id	sid	tid	token	lemma	pos
ejpam-3543	1	1	european	european	PROPN
ejpam-3543	1	2	journal	journal	PROPN
ejpam-3543	1	3	of	of	ADP
ejpam-3543	1	4	pure	pure	ADJ
ejpam-3543	1	5	and	and	CCONJ
ejpam-3543	1	6	applied	apply	VERB
ejpam-3543	1	7	mathematics	mathematic	NOUN
ejpam-3543	1	8	vol	vol	NOUN
ejpam-3543	1	9	.	.	PROPN
ejpam-3543	2	1	12	12	NUM
ejpam-3543	2	2	,	,	PUNCT
ejpam-3543	2	3	no	no	INTJ
ejpam-3543	2	4	.	.	NOUN
ejpam-3543	2	5	4	4	NUM
ejpam-3543	2	6	,	,	PUNCT
ejpam-3543	2	7	2019	2019	NUM
ejpam-3543	2	8	,	,	PUNCT
ejpam-3543	2	9	1382	1382	NUM
ejpam-3543	2	10	-	-	SYM
ejpam-3543	2	11	1409	1409	NUM
ejpam-3543	2	12	issn	issn	PROPN
ejpam-3543	2	13	1307	1307	NUM
ejpam-3543	2	14	-	-	SYM
ejpam-3543	2	15	5543	5543	NUM
ejpam-3543	2	16	–	–	PUNCT
ejpam-3543	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3543	2	18	published	publish	VERB
ejpam-3543	2	19	by	by	ADP
ejpam-3543	2	20	new	new	PROPN
ejpam-3543	2	21	york	york	PROPN
ejpam-3543	2	22	business	business	PROPN
ejpam-3543	2	23	global	global	PROPN
ejpam-3543	2	24	neutrosophic	neutrosophic	PROPN
ejpam-3543	2	25	set	set	PROPN
ejpam-3543	2	26	theory	theory	NOUN
ejpam-3543	2	27	applied	apply	VERB
ejpam-3543	2	28	to	to	ADP
ejpam-3543	2	29	up	up	ADP
ejpam-3543	2	30	-	-	PUNCT
ejpam-3543	2	31	algebras†	algebras†	NOUN
ejpam-3543	2	32	metawee	metawee	NOUN
ejpam-3543	2	33	songsaeng1	songsaeng1	NOUN
ejpam-3543	2	34	,	,	PUNCT
ejpam-3543	2	35	aiyared	aiyare	VERB
ejpam-3543	2	36	iampan1,∗	iampan1,∗	NOUN
ejpam-3543	2	37	1	1	NUM
ejpam-3543	2	38	department	department	NOUN
ejpam-3543	2	39	of	of	ADP
ejpam-3543	2	40	mathematics	mathematic	NOUN
ejpam-3543	2	41	,	,	PUNCT
ejpam-3543	2	42	school	school	NOUN
ejpam-3543	2	43	of	of	ADP
ejpam-3543	2	44	science	science	NOUN
ejpam-3543	2	45	,	,	PUNCT
ejpam-3543	2	46	university	university	NOUN
ejpam-3543	2	47	of	of	ADP
ejpam-3543	2	48	phayao	phayao	NOUN
ejpam-3543	2	49	,	,	PUNCT
ejpam-3543	2	50	phayao	phayao	NOUN
ejpam-3543	2	51	56000	56000	NUM
ejpam-3543	2	52	,	,	PUNCT
ejpam-3543	2	53	thailand	thailand	PROPN
ejpam-3543	2	54	abstract	abstract	NOUN
ejpam-3543	2	55	.	.	PUNCT
ejpam-3543	3	1	the	the	DET
ejpam-3543	3	2	notions	notion	NOUN
ejpam-3543	3	3	of	of	ADP
ejpam-3543	3	4	neutrosophic	neutrosophic	ADJ
ejpam-3543	3	5	up	up	ADP
ejpam-3543	3	6	-	-	PUNCT
ejpam-3543	3	7	subalgebras	subalgebras	PROPN
ejpam-3543	3	8	,	,	PUNCT
ejpam-3543	3	9	neutrosophic	neutrosophic	ADJ
ejpam-3543	3	10	near	near	ADP
ejpam-3543	3	11	up	up	ADP
ejpam-3543	3	12	-	-	PUNCT
ejpam-3543	3	13	filters	filter	NOUN
ejpam-3543	3	14	,	,	PUNCT
ejpam-3543	3	15	neutrosophic	neutrosophic	ADJ
ejpam-3543	3	16	up	up	ADP
ejpam-3543	3	17	-	-	PUNCT
ejpam-3543	3	18	filters	filter	NOUN
ejpam-3543	3	19	,	,	PUNCT
ejpam-3543	3	20	neutrosophic	neutrosophic	ADJ
ejpam-3543	3	21	up	up	ADP
ejpam-3543	3	22	-	-	PUNCT
ejpam-3543	3	23	ideals	ideal	NOUN
ejpam-3543	3	24	,	,	PUNCT
ejpam-3543	3	25	and	and	CCONJ
ejpam-3543	3	26	neutrosophic	neutrosophic	ADJ
ejpam-3543	3	27	strongly	strongly	ADV
ejpam-3543	3	28	up	up	ADP
ejpam-3543	3	29	-	-	PUNCT
ejpam-3543	3	30	ideals	ideal	NOUN
ejpam-3543	3	31	of	of	ADP
ejpam-3543	3	32	up	up	ADV
ejpam-3543	3	33	-	-	PUNCT
ejpam-3543	3	34	algebras	algebra	NOUN
ejpam-3543	3	35	are	be	AUX
ejpam-3543	3	36	introduced	introduce	VERB
ejpam-3543	3	37	,	,	PUNCT
ejpam-3543	3	38	and	and	CCONJ
ejpam-3543	3	39	several	several	ADJ
ejpam-3543	3	40	properties	property	NOUN
ejpam-3543	3	41	are	be	AUX
ejpam-3543	3	42	investigated	investigate	VERB
ejpam-3543	3	43	.	.	PUNCT
ejpam-3543	4	1	conditions	condition	NOUN
ejpam-3543	4	2	for	for	ADP
ejpam-3543	4	3	neutrosophic	neutrosophic	ADJ
ejpam-3543	4	4	sets	set	NOUN
ejpam-3543	4	5	to	to	PART
ejpam-3543	4	6	be	be	AUX
ejpam-3543	4	7	neutrosophic	neutrosophic	ADJ
ejpam-3543	4	8	up	up	ADP
ejpam-3543	4	9	-	-	PUNCT
ejpam-3543	4	10	subalgebras	subalgebras	PROPN
ejpam-3543	4	11	,	,	PUNCT
ejpam-3543	4	12	neutrosophic	neutrosophic	ADJ
ejpam-3543	4	13	near	near	ADP
ejpam-3543	4	14	up	up	ADP
ejpam-3543	4	15	-	-	PUNCT
ejpam-3543	4	16	filters	filter	NOUN
ejpam-3543	4	17	,	,	PUNCT
ejpam-3543	4	18	neutrosophic	neutrosophic	ADJ
ejpam-3543	4	19	up	up	ADP
ejpam-3543	4	20	-	-	PUNCT
ejpam-3543	4	21	filters	filter	NOUN
ejpam-3543	4	22	,	,	PUNCT
ejpam-3543	4	23	neutrosophic	neutrosophic	ADJ
ejpam-3543	4	24	up	up	ADP
ejpam-3543	4	25	-	-	PUNCT
ejpam-3543	4	26	ideals	ideal	NOUN
ejpam-3543	4	27	,	,	PUNCT
ejpam-3543	4	28	and	and	CCONJ
ejpam-3543	4	29	neutrosophic	neutrosophic	ADJ
ejpam-3543	4	30	strongly	strongly	ADV
ejpam-3543	4	31	up	up	ADP
ejpam-3543	4	32	-	-	PUNCT
ejpam-3543	4	33	ideals	ideal	NOUN
ejpam-3543	4	34	of	of	ADP
ejpam-3543	4	35	up	up	ADV
ejpam-3543	4	36	-	-	PUNCT
ejpam-3543	4	37	algebras	algebra	NOUN
ejpam-3543	4	38	are	be	AUX
ejpam-3543	4	39	provided	provide	VERB
ejpam-3543	4	40	.	.	PUNCT
ejpam-3543	5	1	relations	relation	NOUN
ejpam-3543	5	2	between	between	ADP
ejpam-3543	5	3	neutrosophic	neutrosophic	ADJ
ejpam-3543	5	4	up	up	ADP
ejpam-3543	5	5	-	-	PUNCT
ejpam-3543	5	6	subalgebras	subalgebras	PROPN
ejpam-3543	5	7	(	(	PUNCT
ejpam-3543	5	8	resp	resp	PROPN
ejpam-3543	5	9	.	.	PUNCT
ejpam-3543	5	10	,	,	PUNCT
ejpam-3543	5	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	5	12	near	near	ADP
ejpam-3543	5	13	up	up	ADP
ejpam-3543	5	14	-	-	PUNCT
ejpam-3543	5	15	filters	filter	NOUN
ejpam-3543	5	16	,	,	PUNCT
ejpam-3543	5	17	neutrosophic	neutrosophic	ADJ
ejpam-3543	5	18	up	up	ADP
ejpam-3543	5	19	-	-	PUNCT
ejpam-3543	5	20	filters	filter	NOUN
ejpam-3543	5	21	,	,	PUNCT
ejpam-3543	5	22	neutrosophic	neutrosophic	ADJ
ejpam-3543	5	23	up	up	ADP
ejpam-3543	5	24	-	-	PUNCT
ejpam-3543	5	25	ideals	ideal	NOUN
ejpam-3543	5	26	,	,	PUNCT
ejpam-3543	5	27	neutrosophic	neutrosophic	ADJ
ejpam-3543	5	28	strongly	strongly	ADV
ejpam-3543	5	29	up	up	ADP
ejpam-3543	5	30	-	-	PUNCT
ejpam-3543	5	31	ideals	ideal	NOUN
ejpam-3543	5	32	)	)	PUNCT
ejpam-3543	5	33	and	and	CCONJ
ejpam-3543	5	34	their	their	PRON
ejpam-3543	5	35	level	level	NOUN
ejpam-3543	5	36	subsets	subset	NOUN
ejpam-3543	5	37	are	be	AUX
ejpam-3543	5	38	considered	consider	VERB
ejpam-3543	5	39	.	.	PUNCT
ejpam-3543	6	1	2010	2010	NUM
ejpam-3543	6	2	mathematics	mathematic	NOUN
ejpam-3543	6	3	subject	subject	NOUN
ejpam-3543	6	4	classifications	classification	NOUN
ejpam-3543	6	5	:	:	PUNCT
ejpam-3543	6	6	03g25	03g25	NUM
ejpam-3543	6	7	,	,	PUNCT
ejpam-3543	6	8	03b52	03b52	NUM
ejpam-3543	6	9	,	,	PUNCT
ejpam-3543	6	10	03b60	03b60	NOUN
ejpam-3543	6	11	key	key	ADJ
ejpam-3543	6	12	words	word	NOUN
ejpam-3543	6	13	and	and	CCONJ
ejpam-3543	6	14	phrases	phrase	NOUN
ejpam-3543	6	15	:	:	PUNCT
ejpam-3543	6	16	up	up	ADP
ejpam-3543	6	17	-	-	PUNCT
ejpam-3543	6	18	algebra	algebra	NOUN
ejpam-3543	6	19	,	,	PUNCT
ejpam-3543	6	20	neutrosophic	neutrosophic	ADJ
ejpam-3543	6	21	up	up	ADP
ejpam-3543	6	22	-	-	PUNCT
ejpam-3543	6	23	subalgebra	subalgebra	NOUN
ejpam-3543	6	24	,	,	PUNCT
ejpam-3543	6	25	neutrosophic	neutrosophic	ADJ
ejpam-3543	6	26	near	near	ADP
ejpam-3543	6	27	up	up	ADP
ejpam-3543	6	28	-	-	PUNCT
ejpam-3543	6	29	filter	filter	NOUN
ejpam-3543	6	30	,	,	PUNCT
ejpam-3543	6	31	neutrosophic	neutrosophic	ADJ
ejpam-3543	6	32	up	up	ADV
ejpam-3543	6	33	-	-	PUNCT
ejpam-3543	6	34	filter	filter	NOUN
ejpam-3543	6	35	,	,	PUNCT
ejpam-3543	6	36	neutrosophic	neutrosophic	ADJ
ejpam-3543	6	37	up	up	ADV
ejpam-3543	6	38	-	-	PUNCT
ejpam-3543	6	39	ideal	ideal	ADJ
ejpam-3543	6	40	,	,	PUNCT
ejpam-3543	6	41	neutrosophic	neutrosophic	ADJ
ejpam-3543	6	42	strongly	strongly	ADV
ejpam-3543	6	43	up	up	ADP
ejpam-3543	6	44	-	-	PUNCT
ejpam-3543	6	45	ideal	ideal	NOUN
ejpam-3543	6	46	1	1	NUM
ejpam-3543	6	47	.	.	PUNCT
ejpam-3543	7	1	introduction	introduction	NOUN
ejpam-3543	7	2	among	among	ADP
ejpam-3543	7	3	many	many	ADJ
ejpam-3543	7	4	algebraic	algebraic	ADJ
ejpam-3543	7	5	structures	structure	NOUN
ejpam-3543	7	6	,	,	PUNCT
ejpam-3543	7	7	algebras	algebra	NOUN
ejpam-3543	7	8	of	of	ADP
ejpam-3543	7	9	logic	logic	NOUN
ejpam-3543	7	10	form	form	VERB
ejpam-3543	7	11	important	important	ADJ
ejpam-3543	7	12	class	class	NOUN
ejpam-3543	7	13	of	of	ADP
ejpam-3543	7	14	algebras	algebras	PROPN
ejpam-3543	7	15	.	.	PUNCT
ejpam-3543	8	1	examples	example	NOUN
ejpam-3543	8	2	of	of	ADP
ejpam-3543	8	3	these	these	PRON
ejpam-3543	8	4	are	be	AUX
ejpam-3543	8	5	bck	bck	NOUN
ejpam-3543	8	6	-	-	PUNCT
ejpam-3543	8	7	algebras	algebras	NOUN
ejpam-3543	9	1	[	[	X
ejpam-3543	9	2	7	7	NUM
ejpam-3543	9	3	]	]	PUNCT
ejpam-3543	9	4	,	,	PUNCT
ejpam-3543	9	5	bci	bci	NOUN
ejpam-3543	9	6	-	-	PUNCT
ejpam-3543	9	7	algebras	algebras	X
ejpam-3543	9	8	[	[	X
ejpam-3543	9	9	8	8	NUM
ejpam-3543	9	10	]	]	PUNCT
ejpam-3543	9	11	,	,	PUNCT
ejpam-3543	9	12	bch	bch	NOUN
ejpam-3543	9	13	-	-	PUNCT
ejpam-3543	9	14	algebras	algebras	X
ejpam-3543	9	15	[	[	X
ejpam-3543	9	16	4	4	NUM
ejpam-3543	9	17	]	]	PUNCT
ejpam-3543	9	18	,	,	PUNCT
ejpam-3543	9	19	ku	ku	PROPN
ejpam-3543	9	20	-	-	PUNCT
ejpam-3543	9	21	algebras	algebras	PROPN
ejpam-3543	10	1	[	[	X
ejpam-3543	10	2	18	18	NUM
ejpam-3543	10	3	]	]	PUNCT
ejpam-3543	10	4	,	,	PUNCT
ejpam-3543	10	5	su	su	PROPN
ejpam-3543	10	6	-	-	PUNCT
ejpam-3543	10	7	algebras	algebras	X
ejpam-3543	10	8	[	[	X
ejpam-3543	10	9	13	13	NUM
ejpam-3543	10	10	]	]	X
ejpam-3543	10	11	up	up	ADP
ejpam-3543	10	12	-	-	PUNCT
ejpam-3543	10	13	algebras	algebras	X
ejpam-3543	11	1	[	[	X
ejpam-3543	11	2	5	5	NUM
ejpam-3543	11	3	]	]	PUNCT
ejpam-3543	11	4	and	and	CCONJ
ejpam-3543	11	5	so	so	ADV
ejpam-3543	11	6	on	on	ADV
ejpam-3543	11	7	.	.	PUNCT
ejpam-3543	12	1	they	they	PRON
ejpam-3543	12	2	are	be	AUX
ejpam-3543	12	3	strongly	strongly	ADV
ejpam-3543	12	4	connected	connect	VERB
ejpam-3543	12	5	with	with	ADP
ejpam-3543	12	6	logic	logic	NOUN
ejpam-3543	12	7	.	.	PUNCT
ejpam-3543	13	1	for	for	ADP
ejpam-3543	13	2	example	example	NOUN
ejpam-3543	13	3	,	,	PUNCT
ejpam-3543	13	4	bci	bci	PROPN
ejpam-3543	13	5	-	-	PUNCT
ejpam-3543	13	6	algebras	algebras	PROPN
ejpam-3543	13	7	were	be	AUX
ejpam-3543	13	8	introduced	introduce	VERB
ejpam-3543	13	9	by	by	ADP
ejpam-3543	13	10	iséki	iséki	PROPN
ejpam-3543	14	1	[	[	X
ejpam-3543	14	2	8	8	NUM
ejpam-3543	14	3	]	]	PUNCT
ejpam-3543	14	4	in	in	ADP
ejpam-3543	14	5	1966	1966	NUM
ejpam-3543	14	6	have	have	VERB
ejpam-3543	14	7	connections	connection	NOUN
ejpam-3543	14	8	with	with	ADP
ejpam-3543	14	9	bcilogic	bcilogic	ADJ
ejpam-3543	14	10	being	be	AUX
ejpam-3543	14	11	the	the	DET
ejpam-3543	14	12	bci	bci	NOUN
ejpam-3543	14	13	-	-	NOUN
ejpam-3543	14	14	system	system	NOUN
ejpam-3543	14	15	in	in	ADP
ejpam-3543	14	16	combinatory	combinatory	ADJ
ejpam-3543	14	17	logic	logic	NOUN
ejpam-3543	14	18	which	which	PRON
ejpam-3543	14	19	has	have	VERB
ejpam-3543	14	20	application	application	NOUN
ejpam-3543	14	21	in	in	ADP
ejpam-3543	14	22	the	the	DET
ejpam-3543	14	23	language	language	NOUN
ejpam-3543	14	24	of	of	ADP
ejpam-3543	14	25	functional	functional	ADJ
ejpam-3543	14	26	programming	programming	NOUN
ejpam-3543	14	27	.	.	PUNCT
ejpam-3543	15	1	bck	bck	PROPN
ejpam-3543	15	2	and	and	CCONJ
ejpam-3543	15	3	bci	bci	NOUN
ejpam-3543	15	4	-	-	PUNCT
ejpam-3543	15	5	algebras	algebra	NOUN
ejpam-3543	15	6	are	be	AUX
ejpam-3543	15	7	two	two	NUM
ejpam-3543	15	8	classes	class	NOUN
ejpam-3543	15	9	of	of	ADP
ejpam-3543	15	10	logical	logical	ADJ
ejpam-3543	15	11	algebras	algebra	NOUN
ejpam-3543	15	12	.	.	PUNCT
ejpam-3543	16	1	they	they	PRON
ejpam-3543	16	2	were	be	AUX
ejpam-3543	16	3	introduced	introduce	VERB
ejpam-3543	16	4	by	by	ADP
ejpam-3543	16	5	imai	imai	PROPN
ejpam-3543	16	6	and	and	CCONJ
ejpam-3543	16	7	iséki	iséki	NUM
ejpam-3543	17	1	[	[	X
ejpam-3543	17	2	7	7	NUM
ejpam-3543	17	3	,	,	PUNCT
ejpam-3543	17	4	8	8	NUM
ejpam-3543	17	5	]	]	PUNCT
ejpam-3543	17	6	in	in	ADP
ejpam-3543	17	7	1966	1966	NUM
ejpam-3543	17	8	and	and	CCONJ
ejpam-3543	17	9	have	have	AUX
ejpam-3543	17	10	been	be	AUX
ejpam-3543	17	11	extensively	extensively	ADV
ejpam-3543	17	12	investigated	investigate	VERB
ejpam-3543	17	13	by	by	ADP
ejpam-3543	17	14	many	many	ADJ
ejpam-3543	17	15	researchers	researcher	NOUN
ejpam-3543	17	16	.	.	PUNCT
ejpam-3543	18	1	it	it	PRON
ejpam-3543	18	2	is	be	AUX
ejpam-3543	18	3	known	know	VERB
ejpam-3543	18	4	that	that	SCONJ
ejpam-3543	18	5	the	the	DET
ejpam-3543	18	6	class	class	NOUN
ejpam-3543	18	7	of	of	ADP
ejpam-3543	18	8	bck	bck	PROPN
ejpam-3543	18	9	-	-	PUNCT
ejpam-3543	18	10	algebras	algebras	PROPN
ejpam-3543	18	11	is	be	AUX
ejpam-3543	18	12	a	a	DET
ejpam-3543	18	13	proper	proper	ADJ
ejpam-3543	18	14	subclass	subclass	NOUN
ejpam-3543	18	15	of	of	ADP
ejpam-3543	18	16	the	the	DET
ejpam-3543	18	17	class	class	NOUN
ejpam-3543	18	18	of	of	ADP
ejpam-3543	18	19	bci	bci	PROPN
ejpam-3543	18	20	-	-	PUNCT
ejpam-3543	18	21	algebras	algebras	X
ejpam-3543	18	22	.	.	PUNCT
ejpam-3543	19	1	the	the	DET
ejpam-3543	19	2	above	above	ADV
ejpam-3543	19	3	-	-	PUNCT
ejpam-3543	19	4	mentioned	mention	VERB
ejpam-3543	19	5	section	section	NOUN
ejpam-3543	19	6	has	have	AUX
ejpam-3543	19	7	been	be	AUX
ejpam-3543	19	8	derived	derive	VERB
ejpam-3543	19	9	from	from	ADP
ejpam-3543	19	10	[	[	X
ejpam-3543	19	11	12	12	NUM
ejpam-3543	19	12	]	]	PUNCT
ejpam-3543	19	13	.	.	PUNCT
ejpam-3543	20	1	the	the	DET
ejpam-3543	20	2	branch	branch	NOUN
ejpam-3543	20	3	of	of	ADP
ejpam-3543	20	4	the	the	DET
ejpam-3543	20	5	logical	logical	ADJ
ejpam-3543	20	6	algebra	algebra	NOUN
ejpam-3543	20	7	,	,	PUNCT
ejpam-3543	20	8	up	up	ADP
ejpam-3543	20	9	-	-	PUNCT
ejpam-3543	20	10	algebras	algebras	PROPN
ejpam-3543	20	11	were	be	AUX
ejpam-3543	20	12	introduced	introduce	VERB
ejpam-3543	20	13	by	by	ADP
ejpam-3543	20	14	iampan	iampan	NOUN
ejpam-3543	20	15	[	[	X
ejpam-3543	20	16	5	5	NUM
ejpam-3543	20	17	]	]	PUNCT
ejpam-3543	20	18	.	.	PUNCT
ejpam-3543	21	1	later	later	ADV
ejpam-3543	21	2	somjanta	somjanta	VERB
ejpam-3543	21	3	et	et	PROPN
ejpam-3543	21	4	al	al	PROPN
ejpam-3543	21	5	.	.	PUNCT
ejpam-3543	22	1	[	[	X
ejpam-3543	22	2	23	23	NUM
ejpam-3543	22	3	]	]	PUNCT
ejpam-3543	22	4	studied	study	VERB
ejpam-3543	22	5	fuzzy	fuzzy	ADJ
ejpam-3543	22	6	up	up	ADP
ejpam-3543	22	7	-	-	PUNCT
ejpam-3543	22	8	subalgebras	subalgebras	X
ejpam-3543	22	9	,	,	PUNCT
ejpam-3543	22	10	fuzzy	fuzzy	ADJ
ejpam-3543	22	11	up	up	NOUN
ejpam-3543	22	12	-	-	PUNCT
ejpam-3543	22	13	ideals	ideal	NOUN
ejpam-3543	22	14	and	and	CCONJ
ejpam-3543	22	15	fuzzy	fuzzy	ADJ
ejpam-3543	22	16	up	up	NOUN
ejpam-3543	22	17	-	-	PUNCT
ejpam-3543	22	18	filters	filter	NOUN
ejpam-3543	22	19	of	of	ADP
ejpam-3543	22	20	up	up	ADP
ejpam-3543	22	21	-	-	PUNCT
ejpam-3543	22	22	algebras	algebras	X
ejpam-3543	22	23	.	.	PUNCT
ejpam-3543	23	1	guntasow	guntasow	PROPN
ejpam-3543	23	2	et	et	PROPN
ejpam-3543	23	3	al	al	PROPN
ejpam-3543	23	4	.	.	PUNCT
ejpam-3543	24	1	[	[	X
ejpam-3543	24	2	3	3	NUM
ejpam-3543	24	3	]	]	PUNCT
ejpam-3543	24	4	introduced	introduce	VERB
ejpam-3543	24	5	and	and	CCONJ
ejpam-3543	24	6	studied	study	VERB
ejpam-3543	24	7	fuzzy	fuzzy	ADJ
ejpam-3543	24	8	translations	translation	NOUN
ejpam-3543	24	9	of	of	ADP
ejpam-3543	24	10	a	a	DET
ejpam-3543	24	11	fuzzy	fuzzy	ADJ
ejpam-3543	24	12	set	set	NOUN
ejpam-3543	24	13	in	in	ADP
ejpam-3543	24	14	up	up	ADP
ejpam-3543	24	15	-	-	PUNCT
ejpam-3543	24	16	algebras	algebras	X
ejpam-3543	24	17	.	.	PUNCT
ejpam-3543	25	1	kesorn	kesorn	PROPN
ejpam-3543	25	2	et	et	PROPN
ejpam-3543	25	3	al	al	PROPN
ejpam-3543	25	4	.	.	PUNCT
ejpam-3543	26	1	[	[	X
ejpam-3543	26	2	14	14	NUM
ejpam-3543	26	3	]	]	PUNCT
ejpam-3543	26	4	studied	study	VERB
ejpam-3543	26	5	intuitionistic	intuitionistic	ADJ
ejpam-3543	26	6	fuzzy	fuzzy	ADJ
ejpam-3543	26	7	sets	set	NOUN
ejpam-3543	26	8	in	in	ADP
ejpam-3543	26	9	up	up	ADP
ejpam-3543	26	10	-	-	PUNCT
ejpam-3543	26	11	algebras	algebras	X
ejpam-3543	26	12	.	.	PUNCT
ejpam-3543	27	1	kaijae	kaijae	PROPN
ejpam-3543	27	2	et	et	PROPN
ejpam-3543	27	3	al	al	PROPN
ejpam-3543	27	4	.	.	PUNCT
ejpam-3543	28	1	[	[	X
ejpam-3543	28	2	11	11	NUM
ejpam-3543	28	3	]	]	PUNCT
ejpam-3543	28	4	introduced	introduce	VERB
ejpam-3543	28	5	and	and	CCONJ
ejpam-3543	28	6	investigated	investigate	VERB
ejpam-3543	28	7	anti	anti	ADJ
ejpam-3543	28	8	-	-	ADJ
ejpam-3543	28	9	fuzzy	fuzzy	ADJ
ejpam-3543	28	10	up	up	ADJ
ejpam-3543	28	11	-	-	PUNCT
ejpam-3543	28	12	ideals	ideal	NOUN
ejpam-3543	28	13	and	and	CCONJ
ejpam-3543	28	14	anti	anti	ADJ
ejpam-3543	28	15	-	-	ADJ
ejpam-3543	28	16	fuzzy	fuzzy	ADJ
ejpam-3543	28	17	up	up	ADP
ejpam-3543	28	18	-	-	PUNCT
ejpam-3543	28	19	subalgebras	subalgebras	X
ejpam-3543	28	20	.	.	PUNCT
ejpam-3543	29	1	†this	†this	DET
ejpam-3543	29	2	work	work	NOUN
ejpam-3543	29	3	was	be	AUX
ejpam-3543	29	4	supported	support	VERB
ejpam-3543	29	5	by	by	ADP
ejpam-3543	29	6	the	the	DET
ejpam-3543	29	7	unit	unit	NOUN
ejpam-3543	29	8	of	of	ADP
ejpam-3543	29	9	excellence	excellence	PROPN
ejpam-3543	29	10	,	,	PUNCT
ejpam-3543	29	11	university	university	NOUN
ejpam-3543	29	12	of	of	ADP
ejpam-3543	29	13	phayao	phayao	NOUN
ejpam-3543	29	14	.	.	PUNCT
ejpam-3543	30	1	∗corresponding	∗corresponde	VERB
ejpam-3543	30	2	author	author	NOUN
ejpam-3543	30	3	.	.	PUNCT
ejpam-3543	31	1	doi	doi	NOUN
ejpam-3543	31	2	:	:	PUNCT
ejpam-3543	31	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3543	https://doi.org/10.29020/nybg.ejpam.v12i4.3543	PROPN
ejpam-3543	31	4	email	email	NOUN
ejpam-3543	31	5	addresses	address	NOUN
ejpam-3543	31	6	:	:	PUNCT
ejpam-3543	31	7	metawee.faith@gmail.com	metawee.faith@gmail.com	NOUN
ejpam-3543	31	8	(	(	PUNCT
ejpam-3543	31	9	m.	m.	PROPN
ejpam-3543	31	10	songsaeng	songsaeng	PROPN
ejpam-3543	31	11	)	)	PUNCT
ejpam-3543	31	12	,	,	PUNCT
ejpam-3543	31	13	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-3543	31	14	(	(	PUNCT
ejpam-3543	31	15	a.	a.	NOUN
ejpam-3543	31	16	iampan	iampan	PROPN
ejpam-3543	31	17	)	)	PUNCT
ejpam-3543	31	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3543	31	19	1382	1382	NUM
ejpam-3543	32	1	c	c	X
ejpam-3543	32	2	©	©	PROPN
ejpam-3543	32	3	2019	2019	NUM
ejpam-3543	32	4	ejpam	ejpam	NOUN
ejpam-3543	32	5	all	all	DET
ejpam-3543	32	6	rights	right	NOUN
ejpam-3543	32	7	reserved	reserve	VERB
ejpam-3543	32	8	.	.	PUNCT
ejpam-3543	33	1	m.	m.	PROPN
ejpam-3543	33	2	songsaeng	songsaeng	PROPN
ejpam-3543	33	3	,	,	PUNCT
ejpam-3543	33	4	a.	a.	NOUN
ejpam-3543	33	5	iampan	iampan	PROPN
ejpam-3543	33	6	/	/	SYM
ejpam-3543	33	7	eur	eur	PROPN
ejpam-3543	33	8	.	.	PUNCT
ejpam-3543	34	1	j.	j.	PROPN
ejpam-3543	34	2	pure	pure	PROPN
ejpam-3543	34	3	appl	appl	PROPN
ejpam-3543	34	4	.	.	PROPN
ejpam-3543	34	5	math	math	PROPN
ejpam-3543	34	6	,	,	PUNCT
ejpam-3543	34	7	12	12	NUM
ejpam-3543	34	8	(	(	PUNCT
ejpam-3543	34	9	4	4	NUM
ejpam-3543	34	10	)	)	PUNCT
ejpam-3543	34	11	(	(	PUNCT
ejpam-3543	34	12	2019	2019	NUM
ejpam-3543	34	13	)	)	PUNCT
ejpam-3543	34	14	,	,	PUNCT
ejpam-3543	34	15	1382	1382	NUM
ejpam-3543	34	16	-	-	SYM
ejpam-3543	34	17	1409	1409	NUM
ejpam-3543	34	18	1383	1383	NUM
ejpam-3543	34	19	tanamoon	tanamoon	NOUN
ejpam-3543	34	20	et	et	NOUN
ejpam-3543	34	21	al	al	PROPN
ejpam-3543	34	22	.	.	PUNCT
ejpam-3543	35	1	[	[	X
ejpam-3543	35	2	26	26	NUM
ejpam-3543	35	3	]	]	PUNCT
ejpam-3543	35	4	introduced	introduce	VERB
ejpam-3543	35	5	and	and	CCONJ
ejpam-3543	35	6	studied	study	VERB
ejpam-3543	35	7	q	q	ADJ
ejpam-3543	35	8	-	-	PUNCT
ejpam-3543	35	9	fuzzy	fuzzy	ADJ
ejpam-3543	35	10	sets	set	NOUN
ejpam-3543	35	11	in	in	ADP
ejpam-3543	35	12	up	up	ADP
ejpam-3543	35	13	-	-	PUNCT
ejpam-3543	35	14	algebras	algebras	X
ejpam-3543	35	15	.	.	PUNCT
ejpam-3543	36	1	sripaeng	sripaeng	PROPN
ejpam-3543	36	2	et	et	PROPN
ejpam-3543	36	3	al	al	PROPN
ejpam-3543	36	4	.	.	PUNCT
ejpam-3543	37	1	[	[	X
ejpam-3543	37	2	25	25	NUM
ejpam-3543	37	3	]	]	PUNCT
ejpam-3543	37	4	studied	study	VERB
ejpam-3543	37	5	anti	anti	ADJ
ejpam-3543	37	6	q	q	ADJ
ejpam-3543	37	7	-	-	ADJ
ejpam-3543	37	8	fuzzy	fuzzy	ADJ
ejpam-3543	37	9	up	up	NOUN
ejpam-3543	37	10	-	-	PUNCT
ejpam-3543	37	11	ideals	ideal	NOUN
ejpam-3543	37	12	and	and	CCONJ
ejpam-3543	37	13	anti	anti	ADJ
ejpam-3543	37	14	q	q	ADJ
ejpam-3543	37	15	-	-	ADJ
ejpam-3543	37	16	fuzzy	fuzzy	ADJ
ejpam-3543	37	17	up	up	ADP
ejpam-3543	37	18	-	-	PUNCT
ejpam-3543	37	19	subalgebras	subalgebra	NOUN
ejpam-3543	37	20	of	of	ADP
ejpam-3543	37	21	up	up	ADP
ejpam-3543	37	22	-	-	PUNCT
ejpam-3543	37	23	algebras	algebras	X
ejpam-3543	37	24	.	.	PUNCT
ejpam-3543	38	1	dokkhamdang	dokkhamdang	PROPN
ejpam-3543	38	2	et	et	PROPN
ejpam-3543	38	3	al	al	PROPN
ejpam-3543	38	4	.	.	PUNCT
ejpam-3543	39	1	[	[	X
ejpam-3543	39	2	2	2	NUM
ejpam-3543	39	3	]	]	PUNCT
ejpam-3543	39	4	studied	study	VERB
ejpam-3543	39	5	generalized	generalized	ADJ
ejpam-3543	39	6	fuzzy	fuzzy	ADJ
ejpam-3543	39	7	sets	set	NOUN
ejpam-3543	39	8	in	in	ADP
ejpam-3543	39	9	up	up	ADP
ejpam-3543	39	10	-	-	PUNCT
ejpam-3543	39	11	algebras	algebras	X
ejpam-3543	39	12	.	.	PUNCT
ejpam-3543	40	1	songsaeng	songsaeng	PROPN
ejpam-3543	40	2	and	and	CCONJ
ejpam-3543	40	3	iampan	iampan	PROPN
ejpam-3543	40	4	[	[	X
ejpam-3543	40	5	24	24	NUM
ejpam-3543	40	6	]	]	PUNCT
ejpam-3543	40	7	studied	study	VERB
ejpam-3543	40	8	n	n	PRON
ejpam-3543	40	9	-fuzzy	-fuzzy	NOUN
ejpam-3543	40	10	up	up	ADV
ejpam-3543	40	11	-	-	PUNCT
ejpam-3543	40	12	algebras	algebra	NOUN
ejpam-3543	40	13	and	and	CCONJ
ejpam-3543	40	14	their	their	PRON
ejpam-3543	40	15	level	level	NOUN
ejpam-3543	40	16	subsets	subset	NOUN
ejpam-3543	40	17	.	.	PUNCT
ejpam-3543	41	1	the	the	DET
ejpam-3543	41	2	notion	notion	NOUN
ejpam-3543	41	3	of	of	ADP
ejpam-3543	41	4	neutrosophic	neutrosophic	ADJ
ejpam-3543	41	5	sets	set	NOUN
ejpam-3543	41	6	was	be	AUX
ejpam-3543	41	7	introduced	introduce	VERB
ejpam-3543	41	8	by	by	ADP
ejpam-3543	41	9	smarandache	smarandache	NOUN
ejpam-3543	42	1	[	[	X
ejpam-3543	42	2	22	22	NUM
ejpam-3543	42	3	]	]	PUNCT
ejpam-3543	42	4	in	in	ADP
ejpam-3543	42	5	1999	1999	NUM
ejpam-3543	42	6	.	.	PUNCT
ejpam-3543	43	1	wang	wang	PROPN
ejpam-3543	43	2	et	et	PROPN
ejpam-3543	43	3	al	al	PROPN
ejpam-3543	43	4	.	.	PUNCT
ejpam-3543	44	1	[	[	X
ejpam-3543	44	2	28	28	NUM
ejpam-3543	44	3	]	]	PUNCT
ejpam-3543	44	4	introduced	introduce	VERB
ejpam-3543	44	5	the	the	DET
ejpam-3543	44	6	notion	notion	NOUN
ejpam-3543	44	7	of	of	ADP
ejpam-3543	44	8	interval	interval	NOUN
ejpam-3543	44	9	neutrosophic	neutrosophic	ADJ
ejpam-3543	44	10	sets	set	NOUN
ejpam-3543	44	11	in	in	ADP
ejpam-3543	44	12	2005	2005	NUM
ejpam-3543	44	13	.	.	PUNCT
ejpam-3543	45	1	the	the	DET
ejpam-3543	45	2	notion	notion	NOUN
ejpam-3543	45	3	of	of	ADP
ejpam-3543	45	4	neutrosophic	neutrosophic	ADJ
ejpam-3543	45	5	n	n	PRON
ejpam-3543	45	6	-structures	-structure	NOUN
ejpam-3543	45	7	and	and	CCONJ
ejpam-3543	45	8	their	their	PRON
ejpam-3543	45	9	applications	application	NOUN
ejpam-3543	45	10	in	in	ADP
ejpam-3543	45	11	semigroups	semigroup	NOUN
ejpam-3543	45	12	was	be	AUX
ejpam-3543	45	13	introduced	introduce	VERB
ejpam-3543	45	14	by	by	ADP
ejpam-3543	45	15	khan	khan	PROPN
ejpam-3543	45	16	et	et	PROPN
ejpam-3543	45	17	al	al	PROPN
ejpam-3543	45	18	.	.	PUNCT
ejpam-3543	46	1	[	[	X
ejpam-3543	46	2	15	15	NUM
ejpam-3543	46	3	]	]	X
ejpam-3543	46	4	in	in	ADP
ejpam-3543	46	5	2017	2017	NUM
ejpam-3543	46	6	.	.	PUNCT
ejpam-3543	47	1	jun	jun	PROPN
ejpam-3543	47	2	et	et	PROPN
ejpam-3543	47	3	al	al	PROPN
ejpam-3543	47	4	.	.	PUNCT
ejpam-3543	48	1	[	[	X
ejpam-3543	48	2	9	9	NUM
ejpam-3543	48	3	]	]	PUNCT
ejpam-3543	48	4	applied	apply	VERB
ejpam-3543	48	5	the	the	DET
ejpam-3543	48	6	notion	notion	NOUN
ejpam-3543	48	7	of	of	ADP
ejpam-3543	48	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	48	9	n	n	PART
ejpam-3543	48	10	-structures	-structure	NOUN
ejpam-3543	48	11	to	to	PART
ejpam-3543	48	12	bck	bck	VERB
ejpam-3543	48	13	/	/	SYM
ejpam-3543	48	14	bcialgebras	bcialgebra	NOUN
ejpam-3543	48	15	in	in	ADP
ejpam-3543	48	16	2017	2017	NUM
ejpam-3543	48	17	.	.	PUNCT
ejpam-3543	49	1	khan	khan	PROPN
ejpam-3543	49	2	et	et	PROPN
ejpam-3543	49	3	al	al	PROPN
ejpam-3543	49	4	.	.	PUNCT
ejpam-3543	50	1	[	[	X
ejpam-3543	50	2	15	15	NUM
ejpam-3543	50	3	]	]	PUNCT
ejpam-3543	50	4	discussed	discuss	VERB
ejpam-3543	50	5	neutrosophic	neutrosophic	ADJ
ejpam-3543	50	6	n	n	PRON
ejpam-3543	50	7	-structures	-structure	NOUN
ejpam-3543	50	8	and	and	CCONJ
ejpam-3543	50	9	their	their	PRON
ejpam-3543	50	10	applications	application	NOUN
ejpam-3543	50	11	in	in	ADP
ejpam-3543	50	12	semigroups	semigroup	NOUN
ejpam-3543	50	13	in	in	ADP
ejpam-3543	50	14	2017	2017	NUM
ejpam-3543	50	15	.	.	PUNCT
ejpam-3543	51	1	jun	jun	PROPN
ejpam-3543	51	2	et	et	PROPN
ejpam-3543	51	3	al	al	PROPN
ejpam-3543	51	4	.	.	PUNCT
ejpam-3543	52	1	[	[	X
ejpam-3543	52	2	10	10	NUM
ejpam-3543	52	3	]	]	PUNCT
ejpam-3543	52	4	studied	study	VERB
ejpam-3543	52	5	neutrosophic	neutrosophic	ADJ
ejpam-3543	52	6	positive	positive	ADJ
ejpam-3543	52	7	implicative	implicative	ADJ
ejpam-3543	52	8	n	n	PRON
ejpam-3543	52	9	-ideals	-ideal	NOUN
ejpam-3543	52	10	in	in	ADP
ejpam-3543	52	11	bck	bck	NOUN
ejpam-3543	52	12	-	-	PUNCT
ejpam-3543	52	13	algebras	algebras	PROPN
ejpam-3543	52	14	in	in	ADP
ejpam-3543	52	15	2018	2018	NUM
ejpam-3543	52	16	.	.	PUNCT
ejpam-3543	53	1	kim	kim	PROPN
ejpam-3543	53	2	et	et	PROPN
ejpam-3543	53	3	al	al	PROPN
ejpam-3543	53	4	.	.	PUNCT
ejpam-3543	54	1	[	[	X
ejpam-3543	54	2	16	16	NUM
ejpam-3543	54	3	]	]	PUNCT
ejpam-3543	54	4	studied	study	VERB
ejpam-3543	54	5	generalizations	generalization	NOUN
ejpam-3543	54	6	of	of	ADP
ejpam-3543	54	7	neutrosophic	neutrosophic	ADJ
ejpam-3543	54	8	subalgebras	subalgebra	NOUN
ejpam-3543	54	9	in	in	ADP
ejpam-3543	54	10	bck	bck	PROPN
ejpam-3543	54	11	/	/	SYM
ejpam-3543	54	12	bci	bci	NOUN
ejpam-3543	54	13	-	-	PUNCT
ejpam-3543	54	14	algebras	algebras	PROPN
ejpam-3543	54	15	based	base	VERB
ejpam-3543	54	16	on	on	ADP
ejpam-3543	54	17	neutrosophic	neutrosophic	ADJ
ejpam-3543	54	18	points	point	NOUN
ejpam-3543	54	19	in	in	ADP
ejpam-3543	54	20	2018	2018	NUM
ejpam-3543	54	21	.	.	PUNCT
ejpam-3543	55	1	rangsuk	rangsuk	NOUN
ejpam-3543	55	2	et	et	PROPN
ejpam-3543	55	3	al	al	PROPN
ejpam-3543	55	4	.	.	PUNCT
ejpam-3543	56	1	[	[	X
ejpam-3543	56	2	19	19	NUM
ejpam-3543	56	3	]	]	PUNCT
ejpam-3543	56	4	introduced	introduce	VERB
ejpam-3543	56	5	the	the	DET
ejpam-3543	56	6	notions	notion	NOUN
ejpam-3543	56	7	of	of	ADP
ejpam-3543	56	8	(	(	PUNCT
ejpam-3543	56	9	special	special	ADJ
ejpam-3543	56	10	)	)	PUNCT
ejpam-3543	56	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	56	12	n	n	CCONJ
ejpam-3543	56	13	-up	-up	NOUN
ejpam-3543	56	14	-	-	NOUN
ejpam-3543	56	15	subalgebras	subalgebras	X
ejpam-3543	56	16	,	,	PUNCT
ejpam-3543	56	17	(	(	PUNCT
ejpam-3543	56	18	special	special	ADJ
ejpam-3543	56	19	)	)	PUNCT
ejpam-3543	56	20	neutrosophic	neutrosophic	ADJ
ejpam-3543	56	21	n	n	CCONJ
ejpam-3543	56	22	-near	-near	NOUN
ejpam-3543	56	23	up	up	ADP
ejpam-3543	56	24	-	-	PUNCT
ejpam-3543	56	25	filters	filter	NOUN
ejpam-3543	56	26	,	,	PUNCT
ejpam-3543	56	27	(	(	PUNCT
ejpam-3543	56	28	special	special	ADJ
ejpam-3543	56	29	)	)	PUNCT
ejpam-3543	56	30	neutrosophic	neutrosophic	ADJ
ejpam-3543	56	31	n	n	CCONJ
ejpam-3543	56	32	-up	-up	NOUN
ejpam-3543	56	33	-	-	NOUN
ejpam-3543	56	34	filters	filter	NOUN
ejpam-3543	56	35	,	,	PUNCT
ejpam-3543	56	36	(	(	PUNCT
ejpam-3543	56	37	special	special	ADJ
ejpam-3543	56	38	)	)	PUNCT
ejpam-3543	56	39	neutrosophic	neutrosophic	ADJ
ejpam-3543	56	40	n	n	CCONJ
ejpam-3543	56	41	-up	-up	NOUN
ejpam-3543	56	42	-	-	NOUN
ejpam-3543	56	43	ideals	ideal	NOUN
ejpam-3543	56	44	,	,	PUNCT
ejpam-3543	56	45	and	and	CCONJ
ejpam-3543	56	46	(	(	PUNCT
ejpam-3543	56	47	special	special	ADJ
ejpam-3543	56	48	)	)	PUNCT
ejpam-3543	56	49	neutrosophic	neutrosophic	ADJ
ejpam-3543	56	50	n	n	ADP
ejpam-3543	56	51	-strongly	-strongly	ADV
ejpam-3543	56	52	up	up	ADP
ejpam-3543	56	53	-	-	PUNCT
ejpam-3543	56	54	ideals	ideal	NOUN
ejpam-3543	56	55	of	of	ADP
ejpam-3543	56	56	up	up	ADV
ejpam-3543	56	57	-	-	PUNCT
ejpam-3543	56	58	algebras	algebras	NOUN
ejpam-3543	56	59	in	in	ADP
ejpam-3543	56	60	2019	2019	NUM
ejpam-3543	56	61	.	.	PUNCT
ejpam-3543	57	1	in	in	ADP
ejpam-3543	57	2	this	this	DET
ejpam-3543	57	3	paper	paper	NOUN
ejpam-3543	57	4	,	,	PUNCT
ejpam-3543	57	5	the	the	DET
ejpam-3543	57	6	notions	notion	NOUN
ejpam-3543	57	7	of	of	ADP
ejpam-3543	57	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	57	9	up	up	ADP
ejpam-3543	57	10	-	-	PUNCT
ejpam-3543	57	11	subalgebras	subalgebras	PROPN
ejpam-3543	57	12	,	,	PUNCT
ejpam-3543	57	13	neutrosophic	neutrosophic	ADJ
ejpam-3543	57	14	near	near	ADP
ejpam-3543	57	15	upfilters	upfilter	NOUN
ejpam-3543	57	16	,	,	PUNCT
ejpam-3543	57	17	neutrosophic	neutrosophic	ADJ
ejpam-3543	57	18	up	up	ADP
ejpam-3543	57	19	-	-	PUNCT
ejpam-3543	57	20	filters	filter	NOUN
ejpam-3543	57	21	,	,	PUNCT
ejpam-3543	57	22	neutrosophic	neutrosophic	ADJ
ejpam-3543	57	23	up	up	ADP
ejpam-3543	57	24	-	-	PUNCT
ejpam-3543	57	25	ideals	ideal	NOUN
ejpam-3543	57	26	,	,	PUNCT
ejpam-3543	57	27	and	and	CCONJ
ejpam-3543	57	28	neutrosophic	neutrosophic	ADJ
ejpam-3543	57	29	strongly	strongly	ADV
ejpam-3543	57	30	upideals	upideal	NOUN
ejpam-3543	57	31	of	of	ADP
ejpam-3543	57	32	up	up	ADV
ejpam-3543	57	33	-	-	PUNCT
ejpam-3543	57	34	algebras	algebra	NOUN
ejpam-3543	57	35	are	be	AUX
ejpam-3543	57	36	introduced	introduce	VERB
ejpam-3543	57	37	,	,	PUNCT
ejpam-3543	57	38	and	and	CCONJ
ejpam-3543	57	39	several	several	ADJ
ejpam-3543	57	40	properties	property	NOUN
ejpam-3543	57	41	are	be	AUX
ejpam-3543	57	42	investigated	investigate	VERB
ejpam-3543	57	43	.	.	PUNCT
ejpam-3543	58	1	conditions	condition	NOUN
ejpam-3543	58	2	for	for	ADP
ejpam-3543	58	3	neutrosophic	neutrosophic	ADJ
ejpam-3543	58	4	sets	set	NOUN
ejpam-3543	58	5	to	to	PART
ejpam-3543	58	6	be	be	AUX
ejpam-3543	58	7	neutrosophic	neutrosophic	ADJ
ejpam-3543	58	8	up	up	ADP
ejpam-3543	58	9	-	-	PUNCT
ejpam-3543	58	10	subalgebras	subalgebras	PROPN
ejpam-3543	58	11	,	,	PUNCT
ejpam-3543	58	12	neutrosophic	neutrosophic	ADJ
ejpam-3543	58	13	near	near	ADP
ejpam-3543	58	14	up	up	ADP
ejpam-3543	58	15	-	-	PUNCT
ejpam-3543	58	16	filters	filter	NOUN
ejpam-3543	58	17	,	,	PUNCT
ejpam-3543	58	18	neutrosophic	neutrosophic	ADJ
ejpam-3543	58	19	up	up	ADP
ejpam-3543	58	20	-	-	PUNCT
ejpam-3543	58	21	filters	filter	NOUN
ejpam-3543	58	22	,	,	PUNCT
ejpam-3543	58	23	neutrosophic	neutrosophic	ADJ
ejpam-3543	58	24	up	up	ADP
ejpam-3543	58	25	-	-	PUNCT
ejpam-3543	58	26	ideals	ideal	NOUN
ejpam-3543	58	27	,	,	PUNCT
ejpam-3543	58	28	and	and	CCONJ
ejpam-3543	58	29	neutrosophic	neutrosophic	ADJ
ejpam-3543	58	30	strongly	strongly	ADV
ejpam-3543	58	31	up	up	ADP
ejpam-3543	58	32	-	-	PUNCT
ejpam-3543	58	33	ideals	ideal	NOUN
ejpam-3543	58	34	of	of	ADP
ejpam-3543	58	35	up	up	ADV
ejpam-3543	58	36	-	-	PUNCT
ejpam-3543	58	37	algebras	algebra	NOUN
ejpam-3543	58	38	are	be	AUX
ejpam-3543	58	39	provided	provide	VERB
ejpam-3543	58	40	.	.	PUNCT
ejpam-3543	59	1	relations	relation	NOUN
ejpam-3543	59	2	between	between	ADP
ejpam-3543	59	3	neutrosophic	neutrosophic	ADJ
ejpam-3543	59	4	up	up	ADP
ejpam-3543	59	5	-	-	PUNCT
ejpam-3543	59	6	subalgebras	subalgebras	PROPN
ejpam-3543	59	7	(	(	PUNCT
ejpam-3543	59	8	resp	resp	PROPN
ejpam-3543	59	9	.	.	PUNCT
ejpam-3543	59	10	,	,	PUNCT
ejpam-3543	59	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	59	12	near	near	ADP
ejpam-3543	59	13	up	up	ADP
ejpam-3543	59	14	-	-	PUNCT
ejpam-3543	59	15	filters	filter	NOUN
ejpam-3543	59	16	,	,	PUNCT
ejpam-3543	59	17	neutrosophic	neutrosophic	ADJ
ejpam-3543	59	18	up	up	ADP
ejpam-3543	59	19	-	-	PUNCT
ejpam-3543	59	20	filters	filter	NOUN
ejpam-3543	59	21	,	,	PUNCT
ejpam-3543	59	22	neutrosophic	neutrosophic	ADJ
ejpam-3543	59	23	up	up	ADP
ejpam-3543	59	24	-	-	PUNCT
ejpam-3543	59	25	ideals	ideal	NOUN
ejpam-3543	59	26	,	,	PUNCT
ejpam-3543	59	27	neutrosophic	neutrosophic	ADJ
ejpam-3543	59	28	strongly	strongly	ADV
ejpam-3543	59	29	up	up	ADP
ejpam-3543	59	30	-	-	PUNCT
ejpam-3543	59	31	ideals	ideal	NOUN
ejpam-3543	59	32	)	)	PUNCT
ejpam-3543	59	33	and	and	CCONJ
ejpam-3543	59	34	their	their	PRON
ejpam-3543	59	35	level	level	NOUN
ejpam-3543	59	36	subsets	subset	NOUN
ejpam-3543	59	37	are	be	AUX
ejpam-3543	59	38	considered	consider	VERB
ejpam-3543	59	39	.	.	PUNCT
ejpam-3543	60	1	2	2	X
ejpam-3543	60	2	.	.	X
ejpam-3543	60	3	basic	basic	ADJ
ejpam-3543	60	4	results	result	NOUN
ejpam-3543	60	5	on	on	ADP
ejpam-3543	60	6	up	up	ADV
ejpam-3543	60	7	-	-	PUNCT
ejpam-3543	60	8	algebras	algebra	NOUN
ejpam-3543	60	9	before	before	SCONJ
ejpam-3543	60	10	we	we	PRON
ejpam-3543	60	11	begin	begin	VERB
ejpam-3543	60	12	our	our	PRON
ejpam-3543	60	13	study	study	NOUN
ejpam-3543	60	14	,	,	PUNCT
ejpam-3543	60	15	we	we	PRON
ejpam-3543	60	16	will	will	AUX
ejpam-3543	60	17	give	give	VERB
ejpam-3543	60	18	the	the	DET
ejpam-3543	60	19	definition	definition	NOUN
ejpam-3543	60	20	and	and	CCONJ
ejpam-3543	60	21	useful	useful	ADJ
ejpam-3543	60	22	properties	property	NOUN
ejpam-3543	60	23	of	of	ADP
ejpam-3543	60	24	upalgebras	upalgebra	NOUN
ejpam-3543	60	25	.	.	PUNCT
ejpam-3543	61	1	definition	definition	NOUN
ejpam-3543	61	2	1	1	NUM
ejpam-3543	61	3	.	.	PUNCT
ejpam-3543	62	1	[	[	X
ejpam-3543	62	2	5	5	X
ejpam-3543	62	3	]	]	PUNCT
ejpam-3543	62	4	an	an	DET
ejpam-3543	62	5	algebra	algebra	NOUN
ejpam-3543	62	6	x	x	X
ejpam-3543	62	7	=	=	SYM
ejpam-3543	62	8	(	(	PUNCT
ejpam-3543	62	9	x	x	NOUN
ejpam-3543	62	10	,	,	PUNCT
ejpam-3543	62	11	·	·	PUNCT
ejpam-3543	62	12	,	,	PUNCT
ejpam-3543	62	13	0	0	NUM
ejpam-3543	62	14	)	)	PUNCT
ejpam-3543	62	15	of	of	ADP
ejpam-3543	62	16	type	type	NOUN
ejpam-3543	62	17	(	(	PUNCT
ejpam-3543	62	18	2	2	NUM
ejpam-3543	62	19	,	,	PUNCT
ejpam-3543	62	20	0	0	NUM
ejpam-3543	62	21	)	)	PUNCT
ejpam-3543	62	22	is	be	AUX
ejpam-3543	62	23	called	call	VERB
ejpam-3543	62	24	a	a	DET
ejpam-3543	62	25	up	up	NOUN
ejpam-3543	62	26	-	-	PUNCT
ejpam-3543	62	27	algebra	algebra	NOUN
ejpam-3543	62	28	where	where	SCONJ
ejpam-3543	62	29	x	x	PRON
ejpam-3543	62	30	is	be	AUX
ejpam-3543	62	31	a	a	DET
ejpam-3543	62	32	nonempty	nonempty	ADJ
ejpam-3543	62	33	set	set	VERB
ejpam-3543	62	34	,	,	PUNCT
ejpam-3543	62	35	·	·	PUNCT
ejpam-3543	62	36	is	be	AUX
ejpam-3543	62	37	a	a	DET
ejpam-3543	62	38	binary	binary	ADJ
ejpam-3543	62	39	operation	operation	NOUN
ejpam-3543	62	40	on	on	ADP
ejpam-3543	62	41	x	x	NOUN
ejpam-3543	62	42	,	,	PUNCT
ejpam-3543	62	43	and	and	CCONJ
ejpam-3543	62	44	0	0	NUM
ejpam-3543	62	45	is	be	AUX
ejpam-3543	62	46	a	a	DET
ejpam-3543	62	47	fixed	fix	VERB
ejpam-3543	62	48	element	element	NOUN
ejpam-3543	62	49	of	of	ADP
ejpam-3543	62	50	x	x	X
ejpam-3543	62	51	(	(	PUNCT
ejpam-3543	62	52	i.e.	i.e.	X
ejpam-3543	62	53	,	,	PUNCT
ejpam-3543	62	54	a	a	DET
ejpam-3543	62	55	nullary	nullary	ADJ
ejpam-3543	62	56	operation	operation	NOUN
ejpam-3543	62	57	)	)	PUNCT
ejpam-3543	62	58	if	if	SCONJ
ejpam-3543	62	59	it	it	PRON
ejpam-3543	62	60	satisfies	satisfy	VERB
ejpam-3543	62	61	the	the	DET
ejpam-3543	62	62	following	follow	VERB
ejpam-3543	62	63	axioms	axiom	NOUN
ejpam-3543	62	64	:	:	PUNCT
ejpam-3543	62	65	(	(	PUNCT
ejpam-3543	62	66	up-1	up-1	NOUN
ejpam-3543	62	67	)	)	PUNCT
ejpam-3543	62	68	(	(	PUNCT
ejpam-3543	62	69	∀x	∀x	X
ejpam-3543	62	70	,	,	PUNCT
ejpam-3543	62	71	y	y	PROPN
ejpam-3543	62	72	,	,	PUNCT
ejpam-3543	62	73	z	z	PROPN
ejpam-3543	62	74	∈	∈	PROPN
ejpam-3543	62	75	x)((y	x)((y	PROPN
ejpam-3543	62	76	·	·	PUNCT
ejpam-3543	63	1	z	z	X
ejpam-3543	63	2	)	)	PUNCT
ejpam-3543	63	3	·	·	PUNCT
ejpam-3543	63	4	(	(	PUNCT
ejpam-3543	63	5	(	(	PUNCT
ejpam-3543	63	6	x	x	SYM
ejpam-3543	63	7	·	·	PUNCT
ejpam-3543	63	8	y	y	X
ejpam-3543	63	9	)	)	PUNCT
ejpam-3543	63	10	·	·	PUNCT
ejpam-3543	64	1	(	(	PUNCT
ejpam-3543	64	2	x	x	X
ejpam-3543	64	3	·	·	PUNCT
ejpam-3543	64	4	z	z	NOUN
ejpam-3543	64	5	)	)	PUNCT
ejpam-3543	64	6	)	)	PUNCT
ejpam-3543	65	1	=	=	PUNCT
ejpam-3543	65	2	0	0	NUM
ejpam-3543	65	3	)	)	PUNCT
ejpam-3543	65	4	,	,	PUNCT
ejpam-3543	65	5	(	(	PUNCT
ejpam-3543	65	6	up-2	up-2	NUM
ejpam-3543	65	7	)	)	PUNCT
ejpam-3543	65	8	(	(	PUNCT
ejpam-3543	65	9	∀x	∀x	X
ejpam-3543	65	10	∈	∈	NOUN
ejpam-3543	65	11	x)(0	x)(0	X
ejpam-3543	65	12	·	·	PUNCT
ejpam-3543	66	1	x	x	PUNCT
ejpam-3543	66	2	=	=	PUNCT
ejpam-3543	66	3	x	x	NOUN
ejpam-3543	66	4	)	)	PUNCT
ejpam-3543	66	5	,	,	PUNCT
ejpam-3543	66	6	(	(	PUNCT
ejpam-3543	66	7	up-3	up-3	NOUN
ejpam-3543	66	8	)	)	PUNCT
ejpam-3543	66	9	(	(	PUNCT
ejpam-3543	66	10	∀x	∀x	X
ejpam-3543	66	11	∈	∈	PROPN
ejpam-3543	66	12	x)(x	x)(x	PROPN
ejpam-3543	66	13	·	·	PUNCT
ejpam-3543	66	14	0	0	PUNCT
ejpam-3543	67	1	=	=	SYM
ejpam-3543	67	2	0	0	NUM
ejpam-3543	67	3	)	)	PUNCT
ejpam-3543	67	4	,	,	PUNCT
ejpam-3543	67	5	and	and	CCONJ
ejpam-3543	67	6	(	(	PUNCT
ejpam-3543	67	7	up-4	up-4	ADV
ejpam-3543	67	8	)	)	PUNCT
ejpam-3543	67	9	(	(	PUNCT
ejpam-3543	67	10	∀x	∀x	X
ejpam-3543	67	11	,	,	PUNCT
ejpam-3543	67	12	y	y	PROPN
ejpam-3543	67	13	∈	∈	PROPN
ejpam-3543	67	14	x)(x	x)(x	PROPN
ejpam-3543	67	15	·	·	PUNCT
ejpam-3543	67	16	y	y	X
ejpam-3543	67	17	=	=	SYM
ejpam-3543	67	18	0	0	PROPN
ejpam-3543	67	19	,	,	PUNCT
ejpam-3543	67	20	y	y	PROPN
ejpam-3543	67	21	·	·	PUNCT
ejpam-3543	67	22	x	x	PUNCT
ejpam-3543	68	1	=	=	PUNCT
ejpam-3543	68	2	0⇒	0⇒	NUM
ejpam-3543	68	3	x	x	X
ejpam-3543	69	1	=	=	SYM
ejpam-3543	69	2	y	y	PROPN
ejpam-3543	69	3	)	)	PUNCT
ejpam-3543	69	4	.	.	PUNCT
ejpam-3543	70	1	from	from	ADP
ejpam-3543	70	2	[	[	X
ejpam-3543	70	3	5	5	NUM
ejpam-3543	70	4	]	]	PUNCT
ejpam-3543	70	5	,	,	PUNCT
ejpam-3543	70	6	we	we	PRON
ejpam-3543	70	7	know	know	VERB
ejpam-3543	70	8	that	that	SCONJ
ejpam-3543	70	9	the	the	DET
ejpam-3543	70	10	notion	notion	NOUN
ejpam-3543	70	11	of	of	ADP
ejpam-3543	70	12	up	up	ADV
ejpam-3543	70	13	-	-	PUNCT
ejpam-3543	70	14	algebras	algebras	PROPN
ejpam-3543	70	15	is	be	AUX
ejpam-3543	70	16	a	a	DET
ejpam-3543	70	17	generalization	generalization	NOUN
ejpam-3543	70	18	of	of	ADP
ejpam-3543	70	19	ku	ku	PROPN
ejpam-3543	70	20	-	-	PUNCT
ejpam-3543	70	21	algebras	algebras	PROPN
ejpam-3543	70	22	(	(	PUNCT
ejpam-3543	70	23	see	see	VERB
ejpam-3543	70	24	[	[	X
ejpam-3543	70	25	18	18	NUM
ejpam-3543	70	26	]	]	NUM
ejpam-3543	70	27	)	)	PUNCT
ejpam-3543	70	28	.	.	PUNCT
ejpam-3543	71	1	example	example	NOUN
ejpam-3543	72	1	1	1	NUM
ejpam-3543	72	2	.	.	PUNCT
ejpam-3543	73	1	[	[	X
ejpam-3543	73	2	21	21	NUM
ejpam-3543	73	3	]	]	X
ejpam-3543	73	4	let	let	VERB
ejpam-3543	73	5	x	x	PRON
ejpam-3543	73	6	be	be	AUX
ejpam-3543	73	7	a	a	DET
ejpam-3543	73	8	universal	universal	ADJ
ejpam-3543	73	9	set	set	NOUN
ejpam-3543	73	10	and	and	CCONJ
ejpam-3543	73	11	let	let	VERB
ejpam-3543	73	12	ω	ω	NUM
ejpam-3543	73	13	∈	∈	PROPN
ejpam-3543	73	14	p(x	p(x	PROPN
ejpam-3543	73	15	)	)	PUNCT
ejpam-3543	73	16	where	where	SCONJ
ejpam-3543	73	17	p(x	p(x	NOUN
ejpam-3543	73	18	)	)	PUNCT
ejpam-3543	73	19	means	mean	VERB
ejpam-3543	73	20	the	the	DET
ejpam-3543	73	21	power	power	NOUN
ejpam-3543	73	22	set	set	NOUN
ejpam-3543	73	23	of	of	ADP
ejpam-3543	73	24	x.	x.	NOUN
ejpam-3543	73	25	let	let	VERB
ejpam-3543	73	26	pω(x	pω(x	X
ejpam-3543	73	27	)	)	PUNCT
ejpam-3543	73	28	=	=	SYM
ejpam-3543	73	29	{	{	PUNCT
ejpam-3543	73	30	a	a	DET
ejpam-3543	73	31	∈	∈	PROPN
ejpam-3543	73	32	p(x	p(x	NOUN
ejpam-3543	73	33	)	)	PUNCT
ejpam-3543	73	34	|	|	ADV
ejpam-3543	73	35	ω	ω	NUM
ejpam-3543	73	36	⊆	⊆	NUM
ejpam-3543	73	37	a	a	PRON
ejpam-3543	73	38	}	}	PUNCT
ejpam-3543	73	39	.	.	PUNCT
ejpam-3543	74	1	define	define	VERB
ejpam-3543	74	2	a	a	DET
ejpam-3543	74	3	binary	binary	ADJ
ejpam-3543	74	4	operation	operation	NOUN
ejpam-3543	74	5	·	·	PUNCT
ejpam-3543	74	6	on	on	ADP
ejpam-3543	74	7	pω(x	pω(x	NOUN
ejpam-3543	74	8	)	)	PUNCT
ejpam-3543	74	9	by	by	ADP
ejpam-3543	74	10	m.	m.	PROPN
ejpam-3543	74	11	songsaeng	songsaeng	PROPN
ejpam-3543	74	12	,	,	PUNCT
ejpam-3543	74	13	a.	a.	NOUN
ejpam-3543	74	14	iampan	iampan	PROPN
ejpam-3543	74	15	/	/	SYM
ejpam-3543	74	16	eur	eur	PROPN
ejpam-3543	74	17	.	.	PUNCT
ejpam-3543	75	1	j.	j.	PROPN
ejpam-3543	75	2	pure	pure	PROPN
ejpam-3543	75	3	appl	appl	PROPN
ejpam-3543	75	4	.	.	PROPN
ejpam-3543	75	5	math	math	PROPN
ejpam-3543	75	6	,	,	PUNCT
ejpam-3543	75	7	12	12	NUM
ejpam-3543	75	8	(	(	PUNCT
ejpam-3543	75	9	4	4	NUM
ejpam-3543	75	10	)	)	PUNCT
ejpam-3543	75	11	(	(	PUNCT
ejpam-3543	75	12	2019	2019	NUM
ejpam-3543	75	13	)	)	PUNCT
ejpam-3543	75	14	,	,	PUNCT
ejpam-3543	75	15	1382	1382	NUM
ejpam-3543	75	16	-	-	SYM
ejpam-3543	75	17	1409	1409	NUM
ejpam-3543	75	18	1384	1384	NUM
ejpam-3543	75	19	putting	put	VERB
ejpam-3543	75	20	a	a	DET
ejpam-3543	75	21	·	·	PUNCT
ejpam-3543	75	22	b	b	X
ejpam-3543	75	23	=	=	SYM
ejpam-3543	75	24	b	b	PROPN
ejpam-3543	75	25	∩	∩	NOUN
ejpam-3543	75	26	(	(	PUNCT
ejpam-3543	75	27	ac	ac	PROPN
ejpam-3543	75	28	∪	∪	PROPN
ejpam-3543	75	29	ω	ω	PROPN
ejpam-3543	75	30	)	)	PUNCT
ejpam-3543	75	31	for	for	ADP
ejpam-3543	75	32	all	all	DET
ejpam-3543	75	33	a	a	DET
ejpam-3543	75	34	,	,	PUNCT
ejpam-3543	75	35	b	b	NOUN
ejpam-3543	75	36	∈	∈	NOUN
ejpam-3543	75	37	pω(x	pω(x	NOUN
ejpam-3543	75	38	)	)	PUNCT
ejpam-3543	75	39	where	where	SCONJ
ejpam-3543	75	40	ac	ac	PROPN
ejpam-3543	75	41	means	mean	VERB
ejpam-3543	75	42	the	the	DET
ejpam-3543	75	43	complement	complement	NOUN
ejpam-3543	75	44	of	of	ADP
ejpam-3543	75	45	a	a	DET
ejpam-3543	75	46	subset	subset	NOUN
ejpam-3543	75	47	a.	a.	NOUN
ejpam-3543	75	48	then	then	ADV
ejpam-3543	75	49	(	(	PUNCT
ejpam-3543	75	50	pω(x	pω(x	NOUN
ejpam-3543	75	51	)	)	PUNCT
ejpam-3543	75	52	,	,	PUNCT
ejpam-3543	75	53	·	·	PUNCT
ejpam-3543	75	54	,	,	PUNCT
ejpam-3543	75	55	ω	ω	NUM
ejpam-3543	75	56	)	)	PUNCT
ejpam-3543	75	57	is	be	AUX
ejpam-3543	75	58	a	a	DET
ejpam-3543	75	59	up	up	NOUN
ejpam-3543	75	60	-	-	PUNCT
ejpam-3543	75	61	algebra	algebra	NOUN
ejpam-3543	75	62	and	and	CCONJ
ejpam-3543	75	63	we	we	PRON
ejpam-3543	75	64	shall	shall	AUX
ejpam-3543	75	65	call	call	VERB
ejpam-3543	75	66	it	it	PRON
ejpam-3543	75	67	the	the	DET
ejpam-3543	75	68	generalized	generalized	ADJ
ejpam-3543	75	69	power	power	NOUN
ejpam-3543	75	70	up	up	ADP
ejpam-3543	75	71	-	-	PUNCT
ejpam-3543	75	72	algebra	algebra	NOUN
ejpam-3543	75	73	of	of	ADP
ejpam-3543	75	74	type	type	NOUN
ejpam-3543	75	75	1	1	NUM
ejpam-3543	75	76	with	with	ADP
ejpam-3543	75	77	respect	respect	NOUN
ejpam-3543	75	78	to	to	ADP
ejpam-3543	75	79	ω	ω	NUM
ejpam-3543	75	80	.	.	PUNCT
ejpam-3543	76	1	let	let	VERB
ejpam-3543	76	2	pω(x	pω(x	X
ejpam-3543	76	3	)	)	PUNCT
ejpam-3543	76	4	=	=	SYM
ejpam-3543	76	5	{	{	PUNCT
ejpam-3543	76	6	a	a	DET
ejpam-3543	76	7	∈	∈	PROPN
ejpam-3543	76	8	p(x	p(x	NOUN
ejpam-3543	76	9	)	)	PUNCT
ejpam-3543	76	10	|	|	ADV
ejpam-3543	76	11	a	a	DET
ejpam-3543	76	12	⊆	⊆	NUM
ejpam-3543	76	13	ω	ω	NUM
ejpam-3543	76	14	}	}	PUNCT
ejpam-3543	76	15	.	.	PUNCT
ejpam-3543	77	1	define	define	VERB
ejpam-3543	77	2	a	a	DET
ejpam-3543	77	3	binary	binary	ADJ
ejpam-3543	77	4	operation	operation	NOUN
ejpam-3543	77	5	∗	∗	NOUN
ejpam-3543	77	6	on	on	ADP
ejpam-3543	77	7	pω(x	pω(x	NOUN
ejpam-3543	77	8	)	)	PUNCT
ejpam-3543	77	9	by	by	ADP
ejpam-3543	77	10	putting	put	VERB
ejpam-3543	77	11	a	a	DET
ejpam-3543	77	12	∗	∗	NOUN
ejpam-3543	77	13	b	b	NOUN
ejpam-3543	77	14	=	=	SYM
ejpam-3543	77	15	b	b	X
ejpam-3543	77	16	∪	∪	X
ejpam-3543	77	17	(	(	PUNCT
ejpam-3543	77	18	ac	ac	PROPN
ejpam-3543	77	19	∩	∩	PROPN
ejpam-3543	77	20	ω	ω	NOUN
ejpam-3543	77	21	)	)	PUNCT
ejpam-3543	77	22	for	for	ADP
ejpam-3543	77	23	all	all	DET
ejpam-3543	77	24	a	a	DET
ejpam-3543	77	25	,	,	PUNCT
ejpam-3543	77	26	b	b	NOUN
ejpam-3543	77	27	∈	∈	NOUN
ejpam-3543	77	28	pω(x	pω(x	NOUN
ejpam-3543	77	29	)	)	PUNCT
ejpam-3543	77	30	.	.	PUNCT
ejpam-3543	78	1	then	then	ADV
ejpam-3543	78	2	(	(	PUNCT
ejpam-3543	78	3	pω(x	pω(x	NOUN
ejpam-3543	78	4	)	)	PUNCT
ejpam-3543	78	5	,	,	PUNCT
ejpam-3543	78	6	∗,ω	∗,ω	PROPN
ejpam-3543	78	7	)	)	PUNCT
ejpam-3543	78	8	is	be	AUX
ejpam-3543	78	9	a	a	DET
ejpam-3543	78	10	up	up	NOUN
ejpam-3543	78	11	-	-	PUNCT
ejpam-3543	78	12	algebra	algebra	NOUN
ejpam-3543	78	13	and	and	CCONJ
ejpam-3543	78	14	we	we	PRON
ejpam-3543	78	15	shall	shall	AUX
ejpam-3543	78	16	call	call	VERB
ejpam-3543	78	17	it	it	PRON
ejpam-3543	78	18	the	the	DET
ejpam-3543	78	19	generalized	generalized	ADJ
ejpam-3543	78	20	power	power	NOUN
ejpam-3543	78	21	up	up	ADP
ejpam-3543	78	22	-	-	PUNCT
ejpam-3543	78	23	algebra	algebra	NOUN
ejpam-3543	78	24	of	of	ADP
ejpam-3543	78	25	type	type	NOUN
ejpam-3543	78	26	2	2	NUM
ejpam-3543	78	27	with	with	ADP
ejpam-3543	78	28	respect	respect	NOUN
ejpam-3543	78	29	to	to	ADP
ejpam-3543	78	30	ω	ω	NUM
ejpam-3543	78	31	.	.	PUNCT
ejpam-3543	79	1	in	in	ADP
ejpam-3543	79	2	particular	particular	ADJ
ejpam-3543	79	3	,	,	PUNCT
ejpam-3543	79	4	(	(	PUNCT
ejpam-3543	79	5	p(x	p(x	PROPN
ejpam-3543	79	6	)	)	PUNCT
ejpam-3543	79	7	,	,	PUNCT
ejpam-3543	79	8	·	·	PUNCT
ejpam-3543	79	9	,	,	PUNCT
ejpam-3543	79	10	∅	∅	NOUN
ejpam-3543	79	11	)	)	PUNCT
ejpam-3543	79	12	is	be	AUX
ejpam-3543	79	13	a	a	DET
ejpam-3543	79	14	up	up	NOUN
ejpam-3543	79	15	-	-	PUNCT
ejpam-3543	79	16	algebra	algebra	NOUN
ejpam-3543	79	17	and	and	CCONJ
ejpam-3543	79	18	we	we	PRON
ejpam-3543	79	19	shall	shall	AUX
ejpam-3543	79	20	call	call	VERB
ejpam-3543	79	21	it	it	PRON
ejpam-3543	79	22	the	the	DET
ejpam-3543	79	23	power	power	NOUN
ejpam-3543	79	24	up	up	ADP
ejpam-3543	79	25	-	-	PUNCT
ejpam-3543	79	26	algebra	algebra	NOUN
ejpam-3543	79	27	of	of	ADP
ejpam-3543	79	28	type	type	NOUN
ejpam-3543	79	29	1	1	NUM
ejpam-3543	79	30	,	,	PUNCT
ejpam-3543	79	31	and	and	CCONJ
ejpam-3543	79	32	(	(	PUNCT
ejpam-3543	79	33	p(x	p(x	PROPN
ejpam-3543	79	34	)	)	PUNCT
ejpam-3543	79	35	,	,	PUNCT
ejpam-3543	79	36	∗	∗	NOUN
ejpam-3543	79	37	,	,	PUNCT
ejpam-3543	79	38	x	x	X
ejpam-3543	79	39	)	)	PUNCT
ejpam-3543	79	40	is	be	AUX
ejpam-3543	79	41	a	a	DET
ejpam-3543	79	42	up	up	NOUN
ejpam-3543	79	43	-	-	PUNCT
ejpam-3543	79	44	algebra	algebra	NOUN
ejpam-3543	79	45	and	and	CCONJ
ejpam-3543	79	46	we	we	PRON
ejpam-3543	79	47	shall	shall	AUX
ejpam-3543	79	48	call	call	VERB
ejpam-3543	79	49	it	it	PRON
ejpam-3543	79	50	the	the	DET
ejpam-3543	79	51	power	power	NOUN
ejpam-3543	79	52	up	up	ADP
ejpam-3543	79	53	-	-	PUNCT
ejpam-3543	79	54	algebra	algebra	NOUN
ejpam-3543	79	55	of	of	ADP
ejpam-3543	79	56	type	type	NOUN
ejpam-3543	79	57	2	2	NUM
ejpam-3543	79	58	.	.	NOUN
ejpam-3543	79	59	example	example	NOUN
ejpam-3543	80	1	2	2	NUM
ejpam-3543	80	2	.	.	PUNCT
ejpam-3543	81	1	[	[	X
ejpam-3543	81	2	2	2	X
ejpam-3543	81	3	]	]	PUNCT
ejpam-3543	81	4	let	let	VERB
ejpam-3543	81	5	n	n	PRON
ejpam-3543	81	6	be	be	AUX
ejpam-3543	81	7	the	the	DET
ejpam-3543	81	8	set	set	NOUN
ejpam-3543	81	9	of	of	ADP
ejpam-3543	81	10	all	all	DET
ejpam-3543	81	11	natural	natural	ADJ
ejpam-3543	81	12	numbers	number	NOUN
ejpam-3543	81	13	with	with	ADP
ejpam-3543	81	14	two	two	NUM
ejpam-3543	81	15	binary	binary	ADJ
ejpam-3543	81	16	operations	operation	NOUN
ejpam-3543	81	17	◦	◦	NOUN
ejpam-3543	81	18	and	and	CCONJ
ejpam-3543	81	19	•	•	ADV
ejpam-3543	81	20	defined	define	VERB
ejpam-3543	81	21	by	by	ADP
ejpam-3543	81	22	(	(	PUNCT
ejpam-3543	81	23	∀x	∀x	NUM
ejpam-3543	81	24	,	,	PUNCT
ejpam-3543	81	25	y	y	PROPN
ejpam-3543	81	26	∈	∈	PROPN
ejpam-3543	81	27	n	n	CCONJ
ejpam-3543	81	28	)	)	PUNCT
ejpam-3543	81	29	(	(	PUNCT
ejpam-3543	81	30	x	x	X
ejpam-3543	81	31	◦	◦	NOUN
ejpam-3543	81	32	y	y	NOUN
ejpam-3543	81	33	=	=	PRON
ejpam-3543	81	34	{	{	PUNCT
ejpam-3543	81	35	y	y	PROPN
ejpam-3543	81	36	if	if	SCONJ
ejpam-3543	81	37	x	x	X
ejpam-3543	81	38	<	<	X
ejpam-3543	81	39	y	y	PROPN
ejpam-3543	81	40	,	,	PUNCT
ejpam-3543	81	41	0	0	NUM
ejpam-3543	82	1	otherwise	otherwise	ADV
ejpam-3543	82	2	)	)	PUNCT
ejpam-3543	83	1	and	and	CCONJ
ejpam-3543	83	2	(	(	PUNCT
ejpam-3543	83	3	∀x	∀x	X
ejpam-3543	83	4	,	,	PUNCT
ejpam-3543	83	5	y	y	PROPN
ejpam-3543	83	6	∈	∈	PROPN
ejpam-3543	83	7	n	n	CCONJ
ejpam-3543	83	8	)	)	PUNCT
ejpam-3543	83	9	(	(	PUNCT
ejpam-3543	83	10	x	x	X
ejpam-3543	83	11	•	•	NUM
ejpam-3543	83	12	y	y	NOUN
ejpam-3543	83	13	=	=	PRON
ejpam-3543	83	14	{	{	PUNCT
ejpam-3543	83	15	y	y	PROPN
ejpam-3543	83	16	if	if	SCONJ
ejpam-3543	83	17	x	x	PROPN
ejpam-3543	83	18	>	>	X
ejpam-3543	83	19	y	y	PROPN
ejpam-3543	83	20	or	or	CCONJ
ejpam-3543	83	21	x	x	SYM
ejpam-3543	83	22	=	=	SYM
ejpam-3543	83	23	0	0	NUM
ejpam-3543	83	24	,	,	PUNCT
ejpam-3543	83	25	0	0	NUM
ejpam-3543	83	26	otherwise	otherwise	ADV
ejpam-3543	83	27	)	)	PUNCT
ejpam-3543	83	28	.	.	PUNCT
ejpam-3543	84	1	then	then	ADV
ejpam-3543	84	2	(	(	PUNCT
ejpam-3543	84	3	n	n	CCONJ
ejpam-3543	84	4	,	,	PUNCT
ejpam-3543	84	5	◦	◦	NOUN
ejpam-3543	84	6	,	,	PUNCT
ejpam-3543	84	7	0	0	NUM
ejpam-3543	84	8	)	)	PUNCT
ejpam-3543	84	9	and	and	CCONJ
ejpam-3543	84	10	(	(	PUNCT
ejpam-3543	84	11	n	n	CCONJ
ejpam-3543	84	12	,	,	PUNCT
ejpam-3543	84	13	•	•	NUM
ejpam-3543	84	14	,	,	PUNCT
ejpam-3543	84	15	0	0	NUM
ejpam-3543	84	16	)	)	PUNCT
ejpam-3543	84	17	are	be	AUX
ejpam-3543	84	18	up	up	ADV
ejpam-3543	84	19	-	-	PUNCT
ejpam-3543	84	20	algebras	algebras	X
ejpam-3543	84	21	.	.	PUNCT
ejpam-3543	84	22	example	example	NOUN
ejpam-3543	85	1	3	3	NUM
ejpam-3543	85	2	.	.	PUNCT
ejpam-3543	86	1	[	[	X
ejpam-3543	86	2	17	17	NUM
ejpam-3543	86	3	]	]	PUNCT
ejpam-3543	86	4	let	let	VERB
ejpam-3543	86	5	x	x	PUNCT
ejpam-3543	86	6	=	=	PUNCT
ejpam-3543	86	7	{	{	PUNCT
ejpam-3543	86	8	0	0	NUM
ejpam-3543	86	9	,	,	PUNCT
ejpam-3543	86	10	1	1	NUM
ejpam-3543	86	11	,	,	PUNCT
ejpam-3543	86	12	2	2	NUM
ejpam-3543	86	13	,	,	PUNCT
ejpam-3543	86	14	3	3	NUM
ejpam-3543	86	15	,	,	PUNCT
ejpam-3543	86	16	4	4	NUM
ejpam-3543	86	17	,	,	PUNCT
ejpam-3543	86	18	5	5	NUM
ejpam-3543	86	19	}	}	PUNCT
ejpam-3543	86	20	be	be	AUX
ejpam-3543	86	21	a	a	DET
ejpam-3543	86	22	set	set	NOUN
ejpam-3543	86	23	with	with	ADP
ejpam-3543	86	24	a	a	DET
ejpam-3543	86	25	binary	binary	ADJ
ejpam-3543	86	26	operation	operation	NOUN
ejpam-3543	86	27	·	·	PUNCT
ejpam-3543	86	28	defined	define	VERB
ejpam-3543	86	29	by	by	ADP
ejpam-3543	86	30	the	the	DET
ejpam-3543	86	31	following	following	ADJ
ejpam-3543	86	32	cayley	cayley	ADJ
ejpam-3543	86	33	table	table	NOUN
ejpam-3543	86	34	:	:	PUNCT
ejpam-3543	86	35	·	·	PUNCT
ejpam-3543	86	36	0	0	NUM
ejpam-3543	86	37	1	1	NUM
ejpam-3543	86	38	2	2	NUM
ejpam-3543	86	39	3	3	NUM
ejpam-3543	86	40	4	4	NUM
ejpam-3543	86	41	5	5	NUM
ejpam-3543	86	42	0	0	NUM
ejpam-3543	86	43	0	0	NUM
ejpam-3543	86	44	1	1	NUM
ejpam-3543	86	45	2	2	NUM
ejpam-3543	86	46	3	3	NUM
ejpam-3543	86	47	4	4	NUM
ejpam-3543	86	48	5	5	NUM
ejpam-3543	86	49	1	1	NUM
ejpam-3543	86	50	0	0	NUM
ejpam-3543	86	51	0	0	NUM
ejpam-3543	86	52	2	2	NUM
ejpam-3543	86	53	3	3	NUM
ejpam-3543	86	54	2	2	NUM
ejpam-3543	86	55	5	5	NUM
ejpam-3543	86	56	2	2	NUM
ejpam-3543	86	57	0	0	NUM
ejpam-3543	86	58	1	1	NUM
ejpam-3543	86	59	0	0	NUM
ejpam-3543	86	60	3	3	NUM
ejpam-3543	86	61	1	1	NUM
ejpam-3543	86	62	5	5	NUM
ejpam-3543	86	63	3	3	NUM
ejpam-3543	86	64	0	0	NUM
ejpam-3543	86	65	1	1	NUM
ejpam-3543	86	66	2	2	NUM
ejpam-3543	86	67	0	0	NUM
ejpam-3543	86	68	4	4	NUM
ejpam-3543	86	69	5	5	NUM
ejpam-3543	86	70	4	4	NUM
ejpam-3543	86	71	0	0	NUM
ejpam-3543	86	72	0	0	NUM
ejpam-3543	86	73	0	0	NUM
ejpam-3543	86	74	3	3	NUM
ejpam-3543	86	75	0	0	NUM
ejpam-3543	86	76	5	5	NUM
ejpam-3543	86	77	5	5	NUM
ejpam-3543	86	78	0	0	NUM
ejpam-3543	86	79	0	0	NUM
ejpam-3543	86	80	2	2	NUM
ejpam-3543	86	81	0	0	NUM
ejpam-3543	86	82	2	2	NUM
ejpam-3543	86	83	0	0	NUM
ejpam-3543	86	84	then	then	ADV
ejpam-3543	86	85	(	(	PUNCT
ejpam-3543	86	86	x	x	X
ejpam-3543	86	87	,	,	PUNCT
ejpam-3543	86	88	·	·	PUNCT
ejpam-3543	86	89	,	,	PUNCT
ejpam-3543	86	90	0	0	NUM
ejpam-3543	86	91	)	)	PUNCT
ejpam-3543	86	92	is	be	AUX
ejpam-3543	86	93	a	a	DET
ejpam-3543	86	94	up	up	NOUN
ejpam-3543	86	95	-	-	PUNCT
ejpam-3543	86	96	algebra	algebra	NOUN
ejpam-3543	86	97	.	.	PUNCT
ejpam-3543	87	1	for	for	ADP
ejpam-3543	87	2	more	more	ADJ
ejpam-3543	87	3	examples	example	NOUN
ejpam-3543	87	4	of	of	ADP
ejpam-3543	87	5	up	up	ADP
ejpam-3543	87	6	-	-	PUNCT
ejpam-3543	87	7	algebras	algebras	X
ejpam-3543	87	8	,	,	PUNCT
ejpam-3543	87	9	see	see	VERB
ejpam-3543	87	10	[	[	X
ejpam-3543	87	11	1	1	NUM
ejpam-3543	87	12	,	,	PUNCT
ejpam-3543	87	13	6	6	NUM
ejpam-3543	87	14	,	,	PUNCT
ejpam-3543	87	15	20	20	NUM
ejpam-3543	87	16	,	,	PUNCT
ejpam-3543	87	17	21	21	NUM
ejpam-3543	87	18	]	]	PUNCT
ejpam-3543	87	19	.	.	PUNCT
ejpam-3543	88	1	in	in	ADP
ejpam-3543	88	2	a	a	DET
ejpam-3543	88	3	up	up	NOUN
ejpam-3543	88	4	-	-	PUNCT
ejpam-3543	88	5	algebra	algebra	NOUN
ejpam-3543	88	6	x	x	PUNCT
ejpam-3543	88	7	=	=	SYM
ejpam-3543	88	8	(	(	PUNCT
ejpam-3543	88	9	x	x	NOUN
ejpam-3543	88	10	,	,	PUNCT
ejpam-3543	88	11	·	·	PUNCT
ejpam-3543	88	12	,	,	PUNCT
ejpam-3543	88	13	0	0	NUM
ejpam-3543	88	14	)	)	PUNCT
ejpam-3543	88	15	,	,	PUNCT
ejpam-3543	88	16	the	the	DET
ejpam-3543	88	17	following	follow	VERB
ejpam-3543	88	18	assertions	assertion	NOUN
ejpam-3543	88	19	are	be	AUX
ejpam-3543	88	20	valid	valid	ADJ
ejpam-3543	88	21	(	(	PUNCT
ejpam-3543	88	22	see	see	VERB
ejpam-3543	88	23	[	[	X
ejpam-3543	88	24	5	5	NUM
ejpam-3543	88	25	,	,	PUNCT
ejpam-3543	88	26	6	6	NUM
ejpam-3543	88	27	]	]	NUM
ejpam-3543	88	28	)	)	PUNCT
ejpam-3543	88	29	.	.	PUNCT
ejpam-3543	89	1	(	(	PUNCT
ejpam-3543	89	2	∀x	∀x	X
ejpam-3543	89	3	∈	∈	PROPN
ejpam-3543	89	4	x)(x	x)(x	PROPN
ejpam-3543	89	5	·	·	PUNCT
ejpam-3543	89	6	x	x	PUNCT
ejpam-3543	89	7	=	=	PUNCT
ejpam-3543	89	8	0	0	NUM
ejpam-3543	89	9	)	)	PUNCT
ejpam-3543	89	10	,	,	PUNCT
ejpam-3543	89	11	(	(	PUNCT
ejpam-3543	89	12	2.1	2.1	NUM
ejpam-3543	89	13	)	)	PUNCT
ejpam-3543	89	14	(	(	PUNCT
ejpam-3543	89	15	∀x	∀x	X
ejpam-3543	89	16	,	,	PUNCT
ejpam-3543	89	17	y	y	PROPN
ejpam-3543	89	18	,	,	PUNCT
ejpam-3543	89	19	z	z	PROPN
ejpam-3543	89	20	∈	∈	PROPN
ejpam-3543	89	21	x)(x	x)(x	PROPN
ejpam-3543	89	22	·	·	PUNCT
ejpam-3543	89	23	y	y	X
ejpam-3543	89	24	=	=	SYM
ejpam-3543	89	25	0	0	PROPN
ejpam-3543	89	26	,	,	PUNCT
ejpam-3543	89	27	y	y	PROPN
ejpam-3543	89	28	·	·	PUNCT
ejpam-3543	89	29	z	z	X
ejpam-3543	89	30	=	=	SYM
ejpam-3543	89	31	0⇒	0⇒	NUM
ejpam-3543	89	32	x	x	SYM
ejpam-3543	89	33	·	·	PUNCT
ejpam-3543	89	34	z	z	X
ejpam-3543	90	1	=	=	SYM
ejpam-3543	90	2	0	0	NUM
ejpam-3543	90	3	)	)	PUNCT
ejpam-3543	90	4	,	,	PUNCT
ejpam-3543	90	5	(	(	PUNCT
ejpam-3543	90	6	2.2	2.2	NUM
ejpam-3543	90	7	)	)	PUNCT
ejpam-3543	90	8	(	(	PUNCT
ejpam-3543	90	9	∀x	∀x	X
ejpam-3543	90	10	,	,	PUNCT
ejpam-3543	90	11	y	y	PROPN
ejpam-3543	90	12	,	,	PUNCT
ejpam-3543	91	1	z	z	PROPN
ejpam-3543	91	2	∈	∈	PROPN
ejpam-3543	91	3	x)(x	x)(x	PROPN
ejpam-3543	91	4	·	·	PUNCT
ejpam-3543	91	5	y	y	X
ejpam-3543	91	6	=	=	PUNCT
ejpam-3543	91	7	0⇒	0⇒	PROPN
ejpam-3543	91	8	(	(	PUNCT
ejpam-3543	91	9	z	z	NOUN
ejpam-3543	91	10	·	·	PUNCT
ejpam-3543	91	11	x	x	X
ejpam-3543	91	12	)	)	PUNCT
ejpam-3543	91	13	·	·	PUNCT
ejpam-3543	91	14	(	(	PUNCT
ejpam-3543	91	15	z	z	X
ejpam-3543	91	16	·	·	PUNCT
ejpam-3543	91	17	y	y	X
ejpam-3543	91	18	)	)	PUNCT
ejpam-3543	91	19	=	=	NOUN
ejpam-3543	91	20	0	0	NUM
ejpam-3543	91	21	)	)	PUNCT
ejpam-3543	91	22	,	,	PUNCT
ejpam-3543	91	23	(	(	PUNCT
ejpam-3543	91	24	2.3	2.3	NUM
ejpam-3543	91	25	)	)	PUNCT
ejpam-3543	91	26	(	(	PUNCT
ejpam-3543	91	27	∀x	∀x	X
ejpam-3543	91	28	,	,	PUNCT
ejpam-3543	91	29	y	y	PROPN
ejpam-3543	91	30	,	,	PUNCT
ejpam-3543	91	31	z	z	PROPN
ejpam-3543	91	32	∈	∈	PROPN
ejpam-3543	91	33	x)(x	x)(x	PROPN
ejpam-3543	91	34	·	·	PUNCT
ejpam-3543	92	1	y	y	X
ejpam-3543	92	2	=	=	PUNCT
ejpam-3543	92	3	0⇒	0⇒	PROPN
ejpam-3543	92	4	(	(	PUNCT
ejpam-3543	92	5	y	y	PROPN
ejpam-3543	92	6	·	·	PUNCT
ejpam-3543	92	7	z	z	X
ejpam-3543	92	8	)	)	PUNCT
ejpam-3543	92	9	·	·	PUNCT
ejpam-3543	92	10	(	(	PUNCT
ejpam-3543	92	11	x	x	X
ejpam-3543	92	12	·	·	PUNCT
ejpam-3543	93	1	z	z	X
ejpam-3543	93	2	)	)	PUNCT
ejpam-3543	93	3	=	=	SYM
ejpam-3543	93	4	0	0	NUM
ejpam-3543	93	5	)	)	PUNCT
ejpam-3543	93	6	,	,	PUNCT
ejpam-3543	93	7	(	(	PUNCT
ejpam-3543	93	8	2.4	2.4	NUM
ejpam-3543	93	9	)	)	PUNCT
ejpam-3543	93	10	(	(	PUNCT
ejpam-3543	93	11	∀x	∀x	X
ejpam-3543	93	12	,	,	PUNCT
ejpam-3543	93	13	y	y	PROPN
ejpam-3543	93	14	∈	∈	PROPN
ejpam-3543	93	15	x)(x	x)(x	PROPN
ejpam-3543	93	16	·	·	PUNCT
ejpam-3543	93	17	(	(	PUNCT
ejpam-3543	93	18	y	y	PROPN
ejpam-3543	93	19	·	·	PUNCT
ejpam-3543	93	20	x	x	X
ejpam-3543	93	21	)	)	PUNCT
ejpam-3543	93	22	=	=	SYM
ejpam-3543	93	23	0	0	NUM
ejpam-3543	93	24	)	)	PUNCT
ejpam-3543	93	25	,	,	PUNCT
ejpam-3543	93	26	(	(	PUNCT
ejpam-3543	93	27	2.5	2.5	NUM
ejpam-3543	93	28	)	)	PUNCT
ejpam-3543	93	29	(	(	PUNCT
ejpam-3543	93	30	∀x	∀x	X
ejpam-3543	93	31	,	,	PUNCT
ejpam-3543	93	32	y	y	PROPN
ejpam-3543	93	33	∈	∈	PROPN
ejpam-3543	93	34	x)((y	x)((y	PROPN
ejpam-3543	93	35	·	·	PUNCT
ejpam-3543	94	1	x	x	X
ejpam-3543	94	2	)	)	PUNCT
ejpam-3543	94	3	·	·	PUNCT
ejpam-3543	94	4	x	x	PUNCT
ejpam-3543	95	1	=	=	PUNCT
ejpam-3543	95	2	0⇔	0⇔	NOUN
ejpam-3543	95	3	x	x	X
ejpam-3543	96	1	=	=	PUNCT
ejpam-3543	96	2	y	y	PROPN
ejpam-3543	96	3	·	·	PUNCT
ejpam-3543	96	4	x	x	X
ejpam-3543	96	5	)	)	PUNCT
ejpam-3543	96	6	,	,	PUNCT
ejpam-3543	96	7	(	(	PUNCT
ejpam-3543	96	8	2.6	2.6	NUM
ejpam-3543	96	9	)	)	PUNCT
ejpam-3543	96	10	(	(	PUNCT
ejpam-3543	96	11	∀x	∀x	X
ejpam-3543	96	12	,	,	PUNCT
ejpam-3543	96	13	y	y	PROPN
ejpam-3543	96	14	∈	∈	PROPN
ejpam-3543	96	15	x)(x	x)(x	PROPN
ejpam-3543	96	16	·	·	PUNCT
ejpam-3543	96	17	(	(	PUNCT
ejpam-3543	96	18	y	y	PROPN
ejpam-3543	96	19	·	·	PUNCT
ejpam-3543	96	20	y	y	X
ejpam-3543	96	21	)	)	PUNCT
ejpam-3543	96	22	=	=	SYM
ejpam-3543	96	23	0	0	NUM
ejpam-3543	96	24	)	)	PUNCT
ejpam-3543	96	25	,	,	PUNCT
ejpam-3543	96	26	(	(	PUNCT
ejpam-3543	96	27	2.7	2.7	NUM
ejpam-3543	96	28	)	)	PUNCT
ejpam-3543	96	29	m.	m.	NOUN
ejpam-3543	96	30	songsaeng	songsaeng	PROPN
ejpam-3543	96	31	,	,	PUNCT
ejpam-3543	96	32	a.	a.	NOUN
ejpam-3543	96	33	iampan	iampan	PROPN
ejpam-3543	96	34	/	/	SYM
ejpam-3543	96	35	eur	eur	PROPN
ejpam-3543	96	36	.	.	PUNCT
ejpam-3543	97	1	j.	j.	PROPN
ejpam-3543	97	2	pure	pure	PROPN
ejpam-3543	97	3	appl	appl	PROPN
ejpam-3543	97	4	.	.	PROPN
ejpam-3543	97	5	math	math	PROPN
ejpam-3543	97	6	,	,	PUNCT
ejpam-3543	97	7	12	12	NUM
ejpam-3543	97	8	(	(	PUNCT
ejpam-3543	97	9	4	4	NUM
ejpam-3543	97	10	)	)	PUNCT
ejpam-3543	97	11	(	(	PUNCT
ejpam-3543	97	12	2019	2019	NUM
ejpam-3543	97	13	)	)	PUNCT
ejpam-3543	97	14	,	,	PUNCT
ejpam-3543	97	15	1382	1382	NUM
ejpam-3543	97	16	-	-	SYM
ejpam-3543	97	17	1409	1409	NUM
ejpam-3543	97	18	1385	1385	NUM
ejpam-3543	97	19	(	(	PUNCT
ejpam-3543	97	20	∀a	∀a	X
ejpam-3543	97	21	,	,	PUNCT
ejpam-3543	97	22	x	x	X
ejpam-3543	97	23	,	,	PUNCT
ejpam-3543	97	24	y	y	PROPN
ejpam-3543	97	25	,	,	PUNCT
ejpam-3543	97	26	z	z	PROPN
ejpam-3543	97	27	∈	∈	PROPN
ejpam-3543	97	28	x)((x	x)((x	NOUN
ejpam-3543	97	29	·	·	PUNCT
ejpam-3543	97	30	(	(	PUNCT
ejpam-3543	97	31	y	y	PROPN
ejpam-3543	97	32	·	·	PUNCT
ejpam-3543	97	33	z	z	NOUN
ejpam-3543	97	34	)	)	PUNCT
ejpam-3543	97	35	)	)	PUNCT
ejpam-3543	97	36	·	·	PUNCT
ejpam-3543	98	1	(	(	PUNCT
ejpam-3543	98	2	x	x	X
ejpam-3543	98	3	·	·	PUNCT
ejpam-3543	98	4	(	(	PUNCT
ejpam-3543	98	5	(	(	PUNCT
ejpam-3543	98	6	a	a	DET
ejpam-3543	98	7	·	·	PUNCT
ejpam-3543	98	8	y	y	NOUN
ejpam-3543	98	9	)	)	PUNCT
ejpam-3543	98	10	·	·	PUNCT
ejpam-3543	98	11	(	(	PUNCT
ejpam-3543	98	12	a	a	DET
ejpam-3543	98	13	·	·	PUNCT
ejpam-3543	98	14	z	z	NOUN
ejpam-3543	98	15	)	)	PUNCT
ejpam-3543	98	16	)	)	PUNCT
ejpam-3543	98	17	)	)	PUNCT
ejpam-3543	99	1	=	=	PUNCT
ejpam-3543	99	2	0	0	NUM
ejpam-3543	99	3	)	)	PUNCT
ejpam-3543	99	4	,	,	PUNCT
ejpam-3543	99	5	(	(	PUNCT
ejpam-3543	99	6	2.8	2.8	NUM
ejpam-3543	99	7	)	)	PUNCT
ejpam-3543	99	8	(	(	PUNCT
ejpam-3543	99	9	∀a	∀a	X
ejpam-3543	99	10	,	,	PUNCT
ejpam-3543	99	11	x	x	X
ejpam-3543	99	12	,	,	PUNCT
ejpam-3543	99	13	y	y	PROPN
ejpam-3543	99	14	,	,	PUNCT
ejpam-3543	99	15	z	z	PROPN
ejpam-3543	99	16	∈	∈	PROPN
ejpam-3543	99	17	x)((((a	x)((((a	PROPN
ejpam-3543	99	18	·	·	PUNCT
ejpam-3543	99	19	x	x	X
ejpam-3543	99	20	)	)	PUNCT
ejpam-3543	99	21	·	·	PUNCT
ejpam-3543	99	22	(	(	PUNCT
ejpam-3543	99	23	a	a	DET
ejpam-3543	99	24	·	·	PUNCT
ejpam-3543	99	25	y	y	NOUN
ejpam-3543	99	26	)	)	PUNCT
ejpam-3543	99	27	)	)	PUNCT
ejpam-3543	99	28	·	·	PUNCT
ejpam-3543	100	1	z	z	X
ejpam-3543	100	2	)	)	PUNCT
ejpam-3543	100	3	·	·	PUNCT
ejpam-3543	100	4	(	(	PUNCT
ejpam-3543	100	5	(	(	PUNCT
ejpam-3543	100	6	x	x	SYM
ejpam-3543	100	7	·	·	PUNCT
ejpam-3543	100	8	y	y	X
ejpam-3543	100	9	)	)	PUNCT
ejpam-3543	100	10	·	·	PUNCT
ejpam-3543	101	1	z	z	X
ejpam-3543	101	2	)	)	PUNCT
ejpam-3543	101	3	=	=	SYM
ejpam-3543	101	4	0	0	NUM
ejpam-3543	101	5	)	)	PUNCT
ejpam-3543	101	6	,	,	PUNCT
ejpam-3543	101	7	(	(	PUNCT
ejpam-3543	101	8	2.9	2.9	NUM
ejpam-3543	101	9	)	)	PUNCT
ejpam-3543	101	10	(	(	PUNCT
ejpam-3543	101	11	∀x	∀x	X
ejpam-3543	101	12	,	,	PUNCT
ejpam-3543	101	13	y	y	PROPN
ejpam-3543	101	14	,	,	PUNCT
ejpam-3543	101	15	z	z	PROPN
ejpam-3543	101	16	∈	∈	PROPN
ejpam-3543	101	17	x)(((x	x)(((x	SYM
ejpam-3543	101	18	·	·	PUNCT
ejpam-3543	101	19	y	y	X
ejpam-3543	101	20	)	)	PUNCT
ejpam-3543	101	21	·	·	PUNCT
ejpam-3543	102	1	z	z	X
ejpam-3543	102	2	)	)	PUNCT
ejpam-3543	102	3	·	·	PUNCT
ejpam-3543	102	4	(	(	PUNCT
ejpam-3543	102	5	y	y	PROPN
ejpam-3543	102	6	·	·	PUNCT
ejpam-3543	102	7	z	z	X
ejpam-3543	102	8	)	)	PUNCT
ejpam-3543	102	9	=	=	SYM
ejpam-3543	102	10	0	0	NUM
ejpam-3543	102	11	)	)	PUNCT
ejpam-3543	102	12	,	,	PUNCT
ejpam-3543	102	13	(	(	PUNCT
ejpam-3543	102	14	2.10	2.10	NUM
ejpam-3543	102	15	)	)	PUNCT
ejpam-3543	102	16	(	(	PUNCT
ejpam-3543	102	17	∀x	∀x	X
ejpam-3543	102	18	,	,	PUNCT
ejpam-3543	102	19	y	y	PROPN
ejpam-3543	102	20	,	,	PUNCT
ejpam-3543	102	21	z	z	PROPN
ejpam-3543	102	22	∈	∈	PROPN
ejpam-3543	102	23	x)(x	x)(x	PROPN
ejpam-3543	102	24	·	·	PUNCT
ejpam-3543	103	1	y	y	X
ejpam-3543	103	2	=	=	SYM
ejpam-3543	103	3	0⇒	0⇒	PROPN
ejpam-3543	103	4	x	x	SYM
ejpam-3543	103	5	·	·	PUNCT
ejpam-3543	103	6	(	(	PUNCT
ejpam-3543	103	7	z	z	NOUN
ejpam-3543	103	8	·	·	PUNCT
ejpam-3543	103	9	y	y	X
ejpam-3543	103	10	)	)	PUNCT
ejpam-3543	103	11	=	=	NOUN
ejpam-3543	104	1	0	0	NUM
ejpam-3543	104	2	)	)	PUNCT
ejpam-3543	104	3	,	,	PUNCT
ejpam-3543	104	4	(	(	PUNCT
ejpam-3543	104	5	2.11	2.11	NUM
ejpam-3543	104	6	)	)	PUNCT
ejpam-3543	104	7	(	(	PUNCT
ejpam-3543	104	8	∀x	∀x	X
ejpam-3543	104	9	,	,	PUNCT
ejpam-3543	104	10	y	y	PROPN
ejpam-3543	104	11	,	,	PUNCT
ejpam-3543	104	12	z	z	PROPN
ejpam-3543	104	13	∈	∈	PROPN
ejpam-3543	104	14	x)(((x	x)(((x	SYM
ejpam-3543	104	15	·	·	PUNCT
ejpam-3543	104	16	y	y	X
ejpam-3543	104	17	)	)	PUNCT
ejpam-3543	104	18	·	·	PUNCT
ejpam-3543	105	1	z	z	X
ejpam-3543	105	2	)	)	PUNCT
ejpam-3543	105	3	·	·	PUNCT
ejpam-3543	105	4	(	(	PUNCT
ejpam-3543	105	5	x	x	X
ejpam-3543	105	6	·	·	PUNCT
ejpam-3543	105	7	(	(	PUNCT
ejpam-3543	105	8	y	y	PROPN
ejpam-3543	105	9	·	·	PUNCT
ejpam-3543	105	10	z	z	NOUN
ejpam-3543	105	11	)	)	PUNCT
ejpam-3543	105	12	)	)	PUNCT
ejpam-3543	106	1	=	=	PUNCT
ejpam-3543	106	2	0	0	NUM
ejpam-3543	106	3	)	)	PUNCT
ejpam-3543	106	4	,	,	PUNCT
ejpam-3543	106	5	and	and	CCONJ
ejpam-3543	106	6	(	(	PUNCT
ejpam-3543	106	7	2.12	2.12	NUM
ejpam-3543	106	8	)	)	PUNCT
ejpam-3543	106	9	(	(	PUNCT
ejpam-3543	106	10	∀a	∀a	X
ejpam-3543	106	11	,	,	PUNCT
ejpam-3543	106	12	x	x	X
ejpam-3543	106	13	,	,	PUNCT
ejpam-3543	106	14	y	y	PROPN
ejpam-3543	106	15	,	,	PUNCT
ejpam-3543	106	16	z	z	PROPN
ejpam-3543	106	17	∈	∈	PROPN
ejpam-3543	106	18	x)(((x	x)(((x	SYM
ejpam-3543	106	19	·	·	PUNCT
ejpam-3543	106	20	y	y	X
ejpam-3543	106	21	)	)	PUNCT
ejpam-3543	106	22	·	·	PUNCT
ejpam-3543	107	1	z	z	X
ejpam-3543	107	2	)	)	PUNCT
ejpam-3543	107	3	·	·	PUNCT
ejpam-3543	107	4	(	(	PUNCT
ejpam-3543	107	5	y	y	PROPN
ejpam-3543	107	6	·	·	PUNCT
ejpam-3543	107	7	(	(	PUNCT
ejpam-3543	107	8	a	a	DET
ejpam-3543	107	9	·	·	PUNCT
ejpam-3543	107	10	z	z	NOUN
ejpam-3543	107	11	)	)	PUNCT
ejpam-3543	107	12	)	)	PUNCT
ejpam-3543	108	1	=	=	PUNCT
ejpam-3543	108	2	0	0	NUM
ejpam-3543	108	3	)	)	PUNCT
ejpam-3543	108	4	.	.	PUNCT
ejpam-3543	109	1	(	(	PUNCT
ejpam-3543	109	2	2.13	2.13	NUM
ejpam-3543	109	3	)	)	PUNCT
ejpam-3543	109	4	on	on	ADP
ejpam-3543	109	5	a	a	DET
ejpam-3543	109	6	up	up	NOUN
ejpam-3543	109	7	-	-	PUNCT
ejpam-3543	109	8	algebra	algebra	NOUN
ejpam-3543	109	9	x	x	PUNCT
ejpam-3543	109	10	=	=	SYM
ejpam-3543	109	11	(	(	PUNCT
ejpam-3543	109	12	x	x	NOUN
ejpam-3543	109	13	,	,	PUNCT
ejpam-3543	109	14	·	·	PUNCT
ejpam-3543	109	15	,	,	PUNCT
ejpam-3543	109	16	0	0	NUM
ejpam-3543	109	17	)	)	PUNCT
ejpam-3543	109	18	,	,	PUNCT
ejpam-3543	109	19	we	we	PRON
ejpam-3543	109	20	define	define	VERB
ejpam-3543	109	21	a	a	DET
ejpam-3543	109	22	binary	binary	ADJ
ejpam-3543	109	23	relation	relation	NOUN
ejpam-3543	109	24	≤	≤	NOUN
ejpam-3543	109	25	on	on	ADP
ejpam-3543	109	26	x	x	PUNCT
ejpam-3543	110	1	[	[	X
ejpam-3543	110	2	5	5	NUM
ejpam-3543	110	3	]	]	PUNCT
ejpam-3543	110	4	as	as	SCONJ
ejpam-3543	110	5	follows	follow	VERB
ejpam-3543	110	6	:	:	PUNCT
ejpam-3543	110	7	(	(	PUNCT
ejpam-3543	110	8	∀x	∀x	X
ejpam-3543	110	9	,	,	PUNCT
ejpam-3543	110	10	y	y	PROPN
ejpam-3543	110	11	∈	∈	PROPN
ejpam-3543	110	12	x)(x	x)(x	PROPN
ejpam-3543	110	13	≤	≤	PROPN
ejpam-3543	111	1	y	y	PROPN
ejpam-3543	111	2	⇔	⇔	PROPN
ejpam-3543	111	3	x	x	PROPN
ejpam-3543	111	4	·	·	PUNCT
ejpam-3543	111	5	y	y	SYM
ejpam-3543	111	6	=	=	NOUN
ejpam-3543	111	7	0	0	NUM
ejpam-3543	111	8	)	)	PUNCT
ejpam-3543	111	9	.	.	PUNCT
ejpam-3543	112	1	definition	definition	NOUN
ejpam-3543	112	2	2	2	NUM
ejpam-3543	112	3	.	.	PUNCT
ejpam-3543	113	1	[	[	X
ejpam-3543	113	2	3	3	NUM
ejpam-3543	113	3	,	,	PUNCT
ejpam-3543	113	4	5	5	NUM
ejpam-3543	113	5	,	,	PUNCT
ejpam-3543	113	6	23	23	NUM
ejpam-3543	113	7	]	]	PUNCT
ejpam-3543	113	8	a	a	DET
ejpam-3543	113	9	nonempty	nonempty	ADV
ejpam-3543	113	10	subset	subset	VERB
ejpam-3543	113	11	s	s	NOUN
ejpam-3543	113	12	of	of	ADP
ejpam-3543	113	13	a	a	PRON
ejpam-3543	113	14	up	up	NOUN
ejpam-3543	113	15	-	-	PUNCT
ejpam-3543	113	16	algebra	algebra	NOUN
ejpam-3543	113	17	(	(	PUNCT
ejpam-3543	113	18	x	x	X
ejpam-3543	113	19	,	,	PUNCT
ejpam-3543	113	20	·	·	PUNCT
ejpam-3543	113	21	,	,	PUNCT
ejpam-3543	113	22	0	0	NUM
ejpam-3543	113	23	)	)	PUNCT
ejpam-3543	113	24	is	be	AUX
ejpam-3543	113	25	called	call	VERB
ejpam-3543	113	26	(	(	PUNCT
ejpam-3543	113	27	1	1	NUM
ejpam-3543	113	28	)	)	PUNCT
ejpam-3543	113	29	a	a	DET
ejpam-3543	113	30	up	up	ADJ
ejpam-3543	113	31	-	-	PUNCT
ejpam-3543	113	32	subalgebra	subalgebra	NOUN
ejpam-3543	113	33	of	of	ADP
ejpam-3543	113	34	x	x	PRON
ejpam-3543	113	35	if	if	SCONJ
ejpam-3543	113	36	(	(	PUNCT
ejpam-3543	113	37	∀x	∀x	X
ejpam-3543	113	38	,	,	PUNCT
ejpam-3543	113	39	y	y	PROPN
ejpam-3543	113	40	∈	∈	PROPN
ejpam-3543	113	41	s)(x	s)(x	PROPN
ejpam-3543	113	42	·	·	PUNCT
ejpam-3543	114	1	y	y	PROPN
ejpam-3543	114	2	∈	∈	PROPN
ejpam-3543	114	3	s	s	PART
ejpam-3543	114	4	)	)	PUNCT
ejpam-3543	114	5	.	.	PUNCT
ejpam-3543	115	1	(	(	PUNCT
ejpam-3543	115	2	2	2	X
ejpam-3543	115	3	)	)	PUNCT
ejpam-3543	115	4	a	a	DET
ejpam-3543	115	5	near	near	ADJ
ejpam-3543	115	6	up	up	NOUN
ejpam-3543	115	7	-	-	PUNCT
ejpam-3543	115	8	filter	filter	NOUN
ejpam-3543	115	9	of	of	ADP
ejpam-3543	115	10	x	x	SYM
ejpam-3543	115	11	if	if	SCONJ
ejpam-3543	115	12	(	(	PUNCT
ejpam-3543	115	13	i	i	NOUN
ejpam-3543	115	14	)	)	PUNCT
ejpam-3543	115	15	the	the	DET
ejpam-3543	115	16	constant	constant	ADJ
ejpam-3543	115	17	0	0	NUM
ejpam-3543	115	18	of	of	ADP
ejpam-3543	115	19	x	x	PRON
ejpam-3543	115	20	is	be	AUX
ejpam-3543	115	21	in	in	ADP
ejpam-3543	115	22	s	s	PROPN
ejpam-3543	115	23	,	,	PUNCT
ejpam-3543	115	24	and	and	CCONJ
ejpam-3543	115	25	(	(	PUNCT
ejpam-3543	115	26	ii	ii	NOUN
ejpam-3543	115	27	)	)	PUNCT
ejpam-3543	115	28	(	(	PUNCT
ejpam-3543	115	29	∀x	∀x	X
ejpam-3543	115	30	,	,	PUNCT
ejpam-3543	115	31	y	y	PROPN
ejpam-3543	115	32	∈	∈	PROPN
ejpam-3543	115	33	x)(y	x)(y	PUNCT
ejpam-3543	116	1	∈	∈	PROPN
ejpam-3543	116	2	s	s	PART
ejpam-3543	116	3	⇒	⇒	NOUN
ejpam-3543	116	4	x	x	X
ejpam-3543	116	5	·	·	PUNCT
ejpam-3543	116	6	y	y	X
ejpam-3543	116	7	∈	∈	PROPN
ejpam-3543	116	8	s	s	PART
ejpam-3543	116	9	)	)	PUNCT
ejpam-3543	116	10	.	.	PUNCT
ejpam-3543	117	1	(	(	PUNCT
ejpam-3543	117	2	3	3	X
ejpam-3543	117	3	)	)	PUNCT
ejpam-3543	117	4	a	a	DET
ejpam-3543	117	5	up	up	ADJ
ejpam-3543	117	6	-	-	PUNCT
ejpam-3543	117	7	filter	filter	NOUN
ejpam-3543	117	8	of	of	ADP
ejpam-3543	117	9	x	x	SYM
ejpam-3543	117	10	if	if	SCONJ
ejpam-3543	117	11	(	(	PUNCT
ejpam-3543	117	12	i	i	NOUN
ejpam-3543	117	13	)	)	PUNCT
ejpam-3543	117	14	the	the	DET
ejpam-3543	117	15	constant	constant	ADJ
ejpam-3543	117	16	0	0	NUM
ejpam-3543	117	17	of	of	ADP
ejpam-3543	117	18	x	x	PRON
ejpam-3543	117	19	is	be	AUX
ejpam-3543	117	20	in	in	ADP
ejpam-3543	117	21	s	s	PROPN
ejpam-3543	117	22	,	,	PUNCT
ejpam-3543	117	23	and	and	CCONJ
ejpam-3543	117	24	(	(	PUNCT
ejpam-3543	117	25	ii	ii	NOUN
ejpam-3543	117	26	)	)	PUNCT
ejpam-3543	117	27	(	(	PUNCT
ejpam-3543	117	28	∀x	∀x	X
ejpam-3543	117	29	,	,	PUNCT
ejpam-3543	117	30	y	y	PROPN
ejpam-3543	117	31	∈	∈	PROPN
ejpam-3543	117	32	x)(x	x)(x	PROPN
ejpam-3543	117	33	·	·	PUNCT
ejpam-3543	118	1	y	y	PROPN
ejpam-3543	118	2	∈	∈	PROPN
ejpam-3543	118	3	s	s	PROPN
ejpam-3543	118	4	,	,	PUNCT
ejpam-3543	118	5	x	x	SYM
ejpam-3543	118	6	∈	∈	PROPN
ejpam-3543	118	7	s	s	PART
ejpam-3543	118	8	⇒	⇒	NOUN
ejpam-3543	118	9	y	y	PROPN
ejpam-3543	118	10	∈	∈	PROPN
ejpam-3543	118	11	s	s	PART
ejpam-3543	118	12	)	)	PUNCT
ejpam-3543	118	13	.	.	PUNCT
ejpam-3543	119	1	(	(	PUNCT
ejpam-3543	119	2	4	4	X
ejpam-3543	119	3	)	)	PUNCT
ejpam-3543	119	4	a	a	DET
ejpam-3543	119	5	up	up	ADJ
ejpam-3543	119	6	-	-	PUNCT
ejpam-3543	119	7	ideal	ideal	NOUN
ejpam-3543	119	8	of	of	ADP
ejpam-3543	119	9	x	x	PRON
ejpam-3543	119	10	if	if	SCONJ
ejpam-3543	119	11	(	(	PUNCT
ejpam-3543	119	12	i	i	NOUN
ejpam-3543	119	13	)	)	PUNCT
ejpam-3543	119	14	the	the	DET
ejpam-3543	119	15	constant	constant	ADJ
ejpam-3543	119	16	0	0	NUM
ejpam-3543	119	17	of	of	ADP
ejpam-3543	119	18	x	x	PRON
ejpam-3543	119	19	is	be	AUX
ejpam-3543	119	20	in	in	ADP
ejpam-3543	119	21	s	s	PROPN
ejpam-3543	119	22	,	,	PUNCT
ejpam-3543	119	23	and	and	CCONJ
ejpam-3543	119	24	(	(	PUNCT
ejpam-3543	119	25	ii	ii	NOUN
ejpam-3543	119	26	)	)	PUNCT
ejpam-3543	119	27	(	(	PUNCT
ejpam-3543	119	28	∀x	∀x	X
ejpam-3543	119	29	,	,	PUNCT
ejpam-3543	119	30	y	y	PROPN
ejpam-3543	119	31	,	,	PUNCT
ejpam-3543	119	32	z	z	PROPN
ejpam-3543	119	33	∈	∈	PROPN
ejpam-3543	119	34	x)(x	x)(x	PROPN
ejpam-3543	119	35	·	·	PUNCT
ejpam-3543	119	36	(	(	PUNCT
ejpam-3543	119	37	y	y	PROPN
ejpam-3543	119	38	·	·	PUNCT
ejpam-3543	119	39	z	z	X
ejpam-3543	119	40	)	)	PUNCT
ejpam-3543	119	41	∈	∈	PROPN
ejpam-3543	119	42	s	s	PROPN
ejpam-3543	119	43	,	,	PUNCT
ejpam-3543	119	44	y	y	PROPN
ejpam-3543	119	45	∈	∈	PROPN
ejpam-3543	119	46	s	s	PART
ejpam-3543	119	47	⇒	⇒	NOUN
ejpam-3543	119	48	x	x	PUNCT
ejpam-3543	119	49	·	·	PUNCT
ejpam-3543	119	50	z	z	PUNCT
ejpam-3543	119	51	∈	∈	PROPN
ejpam-3543	119	52	s	s	NOUN
ejpam-3543	119	53	)	)	PUNCT
ejpam-3543	119	54	.	.	PUNCT
ejpam-3543	120	1	(	(	PUNCT
ejpam-3543	120	2	5	5	X
ejpam-3543	120	3	)	)	PUNCT
ejpam-3543	120	4	a	a	DET
ejpam-3543	120	5	strongly	strongly	ADV
ejpam-3543	120	6	up	up	ADJ
ejpam-3543	120	7	-	-	PUNCT
ejpam-3543	120	8	ideal	ideal	NOUN
ejpam-3543	120	9	of	of	ADP
ejpam-3543	120	10	x	x	PRON
ejpam-3543	120	11	if	if	SCONJ
ejpam-3543	120	12	(	(	PUNCT
ejpam-3543	120	13	i	i	NOUN
ejpam-3543	120	14	)	)	PUNCT
ejpam-3543	120	15	the	the	DET
ejpam-3543	120	16	constant	constant	ADJ
ejpam-3543	120	17	0	0	NUM
ejpam-3543	120	18	of	of	ADP
ejpam-3543	120	19	x	x	PRON
ejpam-3543	120	20	is	be	AUX
ejpam-3543	120	21	in	in	ADP
ejpam-3543	120	22	s	s	PROPN
ejpam-3543	120	23	,	,	PUNCT
ejpam-3543	120	24	and	and	CCONJ
ejpam-3543	120	25	(	(	PUNCT
ejpam-3543	120	26	ii	ii	NOUN
ejpam-3543	120	27	)	)	PUNCT
ejpam-3543	120	28	(	(	PUNCT
ejpam-3543	120	29	∀x	∀x	X
ejpam-3543	120	30	,	,	PUNCT
ejpam-3543	120	31	y	y	PROPN
ejpam-3543	120	32	,	,	PUNCT
ejpam-3543	120	33	z	z	PROPN
ejpam-3543	120	34	∈	∈	PROPN
ejpam-3543	120	35	x)((z	x)((z	PROPN
ejpam-3543	120	36	·	·	PUNCT
ejpam-3543	121	1	y	y	X
ejpam-3543	121	2	)	)	PUNCT
ejpam-3543	121	3	·	·	PUNCT
ejpam-3543	122	1	(	(	PUNCT
ejpam-3543	122	2	z	z	NOUN
ejpam-3543	122	3	·	·	PUNCT
ejpam-3543	122	4	x	x	X
ejpam-3543	122	5	)	)	PUNCT
ejpam-3543	122	6	∈	∈	PROPN
ejpam-3543	122	7	s	s	PROPN
ejpam-3543	122	8	,	,	PUNCT
ejpam-3543	122	9	y	y	PROPN
ejpam-3543	122	10	∈	∈	PROPN
ejpam-3543	122	11	s	s	PART
ejpam-3543	122	12	⇒	⇒	NOUN
ejpam-3543	122	13	x	x	PUNCT
ejpam-3543	122	14	∈	∈	PROPN
ejpam-3543	122	15	s	s	PART
ejpam-3543	122	16	)	)	PUNCT
ejpam-3543	122	17	.	.	PUNCT
ejpam-3543	123	1	guntasow	guntasow	VERB
ejpam-3543	123	2	et	et	PROPN
ejpam-3543	123	3	al	al	PROPN
ejpam-3543	123	4	.	.	PUNCT
ejpam-3543	124	1	[	[	X
ejpam-3543	124	2	3	3	X
ejpam-3543	124	3	]	]	PUNCT
ejpam-3543	124	4	proved	prove	VERB
ejpam-3543	124	5	that	that	SCONJ
ejpam-3543	124	6	the	the	DET
ejpam-3543	124	7	notion	notion	NOUN
ejpam-3543	124	8	of	of	ADP
ejpam-3543	124	9	up	up	ADV
ejpam-3543	124	10	-	-	PUNCT
ejpam-3543	124	11	subalgebras	subalgebras	PROPN
ejpam-3543	124	12	is	be	AUX
ejpam-3543	124	13	a	a	DET
ejpam-3543	124	14	generalization	generalization	NOUN
ejpam-3543	124	15	of	of	ADP
ejpam-3543	124	16	near	near	ADP
ejpam-3543	124	17	up	up	NOUN
ejpam-3543	124	18	-	-	PUNCT
ejpam-3543	124	19	filters	filter	NOUN
ejpam-3543	124	20	,	,	PUNCT
ejpam-3543	124	21	the	the	DET
ejpam-3543	124	22	notion	notion	NOUN
ejpam-3543	124	23	of	of	ADP
ejpam-3543	124	24	near	near	ADP
ejpam-3543	124	25	up	up	ADP
ejpam-3543	124	26	-	-	PUNCT
ejpam-3543	124	27	filters	filter	NOUN
ejpam-3543	124	28	is	be	AUX
ejpam-3543	124	29	a	a	DET
ejpam-3543	124	30	generalization	generalization	NOUN
ejpam-3543	124	31	of	of	ADP
ejpam-3543	124	32	up	up	ADJ
ejpam-3543	124	33	-	-	PUNCT
ejpam-3543	124	34	filters	filter	NOUN
ejpam-3543	124	35	,	,	PUNCT
ejpam-3543	124	36	the	the	DET
ejpam-3543	124	37	notion	notion	NOUN
ejpam-3543	124	38	of	of	ADP
ejpam-3543	124	39	up	up	ADP
ejpam-3543	124	40	-	-	PUNCT
ejpam-3543	124	41	filters	filter	NOUN
ejpam-3543	124	42	is	be	AUX
ejpam-3543	124	43	a	a	DET
ejpam-3543	124	44	generalization	generalization	NOUN
ejpam-3543	124	45	of	of	ADP
ejpam-3543	124	46	up	up	ADJ
ejpam-3543	124	47	-	-	PUNCT
ejpam-3543	124	48	ideals	ideal	NOUN
ejpam-3543	124	49	,	,	PUNCT
ejpam-3543	124	50	and	and	CCONJ
ejpam-3543	124	51	the	the	DET
ejpam-3543	124	52	notion	notion	NOUN
ejpam-3543	124	53	of	of	ADP
ejpam-3543	124	54	up	up	ADJ
ejpam-3543	124	55	-	-	PUNCT
ejpam-3543	124	56	ideals	ideal	NOUN
ejpam-3543	124	57	is	be	AUX
ejpam-3543	124	58	a	a	DET
ejpam-3543	124	59	generalization	generalization	NOUN
ejpam-3543	124	60	of	of	ADP
ejpam-3543	124	61	strongly	strongly	ADV
ejpam-3543	124	62	up	up	ADJ
ejpam-3543	124	63	-	-	PUNCT
ejpam-3543	124	64	ideals	ideal	NOUN
ejpam-3543	124	65	.	.	PUNCT
ejpam-3543	125	1	moreover	moreover	ADV
ejpam-3543	125	2	,	,	PUNCT
ejpam-3543	125	3	they	they	PRON
ejpam-3543	125	4	also	also	ADV
ejpam-3543	125	5	proved	prove	VERB
ejpam-3543	125	6	that	that	SCONJ
ejpam-3543	125	7	a	a	DET
ejpam-3543	125	8	up	up	NOUN
ejpam-3543	125	9	-	-	PUNCT
ejpam-3543	125	10	algebra	algebra	NOUN
ejpam-3543	125	11	x	x	PUNCT
ejpam-3543	125	12	is	be	AUX
ejpam-3543	125	13	the	the	DET
ejpam-3543	125	14	only	only	ADJ
ejpam-3543	125	15	one	one	NUM
ejpam-3543	125	16	strongly	strongly	ADV
ejpam-3543	125	17	up	up	ADP
ejpam-3543	125	18	-	-	PUNCT
ejpam-3543	125	19	ideal	ideal	NOUN
ejpam-3543	125	20	of	of	ADP
ejpam-3543	125	21	itself	itself	PRON
ejpam-3543	125	22	.	.	PUNCT
ejpam-3543	126	1	m.	m.	PROPN
ejpam-3543	126	2	songsaeng	songsaeng	PROPN
ejpam-3543	126	3	,	,	PUNCT
ejpam-3543	126	4	a.	a.	NOUN
ejpam-3543	126	5	iampan	iampan	PROPN
ejpam-3543	126	6	/	/	SYM
ejpam-3543	126	7	eur	eur	PROPN
ejpam-3543	126	8	.	.	PUNCT
ejpam-3543	127	1	j.	j.	PROPN
ejpam-3543	127	2	pure	pure	PROPN
ejpam-3543	127	3	appl	appl	PROPN
ejpam-3543	127	4	.	.	PROPN
ejpam-3543	127	5	math	math	PROPN
ejpam-3543	127	6	,	,	PUNCT
ejpam-3543	127	7	12	12	NUM
ejpam-3543	127	8	(	(	PUNCT
ejpam-3543	127	9	4	4	NUM
ejpam-3543	127	10	)	)	PUNCT
ejpam-3543	127	11	(	(	PUNCT
ejpam-3543	127	12	2019	2019	NUM
ejpam-3543	127	13	)	)	PUNCT
ejpam-3543	127	14	,	,	PUNCT
ejpam-3543	127	15	1382	1382	NUM
ejpam-3543	127	16	-	-	SYM
ejpam-3543	127	17	1409	1409	NUM
ejpam-3543	127	18	1386	1386	NUM
ejpam-3543	127	19	3	3	NUM
ejpam-3543	127	20	.	.	X
ejpam-3543	127	21	nss	nss	NOUN
ejpam-3543	127	22	in	in	ADP
ejpam-3543	127	23	up	up	ADV
ejpam-3543	127	24	-	-	PUNCT
ejpam-3543	127	25	algebras	algebras	NOUN
ejpam-3543	127	26	in	in	ADP
ejpam-3543	127	27	1965	1965	NUM
ejpam-3543	127	28	,	,	PUNCT
ejpam-3543	127	29	zadeh	zadeh	PROPN
ejpam-3543	128	1	[	[	X
ejpam-3543	128	2	29	29	NUM
ejpam-3543	128	3	]	]	PUNCT
ejpam-3543	128	4	introduced	introduce	VERB
ejpam-3543	128	5	the	the	DET
ejpam-3543	128	6	notion	notion	NOUN
ejpam-3543	128	7	of	of	ADP
ejpam-3543	128	8	fuzzy	fuzzy	ADJ
ejpam-3543	128	9	sets	set	NOUN
ejpam-3543	128	10	as	as	ADP
ejpam-3543	128	11	the	the	DET
ejpam-3543	128	12	following	follow	VERB
ejpam-3543	128	13	definition	definition	NOUN
ejpam-3543	128	14	.	.	PUNCT
ejpam-3543	129	1	a	a	DET
ejpam-3543	129	2	fuzzy	fuzzy	ADJ
ejpam-3543	129	3	set	set	NOUN
ejpam-3543	129	4	(	(	PUNCT
ejpam-3543	129	5	briefly	briefly	ADV
ejpam-3543	129	6	,	,	PUNCT
ejpam-3543	129	7	fs	fs	PROPN
ejpam-3543	129	8	)	)	PUNCT
ejpam-3543	129	9	in	in	ADP
ejpam-3543	129	10	a	a	DET
ejpam-3543	129	11	nonempty	nonempty	ADV
ejpam-3543	129	12	set	set	VERB
ejpam-3543	129	13	x	x	SYM
ejpam-3543	129	14	(	(	PUNCT
ejpam-3543	129	15	or	or	CCONJ
ejpam-3543	129	16	a	a	DET
ejpam-3543	129	17	fuzzy	fuzzy	ADJ
ejpam-3543	129	18	subset	subset	NOUN
ejpam-3543	129	19	of	of	ADP
ejpam-3543	129	20	x	x	X
ejpam-3543	129	21	)	)	PUNCT
ejpam-3543	129	22	is	be	AUX
ejpam-3543	129	23	an	an	DET
ejpam-3543	129	24	arbitrary	arbitrary	ADJ
ejpam-3543	129	25	function	function	NOUN
ejpam-3543	129	26	f	f	NOUN
ejpam-3543	129	27	:	:	PUNCT
ejpam-3543	129	28	x	x	X
ejpam-3543	129	29	→	→	PUNCT
ejpam-3543	129	30	[	[	X
ejpam-3543	129	31	0	0	NUM
ejpam-3543	129	32	,	,	PUNCT
ejpam-3543	129	33	1	1	NUM
ejpam-3543	129	34	]	]	PUNCT
ejpam-3543	129	35	where	where	SCONJ
ejpam-3543	129	36	[	[	X
ejpam-3543	129	37	0	0	NUM
ejpam-3543	129	38	,	,	PUNCT
ejpam-3543	129	39	1	1	NUM
ejpam-3543	129	40	]	]	PUNCT
ejpam-3543	129	41	is	be	AUX
ejpam-3543	129	42	the	the	DET
ejpam-3543	129	43	unit	unit	NOUN
ejpam-3543	129	44	segment	segment	NOUN
ejpam-3543	129	45	of	of	ADP
ejpam-3543	129	46	the	the	DET
ejpam-3543	129	47	real	real	ADJ
ejpam-3543	129	48	line	line	NOUN
ejpam-3543	129	49	,	,	PUNCT
ejpam-3543	129	50	and	and	CCONJ
ejpam-3543	129	51	the	the	DET
ejpam-3543	129	52	fuzzy	fuzzy	ADJ
ejpam-3543	129	53	set	set	NOUN
ejpam-3543	129	54	f	f	PROPN
ejpam-3543	129	55	defined	define	VERB
ejpam-3543	129	56	by	by	ADP
ejpam-3543	129	57	f(x	f(x	PROPN
ejpam-3543	129	58	)	)	PUNCT
ejpam-3543	129	59	=	=	SYM
ejpam-3543	130	1	1−	1−	NUM
ejpam-3543	130	2	f(x	f(x	PROPN
ejpam-3543	130	3	)	)	PUNCT
ejpam-3543	130	4	for	for	ADP
ejpam-3543	130	5	all	all	DET
ejpam-3543	130	6	x	x	SYM
ejpam-3543	130	7	∈	∈	NOUN
ejpam-3543	130	8	x	x	PUNCT
ejpam-3543	130	9	is	be	AUX
ejpam-3543	130	10	said	say	VERB
ejpam-3543	130	11	to	to	PART
ejpam-3543	130	12	be	be	AUX
ejpam-3543	130	13	the	the	DET
ejpam-3543	130	14	complement	complement	NOUN
ejpam-3543	130	15	of	of	ADP
ejpam-3543	130	16	f	f	PROPN
ejpam-3543	130	17	in	in	ADP
ejpam-3543	130	18	x.	x.	PROPN
ejpam-3543	130	19	in	in	ADP
ejpam-3543	130	20	1999	1999	NUM
ejpam-3543	130	21	,	,	PUNCT
ejpam-3543	130	22	smarandache	smarandache	NOUN
ejpam-3543	131	1	[	[	X
ejpam-3543	131	2	22	22	NUM
ejpam-3543	131	3	]	]	PUNCT
ejpam-3543	131	4	introduced	introduce	VERB
ejpam-3543	131	5	the	the	DET
ejpam-3543	131	6	notion	notion	NOUN
ejpam-3543	131	7	of	of	ADP
ejpam-3543	131	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	131	9	sets	set	NOUN
ejpam-3543	131	10	as	as	ADP
ejpam-3543	131	11	the	the	DET
ejpam-3543	131	12	following	follow	VERB
ejpam-3543	131	13	definition	definition	NOUN
ejpam-3543	131	14	.	.	PUNCT
ejpam-3543	132	1	a	a	DET
ejpam-3543	132	2	neutrosophic	neutrosophic	ADJ
ejpam-3543	132	3	set	set	NOUN
ejpam-3543	132	4	(	(	PUNCT
ejpam-3543	132	5	briefly	briefly	ADV
ejpam-3543	132	6	,	,	PUNCT
ejpam-3543	132	7	ns	ns	NUM
ejpam-3543	132	8	)	)	PUNCT
ejpam-3543	132	9	in	in	ADP
ejpam-3543	132	10	a	a	DET
ejpam-3543	132	11	nonempty	nonempty	ADV
ejpam-3543	132	12	set	set	VERB
ejpam-3543	132	13	x	x	PUNCT
ejpam-3543	132	14	is	be	AUX
ejpam-3543	132	15	a	a	DET
ejpam-3543	132	16	structure	structure	NOUN
ejpam-3543	132	17	of	of	ADP
ejpam-3543	132	18	the	the	DET
ejpam-3543	132	19	form	form	NOUN
ejpam-3543	132	20	:	:	PUNCT
ejpam-3543	132	21	λ	λ	X
ejpam-3543	132	22	=	=	PRON
ejpam-3543	132	23	{	{	PUNCT
ejpam-3543	132	24	(	(	PUNCT
ejpam-3543	132	25	x	x	NOUN
ejpam-3543	132	26	,	,	PUNCT
ejpam-3543	132	27	λt	λt	X
ejpam-3543	132	28	(	(	PUNCT
ejpam-3543	132	29	x	x	NOUN
ejpam-3543	132	30	)	)	PUNCT
ejpam-3543	132	31	,	,	PUNCT
ejpam-3543	132	32	λi(x	λi(x	NUM
ejpam-3543	132	33	)	)	PUNCT
ejpam-3543	132	34	,	,	PUNCT
ejpam-3543	132	35	λf	λf	X
ejpam-3543	132	36	(	(	PUNCT
ejpam-3543	132	37	x	x	NOUN
ejpam-3543	132	38	)	)	PUNCT
ejpam-3543	132	39	)	)	PUNCT
ejpam-3543	133	1	|	|	ADV
ejpam-3543	133	2	x	x	SYM
ejpam-3543	133	3	∈	∈	NOUN
ejpam-3543	133	4	x	x	PRON
ejpam-3543	133	5	}	}	PUNCT
ejpam-3543	133	6	(	(	PUNCT
ejpam-3543	133	7	3.1	3.1	NUM
ejpam-3543	133	8	)	)	PUNCT
ejpam-3543	133	9	where	where	SCONJ
ejpam-3543	133	10	λt	λt	ADP
ejpam-3543	133	11	:	:	PUNCT
ejpam-3543	133	12	x	x	X
ejpam-3543	133	13	→	→	SYM
ejpam-3543	134	1	[	[	X
ejpam-3543	134	2	0	0	NUM
ejpam-3543	134	3	,	,	PUNCT
ejpam-3543	134	4	1	1	NUM
ejpam-3543	134	5	]	]	PUNCT
ejpam-3543	134	6	is	be	AUX
ejpam-3543	134	7	a	a	DET
ejpam-3543	134	8	truth	truth	NOUN
ejpam-3543	134	9	membership	membership	NOUN
ejpam-3543	134	10	function	function	NOUN
ejpam-3543	134	11	,	,	PUNCT
ejpam-3543	134	12	λi	λi	ADP
ejpam-3543	134	13	:	:	PUNCT
ejpam-3543	134	14	x	x	X
ejpam-3543	134	15	→	→	SYM
ejpam-3543	135	1	[	[	X
ejpam-3543	135	2	0	0	NUM
ejpam-3543	135	3	,	,	PUNCT
ejpam-3543	135	4	1	1	NUM
ejpam-3543	135	5	]	]	PUNCT
ejpam-3543	135	6	is	be	AUX
ejpam-3543	135	7	an	an	DET
ejpam-3543	135	8	indeterminate	indeterminate	ADJ
ejpam-3543	135	9	membership	membership	NOUN
ejpam-3543	135	10	function	function	NOUN
ejpam-3543	135	11	,	,	PUNCT
ejpam-3543	135	12	and	and	CCONJ
ejpam-3543	135	13	λf	λf	ADP
ejpam-3543	135	14	:	:	PUNCT
ejpam-3543	135	15	x	x	X
ejpam-3543	135	16	→	→	SYM
ejpam-3543	136	1	[	[	X
ejpam-3543	136	2	0	0	NUM
ejpam-3543	136	3	,	,	PUNCT
ejpam-3543	136	4	1	1	NUM
ejpam-3543	136	5	]	]	PUNCT
ejpam-3543	136	6	is	be	AUX
ejpam-3543	136	7	a	a	DET
ejpam-3543	136	8	false	false	ADJ
ejpam-3543	136	9	membership	membership	NOUN
ejpam-3543	136	10	function	function	NOUN
ejpam-3543	136	11	.	.	PUNCT
ejpam-3543	137	1	for	for	ADP
ejpam-3543	137	2	our	our	PRON
ejpam-3543	137	3	convenience	convenience	NOUN
ejpam-3543	137	4	,	,	PUNCT
ejpam-3543	137	5	we	we	PRON
ejpam-3543	137	6	will	will	AUX
ejpam-3543	137	7	denote	denote	VERB
ejpam-3543	137	8	a	a	DET
ejpam-3543	137	9	ns	ns	NOUN
ejpam-3543	137	10	as	as	ADP
ejpam-3543	137	11	λ	λ	X
ejpam-3543	137	12	=	=	SYM
ejpam-3543	137	13	(	(	PUNCT
ejpam-3543	137	14	x	x	X
ejpam-3543	137	15	,	,	PUNCT
ejpam-3543	137	16	λt	λt	INTJ
ejpam-3543	137	17	,	,	PUNCT
ejpam-3543	137	18	λi	λi	INTJ
ejpam-3543	137	19	,	,	PUNCT
ejpam-3543	137	20	λf	λf	PROPN
ejpam-3543	137	21	)	)	PUNCT
ejpam-3543	137	22	=	=	SYM
ejpam-3543	138	1	(	(	PUNCT
ejpam-3543	138	2	x	x	X
ejpam-3543	138	3	,	,	PUNCT
ejpam-3543	138	4	λt	λt	ADP
ejpam-3543	138	5	,	,	PUNCT
ejpam-3543	138	6	i	i	PRON
ejpam-3543	138	7	,	,	PUNCT
ejpam-3543	138	8	f	f	PROPN
ejpam-3543	138	9	)	)	PUNCT
ejpam-3543	138	10	=	=	PRON
ejpam-3543	138	11	{	{	PUNCT
ejpam-3543	138	12	(	(	PUNCT
ejpam-3543	138	13	x	x	NOUN
ejpam-3543	138	14	,	,	PUNCT
ejpam-3543	138	15	λt	λt	X
ejpam-3543	138	16	(	(	PUNCT
ejpam-3543	138	17	x	x	NOUN
ejpam-3543	138	18	)	)	PUNCT
ejpam-3543	138	19	,	,	PUNCT
ejpam-3543	138	20	λi(x	λi(x	NUM
ejpam-3543	138	21	)	)	PUNCT
ejpam-3543	138	22	,	,	PUNCT
ejpam-3543	138	23	λf	λf	X
ejpam-3543	138	24	(	(	PUNCT
ejpam-3543	138	25	x	x	NOUN
ejpam-3543	138	26	)	)	PUNCT
ejpam-3543	138	27	)	)	PUNCT
ejpam-3543	139	1	|	|	ADV
ejpam-3543	139	2	x	x	SYM
ejpam-3543	139	3	∈	∈	NOUN
ejpam-3543	139	4	x	x	X
ejpam-3543	139	5	}	}	PUNCT
ejpam-3543	139	6	.	.	PUNCT
ejpam-3543	140	1	definition	definition	NOUN
ejpam-3543	140	2	3	3	NUM
ejpam-3543	140	3	.	.	PUNCT
ejpam-3543	141	1	[	[	X
ejpam-3543	141	2	22	22	NUM
ejpam-3543	141	3	]	]	PUNCT
ejpam-3543	141	4	let	let	VERB
ejpam-3543	141	5	λ	λ	PART
ejpam-3543	141	6	be	be	AUX
ejpam-3543	141	7	a	a	DET
ejpam-3543	141	8	ns	ns	NOUN
ejpam-3543	141	9	in	in	ADP
ejpam-3543	141	10	a	a	DET
ejpam-3543	141	11	nonempty	nonempty	ADV
ejpam-3543	141	12	set	set	VERB
ejpam-3543	141	13	x.	x.	NOUN
ejpam-3543	141	14	the	the	DET
ejpam-3543	141	15	ns	ns	PROPN
ejpam-3543	141	16	λ	λ	NOUN
ejpam-3543	141	17	=	=	SYM
ejpam-3543	141	18	(	(	PUNCT
ejpam-3543	141	19	x	x	X
ejpam-3543	141	20	,	,	PUNCT
ejpam-3543	141	21	λt	λt	ADP
ejpam-3543	141	22	,	,	PUNCT
ejpam-3543	141	23	i	i	PRON
ejpam-3543	141	24	,	,	PUNCT
ejpam-3543	141	25	f	f	PROPN
ejpam-3543	141	26	)	)	PUNCT
ejpam-3543	141	27	in	in	ADP
ejpam-3543	141	28	x	x	PUNCT
ejpam-3543	141	29	defined	define	VERB
ejpam-3543	141	30	by	by	ADP
ejpam-3543	141	31	(	(	PUNCT
ejpam-3543	141	32	∀x	∀x	X
ejpam-3543	141	33	∈	∈	PROPN
ejpam-3543	141	34	x	x	NOUN
ejpam-3543	141	35	)	)	PUNCT
ejpam-3543	141	36	λt	λt	PROPN
ejpam-3543	141	37	(	(	PUNCT
ejpam-3543	141	38	x	x	NOUN
ejpam-3543	141	39	)	)	PUNCT
ejpam-3543	141	40	=	=	SYM
ejpam-3543	141	41	1−	1−	NUM
ejpam-3543	141	42	λt	λt	ADP
ejpam-3543	141	43	(	(	PUNCT
ejpam-3543	141	44	x	x	NOUN
ejpam-3543	141	45	)	)	PUNCT
ejpam-3543	141	46	λi(x	λi(x	NUM
ejpam-3543	141	47	)	)	PUNCT
ejpam-3543	141	48	=	=	SYM
ejpam-3543	141	49	1−	1−	NUM
ejpam-3543	141	50	λi(x	λi(x	NUM
ejpam-3543	141	51	)	)	PUNCT
ejpam-3543	142	1	λf	λf	X
ejpam-3543	142	2	(	(	PUNCT
ejpam-3543	142	3	x	x	NOUN
ejpam-3543	142	4	)	)	PUNCT
ejpam-3543	142	5	=	=	SYM
ejpam-3543	143	1	1−	1−	NUM
ejpam-3543	143	2	λf	λf	X
ejpam-3543	143	3	(	(	PUNCT
ejpam-3543	143	4	x	x	NOUN
ejpam-3543	143	5	)	)	PUNCT
ejpam-3543	143	6			PROPN
ejpam-3543	143	7	(	(	PUNCT
ejpam-3543	143	8	3.2	3.2	NUM
ejpam-3543	143	9	)	)	PUNCT
ejpam-3543	143	10	is	be	AUX
ejpam-3543	143	11	called	call	VERB
ejpam-3543	143	12	the	the	DET
ejpam-3543	143	13	complement	complement	NOUN
ejpam-3543	143	14	of	of	ADP
ejpam-3543	143	15	λ	λ	PROPN
ejpam-3543	143	16	in	in	ADP
ejpam-3543	143	17	x.	x.	PROPN
ejpam-3543	143	18	remark	remark	PROPN
ejpam-3543	143	19	1	1	NUM
ejpam-3543	143	20	.	.	PUNCT
ejpam-3543	144	1	for	for	ADP
ejpam-3543	144	2	all	all	DET
ejpam-3543	144	3	ns	ns	NUM
ejpam-3543	144	4	λ	λ	NOUN
ejpam-3543	144	5	in	in	ADP
ejpam-3543	144	6	a	a	DET
ejpam-3543	144	7	nonempty	nonempty	ADV
ejpam-3543	144	8	set	set	VERB
ejpam-3543	144	9	x	x	NOUN
ejpam-3543	144	10	,	,	PUNCT
ejpam-3543	144	11	we	we	PRON
ejpam-3543	144	12	have	have	VERB
ejpam-3543	144	13	λ	λ	NOUN
ejpam-3543	144	14	=	=	SYM
ejpam-3543	144	15	λ	λ	PROPN
ejpam-3543	144	16	.	.	PUNCT
ejpam-3543	145	1	lemma	lemma	PROPN
ejpam-3543	145	2	1	1	NUM
ejpam-3543	145	3	.	.	PUNCT
ejpam-3543	146	1	[	[	X
ejpam-3543	146	2	27	27	NUM
ejpam-3543	146	3	]	]	PUNCT
ejpam-3543	146	4	let	let	VERB
ejpam-3543	146	5	a	a	DET
ejpam-3543	146	6	,	,	PUNCT
ejpam-3543	146	7	b	b	NOUN
ejpam-3543	146	8	,	,	PUNCT
ejpam-3543	146	9	c	c	PROPN
ejpam-3543	146	10	∈	∈	PROPN
ejpam-3543	146	11	r.	r.	PROPN
ejpam-3543	146	12	then	then	ADV
ejpam-3543	146	13	the	the	DET
ejpam-3543	146	14	following	follow	VERB
ejpam-3543	146	15	statements	statement	NOUN
ejpam-3543	146	16	hold	hold	VERB
ejpam-3543	146	17	:	:	PUNCT
ejpam-3543	146	18	(	(	PUNCT
ejpam-3543	146	19	1	1	X
ejpam-3543	146	20	)	)	PUNCT
ejpam-3543	146	21	a−min{b	a−min{b	NOUN
ejpam-3543	146	22	,	,	PUNCT
ejpam-3543	146	23	c	c	NOUN
ejpam-3543	146	24	}	}	PUNCT
ejpam-3543	146	25	=	=	SYM
ejpam-3543	146	26	max{a−	max{a−	PROPN
ejpam-3543	146	27	b	b	PROPN
ejpam-3543	146	28	,	,	PUNCT
ejpam-3543	146	29	a−	a−	PROPN
ejpam-3543	146	30	c	c	NOUN
ejpam-3543	146	31	}	}	PUNCT
ejpam-3543	146	32	,	,	PUNCT
ejpam-3543	146	33	and	and	CCONJ
ejpam-3543	146	34	(	(	PUNCT
ejpam-3543	146	35	2	2	NUM
ejpam-3543	146	36	)	)	PUNCT
ejpam-3543	146	37	a−max{b	a−max{b	NOUN
ejpam-3543	146	38	,	,	PUNCT
ejpam-3543	146	39	c	c	NOUN
ejpam-3543	146	40	}	}	PUNCT
ejpam-3543	146	41	=	=	SYM
ejpam-3543	146	42	min{a−	min{a−	PROPN
ejpam-3543	146	43	b	b	PROPN
ejpam-3543	146	44	,	,	PUNCT
ejpam-3543	146	45	a−	a−	PROPN
ejpam-3543	146	46	c	c	NOUN
ejpam-3543	146	47	}	}	PUNCT
ejpam-3543	146	48	.	.	PUNCT
ejpam-3543	147	1	the	the	DET
ejpam-3543	147	2	following	follow	VERB
ejpam-3543	147	3	lemma	lemma	PROPN
ejpam-3543	147	4	is	be	AUX
ejpam-3543	147	5	easily	easily	ADV
ejpam-3543	147	6	proved	prove	VERB
ejpam-3543	147	7	.	.	PUNCT
ejpam-3543	148	1	lemma	lemma	PROPN
ejpam-3543	148	2	2	2	X
ejpam-3543	148	3	.	.	PUNCT
ejpam-3543	149	1	let	let	VERB
ejpam-3543	149	2	f	f	PRON
ejpam-3543	149	3	be	be	AUX
ejpam-3543	149	4	a	a	DET
ejpam-3543	149	5	fuzzy	fuzzy	ADJ
ejpam-3543	149	6	set	set	NOUN
ejpam-3543	149	7	in	in	ADP
ejpam-3543	149	8	a	a	DET
ejpam-3543	149	9	nonempty	nonempty	ADV
ejpam-3543	149	10	set	set	VERB
ejpam-3543	149	11	x.	x.	NOUN
ejpam-3543	149	12	then	then	ADV
ejpam-3543	149	13	the	the	DET
ejpam-3543	149	14	following	follow	VERB
ejpam-3543	149	15	statements	statement	NOUN
ejpam-3543	149	16	hold	hold	VERB
ejpam-3543	149	17	:	:	PUNCT
ejpam-3543	149	18	(	(	PUNCT
ejpam-3543	149	19	1	1	X
ejpam-3543	149	20	)	)	PUNCT
ejpam-3543	149	21	(	(	PUNCT
ejpam-3543	149	22	∀x	∀x	X
ejpam-3543	149	23	,	,	PUNCT
ejpam-3543	149	24	y	y	PROPN
ejpam-3543	149	25	,	,	PUNCT
ejpam-3543	149	26	z	z	NOUN
ejpam-3543	149	27	∈	∈	PROPN
ejpam-3543	149	28	x)(f(x	x)(f(x	PUNCT
ejpam-3543	149	29	)	)	PUNCT
ejpam-3543	149	30	≥	≥	NOUN
ejpam-3543	149	31	min{f(y	min{f(y	NOUN
ejpam-3543	149	32	)	)	PUNCT
ejpam-3543	149	33	,	,	PUNCT
ejpam-3543	149	34	f(z	f(z	NUM
ejpam-3543	149	35	)	)	PUNCT
ejpam-3543	149	36	}	}	PUNCT
ejpam-3543	149	37	⇔	⇔	PROPN
ejpam-3543	149	38	f(x	f(x	PROPN
ejpam-3543	149	39	)	)	PUNCT
ejpam-3543	149	40	≤	≤	NOUN
ejpam-3543	150	1	max{f(y	max{f(y	NUM
ejpam-3543	150	2	)	)	PUNCT
ejpam-3543	151	1	,	,	PUNCT
ejpam-3543	151	2	f(z	f(z	PROPN
ejpam-3543	151	3	)	)	PUNCT
ejpam-3543	151	4	}	}	PUNCT
ejpam-3543	151	5	)	)	PUNCT
ejpam-3543	151	6	,	,	PUNCT
ejpam-3543	151	7	(	(	PUNCT
ejpam-3543	151	8	2	2	X
ejpam-3543	151	9	)	)	PUNCT
ejpam-3543	151	10	(	(	PUNCT
ejpam-3543	151	11	∀x	∀x	X
ejpam-3543	151	12	,	,	PUNCT
ejpam-3543	151	13	y	y	PROPN
ejpam-3543	151	14	,	,	PUNCT
ejpam-3543	151	15	z	z	NOUN
ejpam-3543	151	16	∈	∈	PROPN
ejpam-3543	151	17	x)(f(x	x)(f(x	PUNCT
ejpam-3543	151	18	)	)	PUNCT
ejpam-3543	152	1	≤	≤	NOUN
ejpam-3543	152	2	min{f(y	min{f(y	NOUN
ejpam-3543	152	3	)	)	PUNCT
ejpam-3543	152	4	,	,	PUNCT
ejpam-3543	152	5	f(z	f(z	NUM
ejpam-3543	152	6	)	)	PUNCT
ejpam-3543	152	7	}	}	PUNCT
ejpam-3543	152	8	⇔	⇔	PROPN
ejpam-3543	152	9	f(x	f(x	PROPN
ejpam-3543	152	10	)	)	PUNCT
ejpam-3543	152	11	≥	≥	NOUN
ejpam-3543	152	12	max{f(y	max{f(y	NUM
ejpam-3543	152	13	)	)	PUNCT
ejpam-3543	152	14	,	,	PUNCT
ejpam-3543	152	15	f(z	f(z	PROPN
ejpam-3543	152	16	)	)	PUNCT
ejpam-3543	152	17	}	}	PUNCT
ejpam-3543	152	18	)	)	PUNCT
ejpam-3543	152	19	,	,	PUNCT
ejpam-3543	152	20	(	(	PUNCT
ejpam-3543	152	21	3	3	X
ejpam-3543	152	22	)	)	PUNCT
ejpam-3543	152	23	(	(	PUNCT
ejpam-3543	152	24	∀x	∀x	X
ejpam-3543	152	25	,	,	PUNCT
ejpam-3543	152	26	y	y	PROPN
ejpam-3543	152	27	,	,	PUNCT
ejpam-3543	152	28	z	z	NOUN
ejpam-3543	152	29	∈	∈	PROPN
ejpam-3543	152	30	x)(f(x	x)(f(x	PUNCT
ejpam-3543	152	31	)	)	PUNCT
ejpam-3543	152	32	≥	≥	NOUN
ejpam-3543	152	33	max{f(y	max{f(y	NUM
ejpam-3543	152	34	)	)	PUNCT
ejpam-3543	152	35	,	,	PUNCT
ejpam-3543	152	36	f(z	f(z	NUM
ejpam-3543	152	37	)	)	PUNCT
ejpam-3543	152	38	}	}	PUNCT
ejpam-3543	152	39	⇔	⇔	PROPN
ejpam-3543	152	40	f(x	f(x	PROPN
ejpam-3543	152	41	)	)	PUNCT
ejpam-3543	152	42	≤	≤	NOUN
ejpam-3543	152	43	min{f(y	min{f(y	NUM
ejpam-3543	152	44	)	)	PUNCT
ejpam-3543	152	45	,	,	PUNCT
ejpam-3543	152	46	f(z	f(z	PROPN
ejpam-3543	152	47	)	)	PUNCT
ejpam-3543	152	48	}	}	PUNCT
ejpam-3543	152	49	)	)	PUNCT
ejpam-3543	152	50	,	,	PUNCT
ejpam-3543	152	51	and	and	CCONJ
ejpam-3543	152	52	(	(	PUNCT
ejpam-3543	152	53	4	4	NUM
ejpam-3543	152	54	)	)	PUNCT
ejpam-3543	152	55	(	(	PUNCT
ejpam-3543	152	56	∀x	∀x	X
ejpam-3543	152	57	,	,	PUNCT
ejpam-3543	152	58	y	y	PROPN
ejpam-3543	152	59	,	,	PUNCT
ejpam-3543	152	60	z	z	NOUN
ejpam-3543	152	61	∈	∈	PROPN
ejpam-3543	152	62	x)(f(x	x)(f(x	PUNCT
ejpam-3543	152	63	)	)	PUNCT
ejpam-3543	152	64	≤	≤	NOUN
ejpam-3543	153	1	max{f(y	max{f(y	NUM
ejpam-3543	153	2	)	)	PUNCT
ejpam-3543	153	3	,	,	PUNCT
ejpam-3543	153	4	f(z	f(z	NUM
ejpam-3543	153	5	)	)	PUNCT
ejpam-3543	153	6	}	}	PUNCT
ejpam-3543	153	7	⇔	⇔	PROPN
ejpam-3543	153	8	f(x	f(x	PROPN
ejpam-3543	153	9	)	)	PUNCT
ejpam-3543	153	10	≥	≥	NOUN
ejpam-3543	153	11	min{f(y	min{f(y	NUM
ejpam-3543	153	12	)	)	PUNCT
ejpam-3543	153	13	,	,	PUNCT
ejpam-3543	153	14	f(z	f(z	PROPN
ejpam-3543	153	15	)	)	PUNCT
ejpam-3543	153	16	}	}	PUNCT
ejpam-3543	153	17	)	)	PUNCT
ejpam-3543	153	18	.	.	PUNCT
ejpam-3543	154	1	m.	m.	PROPN
ejpam-3543	154	2	songsaeng	songsaeng	PROPN
ejpam-3543	154	3	,	,	PUNCT
ejpam-3543	154	4	a.	a.	NOUN
ejpam-3543	154	5	iampan	iampan	PROPN
ejpam-3543	154	6	/	/	SYM
ejpam-3543	154	7	eur	eur	PROPN
ejpam-3543	154	8	.	.	PUNCT
ejpam-3543	155	1	j.	j.	PROPN
ejpam-3543	155	2	pure	pure	PROPN
ejpam-3543	155	3	appl	appl	PROPN
ejpam-3543	155	4	.	.	PROPN
ejpam-3543	155	5	math	math	PROPN
ejpam-3543	155	6	,	,	PUNCT
ejpam-3543	155	7	12	12	NUM
ejpam-3543	155	8	(	(	PUNCT
ejpam-3543	155	9	4	4	NUM
ejpam-3543	155	10	)	)	PUNCT
ejpam-3543	155	11	(	(	PUNCT
ejpam-3543	155	12	2019	2019	NUM
ejpam-3543	155	13	)	)	PUNCT
ejpam-3543	155	14	,	,	PUNCT
ejpam-3543	155	15	1382	1382	NUM
ejpam-3543	155	16	-	-	SYM
ejpam-3543	155	17	1409	1409	NUM
ejpam-3543	155	18	1387	1387	NUM
ejpam-3543	155	19	in	in	ADP
ejpam-3543	155	20	what	what	PRON
ejpam-3543	155	21	follows	follow	VERB
ejpam-3543	155	22	,	,	PUNCT
ejpam-3543	155	23	let	let	VERB
ejpam-3543	155	24	x	x	PRON
ejpam-3543	155	25	denote	denote	VERB
ejpam-3543	155	26	a	a	DET
ejpam-3543	155	27	up	up	NOUN
ejpam-3543	155	28	-	-	PUNCT
ejpam-3543	155	29	algebra	algebra	NOUN
ejpam-3543	155	30	(	(	PUNCT
ejpam-3543	155	31	x	x	X
ejpam-3543	155	32	,	,	PUNCT
ejpam-3543	155	33	·	·	PUNCT
ejpam-3543	155	34	,	,	PUNCT
ejpam-3543	155	35	0	0	NUM
ejpam-3543	155	36	)	)	PUNCT
ejpam-3543	155	37	unless	unless	SCONJ
ejpam-3543	155	38	otherwise	otherwise	ADV
ejpam-3543	155	39	specified	specify	VERB
ejpam-3543	155	40	.	.	PUNCT
ejpam-3543	156	1	now	now	ADV
ejpam-3543	156	2	,	,	PUNCT
ejpam-3543	156	3	we	we	PRON
ejpam-3543	156	4	introduce	introduce	VERB
ejpam-3543	156	5	the	the	DET
ejpam-3543	156	6	notions	notion	NOUN
ejpam-3543	156	7	of	of	ADP
ejpam-3543	156	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	156	9	up	up	ADP
ejpam-3543	156	10	-	-	PUNCT
ejpam-3543	156	11	subalgebras	subalgebras	PROPN
ejpam-3543	156	12	,	,	PUNCT
ejpam-3543	156	13	neutrosophic	neutrosophic	ADJ
ejpam-3543	156	14	near	near	ADP
ejpam-3543	156	15	upfilters	upfilter	NOUN
ejpam-3543	156	16	,	,	PUNCT
ejpam-3543	156	17	neutrosophic	neutrosophic	ADJ
ejpam-3543	156	18	up	up	ADP
ejpam-3543	156	19	-	-	PUNCT
ejpam-3543	156	20	filters	filter	NOUN
ejpam-3543	156	21	,	,	PUNCT
ejpam-3543	156	22	neutrosophic	neutrosophic	ADJ
ejpam-3543	156	23	up	up	ADP
ejpam-3543	156	24	-	-	PUNCT
ejpam-3543	156	25	ideals	ideal	NOUN
ejpam-3543	156	26	,	,	PUNCT
ejpam-3543	156	27	and	and	CCONJ
ejpam-3543	156	28	neutrosophic	neutrosophic	ADJ
ejpam-3543	156	29	strongly	strongly	ADV
ejpam-3543	156	30	upideals	upideal	NOUN
ejpam-3543	156	31	of	of	ADP
ejpam-3543	156	32	up	up	ADP
ejpam-3543	156	33	-	-	PUNCT
ejpam-3543	156	34	algebras	algebras	X
ejpam-3543	156	35	,	,	PUNCT
ejpam-3543	156	36	provide	provide	VERB
ejpam-3543	156	37	the	the	DET
ejpam-3543	156	38	necessary	necessary	ADJ
ejpam-3543	156	39	examples	example	NOUN
ejpam-3543	156	40	,	,	PUNCT
ejpam-3543	156	41	investigate	investigate	VERB
ejpam-3543	156	42	their	their	PRON
ejpam-3543	156	43	properties	property	NOUN
ejpam-3543	156	44	,	,	PUNCT
ejpam-3543	156	45	and	and	CCONJ
ejpam-3543	156	46	prove	prove	VERB
ejpam-3543	156	47	their	their	PRON
ejpam-3543	156	48	generalizations	generalization	NOUN
ejpam-3543	156	49	.	.	PUNCT
ejpam-3543	157	1	definition	definition	NOUN
ejpam-3543	157	2	4	4	NUM
ejpam-3543	157	3	.	.	PUNCT
ejpam-3543	158	1	a	a	DET
ejpam-3543	158	2	ns	ns	NUM
ejpam-3543	158	3	λ	λ	NOUN
ejpam-3543	158	4	in	in	ADP
ejpam-3543	158	5	x	x	PROPN
ejpam-3543	158	6	is	be	AUX
ejpam-3543	158	7	called	call	VERB
ejpam-3543	158	8	a	a	DET
ejpam-3543	158	9	neutrosophic	neutrosophic	ADJ
ejpam-3543	158	10	up	up	ADP
ejpam-3543	158	11	-	-	PUNCT
ejpam-3543	158	12	subalgebra	subalgebra	NOUN
ejpam-3543	158	13	of	of	ADP
ejpam-3543	158	14	x	x	PRON
ejpam-3543	158	15	if	if	SCONJ
ejpam-3543	158	16	it	it	PRON
ejpam-3543	158	17	satisfies	satisfy	VERB
ejpam-3543	158	18	the	the	DET
ejpam-3543	158	19	following	follow	VERB
ejpam-3543	158	20	conditions	condition	NOUN
ejpam-3543	158	21	:	:	PUNCT
ejpam-3543	158	22	(	(	PUNCT
ejpam-3543	158	23	∀x	∀x	X
ejpam-3543	158	24	,	,	PUNCT
ejpam-3543	158	25	y	y	PROPN
ejpam-3543	158	26	∈	∈	PROPN
ejpam-3543	158	27	x)(λt	x)(λt	NOUN
ejpam-3543	158	28	(	(	PUNCT
ejpam-3543	158	29	x	x	SYM
ejpam-3543	158	30	·	·	PUNCT
ejpam-3543	158	31	y	y	X
ejpam-3543	158	32	)	)	PUNCT
ejpam-3543	158	33	≥	≥	NOUN
ejpam-3543	158	34	min{λt	min{λt	X
ejpam-3543	158	35	(	(	PUNCT
ejpam-3543	158	36	x	x	X
ejpam-3543	158	37	)	)	PUNCT
ejpam-3543	158	38	,	,	PUNCT
ejpam-3543	158	39	λt	λt	X
ejpam-3543	158	40	(	(	PUNCT
ejpam-3543	158	41	y	y	NOUN
ejpam-3543	158	42	)	)	PUNCT
ejpam-3543	158	43	}	}	PUNCT
ejpam-3543	158	44	)	)	PUNCT
ejpam-3543	158	45	,	,	PUNCT
ejpam-3543	158	46	(	(	PUNCT
ejpam-3543	158	47	3.3	3.3	NUM
ejpam-3543	158	48	)	)	PUNCT
ejpam-3543	158	49	(	(	PUNCT
ejpam-3543	158	50	∀x	∀x	X
ejpam-3543	158	51	,	,	PUNCT
ejpam-3543	158	52	y	y	PROPN
ejpam-3543	158	53	∈	∈	PROPN
ejpam-3543	158	54	x)(λi(x	x)(λi(x	PUNCT
ejpam-3543	158	55	·	·	PUNCT
ejpam-3543	158	56	y	y	X
ejpam-3543	158	57	)	)	PUNCT
ejpam-3543	158	58	≤	≤	NUM
ejpam-3543	158	59	max{λi(x	max{λi(x	NOUN
ejpam-3543	158	60	)	)	PUNCT
ejpam-3543	158	61	,	,	PUNCT
ejpam-3543	158	62	λi(y	λi(y	NUM
ejpam-3543	158	63	)	)	PUNCT
ejpam-3543	158	64	}	}	PUNCT
ejpam-3543	158	65	)	)	PUNCT
ejpam-3543	158	66	,	,	PUNCT
ejpam-3543	158	67	(	(	PUNCT
ejpam-3543	158	68	3.4	3.4	NUM
ejpam-3543	158	69	)	)	PUNCT
ejpam-3543	158	70	(	(	PUNCT
ejpam-3543	158	71	∀x	∀x	X
ejpam-3543	158	72	,	,	PUNCT
ejpam-3543	158	73	y	y	PROPN
ejpam-3543	158	74	∈	∈	PROPN
ejpam-3543	158	75	x)(λf	x)(λf	X
ejpam-3543	158	76	(	(	PUNCT
ejpam-3543	158	77	x	x	SYM
ejpam-3543	158	78	·	·	PUNCT
ejpam-3543	158	79	y	y	X
ejpam-3543	158	80	)	)	PUNCT
ejpam-3543	158	81	≥	≥	NOUN
ejpam-3543	158	82	min{λf	min{λf	X
ejpam-3543	158	83	(	(	PUNCT
ejpam-3543	158	84	x	x	X
ejpam-3543	158	85	)	)	PUNCT
ejpam-3543	158	86	,	,	PUNCT
ejpam-3543	158	87	λf	λf	X
ejpam-3543	158	88	(	(	PUNCT
ejpam-3543	158	89	y	y	NOUN
ejpam-3543	158	90	)	)	PUNCT
ejpam-3543	158	91	}	}	PUNCT
ejpam-3543	158	92	)	)	PUNCT
ejpam-3543	158	93	.	.	PUNCT
ejpam-3543	159	1	(	(	PUNCT
ejpam-3543	159	2	3.5	3.5	NUM
ejpam-3543	159	3	)	)	PUNCT
ejpam-3543	159	4	example	example	NOUN
ejpam-3543	159	5	4	4	NUM
ejpam-3543	159	6	.	.	PUNCT
ejpam-3543	160	1	let	let	VERB
ejpam-3543	160	2	x	x	PUNCT
ejpam-3543	160	3	=	=	PUNCT
ejpam-3543	160	4	{	{	PUNCT
ejpam-3543	160	5	0	0	NUM
ejpam-3543	160	6	,	,	PUNCT
ejpam-3543	160	7	1	1	NUM
ejpam-3543	160	8	,	,	PUNCT
ejpam-3543	160	9	2	2	NUM
ejpam-3543	160	10	,	,	PUNCT
ejpam-3543	160	11	3	3	NUM
ejpam-3543	160	12	,	,	PUNCT
ejpam-3543	160	13	4	4	NUM
ejpam-3543	160	14	}	}	PUNCT
ejpam-3543	160	15	be	be	AUX
ejpam-3543	160	16	a	a	DET
ejpam-3543	160	17	up	up	NOUN
ejpam-3543	160	18	-	-	PUNCT
ejpam-3543	160	19	algebra	algebra	NOUN
ejpam-3543	160	20	with	with	ADP
ejpam-3543	160	21	a	a	DET
ejpam-3543	160	22	fixed	fix	VERB
ejpam-3543	160	23	element	element	NOUN
ejpam-3543	160	24	0	0	PUNCT
ejpam-3543	160	25	and	and	CCONJ
ejpam-3543	160	26	a	a	DET
ejpam-3543	160	27	binary	binary	ADJ
ejpam-3543	160	28	operation	operation	NOUN
ejpam-3543	160	29	·	·	PUNCT
ejpam-3543	160	30	defined	define	VERB
ejpam-3543	160	31	by	by	ADP
ejpam-3543	160	32	the	the	DET
ejpam-3543	160	33	following	following	ADJ
ejpam-3543	160	34	cayley	cayley	ADJ
ejpam-3543	160	35	table	table	NOUN
ejpam-3543	160	36	:	:	PUNCT
ejpam-3543	160	37	·	·	PUNCT
ejpam-3543	160	38	0	0	NUM
ejpam-3543	160	39	1	1	NUM
ejpam-3543	160	40	2	2	NUM
ejpam-3543	160	41	3	3	NUM
ejpam-3543	160	42	4	4	NUM
ejpam-3543	160	43	0	0	NUM
ejpam-3543	160	44	0	0	NUM
ejpam-3543	160	45	1	1	NUM
ejpam-3543	160	46	2	2	NUM
ejpam-3543	160	47	3	3	NUM
ejpam-3543	160	48	4	4	NUM
ejpam-3543	160	49	1	1	NUM
ejpam-3543	160	50	0	0	NUM
ejpam-3543	160	51	0	0	NUM
ejpam-3543	160	52	2	2	NUM
ejpam-3543	160	53	2	2	NUM
ejpam-3543	160	54	4	4	NUM
ejpam-3543	160	55	2	2	NUM
ejpam-3543	160	56	0	0	NUM
ejpam-3543	160	57	0	0	NUM
ejpam-3543	160	58	0	0	NUM
ejpam-3543	160	59	2	2	NUM
ejpam-3543	160	60	4	4	NUM
ejpam-3543	160	61	3	3	NUM
ejpam-3543	160	62	0	0	NUM
ejpam-3543	160	63	0	0	NUM
ejpam-3543	160	64	0	0	NUM
ejpam-3543	160	65	0	0	NUM
ejpam-3543	160	66	4	4	NUM
ejpam-3543	160	67	4	4	NUM
ejpam-3543	160	68	0	0	NUM
ejpam-3543	160	69	1	1	NUM
ejpam-3543	160	70	2	2	NUM
ejpam-3543	160	71	3	3	NUM
ejpam-3543	160	72	0	0	NUM
ejpam-3543	160	73	we	we	PRON
ejpam-3543	160	74	define	define	VERB
ejpam-3543	160	75	a	a	DET
ejpam-3543	160	76	ns	ns	ADJ
ejpam-3543	160	77	λ	λ	NOUN
ejpam-3543	160	78	in	in	ADP
ejpam-3543	160	79	x	x	PUNCT
ejpam-3543	160	80	as	as	SCONJ
ejpam-3543	160	81	follows	follow	VERB
ejpam-3543	160	82	:	:	PUNCT
ejpam-3543	160	83	λt	λt	ADP
ejpam-3543	160	84	=	=	PUNCT
ejpam-3543	160	85	(	(	PUNCT
ejpam-3543	160	86	0	0	NUM
ejpam-3543	160	87	0.9	0.9	NUM
ejpam-3543	160	88	1	1	NUM
ejpam-3543	160	89	0.7	0.7	NUM
ejpam-3543	160	90	2	2	NUM
ejpam-3543	160	91	0.5	0.5	NUM
ejpam-3543	160	92	3	3	NUM
ejpam-3543	160	93	0.3	0.3	NUM
ejpam-3543	160	94	4	4	NUM
ejpam-3543	160	95	0.3	0.3	NUM
ejpam-3543	160	96	)	)	PUNCT
ejpam-3543	160	97	,	,	PUNCT
ejpam-3543	160	98	λi	λi	NOUN
ejpam-3543	160	99	=	=	X
ejpam-3543	160	100	(	(	PUNCT
ejpam-3543	160	101	0	0	NUM
ejpam-3543	160	102	0	0	NUM
ejpam-3543	160	103	1	1	NUM
ejpam-3543	160	104	0.8	0.8	NUM
ejpam-3543	160	105	2	2	NUM
ejpam-3543	160	106	0.4	0.4	NUM
ejpam-3543	160	107	3	3	NUM
ejpam-3543	160	108	0.2	0.2	NUM
ejpam-3543	160	109	4	4	NUM
ejpam-3543	160	110	0.4	0.4	NUM
ejpam-3543	160	111	)	)	PUNCT
ejpam-3543	160	112	,	,	PUNCT
ejpam-3543	160	113	λf	λf	X
ejpam-3543	160	114	=	=	PUNCT
ejpam-3543	160	115	(	(	PUNCT
ejpam-3543	160	116	0	0	NUM
ejpam-3543	160	117	1	1	NUM
ejpam-3543	160	118	1	1	NUM
ejpam-3543	160	119	0.6	0.6	NUM
ejpam-3543	160	120	2	2	NUM
ejpam-3543	160	121	0.8	0.8	NUM
ejpam-3543	160	122	3	3	NUM
ejpam-3543	160	123	0.3	0.3	NUM
ejpam-3543	160	124	4	4	NUM
ejpam-3543	160	125	0.2	0.2	NUM
ejpam-3543	160	126	)	)	PUNCT
ejpam-3543	160	127	.	.	PUNCT
ejpam-3543	161	1	hence	hence	ADV
ejpam-3543	161	2	,	,	PUNCT
ejpam-3543	161	3	λ	λ	PROPN
ejpam-3543	161	4	is	be	AUX
ejpam-3543	161	5	a	a	DET
ejpam-3543	161	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	161	7	up	up	ADP
ejpam-3543	161	8	-	-	PUNCT
ejpam-3543	161	9	subalgebra	subalgebra	NOUN
ejpam-3543	161	10	of	of	ADP
ejpam-3543	161	11	x.	x.	NOUN
ejpam-3543	161	12	definition	definition	NOUN
ejpam-3543	161	13	5	5	NUM
ejpam-3543	161	14	.	.	PUNCT
ejpam-3543	162	1	a	a	DET
ejpam-3543	162	2	ns	ns	NUM
ejpam-3543	162	3	λ	λ	NOUN
ejpam-3543	162	4	in	in	ADP
ejpam-3543	162	5	x	x	PROPN
ejpam-3543	162	6	is	be	AUX
ejpam-3543	162	7	called	call	VERB
ejpam-3543	162	8	a	a	DET
ejpam-3543	162	9	neutrosophic	neutrosophic	ADJ
ejpam-3543	162	10	near	near	ADP
ejpam-3543	162	11	up	up	ADJ
ejpam-3543	162	12	-	-	PUNCT
ejpam-3543	162	13	filter	filter	NOUN
ejpam-3543	162	14	of	of	ADP
ejpam-3543	162	15	x	x	PRON
ejpam-3543	162	16	if	if	SCONJ
ejpam-3543	162	17	it	it	PRON
ejpam-3543	162	18	satisfies	satisfy	VERB
ejpam-3543	162	19	the	the	DET
ejpam-3543	162	20	following	follow	VERB
ejpam-3543	162	21	conditions	condition	NOUN
ejpam-3543	162	22	:	:	PUNCT
ejpam-3543	162	23	(	(	PUNCT
ejpam-3543	162	24	∀x	∀x	X
ejpam-3543	162	25	∈	∈	PROPN
ejpam-3543	162	26	x)(λt	x)(λt	NOUN
ejpam-3543	162	27	(	(	PUNCT
ejpam-3543	162	28	0	0	NUM
ejpam-3543	162	29	)	)	PUNCT
ejpam-3543	162	30	≥	≥	NOUN
ejpam-3543	162	31	λt	λt	X
ejpam-3543	162	32	(	(	PUNCT
ejpam-3543	162	33	x	x	NOUN
ejpam-3543	162	34	)	)	PUNCT
ejpam-3543	162	35	)	)	PUNCT
ejpam-3543	162	36	,	,	PUNCT
ejpam-3543	162	37	(	(	PUNCT
ejpam-3543	162	38	3.6	3.6	NUM
ejpam-3543	162	39	)	)	PUNCT
ejpam-3543	162	40	(	(	PUNCT
ejpam-3543	162	41	∀x	∀x	X
ejpam-3543	162	42	∈	∈	PROPN
ejpam-3543	162	43	x)(λi(0	x)(λi(0	NOUN
ejpam-3543	162	44	)	)	PUNCT
ejpam-3543	162	45	≤	≤	NOUN
ejpam-3543	162	46	λi(x	λi(x	NUM
ejpam-3543	162	47	)	)	PUNCT
ejpam-3543	162	48	)	)	PUNCT
ejpam-3543	162	49	,	,	PUNCT
ejpam-3543	162	50	(	(	PUNCT
ejpam-3543	162	51	3.7	3.7	NUM
ejpam-3543	162	52	)	)	PUNCT
ejpam-3543	162	53	(	(	PUNCT
ejpam-3543	162	54	∀x	∀x	X
ejpam-3543	162	55	∈	∈	PROPN
ejpam-3543	162	56	x)(λf	x)(λf	X
ejpam-3543	162	57	(	(	PUNCT
ejpam-3543	162	58	0	0	NUM
ejpam-3543	162	59	)	)	PUNCT
ejpam-3543	162	60	≥	≥	NOUN
ejpam-3543	162	61	λf	λf	X
ejpam-3543	162	62	(	(	PUNCT
ejpam-3543	162	63	x	x	NOUN
ejpam-3543	162	64	)	)	PUNCT
ejpam-3543	162	65	)	)	PUNCT
ejpam-3543	162	66	,	,	PUNCT
ejpam-3543	162	67	(	(	PUNCT
ejpam-3543	162	68	3.8	3.8	NUM
ejpam-3543	162	69	)	)	PUNCT
ejpam-3543	162	70	(	(	PUNCT
ejpam-3543	162	71	∀x	∀x	X
ejpam-3543	162	72	,	,	PUNCT
ejpam-3543	162	73	y	y	PROPN
ejpam-3543	162	74	∈	∈	PROPN
ejpam-3543	162	75	x)(λt	x)(λt	NOUN
ejpam-3543	162	76	(	(	PUNCT
ejpam-3543	162	77	x	x	SYM
ejpam-3543	162	78	·	·	PUNCT
ejpam-3543	162	79	y	y	X
ejpam-3543	162	80	)	)	PUNCT
ejpam-3543	162	81	≥	≥	NOUN
ejpam-3543	162	82	λt	λt	X
ejpam-3543	162	83	(	(	PUNCT
ejpam-3543	162	84	y	y	NOUN
ejpam-3543	162	85	)	)	PUNCT
ejpam-3543	162	86	)	)	PUNCT
ejpam-3543	162	87	,	,	PUNCT
ejpam-3543	162	88	(	(	PUNCT
ejpam-3543	162	89	3.9	3.9	NUM
ejpam-3543	162	90	)	)	PUNCT
ejpam-3543	162	91	(	(	PUNCT
ejpam-3543	162	92	∀x	∀x	X
ejpam-3543	162	93	,	,	PUNCT
ejpam-3543	162	94	y	y	PROPN
ejpam-3543	162	95	∈	∈	PROPN
ejpam-3543	162	96	x)(λi(x	x)(λi(x	PUNCT
ejpam-3543	162	97	·	·	PUNCT
ejpam-3543	162	98	y	y	X
ejpam-3543	162	99	)	)	PUNCT
ejpam-3543	162	100	≤	≤	NOUN
ejpam-3543	162	101	λi(y	λi(y	NUM
ejpam-3543	162	102	)	)	PUNCT
ejpam-3543	162	103	)	)	PUNCT
ejpam-3543	162	104	,	,	PUNCT
ejpam-3543	162	105	(	(	PUNCT
ejpam-3543	162	106	3.10	3.10	NUM
ejpam-3543	162	107	)	)	PUNCT
ejpam-3543	162	108	(	(	PUNCT
ejpam-3543	162	109	∀x	∀x	X
ejpam-3543	162	110	,	,	PUNCT
ejpam-3543	162	111	y	y	PROPN
ejpam-3543	162	112	∈	∈	PROPN
ejpam-3543	162	113	x)(λf	x)(λf	X
ejpam-3543	162	114	(	(	PUNCT
ejpam-3543	162	115	x	x	SYM
ejpam-3543	162	116	·	·	PUNCT
ejpam-3543	162	117	y	y	X
ejpam-3543	162	118	)	)	PUNCT
ejpam-3543	162	119	≥	≥	NOUN
ejpam-3543	162	120	λf	λf	PROPN
ejpam-3543	162	121	(	(	PUNCT
ejpam-3543	162	122	y	y	NOUN
ejpam-3543	162	123	)	)	PUNCT
ejpam-3543	162	124	)	)	PUNCT
ejpam-3543	162	125	.	.	PUNCT
ejpam-3543	163	1	(	(	PUNCT
ejpam-3543	163	2	3.11	3.11	NUM
ejpam-3543	163	3	)	)	PUNCT
ejpam-3543	163	4	example	example	NOUN
ejpam-3543	163	5	5	5	NUM
ejpam-3543	163	6	.	.	PUNCT
ejpam-3543	164	1	let	let	VERB
ejpam-3543	164	2	x	x	PUNCT
ejpam-3543	164	3	=	=	PUNCT
ejpam-3543	164	4	{	{	PUNCT
ejpam-3543	164	5	0	0	NUM
ejpam-3543	164	6	,	,	PUNCT
ejpam-3543	164	7	1	1	NUM
ejpam-3543	164	8	,	,	PUNCT
ejpam-3543	164	9	2	2	NUM
ejpam-3543	164	10	,	,	PUNCT
ejpam-3543	164	11	3	3	NUM
ejpam-3543	164	12	,	,	PUNCT
ejpam-3543	164	13	4	4	NUM
ejpam-3543	164	14	}	}	PUNCT
ejpam-3543	164	15	be	be	AUX
ejpam-3543	164	16	a	a	DET
ejpam-3543	164	17	up	up	NOUN
ejpam-3543	164	18	-	-	PUNCT
ejpam-3543	164	19	algebra	algebra	NOUN
ejpam-3543	164	20	with	with	ADP
ejpam-3543	164	21	a	a	DET
ejpam-3543	164	22	fixed	fix	VERB
ejpam-3543	164	23	element	element	NOUN
ejpam-3543	164	24	0	0	PUNCT
ejpam-3543	164	25	and	and	CCONJ
ejpam-3543	164	26	a	a	DET
ejpam-3543	164	27	binary	binary	ADJ
ejpam-3543	164	28	operation	operation	NOUN
ejpam-3543	164	29	·	·	PUNCT
ejpam-3543	164	30	defined	define	VERB
ejpam-3543	164	31	by	by	ADP
ejpam-3543	164	32	the	the	DET
ejpam-3543	164	33	following	following	ADJ
ejpam-3543	164	34	cayley	cayley	ADJ
ejpam-3543	164	35	table	table	NOUN
ejpam-3543	164	36	:	:	PUNCT
ejpam-3543	164	37	·	·	PUNCT
ejpam-3543	164	38	0	0	NUM
ejpam-3543	164	39	1	1	NUM
ejpam-3543	164	40	2	2	NUM
ejpam-3543	164	41	3	3	NUM
ejpam-3543	164	42	4	4	NUM
ejpam-3543	164	43	0	0	NUM
ejpam-3543	164	44	0	0	NUM
ejpam-3543	164	45	1	1	NUM
ejpam-3543	164	46	2	2	NUM
ejpam-3543	164	47	3	3	NUM
ejpam-3543	164	48	4	4	NUM
ejpam-3543	164	49	1	1	NUM
ejpam-3543	164	50	0	0	NUM
ejpam-3543	164	51	0	0	NUM
ejpam-3543	164	52	1	1	NUM
ejpam-3543	164	53	2	2	NUM
ejpam-3543	164	54	4	4	NUM
ejpam-3543	164	55	2	2	NUM
ejpam-3543	164	56	0	0	NUM
ejpam-3543	164	57	0	0	NUM
ejpam-3543	164	58	0	0	NUM
ejpam-3543	164	59	1	1	NUM
ejpam-3543	164	60	4	4	NUM
ejpam-3543	164	61	3	3	NUM
ejpam-3543	164	62	0	0	NUM
ejpam-3543	164	63	0	0	NUM
ejpam-3543	164	64	0	0	NUM
ejpam-3543	164	65	0	0	NUM
ejpam-3543	164	66	4	4	NUM
ejpam-3543	164	67	4	4	NUM
ejpam-3543	164	68	0	0	NUM
ejpam-3543	164	69	1	1	NUM
ejpam-3543	164	70	2	2	NUM
ejpam-3543	164	71	3	3	NUM
ejpam-3543	164	72	0	0	NUM
ejpam-3543	164	73	m.	m.	NOUN
ejpam-3543	164	74	songsaeng	songsaeng	PROPN
ejpam-3543	164	75	,	,	PUNCT
ejpam-3543	164	76	a.	a.	NOUN
ejpam-3543	164	77	iampan	iampan	PROPN
ejpam-3543	164	78	/	/	SYM
ejpam-3543	164	79	eur	eur	PROPN
ejpam-3543	164	80	.	.	PUNCT
ejpam-3543	165	1	j.	j.	PROPN
ejpam-3543	165	2	pure	pure	PROPN
ejpam-3543	165	3	appl	appl	PROPN
ejpam-3543	165	4	.	.	PROPN
ejpam-3543	165	5	math	math	PROPN
ejpam-3543	165	6	,	,	PUNCT
ejpam-3543	165	7	12	12	NUM
ejpam-3543	165	8	(	(	PUNCT
ejpam-3543	165	9	4	4	NUM
ejpam-3543	165	10	)	)	PUNCT
ejpam-3543	165	11	(	(	PUNCT
ejpam-3543	165	12	2019	2019	NUM
ejpam-3543	165	13	)	)	PUNCT
ejpam-3543	165	14	,	,	PUNCT
ejpam-3543	165	15	1382	1382	NUM
ejpam-3543	165	16	-	-	SYM
ejpam-3543	165	17	1409	1409	NUM
ejpam-3543	165	18	1388	1388	NUM
ejpam-3543	165	19	we	we	PRON
ejpam-3543	165	20	define	define	VERB
ejpam-3543	165	21	a	a	DET
ejpam-3543	165	22	ns	ns	ADJ
ejpam-3543	165	23	λ	λ	NOUN
ejpam-3543	165	24	in	in	ADP
ejpam-3543	165	25	x	x	PUNCT
ejpam-3543	165	26	as	as	SCONJ
ejpam-3543	165	27	follows	follow	VERB
ejpam-3543	165	28	:	:	PUNCT
ejpam-3543	165	29	λt	λt	ADP
ejpam-3543	165	30	=	=	PUNCT
ejpam-3543	165	31	(	(	PUNCT
ejpam-3543	165	32	0	0	NUM
ejpam-3543	165	33	1	1	NUM
ejpam-3543	165	34	1	1	NUM
ejpam-3543	165	35	0.7	0.7	NUM
ejpam-3543	165	36	2	2	NUM
ejpam-3543	165	37	0.5	0.5	NUM
ejpam-3543	165	38	3	3	NUM
ejpam-3543	165	39	0.4	0.4	NUM
ejpam-3543	165	40	4	4	NUM
ejpam-3543	165	41	0.8	0.8	NUM
ejpam-3543	165	42	)	)	PUNCT
ejpam-3543	165	43	,	,	PUNCT
ejpam-3543	166	1	λi	λi	NOUN
ejpam-3543	166	2	=	=	X
ejpam-3543	166	3	(	(	PUNCT
ejpam-3543	166	4	0	0	NUM
ejpam-3543	166	5	0.1	0.1	NUM
ejpam-3543	166	6	1	1	NUM
ejpam-3543	166	7	0.2	0.2	NUM
ejpam-3543	166	8	2	2	NUM
ejpam-3543	166	9	0.3	0.3	NUM
ejpam-3543	166	10	3	3	NUM
ejpam-3543	166	11	0.7	0.7	NUM
ejpam-3543	166	12	4	4	NUM
ejpam-3543	166	13	0.6	0.6	NUM
ejpam-3543	166	14	)	)	PUNCT
ejpam-3543	166	15	,	,	PUNCT
ejpam-3543	166	16	λf	λf	X
ejpam-3543	166	17	=	=	PUNCT
ejpam-3543	166	18	(	(	PUNCT
ejpam-3543	166	19	0	0	NUM
ejpam-3543	166	20	0.9	0.9	NUM
ejpam-3543	166	21	1	1	NUM
ejpam-3543	166	22	0.8	0.8	NUM
ejpam-3543	166	23	2	2	NUM
ejpam-3543	166	24	0.4	0.4	NUM
ejpam-3543	166	25	3	3	NUM
ejpam-3543	166	26	0.3	0.3	NUM
ejpam-3543	166	27	4	4	NUM
ejpam-3543	166	28	0.5	0.5	NUM
ejpam-3543	166	29	)	)	PUNCT
ejpam-3543	166	30	.	.	PUNCT
ejpam-3543	167	1	hence	hence	ADV
ejpam-3543	167	2	,	,	PUNCT
ejpam-3543	167	3	λ	λ	PROPN
ejpam-3543	167	4	is	be	AUX
ejpam-3543	167	5	a	a	DET
ejpam-3543	167	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	167	7	near	near	ADP
ejpam-3543	167	8	up	up	ADJ
ejpam-3543	167	9	-	-	PUNCT
ejpam-3543	167	10	filter	filter	NOUN
ejpam-3543	167	11	of	of	ADP
ejpam-3543	167	12	x.	x.	NOUN
ejpam-3543	167	13	definition	definition	NOUN
ejpam-3543	167	14	6	6	NUM
ejpam-3543	167	15	.	.	PUNCT
ejpam-3543	168	1	a	a	DET
ejpam-3543	168	2	ns	ns	NUM
ejpam-3543	168	3	λ	λ	NOUN
ejpam-3543	168	4	in	in	ADP
ejpam-3543	168	5	x	x	PROPN
ejpam-3543	168	6	is	be	AUX
ejpam-3543	168	7	called	call	VERB
ejpam-3543	168	8	a	a	DET
ejpam-3543	168	9	neutrosophic	neutrosophic	ADJ
ejpam-3543	168	10	up	up	ADP
ejpam-3543	168	11	-	-	PUNCT
ejpam-3543	168	12	filter	filter	NOUN
ejpam-3543	168	13	of	of	ADP
ejpam-3543	168	14	x	x	PRON
ejpam-3543	168	15	if	if	SCONJ
ejpam-3543	168	16	it	it	PRON
ejpam-3543	168	17	satisfies	satisfy	VERB
ejpam-3543	168	18	the	the	DET
ejpam-3543	168	19	following	follow	VERB
ejpam-3543	168	20	conditions	condition	NOUN
ejpam-3543	168	21	:	:	PUNCT
ejpam-3543	168	22	(	(	PUNCT
ejpam-3543	168	23	3.6	3.6	NUM
ejpam-3543	168	24	)	)	PUNCT
ejpam-3543	168	25	,	,	PUNCT
ejpam-3543	168	26	(	(	PUNCT
ejpam-3543	168	27	3.7	3.7	NUM
ejpam-3543	168	28	)	)	PUNCT
ejpam-3543	168	29	,	,	PUNCT
ejpam-3543	168	30	(	(	PUNCT
ejpam-3543	168	31	3.8	3.8	NUM
ejpam-3543	168	32	)	)	PUNCT
ejpam-3543	168	33	,	,	PUNCT
ejpam-3543	168	34	and	and	CCONJ
ejpam-3543	168	35	(	(	PUNCT
ejpam-3543	168	36	∀x	∀x	X
ejpam-3543	168	37	,	,	PUNCT
ejpam-3543	168	38	y	y	PROPN
ejpam-3543	168	39	∈	∈	PROPN
ejpam-3543	168	40	x)(λt	x)(λt	NOUN
ejpam-3543	168	41	(	(	PUNCT
ejpam-3543	168	42	y	y	NOUN
ejpam-3543	168	43	)	)	PUNCT
ejpam-3543	168	44	≥	≥	NOUN
ejpam-3543	168	45	min{λt	min{λt	X
ejpam-3543	168	46	(	(	PUNCT
ejpam-3543	168	47	x	x	SYM
ejpam-3543	168	48	·	·	PUNCT
ejpam-3543	168	49	y	y	X
ejpam-3543	168	50	)	)	PUNCT
ejpam-3543	168	51	,	,	PUNCT
ejpam-3543	168	52	λt	λt	X
ejpam-3543	168	53	(	(	PUNCT
ejpam-3543	168	54	x	x	NOUN
ejpam-3543	168	55	)	)	PUNCT
ejpam-3543	168	56	}	}	PUNCT
ejpam-3543	168	57	)	)	PUNCT
ejpam-3543	168	58	,	,	PUNCT
ejpam-3543	168	59	(	(	PUNCT
ejpam-3543	168	60	3.12	3.12	NUM
ejpam-3543	168	61	)	)	PUNCT
ejpam-3543	168	62	(	(	PUNCT
ejpam-3543	168	63	∀x	∀x	X
ejpam-3543	168	64	,	,	PUNCT
ejpam-3543	168	65	y	y	PROPN
ejpam-3543	168	66	∈	∈	PROPN
ejpam-3543	168	67	x)(λi(y	x)(λi(y	PROPN
ejpam-3543	168	68	)	)	PUNCT
ejpam-3543	168	69	≤	≤	NUM
ejpam-3543	168	70	max{λi(x	max{λi(x	X
ejpam-3543	168	71	·	·	PUNCT
ejpam-3543	168	72	y	y	X
ejpam-3543	168	73	)	)	PUNCT
ejpam-3543	168	74	,	,	PUNCT
ejpam-3543	168	75	λi(x	λi(x	NUM
ejpam-3543	168	76	)	)	PUNCT
ejpam-3543	168	77	}	}	PUNCT
ejpam-3543	168	78	)	)	PUNCT
ejpam-3543	168	79	,	,	PUNCT
ejpam-3543	168	80	(	(	PUNCT
ejpam-3543	168	81	3.13	3.13	NUM
ejpam-3543	168	82	)	)	PUNCT
ejpam-3543	168	83	(	(	PUNCT
ejpam-3543	168	84	∀x	∀x	X
ejpam-3543	168	85	,	,	PUNCT
ejpam-3543	168	86	y	y	PROPN
ejpam-3543	168	87	∈	∈	PROPN
ejpam-3543	168	88	x)(λf	x)(λf	X
ejpam-3543	168	89	(	(	PUNCT
ejpam-3543	168	90	y	y	PROPN
ejpam-3543	168	91	)	)	PUNCT
ejpam-3543	168	92	≥	≥	NOUN
ejpam-3543	168	93	min{λf	min{λf	X
ejpam-3543	168	94	(	(	PUNCT
ejpam-3543	168	95	x	x	PROPN
ejpam-3543	168	96	·	·	PUNCT
ejpam-3543	168	97	y	y	X
ejpam-3543	168	98	)	)	PUNCT
ejpam-3543	168	99	,	,	PUNCT
ejpam-3543	168	100	λf	λf	X
ejpam-3543	168	101	(	(	PUNCT
ejpam-3543	168	102	x	x	NOUN
ejpam-3543	168	103	)	)	PUNCT
ejpam-3543	168	104	}	}	PUNCT
ejpam-3543	168	105	)	)	PUNCT
ejpam-3543	168	106	.	.	PUNCT
ejpam-3543	169	1	(	(	PUNCT
ejpam-3543	169	2	3.14	3.14	NUM
ejpam-3543	169	3	)	)	PUNCT
ejpam-3543	169	4	example	example	NOUN
ejpam-3543	169	5	6	6	NUM
ejpam-3543	169	6	.	.	PUNCT
ejpam-3543	170	1	let	let	VERB
ejpam-3543	170	2	x	x	PUNCT
ejpam-3543	170	3	=	=	PUNCT
ejpam-3543	170	4	{	{	PUNCT
ejpam-3543	170	5	0	0	NUM
ejpam-3543	170	6	,	,	PUNCT
ejpam-3543	170	7	1	1	NUM
ejpam-3543	170	8	,	,	PUNCT
ejpam-3543	170	9	2	2	NUM
ejpam-3543	170	10	,	,	PUNCT
ejpam-3543	170	11	3	3	NUM
ejpam-3543	170	12	,	,	PUNCT
ejpam-3543	170	13	4	4	NUM
ejpam-3543	170	14	}	}	PUNCT
ejpam-3543	170	15	be	be	AUX
ejpam-3543	170	16	a	a	DET
ejpam-3543	170	17	up	up	NOUN
ejpam-3543	170	18	-	-	PUNCT
ejpam-3543	170	19	algebra	algebra	NOUN
ejpam-3543	170	20	with	with	ADP
ejpam-3543	170	21	a	a	DET
ejpam-3543	170	22	fixed	fix	VERB
ejpam-3543	170	23	element	element	NOUN
ejpam-3543	170	24	0	0	PUNCT
ejpam-3543	170	25	and	and	CCONJ
ejpam-3543	170	26	a	a	DET
ejpam-3543	170	27	binary	binary	ADJ
ejpam-3543	170	28	operation	operation	NOUN
ejpam-3543	170	29	·	·	PUNCT
ejpam-3543	170	30	defined	define	VERB
ejpam-3543	170	31	by	by	ADP
ejpam-3543	170	32	the	the	DET
ejpam-3543	170	33	following	following	ADJ
ejpam-3543	170	34	cayley	cayley	ADJ
ejpam-3543	170	35	table	table	NOUN
ejpam-3543	170	36	:	:	PUNCT
ejpam-3543	170	37	·	·	PUNCT
ejpam-3543	170	38	0	0	NUM
ejpam-3543	170	39	1	1	NUM
ejpam-3543	170	40	2	2	NUM
ejpam-3543	170	41	3	3	NUM
ejpam-3543	170	42	4	4	NUM
ejpam-3543	170	43	0	0	NUM
ejpam-3543	170	44	0	0	NUM
ejpam-3543	170	45	1	1	NUM
ejpam-3543	170	46	2	2	NUM
ejpam-3543	170	47	3	3	NUM
ejpam-3543	170	48	4	4	NUM
ejpam-3543	170	49	1	1	NUM
ejpam-3543	170	50	0	0	NUM
ejpam-3543	170	51	0	0	NUM
ejpam-3543	170	52	2	2	NUM
ejpam-3543	170	53	3	3	NUM
ejpam-3543	170	54	4	4	NUM
ejpam-3543	170	55	2	2	NUM
ejpam-3543	170	56	0	0	NUM
ejpam-3543	170	57	0	0	NUM
ejpam-3543	170	58	0	0	NUM
ejpam-3543	170	59	3	3	NUM
ejpam-3543	170	60	3	3	NUM
ejpam-3543	170	61	3	3	NUM
ejpam-3543	170	62	0	0	NUM
ejpam-3543	170	63	1	1	NUM
ejpam-3543	170	64	2	2	NUM
ejpam-3543	170	65	0	0	NUM
ejpam-3543	170	66	3	3	NUM
ejpam-3543	170	67	4	4	NUM
ejpam-3543	170	68	0	0	NUM
ejpam-3543	170	69	1	1	NUM
ejpam-3543	170	70	2	2	NUM
ejpam-3543	170	71	0	0	NUM
ejpam-3543	170	72	0	0	NUM
ejpam-3543	170	73	we	we	PRON
ejpam-3543	170	74	define	define	VERB
ejpam-3543	170	75	a	a	DET
ejpam-3543	170	76	ns	ns	ADJ
ejpam-3543	170	77	λ	λ	NOUN
ejpam-3543	170	78	in	in	ADP
ejpam-3543	170	79	x	x	PUNCT
ejpam-3543	170	80	as	as	SCONJ
ejpam-3543	170	81	follows	follow	VERB
ejpam-3543	170	82	:	:	PUNCT
ejpam-3543	170	83	λt	λt	ADP
ejpam-3543	170	84	=	=	PUNCT
ejpam-3543	170	85	(	(	PUNCT
ejpam-3543	170	86	0	0	NUM
ejpam-3543	170	87	0.9	0.9	NUM
ejpam-3543	170	88	1	1	NUM
ejpam-3543	170	89	0.4	0.4	NUM
ejpam-3543	170	90	2	2	NUM
ejpam-3543	170	91	0.3	0.3	NUM
ejpam-3543	170	92	3	3	NUM
ejpam-3543	170	93	0.1	0.1	NUM
ejpam-3543	170	94	4	4	NUM
ejpam-3543	170	95	0.1	0.1	NUM
ejpam-3543	170	96	)	)	PUNCT
ejpam-3543	170	97	,	,	PUNCT
ejpam-3543	171	1	λi	λi	NOUN
ejpam-3543	171	2	=	=	X
ejpam-3543	171	3	(	(	PUNCT
ejpam-3543	171	4	0	0	NUM
ejpam-3543	171	5	0.2	0.2	NUM
ejpam-3543	171	6	1	1	NUM
ejpam-3543	171	7	0.3	0.3	NUM
ejpam-3543	171	8	2	2	NUM
ejpam-3543	171	9	0.7	0.7	NUM
ejpam-3543	171	10	3	3	NUM
ejpam-3543	171	11	0.8	0.8	NUM
ejpam-3543	171	12	4	4	NUM
ejpam-3543	171	13	0.8	0.8	NUM
ejpam-3543	171	14	)	)	PUNCT
ejpam-3543	171	15	,	,	PUNCT
ejpam-3543	171	16	λf	λf	NOUN
ejpam-3543	171	17	=	=	PUNCT
ejpam-3543	171	18	(	(	PUNCT
ejpam-3543	171	19	0	0	NUM
ejpam-3543	171	20	0.8	0.8	NUM
ejpam-3543	171	21	1	1	NUM
ejpam-3543	171	22	0.7	0.7	NUM
ejpam-3543	171	23	2	2	NUM
ejpam-3543	171	24	0.4	0.4	NUM
ejpam-3543	171	25	3	3	NUM
ejpam-3543	171	26	0.3	0.3	NUM
ejpam-3543	171	27	4	4	NUM
ejpam-3543	171	28	0.3	0.3	NUM
ejpam-3543	171	29	)	)	PUNCT
ejpam-3543	171	30	.	.	PUNCT
ejpam-3543	172	1	hence	hence	ADV
ejpam-3543	172	2	,	,	PUNCT
ejpam-3543	172	3	λ	λ	PROPN
ejpam-3543	172	4	is	be	AUX
ejpam-3543	172	5	a	a	DET
ejpam-3543	172	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	172	7	up	up	ADJ
ejpam-3543	172	8	-	-	PUNCT
ejpam-3543	172	9	filter	filter	NOUN
ejpam-3543	172	10	of	of	ADP
ejpam-3543	172	11	x.	x.	NOUN
ejpam-3543	172	12	definition	definition	NOUN
ejpam-3543	172	13	7	7	NUM
ejpam-3543	172	14	.	.	PUNCT
ejpam-3543	173	1	a	a	DET
ejpam-3543	173	2	ns	ns	NUM
ejpam-3543	173	3	λ	λ	NOUN
ejpam-3543	173	4	in	in	ADP
ejpam-3543	173	5	x	x	PROPN
ejpam-3543	173	6	is	be	AUX
ejpam-3543	173	7	called	call	VERB
ejpam-3543	173	8	a	a	DET
ejpam-3543	173	9	neutrosophic	neutrosophic	ADJ
ejpam-3543	173	10	up	up	ADP
ejpam-3543	173	11	-	-	PUNCT
ejpam-3543	173	12	ideal	ideal	NOUN
ejpam-3543	173	13	of	of	ADP
ejpam-3543	173	14	x	x	PRON
ejpam-3543	173	15	if	if	SCONJ
ejpam-3543	173	16	it	it	PRON
ejpam-3543	173	17	satisfies	satisfy	VERB
ejpam-3543	173	18	the	the	DET
ejpam-3543	173	19	following	follow	VERB
ejpam-3543	173	20	conditions	condition	NOUN
ejpam-3543	173	21	:	:	PUNCT
ejpam-3543	173	22	(	(	PUNCT
ejpam-3543	173	23	3.6	3.6	NUM
ejpam-3543	173	24	)	)	PUNCT
ejpam-3543	173	25	,	,	PUNCT
ejpam-3543	173	26	(	(	PUNCT
ejpam-3543	173	27	3.7	3.7	NUM
ejpam-3543	173	28	)	)	PUNCT
ejpam-3543	173	29	,	,	PUNCT
ejpam-3543	173	30	(	(	PUNCT
ejpam-3543	173	31	3.8	3.8	NUM
ejpam-3543	173	32	)	)	PUNCT
ejpam-3543	173	33	,	,	PUNCT
ejpam-3543	173	34	and	and	CCONJ
ejpam-3543	173	35	(	(	PUNCT
ejpam-3543	173	36	∀x	∀x	NUM
ejpam-3543	173	37	,	,	PUNCT
ejpam-3543	173	38	y	y	PROPN
ejpam-3543	173	39	,	,	PUNCT
ejpam-3543	173	40	z	z	PROPN
ejpam-3543	173	41	∈	∈	PROPN
ejpam-3543	173	42	x)(λt	x)(λt	NOUN
ejpam-3543	173	43	(	(	PUNCT
ejpam-3543	173	44	x	x	SYM
ejpam-3543	173	45	·	·	PUNCT
ejpam-3543	173	46	z	z	X
ejpam-3543	173	47	)	)	PUNCT
ejpam-3543	173	48	≥	≥	NOUN
ejpam-3543	173	49	min{λt	min{λt	X
ejpam-3543	173	50	(	(	PUNCT
ejpam-3543	173	51	x	x	X
ejpam-3543	173	52	·	·	PUNCT
ejpam-3543	173	53	(	(	PUNCT
ejpam-3543	173	54	y	y	PROPN
ejpam-3543	173	55	·	·	PUNCT
ejpam-3543	173	56	z	z	NOUN
ejpam-3543	173	57	)	)	PUNCT
ejpam-3543	173	58	)	)	PUNCT
ejpam-3543	173	59	,	,	PUNCT
ejpam-3543	173	60	λt	λt	X
ejpam-3543	173	61	(	(	PUNCT
ejpam-3543	173	62	y	y	NOUN
ejpam-3543	173	63	)	)	PUNCT
ejpam-3543	173	64	}	}	PUNCT
ejpam-3543	173	65	)	)	PUNCT
ejpam-3543	173	66	,	,	PUNCT
ejpam-3543	173	67	(	(	PUNCT
ejpam-3543	173	68	3.15	3.15	NUM
ejpam-3543	173	69	)	)	PUNCT
ejpam-3543	173	70	(	(	PUNCT
ejpam-3543	173	71	∀x	∀x	X
ejpam-3543	173	72	,	,	PUNCT
ejpam-3543	173	73	y	y	PROPN
ejpam-3543	173	74	,	,	PUNCT
ejpam-3543	173	75	z	z	NOUN
ejpam-3543	173	76	∈	∈	PROPN
ejpam-3543	174	1	x)(λi(x	x)(λi(x	PUNCT
ejpam-3543	174	2	·	·	PUNCT
ejpam-3543	174	3	z	z	X
ejpam-3543	174	4	)	)	PUNCT
ejpam-3543	174	5	≤	≤	NUM
ejpam-3543	174	6	max{λi(x	max{λi(x	NOUN
ejpam-3543	174	7	·	·	PUNCT
ejpam-3543	174	8	(	(	PUNCT
ejpam-3543	174	9	y	y	PROPN
ejpam-3543	174	10	·	·	PUNCT
ejpam-3543	174	11	z	z	NOUN
ejpam-3543	174	12	)	)	PUNCT
ejpam-3543	174	13	)	)	PUNCT
ejpam-3543	174	14	,	,	PUNCT
ejpam-3543	174	15	λi(y	λi(y	NOUN
ejpam-3543	174	16	)	)	PUNCT
ejpam-3543	174	17	}	}	PUNCT
ejpam-3543	174	18	)	)	PUNCT
ejpam-3543	174	19	,	,	PUNCT
ejpam-3543	174	20	(	(	PUNCT
ejpam-3543	174	21	3.16	3.16	NUM
ejpam-3543	174	22	)	)	PUNCT
ejpam-3543	174	23	(	(	PUNCT
ejpam-3543	174	24	∀x	∀x	X
ejpam-3543	174	25	,	,	PUNCT
ejpam-3543	174	26	y	y	PROPN
ejpam-3543	174	27	,	,	PUNCT
ejpam-3543	174	28	z	z	PROPN
ejpam-3543	174	29	∈	∈	PROPN
ejpam-3543	174	30	x)(λf	x)(λf	X
ejpam-3543	174	31	(	(	PUNCT
ejpam-3543	174	32	x	x	SYM
ejpam-3543	174	33	·	·	PUNCT
ejpam-3543	174	34	z	z	X
ejpam-3543	174	35	)	)	PUNCT
ejpam-3543	174	36	≥	≥	NOUN
ejpam-3543	174	37	min{λf	min{λf	X
ejpam-3543	174	38	(	(	PUNCT
ejpam-3543	174	39	x	x	PART
ejpam-3543	174	40	·	·	PUNCT
ejpam-3543	174	41	(	(	PUNCT
ejpam-3543	174	42	y	y	PROPN
ejpam-3543	174	43	·	·	PUNCT
ejpam-3543	174	44	z	z	NOUN
ejpam-3543	174	45	)	)	PUNCT
ejpam-3543	174	46	)	)	PUNCT
ejpam-3543	174	47	,	,	PUNCT
ejpam-3543	174	48	λf	λf	X
ejpam-3543	174	49	(	(	PUNCT
ejpam-3543	174	50	y	y	NOUN
ejpam-3543	174	51	)	)	PUNCT
ejpam-3543	174	52	}	}	PUNCT
ejpam-3543	174	53	)	)	PUNCT
ejpam-3543	174	54	.	.	PUNCT
ejpam-3543	175	1	(	(	PUNCT
ejpam-3543	175	2	3.17	3.17	NUM
ejpam-3543	175	3	)	)	PUNCT
ejpam-3543	175	4	example	example	NOUN
ejpam-3543	175	5	7	7	NUM
ejpam-3543	175	6	.	.	PUNCT
ejpam-3543	176	1	let	let	VERB
ejpam-3543	176	2	x	x	PUNCT
ejpam-3543	176	3	=	=	PUNCT
ejpam-3543	176	4	{	{	PUNCT
ejpam-3543	176	5	0	0	NUM
ejpam-3543	176	6	,	,	PUNCT
ejpam-3543	176	7	1	1	NUM
ejpam-3543	176	8	,	,	PUNCT
ejpam-3543	176	9	2	2	NUM
ejpam-3543	176	10	,	,	PUNCT
ejpam-3543	176	11	3	3	NUM
ejpam-3543	176	12	,	,	PUNCT
ejpam-3543	176	13	4	4	NUM
ejpam-3543	176	14	}	}	PUNCT
ejpam-3543	176	15	be	be	AUX
ejpam-3543	176	16	a	a	DET
ejpam-3543	176	17	up	up	NOUN
ejpam-3543	176	18	-	-	PUNCT
ejpam-3543	176	19	algebra	algebra	NOUN
ejpam-3543	176	20	with	with	ADP
ejpam-3543	176	21	a	a	DET
ejpam-3543	176	22	fixed	fix	VERB
ejpam-3543	176	23	element	element	NOUN
ejpam-3543	176	24	0	0	PUNCT
ejpam-3543	176	25	and	and	CCONJ
ejpam-3543	176	26	a	a	DET
ejpam-3543	176	27	binary	binary	ADJ
ejpam-3543	176	28	operation	operation	NOUN
ejpam-3543	176	29	·	·	PUNCT
ejpam-3543	176	30	defined	define	VERB
ejpam-3543	176	31	by	by	ADP
ejpam-3543	176	32	the	the	DET
ejpam-3543	176	33	following	following	ADJ
ejpam-3543	176	34	cayley	cayley	ADJ
ejpam-3543	176	35	table	table	NOUN
ejpam-3543	176	36	:	:	PUNCT
ejpam-3543	176	37	·	·	PUNCT
ejpam-3543	176	38	0	0	NUM
ejpam-3543	176	39	1	1	NUM
ejpam-3543	176	40	2	2	NUM
ejpam-3543	176	41	3	3	NUM
ejpam-3543	176	42	4	4	NUM
ejpam-3543	176	43	0	0	NUM
ejpam-3543	176	44	0	0	NUM
ejpam-3543	176	45	1	1	NUM
ejpam-3543	176	46	2	2	NUM
ejpam-3543	176	47	3	3	NUM
ejpam-3543	176	48	4	4	NUM
ejpam-3543	176	49	1	1	NUM
ejpam-3543	176	50	0	0	NUM
ejpam-3543	176	51	0	0	NUM
ejpam-3543	176	52	2	2	NUM
ejpam-3543	176	53	3	3	NUM
ejpam-3543	176	54	4	4	NUM
ejpam-3543	176	55	2	2	NUM
ejpam-3543	176	56	0	0	NUM
ejpam-3543	176	57	0	0	NUM
ejpam-3543	176	58	0	0	NUM
ejpam-3543	176	59	2	2	NUM
ejpam-3543	176	60	4	4	NUM
ejpam-3543	176	61	3	3	NUM
ejpam-3543	176	62	0	0	NUM
ejpam-3543	176	63	0	0	NUM
ejpam-3543	176	64	0	0	NUM
ejpam-3543	176	65	0	0	NUM
ejpam-3543	176	66	4	4	NUM
ejpam-3543	176	67	4	4	NUM
ejpam-3543	176	68	0	0	NUM
ejpam-3543	176	69	1	1	NUM
ejpam-3543	176	70	2	2	NUM
ejpam-3543	176	71	3	3	NUM
ejpam-3543	176	72	0	0	NUM
ejpam-3543	176	73	m.	m.	NOUN
ejpam-3543	176	74	songsaeng	songsaeng	PROPN
ejpam-3543	176	75	,	,	PUNCT
ejpam-3543	176	76	a.	a.	NOUN
ejpam-3543	176	77	iampan	iampan	PROPN
ejpam-3543	176	78	/	/	SYM
ejpam-3543	176	79	eur	eur	PROPN
ejpam-3543	176	80	.	.	PUNCT
ejpam-3543	177	1	j.	j.	PROPN
ejpam-3543	177	2	pure	pure	PROPN
ejpam-3543	177	3	appl	appl	PROPN
ejpam-3543	177	4	.	.	PROPN
ejpam-3543	177	5	math	math	PROPN
ejpam-3543	177	6	,	,	PUNCT
ejpam-3543	177	7	12	12	NUM
ejpam-3543	177	8	(	(	PUNCT
ejpam-3543	177	9	4	4	NUM
ejpam-3543	177	10	)	)	PUNCT
ejpam-3543	177	11	(	(	PUNCT
ejpam-3543	177	12	2019	2019	NUM
ejpam-3543	177	13	)	)	PUNCT
ejpam-3543	177	14	,	,	PUNCT
ejpam-3543	177	15	1382	1382	NUM
ejpam-3543	177	16	-	-	SYM
ejpam-3543	177	17	1409	1409	NUM
ejpam-3543	177	18	1389	1389	NUM
ejpam-3543	177	19	we	we	PRON
ejpam-3543	177	20	define	define	VERB
ejpam-3543	177	21	a	a	DET
ejpam-3543	177	22	ns	ns	ADJ
ejpam-3543	177	23	λ	λ	NOUN
ejpam-3543	177	24	in	in	ADP
ejpam-3543	177	25	x	x	PUNCT
ejpam-3543	177	26	as	as	SCONJ
ejpam-3543	177	27	follows	follow	VERB
ejpam-3543	177	28	:	:	PUNCT
ejpam-3543	177	29	λt	λt	ADP
ejpam-3543	177	30	=	=	PUNCT
ejpam-3543	177	31	(	(	PUNCT
ejpam-3543	177	32	0	0	NUM
ejpam-3543	177	33	1	1	NUM
ejpam-3543	177	34	1	1	NUM
ejpam-3543	177	35	0.7	0.7	NUM
ejpam-3543	177	36	2	2	NUM
ejpam-3543	177	37	0.6	0.6	NUM
ejpam-3543	177	38	3	3	NUM
ejpam-3543	177	39	0.6	0.6	NUM
ejpam-3543	177	40	4	4	NUM
ejpam-3543	177	41	0.4	0.4	NUM
ejpam-3543	177	42	)	)	PUNCT
ejpam-3543	177	43	,	,	PUNCT
ejpam-3543	178	1	λi	λi	NOUN
ejpam-3543	178	2	=	=	X
ejpam-3543	178	3	(	(	PUNCT
ejpam-3543	178	4	0	0	NUM
ejpam-3543	178	5	0	0	NUM
ejpam-3543	178	6	1	1	NUM
ejpam-3543	178	7	0.3	0.3	NUM
ejpam-3543	178	8	2	2	NUM
ejpam-3543	178	9	0.5	0.5	NUM
ejpam-3543	178	10	3	3	NUM
ejpam-3543	178	11	0.5	0.5	NUM
ejpam-3543	178	12	4	4	NUM
ejpam-3543	178	13	0.7	0.7	NUM
ejpam-3543	178	14	)	)	PUNCT
ejpam-3543	178	15	,	,	PUNCT
ejpam-3543	178	16	λf	λf	X
ejpam-3543	178	17	=	=	PUNCT
ejpam-3543	178	18	(	(	PUNCT
ejpam-3543	178	19	0	0	NUM
ejpam-3543	178	20	1	1	NUM
ejpam-3543	178	21	1	1	NUM
ejpam-3543	178	22	0.8	0.8	NUM
ejpam-3543	178	23	2	2	NUM
ejpam-3543	178	24	0.7	0.7	NUM
ejpam-3543	178	25	3	3	NUM
ejpam-3543	178	26	0.7	0.7	NUM
ejpam-3543	178	27	4	4	NUM
ejpam-3543	178	28	0.5	0.5	NUM
ejpam-3543	178	29	)	)	PUNCT
ejpam-3543	178	30	.	.	PUNCT
ejpam-3543	179	1	hence	hence	ADV
ejpam-3543	179	2	,	,	PUNCT
ejpam-3543	179	3	λ	λ	PROPN
ejpam-3543	179	4	is	be	AUX
ejpam-3543	179	5	a	a	DET
ejpam-3543	179	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	179	7	up	up	ADV
ejpam-3543	179	8	-	-	PUNCT
ejpam-3543	179	9	ideal	ideal	NOUN
ejpam-3543	179	10	of	of	ADP
ejpam-3543	179	11	x.	x.	NOUN
ejpam-3543	179	12	definition	definition	NOUN
ejpam-3543	179	13	8	8	NUM
ejpam-3543	179	14	.	.	PUNCT
ejpam-3543	180	1	a	a	DET
ejpam-3543	180	2	ns	ns	NUM
ejpam-3543	180	3	λ	λ	NOUN
ejpam-3543	180	4	in	in	ADP
ejpam-3543	180	5	x	x	AUX
ejpam-3543	180	6	is	be	AUX
ejpam-3543	180	7	called	call	VERB
ejpam-3543	180	8	a	a	DET
ejpam-3543	180	9	neutrosophic	neutrosophic	ADJ
ejpam-3543	180	10	strongly	strongly	ADV
ejpam-3543	180	11	up	up	ADP
ejpam-3543	180	12	-	-	PUNCT
ejpam-3543	180	13	ideal	ideal	NOUN
ejpam-3543	180	14	of	of	ADP
ejpam-3543	180	15	x	x	PRON
ejpam-3543	180	16	if	if	SCONJ
ejpam-3543	180	17	it	it	PRON
ejpam-3543	180	18	satisfies	satisfy	VERB
ejpam-3543	180	19	the	the	DET
ejpam-3543	180	20	following	follow	VERB
ejpam-3543	180	21	conditions	condition	NOUN
ejpam-3543	180	22	:	:	PUNCT
ejpam-3543	180	23	(	(	PUNCT
ejpam-3543	180	24	3.6	3.6	NUM
ejpam-3543	180	25	)	)	PUNCT
ejpam-3543	180	26	,	,	PUNCT
ejpam-3543	180	27	(	(	PUNCT
ejpam-3543	180	28	3.7	3.7	NUM
ejpam-3543	180	29	)	)	PUNCT
ejpam-3543	180	30	,	,	PUNCT
ejpam-3543	180	31	(	(	PUNCT
ejpam-3543	180	32	3.8	3.8	NUM
ejpam-3543	180	33	)	)	PUNCT
ejpam-3543	180	34	,	,	PUNCT
ejpam-3543	180	35	and	and	CCONJ
ejpam-3543	180	36	(	(	PUNCT
ejpam-3543	180	37	∀x	∀x	NUM
ejpam-3543	180	38	,	,	PUNCT
ejpam-3543	180	39	y	y	PROPN
ejpam-3543	180	40	,	,	PUNCT
ejpam-3543	180	41	z	z	PROPN
ejpam-3543	180	42	∈	∈	PROPN
ejpam-3543	180	43	x)(λt	x)(λt	NOUN
ejpam-3543	180	44	(	(	PUNCT
ejpam-3543	180	45	x	x	X
ejpam-3543	180	46	)	)	PUNCT
ejpam-3543	180	47	≥	≥	NOUN
ejpam-3543	180	48	min{λt	min{λt	X
ejpam-3543	180	49	(	(	PUNCT
ejpam-3543	180	50	(	(	PUNCT
ejpam-3543	180	51	z	z	NOUN
ejpam-3543	180	52	·	·	PUNCT
ejpam-3543	180	53	y	y	X
ejpam-3543	180	54	)	)	PUNCT
ejpam-3543	180	55	·	·	PUNCT
ejpam-3543	181	1	(	(	PUNCT
ejpam-3543	181	2	z	z	NOUN
ejpam-3543	181	3	·	·	PUNCT
ejpam-3543	181	4	x	x	X
ejpam-3543	181	5	)	)	PUNCT
ejpam-3543	181	6	)	)	PUNCT
ejpam-3543	181	7	,	,	PUNCT
ejpam-3543	181	8	λt	λt	X
ejpam-3543	181	9	(	(	PUNCT
ejpam-3543	181	10	y	y	NOUN
ejpam-3543	181	11	)	)	PUNCT
ejpam-3543	181	12	}	}	PUNCT
ejpam-3543	181	13	)	)	PUNCT
ejpam-3543	181	14	,	,	PUNCT
ejpam-3543	181	15	(	(	PUNCT
ejpam-3543	181	16	3.18	3.18	NUM
ejpam-3543	181	17	)	)	PUNCT
ejpam-3543	181	18	(	(	PUNCT
ejpam-3543	181	19	∀x	∀x	X
ejpam-3543	181	20	,	,	PUNCT
ejpam-3543	181	21	y	y	PROPN
ejpam-3543	181	22	,	,	PUNCT
ejpam-3543	181	23	z	z	NOUN
ejpam-3543	181	24	∈	∈	PROPN
ejpam-3543	181	25	x)(λi(x	x)(λi(x	PROPN
ejpam-3543	181	26	)	)	PUNCT
ejpam-3543	181	27	≤	≤	NOUN
ejpam-3543	181	28	max{λi((z	max{λi((z	NOUN
ejpam-3543	181	29	·	·	PUNCT
ejpam-3543	181	30	y	y	X
ejpam-3543	181	31	)	)	PUNCT
ejpam-3543	181	32	·	·	PUNCT
ejpam-3543	182	1	(	(	PUNCT
ejpam-3543	182	2	z	z	NOUN
ejpam-3543	182	3	·	·	PUNCT
ejpam-3543	182	4	x	x	X
ejpam-3543	182	5	)	)	PUNCT
ejpam-3543	182	6	)	)	PUNCT
ejpam-3543	182	7	,	,	PUNCT
ejpam-3543	182	8	λi(y	λi(y	NOUN
ejpam-3543	182	9	)	)	PUNCT
ejpam-3543	182	10	}	}	PUNCT
ejpam-3543	182	11	)	)	PUNCT
ejpam-3543	182	12	,	,	PUNCT
ejpam-3543	182	13	(	(	PUNCT
ejpam-3543	182	14	3.19	3.19	NUM
ejpam-3543	182	15	)	)	PUNCT
ejpam-3543	182	16	(	(	PUNCT
ejpam-3543	182	17	∀x	∀x	X
ejpam-3543	182	18	,	,	PUNCT
ejpam-3543	182	19	y	y	PROPN
ejpam-3543	182	20	,	,	PUNCT
ejpam-3543	182	21	z	z	PROPN
ejpam-3543	182	22	∈	∈	PROPN
ejpam-3543	182	23	x)(λf	x)(λf	X
ejpam-3543	182	24	(	(	PUNCT
ejpam-3543	182	25	x	x	X
ejpam-3543	182	26	)	)	PUNCT
ejpam-3543	182	27	≥	≥	X
ejpam-3543	182	28	min{λf	min{λf	X
ejpam-3543	182	29	(	(	PUNCT
ejpam-3543	182	30	(	(	PUNCT
ejpam-3543	182	31	z	z	NOUN
ejpam-3543	182	32	·	·	PUNCT
ejpam-3543	182	33	y	y	X
ejpam-3543	182	34	)	)	PUNCT
ejpam-3543	182	35	·	·	PUNCT
ejpam-3543	183	1	(	(	PUNCT
ejpam-3543	183	2	z	z	NOUN
ejpam-3543	183	3	·	·	PUNCT
ejpam-3543	183	4	x	x	X
ejpam-3543	183	5	)	)	PUNCT
ejpam-3543	183	6	)	)	PUNCT
ejpam-3543	183	7	,	,	PUNCT
ejpam-3543	183	8	λf	λf	X
ejpam-3543	183	9	(	(	PUNCT
ejpam-3543	183	10	y	y	NOUN
ejpam-3543	183	11	)	)	PUNCT
ejpam-3543	183	12	}	}	PUNCT
ejpam-3543	183	13	)	)	PUNCT
ejpam-3543	183	14	.	.	PUNCT
ejpam-3543	184	1	(	(	PUNCT
ejpam-3543	184	2	3.20	3.20	NUM
ejpam-3543	184	3	)	)	PUNCT
ejpam-3543	184	4	example	example	NOUN
ejpam-3543	184	5	8	8	NUM
ejpam-3543	184	6	.	.	PUNCT
ejpam-3543	185	1	let	let	VERB
ejpam-3543	185	2	x	x	PUNCT
ejpam-3543	185	3	=	=	PUNCT
ejpam-3543	185	4	{	{	PUNCT
ejpam-3543	185	5	0	0	NUM
ejpam-3543	185	6	,	,	PUNCT
ejpam-3543	185	7	1	1	NUM
ejpam-3543	185	8	,	,	PUNCT
ejpam-3543	185	9	2	2	NUM
ejpam-3543	185	10	,	,	PUNCT
ejpam-3543	185	11	3	3	NUM
ejpam-3543	185	12	,	,	PUNCT
ejpam-3543	185	13	4	4	NUM
ejpam-3543	185	14	}	}	PUNCT
ejpam-3543	185	15	be	be	AUX
ejpam-3543	185	16	a	a	DET
ejpam-3543	185	17	up	up	NOUN
ejpam-3543	185	18	-	-	PUNCT
ejpam-3543	185	19	algebra	algebra	NOUN
ejpam-3543	185	20	with	with	ADP
ejpam-3543	185	21	a	a	DET
ejpam-3543	185	22	fixed	fix	VERB
ejpam-3543	185	23	element	element	NOUN
ejpam-3543	185	24	0	0	PUNCT
ejpam-3543	185	25	and	and	CCONJ
ejpam-3543	185	26	a	a	DET
ejpam-3543	185	27	binary	binary	ADJ
ejpam-3543	185	28	operation	operation	NOUN
ejpam-3543	185	29	·	·	PUNCT
ejpam-3543	185	30	defined	define	VERB
ejpam-3543	185	31	by	by	ADP
ejpam-3543	185	32	the	the	DET
ejpam-3543	185	33	following	following	ADJ
ejpam-3543	185	34	cayley	cayley	ADJ
ejpam-3543	185	35	table	table	NOUN
ejpam-3543	185	36	:	:	PUNCT
ejpam-3543	185	37	·	·	PUNCT
ejpam-3543	185	38	0	0	NUM
ejpam-3543	185	39	1	1	NUM
ejpam-3543	185	40	2	2	NUM
ejpam-3543	185	41	3	3	NUM
ejpam-3543	185	42	4	4	NUM
ejpam-3543	185	43	0	0	NUM
ejpam-3543	185	44	0	0	NUM
ejpam-3543	185	45	1	1	NUM
ejpam-3543	185	46	2	2	NUM
ejpam-3543	185	47	3	3	NUM
ejpam-3543	185	48	4	4	NUM
ejpam-3543	185	49	1	1	NUM
ejpam-3543	185	50	0	0	NUM
ejpam-3543	185	51	0	0	NUM
ejpam-3543	185	52	2	2	NUM
ejpam-3543	185	53	3	3	NUM
ejpam-3543	185	54	4	4	NUM
ejpam-3543	185	55	2	2	NUM
ejpam-3543	185	56	0	0	NUM
ejpam-3543	185	57	1	1	NUM
ejpam-3543	185	58	0	0	NUM
ejpam-3543	185	59	2	2	NUM
ejpam-3543	185	60	4	4	NUM
ejpam-3543	185	61	3	3	NUM
ejpam-3543	185	62	0	0	NUM
ejpam-3543	185	63	1	1	NUM
ejpam-3543	185	64	0	0	NUM
ejpam-3543	185	65	0	0	NUM
ejpam-3543	185	66	4	4	NUM
ejpam-3543	185	67	4	4	NUM
ejpam-3543	185	68	0	0	NUM
ejpam-3543	185	69	1	1	NUM
ejpam-3543	185	70	0	0	NUM
ejpam-3543	185	71	3	3	NUM
ejpam-3543	185	72	0	0	NUM
ejpam-3543	185	73	we	we	PRON
ejpam-3543	185	74	define	define	VERB
ejpam-3543	185	75	a	a	DET
ejpam-3543	185	76	ns	ns	ADJ
ejpam-3543	185	77	λ	λ	NOUN
ejpam-3543	185	78	in	in	ADP
ejpam-3543	185	79	x	x	PUNCT
ejpam-3543	185	80	as	as	SCONJ
ejpam-3543	185	81	follows	follow	VERB
ejpam-3543	185	82	:	:	PUNCT
ejpam-3543	185	83	(	(	PUNCT
ejpam-3543	186	1	∀x	∀x	X
ejpam-3543	186	2	∈	∈	PROPN
ejpam-3543	186	3	x	x	NOUN
ejpam-3543	186	4	)	)	PUNCT
ejpam-3543	186	5	λt	λt	PROPN
ejpam-3543	186	6	(	(	PUNCT
ejpam-3543	186	7	x	x	NOUN
ejpam-3543	186	8	)	)	PUNCT
ejpam-3543	186	9	=	=	SYM
ejpam-3543	186	10	1	1	NUM
ejpam-3543	186	11	λi(x	λi(x	NUM
ejpam-3543	186	12	)	)	PUNCT
ejpam-3543	186	13	=	=	SYM
ejpam-3543	187	1	0.2	0.2	NUM
ejpam-3543	187	2	λf	λf	PROPN
ejpam-3543	187	3	(	(	PUNCT
ejpam-3543	187	4	x	x	NOUN
ejpam-3543	187	5	)	)	PUNCT
ejpam-3543	187	6	=	=	PUNCT
ejpam-3543	187	7	0.8	0.8	NUM
ejpam-3543	187	8			NOUN
ejpam-3543	187	9	.	.	PUNCT
ejpam-3543	188	1	hence	hence	ADV
ejpam-3543	188	2	,	,	PUNCT
ejpam-3543	188	3	λ	λ	PROPN
ejpam-3543	188	4	is	be	AUX
ejpam-3543	188	5	a	a	DET
ejpam-3543	188	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	188	7	strongly	strongly	ADV
ejpam-3543	188	8	up	up	ADP
ejpam-3543	188	9	-	-	PUNCT
ejpam-3543	188	10	ideal	ideal	NOUN
ejpam-3543	188	11	of	of	ADP
ejpam-3543	188	12	x.	x.	NOUN
ejpam-3543	188	13	definition	definition	NOUN
ejpam-3543	188	14	9	9	NUM
ejpam-3543	188	15	.	.	PUNCT
ejpam-3543	189	1	a	a	DET
ejpam-3543	189	2	ns	ns	NUM
ejpam-3543	189	3	λ	λ	NOUN
ejpam-3543	189	4	in	in	ADP
ejpam-3543	189	5	x	x	VERB
ejpam-3543	189	6	is	be	AUX
ejpam-3543	189	7	said	say	VERB
ejpam-3543	189	8	to	to	PART
ejpam-3543	189	9	be	be	AUX
ejpam-3543	189	10	constant	constant	ADJ
ejpam-3543	189	11	if	if	SCONJ
ejpam-3543	189	12	λ	λ	PROPN
ejpam-3543	189	13	is	be	AUX
ejpam-3543	189	14	a	a	DET
ejpam-3543	189	15	constant	constant	ADJ
ejpam-3543	189	16	function	function	NOUN
ejpam-3543	189	17	from	from	ADP
ejpam-3543	189	18	x	x	X
ejpam-3543	189	19	to	to	ADP
ejpam-3543	189	20	[	[	X
ejpam-3543	189	21	0	0	NUM
ejpam-3543	189	22	,	,	PUNCT
ejpam-3543	189	23	1]3	1]3	NUM
ejpam-3543	189	24	.	.	PUNCT
ejpam-3543	190	1	that	that	PRON
ejpam-3543	190	2	is	be	AUX
ejpam-3543	190	3	,	,	PUNCT
ejpam-3543	190	4	λt	λt	INTJ
ejpam-3543	190	5	,	,	PUNCT
ejpam-3543	190	6	λi	λi	INTJ
ejpam-3543	190	7	,	,	PUNCT
ejpam-3543	190	8	and	and	CCONJ
ejpam-3543	190	9	λf	λf	ADV
ejpam-3543	190	10	are	be	AUX
ejpam-3543	190	11	constant	constant	ADJ
ejpam-3543	190	12	functions	function	NOUN
ejpam-3543	190	13	from	from	ADP
ejpam-3543	190	14	x	x	PUNCT
ejpam-3543	190	15	to	to	ADP
ejpam-3543	190	16	[	[	X
ejpam-3543	190	17	0	0	NUM
ejpam-3543	190	18	,	,	PUNCT
ejpam-3543	190	19	1	1	NUM
ejpam-3543	190	20	]	]	PUNCT
ejpam-3543	190	21	.	.	PUNCT
ejpam-3543	191	1	theorem	theorem	NOUN
ejpam-3543	191	2	1	1	NUM
ejpam-3543	191	3	.	.	PUNCT
ejpam-3543	192	1	every	every	DET
ejpam-3543	192	2	neutrosophic	neutrosophic	ADJ
ejpam-3543	192	3	up	up	ADP
ejpam-3543	192	4	-	-	PUNCT
ejpam-3543	192	5	subalgebra	subalgebra	NOUN
ejpam-3543	192	6	of	of	ADP
ejpam-3543	192	7	x	x	PRON
ejpam-3543	192	8	satisfies	satisfy	VERB
ejpam-3543	192	9	the	the	DET
ejpam-3543	192	10	conditions	condition	NOUN
ejpam-3543	192	11	(	(	PUNCT
ejpam-3543	192	12	3.6	3.6	NUM
ejpam-3543	192	13	)	)	PUNCT
ejpam-3543	192	14	,	,	PUNCT
ejpam-3543	192	15	(	(	PUNCT
ejpam-3543	192	16	3.7	3.7	NUM
ejpam-3543	192	17	)	)	PUNCT
ejpam-3543	192	18	,	,	PUNCT
ejpam-3543	192	19	and	and	CCONJ
ejpam-3543	192	20	(	(	PUNCT
ejpam-3543	192	21	3.8	3.8	NUM
ejpam-3543	192	22	)	)	PUNCT
ejpam-3543	192	23	.	.	PUNCT
ejpam-3543	193	1	proof	proof	NOUN
ejpam-3543	193	2	.	.	PUNCT
ejpam-3543	194	1	assume	assume	VERB
ejpam-3543	194	2	that	that	SCONJ
ejpam-3543	194	3	λ	λ	PROPN
ejpam-3543	194	4	is	be	AUX
ejpam-3543	194	5	a	a	DET
ejpam-3543	194	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	194	7	up	up	ADP
ejpam-3543	194	8	-	-	PUNCT
ejpam-3543	194	9	subalgebra	subalgebra	NOUN
ejpam-3543	194	10	of	of	ADP
ejpam-3543	194	11	x.	x.	NOUN
ejpam-3543	194	12	then	then	ADV
ejpam-3543	194	13	for	for	ADP
ejpam-3543	194	14	all	all	DET
ejpam-3543	194	15	x	x	SYM
ejpam-3543	194	16	∈	∈	PROPN
ejpam-3543	194	17	x	x	NOUN
ejpam-3543	194	18	,	,	PUNCT
ejpam-3543	194	19	λt	λt	X
ejpam-3543	194	20	(	(	PUNCT
ejpam-3543	194	21	0	0	NUM
ejpam-3543	194	22	)	)	PUNCT
ejpam-3543	194	23	=	=	NOUN
ejpam-3543	194	24	λt	λt	X
ejpam-3543	194	25	(	(	PUNCT
ejpam-3543	194	26	x	x	SYM
ejpam-3543	194	27	·	·	PUNCT
ejpam-3543	194	28	x	x	X
ejpam-3543	194	29	)	)	PUNCT
ejpam-3543	194	30	≥	≥	NOUN
ejpam-3543	194	31	min{λt	min{λt	X
ejpam-3543	194	32	(	(	PUNCT
ejpam-3543	194	33	x	x	X
ejpam-3543	194	34	)	)	PUNCT
ejpam-3543	194	35	,	,	PUNCT
ejpam-3543	194	36	λt	λt	X
ejpam-3543	194	37	(	(	PUNCT
ejpam-3543	194	38	x	x	NOUN
ejpam-3543	194	39	)	)	PUNCT
ejpam-3543	194	40	}	}	PUNCT
ejpam-3543	194	41	=	=	SYM
ejpam-3543	194	42	λt	λt	X
ejpam-3543	194	43	(	(	PUNCT
ejpam-3543	194	44	x	x	NOUN
ejpam-3543	194	45	)	)	PUNCT
ejpam-3543	194	46	,	,	PUNCT
ejpam-3543	194	47	(	(	PUNCT
ejpam-3543	194	48	2.1	2.1	NUM
ejpam-3543	194	49	)	)	PUNCT
ejpam-3543	194	50	and	and	CCONJ
ejpam-3543	194	51	(	(	PUNCT
ejpam-3543	194	52	3.3	3.3	NUM
ejpam-3543	194	53	)	)	PUNCT
ejpam-3543	194	54	λi(0	λi(0	X
ejpam-3543	194	55	)	)	PUNCT
ejpam-3543	194	56	=	=	SYM
ejpam-3543	194	57	λi(x	λi(x	NOUN
ejpam-3543	194	58	·	·	PUNCT
ejpam-3543	194	59	x	x	X
ejpam-3543	194	60	)	)	PUNCT
ejpam-3543	194	61	≤	≤	NUM
ejpam-3543	194	62	max{λi(x	max{λi(x	NOUN
ejpam-3543	194	63	)	)	PUNCT
ejpam-3543	194	64	,	,	PUNCT
ejpam-3543	194	65	λi(x	λi(x	NUM
ejpam-3543	194	66	)	)	PUNCT
ejpam-3543	194	67	}	}	PUNCT
ejpam-3543	194	68	=	=	SYM
ejpam-3543	194	69	λi(x	λi(x	NUM
ejpam-3543	194	70	)	)	PUNCT
ejpam-3543	194	71	,	,	PUNCT
ejpam-3543	194	72	(	(	PUNCT
ejpam-3543	194	73	2.1	2.1	NUM
ejpam-3543	194	74	)	)	PUNCT
ejpam-3543	194	75	and	and	CCONJ
ejpam-3543	194	76	(	(	PUNCT
ejpam-3543	194	77	3.4	3.4	NUM
ejpam-3543	194	78	)	)	PUNCT
ejpam-3543	194	79	λf	λf	X
ejpam-3543	194	80	(	(	PUNCT
ejpam-3543	194	81	0	0	NUM
ejpam-3543	194	82	)	)	PUNCT
ejpam-3543	195	1	=	=	NOUN
ejpam-3543	195	2	λf	λf	X
ejpam-3543	195	3	(	(	PUNCT
ejpam-3543	195	4	x	x	SYM
ejpam-3543	195	5	·	·	PUNCT
ejpam-3543	195	6	x	x	X
ejpam-3543	195	7	)	)	PUNCT
ejpam-3543	195	8	≥	≥	X
ejpam-3543	195	9	min{λf	min{λf	X
ejpam-3543	195	10	(	(	PUNCT
ejpam-3543	195	11	x	x	X
ejpam-3543	195	12	)	)	PUNCT
ejpam-3543	195	13	,	,	PUNCT
ejpam-3543	195	14	λf	λf	X
ejpam-3543	195	15	(	(	PUNCT
ejpam-3543	195	16	x	x	NOUN
ejpam-3543	195	17	)	)	PUNCT
ejpam-3543	195	18	}	}	PUNCT
ejpam-3543	196	1	=	=	SYM
ejpam-3543	196	2	λf	λf	X
ejpam-3543	196	3	(	(	PUNCT
ejpam-3543	196	4	x	x	NOUN
ejpam-3543	196	5	)	)	PUNCT
ejpam-3543	196	6	.	.	PUNCT
ejpam-3543	197	1	(	(	PUNCT
ejpam-3543	197	2	2.1	2.1	NUM
ejpam-3543	197	3	)	)	PUNCT
ejpam-3543	197	4	and	and	CCONJ
ejpam-3543	197	5	(	(	PUNCT
ejpam-3543	197	6	3.5	3.5	NUM
ejpam-3543	197	7	)	)	PUNCT
ejpam-3543	197	8	hence	hence	ADV
ejpam-3543	197	9	,	,	PUNCT
ejpam-3543	197	10	λ	λ	PROPN
ejpam-3543	197	11	satisfies	satisfy	VERB
ejpam-3543	197	12	the	the	DET
ejpam-3543	197	13	conditions	condition	NOUN
ejpam-3543	197	14	(	(	PUNCT
ejpam-3543	197	15	3.6	3.6	NUM
ejpam-3543	197	16	)	)	PUNCT
ejpam-3543	197	17	,	,	PUNCT
ejpam-3543	197	18	(	(	PUNCT
ejpam-3543	197	19	3.7	3.7	NUM
ejpam-3543	197	20	)	)	PUNCT
ejpam-3543	197	21	,	,	PUNCT
ejpam-3543	197	22	and	and	CCONJ
ejpam-3543	197	23	(	(	PUNCT
ejpam-3543	197	24	3.8	3.8	NUM
ejpam-3543	197	25	)	)	PUNCT
ejpam-3543	197	26	.	.	PUNCT
ejpam-3543	198	1	m.	m.	PROPN
ejpam-3543	198	2	songsaeng	songsaeng	PROPN
ejpam-3543	198	3	,	,	PUNCT
ejpam-3543	198	4	a.	a.	NOUN
ejpam-3543	198	5	iampan	iampan	PROPN
ejpam-3543	198	6	/	/	SYM
ejpam-3543	198	7	eur	eur	PROPN
ejpam-3543	198	8	.	.	PUNCT
ejpam-3543	199	1	j.	j.	PROPN
ejpam-3543	199	2	pure	pure	PROPN
ejpam-3543	199	3	appl	appl	PROPN
ejpam-3543	199	4	.	.	PROPN
ejpam-3543	199	5	math	math	PROPN
ejpam-3543	199	6	,	,	PUNCT
ejpam-3543	199	7	12	12	NUM
ejpam-3543	199	8	(	(	PUNCT
ejpam-3543	199	9	4	4	NUM
ejpam-3543	199	10	)	)	PUNCT
ejpam-3543	199	11	(	(	PUNCT
ejpam-3543	199	12	2019	2019	NUM
ejpam-3543	199	13	)	)	PUNCT
ejpam-3543	199	14	,	,	PUNCT
ejpam-3543	199	15	1382	1382	NUM
ejpam-3543	199	16	-	-	SYM
ejpam-3543	199	17	1409	1409	NUM
ejpam-3543	199	18	1390	1390	NUM
ejpam-3543	199	19	theorem	theorem	NOUN
ejpam-3543	199	20	2	2	NUM
ejpam-3543	199	21	.	.	PUNCT
ejpam-3543	199	22	a	a	DET
ejpam-3543	199	23	ns	ns	NUM
ejpam-3543	199	24	λ	λ	NOUN
ejpam-3543	199	25	in	in	ADP
ejpam-3543	199	26	x	x	PUNCT
ejpam-3543	199	27	is	be	AUX
ejpam-3543	199	28	constant	constant	ADJ
ejpam-3543	199	29	if	if	SCONJ
ejpam-3543	199	30	and	and	CCONJ
ejpam-3543	199	31	only	only	ADV
ejpam-3543	199	32	if	if	SCONJ
ejpam-3543	199	33	it	it	PRON
ejpam-3543	199	34	is	be	AUX
ejpam-3543	199	35	a	a	DET
ejpam-3543	199	36	neutrosophic	neutrosophic	ADJ
ejpam-3543	199	37	strongly	strongly	ADV
ejpam-3543	199	38	up	up	ADP
ejpam-3543	199	39	-	-	PUNCT
ejpam-3543	199	40	ideal	ideal	NOUN
ejpam-3543	199	41	of	of	ADP
ejpam-3543	199	42	x.	x.	NOUN
ejpam-3543	199	43	proof	proof	PROPN
ejpam-3543	199	44	.	.	PUNCT
ejpam-3543	200	1	assume	assume	VERB
ejpam-3543	200	2	that	that	SCONJ
ejpam-3543	200	3	λ	λ	NOUN
ejpam-3543	200	4	is	be	AUX
ejpam-3543	200	5	constant	constant	ADJ
ejpam-3543	200	6	.	.	PUNCT
ejpam-3543	201	1	then	then	ADV
ejpam-3543	201	2	for	for	ADP
ejpam-3543	201	3	all	all	DET
ejpam-3543	201	4	x	x	SYM
ejpam-3543	201	5	∈	∈	PROPN
ejpam-3543	201	6	x	x	NOUN
ejpam-3543	201	7	,	,	PUNCT
ejpam-3543	201	8	λt	λt	X
ejpam-3543	201	9	(	(	PUNCT
ejpam-3543	201	10	x	x	NOUN
ejpam-3543	201	11	)	)	PUNCT
ejpam-3543	201	12	=	=	SYM
ejpam-3543	201	13	λt	λt	X
ejpam-3543	201	14	(	(	PUNCT
ejpam-3543	201	15	0	0	NUM
ejpam-3543	201	16	)	)	PUNCT
ejpam-3543	201	17	,	,	PUNCT
ejpam-3543	201	18	λi(x	λi(x	NUM
ejpam-3543	201	19	)	)	PUNCT
ejpam-3543	201	20	=	=	PUNCT
ejpam-3543	202	1	λi(0	λi(0	X
ejpam-3543	202	2	)	)	PUNCT
ejpam-3543	202	3	,	,	PUNCT
ejpam-3543	202	4	and	and	CCONJ
ejpam-3543	202	5	λf	λf	INTJ
ejpam-3543	202	6	(	(	PUNCT
ejpam-3543	202	7	x	x	X
ejpam-3543	202	8	)	)	PUNCT
ejpam-3543	202	9	=	=	SYM
ejpam-3543	202	10	λf	λf	X
ejpam-3543	202	11	(	(	PUNCT
ejpam-3543	202	12	0	0	NUM
ejpam-3543	202	13	)	)	PUNCT
ejpam-3543	202	14	and	and	CCONJ
ejpam-3543	202	15	so	so	ADV
ejpam-3543	202	16	λt	λt	ADP
ejpam-3543	202	17	(	(	PUNCT
ejpam-3543	202	18	0	0	NUM
ejpam-3543	202	19	)	)	PUNCT
ejpam-3543	202	20	≥	≥	NOUN
ejpam-3543	202	21	λt	λt	X
ejpam-3543	202	22	(	(	PUNCT
ejpam-3543	202	23	x	x	NOUN
ejpam-3543	202	24	)	)	PUNCT
ejpam-3543	202	25	,	,	PUNCT
ejpam-3543	202	26	λi(0	λi(0	NOUN
ejpam-3543	202	27	)	)	PUNCT
ejpam-3543	202	28	≤	≤	NOUN
ejpam-3543	202	29	λi(x	λi(x	NUM
ejpam-3543	202	30	)	)	PUNCT
ejpam-3543	202	31	,	,	PUNCT
ejpam-3543	202	32	and	and	CCONJ
ejpam-3543	202	33	λf	λf	INTJ
ejpam-3543	202	34	(	(	PUNCT
ejpam-3543	202	35	0	0	NUM
ejpam-3543	202	36	)	)	PUNCT
ejpam-3543	202	37	≥	≥	NOUN
ejpam-3543	202	38	λf	λf	X
ejpam-3543	202	39	(	(	PUNCT
ejpam-3543	202	40	x	x	NOUN
ejpam-3543	202	41	)	)	PUNCT
ejpam-3543	202	42	.	.	PUNCT
ejpam-3543	203	1	next	next	ADV
ejpam-3543	203	2	,	,	PUNCT
ejpam-3543	203	3	for	for	ADP
ejpam-3543	203	4	all	all	DET
ejpam-3543	203	5	x	x	NOUN
ejpam-3543	203	6	,	,	PUNCT
ejpam-3543	203	7	y	y	PROPN
ejpam-3543	203	8	,	,	PUNCT
ejpam-3543	203	9	z	z	PROPN
ejpam-3543	203	10	∈	∈	PROPN
ejpam-3543	203	11	x	x	X
ejpam-3543	203	12	,	,	PUNCT
ejpam-3543	203	13	λt	λt	X
ejpam-3543	203	14	(	(	PUNCT
ejpam-3543	203	15	x	x	NOUN
ejpam-3543	203	16	)	)	PUNCT
ejpam-3543	203	17	=	=	SYM
ejpam-3543	203	18	λt	λt	X
ejpam-3543	203	19	(	(	PUNCT
ejpam-3543	203	20	0	0	NUM
ejpam-3543	203	21	)	)	PUNCT
ejpam-3543	203	22	=	=	SYM
ejpam-3543	203	23	min{λt	min{λt	X
ejpam-3543	203	24	(	(	PUNCT
ejpam-3543	203	25	0	0	NUM
ejpam-3543	203	26	)	)	PUNCT
ejpam-3543	203	27	,	,	PUNCT
ejpam-3543	203	28	λt	λt	X
ejpam-3543	203	29	(	(	PUNCT
ejpam-3543	203	30	0	0	NUM
ejpam-3543	203	31	)	)	PUNCT
ejpam-3543	203	32	}	}	PUNCT
ejpam-3543	203	33	=	=	SYM
ejpam-3543	203	34	min{λt	min{λt	X
ejpam-3543	203	35	(	(	PUNCT
ejpam-3543	203	36	(	(	PUNCT
ejpam-3543	203	37	z	z	NOUN
ejpam-3543	203	38	·	·	PUNCT
ejpam-3543	203	39	y	y	X
ejpam-3543	203	40	)	)	PUNCT
ejpam-3543	203	41	·	·	PUNCT
ejpam-3543	203	42	(	(	PUNCT
ejpam-3543	203	43	z	z	NOUN
ejpam-3543	203	44	·	·	PUNCT
ejpam-3543	203	45	x	x	X
ejpam-3543	203	46	)	)	PUNCT
ejpam-3543	203	47	)	)	PUNCT
ejpam-3543	203	48	,	,	PUNCT
ejpam-3543	203	49	λt	λt	X
ejpam-3543	203	50	(	(	PUNCT
ejpam-3543	203	51	y	y	NOUN
ejpam-3543	203	52	)	)	PUNCT
ejpam-3543	203	53	}	}	PUNCT
ejpam-3543	203	54	,	,	PUNCT
ejpam-3543	203	55	λi(x	λi(x	NUM
ejpam-3543	203	56	)	)	PUNCT
ejpam-3543	203	57	=	=	PUNCT
ejpam-3543	204	1	λi(0	λi(0	X
ejpam-3543	204	2	)	)	PUNCT
ejpam-3543	204	3	=	=	SYM
ejpam-3543	204	4	max{λi(0	max{λi(0	PROPN
ejpam-3543	204	5	)	)	PUNCT
ejpam-3543	204	6	,	,	PUNCT
ejpam-3543	204	7	λi(0	λi(0	NOUN
ejpam-3543	204	8	)	)	PUNCT
ejpam-3543	204	9	}	}	PUNCT
ejpam-3543	205	1	=	=	PUNCT
ejpam-3543	205	2	max{λi((z	max{λi((z	PROPN
ejpam-3543	205	3	·	·	PUNCT
ejpam-3543	205	4	y	y	X
ejpam-3543	205	5	)	)	PUNCT
ejpam-3543	205	6	·	·	PUNCT
ejpam-3543	206	1	(	(	PUNCT
ejpam-3543	206	2	z	z	NOUN
ejpam-3543	206	3	·	·	PUNCT
ejpam-3543	206	4	x	x	X
ejpam-3543	206	5	)	)	PUNCT
ejpam-3543	206	6	)	)	PUNCT
ejpam-3543	206	7	,	,	PUNCT
ejpam-3543	206	8	λi(y	λi(y	NOUN
ejpam-3543	206	9	)	)	PUNCT
ejpam-3543	206	10	}	}	PUNCT
ejpam-3543	206	11	,	,	PUNCT
ejpam-3543	206	12	λf	λf	X
ejpam-3543	206	13	(	(	PUNCT
ejpam-3543	206	14	x	x	NOUN
ejpam-3543	206	15	)	)	PUNCT
ejpam-3543	207	1	=	=	SYM
ejpam-3543	207	2	λf	λf	X
ejpam-3543	207	3	(	(	PUNCT
ejpam-3543	207	4	0	0	NUM
ejpam-3543	207	5	)	)	PUNCT
ejpam-3543	207	6	=	=	SYM
ejpam-3543	207	7	min{λf	min{λf	X
ejpam-3543	207	8	(	(	PUNCT
ejpam-3543	207	9	0	0	NUM
ejpam-3543	207	10	)	)	PUNCT
ejpam-3543	207	11	,	,	PUNCT
ejpam-3543	207	12	λf	λf	X
ejpam-3543	207	13	(	(	PUNCT
ejpam-3543	207	14	0	0	NUM
ejpam-3543	207	15	)	)	PUNCT
ejpam-3543	207	16	}	}	PUNCT
ejpam-3543	207	17	=	=	SYM
ejpam-3543	207	18	min{λf	min{λf	X
ejpam-3543	207	19	(	(	PUNCT
ejpam-3543	207	20	(	(	PUNCT
ejpam-3543	207	21	z	z	NOUN
ejpam-3543	207	22	·	·	PUNCT
ejpam-3543	207	23	y	y	X
ejpam-3543	207	24	)	)	PUNCT
ejpam-3543	207	25	·	·	PUNCT
ejpam-3543	208	1	(	(	PUNCT
ejpam-3543	208	2	z	z	NOUN
ejpam-3543	208	3	·	·	PUNCT
ejpam-3543	208	4	x	x	X
ejpam-3543	208	5	)	)	PUNCT
ejpam-3543	208	6	)	)	PUNCT
ejpam-3543	208	7	,	,	PUNCT
ejpam-3543	208	8	λf	λf	X
ejpam-3543	208	9	(	(	PUNCT
ejpam-3543	208	10	y	y	NOUN
ejpam-3543	208	11	)	)	PUNCT
ejpam-3543	208	12	}	}	PUNCT
ejpam-3543	208	13	.	.	PUNCT
ejpam-3543	209	1	hence	hence	ADV
ejpam-3543	209	2	,	,	PUNCT
ejpam-3543	209	3	λ	λ	PROPN
ejpam-3543	209	4	is	be	AUX
ejpam-3543	209	5	a	a	DET
ejpam-3543	209	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	209	7	strongly	strongly	ADV
ejpam-3543	209	8	up	up	ADP
ejpam-3543	209	9	-	-	PUNCT
ejpam-3543	209	10	ideal	ideal	NOUN
ejpam-3543	209	11	of	of	ADP
ejpam-3543	209	12	x.	x.	NOUN
ejpam-3543	209	13	conversely	conversely	ADV
ejpam-3543	209	14	,	,	PUNCT
ejpam-3543	209	15	assume	assume	VERB
ejpam-3543	209	16	that	that	SCONJ
ejpam-3543	209	17	λ	λ	PROPN
ejpam-3543	209	18	is	be	AUX
ejpam-3543	209	19	a	a	DET
ejpam-3543	209	20	neutrosophic	neutrosophic	ADJ
ejpam-3543	209	21	strongly	strongly	ADV
ejpam-3543	209	22	up	up	ADP
ejpam-3543	209	23	-	-	PUNCT
ejpam-3543	209	24	ideal	ideal	NOUN
ejpam-3543	209	25	of	of	ADP
ejpam-3543	209	26	x.	x.	NOUN
ejpam-3543	209	27	for	for	ADP
ejpam-3543	209	28	any	any	DET
ejpam-3543	209	29	x	x	SYM
ejpam-3543	209	30	∈	∈	PROPN
ejpam-3543	209	31	x	x	NOUN
ejpam-3543	209	32	,	,	PUNCT
ejpam-3543	209	33	we	we	PRON
ejpam-3543	209	34	have	have	VERB
ejpam-3543	209	35	λt	λt	INTJ
ejpam-3543	209	36	(	(	PUNCT
ejpam-3543	209	37	x	x	NOUN
ejpam-3543	209	38	)	)	PUNCT
ejpam-3543	209	39	≥	≥	NOUN
ejpam-3543	209	40	min{λt	min{λt	X
ejpam-3543	209	41	(	(	PUNCT
ejpam-3543	209	42	(	(	PUNCT
ejpam-3543	209	43	x	x	X
ejpam-3543	209	44	·	·	PUNCT
ejpam-3543	209	45	0	0	NUM
ejpam-3543	209	46	)	)	PUNCT
ejpam-3543	209	47	·	·	PUNCT
ejpam-3543	210	1	(	(	PUNCT
ejpam-3543	210	2	x	x	X
ejpam-3543	210	3	·	·	PUNCT
ejpam-3543	210	4	x	x	X
ejpam-3543	210	5	)	)	PUNCT
ejpam-3543	210	6	)	)	PUNCT
ejpam-3543	210	7	,	,	PUNCT
ejpam-3543	210	8	λt	λt	X
ejpam-3543	210	9	(	(	PUNCT
ejpam-3543	210	10	0	0	NUM
ejpam-3543	210	11	)	)	PUNCT
ejpam-3543	210	12	}	}	PUNCT
ejpam-3543	210	13	(	(	PUNCT
ejpam-3543	210	14	3.18	3.18	NUM
ejpam-3543	210	15	)	)	PUNCT
ejpam-3543	210	16	=	=	PUNCT
ejpam-3543	210	17	min{λt	min{λt	X
ejpam-3543	210	18	(	(	PUNCT
ejpam-3543	210	19	0	0	NUM
ejpam-3543	210	20	·	·	PUNCT
ejpam-3543	210	21	(	(	PUNCT
ejpam-3543	210	22	x	x	X
ejpam-3543	210	23	·	·	PUNCT
ejpam-3543	210	24	x	x	X
ejpam-3543	210	25	)	)	PUNCT
ejpam-3543	210	26	)	)	PUNCT
ejpam-3543	210	27	,	,	PUNCT
ejpam-3543	210	28	λt	λt	X
ejpam-3543	210	29	(	(	PUNCT
ejpam-3543	210	30	0	0	NUM
ejpam-3543	210	31	)	)	PUNCT
ejpam-3543	210	32	}	}	PUNCT
ejpam-3543	210	33	(	(	PUNCT
ejpam-3543	210	34	up-3	up-3	NOUN
ejpam-3543	210	35	)	)	PUNCT
ejpam-3543	210	36	=	=	PUNCT
ejpam-3543	210	37	min{λt	min{λt	X
ejpam-3543	210	38	(	(	PUNCT
ejpam-3543	210	39	x	x	SYM
ejpam-3543	210	40	·	·	PUNCT
ejpam-3543	210	41	x	x	X
ejpam-3543	210	42	)	)	PUNCT
ejpam-3543	210	43	,	,	PUNCT
ejpam-3543	210	44	λt	λt	X
ejpam-3543	210	45	(	(	PUNCT
ejpam-3543	210	46	0	0	NUM
ejpam-3543	210	47	)	)	PUNCT
ejpam-3543	210	48	}	}	PUNCT
ejpam-3543	210	49	(	(	PUNCT
ejpam-3543	210	50	up-2	up-2	NUM
ejpam-3543	210	51	)	)	PUNCT
ejpam-3543	210	52	=	=	PUNCT
ejpam-3543	210	53	min{λt	min{λt	X
ejpam-3543	210	54	(	(	PUNCT
ejpam-3543	210	55	0	0	NUM
ejpam-3543	210	56	)	)	PUNCT
ejpam-3543	210	57	,	,	PUNCT
ejpam-3543	210	58	λt	λt	X
ejpam-3543	210	59	(	(	PUNCT
ejpam-3543	210	60	0	0	NUM
ejpam-3543	210	61	)	)	PUNCT
ejpam-3543	210	62	}	}	PUNCT
ejpam-3543	210	63	(	(	PUNCT
ejpam-3543	210	64	2.1	2.1	NUM
ejpam-3543	210	65	)	)	PUNCT
ejpam-3543	210	66	=	=	NOUN
ejpam-3543	210	67	λt	λt	X
ejpam-3543	210	68	(	(	PUNCT
ejpam-3543	210	69	0	0	NUM
ejpam-3543	210	70	)	)	PUNCT
ejpam-3543	210	71	,	,	PUNCT
ejpam-3543	210	72	λi(x	λi(x	NUM
ejpam-3543	210	73	)	)	PUNCT
ejpam-3543	210	74	≤	≤	NOUN
ejpam-3543	210	75	max{λi((x	max{λi((x	NOUN
ejpam-3543	210	76	·	·	PUNCT
ejpam-3543	210	77	0	0	NUM
ejpam-3543	210	78	)	)	PUNCT
ejpam-3543	210	79	·	·	PUNCT
ejpam-3543	210	80	(	(	PUNCT
ejpam-3543	210	81	x	x	X
ejpam-3543	210	82	·	·	PUNCT
ejpam-3543	210	83	x	x	X
ejpam-3543	210	84	)	)	PUNCT
ejpam-3543	210	85	)	)	PUNCT
ejpam-3543	210	86	,	,	PUNCT
ejpam-3543	210	87	λi(0	λi(0	NOUN
ejpam-3543	210	88	)	)	PUNCT
ejpam-3543	210	89	}	}	PUNCT
ejpam-3543	210	90	(	(	PUNCT
ejpam-3543	210	91	3.19	3.19	NUM
ejpam-3543	210	92	)	)	PUNCT
ejpam-3543	211	1	=	=	SYM
ejpam-3543	211	2	max{λi(0	max{λi(0	PROPN
ejpam-3543	211	3	·	·	PUNCT
ejpam-3543	211	4	(	(	PUNCT
ejpam-3543	211	5	x	x	X
ejpam-3543	211	6	·	·	PUNCT
ejpam-3543	211	7	x	x	X
ejpam-3543	211	8	)	)	PUNCT
ejpam-3543	211	9	)	)	PUNCT
ejpam-3543	211	10	,	,	PUNCT
ejpam-3543	211	11	λi(0	λi(0	NOUN
ejpam-3543	211	12	)	)	PUNCT
ejpam-3543	211	13	}	}	PUNCT
ejpam-3543	211	14	(	(	PUNCT
ejpam-3543	211	15	up-3	up-3	NOUN
ejpam-3543	211	16	)	)	PUNCT
ejpam-3543	211	17	=	=	SYM
ejpam-3543	211	18	max{λi(x	max{λi(x	NOUN
ejpam-3543	211	19	·	·	PUNCT
ejpam-3543	211	20	x	x	X
ejpam-3543	211	21	)	)	PUNCT
ejpam-3543	211	22	,	,	PUNCT
ejpam-3543	211	23	λi(0	λi(0	NOUN
ejpam-3543	211	24	)	)	PUNCT
ejpam-3543	211	25	}	}	PUNCT
ejpam-3543	211	26	(	(	PUNCT
ejpam-3543	211	27	up-2	up-2	NUM
ejpam-3543	211	28	)	)	PUNCT
ejpam-3543	211	29	=	=	SYM
ejpam-3543	211	30	max{λi(0	max{λi(0	PROPN
ejpam-3543	211	31	)	)	PUNCT
ejpam-3543	211	32	,	,	PUNCT
ejpam-3543	211	33	λi(0	λi(0	NOUN
ejpam-3543	211	34	)	)	PUNCT
ejpam-3543	211	35	}	}	PUNCT
ejpam-3543	211	36	(	(	PUNCT
ejpam-3543	211	37	2.1	2.1	NUM
ejpam-3543	211	38	)	)	PUNCT
ejpam-3543	211	39	=	=	PUNCT
ejpam-3543	212	1	λi(0	λi(0	X
ejpam-3543	212	2	)	)	PUNCT
ejpam-3543	212	3	,	,	PUNCT
ejpam-3543	212	4	λf	λf	X
ejpam-3543	212	5	(	(	PUNCT
ejpam-3543	212	6	x	x	NOUN
ejpam-3543	212	7	)	)	PUNCT
ejpam-3543	212	8	≥	≥	X
ejpam-3543	212	9	min{λf	min{λf	X
ejpam-3543	212	10	(	(	PUNCT
ejpam-3543	212	11	(	(	PUNCT
ejpam-3543	212	12	x	x	X
ejpam-3543	212	13	·	·	PUNCT
ejpam-3543	212	14	0	0	NUM
ejpam-3543	212	15	)	)	PUNCT
ejpam-3543	212	16	·	·	PUNCT
ejpam-3543	212	17	(	(	PUNCT
ejpam-3543	212	18	x	x	X
ejpam-3543	212	19	·	·	PUNCT
ejpam-3543	212	20	x	x	X
ejpam-3543	212	21	)	)	PUNCT
ejpam-3543	212	22	)	)	PUNCT
ejpam-3543	212	23	,	,	PUNCT
ejpam-3543	212	24	λf	λf	X
ejpam-3543	212	25	(	(	PUNCT
ejpam-3543	212	26	0	0	NUM
ejpam-3543	212	27	)	)	PUNCT
ejpam-3543	212	28	}	}	PUNCT
ejpam-3543	212	29	(	(	PUNCT
ejpam-3543	212	30	3.20	3.20	NUM
ejpam-3543	212	31	)	)	PUNCT
ejpam-3543	212	32	=	=	SYM
ejpam-3543	212	33	min{λf	min{λf	X
ejpam-3543	212	34	(	(	PUNCT
ejpam-3543	212	35	0	0	NUM
ejpam-3543	212	36	·	·	PUNCT
ejpam-3543	212	37	(	(	PUNCT
ejpam-3543	212	38	x	x	X
ejpam-3543	212	39	·	·	PUNCT
ejpam-3543	212	40	x	x	X
ejpam-3543	212	41	)	)	PUNCT
ejpam-3543	212	42	)	)	PUNCT
ejpam-3543	212	43	,	,	PUNCT
ejpam-3543	212	44	λf	λf	X
ejpam-3543	212	45	(	(	PUNCT
ejpam-3543	212	46	0	0	NUM
ejpam-3543	212	47	)	)	PUNCT
ejpam-3543	212	48	}	}	PUNCT
ejpam-3543	212	49	(	(	PUNCT
ejpam-3543	212	50	up-3	up-3	NOUN
ejpam-3543	212	51	)	)	PUNCT
ejpam-3543	212	52	=	=	SYM
ejpam-3543	212	53	min{λf	min{λf	X
ejpam-3543	212	54	(	(	PUNCT
ejpam-3543	212	55	x	x	SYM
ejpam-3543	212	56	·	·	PUNCT
ejpam-3543	212	57	x	x	X
ejpam-3543	212	58	)	)	PUNCT
ejpam-3543	212	59	,	,	PUNCT
ejpam-3543	212	60	λf	λf	X
ejpam-3543	212	61	(	(	PUNCT
ejpam-3543	212	62	0	0	NUM
ejpam-3543	212	63	)	)	PUNCT
ejpam-3543	212	64	}	}	PUNCT
ejpam-3543	212	65	(	(	PUNCT
ejpam-3543	212	66	up-2	up-2	NUM
ejpam-3543	212	67	)	)	PUNCT
ejpam-3543	212	68	=	=	SYM
ejpam-3543	212	69	min{λf	min{λf	X
ejpam-3543	212	70	(	(	PUNCT
ejpam-3543	212	71	0	0	NUM
ejpam-3543	212	72	)	)	PUNCT
ejpam-3543	212	73	,	,	PUNCT
ejpam-3543	212	74	λf	λf	X
ejpam-3543	212	75	(	(	PUNCT
ejpam-3543	212	76	0	0	NUM
ejpam-3543	212	77	)	)	PUNCT
ejpam-3543	212	78	}	}	PUNCT
ejpam-3543	212	79	(	(	PUNCT
ejpam-3543	212	80	2.1	2.1	NUM
ejpam-3543	212	81	)	)	PUNCT
ejpam-3543	212	82	=	=	NOUN
ejpam-3543	212	83	λf	λf	X
ejpam-3543	212	84	(	(	PUNCT
ejpam-3543	212	85	0	0	NUM
ejpam-3543	212	86	)	)	PUNCT
ejpam-3543	212	87	.	.	PUNCT
ejpam-3543	213	1	thus	thus	ADV
ejpam-3543	213	2	λt	λt	X
ejpam-3543	213	3	(	(	PUNCT
ejpam-3543	213	4	x	x	X
ejpam-3543	213	5	)	)	PUNCT
ejpam-3543	213	6	=	=	SYM
ejpam-3543	213	7	λt	λt	X
ejpam-3543	213	8	(	(	PUNCT
ejpam-3543	213	9	0	0	NUM
ejpam-3543	213	10	)	)	PUNCT
ejpam-3543	213	11	,	,	PUNCT
ejpam-3543	213	12	λi(x	λi(x	NUM
ejpam-3543	213	13	)	)	PUNCT
ejpam-3543	213	14	=	=	PUNCT
ejpam-3543	214	1	λi(0	λi(0	X
ejpam-3543	214	2	)	)	PUNCT
ejpam-3543	214	3	,	,	PUNCT
ejpam-3543	214	4	and	and	CCONJ
ejpam-3543	214	5	λf	λf	INTJ
ejpam-3543	214	6	(	(	PUNCT
ejpam-3543	214	7	x	x	X
ejpam-3543	214	8	)	)	PUNCT
ejpam-3543	214	9	=	=	SYM
ejpam-3543	214	10	λf	λf	X
ejpam-3543	214	11	(	(	PUNCT
ejpam-3543	214	12	0	0	NUM
ejpam-3543	214	13	)	)	PUNCT
ejpam-3543	214	14	for	for	ADP
ejpam-3543	214	15	all	all	PRON
ejpam-3543	214	16	x	x	SYM
ejpam-3543	214	17	∈	∈	ADJ
ejpam-3543	214	18	x.	x.	NOUN
ejpam-3543	214	19	hence	hence	ADV
ejpam-3543	214	20	,	,	PUNCT
ejpam-3543	214	21	λ	λ	PROPN
ejpam-3543	214	22	is	be	AUX
ejpam-3543	214	23	constant	constant	ADJ
ejpam-3543	214	24	.	.	PUNCT
ejpam-3543	215	1	theorem	theorem	NOUN
ejpam-3543	215	2	3	3	NUM
ejpam-3543	215	3	.	.	PUNCT
ejpam-3543	216	1	every	every	DET
ejpam-3543	216	2	neutrosophic	neutrosophic	ADJ
ejpam-3543	216	3	strongly	strongly	ADV
ejpam-3543	216	4	up	up	ADP
ejpam-3543	216	5	-	-	PUNCT
ejpam-3543	216	6	ideal	ideal	NOUN
ejpam-3543	216	7	of	of	ADP
ejpam-3543	216	8	x	x	PUNCT
ejpam-3543	216	9	is	be	AUX
ejpam-3543	216	10	a	a	DET
ejpam-3543	216	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	216	12	up	up	ADV
ejpam-3543	216	13	-	-	PUNCT
ejpam-3543	216	14	ideal	ideal	NOUN
ejpam-3543	216	15	.	.	PUNCT
ejpam-3543	217	1	proof	proof	NOUN
ejpam-3543	217	2	.	.	PUNCT
ejpam-3543	218	1	assume	assume	VERB
ejpam-3543	218	2	that	that	SCONJ
ejpam-3543	218	3	λ	λ	PROPN
ejpam-3543	218	4	is	be	AUX
ejpam-3543	218	5	a	a	DET
ejpam-3543	218	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	218	7	strong	strong	ADJ
ejpam-3543	218	8	up	up	NOUN
ejpam-3543	218	9	-	-	PUNCT
ejpam-3543	218	10	ideal	ideal	NOUN
ejpam-3543	218	11	of	of	ADP
ejpam-3543	218	12	x.	x.	NOUN
ejpam-3543	218	13	then	then	ADV
ejpam-3543	218	14	λ	λ	PROPN
ejpam-3543	218	15	satisfies	satisfy	VERB
ejpam-3543	218	16	the	the	DET
ejpam-3543	218	17	conditions	condition	NOUN
ejpam-3543	218	18	(	(	PUNCT
ejpam-3543	218	19	3.6	3.6	NUM
ejpam-3543	218	20	)	)	PUNCT
ejpam-3543	218	21	,	,	PUNCT
ejpam-3543	218	22	(	(	PUNCT
ejpam-3543	218	23	3.7	3.7	NUM
ejpam-3543	218	24	)	)	PUNCT
ejpam-3543	218	25	,	,	PUNCT
ejpam-3543	218	26	and	and	CCONJ
ejpam-3543	218	27	(	(	PUNCT
ejpam-3543	218	28	3.8	3.8	NUM
ejpam-3543	218	29	)	)	PUNCT
ejpam-3543	218	30	.	.	PUNCT
ejpam-3543	219	1	by	by	ADP
ejpam-3543	219	2	theorem	theorem	NOUN
ejpam-3543	219	3	2	2	NUM
ejpam-3543	219	4	,	,	PUNCT
ejpam-3543	219	5	we	we	PRON
ejpam-3543	219	6	have	have	VERB
ejpam-3543	219	7	λ	λ	PROPN
ejpam-3543	219	8	is	be	AUX
ejpam-3543	219	9	constant	constant	ADJ
ejpam-3543	219	10	.	.	PUNCT
ejpam-3543	220	1	then	then	ADV
ejpam-3543	220	2	for	for	ADP
ejpam-3543	220	3	all	all	DET
ejpam-3543	220	4	x	x	SYM
ejpam-3543	220	5	∈	∈	PROPN
ejpam-3543	220	6	x	x	NOUN
ejpam-3543	220	7	,	,	PUNCT
ejpam-3543	220	8	λt	λt	X
ejpam-3543	220	9	(	(	PUNCT
ejpam-3543	220	10	x	x	NOUN
ejpam-3543	220	11	)	)	PUNCT
ejpam-3543	220	12	=	=	SYM
ejpam-3543	220	13	λt	λt	X
ejpam-3543	220	14	(	(	PUNCT
ejpam-3543	220	15	0	0	NUM
ejpam-3543	220	16	)	)	PUNCT
ejpam-3543	220	17	,	,	PUNCT
ejpam-3543	220	18	λi(x	λi(x	NUM
ejpam-3543	220	19	)	)	PUNCT
ejpam-3543	220	20	=	=	PUNCT
ejpam-3543	221	1	λi(0	λi(0	X
ejpam-3543	221	2	)	)	PUNCT
ejpam-3543	221	3	,	,	PUNCT
ejpam-3543	221	4	and	and	CCONJ
ejpam-3543	221	5	λf	λf	INTJ
ejpam-3543	221	6	(	(	PUNCT
ejpam-3543	221	7	x	x	X
ejpam-3543	221	8	)	)	PUNCT
ejpam-3543	221	9	=	=	SYM
ejpam-3543	221	10	λf	λf	X
ejpam-3543	221	11	(	(	PUNCT
ejpam-3543	221	12	0	0	NUM
ejpam-3543	221	13	)	)	PUNCT
ejpam-3543	221	14	.	.	PUNCT
ejpam-3543	222	1	thus	thus	ADV
ejpam-3543	222	2	λt	λt	X
ejpam-3543	222	3	(	(	PUNCT
ejpam-3543	222	4	x	x	X
ejpam-3543	222	5	·	·	PUNCT
ejpam-3543	222	6	z	z	X
ejpam-3543	222	7	)	)	PUNCT
ejpam-3543	222	8	=	=	SYM
ejpam-3543	222	9	min{λt	min{λt	X
ejpam-3543	222	10	(	(	PUNCT
ejpam-3543	222	11	(	(	PUNCT
ejpam-3543	222	12	z	z	NOUN
ejpam-3543	222	13	·	·	PUNCT
ejpam-3543	222	14	y	y	X
ejpam-3543	222	15	)	)	PUNCT
ejpam-3543	222	16	·	·	PUNCT
ejpam-3543	222	17	(	(	PUNCT
ejpam-3543	222	18	z	z	NOUN
ejpam-3543	222	19	·	·	PUNCT
ejpam-3543	222	20	(	(	PUNCT
ejpam-3543	222	21	x	x	X
ejpam-3543	222	22	·	·	PUNCT
ejpam-3543	222	23	z	z	NOUN
ejpam-3543	222	24	)	)	PUNCT
ejpam-3543	222	25	)	)	PUNCT
ejpam-3543	222	26	)	)	PUNCT
ejpam-3543	222	27	,	,	PUNCT
ejpam-3543	222	28	λt	λt	X
ejpam-3543	222	29	(	(	PUNCT
ejpam-3543	222	30	y	y	NOUN
ejpam-3543	222	31	)	)	PUNCT
ejpam-3543	222	32	}	}	PUNCT
ejpam-3543	222	33	(	(	PUNCT
ejpam-3543	222	34	3.18	3.18	NUM
ejpam-3543	222	35	)	)	PUNCT
ejpam-3543	222	36	m.	m.	NOUN
ejpam-3543	222	37	songsaeng	songsaeng	PROPN
ejpam-3543	222	38	,	,	PUNCT
ejpam-3543	222	39	a.	a.	NOUN
ejpam-3543	222	40	iampan	iampan	PROPN
ejpam-3543	222	41	/	/	SYM
ejpam-3543	222	42	eur	eur	PROPN
ejpam-3543	222	43	.	.	PUNCT
ejpam-3543	223	1	j.	j.	PROPN
ejpam-3543	223	2	pure	pure	PROPN
ejpam-3543	223	3	appl	appl	PROPN
ejpam-3543	223	4	.	.	PROPN
ejpam-3543	223	5	math	math	PROPN
ejpam-3543	223	6	,	,	PUNCT
ejpam-3543	223	7	12	12	NUM
ejpam-3543	223	8	(	(	PUNCT
ejpam-3543	223	9	4	4	NUM
ejpam-3543	223	10	)	)	PUNCT
ejpam-3543	223	11	(	(	PUNCT
ejpam-3543	223	12	2019	2019	NUM
ejpam-3543	223	13	)	)	PUNCT
ejpam-3543	223	14	,	,	PUNCT
ejpam-3543	223	15	1382	1382	NUM
ejpam-3543	223	16	-	-	SYM
ejpam-3543	223	17	1409	1409	NUM
ejpam-3543	223	18	1391	1391	NUM
ejpam-3543	223	19	=	=	SYM
ejpam-3543	223	20	min{λt	min{λt	X
ejpam-3543	223	21	(	(	PUNCT
ejpam-3543	223	22	(	(	PUNCT
ejpam-3543	223	23	z	z	NOUN
ejpam-3543	223	24	·	·	PUNCT
ejpam-3543	223	25	y	y	X
ejpam-3543	223	26	)	)	PUNCT
ejpam-3543	223	27	·	·	PUNCT
ejpam-3543	223	28	0	0	NUM
ejpam-3543	223	29	)	)	PUNCT
ejpam-3543	223	30	,	,	PUNCT
ejpam-3543	223	31	λt	λt	X
ejpam-3543	223	32	(	(	PUNCT
ejpam-3543	223	33	y	y	NOUN
ejpam-3543	223	34	)	)	PUNCT
ejpam-3543	223	35	}	}	PUNCT
ejpam-3543	223	36	(	(	PUNCT
ejpam-3543	223	37	2.5	2.5	NUM
ejpam-3543	223	38	)	)	PUNCT
ejpam-3543	223	39	=	=	X
ejpam-3543	223	40	min{λt	min{λt	X
ejpam-3543	223	41	(	(	PUNCT
ejpam-3543	223	42	0	0	NUM
ejpam-3543	223	43	)	)	PUNCT
ejpam-3543	223	44	,	,	PUNCT
ejpam-3543	223	45	λt	λt	X
ejpam-3543	223	46	(	(	PUNCT
ejpam-3543	223	47	y	y	NOUN
ejpam-3543	223	48	)	)	PUNCT
ejpam-3543	223	49	}	}	PUNCT
ejpam-3543	223	50	(	(	PUNCT
ejpam-3543	223	51	up-3	up-3	NOUN
ejpam-3543	223	52	)	)	PUNCT
ejpam-3543	224	1	=	=	SYM
ejpam-3543	224	2	λt	λt	X
ejpam-3543	224	3	(	(	PUNCT
ejpam-3543	224	4	y	y	NOUN
ejpam-3543	224	5	)	)	PUNCT
ejpam-3543	224	6	(	(	PUNCT
ejpam-3543	224	7	3.6	3.6	NUM
ejpam-3543	224	8	)	)	PUNCT
ejpam-3543	224	9	≥	≥	NOUN
ejpam-3543	224	10	min{λt	min{λt	X
ejpam-3543	224	11	(	(	PUNCT
ejpam-3543	224	12	x	x	X
ejpam-3543	224	13	·	·	PUNCT
ejpam-3543	224	14	(	(	PUNCT
ejpam-3543	224	15	y	y	PROPN
ejpam-3543	224	16	·	·	PUNCT
ejpam-3543	224	17	z	z	NOUN
ejpam-3543	224	18	)	)	PUNCT
ejpam-3543	224	19	)	)	PUNCT
ejpam-3543	224	20	,	,	PUNCT
ejpam-3543	224	21	λt	λt	X
ejpam-3543	224	22	(	(	PUNCT
ejpam-3543	224	23	y	y	NOUN
ejpam-3543	224	24	)	)	PUNCT
ejpam-3543	224	25	}	}	PUNCT
ejpam-3543	224	26	,	,	PUNCT
ejpam-3543	224	27	λi(x	λi(x	X
ejpam-3543	224	28	·	·	PUNCT
ejpam-3543	224	29	z	z	X
ejpam-3543	224	30	)	)	PUNCT
ejpam-3543	224	31	=	=	PUNCT
ejpam-3543	224	32	max{λi((z	max{λi((z	PROPN
ejpam-3543	224	33	·	·	PUNCT
ejpam-3543	224	34	y	y	X
ejpam-3543	224	35	)	)	PUNCT
ejpam-3543	224	36	·	·	PUNCT
ejpam-3543	225	1	(	(	PUNCT
ejpam-3543	225	2	z	z	NOUN
ejpam-3543	225	3	·	·	PUNCT
ejpam-3543	225	4	(	(	PUNCT
ejpam-3543	225	5	x	x	X
ejpam-3543	225	6	·	·	PUNCT
ejpam-3543	225	7	z	z	NOUN
ejpam-3543	225	8	)	)	PUNCT
ejpam-3543	225	9	)	)	PUNCT
ejpam-3543	225	10	)	)	PUNCT
ejpam-3543	225	11	,	,	PUNCT
ejpam-3543	225	12	λi(y	λi(y	NOUN
ejpam-3543	225	13	)	)	PUNCT
ejpam-3543	225	14	}	}	PUNCT
ejpam-3543	225	15	(	(	PUNCT
ejpam-3543	225	16	3.19	3.19	NUM
ejpam-3543	225	17	)	)	PUNCT
ejpam-3543	225	18	=	=	PUNCT
ejpam-3543	226	1	max{λi((z	max{λi((z	PROPN
ejpam-3543	226	2	·	·	PUNCT
ejpam-3543	226	3	y	y	X
ejpam-3543	226	4	)	)	PUNCT
ejpam-3543	226	5	·	·	PUNCT
ejpam-3543	226	6	0	0	NUM
ejpam-3543	226	7	)	)	PUNCT
ejpam-3543	226	8	,	,	PUNCT
ejpam-3543	226	9	λi(y	λi(y	NOUN
ejpam-3543	226	10	)	)	PUNCT
ejpam-3543	226	11	}	}	PUNCT
ejpam-3543	226	12	(	(	PUNCT
ejpam-3543	226	13	2.5	2.5	NUM
ejpam-3543	226	14	)	)	PUNCT
ejpam-3543	226	15	=	=	SYM
ejpam-3543	226	16	max{λi(0	max{λi(0	PROPN
ejpam-3543	226	17	)	)	PUNCT
ejpam-3543	226	18	,	,	PUNCT
ejpam-3543	226	19	λi(y	λi(y	NOUN
ejpam-3543	226	20	)	)	PUNCT
ejpam-3543	226	21	}	}	PUNCT
ejpam-3543	226	22	(	(	PUNCT
ejpam-3543	226	23	up-3	up-3	NOUN
ejpam-3543	226	24	)	)	PUNCT
ejpam-3543	226	25	=	=	PUNCT
ejpam-3543	226	26	λi(y	λi(y	X
ejpam-3543	226	27	)	)	PUNCT
ejpam-3543	226	28	(	(	PUNCT
ejpam-3543	226	29	3.7	3.7	NUM
ejpam-3543	226	30	)	)	PUNCT
ejpam-3543	226	31	≤	≤	NUM
ejpam-3543	226	32	max{λi(x	max{λi(x	NOUN
ejpam-3543	226	33	·	·	PUNCT
ejpam-3543	226	34	(	(	PUNCT
ejpam-3543	226	35	y	y	PROPN
ejpam-3543	226	36	·	·	PUNCT
ejpam-3543	226	37	z	z	NOUN
ejpam-3543	226	38	)	)	PUNCT
ejpam-3543	226	39	)	)	PUNCT
ejpam-3543	226	40	,	,	PUNCT
ejpam-3543	226	41	λi(y	λi(y	NOUN
ejpam-3543	226	42	)	)	PUNCT
ejpam-3543	226	43	}	}	PUNCT
ejpam-3543	226	44	,	,	PUNCT
ejpam-3543	226	45	λf	λf	X
ejpam-3543	226	46	(	(	PUNCT
ejpam-3543	226	47	x	x	SYM
ejpam-3543	226	48	·	·	PUNCT
ejpam-3543	226	49	z	z	X
ejpam-3543	226	50	)	)	PUNCT
ejpam-3543	226	51	=	=	SYM
ejpam-3543	226	52	min{λf	min{λf	X
ejpam-3543	226	53	(	(	PUNCT
ejpam-3543	226	54	(	(	PUNCT
ejpam-3543	226	55	z	z	NOUN
ejpam-3543	226	56	·	·	PUNCT
ejpam-3543	226	57	y	y	X
ejpam-3543	226	58	)	)	PUNCT
ejpam-3543	226	59	·	·	PUNCT
ejpam-3543	226	60	(	(	PUNCT
ejpam-3543	226	61	z	z	NOUN
ejpam-3543	226	62	·	·	PUNCT
ejpam-3543	226	63	(	(	PUNCT
ejpam-3543	226	64	x	x	X
ejpam-3543	226	65	·	·	PUNCT
ejpam-3543	226	66	z	z	NOUN
ejpam-3543	226	67	)	)	PUNCT
ejpam-3543	226	68	)	)	PUNCT
ejpam-3543	226	69	)	)	PUNCT
ejpam-3543	226	70	,	,	PUNCT
ejpam-3543	226	71	λf	λf	X
ejpam-3543	226	72	(	(	PUNCT
ejpam-3543	226	73	y	y	NOUN
ejpam-3543	226	74	)	)	PUNCT
ejpam-3543	226	75	}	}	PUNCT
ejpam-3543	226	76	(	(	PUNCT
ejpam-3543	226	77	3.20	3.20	NUM
ejpam-3543	226	78	)	)	PUNCT
ejpam-3543	226	79	=	=	SYM
ejpam-3543	226	80	min{λf	min{λf	X
ejpam-3543	226	81	(	(	PUNCT
ejpam-3543	226	82	(	(	PUNCT
ejpam-3543	226	83	z	z	NOUN
ejpam-3543	226	84	·	·	PUNCT
ejpam-3543	226	85	y	y	X
ejpam-3543	226	86	)	)	PUNCT
ejpam-3543	226	87	·	·	PUNCT
ejpam-3543	226	88	0	0	NUM
ejpam-3543	226	89	)	)	PUNCT
ejpam-3543	226	90	,	,	PUNCT
ejpam-3543	226	91	λf	λf	X
ejpam-3543	226	92	(	(	PUNCT
ejpam-3543	226	93	y	y	NOUN
ejpam-3543	226	94	)	)	PUNCT
ejpam-3543	226	95	}	}	PUNCT
ejpam-3543	226	96	(	(	PUNCT
ejpam-3543	226	97	2.5	2.5	NUM
ejpam-3543	226	98	)	)	PUNCT
ejpam-3543	226	99	=	=	X
ejpam-3543	226	100	min{λf	min{λf	X
ejpam-3543	226	101	(	(	PUNCT
ejpam-3543	226	102	0	0	NUM
ejpam-3543	226	103	)	)	PUNCT
ejpam-3543	226	104	,	,	PUNCT
ejpam-3543	226	105	λf	λf	X
ejpam-3543	226	106	(	(	PUNCT
ejpam-3543	226	107	y	y	NOUN
ejpam-3543	226	108	)	)	PUNCT
ejpam-3543	226	109	}	}	PUNCT
ejpam-3543	226	110	(	(	PUNCT
ejpam-3543	226	111	up-3	up-3	NOUN
ejpam-3543	226	112	)	)	PUNCT
ejpam-3543	227	1	=	=	SYM
ejpam-3543	227	2	λf	λf	X
ejpam-3543	227	3	(	(	PUNCT
ejpam-3543	227	4	y	y	NOUN
ejpam-3543	227	5	)	)	PUNCT
ejpam-3543	227	6	(	(	PUNCT
ejpam-3543	227	7	3.8	3.8	NUM
ejpam-3543	227	8	)	)	PUNCT
ejpam-3543	227	9	≥	≥	X
ejpam-3543	227	10	min{λf	min{λf	X
ejpam-3543	227	11	(	(	PUNCT
ejpam-3543	227	12	x	x	PART
ejpam-3543	227	13	·	·	PUNCT
ejpam-3543	227	14	(	(	PUNCT
ejpam-3543	227	15	y	y	PROPN
ejpam-3543	227	16	·	·	PUNCT
ejpam-3543	227	17	z	z	NOUN
ejpam-3543	227	18	)	)	PUNCT
ejpam-3543	227	19	)	)	PUNCT
ejpam-3543	227	20	,	,	PUNCT
ejpam-3543	227	21	λf	λf	X
ejpam-3543	227	22	(	(	PUNCT
ejpam-3543	227	23	y	y	NOUN
ejpam-3543	227	24	)	)	PUNCT
ejpam-3543	227	25	}	}	PUNCT
ejpam-3543	227	26	.	.	PUNCT
ejpam-3543	228	1	hence	hence	ADV
ejpam-3543	228	2	,	,	PUNCT
ejpam-3543	228	3	λ	λ	PROPN
ejpam-3543	228	4	is	be	AUX
ejpam-3543	228	5	a	a	DET
ejpam-3543	228	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	228	7	up	up	ADV
ejpam-3543	228	8	-	-	PUNCT
ejpam-3543	228	9	ideal	ideal	NOUN
ejpam-3543	228	10	of	of	ADP
ejpam-3543	228	11	x.	x.	NOUN
ejpam-3543	228	12	the	the	DET
ejpam-3543	228	13	following	follow	VERB
ejpam-3543	228	14	example	example	NOUN
ejpam-3543	228	15	show	show	VERB
ejpam-3543	228	16	that	that	SCONJ
ejpam-3543	228	17	the	the	DET
ejpam-3543	228	18	converse	converse	NOUN
ejpam-3543	228	19	of	of	ADP
ejpam-3543	228	20	theorem	theorem	NOUN
ejpam-3543	228	21	3	3	NUM
ejpam-3543	228	22	is	be	AUX
ejpam-3543	228	23	not	not	PART
ejpam-3543	228	24	true	true	ADJ
ejpam-3543	228	25	.	.	PUNCT
ejpam-3543	228	26	example	example	NOUN
ejpam-3543	229	1	9	9	NUM
ejpam-3543	229	2	.	.	PUNCT
ejpam-3543	229	3	from	from	ADP
ejpam-3543	229	4	example	example	NOUN
ejpam-3543	229	5	7	7	NUM
ejpam-3543	229	6	,	,	PUNCT
ejpam-3543	229	7	we	we	PRON
ejpam-3543	229	8	have	have	VERB
ejpam-3543	229	9	λ	λ	PROPN
ejpam-3543	229	10	is	be	AUX
ejpam-3543	229	11	a	a	DET
ejpam-3543	229	12	neutrosophic	neutrosophic	ADJ
ejpam-3543	229	13	up	up	ADV
ejpam-3543	229	14	-	-	PUNCT
ejpam-3543	229	15	ideal	ideal	NOUN
ejpam-3543	229	16	of	of	ADP
ejpam-3543	229	17	x.	x.	NOUN
ejpam-3543	229	18	since	since	SCONJ
ejpam-3543	229	19	λ	λ	PROPN
ejpam-3543	229	20	is	be	AUX
ejpam-3543	229	21	not	not	PART
ejpam-3543	229	22	constant	constant	ADJ
ejpam-3543	229	23	,	,	PUNCT
ejpam-3543	229	24	it	it	PRON
ejpam-3543	229	25	follows	follow	VERB
ejpam-3543	229	26	from	from	ADP
ejpam-3543	229	27	theorem	theorem	ADJ
ejpam-3543	229	28	2	2	NUM
ejpam-3543	229	29	that	that	SCONJ
ejpam-3543	229	30	it	it	PRON
ejpam-3543	229	31	is	be	AUX
ejpam-3543	229	32	not	not	PART
ejpam-3543	229	33	a	a	DET
ejpam-3543	229	34	neutrosophic	neutrosophic	ADJ
ejpam-3543	229	35	strongly	strongly	ADV
ejpam-3543	229	36	up	up	ADP
ejpam-3543	229	37	-	-	PUNCT
ejpam-3543	229	38	ideal	ideal	NOUN
ejpam-3543	229	39	of	of	ADP
ejpam-3543	229	40	x.	x.	PROPN
ejpam-3543	229	41	theorem	theorem	VERB
ejpam-3543	229	42	4	4	NUM
ejpam-3543	229	43	.	.	PUNCT
ejpam-3543	230	1	every	every	DET
ejpam-3543	230	2	neutrosophic	neutrosophic	ADJ
ejpam-3543	230	3	up	up	ADV
ejpam-3543	230	4	-	-	PUNCT
ejpam-3543	230	5	ideal	ideal	NOUN
ejpam-3543	230	6	of	of	ADP
ejpam-3543	230	7	x	x	PUNCT
ejpam-3543	230	8	is	be	AUX
ejpam-3543	230	9	a	a	DET
ejpam-3543	230	10	neutrosophic	neutrosophic	ADJ
ejpam-3543	230	11	up	up	ADJ
ejpam-3543	230	12	-	-	PUNCT
ejpam-3543	230	13	filter	filter	NOUN
ejpam-3543	230	14	.	.	PUNCT
ejpam-3543	231	1	proof	proof	NOUN
ejpam-3543	231	2	.	.	PUNCT
ejpam-3543	232	1	assume	assume	VERB
ejpam-3543	232	2	that	that	SCONJ
ejpam-3543	232	3	λ	λ	PROPN
ejpam-3543	232	4	is	be	AUX
ejpam-3543	232	5	a	a	DET
ejpam-3543	232	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	232	7	up	up	ADV
ejpam-3543	232	8	-	-	PUNCT
ejpam-3543	232	9	ideal	ideal	NOUN
ejpam-3543	232	10	of	of	ADP
ejpam-3543	232	11	x.	x.	NOUN
ejpam-3543	232	12	then	then	ADV
ejpam-3543	232	13	λ	λ	PROPN
ejpam-3543	232	14	satisfies	satisfy	VERB
ejpam-3543	232	15	the	the	DET
ejpam-3543	232	16	conditions	condition	NOUN
ejpam-3543	232	17	(	(	PUNCT
ejpam-3543	232	18	3.6	3.6	NUM
ejpam-3543	232	19	)	)	PUNCT
ejpam-3543	232	20	,	,	PUNCT
ejpam-3543	232	21	(	(	PUNCT
ejpam-3543	232	22	3.7	3.7	NUM
ejpam-3543	232	23	)	)	PUNCT
ejpam-3543	232	24	,	,	PUNCT
ejpam-3543	232	25	and	and	CCONJ
ejpam-3543	232	26	(	(	PUNCT
ejpam-3543	232	27	3.8	3.8	NUM
ejpam-3543	232	28	)	)	PUNCT
ejpam-3543	232	29	.	.	PUNCT
ejpam-3543	233	1	next	next	ADV
ejpam-3543	233	2	,	,	PUNCT
ejpam-3543	233	3	let	let	VERB
ejpam-3543	233	4	x	x	PRON
ejpam-3543	233	5	,	,	PUNCT
ejpam-3543	233	6	y	y	PROPN
ejpam-3543	233	7	∈	∈	PROPN
ejpam-3543	233	8	x.	x.	NOUN
ejpam-3543	233	9	then	then	ADV
ejpam-3543	233	10	λt	λt	ADP
ejpam-3543	233	11	(	(	PUNCT
ejpam-3543	233	12	y	y	NOUN
ejpam-3543	233	13	)	)	PUNCT
ejpam-3543	234	1	=	=	NOUN
ejpam-3543	234	2	λt	λt	X
ejpam-3543	234	3	(	(	PUNCT
ejpam-3543	234	4	0	0	NUM
ejpam-3543	234	5	·	·	PUNCT
ejpam-3543	234	6	y	y	X
ejpam-3543	234	7	)	)	PUNCT
ejpam-3543	234	8	(	(	PUNCT
ejpam-3543	234	9	up-2	up-2	NUM
ejpam-3543	234	10	)	)	PUNCT
ejpam-3543	234	11	≥	≥	NOUN
ejpam-3543	234	12	min{λt	min{λt	X
ejpam-3543	234	13	(	(	PUNCT
ejpam-3543	234	14	0	0	NUM
ejpam-3543	234	15	·	·	PUNCT
ejpam-3543	234	16	(	(	PUNCT
ejpam-3543	234	17	x	x	X
ejpam-3543	234	18	·	·	PUNCT
ejpam-3543	234	19	y	y	NOUN
ejpam-3543	234	20	)	)	PUNCT
ejpam-3543	234	21	)	)	PUNCT
ejpam-3543	234	22	,	,	PUNCT
ejpam-3543	234	23	λt	λt	X
ejpam-3543	234	24	(	(	PUNCT
ejpam-3543	234	25	x	x	NOUN
ejpam-3543	234	26	)	)	PUNCT
ejpam-3543	234	27	}	}	PUNCT
ejpam-3543	234	28	(	(	PUNCT
ejpam-3543	234	29	3.15	3.15	NUM
ejpam-3543	234	30	)	)	PUNCT
ejpam-3543	234	31	=	=	PUNCT
ejpam-3543	234	32	min{λt	min{λt	X
ejpam-3543	234	33	(	(	PUNCT
ejpam-3543	234	34	x	x	SYM
ejpam-3543	234	35	·	·	PUNCT
ejpam-3543	234	36	y	y	X
ejpam-3543	234	37	)	)	PUNCT
ejpam-3543	234	38	,	,	PUNCT
ejpam-3543	234	39	λt	λt	X
ejpam-3543	234	40	(	(	PUNCT
ejpam-3543	234	41	x	x	NOUN
ejpam-3543	234	42	)	)	PUNCT
ejpam-3543	234	43	}	}	PUNCT
ejpam-3543	234	44	,	,	PUNCT
ejpam-3543	234	45	(	(	PUNCT
ejpam-3543	234	46	up-2	up-2	NUM
ejpam-3543	234	47	)	)	PUNCT
ejpam-3543	234	48	λi(y	λi(y	PUNCT
ejpam-3543	234	49	)	)	PUNCT
ejpam-3543	235	1	=	=	PUNCT
ejpam-3543	235	2	λi(0	λi(0	PROPN
ejpam-3543	235	3	·	·	PUNCT
ejpam-3543	235	4	y	y	X
ejpam-3543	235	5	)	)	PUNCT
ejpam-3543	235	6	(	(	PUNCT
ejpam-3543	235	7	up-2	up-2	NUM
ejpam-3543	235	8	)	)	PUNCT
ejpam-3543	235	9	≤	≤	NOUN
ejpam-3543	235	10	max{λi(0	max{λi(0	PROPN
ejpam-3543	235	11	·	·	PUNCT
ejpam-3543	235	12	(	(	PUNCT
ejpam-3543	235	13	x	x	X
ejpam-3543	235	14	·	·	PUNCT
ejpam-3543	235	15	y	y	NOUN
ejpam-3543	235	16	)	)	PUNCT
ejpam-3543	235	17	)	)	PUNCT
ejpam-3543	235	18	,	,	PUNCT
ejpam-3543	235	19	λi(x	λi(x	NUM
ejpam-3543	235	20	)	)	PUNCT
ejpam-3543	235	21	}	}	PUNCT
ejpam-3543	235	22	(	(	PUNCT
ejpam-3543	235	23	3.16	3.16	NUM
ejpam-3543	235	24	)	)	PUNCT
ejpam-3543	235	25	=	=	SYM
ejpam-3543	235	26	max{λi(x	max{λi(x	X
ejpam-3543	235	27	·	·	PUNCT
ejpam-3543	235	28	y	y	X
ejpam-3543	235	29	)	)	PUNCT
ejpam-3543	235	30	,	,	PUNCT
ejpam-3543	235	31	λi(x	λi(x	NUM
ejpam-3543	235	32	)	)	PUNCT
ejpam-3543	235	33	}	}	PUNCT
ejpam-3543	235	34	,	,	PUNCT
ejpam-3543	235	35	(	(	PUNCT
ejpam-3543	235	36	up-2	up-2	NUM
ejpam-3543	235	37	)	)	PUNCT
ejpam-3543	235	38	λf	λf	X
ejpam-3543	235	39	(	(	PUNCT
ejpam-3543	235	40	y	y	NOUN
ejpam-3543	235	41	)	)	PUNCT
ejpam-3543	235	42	=	=	SYM
ejpam-3543	235	43	λf	λf	X
ejpam-3543	235	44	(	(	PUNCT
ejpam-3543	235	45	0	0	NUM
ejpam-3543	235	46	·	·	SYM
ejpam-3543	235	47	y	y	X
ejpam-3543	235	48	)	)	PUNCT
ejpam-3543	235	49	(	(	PUNCT
ejpam-3543	235	50	up-2	up-2	NUM
ejpam-3543	235	51	)	)	PUNCT
ejpam-3543	235	52	≥	≥	NOUN
ejpam-3543	235	53	min{λf	min{λf	X
ejpam-3543	235	54	(	(	PUNCT
ejpam-3543	235	55	0	0	NUM
ejpam-3543	235	56	·	·	PUNCT
ejpam-3543	235	57	(	(	PUNCT
ejpam-3543	235	58	x	x	X
ejpam-3543	235	59	·	·	PUNCT
ejpam-3543	235	60	y	y	NOUN
ejpam-3543	235	61	)	)	PUNCT
ejpam-3543	235	62	)	)	PUNCT
ejpam-3543	235	63	,	,	PUNCT
ejpam-3543	235	64	λf	λf	X
ejpam-3543	235	65	(	(	PUNCT
ejpam-3543	235	66	x	x	NOUN
ejpam-3543	235	67	)	)	PUNCT
ejpam-3543	235	68	}	}	PUNCT
ejpam-3543	235	69	(	(	PUNCT
ejpam-3543	235	70	3.17	3.17	NUM
ejpam-3543	235	71	)	)	PUNCT
ejpam-3543	235	72	=	=	SYM
ejpam-3543	235	73	min{λf	min{λf	X
ejpam-3543	235	74	(	(	PUNCT
ejpam-3543	235	75	x	x	PROPN
ejpam-3543	235	76	·	·	PUNCT
ejpam-3543	235	77	y	y	X
ejpam-3543	235	78	)	)	PUNCT
ejpam-3543	235	79	,	,	PUNCT
ejpam-3543	235	80	λf	λf	X
ejpam-3543	235	81	(	(	PUNCT
ejpam-3543	235	82	x	x	NOUN
ejpam-3543	235	83	)	)	PUNCT
ejpam-3543	235	84	}	}	PUNCT
ejpam-3543	235	85	.	.	PUNCT
ejpam-3543	236	1	(	(	PUNCT
ejpam-3543	236	2	up-2	up-2	NUM
ejpam-3543	236	3	)	)	PUNCT
ejpam-3543	236	4	hence	hence	ADV
ejpam-3543	236	5	,	,	PUNCT
ejpam-3543	236	6	λ	λ	PROPN
ejpam-3543	236	7	is	be	AUX
ejpam-3543	236	8	a	a	DET
ejpam-3543	236	9	neutrosophic	neutrosophic	ADJ
ejpam-3543	236	10	up	up	ADJ
ejpam-3543	236	11	-	-	PUNCT
ejpam-3543	236	12	filter	filter	NOUN
ejpam-3543	236	13	of	of	ADP
ejpam-3543	236	14	x.	x.	NOUN
ejpam-3543	236	15	the	the	DET
ejpam-3543	236	16	following	follow	VERB
ejpam-3543	236	17	example	example	NOUN
ejpam-3543	236	18	show	show	VERB
ejpam-3543	236	19	that	that	SCONJ
ejpam-3543	236	20	the	the	DET
ejpam-3543	236	21	converse	converse	NOUN
ejpam-3543	236	22	of	of	ADP
ejpam-3543	236	23	theorem	theorem	NOUN
ejpam-3543	236	24	4	4	NUM
ejpam-3543	236	25	is	be	AUX
ejpam-3543	236	26	not	not	PART
ejpam-3543	236	27	true	true	ADJ
ejpam-3543	236	28	.	.	PUNCT
ejpam-3543	237	1	m.	m.	PROPN
ejpam-3543	237	2	songsaeng	songsaeng	PROPN
ejpam-3543	237	3	,	,	PUNCT
ejpam-3543	237	4	a.	a.	NOUN
ejpam-3543	237	5	iampan	iampan	PROPN
ejpam-3543	237	6	/	/	SYM
ejpam-3543	237	7	eur	eur	PROPN
ejpam-3543	237	8	.	.	PUNCT
ejpam-3543	238	1	j.	j.	PROPN
ejpam-3543	238	2	pure	pure	PROPN
ejpam-3543	238	3	appl	appl	PROPN
ejpam-3543	238	4	.	.	PROPN
ejpam-3543	238	5	math	math	PROPN
ejpam-3543	238	6	,	,	PUNCT
ejpam-3543	238	7	12	12	NUM
ejpam-3543	238	8	(	(	PUNCT
ejpam-3543	238	9	4	4	NUM
ejpam-3543	238	10	)	)	PUNCT
ejpam-3543	238	11	(	(	PUNCT
ejpam-3543	238	12	2019	2019	NUM
ejpam-3543	238	13	)	)	PUNCT
ejpam-3543	238	14	,	,	PUNCT
ejpam-3543	238	15	1382	1382	NUM
ejpam-3543	238	16	-	-	SYM
ejpam-3543	238	17	1409	1409	NUM
ejpam-3543	238	18	1392	1392	NUM
ejpam-3543	238	19	example	example	NOUN
ejpam-3543	238	20	10	10	NUM
ejpam-3543	238	21	.	.	PUNCT
ejpam-3543	239	1	from	from	ADP
ejpam-3543	239	2	example	example	NOUN
ejpam-3543	239	3	6	6	NUM
ejpam-3543	239	4	,	,	PUNCT
ejpam-3543	239	5	we	we	PRON
ejpam-3543	239	6	have	have	VERB
ejpam-3543	239	7	λ	λ	PROPN
ejpam-3543	239	8	is	be	AUX
ejpam-3543	239	9	a	a	DET
ejpam-3543	239	10	neutrosophic	neutrosophic	ADJ
ejpam-3543	239	11	up	up	ADJ
ejpam-3543	239	12	-	-	PUNCT
ejpam-3543	239	13	filter	filter	NOUN
ejpam-3543	239	14	of	of	ADP
ejpam-3543	239	15	x.	x.	NOUN
ejpam-3543	239	16	since	since	SCONJ
ejpam-3543	239	17	λf	λf	PROPN
ejpam-3543	239	18	(	(	PUNCT
ejpam-3543	239	19	3	3	NUM
ejpam-3543	239	20	·	·	SYM
ejpam-3543	239	21	4	4	NUM
ejpam-3543	239	22	)	)	PUNCT
ejpam-3543	239	23	=	=	PUNCT
ejpam-3543	239	24	0.3	0.3	NUM
ejpam-3543	239	25	<	<	X
ejpam-3543	239	26	0.4	0.4	NUM
ejpam-3543	239	27	=	=	SYM
ejpam-3543	239	28	min{λf	min{λf	X
ejpam-3543	239	29	(	(	PUNCT
ejpam-3543	239	30	3	3	NUM
ejpam-3543	239	31	·	·	PUNCT
ejpam-3543	239	32	(	(	PUNCT
ejpam-3543	239	33	2	2	NUM
ejpam-3543	239	34	·	·	SYM
ejpam-3543	239	35	4	4	NUM
ejpam-3543	239	36	)	)	PUNCT
ejpam-3543	239	37	)	)	PUNCT
ejpam-3543	239	38	,	,	PUNCT
ejpam-3543	239	39	λf	λf	X
ejpam-3543	239	40	(	(	PUNCT
ejpam-3543	239	41	2	2	NUM
ejpam-3543	239	42	)	)	PUNCT
ejpam-3543	239	43	}	}	PUNCT
ejpam-3543	239	44	,	,	PUNCT
ejpam-3543	239	45	we	we	PRON
ejpam-3543	239	46	have	have	VERB
ejpam-3543	239	47	λ	λ	PROPN
ejpam-3543	239	48	is	be	AUX
ejpam-3543	239	49	not	not	PART
ejpam-3543	239	50	a	a	DET
ejpam-3543	239	51	neutrosophic	neutrosophic	ADJ
ejpam-3543	239	52	up	up	ADV
ejpam-3543	239	53	-	-	PUNCT
ejpam-3543	239	54	ideal	ideal	NOUN
ejpam-3543	239	55	of	of	ADP
ejpam-3543	239	56	x.	x.	PROPN
ejpam-3543	239	57	theorem	theorem	VERB
ejpam-3543	239	58	5	5	NUM
ejpam-3543	239	59	.	.	PUNCT
ejpam-3543	240	1	every	every	DET
ejpam-3543	240	2	neutrosophic	neutrosophic	ADJ
ejpam-3543	240	3	up	up	ADP
ejpam-3543	240	4	-	-	PUNCT
ejpam-3543	240	5	filter	filter	NOUN
ejpam-3543	240	6	of	of	ADP
ejpam-3543	240	7	x	x	PUNCT
ejpam-3543	240	8	is	be	AUX
ejpam-3543	240	9	a	a	DET
ejpam-3543	240	10	neutrosophic	neutrosophic	ADJ
ejpam-3543	240	11	near	near	ADP
ejpam-3543	240	12	up	up	ADJ
ejpam-3543	240	13	-	-	PUNCT
ejpam-3543	240	14	filter	filter	NOUN
ejpam-3543	240	15	.	.	PUNCT
ejpam-3543	241	1	proof	proof	NOUN
ejpam-3543	241	2	.	.	PUNCT
ejpam-3543	242	1	assume	assume	VERB
ejpam-3543	242	2	that	that	SCONJ
ejpam-3543	242	3	λ	λ	PROPN
ejpam-3543	242	4	is	be	AUX
ejpam-3543	242	5	a	a	DET
ejpam-3543	242	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	242	7	up	up	ADJ
ejpam-3543	242	8	-	-	PUNCT
ejpam-3543	242	9	filter	filter	NOUN
ejpam-3543	242	10	.	.	PUNCT
ejpam-3543	243	1	then	then	ADV
ejpam-3543	243	2	λ	λ	PROPN
ejpam-3543	243	3	satisfies	satisfy	VERB
ejpam-3543	243	4	the	the	DET
ejpam-3543	243	5	conditions	condition	NOUN
ejpam-3543	243	6	(	(	PUNCT
ejpam-3543	243	7	3.6	3.6	NUM
ejpam-3543	243	8	)	)	PUNCT
ejpam-3543	243	9	,	,	PUNCT
ejpam-3543	243	10	(	(	PUNCT
ejpam-3543	243	11	3.7	3.7	NUM
ejpam-3543	243	12	)	)	PUNCT
ejpam-3543	243	13	,	,	PUNCT
ejpam-3543	243	14	and	and	CCONJ
ejpam-3543	243	15	(	(	PUNCT
ejpam-3543	243	16	3.8	3.8	NUM
ejpam-3543	243	17	)	)	PUNCT
ejpam-3543	243	18	.	.	PUNCT
ejpam-3543	244	1	next	next	ADV
ejpam-3543	244	2	,	,	PUNCT
ejpam-3543	244	3	let	let	VERB
ejpam-3543	244	4	x	x	PRON
ejpam-3543	244	5	,	,	PUNCT
ejpam-3543	244	6	y	y	PROPN
ejpam-3543	244	7	∈	∈	PROPN
ejpam-3543	244	8	x.	x.	NOUN
ejpam-3543	244	9	then	then	ADV
ejpam-3543	244	10	λt	λt	X
ejpam-3543	244	11	(	(	PUNCT
ejpam-3543	244	12	x	x	PROPN
ejpam-3543	244	13	·	·	PUNCT
ejpam-3543	244	14	y	y	X
ejpam-3543	244	15	)	)	PUNCT
ejpam-3543	244	16	≥	≥	NOUN
ejpam-3543	244	17	min{λt	min{λt	X
ejpam-3543	244	18	(	(	PUNCT
ejpam-3543	244	19	y	y	PROPN
ejpam-3543	244	20	·	·	PUNCT
ejpam-3543	244	21	(	(	PUNCT
ejpam-3543	244	22	x	x	X
ejpam-3543	244	23	·	·	PUNCT
ejpam-3543	244	24	y	y	NOUN
ejpam-3543	244	25	)	)	PUNCT
ejpam-3543	244	26	)	)	PUNCT
ejpam-3543	244	27	,	,	PUNCT
ejpam-3543	244	28	λt	λt	X
ejpam-3543	244	29	(	(	PUNCT
ejpam-3543	244	30	y	y	NOUN
ejpam-3543	244	31	)	)	PUNCT
ejpam-3543	244	32	}	}	PUNCT
ejpam-3543	244	33	(	(	PUNCT
ejpam-3543	244	34	3.12	3.12	NUM
ejpam-3543	244	35	)	)	PUNCT
ejpam-3543	244	36	=	=	X
ejpam-3543	244	37	min{λt	min{λt	X
ejpam-3543	244	38	(	(	PUNCT
ejpam-3543	244	39	0	0	NUM
ejpam-3543	244	40	)	)	PUNCT
ejpam-3543	244	41	,	,	PUNCT
ejpam-3543	244	42	λt	λt	X
ejpam-3543	244	43	(	(	PUNCT
ejpam-3543	244	44	y	y	NOUN
ejpam-3543	244	45	)	)	PUNCT
ejpam-3543	244	46	}	}	PUNCT
ejpam-3543	244	47	(	(	PUNCT
ejpam-3543	244	48	2.5	2.5	NUM
ejpam-3543	244	49	)	)	PUNCT
ejpam-3543	244	50	=	=	NOUN
ejpam-3543	245	1	λt	λt	X
ejpam-3543	245	2	(	(	PUNCT
ejpam-3543	245	3	y	y	NOUN
ejpam-3543	245	4	)	)	PUNCT
ejpam-3543	245	5	,	,	PUNCT
ejpam-3543	245	6	(	(	PUNCT
ejpam-3543	245	7	3.6	3.6	NUM
ejpam-3543	245	8	)	)	PUNCT
ejpam-3543	245	9	λi(x	λi(x	X
ejpam-3543	245	10	·	·	PUNCT
ejpam-3543	245	11	y	y	X
ejpam-3543	245	12	)	)	PUNCT
ejpam-3543	245	13	≤	≤	NOUN
ejpam-3543	245	14	max{λi(y	max{λi(y	VERB
ejpam-3543	245	15	·	·	PUNCT
ejpam-3543	245	16	(	(	PUNCT
ejpam-3543	245	17	x	x	X
ejpam-3543	245	18	·	·	PUNCT
ejpam-3543	245	19	y	y	NOUN
ejpam-3543	245	20	)	)	PUNCT
ejpam-3543	245	21	)	)	PUNCT
ejpam-3543	245	22	,	,	PUNCT
ejpam-3543	245	23	λi(y	λi(y	NOUN
ejpam-3543	245	24	)	)	PUNCT
ejpam-3543	245	25	}	}	PUNCT
ejpam-3543	245	26	(	(	PUNCT
ejpam-3543	245	27	3.13	3.13	NUM
ejpam-3543	245	28	)	)	PUNCT
ejpam-3543	245	29	=	=	SYM
ejpam-3543	245	30	max{λi(0	max{λi(0	PROPN
ejpam-3543	245	31	)	)	PUNCT
ejpam-3543	245	32	,	,	PUNCT
ejpam-3543	245	33	λi(y	λi(y	PUNCT
ejpam-3543	245	34	)	)	PUNCT
ejpam-3543	245	35	}	}	PUNCT
ejpam-3543	245	36	(	(	PUNCT
ejpam-3543	245	37	2.5	2.5	NUM
ejpam-3543	245	38	)	)	PUNCT
ejpam-3543	245	39	=	=	PUNCT
ejpam-3543	245	40	λi(y	λi(y	X
ejpam-3543	245	41	)	)	PUNCT
ejpam-3543	245	42	,	,	PUNCT
ejpam-3543	245	43	(	(	PUNCT
ejpam-3543	245	44	3.7	3.7	NUM
ejpam-3543	245	45	)	)	PUNCT
ejpam-3543	245	46	λf	λf	X
ejpam-3543	245	47	(	(	PUNCT
ejpam-3543	245	48	x	x	X
ejpam-3543	245	49	·	·	PUNCT
ejpam-3543	245	50	y	y	X
ejpam-3543	245	51	)	)	PUNCT
ejpam-3543	245	52	≥	≥	NOUN
ejpam-3543	245	53	min{λf	min{λf	X
ejpam-3543	246	1	(	(	PUNCT
ejpam-3543	246	2	y	y	PROPN
ejpam-3543	246	3	·	·	PUNCT
ejpam-3543	246	4	(	(	PUNCT
ejpam-3543	246	5	x	x	X
ejpam-3543	246	6	·	·	PUNCT
ejpam-3543	246	7	y	y	NOUN
ejpam-3543	246	8	)	)	PUNCT
ejpam-3543	246	9	)	)	PUNCT
ejpam-3543	246	10	,	,	PUNCT
ejpam-3543	246	11	λf	λf	X
ejpam-3543	246	12	(	(	PUNCT
ejpam-3543	246	13	y	y	NOUN
ejpam-3543	246	14	)	)	PUNCT
ejpam-3543	246	15	}	}	PUNCT
ejpam-3543	246	16	(	(	PUNCT
ejpam-3543	246	17	3.14	3.14	NUM
ejpam-3543	246	18	)	)	PUNCT
ejpam-3543	246	19	=	=	SYM
ejpam-3543	246	20	min{λf	min{λf	X
ejpam-3543	246	21	(	(	PUNCT
ejpam-3543	246	22	0	0	NUM
ejpam-3543	246	23	)	)	PUNCT
ejpam-3543	246	24	,	,	PUNCT
ejpam-3543	246	25	λf	λf	X
ejpam-3543	246	26	(	(	PUNCT
ejpam-3543	246	27	y	y	NOUN
ejpam-3543	246	28	)	)	PUNCT
ejpam-3543	246	29	}	}	PUNCT
ejpam-3543	246	30	(	(	PUNCT
ejpam-3543	246	31	2.5	2.5	NUM
ejpam-3543	246	32	)	)	PUNCT
ejpam-3543	246	33	=	=	NOUN
ejpam-3543	247	1	λf	λf	X
ejpam-3543	247	2	(	(	PUNCT
ejpam-3543	247	3	y	y	NOUN
ejpam-3543	247	4	)	)	PUNCT
ejpam-3543	247	5	.	.	PUNCT
ejpam-3543	248	1	(	(	PUNCT
ejpam-3543	248	2	3.8	3.8	NUM
ejpam-3543	248	3	)	)	PUNCT
ejpam-3543	248	4	hence	hence	ADV
ejpam-3543	248	5	,	,	PUNCT
ejpam-3543	248	6	λ	λ	PROPN
ejpam-3543	248	7	is	be	AUX
ejpam-3543	248	8	a	a	DET
ejpam-3543	248	9	neutrosophic	neutrosophic	ADJ
ejpam-3543	248	10	near	near	ADP
ejpam-3543	248	11	up	up	ADJ
ejpam-3543	248	12	-	-	PUNCT
ejpam-3543	248	13	filter	filter	NOUN
ejpam-3543	248	14	of	of	ADP
ejpam-3543	248	15	x.	x.	NOUN
ejpam-3543	248	16	the	the	DET
ejpam-3543	248	17	following	follow	VERB
ejpam-3543	248	18	example	example	NOUN
ejpam-3543	248	19	show	show	VERB
ejpam-3543	248	20	that	that	SCONJ
ejpam-3543	248	21	the	the	DET
ejpam-3543	248	22	converse	converse	NOUN
ejpam-3543	248	23	of	of	ADP
ejpam-3543	248	24	theorem	theorem	NOUN
ejpam-3543	248	25	5	5	NUM
ejpam-3543	248	26	is	be	AUX
ejpam-3543	248	27	not	not	PART
ejpam-3543	248	28	true	true	ADJ
ejpam-3543	248	29	.	.	PUNCT
ejpam-3543	248	30	example	example	NOUN
ejpam-3543	249	1	11	11	NUM
ejpam-3543	249	2	.	.	PUNCT
ejpam-3543	250	1	from	from	ADP
ejpam-3543	250	2	example	example	NOUN
ejpam-3543	250	3	5	5	NUM
ejpam-3543	250	4	,	,	PUNCT
ejpam-3543	250	5	we	we	PRON
ejpam-3543	250	6	have	have	VERB
ejpam-3543	250	7	λ	λ	PROPN
ejpam-3543	250	8	is	be	AUX
ejpam-3543	250	9	a	a	DET
ejpam-3543	250	10	neutrosophic	neutrosophic	ADJ
ejpam-3543	250	11	near	near	ADP
ejpam-3543	250	12	up	up	ADJ
ejpam-3543	250	13	-	-	PUNCT
ejpam-3543	250	14	filter	filter	NOUN
ejpam-3543	250	15	of	of	ADP
ejpam-3543	250	16	x.	x.	NOUN
ejpam-3543	250	17	since	since	SCONJ
ejpam-3543	250	18	λi(3	λi(3	NOUN
ejpam-3543	250	19	)	)	PUNCT
ejpam-3543	250	20	=	=	PUNCT
ejpam-3543	250	21	0.7	0.7	NUM
ejpam-3543	250	22	>	>	SYM
ejpam-3543	250	23	0.3	0.3	NUM
ejpam-3543	250	24	=	=	SYM
ejpam-3543	250	25	max{λi(2	max{λi(2	X
ejpam-3543	250	26	·	·	PUNCT
ejpam-3543	250	27	3	3	NUM
ejpam-3543	250	28	)	)	PUNCT
ejpam-3543	250	29	,	,	PUNCT
ejpam-3543	250	30	λi(2	λi(2	PROPN
ejpam-3543	250	31	)	)	PUNCT
ejpam-3543	250	32	}	}	PUNCT
ejpam-3543	250	33	,	,	PUNCT
ejpam-3543	250	34	we	we	PRON
ejpam-3543	250	35	have	have	VERB
ejpam-3543	250	36	λ	λ	PROPN
ejpam-3543	250	37	is	be	AUX
ejpam-3543	250	38	not	not	PART
ejpam-3543	250	39	a	a	DET
ejpam-3543	250	40	neutrosophic	neutrosophic	ADJ
ejpam-3543	250	41	up	up	ADJ
ejpam-3543	250	42	-	-	PUNCT
ejpam-3543	250	43	filter	filter	NOUN
ejpam-3543	250	44	of	of	ADP
ejpam-3543	250	45	x.	x.	PROPN
ejpam-3543	250	46	theorem	theorem	VERB
ejpam-3543	250	47	6	6	NUM
ejpam-3543	250	48	.	.	PUNCT
ejpam-3543	251	1	every	every	DET
ejpam-3543	251	2	neutrosophic	neutrosophic	ADJ
ejpam-3543	251	3	near	near	ADP
ejpam-3543	251	4	up	up	ADP
ejpam-3543	251	5	-	-	PUNCT
ejpam-3543	251	6	filter	filter	NOUN
ejpam-3543	251	7	of	of	ADP
ejpam-3543	251	8	x	x	PUNCT
ejpam-3543	251	9	is	be	AUX
ejpam-3543	251	10	a	a	DET
ejpam-3543	251	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	251	12	up	up	ADJ
ejpam-3543	251	13	-	-	PUNCT
ejpam-3543	251	14	subalgebra	subalgebra	NOUN
ejpam-3543	251	15	.	.	PUNCT
ejpam-3543	252	1	proof	proof	NOUN
ejpam-3543	252	2	.	.	PUNCT
ejpam-3543	253	1	assume	assume	VERB
ejpam-3543	253	2	that	that	SCONJ
ejpam-3543	253	3	λ	λ	PROPN
ejpam-3543	253	4	is	be	AUX
ejpam-3543	253	5	a	a	DET
ejpam-3543	253	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	253	7	near	near	ADP
ejpam-3543	253	8	up	up	ADJ
ejpam-3543	253	9	-	-	PUNCT
ejpam-3543	253	10	filter	filter	NOUN
ejpam-3543	253	11	of	of	ADP
ejpam-3543	253	12	x.	x.	NOUN
ejpam-3543	253	13	then	then	ADV
ejpam-3543	253	14	for	for	ADP
ejpam-3543	253	15	all	all	DET
ejpam-3543	253	16	x	x	NOUN
ejpam-3543	253	17	,	,	PUNCT
ejpam-3543	253	18	y	y	PROPN
ejpam-3543	253	19	∈	∈	PROPN
ejpam-3543	253	20	x	x	X
ejpam-3543	253	21	λt	λt	ADP
ejpam-3543	253	22	(	(	PUNCT
ejpam-3543	253	23	x	x	PROPN
ejpam-3543	253	24	·	·	PUNCT
ejpam-3543	253	25	y	y	X
ejpam-3543	253	26	)	)	PUNCT
ejpam-3543	253	27	≥	≥	NOUN
ejpam-3543	253	28	λt	λt	X
ejpam-3543	253	29	(	(	PUNCT
ejpam-3543	253	30	y	y	NOUN
ejpam-3543	253	31	)	)	PUNCT
ejpam-3543	253	32	≥	≥	NOUN
ejpam-3543	253	33	min{λt	min{λt	X
ejpam-3543	253	34	(	(	PUNCT
ejpam-3543	253	35	x	x	X
ejpam-3543	253	36	)	)	PUNCT
ejpam-3543	253	37	,	,	PUNCT
ejpam-3543	253	38	λt	λt	X
ejpam-3543	253	39	(	(	PUNCT
ejpam-3543	253	40	y	y	NOUN
ejpam-3543	253	41	)	)	PUNCT
ejpam-3543	253	42	}	}	PUNCT
ejpam-3543	253	43	,	,	PUNCT
ejpam-3543	253	44	(	(	PUNCT
ejpam-3543	253	45	3.9	3.9	NUM
ejpam-3543	253	46	)	)	PUNCT
ejpam-3543	253	47	λi(x	λi(x	NOUN
ejpam-3543	253	48	·	·	PUNCT
ejpam-3543	253	49	y	y	X
ejpam-3543	253	50	)	)	PUNCT
ejpam-3543	253	51	≤	≤	NOUN
ejpam-3543	253	52	λi(y	λi(y	NOUN
ejpam-3543	253	53	)	)	PUNCT
ejpam-3543	253	54	≤	≤	NUM
ejpam-3543	253	55	max{λi(x	max{λi(x	NOUN
ejpam-3543	253	56	)	)	PUNCT
ejpam-3543	253	57	,	,	PUNCT
ejpam-3543	253	58	λi(y	λi(y	NOUN
ejpam-3543	253	59	)	)	PUNCT
ejpam-3543	253	60	}	}	PUNCT
ejpam-3543	253	61	,	,	PUNCT
ejpam-3543	253	62	(	(	PUNCT
ejpam-3543	253	63	3.10	3.10	NUM
ejpam-3543	253	64	)	)	PUNCT
ejpam-3543	253	65	λf	λf	X
ejpam-3543	253	66	(	(	PUNCT
ejpam-3543	253	67	x	x	X
ejpam-3543	253	68	·	·	PUNCT
ejpam-3543	253	69	y	y	X
ejpam-3543	253	70	)	)	PUNCT
ejpam-3543	253	71	≥	≥	NOUN
ejpam-3543	253	72	λf	λf	PROPN
ejpam-3543	253	73	(	(	PUNCT
ejpam-3543	253	74	y	y	NOUN
ejpam-3543	253	75	)	)	PUNCT
ejpam-3543	253	76	≥	≥	NOUN
ejpam-3543	253	77	min{λf	min{λf	X
ejpam-3543	253	78	(	(	PUNCT
ejpam-3543	253	79	x	x	X
ejpam-3543	253	80	)	)	PUNCT
ejpam-3543	253	81	,	,	PUNCT
ejpam-3543	253	82	λf	λf	X
ejpam-3543	253	83	(	(	PUNCT
ejpam-3543	253	84	y	y	NOUN
ejpam-3543	253	85	)	)	PUNCT
ejpam-3543	253	86	}	}	PUNCT
ejpam-3543	253	87	.	.	PUNCT
ejpam-3543	254	1	(	(	PUNCT
ejpam-3543	254	2	3.11	3.11	NUM
ejpam-3543	254	3	)	)	PUNCT
ejpam-3543	254	4	hence	hence	ADV
ejpam-3543	254	5	,	,	PUNCT
ejpam-3543	254	6	λ	λ	PROPN
ejpam-3543	254	7	is	be	AUX
ejpam-3543	254	8	a	a	DET
ejpam-3543	254	9	neutrosophic	neutrosophic	ADJ
ejpam-3543	254	10	up	up	ADP
ejpam-3543	254	11	-	-	PUNCT
ejpam-3543	254	12	subalgebra	subalgebra	NOUN
ejpam-3543	254	13	of	of	ADP
ejpam-3543	254	14	x.	x.	NOUN
ejpam-3543	254	15	the	the	DET
ejpam-3543	254	16	following	follow	VERB
ejpam-3543	254	17	example	example	NOUN
ejpam-3543	254	18	show	show	VERB
ejpam-3543	254	19	that	that	SCONJ
ejpam-3543	254	20	the	the	DET
ejpam-3543	254	21	converse	converse	NOUN
ejpam-3543	254	22	of	of	ADP
ejpam-3543	254	23	theorem	theorem	NOUN
ejpam-3543	254	24	6	6	NUM
ejpam-3543	254	25	is	be	AUX
ejpam-3543	254	26	not	not	PART
ejpam-3543	254	27	true	true	ADJ
ejpam-3543	254	28	.	.	PUNCT
ejpam-3543	254	29	example	example	NOUN
ejpam-3543	255	1	12	12	NUM
ejpam-3543	255	2	.	.	PUNCT
ejpam-3543	256	1	from	from	ADP
ejpam-3543	256	2	example	example	NOUN
ejpam-3543	256	3	4	4	NUM
ejpam-3543	256	4	,	,	PUNCT
ejpam-3543	256	5	we	we	PRON
ejpam-3543	256	6	have	have	VERB
ejpam-3543	256	7	λ	λ	PROPN
ejpam-3543	256	8	is	be	AUX
ejpam-3543	256	9	a	a	DET
ejpam-3543	256	10	neutrosophic	neutrosophic	ADJ
ejpam-3543	256	11	up	up	ADP
ejpam-3543	256	12	-	-	PUNCT
ejpam-3543	256	13	subalgebra	subalgebra	NOUN
ejpam-3543	256	14	of	of	ADP
ejpam-3543	256	15	x.	x.	NOUN
ejpam-3543	256	16	since	since	SCONJ
ejpam-3543	256	17	λi(2	λi(2	PROPN
ejpam-3543	256	18	·	·	PUNCT
ejpam-3543	256	19	3	3	X
ejpam-3543	256	20	)	)	PUNCT
ejpam-3543	256	21	=	=	NOUN
ejpam-3543	257	1	0.4	0.4	NUM
ejpam-3543	257	2	>	>	SYM
ejpam-3543	257	3	0.2	0.2	NUM
ejpam-3543	257	4	=	=	SYM
ejpam-3543	257	5	λi(3	λi(3	NOUN
ejpam-3543	257	6	)	)	PUNCT
ejpam-3543	257	7	,	,	PUNCT
ejpam-3543	257	8	we	we	PRON
ejpam-3543	257	9	have	have	VERB
ejpam-3543	257	10	λ	λ	PROPN
ejpam-3543	257	11	is	be	AUX
ejpam-3543	257	12	not	not	PART
ejpam-3543	257	13	a	a	DET
ejpam-3543	257	14	neutrosophic	neutrosophic	ADJ
ejpam-3543	257	15	near	near	ADP
ejpam-3543	257	16	up	up	ADJ
ejpam-3543	257	17	-	-	PUNCT
ejpam-3543	257	18	filter	filter	NOUN
ejpam-3543	257	19	of	of	ADP
ejpam-3543	257	20	x.	x.	NOUN
ejpam-3543	257	21	by	by	ADP
ejpam-3543	257	22	theorems	theorem	NOUN
ejpam-3543	257	23	3	3	NUM
ejpam-3543	257	24	,	,	PUNCT
ejpam-3543	257	25	4	4	NUM
ejpam-3543	257	26	,	,	PUNCT
ejpam-3543	257	27	5	5	NUM
ejpam-3543	257	28	,	,	PUNCT
ejpam-3543	257	29	and	and	CCONJ
ejpam-3543	257	30	6	6	NUM
ejpam-3543	257	31	and	and	CCONJ
ejpam-3543	257	32	examples	example	NOUN
ejpam-3543	257	33	9	9	NUM
ejpam-3543	257	34	,	,	PUNCT
ejpam-3543	257	35	10	10	NUM
ejpam-3543	257	36	,	,	PUNCT
ejpam-3543	257	37	11	11	NUM
ejpam-3543	257	38	,	,	PUNCT
ejpam-3543	257	39	and	and	CCONJ
ejpam-3543	257	40	12	12	NUM
ejpam-3543	257	41	,	,	PUNCT
ejpam-3543	257	42	we	we	PRON
ejpam-3543	257	43	have	have	VERB
ejpam-3543	257	44	that	that	SCONJ
ejpam-3543	257	45	the	the	DET
ejpam-3543	257	46	notion	notion	NOUN
ejpam-3543	257	47	of	of	ADP
ejpam-3543	257	48	neutrosophic	neutrosophic	ADJ
ejpam-3543	257	49	up	up	ADV
ejpam-3543	257	50	-	-	PUNCT
ejpam-3543	257	51	subalgebras	subalgebras	PROPN
ejpam-3543	257	52	is	be	AUX
ejpam-3543	257	53	a	a	DET
ejpam-3543	257	54	generalization	generalization	NOUN
ejpam-3543	257	55	of	of	ADP
ejpam-3543	257	56	neutrosophic	neutrosophic	ADJ
ejpam-3543	257	57	near	near	ADP
ejpam-3543	257	58	up	up	ADP
ejpam-3543	257	59	-	-	PUNCT
ejpam-3543	257	60	filters	filter	NOUN
ejpam-3543	257	61	,	,	PUNCT
ejpam-3543	257	62	the	the	DET
ejpam-3543	257	63	notion	notion	NOUN
ejpam-3543	257	64	of	of	ADP
ejpam-3543	257	65	neutrosophic	neutrosophic	ADJ
ejpam-3543	257	66	near	near	ADP
ejpam-3543	257	67	up	up	ADP
ejpam-3543	257	68	-	-	PUNCT
ejpam-3543	257	69	filters	filter	NOUN
ejpam-3543	257	70	is	be	AUX
ejpam-3543	257	71	a	a	DET
ejpam-3543	257	72	generalization	generalization	NOUN
ejpam-3543	257	73	of	of	ADP
ejpam-3543	257	74	neutrosophic	neutrosophic	ADJ
ejpam-3543	257	75	up	up	ADP
ejpam-3543	257	76	-	-	PUNCT
ejpam-3543	257	77	filters	filter	NOUN
ejpam-3543	257	78	,	,	PUNCT
ejpam-3543	257	79	the	the	DET
ejpam-3543	257	80	notion	notion	NOUN
ejpam-3543	257	81	of	of	ADP
ejpam-3543	257	82	neutrosophic	neutrosophic	ADJ
ejpam-3543	257	83	up	up	PROPN
ejpam-3543	257	84	-	-	PUNCT
ejpam-3543	257	85	filters	filter	NOUN
ejpam-3543	257	86	is	be	AUX
ejpam-3543	257	87	a	a	DET
ejpam-3543	257	88	generalization	generalization	NOUN
ejpam-3543	257	89	of	of	ADP
ejpam-3543	257	90	neutrosophic	neutrosophic	ADJ
ejpam-3543	257	91	up	up	ADJ
ejpam-3543	257	92	-	-	PUNCT
ejpam-3543	257	93	ideals	ideal	NOUN
ejpam-3543	257	94	,	,	PUNCT
ejpam-3543	257	95	and	and	CCONJ
ejpam-3543	257	96	the	the	DET
ejpam-3543	257	97	notion	notion	NOUN
ejpam-3543	257	98	of	of	ADP
ejpam-3543	257	99	neutrosophic	neutrosophic	ADJ
ejpam-3543	257	100	up	up	ADJ
ejpam-3543	257	101	-	-	PUNCT
ejpam-3543	257	102	ideals	ideal	NOUN
ejpam-3543	257	103	is	be	AUX
ejpam-3543	257	104	a	a	DET
ejpam-3543	257	105	generalization	generalization	NOUN
ejpam-3543	257	106	of	of	ADP
ejpam-3543	257	107	neutrosophic	neutrosophic	ADJ
ejpam-3543	257	108	strongly	strongly	ADV
ejpam-3543	257	109	up	up	ADP
ejpam-3543	257	110	-	-	PUNCT
ejpam-3543	257	111	ideals	ideal	NOUN
ejpam-3543	257	112	.	.	PUNCT
ejpam-3543	258	1	moreover	moreover	ADV
ejpam-3543	258	2	,	,	PUNCT
ejpam-3543	258	3	by	by	ADP
ejpam-3543	258	4	theorem	theorem	NOUN
ejpam-3543	258	5	2	2	NUM
ejpam-3543	258	6	,	,	PUNCT
ejpam-3543	258	7	we	we	PRON
ejpam-3543	258	8	obtain	obtain	VERB
ejpam-3543	258	9	that	that	DET
ejpam-3543	258	10	neutrosophic	neutrosophic	ADJ
ejpam-3543	258	11	strongly	strongly	ADV
ejpam-3543	258	12	up	up	ADJ
ejpam-3543	258	13	-	-	PUNCT
ejpam-3543	258	14	ideals	ideal	NOUN
ejpam-3543	258	15	and	and	CCONJ
ejpam-3543	258	16	constant	constant	ADJ
ejpam-3543	258	17	neutrosophic	neutrosophic	ADJ
ejpam-3543	258	18	set	set	NOUN
ejpam-3543	258	19	coincide	coincide	NOUN
ejpam-3543	258	20	.	.	PUNCT
ejpam-3543	259	1	m.	m.	PROPN
ejpam-3543	259	2	songsaeng	songsaeng	PROPN
ejpam-3543	259	3	,	,	PUNCT
ejpam-3543	259	4	a.	a.	NOUN
ejpam-3543	259	5	iampan	iampan	PROPN
ejpam-3543	259	6	/	/	SYM
ejpam-3543	259	7	eur	eur	PROPN
ejpam-3543	259	8	.	.	PUNCT
ejpam-3543	260	1	j.	j.	PROPN
ejpam-3543	260	2	pure	pure	PROPN
ejpam-3543	260	3	appl	appl	PROPN
ejpam-3543	260	4	.	.	PROPN
ejpam-3543	260	5	math	math	PROPN
ejpam-3543	260	6	,	,	PUNCT
ejpam-3543	260	7	12	12	NUM
ejpam-3543	260	8	(	(	PUNCT
ejpam-3543	260	9	4	4	NUM
ejpam-3543	260	10	)	)	PUNCT
ejpam-3543	260	11	(	(	PUNCT
ejpam-3543	260	12	2019	2019	NUM
ejpam-3543	260	13	)	)	PUNCT
ejpam-3543	260	14	,	,	PUNCT
ejpam-3543	260	15	1382	1382	NUM
ejpam-3543	260	16	-	-	SYM
ejpam-3543	260	17	1409	1409	NUM
ejpam-3543	260	18	1393	1393	NUM
ejpam-3543	260	19	theorem	theorem	NOUN
ejpam-3543	260	20	7	7	NUM
ejpam-3543	260	21	.	.	PUNCT
ejpam-3543	261	1	if	if	SCONJ
ejpam-3543	261	2	λ	λ	PROPN
ejpam-3543	261	3	is	be	AUX
ejpam-3543	261	4	a	a	DET
ejpam-3543	261	5	neutrosophic	neutrosophic	ADJ
ejpam-3543	261	6	up	up	ADP
ejpam-3543	261	7	-	-	PUNCT
ejpam-3543	261	8	subalgebra	subalgebra	NOUN
ejpam-3543	261	9	of	of	ADP
ejpam-3543	261	10	x	x	PUNCT
ejpam-3543	261	11	satisfying	satisfy	VERB
ejpam-3543	261	12	the	the	DET
ejpam-3543	261	13	following	follow	VERB
ejpam-3543	261	14	condition	condition	NOUN
ejpam-3543	261	15	:	:	PUNCT
ejpam-3543	261	16	(	(	PUNCT
ejpam-3543	261	17	∀x	∀x	X
ejpam-3543	261	18	,	,	PUNCT
ejpam-3543	261	19	y	y	PROPN
ejpam-3543	261	20	∈	∈	PROPN
ejpam-3543	261	21	x	x	X
ejpam-3543	261	22	)	)	PUNCT
ejpam-3543	262	1	x	x	NOUN
ejpam-3543	262	2	·	·	PUNCT
ejpam-3543	262	3	y	y	PROPN
ejpam-3543	262	4	6=	6=	NUM
ejpam-3543	262	5	0⇒	0⇒	NOUN
ejpam-3543	263	1			PRON
ejpam-3543	263	2	λt	λt	X
ejpam-3543	263	3	(	(	PUNCT
ejpam-3543	263	4	x	x	NOUN
ejpam-3543	263	5	)	)	PUNCT
ejpam-3543	263	6	≥	≥	NOUN
ejpam-3543	263	7	λt	λt	X
ejpam-3543	263	8	(	(	PUNCT
ejpam-3543	263	9	y	y	NOUN
ejpam-3543	263	10	)	)	PUNCT
ejpam-3543	263	11	λi(x	λi(x	NUM
ejpam-3543	263	12	)	)	PUNCT
ejpam-3543	263	13	≤	≤	NOUN
ejpam-3543	263	14	λi(y	λi(y	NOUN
ejpam-3543	263	15	)	)	PUNCT
ejpam-3543	263	16	λf	λf	X
ejpam-3543	263	17	(	(	PUNCT
ejpam-3543	263	18	x	x	NOUN
ejpam-3543	263	19	)	)	PUNCT
ejpam-3543	263	20	≥	≥	NOUN
ejpam-3543	263	21	λf	λf	PROPN
ejpam-3543	263	22	(	(	PUNCT
ejpam-3543	263	23	y	y	NOUN
ejpam-3543	263	24	)	)	PUNCT
ejpam-3543	263	25			NOUN
ejpam-3543	263	26	,	,	PUNCT
ejpam-3543	263	27	(	(	PUNCT
ejpam-3543	263	28	3.21	3.21	NUM
ejpam-3543	263	29	)	)	PUNCT
ejpam-3543	263	30	then	then	ADV
ejpam-3543	263	31	λ	λ	PROPN
ejpam-3543	263	32	is	be	AUX
ejpam-3543	263	33	a	a	DET
ejpam-3543	263	34	neutrosophic	neutrosophic	ADJ
ejpam-3543	263	35	near	near	ADP
ejpam-3543	263	36	up	up	ADJ
ejpam-3543	263	37	-	-	PUNCT
ejpam-3543	263	38	filter	filter	NOUN
ejpam-3543	263	39	of	of	ADP
ejpam-3543	263	40	x.	x.	NOUN
ejpam-3543	263	41	proof	proof	PROPN
ejpam-3543	263	42	.	.	PUNCT
ejpam-3543	264	1	assume	assume	VERB
ejpam-3543	264	2	that	that	SCONJ
ejpam-3543	264	3	λ	λ	PROPN
ejpam-3543	264	4	is	be	AUX
ejpam-3543	264	5	a	a	DET
ejpam-3543	264	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	264	7	up	up	ADP
ejpam-3543	264	8	-	-	PUNCT
ejpam-3543	264	9	subalgebra	subalgebra	NOUN
ejpam-3543	264	10	of	of	ADP
ejpam-3543	264	11	x	x	PUNCT
ejpam-3543	264	12	satisfying	satisfy	VERB
ejpam-3543	264	13	the	the	DET
ejpam-3543	264	14	condition	condition	NOUN
ejpam-3543	264	15	(	(	PUNCT
ejpam-3543	264	16	3.21	3.21	NUM
ejpam-3543	264	17	)	)	PUNCT
ejpam-3543	264	18	.	.	PUNCT
ejpam-3543	265	1	by	by	ADP
ejpam-3543	265	2	theorem	theorem	NOUN
ejpam-3543	265	3	1	1	NUM
ejpam-3543	265	4	,	,	PUNCT
ejpam-3543	265	5	we	we	PRON
ejpam-3543	265	6	have	have	AUX
ejpam-3543	265	7	λ	λ	PROPN
ejpam-3543	265	8	satisfies	satisfie	NOUN
ejpam-3543	265	9	the	the	DET
ejpam-3543	265	10	conditions	condition	NOUN
ejpam-3543	265	11	(	(	PUNCT
ejpam-3543	265	12	3.6	3.6	NUM
ejpam-3543	265	13	)	)	PUNCT
ejpam-3543	265	14	,	,	PUNCT
ejpam-3543	265	15	(	(	PUNCT
ejpam-3543	265	16	3.7	3.7	NUM
ejpam-3543	265	17	)	)	PUNCT
ejpam-3543	265	18	,	,	PUNCT
ejpam-3543	265	19	and	and	CCONJ
ejpam-3543	265	20	(	(	PUNCT
ejpam-3543	265	21	3.8	3.8	NUM
ejpam-3543	265	22	)	)	PUNCT
ejpam-3543	265	23	.	.	PUNCT
ejpam-3543	266	1	next	next	ADV
ejpam-3543	266	2	,	,	PUNCT
ejpam-3543	266	3	let	let	VERB
ejpam-3543	266	4	x	x	PRON
ejpam-3543	266	5	,	,	PUNCT
ejpam-3543	266	6	y	y	PROPN
ejpam-3543	266	7	∈	∈	PROPN
ejpam-3543	266	8	x.	x.	NOUN
ejpam-3543	266	9	case	case	NOUN
ejpam-3543	266	10	1	1	NUM
ejpam-3543	266	11	:	:	PUNCT
ejpam-3543	266	12	x	x	SYM
ejpam-3543	266	13	·	·	PUNCT
ejpam-3543	266	14	y	y	X
ejpam-3543	266	15	=	=	PUNCT
ejpam-3543	267	1	0	0	PROPN
ejpam-3543	267	2	.	.	PUNCT
ejpam-3543	268	1	then	then	ADV
ejpam-3543	268	2	λt	λt	INTJ
ejpam-3543	268	3	(	(	PUNCT
ejpam-3543	268	4	x	x	PROPN
ejpam-3543	268	5	·	·	PUNCT
ejpam-3543	268	6	y	y	X
ejpam-3543	268	7	)	)	PUNCT
ejpam-3543	268	8	=	=	NOUN
ejpam-3543	268	9	λt	λt	X
ejpam-3543	268	10	(	(	PUNCT
ejpam-3543	268	11	0	0	NUM
ejpam-3543	268	12	)	)	PUNCT
ejpam-3543	268	13	≥	≥	NOUN
ejpam-3543	268	14	λt	λt	X
ejpam-3543	268	15	(	(	PUNCT
ejpam-3543	268	16	y	y	NOUN
ejpam-3543	268	17	)	)	PUNCT
ejpam-3543	268	18	,	,	PUNCT
ejpam-3543	268	19	(	(	PUNCT
ejpam-3543	268	20	3.6	3.6	NUM
ejpam-3543	268	21	)	)	PUNCT
ejpam-3543	268	22	λi(x	λi(x	X
ejpam-3543	268	23	·	·	PUNCT
ejpam-3543	268	24	y	y	X
ejpam-3543	268	25	)	)	PUNCT
ejpam-3543	268	26	=	=	SYM
ejpam-3543	269	1	λi(0	λi(0	X
ejpam-3543	269	2	)	)	PUNCT
ejpam-3543	269	3	≤	≤	NOUN
ejpam-3543	269	4	λi(y	λi(y	NUM
ejpam-3543	269	5	)	)	PUNCT
ejpam-3543	269	6	,	,	PUNCT
ejpam-3543	269	7	(	(	PUNCT
ejpam-3543	269	8	3.7	3.7	NUM
ejpam-3543	269	9	)	)	PUNCT
ejpam-3543	269	10	λf	λf	X
ejpam-3543	269	11	(	(	PUNCT
ejpam-3543	269	12	x	x	X
ejpam-3543	269	13	·	·	PUNCT
ejpam-3543	269	14	y	y	X
ejpam-3543	269	15	)	)	PUNCT
ejpam-3543	270	1	=	=	SYM
ejpam-3543	270	2	λf	λf	X
ejpam-3543	270	3	(	(	PUNCT
ejpam-3543	270	4	0	0	NUM
ejpam-3543	270	5	)	)	PUNCT
ejpam-3543	270	6	≥	≥	NOUN
ejpam-3543	270	7	λf	λf	X
ejpam-3543	270	8	(	(	PUNCT
ejpam-3543	270	9	y	y	NOUN
ejpam-3543	270	10	)	)	PUNCT
ejpam-3543	270	11	.	.	PUNCT
ejpam-3543	271	1	(	(	PUNCT
ejpam-3543	271	2	3.8	3.8	NUM
ejpam-3543	271	3	)	)	PUNCT
ejpam-3543	271	4	case	case	NOUN
ejpam-3543	271	5	2	2	NUM
ejpam-3543	271	6	:	:	PUNCT
ejpam-3543	271	7	x	x	SYM
ejpam-3543	271	8	·	·	PUNCT
ejpam-3543	271	9	y	y	PROPN
ejpam-3543	271	10	6=	6=	PROPN
ejpam-3543	271	11	0	0	NUM
ejpam-3543	271	12	.	.	PUNCT
ejpam-3543	272	1	then	then	ADV
ejpam-3543	272	2	λt	λt	INTJ
ejpam-3543	272	3	(	(	PUNCT
ejpam-3543	272	4	x	x	PROPN
ejpam-3543	272	5	·	·	PUNCT
ejpam-3543	272	6	y	y	X
ejpam-3543	272	7	)	)	PUNCT
ejpam-3543	272	8	≥	≥	NOUN
ejpam-3543	272	9	min{λt	min{λt	X
ejpam-3543	272	10	(	(	PUNCT
ejpam-3543	272	11	x	x	X
ejpam-3543	272	12	)	)	PUNCT
ejpam-3543	272	13	,	,	PUNCT
ejpam-3543	272	14	λt	λt	X
ejpam-3543	272	15	(	(	PUNCT
ejpam-3543	272	16	y	y	NOUN
ejpam-3543	272	17	)	)	PUNCT
ejpam-3543	272	18	}	}	PUNCT
ejpam-3543	273	1	=	=	SYM
ejpam-3543	273	2	λt	λt	X
ejpam-3543	273	3	(	(	PUNCT
ejpam-3543	273	4	y	y	NOUN
ejpam-3543	273	5	)	)	PUNCT
ejpam-3543	273	6	,	,	PUNCT
ejpam-3543	273	7	(	(	PUNCT
ejpam-3543	273	8	3.3	3.3	NUM
ejpam-3543	273	9	)	)	PUNCT
ejpam-3543	273	10	and	and	CCONJ
ejpam-3543	273	11	(	(	PUNCT
ejpam-3543	273	12	3.21	3.21	NUM
ejpam-3543	273	13	)	)	PUNCT
ejpam-3543	273	14	for	for	ADP
ejpam-3543	273	15	λt	λt	ADP
ejpam-3543	273	16	λi(x	λi(x	X
ejpam-3543	273	17	·	·	PUNCT
ejpam-3543	273	18	y	y	X
ejpam-3543	273	19	)	)	PUNCT
ejpam-3543	273	20	≤	≤	NUM
ejpam-3543	273	21	max{λi(x	max{λi(x	NOUN
ejpam-3543	273	22	)	)	PUNCT
ejpam-3543	273	23	,	,	PUNCT
ejpam-3543	273	24	λi(y	λi(y	X
ejpam-3543	273	25	)	)	PUNCT
ejpam-3543	273	26	}	}	PUNCT
ejpam-3543	273	27	=	=	SYM
ejpam-3543	273	28	λi(y	λi(y	X
ejpam-3543	273	29	)	)	PUNCT
ejpam-3543	273	30	,	,	PUNCT
ejpam-3543	273	31	(	(	PUNCT
ejpam-3543	273	32	3.4	3.4	NUM
ejpam-3543	273	33	)	)	PUNCT
ejpam-3543	273	34	and	and	CCONJ
ejpam-3543	273	35	(	(	PUNCT
ejpam-3543	273	36	3.21	3.21	NUM
ejpam-3543	273	37	)	)	PUNCT
ejpam-3543	273	38	for	for	ADP
ejpam-3543	273	39	λi	λi	INTJ
ejpam-3543	273	40	λf	λf	X
ejpam-3543	273	41	(	(	PUNCT
ejpam-3543	273	42	x	x	PROPN
ejpam-3543	273	43	·	·	PUNCT
ejpam-3543	273	44	y	y	X
ejpam-3543	273	45	)	)	PUNCT
ejpam-3543	273	46	≥	≥	NOUN
ejpam-3543	273	47	min{λf	min{λf	X
ejpam-3543	273	48	(	(	PUNCT
ejpam-3543	273	49	x	x	X
ejpam-3543	273	50	)	)	PUNCT
ejpam-3543	273	51	,	,	PUNCT
ejpam-3543	273	52	λf	λf	X
ejpam-3543	273	53	(	(	PUNCT
ejpam-3543	273	54	y	y	NOUN
ejpam-3543	273	55	)	)	PUNCT
ejpam-3543	273	56	}	}	PUNCT
ejpam-3543	274	1	=	=	SYM
ejpam-3543	274	2	λf	λf	X
ejpam-3543	274	3	(	(	PUNCT
ejpam-3543	274	4	y	y	NOUN
ejpam-3543	274	5	)	)	PUNCT
ejpam-3543	274	6	.	.	PUNCT
ejpam-3543	275	1	(	(	PUNCT
ejpam-3543	275	2	3.5	3.5	NUM
ejpam-3543	275	3	)	)	PUNCT
ejpam-3543	275	4	and	and	CCONJ
ejpam-3543	275	5	(	(	PUNCT
ejpam-3543	275	6	3.21	3.21	NUM
ejpam-3543	275	7	)	)	PUNCT
ejpam-3543	275	8	for	for	ADP
ejpam-3543	275	9	λf	λf	ADP
ejpam-3543	275	10	hence	hence	ADV
ejpam-3543	275	11	,	,	PUNCT
ejpam-3543	275	12	λ	λ	PROPN
ejpam-3543	275	13	is	be	AUX
ejpam-3543	275	14	a	a	DET
ejpam-3543	275	15	neutrosophic	neutrosophic	ADJ
ejpam-3543	275	16	near	near	ADP
ejpam-3543	275	17	up	up	ADJ
ejpam-3543	275	18	-	-	PUNCT
ejpam-3543	275	19	filter	filter	NOUN
ejpam-3543	275	20	of	of	ADP
ejpam-3543	275	21	x.	x.	PROPN
ejpam-3543	275	22	theorem	theorem	VERB
ejpam-3543	275	23	8	8	NUM
ejpam-3543	275	24	.	.	PUNCT
ejpam-3543	276	1	if	if	SCONJ
ejpam-3543	276	2	λ	λ	PROPN
ejpam-3543	276	3	is	be	AUX
ejpam-3543	276	4	a	a	DET
ejpam-3543	276	5	neutrosophic	neutrosophic	ADJ
ejpam-3543	276	6	near	near	ADP
ejpam-3543	276	7	up	up	ADJ
ejpam-3543	276	8	-	-	PUNCT
ejpam-3543	276	9	filter	filter	NOUN
ejpam-3543	276	10	of	of	ADP
ejpam-3543	276	11	x	x	PUNCT
ejpam-3543	276	12	satisfying	satisfy	VERB
ejpam-3543	276	13	the	the	DET
ejpam-3543	276	14	following	follow	VERB
ejpam-3543	276	15	condition	condition	NOUN
ejpam-3543	276	16	:	:	PUNCT
ejpam-3543	276	17	λt	λt	ADP
ejpam-3543	276	18	=	=	PUNCT
ejpam-3543	276	19	λi	λi	NOUN
ejpam-3543	276	20	=	=	VERB
ejpam-3543	276	21	λf	λf	INTJ
ejpam-3543	276	22	,	,	PUNCT
ejpam-3543	276	23	(	(	PUNCT
ejpam-3543	276	24	3.22	3.22	NUM
ejpam-3543	276	25	)	)	PUNCT
ejpam-3543	276	26	then	then	ADV
ejpam-3543	276	27	λ	λ	PROPN
ejpam-3543	276	28	is	be	AUX
ejpam-3543	276	29	a	a	DET
ejpam-3543	276	30	neutrosophic	neutrosophic	ADJ
ejpam-3543	276	31	up	up	ADJ
ejpam-3543	276	32	-	-	PUNCT
ejpam-3543	276	33	filter	filter	NOUN
ejpam-3543	276	34	of	of	ADP
ejpam-3543	276	35	x.	x.	NOUN
ejpam-3543	276	36	proof	proof	PROPN
ejpam-3543	276	37	.	.	PUNCT
ejpam-3543	277	1	assume	assume	VERB
ejpam-3543	277	2	that	that	SCONJ
ejpam-3543	277	3	λ	λ	PROPN
ejpam-3543	277	4	is	be	AUX
ejpam-3543	277	5	a	a	DET
ejpam-3543	277	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	277	7	near	near	ADP
ejpam-3543	277	8	up	up	ADJ
ejpam-3543	277	9	-	-	PUNCT
ejpam-3543	277	10	filter	filter	NOUN
ejpam-3543	277	11	of	of	ADP
ejpam-3543	277	12	x	x	PUNCT
ejpam-3543	277	13	satisfying	satisfy	VERB
ejpam-3543	277	14	the	the	DET
ejpam-3543	277	15	condition	condition	NOUN
ejpam-3543	277	16	(	(	PUNCT
ejpam-3543	277	17	3.22	3.22	NUM
ejpam-3543	277	18	)	)	PUNCT
ejpam-3543	277	19	.	.	PUNCT
ejpam-3543	278	1	then	then	ADV
ejpam-3543	278	2	λ	λ	PROPN
ejpam-3543	278	3	satisfies	satisfy	VERB
ejpam-3543	278	4	the	the	DET
ejpam-3543	278	5	conditions	condition	NOUN
ejpam-3543	278	6	(	(	PUNCT
ejpam-3543	278	7	3.6	3.6	NUM
ejpam-3543	278	8	)	)	PUNCT
ejpam-3543	278	9	,	,	PUNCT
ejpam-3543	278	10	(	(	PUNCT
ejpam-3543	278	11	3.7	3.7	NUM
ejpam-3543	278	12	)	)	PUNCT
ejpam-3543	278	13	,	,	PUNCT
ejpam-3543	278	14	and	and	CCONJ
ejpam-3543	278	15	(	(	PUNCT
ejpam-3543	278	16	3.8	3.8	NUM
ejpam-3543	278	17	)	)	PUNCT
ejpam-3543	278	18	.	.	PUNCT
ejpam-3543	279	1	next	next	ADV
ejpam-3543	279	2	,	,	PUNCT
ejpam-3543	279	3	let	let	VERB
ejpam-3543	279	4	x	x	PRON
ejpam-3543	279	5	,	,	PUNCT
ejpam-3543	279	6	y	y	PROPN
ejpam-3543	279	7	∈	∈	PROPN
ejpam-3543	279	8	x.	x.	NOUN
ejpam-3543	279	9	then	then	ADV
ejpam-3543	279	10	min{λt	min{λt	X
ejpam-3543	279	11	(	(	PUNCT
ejpam-3543	279	12	x	x	SYM
ejpam-3543	279	13	·	·	PUNCT
ejpam-3543	279	14	y	y	X
ejpam-3543	279	15	)	)	PUNCT
ejpam-3543	279	16	,	,	PUNCT
ejpam-3543	279	17	λt	λt	X
ejpam-3543	279	18	(	(	PUNCT
ejpam-3543	279	19	x	x	NOUN
ejpam-3543	279	20	)	)	PUNCT
ejpam-3543	279	21	}	}	PUNCT
ejpam-3543	279	22	=	=	SYM
ejpam-3543	279	23	min{λi(x	min{λi(x	X
ejpam-3543	279	24	·	·	PUNCT
ejpam-3543	279	25	y	y	X
ejpam-3543	279	26	)	)	PUNCT
ejpam-3543	279	27	,	,	PUNCT
ejpam-3543	279	28	λt	λt	X
ejpam-3543	279	29	(	(	PUNCT
ejpam-3543	279	30	x	x	NOUN
ejpam-3543	279	31	)	)	PUNCT
ejpam-3543	279	32	}	}	PUNCT
ejpam-3543	279	33	(	(	PUNCT
ejpam-3543	279	34	3.22	3.22	NUM
ejpam-3543	279	35	)	)	PUNCT
ejpam-3543	279	36	≤	≤	NOUN
ejpam-3543	279	37	min{λi(y	min{λi(y	NOUN
ejpam-3543	279	38	)	)	PUNCT
ejpam-3543	279	39	,	,	PUNCT
ejpam-3543	279	40	λt	λt	X
ejpam-3543	279	41	(	(	PUNCT
ejpam-3543	279	42	x	x	NOUN
ejpam-3543	279	43	)	)	PUNCT
ejpam-3543	279	44	}	}	PUNCT
ejpam-3543	279	45	(	(	PUNCT
ejpam-3543	279	46	3.10	3.10	NUM
ejpam-3543	279	47	)	)	PUNCT
ejpam-3543	279	48	=	=	PUNCT
ejpam-3543	279	49	min{λt	min{λt	X
ejpam-3543	279	50	(	(	PUNCT
ejpam-3543	279	51	y	y	NOUN
ejpam-3543	279	52	)	)	PUNCT
ejpam-3543	279	53	,	,	PUNCT
ejpam-3543	279	54	λt	λt	X
ejpam-3543	279	55	(	(	PUNCT
ejpam-3543	279	56	x	x	NOUN
ejpam-3543	279	57	)	)	PUNCT
ejpam-3543	279	58	}	}	PUNCT
ejpam-3543	279	59	(	(	PUNCT
ejpam-3543	279	60	3.22	3.22	NUM
ejpam-3543	279	61	)	)	PUNCT
ejpam-3543	279	62	≤	≤	NOUN
ejpam-3543	279	63	λt	λt	ADP
ejpam-3543	279	64	(	(	PUNCT
ejpam-3543	279	65	y	y	NOUN
ejpam-3543	279	66	)	)	PUNCT
ejpam-3543	279	67	,	,	PUNCT
ejpam-3543	279	68	max{λi(x	max{λi(x	PROPN
ejpam-3543	279	69	·	·	PUNCT
ejpam-3543	279	70	y	y	X
ejpam-3543	279	71	)	)	PUNCT
ejpam-3543	279	72	,	,	PUNCT
ejpam-3543	279	73	λi(x	λi(x	NUM
ejpam-3543	279	74	)	)	PUNCT
ejpam-3543	279	75	}	}	PUNCT
ejpam-3543	279	76	=	=	SYM
ejpam-3543	279	77	max{λt	max{λt	NOUN
ejpam-3543	279	78	(	(	PUNCT
ejpam-3543	279	79	x	x	SYM
ejpam-3543	279	80	·	·	PUNCT
ejpam-3543	279	81	y	y	X
ejpam-3543	279	82	)	)	PUNCT
ejpam-3543	279	83	,	,	PUNCT
ejpam-3543	279	84	λi(x	λi(x	NUM
ejpam-3543	279	85	)	)	PUNCT
ejpam-3543	279	86	}	}	PUNCT
ejpam-3543	279	87	(	(	PUNCT
ejpam-3543	279	88	3.22	3.22	NUM
ejpam-3543	279	89	)	)	PUNCT
ejpam-3543	279	90	≥	≥	NOUN
ejpam-3543	279	91	max{λt	max{λt	ADJ
ejpam-3543	279	92	(	(	PUNCT
ejpam-3543	279	93	y	y	NOUN
ejpam-3543	279	94	)	)	PUNCT
ejpam-3543	279	95	,	,	PUNCT
ejpam-3543	279	96	λi(x	λi(x	NUM
ejpam-3543	279	97	)	)	PUNCT
ejpam-3543	279	98	}	}	PUNCT
ejpam-3543	279	99	(	(	PUNCT
ejpam-3543	279	100	3.9	3.9	NUM
ejpam-3543	279	101	)	)	PUNCT
ejpam-3543	279	102	=	=	PUNCT
ejpam-3543	279	103	max{λi(y	max{λi(y	NOUN
ejpam-3543	279	104	)	)	PUNCT
ejpam-3543	279	105	,	,	PUNCT
ejpam-3543	279	106	λi(x	λi(x	NUM
ejpam-3543	279	107	)	)	PUNCT
ejpam-3543	279	108	}	}	PUNCT
ejpam-3543	279	109	(	(	PUNCT
ejpam-3543	279	110	3.22	3.22	NUM
ejpam-3543	279	111	)	)	PUNCT
ejpam-3543	279	112	≥	≥	NOUN
ejpam-3543	279	113	λi(y	λi(y	NUM
ejpam-3543	279	114	)	)	PUNCT
ejpam-3543	279	115	,	,	PUNCT
ejpam-3543	279	116	min{λf	min{λf	X
ejpam-3543	279	117	(	(	PUNCT
ejpam-3543	279	118	x	x	PROPN
ejpam-3543	279	119	·	·	PUNCT
ejpam-3543	279	120	y	y	X
ejpam-3543	279	121	)	)	PUNCT
ejpam-3543	279	122	,	,	PUNCT
ejpam-3543	279	123	λf	λf	X
ejpam-3543	279	124	(	(	PUNCT
ejpam-3543	279	125	x	x	NOUN
ejpam-3543	279	126	)	)	PUNCT
ejpam-3543	279	127	}	}	PUNCT
ejpam-3543	279	128	=	=	SYM
ejpam-3543	279	129	min{λi(x	min{λi(x	X
ejpam-3543	279	130	·	·	PUNCT
ejpam-3543	279	131	y	y	X
ejpam-3543	279	132	)	)	PUNCT
ejpam-3543	279	133	,	,	PUNCT
ejpam-3543	279	134	λf	λf	X
ejpam-3543	279	135	(	(	PUNCT
ejpam-3543	279	136	x	x	NOUN
ejpam-3543	279	137	)	)	PUNCT
ejpam-3543	279	138	}	}	PUNCT
ejpam-3543	279	139	(	(	PUNCT
ejpam-3543	279	140	3.22	3.22	NUM
ejpam-3543	279	141	)	)	PUNCT
ejpam-3543	279	142	m.	m.	NOUN
ejpam-3543	279	143	songsaeng	songsaeng	PROPN
ejpam-3543	279	144	,	,	PUNCT
ejpam-3543	279	145	a.	a.	NOUN
ejpam-3543	279	146	iampan	iampan	PROPN
ejpam-3543	279	147	/	/	SYM
ejpam-3543	279	148	eur	eur	PROPN
ejpam-3543	279	149	.	.	PUNCT
ejpam-3543	280	1	j.	j.	PROPN
ejpam-3543	280	2	pure	pure	PROPN
ejpam-3543	280	3	appl	appl	PROPN
ejpam-3543	280	4	.	.	PROPN
ejpam-3543	280	5	math	math	PROPN
ejpam-3543	280	6	,	,	PUNCT
ejpam-3543	280	7	12	12	NUM
ejpam-3543	280	8	(	(	PUNCT
ejpam-3543	280	9	4	4	NUM
ejpam-3543	280	10	)	)	PUNCT
ejpam-3543	280	11	(	(	PUNCT
ejpam-3543	280	12	2019	2019	NUM
ejpam-3543	280	13	)	)	PUNCT
ejpam-3543	280	14	,	,	PUNCT
ejpam-3543	280	15	1382	1382	NUM
ejpam-3543	280	16	-	-	SYM
ejpam-3543	280	17	1409	1409	NUM
ejpam-3543	280	18	1394	1394	NUM
ejpam-3543	280	19	≤	≤	NOUN
ejpam-3543	280	20	min{λi(y	min{λi(y	NOUN
ejpam-3543	280	21	)	)	PUNCT
ejpam-3543	280	22	,	,	PUNCT
ejpam-3543	280	23	λf	λf	X
ejpam-3543	280	24	(	(	PUNCT
ejpam-3543	280	25	x	x	NOUN
ejpam-3543	280	26	)	)	PUNCT
ejpam-3543	280	27	}	}	PUNCT
ejpam-3543	280	28	(	(	PUNCT
ejpam-3543	280	29	3.10	3.10	NUM
ejpam-3543	280	30	)	)	PUNCT
ejpam-3543	280	31	=	=	SYM
ejpam-3543	280	32	min{λf	min{λf	X
ejpam-3543	280	33	(	(	PUNCT
ejpam-3543	280	34	y	y	NOUN
ejpam-3543	280	35	)	)	PUNCT
ejpam-3543	280	36	,	,	PUNCT
ejpam-3543	280	37	λf	λf	X
ejpam-3543	280	38	(	(	PUNCT
ejpam-3543	280	39	x	x	NOUN
ejpam-3543	280	40	)	)	PUNCT
ejpam-3543	280	41	}	}	PUNCT
ejpam-3543	280	42	(	(	PUNCT
ejpam-3543	280	43	3.22	3.22	NUM
ejpam-3543	280	44	)	)	PUNCT
ejpam-3543	280	45	≤	≤	NOUN
ejpam-3543	280	46	λf	λf	ADP
ejpam-3543	280	47	(	(	PUNCT
ejpam-3543	280	48	y	y	NOUN
ejpam-3543	280	49	)	)	PUNCT
ejpam-3543	280	50	.	.	PUNCT
ejpam-3543	281	1	hence	hence	ADV
ejpam-3543	281	2	,	,	PUNCT
ejpam-3543	281	3	λ	λ	PROPN
ejpam-3543	281	4	is	be	AUX
ejpam-3543	281	5	a	a	DET
ejpam-3543	281	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	281	7	up	up	ADJ
ejpam-3543	281	8	-	-	PUNCT
ejpam-3543	281	9	filter	filter	NOUN
ejpam-3543	281	10	of	of	ADP
ejpam-3543	281	11	x.	x.	NOUN
ejpam-3543	281	12	theorem	theorem	VERB
ejpam-3543	281	13	9	9	NUM
ejpam-3543	281	14	.	.	PUNCT
ejpam-3543	282	1	if	if	SCONJ
ejpam-3543	282	2	λ	λ	PROPN
ejpam-3543	282	3	is	be	AUX
ejpam-3543	282	4	a	a	DET
ejpam-3543	282	5	neutrosophic	neutrosophic	ADJ
ejpam-3543	282	6	up	up	ADJ
ejpam-3543	282	7	-	-	PUNCT
ejpam-3543	282	8	filter	filter	NOUN
ejpam-3543	282	9	of	of	ADP
ejpam-3543	282	10	x	x	PUNCT
ejpam-3543	282	11	satisfying	satisfy	VERB
ejpam-3543	282	12	the	the	DET
ejpam-3543	282	13	following	follow	VERB
ejpam-3543	282	14	condition	condition	NOUN
ejpam-3543	282	15	:	:	PUNCT
ejpam-3543	282	16	(	(	PUNCT
ejpam-3543	282	17	∀x	∀x	X
ejpam-3543	282	18	,	,	PUNCT
ejpam-3543	282	19	y	y	PROPN
ejpam-3543	282	20	,	,	PUNCT
ejpam-3543	282	21	z	z	NOUN
ejpam-3543	282	22	∈	∈	PROPN
ejpam-3543	282	23	x	x	X
ejpam-3543	282	24	)	)	PUNCT
ejpam-3543	282	25	λt	λt	PROPN
ejpam-3543	282	26	(	(	PUNCT
ejpam-3543	282	27	y	y	PROPN
ejpam-3543	282	28	·	·	PUNCT
ejpam-3543	282	29	(	(	PUNCT
ejpam-3543	282	30	x	x	X
ejpam-3543	282	31	·	·	PUNCT
ejpam-3543	282	32	z	z	NOUN
ejpam-3543	282	33	)	)	PUNCT
ejpam-3543	282	34	)	)	PUNCT
ejpam-3543	283	1	=	=	PUNCT
ejpam-3543	283	2	λt	λt	X
ejpam-3543	283	3	(	(	PUNCT
ejpam-3543	283	4	x	x	X
ejpam-3543	283	5	·	·	PUNCT
ejpam-3543	283	6	(	(	PUNCT
ejpam-3543	283	7	y	y	PROPN
ejpam-3543	283	8	·	·	PUNCT
ejpam-3543	283	9	z	z	NOUN
ejpam-3543	283	10	)	)	PUNCT
ejpam-3543	283	11	)	)	PUNCT
ejpam-3543	283	12	λi(y	λi(y	X
ejpam-3543	283	13	·	·	PUNCT
ejpam-3543	283	14	(	(	PUNCT
ejpam-3543	283	15	x	x	X
ejpam-3543	283	16	·	·	PUNCT
ejpam-3543	283	17	z	z	NOUN
ejpam-3543	283	18	)	)	PUNCT
ejpam-3543	283	19	)	)	PUNCT
ejpam-3543	284	1	=	=	SYM
ejpam-3543	284	2	λi(x	λi(x	X
ejpam-3543	284	3	·	·	PUNCT
ejpam-3543	284	4	(	(	PUNCT
ejpam-3543	284	5	y	y	PROPN
ejpam-3543	284	6	·	·	PUNCT
ejpam-3543	284	7	z	z	X
ejpam-3543	284	8	)	)	PUNCT
ejpam-3543	284	9	)	)	PUNCT
ejpam-3543	285	1	λf	λf	X
ejpam-3543	285	2	(	(	PUNCT
ejpam-3543	285	3	y	y	PROPN
ejpam-3543	285	4	·	·	PUNCT
ejpam-3543	285	5	(	(	PUNCT
ejpam-3543	285	6	x	x	X
ejpam-3543	285	7	·	·	PUNCT
ejpam-3543	285	8	z	z	X
ejpam-3543	285	9	)	)	PUNCT
ejpam-3543	285	10	)	)	PUNCT
ejpam-3543	286	1	=	=	PUNCT
ejpam-3543	286	2	λf	λf	X
ejpam-3543	286	3	(	(	PUNCT
ejpam-3543	286	4	x	x	PART
ejpam-3543	286	5	·	·	PUNCT
ejpam-3543	286	6	(	(	PUNCT
ejpam-3543	286	7	y	y	PROPN
ejpam-3543	286	8	·	·	PUNCT
ejpam-3543	286	9	z	z	NOUN
ejpam-3543	286	10	)	)	PUNCT
ejpam-3543	286	11	)	)	PUNCT
ejpam-3543	287	1			NOUN
ejpam-3543	287	2	,	,	PUNCT
ejpam-3543	287	3	(	(	PUNCT
ejpam-3543	287	4	3.23	3.23	NUM
ejpam-3543	287	5	)	)	PUNCT
ejpam-3543	287	6	then	then	ADV
ejpam-3543	287	7	λ	λ	PROPN
ejpam-3543	287	8	is	be	AUX
ejpam-3543	287	9	a	a	DET
ejpam-3543	287	10	neutrosophic	neutrosophic	ADJ
ejpam-3543	287	11	up	up	ADV
ejpam-3543	287	12	-	-	PUNCT
ejpam-3543	287	13	ideal	ideal	NOUN
ejpam-3543	287	14	of	of	ADP
ejpam-3543	287	15	x.	x.	NOUN
ejpam-3543	287	16	proof	proof	PROPN
ejpam-3543	287	17	.	.	PUNCT
ejpam-3543	288	1	assume	assume	VERB
ejpam-3543	288	2	that	that	SCONJ
ejpam-3543	288	3	λ	λ	PROPN
ejpam-3543	288	4	is	be	AUX
ejpam-3543	288	5	a	a	DET
ejpam-3543	288	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	288	7	up	up	ADJ
ejpam-3543	288	8	-	-	PUNCT
ejpam-3543	288	9	filter	filter	NOUN
ejpam-3543	288	10	of	of	ADP
ejpam-3543	288	11	x	x	PUNCT
ejpam-3543	288	12	satisfying	satisfy	VERB
ejpam-3543	288	13	the	the	DET
ejpam-3543	288	14	condition	condition	NOUN
ejpam-3543	288	15	(	(	PUNCT
ejpam-3543	288	16	3.23	3.23	NUM
ejpam-3543	288	17	)	)	PUNCT
ejpam-3543	288	18	.	.	PUNCT
ejpam-3543	289	1	then	then	ADV
ejpam-3543	289	2	λ	λ	PROPN
ejpam-3543	289	3	satisfies	satisfy	VERB
ejpam-3543	289	4	the	the	DET
ejpam-3543	289	5	conditions	condition	NOUN
ejpam-3543	289	6	(	(	PUNCT
ejpam-3543	289	7	3.6	3.6	NUM
ejpam-3543	289	8	)	)	PUNCT
ejpam-3543	289	9	,	,	PUNCT
ejpam-3543	289	10	(	(	PUNCT
ejpam-3543	289	11	3.7	3.7	NUM
ejpam-3543	289	12	)	)	PUNCT
ejpam-3543	289	13	,	,	PUNCT
ejpam-3543	289	14	and	and	CCONJ
ejpam-3543	289	15	(	(	PUNCT
ejpam-3543	289	16	3.8	3.8	NUM
ejpam-3543	289	17	)	)	PUNCT
ejpam-3543	289	18	.	.	PUNCT
ejpam-3543	290	1	next	next	ADV
ejpam-3543	290	2	,	,	PUNCT
ejpam-3543	290	3	let	let	VERB
ejpam-3543	290	4	x	x	PRON
ejpam-3543	290	5	,	,	PUNCT
ejpam-3543	290	6	y	y	PROPN
ejpam-3543	290	7	,	,	PUNCT
ejpam-3543	290	8	z	z	PROPN
ejpam-3543	290	9	∈	∈	PROPN
ejpam-3543	290	10	x.	x.	NOUN
ejpam-3543	290	11	then	then	ADV
ejpam-3543	290	12	λt	λt	X
ejpam-3543	290	13	(	(	PUNCT
ejpam-3543	290	14	x	x	X
ejpam-3543	290	15	·	·	PUNCT
ejpam-3543	290	16	z	z	X
ejpam-3543	290	17	)	)	PUNCT
ejpam-3543	290	18	≥	≥	NOUN
ejpam-3543	290	19	min{λt	min{λt	X
ejpam-3543	290	20	(	(	PUNCT
ejpam-3543	290	21	y	y	PROPN
ejpam-3543	290	22	·	·	PUNCT
ejpam-3543	290	23	(	(	PUNCT
ejpam-3543	290	24	x	x	X
ejpam-3543	290	25	·	·	PUNCT
ejpam-3543	290	26	z	z	NOUN
ejpam-3543	290	27	)	)	PUNCT
ejpam-3543	290	28	)	)	PUNCT
ejpam-3543	290	29	,	,	PUNCT
ejpam-3543	290	30	λt	λt	X
ejpam-3543	290	31	(	(	PUNCT
ejpam-3543	290	32	y	y	NOUN
ejpam-3543	290	33	)	)	PUNCT
ejpam-3543	290	34	}	}	PUNCT
ejpam-3543	290	35	(	(	PUNCT
ejpam-3543	290	36	3.12	3.12	NUM
ejpam-3543	290	37	)	)	PUNCT
ejpam-3543	290	38	=	=	X
ejpam-3543	290	39	min{λt	min{λt	X
ejpam-3543	290	40	(	(	PUNCT
ejpam-3543	290	41	x	x	X
ejpam-3543	290	42	·	·	PUNCT
ejpam-3543	290	43	(	(	PUNCT
ejpam-3543	290	44	y	y	PROPN
ejpam-3543	290	45	·	·	PUNCT
ejpam-3543	290	46	z	z	NOUN
ejpam-3543	290	47	)	)	PUNCT
ejpam-3543	290	48	)	)	PUNCT
ejpam-3543	290	49	,	,	PUNCT
ejpam-3543	290	50	λt	λt	X
ejpam-3543	290	51	(	(	PUNCT
ejpam-3543	290	52	y	y	NOUN
ejpam-3543	290	53	)	)	PUNCT
ejpam-3543	290	54	}	}	PUNCT
ejpam-3543	290	55	,	,	PUNCT
ejpam-3543	290	56	(	(	PUNCT
ejpam-3543	290	57	3.23	3.23	NUM
ejpam-3543	290	58	)	)	PUNCT
ejpam-3543	290	59	for	for	ADP
ejpam-3543	290	60	λt	λt	ADP
ejpam-3543	290	61	λi(x	λi(x	X
ejpam-3543	290	62	·	·	PUNCT
ejpam-3543	290	63	z	z	X
ejpam-3543	290	64	)	)	PUNCT
ejpam-3543	290	65	≤	≤	NOUN
ejpam-3543	290	66	max{λi(y	max{λi(y	VERB
ejpam-3543	290	67	·	·	PUNCT
ejpam-3543	290	68	(	(	PUNCT
ejpam-3543	290	69	x	x	X
ejpam-3543	290	70	·	·	PUNCT
ejpam-3543	290	71	z	z	NOUN
ejpam-3543	290	72	)	)	PUNCT
ejpam-3543	290	73	)	)	PUNCT
ejpam-3543	290	74	,	,	PUNCT
ejpam-3543	290	75	λi(y	λi(y	NOUN
ejpam-3543	290	76	)	)	PUNCT
ejpam-3543	290	77	}	}	PUNCT
ejpam-3543	290	78	(	(	PUNCT
ejpam-3543	290	79	3.13	3.13	NUM
ejpam-3543	290	80	)	)	PUNCT
ejpam-3543	291	1	=	=	SYM
ejpam-3543	291	2	max{λi(x	max{λi(x	NOUN
ejpam-3543	291	3	·	·	PUNCT
ejpam-3543	291	4	(	(	PUNCT
ejpam-3543	291	5	y	y	PROPN
ejpam-3543	291	6	·	·	PUNCT
ejpam-3543	291	7	z	z	NOUN
ejpam-3543	291	8	)	)	PUNCT
ejpam-3543	291	9	)	)	PUNCT
ejpam-3543	291	10	,	,	PUNCT
ejpam-3543	291	11	λi(y	λi(y	NOUN
ejpam-3543	291	12	)	)	PUNCT
ejpam-3543	291	13	}	}	PUNCT
ejpam-3543	291	14	,	,	PUNCT
ejpam-3543	291	15	(	(	PUNCT
ejpam-3543	291	16	3.23	3.23	NUM
ejpam-3543	291	17	)	)	PUNCT
ejpam-3543	291	18	for	for	ADP
ejpam-3543	291	19	λi	λi	INTJ
ejpam-3543	291	20	λf	λf	X
ejpam-3543	291	21	(	(	PUNCT
ejpam-3543	291	22	x	x	SYM
ejpam-3543	291	23	·	·	PUNCT
ejpam-3543	291	24	z	z	X
ejpam-3543	291	25	)	)	PUNCT
ejpam-3543	291	26	≥	≥	NOUN
ejpam-3543	291	27	min{λf	min{λf	X
ejpam-3543	291	28	(	(	PUNCT
ejpam-3543	291	29	y	y	PROPN
ejpam-3543	291	30	·	·	PUNCT
ejpam-3543	291	31	(	(	PUNCT
ejpam-3543	291	32	x	x	X
ejpam-3543	291	33	·	·	PUNCT
ejpam-3543	291	34	z	z	NOUN
ejpam-3543	291	35	)	)	PUNCT
ejpam-3543	291	36	)	)	PUNCT
ejpam-3543	291	37	,	,	PUNCT
ejpam-3543	291	38	λf	λf	X
ejpam-3543	291	39	(	(	PUNCT
ejpam-3543	291	40	y	y	NOUN
ejpam-3543	291	41	)	)	PUNCT
ejpam-3543	291	42	}	}	PUNCT
ejpam-3543	291	43	(	(	PUNCT
ejpam-3543	291	44	3.14	3.14	NUM
ejpam-3543	291	45	)	)	PUNCT
ejpam-3543	291	46	=	=	X
ejpam-3543	291	47	min{λf	min{λf	X
ejpam-3543	291	48	(	(	PUNCT
ejpam-3543	291	49	x	x	PART
ejpam-3543	291	50	·	·	PUNCT
ejpam-3543	291	51	(	(	PUNCT
ejpam-3543	291	52	y	y	PROPN
ejpam-3543	291	53	·	·	PUNCT
ejpam-3543	291	54	z	z	NOUN
ejpam-3543	291	55	)	)	PUNCT
ejpam-3543	291	56	)	)	PUNCT
ejpam-3543	291	57	,	,	PUNCT
ejpam-3543	291	58	λf	λf	X
ejpam-3543	291	59	(	(	PUNCT
ejpam-3543	291	60	y	y	NOUN
ejpam-3543	291	61	)	)	PUNCT
ejpam-3543	291	62	}	}	PUNCT
ejpam-3543	291	63	.	.	PUNCT
ejpam-3543	292	1	(	(	PUNCT
ejpam-3543	292	2	3.23	3.23	NUM
ejpam-3543	292	3	)	)	PUNCT
ejpam-3543	292	4	for	for	ADP
ejpam-3543	292	5	λf	λf	ADP
ejpam-3543	292	6	hence	hence	ADV
ejpam-3543	292	7	,	,	PUNCT
ejpam-3543	292	8	λ	λ	PROPN
ejpam-3543	292	9	is	be	AUX
ejpam-3543	292	10	a	a	DET
ejpam-3543	292	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	292	12	up	up	ADV
ejpam-3543	292	13	-	-	PUNCT
ejpam-3543	292	14	ideal	ideal	NOUN
ejpam-3543	292	15	of	of	ADP
ejpam-3543	292	16	x.	x.	PROPN
ejpam-3543	292	17	theorem	theorem	VERB
ejpam-3543	292	18	10	10	NUM
ejpam-3543	292	19	.	.	PUNCT
ejpam-3543	293	1	if	if	SCONJ
ejpam-3543	293	2	λ	λ	PROPN
ejpam-3543	293	3	is	be	AUX
ejpam-3543	293	4	a	a	DET
ejpam-3543	293	5	ns	ns	NOUN
ejpam-3543	293	6	in	in	ADP
ejpam-3543	293	7	x	x	PUNCT
ejpam-3543	293	8	satisfying	satisfy	VERB
ejpam-3543	293	9	the	the	DET
ejpam-3543	293	10	following	follow	VERB
ejpam-3543	293	11	condition	condition	NOUN
ejpam-3543	293	12	:	:	PUNCT
ejpam-3543	293	13	(	(	PUNCT
ejpam-3543	293	14	∀x	∀x	X
ejpam-3543	293	15	,	,	PUNCT
ejpam-3543	293	16	y	y	PROPN
ejpam-3543	293	17	,	,	PUNCT
ejpam-3543	293	18	z	z	NOUN
ejpam-3543	293	19	∈	∈	PROPN
ejpam-3543	293	20	x	x	X
ejpam-3543	293	21	)	)	PUNCT
ejpam-3543	293	22	z	z	VERB
ejpam-3543	293	23	≤	≤	NOUN
ejpam-3543	293	24	x	x	X
ejpam-3543	293	25	·	·	PUNCT
ejpam-3543	293	26	y	y	PROPN
ejpam-3543	293	27	⇒	⇒	VERB
ejpam-3543	293	28			PRON
ejpam-3543	293	29	λt	λt	ADP
ejpam-3543	293	30	(	(	PUNCT
ejpam-3543	293	31	z	z	NOUN
ejpam-3543	293	32	)	)	PUNCT
ejpam-3543	293	33	≥	≥	NOUN
ejpam-3543	293	34	min{λt	min{λt	X
ejpam-3543	293	35	(	(	PUNCT
ejpam-3543	293	36	x	x	X
ejpam-3543	293	37	)	)	PUNCT
ejpam-3543	293	38	,	,	PUNCT
ejpam-3543	293	39	λt	λt	X
ejpam-3543	293	40	(	(	PUNCT
ejpam-3543	293	41	y	y	NOUN
ejpam-3543	293	42	)	)	PUNCT
ejpam-3543	293	43	}	}	PUNCT
ejpam-3543	293	44	λi(z	λi(z	PROPN
ejpam-3543	293	45	)	)	PUNCT
ejpam-3543	293	46	≤	≤	NUM
ejpam-3543	293	47	max{λi(x	max{λi(x	NOUN
ejpam-3543	293	48	)	)	PUNCT
ejpam-3543	293	49	,	,	PUNCT
ejpam-3543	293	50	λi(y	λi(y	NOUN
ejpam-3543	293	51	)	)	PUNCT
ejpam-3543	293	52	}	}	PUNCT
ejpam-3543	293	53	λf	λf	X
ejpam-3543	293	54	(	(	PUNCT
ejpam-3543	293	55	z	z	NOUN
ejpam-3543	293	56	)	)	PUNCT
ejpam-3543	293	57	≥	≥	NOUN
ejpam-3543	293	58	min{λf	min{λf	X
ejpam-3543	293	59	(	(	PUNCT
ejpam-3543	293	60	x	x	X
ejpam-3543	293	61	)	)	PUNCT
ejpam-3543	293	62	,	,	PUNCT
ejpam-3543	293	63	λf	λf	X
ejpam-3543	293	64	(	(	PUNCT
ejpam-3543	293	65	y	y	NOUN
ejpam-3543	293	66	)	)	PUNCT
ejpam-3543	293	67	}	}	PUNCT
ejpam-3543	293	68			NOUN
ejpam-3543	293	69	,	,	PUNCT
ejpam-3543	293	70	(	(	PUNCT
ejpam-3543	293	71	3.24	3.24	NUM
ejpam-3543	293	72	)	)	PUNCT
ejpam-3543	293	73	then	then	ADV
ejpam-3543	293	74	λ	λ	PROPN
ejpam-3543	293	75	is	be	AUX
ejpam-3543	293	76	a	a	DET
ejpam-3543	293	77	neutrosophic	neutrosophic	ADJ
ejpam-3543	293	78	up	up	ADP
ejpam-3543	293	79	-	-	PUNCT
ejpam-3543	293	80	subalgebra	subalgebra	NOUN
ejpam-3543	293	81	of	of	ADP
ejpam-3543	293	82	x.	x.	NOUN
ejpam-3543	293	83	proof	proof	PROPN
ejpam-3543	293	84	.	.	PUNCT
ejpam-3543	294	1	assume	assume	VERB
ejpam-3543	294	2	that	that	SCONJ
ejpam-3543	294	3	λ	λ	PROPN
ejpam-3543	294	4	is	be	AUX
ejpam-3543	294	5	a	a	DET
ejpam-3543	294	6	ns	ns	NOUN
ejpam-3543	294	7	in	in	ADP
ejpam-3543	294	8	x	x	PUNCT
ejpam-3543	294	9	satisfying	satisfy	VERB
ejpam-3543	294	10	the	the	DET
ejpam-3543	294	11	condition	condition	NOUN
ejpam-3543	294	12	(	(	PUNCT
ejpam-3543	294	13	3.24	3.24	NUM
ejpam-3543	294	14	)	)	PUNCT
ejpam-3543	294	15	.	.	PUNCT
ejpam-3543	295	1	let	let	VERB
ejpam-3543	295	2	x	x	PRON
ejpam-3543	295	3	,	,	PUNCT
ejpam-3543	295	4	y	y	PROPN
ejpam-3543	295	5	∈	∈	PROPN
ejpam-3543	295	6	x.	x.	NOUN
ejpam-3543	295	7	by	by	ADP
ejpam-3543	295	8	(	(	PUNCT
ejpam-3543	295	9	2.1	2.1	NUM
ejpam-3543	295	10	)	)	PUNCT
ejpam-3543	295	11	,	,	PUNCT
ejpam-3543	295	12	we	we	PRON
ejpam-3543	295	13	have	have	VERB
ejpam-3543	295	14	(	(	PUNCT
ejpam-3543	295	15	x	x	X
ejpam-3543	295	16	·	·	PUNCT
ejpam-3543	295	17	y	y	X
ejpam-3543	295	18	)	)	PUNCT
ejpam-3543	295	19	·	·	PUNCT
ejpam-3543	296	1	(	(	PUNCT
ejpam-3543	296	2	x	x	X
ejpam-3543	296	3	·	·	PUNCT
ejpam-3543	296	4	y	y	X
ejpam-3543	296	5	)	)	PUNCT
ejpam-3543	296	6	=	=	SYM
ejpam-3543	296	7	0	0	NUM
ejpam-3543	296	8	,	,	PUNCT
ejpam-3543	296	9	that	that	ADV
ejpam-3543	296	10	is	is	ADV
ejpam-3543	296	11	,	,	PUNCT
ejpam-3543	296	12	x	x	X
ejpam-3543	296	13	·	·	PUNCT
ejpam-3543	296	14	y	y	X
ejpam-3543	296	15	≤	≤	NUM
ejpam-3543	296	16	x	x	X
ejpam-3543	297	1	·	·	PUNCT
ejpam-3543	297	2	y.	y.	NOUN
ejpam-3543	297	3	it	it	PRON
ejpam-3543	297	4	follows	follow	VERB
ejpam-3543	297	5	from	from	ADP
ejpam-3543	297	6	(	(	PUNCT
ejpam-3543	297	7	3.24	3.24	NUM
ejpam-3543	297	8	)	)	PUNCT
ejpam-3543	297	9	that	that	SCONJ
ejpam-3543	298	1	λt	λt	ADP
ejpam-3543	298	2	(	(	PUNCT
ejpam-3543	298	3	x	x	PROPN
ejpam-3543	298	4	·	·	PUNCT
ejpam-3543	298	5	y	y	X
ejpam-3543	298	6	)	)	PUNCT
ejpam-3543	298	7	≥	≥	NOUN
ejpam-3543	298	8	min{λt	min{λt	X
ejpam-3543	298	9	(	(	PUNCT
ejpam-3543	298	10	x	x	X
ejpam-3543	298	11	)	)	PUNCT
ejpam-3543	298	12	,	,	PUNCT
ejpam-3543	298	13	λt	λt	X
ejpam-3543	298	14	(	(	PUNCT
ejpam-3543	298	15	y	y	NOUN
ejpam-3543	298	16	)	)	PUNCT
ejpam-3543	298	17	}	}	PUNCT
ejpam-3543	298	18	,	,	PUNCT
ejpam-3543	298	19	λi(x	λi(x	X
ejpam-3543	298	20	·	·	PUNCT
ejpam-3543	298	21	y	y	X
ejpam-3543	298	22	)	)	PUNCT
ejpam-3543	298	23	≤	≤	NUM
ejpam-3543	298	24	max{λi(x	max{λi(x	NOUN
ejpam-3543	298	25	)	)	PUNCT
ejpam-3543	298	26	,	,	PUNCT
ejpam-3543	298	27	λi(y	λi(y	NOUN
ejpam-3543	298	28	)	)	PUNCT
ejpam-3543	298	29	}	}	PUNCT
ejpam-3543	298	30	,	,	PUNCT
ejpam-3543	298	31	λf	λf	X
ejpam-3543	298	32	(	(	PUNCT
ejpam-3543	298	33	x	x	SYM
ejpam-3543	298	34	·	·	PUNCT
ejpam-3543	298	35	y	y	X
ejpam-3543	298	36	)	)	PUNCT
ejpam-3543	298	37	≥	≥	NOUN
ejpam-3543	298	38	min{λf	min{λf	X
ejpam-3543	298	39	(	(	PUNCT
ejpam-3543	298	40	x	x	X
ejpam-3543	298	41	)	)	PUNCT
ejpam-3543	298	42	,	,	PUNCT
ejpam-3543	298	43	λf	λf	X
ejpam-3543	298	44	(	(	PUNCT
ejpam-3543	298	45	y	y	NOUN
ejpam-3543	298	46	)	)	PUNCT
ejpam-3543	298	47	}	}	PUNCT
ejpam-3543	298	48	.	.	PUNCT
ejpam-3543	299	1	hence	hence	ADV
ejpam-3543	299	2	,	,	PUNCT
ejpam-3543	299	3	λ	λ	PROPN
ejpam-3543	299	4	is	be	AUX
ejpam-3543	299	5	a	a	DET
ejpam-3543	299	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	299	7	up	up	ADP
ejpam-3543	299	8	-	-	PUNCT
ejpam-3543	299	9	subalgebra	subalgebra	NOUN
ejpam-3543	299	10	of	of	ADP
ejpam-3543	299	11	x.	x.	PROPN
ejpam-3543	299	12	m.	m.	PROPN
ejpam-3543	299	13	songsaeng	songsaeng	PROPN
ejpam-3543	299	14	,	,	PUNCT
ejpam-3543	299	15	a.	a.	NOUN
ejpam-3543	299	16	iampan	iampan	PROPN
ejpam-3543	299	17	/	/	SYM
ejpam-3543	299	18	eur	eur	PROPN
ejpam-3543	299	19	.	.	PUNCT
ejpam-3543	300	1	j.	j.	PROPN
ejpam-3543	300	2	pure	pure	PROPN
ejpam-3543	300	3	appl	appl	PROPN
ejpam-3543	300	4	.	.	PROPN
ejpam-3543	300	5	math	math	PROPN
ejpam-3543	300	6	,	,	PUNCT
ejpam-3543	300	7	12	12	NUM
ejpam-3543	300	8	(	(	PUNCT
ejpam-3543	300	9	4	4	NUM
ejpam-3543	300	10	)	)	PUNCT
ejpam-3543	300	11	(	(	PUNCT
ejpam-3543	300	12	2019	2019	NUM
ejpam-3543	300	13	)	)	PUNCT
ejpam-3543	300	14	,	,	PUNCT
ejpam-3543	300	15	1382	1382	NUM
ejpam-3543	300	16	-	-	SYM
ejpam-3543	300	17	1409	1409	NUM
ejpam-3543	300	18	1395	1395	NUM
ejpam-3543	300	19	theorem	theorem	NOUN
ejpam-3543	300	20	11	11	NUM
ejpam-3543	300	21	.	.	PUNCT
ejpam-3543	301	1	if	if	SCONJ
ejpam-3543	301	2	λ	λ	PROPN
ejpam-3543	301	3	is	be	AUX
ejpam-3543	301	4	a	a	DET
ejpam-3543	301	5	ns	ns	NOUN
ejpam-3543	301	6	in	in	ADP
ejpam-3543	301	7	x	x	PUNCT
ejpam-3543	301	8	satisfying	satisfy	VERB
ejpam-3543	301	9	the	the	DET
ejpam-3543	301	10	following	follow	VERB
ejpam-3543	301	11	condition	condition	NOUN
ejpam-3543	301	12	:	:	PUNCT
ejpam-3543	301	13	(	(	PUNCT
ejpam-3543	301	14	∀x	∀x	X
ejpam-3543	301	15	,	,	PUNCT
ejpam-3543	301	16	y	y	PROPN
ejpam-3543	301	17	,	,	PUNCT
ejpam-3543	301	18	z	z	NOUN
ejpam-3543	301	19	∈	∈	PROPN
ejpam-3543	301	20	x	x	X
ejpam-3543	301	21	)	)	PUNCT
ejpam-3543	301	22	z	z	VERB
ejpam-3543	301	23	≤	≤	NOUN
ejpam-3543	301	24	x	x	X
ejpam-3543	301	25	·	·	PUNCT
ejpam-3543	301	26	y	y	PROPN
ejpam-3543	301	27	⇒	⇒	VERB
ejpam-3543	301	28			PRON
ejpam-3543	301	29	λt	λt	ADP
ejpam-3543	301	30	(	(	PUNCT
ejpam-3543	301	31	z	z	NOUN
ejpam-3543	301	32	)	)	PUNCT
ejpam-3543	301	33	≥	≥	NOUN
ejpam-3543	301	34	λt	λt	X
ejpam-3543	301	35	(	(	PUNCT
ejpam-3543	301	36	y	y	NOUN
ejpam-3543	301	37	)	)	PUNCT
ejpam-3543	301	38	λi(z	λi(z	PROPN
ejpam-3543	301	39	)	)	PUNCT
ejpam-3543	301	40	≤	≤	NOUN
ejpam-3543	301	41	λi(y	λi(y	NOUN
ejpam-3543	301	42	)	)	PUNCT
ejpam-3543	301	43	λf	λf	X
ejpam-3543	301	44	(	(	PUNCT
ejpam-3543	301	45	z	z	NOUN
ejpam-3543	301	46	)	)	PUNCT
ejpam-3543	301	47	≥	≥	NOUN
ejpam-3543	301	48	λf	λf	PROPN
ejpam-3543	301	49	(	(	PUNCT
ejpam-3543	301	50	y	y	NOUN
ejpam-3543	301	51	)	)	PUNCT
ejpam-3543	301	52			NOUN
ejpam-3543	301	53	,	,	PUNCT
ejpam-3543	301	54	(	(	PUNCT
ejpam-3543	301	55	3.25	3.25	NUM
ejpam-3543	301	56	)	)	PUNCT
ejpam-3543	301	57	then	then	ADV
ejpam-3543	301	58	λ	λ	PROPN
ejpam-3543	301	59	is	be	AUX
ejpam-3543	301	60	a	a	DET
ejpam-3543	301	61	neutrosophic	neutrosophic	ADJ
ejpam-3543	301	62	near	near	ADP
ejpam-3543	301	63	up	up	ADJ
ejpam-3543	301	64	-	-	PUNCT
ejpam-3543	301	65	filter	filter	NOUN
ejpam-3543	301	66	of	of	ADP
ejpam-3543	301	67	x.	x.	NOUN
ejpam-3543	301	68	proof	proof	PROPN
ejpam-3543	301	69	.	.	PUNCT
ejpam-3543	302	1	assume	assume	VERB
ejpam-3543	302	2	that	that	SCONJ
ejpam-3543	302	3	λ	λ	PROPN
ejpam-3543	302	4	is	be	AUX
ejpam-3543	302	5	a	a	DET
ejpam-3543	302	6	ns	ns	NOUN
ejpam-3543	302	7	in	in	ADP
ejpam-3543	302	8	x	x	PUNCT
ejpam-3543	302	9	satisfying	satisfy	VERB
ejpam-3543	302	10	the	the	DET
ejpam-3543	302	11	condition	condition	NOUN
ejpam-3543	302	12	(	(	PUNCT
ejpam-3543	302	13	3.25	3.25	NUM
ejpam-3543	302	14	)	)	PUNCT
ejpam-3543	302	15	.	.	PUNCT
ejpam-3543	303	1	let	let	VERB
ejpam-3543	303	2	x	x	SYM
ejpam-3543	303	3	∈	∈	PROPN
ejpam-3543	303	4	x.	x.	NOUN
ejpam-3543	303	5	by	by	ADP
ejpam-3543	303	6	(	(	PUNCT
ejpam-3543	303	7	up-2	up-2	NUM
ejpam-3543	303	8	)	)	PUNCT
ejpam-3543	303	9	and	and	CCONJ
ejpam-3543	303	10	(	(	PUNCT
ejpam-3543	303	11	2.1	2.1	NUM
ejpam-3543	303	12	)	)	PUNCT
ejpam-3543	303	13	,	,	PUNCT
ejpam-3543	303	14	we	we	PRON
ejpam-3543	303	15	have	have	VERB
ejpam-3543	303	16	0	0	NUM
ejpam-3543	303	17	·	·	PUNCT
ejpam-3543	303	18	(	(	PUNCT
ejpam-3543	303	19	x	x	X
ejpam-3543	303	20	·	·	PUNCT
ejpam-3543	303	21	x	x	X
ejpam-3543	303	22	)	)	PUNCT
ejpam-3543	303	23	=	=	SYM
ejpam-3543	303	24	0	0	NUM
ejpam-3543	303	25	,	,	PUNCT
ejpam-3543	303	26	that	that	ADV
ejpam-3543	303	27	is	is	ADV
ejpam-3543	303	28	,	,	PUNCT
ejpam-3543	303	29	0	0	NUM
ejpam-3543	303	30	≤	≤	NUM
ejpam-3543	303	31	x	x	X
ejpam-3543	303	32	·	·	PUNCT
ejpam-3543	303	33	x.	x.	NOUN
ejpam-3543	304	1	it	it	PRON
ejpam-3543	304	2	follows	follow	VERB
ejpam-3543	304	3	from	from	ADP
ejpam-3543	304	4	(	(	PUNCT
ejpam-3543	304	5	3.25	3.25	NUM
ejpam-3543	304	6	)	)	PUNCT
ejpam-3543	305	1	that	that	SCONJ
ejpam-3543	305	2	λt	λt	ADP
ejpam-3543	305	3	(	(	PUNCT
ejpam-3543	305	4	0	0	NUM
ejpam-3543	305	5	)	)	PUNCT
ejpam-3543	305	6	≥	≥	NOUN
ejpam-3543	305	7	λt	λt	X
ejpam-3543	305	8	(	(	PUNCT
ejpam-3543	305	9	x	x	NOUN
ejpam-3543	305	10	)	)	PUNCT
ejpam-3543	305	11	,	,	PUNCT
ejpam-3543	305	12	λi(0	λi(0	NOUN
ejpam-3543	305	13	)	)	PUNCT
ejpam-3543	305	14	≤	≤	NOUN
ejpam-3543	305	15	λi(x	λi(x	NUM
ejpam-3543	305	16	)	)	PUNCT
ejpam-3543	305	17	,	,	PUNCT
ejpam-3543	305	18	and	and	CCONJ
ejpam-3543	305	19	λf	λf	INTJ
ejpam-3543	305	20	(	(	PUNCT
ejpam-3543	305	21	0	0	NUM
ejpam-3543	305	22	)	)	PUNCT
ejpam-3543	305	23	≥	≥	NOUN
ejpam-3543	305	24	λf	λf	X
ejpam-3543	305	25	(	(	PUNCT
ejpam-3543	305	26	x	x	NOUN
ejpam-3543	305	27	)	)	PUNCT
ejpam-3543	305	28	.	.	PUNCT
ejpam-3543	306	1	next	next	ADV
ejpam-3543	306	2	,	,	PUNCT
ejpam-3543	306	3	let	let	VERB
ejpam-3543	306	4	x	x	PRON
ejpam-3543	306	5	,	,	PUNCT
ejpam-3543	306	6	y	y	PROPN
ejpam-3543	306	7	∈	∈	PROPN
ejpam-3543	306	8	x.	x.	NOUN
ejpam-3543	306	9	by	by	ADP
ejpam-3543	306	10	(	(	PUNCT
ejpam-3543	306	11	2.1	2.1	NUM
ejpam-3543	306	12	)	)	PUNCT
ejpam-3543	306	13	,	,	PUNCT
ejpam-3543	306	14	we	we	PRON
ejpam-3543	306	15	have	have	VERB
ejpam-3543	306	16	(	(	PUNCT
ejpam-3543	306	17	x	x	X
ejpam-3543	306	18	·	·	PUNCT
ejpam-3543	306	19	y	y	X
ejpam-3543	306	20	)	)	PUNCT
ejpam-3543	306	21	·	·	PUNCT
ejpam-3543	307	1	(	(	PUNCT
ejpam-3543	307	2	x	x	X
ejpam-3543	307	3	·	·	PUNCT
ejpam-3543	307	4	y	y	X
ejpam-3543	307	5	)	)	PUNCT
ejpam-3543	307	6	=	=	SYM
ejpam-3543	307	7	0	0	NUM
ejpam-3543	307	8	,	,	PUNCT
ejpam-3543	307	9	that	that	ADV
ejpam-3543	307	10	is	is	ADV
ejpam-3543	307	11	,	,	PUNCT
ejpam-3543	307	12	x	x	X
ejpam-3543	307	13	·	·	PUNCT
ejpam-3543	307	14	y	y	X
ejpam-3543	307	15	≤	≤	NUM
ejpam-3543	307	16	x	x	X
ejpam-3543	308	1	·	·	PUNCT
ejpam-3543	308	2	y.	y.	NOUN
ejpam-3543	308	3	it	it	PRON
ejpam-3543	308	4	follows	follow	VERB
ejpam-3543	308	5	from	from	ADP
ejpam-3543	308	6	(	(	PUNCT
ejpam-3543	308	7	3.25	3.25	NUM
ejpam-3543	308	8	)	)	PUNCT
ejpam-3543	308	9	that	that	SCONJ
ejpam-3543	308	10	λt	λt	ADP
ejpam-3543	308	11	(	(	PUNCT
ejpam-3543	308	12	x	x	PROPN
ejpam-3543	308	13	·	·	PUNCT
ejpam-3543	308	14	y	y	X
ejpam-3543	308	15	)	)	PUNCT
ejpam-3543	308	16	≥	≥	NOUN
ejpam-3543	308	17	λt	λt	X
ejpam-3543	308	18	(	(	PUNCT
ejpam-3543	308	19	y	y	NOUN
ejpam-3543	308	20	)	)	PUNCT
ejpam-3543	308	21	,	,	PUNCT
ejpam-3543	308	22	λi(x	λi(x	X
ejpam-3543	308	23	·	·	PUNCT
ejpam-3543	308	24	y	y	X
ejpam-3543	308	25	)	)	PUNCT
ejpam-3543	308	26	≤	≤	NOUN
ejpam-3543	308	27	λi(y	λi(y	NUM
ejpam-3543	308	28	)	)	PUNCT
ejpam-3543	308	29	,	,	PUNCT
ejpam-3543	308	30	and	and	CCONJ
ejpam-3543	308	31	λf	λf	INTJ
ejpam-3543	308	32	(	(	PUNCT
ejpam-3543	308	33	x	x	SYM
ejpam-3543	308	34	·	·	PUNCT
ejpam-3543	308	35	y	y	X
ejpam-3543	308	36	)	)	PUNCT
ejpam-3543	308	37	≥	≥	NOUN
ejpam-3543	308	38	λf	λf	PROPN
ejpam-3543	308	39	(	(	PUNCT
ejpam-3543	308	40	y	y	NOUN
ejpam-3543	308	41	)	)	PUNCT
ejpam-3543	308	42	.	.	PUNCT
ejpam-3543	309	1	hence	hence	ADV
ejpam-3543	309	2	,	,	PUNCT
ejpam-3543	309	3	λ	λ	PROPN
ejpam-3543	309	4	is	be	AUX
ejpam-3543	309	5	a	a	DET
ejpam-3543	309	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	309	7	near	near	ADP
ejpam-3543	309	8	up	up	ADJ
ejpam-3543	309	9	-	-	PUNCT
ejpam-3543	309	10	filter	filter	NOUN
ejpam-3543	309	11	of	of	ADP
ejpam-3543	309	12	x.	x.	PROPN
ejpam-3543	309	13	theorem	theorem	VERB
ejpam-3543	309	14	12	12	NUM
ejpam-3543	309	15	.	.	PUNCT
ejpam-3543	310	1	if	if	SCONJ
ejpam-3543	310	2	λ	λ	PROPN
ejpam-3543	310	3	is	be	AUX
ejpam-3543	310	4	a	a	DET
ejpam-3543	310	5	ns	ns	NOUN
ejpam-3543	310	6	in	in	ADP
ejpam-3543	310	7	x	x	PUNCT
ejpam-3543	310	8	satisfying	satisfy	VERB
ejpam-3543	310	9	the	the	DET
ejpam-3543	310	10	following	follow	VERB
ejpam-3543	310	11	condition	condition	NOUN
ejpam-3543	310	12	:	:	PUNCT
ejpam-3543	310	13	(	(	PUNCT
ejpam-3543	310	14	∀x	∀x	X
ejpam-3543	310	15	,	,	PUNCT
ejpam-3543	310	16	y	y	PROPN
ejpam-3543	310	17	,	,	PUNCT
ejpam-3543	310	18	z	z	NOUN
ejpam-3543	310	19	∈	∈	PROPN
ejpam-3543	310	20	x	x	X
ejpam-3543	310	21	)	)	PUNCT
ejpam-3543	310	22	z	z	VERB
ejpam-3543	310	23	≤	≤	NOUN
ejpam-3543	310	24	x	x	X
ejpam-3543	310	25	·	·	PUNCT
ejpam-3543	310	26	y	y	PROPN
ejpam-3543	310	27	⇒	⇒	VERB
ejpam-3543	310	28			PRON
ejpam-3543	310	29	λt	λt	ADP
ejpam-3543	310	30	(	(	PUNCT
ejpam-3543	310	31	y	y	NOUN
ejpam-3543	310	32	)	)	PUNCT
ejpam-3543	310	33	≥	≥	NOUN
ejpam-3543	310	34	min{λt	min{λt	X
ejpam-3543	310	35	(	(	PUNCT
ejpam-3543	310	36	z	z	NOUN
ejpam-3543	310	37	)	)	PUNCT
ejpam-3543	310	38	,	,	PUNCT
ejpam-3543	310	39	λt	λt	X
ejpam-3543	310	40	(	(	PUNCT
ejpam-3543	310	41	x	x	NOUN
ejpam-3543	310	42	)	)	PUNCT
ejpam-3543	310	43	}	}	PUNCT
ejpam-3543	310	44	λi(y	λi(y	NOUN
ejpam-3543	310	45	)	)	PUNCT
ejpam-3543	310	46	≤	≤	NUM
ejpam-3543	310	47	max{λi(z	max{λi(z	NOUN
ejpam-3543	310	48	)	)	PUNCT
ejpam-3543	310	49	,	,	PUNCT
ejpam-3543	310	50	λi(x	λi(x	NUM
ejpam-3543	310	51	)	)	PUNCT
ejpam-3543	310	52	}	}	PUNCT
ejpam-3543	310	53	λf	λf	X
ejpam-3543	310	54	(	(	PUNCT
ejpam-3543	310	55	y	y	NOUN
ejpam-3543	310	56	)	)	PUNCT
ejpam-3543	310	57	≥	≥	NOUN
ejpam-3543	310	58	min{λf	min{λf	X
ejpam-3543	311	1	(	(	PUNCT
ejpam-3543	311	2	z	z	NOUN
ejpam-3543	311	3	)	)	PUNCT
ejpam-3543	311	4	,	,	PUNCT
ejpam-3543	311	5	λf	λf	X
ejpam-3543	311	6	(	(	PUNCT
ejpam-3543	311	7	x	x	NOUN
ejpam-3543	311	8	)	)	PUNCT
ejpam-3543	311	9	}	}	PUNCT
ejpam-3543	311	10			NOUN
ejpam-3543	311	11	,	,	PUNCT
ejpam-3543	311	12	(	(	PUNCT
ejpam-3543	311	13	3.26	3.26	NUM
ejpam-3543	311	14	)	)	PUNCT
ejpam-3543	311	15	then	then	ADV
ejpam-3543	311	16	λ	λ	PROPN
ejpam-3543	311	17	is	be	AUX
ejpam-3543	311	18	a	a	DET
ejpam-3543	311	19	neutrosophic	neutrosophic	ADJ
ejpam-3543	311	20	up	up	ADJ
ejpam-3543	311	21	-	-	PUNCT
ejpam-3543	311	22	filter	filter	NOUN
ejpam-3543	311	23	of	of	ADP
ejpam-3543	311	24	x.	x.	NOUN
ejpam-3543	311	25	proof	proof	PROPN
ejpam-3543	311	26	.	.	PUNCT
ejpam-3543	312	1	assume	assume	VERB
ejpam-3543	312	2	that	that	SCONJ
ejpam-3543	312	3	λ	λ	PROPN
ejpam-3543	312	4	is	be	AUX
ejpam-3543	312	5	a	a	DET
ejpam-3543	312	6	ns	ns	NOUN
ejpam-3543	312	7	in	in	ADP
ejpam-3543	312	8	x	x	PUNCT
ejpam-3543	312	9	satisfying	satisfy	VERB
ejpam-3543	312	10	the	the	DET
ejpam-3543	312	11	condition	condition	NOUN
ejpam-3543	312	12	(	(	PUNCT
ejpam-3543	312	13	3.26	3.26	NUM
ejpam-3543	312	14	)	)	PUNCT
ejpam-3543	312	15	.	.	PUNCT
ejpam-3543	313	1	let	let	VERB
ejpam-3543	313	2	x	x	SYM
ejpam-3543	313	3	∈	∈	PROPN
ejpam-3543	313	4	x.	x.	NOUN
ejpam-3543	313	5	by	by	ADP
ejpam-3543	313	6	(	(	PUNCT
ejpam-3543	313	7	up-3	up-3	NOUN
ejpam-3543	313	8	)	)	PUNCT
ejpam-3543	313	9	,	,	PUNCT
ejpam-3543	313	10	we	we	PRON
ejpam-3543	313	11	have	have	VERB
ejpam-3543	313	12	x	x	X
ejpam-3543	313	13	·	·	PUNCT
ejpam-3543	313	14	(	(	PUNCT
ejpam-3543	313	15	x	x	X
ejpam-3543	313	16	·	·	PUNCT
ejpam-3543	313	17	0	0	NUM
ejpam-3543	313	18	)	)	PUNCT
ejpam-3543	313	19	=	=	SYM
ejpam-3543	314	1	0	0	NUM
ejpam-3543	314	2	,	,	PUNCT
ejpam-3543	314	3	that	that	ADV
ejpam-3543	314	4	is	is	ADV
ejpam-3543	314	5	,	,	PUNCT
ejpam-3543	314	6	x	x	X
ejpam-3543	314	7	≤	≤	X
ejpam-3543	314	8	x	x	SYM
ejpam-3543	314	9	·	·	PUNCT
ejpam-3543	314	10	0	0	X
ejpam-3543	314	11	.	.	PUNCT
ejpam-3543	315	1	it	it	PRON
ejpam-3543	315	2	follows	follow	VERB
ejpam-3543	315	3	from	from	ADP
ejpam-3543	315	4	(	(	PUNCT
ejpam-3543	315	5	3.26	3.26	NUM
ejpam-3543	315	6	)	)	PUNCT
ejpam-3543	315	7	that	that	SCONJ
ejpam-3543	315	8	λt	λt	ADP
ejpam-3543	315	9	(	(	PUNCT
ejpam-3543	315	10	0	0	NUM
ejpam-3543	315	11	)	)	PUNCT
ejpam-3543	315	12	≥	≥	NOUN
ejpam-3543	315	13	min{λt	min{λt	X
ejpam-3543	315	14	(	(	PUNCT
ejpam-3543	315	15	x	x	X
ejpam-3543	315	16	)	)	PUNCT
ejpam-3543	315	17	,	,	PUNCT
ejpam-3543	315	18	λt	λt	X
ejpam-3543	315	19	(	(	PUNCT
ejpam-3543	315	20	x	x	NOUN
ejpam-3543	315	21	)	)	PUNCT
ejpam-3543	315	22	}	}	PUNCT
ejpam-3543	315	23	=	=	SYM
ejpam-3543	315	24	λt	λt	X
ejpam-3543	315	25	(	(	PUNCT
ejpam-3543	315	26	x	x	NOUN
ejpam-3543	315	27	)	)	PUNCT
ejpam-3543	315	28	,	,	PUNCT
ejpam-3543	315	29	λi(0	λi(0	NOUN
ejpam-3543	315	30	)	)	PUNCT
ejpam-3543	315	31	≤	≤	NUM
ejpam-3543	315	32	max{λi(x	max{λi(x	NOUN
ejpam-3543	315	33	)	)	PUNCT
ejpam-3543	315	34	,	,	PUNCT
ejpam-3543	315	35	λi(x	λi(x	NUM
ejpam-3543	315	36	)	)	PUNCT
ejpam-3543	315	37	}	}	PUNCT
ejpam-3543	315	38	=	=	SYM
ejpam-3543	315	39	λi(x	λi(x	NUM
ejpam-3543	315	40	)	)	PUNCT
ejpam-3543	315	41	,	,	PUNCT
ejpam-3543	315	42	λf	λf	X
ejpam-3543	315	43	(	(	PUNCT
ejpam-3543	315	44	0	0	NUM
ejpam-3543	315	45	)	)	PUNCT
ejpam-3543	315	46	≥	≥	NOUN
ejpam-3543	315	47	min{λf	min{λf	X
ejpam-3543	315	48	(	(	PUNCT
ejpam-3543	315	49	x	x	X
ejpam-3543	315	50	)	)	PUNCT
ejpam-3543	315	51	,	,	PUNCT
ejpam-3543	315	52	λf	λf	X
ejpam-3543	315	53	(	(	PUNCT
ejpam-3543	315	54	x	x	NOUN
ejpam-3543	315	55	)	)	PUNCT
ejpam-3543	315	56	}	}	PUNCT
ejpam-3543	316	1	=	=	SYM
ejpam-3543	316	2	λf	λf	X
ejpam-3543	316	3	(	(	PUNCT
ejpam-3543	316	4	x	x	NOUN
ejpam-3543	316	5	)	)	PUNCT
ejpam-3543	316	6	.	.	PUNCT
ejpam-3543	317	1	next	next	ADV
ejpam-3543	317	2	,	,	PUNCT
ejpam-3543	317	3	let	let	VERB
ejpam-3543	317	4	x	x	PRON
ejpam-3543	317	5	,	,	PUNCT
ejpam-3543	317	6	y	y	PROPN
ejpam-3543	317	7	∈	∈	PROPN
ejpam-3543	317	8	x.	x.	NOUN
ejpam-3543	317	9	by	by	ADP
ejpam-3543	317	10	(	(	PUNCT
ejpam-3543	317	11	2.1	2.1	NUM
ejpam-3543	317	12	)	)	PUNCT
ejpam-3543	317	13	,	,	PUNCT
ejpam-3543	317	14	we	we	PRON
ejpam-3543	317	15	have	have	VERB
ejpam-3543	317	16	(	(	PUNCT
ejpam-3543	317	17	x	x	X
ejpam-3543	317	18	·	·	PUNCT
ejpam-3543	317	19	y	y	X
ejpam-3543	317	20	)	)	PUNCT
ejpam-3543	317	21	·	·	PUNCT
ejpam-3543	318	1	(	(	PUNCT
ejpam-3543	318	2	x	x	X
ejpam-3543	318	3	·	·	PUNCT
ejpam-3543	318	4	y	y	X
ejpam-3543	318	5	)	)	PUNCT
ejpam-3543	318	6	=	=	SYM
ejpam-3543	318	7	0	0	NUM
ejpam-3543	318	8	,	,	PUNCT
ejpam-3543	318	9	that	that	ADV
ejpam-3543	318	10	is	is	ADV
ejpam-3543	318	11	,	,	PUNCT
ejpam-3543	318	12	x	x	X
ejpam-3543	318	13	·	·	PUNCT
ejpam-3543	318	14	y	y	X
ejpam-3543	318	15	≤	≤	NUM
ejpam-3543	318	16	x	x	X
ejpam-3543	319	1	·	·	PUNCT
ejpam-3543	319	2	y.	y.	NOUN
ejpam-3543	319	3	it	it	PRON
ejpam-3543	319	4	follows	follow	VERB
ejpam-3543	319	5	from	from	ADP
ejpam-3543	319	6	(	(	PUNCT
ejpam-3543	319	7	3.26	3.26	NUM
ejpam-3543	319	8	)	)	PUNCT
ejpam-3543	320	1	that	that	SCONJ
ejpam-3543	320	2	λt	λt	ADP
ejpam-3543	320	3	(	(	PUNCT
ejpam-3543	320	4	y	y	NOUN
ejpam-3543	320	5	)	)	PUNCT
ejpam-3543	320	6	≥	≥	NOUN
ejpam-3543	320	7	min{λt	min{λt	X
ejpam-3543	320	8	(	(	PUNCT
ejpam-3543	320	9	x	x	SYM
ejpam-3543	320	10	·	·	PUNCT
ejpam-3543	320	11	y	y	X
ejpam-3543	320	12	)	)	PUNCT
ejpam-3543	320	13	,	,	PUNCT
ejpam-3543	320	14	λt	λt	X
ejpam-3543	320	15	(	(	PUNCT
ejpam-3543	320	16	x	x	NOUN
ejpam-3543	320	17	)	)	PUNCT
ejpam-3543	320	18	}	}	PUNCT
ejpam-3543	320	19	,	,	PUNCT
ejpam-3543	320	20	λi(y	λi(y	NUM
ejpam-3543	320	21	)	)	PUNCT
ejpam-3543	320	22	≤	≤	NUM
ejpam-3543	320	23	max{λi(x	max{λi(x	NOUN
ejpam-3543	320	24	·	·	PUNCT
ejpam-3543	320	25	y	y	X
ejpam-3543	320	26	)	)	PUNCT
ejpam-3543	320	27	,	,	PUNCT
ejpam-3543	320	28	λi(x	λi(x	NUM
ejpam-3543	320	29	)	)	PUNCT
ejpam-3543	320	30	}	}	PUNCT
ejpam-3543	320	31	,	,	PUNCT
ejpam-3543	320	32	λf	λf	X
ejpam-3543	320	33	(	(	PUNCT
ejpam-3543	320	34	y	y	NOUN
ejpam-3543	320	35	)	)	PUNCT
ejpam-3543	320	36	≥	≥	NOUN
ejpam-3543	320	37	min{λf	min{λf	X
ejpam-3543	320	38	(	(	PUNCT
ejpam-3543	320	39	x	x	PROPN
ejpam-3543	320	40	·	·	PUNCT
ejpam-3543	320	41	y	y	X
ejpam-3543	320	42	)	)	PUNCT
ejpam-3543	320	43	,	,	PUNCT
ejpam-3543	320	44	λf	λf	X
ejpam-3543	320	45	(	(	PUNCT
ejpam-3543	320	46	x	x	NOUN
ejpam-3543	320	47	)	)	PUNCT
ejpam-3543	320	48	}	}	PUNCT
ejpam-3543	320	49	.	.	PUNCT
ejpam-3543	321	1	hence	hence	ADV
ejpam-3543	321	2	,	,	PUNCT
ejpam-3543	321	3	λ	λ	PROPN
ejpam-3543	321	4	is	be	AUX
ejpam-3543	321	5	a	a	DET
ejpam-3543	321	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	321	7	up	up	ADJ
ejpam-3543	321	8	-	-	PUNCT
ejpam-3543	321	9	filter	filter	NOUN
ejpam-3543	321	10	of	of	ADP
ejpam-3543	321	11	x.	x.	PROPN
ejpam-3543	321	12	theorem	theorem	VERB
ejpam-3543	321	13	13	13	NUM
ejpam-3543	321	14	.	.	PUNCT
ejpam-3543	322	1	if	if	SCONJ
ejpam-3543	322	2	λ	λ	PROPN
ejpam-3543	322	3	is	be	AUX
ejpam-3543	322	4	a	a	DET
ejpam-3543	322	5	ns	ns	NOUN
ejpam-3543	322	6	in	in	ADP
ejpam-3543	322	7	x	x	PUNCT
ejpam-3543	322	8	satisfying	satisfy	VERB
ejpam-3543	322	9	the	the	DET
ejpam-3543	322	10	following	follow	VERB
ejpam-3543	322	11	condition	condition	NOUN
ejpam-3543	322	12	:	:	PUNCT
ejpam-3543	322	13	(	(	PUNCT
ejpam-3543	322	14	∀a	∀a	NOUN
ejpam-3543	322	15	,	,	PUNCT
ejpam-3543	322	16	x	x	X
ejpam-3543	322	17	,	,	PUNCT
ejpam-3543	322	18	y	y	PROPN
ejpam-3543	322	19	,	,	PUNCT
ejpam-3543	322	20	z	z	NOUN
ejpam-3543	322	21	∈	∈	PROPN
ejpam-3543	322	22	x	x	X
ejpam-3543	322	23	)	)	PUNCT
ejpam-3543	322	24	a	a	PROPN
ejpam-3543	322	25	≤	≤	NUM
ejpam-3543	323	1	x	x	SYM
ejpam-3543	323	2	·	·	PUNCT
ejpam-3543	323	3	(	(	PUNCT
ejpam-3543	323	4	y	y	X
ejpam-3543	323	5	·	·	PUNCT
ejpam-3543	323	6	z)⇒	z)⇒	NUM
ejpam-3543	323	7			PRON
ejpam-3543	323	8	λt	λt	ADP
ejpam-3543	323	9	(	(	PUNCT
ejpam-3543	323	10	x	x	X
ejpam-3543	323	11	·	·	PUNCT
ejpam-3543	323	12	z	z	X
ejpam-3543	323	13	)	)	PUNCT
ejpam-3543	323	14	≥	≥	NOUN
ejpam-3543	323	15	min{λt	min{λt	X
ejpam-3543	323	16	(	(	PUNCT
ejpam-3543	323	17	a	a	X
ejpam-3543	323	18	)	)	PUNCT
ejpam-3543	323	19	,	,	PUNCT
ejpam-3543	323	20	λt	λt	X
ejpam-3543	323	21	(	(	PUNCT
ejpam-3543	323	22	y	y	NOUN
ejpam-3543	323	23	)	)	PUNCT
ejpam-3543	323	24	}	}	PUNCT
ejpam-3543	323	25	λi(x	λi(x	PUNCT
ejpam-3543	323	26	·	·	PUNCT
ejpam-3543	323	27	z	z	X
ejpam-3543	323	28	)	)	PUNCT
ejpam-3543	323	29	≤	≤	NUM
ejpam-3543	323	30	max{λi(a	max{λi(a	ADV
ejpam-3543	323	31	)	)	PUNCT
ejpam-3543	323	32	,	,	PUNCT
ejpam-3543	323	33	λi(y	λi(y	NOUN
ejpam-3543	323	34	)	)	PUNCT
ejpam-3543	323	35	}	}	PUNCT
ejpam-3543	323	36	λf	λf	X
ejpam-3543	323	37	(	(	PUNCT
ejpam-3543	323	38	x	x	X
ejpam-3543	323	39	·	·	PUNCT
ejpam-3543	323	40	z	z	X
ejpam-3543	323	41	)	)	PUNCT
ejpam-3543	323	42	≥	≥	NOUN
ejpam-3543	323	43	min{λf	min{λf	X
ejpam-3543	323	44	(	(	PUNCT
ejpam-3543	323	45	a	a	NOUN
ejpam-3543	323	46	)	)	PUNCT
ejpam-3543	323	47	,	,	PUNCT
ejpam-3543	323	48	λf	λf	X
ejpam-3543	323	49	(	(	PUNCT
ejpam-3543	323	50	y	y	NOUN
ejpam-3543	323	51	)	)	PUNCT
ejpam-3543	323	52	}	}	PUNCT
ejpam-3543	323	53			NOUN
ejpam-3543	323	54	,	,	PUNCT
ejpam-3543	323	55	(	(	PUNCT
ejpam-3543	323	56	3.27	3.27	NUM
ejpam-3543	323	57	)	)	PUNCT
ejpam-3543	323	58	then	then	ADV
ejpam-3543	323	59	λ	λ	PROPN
ejpam-3543	323	60	is	be	AUX
ejpam-3543	323	61	a	a	DET
ejpam-3543	323	62	neutrosophic	neutrosophic	ADJ
ejpam-3543	323	63	up	up	ADV
ejpam-3543	323	64	-	-	PUNCT
ejpam-3543	323	65	ideal	ideal	NOUN
ejpam-3543	323	66	of	of	ADP
ejpam-3543	323	67	x.	x.	PROPN
ejpam-3543	323	68	m.	m.	PROPN
ejpam-3543	323	69	songsaeng	songsaeng	PROPN
ejpam-3543	323	70	,	,	PUNCT
ejpam-3543	323	71	a.	a.	NOUN
ejpam-3543	323	72	iampan	iampan	PROPN
ejpam-3543	323	73	/	/	SYM
ejpam-3543	323	74	eur	eur	PROPN
ejpam-3543	323	75	.	.	PUNCT
ejpam-3543	324	1	j.	j.	PROPN
ejpam-3543	324	2	pure	pure	PROPN
ejpam-3543	324	3	appl	appl	PROPN
ejpam-3543	324	4	.	.	PROPN
ejpam-3543	324	5	math	math	PROPN
ejpam-3543	324	6	,	,	PUNCT
ejpam-3543	324	7	12	12	NUM
ejpam-3543	324	8	(	(	PUNCT
ejpam-3543	324	9	4	4	NUM
ejpam-3543	324	10	)	)	PUNCT
ejpam-3543	324	11	(	(	PUNCT
ejpam-3543	324	12	2019	2019	NUM
ejpam-3543	324	13	)	)	PUNCT
ejpam-3543	324	14	,	,	PUNCT
ejpam-3543	324	15	1382	1382	NUM
ejpam-3543	324	16	-	-	SYM
ejpam-3543	324	17	1409	1409	NUM
ejpam-3543	324	18	1396	1396	NUM
ejpam-3543	324	19	proof	proof	NOUN
ejpam-3543	324	20	.	.	PUNCT
ejpam-3543	325	1	assume	assume	VERB
ejpam-3543	325	2	that	that	SCONJ
ejpam-3543	325	3	λ	λ	PROPN
ejpam-3543	325	4	is	be	AUX
ejpam-3543	325	5	a	a	DET
ejpam-3543	325	6	ns	ns	NOUN
ejpam-3543	325	7	in	in	ADP
ejpam-3543	325	8	x	x	PUNCT
ejpam-3543	325	9	satisfying	satisfy	VERB
ejpam-3543	325	10	the	the	DET
ejpam-3543	325	11	condition	condition	NOUN
ejpam-3543	325	12	(	(	PUNCT
ejpam-3543	325	13	3.27	3.27	NUM
ejpam-3543	325	14	)	)	PUNCT
ejpam-3543	325	15	.	.	PUNCT
ejpam-3543	326	1	let	let	VERB
ejpam-3543	326	2	x	x	SYM
ejpam-3543	326	3	∈	∈	PROPN
ejpam-3543	326	4	x.	x.	NOUN
ejpam-3543	326	5	by	by	ADP
ejpam-3543	326	6	(	(	PUNCT
ejpam-3543	326	7	up-3	up-3	NOUN
ejpam-3543	326	8	)	)	PUNCT
ejpam-3543	326	9	,	,	PUNCT
ejpam-3543	326	10	we	we	PRON
ejpam-3543	326	11	have	have	VERB
ejpam-3543	326	12	x	x	X
ejpam-3543	326	13	·	·	PUNCT
ejpam-3543	326	14	(	(	PUNCT
ejpam-3543	326	15	0	0	NUM
ejpam-3543	326	16	·	·	PUNCT
ejpam-3543	326	17	(	(	PUNCT
ejpam-3543	326	18	x	x	X
ejpam-3543	326	19	·	·	PUNCT
ejpam-3543	326	20	0	0	NUM
ejpam-3543	326	21	)	)	PUNCT
ejpam-3543	326	22	=	=	SYM
ejpam-3543	327	1	0	0	NUM
ejpam-3543	327	2	,	,	PUNCT
ejpam-3543	327	3	that	that	ADV
ejpam-3543	327	4	is	is	ADV
ejpam-3543	327	5	,	,	PUNCT
ejpam-3543	327	6	x	x	SYM
ejpam-3543	327	7	≤	≤	ADV
ejpam-3543	327	8	0	0	NUM
ejpam-3543	327	9	·	·	PUNCT
ejpam-3543	327	10	(	(	PUNCT
ejpam-3543	327	11	x	x	X
ejpam-3543	327	12	·	·	PUNCT
ejpam-3543	327	13	0	0	NUM
ejpam-3543	327	14	)	)	PUNCT
ejpam-3543	327	15	.	.	PUNCT
ejpam-3543	328	1	it	it	PRON
ejpam-3543	328	2	follows	follow	VERB
ejpam-3543	328	3	from	from	ADP
ejpam-3543	328	4	(	(	PUNCT
ejpam-3543	328	5	3.27	3.27	NUM
ejpam-3543	328	6	)	)	PUNCT
ejpam-3543	329	1	that	that	SCONJ
ejpam-3543	329	2	λt	λt	ADP
ejpam-3543	329	3	(	(	PUNCT
ejpam-3543	329	4	0	0	NUM
ejpam-3543	329	5	)	)	PUNCT
ejpam-3543	329	6	=	=	NOUN
ejpam-3543	329	7	λt	λt	X
ejpam-3543	329	8	(	(	PUNCT
ejpam-3543	329	9	0	0	NUM
ejpam-3543	329	10	·	·	PUNCT
ejpam-3543	329	11	0	0	NUM
ejpam-3543	329	12	)	)	PUNCT
ejpam-3543	329	13	≥	≥	NOUN
ejpam-3543	329	14	min{λt	min{λt	X
ejpam-3543	329	15	(	(	PUNCT
ejpam-3543	329	16	x	x	X
ejpam-3543	329	17	)	)	PUNCT
ejpam-3543	329	18	,	,	PUNCT
ejpam-3543	329	19	λt	λt	X
ejpam-3543	329	20	(	(	PUNCT
ejpam-3543	329	21	x	x	NOUN
ejpam-3543	329	22	)	)	PUNCT
ejpam-3543	329	23	}	}	PUNCT
ejpam-3543	329	24	=	=	SYM
ejpam-3543	329	25	λt	λt	X
ejpam-3543	329	26	(	(	PUNCT
ejpam-3543	329	27	x	x	NOUN
ejpam-3543	329	28	)	)	PUNCT
ejpam-3543	329	29	,	,	PUNCT
ejpam-3543	329	30	(	(	PUNCT
ejpam-3543	329	31	up-2	up-2	NUM
ejpam-3543	329	32	)	)	PUNCT
ejpam-3543	329	33	λi(0	λi(0	X
ejpam-3543	329	34	)	)	PUNCT
ejpam-3543	330	1	=	=	PUNCT
ejpam-3543	330	2	λi(0	λi(0	PROPN
ejpam-3543	330	3	·	·	PUNCT
ejpam-3543	330	4	0	0	NUM
ejpam-3543	330	5	)	)	PUNCT
ejpam-3543	330	6	≤	≤	NUM
ejpam-3543	330	7	max{λi(x	max{λi(x	NOUN
ejpam-3543	330	8	)	)	PUNCT
ejpam-3543	330	9	,	,	PUNCT
ejpam-3543	330	10	λi(x	λi(x	NUM
ejpam-3543	330	11	)	)	PUNCT
ejpam-3543	330	12	}	}	PUNCT
ejpam-3543	330	13	=	=	SYM
ejpam-3543	330	14	λi(x	λi(x	NUM
ejpam-3543	330	15	)	)	PUNCT
ejpam-3543	330	16	,	,	PUNCT
ejpam-3543	330	17	(	(	PUNCT
ejpam-3543	330	18	up-2	up-2	NUM
ejpam-3543	330	19	)	)	PUNCT
ejpam-3543	331	1	λf	λf	X
ejpam-3543	331	2	(	(	PUNCT
ejpam-3543	331	3	0	0	NUM
ejpam-3543	331	4	)	)	PUNCT
ejpam-3543	331	5	=	=	SYM
ejpam-3543	332	1	λf	λf	X
ejpam-3543	332	2	(	(	PUNCT
ejpam-3543	332	3	0	0	NUM
ejpam-3543	332	4	·	·	SYM
ejpam-3543	332	5	0	0	NUM
ejpam-3543	332	6	)	)	PUNCT
ejpam-3543	332	7	≥	≥	NOUN
ejpam-3543	332	8	min{λf	min{λf	X
ejpam-3543	332	9	(	(	PUNCT
ejpam-3543	332	10	x	x	X
ejpam-3543	332	11	)	)	PUNCT
ejpam-3543	332	12	,	,	PUNCT
ejpam-3543	332	13	λf	λf	X
ejpam-3543	332	14	(	(	PUNCT
ejpam-3543	332	15	x	x	NOUN
ejpam-3543	332	16	)	)	PUNCT
ejpam-3543	332	17	}	}	PUNCT
ejpam-3543	332	18	=	=	SYM
ejpam-3543	332	19	λf	λf	X
ejpam-3543	332	20	(	(	PUNCT
ejpam-3543	332	21	x	x	NOUN
ejpam-3543	332	22	)	)	PUNCT
ejpam-3543	332	23	.	.	PUNCT
ejpam-3543	333	1	(	(	PUNCT
ejpam-3543	333	2	up-2	up-2	NUM
ejpam-3543	333	3	)	)	PUNCT
ejpam-3543	333	4	next	next	ADV
ejpam-3543	333	5	,	,	PUNCT
ejpam-3543	333	6	let	let	VERB
ejpam-3543	333	7	x	x	PRON
ejpam-3543	333	8	,	,	PUNCT
ejpam-3543	333	9	y	y	PROPN
ejpam-3543	333	10	,	,	PUNCT
ejpam-3543	333	11	z	z	NOUN
ejpam-3543	333	12	∈	∈	NOUN
ejpam-3543	333	13	x.	x.	NOUN
ejpam-3543	333	14	by	by	ADP
ejpam-3543	333	15	(	(	PUNCT
ejpam-3543	333	16	2.1	2.1	NUM
ejpam-3543	333	17	)	)	PUNCT
ejpam-3543	333	18	,	,	PUNCT
ejpam-3543	333	19	we	we	PRON
ejpam-3543	333	20	have	have	VERB
ejpam-3543	333	21	(	(	PUNCT
ejpam-3543	333	22	x·(y	x·(y	PUNCT
ejpam-3543	333	23	·	·	PUNCT
ejpam-3543	333	24	z))·(x·(y	z))·(x·(y	X
ejpam-3543	333	25	·	·	PUNCT
ejpam-3543	333	26	z	z	NOUN
ejpam-3543	333	27	)	)	PUNCT
ejpam-3543	333	28	)	)	PUNCT
ejpam-3543	334	1	=	=	SYM
ejpam-3543	334	2	0	0	NUM
ejpam-3543	334	3	,	,	PUNCT
ejpam-3543	334	4	that	that	ADV
ejpam-3543	334	5	is	is	ADV
ejpam-3543	334	6	,	,	PUNCT
ejpam-3543	334	7	x·(y	x·(y	PUNCT
ejpam-3543	334	8	·	·	PUNCT
ejpam-3543	334	9	z	z	X
ejpam-3543	334	10	)	)	PUNCT
ejpam-3543	334	11	≤	≤	NOUN
ejpam-3543	334	12	x·(y	x·(y	PUNCT
ejpam-3543	335	1	·	·	PUNCT
ejpam-3543	335	2	z	z	X
ejpam-3543	335	3	)	)	PUNCT
ejpam-3543	335	4	.	.	PUNCT
ejpam-3543	336	1	it	it	PRON
ejpam-3543	336	2	follows	follow	VERB
ejpam-3543	336	3	from	from	ADP
ejpam-3543	336	4	(	(	PUNCT
ejpam-3543	336	5	3.27	3.27	NUM
ejpam-3543	336	6	)	)	PUNCT
ejpam-3543	337	1	that	that	SCONJ
ejpam-3543	337	2	λt	λt	ADP
ejpam-3543	337	3	(	(	PUNCT
ejpam-3543	337	4	x	x	X
ejpam-3543	337	5	·	·	PUNCT
ejpam-3543	337	6	z	z	X
ejpam-3543	337	7	)	)	PUNCT
ejpam-3543	337	8	≥	≥	NOUN
ejpam-3543	337	9	min{λt	min{λt	X
ejpam-3543	337	10	(	(	PUNCT
ejpam-3543	337	11	x	x	X
ejpam-3543	337	12	·	·	PUNCT
ejpam-3543	337	13	(	(	PUNCT
ejpam-3543	337	14	y	y	PROPN
ejpam-3543	337	15	·	·	PUNCT
ejpam-3543	337	16	z	z	NOUN
ejpam-3543	337	17	)	)	PUNCT
ejpam-3543	337	18	)	)	PUNCT
ejpam-3543	337	19	,	,	PUNCT
ejpam-3543	337	20	λt	λt	X
ejpam-3543	337	21	(	(	PUNCT
ejpam-3543	337	22	y	y	NOUN
ejpam-3543	337	23	)	)	PUNCT
ejpam-3543	337	24	}	}	PUNCT
ejpam-3543	337	25	,	,	PUNCT
ejpam-3543	337	26	λi(x	λi(x	X
ejpam-3543	337	27	·	·	PUNCT
ejpam-3543	337	28	z	z	X
ejpam-3543	337	29	)	)	PUNCT
ejpam-3543	337	30	≤	≤	NUM
ejpam-3543	337	31	max{λi(x	max{λi(x	NOUN
ejpam-3543	337	32	·	·	PUNCT
ejpam-3543	337	33	(	(	PUNCT
ejpam-3543	337	34	y	y	PROPN
ejpam-3543	337	35	·	·	PUNCT
ejpam-3543	337	36	z	z	NOUN
ejpam-3543	337	37	)	)	PUNCT
ejpam-3543	337	38	)	)	PUNCT
ejpam-3543	337	39	,	,	PUNCT
ejpam-3543	337	40	λi(y	λi(y	NOUN
ejpam-3543	337	41	)	)	PUNCT
ejpam-3543	337	42	}	}	PUNCT
ejpam-3543	337	43	,	,	PUNCT
ejpam-3543	337	44	λf	λf	X
ejpam-3543	337	45	(	(	PUNCT
ejpam-3543	337	46	x	x	SYM
ejpam-3543	337	47	·	·	PUNCT
ejpam-3543	337	48	z	z	X
ejpam-3543	337	49	)	)	PUNCT
ejpam-3543	337	50	≥	≥	NOUN
ejpam-3543	337	51	min{λf	min{λf	X
ejpam-3543	337	52	(	(	PUNCT
ejpam-3543	337	53	x	x	PART
ejpam-3543	337	54	·	·	PUNCT
ejpam-3543	337	55	(	(	PUNCT
ejpam-3543	337	56	y	y	PROPN
ejpam-3543	337	57	·	·	PUNCT
ejpam-3543	337	58	z	z	NOUN
ejpam-3543	337	59	)	)	PUNCT
ejpam-3543	337	60	)	)	PUNCT
ejpam-3543	337	61	,	,	PUNCT
ejpam-3543	337	62	λf	λf	X
ejpam-3543	337	63	(	(	PUNCT
ejpam-3543	337	64	y	y	NOUN
ejpam-3543	337	65	)	)	PUNCT
ejpam-3543	337	66	}	}	PUNCT
ejpam-3543	337	67	.	.	PUNCT
ejpam-3543	338	1	hence	hence	ADV
ejpam-3543	338	2	,	,	PUNCT
ejpam-3543	338	3	λ	λ	PROPN
ejpam-3543	338	4	is	be	AUX
ejpam-3543	338	5	a	a	DET
ejpam-3543	338	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	338	7	up	up	ADV
ejpam-3543	338	8	-	-	PUNCT
ejpam-3543	338	9	ideal	ideal	NOUN
ejpam-3543	338	10	of	of	ADP
ejpam-3543	338	11	x.	x.	NOUN
ejpam-3543	338	12	for	for	ADP
ejpam-3543	338	13	any	any	DET
ejpam-3543	338	14	fixed	fix	VERB
ejpam-3543	338	15	numbers	number	NOUN
ejpam-3543	338	16	α+	α+	ADP
ejpam-3543	338	17	,	,	PUNCT
ejpam-3543	338	18	α−	α−	PROPN
ejpam-3543	338	19	,	,	PUNCT
ejpam-3543	338	20	β+	β+	NOUN
ejpam-3543	338	21	,	,	PUNCT
ejpam-3543	338	22	β−	β−	PRON
ejpam-3543	338	23	,	,	PUNCT
ejpam-3543	338	24	γ+	γ+	NUM
ejpam-3543	338	25	,	,	PUNCT
ejpam-3543	338	26	γ−	γ−	PROPN
ejpam-3543	338	27	∈	∈	PROPN
ejpam-3543	339	1	[	[	X
ejpam-3543	339	2	0	0	NUM
ejpam-3543	339	3	,	,	PUNCT
ejpam-3543	339	4	1	1	NUM
ejpam-3543	339	5	]	]	PUNCT
ejpam-3543	340	1	such	such	ADJ
ejpam-3543	340	2	that	that	SCONJ
ejpam-3543	340	3	α+	α+	X
ejpam-3543	340	4	>	>	X
ejpam-3543	340	5	α−	α−	PROPN
ejpam-3543	340	6	,	,	PUNCT
ejpam-3543	340	7	β+	β+	PUNCT
ejpam-3543	340	8	>	>	X
ejpam-3543	340	9	β−	β−	PROPN
ejpam-3543	340	10	,	,	PUNCT
ejpam-3543	340	11	γ+	γ+	PUNCT
ejpam-3543	340	12	>	>	X
ejpam-3543	340	13	γ−	γ−	PROPN
ejpam-3543	340	14	and	and	CCONJ
ejpam-3543	340	15	a	a	DET
ejpam-3543	340	16	nonempty	nonempty	ADJ
ejpam-3543	340	17	subsetg	subsetg	NOUN
ejpam-3543	340	18	ofx	ofx	NOUN
ejpam-3543	340	19	,	,	PUNCT
ejpam-3543	340	20	a	a	DET
ejpam-3543	340	21	ns	ns	ADJ
ejpam-3543	340	22	λg[α	λg[α	PROPN
ejpam-3543	340	23	+	+	PROPN
ejpam-3543	340	24	,	,	PUNCT
ejpam-3543	340	25	β−,γ+	β−,γ+	X
ejpam-3543	340	26	α−,β+,γ−	α−,β+,γ−	NOUN
ejpam-3543	340	27	]	]	PUNCT
ejpam-3543	340	28	=	=	SYM
ejpam-3543	340	29	(	(	PUNCT
ejpam-3543	340	30	x	x	X
ejpam-3543	340	31	,	,	PUNCT
ejpam-3543	340	32	λgt	λgt	PROPN
ejpam-3543	341	1	[	[	X
ejpam-3543	341	2	α	α	X
ejpam-3543	341	3	+	+	X
ejpam-3543	342	1	α−	α−	ADP
ejpam-3543	342	2	]	]	PUNCT
ejpam-3543	342	3	,	,	PUNCT
ejpam-3543	342	4	λgi	λgi	X
ejpam-3543	342	5	[	[	X
ejpam-3543	342	6	β	β	X
ejpam-3543	342	7	−	−	NOUN
ejpam-3543	342	8	β+	β+	PUNCT
ejpam-3543	342	9	]	]	PUNCT
ejpam-3543	342	10	,	,	PUNCT
ejpam-3543	342	11	λgf	λgf	X
ejpam-3543	343	1	[	[	X
ejpam-3543	343	2	γ	γ	X
ejpam-3543	343	3	+	+	X
ejpam-3543	343	4	γ−	γ−	PROPN
ejpam-3543	343	5	]	]	PUNCT
ejpam-3543	343	6	)	)	PUNCT
ejpam-3543	343	7	in	in	ADP
ejpam-3543	343	8	x	x	SYM
ejpam-3543	344	1	where	where	SCONJ
ejpam-3543	344	2	λgt	λgt	PRON
ejpam-3543	345	1	[	[	X
ejpam-3543	345	2	α	α	X
ejpam-3543	345	3	+	+	X
ejpam-3543	346	1	α−	α−	ADP
ejpam-3543	346	2	]	]	PUNCT
ejpam-3543	346	3	,	,	PUNCT
ejpam-3543	346	4	λgi	λgi	X
ejpam-3543	346	5	[	[	X
ejpam-3543	346	6	β	β	X
ejpam-3543	346	7	−	−	NOUN
ejpam-3543	346	8	β+	β+	PUNCT
ejpam-3543	346	9	]	]	X
ejpam-3543	346	10	,	,	PUNCT
ejpam-3543	346	11	and	and	CCONJ
ejpam-3543	346	12	λgf	λgf	X
ejpam-3543	347	1	[	[	X
ejpam-3543	347	2	γ	γ	X
ejpam-3543	347	3	+	+	CCONJ
ejpam-3543	347	4	γ−	γ−	PROPN
ejpam-3543	347	5	]	]	PUNCT
ejpam-3543	347	6	are	be	AUX
ejpam-3543	347	7	functions	function	NOUN
ejpam-3543	347	8	on	on	ADP
ejpam-3543	347	9	x	x	PUNCT
ejpam-3543	347	10	which	which	PRON
ejpam-3543	347	11	are	be	AUX
ejpam-3543	347	12	given	give	VERB
ejpam-3543	347	13	as	as	SCONJ
ejpam-3543	347	14	follows	follow	VERB
ejpam-3543	347	15	:	:	PUNCT
ejpam-3543	347	16	λgt	λgt	PROPN
ejpam-3543	348	1	[	[	X
ejpam-3543	348	2	α	α	X
ejpam-3543	348	3	+	+	X
ejpam-3543	349	1	α−	α−	ADP
ejpam-3543	349	2	]	]	X
ejpam-3543	349	3	(	(	PUNCT
ejpam-3543	349	4	x	x	X
ejpam-3543	349	5	)	)	PUNCT
ejpam-3543	349	6	=	=	PRON
ejpam-3543	349	7	{	{	PUNCT
ejpam-3543	349	8	α+	α+	X
ejpam-3543	349	9	if	if	SCONJ
ejpam-3543	349	10	x	x	SYM
ejpam-3543	349	11	∈	∈	PROPN
ejpam-3543	349	12	g	g	NOUN
ejpam-3543	349	13	,	,	PUNCT
ejpam-3543	349	14	α−	α−	ADP
ejpam-3543	349	15	otherwise	otherwise	ADV
ejpam-3543	349	16	,	,	PUNCT
ejpam-3543	349	17	λgi	λgi	X
ejpam-3543	350	1	[	[	X
ejpam-3543	350	2	β	β	X
ejpam-3543	350	3	−	−	NOUN
ejpam-3543	350	4	β+	β+	PUNCT
ejpam-3543	350	5	]	]	X
ejpam-3543	350	6	(	(	PUNCT
ejpam-3543	350	7	x	x	X
ejpam-3543	350	8	)	)	PUNCT
ejpam-3543	350	9	=	=	NOUN
ejpam-3543	351	1	{	{	PUNCT
ejpam-3543	351	2	β−	β−	INTJ
ejpam-3543	351	3	if	if	SCONJ
ejpam-3543	351	4	x	x	PROPN
ejpam-3543	351	5	∈	∈	PROPN
ejpam-3543	351	6	g	g	PROPN
ejpam-3543	351	7	,	,	PUNCT
ejpam-3543	351	8	β+	β+	PUNCT
ejpam-3543	351	9	otherwise	otherwise	ADV
ejpam-3543	351	10	,	,	PUNCT
ejpam-3543	351	11	λgf	λgf	X
ejpam-3543	352	1	[	[	X
ejpam-3543	352	2	γ	γ	X
ejpam-3543	352	3	+	+	X
ejpam-3543	352	4	γ−	γ−	PROPN
ejpam-3543	352	5	]	]	PUNCT
ejpam-3543	352	6	(	(	PUNCT
ejpam-3543	352	7	x	x	X
ejpam-3543	352	8	)	)	PUNCT
ejpam-3543	352	9	=	=	PRON
ejpam-3543	352	10	{	{	PUNCT
ejpam-3543	352	11	γ+	γ+	PUNCT
ejpam-3543	352	12	if	if	SCONJ
ejpam-3543	352	13	x	x	PROPN
ejpam-3543	352	14	∈	∈	PROPN
ejpam-3543	352	15	g	g	NOUN
ejpam-3543	352	16	,	,	PUNCT
ejpam-3543	352	17	γ−	γ−	PROPN
ejpam-3543	352	18	otherwise	otherwise	ADV
ejpam-3543	352	19	.	.	PUNCT
ejpam-3543	353	1	lemma	lemma	PROPN
ejpam-3543	354	1	3	3	X
ejpam-3543	354	2	.	.	PUNCT
ejpam-3543	355	1	if	if	SCONJ
ejpam-3543	355	2	the	the	DET
ejpam-3543	355	3	constant	constant	ADJ
ejpam-3543	355	4	0	0	NUM
ejpam-3543	355	5	of	of	ADP
ejpam-3543	355	6	x	x	PRON
ejpam-3543	355	7	is	be	AUX
ejpam-3543	355	8	in	in	ADP
ejpam-3543	355	9	a	a	DET
ejpam-3543	355	10	nonempty	nonempty	NOUN
ejpam-3543	355	11	subset	subset	VERB
ejpam-3543	355	12	g	g	NOUN
ejpam-3543	355	13	of	of	ADP
ejpam-3543	355	14	x	x	PROPN
ejpam-3543	355	15	,	,	PUNCT
ejpam-3543	355	16	then	then	ADV
ejpam-3543	355	17	a	a	DET
ejpam-3543	355	18	ns	ns	ADJ
ejpam-3543	355	19	λg[α	λg[α	PROPN
ejpam-3543	355	20	+	+	PROPN
ejpam-3543	355	21	,	,	PUNCT
ejpam-3543	355	22	β−,γ+	β−,γ+	X
ejpam-3543	355	23	α−,β+,γ−	α−,β+,γ−	VERB
ejpam-3543	355	24	]	]	PUNCT
ejpam-3543	355	25	in	in	ADP
ejpam-3543	355	26	x	x	X
ejpam-3543	355	27	satisfies	satisfy	VERB
ejpam-3543	355	28	the	the	DET
ejpam-3543	355	29	conditions	condition	NOUN
ejpam-3543	355	30	(	(	PUNCT
ejpam-3543	355	31	3.6	3.6	NUM
ejpam-3543	355	32	)	)	PUNCT
ejpam-3543	355	33	,	,	PUNCT
ejpam-3543	355	34	(	(	PUNCT
ejpam-3543	355	35	3.7	3.7	NUM
ejpam-3543	355	36	)	)	PUNCT
ejpam-3543	355	37	,	,	PUNCT
ejpam-3543	355	38	and	and	CCONJ
ejpam-3543	355	39	(	(	PUNCT
ejpam-3543	355	40	3.8	3.8	NUM
ejpam-3543	355	41	)	)	PUNCT
ejpam-3543	355	42	.	.	PUNCT
ejpam-3543	356	1	proof	proof	NOUN
ejpam-3543	356	2	.	.	PUNCT
ejpam-3543	357	1	if	if	SCONJ
ejpam-3543	357	2	0	0	NUM
ejpam-3543	357	3	∈	∈	PROPN
ejpam-3543	357	4	g	g	NOUN
ejpam-3543	357	5	,	,	PUNCT
ejpam-3543	357	6	then	then	ADV
ejpam-3543	357	7	λgt	λgt	PRON
ejpam-3543	358	1	[	[	X
ejpam-3543	358	2	α	α	X
ejpam-3543	358	3	+	+	X
ejpam-3543	359	1	α−	α−	ADP
ejpam-3543	359	2	]	]	X
ejpam-3543	359	3	(	(	PUNCT
ejpam-3543	359	4	0	0	NUM
ejpam-3543	359	5	)	)	PUNCT
ejpam-3543	359	6	=	=	SYM
ejpam-3543	359	7	α+	α+	X
ejpam-3543	359	8	,	,	PUNCT
ejpam-3543	359	9	λgi	λgi	X
ejpam-3543	360	1	[	[	X
ejpam-3543	360	2	β	β	X
ejpam-3543	360	3	−	−	NOUN
ejpam-3543	360	4	β+	β+	PUNCT
ejpam-3543	360	5	]	]	X
ejpam-3543	360	6	(	(	PUNCT
ejpam-3543	360	7	0	0	NUM
ejpam-3543	360	8	)	)	PUNCT
ejpam-3543	360	9	=	=	SYM
ejpam-3543	360	10	β−	β−	PROPN
ejpam-3543	360	11	,	,	PUNCT
ejpam-3543	360	12	λgf	λgf	X
ejpam-3543	361	1	[	[	X
ejpam-3543	361	2	γ	γ	X
ejpam-3543	361	3	+	+	X
ejpam-3543	361	4	γ−	γ−	PROPN
ejpam-3543	361	5	]	]	PUNCT
ejpam-3543	361	6	(	(	PUNCT
ejpam-3543	361	7	0	0	NUM
ejpam-3543	361	8	)	)	PUNCT
ejpam-3543	361	9	=	=	PRON
ejpam-3543	361	10	γ+	γ+	PROPN
ejpam-3543	361	11	.	.	PUNCT
ejpam-3543	362	1	thus	thus	ADV
ejpam-3543	362	2	(	(	PUNCT
ejpam-3543	362	3	∀x	∀x	X
ejpam-3543	362	4	∈	∈	PROPN
ejpam-3543	362	5	x	x	NOUN
ejpam-3543	362	6	)	)	PUNCT
ejpam-3543	362	7			NOUN
ejpam-3543	362	8	λgt	λgt	X
ejpam-3543	363	1	[	[	X
ejpam-3543	363	2	α	α	X
ejpam-3543	363	3	+	+	X
ejpam-3543	364	1	α−	α−	ADP
ejpam-3543	364	2	]	]	X
ejpam-3543	364	3	(	(	PUNCT
ejpam-3543	364	4	0	0	NUM
ejpam-3543	364	5	)	)	PUNCT
ejpam-3543	364	6	=	=	SYM
ejpam-3543	364	7	α+	α+	PUNCT
ejpam-3543	364	8	≥	≥	NOUN
ejpam-3543	364	9	λgt	λgt	X
ejpam-3543	365	1	[	[	X
ejpam-3543	365	2	α	α	X
ejpam-3543	365	3	+	+	X
ejpam-3543	366	1	α−	α−	ADP
ejpam-3543	366	2	]	]	X
ejpam-3543	366	3	(	(	PUNCT
ejpam-3543	366	4	x	x	X
ejpam-3543	366	5	)	)	PUNCT
ejpam-3543	366	6	λgi	λgi	NOUN
ejpam-3543	367	1	[	[	X
ejpam-3543	367	2	β	β	X
ejpam-3543	367	3	−	−	NOUN
ejpam-3543	367	4	β+	β+	PUNCT
ejpam-3543	367	5	]	]	X
ejpam-3543	367	6	(	(	PUNCT
ejpam-3543	367	7	0	0	NUM
ejpam-3543	367	8	)	)	PUNCT
ejpam-3543	367	9	=	=	SYM
ejpam-3543	368	1	β−	β−	PUNCT
ejpam-3543	368	2	≤	≤	NUM
ejpam-3543	368	3	λgi	λgi	NOUN
ejpam-3543	369	1	[	[	X
ejpam-3543	369	2	β	β	X
ejpam-3543	369	3	−	−	NOUN
ejpam-3543	369	4	β+	β+	PUNCT
ejpam-3543	369	5	]	]	X
ejpam-3543	369	6	(	(	PUNCT
ejpam-3543	369	7	x	x	X
ejpam-3543	369	8	)	)	PUNCT
ejpam-3543	369	9	λgf	λgf	NOUN
ejpam-3543	370	1	[	[	X
ejpam-3543	370	2	γ	γ	X
ejpam-3543	370	3	+	+	X
ejpam-3543	370	4	γ−	γ−	PROPN
ejpam-3543	370	5	]	]	PUNCT
ejpam-3543	370	6	(	(	PUNCT
ejpam-3543	370	7	0	0	NUM
ejpam-3543	370	8	)	)	PUNCT
ejpam-3543	370	9	=	=	PRON
ejpam-3543	370	10	γ+	γ+	PUNCT
ejpam-3543	370	11	≥	≥	NOUN
ejpam-3543	371	1	λgf	λgf	X
ejpam-3543	372	1	[	[	X
ejpam-3543	372	2	γ	γ	X
ejpam-3543	372	3	+	+	X
ejpam-3543	372	4	γ−	γ−	PROPN
ejpam-3543	372	5	]	]	PUNCT
ejpam-3543	372	6	(	(	PUNCT
ejpam-3543	372	7	x	x	X
ejpam-3543	372	8	)	)	PUNCT
ejpam-3543	372	9			NOUN
ejpam-3543	372	10	.	.	PUNCT
ejpam-3543	373	1	hence	hence	ADV
ejpam-3543	373	2	,	,	PUNCT
ejpam-3543	373	3	λg[α	λg[α	PROPN
ejpam-3543	373	4	+	+	PROPN
ejpam-3543	373	5	,	,	PUNCT
ejpam-3543	373	6	β−,γ+	β−,γ+	X
ejpam-3543	373	7	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	373	8	]	]	PUNCT
ejpam-3543	373	9	satisfies	satisfy	VERB
ejpam-3543	373	10	the	the	DET
ejpam-3543	373	11	conditions	condition	NOUN
ejpam-3543	373	12	(	(	PUNCT
ejpam-3543	373	13	3.6	3.6	NUM
ejpam-3543	373	14	)	)	PUNCT
ejpam-3543	373	15	,	,	PUNCT
ejpam-3543	373	16	(	(	PUNCT
ejpam-3543	373	17	3.7	3.7	NUM
ejpam-3543	373	18	)	)	PUNCT
ejpam-3543	373	19	,	,	PUNCT
ejpam-3543	373	20	and	and	CCONJ
ejpam-3543	373	21	(	(	PUNCT
ejpam-3543	373	22	3.8	3.8	NUM
ejpam-3543	373	23	)	)	PUNCT
ejpam-3543	373	24	.	.	PUNCT
ejpam-3543	374	1	lemma	lemma	PROPN
ejpam-3543	374	2	4	4	X
ejpam-3543	374	3	.	.	PUNCT
ejpam-3543	375	1	if	if	SCONJ
ejpam-3543	375	2	a	a	DET
ejpam-3543	375	3	ns	ns	ADJ
ejpam-3543	375	4	λg[α	λg[α	PROPN
ejpam-3543	375	5	+	+	PROPN
ejpam-3543	375	6	,	,	PUNCT
ejpam-3543	375	7	β−,γ+	β−,γ+	X
ejpam-3543	375	8	α−,β+,γ−	α−,β+,γ−	VERB
ejpam-3543	375	9	]	]	PUNCT
ejpam-3543	375	10	in	in	ADP
ejpam-3543	375	11	x	x	X
ejpam-3543	375	12	satisfies	satisfie	NOUN
ejpam-3543	375	13	the	the	DET
ejpam-3543	375	14	condition	condition	NOUN
ejpam-3543	375	15	(	(	PUNCT
ejpam-3543	375	16	3.6	3.6	NUM
ejpam-3543	375	17	)	)	PUNCT
ejpam-3543	375	18	(	(	PUNCT
ejpam-3543	375	19	resp	resp	NOUN
ejpam-3543	375	20	.	.	PUNCT
ejpam-3543	375	21	,	,	PUNCT
ejpam-3543	375	22	(	(	PUNCT
ejpam-3543	375	23	3.7	3.7	NUM
ejpam-3543	375	24	)	)	PUNCT
ejpam-3543	375	25	,	,	PUNCT
ejpam-3543	375	26	(	(	PUNCT
ejpam-3543	375	27	3.8	3.8	NUM
ejpam-3543	375	28	)	)	PUNCT
ejpam-3543	375	29	)	)	PUNCT
ejpam-3543	375	30	,	,	PUNCT
ejpam-3543	375	31	then	then	ADV
ejpam-3543	375	32	the	the	DET
ejpam-3543	375	33	constant	constant	ADJ
ejpam-3543	375	34	0	0	NUM
ejpam-3543	375	35	of	of	ADP
ejpam-3543	375	36	x	x	PRON
ejpam-3543	375	37	is	be	AUX
ejpam-3543	375	38	in	in	ADP
ejpam-3543	375	39	a	a	DET
ejpam-3543	375	40	nonempty	nonempty	NOUN
ejpam-3543	375	41	subset	subset	VERB
ejpam-3543	375	42	g	g	PROPN
ejpam-3543	375	43	of	of	ADP
ejpam-3543	375	44	x.	x.	PROPN
ejpam-3543	375	45	m.	m.	PROPN
ejpam-3543	375	46	songsaeng	songsaeng	PROPN
ejpam-3543	375	47	,	,	PUNCT
ejpam-3543	375	48	a.	a.	NOUN
ejpam-3543	375	49	iampan	iampan	PROPN
ejpam-3543	375	50	/	/	SYM
ejpam-3543	375	51	eur	eur	PROPN
ejpam-3543	375	52	.	.	PUNCT
ejpam-3543	376	1	j.	j.	PROPN
ejpam-3543	376	2	pure	pure	PROPN
ejpam-3543	376	3	appl	appl	PROPN
ejpam-3543	376	4	.	.	PROPN
ejpam-3543	376	5	math	math	PROPN
ejpam-3543	376	6	,	,	PUNCT
ejpam-3543	376	7	12	12	NUM
ejpam-3543	376	8	(	(	PUNCT
ejpam-3543	376	9	4	4	NUM
ejpam-3543	376	10	)	)	PUNCT
ejpam-3543	376	11	(	(	PUNCT
ejpam-3543	376	12	2019	2019	NUM
ejpam-3543	376	13	)	)	PUNCT
ejpam-3543	376	14	,	,	PUNCT
ejpam-3543	376	15	1382	1382	NUM
ejpam-3543	376	16	-	-	SYM
ejpam-3543	376	17	1409	1409	NUM
ejpam-3543	376	18	1397	1397	NUM
ejpam-3543	376	19	proof	proof	NOUN
ejpam-3543	376	20	.	.	PUNCT
ejpam-3543	377	1	assume	assume	VERB
ejpam-3543	377	2	that	that	SCONJ
ejpam-3543	377	3	the	the	DET
ejpam-3543	377	4	ns	ns	ADJ
ejpam-3543	377	5	λg[α	λg[α	PROPN
ejpam-3543	377	6	+	+	PROPN
ejpam-3543	377	7	,	,	PUNCT
ejpam-3543	377	8	β−,γ+	β−,γ+	X
ejpam-3543	377	9	α−,β+,γ−	α−,β+,γ−	VERB
ejpam-3543	377	10	]	]	PUNCT
ejpam-3543	377	11	in	in	ADP
ejpam-3543	377	12	x	x	X
ejpam-3543	377	13	satisfies	satisfie	NOUN
ejpam-3543	377	14	the	the	DET
ejpam-3543	377	15	condition	condition	NOUN
ejpam-3543	377	16	(	(	PUNCT
ejpam-3543	377	17	3.6	3.6	NUM
ejpam-3543	377	18	)	)	PUNCT
ejpam-3543	377	19	.	.	PUNCT
ejpam-3543	378	1	then	then	ADV
ejpam-3543	378	2	λgt	λgt	PRON
ejpam-3543	379	1	[	[	X
ejpam-3543	379	2	α	α	X
ejpam-3543	379	3	+	+	X
ejpam-3543	380	1	α−	α−	ADP
ejpam-3543	380	2	]	]	X
ejpam-3543	380	3	(	(	PUNCT
ejpam-3543	380	4	0	0	NUM
ejpam-3543	380	5	)	)	PUNCT
ejpam-3543	380	6	≥	≥	NOUN
ejpam-3543	381	1	λgt	λgt	X
ejpam-3543	382	1	[	[	X
ejpam-3543	382	2	α	α	X
ejpam-3543	382	3	+	+	X
ejpam-3543	383	1	α−	α−	ADP
ejpam-3543	383	2	]	]	X
ejpam-3543	383	3	(	(	PUNCT
ejpam-3543	383	4	x	x	X
ejpam-3543	383	5	)	)	PUNCT
ejpam-3543	383	6	for	for	ADP
ejpam-3543	383	7	all	all	DET
ejpam-3543	383	8	x	x	SYM
ejpam-3543	383	9	∈	∈	PROPN
ejpam-3543	383	10	x.	x.	NOUN
ejpam-3543	383	11	since	since	SCONJ
ejpam-3543	383	12	g	g	PROPN
ejpam-3543	383	13	is	be	AUX
ejpam-3543	383	14	nonempty	nonempty	ADJ
ejpam-3543	383	15	,	,	PUNCT
ejpam-3543	383	16	there	there	PRON
ejpam-3543	383	17	exists	exist	VERB
ejpam-3543	383	18	g	g	PROPN
ejpam-3543	383	19	∈	∈	PROPN
ejpam-3543	383	20	g.	g.	NOUN
ejpam-3543	384	1	thus	thus	ADV
ejpam-3543	384	2	λgt	λgt	PRON
ejpam-3543	385	1	[	[	X
ejpam-3543	385	2	α	α	X
ejpam-3543	385	3	+	+	X
ejpam-3543	386	1	α−	α−	ADP
ejpam-3543	386	2	]	]	X
ejpam-3543	386	3	(	(	PUNCT
ejpam-3543	386	4	g	g	NOUN
ejpam-3543	386	5	)	)	PUNCT
ejpam-3543	386	6	=	=	SYM
ejpam-3543	386	7	α+	α+	PUNCT
ejpam-3543	386	8	and	and	CCONJ
ejpam-3543	386	9	so	so	ADV
ejpam-3543	386	10	λgt	λgt	PRON
ejpam-3543	387	1	[	[	X
ejpam-3543	387	2	α	α	X
ejpam-3543	387	3	+	+	X
ejpam-3543	388	1	α−	α−	ADP
ejpam-3543	388	2	]	]	X
ejpam-3543	388	3	(	(	PUNCT
ejpam-3543	388	4	0	0	NUM
ejpam-3543	388	5	)	)	PUNCT
ejpam-3543	388	6	≥	≥	NOUN
ejpam-3543	389	1	λgt	λgt	X
ejpam-3543	390	1	[	[	X
ejpam-3543	390	2	α	α	X
ejpam-3543	390	3	+	+	X
ejpam-3543	391	1	α−	α−	ADP
ejpam-3543	391	2	]	]	X
ejpam-3543	391	3	(	(	PUNCT
ejpam-3543	391	4	g	g	NOUN
ejpam-3543	391	5	)	)	PUNCT
ejpam-3543	391	6	=	=	SYM
ejpam-3543	391	7	α+	α+	PUNCT
ejpam-3543	391	8	≥	≥	NOUN
ejpam-3543	391	9	λgt	λgt	X
ejpam-3543	392	1	[	[	X
ejpam-3543	392	2	α	α	X
ejpam-3543	392	3	+	+	X
ejpam-3543	393	1	α−	α−	ADP
ejpam-3543	393	2	]	]	X
ejpam-3543	393	3	(	(	PUNCT
ejpam-3543	393	4	0	0	NUM
ejpam-3543	393	5	)	)	PUNCT
ejpam-3543	393	6	,	,	PUNCT
ejpam-3543	393	7	that	that	ADV
ejpam-3543	393	8	is	is	ADV
ejpam-3543	393	9	,	,	PUNCT
ejpam-3543	393	10	λgt	λgt	PROPN
ejpam-3543	394	1	[	[	X
ejpam-3543	394	2	α	α	X
ejpam-3543	394	3	+	+	X
ejpam-3543	395	1	α−	α−	ADP
ejpam-3543	395	2	]	]	X
ejpam-3543	395	3	(	(	PUNCT
ejpam-3543	395	4	0	0	NUM
ejpam-3543	395	5	)	)	PUNCT
ejpam-3543	395	6	=	=	SYM
ejpam-3543	395	7	α+	α+	NOUN
ejpam-3543	395	8	.	.	PUNCT
ejpam-3543	396	1	hence	hence	ADV
ejpam-3543	396	2	,	,	PUNCT
ejpam-3543	396	3	0	0	NUM
ejpam-3543	396	4	∈	∈	PROPN
ejpam-3543	396	5	g.	g.	NOUN
ejpam-3543	396	6	theorem	theorem	VERB
ejpam-3543	396	7	14	14	NUM
ejpam-3543	396	8	.	.	PUNCT
ejpam-3543	397	1	a	a	DET
ejpam-3543	397	2	ns	ns	ADJ
ejpam-3543	397	3	λg[α	λg[α	PROPN
ejpam-3543	397	4	+	+	PROPN
ejpam-3543	397	5	,	,	PUNCT
ejpam-3543	397	6	β−,γ+	β−,γ+	X
ejpam-3543	397	7	α−,β+,γ−	α−,β+,γ−	VERB
ejpam-3543	397	8	]	]	PUNCT
ejpam-3543	397	9	in	in	ADP
ejpam-3543	397	10	x	x	SYM
ejpam-3543	397	11	is	be	AUX
ejpam-3543	397	12	a	a	DET
ejpam-3543	397	13	neutrosophic	neutrosophic	ADJ
ejpam-3543	397	14	up	up	ADP
ejpam-3543	397	15	-	-	PUNCT
ejpam-3543	397	16	subalgebra	subalgebra	NOUN
ejpam-3543	397	17	of	of	ADP
ejpam-3543	397	18	x	x	PRON
ejpam-3543	397	19	if	if	SCONJ
ejpam-3543	397	20	and	and	CCONJ
ejpam-3543	397	21	only	only	ADV
ejpam-3543	397	22	if	if	SCONJ
ejpam-3543	397	23	a	a	DET
ejpam-3543	397	24	nonempty	nonempty	NOUN
ejpam-3543	397	25	subset	subset	VERB
ejpam-3543	397	26	g	g	PROPN
ejpam-3543	397	27	of	of	ADP
ejpam-3543	397	28	x	x	PUNCT
ejpam-3543	397	29	is	be	AUX
ejpam-3543	397	30	a	a	DET
ejpam-3543	397	31	up	up	ADJ
ejpam-3543	397	32	-	-	PUNCT
ejpam-3543	397	33	subalgebra	subalgebra	NOUN
ejpam-3543	397	34	of	of	ADP
ejpam-3543	397	35	x.	x.	NOUN
ejpam-3543	397	36	proof	proof	PROPN
ejpam-3543	397	37	.	.	PUNCT
ejpam-3543	398	1	assume	assume	VERB
ejpam-3543	398	2	that	that	SCONJ
ejpam-3543	398	3	λg[α	λg[α	PROPN
ejpam-3543	398	4	+	+	NOUN
ejpam-3543	398	5	,	,	PUNCT
ejpam-3543	398	6	β−,γ+	β−,γ+	X
ejpam-3543	398	7	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	398	8	]	]	PUNCT
ejpam-3543	398	9	is	be	AUX
ejpam-3543	398	10	a	a	DET
ejpam-3543	398	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	398	12	up	up	ADP
ejpam-3543	398	13	-	-	PUNCT
ejpam-3543	398	14	subalgebra	subalgebra	NOUN
ejpam-3543	398	15	of	of	ADP
ejpam-3543	398	16	x.	x.	NOUN
ejpam-3543	398	17	let	let	VERB
ejpam-3543	398	18	x	x	PRON
ejpam-3543	398	19	,	,	PUNCT
ejpam-3543	398	20	y	y	PROPN
ejpam-3543	398	21	∈	∈	PROPN
ejpam-3543	398	22	g.	g.	NOUN
ejpam-3543	399	1	then	then	ADV
ejpam-3543	399	2	λgt	λgt	PRON
ejpam-3543	400	1	[	[	X
ejpam-3543	400	2	α	α	X
ejpam-3543	400	3	+	+	X
ejpam-3543	401	1	α−	α−	ADP
ejpam-3543	401	2	]	]	X
ejpam-3543	401	3	(	(	PUNCT
ejpam-3543	401	4	x	x	X
ejpam-3543	401	5	)	)	PUNCT
ejpam-3543	401	6	=	=	SYM
ejpam-3543	401	7	α+	α+	NOUN
ejpam-3543	401	8	=	=	PUNCT
ejpam-3543	401	9	λgt	λgt	X
ejpam-3543	402	1	[	[	X
ejpam-3543	402	2	α	α	X
ejpam-3543	402	3	+	+	X
ejpam-3543	403	1	α−	α−	ADP
ejpam-3543	403	2	]	]	X
ejpam-3543	403	3	(	(	PUNCT
ejpam-3543	403	4	y	y	NOUN
ejpam-3543	403	5	)	)	PUNCT
ejpam-3543	403	6	.	.	PUNCT
ejpam-3543	404	1	thus	thus	ADV
ejpam-3543	404	2	λgt	λgt	PRON
ejpam-3543	405	1	[	[	X
ejpam-3543	405	2	α	α	X
ejpam-3543	405	3	+	+	X
ejpam-3543	406	1	α−	α−	ADP
ejpam-3543	406	2	]	]	X
ejpam-3543	406	3	(	(	PUNCT
ejpam-3543	406	4	x	x	SYM
ejpam-3543	406	5	·	·	PUNCT
ejpam-3543	406	6	y	y	X
ejpam-3543	406	7	)	)	PUNCT
ejpam-3543	406	8	≥	≥	NOUN
ejpam-3543	406	9	min{λgt	min{λgt	VERB
ejpam-3543	407	1	[	[	X
ejpam-3543	407	2	α	α	X
ejpam-3543	407	3	+	+	X
ejpam-3543	408	1	α−	α−	ADP
ejpam-3543	408	2	]	]	X
ejpam-3543	408	3	(	(	PUNCT
ejpam-3543	408	4	x	x	NOUN
ejpam-3543	408	5	)	)	PUNCT
ejpam-3543	408	6	,	,	PUNCT
ejpam-3543	408	7	λgt	λgt	X
ejpam-3543	409	1	[	[	X
ejpam-3543	409	2	α	α	X
ejpam-3543	409	3	+	+	X
ejpam-3543	410	1	α−	α−	ADP
ejpam-3543	410	2	]	]	X
ejpam-3543	410	3	(	(	PUNCT
ejpam-3543	410	4	y	y	NOUN
ejpam-3543	410	5	)	)	PUNCT
ejpam-3543	410	6	}	}	PUNCT
ejpam-3543	410	7	=	=	SYM
ejpam-3543	410	8	α+	α+	PUNCT
ejpam-3543	410	9	≥	≥	NOUN
ejpam-3543	410	10	λgt	λgt	X
ejpam-3543	411	1	[	[	X
ejpam-3543	411	2	α	α	X
ejpam-3543	411	3	+	+	X
ejpam-3543	412	1	α−	α−	ADP
ejpam-3543	412	2	]	]	X
ejpam-3543	412	3	(	(	PUNCT
ejpam-3543	412	4	x	x	SYM
ejpam-3543	412	5	·	·	PUNCT
ejpam-3543	412	6	y	y	X
ejpam-3543	412	7	)	)	PUNCT
ejpam-3543	412	8	(	(	PUNCT
ejpam-3543	412	9	3.3	3.3	NUM
ejpam-3543	412	10	)	)	PUNCT
ejpam-3543	412	11	and	and	CCONJ
ejpam-3543	412	12	so	so	ADV
ejpam-3543	412	13	λgt	λgt	PRON
ejpam-3543	413	1	[	[	X
ejpam-3543	413	2	α	α	X
ejpam-3543	413	3	+	+	X
ejpam-3543	414	1	α−	α−	ADP
ejpam-3543	414	2	]	]	X
ejpam-3543	414	3	(	(	PUNCT
ejpam-3543	414	4	x	x	SYM
ejpam-3543	414	5	·	·	PUNCT
ejpam-3543	414	6	y	y	X
ejpam-3543	414	7	)	)	PUNCT
ejpam-3543	414	8	=	=	SYM
ejpam-3543	414	9	α+	α+	NOUN
ejpam-3543	414	10	.	.	PUNCT
ejpam-3543	415	1	thus	thus	ADV
ejpam-3543	415	2	x	x	X
ejpam-3543	415	3	·	·	PUNCT
ejpam-3543	415	4	y	y	X
ejpam-3543	415	5	∈	∈	PROPN
ejpam-3543	415	6	g.	g.	NOUN
ejpam-3543	415	7	hence	hence	ADV
ejpam-3543	415	8	,	,	PUNCT
ejpam-3543	415	9	g	g	PROPN
ejpam-3543	415	10	is	be	AUX
ejpam-3543	415	11	a	a	DET
ejpam-3543	415	12	up	up	ADJ
ejpam-3543	415	13	-	-	PUNCT
ejpam-3543	415	14	subalgebra	subalgebra	NOUN
ejpam-3543	415	15	of	of	ADP
ejpam-3543	415	16	x.	x.	NOUN
ejpam-3543	415	17	conversely	conversely	ADV
ejpam-3543	415	18	,	,	PUNCT
ejpam-3543	415	19	assume	assume	VERB
ejpam-3543	415	20	that	that	SCONJ
ejpam-3543	415	21	g	g	PROPN
ejpam-3543	415	22	is	be	AUX
ejpam-3543	415	23	a	a	DET
ejpam-3543	415	24	up	up	ADJ
ejpam-3543	415	25	-	-	PUNCT
ejpam-3543	415	26	subalgebra	subalgebra	NOUN
ejpam-3543	415	27	of	of	ADP
ejpam-3543	415	28	x.	x.	NOUN
ejpam-3543	415	29	let	let	VERB
ejpam-3543	415	30	x	x	PRON
ejpam-3543	415	31	,	,	PUNCT
ejpam-3543	415	32	y	y	PROPN
ejpam-3543	415	33	∈	∈	PROPN
ejpam-3543	415	34	x.	x.	NOUN
ejpam-3543	415	35	case	case	NOUN
ejpam-3543	415	36	1	1	NUM
ejpam-3543	415	37	:	:	PUNCT
ejpam-3543	415	38	x	x	X
ejpam-3543	415	39	,	,	PUNCT
ejpam-3543	415	40	y	y	PROPN
ejpam-3543	415	41	∈	∈	PROPN
ejpam-3543	415	42	g.	g.	NOUN
ejpam-3543	416	1	then	then	ADV
ejpam-3543	416	2	λgt	λgt	PRON
ejpam-3543	417	1	[	[	X
ejpam-3543	417	2	α	α	X
ejpam-3543	417	3	+	+	X
ejpam-3543	418	1	α−	α−	ADP
ejpam-3543	418	2	]	]	X
ejpam-3543	418	3	(	(	PUNCT
ejpam-3543	418	4	x	x	X
ejpam-3543	418	5	)	)	PUNCT
ejpam-3543	418	6	=	=	SYM
ejpam-3543	418	7	α+	α+	NOUN
ejpam-3543	418	8	=	=	PUNCT
ejpam-3543	418	9	λgt	λgt	X
ejpam-3543	419	1	[	[	X
ejpam-3543	419	2	α	α	X
ejpam-3543	419	3	+	+	X
ejpam-3543	420	1	α−	α−	ADP
ejpam-3543	420	2	]	]	X
ejpam-3543	420	3	(	(	PUNCT
ejpam-3543	420	4	y	y	NOUN
ejpam-3543	420	5	)	)	PUNCT
ejpam-3543	420	6	,	,	PUNCT
ejpam-3543	420	7	λgi	λgi	X
ejpam-3543	421	1	[	[	X
ejpam-3543	421	2	β	β	X
ejpam-3543	421	3	−	−	NOUN
ejpam-3543	421	4	β+	β+	PUNCT
ejpam-3543	421	5	]	]	X
ejpam-3543	421	6	(	(	PUNCT
ejpam-3543	421	7	x	x	X
ejpam-3543	421	8	)	)	PUNCT
ejpam-3543	421	9	=	=	SYM
ejpam-3543	421	10	β−	β−	PUNCT
ejpam-3543	422	1	=	=	PUNCT
ejpam-3543	422	2	λgi	λgi	NOUN
ejpam-3543	423	1	[	[	X
ejpam-3543	423	2	β	β	X
ejpam-3543	423	3	−	−	NOUN
ejpam-3543	423	4	β+	β+	PUNCT
ejpam-3543	423	5	]	]	X
ejpam-3543	423	6	(	(	PUNCT
ejpam-3543	423	7	y	y	NOUN
ejpam-3543	423	8	)	)	PUNCT
ejpam-3543	423	9	,	,	PUNCT
ejpam-3543	423	10	λgf	λgf	X
ejpam-3543	424	1	[	[	X
ejpam-3543	424	2	γ	γ	X
ejpam-3543	424	3	+	+	X
ejpam-3543	424	4	γ−	γ−	PROPN
ejpam-3543	424	5	]	]	PUNCT
ejpam-3543	424	6	(	(	PUNCT
ejpam-3543	424	7	x	x	X
ejpam-3543	424	8	)	)	PUNCT
ejpam-3543	424	9	=	=	SYM
ejpam-3543	424	10	γ+	γ+	PUNCT
ejpam-3543	424	11	=	=	SYM
ejpam-3543	424	12	λgf	λgf	X
ejpam-3543	425	1	[	[	X
ejpam-3543	425	2	γ	γ	X
ejpam-3543	425	3	+	+	X
ejpam-3543	425	4	γ−	γ−	PROPN
ejpam-3543	425	5	]	]	PUNCT
ejpam-3543	425	6	(	(	PUNCT
ejpam-3543	425	7	y	y	NOUN
ejpam-3543	425	8	)	)	PUNCT
ejpam-3543	425	9	.	.	PUNCT
ejpam-3543	426	1	thus	thus	ADV
ejpam-3543	426	2	min{λgt	min{λgt	X
ejpam-3543	427	1	[	[	X
ejpam-3543	427	2	α	α	X
ejpam-3543	427	3	+	+	X
ejpam-3543	428	1	α−	α−	ADP
ejpam-3543	428	2	]	]	X
ejpam-3543	428	3	(	(	PUNCT
ejpam-3543	428	4	x	x	NOUN
ejpam-3543	428	5	)	)	PUNCT
ejpam-3543	428	6	,	,	PUNCT
ejpam-3543	428	7	λgt	λgt	X
ejpam-3543	429	1	[	[	X
ejpam-3543	429	2	α	α	X
ejpam-3543	429	3	+	+	X
ejpam-3543	430	1	α−	α−	ADP
ejpam-3543	430	2	]	]	X
ejpam-3543	430	3	(	(	PUNCT
ejpam-3543	430	4	y	y	NOUN
ejpam-3543	430	5	)	)	PUNCT
ejpam-3543	430	6	}	}	PUNCT
ejpam-3543	430	7	=	=	SYM
ejpam-3543	430	8	α+	α+	NOUN
ejpam-3543	430	9	,	,	PUNCT
ejpam-3543	430	10	max{λgi	max{λgi	NOUN
ejpam-3543	431	1	[	[	X
ejpam-3543	431	2	β	β	X
ejpam-3543	431	3	−	−	NOUN
ejpam-3543	431	4	β+	β+	PUNCT
ejpam-3543	431	5	]	]	X
ejpam-3543	431	6	(	(	PUNCT
ejpam-3543	431	7	x	x	NOUN
ejpam-3543	431	8	)	)	PUNCT
ejpam-3543	431	9	,	,	PUNCT
ejpam-3543	431	10	λgi	λgi	X
ejpam-3543	432	1	[	[	X
ejpam-3543	432	2	β	β	X
ejpam-3543	432	3	−	−	NOUN
ejpam-3543	432	4	β+	β+	PUNCT
ejpam-3543	432	5	]	]	X
ejpam-3543	432	6	(	(	PUNCT
ejpam-3543	432	7	y	y	NOUN
ejpam-3543	432	8	)	)	PUNCT
ejpam-3543	432	9	}	}	PUNCT
ejpam-3543	432	10	=	=	SYM
ejpam-3543	432	11	β−	β−	PROPN
ejpam-3543	432	12	,	,	PUNCT
ejpam-3543	432	13	min{λgf	min{λgf	NOUN
ejpam-3543	433	1	[	[	X
ejpam-3543	433	2	γ	γ	X
ejpam-3543	433	3	+	+	X
ejpam-3543	433	4	γ−	γ−	PROPN
ejpam-3543	433	5	]	]	PUNCT
ejpam-3543	433	6	(	(	PUNCT
ejpam-3543	433	7	x	x	NOUN
ejpam-3543	433	8	)	)	PUNCT
ejpam-3543	433	9	,	,	PUNCT
ejpam-3543	433	10	λgf	λgf	X
ejpam-3543	434	1	[	[	X
ejpam-3543	434	2	γ	γ	X
ejpam-3543	434	3	+	+	X
ejpam-3543	434	4	γ−	γ−	PROPN
ejpam-3543	434	5	]	]	PUNCT
ejpam-3543	434	6	(	(	PUNCT
ejpam-3543	434	7	y	y	NOUN
ejpam-3543	434	8	)	)	PUNCT
ejpam-3543	434	9	}	}	PUNCT
ejpam-3543	434	10	=	=	SYM
ejpam-3543	434	11	γ+	γ+	PROPN
ejpam-3543	434	12	.	.	PUNCT
ejpam-3543	435	1	since	since	SCONJ
ejpam-3543	435	2	g	g	PROPN
ejpam-3543	435	3	is	be	AUX
ejpam-3543	435	4	a	a	DET
ejpam-3543	435	5	up	up	ADJ
ejpam-3543	435	6	-	-	PUNCT
ejpam-3543	435	7	subalgebra	subalgebra	NOUN
ejpam-3543	435	8	of	of	ADP
ejpam-3543	435	9	x	x	PRON
ejpam-3543	435	10	,	,	PUNCT
ejpam-3543	435	11	we	we	PRON
ejpam-3543	435	12	have	have	VERB
ejpam-3543	435	13	x·y	x·y	PROPN
ejpam-3543	435	14	∈	∈	PROPN
ejpam-3543	435	15	g	g	PROPN
ejpam-3543	435	16	and	and	CCONJ
ejpam-3543	435	17	so	so	ADV
ejpam-3543	435	18	λgt	λgt	PRON
ejpam-3543	436	1	[	[	X
ejpam-3543	436	2	α	α	X
ejpam-3543	436	3	+	+	X
ejpam-3543	437	1	α−	α−	ADP
ejpam-3543	437	2	]	]	X
ejpam-3543	437	3	(	(	PUNCT
ejpam-3543	437	4	x·y	x·y	PROPN
ejpam-3543	437	5	)	)	PUNCT
ejpam-3543	437	6	=	=	SYM
ejpam-3543	437	7	α+	α+	X
ejpam-3543	437	8	,	,	PUNCT
ejpam-3543	437	9	λgi	λgi	X
ejpam-3543	438	1	[	[	X
ejpam-3543	438	2	β	β	X
ejpam-3543	438	3	−	−	NOUN
ejpam-3543	438	4	β+	β+	PUNCT
ejpam-3543	438	5	]	]	X
ejpam-3543	438	6	(	(	PUNCT
ejpam-3543	438	7	x·y	x·y	PROPN
ejpam-3543	438	8	)	)	PUNCT
ejpam-3543	438	9	=	=	SYM
ejpam-3543	438	10	β−	β−	PROPN
ejpam-3543	438	11	,	,	PUNCT
ejpam-3543	438	12	and	and	CCONJ
ejpam-3543	438	13	λgf	λgf	X
ejpam-3543	439	1	[	[	X
ejpam-3543	439	2	γ	γ	X
ejpam-3543	439	3	+	+	X
ejpam-3543	439	4	γ−	γ−	PROPN
ejpam-3543	439	5	]	]	PUNCT
ejpam-3543	439	6	(	(	PUNCT
ejpam-3543	439	7	x	x	SYM
ejpam-3543	439	8	·	·	PUNCT
ejpam-3543	439	9	y	y	X
ejpam-3543	439	10	)	)	PUNCT
ejpam-3543	439	11	=	=	PRON
ejpam-3543	439	12	γ+	γ+	PROPN
ejpam-3543	439	13	.	.	PUNCT
ejpam-3543	440	1	hence	hence	ADV
ejpam-3543	440	2	,	,	PUNCT
ejpam-3543	440	3	λgt	λgt	PRON
ejpam-3543	441	1	[	[	X
ejpam-3543	441	2	α	α	X
ejpam-3543	441	3	+	+	X
ejpam-3543	442	1	α−	α−	ADP
ejpam-3543	442	2	]	]	X
ejpam-3543	442	3	(	(	PUNCT
ejpam-3543	442	4	x	x	SYM
ejpam-3543	442	5	·	·	PUNCT
ejpam-3543	442	6	y	y	X
ejpam-3543	442	7	)	)	PUNCT
ejpam-3543	442	8	=	=	PRON
ejpam-3543	442	9	α+	α+	PUNCT
ejpam-3543	442	10	≥	≥	X
ejpam-3543	442	11	α+	α+	X
ejpam-3543	442	12	=	=	X
ejpam-3543	442	13	min{λgt	min{λgt	NOUN
ejpam-3543	443	1	[	[	X
ejpam-3543	443	2	α	α	X
ejpam-3543	443	3	+	+	X
ejpam-3543	444	1	α−	α−	ADP
ejpam-3543	444	2	]	]	X
ejpam-3543	444	3	(	(	PUNCT
ejpam-3543	444	4	x	x	NOUN
ejpam-3543	444	5	)	)	PUNCT
ejpam-3543	444	6	,	,	PUNCT
ejpam-3543	444	7	λgt	λgt	X
ejpam-3543	445	1	[	[	X
ejpam-3543	445	2	α	α	X
ejpam-3543	445	3	+	+	X
ejpam-3543	446	1	α−	α−	ADP
ejpam-3543	446	2	]	]	X
ejpam-3543	446	3	(	(	PUNCT
ejpam-3543	446	4	y	y	NOUN
ejpam-3543	446	5	)	)	PUNCT
ejpam-3543	446	6	}	}	PUNCT
ejpam-3543	446	7	,	,	PUNCT
ejpam-3543	446	8	λgi	λgi	X
ejpam-3543	447	1	[	[	X
ejpam-3543	447	2	β	β	X
ejpam-3543	447	3	−	−	NOUN
ejpam-3543	447	4	β+	β+	PUNCT
ejpam-3543	447	5	]	]	X
ejpam-3543	447	6	(	(	PUNCT
ejpam-3543	447	7	x	x	SYM
ejpam-3543	447	8	·	·	PUNCT
ejpam-3543	447	9	y	y	X
ejpam-3543	447	10	)	)	PUNCT
ejpam-3543	448	1	=	=	PUNCT
ejpam-3543	448	2	β−	β−	PUNCT
ejpam-3543	449	1	≤	≤	NUM
ejpam-3543	449	2	β−	β−	PUNCT
ejpam-3543	450	1	=	=	SYM
ejpam-3543	450	2	max{λgi	max{λgi	NOUN
ejpam-3543	451	1	[	[	X
ejpam-3543	451	2	β	β	X
ejpam-3543	451	3	−	−	NOUN
ejpam-3543	451	4	β+	β+	PUNCT
ejpam-3543	451	5	]	]	X
ejpam-3543	451	6	(	(	PUNCT
ejpam-3543	451	7	x	x	NOUN
ejpam-3543	451	8	)	)	PUNCT
ejpam-3543	451	9	,	,	PUNCT
ejpam-3543	451	10	λgi	λgi	X
ejpam-3543	452	1	[	[	X
ejpam-3543	452	2	β	β	X
ejpam-3543	452	3	−	−	NOUN
ejpam-3543	452	4	β+	β+	PUNCT
ejpam-3543	452	5	]	]	X
ejpam-3543	452	6	(	(	PUNCT
ejpam-3543	452	7	y	y	NOUN
ejpam-3543	452	8	)	)	PUNCT
ejpam-3543	452	9	}	}	PUNCT
ejpam-3543	452	10	,	,	PUNCT
ejpam-3543	452	11	λgf	λgf	X
ejpam-3543	453	1	[	[	X
ejpam-3543	453	2	γ	γ	X
ejpam-3543	453	3	+	+	X
ejpam-3543	453	4	γ−	γ−	PROPN
ejpam-3543	453	5	]	]	PUNCT
ejpam-3543	453	6	(	(	PUNCT
ejpam-3543	453	7	x	x	SYM
ejpam-3543	453	8	·	·	PUNCT
ejpam-3543	453	9	y	y	X
ejpam-3543	453	10	)	)	PUNCT
ejpam-3543	453	11	=	=	PRON
ejpam-3543	453	12	γ+	γ+	PUNCT
ejpam-3543	453	13	≥	≥	NOUN
ejpam-3543	453	14	γ+	γ+	X
ejpam-3543	453	15	=	=	PUNCT
ejpam-3543	453	16	min{λgf	min{λgf	PROPN
ejpam-3543	454	1	[	[	X
ejpam-3543	454	2	γ	γ	X
ejpam-3543	454	3	+	+	X
ejpam-3543	454	4	γ−	γ−	PROPN
ejpam-3543	454	5	]	]	PUNCT
ejpam-3543	454	6	(	(	PUNCT
ejpam-3543	454	7	x	x	NOUN
ejpam-3543	454	8	)	)	PUNCT
ejpam-3543	454	9	,	,	PUNCT
ejpam-3543	454	10	λgf	λgf	X
ejpam-3543	455	1	[	[	X
ejpam-3543	455	2	γ	γ	X
ejpam-3543	455	3	+	+	X
ejpam-3543	455	4	γ−	γ−	PROPN
ejpam-3543	455	5	]	]	PUNCT
ejpam-3543	455	6	(	(	PUNCT
ejpam-3543	455	7	y	y	NOUN
ejpam-3543	455	8	)	)	PUNCT
ejpam-3543	455	9	}	}	PUNCT
ejpam-3543	455	10	.	.	PUNCT
ejpam-3543	456	1	case	case	NOUN
ejpam-3543	456	2	2	2	NUM
ejpam-3543	456	3	:	:	PUNCT
ejpam-3543	456	4	x	x	SYM
ejpam-3543	456	5	6∈	6∈	NOUN
ejpam-3543	456	6	g	g	PROPN
ejpam-3543	456	7	or	or	CCONJ
ejpam-3543	456	8	y	y	PROPN
ejpam-3543	456	9	6∈	6∈	PROPN
ejpam-3543	457	1	g.	g.	NOUN
ejpam-3543	457	2	then	then	ADV
ejpam-3543	457	3	λgt	λgt	PRON
ejpam-3543	458	1	[	[	X
ejpam-3543	458	2	α	α	X
ejpam-3543	458	3	−	−	X
ejpam-3543	458	4	α−	α−	ADP
ejpam-3543	458	5	]	]	X
ejpam-3543	458	6	(	(	PUNCT
ejpam-3543	458	7	x	x	X
ejpam-3543	458	8	)	)	PUNCT
ejpam-3543	458	9	=	=	SYM
ejpam-3543	458	10	α−	α−	ADP
ejpam-3543	458	11	or	or	CCONJ
ejpam-3543	458	12	λgt	λgt	PRON
ejpam-3543	458	13	[	[	X
ejpam-3543	458	14	α	α	X
ejpam-3543	458	15	+	+	X
ejpam-3543	459	1	α−	α−	ADP
ejpam-3543	459	2	]	]	X
ejpam-3543	459	3	(	(	PUNCT
ejpam-3543	459	4	y	y	NOUN
ejpam-3543	459	5	)	)	PUNCT
ejpam-3543	459	6	=	=	PUNCT
ejpam-3543	459	7	α−	α−	PROPN
ejpam-3543	459	8	,	,	PUNCT
ejpam-3543	459	9	λgi	λgi	X
ejpam-3543	460	1	[	[	X
ejpam-3543	460	2	β	β	X
ejpam-3543	460	3	−	−	NOUN
ejpam-3543	460	4	β+	β+	PUNCT
ejpam-3543	460	5	]	]	X
ejpam-3543	460	6	(	(	PUNCT
ejpam-3543	460	7	x	x	X
ejpam-3543	460	8	)	)	PUNCT
ejpam-3543	460	9	=	=	SYM
ejpam-3543	460	10	β+	β+	PUNCT
ejpam-3543	460	11	or	or	CCONJ
ejpam-3543	460	12	λgi	λgi	X
ejpam-3543	461	1	[	[	X
ejpam-3543	461	2	β	β	X
ejpam-3543	461	3	−	−	NOUN
ejpam-3543	461	4	β+	β+	PUNCT
ejpam-3543	461	5	]	]	X
ejpam-3543	461	6	(	(	PUNCT
ejpam-3543	461	7	y	y	NOUN
ejpam-3543	461	8	)	)	PUNCT
ejpam-3543	461	9	=	=	SYM
ejpam-3543	462	1	β+	β+	NOUN
ejpam-3543	462	2	,	,	PUNCT
ejpam-3543	462	3	λgf	λgf	NOUN
ejpam-3543	463	1	[	[	X
ejpam-3543	463	2	γ	γ	X
ejpam-3543	463	3	+	+	X
ejpam-3543	463	4	γ−	γ−	PROPN
ejpam-3543	463	5	]	]	PUNCT
ejpam-3543	463	6	(	(	PUNCT
ejpam-3543	463	7	x	x	X
ejpam-3543	463	8	)	)	PUNCT
ejpam-3543	463	9	=	=	SYM
ejpam-3543	463	10	γ−	γ−	PROPN
ejpam-3543	463	11	or	or	CCONJ
ejpam-3543	463	12	λgf	λgf	NOUN
ejpam-3543	464	1	[	[	X
ejpam-3543	464	2	γ	γ	X
ejpam-3543	464	3	+	+	X
ejpam-3543	464	4	γ−	γ−	PROPN
ejpam-3543	464	5	]	]	PUNCT
ejpam-3543	464	6	(	(	PUNCT
ejpam-3543	464	7	y	y	NOUN
ejpam-3543	464	8	)	)	PUNCT
ejpam-3543	464	9	=	=	SYM
ejpam-3543	464	10	γ−.	γ−.	NOUN
ejpam-3543	464	11	m.	m.	NOUN
ejpam-3543	464	12	songsaeng	songsaeng	PROPN
ejpam-3543	464	13	,	,	PUNCT
ejpam-3543	464	14	a.	a.	NOUN
ejpam-3543	464	15	iampan	iampan	PROPN
ejpam-3543	464	16	/	/	SYM
ejpam-3543	464	17	eur	eur	PROPN
ejpam-3543	464	18	.	.	PUNCT
ejpam-3543	465	1	j.	j.	PROPN
ejpam-3543	465	2	pure	pure	PROPN
ejpam-3543	465	3	appl	appl	PROPN
ejpam-3543	465	4	.	.	PROPN
ejpam-3543	465	5	math	math	PROPN
ejpam-3543	465	6	,	,	PUNCT
ejpam-3543	465	7	12	12	NUM
ejpam-3543	465	8	(	(	PUNCT
ejpam-3543	465	9	4	4	NUM
ejpam-3543	465	10	)	)	PUNCT
ejpam-3543	465	11	(	(	PUNCT
ejpam-3543	465	12	2019	2019	NUM
ejpam-3543	465	13	)	)	PUNCT
ejpam-3543	465	14	,	,	PUNCT
ejpam-3543	465	15	1382	1382	NUM
ejpam-3543	465	16	-	-	SYM
ejpam-3543	465	17	1409	1409	NUM
ejpam-3543	465	18	1398	1398	NUM
ejpam-3543	465	19	thus	thus	ADV
ejpam-3543	465	20	min{λgt	min{λgt	X
ejpam-3543	466	1	[	[	X
ejpam-3543	466	2	α	α	X
ejpam-3543	466	3	+	+	X
ejpam-3543	467	1	α−	α−	ADP
ejpam-3543	467	2	]	]	X
ejpam-3543	467	3	(	(	PUNCT
ejpam-3543	467	4	x	x	NOUN
ejpam-3543	467	5	)	)	PUNCT
ejpam-3543	467	6	,	,	PUNCT
ejpam-3543	467	7	λgt	λgt	X
ejpam-3543	468	1	[	[	X
ejpam-3543	468	2	α	α	X
ejpam-3543	468	3	+	+	X
ejpam-3543	469	1	α−	α−	ADP
ejpam-3543	469	2	]	]	X
ejpam-3543	469	3	(	(	PUNCT
ejpam-3543	469	4	y	y	NOUN
ejpam-3543	469	5	)	)	PUNCT
ejpam-3543	469	6	}	}	PUNCT
ejpam-3543	469	7	=	=	SYM
ejpam-3543	469	8	α−	α−	PROPN
ejpam-3543	469	9	,	,	PUNCT
ejpam-3543	469	10	max{λgi	max{λgi	NOUN
ejpam-3543	470	1	[	[	X
ejpam-3543	470	2	β	β	X
ejpam-3543	470	3	−	−	NOUN
ejpam-3543	470	4	β+	β+	PUNCT
ejpam-3543	470	5	]	]	X
ejpam-3543	470	6	(	(	PUNCT
ejpam-3543	470	7	x	x	NOUN
ejpam-3543	470	8	)	)	PUNCT
ejpam-3543	470	9	,	,	PUNCT
ejpam-3543	470	10	λgi	λgi	X
ejpam-3543	471	1	[	[	X
ejpam-3543	471	2	β	β	X
ejpam-3543	471	3	−	−	NOUN
ejpam-3543	471	4	β+	β+	PUNCT
ejpam-3543	471	5	]	]	X
ejpam-3543	471	6	(	(	PUNCT
ejpam-3543	471	7	y	y	NOUN
ejpam-3543	471	8	)	)	PUNCT
ejpam-3543	471	9	}	}	PUNCT
ejpam-3543	472	1	=	=	SYM
ejpam-3543	472	2	β+	β+	NOUN
ejpam-3543	472	3	,	,	PUNCT
ejpam-3543	472	4	min{λgf	min{λgf	NOUN
ejpam-3543	472	5	[	[	X
ejpam-3543	472	6	γ	γ	X
ejpam-3543	472	7	+	+	X
ejpam-3543	472	8	γ−	γ−	PROPN
ejpam-3543	472	9	]	]	PUNCT
ejpam-3543	472	10	(	(	PUNCT
ejpam-3543	472	11	x	x	NOUN
ejpam-3543	472	12	)	)	PUNCT
ejpam-3543	472	13	,	,	PUNCT
ejpam-3543	472	14	λgf	λgf	X
ejpam-3543	473	1	[	[	X
ejpam-3543	473	2	γ	γ	X
ejpam-3543	473	3	+	+	X
ejpam-3543	473	4	γ−	γ−	PROPN
ejpam-3543	473	5	]	]	PUNCT
ejpam-3543	473	6	(	(	PUNCT
ejpam-3543	473	7	y	y	NOUN
ejpam-3543	473	8	)	)	PUNCT
ejpam-3543	473	9	}	}	PUNCT
ejpam-3543	473	10	=	=	SYM
ejpam-3543	473	11	γ−.	γ−.	NOUN
ejpam-3543	473	12	therefore	therefore	ADV
ejpam-3543	473	13	,	,	PUNCT
ejpam-3543	473	14	λgt	λgt	PROPN
ejpam-3543	473	15	[	[	X
ejpam-3543	473	16	α	α	X
ejpam-3543	473	17	+	+	X
ejpam-3543	474	1	α−	α−	ADP
ejpam-3543	474	2	]	]	X
ejpam-3543	474	3	(	(	PUNCT
ejpam-3543	474	4	x	x	SYM
ejpam-3543	474	5	·	·	PUNCT
ejpam-3543	474	6	y	y	X
ejpam-3543	474	7	)	)	PUNCT
ejpam-3543	474	8	≥	≥	NOUN
ejpam-3543	474	9	α−	α−	ADP
ejpam-3543	474	10	=	=	SYM
ejpam-3543	474	11	min{λgt	min{λgt	PROPN
ejpam-3543	475	1	[	[	X
ejpam-3543	475	2	α	α	X
ejpam-3543	475	3	+	+	X
ejpam-3543	476	1	α−	α−	ADP
ejpam-3543	476	2	]	]	X
ejpam-3543	476	3	(	(	PUNCT
ejpam-3543	476	4	x	x	NOUN
ejpam-3543	476	5	)	)	PUNCT
ejpam-3543	476	6	,	,	PUNCT
ejpam-3543	476	7	λgt	λgt	X
ejpam-3543	477	1	[	[	X
ejpam-3543	477	2	α	α	X
ejpam-3543	477	3	+	+	X
ejpam-3543	478	1	α−	α−	ADP
ejpam-3543	478	2	]	]	X
ejpam-3543	478	3	(	(	PUNCT
ejpam-3543	478	4	y	y	NOUN
ejpam-3543	478	5	)	)	PUNCT
ejpam-3543	478	6	}	}	PUNCT
ejpam-3543	478	7	,	,	PUNCT
ejpam-3543	478	8	λgi	λgi	X
ejpam-3543	479	1	[	[	X
ejpam-3543	479	2	β	β	X
ejpam-3543	479	3	−	−	NOUN
ejpam-3543	479	4	β+	β+	PUNCT
ejpam-3543	479	5	]	]	X
ejpam-3543	479	6	(	(	PUNCT
ejpam-3543	479	7	x	x	SYM
ejpam-3543	479	8	·	·	PUNCT
ejpam-3543	479	9	y	y	X
ejpam-3543	479	10	)	)	PUNCT
ejpam-3543	479	11	≤	≤	NOUN
ejpam-3543	479	12	β+	β+	PUNCT
ejpam-3543	479	13	=	=	SYM
ejpam-3543	479	14	max{λgi	max{λgi	NOUN
ejpam-3543	480	1	[	[	X
ejpam-3543	480	2	β	β	X
ejpam-3543	480	3	−	−	NOUN
ejpam-3543	480	4	β+	β+	PUNCT
ejpam-3543	480	5	]	]	X
ejpam-3543	480	6	(	(	PUNCT
ejpam-3543	480	7	x	x	NOUN
ejpam-3543	480	8	)	)	PUNCT
ejpam-3543	480	9	,	,	PUNCT
ejpam-3543	480	10	λgi	λgi	X
ejpam-3543	481	1	[	[	X
ejpam-3543	481	2	β	β	X
ejpam-3543	481	3	−	−	NOUN
ejpam-3543	481	4	β+	β+	PUNCT
ejpam-3543	481	5	]	]	X
ejpam-3543	481	6	(	(	PUNCT
ejpam-3543	481	7	y	y	NOUN
ejpam-3543	481	8	)	)	PUNCT
ejpam-3543	481	9	}	}	PUNCT
ejpam-3543	481	10	,	,	PUNCT
ejpam-3543	481	11	λgf	λgf	X
ejpam-3543	482	1	[	[	X
ejpam-3543	482	2	γ	γ	X
ejpam-3543	482	3	+	+	X
ejpam-3543	482	4	γ−	γ−	PROPN
ejpam-3543	482	5	]	]	PUNCT
ejpam-3543	482	6	(	(	PUNCT
ejpam-3543	482	7	x	x	SYM
ejpam-3543	482	8	·	·	PUNCT
ejpam-3543	482	9	y	y	X
ejpam-3543	482	10	)	)	PUNCT
ejpam-3543	482	11	≥	≥	NOUN
ejpam-3543	482	12	γ−	γ−	NOUN
ejpam-3543	482	13	=	=	NOUN
ejpam-3543	482	14	min{λgf	min{λgf	PROPN
ejpam-3543	483	1	[	[	X
ejpam-3543	483	2	γ	γ	X
ejpam-3543	483	3	+	+	X
ejpam-3543	483	4	γ−	γ−	PROPN
ejpam-3543	483	5	]	]	PUNCT
ejpam-3543	483	6	(	(	PUNCT
ejpam-3543	483	7	x	x	NOUN
ejpam-3543	483	8	)	)	PUNCT
ejpam-3543	483	9	,	,	PUNCT
ejpam-3543	483	10	λgf	λgf	X
ejpam-3543	484	1	[	[	X
ejpam-3543	484	2	γ	γ	X
ejpam-3543	484	3	+	+	X
ejpam-3543	484	4	γ−	γ−	PROPN
ejpam-3543	484	5	]	]	PUNCT
ejpam-3543	484	6	(	(	PUNCT
ejpam-3543	484	7	y	y	NOUN
ejpam-3543	484	8	)	)	PUNCT
ejpam-3543	484	9	}	}	PUNCT
ejpam-3543	484	10	.	.	PUNCT
ejpam-3543	485	1	hence	hence	ADV
ejpam-3543	485	2	,	,	PUNCT
ejpam-3543	485	3	λg[α	λg[α	PROPN
ejpam-3543	485	4	+	+	PROPN
ejpam-3543	485	5	,	,	PUNCT
ejpam-3543	485	6	β−,γ+	β−,γ+	X
ejpam-3543	485	7	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	485	8	]	]	PUNCT
ejpam-3543	485	9	is	be	AUX
ejpam-3543	485	10	a	a	DET
ejpam-3543	485	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	485	12	up	up	ADP
ejpam-3543	485	13	-	-	PUNCT
ejpam-3543	485	14	subalgebra	subalgebra	NOUN
ejpam-3543	485	15	of	of	ADP
ejpam-3543	485	16	x.	x.	PROPN
ejpam-3543	485	17	theorem	theorem	VERB
ejpam-3543	485	18	15	15	NUM
ejpam-3543	485	19	.	.	PUNCT
ejpam-3543	486	1	a	a	DET
ejpam-3543	486	2	ns	ns	ADJ
ejpam-3543	486	3	λg[α	λg[α	PROPN
ejpam-3543	486	4	+	+	PROPN
ejpam-3543	486	5	,	,	PUNCT
ejpam-3543	486	6	β−,γ+	β−,γ+	X
ejpam-3543	486	7	α−,β+,γ−	α−,β+,γ−	VERB
ejpam-3543	486	8	]	]	PUNCT
ejpam-3543	486	9	in	in	ADP
ejpam-3543	486	10	x	x	SYM
ejpam-3543	486	11	is	be	AUX
ejpam-3543	486	12	a	a	DET
ejpam-3543	486	13	neutrosophic	neutrosophic	ADJ
ejpam-3543	486	14	near	near	ADP
ejpam-3543	486	15	up	up	ADJ
ejpam-3543	486	16	-	-	PUNCT
ejpam-3543	486	17	filter	filter	NOUN
ejpam-3543	486	18	of	of	ADP
ejpam-3543	486	19	x	x	SYM
ejpam-3543	486	20	if	if	SCONJ
ejpam-3543	487	1	and	and	CCONJ
ejpam-3543	487	2	only	only	ADV
ejpam-3543	487	3	if	if	SCONJ
ejpam-3543	487	4	a	a	DET
ejpam-3543	487	5	nonempty	nonempty	NOUN
ejpam-3543	487	6	subset	subset	VERB
ejpam-3543	487	7	g	g	PROPN
ejpam-3543	487	8	of	of	ADP
ejpam-3543	487	9	x	x	PUNCT
ejpam-3543	487	10	is	be	AUX
ejpam-3543	487	11	a	a	DET
ejpam-3543	487	12	near	near	ADJ
ejpam-3543	487	13	up	up	NOUN
ejpam-3543	487	14	-	-	PUNCT
ejpam-3543	487	15	filter	filter	NOUN
ejpam-3543	487	16	of	of	ADP
ejpam-3543	487	17	x.	x.	NOUN
ejpam-3543	487	18	proof	proof	PROPN
ejpam-3543	487	19	.	.	PUNCT
ejpam-3543	488	1	assume	assume	VERB
ejpam-3543	488	2	that	that	SCONJ
ejpam-3543	488	3	λg[α	λg[α	PROPN
ejpam-3543	488	4	+	+	NOUN
ejpam-3543	488	5	,	,	PUNCT
ejpam-3543	488	6	β−,γ+	β−,γ+	X
ejpam-3543	488	7	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	488	8	]	]	PUNCT
ejpam-3543	488	9	is	be	AUX
ejpam-3543	488	10	neutrosophic	neutrosophic	ADJ
ejpam-3543	488	11	near	near	ADP
ejpam-3543	488	12	up	up	ADP
ejpam-3543	488	13	-	-	PUNCT
ejpam-3543	488	14	filter	filter	NOUN
ejpam-3543	488	15	ofx	ofx	NOUN
ejpam-3543	488	16	.	.	PUNCT
ejpam-3543	489	1	since	since	SCONJ
ejpam-3543	489	2	λg[α	λg[α	PROPN
ejpam-3543	489	3	+	+	PROPN
ejpam-3543	489	4	,	,	PUNCT
ejpam-3543	489	5	β−,γ+	β−,γ+	X
ejpam-3543	489	6	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	489	7	]	]	PUNCT
ejpam-3543	489	8	satisfies	satisfy	VERB
ejpam-3543	489	9	the	the	DET
ejpam-3543	489	10	condition	condition	NOUN
ejpam-3543	489	11	(	(	PUNCT
ejpam-3543	489	12	3.6	3.6	NUM
ejpam-3543	489	13	)	)	PUNCT
ejpam-3543	489	14	,	,	PUNCT
ejpam-3543	489	15	it	it	PRON
ejpam-3543	489	16	follows	follow	VERB
ejpam-3543	489	17	from	from	ADP
ejpam-3543	489	18	lemma	lemma	PROPN
ejpam-3543	489	19	4	4	NUM
ejpam-3543	489	20	that	that	SCONJ
ejpam-3543	489	21	0	0	NUM
ejpam-3543	489	22	∈	∈	NOUN
ejpam-3543	489	23	g.	g.	NOUN
ejpam-3543	489	24	next	next	ADV
ejpam-3543	489	25	,	,	PUNCT
ejpam-3543	489	26	let	let	VERB
ejpam-3543	489	27	x	x	X
ejpam-3543	489	28	∈	∈	PROPN
ejpam-3543	489	29	x	x	X
ejpam-3543	489	30	and	and	CCONJ
ejpam-3543	489	31	y	y	PROPN
ejpam-3543	489	32	∈	∈	PROPN
ejpam-3543	490	1	g.	g.	NOUN
ejpam-3543	490	2	then	then	ADV
ejpam-3543	490	3	λgt	λgt	PRON
ejpam-3543	491	1	[	[	X
ejpam-3543	491	2	α	α	X
ejpam-3543	491	3	+	+	X
ejpam-3543	492	1	α−	α−	ADP
ejpam-3543	492	2	]	]	X
ejpam-3543	492	3	(	(	PUNCT
ejpam-3543	492	4	y	y	NOUN
ejpam-3543	492	5	)	)	PUNCT
ejpam-3543	492	6	=	=	SYM
ejpam-3543	492	7	α+	α+	NOUN
ejpam-3543	492	8	.	.	PUNCT
ejpam-3543	493	1	thus	thus	ADV
ejpam-3543	493	2	λgt	λgt	PRON
ejpam-3543	494	1	[	[	X
ejpam-3543	494	2	α	α	X
ejpam-3543	494	3	+	+	X
ejpam-3543	495	1	α−	α−	ADP
ejpam-3543	495	2	]	]	X
ejpam-3543	495	3	(	(	PUNCT
ejpam-3543	495	4	x	x	SYM
ejpam-3543	495	5	·	·	PUNCT
ejpam-3543	495	6	y	y	X
ejpam-3543	495	7	)	)	PUNCT
ejpam-3543	495	8	≥	≥	NOUN
ejpam-3543	496	1	λgt	λgt	X
ejpam-3543	497	1	[	[	X
ejpam-3543	497	2	α	α	X
ejpam-3543	497	3	+	+	X
ejpam-3543	498	1	α−	α−	ADP
ejpam-3543	498	2	]	]	X
ejpam-3543	498	3	(	(	PUNCT
ejpam-3543	498	4	y	y	NOUN
ejpam-3543	498	5	)	)	PUNCT
ejpam-3543	498	6	=	=	SYM
ejpam-3543	498	7	α+	α+	PUNCT
ejpam-3543	498	8	≥	≥	NOUN
ejpam-3543	498	9	λgt	λgt	X
ejpam-3543	499	1	[	[	X
ejpam-3543	499	2	α	α	X
ejpam-3543	499	3	+	+	X
ejpam-3543	500	1	α−	α−	ADP
ejpam-3543	500	2	]	]	X
ejpam-3543	500	3	(	(	PUNCT
ejpam-3543	500	4	x	x	SYM
ejpam-3543	500	5	·	·	PUNCT
ejpam-3543	500	6	y	y	X
ejpam-3543	500	7	)	)	PUNCT
ejpam-3543	500	8	(	(	PUNCT
ejpam-3543	500	9	3.9	3.9	NUM
ejpam-3543	500	10	)	)	PUNCT
ejpam-3543	500	11	and	and	CCONJ
ejpam-3543	500	12	so	so	ADV
ejpam-3543	500	13	λgt	λgt	PRON
ejpam-3543	501	1	[	[	X
ejpam-3543	501	2	α	α	X
ejpam-3543	501	3	+	+	X
ejpam-3543	502	1	α−	α−	ADP
ejpam-3543	502	2	]	]	X
ejpam-3543	502	3	(	(	PUNCT
ejpam-3543	502	4	x	x	SYM
ejpam-3543	502	5	·	·	PUNCT
ejpam-3543	502	6	y	y	X
ejpam-3543	502	7	)	)	PUNCT
ejpam-3543	502	8	=	=	SYM
ejpam-3543	502	9	α+	α+	NOUN
ejpam-3543	502	10	.	.	PUNCT
ejpam-3543	503	1	thus	thus	ADV
ejpam-3543	503	2	x	x	X
ejpam-3543	503	3	·	·	PUNCT
ejpam-3543	503	4	y	y	X
ejpam-3543	503	5	∈	∈	PROPN
ejpam-3543	503	6	g.	g.	NOUN
ejpam-3543	503	7	hence	hence	ADV
ejpam-3543	503	8	,	,	PUNCT
ejpam-3543	503	9	g	g	PROPN
ejpam-3543	503	10	is	be	AUX
ejpam-3543	503	11	a	a	DET
ejpam-3543	503	12	near	near	ADJ
ejpam-3543	503	13	up	up	NOUN
ejpam-3543	503	14	-	-	PUNCT
ejpam-3543	503	15	filter	filter	NOUN
ejpam-3543	503	16	of	of	ADP
ejpam-3543	503	17	x.	x.	NOUN
ejpam-3543	503	18	conversely	conversely	ADV
ejpam-3543	503	19	,	,	PUNCT
ejpam-3543	503	20	assume	assume	VERB
ejpam-3543	503	21	that	that	SCONJ
ejpam-3543	503	22	g	g	PROPN
ejpam-3543	503	23	is	be	AUX
ejpam-3543	503	24	a	a	DET
ejpam-3543	503	25	near	near	ADJ
ejpam-3543	503	26	up	up	NOUN
ejpam-3543	503	27	-	-	PUNCT
ejpam-3543	503	28	filter	filter	NOUN
ejpam-3543	503	29	of	of	ADP
ejpam-3543	503	30	x.	x.	NOUN
ejpam-3543	503	31	since	since	SCONJ
ejpam-3543	503	32	0	0	NUM
ejpam-3543	503	33	∈	∈	PROPN
ejpam-3543	503	34	g	g	NOUN
ejpam-3543	503	35	,	,	PUNCT
ejpam-3543	503	36	it	it	PRON
ejpam-3543	503	37	follows	follow	VERB
ejpam-3543	503	38	from	from	ADP
ejpam-3543	503	39	lemma	lemma	PROPN
ejpam-3543	503	40	3	3	NUM
ejpam-3543	503	41	that	that	PRON
ejpam-3543	503	42	λg[α	λg[α	PROPN
ejpam-3543	503	43	+	+	NOUN
ejpam-3543	503	44	,	,	PUNCT
ejpam-3543	503	45	β−,γ+	β−,γ+	X
ejpam-3543	503	46	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	503	47	]	]	PUNCT
ejpam-3543	503	48	satisfies	satisfy	VERB
ejpam-3543	503	49	the	the	DET
ejpam-3543	503	50	conditions	condition	NOUN
ejpam-3543	503	51	(	(	PUNCT
ejpam-3543	503	52	3.6	3.6	NUM
ejpam-3543	503	53	)	)	PUNCT
ejpam-3543	503	54	,	,	PUNCT
ejpam-3543	503	55	(	(	PUNCT
ejpam-3543	503	56	3.7	3.7	NUM
ejpam-3543	503	57	)	)	PUNCT
ejpam-3543	503	58	,	,	PUNCT
ejpam-3543	503	59	and	and	CCONJ
ejpam-3543	503	60	(	(	PUNCT
ejpam-3543	503	61	3.8	3.8	NUM
ejpam-3543	503	62	)	)	PUNCT
ejpam-3543	503	63	.	.	PUNCT
ejpam-3543	504	1	next	next	ADV
ejpam-3543	504	2	,	,	PUNCT
ejpam-3543	504	3	let	let	VERB
ejpam-3543	504	4	x	x	PRON
ejpam-3543	504	5	,	,	PUNCT
ejpam-3543	504	6	y	y	PROPN
ejpam-3543	504	7	∈	∈	PROPN
ejpam-3543	504	8	x.	x.	NOUN
ejpam-3543	504	9	case	case	NOUN
ejpam-3543	504	10	1	1	NUM
ejpam-3543	504	11	:	:	PUNCT
ejpam-3543	504	12	y	y	PROPN
ejpam-3543	504	13	∈	∈	PROPN
ejpam-3543	504	14	g.	g.	NOUN
ejpam-3543	505	1	then	then	ADV
ejpam-3543	505	2	λgt	λgt	PRON
ejpam-3543	506	1	[	[	X
ejpam-3543	506	2	α	α	X
ejpam-3543	506	3	+	+	X
ejpam-3543	507	1	α−	α−	ADP
ejpam-3543	507	2	]	]	X
ejpam-3543	507	3	(	(	PUNCT
ejpam-3543	507	4	y	y	NOUN
ejpam-3543	507	5	)	)	PUNCT
ejpam-3543	507	6	=	=	SYM
ejpam-3543	507	7	α+	α+	X
ejpam-3543	507	8	,	,	PUNCT
ejpam-3543	507	9	λgi	λgi	X
ejpam-3543	508	1	[	[	X
ejpam-3543	508	2	β	β	X
ejpam-3543	508	3	−	−	NOUN
ejpam-3543	508	4	β+	β+	PUNCT
ejpam-3543	508	5	]	]	X
ejpam-3543	508	6	(	(	PUNCT
ejpam-3543	508	7	y	y	NOUN
ejpam-3543	508	8	)	)	PUNCT
ejpam-3543	508	9	=	=	SYM
ejpam-3543	508	10	β−	β−	PROPN
ejpam-3543	508	11	,	,	PUNCT
ejpam-3543	508	12	and	and	CCONJ
ejpam-3543	508	13	λgf	λgf	X
ejpam-3543	509	1	[	[	X
ejpam-3543	509	2	γ	γ	X
ejpam-3543	509	3	+	+	X
ejpam-3543	509	4	γ−	γ−	PROPN
ejpam-3543	509	5	]	]	PUNCT
ejpam-3543	509	6	(	(	PUNCT
ejpam-3543	509	7	y	y	NOUN
ejpam-3543	509	8	)	)	PUNCT
ejpam-3543	509	9	=	=	SYM
ejpam-3543	510	1	γ+	γ+	PROPN
ejpam-3543	510	2	.	.	PUNCT
ejpam-3543	511	1	since	since	SCONJ
ejpam-3543	511	2	g	g	PROPN
ejpam-3543	511	3	is	be	AUX
ejpam-3543	511	4	a	a	DET
ejpam-3543	511	5	near	near	ADJ
ejpam-3543	511	6	up	up	NOUN
ejpam-3543	511	7	-	-	PUNCT
ejpam-3543	511	8	filter	filter	NOUN
ejpam-3543	511	9	of	of	ADP
ejpam-3543	511	10	x	x	PRON
ejpam-3543	511	11	,	,	PUNCT
ejpam-3543	511	12	we	we	PRON
ejpam-3543	511	13	have	have	VERB
ejpam-3543	511	14	x	x	X
ejpam-3543	511	15	·	·	PUNCT
ejpam-3543	511	16	y	y	PROPN
ejpam-3543	511	17	∈	∈	PROPN
ejpam-3543	511	18	g	g	PROPN
ejpam-3543	511	19	and	and	CCONJ
ejpam-3543	511	20	so	so	ADV
ejpam-3543	511	21	λgt	λgt	PRON
ejpam-3543	512	1	[	[	X
ejpam-3543	512	2	α	α	X
ejpam-3543	512	3	+	+	X
ejpam-3543	513	1	α−	α−	ADP
ejpam-3543	513	2	]	]	X
ejpam-3543	513	3	(	(	PUNCT
ejpam-3543	513	4	x	x	SYM
ejpam-3543	513	5	·	·	PUNCT
ejpam-3543	513	6	y	y	X
ejpam-3543	513	7	)	)	PUNCT
ejpam-3543	513	8	=	=	SYM
ejpam-3543	513	9	α+	α+	X
ejpam-3543	513	10	,	,	PUNCT
ejpam-3543	513	11	λgi	λgi	X
ejpam-3543	514	1	[	[	X
ejpam-3543	514	2	β	β	X
ejpam-3543	514	3	−	−	NOUN
ejpam-3543	514	4	β+	β+	PUNCT
ejpam-3543	514	5	]	]	X
ejpam-3543	514	6	(	(	PUNCT
ejpam-3543	514	7	x	x	SYM
ejpam-3543	514	8	·	·	PUNCT
ejpam-3543	514	9	y	y	X
ejpam-3543	514	10	)	)	PUNCT
ejpam-3543	514	11	=	=	SYM
ejpam-3543	514	12	β−	β−	PROPN
ejpam-3543	514	13	,	,	PUNCT
ejpam-3543	514	14	and	and	CCONJ
ejpam-3543	514	15	λgf	λgf	X
ejpam-3543	515	1	[	[	X
ejpam-3543	515	2	γ	γ	X
ejpam-3543	515	3	+	+	X
ejpam-3543	515	4	γ−	γ−	PROPN
ejpam-3543	515	5	]	]	PUNCT
ejpam-3543	515	6	(	(	PUNCT
ejpam-3543	515	7	x	x	SYM
ejpam-3543	515	8	·	·	PUNCT
ejpam-3543	515	9	y	y	X
ejpam-3543	515	10	)	)	PUNCT
ejpam-3543	515	11	=	=	PRON
ejpam-3543	515	12	γ+	γ+	PROPN
ejpam-3543	515	13	.	.	PUNCT
ejpam-3543	516	1	thus	thus	ADV
ejpam-3543	516	2	λgt	λgt	PRON
ejpam-3543	517	1	[	[	X
ejpam-3543	517	2	α	α	X
ejpam-3543	517	3	+	+	X
ejpam-3543	518	1	α−	α−	ADP
ejpam-3543	518	2	]	]	X
ejpam-3543	518	3	(	(	PUNCT
ejpam-3543	518	4	x	x	SYM
ejpam-3543	518	5	·	·	PUNCT
ejpam-3543	518	6	y	y	X
ejpam-3543	518	7	)	)	PUNCT
ejpam-3543	518	8	=	=	PRON
ejpam-3543	518	9	α+	α+	PUNCT
ejpam-3543	518	10	≥	≥	X
ejpam-3543	519	1	α+	α+	X
ejpam-3543	519	2	=	=	PUNCT
ejpam-3543	519	3	λgt	λgt	X
ejpam-3543	520	1	[	[	X
ejpam-3543	520	2	α	α	X
ejpam-3543	520	3	+	+	X
ejpam-3543	521	1	α−	α−	ADP
ejpam-3543	521	2	]	]	X
ejpam-3543	521	3	(	(	PUNCT
ejpam-3543	521	4	y	y	NOUN
ejpam-3543	521	5	)	)	PUNCT
ejpam-3543	521	6	,	,	PUNCT
ejpam-3543	521	7	λgi	λgi	X
ejpam-3543	522	1	[	[	X
ejpam-3543	522	2	β	β	X
ejpam-3543	522	3	−	−	NOUN
ejpam-3543	522	4	β+	β+	PUNCT
ejpam-3543	522	5	]	]	X
ejpam-3543	522	6	(	(	PUNCT
ejpam-3543	522	7	x	x	SYM
ejpam-3543	522	8	·	·	PUNCT
ejpam-3543	522	9	y	y	X
ejpam-3543	522	10	)	)	PUNCT
ejpam-3543	523	1	=	=	PUNCT
ejpam-3543	523	2	β−	β−	PUNCT
ejpam-3543	524	1	≤	≤	NUM
ejpam-3543	524	2	β−	β−	PUNCT
ejpam-3543	525	1	=	=	PUNCT
ejpam-3543	525	2	λgi	λgi	NOUN
ejpam-3543	526	1	[	[	X
ejpam-3543	526	2	β	β	X
ejpam-3543	526	3	−	−	NOUN
ejpam-3543	526	4	β+	β+	PUNCT
ejpam-3543	526	5	]	]	X
ejpam-3543	526	6	(	(	PUNCT
ejpam-3543	526	7	y	y	NOUN
ejpam-3543	526	8	)	)	PUNCT
ejpam-3543	526	9	,	,	PUNCT
ejpam-3543	526	10	λgf	λgf	X
ejpam-3543	527	1	[	[	X
ejpam-3543	527	2	γ	γ	X
ejpam-3543	527	3	+	+	X
ejpam-3543	527	4	γ−	γ−	PROPN
ejpam-3543	527	5	]	]	PUNCT
ejpam-3543	527	6	(	(	PUNCT
ejpam-3543	527	7	x	x	SYM
ejpam-3543	527	8	·	·	PUNCT
ejpam-3543	527	9	y	y	X
ejpam-3543	527	10	)	)	PUNCT
ejpam-3543	527	11	=	=	PRON
ejpam-3543	527	12	γ+	γ+	PUNCT
ejpam-3543	527	13	≥	≥	NOUN
ejpam-3543	527	14	γ+	γ+	PUNCT
ejpam-3543	527	15	=	=	SYM
ejpam-3543	527	16	λgf	λgf	X
ejpam-3543	528	1	[	[	X
ejpam-3543	528	2	γ	γ	X
ejpam-3543	528	3	+	+	X
ejpam-3543	528	4	γ−	γ−	PROPN
ejpam-3543	528	5	]	]	PUNCT
ejpam-3543	528	6	(	(	PUNCT
ejpam-3543	528	7	y	y	NOUN
ejpam-3543	528	8	)	)	PUNCT
ejpam-3543	528	9	.	.	PUNCT
ejpam-3543	529	1	case	case	NOUN
ejpam-3543	529	2	2	2	NUM
ejpam-3543	529	3	:	:	PUNCT
ejpam-3543	530	1	y	y	PROPN
ejpam-3543	530	2	6∈	6∈	PROPN
ejpam-3543	530	3	g.	g.	NOUN
ejpam-3543	530	4	then	then	ADV
ejpam-3543	530	5	λgt	λgt	PRON
ejpam-3543	531	1	[	[	X
ejpam-3543	531	2	α	α	X
ejpam-3543	531	3	+	+	X
ejpam-3543	532	1	α−	α−	ADP
ejpam-3543	532	2	]	]	X
ejpam-3543	532	3	(	(	PUNCT
ejpam-3543	532	4	y	y	NOUN
ejpam-3543	532	5	)	)	PUNCT
ejpam-3543	532	6	=	=	PUNCT
ejpam-3543	532	7	α−	α−	PROPN
ejpam-3543	532	8	,	,	PUNCT
ejpam-3543	532	9	λgi	λgi	X
ejpam-3543	533	1	[	[	X
ejpam-3543	533	2	β	β	X
ejpam-3543	533	3	−	−	NOUN
ejpam-3543	533	4	β+	β+	PUNCT
ejpam-3543	533	5	]	]	X
ejpam-3543	533	6	(	(	PUNCT
ejpam-3543	533	7	y	y	NOUN
ejpam-3543	533	8	)	)	PUNCT
ejpam-3543	533	9	=	=	SYM
ejpam-3543	534	1	β+	β+	NOUN
ejpam-3543	534	2	,	,	PUNCT
ejpam-3543	534	3	and	and	CCONJ
ejpam-3543	534	4	λgf	λgf	X
ejpam-3543	535	1	[	[	X
ejpam-3543	535	2	γ	γ	X
ejpam-3543	535	3	+	+	X
ejpam-3543	535	4	γ−	γ−	PROPN
ejpam-3543	535	5	]	]	PUNCT
ejpam-3543	535	6	(	(	PUNCT
ejpam-3543	535	7	y	y	NOUN
ejpam-3543	535	8	)	)	PUNCT
ejpam-3543	535	9	=	=	VERB
ejpam-3543	535	10	γ−.	γ−.	NOUN
ejpam-3543	535	11	thus	thus	ADV
ejpam-3543	535	12	λgt	λgt	PRON
ejpam-3543	536	1	[	[	X
ejpam-3543	536	2	α	α	X
ejpam-3543	536	3	+	+	X
ejpam-3543	537	1	α−	α−	ADP
ejpam-3543	537	2	]	]	X
ejpam-3543	537	3	(	(	PUNCT
ejpam-3543	537	4	x	x	SYM
ejpam-3543	537	5	·	·	PUNCT
ejpam-3543	537	6	y	y	X
ejpam-3543	537	7	)	)	PUNCT
ejpam-3543	537	8	≥	≥	NOUN
ejpam-3543	537	9	α−	α−	ADP
ejpam-3543	537	10	=	=	PUNCT
ejpam-3543	537	11	λgt	λgt	PROPN
ejpam-3543	538	1	[	[	X
ejpam-3543	538	2	α	α	X
ejpam-3543	538	3	+	+	X
ejpam-3543	539	1	α−	α−	ADP
ejpam-3543	539	2	]	]	X
ejpam-3543	539	3	(	(	PUNCT
ejpam-3543	539	4	y	y	NOUN
ejpam-3543	539	5	)	)	PUNCT
ejpam-3543	539	6	,	,	PUNCT
ejpam-3543	539	7	λgi	λgi	X
ejpam-3543	540	1	[	[	X
ejpam-3543	540	2	β	β	X
ejpam-3543	540	3	−	−	NOUN
ejpam-3543	540	4	β+	β+	PUNCT
ejpam-3543	540	5	]	]	X
ejpam-3543	540	6	(	(	PUNCT
ejpam-3543	540	7	x	x	SYM
ejpam-3543	540	8	·	·	PUNCT
ejpam-3543	540	9	y	y	X
ejpam-3543	540	10	)	)	PUNCT
ejpam-3543	540	11	≤	≤	NOUN
ejpam-3543	540	12	β+	β+	PUNCT
ejpam-3543	540	13	=	=	SYM
ejpam-3543	540	14	λgi	λgi	NOUN
ejpam-3543	541	1	[	[	X
ejpam-3543	541	2	β	β	X
ejpam-3543	541	3	−	−	NOUN
ejpam-3543	541	4	β+	β+	PUNCT
ejpam-3543	541	5	]	]	X
ejpam-3543	541	6	(	(	PUNCT
ejpam-3543	541	7	y	y	NOUN
ejpam-3543	541	8	)	)	PUNCT
ejpam-3543	541	9	,	,	PUNCT
ejpam-3543	541	10	m.	m.	NOUN
ejpam-3543	541	11	songsaeng	songsaeng	PROPN
ejpam-3543	541	12	,	,	PUNCT
ejpam-3543	541	13	a.	a.	NOUN
ejpam-3543	541	14	iampan	iampan	PROPN
ejpam-3543	541	15	/	/	SYM
ejpam-3543	541	16	eur	eur	PROPN
ejpam-3543	541	17	.	.	PUNCT
ejpam-3543	542	1	j.	j.	PROPN
ejpam-3543	542	2	pure	pure	PROPN
ejpam-3543	542	3	appl	appl	PROPN
ejpam-3543	542	4	.	.	PROPN
ejpam-3543	542	5	math	math	PROPN
ejpam-3543	542	6	,	,	PUNCT
ejpam-3543	542	7	12	12	NUM
ejpam-3543	542	8	(	(	PUNCT
ejpam-3543	542	9	4	4	NUM
ejpam-3543	542	10	)	)	PUNCT
ejpam-3543	542	11	(	(	PUNCT
ejpam-3543	542	12	2019	2019	NUM
ejpam-3543	542	13	)	)	PUNCT
ejpam-3543	542	14	,	,	PUNCT
ejpam-3543	542	15	1382	1382	NUM
ejpam-3543	542	16	-	-	SYM
ejpam-3543	542	17	1409	1409	NUM
ejpam-3543	542	18	1399	1399	NUM
ejpam-3543	542	19	λgf	λgf	NOUN
ejpam-3543	543	1	[	[	X
ejpam-3543	543	2	γ	γ	X
ejpam-3543	543	3	+	+	X
ejpam-3543	543	4	γ−	γ−	PROPN
ejpam-3543	543	5	]	]	PUNCT
ejpam-3543	543	6	(	(	PUNCT
ejpam-3543	543	7	x	x	SYM
ejpam-3543	543	8	·	·	PUNCT
ejpam-3543	543	9	y	y	X
ejpam-3543	543	10	)	)	PUNCT
ejpam-3543	543	11	≥	≥	NOUN
ejpam-3543	543	12	γ−	γ−	NUM
ejpam-3543	543	13	=	=	SYM
ejpam-3543	543	14	λgf	λgf	PROPN
ejpam-3543	544	1	[	[	X
ejpam-3543	544	2	γ	γ	X
ejpam-3543	544	3	+	+	X
ejpam-3543	544	4	γ−	γ−	PROPN
ejpam-3543	544	5	]	]	PUNCT
ejpam-3543	544	6	(	(	PUNCT
ejpam-3543	544	7	y	y	NOUN
ejpam-3543	544	8	)	)	PUNCT
ejpam-3543	544	9	.	.	PUNCT
ejpam-3543	545	1	hence	hence	ADV
ejpam-3543	545	2	,	,	PUNCT
ejpam-3543	545	3	λg[α	λg[α	PROPN
ejpam-3543	545	4	+	+	PROPN
ejpam-3543	545	5	,	,	PUNCT
ejpam-3543	545	6	β−,γ+	β−,γ+	X
ejpam-3543	545	7	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	545	8	]	]	PUNCT
ejpam-3543	545	9	is	be	AUX
ejpam-3543	545	10	a	a	DET
ejpam-3543	545	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	545	12	near	near	ADP
ejpam-3543	545	13	up	up	ADJ
ejpam-3543	545	14	-	-	PUNCT
ejpam-3543	545	15	filter	filter	NOUN
ejpam-3543	545	16	of	of	ADP
ejpam-3543	545	17	x.	x.	PROPN
ejpam-3543	545	18	theorem	theorem	VERB
ejpam-3543	545	19	16	16	NUM
ejpam-3543	545	20	.	.	PUNCT
ejpam-3543	546	1	a	a	DET
ejpam-3543	546	2	ns	ns	ADJ
ejpam-3543	546	3	λg[α	λg[α	PROPN
ejpam-3543	546	4	+	+	PROPN
ejpam-3543	546	5	,	,	PUNCT
ejpam-3543	546	6	β−,γ+	β−,γ+	X
ejpam-3543	546	7	α−,β+,γ−	α−,β+,γ−	VERB
ejpam-3543	546	8	]	]	PUNCT
ejpam-3543	546	9	in	in	ADP
ejpam-3543	546	10	x	x	SYM
ejpam-3543	546	11	is	be	AUX
ejpam-3543	546	12	a	a	DET
ejpam-3543	546	13	neutrosophic	neutrosophic	ADJ
ejpam-3543	546	14	up	up	ADJ
ejpam-3543	546	15	-	-	PUNCT
ejpam-3543	546	16	filter	filter	NOUN
ejpam-3543	546	17	of	of	ADP
ejpam-3543	546	18	x	x	SYM
ejpam-3543	546	19	if	if	SCONJ
ejpam-3543	546	20	and	and	CCONJ
ejpam-3543	546	21	only	only	ADV
ejpam-3543	546	22	if	if	SCONJ
ejpam-3543	546	23	a	a	DET
ejpam-3543	546	24	nonempty	nonempty	NOUN
ejpam-3543	546	25	subset	subset	VERB
ejpam-3543	546	26	g	g	PROPN
ejpam-3543	546	27	of	of	ADP
ejpam-3543	546	28	x	x	PUNCT
ejpam-3543	546	29	is	be	AUX
ejpam-3543	546	30	a	a	DET
ejpam-3543	546	31	up	up	ADJ
ejpam-3543	546	32	-	-	PUNCT
ejpam-3543	546	33	filter	filter	NOUN
ejpam-3543	546	34	of	of	ADP
ejpam-3543	546	35	x.	x.	NOUN
ejpam-3543	546	36	proof	proof	PROPN
ejpam-3543	546	37	.	.	PUNCT
ejpam-3543	547	1	assume	assume	VERB
ejpam-3543	547	2	that	that	SCONJ
ejpam-3543	547	3	λg[α	λg[α	PROPN
ejpam-3543	547	4	+	+	NOUN
ejpam-3543	547	5	,	,	PUNCT
ejpam-3543	547	6	β−,γ+	β−,γ+	X
ejpam-3543	547	7	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	547	8	]	]	PUNCT
ejpam-3543	547	9	is	be	AUX
ejpam-3543	547	10	a	a	DET
ejpam-3543	547	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	547	12	up	up	ADJ
ejpam-3543	547	13	-	-	PUNCT
ejpam-3543	547	14	filter	filter	NOUN
ejpam-3543	547	15	of	of	ADP
ejpam-3543	547	16	x.	x.	NOUN
ejpam-3543	547	17	since	since	SCONJ
ejpam-3543	547	18	λg[α	λg[α	PROPN
ejpam-3543	547	19	+	+	PROPN
ejpam-3543	547	20	,	,	PUNCT
ejpam-3543	547	21	β−,γ+	β−,γ+	X
ejpam-3543	547	22	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	547	23	]	]	PUNCT
ejpam-3543	547	24	satisfies	satisfy	VERB
ejpam-3543	547	25	the	the	DET
ejpam-3543	547	26	condition	condition	NOUN
ejpam-3543	547	27	(	(	PUNCT
ejpam-3543	547	28	3.6	3.6	NUM
ejpam-3543	547	29	)	)	PUNCT
ejpam-3543	547	30	,	,	PUNCT
ejpam-3543	547	31	it	it	PRON
ejpam-3543	547	32	follows	follow	VERB
ejpam-3543	547	33	from	from	ADP
ejpam-3543	547	34	lemma	lemma	PROPN
ejpam-3543	547	35	4	4	NUM
ejpam-3543	547	36	that	that	SCONJ
ejpam-3543	547	37	0	0	NUM
ejpam-3543	547	38	∈	∈	NOUN
ejpam-3543	547	39	g.	g.	NOUN
ejpam-3543	547	40	next	next	ADV
ejpam-3543	547	41	,	,	PUNCT
ejpam-3543	547	42	let	let	VERB
ejpam-3543	547	43	x	x	PRON
ejpam-3543	547	44	,	,	PUNCT
ejpam-3543	547	45	y	y	PROPN
ejpam-3543	547	46	∈	∈	PROPN
ejpam-3543	547	47	x	x	AUX
ejpam-3543	547	48	be	be	AUX
ejpam-3543	547	49	such	such	ADJ
ejpam-3543	547	50	that	that	SCONJ
ejpam-3543	547	51	x	x	X
ejpam-3543	547	52	·	·	PUNCT
ejpam-3543	547	53	y	y	PROPN
ejpam-3543	547	54	∈	∈	PROPN
ejpam-3543	547	55	g	g	PROPN
ejpam-3543	547	56	and	and	CCONJ
ejpam-3543	547	57	x	x	PROPN
ejpam-3543	547	58	∈	∈	PROPN
ejpam-3543	547	59	g.	g.	NOUN
ejpam-3543	548	1	then	then	ADV
ejpam-3543	548	2	λgt	λgt	PRON
ejpam-3543	549	1	[	[	X
ejpam-3543	549	2	α	α	X
ejpam-3543	549	3	+	+	X
ejpam-3543	550	1	α−	α−	ADP
ejpam-3543	550	2	]	]	X
ejpam-3543	550	3	(	(	PUNCT
ejpam-3543	550	4	x	x	SYM
ejpam-3543	550	5	·	·	PUNCT
ejpam-3543	550	6	y	y	X
ejpam-3543	550	7	)	)	PUNCT
ejpam-3543	550	8	=	=	PRON
ejpam-3543	551	1	α+	α+	NOUN
ejpam-3543	551	2	=	=	PUNCT
ejpam-3543	552	1	λgt	λgt	X
ejpam-3543	553	1	[	[	X
ejpam-3543	553	2	α	α	X
ejpam-3543	553	3	+	+	X
ejpam-3543	554	1	α−	α−	ADP
ejpam-3543	554	2	]	]	X
ejpam-3543	554	3	(	(	PUNCT
ejpam-3543	554	4	x	x	NOUN
ejpam-3543	554	5	)	)	PUNCT
ejpam-3543	554	6	.	.	PUNCT
ejpam-3543	555	1	thus	thus	ADV
ejpam-3543	555	2	λgt	λgt	PRON
ejpam-3543	556	1	[	[	X
ejpam-3543	556	2	α	α	X
ejpam-3543	556	3	+	+	X
ejpam-3543	557	1	α−	α−	ADP
ejpam-3543	557	2	]	]	X
ejpam-3543	557	3	(	(	PUNCT
ejpam-3543	557	4	y	y	NOUN
ejpam-3543	557	5	)	)	PUNCT
ejpam-3543	557	6	≥	≥	NOUN
ejpam-3543	557	7	min{λgt	min{λgt	VERB
ejpam-3543	558	1	[	[	X
ejpam-3543	558	2	α	α	X
ejpam-3543	558	3	+	+	X
ejpam-3543	559	1	α−	α−	ADP
ejpam-3543	559	2	]	]	X
ejpam-3543	559	3	(	(	PUNCT
ejpam-3543	559	4	x	x	SYM
ejpam-3543	559	5	·	·	PUNCT
ejpam-3543	559	6	y	y	X
ejpam-3543	559	7	)	)	PUNCT
ejpam-3543	559	8	,	,	PUNCT
ejpam-3543	559	9	λgt	λgt	X
ejpam-3543	560	1	[	[	X
ejpam-3543	560	2	α	α	X
ejpam-3543	560	3	+	+	X
ejpam-3543	561	1	α−	α−	ADP
ejpam-3543	561	2	]	]	X
ejpam-3543	561	3	(	(	PUNCT
ejpam-3543	561	4	x	x	NOUN
ejpam-3543	561	5	)	)	PUNCT
ejpam-3543	561	6	}	}	PUNCT
ejpam-3543	561	7	=	=	SYM
ejpam-3543	561	8	α+	α+	PUNCT
ejpam-3543	561	9	≥	≥	NOUN
ejpam-3543	561	10	λgt	λgt	X
ejpam-3543	562	1	[	[	X
ejpam-3543	562	2	α	α	X
ejpam-3543	562	3	+	+	X
ejpam-3543	563	1	α−	α−	ADP
ejpam-3543	563	2	]	]	X
ejpam-3543	563	3	(	(	PUNCT
ejpam-3543	563	4	y	y	NOUN
ejpam-3543	563	5	)	)	PUNCT
ejpam-3543	563	6	(	(	PUNCT
ejpam-3543	563	7	3.12	3.12	NUM
ejpam-3543	563	8	)	)	PUNCT
ejpam-3543	563	9	and	and	CCONJ
ejpam-3543	563	10	so	so	ADV
ejpam-3543	563	11	λgt	λgt	PRON
ejpam-3543	564	1	[	[	X
ejpam-3543	564	2	α	α	X
ejpam-3543	564	3	+	+	X
ejpam-3543	565	1	α−	α−	ADP
ejpam-3543	565	2	]	]	X
ejpam-3543	565	3	(	(	PUNCT
ejpam-3543	565	4	y	y	NOUN
ejpam-3543	565	5	)	)	PUNCT
ejpam-3543	565	6	=	=	SYM
ejpam-3543	565	7	α+	α+	NOUN
ejpam-3543	565	8	.	.	PUNCT
ejpam-3543	566	1	thus	thus	ADV
ejpam-3543	566	2	y	y	PROPN
ejpam-3543	566	3	∈	∈	PROPN
ejpam-3543	566	4	g.	g.	NOUN
ejpam-3543	566	5	hence	hence	ADV
ejpam-3543	566	6	,	,	PUNCT
ejpam-3543	566	7	g	g	PROPN
ejpam-3543	566	8	is	be	AUX
ejpam-3543	566	9	a	a	DET
ejpam-3543	566	10	up	up	ADJ
ejpam-3543	566	11	-	-	PUNCT
ejpam-3543	566	12	filter	filter	NOUN
ejpam-3543	566	13	of	of	ADP
ejpam-3543	566	14	x.	x.	NOUN
ejpam-3543	566	15	conversely	conversely	ADV
ejpam-3543	566	16	,	,	PUNCT
ejpam-3543	566	17	assume	assume	VERB
ejpam-3543	566	18	that	that	SCONJ
ejpam-3543	566	19	g	g	PROPN
ejpam-3543	566	20	is	be	AUX
ejpam-3543	566	21	a	a	DET
ejpam-3543	566	22	up	up	ADJ
ejpam-3543	566	23	-	-	PUNCT
ejpam-3543	566	24	filter	filter	NOUN
ejpam-3543	566	25	of	of	ADP
ejpam-3543	566	26	x.	x.	NOUN
ejpam-3543	566	27	since	since	SCONJ
ejpam-3543	566	28	0	0	NUM
ejpam-3543	566	29	∈	∈	PROPN
ejpam-3543	566	30	g	g	NOUN
ejpam-3543	566	31	,	,	PUNCT
ejpam-3543	566	32	it	it	PRON
ejpam-3543	566	33	follows	follow	VERB
ejpam-3543	566	34	from	from	ADP
ejpam-3543	566	35	lemma	lemma	PROPN
ejpam-3543	566	36	3	3	NUM
ejpam-3543	566	37	that	that	PRON
ejpam-3543	566	38	λg[α	λg[α	PROPN
ejpam-3543	566	39	+	+	NOUN
ejpam-3543	566	40	,	,	PUNCT
ejpam-3543	566	41	β−,γ+	β−,γ+	X
ejpam-3543	566	42	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	566	43	]	]	PUNCT
ejpam-3543	566	44	satisfies	satisfy	VERB
ejpam-3543	566	45	the	the	DET
ejpam-3543	566	46	conditions	condition	NOUN
ejpam-3543	566	47	(	(	PUNCT
ejpam-3543	566	48	3.6	3.6	NUM
ejpam-3543	566	49	)	)	PUNCT
ejpam-3543	566	50	,	,	PUNCT
ejpam-3543	566	51	(	(	PUNCT
ejpam-3543	566	52	3.7	3.7	NUM
ejpam-3543	566	53	)	)	PUNCT
ejpam-3543	566	54	,	,	PUNCT
ejpam-3543	566	55	and	and	CCONJ
ejpam-3543	566	56	(	(	PUNCT
ejpam-3543	566	57	3.8	3.8	NUM
ejpam-3543	566	58	)	)	PUNCT
ejpam-3543	566	59	.	.	PUNCT
ejpam-3543	567	1	next	next	ADV
ejpam-3543	567	2	,	,	PUNCT
ejpam-3543	567	3	let	let	VERB
ejpam-3543	567	4	x	x	PRON
ejpam-3543	567	5	,	,	PUNCT
ejpam-3543	567	6	y	y	PROPN
ejpam-3543	567	7	∈	∈	PROPN
ejpam-3543	567	8	x.	x.	NOUN
ejpam-3543	567	9	case	case	NOUN
ejpam-3543	567	10	1	1	NUM
ejpam-3543	567	11	:	:	PUNCT
ejpam-3543	567	12	x	x	SYM
ejpam-3543	567	13	·	·	PUNCT
ejpam-3543	567	14	y	y	X
ejpam-3543	567	15	∈	∈	PROPN
ejpam-3543	567	16	g	g	PROPN
ejpam-3543	567	17	and	and	CCONJ
ejpam-3543	567	18	x	x	PROPN
ejpam-3543	567	19	∈	∈	PROPN
ejpam-3543	567	20	g.	g.	NOUN
ejpam-3543	568	1	then	then	ADV
ejpam-3543	568	2	λgt	λgt	PRON
ejpam-3543	569	1	[	[	X
ejpam-3543	569	2	α	α	X
ejpam-3543	569	3	+	+	X
ejpam-3543	570	1	α−	α−	ADP
ejpam-3543	570	2	]	]	X
ejpam-3543	570	3	(	(	PUNCT
ejpam-3543	570	4	x	x	SYM
ejpam-3543	570	5	·	·	PUNCT
ejpam-3543	570	6	y	y	X
ejpam-3543	570	7	)	)	PUNCT
ejpam-3543	570	8	=	=	PRON
ejpam-3543	571	1	α+	α+	NOUN
ejpam-3543	571	2	=	=	PUNCT
ejpam-3543	572	1	λgt	λgt	X
ejpam-3543	573	1	[	[	X
ejpam-3543	573	2	α	α	X
ejpam-3543	573	3	+	+	X
ejpam-3543	574	1	α−	α−	ADP
ejpam-3543	574	2	]	]	X
ejpam-3543	574	3	(	(	PUNCT
ejpam-3543	574	4	x	x	NOUN
ejpam-3543	574	5	)	)	PUNCT
ejpam-3543	574	6	,	,	PUNCT
ejpam-3543	574	7	λgi	λgi	X
ejpam-3543	575	1	[	[	X
ejpam-3543	575	2	β	β	X
ejpam-3543	575	3	−	−	NOUN
ejpam-3543	575	4	β+	β+	PUNCT
ejpam-3543	575	5	]	]	X
ejpam-3543	575	6	(	(	PUNCT
ejpam-3543	575	7	x	x	SYM
ejpam-3543	575	8	·	·	PUNCT
ejpam-3543	575	9	y	y	X
ejpam-3543	575	10	)	)	PUNCT
ejpam-3543	575	11	=	=	PUNCT
ejpam-3543	576	1	β−	β−	PUNCT
ejpam-3543	576	2	=	=	PUNCT
ejpam-3543	576	3	λgi	λgi	NOUN
ejpam-3543	577	1	[	[	X
ejpam-3543	577	2	β	β	X
ejpam-3543	577	3	−	−	NOUN
ejpam-3543	577	4	β+	β+	PUNCT
ejpam-3543	577	5	]	]	X
ejpam-3543	577	6	(	(	PUNCT
ejpam-3543	577	7	x	x	NOUN
ejpam-3543	577	8	)	)	PUNCT
ejpam-3543	577	9	,	,	PUNCT
ejpam-3543	577	10	λgf	λgf	X
ejpam-3543	578	1	[	[	X
ejpam-3543	578	2	γ	γ	X
ejpam-3543	578	3	+	+	X
ejpam-3543	578	4	γ−	γ−	PROPN
ejpam-3543	578	5	]	]	PUNCT
ejpam-3543	578	6	(	(	PUNCT
ejpam-3543	578	7	x	x	SYM
ejpam-3543	578	8	·	·	PUNCT
ejpam-3543	578	9	y	y	X
ejpam-3543	578	10	)	)	PUNCT
ejpam-3543	578	11	=	=	PRON
ejpam-3543	578	12	γ+	γ+	PUNCT
ejpam-3543	579	1	=	=	SYM
ejpam-3543	579	2	λgf	λgf	X
ejpam-3543	580	1	[	[	X
ejpam-3543	580	2	γ	γ	X
ejpam-3543	580	3	+	+	X
ejpam-3543	580	4	γ−	γ−	PROPN
ejpam-3543	580	5	]	]	PUNCT
ejpam-3543	580	6	(	(	PUNCT
ejpam-3543	580	7	x	x	NOUN
ejpam-3543	580	8	)	)	PUNCT
ejpam-3543	580	9	.	.	PUNCT
ejpam-3543	581	1	since	since	SCONJ
ejpam-3543	581	2	g	g	PROPN
ejpam-3543	581	3	is	be	AUX
ejpam-3543	581	4	a	a	DET
ejpam-3543	581	5	up	up	ADJ
ejpam-3543	581	6	-	-	PUNCT
ejpam-3543	581	7	filter	filter	NOUN
ejpam-3543	581	8	of	of	ADP
ejpam-3543	581	9	x	x	PRON
ejpam-3543	581	10	,	,	PUNCT
ejpam-3543	581	11	we	we	PRON
ejpam-3543	581	12	have	have	VERB
ejpam-3543	581	13	y	y	PROPN
ejpam-3543	581	14	∈	∈	PROPN
ejpam-3543	581	15	g	g	PROPN
ejpam-3543	582	1	and	and	CCONJ
ejpam-3543	582	2	so	so	ADV
ejpam-3543	582	3	λgt	λgt	PRON
ejpam-3543	583	1	[	[	X
ejpam-3543	583	2	α	α	X
ejpam-3543	583	3	+	+	X
ejpam-3543	584	1	α−	α−	ADP
ejpam-3543	584	2	]	]	X
ejpam-3543	584	3	(	(	PUNCT
ejpam-3543	584	4	y	y	NOUN
ejpam-3543	584	5	)	)	PUNCT
ejpam-3543	584	6	=	=	SYM
ejpam-3543	584	7	α+	α+	X
ejpam-3543	584	8	,	,	PUNCT
ejpam-3543	584	9	λgi	λgi	X
ejpam-3543	585	1	[	[	X
ejpam-3543	585	2	β	β	X
ejpam-3543	585	3	−	−	NOUN
ejpam-3543	585	4	β+	β+	PUNCT
ejpam-3543	585	5	]	]	X
ejpam-3543	585	6	(	(	PUNCT
ejpam-3543	585	7	y	y	NOUN
ejpam-3543	585	8	)	)	PUNCT
ejpam-3543	585	9	=	=	SYM
ejpam-3543	585	10	β−	β−	PROPN
ejpam-3543	585	11	,	,	PUNCT
ejpam-3543	585	12	and	and	CCONJ
ejpam-3543	585	13	λgf	λgf	X
ejpam-3543	586	1	[	[	X
ejpam-3543	586	2	γ	γ	X
ejpam-3543	586	3	+	+	X
ejpam-3543	586	4	γ−	γ−	PROPN
ejpam-3543	586	5	]	]	PUNCT
ejpam-3543	586	6	(	(	PUNCT
ejpam-3543	586	7	y	y	NOUN
ejpam-3543	586	8	)	)	PUNCT
ejpam-3543	586	9	=	=	SYM
ejpam-3543	586	10	γ+	γ+	PROPN
ejpam-3543	586	11	.	.	PUNCT
ejpam-3543	587	1	thus	thus	ADV
ejpam-3543	587	2	λgt	λgt	PRON
ejpam-3543	588	1	[	[	X
ejpam-3543	588	2	α	α	X
ejpam-3543	588	3	+	+	X
ejpam-3543	589	1	α−	α−	ADP
ejpam-3543	589	2	]	]	X
ejpam-3543	589	3	(	(	PUNCT
ejpam-3543	589	4	y	y	NOUN
ejpam-3543	589	5	)	)	PUNCT
ejpam-3543	589	6	=	=	SYM
ejpam-3543	589	7	α+	α+	PUNCT
ejpam-3543	589	8	≥	≥	X
ejpam-3543	589	9	α+	α+	X
ejpam-3543	589	10	=	=	X
ejpam-3543	589	11	min{λgt	min{λgt	NOUN
ejpam-3543	590	1	[	[	X
ejpam-3543	590	2	α	α	X
ejpam-3543	590	3	+	+	X
ejpam-3543	591	1	α−	α−	ADP
ejpam-3543	591	2	]	]	X
ejpam-3543	591	3	(	(	PUNCT
ejpam-3543	591	4	x	x	SYM
ejpam-3543	591	5	·	·	PUNCT
ejpam-3543	591	6	y	y	X
ejpam-3543	591	7	)	)	PUNCT
ejpam-3543	591	8	,	,	PUNCT
ejpam-3543	591	9	λgt	λgt	X
ejpam-3543	592	1	[	[	X
ejpam-3543	592	2	α	α	X
ejpam-3543	592	3	+	+	X
ejpam-3543	593	1	α−	α−	ADP
ejpam-3543	593	2	]	]	X
ejpam-3543	593	3	(	(	PUNCT
ejpam-3543	593	4	x	x	NOUN
ejpam-3543	593	5	)	)	PUNCT
ejpam-3543	593	6	}	}	PUNCT
ejpam-3543	593	7	,	,	PUNCT
ejpam-3543	593	8	λgi	λgi	X
ejpam-3543	594	1	[	[	X
ejpam-3543	594	2	β	β	X
ejpam-3543	594	3	−	−	NOUN
ejpam-3543	594	4	β+	β+	PUNCT
ejpam-3543	594	5	]	]	X
ejpam-3543	594	6	(	(	PUNCT
ejpam-3543	594	7	y	y	NOUN
ejpam-3543	594	8	)	)	PUNCT
ejpam-3543	594	9	=	=	PUNCT
ejpam-3543	595	1	β−	β−	PUNCT
ejpam-3543	595	2	≤	≤	NUM
ejpam-3543	595	3	β−	β−	PUNCT
ejpam-3543	596	1	=	=	SYM
ejpam-3543	596	2	max{λgi	max{λgi	NOUN
ejpam-3543	597	1	[	[	X
ejpam-3543	597	2	β	β	X
ejpam-3543	597	3	−	−	NOUN
ejpam-3543	597	4	β+	β+	PUNCT
ejpam-3543	597	5	]	]	X
ejpam-3543	597	6	(	(	PUNCT
ejpam-3543	597	7	x	x	SYM
ejpam-3543	597	8	·	·	PUNCT
ejpam-3543	597	9	y	y	X
ejpam-3543	597	10	)	)	PUNCT
ejpam-3543	597	11	,	,	PUNCT
ejpam-3543	597	12	λgi	λgi	X
ejpam-3543	598	1	[	[	X
ejpam-3543	598	2	β	β	X
ejpam-3543	598	3	−	−	NOUN
ejpam-3543	598	4	β+	β+	PUNCT
ejpam-3543	598	5	]	]	X
ejpam-3543	598	6	(	(	PUNCT
ejpam-3543	598	7	x	x	NOUN
ejpam-3543	598	8	)	)	PUNCT
ejpam-3543	598	9	}	}	PUNCT
ejpam-3543	598	10	,	,	PUNCT
ejpam-3543	598	11	λgf	λgf	X
ejpam-3543	599	1	[	[	X
ejpam-3543	599	2	γ	γ	X
ejpam-3543	599	3	+	+	X
ejpam-3543	599	4	γ−	γ−	PROPN
ejpam-3543	599	5	]	]	PUNCT
ejpam-3543	599	6	(	(	PUNCT
ejpam-3543	599	7	y	y	NOUN
ejpam-3543	599	8	)	)	PUNCT
ejpam-3543	599	9	=	=	PRON
ejpam-3543	599	10	γ+	γ+	PUNCT
ejpam-3543	599	11	≥	≥	NOUN
ejpam-3543	599	12	γ+	γ+	X
ejpam-3543	600	1	=	=	PUNCT
ejpam-3543	600	2	min{λgf	min{λgf	PROPN
ejpam-3543	600	3	[	[	X
ejpam-3543	600	4	γ	γ	X
ejpam-3543	600	5	+	+	X
ejpam-3543	600	6	γ−	γ−	PROPN
ejpam-3543	600	7	]	]	PUNCT
ejpam-3543	600	8	(	(	PUNCT
ejpam-3543	600	9	x	x	SYM
ejpam-3543	600	10	·	·	PUNCT
ejpam-3543	600	11	y	y	X
ejpam-3543	600	12	)	)	PUNCT
ejpam-3543	600	13	,	,	PUNCT
ejpam-3543	600	14	λgf	λgf	X
ejpam-3543	601	1	[	[	X
ejpam-3543	601	2	γ	γ	X
ejpam-3543	601	3	+	+	X
ejpam-3543	601	4	γ−	γ−	PROPN
ejpam-3543	601	5	]	]	PUNCT
ejpam-3543	601	6	(	(	PUNCT
ejpam-3543	601	7	x	x	NOUN
ejpam-3543	601	8	)	)	PUNCT
ejpam-3543	601	9	}	}	PUNCT
ejpam-3543	601	10	.	.	PUNCT
ejpam-3543	602	1	case	case	NOUN
ejpam-3543	602	2	2	2	NUM
ejpam-3543	602	3	:	:	PUNCT
ejpam-3543	602	4	x	x	SYM
ejpam-3543	602	5	·	·	PUNCT
ejpam-3543	602	6	y	y	NUM
ejpam-3543	602	7	6∈	6∈	NUM
ejpam-3543	602	8	g	g	PROPN
ejpam-3543	602	9	or	or	CCONJ
ejpam-3543	602	10	x	x	ADJ
ejpam-3543	602	11	6∈	6∈	PROPN
ejpam-3543	602	12	g.	g.	NOUN
ejpam-3543	603	1	then	then	ADV
ejpam-3543	603	2	λgt	λgt	PRON
ejpam-3543	604	1	[	[	X
ejpam-3543	604	2	α	α	X
ejpam-3543	604	3	+	+	X
ejpam-3543	605	1	α−	α−	ADP
ejpam-3543	605	2	]	]	X
ejpam-3543	605	3	(	(	PUNCT
ejpam-3543	605	4	x	x	SYM
ejpam-3543	605	5	·	·	PUNCT
ejpam-3543	605	6	y	y	X
ejpam-3543	605	7	)	)	PUNCT
ejpam-3543	605	8	=	=	PUNCT
ejpam-3543	606	1	α−	α−	ADP
ejpam-3543	606	2	or	or	CCONJ
ejpam-3543	606	3	λgt	λgt	PRON
ejpam-3543	607	1	[	[	X
ejpam-3543	607	2	α	α	X
ejpam-3543	607	3	+	+	X
ejpam-3543	608	1	α−	α−	ADP
ejpam-3543	608	2	]	]	X
ejpam-3543	608	3	(	(	PUNCT
ejpam-3543	608	4	x	x	X
ejpam-3543	608	5	)	)	PUNCT
ejpam-3543	608	6	=	=	SYM
ejpam-3543	608	7	α−	α−	PROPN
ejpam-3543	608	8	,	,	PUNCT
ejpam-3543	608	9	λgi	λgi	X
ejpam-3543	609	1	[	[	X
ejpam-3543	609	2	β	β	X
ejpam-3543	609	3	−	−	NOUN
ejpam-3543	609	4	β+	β+	PUNCT
ejpam-3543	609	5	]	]	X
ejpam-3543	609	6	(	(	PUNCT
ejpam-3543	609	7	x	x	SYM
ejpam-3543	609	8	·	·	PUNCT
ejpam-3543	609	9	y	y	X
ejpam-3543	609	10	)	)	PUNCT
ejpam-3543	609	11	=	=	SYM
ejpam-3543	609	12	β+	β+	PUNCT
ejpam-3543	609	13	or	or	CCONJ
ejpam-3543	609	14	λgi	λgi	X
ejpam-3543	610	1	[	[	X
ejpam-3543	610	2	β	β	X
ejpam-3543	610	3	−	−	NOUN
ejpam-3543	610	4	β+	β+	PUNCT
ejpam-3543	610	5	]	]	X
ejpam-3543	610	6	(	(	PUNCT
ejpam-3543	610	7	x	x	X
ejpam-3543	610	8	)	)	PUNCT
ejpam-3543	610	9	=	=	SYM
ejpam-3543	610	10	β+	β+	NOUN
ejpam-3543	610	11	,	,	PUNCT
ejpam-3543	610	12	λgf	λgf	NOUN
ejpam-3543	611	1	[	[	X
ejpam-3543	611	2	γ	γ	X
ejpam-3543	611	3	+	+	X
ejpam-3543	611	4	γ−	γ−	PROPN
ejpam-3543	611	5	]	]	PUNCT
ejpam-3543	611	6	(	(	PUNCT
ejpam-3543	611	7	x	x	SYM
ejpam-3543	611	8	·	·	PUNCT
ejpam-3543	611	9	y	y	X
ejpam-3543	611	10	)	)	PUNCT
ejpam-3543	611	11	=	=	SYM
ejpam-3543	611	12	γ−	γ−	PROPN
ejpam-3543	611	13	or	or	CCONJ
ejpam-3543	611	14	λgf	λgf	NOUN
ejpam-3543	612	1	[	[	X
ejpam-3543	612	2	γ	γ	X
ejpam-3543	612	3	+	+	X
ejpam-3543	612	4	γ−	γ−	PROPN
ejpam-3543	612	5	]	]	PUNCT
ejpam-3543	612	6	(	(	PUNCT
ejpam-3543	612	7	x	x	X
ejpam-3543	612	8	)	)	PUNCT
ejpam-3543	612	9	=	=	VERB
ejpam-3543	612	10	γ−.	γ−.	NOUN
ejpam-3543	612	11	thus	thus	ADV
ejpam-3543	612	12	min{λgt	min{λgt	X
ejpam-3543	613	1	[	[	X
ejpam-3543	613	2	α	α	X
ejpam-3543	613	3	+	+	X
ejpam-3543	614	1	α−	α−	ADP
ejpam-3543	614	2	]	]	X
ejpam-3543	614	3	(	(	PUNCT
ejpam-3543	614	4	x	x	SYM
ejpam-3543	614	5	·	·	PUNCT
ejpam-3543	614	6	y	y	X
ejpam-3543	614	7	)	)	PUNCT
ejpam-3543	614	8	,	,	PUNCT
ejpam-3543	614	9	λgt	λgt	X
ejpam-3543	615	1	[	[	X
ejpam-3543	615	2	α	α	X
ejpam-3543	615	3	+	+	X
ejpam-3543	616	1	α−	α−	ADP
ejpam-3543	616	2	]	]	X
ejpam-3543	616	3	(	(	PUNCT
ejpam-3543	616	4	x	x	NOUN
ejpam-3543	616	5	)	)	PUNCT
ejpam-3543	616	6	}	}	PUNCT
ejpam-3543	616	7	=	=	SYM
ejpam-3543	616	8	α−	α−	PROPN
ejpam-3543	616	9	,	,	PUNCT
ejpam-3543	616	10	max{λgi	max{λgi	NOUN
ejpam-3543	617	1	[	[	X
ejpam-3543	617	2	β	β	X
ejpam-3543	617	3	−	−	NOUN
ejpam-3543	617	4	β+	β+	PUNCT
ejpam-3543	617	5	]	]	X
ejpam-3543	617	6	(	(	PUNCT
ejpam-3543	617	7	x	x	SYM
ejpam-3543	617	8	·	·	PUNCT
ejpam-3543	617	9	y	y	X
ejpam-3543	617	10	)	)	PUNCT
ejpam-3543	617	11	,	,	PUNCT
ejpam-3543	617	12	λgi	λgi	X
ejpam-3543	618	1	[	[	X
ejpam-3543	618	2	β	β	X
ejpam-3543	618	3	−	−	NOUN
ejpam-3543	618	4	β+	β+	PUNCT
ejpam-3543	618	5	]	]	X
ejpam-3543	618	6	(	(	PUNCT
ejpam-3543	618	7	x	x	NOUN
ejpam-3543	618	8	)	)	PUNCT
ejpam-3543	618	9	}	}	PUNCT
ejpam-3543	619	1	=	=	SYM
ejpam-3543	619	2	β+	β+	NOUN
ejpam-3543	619	3	,	,	PUNCT
ejpam-3543	619	4	m.	m.	NOUN
ejpam-3543	619	5	songsaeng	songsaeng	PROPN
ejpam-3543	619	6	,	,	PUNCT
ejpam-3543	619	7	a.	a.	NOUN
ejpam-3543	619	8	iampan	iampan	PROPN
ejpam-3543	619	9	/	/	SYM
ejpam-3543	619	10	eur	eur	PROPN
ejpam-3543	619	11	.	.	PUNCT
ejpam-3543	620	1	j.	j.	PROPN
ejpam-3543	620	2	pure	pure	PROPN
ejpam-3543	620	3	appl	appl	PROPN
ejpam-3543	620	4	.	.	PROPN
ejpam-3543	620	5	math	math	PROPN
ejpam-3543	620	6	,	,	PUNCT
ejpam-3543	620	7	12	12	NUM
ejpam-3543	620	8	(	(	PUNCT
ejpam-3543	620	9	4	4	NUM
ejpam-3543	620	10	)	)	PUNCT
ejpam-3543	620	11	(	(	PUNCT
ejpam-3543	620	12	2019	2019	NUM
ejpam-3543	620	13	)	)	PUNCT
ejpam-3543	620	14	,	,	PUNCT
ejpam-3543	620	15	1382	1382	NUM
ejpam-3543	620	16	-	-	SYM
ejpam-3543	620	17	1409	1409	NUM
ejpam-3543	620	18	1400	1400	NUM
ejpam-3543	620	19	min{λgf	min{λgf	NOUN
ejpam-3543	620	20	[	[	X
ejpam-3543	620	21	γ	γ	X
ejpam-3543	620	22	+	+	X
ejpam-3543	620	23	γ−	γ−	PROPN
ejpam-3543	620	24	]	]	PUNCT
ejpam-3543	620	25	(	(	PUNCT
ejpam-3543	620	26	x	x	SYM
ejpam-3543	620	27	·	·	PUNCT
ejpam-3543	620	28	y	y	X
ejpam-3543	620	29	)	)	PUNCT
ejpam-3543	620	30	,	,	PUNCT
ejpam-3543	620	31	λgf	λgf	X
ejpam-3543	621	1	[	[	X
ejpam-3543	621	2	γ	γ	X
ejpam-3543	621	3	+	+	X
ejpam-3543	621	4	γ−	γ−	PROPN
ejpam-3543	621	5	]	]	PUNCT
ejpam-3543	621	6	(	(	PUNCT
ejpam-3543	621	7	x	x	NOUN
ejpam-3543	621	8	)	)	PUNCT
ejpam-3543	621	9	}	}	PUNCT
ejpam-3543	621	10	=	=	SYM
ejpam-3543	621	11	γ−.	γ−.	NOUN
ejpam-3543	621	12	therefore	therefore	ADV
ejpam-3543	621	13	,	,	PUNCT
ejpam-3543	621	14	λgt	λgt	PROPN
ejpam-3543	621	15	[	[	X
ejpam-3543	621	16	α	α	X
ejpam-3543	621	17	+	+	X
ejpam-3543	622	1	α−	α−	ADP
ejpam-3543	622	2	]	]	X
ejpam-3543	622	3	(	(	PUNCT
ejpam-3543	622	4	y	y	NOUN
ejpam-3543	622	5	)	)	PUNCT
ejpam-3543	622	6	≥	≥	NOUN
ejpam-3543	622	7	α−	α−	ADP
ejpam-3543	622	8	=	=	SYM
ejpam-3543	622	9	min{λgt	min{λgt	PROPN
ejpam-3543	623	1	[	[	X
ejpam-3543	623	2	α	α	X
ejpam-3543	623	3	+	+	X
ejpam-3543	624	1	α−	α−	ADP
ejpam-3543	624	2	]	]	X
ejpam-3543	624	3	(	(	PUNCT
ejpam-3543	624	4	x	x	SYM
ejpam-3543	624	5	·	·	PUNCT
ejpam-3543	624	6	y	y	X
ejpam-3543	624	7	)	)	PUNCT
ejpam-3543	624	8	,	,	PUNCT
ejpam-3543	624	9	λgt	λgt	X
ejpam-3543	625	1	[	[	X
ejpam-3543	625	2	α	α	X
ejpam-3543	625	3	+	+	X
ejpam-3543	626	1	α−	α−	ADP
ejpam-3543	626	2	]	]	X
ejpam-3543	626	3	(	(	PUNCT
ejpam-3543	626	4	x	x	NOUN
ejpam-3543	626	5	)	)	PUNCT
ejpam-3543	626	6	}	}	PUNCT
ejpam-3543	626	7	,	,	PUNCT
ejpam-3543	626	8	λgi	λgi	X
ejpam-3543	627	1	[	[	X
ejpam-3543	627	2	β	β	X
ejpam-3543	627	3	−	−	NOUN
ejpam-3543	627	4	β+	β+	PUNCT
ejpam-3543	627	5	]	]	X
ejpam-3543	627	6	(	(	PUNCT
ejpam-3543	627	7	y	y	NOUN
ejpam-3543	627	8	)	)	PUNCT
ejpam-3543	627	9	≤	≤	NOUN
ejpam-3543	627	10	β+	β+	PUNCT
ejpam-3543	627	11	=	=	SYM
ejpam-3543	627	12	max{λgi	max{λgi	NOUN
ejpam-3543	628	1	[	[	X
ejpam-3543	628	2	β	β	X
ejpam-3543	628	3	−	−	NOUN
ejpam-3543	628	4	β+	β+	PUNCT
ejpam-3543	628	5	]	]	X
ejpam-3543	628	6	(	(	PUNCT
ejpam-3543	628	7	x	x	SYM
ejpam-3543	628	8	·	·	PUNCT
ejpam-3543	628	9	y	y	X
ejpam-3543	628	10	)	)	PUNCT
ejpam-3543	628	11	,	,	PUNCT
ejpam-3543	628	12	λgi	λgi	X
ejpam-3543	629	1	[	[	X
ejpam-3543	629	2	β	β	X
ejpam-3543	629	3	−	−	NOUN
ejpam-3543	629	4	β+	β+	PUNCT
ejpam-3543	629	5	]	]	X
ejpam-3543	629	6	(	(	PUNCT
ejpam-3543	629	7	x	x	NOUN
ejpam-3543	629	8	)	)	PUNCT
ejpam-3543	629	9	}	}	PUNCT
ejpam-3543	629	10	,	,	PUNCT
ejpam-3543	629	11	λgf	λgf	X
ejpam-3543	630	1	[	[	X
ejpam-3543	630	2	γ	γ	X
ejpam-3543	630	3	+	+	X
ejpam-3543	630	4	γ−	γ−	PROPN
ejpam-3543	630	5	]	]	PUNCT
ejpam-3543	630	6	(	(	PUNCT
ejpam-3543	630	7	y	y	NOUN
ejpam-3543	630	8	)	)	PUNCT
ejpam-3543	630	9	≥	≥	NOUN
ejpam-3543	630	10	γ−	γ−	NOUN
ejpam-3543	630	11	=	=	NOUN
ejpam-3543	630	12	min{λgf	min{λgf	PROPN
ejpam-3543	630	13	[	[	X
ejpam-3543	630	14	γ	γ	X
ejpam-3543	630	15	+	+	X
ejpam-3543	630	16	γ−	γ−	PROPN
ejpam-3543	630	17	]	]	PUNCT
ejpam-3543	630	18	(	(	PUNCT
ejpam-3543	630	19	x	x	SYM
ejpam-3543	630	20	·	·	PUNCT
ejpam-3543	630	21	y	y	X
ejpam-3543	630	22	)	)	PUNCT
ejpam-3543	630	23	,	,	PUNCT
ejpam-3543	630	24	λgf	λgf	X
ejpam-3543	631	1	[	[	X
ejpam-3543	631	2	γ	γ	X
ejpam-3543	631	3	+	+	X
ejpam-3543	631	4	γ−	γ−	PROPN
ejpam-3543	631	5	]	]	PUNCT
ejpam-3543	631	6	(	(	PUNCT
ejpam-3543	631	7	x	x	NOUN
ejpam-3543	631	8	)	)	PUNCT
ejpam-3543	631	9	}	}	PUNCT
ejpam-3543	631	10	.	.	PUNCT
ejpam-3543	632	1	hence	hence	ADV
ejpam-3543	632	2	,	,	PUNCT
ejpam-3543	632	3	λg[α	λg[α	PROPN
ejpam-3543	632	4	+	+	PROPN
ejpam-3543	632	5	,	,	PUNCT
ejpam-3543	632	6	β−,γ+	β−,γ+	X
ejpam-3543	632	7	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	632	8	]	]	PUNCT
ejpam-3543	632	9	is	be	AUX
ejpam-3543	632	10	a	a	DET
ejpam-3543	632	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	632	12	up	up	ADJ
ejpam-3543	632	13	-	-	PUNCT
ejpam-3543	632	14	filter	filter	NOUN
ejpam-3543	632	15	of	of	ADP
ejpam-3543	632	16	x.	x.	PROPN
ejpam-3543	632	17	theorem	theorem	VERB
ejpam-3543	632	18	17	17	NUM
ejpam-3543	632	19	.	.	PUNCT
ejpam-3543	633	1	a	a	DET
ejpam-3543	633	2	ns	ns	ADJ
ejpam-3543	633	3	λg[α	λg[α	PROPN
ejpam-3543	633	4	+	+	PROPN
ejpam-3543	633	5	,	,	PUNCT
ejpam-3543	633	6	β−,γ+	β−,γ+	X
ejpam-3543	633	7	α−,β+,γ−	α−,β+,γ−	VERB
ejpam-3543	633	8	]	]	PUNCT
ejpam-3543	633	9	in	in	ADP
ejpam-3543	633	10	x	x	SYM
ejpam-3543	633	11	is	be	AUX
ejpam-3543	633	12	a	a	DET
ejpam-3543	633	13	neutrosophic	neutrosophic	ADJ
ejpam-3543	633	14	up	up	ADV
ejpam-3543	633	15	-	-	PUNCT
ejpam-3543	633	16	ideal	ideal	NOUN
ejpam-3543	633	17	of	of	ADP
ejpam-3543	633	18	x	x	SYM
ejpam-3543	633	19	if	if	SCONJ
ejpam-3543	633	20	and	and	CCONJ
ejpam-3543	633	21	only	only	ADV
ejpam-3543	633	22	if	if	SCONJ
ejpam-3543	633	23	a	a	DET
ejpam-3543	633	24	nonempty	nonempty	NOUN
ejpam-3543	633	25	subset	subset	VERB
ejpam-3543	633	26	g	g	PROPN
ejpam-3543	633	27	of	of	ADP
ejpam-3543	633	28	x	x	PUNCT
ejpam-3543	633	29	is	be	AUX
ejpam-3543	633	30	a	a	DET
ejpam-3543	633	31	up	up	ADJ
ejpam-3543	633	32	-	-	PUNCT
ejpam-3543	633	33	ideal	ideal	NOUN
ejpam-3543	633	34	of	of	ADP
ejpam-3543	633	35	x.	x.	NOUN
ejpam-3543	633	36	proof	proof	PROPN
ejpam-3543	633	37	.	.	PUNCT
ejpam-3543	634	1	assume	assume	VERB
ejpam-3543	634	2	that	that	SCONJ
ejpam-3543	634	3	λg[α	λg[α	PROPN
ejpam-3543	634	4	+	+	NOUN
ejpam-3543	634	5	,	,	PUNCT
ejpam-3543	634	6	β−,γ+	β−,γ+	X
ejpam-3543	634	7	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	634	8	]	]	PUNCT
ejpam-3543	634	9	is	be	AUX
ejpam-3543	634	10	a	a	DET
ejpam-3543	634	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	634	12	up	up	ADV
ejpam-3543	634	13	-	-	PUNCT
ejpam-3543	634	14	ideal	ideal	NOUN
ejpam-3543	634	15	of	of	ADP
ejpam-3543	634	16	x.	x.	NOUN
ejpam-3543	634	17	since	since	SCONJ
ejpam-3543	634	18	λg[α	λg[α	PROPN
ejpam-3543	634	19	+	+	PROPN
ejpam-3543	634	20	,	,	PUNCT
ejpam-3543	634	21	β−,γ+	β−,γ+	X
ejpam-3543	634	22	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	634	23	]	]	PUNCT
ejpam-3543	634	24	satisfies	satisfy	VERB
ejpam-3543	634	25	the	the	DET
ejpam-3543	634	26	condition	condition	NOUN
ejpam-3543	634	27	(	(	PUNCT
ejpam-3543	634	28	3.6	3.6	NUM
ejpam-3543	634	29	)	)	PUNCT
ejpam-3543	634	30	,	,	PUNCT
ejpam-3543	634	31	it	it	PRON
ejpam-3543	634	32	follows	follow	VERB
ejpam-3543	634	33	from	from	ADP
ejpam-3543	634	34	lemma	lemma	PROPN
ejpam-3543	634	35	4	4	NUM
ejpam-3543	634	36	that	that	SCONJ
ejpam-3543	634	37	0	0	NUM
ejpam-3543	634	38	∈	∈	NOUN
ejpam-3543	634	39	g.	g.	NOUN
ejpam-3543	634	40	next	next	ADV
ejpam-3543	634	41	,	,	PUNCT
ejpam-3543	634	42	let	let	VERB
ejpam-3543	634	43	x	x	PRON
ejpam-3543	634	44	,	,	PUNCT
ejpam-3543	634	45	y	y	PROPN
ejpam-3543	634	46	,	,	PUNCT
ejpam-3543	634	47	z	z	NOUN
ejpam-3543	634	48	∈	∈	PROPN
ejpam-3543	634	49	x	x	AUX
ejpam-3543	634	50	be	be	AUX
ejpam-3543	634	51	such	such	ADJ
ejpam-3543	634	52	that	that	SCONJ
ejpam-3543	634	53	x	x	PART
ejpam-3543	634	54	·	·	PUNCT
ejpam-3543	634	55	(	(	PUNCT
ejpam-3543	634	56	y	y	PROPN
ejpam-3543	634	57	·	·	PUNCT
ejpam-3543	634	58	z	z	X
ejpam-3543	634	59	)	)	PUNCT
ejpam-3543	634	60	∈	∈	PROPN
ejpam-3543	634	61	g	g	PROPN
ejpam-3543	634	62	and	and	CCONJ
ejpam-3543	634	63	y	y	PROPN
ejpam-3543	634	64	∈	∈	PROPN
ejpam-3543	635	1	g.	g.	NOUN
ejpam-3543	635	2	then	then	ADV
ejpam-3543	635	3	λgt	λgt	PRON
ejpam-3543	636	1	[	[	X
ejpam-3543	636	2	α	α	X
ejpam-3543	636	3	+	+	X
ejpam-3543	637	1	α−	α−	ADP
ejpam-3543	637	2	]	]	X
ejpam-3543	637	3	(	(	PUNCT
ejpam-3543	637	4	x	x	X
ejpam-3543	637	5	·	·	PUNCT
ejpam-3543	637	6	(	(	PUNCT
ejpam-3543	637	7	y	y	PROPN
ejpam-3543	637	8	·	·	PUNCT
ejpam-3543	637	9	z	z	NOUN
ejpam-3543	637	10	)	)	PUNCT
ejpam-3543	637	11	)	)	PUNCT
ejpam-3543	638	1	=	=	SYM
ejpam-3543	639	1	α+	α+	NOUN
ejpam-3543	639	2	=	=	PUNCT
ejpam-3543	640	1	λgt	λgt	X
ejpam-3543	641	1	[	[	X
ejpam-3543	641	2	α	α	X
ejpam-3543	641	3	+	+	X
ejpam-3543	642	1	α−	α−	ADP
ejpam-3543	642	2	]	]	X
ejpam-3543	642	3	(	(	PUNCT
ejpam-3543	642	4	y	y	NOUN
ejpam-3543	642	5	)	)	PUNCT
ejpam-3543	642	6	.	.	PUNCT
ejpam-3543	643	1	thus	thus	ADV
ejpam-3543	643	2	λgt	λgt	PRON
ejpam-3543	644	1	[	[	X
ejpam-3543	644	2	α	α	X
ejpam-3543	644	3	+	+	X
ejpam-3543	645	1	α−	α−	ADP
ejpam-3543	645	2	]	]	X
ejpam-3543	645	3	(	(	PUNCT
ejpam-3543	645	4	x	x	SYM
ejpam-3543	645	5	·	·	PUNCT
ejpam-3543	645	6	z	z	X
ejpam-3543	645	7	)	)	PUNCT
ejpam-3543	645	8	≥	≥	NOUN
ejpam-3543	645	9	min{λgt	min{λgt	VERB
ejpam-3543	646	1	[	[	X
ejpam-3543	646	2	α	α	X
ejpam-3543	646	3	+	+	X
ejpam-3543	647	1	α−	α−	ADP
ejpam-3543	647	2	]	]	X
ejpam-3543	647	3	(	(	PUNCT
ejpam-3543	647	4	x	x	X
ejpam-3543	647	5	·	·	PUNCT
ejpam-3543	647	6	(	(	PUNCT
ejpam-3543	647	7	y	y	PROPN
ejpam-3543	647	8	·	·	PUNCT
ejpam-3543	647	9	z	z	NOUN
ejpam-3543	647	10	)	)	PUNCT
ejpam-3543	647	11	)	)	PUNCT
ejpam-3543	647	12	,	,	PUNCT
ejpam-3543	647	13	λgt	λgt	X
ejpam-3543	648	1	[	[	X
ejpam-3543	648	2	α	α	X
ejpam-3543	648	3	+	+	X
ejpam-3543	649	1	α−	α−	ADP
ejpam-3543	649	2	]	]	X
ejpam-3543	649	3	(	(	PUNCT
ejpam-3543	649	4	y	y	NOUN
ejpam-3543	649	5	)	)	PUNCT
ejpam-3543	649	6	}	}	PUNCT
ejpam-3543	649	7	=	=	SYM
ejpam-3543	649	8	α+	α+	PUNCT
ejpam-3543	649	9	≥	≥	NOUN
ejpam-3543	649	10	λgt	λgt	X
ejpam-3543	650	1	[	[	X
ejpam-3543	650	2	α	α	X
ejpam-3543	650	3	+	+	X
ejpam-3543	651	1	α−	α−	ADP
ejpam-3543	651	2	]	]	X
ejpam-3543	651	3	(	(	PUNCT
ejpam-3543	651	4	x	x	X
ejpam-3543	651	5	·	·	PUNCT
ejpam-3543	651	6	z	z	X
ejpam-3543	651	7	)	)	PUNCT
ejpam-3543	651	8	(	(	PUNCT
ejpam-3543	651	9	3.18	3.18	NUM
ejpam-3543	651	10	)	)	PUNCT
ejpam-3543	651	11	and	and	CCONJ
ejpam-3543	651	12	so	so	ADV
ejpam-3543	651	13	λgt	λgt	PRON
ejpam-3543	652	1	[	[	X
ejpam-3543	652	2	α	α	X
ejpam-3543	652	3	+	+	X
ejpam-3543	653	1	α−	α−	ADP
ejpam-3543	653	2	]	]	X
ejpam-3543	653	3	(	(	PUNCT
ejpam-3543	653	4	x	x	X
ejpam-3543	653	5	·	·	PUNCT
ejpam-3543	653	6	z	z	X
ejpam-3543	653	7	)	)	PUNCT
ejpam-3543	653	8	=	=	SYM
ejpam-3543	653	9	α+	α+	NOUN
ejpam-3543	653	10	.	.	PUNCT
ejpam-3543	654	1	thus	thus	ADV
ejpam-3543	654	2	x	x	X
ejpam-3543	654	3	·	·	PUNCT
ejpam-3543	654	4	z	z	X
ejpam-3543	654	5	∈	∈	PROPN
ejpam-3543	654	6	g.	g.	NOUN
ejpam-3543	654	7	hence	hence	ADV
ejpam-3543	654	8	,	,	PUNCT
ejpam-3543	654	9	g	g	PROPN
ejpam-3543	654	10	is	be	AUX
ejpam-3543	654	11	a	a	DET
ejpam-3543	654	12	up	up	ADJ
ejpam-3543	654	13	-	-	PUNCT
ejpam-3543	654	14	ideal	ideal	NOUN
ejpam-3543	654	15	of	of	ADP
ejpam-3543	654	16	x.	x.	NOUN
ejpam-3543	654	17	conversely	conversely	ADV
ejpam-3543	654	18	,	,	PUNCT
ejpam-3543	654	19	assume	assume	VERB
ejpam-3543	654	20	that	that	SCONJ
ejpam-3543	654	21	g	g	PROPN
ejpam-3543	654	22	is	be	AUX
ejpam-3543	654	23	a	a	DET
ejpam-3543	654	24	up	up	ADJ
ejpam-3543	654	25	-	-	PUNCT
ejpam-3543	654	26	ideal	ideal	NOUN
ejpam-3543	654	27	of	of	ADP
ejpam-3543	654	28	x.	x.	NOUN
ejpam-3543	654	29	since	since	SCONJ
ejpam-3543	654	30	0	0	NUM
ejpam-3543	654	31	∈	∈	PROPN
ejpam-3543	654	32	g	g	NOUN
ejpam-3543	654	33	,	,	PUNCT
ejpam-3543	654	34	it	it	PRON
ejpam-3543	654	35	follows	follow	VERB
ejpam-3543	654	36	from	from	ADP
ejpam-3543	654	37	lemma	lemma	PROPN
ejpam-3543	654	38	3	3	NUM
ejpam-3543	654	39	that	that	PRON
ejpam-3543	654	40	λg[α	λg[α	PROPN
ejpam-3543	655	1	+	+	NOUN
ejpam-3543	655	2	,	,	PUNCT
ejpam-3543	655	3	β−,γ+	β−,γ+	X
ejpam-3543	655	4	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	655	5	]	]	PUNCT
ejpam-3543	655	6	satisfies	satisfy	VERB
ejpam-3543	655	7	the	the	DET
ejpam-3543	655	8	conditions	condition	NOUN
ejpam-3543	655	9	(	(	PUNCT
ejpam-3543	655	10	3.6	3.6	NUM
ejpam-3543	655	11	)	)	PUNCT
ejpam-3543	655	12	,	,	PUNCT
ejpam-3543	655	13	(	(	PUNCT
ejpam-3543	655	14	3.7	3.7	NUM
ejpam-3543	655	15	)	)	PUNCT
ejpam-3543	655	16	,	,	PUNCT
ejpam-3543	655	17	and	and	CCONJ
ejpam-3543	655	18	(	(	PUNCT
ejpam-3543	655	19	3.8	3.8	NUM
ejpam-3543	655	20	)	)	PUNCT
ejpam-3543	655	21	.	.	PUNCT
ejpam-3543	656	1	next	next	ADV
ejpam-3543	656	2	,	,	PUNCT
ejpam-3543	656	3	let	let	VERB
ejpam-3543	656	4	x	x	PRON
ejpam-3543	656	5	,	,	PUNCT
ejpam-3543	656	6	y	y	PROPN
ejpam-3543	656	7	,	,	PUNCT
ejpam-3543	656	8	z	z	PROPN
ejpam-3543	656	9	∈	∈	NOUN
ejpam-3543	656	10	x.	x.	NOUN
ejpam-3543	656	11	case	case	NOUN
ejpam-3543	656	12	1	1	NUM
ejpam-3543	656	13	:	:	PUNCT
ejpam-3543	656	14	x	x	SYM
ejpam-3543	656	15	·	·	PUNCT
ejpam-3543	656	16	(	(	PUNCT
ejpam-3543	656	17	y	y	PROPN
ejpam-3543	656	18	·	·	PUNCT
ejpam-3543	656	19	z	z	X
ejpam-3543	656	20	)	)	PUNCT
ejpam-3543	656	21	∈	∈	PROPN
ejpam-3543	656	22	g	g	PROPN
ejpam-3543	656	23	and	and	CCONJ
ejpam-3543	656	24	y	y	PROPN
ejpam-3543	656	25	∈	∈	PROPN
ejpam-3543	657	1	g.	g.	NOUN
ejpam-3543	657	2	then	then	ADV
ejpam-3543	657	3	λgt	λgt	PRON
ejpam-3543	658	1	[	[	X
ejpam-3543	658	2	α	α	X
ejpam-3543	658	3	+	+	X
ejpam-3543	659	1	α−	α−	ADP
ejpam-3543	659	2	]	]	X
ejpam-3543	659	3	(	(	PUNCT
ejpam-3543	659	4	x	x	X
ejpam-3543	659	5	·	·	PUNCT
ejpam-3543	659	6	(	(	PUNCT
ejpam-3543	659	7	y	y	PROPN
ejpam-3543	659	8	·	·	PUNCT
ejpam-3543	659	9	z	z	NOUN
ejpam-3543	659	10	)	)	PUNCT
ejpam-3543	659	11	)	)	PUNCT
ejpam-3543	660	1	=	=	SYM
ejpam-3543	661	1	α+	α+	NOUN
ejpam-3543	661	2	=	=	PUNCT
ejpam-3543	662	1	λgt	λgt	X
ejpam-3543	663	1	[	[	X
ejpam-3543	663	2	α	α	X
ejpam-3543	663	3	+	+	X
ejpam-3543	664	1	α−	α−	ADP
ejpam-3543	664	2	]	]	X
ejpam-3543	664	3	(	(	PUNCT
ejpam-3543	664	4	y	y	NOUN
ejpam-3543	664	5	)	)	PUNCT
ejpam-3543	664	6	,	,	PUNCT
ejpam-3543	664	7	λgi	λgi	X
ejpam-3543	665	1	[	[	X
ejpam-3543	665	2	β	β	X
ejpam-3543	665	3	−	−	NOUN
ejpam-3543	665	4	β+	β+	PUNCT
ejpam-3543	665	5	]	]	X
ejpam-3543	665	6	(	(	PUNCT
ejpam-3543	665	7	x	x	X
ejpam-3543	665	8	·	·	PUNCT
ejpam-3543	665	9	(	(	PUNCT
ejpam-3543	665	10	y	y	PROPN
ejpam-3543	665	11	·	·	PUNCT
ejpam-3543	665	12	z	z	X
ejpam-3543	665	13	)	)	PUNCT
ejpam-3543	665	14	)	)	PUNCT
ejpam-3543	666	1	=	=	PUNCT
ejpam-3543	666	2	β−	β−	PUNCT
ejpam-3543	666	3	=	=	PUNCT
ejpam-3543	666	4	λgi	λgi	NOUN
ejpam-3543	666	5	[	[	X
ejpam-3543	666	6	β	β	X
ejpam-3543	666	7	−	−	NOUN
ejpam-3543	666	8	β+	β+	PUNCT
ejpam-3543	666	9	]	]	X
ejpam-3543	666	10	(	(	PUNCT
ejpam-3543	666	11	y	y	NOUN
ejpam-3543	666	12	)	)	PUNCT
ejpam-3543	666	13	,	,	PUNCT
ejpam-3543	667	1	λgf	λgf	X
ejpam-3543	668	1	[	[	X
ejpam-3543	668	2	γ	γ	X
ejpam-3543	668	3	+	+	X
ejpam-3543	668	4	γ−	γ−	PROPN
ejpam-3543	668	5	]	]	PUNCT
ejpam-3543	668	6	(	(	PUNCT
ejpam-3543	668	7	x	x	X
ejpam-3543	668	8	·	·	PUNCT
ejpam-3543	668	9	(	(	PUNCT
ejpam-3543	668	10	y	y	PROPN
ejpam-3543	668	11	·	·	PUNCT
ejpam-3543	668	12	z	z	NOUN
ejpam-3543	668	13	)	)	PUNCT
ejpam-3543	668	14	)	)	PUNCT
ejpam-3543	669	1	=	=	PRON
ejpam-3543	669	2	γ+	γ+	PUNCT
ejpam-3543	669	3	=	=	SYM
ejpam-3543	669	4	λgf	λgf	X
ejpam-3543	670	1	[	[	X
ejpam-3543	670	2	γ	γ	X
ejpam-3543	670	3	+	+	X
ejpam-3543	670	4	γ−	γ−	PROPN
ejpam-3543	670	5	]	]	PUNCT
ejpam-3543	670	6	(	(	PUNCT
ejpam-3543	670	7	y	y	NOUN
ejpam-3543	670	8	)	)	PUNCT
ejpam-3543	670	9	.	.	PUNCT
ejpam-3543	671	1	thus	thus	ADV
ejpam-3543	671	2	min{λgt	min{λgt	X
ejpam-3543	672	1	[	[	X
ejpam-3543	672	2	α	α	X
ejpam-3543	672	3	+	+	X
ejpam-3543	673	1	α−	α−	ADP
ejpam-3543	673	2	]	]	X
ejpam-3543	673	3	(	(	PUNCT
ejpam-3543	673	4	x	x	X
ejpam-3543	673	5	·	·	PUNCT
ejpam-3543	673	6	(	(	PUNCT
ejpam-3543	673	7	y	y	PROPN
ejpam-3543	673	8	·	·	PUNCT
ejpam-3543	673	9	z	z	NOUN
ejpam-3543	673	10	)	)	PUNCT
ejpam-3543	673	11	)	)	PUNCT
ejpam-3543	673	12	,	,	PUNCT
ejpam-3543	673	13	λgt	λgt	X
ejpam-3543	674	1	[	[	X
ejpam-3543	674	2	α	α	X
ejpam-3543	674	3	+	+	X
ejpam-3543	675	1	α−	α−	ADP
ejpam-3543	675	2	]	]	X
ejpam-3543	675	3	(	(	PUNCT
ejpam-3543	675	4	y	y	NOUN
ejpam-3543	675	5	)	)	PUNCT
ejpam-3543	675	6	}	}	PUNCT
ejpam-3543	675	7	=	=	SYM
ejpam-3543	675	8	α+	α+	NOUN
ejpam-3543	675	9	,	,	PUNCT
ejpam-3543	675	10	max{λgi	max{λgi	NOUN
ejpam-3543	676	1	[	[	X
ejpam-3543	676	2	β	β	X
ejpam-3543	676	3	−	−	NOUN
ejpam-3543	676	4	β+	β+	PUNCT
ejpam-3543	676	5	]	]	X
ejpam-3543	676	6	(	(	PUNCT
ejpam-3543	676	7	x	x	X
ejpam-3543	676	8	·	·	PUNCT
ejpam-3543	676	9	(	(	PUNCT
ejpam-3543	676	10	y	y	PROPN
ejpam-3543	676	11	·	·	PUNCT
ejpam-3543	676	12	z	z	NOUN
ejpam-3543	676	13	)	)	PUNCT
ejpam-3543	676	14	)	)	PUNCT
ejpam-3543	676	15	,	,	PUNCT
ejpam-3543	676	16	λgi	λgi	X
ejpam-3543	677	1	[	[	X
ejpam-3543	677	2	β	β	X
ejpam-3543	677	3	−	−	NOUN
ejpam-3543	677	4	β+	β+	PUNCT
ejpam-3543	677	5	]	]	X
ejpam-3543	677	6	(	(	PUNCT
ejpam-3543	677	7	y	y	NOUN
ejpam-3543	677	8	)	)	PUNCT
ejpam-3543	677	9	}	}	PUNCT
ejpam-3543	677	10	=	=	SYM
ejpam-3543	677	11	β−	β−	PROPN
ejpam-3543	677	12	,	,	PUNCT
ejpam-3543	677	13	min{λgf	min{λgf	NOUN
ejpam-3543	678	1	[	[	X
ejpam-3543	678	2	γ	γ	X
ejpam-3543	678	3	+	+	X
ejpam-3543	678	4	γ−	γ−	PROPN
ejpam-3543	678	5	]	]	PUNCT
ejpam-3543	678	6	(	(	PUNCT
ejpam-3543	678	7	x	x	X
ejpam-3543	678	8	·	·	PUNCT
ejpam-3543	678	9	(	(	PUNCT
ejpam-3543	678	10	y	y	PROPN
ejpam-3543	678	11	·	·	PUNCT
ejpam-3543	678	12	z	z	NOUN
ejpam-3543	678	13	)	)	PUNCT
ejpam-3543	678	14	)	)	PUNCT
ejpam-3543	678	15	,	,	PUNCT
ejpam-3543	678	16	λgf	λgf	X
ejpam-3543	679	1	[	[	X
ejpam-3543	679	2	γ	γ	X
ejpam-3543	679	3	+	+	X
ejpam-3543	679	4	γ−	γ−	PROPN
ejpam-3543	679	5	]	]	PUNCT
ejpam-3543	679	6	(	(	PUNCT
ejpam-3543	679	7	y	y	NOUN
ejpam-3543	679	8	)	)	PUNCT
ejpam-3543	679	9	}	}	PUNCT
ejpam-3543	679	10	=	=	SYM
ejpam-3543	679	11	γ+	γ+	PROPN
ejpam-3543	679	12	.	.	PUNCT
ejpam-3543	680	1	since	since	SCONJ
ejpam-3543	680	2	g	g	PROPN
ejpam-3543	680	3	is	be	AUX
ejpam-3543	680	4	a	a	DET
ejpam-3543	680	5	up	up	ADJ
ejpam-3543	680	6	-	-	PUNCT
ejpam-3543	680	7	ideal	ideal	NOUN
ejpam-3543	680	8	of	of	ADP
ejpam-3543	680	9	x	x	SYM
ejpam-3543	680	10	,	,	PUNCT
ejpam-3543	680	11	we	we	PRON
ejpam-3543	680	12	have	have	VERB
ejpam-3543	680	13	x	x	X
ejpam-3543	680	14	·	·	PUNCT
ejpam-3543	680	15	z	z	NOUN
ejpam-3543	680	16	∈	∈	PROPN
ejpam-3543	680	17	g	g	PROPN
ejpam-3543	680	18	and	and	CCONJ
ejpam-3543	681	1	so	so	ADV
ejpam-3543	681	2	λgt	λgt	PRON
ejpam-3543	682	1	[	[	X
ejpam-3543	682	2	α	α	X
ejpam-3543	682	3	+	+	X
ejpam-3543	683	1	α−	α−	ADP
ejpam-3543	683	2	]	]	X
ejpam-3543	683	3	(	(	PUNCT
ejpam-3543	683	4	x	x	SYM
ejpam-3543	683	5	·	·	SYM
ejpam-3543	683	6	z	z	NOUN
ejpam-3543	683	7	)	)	PUNCT
ejpam-3543	683	8	=	=	SYM
ejpam-3543	683	9	α+	α+	X
ejpam-3543	683	10	,	,	PUNCT
ejpam-3543	683	11	λgi	λgi	X
ejpam-3543	684	1	[	[	X
ejpam-3543	684	2	β	β	X
ejpam-3543	684	3	−	−	NOUN
ejpam-3543	684	4	β+	β+	PUNCT
ejpam-3543	684	5	]	]	X
ejpam-3543	684	6	(	(	PUNCT
ejpam-3543	684	7	x	x	SYM
ejpam-3543	684	8	·	·	SYM
ejpam-3543	684	9	z	z	NOUN
ejpam-3543	684	10	)	)	PUNCT
ejpam-3543	684	11	=	=	SYM
ejpam-3543	684	12	β−	β−	PROPN
ejpam-3543	684	13	,	,	PUNCT
ejpam-3543	684	14	and	and	CCONJ
ejpam-3543	684	15	λgf	λgf	X
ejpam-3543	685	1	[	[	X
ejpam-3543	685	2	γ	γ	X
ejpam-3543	685	3	+	+	X
ejpam-3543	685	4	γ−	γ−	PROPN
ejpam-3543	685	5	]	]	PUNCT
ejpam-3543	685	6	(	(	PUNCT
ejpam-3543	685	7	x	x	X
ejpam-3543	685	8	·	·	PUNCT
ejpam-3543	685	9	z	z	X
ejpam-3543	685	10	)	)	PUNCT
ejpam-3543	685	11	=	=	SYM
ejpam-3543	685	12	γ+	γ+	PROPN
ejpam-3543	685	13	.	.	PUNCT
ejpam-3543	686	1	thus	thus	ADV
ejpam-3543	686	2	λgt	λgt	PRON
ejpam-3543	687	1	[	[	X
ejpam-3543	687	2	α	α	X
ejpam-3543	687	3	+	+	X
ejpam-3543	688	1	α−	α−	ADP
ejpam-3543	688	2	]	]	X
ejpam-3543	688	3	(	(	PUNCT
ejpam-3543	688	4	x	x	X
ejpam-3543	688	5	·	·	PUNCT
ejpam-3543	688	6	z	z	X
ejpam-3543	688	7	)	)	PUNCT
ejpam-3543	688	8	=	=	SYM
ejpam-3543	688	9	α+	α+	PUNCT
ejpam-3543	688	10	≥	≥	X
ejpam-3543	688	11	α+	α+	X
ejpam-3543	688	12	=	=	X
ejpam-3543	688	13	min{λgt	min{λgt	NOUN
ejpam-3543	689	1	[	[	X
ejpam-3543	689	2	α	α	X
ejpam-3543	689	3	+	+	X
ejpam-3543	690	1	α−	α−	ADP
ejpam-3543	690	2	]	]	X
ejpam-3543	690	3	(	(	PUNCT
ejpam-3543	690	4	x	x	X
ejpam-3543	690	5	·	·	PUNCT
ejpam-3543	690	6	(	(	PUNCT
ejpam-3543	690	7	y	y	PROPN
ejpam-3543	690	8	·	·	PUNCT
ejpam-3543	690	9	z	z	NOUN
ejpam-3543	690	10	)	)	PUNCT
ejpam-3543	690	11	)	)	PUNCT
ejpam-3543	690	12	,	,	PUNCT
ejpam-3543	690	13	λgt	λgt	X
ejpam-3543	691	1	[	[	X
ejpam-3543	691	2	α	α	X
ejpam-3543	691	3	+	+	X
ejpam-3543	692	1	α−	α−	ADP
ejpam-3543	692	2	]	]	X
ejpam-3543	692	3	(	(	PUNCT
ejpam-3543	692	4	y	y	NOUN
ejpam-3543	692	5	)	)	PUNCT
ejpam-3543	692	6	}	}	PUNCT
ejpam-3543	692	7	,	,	PUNCT
ejpam-3543	692	8	λgi	λgi	X
ejpam-3543	693	1	[	[	X
ejpam-3543	693	2	β	β	X
ejpam-3543	693	3	−	−	NOUN
ejpam-3543	693	4	β+	β+	PUNCT
ejpam-3543	693	5	]	]	X
ejpam-3543	693	6	(	(	PUNCT
ejpam-3543	693	7	x	x	SYM
ejpam-3543	693	8	·	·	PUNCT
ejpam-3543	693	9	z	z	X
ejpam-3543	693	10	)	)	PUNCT
ejpam-3543	693	11	=	=	PUNCT
ejpam-3543	694	1	β−	β−	PUNCT
ejpam-3543	694	2	≤	≤	NUM
ejpam-3543	694	3	β−	β−	PUNCT
ejpam-3543	695	1	=	=	SYM
ejpam-3543	695	2	max{λgi	max{λgi	NOUN
ejpam-3543	696	1	[	[	X
ejpam-3543	696	2	β	β	X
ejpam-3543	696	3	−	−	NOUN
ejpam-3543	696	4	β+	β+	PUNCT
ejpam-3543	696	5	]	]	X
ejpam-3543	696	6	(	(	PUNCT
ejpam-3543	696	7	x	x	X
ejpam-3543	696	8	·	·	PUNCT
ejpam-3543	696	9	(	(	PUNCT
ejpam-3543	696	10	y	y	PROPN
ejpam-3543	696	11	·	·	PUNCT
ejpam-3543	696	12	z	z	NOUN
ejpam-3543	696	13	)	)	PUNCT
ejpam-3543	696	14	)	)	PUNCT
ejpam-3543	696	15	,	,	PUNCT
ejpam-3543	696	16	λgi	λgi	X
ejpam-3543	697	1	[	[	X
ejpam-3543	697	2	β	β	X
ejpam-3543	697	3	−	−	NOUN
ejpam-3543	697	4	β+	β+	PUNCT
ejpam-3543	697	5	]	]	X
ejpam-3543	697	6	(	(	PUNCT
ejpam-3543	697	7	y	y	NOUN
ejpam-3543	697	8	)	)	PUNCT
ejpam-3543	697	9	}	}	PUNCT
ejpam-3543	697	10	,	,	PUNCT
ejpam-3543	697	11	m.	m.	NOUN
ejpam-3543	697	12	songsaeng	songsaeng	PROPN
ejpam-3543	697	13	,	,	PUNCT
ejpam-3543	697	14	a.	a.	NOUN
ejpam-3543	697	15	iampan	iampan	PROPN
ejpam-3543	697	16	/	/	SYM
ejpam-3543	697	17	eur	eur	PROPN
ejpam-3543	697	18	.	.	PUNCT
ejpam-3543	698	1	j.	j.	PROPN
ejpam-3543	698	2	pure	pure	PROPN
ejpam-3543	698	3	appl	appl	PROPN
ejpam-3543	698	4	.	.	PROPN
ejpam-3543	698	5	math	math	PROPN
ejpam-3543	698	6	,	,	PUNCT
ejpam-3543	698	7	12	12	NUM
ejpam-3543	698	8	(	(	PUNCT
ejpam-3543	698	9	4	4	NUM
ejpam-3543	698	10	)	)	PUNCT
ejpam-3543	698	11	(	(	PUNCT
ejpam-3543	698	12	2019	2019	NUM
ejpam-3543	698	13	)	)	PUNCT
ejpam-3543	698	14	,	,	PUNCT
ejpam-3543	698	15	1382	1382	NUM
ejpam-3543	698	16	-	-	SYM
ejpam-3543	698	17	1409	1409	NUM
ejpam-3543	698	18	1401	1401	NUM
ejpam-3543	698	19	λgf	λgf	NOUN
ejpam-3543	699	1	[	[	X
ejpam-3543	699	2	γ	γ	X
ejpam-3543	699	3	+	+	X
ejpam-3543	699	4	γ−	γ−	PROPN
ejpam-3543	699	5	]	]	PUNCT
ejpam-3543	699	6	(	(	PUNCT
ejpam-3543	699	7	x	x	X
ejpam-3543	699	8	·	·	PUNCT
ejpam-3543	700	1	z	z	X
ejpam-3543	700	2	)	)	PUNCT
ejpam-3543	700	3	=	=	PRON
ejpam-3543	700	4	γ+	γ+	PUNCT
ejpam-3543	700	5	≥	≥	NOUN
ejpam-3543	700	6	γ+	γ+	X
ejpam-3543	700	7	=	=	PUNCT
ejpam-3543	700	8	min{λgf	min{λgf	PROPN
ejpam-3543	701	1	[	[	X
ejpam-3543	701	2	γ	γ	X
ejpam-3543	701	3	+	+	X
ejpam-3543	701	4	γ−	γ−	PROPN
ejpam-3543	701	5	]	]	PUNCT
ejpam-3543	701	6	(	(	PUNCT
ejpam-3543	701	7	x	x	X
ejpam-3543	701	8	·	·	PUNCT
ejpam-3543	701	9	(	(	PUNCT
ejpam-3543	701	10	y	y	PROPN
ejpam-3543	701	11	·	·	PUNCT
ejpam-3543	701	12	z	z	NOUN
ejpam-3543	701	13	)	)	PUNCT
ejpam-3543	701	14	)	)	PUNCT
ejpam-3543	701	15	,	,	PUNCT
ejpam-3543	701	16	λgf	λgf	X
ejpam-3543	702	1	[	[	X
ejpam-3543	702	2	γ	γ	X
ejpam-3543	702	3	+	+	X
ejpam-3543	702	4	γ−	γ−	PROPN
ejpam-3543	702	5	]	]	PUNCT
ejpam-3543	702	6	(	(	PUNCT
ejpam-3543	702	7	y	y	NOUN
ejpam-3543	702	8	)	)	PUNCT
ejpam-3543	702	9	}	}	PUNCT
ejpam-3543	702	10	.	.	PUNCT
ejpam-3543	703	1	case	case	NOUN
ejpam-3543	703	2	2	2	NUM
ejpam-3543	703	3	:	:	PUNCT
ejpam-3543	703	4	x	x	SYM
ejpam-3543	703	5	·	·	PUNCT
ejpam-3543	703	6	(	(	PUNCT
ejpam-3543	703	7	y	y	PROPN
ejpam-3543	703	8	·	·	PUNCT
ejpam-3543	703	9	z	z	X
ejpam-3543	703	10	)	)	PUNCT
ejpam-3543	703	11	6∈	6∈	PROPN
ejpam-3543	703	12	g	g	PROPN
ejpam-3543	703	13	or	or	CCONJ
ejpam-3543	703	14	y	y	PROPN
ejpam-3543	703	15	6∈	6∈	PROPN
ejpam-3543	704	1	g.	g.	NOUN
ejpam-3543	704	2	then	then	ADV
ejpam-3543	704	3	λgt	λgt	PRON
ejpam-3543	705	1	[	[	X
ejpam-3543	705	2	α	α	X
ejpam-3543	705	3	+	+	X
ejpam-3543	706	1	α−	α−	ADP
ejpam-3543	706	2	]	]	X
ejpam-3543	706	3	(	(	PUNCT
ejpam-3543	706	4	x	x	X
ejpam-3543	706	5	·	·	PUNCT
ejpam-3543	706	6	(	(	PUNCT
ejpam-3543	706	7	y	y	PROPN
ejpam-3543	706	8	·	·	PUNCT
ejpam-3543	706	9	z	z	NOUN
ejpam-3543	706	10	)	)	PUNCT
ejpam-3543	706	11	)	)	PUNCT
ejpam-3543	707	1	=	=	PUNCT
ejpam-3543	708	1	α−	α−	ADP
ejpam-3543	708	2	or	or	CCONJ
ejpam-3543	708	3	λgt	λgt	PRON
ejpam-3543	709	1	[	[	X
ejpam-3543	709	2	α	α	X
ejpam-3543	709	3	+	+	X
ejpam-3543	710	1	α−	α−	ADP
ejpam-3543	710	2	]	]	X
ejpam-3543	710	3	(	(	PUNCT
ejpam-3543	710	4	y	y	NOUN
ejpam-3543	710	5	)	)	PUNCT
ejpam-3543	710	6	=	=	PUNCT
ejpam-3543	710	7	α−	α−	PROPN
ejpam-3543	710	8	,	,	PUNCT
ejpam-3543	710	9	λgi	λgi	X
ejpam-3543	711	1	[	[	X
ejpam-3543	711	2	β	β	X
ejpam-3543	711	3	−	−	NOUN
ejpam-3543	711	4	β+	β+	PUNCT
ejpam-3543	711	5	]	]	X
ejpam-3543	711	6	(	(	PUNCT
ejpam-3543	711	7	x	x	X
ejpam-3543	711	8	·	·	PUNCT
ejpam-3543	711	9	(	(	PUNCT
ejpam-3543	711	10	y	y	PROPN
ejpam-3543	711	11	·	·	PUNCT
ejpam-3543	711	12	z	z	NOUN
ejpam-3543	711	13	)	)	PUNCT
ejpam-3543	711	14	)	)	PUNCT
ejpam-3543	712	1	=	=	SYM
ejpam-3543	712	2	β+	β+	PUNCT
ejpam-3543	712	3	or	or	CCONJ
ejpam-3543	712	4	λgi	λgi	X
ejpam-3543	713	1	[	[	X
ejpam-3543	713	2	β	β	X
ejpam-3543	713	3	−	−	NOUN
ejpam-3543	713	4	β+	β+	PUNCT
ejpam-3543	713	5	]	]	X
ejpam-3543	713	6	(	(	PUNCT
ejpam-3543	713	7	y	y	NOUN
ejpam-3543	713	8	)	)	PUNCT
ejpam-3543	713	9	=	=	SYM
ejpam-3543	714	1	β+	β+	NOUN
ejpam-3543	714	2	,	,	PUNCT
ejpam-3543	714	3	λgf	λgf	NOUN
ejpam-3543	715	1	[	[	X
ejpam-3543	715	2	γ	γ	X
ejpam-3543	715	3	+	+	X
ejpam-3543	715	4	γ−	γ−	PROPN
ejpam-3543	715	5	]	]	PUNCT
ejpam-3543	715	6	(	(	PUNCT
ejpam-3543	715	7	x	x	X
ejpam-3543	715	8	·	·	PUNCT
ejpam-3543	715	9	(	(	PUNCT
ejpam-3543	715	10	y	y	PROPN
ejpam-3543	715	11	·	·	PUNCT
ejpam-3543	715	12	z	z	NOUN
ejpam-3543	715	13	)	)	PUNCT
ejpam-3543	715	14	)	)	PUNCT
ejpam-3543	716	1	=	=	SYM
ejpam-3543	716	2	γ−	γ−	PROPN
ejpam-3543	716	3	or	or	CCONJ
ejpam-3543	716	4	λgf	λgf	NOUN
ejpam-3543	717	1	[	[	X
ejpam-3543	717	2	γ	γ	X
ejpam-3543	717	3	+	+	X
ejpam-3543	717	4	γ−	γ−	PROPN
ejpam-3543	717	5	]	]	PUNCT
ejpam-3543	717	6	(	(	PUNCT
ejpam-3543	717	7	y	y	NOUN
ejpam-3543	717	8	)	)	PUNCT
ejpam-3543	717	9	=	=	VERB
ejpam-3543	717	10	γ−.	γ−.	NOUN
ejpam-3543	717	11	thus	thus	ADV
ejpam-3543	717	12	min{λgt	min{λgt	X
ejpam-3543	718	1	[	[	X
ejpam-3543	718	2	α	α	X
ejpam-3543	718	3	+	+	X
ejpam-3543	719	1	α−	α−	ADP
ejpam-3543	719	2	]	]	X
ejpam-3543	719	3	(	(	PUNCT
ejpam-3543	719	4	x	x	X
ejpam-3543	719	5	·	·	PUNCT
ejpam-3543	719	6	(	(	PUNCT
ejpam-3543	719	7	y	y	PROPN
ejpam-3543	719	8	·	·	PUNCT
ejpam-3543	719	9	z	z	NOUN
ejpam-3543	719	10	)	)	PUNCT
ejpam-3543	719	11	)	)	PUNCT
ejpam-3543	719	12	,	,	PUNCT
ejpam-3543	719	13	λgt	λgt	X
ejpam-3543	720	1	[	[	X
ejpam-3543	720	2	α	α	X
ejpam-3543	720	3	+	+	X
ejpam-3543	721	1	α−	α−	ADP
ejpam-3543	721	2	]	]	X
ejpam-3543	721	3	(	(	PUNCT
ejpam-3543	721	4	y	y	NOUN
ejpam-3543	721	5	)	)	PUNCT
ejpam-3543	721	6	}	}	PUNCT
ejpam-3543	721	7	=	=	SYM
ejpam-3543	721	8	α−	α−	PROPN
ejpam-3543	721	9	,	,	PUNCT
ejpam-3543	721	10	max{λgi	max{λgi	NOUN
ejpam-3543	722	1	[	[	X
ejpam-3543	722	2	β	β	X
ejpam-3543	722	3	−	−	NOUN
ejpam-3543	722	4	β+	β+	PUNCT
ejpam-3543	722	5	]	]	X
ejpam-3543	722	6	(	(	PUNCT
ejpam-3543	722	7	x	x	X
ejpam-3543	722	8	·	·	PUNCT
ejpam-3543	722	9	(	(	PUNCT
ejpam-3543	722	10	y	y	PROPN
ejpam-3543	722	11	·	·	PUNCT
ejpam-3543	722	12	z	z	NOUN
ejpam-3543	722	13	)	)	PUNCT
ejpam-3543	722	14	)	)	PUNCT
ejpam-3543	722	15	,	,	PUNCT
ejpam-3543	722	16	λgi	λgi	X
ejpam-3543	723	1	[	[	X
ejpam-3543	723	2	β	β	X
ejpam-3543	723	3	−	−	NOUN
ejpam-3543	723	4	β+	β+	PUNCT
ejpam-3543	723	5	]	]	X
ejpam-3543	723	6	(	(	PUNCT
ejpam-3543	723	7	y	y	NOUN
ejpam-3543	723	8	)	)	PUNCT
ejpam-3543	723	9	}	}	PUNCT
ejpam-3543	724	1	=	=	SYM
ejpam-3543	724	2	β+	β+	NOUN
ejpam-3543	724	3	,	,	PUNCT
ejpam-3543	724	4	min{λgf	min{λgf	NOUN
ejpam-3543	724	5	[	[	X
ejpam-3543	724	6	γ	γ	X
ejpam-3543	724	7	+	+	X
ejpam-3543	724	8	γ−	γ−	PROPN
ejpam-3543	724	9	]	]	PUNCT
ejpam-3543	724	10	(	(	PUNCT
ejpam-3543	724	11	x	x	X
ejpam-3543	724	12	·	·	PUNCT
ejpam-3543	724	13	(	(	PUNCT
ejpam-3543	724	14	y	y	PROPN
ejpam-3543	724	15	·	·	PUNCT
ejpam-3543	724	16	z	z	NOUN
ejpam-3543	724	17	)	)	PUNCT
ejpam-3543	724	18	)	)	PUNCT
ejpam-3543	724	19	,	,	PUNCT
ejpam-3543	724	20	λgf	λgf	X
ejpam-3543	725	1	[	[	X
ejpam-3543	725	2	γ	γ	X
ejpam-3543	725	3	+	+	X
ejpam-3543	725	4	γ−	γ−	PROPN
ejpam-3543	725	5	]	]	PUNCT
ejpam-3543	725	6	(	(	PUNCT
ejpam-3543	725	7	y	y	NOUN
ejpam-3543	725	8	)	)	PUNCT
ejpam-3543	725	9	}	}	PUNCT
ejpam-3543	725	10	=	=	SYM
ejpam-3543	725	11	γ−.	γ−.	NOUN
ejpam-3543	725	12	therefore	therefore	ADV
ejpam-3543	725	13	,	,	PUNCT
ejpam-3543	725	14	λgt	λgt	PROPN
ejpam-3543	725	15	[	[	X
ejpam-3543	725	16	α	α	X
ejpam-3543	725	17	+	+	X
ejpam-3543	726	1	α−	α−	ADP
ejpam-3543	726	2	]	]	X
ejpam-3543	726	3	(	(	PUNCT
ejpam-3543	726	4	x	x	SYM
ejpam-3543	726	5	·	·	PUNCT
ejpam-3543	726	6	z	z	X
ejpam-3543	726	7	)	)	PUNCT
ejpam-3543	726	8	≥	≥	NOUN
ejpam-3543	726	9	α−	α−	ADP
ejpam-3543	726	10	=	=	SYM
ejpam-3543	726	11	min{λgt	min{λgt	PROPN
ejpam-3543	727	1	[	[	X
ejpam-3543	727	2	α	α	X
ejpam-3543	727	3	+	+	X
ejpam-3543	728	1	α−	α−	ADP
ejpam-3543	728	2	]	]	X
ejpam-3543	728	3	(	(	PUNCT
ejpam-3543	728	4	x	x	X
ejpam-3543	728	5	·	·	PUNCT
ejpam-3543	728	6	(	(	PUNCT
ejpam-3543	728	7	y	y	PROPN
ejpam-3543	728	8	·	·	PUNCT
ejpam-3543	728	9	z	z	NOUN
ejpam-3543	728	10	)	)	PUNCT
ejpam-3543	728	11	)	)	PUNCT
ejpam-3543	728	12	,	,	PUNCT
ejpam-3543	728	13	λgt	λgt	X
ejpam-3543	729	1	[	[	X
ejpam-3543	729	2	α	α	X
ejpam-3543	729	3	+	+	X
ejpam-3543	730	1	α−	α−	ADP
ejpam-3543	730	2	]	]	X
ejpam-3543	730	3	(	(	PUNCT
ejpam-3543	730	4	y	y	NOUN
ejpam-3543	730	5	)	)	PUNCT
ejpam-3543	730	6	}	}	PUNCT
ejpam-3543	730	7	,	,	PUNCT
ejpam-3543	730	8	λgi	λgi	X
ejpam-3543	731	1	[	[	X
ejpam-3543	731	2	β	β	X
ejpam-3543	731	3	−	−	NOUN
ejpam-3543	731	4	β+	β+	PUNCT
ejpam-3543	731	5	]	]	X
ejpam-3543	731	6	(	(	PUNCT
ejpam-3543	731	7	x	x	SYM
ejpam-3543	731	8	·	·	PUNCT
ejpam-3543	731	9	z	z	X
ejpam-3543	731	10	)	)	PUNCT
ejpam-3543	731	11	≤	≤	NOUN
ejpam-3543	731	12	β+	β+	PUNCT
ejpam-3543	731	13	=	=	SYM
ejpam-3543	731	14	max{λgi	max{λgi	NOUN
ejpam-3543	732	1	[	[	X
ejpam-3543	732	2	β	β	X
ejpam-3543	732	3	−	−	NOUN
ejpam-3543	732	4	β+	β+	PUNCT
ejpam-3543	732	5	]	]	X
ejpam-3543	732	6	(	(	PUNCT
ejpam-3543	732	7	x	x	X
ejpam-3543	732	8	·	·	PUNCT
ejpam-3543	732	9	(	(	PUNCT
ejpam-3543	732	10	y	y	PROPN
ejpam-3543	732	11	·	·	PUNCT
ejpam-3543	732	12	z	z	NOUN
ejpam-3543	732	13	)	)	PUNCT
ejpam-3543	732	14	)	)	PUNCT
ejpam-3543	732	15	,	,	PUNCT
ejpam-3543	732	16	λgi	λgi	X
ejpam-3543	733	1	[	[	X
ejpam-3543	733	2	β	β	X
ejpam-3543	733	3	−	−	NOUN
ejpam-3543	733	4	β+	β+	PUNCT
ejpam-3543	733	5	]	]	X
ejpam-3543	733	6	(	(	PUNCT
ejpam-3543	733	7	y	y	NOUN
ejpam-3543	733	8	)	)	PUNCT
ejpam-3543	733	9	}	}	PUNCT
ejpam-3543	733	10	,	,	PUNCT
ejpam-3543	733	11	λgf	λgf	X
ejpam-3543	734	1	[	[	X
ejpam-3543	734	2	γ	γ	X
ejpam-3543	734	3	+	+	X
ejpam-3543	734	4	γ−	γ−	PROPN
ejpam-3543	734	5	]	]	PUNCT
ejpam-3543	734	6	(	(	PUNCT
ejpam-3543	734	7	x	x	X
ejpam-3543	734	8	·	·	PUNCT
ejpam-3543	734	9	z	z	X
ejpam-3543	734	10	)	)	PUNCT
ejpam-3543	734	11	≥	≥	NOUN
ejpam-3543	734	12	γ−	γ−	NOUN
ejpam-3543	734	13	=	=	NOUN
ejpam-3543	734	14	min{λgf	min{λgf	PROPN
ejpam-3543	735	1	[	[	X
ejpam-3543	735	2	γ	γ	X
ejpam-3543	735	3	+	+	X
ejpam-3543	735	4	γ−	γ−	PROPN
ejpam-3543	735	5	]	]	PUNCT
ejpam-3543	735	6	(	(	PUNCT
ejpam-3543	735	7	x	x	X
ejpam-3543	735	8	·	·	PUNCT
ejpam-3543	735	9	(	(	PUNCT
ejpam-3543	735	10	y	y	PROPN
ejpam-3543	735	11	·	·	PUNCT
ejpam-3543	735	12	z	z	NOUN
ejpam-3543	735	13	)	)	PUNCT
ejpam-3543	735	14	)	)	PUNCT
ejpam-3543	735	15	,	,	PUNCT
ejpam-3543	735	16	λgf	λgf	X
ejpam-3543	736	1	[	[	X
ejpam-3543	736	2	γ	γ	X
ejpam-3543	736	3	+	+	X
ejpam-3543	736	4	γ−	γ−	PROPN
ejpam-3543	736	5	]	]	PUNCT
ejpam-3543	736	6	(	(	PUNCT
ejpam-3543	736	7	y	y	NOUN
ejpam-3543	736	8	)	)	PUNCT
ejpam-3543	736	9	}	}	PUNCT
ejpam-3543	736	10	.	.	PUNCT
ejpam-3543	737	1	hence	hence	ADV
ejpam-3543	737	2	,	,	PUNCT
ejpam-3543	737	3	λg[α	λg[α	PROPN
ejpam-3543	737	4	+	+	PROPN
ejpam-3543	737	5	,	,	PUNCT
ejpam-3543	737	6	β−,γ+	β−,γ+	X
ejpam-3543	737	7	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	737	8	]	]	PUNCT
ejpam-3543	737	9	is	be	AUX
ejpam-3543	737	10	a	a	DET
ejpam-3543	737	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	737	12	up	up	ADV
ejpam-3543	737	13	-	-	PUNCT
ejpam-3543	737	14	ideal	ideal	NOUN
ejpam-3543	737	15	of	of	ADP
ejpam-3543	737	16	x.	x.	PROPN
ejpam-3543	737	17	theorem	theorem	VERB
ejpam-3543	737	18	18	18	NUM
ejpam-3543	737	19	.	.	PUNCT
ejpam-3543	738	1	a	a	DET
ejpam-3543	738	2	ns	ns	ADJ
ejpam-3543	738	3	λg[α	λg[α	PROPN
ejpam-3543	738	4	+	+	PROPN
ejpam-3543	738	5	,	,	PUNCT
ejpam-3543	738	6	β−,γ+	β−,γ+	X
ejpam-3543	738	7	α−,β+,γ−	α−,β+,γ−	VERB
ejpam-3543	738	8	]	]	PUNCT
ejpam-3543	738	9	in	in	ADP
ejpam-3543	738	10	x	x	SYM
ejpam-3543	738	11	is	be	AUX
ejpam-3543	738	12	a	a	DET
ejpam-3543	738	13	neutrosophic	neutrosophic	ADJ
ejpam-3543	738	14	strongly	strongly	ADV
ejpam-3543	738	15	up	up	ADP
ejpam-3543	738	16	-	-	PUNCT
ejpam-3543	738	17	ideal	ideal	NOUN
ejpam-3543	738	18	of	of	ADP
ejpam-3543	738	19	x	x	SYM
ejpam-3543	738	20	if	if	SCONJ
ejpam-3543	738	21	and	and	CCONJ
ejpam-3543	738	22	only	only	ADV
ejpam-3543	738	23	if	if	SCONJ
ejpam-3543	738	24	a	a	DET
ejpam-3543	738	25	nonempty	nonempty	NOUN
ejpam-3543	738	26	subset	subset	VERB
ejpam-3543	738	27	g	g	PROPN
ejpam-3543	738	28	of	of	ADP
ejpam-3543	738	29	x	x	PUNCT
ejpam-3543	738	30	is	be	AUX
ejpam-3543	738	31	a	a	DET
ejpam-3543	738	32	strongly	strongly	ADV
ejpam-3543	738	33	up	up	ADJ
ejpam-3543	738	34	-	-	PUNCT
ejpam-3543	738	35	ideal	ideal	NOUN
ejpam-3543	738	36	of	of	ADP
ejpam-3543	738	37	x.	x.	NOUN
ejpam-3543	738	38	proof	proof	PROPN
ejpam-3543	738	39	.	.	PUNCT
ejpam-3543	739	1	assume	assume	VERB
ejpam-3543	739	2	that	that	SCONJ
ejpam-3543	739	3	λg[α	λg[α	PROPN
ejpam-3543	739	4	+	+	NOUN
ejpam-3543	739	5	,	,	PUNCT
ejpam-3543	739	6	β−,γ+	β−,γ+	X
ejpam-3543	739	7	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	739	8	]	]	PUNCT
ejpam-3543	739	9	is	be	AUX
ejpam-3543	739	10	a	a	DET
ejpam-3543	739	11	neutrosophic	neutrosophic	ADJ
ejpam-3543	739	12	strongly	strongly	ADV
ejpam-3543	739	13	up	up	ADP
ejpam-3543	739	14	-	-	PUNCT
ejpam-3543	739	15	ideal	ideal	NOUN
ejpam-3543	739	16	of	of	ADP
ejpam-3543	739	17	x.	x.	NOUN
ejpam-3543	739	18	by	by	ADP
ejpam-3543	739	19	theorem	theorem	NOUN
ejpam-3543	739	20	2	2	NUM
ejpam-3543	739	21	,	,	PUNCT
ejpam-3543	739	22	we	we	PRON
ejpam-3543	739	23	have	have	VERB
ejpam-3543	739	24	λg[α	λg[α	PROPN
ejpam-3543	739	25	+	+	NOUN
ejpam-3543	739	26	,	,	PUNCT
ejpam-3543	739	27	β−,γ+	β−,γ+	X
ejpam-3543	739	28	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	739	29	]	]	PUNCT
ejpam-3543	739	30	is	be	AUX
ejpam-3543	739	31	constant	constant	ADJ
ejpam-3543	739	32	,	,	PUNCT
ejpam-3543	739	33	that	that	ADV
ejpam-3543	739	34	is	is	ADV
ejpam-3543	739	35	,	,	PUNCT
ejpam-3543	739	36	λgt	λgt	PROPN
ejpam-3543	740	1	[	[	X
ejpam-3543	740	2	α	α	X
ejpam-3543	740	3	+	+	X
ejpam-3543	740	4	α−	α−	ADP
ejpam-3543	740	5	]	]	PUNCT
ejpam-3543	740	6	is	be	AUX
ejpam-3543	740	7	constant	constant	ADJ
ejpam-3543	740	8	.	.	PUNCT
ejpam-3543	741	1	since	since	SCONJ
ejpam-3543	741	2	g	g	PROPN
ejpam-3543	741	3	is	be	AUX
ejpam-3543	741	4	nonempty	nonempty	ADJ
ejpam-3543	741	5	,	,	PUNCT
ejpam-3543	741	6	we	we	PRON
ejpam-3543	741	7	have	have	VERB
ejpam-3543	741	8	λgt	λgt	PRON
ejpam-3543	742	1	[	[	X
ejpam-3543	742	2	α	α	X
ejpam-3543	742	3	+	+	X
ejpam-3543	743	1	α−	α−	ADP
ejpam-3543	743	2	]	]	X
ejpam-3543	743	3	(	(	PUNCT
ejpam-3543	743	4	x	x	X
ejpam-3543	743	5	)	)	PUNCT
ejpam-3543	743	6	=	=	SYM
ejpam-3543	743	7	α+	α+	X
ejpam-3543	743	8	for	for	ADP
ejpam-3543	743	9	all	all	PRON
ejpam-3543	743	10	x	x	SYM
ejpam-3543	743	11	∈	∈	NOUN
ejpam-3543	743	12	x.	x.	NOUN
ejpam-3543	743	13	thus	thus	ADV
ejpam-3543	743	14	g	g	PROPN
ejpam-3543	743	15	=	=	NOUN
ejpam-3543	743	16	x.	x.	NOUN
ejpam-3543	743	17	hence	hence	ADV
ejpam-3543	743	18	,	,	PUNCT
ejpam-3543	743	19	g	g	PROPN
ejpam-3543	743	20	is	be	AUX
ejpam-3543	743	21	a	a	DET
ejpam-3543	743	22	strongly	strongly	ADV
ejpam-3543	743	23	up	up	ADJ
ejpam-3543	743	24	-	-	PUNCT
ejpam-3543	743	25	ideal	ideal	NOUN
ejpam-3543	743	26	of	of	ADP
ejpam-3543	743	27	x.	x.	NOUN
ejpam-3543	743	28	conversely	conversely	ADV
ejpam-3543	743	29	,	,	PUNCT
ejpam-3543	743	30	assume	assume	VERB
ejpam-3543	743	31	that	that	SCONJ
ejpam-3543	743	32	g	g	PROPN
ejpam-3543	743	33	is	be	AUX
ejpam-3543	743	34	a	a	DET
ejpam-3543	743	35	strongly	strongly	ADV
ejpam-3543	743	36	up	up	ADJ
ejpam-3543	743	37	-	-	PUNCT
ejpam-3543	743	38	ideal	ideal	NOUN
ejpam-3543	743	39	of	of	ADP
ejpam-3543	743	40	x.	x.	NOUN
ejpam-3543	743	41	then	then	ADV
ejpam-3543	743	42	g	g	PROPN
ejpam-3543	743	43	=	=	SYM
ejpam-3543	743	44	x	x	PROPN
ejpam-3543	743	45	,	,	PUNCT
ejpam-3543	743	46	so	so	CCONJ
ejpam-3543	743	47	(	(	PUNCT
ejpam-3543	743	48	∀x	∀x	X
ejpam-3543	743	49	∈	∈	PROPN
ejpam-3543	743	50	x	x	NOUN
ejpam-3543	743	51	)	)	PUNCT
ejpam-3543	744	1			NOUN
ejpam-3543	745	1	λgt	λgt	X
ejpam-3543	746	1	[	[	X
ejpam-3543	746	2	α	α	X
ejpam-3543	746	3	+	+	X
ejpam-3543	747	1	α−	α−	ADP
ejpam-3543	747	2	]	]	X
ejpam-3543	747	3	(	(	PUNCT
ejpam-3543	747	4	x	x	X
ejpam-3543	747	5	)	)	PUNCT
ejpam-3543	747	6	=	=	SYM
ejpam-3543	747	7	α+	α+	PUNCT
ejpam-3543	747	8	λgi	λgi	X
ejpam-3543	747	9	[	[	X
ejpam-3543	747	10	β	β	X
ejpam-3543	747	11	−	−	NOUN
ejpam-3543	747	12	β+	β+	PUNCT
ejpam-3543	747	13	]	]	X
ejpam-3543	747	14	(	(	PUNCT
ejpam-3543	747	15	x	x	X
ejpam-3543	747	16	)	)	PUNCT
ejpam-3543	747	17	=	=	SYM
ejpam-3543	747	18	β−	β−	NUM
ejpam-3543	747	19	λgf	λgf	NOUN
ejpam-3543	748	1	[	[	X
ejpam-3543	748	2	γ	γ	X
ejpam-3543	748	3	+	+	X
ejpam-3543	748	4	γ−	γ−	PROPN
ejpam-3543	748	5	]	]	PUNCT
ejpam-3543	748	6	(	(	PUNCT
ejpam-3543	748	7	x	x	X
ejpam-3543	748	8	)	)	PUNCT
ejpam-3543	748	9	=	=	PRON
ejpam-3543	748	10	γ+	γ+	PUNCT
ejpam-3543	748	11			NOUN
ejpam-3543	748	12	.	.	PUNCT
ejpam-3543	749	1	thus	thus	ADV
ejpam-3543	749	2	λgt	λgt	PRON
ejpam-3543	750	1	[	[	X
ejpam-3543	750	2	α	α	X
ejpam-3543	750	3	+	+	X
ejpam-3543	751	1	α−	α−	ADP
ejpam-3543	751	2	]	]	PUNCT
ejpam-3543	751	3	,	,	PUNCT
ejpam-3543	751	4	λgi	λgi	X
ejpam-3543	751	5	[	[	X
ejpam-3543	751	6	β	β	X
ejpam-3543	751	7	−	−	NOUN
ejpam-3543	751	8	β+	β+	PUNCT
ejpam-3543	751	9	]	]	X
ejpam-3543	751	10	,	,	PUNCT
ejpam-3543	751	11	and	and	CCONJ
ejpam-3543	751	12	λgf	λgf	X
ejpam-3543	752	1	[	[	X
ejpam-3543	752	2	γ	γ	X
ejpam-3543	752	3	+	+	CCONJ
ejpam-3543	752	4	γ−	γ−	PROPN
ejpam-3543	752	5	]	]	PUNCT
ejpam-3543	752	6	are	be	AUX
ejpam-3543	752	7	constant	constant	ADJ
ejpam-3543	752	8	,	,	PUNCT
ejpam-3543	752	9	that	that	ADV
ejpam-3543	752	10	is	is	ADV
ejpam-3543	752	11	,	,	PUNCT
ejpam-3543	752	12	λg[α	λg[α	PROPN
ejpam-3543	752	13	+	+	PROPN
ejpam-3543	752	14	,	,	PUNCT
ejpam-3543	752	15	β−,γ+	β−,γ+	X
ejpam-3543	752	16	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	752	17	]	]	PUNCT
ejpam-3543	752	18	is	be	AUX
ejpam-3543	752	19	constant	constant	ADJ
ejpam-3543	752	20	.	.	PUNCT
ejpam-3543	753	1	by	by	ADP
ejpam-3543	753	2	theorem	theorem	NOUN
ejpam-3543	753	3	2	2	NUM
ejpam-3543	753	4	,	,	PUNCT
ejpam-3543	753	5	we	we	PRON
ejpam-3543	753	6	have	have	VERB
ejpam-3543	753	7	λg[α	λg[α	PROPN
ejpam-3543	753	8	+	+	NOUN
ejpam-3543	753	9	,	,	PUNCT
ejpam-3543	753	10	β−,γ+	β−,γ+	X
ejpam-3543	753	11	α−,β+,γ−	α−,β+,γ−	X
ejpam-3543	753	12	]	]	PUNCT
ejpam-3543	753	13	is	be	AUX
ejpam-3543	753	14	a	a	DET
ejpam-3543	753	15	neutrosophic	neutrosophic	ADJ
ejpam-3543	753	16	strongly	strongly	ADV
ejpam-3543	753	17	up	up	ADP
ejpam-3543	753	18	-	-	PUNCT
ejpam-3543	753	19	ideal	ideal	NOUN
ejpam-3543	753	20	of	of	ADP
ejpam-3543	753	21	x.	x.	PROPN
ejpam-3543	753	22	m.	m.	PROPN
ejpam-3543	753	23	songsaeng	songsaeng	PROPN
ejpam-3543	753	24	,	,	PUNCT
ejpam-3543	753	25	a.	a.	NOUN
ejpam-3543	753	26	iampan	iampan	PROPN
ejpam-3543	753	27	/	/	SYM
ejpam-3543	753	28	eur	eur	PROPN
ejpam-3543	753	29	.	.	PUNCT
ejpam-3543	754	1	j.	j.	PROPN
ejpam-3543	754	2	pure	pure	PROPN
ejpam-3543	754	3	appl	appl	PROPN
ejpam-3543	754	4	.	.	PROPN
ejpam-3543	754	5	math	math	PROPN
ejpam-3543	754	6	,	,	PUNCT
ejpam-3543	754	7	12	12	NUM
ejpam-3543	754	8	(	(	PUNCT
ejpam-3543	754	9	4	4	NUM
ejpam-3543	754	10	)	)	PUNCT
ejpam-3543	754	11	(	(	PUNCT
ejpam-3543	754	12	2019	2019	NUM
ejpam-3543	754	13	)	)	PUNCT
ejpam-3543	754	14	,	,	PUNCT
ejpam-3543	754	15	1382	1382	NUM
ejpam-3543	754	16	-	-	SYM
ejpam-3543	754	17	1409	1409	NUM
ejpam-3543	754	18	1402	1402	NUM
ejpam-3543	754	19	4	4	NUM
ejpam-3543	754	20	.	.	PUNCT
ejpam-3543	754	21	level	level	NOUN
ejpam-3543	754	22	subsets	subset	NOUN
ejpam-3543	754	23	of	of	ADP
ejpam-3543	754	24	a	a	DET
ejpam-3543	754	25	ns	ns	NOUN
ejpam-3543	754	26	in	in	ADP
ejpam-3543	754	27	this	this	DET
ejpam-3543	754	28	section	section	NOUN
ejpam-3543	755	1	,	,	PUNCT
ejpam-3543	755	2	we	we	PRON
ejpam-3543	755	3	discuss	discuss	VERB
ejpam-3543	755	4	the	the	DET
ejpam-3543	755	5	relationships	relationship	NOUN
ejpam-3543	755	6	between	between	ADP
ejpam-3543	755	7	neutrosophic	neutrosophic	ADJ
ejpam-3543	755	8	up	up	ADP
ejpam-3543	755	9	-	-	PUNCT
ejpam-3543	755	10	subalgebras	subalgebras	PROPN
ejpam-3543	755	11	(	(	PUNCT
ejpam-3543	755	12	resp	resp	PROPN
ejpam-3543	755	13	.	.	PUNCT
ejpam-3543	755	14	,	,	PUNCT
ejpam-3543	755	15	neutrosophic	neutrosophic	ADJ
ejpam-3543	755	16	near	near	ADP
ejpam-3543	755	17	up	up	ADP
ejpam-3543	755	18	-	-	PUNCT
ejpam-3543	755	19	filters	filter	NOUN
ejpam-3543	755	20	,	,	PUNCT
ejpam-3543	755	21	neutrosophic	neutrosophic	ADJ
ejpam-3543	755	22	up	up	ADP
ejpam-3543	755	23	-	-	PUNCT
ejpam-3543	755	24	filters	filter	NOUN
ejpam-3543	755	25	,	,	PUNCT
ejpam-3543	755	26	neutrosophic	neutrosophic	ADJ
ejpam-3543	755	27	up	up	ADP
ejpam-3543	755	28	-	-	PUNCT
ejpam-3543	755	29	ideals	ideal	NOUN
ejpam-3543	755	30	,	,	PUNCT
ejpam-3543	755	31	neutrosophic	neutrosophic	ADJ
ejpam-3543	755	32	strongly	strongly	ADV
ejpam-3543	755	33	up	up	ADP
ejpam-3543	755	34	-	-	PUNCT
ejpam-3543	755	35	ideals	ideal	NOUN
ejpam-3543	755	36	)	)	PUNCT
ejpam-3543	755	37	of	of	ADP
ejpam-3543	755	38	up	up	ADV
ejpam-3543	755	39	-	-	PUNCT
ejpam-3543	755	40	algebras	algebra	NOUN
ejpam-3543	755	41	and	and	CCONJ
ejpam-3543	755	42	their	their	PRON
ejpam-3543	755	43	level	level	NOUN
ejpam-3543	755	44	subsets	subset	NOUN
ejpam-3543	755	45	.	.	PUNCT
ejpam-3543	756	1	definition	definition	NOUN
ejpam-3543	756	2	10	10	NUM
ejpam-3543	756	3	.	.	PUNCT
ejpam-3543	757	1	[	[	X
ejpam-3543	757	2	23	23	NUM
ejpam-3543	757	3	]	]	PUNCT
ejpam-3543	757	4	let	let	VERB
ejpam-3543	757	5	f	f	PRON
ejpam-3543	757	6	be	be	AUX
ejpam-3543	757	7	a	a	DET
ejpam-3543	757	8	fuzzy	fuzzy	ADJ
ejpam-3543	757	9	set	set	NOUN
ejpam-3543	757	10	in	in	ADP
ejpam-3543	757	11	a.	a.	NOUN
ejpam-3543	757	12	for	for	ADP
ejpam-3543	757	13	any	any	DET
ejpam-3543	757	14	t	t	NOUN
ejpam-3543	757	15	∈	∈	PROPN
ejpam-3543	758	1	[	[	X
ejpam-3543	758	2	0	0	NUM
ejpam-3543	758	3	,	,	PUNCT
ejpam-3543	758	4	1	1	NUM
ejpam-3543	758	5	]	]	PUNCT
ejpam-3543	758	6	,	,	PUNCT
ejpam-3543	758	7	the	the	DET
ejpam-3543	758	8	sets	set	VERB
ejpam-3543	758	9	u(f	u(f	PROPN
ejpam-3543	758	10	;	;	PUNCT
ejpam-3543	758	11	t	t	X
ejpam-3543	758	12	)	)	PUNCT
ejpam-3543	758	13	=	=	PRON
ejpam-3543	759	1	{	{	PUNCT
ejpam-3543	759	2	x	x	PUNCT
ejpam-3543	759	3	∈	∈	PROPN
ejpam-3543	759	4	x	x	X
ejpam-3543	759	5	|	|	ADV
ejpam-3543	759	6	f(x	f(x	PROPN
ejpam-3543	759	7	)	)	PUNCT
ejpam-3543	759	8	≥	≥	NOUN
ejpam-3543	759	9	t	t	PROPN
ejpam-3543	759	10	}	}	PUNCT
ejpam-3543	759	11	,	,	PUNCT
ejpam-3543	759	12	l(f	l(f	PROPN
ejpam-3543	759	13	;	;	PUNCT
ejpam-3543	759	14	t	t	X
ejpam-3543	759	15	)	)	PUNCT
ejpam-3543	759	16	=	=	PRON
ejpam-3543	759	17	{	{	PUNCT
ejpam-3543	759	18	x	x	PUNCT
ejpam-3543	759	19	∈	∈	PROPN
ejpam-3543	759	20	x	x	X
ejpam-3543	759	21	|	|	ADV
ejpam-3543	759	22	f(x	f(x	PROPN
ejpam-3543	759	23	)	)	PUNCT
ejpam-3543	759	24	≤	≤	NOUN
ejpam-3543	759	25	t	t	PROPN
ejpam-3543	759	26	}	}	PUNCT
ejpam-3543	759	27	,	,	PUNCT
ejpam-3543	759	28	e(f	e(f	PROPN
ejpam-3543	759	29	;	;	PUNCT
ejpam-3543	759	30	t	t	PROPN
ejpam-3543	759	31	)	)	PUNCT
ejpam-3543	759	32	=	=	PRON
ejpam-3543	759	33	{	{	PUNCT
ejpam-3543	759	34	x	x	PUNCT
ejpam-3543	759	35	∈	∈	PROPN
ejpam-3543	759	36	x	x	X
ejpam-3543	759	37	|	|	ADV
ejpam-3543	759	38	f(x	f(x	PROPN
ejpam-3543	759	39	)	)	PUNCT
ejpam-3543	759	40	=	=	SYM
ejpam-3543	760	1	t	t	PROPN
ejpam-3543	760	2	}	}	PUNCT
ejpam-3543	760	3	are	be	AUX
ejpam-3543	760	4	called	call	VERB
ejpam-3543	760	5	an	an	DET
ejpam-3543	760	6	upper	upper	ADJ
ejpam-3543	760	7	t	t	NOUN
ejpam-3543	760	8	-	-	PUNCT
ejpam-3543	760	9	level	level	NOUN
ejpam-3543	760	10	subset	subset	NOUN
ejpam-3543	760	11	,	,	PUNCT
ejpam-3543	760	12	a	a	DET
ejpam-3543	760	13	lower	low	ADJ
ejpam-3543	760	14	t	t	NOUN
ejpam-3543	760	15	-	-	PUNCT
ejpam-3543	760	16	level	level	NOUN
ejpam-3543	760	17	subset	subset	NOUN
ejpam-3543	760	18	,	,	PUNCT
ejpam-3543	760	19	and	and	CCONJ
ejpam-3543	760	20	an	an	DET
ejpam-3543	760	21	equal	equal	ADJ
ejpam-3543	760	22	t	t	NOUN
ejpam-3543	760	23	-	-	PUNCT
ejpam-3543	760	24	level	level	NOUN
ejpam-3543	760	25	subset	subset	NOUN
ejpam-3543	760	26	of	of	ADP
ejpam-3543	760	27	f	f	PROPN
ejpam-3543	760	28	,	,	PUNCT
ejpam-3543	760	29	respectively	respectively	ADV
ejpam-3543	760	30	.	.	PUNCT
ejpam-3543	761	1	theorem	theorem	VERB
ejpam-3543	761	2	19	19	NUM
ejpam-3543	761	3	.	.	PUNCT
ejpam-3543	762	1	a	a	DET
ejpam-3543	762	2	ns	ns	NUM
ejpam-3543	762	3	λ	λ	NOUN
ejpam-3543	762	4	in	in	ADP
ejpam-3543	762	5	x	x	PROPN
ejpam-3543	762	6	is	be	AUX
ejpam-3543	762	7	a	a	DET
ejpam-3543	762	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	762	9	up	up	ADP
ejpam-3543	762	10	-	-	PUNCT
ejpam-3543	762	11	subalgebra	subalgebra	NOUN
ejpam-3543	762	12	of	of	ADP
ejpam-3543	762	13	x	x	PRON
ejpam-3543	762	14	if	if	SCONJ
ejpam-3543	762	15	and	and	CCONJ
ejpam-3543	762	16	only	only	ADV
ejpam-3543	762	17	if	if	SCONJ
ejpam-3543	762	18	for	for	ADP
ejpam-3543	762	19	all	all	DET
ejpam-3543	762	20	α	α	NOUN
ejpam-3543	762	21	,	,	PUNCT
ejpam-3543	762	22	β	β	X
ejpam-3543	762	23	,	,	PUNCT
ejpam-3543	762	24	γ	γ	PROPN
ejpam-3543	762	25	∈	∈	PROPN
ejpam-3543	763	1	[	[	X
ejpam-3543	763	2	0	0	NUM
ejpam-3543	763	3	,	,	PUNCT
ejpam-3543	763	4	1	1	NUM
ejpam-3543	763	5	]	]	PUNCT
ejpam-3543	763	6	,	,	PUNCT
ejpam-3543	763	7	the	the	PRON
ejpam-3543	763	8	sets	set	NOUN
ejpam-3543	763	9	u(λt	u(λt	NOUN
ejpam-3543	763	10	;	;	PUNCT
ejpam-3543	763	11	α	α	X
ejpam-3543	763	12	)	)	PUNCT
ejpam-3543	763	13	,	,	PUNCT
ejpam-3543	763	14	l(λi	l(λi	PROPN
ejpam-3543	763	15	;	;	PUNCT
ejpam-3543	763	16	β	β	X
ejpam-3543	763	17	)	)	PUNCT
ejpam-3543	763	18	,	,	PUNCT
ejpam-3543	763	19	and	and	CCONJ
ejpam-3543	763	20	u(λf	u(λf	ADV
ejpam-3543	763	21	;	;	PUNCT
ejpam-3543	763	22	γ	γ	X
ejpam-3543	763	23	)	)	PUNCT
ejpam-3543	763	24	are	be	AUX
ejpam-3543	763	25	up	up	ADV
ejpam-3543	763	26	-	-	PUNCT
ejpam-3543	763	27	subalgebras	subalgebra	NOUN
ejpam-3543	763	28	of	of	ADP
ejpam-3543	763	29	x	x	PRON
ejpam-3543	763	30	if	if	SCONJ
ejpam-3543	763	31	u(λt	u(λt	NOUN
ejpam-3543	763	32	;	;	PUNCT
ejpam-3543	763	33	α	α	X
ejpam-3543	763	34	)	)	PUNCT
ejpam-3543	763	35	,	,	PUNCT
ejpam-3543	763	36	l(λi	l(λi	PROPN
ejpam-3543	763	37	;	;	PUNCT
ejpam-3543	763	38	β	β	X
ejpam-3543	763	39	)	)	PUNCT
ejpam-3543	763	40	,	,	PUNCT
ejpam-3543	763	41	and	and	CCONJ
ejpam-3543	763	42	u(λf	u(λf	ADV
ejpam-3543	763	43	;	;	PUNCT
ejpam-3543	763	44	γ	γ	X
ejpam-3543	763	45	)	)	PUNCT
ejpam-3543	763	46	are	be	AUX
ejpam-3543	763	47	nonempty	nonempty	ADJ
ejpam-3543	763	48	.	.	PUNCT
ejpam-3543	764	1	proof	proof	NOUN
ejpam-3543	764	2	.	.	PUNCT
ejpam-3543	765	1	assume	assume	VERB
ejpam-3543	765	2	that	that	SCONJ
ejpam-3543	765	3	λ	λ	PROPN
ejpam-3543	765	4	is	be	AUX
ejpam-3543	765	5	a	a	DET
ejpam-3543	765	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	765	7	up	up	ADP
ejpam-3543	765	8	-	-	PUNCT
ejpam-3543	765	9	subalgebra	subalgebra	NOUN
ejpam-3543	765	10	of	of	ADP
ejpam-3543	765	11	x.	x.	NOUN
ejpam-3543	765	12	let	let	VERB
ejpam-3543	765	13	α	α	PRON
ejpam-3543	765	14	,	,	PUNCT
ejpam-3543	765	15	β	β	X
ejpam-3543	765	16	,	,	PUNCT
ejpam-3543	765	17	γ	γ	PROPN
ejpam-3543	765	18	∈	∈	PROPN
ejpam-3543	766	1	[	[	X
ejpam-3543	766	2	0	0	NUM
ejpam-3543	766	3	,	,	PUNCT
ejpam-3543	766	4	1	1	NUM
ejpam-3543	766	5	]	]	PUNCT
ejpam-3543	766	6	be	be	AUX
ejpam-3543	766	7	such	such	ADJ
ejpam-3543	766	8	that	that	SCONJ
ejpam-3543	766	9	u(λt	u(λt	NOUN
ejpam-3543	766	10	;	;	PUNCT
ejpam-3543	766	11	α	α	X
ejpam-3543	766	12	)	)	PUNCT
ejpam-3543	766	13	,	,	PUNCT
ejpam-3543	766	14	l(λi	l(λi	PROPN
ejpam-3543	766	15	;	;	PUNCT
ejpam-3543	766	16	β	β	X
ejpam-3543	766	17	)	)	PUNCT
ejpam-3543	766	18	,	,	PUNCT
ejpam-3543	766	19	and	and	CCONJ
ejpam-3543	766	20	u(λf	u(λf	ADV
ejpam-3543	766	21	;	;	PUNCT
ejpam-3543	766	22	γ	γ	X
ejpam-3543	766	23	)	)	PUNCT
ejpam-3543	766	24	are	be	AUX
ejpam-3543	766	25	nonempty	nonempty	ADJ
ejpam-3543	766	26	.	.	PUNCT
ejpam-3543	767	1	let	let	VERB
ejpam-3543	767	2	x	x	PRON
ejpam-3543	767	3	,	,	PUNCT
ejpam-3543	767	4	y	y	PROPN
ejpam-3543	767	5	∈	∈	PROPN
ejpam-3543	767	6	u(λt	u(λt	PROPN
ejpam-3543	767	7	;	;	PUNCT
ejpam-3543	767	8	α	α	X
ejpam-3543	767	9	)	)	PUNCT
ejpam-3543	767	10	.	.	PUNCT
ejpam-3543	768	1	then	then	ADV
ejpam-3543	768	2	λt	λt	INTJ
ejpam-3543	768	3	(	(	PUNCT
ejpam-3543	768	4	x	x	X
ejpam-3543	768	5	)	)	PUNCT
ejpam-3543	768	6	≥	≥	NOUN
ejpam-3543	768	7	α	α	NOUN
ejpam-3543	768	8	and	and	CCONJ
ejpam-3543	768	9	λt	λt	X
ejpam-3543	768	10	(	(	PUNCT
ejpam-3543	768	11	y	y	NOUN
ejpam-3543	768	12	)	)	PUNCT
ejpam-3543	768	13	≥	≥	NOUN
ejpam-3543	768	14	α	α	NOUN
ejpam-3543	768	15	,	,	PUNCT
ejpam-3543	768	16	so	so	ADV
ejpam-3543	768	17	α	α	PRON
ejpam-3543	768	18	is	be	AUX
ejpam-3543	768	19	an	an	DET
ejpam-3543	768	20	lower	low	ADJ
ejpam-3543	768	21	bound	bind	VERB
ejpam-3543	768	22	of	of	ADP
ejpam-3543	768	23	{	{	PUNCT
ejpam-3543	768	24	λt	λt	X
ejpam-3543	768	25	(	(	PUNCT
ejpam-3543	768	26	x	x	NOUN
ejpam-3543	768	27	)	)	PUNCT
ejpam-3543	768	28	,	,	PUNCT
ejpam-3543	768	29	λt	λt	X
ejpam-3543	768	30	(	(	PUNCT
ejpam-3543	768	31	y	y	NOUN
ejpam-3543	768	32	)	)	PUNCT
ejpam-3543	768	33	}	}	PUNCT
ejpam-3543	768	34	.	.	PUNCT
ejpam-3543	769	1	by	by	ADP
ejpam-3543	769	2	(	(	PUNCT
ejpam-3543	769	3	3.3	3.3	NUM
ejpam-3543	769	4	)	)	PUNCT
ejpam-3543	769	5	,	,	PUNCT
ejpam-3543	769	6	we	we	PRON
ejpam-3543	769	7	have	have	VERB
ejpam-3543	769	8	λt	λt	INTJ
ejpam-3543	769	9	(	(	PUNCT
ejpam-3543	769	10	x	x	PROPN
ejpam-3543	769	11	·	·	PUNCT
ejpam-3543	769	12	y	y	X
ejpam-3543	769	13	)	)	PUNCT
ejpam-3543	769	14	≥	≥	NOUN
ejpam-3543	769	15	min{λt	min{λt	X
ejpam-3543	769	16	(	(	PUNCT
ejpam-3543	769	17	x	x	X
ejpam-3543	769	18	)	)	PUNCT
ejpam-3543	769	19	,	,	PUNCT
ejpam-3543	769	20	λt	λt	X
ejpam-3543	769	21	(	(	PUNCT
ejpam-3543	769	22	y	y	NOUN
ejpam-3543	769	23	)	)	PUNCT
ejpam-3543	769	24	}	}	PUNCT
ejpam-3543	769	25	≥	≥	NUM
ejpam-3543	769	26	α	α	NOUN
ejpam-3543	769	27	.	.	PUNCT
ejpam-3543	770	1	thus	thus	ADV
ejpam-3543	770	2	x	x	X
ejpam-3543	770	3	·	·	PUNCT
ejpam-3543	770	4	y	y	PROPN
ejpam-3543	770	5	∈	∈	PROPN
ejpam-3543	770	6	u(λt	u(λt	PROPN
ejpam-3543	770	7	;	;	PUNCT
ejpam-3543	770	8	α	α	X
ejpam-3543	770	9	)	)	PUNCT
ejpam-3543	770	10	.	.	PUNCT
ejpam-3543	771	1	let	let	VERB
ejpam-3543	771	2	x	x	PRON
ejpam-3543	771	3	,	,	PUNCT
ejpam-3543	771	4	y	y	PROPN
ejpam-3543	771	5	∈	∈	PROPN
ejpam-3543	771	6	l(λi	l(λi	X
ejpam-3543	771	7	;	;	PUNCT
ejpam-3543	771	8	β	β	X
ejpam-3543	771	9	)	)	PUNCT
ejpam-3543	771	10	.	.	PUNCT
ejpam-3543	772	1	then	then	ADV
ejpam-3543	772	2	λi(x	λi(x	X
ejpam-3543	772	3	)	)	PUNCT
ejpam-3543	772	4	≤	≤	NUM
ejpam-3543	772	5	β	β	X
ejpam-3543	772	6	and	and	CCONJ
ejpam-3543	772	7	λi(y	λi(y	NUM
ejpam-3543	772	8	)	)	PUNCT
ejpam-3543	772	9	≤	≤	NOUN
ejpam-3543	772	10	β	β	NOUN
ejpam-3543	772	11	,	,	PUNCT
ejpam-3543	772	12	so	so	SCONJ
ejpam-3543	772	13	β	β	X
ejpam-3543	772	14	is	be	AUX
ejpam-3543	772	15	a	a	DET
ejpam-3543	772	16	upper	upper	ADJ
ejpam-3543	772	17	bound	bind	VERB
ejpam-3543	772	18	of	of	ADP
ejpam-3543	772	19	{	{	PUNCT
ejpam-3543	772	20	λi(x	λi(x	NUM
ejpam-3543	772	21	)	)	PUNCT
ejpam-3543	772	22	,	,	PUNCT
ejpam-3543	772	23	λi(y	λi(y	NOUN
ejpam-3543	772	24	)	)	PUNCT
ejpam-3543	772	25	}	}	PUNCT
ejpam-3543	772	26	.	.	PUNCT
ejpam-3543	773	1	by	by	ADP
ejpam-3543	773	2	(	(	PUNCT
ejpam-3543	773	3	3.4	3.4	NUM
ejpam-3543	773	4	)	)	PUNCT
ejpam-3543	773	5	,	,	PUNCT
ejpam-3543	773	6	we	we	PRON
ejpam-3543	773	7	have	have	AUX
ejpam-3543	773	8	λi(x·y	λi(x·y	VERB
ejpam-3543	773	9	)	)	PUNCT
ejpam-3543	773	10	≤	≤	NUM
ejpam-3543	773	11	max{λi(x	max{λi(x	NOUN
ejpam-3543	773	12	)	)	PUNCT
ejpam-3543	773	13	,	,	PUNCT
ejpam-3543	773	14	λi(y	λi(y	X
ejpam-3543	773	15	)	)	PUNCT
ejpam-3543	773	16	}	}	PUNCT
ejpam-3543	773	17	≤	≤	NOUN
ejpam-3543	774	1	β	β	X
ejpam-3543	774	2	.	.	PUNCT
ejpam-3543	775	1	thus	thus	ADV
ejpam-3543	775	2	x·y	x·y	PROPN
ejpam-3543	775	3	∈	∈	PROPN
ejpam-3543	775	4	l(λi	l(λi	X
ejpam-3543	775	5	;	;	PUNCT
ejpam-3543	775	6	β	β	X
ejpam-3543	775	7	)	)	PUNCT
ejpam-3543	775	8	.	.	PUNCT
ejpam-3543	776	1	let	let	VERB
ejpam-3543	776	2	x	x	PRON
ejpam-3543	776	3	,	,	PUNCT
ejpam-3543	776	4	y	y	PROPN
ejpam-3543	776	5	∈	∈	PROPN
ejpam-3543	776	6	u(λf	u(λf	ADV
ejpam-3543	776	7	;	;	PUNCT
ejpam-3543	776	8	γ	γ	X
ejpam-3543	776	9	)	)	PUNCT
ejpam-3543	776	10	.	.	PUNCT
ejpam-3543	777	1	then	then	ADV
ejpam-3543	777	2	λf	λf	INTJ
ejpam-3543	777	3	(	(	PUNCT
ejpam-3543	777	4	x	x	NOUN
ejpam-3543	777	5	)	)	PUNCT
ejpam-3543	777	6	≥	≥	PROPN
ejpam-3543	777	7	γ	γ	NOUN
ejpam-3543	777	8	and	and	CCONJ
ejpam-3543	777	9	λf	λf	PROPN
ejpam-3543	777	10	(	(	PUNCT
ejpam-3543	777	11	y	y	PROPN
ejpam-3543	777	12	)	)	PUNCT
ejpam-3543	777	13	≥	≥	PROPN
ejpam-3543	777	14	γ	γ	PROPN
ejpam-3543	777	15	,	,	PUNCT
ejpam-3543	777	16	so	so	ADV
ejpam-3543	777	17	γ	γ	NOUN
ejpam-3543	777	18	is	be	AUX
ejpam-3543	777	19	an	an	DET
ejpam-3543	777	20	lower	low	ADJ
ejpam-3543	777	21	bound	bind	VERB
ejpam-3543	777	22	of	of	ADP
ejpam-3543	777	23	{	{	PUNCT
ejpam-3543	777	24	λf	λf	PROPN
ejpam-3543	777	25	(	(	PUNCT
ejpam-3543	777	26	x	x	NOUN
ejpam-3543	777	27	)	)	PUNCT
ejpam-3543	777	28	,	,	PUNCT
ejpam-3543	777	29	λf	λf	X
ejpam-3543	777	30	(	(	PUNCT
ejpam-3543	777	31	y	y	NOUN
ejpam-3543	777	32	)	)	PUNCT
ejpam-3543	777	33	}	}	PUNCT
ejpam-3543	777	34	.	.	PUNCT
ejpam-3543	778	1	by	by	ADP
ejpam-3543	778	2	(	(	PUNCT
ejpam-3543	778	3	3.5	3.5	NUM
ejpam-3543	778	4	)	)	PUNCT
ejpam-3543	778	5	,	,	PUNCT
ejpam-3543	778	6	we	we	PRON
ejpam-3543	778	7	have	have	VERB
ejpam-3543	778	8	λf	λf	INTJ
ejpam-3543	778	9	(	(	PUNCT
ejpam-3543	778	10	x	x	SYM
ejpam-3543	778	11	·	·	PUNCT
ejpam-3543	778	12	y	y	X
ejpam-3543	778	13	)	)	PUNCT
ejpam-3543	778	14	≥	≥	NOUN
ejpam-3543	778	15	min{λf	min{λf	X
ejpam-3543	778	16	(	(	PUNCT
ejpam-3543	778	17	x	x	X
ejpam-3543	778	18	)	)	PUNCT
ejpam-3543	778	19	,	,	PUNCT
ejpam-3543	778	20	λf	λf	X
ejpam-3543	778	21	(	(	PUNCT
ejpam-3543	778	22	y	y	NOUN
ejpam-3543	778	23	)	)	PUNCT
ejpam-3543	778	24	}	}	PUNCT
ejpam-3543	778	25	≥	≥	PROPN
ejpam-3543	778	26	γ	γ	X
ejpam-3543	778	27	.	.	PUNCT
ejpam-3543	779	1	thus	thus	ADV
ejpam-3543	779	2	x	x	X
ejpam-3543	779	3	·	·	PUNCT
ejpam-3543	779	4	y	y	X
ejpam-3543	779	5	∈	∈	PROPN
ejpam-3543	779	6	u(λf	u(λf	ADV
ejpam-3543	779	7	;	;	PUNCT
ejpam-3543	779	8	γ	γ	X
ejpam-3543	779	9	)	)	PUNCT
ejpam-3543	779	10	.	.	PUNCT
ejpam-3543	780	1	hence	hence	ADV
ejpam-3543	780	2	,	,	PUNCT
ejpam-3543	780	3	u(λt	u(λt	PROPN
ejpam-3543	780	4	;	;	PUNCT
ejpam-3543	780	5	α	α	X
ejpam-3543	780	6	)	)	PUNCT
ejpam-3543	780	7	,	,	PUNCT
ejpam-3543	780	8	l(λi	l(λi	PROPN
ejpam-3543	780	9	;	;	PUNCT
ejpam-3543	780	10	β	β	X
ejpam-3543	780	11	)	)	PUNCT
ejpam-3543	780	12	,	,	PUNCT
ejpam-3543	780	13	and	and	CCONJ
ejpam-3543	780	14	u(λf	u(λf	ADV
ejpam-3543	780	15	;	;	PUNCT
ejpam-3543	780	16	γ	γ	X
ejpam-3543	780	17	)	)	PUNCT
ejpam-3543	780	18	are	be	AUX
ejpam-3543	780	19	up	up	ADV
ejpam-3543	780	20	-	-	PUNCT
ejpam-3543	780	21	subalgebras	subalgebra	NOUN
ejpam-3543	780	22	of	of	ADP
ejpam-3543	780	23	x.	x.	NOUN
ejpam-3543	780	24	conversely	conversely	ADV
ejpam-3543	780	25	,	,	PUNCT
ejpam-3543	780	26	assume	assume	VERB
ejpam-3543	780	27	that	that	SCONJ
ejpam-3543	780	28	for	for	ADP
ejpam-3543	780	29	all	all	DET
ejpam-3543	780	30	α	α	NOUN
ejpam-3543	780	31	,	,	PUNCT
ejpam-3543	780	32	β	β	X
ejpam-3543	780	33	,	,	PUNCT
ejpam-3543	780	34	γ	γ	PROPN
ejpam-3543	780	35	∈	∈	PROPN
ejpam-3543	781	1	[	[	X
ejpam-3543	781	2	0	0	NUM
ejpam-3543	781	3	,	,	PUNCT
ejpam-3543	781	4	1	1	NUM
ejpam-3543	781	5	]	]	PUNCT
ejpam-3543	781	6	,	,	PUNCT
ejpam-3543	781	7	the	the	PRON
ejpam-3543	781	8	sets	set	NOUN
ejpam-3543	781	9	u(λt	u(λt	NOUN
ejpam-3543	781	10	;	;	PUNCT
ejpam-3543	781	11	α	α	X
ejpam-3543	781	12	)	)	PUNCT
ejpam-3543	781	13	,	,	PUNCT
ejpam-3543	781	14	l(λi	l(λi	PROPN
ejpam-3543	781	15	;	;	PUNCT
ejpam-3543	781	16	β	β	X
ejpam-3543	781	17	)	)	PUNCT
ejpam-3543	781	18	,	,	PUNCT
ejpam-3543	781	19	and	and	CCONJ
ejpam-3543	781	20	u(λf	u(λf	ADV
ejpam-3543	781	21	;	;	PUNCT
ejpam-3543	781	22	γ	γ	X
ejpam-3543	781	23	)	)	PUNCT
ejpam-3543	781	24	are	be	AUX
ejpam-3543	781	25	up	up	ADV
ejpam-3543	781	26	-	-	PUNCT
ejpam-3543	781	27	subalgebras	subalgebra	NOUN
ejpam-3543	781	28	of	of	ADP
ejpam-3543	781	29	x	x	PRON
ejpam-3543	781	30	if	if	SCONJ
ejpam-3543	781	31	u(λt	u(λt	NOUN
ejpam-3543	781	32	;	;	PUNCT
ejpam-3543	781	33	α	α	X
ejpam-3543	781	34	)	)	PUNCT
ejpam-3543	781	35	,	,	PUNCT
ejpam-3543	781	36	l(λi	l(λi	PROPN
ejpam-3543	781	37	;	;	PUNCT
ejpam-3543	781	38	β	β	X
ejpam-3543	781	39	)	)	PUNCT
ejpam-3543	781	40	,	,	PUNCT
ejpam-3543	781	41	and	and	CCONJ
ejpam-3543	781	42	u(λf	u(λf	ADV
ejpam-3543	781	43	;	;	PUNCT
ejpam-3543	781	44	γ	γ	X
ejpam-3543	781	45	)	)	PUNCT
ejpam-3543	781	46	are	be	AUX
ejpam-3543	781	47	nonempty	nonempty	ADJ
ejpam-3543	781	48	.	.	PUNCT
ejpam-3543	782	1	let	let	VERB
ejpam-3543	782	2	x	x	PRON
ejpam-3543	782	3	,	,	PUNCT
ejpam-3543	782	4	y	y	PROPN
ejpam-3543	782	5	∈	∈	PROPN
ejpam-3543	782	6	x.	x.	NOUN
ejpam-3543	783	1	then	then	ADV
ejpam-3543	783	2	λt	λt	ADP
ejpam-3543	783	3	(	(	PUNCT
ejpam-3543	783	4	x	x	NOUN
ejpam-3543	783	5	)	)	PUNCT
ejpam-3543	783	6	,	,	PUNCT
ejpam-3543	783	7	λt	λt	X
ejpam-3543	783	8	(	(	PUNCT
ejpam-3543	783	9	y	y	NOUN
ejpam-3543	783	10	)	)	PUNCT
ejpam-3543	783	11	∈	∈	PROPN
ejpam-3543	784	1	[	[	X
ejpam-3543	784	2	0	0	NUM
ejpam-3543	784	3	,	,	PUNCT
ejpam-3543	784	4	1	1	NUM
ejpam-3543	784	5	]	]	PUNCT
ejpam-3543	784	6	.	.	PUNCT
ejpam-3543	785	1	choose	choose	VERB
ejpam-3543	785	2	α	α	NOUN
ejpam-3543	785	3	=	=	PUNCT
ejpam-3543	785	4	min{λt	min{λt	X
ejpam-3543	785	5	(	(	PUNCT
ejpam-3543	785	6	x	x	X
ejpam-3543	785	7	)	)	PUNCT
ejpam-3543	785	8	,	,	PUNCT
ejpam-3543	785	9	λt	λt	X
ejpam-3543	785	10	(	(	PUNCT
ejpam-3543	785	11	y	y	NOUN
ejpam-3543	785	12	)	)	PUNCT
ejpam-3543	785	13	}	}	PUNCT
ejpam-3543	785	14	.	.	PUNCT
ejpam-3543	786	1	thus	thus	ADV
ejpam-3543	786	2	λt	λt	X
ejpam-3543	786	3	(	(	PUNCT
ejpam-3543	786	4	x	x	NOUN
ejpam-3543	786	5	)	)	PUNCT
ejpam-3543	786	6	≥	≥	NOUN
ejpam-3543	786	7	α	α	NOUN
ejpam-3543	786	8	and	and	CCONJ
ejpam-3543	786	9	λt	λt	X
ejpam-3543	786	10	(	(	PUNCT
ejpam-3543	786	11	y	y	NOUN
ejpam-3543	786	12	)	)	PUNCT
ejpam-3543	786	13	≥	≥	NOUN
ejpam-3543	786	14	α	α	NOUN
ejpam-3543	786	15	,	,	PUNCT
ejpam-3543	786	16	so	so	SCONJ
ejpam-3543	786	17	x	x	X
ejpam-3543	786	18	,	,	PUNCT
ejpam-3543	786	19	y	y	PROPN
ejpam-3543	786	20	∈	∈	PROPN
ejpam-3543	786	21	u(λt	u(λt	PROPN
ejpam-3543	786	22	;	;	PUNCT
ejpam-3543	786	23	α	α	X
ejpam-3543	786	24	)	)	PUNCT
ejpam-3543	786	25	6=	6=	ADP
ejpam-3543	786	26	∅.	∅.	ADP
ejpam-3543	786	27	by	by	ADP
ejpam-3543	786	28	assumption	assumption	NOUN
ejpam-3543	786	29	,	,	PUNCT
ejpam-3543	786	30	we	we	PRON
ejpam-3543	786	31	have	have	VERB
ejpam-3543	786	32	u(λt	u(λt	NOUN
ejpam-3543	786	33	;	;	PUNCT
ejpam-3543	786	34	α	α	X
ejpam-3543	786	35	)	)	PUNCT
ejpam-3543	786	36	is	be	AUX
ejpam-3543	786	37	a	a	DET
ejpam-3543	786	38	up	up	ADJ
ejpam-3543	786	39	-	-	PUNCT
ejpam-3543	786	40	subalgebra	subalgebra	NOUN
ejpam-3543	786	41	of	of	ADP
ejpam-3543	786	42	x	x	X
ejpam-3543	786	43	and	and	CCONJ
ejpam-3543	786	44	so	so	ADV
ejpam-3543	786	45	x	x	SYM
ejpam-3543	786	46	·	·	PUNCT
ejpam-3543	786	47	y	y	PROPN
ejpam-3543	786	48	∈	∈	PROPN
ejpam-3543	786	49	u(λt	u(λt	PROPN
ejpam-3543	786	50	;	;	PUNCT
ejpam-3543	786	51	α	α	X
ejpam-3543	786	52	)	)	PUNCT
ejpam-3543	786	53	.	.	PUNCT
ejpam-3543	787	1	thus	thus	ADV
ejpam-3543	787	2	λt	λt	X
ejpam-3543	787	3	(	(	PUNCT
ejpam-3543	787	4	x	x	X
ejpam-3543	787	5	·	·	PUNCT
ejpam-3543	787	6	y	y	X
ejpam-3543	787	7	)	)	PUNCT
ejpam-3543	787	8	≥	≥	NOUN
ejpam-3543	787	9	α	α	NOUN
ejpam-3543	787	10	=	=	PUNCT
ejpam-3543	787	11	min{λt	min{λt	X
ejpam-3543	787	12	(	(	PUNCT
ejpam-3543	787	13	x	x	X
ejpam-3543	787	14	)	)	PUNCT
ejpam-3543	787	15	,	,	PUNCT
ejpam-3543	787	16	λt	λt	X
ejpam-3543	787	17	(	(	PUNCT
ejpam-3543	787	18	y	y	NOUN
ejpam-3543	787	19	)	)	PUNCT
ejpam-3543	787	20	}	}	PUNCT
ejpam-3543	787	21	.	.	PUNCT
ejpam-3543	788	1	let	let	VERB
ejpam-3543	788	2	x	x	PRON
ejpam-3543	788	3	,	,	PUNCT
ejpam-3543	788	4	y	y	PROPN
ejpam-3543	788	5	∈	∈	PROPN
ejpam-3543	788	6	x.	x.	NOUN
ejpam-3543	788	7	then	then	ADV
ejpam-3543	788	8	λi(x	λi(x	NUM
ejpam-3543	788	9	)	)	PUNCT
ejpam-3543	788	10	,	,	PUNCT
ejpam-3543	788	11	λi(y	λi(y	X
ejpam-3543	788	12	)	)	PUNCT
ejpam-3543	788	13	∈	∈	PROPN
ejpam-3543	789	1	[	[	X
ejpam-3543	789	2	0	0	NUM
ejpam-3543	789	3	,	,	PUNCT
ejpam-3543	789	4	1	1	NUM
ejpam-3543	789	5	]	]	PUNCT
ejpam-3543	789	6	.	.	PUNCT
ejpam-3543	790	1	choose	choose	VERB
ejpam-3543	790	2	β	β	X
ejpam-3543	790	3	=	=	SYM
ejpam-3543	790	4	max{λi(x	max{λi(x	PROPN
ejpam-3543	790	5	)	)	PUNCT
ejpam-3543	790	6	,	,	PUNCT
ejpam-3543	790	7	λi(y	λi(y	NOUN
ejpam-3543	790	8	)	)	PUNCT
ejpam-3543	790	9	}	}	PUNCT
ejpam-3543	790	10	.	.	PUNCT
ejpam-3543	791	1	thus	thus	ADV
ejpam-3543	791	2	λi(x	λi(x	NUM
ejpam-3543	791	3	)	)	PUNCT
ejpam-3543	791	4	≤	≤	NUM
ejpam-3543	791	5	β	β	X
ejpam-3543	791	6	and	and	CCONJ
ejpam-3543	791	7	λi(y	λi(y	NUM
ejpam-3543	791	8	)	)	PUNCT
ejpam-3543	791	9	≤	≤	NOUN
ejpam-3543	791	10	β	β	NOUN
ejpam-3543	791	11	,	,	PUNCT
ejpam-3543	791	12	so	so	SCONJ
ejpam-3543	791	13	x	x	X
ejpam-3543	791	14	,	,	PUNCT
ejpam-3543	791	15	y	y	PROPN
ejpam-3543	791	16	∈	∈	PROPN
ejpam-3543	791	17	l(λi	l(λi	X
ejpam-3543	791	18	;	;	PUNCT
ejpam-3543	791	19	β	β	X
ejpam-3543	791	20	)	)	PUNCT
ejpam-3543	791	21	6=	6=	ADP
ejpam-3543	791	22	∅.	∅.	ADP
ejpam-3543	791	23	by	by	ADP
ejpam-3543	791	24	assumption	assumption	NOUN
ejpam-3543	791	25	,	,	PUNCT
ejpam-3543	791	26	we	we	PRON
ejpam-3543	791	27	have	have	VERB
ejpam-3543	791	28	l(λi	l(λi	NOUN
ejpam-3543	791	29	;	;	PUNCT
ejpam-3543	791	30	β	β	X
ejpam-3543	791	31	)	)	PUNCT
ejpam-3543	791	32	is	be	AUX
ejpam-3543	791	33	a	a	DET
ejpam-3543	791	34	up	up	ADJ
ejpam-3543	791	35	-	-	PUNCT
ejpam-3543	791	36	subalgebra	subalgebra	NOUN
ejpam-3543	791	37	of	of	ADP
ejpam-3543	791	38	x	x	X
ejpam-3543	791	39	and	and	CCONJ
ejpam-3543	791	40	so	so	ADV
ejpam-3543	791	41	x	x	SYM
ejpam-3543	791	42	·	·	PUNCT
ejpam-3543	791	43	y	y	SYM
ejpam-3543	791	44	∈	∈	PROPN
ejpam-3543	791	45	l(λi	l(λi	X
ejpam-3543	791	46	;	;	PUNCT
ejpam-3543	791	47	β	β	X
ejpam-3543	791	48	)	)	PUNCT
ejpam-3543	791	49	.	.	PUNCT
ejpam-3543	792	1	thus	thus	ADV
ejpam-3543	792	2	λi(x	λi(x	X
ejpam-3543	792	3	·	·	PUNCT
ejpam-3543	792	4	y	y	X
ejpam-3543	792	5	)	)	PUNCT
ejpam-3543	792	6	≤	≤	NOUN
ejpam-3543	792	7	β	β	X
ejpam-3543	792	8	=	=	SYM
ejpam-3543	792	9	max{λi(x	max{λi(x	PROPN
ejpam-3543	792	10	)	)	PUNCT
ejpam-3543	792	11	,	,	PUNCT
ejpam-3543	792	12	λi(y	λi(y	NOUN
ejpam-3543	792	13	)	)	PUNCT
ejpam-3543	792	14	}	}	PUNCT
ejpam-3543	792	15	.	.	PUNCT
ejpam-3543	793	1	let	let	VERB
ejpam-3543	793	2	x	x	PRON
ejpam-3543	793	3	,	,	PUNCT
ejpam-3543	793	4	y	y	PROPN
ejpam-3543	793	5	∈	∈	PROPN
ejpam-3543	793	6	x.	x.	NOUN
ejpam-3543	794	1	then	then	ADV
ejpam-3543	794	2	λf	λf	INTJ
ejpam-3543	794	3	(	(	PUNCT
ejpam-3543	794	4	x	x	NOUN
ejpam-3543	794	5	)	)	PUNCT
ejpam-3543	794	6	,	,	PUNCT
ejpam-3543	794	7	λf	λf	X
ejpam-3543	794	8	(	(	PUNCT
ejpam-3543	794	9	y	y	NOUN
ejpam-3543	794	10	)	)	PUNCT
ejpam-3543	794	11	∈	∈	PROPN
ejpam-3543	795	1	[	[	X
ejpam-3543	795	2	0	0	NUM
ejpam-3543	795	3	,	,	PUNCT
ejpam-3543	795	4	1	1	NUM
ejpam-3543	795	5	]	]	PUNCT
ejpam-3543	795	6	.	.	PUNCT
ejpam-3543	796	1	choose	choose	VERB
ejpam-3543	796	2	γ	γ	X
ejpam-3543	796	3	=	=	SYM
ejpam-3543	796	4	min{λf	min{λf	X
ejpam-3543	796	5	(	(	PUNCT
ejpam-3543	796	6	x	x	NOUN
ejpam-3543	796	7	)	)	PUNCT
ejpam-3543	796	8	,	,	PUNCT
ejpam-3543	796	9	λf	λf	X
ejpam-3543	796	10	(	(	PUNCT
ejpam-3543	796	11	y	y	NOUN
ejpam-3543	796	12	)	)	PUNCT
ejpam-3543	796	13	}	}	PUNCT
ejpam-3543	796	14	.	.	PUNCT
ejpam-3543	797	1	thus	thus	ADV
ejpam-3543	797	2	λf	λf	X
ejpam-3543	797	3	(	(	PUNCT
ejpam-3543	797	4	x	x	NOUN
ejpam-3543	797	5	)	)	PUNCT
ejpam-3543	797	6	≥	≥	PROPN
ejpam-3543	797	7	γ	γ	NOUN
ejpam-3543	797	8	and	and	CCONJ
ejpam-3543	797	9	λf	λf	PROPN
ejpam-3543	797	10	(	(	PUNCT
ejpam-3543	797	11	y	y	PROPN
ejpam-3543	797	12	)	)	PUNCT
ejpam-3543	797	13	≥	≥	PROPN
ejpam-3543	797	14	γ	γ	NOUN
ejpam-3543	797	15	,	,	PUNCT
ejpam-3543	797	16	so	so	ADV
ejpam-3543	797	17	x	x	NOUN
ejpam-3543	797	18	,	,	PUNCT
ejpam-3543	797	19	y	y	PROPN
ejpam-3543	797	20	∈	∈	PROPN
ejpam-3543	797	21	u(λf	u(λf	ADV
ejpam-3543	797	22	;	;	PUNCT
ejpam-3543	797	23	γ	γ	X
ejpam-3543	797	24	)	)	PUNCT
ejpam-3543	797	25	6=	6=	ADP
ejpam-3543	797	26	∅.	∅.	ADP
ejpam-3543	797	27	by	by	ADP
ejpam-3543	797	28	assumption	assumption	NOUN
ejpam-3543	797	29	,	,	PUNCT
ejpam-3543	797	30	we	we	PRON
ejpam-3543	797	31	have	have	VERB
ejpam-3543	797	32	u(λf	u(λf	ADV
ejpam-3543	797	33	;	;	PUNCT
ejpam-3543	797	34	γ	γ	X
ejpam-3543	797	35	)	)	PUNCT
ejpam-3543	797	36	is	be	AUX
ejpam-3543	797	37	a	a	DET
ejpam-3543	797	38	up	up	ADJ
ejpam-3543	797	39	-	-	PUNCT
ejpam-3543	797	40	subalgebra	subalgebra	NOUN
ejpam-3543	797	41	of	of	ADP
ejpam-3543	797	42	x	x	X
ejpam-3543	797	43	and	and	CCONJ
ejpam-3543	797	44	so	so	ADV
ejpam-3543	797	45	x	x	SYM
ejpam-3543	797	46	·	·	PUNCT
ejpam-3543	797	47	y	y	X
ejpam-3543	797	48	∈	∈	PROPN
ejpam-3543	797	49	u(λf	u(λf	ADV
ejpam-3543	797	50	;	;	PUNCT
ejpam-3543	797	51	γ	γ	X
ejpam-3543	797	52	)	)	PUNCT
ejpam-3543	797	53	.	.	PUNCT
ejpam-3543	798	1	thus	thus	ADV
ejpam-3543	798	2	λf	λf	X
ejpam-3543	798	3	(	(	PUNCT
ejpam-3543	798	4	x	x	SYM
ejpam-3543	798	5	·	·	PUNCT
ejpam-3543	798	6	y	y	X
ejpam-3543	798	7	)	)	PUNCT
ejpam-3543	798	8	≥	≥	PROPN
ejpam-3543	798	9	γ	γ	X
ejpam-3543	798	10	=	=	SYM
ejpam-3543	798	11	min{λf	min{λf	X
ejpam-3543	798	12	(	(	PUNCT
ejpam-3543	798	13	x	x	NOUN
ejpam-3543	798	14	)	)	PUNCT
ejpam-3543	798	15	,	,	PUNCT
ejpam-3543	798	16	λf	λf	X
ejpam-3543	798	17	(	(	PUNCT
ejpam-3543	798	18	y	y	NOUN
ejpam-3543	798	19	)	)	PUNCT
ejpam-3543	798	20	}	}	PUNCT
ejpam-3543	798	21	.	.	PUNCT
ejpam-3543	799	1	therefore	therefore	ADV
ejpam-3543	799	2	,	,	PUNCT
ejpam-3543	799	3	λ	λ	PROPN
ejpam-3543	799	4	is	be	AUX
ejpam-3543	799	5	a	a	DET
ejpam-3543	799	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	799	7	up	up	ADP
ejpam-3543	799	8	-	-	PUNCT
ejpam-3543	799	9	subalgebra	subalgebra	NOUN
ejpam-3543	799	10	of	of	ADP
ejpam-3543	799	11	x.	x.	PROPN
ejpam-3543	799	12	m.	m.	PROPN
ejpam-3543	799	13	songsaeng	songsaeng	PROPN
ejpam-3543	799	14	,	,	PUNCT
ejpam-3543	799	15	a.	a.	NOUN
ejpam-3543	799	16	iampan	iampan	PROPN
ejpam-3543	799	17	/	/	SYM
ejpam-3543	799	18	eur	eur	PROPN
ejpam-3543	799	19	.	.	PUNCT
ejpam-3543	800	1	j.	j.	PROPN
ejpam-3543	800	2	pure	pure	PROPN
ejpam-3543	800	3	appl	appl	PROPN
ejpam-3543	800	4	.	.	PROPN
ejpam-3543	800	5	math	math	PROPN
ejpam-3543	800	6	,	,	PUNCT
ejpam-3543	800	7	12	12	NUM
ejpam-3543	800	8	(	(	PUNCT
ejpam-3543	800	9	4	4	NUM
ejpam-3543	800	10	)	)	PUNCT
ejpam-3543	800	11	(	(	PUNCT
ejpam-3543	800	12	2019	2019	NUM
ejpam-3543	800	13	)	)	PUNCT
ejpam-3543	800	14	,	,	PUNCT
ejpam-3543	800	15	1382	1382	NUM
ejpam-3543	800	16	-	-	SYM
ejpam-3543	800	17	1409	1409	NUM
ejpam-3543	800	18	1403	1403	NUM
ejpam-3543	800	19	theorem	theorem	VERB
ejpam-3543	800	20	20	20	NUM
ejpam-3543	800	21	.	.	PUNCT
ejpam-3543	801	1	a	a	DET
ejpam-3543	801	2	ns	ns	NUM
ejpam-3543	801	3	λ	λ	NOUN
ejpam-3543	801	4	in	in	ADP
ejpam-3543	801	5	x	x	PROPN
ejpam-3543	801	6	is	be	AUX
ejpam-3543	801	7	a	a	DET
ejpam-3543	801	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	801	9	near	near	ADP
ejpam-3543	801	10	up	up	ADJ
ejpam-3543	801	11	-	-	PUNCT
ejpam-3543	801	12	filter	filter	NOUN
ejpam-3543	801	13	of	of	ADP
ejpam-3543	801	14	x	x	SYM
ejpam-3543	801	15	if	if	SCONJ
ejpam-3543	802	1	and	and	CCONJ
ejpam-3543	802	2	only	only	ADV
ejpam-3543	802	3	if	if	SCONJ
ejpam-3543	802	4	for	for	ADP
ejpam-3543	802	5	all	all	DET
ejpam-3543	802	6	α	α	NOUN
ejpam-3543	802	7	,	,	PUNCT
ejpam-3543	802	8	β	β	X
ejpam-3543	802	9	,	,	PUNCT
ejpam-3543	802	10	γ	γ	PROPN
ejpam-3543	802	11	∈	∈	PROPN
ejpam-3543	803	1	[	[	X
ejpam-3543	803	2	0	0	NUM
ejpam-3543	803	3	,	,	PUNCT
ejpam-3543	803	4	1	1	NUM
ejpam-3543	803	5	]	]	PUNCT
ejpam-3543	803	6	,	,	PUNCT
ejpam-3543	803	7	the	the	PRON
ejpam-3543	803	8	sets	set	NOUN
ejpam-3543	803	9	u(λt	u(λt	NOUN
ejpam-3543	803	10	;	;	PUNCT
ejpam-3543	803	11	α	α	X
ejpam-3543	803	12	)	)	PUNCT
ejpam-3543	803	13	,	,	PUNCT
ejpam-3543	803	14	l(λi	l(λi	PROPN
ejpam-3543	803	15	;	;	PUNCT
ejpam-3543	803	16	β	β	X
ejpam-3543	803	17	)	)	PUNCT
ejpam-3543	803	18	,	,	PUNCT
ejpam-3543	803	19	and	and	CCONJ
ejpam-3543	803	20	u(λf	u(λf	ADV
ejpam-3543	803	21	;	;	PUNCT
ejpam-3543	803	22	γ	γ	X
ejpam-3543	803	23	)	)	PUNCT
ejpam-3543	803	24	are	be	AUX
ejpam-3543	803	25	near	near	ADP
ejpam-3543	803	26	up	up	ADP
ejpam-3543	803	27	-	-	PUNCT
ejpam-3543	803	28	filters	filter	NOUN
ejpam-3543	803	29	of	of	ADP
ejpam-3543	803	30	x	x	PRON
ejpam-3543	803	31	if	if	SCONJ
ejpam-3543	803	32	u(λt	u(λt	NOUN
ejpam-3543	803	33	;	;	PUNCT
ejpam-3543	803	34	α	α	X
ejpam-3543	803	35	)	)	PUNCT
ejpam-3543	803	36	,	,	PUNCT
ejpam-3543	803	37	l(λi	l(λi	PROPN
ejpam-3543	803	38	;	;	PUNCT
ejpam-3543	803	39	β	β	X
ejpam-3543	803	40	)	)	PUNCT
ejpam-3543	803	41	,	,	PUNCT
ejpam-3543	803	42	and	and	CCONJ
ejpam-3543	803	43	u(λf	u(λf	ADV
ejpam-3543	803	44	;	;	PUNCT
ejpam-3543	803	45	γ	γ	X
ejpam-3543	803	46	)	)	PUNCT
ejpam-3543	803	47	are	be	AUX
ejpam-3543	803	48	nonempty	nonempty	ADJ
ejpam-3543	803	49	.	.	PUNCT
ejpam-3543	804	1	proof	proof	NOUN
ejpam-3543	804	2	.	.	PUNCT
ejpam-3543	805	1	assume	assume	VERB
ejpam-3543	805	2	that	that	SCONJ
ejpam-3543	805	3	λ	λ	PROPN
ejpam-3543	805	4	is	be	AUX
ejpam-3543	805	5	a	a	DET
ejpam-3543	805	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	805	7	near	near	ADP
ejpam-3543	805	8	up	up	ADJ
ejpam-3543	805	9	-	-	PUNCT
ejpam-3543	805	10	filter	filter	NOUN
ejpam-3543	805	11	of	of	ADP
ejpam-3543	805	12	x.	x.	NOUN
ejpam-3543	805	13	let	let	VERB
ejpam-3543	805	14	α	α	PRON
ejpam-3543	805	15	,	,	PUNCT
ejpam-3543	805	16	β	β	X
ejpam-3543	805	17	,	,	PUNCT
ejpam-3543	805	18	γ	γ	PROPN
ejpam-3543	805	19	∈	∈	PROPN
ejpam-3543	806	1	[	[	X
ejpam-3543	806	2	0	0	NUM
ejpam-3543	806	3	,	,	PUNCT
ejpam-3543	806	4	1	1	NUM
ejpam-3543	806	5	]	]	PUNCT
ejpam-3543	806	6	be	be	AUX
ejpam-3543	806	7	such	such	ADJ
ejpam-3543	806	8	that	that	SCONJ
ejpam-3543	806	9	u(λt	u(λt	NOUN
ejpam-3543	806	10	;	;	PUNCT
ejpam-3543	806	11	α	α	X
ejpam-3543	806	12	)	)	PUNCT
ejpam-3543	806	13	,	,	PUNCT
ejpam-3543	806	14	l(λi	l(λi	PROPN
ejpam-3543	806	15	;	;	PUNCT
ejpam-3543	806	16	β	β	X
ejpam-3543	806	17	)	)	PUNCT
ejpam-3543	806	18	,	,	PUNCT
ejpam-3543	806	19	and	and	CCONJ
ejpam-3543	806	20	u(λf	u(λf	ADV
ejpam-3543	806	21	;	;	PUNCT
ejpam-3543	806	22	γ	γ	X
ejpam-3543	806	23	)	)	PUNCT
ejpam-3543	806	24	are	be	AUX
ejpam-3543	806	25	nonempty	nonempty	ADJ
ejpam-3543	806	26	.	.	PUNCT
ejpam-3543	807	1	let	let	VERB
ejpam-3543	807	2	x	x	SYM
ejpam-3543	807	3	∈	∈	PROPN
ejpam-3543	807	4	u(λt	u(λt	NOUN
ejpam-3543	807	5	;	;	PUNCT
ejpam-3543	807	6	α	α	X
ejpam-3543	807	7	)	)	PUNCT
ejpam-3543	807	8	.	.	PUNCT
ejpam-3543	808	1	then	then	ADV
ejpam-3543	808	2	λt	λt	INTJ
ejpam-3543	808	3	(	(	PUNCT
ejpam-3543	808	4	x	x	X
ejpam-3543	808	5	)	)	PUNCT
ejpam-3543	808	6	≥	≥	PROPN
ejpam-3543	808	7	α	α	NOUN
ejpam-3543	808	8	.	.	PUNCT
ejpam-3543	809	1	by	by	ADP
ejpam-3543	809	2	(	(	PUNCT
ejpam-3543	809	3	3.6	3.6	NUM
ejpam-3543	809	4	)	)	PUNCT
ejpam-3543	809	5	,	,	PUNCT
ejpam-3543	809	6	we	we	PRON
ejpam-3543	809	7	have	have	VERB
ejpam-3543	809	8	λt	λt	X
ejpam-3543	809	9	(	(	PUNCT
ejpam-3543	809	10	0	0	NUM
ejpam-3543	809	11	)	)	PUNCT
ejpam-3543	809	12	≥	≥	NOUN
ejpam-3543	809	13	λt	λt	X
ejpam-3543	809	14	(	(	PUNCT
ejpam-3543	809	15	x	x	NOUN
ejpam-3543	809	16	)	)	PUNCT
ejpam-3543	809	17	≥	≥	PROPN
ejpam-3543	809	18	α	α	NOUN
ejpam-3543	809	19	.	.	PUNCT
ejpam-3543	810	1	thus	thus	ADV
ejpam-3543	810	2	0	0	NUM
ejpam-3543	810	3	∈	∈	PROPN
ejpam-3543	810	4	u(λt	u(λt	NOUN
ejpam-3543	810	5	;	;	PUNCT
ejpam-3543	810	6	α	α	X
ejpam-3543	810	7	)	)	PUNCT
ejpam-3543	810	8	.	.	PUNCT
ejpam-3543	811	1	next	next	ADV
ejpam-3543	811	2	,	,	PUNCT
ejpam-3543	811	3	let	let	VERB
ejpam-3543	811	4	x	x	X
ejpam-3543	811	5	∈	∈	PROPN
ejpam-3543	811	6	x	x	X
ejpam-3543	811	7	and	and	CCONJ
ejpam-3543	811	8	y	y	PROPN
ejpam-3543	811	9	∈	∈	PROPN
ejpam-3543	811	10	u(λt	u(λt	PROPN
ejpam-3543	811	11	;	;	PUNCT
ejpam-3543	811	12	α	α	X
ejpam-3543	811	13	)	)	PUNCT
ejpam-3543	811	14	.	.	PUNCT
ejpam-3543	812	1	then	then	ADV
ejpam-3543	812	2	λt	λt	INTJ
ejpam-3543	812	3	(	(	PUNCT
ejpam-3543	812	4	y	y	NOUN
ejpam-3543	812	5	)	)	PUNCT
ejpam-3543	812	6	≥	≥	PROPN
ejpam-3543	812	7	α	α	NOUN
ejpam-3543	812	8	.	.	PUNCT
ejpam-3543	813	1	by	by	ADP
ejpam-3543	813	2	(	(	PUNCT
ejpam-3543	813	3	3.9	3.9	NUM
ejpam-3543	813	4	)	)	PUNCT
ejpam-3543	813	5	,	,	PUNCT
ejpam-3543	813	6	we	we	PRON
ejpam-3543	813	7	have	have	VERB
ejpam-3543	813	8	λt	λt	INTJ
ejpam-3543	813	9	(	(	PUNCT
ejpam-3543	813	10	x	x	PROPN
ejpam-3543	813	11	·	·	PUNCT
ejpam-3543	813	12	y	y	X
ejpam-3543	813	13	)	)	PUNCT
ejpam-3543	813	14	≥	≥	NOUN
ejpam-3543	813	15	λt	λt	X
ejpam-3543	813	16	(	(	PUNCT
ejpam-3543	813	17	y	y	NOUN
ejpam-3543	813	18	)	)	PUNCT
ejpam-3543	813	19	≥	≥	PROPN
ejpam-3543	813	20	α	α	NOUN
ejpam-3543	813	21	.	.	PUNCT
ejpam-3543	814	1	thus	thus	ADV
ejpam-3543	814	2	x	x	X
ejpam-3543	814	3	·	·	PUNCT
ejpam-3543	814	4	y	y	PROPN
ejpam-3543	814	5	∈	∈	PROPN
ejpam-3543	814	6	u(λt	u(λt	PROPN
ejpam-3543	814	7	;	;	PUNCT
ejpam-3543	814	8	α	α	X
ejpam-3543	814	9	)	)	PUNCT
ejpam-3543	814	10	.	.	PUNCT
ejpam-3543	815	1	let	let	VERB
ejpam-3543	815	2	x	x	SYM
ejpam-3543	815	3	∈	∈	NOUN
ejpam-3543	815	4	l(λi	l(λi	X
ejpam-3543	815	5	;	;	PUNCT
ejpam-3543	815	6	β	β	X
ejpam-3543	815	7	)	)	PUNCT
ejpam-3543	815	8	.	.	PUNCT
ejpam-3543	816	1	then	then	ADV
ejpam-3543	816	2	λi(x	λi(x	NUM
ejpam-3543	816	3	)	)	PUNCT
ejpam-3543	816	4	≤	≤	NOUN
ejpam-3543	817	1	β	β	X
ejpam-3543	817	2	.	.	PUNCT
ejpam-3543	818	1	by	by	ADP
ejpam-3543	818	2	(	(	PUNCT
ejpam-3543	818	3	3.7	3.7	NUM
ejpam-3543	818	4	)	)	PUNCT
ejpam-3543	818	5	,	,	PUNCT
ejpam-3543	818	6	we	we	PRON
ejpam-3543	818	7	have	have	VERB
ejpam-3543	818	8	λi(0	λi(0	NOUN
ejpam-3543	818	9	)	)	PUNCT
ejpam-3543	818	10	≤	≤	NOUN
ejpam-3543	818	11	λi(x	λi(x	NUM
ejpam-3543	818	12	)	)	PUNCT
ejpam-3543	818	13	≤	≤	NOUN
ejpam-3543	818	14	β	β	X
ejpam-3543	818	15	.	.	PUNCT
ejpam-3543	819	1	thus	thus	ADV
ejpam-3543	819	2	0	0	NUM
ejpam-3543	819	3	∈	∈	NOUN
ejpam-3543	819	4	l(λi	l(λi	NOUN
ejpam-3543	819	5	;	;	PUNCT
ejpam-3543	819	6	β	β	X
ejpam-3543	819	7	)	)	PUNCT
ejpam-3543	819	8	.	.	PUNCT
ejpam-3543	820	1	next	next	ADV
ejpam-3543	820	2	,	,	PUNCT
ejpam-3543	820	3	let	let	VERB
ejpam-3543	820	4	x	x	X
ejpam-3543	820	5	∈	∈	PROPN
ejpam-3543	820	6	x	x	X
ejpam-3543	820	7	and	and	CCONJ
ejpam-3543	820	8	y	y	PROPN
ejpam-3543	820	9	∈	∈	PROPN
ejpam-3543	820	10	l(λi	l(λi	X
ejpam-3543	820	11	;	;	PUNCT
ejpam-3543	820	12	β	β	X
ejpam-3543	820	13	)	)	PUNCT
ejpam-3543	820	14	.	.	PUNCT
ejpam-3543	821	1	then	then	ADV
ejpam-3543	821	2	λi(y	λi(y	NOUN
ejpam-3543	821	3	)	)	PUNCT
ejpam-3543	821	4	≤	≤	NOUN
ejpam-3543	821	5	β	β	X
ejpam-3543	821	6	.	.	PUNCT
ejpam-3543	822	1	by	by	ADP
ejpam-3543	822	2	(	(	PUNCT
ejpam-3543	822	3	3.10	3.10	NUM
ejpam-3543	822	4	)	)	PUNCT
ejpam-3543	822	5	,	,	PUNCT
ejpam-3543	822	6	we	we	PRON
ejpam-3543	822	7	have	have	VERB
ejpam-3543	822	8	λi(x	λi(x	NUM
ejpam-3543	822	9	·	·	PUNCT
ejpam-3543	822	10	y	y	X
ejpam-3543	822	11	)	)	PUNCT
ejpam-3543	822	12	≤	≤	NOUN
ejpam-3543	822	13	λi(y	λi(y	NOUN
ejpam-3543	822	14	)	)	PUNCT
ejpam-3543	822	15	≤	≤	NOUN
ejpam-3543	822	16	β	β	X
ejpam-3543	822	17	.	.	PUNCT
ejpam-3543	823	1	thus	thus	ADV
ejpam-3543	823	2	x	x	X
ejpam-3543	823	3	·	·	PUNCT
ejpam-3543	823	4	y	y	X
ejpam-3543	823	5	∈	∈	PROPN
ejpam-3543	823	6	l(λi	l(λi	X
ejpam-3543	823	7	;	;	PUNCT
ejpam-3543	823	8	β	β	X
ejpam-3543	823	9	)	)	PUNCT
ejpam-3543	823	10	.	.	PUNCT
ejpam-3543	824	1	let	let	VERB
ejpam-3543	824	2	x	x	PUNCT
ejpam-3543	824	3	∈	∈	PROPN
ejpam-3543	824	4	u(λf	u(λf	NOUN
ejpam-3543	824	5	;	;	PUNCT
ejpam-3543	824	6	γ	γ	X
ejpam-3543	824	7	)	)	PUNCT
ejpam-3543	824	8	.	.	PUNCT
ejpam-3543	825	1	then	then	ADV
ejpam-3543	825	2	λf	λf	INTJ
ejpam-3543	825	3	(	(	PUNCT
ejpam-3543	825	4	x	x	NOUN
ejpam-3543	825	5	)	)	PUNCT
ejpam-3543	825	6	≥	≥	PROPN
ejpam-3543	825	7	γ	γ	PROPN
ejpam-3543	825	8	.	.	PUNCT
ejpam-3543	825	9	by	by	ADP
ejpam-3543	825	10	(	(	PUNCT
ejpam-3543	825	11	3.8	3.8	NUM
ejpam-3543	825	12	)	)	PUNCT
ejpam-3543	825	13	,	,	PUNCT
ejpam-3543	825	14	we	we	PRON
ejpam-3543	825	15	have	have	VERB
ejpam-3543	825	16	λf	λf	VERB
ejpam-3543	825	17	(	(	PUNCT
ejpam-3543	825	18	0	0	NUM
ejpam-3543	825	19	)	)	PUNCT
ejpam-3543	825	20	≥	≥	NOUN
ejpam-3543	826	1	λf	λf	X
ejpam-3543	826	2	(	(	PUNCT
ejpam-3543	826	3	x	x	NOUN
ejpam-3543	826	4	)	)	PUNCT
ejpam-3543	826	5	≥	≥	PROPN
ejpam-3543	826	6	γ	γ	X
ejpam-3543	826	7	.	.	PUNCT
ejpam-3543	827	1	thus	thus	ADV
ejpam-3543	827	2	0	0	NUM
ejpam-3543	827	3	∈	∈	PROPN
ejpam-3543	827	4	u(λf	u(λf	NOUN
ejpam-3543	827	5	;	;	PUNCT
ejpam-3543	827	6	γ	γ	X
ejpam-3543	827	7	)	)	PUNCT
ejpam-3543	827	8	.	.	PUNCT
ejpam-3543	828	1	next	next	ADV
ejpam-3543	828	2	,	,	PUNCT
ejpam-3543	828	3	let	let	VERB
ejpam-3543	828	4	x	x	X
ejpam-3543	828	5	∈	∈	PROPN
ejpam-3543	828	6	x	x	X
ejpam-3543	828	7	and	and	CCONJ
ejpam-3543	828	8	y	y	PROPN
ejpam-3543	828	9	∈	∈	PROPN
ejpam-3543	828	10	u(λf	u(λf	ADV
ejpam-3543	828	11	;	;	PUNCT
ejpam-3543	828	12	γ	γ	X
ejpam-3543	828	13	)	)	PUNCT
ejpam-3543	828	14	.	.	PUNCT
ejpam-3543	829	1	then	then	ADV
ejpam-3543	829	2	λf	λf	INTJ
ejpam-3543	829	3	(	(	PUNCT
ejpam-3543	829	4	y	y	PROPN
ejpam-3543	829	5	)	)	PUNCT
ejpam-3543	829	6	≥	≥	PROPN
ejpam-3543	829	7	γ	γ	X
ejpam-3543	829	8	.	.	PUNCT
ejpam-3543	829	9	by	by	ADP
ejpam-3543	829	10	(	(	PUNCT
ejpam-3543	829	11	3.11	3.11	NUM
ejpam-3543	829	12	)	)	PUNCT
ejpam-3543	829	13	,	,	PUNCT
ejpam-3543	829	14	we	we	PRON
ejpam-3543	829	15	have	have	VERB
ejpam-3543	829	16	λf	λf	INTJ
ejpam-3543	829	17	(	(	PUNCT
ejpam-3543	829	18	x	x	SYM
ejpam-3543	829	19	·	·	PUNCT
ejpam-3543	829	20	y	y	X
ejpam-3543	829	21	)	)	PUNCT
ejpam-3543	829	22	≥	≥	NOUN
ejpam-3543	829	23	λf	λf	PROPN
ejpam-3543	829	24	(	(	PUNCT
ejpam-3543	829	25	y	y	NOUN
ejpam-3543	829	26	)	)	PUNCT
ejpam-3543	829	27	≥	≥	PROPN
ejpam-3543	829	28	γ	γ	X
ejpam-3543	829	29	.	.	PUNCT
ejpam-3543	830	1	thus	thus	ADV
ejpam-3543	830	2	x	x	X
ejpam-3543	830	3	·	·	PUNCT
ejpam-3543	830	4	y	y	X
ejpam-3543	830	5	∈	∈	PROPN
ejpam-3543	830	6	u(λf	u(λf	ADV
ejpam-3543	830	7	;	;	PUNCT
ejpam-3543	830	8	γ	γ	X
ejpam-3543	830	9	)	)	PUNCT
ejpam-3543	830	10	.	.	PUNCT
ejpam-3543	831	1	hence	hence	ADV
ejpam-3543	831	2	,	,	PUNCT
ejpam-3543	831	3	u(λt	u(λt	PROPN
ejpam-3543	831	4	;	;	PUNCT
ejpam-3543	831	5	α	α	X
ejpam-3543	831	6	)	)	PUNCT
ejpam-3543	831	7	,	,	PUNCT
ejpam-3543	831	8	l(λi	l(λi	PROPN
ejpam-3543	831	9	;	;	PUNCT
ejpam-3543	831	10	β	β	X
ejpam-3543	831	11	)	)	PUNCT
ejpam-3543	831	12	,	,	PUNCT
ejpam-3543	831	13	and	and	CCONJ
ejpam-3543	831	14	u(λf	u(λf	ADV
ejpam-3543	831	15	;	;	PUNCT
ejpam-3543	831	16	γ	γ	X
ejpam-3543	831	17	)	)	PUNCT
ejpam-3543	831	18	are	be	AUX
ejpam-3543	831	19	near	near	ADP
ejpam-3543	831	20	up	up	ADP
ejpam-3543	831	21	-	-	PUNCT
ejpam-3543	831	22	filters	filter	NOUN
ejpam-3543	831	23	of	of	ADP
ejpam-3543	831	24	x.	x.	NOUN
ejpam-3543	831	25	conversely	conversely	ADV
ejpam-3543	831	26	,	,	PUNCT
ejpam-3543	831	27	assume	assume	VERB
ejpam-3543	831	28	that	that	SCONJ
ejpam-3543	831	29	for	for	ADP
ejpam-3543	831	30	all	all	DET
ejpam-3543	831	31	α	α	NOUN
ejpam-3543	831	32	,	,	PUNCT
ejpam-3543	831	33	β	β	X
ejpam-3543	831	34	,	,	PUNCT
ejpam-3543	831	35	γ	γ	PROPN
ejpam-3543	831	36	∈	∈	PROPN
ejpam-3543	832	1	[	[	X
ejpam-3543	832	2	0	0	NUM
ejpam-3543	832	3	,	,	PUNCT
ejpam-3543	832	4	1	1	NUM
ejpam-3543	832	5	]	]	PUNCT
ejpam-3543	832	6	,	,	PUNCT
ejpam-3543	832	7	the	the	PRON
ejpam-3543	832	8	sets	set	NOUN
ejpam-3543	832	9	u(λt	u(λt	NOUN
ejpam-3543	832	10	;	;	PUNCT
ejpam-3543	832	11	α	α	X
ejpam-3543	832	12	)	)	PUNCT
ejpam-3543	832	13	,	,	PUNCT
ejpam-3543	832	14	l(λi	l(λi	PROPN
ejpam-3543	832	15	;	;	PUNCT
ejpam-3543	832	16	β	β	X
ejpam-3543	832	17	)	)	PUNCT
ejpam-3543	832	18	,	,	PUNCT
ejpam-3543	832	19	and	and	CCONJ
ejpam-3543	832	20	u(λf	u(λf	ADV
ejpam-3543	832	21	;	;	PUNCT
ejpam-3543	832	22	γ	γ	X
ejpam-3543	832	23	)	)	PUNCT
ejpam-3543	832	24	are	be	AUX
ejpam-3543	832	25	near	near	ADP
ejpam-3543	832	26	up	up	ADP
ejpam-3543	832	27	-	-	PUNCT
ejpam-3543	832	28	filters	filter	NOUN
ejpam-3543	832	29	of	of	ADP
ejpam-3543	832	30	x	x	PRON
ejpam-3543	832	31	if	if	SCONJ
ejpam-3543	832	32	u(λt	u(λt	NOUN
ejpam-3543	832	33	;	;	PUNCT
ejpam-3543	832	34	α	α	X
ejpam-3543	832	35	)	)	PUNCT
ejpam-3543	832	36	,	,	PUNCT
ejpam-3543	832	37	l(λi	l(λi	PROPN
ejpam-3543	832	38	;	;	PUNCT
ejpam-3543	832	39	β	β	X
ejpam-3543	832	40	)	)	PUNCT
ejpam-3543	832	41	,	,	PUNCT
ejpam-3543	832	42	and	and	CCONJ
ejpam-3543	832	43	u(λf	u(λf	ADV
ejpam-3543	832	44	;	;	PUNCT
ejpam-3543	832	45	γ	γ	X
ejpam-3543	832	46	)	)	PUNCT
ejpam-3543	832	47	are	be	AUX
ejpam-3543	832	48	nonempty	nonempty	ADJ
ejpam-3543	832	49	.	.	PUNCT
ejpam-3543	833	1	let	let	VERB
ejpam-3543	833	2	x	x	SYM
ejpam-3543	833	3	∈	∈	PROPN
ejpam-3543	833	4	x.	x.	NOUN
ejpam-3543	833	5	then	then	ADV
ejpam-3543	833	6	λt	λt	INTJ
ejpam-3543	833	7	(	(	PUNCT
ejpam-3543	833	8	x	x	X
ejpam-3543	833	9	)	)	PUNCT
ejpam-3543	833	10	∈	∈	PROPN
ejpam-3543	834	1	[	[	X
ejpam-3543	834	2	0	0	NUM
ejpam-3543	834	3	,	,	PUNCT
ejpam-3543	834	4	1	1	NUM
ejpam-3543	834	5	]	]	PUNCT
ejpam-3543	834	6	.	.	PUNCT
ejpam-3543	835	1	choose	choose	VERB
ejpam-3543	835	2	α	α	X
ejpam-3543	835	3	=	=	PUNCT
ejpam-3543	835	4	λt	λt	X
ejpam-3543	835	5	(	(	PUNCT
ejpam-3543	835	6	x	x	NOUN
ejpam-3543	835	7	)	)	PUNCT
ejpam-3543	835	8	.	.	PUNCT
ejpam-3543	836	1	thus	thus	ADV
ejpam-3543	836	2	λt	λt	X
ejpam-3543	836	3	(	(	PUNCT
ejpam-3543	836	4	x	x	NOUN
ejpam-3543	836	5	)	)	PUNCT
ejpam-3543	836	6	≥	≥	NUM
ejpam-3543	836	7	α	α	NOUN
ejpam-3543	836	8	,	,	PUNCT
ejpam-3543	836	9	so	so	ADV
ejpam-3543	836	10	x	x	SYM
ejpam-3543	836	11	∈	∈	NOUN
ejpam-3543	836	12	u(λt	u(λt	NOUN
ejpam-3543	836	13	;	;	PUNCT
ejpam-3543	836	14	α	α	X
ejpam-3543	836	15	)	)	PUNCT
ejpam-3543	836	16	6=	6=	ADP
ejpam-3543	836	17	∅.	∅.	ADP
ejpam-3543	836	18	by	by	ADP
ejpam-3543	836	19	assumption	assumption	NOUN
ejpam-3543	836	20	,	,	PUNCT
ejpam-3543	836	21	we	we	PRON
ejpam-3543	836	22	have	have	VERB
ejpam-3543	836	23	u(λt	u(λt	NOUN
ejpam-3543	836	24	;	;	PUNCT
ejpam-3543	836	25	α	α	X
ejpam-3543	836	26	)	)	PUNCT
ejpam-3543	836	27	is	be	AUX
ejpam-3543	836	28	a	a	DET
ejpam-3543	836	29	near	near	ADJ
ejpam-3543	836	30	up	up	NOUN
ejpam-3543	836	31	-	-	PUNCT
ejpam-3543	836	32	filter	filter	NOUN
ejpam-3543	836	33	of	of	ADP
ejpam-3543	836	34	x	x	PUNCT
ejpam-3543	836	35	and	and	CCONJ
ejpam-3543	836	36	so	so	ADV
ejpam-3543	836	37	0	0	NUM
ejpam-3543	836	38	∈	∈	PROPN
ejpam-3543	836	39	u(λt	u(λt	NOUN
ejpam-3543	836	40	;	;	PUNCT
ejpam-3543	836	41	α	α	X
ejpam-3543	836	42	)	)	PUNCT
ejpam-3543	836	43	.	.	PUNCT
ejpam-3543	837	1	thus	thus	ADV
ejpam-3543	837	2	λt	λt	X
ejpam-3543	837	3	(	(	PUNCT
ejpam-3543	837	4	0	0	NUM
ejpam-3543	837	5	)	)	PUNCT
ejpam-3543	837	6	≥	≥	NOUN
ejpam-3543	837	7	α	α	X
ejpam-3543	837	8	=	=	PUNCT
ejpam-3543	837	9	λt	λt	X
ejpam-3543	837	10	(	(	PUNCT
ejpam-3543	837	11	x	x	NOUN
ejpam-3543	837	12	)	)	PUNCT
ejpam-3543	837	13	.	.	PUNCT
ejpam-3543	838	1	next	next	ADV
ejpam-3543	838	2	,	,	PUNCT
ejpam-3543	838	3	let	let	VERB
ejpam-3543	838	4	x	x	PRON
ejpam-3543	838	5	,	,	PUNCT
ejpam-3543	838	6	y	y	PROPN
ejpam-3543	838	7	∈	∈	PROPN
ejpam-3543	838	8	x.	x.	NOUN
ejpam-3543	839	1	then	then	ADV
ejpam-3543	839	2	λt	λt	ADP
ejpam-3543	839	3	(	(	PUNCT
ejpam-3543	839	4	y	y	NOUN
ejpam-3543	839	5	)	)	PUNCT
ejpam-3543	839	6	∈	∈	PROPN
ejpam-3543	840	1	[	[	X
ejpam-3543	840	2	0	0	NUM
ejpam-3543	840	3	,	,	PUNCT
ejpam-3543	840	4	1	1	NUM
ejpam-3543	840	5	]	]	PUNCT
ejpam-3543	840	6	.	.	PUNCT
ejpam-3543	841	1	choose	choose	VERB
ejpam-3543	841	2	α	α	X
ejpam-3543	841	3	=	=	PUNCT
ejpam-3543	841	4	λt	λt	X
ejpam-3543	841	5	(	(	PUNCT
ejpam-3543	841	6	y	y	NOUN
ejpam-3543	841	7	)	)	PUNCT
ejpam-3543	841	8	.	.	PUNCT
ejpam-3543	842	1	thus	thus	ADV
ejpam-3543	842	2	λt	λt	X
ejpam-3543	842	3	(	(	PUNCT
ejpam-3543	842	4	y	y	NOUN
ejpam-3543	842	5	)	)	PUNCT
ejpam-3543	842	6	≥	≥	NOUN
ejpam-3543	842	7	α	α	NOUN
ejpam-3543	842	8	,	,	PUNCT
ejpam-3543	842	9	so	so	ADV
ejpam-3543	842	10	y	y	PROPN
ejpam-3543	842	11	∈	∈	PROPN
ejpam-3543	842	12	u(λt	u(λt	PROPN
ejpam-3543	842	13	;	;	PUNCT
ejpam-3543	842	14	α	α	X
ejpam-3543	842	15	)	)	PUNCT
ejpam-3543	842	16	6=	6=	ADP
ejpam-3543	842	17	∅.	∅.	ADP
ejpam-3543	842	18	by	by	ADP
ejpam-3543	842	19	assumption	assumption	NOUN
ejpam-3543	842	20	,	,	PUNCT
ejpam-3543	842	21	we	we	PRON
ejpam-3543	842	22	have	have	VERB
ejpam-3543	842	23	u(λt	u(λt	NOUN
ejpam-3543	842	24	;	;	PUNCT
ejpam-3543	842	25	α	α	X
ejpam-3543	842	26	)	)	PUNCT
ejpam-3543	842	27	is	be	AUX
ejpam-3543	842	28	a	a	DET
ejpam-3543	842	29	near	near	ADJ
ejpam-3543	842	30	up	up	NOUN
ejpam-3543	842	31	-	-	PUNCT
ejpam-3543	842	32	filter	filter	NOUN
ejpam-3543	842	33	of	of	ADP
ejpam-3543	842	34	x	x	PUNCT
ejpam-3543	842	35	and	and	CCONJ
ejpam-3543	842	36	so	so	ADV
ejpam-3543	842	37	x	x	SYM
ejpam-3543	842	38	·	·	PUNCT
ejpam-3543	842	39	y	y	PROPN
ejpam-3543	842	40	∈	∈	PROPN
ejpam-3543	842	41	u(λt	u(λt	PROPN
ejpam-3543	842	42	;	;	PUNCT
ejpam-3543	842	43	α	α	X
ejpam-3543	842	44	)	)	PUNCT
ejpam-3543	842	45	.	.	PUNCT
ejpam-3543	843	1	thus	thus	ADV
ejpam-3543	843	2	λt	λt	X
ejpam-3543	843	3	(	(	PUNCT
ejpam-3543	843	4	x	x	X
ejpam-3543	843	5	·	·	PUNCT
ejpam-3543	843	6	y	y	X
ejpam-3543	843	7	)	)	PUNCT
ejpam-3543	843	8	≥	≥	NOUN
ejpam-3543	843	9	α	α	X
ejpam-3543	843	10	=	=	PUNCT
ejpam-3543	843	11	λt	λt	X
ejpam-3543	843	12	(	(	PUNCT
ejpam-3543	843	13	y	y	NOUN
ejpam-3543	843	14	)	)	PUNCT
ejpam-3543	843	15	.	.	PUNCT
ejpam-3543	844	1	let	let	VERB
ejpam-3543	844	2	x	x	SYM
ejpam-3543	844	3	∈	∈	PROPN
ejpam-3543	844	4	x.	x.	NOUN
ejpam-3543	844	5	then	then	ADV
ejpam-3543	844	6	λi(x	λi(x	X
ejpam-3543	844	7	)	)	PUNCT
ejpam-3543	844	8	∈	∈	PROPN
ejpam-3543	845	1	[	[	X
ejpam-3543	845	2	0	0	NUM
ejpam-3543	845	3	,	,	PUNCT
ejpam-3543	845	4	1	1	NUM
ejpam-3543	845	5	]	]	PUNCT
ejpam-3543	845	6	.	.	PUNCT
ejpam-3543	846	1	choose	choose	VERB
ejpam-3543	846	2	β	β	X
ejpam-3543	846	3	=	=	SYM
ejpam-3543	846	4	λi(x	λi(x	NUM
ejpam-3543	846	5	)	)	PUNCT
ejpam-3543	846	6	.	.	PUNCT
ejpam-3543	847	1	thus	thus	ADV
ejpam-3543	847	2	λi(x	λi(x	NUM
ejpam-3543	847	3	)	)	PUNCT
ejpam-3543	847	4	≤	≤	NUM
ejpam-3543	848	1	β	β	NOUN
ejpam-3543	848	2	,	,	PUNCT
ejpam-3543	848	3	so	so	CCONJ
ejpam-3543	848	4	x	x	SYM
ejpam-3543	848	5	∈	∈	NOUN
ejpam-3543	848	6	l(λi	l(λi	NOUN
ejpam-3543	848	7	;	;	PUNCT
ejpam-3543	848	8	β	β	X
ejpam-3543	848	9	)	)	PUNCT
ejpam-3543	848	10	6=	6=	ADP
ejpam-3543	848	11	∅.	∅.	ADP
ejpam-3543	848	12	by	by	ADP
ejpam-3543	848	13	assumption	assumption	NOUN
ejpam-3543	848	14	,	,	PUNCT
ejpam-3543	848	15	we	we	PRON
ejpam-3543	848	16	have	have	VERB
ejpam-3543	848	17	l(λi	l(λi	NOUN
ejpam-3543	848	18	;	;	PUNCT
ejpam-3543	848	19	β	β	X
ejpam-3543	848	20	)	)	PUNCT
ejpam-3543	848	21	is	be	AUX
ejpam-3543	848	22	a	a	DET
ejpam-3543	848	23	near	near	ADJ
ejpam-3543	848	24	up	up	NOUN
ejpam-3543	848	25	-	-	PUNCT
ejpam-3543	848	26	filter	filter	NOUN
ejpam-3543	848	27	of	of	ADP
ejpam-3543	848	28	x	x	PUNCT
ejpam-3543	848	29	and	and	CCONJ
ejpam-3543	848	30	so	so	ADV
ejpam-3543	848	31	0	0	NUM
ejpam-3543	848	32	∈	∈	NOUN
ejpam-3543	848	33	l(λi	l(λi	NOUN
ejpam-3543	848	34	;	;	PUNCT
ejpam-3543	848	35	β	β	X
ejpam-3543	848	36	)	)	PUNCT
ejpam-3543	848	37	.	.	PUNCT
ejpam-3543	849	1	thus	thus	ADV
ejpam-3543	849	2	λi(0	λi(0	X
ejpam-3543	849	3	)	)	PUNCT
ejpam-3543	849	4	≤	≤	NOUN
ejpam-3543	849	5	β	β	X
ejpam-3543	849	6	=	=	SYM
ejpam-3543	849	7	λi(x	λi(x	NUM
ejpam-3543	849	8	)	)	PUNCT
ejpam-3543	849	9	.	.	PUNCT
ejpam-3543	850	1	next	next	ADV
ejpam-3543	850	2	,	,	PUNCT
ejpam-3543	850	3	let	let	VERB
ejpam-3543	850	4	x	x	PRON
ejpam-3543	850	5	,	,	PUNCT
ejpam-3543	850	6	y	y	PROPN
ejpam-3543	850	7	∈	∈	PROPN
ejpam-3543	850	8	x.	x.	NOUN
ejpam-3543	850	9	then	then	ADV
ejpam-3543	850	10	λi(y	λi(y	NOUN
ejpam-3543	850	11	)	)	PUNCT
ejpam-3543	850	12	∈	∈	PROPN
ejpam-3543	851	1	[	[	X
ejpam-3543	851	2	0	0	NUM
ejpam-3543	851	3	,	,	PUNCT
ejpam-3543	851	4	1	1	NUM
ejpam-3543	851	5	]	]	PUNCT
ejpam-3543	851	6	.	.	PUNCT
ejpam-3543	852	1	choose	choose	VERB
ejpam-3543	852	2	β	β	X
ejpam-3543	852	3	=	=	PUNCT
ejpam-3543	852	4	λi(y	λi(y	X
ejpam-3543	852	5	)	)	PUNCT
ejpam-3543	852	6	.	.	PUNCT
ejpam-3543	853	1	thus	thus	ADV
ejpam-3543	853	2	λi(y	λi(y	NOUN
ejpam-3543	853	3	)	)	PUNCT
ejpam-3543	853	4	≤	≤	NOUN
ejpam-3543	853	5	β	β	NOUN
ejpam-3543	853	6	,	,	PUNCT
ejpam-3543	853	7	so	so	ADV
ejpam-3543	853	8	y	y	PROPN
ejpam-3543	853	9	∈	∈	PROPN
ejpam-3543	853	10	l(λi	l(λi	X
ejpam-3543	853	11	;	;	PUNCT
ejpam-3543	853	12	β	β	X
ejpam-3543	853	13	)	)	PUNCT
ejpam-3543	853	14	6=	6=	ADP
ejpam-3543	853	15	∅.	∅.	ADP
ejpam-3543	853	16	by	by	ADP
ejpam-3543	853	17	assumption	assumption	NOUN
ejpam-3543	853	18	,	,	PUNCT
ejpam-3543	853	19	we	we	PRON
ejpam-3543	853	20	have	have	VERB
ejpam-3543	853	21	l(λi	l(λi	NOUN
ejpam-3543	853	22	;	;	PUNCT
ejpam-3543	853	23	β	β	X
ejpam-3543	853	24	)	)	PUNCT
ejpam-3543	853	25	is	be	AUX
ejpam-3543	853	26	a	a	DET
ejpam-3543	853	27	near	near	ADJ
ejpam-3543	853	28	up	up	NOUN
ejpam-3543	853	29	-	-	PUNCT
ejpam-3543	853	30	filter	filter	NOUN
ejpam-3543	853	31	of	of	ADP
ejpam-3543	853	32	x	x	PUNCT
ejpam-3543	853	33	and	and	CCONJ
ejpam-3543	853	34	so	so	ADV
ejpam-3543	853	35	x	x	SYM
ejpam-3543	853	36	·	·	PUNCT
ejpam-3543	853	37	y	y	SYM
ejpam-3543	853	38	∈	∈	PROPN
ejpam-3543	853	39	l(λi	l(λi	X
ejpam-3543	853	40	;	;	PUNCT
ejpam-3543	853	41	β	β	X
ejpam-3543	853	42	)	)	PUNCT
ejpam-3543	853	43	.	.	PUNCT
ejpam-3543	854	1	thus	thus	ADV
ejpam-3543	854	2	λi(x	λi(x	X
ejpam-3543	854	3	·	·	PUNCT
ejpam-3543	854	4	y	y	X
ejpam-3543	854	5	)	)	PUNCT
ejpam-3543	854	6	≤	≤	NOUN
ejpam-3543	854	7	β	β	X
ejpam-3543	854	8	=	=	PUNCT
ejpam-3543	854	9	λi(y	λi(y	X
ejpam-3543	854	10	)	)	PUNCT
ejpam-3543	854	11	.	.	PUNCT
ejpam-3543	855	1	let	let	VERB
ejpam-3543	855	2	x	x	SYM
ejpam-3543	855	3	∈	∈	PROPN
ejpam-3543	855	4	x.	x.	NOUN
ejpam-3543	855	5	then	then	ADV
ejpam-3543	856	1	λf	λf	INTJ
ejpam-3543	856	2	(	(	PUNCT
ejpam-3543	856	3	x	x	X
ejpam-3543	856	4	)	)	PUNCT
ejpam-3543	856	5	∈	∈	PROPN
ejpam-3543	857	1	[	[	X
ejpam-3543	857	2	0	0	NUM
ejpam-3543	857	3	,	,	PUNCT
ejpam-3543	857	4	1	1	NUM
ejpam-3543	857	5	]	]	PUNCT
ejpam-3543	857	6	.	.	PUNCT
ejpam-3543	858	1	choose	choose	VERB
ejpam-3543	858	2	γ	γ	X
ejpam-3543	858	3	=	=	PUNCT
ejpam-3543	858	4	λf	λf	PROPN
ejpam-3543	858	5	(	(	PUNCT
ejpam-3543	858	6	x	x	NOUN
ejpam-3543	858	7	)	)	PUNCT
ejpam-3543	858	8	.	.	PUNCT
ejpam-3543	859	1	thus	thus	ADV
ejpam-3543	859	2	λf	λf	X
ejpam-3543	859	3	(	(	PUNCT
ejpam-3543	859	4	x	x	NOUN
ejpam-3543	859	5	)	)	PUNCT
ejpam-3543	859	6	≥	≥	PROPN
ejpam-3543	859	7	γ	γ	NOUN
ejpam-3543	859	8	,	,	PUNCT
ejpam-3543	859	9	so	so	ADV
ejpam-3543	859	10	x	x	SYM
ejpam-3543	859	11	∈	∈	PROPN
ejpam-3543	859	12	u(λf	u(λf	NOUN
ejpam-3543	859	13	;	;	PUNCT
ejpam-3543	859	14	γ	γ	X
ejpam-3543	859	15	)	)	PUNCT
ejpam-3543	859	16	6=	6=	ADP
ejpam-3543	859	17	∅.	∅.	ADP
ejpam-3543	859	18	by	by	ADP
ejpam-3543	859	19	assumption	assumption	NOUN
ejpam-3543	859	20	,	,	PUNCT
ejpam-3543	859	21	we	we	PRON
ejpam-3543	859	22	have	have	VERB
ejpam-3543	859	23	u(λf	u(λf	ADV
ejpam-3543	859	24	;	;	PUNCT
ejpam-3543	859	25	γ	γ	X
ejpam-3543	859	26	)	)	PUNCT
ejpam-3543	859	27	is	be	AUX
ejpam-3543	859	28	a	a	DET
ejpam-3543	859	29	near	near	ADJ
ejpam-3543	859	30	up	up	NOUN
ejpam-3543	859	31	-	-	PUNCT
ejpam-3543	859	32	filter	filter	NOUN
ejpam-3543	859	33	of	of	ADP
ejpam-3543	859	34	x	x	PUNCT
ejpam-3543	859	35	and	and	CCONJ
ejpam-3543	859	36	so	so	ADV
ejpam-3543	859	37	0	0	NUM
ejpam-3543	859	38	∈	∈	PROPN
ejpam-3543	859	39	u(λf	u(λf	NOUN
ejpam-3543	859	40	;	;	PUNCT
ejpam-3543	859	41	γ	γ	X
ejpam-3543	859	42	)	)	PUNCT
ejpam-3543	859	43	.	.	PUNCT
ejpam-3543	860	1	thus	thus	ADV
ejpam-3543	860	2	λf	λf	X
ejpam-3543	860	3	(	(	PUNCT
ejpam-3543	860	4	0	0	NUM
ejpam-3543	860	5	)	)	PUNCT
ejpam-3543	860	6	≥	≥	NOUN
ejpam-3543	860	7	γ	γ	X
ejpam-3543	860	8	=	=	PUNCT
ejpam-3543	860	9	λf	λf	PROPN
ejpam-3543	860	10	(	(	PUNCT
ejpam-3543	860	11	x	x	NOUN
ejpam-3543	860	12	)	)	PUNCT
ejpam-3543	860	13	.	.	PUNCT
ejpam-3543	861	1	next	next	ADV
ejpam-3543	861	2	,	,	PUNCT
ejpam-3543	861	3	let	let	VERB
ejpam-3543	861	4	x	x	PRON
ejpam-3543	861	5	,	,	PUNCT
ejpam-3543	861	6	y	y	PROPN
ejpam-3543	861	7	∈	∈	PROPN
ejpam-3543	861	8	x.	x.	NOUN
ejpam-3543	862	1	then	then	ADV
ejpam-3543	862	2	λf	λf	PROPN
ejpam-3543	862	3	(	(	PUNCT
ejpam-3543	862	4	y	y	NOUN
ejpam-3543	862	5	)	)	PUNCT
ejpam-3543	862	6	∈	∈	PROPN
ejpam-3543	863	1	[	[	X
ejpam-3543	863	2	0	0	NUM
ejpam-3543	863	3	,	,	PUNCT
ejpam-3543	863	4	1	1	NUM
ejpam-3543	863	5	]	]	PUNCT
ejpam-3543	863	6	.	.	PUNCT
ejpam-3543	864	1	choose	choose	VERB
ejpam-3543	864	2	γ	γ	X
ejpam-3543	864	3	=	=	SYM
ejpam-3543	864	4	λf	λf	PROPN
ejpam-3543	864	5	(	(	PUNCT
ejpam-3543	864	6	y	y	NOUN
ejpam-3543	864	7	)	)	PUNCT
ejpam-3543	864	8	.	.	PUNCT
ejpam-3543	865	1	thus	thus	ADV
ejpam-3543	865	2	λf	λf	X
ejpam-3543	865	3	(	(	PUNCT
ejpam-3543	865	4	y	y	NOUN
ejpam-3543	865	5	)	)	PUNCT
ejpam-3543	865	6	≥	≥	PROPN
ejpam-3543	865	7	γ	γ	NOUN
ejpam-3543	865	8	,	,	PUNCT
ejpam-3543	865	9	so	so	ADV
ejpam-3543	865	10	y	y	PROPN
ejpam-3543	865	11	∈	∈	PROPN
ejpam-3543	865	12	u(λf	u(λf	ADV
ejpam-3543	865	13	;	;	PUNCT
ejpam-3543	865	14	γ	γ	X
ejpam-3543	865	15	)	)	PUNCT
ejpam-3543	865	16	6=	6=	ADP
ejpam-3543	865	17	∅.	∅.	ADP
ejpam-3543	865	18	by	by	ADP
ejpam-3543	865	19	assumption	assumption	NOUN
ejpam-3543	865	20	,	,	PUNCT
ejpam-3543	865	21	we	we	PRON
ejpam-3543	865	22	have	have	VERB
ejpam-3543	865	23	l(λf	l(λf	PROPN
ejpam-3543	865	24	;	;	PUNCT
ejpam-3543	865	25	γ	γ	X
ejpam-3543	865	26	)	)	PUNCT
ejpam-3543	865	27	is	be	AUX
ejpam-3543	865	28	a	a	DET
ejpam-3543	865	29	near	near	ADJ
ejpam-3543	865	30	up	up	NOUN
ejpam-3543	865	31	-	-	PUNCT
ejpam-3543	865	32	filter	filter	NOUN
ejpam-3543	865	33	of	of	ADP
ejpam-3543	865	34	x	x	PUNCT
ejpam-3543	865	35	and	and	CCONJ
ejpam-3543	865	36	so	so	ADV
ejpam-3543	865	37	x	x	SYM
ejpam-3543	865	38	·	·	PUNCT
ejpam-3543	865	39	y	y	X
ejpam-3543	865	40	∈	∈	PROPN
ejpam-3543	865	41	u(λf	u(λf	ADV
ejpam-3543	865	42	;	;	PUNCT
ejpam-3543	865	43	γ	γ	X
ejpam-3543	865	44	)	)	PUNCT
ejpam-3543	865	45	.	.	PUNCT
ejpam-3543	866	1	thus	thus	ADV
ejpam-3543	866	2	λf	λf	X
ejpam-3543	866	3	(	(	PUNCT
ejpam-3543	866	4	x	x	SYM
ejpam-3543	866	5	·	·	PUNCT
ejpam-3543	866	6	y	y	X
ejpam-3543	866	7	)	)	PUNCT
ejpam-3543	866	8	≥	≥	PROPN
ejpam-3543	866	9	γ	γ	X
ejpam-3543	866	10	=	=	SYM
ejpam-3543	866	11	λf	λf	PROPN
ejpam-3543	866	12	(	(	PUNCT
ejpam-3543	866	13	y	y	NOUN
ejpam-3543	866	14	)	)	PUNCT
ejpam-3543	866	15	.	.	PUNCT
ejpam-3543	867	1	therefore	therefore	ADV
ejpam-3543	867	2	,	,	PUNCT
ejpam-3543	867	3	λ	λ	PROPN
ejpam-3543	867	4	is	be	AUX
ejpam-3543	867	5	a	a	DET
ejpam-3543	867	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	867	7	near	near	ADP
ejpam-3543	867	8	up	up	ADJ
ejpam-3543	867	9	-	-	PUNCT
ejpam-3543	867	10	filter	filter	NOUN
ejpam-3543	867	11	of	of	ADP
ejpam-3543	867	12	x.	x.	PROPN
ejpam-3543	867	13	theorem	theorem	VERB
ejpam-3543	867	14	21	21	NUM
ejpam-3543	867	15	.	.	PUNCT
ejpam-3543	868	1	a	a	DET
ejpam-3543	868	2	ns	ns	NUM
ejpam-3543	868	3	λ	λ	NOUN
ejpam-3543	868	4	in	in	ADP
ejpam-3543	868	5	x	x	PROPN
ejpam-3543	868	6	is	be	AUX
ejpam-3543	868	7	a	a	DET
ejpam-3543	868	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	868	9	up	up	ADJ
ejpam-3543	868	10	-	-	PUNCT
ejpam-3543	868	11	filter	filter	NOUN
ejpam-3543	868	12	of	of	ADP
ejpam-3543	868	13	x	x	SYM
ejpam-3543	868	14	if	if	SCONJ
ejpam-3543	868	15	and	and	CCONJ
ejpam-3543	868	16	only	only	ADV
ejpam-3543	868	17	if	if	SCONJ
ejpam-3543	868	18	for	for	ADP
ejpam-3543	868	19	all	all	DET
ejpam-3543	868	20	α	α	NOUN
ejpam-3543	868	21	,	,	PUNCT
ejpam-3543	868	22	β	β	X
ejpam-3543	868	23	,	,	PUNCT
ejpam-3543	868	24	γ	γ	PROPN
ejpam-3543	868	25	∈	∈	PROPN
ejpam-3543	869	1	[	[	X
ejpam-3543	869	2	0	0	NUM
ejpam-3543	869	3	,	,	PUNCT
ejpam-3543	869	4	1	1	NUM
ejpam-3543	869	5	]	]	PUNCT
ejpam-3543	869	6	,	,	PUNCT
ejpam-3543	869	7	the	the	PRON
ejpam-3543	869	8	sets	set	NOUN
ejpam-3543	869	9	u(λt	u(λt	NOUN
ejpam-3543	869	10	;	;	PUNCT
ejpam-3543	869	11	α	α	X
ejpam-3543	869	12	)	)	PUNCT
ejpam-3543	869	13	,	,	PUNCT
ejpam-3543	869	14	l(λi	l(λi	PROPN
ejpam-3543	869	15	;	;	PUNCT
ejpam-3543	869	16	β	β	X
ejpam-3543	869	17	)	)	PUNCT
ejpam-3543	869	18	,	,	PUNCT
ejpam-3543	869	19	and	and	CCONJ
ejpam-3543	869	20	u(λf	u(λf	ADV
ejpam-3543	869	21	;	;	PUNCT
ejpam-3543	869	22	γ	γ	X
ejpam-3543	869	23	)	)	PUNCT
ejpam-3543	869	24	are	be	AUX
ejpam-3543	869	25	up	up	ADP
ejpam-3543	869	26	-	-	PUNCT
ejpam-3543	869	27	filters	filter	NOUN
ejpam-3543	869	28	of	of	ADP
ejpam-3543	869	29	x	x	PRON
ejpam-3543	869	30	if	if	SCONJ
ejpam-3543	869	31	u(λt	u(λt	NOUN
ejpam-3543	869	32	;	;	PUNCT
ejpam-3543	869	33	α	α	X
ejpam-3543	869	34	)	)	PUNCT
ejpam-3543	869	35	,	,	PUNCT
ejpam-3543	869	36	l(λi	l(λi	PROPN
ejpam-3543	869	37	;	;	PUNCT
ejpam-3543	869	38	β	β	X
ejpam-3543	869	39	)	)	PUNCT
ejpam-3543	869	40	,	,	PUNCT
ejpam-3543	869	41	and	and	CCONJ
ejpam-3543	869	42	u(λf	u(λf	ADV
ejpam-3543	869	43	;	;	PUNCT
ejpam-3543	869	44	γ	γ	X
ejpam-3543	869	45	)	)	PUNCT
ejpam-3543	869	46	are	be	AUX
ejpam-3543	869	47	nonempty	nonempty	ADJ
ejpam-3543	869	48	.	.	PUNCT
ejpam-3543	870	1	proof	proof	NOUN
ejpam-3543	870	2	.	.	PUNCT
ejpam-3543	871	1	assume	assume	VERB
ejpam-3543	871	2	that	that	SCONJ
ejpam-3543	871	3	λ	λ	PROPN
ejpam-3543	871	4	is	be	AUX
ejpam-3543	871	5	a	a	DET
ejpam-3543	871	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	871	7	up	up	ADJ
ejpam-3543	871	8	-	-	PUNCT
ejpam-3543	871	9	filter	filter	NOUN
ejpam-3543	871	10	of	of	ADP
ejpam-3543	871	11	x.	x.	NOUN
ejpam-3543	871	12	let	let	VERB
ejpam-3543	871	13	α	α	PRON
ejpam-3543	871	14	,	,	PUNCT
ejpam-3543	871	15	β	β	X
ejpam-3543	871	16	,	,	PUNCT
ejpam-3543	871	17	γ	γ	PROPN
ejpam-3543	871	18	∈	∈	PROPN
ejpam-3543	872	1	[	[	X
ejpam-3543	872	2	0	0	NUM
ejpam-3543	872	3	,	,	PUNCT
ejpam-3543	872	4	1	1	NUM
ejpam-3543	872	5	]	]	PUNCT
ejpam-3543	872	6	be	be	AUX
ejpam-3543	872	7	such	such	ADJ
ejpam-3543	872	8	that	that	SCONJ
ejpam-3543	872	9	u(λt	u(λt	NOUN
ejpam-3543	872	10	;	;	PUNCT
ejpam-3543	872	11	α	α	X
ejpam-3543	872	12	)	)	PUNCT
ejpam-3543	872	13	,	,	PUNCT
ejpam-3543	872	14	l(λi	l(λi	PROPN
ejpam-3543	872	15	;	;	PUNCT
ejpam-3543	872	16	β	β	X
ejpam-3543	872	17	)	)	PUNCT
ejpam-3543	872	18	,	,	PUNCT
ejpam-3543	872	19	and	and	CCONJ
ejpam-3543	872	20	u(λf	u(λf	ADV
ejpam-3543	872	21	;	;	PUNCT
ejpam-3543	872	22	γ	γ	X
ejpam-3543	872	23	)	)	PUNCT
ejpam-3543	872	24	are	be	AUX
ejpam-3543	872	25	nonempty	nonempty	ADJ
ejpam-3543	872	26	.	.	PUNCT
ejpam-3543	873	1	let	let	VERB
ejpam-3543	873	2	x	x	SYM
ejpam-3543	873	3	∈	∈	PROPN
ejpam-3543	873	4	u(λt	u(λt	NOUN
ejpam-3543	873	5	;	;	PUNCT
ejpam-3543	873	6	α	α	X
ejpam-3543	873	7	)	)	PUNCT
ejpam-3543	873	8	.	.	PUNCT
ejpam-3543	874	1	then	then	ADV
ejpam-3543	874	2	λt	λt	INTJ
ejpam-3543	874	3	(	(	PUNCT
ejpam-3543	874	4	x	x	X
ejpam-3543	874	5	)	)	PUNCT
ejpam-3543	874	6	≥	≥	PROPN
ejpam-3543	874	7	α	α	NOUN
ejpam-3543	874	8	.	.	PUNCT
ejpam-3543	875	1	by	by	ADP
ejpam-3543	875	2	(	(	PUNCT
ejpam-3543	875	3	3.6	3.6	NUM
ejpam-3543	875	4	)	)	PUNCT
ejpam-3543	875	5	,	,	PUNCT
ejpam-3543	875	6	we	we	PRON
ejpam-3543	875	7	have	have	VERB
ejpam-3543	875	8	λt	λt	X
ejpam-3543	875	9	(	(	PUNCT
ejpam-3543	875	10	0	0	NUM
ejpam-3543	875	11	)	)	PUNCT
ejpam-3543	875	12	≥	≥	NOUN
ejpam-3543	875	13	λt	λt	X
ejpam-3543	875	14	(	(	PUNCT
ejpam-3543	875	15	x	x	NOUN
ejpam-3543	875	16	)	)	PUNCT
ejpam-3543	875	17	≥	≥	PROPN
ejpam-3543	875	18	α	α	NOUN
ejpam-3543	875	19	.	.	PUNCT
ejpam-3543	876	1	thus	thus	ADV
ejpam-3543	876	2	0	0	NUM
ejpam-3543	876	3	∈	∈	PROPN
ejpam-3543	876	4	u(λt	u(λt	NOUN
ejpam-3543	876	5	;	;	PUNCT
ejpam-3543	876	6	α	α	X
ejpam-3543	876	7	)	)	PUNCT
ejpam-3543	876	8	.	.	PUNCT
ejpam-3543	877	1	next	next	ADV
ejpam-3543	877	2	,	,	PUNCT
ejpam-3543	877	3	let	let	VERB
ejpam-3543	877	4	x	x	PRON
ejpam-3543	877	5	,	,	PUNCT
ejpam-3543	877	6	y	y	PROPN
ejpam-3543	877	7	∈	∈	PROPN
ejpam-3543	877	8	x	x	AUX
ejpam-3543	877	9	be	be	AUX
ejpam-3543	877	10	such	such	ADJ
ejpam-3543	877	11	that	that	SCONJ
ejpam-3543	877	12	x	x	X
ejpam-3543	877	13	·	·	PUNCT
ejpam-3543	877	14	y	y	PROPN
ejpam-3543	877	15	∈	∈	PROPN
ejpam-3543	877	16	u(λt	u(λt	PROPN
ejpam-3543	877	17	;	;	PUNCT
ejpam-3543	877	18	α	α	X
ejpam-3543	877	19	)	)	PUNCT
ejpam-3543	877	20	and	and	CCONJ
ejpam-3543	877	21	x	x	PART
ejpam-3543	877	22	∈	∈	NOUN
ejpam-3543	877	23	u(λt	u(λt	NOUN
ejpam-3543	877	24	;	;	PUNCT
ejpam-3543	877	25	α	α	X
ejpam-3543	877	26	)	)	PUNCT
ejpam-3543	877	27	.	.	PUNCT
ejpam-3543	878	1	then	then	ADV
ejpam-3543	878	2	m.	m.	PROPN
ejpam-3543	878	3	songsaeng	songsaeng	PROPN
ejpam-3543	878	4	,	,	PUNCT
ejpam-3543	878	5	a.	a.	NOUN
ejpam-3543	878	6	iampan	iampan	PROPN
ejpam-3543	878	7	/	/	SYM
ejpam-3543	878	8	eur	eur	PROPN
ejpam-3543	878	9	.	.	PUNCT
ejpam-3543	879	1	j.	j.	PROPN
ejpam-3543	879	2	pure	pure	PROPN
ejpam-3543	879	3	appl	appl	PROPN
ejpam-3543	879	4	.	.	PROPN
ejpam-3543	879	5	math	math	PROPN
ejpam-3543	879	6	,	,	PUNCT
ejpam-3543	879	7	12	12	NUM
ejpam-3543	879	8	(	(	PUNCT
ejpam-3543	879	9	4	4	NUM
ejpam-3543	879	10	)	)	PUNCT
ejpam-3543	879	11	(	(	PUNCT
ejpam-3543	879	12	2019	2019	NUM
ejpam-3543	879	13	)	)	PUNCT
ejpam-3543	879	14	,	,	PUNCT
ejpam-3543	879	15	1382	1382	NUM
ejpam-3543	879	16	-	-	SYM
ejpam-3543	879	17	1409	1409	NUM
ejpam-3543	879	18	1404	1404	NUM
ejpam-3543	879	19	λt	λt	ADP
ejpam-3543	879	20	(	(	PUNCT
ejpam-3543	879	21	x	x	PROPN
ejpam-3543	879	22	·	·	PUNCT
ejpam-3543	879	23	y	y	X
ejpam-3543	879	24	)	)	PUNCT
ejpam-3543	879	25	≥	≥	NOUN
ejpam-3543	879	26	α	α	NOUN
ejpam-3543	879	27	and	and	CCONJ
ejpam-3543	879	28	λt	λt	X
ejpam-3543	879	29	(	(	PUNCT
ejpam-3543	879	30	x	x	NOUN
ejpam-3543	879	31	)	)	PUNCT
ejpam-3543	879	32	≥	≥	NUM
ejpam-3543	879	33	α	α	NOUN
ejpam-3543	879	34	,	,	PUNCT
ejpam-3543	879	35	so	so	ADV
ejpam-3543	879	36	α	α	PRON
ejpam-3543	879	37	is	be	AUX
ejpam-3543	879	38	an	an	DET
ejpam-3543	879	39	lower	low	ADJ
ejpam-3543	879	40	bound	bind	VERB
ejpam-3543	879	41	of	of	ADP
ejpam-3543	879	42	{	{	PUNCT
ejpam-3543	879	43	λt	λt	X
ejpam-3543	879	44	(	(	PUNCT
ejpam-3543	879	45	x	x	PROPN
ejpam-3543	879	46	·	·	PUNCT
ejpam-3543	879	47	y	y	X
ejpam-3543	879	48	)	)	PUNCT
ejpam-3543	879	49	,	,	PUNCT
ejpam-3543	879	50	λt	λt	X
ejpam-3543	879	51	(	(	PUNCT
ejpam-3543	879	52	x	x	NOUN
ejpam-3543	879	53	)	)	PUNCT
ejpam-3543	879	54	}	}	PUNCT
ejpam-3543	879	55	.	.	PUNCT
ejpam-3543	880	1	by	by	ADP
ejpam-3543	880	2	(	(	PUNCT
ejpam-3543	880	3	3.12	3.12	NUM
ejpam-3543	880	4	)	)	PUNCT
ejpam-3543	880	5	,	,	PUNCT
ejpam-3543	880	6	we	we	PRON
ejpam-3543	880	7	have	have	VERB
ejpam-3543	880	8	λt	λt	INTJ
ejpam-3543	880	9	(	(	PUNCT
ejpam-3543	880	10	y	y	NOUN
ejpam-3543	880	11	)	)	PUNCT
ejpam-3543	880	12	≥	≥	NOUN
ejpam-3543	880	13	min{λt	min{λt	X
ejpam-3543	880	14	(	(	PUNCT
ejpam-3543	880	15	x	x	SYM
ejpam-3543	880	16	·	·	PUNCT
ejpam-3543	880	17	y	y	X
ejpam-3543	880	18	)	)	PUNCT
ejpam-3543	880	19	,	,	PUNCT
ejpam-3543	880	20	λt	λt	X
ejpam-3543	880	21	(	(	PUNCT
ejpam-3543	880	22	x	x	NOUN
ejpam-3543	880	23	)	)	PUNCT
ejpam-3543	880	24	}	}	PUNCT
ejpam-3543	880	25	≥	≥	PROPN
ejpam-3543	880	26	α	α	NOUN
ejpam-3543	880	27	.	.	PUNCT
ejpam-3543	881	1	thus	thus	ADV
ejpam-3543	881	2	y	y	PROPN
ejpam-3543	881	3	∈	∈	PROPN
ejpam-3543	881	4	u(λt	u(λt	PROPN
ejpam-3543	881	5	;	;	PUNCT
ejpam-3543	881	6	α	α	X
ejpam-3543	881	7	)	)	PUNCT
ejpam-3543	881	8	.	.	PUNCT
ejpam-3543	882	1	let	let	VERB
ejpam-3543	882	2	x	x	SYM
ejpam-3543	882	3	∈	∈	NOUN
ejpam-3543	882	4	l(λi	l(λi	X
ejpam-3543	882	5	;	;	PUNCT
ejpam-3543	882	6	β	β	X
ejpam-3543	882	7	)	)	PUNCT
ejpam-3543	882	8	.	.	PUNCT
ejpam-3543	883	1	then	then	ADV
ejpam-3543	883	2	λi(x	λi(x	NUM
ejpam-3543	883	3	)	)	PUNCT
ejpam-3543	883	4	≤	≤	NOUN
ejpam-3543	884	1	β	β	X
ejpam-3543	884	2	.	.	PUNCT
ejpam-3543	885	1	by	by	ADP
ejpam-3543	885	2	(	(	PUNCT
ejpam-3543	885	3	3.7	3.7	NUM
ejpam-3543	885	4	)	)	PUNCT
ejpam-3543	885	5	,	,	PUNCT
ejpam-3543	885	6	we	we	PRON
ejpam-3543	885	7	have	have	VERB
ejpam-3543	885	8	λi(0	λi(0	NOUN
ejpam-3543	885	9	)	)	PUNCT
ejpam-3543	885	10	≤	≤	NOUN
ejpam-3543	885	11	λi(x	λi(x	NUM
ejpam-3543	885	12	)	)	PUNCT
ejpam-3543	885	13	≤	≤	NOUN
ejpam-3543	885	14	β	β	X
ejpam-3543	885	15	.	.	PUNCT
ejpam-3543	886	1	thus	thus	ADV
ejpam-3543	886	2	0	0	NUM
ejpam-3543	886	3	∈	∈	NOUN
ejpam-3543	886	4	l(λi	l(λi	NOUN
ejpam-3543	886	5	;	;	PUNCT
ejpam-3543	886	6	β	β	X
ejpam-3543	886	7	)	)	PUNCT
ejpam-3543	886	8	.	.	PUNCT
ejpam-3543	887	1	next	next	ADV
ejpam-3543	887	2	,	,	PUNCT
ejpam-3543	887	3	let	let	VERB
ejpam-3543	887	4	x	x	PRON
ejpam-3543	887	5	,	,	PUNCT
ejpam-3543	887	6	y	y	PROPN
ejpam-3543	887	7	∈	∈	PROPN
ejpam-3543	887	8	x	x	AUX
ejpam-3543	887	9	be	be	AUX
ejpam-3543	887	10	such	such	ADJ
ejpam-3543	887	11	that	that	SCONJ
ejpam-3543	887	12	x	x	X
ejpam-3543	887	13	·	·	PUNCT
ejpam-3543	887	14	y	y	SYM
ejpam-3543	887	15	∈	∈	PROPN
ejpam-3543	887	16	l(λi	l(λi	X
ejpam-3543	887	17	;	;	PUNCT
ejpam-3543	887	18	β	β	X
ejpam-3543	887	19	)	)	PUNCT
ejpam-3543	887	20	and	and	CCONJ
ejpam-3543	887	21	x	x	PUNCT
ejpam-3543	887	22	∈	∈	NOUN
ejpam-3543	887	23	l(λi	l(λi	NOUN
ejpam-3543	887	24	;	;	PUNCT
ejpam-3543	887	25	β	β	X
ejpam-3543	887	26	)	)	PUNCT
ejpam-3543	887	27	.	.	PUNCT
ejpam-3543	888	1	then	then	ADV
ejpam-3543	888	2	λi(x	λi(x	X
ejpam-3543	888	3	·	·	PUNCT
ejpam-3543	888	4	y	y	X
ejpam-3543	888	5	)	)	PUNCT
ejpam-3543	888	6	≤	≤	NOUN
ejpam-3543	888	7	β	β	X
ejpam-3543	888	8	and	and	CCONJ
ejpam-3543	888	9	λi(x	λi(x	NUM
ejpam-3543	888	10	)	)	PUNCT
ejpam-3543	888	11	≤	≤	NUM
ejpam-3543	889	1	β	β	NOUN
ejpam-3543	889	2	,	,	PUNCT
ejpam-3543	889	3	so	so	SCONJ
ejpam-3543	889	4	β	β	X
ejpam-3543	889	5	is	be	AUX
ejpam-3543	889	6	a	a	DET
ejpam-3543	889	7	upper	upper	ADJ
ejpam-3543	889	8	bound	bind	VERB
ejpam-3543	889	9	of	of	ADP
ejpam-3543	889	10	{	{	PUNCT
ejpam-3543	889	11	λi(x	λi(x	X
ejpam-3543	889	12	·	·	PUNCT
ejpam-3543	889	13	y	y	X
ejpam-3543	889	14	)	)	PUNCT
ejpam-3543	889	15	,	,	PUNCT
ejpam-3543	889	16	λi(x	λi(x	NUM
ejpam-3543	889	17	)	)	PUNCT
ejpam-3543	889	18	}	}	PUNCT
ejpam-3543	889	19	.	.	PUNCT
ejpam-3543	890	1	by	by	ADP
ejpam-3543	890	2	(	(	PUNCT
ejpam-3543	890	3	3.13	3.13	NUM
ejpam-3543	890	4	)	)	PUNCT
ejpam-3543	890	5	,	,	PUNCT
ejpam-3543	890	6	we	we	PRON
ejpam-3543	890	7	have	have	VERB
ejpam-3543	890	8	λi(y	λi(y	NOUN
ejpam-3543	890	9	)	)	PUNCT
ejpam-3543	890	10	≤	≤	NUM
ejpam-3543	890	11	max{λi(x	max{λi(x	X
ejpam-3543	890	12	·	·	PUNCT
ejpam-3543	890	13	y	y	X
ejpam-3543	890	14	)	)	PUNCT
ejpam-3543	890	15	,	,	PUNCT
ejpam-3543	890	16	λi(x	λi(x	NUM
ejpam-3543	890	17	)	)	PUNCT
ejpam-3543	890	18	}	}	PUNCT
ejpam-3543	890	19	≤	≤	NOUN
ejpam-3543	890	20	β	β	X
ejpam-3543	890	21	thus	thus	ADV
ejpam-3543	890	22	y	y	PROPN
ejpam-3543	890	23	∈	∈	PROPN
ejpam-3543	890	24	l(λi	l(λi	X
ejpam-3543	890	25	;	;	PUNCT
ejpam-3543	890	26	β	β	X
ejpam-3543	890	27	)	)	PUNCT
ejpam-3543	890	28	.	.	PUNCT
ejpam-3543	891	1	let	let	VERB
ejpam-3543	891	2	x	x	PUNCT
ejpam-3543	891	3	∈	∈	PROPN
ejpam-3543	891	4	u(λf	u(λf	NOUN
ejpam-3543	891	5	;	;	PUNCT
ejpam-3543	891	6	γ	γ	X
ejpam-3543	891	7	)	)	PUNCT
ejpam-3543	891	8	.	.	PUNCT
ejpam-3543	892	1	then	then	ADV
ejpam-3543	892	2	λf	λf	INTJ
ejpam-3543	892	3	(	(	PUNCT
ejpam-3543	892	4	x	x	NOUN
ejpam-3543	892	5	)	)	PUNCT
ejpam-3543	892	6	≥	≥	PROPN
ejpam-3543	892	7	γ	γ	PROPN
ejpam-3543	892	8	.	.	PUNCT
ejpam-3543	892	9	by	by	ADP
ejpam-3543	892	10	(	(	PUNCT
ejpam-3543	892	11	3.8	3.8	NUM
ejpam-3543	892	12	)	)	PUNCT
ejpam-3543	892	13	,	,	PUNCT
ejpam-3543	892	14	we	we	PRON
ejpam-3543	892	15	have	have	VERB
ejpam-3543	892	16	λf	λf	VERB
ejpam-3543	892	17	(	(	PUNCT
ejpam-3543	892	18	0	0	NUM
ejpam-3543	892	19	)	)	PUNCT
ejpam-3543	892	20	≥	≥	NOUN
ejpam-3543	893	1	λf	λf	X
ejpam-3543	893	2	(	(	PUNCT
ejpam-3543	893	3	x	x	NOUN
ejpam-3543	893	4	)	)	PUNCT
ejpam-3543	893	5	≥	≥	PROPN
ejpam-3543	893	6	γ	γ	X
ejpam-3543	893	7	.	.	PUNCT
ejpam-3543	894	1	thus	thus	ADV
ejpam-3543	894	2	0	0	NUM
ejpam-3543	894	3	∈	∈	PROPN
ejpam-3543	894	4	u(λf	u(λf	NOUN
ejpam-3543	894	5	;	;	PUNCT
ejpam-3543	894	6	γ	γ	X
ejpam-3543	894	7	)	)	PUNCT
ejpam-3543	894	8	.	.	PUNCT
ejpam-3543	895	1	next	next	ADV
ejpam-3543	895	2	,	,	PUNCT
ejpam-3543	895	3	let	let	VERB
ejpam-3543	895	4	x	x	PRON
ejpam-3543	895	5	,	,	PUNCT
ejpam-3543	895	6	y	y	PROPN
ejpam-3543	895	7	∈	∈	PROPN
ejpam-3543	895	8	x	x	AUX
ejpam-3543	895	9	be	be	AUX
ejpam-3543	895	10	such	such	ADJ
ejpam-3543	895	11	that	that	SCONJ
ejpam-3543	895	12	x	x	X
ejpam-3543	895	13	·	·	PUNCT
ejpam-3543	895	14	y	y	X
ejpam-3543	895	15	∈	∈	PROPN
ejpam-3543	895	16	u(λf	u(λf	ADV
ejpam-3543	895	17	;	;	PUNCT
ejpam-3543	895	18	γ	γ	X
ejpam-3543	895	19	)	)	PUNCT
ejpam-3543	895	20	and	and	CCONJ
ejpam-3543	895	21	x	x	PUNCT
ejpam-3543	895	22	∈	∈	PROPN
ejpam-3543	895	23	u(λf	u(λf	NOUN
ejpam-3543	895	24	;	;	PUNCT
ejpam-3543	895	25	γ	γ	X
ejpam-3543	895	26	)	)	PUNCT
ejpam-3543	895	27	.	.	PUNCT
ejpam-3543	896	1	then	then	ADV
ejpam-3543	896	2	λf	λf	INTJ
ejpam-3543	896	3	(	(	PUNCT
ejpam-3543	896	4	x	x	SYM
ejpam-3543	896	5	·	·	PUNCT
ejpam-3543	896	6	y	y	X
ejpam-3543	896	7	)	)	PUNCT
ejpam-3543	896	8	≥	≥	PROPN
ejpam-3543	896	9	γ	γ	NOUN
ejpam-3543	896	10	and	and	CCONJ
ejpam-3543	896	11	λf	λf	PROPN
ejpam-3543	896	12	(	(	PUNCT
ejpam-3543	896	13	x	x	NOUN
ejpam-3543	896	14	)	)	PUNCT
ejpam-3543	896	15	≥	≥	PROPN
ejpam-3543	896	16	γ	γ	NOUN
ejpam-3543	896	17	,	,	PUNCT
ejpam-3543	896	18	so	so	ADV
ejpam-3543	896	19	γ	γ	NOUN
ejpam-3543	896	20	is	be	AUX
ejpam-3543	896	21	an	an	DET
ejpam-3543	896	22	lower	low	ADJ
ejpam-3543	896	23	bound	bind	VERB
ejpam-3543	896	24	of	of	ADP
ejpam-3543	896	25	{	{	PUNCT
ejpam-3543	896	26	λf	λf	PROPN
ejpam-3543	896	27	(	(	PUNCT
ejpam-3543	896	28	x	x	SYM
ejpam-3543	896	29	·	·	PUNCT
ejpam-3543	896	30	y	y	X
ejpam-3543	896	31	)	)	PUNCT
ejpam-3543	896	32	,	,	PUNCT
ejpam-3543	896	33	λf	λf	X
ejpam-3543	896	34	(	(	PUNCT
ejpam-3543	896	35	x	x	NOUN
ejpam-3543	896	36	)	)	PUNCT
ejpam-3543	896	37	}	}	PUNCT
ejpam-3543	896	38	.	.	PUNCT
ejpam-3543	897	1	by	by	ADP
ejpam-3543	897	2	(	(	PUNCT
ejpam-3543	897	3	3.14	3.14	NUM
ejpam-3543	897	4	)	)	PUNCT
ejpam-3543	897	5	,	,	PUNCT
ejpam-3543	897	6	we	we	PRON
ejpam-3543	897	7	have	have	VERB
ejpam-3543	897	8	λf	λf	PROPN
ejpam-3543	897	9	(	(	PUNCT
ejpam-3543	897	10	y	y	NOUN
ejpam-3543	897	11	)	)	PUNCT
ejpam-3543	897	12	≥	≥	NOUN
ejpam-3543	897	13	min{λf	min{λf	X
ejpam-3543	898	1	(	(	PUNCT
ejpam-3543	898	2	x	x	PROPN
ejpam-3543	898	3	·	·	PUNCT
ejpam-3543	898	4	y	y	X
ejpam-3543	898	5	)	)	PUNCT
ejpam-3543	898	6	,	,	PUNCT
ejpam-3543	898	7	λf	λf	X
ejpam-3543	898	8	(	(	PUNCT
ejpam-3543	898	9	x	x	NOUN
ejpam-3543	898	10	)	)	PUNCT
ejpam-3543	898	11	}	}	PUNCT
ejpam-3543	898	12	≥	≥	PROPN
ejpam-3543	898	13	γ	γ	X
ejpam-3543	898	14	.	.	PUNCT
ejpam-3543	898	15	thus	thus	ADV
ejpam-3543	898	16	y	y	PROPN
ejpam-3543	898	17	∈	∈	PROPN
ejpam-3543	898	18	u(λf	u(λf	ADV
ejpam-3543	898	19	;	;	PUNCT
ejpam-3543	898	20	γ	γ	X
ejpam-3543	898	21	)	)	PUNCT
ejpam-3543	898	22	.	.	PUNCT
ejpam-3543	899	1	hence	hence	ADV
ejpam-3543	899	2	,	,	PUNCT
ejpam-3543	899	3	u(λt	u(λt	PROPN
ejpam-3543	899	4	;	;	PUNCT
ejpam-3543	899	5	α	α	X
ejpam-3543	899	6	)	)	PUNCT
ejpam-3543	899	7	,	,	PUNCT
ejpam-3543	899	8	l(λi	l(λi	PROPN
ejpam-3543	899	9	;	;	PUNCT
ejpam-3543	899	10	β	β	X
ejpam-3543	899	11	)	)	PUNCT
ejpam-3543	899	12	,	,	PUNCT
ejpam-3543	899	13	and	and	CCONJ
ejpam-3543	899	14	u(λf	u(λf	ADV
ejpam-3543	899	15	;	;	PUNCT
ejpam-3543	899	16	γ	γ	X
ejpam-3543	899	17	)	)	PUNCT
ejpam-3543	899	18	are	be	AUX
ejpam-3543	899	19	up	up	ADP
ejpam-3543	899	20	-	-	PUNCT
ejpam-3543	899	21	filters	filter	NOUN
ejpam-3543	899	22	of	of	ADP
ejpam-3543	899	23	x.	x.	NOUN
ejpam-3543	899	24	conversely	conversely	ADV
ejpam-3543	899	25	,	,	PUNCT
ejpam-3543	899	26	assume	assume	VERB
ejpam-3543	899	27	that	that	SCONJ
ejpam-3543	899	28	for	for	ADP
ejpam-3543	899	29	all	all	DET
ejpam-3543	899	30	α	α	NOUN
ejpam-3543	899	31	,	,	PUNCT
ejpam-3543	899	32	β	β	X
ejpam-3543	899	33	,	,	PUNCT
ejpam-3543	899	34	γ	γ	PROPN
ejpam-3543	899	35	∈	∈	PROPN
ejpam-3543	900	1	[	[	X
ejpam-3543	900	2	0	0	NUM
ejpam-3543	900	3	,	,	PUNCT
ejpam-3543	900	4	1	1	NUM
ejpam-3543	900	5	]	]	PUNCT
ejpam-3543	900	6	,	,	PUNCT
ejpam-3543	900	7	the	the	PRON
ejpam-3543	900	8	sets	set	NOUN
ejpam-3543	900	9	u(λt	u(λt	NOUN
ejpam-3543	900	10	;	;	PUNCT
ejpam-3543	900	11	α	α	X
ejpam-3543	900	12	)	)	PUNCT
ejpam-3543	900	13	,	,	PUNCT
ejpam-3543	900	14	l(λi	l(λi	PROPN
ejpam-3543	900	15	;	;	PUNCT
ejpam-3543	900	16	β	β	X
ejpam-3543	900	17	)	)	PUNCT
ejpam-3543	900	18	,	,	PUNCT
ejpam-3543	900	19	and	and	CCONJ
ejpam-3543	900	20	u(λf	u(λf	ADV
ejpam-3543	900	21	;	;	PUNCT
ejpam-3543	900	22	γ	γ	X
ejpam-3543	900	23	)	)	PUNCT
ejpam-3543	900	24	are	be	AUX
ejpam-3543	900	25	up	up	ADP
ejpam-3543	900	26	-	-	PUNCT
ejpam-3543	900	27	filters	filter	NOUN
ejpam-3543	900	28	of	of	ADP
ejpam-3543	900	29	x	x	PRON
ejpam-3543	900	30	if	if	SCONJ
ejpam-3543	900	31	u(λt	u(λt	NOUN
ejpam-3543	900	32	;	;	PUNCT
ejpam-3543	900	33	α	α	X
ejpam-3543	900	34	)	)	PUNCT
ejpam-3543	900	35	,	,	PUNCT
ejpam-3543	900	36	l(λi	l(λi	PROPN
ejpam-3543	900	37	;	;	PUNCT
ejpam-3543	900	38	β	β	X
ejpam-3543	900	39	)	)	PUNCT
ejpam-3543	900	40	,	,	PUNCT
ejpam-3543	900	41	and	and	CCONJ
ejpam-3543	900	42	u(λf	u(λf	ADV
ejpam-3543	900	43	;	;	PUNCT
ejpam-3543	900	44	γ	γ	X
ejpam-3543	900	45	)	)	PUNCT
ejpam-3543	900	46	are	be	AUX
ejpam-3543	900	47	nonempty	nonempty	ADJ
ejpam-3543	900	48	.	.	PUNCT
ejpam-3543	901	1	let	let	VERB
ejpam-3543	901	2	x	x	SYM
ejpam-3543	901	3	∈	∈	PROPN
ejpam-3543	901	4	x.	x.	NOUN
ejpam-3543	901	5	then	then	ADV
ejpam-3543	901	6	λt	λt	INTJ
ejpam-3543	901	7	(	(	PUNCT
ejpam-3543	901	8	x	x	X
ejpam-3543	901	9	)	)	PUNCT
ejpam-3543	901	10	∈	∈	PROPN
ejpam-3543	902	1	[	[	X
ejpam-3543	902	2	0	0	NUM
ejpam-3543	902	3	,	,	PUNCT
ejpam-3543	902	4	1	1	NUM
ejpam-3543	902	5	]	]	PUNCT
ejpam-3543	902	6	.	.	PUNCT
ejpam-3543	903	1	choose	choose	VERB
ejpam-3543	903	2	α	α	X
ejpam-3543	903	3	=	=	PUNCT
ejpam-3543	903	4	λt	λt	X
ejpam-3543	903	5	(	(	PUNCT
ejpam-3543	903	6	x	x	NOUN
ejpam-3543	903	7	)	)	PUNCT
ejpam-3543	903	8	.	.	PUNCT
ejpam-3543	904	1	thus	thus	ADV
ejpam-3543	904	2	λt	λt	X
ejpam-3543	904	3	(	(	PUNCT
ejpam-3543	904	4	x	x	NOUN
ejpam-3543	904	5	)	)	PUNCT
ejpam-3543	904	6	≥	≥	NUM
ejpam-3543	904	7	α	α	NOUN
ejpam-3543	904	8	,	,	PUNCT
ejpam-3543	904	9	so	so	ADV
ejpam-3543	904	10	x	x	SYM
ejpam-3543	904	11	∈	∈	NOUN
ejpam-3543	904	12	u(λt	u(λt	NOUN
ejpam-3543	904	13	;	;	PUNCT
ejpam-3543	904	14	α	α	X
ejpam-3543	904	15	)	)	PUNCT
ejpam-3543	904	16	6=	6=	ADP
ejpam-3543	904	17	∅.	∅.	ADP
ejpam-3543	904	18	by	by	ADP
ejpam-3543	904	19	assumption	assumption	NOUN
ejpam-3543	904	20	,	,	PUNCT
ejpam-3543	904	21	we	we	PRON
ejpam-3543	904	22	have	have	VERB
ejpam-3543	904	23	u(λt	u(λt	NOUN
ejpam-3543	904	24	;	;	PUNCT
ejpam-3543	904	25	α	α	X
ejpam-3543	904	26	)	)	PUNCT
ejpam-3543	904	27	is	be	AUX
ejpam-3543	904	28	a	a	DET
ejpam-3543	904	29	up	up	ADJ
ejpam-3543	904	30	-	-	PUNCT
ejpam-3543	904	31	filter	filter	NOUN
ejpam-3543	904	32	of	of	ADP
ejpam-3543	904	33	x	x	PUNCT
ejpam-3543	904	34	and	and	CCONJ
ejpam-3543	904	35	so	so	ADV
ejpam-3543	904	36	0	0	NUM
ejpam-3543	904	37	∈	∈	PROPN
ejpam-3543	904	38	u(λt	u(λt	NOUN
ejpam-3543	904	39	;	;	PUNCT
ejpam-3543	904	40	α	α	X
ejpam-3543	904	41	)	)	PUNCT
ejpam-3543	904	42	.	.	PUNCT
ejpam-3543	905	1	thus	thus	ADV
ejpam-3543	905	2	λt	λt	X
ejpam-3543	905	3	(	(	PUNCT
ejpam-3543	905	4	0	0	NUM
ejpam-3543	905	5	)	)	PUNCT
ejpam-3543	905	6	≥	≥	NOUN
ejpam-3543	905	7	α	α	X
ejpam-3543	905	8	=	=	PUNCT
ejpam-3543	905	9	λt	λt	X
ejpam-3543	905	10	(	(	PUNCT
ejpam-3543	905	11	x	x	NOUN
ejpam-3543	905	12	)	)	PUNCT
ejpam-3543	905	13	.	.	PUNCT
ejpam-3543	906	1	next	next	ADV
ejpam-3543	906	2	,	,	PUNCT
ejpam-3543	906	3	let	let	VERB
ejpam-3543	906	4	x	x	PRON
ejpam-3543	906	5	,	,	PUNCT
ejpam-3543	906	6	y	y	PROPN
ejpam-3543	906	7	∈	∈	PROPN
ejpam-3543	906	8	x.	x.	NOUN
ejpam-3543	906	9	then	then	ADV
ejpam-3543	906	10	λt	λt	X
ejpam-3543	906	11	(	(	PUNCT
ejpam-3543	906	12	x	x	PROPN
ejpam-3543	906	13	·	·	PUNCT
ejpam-3543	906	14	y	y	X
ejpam-3543	906	15	)	)	PUNCT
ejpam-3543	906	16	,	,	PUNCT
ejpam-3543	907	1	λt	λt	X
ejpam-3543	907	2	(	(	PUNCT
ejpam-3543	907	3	x	x	X
ejpam-3543	907	4	)	)	PUNCT
ejpam-3543	907	5	∈	∈	PROPN
ejpam-3543	908	1	[	[	X
ejpam-3543	908	2	0	0	NUM
ejpam-3543	908	3	,	,	PUNCT
ejpam-3543	908	4	1	1	NUM
ejpam-3543	908	5	]	]	PUNCT
ejpam-3543	908	6	.	.	PUNCT
ejpam-3543	909	1	choose	choose	VERB
ejpam-3543	909	2	α	α	X
ejpam-3543	909	3	=	=	PUNCT
ejpam-3543	909	4	min{λt	min{λt	X
ejpam-3543	909	5	(	(	PUNCT
ejpam-3543	909	6	x	x	SYM
ejpam-3543	909	7	·	·	PUNCT
ejpam-3543	909	8	y	y	X
ejpam-3543	909	9	)	)	PUNCT
ejpam-3543	909	10	,	,	PUNCT
ejpam-3543	909	11	λt	λt	X
ejpam-3543	909	12	(	(	PUNCT
ejpam-3543	909	13	x	x	NOUN
ejpam-3543	909	14	)	)	PUNCT
ejpam-3543	909	15	}	}	PUNCT
ejpam-3543	909	16	.	.	PUNCT
ejpam-3543	910	1	thus	thus	ADV
ejpam-3543	910	2	λt	λt	X
ejpam-3543	910	3	(	(	PUNCT
ejpam-3543	910	4	x	x	X
ejpam-3543	910	5	·	·	PUNCT
ejpam-3543	910	6	y	y	X
ejpam-3543	910	7	)	)	PUNCT
ejpam-3543	910	8	≥	≥	NOUN
ejpam-3543	910	9	α	α	NOUN
ejpam-3543	910	10	and	and	CCONJ
ejpam-3543	910	11	λt	λt	X
ejpam-3543	910	12	(	(	PUNCT
ejpam-3543	910	13	x	x	NOUN
ejpam-3543	910	14	)	)	PUNCT
ejpam-3543	910	15	≥	≥	NUM
ejpam-3543	910	16	α	α	NOUN
ejpam-3543	910	17	,	,	PUNCT
ejpam-3543	910	18	so	so	ADV
ejpam-3543	910	19	x	x	SYM
ejpam-3543	910	20	·	·	PUNCT
ejpam-3543	910	21	y	y	X
ejpam-3543	910	22	,	,	PUNCT
ejpam-3543	910	23	x	x	SYM
ejpam-3543	910	24	∈	∈	NOUN
ejpam-3543	910	25	u(λt	u(λt	NOUN
ejpam-3543	910	26	;	;	PUNCT
ejpam-3543	910	27	α	α	X
ejpam-3543	910	28	)	)	PUNCT
ejpam-3543	910	29	6=	6=	ADP
ejpam-3543	910	30	∅.	∅.	ADP
ejpam-3543	910	31	by	by	ADP
ejpam-3543	910	32	assumption	assumption	NOUN
ejpam-3543	910	33	,	,	PUNCT
ejpam-3543	910	34	we	we	PRON
ejpam-3543	910	35	have	have	VERB
ejpam-3543	910	36	u(λt	u(λt	NOUN
ejpam-3543	910	37	;	;	PUNCT
ejpam-3543	910	38	α	α	X
ejpam-3543	910	39	)	)	PUNCT
ejpam-3543	910	40	is	be	AUX
ejpam-3543	910	41	a	a	DET
ejpam-3543	910	42	up	up	ADJ
ejpam-3543	910	43	-	-	PUNCT
ejpam-3543	910	44	filter	filter	NOUN
ejpam-3543	910	45	of	of	ADP
ejpam-3543	910	46	x	x	PUNCT
ejpam-3543	910	47	and	and	CCONJ
ejpam-3543	910	48	so	so	ADV
ejpam-3543	910	49	y	y	PROPN
ejpam-3543	910	50	∈	∈	PROPN
ejpam-3543	910	51	u(λt	u(λt	PROPN
ejpam-3543	910	52	;	;	PUNCT
ejpam-3543	910	53	α	α	X
ejpam-3543	910	54	)	)	PUNCT
ejpam-3543	910	55	.	.	PUNCT
ejpam-3543	911	1	thus	thus	ADV
ejpam-3543	911	2	λt	λt	X
ejpam-3543	911	3	(	(	PUNCT
ejpam-3543	911	4	y	y	NOUN
ejpam-3543	911	5	)	)	PUNCT
ejpam-3543	911	6	≥	≥	NOUN
ejpam-3543	911	7	α	α	NOUN
ejpam-3543	911	8	=	=	PUNCT
ejpam-3543	911	9	min{λt	min{λt	X
ejpam-3543	911	10	(	(	PUNCT
ejpam-3543	911	11	x	x	SYM
ejpam-3543	911	12	·	·	PUNCT
ejpam-3543	911	13	y	y	X
ejpam-3543	911	14	)	)	PUNCT
ejpam-3543	911	15	,	,	PUNCT
ejpam-3543	911	16	λt	λt	X
ejpam-3543	911	17	(	(	PUNCT
ejpam-3543	911	18	x	x	NOUN
ejpam-3543	911	19	)	)	PUNCT
ejpam-3543	911	20	}	}	PUNCT
ejpam-3543	911	21	.	.	PUNCT
ejpam-3543	912	1	let	let	VERB
ejpam-3543	912	2	x	x	SYM
ejpam-3543	912	3	∈	∈	PROPN
ejpam-3543	912	4	x.	x.	NOUN
ejpam-3543	912	5	then	then	ADV
ejpam-3543	912	6	λi(x	λi(x	X
ejpam-3543	912	7	)	)	PUNCT
ejpam-3543	912	8	∈	∈	PROPN
ejpam-3543	913	1	[	[	X
ejpam-3543	913	2	0	0	NUM
ejpam-3543	913	3	,	,	PUNCT
ejpam-3543	913	4	1	1	NUM
ejpam-3543	913	5	]	]	PUNCT
ejpam-3543	913	6	.	.	PUNCT
ejpam-3543	914	1	choose	choose	VERB
ejpam-3543	914	2	β	β	X
ejpam-3543	914	3	=	=	SYM
ejpam-3543	914	4	λi(x	λi(x	NUM
ejpam-3543	914	5	)	)	PUNCT
ejpam-3543	914	6	.	.	PUNCT
ejpam-3543	915	1	thus	thus	ADV
ejpam-3543	915	2	λi(x	λi(x	NUM
ejpam-3543	915	3	)	)	PUNCT
ejpam-3543	915	4	≤	≤	NUM
ejpam-3543	916	1	β	β	NOUN
ejpam-3543	916	2	,	,	PUNCT
ejpam-3543	916	3	so	so	CCONJ
ejpam-3543	916	4	x	x	SYM
ejpam-3543	916	5	∈	∈	NOUN
ejpam-3543	916	6	l(λi	l(λi	NOUN
ejpam-3543	916	7	;	;	PUNCT
ejpam-3543	916	8	β	β	X
ejpam-3543	916	9	)	)	PUNCT
ejpam-3543	916	10	6=	6=	ADP
ejpam-3543	916	11	∅.	∅.	ADP
ejpam-3543	916	12	by	by	ADP
ejpam-3543	916	13	assumption	assumption	NOUN
ejpam-3543	916	14	,	,	PUNCT
ejpam-3543	916	15	we	we	PRON
ejpam-3543	916	16	have	have	VERB
ejpam-3543	916	17	l(λi	l(λi	NOUN
ejpam-3543	916	18	;	;	PUNCT
ejpam-3543	916	19	β	β	X
ejpam-3543	916	20	)	)	PUNCT
ejpam-3543	916	21	is	be	AUX
ejpam-3543	916	22	a	a	DET
ejpam-3543	916	23	up	up	ADJ
ejpam-3543	916	24	-	-	PUNCT
ejpam-3543	916	25	filter	filter	NOUN
ejpam-3543	916	26	of	of	ADP
ejpam-3543	916	27	x	x	PUNCT
ejpam-3543	916	28	and	and	CCONJ
ejpam-3543	916	29	so	so	ADV
ejpam-3543	916	30	0	0	NUM
ejpam-3543	916	31	∈	∈	NOUN
ejpam-3543	916	32	l(λi	l(λi	NOUN
ejpam-3543	916	33	;	;	PUNCT
ejpam-3543	916	34	β	β	X
ejpam-3543	916	35	)	)	PUNCT
ejpam-3543	916	36	.	.	PUNCT
ejpam-3543	917	1	thus	thus	ADV
ejpam-3543	917	2	λi(0	λi(0	X
ejpam-3543	917	3	)	)	PUNCT
ejpam-3543	917	4	≤	≤	NOUN
ejpam-3543	917	5	β	β	X
ejpam-3543	917	6	=	=	SYM
ejpam-3543	917	7	λi(x	λi(x	NUM
ejpam-3543	917	8	)	)	PUNCT
ejpam-3543	917	9	.	.	PUNCT
ejpam-3543	918	1	next	next	ADV
ejpam-3543	918	2	,	,	PUNCT
ejpam-3543	918	3	let	let	VERB
ejpam-3543	918	4	x	x	PRON
ejpam-3543	918	5	,	,	PUNCT
ejpam-3543	918	6	y	y	PROPN
ejpam-3543	918	7	∈	∈	PROPN
ejpam-3543	918	8	x.	x.	NOUN
ejpam-3543	918	9	then	then	ADV
ejpam-3543	918	10	λi(x	λi(x	X
ejpam-3543	918	11	·	·	PUNCT
ejpam-3543	918	12	y	y	X
ejpam-3543	918	13	)	)	PUNCT
ejpam-3543	918	14	,	,	PUNCT
ejpam-3543	918	15	λi(x	λi(x	NUM
ejpam-3543	918	16	)	)	PUNCT
ejpam-3543	918	17	∈	∈	PROPN
ejpam-3543	919	1	[	[	X
ejpam-3543	919	2	0	0	NUM
ejpam-3543	919	3	,	,	PUNCT
ejpam-3543	919	4	1	1	NUM
ejpam-3543	919	5	]	]	PUNCT
ejpam-3543	919	6	.	.	PUNCT
ejpam-3543	920	1	choose	choose	VERB
ejpam-3543	920	2	β	β	X
ejpam-3543	920	3	=	=	SYM
ejpam-3543	920	4	max{λi(x	max{λi(x	X
ejpam-3543	920	5	·	·	PUNCT
ejpam-3543	920	6	y	y	X
ejpam-3543	920	7	)	)	PUNCT
ejpam-3543	920	8	,	,	PUNCT
ejpam-3543	920	9	λi(x	λi(x	NUM
ejpam-3543	920	10	)	)	PUNCT
ejpam-3543	920	11	}	}	PUNCT
ejpam-3543	920	12	.	.	PUNCT
ejpam-3543	921	1	thus	thus	ADV
ejpam-3543	921	2	λi(x	λi(x	X
ejpam-3543	921	3	·	·	PUNCT
ejpam-3543	921	4	y	y	X
ejpam-3543	921	5	)	)	PUNCT
ejpam-3543	921	6	≤	≤	NOUN
ejpam-3543	921	7	β	β	X
ejpam-3543	921	8	and	and	CCONJ
ejpam-3543	921	9	λi(x	λi(x	NUM
ejpam-3543	921	10	)	)	PUNCT
ejpam-3543	921	11	≤	≤	NUM
ejpam-3543	921	12	β	β	NOUN
ejpam-3543	921	13	,	,	PUNCT
ejpam-3543	921	14	so	so	SCONJ
ejpam-3543	921	15	x	x	SYM
ejpam-3543	921	16	·	·	PUNCT
ejpam-3543	921	17	y	y	X
ejpam-3543	921	18	,	,	PUNCT
ejpam-3543	921	19	x	x	SYM
ejpam-3543	921	20	∈	∈	NOUN
ejpam-3543	921	21	l(λi	l(λi	NOUN
ejpam-3543	921	22	;	;	PUNCT
ejpam-3543	921	23	β	β	X
ejpam-3543	921	24	)	)	PUNCT
ejpam-3543	921	25	6=	6=	ADP
ejpam-3543	921	26	∅.	∅.	ADP
ejpam-3543	921	27	by	by	ADP
ejpam-3543	921	28	assumption	assumption	NOUN
ejpam-3543	921	29	,	,	PUNCT
ejpam-3543	921	30	we	we	PRON
ejpam-3543	921	31	have	have	VERB
ejpam-3543	921	32	l(λi	l(λi	NOUN
ejpam-3543	921	33	;	;	PUNCT
ejpam-3543	921	34	β	β	X
ejpam-3543	921	35	)	)	PUNCT
ejpam-3543	921	36	is	be	AUX
ejpam-3543	921	37	a	a	DET
ejpam-3543	921	38	up	up	ADJ
ejpam-3543	921	39	-	-	PUNCT
ejpam-3543	921	40	filter	filter	NOUN
ejpam-3543	921	41	of	of	ADP
ejpam-3543	921	42	x	x	PUNCT
ejpam-3543	921	43	and	and	CCONJ
ejpam-3543	921	44	so	so	ADV
ejpam-3543	921	45	y	y	PROPN
ejpam-3543	921	46	∈	∈	PROPN
ejpam-3543	921	47	l(λi	l(λi	X
ejpam-3543	921	48	;	;	PUNCT
ejpam-3543	921	49	β	β	X
ejpam-3543	921	50	)	)	PUNCT
ejpam-3543	921	51	.	.	PUNCT
ejpam-3543	922	1	thus	thus	ADV
ejpam-3543	922	2	λi(y	λi(y	NOUN
ejpam-3543	922	3	)	)	PUNCT
ejpam-3543	922	4	≤	≤	NOUN
ejpam-3543	922	5	β	β	X
ejpam-3543	922	6	=	=	SYM
ejpam-3543	922	7	max{λi(x	max{λi(x	X
ejpam-3543	922	8	·	·	PUNCT
ejpam-3543	922	9	y	y	X
ejpam-3543	922	10	)	)	PUNCT
ejpam-3543	922	11	,	,	PUNCT
ejpam-3543	922	12	λi(x	λi(x	NUM
ejpam-3543	922	13	)	)	PUNCT
ejpam-3543	922	14	}	}	PUNCT
ejpam-3543	922	15	.	.	PUNCT
ejpam-3543	923	1	let	let	VERB
ejpam-3543	923	2	x	x	SYM
ejpam-3543	923	3	∈	∈	PROPN
ejpam-3543	923	4	x.	x.	NOUN
ejpam-3543	923	5	then	then	ADV
ejpam-3543	924	1	λf	λf	INTJ
ejpam-3543	924	2	(	(	PUNCT
ejpam-3543	924	3	x	x	X
ejpam-3543	924	4	)	)	PUNCT
ejpam-3543	924	5	∈	∈	PROPN
ejpam-3543	925	1	[	[	X
ejpam-3543	925	2	0	0	NUM
ejpam-3543	925	3	,	,	PUNCT
ejpam-3543	925	4	1	1	NUM
ejpam-3543	925	5	]	]	PUNCT
ejpam-3543	925	6	.	.	PUNCT
ejpam-3543	926	1	choose	choose	VERB
ejpam-3543	926	2	γ	γ	X
ejpam-3543	926	3	=	=	PUNCT
ejpam-3543	926	4	λf	λf	PROPN
ejpam-3543	926	5	(	(	PUNCT
ejpam-3543	926	6	x	x	NOUN
ejpam-3543	926	7	)	)	PUNCT
ejpam-3543	926	8	.	.	PUNCT
ejpam-3543	927	1	thus	thus	ADV
ejpam-3543	927	2	λf	λf	X
ejpam-3543	927	3	(	(	PUNCT
ejpam-3543	927	4	x	x	NOUN
ejpam-3543	927	5	)	)	PUNCT
ejpam-3543	927	6	≥	≥	PROPN
ejpam-3543	927	7	γ	γ	NOUN
ejpam-3543	927	8	,	,	PUNCT
ejpam-3543	927	9	so	so	ADV
ejpam-3543	927	10	x	x	SYM
ejpam-3543	927	11	∈	∈	PROPN
ejpam-3543	927	12	u(λf	u(λf	NOUN
ejpam-3543	927	13	;	;	PUNCT
ejpam-3543	927	14	γ	γ	X
ejpam-3543	927	15	)	)	PUNCT
ejpam-3543	927	16	6=	6=	ADP
ejpam-3543	927	17	∅.	∅.	ADP
ejpam-3543	927	18	by	by	ADP
ejpam-3543	927	19	assumption	assumption	NOUN
ejpam-3543	927	20	,	,	PUNCT
ejpam-3543	927	21	we	we	PRON
ejpam-3543	927	22	have	have	VERB
ejpam-3543	927	23	u(λf	u(λf	ADV
ejpam-3543	927	24	;	;	PUNCT
ejpam-3543	927	25	γ	γ	X
ejpam-3543	927	26	)	)	PUNCT
ejpam-3543	927	27	is	be	AUX
ejpam-3543	927	28	a	a	DET
ejpam-3543	927	29	up	up	ADJ
ejpam-3543	927	30	-	-	PUNCT
ejpam-3543	927	31	filter	filter	NOUN
ejpam-3543	927	32	of	of	ADP
ejpam-3543	927	33	x	x	PUNCT
ejpam-3543	927	34	and	and	CCONJ
ejpam-3543	927	35	so	so	ADV
ejpam-3543	927	36	0	0	NUM
ejpam-3543	927	37	∈	∈	PROPN
ejpam-3543	927	38	u(λf	u(λf	NOUN
ejpam-3543	927	39	;	;	PUNCT
ejpam-3543	927	40	γ	γ	X
ejpam-3543	927	41	)	)	PUNCT
ejpam-3543	927	42	.	.	PUNCT
ejpam-3543	928	1	thus	thus	ADV
ejpam-3543	928	2	λf	λf	X
ejpam-3543	928	3	(	(	PUNCT
ejpam-3543	928	4	0	0	NUM
ejpam-3543	928	5	)	)	PUNCT
ejpam-3543	928	6	≥	≥	NOUN
ejpam-3543	928	7	γ	γ	X
ejpam-3543	928	8	=	=	PUNCT
ejpam-3543	928	9	λf	λf	PROPN
ejpam-3543	928	10	(	(	PUNCT
ejpam-3543	928	11	x	x	NOUN
ejpam-3543	928	12	)	)	PUNCT
ejpam-3543	928	13	.	.	PUNCT
ejpam-3543	929	1	next	next	ADV
ejpam-3543	929	2	,	,	PUNCT
ejpam-3543	929	3	let	let	VERB
ejpam-3543	929	4	x	x	PRON
ejpam-3543	929	5	,	,	PUNCT
ejpam-3543	929	6	y	y	PROPN
ejpam-3543	929	7	∈	∈	PROPN
ejpam-3543	929	8	x.	x.	NOUN
ejpam-3543	930	1	then	then	ADV
ejpam-3543	930	2	λf	λf	INTJ
ejpam-3543	930	3	(	(	PUNCT
ejpam-3543	930	4	x	x	PROPN
ejpam-3543	930	5	·	·	PUNCT
ejpam-3543	930	6	y	y	X
ejpam-3543	930	7	)	)	PUNCT
ejpam-3543	930	8	,	,	PUNCT
ejpam-3543	930	9	λf	λf	X
ejpam-3543	930	10	(	(	PUNCT
ejpam-3543	930	11	x	x	X
ejpam-3543	930	12	)	)	PUNCT
ejpam-3543	930	13	∈	∈	PROPN
ejpam-3543	931	1	[	[	X
ejpam-3543	931	2	0	0	NUM
ejpam-3543	931	3	,	,	PUNCT
ejpam-3543	931	4	1	1	NUM
ejpam-3543	931	5	]	]	PUNCT
ejpam-3543	931	6	.	.	PUNCT
ejpam-3543	932	1	choose	choose	VERB
ejpam-3543	932	2	γ	γ	X
ejpam-3543	932	3	=	=	SYM
ejpam-3543	932	4	min{λf	min{λf	X
ejpam-3543	932	5	(	(	PUNCT
ejpam-3543	932	6	x	x	PROPN
ejpam-3543	932	7	·	·	PUNCT
ejpam-3543	932	8	y	y	X
ejpam-3543	932	9	)	)	PUNCT
ejpam-3543	932	10	,	,	PUNCT
ejpam-3543	932	11	λf	λf	X
ejpam-3543	932	12	(	(	PUNCT
ejpam-3543	932	13	x	x	NOUN
ejpam-3543	932	14	)	)	PUNCT
ejpam-3543	932	15	}	}	PUNCT
ejpam-3543	932	16	.	.	PUNCT
ejpam-3543	933	1	thus	thus	ADV
ejpam-3543	933	2	λf	λf	X
ejpam-3543	933	3	(	(	PUNCT
ejpam-3543	933	4	x	x	SYM
ejpam-3543	933	5	·	·	PUNCT
ejpam-3543	933	6	y	y	X
ejpam-3543	933	7	)	)	PUNCT
ejpam-3543	933	8	≥	≥	PROPN
ejpam-3543	933	9	γ	γ	NOUN
ejpam-3543	933	10	and	and	CCONJ
ejpam-3543	933	11	λf	λf	PROPN
ejpam-3543	933	12	(	(	PUNCT
ejpam-3543	933	13	x	x	NOUN
ejpam-3543	933	14	)	)	PUNCT
ejpam-3543	933	15	≥	≥	PROPN
ejpam-3543	933	16	γ	γ	NOUN
ejpam-3543	933	17	,	,	PUNCT
ejpam-3543	933	18	so	so	ADV
ejpam-3543	933	19	x	x	SYM
ejpam-3543	933	20	·	·	PUNCT
ejpam-3543	933	21	y	y	X
ejpam-3543	933	22	,	,	PUNCT
ejpam-3543	933	23	x	x	SYM
ejpam-3543	933	24	∈	∈	PROPN
ejpam-3543	933	25	u(λf	u(λf	NOUN
ejpam-3543	933	26	;	;	PUNCT
ejpam-3543	933	27	γ	γ	X
ejpam-3543	933	28	)	)	PUNCT
ejpam-3543	933	29	6=	6=	ADP
ejpam-3543	933	30	∅.	∅.	ADP
ejpam-3543	933	31	by	by	ADP
ejpam-3543	933	32	assumption	assumption	NOUN
ejpam-3543	933	33	,	,	PUNCT
ejpam-3543	933	34	we	we	PRON
ejpam-3543	933	35	have	have	VERB
ejpam-3543	933	36	u(λf	u(λf	ADV
ejpam-3543	933	37	;	;	PUNCT
ejpam-3543	933	38	γ	γ	X
ejpam-3543	933	39	)	)	PUNCT
ejpam-3543	933	40	is	be	AUX
ejpam-3543	933	41	a	a	DET
ejpam-3543	933	42	up	up	ADJ
ejpam-3543	933	43	-	-	PUNCT
ejpam-3543	933	44	filter	filter	NOUN
ejpam-3543	933	45	of	of	ADP
ejpam-3543	933	46	x	x	PUNCT
ejpam-3543	933	47	and	and	CCONJ
ejpam-3543	933	48	so	so	ADV
ejpam-3543	933	49	y	y	PROPN
ejpam-3543	933	50	∈	∈	PROPN
ejpam-3543	933	51	u(λf	u(λf	ADV
ejpam-3543	933	52	;	;	PUNCT
ejpam-3543	933	53	γ	γ	X
ejpam-3543	933	54	)	)	PUNCT
ejpam-3543	933	55	.	.	PUNCT
ejpam-3543	934	1	thus	thus	ADV
ejpam-3543	934	2	λf	λf	X
ejpam-3543	934	3	(	(	PUNCT
ejpam-3543	934	4	y	y	NOUN
ejpam-3543	934	5	)	)	PUNCT
ejpam-3543	934	6	≥	≥	PROPN
ejpam-3543	934	7	γ	γ	X
ejpam-3543	934	8	=	=	SYM
ejpam-3543	934	9	min{λf	min{λf	X
ejpam-3543	934	10	(	(	PUNCT
ejpam-3543	934	11	x	x	PROPN
ejpam-3543	934	12	·	·	PUNCT
ejpam-3543	934	13	y	y	X
ejpam-3543	934	14	)	)	PUNCT
ejpam-3543	934	15	,	,	PUNCT
ejpam-3543	934	16	λf	λf	X
ejpam-3543	934	17	(	(	PUNCT
ejpam-3543	934	18	x	x	NOUN
ejpam-3543	934	19	)	)	PUNCT
ejpam-3543	934	20	}	}	PUNCT
ejpam-3543	934	21	.	.	PUNCT
ejpam-3543	935	1	therefore	therefore	ADV
ejpam-3543	935	2	,	,	PUNCT
ejpam-3543	935	3	λ	λ	PROPN
ejpam-3543	935	4	is	be	AUX
ejpam-3543	935	5	a	a	DET
ejpam-3543	935	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	935	7	up	up	ADJ
ejpam-3543	935	8	-	-	PUNCT
ejpam-3543	935	9	filter	filter	NOUN
ejpam-3543	935	10	of	of	ADP
ejpam-3543	935	11	x.	x.	PROPN
ejpam-3543	935	12	theorem	theorem	VERB
ejpam-3543	935	13	22	22	NUM
ejpam-3543	935	14	.	.	PUNCT
ejpam-3543	936	1	a	a	DET
ejpam-3543	936	2	ns	ns	NUM
ejpam-3543	936	3	λ	λ	NOUN
ejpam-3543	936	4	in	in	ADP
ejpam-3543	936	5	x	x	PROPN
ejpam-3543	936	6	is	be	AUX
ejpam-3543	936	7	a	a	DET
ejpam-3543	936	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	936	9	up	up	ADV
ejpam-3543	936	10	-	-	PUNCT
ejpam-3543	936	11	ideal	ideal	NOUN
ejpam-3543	936	12	of	of	ADP
ejpam-3543	936	13	x	x	SYM
ejpam-3543	936	14	if	if	SCONJ
ejpam-3543	936	15	and	and	CCONJ
ejpam-3543	936	16	only	only	ADV
ejpam-3543	936	17	if	if	SCONJ
ejpam-3543	936	18	for	for	ADP
ejpam-3543	936	19	all	all	DET
ejpam-3543	936	20	α	α	NOUN
ejpam-3543	936	21	,	,	PUNCT
ejpam-3543	936	22	β	β	X
ejpam-3543	936	23	,	,	PUNCT
ejpam-3543	936	24	γ	γ	PROPN
ejpam-3543	936	25	∈	∈	PROPN
ejpam-3543	937	1	[	[	X
ejpam-3543	937	2	0	0	NUM
ejpam-3543	937	3	,	,	PUNCT
ejpam-3543	937	4	1	1	NUM
ejpam-3543	937	5	]	]	PUNCT
ejpam-3543	937	6	,	,	PUNCT
ejpam-3543	937	7	the	the	PRON
ejpam-3543	937	8	sets	set	NOUN
ejpam-3543	937	9	u(λt	u(λt	NOUN
ejpam-3543	937	10	;	;	PUNCT
ejpam-3543	937	11	α	α	X
ejpam-3543	937	12	)	)	PUNCT
ejpam-3543	937	13	,	,	PUNCT
ejpam-3543	937	14	l(λi	l(λi	PROPN
ejpam-3543	937	15	;	;	PUNCT
ejpam-3543	937	16	β	β	X
ejpam-3543	937	17	)	)	PUNCT
ejpam-3543	937	18	,	,	PUNCT
ejpam-3543	937	19	and	and	CCONJ
ejpam-3543	937	20	u(λf	u(λf	ADV
ejpam-3543	937	21	;	;	PUNCT
ejpam-3543	937	22	γ	γ	X
ejpam-3543	937	23	)	)	PUNCT
ejpam-3543	937	24	are	be	AUX
ejpam-3543	937	25	up	up	ADP
ejpam-3543	937	26	-	-	PUNCT
ejpam-3543	937	27	ideals	ideal	NOUN
ejpam-3543	937	28	of	of	ADP
ejpam-3543	937	29	x	x	SYM
ejpam-3543	937	30	if	if	SCONJ
ejpam-3543	937	31	u(λt	u(λt	NOUN
ejpam-3543	937	32	;	;	PUNCT
ejpam-3543	937	33	α	α	X
ejpam-3543	937	34	)	)	PUNCT
ejpam-3543	937	35	,	,	PUNCT
ejpam-3543	937	36	l(λi	l(λi	PROPN
ejpam-3543	937	37	;	;	PUNCT
ejpam-3543	937	38	β	β	X
ejpam-3543	937	39	)	)	PUNCT
ejpam-3543	937	40	,	,	PUNCT
ejpam-3543	937	41	and	and	CCONJ
ejpam-3543	937	42	u(λf	u(λf	ADV
ejpam-3543	937	43	;	;	PUNCT
ejpam-3543	937	44	γ	γ	X
ejpam-3543	937	45	)	)	PUNCT
ejpam-3543	937	46	are	be	AUX
ejpam-3543	937	47	nonempty	nonempty	ADJ
ejpam-3543	937	48	.	.	PUNCT
ejpam-3543	938	1	proof	proof	NOUN
ejpam-3543	938	2	.	.	PUNCT
ejpam-3543	939	1	assume	assume	VERB
ejpam-3543	939	2	that	that	SCONJ
ejpam-3543	939	3	λ	λ	PROPN
ejpam-3543	939	4	is	be	AUX
ejpam-3543	939	5	a	a	DET
ejpam-3543	939	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	939	7	up	up	ADV
ejpam-3543	939	8	-	-	PUNCT
ejpam-3543	939	9	ideal	ideal	NOUN
ejpam-3543	939	10	of	of	ADP
ejpam-3543	939	11	x.	x.	NOUN
ejpam-3543	939	12	let	let	VERB
ejpam-3543	939	13	α	α	PRON
ejpam-3543	939	14	,	,	PUNCT
ejpam-3543	939	15	β	β	X
ejpam-3543	939	16	,	,	PUNCT
ejpam-3543	939	17	γ	γ	PROPN
ejpam-3543	939	18	∈	∈	PROPN
ejpam-3543	940	1	[	[	X
ejpam-3543	940	2	0	0	NUM
ejpam-3543	940	3	,	,	PUNCT
ejpam-3543	940	4	1	1	NUM
ejpam-3543	940	5	]	]	PUNCT
ejpam-3543	940	6	be	be	AUX
ejpam-3543	940	7	such	such	ADJ
ejpam-3543	940	8	that	that	SCONJ
ejpam-3543	940	9	u(λt	u(λt	NOUN
ejpam-3543	940	10	;	;	PUNCT
ejpam-3543	940	11	α	α	X
ejpam-3543	940	12	)	)	PUNCT
ejpam-3543	940	13	,	,	PUNCT
ejpam-3543	940	14	l(λi	l(λi	PROPN
ejpam-3543	940	15	;	;	PUNCT
ejpam-3543	940	16	β	β	X
ejpam-3543	940	17	)	)	PUNCT
ejpam-3543	940	18	,	,	PUNCT
ejpam-3543	940	19	and	and	CCONJ
ejpam-3543	940	20	u(λf	u(λf	ADV
ejpam-3543	940	21	;	;	PUNCT
ejpam-3543	940	22	γ	γ	X
ejpam-3543	940	23	)	)	PUNCT
ejpam-3543	940	24	are	be	AUX
ejpam-3543	940	25	nonempty	nonempty	ADJ
ejpam-3543	940	26	.	.	PUNCT
ejpam-3543	941	1	let	let	VERB
ejpam-3543	941	2	x	x	SYM
ejpam-3543	941	3	∈	∈	PROPN
ejpam-3543	941	4	u(λt	u(λt	NOUN
ejpam-3543	941	5	;	;	PUNCT
ejpam-3543	941	6	α	α	X
ejpam-3543	941	7	)	)	PUNCT
ejpam-3543	941	8	.	.	PUNCT
ejpam-3543	942	1	then	then	ADV
ejpam-3543	942	2	λt	λt	INTJ
ejpam-3543	942	3	(	(	PUNCT
ejpam-3543	942	4	x	x	X
ejpam-3543	942	5	)	)	PUNCT
ejpam-3543	942	6	≥	≥	PROPN
ejpam-3543	942	7	α	α	NOUN
ejpam-3543	942	8	.	.	PUNCT
ejpam-3543	943	1	by	by	ADP
ejpam-3543	943	2	(	(	PUNCT
ejpam-3543	943	3	3.6	3.6	NUM
ejpam-3543	943	4	)	)	PUNCT
ejpam-3543	943	5	,	,	PUNCT
ejpam-3543	943	6	we	we	PRON
ejpam-3543	943	7	have	have	VERB
ejpam-3543	943	8	λt	λt	X
ejpam-3543	943	9	(	(	PUNCT
ejpam-3543	943	10	0	0	NUM
ejpam-3543	943	11	)	)	PUNCT
ejpam-3543	943	12	≥	≥	NOUN
ejpam-3543	943	13	λt	λt	X
ejpam-3543	943	14	(	(	PUNCT
ejpam-3543	943	15	x	x	NOUN
ejpam-3543	943	16	)	)	PUNCT
ejpam-3543	943	17	≥	≥	PROPN
ejpam-3543	943	18	α	α	NOUN
ejpam-3543	943	19	.	.	PUNCT
ejpam-3543	944	1	thus	thus	ADV
ejpam-3543	944	2	0	0	NUM
ejpam-3543	944	3	∈	∈	PROPN
ejpam-3543	944	4	u(λt	u(λt	NOUN
ejpam-3543	944	5	;	;	PUNCT
ejpam-3543	944	6	α	α	X
ejpam-3543	944	7	)	)	PUNCT
ejpam-3543	944	8	.	.	PUNCT
ejpam-3543	945	1	next	next	ADV
ejpam-3543	945	2	,	,	PUNCT
ejpam-3543	945	3	let	let	VERB
ejpam-3543	945	4	x	x	PRON
ejpam-3543	945	5	,	,	PUNCT
ejpam-3543	945	6	y	y	PROPN
ejpam-3543	945	7	,	,	PUNCT
ejpam-3543	945	8	z	z	NOUN
ejpam-3543	945	9	∈	∈	PROPN
ejpam-3543	945	10	x	x	AUX
ejpam-3543	945	11	be	be	AUX
ejpam-3543	945	12	such	such	ADJ
ejpam-3543	945	13	that	that	SCONJ
ejpam-3543	945	14	x	x	PART
ejpam-3543	945	15	·	·	PUNCT
ejpam-3543	945	16	(	(	PUNCT
ejpam-3543	945	17	y	y	PROPN
ejpam-3543	945	18	·	·	PUNCT
ejpam-3543	945	19	z	z	X
ejpam-3543	945	20	)	)	PUNCT
ejpam-3543	945	21	∈	∈	PROPN
ejpam-3543	945	22	u(λt	u(λt	NOUN
ejpam-3543	945	23	;	;	PUNCT
ejpam-3543	945	24	α	α	X
ejpam-3543	945	25	)	)	PUNCT
ejpam-3543	945	26	and	and	CCONJ
ejpam-3543	945	27	y	y	PROPN
ejpam-3543	945	28	∈	∈	PROPN
ejpam-3543	945	29	u(λt	u(λt	PROPN
ejpam-3543	945	30	;	;	PUNCT
ejpam-3543	945	31	α	α	X
ejpam-3543	945	32	)	)	PUNCT
ejpam-3543	945	33	.	.	PUNCT
ejpam-3543	946	1	then	then	ADV
ejpam-3543	946	2	λt	λt	INTJ
ejpam-3543	946	3	(	(	PUNCT
ejpam-3543	946	4	x	x	X
ejpam-3543	946	5	·	·	PUNCT
ejpam-3543	946	6	(	(	PUNCT
ejpam-3543	946	7	y	y	PROPN
ejpam-3543	946	8	·	·	PUNCT
ejpam-3543	946	9	z	z	NOUN
ejpam-3543	946	10	)	)	PUNCT
ejpam-3543	946	11	)	)	PUNCT
ejpam-3543	946	12	≥	≥	PROPN
ejpam-3543	946	13	α	α	NOUN
ejpam-3543	946	14	and	and	CCONJ
ejpam-3543	946	15	λt	λt	X
ejpam-3543	946	16	(	(	PUNCT
ejpam-3543	946	17	y	y	NOUN
ejpam-3543	946	18	)	)	PUNCT
ejpam-3543	946	19	≥	≥	NOUN
ejpam-3543	946	20	α	α	NOUN
ejpam-3543	946	21	,	,	PUNCT
ejpam-3543	946	22	so	so	ADV
ejpam-3543	946	23	α	α	PRON
ejpam-3543	946	24	is	be	AUX
ejpam-3543	946	25	an	an	DET
ejpam-3543	946	26	lower	low	ADJ
ejpam-3543	946	27	bound	bind	VERB
ejpam-3543	946	28	of	of	ADP
ejpam-3543	946	29	{	{	PUNCT
ejpam-3543	946	30	λt	λt	X
ejpam-3543	946	31	(	(	PUNCT
ejpam-3543	946	32	x	x	X
ejpam-3543	946	33	·	·	PUNCT
ejpam-3543	946	34	(	(	PUNCT
ejpam-3543	946	35	y	y	PROPN
ejpam-3543	946	36	·	·	PUNCT
ejpam-3543	946	37	z	z	NOUN
ejpam-3543	946	38	)	)	PUNCT
ejpam-3543	946	39	)	)	PUNCT
ejpam-3543	946	40	,	,	PUNCT
ejpam-3543	946	41	λt	λt	X
ejpam-3543	946	42	(	(	PUNCT
ejpam-3543	946	43	y	y	NOUN
ejpam-3543	946	44	)	)	PUNCT
ejpam-3543	946	45	}	}	PUNCT
ejpam-3543	946	46	.	.	PUNCT
ejpam-3543	947	1	by	by	ADP
ejpam-3543	947	2	(	(	PUNCT
ejpam-3543	947	3	3.15	3.15	NUM
ejpam-3543	947	4	)	)	PUNCT
ejpam-3543	947	5	,	,	PUNCT
ejpam-3543	947	6	we	we	PRON
ejpam-3543	947	7	have	have	VERB
ejpam-3543	947	8	λt	λt	INTJ
ejpam-3543	947	9	(	(	PUNCT
ejpam-3543	947	10	x	x	X
ejpam-3543	947	11	·	·	PUNCT
ejpam-3543	947	12	z	z	X
ejpam-3543	947	13	)	)	PUNCT
ejpam-3543	947	14	≥	≥	NOUN
ejpam-3543	947	15	min{λt	min{λt	X
ejpam-3543	947	16	(	(	PUNCT
ejpam-3543	947	17	x	x	X
ejpam-3543	947	18	·	·	PUNCT
ejpam-3543	947	19	(	(	PUNCT
ejpam-3543	947	20	y	y	PROPN
ejpam-3543	947	21	·	·	PUNCT
ejpam-3543	947	22	z	z	NOUN
ejpam-3543	947	23	)	)	PUNCT
ejpam-3543	947	24	)	)	PUNCT
ejpam-3543	947	25	,	,	PUNCT
ejpam-3543	947	26	λt	λt	X
ejpam-3543	947	27	(	(	PUNCT
ejpam-3543	947	28	y	y	NOUN
ejpam-3543	947	29	)	)	PUNCT
ejpam-3543	947	30	}	}	PUNCT
ejpam-3543	947	31	≥	≥	NUM
ejpam-3543	948	1	α	α	NOUN
ejpam-3543	948	2	.	.	PUNCT
ejpam-3543	949	1	thus	thus	ADV
ejpam-3543	949	2	x	x	X
ejpam-3543	949	3	·	·	PUNCT
ejpam-3543	949	4	z	z	X
ejpam-3543	949	5	∈	∈	PROPN
ejpam-3543	949	6	u(λt	u(λt	NOUN
ejpam-3543	949	7	;	;	PUNCT
ejpam-3543	949	8	α	α	X
ejpam-3543	949	9	)	)	PUNCT
ejpam-3543	949	10	.	.	PUNCT
ejpam-3543	950	1	m.	m.	PROPN
ejpam-3543	950	2	songsaeng	songsaeng	PROPN
ejpam-3543	950	3	,	,	PUNCT
ejpam-3543	950	4	a.	a.	NOUN
ejpam-3543	950	5	iampan	iampan	PROPN
ejpam-3543	950	6	/	/	SYM
ejpam-3543	950	7	eur	eur	PROPN
ejpam-3543	950	8	.	.	PUNCT
ejpam-3543	951	1	j.	j.	PROPN
ejpam-3543	951	2	pure	pure	PROPN
ejpam-3543	951	3	appl	appl	PROPN
ejpam-3543	951	4	.	.	PROPN
ejpam-3543	951	5	math	math	PROPN
ejpam-3543	951	6	,	,	PUNCT
ejpam-3543	951	7	12	12	NUM
ejpam-3543	951	8	(	(	PUNCT
ejpam-3543	951	9	4	4	NUM
ejpam-3543	951	10	)	)	PUNCT
ejpam-3543	951	11	(	(	PUNCT
ejpam-3543	951	12	2019	2019	NUM
ejpam-3543	951	13	)	)	PUNCT
ejpam-3543	951	14	,	,	PUNCT
ejpam-3543	951	15	1382	1382	NUM
ejpam-3543	951	16	-	-	SYM
ejpam-3543	951	17	1409	1409	NUM
ejpam-3543	951	18	1405	1405	NUM
ejpam-3543	951	19	let	let	VERB
ejpam-3543	951	20	x	x	SYM
ejpam-3543	951	21	∈	∈	NOUN
ejpam-3543	951	22	l(λi	l(λi	NOUN
ejpam-3543	951	23	;	;	PUNCT
ejpam-3543	951	24	α	α	X
ejpam-3543	951	25	)	)	PUNCT
ejpam-3543	951	26	.	.	PUNCT
ejpam-3543	952	1	then	then	ADV
ejpam-3543	952	2	λi(x	λi(x	NUM
ejpam-3543	952	3	)	)	PUNCT
ejpam-3543	952	4	≤	≤	NOUN
ejpam-3543	953	1	β	β	X
ejpam-3543	953	2	.	.	PUNCT
ejpam-3543	954	1	by	by	ADP
ejpam-3543	954	2	(	(	PUNCT
ejpam-3543	954	3	3.7	3.7	NUM
ejpam-3543	954	4	)	)	PUNCT
ejpam-3543	954	5	,	,	PUNCT
ejpam-3543	954	6	we	we	PRON
ejpam-3543	954	7	have	have	VERB
ejpam-3543	954	8	λi(0	λi(0	NOUN
ejpam-3543	954	9	)	)	PUNCT
ejpam-3543	954	10	≤	≤	NOUN
ejpam-3543	954	11	λi(x	λi(x	NUM
ejpam-3543	954	12	)	)	PUNCT
ejpam-3543	954	13	≤	≤	NOUN
ejpam-3543	954	14	β	β	X
ejpam-3543	954	15	.	.	PUNCT
ejpam-3543	955	1	thus	thus	ADV
ejpam-3543	955	2	0	0	NUM
ejpam-3543	955	3	∈	∈	NOUN
ejpam-3543	955	4	l(λi	l(λi	NOUN
ejpam-3543	955	5	;	;	PUNCT
ejpam-3543	955	6	β	β	X
ejpam-3543	955	7	)	)	PUNCT
ejpam-3543	955	8	.	.	PUNCT
ejpam-3543	956	1	next	next	ADV
ejpam-3543	956	2	,	,	PUNCT
ejpam-3543	956	3	let	let	VERB
ejpam-3543	956	4	x	x	PRON
ejpam-3543	956	5	,	,	PUNCT
ejpam-3543	956	6	y	y	PROPN
ejpam-3543	956	7	,	,	PUNCT
ejpam-3543	956	8	z	z	NOUN
ejpam-3543	956	9	∈	∈	PROPN
ejpam-3543	956	10	x	x	AUX
ejpam-3543	956	11	be	be	AUX
ejpam-3543	956	12	such	such	ADJ
ejpam-3543	956	13	that	that	SCONJ
ejpam-3543	956	14	x	x	PART
ejpam-3543	956	15	·	·	PUNCT
ejpam-3543	956	16	(	(	PUNCT
ejpam-3543	956	17	y	y	PROPN
ejpam-3543	956	18	·	·	PUNCT
ejpam-3543	956	19	z	z	X
ejpam-3543	956	20	)	)	PUNCT
ejpam-3543	956	21	∈	∈	PROPN
ejpam-3543	956	22	l(λi	l(λi	NOUN
ejpam-3543	956	23	;	;	PUNCT
ejpam-3543	956	24	β	β	X
ejpam-3543	956	25	)	)	PUNCT
ejpam-3543	956	26	and	and	CCONJ
ejpam-3543	956	27	y	y	PROPN
ejpam-3543	956	28	∈	∈	PROPN
ejpam-3543	956	29	l(λi	l(λi	X
ejpam-3543	956	30	;	;	PUNCT
ejpam-3543	956	31	β	β	X
ejpam-3543	956	32	)	)	PUNCT
ejpam-3543	956	33	.	.	PUNCT
ejpam-3543	957	1	then	then	ADV
ejpam-3543	957	2	λi(x	λi(x	X
ejpam-3543	957	3	·	·	PUNCT
ejpam-3543	957	4	(	(	PUNCT
ejpam-3543	957	5	y	y	PROPN
ejpam-3543	957	6	·	·	PUNCT
ejpam-3543	957	7	z	z	NOUN
ejpam-3543	957	8	)	)	PUNCT
ejpam-3543	957	9	)	)	PUNCT
ejpam-3543	957	10	≤	≤	NUM
ejpam-3543	957	11	β	β	X
ejpam-3543	957	12	and	and	CCONJ
ejpam-3543	957	13	λi(y	λi(y	NUM
ejpam-3543	957	14	)	)	PUNCT
ejpam-3543	957	15	≤	≤	NOUN
ejpam-3543	957	16	β	β	NOUN
ejpam-3543	957	17	,	,	PUNCT
ejpam-3543	957	18	so	so	SCONJ
ejpam-3543	957	19	β	β	X
ejpam-3543	957	20	is	be	AUX
ejpam-3543	957	21	a	a	DET
ejpam-3543	957	22	upper	upper	ADJ
ejpam-3543	957	23	bound	bind	VERB
ejpam-3543	957	24	of	of	ADP
ejpam-3543	957	25	{	{	PUNCT
ejpam-3543	957	26	λi(x	λi(x	X
ejpam-3543	957	27	·	·	PUNCT
ejpam-3543	957	28	(	(	PUNCT
ejpam-3543	957	29	y	y	PROPN
ejpam-3543	957	30	·	·	PUNCT
ejpam-3543	957	31	z	z	NOUN
ejpam-3543	957	32	)	)	PUNCT
ejpam-3543	957	33	)	)	PUNCT
ejpam-3543	957	34	,	,	PUNCT
ejpam-3543	957	35	λi(y	λi(y	NOUN
ejpam-3543	957	36	)	)	PUNCT
ejpam-3543	957	37	}	}	PUNCT
ejpam-3543	957	38	.	.	PUNCT
ejpam-3543	958	1	by	by	ADP
ejpam-3543	958	2	(	(	PUNCT
ejpam-3543	958	3	3.16	3.16	NUM
ejpam-3543	958	4	)	)	PUNCT
ejpam-3543	958	5	,	,	PUNCT
ejpam-3543	958	6	we	we	PRON
ejpam-3543	958	7	have	have	VERB
ejpam-3543	958	8	λi(x	λi(x	NUM
ejpam-3543	958	9	·	·	PUNCT
ejpam-3543	958	10	z	z	X
ejpam-3543	958	11	)	)	PUNCT
ejpam-3543	958	12	≤	≤	NUM
ejpam-3543	958	13	max{λi(x	max{λi(x	NOUN
ejpam-3543	958	14	·	·	PUNCT
ejpam-3543	958	15	(	(	PUNCT
ejpam-3543	958	16	y	y	PROPN
ejpam-3543	958	17	·	·	PUNCT
ejpam-3543	958	18	z	z	NOUN
ejpam-3543	958	19	)	)	PUNCT
ejpam-3543	958	20	)	)	PUNCT
ejpam-3543	958	21	,	,	PUNCT
ejpam-3543	958	22	λi(y	λi(y	NOUN
ejpam-3543	958	23	)	)	PUNCT
ejpam-3543	958	24	}	}	PUNCT
ejpam-3543	958	25	≤	≤	NOUN
ejpam-3543	958	26	β	β	X
ejpam-3543	958	27	.	.	PUNCT
ejpam-3543	959	1	thus	thus	ADV
ejpam-3543	959	2	x	x	X
ejpam-3543	959	3	·	·	PUNCT
ejpam-3543	959	4	z	z	X
ejpam-3543	959	5	∈	∈	PROPN
ejpam-3543	959	6	l(λi	l(λi	NOUN
ejpam-3543	959	7	;	;	PUNCT
ejpam-3543	959	8	β	β	X
ejpam-3543	959	9	)	)	PUNCT
ejpam-3543	959	10	.	.	PUNCT
ejpam-3543	960	1	let	let	VERB
ejpam-3543	960	2	x	x	PUNCT
ejpam-3543	960	3	∈	∈	PROPN
ejpam-3543	960	4	u(λf	u(λf	NOUN
ejpam-3543	960	5	;	;	PUNCT
ejpam-3543	960	6	γ	γ	X
ejpam-3543	960	7	)	)	PUNCT
ejpam-3543	960	8	.	.	PUNCT
ejpam-3543	961	1	then	then	ADV
ejpam-3543	961	2	λf	λf	INTJ
ejpam-3543	961	3	(	(	PUNCT
ejpam-3543	961	4	x	x	NOUN
ejpam-3543	961	5	)	)	PUNCT
ejpam-3543	961	6	≥	≥	PROPN
ejpam-3543	961	7	γ	γ	PROPN
ejpam-3543	961	8	.	.	PUNCT
ejpam-3543	961	9	by	by	ADP
ejpam-3543	961	10	(	(	PUNCT
ejpam-3543	961	11	3.8	3.8	NUM
ejpam-3543	961	12	)	)	PUNCT
ejpam-3543	961	13	,	,	PUNCT
ejpam-3543	961	14	we	we	PRON
ejpam-3543	961	15	have	have	VERB
ejpam-3543	961	16	λf	λf	VERB
ejpam-3543	961	17	(	(	PUNCT
ejpam-3543	961	18	0	0	NUM
ejpam-3543	961	19	)	)	PUNCT
ejpam-3543	961	20	≥	≥	NOUN
ejpam-3543	962	1	λf	λf	X
ejpam-3543	962	2	(	(	PUNCT
ejpam-3543	962	3	x	x	NOUN
ejpam-3543	962	4	)	)	PUNCT
ejpam-3543	962	5	≥	≥	PROPN
ejpam-3543	962	6	γ	γ	X
ejpam-3543	962	7	.	.	PUNCT
ejpam-3543	963	1	thus	thus	ADV
ejpam-3543	963	2	0	0	NUM
ejpam-3543	963	3	∈	∈	PROPN
ejpam-3543	963	4	u(λf	u(λf	NOUN
ejpam-3543	963	5	;	;	PUNCT
ejpam-3543	963	6	γ	γ	X
ejpam-3543	963	7	)	)	PUNCT
ejpam-3543	963	8	.	.	PUNCT
ejpam-3543	964	1	next	next	ADV
ejpam-3543	964	2	,	,	PUNCT
ejpam-3543	964	3	let	let	VERB
ejpam-3543	964	4	x	x	PRON
ejpam-3543	964	5	,	,	PUNCT
ejpam-3543	964	6	y	y	PROPN
ejpam-3543	964	7	,	,	PUNCT
ejpam-3543	964	8	z	z	NOUN
ejpam-3543	964	9	∈	∈	PROPN
ejpam-3543	964	10	x	x	AUX
ejpam-3543	964	11	be	be	AUX
ejpam-3543	964	12	such	such	ADJ
ejpam-3543	964	13	that	that	SCONJ
ejpam-3543	964	14	x	x	PART
ejpam-3543	964	15	·	·	PUNCT
ejpam-3543	964	16	(	(	PUNCT
ejpam-3543	964	17	y	y	PROPN
ejpam-3543	964	18	·	·	PUNCT
ejpam-3543	964	19	z	z	X
ejpam-3543	964	20	)	)	PUNCT
ejpam-3543	964	21	∈	∈	PROPN
ejpam-3543	964	22	u(λf	u(λf	NOUN
ejpam-3543	964	23	;	;	PUNCT
ejpam-3543	964	24	γ	γ	X
ejpam-3543	964	25	)	)	PUNCT
ejpam-3543	964	26	and	and	CCONJ
ejpam-3543	964	27	y	y	PROPN
ejpam-3543	964	28	∈	∈	PROPN
ejpam-3543	964	29	u(λf	u(λf	ADV
ejpam-3543	964	30	;	;	PUNCT
ejpam-3543	964	31	γ	γ	X
ejpam-3543	964	32	)	)	PUNCT
ejpam-3543	964	33	.	.	PUNCT
ejpam-3543	965	1	then	then	ADV
ejpam-3543	965	2	λf	λf	INTJ
ejpam-3543	965	3	(	(	PUNCT
ejpam-3543	965	4	x	x	PART
ejpam-3543	965	5	·	·	PUNCT
ejpam-3543	965	6	(	(	PUNCT
ejpam-3543	965	7	y	y	PROPN
ejpam-3543	965	8	·	·	PUNCT
ejpam-3543	965	9	z	z	NOUN
ejpam-3543	965	10	)	)	PUNCT
ejpam-3543	965	11	)	)	PUNCT
ejpam-3543	965	12	≥	≥	PROPN
ejpam-3543	965	13	γ	γ	X
ejpam-3543	965	14	and	and	CCONJ
ejpam-3543	965	15	λf	λf	PROPN
ejpam-3543	965	16	(	(	PUNCT
ejpam-3543	965	17	y	y	PROPN
ejpam-3543	965	18	)	)	PUNCT
ejpam-3543	965	19	≥	≥	PROPN
ejpam-3543	965	20	γ	γ	PROPN
ejpam-3543	965	21	,	,	PUNCT
ejpam-3543	965	22	so	so	ADV
ejpam-3543	965	23	γ	γ	NOUN
ejpam-3543	965	24	is	be	AUX
ejpam-3543	965	25	an	an	DET
ejpam-3543	965	26	lower	low	ADJ
ejpam-3543	965	27	bound	bind	VERB
ejpam-3543	965	28	of	of	ADP
ejpam-3543	965	29	{	{	PUNCT
ejpam-3543	965	30	λf	λf	PROPN
ejpam-3543	965	31	(	(	PUNCT
ejpam-3543	965	32	x	x	PART
ejpam-3543	965	33	·	·	PUNCT
ejpam-3543	965	34	(	(	PUNCT
ejpam-3543	965	35	y	y	PROPN
ejpam-3543	965	36	·	·	PUNCT
ejpam-3543	965	37	z	z	NOUN
ejpam-3543	965	38	)	)	PUNCT
ejpam-3543	965	39	)	)	PUNCT
ejpam-3543	965	40	,	,	PUNCT
ejpam-3543	965	41	λf	λf	X
ejpam-3543	965	42	(	(	PUNCT
ejpam-3543	965	43	y	y	NOUN
ejpam-3543	965	44	)	)	PUNCT
ejpam-3543	965	45	}	}	PUNCT
ejpam-3543	965	46	.	.	PUNCT
ejpam-3543	966	1	by	by	ADP
ejpam-3543	966	2	(	(	PUNCT
ejpam-3543	966	3	3.17	3.17	NUM
ejpam-3543	966	4	)	)	PUNCT
ejpam-3543	966	5	,	,	PUNCT
ejpam-3543	966	6	we	we	PRON
ejpam-3543	966	7	have	have	VERB
ejpam-3543	966	8	λf	λf	INTJ
ejpam-3543	966	9	(	(	PUNCT
ejpam-3543	966	10	x	x	SYM
ejpam-3543	966	11	·	·	PUNCT
ejpam-3543	966	12	z	z	X
ejpam-3543	966	13	)	)	PUNCT
ejpam-3543	966	14	≥	≥	NOUN
ejpam-3543	966	15	min{λf	min{λf	X
ejpam-3543	967	1	(	(	PUNCT
ejpam-3543	967	2	x	x	PART
ejpam-3543	967	3	·	·	PUNCT
ejpam-3543	967	4	(	(	PUNCT
ejpam-3543	967	5	y	y	PROPN
ejpam-3543	967	6	·	·	PUNCT
ejpam-3543	967	7	z	z	NOUN
ejpam-3543	967	8	)	)	PUNCT
ejpam-3543	967	9	)	)	PUNCT
ejpam-3543	967	10	,	,	PUNCT
ejpam-3543	967	11	λf	λf	X
ejpam-3543	967	12	(	(	PUNCT
ejpam-3543	967	13	y	y	NOUN
ejpam-3543	967	14	)	)	PUNCT
ejpam-3543	967	15	}	}	PUNCT
ejpam-3543	967	16	≥	≥	PROPN
ejpam-3543	967	17	γ	γ	X
ejpam-3543	967	18	.	.	PUNCT
ejpam-3543	967	19	thus	thus	ADV
ejpam-3543	967	20	x	x	X
ejpam-3543	967	21	·	·	PUNCT
ejpam-3543	967	22	z	z	X
ejpam-3543	967	23	∈	∈	PROPN
ejpam-3543	967	24	u(λf	u(λf	NOUN
ejpam-3543	967	25	;	;	PUNCT
ejpam-3543	967	26	γ	γ	X
ejpam-3543	967	27	)	)	PUNCT
ejpam-3543	967	28	.	.	PUNCT
ejpam-3543	968	1	hence	hence	ADV
ejpam-3543	968	2	,	,	PUNCT
ejpam-3543	968	3	u(λt	u(λt	PROPN
ejpam-3543	968	4	;	;	PUNCT
ejpam-3543	968	5	α	α	X
ejpam-3543	968	6	)	)	PUNCT
ejpam-3543	968	7	,	,	PUNCT
ejpam-3543	968	8	l(λi	l(λi	PROPN
ejpam-3543	968	9	;	;	PUNCT
ejpam-3543	968	10	β	β	X
ejpam-3543	968	11	)	)	PUNCT
ejpam-3543	968	12	,	,	PUNCT
ejpam-3543	968	13	and	and	CCONJ
ejpam-3543	968	14	u(λf	u(λf	ADV
ejpam-3543	968	15	;	;	PUNCT
ejpam-3543	968	16	γ	γ	X
ejpam-3543	968	17	)	)	PUNCT
ejpam-3543	968	18	are	be	AUX
ejpam-3543	968	19	up	up	ADP
ejpam-3543	968	20	-	-	PUNCT
ejpam-3543	968	21	ideals	ideal	NOUN
ejpam-3543	968	22	of	of	ADP
ejpam-3543	968	23	x.	x.	NOUN
ejpam-3543	968	24	conversely	conversely	ADV
ejpam-3543	968	25	,	,	PUNCT
ejpam-3543	968	26	assume	assume	VERB
ejpam-3543	968	27	that	that	SCONJ
ejpam-3543	968	28	for	for	ADP
ejpam-3543	968	29	all	all	DET
ejpam-3543	968	30	α	α	NOUN
ejpam-3543	968	31	,	,	PUNCT
ejpam-3543	968	32	β	β	X
ejpam-3543	968	33	,	,	PUNCT
ejpam-3543	968	34	γ	γ	PROPN
ejpam-3543	968	35	∈	∈	PROPN
ejpam-3543	969	1	[	[	X
ejpam-3543	969	2	0	0	NUM
ejpam-3543	969	3	,	,	PUNCT
ejpam-3543	969	4	1	1	NUM
ejpam-3543	969	5	]	]	PUNCT
ejpam-3543	969	6	,	,	PUNCT
ejpam-3543	969	7	the	the	PRON
ejpam-3543	969	8	sets	set	NOUN
ejpam-3543	969	9	u(λt	u(λt	NOUN
ejpam-3543	969	10	;	;	PUNCT
ejpam-3543	969	11	α	α	X
ejpam-3543	969	12	)	)	PUNCT
ejpam-3543	969	13	,	,	PUNCT
ejpam-3543	969	14	l(λi	l(λi	PROPN
ejpam-3543	969	15	;	;	PUNCT
ejpam-3543	969	16	β	β	X
ejpam-3543	969	17	)	)	PUNCT
ejpam-3543	969	18	,	,	PUNCT
ejpam-3543	969	19	and	and	CCONJ
ejpam-3543	969	20	u(λf	u(λf	ADV
ejpam-3543	969	21	;	;	PUNCT
ejpam-3543	969	22	γ	γ	X
ejpam-3543	969	23	)	)	PUNCT
ejpam-3543	969	24	are	be	AUX
ejpam-3543	969	25	up	up	ADP
ejpam-3543	969	26	-	-	PUNCT
ejpam-3543	969	27	ideals	ideal	NOUN
ejpam-3543	969	28	of	of	ADP
ejpam-3543	969	29	x	x	SYM
ejpam-3543	969	30	if	if	SCONJ
ejpam-3543	969	31	u(λt	u(λt	NOUN
ejpam-3543	969	32	;	;	PUNCT
ejpam-3543	969	33	α	α	X
ejpam-3543	969	34	)	)	PUNCT
ejpam-3543	969	35	,	,	PUNCT
ejpam-3543	969	36	l(λi	l(λi	PROPN
ejpam-3543	969	37	;	;	PUNCT
ejpam-3543	969	38	β	β	X
ejpam-3543	969	39	)	)	PUNCT
ejpam-3543	969	40	,	,	PUNCT
ejpam-3543	969	41	and	and	CCONJ
ejpam-3543	969	42	u(λf	u(λf	ADV
ejpam-3543	969	43	;	;	PUNCT
ejpam-3543	969	44	γ	γ	X
ejpam-3543	969	45	)	)	PUNCT
ejpam-3543	969	46	are	be	AUX
ejpam-3543	969	47	nonempty	nonempty	ADJ
ejpam-3543	969	48	.	.	PUNCT
ejpam-3543	970	1	let	let	VERB
ejpam-3543	970	2	x	x	SYM
ejpam-3543	970	3	∈	∈	PROPN
ejpam-3543	970	4	x.	x.	NOUN
ejpam-3543	970	5	then	then	ADV
ejpam-3543	970	6	λt	λt	INTJ
ejpam-3543	970	7	(	(	PUNCT
ejpam-3543	970	8	x	x	X
ejpam-3543	970	9	)	)	PUNCT
ejpam-3543	970	10	∈	∈	PROPN
ejpam-3543	971	1	[	[	X
ejpam-3543	971	2	0	0	NUM
ejpam-3543	971	3	,	,	PUNCT
ejpam-3543	971	4	1	1	NUM
ejpam-3543	971	5	]	]	PUNCT
ejpam-3543	971	6	.	.	PUNCT
ejpam-3543	972	1	choose	choose	VERB
ejpam-3543	972	2	α	α	X
ejpam-3543	972	3	=	=	PUNCT
ejpam-3543	972	4	λt	λt	X
ejpam-3543	972	5	(	(	PUNCT
ejpam-3543	972	6	x	x	NOUN
ejpam-3543	972	7	)	)	PUNCT
ejpam-3543	972	8	.	.	PUNCT
ejpam-3543	973	1	thus	thus	ADV
ejpam-3543	973	2	λt	λt	X
ejpam-3543	973	3	(	(	PUNCT
ejpam-3543	973	4	x	x	NOUN
ejpam-3543	973	5	)	)	PUNCT
ejpam-3543	973	6	≥	≥	NUM
ejpam-3543	973	7	α	α	NOUN
ejpam-3543	973	8	,	,	PUNCT
ejpam-3543	973	9	so	so	ADV
ejpam-3543	973	10	x	x	SYM
ejpam-3543	973	11	∈	∈	NOUN
ejpam-3543	973	12	u(λt	u(λt	NOUN
ejpam-3543	973	13	;	;	PUNCT
ejpam-3543	973	14	α	α	X
ejpam-3543	973	15	)	)	PUNCT
ejpam-3543	973	16	6=	6=	ADP
ejpam-3543	973	17	∅.	∅.	ADP
ejpam-3543	973	18	by	by	ADP
ejpam-3543	973	19	assumption	assumption	NOUN
ejpam-3543	973	20	,	,	PUNCT
ejpam-3543	973	21	we	we	PRON
ejpam-3543	973	22	have	have	VERB
ejpam-3543	973	23	u(λt	u(λt	NOUN
ejpam-3543	973	24	;	;	PUNCT
ejpam-3543	973	25	α	α	X
ejpam-3543	973	26	)	)	PUNCT
ejpam-3543	973	27	is	be	AUX
ejpam-3543	973	28	a	a	DET
ejpam-3543	973	29	up	up	ADJ
ejpam-3543	973	30	-	-	PUNCT
ejpam-3543	973	31	ideal	ideal	NOUN
ejpam-3543	973	32	of	of	ADP
ejpam-3543	973	33	x	x	X
ejpam-3543	973	34	and	and	CCONJ
ejpam-3543	973	35	so	so	ADV
ejpam-3543	973	36	0	0	NUM
ejpam-3543	973	37	∈	∈	PROPN
ejpam-3543	973	38	u(λt	u(λt	NOUN
ejpam-3543	973	39	;	;	PUNCT
ejpam-3543	973	40	α	α	X
ejpam-3543	973	41	)	)	PUNCT
ejpam-3543	973	42	.	.	PUNCT
ejpam-3543	974	1	thus	thus	ADV
ejpam-3543	974	2	λt	λt	X
ejpam-3543	974	3	(	(	PUNCT
ejpam-3543	974	4	0	0	NUM
ejpam-3543	974	5	)	)	PUNCT
ejpam-3543	974	6	≥	≥	NOUN
ejpam-3543	974	7	α	α	X
ejpam-3543	974	8	=	=	PUNCT
ejpam-3543	974	9	λt	λt	X
ejpam-3543	974	10	(	(	PUNCT
ejpam-3543	974	11	x	x	NOUN
ejpam-3543	974	12	)	)	PUNCT
ejpam-3543	974	13	.	.	PUNCT
ejpam-3543	975	1	next	next	ADV
ejpam-3543	975	2	,	,	PUNCT
ejpam-3543	975	3	let	let	VERB
ejpam-3543	975	4	x	x	PRON
ejpam-3543	975	5	,	,	PUNCT
ejpam-3543	975	6	y	y	PROPN
ejpam-3543	975	7	,	,	PUNCT
ejpam-3543	975	8	z	z	PROPN
ejpam-3543	975	9	∈	∈	PROPN
ejpam-3543	975	10	x.	x.	NOUN
ejpam-3543	975	11	then	then	ADV
ejpam-3543	975	12	λt	λt	X
ejpam-3543	975	13	(	(	PUNCT
ejpam-3543	975	14	x	x	X
ejpam-3543	975	15	·	·	PUNCT
ejpam-3543	975	16	(	(	PUNCT
ejpam-3543	975	17	y	y	PROPN
ejpam-3543	975	18	·	·	PUNCT
ejpam-3543	975	19	z	z	NOUN
ejpam-3543	975	20	)	)	PUNCT
ejpam-3543	975	21	)	)	PUNCT
ejpam-3543	975	22	,	,	PUNCT
ejpam-3543	975	23	λt	λt	X
ejpam-3543	975	24	(	(	PUNCT
ejpam-3543	975	25	y	y	NOUN
ejpam-3543	975	26	)	)	PUNCT
ejpam-3543	975	27	∈	∈	PROPN
ejpam-3543	976	1	[	[	X
ejpam-3543	976	2	0	0	NUM
ejpam-3543	976	3	,	,	PUNCT
ejpam-3543	976	4	1	1	NUM
ejpam-3543	976	5	]	]	PUNCT
ejpam-3543	976	6	.	.	PUNCT
ejpam-3543	977	1	choose	choose	VERB
ejpam-3543	977	2	α	α	X
ejpam-3543	977	3	=	=	PUNCT
ejpam-3543	977	4	min{λt	min{λt	X
ejpam-3543	977	5	(	(	PUNCT
ejpam-3543	977	6	x	x	X
ejpam-3543	977	7	·	·	PUNCT
ejpam-3543	977	8	(	(	PUNCT
ejpam-3543	977	9	y	y	PROPN
ejpam-3543	977	10	·	·	PUNCT
ejpam-3543	977	11	z	z	NOUN
ejpam-3543	977	12	)	)	PUNCT
ejpam-3543	977	13	)	)	PUNCT
ejpam-3543	977	14	,	,	PUNCT
ejpam-3543	977	15	λt	λt	X
ejpam-3543	977	16	(	(	PUNCT
ejpam-3543	977	17	y	y	NOUN
ejpam-3543	977	18	)	)	PUNCT
ejpam-3543	977	19	}	}	PUNCT
ejpam-3543	977	20	.	.	PUNCT
ejpam-3543	978	1	thus	thus	ADV
ejpam-3543	978	2	λt	λt	X
ejpam-3543	978	3	(	(	PUNCT
ejpam-3543	978	4	x	x	X
ejpam-3543	978	5	·	·	PUNCT
ejpam-3543	978	6	(	(	PUNCT
ejpam-3543	978	7	y	y	PROPN
ejpam-3543	978	8	·	·	PUNCT
ejpam-3543	978	9	z	z	NOUN
ejpam-3543	978	10	)	)	PUNCT
ejpam-3543	978	11	)	)	PUNCT
ejpam-3543	978	12	≥	≥	PROPN
ejpam-3543	978	13	α	α	NOUN
ejpam-3543	978	14	and	and	CCONJ
ejpam-3543	978	15	λt	λt	X
ejpam-3543	978	16	(	(	PUNCT
ejpam-3543	978	17	y	y	NOUN
ejpam-3543	978	18	)	)	PUNCT
ejpam-3543	978	19	≥	≥	NOUN
ejpam-3543	978	20	α	α	NOUN
ejpam-3543	978	21	,	,	PUNCT
ejpam-3543	978	22	so	so	ADV
ejpam-3543	978	23	x	x	X
ejpam-3543	978	24	·	·	PUNCT
ejpam-3543	978	25	(	(	PUNCT
ejpam-3543	978	26	y	y	PROPN
ejpam-3543	978	27	·	·	PUNCT
ejpam-3543	978	28	z	z	X
ejpam-3543	978	29	)	)	PUNCT
ejpam-3543	978	30	,	,	PUNCT
ejpam-3543	978	31	y	y	PROPN
ejpam-3543	978	32	∈	∈	PROPN
ejpam-3543	978	33	u(λt	u(λt	PROPN
ejpam-3543	978	34	;	;	PUNCT
ejpam-3543	978	35	α	α	X
ejpam-3543	978	36	)	)	PUNCT
ejpam-3543	978	37	6=	6=	ADP
ejpam-3543	978	38	∅.	∅.	ADP
ejpam-3543	978	39	by	by	ADP
ejpam-3543	978	40	assumption	assumption	NOUN
ejpam-3543	978	41	,	,	PUNCT
ejpam-3543	978	42	we	we	PRON
ejpam-3543	978	43	have	have	VERB
ejpam-3543	978	44	u(λt	u(λt	NOUN
ejpam-3543	978	45	;	;	PUNCT
ejpam-3543	978	46	α	α	X
ejpam-3543	978	47	)	)	PUNCT
ejpam-3543	978	48	is	be	AUX
ejpam-3543	978	49	a	a	DET
ejpam-3543	978	50	up	up	ADJ
ejpam-3543	978	51	-	-	PUNCT
ejpam-3543	978	52	ideal	ideal	NOUN
ejpam-3543	978	53	of	of	ADP
ejpam-3543	978	54	x	x	PUNCT
ejpam-3543	978	55	and	and	CCONJ
ejpam-3543	978	56	so	so	ADV
ejpam-3543	978	57	x	x	X
ejpam-3543	978	58	·	·	PUNCT
ejpam-3543	978	59	z	z	SYM
ejpam-3543	978	60	∈	∈	PROPN
ejpam-3543	978	61	u(λt	u(λt	NOUN
ejpam-3543	978	62	;	;	PUNCT
ejpam-3543	978	63	α	α	X
ejpam-3543	978	64	)	)	PUNCT
ejpam-3543	978	65	.	.	PUNCT
ejpam-3543	979	1	thus	thus	ADV
ejpam-3543	979	2	λt	λt	X
ejpam-3543	979	3	(	(	PUNCT
ejpam-3543	979	4	x	x	X
ejpam-3543	979	5	·	·	PUNCT
ejpam-3543	979	6	z	z	X
ejpam-3543	979	7	)	)	PUNCT
ejpam-3543	979	8	≥	≥	NOUN
ejpam-3543	979	9	α	α	NOUN
ejpam-3543	979	10	=	=	PUNCT
ejpam-3543	979	11	min{λt	min{λt	X
ejpam-3543	979	12	(	(	PUNCT
ejpam-3543	979	13	x	x	X
ejpam-3543	979	14	·	·	PUNCT
ejpam-3543	979	15	(	(	PUNCT
ejpam-3543	979	16	y	y	PROPN
ejpam-3543	979	17	·	·	PUNCT
ejpam-3543	979	18	z	z	NOUN
ejpam-3543	979	19	)	)	PUNCT
ejpam-3543	979	20	)	)	PUNCT
ejpam-3543	979	21	,	,	PUNCT
ejpam-3543	979	22	λt	λt	X
ejpam-3543	979	23	(	(	PUNCT
ejpam-3543	979	24	y	y	NOUN
ejpam-3543	979	25	)	)	PUNCT
ejpam-3543	979	26	}	}	PUNCT
ejpam-3543	979	27	.	.	PUNCT
ejpam-3543	980	1	let	let	VERB
ejpam-3543	980	2	x	x	SYM
ejpam-3543	980	3	∈	∈	PROPN
ejpam-3543	980	4	x.	x.	NOUN
ejpam-3543	980	5	then	then	ADV
ejpam-3543	980	6	λi(x	λi(x	X
ejpam-3543	980	7	)	)	PUNCT
ejpam-3543	980	8	∈	∈	PROPN
ejpam-3543	981	1	[	[	X
ejpam-3543	981	2	0	0	NUM
ejpam-3543	981	3	,	,	PUNCT
ejpam-3543	981	4	1	1	NUM
ejpam-3543	981	5	]	]	PUNCT
ejpam-3543	981	6	.	.	PUNCT
ejpam-3543	982	1	choose	choose	VERB
ejpam-3543	982	2	β	β	X
ejpam-3543	982	3	=	=	SYM
ejpam-3543	982	4	λi(x	λi(x	NUM
ejpam-3543	982	5	)	)	PUNCT
ejpam-3543	982	6	.	.	PUNCT
ejpam-3543	983	1	thus	thus	ADV
ejpam-3543	983	2	λi(x	λi(x	NUM
ejpam-3543	983	3	)	)	PUNCT
ejpam-3543	983	4	≤	≤	NUM
ejpam-3543	984	1	β	β	NOUN
ejpam-3543	984	2	,	,	PUNCT
ejpam-3543	984	3	so	so	CCONJ
ejpam-3543	984	4	x	x	SYM
ejpam-3543	984	5	∈	∈	NOUN
ejpam-3543	984	6	l(λi	l(λi	NOUN
ejpam-3543	984	7	;	;	PUNCT
ejpam-3543	984	8	β	β	X
ejpam-3543	984	9	)	)	PUNCT
ejpam-3543	984	10	6=	6=	ADP
ejpam-3543	984	11	∅.	∅.	ADP
ejpam-3543	984	12	by	by	ADP
ejpam-3543	984	13	assumption	assumption	NOUN
ejpam-3543	984	14	,	,	PUNCT
ejpam-3543	984	15	we	we	PRON
ejpam-3543	984	16	have	have	VERB
ejpam-3543	984	17	l(λi	l(λi	NOUN
ejpam-3543	984	18	;	;	PUNCT
ejpam-3543	984	19	β	β	X
ejpam-3543	984	20	)	)	PUNCT
ejpam-3543	984	21	is	be	AUX
ejpam-3543	984	22	a	a	DET
ejpam-3543	984	23	up	up	ADJ
ejpam-3543	984	24	-	-	PUNCT
ejpam-3543	984	25	ideal	ideal	NOUN
ejpam-3543	984	26	of	of	ADP
ejpam-3543	984	27	x	x	X
ejpam-3543	984	28	and	and	CCONJ
ejpam-3543	984	29	so	so	ADV
ejpam-3543	984	30	0	0	NUM
ejpam-3543	984	31	∈	∈	NOUN
ejpam-3543	984	32	l(λi	l(λi	NOUN
ejpam-3543	984	33	;	;	PUNCT
ejpam-3543	984	34	β	β	X
ejpam-3543	984	35	)	)	PUNCT
ejpam-3543	984	36	.	.	PUNCT
ejpam-3543	985	1	thus	thus	ADV
ejpam-3543	985	2	λi(0	λi(0	X
ejpam-3543	985	3	)	)	PUNCT
ejpam-3543	985	4	≤	≤	NOUN
ejpam-3543	985	5	β	β	X
ejpam-3543	985	6	=	=	SYM
ejpam-3543	985	7	λi(x	λi(x	NUM
ejpam-3543	985	8	)	)	PUNCT
ejpam-3543	985	9	.	.	PUNCT
ejpam-3543	986	1	next	next	ADV
ejpam-3543	986	2	,	,	PUNCT
ejpam-3543	986	3	let	let	VERB
ejpam-3543	986	4	x	x	PRON
ejpam-3543	986	5	,	,	PUNCT
ejpam-3543	986	6	y	y	PROPN
ejpam-3543	986	7	,	,	PUNCT
ejpam-3543	986	8	z	z	PROPN
ejpam-3543	986	9	∈	∈	PROPN
ejpam-3543	986	10	x.	x.	NOUN
ejpam-3543	986	11	then	then	ADV
ejpam-3543	986	12	λi(x	λi(x	X
ejpam-3543	986	13	·	·	PUNCT
ejpam-3543	986	14	(	(	PUNCT
ejpam-3543	986	15	y	y	PROPN
ejpam-3543	986	16	·	·	PUNCT
ejpam-3543	986	17	z	z	NOUN
ejpam-3543	986	18	)	)	PUNCT
ejpam-3543	986	19	)	)	PUNCT
ejpam-3543	986	20	,	,	PUNCT
ejpam-3543	986	21	λi(y	λi(y	X
ejpam-3543	986	22	)	)	PUNCT
ejpam-3543	986	23	∈	∈	PROPN
ejpam-3543	987	1	[	[	X
ejpam-3543	987	2	0	0	NUM
ejpam-3543	987	3	,	,	PUNCT
ejpam-3543	987	4	1	1	NUM
ejpam-3543	987	5	]	]	PUNCT
ejpam-3543	987	6	.	.	PUNCT
ejpam-3543	988	1	choose	choose	VERB
ejpam-3543	988	2	β	β	X
ejpam-3543	988	3	=	=	SYM
ejpam-3543	988	4	max{λi(x	max{λi(x	X
ejpam-3543	988	5	·	·	PUNCT
ejpam-3543	988	6	(	(	PUNCT
ejpam-3543	988	7	y	y	PROPN
ejpam-3543	988	8	·	·	PUNCT
ejpam-3543	988	9	z	z	NOUN
ejpam-3543	988	10	)	)	PUNCT
ejpam-3543	988	11	)	)	PUNCT
ejpam-3543	988	12	,	,	PUNCT
ejpam-3543	988	13	λi(y	λi(y	NOUN
ejpam-3543	988	14	)	)	PUNCT
ejpam-3543	988	15	}	}	PUNCT
ejpam-3543	988	16	.	.	PUNCT
ejpam-3543	989	1	thus	thus	ADV
ejpam-3543	989	2	λi(x	λi(x	X
ejpam-3543	989	3	·	·	PUNCT
ejpam-3543	989	4	(	(	PUNCT
ejpam-3543	989	5	y	y	PROPN
ejpam-3543	989	6	·	·	PUNCT
ejpam-3543	989	7	z	z	NOUN
ejpam-3543	989	8	)	)	PUNCT
ejpam-3543	989	9	)	)	PUNCT
ejpam-3543	989	10	≤	≤	NUM
ejpam-3543	989	11	β	β	X
ejpam-3543	989	12	and	and	CCONJ
ejpam-3543	989	13	λi(y	λi(y	NUM
ejpam-3543	989	14	)	)	PUNCT
ejpam-3543	989	15	≤	≤	NOUN
ejpam-3543	989	16	β	β	NOUN
ejpam-3543	989	17	,	,	PUNCT
ejpam-3543	989	18	so	so	SCONJ
ejpam-3543	989	19	x	x	X
ejpam-3543	989	20	·	·	PUNCT
ejpam-3543	989	21	(	(	PUNCT
ejpam-3543	989	22	y	y	PROPN
ejpam-3543	989	23	·	·	PUNCT
ejpam-3543	989	24	z	z	X
ejpam-3543	989	25	)	)	PUNCT
ejpam-3543	989	26	,	,	PUNCT
ejpam-3543	989	27	y	y	PROPN
ejpam-3543	989	28	∈	∈	PROPN
ejpam-3543	989	29	l(λi	l(λi	X
ejpam-3543	989	30	;	;	PUNCT
ejpam-3543	989	31	β	β	X
ejpam-3543	989	32	)	)	PUNCT
ejpam-3543	989	33	6=	6=	ADP
ejpam-3543	989	34	∅.	∅.	ADP
ejpam-3543	989	35	by	by	ADP
ejpam-3543	989	36	assumption	assumption	NOUN
ejpam-3543	989	37	,	,	PUNCT
ejpam-3543	989	38	we	we	PRON
ejpam-3543	989	39	have	have	VERB
ejpam-3543	989	40	l(λi	l(λi	NOUN
ejpam-3543	989	41	;	;	PUNCT
ejpam-3543	989	42	β	β	X
ejpam-3543	989	43	)	)	PUNCT
ejpam-3543	989	44	is	be	AUX
ejpam-3543	989	45	a	a	DET
ejpam-3543	989	46	up	up	ADJ
ejpam-3543	989	47	-	-	PUNCT
ejpam-3543	989	48	ideal	ideal	NOUN
ejpam-3543	989	49	of	of	ADP
ejpam-3543	989	50	x	x	PUNCT
ejpam-3543	989	51	and	and	CCONJ
ejpam-3543	989	52	so	so	ADV
ejpam-3543	989	53	x	x	X
ejpam-3543	989	54	·	·	PUNCT
ejpam-3543	989	55	z	z	SYM
ejpam-3543	989	56	∈	∈	PROPN
ejpam-3543	989	57	l(λi	l(λi	NOUN
ejpam-3543	989	58	;	;	PUNCT
ejpam-3543	989	59	β	β	X
ejpam-3543	989	60	)	)	PUNCT
ejpam-3543	989	61	.	.	PUNCT
ejpam-3543	990	1	thus	thus	ADV
ejpam-3543	990	2	λi(x	λi(x	X
ejpam-3543	990	3	·	·	PUNCT
ejpam-3543	990	4	z	z	X
ejpam-3543	990	5	)	)	PUNCT
ejpam-3543	990	6	≤	≤	NOUN
ejpam-3543	990	7	β	β	X
ejpam-3543	990	8	=	=	SYM
ejpam-3543	990	9	max{λi(x	max{λi(x	X
ejpam-3543	990	10	·	·	PUNCT
ejpam-3543	990	11	(	(	PUNCT
ejpam-3543	990	12	y	y	PROPN
ejpam-3543	990	13	·	·	PUNCT
ejpam-3543	990	14	z	z	NOUN
ejpam-3543	990	15	)	)	PUNCT
ejpam-3543	990	16	)	)	PUNCT
ejpam-3543	990	17	,	,	PUNCT
ejpam-3543	990	18	λi(y	λi(y	NOUN
ejpam-3543	990	19	)	)	PUNCT
ejpam-3543	990	20	}	}	PUNCT
ejpam-3543	990	21	.	.	PUNCT
ejpam-3543	991	1	let	let	VERB
ejpam-3543	991	2	x	x	SYM
ejpam-3543	991	3	∈	∈	PROPN
ejpam-3543	991	4	x.	x.	NOUN
ejpam-3543	991	5	then	then	ADV
ejpam-3543	992	1	λf	λf	INTJ
ejpam-3543	992	2	(	(	PUNCT
ejpam-3543	992	3	x	x	X
ejpam-3543	992	4	)	)	PUNCT
ejpam-3543	992	5	∈	∈	PROPN
ejpam-3543	993	1	[	[	X
ejpam-3543	993	2	0	0	NUM
ejpam-3543	993	3	,	,	PUNCT
ejpam-3543	993	4	1	1	NUM
ejpam-3543	993	5	]	]	PUNCT
ejpam-3543	993	6	.	.	PUNCT
ejpam-3543	994	1	choose	choose	VERB
ejpam-3543	994	2	γ	γ	X
ejpam-3543	994	3	=	=	PUNCT
ejpam-3543	994	4	λf	λf	PROPN
ejpam-3543	994	5	(	(	PUNCT
ejpam-3543	994	6	x	x	NOUN
ejpam-3543	994	7	)	)	PUNCT
ejpam-3543	994	8	.	.	PUNCT
ejpam-3543	995	1	thus	thus	ADV
ejpam-3543	995	2	λf	λf	X
ejpam-3543	995	3	(	(	PUNCT
ejpam-3543	995	4	x	x	NOUN
ejpam-3543	995	5	)	)	PUNCT
ejpam-3543	995	6	≥	≥	PROPN
ejpam-3543	995	7	γ	γ	NOUN
ejpam-3543	995	8	,	,	PUNCT
ejpam-3543	995	9	so	so	ADV
ejpam-3543	995	10	x	x	SYM
ejpam-3543	995	11	∈	∈	PROPN
ejpam-3543	995	12	u(λf	u(λf	NOUN
ejpam-3543	995	13	;	;	PUNCT
ejpam-3543	995	14	γ	γ	X
ejpam-3543	995	15	)	)	PUNCT
ejpam-3543	995	16	6=	6=	ADP
ejpam-3543	995	17	∅.	∅.	ADP
ejpam-3543	995	18	by	by	ADP
ejpam-3543	995	19	assumption	assumption	NOUN
ejpam-3543	995	20	,	,	PUNCT
ejpam-3543	995	21	we	we	PRON
ejpam-3543	995	22	have	have	VERB
ejpam-3543	995	23	u(λf	u(λf	ADV
ejpam-3543	995	24	;	;	PUNCT
ejpam-3543	995	25	γ	γ	X
ejpam-3543	995	26	)	)	PUNCT
ejpam-3543	995	27	is	be	AUX
ejpam-3543	995	28	a	a	DET
ejpam-3543	995	29	up	up	ADJ
ejpam-3543	995	30	-	-	PUNCT
ejpam-3543	995	31	ideal	ideal	NOUN
ejpam-3543	995	32	of	of	ADP
ejpam-3543	995	33	x	x	X
ejpam-3543	995	34	and	and	CCONJ
ejpam-3543	995	35	so	so	ADV
ejpam-3543	995	36	0	0	NUM
ejpam-3543	995	37	∈	∈	PROPN
ejpam-3543	995	38	u(λf	u(λf	NOUN
ejpam-3543	995	39	;	;	PUNCT
ejpam-3543	995	40	γ	γ	X
ejpam-3543	995	41	)	)	PUNCT
ejpam-3543	995	42	.	.	PUNCT
ejpam-3543	996	1	thus	thus	ADV
ejpam-3543	996	2	λf	λf	X
ejpam-3543	996	3	(	(	PUNCT
ejpam-3543	996	4	0	0	NUM
ejpam-3543	996	5	)	)	PUNCT
ejpam-3543	996	6	≥	≥	NOUN
ejpam-3543	996	7	γ	γ	X
ejpam-3543	996	8	=	=	PUNCT
ejpam-3543	996	9	λf	λf	PROPN
ejpam-3543	996	10	(	(	PUNCT
ejpam-3543	996	11	x	x	NOUN
ejpam-3543	996	12	)	)	PUNCT
ejpam-3543	996	13	.	.	PUNCT
ejpam-3543	997	1	next	next	ADV
ejpam-3543	997	2	,	,	PUNCT
ejpam-3543	997	3	let	let	VERB
ejpam-3543	997	4	x	x	PRON
ejpam-3543	997	5	,	,	PUNCT
ejpam-3543	997	6	y	y	PROPN
ejpam-3543	997	7	,	,	PUNCT
ejpam-3543	997	8	z	z	PROPN
ejpam-3543	997	9	∈	∈	PROPN
ejpam-3543	997	10	x.	x.	NOUN
ejpam-3543	998	1	then	then	ADV
ejpam-3543	998	2	λf	λf	INTJ
ejpam-3543	998	3	(	(	PUNCT
ejpam-3543	998	4	x	x	PART
ejpam-3543	998	5	·	·	PUNCT
ejpam-3543	998	6	(	(	PUNCT
ejpam-3543	998	7	y	y	PROPN
ejpam-3543	998	8	·	·	PUNCT
ejpam-3543	998	9	z	z	NOUN
ejpam-3543	998	10	)	)	PUNCT
ejpam-3543	998	11	)	)	PUNCT
ejpam-3543	998	12	,	,	PUNCT
ejpam-3543	998	13	λf	λf	X
ejpam-3543	998	14	(	(	PUNCT
ejpam-3543	998	15	y	y	NOUN
ejpam-3543	998	16	)	)	PUNCT
ejpam-3543	998	17	∈	∈	PROPN
ejpam-3543	999	1	[	[	X
ejpam-3543	999	2	0	0	NUM
ejpam-3543	999	3	,	,	PUNCT
ejpam-3543	999	4	1	1	NUM
ejpam-3543	999	5	]	]	PUNCT
ejpam-3543	999	6	.	.	PUNCT
ejpam-3543	1000	1	choose	choose	VERB
ejpam-3543	1000	2	γ	γ	X
ejpam-3543	1000	3	=	=	SYM
ejpam-3543	1000	4	min{λf	min{λf	X
ejpam-3543	1000	5	(	(	PUNCT
ejpam-3543	1000	6	x	x	PART
ejpam-3543	1000	7	·	·	PUNCT
ejpam-3543	1000	8	(	(	PUNCT
ejpam-3543	1000	9	y	y	PROPN
ejpam-3543	1000	10	·	·	PUNCT
ejpam-3543	1000	11	z	z	NOUN
ejpam-3543	1000	12	)	)	PUNCT
ejpam-3543	1000	13	)	)	PUNCT
ejpam-3543	1000	14	,	,	PUNCT
ejpam-3543	1000	15	λf	λf	X
ejpam-3543	1000	16	(	(	PUNCT
ejpam-3543	1000	17	y	y	NOUN
ejpam-3543	1000	18	)	)	PUNCT
ejpam-3543	1000	19	}	}	PUNCT
ejpam-3543	1000	20	.	.	PUNCT
ejpam-3543	1001	1	thus	thus	ADV
ejpam-3543	1001	2	λf	λf	X
ejpam-3543	1001	3	(	(	PUNCT
ejpam-3543	1001	4	x	x	PART
ejpam-3543	1001	5	·	·	PUNCT
ejpam-3543	1001	6	(	(	PUNCT
ejpam-3543	1001	7	y	y	PROPN
ejpam-3543	1001	8	·	·	PUNCT
ejpam-3543	1001	9	z	z	NOUN
ejpam-3543	1001	10	)	)	PUNCT
ejpam-3543	1001	11	)	)	PUNCT
ejpam-3543	1001	12	≥	≥	PROPN
ejpam-3543	1001	13	γ	γ	X
ejpam-3543	1001	14	and	and	CCONJ
ejpam-3543	1001	15	λf	λf	PROPN
ejpam-3543	1001	16	(	(	PUNCT
ejpam-3543	1001	17	y	y	PROPN
ejpam-3543	1001	18	)	)	PUNCT
ejpam-3543	1001	19	≥	≥	PROPN
ejpam-3543	1001	20	γ	γ	NOUN
ejpam-3543	1001	21	,	,	PUNCT
ejpam-3543	1001	22	so	so	ADV
ejpam-3543	1001	23	x	x	X
ejpam-3543	1001	24	·	·	PUNCT
ejpam-3543	1001	25	(	(	PUNCT
ejpam-3543	1001	26	y	y	PROPN
ejpam-3543	1001	27	·	·	PUNCT
ejpam-3543	1001	28	z	z	X
ejpam-3543	1001	29	)	)	PUNCT
ejpam-3543	1001	30	,	,	PUNCT
ejpam-3543	1001	31	y	y	PROPN
ejpam-3543	1001	32	∈	∈	PROPN
ejpam-3543	1001	33	u(λf	u(λf	ADV
ejpam-3543	1001	34	;	;	PUNCT
ejpam-3543	1001	35	γ	γ	X
ejpam-3543	1001	36	)	)	PUNCT
ejpam-3543	1001	37	6=	6=	ADP
ejpam-3543	1001	38	∅.	∅.	ADP
ejpam-3543	1001	39	by	by	ADP
ejpam-3543	1001	40	assumption	assumption	NOUN
ejpam-3543	1001	41	,	,	PUNCT
ejpam-3543	1001	42	we	we	PRON
ejpam-3543	1001	43	have	have	VERB
ejpam-3543	1001	44	u(λf	u(λf	ADV
ejpam-3543	1001	45	;	;	PUNCT
ejpam-3543	1001	46	γ	γ	X
ejpam-3543	1001	47	)	)	PUNCT
ejpam-3543	1001	48	is	be	AUX
ejpam-3543	1001	49	a	a	DET
ejpam-3543	1001	50	up	up	ADJ
ejpam-3543	1001	51	-	-	PUNCT
ejpam-3543	1001	52	ideal	ideal	NOUN
ejpam-3543	1001	53	of	of	ADP
ejpam-3543	1001	54	x	x	PUNCT
ejpam-3543	1001	55	and	and	CCONJ
ejpam-3543	1001	56	so	so	ADV
ejpam-3543	1001	57	x	x	X
ejpam-3543	1001	58	·	·	PUNCT
ejpam-3543	1001	59	z	z	X
ejpam-3543	1001	60	∈	∈	PROPN
ejpam-3543	1001	61	u(λf	u(λf	NOUN
ejpam-3543	1001	62	;	;	PUNCT
ejpam-3543	1001	63	γ	γ	X
ejpam-3543	1001	64	)	)	PUNCT
ejpam-3543	1001	65	.	.	PUNCT
ejpam-3543	1002	1	thus	thus	ADV
ejpam-3543	1002	2	λf	λf	X
ejpam-3543	1002	3	(	(	PUNCT
ejpam-3543	1002	4	x	x	SYM
ejpam-3543	1002	5	·	·	PUNCT
ejpam-3543	1002	6	z	z	X
ejpam-3543	1002	7	)	)	PUNCT
ejpam-3543	1002	8	≥	≥	NOUN
ejpam-3543	1002	9	γ	γ	X
ejpam-3543	1002	10	=	=	SYM
ejpam-3543	1002	11	min{λf	min{λf	X
ejpam-3543	1002	12	(	(	PUNCT
ejpam-3543	1002	13	x	x	PART
ejpam-3543	1002	14	·	·	PUNCT
ejpam-3543	1002	15	(	(	PUNCT
ejpam-3543	1002	16	y	y	PROPN
ejpam-3543	1002	17	·	·	PUNCT
ejpam-3543	1002	18	z	z	NOUN
ejpam-3543	1002	19	)	)	PUNCT
ejpam-3543	1002	20	)	)	PUNCT
ejpam-3543	1002	21	,	,	PUNCT
ejpam-3543	1002	22	λf	λf	X
ejpam-3543	1002	23	(	(	PUNCT
ejpam-3543	1002	24	y	y	NOUN
ejpam-3543	1002	25	)	)	PUNCT
ejpam-3543	1002	26	}	}	PUNCT
ejpam-3543	1002	27	.	.	PUNCT
ejpam-3543	1003	1	therefore	therefore	ADV
ejpam-3543	1003	2	,	,	PUNCT
ejpam-3543	1003	3	λ	λ	PROPN
ejpam-3543	1003	4	is	be	AUX
ejpam-3543	1003	5	a	a	DET
ejpam-3543	1003	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	1003	7	up	up	ADV
ejpam-3543	1003	8	-	-	PUNCT
ejpam-3543	1003	9	ideal	ideal	NOUN
ejpam-3543	1003	10	of	of	ADP
ejpam-3543	1003	11	x.	x.	PROPN
ejpam-3543	1003	12	theorem	theorem	VERB
ejpam-3543	1003	13	23	23	NUM
ejpam-3543	1003	14	.	.	PUNCT
ejpam-3543	1004	1	a	a	DET
ejpam-3543	1004	2	ns	ns	NUM
ejpam-3543	1004	3	λ	λ	NOUN
ejpam-3543	1004	4	in	in	ADP
ejpam-3543	1004	5	x	x	PROPN
ejpam-3543	1004	6	is	be	AUX
ejpam-3543	1004	7	a	a	DET
ejpam-3543	1004	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	1004	9	strongly	strongly	ADV
ejpam-3543	1004	10	up	up	ADP
ejpam-3543	1004	11	-	-	PUNCT
ejpam-3543	1004	12	ideal	ideal	NOUN
ejpam-3543	1004	13	of	of	ADP
ejpam-3543	1004	14	x	x	SYM
ejpam-3543	1004	15	if	if	SCONJ
ejpam-3543	1004	16	and	and	CCONJ
ejpam-3543	1004	17	only	only	ADV
ejpam-3543	1004	18	if	if	SCONJ
ejpam-3543	1004	19	the	the	PRON
ejpam-3543	1004	20	sets	set	VERB
ejpam-3543	1004	21	e(λt	e(λt	PROPN
ejpam-3543	1004	22	;	;	PUNCT
ejpam-3543	1004	23	λt	λt	X
ejpam-3543	1004	24	(	(	PUNCT
ejpam-3543	1004	25	0	0	NUM
ejpam-3543	1004	26	)	)	PUNCT
ejpam-3543	1004	27	)	)	PUNCT
ejpam-3543	1004	28	,	,	PUNCT
ejpam-3543	1004	29	e(λi	e(λi	PROPN
ejpam-3543	1004	30	;	;	PUNCT
ejpam-3543	1004	31	λi(0	λi(0	X
ejpam-3543	1004	32	)	)	PUNCT
ejpam-3543	1004	33	)	)	PUNCT
ejpam-3543	1004	34	,	,	PUNCT
ejpam-3543	1004	35	and	and	CCONJ
ejpam-3543	1004	36	e(λf	e(λf	PROPN
ejpam-3543	1004	37	;	;	PUNCT
ejpam-3543	1004	38	λf	λf	X
ejpam-3543	1004	39	(	(	PUNCT
ejpam-3543	1004	40	0	0	NUM
ejpam-3543	1004	41	)	)	PUNCT
ejpam-3543	1004	42	)	)	PUNCT
ejpam-3543	1005	1	are	be	AUX
ejpam-3543	1005	2	strongly	strongly	ADV
ejpam-3543	1005	3	up	up	ADP
ejpam-3543	1005	4	-	-	PUNCT
ejpam-3543	1005	5	ideals	ideal	NOUN
ejpam-3543	1005	6	of	of	ADP
ejpam-3543	1005	7	x.	x.	NOUN
ejpam-3543	1005	8	proof	proof	NOUN
ejpam-3543	1005	9	.	.	PUNCT
ejpam-3543	1006	1	assume	assume	VERB
ejpam-3543	1006	2	that	that	SCONJ
ejpam-3543	1006	3	λ	λ	PROPN
ejpam-3543	1006	4	is	be	AUX
ejpam-3543	1006	5	a	a	DET
ejpam-3543	1006	6	neutrosophic	neutrosophic	ADJ
ejpam-3543	1006	7	strongly	strongly	ADV
ejpam-3543	1006	8	up	up	ADP
ejpam-3543	1006	9	-	-	PUNCT
ejpam-3543	1006	10	ideal	ideal	NOUN
ejpam-3543	1006	11	of	of	ADP
ejpam-3543	1006	12	x.	x.	NOUN
ejpam-3543	1006	13	by	by	ADP
ejpam-3543	1006	14	theorem	theorem	NOUN
ejpam-3543	1006	15	2	2	NUM
ejpam-3543	1006	16	,	,	PUNCT
ejpam-3543	1006	17	we	we	PRON
ejpam-3543	1006	18	have	have	VERB
ejpam-3543	1006	19	λ	λ	PROPN
ejpam-3543	1006	20	is	be	AUX
ejpam-3543	1006	21	constant	constant	ADJ
ejpam-3543	1006	22	,	,	PUNCT
ejpam-3543	1006	23	that	that	ADV
ejpam-3543	1006	24	is	is	ADV
ejpam-3543	1006	25	,	,	PUNCT
ejpam-3543	1006	26	λt	λt	INTJ
ejpam-3543	1006	27	,	,	PUNCT
ejpam-3543	1006	28	λi	λi	INTJ
ejpam-3543	1006	29	,	,	PUNCT
ejpam-3543	1006	30	and	and	CCONJ
ejpam-3543	1006	31	λf	λf	PROPN
ejpam-3543	1006	32	are	be	AUX
ejpam-3543	1006	33	constant	constant	ADJ
ejpam-3543	1006	34	.	.	PUNCT
ejpam-3543	1007	1	thus	thus	ADV
ejpam-3543	1007	2	(	(	PUNCT
ejpam-3543	1007	3	∀x	∀x	X
ejpam-3543	1007	4	∈	∈	PROPN
ejpam-3543	1007	5	x	x	NOUN
ejpam-3543	1007	6	)	)	PUNCT
ejpam-3543	1007	7	λt	λt	PROPN
ejpam-3543	1007	8	(	(	PUNCT
ejpam-3543	1007	9	x	x	NOUN
ejpam-3543	1007	10	)	)	PUNCT
ejpam-3543	1007	11	=	=	SYM
ejpam-3543	1007	12	λt	λt	X
ejpam-3543	1007	13	(	(	PUNCT
ejpam-3543	1007	14	0	0	NUM
ejpam-3543	1007	15	)	)	PUNCT
ejpam-3543	1007	16	λi(x	λi(x	NUM
ejpam-3543	1007	17	)	)	PUNCT
ejpam-3543	1007	18	=	=	PUNCT
ejpam-3543	1008	1	λi(0	λi(0	X
ejpam-3543	1008	2	)	)	PUNCT
ejpam-3543	1008	3	λf	λf	X
ejpam-3543	1008	4	(	(	PUNCT
ejpam-3543	1008	5	x	x	X
ejpam-3543	1008	6	)	)	PUNCT
ejpam-3543	1008	7	=	=	SYM
ejpam-3543	1008	8	λf	λf	X
ejpam-3543	1008	9	(	(	PUNCT
ejpam-3543	1008	10	0	0	NUM
ejpam-3543	1008	11	)	)	PUNCT
ejpam-3543	1008	12			NOUN
ejpam-3543	1008	13	.	.	PUNCT
ejpam-3543	1009	1	hence	hence	ADV
ejpam-3543	1009	2	,	,	PUNCT
ejpam-3543	1009	3	e(λt	e(λt	PROPN
ejpam-3543	1009	4	;	;	PUNCT
ejpam-3543	1009	5	λt	λt	X
ejpam-3543	1009	6	(	(	PUNCT
ejpam-3543	1009	7	0	0	NUM
ejpam-3543	1009	8	)	)	PUNCT
ejpam-3543	1009	9	)	)	PUNCT
ejpam-3543	1009	10	=	=	SYM
ejpam-3543	1010	1	x	x	X
ejpam-3543	1010	2	,	,	PUNCT
ejpam-3543	1010	3	e(λi	e(λi	PROPN
ejpam-3543	1010	4	;	;	PUNCT
ejpam-3543	1010	5	λi(0	λi(0	X
ejpam-3543	1010	6	)	)	PUNCT
ejpam-3543	1010	7	)	)	PUNCT
ejpam-3543	1010	8	=	=	SYM
ejpam-3543	1011	1	x	x	NOUN
ejpam-3543	1011	2	,	,	PUNCT
ejpam-3543	1011	3	and	and	CCONJ
ejpam-3543	1011	4	e(λf	e(λf	PROPN
ejpam-3543	1011	5	;	;	PUNCT
ejpam-3543	1011	6	λf	λf	X
ejpam-3543	1011	7	(	(	PUNCT
ejpam-3543	1011	8	0	0	NUM
ejpam-3543	1011	9	)	)	PUNCT
ejpam-3543	1011	10	)	)	PUNCT
ejpam-3543	1012	1	=	=	PUNCT
ejpam-3543	1013	1	x	x	PUNCT
ejpam-3543	1013	2	and	and	CCONJ
ejpam-3543	1013	3	so	so	ADV
ejpam-3543	1013	4	e(λt	e(λt	PROPN
ejpam-3543	1013	5	;	;	PUNCT
ejpam-3543	1013	6	λt	λt	X
ejpam-3543	1013	7	(	(	PUNCT
ejpam-3543	1013	8	0	0	NUM
ejpam-3543	1013	9	)	)	PUNCT
ejpam-3543	1013	10	)	)	PUNCT
ejpam-3543	1013	11	,	,	PUNCT
ejpam-3543	1013	12	e(λi	e(λi	PROPN
ejpam-3543	1013	13	;	;	PUNCT
ejpam-3543	1013	14	λi(0	λi(0	X
ejpam-3543	1013	15	)	)	PUNCT
ejpam-3543	1013	16	)	)	PUNCT
ejpam-3543	1013	17	,	,	PUNCT
ejpam-3543	1013	18	and	and	CCONJ
ejpam-3543	1013	19	e(λf	e(λf	PROPN
ejpam-3543	1013	20	;	;	PUNCT
ejpam-3543	1013	21	λf	λf	X
ejpam-3543	1013	22	(	(	PUNCT
ejpam-3543	1013	23	0	0	NUM
ejpam-3543	1013	24	)	)	PUNCT
ejpam-3543	1013	25	)	)	PUNCT
ejpam-3543	1013	26	are	be	AUX
ejpam-3543	1013	27	strongly	strongly	ADV
ejpam-3543	1013	28	up	up	ADP
ejpam-3543	1013	29	-	-	PUNCT
ejpam-3543	1013	30	ideals	ideal	NOUN
ejpam-3543	1013	31	of	of	ADP
ejpam-3543	1013	32	x.	x.	PROPN
ejpam-3543	1013	33	m.	m.	PROPN
ejpam-3543	1013	34	songsaeng	songsaeng	PROPN
ejpam-3543	1013	35	,	,	PUNCT
ejpam-3543	1013	36	a.	a.	NOUN
ejpam-3543	1013	37	iampan	iampan	PROPN
ejpam-3543	1013	38	/	/	SYM
ejpam-3543	1013	39	eur	eur	PROPN
ejpam-3543	1013	40	.	.	PUNCT
ejpam-3543	1014	1	j.	j.	PROPN
ejpam-3543	1014	2	pure	pure	PROPN
ejpam-3543	1014	3	appl	appl	PROPN
ejpam-3543	1014	4	.	.	PROPN
ejpam-3543	1014	5	math	math	PROPN
ejpam-3543	1014	6	,	,	PUNCT
ejpam-3543	1014	7	12	12	NUM
ejpam-3543	1014	8	(	(	PUNCT
ejpam-3543	1014	9	4	4	NUM
ejpam-3543	1014	10	)	)	PUNCT
ejpam-3543	1014	11	(	(	PUNCT
ejpam-3543	1014	12	2019	2019	NUM
ejpam-3543	1014	13	)	)	PUNCT
ejpam-3543	1014	14	,	,	PUNCT
ejpam-3543	1014	15	1382	1382	NUM
ejpam-3543	1014	16	-	-	SYM
ejpam-3543	1014	17	1409	1409	NUM
ejpam-3543	1014	18	1406	1406	NUM
ejpam-3543	1014	19	conversely	conversely	ADV
ejpam-3543	1014	20	,	,	PUNCT
ejpam-3543	1014	21	assume	assume	VERB
ejpam-3543	1014	22	that	that	SCONJ
ejpam-3543	1014	23	e(λt	e(λt	NOUN
ejpam-3543	1014	24	;	;	PUNCT
ejpam-3543	1014	25	λt	λt	X
ejpam-3543	1014	26	(	(	PUNCT
ejpam-3543	1014	27	0	0	NUM
ejpam-3543	1014	28	)	)	PUNCT
ejpam-3543	1014	29	)	)	PUNCT
ejpam-3543	1014	30	,	,	PUNCT
ejpam-3543	1014	31	e(λi	e(λi	PROPN
ejpam-3543	1014	32	;	;	PUNCT
ejpam-3543	1014	33	λi(0	λi(0	X
ejpam-3543	1014	34	)	)	PUNCT
ejpam-3543	1014	35	)	)	PUNCT
ejpam-3543	1014	36	,	,	PUNCT
ejpam-3543	1014	37	and	and	CCONJ
ejpam-3543	1014	38	e(λf	e(λf	PROPN
ejpam-3543	1014	39	;	;	PUNCT
ejpam-3543	1014	40	λf	λf	X
ejpam-3543	1014	41	(	(	PUNCT
ejpam-3543	1014	42	0	0	NUM
ejpam-3543	1014	43	)	)	PUNCT
ejpam-3543	1014	44	)	)	PUNCT
ejpam-3543	1014	45	are	be	AUX
ejpam-3543	1014	46	strongly	strongly	ADV
ejpam-3543	1014	47	up	up	ADP
ejpam-3543	1014	48	-	-	PUNCT
ejpam-3543	1014	49	ideals	ideal	NOUN
ejpam-3543	1014	50	of	of	ADP
ejpam-3543	1014	51	x.	x.	NOUN
ejpam-3543	1014	52	then	then	ADV
ejpam-3543	1014	53	e(λt	e(λt	NOUN
ejpam-3543	1014	54	;	;	PUNCT
ejpam-3543	1014	55	λt	λt	X
ejpam-3543	1014	56	(	(	PUNCT
ejpam-3543	1014	57	0	0	NUM
ejpam-3543	1014	58	)	)	PUNCT
ejpam-3543	1014	59	)	)	PUNCT
ejpam-3543	1015	1	=	=	SYM
ejpam-3543	1015	2	x	x	X
ejpam-3543	1015	3	,	,	PUNCT
ejpam-3543	1015	4	e(λi	e(λi	PROPN
ejpam-3543	1015	5	;	;	PUNCT
ejpam-3543	1015	6	λi(0	λi(0	X
ejpam-3543	1015	7	)	)	PUNCT
ejpam-3543	1015	8	)	)	PUNCT
ejpam-3543	1015	9	=	=	SYM
ejpam-3543	1016	1	x	x	X
ejpam-3543	1016	2	,	,	PUNCT
ejpam-3543	1016	3	e(λf	e(λf	PROPN
ejpam-3543	1016	4	;	;	PUNCT
ejpam-3543	1016	5	λf	λf	X
ejpam-3543	1016	6	(	(	PUNCT
ejpam-3543	1016	7	0	0	NUM
ejpam-3543	1016	8	)	)	PUNCT
ejpam-3543	1016	9	)	)	PUNCT
ejpam-3543	1017	1	=	=	PUNCT
ejpam-3543	1018	1	x	x	PUNCT
ejpam-3543	1019	1	and	and	CCONJ
ejpam-3543	1019	2	so	so	ADV
ejpam-3543	1019	3	(	(	PUNCT
ejpam-3543	1019	4	∀x	∀x	X
ejpam-3543	1019	5	∈	∈	PROPN
ejpam-3543	1019	6	x	x	NOUN
ejpam-3543	1019	7	)	)	PUNCT
ejpam-3543	1019	8	λt	λt	PROPN
ejpam-3543	1019	9	(	(	PUNCT
ejpam-3543	1019	10	x	x	NOUN
ejpam-3543	1019	11	)	)	PUNCT
ejpam-3543	1019	12	=	=	SYM
ejpam-3543	1019	13	λt	λt	X
ejpam-3543	1019	14	(	(	PUNCT
ejpam-3543	1019	15	0	0	NUM
ejpam-3543	1019	16	)	)	PUNCT
ejpam-3543	1019	17	λi(x	λi(x	NUM
ejpam-3543	1019	18	)	)	PUNCT
ejpam-3543	1020	1	=	=	PUNCT
ejpam-3543	1020	2	λi(0	λi(0	X
ejpam-3543	1020	3	)	)	PUNCT
ejpam-3543	1020	4	λf	λf	X
ejpam-3543	1020	5	(	(	PUNCT
ejpam-3543	1020	6	x	x	X
ejpam-3543	1020	7	)	)	PUNCT
ejpam-3543	1020	8	=	=	SYM
ejpam-3543	1020	9	λf	λf	X
ejpam-3543	1020	10	(	(	PUNCT
ejpam-3543	1020	11	0	0	NUM
ejpam-3543	1020	12	)	)	PUNCT
ejpam-3543	1020	13			NOUN
ejpam-3543	1020	14	.	.	PUNCT
ejpam-3543	1021	1	thus	thus	ADV
ejpam-3543	1021	2	λt	λt	ADP
ejpam-3543	1021	3	,	,	PUNCT
ejpam-3543	1021	4	λi	λi	INTJ
ejpam-3543	1021	5	,	,	PUNCT
ejpam-3543	1021	6	and	and	CCONJ
ejpam-3543	1021	7	λf	λf	PROPN
ejpam-3543	1021	8	are	be	AUX
ejpam-3543	1021	9	constant	constant	ADJ
ejpam-3543	1021	10	,	,	PUNCT
ejpam-3543	1021	11	that	that	ADV
ejpam-3543	1021	12	is	is	ADV
ejpam-3543	1021	13	,	,	PUNCT
ejpam-3543	1021	14	λ	λ	PROPN
ejpam-3543	1021	15	is	be	AUX
ejpam-3543	1021	16	constant	constant	ADJ
ejpam-3543	1021	17	.	.	PUNCT
ejpam-3543	1022	1	by	by	ADP
ejpam-3543	1022	2	theorem	theorem	NOUN
ejpam-3543	1022	3	2	2	NUM
ejpam-3543	1022	4	,	,	PUNCT
ejpam-3543	1022	5	we	we	PRON
ejpam-3543	1022	6	have	have	VERB
ejpam-3543	1022	7	λ	λ	PROPN
ejpam-3543	1022	8	is	be	AUX
ejpam-3543	1022	9	a	a	DET
ejpam-3543	1022	10	neutrosophic	neutrosophic	ADJ
ejpam-3543	1022	11	strongly	strongly	ADV
ejpam-3543	1022	12	up	up	ADP
ejpam-3543	1022	13	-	-	PUNCT
ejpam-3543	1022	14	ideal	ideal	NOUN
ejpam-3543	1022	15	of	of	ADP
ejpam-3543	1022	16	x.	x.	NOUN
ejpam-3543	1022	17	definition	definition	NOUN
ejpam-3543	1022	18	11	11	NUM
ejpam-3543	1022	19	.	.	PUNCT
ejpam-3543	1023	1	let	let	VERB
ejpam-3543	1023	2	λ	λ	PRON
ejpam-3543	1023	3	be	be	AUX
ejpam-3543	1023	4	a	a	DET
ejpam-3543	1023	5	ns	ns	NOUN
ejpam-3543	1023	6	in	in	ADP
ejpam-3543	1023	7	x.	x.	NOUN
ejpam-3543	1023	8	for	for	ADP
ejpam-3543	1023	9	α	α	PROPN
ejpam-3543	1023	10	,	,	PUNCT
ejpam-3543	1023	11	β	β	X
ejpam-3543	1023	12	,	,	PUNCT
ejpam-3543	1023	13	γ	γ	PROPN
ejpam-3543	1023	14	∈	∈	PROPN
ejpam-3543	1024	1	[	[	X
ejpam-3543	1024	2	0	0	NUM
ejpam-3543	1024	3	,	,	PUNCT
ejpam-3543	1024	4	1	1	NUM
ejpam-3543	1024	5	]	]	PUNCT
ejpam-3543	1024	6	,	,	PUNCT
ejpam-3543	1024	7	the	the	DET
ejpam-3543	1024	8	sets	set	NOUN
ejpam-3543	1024	9	uluλ(α	uluλ(α	PROPN
ejpam-3543	1024	10	,	,	PUNCT
ejpam-3543	1024	11	β	β	PROPN
ejpam-3543	1024	12	,	,	PUNCT
ejpam-3543	1024	13	γ	γ	NOUN
ejpam-3543	1024	14	)	)	PUNCT
ejpam-3543	1024	15	=	=	SYM
ejpam-3543	1024	16	{	{	PUNCT
ejpam-3543	1024	17	x	x	PUNCT
ejpam-3543	1024	18	∈	∈	NOUN
ejpam-3543	1024	19	x	x	INTJ
ejpam-3543	1024	20	|	|	ADV
ejpam-3543	1024	21	λt	λt	INTJ
ejpam-3543	1024	22	≥	≥	NOUN
ejpam-3543	1024	23	α	α	NOUN
ejpam-3543	1024	24	,	,	PUNCT
ejpam-3543	1024	25	λi	λi	ADP
ejpam-3543	1024	26	≤	≤	ADJ
ejpam-3543	1024	27	β	β	NOUN
ejpam-3543	1024	28	,	,	PUNCT
ejpam-3543	1024	29	λf	λf	PROPN
ejpam-3543	1024	30	≥	≥	X
ejpam-3543	1024	31	γ	γ	NOUN
ejpam-3543	1024	32	}	}	PUNCT
ejpam-3543	1024	33	,	,	PUNCT
ejpam-3543	1024	34	lulλ(α	lulλ(α	PROPN
ejpam-3543	1024	35	,	,	PUNCT
ejpam-3543	1024	36	β	β	X
ejpam-3543	1024	37	,	,	PUNCT
ejpam-3543	1024	38	γ	γ	NOUN
ejpam-3543	1024	39	)	)	PUNCT
ejpam-3543	1024	40	=	=	SYM
ejpam-3543	1024	41	{	{	PUNCT
ejpam-3543	1024	42	x	x	PUNCT
ejpam-3543	1024	43	∈	∈	NOUN
ejpam-3543	1024	44	x	x	INTJ
ejpam-3543	1024	45	|	|	ADV
ejpam-3543	1024	46	λt	λt	ADP
ejpam-3543	1024	47	≤	≤	NUM
ejpam-3543	1024	48	α	α	NOUN
ejpam-3543	1024	49	,	,	PUNCT
ejpam-3543	1024	50	λi	λi	ADP
ejpam-3543	1024	51	≥	≥	NOUN
ejpam-3543	1024	52	β	β	NOUN
ejpam-3543	1024	53	,	,	PUNCT
ejpam-3543	1024	54	λf	λf	ADP
ejpam-3543	1024	55	≤	≤	PROPN
ejpam-3543	1024	56	γ	γ	X
ejpam-3543	1024	57	}	}	PUNCT
ejpam-3543	1024	58	,	,	PUNCT
ejpam-3543	1024	59	eλ(α	eλ(α	X
ejpam-3543	1024	60	,	,	PUNCT
ejpam-3543	1024	61	β	β	X
ejpam-3543	1024	62	,	,	PUNCT
ejpam-3543	1024	63	γ	γ	NOUN
ejpam-3543	1024	64	)	)	PUNCT
ejpam-3543	1024	65	=	=	SYM
ejpam-3543	1024	66	{	{	PUNCT
ejpam-3543	1024	67	x	x	PUNCT
ejpam-3543	1024	68	∈	∈	NOUN
ejpam-3543	1024	69	x	x	INTJ
ejpam-3543	1024	70	|	|	ADV
ejpam-3543	1024	71	λt	λt	ADP
ejpam-3543	1024	72	=	=	NOUN
ejpam-3543	1024	73	α	α	PROPN
ejpam-3543	1024	74	,	,	PUNCT
ejpam-3543	1024	75	λi	λi	X
ejpam-3543	1024	76	=	=	SYM
ejpam-3543	1024	77	β	β	X
ejpam-3543	1024	78	,	,	PUNCT
ejpam-3543	1024	79	λf	λf	X
ejpam-3543	1024	80	=	=	SYM
ejpam-3543	1024	81	γ	γ	X
ejpam-3543	1024	82	}	}	PUNCT
ejpam-3543	1024	83	are	be	AUX
ejpam-3543	1024	84	called	call	VERB
ejpam-3543	1024	85	a	a	DET
ejpam-3543	1024	86	ulu	ulu	PROPN
ejpam-3543	1024	87	-(α	-(α	PUNCT
ejpam-3543	1024	88	,	,	PUNCT
ejpam-3543	1024	89	β	β	X
ejpam-3543	1024	90	,	,	PUNCT
ejpam-3543	1024	91	γ)-level	γ)-level	PROPN
ejpam-3543	1024	92	subset	subset	NOUN
ejpam-3543	1024	93	,	,	PUNCT
ejpam-3543	1024	94	a	a	DET
ejpam-3543	1024	95	lul-(α	lul-(α	NOUN
ejpam-3543	1024	96	,	,	PUNCT
ejpam-3543	1024	97	β	β	X
ejpam-3543	1024	98	,	,	PUNCT
ejpam-3543	1024	99	γ)-level	γ)-level	PROPN
ejpam-3543	1024	100	subset	subset	NOUN
ejpam-3543	1024	101	,	,	PUNCT
ejpam-3543	1024	102	and	and	CCONJ
ejpam-3543	1024	103	an	an	DET
ejpam-3543	1024	104	e-(α	e-(α	ADJ
ejpam-3543	1024	105	,	,	PUNCT
ejpam-3543	1024	106	β	β	NOUN
ejpam-3543	1024	107	,	,	PUNCT
ejpam-3543	1024	108	γ)level	γ)level	PROPN
ejpam-3543	1024	109	subset	subset	NOUN
ejpam-3543	1024	110	of	of	ADP
ejpam-3543	1024	111	λ	λ	PROPN
ejpam-3543	1024	112	,	,	PUNCT
ejpam-3543	1024	113	respectively	respectively	ADV
ejpam-3543	1024	114	.	.	PUNCT
ejpam-3543	1025	1	then	then	ADV
ejpam-3543	1025	2	we	we	PRON
ejpam-3543	1025	3	see	see	VERB
ejpam-3543	1025	4	that	that	SCONJ
ejpam-3543	1025	5	uluλ(α	uluλ(α	PROPN
ejpam-3543	1025	6	,	,	PUNCT
ejpam-3543	1025	7	β	β	PROPN
ejpam-3543	1025	8	,	,	PUNCT
ejpam-3543	1025	9	γ	γ	NOUN
ejpam-3543	1025	10	)	)	PUNCT
ejpam-3543	1025	11	=	=	PROPN
ejpam-3543	1025	12	u(λt	u(λt	NOUN
ejpam-3543	1025	13	;	;	PUNCT
ejpam-3543	1025	14	α	α	X
ejpam-3543	1025	15	)	)	PUNCT
ejpam-3543	1025	16	∩	∩	NOUN
ejpam-3543	1025	17	l(λi	l(λi	NOUN
ejpam-3543	1025	18	;	;	PUNCT
ejpam-3543	1025	19	β	β	X
ejpam-3543	1025	20	)	)	PUNCT
ejpam-3543	1025	21	∩	∩	NOUN
ejpam-3543	1025	22	u(λf	u(λf	NOUN
ejpam-3543	1025	23	;	;	PUNCT
ejpam-3543	1025	24	γ	γ	X
ejpam-3543	1025	25	)	)	PUNCT
ejpam-3543	1025	26	,	,	PUNCT
ejpam-3543	1025	27	lulλ(α	lulλ(α	PROPN
ejpam-3543	1025	28	,	,	PUNCT
ejpam-3543	1025	29	β	β	X
ejpam-3543	1025	30	,	,	PUNCT
ejpam-3543	1025	31	γ	γ	NOUN
ejpam-3543	1025	32	)	)	PUNCT
ejpam-3543	1025	33	=	=	NOUN
ejpam-3543	1025	34	l(λt	l(λt	NOUN
ejpam-3543	1025	35	;	;	PUNCT
ejpam-3543	1025	36	α	α	X
ejpam-3543	1025	37	)	)	PUNCT
ejpam-3543	1025	38	∩	∩	NOUN
ejpam-3543	1025	39	u(λi	u(λi	ADJ
ejpam-3543	1025	40	;	;	PUNCT
ejpam-3543	1025	41	β	β	X
ejpam-3543	1025	42	)	)	PUNCT
ejpam-3543	1025	43	∩	∩	NOUN
ejpam-3543	1025	44	l(λf	l(λf	PROPN
ejpam-3543	1025	45	;	;	PUNCT
ejpam-3543	1025	46	γ	γ	X
ejpam-3543	1025	47	)	)	PUNCT
ejpam-3543	1025	48	,	,	PUNCT
ejpam-3543	1025	49	eλ(α	eλ(α	X
ejpam-3543	1025	50	,	,	PUNCT
ejpam-3543	1025	51	β	β	X
ejpam-3543	1025	52	,	,	PUNCT
ejpam-3543	1025	53	γ	γ	NOUN
ejpam-3543	1025	54	)	)	PUNCT
ejpam-3543	1025	55	=	=	NOUN
ejpam-3543	1025	56	e(λt	e(λt	PROPN
ejpam-3543	1025	57	;	;	PUNCT
ejpam-3543	1025	58	α	α	X
ejpam-3543	1025	59	)	)	PUNCT
ejpam-3543	1025	60	∩	∩	NOUN
ejpam-3543	1025	61	e(λi	e(λi	PROPN
ejpam-3543	1025	62	;	;	PUNCT
ejpam-3543	1025	63	β	β	X
ejpam-3543	1025	64	)	)	PUNCT
ejpam-3543	1025	65	∩	∩	NOUN
ejpam-3543	1025	66	e(λf	e(λf	NOUN
ejpam-3543	1025	67	;	;	PUNCT
ejpam-3543	1025	68	γ	γ	X
ejpam-3543	1025	69	)	)	PUNCT
ejpam-3543	1025	70	.	.	PUNCT
ejpam-3543	1026	1	corollary	corollary	ADJ
ejpam-3543	1026	2	1	1	NUM
ejpam-3543	1026	3	.	.	PUNCT
ejpam-3543	1027	1	a	a	DET
ejpam-3543	1027	2	ns	ns	NUM
ejpam-3543	1027	3	λ	λ	NOUN
ejpam-3543	1027	4	in	in	ADP
ejpam-3543	1027	5	x	x	PROPN
ejpam-3543	1027	6	is	be	AUX
ejpam-3543	1027	7	a	a	DET
ejpam-3543	1027	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	1027	9	up	up	ADP
ejpam-3543	1027	10	-	-	PUNCT
ejpam-3543	1027	11	subalgebra	subalgebra	NOUN
ejpam-3543	1027	12	of	of	ADP
ejpam-3543	1027	13	x	x	PRON
ejpam-3543	1027	14	if	if	SCONJ
ejpam-3543	1027	15	and	and	CCONJ
ejpam-3543	1027	16	only	only	ADV
ejpam-3543	1027	17	if	if	SCONJ
ejpam-3543	1027	18	for	for	ADP
ejpam-3543	1027	19	all	all	DET
ejpam-3543	1027	20	α	α	NOUN
ejpam-3543	1027	21	,	,	PUNCT
ejpam-3543	1027	22	β	β	X
ejpam-3543	1027	23	,	,	PUNCT
ejpam-3543	1027	24	γ	γ	PROPN
ejpam-3543	1027	25	∈	∈	PROPN
ejpam-3543	1028	1	[	[	X
ejpam-3543	1028	2	0	0	NUM
ejpam-3543	1028	3	,	,	PUNCT
ejpam-3543	1028	4	1	1	NUM
ejpam-3543	1028	5	]	]	PUNCT
ejpam-3543	1028	6	,	,	PUNCT
ejpam-3543	1028	7	uluλ(α	uluλ(α	PROPN
ejpam-3543	1028	8	,	,	PUNCT
ejpam-3543	1028	9	β	β	PROPN
ejpam-3543	1028	10	,	,	PUNCT
ejpam-3543	1028	11	γ	γ	X
ejpam-3543	1028	12	)	)	PUNCT
ejpam-3543	1028	13	is	be	AUX
ejpam-3543	1028	14	a	a	DET
ejpam-3543	1028	15	up	up	ADJ
ejpam-3543	1028	16	-	-	PUNCT
ejpam-3543	1028	17	subalgebra	subalgebra	NOUN
ejpam-3543	1028	18	of	of	ADP
ejpam-3543	1028	19	x	x	SYM
ejpam-3543	1028	20	where	where	SCONJ
ejpam-3543	1028	21	uluλ(α	uluλ(α	PROPN
ejpam-3543	1028	22	,	,	PUNCT
ejpam-3543	1028	23	β	β	PROPN
ejpam-3543	1028	24	,	,	PUNCT
ejpam-3543	1028	25	γ	γ	PROPN
ejpam-3543	1028	26	)	)	PUNCT
ejpam-3543	1028	27	is	be	AUX
ejpam-3543	1028	28	nonempty	nonempty	ADJ
ejpam-3543	1028	29	.	.	PUNCT
ejpam-3543	1029	1	proof	proof	NOUN
ejpam-3543	1029	2	.	.	PUNCT
ejpam-3543	1030	1	it	it	PRON
ejpam-3543	1030	2	is	be	AUX
ejpam-3543	1030	3	straightforward	straightforward	ADJ
ejpam-3543	1030	4	by	by	ADP
ejpam-3543	1030	5	theorem	theorem	NOUN
ejpam-3543	1030	6	19	19	NUM
ejpam-3543	1030	7	.	.	PUNCT
ejpam-3543	1030	8	corollary	corollary	ADJ
ejpam-3543	1030	9	2	2	NUM
ejpam-3543	1030	10	.	.	PUNCT
ejpam-3543	1031	1	a	a	DET
ejpam-3543	1031	2	ns	ns	NUM
ejpam-3543	1031	3	λ	λ	NOUN
ejpam-3543	1031	4	in	in	ADP
ejpam-3543	1031	5	x	x	PROPN
ejpam-3543	1031	6	is	be	AUX
ejpam-3543	1031	7	a	a	DET
ejpam-3543	1031	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	1031	9	near	near	ADP
ejpam-3543	1031	10	up	up	ADJ
ejpam-3543	1031	11	-	-	PUNCT
ejpam-3543	1031	12	filter	filter	NOUN
ejpam-3543	1031	13	of	of	ADP
ejpam-3543	1031	14	x	x	SYM
ejpam-3543	1031	15	if	if	SCONJ
ejpam-3543	1032	1	and	and	CCONJ
ejpam-3543	1032	2	only	only	ADV
ejpam-3543	1032	3	if	if	SCONJ
ejpam-3543	1032	4	for	for	ADP
ejpam-3543	1032	5	all	all	DET
ejpam-3543	1032	6	α	α	NOUN
ejpam-3543	1032	7	,	,	PUNCT
ejpam-3543	1032	8	β	β	X
ejpam-3543	1032	9	,	,	PUNCT
ejpam-3543	1032	10	γ	γ	PROPN
ejpam-3543	1032	11	∈	∈	PROPN
ejpam-3543	1033	1	[	[	X
ejpam-3543	1033	2	0	0	NUM
ejpam-3543	1033	3	,	,	PUNCT
ejpam-3543	1033	4	1	1	NUM
ejpam-3543	1033	5	]	]	PUNCT
ejpam-3543	1033	6	,	,	PUNCT
ejpam-3543	1033	7	uluλ(α	uluλ(α	PROPN
ejpam-3543	1033	8	,	,	PUNCT
ejpam-3543	1033	9	β	β	PROPN
ejpam-3543	1033	10	,	,	PUNCT
ejpam-3543	1033	11	γ	γ	X
ejpam-3543	1033	12	)	)	PUNCT
ejpam-3543	1033	13	is	be	AUX
ejpam-3543	1033	14	a	a	DET
ejpam-3543	1033	15	near	near	ADJ
ejpam-3543	1033	16	up	up	NOUN
ejpam-3543	1033	17	-	-	PUNCT
ejpam-3543	1033	18	filter	filter	NOUN
ejpam-3543	1033	19	of	of	ADP
ejpam-3543	1033	20	x	x	SYM
ejpam-3543	1033	21	where	where	SCONJ
ejpam-3543	1033	22	uluλ(α	uluλ(α	PROPN
ejpam-3543	1033	23	,	,	PUNCT
ejpam-3543	1033	24	β	β	PROPN
ejpam-3543	1033	25	,	,	PUNCT
ejpam-3543	1033	26	γ	γ	PROPN
ejpam-3543	1033	27	)	)	PUNCT
ejpam-3543	1033	28	is	be	AUX
ejpam-3543	1033	29	nonempty	nonempty	ADJ
ejpam-3543	1033	30	.	.	PUNCT
ejpam-3543	1034	1	proof	proof	NOUN
ejpam-3543	1034	2	.	.	PUNCT
ejpam-3543	1035	1	it	it	PRON
ejpam-3543	1035	2	is	be	AUX
ejpam-3543	1035	3	straightforward	straightforward	ADJ
ejpam-3543	1035	4	by	by	ADP
ejpam-3543	1035	5	theorem	theorem	ADJ
ejpam-3543	1035	6	20	20	NUM
ejpam-3543	1035	7	.	.	PUNCT
ejpam-3543	1035	8	corollary	corollary	ADJ
ejpam-3543	1035	9	3	3	NUM
ejpam-3543	1035	10	.	.	PUNCT
ejpam-3543	1036	1	a	a	DET
ejpam-3543	1036	2	ns	ns	NUM
ejpam-3543	1036	3	λ	λ	NOUN
ejpam-3543	1036	4	in	in	ADP
ejpam-3543	1036	5	x	x	PROPN
ejpam-3543	1036	6	is	be	AUX
ejpam-3543	1036	7	a	a	DET
ejpam-3543	1036	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	1036	9	up	up	ADJ
ejpam-3543	1036	10	-	-	PUNCT
ejpam-3543	1036	11	filter	filter	NOUN
ejpam-3543	1036	12	of	of	ADP
ejpam-3543	1036	13	x	x	SYM
ejpam-3543	1036	14	if	if	SCONJ
ejpam-3543	1036	15	and	and	CCONJ
ejpam-3543	1036	16	only	only	ADV
ejpam-3543	1036	17	if	if	SCONJ
ejpam-3543	1036	18	for	for	ADP
ejpam-3543	1036	19	all	all	DET
ejpam-3543	1036	20	α	α	NOUN
ejpam-3543	1036	21	,	,	PUNCT
ejpam-3543	1036	22	β	β	X
ejpam-3543	1036	23	,	,	PUNCT
ejpam-3543	1036	24	γ	γ	PROPN
ejpam-3543	1036	25	∈	∈	PROPN
ejpam-3543	1037	1	[	[	X
ejpam-3543	1037	2	0	0	NUM
ejpam-3543	1037	3	,	,	PUNCT
ejpam-3543	1037	4	1	1	NUM
ejpam-3543	1037	5	]	]	PUNCT
ejpam-3543	1037	6	,	,	PUNCT
ejpam-3543	1037	7	uluλ(α	uluλ(α	PROPN
ejpam-3543	1037	8	,	,	PUNCT
ejpam-3543	1037	9	β	β	PROPN
ejpam-3543	1037	10	,	,	PUNCT
ejpam-3543	1037	11	γ	γ	X
ejpam-3543	1037	12	)	)	PUNCT
ejpam-3543	1037	13	is	be	AUX
ejpam-3543	1037	14	a	a	DET
ejpam-3543	1037	15	up	up	ADJ
ejpam-3543	1037	16	-	-	PUNCT
ejpam-3543	1037	17	filter	filter	NOUN
ejpam-3543	1037	18	of	of	ADP
ejpam-3543	1037	19	x	x	SYM
ejpam-3543	1037	20	where	where	SCONJ
ejpam-3543	1037	21	uluλ(α	uluλ(α	PROPN
ejpam-3543	1037	22	,	,	PUNCT
ejpam-3543	1037	23	β	β	PROPN
ejpam-3543	1037	24	,	,	PUNCT
ejpam-3543	1037	25	γ	γ	PROPN
ejpam-3543	1037	26	)	)	PUNCT
ejpam-3543	1037	27	is	be	AUX
ejpam-3543	1037	28	nonempty	nonempty	ADJ
ejpam-3543	1037	29	.	.	PUNCT
ejpam-3543	1038	1	proof	proof	NOUN
ejpam-3543	1038	2	.	.	PUNCT
ejpam-3543	1039	1	it	it	PRON
ejpam-3543	1039	2	is	be	AUX
ejpam-3543	1039	3	straightforward	straightforward	ADJ
ejpam-3543	1039	4	by	by	ADP
ejpam-3543	1039	5	theorem	theorem	NOUN
ejpam-3543	1039	6	21	21	NUM
ejpam-3543	1039	7	.	.	PUNCT
ejpam-3543	1039	8	corollary	corollary	ADJ
ejpam-3543	1039	9	4	4	NUM
ejpam-3543	1039	10	.	.	PUNCT
ejpam-3543	1040	1	a	a	DET
ejpam-3543	1040	2	ns	ns	NUM
ejpam-3543	1040	3	λ	λ	NOUN
ejpam-3543	1040	4	in	in	ADP
ejpam-3543	1040	5	x	x	PROPN
ejpam-3543	1040	6	is	be	AUX
ejpam-3543	1040	7	a	a	DET
ejpam-3543	1040	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	1040	9	up	up	ADV
ejpam-3543	1040	10	-	-	PUNCT
ejpam-3543	1040	11	ideal	ideal	NOUN
ejpam-3543	1040	12	of	of	ADP
ejpam-3543	1040	13	x	x	SYM
ejpam-3543	1040	14	if	if	SCONJ
ejpam-3543	1040	15	and	and	CCONJ
ejpam-3543	1040	16	only	only	ADV
ejpam-3543	1040	17	if	if	SCONJ
ejpam-3543	1040	18	for	for	ADP
ejpam-3543	1040	19	all	all	DET
ejpam-3543	1040	20	α	α	NOUN
ejpam-3543	1040	21	,	,	PUNCT
ejpam-3543	1040	22	β	β	X
ejpam-3543	1040	23	,	,	PUNCT
ejpam-3543	1040	24	γ	γ	PROPN
ejpam-3543	1040	25	∈	∈	PROPN
ejpam-3543	1041	1	[	[	X
ejpam-3543	1041	2	0	0	NUM
ejpam-3543	1041	3	,	,	PUNCT
ejpam-3543	1041	4	1	1	NUM
ejpam-3543	1041	5	]	]	PUNCT
ejpam-3543	1041	6	,	,	PUNCT
ejpam-3543	1041	7	uluλ(α	uluλ(α	PROPN
ejpam-3543	1041	8	,	,	PUNCT
ejpam-3543	1041	9	β	β	PROPN
ejpam-3543	1041	10	,	,	PUNCT
ejpam-3543	1041	11	γ	γ	X
ejpam-3543	1041	12	)	)	PUNCT
ejpam-3543	1041	13	is	be	AUX
ejpam-3543	1041	14	a	a	DET
ejpam-3543	1041	15	up	up	ADJ
ejpam-3543	1041	16	-	-	PUNCT
ejpam-3543	1041	17	ideal	ideal	NOUN
ejpam-3543	1041	18	of	of	ADP
ejpam-3543	1041	19	x	x	SYM
ejpam-3543	1041	20	where	where	SCONJ
ejpam-3543	1041	21	uluλ(α	uluλ(α	PROPN
ejpam-3543	1041	22	,	,	PUNCT
ejpam-3543	1041	23	β	β	PROPN
ejpam-3543	1041	24	,	,	PUNCT
ejpam-3543	1041	25	γ	γ	PROPN
ejpam-3543	1041	26	)	)	PUNCT
ejpam-3543	1041	27	is	be	AUX
ejpam-3543	1041	28	nonempty	nonempty	ADJ
ejpam-3543	1041	29	.	.	PUNCT
ejpam-3543	1042	1	proof	proof	NOUN
ejpam-3543	1042	2	.	.	PUNCT
ejpam-3543	1043	1	it	it	PRON
ejpam-3543	1043	2	is	be	AUX
ejpam-3543	1043	3	straightforward	straightforward	ADJ
ejpam-3543	1043	4	by	by	ADP
ejpam-3543	1043	5	theorem	theorem	NOUN
ejpam-3543	1043	6	22	22	NUM
ejpam-3543	1043	7	.	.	PUNCT
ejpam-3543	1044	1	corollary	corollary	ADJ
ejpam-3543	1044	2	5	5	NUM
ejpam-3543	1044	3	.	.	PUNCT
ejpam-3543	1045	1	a	a	DET
ejpam-3543	1045	2	ns	ns	NUM
ejpam-3543	1045	3	λ	λ	NOUN
ejpam-3543	1045	4	in	in	ADP
ejpam-3543	1045	5	x	x	PROPN
ejpam-3543	1045	6	is	be	AUX
ejpam-3543	1045	7	a	a	DET
ejpam-3543	1045	8	neutrosophic	neutrosophic	ADJ
ejpam-3543	1045	9	strongly	strongly	ADV
ejpam-3543	1045	10	up	up	ADP
ejpam-3543	1045	11	-	-	PUNCT
ejpam-3543	1045	12	ideal	ideal	NOUN
ejpam-3543	1045	13	of	of	ADP
ejpam-3543	1045	14	x	x	SYM
ejpam-3543	1045	15	if	if	SCONJ
ejpam-3543	1045	16	and	and	CCONJ
ejpam-3543	1045	17	only	only	ADV
ejpam-3543	1045	18	if	if	SCONJ
ejpam-3543	1045	19	e(λt	e(λt	NOUN
ejpam-3543	1045	20	,	,	PUNCT
ejpam-3543	1045	21	λt	λt	X
ejpam-3543	1045	22	(	(	PUNCT
ejpam-3543	1045	23	0	0	NUM
ejpam-3543	1045	24	)	)	PUNCT
ejpam-3543	1045	25	)	)	PUNCT
ejpam-3543	1045	26	,	,	PUNCT
ejpam-3543	1045	27	e(λi	e(λi	PROPN
ejpam-3543	1045	28	,	,	PUNCT
ejpam-3543	1045	29	λi(0	λi(0	NOUN
ejpam-3543	1045	30	)	)	PUNCT
ejpam-3543	1045	31	)	)	PUNCT
ejpam-3543	1045	32	,	,	PUNCT
ejpam-3543	1045	33	and	and	CCONJ
ejpam-3543	1045	34	e(λf	e(λf	PROPN
ejpam-3543	1045	35	,	,	PUNCT
ejpam-3543	1045	36	λf	λf	X
ejpam-3543	1045	37	(	(	PUNCT
ejpam-3543	1045	38	0	0	NUM
ejpam-3543	1045	39	)	)	PUNCT
ejpam-3543	1045	40	)	)	PUNCT
ejpam-3543	1045	41	are	be	AUX
ejpam-3543	1045	42	strongly	strongly	ADV
ejpam-3543	1045	43	up	up	ADP
ejpam-3543	1045	44	-	-	PUNCT
ejpam-3543	1045	45	ideals	ideal	NOUN
ejpam-3543	1045	46	of	of	ADP
ejpam-3543	1045	47	x	x	PRON
ejpam-3543	1045	48	,	,	PUNCT
ejpam-3543	1045	49	that	that	ADV
ejpam-3543	1045	50	is	is	ADV
ejpam-3543	1045	51	,	,	PUNCT
ejpam-3543	1045	52	e(λt	e(λt	NOUN
ejpam-3543	1045	53	,	,	PUNCT
ejpam-3543	1045	54	λt	λt	X
ejpam-3543	1045	55	(	(	PUNCT
ejpam-3543	1045	56	0	0	NUM
ejpam-3543	1045	57	)	)	PUNCT
ejpam-3543	1045	58	)	)	PUNCT
ejpam-3543	1046	1	=	=	SYM
ejpam-3543	1046	2	x	x	X
ejpam-3543	1046	3	,	,	PUNCT
ejpam-3543	1046	4	e(λi	e(λi	PROPN
ejpam-3543	1046	5	,	,	PUNCT
ejpam-3543	1046	6	λi(0	λi(0	NOUN
ejpam-3543	1046	7	)	)	PUNCT
ejpam-3543	1046	8	)	)	PUNCT
ejpam-3543	1047	1	=	=	SYM
ejpam-3543	1047	2	x	x	NOUN
ejpam-3543	1047	3	,	,	PUNCT
ejpam-3543	1047	4	and	and	CCONJ
ejpam-3543	1047	5	e(λf	e(λf	PROPN
ejpam-3543	1047	6	,	,	PUNCT
ejpam-3543	1047	7	λf	λf	X
ejpam-3543	1047	8	(	(	PUNCT
ejpam-3543	1047	9	0	0	NUM
ejpam-3543	1047	10	)	)	PUNCT
ejpam-3543	1047	11	)	)	PUNCT
ejpam-3543	1048	1	=	=	PUNCT
ejpam-3543	1048	2	x.	x.	NOUN
ejpam-3543	1048	3	proof	proof	NOUN
ejpam-3543	1048	4	.	.	PUNCT
ejpam-3543	1049	1	it	it	PRON
ejpam-3543	1049	2	is	be	AUX
ejpam-3543	1049	3	straightforward	straightforward	ADJ
ejpam-3543	1049	4	by	by	ADP
ejpam-3543	1049	5	theorem	theorem	NOUN
ejpam-3543	1049	6	23	23	NUM
ejpam-3543	1049	7	.	.	PUNCT
ejpam-3543	1050	1	references	reference	NOUN
ejpam-3543	1050	2	1407	1407	NUM
ejpam-3543	1050	3	5	5	NUM
ejpam-3543	1050	4	.	.	PUNCT
ejpam-3543	1050	5	conclusions	conclusion	NOUN
ejpam-3543	1050	6	in	in	ADP
ejpam-3543	1050	7	this	this	DET
ejpam-3543	1050	8	paper	paper	NOUN
ejpam-3543	1050	9	,	,	PUNCT
ejpam-3543	1050	10	we	we	PRON
ejpam-3543	1050	11	have	have	AUX
ejpam-3543	1050	12	introduced	introduce	VERB
ejpam-3543	1050	13	the	the	DET
ejpam-3543	1050	14	notions	notion	NOUN
ejpam-3543	1050	15	of	of	ADP
ejpam-3543	1050	16	neutrosophic	neutrosophic	ADJ
ejpam-3543	1050	17	up	up	ADP
ejpam-3543	1050	18	-	-	PUNCT
ejpam-3543	1050	19	subalgebras	subalgebras	PROPN
ejpam-3543	1050	20	,	,	PUNCT
ejpam-3543	1050	21	neutrosophic	neutrosophic	ADJ
ejpam-3543	1050	22	near	near	ADP
ejpam-3543	1050	23	up	up	ADP
ejpam-3543	1050	24	-	-	PUNCT
ejpam-3543	1050	25	filters	filter	NOUN
ejpam-3543	1050	26	,	,	PUNCT
ejpam-3543	1050	27	neutrosophic	neutrosophic	ADJ
ejpam-3543	1050	28	up	up	ADP
ejpam-3543	1050	29	-	-	PUNCT
ejpam-3543	1050	30	filters	filter	NOUN
ejpam-3543	1050	31	,	,	PUNCT
ejpam-3543	1050	32	neutrosophic	neutrosophic	ADJ
ejpam-3543	1050	33	up	up	ADP
ejpam-3543	1050	34	-	-	PUNCT
ejpam-3543	1050	35	ideals	ideal	NOUN
ejpam-3543	1050	36	,	,	PUNCT
ejpam-3543	1050	37	and	and	CCONJ
ejpam-3543	1050	38	neutrosophic	neutrosophic	ADJ
ejpam-3543	1050	39	strongly	strongly	ADV
ejpam-3543	1050	40	up	up	ADP
ejpam-3543	1050	41	-	-	PUNCT
ejpam-3543	1050	42	ideals	ideal	NOUN
ejpam-3543	1050	43	of	of	ADP
ejpam-3543	1050	44	up	up	ADV
ejpam-3543	1050	45	-	-	PUNCT
ejpam-3543	1050	46	algebras	algebras	PROPN
ejpam-3543	1050	47	and	and	CCONJ
ejpam-3543	1050	48	investigated	investigate	VERB
ejpam-3543	1050	49	some	some	PRON
ejpam-3543	1050	50	of	of	ADP
ejpam-3543	1050	51	their	their	PRON
ejpam-3543	1050	52	important	important	ADJ
ejpam-3543	1050	53	properties	property	NOUN
ejpam-3543	1050	54	.	.	PUNCT
ejpam-3543	1051	1	then	then	ADV
ejpam-3543	1051	2	,	,	PUNCT
ejpam-3543	1051	3	we	we	PRON
ejpam-3543	1051	4	get	get	VERB
ejpam-3543	1051	5	the	the	DET
ejpam-3543	1051	6	diagram	diagram	NOUN
ejpam-3543	1051	7	of	of	ADP
ejpam-3543	1051	8	generalization	generalization	NOUN
ejpam-3543	1051	9	of	of	ADP
ejpam-3543	1051	10	nss	nss	NOUN
ejpam-3543	1051	11	in	in	ADP
ejpam-3543	1051	12	up	up	ADV
ejpam-3543	1051	13	-	-	PUNCT
ejpam-3543	1051	14	algebras	algebra	NOUN
ejpam-3543	1051	15	as	as	SCONJ
ejpam-3543	1051	16	shown	show	VERB
ejpam-3543	1051	17	in	in	ADP
ejpam-3543	1051	18	figure	figure	NOUN
ejpam-3543	1051	19	1	1	NUM
ejpam-3543	1051	20	.	.	PUNCT
ejpam-3543	1051	21	figure	figure	NOUN
ejpam-3543	1051	22	1	1	NUM
ejpam-3543	1051	23	:	:	PUNCT
ejpam-3543	1051	24	nss	nss	VERB
ejpam-3543	1051	25	in	in	ADV
ejpam-3543	1051	26	up	up	ADV
ejpam-3543	1051	27	-	-	PUNCT
ejpam-3543	1051	28	algebras	algebras	NOUN
ejpam-3543	1051	29	in	in	ADP
ejpam-3543	1051	30	our	our	PRON
ejpam-3543	1051	31	future	future	ADJ
ejpam-3543	1051	32	study	study	NOUN
ejpam-3543	1051	33	,	,	PUNCT
ejpam-3543	1051	34	we	we	PRON
ejpam-3543	1051	35	will	will	AUX
ejpam-3543	1051	36	apply	apply	VERB
ejpam-3543	1051	37	this	this	DET
ejpam-3543	1051	38	notion	notion	NOUN
ejpam-3543	1051	39	/	/	SYM
ejpam-3543	1051	40	results	result	NOUN
ejpam-3543	1051	41	to	to	ADP
ejpam-3543	1051	42	other	other	ADJ
ejpam-3543	1051	43	type	type	NOUN
ejpam-3543	1051	44	of	of	ADP
ejpam-3543	1051	45	nss	nss	NOUN
ejpam-3543	1051	46	in	in	ADP
ejpam-3543	1051	47	upalgebras	upalgebra	NOUN
ejpam-3543	1051	48	.	.	PUNCT
ejpam-3543	1052	1	also	also	ADV
ejpam-3543	1052	2	,	,	PUNCT
ejpam-3543	1052	3	we	we	PRON
ejpam-3543	1052	4	will	will	AUX
ejpam-3543	1052	5	study	study	VERB
ejpam-3543	1052	6	the	the	DET
ejpam-3543	1052	7	soft	soft	ADJ
ejpam-3543	1052	8	set	set	NOUN
ejpam-3543	1052	9	theory	theory	NOUN
ejpam-3543	1052	10	/	/	SYM
ejpam-3543	1052	11	cubic	cubic	ADJ
ejpam-3543	1052	12	set	set	NOUN
ejpam-3543	1052	13	theory	theory	NOUN
ejpam-3543	1052	14	of	of	ADP
ejpam-3543	1052	15	neutrosophic	neutrosophic	ADJ
ejpam-3543	1052	16	upsubalgebras	upsubalgebra	NOUN
ejpam-3543	1052	17	,	,	PUNCT
ejpam-3543	1052	18	neutrosophic	neutrosophic	ADJ
ejpam-3543	1052	19	near	near	ADP
ejpam-3543	1052	20	up	up	ADP
ejpam-3543	1052	21	-	-	PUNCT
ejpam-3543	1052	22	filters	filter	NOUN
ejpam-3543	1052	23	,	,	PUNCT
ejpam-3543	1052	24	neutrosophic	neutrosophic	ADJ
ejpam-3543	1052	25	up	up	ADP
ejpam-3543	1052	26	-	-	PUNCT
ejpam-3543	1052	27	filters	filter	NOUN
ejpam-3543	1052	28	,	,	PUNCT
ejpam-3543	1052	29	neutrosophic	neutrosophic	ADJ
ejpam-3543	1052	30	up	up	ADP
ejpam-3543	1052	31	-	-	PUNCT
ejpam-3543	1052	32	ideals	ideal	NOUN
ejpam-3543	1052	33	,	,	PUNCT
ejpam-3543	1052	34	and	and	CCONJ
ejpam-3543	1052	35	neutrosophic	neutrosophic	ADJ
ejpam-3543	1052	36	strongly	strongly	ADV
ejpam-3543	1052	37	up	up	ADP
ejpam-3543	1052	38	-	-	PUNCT
ejpam-3543	1052	39	ideals	ideal	NOUN
ejpam-3543	1052	40	.	.	PUNCT
ejpam-3543	1053	1	acknowledgements	acknowledgement	NOUN
ejpam-3543	1053	2	the	the	DET
ejpam-3543	1053	3	authors	author	NOUN
ejpam-3543	1053	4	would	would	AUX
ejpam-3543	1053	5	also	also	ADV
ejpam-3543	1053	6	like	like	VERB
ejpam-3543	1053	7	to	to	PART
ejpam-3543	1053	8	thank	thank	VERB
ejpam-3543	1053	9	the	the	DET
ejpam-3543	1053	10	anonymous	anonymous	ADJ
ejpam-3543	1053	11	referee	referee	NOUN
ejpam-3543	1053	12	for	for	ADP
ejpam-3543	1053	13	giving	give	VERB
ejpam-3543	1053	14	many	many	ADJ
ejpam-3543	1053	15	helpful	helpful	ADJ
ejpam-3543	1053	16	suggestion	suggestion	NOUN
ejpam-3543	1053	17	on	on	ADP
ejpam-3543	1053	18	the	the	DET
ejpam-3543	1053	19	revision	revision	NOUN
ejpam-3543	1053	20	of	of	ADP
ejpam-3543	1053	21	present	present	ADJ
ejpam-3543	1053	22	paper	paper	NOUN
ejpam-3543	1053	23	.	.	PUNCT
ejpam-3543	1054	1	references	reference	NOUN
ejpam-3543	1054	2	[	[	X
ejpam-3543	1054	3	1	1	NUM
ejpam-3543	1054	4	]	]	PUNCT
ejpam-3543	1054	5	m.	m.	NOUN
ejpam-3543	1054	6	a.	a.	NOUN
ejpam-3543	1054	7	ansari	ansari	PROPN
ejpam-3543	1054	8	,	,	PUNCT
ejpam-3543	1054	9	a.	a.	PROPN
ejpam-3543	1054	10	haidar	haidar	NOUN
ejpam-3543	1054	11	,	,	PUNCT
ejpam-3543	1054	12	and	and	CCONJ
ejpam-3543	1054	13	a.	a.	PROPN
ejpam-3543	1054	14	n.	n.	PROPN
ejpam-3543	1054	15	a.	a.	PROPN
ejpam-3543	1054	16	koam	koam	PROPN
ejpam-3543	1054	17	.	.	PUNCT
ejpam-3543	1055	1	on	on	ADP
ejpam-3543	1055	2	a	a	DET
ejpam-3543	1055	3	graph	graph	NOUN
ejpam-3543	1055	4	associated	associate	VERB
ejpam-3543	1055	5	to	to	ADP
ejpam-3543	1055	6	up	up	ADV
ejpam-3543	1055	7	-	-	PUNCT
ejpam-3543	1055	8	algebras	algebras	PROPN
ejpam-3543	1055	9	.	.	PUNCT
ejpam-3543	1055	10	math	math	NOUN
ejpam-3543	1055	11	.	.	PUNCT
ejpam-3543	1056	1	comput	comput	NOUN
ejpam-3543	1056	2	.	.	PUNCT
ejpam-3543	1057	1	appl	appl	PROPN
ejpam-3543	1057	2	.	.	PROPN
ejpam-3543	1058	1	,	,	PUNCT
ejpam-3543	1058	2	23(4):61	23(4):61	NUM
ejpam-3543	1058	3	,	,	PUNCT
ejpam-3543	1058	4	2018	2018	NUM
ejpam-3543	1058	5	.	.	PUNCT
ejpam-3543	1059	1	[	[	X
ejpam-3543	1059	2	2	2	NUM
ejpam-3543	1059	3	]	]	X
ejpam-3543	1059	4	n.	n.	PROPN
ejpam-3543	1059	5	dokkhamdang	dokkhamdang	PROPN
ejpam-3543	1059	6	,	,	PUNCT
ejpam-3543	1059	7	a.	a.	PROPN
ejpam-3543	1059	8	kesorn	kesorn	PROPN
ejpam-3543	1059	9	,	,	PUNCT
ejpam-3543	1059	10	and	and	CCONJ
ejpam-3543	1059	11	a.	a.	NOUN
ejpam-3543	1059	12	iampan	iampan	PROPN
ejpam-3543	1059	13	.	.	PUNCT
ejpam-3543	1060	1	generalized	generalize	VERB
ejpam-3543	1060	2	fuzzy	fuzzy	ADJ
ejpam-3543	1060	3	sets	set	NOUN
ejpam-3543	1060	4	in	in	ADP
ejpam-3543	1060	5	up	up	ADP
ejpam-3543	1060	6	-	-	PUNCT
ejpam-3543	1060	7	algebras	algebras	X
ejpam-3543	1060	8	.	.	PUNCT
ejpam-3543	1061	1	ann	ann	PROPN
ejpam-3543	1061	2	.	.	PUNCT
ejpam-3543	1061	3	fuzzy	fuzzy	ADJ
ejpam-3543	1061	4	math	math	NOUN
ejpam-3543	1061	5	.	.	PUNCT
ejpam-3543	1062	1	inform	inform	NOUN
ejpam-3543	1062	2	.	.	PUNCT
ejpam-3543	1062	3	,	,	PUNCT
ejpam-3543	1062	4	16(2):171–190	16(2):171–190	NUM
ejpam-3543	1062	5	,	,	PUNCT
ejpam-3543	1062	6	2018	2018	NUM
ejpam-3543	1062	7	.	.	PUNCT
ejpam-3543	1063	1	references	reference	NOUN
ejpam-3543	1063	2	1408	1408	NUM
ejpam-3543	1063	3	[	[	X
ejpam-3543	1063	4	3	3	NUM
ejpam-3543	1063	5	]	]	X
ejpam-3543	1063	6	t.	t.	NOUN
ejpam-3543	1063	7	guntasow	guntasow	NOUN
ejpam-3543	1063	8	,	,	PUNCT
ejpam-3543	1063	9	s.	s.	PROPN
ejpam-3543	1063	10	sajak	sajak	PROPN
ejpam-3543	1063	11	,	,	PUNCT
ejpam-3543	1063	12	a.	a.	PROPN
ejpam-3543	1063	13	jomkham	jomkham	PROPN
ejpam-3543	1063	14	,	,	PUNCT
ejpam-3543	1063	15	and	and	CCONJ
ejpam-3543	1063	16	a.	a.	NOUN
ejpam-3543	1063	17	iampan	iampan	PROPN
ejpam-3543	1063	18	.	.	PUNCT
ejpam-3543	1064	1	fuzzy	fuzzy	ADJ
ejpam-3543	1064	2	translations	translation	NOUN
ejpam-3543	1064	3	of	of	ADP
ejpam-3543	1064	4	a	a	DET
ejpam-3543	1064	5	fuzzy	fuzzy	ADJ
ejpam-3543	1064	6	set	set	NOUN
ejpam-3543	1064	7	in	in	ADP
ejpam-3543	1064	8	up	up	ADP
ejpam-3543	1064	9	-	-	PUNCT
ejpam-3543	1064	10	algebras	algebras	X
ejpam-3543	1064	11	.	.	PUNCT
ejpam-3543	1065	1	j.	j.	PROPN
ejpam-3543	1065	2	indones	indones	PROPN
ejpam-3543	1065	3	.	.	PUNCT
ejpam-3543	1066	1	math	math	NOUN
ejpam-3543	1066	2	.	.	PUNCT
ejpam-3543	1067	1	soc	soc	PROPN
ejpam-3543	1067	2	.	.	PROPN
ejpam-3543	1067	3	,	,	PUNCT
ejpam-3543	1067	4	23(2):1–19	23(2):1–19	NUM
ejpam-3543	1067	5	,	,	PUNCT
ejpam-3543	1067	6	2017	2017	NUM
ejpam-3543	1067	7	.	.	PUNCT
ejpam-3543	1068	1	[	[	X
ejpam-3543	1068	2	4	4	NUM
ejpam-3543	1068	3	]	]	PUNCT
ejpam-3543	1068	4	q.	q.	PROPN
ejpam-3543	1068	5	p.	p.	PROPN
ejpam-3543	1068	6	hu	hu	PROPN
ejpam-3543	1069	1	and	and	CCONJ
ejpam-3543	1070	1	x.	x.	PROPN
ejpam-3543	1070	2	li	li	PROPN
ejpam-3543	1070	3	.	.	PROPN
ejpam-3543	1071	1	on	on	ADP
ejpam-3543	1071	2	bch	bch	PROPN
ejpam-3543	1071	3	-	-	PUNCT
ejpam-3543	1071	4	algebras	algebras	PROPN
ejpam-3543	1071	5	.	.	PUNCT
ejpam-3543	1071	6	math	math	PROPN
ejpam-3543	1071	7	.	.	PUNCT
ejpam-3543	1072	1	sem	sem	PROPN
ejpam-3543	1072	2	.	.	PUNCT
ejpam-3543	1073	1	notes	notes	PROPN
ejpam-3543	1073	2	kobe	kobe	PROPN
ejpam-3543	1073	3	univ	univ	PROPN
ejpam-3543	1073	4	.	.	PROPN
ejpam-3543	1073	5	,	,	PUNCT
ejpam-3543	1073	6	11(2):313–320	11(2):313–320	PROPN
ejpam-3543	1073	7	,	,	PUNCT
ejpam-3543	1073	8	1983	1983	NUM
ejpam-3543	1073	9	.	.	PUNCT
ejpam-3543	1074	1	[	[	X
ejpam-3543	1074	2	5	5	NUM
ejpam-3543	1074	3	]	]	PUNCT
ejpam-3543	1074	4	a.	a.	NOUN
ejpam-3543	1074	5	iampan	iampan	PROPN
ejpam-3543	1074	6	.	.	PUNCT
ejpam-3543	1075	1	a	a	DET
ejpam-3543	1075	2	new	new	ADJ
ejpam-3543	1075	3	branch	branch	NOUN
ejpam-3543	1075	4	of	of	ADP
ejpam-3543	1075	5	the	the	DET
ejpam-3543	1075	6	logical	logical	ADJ
ejpam-3543	1075	7	algebra	algebra	NOUN
ejpam-3543	1075	8	:	:	PUNCT
ejpam-3543	1075	9	up	up	ADP
ejpam-3543	1075	10	-	-	PUNCT
ejpam-3543	1075	11	algebras	algebras	X
ejpam-3543	1075	12	.	.	PUNCT
ejpam-3543	1076	1	j.	j.	PROPN
ejpam-3543	1076	2	algebra	algebra	PROPN
ejpam-3543	1076	3	relat	relat	PROPN
ejpam-3543	1076	4	.	.	PUNCT
ejpam-3543	1077	1	top	top	PROPN
ejpam-3543	1077	2	.	.	PROPN
ejpam-3543	1077	3	,	,	PUNCT
ejpam-3543	1077	4	5(1):35–54	5(1):35–54	NUM
ejpam-3543	1077	5	,	,	PUNCT
ejpam-3543	1077	6	2017	2017	NUM
ejpam-3543	1077	7	.	.	PUNCT
ejpam-3543	1078	1	[	[	X
ejpam-3543	1078	2	6	6	NUM
ejpam-3543	1078	3	]	]	PUNCT
ejpam-3543	1078	4	a.	a.	NOUN
ejpam-3543	1078	5	iampan	iampan	PROPN
ejpam-3543	1078	6	.	.	PUNCT
ejpam-3543	1079	1	introducing	introduce	VERB
ejpam-3543	1079	2	fully	fully	ADV
ejpam-3543	1079	3	up	up	ADP
ejpam-3543	1079	4	-	-	PUNCT
ejpam-3543	1079	5	semigroups	semigroup	NOUN
ejpam-3543	1079	6	.	.	PUNCT
ejpam-3543	1080	1	discuss	discuss	PROPN
ejpam-3543	1080	2	.	.	PUNCT
ejpam-3543	1080	3	math	math	PROPN
ejpam-3543	1080	4	.	.	PUNCT
ejpam-3543	1080	5	,	,	PUNCT
ejpam-3543	1081	1	gen	gen	PROPN
ejpam-3543	1081	2	.	.	PROPN
ejpam-3543	1081	3	algebra	algebra	PROPN
ejpam-3543	1081	4	appl	appl	PROPN
ejpam-3543	1081	5	.	.	PROPN
ejpam-3543	1081	6	,	,	PUNCT
ejpam-3543	1081	7	38(2):297–306	38(2):297–306	NUM
ejpam-3543	1081	8	,	,	PUNCT
ejpam-3543	1081	9	2018	2018	NUM
ejpam-3543	1081	10	.	.	PUNCT
ejpam-3543	1082	1	[	[	X
ejpam-3543	1082	2	7	7	X
ejpam-3543	1082	3	]	]	X
ejpam-3543	1082	4	y.	y.	PROPN
ejpam-3543	1082	5	imai	imai	PROPN
ejpam-3543	1082	6	and	and	CCONJ
ejpam-3543	1082	7	k.	k.	PROPN
ejpam-3543	1082	8	iséki	iséki	PROPN
ejpam-3543	1082	9	.	.	PROPN
ejpam-3543	1083	1	on	on	ADP
ejpam-3543	1083	2	axiom	axiom	NOUN
ejpam-3543	1083	3	system	system	NOUN
ejpam-3543	1083	4	of	of	ADP
ejpam-3543	1083	5	propositional	propositional	ADJ
ejpam-3543	1083	6	calculi	calculi	PROPN
ejpam-3543	1083	7	,	,	PUNCT
ejpam-3543	1083	8	xiv	xiv	PROPN
ejpam-3543	1083	9	.	.	PUNCT
ejpam-3543	1084	1	proc	proc	PROPN
ejpam-3543	1084	2	.	.	PUNCT
ejpam-3543	1085	1	japan	japan	PROPN
ejpam-3543	1085	2	acad	acad	PROPN
ejpam-3543	1085	3	.	.	PROPN
ejpam-3543	1085	4	,	,	PUNCT
ejpam-3543	1085	5	42(1):19–22	42(1):19–22	NUM
ejpam-3543	1085	6	,	,	PUNCT
ejpam-3543	1085	7	1966	1966	NUM
ejpam-3543	1085	8	.	.	PUNCT
ejpam-3543	1086	1	[	[	X
ejpam-3543	1086	2	8	8	NUM
ejpam-3543	1086	3	]	]	PUNCT
ejpam-3543	1086	4	k.	k.	PROPN
ejpam-3543	1086	5	iséki	iséki	PROPN
ejpam-3543	1086	6	.	.	PUNCT
ejpam-3543	1087	1	an	an	DET
ejpam-3543	1087	2	algebra	algebra	NOUN
ejpam-3543	1087	3	related	relate	VERB
ejpam-3543	1087	4	with	with	ADP
ejpam-3543	1087	5	a	a	DET
ejpam-3543	1087	6	propositional	propositional	ADJ
ejpam-3543	1087	7	calculus	calculus	NOUN
ejpam-3543	1087	8	.	.	PUNCT
ejpam-3543	1088	1	proc	proc	PROPN
ejpam-3543	1088	2	.	.	PUNCT
ejpam-3543	1089	1	japan	japan	PROPN
ejpam-3543	1089	2	acad	acad	PROPN
ejpam-3543	1089	3	.	.	PROPN
ejpam-3543	1089	4	,	,	PUNCT
ejpam-3543	1089	5	42(1):26–29	42(1):26–29	NUM
ejpam-3543	1089	6	,	,	PUNCT
ejpam-3543	1089	7	1966	1966	NUM
ejpam-3543	1089	8	.	.	PUNCT
ejpam-3543	1090	1	[	[	X
ejpam-3543	1090	2	9	9	X
ejpam-3543	1090	3	]	]	X
ejpam-3543	1090	4	y.	y.	PROPN
ejpam-3543	1090	5	b.	b.	PROPN
ejpam-3543	1090	6	jun	jun	PROPN
ejpam-3543	1090	7	,	,	PUNCT
ejpam-3543	1090	8	f.	f.	PROPN
ejpam-3543	1090	9	smarandache	smarandache	PROPN
ejpam-3543	1090	10	,	,	PUNCT
ejpam-3543	1090	11	and	and	CCONJ
ejpam-3543	1090	12	h.	h.	PROPN
ejpam-3543	1090	13	bordbar	bordbar	PROPN
ejpam-3543	1090	14	.	.	PUNCT
ejpam-3543	1091	1	neutrosophic	neutrosophic	PROPN
ejpam-3543	1091	2	n	n	PRON
ejpam-3543	1091	3	-structures	-structure	NOUN
ejpam-3543	1091	4	applied	apply	VERB
ejpam-3543	1091	5	to	to	PART
ejpam-3543	1091	6	bck	bck	VERB
ejpam-3543	1091	7	/	/	SYM
ejpam-3543	1091	8	bci	bci	NOUN
ejpam-3543	1091	9	-	-	PUNCT
ejpam-3543	1091	10	algebras	algebra	NOUN
ejpam-3543	1091	11	.	.	PUNCT
ejpam-3543	1092	1	inform	inform	NOUN
ejpam-3543	1092	2	.	.	PUNCT
ejpam-3543	1092	3	,	,	PUNCT
ejpam-3543	1092	4	8(4):128	8(4):128	NUM
ejpam-3543	1092	5	,	,	PUNCT
ejpam-3543	1092	6	2017	2017	NUM
ejpam-3543	1092	7	.	.	PUNCT
ejpam-3543	1093	1	[	[	X
ejpam-3543	1093	2	10	10	NUM
ejpam-3543	1093	3	]	]	X
ejpam-3543	1093	4	y.	y.	PROPN
ejpam-3543	1093	5	b.	b.	PROPN
ejpam-3543	1093	6	jun	jun	PROPN
ejpam-3543	1093	7	,	,	PUNCT
ejpam-3543	1093	8	f.	f.	PROPN
ejpam-3543	1093	9	smarandache	smarandache	PROPN
ejpam-3543	1093	10	,	,	PUNCT
ejpam-3543	1093	11	s.-z	s.-z	PROPN
ejpam-3543	1093	12	.	.	PUNCT
ejpam-3543	1094	1	song	song	NOUN
ejpam-3543	1094	2	,	,	PUNCT
ejpam-3543	1094	3	and	and	CCONJ
ejpam-3543	1094	4	m.	m.	PROPN
ejpam-3543	1094	5	khan	khan	PROPN
ejpam-3543	1094	6	.	.	PUNCT
ejpam-3543	1095	1	neutrosophic	neutrosophic	ADJ
ejpam-3543	1095	2	positive	positive	ADJ
ejpam-3543	1095	3	implicative	implicative	ADJ
ejpam-3543	1095	4	n	n	PRON
ejpam-3543	1095	5	-ideals	-ideal	NOUN
ejpam-3543	1095	6	in	in	ADP
ejpam-3543	1095	7	bck	bck	NOUN
ejpam-3543	1095	8	-	-	PUNCT
ejpam-3543	1095	9	algebras	algebra	NOUN
ejpam-3543	1095	10	.	.	PUNCT
ejpam-3543	1096	1	axioms	axiom	NOUN
ejpam-3543	1096	2	,	,	PUNCT
ejpam-3543	1096	3	7(1):3	7(1):3	PROPN
ejpam-3543	1096	4	,	,	PUNCT
ejpam-3543	1096	5	2018	2018	NUM
ejpam-3543	1096	6	.	.	PUNCT
ejpam-3543	1097	1	[	[	X
ejpam-3543	1097	2	11	11	NUM
ejpam-3543	1097	3	]	]	X
ejpam-3543	1097	4	w.	w.	PROPN
ejpam-3543	1097	5	kaijae	kaijae	PROPN
ejpam-3543	1097	6	,	,	PUNCT
ejpam-3543	1097	7	p.	p.	PROPN
ejpam-3543	1097	8	poungsumpao	poungsumpao	PROPN
ejpam-3543	1097	9	,	,	PUNCT
ejpam-3543	1097	10	s.	s.	PROPN
ejpam-3543	1097	11	arayarangsi	arayarangsi	PROPN
ejpam-3543	1097	12	,	,	PUNCT
ejpam-3543	1097	13	and	and	CCONJ
ejpam-3543	1097	14	a.	a.	NOUN
ejpam-3543	1097	15	iampan	iampan	PROPN
ejpam-3543	1097	16	.	.	PUNCT
ejpam-3543	1098	1	up	up	ADV
ejpam-3543	1098	2	-	-	PUNCT
ejpam-3543	1098	3	algebras	algebras	PROPN
ejpam-3543	1098	4	characterized	characterize	VERB
ejpam-3543	1098	5	by	by	ADP
ejpam-3543	1098	6	their	their	PRON
ejpam-3543	1098	7	anti	anti	ADJ
ejpam-3543	1098	8	-	-	ADJ
ejpam-3543	1098	9	fuzzy	fuzzy	ADJ
ejpam-3543	1098	10	up	up	ADJ
ejpam-3543	1098	11	-	-	PUNCT
ejpam-3543	1098	12	ideals	ideal	NOUN
ejpam-3543	1098	13	and	and	CCONJ
ejpam-3543	1098	14	anti	anti	ADJ
ejpam-3543	1098	15	-	-	ADJ
ejpam-3543	1098	16	fuzzy	fuzzy	ADJ
ejpam-3543	1098	17	up	up	ADP
ejpam-3543	1098	18	-	-	PUNCT
ejpam-3543	1098	19	subalgebras	subalgebras	PROPN
ejpam-3543	1098	20	.	.	PUNCT
ejpam-3543	1099	1	ital	ital	PROPN
ejpam-3543	1099	2	.	.	PUNCT
ejpam-3543	1100	1	j.	j.	PROPN
ejpam-3543	1100	2	pure	pure	PROPN
ejpam-3543	1100	3	appl	appl	PROPN
ejpam-3543	1100	4	.	.	PUNCT
ejpam-3543	1100	5	math	math	PROPN
ejpam-3543	1100	6	.	.	PUNCT
ejpam-3543	1100	7	,	,	PUNCT
ejpam-3543	1101	1	36:667–692	36:667–692	NUM
ejpam-3543	1101	2	,	,	PUNCT
ejpam-3543	1101	3	2016	2016	NUM
ejpam-3543	1101	4	.	.	PUNCT
ejpam-3543	1102	1	[	[	X
ejpam-3543	1102	2	12	12	NUM
ejpam-3543	1102	3	]	]	PUNCT
ejpam-3543	1102	4	k.	k.	PROPN
ejpam-3543	1102	5	kawila	kawila	PROPN
ejpam-3543	1102	6	,	,	PUNCT
ejpam-3543	1102	7	c.	c.	PROPN
ejpam-3543	1102	8	udomsetchai	udomsetchai	PROPN
ejpam-3543	1102	9	,	,	PUNCT
ejpam-3543	1102	10	and	and	CCONJ
ejpam-3543	1102	11	a.	a.	NOUN
ejpam-3543	1102	12	iampan	iampan	PROPN
ejpam-3543	1102	13	.	.	PUNCT
ejpam-3543	1103	1	bipolar	bipolar	ADJ
ejpam-3543	1103	2	fuzzy	fuzzy	ADJ
ejpam-3543	1103	3	up	up	ADP
ejpam-3543	1103	4	-	-	PUNCT
ejpam-3543	1103	5	algebras	algebras	PROPN
ejpam-3543	1103	6	.	.	PUNCT
ejpam-3543	1104	1	math	math	NOUN
ejpam-3543	1104	2	.	.	PUNCT
ejpam-3543	1105	1	comput	comput	NOUN
ejpam-3543	1105	2	.	.	PUNCT
ejpam-3543	1106	1	appl	appl	PROPN
ejpam-3543	1106	2	.	.	PROPN
ejpam-3543	1106	3	,	,	PUNCT
ejpam-3543	1106	4	23(4):69	23(4):69	PROPN
ejpam-3543	1106	5	,	,	PUNCT
ejpam-3543	1106	6	2018	2018	NUM
ejpam-3543	1106	7	.	.	PUNCT
ejpam-3543	1107	1	[	[	X
ejpam-3543	1107	2	13	13	NUM
ejpam-3543	1107	3	]	]	PUNCT
ejpam-3543	1107	4	s.	s.	PROPN
ejpam-3543	1107	5	keawrahun	keawrahun	PROPN
ejpam-3543	1107	6	and	and	CCONJ
ejpam-3543	1107	7	u.	u.	PROPN
ejpam-3543	1107	8	leerawat	leerawat	PROPN
ejpam-3543	1107	9	.	.	PUNCT
ejpam-3543	1108	1	on	on	ADP
ejpam-3543	1108	2	isomorphisms	isomorphisms	PROPN
ejpam-3543	1108	3	of	of	ADP
ejpam-3543	1108	4	su	su	PROPN
ejpam-3543	1108	5	-	-	PUNCT
ejpam-3543	1108	6	algebras	algebras	PROPN
ejpam-3543	1108	7	.	.	PUNCT
ejpam-3543	1109	1	sci	sci	PROPN
ejpam-3543	1109	2	.	.	PUNCT
ejpam-3543	1109	3	magna	magna	PROPN
ejpam-3543	1109	4	.	.	PROPN
ejpam-3543	1109	5	,	,	PUNCT
ejpam-3543	1109	6	7(2):39–44	7(2):39–44	NUM
ejpam-3543	1109	7	,	,	PUNCT
ejpam-3543	1109	8	2011	2011	NUM
ejpam-3543	1109	9	.	.	PUNCT
ejpam-3543	1110	1	[	[	X
ejpam-3543	1110	2	14	14	NUM
ejpam-3543	1110	3	]	]	X
ejpam-3543	1110	4	b.	b.	PROPN
ejpam-3543	1110	5	kesorn	kesorn	PROPN
ejpam-3543	1110	6	,	,	PUNCT
ejpam-3543	1110	7	k.	k.	PROPN
ejpam-3543	1110	8	maimun	maimun	PROPN
ejpam-3543	1110	9	,	,	PUNCT
ejpam-3543	1110	10	w.	w.	PROPN
ejpam-3543	1110	11	ratbandan	ratbandan	PROPN
ejpam-3543	1110	12	,	,	PUNCT
ejpam-3543	1110	13	and	and	CCONJ
ejpam-3543	1110	14	a.	a.	NOUN
ejpam-3543	1110	15	iampan	iampan	PROPN
ejpam-3543	1110	16	.	.	PUNCT
ejpam-3543	1111	1	intuitionistic	intuitionistic	ADJ
ejpam-3543	1111	2	fuzzy	fuzzy	ADJ
ejpam-3543	1111	3	sets	set	NOUN
ejpam-3543	1111	4	in	in	ADP
ejpam-3543	1111	5	up	up	ADP
ejpam-3543	1111	6	-	-	PUNCT
ejpam-3543	1111	7	algebras	algebras	X
ejpam-3543	1111	8	.	.	PUNCT
ejpam-3543	1112	1	ital	ital	PROPN
ejpam-3543	1112	2	.	.	PUNCT
ejpam-3543	1113	1	j.	j.	PROPN
ejpam-3543	1113	2	pure	pure	PROPN
ejpam-3543	1113	3	appl	appl	PROPN
ejpam-3543	1113	4	.	.	PUNCT
ejpam-3543	1113	5	math	math	PROPN
ejpam-3543	1113	6	.	.	PUNCT
ejpam-3543	1113	7	,	,	PUNCT
ejpam-3543	1114	1	34:339–364	34:339–364	NUM
ejpam-3543	1114	2	,	,	PUNCT
ejpam-3543	1114	3	2015	2015	NUM
ejpam-3543	1114	4	.	.	PUNCT
ejpam-3543	1115	1	[	[	X
ejpam-3543	1115	2	15	15	NUM
ejpam-3543	1115	3	]	]	X
ejpam-3543	1115	4	m.	m.	NOUN
ejpam-3543	1115	5	khan	khan	PROPN
ejpam-3543	1115	6	,	,	PUNCT
ejpam-3543	1115	7	s.	s.	PROPN
ejpam-3543	1115	8	anis	anis	PROPN
ejpam-3543	1115	9	,	,	PUNCT
ejpam-3543	1115	10	f.	f.	PROPN
ejpam-3543	1115	11	smarandache	smarandache	PROPN
ejpam-3543	1115	12	,	,	PUNCT
ejpam-3543	1115	13	and	and	CCONJ
ejpam-3543	1115	14	y.	y.	PROPN
ejpam-3543	1115	15	b.	b.	PROPN
ejpam-3543	1115	16	jun	jun	PROPN
ejpam-3543	1115	17	.	.	PROPN
ejpam-3543	1115	18	neutrosophic	neutrosophic	PROPN
ejpam-3543	1115	19	n	n	PRON
ejpam-3543	1115	20	-structures	-structure	NOUN
ejpam-3543	1115	21	and	and	CCONJ
ejpam-3543	1115	22	their	their	PRON
ejpam-3543	1115	23	applications	application	NOUN
ejpam-3543	1115	24	in	in	ADP
ejpam-3543	1115	25	semigroups	semigroup	NOUN
ejpam-3543	1115	26	.	.	PUNCT
ejpam-3543	1116	1	ann	ann	PROPN
ejpam-3543	1116	2	.	.	PUNCT
ejpam-3543	1116	3	fuzzy	fuzzy	ADJ
ejpam-3543	1116	4	math	math	NOUN
ejpam-3543	1116	5	.	.	PUNCT
ejpam-3543	1117	1	inform	inform	NOUN
ejpam-3543	1117	2	.	.	PUNCT
ejpam-3543	1117	3	,	,	PUNCT
ejpam-3543	1117	4	14:583–598	14:583–598	PROPN
ejpam-3543	1117	5	,	,	PUNCT
ejpam-3543	1117	6	2017	2017	NUM
ejpam-3543	1117	7	.	.	PUNCT
ejpam-3543	1118	1	[	[	X
ejpam-3543	1118	2	16	16	NUM
ejpam-3543	1118	3	]	]	PUNCT
ejpam-3543	1118	4	s.	s.	PROPN
ejpam-3543	1118	5	j.	j.	PROPN
ejpam-3543	1118	6	ki	ki	PROPN
ejpam-3543	1118	7	,	,	PUNCT
ejpam-3543	1118	8	s.-z	s.-z	PROPN
ejpam-3543	1118	9	.	.	PUNCT
ejpam-3543	1119	1	song	song	NOUN
ejpam-3543	1119	2	,	,	PUNCT
ejpam-3543	1119	3	and	and	CCONJ
ejpam-3543	1119	4	y.	y.	PROPN
ejpam-3543	1119	5	b.	b.	PROPN
ejpam-3543	1119	6	jun	jun	PROPN
ejpam-3543	1119	7	.	.	PUNCT
ejpam-3543	1120	1	generalizations	generalization	NOUN
ejpam-3543	1120	2	of	of	ADP
ejpam-3543	1120	3	neutrosophic	neutrosophic	ADJ
ejpam-3543	1120	4	subalgebras	subalgebras	PROPN
ejpam-3543	1120	5	in	in	ADP
ejpam-3543	1120	6	bck	bck	PROPN
ejpam-3543	1120	7	/	/	SYM
ejpam-3543	1120	8	bci	bci	NOUN
ejpam-3543	1120	9	-	-	PUNCT
ejpam-3543	1120	10	algebras	algebras	PROPN
ejpam-3543	1120	11	based	base	VERB
ejpam-3543	1120	12	on	on	ADP
ejpam-3543	1120	13	neutrosophic	neutrosophic	ADJ
ejpam-3543	1120	14	points	point	NOUN
ejpam-3543	1120	15	.	.	PUNCT
ejpam-3543	1121	1	neutrosophic	neutrosophic	ADJ
ejpam-3543	1121	2	sets	set	VERB
ejpam-3543	1121	3	syst	syst	PROPN
ejpam-3543	1121	4	.	.	PUNCT
ejpam-3543	1121	5	,	,	PUNCT
ejpam-3543	1121	6	20:26–35	20:26–35	NUM
ejpam-3543	1121	7	,	,	PUNCT
ejpam-3543	1121	8	2018	2018	NUM
ejpam-3543	1121	9	.	.	PUNCT
ejpam-3543	1122	1	[	[	X
ejpam-3543	1122	2	17	17	NUM
ejpam-3543	1122	3	]	]	PUNCT
ejpam-3543	1122	4	t.	t.	PROPN
ejpam-3543	1122	5	klinseesook	klinseesook	PROPN
ejpam-3543	1122	6	,	,	PUNCT
ejpam-3543	1122	7	s.	s.	PROPN
ejpam-3543	1122	8	bukok	bukok	PROPN
ejpam-3543	1122	9	,	,	PUNCT
ejpam-3543	1122	10	and	and	CCONJ
ejpam-3543	1122	11	a.	a.	NOUN
ejpam-3543	1122	12	iampan	iampan	PROPN
ejpam-3543	1122	13	.	.	PUNCT
ejpam-3543	1123	1	rough	rough	ADJ
ejpam-3543	1123	2	set	set	NOUN
ejpam-3543	1123	3	theory	theory	NOUN
ejpam-3543	1123	4	applied	apply	VERB
ejpam-3543	1123	5	to	to	ADP
ejpam-3543	1123	6	up	up	ADV
ejpam-3543	1123	7	-	-	PUNCT
ejpam-3543	1123	8	algebras	algebras	X
ejpam-3543	1123	9	.	.	PUNCT
ejpam-3543	1124	1	manuscript	manuscript	NOUN
ejpam-3543	1124	2	accepted	accept	VERB
ejpam-3543	1124	3	for	for	ADP
ejpam-3543	1124	4	publication	publication	NOUN
ejpam-3543	1124	5	in	in	ADP
ejpam-3543	1124	6	j.	j.	PROPN
ejpam-3543	1124	7	inf	inf	PROPN
ejpam-3543	1124	8	.	.	PROPN
ejpam-3543	1125	1	optim	optim	PROPN
ejpam-3543	1125	2	.	.	PUNCT
ejpam-3543	1126	1	sci	sci	PROPN
ejpam-3543	1126	2	.	.	PROPN
ejpam-3543	1126	3	,	,	PUNCT
ejpam-3543	1126	4	november	november	PROPN
ejpam-3543	1126	5	2018	2018	NUM
ejpam-3543	1126	6	.	.	PUNCT
ejpam-3543	1127	1	[	[	X
ejpam-3543	1127	2	18	18	NUM
ejpam-3543	1127	3	]	]	PUNCT
ejpam-3543	1127	4	c.	c.	NOUN
ejpam-3543	1127	5	prabpayak	prabpayak	NOUN
ejpam-3543	1127	6	and	and	CCONJ
ejpam-3543	1127	7	u.	u.	NOUN
ejpam-3543	1127	8	leerawat	leerawat	PROPN
ejpam-3543	1127	9	.	.	PUNCT
ejpam-3543	1128	1	on	on	ADP
ejpam-3543	1128	2	ideals	ideal	NOUN
ejpam-3543	1128	3	and	and	CCONJ
ejpam-3543	1128	4	congruences	congruence	NOUN
ejpam-3543	1128	5	in	in	ADP
ejpam-3543	1128	6	ku	ku	PROPN
ejpam-3543	1128	7	-	-	PUNCT
ejpam-3543	1128	8	algebras	algebras	PROPN
ejpam-3543	1128	9	.	.	PUNCT
ejpam-3543	1129	1	sci	sci	PROPN
ejpam-3543	1129	2	.	.	PROPN
ejpam-3543	1129	3	magna	magna	PROPN
ejpam-3543	1129	4	,	,	PUNCT
ejpam-3543	1129	5	5(1):54–57	5(1):54–57	NUM
ejpam-3543	1129	6	,	,	PUNCT
ejpam-3543	1129	7	2009	2009	NUM
ejpam-3543	1129	8	.	.	PUNCT
ejpam-3543	1130	1	references	reference	NOUN
ejpam-3543	1130	2	1409	1409	NUM
ejpam-3543	1130	3	[	[	X
ejpam-3543	1130	4	19	19	NUM
ejpam-3543	1130	5	]	]	PUNCT
ejpam-3543	1130	6	p.	p.	NOUN
ejpam-3543	1130	7	rangsuk	rangsuk	PROPN
ejpam-3543	1130	8	,	,	PUNCT
ejpam-3543	1130	9	p.	p.	NOUN
ejpam-3543	1130	10	huana	huana	PROPN
ejpam-3543	1130	11	,	,	PUNCT
ejpam-3543	1130	12	and	and	CCONJ
ejpam-3543	1130	13	a.	a.	NOUN
ejpam-3543	1130	14	iampan	iampan	PROPN
ejpam-3543	1130	15	.	.	PUNCT
ejpam-3543	1131	1	neutrosophic	neutrosophic	ADJ
ejpam-3543	1131	2	n	n	PRON
ejpam-3543	1131	3	-structures	-structure	NOUN
ejpam-3543	1131	4	over	over	ADP
ejpam-3543	1131	5	up	up	ADV
ejpam-3543	1131	6	-	-	PUNCT
ejpam-3543	1131	7	algebras	algebras	X
ejpam-3543	1131	8	.	.	PUNCT
ejpam-3543	1132	1	neutrosophic	neutrosophic	PROPN
ejpam-3543	1132	2	sets	set	VERB
ejpam-3543	1132	3	syst	syst	PROPN
ejpam-3543	1132	4	.	.	PUNCT
ejpam-3543	1132	5	,	,	PUNCT
ejpam-3543	1132	6	28:87–127	28:87–127	NUM
ejpam-3543	1132	7	,	,	PUNCT
ejpam-3543	1132	8	2019	2019	NUM
ejpam-3543	1132	9	.	.	PUNCT
ejpam-3543	1133	1	[	[	X
ejpam-3543	1133	2	20	20	NUM
ejpam-3543	1133	3	]	]	PUNCT
ejpam-3543	1133	4	a.	a.	NOUN
ejpam-3543	1133	5	satirad	satirad	PROPN
ejpam-3543	1133	6	,	,	PUNCT
ejpam-3543	1133	7	p.	p.	PROPN
ejpam-3543	1133	8	mosrijai	mosrijai	PROPN
ejpam-3543	1133	9	,	,	PUNCT
ejpam-3543	1133	10	and	and	CCONJ
ejpam-3543	1133	11	a.	a.	NOUN
ejpam-3543	1133	12	iampan	iampan	PROPN
ejpam-3543	1133	13	.	.	PUNCT
ejpam-3543	1134	1	formulas	formula	NOUN
ejpam-3543	1134	2	for	for	ADP
ejpam-3543	1134	3	finding	find	VERB
ejpam-3543	1134	4	up	up	ADP
ejpam-3543	1134	5	-	-	PUNCT
ejpam-3543	1134	6	algebras	algebras	X
ejpam-3543	1134	7	.	.	PUNCT
ejpam-3543	1135	1	int	int	NOUN
ejpam-3543	1135	2	.	.	PUNCT
ejpam-3543	1136	1	j.	j.	PROPN
ejpam-3543	1136	2	math	math	PROPN
ejpam-3543	1136	3	.	.	PUNCT
ejpam-3543	1137	1	comput	comput	NOUN
ejpam-3543	1137	2	.	.	PUNCT
ejpam-3543	1138	1	sci	sci	PROPN
ejpam-3543	1138	2	.	.	PROPN
ejpam-3543	1138	3	,	,	PUNCT
ejpam-3543	1138	4	14(2):403–409	14(2):403–409	PROPN
ejpam-3543	1138	5	,	,	PUNCT
ejpam-3543	1138	6	2019	2019	NUM
ejpam-3543	1138	7	.	.	PUNCT
ejpam-3543	1139	1	[	[	X
ejpam-3543	1139	2	21	21	NUM
ejpam-3543	1139	3	]	]	PUNCT
ejpam-3543	1139	4	a.	a.	NOUN
ejpam-3543	1139	5	satirad	satirad	PROPN
ejpam-3543	1139	6	,	,	PUNCT
ejpam-3543	1139	7	p.	p.	PROPN
ejpam-3543	1139	8	mosrijai	mosrijai	PROPN
ejpam-3543	1139	9	,	,	PUNCT
ejpam-3543	1139	10	and	and	CCONJ
ejpam-3543	1139	11	a.	a.	NOUN
ejpam-3543	1139	12	iampan	iampan	PROPN
ejpam-3543	1139	13	.	.	PUNCT
ejpam-3543	1140	1	generalized	generalized	ADJ
ejpam-3543	1140	2	power	power	NOUN
ejpam-3543	1140	3	up	up	ADP
ejpam-3543	1140	4	-	-	PUNCT
ejpam-3543	1140	5	algebras	algebras	PROPN
ejpam-3543	1140	6	.	.	PUNCT
ejpam-3543	1141	1	int	int	NOUN
ejpam-3543	1141	2	.	.	PUNCT
ejpam-3543	1142	1	j.	j.	PROPN
ejpam-3543	1142	2	math	math	PROPN
ejpam-3543	1142	3	.	.	PUNCT
ejpam-3543	1143	1	comput	comput	NOUN
ejpam-3543	1143	2	.	.	PUNCT
ejpam-3543	1144	1	sci	sci	PROPN
ejpam-3543	1144	2	.	.	PROPN
ejpam-3543	1144	3	,	,	PUNCT
ejpam-3543	1144	4	14(1):17–25	14(1):17–25	NUM
ejpam-3543	1144	5	,	,	PUNCT
ejpam-3543	1144	6	2019	2019	NUM
ejpam-3543	1144	7	.	.	PUNCT
ejpam-3543	1145	1	[	[	X
ejpam-3543	1145	2	22	22	NUM
ejpam-3543	1145	3	]	]	X
ejpam-3543	1145	4	f.	f.	PROPN
ejpam-3543	1145	5	smarandache	smarandache	PROPN
ejpam-3543	1145	6	.	.	PUNCT
ejpam-3543	1146	1	a	a	DET
ejpam-3543	1146	2	unifying	unifying	ADJ
ejpam-3543	1146	3	field	field	NOUN
ejpam-3543	1146	4	in	in	ADP
ejpam-3543	1146	5	logics	logic	NOUN
ejpam-3543	1146	6	:	:	PUNCT
ejpam-3543	1146	7	neutrosophic	neutrosophic	ADJ
ejpam-3543	1146	8	logic	logic	NOUN
ejpam-3543	1146	9	,	,	PUNCT
ejpam-3543	1146	10	neutrosophy	neutrosophy	NOUN
ejpam-3543	1146	11	,	,	PUNCT
ejpam-3543	1146	12	neutrosophic	neutrosophic	ADJ
ejpam-3543	1146	13	set	set	NOUN
ejpam-3543	1146	14	,	,	PUNCT
ejpam-3543	1146	15	neutrosophic	neutrosophic	ADJ
ejpam-3543	1146	16	probability	probability	NOUN
ejpam-3543	1146	17	.	.	PUNCT
ejpam-3543	1147	1	american	american	PROPN
ejpam-3543	1147	2	research	research	PROPN
ejpam-3543	1147	3	press	press	PROPN
ejpam-3543	1147	4	,	,	PUNCT
ejpam-3543	1147	5	1999	1999	NUM
ejpam-3543	1147	6	.	.	PUNCT
ejpam-3543	1148	1	[	[	X
ejpam-3543	1148	2	23	23	NUM
ejpam-3543	1148	3	]	]	PUNCT
ejpam-3543	1148	4	j.	j.	PROPN
ejpam-3543	1148	5	somjanta	somjanta	PROPN
ejpam-3543	1148	6	,	,	PUNCT
ejpam-3543	1148	7	n.	n.	PROPN
ejpam-3543	1148	8	thuekaew	thuekaew	PROPN
ejpam-3543	1148	9	,	,	PUNCT
ejpam-3543	1148	10	p.	p.	NOUN
ejpam-3543	1148	11	kumpeangkeaw	kumpeangkeaw	PROPN
ejpam-3543	1148	12	,	,	PUNCT
ejpam-3543	1148	13	and	and	CCONJ
ejpam-3543	1148	14	a.	a.	NOUN
ejpam-3543	1148	15	iampan	iampan	PROPN
ejpam-3543	1148	16	.	.	PUNCT
ejpam-3543	1149	1	fuzzy	fuzzy	ADJ
ejpam-3543	1149	2	sets	set	NOUN
ejpam-3543	1149	3	in	in	ADP
ejpam-3543	1149	4	upalgebras	upalgebra	NOUN
ejpam-3543	1149	5	.	.	PUNCT
ejpam-3543	1150	1	ann	ann	PROPN
ejpam-3543	1150	2	.	.	PUNCT
ejpam-3543	1150	3	fuzzy	fuzzy	ADJ
ejpam-3543	1150	4	math	math	NOUN
ejpam-3543	1150	5	.	.	PUNCT
ejpam-3543	1151	1	inform	inform	NOUN
ejpam-3543	1151	2	.	.	PUNCT
ejpam-3543	1151	3	,	,	PUNCT
ejpam-3543	1151	4	12(6):739–756	12(6):739–756	PROPN
ejpam-3543	1151	5	,	,	PUNCT
ejpam-3543	1151	6	2016	2016	NUM
ejpam-3543	1151	7	.	.	PUNCT
ejpam-3543	1152	1	[	[	X
ejpam-3543	1152	2	24	24	NUM
ejpam-3543	1152	3	]	]	PUNCT
ejpam-3543	1152	4	m.	m.	NOUN
ejpam-3543	1152	5	songsaeng	songsaeng	PROPN
ejpam-3543	1152	6	and	and	CCONJ
ejpam-3543	1152	7	a.	a.	NOUN
ejpam-3543	1152	8	iampan	iampan	PROPN
ejpam-3543	1152	9	.	.	PUNCT
ejpam-3543	1153	1	n	n	PRON
ejpam-3543	1153	2	-fuzzy	-fuzzy	NOUN
ejpam-3543	1153	3	up	up	ADV
ejpam-3543	1153	4	-	-	PUNCT
ejpam-3543	1153	5	algebras	algebra	NOUN
ejpam-3543	1153	6	and	and	CCONJ
ejpam-3543	1153	7	its	its	PRON
ejpam-3543	1153	8	level	level	NOUN
ejpam-3543	1153	9	subsets	subset	NOUN
ejpam-3543	1153	10	.	.	PUNCT
ejpam-3543	1154	1	j.	j.	PROPN
ejpam-3543	1154	2	algebra	algebra	PROPN
ejpam-3543	1154	3	relat	relat	PROPN
ejpam-3543	1154	4	.	.	PUNCT
ejpam-3543	1155	1	top	top	NOUN
ejpam-3543	1155	2	.	.	PUNCT
ejpam-3543	1155	3	,	,	PUNCT
ejpam-3543	1155	4	6(1):1–24	6(1):1–24	NUM
ejpam-3543	1155	5	,	,	PUNCT
ejpam-3543	1155	6	2018	2018	NUM
ejpam-3543	1155	7	.	.	PUNCT
ejpam-3543	1156	1	[	[	X
ejpam-3543	1156	2	25	25	NUM
ejpam-3543	1156	3	]	]	PUNCT
ejpam-3543	1156	4	s.	s.	PROPN
ejpam-3543	1156	5	sripaeng	sripaeng	PROPN
ejpam-3543	1156	6	,	,	PUNCT
ejpam-3543	1156	7	k.	k.	PROPN
ejpam-3543	1156	8	tanamoon	tanamoon	PROPN
ejpam-3543	1156	9	,	,	PUNCT
ejpam-3543	1156	10	and	and	CCONJ
ejpam-3543	1156	11	a.	a.	NOUN
ejpam-3543	1156	12	iampan	iampan	PROPN
ejpam-3543	1156	13	.	.	PUNCT
ejpam-3543	1157	1	on	on	ADP
ejpam-3543	1157	2	anti	anti	ADJ
ejpam-3543	1157	3	q	q	ADJ
ejpam-3543	1157	4	-	-	ADJ
ejpam-3543	1157	5	fuzzy	fuzzy	ADJ
ejpam-3543	1157	6	up	up	NOUN
ejpam-3543	1157	7	-	-	PUNCT
ejpam-3543	1157	8	ideals	ideal	NOUN
ejpam-3543	1157	9	and	and	CCONJ
ejpam-3543	1157	10	anti	anti	ADJ
ejpam-3543	1157	11	q	q	ADJ
ejpam-3543	1157	12	-	-	ADJ
ejpam-3543	1157	13	fuzzy	fuzzy	ADJ
ejpam-3543	1157	14	up	up	ADP
ejpam-3543	1157	15	-	-	PUNCT
ejpam-3543	1157	16	subalgebras	subalgebra	NOUN
ejpam-3543	1157	17	of	of	ADP
ejpam-3543	1157	18	up	up	ADP
ejpam-3543	1157	19	-	-	PUNCT
ejpam-3543	1157	20	algebras	algebras	X
ejpam-3543	1157	21	.	.	PUNCT
ejpam-3543	1158	1	j.	j.	PROPN
ejpam-3543	1158	2	inf	inf	PROPN
ejpam-3543	1158	3	.	.	PROPN
ejpam-3543	1158	4	optim	optim	PROPN
ejpam-3543	1158	5	.	.	PUNCT
ejpam-3543	1159	1	sci	sci	PROPN
ejpam-3543	1159	2	.	.	PROPN
ejpam-3543	1159	3	,	,	PUNCT
ejpam-3543	1159	4	39(5):1095–1127	39(5):1095–1127	NUM
ejpam-3543	1159	5	,	,	PUNCT
ejpam-3543	1159	6	2018	2018	NUM
ejpam-3543	1159	7	.	.	PUNCT
ejpam-3543	1160	1	[	[	X
ejpam-3543	1160	2	26	26	NUM
ejpam-3543	1160	3	]	]	PUNCT
ejpam-3543	1160	4	k.	k.	PROPN
ejpam-3543	1160	5	tanamoon	tanamoon	PROPN
ejpam-3543	1160	6	,	,	PUNCT
ejpam-3543	1160	7	s.	s.	PROPN
ejpam-3543	1160	8	sripaeng	sripaeng	PROPN
ejpam-3543	1160	9	,	,	PUNCT
ejpam-3543	1160	10	and	and	CCONJ
ejpam-3543	1160	11	a.	a.	NOUN
ejpam-3543	1160	12	iampan	iampan	PROPN
ejpam-3543	1160	13	.	.	PUNCT
ejpam-3543	1161	1	q	q	ADJ
ejpam-3543	1161	2	-	-	ADJ
ejpam-3543	1161	3	fuzzy	fuzzy	ADJ
ejpam-3543	1161	4	sets	set	NOUN
ejpam-3543	1161	5	in	in	ADP
ejpam-3543	1161	6	up	up	ADP
ejpam-3543	1161	7	-	-	PUNCT
ejpam-3543	1161	8	algebras	algebras	X
ejpam-3543	1161	9	.	.	PUNCT
ejpam-3543	1162	1	songklanakarin	songklanakarin	PROPN
ejpam-3543	1162	2	j.	j.	PROPN
ejpam-3543	1162	3	sci	sci	PROPN
ejpam-3543	1162	4	.	.	PROPN
ejpam-3543	1162	5	technol	technol	PROPN
ejpam-3543	1162	6	.	.	PROPN
ejpam-3543	1162	7	,	,	PUNCT
ejpam-3543	1162	8	40(1):9–29	40(1):9–29	NUM
ejpam-3543	1162	9	,	,	PUNCT
ejpam-3543	1162	10	2018	2018	NUM
ejpam-3543	1162	11	.	.	PUNCT
ejpam-3543	1163	1	[	[	X
ejpam-3543	1163	2	27	27	NUM
ejpam-3543	1163	3	]	]	X
ejpam-3543	1163	4	n.	n.	NOUN
ejpam-3543	1163	5	udten	udten	PROPN
ejpam-3543	1163	6	,	,	PUNCT
ejpam-3543	1163	7	n.	n.	PROPN
ejpam-3543	1163	8	songseang	songseang	PROPN
ejpam-3543	1163	9	,	,	PUNCT
ejpam-3543	1163	10	and	and	CCONJ
ejpam-3543	1163	11	a.	a.	NOUN
ejpam-3543	1163	12	iampan	iampan	PROPN
ejpam-3543	1163	13	.	.	PUNCT
ejpam-3543	1164	1	translation	translation	NOUN
ejpam-3543	1164	2	and	and	CCONJ
ejpam-3543	1164	3	density	density	NOUN
ejpam-3543	1164	4	of	of	ADP
ejpam-3543	1164	5	a	a	DET
ejpam-3543	1164	6	bipolar	bipolar	ADV
ejpam-3543	1164	7	-	-	PUNCT
ejpam-3543	1164	8	valued	value	VERB
ejpam-3543	1164	9	fuzzy	fuzzy	ADJ
ejpam-3543	1164	10	set	set	VERB
ejpam-3543	1164	11	in	in	ADP
ejpam-3543	1164	12	up	up	ADP
ejpam-3543	1164	13	-	-	PUNCT
ejpam-3543	1164	14	algebras	algebras	X
ejpam-3543	1164	15	.	.	PUNCT
ejpam-3543	1165	1	ital	ital	PROPN
ejpam-3543	1165	2	.	.	PUNCT
ejpam-3543	1166	1	j.	j.	PROPN
ejpam-3543	1166	2	pure	pure	PROPN
ejpam-3543	1166	3	appl	appl	PROPN
ejpam-3543	1166	4	.	.	PUNCT
ejpam-3543	1166	5	math	math	PROPN
ejpam-3543	1166	6	.	.	PUNCT
ejpam-3543	1166	7	,	,	PUNCT
ejpam-3543	1166	8	41:469–496	41:469–496	PROPN
ejpam-3543	1166	9	,	,	PUNCT
ejpam-3543	1166	10	2019	2019	NUM
ejpam-3543	1166	11	.	.	PUNCT
ejpam-3543	1167	1	[	[	X
ejpam-3543	1167	2	28	28	NUM
ejpam-3543	1167	3	]	]	X
ejpam-3543	1167	4	h.	h.	PROPN
ejpam-3543	1167	5	wang	wang	PROPN
ejpam-3543	1167	6	,	,	PUNCT
ejpam-3543	1167	7	f.	f.	PROPN
ejpam-3543	1167	8	smarandache	smarandache	PROPN
ejpam-3543	1167	9	,	,	PUNCT
ejpam-3543	1167	10	y.	y.	PROPN
ejpam-3543	1167	11	q.	q.	PROPN
ejpam-3543	1167	12	zhang	zhang	PROPN
ejpam-3543	1167	13	,	,	PUNCT
ejpam-3543	1167	14	and	and	CCONJ
ejpam-3543	1167	15	r.	r.	PROPN
ejpam-3543	1167	16	sunderraman	sunderraman	PROPN
ejpam-3543	1167	17	.	.	PUNCT
ejpam-3543	1168	1	interval	interval	NOUN
ejpam-3543	1168	2	neutrosophic	neutrosophic	ADJ
ejpam-3543	1168	3	sets	set	NOUN
ejpam-3543	1168	4	and	and	CCONJ
ejpam-3543	1168	5	logic	logic	NOUN
ejpam-3543	1168	6	:	:	PUNCT
ejpam-3543	1168	7	theory	theory	NOUN
ejpam-3543	1168	8	and	and	CCONJ
ejpam-3543	1168	9	applications	application	NOUN
ejpam-3543	1168	10	in	in	ADP
ejpam-3543	1168	11	computing	computing	NOUN
ejpam-3543	1168	12	.	.	PUNCT
ejpam-3543	1169	1	hexis	hexis	PROPN
ejpam-3543	1169	2	,	,	PUNCT
ejpam-3543	1169	3	phoenix	phoenix	PROPN
ejpam-3543	1169	4	,	,	PUNCT
ejpam-3543	1169	5	ariz	ariz	PROPN
ejpam-3543	1169	6	,	,	PUNCT
ejpam-3543	1169	7	usa	usa	PROPN
ejpam-3543	1169	8	,	,	PUNCT
ejpam-3543	1169	9	2005	2005	NUM
ejpam-3543	1169	10	.	.	PUNCT
ejpam-3543	1170	1	[	[	X
ejpam-3543	1170	2	29	29	NUM
ejpam-3543	1170	3	]	]	X
ejpam-3543	1170	4	l.	l.	PROPN
ejpam-3543	1170	5	a.	a.	PROPN
ejpam-3543	1170	6	zadeh	zadeh	PROPN
ejpam-3543	1170	7	.	.	PUNCT
ejpam-3543	1170	8	fuzzy	fuzzy	ADJ
ejpam-3543	1170	9	sets	set	NOUN
ejpam-3543	1170	10	.	.	PUNCT
ejpam-3543	1171	1	inf	inf	PROPN
ejpam-3543	1171	2	.	.	PUNCT
ejpam-3543	1171	3	cont	cont	PROPN
ejpam-3543	1171	4	.	.	PROPN
ejpam-3543	1171	5	,	,	PUNCT
ejpam-3543	1171	6	8:338–353	8:338–353	NUM
ejpam-3543	1171	7	,	,	PUNCT
ejpam-3543	1171	8	1965	1965	NUM
ejpam-3543	1171	9	.	.	PUNCT