	13	x	x	X
ejpam-5857	965	14	·	·	PUNCT
ejpam-5857	965	15	(	(	PUNCT
ejpam-5857	965	16	y	y	PROPN
ejpam-5857	965	17	·	·	SYM
ejpam-5857	965	18	z))∧ψt	z))∧ψt	PROPN
ejpam-5857	965	19	(	(	PUNCT
ejpam-5857	965	20	y))∨0.5	y))∨0.5	PROPN
ejpam-5857	965	21	.	.	PUNCT
ejpam-5857	966	1	let	let	VERB
ejpam-5857	966	2	α	α	NOUN
ejpam-5857	966	3	=	=	VERB
ejpam-5857	966	4	ψt	ψt	ADJ
ejpam-5857	966	5	(	(	PUNCT
ejpam-5857	966	6	x	x	X
ejpam-5857	966	7	·	·	PUNCT
ejpam-5857	966	8	z	z	X
ejpam-5857	966	9	)	)	PUNCT
ejpam-5857	966	10	.	.	PUNCT
ejpam-5857	967	1	if	if	SCONJ
ejpam-5857	967	2	(	(	PUNCT
ejpam-5857	967	3	ψt	ψt	VERB
ejpam-5857	967	4	(	(	PUNCT
ejpam-5857	967	5	x	x	X
ejpam-5857	967	6	·	·	PUNCT
ejpam-5857	967	7	(	(	PUNCT
ejpam-5857	967	8	y	y	PROPN
ejpam-5857	967	9	·	·	PUNCT
ejpam-5857	967	10	z	z	NOUN
ejpam-5857	967	11	)	)	PUNCT
ejpam-5857	967	12	)	)	PUNCT
ejpam-5857	967	13	∧	∧	NOUN
ejpam-5857	967	14	ψt	ψt	NOUN
ejpam-5857	967	15	(	(	PUNCT
ejpam-5857	967	16	y	y	NOUN
ejpam-5857	967	17	)	)	PUNCT
ejpam-5857	967	18	)	)	PUNCT
ejpam-5857	967	19	∨	∨	NUM
ejpam-5857	967	20	0.5	0.5	NUM
ejpam-5857	967	21	=	=	SYM
ejpam-5857	967	22	ψt	ψt	ADJ
ejpam-5857	967	23	(	(	PUNCT
ejpam-5857	967	24	x	x	X
ejpam-5857	967	25	·	·	PUNCT
ejpam-5857	967	26	(	(	PUNCT
ejpam-5857	967	27	y	y	PROPN
ejpam-5857	967	28	·	·	PUNCT
ejpam-5857	967	29	z	z	NOUN
ejpam-5857	967	30	)	)	PUNCT
ejpam-5857	967	31	)	)	PUNCT
ejpam-5857	968	1	∧	∧	NOUN
ejpam-5857	968	2	ψt	ψt	NOUN
ejpam-5857	968	3	(	(	PUNCT
ejpam-5857	968	4	y	y	NOUN
ejpam-5857	968	5	)	)	PUNCT
ejpam-5857	968	6	,	,	PUNCT
ejpam-5857	968	7	then	then	ADV
ejpam-5857	968	8	x	x	X
ejpam-5857	968	9	·	·	PUNCT
ejpam-5857	968	10	(	(	PUNCT
ejpam-5857	968	11	y	y	PROPN
ejpam-5857	968	12	·	·	PUNCT
ejpam-5857	968	13	z	z	X
ejpam-5857	968	14	)	)	PUNCT
ejpam-5857	968	15	,	,	PUNCT
ejpam-5857	968	16	y	y	PROPN
ejpam-5857	968	17	∈	∈	PROPN
ejpam-5857	968	18	u	u	PROPN
ejpam-5857	968	19	+	+	X
ejpam-5857	968	20	(	(	PUNCT
ejpam-5857	968	21	ψt	ψt	NUM
ejpam-5857	968	22	;	;	PUNCT
ejpam-5857	968	23	α	α	X
ejpam-5857	968	24	)	)	PUNCT
ejpam-5857	968	25	̸=	̸=	PROPN
ejpam-5857	968	26	∅.	∅.	NOUN
ejpam-5857	968	27	by	by	ADP
ejpam-5857	968	28	assumption	assumption	NOUN
ejpam-5857	968	29	,	,	PUNCT
ejpam-5857	968	30	we	we	PRON
ejpam-5857	968	31	have	have	VERB
ejpam-5857	968	32	u	u	NOUN
ejpam-5857	968	33	+	+	PUNCT
ejpam-5857	968	34	(	(	PUNCT
ejpam-5857	968	35	ψt	ψt	NUM
ejpam-5857	968	36	;	;	PUNCT
ejpam-5857	968	37	α	α	X
ejpam-5857	968	38	)	)	PUNCT
ejpam-5857	968	39	is	be	AUX
ejpam-5857	968	40	an	an	DET
ejpam-5857	968	41	iup	iup	NOUN
ejpam-5857	968	42	-	-	PUNCT
ejpam-5857	968	43	ideal	ideal	NOUN
ejpam-5857	968	44	of	of	ADP
ejpam-5857	968	45	x.	x.	NOUN
ejpam-5857	968	46	by	by	ADP
ejpam-5857	968	47	the	the	DET
ejpam-5857	968	48	condition	condition	NOUN
ejpam-5857	968	49	(	(	PUNCT
ejpam-5857	968	50	2.20	2.20	NUM
ejpam-5857	968	51	)	)	PUNCT
ejpam-5857	968	52	,	,	PUNCT
ejpam-5857	968	53	we	we	PRON
ejpam-5857	968	54	have	have	VERB
ejpam-5857	968	55	x	x	X
ejpam-5857	968	56	·	·	PUNCT
ejpam-5857	968	57	z	z	PUNCT
ejpam-5857	968	58	∈	∈	PROPN
ejpam-5857	968	59	u	u	NOUN
ejpam-5857	968	60	+	+	X
ejpam-5857	968	61	(	(	PUNCT
ejpam-5857	968	62	ψt	ψt	NUM
ejpam-5857	968	63	;	;	PUNCT
ejpam-5857	968	64	α	α	X
ejpam-5857	968	65	)	)	PUNCT
ejpam-5857	968	66	.	.	PUNCT
ejpam-5857	969	1	so	so	ADV
ejpam-5857	969	2	ψt	ψt	VERB
ejpam-5857	969	3	(	(	PUNCT
ejpam-5857	969	4	x	x	X
ejpam-5857	969	5	·	·	PUNCT
ejpam-5857	969	6	z	z	X
ejpam-5857	969	7	)	)	PUNCT
ejpam-5857	969	8	>	>	X
ejpam-5857	970	1	α	α	X
ejpam-5857	970	2	=	=	X
ejpam-5857	970	3	ψt	ψt	ADJ
ejpam-5857	970	4	(	(	PUNCT
ejpam-5857	970	5	x	x	X
ejpam-5857	970	6	·	·	PUNCT
ejpam-5857	970	7	z	z	X
ejpam-5857	970	8	)	)	PUNCT
ejpam-5857	970	9	,	,	PUNCT
ejpam-5857	970	10	which	which	PRON
ejpam-5857	970	11	is	be	AUX
ejpam-5857	970	12	a	a	DET
ejpam-5857	970	13	contradiction	contradiction	NOUN
ejpam-5857	970	14	.	.	PUNCT
ejpam-5857	971	1	if	if	SCONJ
ejpam-5857	971	2	(	(	PUNCT
ejpam-5857	971	3	ψt	ψt	VERB
ejpam-5857	971	4	(	(	PUNCT
ejpam-5857	971	5	x	x	X
ejpam-5857	971	6	·	·	PUNCT
ejpam-5857	971	7	(	(	PUNCT
ejpam-5857	971	8	y	y	PROPN
ejpam-5857	971	9	·	·	PUNCT
ejpam-5857	971	10	z	z	NOUN
ejpam-5857	971	11	)	)	PUNCT
ejpam-5857	971	12	)	)	PUNCT
ejpam-5857	971	13	∧	∧	NOUN
ejpam-5857	971	14	ψt	ψt	NOUN
ejpam-5857	971	15	(	(	PUNCT
ejpam-5857	971	16	y	y	NOUN
ejpam-5857	971	17	)	)	PUNCT
ejpam-5857	971	18	)	)	PUNCT
ejpam-5857	971	19	∨	∨	NUM
ejpam-5857	971	20	0.5	0.5	NUM
ejpam-5857	971	21	=	=	SYM
ejpam-5857	971	22	0.5	0.5	NUM
ejpam-5857	971	23	,	,	PUNCT
ejpam-5857	971	24	then	then	ADV
ejpam-5857	971	25	α	α	PROPN
ejpam-5857	971	26	=	=	NOUN
ejpam-5857	971	27	ψt	ψt	ADJ
ejpam-5857	971	28	(	(	PUNCT
ejpam-5857	971	29	x	x	X
ejpam-5857	971	30	·	·	PUNCT
ejpam-5857	971	31	z	z	X
ejpam-5857	971	32	)	)	PUNCT
ejpam-5857	971	33	<	<	X
ejpam-5857	971	34	0.5	0.5	NUM
ejpam-5857	971	35	,	,	PUNCT
ejpam-5857	971	36	which	which	PRON
ejpam-5857	971	37	is	be	AUX
ejpam-5857	971	38	a	a	DET
ejpam-5857	971	39	contradiction	contradiction	NOUN
ejpam-5857	971	40	.	.	PUNCT
ejpam-5857	972	1	thus	thus	ADV
ejpam-5857	972	2	,	,	PUNCT
ejpam-5857	972	3	ψt	ψt	VERB
ejpam-5857	972	4	(	(	PUNCT
ejpam-5857	972	5	x	x	X
ejpam-5857	972	6	·	·	PUNCT
ejpam-5857	972	7	z	z	X
ejpam-5857	972	8	)	)	PUNCT
ejpam-5857	972	9	≥	≥	NOUN
ejpam-5857	972	10	(	(	PUNCT
ejpam-5857	972	11	ψt	ψt	VERB
ejpam-5857	972	12	(	(	PUNCT
ejpam-5857	972	13	x	x	X
ejpam-5857	972	14	·	·	PUNCT
ejpam-5857	972	15	(	(	PUNCT
ejpam-5857	972	16	y	y	PROPN
ejpam-5857	972	17	·	·	PUNCT
ejpam-5857	972	18	z	z	NOUN
ejpam-5857	972	19	)	)	PUNCT
ejpam-5857	972	20	)	)	PUNCT
ejpam-5857	973	1	∧	∧	NOUN
ejpam-5857	973	2	ψt	ψt	NOUN
ejpam-5857	973	3	(	(	PUNCT
ejpam-5857	973	4	y	y	NOUN
ejpam-5857	973	5	)	)	PUNCT
ejpam-5857	973	6	)	)	PUNCT
ejpam-5857	974	1	∨	∨	NUM
ejpam-5857	974	2	0.5	0.5	NUM
ejpam-5857	974	3	.	.	PUNCT
ejpam-5857	975	1	let	let	VERB
ejpam-5857	975	2	x	x	SYM
ejpam-5857	975	3	∈	∈	PROPN
ejpam-5857	975	4	x.	x.	NOUN
ejpam-5857	975	5	assume	assume	VERB
ejpam-5857	975	6	that	that	SCONJ
ejpam-5857	975	7	ψi(0	ψi(0	PROPN
ejpam-5857	975	8	)	)	PUNCT
ejpam-5857	975	9	>	>	X
ejpam-5857	975	10	ψi(x	ψi(x	PROPN
ejpam-5857	975	11	)	)	PUNCT
ejpam-5857	975	12	.	.	PUNCT
ejpam-5857	976	1	let	let	VERB
ejpam-5857	976	2	β	β	X
ejpam-5857	976	3	=	=	VERB
ejpam-5857	976	4	ψi(0	ψi(0	PROPN
ejpam-5857	976	5	)	)	PUNCT
ejpam-5857	976	6	.	.	PUNCT
ejpam-5857	977	1	then	then	ADV
ejpam-5857	977	2	x	x	SYM
ejpam-5857	977	3	∈	∈	PROPN
ejpam-5857	977	4	l	l	NOUN
ejpam-5857	977	5	−	−	PROPN
ejpam-5857	977	6	(	(	PUNCT
ejpam-5857	977	7	ψi	ψi	ADP
ejpam-5857	977	8	;	;	PUNCT
ejpam-5857	977	9	β	β	X
ejpam-5857	977	10	)	)	PUNCT
ejpam-5857	977	11	̸=	̸=	PROPN
ejpam-5857	977	12	∅.	∅.	VERB
ejpam-5857	977	13	by	by	ADP
ejpam-5857	977	14	assumption	assumption	NOUN
ejpam-5857	977	15	,	,	PUNCT
ejpam-5857	977	16	we	we	PRON
ejpam-5857	977	17	have	have	VERB
ejpam-5857	977	18	l	l	NOUN
ejpam-5857	977	19	−	−	PROPN
ejpam-5857	977	20	(	(	PUNCT
ejpam-5857	977	21	ψi	ψi	ADP
ejpam-5857	977	22	;	;	PUNCT
ejpam-5857	977	23	β	β	X
ejpam-5857	977	24	)	)	PUNCT
ejpam-5857	977	25	is	be	AUX
ejpam-5857	977	26	an	an	DET
ejpam-5857	977	27	iup	iup	NOUN
ejpam-5857	977	28	-	-	PUNCT
ejpam-5857	977	29	ideal	ideal	NOUN
ejpam-5857	977	30	of	of	ADP
ejpam-5857	977	31	x.	x.	NOUN
ejpam-5857	977	32	by	by	ADP
ejpam-5857	977	33	the	the	DET
ejpam-5857	977	34	condition	condition	NOUN
ejpam-5857	977	35	(	(	PUNCT
ejpam-5857	977	36	2.18	2.18	NUM
ejpam-5857	977	37	)	)	PUNCT
ejpam-5857	977	38	,	,	PUNCT
ejpam-5857	977	39	we	we	PRON
ejpam-5857	977	40	have	have	VERB
ejpam-5857	977	41	0	0	NUM
ejpam-5857	977	42	∈	∈	NOUN
ejpam-5857	977	43	l	l	NOUN
ejpam-5857	977	44	−	−	PROPN
ejpam-5857	977	45	(	(	PUNCT
ejpam-5857	977	46	ψi	ψi	ADP
ejpam-5857	977	47	;	;	PUNCT
ejpam-5857	977	48	β	β	X
ejpam-5857	977	49	)	)	PUNCT
ejpam-5857	977	50	.	.	PUNCT
ejpam-5857	978	1	so	so	ADV
ejpam-5857	978	2	ψi(0	ψi(0	PROPN
ejpam-5857	978	3	)	)	PUNCT
ejpam-5857	978	4	<	<	X
ejpam-5857	978	5	β	β	X
ejpam-5857	978	6	=	=	SYM
ejpam-5857	978	7	ψi(0	ψi(0	PROPN
ejpam-5857	978	8	)	)	PUNCT
ejpam-5857	978	9	,	,	PUNCT
ejpam-5857	978	10	which	which	PRON
ejpam-5857	978	11	is	be	AUX
ejpam-5857	978	12	a	a	DET
ejpam-5857	978	13	contradiction	contradiction	NOUN
ejpam-5857	978	14	.	.	PUNCT
ejpam-5857	979	1	thus	thus	ADV
ejpam-5857	979	2	,	,	PUNCT
ejpam-5857	979	3	ψi(0	ψi(0	PROPN
ejpam-5857	979	4	)	)	PUNCT
ejpam-5857	979	5	≤	≤	NOUN
ejpam-5857	979	6	ψi(x	ψi(x	NUM
ejpam-5857	979	7	)	)	PUNCT
ejpam-5857	979	8	.	.	PUNCT
ejpam-5857	980	1	let	let	VERB
ejpam-5857	980	2	x	x	PRON
ejpam-5857	980	3	,	,	PUNCT
ejpam-5857	980	4	y	y	PROPN
ejpam-5857	980	5	,	,	PUNCT
ejpam-5857	980	6	z	z	NOUN
ejpam-5857	980	7	∈	∈	PROPN
ejpam-5857	980	8	x	x	AUX
ejpam-5857	980	9	be	be	AUX
ejpam-5857	980	10	such	such	ADJ
ejpam-5857	980	11	that	that	SCONJ
ejpam-5857	980	12	ψi(x	ψi(x	NUM
ejpam-5857	980	13	·	·	PUNCT
ejpam-5857	980	14	(	(	PUNCT
ejpam-5857	980	15	y	y	PROPN
ejpam-5857	980	16	·	·	PROPN
ejpam-5857	980	17	z	z	NOUN
ejpam-5857	980	18	)	)	PUNCT
ejpam-5857	980	19	)	)	PUNCT
ejpam-5857	980	20	<	<	X
ejpam-5857	980	21	0.5	0.5	NUM
ejpam-5857	980	22	and	and	CCONJ
ejpam-5857	980	23	ψi(y	ψi(y	NUM
ejpam-5857	980	24	)	)	PUNCT
ejpam-5857	980	25	<	<	X
ejpam-5857	980	26	0.5	0.5	NUM
ejpam-5857	980	27	.	.	PUNCT
ejpam-5857	980	28	assume	assume	VERB
ejpam-5857	980	29	that	that	SCONJ
ejpam-5857	980	30	ψi(x	ψi(x	NOUN
ejpam-5857	980	31	·	·	PUNCT
ejpam-5857	980	32	z	z	X
ejpam-5857	980	33	)	)	PUNCT
ejpam-5857	980	34	>	>	X
ejpam-5857	980	35	ψi(x	ψi(x	PUNCT
ejpam-5857	980	36	·	·	PUNCT
ejpam-5857	980	37	(	(	PUNCT
ejpam-5857	980	38	y	y	PROPN
ejpam-5857	980	39	·	·	PUNCT
ejpam-5857	981	1	z))∨ψi(y))∧0.5	z))∨ψi(y))∧0.5	PROPN
ejpam-5857	981	2	.	.	PUNCT
ejpam-5857	982	1	let	let	VERB
ejpam-5857	982	2	β	β	X
ejpam-5857	982	3	=	=	SYM
ejpam-5857	982	4	ψi(x·z	ψi(x·z	X
ejpam-5857	982	5	)	)	PUNCT
ejpam-5857	982	6	.	.	PUNCT
ejpam-5857	983	1	if	if	SCONJ
ejpam-5857	983	2	(	(	PUNCT
ejpam-5857	983	3	ψi(x·(y	ψi(x·(y	NOUN
ejpam-5857	983	4	·	·	SYM
ejpam-5857	983	5	z))∨ψi(y))∧0.5	z))∨ψi(y))∧0.5	NOUN
ejpam-5857	983	6	=	=	PRON
ejpam-5857	983	7	ψi(x·(y	ψi(x·(y	VERB
ejpam-5857	983	8	·	·	PUNCT
ejpam-5857	983	9	z))∨ψi(y	z))∨ψi(y	NUM
ejpam-5857	983	10	)	)	PUNCT
ejpam-5857	983	11	,	,	PUNCT
ejpam-5857	983	12	then	then	ADV
ejpam-5857	983	13	x	x	X
ejpam-5857	983	14	·	·	PUNCT
ejpam-5857	983	15	(	(	PUNCT
ejpam-5857	983	16	y	y	PROPN
ejpam-5857	983	17	·	·	PUNCT
ejpam-5857	983	18	z	z	X
ejpam-5857	983	19	)	)	PUNCT
ejpam-5857	983	20	,	,	PUNCT
ejpam-5857	983	21	y	y	PROPN
ejpam-5857	983	22	∈	∈	PROPN
ejpam-5857	983	23	l	l	NOUN
ejpam-5857	984	1	−	−	PROPN
ejpam-5857	984	2	(	(	PUNCT
ejpam-5857	984	3	ψi	ψi	ADP
ejpam-5857	984	4	;	;	PUNCT
ejpam-5857	984	5	β	β	X
ejpam-5857	984	6	)	)	PUNCT
ejpam-5857	984	7	̸=	̸=	PROPN
ejpam-5857	984	8	∅.	∅.	VERB
ejpam-5857	984	9	by	by	ADP
ejpam-5857	984	10	assumption	assumption	NOUN
ejpam-5857	984	11	,	,	PUNCT
ejpam-5857	984	12	we	we	PRON
ejpam-5857	984	13	have	have	VERB
ejpam-5857	984	14	l	l	NOUN
ejpam-5857	984	15	−	−	PROPN
ejpam-5857	984	16	(	(	PUNCT
ejpam-5857	984	17	ψi	ψi	ADP
ejpam-5857	984	18	;	;	PUNCT
ejpam-5857	984	19	β	β	X
ejpam-5857	984	20	)	)	PUNCT
ejpam-5857	984	21	is	be	AUX
ejpam-5857	984	22	an	an	DET
ejpam-5857	984	23	iup	iup	NOUN
ejpam-5857	984	24	-	-	PUNCT
ejpam-5857	984	25	ideal	ideal	NOUN
ejpam-5857	984	26	of	of	ADP
ejpam-5857	984	27	x.	x.	NOUN
ejpam-5857	984	28	by	by	ADP
ejpam-5857	984	29	the	the	DET
ejpam-5857	984	30	condition	condition	NOUN
ejpam-5857	984	31	(	(	PUNCT
ejpam-5857	984	32	2.20	2.20	NUM
ejpam-5857	984	33	)	)	PUNCT
ejpam-5857	984	34	,	,	PUNCT
ejpam-5857	984	35	we	we	PRON
ejpam-5857	984	36	have	have	VERB
ejpam-5857	984	37	x	x	X
ejpam-5857	984	38	·	·	PUNCT
ejpam-5857	984	39	z	z	SYM
ejpam-5857	984	40	∈	∈	PROPN
ejpam-5857	984	41	l	l	NOUN
ejpam-5857	984	42	−	−	PROPN
ejpam-5857	984	43	(	(	PUNCT
ejpam-5857	984	44	ψi	ψi	ADP
ejpam-5857	984	45	;	;	PUNCT
ejpam-5857	984	46	β	β	X
ejpam-5857	984	47	)	)	PUNCT
ejpam-5857	984	48	.	.	PUNCT
ejpam-5857	985	1	so	so	ADV
ejpam-5857	985	2	ψi(x	ψi(x	NOUN
ejpam-5857	985	3	·	·	PUNCT
ejpam-5857	986	1	z	z	X
ejpam-5857	986	2	)	)	PUNCT
ejpam-5857	986	3	<	<	X
ejpam-5857	986	4	β	β	X
ejpam-5857	986	5	=	=	SYM
ejpam-5857	986	6	ψi(x	ψi(x	X
ejpam-5857	986	7	·	·	PUNCT
ejpam-5857	986	8	z	z	X
ejpam-5857	986	9	)	)	PUNCT
ejpam-5857	986	10	,	,	PUNCT
ejpam-5857	986	11	which	which	PRON
ejpam-5857	986	12	is	be	AUX
ejpam-5857	986	13	a	a	DET
ejpam-5857	986	14	contradiction	contradiction	NOUN
ejpam-5857	986	15	.	.	PUNCT
ejpam-5857	987	1	if	if	SCONJ
ejpam-5857	987	2	(	(	PUNCT
ejpam-5857	987	3	ψi(x	ψi(x	X
ejpam-5857	987	4	·	·	PUNCT
ejpam-5857	987	5	(	(	PUNCT
ejpam-5857	987	6	y	y	PROPN
ejpam-5857	987	7	·	·	PUNCT
ejpam-5857	987	8	z	z	NOUN
ejpam-5857	987	9	)	)	PUNCT
ejpam-5857	987	10	)	)	PUNCT
ejpam-5857	987	11	∨	∨	NUM
ejpam-5857	987	12	ψi(y	ψi(y	NUM
ejpam-5857	987	13	)	)	PUNCT
ejpam-5857	987	14	)	)	PUNCT
ejpam-5857	988	1	∧	∧	NOUN
ejpam-5857	988	2	0.5	0.5	NUM
ejpam-5857	988	3	=	=	SYM
ejpam-5857	988	4	0.5	0.5	NUM
ejpam-5857	988	5	,	,	PUNCT
ejpam-5857	988	6	then	then	ADV
ejpam-5857	988	7	β	β	X
ejpam-5857	988	8	=	=	SYM
ejpam-5857	988	9	ψi(x	ψi(x	X
ejpam-5857	988	10	·	·	PUNCT
ejpam-5857	988	11	z	z	X
ejpam-5857	988	12	)	)	PUNCT
ejpam-5857	988	13	≥	≥	NOUN
ejpam-5857	988	14	0.5	0.5	NUM
ejpam-5857	988	15	,	,	PUNCT
ejpam-5857	988	16	which	which	PRON
ejpam-5857	988	17	is	be	AUX
ejpam-5857	988	18	a	a	DET
ejpam-5857	988	19	contradiction	contradiction	NOUN
ejpam-5857	988	20	.	.	PUNCT
ejpam-5857	989	1	thus	thus	ADV
ejpam-5857	989	2	,	,	PUNCT
ejpam-5857	989	3	ψi(x	ψi(x	X
ejpam-5857	989	4	·	·	PUNCT
ejpam-5857	989	5	z	z	X
ejpam-5857	989	6	)	)	PUNCT
ejpam-5857	989	7	≤	≤	NOUN
ejpam-5857	989	8	(	(	PUNCT
ejpam-5857	989	9	ψi(x	ψi(x	X
ejpam-5857	989	10	·	·	PUNCT
ejpam-5857	989	11	(	(	PUNCT
ejpam-5857	989	12	y	y	PROPN
ejpam-5857	989	13	·	·	PUNCT
ejpam-5857	989	14	z	z	NOUN
ejpam-5857	989	15	)	)	PUNCT
ejpam-5857	989	16	)	)	PUNCT
ejpam-5857	989	17	∨	∨	NUM
ejpam-5857	989	18	ψi(y	ψi(y	NUM
ejpam-5857	989	19	)	)	PUNCT
ejpam-5857	989	20	)	)	PUNCT
ejpam-5857	990	1	∧	∧	NOUN
ejpam-5857	990	2	0.5	0.5	NUM
ejpam-5857	990	3	.	.	PUNCT
ejpam-5857	991	1	k.	k.	PROPN
ejpam-5857	991	2	suayngam	suayngam	PROPN
ejpam-5857	991	3	,	,	PUNCT
ejpam-5857	991	4	p.	p.	NOUN
ejpam-5857	991	5	julatha	julatha	PROPN
ejpam-5857	991	6	,	,	PUNCT
ejpam-5857	991	7	w.	w.	PROPN
ejpam-5857	991	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	991	9	,	,	PUNCT
ejpam-5857	991	10	a.	a.	NOUN
ejpam-5857	991	11	iampan	iampan	PROPN
ejpam-5857	991	12	/	/	SYM
ejpam-5857	991	13	eur	eur	PROPN
ejpam-5857	991	14	.	.	PUNCT
ejpam-5857	992	1	j.	j.	PROPN
ejpam-5857	992	2	pure	pure	PROPN
ejpam-5857	992	3	appl	appl	PROPN
ejpam-5857	992	4	.	.	PROPN
ejpam-5857	992	5	math	math	PROPN
ejpam-5857	992	6	,	,	PUNCT
ejpam-5857	992	7	18	18	NUM
ejpam-5857	992	8	(	(	PUNCT
ejpam-5857	992	9	2	2	NUM
ejpam-5857	992	10	)	)	PUNCT
ejpam-5857	992	11	(	(	PUNCT
ejpam-5857	992	12	2025	2025	NUM
ejpam-5857	992	13	)	)	PUNCT
ejpam-5857	992	14	,	,	PUNCT
ejpam-5857	992	15	5857	5857	NUM
ejpam-5857	992	16	28	28	NUM
ejpam-5857	992	17	of	of	ADP
ejpam-5857	992	18	30	30	NUM
ejpam-5857	992	19	let	let	VERB
ejpam-5857	992	20	x	x	SYM
ejpam-5857	992	21	∈	∈	PROPN
ejpam-5857	992	22	x.	x.	NOUN
ejpam-5857	992	23	assume	assume	VERB
ejpam-5857	992	24	that	that	SCONJ
ejpam-5857	992	25	ψf	ψf	X
ejpam-5857	992	26	(	(	PUNCT
ejpam-5857	992	27	0	0	NUM
ejpam-5857	992	28	)	)	PUNCT
ejpam-5857	992	29	<	<	X
ejpam-5857	992	30	ψf	ψf	X
ejpam-5857	992	31	(	(	PUNCT
ejpam-5857	992	32	x	x	NOUN
ejpam-5857	992	33	)	)	PUNCT
ejpam-5857	992	34	.	.	PUNCT
ejpam-5857	993	1	let	let	VERB
ejpam-5857	993	2	γ	γ	X
ejpam-5857	993	3	=	=	PRON
ejpam-5857	993	4	ψf	ψf	X
ejpam-5857	993	5	(	(	PUNCT
ejpam-5857	993	6	0	0	NUM
ejpam-5857	993	7	)	)	PUNCT
ejpam-5857	993	8	.	.	PUNCT
ejpam-5857	994	1	then	then	ADV
ejpam-5857	994	2	x	x	SYM
ejpam-5857	994	3	∈	∈	PROPN
ejpam-5857	994	4	u	u	NOUN
ejpam-5857	994	5	+	+	X
ejpam-5857	994	6	(	(	PUNCT
ejpam-5857	994	7	ψf	ψf	X
ejpam-5857	994	8	;	;	PUNCT
ejpam-5857	994	9	γ	γ	X
ejpam-5857	994	10	)	)	PUNCT
ejpam-5857	994	11	̸=	̸=	PROPN
ejpam-5857	994	12	∅.	∅.	VERB
ejpam-5857	994	13	by	by	ADP
ejpam-5857	994	14	assumption	assumption	NOUN
ejpam-5857	994	15	,	,	PUNCT
ejpam-5857	994	16	we	we	PRON
ejpam-5857	994	17	have	have	VERB
ejpam-5857	994	18	u	u	NOUN
ejpam-5857	994	19	+	+	CCONJ
ejpam-5857	994	20	(	(	PUNCT
ejpam-5857	994	21	ψf	ψf	X
ejpam-5857	994	22	;	;	PUNCT
ejpam-5857	994	23	γ	γ	X
ejpam-5857	994	24	)	)	PUNCT
ejpam-5857	994	25	is	be	AUX
ejpam-5857	994	26	an	an	DET
ejpam-5857	994	27	iup	iup	NOUN
ejpam-5857	994	28	-	-	PUNCT
ejpam-5857	994	29	ideal	ideal	NOUN
ejpam-5857	994	30	of	of	ADP
ejpam-5857	994	31	x.	x.	NOUN
ejpam-5857	994	32	by	by	ADP
ejpam-5857	994	33	the	the	DET
ejpam-5857	994	34	condition	condition	NOUN
ejpam-5857	994	35	(	(	PUNCT
ejpam-5857	994	36	2.18	2.18	NUM
ejpam-5857	994	37	)	)	PUNCT
ejpam-5857	994	38	,	,	PUNCT
ejpam-5857	994	39	we	we	PRON
ejpam-5857	994	40	have	have	VERB
ejpam-5857	994	41	0	0	NUM
ejpam-5857	994	42	∈	∈	PROPN
ejpam-5857	994	43	u	u	NOUN
ejpam-5857	994	44	+	+	X
ejpam-5857	994	45	(	(	PUNCT
ejpam-5857	994	46	ψf	ψf	X
ejpam-5857	994	47	;	;	PUNCT
ejpam-5857	994	48	γ	γ	X
ejpam-5857	994	49	)	)	PUNCT
ejpam-5857	994	50	.	.	PUNCT
ejpam-5857	995	1	so	so	ADV
ejpam-5857	995	2	ψf	ψf	X
ejpam-5857	995	3	(	(	PUNCT
ejpam-5857	995	4	0	0	NUM
ejpam-5857	995	5	)	)	PUNCT
ejpam-5857	995	6	>	>	X
ejpam-5857	995	7	γ	γ	X
ejpam-5857	995	8	=	=	X
ejpam-5857	995	9	ψf	ψf	X
ejpam-5857	995	10	(	(	PUNCT
ejpam-5857	995	11	0	0	NUM
ejpam-5857	995	12	)	)	PUNCT
ejpam-5857	995	13	,	,	PUNCT
ejpam-5857	995	14	which	which	PRON
ejpam-5857	995	15	is	be	AUX
ejpam-5857	995	16	a	a	DET
ejpam-5857	995	17	contradiction	contradiction	NOUN
ejpam-5857	995	18	.	.	PUNCT
ejpam-5857	996	1	thus	thus	ADV
ejpam-5857	996	2	,	,	PUNCT
ejpam-5857	996	3	ψf	ψf	X
ejpam-5857	996	4	(	(	PUNCT
ejpam-5857	996	5	0	0	NUM
ejpam-5857	996	6	)	)	PUNCT
ejpam-5857	996	7	≥	≥	NOUN
ejpam-5857	996	8	ψf	ψf	X
ejpam-5857	996	9	(	(	PUNCT
ejpam-5857	996	10	x	x	NOUN
ejpam-5857	996	11	)	)	PUNCT
ejpam-5857	996	12	.	.	PUNCT
ejpam-5857	997	1	let	let	VERB
ejpam-5857	997	2	x	x	PRON
ejpam-5857	997	3	,	,	PUNCT
ejpam-5857	997	4	y	y	PROPN
ejpam-5857	997	5	,	,	PUNCT
ejpam-5857	997	6	z	z	NOUN
ejpam-5857	997	7	∈	∈	PROPN
ejpam-5857	997	8	x	x	AUX
ejpam-5857	997	9	be	be	AUX
ejpam-5857	997	10	such	such	ADJ
ejpam-5857	997	11	that	that	SCONJ
ejpam-5857	997	12	ψf	ψf	X
ejpam-5857	997	13	(	(	PUNCT
ejpam-5857	997	14	x	x	X
ejpam-5857	997	15	·	·	PUNCT
ejpam-5857	997	16	(	(	PUNCT
ejpam-5857	997	17	y	y	PROPN
ejpam-5857	997	18	·	·	PROPN
ejpam-5857	997	19	z	z	NOUN
ejpam-5857	997	20	)	)	PUNCT
ejpam-5857	997	21	)	)	PUNCT
ejpam-5857	997	22	≥	≥	NOUN
ejpam-5857	997	23	0.5	0.5	NUM
ejpam-5857	997	24	and	and	CCONJ
ejpam-5857	997	25	ψf	ψf	X
ejpam-5857	997	26	(	(	PUNCT
ejpam-5857	997	27	y	y	PROPN
ejpam-5857	997	28	)	)	PUNCT
ejpam-5857	997	29	≥	≥	NOUN
ejpam-5857	997	30	0.5	0.5	NUM
ejpam-5857	997	31	.	.	PUNCT
ejpam-5857	998	1	assume	assume	VERB
ejpam-5857	998	2	that	that	SCONJ
ejpam-5857	998	3	ψf	ψf	X
ejpam-5857	998	4	(	(	PUNCT
ejpam-5857	998	5	x	x	X
ejpam-5857	998	6	·	·	SYM
ejpam-5857	998	7	z	z	X
ejpam-5857	998	8	)	)	PUNCT
ejpam-5857	998	9	<	<	X
ejpam-5857	998	10	(	(	PUNCT
ejpam-5857	998	11	ψf	ψf	X
ejpam-5857	998	12	(	(	PUNCT
ejpam-5857	998	13	x	x	X
ejpam-5857	998	14	·	·	PUNCT
ejpam-5857	998	15	(	(	PUNCT
ejpam-5857	998	16	y	y	PROPN
ejpam-5857	998	17	·	·	PUNCT
ejpam-5857	998	18	z	z	NOUN
ejpam-5857	998	19	)	)	PUNCT
ejpam-5857	998	20	)	)	PUNCT
ejpam-5857	998	21	∧	∧	NOUN
ejpam-5857	998	22	ψf	ψf	X
ejpam-5857	998	23	(	(	PUNCT
ejpam-5857	998	24	y	y	NOUN
ejpam-5857	998	25	)	)	PUNCT
ejpam-5857	998	26	)	)	PUNCT
ejpam-5857	999	1	∨	∨	NUM
ejpam-5857	999	2	0.5	0.5	NUM
ejpam-5857	999	3	.	.	PUNCT
ejpam-5857	1000	1	let	let	VERB
ejpam-5857	1000	2	γ	γ	X
ejpam-5857	1000	3	=	=	PRON
ejpam-5857	1000	4	ψf	ψf	X
ejpam-5857	1000	5	(	(	PUNCT
ejpam-5857	1000	6	x	x	X
ejpam-5857	1000	7	·	·	PUNCT
ejpam-5857	1000	8	z	z	X
ejpam-5857	1000	9	)	)	PUNCT
ejpam-5857	1000	10	.	.	PUNCT
ejpam-5857	1001	1	if	if	SCONJ
ejpam-5857	1001	2	(	(	PUNCT
ejpam-5857	1001	3	ψf	ψf	X
ejpam-5857	1001	4	(	(	PUNCT
ejpam-5857	1001	5	x	x	X
ejpam-5857	1001	6	·	·	PUNCT
ejpam-5857	1001	7	(	(	PUNCT
ejpam-5857	1001	8	y	y	PROPN
ejpam-5857	1001	9	·	·	PUNCT
ejpam-5857	1001	10	z	z	NOUN
ejpam-5857	1001	11	)	)	PUNCT
ejpam-5857	1001	12	)	)	PUNCT
ejpam-5857	1001	13	∧	∧	NOUN
ejpam-5857	1001	14	ψf	ψf	X
ejpam-5857	1001	15	(	(	PUNCT
ejpam-5857	1001	16	y	y	NOUN
ejpam-5857	1001	17	)	)	PUNCT
ejpam-5857	1001	18	)	)	PUNCT
ejpam-5857	1001	19	∨	∨	NOUN
ejpam-5857	1001	20	0.5	0.5	NUM
ejpam-5857	1001	21	=	=	SYM
ejpam-5857	1001	22	ψf	ψf	X
ejpam-5857	1001	23	(	(	PUNCT
ejpam-5857	1001	24	x	x	X
ejpam-5857	1001	25	·	·	PUNCT
ejpam-5857	1001	26	(	(	PUNCT
ejpam-5857	1001	27	y	y	PROPN
ejpam-5857	1001	28	·	·	PUNCT
ejpam-5857	1001	29	z	z	NOUN
ejpam-5857	1001	30	)	)	PUNCT
ejpam-5857	1001	31	)	)	PUNCT
ejpam-5857	1001	32	∧	∧	NOUN
ejpam-5857	1001	33	ψf	ψf	X
ejpam-5857	1001	34	(	(	PUNCT
ejpam-5857	1001	35	y	y	NOUN
ejpam-5857	1001	36	)	)	PUNCT
ejpam-5857	1001	37	,	,	PUNCT
ejpam-5857	1001	38	then	then	ADV
ejpam-5857	1001	39	x	x	X
ejpam-5857	1001	40	·	·	PUNCT
ejpam-5857	1001	41	(	(	PUNCT
ejpam-5857	1001	42	y	y	PROPN
ejpam-5857	1001	43	·	·	PUNCT
ejpam-5857	1001	44	z	z	X
ejpam-5857	1001	45	)	)	PUNCT
ejpam-5857	1001	46	,	,	PUNCT
ejpam-5857	1001	47	y	y	PROPN
ejpam-5857	1001	48	∈	∈	PROPN
ejpam-5857	1001	49	u	u	PROPN
ejpam-5857	1001	50	+	+	X
ejpam-5857	1001	51	(	(	PUNCT
ejpam-5857	1001	52	ψf	ψf	X
ejpam-5857	1001	53	;	;	PUNCT
ejpam-5857	1001	54	γ	γ	X
ejpam-5857	1001	55	)	)	PUNCT
ejpam-5857	1001	56	̸=	̸=	PROPN
ejpam-5857	1001	57	∅.	∅.	VERB
ejpam-5857	1001	58	by	by	ADP
ejpam-5857	1001	59	assumption	assumption	NOUN
ejpam-5857	1001	60	,	,	PUNCT
ejpam-5857	1001	61	we	we	PRON
ejpam-5857	1001	62	have	have	VERB
ejpam-5857	1001	63	u	u	NOUN
ejpam-5857	1001	64	+	+	CCONJ
ejpam-5857	1001	65	(	(	PUNCT
ejpam-5857	1001	66	ψf	ψf	X
ejpam-5857	1001	67	;	;	PUNCT
ejpam-5857	1001	68	γ	γ	X
ejpam-5857	1001	69	)	)	PUNCT
ejpam-5857	1001	70	is	be	AUX
ejpam-5857	1001	71	an	an	DET
ejpam-5857	1001	72	iup	iup	NOUN
ejpam-5857	1001	73	-	-	PUNCT
ejpam-5857	1001	74	ideal	ideal	NOUN
ejpam-5857	1001	75	of	of	ADP
ejpam-5857	1001	76	x.	x.	NOUN
ejpam-5857	1001	77	by	by	ADP
ejpam-5857	1001	78	the	the	DET
ejpam-5857	1001	79	condition	condition	NOUN
ejpam-5857	1001	80	(	(	PUNCT
ejpam-5857	1001	81	2.20	2.20	NUM
ejpam-5857	1001	82	)	)	PUNCT
ejpam-5857	1001	83	,	,	PUNCT
ejpam-5857	1001	84	we	we	PRON
ejpam-5857	1001	85	have	have	VERB
ejpam-5857	1001	86	x	x	X
ejpam-5857	1001	87	·	·	PUNCT
ejpam-5857	1001	88	z	z	PUNCT
ejpam-5857	1001	89	∈	∈	PROPN
ejpam-5857	1001	90	u	u	NOUN
ejpam-5857	1001	91	+	+	X
ejpam-5857	1001	92	(	(	PUNCT
ejpam-5857	1001	93	ψf	ψf	X
ejpam-5857	1001	94	;	;	PUNCT
ejpam-5857	1001	95	γ	γ	X
ejpam-5857	1001	96	)	)	PUNCT
ejpam-5857	1001	97	.	.	PUNCT
ejpam-5857	1002	1	so	so	ADV
ejpam-5857	1002	2	ψf	ψf	X
ejpam-5857	1002	3	(	(	PUNCT
ejpam-5857	1002	4	x·z	x·z	PROPN
ejpam-5857	1002	5	)	)	PUNCT
ejpam-5857	1002	6	>	>	X
ejpam-5857	1003	1	γ	γ	X
ejpam-5857	1003	2	=	=	PRON
ejpam-5857	1003	3	ψf	ψf	X
ejpam-5857	1003	4	(	(	PUNCT
ejpam-5857	1003	5	x·z	x·z	PROPN
ejpam-5857	1003	6	)	)	PUNCT
ejpam-5857	1003	7	,	,	PUNCT
ejpam-5857	1003	8	which	which	PRON
ejpam-5857	1003	9	is	be	AUX
ejpam-5857	1003	10	a	a	DET
ejpam-5857	1003	11	contradiction	contradiction	NOUN
ejpam-5857	1003	12	.	.	PUNCT
ejpam-5857	1004	1	if	if	SCONJ
ejpam-5857	1004	2	(	(	PUNCT
ejpam-5857	1004	3	ψf	ψf	X
ejpam-5857	1004	4	(	(	PUNCT
ejpam-5857	1004	5	x·(y·z))∧ψf	x·(y·z))∧ψf	PROPN
ejpam-5857	1004	6	(	(	PUNCT
ejpam-5857	1004	7	y))∨0.5	y))∨0.5	PROPN
ejpam-5857	1004	8	=	=	SYM
ejpam-5857	1004	9	0.5	0.5	NUM
ejpam-5857	1004	10	,	,	PUNCT
ejpam-5857	1004	11	then	then	ADV
ejpam-5857	1004	12	γ	γ	X
ejpam-5857	1004	13	=	=	PRON
ejpam-5857	1004	14	ψf	ψf	X
ejpam-5857	1004	15	(	(	PUNCT
ejpam-5857	1004	16	x·z	x·z	PROPN
ejpam-5857	1004	17	)	)	PUNCT
ejpam-5857	1004	18	<	<	X
ejpam-5857	1004	19	0.5	0.5	NUM
ejpam-5857	1004	20	,	,	PUNCT
ejpam-5857	1004	21	which	which	PRON
ejpam-5857	1004	22	is	be	AUX
ejpam-5857	1004	23	a	a	DET
ejpam-5857	1004	24	contradiction	contradiction	NOUN
ejpam-5857	1004	25	.	.	PUNCT
ejpam-5857	1005	1	thus	thus	ADV
ejpam-5857	1005	2	,	,	PUNCT
ejpam-5857	1005	3	ψf	ψf	X
ejpam-5857	1005	4	(	(	PUNCT
ejpam-5857	1005	5	x·z	x·z	PROPN
ejpam-5857	1005	6	)	)	PUNCT
ejpam-5857	1005	7	≥	≥	PROPN
ejpam-5857	1005	8	(	(	PUNCT
ejpam-5857	1005	9	ψf	ψf	X
ejpam-5857	1005	10	(	(	PUNCT
ejpam-5857	1005	11	x·(y	x·(y	NOUN
ejpam-5857	1005	12	·	·	PUNCT
ejpam-5857	1005	13	z))∧ψf	z))∧ψf	X
ejpam-5857	1005	14	(	(	PUNCT
ejpam-5857	1005	15	y))∨0.5	y))∨0.5	PROPN
ejpam-5857	1005	16	.	.	PROPN
ejpam-5857	1005	17	hence	hence	ADV
ejpam-5857	1005	18	,	,	PUNCT
ejpam-5857	1005	19	ψ	ψ	X
ejpam-5857	1005	20	is	be	AUX
ejpam-5857	1005	21	an	an	DET
ejpam-5857	1005	22	intuitionistic	intuitionistic	ADJ
ejpam-5857	1005	23	neutrosophic	neutrosophic	ADJ
ejpam-5857	1005	24	iup	iup	NOUN
ejpam-5857	1005	25	-	-	PUNCT
ejpam-5857	1005	26	ideal	ideal	NOUN
ejpam-5857	1005	27	of	of	ADP
ejpam-5857	1005	28	x.	x.	PROPN
ejpam-5857	1005	29	theorem	theorem	VERB
ejpam-5857	1005	30	32	32	NUM
ejpam-5857	1005	31	.	.	PUNCT
ejpam-5857	1006	1	let	let	VERB
ejpam-5857	1006	2	for	for	ADP
ejpam-5857	1006	3	all	all	DET
ejpam-5857	1006	4	α	α	NOUN
ejpam-5857	1006	5	,	,	PUNCT
ejpam-5857	1006	6	γ	γ	PROPN
ejpam-5857	1006	7	∈	∈	PROPN
ejpam-5857	1007	1	[	[	X
ejpam-5857	1007	2	0.5	0.5	NUM
ejpam-5857	1007	3	,	,	PUNCT
ejpam-5857	1007	4	1	1	NUM
ejpam-5857	1007	5	]	]	PUNCT
ejpam-5857	1007	6	and	and	CCONJ
ejpam-5857	1007	7	β	β	X
ejpam-5857	1007	8	∈	∈	PROPN
ejpam-5857	1007	9	[	[	X
ejpam-5857	1007	10	0	0	NUM
ejpam-5857	1007	11	,	,	PUNCT
ejpam-5857	1007	12	0.5	0.5	NUM
ejpam-5857	1007	13	)	)	PUNCT
ejpam-5857	1007	14	,	,	PUNCT
ejpam-5857	1007	15	the	the	DET
ejpam-5857	1007	16	sets	set	NOUN
ejpam-5857	1007	17	u	u	NOUN
ejpam-5857	1007	18	+	+	X
ejpam-5857	1007	19	(	(	PUNCT
ejpam-5857	1007	20	ψt	ψt	NUM
ejpam-5857	1007	21	;	;	PUNCT
ejpam-5857	1007	22	α	α	X
ejpam-5857	1007	23	)	)	PUNCT
ejpam-5857	1007	24	,	,	PUNCT
ejpam-5857	1007	25	l	l	NOUN
ejpam-5857	1007	26	−	−	PROPN
ejpam-5857	1007	27	(	(	PUNCT
ejpam-5857	1007	28	ψi	ψi	ADP
ejpam-5857	1007	29	;	;	PUNCT
ejpam-5857	1007	30	β	β	X
ejpam-5857	1007	31	)	)	PUNCT
ejpam-5857	1007	32	and	and	CCONJ
ejpam-5857	1007	33	u	u	PRON
ejpam-5857	1007	34	+	+	X
ejpam-5857	1007	35	(	(	PUNCT
ejpam-5857	1007	36	ψf	ψf	X
ejpam-5857	1007	37	;	;	PUNCT
ejpam-5857	1007	38	γ	γ	X
ejpam-5857	1007	39	)	)	PUNCT
ejpam-5857	1007	40	are	be	AUX
ejpam-5857	1007	41	either	either	CCONJ
ejpam-5857	1007	42	empty	empty	ADJ
ejpam-5857	1007	43	or	or	CCONJ
ejpam-5857	1007	44	iup	iup	NOUN
ejpam-5857	1007	45	-	-	PUNCT
ejpam-5857	1007	46	filters	filter	NOUN
ejpam-5857	1007	47	of	of	ADP
ejpam-5857	1007	48	x.	x.	NOUN
ejpam-5857	1007	49	if	if	SCONJ
ejpam-5857	1007	50	ψt	ψt	VERB
ejpam-5857	1007	51	(	(	PUNCT
ejpam-5857	1007	52	x	x	NOUN
ejpam-5857	1007	53	)	)	PUNCT
ejpam-5857	1007	54	≥	≥	NOUN
ejpam-5857	1007	55	0.5	0.5	NUM
ejpam-5857	1007	56	,	,	PUNCT
ejpam-5857	1007	57	ψi(x	ψi(x	NUM
ejpam-5857	1007	58	)	)	PUNCT
ejpam-5857	1007	59	<	<	X
ejpam-5857	1007	60	0.5	0.5	NUM
ejpam-5857	1007	61	and	and	CCONJ
ejpam-5857	1007	62	ψf	ψf	X
ejpam-5857	1007	63	(	(	PUNCT
ejpam-5857	1007	64	x	x	X
ejpam-5857	1007	65	)	)	PUNCT
ejpam-5857	1007	66	≥	≥	NOUN
ejpam-5857	1007	67	0.5	0.5	NUM
ejpam-5857	1007	68	for	for	ADP
ejpam-5857	1007	69	all	all	DET
ejpam-5857	1007	70	x	x	SYM
ejpam-5857	1007	71	∈	∈	NOUN
ejpam-5857	1007	72	x	x	NOUN
ejpam-5857	1007	73	,	,	PUNCT
ejpam-5857	1007	74	then	then	ADV
ejpam-5857	1007	75	ψ	ψ	NOUN
ejpam-5857	1007	76	is	be	AUX
ejpam-5857	1007	77	an	an	DET
ejpam-5857	1007	78	intuitionistic	intuitionistic	ADJ
ejpam-5857	1007	79	neutrosophic	neutrosophic	ADJ
ejpam-5857	1007	80	iup	iup	NOUN
ejpam-5857	1007	81	-	-	PUNCT
ejpam-5857	1007	82	filter	filter	NOUN
ejpam-5857	1007	83	of	of	ADP
ejpam-5857	1007	84	x.	x.	NOUN
ejpam-5857	1007	85	proof	proof	PROPN
ejpam-5857	1007	86	.	.	PUNCT
ejpam-5857	1008	1	assume	assume	VERB
ejpam-5857	1008	2	that	that	SCONJ
ejpam-5857	1008	3	for	for	ADP
ejpam-5857	1008	4	all	all	DET
ejpam-5857	1008	5	α	α	NOUN
ejpam-5857	1008	6	,	,	PUNCT
ejpam-5857	1008	7	γ	γ	PROPN
ejpam-5857	1008	8	∈	∈	PROPN
ejpam-5857	1009	1	[	[	X
ejpam-5857	1009	2	0.5	0.5	NUM
ejpam-5857	1009	3	,	,	PUNCT
ejpam-5857	1009	4	1	1	NUM
ejpam-5857	1009	5	]	]	PUNCT
ejpam-5857	1009	6	and	and	CCONJ
ejpam-5857	1009	7	β	β	X
ejpam-5857	1009	8	∈	∈	PROPN
ejpam-5857	1010	1	[	[	X
ejpam-5857	1010	2	0	0	NUM
ejpam-5857	1010	3	,	,	PUNCT
ejpam-5857	1010	4	0.5	0.5	NUM
ejpam-5857	1010	5	)	)	PUNCT
ejpam-5857	1010	6	,	,	PUNCT
ejpam-5857	1010	7	the	the	DET
ejpam-5857	1010	8	sets	set	NOUN
ejpam-5857	1010	9	u	u	NOUN
ejpam-5857	1010	10	+	+	X
ejpam-5857	1010	11	(	(	PUNCT
ejpam-5857	1010	12	ψt	ψt	NUM
ejpam-5857	1010	13	;	;	PUNCT
ejpam-5857	1010	14	α	α	X
ejpam-5857	1010	15	)	)	PUNCT
ejpam-5857	1010	16	,	,	PUNCT
ejpam-5857	1010	17	l	l	NOUN
ejpam-5857	1010	18	−	−	PROPN
ejpam-5857	1010	19	(	(	PUNCT
ejpam-5857	1010	20	ψi	ψi	ADP
ejpam-5857	1010	21	;	;	PUNCT
ejpam-5857	1010	22	β	β	X
ejpam-5857	1010	23	)	)	PUNCT
ejpam-5857	1010	24	and	and	CCONJ
ejpam-5857	1010	25	u	u	PRON
ejpam-5857	1010	26	+	+	X
ejpam-5857	1010	27	(	(	PUNCT
ejpam-5857	1010	28	ψf	ψf	X
ejpam-5857	1010	29	;	;	PUNCT
ejpam-5857	1010	30	γ	γ	X
ejpam-5857	1010	31	)	)	PUNCT
ejpam-5857	1010	32	are	be	AUX
ejpam-5857	1010	33	either	either	CCONJ
ejpam-5857	1010	34	empty	empty	ADJ
ejpam-5857	1010	35	or	or	CCONJ
ejpam-5857	1010	36	iup	iup	NOUN
ejpam-5857	1010	37	-	-	PUNCT
ejpam-5857	1010	38	filters	filter	NOUN
ejpam-5857	1010	39	of	of	ADP
ejpam-5857	1010	40	x.	x.	NOUN
ejpam-5857	1010	41	let	let	VERB
ejpam-5857	1010	42	x	x	SYM
ejpam-5857	1010	43	∈	∈	PROPN
ejpam-5857	1010	44	x.	x.	NOUN
ejpam-5857	1010	45	assume	assume	VERB
ejpam-5857	1010	46	that	that	SCONJ
ejpam-5857	1010	47	ψt	ψt	VERB
ejpam-5857	1010	48	(	(	PUNCT
ejpam-5857	1010	49	0	0	NUM
ejpam-5857	1010	50	)	)	PUNCT
ejpam-5857	1010	51	<	<	X
ejpam-5857	1011	1	ψt	ψt	X
ejpam-5857	1011	2	(	(	PUNCT
ejpam-5857	1011	3	x	x	NOUN
ejpam-5857	1011	4	)	)	PUNCT
ejpam-5857	1011	5	.	.	PUNCT
ejpam-5857	1012	1	let	let	VERB
ejpam-5857	1012	2	α	α	NOUN
ejpam-5857	1012	3	=	=	VERB
ejpam-5857	1012	4	ψt	ψt	ADJ
ejpam-5857	1012	5	(	(	PUNCT
ejpam-5857	1012	6	0	0	NUM
ejpam-5857	1012	7	)	)	PUNCT
ejpam-5857	1012	8	.	.	PUNCT
ejpam-5857	1013	1	then	then	ADV
ejpam-5857	1013	2	x	x	SYM
ejpam-5857	1013	3	∈	∈	PROPN
ejpam-5857	1013	4	u	u	NOUN
ejpam-5857	1013	5	+	+	X
ejpam-5857	1013	6	(	(	PUNCT
ejpam-5857	1013	7	ψt	ψt	NUM
ejpam-5857	1013	8	;	;	PUNCT
ejpam-5857	1013	9	α	α	X
ejpam-5857	1013	10	)	)	PUNCT
ejpam-5857	1013	11	̸=	̸=	PROPN
ejpam-5857	1013	12	∅.	∅.	NOUN
ejpam-5857	1013	13	by	by	ADP
ejpam-5857	1013	14	assumption	assumption	NOUN
ejpam-5857	1013	15	,	,	PUNCT
ejpam-5857	1013	16	we	we	PRON
ejpam-5857	1013	17	have	have	VERB
ejpam-5857	1013	18	u	u	NOUN
ejpam-5857	1013	19	+	+	PUNCT
ejpam-5857	1013	20	(	(	PUNCT
ejpam-5857	1013	21	ψt	ψt	NUM
ejpam-5857	1013	22	;	;	PUNCT
ejpam-5857	1013	23	α	α	X
ejpam-5857	1013	24	)	)	PUNCT
ejpam-5857	1013	25	is	be	AUX
ejpam-5857	1013	26	an	an	DET
ejpam-5857	1013	27	iup	iup	NOUN
ejpam-5857	1013	28	-	-	PUNCT
ejpam-5857	1013	29	ideal	ideal	NOUN
ejpam-5857	1013	30	of	of	ADP
ejpam-5857	1013	31	x.	x.	NOUN
ejpam-5857	1013	32	by	by	ADP
ejpam-5857	1013	33	the	the	DET
ejpam-5857	1013	34	condition	condition	NOUN
ejpam-5857	1013	35	(	(	PUNCT
ejpam-5857	1013	36	2.18	2.18	NUM
ejpam-5857	1013	37	)	)	PUNCT
ejpam-5857	1013	38	,	,	PUNCT
ejpam-5857	1013	39	we	we	PRON
ejpam-5857	1013	40	have	have	VERB
ejpam-5857	1013	41	0	0	NUM
ejpam-5857	1013	42	∈	∈	PROPN
ejpam-5857	1013	43	u	u	NOUN
ejpam-5857	1013	44	+	+	X
ejpam-5857	1013	45	(	(	PUNCT
ejpam-5857	1013	46	ψt	ψt	NUM
ejpam-5857	1013	47	;	;	PUNCT
ejpam-5857	1013	48	α	α	X
ejpam-5857	1013	49	)	)	PUNCT
ejpam-5857	1013	50	.	.	PUNCT
ejpam-5857	1014	1	so	so	ADV
ejpam-5857	1014	2	ψt	ψt	VERB
ejpam-5857	1014	3	(	(	PUNCT
ejpam-5857	1014	4	0	0	NUM
ejpam-5857	1014	5	)	)	PUNCT
ejpam-5857	1014	6	>	>	X
ejpam-5857	1015	1	α	α	X
ejpam-5857	1015	2	=	=	X
ejpam-5857	1015	3	ψt	ψt	NOUN
ejpam-5857	1015	4	(	(	PUNCT
ejpam-5857	1015	5	0	0	NUM
ejpam-5857	1015	6	)	)	PUNCT
ejpam-5857	1015	7	,	,	PUNCT
ejpam-5857	1015	8	which	which	PRON
ejpam-5857	1015	9	is	be	AUX
ejpam-5857	1015	10	a	a	DET
ejpam-5857	1015	11	contradiction	contradiction	NOUN
ejpam-5857	1015	12	.	.	PUNCT
ejpam-5857	1016	1	thus	thus	ADV
ejpam-5857	1016	2	,	,	PUNCT
ejpam-5857	1016	3	ψt	ψt	VERB
ejpam-5857	1016	4	(	(	PUNCT
ejpam-5857	1016	5	0	0	NUM
ejpam-5857	1016	6	)	)	PUNCT
ejpam-5857	1016	7	≥	≥	PRON
ejpam-5857	1016	8	ψt	ψt	VERB
ejpam-5857	1016	9	(	(	PUNCT
ejpam-5857	1016	10	x	x	NOUN
ejpam-5857	1016	11	)	)	PUNCT
ejpam-5857	1016	12	.	.	PUNCT
ejpam-5857	1017	1	let	let	VERB
ejpam-5857	1017	2	x	x	PRON
ejpam-5857	1017	3	,	,	PUNCT
ejpam-5857	1017	4	y	y	PROPN
ejpam-5857	1017	5	∈	∈	PROPN
ejpam-5857	1017	6	x	x	AUX
ejpam-5857	1017	7	be	be	AUX
ejpam-5857	1017	8	such	such	ADJ
ejpam-5857	1017	9	that	that	SCONJ
ejpam-5857	1017	10	ψt	ψt	NOUN
ejpam-5857	1017	11	(	(	PUNCT
ejpam-5857	1017	12	x	x	PROPN
ejpam-5857	1017	13	·	·	PUNCT
ejpam-5857	1017	14	y	y	X
ejpam-5857	1017	15	)	)	PUNCT
ejpam-5857	1017	16	≥	≥	NOUN
ejpam-5857	1017	17	0.5	0.5	NUM
ejpam-5857	1017	18	and	and	CCONJ
ejpam-5857	1017	19	ψt	ψt	ADJ
ejpam-5857	1017	20	(	(	PUNCT
ejpam-5857	1017	21	x	x	NOUN
ejpam-5857	1017	22	)	)	PUNCT
ejpam-5857	1017	23	≥	≥	NOUN
ejpam-5857	1017	24	0.5	0.5	NUM
ejpam-5857	1017	25	.	.	PUNCT
ejpam-5857	1018	1	assume	assume	VERB
ejpam-5857	1018	2	that	that	SCONJ
ejpam-5857	1018	3	ψt	ψt	VERB
ejpam-5857	1018	4	(	(	PUNCT
ejpam-5857	1018	5	y	y	NOUN
ejpam-5857	1018	6	)	)	PUNCT
ejpam-5857	1018	7	<	<	X
ejpam-5857	1018	8	(	(	PUNCT
ejpam-5857	1018	9	ψt	ψt	ADJ
ejpam-5857	1018	10	(	(	PUNCT
ejpam-5857	1018	11	x	x	PROPN
ejpam-5857	1018	12	·	·	PUNCT
ejpam-5857	1018	13	y	y	X
ejpam-5857	1018	14	)	)	PUNCT
ejpam-5857	1018	15	∧	∧	NOUN
ejpam-5857	1018	16	ψt	ψt	NOUN
ejpam-5857	1018	17	(	(	PUNCT
ejpam-5857	1018	18	x	x	NOUN
ejpam-5857	1018	19	)	)	PUNCT
ejpam-5857	1018	20	)	)	PUNCT
ejpam-5857	1019	1	∨	∨	NUM
ejpam-5857	1019	2	0.5	0.5	NUM
ejpam-5857	1019	3	.	.	PUNCT
ejpam-5857	1020	1	let	let	VERB
ejpam-5857	1020	2	α	α	NOUN
ejpam-5857	1020	3	=	=	VERB
ejpam-5857	1020	4	ψt	ψt	ADJ
ejpam-5857	1020	5	(	(	PUNCT
ejpam-5857	1020	6	y	y	NOUN
ejpam-5857	1020	7	)	)	PUNCT
ejpam-5857	1020	8	.	.	PUNCT
ejpam-5857	1021	1	if	if	SCONJ
ejpam-5857	1021	2	(	(	PUNCT
ejpam-5857	1021	3	ψt	ψt	VERB
ejpam-5857	1021	4	(	(	PUNCT
ejpam-5857	1021	5	x	x	X
ejpam-5857	1021	6	·	·	PUNCT
ejpam-5857	1021	7	y)∧ψt	y)∧ψt	PROPN
ejpam-5857	1021	8	(	(	PUNCT
ejpam-5857	1021	9	x))∨0.5	x))∨0.5	PROPN
ejpam-5857	1021	10	=	=	SYM
ejpam-5857	1021	11	ψt	ψt	NUM
ejpam-5857	1021	12	(	(	PUNCT
ejpam-5857	1021	13	x	x	PROPN
ejpam-5857	1021	14	·	·	PUNCT
ejpam-5857	1021	15	y)∧ψt	y)∧ψt	PROPN
ejpam-5857	1021	16	(	(	PUNCT
ejpam-5857	1021	17	x	x	NOUN
ejpam-5857	1021	18	)	)	PUNCT
ejpam-5857	1021	19	,	,	PUNCT
ejpam-5857	1021	20	then	then	ADV
ejpam-5857	1021	21	x	x	X
ejpam-5857	1021	22	·	·	PUNCT
ejpam-5857	1021	23	y	y	PROPN
ejpam-5857	1021	24	,	,	PUNCT
ejpam-5857	1021	25	x	x	SYM
ejpam-5857	1021	26	∈	∈	PROPN
ejpam-5857	1021	27	u	u	NOUN
ejpam-5857	1021	28	+	+	X
ejpam-5857	1021	29	(	(	PUNCT
ejpam-5857	1021	30	ψt	ψt	NUM
ejpam-5857	1021	31	;	;	PUNCT
ejpam-5857	1021	32	α	α	X
ejpam-5857	1021	33	)	)	PUNCT
ejpam-5857	1021	34	̸=	̸=	PROPN
ejpam-5857	1021	35	∅.	∅.	NOUN
ejpam-5857	1021	36	by	by	ADP
ejpam-5857	1021	37	assumption	assumption	NOUN
ejpam-5857	1021	38	,	,	PUNCT
ejpam-5857	1021	39	we	we	PRON
ejpam-5857	1021	40	have	have	VERB
ejpam-5857	1021	41	u	u	NOUN
ejpam-5857	1021	42	+	+	PUNCT
ejpam-5857	1021	43	(	(	PUNCT
ejpam-5857	1021	44	ψt	ψt	NUM
ejpam-5857	1021	45	;	;	PUNCT
ejpam-5857	1021	46	α	α	X
ejpam-5857	1021	47	)	)	PUNCT
ejpam-5857	1021	48	is	be	AUX
ejpam-5857	1021	49	an	an	DET
ejpam-5857	1021	50	iup	iup	NOUN
ejpam-5857	1021	51	-	-	PUNCT
ejpam-5857	1021	52	filter	filter	NOUN
ejpam-5857	1021	53	of	of	ADP
ejpam-5857	1021	54	x.	x.	NOUN
ejpam-5857	1021	55	by	by	ADP
ejpam-5857	1021	56	the	the	DET
ejpam-5857	1021	57	condition	condition	NOUN
ejpam-5857	1021	58	(	(	PUNCT
ejpam-5857	1021	59	2.19	2.19	NUM
ejpam-5857	1021	60	)	)	PUNCT
ejpam-5857	1021	61	,	,	PUNCT
ejpam-5857	1021	62	we	we	PRON
ejpam-5857	1021	63	have	have	VERB
ejpam-5857	1021	64	y	y	PROPN
ejpam-5857	1021	65	∈	∈	PROPN
ejpam-5857	1021	66	u	u	NOUN
ejpam-5857	1021	67	+	+	X
ejpam-5857	1021	68	(	(	PUNCT
ejpam-5857	1021	69	ψt	ψt	NUM
ejpam-5857	1021	70	;	;	PUNCT
ejpam-5857	1021	71	α	α	X
ejpam-5857	1021	72	)	)	PUNCT
ejpam-5857	1021	73	.	.	PUNCT
ejpam-5857	1022	1	so	so	ADV
ejpam-5857	1022	2	ψt	ψt	VERB
ejpam-5857	1022	3	(	(	PUNCT
ejpam-5857	1022	4	y	y	NOUN
ejpam-5857	1022	5	)	)	PUNCT
ejpam-5857	1022	6	>	>	X
ejpam-5857	1023	1	α	α	X
ejpam-5857	1023	2	=	=	X
ejpam-5857	1023	3	ψt	ψt	ADJ
ejpam-5857	1023	4	(	(	PUNCT
ejpam-5857	1023	5	y	y	NOUN
ejpam-5857	1023	6	)	)	PUNCT
ejpam-5857	1023	7	,	,	PUNCT
ejpam-5857	1023	8	which	which	PRON
ejpam-5857	1023	9	is	be	AUX
ejpam-5857	1023	10	a	a	DET
ejpam-5857	1023	11	contradiction	contradiction	NOUN
ejpam-5857	1023	12	.	.	PUNCT
ejpam-5857	1024	1	if	if	SCONJ
ejpam-5857	1024	2	(	(	PUNCT
ejpam-5857	1024	3	ψt	ψt	VERB
ejpam-5857	1024	4	(	(	PUNCT
ejpam-5857	1024	5	x	x	PROPN
ejpam-5857	1024	6	·	·	PUNCT
ejpam-5857	1024	7	y	y	X
ejpam-5857	1024	8	)	)	PUNCT
ejpam-5857	1024	9	∧	∧	NOUN
ejpam-5857	1024	10	ψt	ψt	NOUN
ejpam-5857	1024	11	(	(	PUNCT
ejpam-5857	1024	12	x	x	NOUN
ejpam-5857	1024	13	)	)	PUNCT
ejpam-5857	1024	14	)	)	PUNCT
ejpam-5857	1024	15	∨	∨	NOUN
ejpam-5857	1024	16	0.5	0.5	NUM
ejpam-5857	1024	17	=	=	SYM
ejpam-5857	1024	18	0.5	0.5	NUM
ejpam-5857	1024	19	,	,	PUNCT
ejpam-5857	1024	20	then	then	ADV
ejpam-5857	1024	21	α	α	PROPN
ejpam-5857	1024	22	=	=	NOUN
ejpam-5857	1024	23	ψt	ψt	ADJ
ejpam-5857	1024	24	(	(	PUNCT
ejpam-5857	1024	25	y	y	NOUN
ejpam-5857	1024	26	)	)	PUNCT
ejpam-5857	1024	27	<	<	X
ejpam-5857	1024	28	0.5	0.5	NUM
ejpam-5857	1024	29	,	,	PUNCT
ejpam-5857	1024	30	which	which	PRON
ejpam-5857	1024	31	is	be	AUX
ejpam-5857	1024	32	a	a	DET
ejpam-5857	1024	33	contradiction	contradiction	NOUN
ejpam-5857	1024	34	.	.	PUNCT
ejpam-5857	1025	1	thus	thus	ADV
ejpam-5857	1025	2	,	,	PUNCT
ejpam-5857	1025	3	ψt	ψt	NUM
ejpam-5857	1025	4	(	(	PUNCT
ejpam-5857	1025	5	y	y	NOUN
ejpam-5857	1025	6	)	)	PUNCT
ejpam-5857	1025	7	≥	≥	NOUN
ejpam-5857	1025	8	(	(	PUNCT
ejpam-5857	1025	9	ψt	ψt	VERB
ejpam-5857	1025	10	(	(	PUNCT
ejpam-5857	1025	11	x	x	PROPN
ejpam-5857	1025	12	·	·	PUNCT
ejpam-5857	1025	13	y	y	X
ejpam-5857	1025	14	)	)	PUNCT
ejpam-5857	1025	15	∧	∧	NOUN
ejpam-5857	1025	16	ψt	ψt	NOUN
ejpam-5857	1025	17	(	(	PUNCT
ejpam-5857	1025	18	x	x	NOUN
ejpam-5857	1025	19	)	)	PUNCT
ejpam-5857	1025	20	)	)	PUNCT
ejpam-5857	1025	21	∨	∨	NUM
ejpam-5857	1025	22	0.5	0.5	NUM
ejpam-5857	1025	23	.	.	PUNCT
ejpam-5857	1026	1	let	let	VERB
ejpam-5857	1026	2	x	x	SYM
ejpam-5857	1026	3	∈	∈	PROPN
ejpam-5857	1026	4	x.	x.	NOUN
ejpam-5857	1026	5	assume	assume	VERB
ejpam-5857	1026	6	that	that	SCONJ
ejpam-5857	1026	7	ψi(0	ψi(0	PROPN
ejpam-5857	1026	8	)	)	PUNCT
ejpam-5857	1026	9	>	>	X
ejpam-5857	1026	10	ψi(x	ψi(x	PROPN
ejpam-5857	1026	11	)	)	PUNCT
ejpam-5857	1026	12	.	.	PUNCT
ejpam-5857	1027	1	let	let	VERB
ejpam-5857	1027	2	β	β	X
ejpam-5857	1027	3	=	=	VERB
ejpam-5857	1027	4	ψi(0	ψi(0	PROPN
ejpam-5857	1027	5	)	)	PUNCT
ejpam-5857	1027	6	.	.	PUNCT
ejpam-5857	1028	1	then	then	ADV
ejpam-5857	1028	2	x	x	SYM
ejpam-5857	1028	3	∈	∈	PROPN
ejpam-5857	1028	4	l	l	NOUN
ejpam-5857	1028	5	−	−	PROPN
ejpam-5857	1028	6	(	(	PUNCT
ejpam-5857	1028	7	ψi	ψi	ADP
ejpam-5857	1028	8	;	;	PUNCT
ejpam-5857	1028	9	β	β	X
ejpam-5857	1028	10	)	)	PUNCT
ejpam-5857	1028	11	̸=	̸=	PROPN
ejpam-5857	1028	12	∅.	∅.	VERB
ejpam-5857	1028	13	by	by	ADP
ejpam-5857	1028	14	assumption	assumption	NOUN
ejpam-5857	1028	15	,	,	PUNCT
ejpam-5857	1028	16	we	we	PRON
ejpam-5857	1028	17	have	have	VERB
ejpam-5857	1028	18	l	l	NOUN
ejpam-5857	1028	19	−	−	PROPN
ejpam-5857	1028	20	(	(	PUNCT
ejpam-5857	1028	21	ψi	ψi	ADP
ejpam-5857	1028	22	;	;	PUNCT
ejpam-5857	1028	23	β	β	X
ejpam-5857	1028	24	)	)	PUNCT
ejpam-5857	1028	25	is	be	AUX
ejpam-5857	1028	26	an	an	DET
ejpam-5857	1028	27	iup	iup	NOUN
ejpam-5857	1028	28	-	-	PUNCT
ejpam-5857	1028	29	filter	filter	NOUN
ejpam-5857	1028	30	of	of	ADP
ejpam-5857	1028	31	x.	x.	NOUN
ejpam-5857	1028	32	by	by	ADP
ejpam-5857	1028	33	the	the	DET
ejpam-5857	1028	34	condition	condition	NOUN
ejpam-5857	1028	35	(	(	PUNCT
ejpam-5857	1028	36	2.18	2.18	NUM
ejpam-5857	1028	37	)	)	PUNCT
ejpam-5857	1028	38	,	,	PUNCT
ejpam-5857	1028	39	we	we	PRON
ejpam-5857	1028	40	have	have	VERB
ejpam-5857	1028	41	0	0	NUM
ejpam-5857	1028	42	∈	∈	NOUN
ejpam-5857	1028	43	l	l	NOUN
ejpam-5857	1028	44	−	−	PROPN
ejpam-5857	1028	45	(	(	PUNCT
ejpam-5857	1028	46	ψi	ψi	ADP
ejpam-5857	1028	47	;	;	PUNCT
ejpam-5857	1028	48	β	β	X
ejpam-5857	1028	49	)	)	PUNCT
ejpam-5857	1028	50	.	.	PUNCT
ejpam-5857	1029	1	so	so	ADV
ejpam-5857	1029	2	ψi(0	ψi(0	PROPN
ejpam-5857	1029	3	)	)	PUNCT
ejpam-5857	1029	4	<	<	X
ejpam-5857	1029	5	β	β	X
ejpam-5857	1029	6	=	=	SYM
ejpam-5857	1029	7	ψi(0	ψi(0	PROPN
ejpam-5857	1029	8	)	)	PUNCT
ejpam-5857	1029	9	,	,	PUNCT
ejpam-5857	1029	10	which	which	PRON
ejpam-5857	1029	11	is	be	AUX
ejpam-5857	1029	12	a	a	DET
ejpam-5857	1029	13	contradiction	contradiction	NOUN
ejpam-5857	1029	14	.	.	PUNCT
ejpam-5857	1030	1	thus	thus	ADV
ejpam-5857	1030	2	,	,	PUNCT
ejpam-5857	1030	3	ψi(0	ψi(0	PROPN
ejpam-5857	1030	4	)	)	PUNCT
ejpam-5857	1030	5	≤	≤	NOUN
ejpam-5857	1030	6	ψi(x	ψi(x	NUM
ejpam-5857	1030	7	)	)	PUNCT
ejpam-5857	1030	8	.	.	PUNCT
ejpam-5857	1031	1	let	let	VERB
ejpam-5857	1031	2	x	x	PRON
ejpam-5857	1031	3	,	,	PUNCT
ejpam-5857	1031	4	y	y	PROPN
ejpam-5857	1031	5	∈	∈	PROPN
ejpam-5857	1031	6	x	x	AUX
ejpam-5857	1031	7	be	be	AUX
ejpam-5857	1031	8	such	such	ADJ
ejpam-5857	1031	9	that	that	SCONJ
ejpam-5857	1031	10	ψi(x	ψi(x	NUM
ejpam-5857	1031	11	·	·	PUNCT
ejpam-5857	1031	12	y	y	X
ejpam-5857	1031	13	)	)	PUNCT
ejpam-5857	1031	14	<	<	X
ejpam-5857	1031	15	0.5	0.5	NUM
ejpam-5857	1031	16	and	and	CCONJ
ejpam-5857	1031	17	ψi(x	ψi(x	NUM
ejpam-5857	1031	18	)	)	PUNCT
ejpam-5857	1031	19	<	<	X
ejpam-5857	1031	20	0.5	0.5	NUM
ejpam-5857	1031	21	.	.	PUNCT
ejpam-5857	1031	22	assume	assume	VERB
ejpam-5857	1031	23	that	that	SCONJ
ejpam-5857	1031	24	ψi(y	ψi(y	VERB
ejpam-5857	1031	25	)	)	PUNCT
ejpam-5857	1031	26	>	>	PUNCT
ejpam-5857	1032	1	(	(	PUNCT
ejpam-5857	1032	2	ψi(x	ψi(x	X
ejpam-5857	1032	3	·	·	SYM
ejpam-5857	1032	4	y)∨ψi(x))∧0.5	y)∨ψi(x))∧0.5	NOUN
ejpam-5857	1032	5	.	.	PUNCT
ejpam-5857	1033	1	let	let	VERB
ejpam-5857	1033	2	β	β	X
ejpam-5857	1033	3	=	=	NOUN
ejpam-5857	1033	4	ψi(y	ψi(y	NUM
ejpam-5857	1033	5	)	)	PUNCT
ejpam-5857	1033	6	.	.	PUNCT
ejpam-5857	1034	1	if	if	SCONJ
ejpam-5857	1034	2	(	(	PUNCT
ejpam-5857	1034	3	ψi(x	ψi(x	X
ejpam-5857	1034	4	·	·	PUNCT
ejpam-5857	1034	5	y)∨ψi(x))∧0.5	y)∨ψi(x))∧0.5	NOUN
ejpam-5857	1034	6	=	=	SYM
ejpam-5857	1034	7	ψi(x	ψi(x	X
ejpam-5857	1034	8	·	·	SYM
ejpam-5857	1034	9	y)∨ψi(x	y)∨ψi(x	NUM
ejpam-5857	1034	10	)	)	PUNCT
ejpam-5857	1034	11	,	,	PUNCT
ejpam-5857	1034	12	then	then	ADV
ejpam-5857	1034	13	x	x	X
ejpam-5857	1034	14	·	·	PUNCT
ejpam-5857	1034	15	y	y	X
ejpam-5857	1034	16	,	,	PUNCT
ejpam-5857	1034	17	x	x	X
ejpam-5857	1034	18	∈	∈	NOUN
ejpam-5857	1034	19	l	l	NOUN
ejpam-5857	1034	20	−	−	PROPN
ejpam-5857	1034	21	(	(	PUNCT
ejpam-5857	1034	22	ψi	ψi	ADP
ejpam-5857	1034	23	;	;	PUNCT
ejpam-5857	1034	24	β	β	X
ejpam-5857	1034	25	)	)	PUNCT
ejpam-5857	1034	26	̸=	̸=	PROPN
ejpam-5857	1034	27	∅.	∅.	VERB
ejpam-5857	1034	28	by	by	ADP
ejpam-5857	1034	29	assumption	assumption	NOUN
ejpam-5857	1034	30	,	,	PUNCT
ejpam-5857	1034	31	we	we	PRON
ejpam-5857	1034	32	have	have	VERB
ejpam-5857	1034	33	l	l	NOUN
ejpam-5857	1034	34	−	−	PROPN
ejpam-5857	1034	35	(	(	PUNCT
ejpam-5857	1034	36	ψi	ψi	ADP
ejpam-5857	1034	37	;	;	PUNCT
ejpam-5857	1034	38	β	β	X
ejpam-5857	1034	39	)	)	PUNCT
ejpam-5857	1034	40	is	be	AUX
ejpam-5857	1034	41	an	an	DET
ejpam-5857	1034	42	iup	iup	NOUN
ejpam-5857	1034	43	-	-	PUNCT
ejpam-5857	1034	44	filter	filter	NOUN
ejpam-5857	1034	45	of	of	ADP
ejpam-5857	1034	46	x.	x.	NOUN
ejpam-5857	1034	47	by	by	ADP
ejpam-5857	1034	48	the	the	DET
ejpam-5857	1034	49	condition	condition	NOUN
ejpam-5857	1034	50	(	(	PUNCT
ejpam-5857	1034	51	2.19	2.19	NUM
ejpam-5857	1034	52	)	)	PUNCT
ejpam-5857	1034	53	,	,	PUNCT
ejpam-5857	1034	54	we	we	PRON
ejpam-5857	1034	55	have	have	VERB
ejpam-5857	1034	56	y	y	PROPN
ejpam-5857	1034	57	∈	∈	PROPN
ejpam-5857	1034	58	l	l	NOUN
ejpam-5857	1034	59	−	−	PROPN
ejpam-5857	1035	1	(	(	PUNCT
ejpam-5857	1035	2	ψi	ψi	ADP
ejpam-5857	1035	3	;	;	PUNCT
ejpam-5857	1035	4	β	β	X
ejpam-5857	1035	5	)	)	PUNCT
ejpam-5857	1035	6	.	.	PUNCT
ejpam-5857	1036	1	so	so	ADV
ejpam-5857	1036	2	ψi(y	ψi(y	NOUN
ejpam-5857	1036	3	)	)	PUNCT
ejpam-5857	1036	4	<	<	X
ejpam-5857	1036	5	β	β	X
ejpam-5857	1036	6	=	=	PUNCT
ejpam-5857	1036	7	ψi(y	ψi(y	NUM
ejpam-5857	1036	8	)	)	PUNCT
ejpam-5857	1036	9	,	,	PUNCT
ejpam-5857	1036	10	which	which	PRON
ejpam-5857	1036	11	is	be	AUX
ejpam-5857	1036	12	a	a	DET
ejpam-5857	1036	13	contradiction	contradiction	NOUN
ejpam-5857	1036	14	.	.	PUNCT
ejpam-5857	1037	1	if	if	SCONJ
ejpam-5857	1037	2	(	(	PUNCT
ejpam-5857	1037	3	ψi(x	ψi(x	X
ejpam-5857	1037	4	·	·	PUNCT
ejpam-5857	1037	5	y	y	X
ejpam-5857	1037	6	)	)	PUNCT
ejpam-5857	1037	7	∨	∨	NUM
ejpam-5857	1037	8	ψi(x	ψi(x	NUM
ejpam-5857	1037	9	)	)	PUNCT
ejpam-5857	1037	10	)	)	PUNCT
ejpam-5857	1038	1	∧	∧	NOUN
ejpam-5857	1038	2	0.5	0.5	NUM
ejpam-5857	1038	3	=	=	SYM
ejpam-5857	1038	4	0.5	0.5	NUM
ejpam-5857	1038	5	,	,	PUNCT
ejpam-5857	1038	6	then	then	ADV
ejpam-5857	1038	7	β	β	X
ejpam-5857	1038	8	=	=	PUNCT
ejpam-5857	1038	9	ψi(y	ψi(y	PROPN
ejpam-5857	1038	10	)	)	PUNCT
ejpam-5857	1038	11	>	>	X
ejpam-5857	1038	12	0.5	0.5	NUM
ejpam-5857	1038	13	,	,	PUNCT
ejpam-5857	1038	14	which	which	PRON
ejpam-5857	1038	15	is	be	AUX
ejpam-5857	1038	16	a	a	DET
ejpam-5857	1038	17	contradiction	contradiction	NOUN
ejpam-5857	1038	18	.	.	PUNCT
ejpam-5857	1039	1	thus	thus	ADV
ejpam-5857	1039	2	,	,	PUNCT
ejpam-5857	1039	3	ψi(y	ψi(y	NUM
ejpam-5857	1039	4	)	)	PUNCT
ejpam-5857	1039	5	≤	≤	NOUN
ejpam-5857	1039	6	(	(	PUNCT
ejpam-5857	1039	7	ψi(x	ψi(x	X
ejpam-5857	1039	8	·	·	PUNCT
ejpam-5857	1039	9	y	y	X
ejpam-5857	1039	10	)	)	PUNCT
ejpam-5857	1039	11	∨	∨	NUM
ejpam-5857	1039	12	ψi(x	ψi(x	NUM
ejpam-5857	1039	13	)	)	PUNCT
ejpam-5857	1039	14	)	)	PUNCT
ejpam-5857	1039	15	∧	∧	NOUN
ejpam-5857	1039	16	0.5	0.5	NUM
ejpam-5857	1039	17	)	)	PUNCT
ejpam-5857	1039	18	.	.	PUNCT
ejpam-5857	1040	1	let	let	VERB
ejpam-5857	1040	2	x	x	SYM
ejpam-5857	1040	3	∈	∈	PROPN
ejpam-5857	1040	4	x.	x.	NOUN
ejpam-5857	1040	5	assume	assume	VERB
ejpam-5857	1040	6	that	that	SCONJ
ejpam-5857	1040	7	ψf	ψf	X
ejpam-5857	1040	8	(	(	PUNCT
ejpam-5857	1040	9	0	0	NUM
ejpam-5857	1040	10	)	)	PUNCT
ejpam-5857	1040	11	<	<	X
ejpam-5857	1040	12	ψf	ψf	X
ejpam-5857	1040	13	(	(	PUNCT
ejpam-5857	1040	14	x	x	NOUN
ejpam-5857	1040	15	)	)	PUNCT
ejpam-5857	1040	16	.	.	PUNCT
ejpam-5857	1041	1	let	let	VERB
ejpam-5857	1041	2	γ	γ	X
ejpam-5857	1041	3	=	=	PRON
ejpam-5857	1041	4	ψf	ψf	X
ejpam-5857	1041	5	(	(	PUNCT
ejpam-5857	1041	6	0	0	NUM
ejpam-5857	1041	7	)	)	PUNCT
ejpam-5857	1041	8	.	.	PUNCT
ejpam-5857	1042	1	then	then	ADV
ejpam-5857	1042	2	x	x	SYM
ejpam-5857	1042	3	∈	∈	PROPN
ejpam-5857	1042	4	u	u	NOUN
ejpam-5857	1042	5	+	+	X
ejpam-5857	1042	6	(	(	PUNCT
ejpam-5857	1042	7	ψf	ψf	X
ejpam-5857	1042	8	;	;	PUNCT
ejpam-5857	1042	9	γ	γ	X
ejpam-5857	1042	10	)	)	PUNCT
ejpam-5857	1042	11	̸=	̸=	PROPN
ejpam-5857	1042	12	∅.	∅.	VERB
ejpam-5857	1042	13	by	by	ADP
ejpam-5857	1042	14	assumption	assumption	NOUN
ejpam-5857	1042	15	,	,	PUNCT
ejpam-5857	1042	16	we	we	PRON
ejpam-5857	1042	17	have	have	VERB
ejpam-5857	1042	18	u	u	NOUN
ejpam-5857	1042	19	+	+	CCONJ
ejpam-5857	1042	20	(	(	PUNCT
ejpam-5857	1042	21	ψf	ψf	X
ejpam-5857	1042	22	;	;	PUNCT
ejpam-5857	1042	23	γ	γ	X
ejpam-5857	1042	24	)	)	PUNCT
ejpam-5857	1042	25	is	be	AUX
ejpam-5857	1042	26	an	an	DET
ejpam-5857	1042	27	iup	iup	NOUN
ejpam-5857	1042	28	-	-	PUNCT
ejpam-5857	1042	29	filter	filter	NOUN
ejpam-5857	1042	30	of	of	ADP
ejpam-5857	1042	31	x.	x.	NOUN
ejpam-5857	1042	32	by	by	ADP
ejpam-5857	1042	33	the	the	DET
ejpam-5857	1042	34	condition	condition	NOUN
ejpam-5857	1042	35	(	(	PUNCT
ejpam-5857	1042	36	2.18	2.18	NUM
ejpam-5857	1042	37	)	)	PUNCT
ejpam-5857	1042	38	,	,	PUNCT
ejpam-5857	1042	39	we	we	PRON
ejpam-5857	1042	40	have	have	VERB
ejpam-5857	1042	41	0	0	NUM
ejpam-5857	1042	42	∈	∈	PROPN
ejpam-5857	1042	43	u	u	NOUN
ejpam-5857	1042	44	+	+	X
ejpam-5857	1042	45	(	(	PUNCT
ejpam-5857	1042	46	ψf	ψf	X
ejpam-5857	1042	47	;	;	PUNCT
ejpam-5857	1042	48	γ	γ	X
ejpam-5857	1042	49	)	)	PUNCT
ejpam-5857	1042	50	.	.	PUNCT
ejpam-5857	1043	1	so	so	ADV
ejpam-5857	1043	2	ψf	ψf	X
ejpam-5857	1043	3	(	(	PUNCT
ejpam-5857	1043	4	0	0	NUM
ejpam-5857	1043	5	)	)	PUNCT
ejpam-5857	1043	6	>	>	X
ejpam-5857	1043	7	γ	γ	X
ejpam-5857	1043	8	=	=	X
ejpam-5857	1043	9	ψf	ψf	X
ejpam-5857	1043	10	(	(	PUNCT
ejpam-5857	1043	11	0	0	NUM
ejpam-5857	1043	12	)	)	PUNCT
ejpam-5857	1043	13	,	,	PUNCT
ejpam-5857	1043	14	which	which	PRON
ejpam-5857	1043	15	is	be	AUX
ejpam-5857	1043	16	a	a	DET
ejpam-5857	1043	17	contradiction	contradiction	NOUN
ejpam-5857	1043	18	.	.	PUNCT
ejpam-5857	1044	1	thus	thus	ADV
ejpam-5857	1044	2	,	,	PUNCT
ejpam-5857	1044	3	ψf	ψf	X
ejpam-5857	1044	4	(	(	PUNCT
ejpam-5857	1044	5	0	0	NUM
ejpam-5857	1044	6	)	)	PUNCT
ejpam-5857	1044	7	≥	≥	NOUN
ejpam-5857	1044	8	ψf	ψf	X
ejpam-5857	1044	9	(	(	PUNCT
ejpam-5857	1044	10	x	x	NOUN
ejpam-5857	1044	11	)	)	PUNCT
ejpam-5857	1044	12	.	.	PUNCT
ejpam-5857	1045	1	let	let	VERB
ejpam-5857	1045	2	x	x	PRON
ejpam-5857	1045	3	,	,	PUNCT
ejpam-5857	1045	4	y	y	PROPN
ejpam-5857	1045	5	∈	∈	PROPN
ejpam-5857	1045	6	x	x	AUX
ejpam-5857	1045	7	be	be	AUX
ejpam-5857	1045	8	such	such	ADJ
ejpam-5857	1045	9	that	that	SCONJ
ejpam-5857	1045	10	ψf	ψf	X
ejpam-5857	1045	11	(	(	PUNCT
ejpam-5857	1045	12	x	x	X
ejpam-5857	1045	13	·	·	PUNCT
ejpam-5857	1045	14	y	y	X
ejpam-5857	1045	15	)	)	PUNCT
ejpam-5857	1045	16	≥	≥	NOUN
ejpam-5857	1045	17	0.5	0.5	NUM
ejpam-5857	1045	18	and	and	CCONJ
ejpam-5857	1045	19	ψf	ψf	X
ejpam-5857	1045	20	(	(	PUNCT
ejpam-5857	1045	21	x	x	X
ejpam-5857	1045	22	)	)	PUNCT
ejpam-5857	1045	23	≥	≥	NOUN
ejpam-5857	1045	24	0.5	0.5	NUM
ejpam-5857	1045	25	.	.	PUNCT
ejpam-5857	1046	1	assume	assume	VERB
ejpam-5857	1046	2	that	that	SCONJ
ejpam-5857	1046	3	ψf	ψf	X
ejpam-5857	1046	4	(	(	PUNCT
ejpam-5857	1046	5	y	y	NOUN
ejpam-5857	1046	6	)	)	PUNCT
ejpam-5857	1046	7	<	<	X
ejpam-5857	1046	8	(	(	PUNCT
ejpam-5857	1046	9	ψf	ψf	X
ejpam-5857	1046	10	(	(	PUNCT
ejpam-5857	1046	11	x	x	X
ejpam-5857	1046	12	·	·	PUNCT
ejpam-5857	1046	13	y)∧ψf	y)∧ψf	NOUN
ejpam-5857	1046	14	(	(	PUNCT
ejpam-5857	1046	15	x))∨	x))∨	PROPN
ejpam-5857	1046	16	0.5	0.5	NUM
ejpam-5857	1046	17	.	.	PUNCT
ejpam-5857	1047	1	let	let	VERB
ejpam-5857	1047	2	γ	γ	X
ejpam-5857	1047	3	=	=	PRON
ejpam-5857	1047	4	ψf	ψf	X
ejpam-5857	1047	5	(	(	PUNCT
ejpam-5857	1047	6	y	y	NOUN
ejpam-5857	1047	7	)	)	PUNCT
ejpam-5857	1047	8	.	.	PUNCT
ejpam-5857	1048	1	if	if	SCONJ
ejpam-5857	1048	2	(	(	PUNCT
ejpam-5857	1048	3	ψf	ψf	X
ejpam-5857	1048	4	(	(	PUNCT
ejpam-5857	1048	5	x	x	X
ejpam-5857	1048	6	·	·	PUNCT
ejpam-5857	1048	7	y)∧ψf	y)∧ψf	NOUN
ejpam-5857	1048	8	(	(	PUNCT
ejpam-5857	1048	9	x))∨	x))∨	PROPN
ejpam-5857	1048	10	0.5	0.5	NUM
ejpam-5857	1048	11	=	=	SYM
ejpam-5857	1048	12	ψf	ψf	X
ejpam-5857	1048	13	(	(	PUNCT
ejpam-5857	1048	14	x	x	X
ejpam-5857	1048	15	·	·	PUNCT
ejpam-5857	1048	16	y)∧ψf	y)∧ψf	NOUN
ejpam-5857	1048	17	(	(	PUNCT
ejpam-5857	1048	18	x	x	NOUN
ejpam-5857	1048	19	)	)	PUNCT
ejpam-5857	1048	20	,	,	PUNCT
ejpam-5857	1048	21	then	then	ADV
ejpam-5857	1048	22	x	x	X
ejpam-5857	1048	23	·	·	PUNCT
ejpam-5857	1048	24	y	y	X
ejpam-5857	1048	25	,	,	PUNCT
ejpam-5857	1048	26	x	x	SYM
ejpam-5857	1048	27	∈	∈	PROPN
ejpam-5857	1048	28	u	u	NOUN
ejpam-5857	1048	29	+	+	X
ejpam-5857	1048	30	(	(	PUNCT
ejpam-5857	1048	31	ψf	ψf	X
ejpam-5857	1048	32	;	;	PUNCT
ejpam-5857	1048	33	γ	γ	X
ejpam-5857	1048	34	)	)	PUNCT
ejpam-5857	1048	35	̸=	̸=	PROPN
ejpam-5857	1048	36	∅.	∅.	VERB
ejpam-5857	1048	37	by	by	ADP
ejpam-5857	1048	38	assumption	assumption	NOUN
ejpam-5857	1048	39	,	,	PUNCT
ejpam-5857	1048	40	we	we	PRON
ejpam-5857	1048	41	have	have	VERB
ejpam-5857	1048	42	u	u	NOUN
ejpam-5857	1048	43	+	+	CCONJ
ejpam-5857	1048	44	(	(	PUNCT
ejpam-5857	1048	45	ψf	ψf	X
ejpam-5857	1048	46	;	;	PUNCT
ejpam-5857	1048	47	γ	γ	X
ejpam-5857	1048	48	)	)	PUNCT
ejpam-5857	1048	49	is	be	AUX
ejpam-5857	1048	50	an	an	DET
ejpam-5857	1048	51	iup	iup	NOUN
ejpam-5857	1048	52	-	-	PUNCT
ejpam-5857	1048	53	filter	filter	NOUN
ejpam-5857	1048	54	of	of	ADP
ejpam-5857	1048	55	x.	x.	NOUN
ejpam-5857	1048	56	by	by	ADP
ejpam-5857	1048	57	the	the	DET
ejpam-5857	1048	58	condition	condition	NOUN
ejpam-5857	1048	59	(	(	PUNCT
ejpam-5857	1048	60	2.19	2.19	NUM
ejpam-5857	1048	61	)	)	PUNCT
ejpam-5857	1048	62	,	,	PUNCT
ejpam-5857	1048	63	we	we	PRON
ejpam-5857	1048	64	have	have	VERB
ejpam-5857	1048	65	y	y	PROPN
ejpam-5857	1048	66	∈	∈	PROPN
ejpam-5857	1048	67	u	u	NOUN
ejpam-5857	1048	68	+	+	X
ejpam-5857	1048	69	(	(	PUNCT
ejpam-5857	1048	70	ψf	ψf	X
ejpam-5857	1048	71	;	;	PUNCT
ejpam-5857	1048	72	γ	γ	X
ejpam-5857	1048	73	)	)	PUNCT
ejpam-5857	1048	74	.	.	PUNCT
ejpam-5857	1049	1	so	so	ADV
ejpam-5857	1049	2	ψf	ψf	X
ejpam-5857	1049	3	(	(	PUNCT
ejpam-5857	1049	4	y	y	NOUN
ejpam-5857	1049	5	)	)	PUNCT
ejpam-5857	1049	6	>	>	X
ejpam-5857	1050	1	γ	γ	X
ejpam-5857	1050	2	=	=	X
ejpam-5857	1050	3	ψf	ψf	X
ejpam-5857	1050	4	(	(	PUNCT
ejpam-5857	1050	5	y	y	NOUN
ejpam-5857	1050	6	)	)	PUNCT
ejpam-5857	1050	7	,	,	PUNCT
ejpam-5857	1050	8	which	which	PRON
ejpam-5857	1050	9	is	be	AUX
ejpam-5857	1050	10	a	a	DET
ejpam-5857	1050	11	contradiction	contradiction	NOUN
ejpam-5857	1050	12	.	.	PUNCT
ejpam-5857	1051	1	if	if	SCONJ
ejpam-5857	1051	2	(	(	PUNCT
ejpam-5857	1051	3	ψf	ψf	X
ejpam-5857	1051	4	(	(	PUNCT
ejpam-5857	1051	5	x	x	PROPN
ejpam-5857	1051	6	·	·	PUNCT
ejpam-5857	1051	7	y	y	X
ejpam-5857	1051	8	)	)	PUNCT
ejpam-5857	1051	9	∧	∧	NOUN
ejpam-5857	1051	10	ψf	ψf	X
ejpam-5857	1051	11	(	(	PUNCT
ejpam-5857	1051	12	x	x	NOUN
ejpam-5857	1051	13	)	)	PUNCT
ejpam-5857	1051	14	)	)	PUNCT
ejpam-5857	1051	15	∨	∨	NOUN
ejpam-5857	1051	16	0.5	0.5	NUM
ejpam-5857	1051	17	=	=	SYM
ejpam-5857	1051	18	0.5	0.5	NUM
ejpam-5857	1051	19	,	,	PUNCT
ejpam-5857	1051	20	then	then	ADV
ejpam-5857	1051	21	γ	γ	X
ejpam-5857	1051	22	=	=	PUNCT
ejpam-5857	1051	23	ψf	ψf	X
ejpam-5857	1051	24	(	(	PUNCT
ejpam-5857	1051	25	y	y	NOUN
ejpam-5857	1051	26	)	)	PUNCT
ejpam-5857	1051	27	<	<	X
ejpam-5857	1051	28	0.5	0.5	NUM
ejpam-5857	1051	29	,	,	PUNCT
ejpam-5857	1051	30	which	which	PRON
ejpam-5857	1051	31	is	be	AUX
ejpam-5857	1051	32	a	a	DET
ejpam-5857	1051	33	contradiction	contradiction	NOUN
ejpam-5857	1051	34	.	.	PUNCT
ejpam-5857	1052	1	thus	thus	ADV
ejpam-5857	1052	2	,	,	PUNCT
ejpam-5857	1052	3	ψf	ψf	X
ejpam-5857	1052	4	(	(	PUNCT
ejpam-5857	1052	5	y	y	NOUN
ejpam-5857	1052	6	)	)	PUNCT
ejpam-5857	1052	7	≥	≥	NOUN
ejpam-5857	1052	8	(	(	PUNCT
ejpam-5857	1052	9	ψf	ψf	X
ejpam-5857	1052	10	(	(	PUNCT
ejpam-5857	1052	11	x	x	PROPN
ejpam-5857	1052	12	·	·	PUNCT
ejpam-5857	1052	13	y	y	X
ejpam-5857	1052	14	)	)	PUNCT
ejpam-5857	1052	15	∧	∧	NOUN
ejpam-5857	1052	16	ψf	ψf	X
ejpam-5857	1052	17	(	(	PUNCT
ejpam-5857	1052	18	x	x	NOUN
ejpam-5857	1052	19	)	)	PUNCT
ejpam-5857	1052	20	)	)	PUNCT
ejpam-5857	1052	21	∨	∨	NUM
ejpam-5857	1052	22	0.5	0.5	NUM
ejpam-5857	1052	23	.	.	PUNCT
ejpam-5857	1052	24	k.	k.	PROPN
ejpam-5857	1052	25	suayngam	suayngam	PROPN
ejpam-5857	1052	26	,	,	PUNCT
ejpam-5857	1052	27	p.	p.	NOUN
ejpam-5857	1052	28	julatha	julatha	PROPN
ejpam-5857	1052	29	,	,	PUNCT
ejpam-5857	1052	30	w.	w.	PROPN
ejpam-5857	1052	31	nakkhasen	nakkhasen	PROPN
ejpam-5857	1052	32	,	,	PUNCT
ejpam-5857	1052	33	a.	a.	NOUN
ejpam-5857	1052	34	iampan	iampan	PROPN
ejpam-5857	1052	35	/	/	SYM
ejpam-5857	1052	36	eur	eur	PROPN
ejpam-5857	1052	37	.	.	PUNCT
ejpam-5857	1053	1	j.	j.	PROPN
ejpam-5857	1053	2	pure	pure	PROPN
ejpam-5857	1053	3	appl	appl	PROPN
ejpam-5857	1053	4	.	.	PROPN
ejpam-5857	1053	5	math	math	PROPN
ejpam-5857	1053	6	,	,	PUNCT
ejpam-5857	1053	7	18	18	NUM
ejpam-5857	1053	8	(	(	PUNCT
ejpam-5857	1053	9	2	2	NUM
ejpam-5857	1053	10	)	)	PUNCT
ejpam-5857	1053	11	(	(	PUNCT
ejpam-5857	1053	12	2025	2025	NUM
ejpam-5857	1053	13	)	)	PUNCT
ejpam-5857	1053	14	,	,	PUNCT
ejpam-5857	1053	15	5857	5857	NUM
ejpam-5857	1053	16	29	29	NUM
ejpam-5857	1053	17	of	of	ADP
ejpam-5857	1053	18	30	30	NUM
ejpam-5857	1053	19	hence	hence	ADV
ejpam-5857	1053	20	,	,	PUNCT
ejpam-5857	1053	21	ψ	ψ	X
ejpam-5857	1053	22	is	be	AUX
ejpam-5857	1053	23	an	an	DET
ejpam-5857	1053	24	intuitionistic	intuitionistic	ADJ
ejpam-5857	1053	25	neutrosophic	neutrosophic	ADJ
ejpam-5857	1053	26	iup	iup	NOUN
ejpam-5857	1053	27	-	-	PUNCT
ejpam-5857	1053	28	filter	filter	NOUN
ejpam-5857	1053	29	of	of	ADP
ejpam-5857	1053	30	x.	x.	PROPN
ejpam-5857	1053	31	theorem	theorem	VERB
ejpam-5857	1053	32	33	33	NUM
ejpam-5857	1053	33	.	.	PUNCT
ejpam-5857	1054	1	let	let	VERB
ejpam-5857	1054	2	for	for	ADP
ejpam-5857	1054	3	all	all	DET
ejpam-5857	1054	4	α	α	NOUN
ejpam-5857	1054	5	,	,	PUNCT
ejpam-5857	1054	6	γ	γ	PROPN
ejpam-5857	1054	7	∈	∈	PROPN
ejpam-5857	1055	1	[	[	X
ejpam-5857	1055	2	0.5	0.5	NUM
ejpam-5857	1055	3	,	,	PUNCT
ejpam-5857	1055	4	1	1	NUM
ejpam-5857	1055	5	]	]	PUNCT
ejpam-5857	1055	6	and	and	CCONJ
ejpam-5857	1055	7	β	β	X
ejpam-5857	1055	8	∈	∈	PROPN
ejpam-5857	1055	9	[	[	X
ejpam-5857	1055	10	0	0	NUM
ejpam-5857	1055	11	,	,	PUNCT
ejpam-5857	1055	12	0.5	0.5	NUM
ejpam-5857	1055	13	)	)	PUNCT
ejpam-5857	1055	14	,	,	PUNCT
ejpam-5857	1055	15	the	the	DET
ejpam-5857	1055	16	sets	set	NOUN
ejpam-5857	1055	17	u	u	NOUN
ejpam-5857	1055	18	+	+	X
ejpam-5857	1055	19	(	(	PUNCT
ejpam-5857	1055	20	ψt	ψt	NUM
ejpam-5857	1055	21	;	;	PUNCT
ejpam-5857	1055	22	α	α	X
ejpam-5857	1055	23	)	)	PUNCT
ejpam-5857	1055	24	,	,	PUNCT
ejpam-5857	1055	25	l	l	NOUN
ejpam-5857	1055	26	−	−	PROPN
ejpam-5857	1055	27	(	(	PUNCT
ejpam-5857	1055	28	ψi	ψi	ADP
ejpam-5857	1055	29	;	;	PUNCT
ejpam-5857	1055	30	β	β	X
ejpam-5857	1055	31	)	)	PUNCT
ejpam-5857	1055	32	and	and	CCONJ
ejpam-5857	1055	33	u	u	PRON
ejpam-5857	1055	34	+	+	X
ejpam-5857	1055	35	(	(	PUNCT
ejpam-5857	1055	36	ψf	ψf	X
ejpam-5857	1055	37	;	;	PUNCT
ejpam-5857	1055	38	γ	γ	X
ejpam-5857	1055	39	)	)	PUNCT
ejpam-5857	1055	40	are	be	AUX
ejpam-5857	1055	41	either	either	CCONJ
ejpam-5857	1055	42	empty	empty	ADJ
ejpam-5857	1055	43	or	or	CCONJ
ejpam-5857	1055	44	strong	strong	ADJ
ejpam-5857	1055	45	iup	iup	NOUN
ejpam-5857	1055	46	-	-	PUNCT
ejpam-5857	1055	47	ideals	ideal	NOUN
ejpam-5857	1055	48	of	of	ADP
ejpam-5857	1055	49	x.	x.	NOUN
ejpam-5857	1055	50	if	if	SCONJ
ejpam-5857	1055	51	ψt	ψt	VERB
ejpam-5857	1055	52	(	(	PUNCT
ejpam-5857	1055	53	x	x	NOUN
ejpam-5857	1055	54	)	)	PUNCT
ejpam-5857	1055	55	≥	≥	NOUN
ejpam-5857	1055	56	0.5	0.5	NUM
ejpam-5857	1055	57	,	,	PUNCT
ejpam-5857	1055	58	ψi(x	ψi(x	NUM
ejpam-5857	1055	59	)	)	PUNCT
ejpam-5857	1055	60	<	<	X
ejpam-5857	1055	61	0.5	0.5	NUM
ejpam-5857	1055	62	and	and	CCONJ
ejpam-5857	1055	63	ψf	ψf	X
ejpam-5857	1055	64	(	(	PUNCT
ejpam-5857	1055	65	x	x	X
ejpam-5857	1055	66	)	)	PUNCT
ejpam-5857	1055	67	≥	≥	NOUN
ejpam-5857	1055	68	0.5	0.5	NUM
ejpam-5857	1055	69	for	for	ADP
ejpam-5857	1055	70	all	all	DET
ejpam-5857	1055	71	x	x	SYM
ejpam-5857	1055	72	∈	∈	NOUN
ejpam-5857	1055	73	x	x	NOUN
ejpam-5857	1055	74	,	,	PUNCT
ejpam-5857	1055	75	then	then	ADV
ejpam-5857	1055	76	ψ	ψ	NOUN
ejpam-5857	1055	77	is	be	AUX
ejpam-5857	1055	78	an	an	DET
ejpam-5857	1055	79	intuitionistic	intuitionistic	ADJ
ejpam-5857	1055	80	neutrosophic	neutrosophic	ADJ
ejpam-5857	1055	81	strong	strong	ADJ
ejpam-5857	1055	82	iup	iup	NOUN
ejpam-5857	1055	83	-	-	PUNCT
ejpam-5857	1055	84	ideal	ideal	NOUN
ejpam-5857	1055	85	of	of	ADP
ejpam-5857	1055	86	x.	x.	NOUN
ejpam-5857	1055	87	proof	proof	NOUN
ejpam-5857	1055	88	.	.	PUNCT
ejpam-5857	1056	1	it	it	PRON
ejpam-5857	1056	2	is	be	AUX
ejpam-5857	1056	3	straightforward	straightforward	ADJ
ejpam-5857	1056	4	by	by	ADP
ejpam-5857	1056	5	theorem	theorem	NOUN
ejpam-5857	1056	6	1	1	NUM
ejpam-5857	1056	7	.	.	NOUN
ejpam-5857	1056	8	4	4	NUM
ejpam-5857	1056	9	.	.	PUNCT
ejpam-5857	1057	1	conclusions	conclusion	NOUN
ejpam-5857	1057	2	this	this	DET
ejpam-5857	1057	3	study	study	NOUN
ejpam-5857	1057	4	has	have	AUX
ejpam-5857	1057	5	introduced	introduce	VERB
ejpam-5857	1057	6	the	the	DET
ejpam-5857	1057	7	foundational	foundational	ADJ
ejpam-5857	1057	8	concepts	concept	NOUN
ejpam-5857	1057	9	of	of	ADP
ejpam-5857	1057	10	intuitionistic	intuitionistic	ADJ
ejpam-5857	1057	11	neutrosophic	neutrosophic	ADJ
ejpam-5857	1057	12	iupsubalgebras	iupsubalgebra	NOUN
ejpam-5857	1057	13	,	,	PUNCT
ejpam-5857	1057	14	intuitionistic	intuitionistic	ADJ
ejpam-5857	1057	15	neutrosophic	neutrosophic	ADJ
ejpam-5857	1057	16	iup	iup	NOUN
ejpam-5857	1057	17	-	-	PUNCT
ejpam-5857	1057	18	ideals	ideal	NOUN
ejpam-5857	1057	19	,	,	PUNCT
ejpam-5857	1057	20	intuitionistic	intuitionistic	ADJ
ejpam-5857	1057	21	neutrosophic	neutrosophic	ADJ
ejpam-5857	1057	22	iup	iup	NOUN
ejpam-5857	1057	23	-	-	PUNCT
ejpam-5857	1057	24	filters	filter	NOUN
ejpam-5857	1057	25	and	and	CCONJ
ejpam-5857	1057	26	intuitionistic	intuitionistic	ADJ
ejpam-5857	1057	27	neutrosophic	neutrosophic	ADJ
ejpam-5857	1057	28	strong	strong	ADJ
ejpam-5857	1057	29	iup	iup	NOUN
ejpam-5857	1057	30	-	-	PUNCT
ejpam-5857	1057	31	ideals	ideal	NOUN
ejpam-5857	1057	32	within	within	ADP
ejpam-5857	1057	33	the	the	DET
ejpam-5857	1057	34	framework	framework	NOUN
ejpam-5857	1057	35	of	of	ADP
ejpam-5857	1057	36	iup	iup	NOUN
ejpam-5857	1057	37	-	-	PUNCT
ejpam-5857	1057	38	algebras	algebras	PROPN
ejpam-5857	1057	39	.	.	PUNCT
ejpam-5857	1058	1	through	through	ADP
ejpam-5857	1058	2	rigorous	rigorous	ADJ
ejpam-5857	1058	3	analysis	analysis	NOUN
ejpam-5857	1058	4	,	,	PUNCT
ejpam-5857	1058	5	we	we	PRON
ejpam-5857	1058	6	explored	explore	VERB
ejpam-5857	1058	7	their	their	PRON
ejpam-5857	1058	8	intrinsic	intrinsic	ADJ
ejpam-5857	1058	9	properties	property	NOUN
ejpam-5857	1058	10	and	and	CCONJ
ejpam-5857	1058	11	established	establish	VERB
ejpam-5857	1058	12	their	their	PRON
ejpam-5857	1058	13	relationships	relationship	NOUN
ejpam-5857	1058	14	with	with	ADP
ejpam-5857	1058	15	the	the	DET
ejpam-5857	1058	16	notions	notion	NOUN
ejpam-5857	1058	17	of	of	ADP
ejpam-5857	1058	18	characteristic	characteristic	NOUN
ejpam-5857	1058	19	,	,	PUNCT
ejpam-5857	1058	20	complement	complement	NOUN
ejpam-5857	1058	21	and	and	CCONJ
ejpam-5857	1058	22	level	level	NOUN
ejpam-5857	1058	23	subsets	subset	NOUN
ejpam-5857	1058	24	.	.	PUNCT
ejpam-5857	1059	1	a	a	DET
ejpam-5857	1059	2	key	key	ADJ
ejpam-5857	1059	3	contribution	contribution	NOUN
ejpam-5857	1059	4	of	of	ADP
ejpam-5857	1059	5	this	this	DET
ejpam-5857	1059	6	work	work	NOUN
ejpam-5857	1059	7	is	be	AUX
ejpam-5857	1059	8	the	the	DET
ejpam-5857	1059	9	derivation	derivation	NOUN
ejpam-5857	1059	10	of	of	ADP
ejpam-5857	1059	11	a	a	DET
ejpam-5857	1059	12	comprehensive	comprehensive	ADJ
ejpam-5857	1059	13	diagram	diagram	NOUN
ejpam-5857	1059	14	,	,	PUNCT
ejpam-5857	1059	15	as	as	SCONJ
ejpam-5857	1059	16	depicted	depict	VERB
ejpam-5857	1059	17	in	in	ADP
ejpam-5857	1059	18	figure	figure	NOUN
ejpam-5857	1059	19	2	2	NUM
ejpam-5857	1059	20	,	,	PUNCT
ejpam-5857	1059	21	which	which	PRON
ejpam-5857	1059	22	illustrates	illustrate	VERB
ejpam-5857	1059	23	the	the	DET
ejpam-5857	1059	24	hierarchical	hierarchical	ADJ
ejpam-5857	1059	25	structure	structure	NOUN
ejpam-5857	1059	26	and	and	CCONJ
ejpam-5857	1059	27	interactions	interaction	NOUN
ejpam-5857	1059	28	among	among	ADP
ejpam-5857	1059	29	these	these	DET
ejpam-5857	1059	30	subsets	subset	NOUN
ejpam-5857	1059	31	.	.	PUNCT
ejpam-5857	1060	1	this	this	DET
ejpam-5857	1060	2	visualization	visualization	NOUN
ejpam-5857	1060	3	provides	provide	VERB
ejpam-5857	1060	4	an	an	DET
ejpam-5857	1060	5	intuitive	intuitive	ADJ
ejpam-5857	1060	6	framework	framework	NOUN
ejpam-5857	1060	7	for	for	ADP
ejpam-5857	1060	8	understanding	understand	VERB
ejpam-5857	1060	9	the	the	DET
ejpam-5857	1060	10	interconnections	interconnection	NOUN
ejpam-5857	1060	11	within	within	ADP
ejpam-5857	1060	12	the	the	DET
ejpam-5857	1060	13	intuitionistic	intuitionistic	ADJ
ejpam-5857	1060	14	neutrosophic	neutrosophic	ADJ
ejpam-5857	1060	15	iup	iup	PROPN
ejpam-5857	1060	16	-	-	PUNCT
ejpam-5857	1060	17	algebraic	algebraic	ADJ
ejpam-5857	1060	18	system	system	NOUN
ejpam-5857	1060	19	.	.	PUNCT
ejpam-5857	1061	1	figure	figure	NOUN
ejpam-5857	1061	2	2	2	NUM
ejpam-5857	1061	3	:	:	PUNCT
ejpam-5857	1061	4	inss	ins	NOUN
ejpam-5857	1061	5	in	in	ADP
ejpam-5857	1061	6	iup	iup	NOUN
ejpam-5857	1061	7	-	-	PUNCT
ejpam-5857	1061	8	algebras	algebra	NOUN
ejpam-5857	1061	9	the	the	DET
ejpam-5857	1061	10	findings	finding	NOUN
ejpam-5857	1061	11	presented	present	VERB
ejpam-5857	1061	12	herein	herein	NOUN
ejpam-5857	1061	13	mark	mark	VERB
ejpam-5857	1061	14	a	a	DET
ejpam-5857	1061	15	significant	significant	ADJ
ejpam-5857	1061	16	advancement	advancement	NOUN
ejpam-5857	1061	17	in	in	ADP
ejpam-5857	1061	18	ins	in	NOUN
ejpam-5857	1061	19	theory	theory	NOUN
ejpam-5857	1061	20	as	as	SCONJ
ejpam-5857	1061	21	applied	apply	VERB
ejpam-5857	1061	22	to	to	ADP
ejpam-5857	1061	23	iup	iup	VERB
ejpam-5857	1061	24	-	-	PUNCT
ejpam-5857	1061	25	algebras	algebra	NOUN
ejpam-5857	1061	26	,	,	PUNCT
ejpam-5857	1061	27	offering	offer	VERB
ejpam-5857	1061	28	both	both	CCONJ
ejpam-5857	1061	29	theoretical	theoretical	ADJ
ejpam-5857	1061	30	and	and	CCONJ
ejpam-5857	1061	31	practical	practical	ADJ
ejpam-5857	1061	32	insights	insight	NOUN
ejpam-5857	1061	33	.	.	PUNCT
ejpam-5857	1062	1	by	by	ADP
ejpam-5857	1062	2	systematically	systematically	ADV
ejpam-5857	1062	3	bridging	bridge	VERB
ejpam-5857	1062	4	these	these	DET
ejpam-5857	1062	5	concepts	concept	NOUN
ejpam-5857	1062	6	,	,	PUNCT
ejpam-5857	1062	7	this	this	DET
ejpam-5857	1062	8	study	study	NOUN
ejpam-5857	1062	9	lays	lay	VERB
ejpam-5857	1062	10	the	the	DET
ejpam-5857	1062	11	groundwork	groundwork	NOUN
ejpam-5857	1062	12	for	for	ADP
ejpam-5857	1062	13	future	future	ADJ
ejpam-5857	1062	14	explorations	exploration	NOUN
ejpam-5857	1062	15	,	,	PUNCT
ejpam-5857	1062	16	including	include	VERB
ejpam-5857	1062	17	the	the	DET
ejpam-5857	1062	18	potential	potential	ADJ
ejpam-5857	1062	19	application	application	NOUN
ejpam-5857	1062	20	of	of	ADP
ejpam-5857	1062	21	ins	in	NOUN
ejpam-5857	1062	22	theory	theory	NOUN
ejpam-5857	1062	23	to	to	ADP
ejpam-5857	1062	24	other	other	ADJ
ejpam-5857	1062	25	algebraic	algebraic	ADJ
ejpam-5857	1062	26	systems	system	NOUN
ejpam-5857	1062	27	and	and	CCONJ
ejpam-5857	1062	28	the	the	DET
ejpam-5857	1062	29	extension	extension	NOUN
ejpam-5857	1062	30	of	of	ADP
ejpam-5857	1062	31	these	these	DET
ejpam-5857	1062	32	ideas	idea	NOUN
ejpam-5857	1062	33	into	into	ADP
ejpam-5857	1062	34	more	more	ADJ
ejpam-5857	1062	35	generalized	generalized	ADJ
ejpam-5857	1062	36	frameworks	framework	NOUN
ejpam-5857	1062	37	.	.	PUNCT
ejpam-5857	1063	1	in	in	ADP
ejpam-5857	1063	2	future	future	ADJ
ejpam-5857	1063	3	work	work	NOUN
ejpam-5857	1063	4	,	,	PUNCT
ejpam-5857	1063	5	we	we	PRON
ejpam-5857	1063	6	aim	aim	VERB
ejpam-5857	1063	7	to	to	PART
ejpam-5857	1063	8	expand	expand	VERB
ejpam-5857	1063	9	upon	upon	SCONJ
ejpam-5857	1063	10	this	this	DET
ejpam-5857	1063	11	foundation	foundation	NOUN
ejpam-5857	1063	12	by	by	ADP
ejpam-5857	1063	13	examining	examine	VERB
ejpam-5857	1063	14	the	the	DET
ejpam-5857	1063	15	integration	integration	NOUN
ejpam-5857	1063	16	of	of	ADP
ejpam-5857	1063	17	soft	soft	ADJ
ejpam-5857	1063	18	set	set	NOUN
ejpam-5857	1063	19	theory	theory	NOUN
ejpam-5857	1063	20	and	and	CCONJ
ejpam-5857	1063	21	cubic	cubic	ADJ
ejpam-5857	1063	22	set	set	NOUN
ejpam-5857	1063	23	theory	theory	NOUN
ejpam-5857	1063	24	with	with	ADP
ejpam-5857	1063	25	neutrosophic	neutrosophic	ADJ
ejpam-5857	1063	26	iup	iup	NOUN
ejpam-5857	1063	27	-	-	PUNCT
ejpam-5857	1063	28	algebras	algebras	PROPN
ejpam-5857	1063	29	.	.	PUNCT
ejpam-5857	1064	1	these	these	DET
ejpam-5857	1064	2	efforts	effort	NOUN
ejpam-5857	1064	3	will	will	AUX
ejpam-5857	1064	4	involve	involve	VERB
ejpam-5857	1064	5	investigating	investigate	VERB
ejpam-5857	1064	6	neutrosophic	neutrosophic	ADJ
ejpam-5857	1064	7	iup	iup	NOUN
ejpam-5857	1064	8	-	-	PUNCT
ejpam-5857	1064	9	subalgebras	subalgebras	PROPN
ejpam-5857	1064	10	,	,	PUNCT
ejpam-5857	1064	11	iup	iup	NOUN
ejpam-5857	1064	12	-	-	PUNCT
ejpam-5857	1064	13	ideals	ideal	NOUN
ejpam-5857	1064	14	,	,	PUNCT
ejpam-5857	1064	15	iup	iup	NOUN
ejpam-5857	1064	16	-	-	PUNCT
ejpam-5857	1064	17	filters	filter	NOUN
ejpam-5857	1064	18	and	and	CCONJ
ejpam-5857	1064	19	strong	strong	ADJ
ejpam-5857	1064	20	iup	iup	NOUN
ejpam-5857	1064	21	-	-	PUNCT
ejpam-5857	1064	22	ideals	ideal	NOUN
ejpam-5857	1064	23	within	within	ADP
ejpam-5857	1064	24	these	these	DET
ejpam-5857	1064	25	alternative	alternative	ADJ
ejpam-5857	1064	26	frameworks	framework	NOUN
ejpam-5857	1064	27	.	.	PUNCT
ejpam-5857	1065	1	the	the	DET
ejpam-5857	1065	2	hierarchical	hierarchical	ADJ
ejpam-5857	1065	3	relationships	relationship	NOUN
ejpam-5857	1065	4	,	,	PUNCT
ejpam-5857	1065	5	as	as	SCONJ
ejpam-5857	1065	6	detailed	detailed	ADJ
ejpam-5857	1065	7	in	in	ADP
ejpam-5857	1065	8	figure	figure	NOUN
ejpam-5857	1065	9	2	2	NUM
ejpam-5857	1065	10	,	,	PUNCT
ejpam-5857	1065	11	will	will	AUX
ejpam-5857	1065	12	serve	serve	VERB
ejpam-5857	1065	13	as	as	ADP
ejpam-5857	1065	14	a	a	DET
ejpam-5857	1065	15	critical	critical	ADJ
ejpam-5857	1065	16	reference	reference	NOUN
ejpam-5857	1065	17	point	point	NOUN
ejpam-5857	1065	18	for	for	ADP
ejpam-5857	1065	19	further	further	ADJ
ejpam-5857	1065	20	studies	study	NOUN
ejpam-5857	1065	21	into	into	ADP
ejpam-5857	1065	22	the	the	DET
ejpam-5857	1065	23	algebraic	algebraic	ADJ
ejpam-5857	1065	24	and	and	CCONJ
ejpam-5857	1065	25	logical	logical	ADJ
ejpam-5857	1065	26	underpinnings	underpinning	NOUN
ejpam-5857	1065	27	of	of	ADP
ejpam-5857	1065	28	iup	iup	NOUN
ejpam-5857	1065	29	-	-	PUNCT
ejpam-5857	1065	30	algebras	algebras	X
ejpam-5857	1065	31	,	,	PUNCT
ejpam-5857	1065	32	ultimately	ultimately	ADV
ejpam-5857	1065	33	enhancing	enhance	VERB
ejpam-5857	1065	34	their	their	PRON
ejpam-5857	1065	35	utility	utility	NOUN
ejpam-5857	1065	36	in	in	ADP
ejpam-5857	1065	37	modeling	modeling	NOUN
ejpam-5857	1065	38	and	and	CCONJ
ejpam-5857	1065	39	decision	decision	NOUN
ejpam-5857	1065	40	-	-	PUNCT
ejpam-5857	1065	41	making	making	NOUN
ejpam-5857	1065	42	under	under	ADP
ejpam-5857	1065	43	conditions	condition	NOUN
ejpam-5857	1065	44	of	of	ADP
ejpam-5857	1065	45	uncertainty	uncertainty	NOUN
ejpam-5857	1065	46	.	.	PUNCT
ejpam-5857	1066	1	k.	k.	PROPN
ejpam-5857	1066	2	suayngam	suayngam	PROPN
ejpam-5857	1066	3	,	,	PUNCT
ejpam-5857	1066	4	p.	p.	NOUN
ejpam-5857	1066	5	julatha	julatha	PROPN
ejpam-5857	1066	6	,	,	PUNCT
ejpam-5857	1066	7	w.	w.	PROPN
ejpam-5857	1066	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	1066	9	,	,	PUNCT
ejpam-5857	1066	10	a.	a.	NOUN
ejpam-5857	1066	11	iampan	iampan	PROPN
ejpam-5857	1066	12	/	/	SYM
ejpam-5857	1066	13	eur	eur	PROPN
ejpam-5857	1066	14	.	.	PUNCT
ejpam-5857	1067	1	j.	j.	PROPN
ejpam-5857	1067	2	pure	pure	PROPN
ejpam-5857	1067	3	appl	appl	PROPN
ejpam-5857	1067	4	.	.	PROPN
ejpam-5857	1067	5	math	math	PROPN
ejpam-5857	1067	6	,	,	PUNCT
ejpam-5857	1067	7	18	18	NUM
ejpam-5857	1067	8	(	(	PUNCT
ejpam-5857	1067	9	2	2	NUM
ejpam-5857	1067	10	)	)	PUNCT
ejpam-5857	1067	11	(	(	PUNCT
ejpam-5857	1067	12	2025	2025	NUM
ejpam-5857	1067	13	)	)	PUNCT
ejpam-5857	1067	14	,	,	PUNCT
ejpam-5857	1067	15	5857	5857	NUM
ejpam-5857	1067	16	30	30	NUM
ejpam-5857	1067	17	of	of	ADP
ejpam-5857	1067	18	30	30	NUM
ejpam-5857	1067	19	acknowledgements	acknowledgement	NOUN
ejpam-5857	1067	20	this	this	DET
ejpam-5857	1067	21	research	research	NOUN
ejpam-5857	1067	22	was	be	AUX
ejpam-5857	1067	23	supported	support	VERB
ejpam-5857	1067	24	by	by	ADP
ejpam-5857	1067	25	university	university	NOUN
ejpam-5857	1067	26	of	of	ADP
ejpam-5857	1067	27	phayao	phayao	NOUN
ejpam-5857	1067	28	and	and	CCONJ
ejpam-5857	1067	29	thailand	thailand	PROPN
ejpam-5857	1067	30	science	science	PROPN
ejpam-5857	1067	31	research	research	PROPN
ejpam-5857	1067	32	and	and	CCONJ
ejpam-5857	1067	33	innovation	innovation	NOUN
ejpam-5857	1067	34	fund	fund	NOUN
ejpam-5857	1067	35	(	(	PUNCT
ejpam-5857	1067	36	fundamental	fundamental	ADJ
ejpam-5857	1067	37	fund	fund	NOUN
ejpam-5857	1067	38	2025	2025	NUM
ejpam-5857	1067	39	,	,	PUNCT
ejpam-5857	1067	40	grant	grant	VERB
ejpam-5857	1067	41	no	no	NOUN
ejpam-5857	1067	42	.	.	PROPN
ejpam-5857	1068	1	5027/2567	5027/2567	NUM
ejpam-5857	1068	2	)	)	PUNCT
ejpam-5857	1068	3	.	.	PUNCT
ejpam-5857	1069	1	references	reference	NOUN
ejpam-5857	1069	2	[	[	X
ejpam-5857	1069	3	1	1	NUM
ejpam-5857	1069	4	]	]	PUNCT
ejpam-5857	1069	5	k.	k.	PROPN
ejpam-5857	1069	6	t.	t.	PROPN
ejpam-5857	1069	7	atanassov	atanassov	PROPN
ejpam-5857	1069	8	.	.	PUNCT
ejpam-5857	1070	1	intuitionistic	intuitionistic	ADJ
ejpam-5857	1070	2	fuzzy	fuzzy	ADJ
ejpam-5857	1070	3	sets	set	NOUN
ejpam-5857	1070	4	.	.	PUNCT
ejpam-5857	1071	1	fuzzy	fuzzy	ADJ
ejpam-5857	1071	2	sets	set	NOUN
ejpam-5857	1071	3	syst	syst	PROPN
ejpam-5857	1071	4	.	.	PUNCT
ejpam-5857	1071	5	,	,	PUNCT
ejpam-5857	1071	6	20(1):87–96	20(1):87–96	NUM
ejpam-5857	1071	7	,	,	PUNCT
ejpam-5857	1071	8	1986	1986	NUM
ejpam-5857	1071	9	.	.	PUNCT
ejpam-5857	1072	1	[	[	X
ejpam-5857	1072	2	2	2	NUM
ejpam-5857	1072	3	]	]	PUNCT
ejpam-5857	1072	4	m.	m.	NOUN
ejpam-5857	1072	5	bhowmik	bhowmik	ADJ
ejpam-5857	1072	6	and	and	CCONJ
ejpam-5857	1072	7	m.	m.	NOUN
ejpam-5857	1072	8	pal	pal	NOUN
ejpam-5857	1072	9	.	.	PUNCT
ejpam-5857	1073	1	intuitionistic	intuitionistic	ADJ
ejpam-5857	1073	2	neutrosophic	neutrosophic	ADJ
ejpam-5857	1073	3	set	set	NOUN
ejpam-5857	1073	4	.	.	PUNCT
ejpam-5857	1074	1	j.	j.	PROPN
ejpam-5857	1074	2	inf	inf	PROPN
ejpam-5857	1074	3	.	.	PUNCT
ejpam-5857	1075	1	comput	comput	PROPN
ejpam-5857	1075	2	.	.	PUNCT
ejpam-5857	1076	1	inf	inf	PROPN
ejpam-5857	1076	2	.	.	PUNCT
ejpam-5857	1077	1	sci	sci	PROPN
ejpam-5857	1077	2	.	.	PUNCT
ejpam-5857	1078	1	eng	eng	PROPN
ejpam-5857	1078	2	.	.	PROPN
ejpam-5857	1078	3	,	,	PUNCT
ejpam-5857	1078	4	4(2):142–152	4(2):142–152	NUM
ejpam-5857	1078	5	,	,	PUNCT
ejpam-5857	1078	6	2009	2009	NUM
ejpam-5857	1078	7	.	.	PUNCT
ejpam-5857	1079	1	[	[	X
ejpam-5857	1079	2	3	3	X
ejpam-5857	1079	3	]	]	PUNCT
ejpam-5857	1079	4	m.	m.	NOUN
ejpam-5857	1079	5	bhowmik	bhowmik	ADJ
ejpam-5857	1079	6	and	and	CCONJ
ejpam-5857	1079	7	m.	m.	NOUN
ejpam-5857	1079	8	pal	pal	NOUN
ejpam-5857	1079	9	.	.	PUNCT
ejpam-5857	1080	1	intuitionistic	intuitionistic	ADJ
ejpam-5857	1080	2	neutrosophic	neutrosophic	ADJ
ejpam-5857	1080	3	set	set	NOUN
ejpam-5857	1080	4	relations	relation	NOUN
ejpam-5857	1080	5	and	and	CCONJ
ejpam-5857	1080	6	some	some	PRON
ejpam-5857	1080	7	of	of	ADP
ejpam-5857	1080	8	its	its	PRON
ejpam-5857	1080	9	properties	property	NOUN
ejpam-5857	1080	10	.	.	PUNCT
ejpam-5857	1081	1	j.	j.	PROPN
ejpam-5857	1081	2	inf	inf	PROPN
ejpam-5857	1081	3	.	.	PUNCT
ejpam-5857	1082	1	comput	comput	PROPN
ejpam-5857	1082	2	.	.	PUNCT
ejpam-5857	1083	1	inf	inf	PROPN
ejpam-5857	1083	2	.	.	PUNCT
ejpam-5857	1084	1	sci	sci	PROPN
ejpam-5857	1084	2	.	.	PUNCT
ejpam-5857	1085	1	eng	eng	PROPN
ejpam-5857	1085	2	.	.	PROPN
ejpam-5857	1085	3	,	,	PUNCT
ejpam-5857	1085	4	5(3):183–192	5(3):183–192	NUM
ejpam-5857	1085	5	,	,	PUNCT
ejpam-5857	1085	6	2010	2010	NUM
ejpam-5857	1085	7	.	.	PUNCT
ejpam-5857	1086	1	[	[	X
ejpam-5857	1086	2	4	4	X
ejpam-5857	1086	3	]	]	PUNCT
ejpam-5857	1086	4	s.	s.	PROPN
ejpam-5857	1086	5	broumi	broumi	PROPN
ejpam-5857	1086	6	and	and	CCONJ
ejpam-5857	1086	7	f.	f.	PROPN
ejpam-5857	1086	8	smarandache	smarandache	PROPN
ejpam-5857	1086	9	.	.	PUNCT
ejpam-5857	1087	1	intuitionistic	intuitionistic	ADJ
ejpam-5857	1087	2	neutrosophic	neutrosophic	ADJ
ejpam-5857	1087	3	soft	soft	ADJ
ejpam-5857	1087	4	set	set	NOUN
ejpam-5857	1087	5	.	.	PUNCT
ejpam-5857	1088	1	j.	j.	PROPN
ejpam-5857	1088	2	inf	inf	PROPN
ejpam-5857	1088	3	.	.	PUNCT
ejpam-5857	1088	4	comput	comput	PROPN
ejpam-5857	1088	5	.	.	PUNCT
ejpam-5857	1089	1	sci	sci	PROPN
ejpam-5857	1089	2	.	.	PROPN
ejpam-5857	1089	3	,	,	PUNCT
ejpam-5857	1089	4	8(2):130–140	8(2):130–140	NUM
ejpam-5857	1089	5	,	,	PUNCT
ejpam-5857	1089	6	2013	2013	NUM
ejpam-5857	1089	7	.	.	PUNCT
ejpam-5857	1090	1	[	[	X
ejpam-5857	1090	2	5	5	X
ejpam-5857	1090	3	]	]	PUNCT
ejpam-5857	1090	4	s.	s.	PROPN
ejpam-5857	1090	5	broumi	broumi	PROPN
ejpam-5857	1090	6	and	and	CCONJ
ejpam-5857	1090	7	f.	f.	PROPN
ejpam-5857	1090	8	smarandache	smarandache	PROPN
ejpam-5857	1090	9	.	.	PUNCT
ejpam-5857	1091	1	more	more	ADJ
ejpam-5857	1091	2	on	on	ADP
ejpam-5857	1091	3	intuitionistic	intuitionistic	ADJ
ejpam-5857	1091	4	neutrosophic	neutrosophic	ADJ
ejpam-5857	1091	5	soft	soft	ADJ
ejpam-5857	1091	6	sets	set	NOUN
ejpam-5857	1091	7	.	.	PUNCT
ejpam-5857	1092	1	comp	comp	NOUN
ejpam-5857	1092	2	.	.	PUNCT
ejpam-5857	1093	1	sci	sci	PROPN
ejpam-5857	1093	2	.	.	PROPN
ejpam-5857	1093	3	inf	inf	PROPN
ejpam-5857	1093	4	.	.	PUNCT
ejpam-5857	1093	5	tech	tech	PROPN
ejpam-5857	1093	6	.	.	PUNCT
ejpam-5857	1093	7	,	,	PUNCT
ejpam-5857	1093	8	1(4):257–268	1(4):257–268	NUM
ejpam-5857	1093	9	,	,	PUNCT
ejpam-5857	1093	10	2013	2013	NUM
ejpam-5857	1093	11	.	.	PUNCT
ejpam-5857	1094	1	[	[	X
ejpam-5857	1094	2	6	6	NUM
ejpam-5857	1094	3	]	]	PUNCT
ejpam-5857	1094	4	s.	s.	PROPN
ejpam-5857	1094	5	broumi	broumi	PROPN
ejpam-5857	1094	6	,	,	PUNCT
ejpam-5857	1094	7	f.	f.	PROPN
ejpam-5857	1094	8	smarandache	smarandache	PROPN
ejpam-5857	1094	9	,	,	PUNCT
ejpam-5857	1094	10	and	and	CCONJ
ejpam-5857	1094	11	p.	p.	PROPN
ejpam-5857	1094	12	k.	k.	PROPN
ejpam-5857	1095	1	maji	maji	PROPN
ejpam-5857	1095	2	.	.	PUNCT
ejpam-5857	1096	1	intuitionistic	intuitionistic	ADJ
ejpam-5857	1096	2	neutrosphic	neutrosphic	ADJ
ejpam-5857	1096	3	soft	soft	ADJ
ejpam-5857	1096	4	set	set	NOUN
ejpam-5857	1096	5	over	over	ADP
ejpam-5857	1096	6	rings	ring	NOUN
ejpam-5857	1096	7	.	.	PUNCT
ejpam-5857	1097	1	math	math	NOUN
ejpam-5857	1097	2	.	.	PUNCT
ejpam-5857	1098	1	stat	stat	PROPN
ejpam-5857	1098	2	.	.	PUNCT
ejpam-5857	1098	3	,	,	PUNCT
ejpam-5857	1098	4	2(3):120–126	2(3):120–126	NOUN
ejpam-5857	1098	5	,	,	PUNCT
ejpam-5857	1098	6	2014	2014	NUM
ejpam-5857	1098	7	.	.	PUNCT
ejpam-5857	1099	1	[	[	X
ejpam-5857	1099	2	7	7	X
ejpam-5857	1099	3	]	]	X
ejpam-5857	1099	4	c.	c.	PROPN
ejpam-5857	1099	5	chanmanee	chanmanee	PROPN
ejpam-5857	1099	6	,	,	PUNCT
ejpam-5857	1099	7	w.	w.	PROPN
ejpam-5857	1099	8	nakkhasen	nakkhasen	PROPN
ejpam-5857	1099	9	,	,	PUNCT
ejpam-5857	1099	10	r.	r.	PROPN
ejpam-5857	1099	11	prasertpong	prasertpong	PROPN
ejpam-5857	1099	12	,	,	PUNCT
ejpam-5857	1099	13	p.	p.	PROPN
ejpam-5857	1099	14	julatha	julatha	PROPN
ejpam-5857	1099	15	,	,	PUNCT
ejpam-5857	1099	16	and	and	CCONJ
ejpam-5857	1099	17	a.	a.	NOUN
ejpam-5857	1099	18	iampan	iampan	PROPN
ejpam-5857	1099	19	.	.	PUNCT
ejpam-5857	1100	1	notes	note	NOUN
ejpam-5857	1100	2	on	on	ADP
ejpam-5857	1100	3	external	external	ADJ
ejpam-5857	1100	4	direct	direct	ADJ
ejpam-5857	1100	5	products	product	NOUN
ejpam-5857	1100	6	of	of	ADP
ejpam-5857	1100	7	dual	dual	ADJ
ejpam-5857	1100	8	iup	iup	NOUN
ejpam-5857	1100	9	-	-	PUNCT
ejpam-5857	1100	10	algebras	algebras	PROPN
ejpam-5857	1100	11	.	.	PUNCT
ejpam-5857	1101	1	south	south	PROPN
ejpam-5857	1101	2	east	east	PROPN
ejpam-5857	1101	3	asian	asian	PROPN
ejpam-5857	1101	4	j.	j.	PROPN
ejpam-5857	1101	5	math	math	PROPN
ejpam-5857	1101	6	.	.	PUNCT
ejpam-5857	1102	1	math	math	NOUN
ejpam-5857	1102	2	.	.	PUNCT
ejpam-5857	1103	1	sci	sci	PROPN
ejpam-5857	1103	2	.	.	PROPN
ejpam-5857	1103	3	,	,	PUNCT
ejpam-5857	1103	4	19(3):13–30	19(3):13–30	NUM
ejpam-5857	1103	5	,	,	PUNCT
ejpam-5857	1103	6	2023	2023	NUM
ejpam-5857	1103	7	.	.	PUNCT
ejpam-5857	1104	1	[	[	X
ejpam-5857	1104	2	8	8	NUM
ejpam-5857	1104	3	]	]	X
ejpam-5857	1104	4	c.	c.	PROPN
ejpam-5857	1104	5	chanmanee	chanmanee	PROPN
ejpam-5857	1104	6	,	,	PUNCT
ejpam-5857	1104	7	r.	r.	PROPN
ejpam-5857	1104	8	prasertpong	prasertpong	PROPN
ejpam-5857	1104	9	,	,	PUNCT
ejpam-5857	1104	10	p.	p.	PROPN
ejpam-5857	1104	11	julatha	julatha	PROPN
ejpam-5857	1104	12	,	,	PUNCT
ejpam-5857	1104	13	n.	n.	PROPN
ejpam-5857	1104	14	lekkoksung	lekkoksung	PROPN
ejpam-5857	1104	15	,	,	PUNCT
ejpam-5857	1104	16	and	and	CCONJ
ejpam-5857	1104	17	a.	a.	NOUN
ejpam-5857	1104	18	iampan	iampan	PROPN
ejpam-5857	1104	19	.	.	PUNCT
ejpam-5857	1105	1	on	on	ADP
ejpam-5857	1105	2	external	external	ADJ
ejpam-5857	1105	3	direct	direct	ADJ
ejpam-5857	1105	4	products	product	NOUN
ejpam-5857	1105	5	of	of	ADP
ejpam-5857	1105	6	iup	iup	NOUN
ejpam-5857	1105	7	-	-	PUNCT
ejpam-5857	1105	8	algebras	algebras	PROPN
ejpam-5857	1105	9	.	.	PUNCT
ejpam-5857	1106	1	int	int	NOUN
ejpam-5857	1106	2	.	.	PUNCT
ejpam-5857	1107	1	j.	j.	PROPN
ejpam-5857	1107	2	innov	innov	PROPN
ejpam-5857	1107	3	.	.	PUNCT
ejpam-5857	1108	1	comput	comput	PROPN
ejpam-5857	1108	2	.	.	PUNCT
ejpam-5857	1109	1	inf	inf	PROPN
ejpam-5857	1109	2	.	.	PUNCT
ejpam-5857	1109	3	control	control	PROPN
ejpam-5857	1109	4	,	,	PUNCT
ejpam-5857	1109	5	19(3):775	19(3):775	NUM
ejpam-5857	1109	6	–	–	PUNCT
ejpam-5857	1109	7	787	787	NUM
ejpam-5857	1109	8	,	,	PUNCT
ejpam-5857	1109	9	2023	2023	NUM
ejpam-5857	1109	10	.	.	PUNCT
ejpam-5857	1110	1	[	[	X
ejpam-5857	1110	2	9	9	NUM
ejpam-5857	1110	3	]	]	PUNCT
ejpam-5857	1110	4	a.	a.	NOUN
ejpam-5857	1110	5	iampan	iampan	PROPN
ejpam-5857	1110	6	,	,	PUNCT
ejpam-5857	1110	7	p.	p.	PROPN
ejpam-5857	1110	8	julatha	julatha	PROPN
ejpam-5857	1110	9	,	,	PUNCT
ejpam-5857	1110	10	p.	p.	NOUN
ejpam-5857	1110	11	khamrot	khamrot	NOUN
ejpam-5857	1110	12	,	,	PUNCT
ejpam-5857	1110	13	and	and	CCONJ
ejpam-5857	1110	14	d.	d.	PROPN
ejpam-5857	1110	15	a.	a.	PROPN
ejpam-5857	1110	16	romano	romano	PROPN
ejpam-5857	1110	17	.	.	PUNCT
ejpam-5857	1111	1	independent	independent	ADJ
ejpam-5857	1111	2	up	up	ADP
ejpam-5857	1111	3	-	-	PUNCT
ejpam-5857	1111	4	algebras	algebras	X
ejpam-5857	1111	5	.	.	PUNCT
ejpam-5857	1112	1	j.	j.	PROPN
ejpam-5857	1112	2	math	math	PROPN
ejpam-5857	1112	3	.	.	PUNCT
ejpam-5857	1113	1	comput	comput	NOUN
ejpam-5857	1113	2	.	.	PUNCT
ejpam-5857	1114	1	sci	sci	PROPN
ejpam-5857	1114	2	.	.	PROPN
ejpam-5857	1114	3	,	,	PUNCT
ejpam-5857	1114	4	jmcs	jmcs	NOUN
ejpam-5857	1114	5	,	,	PUNCT
ejpam-5857	1114	6	27(1):65–76	27(1):65–76	NUM
ejpam-5857	1114	7	,	,	PUNCT
ejpam-5857	1114	8	2022	2022	NUM
ejpam-5857	1114	9	.	.	PUNCT
ejpam-5857	1115	1	[	[	X
ejpam-5857	1115	2	10	10	NUM
ejpam-5857	1115	3	]	]	PUNCT
ejpam-5857	1115	4	k.	k.	PROPN
ejpam-5857	1115	5	kuntama	kuntama	PROPN
ejpam-5857	1115	6	,	,	PUNCT
ejpam-5857	1115	7	p.	p.	NOUN
ejpam-5857	1115	8	krongchai	krongchai	PROPN
ejpam-5857	1115	9	,	,	PUNCT
ejpam-5857	1115	10	r.	r.	PROPN
ejpam-5857	1115	11	prasertpong	prasertpong	PROPN
ejpam-5857	1115	12	,	,	PUNCT
ejpam-5857	1115	13	p.	p.	PROPN
ejpam-5857	1115	14	julatha	julatha	PROPN
ejpam-5857	1115	15	,	,	PUNCT
ejpam-5857	1115	16	and	and	CCONJ
ejpam-5857	1115	17	a.	a.	NOUN
ejpam-5857	1115	18	iampan	iampan	PROPN
ejpam-5857	1115	19	.	.	PUNCT
ejpam-5857	1116	1	fuzzy	fuzzy	ADJ
ejpam-5857	1116	2	set	set	VERB
ejpam-5857	1116	3	theory	theory	NOUN
ejpam-5857	1116	4	applied	apply	VERB
ejpam-5857	1116	5	to	to	ADP
ejpam-5857	1116	6	iup	iup	VERB
ejpam-5857	1116	7	-	-	PUNCT
ejpam-5857	1116	8	algebras	algebras	PROPN
ejpam-5857	1116	9	.	.	PUNCT
ejpam-5857	1117	1	j.	j.	PROPN
ejpam-5857	1117	2	math	math	PROPN
ejpam-5857	1117	3	.	.	PUNCT
ejpam-5857	1118	1	comput	comput	NOUN
ejpam-5857	1118	2	.	.	PUNCT
ejpam-5857	1119	1	sci	sci	PROPN
ejpam-5857	1119	2	.	.	PROPN
ejpam-5857	1119	3	,	,	PUNCT
ejpam-5857	1119	4	jmcs	jmcs	NOUN
ejpam-5857	1119	5	,	,	PUNCT
ejpam-5857	1119	6	34(2):128–143	34(2):128–143	PROPN
ejpam-5857	1119	7	,	,	PUNCT
ejpam-5857	1119	8	2024	2024	NUM
ejpam-5857	1119	9	.	.	PUNCT
ejpam-5857	1120	1	[	[	X
ejpam-5857	1120	2	11	11	NUM
ejpam-5857	1120	3	]	]	X
ejpam-5857	1120	4	f.	f.	PROPN
ejpam-5857	1120	5	smarandache	smarandache	PROPN
ejpam-5857	1120	6	.	.	PUNCT
ejpam-5857	1121	1	neutrosophic	neutrosophic	PROPN
ejpam-5857	1121	2	set	set	VERB
ejpam-5857	1121	3	–	–	PUNCT
ejpam-5857	1121	4	a	a	DET
ejpam-5857	1121	5	generalization	generalization	NOUN
ejpam-5857	1121	6	of	of	ADP
ejpam-5857	1121	7	the	the	DET
ejpam-5857	1121	8	intuitionistic	intuitionistic	ADJ
ejpam-5857	1121	9	fuzzy	fuzzy	ADJ
ejpam-5857	1121	10	set	set	NOUN
ejpam-5857	1121	11	.	.	PUNCT
ejpam-5857	1122	1	2006	2006	NUM
ejpam-5857	1122	2	ieee	ieee	PROPN
ejpam-5857	1122	3	international	international	ADJ
ejpam-5857	1122	4	conference	conference	NOUN
ejpam-5857	1122	5	on	on	ADP
ejpam-5857	1122	6	granular	granular	ADJ
ejpam-5857	1122	7	computing	computing	NOUN
ejpam-5857	1122	8	,	,	PUNCT
ejpam-5857	1122	9	pages	page	NOUN
ejpam-5857	1122	10	38–42	38–42	NUM
ejpam-5857	1122	11	,	,	PUNCT
ejpam-5857	1122	12	2006	2006	NUM
ejpam-5857	1122	13	.	.	PUNCT
ejpam-5857	1123	1	[	[	X
ejpam-5857	1123	2	12	12	NUM
ejpam-5857	1123	3	]	]	PUNCT
ejpam-5857	1123	4	k.	k.	PROPN
ejpam-5857	1123	5	suayngam	suayngam	PROPN
ejpam-5857	1123	6	,	,	PUNCT
ejpam-5857	1123	7	p.	p.	NOUN
ejpam-5857	1123	8	julatha	julatha	PROPN
ejpam-5857	1123	9	,	,	PUNCT
ejpam-5857	1123	10	r.	r.	PROPN
ejpam-5857	1123	11	prasertpong	prasertpong	PROPN
ejpam-5857	1123	12	,	,	PUNCT
ejpam-5857	1123	13	and	and	CCONJ
ejpam-5857	1123	14	a.	a.	NOUN
ejpam-5857	1123	15	iampan	iampan	PROPN
ejpam-5857	1123	16	.	.	PUNCT
ejpam-5857	1124	1	neutrosophic	neutrosophic	ADJ
ejpam-5857	1124	2	sets	set	NOUN
ejpam-5857	1124	3	in	in	ADP
ejpam-5857	1124	4	iup	iup	NOUN
ejpam-5857	1124	5	-	-	PUNCT
ejpam-5857	1124	6	algebras	algebras	PROPN
ejpam-5857	1124	7	:	:	PUNCT
ejpam-5857	1124	8	a	a	DET
ejpam-5857	1124	9	new	new	ADJ
ejpam-5857	1124	10	exploration	exploration	NOUN
ejpam-5857	1124	11	.	.	PUNCT
ejpam-5857	1125	1	int	int	NOUN
ejpam-5857	1125	2	.	.	PUNCT
ejpam-5857	1126	1	j.	j.	PROPN
ejpam-5857	1126	2	neutrosophic	neutrosophic	PROPN
ejpam-5857	1126	3	sci	sci	PROPN
ejpam-5857	1126	4	.	.	PROPN
ejpam-5857	1126	5	,	,	PUNCT
ejpam-5857	1126	6	25(3):540–560	25(3):540–560	PROPN
ejpam-5857	1126	7	,	,	PUNCT
ejpam-5857	1126	8	2025	2025	NUM
ejpam-5857	1126	9	.	.	PUNCT
ejpam-5857	1127	1	[	[	X
ejpam-5857	1127	2	13	13	NUM
ejpam-5857	1127	3	]	]	PUNCT
ejpam-5857	1127	4	k.	k.	PROPN
ejpam-5857	1127	5	suayngam	suayngam	PROPN
ejpam-5857	1127	6	,	,	PUNCT
ejpam-5857	1127	7	r.	r.	PROPN
ejpam-5857	1127	8	prasertpong	prasertpong	PROPN
ejpam-5857	1127	9	,	,	PUNCT
ejpam-5857	1127	10	n.	n.	PROPN
ejpam-5857	1127	11	lekkoksung	lekkoksung	PROPN
ejpam-5857	1127	12	,	,	PUNCT
ejpam-5857	1127	13	p.	p.	PROPN
ejpam-5857	1127	14	julatha	julatha	PROPN
ejpam-5857	1127	15	,	,	PUNCT
ejpam-5857	1127	16	and	and	CCONJ
ejpam-5857	1127	17	a.	a.	NOUN
ejpam-5857	1127	18	iampan	iampan	PROPN
ejpam-5857	1127	19	.	.	PUNCT
ejpam-5857	1128	1	fermatean	fermatean	PROPN
ejpam-5857	1128	2	fuzzy	fuzzy	ADJ
ejpam-5857	1128	3	set	set	NOUN
ejpam-5857	1128	4	theory	theory	NOUN
ejpam-5857	1128	5	applied	apply	VERB
ejpam-5857	1128	6	to	to	ADP
ejpam-5857	1128	7	iup	iup	VERB
ejpam-5857	1128	8	-	-	PUNCT
ejpam-5857	1128	9	algebras	algebras	PROPN
ejpam-5857	1128	10	.	.	PUNCT
ejpam-5857	1129	1	european	european	PROPN
ejpam-5857	1129	2	j.	j.	PROPN
ejpam-5857	1129	3	pure	pure	PROPN
ejpam-5857	1129	4	app	app	PROPN
ejpam-5857	1129	5	.	.	PROPN
ejpam-5857	1129	6	math	math	PROPN
ejpam-5857	1129	7	.	.	PUNCT
ejpam-5857	1129	8	,	,	PUNCT
ejpam-5857	1129	9	17(4):3022	17(4):3022	NUM
ejpam-5857	1129	10	–	–	PUNCT
ejpam-5857	1129	11	3042	3042	NUM
ejpam-5857	1129	12	,	,	PUNCT
ejpam-5857	1129	13	2024	2024	NUM
ejpam-5857	1129	14	.	.	PUNCT
ejpam-5857	1130	1	[	[	X
ejpam-5857	1130	2	14	14	NUM
ejpam-5857	1130	3	]	]	PUNCT
ejpam-5857	1130	4	k.	k.	PROPN
ejpam-5857	1130	5	suayngam	suayngam	PROPN
ejpam-5857	1130	6	,	,	PUNCT
ejpam-5857	1130	7	r.	r.	PROPN
ejpam-5857	1130	8	prasertpong	prasertpong	PROPN
ejpam-5857	1130	9	,	,	PUNCT
ejpam-5857	1130	10	w.	w.	PROPN
ejpam-5857	1130	11	nakkhasen	nakkhasen	PROPN
ejpam-5857	1130	12	,	,	PUNCT
ejpam-5857	1130	13	p.	p.	NOUN
ejpam-5857	1130	14	julatha	julatha	PROPN
ejpam-5857	1130	15	,	,	PUNCT
ejpam-5857	1130	16	and	and	CCONJ
ejpam-5857	1130	17	a.	a.	NOUN
ejpam-5857	1130	18	iampan	iampan	PROPN
ejpam-5857	1130	19	.	.	PUNCT
ejpam-5857	1131	1	pythagorean	pythagorean	PROPN
ejpam-5857	1131	2	fuzzy	fuzzy	ADJ
ejpam-5857	1131	3	sets	set	NOUN
ejpam-5857	1131	4	:	:	PUNCT
ejpam-5857	1131	5	a	a	DET
ejpam-5857	1131	6	new	new	ADJ
ejpam-5857	1131	7	perspective	perspective	NOUN
ejpam-5857	1131	8	on	on	ADP
ejpam-5857	1131	9	iup	iup	NOUN
ejpam-5857	1131	10	-	-	PUNCT
ejpam-5857	1131	11	algebras	algebras	PROPN
ejpam-5857	1131	12	.	.	PUNCT
ejpam-5857	1132	1	int	int	NOUN
ejpam-5857	1132	2	.	.	PUNCT
ejpam-5857	1133	1	j.	j.	PROPN
ejpam-5857	1133	2	innov	innov	PROPN
ejpam-5857	1133	3	.	.	PUNCT
ejpam-5857	1134	1	comput	comput	PROPN
ejpam-5857	1134	2	.	.	PUNCT
ejpam-5857	1135	1	inf	inf	PROPN
ejpam-5857	1135	2	.	.	PUNCT
ejpam-5857	1135	3	control	control	PROPN
ejpam-5857	1135	4	,	,	PUNCT
ejpam-5857	1135	5	21(2):accepted	21(2):accepted	PROPN
ejpam-5857	1135	6	,	,	PUNCT
ejpam-5857	1135	7	2025	2025	NUM
ejpam-5857	1135	8	.	.	PUNCT
ejpam-5857	1136	1	[	[	X
ejpam-5857	1136	2	15	15	NUM
ejpam-5857	1136	3	]	]	X
ejpam-5857	1136	4	k.	k.	NOUN
ejpam-5857	1136	5	suayngam	suayngam	PROPN
ejpam-5857	1136	6	,	,	PUNCT
ejpam-5857	1136	7	t.	t.	PROPN
ejpam-5857	1136	8	suwanklang	suwanklang	PROPN
ejpam-5857	1136	9	,	,	PUNCT
ejpam-5857	1136	10	p.	p.	PROPN
ejpam-5857	1136	11	julatha	julatha	PROPN
ejpam-5857	1136	12	,	,	PUNCT
ejpam-5857	1136	13	r.	r.	PROPN
ejpam-5857	1136	14	prasertpong	prasertpong	PROPN
ejpam-5857	1136	15	,	,	PUNCT
ejpam-5857	1136	16	and	and	CCONJ
ejpam-5857	1136	17	a.	a.	NOUN
ejpam-5857	1136	18	iampan	iampan	PROPN
ejpam-5857	1136	19	.	.	PUNCT
ejpam-5857	1137	1	new	new	ADJ
ejpam-5857	1137	2	results	result	NOUN
ejpam-5857	1137	3	on	on	ADP
ejpam-5857	1137	4	intuitionistic	intuitionistic	ADJ
ejpam-5857	1137	5	fuzzy	fuzzy	ADJ
ejpam-5857	1137	6	sets	set	NOUN
ejpam-5857	1137	7	in	in	ADP
ejpam-5857	1137	8	iup	iup	NOUN
ejpam-5857	1137	9	-	-	PUNCT
ejpam-5857	1137	10	algebras	algebras	PROPN
ejpam-5857	1137	11	.	.	PUNCT
ejpam-5857	1138	1	int	int	NOUN
ejpam-5857	1138	2	.	.	PUNCT
ejpam-5857	1139	1	j.	j.	PROPN
ejpam-5857	1139	2	innov	innov	PROPN
ejpam-5857	1139	3	.	.	PUNCT
ejpam-5857	1140	1	comput	comput	PROPN
ejpam-5857	1140	2	.	.	PUNCT
ejpam-5857	1141	1	inf	inf	PROPN
ejpam-5857	1141	2	.	.	PUNCT
ejpam-5857	1141	3	control	control	PROPN
ejpam-5857	1141	4	,	,	PUNCT
ejpam-5857	1141	5	20(4):1125–1141	20(4):1125–1141	NUM
ejpam-5857	1141	6	,	,	PUNCT
ejpam-5857	1141	7	2024	2024	NUM
ejpam-5857	1141	8	.	.	PUNCT
ejpam-5857	1142	1	[	[	X
ejpam-5857	1142	2	16	16	NUM
ejpam-5857	1142	3	]	]	X
ejpam-5857	1142	4	l.	l.	PROPN
ejpam-5857	1142	5	a.	a.	PROPN
ejpam-5857	1142	6	zadeh	zadeh	PROPN
ejpam-5857	1142	7	.	.	PUNCT
ejpam-5857	1142	8	fuzzy	fuzzy	ADJ
ejpam-5857	1142	9	sets	set	NOUN
ejpam-5857	1142	10	.	.	PUNCT
ejpam-5857	1143	1	inf	inf	PROPN
ejpam-5857	1143	2	.	.	PUNCT
ejpam-5857	1143	3	cont	cont	PROPN
ejpam-5857	1143	4	.	.	PROPN
ejpam-5857	1143	5	,	,	PUNCT
ejpam-5857	1143	6	8(3):338–353	8(3):338–353	NUM
ejpam-5857	1143	7	,	,	PUNCT
ejpam-5857	1143	8	1965	1965	NUM
ejpam-5857	1143	9	.	.	PUNCT