id	sid	tid	token	lemma	pos
ejpam-5894	1	1	european	european	PROPN
ejpam-5894	1	2	journal	journal	PROPN
ejpam-5894	1	3	of	of	ADP
ejpam-5894	1	4	pure	pure	ADJ
ejpam-5894	1	5	and	and	CCONJ
ejpam-5894	1	6	applied	applied	ADJ
ejpam-5894	1	7	mathematics	mathematic	NOUN
ejpam-5894	1	8	2025	2025	NUM
ejpam-5894	1	9	,	,	PUNCT
ejpam-5894	1	10	vol	vol	NOUN
ejpam-5894	1	11	.	.	PROPN
ejpam-5894	1	12	18	18	NUM
ejpam-5894	1	13	,	,	PUNCT
ejpam-5894	1	14	issue	issue	NOUN
ejpam-5894	1	15	3	3	NUM
ejpam-5894	1	16	,	,	PUNCT
ejpam-5894	1	17	article	article	NOUN
ejpam-5894	1	18	number	number	NOUN
ejpam-5894	1	19	5894	5894	NUM
ejpam-5894	1	20	issn	issn	PROPN
ejpam-5894	1	21	1307	1307	NUM
ejpam-5894	1	22	-	-	SYM
ejpam-5894	1	23	5543	5543	NUM
ejpam-5894	1	24	–	–	PUNCT
ejpam-5894	1	25	ejpam.com	ejpam.com	X
ejpam-5894	1	26	published	publish	VERB
ejpam-5894	1	27	by	by	ADP
ejpam-5894	1	28	new	new	PROPN
ejpam-5894	1	29	york	york	PROPN
ejpam-5894	1	30	business	business	PROPN
ejpam-5894	1	31	global	global	ADJ
ejpam-5894	1	32	structural	structural	ADJ
ejpam-5894	1	33	analysis	analysis	NOUN
ejpam-5894	1	34	of	of	ADP
ejpam-5894	1	35	intuitionistic	intuitionistic	ADJ
ejpam-5894	1	36	fuzzy	fuzzy	ADJ
ejpam-5894	1	37	implicative	implicative	ADJ
ejpam-5894	1	38	wsbg	wsbg	NOUN
ejpam-5894	1	39	-	-	PUNCT
ejpam-5894	1	40	ideals	ideal	NOUN
ejpam-5894	1	41	tahsin	tahsin	VERB
ejpam-5894	1	42	oner1	oner1	NOUN
ejpam-5894	1	43	,	,	PUNCT
ejpam-5894	1	44	aiyared	aiyare	VERB
ejpam-5894	1	45	iampan2,∗	iampan2,∗	PROPN
ejpam-5894	1	46	,	,	PUNCT
ejpam-5894	1	47	neelamegarajan	neelamegarajan	NOUN
ejpam-5894	1	48	rajesh3	rajesh3	PROPN
ejpam-5894	1	49	,	,	PUNCT
ejpam-5894	1	50	ibrahim	ibrahim	PROPN
ejpam-5894	1	51	senturk1	senturk1	X
ejpam-5894	2	1	1	1	NUM
ejpam-5894	2	2	department	department	NOUN
ejpam-5894	2	3	of	of	ADP
ejpam-5894	2	4	mathematics	mathematic	NOUN
ejpam-5894	2	5	,	,	PUNCT
ejpam-5894	2	6	faculty	faculty	NOUN
ejpam-5894	2	7	of	of	ADP
ejpam-5894	2	8	science	science	NOUN
ejpam-5894	2	9	,	,	PUNCT
ejpam-5894	2	10	ege	ege	PROPN
ejpam-5894	2	11	university	university	NOUN
ejpam-5894	2	12	,	,	PUNCT
ejpam-5894	2	13	35100	35100	NUM
ejpam-5894	2	14	izmir	izmir	PROPN
ejpam-5894	2	15	,	,	PUNCT
ejpam-5894	2	16	turkey	turkey	PROPN
ejpam-5894	2	17	2	2	NUM
ejpam-5894	2	18	department	department	NOUN
ejpam-5894	2	19	of	of	ADP
ejpam-5894	2	20	mathematics	mathematic	NOUN
ejpam-5894	2	21	,	,	PUNCT
ejpam-5894	2	22	school	school	NOUN
ejpam-5894	2	23	of	of	ADP
ejpam-5894	2	24	science	science	NOUN
ejpam-5894	2	25	,	,	PUNCT
ejpam-5894	2	26	university	university	NOUN
ejpam-5894	2	27	of	of	ADP
ejpam-5894	2	28	phayao	phayao	NOUN
ejpam-5894	2	29	,	,	PUNCT
ejpam-5894	2	30	mae	mae	PROPN
ejpam-5894	2	31	ka	ka	PROPN
ejpam-5894	2	32	,	,	PUNCT
ejpam-5894	2	33	mueang	mueang	PROPN
ejpam-5894	2	34	,	,	PUNCT
ejpam-5894	2	35	phayao	phayao	NOUN
ejpam-5894	2	36	56000	56000	NUM
ejpam-5894	2	37	,	,	PUNCT
ejpam-5894	2	38	thailand	thailand	PROPN
ejpam-5894	2	39	3	3	NUM
ejpam-5894	2	40	department	department	PROPN
ejpam-5894	2	41	of	of	ADP
ejpam-5894	2	42	mathematics	mathematic	NOUN
ejpam-5894	2	43	,	,	PUNCT
ejpam-5894	2	44	rajah	rajah	NOUN
ejpam-5894	2	45	serfoji	serfoji	ADJ
ejpam-5894	2	46	government	government	NOUN
ejpam-5894	2	47	college	college	NOUN
ejpam-5894	2	48	,	,	PUNCT
ejpam-5894	2	49	thanjavur-613005	thanjavur-613005	NOUN
ejpam-5894	2	50	,	,	PUNCT
ejpam-5894	2	51	tamil	tamil	PROPN
ejpam-5894	2	52	nadu	nadu	NOUN
ejpam-5894	2	53	,	,	PUNCT
ejpam-5894	2	54	india	india	PROPN
ejpam-5894	2	55	abstract	abstract	NOUN
ejpam-5894	2	56	.	.	PUNCT
ejpam-5894	3	1	in	in	ADP
ejpam-5894	3	2	this	this	DET
ejpam-5894	3	3	paper	paper	NOUN
ejpam-5894	3	4	,	,	PUNCT
ejpam-5894	3	5	we	we	PRON
ejpam-5894	3	6	investigate	investigate	VERB
ejpam-5894	3	7	intuitionistic	intuitionistic	ADJ
ejpam-5894	3	8	fuzzy	fuzzy	ADJ
ejpam-5894	3	9	wsbg	wsbg	NOUN
ejpam-5894	3	10	-	-	PUNCT
ejpam-5894	3	11	ideals	ideal	NOUN
ejpam-5894	3	12	and	and	CCONJ
ejpam-5894	3	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	3	14	fuzzy	fuzzy	ADJ
ejpam-5894	3	15	implicative	implicative	ADJ
ejpam-5894	3	16	wsbg	wsbg	NOUN
ejpam-5894	3	17	-	-	PUNCT
ejpam-5894	3	18	ideals	ideal	NOUN
ejpam-5894	3	19	within	within	ADP
ejpam-5894	3	20	the	the	DET
ejpam-5894	3	21	framework	framework	NOUN
ejpam-5894	3	22	of	of	ADP
ejpam-5894	3	23	sheffer	sheffer	PROPN
ejpam-5894	3	24	stroke	stroke	PROPN
ejpam-5894	3	25	bg	bg	PROPN
ejpam-5894	3	26	-	-	PUNCT
ejpam-5894	3	27	algebras	algebras	PROPN
ejpam-5894	3	28	.	.	PUNCT
ejpam-5894	4	1	we	we	PRON
ejpam-5894	4	2	establish	establish	VERB
ejpam-5894	4	3	new	new	ADJ
ejpam-5894	4	4	algebraic	algebraic	ADJ
ejpam-5894	4	5	structures	structure	NOUN
ejpam-5894	4	6	that	that	PRON
ejpam-5894	4	7	extend	extend	VERB
ejpam-5894	4	8	classical	classical	ADJ
ejpam-5894	4	9	boolean	boolean	NOUN
ejpam-5894	4	10	and	and	CCONJ
ejpam-5894	4	11	bg	bg	NOUN
ejpam-5894	4	12	-	-	PUNCT
ejpam-5894	4	13	algebra	algebra	NOUN
ejpam-5894	4	14	frameworks	framework	NOUN
ejpam-5894	4	15	by	by	ADP
ejpam-5894	4	16	synthesizing	synthesize	VERB
ejpam-5894	4	17	intuitionistic	intuitionistic	ADJ
ejpam-5894	4	18	fuzzy	fuzzy	ADJ
ejpam-5894	4	19	set	set	NOUN
ejpam-5894	4	20	theory	theory	NOUN
ejpam-5894	4	21	,	,	PUNCT
ejpam-5894	4	22	introduced	introduce	VERB
ejpam-5894	4	23	by	by	ADP
ejpam-5894	4	24	atanassov	atanassov	NOUN
ejpam-5894	4	25	,	,	PUNCT
ejpam-5894	4	26	with	with	ADP
ejpam-5894	4	27	the	the	DET
ejpam-5894	4	28	sheffer	sheffer	NOUN
ejpam-5894	4	29	stroke	stroke	NOUN
ejpam-5894	4	30	operation	operation	NOUN
ejpam-5894	4	31	.	.	PUNCT
ejpam-5894	5	1	we	we	PRON
ejpam-5894	5	2	demonstrate	demonstrate	VERB
ejpam-5894	5	3	a	a	DET
ejpam-5894	5	4	fundamental	fundamental	ADJ
ejpam-5894	5	5	connection	connection	NOUN
ejpam-5894	5	6	between	between	ADP
ejpam-5894	5	7	intuitionistic	intuitionistic	ADJ
ejpam-5894	5	8	fuzzy	fuzzy	ADJ
ejpam-5894	5	9	implicative	implicative	ADJ
ejpam-5894	5	10	wsbg	wsbg	NOUN
ejpam-5894	5	11	-	-	PUNCT
ejpam-5894	5	12	ideals	ideal	NOUN
ejpam-5894	5	13	and	and	CCONJ
ejpam-5894	5	14	their	their	PRON
ejpam-5894	5	15	level	level	NOUN
ejpam-5894	5	16	sets	set	NOUN
ejpam-5894	5	17	,	,	PUNCT
ejpam-5894	5	18	showing	show	VERB
ejpam-5894	5	19	that	that	SCONJ
ejpam-5894	5	20	the	the	DET
ejpam-5894	5	21	level	level	NOUN
ejpam-5894	5	22	set	set	NOUN
ejpam-5894	5	23	of	of	ADP
ejpam-5894	5	24	an	an	DET
ejpam-5894	5	25	intuitionistic	intuitionistic	ADJ
ejpam-5894	5	26	fuzzy	fuzzy	ADJ
ejpam-5894	5	27	implicative	implicative	ADJ
ejpam-5894	5	28	wsbg	wsbg	ADV
ejpam-5894	5	29	-	-	PUNCT
ejpam-5894	5	30	ideal	ideal	ADJ
ejpam-5894	5	31	corresponds	correspond	NOUN
ejpam-5894	5	32	to	to	ADP
ejpam-5894	5	33	an	an	DET
ejpam-5894	5	34	implicative	implicative	ADJ
ejpam-5894	5	35	wsbg	wsbg	NOUN
ejpam-5894	5	36	-	-	PUNCT
ejpam-5894	5	37	ideal	ideal	NOUN
ejpam-5894	5	38	of	of	ADP
ejpam-5894	5	39	the	the	DET
ejpam-5894	5	40	sheffer	sheffer	NOUN
ejpam-5894	5	41	stroke	stroke	NOUN
ejpam-5894	5	42	bg	bg	PROPN
ejpam-5894	5	43	-	-	NOUN
ejpam-5894	5	44	algebra	algebra	PROPN
ejpam-5894	5	45	.	.	PUNCT
ejpam-5894	6	1	furthermore	furthermore	ADV
ejpam-5894	6	2	,	,	PUNCT
ejpam-5894	6	3	we	we	PRON
ejpam-5894	6	4	explore	explore	VERB
ejpam-5894	6	5	the	the	DET
ejpam-5894	6	6	properties	property	NOUN
ejpam-5894	6	7	of	of	ADP
ejpam-5894	6	8	intuitionistic	intuitionistic	ADJ
ejpam-5894	6	9	fuzzy	fuzzy	ADJ
ejpam-5894	6	10	wsbg	wsbg	NOUN
ejpam-5894	6	11	-	-	PUNCT
ejpam-5894	6	12	ideals	ideal	NOUN
ejpam-5894	6	13	,	,	PUNCT
ejpam-5894	6	14	proving	prove	VERB
ejpam-5894	6	15	that	that	SCONJ
ejpam-5894	6	16	every	every	DET
ejpam-5894	6	17	intuitionistic	intuitionistic	ADJ
ejpam-5894	6	18	fuzzy	fuzzy	ADJ
ejpam-5894	6	19	implicative	implicative	ADJ
ejpam-5894	6	20	wsbg	wsbg	PROPN
ejpam-5894	6	21	-	-	PUNCT
ejpam-5894	6	22	ideal	ideal	NOUN
ejpam-5894	6	23	is	be	AUX
ejpam-5894	6	24	also	also	ADV
ejpam-5894	6	25	an	an	DET
ejpam-5894	6	26	intuitionistic	intuitionistic	ADJ
ejpam-5894	6	27	fuzzy	fuzzy	ADJ
ejpam-5894	6	28	wsbg	wsbg	NOUN
ejpam-5894	6	29	-	-	PUNCT
ejpam-5894	6	30	ideal	ideal	ADJ
ejpam-5894	6	31	.	.	PUNCT
ejpam-5894	7	1	however	however	ADV
ejpam-5894	7	2	,	,	PUNCT
ejpam-5894	7	3	the	the	DET
ejpam-5894	7	4	converse	converse	NOUN
ejpam-5894	7	5	does	do	AUX
ejpam-5894	7	6	not	not	PART
ejpam-5894	7	7	always	always	ADV
ejpam-5894	7	8	hold	hold	VERB
ejpam-5894	7	9	.	.	PUNCT
ejpam-5894	8	1	this	this	DET
ejpam-5894	8	2	work	work	NOUN
ejpam-5894	8	3	provides	provide	VERB
ejpam-5894	8	4	new	new	ADJ
ejpam-5894	8	5	insights	insight	NOUN
ejpam-5894	8	6	into	into	ADP
ejpam-5894	8	7	the	the	DET
ejpam-5894	8	8	algebraic	algebraic	ADJ
ejpam-5894	8	9	properties	property	NOUN
ejpam-5894	8	10	of	of	ADP
ejpam-5894	8	11	sheffer	sheffer	PROPN
ejpam-5894	8	12	stroke	stroke	PROPN
ejpam-5894	8	13	bg	bg	PROPN
ejpam-5894	8	14	-	-	PUNCT
ejpam-5894	8	15	algebras	algebras	PROPN
ejpam-5894	8	16	,	,	PUNCT
ejpam-5894	8	17	enabling	enable	VERB
ejpam-5894	8	18	novel	novel	ADJ
ejpam-5894	8	19	reasoning	reasoning	NOUN
ejpam-5894	8	20	methods	method	NOUN
ejpam-5894	8	21	under	under	ADP
ejpam-5894	8	22	uncertainty	uncertainty	NOUN
ejpam-5894	8	23	and	and	CCONJ
ejpam-5894	8	24	paving	pave	VERB
ejpam-5894	8	25	the	the	DET
ejpam-5894	8	26	way	way	NOUN
ejpam-5894	8	27	for	for	ADP
ejpam-5894	8	28	further	further	ADJ
ejpam-5894	8	29	applications	application	NOUN
ejpam-5894	8	30	in	in	ADP
ejpam-5894	8	31	fuzzy	fuzzy	ADJ
ejpam-5894	8	32	logic	logic	NOUN
ejpam-5894	8	33	and	and	CCONJ
ejpam-5894	8	34	computational	computational	ADJ
ejpam-5894	8	35	models	model	NOUN
ejpam-5894	8	36	.	.	PUNCT
ejpam-5894	9	1	2020	2020	NUM
ejpam-5894	9	2	mathematics	mathematic	NOUN
ejpam-5894	9	3	subject	subject	NOUN
ejpam-5894	9	4	classifications	classification	NOUN
ejpam-5894	9	5	:	:	PUNCT
ejpam-5894	9	6	06f05	06f05	NUM
ejpam-5894	9	7	,	,	PUNCT
ejpam-5894	9	8	03g25	03g25	NUM
ejpam-5894	9	9	,	,	PUNCT
ejpam-5894	9	10	03g10	03g10	NUM
ejpam-5894	9	11	.	.	PUNCT
ejpam-5894	10	1	key	key	ADJ
ejpam-5894	10	2	words	word	NOUN
ejpam-5894	10	3	and	and	CCONJ
ejpam-5894	10	4	phrases	phrase	NOUN
ejpam-5894	10	5	:	:	PUNCT
ejpam-5894	10	6	weak	weak	ADJ
ejpam-5894	10	7	sheffer	sheffer	NOUN
ejpam-5894	10	8	stroke	stroke	NOUN
ejpam-5894	10	9	bg	bg	PROPN
ejpam-5894	10	10	-	-	PROPN
ejpam-5894	10	11	algebra	algebra	PROPN
ejpam-5894	10	12	(	(	PUNCT
ejpam-5894	10	13	wsbg	wsbg	NOUN
ejpam-5894	10	14	-	-	PUNCT
ejpam-5894	10	15	algebra	algebra	NOUN
ejpam-5894	10	16	)	)	PUNCT
ejpam-5894	10	17	,	,	PUNCT
ejpam-5894	10	18	intuitionistic	intuitionistic	ADJ
ejpam-5894	10	19	fuzzy	fuzzy	ADJ
ejpam-5894	10	20	wsbg	wsbg	NOUN
ejpam-5894	10	21	-	-	PUNCT
ejpam-5894	10	22	ideal	ideal	ADJ
ejpam-5894	10	23	,	,	PUNCT
ejpam-5894	10	24	intuitionistic	intuitionistic	ADJ
ejpam-5894	10	25	fuzzy	fuzzy	ADJ
ejpam-5894	10	26	implicative	implicative	ADJ
ejpam-5894	10	27	wsbg	wsbg	NOUN
ejpam-5894	10	28	-	-	PUNCT
ejpam-5894	10	29	ideal	ideal	ADJ
ejpam-5894	10	30	.	.	PUNCT
ejpam-5894	11	1	1	1	X
ejpam-5894	11	2	.	.	X
ejpam-5894	11	3	introduction	introduction	NOUN
ejpam-5894	11	4	bg	bg	PROPN
ejpam-5894	11	5	-	-	PUNCT
ejpam-5894	11	6	algebras	algebras	PROPN
ejpam-5894	11	7	,	,	PUNCT
ejpam-5894	11	8	a	a	DET
ejpam-5894	11	9	generalization	generalization	NOUN
ejpam-5894	11	10	of	of	ADP
ejpam-5894	11	11	b	b	PROPN
ejpam-5894	11	12	-	-	PUNCT
ejpam-5894	11	13	algebras	algebras	X
ejpam-5894	11	14	,	,	PUNCT
ejpam-5894	11	15	extend	extend	VERB
ejpam-5894	11	16	the	the	DET
ejpam-5894	11	17	classical	classical	ADJ
ejpam-5894	11	18	boolean	boolean	ADJ
ejpam-5894	11	19	algebra	algebra	NOUN
ejpam-5894	11	20	framework	framework	NOUN
ejpam-5894	11	21	by	by	ADP
ejpam-5894	11	22	incorporating	incorporate	VERB
ejpam-5894	11	23	more	more	ADV
ejpam-5894	11	24	complex	complex	ADJ
ejpam-5894	11	25	operations	operation	NOUN
ejpam-5894	11	26	and	and	CCONJ
ejpam-5894	11	27	properties	property	NOUN
ejpam-5894	11	28	[	[	X
ejpam-5894	11	29	1	1	NUM
ejpam-5894	11	30	]	]	PUNCT
ejpam-5894	11	31	.	.	PUNCT
ejpam-5894	12	1	this	this	DET
ejpam-5894	12	2	extension	extension	NOUN
ejpam-5894	12	3	provides	provide	VERB
ejpam-5894	12	4	a	a	DET
ejpam-5894	12	5	robust	robust	ADJ
ejpam-5894	12	6	foundation	foundation	NOUN
ejpam-5894	12	7	for	for	ADP
ejpam-5894	12	8	modeling	modeling	NOUN
ejpam-5894	12	9	and	and	CCONJ
ejpam-5894	12	10	analyzing	analyze	VERB
ejpam-5894	12	11	logical	logical	ADJ
ejpam-5894	12	12	and	and	CCONJ
ejpam-5894	12	13	algebraic	algebraic	ADJ
ejpam-5894	12	14	systems	system	NOUN
ejpam-5894	12	15	that	that	PRON
ejpam-5894	12	16	go	go	VERB
ejpam-5894	12	17	beyond	beyond	ADP
ejpam-5894	12	18	the	the	DET
ejpam-5894	12	19	limitations	limitation	NOUN
ejpam-5894	12	20	of	of	ADP
ejpam-5894	12	21	traditional	traditional	ADJ
ejpam-5894	12	22	boolean	boolean	ADJ
ejpam-5894	12	23	logic	logic	NOUN
ejpam-5894	12	24	.	.	PUNCT
ejpam-5894	13	1	such	such	ADJ
ejpam-5894	13	2	generalizations	generalization	NOUN
ejpam-5894	13	3	enable	enable	VERB
ejpam-5894	13	4	the	the	DET
ejpam-5894	13	5	study	study	NOUN
ejpam-5894	13	6	of	of	ADP
ejpam-5894	13	7	intricate	intricate	ADJ
ejpam-5894	13	8	logical	logical	ADJ
ejpam-5894	13	9	structures	structure	NOUN
ejpam-5894	13	10	and	and	CCONJ
ejpam-5894	13	11	have	have	VERB
ejpam-5894	13	12	applications	application	NOUN
ejpam-5894	13	13	in	in	ADP
ejpam-5894	13	14	advanced	advanced	ADJ
ejpam-5894	13	15	mathematics	mathematic	NOUN
ejpam-5894	13	16	and	and	CCONJ
ejpam-5894	13	17	fuzzy	fuzzy	ADJ
ejpam-5894	13	18	logic	logic	NOUN
ejpam-5894	13	19	,	,	PUNCT
ejpam-5894	13	20	addressing	address	VERB
ejpam-5894	13	21	subtleties	subtlety	NOUN
ejpam-5894	13	22	in	in	ADP
ejpam-5894	13	23	reasoning	reason	VERB
ejpam-5894	13	24	that	that	SCONJ
ejpam-5894	13	25	conventional	conventional	ADJ
ejpam-5894	13	26	boolean	boolean	ADJ
ejpam-5894	13	27	algebras	algebra	NOUN
ejpam-5894	13	28	can	can	AUX
ejpam-5894	13	29	not	not	PART
ejpam-5894	13	30	handle	handle	VERB
ejpam-5894	13	31	.	.	PUNCT
ejpam-5894	14	1	∗corresponding	∗corresponde	VERB
ejpam-5894	14	2	author	author	NOUN
ejpam-5894	14	3	.	.	PUNCT
ejpam-5894	15	1	doi	doi	NOUN
ejpam-5894	15	2	:	:	PUNCT
ejpam-5894	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.5894	https://doi.org/10.29020/nybg.ejpam.v18i3.5894	PROPN
ejpam-5894	15	4	email	email	NOUN
ejpam-5894	15	5	addresses	address	NOUN
ejpam-5894	15	6	:	:	PUNCT
ejpam-5894	15	7	tahsin.oner@ege.edu.tr	tahsin.oner@ege.edu.tr	NOUN
ejpam-5894	15	8	(	(	PUNCT
ejpam-5894	15	9	t.	t.	NOUN
ejpam-5894	15	10	oner	oner	PROPN
ejpam-5894	15	11	)	)	PUNCT
ejpam-5894	15	12	,	,	PUNCT
ejpam-5894	15	13	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-5894	15	14	(	(	PUNCT
ejpam-5894	15	15	a.	a.	NOUN
ejpam-5894	15	16	iampan	iampan	PROPN
ejpam-5894	15	17	)	)	PUNCT
ejpam-5894	15	18	,	,	PUNCT
ejpam-5894	15	19	nrajesh	nrajesh	PROPN
ejpam-5894	15	20	topology@yahoo.co.in	topology@yahoo.co.in	PROPN
ejpam-5894	15	21	(	(	PUNCT
ejpam-5894	15	22	n.	n.	PROPN
ejpam-5894	15	23	rajesh	rajesh	PROPN
ejpam-5894	15	24	)	)	PUNCT
ejpam-5894	15	25	,	,	PUNCT
ejpam-5894	15	26	ibrahim.senturk@ege.edu.tr	ibrahim.senturk@ege.edu.tr	PROPN
ejpam-5894	15	27	(	(	PUNCT
ejpam-5894	15	28	i.	i.	PROPN
ejpam-5894	15	29	senturk	senturk	PROPN
ejpam-5894	15	30	)	)	PUNCT
ejpam-5894	15	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5894	15	32	1	1	NUM
ejpam-5894	15	33	copyright	copyright	NOUN
ejpam-5894	15	34	:	:	PUNCT
ejpam-5894	16	1	©	©	PROPN
ejpam-5894	16	2	2025	2025	NUM
ejpam-5894	16	3	the	the	DET
ejpam-5894	16	4	author(s	author(s	NOUN
ejpam-5894	16	5	)	)	PUNCT
ejpam-5894	16	6	.	.	PUNCT
ejpam-5894	17	1	(	(	PUNCT
ejpam-5894	17	2	cc	cc	NOUN
ejpam-5894	17	3	by	by	ADP
ejpam-5894	17	4	-	-	PUNCT
ejpam-5894	17	5	nc	nc	PROPN
ejpam-5894	17	6	4.0	4.0	NUM
ejpam-5894	17	7	)	)	PUNCT
ejpam-5894	17	8	t.	t.	NOUN
ejpam-5894	17	9	oner	oner	NOUN
ejpam-5894	17	10	et	et	PROPN
ejpam-5894	17	11	al	al	PROPN
ejpam-5894	17	12	.	.	PUNCT
ejpam-5894	17	13	/	/	SYM
ejpam-5894	17	14	eur	eur	PROPN
ejpam-5894	17	15	.	.	PUNCT
ejpam-5894	18	1	j.	j.	PROPN
ejpam-5894	18	2	pure	pure	PROPN
ejpam-5894	18	3	appl	appl	PROPN
ejpam-5894	18	4	.	.	PROPN
ejpam-5894	18	5	math	math	PROPN
ejpam-5894	18	6	,	,	PUNCT
ejpam-5894	18	7	18	18	NUM
ejpam-5894	18	8	(	(	PUNCT
ejpam-5894	18	9	3	3	NUM
ejpam-5894	18	10	)	)	PUNCT
ejpam-5894	18	11	(	(	PUNCT
ejpam-5894	18	12	2025	2025	NUM
ejpam-5894	18	13	)	)	PUNCT
ejpam-5894	18	14	,	,	PUNCT
ejpam-5894	18	15	5894	5894	NUM
ejpam-5894	18	16	2	2	NUM
ejpam-5894	18	17	of	of	ADP
ejpam-5894	18	18	33	33	NUM
ejpam-5894	18	19	guntasow	guntasow	NOUN
ejpam-5894	18	20	et	et	PROPN
ejpam-5894	18	21	al	al	PROPN
ejpam-5894	18	22	.	.	PUNCT
ejpam-5894	19	1	[	[	X
ejpam-5894	19	2	2	2	X
ejpam-5894	19	3	]	]	PUNCT
ejpam-5894	19	4	introduced	introduce	VERB
ejpam-5894	19	5	fuzzy	fuzzy	ADJ
ejpam-5894	19	6	α	α	NOUN
ejpam-5894	19	7	and	and	CCONJ
ejpam-5894	19	8	β	β	NOUN
ejpam-5894	19	9	-	-	NOUN
ejpam-5894	19	10	translations	translation	NOUN
ejpam-5894	19	11	of	of	ADP
ejpam-5894	19	12	µ	µ	DET
ejpam-5894	19	13	types	type	NOUN
ejpam-5894	19	14	i	i	PRON
ejpam-5894	19	15	and	and	CCONJ
ejpam-5894	19	16	ii	ii	PROPN
ejpam-5894	19	17	,	,	PUNCT
ejpam-5894	19	18	while	while	SCONJ
ejpam-5894	19	19	kim	kim	PROPN
ejpam-5894	19	20	et	et	PROPN
ejpam-5894	19	21	al	al	PROPN
ejpam-5894	19	22	.	.	PUNCT
ejpam-5894	20	1	[	[	X
ejpam-5894	20	2	1	1	X
ejpam-5894	20	3	]	]	PUNCT
ejpam-5894	20	4	proposed	propose	VERB
ejpam-5894	20	5	bg	bg	PROPN
ejpam-5894	20	6	-	-	PUNCT
ejpam-5894	20	7	algebras	algebras	PROPN
ejpam-5894	20	8	as	as	ADP
ejpam-5894	20	9	a	a	DET
ejpam-5894	20	10	broader	broad	ADJ
ejpam-5894	20	11	generalization	generalization	NOUN
ejpam-5894	20	12	of	of	ADP
ejpam-5894	20	13	b	b	PROPN
ejpam-5894	20	14	-	-	PUNCT
ejpam-5894	20	15	algebras	algebras	X
ejpam-5894	20	16	.	.	PUNCT
ejpam-5894	21	1	udten	udten	VERB
ejpam-5894	21	2	et	et	PROPN
ejpam-5894	21	3	al	al	PROPN
ejpam-5894	21	4	.	.	PUNCT
ejpam-5894	22	1	[	[	X
ejpam-5894	22	2	3	3	NUM
ejpam-5894	22	3	]	]	PUNCT
ejpam-5894	22	4	investigated	investigate	VERB
ejpam-5894	22	5	the	the	DET
ejpam-5894	22	6	concepts	concept	NOUN
ejpam-5894	22	7	of	of	ADP
ejpam-5894	22	8	translation	translation	NOUN
ejpam-5894	22	9	and	and	CCONJ
ejpam-5894	22	10	density	density	NOUN
ejpam-5894	22	11	within	within	ADP
ejpam-5894	22	12	the	the	DET
ejpam-5894	22	13	framework	framework	NOUN
ejpam-5894	22	14	of	of	ADP
ejpam-5894	22	15	intuitionistic	intuitionistic	ADJ
ejpam-5894	22	16	fuzzy	fuzzy	ADJ
ejpam-5894	22	17	sets	set	NOUN
ejpam-5894	22	18	in	in	ADP
ejpam-5894	22	19	up	up	ADP
ejpam-5894	22	20	-	-	PUNCT
ejpam-5894	22	21	algebras	algebras	X
ejpam-5894	22	22	.	.	PUNCT
ejpam-5894	23	1	furthermore	furthermore	ADV
ejpam-5894	23	2	,	,	PUNCT
ejpam-5894	23	3	lee	lee	PROPN
ejpam-5894	23	4	et	et	PROPN
ejpam-5894	23	5	al	al	PROPN
ejpam-5894	23	6	.	.	PUNCT
ejpam-5894	24	1	[	[	X
ejpam-5894	24	2	4	4	X
ejpam-5894	24	3	]	]	PUNCT
ejpam-5894	24	4	explored	explore	VERB
ejpam-5894	24	5	the	the	DET
ejpam-5894	24	6	integration	integration	NOUN
ejpam-5894	24	7	of	of	ADP
ejpam-5894	24	8	fuzzy	fuzzy	ADJ
ejpam-5894	24	9	set	set	NOUN
ejpam-5894	24	10	theory	theory	NOUN
ejpam-5894	24	11	into	into	ADP
ejpam-5894	24	12	bck	bck	PROPN
ejpam-5894	24	13	/	/	SYM
ejpam-5894	24	14	bci	bci	NOUN
ejpam-5894	24	15	-	-	PUNCT
ejpam-5894	24	16	algebras	algebra	NOUN
ejpam-5894	24	17	,	,	PUNCT
ejpam-5894	24	18	extending	extend	VERB
ejpam-5894	24	19	classical	classical	ADJ
ejpam-5894	24	20	algebraic	algebraic	ADJ
ejpam-5894	24	21	frameworks	framework	NOUN
ejpam-5894	24	22	to	to	PART
ejpam-5894	24	23	account	account	VERB
ejpam-5894	24	24	for	for	ADP
ejpam-5894	24	25	vagueness	vagueness	NOUN
ejpam-5894	24	26	and	and	CCONJ
ejpam-5894	24	27	uncertainty	uncertainty	NOUN
ejpam-5894	24	28	.	.	PUNCT
ejpam-5894	25	1	similarly	similarly	ADV
ejpam-5894	25	2	,	,	PUNCT
ejpam-5894	25	3	balamurugan	balamurugan	VERB
ejpam-5894	25	4	et	et	PROPN
ejpam-5894	25	5	al	al	PROPN
ejpam-5894	25	6	.	.	PUNCT
ejpam-5894	26	1	[	[	X
ejpam-5894	26	2	5	5	NUM
ejpam-5894	26	3	]	]	PUNCT
ejpam-5894	26	4	developed	develop	VERB
ejpam-5894	26	5	translations	translation	NOUN
ejpam-5894	26	6	of	of	ADP
ejpam-5894	26	7	intuitionistic	intuitionistic	ADJ
ejpam-5894	26	8	fuzzy	fuzzy	ADJ
ejpam-5894	26	9	soft	soft	ADJ
ejpam-5894	26	10	structures	structure	NOUN
ejpam-5894	26	11	in	in	ADP
ejpam-5894	26	12	b	b	NOUN
ejpam-5894	26	13	-	-	PUNCT
ejpam-5894	26	14	algebras	algebras	X
ejpam-5894	26	15	,	,	PUNCT
ejpam-5894	26	16	combining	combine	VERB
ejpam-5894	26	17	intuitionistic	intuitionistic	ADJ
ejpam-5894	26	18	fuzzy	fuzzy	ADJ
ejpam-5894	26	19	sets	set	NOUN
ejpam-5894	26	20	with	with	ADP
ejpam-5894	26	21	soft	soft	ADJ
ejpam-5894	26	22	set	set	NOUN
ejpam-5894	26	23	theory	theory	NOUN
ejpam-5894	26	24	to	to	PART
ejpam-5894	26	25	address	address	VERB
ejpam-5894	26	26	imprecision	imprecision	NOUN
ejpam-5894	26	27	in	in	ADP
ejpam-5894	26	28	algebraic	algebraic	ADJ
ejpam-5894	26	29	systems	system	NOUN
ejpam-5894	26	30	.	.	PUNCT
ejpam-5894	27	1	the	the	DET
ejpam-5894	27	2	sheffer	sheffer	PROPN
ejpam-5894	27	3	stroke	stroke	NOUN
ejpam-5894	27	4	operation	operation	NOUN
ejpam-5894	27	5	,	,	PUNCT
ejpam-5894	27	6	also	also	ADV
ejpam-5894	27	7	known	know	VERB
ejpam-5894	27	8	as	as	ADP
ejpam-5894	27	9	the	the	DET
ejpam-5894	27	10	nand	nand	NOUN
ejpam-5894	27	11	operator	operator	NOUN
ejpam-5894	27	12	,	,	PUNCT
ejpam-5894	27	13	was	be	AUX
ejpam-5894	27	14	introduced	introduce	VERB
ejpam-5894	27	15	by	by	ADP
ejpam-5894	27	16	sheffer	sheffer	NOUN
ejpam-5894	27	17	[	[	X
ejpam-5894	27	18	6	6	NUM
ejpam-5894	27	19	]	]	PUNCT
ejpam-5894	27	20	.	.	PUNCT
ejpam-5894	28	1	as	as	ADP
ejpam-5894	28	2	a	a	DET
ejpam-5894	28	3	functionally	functionally	ADV
ejpam-5894	28	4	complete	complete	ADJ
ejpam-5894	28	5	operation	operation	NOUN
ejpam-5894	28	6	,	,	PUNCT
ejpam-5894	28	7	it	it	PRON
ejpam-5894	28	8	allows	allow	VERB
ejpam-5894	28	9	any	any	DET
ejpam-5894	28	10	logical	logical	ADJ
ejpam-5894	28	11	expression	expression	NOUN
ejpam-5894	28	12	or	or	CCONJ
ejpam-5894	28	13	axiom	axiom	NOUN
ejpam-5894	28	14	in	in	ADP
ejpam-5894	28	15	a	a	DET
ejpam-5894	28	16	logical	logical	ADJ
ejpam-5894	28	17	system	system	NOUN
ejpam-5894	28	18	to	to	PART
ejpam-5894	28	19	be	be	AUX
ejpam-5894	28	20	expressed	express	VERB
ejpam-5894	28	21	solely	solely	ADV
ejpam-5894	28	22	using	use	VERB
ejpam-5894	28	23	the	the	DET
ejpam-5894	28	24	sheffer	sheffer	NOUN
ejpam-5894	28	25	stroke	stroke	NOUN
ejpam-5894	29	1	[	[	X
ejpam-5894	29	2	7	7	NUM
ejpam-5894	29	3	]	]	PUNCT
ejpam-5894	29	4	.	.	PUNCT
ejpam-5894	30	1	this	this	DET
ejpam-5894	30	2	property	property	NOUN
ejpam-5894	30	3	simplifies	simplify	VERB
ejpam-5894	30	4	the	the	DET
ejpam-5894	30	5	study	study	NOUN
ejpam-5894	30	6	of	of	ADP
ejpam-5894	30	7	logical	logical	ADJ
ejpam-5894	30	8	systems	system	NOUN
ejpam-5894	30	9	by	by	ADP
ejpam-5894	30	10	reducing	reduce	VERB
ejpam-5894	30	11	the	the	DET
ejpam-5894	30	12	number	number	NOUN
ejpam-5894	30	13	of	of	ADP
ejpam-5894	30	14	required	require	VERB
ejpam-5894	30	15	fundamental	fundamental	ADJ
ejpam-5894	30	16	operations	operation	NOUN
ejpam-5894	30	17	and	and	CCONJ
ejpam-5894	30	18	has	have	VERB
ejpam-5894	30	19	significant	significant	ADJ
ejpam-5894	30	20	implications	implication	NOUN
ejpam-5894	30	21	for	for	ADP
ejpam-5894	30	22	both	both	CCONJ
ejpam-5894	30	23	algebraic	algebraic	ADJ
ejpam-5894	30	24	and	and	CCONJ
ejpam-5894	30	25	logical	logical	ADJ
ejpam-5894	30	26	frameworks	framework	NOUN
ejpam-5894	30	27	.	.	PUNCT
ejpam-5894	31	1	the	the	DET
ejpam-5894	31	2	sheffer	sheffer	PROPN
ejpam-5894	31	3	stroke	stroke	NOUN
ejpam-5894	31	4	’s	’s	PART
ejpam-5894	31	5	ability	ability	NOUN
ejpam-5894	31	6	to	to	PART
ejpam-5894	31	7	encapsulate	encapsulate	VERB
ejpam-5894	31	8	all	all	DET
ejpam-5894	31	9	boolean	boolean	ADJ
ejpam-5894	31	10	algebra	algebra	NOUN
ejpam-5894	31	11	axioms	axiom	NOUN
ejpam-5894	31	12	highlights	highlight	VERB
ejpam-5894	31	13	its	its	PRON
ejpam-5894	31	14	foundational	foundational	ADJ
ejpam-5894	31	15	importance	importance	NOUN
ejpam-5894	31	16	and	and	CCONJ
ejpam-5894	31	17	versatility	versatility	NOUN
ejpam-5894	31	18	.	.	PUNCT
ejpam-5894	32	1	the	the	DET
ejpam-5894	32	2	integration	integration	NOUN
ejpam-5894	32	3	of	of	ADP
ejpam-5894	32	4	the	the	DET
ejpam-5894	32	5	sheffer	sheffer	NOUN
ejpam-5894	32	6	stroke	stroke	NOUN
ejpam-5894	32	7	into	into	ADP
ejpam-5894	32	8	various	various	ADJ
ejpam-5894	32	9	algebraic	algebraic	ADJ
ejpam-5894	32	10	structures	structure	NOUN
ejpam-5894	32	11	has	have	AUX
ejpam-5894	32	12	attracted	attract	VERB
ejpam-5894	32	13	considerable	considerable	ADJ
ejpam-5894	32	14	academic	academic	ADJ
ejpam-5894	32	15	attention	attention	NOUN
ejpam-5894	32	16	.	.	PUNCT
ejpam-5894	33	1	studies	study	NOUN
ejpam-5894	33	2	have	have	AUX
ejpam-5894	33	3	examined	examine	VERB
ejpam-5894	33	4	sheffer	sheffer	NOUN
ejpam-5894	33	5	stroke	stroke	NOUN
ejpam-5894	33	6	operation	operation	NOUN
ejpam-5894	33	7	reducts	reduct	NOUN
ejpam-5894	33	8	of	of	ADP
ejpam-5894	33	9	basic	basic	ADJ
ejpam-5894	33	10	algebras	algebra	NOUN
ejpam-5894	33	11	and	and	CCONJ
ejpam-5894	33	12	their	their	PRON
ejpam-5894	33	13	congruences	congruence	NOUN
ejpam-5894	33	14	[	[	X
ejpam-5894	33	15	8	8	NUM
ejpam-5894	33	16	,	,	PUNCT
ejpam-5894	33	17	9	9	NUM
ejpam-5894	33	18	]	]	PUNCT
ejpam-5894	33	19	,	,	PUNCT
ejpam-5894	33	20	sheffer	sheffer	PROPN
ejpam-5894	33	21	stroke	stroke	NOUN
ejpam-5894	33	22	mtl	mtl	PROPN
ejpam-5894	33	23	-	-	PUNCT
ejpam-5894	33	24	algebras	algebras	X
ejpam-5894	34	1	[	[	X
ejpam-5894	34	2	10	10	NUM
ejpam-5894	34	3	]	]	PUNCT
ejpam-5894	34	4	,	,	PUNCT
ejpam-5894	34	5	ortholattices	ortholattice	VERB
ejpam-5894	34	6	[	[	X
ejpam-5894	34	7	11	11	NUM
ejpam-5894	34	8	]	]	PUNCT
ejpam-5894	34	9	,	,	PUNCT
ejpam-5894	34	10	new	new	ADJ
ejpam-5894	34	11	state	state	NOUN
ejpam-5894	34	12	operators	operator	NOUN
ejpam-5894	34	13	in	in	ADP
ejpam-5894	34	14	sheffer	sheffer	PROPN
ejpam-5894	34	15	stroke	stroke	NOUN
ejpam-5894	34	16	basic	basic	ADJ
ejpam-5894	34	17	algebras	algebra	NOUN
ejpam-5894	34	18	and	and	CCONJ
ejpam-5894	34	19	their	their	PRON
ejpam-5894	34	20	filters	filter	NOUN
ejpam-5894	35	1	[	[	X
ejpam-5894	35	2	12	12	NUM
ejpam-5894	35	3	]	]	PUNCT
ejpam-5894	35	4	,	,	PUNCT
ejpam-5894	35	5	riečan	riečan	NOUN
ejpam-5894	35	6	and	and	CCONJ
ejpam-5894	35	7	bosbach	bosbach	ADJ
ejpam-5894	35	8	state	state	NOUN
ejpam-5894	35	9	operators	operator	NOUN
ejpam-5894	35	10	on	on	ADP
ejpam-5894	35	11	sheffer	sheffer	PROPN
ejpam-5894	35	12	stroke	stroke	NOUN
ejpam-5894	35	13	mtl	mtl	PROPN
ejpam-5894	35	14	-	-	PUNCT
ejpam-5894	35	15	algebras	algebras	X
ejpam-5894	35	16	[	[	X
ejpam-5894	35	17	13	13	NUM
ejpam-5894	35	18	]	]	PUNCT
ejpam-5894	35	19	,	,	PUNCT
ejpam-5894	35	20	fuzzy	fuzzy	ADJ
ejpam-5894	35	21	set	set	VERB
ejpam-5894	35	22	approaches	approach	NOUN
ejpam-5894	35	23	to	to	PART
ejpam-5894	35	24	sheffer	sheffer	VERB
ejpam-5894	35	25	stroke	stroke	NOUN
ejpam-5894	35	26	be	be	AUX
ejpam-5894	35	27	-	-	PUNCT
ejpam-5894	35	28	algebras	algebras	X
ejpam-5894	35	29	[	[	X
ejpam-5894	35	30	14	14	NUM
ejpam-5894	35	31	]	]	PUNCT
ejpam-5894	35	32	,	,	PUNCT
ejpam-5894	35	33	and	and	CCONJ
ejpam-5894	35	34	,	,	PUNCT
ejpam-5894	35	35	notably	notably	ADV
ejpam-5894	35	36	,	,	PUNCT
ejpam-5894	35	37	sheffer	sheffer	PROPN
ejpam-5894	35	38	stroke	stroke	NOUN
ejpam-5894	35	39	bg	bg	PROPN
ejpam-5894	35	40	-	-	PUNCT
ejpam-5894	35	41	algebras	algebras	X
ejpam-5894	36	1	[	[	X
ejpam-5894	36	2	15	15	NUM
ejpam-5894	36	3	]	]	PUNCT
ejpam-5894	36	4	.	.	PUNCT
ejpam-5894	37	1	the	the	DET
ejpam-5894	37	2	study	study	NOUN
ejpam-5894	37	3	of	of	ADP
ejpam-5894	37	4	sheffer	sheffer	PROPN
ejpam-5894	37	5	stroke	stroke	PROPN
ejpam-5894	37	6	bg	bg	PROPN
ejpam-5894	37	7	-	-	PUNCT
ejpam-5894	37	8	algebras	algebras	PROPN
ejpam-5894	37	9	is	be	AUX
ejpam-5894	37	10	motivated	motivate	VERB
ejpam-5894	37	11	by	by	ADP
ejpam-5894	37	12	their	their	PRON
ejpam-5894	37	13	theoretical	theoretical	ADJ
ejpam-5894	37	14	significance	significance	NOUN
ejpam-5894	37	15	and	and	CCONJ
ejpam-5894	37	16	practical	practical	ADJ
ejpam-5894	37	17	applications	application	NOUN
ejpam-5894	37	18	.	.	PUNCT
ejpam-5894	38	1	these	these	DET
ejpam-5894	38	2	structures	structure	NOUN
ejpam-5894	38	3	deepen	deepen	VERB
ejpam-5894	38	4	our	our	PRON
ejpam-5894	38	5	understanding	understanding	NOUN
ejpam-5894	38	6	of	of	ADP
ejpam-5894	38	7	non	non	ADJ
ejpam-5894	38	8	-	-	ADJ
ejpam-5894	38	9	classical	classical	ADJ
ejpam-5894	38	10	logics	logic	NOUN
ejpam-5894	38	11	and	and	CCONJ
ejpam-5894	38	12	offer	offer	VERB
ejpam-5894	38	13	valuable	valuable	ADJ
ejpam-5894	38	14	insights	insight	NOUN
ejpam-5894	38	15	into	into	ADP
ejpam-5894	38	16	computational	computational	ADJ
ejpam-5894	38	17	models	model	NOUN
ejpam-5894	38	18	,	,	PUNCT
ejpam-5894	38	19	particularly	particularly	ADV
ejpam-5894	38	20	in	in	ADP
ejpam-5894	38	21	fields	field	NOUN
ejpam-5894	38	22	such	such	ADJ
ejpam-5894	38	23	as	as	ADP
ejpam-5894	38	24	quantum	quantum	NOUN
ejpam-5894	38	25	computing	computing	NOUN
ejpam-5894	38	26	and	and	CCONJ
ejpam-5894	38	27	intuitionistic	intuitionistic	ADJ
ejpam-5894	38	28	fuzzy	fuzzy	ADJ
ejpam-5894	38	29	sets	set	NOUN
ejpam-5894	38	30	[	[	X
ejpam-5894	38	31	16	16	NUM
ejpam-5894	38	32	]	]	PUNCT
ejpam-5894	38	33	.	.	PUNCT
ejpam-5894	39	1	oner	oner	NOUN
ejpam-5894	39	2	et	et	PROPN
ejpam-5894	39	3	al	al	PROPN
ejpam-5894	39	4	.	.	PROPN
ejpam-5894	39	5	have	have	AUX
ejpam-5894	39	6	extensively	extensively	ADV
ejpam-5894	39	7	investigated	investigate	VERB
ejpam-5894	39	8	the	the	DET
ejpam-5894	39	9	theoretical	theoretical	ADJ
ejpam-5894	39	10	and	and	CCONJ
ejpam-5894	39	11	axiomatic	axiomatic	ADJ
ejpam-5894	39	12	properties	property	NOUN
ejpam-5894	39	13	of	of	ADP
ejpam-5894	39	14	various	various	ADJ
ejpam-5894	39	15	algebraic	algebraic	ADJ
ejpam-5894	39	16	systems	system	NOUN
ejpam-5894	39	17	and	and	CCONJ
ejpam-5894	39	18	their	their	PRON
ejpam-5894	39	19	interrelations	interrelation	NOUN
ejpam-5894	39	20	,	,	PUNCT
ejpam-5894	39	21	such	such	ADJ
ejpam-5894	39	22	as	as	ADP
ejpam-5894	39	23	sheffer	sheffer	NOUN
ejpam-5894	39	24	stroke	stroke	NOUN
ejpam-5894	39	25	bg	bg	PROPN
ejpam-5894	39	26	-	-	PUNCT
ejpam-5894	39	27	algebras	algebras	PROPN
ejpam-5894	39	28	(	(	PUNCT
ejpam-5894	39	29	see	see	VERB
ejpam-5894	39	30	[	[	X
ejpam-5894	39	31	15	15	NUM
ejpam-5894	39	32	]	]	PUNCT
ejpam-5894	39	33	)	)	PUNCT
ejpam-5894	39	34	sheffer	sheffer	NOUN
ejpam-5894	39	35	stroke	stroke	NOUN
ejpam-5894	39	36	be	be	VERB
ejpam-5894	39	37	-	-	PUNCT
ejpam-5894	39	38	algebras	algebras	X
ejpam-5894	39	39	(	(	PUNCT
ejpam-5894	39	40	see	see	VERB
ejpam-5894	39	41	[	[	X
ejpam-5894	39	42	17	17	NUM
ejpam-5894	39	43	,	,	PUNCT
ejpam-5894	39	44	18	18	NUM
ejpam-5894	39	45	]	]	NUM
ejpam-5894	39	46	)	)	PUNCT
ejpam-5894	39	47	,	,	PUNCT
ejpam-5894	39	48	sheffer	sheffer	NOUN
ejpam-5894	39	49	stroke	stroke	PROPN
ejpam-5894	39	50	hilbert	hilbert	PROPN
ejpam-5894	39	51	algebras	algebras	PROPN
ejpam-5894	39	52	(	(	PUNCT
ejpam-5894	39	53	see	see	VERB
ejpam-5894	39	54	[	[	X
ejpam-5894	39	55	19–22	19–22	NUM
ejpam-5894	39	56	]	]	X
ejpam-5894	39	57	)	)	PUNCT
ejpam-5894	39	58	,	,	PUNCT
ejpam-5894	39	59	sheffer	sheffer	NOUN
ejpam-5894	39	60	stroke	stroke	NOUN
ejpam-5894	39	61	bck	bck	PROPN
ejpam-5894	39	62	-	-	PUNCT
ejpam-5894	39	63	algebras	algebras	X
ejpam-5894	39	64	(	(	PUNCT
ejpam-5894	39	65	see	see	VERB
ejpam-5894	39	66	[	[	X
ejpam-5894	39	67	23	23	NUM
ejpam-5894	39	68	]	]	NUM
ejpam-5894	39	69	)	)	PUNCT
ejpam-5894	39	70	,	,	PUNCT
ejpam-5894	39	71	sheffer	sheffer	NOUN
ejpam-5894	39	72	stroke	stroke	NOUN
ejpam-5894	39	73	mtl	mtl	PROPN
ejpam-5894	39	74	-	-	PUNCT
ejpam-5894	39	75	algebras	algebras	PROPN
ejpam-5894	39	76	(	(	PUNCT
ejpam-5894	39	77	see	see	VERB
ejpam-5894	39	78	[	[	X
ejpam-5894	39	79	24	24	NUM
ejpam-5894	39	80	]	]	NUM
ejpam-5894	39	81	)	)	PUNCT
ejpam-5894	39	82	,	,	PUNCT
ejpam-5894	39	83	sheffer	sheffer	NOUN
ejpam-5894	39	84	stroke	stroke	NOUN
ejpam-5894	39	85	bl	bl	PROPN
ejpam-5894	39	86	-	-	PUNCT
ejpam-5894	39	87	algebras	algebras	PROPN
ejpam-5894	39	88	(	(	PUNCT
ejpam-5894	39	89	see	see	VERB
ejpam-5894	39	90	[	[	X
ejpam-5894	39	91	25	25	NUM
ejpam-5894	39	92	]	]	NUM
ejpam-5894	39	93	)	)	PUNCT
ejpam-5894	39	94	,	,	PUNCT
ejpam-5894	39	95	sheffer	sheffer	NOUN
ejpam-5894	39	96	stroke	stroke	NOUN
ejpam-5894	39	97	basic	basic	ADJ
ejpam-5894	39	98	algebras	algebra	NOUN
ejpam-5894	39	99	(	(	PUNCT
ejpam-5894	39	100	see	see	VERB
ejpam-5894	39	101	[	[	X
ejpam-5894	39	102	26	26	NUM
ejpam-5894	39	103	]	]	NUM
ejpam-5894	39	104	)	)	PUNCT
ejpam-5894	39	105	,	,	PUNCT
ejpam-5894	39	106	sheffer	sheffer	NOUN
ejpam-5894	39	107	stroke	stroke	PROPN
ejpam-5894	39	108	bch	bch	PROPN
ejpam-5894	39	109	-	-	PUNCT
ejpam-5894	39	110	algebras	algebras	PROPN
ejpam-5894	39	111	(	(	PUNCT
ejpam-5894	39	112	see	see	VERB
ejpam-5894	39	113	[	[	X
ejpam-5894	39	114	27	27	NUM
ejpam-5894	39	115	]	]	NUM
ejpam-5894	39	116	)	)	PUNCT
ejpam-5894	39	117	,	,	PUNCT
ejpam-5894	39	118	sheffer	sheffer	NOUN
ejpam-5894	39	119	stroke	stroke	NOUN
ejpam-5894	39	120	bhalgebras	bhalgebras	X
ejpam-5894	39	121	(	(	PUNCT
ejpam-5894	39	122	see	see	VERB
ejpam-5894	39	123	[	[	X
ejpam-5894	39	124	28	28	NUM
ejpam-5894	39	125	]	]	NUM
ejpam-5894	39	126	)	)	PUNCT
ejpam-5894	39	127	,	,	PUNCT
ejpam-5894	39	128	sheffer	sheffer	VERB
ejpam-5894	39	129	stroke	stroke	NOUN
ejpam-5894	39	130	up	up	ADP
ejpam-5894	39	131	-	-	PUNCT
ejpam-5894	39	132	algebras	algebras	X
ejpam-5894	39	133	(	(	PUNCT
ejpam-5894	39	134	see	see	VERB
ejpam-5894	39	135	[	[	X
ejpam-5894	39	136	29	29	NUM
ejpam-5894	39	137	,	,	PUNCT
ejpam-5894	39	138	30	30	NUM
ejpam-5894	39	139	]	]	PUNCT
ejpam-5894	39	140	)	)	PUNCT
ejpam-5894	39	141	.	.	PUNCT
ejpam-5894	40	1	by	by	ADP
ejpam-5894	40	2	leveraging	leverage	VERB
ejpam-5894	40	3	the	the	DET
ejpam-5894	40	4	unique	unique	ADJ
ejpam-5894	40	5	properties	property	NOUN
ejpam-5894	40	6	of	of	ADP
ejpam-5894	40	7	the	the	DET
ejpam-5894	40	8	sheffer	sheffer	NOUN
ejpam-5894	40	9	stroke	stroke	NOUN
ejpam-5894	40	10	,	,	PUNCT
ejpam-5894	40	11	sheffer	sheffer	PROPN
ejpam-5894	40	12	stroke	stroke	NOUN
ejpam-5894	40	13	bg	bg	PROPN
ejpam-5894	40	14	-	-	PUNCT
ejpam-5894	40	15	algebras	algebras	PROPN
ejpam-5894	40	16	enable	enable	VERB
ejpam-5894	40	17	the	the	DET
ejpam-5894	40	18	development	development	NOUN
ejpam-5894	40	19	of	of	ADP
ejpam-5894	40	20	novel	novel	ADJ
ejpam-5894	40	21	reasoning	reasoning	NOUN
ejpam-5894	40	22	methods	method	NOUN
ejpam-5894	40	23	that	that	PRON
ejpam-5894	40	24	extend	extend	VERB
ejpam-5894	40	25	beyond	beyond	ADP
ejpam-5894	40	26	classical	classical	ADJ
ejpam-5894	40	27	boolean	boolean	ADJ
ejpam-5894	40	28	frameworks	framework	NOUN
ejpam-5894	40	29	.	.	PUNCT
ejpam-5894	41	1	in	in	ADP
ejpam-5894	41	2	this	this	DET
ejpam-5894	41	3	paper	paper	NOUN
ejpam-5894	41	4	,	,	PUNCT
ejpam-5894	41	5	we	we	PRON
ejpam-5894	41	6	introduce	introduce	VERB
ejpam-5894	41	7	and	and	CCONJ
ejpam-5894	41	8	analyze	analyze	VERB
ejpam-5894	41	9	the	the	DET
ejpam-5894	41	10	concepts	concept	NOUN
ejpam-5894	41	11	of	of	ADP
ejpam-5894	41	12	intuitionistic	intuitionistic	ADJ
ejpam-5894	41	13	fuzzy	fuzzy	ADJ
ejpam-5894	41	14	wsbgideals	wsbgideal	NOUN
ejpam-5894	41	15	within	within	ADP
ejpam-5894	41	16	the	the	DET
ejpam-5894	41	17	framework	framework	NOUN
ejpam-5894	41	18	of	of	ADP
ejpam-5894	41	19	sheffer	sheffer	PROPN
ejpam-5894	41	20	stroke	stroke	PROPN
ejpam-5894	41	21	bg	bg	PROPN
ejpam-5894	41	22	-	-	PUNCT
ejpam-5894	41	23	algebras	algebras	PROPN
ejpam-5894	41	24	.	.	PUNCT
ejpam-5894	42	1	intuitionistic	intuitionistic	ADJ
ejpam-5894	42	2	fuzzy	fuzzy	ADJ
ejpam-5894	42	3	sets	set	NOUN
ejpam-5894	42	4	,	,	PUNCT
ejpam-5894	42	5	as	as	SCONJ
ejpam-5894	42	6	formulated	formulate	VERB
ejpam-5894	42	7	by	by	ADP
ejpam-5894	42	8	atanassov	atanassov	NOUN
ejpam-5894	42	9	,	,	PUNCT
ejpam-5894	42	10	generalize	generalize	VERB
ejpam-5894	42	11	fuzzy	fuzzy	ADJ
ejpam-5894	42	12	sets	set	NOUN
ejpam-5894	42	13	by	by	ADP
ejpam-5894	42	14	considering	consider	VERB
ejpam-5894	42	15	both	both	CCONJ
ejpam-5894	42	16	membership	membership	NOUN
ejpam-5894	42	17	and	and	CCONJ
ejpam-5894	42	18	nonmembership	nonmembership	NOUN
ejpam-5894	42	19	degrees	degree	NOUN
ejpam-5894	42	20	independently	independently	ADV
ejpam-5894	42	21	,	,	PUNCT
ejpam-5894	42	22	making	make	VERB
ejpam-5894	42	23	them	they	PRON
ejpam-5894	42	24	particularly	particularly	ADV
ejpam-5894	42	25	effective	effective	ADJ
ejpam-5894	42	26	for	for	ADP
ejpam-5894	42	27	handling	handle	VERB
ejpam-5894	42	28	incomplete	incomplete	ADJ
ejpam-5894	42	29	or	or	CCONJ
ejpam-5894	42	30	hesitant	hesitant	ADJ
ejpam-5894	42	31	information	information	NOUN
ejpam-5894	42	32	.	.	PUNCT
ejpam-5894	43	1	we	we	PRON
ejpam-5894	43	2	establish	establish	VERB
ejpam-5894	43	3	a	a	DET
ejpam-5894	43	4	fundamental	fundamental	ADJ
ejpam-5894	43	5	connection	connection	NOUN
ejpam-5894	43	6	between	between	ADP
ejpam-5894	43	7	intuitionistic	intuitionistic	ADJ
ejpam-5894	43	8	fuzzywsbg	fuzzywsbg	NOUN
ejpam-5894	43	9	-	-	NOUN
ejpam-5894	43	10	subalgebras	subalgebra	NOUN
ejpam-5894	43	11	and	and	CCONJ
ejpam-5894	43	12	their	their	PRON
ejpam-5894	43	13	level	level	NOUN
ejpam-5894	43	14	sets	set	NOUN
ejpam-5894	43	15	,	,	PUNCT
ejpam-5894	43	16	showing	show	VERB
ejpam-5894	43	17	that	that	SCONJ
ejpam-5894	43	18	the	the	DET
ejpam-5894	43	19	level	level	NOUN
ejpam-5894	43	20	set	set	NOUN
ejpam-5894	43	21	of	of	ADP
ejpam-5894	43	22	an	an	DET
ejpam-5894	43	23	intuitionistic	intuitionistic	ADJ
ejpam-5894	43	24	fuzzy	fuzzy	ADJ
ejpam-5894	43	25	wsbg	wsbg	NOUN
ejpam-5894	43	26	-	-	PUNCT
ejpam-5894	43	27	subalgebra	subalgebra	NOUN
ejpam-5894	43	28	corresponds	correspond	VERB
ejpam-5894	43	29	to	to	ADP
ejpam-5894	43	30	a	a	DET
ejpam-5894	43	31	subalgebra	subalgebra	NOUN
ejpam-5894	43	32	of	of	ADP
ejpam-5894	43	33	the	the	DET
ejpam-5894	43	34	sheffer	sheffer	NOUN
ejpam-5894	43	35	stroke	stroke	NOUN
ejpam-5894	43	36	bg	bg	PROPN
ejpam-5894	43	37	-	-	NOUN
ejpam-5894	43	38	algebra	algebra	PROPN
ejpam-5894	43	39	,	,	PUNCT
ejpam-5894	43	40	and	and	CCONJ
ejpam-5894	43	41	vice	vice	ADV
ejpam-5894	43	42	versa	versa	ADV
ejpam-5894	43	43	.	.	PUNCT
ejpam-5894	44	1	this	this	DET
ejpam-5894	44	2	relationship	relationship	NOUN
ejpam-5894	44	3	provides	provide	VERB
ejpam-5894	44	4	a	a	DET
ejpam-5894	44	5	systematic	systematic	ADJ
ejpam-5894	44	6	framework	framework	NOUN
ejpam-5894	44	7	for	for	ADP
ejpam-5894	44	8	analyzing	analyze	VERB
ejpam-5894	44	9	the	the	DET
ejpam-5894	44	10	structure	structure	NOUN
ejpam-5894	44	11	of	of	ADP
ejpam-5894	44	12	these	these	DET
ejpam-5894	44	13	subalgebras	subalgebra	NOUN
ejpam-5894	44	14	,	,	PUNCT
ejpam-5894	44	15	t.	t.	PROPN
ejpam-5894	44	16	oner	oner	NOUN
ejpam-5894	44	17	et	et	PROPN
ejpam-5894	44	18	al	al	PROPN
ejpam-5894	44	19	.	.	PUNCT
ejpam-5894	44	20	/	/	SYM
ejpam-5894	44	21	eur	eur	PROPN
ejpam-5894	44	22	.	.	PUNCT
ejpam-5894	45	1	j.	j.	PROPN
ejpam-5894	45	2	pure	pure	PROPN
ejpam-5894	45	3	appl	appl	PROPN
ejpam-5894	45	4	.	.	PROPN
ejpam-5894	45	5	math	math	PROPN
ejpam-5894	45	6	,	,	PUNCT
ejpam-5894	45	7	18	18	NUM
ejpam-5894	45	8	(	(	PUNCT
ejpam-5894	45	9	3	3	NUM
ejpam-5894	45	10	)	)	PUNCT
ejpam-5894	45	11	(	(	PUNCT
ejpam-5894	45	12	2025	2025	NUM
ejpam-5894	45	13	)	)	PUNCT
ejpam-5894	45	14	,	,	PUNCT
ejpam-5894	45	15	5894	5894	NUM
ejpam-5894	45	16	3	3	NUM
ejpam-5894	45	17	of	of	ADP
ejpam-5894	45	18	33	33	NUM
ejpam-5894	45	19	thereby	thereby	ADV
ejpam-5894	45	20	deepening	deepen	VERB
ejpam-5894	45	21	our	our	PRON
ejpam-5894	45	22	understanding	understanding	NOUN
ejpam-5894	45	23	of	of	ADP
ejpam-5894	45	24	the	the	DET
ejpam-5894	45	25	underlying	underlying	ADJ
ejpam-5894	45	26	algebraic	algebraic	ADJ
ejpam-5894	45	27	framework	framework	NOUN
ejpam-5894	45	28	.	.	PUNCT
ejpam-5894	46	1	additionally	additionally	ADV
ejpam-5894	46	2	,	,	PUNCT
ejpam-5894	46	3	we	we	PRON
ejpam-5894	46	4	investigate	investigate	VERB
ejpam-5894	46	5	the	the	DET
ejpam-5894	46	6	properties	property	NOUN
ejpam-5894	46	7	of	of	ADP
ejpam-5894	46	8	intuitionistic	intuitionistic	ADJ
ejpam-5894	46	9	fuzzy	fuzzy	ADJ
ejpam-5894	46	10	wsbg	wsbg	NOUN
ejpam-5894	46	11	-	-	PUNCT
ejpam-5894	46	12	ideals	ideal	NOUN
ejpam-5894	46	13	,	,	PUNCT
ejpam-5894	46	14	demonstrating	demonstrate	VERB
ejpam-5894	46	15	that	that	SCONJ
ejpam-5894	46	16	every	every	DET
ejpam-5894	46	17	intuitionistic	intuitionistic	ADJ
ejpam-5894	46	18	fuzzy	fuzzy	ADJ
ejpam-5894	46	19	wsbg	wsbg	NOUN
ejpam-5894	46	20	-	-	PUNCT
ejpam-5894	46	21	ideal	ideal	NOUN
ejpam-5894	46	22	is	be	AUX
ejpam-5894	46	23	also	also	ADV
ejpam-5894	46	24	an	an	DET
ejpam-5894	46	25	intuitionistic	intuitionistic	ADJ
ejpam-5894	46	26	fuzzy	fuzzy	ADJ
ejpam-5894	46	27	wsbgsubalgebra	wsbgsubalgebra	NOUN
ejpam-5894	46	28	.	.	PUNCT
ejpam-5894	47	1	however	however	ADV
ejpam-5894	47	2	,	,	PUNCT
ejpam-5894	47	3	the	the	DET
ejpam-5894	47	4	converse	converse	NOUN
ejpam-5894	47	5	does	do	AUX
ejpam-5894	47	6	not	not	PART
ejpam-5894	47	7	always	always	ADV
ejpam-5894	47	8	hold	hold	VERB
ejpam-5894	47	9	.	.	PUNCT
ejpam-5894	48	1	this	this	DET
ejpam-5894	48	2	distinction	distinction	NOUN
ejpam-5894	48	3	illuminates	illuminate	VERB
ejpam-5894	48	4	the	the	DET
ejpam-5894	48	5	unique	unique	ADJ
ejpam-5894	48	6	characteristics	characteristic	NOUN
ejpam-5894	48	7	of	of	ADP
ejpam-5894	48	8	intuitionistic	intuitionistic	ADJ
ejpam-5894	48	9	fuzzy	fuzzy	ADJ
ejpam-5894	48	10	wsbg	wsbg	NOUN
ejpam-5894	48	11	-	-	NOUN
ejpam-5894	48	12	ideals	ideal	NOUN
ejpam-5894	48	13	within	within	ADP
ejpam-5894	48	14	the	the	DET
ejpam-5894	48	15	algebraic	algebraic	ADJ
ejpam-5894	48	16	context	context	NOUN
ejpam-5894	48	17	.	.	PUNCT
ejpam-5894	49	1	the	the	DET
ejpam-5894	49	2	novelty	novelty	NOUN
ejpam-5894	49	3	of	of	ADP
ejpam-5894	49	4	this	this	DET
ejpam-5894	49	5	work	work	NOUN
ejpam-5894	49	6	lies	lie	VERB
ejpam-5894	49	7	in	in	ADP
ejpam-5894	49	8	the	the	DET
ejpam-5894	49	9	integration	integration	NOUN
ejpam-5894	49	10	of	of	ADP
ejpam-5894	49	11	intuitionistic	intuitionistic	ADJ
ejpam-5894	49	12	fuzzy	fuzzy	ADJ
ejpam-5894	49	13	set	set	NOUN
ejpam-5894	49	14	theory	theory	NOUN
ejpam-5894	49	15	with	with	ADP
ejpam-5894	49	16	sheffer	sheffer	PROPN
ejpam-5894	49	17	stroke	stroke	PROPN
ejpam-5894	49	18	bg	bg	PROPN
ejpam-5894	49	19	-	-	PUNCT
ejpam-5894	49	20	algebras	algebras	PROPN
ejpam-5894	49	21	,	,	PUNCT
ejpam-5894	49	22	an	an	DET
ejpam-5894	49	23	area	area	NOUN
ejpam-5894	49	24	that	that	PRON
ejpam-5894	49	25	,	,	PUNCT
ejpam-5894	49	26	to	to	ADP
ejpam-5894	49	27	the	the	DET
ejpam-5894	49	28	best	good	ADJ
ejpam-5894	49	29	of	of	ADP
ejpam-5894	49	30	our	our	PRON
ejpam-5894	49	31	knowledge	knowledge	NOUN
ejpam-5894	49	32	,	,	PUNCT
ejpam-5894	49	33	remains	remain	VERB
ejpam-5894	49	34	underexplored	underexplored	ADJ
ejpam-5894	49	35	.	.	PUNCT
ejpam-5894	50	1	this	this	DET
ejpam-5894	50	2	synthesis	synthesis	NOUN
ejpam-5894	50	3	opens	open	VERB
ejpam-5894	50	4	new	new	ADJ
ejpam-5894	50	5	avenues	avenue	NOUN
ejpam-5894	50	6	for	for	ADP
ejpam-5894	50	7	research	research	NOUN
ejpam-5894	50	8	in	in	ADP
ejpam-5894	50	9	algebraic	algebraic	ADJ
ejpam-5894	50	10	logic	logic	NOUN
ejpam-5894	50	11	and	and	CCONJ
ejpam-5894	50	12	its	its	PRON
ejpam-5894	50	13	applications	application	NOUN
ejpam-5894	50	14	,	,	PUNCT
ejpam-5894	50	15	especially	especially	ADV
ejpam-5894	50	16	in	in	ADP
ejpam-5894	50	17	scenarios	scenario	NOUN
ejpam-5894	50	18	where	where	SCONJ
ejpam-5894	50	19	reasoning	reason	VERB
ejpam-5894	50	20	under	under	ADP
ejpam-5894	50	21	uncertainty	uncertainty	NOUN
ejpam-5894	50	22	is	be	AUX
ejpam-5894	50	23	crucial	crucial	ADJ
ejpam-5894	50	24	.	.	PUNCT
ejpam-5894	51	1	as	as	ADP
ejpam-5894	51	2	part	part	NOUN
ejpam-5894	51	3	of	of	ADP
ejpam-5894	51	4	this	this	DET
ejpam-5894	51	5	study	study	NOUN
ejpam-5894	51	6	,	,	PUNCT
ejpam-5894	51	7	we	we	PRON
ejpam-5894	51	8	present	present	VERB
ejpam-5894	51	9	a	a	DET
ejpam-5894	51	10	theorem	theorem	NOUN
ejpam-5894	51	11	and	and	CCONJ
ejpam-5894	51	12	its	its	PRON
ejpam-5894	51	13	proof	proof	NOUN
ejpam-5894	51	14	concerning	concern	VERB
ejpam-5894	51	15	intuitionistic	intuitionistic	ADJ
ejpam-5894	51	16	fuzzy	fuzzy	ADJ
ejpam-5894	51	17	implicative	implicative	ADJ
ejpam-5894	51	18	wsbg	wsbg	NOUN
ejpam-5894	51	19	-	-	PUNCT
ejpam-5894	51	20	ideals	ideal	NOUN
ejpam-5894	51	21	in	in	ADP
ejpam-5894	51	22	the	the	DET
ejpam-5894	51	23	lattice	lattice	PROPN
ejpam-5894	51	24	l.	l.	PROPN
ejpam-5894	51	25	the	the	DET
ejpam-5894	51	26	theorem	theorem	ADJ
ejpam-5894	51	27	states	state	NOUN
ejpam-5894	51	28	that	that	SCONJ
ejpam-5894	51	29	an	an	DET
ejpam-5894	51	30	intuitionistic	intuitionistic	ADJ
ejpam-5894	51	31	fuzzy	fuzzy	ADJ
ejpam-5894	51	32	set	set	NOUN
ejpam-5894	51	33	l	l	NOUN
ejpam-5894	51	34	=	=	SYM
ejpam-5894	51	35	(	(	PUNCT
ejpam-5894	51	36	l	l	NOUN
ejpam-5894	51	37	,	,	PUNCT
ejpam-5894	51	38	α	α	X
ejpam-5894	51	39	,	,	PUNCT
ejpam-5894	51	40	β	β	NOUN
ejpam-5894	51	41	)	)	PUNCT
ejpam-5894	51	42	is	be	AUX
ejpam-5894	51	43	an	an	DET
ejpam-5894	51	44	intuitionistic	intuitionistic	ADJ
ejpam-5894	51	45	fuzzy	fuzzy	ADJ
ejpam-5894	51	46	implicative	implicative	ADJ
ejpam-5894	51	47	wsbg	wsbg	NOUN
ejpam-5894	51	48	-	-	PUNCT
ejpam-5894	51	49	ideal	ideal	NOUN
ejpam-5894	51	50	of	of	ADP
ejpam-5894	51	51	l	l	NOUN
ejpam-5894	51	52	if	if	SCONJ
ejpam-5894	52	1	and	and	CCONJ
ejpam-5894	52	2	only	only	ADV
ejpam-5894	52	3	if	if	SCONJ
ejpam-5894	52	4	,	,	PUNCT
ejpam-5894	52	5	for	for	ADP
ejpam-5894	52	6	all	all	DET
ejpam-5894	52	7	t	t	PROPN
ejpam-5894	52	8	,	,	PUNCT
ejpam-5894	52	9	s	s	PART
ejpam-5894	52	10	∈	∈	PROPN
ejpam-5894	53	1	[	[	X
ejpam-5894	53	2	0	0	NUM
ejpam-5894	53	3	,	,	PUNCT
ejpam-5894	53	4	1	1	NUM
ejpam-5894	53	5	]	]	PUNCT
ejpam-5894	53	6	,	,	PUNCT
ejpam-5894	53	7	the	the	DET
ejpam-5894	53	8	sets	set	NOUN
ejpam-5894	53	9	u(β	u(β	ADV
ejpam-5894	53	10	,	,	PUNCT
ejpam-5894	53	11	t	t	PROPN
ejpam-5894	53	12	)	)	PUNCT
ejpam-5894	53	13	and	and	CCONJ
ejpam-5894	53	14	l(α	l(α	PROPN
ejpam-5894	53	15	,	,	PUNCT
ejpam-5894	53	16	s	s	X
ejpam-5894	53	17	)	)	PUNCT
ejpam-5894	53	18	are	be	AUX
ejpam-5894	53	19	implicative	implicative	ADJ
ejpam-5894	53	20	wsbg	wsbg	NOUN
ejpam-5894	53	21	-	-	PUNCT
ejpam-5894	53	22	ideals	ideal	NOUN
ejpam-5894	53	23	of	of	ADP
ejpam-5894	53	24	l	l	NOUN
ejpam-5894	53	25	,	,	PUNCT
ejpam-5894	53	26	provided	provide	VERB
ejpam-5894	53	27	they	they	PRON
ejpam-5894	53	28	are	be	AUX
ejpam-5894	53	29	nonempty	nonempty	ADJ
ejpam-5894	53	30	.	.	PUNCT
ejpam-5894	54	1	the	the	DET
ejpam-5894	54	2	proof	proof	NOUN
ejpam-5894	54	3	is	be	AUX
ejpam-5894	54	4	divided	divide	VERB
ejpam-5894	54	5	into	into	ADP
ejpam-5894	54	6	two	two	NUM
ejpam-5894	54	7	cases	case	NOUN
ejpam-5894	54	8	:	:	PUNCT
ejpam-5894	54	9	the	the	DET
ejpam-5894	54	10	first	first	ADJ
ejpam-5894	54	11	case	case	NOUN
ejpam-5894	54	12	verifies	verifie	NOUN
ejpam-5894	54	13	that	that	SCONJ
ejpam-5894	54	14	u(β	u(β	ADV
ejpam-5894	54	15	,	,	PUNCT
ejpam-5894	54	16	t	t	PROPN
ejpam-5894	54	17	)	)	PUNCT
ejpam-5894	54	18	satisfies	satisfy	VERB
ejpam-5894	54	19	the	the	DET
ejpam-5894	54	20	implicative	implicative	ADJ
ejpam-5894	54	21	wsbg	wsbg	ADV
ejpam-5894	54	22	-	-	PUNCT
ejpam-5894	54	23	ideal	ideal	ADJ
ejpam-5894	54	24	property	property	NOUN
ejpam-5894	54	25	using	use	VERB
ejpam-5894	54	26	the	the	DET
ejpam-5894	54	27	membership	membership	NOUN
ejpam-5894	54	28	function	function	VERB
ejpam-5894	54	29	β	β	NOUN
ejpam-5894	54	30	,	,	PUNCT
ejpam-5894	54	31	while	while	SCONJ
ejpam-5894	54	32	the	the	DET
ejpam-5894	54	33	second	second	ADJ
ejpam-5894	54	34	case	case	NOUN
ejpam-5894	54	35	establishes	establish	VERB
ejpam-5894	54	36	the	the	DET
ejpam-5894	54	37	same	same	ADJ
ejpam-5894	54	38	for	for	ADP
ejpam-5894	54	39	l(α	l(α	PROPN
ejpam-5894	54	40	,	,	PUNCT
ejpam-5894	54	41	s	s	X
ejpam-5894	54	42	)	)	PUNCT
ejpam-5894	54	43	using	use	VERB
ejpam-5894	54	44	α	α	NOUN
ejpam-5894	54	45	.	.	PUNCT
ejpam-5894	55	1	the	the	DET
ejpam-5894	55	2	converse	converse	NOUN
ejpam-5894	55	3	is	be	AUX
ejpam-5894	55	4	also	also	ADV
ejpam-5894	55	5	proven	prove	VERB
ejpam-5894	55	6	by	by	ADP
ejpam-5894	55	7	assuming	assume	VERB
ejpam-5894	55	8	the	the	DET
ejpam-5894	55	9	implicative	implicative	ADJ
ejpam-5894	55	10	wsbg	wsbg	ADV
ejpam-5894	55	11	-	-	PUNCT
ejpam-5894	55	12	ideal	ideal	ADJ
ejpam-5894	55	13	properties	property	NOUN
ejpam-5894	55	14	of	of	ADP
ejpam-5894	55	15	u(β	u(β	PROPN
ejpam-5894	55	16	,	,	PUNCT
ejpam-5894	55	17	t	t	PROPN
ejpam-5894	55	18	)	)	PUNCT
ejpam-5894	55	19	and	and	CCONJ
ejpam-5894	55	20	l(α	l(α	PROPN
ejpam-5894	55	21	,	,	PUNCT
ejpam-5894	55	22	s	s	X
ejpam-5894	55	23	)	)	PUNCT
ejpam-5894	55	24	,	,	PUNCT
ejpam-5894	55	25	showing	show	VERB
ejpam-5894	55	26	that	that	SCONJ
ejpam-5894	55	27	they	they	PRON
ejpam-5894	55	28	imply	imply	VERB
ejpam-5894	55	29	l	l	NOUN
ejpam-5894	55	30	is	be	AUX
ejpam-5894	55	31	an	an	DET
ejpam-5894	55	32	intuitionistic	intuitionistic	ADJ
ejpam-5894	55	33	fuzzy	fuzzy	ADJ
ejpam-5894	55	34	implicative	implicative	ADJ
ejpam-5894	55	35	wsbg	wsbg	NOUN
ejpam-5894	55	36	-	-	PUNCT
ejpam-5894	55	37	ideal	ideal	ADJ
ejpam-5894	55	38	.	.	PUNCT
ejpam-5894	56	1	this	this	DET
ejpam-5894	56	2	proof	proof	NOUN
ejpam-5894	56	3	employs	employ	VERB
ejpam-5894	56	4	symbolic	symbolic	ADJ
ejpam-5894	56	5	reasoning	reasoning	NOUN
ejpam-5894	56	6	and	and	CCONJ
ejpam-5894	56	7	logical	logical	ADJ
ejpam-5894	56	8	deductions	deduction	NOUN
ejpam-5894	56	9	,	,	PUNCT
ejpam-5894	56	10	offering	offer	VERB
ejpam-5894	56	11	a	a	DET
ejpam-5894	56	12	comprehensive	comprehensive	ADJ
ejpam-5894	56	13	theoretical	theoretical	ADJ
ejpam-5894	56	14	foundation	foundation	NOUN
ejpam-5894	56	15	for	for	ADP
ejpam-5894	56	16	further	further	ADJ
ejpam-5894	56	17	exploration	exploration	NOUN
ejpam-5894	56	18	.	.	PUNCT
ejpam-5894	57	1	2	2	X
ejpam-5894	57	2	.	.	X
ejpam-5894	57	3	preliminaries	preliminary	NOUN
ejpam-5894	57	4	this	this	DET
ejpam-5894	57	5	section	section	NOUN
ejpam-5894	57	6	provides	provide	VERB
ejpam-5894	57	7	fundamental	fundamental	ADJ
ejpam-5894	57	8	definitions	definition	NOUN
ejpam-5894	57	9	and	and	CCONJ
ejpam-5894	57	10	concepts	concept	NOUN
ejpam-5894	57	11	related	relate	VERB
ejpam-5894	57	12	to	to	PART
ejpam-5894	57	13	sheffer	sheffer	VERB
ejpam-5894	57	14	stroke	stroke	PROPN
ejpam-5894	57	15	bg	bg	PROPN
ejpam-5894	57	16	-	-	PUNCT
ejpam-5894	57	17	algebras	algebras	PROPN
ejpam-5894	57	18	and	and	CCONJ
ejpam-5894	57	19	intuitionistic	intuitionistic	ADJ
ejpam-5894	57	20	fuzzy	fuzzy	ADJ
ejpam-5894	57	21	structures	structure	NOUN
ejpam-5894	57	22	.	.	PUNCT
ejpam-5894	58	1	definition	definition	NOUN
ejpam-5894	58	2	1	1	NUM
ejpam-5894	58	3	.	.	PUNCT
ejpam-5894	59	1	[	[	X
ejpam-5894	59	2	6	6	NUM
ejpam-5894	59	3	]	]	PUNCT
ejpam-5894	59	4	let	let	NOUN
ejpam-5894	59	5	h	h	NOUN
ejpam-5894	59	6	=	=	SYM
ejpam-5894	59	7	⟨h	⟨h	PROPN
ejpam-5894	59	8	;	;	PUNCT
ejpam-5894	59	9	|⟩	|⟩	PROPN
ejpam-5894	59	10	be	be	VERB
ejpam-5894	59	11	a	a	DET
ejpam-5894	59	12	groupoid	groupoid	NOUN
ejpam-5894	59	13	.	.	PUNCT
ejpam-5894	60	1	the	the	DET
ejpam-5894	60	2	operation	operation	NOUN
ejpam-5894	60	3	|	|	ADV
ejpam-5894	60	4	is	be	AUX
ejpam-5894	60	5	called	call	VERB
ejpam-5894	60	6	a	a	DET
ejpam-5894	60	7	sheffer	sheffer	NOUN
ejpam-5894	60	8	stroke	stroke	NOUN
ejpam-5894	60	9	operation	operation	NOUN
ejpam-5894	60	10	if	if	SCONJ
ejpam-5894	60	11	it	it	PRON
ejpam-5894	60	12	satisfies	satisfy	VERB
ejpam-5894	60	13	the	the	DET
ejpam-5894	60	14	following	follow	VERB
ejpam-5894	60	15	axioms	axiom	NOUN
ejpam-5894	60	16	:	:	PUNCT
ejpam-5894	60	17	for	for	ADP
ejpam-5894	60	18	all	all	DET
ejpam-5894	60	19	x	x	NOUN
ejpam-5894	60	20	,	,	PUNCT
ejpam-5894	60	21	y	y	PROPN
ejpam-5894	60	22	,	,	PUNCT
ejpam-5894	60	23	z	z	PROPN
ejpam-5894	60	24	∈	∈	PROPN
ejpam-5894	60	25	h	h	NOUN
ejpam-5894	60	26	,	,	PUNCT
ejpam-5894	60	27	(	(	PUNCT
ejpam-5894	60	28	s1	s1	NOUN
ejpam-5894	60	29	)	)	PUNCT
ejpam-5894	60	30	x|y	x|y	PUNCT
ejpam-5894	61	1	=	=	SYM
ejpam-5894	61	2	y|x	y|x	NOUN
ejpam-5894	61	3	,	,	PUNCT
ejpam-5894	61	4	(	(	PUNCT
ejpam-5894	61	5	s2	s2	PROPN
ejpam-5894	61	6	)	)	PUNCT
ejpam-5894	61	7	(	(	PUNCT
ejpam-5894	61	8	x|x)|(x|y	x|x)|(x|y	PROPN
ejpam-5894	61	9	)	)	PUNCT
ejpam-5894	61	10	=	=	SYM
ejpam-5894	62	1	x	x	X
ejpam-5894	62	2	,	,	PUNCT
ejpam-5894	62	3	(	(	PUNCT
ejpam-5894	62	4	s3	s3	PROPN
ejpam-5894	62	5	)	)	PUNCT
ejpam-5894	62	6	x|((y|z)|(y|z	x|((y|z)|(y|z	NUM
ejpam-5894	62	7	)	)	PUNCT
ejpam-5894	62	8	)	)	PUNCT
ejpam-5894	63	1	=	=	SYM
ejpam-5894	63	2	(	(	PUNCT
ejpam-5894	63	3	(	(	PUNCT
ejpam-5894	63	4	x|y)|(x|y))|z	x|y)|(x|y))|z	NOUN
ejpam-5894	63	5	,	,	PUNCT
ejpam-5894	63	6	(	(	PUNCT
ejpam-5894	63	7	s4	s4	PROPN
ejpam-5894	63	8	)	)	PUNCT
ejpam-5894	63	9	(	(	PUNCT
ejpam-5894	63	10	x|((x|x)|(y|y)))|(x|((x|x)|(y|y	x|((x|x)|(y|y)))|(x|((x|x)|(y|y	NUM
ejpam-5894	63	11	)	)	PUNCT
ejpam-5894	63	12	)	)	PUNCT
ejpam-5894	63	13	)	)	PUNCT
ejpam-5894	63	14	=	=	PUNCT
ejpam-5894	64	1	x.	x.	NOUN
ejpam-5894	64	2	definition	definition	NOUN
ejpam-5894	64	3	2	2	NUM
ejpam-5894	64	4	.	.	PUNCT
ejpam-5894	65	1	[	[	X
ejpam-5894	65	2	15	15	NUM
ejpam-5894	65	3	]	]	X
ejpam-5894	65	4	a	a	DET
ejpam-5894	65	5	sheffer	sheffer	NOUN
ejpam-5894	65	6	stroke	stroke	NOUN
ejpam-5894	65	7	bg	bg	NOUN
ejpam-5894	65	8	-	-	PROPN
ejpam-5894	65	9	algebra	algebra	PROPN
ejpam-5894	65	10	(	(	PUNCT
ejpam-5894	65	11	abbreviated	abbreviate	VERB
ejpam-5894	65	12	as	as	ADP
ejpam-5894	65	13	sbg	sbg	NOUN
ejpam-5894	65	14	-	-	PUNCT
ejpam-5894	65	15	algebra	algebra	NOUN
ejpam-5894	65	16	)	)	PUNCT
ejpam-5894	65	17	is	be	AUX
ejpam-5894	65	18	a	a	DET
ejpam-5894	65	19	structure	structure	NOUN
ejpam-5894	65	20	⟨l	⟨l	NOUN
ejpam-5894	65	21	;	;	PUNCT
ejpam-5894	65	22	|	|	ADV
ejpam-5894	65	23	,	,	PUNCT
ejpam-5894	65	24	0⟩	0⟩	PROPN
ejpam-5894	65	25	of	of	ADP
ejpam-5894	65	26	type	type	NOUN
ejpam-5894	65	27	(	(	PUNCT
ejpam-5894	65	28	2	2	NUM
ejpam-5894	65	29	,	,	PUNCT
ejpam-5894	65	30	0	0	NUM
ejpam-5894	65	31	)	)	PUNCT
ejpam-5894	65	32	,	,	PUNCT
ejpam-5894	65	33	where	where	SCONJ
ejpam-5894	65	34	|	|	ADV
ejpam-5894	65	35	is	be	AUX
ejpam-5894	65	36	a	a	DET
ejpam-5894	65	37	sheffer	sheffer	NOUN
ejpam-5894	65	38	stroke	stroke	NOUN
ejpam-5894	65	39	operation	operation	NOUN
ejpam-5894	65	40	,	,	PUNCT
ejpam-5894	65	41	i.e.	i.e.	X
ejpam-5894	65	42	,	,	PUNCT
ejpam-5894	65	43	it	it	PRON
ejpam-5894	65	44	satisfies	satisfy	VERB
ejpam-5894	65	45	the	the	DET
ejpam-5894	65	46	axioms	axiom	NOUN
ejpam-5894	65	47	(	(	PUNCT
ejpam-5894	65	48	s1)(s4	s1)(s4	NOUN
ejpam-5894	65	49	)	)	PUNCT
ejpam-5894	65	50	,	,	PUNCT
ejpam-5894	65	51	on	on	ADP
ejpam-5894	65	52	l	l	NOUN
ejpam-5894	65	53	and	and	CCONJ
ejpam-5894	65	54	0	0	NUM
ejpam-5894	65	55	is	be	AUX
ejpam-5894	65	56	a	a	DET
ejpam-5894	65	57	distinguished	distinguished	ADJ
ejpam-5894	65	58	element	element	NOUN
ejpam-5894	65	59	in	in	ADP
ejpam-5894	65	60	l	l	PROPN
ejpam-5894	65	61	,	,	PUNCT
ejpam-5894	65	62	and	and	CCONJ
ejpam-5894	65	63	the	the	DET
ejpam-5894	65	64	following	follow	VERB
ejpam-5894	65	65	conditions	condition	NOUN
ejpam-5894	65	66	hold	hold	VERB
ejpam-5894	65	67	:	:	PUNCT
ejpam-5894	65	68	for	for	ADP
ejpam-5894	65	69	all	all	DET
ejpam-5894	65	70	x	x	NOUN
ejpam-5894	65	71	,	,	PUNCT
ejpam-5894	65	72	y	y	PROPN
ejpam-5894	65	73	∈	∈	PROPN
ejpam-5894	65	74	l	l	PROPN
ejpam-5894	65	75	,	,	PUNCT
ejpam-5894	65	76	(	(	PUNCT
ejpam-5894	65	77	sbg1	sbg1	PROPN
ejpam-5894	65	78	)	)	PUNCT
ejpam-5894	65	79	(	(	PUNCT
ejpam-5894	65	80	x|(x|x))|(x|(x|x	x|(x|x))|(x|(x|x	NOUN
ejpam-5894	65	81	)	)	PUNCT
ejpam-5894	65	82	)	)	PUNCT
ejpam-5894	66	1	=	=	SYM
ejpam-5894	66	2	0	0	NUM
ejpam-5894	66	3	,	,	PUNCT
ejpam-5894	66	4	(	(	PUNCT
ejpam-5894	66	5	sbg2	sbg2	PROPN
ejpam-5894	66	6	)	)	PUNCT
ejpam-5894	66	7	(	(	PUNCT
ejpam-5894	66	8	0|(y|y))|((x|(y|y))|(x|(y|y	0|(y|y))|((x|(y|y))|(x|(y|y	NUM
ejpam-5894	66	9	)	)	PUNCT
ejpam-5894	66	10	)	)	PUNCT
ejpam-5894	66	11	)	)	PUNCT
ejpam-5894	67	1	=	=	PUNCT
ejpam-5894	67	2	x|x	x|x	PROPN
ejpam-5894	67	3	.	.	PUNCT
ejpam-5894	68	1	definition	definition	NOUN
ejpam-5894	68	2	3	3	NUM
ejpam-5894	68	3	.	.	PUNCT
ejpam-5894	69	1	a	a	DET
ejpam-5894	69	2	weak	weak	ADJ
ejpam-5894	69	3	sheffer	sheffer	NOUN
ejpam-5894	69	4	stroke	stroke	NOUN
ejpam-5894	69	5	bg	bg	PROPN
ejpam-5894	69	6	-	-	PROPN
ejpam-5894	69	7	algebra	algebra	PROPN
ejpam-5894	69	8	(	(	PUNCT
ejpam-5894	69	9	abbreviated	abbreviate	VERB
ejpam-5894	69	10	as	as	ADP
ejpam-5894	69	11	wsbg	wsbg	NOUN
ejpam-5894	69	12	-	-	PUNCT
ejpam-5894	69	13	algebra	algebra	NOUN
ejpam-5894	69	14	)	)	PUNCT
ejpam-5894	69	15	is	be	AUX
ejpam-5894	69	16	a	a	DET
ejpam-5894	69	17	structure	structure	NOUN
ejpam-5894	69	18	⟨l	⟨l	NOUN
ejpam-5894	69	19	;	;	PUNCT
ejpam-5894	69	20	|	|	ADV
ejpam-5894	69	21	,	,	PUNCT
ejpam-5894	69	22	0⟩	0⟩	PROPN
ejpam-5894	69	23	of	of	ADP
ejpam-5894	69	24	type	type	NOUN
ejpam-5894	69	25	(	(	PUNCT
ejpam-5894	69	26	2	2	NUM
ejpam-5894	69	27	,	,	PUNCT
ejpam-5894	69	28	0	0	NUM
ejpam-5894	69	29	)	)	PUNCT
ejpam-5894	69	30	,	,	PUNCT
ejpam-5894	69	31	where	where	SCONJ
ejpam-5894	69	32	|	|	ADV
ejpam-5894	69	33	is	be	AUX
ejpam-5894	69	34	a	a	DET
ejpam-5894	69	35	binary	binary	ADJ
ejpam-5894	69	36	operation	operation	NOUN
ejpam-5894	69	37	,	,	PUNCT
ejpam-5894	69	38	i.e.	i.e.	X
ejpam-5894	69	39	,	,	PUNCT
ejpam-5894	69	40	it	it	PRON
ejpam-5894	69	41	satisfies	satisfy	VERB
ejpam-5894	69	42	the	the	DET
ejpam-5894	69	43	axioms	axiom	NOUN
ejpam-5894	69	44	(	(	PUNCT
ejpam-5894	69	45	sbg1	sbg1	PROPN
ejpam-5894	69	46	)	)	PUNCT
ejpam-5894	69	47	and	and	CCONJ
ejpam-5894	69	48	(	(	PUNCT
ejpam-5894	69	49	sbg2	sbg2	PROPN
ejpam-5894	69	50	)	)	PUNCT
ejpam-5894	69	51	,	,	PUNCT
ejpam-5894	69	52	on	on	ADP
ejpam-5894	69	53	l	l	NOUN
ejpam-5894	69	54	and	and	CCONJ
ejpam-5894	69	55	0	0	NUM
ejpam-5894	69	56	is	be	AUX
ejpam-5894	69	57	a	a	DET
ejpam-5894	69	58	distinguished	distinguished	ADJ
ejpam-5894	69	59	element	element	NOUN
ejpam-5894	69	60	in	in	ADP
ejpam-5894	69	61	l.	l.	PROPN
ejpam-5894	69	62	t.	t.	PROPN
ejpam-5894	69	63	oner	oner	PROPN
ejpam-5894	69	64	et	et	PROPN
ejpam-5894	69	65	al	al	PROPN
ejpam-5894	69	66	.	.	PUNCT
ejpam-5894	69	67	/	/	SYM
ejpam-5894	69	68	eur	eur	PROPN
ejpam-5894	69	69	.	.	PUNCT
ejpam-5894	70	1	j.	j.	PROPN
ejpam-5894	70	2	pure	pure	PROPN
ejpam-5894	70	3	appl	appl	PROPN
ejpam-5894	70	4	.	.	PROPN
ejpam-5894	70	5	math	math	PROPN
ejpam-5894	70	6	,	,	PUNCT
ejpam-5894	70	7	18	18	NUM
ejpam-5894	70	8	(	(	PUNCT
ejpam-5894	70	9	3	3	NUM
ejpam-5894	70	10	)	)	PUNCT
ejpam-5894	70	11	(	(	PUNCT
ejpam-5894	70	12	2025	2025	NUM
ejpam-5894	70	13	)	)	PUNCT
ejpam-5894	70	14	,	,	PUNCT
ejpam-5894	70	15	5894	5894	NUM
ejpam-5894	70	16	4	4	NUM
ejpam-5894	70	17	of	of	ADP
ejpam-5894	70	18	33	33	NUM
ejpam-5894	70	19	example	example	NOUN
ejpam-5894	71	1	1	1	NUM
ejpam-5894	71	2	.	.	PUNCT
ejpam-5894	72	1	let	let	VERB
ejpam-5894	72	2	l	l	NOUN
ejpam-5894	72	3	=	=	PUNCT
ejpam-5894	72	4	{	{	PUNCT
ejpam-5894	72	5	0	0	NUM
ejpam-5894	72	6	,	,	PUNCT
ejpam-5894	72	7	1	1	NUM
ejpam-5894	72	8	,	,	PUNCT
ejpam-5894	72	9	2	2	NUM
ejpam-5894	72	10	,	,	PUNCT
ejpam-5894	72	11	3	3	NUM
ejpam-5894	72	12	,	,	PUNCT
ejpam-5894	72	13	4	4	NUM
ejpam-5894	72	14	,	,	PUNCT
ejpam-5894	72	15	5	5	NUM
ejpam-5894	72	16	}	}	PUNCT
ejpam-5894	72	17	be	be	AUX
ejpam-5894	72	18	a	a	DET
ejpam-5894	72	19	set	set	NOUN
ejpam-5894	72	20	with	with	ADP
ejpam-5894	72	21	the	the	DET
ejpam-5894	72	22	binary	binary	PROPN
ejpam-5894	72	23	operation	operation	NOUN
ejpam-5894	72	24	|	|	ADV
ejpam-5894	72	25	defined	define	VERB
ejpam-5894	72	26	by	by	ADP
ejpam-5894	72	27	the	the	DET
ejpam-5894	72	28	following	following	ADJ
ejpam-5894	72	29	cayley	cayley	ADJ
ejpam-5894	72	30	table	table	NOUN
ejpam-5894	72	31	:	:	PUNCT
ejpam-5894	73	1	|	|	ADV
ejpam-5894	73	2	0	0	NUM
ejpam-5894	73	3	1	1	NUM
ejpam-5894	73	4	2	2	NUM
ejpam-5894	73	5	3	3	NUM
ejpam-5894	73	6	4	4	NUM
ejpam-5894	73	7	5	5	NUM
ejpam-5894	73	8	0	0	NUM
ejpam-5894	73	9	0	0	NUM
ejpam-5894	73	10	0	0	NUM
ejpam-5894	73	11	2	2	NUM
ejpam-5894	73	12	3	3	NUM
ejpam-5894	73	13	0	0	NUM
ejpam-5894	73	14	0	0	NUM
ejpam-5894	73	15	1	1	NUM
ejpam-5894	73	16	1	1	NUM
ejpam-5894	73	17	2	2	NUM
ejpam-5894	73	18	0	0	NUM
ejpam-5894	73	19	2	2	NUM
ejpam-5894	73	20	0	0	NUM
ejpam-5894	73	21	0	0	NUM
ejpam-5894	73	22	2	2	NUM
ejpam-5894	73	23	2	2	NUM
ejpam-5894	73	24	0	0	NUM
ejpam-5894	73	25	3	3	NUM
ejpam-5894	73	26	0	0	NUM
ejpam-5894	73	27	0	0	NUM
ejpam-5894	73	28	0	0	NUM
ejpam-5894	73	29	3	3	NUM
ejpam-5894	73	30	3	3	NUM
ejpam-5894	73	31	0	0	NUM
ejpam-5894	73	32	0	0	NUM
ejpam-5894	73	33	2	2	NUM
ejpam-5894	73	34	0	0	NUM
ejpam-5894	73	35	0	0	NUM
ejpam-5894	73	36	4	4	NUM
ejpam-5894	73	37	0	0	NUM
ejpam-5894	73	38	0	0	NUM
ejpam-5894	73	39	2	2	NUM
ejpam-5894	73	40	1	1	NUM
ejpam-5894	73	41	0	0	NUM
ejpam-5894	73	42	0	0	NUM
ejpam-5894	73	43	5	5	NUM
ejpam-5894	73	44	0	0	NUM
ejpam-5894	73	45	0	0	NUM
ejpam-5894	73	46	2	2	NUM
ejpam-5894	73	47	1	1	NUM
ejpam-5894	73	48	0	0	NUM
ejpam-5894	73	49	0	0	NUM
ejpam-5894	73	50	hence	hence	ADV
ejpam-5894	73	51	,	,	PUNCT
ejpam-5894	73	52	⟨l	⟨l	NOUN
ejpam-5894	73	53	;	;	PUNCT
ejpam-5894	73	54	|	|	X
ejpam-5894	73	55	,	,	PUNCT
ejpam-5894	73	56	0⟩	0⟩	PROPN
ejpam-5894	73	57	is	be	AUX
ejpam-5894	73	58	a	a	DET
ejpam-5894	73	59	wsbg	wsbg	ADV
ejpam-5894	73	60	-	-	PUNCT
ejpam-5894	73	61	algebra	algebra	NOUN
ejpam-5894	73	62	.	.	PUNCT
ejpam-5894	74	1	definition	definition	NOUN
ejpam-5894	74	2	4	4	NUM
ejpam-5894	74	3	.	.	PUNCT
ejpam-5894	75	1	a	a	DET
ejpam-5894	75	2	nonempty	nonempty	ADV
ejpam-5894	75	3	subset	subset	VERB
ejpam-5894	75	4	h	h	NOUN
ejpam-5894	75	5	of	of	ADP
ejpam-5894	75	6	a	a	DET
ejpam-5894	75	7	wsbg	wsbg	ADV
ejpam-5894	75	8	-	-	PUNCT
ejpam-5894	75	9	algebra	algebra	NOUN
ejpam-5894	75	10	l	l	NOUN
ejpam-5894	75	11	=	=	PUNCT
ejpam-5894	75	12	⟨l	⟨l	NOUN
ejpam-5894	75	13	;	;	PUNCT
ejpam-5894	75	14	|	|	ADV
ejpam-5894	75	15	,	,	PUNCT
ejpam-5894	75	16	0⟩	0⟩	PROPN
ejpam-5894	75	17	is	be	AUX
ejpam-5894	75	18	called	call	VERB
ejpam-5894	75	19	a	a	DET
ejpam-5894	75	20	wsbgsubalgebra	wsbgsubalgebra	NOUN
ejpam-5894	75	21	of	of	ADP
ejpam-5894	75	22	l	l	NOUN
ejpam-5894	75	23	if	if	SCONJ
ejpam-5894	75	24	(	(	PUNCT
ejpam-5894	75	25	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5894	75	26	)	)	PUNCT
ejpam-5894	75	27	)	)	PUNCT
ejpam-5894	76	1	∈	∈	PROPN
ejpam-5894	76	2	h	h	NOUN
ejpam-5894	76	3	,	,	PUNCT
ejpam-5894	76	4	∀x	∀x	X
ejpam-5894	76	5	,	,	PUNCT
ejpam-5894	76	6	y	y	PROPN
ejpam-5894	76	7	∈	∈	PROPN
ejpam-5894	76	8	h.	h.	PROPN
ejpam-5894	76	9	example	example	NOUN
ejpam-5894	77	1	2	2	NUM
ejpam-5894	77	2	.	.	X
ejpam-5894	77	3	from	from	ADP
ejpam-5894	77	4	the	the	DET
ejpam-5894	77	5	wsbg	wsbg	NOUN
ejpam-5894	77	6	-	-	PUNCT
ejpam-5894	77	7	algebra	algebra	NOUN
ejpam-5894	77	8	in	in	ADP
ejpam-5894	77	9	example	example	NOUN
ejpam-5894	77	10	1	1	NUM
ejpam-5894	77	11	,	,	PUNCT
ejpam-5894	77	12	the	the	DET
ejpam-5894	77	13	following	follow	VERB
ejpam-5894	77	14	subsets	subset	NOUN
ejpam-5894	77	15	are	be	AUX
ejpam-5894	77	16	wsbgsubalgebras	wsbgsubalgebras	ADJ
ejpam-5894	77	17	:	:	PUNCT
ejpam-5894	77	18	h1	h1	PROPN
ejpam-5894	77	19	=	=	SYM
ejpam-5894	77	20	{	{	PUNCT
ejpam-5894	77	21	0	0	NUM
ejpam-5894	77	22	}	}	PUNCT
ejpam-5894	77	23	,	,	PUNCT
ejpam-5894	77	24	h2	h2	NOUN
ejpam-5894	77	25	=	=	PUNCT
ejpam-5894	77	26	{	{	PUNCT
ejpam-5894	77	27	0	0	NUM
ejpam-5894	77	28	,	,	PUNCT
ejpam-5894	77	29	4	4	NUM
ejpam-5894	77	30	}	}	PUNCT
ejpam-5894	77	31	,	,	PUNCT
ejpam-5894	77	32	h3	h3	NOUN
ejpam-5894	77	33	=	=	SYM
ejpam-5894	77	34	{	{	PUNCT
ejpam-5894	77	35	0	0	NUM
ejpam-5894	77	36	,	,	PUNCT
ejpam-5894	77	37	5	5	NUM
ejpam-5894	77	38	}	}	PUNCT
ejpam-5894	77	39	,	,	PUNCT
ejpam-5894	77	40	h4	h4	PROPN
ejpam-5894	77	41	=	=	SYM
ejpam-5894	77	42	{	{	PUNCT
ejpam-5894	77	43	0	0	NUM
ejpam-5894	77	44	,	,	PUNCT
ejpam-5894	77	45	2	2	NUM
ejpam-5894	77	46	,	,	PUNCT
ejpam-5894	77	47	3	3	NUM
ejpam-5894	77	48	}	}	PUNCT
ejpam-5894	77	49	,	,	PUNCT
ejpam-5894	77	50	h5	h5	PROPN
ejpam-5894	77	51	=	=	SYM
ejpam-5894	77	52	{	{	PUNCT
ejpam-5894	77	53	0	0	NUM
ejpam-5894	77	54	,	,	PUNCT
ejpam-5894	77	55	4	4	NUM
ejpam-5894	77	56	,	,	PUNCT
ejpam-5894	77	57	5	5	NUM
ejpam-5894	77	58	}	}	PUNCT
ejpam-5894	77	59	,	,	PUNCT
ejpam-5894	77	60	h6	h6	PROPN
ejpam-5894	77	61	=	=	PUNCT
ejpam-5894	77	62	{	{	PUNCT
ejpam-5894	77	63	0	0	NUM
ejpam-5894	77	64	,	,	PUNCT
ejpam-5894	77	65	1	1	NUM
ejpam-5894	77	66	,	,	PUNCT
ejpam-5894	77	67	2	2	NUM
ejpam-5894	77	68	,	,	PUNCT
ejpam-5894	77	69	3	3	NUM
ejpam-5894	77	70	}	}	PUNCT
ejpam-5894	77	71	,	,	PUNCT
ejpam-5894	77	72	h7	h7	X
ejpam-5894	77	73	=	=	PUNCT
ejpam-5894	77	74	{	{	PUNCT
ejpam-5894	77	75	0	0	NUM
ejpam-5894	77	76	,	,	PUNCT
ejpam-5894	77	77	2	2	NUM
ejpam-5894	77	78	,	,	PUNCT
ejpam-5894	77	79	3	3	NUM
ejpam-5894	77	80	,	,	PUNCT
ejpam-5894	77	81	4	4	NUM
ejpam-5894	77	82	}	}	PUNCT
ejpam-5894	77	83	,	,	PUNCT
ejpam-5894	77	84	h8	h8	PROPN
ejpam-5894	77	85	=	=	PUNCT
ejpam-5894	77	86	{	{	PUNCT
ejpam-5894	77	87	0	0	NUM
ejpam-5894	77	88	,	,	PUNCT
ejpam-5894	77	89	2	2	NUM
ejpam-5894	77	90	,	,	PUNCT
ejpam-5894	77	91	3	3	NUM
ejpam-5894	77	92	,	,	PUNCT
ejpam-5894	77	93	5	5	NUM
ejpam-5894	77	94	}	}	PUNCT
ejpam-5894	77	95	,	,	PUNCT
ejpam-5894	77	96	h9	h9	NOUN
ejpam-5894	77	97	=	=	SYM
ejpam-5894	77	98	{	{	PUNCT
ejpam-5894	77	99	0	0	NUM
ejpam-5894	77	100	,	,	PUNCT
ejpam-5894	77	101	1	1	NUM
ejpam-5894	77	102	,	,	PUNCT
ejpam-5894	77	103	2	2	NUM
ejpam-5894	77	104	,	,	PUNCT
ejpam-5894	77	105	3	3	NUM
ejpam-5894	77	106	,	,	PUNCT
ejpam-5894	77	107	4	4	NUM
ejpam-5894	77	108	}	}	PUNCT
ejpam-5894	77	109	,	,	PUNCT
ejpam-5894	77	110	h10	h10	NOUN
ejpam-5894	77	111	=	=	SYM
ejpam-5894	77	112	{	{	PUNCT
ejpam-5894	77	113	0	0	NUM
ejpam-5894	77	114	,	,	PUNCT
ejpam-5894	77	115	1	1	NUM
ejpam-5894	77	116	,	,	PUNCT
ejpam-5894	77	117	2	2	NUM
ejpam-5894	77	118	,	,	PUNCT
ejpam-5894	77	119	3	3	NUM
ejpam-5894	77	120	,	,	PUNCT
ejpam-5894	77	121	5	5	NUM
ejpam-5894	77	122	}	}	PUNCT
ejpam-5894	77	123	,	,	PUNCT
ejpam-5894	77	124	h11	h11	NOUN
ejpam-5894	77	125	=	=	PUNCT
ejpam-5894	77	126	{	{	PUNCT
ejpam-5894	77	127	0	0	NUM
ejpam-5894	77	128	,	,	PUNCT
ejpam-5894	77	129	2	2	NUM
ejpam-5894	77	130	,	,	PUNCT
ejpam-5894	77	131	3	3	NUM
ejpam-5894	77	132	,	,	PUNCT
ejpam-5894	77	133	4	4	NUM
ejpam-5894	77	134	,	,	PUNCT
ejpam-5894	77	135	5	5	NUM
ejpam-5894	77	136	}	}	PUNCT
ejpam-5894	77	137	,	,	PUNCT
ejpam-5894	77	138	h12	h12	NOUN
ejpam-5894	77	139	=	=	SYM
ejpam-5894	77	140	l.	l.	PROPN
ejpam-5894	77	141	definition	definition	NOUN
ejpam-5894	77	142	5	5	NUM
ejpam-5894	77	143	.	.	PUNCT
ejpam-5894	78	1	a	a	DET
ejpam-5894	78	2	nonempty	nonempty	ADV
ejpam-5894	78	3	subset	subset	VERB
ejpam-5894	78	4	h	h	NOUN
ejpam-5894	78	5	of	of	ADP
ejpam-5894	78	6	a	a	DET
ejpam-5894	78	7	wsbg	wsbg	ADV
ejpam-5894	78	8	-	-	PUNCT
ejpam-5894	78	9	algebra	algebra	NOUN
ejpam-5894	78	10	l	l	NOUN
ejpam-5894	78	11	=	=	PUNCT
ejpam-5894	78	12	⟨l	⟨l	NOUN
ejpam-5894	78	13	;	;	PUNCT
ejpam-5894	78	14	|	|	ADV
ejpam-5894	78	15	,	,	PUNCT
ejpam-5894	78	16	0⟩	0⟩	PROPN
ejpam-5894	78	17	is	be	AUX
ejpam-5894	78	18	called	call	VERB
ejpam-5894	78	19	a	a	DET
ejpam-5894	78	20	wsbgideal	wsbgideal	NOUN
ejpam-5894	78	21	of	of	ADP
ejpam-5894	78	22	l	l	NOUN
ejpam-5894	78	23	if	if	SCONJ
ejpam-5894	78	24	the	the	DET
ejpam-5894	78	25	following	follow	VERB
ejpam-5894	78	26	conditions	condition	NOUN
ejpam-5894	78	27	are	be	AUX
ejpam-5894	78	28	satisfied	satisfied	ADJ
ejpam-5894	78	29	:	:	PUNCT
ejpam-5894	78	30	for	for	ADP
ejpam-5894	78	31	all	all	DET
ejpam-5894	78	32	x	x	NOUN
ejpam-5894	78	33	,	,	PUNCT
ejpam-5894	78	34	y	y	PROPN
ejpam-5894	78	35	∈	∈	PROPN
ejpam-5894	78	36	l	l	PROPN
ejpam-5894	78	37	,	,	PUNCT
ejpam-5894	78	38	(	(	PUNCT
ejpam-5894	78	39	i	i	NOUN
ejpam-5894	78	40	)	)	PUNCT
ejpam-5894	78	41	0	0	PUNCT
ejpam-5894	79	1	∈	∈	PROPN
ejpam-5894	79	2	h	h	NOUN
ejpam-5894	79	3	,	,	PUNCT
ejpam-5894	79	4	(	(	PUNCT
ejpam-5894	79	5	ii	ii	NOUN
ejpam-5894	79	6	)	)	PUNCT
ejpam-5894	79	7	(	(	PUNCT
ejpam-5894	79	8	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	PROPN
ejpam-5894	79	9	)	)	PUNCT
ejpam-5894	79	10	)	)	PUNCT
ejpam-5894	80	1	∈	∈	PROPN
ejpam-5894	80	2	h	h	NOUN
ejpam-5894	80	3	and	and	CCONJ
ejpam-5894	80	4	y	y	PROPN
ejpam-5894	80	5	∈	∈	PROPN
ejpam-5894	80	6	h	h	NOUN
ejpam-5894	80	7	⇒	⇒	VERB
ejpam-5894	80	8	x	x	SYM
ejpam-5894	80	9	∈	∈	PROPN
ejpam-5894	80	10	h.	h.	NOUN
ejpam-5894	80	11	definition	definition	NOUN
ejpam-5894	80	12	6	6	NUM
ejpam-5894	80	13	.	.	PUNCT
ejpam-5894	81	1	a	a	DET
ejpam-5894	81	2	nonempty	nonempty	ADV
ejpam-5894	81	3	subset	subset	VERB
ejpam-5894	81	4	h	h	NOUN
ejpam-5894	81	5	of	of	ADP
ejpam-5894	81	6	a	a	DET
ejpam-5894	81	7	wsbg	wsbg	ADV
ejpam-5894	81	8	-	-	PUNCT
ejpam-5894	81	9	algebra	algebra	NOUN
ejpam-5894	81	10	l	l	NOUN
ejpam-5894	81	11	=	=	PUNCT
ejpam-5894	81	12	⟨l	⟨l	NOUN
ejpam-5894	81	13	;	;	PUNCT
ejpam-5894	81	14	|	|	ADV
ejpam-5894	81	15	,	,	PUNCT
ejpam-5894	81	16	0⟩	0⟩	PROPN
ejpam-5894	81	17	is	be	AUX
ejpam-5894	81	18	called	call	VERB
ejpam-5894	81	19	an	an	DET
ejpam-5894	81	20	implication	implication	NOUN
ejpam-5894	81	21	wsbg	wsbg	ADV
ejpam-5894	81	22	-	-	PUNCT
ejpam-5894	81	23	ideal	ideal	NOUN
ejpam-5894	81	24	of	of	ADP
ejpam-5894	81	25	l	l	NOUN
ejpam-5894	81	26	if	if	SCONJ
ejpam-5894	81	27	the	the	DET
ejpam-5894	81	28	following	follow	VERB
ejpam-5894	81	29	conditions	condition	NOUN
ejpam-5894	81	30	are	be	AUX
ejpam-5894	81	31	satisfied	satisfied	ADJ
ejpam-5894	81	32	:	:	PUNCT
ejpam-5894	81	33	for	for	ADP
ejpam-5894	81	34	all	all	DET
ejpam-5894	81	35	x	x	NOUN
ejpam-5894	81	36	,	,	PUNCT
ejpam-5894	81	37	y	y	PROPN
ejpam-5894	81	38	,	,	PUNCT
ejpam-5894	81	39	z	z	PROPN
ejpam-5894	81	40	∈	∈	PROPN
ejpam-5894	81	41	l	l	NOUN
ejpam-5894	81	42	,	,	PUNCT
ejpam-5894	81	43	(	(	PUNCT
ejpam-5894	81	44	i	i	NOUN
ejpam-5894	81	45	)	)	PUNCT
ejpam-5894	81	46	0	0	PUNCT
ejpam-5894	82	1	∈	∈	PROPN
ejpam-5894	82	2	h	h	NOUN
ejpam-5894	82	3	,	,	PUNCT
ejpam-5894	82	4	(	(	PUNCT
ejpam-5894	82	5	ii	ii	NOUN
ejpam-5894	82	6	)	)	PUNCT
ejpam-5894	82	7	(	(	PUNCT
ejpam-5894	82	8	(	(	PUNCT
ejpam-5894	82	9	(	(	PUNCT
ejpam-5894	82	10	(	(	PUNCT
ejpam-5894	82	11	y|(x|(y|y)))|(y|(x|(y|y))))|(z|z))|(((y|(x|(y|y)))|(y|(x|(y|y))))|(z|z	y|(x|(y|y)))|(y|(x|(y|y))))|(z|z))|(((y|(x|(y|y)))|(y|(x|(y|y))))|(z|z	NOUN
ejpam-5894	82	12	)	)	PUNCT
ejpam-5894	82	13	)	)	PUNCT
ejpam-5894	82	14	)	)	PUNCT
ejpam-5894	83	1	∈	∈	PROPN
ejpam-5894	83	2	h	h	NOUN
ejpam-5894	83	3	and	and	CCONJ
ejpam-5894	83	4	z	z	NOUN
ejpam-5894	83	5	∈	∈	PROPN
ejpam-5894	83	6	h	h	NOUN
ejpam-5894	83	7	⇒	⇒	VERB
ejpam-5894	83	8	y	y	PROPN
ejpam-5894	83	9	∈	∈	PROPN
ejpam-5894	83	10	h.	h.	PROPN
ejpam-5894	83	11	example	example	NOUN
ejpam-5894	84	1	3	3	X
ejpam-5894	84	2	.	.	X
ejpam-5894	84	3	from	from	ADP
ejpam-5894	84	4	the	the	DET
ejpam-5894	84	5	wsbg	wsbg	NOUN
ejpam-5894	84	6	-	-	PUNCT
ejpam-5894	84	7	algebra	algebra	NOUN
ejpam-5894	84	8	in	in	ADP
ejpam-5894	84	9	example	example	NOUN
ejpam-5894	84	10	1	1	NUM
ejpam-5894	84	11	,	,	PUNCT
ejpam-5894	84	12	the	the	DET
ejpam-5894	84	13	subset	subset	NOUN
ejpam-5894	84	14	h5	h5	NOUN
ejpam-5894	84	15	=	=	SYM
ejpam-5894	84	16	{	{	PUNCT
ejpam-5894	84	17	0	0	NUM
ejpam-5894	84	18	,	,	PUNCT
ejpam-5894	84	19	4	4	NUM
ejpam-5894	84	20	,	,	PUNCT
ejpam-5894	84	21	5	5	NUM
ejpam-5894	84	22	}	}	PUNCT
ejpam-5894	84	23	is	be	AUX
ejpam-5894	84	24	a	a	DET
ejpam-5894	84	25	wsbgideal	wsbgideal	NOUN
ejpam-5894	84	26	,	,	PUNCT
ejpam-5894	84	27	but	but	CCONJ
ejpam-5894	84	28	not	not	PART
ejpam-5894	84	29	an	an	DET
ejpam-5894	84	30	implication	implication	NOUN
ejpam-5894	84	31	wsbg	wsbg	ADV
ejpam-5894	84	32	-	-	PUNCT
ejpam-5894	84	33	ideal	ideal	NOUN
ejpam-5894	84	34	of	of	ADP
ejpam-5894	84	35	l.	l.	PROPN
ejpam-5894	84	36	the	the	DET
ejpam-5894	84	37	subset	subset	NOUN
ejpam-5894	84	38	h12	h12	NOUN
ejpam-5894	84	39	=	=	PUNCT
ejpam-5894	84	40	l	l	NOUN
ejpam-5894	84	41	is	be	AUX
ejpam-5894	84	42	both	both	PRON
ejpam-5894	84	43	a	a	DET
ejpam-5894	84	44	wsbg	wsbg	ADV
ejpam-5894	84	45	-	-	PUNCT
ejpam-5894	84	46	ideal	ideal	NOUN
ejpam-5894	84	47	and	and	CCONJ
ejpam-5894	84	48	an	an	DET
ejpam-5894	84	49	implication	implication	NOUN
ejpam-5894	84	50	wsbg	wsbg	ADV
ejpam-5894	84	51	-	-	PUNCT
ejpam-5894	84	52	ideal	ideal	NOUN
ejpam-5894	84	53	of	of	ADP
ejpam-5894	84	54	l.	l.	PROPN
ejpam-5894	84	55	definition	definition	NOUN
ejpam-5894	84	56	7	7	NUM
ejpam-5894	84	57	.	.	PUNCT
ejpam-5894	85	1	[	[	X
ejpam-5894	85	2	16	16	NUM
ejpam-5894	85	3	]	]	X
ejpam-5894	85	4	let	let	VERB
ejpam-5894	85	5	l	l	NOUN
ejpam-5894	85	6	be	be	AUX
ejpam-5894	85	7	a	a	DET
ejpam-5894	85	8	nonempty	nonempty	ADV
ejpam-5894	85	9	set	set	VERB
ejpam-5894	85	10	.	.	PUNCT
ejpam-5894	86	1	an	an	DET
ejpam-5894	86	2	intuitionistic	intuitionistic	ADJ
ejpam-5894	86	3	fuzzy	fuzzy	ADJ
ejpam-5894	86	4	structure	structure	NOUN
ejpam-5894	86	5	on	on	ADP
ejpam-5894	86	6	l	l	PROPN
ejpam-5894	86	7	is	be	AUX
ejpam-5894	86	8	defined	define	VERB
ejpam-5894	86	9	as	as	ADP
ejpam-5894	86	10	:	:	PUNCT
ejpam-5894	86	11	a	a	PRON
ejpam-5894	86	12	:	:	PUNCT
ejpam-5894	86	13	=	=	X
ejpam-5894	86	14	{	{	PUNCT
ejpam-5894	86	15	⟨x	⟨x	VERB
ejpam-5894	86	16	,	,	PUNCT
ejpam-5894	86	17	µ(x	µ(x	NUM
ejpam-5894	86	18	)	)	PUNCT
ejpam-5894	86	19	,	,	PUNCT
ejpam-5894	86	20	ν(x)⟩	ν(x)⟩	VERB
ejpam-5894	86	21	|	|	ADV
ejpam-5894	86	22	x	x	SYM
ejpam-5894	86	23	∈	∈	PROPN
ejpam-5894	86	24	l	l	NOUN
ejpam-5894	86	25	}	}	PUNCT
ejpam-5894	86	26	,	,	PUNCT
ejpam-5894	86	27	(	(	PUNCT
ejpam-5894	86	28	1	1	X
ejpam-5894	86	29	)	)	PUNCT
ejpam-5894	86	30	where	where	SCONJ
ejpam-5894	86	31	µ	µ	X
ejpam-5894	86	32	:	:	PUNCT
ejpam-5894	86	33	l	l	X
ejpam-5894	86	34	→	→	PUNCT
ejpam-5894	86	35	[	[	X
ejpam-5894	86	36	0	0	NUM
ejpam-5894	86	37	,	,	PUNCT
ejpam-5894	86	38	1	1	NUM
ejpam-5894	86	39	]	]	PUNCT
ejpam-5894	86	40	denotes	denote	VERB
ejpam-5894	86	41	the	the	DET
ejpam-5894	86	42	membership	membership	NOUN
ejpam-5894	86	43	degree	degree	NOUN
ejpam-5894	86	44	of	of	ADP
ejpam-5894	86	45	x	x	PUNCT
ejpam-5894	86	46	in	in	ADP
ejpam-5894	86	47	l	l	NOUN
ejpam-5894	86	48	,	,	PUNCT
ejpam-5894	86	49	and	and	CCONJ
ejpam-5894	86	50	ν	ν	X
ejpam-5894	86	51	:	:	PUNCT
ejpam-5894	87	1	l	l	X
ejpam-5894	87	2	→	→	PUNCT
ejpam-5894	87	3	[	[	X
ejpam-5894	87	4	0	0	NUM
ejpam-5894	87	5	,	,	PUNCT
ejpam-5894	87	6	1	1	NUM
ejpam-5894	87	7	]	]	PUNCT
ejpam-5894	87	8	denotes	denote	VERB
ejpam-5894	87	9	the	the	DET
ejpam-5894	87	10	non	non	ADJ
ejpam-5894	87	11	-	-	ADJ
ejpam-5894	87	12	membership	membership	ADJ
ejpam-5894	87	13	degree	degree	NOUN
ejpam-5894	87	14	of	of	ADP
ejpam-5894	87	15	x	x	PUNCT
ejpam-5894	87	16	in	in	ADP
ejpam-5894	87	17	l	l	NOUN
ejpam-5894	87	18	,	,	PUNCT
ejpam-5894	87	19	with	with	ADP
ejpam-5894	87	20	the	the	DET
ejpam-5894	87	21	condition	condition	NOUN
ejpam-5894	87	22	0	0	NUM
ejpam-5894	87	23	≤	≤	NOUN
ejpam-5894	87	24	µ(x	µ(x	NOUN
ejpam-5894	87	25	)	)	PUNCT
ejpam-5894	87	26	+	+	NUM
ejpam-5894	87	27	ν(x	ν(x	PROPN
ejpam-5894	87	28	)	)	PUNCT
ejpam-5894	87	29	≤	≤	NUM
ejpam-5894	87	30	1	1	NUM
ejpam-5894	87	31	.	.	PUNCT
ejpam-5894	88	1	definition	definition	NOUN
ejpam-5894	88	2	8	8	NUM
ejpam-5894	88	3	.	.	PUNCT
ejpam-5894	89	1	let	let	VERB
ejpam-5894	89	2	⟨p	⟨p	NOUN
ejpam-5894	89	3	;	;	PUNCT
ejpam-5894	89	4	|	|	ADV
ejpam-5894	89	5	,	,	PUNCT
ejpam-5894	89	6	0p	0p	NUM
ejpam-5894	89	7	⟩	⟩	PROPN
ejpam-5894	89	8	and	and	CCONJ
ejpam-5894	89	9	⟨q	⟨q	PROPN
ejpam-5894	89	10	;	;	PUNCT
ejpam-5894	89	11	|	|	ADV
ejpam-5894	89	12	,	,	PUNCT
ejpam-5894	89	13	0q⟩	0q⟩	PRON
ejpam-5894	89	14	be	be	AUX
ejpam-5894	89	15	wsbg	wsbg	NOUN
ejpam-5894	89	16	-	-	PUNCT
ejpam-5894	89	17	algebras	algebras	X
ejpam-5894	89	18	.	.	PUNCT
ejpam-5894	90	1	a	a	DET
ejpam-5894	90	2	mapping	mapping	NOUN
ejpam-5894	90	3	g	g	NOUN
ejpam-5894	90	4	:	:	PUNCT
ejpam-5894	90	5	p	p	X
ejpam-5894	90	6	→	→	PUNCT
ejpam-5894	90	7	q	q	X
ejpam-5894	90	8	is	be	AUX
ejpam-5894	90	9	called	call	VERB
ejpam-5894	90	10	a	a	DET
ejpam-5894	90	11	homomorphism	homomorphism	NOUN
ejpam-5894	90	12	if	if	SCONJ
ejpam-5894	90	13	it	it	PRON
ejpam-5894	90	14	satisfies	satisfy	VERB
ejpam-5894	90	15	g(x|y	g(x|y	NUM
ejpam-5894	90	16	)	)	PUNCT
ejpam-5894	90	17	=	=	SYM
ejpam-5894	90	18	g(x)|g(y	g(x)|g(y	NOUN
ejpam-5894	90	19	)	)	PUNCT
ejpam-5894	90	20	,	,	PUNCT
ejpam-5894	90	21	∀x	∀x	X
ejpam-5894	90	22	,	,	PUNCT
ejpam-5894	90	23	y	y	PROPN
ejpam-5894	90	24	∈	∈	PROPN
ejpam-5894	90	25	p	p	X
ejpam-5894	90	26	,	,	PUNCT
ejpam-5894	90	27	and	and	CCONJ
ejpam-5894	90	28	g(0p	g(0p	X
ejpam-5894	90	29	)	)	PUNCT
ejpam-5894	90	30	=	=	SYM
ejpam-5894	90	31	0q	0q	NOUN
ejpam-5894	90	32	.	.	PUNCT
ejpam-5894	91	1	t.	t.	PROPN
ejpam-5894	91	2	oner	oner	PROPN
ejpam-5894	91	3	et	et	PROPN
ejpam-5894	91	4	al	al	PROPN
ejpam-5894	91	5	.	.	PUNCT
ejpam-5894	91	6	/	/	SYM
ejpam-5894	91	7	eur	eur	PROPN
ejpam-5894	91	8	.	.	PUNCT
ejpam-5894	92	1	j.	j.	PROPN
ejpam-5894	92	2	pure	pure	PROPN
ejpam-5894	92	3	appl	appl	PROPN
ejpam-5894	92	4	.	.	PROPN
ejpam-5894	92	5	math	math	PROPN
ejpam-5894	92	6	,	,	PUNCT
ejpam-5894	92	7	18	18	NUM
ejpam-5894	92	8	(	(	PUNCT
ejpam-5894	92	9	3	3	NUM
ejpam-5894	92	10	)	)	PUNCT
ejpam-5894	92	11	(	(	PUNCT
ejpam-5894	92	12	2025	2025	NUM
ejpam-5894	92	13	)	)	PUNCT
ejpam-5894	92	14	,	,	PUNCT
ejpam-5894	92	15	5894	5894	NUM
ejpam-5894	92	16	5	5	NUM
ejpam-5894	92	17	of	of	ADP
ejpam-5894	92	18	33	33	NUM
ejpam-5894	92	19	3	3	NUM
ejpam-5894	92	20	.	.	PUNCT
ejpam-5894	92	21	intuitionistic	intuitionistic	ADJ
ejpam-5894	92	22	fuzzy	fuzzy	ADJ
ejpam-5894	92	23	implicative	implicative	ADJ
ejpam-5894	92	24	and	and	CCONJ
ejpam-5894	92	25	related	related	ADJ
ejpam-5894	92	26	wsbg	wsbg	NOUN
ejpam-5894	92	27	-	-	PUNCT
ejpam-5894	92	28	ideals	ideal	NOUN
ejpam-5894	92	29	this	this	DET
ejpam-5894	92	30	section	section	NOUN
ejpam-5894	92	31	presents	present	VERB
ejpam-5894	92	32	a	a	DET
ejpam-5894	92	33	theorem	theorem	NOUN
ejpam-5894	92	34	and	and	CCONJ
ejpam-5894	92	35	its	its	PRON
ejpam-5894	92	36	proof	proof	NOUN
ejpam-5894	92	37	concerning	concern	VERB
ejpam-5894	92	38	intuitionistic	intuitionistic	ADJ
ejpam-5894	92	39	fuzzy	fuzzy	ADJ
ejpam-5894	92	40	implicative	implicative	ADJ
ejpam-5894	92	41	wsbg	wsbg	NOUN
ejpam-5894	92	42	-	-	PUNCT
ejpam-5894	92	43	ideals	ideal	NOUN
ejpam-5894	92	44	in	in	ADP
ejpam-5894	92	45	a	a	DET
ejpam-5894	92	46	lattice	lattice	NOUN
ejpam-5894	92	47	l.	l.	NOUN
ejpam-5894	92	48	the	the	DET
ejpam-5894	92	49	theorem	theorem	NOUN
ejpam-5894	92	50	establishes	establish	VERB
ejpam-5894	92	51	that	that	SCONJ
ejpam-5894	92	52	an	an	DET
ejpam-5894	92	53	intuitionistic	intuitionistic	ADJ
ejpam-5894	92	54	fuzzy	fuzzy	ADJ
ejpam-5894	92	55	set	set	NOUN
ejpam-5894	92	56	l	l	NOUN
ejpam-5894	92	57	=	=	SYM
ejpam-5894	92	58	(	(	PUNCT
ejpam-5894	92	59	l	l	NOUN
ejpam-5894	92	60	,	,	PUNCT
ejpam-5894	92	61	α	α	X
ejpam-5894	92	62	,	,	PUNCT
ejpam-5894	92	63	β	β	NOUN
ejpam-5894	92	64	)	)	PUNCT
ejpam-5894	92	65	is	be	AUX
ejpam-5894	92	66	an	an	DET
ejpam-5894	92	67	intuitionistic	intuitionistic	ADJ
ejpam-5894	92	68	fuzzy	fuzzy	ADJ
ejpam-5894	92	69	implicative	implicative	ADJ
ejpam-5894	92	70	wsbg	wsbg	NOUN
ejpam-5894	92	71	-	-	PUNCT
ejpam-5894	92	72	ideal	ideal	NOUN
ejpam-5894	92	73	of	of	ADP
ejpam-5894	92	74	l	l	NOUN
ejpam-5894	92	75	if	if	SCONJ
ejpam-5894	93	1	and	and	CCONJ
ejpam-5894	93	2	only	only	ADV
ejpam-5894	93	3	if	if	SCONJ
ejpam-5894	93	4	,	,	PUNCT
ejpam-5894	93	5	for	for	ADP
ejpam-5894	93	6	all	all	DET
ejpam-5894	93	7	t	t	PROPN
ejpam-5894	93	8	,	,	PUNCT
ejpam-5894	93	9	s	s	PART
ejpam-5894	93	10	∈	∈	PROPN
ejpam-5894	94	1	[	[	X
ejpam-5894	94	2	0	0	NUM
ejpam-5894	94	3	,	,	PUNCT
ejpam-5894	94	4	1	1	NUM
ejpam-5894	94	5	]	]	PUNCT
ejpam-5894	94	6	,	,	PUNCT
ejpam-5894	94	7	the	the	DET
ejpam-5894	94	8	sets	set	NOUN
ejpam-5894	94	9	u(β	u(β	ADV
ejpam-5894	94	10	,	,	PUNCT
ejpam-5894	94	11	t	t	PROPN
ejpam-5894	94	12	)	)	PUNCT
ejpam-5894	94	13	and	and	CCONJ
ejpam-5894	94	14	l(α	l(α	PROPN
ejpam-5894	94	15	,	,	PUNCT
ejpam-5894	94	16	s	s	X
ejpam-5894	94	17	)	)	PUNCT
ejpam-5894	94	18	are	be	AUX
ejpam-5894	94	19	implicative	implicative	ADJ
ejpam-5894	94	20	wsbg	wsbg	NOUN
ejpam-5894	94	21	-	-	PUNCT
ejpam-5894	94	22	ideals	ideal	NOUN
ejpam-5894	94	23	of	of	ADP
ejpam-5894	94	24	l	l	NOUN
ejpam-5894	94	25	,	,	PUNCT
ejpam-5894	94	26	provided	provide	VERB
ejpam-5894	94	27	they	they	PRON
ejpam-5894	94	28	are	be	AUX
ejpam-5894	94	29	nonempty	nonempty	ADJ
ejpam-5894	94	30	.	.	PUNCT
ejpam-5894	95	1	the	the	DET
ejpam-5894	95	2	proof	proof	NOUN
ejpam-5894	95	3	is	be	AUX
ejpam-5894	95	4	divided	divide	VERB
ejpam-5894	95	5	into	into	ADP
ejpam-5894	95	6	two	two	NUM
ejpam-5894	95	7	cases	case	NOUN
ejpam-5894	95	8	:	:	PUNCT
ejpam-5894	95	9	the	the	DET
ejpam-5894	95	10	first	first	ADJ
ejpam-5894	95	11	case	case	NOUN
ejpam-5894	95	12	demonstrates	demonstrate	VERB
ejpam-5894	95	13	that	that	SCONJ
ejpam-5894	95	14	u(β	u(β	PROPN
ejpam-5894	95	15	,	,	PUNCT
ejpam-5894	95	16	t	t	PROPN
ejpam-5894	95	17	)	)	PUNCT
ejpam-5894	95	18	satisfies	satisfy	VERB
ejpam-5894	95	19	the	the	DET
ejpam-5894	95	20	implicative	implicative	ADJ
ejpam-5894	95	21	wsbg	wsbg	ADV
ejpam-5894	95	22	-	-	PUNCT
ejpam-5894	95	23	ideal	ideal	ADJ
ejpam-5894	95	24	property	property	NOUN
ejpam-5894	95	25	by	by	ADP
ejpam-5894	95	26	verifying	verify	VERB
ejpam-5894	95	27	that	that	SCONJ
ejpam-5894	95	28	certain	certain	ADJ
ejpam-5894	95	29	conditions	condition	NOUN
ejpam-5894	95	30	involving	involve	VERB
ejpam-5894	95	31	the	the	DET
ejpam-5894	95	32	membership	membership	NOUN
ejpam-5894	95	33	function	function	NOUN
ejpam-5894	95	34	β	β	PART
ejpam-5894	95	35	hold	hold	VERB
ejpam-5894	95	36	for	for	ADP
ejpam-5894	95	37	elements	element	NOUN
ejpam-5894	95	38	of	of	ADP
ejpam-5894	95	39	l.	l.	NOUN
ejpam-5894	95	40	the	the	DET
ejpam-5894	95	41	second	second	ADJ
ejpam-5894	95	42	case	case	NOUN
ejpam-5894	95	43	similarly	similarly	ADV
ejpam-5894	95	44	proves	prove	VERB
ejpam-5894	95	45	that	that	SCONJ
ejpam-5894	95	46	l(α	l(α	PROPN
ejpam-5894	95	47	,	,	PUNCT
ejpam-5894	95	48	s	s	X
ejpam-5894	95	49	)	)	PUNCT
ejpam-5894	95	50	satisfies	satisfy	VERB
ejpam-5894	95	51	the	the	DET
ejpam-5894	95	52	implicative	implicative	ADJ
ejpam-5894	95	53	wsbg	wsbg	ADV
ejpam-5894	95	54	-	-	PUNCT
ejpam-5894	95	55	ideal	ideal	ADJ
ejpam-5894	95	56	property	property	NOUN
ejpam-5894	95	57	using	use	VERB
ejpam-5894	95	58	the	the	DET
ejpam-5894	95	59	membership	membership	NOUN
ejpam-5894	95	60	function	function	NOUN
ejpam-5894	95	61	α	α	NOUN
ejpam-5894	95	62	.	.	PUNCT
ejpam-5894	96	1	the	the	DET
ejpam-5894	96	2	converse	converse	NOUN
ejpam-5894	96	3	is	be	AUX
ejpam-5894	96	4	also	also	ADV
ejpam-5894	96	5	proven	prove	VERB
ejpam-5894	96	6	by	by	ADP
ejpam-5894	96	7	assuming	assume	VERB
ejpam-5894	96	8	the	the	DET
ejpam-5894	96	9	implicative	implicative	ADJ
ejpam-5894	96	10	wsbg	wsbg	ADV
ejpam-5894	96	11	-	-	PUNCT
ejpam-5894	96	12	ideal	ideal	ADJ
ejpam-5894	96	13	properties	property	NOUN
ejpam-5894	96	14	of	of	ADP
ejpam-5894	96	15	u(β	u(β	PROPN
ejpam-5894	96	16	,	,	PUNCT
ejpam-5894	96	17	t	t	PROPN
ejpam-5894	96	18	)	)	PUNCT
ejpam-5894	96	19	and	and	CCONJ
ejpam-5894	96	20	l(α	l(α	PROPN
ejpam-5894	96	21	,	,	PUNCT
ejpam-5894	96	22	s	s	X
ejpam-5894	96	23	)	)	PUNCT
ejpam-5894	96	24	and	and	CCONJ
ejpam-5894	96	25	showing	show	VERB
ejpam-5894	96	26	that	that	SCONJ
ejpam-5894	96	27	they	they	PRON
ejpam-5894	96	28	imply	imply	VERB
ejpam-5894	96	29	l	l	NOUN
ejpam-5894	96	30	is	be	AUX
ejpam-5894	96	31	an	an	DET
ejpam-5894	96	32	intuitionistic	intuitionistic	ADJ
ejpam-5894	96	33	fuzzy	fuzzy	ADJ
ejpam-5894	96	34	implicative	implicative	ADJ
ejpam-5894	96	35	wsbg	wsbg	NOUN
ejpam-5894	96	36	-	-	PUNCT
ejpam-5894	96	37	ideal	ideal	ADJ
ejpam-5894	96	38	.	.	PUNCT
ejpam-5894	97	1	the	the	DET
ejpam-5894	97	2	proof	proof	NOUN
ejpam-5894	97	3	employs	employ	VERB
ejpam-5894	97	4	symbolic	symbolic	ADJ
ejpam-5894	97	5	reasoning	reasoning	NOUN
ejpam-5894	97	6	and	and	CCONJ
ejpam-5894	97	7	logical	logical	ADJ
ejpam-5894	97	8	deductions	deduction	NOUN
ejpam-5894	97	9	using	use	VERB
ejpam-5894	97	10	variables	variable	NOUN
ejpam-5894	97	11	ζ	ζ	PROPN
ejpam-5894	97	12	,	,	PUNCT
ejpam-5894	97	13	η	η	NOUN
ejpam-5894	97	14	,	,	PUNCT
ejpam-5894	97	15	and	and	CCONJ
ejpam-5894	97	16	θ	θ	NOUN
ejpam-5894	97	17	to	to	PART
ejpam-5894	97	18	represent	represent	VERB
ejpam-5894	97	19	elements	element	NOUN
ejpam-5894	97	20	of	of	ADP
ejpam-5894	97	21	the	the	DET
ejpam-5894	97	22	lattice	lattice	PROPN
ejpam-5894	97	23	l.	l.	PROPN
ejpam-5894	97	24	definition	definition	NOUN
ejpam-5894	97	25	9	9	NUM
ejpam-5894	97	26	.	.	PUNCT
ejpam-5894	98	1	an	an	DET
ejpam-5894	98	2	intuitionistic	intuitionistic	ADJ
ejpam-5894	98	3	fuzzy	fuzzy	ADJ
ejpam-5894	98	4	set	set	NOUN
ejpam-5894	98	5	l	l	NOUN
ejpam-5894	98	6	=	=	SYM
ejpam-5894	98	7	(	(	PUNCT
ejpam-5894	98	8	l	l	NOUN
ejpam-5894	98	9	,	,	PUNCT
ejpam-5894	98	10	α	α	X
ejpam-5894	98	11	,	,	PUNCT
ejpam-5894	98	12	β	β	NOUN
ejpam-5894	98	13	)	)	PUNCT
ejpam-5894	98	14	of	of	ADP
ejpam-5894	98	15	a	a	DET
ejpam-5894	98	16	wsbg	wsbg	ADV
ejpam-5894	98	17	-	-	PUNCT
ejpam-5894	98	18	algebra	algebra	NOUN
ejpam-5894	98	19	l	l	NOUN
ejpam-5894	98	20	=	=	PUNCT
ejpam-5894	98	21	⟨l	⟨l	NOUN
ejpam-5894	98	22	;	;	PUNCT
ejpam-5894	98	23	|	|	ADV
ejpam-5894	98	24	,	,	PUNCT
ejpam-5894	98	25	0⟩	0⟩	PROPN
ejpam-5894	98	26	is	be	AUX
ejpam-5894	98	27	referred	refer	VERB
ejpam-5894	98	28	to	to	ADP
ejpam-5894	98	29	as	as	ADP
ejpam-5894	98	30	an	an	DET
ejpam-5894	98	31	intuitionistic	intuitionistic	ADJ
ejpam-5894	98	32	fuzzy	fuzzy	ADJ
ejpam-5894	98	33	wsbg	wsbg	NOUN
ejpam-5894	98	34	-	-	PUNCT
ejpam-5894	98	35	ideal	ideal	NOUN
ejpam-5894	98	36	of	of	ADP
ejpam-5894	98	37	l	l	NOUN
ejpam-5894	98	38	if	if	SCONJ
ejpam-5894	98	39	the	the	DET
ejpam-5894	98	40	following	follow	VERB
ejpam-5894	98	41	conditions	condition	NOUN
ejpam-5894	98	42	hold	hold	VERB
ejpam-5894	98	43	:	:	PUNCT
ejpam-5894	98	44	(	(	PUNCT
ejpam-5894	98	45	∀ζ	∀ζ	PROPN
ejpam-5894	98	46	,	,	PUNCT
ejpam-5894	98	47	η	η	PROPN
ejpam-5894	98	48	∈	∈	PROPN
ejpam-5894	98	49	l	l	NOUN
ejpam-5894	98	50	)	)	PUNCT
ejpam-5894	98	51	(	(	PUNCT
ejpam-5894	98	52	α(0	α(0	PROPN
ejpam-5894	98	53	)	)	PUNCT
ejpam-5894	98	54	≥	≥	NOUN
ejpam-5894	98	55	α(ζ	α(ζ	PROPN
ejpam-5894	98	56	)	)	PUNCT
ejpam-5894	98	57	≥	≥	NOUN
ejpam-5894	98	58	min{α(η	min{α(η	PROPN
ejpam-5894	98	59	)	)	PUNCT
ejpam-5894	98	60	,	,	PUNCT
ejpam-5894	98	61	α((ζ|(η|η))|(ζ|(η|η	α((ζ|(η|η))|(ζ|(η|η	VERB
ejpam-5894	98	62	)	)	PUNCT
ejpam-5894	98	63	)	)	PUNCT
ejpam-5894	98	64	)	)	PUNCT
ejpam-5894	99	1	}	}	PUNCT
ejpam-5894	99	2	,	,	PUNCT
ejpam-5894	99	3	β(0	β(0	PROPN
ejpam-5894	99	4	)	)	PUNCT
ejpam-5894	99	5	≤	≤	NOUN
ejpam-5894	99	6	β(ζ	β(ζ	PROPN
ejpam-5894	99	7	)	)	PUNCT
ejpam-5894	99	8	≤	≤	NOUN
ejpam-5894	99	9	max{β(η	max{β(η	PROPN
ejpam-5894	99	10	)	)	PUNCT
ejpam-5894	99	11	,	,	PUNCT
ejpam-5894	99	12	β((ζ|(η|η))|(ζ|(η|η	β((ζ|(η|η))|(ζ|(η|η	ADJ
ejpam-5894	99	13	)	)	PUNCT
ejpam-5894	99	14	)	)	PUNCT
ejpam-5894	99	15	)	)	PUNCT
ejpam-5894	99	16	}	}	PUNCT
ejpam-5894	99	17	)	)	PUNCT
ejpam-5894	99	18	.	.	PUNCT
ejpam-5894	100	1	(	(	PUNCT
ejpam-5894	100	2	2	2	X
ejpam-5894	100	3	)	)	PUNCT
ejpam-5894	100	4	in	in	ADP
ejpam-5894	100	5	this	this	DET
ejpam-5894	100	6	case	case	NOUN
ejpam-5894	100	7	,	,	PUNCT
ejpam-5894	100	8	the	the	DET
ejpam-5894	100	9	membership	membership	NOUN
ejpam-5894	100	10	function	function	NOUN
ejpam-5894	100	11	α	α	PROPN
ejpam-5894	100	12	is	be	AUX
ejpam-5894	100	13	referred	refer	VERB
ejpam-5894	100	14	to	to	ADP
ejpam-5894	100	15	as	as	ADP
ejpam-5894	100	16	the	the	DET
ejpam-5894	100	17	fuzzy	fuzzy	ADJ
ejpam-5894	100	18	wsbg	wsbg	NOUN
ejpam-5894	100	19	-	-	PUNCT
ejpam-5894	100	20	ideal	ideal	NOUN
ejpam-5894	100	21	of	of	ADP
ejpam-5894	100	22	l.	l.	PROPN
ejpam-5894	100	23	example	example	PROPN
ejpam-5894	100	24	4	4	X
ejpam-5894	100	25	.	.	PUNCT
ejpam-5894	101	1	consider	consider	VERB
ejpam-5894	101	2	the	the	DET
ejpam-5894	101	3	wsbg	wsbg	NOUN
ejpam-5894	101	4	-	-	PUNCT
ejpam-5894	101	5	algebra	algebra	NOUN
ejpam-5894	101	6	l	l	NOUN
ejpam-5894	101	7	=	=	PUNCT
ejpam-5894	101	8	⟨l	⟨l	NOUN
ejpam-5894	101	9	;	;	PUNCT
ejpam-5894	102	1	|	|	ADV
ejpam-5894	102	2	,	,	PUNCT
ejpam-5894	102	3	0⟩	0⟩	PROPN
ejpam-5894	102	4	where	where	SCONJ
ejpam-5894	102	5	l	l	NOUN
ejpam-5894	102	6	=	=	PUNCT
ejpam-5894	102	7	{	{	PUNCT
ejpam-5894	102	8	0	0	NUM
ejpam-5894	102	9	,	,	PUNCT
ejpam-5894	102	10	a	a	DET
ejpam-5894	102	11	,	,	PUNCT
ejpam-5894	102	12	b	b	NOUN
ejpam-5894	102	13	}	}	PUNCT
ejpam-5894	102	14	with	with	ADP
ejpam-5894	102	15	the	the	DET
ejpam-5894	102	16	following	follow	VERB
ejpam-5894	102	17	operation	operation	NOUN
ejpam-5894	102	18	table	table	NOUN
ejpam-5894	102	19	:	:	PUNCT
ejpam-5894	102	20	|	|	ADV
ejpam-5894	102	21	0	0	PUNCT
ejpam-5894	102	22	a	a	DET
ejpam-5894	102	23	b	b	NOUN
ejpam-5894	102	24	0	0	NUM
ejpam-5894	102	25	0	0	NUM
ejpam-5894	102	26	b	b	NOUN
ejpam-5894	102	27	a	a	PRON
ejpam-5894	102	28	a	a	PRON
ejpam-5894	102	29	b	b	NOUN
ejpam-5894	102	30	0	0	NUM
ejpam-5894	102	31	0	0	NUM
ejpam-5894	102	32	b	b	NOUN
ejpam-5894	102	33	a	a	DET
ejpam-5894	102	34	0	0	NUM
ejpam-5894	102	35	0	0	NUM
ejpam-5894	102	36	define	define	VERB
ejpam-5894	102	37	the	the	DET
ejpam-5894	102	38	intuitionistic	intuitionistic	ADJ
ejpam-5894	102	39	fuzzy	fuzzy	ADJ
ejpam-5894	102	40	set	set	NOUN
ejpam-5894	102	41	l	l	NOUN
ejpam-5894	102	42	=	=	SYM
ejpam-5894	102	43	(	(	PUNCT
ejpam-5894	102	44	l	l	NOUN
ejpam-5894	102	45	,	,	PUNCT
ejpam-5894	102	46	α	α	X
ejpam-5894	102	47	,	,	PUNCT
ejpam-5894	102	48	β	β	NOUN
ejpam-5894	102	49	)	)	PUNCT
ejpam-5894	102	50	by	by	ADP
ejpam-5894	102	51	:	:	PUNCT
ejpam-5894	102	52	α(x	α(x	NOUN
ejpam-5894	102	53	)	)	PUNCT
ejpam-5894	102	54	=	=	SYM
ejpam-5894	102	55	0.5	0.5	NUM
ejpam-5894	102	56	,	,	PUNCT
ejpam-5894	102	57	β(x	β(x	NOUN
ejpam-5894	102	58	)	)	PUNCT
ejpam-5894	102	59	=	=	SYM
ejpam-5894	102	60	0	0	NUM
ejpam-5894	102	61	,	,	PUNCT
ejpam-5894	102	62	∀x	∀x	X
ejpam-5894	102	63	∈	∈	PROPN
ejpam-5894	102	64	l.	l.	NOUN
ejpam-5894	102	65	then	then	ADV
ejpam-5894	102	66	l	l	PROPN
ejpam-5894	103	1	=	=	PUNCT
ejpam-5894	104	1	(	(	PUNCT
ejpam-5894	104	2	l	l	NOUN
ejpam-5894	104	3	,	,	PUNCT
ejpam-5894	104	4	α	α	X
ejpam-5894	104	5	,	,	PUNCT
ejpam-5894	104	6	β	β	NOUN
ejpam-5894	104	7	)	)	PUNCT
ejpam-5894	104	8	is	be	AUX
ejpam-5894	104	9	an	an	DET
ejpam-5894	104	10	intuitionistic	intuitionistic	ADJ
ejpam-5894	104	11	fuzzy	fuzzy	ADJ
ejpam-5894	104	12	wsbg	wsbg	NOUN
ejpam-5894	104	13	-	-	PUNCT
ejpam-5894	104	14	ideal	ideal	NOUN
ejpam-5894	104	15	of	of	ADP
ejpam-5894	104	16	the	the	DET
ejpam-5894	104	17	given	give	VERB
ejpam-5894	104	18	wsbg	wsbg	NOUN
ejpam-5894	104	19	-	-	PUNCT
ejpam-5894	104	20	algebra	algebra	NOUN
ejpam-5894	104	21	.	.	PUNCT
ejpam-5894	105	1	definition	definition	NOUN
ejpam-5894	105	2	10	10	NUM
ejpam-5894	105	3	.	.	PUNCT
ejpam-5894	106	1	an	an	DET
ejpam-5894	106	2	intuitionistic	intuitionistic	ADJ
ejpam-5894	106	3	fuzzy	fuzzy	ADJ
ejpam-5894	106	4	set	set	NOUN
ejpam-5894	106	5	l	l	NOUN
ejpam-5894	106	6	=	=	SYM
ejpam-5894	106	7	(	(	PUNCT
ejpam-5894	106	8	l	l	NOUN
ejpam-5894	106	9	,	,	PUNCT
ejpam-5894	106	10	α	α	X
ejpam-5894	106	11	,	,	PUNCT
ejpam-5894	106	12	β	β	NOUN
ejpam-5894	106	13	)	)	PUNCT
ejpam-5894	106	14	of	of	ADP
ejpam-5894	106	15	a	a	DET
ejpam-5894	106	16	wsbg	wsbg	ADV
ejpam-5894	106	17	-	-	PUNCT
ejpam-5894	106	18	algebra	algebra	NOUN
ejpam-5894	106	19	l	l	NOUN
ejpam-5894	106	20	=	=	PUNCT
ejpam-5894	106	21	⟨l	⟨l	NOUN
ejpam-5894	106	22	;	;	PUNCT
ejpam-5894	106	23	|	|	ADV
ejpam-5894	106	24	,	,	PUNCT
ejpam-5894	106	25	0⟩	0⟩	PROPN
ejpam-5894	106	26	is	be	AUX
ejpam-5894	106	27	referred	refer	VERB
ejpam-5894	106	28	to	to	ADP
ejpam-5894	106	29	as	as	ADP
ejpam-5894	106	30	an	an	DET
ejpam-5894	106	31	intuitionistic	intuitionistic	ADJ
ejpam-5894	106	32	fuzzy	fuzzy	ADJ
ejpam-5894	106	33	implicative	implicative	ADJ
ejpam-5894	106	34	wsbg	wsbg	NOUN
ejpam-5894	106	35	-	-	PUNCT
ejpam-5894	106	36	ideal	ideal	NOUN
ejpam-5894	106	37	of	of	ADP
ejpam-5894	106	38	l	l	NOUN
ejpam-5894	106	39	if	if	SCONJ
ejpam-5894	106	40	the	the	DET
ejpam-5894	106	41	following	follow	VERB
ejpam-5894	106	42	conditions	condition	NOUN
ejpam-5894	106	43	hold	hold	VERB
ejpam-5894	106	44	:	:	PUNCT
ejpam-5894	106	45	(	(	PUNCT
ejpam-5894	106	46	∀ζ	∀ζ	PROPN
ejpam-5894	106	47	,	,	PUNCT
ejpam-5894	106	48	η	η	PROPN
ejpam-5894	106	49	,	,	PUNCT
ejpam-5894	106	50	θ	θ	PROPN
ejpam-5894	106	51	∈	∈	PROPN
ejpam-5894	106	52	l	l	NOUN
ejpam-5894	106	53	)	)	PUNCT
ejpam-5894	106	54			PROPN
ejpam-5894	106	55	α(0	α(0	PROPN
ejpam-5894	106	56	)	)	PUNCT
ejpam-5894	106	57	≥	≥	NOUN
ejpam-5894	106	58	α(ζ	α(ζ	PROPN
ejpam-5894	106	59	)	)	PUNCT
ejpam-5894	106	60	≥	≥	NOUN
ejpam-5894	107	1	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|	PROPN
ejpam-5894	107	2	(	(	PUNCT
ejpam-5894	107	3	(	(	PUNCT
ejpam-5894	107	4	(	(	PUNCT
ejpam-5894	107	5	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	107	6	)	)	PUNCT
ejpam-5894	107	7	)	)	PUNCT
ejpam-5894	107	8	)	)	PUNCT
ejpam-5894	107	9	,	,	PUNCT
ejpam-5894	107	10	α(θ	α(θ	NOUN
ejpam-5894	107	11	)	)	PUNCT
ejpam-5894	107	12	}	}	PUNCT
ejpam-5894	107	13	,	,	PUNCT
ejpam-5894	107	14	β(0	β(0	PROPN
ejpam-5894	107	15	)	)	PUNCT
ejpam-5894	107	16	≤	≤	NOUN
ejpam-5894	107	17	β(ζ	β(ζ	PROPN
ejpam-5894	107	18	)	)	PUNCT
ejpam-5894	107	19	≤	≤	NUM
ejpam-5894	108	1	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|	PROPN
ejpam-5894	108	2	(	(	PUNCT
ejpam-5894	108	3	(	(	PUNCT
ejpam-5894	108	4	(	(	PUNCT
ejpam-5894	108	5	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	108	6	)	)	PUNCT
ejpam-5894	108	7	)	)	PUNCT
ejpam-5894	108	8	)	)	PUNCT
ejpam-5894	108	9	,	,	PUNCT
ejpam-5894	108	10	β(θ	β(θ	NUM
ejpam-5894	108	11	)	)	PUNCT
ejpam-5894	108	12	}	}	PUNCT
ejpam-5894	108	13			NOUN
ejpam-5894	108	14	.	.	PUNCT
ejpam-5894	109	1	(	(	PUNCT
ejpam-5894	109	2	3	3	X
ejpam-5894	109	3	)	)	PUNCT
ejpam-5894	109	4	in	in	ADP
ejpam-5894	109	5	this	this	DET
ejpam-5894	109	6	case	case	NOUN
ejpam-5894	109	7	,	,	PUNCT
ejpam-5894	109	8	the	the	DET
ejpam-5894	109	9	membership	membership	NOUN
ejpam-5894	109	10	function	function	NOUN
ejpam-5894	109	11	α	α	PROPN
ejpam-5894	109	12	is	be	AUX
ejpam-5894	109	13	referred	refer	VERB
ejpam-5894	109	14	to	to	ADP
ejpam-5894	109	15	as	as	ADP
ejpam-5894	109	16	the	the	DET
ejpam-5894	109	17	fuzzy	fuzzy	ADJ
ejpam-5894	109	18	implicative	implicative	ADJ
ejpam-5894	109	19	wsbg	wsbg	NOUN
ejpam-5894	109	20	-	-	PUNCT
ejpam-5894	109	21	ideal	ideal	NOUN
ejpam-5894	109	22	of	of	ADP
ejpam-5894	109	23	l.	l.	PROPN
ejpam-5894	109	24	t.	t.	PROPN
ejpam-5894	109	25	oner	oner	PROPN
ejpam-5894	109	26	et	et	PROPN
ejpam-5894	109	27	al	al	PROPN
ejpam-5894	109	28	.	.	PUNCT
ejpam-5894	109	29	/	/	SYM
ejpam-5894	109	30	eur	eur	PROPN
ejpam-5894	109	31	.	.	PUNCT
ejpam-5894	110	1	j.	j.	PROPN
ejpam-5894	110	2	pure	pure	PROPN
ejpam-5894	110	3	appl	appl	PROPN
ejpam-5894	110	4	.	.	PROPN
ejpam-5894	110	5	math	math	PROPN
ejpam-5894	110	6	,	,	PUNCT
ejpam-5894	110	7	18	18	NUM
ejpam-5894	110	8	(	(	PUNCT
ejpam-5894	110	9	3	3	NUM
ejpam-5894	110	10	)	)	PUNCT
ejpam-5894	110	11	(	(	PUNCT
ejpam-5894	110	12	2025	2025	NUM
ejpam-5894	110	13	)	)	PUNCT
ejpam-5894	110	14	,	,	PUNCT
ejpam-5894	110	15	5894	5894	NUM
ejpam-5894	110	16	6	6	NUM
ejpam-5894	110	17	of	of	ADP
ejpam-5894	110	18	33	33	NUM
ejpam-5894	110	19	example	example	NOUN
ejpam-5894	110	20	5	5	NUM
ejpam-5894	110	21	.	.	PUNCT
ejpam-5894	110	22	from	from	ADP
ejpam-5894	110	23	the	the	DET
ejpam-5894	110	24	wsbg	wsbg	NOUN
ejpam-5894	110	25	-	-	PUNCT
ejpam-5894	110	26	algebra	algebra	NOUN
ejpam-5894	110	27	in	in	ADP
ejpam-5894	110	28	example	example	NOUN
ejpam-5894	110	29	1	1	NUM
ejpam-5894	110	30	,	,	PUNCT
ejpam-5894	110	31	define	define	VERB
ejpam-5894	110	32	the	the	DET
ejpam-5894	110	33	intuitionistic	intuitionistic	ADJ
ejpam-5894	110	34	fuzzy	fuzzy	ADJ
ejpam-5894	110	35	set	set	NOUN
ejpam-5894	110	36	l	l	NOUN
ejpam-5894	110	37	=	=	SYM
ejpam-5894	110	38	(	(	PUNCT
ejpam-5894	110	39	l	l	NOUN
ejpam-5894	110	40	,	,	PUNCT
ejpam-5894	110	41	α	α	X
ejpam-5894	110	42	,	,	PUNCT
ejpam-5894	110	43	β	β	NOUN
ejpam-5894	110	44	)	)	PUNCT
ejpam-5894	110	45	with	with	ADP
ejpam-5894	110	46	membership	membership	NOUN
ejpam-5894	110	47	and	and	CCONJ
ejpam-5894	110	48	non	non	ADJ
ejpam-5894	110	49	-	-	ADJ
ejpam-5894	110	50	membership	membership	ADJ
ejpam-5894	110	51	functions	function	NOUN
ejpam-5894	110	52	:	:	PUNCT
ejpam-5894	110	53	α(x	α(x	NUM
ejpam-5894	110	54	)	)	PUNCT
ejpam-5894	110	55	=	=	SYM
ejpam-5894	110	56	0.5	0.5	NUM
ejpam-5894	110	57	,	,	PUNCT
ejpam-5894	110	58	β(x	β(x	NOUN
ejpam-5894	110	59	)	)	PUNCT
ejpam-5894	110	60	=	=	SYM
ejpam-5894	110	61	0.25	0.25	NUM
ejpam-5894	110	62	,	,	PUNCT
ejpam-5894	110	63	∀x	∀x	PROPN
ejpam-5894	110	64	∈	∈	PROPN
ejpam-5894	110	65	l.	l.	NOUN
ejpam-5894	110	66	then	then	ADV
ejpam-5894	110	67	l	l	PROPN
ejpam-5894	110	68	=	=	PUNCT
ejpam-5894	110	69	(	(	PUNCT
ejpam-5894	110	70	l	l	NOUN
ejpam-5894	110	71	,	,	PUNCT
ejpam-5894	110	72	α	α	X
ejpam-5894	110	73	,	,	PUNCT
ejpam-5894	110	74	β	β	NOUN
ejpam-5894	110	75	)	)	PUNCT
ejpam-5894	110	76	is	be	AUX
ejpam-5894	110	77	an	an	DET
ejpam-5894	110	78	intuitionistic	intuitionistic	ADJ
ejpam-5894	110	79	fuzzy	fuzzy	ADJ
ejpam-5894	110	80	implicative	implicative	ADJ
ejpam-5894	110	81	wsbg	wsbg	NOUN
ejpam-5894	110	82	-	-	PUNCT
ejpam-5894	110	83	ideal	ideal	NOUN
ejpam-5894	110	84	of	of	ADP
ejpam-5894	110	85	the	the	DET
ejpam-5894	110	86	wsbg	wsbg	NOUN
ejpam-5894	110	87	-	-	PUNCT
ejpam-5894	110	88	algebra	algebra	NOUN
ejpam-5894	110	89	in	in	ADP
ejpam-5894	110	90	example	example	NOUN
ejpam-5894	110	91	1	1	NUM
ejpam-5894	110	92	.	.	X
ejpam-5894	110	93	proposition	proposition	NOUN
ejpam-5894	110	94	1	1	NUM
ejpam-5894	110	95	.	.	PUNCT
ejpam-5894	111	1	every	every	DET
ejpam-5894	111	2	intuitionistic	intuitionistic	ADJ
ejpam-5894	111	3	fuzzy	fuzzy	ADJ
ejpam-5894	111	4	implicative	implicative	ADJ
ejpam-5894	111	5	wsbg	wsbg	NOUN
ejpam-5894	111	6	-	-	PUNCT
ejpam-5894	111	7	ideal	ideal	NOUN
ejpam-5894	111	8	of	of	ADP
ejpam-5894	111	9	a	a	DET
ejpam-5894	111	10	wsbg	wsbg	ADV
ejpam-5894	111	11	-	-	PUNCT
ejpam-5894	111	12	algebra	algebra	NOUN
ejpam-5894	111	13	l	l	NOUN
ejpam-5894	111	14	=	=	PUNCT
ejpam-5894	111	15	⟨l	⟨l	NOUN
ejpam-5894	111	16	;	;	PUNCT
ejpam-5894	111	17	|	|	ADV
ejpam-5894	111	18	,	,	PUNCT
ejpam-5894	111	19	0⟩	0⟩	PROPN
ejpam-5894	111	20	is	be	AUX
ejpam-5894	111	21	also	also	ADV
ejpam-5894	111	22	an	an	DET
ejpam-5894	111	23	intuitionistic	intuitionistic	ADJ
ejpam-5894	111	24	fuzzy	fuzzy	ADJ
ejpam-5894	111	25	wsbg	wsbg	NOUN
ejpam-5894	111	26	-	-	PUNCT
ejpam-5894	111	27	ideal	ideal	NOUN
ejpam-5894	111	28	of	of	ADP
ejpam-5894	111	29	l.	l.	PROPN
ejpam-5894	111	30	proof	proof	PROPN
ejpam-5894	111	31	.	.	PUNCT
ejpam-5894	112	1	let	let	VERB
ejpam-5894	112	2	l	l	NOUN
ejpam-5894	112	3	=	=	SYM
ejpam-5894	112	4	(	(	PUNCT
ejpam-5894	112	5	l	l	NOUN
ejpam-5894	112	6	,	,	PUNCT
ejpam-5894	112	7	α	α	X
ejpam-5894	112	8	,	,	PUNCT
ejpam-5894	112	9	β	β	NOUN
ejpam-5894	112	10	)	)	PUNCT
ejpam-5894	112	11	be	be	VERB
ejpam-5894	112	12	an	an	DET
ejpam-5894	112	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	112	14	fuzzy	fuzzy	ADJ
ejpam-5894	112	15	implicative	implicative	ADJ
ejpam-5894	112	16	wsbg	wsbg	NOUN
ejpam-5894	112	17	-	-	PUNCT
ejpam-5894	112	18	ideal	ideal	NOUN
ejpam-5894	112	19	of	of	ADP
ejpam-5894	112	20	l	l	NOUN
ejpam-5894	112	21	=	=	SYM
ejpam-5894	112	22	⟨l	⟨l	NOUN
ejpam-5894	112	23	;	;	PUNCT
ejpam-5894	112	24	|	|	ADV
ejpam-5894	112	25	,	,	PUNCT
ejpam-5894	112	26	0⟩.	0⟩.	PROPN
ejpam-5894	112	27	then	then	ADV
ejpam-5894	112	28	,	,	PUNCT
ejpam-5894	112	29	it	it	PRON
ejpam-5894	112	30	follows	follow	VERB
ejpam-5894	112	31	that	that	SCONJ
ejpam-5894	112	32	α(0	α(0	PROPN
ejpam-5894	112	33	)	)	PUNCT
ejpam-5894	112	34	≥	≥	NOUN
ejpam-5894	112	35	α(ζ	α(ζ	PROPN
ejpam-5894	112	36	)	)	PUNCT
ejpam-5894	112	37	and	and	CCONJ
ejpam-5894	112	38	β(0	β(0	PROPN
ejpam-5894	112	39	)	)	PUNCT
ejpam-5894	112	40	≤	≤	NOUN
ejpam-5894	112	41	β(ζ	β(ζ	PROPN
ejpam-5894	112	42	)	)	PUNCT
ejpam-5894	112	43	.	.	PUNCT
ejpam-5894	113	1	furthermore	furthermore	ADV
ejpam-5894	113	2	,	,	PUNCT
ejpam-5894	113	3	we	we	PRON
ejpam-5894	113	4	have	have	VERB
ejpam-5894	113	5	α(ζ	α(ζ	PROPN
ejpam-5894	113	6	)	)	PUNCT
ejpam-5894	113	7	≥	≥	NOUN
ejpam-5894	113	8	min{α(η	min{α(η	PROPN
ejpam-5894	113	9	)	)	PUNCT
ejpam-5894	113	10	,	,	PUNCT
ejpam-5894	113	11	α((((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(η|η))|	α((((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(η|η))|	PROPN
ejpam-5894	113	12	(	(	PUNCT
ejpam-5894	113	13	(	(	PUNCT
ejpam-5894	113	14	(	(	PUNCT
ejpam-5894	113	15	ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(η|η	ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(η|η	PROPN
ejpam-5894	113	16	)	)	PUNCT
ejpam-5894	113	17	)	)	PUNCT
ejpam-5894	113	18	)	)	PUNCT
ejpam-5894	113	19	}	}	PUNCT
ejpam-5894	113	20	=	=	SYM
ejpam-5894	113	21	min{α(η	min{α(η	NOUN
ejpam-5894	113	22	)	)	PUNCT
ejpam-5894	113	23	,	,	PUNCT
ejpam-5894	113	24	α((((ζ|(0|0))|(ζ|(0|0)))|(η|η))|	α((((ζ|(0|0))|(ζ|(0|0)))|(η|η))|	NUM
ejpam-5894	113	25	(	(	PUNCT
ejpam-5894	113	26	(	(	PUNCT
ejpam-5894	113	27	(	(	PUNCT
ejpam-5894	113	28	ζ|(0|0))|(ζ|(0|0)))|(η|η	ζ|(0|0))|(ζ|(0|0)))|(η|η	NOUN
ejpam-5894	113	29	)	)	PUNCT
ejpam-5894	113	30	)	)	PUNCT
ejpam-5894	113	31	)	)	PUNCT
ejpam-5894	113	32	}	}	PUNCT
ejpam-5894	113	33	=	=	SYM
ejpam-5894	113	34	min{α(η	min{α(η	NOUN
ejpam-5894	113	35	)	)	PUNCT
ejpam-5894	113	36	,	,	PUNCT
ejpam-5894	113	37	α((ζ|(η|η))|(ζ|(η|η	α((ζ|(η|η))|(ζ|(η|η	VERB
ejpam-5894	113	38	)	)	PUNCT
ejpam-5894	113	39	)	)	PUNCT
ejpam-5894	113	40	)	)	PUNCT
ejpam-5894	113	41	}	}	PUNCT
ejpam-5894	113	42	,	,	PUNCT
ejpam-5894	113	43	β(ζ	β(ζ	PROPN
ejpam-5894	113	44	)	)	PUNCT
ejpam-5894	113	45	≤	≤	NOUN
ejpam-5894	113	46	max{β(η	max{β(η	PROPN
ejpam-5894	113	47	)	)	PUNCT
ejpam-5894	113	48	,	,	PUNCT
ejpam-5894	113	49	β((((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(η|η))|	β((((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(η|η))|	PROPN
ejpam-5894	113	50	(	(	PUNCT
ejpam-5894	113	51	(	(	PUNCT
ejpam-5894	113	52	(	(	PUNCT
ejpam-5894	113	53	ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(η|η	ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(η|η	PROPN
ejpam-5894	113	54	)	)	PUNCT
ejpam-5894	113	55	)	)	PUNCT
ejpam-5894	113	56	)	)	PUNCT
ejpam-5894	113	57	}	}	PUNCT
ejpam-5894	113	58	=	=	SYM
ejpam-5894	113	59	max{β(η	max{β(η	PROPN
ejpam-5894	113	60	)	)	PUNCT
ejpam-5894	113	61	,	,	PUNCT
ejpam-5894	113	62	β((((ζ|(0|0))|(ζ|(0|0)))|(η|η))|	β((((ζ|(0|0))|(ζ|(0|0)))|(η|η))|	PUNCT
ejpam-5894	113	63	(	(	PUNCT
ejpam-5894	113	64	(	(	PUNCT
ejpam-5894	113	65	(	(	PUNCT
ejpam-5894	113	66	ζ|(0|0))|(ζ|(0|0)))|(η|η	ζ|(0|0))|(ζ|(0|0)))|(η|η	NOUN
ejpam-5894	113	67	)	)	PUNCT
ejpam-5894	113	68	)	)	PUNCT
ejpam-5894	113	69	)	)	PUNCT
ejpam-5894	113	70	}	}	PUNCT
ejpam-5894	114	1	=	=	SYM
ejpam-5894	114	2	max{β(η	max{β(η	PROPN
ejpam-5894	114	3	)	)	PUNCT
ejpam-5894	114	4	,	,	PUNCT
ejpam-5894	114	5	β((ζ|(η|η))|(ζ|(η|η	β((ζ|(η|η))|(ζ|(η|η	ADJ
ejpam-5894	114	6	)	)	PUNCT
ejpam-5894	114	7	)	)	PUNCT
ejpam-5894	114	8	)	)	PUNCT
ejpam-5894	114	9	}	}	PUNCT
ejpam-5894	114	10	.	.	PUNCT
ejpam-5894	115	1	therefore	therefore	ADV
ejpam-5894	115	2	,	,	PUNCT
ejpam-5894	115	3	l	l	NOUN
ejpam-5894	115	4	=	=	SYM
ejpam-5894	115	5	(	(	PUNCT
ejpam-5894	115	6	l	l	NOUN
ejpam-5894	115	7	,	,	PUNCT
ejpam-5894	115	8	α	α	X
ejpam-5894	115	9	,	,	PUNCT
ejpam-5894	115	10	β	β	NOUN
ejpam-5894	115	11	)	)	PUNCT
ejpam-5894	115	12	is	be	AUX
ejpam-5894	115	13	an	an	DET
ejpam-5894	115	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	115	15	fuzzy	fuzzy	ADJ
ejpam-5894	115	16	wsbg	wsbg	NOUN
ejpam-5894	115	17	-	-	PUNCT
ejpam-5894	115	18	ideal	ideal	NOUN
ejpam-5894	115	19	of	of	ADP
ejpam-5894	115	20	l.	l.	PROPN
ejpam-5894	115	21	theorem	theorem	PROPN
ejpam-5894	115	22	1	1	NUM
ejpam-5894	115	23	.	.	PUNCT
ejpam-5894	115	24	an	an	DET
ejpam-5894	115	25	intuitionistic	intuitionistic	ADJ
ejpam-5894	115	26	fuzzy	fuzzy	ADJ
ejpam-5894	115	27	set	set	NOUN
ejpam-5894	115	28	l	l	NOUN
ejpam-5894	115	29	=	=	SYM
ejpam-5894	115	30	(	(	PUNCT
ejpam-5894	115	31	l	l	NOUN
ejpam-5894	115	32	,	,	PUNCT
ejpam-5894	115	33	α	α	X
ejpam-5894	115	34	,	,	PUNCT
ejpam-5894	115	35	β	β	NOUN
ejpam-5894	115	36	)	)	PUNCT
ejpam-5894	115	37	in	in	ADP
ejpam-5894	115	38	a	a	DET
ejpam-5894	115	39	wsbg	wsbg	ADV
ejpam-5894	115	40	-	-	PUNCT
ejpam-5894	115	41	algebra	algebra	NOUN
ejpam-5894	115	42	l	l	NOUN
ejpam-5894	115	43	=	=	PUNCT
ejpam-5894	115	44	⟨l	⟨l	NOUN
ejpam-5894	115	45	;	;	PUNCT
ejpam-5894	115	46	|	|	ADV
ejpam-5894	115	47	,	,	PUNCT
ejpam-5894	115	48	0⟩	0⟩	PROPN
ejpam-5894	115	49	is	be	AUX
ejpam-5894	115	50	an	an	DET
ejpam-5894	115	51	intuitionistic	intuitionistic	ADJ
ejpam-5894	115	52	fuzzy	fuzzy	ADJ
ejpam-5894	115	53	implicative	implicative	ADJ
ejpam-5894	115	54	wsbg	wsbg	NOUN
ejpam-5894	115	55	-	-	PUNCT
ejpam-5894	115	56	ideal	ideal	NOUN
ejpam-5894	115	57	of	of	ADP
ejpam-5894	115	58	l	l	NOUN
ejpam-5894	115	59	if	if	SCONJ
ejpam-5894	116	1	and	and	CCONJ
ejpam-5894	116	2	only	only	ADV
ejpam-5894	116	3	if	if	SCONJ
ejpam-5894	116	4	the	the	DET
ejpam-5894	116	5	sets	set	NOUN
ejpam-5894	116	6	l(β	l(β	PROPN
ejpam-5894	116	7	,	,	PUNCT
ejpam-5894	116	8	s	s	NOUN
ejpam-5894	116	9	)	)	PUNCT
ejpam-5894	116	10	and	and	CCONJ
ejpam-5894	116	11	u(α	u(α	PROPN
ejpam-5894	116	12	,	,	PUNCT
ejpam-5894	116	13	t	t	PROPN
ejpam-5894	116	14	)	)	PUNCT
ejpam-5894	116	15	are	be	AUX
ejpam-5894	116	16	implicative	implicative	ADJ
ejpam-5894	116	17	wsbg	wsbg	NOUN
ejpam-5894	116	18	-	-	PUNCT
ejpam-5894	116	19	ideals	ideal	NOUN
ejpam-5894	116	20	of	of	ADP
ejpam-5894	116	21	l	l	NOUN
ejpam-5894	116	22	whenever	whenever	SCONJ
ejpam-5894	116	23	they	they	PRON
ejpam-5894	116	24	are	be	AUX
ejpam-5894	116	25	nonempty	nonempty	ADJ
ejpam-5894	116	26	for	for	ADP
ejpam-5894	116	27	all	all	DET
ejpam-5894	116	28	s	s	PROPN
ejpam-5894	116	29	,	,	PUNCT
ejpam-5894	116	30	t	t	PROPN
ejpam-5894	116	31	∈	∈	PROPN
ejpam-5894	117	1	[	[	X
ejpam-5894	117	2	0	0	NUM
ejpam-5894	117	3	,	,	PUNCT
ejpam-5894	117	4	1	1	NUM
ejpam-5894	117	5	]	]	PUNCT
ejpam-5894	117	6	.	.	PUNCT
ejpam-5894	118	1	proof	proof	NOUN
ejpam-5894	118	2	.	.	PUNCT
ejpam-5894	119	1	assume	assume	VERB
ejpam-5894	119	2	that	that	SCONJ
ejpam-5894	119	3	l	l	NOUN
ejpam-5894	119	4	=	=	SYM
ejpam-5894	119	5	(	(	PUNCT
ejpam-5894	119	6	l	l	NOUN
ejpam-5894	119	7	,	,	PUNCT
ejpam-5894	119	8	α	α	X
ejpam-5894	119	9	,	,	PUNCT
ejpam-5894	119	10	β	β	NOUN
ejpam-5894	119	11	)	)	PUNCT
ejpam-5894	119	12	is	be	AUX
ejpam-5894	119	13	an	an	DET
ejpam-5894	119	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	119	15	fuzzy	fuzzy	ADJ
ejpam-5894	119	16	implicative	implicative	ADJ
ejpam-5894	119	17	wsbg	wsbg	NOUN
ejpam-5894	119	18	-	-	PUNCT
ejpam-5894	119	19	ideal	ideal	NOUN
ejpam-5894	119	20	of	of	ADP
ejpam-5894	119	21	l	l	NOUN
ejpam-5894	119	22	=	=	SYM
ejpam-5894	119	23	⟨l	⟨l	NOUN
ejpam-5894	119	24	;	;	PUNCT
ejpam-5894	119	25	|	|	ADV
ejpam-5894	119	26	,	,	PUNCT
ejpam-5894	119	27	0⟩	0⟩	PROPN
ejpam-5894	119	28	,	,	PUNCT
ejpam-5894	119	29	and	and	CCONJ
ejpam-5894	119	30	let	let	VERB
ejpam-5894	119	31	l(β	l(β	PROPN
ejpam-5894	119	32	,	,	PUNCT
ejpam-5894	119	33	s	s	X
ejpam-5894	119	34	)	)	PUNCT
ejpam-5894	119	35	̸=	̸=	PROPN
ejpam-5894	119	36	∅	∅	NOUN
ejpam-5894	119	37	=	=	NOUN
ejpam-5894	119	38	̸	̸	PUNCT
ejpam-5894	119	39	u(α	u(α	NOUN
ejpam-5894	119	40	,	,	PUNCT
ejpam-5894	119	41	t	t	PROPN
ejpam-5894	119	42	)	)	PUNCT
ejpam-5894	119	43	for	for	ADP
ejpam-5894	119	44	all	all	DET
ejpam-5894	119	45	s	s	PROPN
ejpam-5894	119	46	,	,	PUNCT
ejpam-5894	119	47	t	t	PROPN
ejpam-5894	119	48	∈	∈	PROPN
ejpam-5894	120	1	[	[	X
ejpam-5894	120	2	0	0	NUM
ejpam-5894	120	3	,	,	PUNCT
ejpam-5894	120	4	1	1	NUM
ejpam-5894	120	5	]	]	PUNCT
ejpam-5894	120	6	.	.	PUNCT
ejpam-5894	121	1	let	let	VERB
ejpam-5894	121	2	ζ	ζ	NOUN
ejpam-5894	121	3	,	,	PUNCT
ejpam-5894	121	4	η	η	PROPN
ejpam-5894	121	5	∈	∈	PROPN
ejpam-5894	121	6	l	l	NOUN
ejpam-5894	121	7	be	be	AUX
ejpam-5894	121	8	such	such	ADJ
ejpam-5894	121	9	that	that	SCONJ
ejpam-5894	121	10	(	(	PUNCT
ejpam-5894	121	11	ζ	ζ	NOUN
ejpam-5894	121	12	,	,	PUNCT
ejpam-5894	121	13	η	η	NOUN
ejpam-5894	121	14	)	)	PUNCT
ejpam-5894	121	15	∈	∈	PROPN
ejpam-5894	121	16	l(β	l(β	PROPN
ejpam-5894	121	17	,	,	PUNCT
ejpam-5894	121	18	s	s	X
ejpam-5894	121	19	)	)	PUNCT
ejpam-5894	121	20	×	×	PROPN
ejpam-5894	121	21	u(α	u(α	PROPN
ejpam-5894	121	22	,	,	PUNCT
ejpam-5894	121	23	t	t	PROPN
ejpam-5894	121	24	)	)	PUNCT
ejpam-5894	121	25	.	.	PUNCT
ejpam-5894	122	1	then	then	ADV
ejpam-5894	122	2	,	,	PUNCT
ejpam-5894	122	3	by	by	ADP
ejpam-5894	122	4	definition	definition	NOUN
ejpam-5894	122	5	,	,	PUNCT
ejpam-5894	122	6	β(ζ	β(ζ	PROPN
ejpam-5894	122	7	)	)	PUNCT
ejpam-5894	122	8	≤	≤	PROPN
ejpam-5894	122	9	s	s	NOUN
ejpam-5894	122	10	and	and	CCONJ
ejpam-5894	122	11	α(η	α(η	PROPN
ejpam-5894	122	12	)	)	PUNCT
ejpam-5894	122	13	≥	≥	NOUN
ejpam-5894	122	14	t.	t.	NOUN
ejpam-5894	122	15	since	since	SCONJ
ejpam-5894	122	16	β(0	β(0	PROPN
ejpam-5894	122	17	)	)	PUNCT
ejpam-5894	122	18	≤	≤	NOUN
ejpam-5894	122	19	β(ζ	β(ζ	PROPN
ejpam-5894	122	20	)	)	PUNCT
ejpam-5894	122	21	≤	≤	PROPN
ejpam-5894	122	22	s	s	NOUN
ejpam-5894	122	23	and	and	CCONJ
ejpam-5894	122	24	α(0	α(0	PROPN
ejpam-5894	122	25	)	)	PUNCT
ejpam-5894	122	26	≥	≥	PROPN
ejpam-5894	122	27	α(η	α(η	PROPN
ejpam-5894	122	28	)	)	PUNCT
ejpam-5894	122	29	≥	≥	PROPN
ejpam-5894	122	30	t	t	PROPN
ejpam-5894	122	31	,	,	PUNCT
ejpam-5894	122	32	it	it	PRON
ejpam-5894	122	33	follows	follow	VERB
ejpam-5894	122	34	that	that	SCONJ
ejpam-5894	122	35	(	(	PUNCT
ejpam-5894	122	36	0	0	NUM
ejpam-5894	122	37	,	,	PUNCT
ejpam-5894	122	38	0	0	NUM
ejpam-5894	122	39	)	)	PUNCT
ejpam-5894	122	40	∈	∈	PROPN
ejpam-5894	122	41	l(β	l(β	PROPN
ejpam-5894	122	42	,	,	PUNCT
ejpam-5894	122	43	s)×	s)×	CCONJ
ejpam-5894	122	44	u(α	u(α	NUM
ejpam-5894	122	45	,	,	PUNCT
ejpam-5894	122	46	t	t	PROPN
ejpam-5894	122	47	)	)	PUNCT
ejpam-5894	122	48	.	.	PUNCT
ejpam-5894	123	1	now	now	ADV
ejpam-5894	123	2	,	,	PUNCT
ejpam-5894	123	3	let	let	VERB
ejpam-5894	123	4	ζ	ζ	NOUN
ejpam-5894	123	5	,	,	PUNCT
ejpam-5894	123	6	η	η	PROPN
ejpam-5894	123	7	,	,	PUNCT
ejpam-5894	123	8	θ	θ	PROPN
ejpam-5894	123	9	,	,	PUNCT
ejpam-5894	123	10	ξ	ξ	PROPN
ejpam-5894	123	11	,	,	PUNCT
ejpam-5894	123	12	ϕ	ϕ	NOUN
ejpam-5894	123	13	,	,	PUNCT
ejpam-5894	123	14	ψ	ψ	AUX
ejpam-5894	123	15	∈	∈	PROPN
ejpam-5894	123	16	l	l	NOUN
ejpam-5894	123	17	be	be	AUX
ejpam-5894	123	18	such	such	ADJ
ejpam-5894	123	19	that	that	SCONJ
ejpam-5894	123	20	(	(	PUNCT
ejpam-5894	123	21	(	(	PUNCT
ejpam-5894	123	22	(	(	PUNCT
ejpam-5894	123	23	(	(	PUNCT
ejpam-5894	123	24	(	(	PUNCT
ejpam-5894	123	25	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	123	26	)	)	PUNCT
ejpam-5894	123	27	)	)	PUNCT
ejpam-5894	123	28	)	)	PUNCT
ejpam-5894	123	29	,	,	PUNCT
ejpam-5894	123	30	(	(	PUNCT
ejpam-5894	123	31	(	(	PUNCT
ejpam-5894	123	32	(	(	PUNCT
ejpam-5894	123	33	(	(	PUNCT
ejpam-5894	123	34	(	(	PUNCT
ejpam-5894	123	35	ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ))|(((ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ	ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ))|(((ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ	NOUN
ejpam-5894	123	36	)	)	PUNCT
ejpam-5894	123	37	)	)	PUNCT
ejpam-5894	123	38	)	)	PUNCT
ejpam-5894	123	39	)	)	PUNCT
ejpam-5894	123	40	)	)	PUNCT
ejpam-5894	124	1	∈	∈	PROPN
ejpam-5894	124	2	l(β	l(β	PROPN
ejpam-5894	124	3	,	,	PUNCT
ejpam-5894	124	4	s)×	s)×	CCONJ
ejpam-5894	124	5	u(α	u(α	NUM
ejpam-5894	124	6	,	,	PUNCT
ejpam-5894	124	7	t	t	PROPN
ejpam-5894	124	8	)	)	PUNCT
ejpam-5894	124	9	and	and	CCONJ
ejpam-5894	124	10	(	(	PUNCT
ejpam-5894	124	11	θ	θ	NOUN
ejpam-5894	124	12	,	,	PUNCT
ejpam-5894	124	13	ψ	ψ	NOUN
ejpam-5894	124	14	)	)	PUNCT
ejpam-5894	124	15	∈	∈	PROPN
ejpam-5894	124	16	l(β	l(β	PROPN
ejpam-5894	124	17	,	,	PUNCT
ejpam-5894	124	18	s)×	s)×	CCONJ
ejpam-5894	124	19	u(α	u(α	NUM
ejpam-5894	124	20	,	,	PUNCT
ejpam-5894	124	21	t	t	PROPN
ejpam-5894	124	22	)	)	PUNCT
ejpam-5894	124	23	.	.	PUNCT
ejpam-5894	125	1	then	then	ADV
ejpam-5894	125	2	,	,	PUNCT
ejpam-5894	125	3	by	by	ADP
ejpam-5894	125	4	definition	definition	NOUN
ejpam-5894	125	5	,	,	PUNCT
ejpam-5894	125	6	we	we	PRON
ejpam-5894	125	7	have	have	VERB
ejpam-5894	125	8	β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	125	9	)	)	PUNCT
ejpam-5894	125	10	)	)	PUNCT
ejpam-5894	125	11	)	)	PUNCT
ejpam-5894	125	12	)	)	PUNCT
ejpam-5894	126	1	≤	≤	PROPN
ejpam-5894	126	2	s	s	X
ejpam-5894	126	3	,	,	PUNCT
ejpam-5894	126	4	β(θ	β(θ	NUM
ejpam-5894	126	5	)	)	PUNCT
ejpam-5894	126	6	≤	≤	NOUN
ejpam-5894	126	7	s	s	PROPN
ejpam-5894	126	8	,	,	PUNCT
ejpam-5894	126	9	t.	t.	PROPN
ejpam-5894	126	10	oner	oner	NOUN
ejpam-5894	126	11	et	et	PROPN
ejpam-5894	126	12	al	al	PROPN
ejpam-5894	126	13	.	.	PUNCT
ejpam-5894	126	14	/	/	SYM
ejpam-5894	126	15	eur	eur	PROPN
ejpam-5894	126	16	.	.	PUNCT
ejpam-5894	127	1	j.	j.	PROPN
ejpam-5894	127	2	pure	pure	PROPN
ejpam-5894	127	3	appl	appl	PROPN
ejpam-5894	127	4	.	.	PROPN
ejpam-5894	127	5	math	math	PROPN
ejpam-5894	127	6	,	,	PUNCT
ejpam-5894	127	7	18	18	NUM
ejpam-5894	127	8	(	(	PUNCT
ejpam-5894	127	9	3	3	NUM
ejpam-5894	127	10	)	)	PUNCT
ejpam-5894	127	11	(	(	PUNCT
ejpam-5894	127	12	2025	2025	NUM
ejpam-5894	127	13	)	)	PUNCT
ejpam-5894	127	14	,	,	PUNCT
ejpam-5894	127	15	5894	5894	NUM
ejpam-5894	127	16	7	7	NUM
ejpam-5894	127	17	of	of	ADP
ejpam-5894	127	18	33	33	NUM
ejpam-5894	127	19	α(((((ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ))|(((ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ	α(((((ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ))|(((ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ	NOUN
ejpam-5894	127	20	)	)	PUNCT
ejpam-5894	127	21	)	)	PUNCT
ejpam-5894	127	22	)	)	PUNCT
ejpam-5894	127	23	)	)	PUNCT
ejpam-5894	128	1	≥	≥	PROPN
ejpam-5894	128	2	t	t	PROPN
ejpam-5894	128	3	,	,	PUNCT
ejpam-5894	128	4	and	and	CCONJ
ejpam-5894	128	5	also	also	ADV
ejpam-5894	128	6	α(ψ	α(ψ	PROPN
ejpam-5894	128	7	)	)	PUNCT
ejpam-5894	128	8	≥	≥	NOUN
ejpam-5894	128	9	t.	t.	PROPN
ejpam-5894	129	1	thus	thus	ADV
ejpam-5894	129	2	,	,	PUNCT
ejpam-5894	129	3	it	it	PRON
ejpam-5894	129	4	follows	follow	VERB
ejpam-5894	129	5	that	that	SCONJ
ejpam-5894	129	6	β(ζ	β(ζ	PRON
ejpam-5894	129	7	)	)	PUNCT
ejpam-5894	129	8	≤	≤	NUM
ejpam-5894	129	9	max{β((ζ|(η|η))|(ζ|(η|η	max{β((ζ|(η|η))|(ζ|(η|η	NOUN
ejpam-5894	129	10	)	)	PUNCT
ejpam-5894	129	11	)	)	PUNCT
ejpam-5894	129	12	)	)	PUNCT
ejpam-5894	129	13	,	,	PUNCT
ejpam-5894	129	14	β(θ	β(θ	NUM
ejpam-5894	129	15	)	)	PUNCT
ejpam-5894	129	16	}	}	PUNCT
ejpam-5894	129	17	≤	≤	NUM
ejpam-5894	129	18	s	s	PROPN
ejpam-5894	129	19	,	,	PUNCT
ejpam-5894	129	20	and	and	CCONJ
ejpam-5894	129	21	α(ξ	α(ξ	PROPN
ejpam-5894	129	22	)	)	PUNCT
ejpam-5894	129	23	≥	≥	NOUN
ejpam-5894	129	24	min{α((((ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ))|(((ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ	min{α((((ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ))|(((ξ|(ϕ|(ξ|ξ)))|(ξ|(ϕ|(ξ|ξ))))|(ψ|ψ	NOUN
ejpam-5894	129	25	)	)	PUNCT
ejpam-5894	129	26	)	)	PUNCT
ejpam-5894	129	27	)	)	PUNCT
ejpam-5894	129	28	,	,	PUNCT
ejpam-5894	129	29	α(ψ	α(ψ	PROPN
ejpam-5894	129	30	)	)	PUNCT
ejpam-5894	129	31	}	}	PUNCT
ejpam-5894	129	32	≥	≥	X
ejpam-5894	129	33	t.	t.	NOUN
ejpam-5894	129	34	hence	hence	ADV
ejpam-5894	129	35	,	,	PUNCT
ejpam-5894	129	36	(	(	PUNCT
ejpam-5894	129	37	ζ	ζ	X
ejpam-5894	129	38	,	,	PUNCT
ejpam-5894	129	39	ξ	ξ	NOUN
ejpam-5894	129	40	)	)	PUNCT
ejpam-5894	129	41	∈	∈	PROPN
ejpam-5894	129	42	l(β	l(β	PROPN
ejpam-5894	129	43	,	,	PUNCT
ejpam-5894	129	44	s	s	X
ejpam-5894	129	45	)	)	PUNCT
ejpam-5894	129	46	×	×	PROPN
ejpam-5894	129	47	u(α	u(α	PROPN
ejpam-5894	129	48	,	,	PUNCT
ejpam-5894	129	49	t	t	PROPN
ejpam-5894	129	50	)	)	PUNCT
ejpam-5894	129	51	.	.	PUNCT
ejpam-5894	130	1	therefore	therefore	ADV
ejpam-5894	130	2	,	,	PUNCT
ejpam-5894	130	3	l(β	l(β	PROPN
ejpam-5894	130	4	,	,	PUNCT
ejpam-5894	130	5	s	s	AUX
ejpam-5894	130	6	)	)	PUNCT
ejpam-5894	130	7	and	and	CCONJ
ejpam-5894	130	8	u(α	u(α	PROPN
ejpam-5894	130	9	,	,	PUNCT
ejpam-5894	130	10	t	t	PROPN
ejpam-5894	130	11	)	)	PUNCT
ejpam-5894	130	12	are	be	AUX
ejpam-5894	130	13	implicative	implicative	ADJ
ejpam-5894	130	14	wsbgideals	wsbgideal	NOUN
ejpam-5894	130	15	of	of	ADP
ejpam-5894	130	16	l.	l.	NOUN
ejpam-5894	130	17	conversely	conversely	ADV
ejpam-5894	130	18	,	,	PUNCT
ejpam-5894	130	19	assume	assume	VERB
ejpam-5894	130	20	that	that	SCONJ
ejpam-5894	130	21	l	l	NOUN
ejpam-5894	130	22	=	=	SYM
ejpam-5894	130	23	(	(	PUNCT
ejpam-5894	130	24	l	l	NOUN
ejpam-5894	130	25	,	,	PUNCT
ejpam-5894	130	26	α	α	X
ejpam-5894	130	27	,	,	PUNCT
ejpam-5894	130	28	β	β	NOUN
ejpam-5894	130	29	)	)	PUNCT
ejpam-5894	130	30	is	be	AUX
ejpam-5894	130	31	an	an	DET
ejpam-5894	130	32	intuitionistic	intuitionistic	ADJ
ejpam-5894	130	33	fuzzy	fuzzy	ADJ
ejpam-5894	130	34	set	set	NOUN
ejpam-5894	130	35	in	in	ADP
ejpam-5894	130	36	l	l	NOUN
ejpam-5894	130	37	such	such	ADJ
ejpam-5894	130	38	that	that	SCONJ
ejpam-5894	130	39	l(β	l(β	PROPN
ejpam-5894	130	40	,	,	PUNCT
ejpam-5894	130	41	s	s	PART
ejpam-5894	130	42	)	)	PUNCT
ejpam-5894	130	43	and	and	CCONJ
ejpam-5894	130	44	u(α	u(α	PROPN
ejpam-5894	130	45	,	,	PUNCT
ejpam-5894	130	46	t	t	PROPN
ejpam-5894	130	47	)	)	PUNCT
ejpam-5894	130	48	are	be	AUX
ejpam-5894	130	49	implicative	implicative	ADJ
ejpam-5894	130	50	wsbg	wsbg	NOUN
ejpam-5894	130	51	-	-	PUNCT
ejpam-5894	130	52	ideals	ideal	NOUN
ejpam-5894	130	53	of	of	ADP
ejpam-5894	130	54	l	l	NOUN
ejpam-5894	130	55	=	=	SYM
ejpam-5894	130	56	⟨l	⟨l	NOUN
ejpam-5894	130	57	;	;	PUNCT
ejpam-5894	130	58	|	|	ADV
ejpam-5894	130	59	,	,	PUNCT
ejpam-5894	130	60	0⟩	0⟩	PROPN
ejpam-5894	130	61	whenever	whenever	SCONJ
ejpam-5894	130	62	they	they	PRON
ejpam-5894	130	63	are	be	AUX
ejpam-5894	130	64	nonempty	nonempty	ADJ
ejpam-5894	130	65	for	for	ADP
ejpam-5894	130	66	all	all	DET
ejpam-5894	130	67	s	s	PROPN
ejpam-5894	130	68	,	,	PUNCT
ejpam-5894	130	69	t	t	PROPN
ejpam-5894	130	70	∈	∈	PROPN
ejpam-5894	131	1	[	[	X
ejpam-5894	131	2	0	0	NUM
ejpam-5894	131	3	,	,	PUNCT
ejpam-5894	131	4	1	1	NUM
ejpam-5894	131	5	]	]	PUNCT
ejpam-5894	131	6	.	.	PUNCT
ejpam-5894	132	1	suppose	suppose	VERB
ejpam-5894	132	2	that	that	SCONJ
ejpam-5894	132	3	β(0	β(0	NOUN
ejpam-5894	132	4	)	)	PUNCT
ejpam-5894	132	5	>	>	PUNCT
ejpam-5894	132	6	β(η	β(η	PROPN
ejpam-5894	132	7	)	)	PUNCT
ejpam-5894	132	8	for	for	ADP
ejpam-5894	132	9	some	some	DET
ejpam-5894	132	10	η	η	PROPN
ejpam-5894	132	11	∈	∈	PROPN
ejpam-5894	132	12	l.	l.	PROPN
ejpam-5894	132	13	then	then	ADV
ejpam-5894	132	14	η	η	PROPN
ejpam-5894	132	15	∈	∈	PROPN
ejpam-5894	132	16	l(β	l(β	PROPN
ejpam-5894	132	17	,	,	PUNCT
ejpam-5894	132	18	β(η	β(η	PROPN
ejpam-5894	132	19	)	)	PUNCT
ejpam-5894	132	20	)	)	PUNCT
ejpam-5894	133	1	but	but	CCONJ
ejpam-5894	133	2	0	0	NUM
ejpam-5894	133	3	/∈	/∈	PUNCT
ejpam-5894	134	1	l(β	l(β	PROPN
ejpam-5894	134	2	,	,	PUNCT
ejpam-5894	134	3	β(η	β(η	PROPN
ejpam-5894	134	4	)	)	PUNCT
ejpam-5894	134	5	)	)	PUNCT
ejpam-5894	134	6	,	,	PUNCT
ejpam-5894	134	7	a	a	DET
ejpam-5894	134	8	contradiction	contradiction	NOUN
ejpam-5894	134	9	.	.	PUNCT
ejpam-5894	135	1	hence	hence	ADV
ejpam-5894	135	2	,	,	PUNCT
ejpam-5894	135	3	β(0	β(0	PROPN
ejpam-5894	135	4	)	)	PUNCT
ejpam-5894	135	5	≤	≤	NOUN
ejpam-5894	135	6	β(ζ	β(ζ	PROPN
ejpam-5894	135	7	)	)	PUNCT
ejpam-5894	135	8	for	for	ADP
ejpam-5894	135	9	all	all	DET
ejpam-5894	135	10	ζ	ζ	PROPN
ejpam-5894	135	11	∈	∈	PROPN
ejpam-5894	135	12	l.	l.	NOUN
ejpam-5894	135	13	similarly	similarly	ADV
ejpam-5894	135	14	,	,	PUNCT
ejpam-5894	135	15	suppose	suppose	VERB
ejpam-5894	135	16	that	that	SCONJ
ejpam-5894	135	17	α(0	α(0	NOUN
ejpam-5894	135	18	)	)	PUNCT
ejpam-5894	135	19	<	<	X
ejpam-5894	135	20	α(ζ	α(ζ	NOUN
ejpam-5894	135	21	)	)	PUNCT
ejpam-5894	135	22	for	for	ADP
ejpam-5894	135	23	some	some	DET
ejpam-5894	135	24	ζ	ζ	PROPN
ejpam-5894	135	25	∈	∈	NOUN
ejpam-5894	135	26	l.	l.	NOUN
ejpam-5894	135	27	then	then	ADV
ejpam-5894	135	28	ζ	ζ	PROPN
ejpam-5894	135	29	∈	∈	PROPN
ejpam-5894	135	30	u(α	u(α	NOUN
ejpam-5894	135	31	,	,	PUNCT
ejpam-5894	135	32	α(ζ	α(ζ	NOUN
ejpam-5894	135	33	)	)	PUNCT
ejpam-5894	135	34	)	)	PUNCT
ejpam-5894	136	1	but	but	CCONJ
ejpam-5894	136	2	0	0	NUM
ejpam-5894	136	3	/∈	/∈	PUNCT
ejpam-5894	136	4	u(α	u(α	NOUN
ejpam-5894	136	5	,	,	PUNCT
ejpam-5894	136	6	α(ζ	α(ζ	NOUN
ejpam-5894	136	7	)	)	PUNCT
ejpam-5894	136	8	)	)	PUNCT
ejpam-5894	136	9	,	,	PUNCT
ejpam-5894	136	10	a	a	DET
ejpam-5894	136	11	contradiction	contradiction	NOUN
ejpam-5894	136	12	.	.	PUNCT
ejpam-5894	137	1	hence	hence	ADV
ejpam-5894	137	2	,	,	PUNCT
ejpam-5894	137	3	α(0	α(0	PROPN
ejpam-5894	137	4	)	)	PUNCT
ejpam-5894	137	5	≥	≥	NOUN
ejpam-5894	137	6	α(ζ	α(ζ	PROPN
ejpam-5894	137	7	)	)	PUNCT
ejpam-5894	137	8	for	for	ADP
ejpam-5894	137	9	all	all	DET
ejpam-5894	137	10	ζ	ζ	PROPN
ejpam-5894	137	11	∈	∈	PROPN
ejpam-5894	137	12	l.	l.	NOUN
ejpam-5894	137	13	next	next	ADV
ejpam-5894	137	14	,	,	PUNCT
ejpam-5894	137	15	suppose	suppose	VERB
ejpam-5894	137	16	that	that	SCONJ
ejpam-5894	137	17	β(η	β(η	PROPN
ejpam-5894	137	18	)	)	PUNCT
ejpam-5894	137	19	>	>	X
ejpam-5894	137	20	max{β((((η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ))|(((η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ	max{β((((η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ))|(((η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ	NOUN
ejpam-5894	137	21	)	)	PUNCT
ejpam-5894	137	22	)	)	PUNCT
ejpam-5894	137	23	)	)	PUNCT
ejpam-5894	137	24	,	,	PUNCT
ejpam-5894	137	25	β(ψ	β(ψ	NUM
ejpam-5894	137	26	)	)	PUNCT
ejpam-5894	137	27	}	}	PUNCT
ejpam-5894	137	28	or	or	CCONJ
ejpam-5894	137	29	α(ζ	α(ζ	NOUN
ejpam-5894	137	30	)	)	PUNCT
ejpam-5894	137	31	<	<	X
ejpam-5894	137	32	min{α((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	min{α((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NUM
ejpam-5894	137	33	)	)	PUNCT
ejpam-5894	137	34	)	)	PUNCT
ejpam-5894	137	35	)	)	PUNCT
ejpam-5894	137	36	,	,	PUNCT
ejpam-5894	137	37	α(θ	α(θ	NOUN
ejpam-5894	137	38	)	)	PUNCT
ejpam-5894	137	39	}	}	PUNCT
ejpam-5894	137	40	for	for	ADP
ejpam-5894	137	41	some	some	DET
ejpam-5894	137	42	η	η	PROPN
ejpam-5894	137	43	,	,	PUNCT
ejpam-5894	137	44	ϕ	ϕ	PROPN
ejpam-5894	137	45	,	,	PUNCT
ejpam-5894	137	46	ψ	ψ	NOUN
ejpam-5894	137	47	,	,	PUNCT
ejpam-5894	137	48	ζ	ζ	NOUN
ejpam-5894	137	49	,	,	PUNCT
ejpam-5894	137	50	η	η	PROPN
ejpam-5894	137	51	,	,	PUNCT
ejpam-5894	137	52	θ	θ	PROPN
ejpam-5894	137	53	∈	∈	PROPN
ejpam-5894	137	54	l.	l.	NOUN
ejpam-5894	137	55	then	then	ADV
ejpam-5894	137	56	(	(	PUNCT
ejpam-5894	137	57	(	(	PUNCT
ejpam-5894	137	58	(	(	PUNCT
ejpam-5894	137	59	(	(	PUNCT
ejpam-5894	137	60	(	(	PUNCT
ejpam-5894	137	61	η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ))|(((η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ	η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ))|(((η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ	NOUN
ejpam-5894	137	62	)	)	PUNCT
ejpam-5894	137	63	)	)	PUNCT
ejpam-5894	137	64	)	)	PUNCT
ejpam-5894	137	65	,	,	PUNCT
ejpam-5894	137	66	ψ	ψ	X
ejpam-5894	137	67	)	)	PUNCT
ejpam-5894	137	68	∈	∈	PROPN
ejpam-5894	137	69	l(β	l(β	PROPN
ejpam-5894	137	70	,	,	PUNCT
ejpam-5894	137	71	s	s	NOUN
ejpam-5894	137	72	)	)	PUNCT
ejpam-5894	137	73	,	,	PUNCT
ejpam-5894	137	74	or	or	CCONJ
ejpam-5894	137	75	(	(	PUNCT
ejpam-5894	137	76	(	(	PUNCT
ejpam-5894	137	77	(	(	PUNCT
ejpam-5894	137	78	(	(	PUNCT
ejpam-5894	137	79	(	(	PUNCT
ejpam-5894	137	80	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	137	81	)	)	PUNCT
ejpam-5894	137	82	)	)	PUNCT
ejpam-5894	137	83	)	)	PUNCT
ejpam-5894	137	84	,	,	PUNCT
ejpam-5894	137	85	θ	θ	X
ejpam-5894	137	86	)	)	PUNCT
ejpam-5894	137	87	∈	∈	PROPN
ejpam-5894	137	88	u(α	u(α	PROPN
ejpam-5894	137	89	,	,	PUNCT
ejpam-5894	137	90	t	t	PROPN
ejpam-5894	137	91	)	)	PUNCT
ejpam-5894	137	92	,	,	PUNCT
ejpam-5894	137	93	where	where	SCONJ
ejpam-5894	137	94	s	s	NOUN
ejpam-5894	137	95	=	=	SYM
ejpam-5894	137	96	max{β((((η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ))|(((η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ	max{β((((η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ))|(((η|(ϕ|(η|η)))|(η|(ϕ|(η|η))))|(ψ|ψ	NUM
ejpam-5894	137	97	)	)	PUNCT
ejpam-5894	137	98	)	)	PUNCT
ejpam-5894	137	99	)	)	PUNCT
ejpam-5894	137	100	,	,	PUNCT
ejpam-5894	137	101	β(ψ	β(ψ	NUM
ejpam-5894	137	102	)	)	PUNCT
ejpam-5894	137	103	}	}	PUNCT
ejpam-5894	137	104	and	and	CCONJ
ejpam-5894	137	105	t	t	X
ejpam-5894	137	106	=	=	SYM
ejpam-5894	137	107	min{α((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	min{α((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NUM
ejpam-5894	137	108	)	)	PUNCT
ejpam-5894	137	109	)	)	PUNCT
ejpam-5894	137	110	)	)	PUNCT
ejpam-5894	137	111	,	,	PUNCT
ejpam-5894	137	112	α(θ	α(θ	NOUN
ejpam-5894	137	113	)	)	PUNCT
ejpam-5894	137	114	}	}	PUNCT
ejpam-5894	137	115	.	.	PUNCT
ejpam-5894	138	1	but	but	CCONJ
ejpam-5894	138	2	η	η	PROPN
ejpam-5894	138	3	/∈	/∈	PROPN
ejpam-5894	138	4	l(β	l(β	PROPN
ejpam-5894	138	5	,	,	PUNCT
ejpam-5894	138	6	s	s	NOUN
ejpam-5894	138	7	)	)	PUNCT
ejpam-5894	138	8	or	or	CCONJ
ejpam-5894	138	9	ζ	ζ	NOUN
ejpam-5894	138	10	/∈	/∈	PUNCT
ejpam-5894	138	11	u(α	u(α	NOUN
ejpam-5894	138	12	,	,	PUNCT
ejpam-5894	138	13	t	t	PROPN
ejpam-5894	138	14	)	)	PUNCT
ejpam-5894	138	15	,	,	PUNCT
ejpam-5894	138	16	a	a	DET
ejpam-5894	138	17	contradiction	contradiction	NOUN
ejpam-5894	138	18	.	.	PUNCT
ejpam-5894	139	1	hence	hence	ADV
ejpam-5894	139	2	,	,	PUNCT
ejpam-5894	139	3	β(ζ	β(ζ	PROPN
ejpam-5894	139	4	)	)	PUNCT
ejpam-5894	139	5	≤	≤	NOUN
ejpam-5894	139	6	max{β((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	max{β((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	139	7	)	)	PUNCT
ejpam-5894	139	8	)	)	PUNCT
ejpam-5894	139	9	)	)	PUNCT
ejpam-5894	139	10	,	,	PUNCT
ejpam-5894	139	11	β(θ	β(θ	NUM
ejpam-5894	139	12	)	)	PUNCT
ejpam-5894	139	13	}	}	PUNCT
ejpam-5894	139	14	,	,	PUNCT
ejpam-5894	139	15	and	and	CCONJ
ejpam-5894	139	16	α(ζ	α(ζ	NOUN
ejpam-5894	139	17	)	)	PUNCT
ejpam-5894	139	18	≥	≥	NOUN
ejpam-5894	139	19	min{α((ζ|(η|η))|(ζ|(η|η	min{α((ζ|(η|η))|(ζ|(η|η	PROPN
ejpam-5894	139	20	)	)	PUNCT
ejpam-5894	139	21	)	)	PUNCT
ejpam-5894	139	22	)	)	PUNCT
ejpam-5894	139	23	,	,	PUNCT
ejpam-5894	139	24	α(θ	α(θ	NOUN
ejpam-5894	139	25	)	)	PUNCT
ejpam-5894	139	26	}	}	PUNCT
ejpam-5894	139	27	for	for	ADP
ejpam-5894	139	28	all	all	DET
ejpam-5894	139	29	ζ	ζ	NOUN
ejpam-5894	139	30	,	,	PUNCT
ejpam-5894	139	31	η	η	PROPN
ejpam-5894	139	32	,	,	PUNCT
ejpam-5894	139	33	θ	θ	PROPN
ejpam-5894	139	34	∈	∈	PROPN
ejpam-5894	139	35	l.	l.	PROPN
ejpam-5894	139	36	consequently	consequently	ADV
ejpam-5894	139	37	,	,	PUNCT
ejpam-5894	139	38	l	l	PROPN
ejpam-5894	139	39	=	=	SYM
ejpam-5894	139	40	(	(	PUNCT
ejpam-5894	139	41	l	l	NOUN
ejpam-5894	139	42	,	,	PUNCT
ejpam-5894	139	43	α	α	X
ejpam-5894	139	44	,	,	PUNCT
ejpam-5894	139	45	β	β	NOUN
ejpam-5894	139	46	)	)	PUNCT
ejpam-5894	139	47	is	be	AUX
ejpam-5894	139	48	an	an	DET
ejpam-5894	139	49	intuitionistic	intuitionistic	ADJ
ejpam-5894	139	50	fuzzy	fuzzy	ADJ
ejpam-5894	139	51	implicative	implicative	ADJ
ejpam-5894	139	52	wsbgideal	wsbgideal	NOUN
ejpam-5894	139	53	of	of	ADP
ejpam-5894	139	54	l.	l.	PROPN
ejpam-5894	139	55	t.	t.	PROPN
ejpam-5894	139	56	oner	oner	PROPN
ejpam-5894	139	57	et	et	PROPN
ejpam-5894	139	58	al	al	PROPN
ejpam-5894	139	59	.	.	PUNCT
ejpam-5894	139	60	/	/	SYM
ejpam-5894	139	61	eur	eur	PROPN
ejpam-5894	139	62	.	.	PUNCT
ejpam-5894	140	1	j.	j.	PROPN
ejpam-5894	140	2	pure	pure	PROPN
ejpam-5894	140	3	appl	appl	PROPN
ejpam-5894	140	4	.	.	PROPN
ejpam-5894	140	5	math	math	PROPN
ejpam-5894	140	6	,	,	PUNCT
ejpam-5894	140	7	18	18	NUM
ejpam-5894	140	8	(	(	PUNCT
ejpam-5894	140	9	3	3	NUM
ejpam-5894	140	10	)	)	PUNCT
ejpam-5894	140	11	(	(	PUNCT
ejpam-5894	140	12	2025	2025	NUM
ejpam-5894	140	13	)	)	PUNCT
ejpam-5894	140	14	,	,	PUNCT
ejpam-5894	140	15	5894	5894	NUM
ejpam-5894	140	16	8	8	NUM
ejpam-5894	140	17	of	of	ADP
ejpam-5894	140	18	33	33	NUM
ejpam-5894	140	19	theorem	theorem	NOUN
ejpam-5894	140	20	2	2	NUM
ejpam-5894	140	21	.	.	PUNCT
ejpam-5894	140	22	an	an	DET
ejpam-5894	140	23	intuitionistic	intuitionistic	ADJ
ejpam-5894	140	24	fuzzy	fuzzy	ADJ
ejpam-5894	140	25	set	set	NOUN
ejpam-5894	140	26	l	l	NOUN
ejpam-5894	140	27	=	=	SYM
ejpam-5894	140	28	(	(	PUNCT
ejpam-5894	140	29	l	l	NOUN
ejpam-5894	140	30	,	,	PUNCT
ejpam-5894	140	31	α	α	X
ejpam-5894	140	32	,	,	PUNCT
ejpam-5894	140	33	β	β	NOUN
ejpam-5894	140	34	)	)	PUNCT
ejpam-5894	140	35	in	in	ADP
ejpam-5894	140	36	a	a	DET
ejpam-5894	140	37	wsbg	wsbg	ADV
ejpam-5894	140	38	-	-	PUNCT
ejpam-5894	140	39	algebra	algebra	NOUN
ejpam-5894	140	40	l	l	NOUN
ejpam-5894	140	41	=	=	PUNCT
ejpam-5894	140	42	⟨l	⟨l	NOUN
ejpam-5894	140	43	;	;	PUNCT
ejpam-5894	140	44	|	|	ADV
ejpam-5894	140	45	,	,	PUNCT
ejpam-5894	140	46	0⟩	0⟩	PROPN
ejpam-5894	140	47	is	be	AUX
ejpam-5894	140	48	an	an	DET
ejpam-5894	140	49	intuitionistic	intuitionistic	ADJ
ejpam-5894	140	50	fuzzy	fuzzy	ADJ
ejpam-5894	140	51	implicative	implicative	ADJ
ejpam-5894	140	52	wsbg	wsbg	NOUN
ejpam-5894	140	53	-	-	PUNCT
ejpam-5894	140	54	ideal	ideal	NOUN
ejpam-5894	140	55	of	of	ADP
ejpam-5894	140	56	l	l	NOUN
ejpam-5894	140	57	if	if	SCONJ
ejpam-5894	141	1	and	and	CCONJ
ejpam-5894	141	2	only	only	ADV
ejpam-5894	141	3	if	if	SCONJ
ejpam-5894	141	4	the	the	DET
ejpam-5894	141	5	fuzzy	fuzzy	ADJ
ejpam-5894	141	6	sets	set	VERB
ejpam-5894	141	7	β	β	PROPN
ejpam-5894	141	8	and	and	CCONJ
ejpam-5894	141	9	α	α	PROPN
ejpam-5894	141	10	are	be	AUX
ejpam-5894	141	11	fuzzy	fuzzy	ADJ
ejpam-5894	141	12	implicative	implicative	ADJ
ejpam-5894	141	13	wsbg	wsbg	NOUN
ejpam-5894	141	14	-	-	PUNCT
ejpam-5894	141	15	ideals	ideal	NOUN
ejpam-5894	141	16	of	of	ADP
ejpam-5894	141	17	l	l	NOUN
ejpam-5894	141	18	,	,	PUNCT
ejpam-5894	141	19	where	where	SCONJ
ejpam-5894	141	20	β	β	X
ejpam-5894	141	21	:	:	PUNCT
ejpam-5894	141	22	l→	l→	X
ejpam-5894	142	1	[	[	X
ejpam-5894	142	2	0	0	NUM
ejpam-5894	142	3	,	,	PUNCT
ejpam-5894	142	4	1	1	NUM
ejpam-5894	142	5	]	]	PUNCT
ejpam-5894	142	6	is	be	AUX
ejpam-5894	142	7	defined	define	VERB
ejpam-5894	142	8	by	by	ADP
ejpam-5894	142	9	β(ζ	β(ζ	PROPN
ejpam-5894	142	10	)	)	PUNCT
ejpam-5894	143	1	=	=	SYM
ejpam-5894	143	2	1−β(ζ	1−β(ζ	NUM
ejpam-5894	143	3	)	)	PUNCT
ejpam-5894	143	4	for	for	ADP
ejpam-5894	143	5	all	all	DET
ejpam-5894	143	6	ζ	ζ	PROPN
ejpam-5894	143	7	∈	∈	NOUN
ejpam-5894	143	8	l.	l.	NOUN
ejpam-5894	143	9	proof	proof	PROPN
ejpam-5894	143	10	.	.	PUNCT
ejpam-5894	144	1	assume	assume	VERB
ejpam-5894	144	2	that	that	SCONJ
ejpam-5894	144	3	l	l	NOUN
ejpam-5894	144	4	=	=	SYM
ejpam-5894	144	5	(	(	PUNCT
ejpam-5894	144	6	l	l	NOUN
ejpam-5894	144	7	,	,	PUNCT
ejpam-5894	144	8	α	α	X
ejpam-5894	144	9	,	,	PUNCT
ejpam-5894	144	10	β	β	NOUN
ejpam-5894	144	11	)	)	PUNCT
ejpam-5894	144	12	is	be	AUX
ejpam-5894	144	13	an	an	DET
ejpam-5894	144	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	144	15	fuzzy	fuzzy	ADJ
ejpam-5894	144	16	implicative	implicative	ADJ
ejpam-5894	144	17	wsbg	wsbg	NOUN
ejpam-5894	144	18	-	-	PUNCT
ejpam-5894	144	19	ideal	ideal	NOUN
ejpam-5894	144	20	of	of	ADP
ejpam-5894	144	21	l	l	NOUN
ejpam-5894	144	22	=	=	SYM
ejpam-5894	144	23	⟨l	⟨l	NOUN
ejpam-5894	144	24	;	;	PUNCT
ejpam-5894	144	25	|	|	ADV
ejpam-5894	144	26	,	,	PUNCT
ejpam-5894	144	27	0⟩.	0⟩.	VERB
ejpam-5894	144	28	by	by	ADP
ejpam-5894	144	29	definition	definition	NOUN
ejpam-5894	144	30	,	,	PUNCT
ejpam-5894	144	31	α	α	PROPN
ejpam-5894	144	32	is	be	AUX
ejpam-5894	144	33	a	a	DET
ejpam-5894	144	34	fuzzy	fuzzy	ADJ
ejpam-5894	144	35	implicative	implicative	ADJ
ejpam-5894	144	36	wsbg	wsbg	NOUN
ejpam-5894	144	37	-	-	PUNCT
ejpam-5894	144	38	ideal	ideal	NOUN
ejpam-5894	144	39	of	of	ADP
ejpam-5894	144	40	l.	l.	PROPN
ejpam-5894	144	41	we	we	PRON
ejpam-5894	144	42	now	now	ADV
ejpam-5894	144	43	show	show	VERB
ejpam-5894	144	44	that	that	SCONJ
ejpam-5894	144	45	β	β	NOUN
ejpam-5894	144	46	is	be	AUX
ejpam-5894	144	47	also	also	ADV
ejpam-5894	144	48	a	a	DET
ejpam-5894	144	49	fuzzy	fuzzy	ADJ
ejpam-5894	144	50	implicative	implicative	ADJ
ejpam-5894	144	51	wsbg	wsbg	NOUN
ejpam-5894	144	52	-	-	PUNCT
ejpam-5894	144	53	ideal	ideal	NOUN
ejpam-5894	144	54	of	of	ADP
ejpam-5894	144	55	l.	l.	NOUN
ejpam-5894	144	56	for	for	ADP
ejpam-5894	144	57	all	all	DET
ejpam-5894	144	58	ζ	ζ	PROPN
ejpam-5894	144	59	,	,	PUNCT
ejpam-5894	144	60	η	η	PROPN
ejpam-5894	144	61	,	,	PUNCT
ejpam-5894	144	62	θ	θ	PROPN
ejpam-5894	144	63	∈	∈	PROPN
ejpam-5894	144	64	l	l	NOUN
ejpam-5894	144	65	,	,	PUNCT
ejpam-5894	144	66	we	we	PRON
ejpam-5894	144	67	have	have	VERB
ejpam-5894	144	68	β(0	β(0	NOUN
ejpam-5894	144	69	)	)	PUNCT
ejpam-5894	145	1	=	=	SYM
ejpam-5894	145	2	1−	1−	NUM
ejpam-5894	145	3	β(0	β(0	PROPN
ejpam-5894	145	4	)	)	PUNCT
ejpam-5894	145	5	≥	≥	NOUN
ejpam-5894	145	6	1−	1−	NUM
ejpam-5894	145	7	β(ζ	β(ζ	PROPN
ejpam-5894	145	8	)	)	PUNCT
ejpam-5894	145	9	=	=	SYM
ejpam-5894	145	10	β(ζ	β(ζ	PROPN
ejpam-5894	145	11	)	)	PUNCT
ejpam-5894	145	12	,	,	PUNCT
ejpam-5894	145	13	and	and	CCONJ
ejpam-5894	145	14	β(ζ	β(ζ	NUM
ejpam-5894	145	15	)	)	PUNCT
ejpam-5894	145	16	=	=	SYM
ejpam-5894	146	1	1−	1−	NUM
ejpam-5894	146	2	β(ζ	β(ζ	NUM
ejpam-5894	146	3	)	)	PUNCT
ejpam-5894	146	4	≥	≥	NOUN
ejpam-5894	146	5	1−max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	1−max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NUM
ejpam-5894	146	6	)	)	PUNCT
ejpam-5894	146	7	)	)	PUNCT
ejpam-5894	146	8	)	)	PUNCT
ejpam-5894	146	9	)	)	PUNCT
ejpam-5894	146	10	,	,	PUNCT
ejpam-5894	146	11	β(θ	β(θ	NUM
ejpam-5894	146	12	)	)	PUNCT
ejpam-5894	146	13	}	}	PUNCT
ejpam-5894	146	14	=	=	PUNCT
ejpam-5894	146	15	min{1−	min{1−	VERB
ejpam-5894	146	16	β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	146	17	)	)	PUNCT
ejpam-5894	146	18	)	)	PUNCT
ejpam-5894	146	19	)	)	PUNCT
ejpam-5894	146	20	)	)	PUNCT
ejpam-5894	146	21	,	,	PUNCT
ejpam-5894	146	22	1−	1−	NUM
ejpam-5894	146	23	β(θ	β(θ	NUM
ejpam-5894	146	24	)	)	PUNCT
ejpam-5894	146	25	}	}	PUNCT
ejpam-5894	146	26	=	=	SYM
ejpam-5894	146	27	min{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	min{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	146	28	)	)	PUNCT
ejpam-5894	146	29	)	)	PUNCT
ejpam-5894	146	30	)	)	PUNCT
ejpam-5894	146	31	)	)	PUNCT
ejpam-5894	146	32	,	,	PUNCT
ejpam-5894	146	33	β(θ	β(θ	NUM
ejpam-5894	146	34	)	)	PUNCT
ejpam-5894	146	35	}	}	PUNCT
ejpam-5894	146	36	.	.	PUNCT
ejpam-5894	147	1	thus	thus	ADV
ejpam-5894	147	2	,	,	PUNCT
ejpam-5894	147	3	β	β	X
ejpam-5894	147	4	is	be	AUX
ejpam-5894	147	5	a	a	DET
ejpam-5894	147	6	fuzzy	fuzzy	ADJ
ejpam-5894	147	7	implicative	implicative	ADJ
ejpam-5894	147	8	wsbg	wsbg	NOUN
ejpam-5894	147	9	-	-	PUNCT
ejpam-5894	147	10	ideal	ideal	NOUN
ejpam-5894	147	11	of	of	ADP
ejpam-5894	147	12	l.	l.	NOUN
ejpam-5894	147	13	conversely	conversely	ADV
ejpam-5894	147	14	,	,	PUNCT
ejpam-5894	147	15	assume	assume	VERB
ejpam-5894	147	16	that	that	SCONJ
ejpam-5894	147	17	β	β	PROPN
ejpam-5894	147	18	and	and	CCONJ
ejpam-5894	147	19	α	α	PROPN
ejpam-5894	147	20	are	be	AUX
ejpam-5894	147	21	fuzzy	fuzzy	ADJ
ejpam-5894	147	22	implicative	implicative	ADJ
ejpam-5894	147	23	wsbg	wsbg	NOUN
ejpam-5894	147	24	-	-	PUNCT
ejpam-5894	147	25	ideals	ideal	NOUN
ejpam-5894	147	26	of	of	ADP
ejpam-5894	147	27	l	l	NOUN
ejpam-5894	147	28	=	=	SYM
ejpam-5894	147	29	⟨l	⟨l	NOUN
ejpam-5894	147	30	;	;	PUNCT
ejpam-5894	147	31	|	|	ADV
ejpam-5894	147	32	,	,	PUNCT
ejpam-5894	147	33	0⟩.	0⟩.	NOUN
ejpam-5894	147	34	to	to	PART
ejpam-5894	147	35	show	show	VERB
ejpam-5894	147	36	that	that	SCONJ
ejpam-5894	147	37	l	l	NOUN
ejpam-5894	147	38	=	=	SYM
ejpam-5894	147	39	(	(	PUNCT
ejpam-5894	147	40	l	l	NOUN
ejpam-5894	147	41	,	,	PUNCT
ejpam-5894	147	42	α	α	X
ejpam-5894	147	43	,	,	PUNCT
ejpam-5894	147	44	β	β	NOUN
ejpam-5894	147	45	)	)	PUNCT
ejpam-5894	147	46	is	be	AUX
ejpam-5894	147	47	an	an	DET
ejpam-5894	147	48	intuitionistic	intuitionistic	ADJ
ejpam-5894	147	49	fuzzy	fuzzy	ADJ
ejpam-5894	147	50	implicative	implicative	ADJ
ejpam-5894	147	51	wsbg	wsbg	NOUN
ejpam-5894	147	52	-	-	PUNCT
ejpam-5894	147	53	ideal	ideal	ADJ
ejpam-5894	147	54	,	,	PUNCT
ejpam-5894	147	55	let	let	VERB
ejpam-5894	147	56	ζ	ζ	NOUN
ejpam-5894	147	57	,	,	PUNCT
ejpam-5894	147	58	η	η	PROPN
ejpam-5894	147	59	,	,	PUNCT
ejpam-5894	147	60	θ	θ	PROPN
ejpam-5894	147	61	∈	∈	PROPN
ejpam-5894	147	62	l.	l.	NOUN
ejpam-5894	147	63	then	then	ADV
ejpam-5894	147	64	:	:	PUNCT
ejpam-5894	147	65	1−	1−	NUM
ejpam-5894	147	66	β(0	β(0	NOUN
ejpam-5894	147	67	)	)	PUNCT
ejpam-5894	147	68	=	=	SYM
ejpam-5894	147	69	β(0	β(0	PROPN
ejpam-5894	147	70	)	)	PUNCT
ejpam-5894	147	71	≥	≥	NOUN
ejpam-5894	147	72	β(ζ	β(ζ	NUM
ejpam-5894	147	73	)	)	PUNCT
ejpam-5894	147	74	=	=	SYM
ejpam-5894	148	1	1−	1−	NUM
ejpam-5894	148	2	β(ζ	β(ζ	NUM
ejpam-5894	148	3	)	)	PUNCT
ejpam-5894	148	4	,	,	PUNCT
ejpam-5894	148	5	β(0	β(0	PROPN
ejpam-5894	148	6	)	)	PUNCT
ejpam-5894	148	7	≤	≤	NOUN
ejpam-5894	148	8	β(ζ	β(ζ	PROPN
ejpam-5894	148	9	)	)	PUNCT
ejpam-5894	148	10	.	.	PUNCT
ejpam-5894	149	1	furthermore	furthermore	ADV
ejpam-5894	149	2	,	,	PUNCT
ejpam-5894	149	3	we	we	PRON
ejpam-5894	149	4	have	have	VERB
ejpam-5894	149	5	1−	1−	NUM
ejpam-5894	149	6	β(ζ	β(ζ	NUM
ejpam-5894	149	7	)	)	PUNCT
ejpam-5894	149	8	=	=	SYM
ejpam-5894	149	9	β(ζ	β(ζ	PROPN
ejpam-5894	149	10	)	)	PUNCT
ejpam-5894	149	11	≥	≥	NOUN
ejpam-5894	149	12	min{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	min{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	149	13	)	)	PUNCT
ejpam-5894	149	14	)	)	PUNCT
ejpam-5894	149	15	)	)	PUNCT
ejpam-5894	149	16	)	)	PUNCT
ejpam-5894	149	17	,	,	PUNCT
ejpam-5894	149	18	β(θ	β(θ	NUM
ejpam-5894	149	19	)	)	PUNCT
ejpam-5894	149	20	}	}	PUNCT
ejpam-5894	149	21	=	=	PUNCT
ejpam-5894	149	22	min{1−	min{1−	VERB
ejpam-5894	149	23	β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	149	24	)	)	PUNCT
ejpam-5894	149	25	)	)	PUNCT
ejpam-5894	149	26	)	)	PUNCT
ejpam-5894	149	27	)	)	PUNCT
ejpam-5894	149	28	,	,	PUNCT
ejpam-5894	149	29	1−	1−	NUM
ejpam-5894	149	30	β(θ	β(θ	NUM
ejpam-5894	149	31	)	)	PUNCT
ejpam-5894	149	32	}	}	PUNCT
ejpam-5894	149	33	=	=	SYM
ejpam-5894	149	34	1−max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	1−max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NUM
ejpam-5894	149	35	)	)	PUNCT
ejpam-5894	149	36	)	)	PUNCT
ejpam-5894	149	37	)	)	PUNCT
ejpam-5894	149	38	)	)	PUNCT
ejpam-5894	149	39	,	,	PUNCT
ejpam-5894	149	40	β(θ	β(θ	NUM
ejpam-5894	149	41	)	)	PUNCT
ejpam-5894	149	42	}	}	PUNCT
ejpam-5894	149	43	,	,	PUNCT
ejpam-5894	149	44	β(ζ	β(ζ	PROPN
ejpam-5894	149	45	)	)	PUNCT
ejpam-5894	149	46	≤	≤	NOUN
ejpam-5894	149	47	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	149	48	)	)	PUNCT
ejpam-5894	149	49	)	)	PUNCT
ejpam-5894	149	50	)	)	PUNCT
ejpam-5894	149	51	)	)	PUNCT
ejpam-5894	149	52	,	,	PUNCT
ejpam-5894	149	53	β(θ	β(θ	NUM
ejpam-5894	149	54	)	)	PUNCT
ejpam-5894	149	55	}	}	PUNCT
ejpam-5894	149	56	.	.	PUNCT
ejpam-5894	150	1	thus	thus	ADV
ejpam-5894	150	2	,	,	PUNCT
ejpam-5894	150	3	l	l	NOUN
ejpam-5894	150	4	=	=	SYM
ejpam-5894	150	5	(	(	PUNCT
ejpam-5894	150	6	l	l	NOUN
ejpam-5894	150	7	,	,	PUNCT
ejpam-5894	150	8	α	α	X
ejpam-5894	150	9	,	,	PUNCT
ejpam-5894	150	10	β	β	NOUN
ejpam-5894	150	11	)	)	PUNCT
ejpam-5894	150	12	is	be	AUX
ejpam-5894	150	13	an	an	DET
ejpam-5894	150	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	150	15	fuzzy	fuzzy	ADJ
ejpam-5894	150	16	implicative	implicative	ADJ
ejpam-5894	150	17	wsbg	wsbg	NOUN
ejpam-5894	150	18	-	-	PUNCT
ejpam-5894	150	19	ideal	ideal	NOUN
ejpam-5894	150	20	of	of	ADP
ejpam-5894	150	21	l.	l.	PROPN
ejpam-5894	150	22	theorem	theorem	PROPN
ejpam-5894	150	23	3	3	X
ejpam-5894	150	24	.	.	PUNCT
ejpam-5894	151	1	let	let	VERB
ejpam-5894	151	2	f	f	PRON
ejpam-5894	151	3	be	be	AUX
ejpam-5894	151	4	a	a	DET
ejpam-5894	151	5	nonempty	nonempty	ADJ
ejpam-5894	151	6	subset	subset	NOUN
ejpam-5894	151	7	of	of	ADP
ejpam-5894	151	8	a	a	DET
ejpam-5894	151	9	wsbg	wsbg	ADV
ejpam-5894	151	10	-	-	PUNCT
ejpam-5894	151	11	algebra	algebra	NOUN
ejpam-5894	151	12	l	l	NOUN
ejpam-5894	151	13	=	=	PUNCT
ejpam-5894	151	14	⟨l	⟨l	NOUN
ejpam-5894	151	15	;	;	PUNCT
ejpam-5894	151	16	|	|	ADV
ejpam-5894	151	17	,	,	PUNCT
ejpam-5894	151	18	0⟩.	0⟩.	PROPN
ejpam-5894	151	19	define	define	VERB
ejpam-5894	151	20	an	an	DET
ejpam-5894	151	21	intuitionistic	intuitionistic	ADJ
ejpam-5894	151	22	fuzzy	fuzzy	ADJ
ejpam-5894	151	23	set	set	VERB
ejpam-5894	151	24	lf	lf	NOUN
ejpam-5894	151	25	=	=	SYM
ejpam-5894	151	26	(	(	PUNCT
ejpam-5894	151	27	l	l	NOUN
ejpam-5894	151	28	,	,	PUNCT
ejpam-5894	151	29	βf	βf	INTJ
ejpam-5894	151	30	,	,	PUNCT
ejpam-5894	151	31	αf	αf	NOUN
ejpam-5894	151	32	)	)	PUNCT
ejpam-5894	151	33	in	in	ADP
ejpam-5894	151	34	l	l	NOUN
ejpam-5894	151	35	as	as	SCONJ
ejpam-5894	151	36	follows	follow	VERB
ejpam-5894	151	37	:	:	PUNCT
ejpam-5894	151	38	αf	αf	ADP
ejpam-5894	151	39	:	:	PUNCT
ejpam-5894	151	40	l→	l→	NOUN
ejpam-5894	151	41	[	[	X
ejpam-5894	151	42	0	0	NUM
ejpam-5894	151	43	,	,	PUNCT
ejpam-5894	151	44	1	1	NUM
ejpam-5894	151	45	]	]	PUNCT
ejpam-5894	151	46	,	,	PUNCT
ejpam-5894	151	47	ζ	ζ	PROPN
ejpam-5894	151	48	7→	7→	NUM
ejpam-5894	151	49	{	{	PUNCT
ejpam-5894	151	50	α0	α0	ADJ
ejpam-5894	151	51	if	if	SCONJ
ejpam-5894	151	52	ζ	ζ	NOUN
ejpam-5894	151	53	∈	∈	PROPN
ejpam-5894	151	54	f	f	X
ejpam-5894	151	55	,	,	PUNCT
ejpam-5894	151	56	α1	α1	PROPN
ejpam-5894	151	57	otherwise	otherwise	ADV
ejpam-5894	151	58	,	,	PUNCT
ejpam-5894	151	59	t.	t.	PROPN
ejpam-5894	151	60	oner	oner	NOUN
ejpam-5894	151	61	et	et	PROPN
ejpam-5894	151	62	al	al	PROPN
ejpam-5894	151	63	.	.	PUNCT
ejpam-5894	151	64	/	/	SYM
ejpam-5894	151	65	eur	eur	PROPN
ejpam-5894	151	66	.	.	PUNCT
ejpam-5894	152	1	j.	j.	PROPN
ejpam-5894	152	2	pure	pure	PROPN
ejpam-5894	152	3	appl	appl	PROPN
ejpam-5894	152	4	.	.	PROPN
ejpam-5894	152	5	math	math	PROPN
ejpam-5894	152	6	,	,	PUNCT
ejpam-5894	152	7	18	18	NUM
ejpam-5894	152	8	(	(	PUNCT
ejpam-5894	152	9	3	3	NUM
ejpam-5894	152	10	)	)	PUNCT
ejpam-5894	152	11	(	(	PUNCT
ejpam-5894	152	12	2025	2025	NUM
ejpam-5894	152	13	)	)	PUNCT
ejpam-5894	152	14	,	,	PUNCT
ejpam-5894	152	15	5894	5894	NUM
ejpam-5894	152	16	9	9	NUM
ejpam-5894	152	17	of	of	ADP
ejpam-5894	152	18	33	33	NUM
ejpam-5894	152	19	βf	βf	NOUN
ejpam-5894	152	20	:	:	PUNCT
ejpam-5894	152	21	l→	l→	NOUN
ejpam-5894	153	1	[	[	X
ejpam-5894	153	2	0	0	NUM
ejpam-5894	153	3	,	,	PUNCT
ejpam-5894	153	4	1	1	NUM
ejpam-5894	153	5	]	]	PUNCT
ejpam-5894	153	6	,	,	PUNCT
ejpam-5894	153	7	ζ	ζ	PROPN
ejpam-5894	153	8	7→	7→	NUM
ejpam-5894	153	9	{	{	PUNCT
ejpam-5894	153	10	β0	β0	NOUN
ejpam-5894	153	11	if	if	SCONJ
ejpam-5894	153	12	ζ	ζ	NOUN
ejpam-5894	153	13	∈	∈	PROPN
ejpam-5894	153	14	f	f	NOUN
ejpam-5894	153	15	,	,	PUNCT
ejpam-5894	153	16	β1	β1	PROPN
ejpam-5894	153	17	otherwise	otherwise	ADV
ejpam-5894	153	18	,	,	PUNCT
ejpam-5894	153	19	for	for	ADP
ejpam-5894	153	20	all	all	DET
ejpam-5894	153	21	ζ	ζ	NOUN
ejpam-5894	153	22	∈	∈	PROPN
ejpam-5894	153	23	l	l	NOUN
ejpam-5894	153	24	,	,	PUNCT
ejpam-5894	153	25	where	where	SCONJ
ejpam-5894	153	26	αi	αi	VERB
ejpam-5894	153	27	,	,	PUNCT
ejpam-5894	153	28	βi	βi	PRON
ejpam-5894	153	29	∈	∈	PROPN
ejpam-5894	154	1	[	[	X
ejpam-5894	154	2	0	0	NUM
ejpam-5894	154	3	,	,	PUNCT
ejpam-5894	154	4	1	1	NUM
ejpam-5894	154	5	]	]	PUNCT
ejpam-5894	154	6	satisfy	satisfy	NOUN
ejpam-5894	154	7	α0	α0	PROPN
ejpam-5894	154	8	>	>	X
ejpam-5894	154	9	α1	α1	PROPN
ejpam-5894	154	10	,	,	PUNCT
ejpam-5894	154	11	β0	β0	NOUN
ejpam-5894	154	12	<	<	X
ejpam-5894	154	13	β1	β1	PROPN
ejpam-5894	154	14	,	,	PUNCT
ejpam-5894	154	15	and	and	CCONJ
ejpam-5894	154	16	αi	αi	VERB
ejpam-5894	155	1	+	+	CCONJ
ejpam-5894	155	2	βi	βi	VERB
ejpam-5894	155	3	≤	≤	NUM
ejpam-5894	155	4	1	1	NUM
ejpam-5894	155	5	for	for	ADP
ejpam-5894	155	6	i	i	PRON
ejpam-5894	155	7	=	=	SYM
ejpam-5894	155	8	0	0	NUM
ejpam-5894	155	9	,	,	PUNCT
ejpam-5894	155	10	1	1	NUM
ejpam-5894	155	11	.	.	PUNCT
ejpam-5894	155	12	then	then	ADV
ejpam-5894	155	13	lf	lf	ADV
ejpam-5894	155	14	=	=	SYM
ejpam-5894	155	15	(	(	PUNCT
ejpam-5894	155	16	l	l	NOUN
ejpam-5894	155	17	,	,	PUNCT
ejpam-5894	155	18	βf	βf	INTJ
ejpam-5894	155	19	,	,	PUNCT
ejpam-5894	155	20	αf	αf	PROPN
ejpam-5894	155	21	)	)	PUNCT
ejpam-5894	155	22	is	be	AUX
ejpam-5894	155	23	an	an	DET
ejpam-5894	155	24	intuitionistic	intuitionistic	ADJ
ejpam-5894	155	25	fuzzy	fuzzy	ADJ
ejpam-5894	155	26	implicative	implicative	ADJ
ejpam-5894	155	27	wsbg	wsbg	NOUN
ejpam-5894	155	28	-	-	PUNCT
ejpam-5894	155	29	ideal	ideal	NOUN
ejpam-5894	155	30	of	of	ADP
ejpam-5894	155	31	l	l	NOUN
ejpam-5894	155	32	if	if	SCONJ
ejpam-5894	156	1	and	and	CCONJ
ejpam-5894	156	2	only	only	ADV
ejpam-5894	156	3	if	if	SCONJ
ejpam-5894	156	4	f	f	PROPN
ejpam-5894	156	5	is	be	AUX
ejpam-5894	156	6	an	an	DET
ejpam-5894	156	7	implicative	implicative	ADJ
ejpam-5894	156	8	wsbg	wsbg	ADV
ejpam-5894	156	9	-	-	PUNCT
ejpam-5894	156	10	ideal	ideal	NOUN
ejpam-5894	156	11	of	of	ADP
ejpam-5894	156	12	l.	l.	PROPN
ejpam-5894	156	13	proof	proof	PROPN
ejpam-5894	156	14	.	.	PUNCT
ejpam-5894	157	1	assume	assume	VERB
ejpam-5894	157	2	that	that	SCONJ
ejpam-5894	157	3	lf	lf	NOUN
ejpam-5894	157	4	=	=	SYM
ejpam-5894	157	5	(	(	PUNCT
ejpam-5894	157	6	l	l	NOUN
ejpam-5894	157	7	,	,	PUNCT
ejpam-5894	157	8	βf	βf	INTJ
ejpam-5894	157	9	,	,	PUNCT
ejpam-5894	157	10	αf	αf	PROPN
ejpam-5894	157	11	)	)	PUNCT
ejpam-5894	157	12	is	be	AUX
ejpam-5894	157	13	an	an	DET
ejpam-5894	157	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	157	15	fuzzy	fuzzy	ADJ
ejpam-5894	157	16	implicative	implicative	ADJ
ejpam-5894	157	17	wsbg	wsbg	NOUN
ejpam-5894	157	18	-	-	PUNCT
ejpam-5894	157	19	ideal	ideal	NOUN
ejpam-5894	157	20	of	of	ADP
ejpam-5894	157	21	l	l	NOUN
ejpam-5894	157	22	=	=	SYM
ejpam-5894	157	23	⟨l	⟨l	NOUN
ejpam-5894	157	24	;	;	PUNCT
ejpam-5894	157	25	|	|	ADV
ejpam-5894	157	26	,	,	PUNCT
ejpam-5894	157	27	0⟩.	0⟩.	PROPN
ejpam-5894	157	28	let	let	VERB
ejpam-5894	157	29	ζ	ζ	NOUN
ejpam-5894	157	30	,	,	PUNCT
ejpam-5894	157	31	η	η	PROPN
ejpam-5894	157	32	,	,	PUNCT
ejpam-5894	157	33	θ	θ	PROPN
ejpam-5894	157	34	∈	∈	PROPN
ejpam-5894	157	35	l	l	NOUN
ejpam-5894	157	36	be	be	AUX
ejpam-5894	157	37	such	such	ADJ
ejpam-5894	157	38	that	that	SCONJ
ejpam-5894	157	39	ζ	ζ	NOUN
ejpam-5894	157	40	,	,	PUNCT
ejpam-5894	157	41	η	η	PROPN
ejpam-5894	157	42	∈	∈	PROPN
ejpam-5894	157	43	f	f	X
ejpam-5894	157	44	.	.	PUNCT
ejpam-5894	158	1	then	then	ADV
ejpam-5894	158	2	αf	αf	VERB
ejpam-5894	158	3	(	(	PUNCT
ejpam-5894	158	4	0	0	NUM
ejpam-5894	158	5	)	)	PUNCT
ejpam-5894	158	6	≥	≥	NOUN
ejpam-5894	158	7	αf	αf	X
ejpam-5894	158	8	(	(	PUNCT
ejpam-5894	158	9	ζ	ζ	NOUN
ejpam-5894	158	10	)	)	PUNCT
ejpam-5894	158	11	=	=	SYM
ejpam-5894	159	1	α0	α0	ADJ
ejpam-5894	159	2	and	and	CCONJ
ejpam-5894	159	3	βf	βf	INTJ
ejpam-5894	159	4	(	(	PUNCT
ejpam-5894	159	5	0	0	X
ejpam-5894	159	6	)	)	PUNCT
ejpam-5894	159	7	≤	≤	NOUN
ejpam-5894	160	1	βf	βf	CCONJ
ejpam-5894	160	2	(	(	PUNCT
ejpam-5894	160	3	ζ	ζ	NOUN
ejpam-5894	160	4	)	)	PUNCT
ejpam-5894	160	5	=	=	SYM
ejpam-5894	160	6	β0	β0	NOUN
ejpam-5894	160	7	.	.	PUNCT
ejpam-5894	161	1	thus	thus	ADV
ejpam-5894	161	2	,	,	PUNCT
ejpam-5894	161	3	αf	αf	ADP
ejpam-5894	161	4	(	(	PUNCT
ejpam-5894	161	5	0	0	NUM
ejpam-5894	161	6	)	)	PUNCT
ejpam-5894	161	7	=	=	SYM
ejpam-5894	162	1	α0	α0	ADJ
ejpam-5894	162	2	and	and	CCONJ
ejpam-5894	162	3	βf	βf	INTJ
ejpam-5894	162	4	(	(	PUNCT
ejpam-5894	162	5	0	0	NUM
ejpam-5894	162	6	)	)	PUNCT
ejpam-5894	162	7	=	=	SYM
ejpam-5894	162	8	β0	β0	NOUN
ejpam-5894	162	9	,	,	PUNCT
ejpam-5894	162	10	which	which	PRON
ejpam-5894	162	11	implies	imply	VERB
ejpam-5894	162	12	0	0	NUM
ejpam-5894	162	13	∈	∈	PROPN
ejpam-5894	162	14	f	f	PROPN
ejpam-5894	162	15	.	.	PUNCT
ejpam-5894	163	1	now	now	ADV
ejpam-5894	163	2	,	,	PUNCT
ejpam-5894	163	3	consider	consider	VERB
ejpam-5894	163	4	αf	αf	NOUN
ejpam-5894	163	5	(	(	PUNCT
ejpam-5894	163	6	ζ	ζ	NOUN
ejpam-5894	163	7	)	)	PUNCT
ejpam-5894	163	8	≥	≥	NOUN
ejpam-5894	163	9	min{αf	min{αf	PUNCT
ejpam-5894	163	10	(	(	PUNCT
ejpam-5894	163	11	(	(	PUNCT
ejpam-5894	163	12	(	(	PUNCT
ejpam-5894	163	13	(	(	PUNCT
ejpam-5894	163	14	(	(	PUNCT
ejpam-5894	163	15	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	163	16	)	)	PUNCT
ejpam-5894	163	17	)	)	PUNCT
ejpam-5894	163	18	)	)	PUNCT
ejpam-5894	163	19	)	)	PUNCT
ejpam-5894	163	20	,	,	PUNCT
ejpam-5894	163	21	αf	αf	PROPN
ejpam-5894	163	22	(	(	PUNCT
ejpam-5894	163	23	η	η	NOUN
ejpam-5894	163	24	)	)	PUNCT
ejpam-5894	163	25	}	}	PUNCT
ejpam-5894	163	26	=	=	SYM
ejpam-5894	164	1	α0	α0	ADJ
ejpam-5894	164	2	and	and	CCONJ
ejpam-5894	164	3	βf	βf	INTJ
ejpam-5894	164	4	(	(	PUNCT
ejpam-5894	164	5	ζ	ζ	NOUN
ejpam-5894	164	6	)	)	PUNCT
ejpam-5894	164	7	≤	≤	NUM
ejpam-5894	164	8	max{βf	max{βf	INTJ
ejpam-5894	164	9	(	(	PUNCT
ejpam-5894	164	10	(	(	PUNCT
ejpam-5894	164	11	(	(	PUNCT
ejpam-5894	164	12	(	(	PUNCT
ejpam-5894	164	13	(	(	PUNCT
ejpam-5894	164	14	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	164	15	)	)	PUNCT
ejpam-5894	164	16	)	)	PUNCT
ejpam-5894	164	17	)	)	PUNCT
ejpam-5894	164	18	)	)	PUNCT
ejpam-5894	164	19	,	,	PUNCT
ejpam-5894	164	20	βf	βf	CCONJ
ejpam-5894	164	21	(	(	PUNCT
ejpam-5894	164	22	η	η	NOUN
ejpam-5894	164	23	)	)	PUNCT
ejpam-5894	164	24	}	}	PUNCT
ejpam-5894	164	25	=	=	SYM
ejpam-5894	164	26	β0	β0	NOUN
ejpam-5894	164	27	.	.	PUNCT
ejpam-5894	165	1	thus	thus	ADV
ejpam-5894	165	2	,	,	PUNCT
ejpam-5894	165	3	αf	αf	ADP
ejpam-5894	165	4	(	(	PUNCT
ejpam-5894	165	5	ζ	ζ	NOUN
ejpam-5894	165	6	)	)	PUNCT
ejpam-5894	165	7	=	=	SYM
ejpam-5894	165	8	α0	α0	ADJ
ejpam-5894	165	9	and	and	CCONJ
ejpam-5894	165	10	βf	βf	INTJ
ejpam-5894	165	11	(	(	PUNCT
ejpam-5894	165	12	ζ	ζ	NOUN
ejpam-5894	165	13	)	)	PUNCT
ejpam-5894	165	14	=	=	SYM
ejpam-5894	165	15	β0	β0	NOUN
ejpam-5894	165	16	,	,	PUNCT
ejpam-5894	165	17	which	which	PRON
ejpam-5894	165	18	implies	imply	VERB
ejpam-5894	165	19	ζ	ζ	PROPN
ejpam-5894	165	20	∈	∈	PROPN
ejpam-5894	165	21	f	f	X
ejpam-5894	165	22	.	.	PUNCT
ejpam-5894	166	1	therefore	therefore	ADV
ejpam-5894	166	2	,	,	PUNCT
ejpam-5894	166	3	f	f	PROPN
ejpam-5894	166	4	is	be	AUX
ejpam-5894	166	5	an	an	DET
ejpam-5894	166	6	implicative	implicative	ADJ
ejpam-5894	166	7	wsbg	wsbg	ADV
ejpam-5894	166	8	-	-	PUNCT
ejpam-5894	166	9	ideal	ideal	NOUN
ejpam-5894	166	10	of	of	ADP
ejpam-5894	166	11	l.	l.	NOUN
ejpam-5894	166	12	conversely	conversely	ADV
ejpam-5894	166	13	,	,	PUNCT
ejpam-5894	166	14	assume	assume	VERB
ejpam-5894	166	15	that	that	SCONJ
ejpam-5894	166	16	f	f	PROPN
ejpam-5894	166	17	is	be	AUX
ejpam-5894	166	18	an	an	DET
ejpam-5894	166	19	implicative	implicative	ADJ
ejpam-5894	166	20	wsbg	wsbg	ADV
ejpam-5894	166	21	-	-	PUNCT
ejpam-5894	166	22	ideal	ideal	NOUN
ejpam-5894	166	23	of	of	ADP
ejpam-5894	166	24	l	l	NOUN
ejpam-5894	166	25	=	=	SYM
ejpam-5894	166	26	⟨l	⟨l	NOUN
ejpam-5894	166	27	;	;	PUNCT
ejpam-5894	166	28	|	|	ADV
ejpam-5894	166	29	,	,	PUNCT
ejpam-5894	166	30	0⟩.	0⟩.	PROPN
ejpam-5894	166	31	let	let	VERB
ejpam-5894	166	32	ζ	ζ	NOUN
ejpam-5894	166	33	,	,	PUNCT
ejpam-5894	166	34	η	η	PROPN
ejpam-5894	166	35	∈	∈	PROPN
ejpam-5894	166	36	l.	l.	NOUN
ejpam-5894	167	1	if	if	SCONJ
ejpam-5894	167	2	ζ	ζ	NOUN
ejpam-5894	167	3	∈	∈	PROPN
ejpam-5894	167	4	f	f	X
ejpam-5894	167	5	,	,	PUNCT
ejpam-5894	167	6	then	then	ADV
ejpam-5894	167	7	0	0	NUM
ejpam-5894	167	8	∈	∈	PROPN
ejpam-5894	167	9	f	f	PROPN
ejpam-5894	167	10	,	,	PUNCT
ejpam-5894	167	11	which	which	PRON
ejpam-5894	167	12	implies	imply	VERB
ejpam-5894	167	13	αf	αf	NUM
ejpam-5894	167	14	(	(	PUNCT
ejpam-5894	167	15	0	0	NUM
ejpam-5894	167	16	)	)	PUNCT
ejpam-5894	167	17	=	=	SYM
ejpam-5894	168	1	α0	α0	VERB
ejpam-5894	168	2	=	=	SYM
ejpam-5894	168	3	αf	αf	X
ejpam-5894	168	4	(	(	PUNCT
ejpam-5894	168	5	ζ	ζ	NOUN
ejpam-5894	168	6	)	)	PUNCT
ejpam-5894	168	7	and	and	CCONJ
ejpam-5894	168	8	βf	βf	INTJ
ejpam-5894	168	9	(	(	PUNCT
ejpam-5894	168	10	0	0	NUM
ejpam-5894	168	11	)	)	PUNCT
ejpam-5894	169	1	=	=	SYM
ejpam-5894	169	2	β0	β0	NOUN
ejpam-5894	169	3	=	=	NOUN
ejpam-5894	169	4	βf	βf	INTJ
ejpam-5894	169	5	(	(	PUNCT
ejpam-5894	169	6	ζ	ζ	NOUN
ejpam-5894	169	7	)	)	PUNCT
ejpam-5894	169	8	.	.	PUNCT
ejpam-5894	170	1	if	if	SCONJ
ejpam-5894	170	2	0	0	NUM
ejpam-5894	170	3	/∈	/∈	NUM
ejpam-5894	171	1	f	f	PROPN
ejpam-5894	171	2	,	,	PUNCT
ejpam-5894	171	3	then	then	ADV
ejpam-5894	171	4	αf	αf	VERB
ejpam-5894	171	5	(	(	PUNCT
ejpam-5894	171	6	0	0	NUM
ejpam-5894	171	7	)	)	PUNCT
ejpam-5894	171	8	=	=	SYM
ejpam-5894	172	1	α1	α1	PROPN
ejpam-5894	172	2	<	<	X
ejpam-5894	172	3	αf	αf	X
ejpam-5894	172	4	(	(	PUNCT
ejpam-5894	172	5	ζ	ζ	NOUN
ejpam-5894	172	6	)	)	PUNCT
ejpam-5894	172	7	and	and	CCONJ
ejpam-5894	172	8	βf	βf	INTJ
ejpam-5894	172	9	(	(	PUNCT
ejpam-5894	172	10	0	0	X
ejpam-5894	172	11	)	)	PUNCT
ejpam-5894	172	12	=	=	SYM
ejpam-5894	173	1	β1	β1	PROPN
ejpam-5894	173	2	>	>	X
ejpam-5894	174	1	βf	βf	INTJ
ejpam-5894	174	2	(	(	PUNCT
ejpam-5894	174	3	ζ	ζ	NOUN
ejpam-5894	174	4	)	)	PUNCT
ejpam-5894	174	5	.	.	PUNCT
ejpam-5894	175	1	for	for	ADP
ejpam-5894	175	2	every	every	DET
ejpam-5894	175	3	ζ	ζ	PROPN
ejpam-5894	175	4	,	,	PUNCT
ejpam-5894	175	5	η	η	PROPN
ejpam-5894	175	6	,	,	PUNCT
ejpam-5894	175	7	θ	θ	PROPN
ejpam-5894	175	8	∈	∈	PROPN
ejpam-5894	175	9	l	l	NOUN
ejpam-5894	175	10	,	,	PUNCT
ejpam-5894	175	11	if	if	SCONJ
ejpam-5894	175	12	(	(	PUNCT
ejpam-5894	175	13	(	(	PUNCT
ejpam-5894	175	14	(	(	PUNCT
ejpam-5894	175	15	(	(	PUNCT
ejpam-5894	175	16	(	(	PUNCT
ejpam-5894	175	17	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	175	18	)	)	PUNCT
ejpam-5894	175	19	)	)	PUNCT
ejpam-5894	175	20	)	)	PUNCT
ejpam-5894	175	21	,	,	PUNCT
ejpam-5894	175	22	θ	θ	X
ejpam-5894	175	23	)	)	PUNCT
ejpam-5894	175	24	∈	∈	PROPN
ejpam-5894	175	25	f	f	X
ejpam-5894	175	26	,	,	PUNCT
ejpam-5894	175	27	then	then	ADV
ejpam-5894	175	28	ζ	ζ	PROPN
ejpam-5894	175	29	∈	∈	PROPN
ejpam-5894	175	30	f	f	X
ejpam-5894	175	31	,	,	PUNCT
ejpam-5894	175	32	which	which	PRON
ejpam-5894	175	33	implies	imply	VERB
ejpam-5894	175	34	αf	αf	X
ejpam-5894	175	35	(	(	PUNCT
ejpam-5894	175	36	ζ	ζ	NOUN
ejpam-5894	175	37	)	)	PUNCT
ejpam-5894	175	38	=	=	SYM
ejpam-5894	175	39	α0	α0	ADJ
ejpam-5894	175	40	=	=	SYM
ejpam-5894	175	41	min{αf	min{αf	X
ejpam-5894	175	42	(	(	PUNCT
ejpam-5894	175	43	(	(	PUNCT
ejpam-5894	175	44	(	(	PUNCT
ejpam-5894	175	45	(	(	PUNCT
ejpam-5894	175	46	(	(	PUNCT
ejpam-5894	175	47	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	175	48	)	)	PUNCT
ejpam-5894	175	49	)	)	PUNCT
ejpam-5894	175	50	)	)	PUNCT
ejpam-5894	175	51	)	)	PUNCT
ejpam-5894	175	52	,	,	PUNCT
ejpam-5894	175	53	αf	αf	X
ejpam-5894	175	54	(	(	PUNCT
ejpam-5894	175	55	θ	θ	NOUN
ejpam-5894	175	56	)	)	PUNCT
ejpam-5894	175	57	}	}	PUNCT
ejpam-5894	176	1	t.	t.	NOUN
ejpam-5894	176	2	oner	oner	NOUN
ejpam-5894	176	3	et	et	PROPN
ejpam-5894	176	4	al	al	PROPN
ejpam-5894	176	5	.	.	PUNCT
ejpam-5894	176	6	/	/	SYM
ejpam-5894	176	7	eur	eur	PROPN
ejpam-5894	176	8	.	.	PUNCT
ejpam-5894	177	1	j.	j.	PROPN
ejpam-5894	177	2	pure	pure	PROPN
ejpam-5894	177	3	appl	appl	PROPN
ejpam-5894	177	4	.	.	PROPN
ejpam-5894	177	5	math	math	PROPN
ejpam-5894	177	6	,	,	PUNCT
ejpam-5894	177	7	18	18	NUM
ejpam-5894	177	8	(	(	PUNCT
ejpam-5894	177	9	3	3	NUM
ejpam-5894	177	10	)	)	PUNCT
ejpam-5894	177	11	(	(	PUNCT
ejpam-5894	177	12	2025	2025	NUM
ejpam-5894	177	13	)	)	PUNCT
ejpam-5894	177	14	,	,	PUNCT
ejpam-5894	177	15	5894	5894	NUM
ejpam-5894	177	16	10	10	NUM
ejpam-5894	177	17	of	of	ADP
ejpam-5894	177	18	33	33	NUM
ejpam-5894	177	19	and	and	CCONJ
ejpam-5894	177	20	βf	βf	NOUN
ejpam-5894	177	21	(	(	PUNCT
ejpam-5894	177	22	ζ	ζ	NOUN
ejpam-5894	177	23	)	)	PUNCT
ejpam-5894	177	24	=	=	SYM
ejpam-5894	178	1	β0	β0	NOUN
ejpam-5894	178	2	=	=	SYM
ejpam-5894	178	3	max{βf	max{βf	X
ejpam-5894	178	4	(	(	PUNCT
ejpam-5894	178	5	(	(	PUNCT
ejpam-5894	178	6	(	(	PUNCT
ejpam-5894	178	7	(	(	PUNCT
ejpam-5894	178	8	(	(	PUNCT
ejpam-5894	178	9	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	178	10	)	)	PUNCT
ejpam-5894	178	11	)	)	PUNCT
ejpam-5894	178	12	)	)	PUNCT
ejpam-5894	178	13	)	)	PUNCT
ejpam-5894	178	14	,	,	PUNCT
ejpam-5894	178	15	βf	βf	CCONJ
ejpam-5894	178	16	(	(	PUNCT
ejpam-5894	178	17	θ	θ	NOUN
ejpam-5894	178	18	)	)	PUNCT
ejpam-5894	178	19	}	}	PUNCT
ejpam-5894	178	20	.	.	PUNCT
ejpam-5894	179	1	if	if	SCONJ
ejpam-5894	179	2	(	(	PUNCT
ejpam-5894	179	3	(	(	PUNCT
ejpam-5894	179	4	(	(	PUNCT
ejpam-5894	179	5	(	(	PUNCT
ejpam-5894	179	6	(	(	PUNCT
ejpam-5894	179	7	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	179	8	)	)	PUNCT
ejpam-5894	179	9	)	)	PUNCT
ejpam-5894	179	10	)	)	PUNCT
ejpam-5894	179	11	/∈	/∈	PUNCT
ejpam-5894	180	1	f	f	NOUN
ejpam-5894	180	2	or	or	CCONJ
ejpam-5894	180	3	θ	θ	PROPN
ejpam-5894	180	4	/∈	/∈	PUNCT
ejpam-5894	181	1	f	f	PROPN
ejpam-5894	181	2	,	,	PUNCT
ejpam-5894	181	3	then	then	ADV
ejpam-5894	181	4	αf	αf	VERB
ejpam-5894	181	5	(	(	PUNCT
ejpam-5894	181	6	ζ	ζ	NOUN
ejpam-5894	181	7	)	)	PUNCT
ejpam-5894	181	8	≥	≥	NOUN
ejpam-5894	181	9	α1	α1	PROPN
ejpam-5894	181	10	=	=	SYM
ejpam-5894	181	11	min{αf	min{αf	X
ejpam-5894	181	12	(	(	PUNCT
ejpam-5894	181	13	(	(	PUNCT
ejpam-5894	181	14	(	(	PUNCT
ejpam-5894	181	15	(	(	PUNCT
ejpam-5894	181	16	(	(	PUNCT
ejpam-5894	181	17	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	181	18	)	)	PUNCT
ejpam-5894	181	19	)	)	PUNCT
ejpam-5894	181	20	)	)	PUNCT
ejpam-5894	181	21	)	)	PUNCT
ejpam-5894	181	22	,	,	PUNCT
ejpam-5894	181	23	αf	αf	X
ejpam-5894	181	24	(	(	PUNCT
ejpam-5894	181	25	θ	θ	NOUN
ejpam-5894	181	26	)	)	PUNCT
ejpam-5894	181	27	}	}	PUNCT
ejpam-5894	181	28	and	and	CCONJ
ejpam-5894	181	29	βf	βf	INTJ
ejpam-5894	181	30	(	(	PUNCT
ejpam-5894	181	31	ζ	ζ	NOUN
ejpam-5894	181	32	)	)	PUNCT
ejpam-5894	181	33	≤	≤	NOUN
ejpam-5894	182	1	β1	β1	NOUN
ejpam-5894	182	2	=	=	PUNCT
ejpam-5894	182	3	max{βf	max{βf	PROPN
ejpam-5894	182	4	(	(	PUNCT
ejpam-5894	182	5	(	(	PUNCT
ejpam-5894	182	6	(	(	PUNCT
ejpam-5894	182	7	(	(	PUNCT
ejpam-5894	182	8	(	(	PUNCT
ejpam-5894	182	9	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	182	10	)	)	PUNCT
ejpam-5894	182	11	)	)	PUNCT
ejpam-5894	182	12	)	)	PUNCT
ejpam-5894	182	13	)	)	PUNCT
ejpam-5894	182	14	,	,	PUNCT
ejpam-5894	182	15	βf	βf	CCONJ
ejpam-5894	182	16	(	(	PUNCT
ejpam-5894	182	17	θ	θ	NOUN
ejpam-5894	182	18	)	)	PUNCT
ejpam-5894	182	19	}	}	PUNCT
ejpam-5894	182	20	.	.	PUNCT
ejpam-5894	183	1	thus	thus	ADV
ejpam-5894	183	2	,	,	PUNCT
ejpam-5894	183	3	lf	lf	ADP
ejpam-5894	183	4	=	=	SYM
ejpam-5894	183	5	(	(	PUNCT
ejpam-5894	183	6	l	l	NOUN
ejpam-5894	183	7	,	,	PUNCT
ejpam-5894	183	8	βf	βf	INTJ
ejpam-5894	183	9	,	,	PUNCT
ejpam-5894	183	10	αf	αf	PROPN
ejpam-5894	183	11	)	)	PUNCT
ejpam-5894	183	12	is	be	AUX
ejpam-5894	183	13	an	an	DET
ejpam-5894	183	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	183	15	fuzzy	fuzzy	ADJ
ejpam-5894	183	16	implicative	implicative	ADJ
ejpam-5894	183	17	wsbg	wsbg	NOUN
ejpam-5894	183	18	-	-	PUNCT
ejpam-5894	183	19	ideal	ideal	NOUN
ejpam-5894	183	20	of	of	ADP
ejpam-5894	183	21	l.	l.	PROPN
ejpam-5894	183	22	proposition	proposition	PROPN
ejpam-5894	183	23	2	2	X
ejpam-5894	183	24	.	.	PUNCT
ejpam-5894	184	1	if	if	SCONJ
ejpam-5894	184	2	li	li	PROPN
ejpam-5894	184	3	=	=	SYM
ejpam-5894	184	4	{	{	PUNCT
ejpam-5894	184	5	(	(	PUNCT
ejpam-5894	184	6	l	l	NOUN
ejpam-5894	184	7	,	,	PUNCT
ejpam-5894	184	8	αi	αi	NOUN
ejpam-5894	184	9	,	,	PUNCT
ejpam-5894	184	10	βi	βi	PROPN
ejpam-5894	184	11	)	)	PUNCT
ejpam-5894	184	12	:	:	PUNCT
ejpam-5894	184	13	i	i	PRON
ejpam-5894	184	14	∈	∈	PROPN
ejpam-5894	184	15	∆	∆	PROPN
ejpam-5894	184	16	}	}	PUNCT
ejpam-5894	184	17	is	be	AUX
ejpam-5894	184	18	a	a	DET
ejpam-5894	184	19	family	family	NOUN
ejpam-5894	184	20	of	of	ADP
ejpam-5894	184	21	intuitionistic	intuitionistic	ADJ
ejpam-5894	184	22	fuzzy	fuzzy	ADJ
ejpam-5894	184	23	implicative	implicative	ADJ
ejpam-5894	184	24	wsbg	wsbg	NOUN
ejpam-5894	184	25	-	-	PUNCT
ejpam-5894	184	26	ideals	ideal	NOUN
ejpam-5894	184	27	of	of	ADP
ejpam-5894	184	28	a	a	DET
ejpam-5894	184	29	wsbg	wsbg	ADV
ejpam-5894	184	30	-	-	PUNCT
ejpam-5894	184	31	algebra	algebra	NOUN
ejpam-5894	184	32	l	l	NOUN
ejpam-5894	184	33	=	=	PUNCT
ejpam-5894	184	34	⟨l	⟨l	NOUN
ejpam-5894	184	35	;	;	PUNCT
ejpam-5894	184	36	|	|	ADV
ejpam-5894	184	37	,	,	PUNCT
ejpam-5894	184	38	0⟩	0⟩	PROPN
ejpam-5894	184	39	,	,	PUNCT
ejpam-5894	184	40	then	then	ADV
ejpam-5894	184	41	∧	∧	PROPN
ejpam-5894	184	42	i∈∆	i∈∆	PROPN
ejpam-5894	184	43	li	li	PROPN
ejpam-5894	184	44	is	be	AUX
ejpam-5894	184	45	an	an	DET
ejpam-5894	184	46	intuitionistic	intuitionistic	ADJ
ejpam-5894	184	47	fuzzy	fuzzy	ADJ
ejpam-5894	184	48	implicative	implicative	ADJ
ejpam-5894	184	49	wsbg	wsbg	NOUN
ejpam-5894	184	50	-	-	PUNCT
ejpam-5894	184	51	ideal	ideal	NOUN
ejpam-5894	184	52	of	of	ADP
ejpam-5894	184	53	l.	l.	PROPN
ejpam-5894	184	54	proof	proof	PROPN
ejpam-5894	184	55	.	.	PUNCT
ejpam-5894	185	1	let	let	VERB
ejpam-5894	185	2	li	li	PROPN
ejpam-5894	185	3	=	=	VERB
ejpam-5894	185	4	{	{	PUNCT
ejpam-5894	185	5	(	(	PUNCT
ejpam-5894	185	6	l	l	NOUN
ejpam-5894	185	7	,	,	PUNCT
ejpam-5894	185	8	αi	αi	NOUN
ejpam-5894	185	9	,	,	PUNCT
ejpam-5894	185	10	βi	βi	PROPN
ejpam-5894	185	11	)	)	PUNCT
ejpam-5894	185	12	:	:	PUNCT
ejpam-5894	185	13	i	i	PRON
ejpam-5894	185	14	∈	∈	PROPN
ejpam-5894	185	15	∆	∆	PROPN
ejpam-5894	185	16	}	}	PUNCT
ejpam-5894	185	17	be	be	AUX
ejpam-5894	185	18	a	a	DET
ejpam-5894	185	19	family	family	NOUN
ejpam-5894	185	20	of	of	ADP
ejpam-5894	185	21	intuitionistic	intuitionistic	ADJ
ejpam-5894	185	22	fuzzy	fuzzy	ADJ
ejpam-5894	185	23	implicative	implicative	ADJ
ejpam-5894	185	24	wsbg	wsbg	NOUN
ejpam-5894	185	25	-	-	PUNCT
ejpam-5894	185	26	ideals	ideal	NOUN
ejpam-5894	185	27	of	of	ADP
ejpam-5894	185	28	l	l	NOUN
ejpam-5894	185	29	=	=	SYM
ejpam-5894	185	30	⟨l	⟨l	NOUN
ejpam-5894	185	31	;	;	PUNCT
ejpam-5894	185	32	|	|	ADV
ejpam-5894	185	33	,	,	PUNCT
ejpam-5894	185	34	0⟩.	0⟩.	PROPN
ejpam-5894	185	35	for	for	ADP
ejpam-5894	185	36	all	all	DET
ejpam-5894	185	37	ζ	ζ	PROPN
ejpam-5894	185	38	,	,	PUNCT
ejpam-5894	185	39	η	η	PROPN
ejpam-5894	185	40	,	,	PUNCT
ejpam-5894	185	41	θ	θ	PROPN
ejpam-5894	185	42	∈	∈	PROPN
ejpam-5894	185	43	l	l	NOUN
ejpam-5894	185	44	,	,	PUNCT
ejpam-5894	185	45	we	we	PRON
ejpam-5894	185	46	have	have	VERB
ejpam-5894	185	47	(	(	PUNCT
ejpam-5894	185	48	∧	∧	PROPN
ejpam-5894	185	49	i∈∆	i∈∆	NOUN
ejpam-5894	185	50	αi	αi	PART
ejpam-5894	185	51	)	)	PUNCT
ejpam-5894	186	1	(	(	PUNCT
ejpam-5894	186	2	0	0	X
ejpam-5894	186	3	)	)	PUNCT
ejpam-5894	186	4	=	=	VERB
ejpam-5894	186	5	inf	inf	PROPN
ejpam-5894	186	6	i∈∆	i∈∆	PROPN
ejpam-5894	186	7	αi(0	αi(0	NOUN
ejpam-5894	186	8	)	)	PUNCT
ejpam-5894	186	9	≥	≥	NOUN
ejpam-5894	186	10	inf	inf	NOUN
ejpam-5894	186	11	i∈∆	i∈∆	PROPN
ejpam-5894	186	12	αi(ζ	αi(ζ	ADJ
ejpam-5894	186	13	)	)	PUNCT
ejpam-5894	187	1	=	=	SYM
ejpam-5894	187	2	(	(	PUNCT
ejpam-5894	187	3	∧	∧	PROPN
ejpam-5894	187	4	i∈∆	i∈∆	NOUN
ejpam-5894	187	5	αi	αi	PART
ejpam-5894	187	6	)	)	PUNCT
ejpam-5894	188	1	(	(	PUNCT
ejpam-5894	188	2	ζ	ζ	NOUN
ejpam-5894	188	3	)	)	PUNCT
ejpam-5894	188	4	and	and	CCONJ
ejpam-5894	188	5	(	(	PUNCT
ejpam-5894	188	6	∧	∧	PROPN
ejpam-5894	188	7	i∈∆	i∈∆	NOUN
ejpam-5894	188	8	βi	βi	PRON
ejpam-5894	188	9	)	)	PUNCT
ejpam-5894	188	10	(	(	PUNCT
ejpam-5894	188	11	0	0	X
ejpam-5894	188	12	)	)	PUNCT
ejpam-5894	188	13	=	=	NOUN
ejpam-5894	189	1	sup	sup	NOUN
ejpam-5894	189	2	i∈∆	i∈∆	PROPN
ejpam-5894	189	3	βi(0	βi(0	PROPN
ejpam-5894	189	4	)	)	PUNCT
ejpam-5894	189	5	≤	≤	NUM
ejpam-5894	189	6	sup	sup	NOUN
ejpam-5894	189	7	i∈∆	i∈∆	NOUN
ejpam-5894	189	8	βi(ζ	βi(ζ	NOUN
ejpam-5894	189	9	)	)	PUNCT
ejpam-5894	190	1	=	=	SYM
ejpam-5894	190	2	(	(	PUNCT
ejpam-5894	190	3	∧	∧	NOUN
ejpam-5894	190	4	i∈∆	i∈∆	NOUN
ejpam-5894	190	5	βi	βi	PRON
ejpam-5894	190	6	)	)	PUNCT
ejpam-5894	190	7	(	(	PUNCT
ejpam-5894	190	8	ζ	ζ	NOUN
ejpam-5894	190	9	)	)	PUNCT
ejpam-5894	190	10	.	.	PUNCT
ejpam-5894	191	1	next	next	ADV
ejpam-5894	191	2	,	,	PUNCT
ejpam-5894	191	3	for	for	ADP
ejpam-5894	191	4	all	all	DET
ejpam-5894	191	5	ζ	ζ	NOUN
ejpam-5894	191	6	,	,	PUNCT
ejpam-5894	191	7	η	η	PROPN
ejpam-5894	191	8	,	,	PUNCT
ejpam-5894	191	9	θ	θ	PROPN
ejpam-5894	191	10	∈	∈	PROPN
ejpam-5894	191	11	l	l	NOUN
ejpam-5894	191	12	,	,	PUNCT
ejpam-5894	191	13	we	we	PRON
ejpam-5894	191	14	compute	compute	VERB
ejpam-5894	191	15	(	(	PUNCT
ejpam-5894	191	16	∧	∧	PROPN
ejpam-5894	191	17	i∈∆	i∈∆	NOUN
ejpam-5894	191	18	αi	αi	PART
ejpam-5894	191	19	)	)	PUNCT
ejpam-5894	192	1	(	(	PUNCT
ejpam-5894	192	2	ζ	ζ	NOUN
ejpam-5894	192	3	)	)	PUNCT
ejpam-5894	192	4	=	=	SYM
ejpam-5894	192	5	inf	inf	NOUN
ejpam-5894	192	6	i∈∆	i∈∆	PROPN
ejpam-5894	192	7	αi(ζ	αi(ζ	ADJ
ejpam-5894	192	8	)	)	PUNCT
ejpam-5894	192	9	≥	≥	PROPN
ejpam-5894	193	1	inf	inf	PROPN
ejpam-5894	193	2	i∈∆	i∈∆	PROPN
ejpam-5894	193	3	min	min	NOUN
ejpam-5894	193	4	{	{	PUNCT
ejpam-5894	193	5	αi(φ(ζ	αi(φ(ζ	ADJ
ejpam-5894	193	6	,	,	PUNCT
ejpam-5894	193	7	η	η	NOUN
ejpam-5894	193	8	,	,	PUNCT
ejpam-5894	193	9	θ	θ	NOUN
ejpam-5894	193	10	)	)	PUNCT
ejpam-5894	193	11	)	)	PUNCT
ejpam-5894	193	12	,	,	PUNCT
ejpam-5894	193	13	αi(θ	αi(θ	NOUN
ejpam-5894	193	14	)	)	PUNCT
ejpam-5894	193	15	}	}	PUNCT
ejpam-5894	193	16	,	,	PUNCT
ejpam-5894	193	17	where	where	SCONJ
ejpam-5894	193	18	φ(ζ	φ(ζ	NOUN
ejpam-5894	193	19	,	,	PUNCT
ejpam-5894	193	20	η	η	NOUN
ejpam-5894	193	21	,	,	PUNCT
ejpam-5894	193	22	θ	θ	NOUN
ejpam-5894	193	23	)	)	PUNCT
ejpam-5894	193	24	=	=	SYM
ejpam-5894	193	25	(	(	PUNCT
ejpam-5894	193	26	(	(	PUNCT
ejpam-5894	193	27	(	(	PUNCT
ejpam-5894	193	28	(	(	PUNCT
ejpam-5894	193	29	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	193	30	)	)	PUNCT
ejpam-5894	193	31	)	)	PUNCT
ejpam-5894	193	32	)	)	PUNCT
ejpam-5894	193	33	.	.	PUNCT
ejpam-5894	194	1	using	use	VERB
ejpam-5894	194	2	the	the	DET
ejpam-5894	194	3	properties	property	NOUN
ejpam-5894	194	4	of	of	ADP
ejpam-5894	194	5	inf	inf	NOUN
ejpam-5894	194	6	,	,	PUNCT
ejpam-5894	194	7	we	we	PRON
ejpam-5894	194	8	can	can	AUX
ejpam-5894	194	9	separate	separate	VERB
ejpam-5894	194	10	the	the	DET
ejpam-5894	194	11	terms	term	NOUN
ejpam-5894	194	12	inf	inf	PROPN
ejpam-5894	195	1	i∈∆	i∈∆	PROPN
ejpam-5894	195	2	min{αi(φ(ζ	min{αi(φ(ζ	PROPN
ejpam-5894	195	3	,	,	PUNCT
ejpam-5894	195	4	η	η	NOUN
ejpam-5894	195	5	,	,	PUNCT
ejpam-5894	195	6	θ	θ	NOUN
ejpam-5894	195	7	)	)	PUNCT
ejpam-5894	195	8	)	)	PUNCT
ejpam-5894	195	9	,	,	PUNCT
ejpam-5894	195	10	αi(θ	αi(θ	NOUN
ejpam-5894	195	11	)	)	PUNCT
ejpam-5894	195	12	}	}	PUNCT
ejpam-5894	195	13	=	=	SYM
ejpam-5894	195	14	min	min	PROPN
ejpam-5894	195	15	{	{	PUNCT
ejpam-5894	195	16	inf	inf	NOUN
ejpam-5894	195	17	i∈∆	i∈∆	PROPN
ejpam-5894	195	18	αi(φ(ζ	αi(φ(ζ	ADJ
ejpam-5894	195	19	,	,	PUNCT
ejpam-5894	195	20	η	η	NOUN
ejpam-5894	195	21	,	,	PUNCT
ejpam-5894	195	22	θ	θ	NOUN
ejpam-5894	195	23	)	)	PUNCT
ejpam-5894	195	24	)	)	PUNCT
ejpam-5894	195	25	,	,	PUNCT
ejpam-5894	195	26	inf	inf	PROPN
ejpam-5894	195	27	i∈∆	i∈∆	PROPN
ejpam-5894	195	28	αi(θ	αi(θ	NOUN
ejpam-5894	195	29	)	)	PUNCT
ejpam-5894	195	30	}	}	PUNCT
ejpam-5894	195	31	.	.	PUNCT
ejpam-5894	196	1	t.	t.	PROPN
ejpam-5894	196	2	oner	oner	PROPN
ejpam-5894	196	3	et	et	PROPN
ejpam-5894	196	4	al	al	PROPN
ejpam-5894	196	5	.	.	PUNCT
ejpam-5894	196	6	/	/	SYM
ejpam-5894	196	7	eur	eur	PROPN
ejpam-5894	196	8	.	.	PUNCT
ejpam-5894	197	1	j.	j.	PROPN
ejpam-5894	197	2	pure	pure	PROPN
ejpam-5894	197	3	appl	appl	PROPN
ejpam-5894	197	4	.	.	PROPN
ejpam-5894	197	5	math	math	PROPN
ejpam-5894	197	6	,	,	PUNCT
ejpam-5894	197	7	18	18	NUM
ejpam-5894	197	8	(	(	PUNCT
ejpam-5894	197	9	3	3	NUM
ejpam-5894	197	10	)	)	PUNCT
ejpam-5894	197	11	(	(	PUNCT
ejpam-5894	197	12	2025	2025	NUM
ejpam-5894	197	13	)	)	PUNCT
ejpam-5894	197	14	,	,	PUNCT
ejpam-5894	197	15	5894	5894	NUM
ejpam-5894	197	16	11	11	NUM
ejpam-5894	197	17	of	of	ADP
ejpam-5894	197	18	33	33	NUM
ejpam-5894	197	19	thus	thus	ADV
ejpam-5894	197	20	,	,	PUNCT
ejpam-5894	197	21	(	(	PUNCT
ejpam-5894	197	22	∧	∧	NOUN
ejpam-5894	197	23	i∈∆	i∈∆	NOUN
ejpam-5894	197	24	αi	αi	PART
ejpam-5894	197	25	)	)	PUNCT
ejpam-5894	198	1	(	(	PUNCT
ejpam-5894	198	2	ζ	ζ	X
ejpam-5894	198	3	)	)	PUNCT
ejpam-5894	198	4	≥	≥	NOUN
ejpam-5894	198	5	min	min	NOUN
ejpam-5894	198	6	{	{	PUNCT
ejpam-5894	198	7	(	(	PUNCT
ejpam-5894	198	8	∧	∧	PROPN
ejpam-5894	198	9	i∈∆	i∈∆	NOUN
ejpam-5894	198	10	αi	αi	PART
ejpam-5894	198	11	)	)	PUNCT
ejpam-5894	198	12	(	(	PUNCT
ejpam-5894	198	13	φ(ζ	φ(ζ	NOUN
ejpam-5894	198	14	,	,	PUNCT
ejpam-5894	198	15	η	η	NOUN
ejpam-5894	198	16	,	,	PUNCT
ejpam-5894	198	17	θ	θ	NOUN
ejpam-5894	198	18	)	)	PUNCT
ejpam-5894	198	19	)	)	PUNCT
ejpam-5894	198	20	,	,	PUNCT
ejpam-5894	198	21	(	(	PUNCT
ejpam-5894	198	22	∧	∧	NOUN
ejpam-5894	198	23	i∈∆	i∈∆	NOUN
ejpam-5894	198	24	αi	αi	PART
ejpam-5894	198	25	)	)	PUNCT
ejpam-5894	198	26	(	(	PUNCT
ejpam-5894	198	27	θ	θ	NOUN
ejpam-5894	198	28	)	)	PUNCT
ejpam-5894	198	29	}	}	PUNCT
ejpam-5894	198	30	.	.	PUNCT
ejpam-5894	199	1	similarly	similarly	ADV
ejpam-5894	199	2	,	,	PUNCT
ejpam-5894	199	3	for	for	ADP
ejpam-5894	199	4	βi	βi	PRON
ejpam-5894	199	5	,	,	PUNCT
ejpam-5894	199	6	we	we	PRON
ejpam-5894	199	7	have	have	VERB
ejpam-5894	199	8	(	(	PUNCT
ejpam-5894	199	9	∧	∧	PROPN
ejpam-5894	199	10	i∈∆	i∈∆	NOUN
ejpam-5894	199	11	βi	βi	PRON
ejpam-5894	199	12	)	)	PUNCT
ejpam-5894	200	1	(	(	PUNCT
ejpam-5894	200	2	ζ	ζ	NOUN
ejpam-5894	200	3	)	)	PUNCT
ejpam-5894	200	4	=	=	NOUN
ejpam-5894	200	5	sup	sup	NOUN
ejpam-5894	200	6	i∈∆	i∈∆	ADV
ejpam-5894	200	7	βi(ζ	βi(ζ	NOUN
ejpam-5894	200	8	)	)	PUNCT
ejpam-5894	200	9	≤	≤	NUM
ejpam-5894	200	10	sup	sup	NOUN
ejpam-5894	200	11	i∈∆	i∈∆	PROPN
ejpam-5894	200	12	max{βi(φ(ζ	max{βi(φ(ζ	PROPN
ejpam-5894	200	13	,	,	PUNCT
ejpam-5894	200	14	η	η	PROPN
ejpam-5894	200	15	,	,	PUNCT
ejpam-5894	200	16	θ	θ	NOUN
ejpam-5894	200	17	)	)	PUNCT
ejpam-5894	200	18	)	)	PUNCT
ejpam-5894	200	19	,	,	PUNCT
ejpam-5894	200	20	βi(θ	βi(θ	NOUN
ejpam-5894	200	21	)	)	PUNCT
ejpam-5894	200	22	}	}	PUNCT
ejpam-5894	200	23	.	.	PUNCT
ejpam-5894	201	1	using	use	VERB
ejpam-5894	201	2	the	the	DET
ejpam-5894	201	3	properties	property	NOUN
ejpam-5894	201	4	of	of	ADP
ejpam-5894	201	5	sup	sup	NOUN
ejpam-5894	201	6	,	,	PUNCT
ejpam-5894	201	7	we	we	PRON
ejpam-5894	201	8	separate	separate	VERB
ejpam-5894	201	9	the	the	DET
ejpam-5894	201	10	terms	term	NOUN
ejpam-5894	201	11	sup	sup	VERB
ejpam-5894	201	12	i∈∆	i∈∆	PROPN
ejpam-5894	201	13	max{βi(φ(ζ	max{βi(φ(ζ	PROPN
ejpam-5894	201	14	,	,	PUNCT
ejpam-5894	201	15	η	η	PROPN
ejpam-5894	201	16	,	,	PUNCT
ejpam-5894	201	17	θ	θ	NOUN
ejpam-5894	201	18	)	)	PUNCT
ejpam-5894	201	19	)	)	PUNCT
ejpam-5894	201	20	,	,	PUNCT
ejpam-5894	201	21	βi(θ	βi(θ	NOUN
ejpam-5894	201	22	)	)	PUNCT
ejpam-5894	201	23	}	}	PUNCT
ejpam-5894	202	1	=	=	PUNCT
ejpam-5894	202	2	max{sup	max{sup	ADV
ejpam-5894	202	3	i∈∆	i∈∆	PROPN
ejpam-5894	202	4	βi(φ(ζ	βi(φ(ζ	PART
ejpam-5894	202	5	,	,	PUNCT
ejpam-5894	202	6	η	η	NOUN
ejpam-5894	202	7	,	,	PUNCT
ejpam-5894	202	8	θ	θ	NOUN
ejpam-5894	202	9	)	)	PUNCT
ejpam-5894	202	10	)	)	PUNCT
ejpam-5894	202	11	,	,	PUNCT
ejpam-5894	202	12	sup	sup	NOUN
ejpam-5894	202	13	i∈∆	i∈∆	PROPN
ejpam-5894	202	14	βi(θ	βi(θ	NOUN
ejpam-5894	202	15	)	)	PUNCT
ejpam-5894	202	16	}	}	PUNCT
ejpam-5894	202	17	.	.	PUNCT
ejpam-5894	203	1	thus	thus	ADV
ejpam-5894	203	2	,	,	PUNCT
ejpam-5894	203	3	(	(	PUNCT
ejpam-5894	203	4	∧	∧	NOUN
ejpam-5894	203	5	i∈∆	i∈∆	NOUN
ejpam-5894	203	6	βi	βi	PRON
ejpam-5894	203	7	)	)	PUNCT
ejpam-5894	203	8	(	(	PUNCT
ejpam-5894	203	9	ζ	ζ	NOUN
ejpam-5894	203	10	)	)	PUNCT
ejpam-5894	203	11	≤	≤	NUM
ejpam-5894	203	12	max	max	NOUN
ejpam-5894	203	13	{	{	PUNCT
ejpam-5894	203	14	(	(	PUNCT
ejpam-5894	203	15	∧	∧	PROPN
ejpam-5894	203	16	i∈∆	i∈∆	NOUN
ejpam-5894	203	17	βi	βi	PRON
ejpam-5894	203	18	)	)	PUNCT
ejpam-5894	203	19	(	(	PUNCT
ejpam-5894	203	20	φ(ζ	φ(ζ	NOUN
ejpam-5894	203	21	,	,	PUNCT
ejpam-5894	203	22	η	η	NOUN
ejpam-5894	203	23	,	,	PUNCT
ejpam-5894	203	24	θ	θ	NOUN
ejpam-5894	203	25	)	)	PUNCT
ejpam-5894	203	26	)	)	PUNCT
ejpam-5894	203	27	,	,	PUNCT
ejpam-5894	203	28	(	(	PUNCT
ejpam-5894	203	29	∧	∧	NOUN
ejpam-5894	203	30	i∈∆	i∈∆	NOUN
ejpam-5894	203	31	βi	βi	PRON
ejpam-5894	203	32	)	)	PUNCT
ejpam-5894	203	33	(	(	PUNCT
ejpam-5894	203	34	θ	θ	NOUN
ejpam-5894	203	35	)	)	PUNCT
ejpam-5894	203	36	}	}	PUNCT
ejpam-5894	203	37	.	.	PUNCT
ejpam-5894	204	1	hence	hence	ADV
ejpam-5894	204	2	,	,	PUNCT
ejpam-5894	204	3	∧	∧	PROPN
ejpam-5894	204	4	i∈∆	i∈∆	PROPN
ejpam-5894	204	5	li	li	PROPN
ejpam-5894	204	6	is	be	AUX
ejpam-5894	204	7	an	an	DET
ejpam-5894	204	8	intuitionistic	intuitionistic	ADJ
ejpam-5894	204	9	fuzzy	fuzzy	ADJ
ejpam-5894	204	10	implicative	implicative	ADJ
ejpam-5894	204	11	wsbg	wsbg	NOUN
ejpam-5894	204	12	-	-	PUNCT
ejpam-5894	204	13	ideal	ideal	NOUN
ejpam-5894	204	14	of	of	ADP
ejpam-5894	204	15	l.	l.	PROPN
ejpam-5894	204	16	definition	definition	NOUN
ejpam-5894	204	17	11	11	NUM
ejpam-5894	204	18	.	.	PUNCT
ejpam-5894	205	1	an	an	DET
ejpam-5894	205	2	intuitionistic	intuitionistic	ADJ
ejpam-5894	205	3	fuzzy	fuzzy	ADJ
ejpam-5894	205	4	set	set	NOUN
ejpam-5894	205	5	l	l	NOUN
ejpam-5894	205	6	=	=	SYM
ejpam-5894	205	7	(	(	PUNCT
ejpam-5894	205	8	l	l	NOUN
ejpam-5894	205	9	,	,	PUNCT
ejpam-5894	205	10	α	α	X
ejpam-5894	205	11	,	,	PUNCT
ejpam-5894	205	12	β	β	NOUN
ejpam-5894	205	13	)	)	PUNCT
ejpam-5894	205	14	of	of	ADP
ejpam-5894	205	15	a	a	DET
ejpam-5894	205	16	wsbg	wsbg	ADV
ejpam-5894	205	17	-	-	PUNCT
ejpam-5894	205	18	algebra	algebra	NOUN
ejpam-5894	205	19	l	l	NOUN
ejpam-5894	205	20	=	=	PUNCT
ejpam-5894	205	21	⟨l	⟨l	NOUN
ejpam-5894	205	22	;	;	PUNCT
ejpam-5894	205	23	|	|	ADV
ejpam-5894	205	24	,	,	PUNCT
ejpam-5894	205	25	0⟩	0⟩	PROPN
ejpam-5894	205	26	is	be	AUX
ejpam-5894	205	27	called	call	VERB
ejpam-5894	205	28	an	an	DET
ejpam-5894	205	29	intuitionistic	intuitionistic	ADJ
ejpam-5894	205	30	fuzzy	fuzzy	ADJ
ejpam-5894	205	31	sub	sub	ADJ
ejpam-5894	205	32	-	-	ADJ
ejpam-5894	205	33	implicative	implicative	ADJ
ejpam-5894	205	34	wsbg	wsbg	NOUN
ejpam-5894	205	35	-	-	PUNCT
ejpam-5894	205	36	ideal	ideal	NOUN
ejpam-5894	205	37	of	of	ADP
ejpam-5894	205	38	l	l	NOUN
ejpam-5894	205	39	if	if	SCONJ
ejpam-5894	205	40	it	it	PRON
ejpam-5894	205	41	satisfies	satisfy	VERB
ejpam-5894	205	42	the	the	DET
ejpam-5894	205	43	following	follow	VERB
ejpam-5894	205	44	conditions	condition	NOUN
ejpam-5894	205	45	:	:	PUNCT
ejpam-5894	205	46	for	for	ADP
ejpam-5894	205	47	all	all	DET
ejpam-5894	205	48	ζ	ζ	PROPN
ejpam-5894	205	49	,	,	PUNCT
ejpam-5894	205	50	η	η	PROPN
ejpam-5894	205	51	,	,	PUNCT
ejpam-5894	205	52	θ	θ	PROPN
ejpam-5894	205	53	∈	∈	PROPN
ejpam-5894	205	54	l	l	NOUN
ejpam-5894	205	55	,	,	PUNCT
ejpam-5894	205	56	α(0	α(0	PROPN
ejpam-5894	205	57	)	)	PUNCT
ejpam-5894	205	58	≥	≥	NOUN
ejpam-5894	205	59	α(ζ	α(ζ	PROPN
ejpam-5894	205	60	)	)	PUNCT
ejpam-5894	205	61	and	and	CCONJ
ejpam-5894	205	62	β(0	β(0	PROPN
ejpam-5894	205	63	)	)	PUNCT
ejpam-5894	205	64	≤	≤	NOUN
ejpam-5894	205	65	β(ζ	β(ζ	PROPN
ejpam-5894	205	66	)	)	PUNCT
ejpam-5894	205	67	,	,	PUNCT
ejpam-5894	205	68	(	(	PUNCT
ejpam-5894	205	69	1	1	X
ejpam-5894	205	70	)	)	PUNCT
ejpam-5894	205	71	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	205	72	)	)	PUNCT
ejpam-5894	205	73	)	)	PUNCT
ejpam-5894	205	74	)	)	PUNCT
ejpam-5894	205	75	)	)	PUNCT
ejpam-5894	205	76	≥	≥	PROPN
ejpam-5894	205	77	min{α(φ(ζ	min{α(φ(ζ	PROPN
ejpam-5894	205	78	,	,	PUNCT
ejpam-5894	205	79	η	η	PROPN
ejpam-5894	205	80	,	,	PUNCT
ejpam-5894	205	81	θ	θ	NOUN
ejpam-5894	205	82	)	)	PUNCT
ejpam-5894	205	83	)	)	PUNCT
ejpam-5894	205	84	,	,	PUNCT
ejpam-5894	205	85	α(θ	α(θ	NOUN
ejpam-5894	205	86	)	)	PUNCT
ejpam-5894	205	87	}	}	PUNCT
ejpam-5894	205	88	,	,	PUNCT
ejpam-5894	205	89	(	(	PUNCT
ejpam-5894	205	90	2	2	X
ejpam-5894	205	91	)	)	PUNCT
ejpam-5894	205	92	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	205	93	)	)	PUNCT
ejpam-5894	205	94	)	)	PUNCT
ejpam-5894	205	95	)	)	PUNCT
ejpam-5894	205	96	)	)	PUNCT
ejpam-5894	206	1	≤	≤	PROPN
ejpam-5894	206	2	max{β(φ(ζ	max{β(φ(ζ	PROPN
ejpam-5894	206	3	,	,	PUNCT
ejpam-5894	206	4	η	η	NOUN
ejpam-5894	206	5	,	,	PUNCT
ejpam-5894	206	6	θ	θ	NOUN
ejpam-5894	206	7	)	)	PUNCT
ejpam-5894	206	8	)	)	PUNCT
ejpam-5894	206	9	,	,	PUNCT
ejpam-5894	206	10	β(θ	β(θ	NUM
ejpam-5894	206	11	)	)	PUNCT
ejpam-5894	206	12	}	}	PUNCT
ejpam-5894	206	13	,	,	PUNCT
ejpam-5894	206	14	(	(	PUNCT
ejpam-5894	206	15	3	3	X
ejpam-5894	206	16	)	)	PUNCT
ejpam-5894	206	17	where	where	SCONJ
ejpam-5894	206	18	φ(ζ	φ(ζ	NOUN
ejpam-5894	206	19	,	,	PUNCT
ejpam-5894	206	20	η	η	NOUN
ejpam-5894	206	21	,	,	PUNCT
ejpam-5894	206	22	θ	θ	NOUN
ejpam-5894	206	23	)	)	PUNCT
ejpam-5894	206	24	=	=	SYM
ejpam-5894	206	25	(	(	PUNCT
ejpam-5894	206	26	(	(	PUNCT
ejpam-5894	206	27	(	(	PUNCT
ejpam-5894	206	28	(	(	PUNCT
ejpam-5894	206	29	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ))|(((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ))|(((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ	NOUN
ejpam-5894	206	30	)	)	PUNCT
ejpam-5894	206	31	)	)	PUNCT
ejpam-5894	206	32	)	)	PUNCT
ejpam-5894	206	33	.	.	PUNCT
ejpam-5894	207	1	example	example	NOUN
ejpam-5894	208	1	6	6	NUM
ejpam-5894	208	2	.	.	PUNCT
ejpam-5894	209	1	let	let	VERB
ejpam-5894	209	2	l	l	NOUN
ejpam-5894	209	3	=	=	PUNCT
ejpam-5894	209	4	{	{	PUNCT
ejpam-5894	209	5	0	0	NUM
ejpam-5894	209	6	,	,	PUNCT
ejpam-5894	209	7	1	1	NUM
ejpam-5894	209	8	,	,	PUNCT
ejpam-5894	209	9	2	2	NUM
ejpam-5894	209	10	,	,	PUNCT
ejpam-5894	209	11	3	3	NUM
ejpam-5894	209	12	}	}	PUNCT
ejpam-5894	209	13	be	be	AUX
ejpam-5894	209	14	a	a	DET
ejpam-5894	209	15	wsbg	wsbg	NOUN
ejpam-5894	209	16	-	-	PUNCT
ejpam-5894	209	17	algebra	algebra	NOUN
ejpam-5894	209	18	with	with	ADP
ejpam-5894	209	19	the	the	DET
ejpam-5894	209	20	binary	binary	PROPN
ejpam-5894	209	21	operation	operation	NOUN
ejpam-5894	209	22	|	|	ADV
ejpam-5894	209	23	defined	define	VERB
ejpam-5894	209	24	by	by	ADP
ejpam-5894	209	25	the	the	DET
ejpam-5894	209	26	following	following	ADJ
ejpam-5894	209	27	cayley	cayley	ADJ
ejpam-5894	209	28	table	table	NOUN
ejpam-5894	209	29	:	:	PUNCT
ejpam-5894	209	30	|	|	ADV
ejpam-5894	209	31	0	0	NUM
ejpam-5894	209	32	1	1	NUM
ejpam-5894	209	33	2	2	NUM
ejpam-5894	209	34	3	3	NUM
ejpam-5894	209	35	0	0	NUM
ejpam-5894	209	36	0	0	NUM
ejpam-5894	209	37	0	0	NUM
ejpam-5894	209	38	2	2	NUM
ejpam-5894	209	39	3	3	NUM
ejpam-5894	209	40	1	1	NUM
ejpam-5894	209	41	1	1	NUM
ejpam-5894	209	42	2	2	NUM
ejpam-5894	209	43	0	0	NUM
ejpam-5894	209	44	2	2	NUM
ejpam-5894	209	45	2	2	NUM
ejpam-5894	209	46	2	2	NUM
ejpam-5894	209	47	0	0	NUM
ejpam-5894	209	48	3	3	NUM
ejpam-5894	209	49	0	0	NUM
ejpam-5894	209	50	3	3	NUM
ejpam-5894	209	51	3	3	NUM
ejpam-5894	209	52	0	0	NUM
ejpam-5894	209	53	0	0	NUM
ejpam-5894	209	54	2	2	NUM
ejpam-5894	209	55	define	define	VERB
ejpam-5894	209	56	the	the	DET
ejpam-5894	209	57	intuitionistic	intuitionistic	ADJ
ejpam-5894	209	58	fuzzy	fuzzy	ADJ
ejpam-5894	209	59	set	set	NOUN
ejpam-5894	209	60	l	l	NOUN
ejpam-5894	209	61	=	=	SYM
ejpam-5894	209	62	(	(	PUNCT
ejpam-5894	209	63	l	l	NOUN
ejpam-5894	209	64	,	,	PUNCT
ejpam-5894	209	65	α	α	X
ejpam-5894	209	66	,	,	PUNCT
ejpam-5894	209	67	β	β	NOUN
ejpam-5894	209	68	)	)	PUNCT
ejpam-5894	209	69	by	by	ADP
ejpam-5894	209	70	:	:	PUNCT
ejpam-5894	209	71	α(0	α(0	NOUN
ejpam-5894	209	72	)	)	PUNCT
ejpam-5894	209	73	=	=	SYM
ejpam-5894	209	74	α(2	α(2	PROPN
ejpam-5894	209	75	)	)	PUNCT
ejpam-5894	209	76	=	=	SYM
ejpam-5894	209	77	α(3	α(3	PROPN
ejpam-5894	209	78	)	)	PUNCT
ejpam-5894	209	79	=	=	NOUN
ejpam-5894	209	80	0.5	0.5	NUM
ejpam-5894	209	81	,	,	PUNCT
ejpam-5894	209	82	α(1	α(1	PROPN
ejpam-5894	209	83	)	)	PUNCT
ejpam-5894	209	84	=	=	SYM
ejpam-5894	210	1	0.25	0.25	NUM
ejpam-5894	210	2	,	,	PUNCT
ejpam-5894	210	3	β(0	β(0	PROPN
ejpam-5894	210	4	)	)	PUNCT
ejpam-5894	210	5	=	=	SYM
ejpam-5894	210	6	β(2	β(2	PROPN
ejpam-5894	210	7	)	)	PUNCT
ejpam-5894	210	8	=	=	PUNCT
ejpam-5894	211	1	β(3	β(3	PROPN
ejpam-5894	211	2	)	)	PUNCT
ejpam-5894	211	3	=	=	SYM
ejpam-5894	211	4	0.25	0.25	NUM
ejpam-5894	211	5	,	,	PUNCT
ejpam-5894	211	6	β(1	β(1	PROPN
ejpam-5894	211	7	)	)	PUNCT
ejpam-5894	211	8	=	=	NUM
ejpam-5894	211	9	0.5	0.5	NUM
ejpam-5894	211	10	.	.	PUNCT
ejpam-5894	212	1	therefore	therefore	ADV
ejpam-5894	212	2	,	,	PUNCT
ejpam-5894	212	3	l	l	NOUN
ejpam-5894	212	4	=	=	SYM
ejpam-5894	212	5	(	(	PUNCT
ejpam-5894	212	6	l	l	NOUN
ejpam-5894	212	7	,	,	PUNCT
ejpam-5894	212	8	α	α	X
ejpam-5894	212	9	,	,	PUNCT
ejpam-5894	212	10	β	β	NOUN
ejpam-5894	212	11	)	)	PUNCT
ejpam-5894	212	12	is	be	AUX
ejpam-5894	212	13	an	an	DET
ejpam-5894	212	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	212	15	fuzzy	fuzzy	ADJ
ejpam-5894	212	16	sub	sub	ADJ
ejpam-5894	212	17	-	-	ADJ
ejpam-5894	212	18	implicative	implicative	ADJ
ejpam-5894	212	19	wsbg	wsbg	NOUN
ejpam-5894	212	20	-	-	PUNCT
ejpam-5894	212	21	ideal	ideal	NOUN
ejpam-5894	212	22	of	of	ADP
ejpam-5894	212	23	l.	l.	PROPN
ejpam-5894	212	24	proposition	proposition	PROPN
ejpam-5894	212	25	3	3	NUM
ejpam-5894	212	26	.	.	PUNCT
ejpam-5894	213	1	every	every	DET
ejpam-5894	213	2	intuitionistic	intuitionistic	ADJ
ejpam-5894	213	3	fuzzy	fuzzy	ADJ
ejpam-5894	213	4	sub	sub	ADJ
ejpam-5894	213	5	-	-	ADJ
ejpam-5894	213	6	implicative	implicative	ADJ
ejpam-5894	213	7	wsbg	wsbg	NOUN
ejpam-5894	213	8	-	-	PUNCT
ejpam-5894	213	9	ideal	ideal	NOUN
ejpam-5894	213	10	of	of	ADP
ejpam-5894	213	11	a	a	DET
ejpam-5894	213	12	wsbg	wsbg	ADV
ejpam-5894	213	13	-	-	PUNCT
ejpam-5894	213	14	algebra	algebra	NOUN
ejpam-5894	213	15	l	l	NOUN
ejpam-5894	213	16	=	=	PUNCT
ejpam-5894	213	17	⟨l	⟨l	NOUN
ejpam-5894	213	18	;	;	PUNCT
ejpam-5894	213	19	|	|	ADV
ejpam-5894	213	20	,	,	PUNCT
ejpam-5894	213	21	0⟩	0⟩	PROPN
ejpam-5894	213	22	is	be	AUX
ejpam-5894	213	23	an	an	DET
ejpam-5894	213	24	intuitionistic	intuitionistic	ADJ
ejpam-5894	213	25	fuzzy	fuzzy	ADJ
ejpam-5894	213	26	wsbg	wsbg	NOUN
ejpam-5894	213	27	-	-	PUNCT
ejpam-5894	213	28	ideal	ideal	NOUN
ejpam-5894	213	29	of	of	ADP
ejpam-5894	213	30	l.	l.	PROPN
ejpam-5894	213	31	t.	t.	PROPN
ejpam-5894	213	32	oner	oner	PROPN
ejpam-5894	213	33	et	et	PROPN
ejpam-5894	213	34	al	al	PROPN
ejpam-5894	213	35	.	.	PUNCT
ejpam-5894	213	36	/	/	SYM
ejpam-5894	213	37	eur	eur	PROPN
ejpam-5894	213	38	.	.	PUNCT
ejpam-5894	214	1	j.	j.	PROPN
ejpam-5894	214	2	pure	pure	PROPN
ejpam-5894	214	3	appl	appl	PROPN
ejpam-5894	214	4	.	.	PROPN
ejpam-5894	214	5	math	math	PROPN
ejpam-5894	214	6	,	,	PUNCT
ejpam-5894	214	7	18	18	NUM
ejpam-5894	214	8	(	(	PUNCT
ejpam-5894	214	9	3	3	NUM
ejpam-5894	214	10	)	)	PUNCT
ejpam-5894	214	11	(	(	PUNCT
ejpam-5894	214	12	2025	2025	NUM
ejpam-5894	214	13	)	)	PUNCT
ejpam-5894	214	14	,	,	PUNCT
ejpam-5894	214	15	5894	5894	NUM
ejpam-5894	214	16	12	12	NUM
ejpam-5894	214	17	of	of	ADP
ejpam-5894	214	18	33	33	NUM
ejpam-5894	214	19	proof	proof	NOUN
ejpam-5894	214	20	.	.	PUNCT
ejpam-5894	215	1	let	let	VERB
ejpam-5894	215	2	l	l	NOUN
ejpam-5894	215	3	=	=	SYM
ejpam-5894	215	4	(	(	PUNCT
ejpam-5894	215	5	l	l	NOUN
ejpam-5894	215	6	,	,	PUNCT
ejpam-5894	215	7	α	α	X
ejpam-5894	215	8	,	,	PUNCT
ejpam-5894	215	9	β	β	NOUN
ejpam-5894	215	10	)	)	PUNCT
ejpam-5894	215	11	be	be	VERB
ejpam-5894	215	12	an	an	DET
ejpam-5894	215	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	215	14	fuzzy	fuzzy	ADJ
ejpam-5894	215	15	sub	sub	ADJ
ejpam-5894	215	16	-	-	ADJ
ejpam-5894	215	17	implicative	implicative	ADJ
ejpam-5894	215	18	wsbg	wsbg	NOUN
ejpam-5894	215	19	-	-	PUNCT
ejpam-5894	215	20	ideal	ideal	NOUN
ejpam-5894	215	21	of	of	ADP
ejpam-5894	215	22	l	l	NOUN
ejpam-5894	215	23	=	=	SYM
ejpam-5894	215	24	⟨l	⟨l	NOUN
ejpam-5894	215	25	;	;	PUNCT
ejpam-5894	215	26	|	|	ADV
ejpam-5894	215	27	,	,	PUNCT
ejpam-5894	215	28	0⟩.	0⟩.	VERB
ejpam-5894	215	29	by	by	ADP
ejpam-5894	215	30	definition	definition	NOUN
ejpam-5894	215	31	,	,	PUNCT
ejpam-5894	215	32	we	we	PRON
ejpam-5894	215	33	have	have	VERB
ejpam-5894	215	34	α(0	α(0	PROPN
ejpam-5894	215	35	)	)	PUNCT
ejpam-5894	215	36	≥	≥	NOUN
ejpam-5894	215	37	α(ζ	α(ζ	PROPN
ejpam-5894	215	38	)	)	PUNCT
ejpam-5894	215	39	and	and	CCONJ
ejpam-5894	215	40	β(0	β(0	PROPN
ejpam-5894	215	41	)	)	PUNCT
ejpam-5894	215	42	≤	≤	NOUN
ejpam-5894	215	43	β(ζ	β(ζ	PROPN
ejpam-5894	215	44	)	)	PUNCT
ejpam-5894	215	45	,	,	PUNCT
ejpam-5894	215	46	and	and	CCONJ
ejpam-5894	215	47	the	the	DET
ejpam-5894	215	48	following	follow	VERB
ejpam-5894	215	49	conditions	condition	NOUN
ejpam-5894	215	50	hold	hold	VERB
ejpam-5894	215	51	:	:	PUNCT
ejpam-5894	215	52	for	for	ADP
ejpam-5894	215	53	all	all	DET
ejpam-5894	215	54	ζ	ζ	NOUN
ejpam-5894	215	55	,	,	PUNCT
ejpam-5894	215	56	θ	θ	PROPN
ejpam-5894	215	57	∈	∈	PROPN
ejpam-5894	215	58	l	l	NOUN
ejpam-5894	215	59	,	,	PUNCT
ejpam-5894	215	60	α((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ	α((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ	NOUN
ejpam-5894	215	61	)	)	PUNCT
ejpam-5894	215	62	)	)	PUNCT
ejpam-5894	215	63	)	)	PUNCT
ejpam-5894	215	64	)	)	PUNCT
ejpam-5894	216	1	≥	≥	PROPN
ejpam-5894	216	2	min{α(φ(ζ	min{α(φ(ζ	NOUN
ejpam-5894	216	3	,	,	PUNCT
ejpam-5894	216	4	ζ	ζ	NOUN
ejpam-5894	216	5	,	,	PUNCT
ejpam-5894	216	6	θ	θ	NOUN
ejpam-5894	216	7	)	)	PUNCT
ejpam-5894	216	8	)	)	PUNCT
ejpam-5894	216	9	,	,	PUNCT
ejpam-5894	216	10	α(θ	α(θ	NOUN
ejpam-5894	216	11	)	)	PUNCT
ejpam-5894	216	12	}	}	PUNCT
ejpam-5894	216	13	,	,	PUNCT
ejpam-5894	216	14	β((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ	β((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ	PROPN
ejpam-5894	216	15	)	)	PUNCT
ejpam-5894	216	16	)	)	PUNCT
ejpam-5894	216	17	)	)	PUNCT
ejpam-5894	216	18	)	)	PUNCT
ejpam-5894	217	1	≤	≤	PROPN
ejpam-5894	217	2	max{β(φ(ζ	max{β(φ(ζ	NOUN
ejpam-5894	217	3	,	,	PUNCT
ejpam-5894	217	4	ζ	ζ	NOUN
ejpam-5894	217	5	,	,	PUNCT
ejpam-5894	217	6	θ	θ	NOUN
ejpam-5894	217	7	)	)	PUNCT
ejpam-5894	217	8	)	)	PUNCT
ejpam-5894	217	9	,	,	PUNCT
ejpam-5894	217	10	β(θ	β(θ	NUM
ejpam-5894	217	11	)	)	PUNCT
ejpam-5894	217	12	}	}	PUNCT
ejpam-5894	217	13	,	,	PUNCT
ejpam-5894	217	14	where	where	SCONJ
ejpam-5894	217	15	φ(ζ	φ(ζ	NOUN
ejpam-5894	217	16	,	,	PUNCT
ejpam-5894	217	17	ζ	ζ	NOUN
ejpam-5894	217	18	,	,	PUNCT
ejpam-5894	217	19	θ	θ	NOUN
ejpam-5894	217	20	)	)	PUNCT
ejpam-5894	217	21	=	=	SYM
ejpam-5894	217	22	(	(	PUNCT
ejpam-5894	217	23	(	(	PUNCT
ejpam-5894	217	24	(	(	PUNCT
ejpam-5894	217	25	(	(	PUNCT
ejpam-5894	217	26	ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(θ|θ))|(((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(θ|θ	ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(θ|θ))|(((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	217	27	)	)	PUNCT
ejpam-5894	217	28	)	)	PUNCT
ejpam-5894	217	29	)	)	PUNCT
ejpam-5894	217	30	.	.	PUNCT
ejpam-5894	218	1	now	now	ADV
ejpam-5894	218	2	,	,	PUNCT
ejpam-5894	218	3	for	for	ADP
ejpam-5894	218	4	all	all	DET
ejpam-5894	218	5	ζ	ζ	NOUN
ejpam-5894	218	6	,	,	PUNCT
ejpam-5894	218	7	θ	θ	PROPN
ejpam-5894	218	8	∈	∈	PROPN
ejpam-5894	218	9	l	l	NOUN
ejpam-5894	218	10	,	,	PUNCT
ejpam-5894	218	11	we	we	PRON
ejpam-5894	218	12	compute	compute	VERB
ejpam-5894	218	13	1	1	NUM
ejpam-5894	218	14	.	.	PUNCT
ejpam-5894	219	1	for	for	ADP
ejpam-5894	219	2	α(ζ	α(ζ	NOUN
ejpam-5894	219	3	):	):	PUNCT
ejpam-5894	219	4	α(ζ	α(ζ	PROPN
ejpam-5894	219	5	)	)	PUNCT
ejpam-5894	219	6	=	=	SYM
ejpam-5894	219	7	α((ζ|(0|0))|(ζ|(0|0	α((ζ|(0|0))|(ζ|(0|0	PROPN
ejpam-5894	219	8	)	)	PUNCT
ejpam-5894	219	9	)	)	PUNCT
ejpam-5894	219	10	)	)	PUNCT
ejpam-5894	220	1	=	=	SYM
ejpam-5894	220	2	α((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ	α((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ	NOUN
ejpam-5894	220	3	)	)	PUNCT
ejpam-5894	220	4	)	)	PUNCT
ejpam-5894	220	5	)	)	PUNCT
ejpam-5894	220	6	)	)	PUNCT
ejpam-5894	221	1	≥	≥	PROPN
ejpam-5894	221	2	min{α(φ(ζ	min{α(φ(ζ	NOUN
ejpam-5894	221	3	,	,	PUNCT
ejpam-5894	221	4	ζ	ζ	NOUN
ejpam-5894	221	5	,	,	PUNCT
ejpam-5894	221	6	θ	θ	NOUN
ejpam-5894	221	7	)	)	PUNCT
ejpam-5894	221	8	)	)	PUNCT
ejpam-5894	221	9	,	,	PUNCT
ejpam-5894	221	10	α(θ	α(θ	NOUN
ejpam-5894	221	11	)	)	PUNCT
ejpam-5894	221	12	}	}	PUNCT
ejpam-5894	221	13	=	=	PUNCT
ejpam-5894	222	1	min{α((ζ|(θ|θ))|(ζ|(θ|θ	min{α((ζ|(θ|θ))|(ζ|(θ|θ	ADJ
ejpam-5894	222	2	)	)	PUNCT
ejpam-5894	222	3	)	)	PUNCT
ejpam-5894	222	4	)	)	PUNCT
ejpam-5894	222	5	,	,	PUNCT
ejpam-5894	222	6	α(θ	α(θ	NOUN
ejpam-5894	222	7	)	)	PUNCT
ejpam-5894	222	8	}	}	PUNCT
ejpam-5894	222	9	.	.	PUNCT
ejpam-5894	223	1	2	2	X
ejpam-5894	223	2	.	.	X
ejpam-5894	223	3	for	for	ADP
ejpam-5894	223	4	β(ζ	β(ζ	NUM
ejpam-5894	223	5	):	):	PUNCT
ejpam-5894	223	6	β(ζ	β(ζ	PROPN
ejpam-5894	223	7	)	)	PUNCT
ejpam-5894	223	8	=	=	SYM
ejpam-5894	223	9	β((ζ|(0|0))|(ζ|(0|0	β((ζ|(0|0))|(ζ|(0|0	NOUN
ejpam-5894	223	10	)	)	PUNCT
ejpam-5894	223	11	)	)	PUNCT
ejpam-5894	223	12	)	)	PUNCT
ejpam-5894	224	1	=	=	PUNCT
ejpam-5894	224	2	β((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ	β((ζ|(ζ|(ζ|ζ)))|(ζ|(ζ|(ζ|ζ	PROPN
ejpam-5894	224	3	)	)	PUNCT
ejpam-5894	224	4	)	)	PUNCT
ejpam-5894	224	5	)	)	PUNCT
ejpam-5894	224	6	)	)	PUNCT
ejpam-5894	225	1	≤	≤	PROPN
ejpam-5894	225	2	max{β(φ(ζ	max{β(φ(ζ	NOUN
ejpam-5894	225	3	,	,	PUNCT
ejpam-5894	225	4	ζ	ζ	NOUN
ejpam-5894	225	5	,	,	PUNCT
ejpam-5894	225	6	θ	θ	NOUN
ejpam-5894	225	7	)	)	PUNCT
ejpam-5894	225	8	)	)	PUNCT
ejpam-5894	225	9	,	,	PUNCT
ejpam-5894	225	10	β(θ	β(θ	NUM
ejpam-5894	225	11	)	)	PUNCT
ejpam-5894	225	12	}	}	PUNCT
ejpam-5894	225	13	=	=	SYM
ejpam-5894	225	14	max{β((ζ|(θ|θ))|(ζ|(θ|θ	max{β((ζ|(θ|θ))|(ζ|(θ|θ	NOUN
ejpam-5894	225	15	)	)	PUNCT
ejpam-5894	225	16	)	)	PUNCT
ejpam-5894	225	17	)	)	PUNCT
ejpam-5894	225	18	,	,	PUNCT
ejpam-5894	225	19	β(θ	β(θ	NUM
ejpam-5894	225	20	)	)	PUNCT
ejpam-5894	225	21	}	}	PUNCT
ejpam-5894	225	22	.	.	PUNCT
ejpam-5894	226	1	thus	thus	ADV
ejpam-5894	226	2	,	,	PUNCT
ejpam-5894	226	3	l	l	NOUN
ejpam-5894	226	4	=	=	SYM
ejpam-5894	226	5	(	(	PUNCT
ejpam-5894	226	6	l	l	NOUN
ejpam-5894	226	7	,	,	PUNCT
ejpam-5894	226	8	α	α	X
ejpam-5894	226	9	,	,	PUNCT
ejpam-5894	226	10	β	β	NOUN
ejpam-5894	226	11	)	)	PUNCT
ejpam-5894	226	12	is	be	AUX
ejpam-5894	226	13	an	an	DET
ejpam-5894	226	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	226	15	fuzzy	fuzzy	ADJ
ejpam-5894	226	16	wsbg	wsbg	NOUN
ejpam-5894	226	17	-	-	PUNCT
ejpam-5894	226	18	ideal	ideal	NOUN
ejpam-5894	226	19	of	of	ADP
ejpam-5894	226	20	l.	l.	PROPN
ejpam-5894	226	21	therefore	therefore	ADV
ejpam-5894	226	22	,	,	PUNCT
ejpam-5894	226	23	every	every	DET
ejpam-5894	226	24	intuitionistic	intuitionistic	ADJ
ejpam-5894	226	25	fuzzy	fuzzy	ADJ
ejpam-5894	226	26	sub	sub	ADJ
ejpam-5894	226	27	-	-	ADJ
ejpam-5894	226	28	implicative	implicative	ADJ
ejpam-5894	226	29	wsbg	wsbg	NOUN
ejpam-5894	226	30	-	-	PUNCT
ejpam-5894	226	31	ideal	ideal	NOUN
ejpam-5894	226	32	of	of	ADP
ejpam-5894	226	33	l	l	NOUN
ejpam-5894	226	34	is	be	AUX
ejpam-5894	226	35	an	an	DET
ejpam-5894	226	36	intuitionistic	intuitionistic	ADJ
ejpam-5894	226	37	fuzzy	fuzzy	ADJ
ejpam-5894	226	38	wsbg	wsbg	NOUN
ejpam-5894	226	39	-	-	PUNCT
ejpam-5894	226	40	ideal	ideal	NOUN
ejpam-5894	226	41	of	of	ADP
ejpam-5894	226	42	l.	l.	PROPN
ejpam-5894	226	43	example	example	PROPN
ejpam-5894	226	44	7	7	NUM
ejpam-5894	226	45	.	.	PUNCT
ejpam-5894	226	46	from	from	ADP
ejpam-5894	226	47	the	the	DET
ejpam-5894	226	48	wsbg	wsbg	ADV
ejpam-5894	226	49	-	-	PUNCT
ejpam-5894	226	50	algebra	algebra	NOUN
ejpam-5894	226	51	l	l	NOUN
ejpam-5894	226	52	=	=	PUNCT
ejpam-5894	226	53	⟨l	⟨l	NOUN
ejpam-5894	226	54	;	;	PUNCT
ejpam-5894	226	55	|	|	ADV
ejpam-5894	226	56	,	,	PUNCT
ejpam-5894	226	57	0⟩	0⟩	PROPN
ejpam-5894	226	58	where	where	SCONJ
ejpam-5894	226	59	l	l	NOUN
ejpam-5894	226	60	=	=	PUNCT
ejpam-5894	226	61	{	{	PUNCT
ejpam-5894	226	62	0	0	NUM
ejpam-5894	226	63	,	,	PUNCT
ejpam-5894	226	64	a	a	DET
ejpam-5894	226	65	,	,	PUNCT
ejpam-5894	226	66	b	b	NOUN
ejpam-5894	226	67	}	}	PUNCT
ejpam-5894	226	68	in	in	ADP
ejpam-5894	226	69	example	example	NOUN
ejpam-5894	226	70	4	4	NUM
ejpam-5894	226	71	,	,	PUNCT
ejpam-5894	226	72	define	define	VERB
ejpam-5894	226	73	an	an	DET
ejpam-5894	226	74	intuitionistic	intuitionistic	ADJ
ejpam-5894	226	75	fuzzy	fuzzy	ADJ
ejpam-5894	226	76	set	set	NOUN
ejpam-5894	226	77	l	l	NOUN
ejpam-5894	226	78	=	=	SYM
ejpam-5894	226	79	(	(	PUNCT
ejpam-5894	226	80	l	l	NOUN
ejpam-5894	226	81	,	,	PUNCT
ejpam-5894	226	82	α	α	X
ejpam-5894	226	83	,	,	PUNCT
ejpam-5894	226	84	β	β	NOUN
ejpam-5894	226	85	)	)	PUNCT
ejpam-5894	226	86	where	where	SCONJ
ejpam-5894	226	87	:	:	PUNCT
ejpam-5894	226	88	α(0	α(0	NOUN
ejpam-5894	226	89	)	)	PUNCT
ejpam-5894	226	90	=	=	SYM
ejpam-5894	226	91	α(a	α(a	NOUN
ejpam-5894	226	92	)	)	PUNCT
ejpam-5894	226	93	=	=	PUNCT
ejpam-5894	226	94	α(b	α(b	NOUN
ejpam-5894	226	95	)	)	PUNCT
ejpam-5894	226	96	=	=	SYM
ejpam-5894	226	97	0.5	0.5	NUM
ejpam-5894	226	98	,	,	PUNCT
ejpam-5894	226	99	β(0	β(0	PROPN
ejpam-5894	226	100	)	)	PUNCT
ejpam-5894	226	101	=	=	NOUN
ejpam-5894	226	102	0.25	0.25	NUM
ejpam-5894	226	103	,	,	PUNCT
ejpam-5894	226	104	β(a	β(a	PROPN
ejpam-5894	226	105	)	)	PUNCT
ejpam-5894	226	106	=	=	PUNCT
ejpam-5894	226	107	β(b	β(b	PUNCT
ejpam-5894	226	108	)	)	PUNCT
ejpam-5894	227	1	=	=	SYM
ejpam-5894	227	2	0	0	X
ejpam-5894	227	3	.	.	PUNCT
ejpam-5894	228	1	then	then	ADV
ejpam-5894	228	2	l	l	PROPN
ejpam-5894	228	3	is	be	AUX
ejpam-5894	228	4	an	an	DET
ejpam-5894	228	5	intuitionistic	intuitionistic	ADJ
ejpam-5894	228	6	fuzzy	fuzzy	ADJ
ejpam-5894	228	7	wsbg	wsbg	NOUN
ejpam-5894	228	8	-	-	PUNCT
ejpam-5894	228	9	ideal	ideal	NOUN
ejpam-5894	228	10	of	of	ADP
ejpam-5894	228	11	l.	l.	PROPN
ejpam-5894	228	12	however	however	ADV
ejpam-5894	228	13	,	,	PUNCT
ejpam-5894	228	14	l	l	NOUN
ejpam-5894	228	15	is	be	AUX
ejpam-5894	228	16	not	not	PART
ejpam-5894	228	17	an	an	DET
ejpam-5894	228	18	intuitionistic	intuitionistic	ADJ
ejpam-5894	228	19	fuzzy	fuzzy	ADJ
ejpam-5894	228	20	sub	sub	ADJ
ejpam-5894	228	21	-	-	ADJ
ejpam-5894	228	22	implicative	implicative	ADJ
ejpam-5894	228	23	wsbg	wsbg	NOUN
ejpam-5894	228	24	-	-	PUNCT
ejpam-5894	228	25	ideal	ideal	ADJ
ejpam-5894	228	26	because	because	SCONJ
ejpam-5894	228	27	it	it	PRON
ejpam-5894	228	28	violates	violate	VERB
ejpam-5894	228	29	the	the	DET
ejpam-5894	228	30	condition	condition	NOUN
ejpam-5894	228	31	:	:	PUNCT
ejpam-5894	228	32	β(0	β(0	NOUN
ejpam-5894	228	33	)	)	PUNCT
ejpam-5894	228	34	≤	≤	NOUN
ejpam-5894	228	35	β(ζ	β(ζ	PROPN
ejpam-5894	228	36	)	)	PUNCT
ejpam-5894	228	37	,	,	PUNCT
ejpam-5894	228	38	∀ζ	∀ζ	PROPN
ejpam-5894	228	39	∈	∈	PROPN
ejpam-5894	228	40	l	l	NOUN
ejpam-5894	228	41	,	,	PUNCT
ejpam-5894	228	42	which	which	PRON
ejpam-5894	228	43	fails	fail	VERB
ejpam-5894	228	44	at	at	ADP
ejpam-5894	228	45	ζ	ζ	NOUN
ejpam-5894	228	46	=	=	SYM
ejpam-5894	228	47	a	a	NOUN
ejpam-5894	228	48	,	,	PUNCT
ejpam-5894	228	49	since	since	SCONJ
ejpam-5894	228	50	:	:	PUNCT
ejpam-5894	228	51	β(0	β(0	NOUN
ejpam-5894	228	52	)	)	PUNCT
ejpam-5894	228	53	=	=	PUNCT
ejpam-5894	228	54	0.25	0.25	NUM
ejpam-5894	228	55	>	>	PUNCT
ejpam-5894	228	56	β(a	β(a	PROPN
ejpam-5894	228	57	)	)	PUNCT
ejpam-5894	228	58	=	=	SYM
ejpam-5894	229	1	0	0	X
ejpam-5894	229	2	.	.	PUNCT
ejpam-5894	230	1	therefore	therefore	ADV
ejpam-5894	230	2	,	,	PUNCT
ejpam-5894	230	3	this	this	DET
ejpam-5894	230	4	example	example	NOUN
ejpam-5894	230	5	demonstrates	demonstrate	VERB
ejpam-5894	230	6	that	that	SCONJ
ejpam-5894	230	7	an	an	DET
ejpam-5894	230	8	intuitionistic	intuitionistic	ADJ
ejpam-5894	230	9	fuzzy	fuzzy	ADJ
ejpam-5894	230	10	wsbg	wsbg	NOUN
ejpam-5894	230	11	-	-	PUNCT
ejpam-5894	230	12	ideal	ideal	NOUN
ejpam-5894	230	13	is	be	AUX
ejpam-5894	230	14	not	not	PART
ejpam-5894	230	15	necessarily	necessarily	ADV
ejpam-5894	230	16	an	an	DET
ejpam-5894	230	17	intuitionistic	intuitionistic	ADJ
ejpam-5894	230	18	fuzzy	fuzzy	ADJ
ejpam-5894	230	19	sub	sub	ADJ
ejpam-5894	230	20	-	-	ADJ
ejpam-5894	230	21	implicative	implicative	ADJ
ejpam-5894	230	22	wsbg	wsbg	NOUN
ejpam-5894	230	23	-	-	PUNCT
ejpam-5894	230	24	ideal	ideal	ADJ
ejpam-5894	230	25	.	.	PUNCT
ejpam-5894	231	1	t.	t.	PROPN
ejpam-5894	231	2	oner	oner	PROPN
ejpam-5894	231	3	et	et	PROPN
ejpam-5894	231	4	al	al	PROPN
ejpam-5894	231	5	.	.	PUNCT
ejpam-5894	231	6	/	/	SYM
ejpam-5894	231	7	eur	eur	PROPN
ejpam-5894	231	8	.	.	PUNCT
ejpam-5894	232	1	j.	j.	PROPN
ejpam-5894	232	2	pure	pure	PROPN
ejpam-5894	232	3	appl	appl	PROPN
ejpam-5894	232	4	.	.	PROPN
ejpam-5894	232	5	math	math	PROPN
ejpam-5894	232	6	,	,	PUNCT
ejpam-5894	232	7	18	18	NUM
ejpam-5894	232	8	(	(	PUNCT
ejpam-5894	232	9	3	3	NUM
ejpam-5894	232	10	)	)	PUNCT
ejpam-5894	232	11	(	(	PUNCT
ejpam-5894	232	12	2025	2025	NUM
ejpam-5894	232	13	)	)	PUNCT
ejpam-5894	232	14	,	,	PUNCT
ejpam-5894	232	15	5894	5894	NUM
ejpam-5894	232	16	13	13	NUM
ejpam-5894	232	17	of	of	ADP
ejpam-5894	232	18	33	33	NUM
ejpam-5894	232	19	theorem	theorem	NOUN
ejpam-5894	232	20	4	4	NUM
ejpam-5894	232	21	.	.	PUNCT
ejpam-5894	233	1	let	let	AUX
ejpam-5894	233	2	l	l	NOUN
ejpam-5894	233	3	=	=	SYM
ejpam-5894	233	4	(	(	PUNCT
ejpam-5894	233	5	l	l	NOUN
ejpam-5894	233	6	,	,	PUNCT
ejpam-5894	233	7	α	α	X
ejpam-5894	233	8	,	,	PUNCT
ejpam-5894	233	9	β	β	NOUN
ejpam-5894	233	10	)	)	PUNCT
ejpam-5894	233	11	be	be	VERB
ejpam-5894	233	12	an	an	DET
ejpam-5894	233	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	233	14	fuzzy	fuzzy	ADJ
ejpam-5894	233	15	wsbg	wsbg	NOUN
ejpam-5894	233	16	-	-	PUNCT
ejpam-5894	233	17	ideal	ideal	NOUN
ejpam-5894	233	18	of	of	ADP
ejpam-5894	233	19	a	a	DET
ejpam-5894	233	20	wsbg	wsbg	ADV
ejpam-5894	233	21	-	-	PUNCT
ejpam-5894	233	22	algebra	algebra	NOUN
ejpam-5894	233	23	l	l	NOUN
ejpam-5894	233	24	=	=	PUNCT
ejpam-5894	233	25	⟨l	⟨l	NOUN
ejpam-5894	233	26	;	;	PUNCT
ejpam-5894	233	27	|	|	ADV
ejpam-5894	233	28	,	,	PUNCT
ejpam-5894	233	29	0⟩.	0⟩.	PROPN
ejpam-5894	233	30	then	then	ADV
ejpam-5894	233	31	l	l	PROPN
ejpam-5894	234	1	=	=	PUNCT
ejpam-5894	234	2	(	(	PUNCT
ejpam-5894	234	3	l	l	NOUN
ejpam-5894	234	4	,	,	PUNCT
ejpam-5894	234	5	α	α	X
ejpam-5894	234	6	,	,	PUNCT
ejpam-5894	234	7	β	β	NOUN
ejpam-5894	234	8	)	)	PUNCT
ejpam-5894	234	9	is	be	AUX
ejpam-5894	234	10	an	an	DET
ejpam-5894	234	11	intuitionistic	intuitionistic	ADJ
ejpam-5894	234	12	fuzzy	fuzzy	ADJ
ejpam-5894	234	13	sub	sub	ADJ
ejpam-5894	234	14	-	-	ADJ
ejpam-5894	234	15	implicative	implicative	ADJ
ejpam-5894	234	16	wsbg	wsbg	NOUN
ejpam-5894	234	17	-	-	PUNCT
ejpam-5894	234	18	ideal	ideal	NOUN
ejpam-5894	234	19	of	of	ADP
ejpam-5894	234	20	l	l	NOUN
ejpam-5894	234	21	if	if	SCONJ
ejpam-5894	234	22	and	and	CCONJ
ejpam-5894	234	23	only	only	ADV
ejpam-5894	234	24	if	if	SCONJ
ejpam-5894	234	25	for	for	ADP
ejpam-5894	234	26	all	all	DET
ejpam-5894	234	27	ζ	ζ	NOUN
ejpam-5894	234	28	,	,	PUNCT
ejpam-5894	234	29	η	η	PROPN
ejpam-5894	234	30	∈	∈	PROPN
ejpam-5894	234	31	l	l	NOUN
ejpam-5894	234	32	,	,	PUNCT
ejpam-5894	234	33	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	234	34	)	)	PUNCT
ejpam-5894	234	35	)	)	PUNCT
ejpam-5894	234	36	)	)	PUNCT
ejpam-5894	234	37	)	)	PUNCT
ejpam-5894	234	38	≥	≥	PROPN
ejpam-5894	234	39	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	234	40	)	)	PUNCT
ejpam-5894	234	41	)	)	PUNCT
ejpam-5894	234	42	)	)	PUNCT
ejpam-5894	234	43	)	)	PUNCT
ejpam-5894	234	44	and	and	CCONJ
ejpam-5894	234	45	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	PROPN
ejpam-5894	234	46	)	)	PUNCT
ejpam-5894	234	47	)	)	PUNCT
ejpam-5894	234	48	)	)	PUNCT
ejpam-5894	234	49	)	)	PUNCT
ejpam-5894	234	50	≤	≤	NUM
ejpam-5894	234	51	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	234	52	)	)	PUNCT
ejpam-5894	234	53	)	)	PUNCT
ejpam-5894	234	54	)	)	PUNCT
ejpam-5894	234	55	)	)	PUNCT
ejpam-5894	234	56	.	.	PUNCT
ejpam-5894	235	1	proof	proof	NOUN
ejpam-5894	235	2	.	.	PUNCT
ejpam-5894	236	1	let	let	VERB
ejpam-5894	236	2	l	l	NOUN
ejpam-5894	236	3	=	=	SYM
ejpam-5894	236	4	(	(	PUNCT
ejpam-5894	236	5	l	l	NOUN
ejpam-5894	236	6	,	,	PUNCT
ejpam-5894	236	7	α	α	X
ejpam-5894	236	8	,	,	PUNCT
ejpam-5894	236	9	β	β	NOUN
ejpam-5894	236	10	)	)	PUNCT
ejpam-5894	236	11	be	be	VERB
ejpam-5894	236	12	an	an	DET
ejpam-5894	236	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	236	14	fuzzy	fuzzy	ADJ
ejpam-5894	236	15	sub	sub	ADJ
ejpam-5894	236	16	-	-	ADJ
ejpam-5894	236	17	implicative	implicative	ADJ
ejpam-5894	236	18	wsbg	wsbg	NOUN
ejpam-5894	236	19	-	-	PUNCT
ejpam-5894	236	20	ideal	ideal	NOUN
ejpam-5894	236	21	of	of	ADP
ejpam-5894	236	22	l	l	NOUN
ejpam-5894	236	23	=	=	SYM
ejpam-5894	236	24	⟨l	⟨l	NOUN
ejpam-5894	236	25	;	;	PUNCT
ejpam-5894	236	26	|	|	ADV
ejpam-5894	236	27	,	,	PUNCT
ejpam-5894	236	28	0⟩.	0⟩.	VERB
ejpam-5894	236	29	by	by	ADP
ejpam-5894	236	30	definition	definition	NOUN
ejpam-5894	236	31	,	,	PUNCT
ejpam-5894	236	32	we	we	PRON
ejpam-5894	236	33	have	have	VERB
ejpam-5894	236	34	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	VERB
ejpam-5894	236	35	)	)	PUNCT
ejpam-5894	236	36	)	)	PUNCT
ejpam-5894	236	37	)	)	PUNCT
ejpam-5894	236	38	)	)	PUNCT
ejpam-5894	237	1	≥	≥	PROPN
ejpam-5894	237	2	min{α(φ(ζ	min{α(φ(ζ	PROPN
ejpam-5894	237	3	,	,	PUNCT
ejpam-5894	237	4	η	η	PROPN
ejpam-5894	237	5	,	,	PUNCT
ejpam-5894	237	6	0	0	NUM
ejpam-5894	237	7	)	)	PUNCT
ejpam-5894	237	8	)	)	PUNCT
ejpam-5894	237	9	,	,	PUNCT
ejpam-5894	237	10	α(0	α(0	NOUN
ejpam-5894	237	11	)	)	PUNCT
ejpam-5894	237	12	}	}	PUNCT
ejpam-5894	237	13	,	,	PUNCT
ejpam-5894	237	14	where	where	SCONJ
ejpam-5894	237	15	φ(ζ	φ(ζ	NOUN
ejpam-5894	237	16	,	,	PUNCT
ejpam-5894	237	17	η	η	NOUN
ejpam-5894	237	18	,	,	PUNCT
ejpam-5894	237	19	0	0	NUM
ejpam-5894	237	20	)	)	PUNCT
ejpam-5894	237	21	=	=	SYM
ejpam-5894	237	22	(	(	PUNCT
ejpam-5894	237	23	(	(	PUNCT
ejpam-5894	237	24	(	(	PUNCT
ejpam-5894	237	25	(	(	PUNCT
ejpam-5894	237	26	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(0|0))|(((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(0|0	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(0|0))|(((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(0|0	X
ejpam-5894	237	27	)	)	PUNCT
ejpam-5894	237	28	)	)	PUNCT
ejpam-5894	237	29	)	)	PUNCT
ejpam-5894	237	30	.	.	PUNCT
ejpam-5894	238	1	this	this	DET
ejpam-5894	238	2	simplifies	simplifie	NOUN
ejpam-5894	238	3	to	to	ADP
ejpam-5894	238	4	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	238	5	)	)	PUNCT
ejpam-5894	238	6	)	)	PUNCT
ejpam-5894	238	7	)	)	PUNCT
ejpam-5894	238	8	)	)	PUNCT
ejpam-5894	238	9	≥	≥	PROPN
ejpam-5894	238	10	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	238	11	)	)	PUNCT
ejpam-5894	238	12	)	)	PUNCT
ejpam-5894	238	13	)	)	PUNCT
ejpam-5894	238	14	)	)	PUNCT
ejpam-5894	238	15	.	.	PUNCT
ejpam-5894	239	1	similarly	similarly	ADV
ejpam-5894	239	2	,	,	PUNCT
ejpam-5894	239	3	for	for	ADP
ejpam-5894	239	4	β	β	X
ejpam-5894	239	5	,	,	PUNCT
ejpam-5894	239	6	we	we	PRON
ejpam-5894	239	7	have	have	VERB
ejpam-5894	239	8	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	239	9	)	)	PUNCT
ejpam-5894	239	10	)	)	PUNCT
ejpam-5894	239	11	)	)	PUNCT
ejpam-5894	239	12	)	)	PUNCT
ejpam-5894	240	1	≤	≤	PROPN
ejpam-5894	240	2	max{β(φ(ζ	max{β(φ(ζ	PROPN
ejpam-5894	240	3	,	,	PUNCT
ejpam-5894	240	4	η	η	PROPN
ejpam-5894	240	5	,	,	PUNCT
ejpam-5894	240	6	0	0	NUM
ejpam-5894	240	7	)	)	PUNCT
ejpam-5894	240	8	)	)	PUNCT
ejpam-5894	240	9	,	,	PUNCT
ejpam-5894	240	10	β(0	β(0	PROPN
ejpam-5894	240	11	)	)	PUNCT
ejpam-5894	240	12	}	}	PUNCT
ejpam-5894	240	13	.	.	PUNCT
ejpam-5894	241	1	this	this	DET
ejpam-5894	241	2	simplifies	simplifie	NOUN
ejpam-5894	241	3	to	to	ADP
ejpam-5894	241	4	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	241	5	)	)	PUNCT
ejpam-5894	241	6	)	)	PUNCT
ejpam-5894	241	7	)	)	PUNCT
ejpam-5894	241	8	)	)	PUNCT
ejpam-5894	241	9	≤	≤	NUM
ejpam-5894	241	10	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	241	11	)	)	PUNCT
ejpam-5894	241	12	)	)	PUNCT
ejpam-5894	241	13	)	)	PUNCT
ejpam-5894	241	14	)	)	PUNCT
ejpam-5894	241	15	.	.	PUNCT
ejpam-5894	242	1	conversely	conversely	ADV
ejpam-5894	242	2	,	,	PUNCT
ejpam-5894	242	3	assume	assume	VERB
ejpam-5894	242	4	that	that	SCONJ
ejpam-5894	242	5	the	the	DET
ejpam-5894	242	6	conditions	condition	NOUN
ejpam-5894	242	7	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	VERB
ejpam-5894	242	8	)	)	PUNCT
ejpam-5894	242	9	)	)	PUNCT
ejpam-5894	242	10	)	)	PUNCT
ejpam-5894	242	11	)	)	PUNCT
ejpam-5894	242	12	≥	≥	PROPN
ejpam-5894	242	13	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	242	14	)	)	PUNCT
ejpam-5894	242	15	)	)	PUNCT
ejpam-5894	242	16	)	)	PUNCT
ejpam-5894	242	17	)	)	PUNCT
ejpam-5894	242	18	and	and	CCONJ
ejpam-5894	242	19	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	PROPN
ejpam-5894	242	20	)	)	PUNCT
ejpam-5894	242	21	)	)	PUNCT
ejpam-5894	242	22	)	)	PUNCT
ejpam-5894	242	23	)	)	PUNCT
ejpam-5894	242	24	≤	≤	NUM
ejpam-5894	242	25	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	242	26	)	)	PUNCT
ejpam-5894	242	27	)	)	PUNCT
ejpam-5894	242	28	)	)	PUNCT
ejpam-5894	242	29	)	)	PUNCT
ejpam-5894	242	30	hold	hold	VERB
ejpam-5894	242	31	.	.	PUNCT
ejpam-5894	243	1	since	since	SCONJ
ejpam-5894	243	2	l	l	NOUN
ejpam-5894	243	3	=	=	SYM
ejpam-5894	243	4	(	(	PUNCT
ejpam-5894	243	5	l	l	NOUN
ejpam-5894	243	6	,	,	PUNCT
ejpam-5894	243	7	α	α	X
ejpam-5894	243	8	,	,	PUNCT
ejpam-5894	243	9	β	β	NOUN
ejpam-5894	243	10	)	)	PUNCT
ejpam-5894	243	11	is	be	AUX
ejpam-5894	243	12	an	an	DET
ejpam-5894	243	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	243	14	fuzzy	fuzzy	ADJ
ejpam-5894	243	15	wsbg	wsbg	NOUN
ejpam-5894	243	16	-	-	PUNCT
ejpam-5894	243	17	ideal	ideal	NOUN
ejpam-5894	243	18	of	of	ADP
ejpam-5894	243	19	l	l	NOUN
ejpam-5894	243	20	,	,	PUNCT
ejpam-5894	243	21	we	we	PRON
ejpam-5894	243	22	know	know	VERB
ejpam-5894	243	23	α(0	α(0	PROPN
ejpam-5894	243	24	)	)	PUNCT
ejpam-5894	243	25	≥	≥	NOUN
ejpam-5894	243	26	α(ζ	α(ζ	PROPN
ejpam-5894	243	27	)	)	PUNCT
ejpam-5894	243	28	and	and	CCONJ
ejpam-5894	243	29	β(0	β(0	PROPN
ejpam-5894	243	30	)	)	PUNCT
ejpam-5894	243	31	≤	≤	NOUN
ejpam-5894	243	32	β(ζ	β(ζ	NUM
ejpam-5894	243	33	)	)	PUNCT
ejpam-5894	243	34	.	.	PUNCT
ejpam-5894	244	1	using	use	VERB
ejpam-5894	244	2	these	these	DET
ejpam-5894	244	3	properties	property	NOUN
ejpam-5894	244	4	,	,	PUNCT
ejpam-5894	244	5	we	we	PRON
ejpam-5894	244	6	verify	verify	VERB
ejpam-5894	244	7	that	that	SCONJ
ejpam-5894	244	8	l	l	NOUN
ejpam-5894	244	9	=	=	SYM
ejpam-5894	244	10	(	(	PUNCT
ejpam-5894	244	11	l	l	NOUN
ejpam-5894	244	12	,	,	PUNCT
ejpam-5894	244	13	α	α	X
ejpam-5894	244	14	,	,	PUNCT
ejpam-5894	244	15	β	β	NOUN
ejpam-5894	244	16	)	)	PUNCT
ejpam-5894	244	17	satisfies	satisfy	VERB
ejpam-5894	244	18	the	the	DET
ejpam-5894	244	19	conditions	condition	NOUN
ejpam-5894	244	20	of	of	ADP
ejpam-5894	244	21	an	an	DET
ejpam-5894	244	22	intuitionistic	intuitionistic	ADJ
ejpam-5894	244	23	fuzzy	fuzzy	ADJ
ejpam-5894	244	24	sub	sub	ADJ
ejpam-5894	244	25	-	-	ADJ
ejpam-5894	244	26	implicative	implicative	ADJ
ejpam-5894	244	27	wsbg	wsbg	NOUN
ejpam-5894	244	28	-	-	PUNCT
ejpam-5894	244	29	ideal	ideal	NOUN
ejpam-5894	244	30	of	of	ADP
ejpam-5894	244	31	l.	l.	NOUN
ejpam-5894	244	32	for	for	ADP
ejpam-5894	244	33	α	α	NOUN
ejpam-5894	244	34	,	,	PUNCT
ejpam-5894	244	35	we	we	PRON
ejpam-5894	244	36	compute	compute	VERB
ejpam-5894	244	37	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	244	38	)	)	PUNCT
ejpam-5894	244	39	)	)	PUNCT
ejpam-5894	244	40	)	)	PUNCT
ejpam-5894	244	41	)	)	PUNCT
ejpam-5894	245	1	≥	≥	PROPN
ejpam-5894	245	2	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	245	3	)	)	PUNCT
ejpam-5894	245	4	)	)	PUNCT
ejpam-5894	245	5	)	)	PUNCT
ejpam-5894	245	6	)	)	PUNCT
ejpam-5894	245	7	≥	≥	PROPN
ejpam-5894	245	8	min{α(φ(ζ	min{α(φ(ζ	PROPN
ejpam-5894	245	9	,	,	PUNCT
ejpam-5894	245	10	η	η	PROPN
ejpam-5894	245	11	,	,	PUNCT
ejpam-5894	245	12	θ	θ	NOUN
ejpam-5894	245	13	)	)	PUNCT
ejpam-5894	245	14	)	)	PUNCT
ejpam-5894	245	15	,	,	PUNCT
ejpam-5894	245	16	α(θ	α(θ	NOUN
ejpam-5894	245	17	)	)	PUNCT
ejpam-5894	245	18	}	}	PUNCT
ejpam-5894	245	19	.	.	PUNCT
ejpam-5894	246	1	for	for	ADP
ejpam-5894	246	2	β	β	X
ejpam-5894	246	3	,	,	PUNCT
ejpam-5894	246	4	we	we	PRON
ejpam-5894	246	5	compute	compute	VERB
ejpam-5894	246	6	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	PROPN
ejpam-5894	246	7	)	)	PUNCT
ejpam-5894	246	8	)	)	PUNCT
ejpam-5894	246	9	)	)	PUNCT
ejpam-5894	246	10	)	)	PUNCT
ejpam-5894	247	1	≤	≤	NUM
ejpam-5894	247	2	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	247	3	)	)	PUNCT
ejpam-5894	247	4	)	)	PUNCT
ejpam-5894	247	5	)	)	PUNCT
ejpam-5894	247	6	)	)	PUNCT
ejpam-5894	248	1	≤	≤	PROPN
ejpam-5894	248	2	max{β(φ(ζ	max{β(φ(ζ	PROPN
ejpam-5894	248	3	,	,	PUNCT
ejpam-5894	248	4	η	η	NOUN
ejpam-5894	248	5	,	,	PUNCT
ejpam-5894	248	6	θ	θ	NOUN
ejpam-5894	248	7	)	)	PUNCT
ejpam-5894	248	8	)	)	PUNCT
ejpam-5894	248	9	,	,	PUNCT
ejpam-5894	248	10	β(θ	β(θ	NUM
ejpam-5894	248	11	)	)	PUNCT
ejpam-5894	248	12	}	}	PUNCT
ejpam-5894	248	13	.	.	PUNCT
ejpam-5894	249	1	thus	thus	ADV
ejpam-5894	249	2	,	,	PUNCT
ejpam-5894	249	3	l	l	NOUN
ejpam-5894	249	4	=	=	SYM
ejpam-5894	249	5	(	(	PUNCT
ejpam-5894	249	6	l	l	NOUN
ejpam-5894	249	7	,	,	PUNCT
ejpam-5894	249	8	α	α	X
ejpam-5894	249	9	,	,	PUNCT
ejpam-5894	249	10	β	β	NOUN
ejpam-5894	249	11	)	)	PUNCT
ejpam-5894	249	12	is	be	AUX
ejpam-5894	249	13	an	an	DET
ejpam-5894	249	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	249	15	fuzzy	fuzzy	ADJ
ejpam-5894	249	16	sub	sub	ADJ
ejpam-5894	249	17	-	-	ADJ
ejpam-5894	249	18	implicative	implicative	ADJ
ejpam-5894	249	19	wsbg	wsbg	NOUN
ejpam-5894	249	20	-	-	PUNCT
ejpam-5894	249	21	ideal	ideal	NOUN
ejpam-5894	249	22	of	of	ADP
ejpam-5894	249	23	l.	l.	PROPN
ejpam-5894	249	24	this	this	PRON
ejpam-5894	249	25	completes	complete	VERB
ejpam-5894	249	26	the	the	DET
ejpam-5894	249	27	proof	proof	NOUN
ejpam-5894	249	28	.	.	PUNCT
ejpam-5894	250	1	the	the	DET
ejpam-5894	250	2	identity	identity	NOUN
ejpam-5894	250	3	used	use	VERB
ejpam-5894	250	4	in	in	ADP
ejpam-5894	250	5	theorem	theorem	NOUN
ejpam-5894	250	6	4	4	NUM
ejpam-5894	250	7	is	be	AUX
ejpam-5894	250	8	not	not	PART
ejpam-5894	250	9	an	an	DET
ejpam-5894	250	10	assumption	assumption	NOUN
ejpam-5894	250	11	but	but	CCONJ
ejpam-5894	250	12	a	a	DET
ejpam-5894	250	13	necessary	necessary	ADJ
ejpam-5894	250	14	and	and	CCONJ
ejpam-5894	250	15	sufficient	sufficient	ADJ
ejpam-5894	250	16	condition	condition	NOUN
ejpam-5894	250	17	that	that	PRON
ejpam-5894	250	18	fully	fully	ADV
ejpam-5894	250	19	characterizes	characterize	VERB
ejpam-5894	250	20	when	when	SCONJ
ejpam-5894	250	21	an	an	DET
ejpam-5894	250	22	intuitionistic	intuitionistic	ADJ
ejpam-5894	250	23	fuzzy	fuzzy	ADJ
ejpam-5894	250	24	wsbg	wsbg	NOUN
ejpam-5894	250	25	-	-	PUNCT
ejpam-5894	250	26	ideal	ideal	NOUN
ejpam-5894	250	27	becomes	become	VERB
ejpam-5894	250	28	a	a	DET
ejpam-5894	250	29	sub	sub	ADJ
ejpam-5894	250	30	-	-	ADJ
ejpam-5894	250	31	implicative	implicative	ADJ
ejpam-5894	250	32	wsbg	wsbg	NOUN
ejpam-5894	250	33	-	-	PUNCT
ejpam-5894	250	34	ideal	ideal	ADJ
ejpam-5894	250	35	.	.	PUNCT
ejpam-5894	251	1	t.	t.	PROPN
ejpam-5894	251	2	oner	oner	PROPN
ejpam-5894	251	3	et	et	PROPN
ejpam-5894	251	4	al	al	PROPN
ejpam-5894	251	5	.	.	PUNCT
ejpam-5894	251	6	/	/	SYM
ejpam-5894	251	7	eur	eur	PROPN
ejpam-5894	251	8	.	.	PUNCT
ejpam-5894	252	1	j.	j.	PROPN
ejpam-5894	252	2	pure	pure	PROPN
ejpam-5894	252	3	appl	appl	PROPN
ejpam-5894	252	4	.	.	PROPN
ejpam-5894	252	5	math	math	PROPN
ejpam-5894	252	6	,	,	PUNCT
ejpam-5894	252	7	18	18	NUM
ejpam-5894	252	8	(	(	PUNCT
ejpam-5894	252	9	3	3	NUM
ejpam-5894	252	10	)	)	PUNCT
ejpam-5894	252	11	(	(	PUNCT
ejpam-5894	252	12	2025	2025	NUM
ejpam-5894	252	13	)	)	PUNCT
ejpam-5894	252	14	,	,	PUNCT
ejpam-5894	252	15	5894	5894	NUM
ejpam-5894	252	16	14	14	NUM
ejpam-5894	252	17	of	of	ADP
ejpam-5894	252	18	33	33	NUM
ejpam-5894	252	19	definition	definition	NOUN
ejpam-5894	252	20	12	12	NUM
ejpam-5894	252	21	.	.	PUNCT
ejpam-5894	253	1	a	a	DET
ejpam-5894	253	2	wsbg	wsbg	ADV
ejpam-5894	253	3	-	-	PUNCT
ejpam-5894	253	4	algebra	algebra	NOUN
ejpam-5894	253	5	is	be	AUX
ejpam-5894	253	6	said	say	VERB
ejpam-5894	253	7	to	to	PART
ejpam-5894	253	8	be	be	AUX
ejpam-5894	253	9	implicative	implicative	ADJ
ejpam-5894	253	10	if	if	SCONJ
ejpam-5894	253	11	it	it	PRON
ejpam-5894	253	12	satisfies	satisfy	VERB
ejpam-5894	253	13	the	the	DET
ejpam-5894	253	14	following	follow	VERB
ejpam-5894	253	15	condition	condition	NOUN
ejpam-5894	253	16	:	:	PUNCT
ejpam-5894	253	17	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	253	18	)	)	PUNCT
ejpam-5894	253	19	)	)	PUNCT
ejpam-5894	254	1	=	=	SYM
ejpam-5894	254	2	η|(η|(ζ|ζ	η|(η|(ζ|ζ	NOUN
ejpam-5894	254	3	)	)	PUNCT
ejpam-5894	254	4	)	)	PUNCT
ejpam-5894	254	5	,	,	PUNCT
ejpam-5894	254	6	∀ζ	∀ζ	PROPN
ejpam-5894	254	7	,	,	PUNCT
ejpam-5894	254	8	η	η	PROPN
ejpam-5894	254	9	∈	∈	PROPN
ejpam-5894	254	10	l.	l.	PROPN
ejpam-5894	254	11	example	example	NOUN
ejpam-5894	254	12	8	8	NUM
ejpam-5894	254	13	.	.	PUNCT
ejpam-5894	254	14	consider	consider	VERB
ejpam-5894	254	15	the	the	DET
ejpam-5894	254	16	algebra	algebra	NOUN
ejpam-5894	254	17	l	l	NOUN
ejpam-5894	254	18	=	=	PUNCT
ejpam-5894	254	19	⟨l	⟨l	NOUN
ejpam-5894	254	20	;	;	PUNCT
ejpam-5894	254	21	|	|	ADV
ejpam-5894	254	22	,	,	PUNCT
ejpam-5894	254	23	0⟩	0⟩	PROPN
ejpam-5894	254	24	with	with	ADP
ejpam-5894	254	25	l	l	NOUN
ejpam-5894	254	26	=	=	PUNCT
ejpam-5894	254	27	{	{	PUNCT
ejpam-5894	254	28	0	0	NUM
ejpam-5894	254	29	,	,	PUNCT
ejpam-5894	254	30	1	1	NUM
ejpam-5894	254	31	,	,	PUNCT
ejpam-5894	254	32	2	2	NUM
ejpam-5894	254	33	,	,	PUNCT
ejpam-5894	254	34	3	3	NUM
ejpam-5894	254	35	,	,	PUNCT
ejpam-5894	254	36	4	4	NUM
ejpam-5894	254	37	}	}	PUNCT
ejpam-5894	254	38	and	and	CCONJ
ejpam-5894	254	39	binary	binary	ADJ
ejpam-5894	254	40	operation	operation	NOUN
ejpam-5894	254	41	|	|	ADV
ejpam-5894	254	42	defined	define	VERB
ejpam-5894	254	43	by	by	ADP
ejpam-5894	254	44	the	the	DET
ejpam-5894	254	45	cayley	cayley	ADJ
ejpam-5894	254	46	table	table	NOUN
ejpam-5894	254	47	:	:	PUNCT
ejpam-5894	255	1	|	|	ADV
ejpam-5894	255	2	0	0	NUM
ejpam-5894	255	3	1	1	NUM
ejpam-5894	255	4	2	2	NUM
ejpam-5894	255	5	3	3	NUM
ejpam-5894	255	6	4	4	NUM
ejpam-5894	255	7	0	0	NUM
ejpam-5894	255	8	0	0	NUM
ejpam-5894	255	9	0	0	NUM
ejpam-5894	255	10	2	2	NUM
ejpam-5894	255	11	3	3	NUM
ejpam-5894	255	12	0	0	NUM
ejpam-5894	255	13	1	1	NUM
ejpam-5894	255	14	2	2	NUM
ejpam-5894	255	15	3	3	NUM
ejpam-5894	255	16	3	3	NUM
ejpam-5894	255	17	0	0	NUM
ejpam-5894	255	18	0	0	NUM
ejpam-5894	255	19	2	2	NUM
ejpam-5894	255	20	2	2	NUM
ejpam-5894	255	21	0	0	NUM
ejpam-5894	255	22	3	3	NUM
ejpam-5894	255	23	0	0	NUM
ejpam-5894	255	24	0	0	NUM
ejpam-5894	255	25	3	3	NUM
ejpam-5894	255	26	3	3	NUM
ejpam-5894	255	27	0	0	NUM
ejpam-5894	255	28	0	0	NUM
ejpam-5894	255	29	2	2	NUM
ejpam-5894	255	30	1	1	NUM
ejpam-5894	255	31	4	4	NUM
ejpam-5894	255	32	0	0	NUM
ejpam-5894	255	33	2	2	NUM
ejpam-5894	255	34	1	1	NUM
ejpam-5894	255	35	3	3	NUM
ejpam-5894	255	36	0	0	NUM
ejpam-5894	255	37	hence	hence	ADV
ejpam-5894	255	38	,	,	PUNCT
ejpam-5894	255	39	this	this	DET
ejpam-5894	255	40	algebra	algebra	NOUN
ejpam-5894	255	41	is	be	AUX
ejpam-5894	255	42	an	an	DET
ejpam-5894	255	43	implicative	implicative	ADJ
ejpam-5894	255	44	wsbg	wsbg	NOUN
ejpam-5894	255	45	-	-	PUNCT
ejpam-5894	255	46	algebra	algebra	NOUN
ejpam-5894	255	47	.	.	PUNCT
ejpam-5894	256	1	theorem	theorem	NOUN
ejpam-5894	256	2	5	5	NUM
ejpam-5894	256	3	.	.	PUNCT
ejpam-5894	257	1	let	let	VERB
ejpam-5894	257	2	l	l	NOUN
ejpam-5894	257	3	=	=	SYM
ejpam-5894	257	4	⟨l	⟨l	NOUN
ejpam-5894	257	5	;	;	PUNCT
ejpam-5894	257	6	|	|	ADV
ejpam-5894	257	7	,	,	PUNCT
ejpam-5894	257	8	0⟩	0⟩	PROPN
ejpam-5894	257	9	be	be	VERB
ejpam-5894	257	10	an	an	DET
ejpam-5894	257	11	implicative	implicative	ADJ
ejpam-5894	257	12	wsbg	wsbg	NOUN
ejpam-5894	257	13	-	-	PUNCT
ejpam-5894	257	14	algebra	algebra	NOUN
ejpam-5894	257	15	.	.	PUNCT
ejpam-5894	258	1	then	then	ADV
ejpam-5894	258	2	every	every	DET
ejpam-5894	258	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	258	4	fuzzy	fuzzy	ADJ
ejpam-5894	258	5	wsbg	wsbg	NOUN
ejpam-5894	258	6	-	-	PUNCT
ejpam-5894	258	7	ideal	ideal	NOUN
ejpam-5894	258	8	of	of	ADP
ejpam-5894	258	9	l	l	NOUN
ejpam-5894	258	10	is	be	AUX
ejpam-5894	258	11	an	an	DET
ejpam-5894	258	12	intuitionistic	intuitionistic	ADJ
ejpam-5894	258	13	fuzzy	fuzzy	ADJ
ejpam-5894	258	14	sub	sub	ADJ
ejpam-5894	258	15	-	-	ADJ
ejpam-5894	258	16	implicative	implicative	ADJ
ejpam-5894	258	17	wsbg	wsbg	NOUN
ejpam-5894	258	18	-	-	PUNCT
ejpam-5894	258	19	ideal	ideal	NOUN
ejpam-5894	258	20	of	of	ADP
ejpam-5894	258	21	l.	l.	PROPN
ejpam-5894	258	22	proof	proof	PROPN
ejpam-5894	258	23	.	.	PUNCT
ejpam-5894	259	1	let	let	VERB
ejpam-5894	259	2	l	l	NOUN
ejpam-5894	259	3	=	=	SYM
ejpam-5894	259	4	(	(	PUNCT
ejpam-5894	259	5	l	l	NOUN
ejpam-5894	259	6	,	,	PUNCT
ejpam-5894	259	7	α	α	X
ejpam-5894	259	8	,	,	PUNCT
ejpam-5894	259	9	β	β	NOUN
ejpam-5894	259	10	)	)	PUNCT
ejpam-5894	259	11	be	be	VERB
ejpam-5894	259	12	an	an	DET
ejpam-5894	259	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	259	14	fuzzy	fuzzy	ADJ
ejpam-5894	259	15	wsbg	wsbg	NOUN
ejpam-5894	259	16	-	-	PUNCT
ejpam-5894	259	17	ideal	ideal	NOUN
ejpam-5894	259	18	of	of	ADP
ejpam-5894	259	19	l	l	NOUN
ejpam-5894	259	20	=	=	SYM
ejpam-5894	259	21	⟨l	⟨l	NOUN
ejpam-5894	259	22	;	;	PUNCT
ejpam-5894	259	23	|	|	ADV
ejpam-5894	259	24	,	,	PUNCT
ejpam-5894	259	25	0⟩.	0⟩.	VERB
ejpam-5894	259	26	by	by	ADP
ejpam-5894	259	27	definition	definition	NOUN
ejpam-5894	259	28	,	,	PUNCT
ejpam-5894	259	29	we	we	PRON
ejpam-5894	259	30	have	have	VERB
ejpam-5894	259	31	α(0	α(0	PROPN
ejpam-5894	259	32	)	)	PUNCT
ejpam-5894	259	33	≥	≥	NOUN
ejpam-5894	259	34	α(ζ	α(ζ	PROPN
ejpam-5894	259	35	)	)	PUNCT
ejpam-5894	259	36	and	and	CCONJ
ejpam-5894	259	37	β(0	β(0	PROPN
ejpam-5894	259	38	)	)	PUNCT
ejpam-5894	259	39	≤	≤	NOUN
ejpam-5894	259	40	β(ζ	β(ζ	PROPN
ejpam-5894	259	41	)	)	PUNCT
ejpam-5894	259	42	,	,	PUNCT
ejpam-5894	259	43	∀ζ	∀ζ	PROPN
ejpam-5894	259	44	∈	∈	PROPN
ejpam-5894	259	45	l.	l.	NOUN
ejpam-5894	259	46	now	now	ADV
ejpam-5894	259	47	,	,	PUNCT
ejpam-5894	259	48	consider	consider	VERB
ejpam-5894	259	49	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	259	50	)	)	PUNCT
ejpam-5894	259	51	)	)	PUNCT
ejpam-5894	259	52	)	)	PUNCT
ejpam-5894	259	53	)	)	PUNCT
ejpam-5894	259	54	.	.	PUNCT
ejpam-5894	260	1	using	use	VERB
ejpam-5894	260	2	the	the	DET
ejpam-5894	260	3	implicative	implicative	ADJ
ejpam-5894	260	4	property	property	NOUN
ejpam-5894	260	5	(	(	PUNCT
ejpam-5894	260	6	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	260	7	)	)	PUNCT
ejpam-5894	260	8	)	)	PUNCT
ejpam-5894	261	1	=	=	SYM
ejpam-5894	261	2	η|(η|(ζ|ζ	η|(η|(ζ|ζ	NOUN
ejpam-5894	261	3	)	)	PUNCT
ejpam-5894	261	4	)	)	PUNCT
ejpam-5894	261	5	)	)	PUNCT
ejpam-5894	261	6	,	,	PUNCT
ejpam-5894	261	7	we	we	PRON
ejpam-5894	261	8	have	have	VERB
ejpam-5894	261	9	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	VERB
ejpam-5894	261	10	)	)	PUNCT
ejpam-5894	261	11	)	)	PUNCT
ejpam-5894	261	12	)	)	PUNCT
ejpam-5894	261	13	)	)	PUNCT
ejpam-5894	262	1	≥	≥	PROPN
ejpam-5894	262	2	min{α(φ(ζ	min{α(φ(ζ	PROPN
ejpam-5894	262	3	,	,	PUNCT
ejpam-5894	262	4	η	η	PROPN
ejpam-5894	262	5	,	,	PUNCT
ejpam-5894	262	6	θ	θ	NOUN
ejpam-5894	262	7	)	)	PUNCT
ejpam-5894	262	8	)	)	PUNCT
ejpam-5894	262	9	,	,	PUNCT
ejpam-5894	262	10	α(θ	α(θ	NOUN
ejpam-5894	262	11	)	)	PUNCT
ejpam-5894	262	12	}	}	PUNCT
ejpam-5894	262	13	,	,	PUNCT
ejpam-5894	262	14	where	where	SCONJ
ejpam-5894	262	15	φ(ζ	φ(ζ	NOUN
ejpam-5894	262	16	,	,	PUNCT
ejpam-5894	262	17	η	η	NOUN
ejpam-5894	262	18	,	,	PUNCT
ejpam-5894	262	19	θ	θ	NOUN
ejpam-5894	262	20	)	)	PUNCT
ejpam-5894	262	21	=	=	SYM
ejpam-5894	262	22	(	(	PUNCT
ejpam-5894	262	23	(	(	PUNCT
ejpam-5894	262	24	(	(	PUNCT
ejpam-5894	262	25	(	(	PUNCT
ejpam-5894	262	26	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ))|(((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ))|(((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ	NOUN
ejpam-5894	262	27	)	)	PUNCT
ejpam-5894	262	28	)	)	PUNCT
ejpam-5894	262	29	)	)	PUNCT
ejpam-5894	262	30	.	.	PUNCT
ejpam-5894	263	1	by	by	ADP
ejpam-5894	263	2	the	the	DET
ejpam-5894	263	3	implicative	implicative	ADJ
ejpam-5894	263	4	property	property	NOUN
ejpam-5894	263	5	,	,	PUNCT
ejpam-5894	263	6	this	this	DET
ejpam-5894	263	7	simplifies	simplifie	NOUN
ejpam-5894	263	8	to	to	ADP
ejpam-5894	263	9	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	263	10	)	)	PUNCT
ejpam-5894	263	11	)	)	PUNCT
ejpam-5894	263	12	)	)	PUNCT
ejpam-5894	263	13	)	)	PUNCT
ejpam-5894	263	14	≥	≥	PROPN
ejpam-5894	263	15	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	263	16	)	)	PUNCT
ejpam-5894	263	17	)	)	PUNCT
ejpam-5894	263	18	)	)	PUNCT
ejpam-5894	263	19	)	)	PUNCT
ejpam-5894	263	20	.	.	PUNCT
ejpam-5894	264	1	similarly	similarly	ADV
ejpam-5894	264	2	,	,	PUNCT
ejpam-5894	264	3	for	for	ADP
ejpam-5894	264	4	β	β	X
ejpam-5894	264	5	,	,	PUNCT
ejpam-5894	264	6	we	we	PRON
ejpam-5894	264	7	have	have	VERB
ejpam-5894	264	8	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	264	9	)	)	PUNCT
ejpam-5894	264	10	)	)	PUNCT
ejpam-5894	264	11	)	)	PUNCT
ejpam-5894	264	12	)	)	PUNCT
ejpam-5894	264	13	.	.	PUNCT
ejpam-5894	265	1	using	use	VERB
ejpam-5894	265	2	the	the	DET
ejpam-5894	265	3	same	same	ADJ
ejpam-5894	265	4	property	property	NOUN
ejpam-5894	265	5	,	,	PUNCT
ejpam-5894	265	6	we	we	PRON
ejpam-5894	265	7	get	get	VERB
ejpam-5894	265	8	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	265	9	)	)	PUNCT
ejpam-5894	265	10	)	)	PUNCT
ejpam-5894	265	11	)	)	PUNCT
ejpam-5894	265	12	)	)	PUNCT
ejpam-5894	266	1	≤	≤	PROPN
ejpam-5894	266	2	max{β(φ(ζ	max{β(φ(ζ	PROPN
ejpam-5894	266	3	,	,	PUNCT
ejpam-5894	266	4	η	η	NOUN
ejpam-5894	266	5	,	,	PUNCT
ejpam-5894	266	6	θ	θ	NOUN
ejpam-5894	266	7	)	)	PUNCT
ejpam-5894	266	8	)	)	PUNCT
ejpam-5894	266	9	,	,	PUNCT
ejpam-5894	266	10	β(θ	β(θ	NUM
ejpam-5894	266	11	)	)	PUNCT
ejpam-5894	266	12	}	}	PUNCT
ejpam-5894	266	13	.	.	PUNCT
ejpam-5894	267	1	this	this	DET
ejpam-5894	267	2	simplifies	simplifie	NOUN
ejpam-5894	267	3	to	to	ADP
ejpam-5894	267	4	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	267	5	)	)	PUNCT
ejpam-5894	267	6	)	)	PUNCT
ejpam-5894	267	7	)	)	PUNCT
ejpam-5894	267	8	)	)	PUNCT
ejpam-5894	267	9	≤	≤	NUM
ejpam-5894	267	10	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	267	11	)	)	PUNCT
ejpam-5894	267	12	)	)	PUNCT
ejpam-5894	267	13	)	)	PUNCT
ejpam-5894	267	14	)	)	PUNCT
ejpam-5894	267	15	.	.	PUNCT
ejpam-5894	268	1	thus	thus	ADV
ejpam-5894	268	2	,	,	PUNCT
ejpam-5894	268	3	l	l	NOUN
ejpam-5894	268	4	=	=	SYM
ejpam-5894	268	5	(	(	PUNCT
ejpam-5894	268	6	l	l	NOUN
ejpam-5894	268	7	,	,	PUNCT
ejpam-5894	268	8	α	α	X
ejpam-5894	268	9	,	,	PUNCT
ejpam-5894	268	10	β	β	NOUN
ejpam-5894	268	11	)	)	PUNCT
ejpam-5894	268	12	is	be	AUX
ejpam-5894	268	13	an	an	DET
ejpam-5894	268	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	268	15	fuzzy	fuzzy	ADJ
ejpam-5894	268	16	sub	sub	ADJ
ejpam-5894	268	17	-	-	ADJ
ejpam-5894	268	18	implicative	implicative	ADJ
ejpam-5894	268	19	wsbg	wsbg	NOUN
ejpam-5894	268	20	-	-	PUNCT
ejpam-5894	268	21	ideal	ideal	NOUN
ejpam-5894	268	22	of	of	ADP
ejpam-5894	268	23	l.	l.	PROPN
ejpam-5894	268	24	t.	t.	PROPN
ejpam-5894	268	25	oner	oner	PROPN
ejpam-5894	268	26	et	et	PROPN
ejpam-5894	268	27	al	al	PROPN
ejpam-5894	268	28	.	.	PUNCT
ejpam-5894	268	29	/	/	SYM
ejpam-5894	268	30	eur	eur	PROPN
ejpam-5894	268	31	.	.	PUNCT
ejpam-5894	269	1	j.	j.	PROPN
ejpam-5894	269	2	pure	pure	PROPN
ejpam-5894	269	3	appl	appl	PROPN
ejpam-5894	269	4	.	.	PROPN
ejpam-5894	269	5	math	math	PROPN
ejpam-5894	269	6	,	,	PUNCT
ejpam-5894	269	7	18	18	NUM
ejpam-5894	269	8	(	(	PUNCT
ejpam-5894	269	9	3	3	NUM
ejpam-5894	269	10	)	)	PUNCT
ejpam-5894	269	11	(	(	PUNCT
ejpam-5894	269	12	2025	2025	NUM
ejpam-5894	269	13	)	)	PUNCT
ejpam-5894	269	14	,	,	PUNCT
ejpam-5894	269	15	5894	5894	NUM
ejpam-5894	269	16	15	15	NUM
ejpam-5894	269	17	of	of	ADP
ejpam-5894	269	18	33	33	NUM
ejpam-5894	269	19	example	example	NOUN
ejpam-5894	269	20	9	9	NUM
ejpam-5894	269	21	.	.	X
ejpam-5894	269	22	consider	consider	VERB
ejpam-5894	269	23	the	the	DET
ejpam-5894	269	24	set	set	NOUN
ejpam-5894	269	25	l	l	NOUN
ejpam-5894	269	26	=	=	PUNCT
ejpam-5894	269	27	{	{	PUNCT
ejpam-5894	269	28	0	0	NUM
ejpam-5894	269	29	,	,	PUNCT
ejpam-5894	269	30	a	a	PRON
ejpam-5894	269	31	,	,	PUNCT
ejpam-5894	269	32	b	b	NOUN
ejpam-5894	269	33	,	,	PUNCT
ejpam-5894	269	34	c	c	NOUN
ejpam-5894	269	35	}	}	PUNCT
ejpam-5894	269	36	equipped	equip	VERB
ejpam-5894	269	37	with	with	ADP
ejpam-5894	269	38	the	the	DET
ejpam-5894	269	39	binary	binary	PROPN
ejpam-5894	269	40	operation	operation	NOUN
ejpam-5894	269	41	|	|	ADV
ejpam-5894	269	42	defined	define	VERB
ejpam-5894	269	43	by	by	ADP
ejpam-5894	269	44	the	the	DET
ejpam-5894	269	45	following	following	ADJ
ejpam-5894	269	46	cayley	cayley	ADJ
ejpam-5894	269	47	table	table	NOUN
ejpam-5894	269	48	:	:	PUNCT
ejpam-5894	269	49	|	|	ADV
ejpam-5894	269	50	0	0	PUNCT
ejpam-5894	269	51	a	a	DET
ejpam-5894	269	52	b	b	NOUN
ejpam-5894	269	53	c	c	NOUN
ejpam-5894	269	54	0	0	NUM
ejpam-5894	269	55	0	0	NUM
ejpam-5894	270	1	b	b	X
ejpam-5894	270	2	c	c	NOUN
ejpam-5894	270	3	a	a	PRON
ejpam-5894	270	4	a	a	DET
ejpam-5894	270	5	b	b	NOUN
ejpam-5894	270	6	0	0	NUM
ejpam-5894	270	7	c	c	PROPN
ejpam-5894	270	8	b	b	PROPN
ejpam-5894	270	9	b	b	PROPN
ejpam-5894	270	10	c	c	PROPN
ejpam-5894	270	11	a	a	DET
ejpam-5894	270	12	0	0	NUM
ejpam-5894	270	13	b	b	NOUN
ejpam-5894	270	14	c	c	NOUN
ejpam-5894	270	15	a	a	DET
ejpam-5894	270	16	c	c	NOUN
ejpam-5894	270	17	0	0	NUM
ejpam-5894	270	18	0	0	NUM
ejpam-5894	270	19	hence	hence	ADV
ejpam-5894	270	20	,	,	PUNCT
ejpam-5894	270	21	l	l	NOUN
ejpam-5894	270	22	=	=	SYM
ejpam-5894	270	23	⟨l	⟨l	NOUN
ejpam-5894	270	24	;	;	PUNCT
ejpam-5894	270	25	|	|	ADV
ejpam-5894	270	26	,	,	PUNCT
ejpam-5894	270	27	0⟩	0⟩	PROPN
ejpam-5894	270	28	is	be	AUX
ejpam-5894	270	29	a	a	DET
ejpam-5894	270	30	wsbg	wsbg	ADV
ejpam-5894	270	31	-	-	PUNCT
ejpam-5894	270	32	algebra	algebra	NOUN
ejpam-5894	270	33	.	.	PUNCT
ejpam-5894	271	1	we	we	PRON
ejpam-5894	271	2	check	check	VERB
ejpam-5894	271	3	whether	whether	SCONJ
ejpam-5894	271	4	the	the	DET
ejpam-5894	271	5	algebra	algebra	NOUN
ejpam-5894	271	6	is	be	AUX
ejpam-5894	271	7	implicative	implicative	ADJ
ejpam-5894	271	8	according	accord	VERB
ejpam-5894	271	9	to	to	ADP
ejpam-5894	271	10	the	the	DET
ejpam-5894	271	11	definition	definition	NOUN
ejpam-5894	271	12	:	:	PUNCT
ejpam-5894	271	13	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	271	14	)	)	PUNCT
ejpam-5894	271	15	)	)	PUNCT
ejpam-5894	272	1	=	=	SYM
ejpam-5894	272	2	η|(η|(ζ|ζ	η|(η|(ζ|ζ	NOUN
ejpam-5894	272	3	)	)	PUNCT
ejpam-5894	272	4	)	)	PUNCT
ejpam-5894	272	5	,	,	PUNCT
ejpam-5894	272	6	∀ζ	∀ζ	PROPN
ejpam-5894	272	7	,	,	PUNCT
ejpam-5894	272	8	η	η	PROPN
ejpam-5894	272	9	∈	∈	PROPN
ejpam-5894	272	10	l.	l.	PROPN
ejpam-5894	272	11	direct	direct	PROPN
ejpam-5894	272	12	computation	computation	NOUN
ejpam-5894	272	13	shows	show	VERB
ejpam-5894	272	14	this	this	DET
ejpam-5894	272	15	condition	condition	NOUN
ejpam-5894	272	16	fails	fail	VERB
ejpam-5894	272	17	for	for	ADP
ejpam-5894	272	18	ζ	ζ	NOUN
ejpam-5894	272	19	=	=	SYM
ejpam-5894	272	20	0	0	NUM
ejpam-5894	272	21	and	and	CCONJ
ejpam-5894	272	22	η	η	PROPN
ejpam-5894	272	23	=	=	PROPN
ejpam-5894	272	24	a.	a.	NOUN
ejpam-5894	272	25	therefore	therefore	ADV
ejpam-5894	272	26	,	,	PUNCT
ejpam-5894	272	27	the	the	DET
ejpam-5894	272	28	algebra	algebra	NOUN
ejpam-5894	272	29	is	be	AUX
ejpam-5894	272	30	not	not	PART
ejpam-5894	272	31	implicative	implicative	ADJ
ejpam-5894	272	32	.	.	PUNCT
ejpam-5894	273	1	define	define	VERB
ejpam-5894	273	2	an	an	DET
ejpam-5894	273	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	273	4	fuzzy	fuzzy	ADJ
ejpam-5894	273	5	set	set	NOUN
ejpam-5894	273	6	l	l	NOUN
ejpam-5894	273	7	=	=	SYM
ejpam-5894	273	8	(	(	PUNCT
ejpam-5894	273	9	l	l	NOUN
ejpam-5894	273	10	,	,	PUNCT
ejpam-5894	273	11	α	α	X
ejpam-5894	273	12	,	,	PUNCT
ejpam-5894	273	13	β	β	NOUN
ejpam-5894	273	14	)	)	PUNCT
ejpam-5894	273	15	as	as	ADP
ejpam-5894	273	16	:	:	PUNCT
ejpam-5894	273	17	α(x	α(x	NOUN
ejpam-5894	273	18	)	)	PUNCT
ejpam-5894	273	19	=	=	SYM
ejpam-5894	273	20	0.5	0.5	NUM
ejpam-5894	273	21	,	,	PUNCT
ejpam-5894	273	22	∀x	∀x	X
ejpam-5894	273	23	∈	∈	PROPN
ejpam-5894	273	24	l	l	NOUN
ejpam-5894	273	25	;	;	PUNCT
ejpam-5894	273	26	β(0	β(0	PROPN
ejpam-5894	273	27	)	)	PUNCT
ejpam-5894	273	28	=	=	PUNCT
ejpam-5894	273	29	β(b	β(b	PUNCT
ejpam-5894	273	30	)	)	PUNCT
ejpam-5894	273	31	=	=	SYM
ejpam-5894	273	32	0.25	0.25	NUM
ejpam-5894	273	33	,	,	PUNCT
ejpam-5894	273	34	β(a	β(a	PROPN
ejpam-5894	273	35	)	)	PUNCT
ejpam-5894	273	36	=	=	SYM
ejpam-5894	273	37	β(c	β(c	PROPN
ejpam-5894	273	38	)	)	PUNCT
ejpam-5894	273	39	=	=	SYM
ejpam-5894	274	1	0	0	X
ejpam-5894	274	2	.	.	PUNCT
ejpam-5894	275	1	it	it	PRON
ejpam-5894	275	2	can	can	AUX
ejpam-5894	275	3	be	be	AUX
ejpam-5894	275	4	verified	verify	VERB
ejpam-5894	275	5	that	that	SCONJ
ejpam-5894	275	6	l	l	NOUN
ejpam-5894	275	7	=	=	SYM
ejpam-5894	275	8	(	(	PUNCT
ejpam-5894	275	9	l	l	NOUN
ejpam-5894	275	10	,	,	PUNCT
ejpam-5894	275	11	α	α	X
ejpam-5894	275	12	,	,	PUNCT
ejpam-5894	275	13	β	β	NOUN
ejpam-5894	275	14	)	)	PUNCT
ejpam-5894	275	15	is	be	AUX
ejpam-5894	275	16	an	an	DET
ejpam-5894	275	17	intuitionistic	intuitionistic	ADJ
ejpam-5894	275	18	fuzzy	fuzzy	ADJ
ejpam-5894	275	19	wsbg	wsbg	NOUN
ejpam-5894	275	20	-	-	PUNCT
ejpam-5894	275	21	ideal	ideal	NOUN
ejpam-5894	275	22	of	of	ADP
ejpam-5894	275	23	l.	l.	PROPN
ejpam-5894	275	24	however	however	ADV
ejpam-5894	275	25	,	,	PUNCT
ejpam-5894	275	26	l	l	PROPN
ejpam-5894	275	27	=	=	SYM
ejpam-5894	275	28	(	(	PUNCT
ejpam-5894	275	29	l	l	NOUN
ejpam-5894	275	30	,	,	PUNCT
ejpam-5894	275	31	α	α	X
ejpam-5894	275	32	,	,	PUNCT
ejpam-5894	275	33	β	β	NOUN
ejpam-5894	275	34	)	)	PUNCT
ejpam-5894	275	35	is	be	AUX
ejpam-5894	275	36	not	not	PART
ejpam-5894	275	37	an	an	DET
ejpam-5894	275	38	intuitionistic	intuitionistic	ADJ
ejpam-5894	275	39	fuzzy	fuzzy	ADJ
ejpam-5894	275	40	sub	sub	ADJ
ejpam-5894	275	41	-	-	ADJ
ejpam-5894	275	42	implicative	implicative	ADJ
ejpam-5894	275	43	wsbg	wsbg	NOUN
ejpam-5894	275	44	-	-	PUNCT
ejpam-5894	275	45	ideal	ideal	ADJ
ejpam-5894	275	46	because	because	SCONJ
ejpam-5894	275	47	it	it	PRON
ejpam-5894	275	48	fails	fail	VERB
ejpam-5894	275	49	the	the	DET
ejpam-5894	275	50	bound	bound	ADJ
ejpam-5894	275	51	condition	condition	NOUN
ejpam-5894	275	52	:	:	PUNCT
ejpam-5894	275	53	β(0	β(0	NOUN
ejpam-5894	275	54	)	)	PUNCT
ejpam-5894	275	55	=	=	NUM
ejpam-5894	275	56	0.25	0.25	NUM
ejpam-5894	275	57	>	>	PUNCT
ejpam-5894	275	58	β(a	β(a	PROPN
ejpam-5894	275	59	)	)	PUNCT
ejpam-5894	275	60	=	=	PUNCT
ejpam-5894	276	1	0	0	X
ejpam-5894	276	2	.	.	PUNCT
ejpam-5894	277	1	this	this	DET
ejpam-5894	277	2	example	example	NOUN
ejpam-5894	277	3	demonstrates	demonstrate	VERB
ejpam-5894	277	4	that	that	SCONJ
ejpam-5894	277	5	in	in	ADP
ejpam-5894	277	6	a	a	DET
ejpam-5894	277	7	wsbg	wsbg	NOUN
ejpam-5894	277	8	-	-	PUNCT
ejpam-5894	277	9	algebra	algebra	NOUN
ejpam-5894	277	10	that	that	PRON
ejpam-5894	277	11	is	be	AUX
ejpam-5894	277	12	not	not	PART
ejpam-5894	277	13	implicative	implicative	ADJ
ejpam-5894	277	14	,	,	PUNCT
ejpam-5894	277	15	an	an	DET
ejpam-5894	277	16	intuitionistic	intuitionistic	ADJ
ejpam-5894	277	17	fuzzy	fuzzy	ADJ
ejpam-5894	277	18	wsbg	wsbg	NOUN
ejpam-5894	277	19	-	-	PUNCT
ejpam-5894	277	20	ideal	ideal	NOUN
ejpam-5894	277	21	may	may	AUX
ejpam-5894	277	22	not	not	PART
ejpam-5894	277	23	be	be	AUX
ejpam-5894	277	24	a	a	DET
ejpam-5894	277	25	sub	sub	ADJ
ejpam-5894	277	26	-	-	ADJ
ejpam-5894	277	27	implicative	implicative	ADJ
ejpam-5894	277	28	fuzzy	fuzzy	ADJ
ejpam-5894	277	29	wsbg	wsbg	NOUN
ejpam-5894	277	30	-	-	PUNCT
ejpam-5894	277	31	ideal	ideal	ADJ
ejpam-5894	277	32	.	.	PUNCT
ejpam-5894	278	1	definition	definition	NOUN
ejpam-5894	278	2	13	13	NUM
ejpam-5894	278	3	.	.	PUNCT
ejpam-5894	279	1	a	a	DET
ejpam-5894	279	2	wsbg	wsbg	ADV
ejpam-5894	279	3	-	-	PUNCT
ejpam-5894	279	4	algebra	algebra	NOUN
ejpam-5894	279	5	l	l	NOUN
ejpam-5894	279	6	=	=	PUNCT
ejpam-5894	279	7	⟨l	⟨l	NOUN
ejpam-5894	279	8	;	;	PUNCT
ejpam-5894	279	9	|	|	ADV
ejpam-5894	279	10	,	,	PUNCT
ejpam-5894	279	11	0⟩	0⟩	PROPN
ejpam-5894	279	12	is	be	AUX
ejpam-5894	279	13	called	call	VERB
ejpam-5894	279	14	medial	medial	ADJ
ejpam-5894	279	15	if	if	SCONJ
ejpam-5894	279	16	it	it	PRON
ejpam-5894	279	17	satisfies	satisfy	VERB
ejpam-5894	279	18	the	the	DET
ejpam-5894	279	19	following	follow	VERB
ejpam-5894	279	20	condition	condition	NOUN
ejpam-5894	279	21	:	:	PUNCT
ejpam-5894	279	22	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	279	23	)	)	PUNCT
ejpam-5894	279	24	)	)	PUNCT
ejpam-5894	280	1	=	=	SYM
ejpam-5894	280	2	η|η	η|η	PROPN
ejpam-5894	280	3	,	,	PUNCT
ejpam-5894	280	4	∀ζ	∀ζ	PROPN
ejpam-5894	280	5	,	,	PUNCT
ejpam-5894	280	6	η	η	PROPN
ejpam-5894	280	7	∈	∈	PROPN
ejpam-5894	280	8	l.	l.	PROPN
ejpam-5894	280	9	example	example	NOUN
ejpam-5894	280	10	10	10	NUM
ejpam-5894	280	11	.	.	PUNCT
ejpam-5894	280	12	consider	consider	VERB
ejpam-5894	280	13	the	the	DET
ejpam-5894	280	14	algebra	algebra	NOUN
ejpam-5894	280	15	l	l	NOUN
ejpam-5894	280	16	=	=	PUNCT
ejpam-5894	280	17	⟨l	⟨l	NOUN
ejpam-5894	280	18	;	;	PUNCT
ejpam-5894	280	19	|	|	ADV
ejpam-5894	280	20	,	,	PUNCT
ejpam-5894	280	21	0⟩	0⟩	PROPN
ejpam-5894	280	22	with	with	ADP
ejpam-5894	280	23	l	l	NOUN
ejpam-5894	280	24	=	=	PUNCT
ejpam-5894	280	25	{	{	PUNCT
ejpam-5894	280	26	0	0	NUM
ejpam-5894	280	27	,	,	PUNCT
ejpam-5894	280	28	1	1	NUM
ejpam-5894	280	29	,	,	PUNCT
ejpam-5894	280	30	2	2	NUM
ejpam-5894	280	31	}	}	PUNCT
ejpam-5894	280	32	and	and	CCONJ
ejpam-5894	280	33	binary	binary	ADJ
ejpam-5894	280	34	operation	operation	NOUN
ejpam-5894	280	35	|	|	ADV
ejpam-5894	280	36	defined	define	VERB
ejpam-5894	280	37	by	by	ADP
ejpam-5894	280	38	the	the	DET
ejpam-5894	280	39	cayley	cayley	ADJ
ejpam-5894	280	40	table	table	NOUN
ejpam-5894	280	41	:	:	PUNCT
ejpam-5894	281	1	|	|	ADV
ejpam-5894	281	2	0	0	NUM
ejpam-5894	281	3	1	1	NUM
ejpam-5894	281	4	2	2	NUM
ejpam-5894	281	5	0	0	NUM
ejpam-5894	281	6	0	0	NUM
ejpam-5894	281	7	1	1	NUM
ejpam-5894	281	8	0	0	NUM
ejpam-5894	281	9	1	1	NUM
ejpam-5894	281	10	0	0	NUM
ejpam-5894	281	11	0	0	NUM
ejpam-5894	281	12	0	0	NUM
ejpam-5894	281	13	2	2	NUM
ejpam-5894	281	14	0	0	NUM
ejpam-5894	281	15	0	0	NUM
ejpam-5894	281	16	0	0	NUM
ejpam-5894	282	1	hence	hence	ADV
ejpam-5894	282	2	,	,	PUNCT
ejpam-5894	282	3	this	this	DET
ejpam-5894	282	4	algebra	algebra	NOUN
ejpam-5894	282	5	is	be	AUX
ejpam-5894	282	6	a	a	DET
ejpam-5894	282	7	medial	medial	ADJ
ejpam-5894	282	8	wsbg	wsbg	NOUN
ejpam-5894	282	9	-	-	PUNCT
ejpam-5894	282	10	algebra	algebra	NOUN
ejpam-5894	282	11	.	.	PUNCT
ejpam-5894	283	1	lemma	lemma	PROPN
ejpam-5894	283	2	1	1	NUM
ejpam-5894	283	3	.	.	PUNCT
ejpam-5894	284	1	in	in	ADP
ejpam-5894	284	2	a	a	DET
ejpam-5894	284	3	medial	medial	ADJ
ejpam-5894	284	4	wsbg	wsbg	NOUN
ejpam-5894	284	5	-	-	PUNCT
ejpam-5894	284	6	algebra	algebra	NOUN
ejpam-5894	284	7	l	l	NOUN
ejpam-5894	284	8	=	=	PUNCT
ejpam-5894	284	9	⟨l	⟨l	NOUN
ejpam-5894	284	10	;	;	PUNCT
ejpam-5894	284	11	|	|	ADV
ejpam-5894	284	12	,	,	PUNCT
ejpam-5894	284	13	0⟩	0⟩	PROPN
ejpam-5894	284	14	,	,	PUNCT
ejpam-5894	284	15	the	the	DET
ejpam-5894	284	16	following	follow	VERB
ejpam-5894	284	17	property	property	NOUN
ejpam-5894	284	18	holds	hold	VERB
ejpam-5894	284	19	:	:	PUNCT
ejpam-5894	284	20	(	(	PUNCT
ejpam-5894	284	21	(	(	PUNCT
ejpam-5894	284	22	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(η|(ζ|ζ	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(η|(ζ|ζ	NOUN
ejpam-5894	284	23	)	)	PUNCT
ejpam-5894	284	24	)	)	PUNCT
ejpam-5894	284	25	=	=	SYM
ejpam-5894	285	1	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	285	2	)	)	PUNCT
ejpam-5894	285	3	)	)	PUNCT
ejpam-5894	285	4	,	,	PUNCT
ejpam-5894	285	5	∀ζ	∀ζ	PROPN
ejpam-5894	285	6	,	,	PUNCT
ejpam-5894	285	7	η	η	PROPN
ejpam-5894	285	8	∈	∈	PROPN
ejpam-5894	285	9	l.	l.	NOUN
ejpam-5894	285	10	proof	proof	PROPN
ejpam-5894	285	11	.	.	PUNCT
ejpam-5894	286	1	let	let	VERB
ejpam-5894	286	2	a	a	DET
ejpam-5894	286	3	=	=	SYM
ejpam-5894	286	4	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	286	5	)	)	PUNCT
ejpam-5894	286	6	)	)	PUNCT
ejpam-5894	286	7	.	.	PUNCT
ejpam-5894	287	1	then	then	ADV
ejpam-5894	287	2	,	,	PUNCT
ejpam-5894	287	3	using	use	VERB
ejpam-5894	287	4	this	this	DET
ejpam-5894	287	5	shorthand	shorthand	NOUN
ejpam-5894	287	6	:	:	PUNCT
ejpam-5894	287	7	(	(	PUNCT
ejpam-5894	287	8	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	NOUN
ejpam-5894	287	9	)	)	PUNCT
ejpam-5894	287	10	)	)	PUNCT
ejpam-5894	287	11	)	)	PUNCT
ejpam-5894	288	1	=	=	PUNCT
ejpam-5894	288	2	a|a	a|a	NOUN
ejpam-5894	288	3	and	and	CCONJ
ejpam-5894	288	4	η|(ζ|ζ	η|(ζ|ζ	PROPN
ejpam-5894	288	5	)	)	PUNCT
ejpam-5894	289	1	=	=	SYM
ejpam-5894	289	2	b.	b.	PROPN
ejpam-5894	289	3	then	then	ADV
ejpam-5894	289	4	the	the	DET
ejpam-5894	289	5	left	left	ADJ
ejpam-5894	289	6	-	-	PUNCT
ejpam-5894	289	7	hand	hand	NOUN
ejpam-5894	289	8	side	side	NOUN
ejpam-5894	289	9	becomes	become	VERB
ejpam-5894	289	10	:	:	PUNCT
ejpam-5894	289	11	(	(	PUNCT
ejpam-5894	289	12	a|a)|b	a|a)|b	PROPN
ejpam-5894	289	13	.	.	PUNCT
ejpam-5894	290	1	t.	t.	PROPN
ejpam-5894	290	2	oner	oner	PROPN
ejpam-5894	290	3	et	et	PROPN
ejpam-5894	290	4	al	al	PROPN
ejpam-5894	290	5	.	.	PUNCT
ejpam-5894	290	6	/	/	SYM
ejpam-5894	290	7	eur	eur	PROPN
ejpam-5894	290	8	.	.	PUNCT
ejpam-5894	291	1	j.	j.	PROPN
ejpam-5894	291	2	pure	pure	PROPN
ejpam-5894	291	3	appl	appl	PROPN
ejpam-5894	291	4	.	.	PROPN
ejpam-5894	291	5	math	math	PROPN
ejpam-5894	291	6	,	,	PUNCT
ejpam-5894	291	7	18	18	NUM
ejpam-5894	291	8	(	(	PUNCT
ejpam-5894	291	9	3	3	NUM
ejpam-5894	291	10	)	)	PUNCT
ejpam-5894	291	11	(	(	PUNCT
ejpam-5894	291	12	2025	2025	NUM
ejpam-5894	291	13	)	)	PUNCT
ejpam-5894	291	14	,	,	PUNCT
ejpam-5894	291	15	5894	5894	NUM
ejpam-5894	291	16	16	16	NUM
ejpam-5894	291	17	of	of	ADP
ejpam-5894	291	18	33	33	NUM
ejpam-5894	291	19	now	now	ADV
ejpam-5894	291	20	,	,	PUNCT
ejpam-5894	291	21	if	if	SCONJ
ejpam-5894	291	22	the	the	DET
ejpam-5894	291	23	operation	operation	NOUN
ejpam-5894	291	24	|	|	ADV
ejpam-5894	291	25	satisfies	satisfy	VERB
ejpam-5894	291	26	the	the	DET
ejpam-5894	291	27	medial	medial	ADJ
ejpam-5894	291	28	-	-	PUNCT
ejpam-5894	291	29	like	like	ADJ
ejpam-5894	291	30	identity	identity	NOUN
ejpam-5894	291	31	:	:	PUNCT
ejpam-5894	291	32	(	(	PUNCT
ejpam-5894	291	33	a|a)|b	a|a)|b	PROPN
ejpam-5894	291	34	=	=	SYM
ejpam-5894	291	35	a	a	PROPN
ejpam-5894	291	36	,	,	PUNCT
ejpam-5894	291	37	then	then	ADV
ejpam-5894	291	38	:	:	PUNCT
ejpam-5894	291	39	(	(	PUNCT
ejpam-5894	291	40	(	(	PUNCT
ejpam-5894	291	41	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(η|(ζ|ζ	ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(η|(ζ|ζ	NOUN
ejpam-5894	291	42	)	)	PUNCT
ejpam-5894	291	43	)	)	PUNCT
ejpam-5894	291	44	=	=	SYM
ejpam-5894	291	45	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	291	46	)	)	PUNCT
ejpam-5894	291	47	)	)	PUNCT
ejpam-5894	291	48	.	.	PUNCT
ejpam-5894	292	1	theorem	theorem	VERB
ejpam-5894	292	2	6	6	NUM
ejpam-5894	292	3	.	.	PUNCT
ejpam-5894	293	1	every	every	DET
ejpam-5894	293	2	intuitionistic	intuitionistic	ADJ
ejpam-5894	293	3	fuzzy	fuzzy	ADJ
ejpam-5894	293	4	wsbg	wsbg	NOUN
ejpam-5894	293	5	-	-	PUNCT
ejpam-5894	293	6	ideal	ideal	NOUN
ejpam-5894	293	7	of	of	ADP
ejpam-5894	293	8	a	a	DET
ejpam-5894	293	9	medial	medial	ADJ
ejpam-5894	293	10	wsbg	wsbg	NOUN
ejpam-5894	293	11	-	-	PUNCT
ejpam-5894	293	12	algebra	algebra	NOUN
ejpam-5894	293	13	l	l	NOUN
ejpam-5894	293	14	=	=	PUNCT
ejpam-5894	293	15	⟨l	⟨l	NOUN
ejpam-5894	293	16	;	;	PUNCT
ejpam-5894	293	17	|	|	ADV
ejpam-5894	293	18	,	,	PUNCT
ejpam-5894	293	19	0⟩	0⟩	PROPN
ejpam-5894	293	20	is	be	AUX
ejpam-5894	293	21	an	an	DET
ejpam-5894	293	22	intuitionistic	intuitionistic	ADJ
ejpam-5894	293	23	fuzzy	fuzzy	ADJ
ejpam-5894	293	24	sub	sub	ADJ
ejpam-5894	293	25	-	-	ADJ
ejpam-5894	293	26	implicative	implicative	ADJ
ejpam-5894	293	27	wsbg	wsbg	NOUN
ejpam-5894	293	28	-	-	PUNCT
ejpam-5894	293	29	ideal	ideal	NOUN
ejpam-5894	293	30	of	of	ADP
ejpam-5894	293	31	l.	l.	PROPN
ejpam-5894	293	32	proof	proof	PROPN
ejpam-5894	293	33	.	.	PUNCT
ejpam-5894	294	1	let	let	VERB
ejpam-5894	294	2	l	l	NOUN
ejpam-5894	294	3	=	=	SYM
ejpam-5894	294	4	(	(	PUNCT
ejpam-5894	294	5	l	l	NOUN
ejpam-5894	294	6	,	,	PUNCT
ejpam-5894	294	7	α	α	X
ejpam-5894	294	8	,	,	PUNCT
ejpam-5894	294	9	β	β	NOUN
ejpam-5894	294	10	)	)	PUNCT
ejpam-5894	294	11	be	be	VERB
ejpam-5894	294	12	an	an	DET
ejpam-5894	294	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	294	14	fuzzy	fuzzy	ADJ
ejpam-5894	294	15	wsbg	wsbg	NOUN
ejpam-5894	294	16	-	-	PUNCT
ejpam-5894	294	17	ideal	ideal	NOUN
ejpam-5894	294	18	of	of	ADP
ejpam-5894	294	19	a	a	DET
ejpam-5894	294	20	medial	medial	ADJ
ejpam-5894	294	21	wsbgalgebra	wsbgalgebra	NOUN
ejpam-5894	294	22	l	l	NOUN
ejpam-5894	294	23	=	=	PUNCT
ejpam-5894	294	24	⟨l	⟨l	NOUN
ejpam-5894	294	25	;	;	PUNCT
ejpam-5894	294	26	|	|	ADV
ejpam-5894	294	27	,	,	PUNCT
ejpam-5894	294	28	0⟩.	0⟩.	VERB
ejpam-5894	294	29	by	by	ADP
ejpam-5894	294	30	definition	definition	NOUN
ejpam-5894	294	31	,	,	PUNCT
ejpam-5894	294	32	we	we	PRON
ejpam-5894	294	33	have	have	VERB
ejpam-5894	294	34	α(0	α(0	PROPN
ejpam-5894	294	35	)	)	PUNCT
ejpam-5894	294	36	≥	≥	NOUN
ejpam-5894	294	37	α(ζ	α(ζ	PROPN
ejpam-5894	294	38	)	)	PUNCT
ejpam-5894	294	39	and	and	CCONJ
ejpam-5894	294	40	β(0	β(0	PROPN
ejpam-5894	294	41	)	)	PUNCT
ejpam-5894	294	42	≤	≤	NOUN
ejpam-5894	294	43	β(ζ	β(ζ	PROPN
ejpam-5894	294	44	)	)	PUNCT
ejpam-5894	294	45	,	,	PUNCT
ejpam-5894	294	46	∀ζ	∀ζ	PROPN
ejpam-5894	294	47	∈	∈	PROPN
ejpam-5894	294	48	l.	l.	NOUN
ejpam-5894	294	49	now	now	ADV
ejpam-5894	294	50	,	,	PUNCT
ejpam-5894	294	51	consider	consider	VERB
ejpam-5894	294	52	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	294	53	)	)	PUNCT
ejpam-5894	294	54	)	)	PUNCT
ejpam-5894	294	55	)	)	PUNCT
ejpam-5894	294	56	)	)	PUNCT
ejpam-5894	294	57	.	.	PUNCT
ejpam-5894	295	1	using	use	VERB
ejpam-5894	295	2	the	the	DET
ejpam-5894	295	3	medial	medial	ADJ
ejpam-5894	295	4	property	property	NOUN
ejpam-5894	295	5	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	295	6	)	)	PUNCT
ejpam-5894	295	7	)	)	PUNCT
ejpam-5894	296	1	=	=	SYM
ejpam-5894	296	2	η|η	η|η	PROPN
ejpam-5894	296	3	,	,	PUNCT
ejpam-5894	296	4	we	we	PRON
ejpam-5894	296	5	get	get	VERB
ejpam-5894	296	6	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	VERB
ejpam-5894	296	7	)	)	PUNCT
ejpam-5894	296	8	)	)	PUNCT
ejpam-5894	296	9	)	)	PUNCT
ejpam-5894	296	10	)	)	PUNCT
ejpam-5894	297	1	=	=	SYM
ejpam-5894	297	2	α(ζ	α(ζ	NOUN
ejpam-5894	297	3	)	)	PUNCT
ejpam-5894	297	4	.	.	PUNCT
ejpam-5894	298	1	furthermore	furthermore	ADV
ejpam-5894	298	2	,	,	PUNCT
ejpam-5894	298	3	α(ζ	α(ζ	PROPN
ejpam-5894	298	4	)	)	PUNCT
ejpam-5894	298	5	≥	≥	NOUN
ejpam-5894	298	6	min{α((ζ|(θ|θ))|(ζ|(θ|θ	min{α((ζ|(θ|θ))|(ζ|(θ|θ	ADV
ejpam-5894	298	7	)	)	PUNCT
ejpam-5894	298	8	)	)	PUNCT
ejpam-5894	298	9	)	)	PUNCT
ejpam-5894	298	10	,	,	PUNCT
ejpam-5894	298	11	α(θ	α(θ	NOUN
ejpam-5894	298	12	)	)	PUNCT
ejpam-5894	298	13	}	}	PUNCT
ejpam-5894	298	14	.	.	PUNCT
ejpam-5894	299	1	by	by	ADP
ejpam-5894	299	2	expanding	expand	VERB
ejpam-5894	299	3	this	this	PRON
ejpam-5894	299	4	,	,	PUNCT
ejpam-5894	299	5	we	we	PRON
ejpam-5894	299	6	have	have	VERB
ejpam-5894	299	7	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	VERB
ejpam-5894	299	8	)	)	PUNCT
ejpam-5894	299	9	)	)	PUNCT
ejpam-5894	299	10	)	)	PUNCT
ejpam-5894	299	11	)	)	PUNCT
ejpam-5894	299	12	≥	≥	NOUN
ejpam-5894	299	13	min{α((((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ))|(((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ	min{α((((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ))|(((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ	NUM
ejpam-5894	299	14	)	)	PUNCT
ejpam-5894	299	15	)	)	PUNCT
ejpam-5894	299	16	)	)	PUNCT
ejpam-5894	299	17	,	,	PUNCT
ejpam-5894	299	18	α(θ	α(θ	NOUN
ejpam-5894	299	19	)	)	PUNCT
ejpam-5894	299	20	}	}	PUNCT
ejpam-5894	299	21	.	.	PUNCT
ejpam-5894	300	1	finally	finally	ADV
ejpam-5894	300	2	,	,	PUNCT
ejpam-5894	300	3	by	by	ADP
ejpam-5894	300	4	the	the	DET
ejpam-5894	300	5	lemma	lemma	PROPN
ejpam-5894	300	6	,	,	PUNCT
ejpam-5894	300	7	this	this	DET
ejpam-5894	300	8	simplifies	simplifie	NOUN
ejpam-5894	300	9	to	to	ADP
ejpam-5894	300	10	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	300	11	)	)	PUNCT
ejpam-5894	300	12	)	)	PUNCT
ejpam-5894	300	13	)	)	PUNCT
ejpam-5894	300	14	)	)	PUNCT
ejpam-5894	300	15	≥	≥	PROPN
ejpam-5894	300	16	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	α((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	300	17	)	)	PUNCT
ejpam-5894	300	18	)	)	PUNCT
ejpam-5894	300	19	)	)	PUNCT
ejpam-5894	300	20	)	)	PUNCT
ejpam-5894	300	21	.	.	PUNCT
ejpam-5894	301	1	similarly	similarly	ADV
ejpam-5894	301	2	,	,	PUNCT
ejpam-5894	301	3	for	for	ADP
ejpam-5894	301	4	β	β	X
ejpam-5894	301	5	,	,	PUNCT
ejpam-5894	301	6	we	we	PRON
ejpam-5894	301	7	have	have	VERB
ejpam-5894	301	8	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	301	9	)	)	PUNCT
ejpam-5894	301	10	)	)	PUNCT
ejpam-5894	301	11	)	)	PUNCT
ejpam-5894	301	12	)	)	PUNCT
ejpam-5894	301	13	.	.	PUNCT
ejpam-5894	302	1	using	use	VERB
ejpam-5894	302	2	the	the	DET
ejpam-5894	302	3	medial	medial	ADJ
ejpam-5894	302	4	property	property	NOUN
ejpam-5894	302	5	,	,	PUNCT
ejpam-5894	302	6	we	we	PRON
ejpam-5894	302	7	get	get	VERB
ejpam-5894	302	8	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	302	9	)	)	PUNCT
ejpam-5894	302	10	)	)	PUNCT
ejpam-5894	302	11	)	)	PUNCT
ejpam-5894	302	12	)	)	PUNCT
ejpam-5894	303	1	=	=	SYM
ejpam-5894	303	2	β(ζ	β(ζ	PROPN
ejpam-5894	303	3	)	)	PUNCT
ejpam-5894	303	4	.	.	PUNCT
ejpam-5894	304	1	furthermore	furthermore	ADV
ejpam-5894	304	2	,	,	PUNCT
ejpam-5894	304	3	β(ζ	β(ζ	PROPN
ejpam-5894	304	4	)	)	PUNCT
ejpam-5894	304	5	≤	≤	NUM
ejpam-5894	304	6	max{β((ζ|(θ|θ))|(ζ|(θ|θ	max{β((ζ|(θ|θ))|(ζ|(θ|θ	NOUN
ejpam-5894	304	7	)	)	PUNCT
ejpam-5894	304	8	)	)	PUNCT
ejpam-5894	304	9	)	)	PUNCT
ejpam-5894	304	10	,	,	PUNCT
ejpam-5894	304	11	β(θ	β(θ	NUM
ejpam-5894	304	12	)	)	PUNCT
ejpam-5894	304	13	}	}	PUNCT
ejpam-5894	304	14	.	.	PUNCT
ejpam-5894	305	1	by	by	ADP
ejpam-5894	305	2	expanding	expand	VERB
ejpam-5894	305	3	this	this	PRON
ejpam-5894	305	4	,	,	PUNCT
ejpam-5894	305	5	we	we	PRON
ejpam-5894	305	6	have	have	VERB
ejpam-5894	305	7	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	305	8	)	)	PUNCT
ejpam-5894	305	9	)	)	PUNCT
ejpam-5894	305	10	)	)	PUNCT
ejpam-5894	305	11	)	)	PUNCT
ejpam-5894	306	1	≤	≤	NUM
ejpam-5894	306	2	max{β((((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ))|(((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ	max{β((((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ))|(((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η))))|(θ|θ	NUM
ejpam-5894	306	3	)	)	PUNCT
ejpam-5894	306	4	)	)	PUNCT
ejpam-5894	306	5	)	)	PUNCT
ejpam-5894	306	6	,	,	PUNCT
ejpam-5894	306	7	β(θ	β(θ	NUM
ejpam-5894	306	8	)	)	PUNCT
ejpam-5894	306	9	}	}	PUNCT
ejpam-5894	306	10	.	.	PUNCT
ejpam-5894	307	1	finally	finally	ADV
ejpam-5894	307	2	,	,	PUNCT
ejpam-5894	307	3	by	by	ADP
ejpam-5894	307	4	the	the	DET
ejpam-5894	307	5	lemma	lemma	PROPN
ejpam-5894	307	6	,	,	PUNCT
ejpam-5894	307	7	this	this	DET
ejpam-5894	307	8	simplifies	simplifie	NOUN
ejpam-5894	307	9	to	to	ADP
ejpam-5894	307	10	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	β((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	307	11	)	)	PUNCT
ejpam-5894	307	12	)	)	PUNCT
ejpam-5894	307	13	)	)	PUNCT
ejpam-5894	307	14	)	)	PUNCT
ejpam-5894	308	1	≤	≤	NUM
ejpam-5894	308	2	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	β((ζ|(ζ|(η|η)))|(ζ|(ζ|(η|η	PROPN
ejpam-5894	308	3	)	)	PUNCT
ejpam-5894	308	4	)	)	PUNCT
ejpam-5894	308	5	)	)	PUNCT
ejpam-5894	308	6	)	)	PUNCT
ejpam-5894	308	7	.	.	PUNCT
ejpam-5894	309	1	thus	thus	ADV
ejpam-5894	309	2	,	,	PUNCT
ejpam-5894	309	3	l	l	NOUN
ejpam-5894	309	4	=	=	SYM
ejpam-5894	309	5	(	(	PUNCT
ejpam-5894	309	6	l	l	NOUN
ejpam-5894	309	7	,	,	PUNCT
ejpam-5894	309	8	α	α	X
ejpam-5894	309	9	,	,	PUNCT
ejpam-5894	309	10	β	β	NOUN
ejpam-5894	309	11	)	)	PUNCT
ejpam-5894	309	12	is	be	AUX
ejpam-5894	309	13	an	an	DET
ejpam-5894	309	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	309	15	fuzzy	fuzzy	ADJ
ejpam-5894	309	16	sub	sub	ADJ
ejpam-5894	309	17	-	-	ADJ
ejpam-5894	309	18	implicative	implicative	ADJ
ejpam-5894	309	19	wsbg	wsbg	NOUN
ejpam-5894	309	20	-	-	PUNCT
ejpam-5894	309	21	ideal	ideal	NOUN
ejpam-5894	309	22	of	of	ADP
ejpam-5894	309	23	l.	l.	PROPN
ejpam-5894	309	24	t.	t.	PROPN
ejpam-5894	309	25	oner	oner	PROPN
ejpam-5894	309	26	et	et	PROPN
ejpam-5894	309	27	al	al	PROPN
ejpam-5894	309	28	.	.	PUNCT
ejpam-5894	309	29	/	/	SYM
ejpam-5894	309	30	eur	eur	PROPN
ejpam-5894	309	31	.	.	PUNCT
ejpam-5894	310	1	j.	j.	PROPN
ejpam-5894	310	2	pure	pure	PROPN
ejpam-5894	310	3	appl	appl	PROPN
ejpam-5894	310	4	.	.	PROPN
ejpam-5894	310	5	math	math	PROPN
ejpam-5894	310	6	,	,	PUNCT
ejpam-5894	310	7	18	18	NUM
ejpam-5894	310	8	(	(	PUNCT
ejpam-5894	310	9	3	3	NUM
ejpam-5894	310	10	)	)	PUNCT
ejpam-5894	310	11	(	(	PUNCT
ejpam-5894	310	12	2025	2025	NUM
ejpam-5894	310	13	)	)	PUNCT
ejpam-5894	310	14	,	,	PUNCT
ejpam-5894	310	15	5894	5894	NUM
ejpam-5894	310	16	17	17	NUM
ejpam-5894	310	17	of	of	ADP
ejpam-5894	310	18	33	33	NUM
ejpam-5894	310	19	example	example	NOUN
ejpam-5894	310	20	11	11	NUM
ejpam-5894	310	21	.	.	PUNCT
ejpam-5894	311	1	consider	consider	VERB
ejpam-5894	311	2	the	the	DET
ejpam-5894	311	3	set	set	NOUN
ejpam-5894	311	4	l	l	NOUN
ejpam-5894	311	5	=	=	PUNCT
ejpam-5894	311	6	{	{	PUNCT
ejpam-5894	311	7	0	0	NUM
ejpam-5894	311	8	,	,	PUNCT
ejpam-5894	311	9	a	a	DET
ejpam-5894	311	10	,	,	PUNCT
ejpam-5894	311	11	b	b	NOUN
ejpam-5894	311	12	}	}	PUNCT
ejpam-5894	311	13	equipped	equip	VERB
ejpam-5894	311	14	with	with	ADP
ejpam-5894	311	15	the	the	DET
ejpam-5894	311	16	binary	binary	PROPN
ejpam-5894	311	17	operation	operation	NOUN
ejpam-5894	312	1	|	|	ADV
ejpam-5894	312	2	defined	define	VERB
ejpam-5894	312	3	by	by	ADP
ejpam-5894	312	4	the	the	DET
ejpam-5894	312	5	following	following	ADJ
ejpam-5894	312	6	cayley	cayley	ADJ
ejpam-5894	312	7	table	table	NOUN
ejpam-5894	312	8	:	:	PUNCT
ejpam-5894	312	9	|	|	ADV
ejpam-5894	312	10	0	0	PUNCT
ejpam-5894	312	11	a	a	DET
ejpam-5894	312	12	b	b	NOUN
ejpam-5894	312	13	0	0	NUM
ejpam-5894	312	14	0	0	NUM
ejpam-5894	312	15	b	b	NOUN
ejpam-5894	312	16	a	a	PRON
ejpam-5894	312	17	a	a	DET
ejpam-5894	312	18	b	b	NOUN
ejpam-5894	312	19	0	0	NUM
ejpam-5894	312	20	a	a	DET
ejpam-5894	312	21	b	b	NOUN
ejpam-5894	312	22	a	a	DET
ejpam-5894	312	23	b	b	NOUN
ejpam-5894	312	24	0	0	PUNCT
ejpam-5894	312	25	thus	thus	ADV
ejpam-5894	312	26	,	,	PUNCT
ejpam-5894	312	27	l	l	NOUN
ejpam-5894	312	28	=	=	SYM
ejpam-5894	312	29	⟨l	⟨l	NOUN
ejpam-5894	312	30	;	;	PUNCT
ejpam-5894	312	31	|	|	ADV
ejpam-5894	312	32	,	,	PUNCT
ejpam-5894	312	33	0⟩	0⟩	PROPN
ejpam-5894	312	34	is	be	AUX
ejpam-5894	312	35	a	a	DET
ejpam-5894	312	36	wsbg	wsbg	ADV
ejpam-5894	312	37	-	-	PUNCT
ejpam-5894	312	38	algebra	algebra	NOUN
ejpam-5894	312	39	.	.	PUNCT
ejpam-5894	313	1	we	we	PRON
ejpam-5894	313	2	check	check	VERB
ejpam-5894	313	3	the	the	DET
ejpam-5894	313	4	medial	medial	ADJ
ejpam-5894	313	5	condition	condition	NOUN
ejpam-5894	313	6	:	:	PUNCT
ejpam-5894	313	7	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	313	8	)	)	PUNCT
ejpam-5894	313	9	)	)	PUNCT
ejpam-5894	314	1	=	=	SYM
ejpam-5894	314	2	η|η	η|η	PROPN
ejpam-5894	314	3	,	,	PUNCT
ejpam-5894	314	4	∀ζ	∀ζ	PROPN
ejpam-5894	314	5	,	,	PUNCT
ejpam-5894	314	6	η	η	PROPN
ejpam-5894	314	7	∈	∈	PROPN
ejpam-5894	314	8	l.	l.	NOUN
ejpam-5894	314	9	it	it	PRON
ejpam-5894	314	10	fails	fail	VERB
ejpam-5894	314	11	for	for	ADP
ejpam-5894	314	12	ζ	ζ	NOUN
ejpam-5894	314	13	=	=	SYM
ejpam-5894	314	14	a	a	PROPN
ejpam-5894	314	15	,	,	PUNCT
ejpam-5894	314	16	η	η	X
ejpam-5894	314	17	=	=	SYM
ejpam-5894	314	18	0	0	NUM
ejpam-5894	314	19	:	:	PUNCT
ejpam-5894	314	20	a|(a|(0|0	a|(a|(0|0	VERB
ejpam-5894	314	21	)	)	PUNCT
ejpam-5894	314	22	)	)	PUNCT
ejpam-5894	314	23	=	=	PUNCT
ejpam-5894	314	24	a|(a|0	a|(a|0	ADJ
ejpam-5894	314	25	)	)	PUNCT
ejpam-5894	314	26	=	=	SYM
ejpam-5894	314	27	a|b	a|b	X
ejpam-5894	314	28	=	=	PUNCT
ejpam-5894	314	29	a	a	DET
ejpam-5894	314	30	̸=	̸=	PROPN
ejpam-5894	314	31	0	0	NUM
ejpam-5894	314	32	=	=	SYM
ejpam-5894	314	33	0|0	0|0	PROPN
ejpam-5894	314	34	.	.	PUNCT
ejpam-5894	315	1	hence	hence	ADV
ejpam-5894	315	2	,	,	PUNCT
ejpam-5894	315	3	l	l	NOUN
ejpam-5894	315	4	is	be	AUX
ejpam-5894	315	5	not	not	PART
ejpam-5894	315	6	medial	medial	ADJ
ejpam-5894	315	7	.	.	PUNCT
ejpam-5894	316	1	define	define	VERB
ejpam-5894	316	2	an	an	DET
ejpam-5894	316	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	316	4	fuzzy	fuzzy	ADJ
ejpam-5894	316	5	set	set	NOUN
ejpam-5894	316	6	l	l	NOUN
ejpam-5894	316	7	=	=	SYM
ejpam-5894	316	8	(	(	PUNCT
ejpam-5894	316	9	l	l	NOUN
ejpam-5894	316	10	,	,	PUNCT
ejpam-5894	316	11	α	α	X
ejpam-5894	316	12	,	,	PUNCT
ejpam-5894	316	13	β	β	NOUN
ejpam-5894	316	14	):	):	PUNCT
ejpam-5894	316	15	α(x	α(x	NOUN
ejpam-5894	316	16	)	)	PUNCT
ejpam-5894	316	17	=	=	NUM
ejpam-5894	316	18	0.5	0.5	NUM
ejpam-5894	316	19	,	,	PUNCT
ejpam-5894	316	20	∀x	∀x	X
ejpam-5894	316	21	∈	∈	PROPN
ejpam-5894	316	22	l	l	NOUN
ejpam-5894	316	23	,	,	PUNCT
ejpam-5894	316	24	β(0	β(0	PROPN
ejpam-5894	316	25	)	)	PUNCT
ejpam-5894	316	26	=	=	PUNCT
ejpam-5894	316	27	β(b	β(b	PUNCT
ejpam-5894	316	28	)	)	PUNCT
ejpam-5894	316	29	=	=	SYM
ejpam-5894	316	30	0.25	0.25	NUM
ejpam-5894	316	31	,	,	PUNCT
ejpam-5894	316	32	β(a	β(a	PROPN
ejpam-5894	316	33	)	)	PUNCT
ejpam-5894	317	1	=	=	PUNCT
ejpam-5894	317	2	0	0	X
ejpam-5894	317	3	.	.	PUNCT
ejpam-5894	318	1	then	then	ADV
ejpam-5894	318	2	l	l	NOUN
ejpam-5894	318	3	=	=	PUNCT
ejpam-5894	318	4	(	(	PUNCT
ejpam-5894	318	5	l	l	NOUN
ejpam-5894	318	6	,	,	PUNCT
ejpam-5894	318	7	α	α	X
ejpam-5894	318	8	,	,	PUNCT
ejpam-5894	318	9	β	β	NOUN
ejpam-5894	318	10	)	)	PUNCT
ejpam-5894	318	11	is	be	AUX
ejpam-5894	318	12	an	an	DET
ejpam-5894	318	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	318	14	fuzzy	fuzzy	ADJ
ejpam-5894	318	15	wsbg	wsbg	NOUN
ejpam-5894	318	16	-	-	PUNCT
ejpam-5894	318	17	ideal	ideal	NOUN
ejpam-5894	318	18	of	of	ADP
ejpam-5894	318	19	l.	l.	PROPN
ejpam-5894	318	20	however	however	ADV
ejpam-5894	318	21	,	,	PUNCT
ejpam-5894	318	22	l	l	PROPN
ejpam-5894	318	23	=	=	SYM
ejpam-5894	318	24	(	(	PUNCT
ejpam-5894	318	25	l	l	NOUN
ejpam-5894	318	26	,	,	PUNCT
ejpam-5894	318	27	α	α	X
ejpam-5894	318	28	,	,	PUNCT
ejpam-5894	318	29	β	β	NOUN
ejpam-5894	318	30	)	)	PUNCT
ejpam-5894	318	31	fails	fail	VERB
ejpam-5894	318	32	the	the	DET
ejpam-5894	318	33	bound	bound	ADJ
ejpam-5894	318	34	condition	condition	NOUN
ejpam-5894	318	35	for	for	ADP
ejpam-5894	318	36	an	an	DET
ejpam-5894	318	37	intuitionistic	intuitionistic	ADJ
ejpam-5894	318	38	fuzzy	fuzzy	ADJ
ejpam-5894	318	39	sub	sub	ADJ
ejpam-5894	318	40	-	-	ADJ
ejpam-5894	318	41	implicative	implicative	ADJ
ejpam-5894	318	42	wsbg	wsbg	NOUN
ejpam-5894	318	43	-	-	PUNCT
ejpam-5894	318	44	ideal	ideal	ADJ
ejpam-5894	318	45	:	:	PUNCT
ejpam-5894	318	46	β(0	β(0	NOUN
ejpam-5894	318	47	)	)	PUNCT
ejpam-5894	318	48	=	=	NUM
ejpam-5894	318	49	0.25	0.25	NUM
ejpam-5894	318	50	>	>	PUNCT
ejpam-5894	318	51	β(a	β(a	PROPN
ejpam-5894	318	52	)	)	PUNCT
ejpam-5894	318	53	=	=	SYM
ejpam-5894	319	1	0	0	X
ejpam-5894	319	2	.	.	PUNCT
ejpam-5894	320	1	thus	thus	ADV
ejpam-5894	320	2	,	,	PUNCT
ejpam-5894	320	3	l	l	NOUN
ejpam-5894	320	4	=	=	SYM
ejpam-5894	320	5	(	(	PUNCT
ejpam-5894	320	6	l	l	NOUN
ejpam-5894	320	7	,	,	PUNCT
ejpam-5894	320	8	α	α	X
ejpam-5894	320	9	,	,	PUNCT
ejpam-5894	320	10	β	β	NOUN
ejpam-5894	320	11	)	)	PUNCT
ejpam-5894	320	12	is	be	AUX
ejpam-5894	320	13	not	not	PART
ejpam-5894	320	14	an	an	DET
ejpam-5894	320	15	intuitionistic	intuitionistic	ADJ
ejpam-5894	320	16	fuzzy	fuzzy	ADJ
ejpam-5894	320	17	sub	sub	ADJ
ejpam-5894	320	18	-	-	ADJ
ejpam-5894	320	19	implicative	implicative	ADJ
ejpam-5894	320	20	wsbg	wsbg	NOUN
ejpam-5894	320	21	-	-	PUNCT
ejpam-5894	320	22	ideal	ideal	ADJ
ejpam-5894	320	23	.	.	PUNCT
ejpam-5894	321	1	this	this	DET
ejpam-5894	321	2	example	example	NOUN
ejpam-5894	321	3	demonstrates	demonstrate	VERB
ejpam-5894	321	4	that	that	SCONJ
ejpam-5894	321	5	in	in	ADP
ejpam-5894	321	6	a	a	DET
ejpam-5894	321	7	wsbg	wsbg	ADV
ejpam-5894	321	8	-	-	PUNCT
ejpam-5894	321	9	algebra	algebra	NOUN
ejpam-5894	321	10	which	which	PRON
ejpam-5894	321	11	is	be	AUX
ejpam-5894	321	12	not	not	PART
ejpam-5894	321	13	medial	medial	ADJ
ejpam-5894	321	14	,	,	PUNCT
ejpam-5894	321	15	an	an	DET
ejpam-5894	321	16	intuitionistic	intuitionistic	ADJ
ejpam-5894	321	17	fuzzy	fuzzy	ADJ
ejpam-5894	321	18	wsbg	wsbg	ADV
ejpam-5894	321	19	-	-	PUNCT
ejpam-5894	321	20	ideal	ideal	NOUN
ejpam-5894	321	21	need	need	AUX
ejpam-5894	321	22	not	not	PART
ejpam-5894	321	23	be	be	AUX
ejpam-5894	321	24	an	an	DET
ejpam-5894	321	25	intuitionistic	intuitionistic	ADJ
ejpam-5894	321	26	fuzzy	fuzzy	ADJ
ejpam-5894	321	27	sub	sub	ADJ
ejpam-5894	321	28	-	-	ADJ
ejpam-5894	321	29	implicative	implicative	ADJ
ejpam-5894	321	30	wsbg	wsbg	ADV
ejpam-5894	321	31	-	-	PUNCT
ejpam-5894	321	32	ideal	ideal	ADJ
ejpam-5894	321	33	.	.	PUNCT
ejpam-5894	322	1	theorem	theorem	VERB
ejpam-5894	322	2	7	7	NUM
ejpam-5894	322	3	.	.	PUNCT
ejpam-5894	323	1	every	every	DET
ejpam-5894	323	2	medial	medial	ADJ
ejpam-5894	323	3	wsbg	wsbg	NOUN
ejpam-5894	323	4	-	-	PUNCT
ejpam-5894	323	5	algebra	algebra	NOUN
ejpam-5894	323	6	is	be	AUX
ejpam-5894	323	7	an	an	DET
ejpam-5894	323	8	implicative	implicative	ADJ
ejpam-5894	323	9	wsbg	wsbg	NOUN
ejpam-5894	323	10	-	-	PUNCT
ejpam-5894	323	11	algebra	algebra	NOUN
ejpam-5894	323	12	.	.	PUNCT
ejpam-5894	324	1	proof	proof	NOUN
ejpam-5894	324	2	.	.	PUNCT
ejpam-5894	325	1	let	let	VERB
ejpam-5894	325	2	l	l	NOUN
ejpam-5894	325	3	=	=	SYM
ejpam-5894	325	4	⟨l	⟨l	NOUN
ejpam-5894	325	5	;	;	PUNCT
ejpam-5894	325	6	|	|	ADV
ejpam-5894	325	7	,	,	PUNCT
ejpam-5894	325	8	0⟩	0⟩	PROPN
ejpam-5894	325	9	be	be	VERB
ejpam-5894	325	10	a	a	DET
ejpam-5894	325	11	medial	medial	ADJ
ejpam-5894	325	12	wsbg	wsbg	NOUN
ejpam-5894	325	13	-	-	PUNCT
ejpam-5894	325	14	algebra	algebra	NOUN
ejpam-5894	325	15	.	.	PUNCT
ejpam-5894	326	1	we	we	PRON
ejpam-5894	326	2	aim	aim	VERB
ejpam-5894	326	3	to	to	PART
ejpam-5894	326	4	prove	prove	VERB
ejpam-5894	326	5	the	the	DET
ejpam-5894	326	6	identity	identity	NOUN
ejpam-5894	326	7	:	:	PUNCT
ejpam-5894	326	8	x|(x|(y|y	x|(x|(y|y	NUM
ejpam-5894	326	9	)	)	PUNCT
ejpam-5894	326	10	)	)	PUNCT
ejpam-5894	327	1	=	=	SYM
ejpam-5894	327	2	y|(y|(x|x	y|(y|(x|x	NOUN
ejpam-5894	327	3	)	)	PUNCT
ejpam-5894	327	4	)	)	PUNCT
ejpam-5894	327	5	,	,	PUNCT
ejpam-5894	327	6	∀x	∀x	X
ejpam-5894	327	7	,	,	PUNCT
ejpam-5894	327	8	y	y	PROPN
ejpam-5894	327	9	∈	∈	PROPN
ejpam-5894	327	10	l.	l.	NOUN
ejpam-5894	327	11	(	(	PUNCT
ejpam-5894	327	12	4	4	X
ejpam-5894	327	13	)	)	PUNCT
ejpam-5894	327	14	assume	assume	VERB
ejpam-5894	327	15	that	that	SCONJ
ejpam-5894	327	16	the	the	DET
ejpam-5894	327	17	identity	identity	NOUN
ejpam-5894	327	18	is	be	AUX
ejpam-5894	327	19	not	not	PART
ejpam-5894	327	20	valid	valid	ADJ
ejpam-5894	327	21	.	.	PUNCT
ejpam-5894	328	1	there	there	PRON
ejpam-5894	328	2	exist	exist	VERB
ejpam-5894	328	3	c1	c1	NOUN
ejpam-5894	328	4	,	,	PUNCT
ejpam-5894	328	5	c2	c2	PROPN
ejpam-5894	328	6	∈	∈	PROPN
ejpam-5894	328	7	l	l	NOUN
ejpam-5894	328	8	such	such	ADJ
ejpam-5894	328	9	that	that	SCONJ
ejpam-5894	328	10	c2|(c2|(c1|c1	c2|(c2|(c1|c1	NOUN
ejpam-5894	328	11	)	)	PUNCT
ejpam-5894	328	12	)	)	PUNCT
ejpam-5894	328	13	̸=	̸=	PROPN
ejpam-5894	328	14	c1|(c1|(c2|c2	c1|(c1|(c2|c2	PROPN
ejpam-5894	328	15	)	)	PUNCT
ejpam-5894	328	16	)	)	PUNCT
ejpam-5894	328	17	.	.	PUNCT
ejpam-5894	329	1	by	by	ADP
ejpam-5894	329	2	the	the	DET
ejpam-5894	329	3	medial	medial	ADJ
ejpam-5894	329	4	property	property	NOUN
ejpam-5894	329	5	,	,	PUNCT
ejpam-5894	329	6	we	we	PRON
ejpam-5894	329	7	have	have	VERB
ejpam-5894	329	8	c2|c2	c2|c2	NOUN
ejpam-5894	329	9	̸=	̸=	PROPN
ejpam-5894	329	10	c1|c1	c1|c1	PROPN
ejpam-5894	329	11	.	.	PUNCT
ejpam-5894	330	1	(	(	PUNCT
ejpam-5894	330	2	5	5	NUM
ejpam-5894	330	3	)	)	PUNCT
ejpam-5894	330	4	by	by	ADP
ejpam-5894	330	5	(	(	PUNCT
ejpam-5894	330	6	sbg1	sbg1	PROPN
ejpam-5894	330	7	)	)	PUNCT
ejpam-5894	330	8	,	,	PUNCT
ejpam-5894	330	9	we	we	PRON
ejpam-5894	330	10	have	have	VERB
ejpam-5894	330	11	(	(	PUNCT
ejpam-5894	330	12	(	(	PUNCT
ejpam-5894	330	13	x|(x|x))|0)|((x|(x|x))|0	x|(x|x))|0)|((x|(x|x))|0	PROPN
ejpam-5894	330	14	)	)	PUNCT
ejpam-5894	330	15	=	=	PUNCT
ejpam-5894	331	1	0	0	X
ejpam-5894	331	2	.	.	PUNCT
ejpam-5894	332	1	(	(	PUNCT
ejpam-5894	332	2	6	6	X
ejpam-5894	332	3	)	)	PUNCT
ejpam-5894	332	4	combining	combine	VERB
ejpam-5894	332	5	(	(	PUNCT
ejpam-5894	332	6	sbg1	sbg1	PROPN
ejpam-5894	332	7	)	)	PUNCT
ejpam-5894	332	8	and	and	CCONJ
ejpam-5894	332	9	(	(	PUNCT
ejpam-5894	332	10	sbg2	sbg2	PROPN
ejpam-5894	332	11	)	)	PUNCT
ejpam-5894	332	12	,	,	PUNCT
ejpam-5894	332	13	we	we	PRON
ejpam-5894	332	14	get	get	VERB
ejpam-5894	332	15	(	(	PUNCT
ejpam-5894	332	16	0|(x|x))|0	0|(x|x))|0	NOUN
ejpam-5894	332	17	=	=	PUNCT
ejpam-5894	332	18	x|x	x|x	PROPN
ejpam-5894	332	19	.	.	PUNCT
ejpam-5894	333	1	(	(	PUNCT
ejpam-5894	333	2	7	7	X
ejpam-5894	333	3	)	)	PUNCT
ejpam-5894	333	4	t.	t.	NOUN
ejpam-5894	333	5	oner	oner	NOUN
ejpam-5894	333	6	et	et	PROPN
ejpam-5894	333	7	al	al	PROPN
ejpam-5894	333	8	.	.	PUNCT
ejpam-5894	333	9	/	/	SYM
ejpam-5894	333	10	eur	eur	PROPN
ejpam-5894	333	11	.	.	PUNCT
ejpam-5894	334	1	j.	j.	PROPN
ejpam-5894	334	2	pure	pure	PROPN
ejpam-5894	334	3	appl	appl	PROPN
ejpam-5894	334	4	.	.	PROPN
ejpam-5894	334	5	math	math	PROPN
ejpam-5894	334	6	,	,	PUNCT
ejpam-5894	334	7	18	18	NUM
ejpam-5894	334	8	(	(	PUNCT
ejpam-5894	334	9	3	3	NUM
ejpam-5894	334	10	)	)	PUNCT
ejpam-5894	334	11	(	(	PUNCT
ejpam-5894	334	12	2025	2025	NUM
ejpam-5894	334	13	)	)	PUNCT
ejpam-5894	334	14	,	,	PUNCT
ejpam-5894	334	15	5894	5894	NUM
ejpam-5894	334	16	18	18	NUM
ejpam-5894	334	17	of	of	ADP
ejpam-5894	334	18	33	33	NUM
ejpam-5894	334	19	combining	combine	VERB
ejpam-5894	334	20	(	(	PUNCT
ejpam-5894	334	21	sbg1	sbg1	PROPN
ejpam-5894	334	22	)	)	PUNCT
ejpam-5894	334	23	and	and	CCONJ
ejpam-5894	334	24	the	the	DET
ejpam-5894	334	25	medial	medial	ADJ
ejpam-5894	334	26	property	property	NOUN
ejpam-5894	334	27	,	,	PUNCT
ejpam-5894	334	28	we	we	PRON
ejpam-5894	334	29	have	have	AUX
ejpam-5894	334	30	(	(	PUNCT
ejpam-5894	334	31	x|x)|(x|x	x|x)|(x|x	ADJ
ejpam-5894	334	32	)	)	PUNCT
ejpam-5894	334	33	=	=	SYM
ejpam-5894	335	1	0	0	X
ejpam-5894	335	2	.	.	PUNCT
ejpam-5894	336	1	(	(	PUNCT
ejpam-5894	336	2	8)	8)	NUM
ejpam-5894	336	3	combining	combine	VERB
ejpam-5894	336	4	(	(	PUNCT
ejpam-5894	336	5	sbg1	sbg1	PROPN
ejpam-5894	336	6	)	)	PUNCT
ejpam-5894	336	7	and	and	CCONJ
ejpam-5894	336	8	the	the	DET
ejpam-5894	336	9	medial	medial	ADJ
ejpam-5894	336	10	property	property	NOUN
ejpam-5894	336	11	again	again	ADV
ejpam-5894	336	12	,	,	PUNCT
ejpam-5894	336	13	we	we	PRON
ejpam-5894	336	14	have	have	VERB
ejpam-5894	336	15	x|(x|0	x|(x|0	NOUN
ejpam-5894	336	16	)	)	PUNCT
ejpam-5894	336	17	=	=	SYM
ejpam-5894	337	1	0	0	X
ejpam-5894	337	2	.	.	PUNCT
ejpam-5894	338	1	(	(	PUNCT
ejpam-5894	338	2	9	9	X
ejpam-5894	338	3	)	)	PUNCT
ejpam-5894	338	4	combining	combine	VERB
ejpam-5894	338	5	(	(	PUNCT
ejpam-5894	338	6	sbg2	sbg2	ADJ
ejpam-5894	338	7	)	)	PUNCT
ejpam-5894	338	8	and	and	CCONJ
ejpam-5894	338	9	the	the	DET
ejpam-5894	338	10	medial	medial	ADJ
ejpam-5894	338	11	property	property	NOUN
ejpam-5894	338	12	,	,	PUNCT
ejpam-5894	338	13	we	we	PRON
ejpam-5894	338	14	have	have	VERB
ejpam-5894	338	15	(	(	PUNCT
ejpam-5894	338	16	0|((x|x)|(x|x)))|((x|x)|((x|x)|((x|x)|(x|x	0|((x|x)|(x|x)))|((x|x)|((x|x)|((x|x)|(x|x	NOUN
ejpam-5894	338	17	)	)	PUNCT
ejpam-5894	338	18	)	)	PUNCT
ejpam-5894	338	19	)	)	PUNCT
ejpam-5894	338	20	)	)	PUNCT
ejpam-5894	339	1	=	=	PRON
ejpam-5894	339	2	(	(	PUNCT
ejpam-5894	339	3	x|x)|(x|x	x|x)|(x|x	PROPN
ejpam-5894	339	4	)	)	PUNCT
ejpam-5894	339	5	.	.	PUNCT
ejpam-5894	340	1	(	(	PUNCT
ejpam-5894	340	2	10	10	NUM
ejpam-5894	340	3	)	)	PUNCT
ejpam-5894	340	4	by	by	ADP
ejpam-5894	340	5	(	(	PUNCT
ejpam-5894	340	6	8)	8)	NUM
ejpam-5894	340	7	and	and	CCONJ
ejpam-5894	340	8	(	(	PUNCT
ejpam-5894	340	9	10	10	NUM
ejpam-5894	340	10	)	)	PUNCT
ejpam-5894	340	11	,	,	PUNCT
ejpam-5894	340	12	we	we	PRON
ejpam-5894	340	13	have	have	VERB
ejpam-5894	340	14	(	(	PUNCT
ejpam-5894	340	15	0|0)|((x|x)|((x|x)|((x|x)|(x|x	0|0)|((x|x)|((x|x)|((x|x)|(x|x	NOUN
ejpam-5894	340	16	)	)	PUNCT
ejpam-5894	340	17	)	)	PUNCT
ejpam-5894	340	18	)	)	PUNCT
ejpam-5894	340	19	)	)	PUNCT
ejpam-5894	341	1	=	=	PRON
ejpam-5894	341	2	(	(	PUNCT
ejpam-5894	341	3	x|x)|(x|x	x|x)|(x|x	PROPN
ejpam-5894	341	4	)	)	PUNCT
ejpam-5894	341	5	.	.	PUNCT
ejpam-5894	342	1	(	(	PUNCT
ejpam-5894	342	2	11	11	NUM
ejpam-5894	342	3	)	)	PUNCT
ejpam-5894	342	4	by	by	ADP
ejpam-5894	342	5	(	(	PUNCT
ejpam-5894	342	6	8)	8)	NUM
ejpam-5894	342	7	and	and	CCONJ
ejpam-5894	342	8	(	(	PUNCT
ejpam-5894	342	9	11	11	NUM
ejpam-5894	342	10	)	)	PUNCT
ejpam-5894	342	11	,	,	PUNCT
ejpam-5894	342	12	we	we	PRON
ejpam-5894	342	13	have	have	VERB
ejpam-5894	342	14	(	(	PUNCT
ejpam-5894	342	15	0|0)|((x|x)|((x|x)|0	0|0)|((x|x)|((x|x)|0	PROPN
ejpam-5894	342	16	)	)	PUNCT
ejpam-5894	342	17	)	)	PUNCT
ejpam-5894	343	1	=	=	PRON
ejpam-5894	343	2	(	(	PUNCT
ejpam-5894	343	3	x|x)|(x|x	x|x)|(x|x	PROPN
ejpam-5894	343	4	)	)	PUNCT
ejpam-5894	343	5	.	.	PUNCT
ejpam-5894	344	1	(	(	PUNCT
ejpam-5894	344	2	12	12	NUM
ejpam-5894	344	3	)	)	PUNCT
ejpam-5894	344	4	by	by	ADP
ejpam-5894	344	5	(	(	PUNCT
ejpam-5894	344	6	9	9	NUM
ejpam-5894	344	7	)	)	PUNCT
ejpam-5894	344	8	and	and	CCONJ
ejpam-5894	344	9	(	(	PUNCT
ejpam-5894	344	10	12	12	NUM
ejpam-5894	344	11	)	)	PUNCT
ejpam-5894	344	12	,	,	PUNCT
ejpam-5894	344	13	we	we	PRON
ejpam-5894	344	14	have	have	VERB
ejpam-5894	344	15	(	(	PUNCT
ejpam-5894	344	16	0|0)|0	0|0)|0	PUNCT
ejpam-5894	344	17	=	=	SYM
ejpam-5894	344	18	(	(	PUNCT
ejpam-5894	344	19	x|x)|(x|x	x|x)|(x|x	PROPN
ejpam-5894	344	20	)	)	PUNCT
ejpam-5894	344	21	.	.	PUNCT
ejpam-5894	345	1	(	(	PUNCT
ejpam-5894	345	2	13	13	NUM
ejpam-5894	345	3	)	)	PUNCT
ejpam-5894	345	4	by	by	ADP
ejpam-5894	345	5	(	(	PUNCT
ejpam-5894	345	6	8)	8)	NUM
ejpam-5894	345	7	and	and	CCONJ
ejpam-5894	345	8	(	(	PUNCT
ejpam-5894	345	9	13	13	NUM
ejpam-5894	345	10	)	)	PUNCT
ejpam-5894	345	11	,	,	PUNCT
ejpam-5894	345	12	we	we	PRON
ejpam-5894	345	13	have	have	VERB
ejpam-5894	345	14	(	(	PUNCT
ejpam-5894	345	15	0|0)|0	0|0)|0	PUNCT
ejpam-5894	345	16	=	=	SYM
ejpam-5894	345	17	0	0	NUM
ejpam-5894	345	18	.	.	PUNCT
ejpam-5894	346	1	(	(	PUNCT
ejpam-5894	346	2	14	14	X
ejpam-5894	346	3	)	)	PUNCT
ejpam-5894	346	4	combining	combine	VERB
ejpam-5894	346	5	(	(	PUNCT
ejpam-5894	346	6	sbg2	sbg2	ADJ
ejpam-5894	346	7	)	)	PUNCT
ejpam-5894	346	8	and	and	CCONJ
ejpam-5894	346	9	(	(	PUNCT
ejpam-5894	346	10	6	6	NUM
ejpam-5894	346	11	)	)	PUNCT
ejpam-5894	346	12	,	,	PUNCT
ejpam-5894	346	13	we	we	PRON
ejpam-5894	346	14	have	have	VERB
ejpam-5894	346	15	(	(	PUNCT
ejpam-5894	346	16	(	(	PUNCT
ejpam-5894	346	17	0|0)|0)|(((0|(x|x))|((0|(x|x))|(0|(x|x))))|0	0|0)|0)|(((0|(x|x))|((0|(x|x))|(0|(x|x))))|0	NOUN
ejpam-5894	346	18	)	)	PUNCT
ejpam-5894	346	19	=	=	SYM
ejpam-5894	347	1	0	0	X
ejpam-5894	347	2	.	.	PUNCT
ejpam-5894	348	1	(	(	PUNCT
ejpam-5894	348	2	15	15	NUM
ejpam-5894	348	3	)	)	PUNCT
ejpam-5894	348	4	by	by	ADP
ejpam-5894	348	5	(	(	PUNCT
ejpam-5894	348	6	14	14	NUM
ejpam-5894	348	7	)	)	PUNCT
ejpam-5894	348	8	and	and	CCONJ
ejpam-5894	348	9	(	(	PUNCT
ejpam-5894	348	10	15	15	NUM
ejpam-5894	348	11	)	)	PUNCT
ejpam-5894	348	12	,	,	PUNCT
ejpam-5894	348	13	we	we	PRON
ejpam-5894	348	14	have	have	VERB
ejpam-5894	348	15	0|(((0|(x|x))|((0|(x|x))|(0|(x|x))))|0	0|(((0|(x|x))|((0|(x|x))|(0|(x|x))))|0	NOUN
ejpam-5894	348	16	)	)	PUNCT
ejpam-5894	349	1	=	=	SYM
ejpam-5894	349	2	0	0	X
ejpam-5894	349	3	.	.	PUNCT
ejpam-5894	350	1	(	(	PUNCT
ejpam-5894	350	2	16	16	X
ejpam-5894	350	3	)	)	PUNCT
ejpam-5894	350	4	combining	combine	VERB
ejpam-5894	350	5	(	(	PUNCT
ejpam-5894	350	6	sbg2	sbg2	ADJ
ejpam-5894	350	7	)	)	PUNCT
ejpam-5894	350	8	and	and	CCONJ
ejpam-5894	350	9	(	(	PUNCT
ejpam-5894	350	10	16	16	NUM
ejpam-5894	350	11	)	)	PUNCT
ejpam-5894	350	12	,	,	PUNCT
ejpam-5894	350	13	we	we	PRON
ejpam-5894	350	14	have	have	VERB
ejpam-5894	350	15	0|((0|0)|0	0|((0|0)|0	NUM
ejpam-5894	350	16	)	)	PUNCT
ejpam-5894	351	1	=	=	SYM
ejpam-5894	352	1	0	0	X
ejpam-5894	352	2	.	.	PUNCT
ejpam-5894	353	1	(	(	PUNCT
ejpam-5894	353	2	17	17	NUM
ejpam-5894	353	3	)	)	PUNCT
ejpam-5894	353	4	by	by	ADP
ejpam-5894	353	5	(	(	PUNCT
ejpam-5894	353	6	14	14	NUM
ejpam-5894	353	7	)	)	PUNCT
ejpam-5894	353	8	and	and	CCONJ
ejpam-5894	353	9	(	(	PUNCT
ejpam-5894	353	10	17	17	NUM
ejpam-5894	353	11	)	)	PUNCT
ejpam-5894	353	12	,	,	PUNCT
ejpam-5894	353	13	we	we	PRON
ejpam-5894	353	14	have	have	VERB
ejpam-5894	353	15	0|0	0|0	NUM
ejpam-5894	353	16	=	=	SYM
ejpam-5894	353	17	0	0	NUM
ejpam-5894	353	18	.	.	PUNCT
ejpam-5894	354	1	(	(	PUNCT
ejpam-5894	354	2	18	18	NUM
ejpam-5894	354	3	)	)	PUNCT
ejpam-5894	354	4	combining	combine	VERB
ejpam-5894	354	5	(	(	PUNCT
ejpam-5894	354	6	sbg2	sbg2	ADJ
ejpam-5894	354	7	)	)	PUNCT
ejpam-5894	354	8	and	and	CCONJ
ejpam-5894	354	9	(	(	PUNCT
ejpam-5894	354	10	8)	8)	NUM
ejpam-5894	354	11	,	,	PUNCT
ejpam-5894	354	12	we	we	PRON
ejpam-5894	354	13	have	have	VERB
ejpam-5894	354	14	(	(	PUNCT
ejpam-5894	354	15	0|(x|x))|(0|((x|x)|(x|x	0|(x|x))|(0|((x|x)|(x|x	NUM
ejpam-5894	354	16	)	)	PUNCT
ejpam-5894	354	17	)	)	PUNCT
ejpam-5894	354	18	)	)	PUNCT
ejpam-5894	355	1	=	=	PRON
ejpam-5894	355	2	(	(	PUNCT
ejpam-5894	355	3	x|x)|(x|x	x|x)|(x|x	PROPN
ejpam-5894	355	4	)	)	PUNCT
ejpam-5894	355	5	.	.	PUNCT
ejpam-5894	356	1	(	(	PUNCT
ejpam-5894	356	2	19	19	NUM
ejpam-5894	356	3	)	)	PUNCT
ejpam-5894	356	4	t.	t.	NOUN
ejpam-5894	356	5	oner	oner	NOUN
ejpam-5894	356	6	et	et	PROPN
ejpam-5894	356	7	al	al	PROPN
ejpam-5894	356	8	.	.	PUNCT
ejpam-5894	356	9	/	/	SYM
ejpam-5894	356	10	eur	eur	PROPN
ejpam-5894	356	11	.	.	PUNCT
ejpam-5894	357	1	j.	j.	PROPN
ejpam-5894	357	2	pure	pure	PROPN
ejpam-5894	357	3	appl	appl	PROPN
ejpam-5894	357	4	.	.	PROPN
ejpam-5894	357	5	math	math	PROPN
ejpam-5894	357	6	,	,	PUNCT
ejpam-5894	357	7	18	18	NUM
ejpam-5894	357	8	(	(	PUNCT
ejpam-5894	357	9	3	3	NUM
ejpam-5894	357	10	)	)	PUNCT
ejpam-5894	357	11	(	(	PUNCT
ejpam-5894	357	12	2025	2025	NUM
ejpam-5894	357	13	)	)	PUNCT
ejpam-5894	357	14	,	,	PUNCT
ejpam-5894	357	15	5894	5894	NUM
ejpam-5894	357	16	19	19	NUM
ejpam-5894	357	17	of	of	ADP
ejpam-5894	357	18	33	33	NUM
ejpam-5894	357	19	by	by	ADP
ejpam-5894	357	20	(	(	PUNCT
ejpam-5894	357	21	8)	8)	NUM
ejpam-5894	357	22	and	and	CCONJ
ejpam-5894	357	23	(	(	PUNCT
ejpam-5894	357	24	19	19	NUM
ejpam-5894	357	25	)	)	PUNCT
ejpam-5894	357	26	,	,	PUNCT
ejpam-5894	357	27	we	we	PRON
ejpam-5894	357	28	have	have	VERB
ejpam-5894	357	29	(	(	PUNCT
ejpam-5894	357	30	0|(x|x))|(0|0	0|(x|x))|(0|0	NUM
ejpam-5894	357	31	)	)	PUNCT
ejpam-5894	357	32	=	=	PRON
ejpam-5894	357	33	(	(	PUNCT
ejpam-5894	357	34	x|x)|(x|x	x|x)|(x|x	PROPN
ejpam-5894	357	35	)	)	PUNCT
ejpam-5894	357	36	.	.	PUNCT
ejpam-5894	358	1	(	(	PUNCT
ejpam-5894	358	2	20	20	NUM
ejpam-5894	358	3	)	)	PUNCT
ejpam-5894	358	4	by	by	ADP
ejpam-5894	358	5	(	(	PUNCT
ejpam-5894	358	6	18	18	NUM
ejpam-5894	358	7	)	)	PUNCT
ejpam-5894	358	8	and	and	CCONJ
ejpam-5894	358	9	(	(	PUNCT
ejpam-5894	358	10	20	20	NUM
ejpam-5894	358	11	)	)	PUNCT
ejpam-5894	358	12	,	,	PUNCT
ejpam-5894	358	13	we	we	PRON
ejpam-5894	358	14	have	have	VERB
ejpam-5894	358	15	(	(	PUNCT
ejpam-5894	358	16	0|(x|x))|0	0|(x|x))|0	NOUN
ejpam-5894	358	17	=	=	SYM
ejpam-5894	358	18	(	(	PUNCT
ejpam-5894	358	19	x|x)|(x|x	x|x)|(x|x	PROPN
ejpam-5894	358	20	)	)	PUNCT
ejpam-5894	358	21	.	.	PUNCT
ejpam-5894	359	1	(	(	PUNCT
ejpam-5894	359	2	21	21	NUM
ejpam-5894	359	3	)	)	PUNCT
ejpam-5894	359	4	by	by	ADP
ejpam-5894	359	5	(	(	PUNCT
ejpam-5894	359	6	7	7	NUM
ejpam-5894	359	7	)	)	PUNCT
ejpam-5894	359	8	and	and	CCONJ
ejpam-5894	359	9	(	(	PUNCT
ejpam-5894	359	10	21	21	NUM
ejpam-5894	359	11	)	)	PUNCT
ejpam-5894	359	12	,	,	PUNCT
ejpam-5894	359	13	we	we	PRON
ejpam-5894	359	14	have	have	VERB
ejpam-5894	359	15	x|x	x|x	PUNCT
ejpam-5894	360	1	=	=	SYM
ejpam-5894	360	2	(	(	PUNCT
ejpam-5894	360	3	x|x)|(x|x	x|x)|(x|x	PROPN
ejpam-5894	360	4	)	)	PUNCT
ejpam-5894	360	5	.	.	PUNCT
ejpam-5894	361	1	(	(	PUNCT
ejpam-5894	361	2	22	22	NUM
ejpam-5894	361	3	)	)	PUNCT
ejpam-5894	361	4	by	by	ADP
ejpam-5894	361	5	(	(	PUNCT
ejpam-5894	361	6	8)	8)	NUM
ejpam-5894	361	7	and	and	CCONJ
ejpam-5894	361	8	(	(	PUNCT
ejpam-5894	361	9	22	22	NUM
ejpam-5894	361	10	)	)	PUNCT
ejpam-5894	361	11	,	,	PUNCT
ejpam-5894	361	12	we	we	PRON
ejpam-5894	361	13	have	have	VERB
ejpam-5894	361	14	x|x	x|x	PUNCT
ejpam-5894	362	1	=	=	SYM
ejpam-5894	362	2	0	0	NUM
ejpam-5894	362	3	,	,	PUNCT
ejpam-5894	362	4	∀x	∀x	X
ejpam-5894	362	5	∈	∈	PROPN
ejpam-5894	362	6	l.	l.	NOUN
ejpam-5894	362	7	(	(	PUNCT
ejpam-5894	362	8	23	23	NUM
ejpam-5894	362	9	)	)	PUNCT
ejpam-5894	362	10	by	by	ADP
ejpam-5894	362	11	(	(	PUNCT
ejpam-5894	362	12	23	23	NUM
ejpam-5894	362	13	)	)	PUNCT
ejpam-5894	362	14	and	and	CCONJ
ejpam-5894	362	15	(	(	PUNCT
ejpam-5894	362	16	5	5	NUM
ejpam-5894	362	17	)	)	PUNCT
ejpam-5894	362	18	,	,	PUNCT
ejpam-5894	362	19	we	we	PRON
ejpam-5894	362	20	have	have	VERB
ejpam-5894	362	21	0	0	NUM
ejpam-5894	362	22	̸=	̸=	NOUN
ejpam-5894	362	23	0	0	NUM
ejpam-5894	362	24	,	,	PUNCT
ejpam-5894	362	25	which	which	PRON
ejpam-5894	362	26	is	be	AUX
ejpam-5894	362	27	a	a	DET
ejpam-5894	362	28	contradiction	contradiction	NOUN
ejpam-5894	362	29	.	.	PUNCT
ejpam-5894	363	1	so	so	ADV
ejpam-5894	363	2	,	,	PUNCT
ejpam-5894	363	3	(	(	PUNCT
ejpam-5894	363	4	4	4	X
ejpam-5894	363	5	)	)	PUNCT
ejpam-5894	363	6	is	be	AUX
ejpam-5894	363	7	true	true	ADJ
ejpam-5894	363	8	,	,	PUNCT
ejpam-5894	363	9	that	that	ADV
ejpam-5894	363	10	is	is	ADV
ejpam-5894	363	11	,	,	PUNCT
ejpam-5894	363	12	l	l	NOUN
ejpam-5894	363	13	is	be	AUX
ejpam-5894	363	14	an	an	DET
ejpam-5894	363	15	implicative	implicative	ADJ
ejpam-5894	363	16	wsbg	wsbg	NOUN
ejpam-5894	363	17	-	-	PUNCT
ejpam-5894	363	18	algebra	algebra	NOUN
ejpam-5894	363	19	.	.	PUNCT
ejpam-5894	364	1	example	example	NOUN
ejpam-5894	364	2	12	12	NUM
ejpam-5894	364	3	.	.	PUNCT
ejpam-5894	365	1	consider	consider	VERB
ejpam-5894	365	2	the	the	DET
ejpam-5894	365	3	algebra	algebra	NOUN
ejpam-5894	365	4	l	l	NOUN
ejpam-5894	365	5	=	=	PUNCT
ejpam-5894	365	6	⟨l	⟨l	NOUN
ejpam-5894	365	7	;	;	PUNCT
ejpam-5894	365	8	|	|	ADV
ejpam-5894	365	9	,	,	PUNCT
ejpam-5894	365	10	0⟩	0⟩	PROPN
ejpam-5894	365	11	with	with	ADP
ejpam-5894	365	12	l	l	NOUN
ejpam-5894	365	13	=	=	PUNCT
ejpam-5894	365	14	{	{	PUNCT
ejpam-5894	365	15	0	0	NUM
ejpam-5894	365	16	,	,	PUNCT
ejpam-5894	365	17	1	1	NUM
ejpam-5894	365	18	,	,	PUNCT
ejpam-5894	365	19	2	2	NUM
ejpam-5894	365	20	}	}	PUNCT
ejpam-5894	365	21	and	and	CCONJ
ejpam-5894	365	22	binary	binary	ADJ
ejpam-5894	365	23	operation	operation	NOUN
ejpam-5894	365	24	|	|	ADV
ejpam-5894	365	25	defined	define	VERB
ejpam-5894	365	26	by	by	ADP
ejpam-5894	365	27	the	the	DET
ejpam-5894	365	28	cayley	cayley	ADJ
ejpam-5894	365	29	table	table	NOUN
ejpam-5894	365	30	:	:	PUNCT
ejpam-5894	365	31	|	|	ADV
ejpam-5894	365	32	0	0	NUM
ejpam-5894	365	33	1	1	NUM
ejpam-5894	365	34	2	2	NUM
ejpam-5894	365	35	0	0	NUM
ejpam-5894	365	36	0	0	NUM
ejpam-5894	365	37	1	1	NUM
ejpam-5894	365	38	2	2	NUM
ejpam-5894	365	39	1	1	NUM
ejpam-5894	365	40	1	1	NUM
ejpam-5894	365	41	2	2	NUM
ejpam-5894	365	42	0	0	NUM
ejpam-5894	365	43	2	2	NUM
ejpam-5894	365	44	2	2	NUM
ejpam-5894	365	45	0	0	NUM
ejpam-5894	365	46	1	1	NUM
ejpam-5894	365	47	hence	hence	ADV
ejpam-5894	365	48	,	,	PUNCT
ejpam-5894	365	49	the	the	DET
ejpam-5894	365	50	algebra	algebra	NOUN
ejpam-5894	365	51	is	be	AUX
ejpam-5894	365	52	an	an	DET
ejpam-5894	365	53	implicative	implicative	ADJ
ejpam-5894	365	54	wsbg	wsbg	NOUN
ejpam-5894	365	55	-	-	PUNCT
ejpam-5894	365	56	algebra	algebra	NOUN
ejpam-5894	365	57	.	.	PUNCT
ejpam-5894	366	1	we	we	PRON
ejpam-5894	366	2	found	find	VERB
ejpam-5894	366	3	that	that	SCONJ
ejpam-5894	366	4	for	for	ADP
ejpam-5894	366	5	ζ	ζ	NOUN
ejpam-5894	366	6	=	=	SYM
ejpam-5894	366	7	1	1	NUM
ejpam-5894	366	8	,	,	PUNCT
ejpam-5894	366	9	η	η	X
ejpam-5894	366	10	=	=	PROPN
ejpam-5894	366	11	0	0	NUM
ejpam-5894	366	12	:	:	PUNCT
ejpam-5894	366	13	1|(1|(0|0	1|(1|(0|0	NUM
ejpam-5894	366	14	)	)	PUNCT
ejpam-5894	366	15	)	)	PUNCT
ejpam-5894	367	1	=	=	SYM
ejpam-5894	367	2	1|(1|0	1|(1|0	NUM
ejpam-5894	367	3	)	)	PUNCT
ejpam-5894	367	4	=	=	SYM
ejpam-5894	368	1	1|1	1|1	NUM
ejpam-5894	368	2	=	=	SYM
ejpam-5894	368	3	2	2	NUM
ejpam-5894	368	4	̸=	̸=	PROPN
ejpam-5894	368	5	0	0	NUM
ejpam-5894	368	6	=	=	SYM
ejpam-5894	368	7	0|0	0|0	PROPN
ejpam-5894	368	8	.	.	PUNCT
ejpam-5894	369	1	therefore	therefore	ADV
ejpam-5894	369	2	,	,	PUNCT
ejpam-5894	369	3	the	the	DET
ejpam-5894	369	4	algebra	algebra	NOUN
ejpam-5894	369	5	is	be	AUX
ejpam-5894	369	6	not	not	PART
ejpam-5894	369	7	a	a	DET
ejpam-5894	369	8	medial	medial	ADJ
ejpam-5894	369	9	wsbg	wsbg	NOUN
ejpam-5894	369	10	-	-	PUNCT
ejpam-5894	369	11	algebra	algebra	NOUN
ejpam-5894	369	12	.	.	PUNCT
ejpam-5894	370	1	theorem	theorem	ADJ
ejpam-5894	370	2	8	8	NUM
ejpam-5894	370	3	.	.	PUNCT
ejpam-5894	371	1	let	let	VERB
ejpam-5894	371	2	l	l	NOUN
ejpam-5894	371	3	=	=	SYM
ejpam-5894	371	4	(	(	PUNCT
ejpam-5894	371	5	l	l	NOUN
ejpam-5894	371	6	,	,	PUNCT
ejpam-5894	371	7	α	α	X
ejpam-5894	371	8	,	,	PUNCT
ejpam-5894	371	9	β	β	NOUN
ejpam-5894	371	10	)	)	PUNCT
ejpam-5894	371	11	be	be	VERB
ejpam-5894	371	12	an	an	DET
ejpam-5894	371	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	371	14	fuzzy	fuzzy	ADJ
ejpam-5894	371	15	set	set	NOUN
ejpam-5894	371	16	of	of	ADP
ejpam-5894	371	17	l	l	NOUN
ejpam-5894	371	18	=	=	PUNCT
ejpam-5894	371	19	⟨l	⟨l	NOUN
ejpam-5894	371	20	;	;	PUNCT
ejpam-5894	371	21	|	|	ADV
ejpam-5894	371	22	,	,	PUNCT
ejpam-5894	371	23	0⟩.	0⟩.	PROPN
ejpam-5894	371	24	then	then	ADV
ejpam-5894	371	25	l	l	PROPN
ejpam-5894	372	1	=	=	PUNCT
ejpam-5894	372	2	(	(	PUNCT
ejpam-5894	372	3	l	l	NOUN
ejpam-5894	372	4	,	,	PUNCT
ejpam-5894	372	5	α	α	X
ejpam-5894	372	6	,	,	PUNCT
ejpam-5894	372	7	β	β	NOUN
ejpam-5894	372	8	)	)	PUNCT
ejpam-5894	372	9	is	be	AUX
ejpam-5894	372	10	an	an	DET
ejpam-5894	372	11	intuitionistic	intuitionistic	ADJ
ejpam-5894	372	12	fuzzy	fuzzy	ADJ
ejpam-5894	372	13	implicative	implicative	ADJ
ejpam-5894	372	14	wsbg	wsbg	NOUN
ejpam-5894	372	15	-	-	PUNCT
ejpam-5894	372	16	ideal	ideal	NOUN
ejpam-5894	372	17	of	of	ADP
ejpam-5894	372	18	l	l	NOUN
ejpam-5894	372	19	if	if	SCONJ
ejpam-5894	372	20	and	and	CCONJ
ejpam-5894	372	21	only	only	ADV
ejpam-5894	372	22	if	if	SCONJ
ejpam-5894	372	23	(	(	PUNCT
ejpam-5894	372	24	∀ζ	∀ζ	PROPN
ejpam-5894	372	25	,	,	PUNCT
ejpam-5894	372	26	η	η	PROPN
ejpam-5894	372	27	∈	∈	PROPN
ejpam-5894	372	28	l	l	NOUN
ejpam-5894	372	29	)	)	PUNCT
ejpam-5894	372	30	(	(	PUNCT
ejpam-5894	372	31	α(ζ	α(ζ	PROPN
ejpam-5894	372	32	)	)	PUNCT
ejpam-5894	372	33	≥	≥	NOUN
ejpam-5894	372	34	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	372	35	)	)	PUNCT
ejpam-5894	372	36	)	)	PUNCT
ejpam-5894	372	37	)	)	PUNCT
ejpam-5894	372	38	)	)	PUNCT
ejpam-5894	372	39	,	,	PUNCT
ejpam-5894	372	40	β(ζ	β(ζ	PROPN
ejpam-5894	372	41	)	)	PUNCT
ejpam-5894	372	42	≤	≤	ADV
ejpam-5894	372	43	β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	372	44	)	)	PUNCT
ejpam-5894	372	45	)	)	PUNCT
ejpam-5894	372	46	)	)	PUNCT
ejpam-5894	372	47	)	)	PUNCT
ejpam-5894	372	48	)	)	PUNCT
ejpam-5894	372	49	.	.	PUNCT
ejpam-5894	373	1	(	(	PUNCT
ejpam-5894	373	2	24	24	NUM
ejpam-5894	373	3	)	)	PUNCT
ejpam-5894	373	4	proof	proof	NOUN
ejpam-5894	373	5	.	.	PUNCT
ejpam-5894	374	1	let	let	VERB
ejpam-5894	374	2	l	l	NOUN
ejpam-5894	374	3	=	=	SYM
ejpam-5894	374	4	(	(	PUNCT
ejpam-5894	374	5	l	l	NOUN
ejpam-5894	374	6	,	,	PUNCT
ejpam-5894	374	7	α	α	X
ejpam-5894	374	8	,	,	PUNCT
ejpam-5894	374	9	β	β	NOUN
ejpam-5894	374	10	)	)	PUNCT
ejpam-5894	374	11	be	be	VERB
ejpam-5894	374	12	an	an	DET
ejpam-5894	374	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	374	14	fuzzy	fuzzy	ADJ
ejpam-5894	374	15	implicative	implicative	ADJ
ejpam-5894	374	16	wsbg	wsbg	NOUN
ejpam-5894	374	17	-	-	PUNCT
ejpam-5894	374	18	ideal	ideal	NOUN
ejpam-5894	374	19	of	of	ADP
ejpam-5894	374	20	l	l	NOUN
ejpam-5894	374	21	=	=	SYM
ejpam-5894	374	22	⟨l	⟨l	NOUN
ejpam-5894	374	23	;	;	PUNCT
ejpam-5894	374	24	|	|	ADV
ejpam-5894	374	25	,	,	PUNCT
ejpam-5894	374	26	0⟩.	0⟩.	PROPN
ejpam-5894	374	27	then	then	ADV
ejpam-5894	374	28	,	,	PUNCT
ejpam-5894	374	29	for	for	ADP
ejpam-5894	374	30	all	all	DET
ejpam-5894	374	31	ζ	ζ	NOUN
ejpam-5894	374	32	,	,	PUNCT
ejpam-5894	374	33	η	η	PROPN
ejpam-5894	374	34	∈	∈	PROPN
ejpam-5894	374	35	l	l	NOUN
ejpam-5894	374	36	,	,	PUNCT
ejpam-5894	374	37	we	we	PRON
ejpam-5894	374	38	have	have	VERB
ejpam-5894	374	39	α(ζ	α(ζ	PROPN
ejpam-5894	374	40	)	)	PUNCT
ejpam-5894	374	41	≥	≥	NOUN
ejpam-5894	374	42	min{α(0	min{α(0	NOUN
ejpam-5894	374	43	)	)	PUNCT
ejpam-5894	374	44	,	,	PUNCT
ejpam-5894	374	45	α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0	α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0	NUM
ejpam-5894	374	46	)	)	PUNCT
ejpam-5894	374	47	)	)	PUNCT
ejpam-5894	374	48	)	)	PUNCT
ejpam-5894	374	49	)	)	PUNCT
ejpam-5894	374	50	}	}	PUNCT
ejpam-5894	374	51	.	.	PUNCT
ejpam-5894	375	1	since	since	SCONJ
ejpam-5894	375	2	α(0	α(0	PROPN
ejpam-5894	375	3	)	)	PUNCT
ejpam-5894	375	4	≥	≥	NOUN
ejpam-5894	375	5	α(ζ	α(ζ	PROPN
ejpam-5894	375	6	)	)	PUNCT
ejpam-5894	375	7	,	,	PUNCT
ejpam-5894	375	8	this	this	DET
ejpam-5894	375	9	simplifies	simplifie	NOUN
ejpam-5894	375	10	to	to	ADP
ejpam-5894	375	11	α(ζ	α(ζ	PROPN
ejpam-5894	375	12	)	)	PUNCT
ejpam-5894	375	13	≥	≥	NOUN
ejpam-5894	375	14	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	375	15	)	)	PUNCT
ejpam-5894	375	16	)	)	PUNCT
ejpam-5894	375	17	)	)	PUNCT
ejpam-5894	375	18	)	)	PUNCT
ejpam-5894	375	19	.	.	PUNCT
ejpam-5894	376	1	t.	t.	PROPN
ejpam-5894	376	2	oner	oner	PROPN
ejpam-5894	376	3	et	et	PROPN
ejpam-5894	376	4	al	al	PROPN
ejpam-5894	376	5	.	.	PUNCT
ejpam-5894	376	6	/	/	SYM
ejpam-5894	376	7	eur	eur	PROPN
ejpam-5894	376	8	.	.	PUNCT
ejpam-5894	377	1	j.	j.	PROPN
ejpam-5894	377	2	pure	pure	PROPN
ejpam-5894	377	3	appl	appl	PROPN
ejpam-5894	377	4	.	.	PROPN
ejpam-5894	377	5	math	math	PROPN
ejpam-5894	377	6	,	,	PUNCT
ejpam-5894	377	7	18	18	NUM
ejpam-5894	377	8	(	(	PUNCT
ejpam-5894	377	9	3	3	NUM
ejpam-5894	377	10	)	)	PUNCT
ejpam-5894	377	11	(	(	PUNCT
ejpam-5894	377	12	2025	2025	NUM
ejpam-5894	377	13	)	)	PUNCT
ejpam-5894	377	14	,	,	PUNCT
ejpam-5894	377	15	5894	5894	NUM
ejpam-5894	377	16	20	20	NUM
ejpam-5894	377	17	of	of	ADP
ejpam-5894	377	18	33	33	NUM
ejpam-5894	377	19	similarly	similarly	ADV
ejpam-5894	377	20	,	,	PUNCT
ejpam-5894	377	21	for	for	ADP
ejpam-5894	377	22	β(ζ	β(ζ	PROPN
ejpam-5894	377	23	)	)	PUNCT
ejpam-5894	377	24	,	,	PUNCT
ejpam-5894	377	25	we	we	PRON
ejpam-5894	377	26	have	have	VERB
ejpam-5894	377	27	β(ζ	β(ζ	NUM
ejpam-5894	377	28	)	)	PUNCT
ejpam-5894	377	29	≤	≤	NOUN
ejpam-5894	377	30	max{β(0	max{β(0	NOUN
ejpam-5894	377	31	)	)	PUNCT
ejpam-5894	377	32	,	,	PUNCT
ejpam-5894	377	33	β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0	β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0	PUNCT
ejpam-5894	377	34	)	)	PUNCT
ejpam-5894	377	35	)	)	PUNCT
ejpam-5894	377	36	)	)	PUNCT
ejpam-5894	377	37	)	)	PUNCT
ejpam-5894	377	38	}	}	PUNCT
ejpam-5894	377	39	.	.	PUNCT
ejpam-5894	378	1	since	since	SCONJ
ejpam-5894	378	2	β(0	β(0	PROPN
ejpam-5894	378	3	)	)	PUNCT
ejpam-5894	378	4	≤	≤	NOUN
ejpam-5894	378	5	β(ζ	β(ζ	PROPN
ejpam-5894	378	6	)	)	PUNCT
ejpam-5894	378	7	,	,	PUNCT
ejpam-5894	378	8	this	this	DET
ejpam-5894	378	9	simplifies	simplifie	NOUN
ejpam-5894	378	10	to	to	ADP
ejpam-5894	378	11	β(ζ	β(ζ	PROPN
ejpam-5894	378	12	)	)	PUNCT
ejpam-5894	378	13	≤	≤	ADV
ejpam-5894	378	14	β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	378	15	)	)	PUNCT
ejpam-5894	378	16	)	)	PUNCT
ejpam-5894	378	17	)	)	PUNCT
ejpam-5894	378	18	)	)	PUNCT
ejpam-5894	378	19	.	.	PUNCT
ejpam-5894	379	1	thus	thus	ADV
ejpam-5894	379	2	,	,	PUNCT
ejpam-5894	379	3	l	l	NOUN
ejpam-5894	379	4	=	=	SYM
ejpam-5894	379	5	(	(	PUNCT
ejpam-5894	379	6	l	l	NOUN
ejpam-5894	379	7	,	,	PUNCT
ejpam-5894	379	8	α	α	X
ejpam-5894	379	9	,	,	PUNCT
ejpam-5894	379	10	β	β	NOUN
ejpam-5894	379	11	)	)	PUNCT
ejpam-5894	379	12	satisfies	satisfy	VERB
ejpam-5894	379	13	condition	condition	NOUN
ejpam-5894	379	14	(	(	PUNCT
ejpam-5894	379	15	24	24	NUM
ejpam-5894	379	16	)	)	PUNCT
ejpam-5894	379	17	.	.	PUNCT
ejpam-5894	380	1	conversely	conversely	ADV
ejpam-5894	380	2	,	,	PUNCT
ejpam-5894	380	3	let	let	VERB
ejpam-5894	380	4	l	l	NOUN
ejpam-5894	380	5	=	=	SYM
ejpam-5894	380	6	(	(	PUNCT
ejpam-5894	380	7	l	l	NOUN
ejpam-5894	380	8	,	,	PUNCT
ejpam-5894	380	9	α	α	X
ejpam-5894	380	10	,	,	PUNCT
ejpam-5894	380	11	β	β	NOUN
ejpam-5894	380	12	)	)	PUNCT
ejpam-5894	380	13	be	be	VERB
ejpam-5894	380	14	an	an	DET
ejpam-5894	380	15	intuitionistic	intuitionistic	ADJ
ejpam-5894	380	16	fuzzy	fuzzy	ADJ
ejpam-5894	380	17	wsbg	wsbg	NOUN
ejpam-5894	380	18	-	-	PUNCT
ejpam-5894	380	19	ideal	ideal	NOUN
ejpam-5894	380	20	of	of	ADP
ejpam-5894	380	21	l	l	NOUN
ejpam-5894	380	22	=	=	SYM
ejpam-5894	380	23	⟨l	⟨l	NOUN
ejpam-5894	380	24	;	;	PUNCT
ejpam-5894	380	25	|	|	ADV
ejpam-5894	380	26	,	,	PUNCT
ejpam-5894	380	27	0⟩	0⟩	PROPN
ejpam-5894	380	28	and	and	CCONJ
ejpam-5894	380	29	assume	assume	VERB
ejpam-5894	380	30	that	that	SCONJ
ejpam-5894	380	31	condition	condition	NOUN
ejpam-5894	380	32	(	(	PUNCT
ejpam-5894	380	33	24	24	NUM
ejpam-5894	380	34	)	)	PUNCT
ejpam-5894	380	35	holds	hold	VERB
ejpam-5894	380	36	.	.	PUNCT
ejpam-5894	381	1	then	then	ADV
ejpam-5894	381	2	,	,	PUNCT
ejpam-5894	381	3	for	for	ADP
ejpam-5894	381	4	all	all	DET
ejpam-5894	381	5	ζ	ζ	NOUN
ejpam-5894	381	6	,	,	PUNCT
ejpam-5894	381	7	η	η	PROPN
ejpam-5894	381	8	,	,	PUNCT
ejpam-5894	381	9	θ	θ	PROPN
ejpam-5894	381	10	∈	∈	PROPN
ejpam-5894	381	11	l	l	NOUN
ejpam-5894	381	12	,	,	PUNCT
ejpam-5894	381	13	we	we	PRON
ejpam-5894	381	14	have	have	VERB
ejpam-5894	381	15	α(ζ	α(ζ	PROPN
ejpam-5894	381	16	)	)	PUNCT
ejpam-5894	381	17	≥	≥	NOUN
ejpam-5894	381	18	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	381	19	)	)	PUNCT
ejpam-5894	381	20	)	)	PUNCT
ejpam-5894	381	21	)	)	PUNCT
ejpam-5894	381	22	)	)	PUNCT
ejpam-5894	381	23	.	.	PUNCT
ejpam-5894	382	1	moreover	moreover	ADV
ejpam-5894	382	2	,	,	PUNCT
ejpam-5894	382	3	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	382	4	)	)	PUNCT
ejpam-5894	382	5	)	)	PUNCT
ejpam-5894	382	6	)	)	PUNCT
ejpam-5894	382	7	)	)	PUNCT
ejpam-5894	382	8	can	can	AUX
ejpam-5894	382	9	be	be	AUX
ejpam-5894	382	10	bounded	bound	VERB
ejpam-5894	382	11	as	as	SCONJ
ejpam-5894	382	12	follows	follow	VERB
ejpam-5894	382	13	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	382	14	)	)	PUNCT
ejpam-5894	382	15	)	)	PUNCT
ejpam-5894	382	16	)	)	PUNCT
ejpam-5894	382	17	)	)	PUNCT
ejpam-5894	382	18	≥	≥	NOUN
ejpam-5894	382	19	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NUM
ejpam-5894	382	20	)	)	PUNCT
ejpam-5894	382	21	)	)	PUNCT
ejpam-5894	382	22	)	)	PUNCT
ejpam-5894	382	23	)	)	PUNCT
ejpam-5894	382	24	,	,	PUNCT
ejpam-5894	382	25	α(θ	α(θ	NOUN
ejpam-5894	382	26	)	)	PUNCT
ejpam-5894	382	27	}	}	PUNCT
ejpam-5894	382	28	.	.	PUNCT
ejpam-5894	383	1	thus	thus	ADV
ejpam-5894	383	2	,	,	PUNCT
ejpam-5894	383	3	we	we	PRON
ejpam-5894	383	4	get	get	VERB
ejpam-5894	383	5	α(ζ	α(ζ	NOUN
ejpam-5894	383	6	)	)	PUNCT
ejpam-5894	383	7	≥	≥	NOUN
ejpam-5894	383	8	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NUM
ejpam-5894	383	9	)	)	PUNCT
ejpam-5894	383	10	)	)	PUNCT
ejpam-5894	383	11	)	)	PUNCT
ejpam-5894	383	12	)	)	PUNCT
ejpam-5894	383	13	,	,	PUNCT
ejpam-5894	383	14	α(θ	α(θ	NOUN
ejpam-5894	383	15	)	)	PUNCT
ejpam-5894	383	16	}	}	PUNCT
ejpam-5894	383	17	.	.	PUNCT
ejpam-5894	384	1	similarly	similarly	ADV
ejpam-5894	384	2	,	,	PUNCT
ejpam-5894	384	3	for	for	ADP
ejpam-5894	384	4	β(ζ	β(ζ	PROPN
ejpam-5894	384	5	)	)	PUNCT
ejpam-5894	384	6	,	,	PUNCT
ejpam-5894	384	7	we	we	PRON
ejpam-5894	384	8	have	have	VERB
ejpam-5894	384	9	β(ζ	β(ζ	NUM
ejpam-5894	384	10	)	)	PUNCT
ejpam-5894	384	11	≤	≤	ADV
ejpam-5894	384	12	β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	384	13	)	)	PUNCT
ejpam-5894	384	14	)	)	PUNCT
ejpam-5894	384	15	)	)	PUNCT
ejpam-5894	384	16	)	)	PUNCT
ejpam-5894	384	17	.	.	PUNCT
ejpam-5894	385	1	and	and	CCONJ
ejpam-5894	385	2	also	also	ADV
ejpam-5894	385	3	,	,	PUNCT
ejpam-5894	385	4	we	we	PRON
ejpam-5894	385	5	attain	attain	VERB
ejpam-5894	385	6	β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	PROPN
ejpam-5894	385	7	)	)	PUNCT
ejpam-5894	385	8	)	)	PUNCT
ejpam-5894	385	9	)	)	PUNCT
ejpam-5894	385	10	)	)	PUNCT
ejpam-5894	386	1	≤	≤	NOUN
ejpam-5894	386	2	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	386	3	)	)	PUNCT
ejpam-5894	386	4	)	)	PUNCT
ejpam-5894	386	5	)	)	PUNCT
ejpam-5894	386	6	)	)	PUNCT
ejpam-5894	386	7	,	,	PUNCT
ejpam-5894	386	8	β(θ	β(θ	NUM
ejpam-5894	386	9	)	)	PUNCT
ejpam-5894	386	10	}	}	PUNCT
ejpam-5894	386	11	.	.	PUNCT
ejpam-5894	387	1	thus	thus	ADV
ejpam-5894	387	2	,	,	PUNCT
ejpam-5894	387	3	we	we	PRON
ejpam-5894	387	4	obtain	obtain	VERB
ejpam-5894	387	5	β(ζ	β(ζ	NOUN
ejpam-5894	387	6	)	)	PUNCT
ejpam-5894	387	7	≤	≤	NOUN
ejpam-5894	387	8	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	387	9	)	)	PUNCT
ejpam-5894	387	10	)	)	PUNCT
ejpam-5894	387	11	)	)	PUNCT
ejpam-5894	387	12	)	)	PUNCT
ejpam-5894	387	13	,	,	PUNCT
ejpam-5894	387	14	β(θ	β(θ	NUM
ejpam-5894	387	15	)	)	PUNCT
ejpam-5894	387	16	}	}	PUNCT
ejpam-5894	387	17	.	.	PUNCT
ejpam-5894	388	1	therefore	therefore	ADV
ejpam-5894	388	2	,	,	PUNCT
ejpam-5894	388	3	l	l	NOUN
ejpam-5894	388	4	=	=	SYM
ejpam-5894	388	5	(	(	PUNCT
ejpam-5894	388	6	l	l	NOUN
ejpam-5894	388	7	,	,	PUNCT
ejpam-5894	388	8	α	α	X
ejpam-5894	388	9	,	,	PUNCT
ejpam-5894	388	10	β	β	NOUN
ejpam-5894	388	11	)	)	PUNCT
ejpam-5894	388	12	is	be	AUX
ejpam-5894	388	13	an	an	DET
ejpam-5894	388	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	388	15	fuzzy	fuzzy	ADJ
ejpam-5894	388	16	implicative	implicative	ADJ
ejpam-5894	388	17	wsbg	wsbg	NOUN
ejpam-5894	388	18	-	-	PUNCT
ejpam-5894	388	19	ideal	ideal	NOUN
ejpam-5894	388	20	of	of	ADP
ejpam-5894	388	21	l.	l.	PROPN
ejpam-5894	388	22	the	the	DET
ejpam-5894	388	23	identity	identity	NOUN
ejpam-5894	388	24	used	use	VERB
ejpam-5894	388	25	in	in	ADP
ejpam-5894	388	26	theorem	theorem	ADJ
ejpam-5894	388	27	8	8	NUM
ejpam-5894	388	28	is	be	AUX
ejpam-5894	388	29	not	not	PART
ejpam-5894	388	30	an	an	DET
ejpam-5894	388	31	assumption	assumption	NOUN
ejpam-5894	388	32	but	but	CCONJ
ejpam-5894	388	33	a	a	DET
ejpam-5894	388	34	necessary	necessary	ADJ
ejpam-5894	388	35	and	and	CCONJ
ejpam-5894	388	36	sufficient	sufficient	ADJ
ejpam-5894	388	37	condition	condition	NOUN
ejpam-5894	388	38	that	that	PRON
ejpam-5894	388	39	fully	fully	ADV
ejpam-5894	388	40	characterizes	characterize	VERB
ejpam-5894	388	41	when	when	SCONJ
ejpam-5894	388	42	an	an	DET
ejpam-5894	388	43	intuitionistic	intuitionistic	ADJ
ejpam-5894	388	44	fuzzy	fuzzy	ADJ
ejpam-5894	388	45	set	set	NOUN
ejpam-5894	388	46	becomes	become	VERB
ejpam-5894	388	47	an	an	DET
ejpam-5894	388	48	intuitionistic	intuitionistic	ADJ
ejpam-5894	388	49	fuzzy	fuzzy	ADJ
ejpam-5894	388	50	implicative	implicative	ADJ
ejpam-5894	388	51	wsbg	wsbg	ADV
ejpam-5894	388	52	-	-	PUNCT
ejpam-5894	388	53	ideal	ideal	ADJ
ejpam-5894	388	54	.	.	PUNCT
ejpam-5894	389	1	theorem	theorem	NOUN
ejpam-5894	389	2	9	9	NUM
ejpam-5894	389	3	.	.	PUNCT
ejpam-5894	390	1	let	let	VERB
ejpam-5894	390	2	l	l	NOUN
ejpam-5894	390	3	=	=	SYM
ejpam-5894	390	4	⟨l	⟨l	NOUN
ejpam-5894	390	5	;	;	PUNCT
ejpam-5894	390	6	|	|	ADV
ejpam-5894	390	7	,	,	PUNCT
ejpam-5894	390	8	0⟩	0⟩	PROPN
ejpam-5894	390	9	be	be	VERB
ejpam-5894	390	10	a	a	DET
ejpam-5894	390	11	medial	medial	ADJ
ejpam-5894	390	12	wsbg	wsbg	NOUN
ejpam-5894	390	13	-	-	PUNCT
ejpam-5894	390	14	algebra	algebra	NOUN
ejpam-5894	390	15	.	.	PUNCT
ejpam-5894	391	1	then	then	ADV
ejpam-5894	391	2	every	every	DET
ejpam-5894	391	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	391	4	fuzzy	fuzzy	ADJ
ejpam-5894	391	5	implicative	implicative	ADJ
ejpam-5894	391	6	wsbg	wsbg	NOUN
ejpam-5894	391	7	-	-	PUNCT
ejpam-5894	391	8	ideal	ideal	NOUN
ejpam-5894	391	9	of	of	ADP
ejpam-5894	391	10	l	l	NOUN
ejpam-5894	391	11	is	be	AUX
ejpam-5894	391	12	an	an	DET
ejpam-5894	391	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	391	14	fuzzy	fuzzy	ADJ
ejpam-5894	391	15	sub	sub	ADJ
ejpam-5894	391	16	-	-	ADJ
ejpam-5894	391	17	implicative	implicative	ADJ
ejpam-5894	391	18	wsbg	wsbg	NOUN
ejpam-5894	391	19	-	-	PUNCT
ejpam-5894	391	20	ideal	ideal	NOUN
ejpam-5894	391	21	of	of	ADP
ejpam-5894	391	22	l.	l.	PROPN
ejpam-5894	391	23	t.	t.	PROPN
ejpam-5894	391	24	oner	oner	PROPN
ejpam-5894	391	25	et	et	PROPN
ejpam-5894	391	26	al	al	PROPN
ejpam-5894	391	27	.	.	PUNCT
ejpam-5894	391	28	/	/	SYM
ejpam-5894	391	29	eur	eur	PROPN
ejpam-5894	391	30	.	.	PUNCT
ejpam-5894	392	1	j.	j.	PROPN
ejpam-5894	392	2	pure	pure	PROPN
ejpam-5894	392	3	appl	appl	PROPN
ejpam-5894	392	4	.	.	PROPN
ejpam-5894	392	5	math	math	PROPN
ejpam-5894	392	6	,	,	PUNCT
ejpam-5894	392	7	18	18	NUM
ejpam-5894	392	8	(	(	PUNCT
ejpam-5894	392	9	3	3	NUM
ejpam-5894	392	10	)	)	PUNCT
ejpam-5894	392	11	(	(	PUNCT
ejpam-5894	392	12	2025	2025	NUM
ejpam-5894	392	13	)	)	PUNCT
ejpam-5894	392	14	,	,	PUNCT
ejpam-5894	392	15	5894	5894	NUM
ejpam-5894	392	16	21	21	NUM
ejpam-5894	392	17	of	of	ADP
ejpam-5894	392	18	33	33	NUM
ejpam-5894	392	19	proof	proof	NOUN
ejpam-5894	392	20	.	.	PUNCT
ejpam-5894	393	1	by	by	ADP
ejpam-5894	393	2	assumption	assumption	NOUN
ejpam-5894	393	3	,	,	PUNCT
ejpam-5894	393	4	l	l	NOUN
ejpam-5894	393	5	=	=	SYM
ejpam-5894	393	6	(	(	PUNCT
ejpam-5894	393	7	l	l	NOUN
ejpam-5894	393	8	,	,	PUNCT
ejpam-5894	393	9	α	α	X
ejpam-5894	393	10	,	,	PUNCT
ejpam-5894	393	11	β	β	NOUN
ejpam-5894	393	12	)	)	PUNCT
ejpam-5894	393	13	is	be	AUX
ejpam-5894	393	14	an	an	DET
ejpam-5894	393	15	intuitionistic	intuitionistic	ADJ
ejpam-5894	393	16	fuzzy	fuzzy	ADJ
ejpam-5894	393	17	implicative	implicative	ADJ
ejpam-5894	393	18	wsbg	wsbg	NOUN
ejpam-5894	393	19	-	-	PUNCT
ejpam-5894	393	20	ideal	ideal	NOUN
ejpam-5894	393	21	of	of	ADP
ejpam-5894	393	22	l.	l.	PROPN
ejpam-5894	393	23	then	then	ADV
ejpam-5894	393	24	,	,	PUNCT
ejpam-5894	393	25	for	for	ADP
ejpam-5894	393	26	all	all	DET
ejpam-5894	393	27	ζ	ζ	NOUN
ejpam-5894	393	28	,	,	PUNCT
ejpam-5894	393	29	η	η	PROPN
ejpam-5894	393	30	,	,	PUNCT
ejpam-5894	393	31	θ	θ	PROPN
ejpam-5894	393	32	∈	∈	PROPN
ejpam-5894	393	33	l	l	NOUN
ejpam-5894	393	34	,	,	PUNCT
ejpam-5894	393	35	we	we	PRON
ejpam-5894	393	36	have	have	VERB
ejpam-5894	393	37	α(0	α(0	PROPN
ejpam-5894	393	38	)	)	PUNCT
ejpam-5894	393	39	≥	≥	NOUN
ejpam-5894	393	40	α(ζ	α(ζ	PROPN
ejpam-5894	393	41	)	)	PUNCT
ejpam-5894	393	42	≥	≥	NOUN
ejpam-5894	393	43	min{α(ψ(ζ	min{α(ψ(ζ	NOUN
ejpam-5894	393	44	,	,	PUNCT
ejpam-5894	393	45	η	η	PROPN
ejpam-5894	393	46	,	,	PUNCT
ejpam-5894	393	47	θ	θ	NOUN
ejpam-5894	393	48	)	)	PUNCT
ejpam-5894	393	49	)	)	PUNCT
ejpam-5894	393	50	,	,	PUNCT
ejpam-5894	393	51	α(θ	α(θ	NOUN
ejpam-5894	393	52	)	)	PUNCT
ejpam-5894	393	53	}	}	PUNCT
ejpam-5894	393	54	,	,	PUNCT
ejpam-5894	393	55	β(0	β(0	PROPN
ejpam-5894	393	56	)	)	PUNCT
ejpam-5894	393	57	≤	≤	NOUN
ejpam-5894	393	58	β(ζ	β(ζ	PROPN
ejpam-5894	393	59	)	)	PUNCT
ejpam-5894	393	60	≤	≤	PUNCT
ejpam-5894	394	1	max{β(ψ(ζ	max{β(ψ(ζ	PROPN
ejpam-5894	394	2	,	,	PUNCT
ejpam-5894	394	3	η	η	PROPN
ejpam-5894	394	4	,	,	PUNCT
ejpam-5894	394	5	θ	θ	NOUN
ejpam-5894	394	6	)	)	PUNCT
ejpam-5894	394	7	)	)	PUNCT
ejpam-5894	394	8	,	,	PUNCT
ejpam-5894	394	9	β(θ	β(θ	NUM
ejpam-5894	394	10	)	)	PUNCT
ejpam-5894	394	11	}	}	PUNCT
ejpam-5894	394	12	.	.	PUNCT
ejpam-5894	395	1	we	we	PRON
ejpam-5894	395	2	aim	aim	VERB
ejpam-5894	395	3	to	to	PART
ejpam-5894	395	4	prove	prove	VERB
ejpam-5894	395	5	that	that	DET
ejpam-5894	395	6	l	l	NOUN
ejpam-5894	395	7	=	=	SYM
ejpam-5894	395	8	(	(	PUNCT
ejpam-5894	395	9	l	l	NOUN
ejpam-5894	395	10	,	,	PUNCT
ejpam-5894	395	11	α	α	X
ejpam-5894	395	12	,	,	PUNCT
ejpam-5894	395	13	β	β	NOUN
ejpam-5894	395	14	)	)	PUNCT
ejpam-5894	395	15	satisfies	satisfy	VERB
ejpam-5894	395	16	the	the	DET
ejpam-5894	395	17	sub	sub	ADJ
ejpam-5894	395	18	-	-	ADJ
ejpam-5894	395	19	implicative	implicative	ADJ
ejpam-5894	395	20	condition	condition	NOUN
ejpam-5894	395	21	,	,	PUNCT
ejpam-5894	395	22	i.e.	i.e.	X
ejpam-5894	395	23	,	,	PUNCT
ejpam-5894	395	24	for	for	ADP
ejpam-5894	395	25	all	all	DET
ejpam-5894	395	26	ζ	ζ	NOUN
ejpam-5894	395	27	,	,	PUNCT
ejpam-5894	395	28	η	η	PROPN
ejpam-5894	395	29	,	,	PUNCT
ejpam-5894	395	30	θ	θ	PROPN
ejpam-5894	395	31	∈	∈	PROPN
ejpam-5894	395	32	l	l	NOUN
ejpam-5894	395	33	,	,	PUNCT
ejpam-5894	395	34	α(x	α(x	NOUN
ejpam-5894	395	35	)	)	PUNCT
ejpam-5894	395	36	≥	≥	NOUN
ejpam-5894	395	37	min{α(φ(ζ	min{α(φ(ζ	PROPN
ejpam-5894	395	38	,	,	PUNCT
ejpam-5894	395	39	η	η	PROPN
ejpam-5894	395	40	,	,	PUNCT
ejpam-5894	395	41	θ	θ	NOUN
ejpam-5894	395	42	)	)	PUNCT
ejpam-5894	395	43	)	)	PUNCT
ejpam-5894	395	44	,	,	PUNCT
ejpam-5894	395	45	α(θ	α(θ	NOUN
ejpam-5894	395	46	)	)	PUNCT
ejpam-5894	395	47	}	}	PUNCT
ejpam-5894	395	48	,	,	PUNCT
ejpam-5894	395	49	where	where	SCONJ
ejpam-5894	395	50	x	x	X
ejpam-5894	395	51	=	=	PRON
ejpam-5894	395	52	(	(	PUNCT
ejpam-5894	395	53	η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	395	54	)	)	PUNCT
ejpam-5894	395	55	)	)	PUNCT
ejpam-5894	395	56	)	)	PUNCT
ejpam-5894	395	57	β(x	β(x	NOUN
ejpam-5894	395	58	)	)	PUNCT
ejpam-5894	395	59	≤	≤	NOUN
ejpam-5894	395	60	max{β(φ(ζ	max{β(φ(ζ	NOUN
ejpam-5894	395	61	,	,	PUNCT
ejpam-5894	395	62	η	η	NOUN
ejpam-5894	395	63	,	,	PUNCT
ejpam-5894	395	64	θ	θ	NOUN
ejpam-5894	395	65	)	)	PUNCT
ejpam-5894	395	66	)	)	PUNCT
ejpam-5894	395	67	,	,	PUNCT
ejpam-5894	395	68	β(θ	β(θ	NUM
ejpam-5894	395	69	)	)	PUNCT
ejpam-5894	395	70	}	}	PUNCT
ejpam-5894	395	71	.	.	PUNCT
ejpam-5894	396	1	from	from	ADP
ejpam-5894	396	2	the	the	DET
ejpam-5894	396	3	medial	medial	ADJ
ejpam-5894	396	4	identity	identity	NOUN
ejpam-5894	396	5	:	:	PUNCT
ejpam-5894	396	6	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	396	7	)	)	PUNCT
ejpam-5894	396	8	)	)	PUNCT
ejpam-5894	396	9	=	=	SYM
ejpam-5894	396	10	η|η	η|η	PROPN
ejpam-5894	396	11	.	.	PROPN
ejpam-5894	396	12	apply	apply	VERB
ejpam-5894	396	13	this	this	DET
ejpam-5894	396	14	identity	identity	NOUN
ejpam-5894	396	15	twice	twice	ADV
ejpam-5894	396	16	:	:	PUNCT
ejpam-5894	396	17	let	let	VERB
ejpam-5894	396	18	a	a	PRON
ejpam-5894	396	19	:	:	PUNCT
ejpam-5894	396	20	=	=	SYM
ejpam-5894	396	21	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	396	22	)	)	PUNCT
ejpam-5894	396	23	)	)	PUNCT
ejpam-5894	396	24	,	,	PUNCT
ejpam-5894	396	25	then	then	ADV
ejpam-5894	396	26	by	by	ADP
ejpam-5894	396	27	medial	medial	ADJ
ejpam-5894	396	28	property	property	NOUN
ejpam-5894	396	29	:	:	PUNCT
ejpam-5894	396	30	a	a	DET
ejpam-5894	396	31	=	=	SYM
ejpam-5894	396	32	η|η	η|η	PROPN
ejpam-5894	396	33	.	.	PUNCT
ejpam-5894	397	1	thus	thus	ADV
ejpam-5894	397	2	,	,	PUNCT
ejpam-5894	397	3	a|a	a|a	PUNCT
ejpam-5894	397	4	=	=	PUNCT
ejpam-5894	397	5	(	(	PUNCT
ejpam-5894	397	6	η|η)|(η|η	η|η)|(η|η	PROPN
ejpam-5894	397	7	)	)	PUNCT
ejpam-5894	397	8	.	.	PUNCT
ejpam-5894	398	1	also	also	ADV
ejpam-5894	398	2	,	,	PUNCT
ejpam-5894	398	3	let	let	VERB
ejpam-5894	398	4	b	b	X
ejpam-5894	398	5	:	:	PUNCT
ejpam-5894	398	6	=	=	SYM
ejpam-5894	398	7	θ|θ	θ|θ	NOUN
ejpam-5894	398	8	,	,	PUNCT
ejpam-5894	398	9	φ	φ	X
ejpam-5894	398	10	:	:	PUNCT
ejpam-5894	398	11	=	=	SYM
ejpam-5894	398	12	(	(	PUNCT
ejpam-5894	398	13	a|a)|b	a|a)|b	PROPN
ejpam-5894	398	14	,	,	PUNCT
ejpam-5894	398	15	φ	φ	NOUN
ejpam-5894	398	16	=	=	SYM
ejpam-5894	398	17	ψ(ζ	ψ(ζ	PROPN
ejpam-5894	398	18	,	,	PUNCT
ejpam-5894	398	19	η	η	PROPN
ejpam-5894	398	20	,	,	PUNCT
ejpam-5894	398	21	θ	θ	NOUN
ejpam-5894	398	22	)	)	PUNCT
ejpam-5894	398	23	.	.	PUNCT
ejpam-5894	399	1	now	now	ADV
ejpam-5894	399	2	define	define	VERB
ejpam-5894	399	3	x	x	PUNCT
ejpam-5894	399	4	:	:	PUNCT
ejpam-5894	399	5	=	=	SYM
ejpam-5894	399	6	(	(	PUNCT
ejpam-5894	399	7	η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ	NOUN
ejpam-5894	399	8	)	)	PUNCT
ejpam-5894	399	9	)	)	PUNCT
ejpam-5894	399	10	)	)	PUNCT
ejpam-5894	400	1	=	=	PUNCT
ejpam-5894	400	2	y|y	y|y	PROPN
ejpam-5894	400	3	.	.	PUNCT
ejpam-5894	401	1	let	let	VERB
ejpam-5894	401	2	us	we	PRON
ejpam-5894	401	3	show	show	VERB
ejpam-5894	401	4	that	that	SCONJ
ejpam-5894	401	5	y	y	PROPN
ejpam-5894	401	6	=	=	PRON
ejpam-5894	401	7	ζ|(ζ|(η|η	ζ|(ζ|(η|η	X
ejpam-5894	401	8	)	)	PUNCT
ejpam-5894	401	9	)	)	PUNCT
ejpam-5894	402	1	=	=	PUNCT
ejpam-5894	402	2	a	a	PRON
ejpam-5894	402	3	=	=	PUNCT
ejpam-5894	402	4	η|η	η|η	PROPN
ejpam-5894	402	5	⇒	⇒	VERB
ejpam-5894	402	6	x	x	PUNCT
ejpam-5894	403	1	=	=	SYM
ejpam-5894	403	2	(	(	PUNCT
ejpam-5894	403	3	η|η)|(η|η	η|η)|(η|η	NOUN
ejpam-5894	403	4	)	)	PUNCT
ejpam-5894	403	5	⇒	⇒	NOUN
ejpam-5894	403	6	x	x	PUNCT
ejpam-5894	403	7	=	=	PUNCT
ejpam-5894	403	8	a|a	a|a	NOUN
ejpam-5894	403	9	.	.	PUNCT
ejpam-5894	404	1	hence	hence	ADV
ejpam-5894	404	2	,	,	PUNCT
ejpam-5894	404	3	x	x	PUNCT
ejpam-5894	404	4	=	=	SYM
ejpam-5894	404	5	a|a	a|a	NOUN
ejpam-5894	404	6	,	,	PUNCT
ejpam-5894	404	7	φ	φ	NOUN
ejpam-5894	404	8	=	=	SYM
ejpam-5894	404	9	(	(	PUNCT
ejpam-5894	404	10	a|a)|b⇒	a|a)|b⇒	PUNCT
ejpam-5894	404	11	and	and	CCONJ
ejpam-5894	404	12	the	the	DET
ejpam-5894	404	13	same	same	ADJ
ejpam-5894	404	14	value	value	NOUN
ejpam-5894	404	15	of	of	ADP
ejpam-5894	404	16	a	a	DET
ejpam-5894	404	17	links	link	NOUN
ejpam-5894	404	18	both	both	DET
ejpam-5894	404	19	sides	side	NOUN
ejpam-5894	404	20	.	.	PUNCT
ejpam-5894	405	1	therefore	therefore	ADV
ejpam-5894	405	2	,	,	PUNCT
ejpam-5894	405	3	α(x	α(x	NOUN
ejpam-5894	405	4	)	)	PUNCT
ejpam-5894	405	5	=	=	SYM
ejpam-5894	405	6	α(a|a	α(a|a	NUM
ejpam-5894	405	7	)	)	PUNCT
ejpam-5894	405	8	≥	≥	NOUN
ejpam-5894	405	9	min{α(φ	min{α(φ	NUM
ejpam-5894	405	10	)	)	PUNCT
ejpam-5894	405	11	,	,	PUNCT
ejpam-5894	405	12	α(θ	α(θ	NOUN
ejpam-5894	405	13	)	)	PUNCT
ejpam-5894	405	14	}	}	PUNCT
ejpam-5894	405	15	,	,	PUNCT
ejpam-5894	405	16	β(x	β(x	NOUN
ejpam-5894	405	17	)	)	PUNCT
ejpam-5894	405	18	=	=	PUNCT
ejpam-5894	405	19	β(a|a	β(a|a	NUM
ejpam-5894	405	20	)	)	PUNCT
ejpam-5894	405	21	≤	≤	NOUN
ejpam-5894	405	22	max{β(φ	max{β(φ	PROPN
ejpam-5894	405	23	)	)	PUNCT
ejpam-5894	405	24	,	,	PUNCT
ejpam-5894	405	25	β(θ	β(θ	NUM
ejpam-5894	405	26	)	)	PUNCT
ejpam-5894	405	27	}	}	PUNCT
ejpam-5894	405	28	.	.	PUNCT
ejpam-5894	406	1	this	this	PRON
ejpam-5894	406	2	completes	complete	VERB
ejpam-5894	406	3	the	the	DET
ejpam-5894	406	4	proof	proof	NOUN
ejpam-5894	406	5	that	that	SCONJ
ejpam-5894	406	6	l	l	NOUN
ejpam-5894	406	7	=	=	SYM
ejpam-5894	406	8	(	(	PUNCT
ejpam-5894	406	9	l	l	NOUN
ejpam-5894	406	10	,	,	PUNCT
ejpam-5894	406	11	α	α	X
ejpam-5894	406	12	,	,	PUNCT
ejpam-5894	406	13	β	β	NOUN
ejpam-5894	406	14	)	)	PUNCT
ejpam-5894	406	15	is	be	AUX
ejpam-5894	406	16	an	an	DET
ejpam-5894	406	17	intuitionistic	intuitionistic	ADJ
ejpam-5894	406	18	fuzzy	fuzzy	ADJ
ejpam-5894	406	19	sub	sub	ADJ
ejpam-5894	406	20	-	-	ADJ
ejpam-5894	406	21	implicative	implicative	ADJ
ejpam-5894	406	22	wsbg	wsbg	NOUN
ejpam-5894	406	23	-	-	PUNCT
ejpam-5894	406	24	ideal	ideal	NOUN
ejpam-5894	406	25	of	of	ADP
ejpam-5894	406	26	l.	l.	PROPN
ejpam-5894	406	27	example	example	PROPN
ejpam-5894	406	28	13	13	NUM
ejpam-5894	406	29	.	.	PUNCT
ejpam-5894	407	1	from	from	ADP
ejpam-5894	407	2	example	example	NOUN
ejpam-5894	407	3	10	10	NUM
ejpam-5894	407	4	,	,	PUNCT
ejpam-5894	407	5	the	the	DET
ejpam-5894	407	6	algebra	algebra	NOUN
ejpam-5894	407	7	l	l	NOUN
ejpam-5894	407	8	=	=	PUNCT
ejpam-5894	407	9	⟨l	⟨l	NOUN
ejpam-5894	407	10	;	;	PUNCT
ejpam-5894	407	11	|	|	ADV
ejpam-5894	407	12	,	,	PUNCT
ejpam-5894	407	13	0⟩	0⟩	PROPN
ejpam-5894	407	14	with	with	ADP
ejpam-5894	407	15	l	l	NOUN
ejpam-5894	407	16	=	=	PUNCT
ejpam-5894	407	17	{	{	PUNCT
ejpam-5894	407	18	0	0	NUM
ejpam-5894	407	19	,	,	PUNCT
ejpam-5894	407	20	1	1	NUM
ejpam-5894	407	21	,	,	PUNCT
ejpam-5894	407	22	2	2	NUM
ejpam-5894	407	23	}	}	PUNCT
ejpam-5894	407	24	is	be	AUX
ejpam-5894	407	25	a	a	DET
ejpam-5894	407	26	medial	medial	ADJ
ejpam-5894	407	27	wsbg	wsbg	NOUN
ejpam-5894	407	28	-	-	PUNCT
ejpam-5894	407	29	algebra	algebra	NOUN
ejpam-5894	407	30	.	.	PUNCT
ejpam-5894	408	1	define	define	VERB
ejpam-5894	408	2	an	an	DET
ejpam-5894	408	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	408	4	fuzzy	fuzzy	ADJ
ejpam-5894	408	5	set	set	NOUN
ejpam-5894	408	6	l	l	NOUN
ejpam-5894	408	7	=	=	SYM
ejpam-5894	408	8	(	(	PUNCT
ejpam-5894	408	9	l	l	NOUN
ejpam-5894	408	10	,	,	PUNCT
ejpam-5894	408	11	α	α	X
ejpam-5894	408	12	,	,	PUNCT
ejpam-5894	408	13	β	β	NOUN
ejpam-5894	408	14	)	)	PUNCT
ejpam-5894	408	15	by	by	ADP
ejpam-5894	408	16	:	:	PUNCT
ejpam-5894	408	17	α(x	α(x	NOUN
ejpam-5894	408	18	)	)	PUNCT
ejpam-5894	408	19	=	=	SYM
ejpam-5894	408	20	0.5	0.5	NUM
ejpam-5894	408	21	,	,	PUNCT
ejpam-5894	408	22	∀x	∀x	X
ejpam-5894	408	23	∈	∈	PROPN
ejpam-5894	408	24	l	l	NOUN
ejpam-5894	408	25	,	,	PUNCT
ejpam-5894	408	26	β(0	β(0	PROPN
ejpam-5894	408	27	)	)	PUNCT
ejpam-5894	408	28	=	=	SYM
ejpam-5894	408	29	β(2	β(2	PROPN
ejpam-5894	408	30	)	)	PUNCT
ejpam-5894	409	1	=	=	SYM
ejpam-5894	409	2	0.25	0.25	NUM
ejpam-5894	409	3	,	,	PUNCT
ejpam-5894	409	4	β(1	β(1	PROPN
ejpam-5894	409	5	)	)	PUNCT
ejpam-5894	409	6	=	=	SYM
ejpam-5894	410	1	0	0	X
ejpam-5894	410	2	.	.	PUNCT
ejpam-5894	411	1	we	we	PRON
ejpam-5894	411	2	verified	verify	VERB
ejpam-5894	411	3	that	that	SCONJ
ejpam-5894	411	4	l	l	NOUN
ejpam-5894	411	5	=	=	SYM
ejpam-5894	411	6	(	(	PUNCT
ejpam-5894	411	7	l	l	NOUN
ejpam-5894	411	8	,	,	PUNCT
ejpam-5894	411	9	α	α	X
ejpam-5894	411	10	,	,	PUNCT
ejpam-5894	411	11	β	β	NOUN
ejpam-5894	411	12	)	)	PUNCT
ejpam-5894	411	13	is	be	AUX
ejpam-5894	411	14	an	an	DET
ejpam-5894	411	15	intuitionistic	intuitionistic	ADJ
ejpam-5894	411	16	fuzzy	fuzzy	ADJ
ejpam-5894	411	17	sub	sub	ADJ
ejpam-5894	411	18	-	-	ADJ
ejpam-5894	411	19	implicative	implicative	ADJ
ejpam-5894	411	20	wsbg	wsbg	NOUN
ejpam-5894	411	21	-	-	PUNCT
ejpam-5894	411	22	ideal	ideal	NOUN
ejpam-5894	411	23	of	of	ADP
ejpam-5894	411	24	l	l	NOUN
ejpam-5894	411	25	,	,	PUNCT
ejpam-5894	411	26	but	but	CCONJ
ejpam-5894	411	27	not	not	PART
ejpam-5894	411	28	an	an	DET
ejpam-5894	411	29	intuitionistic	intuitionistic	ADJ
ejpam-5894	411	30	fuzzy	fuzzy	ADJ
ejpam-5894	411	31	implicative	implicative	ADJ
ejpam-5894	411	32	wsbg	wsbg	NOUN
ejpam-5894	411	33	-	-	PUNCT
ejpam-5894	411	34	ideal	ideal	ADJ
ejpam-5894	411	35	because	because	SCONJ
ejpam-5894	411	36	β(0	β(0	NOUN
ejpam-5894	411	37	)	)	PUNCT
ejpam-5894	411	38	=	=	NUM
ejpam-5894	411	39	0.25	0.25	NUM
ejpam-5894	411	40	>	>	PUNCT
ejpam-5894	411	41	β(1	β(1	PROPN
ejpam-5894	411	42	)	)	PUNCT
ejpam-5894	411	43	=	=	SYM
ejpam-5894	412	1	0	0	X
ejpam-5894	412	2	.	.	PUNCT
ejpam-5894	413	1	t.	t.	PROPN
ejpam-5894	413	2	oner	oner	PROPN
ejpam-5894	413	3	et	et	PROPN
ejpam-5894	413	4	al	al	PROPN
ejpam-5894	413	5	.	.	PUNCT
ejpam-5894	413	6	/	/	SYM
ejpam-5894	413	7	eur	eur	PROPN
ejpam-5894	413	8	.	.	PUNCT
ejpam-5894	414	1	j.	j.	PROPN
ejpam-5894	414	2	pure	pure	PROPN
ejpam-5894	414	3	appl	appl	PROPN
ejpam-5894	414	4	.	.	PROPN
ejpam-5894	414	5	math	math	PROPN
ejpam-5894	414	6	,	,	PUNCT
ejpam-5894	414	7	18	18	NUM
ejpam-5894	414	8	(	(	PUNCT
ejpam-5894	414	9	3	3	NUM
ejpam-5894	414	10	)	)	PUNCT
ejpam-5894	414	11	(	(	PUNCT
ejpam-5894	414	12	2025	2025	NUM
ejpam-5894	414	13	)	)	PUNCT
ejpam-5894	414	14	,	,	PUNCT
ejpam-5894	414	15	5894	5894	NUM
ejpam-5894	414	16	22	22	NUM
ejpam-5894	414	17	of	of	ADP
ejpam-5894	414	18	33	33	NUM
ejpam-5894	414	19	definition	definition	NOUN
ejpam-5894	414	20	14	14	NUM
ejpam-5894	414	21	.	.	PUNCT
ejpam-5894	415	1	an	an	DET
ejpam-5894	415	2	intuitionistic	intuitionistic	ADJ
ejpam-5894	415	3	fuzzy	fuzzy	ADJ
ejpam-5894	415	4	wsbg	wsbg	ADJ
ejpam-5894	415	5	-	-	PUNCT
ejpam-5894	415	6	ideal	ideal	NOUN
ejpam-5894	415	7	l	l	NOUN
ejpam-5894	415	8	=	=	SYM
ejpam-5894	415	9	(	(	PUNCT
ejpam-5894	415	10	l	l	NOUN
ejpam-5894	415	11	,	,	PUNCT
ejpam-5894	415	12	α	α	X
ejpam-5894	415	13	,	,	PUNCT
ejpam-5894	415	14	β	β	NOUN
ejpam-5894	415	15	)	)	PUNCT
ejpam-5894	415	16	of	of	ADP
ejpam-5894	415	17	a	a	DET
ejpam-5894	415	18	wsbg	wsbg	ADV
ejpam-5894	415	19	-	-	PUNCT
ejpam-5894	415	20	algebra	algebra	NOUN
ejpam-5894	415	21	l	l	NOUN
ejpam-5894	415	22	=	=	PUNCT
ejpam-5894	415	23	⟨l	⟨l	NOUN
ejpam-5894	415	24	;	;	PUNCT
ejpam-5894	415	25	|	|	ADV
ejpam-5894	415	26	,	,	PUNCT
ejpam-5894	415	27	0⟩	0⟩	PROPN
ejpam-5894	415	28	is	be	AUX
ejpam-5894	415	29	said	say	VERB
ejpam-5894	415	30	to	to	PART
ejpam-5894	415	31	be	be	AUX
ejpam-5894	415	32	an	an	DET
ejpam-5894	415	33	intuitionistic	intuitionistic	ADJ
ejpam-5894	415	34	fuzzy	fuzzy	ADJ
ejpam-5894	415	35	closed	close	VERB
ejpam-5894	415	36	wsbg	wsbg	ADV
ejpam-5894	415	37	-	-	PUNCT
ejpam-5894	415	38	ideal	ideal	ADJ
ejpam-5894	415	39	if	if	SCONJ
ejpam-5894	415	40	(	(	PUNCT
ejpam-5894	415	41	∀ζ	∀ζ	PROPN
ejpam-5894	415	42	∈	∈	PROPN
ejpam-5894	415	43	l	l	NOUN
ejpam-5894	415	44	)	)	PUNCT
ejpam-5894	415	45	(	(	PUNCT
ejpam-5894	415	46	α((0|(ζ|ζ))|(0|(ζ|ζ	α((0|(ζ|ζ))|(0|(ζ|ζ	PROPN
ejpam-5894	415	47	)	)	PUNCT
ejpam-5894	415	48	)	)	PUNCT
ejpam-5894	415	49	)	)	PUNCT
ejpam-5894	415	50	≥	≥	PROPN
ejpam-5894	415	51	α(ζ	α(ζ	NOUN
ejpam-5894	415	52	)	)	PUNCT
ejpam-5894	415	53	,	,	PUNCT
ejpam-5894	415	54	β((0|(ζ|ζ))|(0|(ζ|ζ	β((0|(ζ|ζ))|(0|(ζ|ζ	PROPN
ejpam-5894	415	55	)	)	PUNCT
ejpam-5894	415	56	)	)	PUNCT
ejpam-5894	415	57	)	)	PUNCT
ejpam-5894	416	1	≤	≤	NUM
ejpam-5894	416	2	β(ζ	β(ζ	PROPN
ejpam-5894	416	3	)	)	PUNCT
ejpam-5894	416	4	)	)	PUNCT
ejpam-5894	416	5	.	.	PUNCT
ejpam-5894	417	1	(	(	PUNCT
ejpam-5894	417	2	25	25	NUM
ejpam-5894	417	3	)	)	PUNCT
ejpam-5894	417	4	example	example	NOUN
ejpam-5894	417	5	14	14	NUM
ejpam-5894	417	6	.	.	PUNCT
ejpam-5894	418	1	from	from	ADP
ejpam-5894	418	2	the	the	DET
ejpam-5894	418	3	wsbg	wsbg	ADV
ejpam-5894	418	4	-	-	PUNCT
ejpam-5894	418	5	algebra	algebra	NOUN
ejpam-5894	418	6	l	l	NOUN
ejpam-5894	418	7	=	=	PUNCT
ejpam-5894	418	8	⟨l	⟨l	NOUN
ejpam-5894	418	9	;	;	PUNCT
ejpam-5894	418	10	|	|	ADV
ejpam-5894	418	11	,	,	PUNCT
ejpam-5894	418	12	0⟩	0⟩	PROPN
ejpam-5894	418	13	where	where	SCONJ
ejpam-5894	418	14	l	l	NOUN
ejpam-5894	418	15	=	=	PUNCT
ejpam-5894	418	16	{	{	PUNCT
ejpam-5894	418	17	0	0	NUM
ejpam-5894	418	18	,	,	PUNCT
ejpam-5894	418	19	a	a	DET
ejpam-5894	418	20	,	,	PUNCT
ejpam-5894	418	21	b	b	NOUN
ejpam-5894	418	22	}	}	PUNCT
ejpam-5894	418	23	in	in	ADP
ejpam-5894	418	24	example	example	NOUN
ejpam-5894	418	25	4	4	NUM
ejpam-5894	418	26	,	,	PUNCT
ejpam-5894	418	27	define	define	VERB
ejpam-5894	418	28	an	an	DET
ejpam-5894	418	29	intuitionistic	intuitionistic	ADJ
ejpam-5894	418	30	fuzzy	fuzzy	ADJ
ejpam-5894	418	31	set	set	NOUN
ejpam-5894	418	32	l	l	NOUN
ejpam-5894	418	33	=	=	SYM
ejpam-5894	418	34	(	(	PUNCT
ejpam-5894	418	35	l	l	NOUN
ejpam-5894	418	36	,	,	PUNCT
ejpam-5894	418	37	α	α	X
ejpam-5894	418	38	,	,	PUNCT
ejpam-5894	418	39	β	β	NOUN
ejpam-5894	418	40	)	)	PUNCT
ejpam-5894	418	41	by	by	ADP
ejpam-5894	418	42	:	:	PUNCT
ejpam-5894	418	43	α(0	α(0	NOUN
ejpam-5894	418	44	)	)	PUNCT
ejpam-5894	418	45	=	=	SYM
ejpam-5894	418	46	0.9	0.9	NUM
ejpam-5894	418	47	,	,	PUNCT
ejpam-5894	418	48	α(a	α(a	NOUN
ejpam-5894	418	49	)	)	PUNCT
ejpam-5894	418	50	=	=	SYM
ejpam-5894	418	51	0.7	0.7	NUM
ejpam-5894	418	52	,	,	PUNCT
ejpam-5894	418	53	α(b	α(b	NOUN
ejpam-5894	418	54	)	)	PUNCT
ejpam-5894	418	55	=	=	SYM
ejpam-5894	418	56	0.5	0.5	NUM
ejpam-5894	418	57	,	,	PUNCT
ejpam-5894	418	58	β(0	β(0	PROPN
ejpam-5894	418	59	)	)	PUNCT
ejpam-5894	418	60	=	=	NOUN
ejpam-5894	418	61	0.1	0.1	NUM
ejpam-5894	418	62	,	,	PUNCT
ejpam-5894	418	63	β(a	β(a	PROPN
ejpam-5894	418	64	)	)	PUNCT
ejpam-5894	418	65	=	=	NUM
ejpam-5894	418	66	0.4	0.4	NUM
ejpam-5894	418	67	,	,	PUNCT
ejpam-5894	418	68	β(b	β(b	PUNCT
ejpam-5894	418	69	)	)	PUNCT
ejpam-5894	418	70	=	=	SYM
ejpam-5894	418	71	0.6	0.6	NUM
ejpam-5894	418	72	.	.	PUNCT
ejpam-5894	419	1	thus	thus	ADV
ejpam-5894	419	2	,	,	PUNCT
ejpam-5894	419	3	l	l	NOUN
ejpam-5894	419	4	=	=	SYM
ejpam-5894	419	5	(	(	PUNCT
ejpam-5894	419	6	l	l	NOUN
ejpam-5894	419	7	,	,	PUNCT
ejpam-5894	419	8	α	α	X
ejpam-5894	419	9	,	,	PUNCT
ejpam-5894	419	10	β	β	NOUN
ejpam-5894	419	11	)	)	PUNCT
ejpam-5894	419	12	is	be	AUX
ejpam-5894	419	13	an	an	DET
ejpam-5894	419	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	419	15	fuzzy	fuzzy	ADJ
ejpam-5894	419	16	closed	close	VERB
ejpam-5894	419	17	wsbg	wsbg	ADV
ejpam-5894	419	18	-	-	PUNCT
ejpam-5894	419	19	ideal	ideal	NOUN
ejpam-5894	419	20	of	of	ADP
ejpam-5894	419	21	l.	l.	PROPN
ejpam-5894	419	22	4	4	NUM
ejpam-5894	419	23	.	.	PUNCT
ejpam-5894	419	24	special	special	ADJ
ejpam-5894	419	25	classes	class	NOUN
ejpam-5894	419	26	of	of	ADP
ejpam-5894	419	27	intuitionistic	intuitionistic	ADJ
ejpam-5894	419	28	fuzzy	fuzzy	ADJ
ejpam-5894	419	29	implicative	implicative	ADJ
ejpam-5894	419	30	wsbg	wsbg	NOUN
ejpam-5894	419	31	-	-	PUNCT
ejpam-5894	419	32	ideals	ideal	NOUN
ejpam-5894	419	33	in	in	ADP
ejpam-5894	419	34	this	this	DET
ejpam-5894	419	35	section	section	NOUN
ejpam-5894	419	36	,	,	PUNCT
ejpam-5894	419	37	we	we	PRON
ejpam-5894	419	38	investigate	investigate	VERB
ejpam-5894	419	39	specialized	specialized	ADJ
ejpam-5894	419	40	subclasses	subclass	NOUN
ejpam-5894	419	41	of	of	ADP
ejpam-5894	419	42	intuitionistic	intuitionistic	ADJ
ejpam-5894	419	43	fuzzy	fuzzy	ADJ
ejpam-5894	419	44	implicative	implicative	ADJ
ejpam-5894	419	45	wsbg	wsbg	NOUN
ejpam-5894	419	46	-	-	PUNCT
ejpam-5894	419	47	ideals	ideal	NOUN
ejpam-5894	419	48	in	in	ADP
ejpam-5894	419	49	wsbg	wsbg	NOUN
ejpam-5894	419	50	-	-	PUNCT
ejpam-5894	419	51	algebras	algebras	X
ejpam-5894	419	52	.	.	PUNCT
ejpam-5894	420	1	while	while	SCONJ
ejpam-5894	420	2	the	the	DET
ejpam-5894	420	3	general	general	ADJ
ejpam-5894	420	4	notion	notion	NOUN
ejpam-5894	420	5	of	of	ADP
ejpam-5894	420	6	an	an	DET
ejpam-5894	420	7	intuitionistic	intuitionistic	ADJ
ejpam-5894	420	8	fuzzy	fuzzy	ADJ
ejpam-5894	420	9	implicative	implicative	ADJ
ejpam-5894	420	10	wsbg	wsbg	ADV
ejpam-5894	420	11	-	-	PUNCT
ejpam-5894	420	12	ideal	ideal	NOUN
ejpam-5894	420	13	captures	capture	VERB
ejpam-5894	420	14	a	a	DET
ejpam-5894	420	15	broad	broad	ADJ
ejpam-5894	420	16	range	range	NOUN
ejpam-5894	420	17	of	of	ADP
ejpam-5894	420	18	structural	structural	ADJ
ejpam-5894	420	19	behaviors	behavior	NOUN
ejpam-5894	420	20	,	,	PUNCT
ejpam-5894	420	21	certain	certain	ADJ
ejpam-5894	420	22	algebraic	algebraic	ADJ
ejpam-5894	420	23	and	and	CCONJ
ejpam-5894	420	24	fuzzy	fuzzy	ADJ
ejpam-5894	420	25	-	-	PUNCT
ejpam-5894	420	26	theoretic	theoretic	NOUN
ejpam-5894	420	27	applications	application	NOUN
ejpam-5894	420	28	require	require	VERB
ejpam-5894	420	29	stronger	strong	ADJ
ejpam-5894	420	30	or	or	CCONJ
ejpam-5894	420	31	more	more	ADJ
ejpam-5894	420	32	refined	refined	ADJ
ejpam-5894	420	33	conditions	condition	NOUN
ejpam-5894	420	34	.	.	PUNCT
ejpam-5894	421	1	we	we	PRON
ejpam-5894	421	2	therefore	therefore	ADV
ejpam-5894	421	3	introduce	introduce	VERB
ejpam-5894	421	4	and	and	CCONJ
ejpam-5894	421	5	examine	examine	VERB
ejpam-5894	421	6	notions	notion	NOUN
ejpam-5894	421	7	such	such	ADJ
ejpam-5894	421	8	as	as	ADP
ejpam-5894	421	9	intuitionistic	intuitionistic	ADJ
ejpam-5894	421	10	fuzzy	fuzzy	ADJ
ejpam-5894	421	11	completely	completely	ADV
ejpam-5894	421	12	closed	close	VERB
ejpam-5894	421	13	wsbg	wsbg	NOUN
ejpam-5894	421	14	-	-	PUNCT
ejpam-5894	421	15	ideals	ideal	NOUN
ejpam-5894	421	16	,	,	PUNCT
ejpam-5894	421	17	intuitionistic	intuitionistic	ADJ
ejpam-5894	421	18	fuzzy	fuzzy	ADJ
ejpam-5894	421	19	closed	close	VERB
ejpam-5894	421	20	wsbg	wsbg	NOUN
ejpam-5894	421	21	-	-	PUNCT
ejpam-5894	421	22	ideals	ideal	NOUN
ejpam-5894	421	23	,	,	PUNCT
ejpam-5894	421	24	and	and	CCONJ
ejpam-5894	421	25	intuitionistic	intuitionistic	ADJ
ejpam-5894	421	26	fuzzy	fuzzy	ADJ
ejpam-5894	421	27	p	p	NOUN
ejpam-5894	421	28	-	-	PUNCT
ejpam-5894	421	29	ideals	ideal	NOUN
ejpam-5894	421	30	.	.	PUNCT
ejpam-5894	422	1	these	these	DET
ejpam-5894	422	2	classes	class	NOUN
ejpam-5894	422	3	serve	serve	VERB
ejpam-5894	422	4	not	not	PART
ejpam-5894	422	5	only	only	ADV
ejpam-5894	422	6	to	to	PART
ejpam-5894	422	7	enrich	enrich	VERB
ejpam-5894	422	8	the	the	DET
ejpam-5894	422	9	theory	theory	NOUN
ejpam-5894	422	10	but	but	CCONJ
ejpam-5894	422	11	also	also	ADV
ejpam-5894	422	12	to	to	PART
ejpam-5894	422	13	provide	provide	VERB
ejpam-5894	422	14	a	a	DET
ejpam-5894	422	15	finer	fine	ADJ
ejpam-5894	422	16	framework	framework	NOUN
ejpam-5894	422	17	for	for	ADP
ejpam-5894	422	18	analyzing	analyze	VERB
ejpam-5894	422	19	hierarchical	hierarchical	ADJ
ejpam-5894	422	20	relationships	relationship	NOUN
ejpam-5894	422	21	among	among	ADP
ejpam-5894	422	22	fuzzy	fuzzy	ADJ
ejpam-5894	422	23	ideal	ideal	ADJ
ejpam-5894	422	24	structures	structure	NOUN
ejpam-5894	422	25	in	in	ADP
ejpam-5894	422	26	wsbg	wsbg	NOUN
ejpam-5894	422	27	-	-	PUNCT
ejpam-5894	422	28	algebras	algebra	NOUN
ejpam-5894	422	29	.	.	PUNCT
ejpam-5894	423	1	connections	connection	NOUN
ejpam-5894	423	2	between	between	ADP
ejpam-5894	423	3	these	these	DET
ejpam-5894	423	4	classes	class	NOUN
ejpam-5894	423	5	and	and	CCONJ
ejpam-5894	423	6	the	the	DET
ejpam-5894	423	7	foundational	foundational	ADJ
ejpam-5894	423	8	concepts	concept	NOUN
ejpam-5894	423	9	introduced	introduce	VERB
ejpam-5894	423	10	in	in	ADP
ejpam-5894	423	11	the	the	DET
ejpam-5894	423	12	previous	previous	ADJ
ejpam-5894	423	13	section	section	NOUN
ejpam-5894	423	14	are	be	AUX
ejpam-5894	423	15	also	also	ADV
ejpam-5894	423	16	explored	explore	VERB
ejpam-5894	423	17	.	.	PUNCT
ejpam-5894	424	1	definition	definition	NOUN
ejpam-5894	424	2	15	15	NUM
ejpam-5894	424	3	.	.	PUNCT
ejpam-5894	425	1	let	let	VERB
ejpam-5894	425	2	l	l	NOUN
ejpam-5894	425	3	=	=	SYM
ejpam-5894	425	4	(	(	PUNCT
ejpam-5894	425	5	l	l	NOUN
ejpam-5894	425	6	,	,	PUNCT
ejpam-5894	425	7	α	α	X
ejpam-5894	425	8	,	,	PUNCT
ejpam-5894	425	9	β	β	NOUN
ejpam-5894	425	10	)	)	PUNCT
ejpam-5894	425	11	be	be	VERB
ejpam-5894	425	12	an	an	DET
ejpam-5894	425	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	425	14	fuzzy	fuzzy	ADJ
ejpam-5894	425	15	wsbg	wsbg	NOUN
ejpam-5894	425	16	-	-	PUNCT
ejpam-5894	425	17	ideal	ideal	NOUN
ejpam-5894	425	18	of	of	ADP
ejpam-5894	425	19	a	a	DET
ejpam-5894	425	20	wsbgalgebra	wsbgalgebra	NOUN
ejpam-5894	425	21	l	l	NOUN
ejpam-5894	425	22	=	=	SYM
ejpam-5894	425	23	⟨l	⟨l	NOUN
ejpam-5894	425	24	;	;	PUNCT
ejpam-5894	425	25	|	|	ADV
ejpam-5894	425	26	,	,	PUNCT
ejpam-5894	425	27	0⟩.	0⟩.	PROPN
ejpam-5894	425	28	then	then	ADV
ejpam-5894	425	29	l	l	PROPN
ejpam-5894	425	30	=	=	PUNCT
ejpam-5894	425	31	(	(	PUNCT
ejpam-5894	425	32	l	l	NOUN
ejpam-5894	425	33	,	,	PUNCT
ejpam-5894	425	34	α	α	X
ejpam-5894	425	35	,	,	PUNCT
ejpam-5894	425	36	β	β	NOUN
ejpam-5894	425	37	)	)	PUNCT
ejpam-5894	425	38	is	be	AUX
ejpam-5894	425	39	called	call	VERB
ejpam-5894	425	40	an	an	DET
ejpam-5894	425	41	intuitionistic	intuitionistic	ADJ
ejpam-5894	425	42	fuzzy	fuzzy	NOUN
ejpam-5894	425	43	completely	completely	ADV
ejpam-5894	425	44	closed	close	VERB
ejpam-5894	425	45	wsbg	wsbg	ADV
ejpam-5894	425	46	-	-	PUNCT
ejpam-5894	425	47	ideal	ideal	NOUN
ejpam-5894	425	48	of	of	ADP
ejpam-5894	425	49	l	l	NOUN
ejpam-5894	426	1	if	if	SCONJ
ejpam-5894	426	2	(	(	PUNCT
ejpam-5894	426	3	∀ζ	∀ζ	PROPN
ejpam-5894	426	4	,	,	PUNCT
ejpam-5894	426	5	η	η	PROPN
ejpam-5894	426	6	∈	∈	PROPN
ejpam-5894	426	7	l	l	NOUN
ejpam-5894	426	8	)	)	PUNCT
ejpam-5894	426	9	(	(	PUNCT
ejpam-5894	426	10	α((ζ|(η|η))|(ζ|(η|η	α((ζ|(η|η))|(ζ|(η|η	ADJ
ejpam-5894	426	11	)	)	PUNCT
ejpam-5894	426	12	)	)	PUNCT
ejpam-5894	426	13	)	)	PUNCT
ejpam-5894	426	14	≥	≥	NOUN
ejpam-5894	427	1	min{α(ζ	min{α(ζ	PROPN
ejpam-5894	427	2	)	)	PUNCT
ejpam-5894	427	3	,	,	PUNCT
ejpam-5894	427	4	α(η	α(η	PROPN
ejpam-5894	427	5	)	)	PUNCT
ejpam-5894	427	6	}	}	PUNCT
ejpam-5894	427	7	,	,	PUNCT
ejpam-5894	427	8	β((ζ|(η|η))|(ζ|(η|η	β((ζ|(η|η))|(ζ|(η|η	ADJ
ejpam-5894	427	9	)	)	PUNCT
ejpam-5894	427	10	)	)	PUNCT
ejpam-5894	427	11	)	)	PUNCT
ejpam-5894	428	1	≤	≤	NUM
ejpam-5894	428	2	max{β(ζ	max{β(ζ	PROPN
ejpam-5894	428	3	)	)	PUNCT
ejpam-5894	428	4	,	,	PUNCT
ejpam-5894	428	5	β(η	β(η	PROPN
ejpam-5894	428	6	)	)	PUNCT
ejpam-5894	428	7	}	}	PUNCT
ejpam-5894	428	8	)	)	PUNCT
ejpam-5894	428	9	.	.	PUNCT
ejpam-5894	429	1	(	(	PUNCT
ejpam-5894	429	2	26	26	NUM
ejpam-5894	429	3	)	)	PUNCT
ejpam-5894	429	4	example	example	NOUN
ejpam-5894	429	5	15	15	NUM
ejpam-5894	429	6	.	.	PUNCT
ejpam-5894	430	1	from	from	ADP
ejpam-5894	430	2	the	the	DET
ejpam-5894	430	3	wsbg	wsbg	ADV
ejpam-5894	430	4	-	-	PUNCT
ejpam-5894	430	5	algebra	algebra	NOUN
ejpam-5894	430	6	l	l	NOUN
ejpam-5894	430	7	=	=	PUNCT
ejpam-5894	430	8	⟨l	⟨l	NOUN
ejpam-5894	430	9	;	;	PUNCT
ejpam-5894	430	10	|	|	ADV
ejpam-5894	430	11	,	,	PUNCT
ejpam-5894	430	12	0⟩	0⟩	PROPN
ejpam-5894	430	13	where	where	SCONJ
ejpam-5894	430	14	l	l	NOUN
ejpam-5894	430	15	=	=	PUNCT
ejpam-5894	430	16	{	{	PUNCT
ejpam-5894	430	17	0	0	NUM
ejpam-5894	430	18	,	,	PUNCT
ejpam-5894	430	19	a	a	DET
ejpam-5894	430	20	,	,	PUNCT
ejpam-5894	430	21	b	b	NOUN
ejpam-5894	430	22	}	}	PUNCT
ejpam-5894	430	23	in	in	ADP
ejpam-5894	430	24	example	example	NOUN
ejpam-5894	430	25	4	4	NUM
ejpam-5894	430	26	,	,	PUNCT
ejpam-5894	430	27	define	define	VERB
ejpam-5894	430	28	the	the	DET
ejpam-5894	430	29	intuitionistic	intuitionistic	ADJ
ejpam-5894	430	30	fuzzy	fuzzy	ADJ
ejpam-5894	430	31	set	set	NOUN
ejpam-5894	430	32	l	l	NOUN
ejpam-5894	430	33	=	=	SYM
ejpam-5894	430	34	(	(	PUNCT
ejpam-5894	430	35	l	l	NOUN
ejpam-5894	430	36	,	,	PUNCT
ejpam-5894	430	37	α	α	X
ejpam-5894	430	38	,	,	PUNCT
ejpam-5894	430	39	β	β	NOUN
ejpam-5894	430	40	)	)	PUNCT
ejpam-5894	430	41	by	by	ADP
ejpam-5894	430	42	:	:	PUNCT
ejpam-5894	430	43	α(0	α(0	NOUN
ejpam-5894	430	44	)	)	PUNCT
ejpam-5894	430	45	=	=	SYM
ejpam-5894	430	46	1	1	NUM
ejpam-5894	430	47	,	,	PUNCT
ejpam-5894	430	48	α(a	α(a	NOUN
ejpam-5894	430	49	)	)	PUNCT
ejpam-5894	430	50	=	=	SYM
ejpam-5894	430	51	0.6	0.6	NUM
ejpam-5894	430	52	,	,	PUNCT
ejpam-5894	430	53	α(b	α(b	NOUN
ejpam-5894	430	54	)	)	PUNCT
ejpam-5894	430	55	=	=	SYM
ejpam-5894	430	56	0.4	0.4	NUM
ejpam-5894	430	57	,	,	PUNCT
ejpam-5894	430	58	β(0	β(0	PROPN
ejpam-5894	430	59	)	)	PUNCT
ejpam-5894	430	60	=	=	SYM
ejpam-5894	430	61	0	0	NUM
ejpam-5894	430	62	,	,	PUNCT
ejpam-5894	430	63	β(a	β(a	PROPN
ejpam-5894	430	64	)	)	PUNCT
ejpam-5894	430	65	=	=	PUNCT
ejpam-5894	430	66	0.3	0.3	NUM
ejpam-5894	430	67	,	,	PUNCT
ejpam-5894	430	68	β(b	β(b	PUNCT
ejpam-5894	430	69	)	)	PUNCT
ejpam-5894	430	70	=	=	PUNCT
ejpam-5894	430	71	0.7	0.7	NUM
ejpam-5894	430	72	.	.	PUNCT
ejpam-5894	431	1	therefore	therefore	ADV
ejpam-5894	431	2	,	,	PUNCT
ejpam-5894	431	3	l	l	NOUN
ejpam-5894	431	4	=	=	SYM
ejpam-5894	431	5	(	(	PUNCT
ejpam-5894	431	6	l	l	NOUN
ejpam-5894	431	7	,	,	PUNCT
ejpam-5894	431	8	α	α	X
ejpam-5894	431	9	,	,	PUNCT
ejpam-5894	431	10	β	β	NOUN
ejpam-5894	431	11	)	)	PUNCT
ejpam-5894	431	12	is	be	AUX
ejpam-5894	431	13	an	an	DET
ejpam-5894	431	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	431	15	fuzzy	fuzzy	NOUN
ejpam-5894	431	16	completely	completely	ADV
ejpam-5894	431	17	closed	close	VERB
ejpam-5894	431	18	wsbg	wsbg	ADV
ejpam-5894	431	19	-	-	PUNCT
ejpam-5894	431	20	ideal	ideal	NOUN
ejpam-5894	431	21	of	of	ADP
ejpam-5894	431	22	l.	l.	PROPN
ejpam-5894	431	23	note	note	PROPN
ejpam-5894	431	24	that	that	SCONJ
ejpam-5894	431	25	an	an	DET
ejpam-5894	431	26	intuitionistic	intuitionistic	ADJ
ejpam-5894	431	27	fuzzy	fuzzy	ADJ
ejpam-5894	431	28	closed	close	VERB
ejpam-5894	431	29	wsbg	wsbg	ADV
ejpam-5894	431	30	-	-	PUNCT
ejpam-5894	431	31	ideal	ideal	NOUN
ejpam-5894	431	32	is	be	AUX
ejpam-5894	431	33	not	not	PART
ejpam-5894	431	34	necessarily	necessarily	ADV
ejpam-5894	431	35	an	an	DET
ejpam-5894	431	36	intuitionistic	intuitionistic	ADJ
ejpam-5894	431	37	fuzzy	fuzzy	ADJ
ejpam-5894	431	38	implicative	implicative	ADJ
ejpam-5894	431	39	wsbg	wsbg	NOUN
ejpam-5894	431	40	-	-	PUNCT
ejpam-5894	431	41	ideal	ideal	ADJ
ejpam-5894	431	42	,	,	PUNCT
ejpam-5894	431	43	unless	unless	SCONJ
ejpam-5894	431	44	the	the	DET
ejpam-5894	431	45	underlying	underlying	ADJ
ejpam-5894	431	46	wsbg	wsbg	ADV
ejpam-5894	431	47	-	-	PUNCT
ejpam-5894	431	48	algebra	algebra	NOUN
ejpam-5894	431	49	satisfies	satisfie	NOUN
ejpam-5894	431	50	additional	additional	ADJ
ejpam-5894	431	51	conditions	condition	NOUN
ejpam-5894	431	52	such	such	ADJ
ejpam-5894	431	53	as	as	ADP
ejpam-5894	431	54	implicativity	implicativity	NOUN
ejpam-5894	431	55	.	.	PUNCT
ejpam-5894	432	1	the	the	DET
ejpam-5894	432	2	following	follow	VERB
ejpam-5894	432	3	theorem	theorem	ADJ
ejpam-5894	432	4	presents	present	NOUN
ejpam-5894	432	5	one	one	NUM
ejpam-5894	432	6	such	such	ADJ
ejpam-5894	432	7	sufficient	sufficient	ADJ
ejpam-5894	432	8	condition	condition	NOUN
ejpam-5894	432	9	.	.	PUNCT
ejpam-5894	433	1	t.	t.	PROPN
ejpam-5894	433	2	oner	oner	PROPN
ejpam-5894	433	3	et	et	PROPN
ejpam-5894	433	4	al	al	PROPN
ejpam-5894	433	5	.	.	PUNCT
ejpam-5894	433	6	/	/	SYM
ejpam-5894	433	7	eur	eur	PROPN
ejpam-5894	433	8	.	.	PUNCT
ejpam-5894	434	1	j.	j.	PROPN
ejpam-5894	434	2	pure	pure	PROPN
ejpam-5894	434	3	appl	appl	PROPN
ejpam-5894	434	4	.	.	PROPN
ejpam-5894	434	5	math	math	PROPN
ejpam-5894	434	6	,	,	PUNCT
ejpam-5894	434	7	18	18	NUM
ejpam-5894	434	8	(	(	PUNCT
ejpam-5894	434	9	3	3	NUM
ejpam-5894	434	10	)	)	PUNCT
ejpam-5894	434	11	(	(	PUNCT
ejpam-5894	434	12	2025	2025	NUM
ejpam-5894	434	13	)	)	PUNCT
ejpam-5894	434	14	,	,	PUNCT
ejpam-5894	434	15	5894	5894	NUM
ejpam-5894	434	16	23	23	NUM
ejpam-5894	434	17	of	of	ADP
ejpam-5894	434	18	33	33	NUM
ejpam-5894	434	19	theorem	theorem	ADJ
ejpam-5894	434	20	10	10	NUM
ejpam-5894	434	21	.	.	PUNCT
ejpam-5894	435	1	let	let	VERB
ejpam-5894	435	2	l	l	NOUN
ejpam-5894	435	3	=	=	SYM
ejpam-5894	435	4	⟨l	⟨l	NOUN
ejpam-5894	435	5	;	;	PUNCT
ejpam-5894	435	6	|	|	ADV
ejpam-5894	435	7	,	,	PUNCT
ejpam-5894	435	8	0⟩	0⟩	PROPN
ejpam-5894	435	9	be	be	VERB
ejpam-5894	435	10	a	a	DET
ejpam-5894	435	11	wsbg	wsbg	ADV
ejpam-5894	435	12	-	-	PUNCT
ejpam-5894	435	13	algebra	algebra	NOUN
ejpam-5894	435	14	satisfying	satisfying	NOUN
ejpam-5894	435	15	(	(	PUNCT
ejpam-5894	435	16	∀ζ	∀ζ	PROPN
ejpam-5894	435	17	,	,	PUNCT
ejpam-5894	435	18	η	η	PROPN
ejpam-5894	435	19	,	,	PUNCT
ejpam-5894	435	20	θ	θ	PROPN
ejpam-5894	435	21	∈	∈	PROPN
ejpam-5894	435	22	l	l	NOUN
ejpam-5894	435	23	)	)	PUNCT
ejpam-5894	435	24	(	(	PUNCT
ejpam-5894	435	25	(	(	PUNCT
ejpam-5894	435	26	(	(	PUNCT
ejpam-5894	435	27	(	(	PUNCT
ejpam-5894	435	28	(	(	PUNCT
ejpam-5894	435	29	ζ|(η|η))|(ζ|(η|η)))|(ζ|(θ|θ)))|	ζ|(η|η))|(ζ|(η|η)))|(ζ|(θ|θ)))|	PROPN
ejpam-5894	435	30	(	(	PUNCT
ejpam-5894	435	31	(	(	PUNCT
ejpam-5894	435	32	(	(	PUNCT
ejpam-5894	435	33	ζ|(η|η))|(ζ|(η|η)))|(ζ|(θ|θ))))|(θ|(η|η	ζ|(η|η))|(ζ|(η|η)))|(ζ|(θ|θ))))|(θ|(η|η	PROPN
ejpam-5894	435	34	)	)	PUNCT
ejpam-5894	435	35	)	)	PUNCT
ejpam-5894	436	1	=	=	SYM
ejpam-5894	436	2	0|0	0|0	NUM
ejpam-5894	436	3	)	)	PUNCT
ejpam-5894	436	4	.	.	PUNCT
ejpam-5894	437	1	(	(	PUNCT
ejpam-5894	437	2	27	27	NUM
ejpam-5894	437	3	)	)	PUNCT
ejpam-5894	437	4	then	then	ADV
ejpam-5894	437	5	l	l	NOUN
ejpam-5894	437	6	is	be	AUX
ejpam-5894	437	7	implicative	implicative	ADJ
ejpam-5894	437	8	if	if	SCONJ
ejpam-5894	438	1	and	and	CCONJ
ejpam-5894	438	2	only	only	ADV
ejpam-5894	438	3	if	if	SCONJ
ejpam-5894	438	4	every	every	DET
ejpam-5894	438	5	intuitionistic	intuitionistic	ADJ
ejpam-5894	438	6	fuzzy	fuzzy	NOUN
ejpam-5894	438	7	closed	close	VERB
ejpam-5894	438	8	wsbg	wsbg	ADV
ejpam-5894	438	9	-	-	PUNCT
ejpam-5894	438	10	ideal	ideal	NOUN
ejpam-5894	438	11	of	of	ADP
ejpam-5894	438	12	l	l	NOUN
ejpam-5894	438	13	is	be	AUX
ejpam-5894	438	14	an	an	DET
ejpam-5894	438	15	intuitionistic	intuitionistic	ADJ
ejpam-5894	438	16	fuzzy	fuzzy	ADJ
ejpam-5894	438	17	implicative	implicative	ADJ
ejpam-5894	438	18	wsbg	wsbg	NOUN
ejpam-5894	438	19	-	-	PUNCT
ejpam-5894	438	20	ideal	ideal	NOUN
ejpam-5894	438	21	of	of	ADP
ejpam-5894	438	22	l.	l.	PROPN
ejpam-5894	438	23	proof	proof	PROPN
ejpam-5894	438	24	.	.	PUNCT
ejpam-5894	439	1	let	let	VERB
ejpam-5894	439	2	l	l	NOUN
ejpam-5894	439	3	=	=	SYM
ejpam-5894	439	4	⟨l	⟨l	NOUN
ejpam-5894	439	5	;	;	PUNCT
ejpam-5894	439	6	|	|	ADV
ejpam-5894	439	7	,	,	PUNCT
ejpam-5894	439	8	0⟩	0⟩	PROPN
ejpam-5894	439	9	be	be	VERB
ejpam-5894	439	10	a	a	DET
ejpam-5894	439	11	wsbg	wsbg	ADV
ejpam-5894	439	12	-	-	PUNCT
ejpam-5894	439	13	algebra	algebra	NOUN
ejpam-5894	439	14	satisfying	satisfying	NOUN
ejpam-5894	439	15	(	(	PUNCT
ejpam-5894	439	16	27	27	NUM
ejpam-5894	439	17	)	)	PUNCT
ejpam-5894	439	18	.	.	PUNCT
ejpam-5894	440	1	assume	assume	VERB
ejpam-5894	440	2	that	that	SCONJ
ejpam-5894	440	3	l	l	NOUN
ejpam-5894	440	4	is	be	AUX
ejpam-5894	440	5	implicative	implicative	ADJ
ejpam-5894	440	6	and	and	CCONJ
ejpam-5894	440	7	l	l	NOUN
ejpam-5894	440	8	=	=	SYM
ejpam-5894	440	9	(	(	PUNCT
ejpam-5894	440	10	l	l	NOUN
ejpam-5894	440	11	,	,	PUNCT
ejpam-5894	440	12	α	α	X
ejpam-5894	440	13	,	,	PUNCT
ejpam-5894	440	14	β	β	NOUN
ejpam-5894	440	15	)	)	PUNCT
ejpam-5894	440	16	is	be	AUX
ejpam-5894	440	17	an	an	DET
ejpam-5894	440	18	intuitionistic	intuitionistic	ADJ
ejpam-5894	440	19	fuzzy	fuzzy	ADJ
ejpam-5894	440	20	closed	close	VERB
ejpam-5894	440	21	wsbg	wsbg	ADV
ejpam-5894	440	22	-	-	PUNCT
ejpam-5894	440	23	ideal	ideal	NOUN
ejpam-5894	440	24	of	of	ADP
ejpam-5894	440	25	l.	l.	PROPN
ejpam-5894	440	26	then	then	ADV
ejpam-5894	440	27	l	l	PROPN
ejpam-5894	440	28	=	=	PUNCT
ejpam-5894	440	29	(	(	PUNCT
ejpam-5894	440	30	l	l	NOUN
ejpam-5894	440	31	,	,	PUNCT
ejpam-5894	440	32	α	α	X
ejpam-5894	440	33	,	,	PUNCT
ejpam-5894	440	34	β	β	NOUN
ejpam-5894	440	35	)	)	PUNCT
ejpam-5894	440	36	is	be	AUX
ejpam-5894	440	37	an	an	DET
ejpam-5894	440	38	intuitionistic	intuitionistic	ADJ
ejpam-5894	440	39	fuzzy	fuzzy	ADJ
ejpam-5894	440	40	wsbg	wsbg	NOUN
ejpam-5894	440	41	-	-	PUNCT
ejpam-5894	440	42	ideal	ideal	NOUN
ejpam-5894	440	43	of	of	ADP
ejpam-5894	440	44	l.	l.	PROPN
ejpam-5894	440	45	thus	thus	ADV
ejpam-5894	440	46	,	,	PUNCT
ejpam-5894	440	47	α(0	α(0	PROPN
ejpam-5894	440	48	)	)	PUNCT
ejpam-5894	440	49	≥	≥	NOUN
ejpam-5894	440	50	α(ζ	α(ζ	PROPN
ejpam-5894	440	51	)	)	PUNCT
ejpam-5894	440	52	and	and	CCONJ
ejpam-5894	440	53	β(0	β(0	PROPN
ejpam-5894	440	54	)	)	PUNCT
ejpam-5894	440	55	≤	≤	NOUN
ejpam-5894	440	56	β(ζ	β(ζ	PROPN
ejpam-5894	440	57	)	)	PUNCT
ejpam-5894	440	58	.	.	PUNCT
ejpam-5894	441	1	also	also	ADV
ejpam-5894	441	2	,	,	PUNCT
ejpam-5894	441	3	α(ζ	α(ζ	PROPN
ejpam-5894	441	4	)	)	PUNCT
ejpam-5894	441	5	≥	≥	NOUN
ejpam-5894	441	6	min{α(θ	min{α(θ	NOUN
ejpam-5894	441	7	)	)	PUNCT
ejpam-5894	441	8	,	,	PUNCT
ejpam-5894	441	9	α((ζ|(θ|θ))|(ζ|(θ|θ	α((ζ|(θ|θ))|(ζ|(θ|θ	NOUN
ejpam-5894	441	10	)	)	PUNCT
ejpam-5894	441	11	)	)	PUNCT
ejpam-5894	441	12	)	)	PUNCT
ejpam-5894	441	13	}	}	PUNCT
ejpam-5894	442	1	=	=	SYM
ejpam-5894	442	2	min{α(θ	min{α(θ	NOUN
ejpam-5894	442	3	)	)	PUNCT
ejpam-5894	442	4	,	,	PUNCT
ejpam-5894	442	5	α(((((ζ|ζ)|(ζ|ζ))|((ζ|ζ)|η))|(θ|θ))|	α(((((ζ|ζ)|(ζ|ζ))|((ζ|ζ)|η))|(θ|θ))|	NUM
ejpam-5894	442	6	(	(	PUNCT
ejpam-5894	442	7	(	(	PUNCT
ejpam-5894	442	8	(	(	PUNCT
ejpam-5894	442	9	(	(	PUNCT
ejpam-5894	442	10	ζ|ζ)|(ζ|ζ))|((ζ|ζ)|η))|(θ|θ	ζ|ζ)|(ζ|ζ))|((ζ|ζ)|η))|(θ|θ	NUM
ejpam-5894	442	11	)	)	PUNCT
ejpam-5894	442	12	)	)	PUNCT
ejpam-5894	442	13	)	)	PUNCT
ejpam-5894	442	14	}	}	PUNCT
ejpam-5894	443	1	=	=	SYM
ejpam-5894	443	2	min{α(θ	min{α(θ	NOUN
ejpam-5894	443	3	)	)	PUNCT
ejpam-5894	443	4	,	,	PUNCT
ejpam-5894	443	5	α((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|	α((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|	PROPN
ejpam-5894	443	6	(	(	PUNCT
ejpam-5894	443	7	(	(	PUNCT
ejpam-5894	443	8	(	(	PUNCT
ejpam-5894	443	9	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	443	10	)	)	PUNCT
ejpam-5894	443	11	)	)	PUNCT
ejpam-5894	443	12	)	)	PUNCT
ejpam-5894	443	13	}	}	PUNCT
ejpam-5894	443	14	,	,	PUNCT
ejpam-5894	443	15	β(ζ	β(ζ	PROPN
ejpam-5894	443	16	)	)	PUNCT
ejpam-5894	443	17	≤	≤	NOUN
ejpam-5894	443	18	max{β(θ	max{β(θ	PROPN
ejpam-5894	443	19	)	)	PUNCT
ejpam-5894	443	20	,	,	PUNCT
ejpam-5894	443	21	β((ζ|(θ|θ))|(ζ|(θ|θ	β((ζ|(θ|θ))|(ζ|(θ|θ	NOUN
ejpam-5894	443	22	)	)	PUNCT
ejpam-5894	443	23	)	)	PUNCT
ejpam-5894	443	24	)	)	PUNCT
ejpam-5894	443	25	}	}	PUNCT
ejpam-5894	444	1	=	=	SYM
ejpam-5894	444	2	max{β(θ	max{β(θ	PROPN
ejpam-5894	444	3	)	)	PUNCT
ejpam-5894	444	4	,	,	PUNCT
ejpam-5894	444	5	β(((((ζ|ζ)|(ζ|ζ))|((ζ|ζ)|η))|(θ|θ))|	β(((((ζ|ζ)|(ζ|ζ))|((ζ|ζ)|η))|(θ|θ))|	NUM
ejpam-5894	444	6	(	(	PUNCT
ejpam-5894	444	7	(	(	PUNCT
ejpam-5894	444	8	(	(	PUNCT
ejpam-5894	444	9	(	(	PUNCT
ejpam-5894	444	10	ζ|ζ)|(ζ|ζ))|((ζ|ζ)|η))|(θ|θ	ζ|ζ)|(ζ|ζ))|((ζ|ζ)|η))|(θ|θ	NUM
ejpam-5894	444	11	)	)	PUNCT
ejpam-5894	444	12	)	)	PUNCT
ejpam-5894	444	13	)	)	PUNCT
ejpam-5894	444	14	}	}	PUNCT
ejpam-5894	444	15	=	=	SYM
ejpam-5894	444	16	max{β(θ	max{β(θ	PROPN
ejpam-5894	444	17	)	)	PUNCT
ejpam-5894	444	18	,	,	PUNCT
ejpam-5894	444	19	β((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|	β((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|	PROPN
ejpam-5894	444	20	(	(	PUNCT
ejpam-5894	444	21	(	(	PUNCT
ejpam-5894	444	22	(	(	PUNCT
ejpam-5894	444	23	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	444	24	)	)	PUNCT
ejpam-5894	444	25	)	)	PUNCT
ejpam-5894	444	26	)	)	PUNCT
ejpam-5894	444	27	}	}	PUNCT
ejpam-5894	444	28	,	,	PUNCT
ejpam-5894	444	29	which	which	PRON
ejpam-5894	444	30	means	mean	VERB
ejpam-5894	444	31	that	that	SCONJ
ejpam-5894	444	32	l	l	NOUN
ejpam-5894	444	33	=	=	SYM
ejpam-5894	444	34	(	(	PUNCT
ejpam-5894	444	35	l	l	NOUN
ejpam-5894	444	36	,	,	PUNCT
ejpam-5894	444	37	α	α	X
ejpam-5894	444	38	,	,	PUNCT
ejpam-5894	444	39	β	β	NOUN
ejpam-5894	444	40	)	)	PUNCT
ejpam-5894	444	41	is	be	AUX
ejpam-5894	444	42	an	an	DET
ejpam-5894	444	43	intuitionistic	intuitionistic	ADJ
ejpam-5894	444	44	fuzzy	fuzzy	ADJ
ejpam-5894	444	45	implicative	implicative	ADJ
ejpam-5894	444	46	wsbg	wsbg	NOUN
ejpam-5894	444	47	-	-	PUNCT
ejpam-5894	444	48	ideal	ideal	NOUN
ejpam-5894	444	49	of	of	ADP
ejpam-5894	444	50	l.	l.	NOUN
ejpam-5894	444	51	conversely	conversely	ADV
ejpam-5894	444	52	,	,	PUNCT
ejpam-5894	444	53	suppose	suppose	VERB
ejpam-5894	444	54	that	that	SCONJ
ejpam-5894	444	55	every	every	DET
ejpam-5894	444	56	intuitionistic	intuitionistic	ADJ
ejpam-5894	444	57	fuzzy	fuzzy	NOUN
ejpam-5894	444	58	closed	close	VERB
ejpam-5894	444	59	wsbg	wsbg	ADV
ejpam-5894	444	60	-	-	PUNCT
ejpam-5894	444	61	ideal	ideal	NOUN
ejpam-5894	444	62	of	of	ADP
ejpam-5894	444	63	l	l	NOUN
ejpam-5894	444	64	=	=	SYM
ejpam-5894	444	65	⟨l	⟨l	NOUN
ejpam-5894	444	66	;	;	PUNCT
ejpam-5894	444	67	|	|	ADV
ejpam-5894	444	68	,	,	PUNCT
ejpam-5894	444	69	0⟩	0⟩	PROPN
ejpam-5894	444	70	is	be	AUX
ejpam-5894	444	71	an	an	DET
ejpam-5894	444	72	intuitionistic	intuitionistic	ADJ
ejpam-5894	444	73	fuzzy	fuzzy	ADJ
ejpam-5894	444	74	implicative	implicative	ADJ
ejpam-5894	444	75	wsbg	wsbg	NOUN
ejpam-5894	444	76	-	-	PUNCT
ejpam-5894	444	77	ideal	ideal	NOUN
ejpam-5894	444	78	of	of	ADP
ejpam-5894	444	79	l.	l.	PROPN
ejpam-5894	444	80	so	so	ADV
ejpam-5894	444	81	,	,	PUNCT
ejpam-5894	444	82	it	it	PRON
ejpam-5894	444	83	follows	follow	VERB
ejpam-5894	444	84	from	from	ADP
ejpam-5894	444	85	the	the	DET
ejpam-5894	444	86	equation	equation	NOUN
ejpam-5894	444	87	(	(	PUNCT
ejpam-5894	444	88	27	27	NUM
ejpam-5894	444	89	)	)	PUNCT
ejpam-5894	444	90	that	that	SCONJ
ejpam-5894	444	91	θ|(η|η	θ|(η|η	PROPN
ejpam-5894	444	92	)	)	PUNCT
ejpam-5894	444	93	=	=	SYM
ejpam-5894	444	94	(	(	PUNCT
ejpam-5894	444	95	ζ|(θ|θ))|((ζ|(η|η))|(ζ|(η|η	ζ|(θ|θ))|((ζ|(η|η))|(ζ|(η|η	ADJ
ejpam-5894	444	96	)	)	PUNCT
ejpam-5894	444	97	)	)	PUNCT
ejpam-5894	444	98	)	)	PUNCT
ejpam-5894	444	99	.	.	PUNCT
ejpam-5894	445	1	since	since	SCONJ
ejpam-5894	445	2	θ|(η|η	θ|(η|η	PROPN
ejpam-5894	445	3	)	)	PUNCT
ejpam-5894	445	4	=	=	SYM
ejpam-5894	445	5	(	(	PUNCT
ejpam-5894	445	6	ζ|(θ|θ))|((ζ|(η|η))|(ζ|(η|η	ζ|(θ|θ))|((ζ|(η|η))|(ζ|(η|η	ADJ
ejpam-5894	445	7	)	)	PUNCT
ejpam-5894	445	8	)	)	PUNCT
ejpam-5894	445	9	)	)	PUNCT
ejpam-5894	446	1	=	=	SYM
ejpam-5894	446	2	(	(	PUNCT
ejpam-5894	446	3	(	(	PUNCT
ejpam-5894	446	4	ζ|(ζ|(θ|θ)))|(ζ|(ζ|(θ|θ))))|(η|η	ζ|(ζ|(θ|θ)))|(ζ|(ζ|(θ|θ))))|(η|η	NOUN
ejpam-5894	446	5	)	)	PUNCT
ejpam-5894	446	6	from	from	ADP
ejpam-5894	446	7	(	(	PUNCT
ejpam-5894	446	8	s1	s1	NOUN
ejpam-5894	446	9	)	)	PUNCT
ejpam-5894	446	10	and	and	CCONJ
ejpam-5894	446	11	(	(	PUNCT
ejpam-5894	446	12	s3	s3	PROPN
ejpam-5894	446	13	)	)	PUNCT
ejpam-5894	446	14	,	,	PUNCT
ejpam-5894	446	15	it	it	PRON
ejpam-5894	446	16	is	be	AUX
ejpam-5894	446	17	obtained	obtain	VERB
ejpam-5894	446	18	from	from	ADP
ejpam-5894	446	19	(	(	PUNCT
ejpam-5894	446	20	s2	s2	PROPN
ejpam-5894	446	21	)	)	PUNCT
ejpam-5894	446	22	that	that	PRON
ejpam-5894	446	23	θ	θ	X
ejpam-5894	447	1	=	=	PUNCT
ejpam-5894	447	2	(	(	PUNCT
ejpam-5894	447	3	ζ|(ζ|(θ|θ)))|(ζ|(ζ|(θ|θ	ζ|(ζ|(θ|θ)))|(ζ|(ζ|(θ|θ	NOUN
ejpam-5894	447	4	)	)	PUNCT
ejpam-5894	447	5	)	)	PUNCT
ejpam-5894	447	6	)	)	PUNCT
ejpam-5894	447	7	.	.	PUNCT
ejpam-5894	448	1	thus	thus	ADV
ejpam-5894	448	2	,	,	PUNCT
ejpam-5894	448	3	we	we	PRON
ejpam-5894	448	4	get	get	VERB
ejpam-5894	448	5	from	from	ADP
ejpam-5894	448	6	(	(	PUNCT
ejpam-5894	448	7	s1)-(s3	s1)-(s3	NUM
ejpam-5894	448	8	)	)	PUNCT
ejpam-5894	448	9	that	that	SCONJ
ejpam-5894	448	10	ζ|(ζ|(η|η	ζ|(ζ|(η|η	NOUN
ejpam-5894	448	11	)	)	PUNCT
ejpam-5894	448	12	)	)	PUNCT
ejpam-5894	449	1	=	=	SYM
ejpam-5894	449	2	(	(	PUNCT
ejpam-5894	449	3	(	(	PUNCT
ejpam-5894	449	4	η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ))))|(((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ))))|(η|η	η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ))))|(((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ))))|(η|η	NOUN
ejpam-5894	449	5	)	)	PUNCT
ejpam-5894	449	6	)	)	PUNCT
ejpam-5894	450	1	=	=	SYM
ejpam-5894	450	2	(	(	PUNCT
ejpam-5894	450	3	(	(	PUNCT
ejpam-5894	450	4	η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ))))|(η|(((η|η)|(η|(ζ|ζ)))|((η|η)|(η|(ζ|ζ	η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ))))|(η|(((η|η)|(η|(ζ|ζ)))|((η|η)|(η|(ζ|ζ	NOUN
ejpam-5894	450	5	)	)	PUNCT
ejpam-5894	450	6	)	)	PUNCT
ejpam-5894	450	7	)	)	PUNCT
ejpam-5894	450	8	)	)	PUNCT
ejpam-5894	450	9	)	)	PUNCT
ejpam-5894	451	1	=	=	PUNCT
ejpam-5894	451	2	(	(	PUNCT
ejpam-5894	451	3	(	(	PUNCT
ejpam-5894	451	4	η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ))))|(η|(η|η	η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ))))|(η|(η|η	NUM
ejpam-5894	451	5	)	)	PUNCT
ejpam-5894	451	6	)	)	PUNCT
ejpam-5894	452	1	=	=	PUNCT
ejpam-5894	452	2	(	(	PUNCT
ejpam-5894	452	3	(	(	PUNCT
ejpam-5894	452	4	(	(	PUNCT
ejpam-5894	452	5	η|(η|η))|((η|η)|(η|η)))|((η|(η|η))|((η|η)|(η|η))))|(η|(ζ|ζ	η|(η|η))|((η|η)|(η|η)))|((η|(η|η))|((η|η)|(η|η))))|(η|(ζ|ζ	NOUN
ejpam-5894	452	6	)	)	PUNCT
ejpam-5894	452	7	)	)	PUNCT
ejpam-5894	453	1	=	=	SYM
ejpam-5894	453	2	η|(η|(ζ|ζ	η|(η|(ζ|ζ	NOUN
ejpam-5894	453	3	)	)	PUNCT
ejpam-5894	453	4	)	)	PUNCT
ejpam-5894	453	5	,	,	PUNCT
ejpam-5894	453	6	for	for	ADP
ejpam-5894	453	7	all	all	DET
ejpam-5894	453	8	ζ	ζ	NOUN
ejpam-5894	453	9	,	,	PUNCT
ejpam-5894	453	10	η	η	PROPN
ejpam-5894	453	11	∈	∈	PROPN
ejpam-5894	453	12	l	l	NOUN
ejpam-5894	453	13	,	,	PUNCT
ejpam-5894	453	14	which	which	PRON
ejpam-5894	453	15	means	mean	VERB
ejpam-5894	453	16	that	that	SCONJ
ejpam-5894	453	17	l	l	NOUN
ejpam-5894	453	18	is	be	AUX
ejpam-5894	453	19	implicative	implicative	ADJ
ejpam-5894	453	20	.	.	PUNCT
ejpam-5894	454	1	the	the	DET
ejpam-5894	454	2	identity	identity	NOUN
ejpam-5894	454	3	used	use	VERB
ejpam-5894	454	4	in	in	ADP
ejpam-5894	454	5	theorem	theorem	ADJ
ejpam-5894	454	6	8	8	NUM
ejpam-5894	454	7	is	be	AUX
ejpam-5894	454	8	not	not	PART
ejpam-5894	454	9	an	an	DET
ejpam-5894	454	10	assumption	assumption	NOUN
ejpam-5894	454	11	but	but	CCONJ
ejpam-5894	454	12	a	a	DET
ejpam-5894	454	13	necessary	necessary	ADJ
ejpam-5894	454	14	and	and	CCONJ
ejpam-5894	454	15	sufficient	sufficient	ADJ
ejpam-5894	454	16	condition	condition	NOUN
ejpam-5894	454	17	that	that	PRON
ejpam-5894	454	18	fully	fully	ADV
ejpam-5894	454	19	characterizes	characterize	VERB
ejpam-5894	454	20	when	when	SCONJ
ejpam-5894	454	21	an	an	DET
ejpam-5894	454	22	intuitionistic	intuitionistic	ADJ
ejpam-5894	454	23	fuzzy	fuzzy	ADJ
ejpam-5894	454	24	set	set	NOUN
ejpam-5894	454	25	becomes	become	VERB
ejpam-5894	454	26	an	an	DET
ejpam-5894	454	27	intuitionistic	intuitionistic	ADJ
ejpam-5894	454	28	fuzzy	fuzzy	ADJ
ejpam-5894	454	29	implicative	implicative	ADJ
ejpam-5894	454	30	wsbg	wsbg	ADV
ejpam-5894	454	31	-	-	PUNCT
ejpam-5894	454	32	ideal	ideal	ADJ
ejpam-5894	454	33	.	.	PUNCT
ejpam-5894	455	1	proposition	proposition	NOUN
ejpam-5894	455	2	4	4	NUM
ejpam-5894	455	3	.	.	PUNCT
ejpam-5894	456	1	let	let	VERB
ejpam-5894	456	2	l	l	NOUN
ejpam-5894	456	3	=	=	SYM
ejpam-5894	456	4	⟨l	⟨l	NOUN
ejpam-5894	456	5	;	;	PUNCT
ejpam-5894	456	6	|	|	ADV
ejpam-5894	456	7	,	,	PUNCT
ejpam-5894	456	8	0⟩	0⟩	PROPN
ejpam-5894	456	9	be	be	VERB
ejpam-5894	456	10	an	an	DET
ejpam-5894	456	11	implicative	implicative	ADJ
ejpam-5894	456	12	wsbg	wsbg	NOUN
ejpam-5894	456	13	-	-	PUNCT
ejpam-5894	456	14	algebra	algebra	NOUN
ejpam-5894	456	15	.	.	PUNCT
ejpam-5894	457	1	then	then	ADV
ejpam-5894	457	2	every	every	DET
ejpam-5894	457	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	457	4	fuzzy	fuzzy	NOUN
ejpam-5894	457	5	completely	completely	ADV
ejpam-5894	457	6	closed	close	VERB
ejpam-5894	457	7	wsbg	wsbg	ADV
ejpam-5894	457	8	-	-	PUNCT
ejpam-5894	457	9	ideal	ideal	NOUN
ejpam-5894	457	10	of	of	ADP
ejpam-5894	457	11	l	l	NOUN
ejpam-5894	457	12	is	be	AUX
ejpam-5894	457	13	an	an	DET
ejpam-5894	457	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	457	15	fuzzy	fuzzy	ADJ
ejpam-5894	457	16	implicative	implicative	ADJ
ejpam-5894	457	17	ideal	ideal	NOUN
ejpam-5894	457	18	of	of	ADP
ejpam-5894	457	19	l.	l.	PROPN
ejpam-5894	457	20	t.	t.	PROPN
ejpam-5894	457	21	oner	oner	PROPN
ejpam-5894	457	22	et	et	PROPN
ejpam-5894	457	23	al	al	PROPN
ejpam-5894	457	24	.	.	PUNCT
ejpam-5894	457	25	/	/	SYM
ejpam-5894	457	26	eur	eur	PROPN
ejpam-5894	457	27	.	.	PUNCT
ejpam-5894	458	1	j.	j.	PROPN
ejpam-5894	458	2	pure	pure	PROPN
ejpam-5894	458	3	appl	appl	PROPN
ejpam-5894	458	4	.	.	PROPN
ejpam-5894	458	5	math	math	PROPN
ejpam-5894	458	6	,	,	PUNCT
ejpam-5894	458	7	18	18	NUM
ejpam-5894	458	8	(	(	PUNCT
ejpam-5894	458	9	3	3	NUM
ejpam-5894	458	10	)	)	PUNCT
ejpam-5894	458	11	(	(	PUNCT
ejpam-5894	458	12	2025	2025	NUM
ejpam-5894	458	13	)	)	PUNCT
ejpam-5894	458	14	,	,	PUNCT
ejpam-5894	458	15	5894	5894	NUM
ejpam-5894	458	16	24	24	NUM
ejpam-5894	458	17	of	of	ADP
ejpam-5894	458	18	33	33	NUM
ejpam-5894	458	19	proof	proof	NOUN
ejpam-5894	458	20	.	.	PUNCT
ejpam-5894	459	1	let	let	VERB
ejpam-5894	459	2	l	l	NOUN
ejpam-5894	459	3	=	=	SYM
ejpam-5894	459	4	(	(	PUNCT
ejpam-5894	459	5	l	l	NOUN
ejpam-5894	459	6	,	,	PUNCT
ejpam-5894	459	7	α	α	X
ejpam-5894	459	8	,	,	PUNCT
ejpam-5894	459	9	β	β	NOUN
ejpam-5894	459	10	)	)	PUNCT
ejpam-5894	459	11	be	be	VERB
ejpam-5894	459	12	an	an	DET
ejpam-5894	459	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	459	14	fuzzy	fuzzy	NOUN
ejpam-5894	459	15	completely	completely	ADV
ejpam-5894	459	16	closed	close	VERB
ejpam-5894	459	17	wsbg	wsbg	NOUN
ejpam-5894	459	18	-	-	PUNCT
ejpam-5894	459	19	ideal	ideal	NOUN
ejpam-5894	459	20	of	of	ADP
ejpam-5894	459	21	an	an	DET
ejpam-5894	459	22	implicative	implicative	ADJ
ejpam-5894	459	23	wsbg	wsbg	ADV
ejpam-5894	459	24	-	-	PUNCT
ejpam-5894	459	25	algebra	algebra	NOUN
ejpam-5894	459	26	l	l	NOUN
ejpam-5894	459	27	=	=	PUNCT
ejpam-5894	459	28	⟨l	⟨l	NOUN
ejpam-5894	459	29	;	;	PUNCT
ejpam-5894	459	30	|	|	ADV
ejpam-5894	459	31	,	,	PUNCT
ejpam-5894	459	32	0⟩.	0⟩.	PROPN
ejpam-5894	459	33	then	then	ADV
ejpam-5894	459	34	l	l	PROPN
ejpam-5894	459	35	=	=	PUNCT
ejpam-5894	459	36	(	(	PUNCT
ejpam-5894	459	37	l	l	NOUN
ejpam-5894	459	38	,	,	PUNCT
ejpam-5894	459	39	α	α	X
ejpam-5894	459	40	,	,	PUNCT
ejpam-5894	459	41	β	β	NOUN
ejpam-5894	459	42	)	)	PUNCT
ejpam-5894	459	43	is	be	AUX
ejpam-5894	459	44	an	an	DET
ejpam-5894	459	45	intuitionistic	intuitionistic	ADJ
ejpam-5894	459	46	fuzzy	fuzzy	ADJ
ejpam-5894	459	47	wsbg	wsbg	NOUN
ejpam-5894	459	48	-	-	PUNCT
ejpam-5894	459	49	ideal	ideal	NOUN
ejpam-5894	459	50	of	of	ADP
ejpam-5894	459	51	l.	l.	PROPN
ejpam-5894	459	52	since	since	SCONJ
ejpam-5894	459	53	β((0|(η|η))|(0|(η|η	β((0|(η|η))|(0|(η|η	PROPN
ejpam-5894	459	54	)	)	PUNCT
ejpam-5894	459	55	)	)	PUNCT
ejpam-5894	459	56	)	)	PUNCT
ejpam-5894	460	1	≤	≤	NUM
ejpam-5894	460	2	max{β(0	max{β(0	NOUN
ejpam-5894	460	3	)	)	PUNCT
ejpam-5894	460	4	,	,	PUNCT
ejpam-5894	460	5	β(η	β(η	PROPN
ejpam-5894	460	6	)	)	PUNCT
ejpam-5894	460	7	}	}	PUNCT
ejpam-5894	460	8	=	=	SYM
ejpam-5894	460	9	β(η	β(η	NOUN
ejpam-5894	460	10	)	)	PUNCT
ejpam-5894	460	11	and	and	CCONJ
ejpam-5894	460	12	α((0|(η|η))|(0|(η|η	α((0|(η|η))|(0|(η|η	NUM
ejpam-5894	460	13	)	)	PUNCT
ejpam-5894	460	14	)	)	PUNCT
ejpam-5894	460	15	)	)	PUNCT
ejpam-5894	460	16	≥	≥	NOUN
ejpam-5894	460	17	min{α(0	min{α(0	NOUN
ejpam-5894	460	18	)	)	PUNCT
ejpam-5894	460	19	,	,	PUNCT
ejpam-5894	460	20	α(η	α(η	PROPN
ejpam-5894	460	21	)	)	PUNCT
ejpam-5894	460	22	}	}	PUNCT
ejpam-5894	460	23	=	=	SYM
ejpam-5894	460	24	α(η	α(η	X
ejpam-5894	460	25	)	)	PUNCT
ejpam-5894	460	26	,	,	PUNCT
ejpam-5894	460	27	it	it	PRON
ejpam-5894	460	28	is	be	AUX
ejpam-5894	460	29	obtained	obtain	VERB
ejpam-5894	460	30	that	that	SCONJ
ejpam-5894	460	31	l	l	NOUN
ejpam-5894	460	32	is	be	AUX
ejpam-5894	460	33	an	an	DET
ejpam-5894	460	34	intuitionistic	intuitionistic	ADJ
ejpam-5894	460	35	fuzzy	fuzzy	ADJ
ejpam-5894	460	36	closed	close	VERB
ejpam-5894	460	37	wsbg	wsbg	ADV
ejpam-5894	460	38	-	-	PUNCT
ejpam-5894	460	39	ideal	ideal	NOUN
ejpam-5894	460	40	of	of	ADP
ejpam-5894	460	41	l.	l.	PROPN
ejpam-5894	460	42	therefore	therefore	ADV
ejpam-5894	460	43	,	,	PUNCT
ejpam-5894	460	44	l	l	NOUN
ejpam-5894	460	45	=	=	SYM
ejpam-5894	460	46	(	(	PUNCT
ejpam-5894	460	47	l	l	NOUN
ejpam-5894	460	48	,	,	PUNCT
ejpam-5894	460	49	α	α	X
ejpam-5894	460	50	,	,	PUNCT
ejpam-5894	460	51	β	β	NOUN
ejpam-5894	460	52	)	)	PUNCT
ejpam-5894	460	53	is	be	AUX
ejpam-5894	460	54	an	an	DET
ejpam-5894	460	55	intuitionistic	intuitionistic	ADJ
ejpam-5894	460	56	fuzzy	fuzzy	ADJ
ejpam-5894	460	57	implicative	implicative	ADJ
ejpam-5894	460	58	wsbg	wsbg	NOUN
ejpam-5894	460	59	-	-	PUNCT
ejpam-5894	460	60	ideal	ideal	NOUN
ejpam-5894	460	61	of	of	ADP
ejpam-5894	460	62	l.	l.	PROPN
ejpam-5894	460	63	example	example	PROPN
ejpam-5894	460	64	16	16	NUM
ejpam-5894	460	65	.	.	PUNCT
ejpam-5894	461	1	let	let	VERB
ejpam-5894	461	2	us	we	PRON
ejpam-5894	461	3	consider	consider	VERB
ejpam-5894	461	4	the	the	DET
ejpam-5894	461	5	following	follow	VERB
ejpam-5894	461	6	algebra	algebra	NOUN
ejpam-5894	461	7	l	l	NOUN
ejpam-5894	461	8	=	=	PUNCT
ejpam-5894	461	9	{	{	PUNCT
ejpam-5894	461	10	0	0	NUM
ejpam-5894	461	11	,	,	PUNCT
ejpam-5894	461	12	1	1	NUM
ejpam-5894	461	13	,	,	PUNCT
ejpam-5894	461	14	2	2	NUM
ejpam-5894	461	15	,	,	PUNCT
ejpam-5894	461	16	3	3	NUM
ejpam-5894	461	17	}	}	PUNCT
ejpam-5894	461	18	with	with	ADP
ejpam-5894	461	19	a	a	DET
ejpam-5894	461	20	binary	binary	ADJ
ejpam-5894	461	21	operation	operation	NOUN
ejpam-5894	461	22	|	|	ADV
ejpam-5894	461	23	given	give	VERB
ejpam-5894	461	24	by	by	ADP
ejpam-5894	461	25	the	the	DET
ejpam-5894	461	26	cayley	cayley	ADJ
ejpam-5894	461	27	table	table	NOUN
ejpam-5894	461	28	:	:	PUNCT
ejpam-5894	462	1	|	|	ADV
ejpam-5894	462	2	0	0	NUM
ejpam-5894	462	3	1	1	NUM
ejpam-5894	462	4	2	2	NUM
ejpam-5894	462	5	3	3	NUM
ejpam-5894	462	6	0	0	NUM
ejpam-5894	462	7	0	0	NUM
ejpam-5894	462	8	0	0	NUM
ejpam-5894	462	9	0	0	NUM
ejpam-5894	462	10	0	0	NUM
ejpam-5894	462	11	1	1	NUM
ejpam-5894	462	12	2	2	NUM
ejpam-5894	462	13	0	0	NUM
ejpam-5894	462	14	1	1	NUM
ejpam-5894	462	15	0	0	NUM
ejpam-5894	462	16	2	2	NUM
ejpam-5894	462	17	0	0	NUM
ejpam-5894	462	18	0	0	NUM
ejpam-5894	462	19	0	0	NUM
ejpam-5894	462	20	0	0	NUM
ejpam-5894	462	21	3	3	NUM
ejpam-5894	462	22	0	0	NUM
ejpam-5894	462	23	0	0	NUM
ejpam-5894	462	24	0	0	NUM
ejpam-5894	462	25	0	0	PUNCT
ejpam-5894	462	26	then	then	ADV
ejpam-5894	462	27	l	l	NOUN
ejpam-5894	462	28	=	=	PUNCT
ejpam-5894	462	29	⟨l	⟨l	NOUN
ejpam-5894	462	30	;	;	PUNCT
ejpam-5894	462	31	|	|	ADV
ejpam-5894	462	32	,	,	PUNCT
ejpam-5894	462	33	0⟩	0⟩	PROPN
ejpam-5894	462	34	is	be	AUX
ejpam-5894	462	35	a	a	DET
ejpam-5894	462	36	wsbg	wsbg	ADV
ejpam-5894	462	37	-	-	PUNCT
ejpam-5894	462	38	algebra	algebra	NOUN
ejpam-5894	462	39	.	.	PUNCT
ejpam-5894	463	1	next	next	ADV
ejpam-5894	463	2	,	,	PUNCT
ejpam-5894	463	3	define	define	VERB
ejpam-5894	463	4	an	an	DET
ejpam-5894	463	5	intuitionistic	intuitionistic	ADJ
ejpam-5894	463	6	fuzzy	fuzzy	ADJ
ejpam-5894	463	7	set	set	NOUN
ejpam-5894	463	8	l	l	NOUN
ejpam-5894	463	9	=	=	SYM
ejpam-5894	463	10	(	(	PUNCT
ejpam-5894	463	11	l	l	NOUN
ejpam-5894	463	12	,	,	PUNCT
ejpam-5894	463	13	α	α	X
ejpam-5894	463	14	,	,	PUNCT
ejpam-5894	463	15	β	β	NOUN
ejpam-5894	463	16	)	)	PUNCT
ejpam-5894	463	17	with	with	ADP
ejpam-5894	463	18	:	:	PUNCT
ejpam-5894	463	19	α(0	α(0	NOUN
ejpam-5894	463	20	)	)	PUNCT
ejpam-5894	463	21	=	=	SYM
ejpam-5894	463	22	1	1	X
ejpam-5894	463	23	,	,	PUNCT
ejpam-5894	463	24	α(1	α(1	PROPN
ejpam-5894	463	25	)	)	PUNCT
ejpam-5894	463	26	=	=	SYM
ejpam-5894	463	27	0.7	0.7	NUM
ejpam-5894	463	28	,	,	PUNCT
ejpam-5894	463	29	α(2	α(2	PROPN
ejpam-5894	463	30	)	)	PUNCT
ejpam-5894	463	31	=	=	NOUN
ejpam-5894	463	32	0.5	0.5	NUM
ejpam-5894	463	33	,	,	PUNCT
ejpam-5894	463	34	α(3	α(3	PROPN
ejpam-5894	463	35	)	)	PUNCT
ejpam-5894	463	36	=	=	NOUN
ejpam-5894	463	37	0.4	0.4	NUM
ejpam-5894	463	38	,	,	PUNCT
ejpam-5894	463	39	β(0	β(0	PROPN
ejpam-5894	463	40	)	)	PUNCT
ejpam-5894	463	41	=	=	SYM
ejpam-5894	463	42	0	0	NUM
ejpam-5894	463	43	,	,	PUNCT
ejpam-5894	463	44	β(1	β(1	PROPN
ejpam-5894	463	45	)	)	PUNCT
ejpam-5894	463	46	=	=	NOUN
ejpam-5894	463	47	0.2	0.2	NUM
ejpam-5894	463	48	,	,	PUNCT
ejpam-5894	463	49	β(2	β(2	PROPN
ejpam-5894	463	50	)	)	PUNCT
ejpam-5894	464	1	=	=	PUNCT
ejpam-5894	464	2	0.3	0.3	NUM
ejpam-5894	464	3	,	,	PUNCT
ejpam-5894	464	4	β(3	β(3	PROPN
ejpam-5894	464	5	)	)	PUNCT
ejpam-5894	464	6	=	=	SYM
ejpam-5894	464	7	0.4	0.4	NUM
ejpam-5894	464	8	.	.	PUNCT
ejpam-5894	465	1	we	we	PRON
ejpam-5894	465	2	verify	verify	VERB
ejpam-5894	465	3	that	that	SCONJ
ejpam-5894	465	4	l	l	NOUN
ejpam-5894	465	5	is	be	AUX
ejpam-5894	465	6	an	an	DET
ejpam-5894	465	7	intuitionistic	intuitionistic	ADJ
ejpam-5894	465	8	fuzzy	fuzzy	NOUN
ejpam-5894	465	9	completely	completely	ADV
ejpam-5894	465	10	closed	close	VERB
ejpam-5894	465	11	wsbg	wsbg	NOUN
ejpam-5894	465	12	-	-	PUNCT
ejpam-5894	465	13	ideal	ideal	ADJ
ejpam-5894	465	14	,	,	PUNCT
ejpam-5894	465	15	but	but	CCONJ
ejpam-5894	465	16	it	it	PRON
ejpam-5894	465	17	is	be	AUX
ejpam-5894	465	18	not	not	PART
ejpam-5894	465	19	an	an	DET
ejpam-5894	465	20	intuitionistic	intuitionistic	ADJ
ejpam-5894	465	21	fuzzy	fuzzy	ADJ
ejpam-5894	465	22	implicative	implicative	ADJ
ejpam-5894	465	23	ideal	ideal	NOUN
ejpam-5894	465	24	of	of	ADP
ejpam-5894	465	25	l.	l.	PROPN
ejpam-5894	465	26	it	it	PRON
ejpam-5894	465	27	must	must	AUX
ejpam-5894	465	28	also	also	ADV
ejpam-5894	465	29	satisfy	satisfy	VERB
ejpam-5894	465	30	:	:	PUNCT
ejpam-5894	465	31	α(0	α(0	NUM
ejpam-5894	465	32	)	)	PUNCT
ejpam-5894	465	33	≥	≥	NOUN
ejpam-5894	465	34	α(ζ	α(ζ	PROPN
ejpam-5894	465	35	)	)	PUNCT
ejpam-5894	465	36	≥	≥	NOUN
ejpam-5894	465	37	min{α(φ(ζ	min{α(φ(ζ	PROPN
ejpam-5894	465	38	,	,	PUNCT
ejpam-5894	465	39	η	η	PROPN
ejpam-5894	465	40	,	,	PUNCT
ejpam-5894	465	41	θ	θ	NOUN
ejpam-5894	465	42	)	)	PUNCT
ejpam-5894	465	43	)	)	PUNCT
ejpam-5894	465	44	,	,	PUNCT
ejpam-5894	465	45	α(θ	α(θ	NOUN
ejpam-5894	465	46	)	)	PUNCT
ejpam-5894	465	47	}	}	PUNCT
ejpam-5894	465	48	for	for	ADP
ejpam-5894	465	49	all	all	DET
ejpam-5894	465	50	ζ	ζ	NOUN
ejpam-5894	465	51	,	,	PUNCT
ejpam-5894	465	52	η	η	PROPN
ejpam-5894	465	53	,	,	PUNCT
ejpam-5894	465	54	θ	θ	PROPN
ejpam-5894	465	55	∈	∈	PROPN
ejpam-5894	465	56	l	l	NOUN
ejpam-5894	465	57	,	,	PUNCT
ejpam-5894	465	58	where	where	SCONJ
ejpam-5894	465	59	:	:	PUNCT
ejpam-5894	465	60	φ(ζ	φ(ζ	NOUN
ejpam-5894	465	61	,	,	PUNCT
ejpam-5894	465	62	η	η	NOUN
ejpam-5894	465	63	,	,	PUNCT
ejpam-5894	465	64	θ	θ	NOUN
ejpam-5894	465	65	)	)	PUNCT
ejpam-5894	465	66	=	=	SYM
ejpam-5894	465	67	(	(	PUNCT
ejpam-5894	465	68	(	(	PUNCT
ejpam-5894	465	69	(	(	PUNCT
ejpam-5894	465	70	(	(	PUNCT
ejpam-5894	465	71	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	465	72	)	)	PUNCT
ejpam-5894	465	73	)	)	PUNCT
ejpam-5894	465	74	)	)	PUNCT
ejpam-5894	465	75	.	.	PUNCT
ejpam-5894	466	1	however	however	ADV
ejpam-5894	466	2	,	,	PUNCT
ejpam-5894	466	3	this	this	DET
ejpam-5894	466	4	condition	condition	NOUN
ejpam-5894	466	5	fails	fail	VERB
ejpam-5894	466	6	at	at	ADP
ejpam-5894	466	7	ζ	ζ	NOUN
ejpam-5894	466	8	=	=	SYM
ejpam-5894	466	9	1	1	NUM
ejpam-5894	466	10	,	,	PUNCT
ejpam-5894	466	11	η	η	X
ejpam-5894	466	12	=	=	SYM
ejpam-5894	466	13	0	0	PROPN
ejpam-5894	466	14	,	,	PUNCT
ejpam-5894	466	15	θ	θ	X
ejpam-5894	466	16	=	=	SYM
ejpam-5894	466	17	0	0	X
ejpam-5894	466	18	.	.	PUNCT
ejpam-5894	467	1	corollary	corollary	ADJ
ejpam-5894	467	2	1	1	NUM
ejpam-5894	467	3	.	.	PUNCT
ejpam-5894	468	1	let	let	VERB
ejpam-5894	468	2	l	l	NOUN
ejpam-5894	468	3	=	=	SYM
ejpam-5894	468	4	⟨l	⟨l	NOUN
ejpam-5894	468	5	;	;	PUNCT
ejpam-5894	468	6	|	|	ADV
ejpam-5894	468	7	,	,	PUNCT
ejpam-5894	468	8	0⟩	0⟩	PROPN
ejpam-5894	468	9	be	be	VERB
ejpam-5894	468	10	a	a	DET
ejpam-5894	468	11	medial	medial	ADJ
ejpam-5894	468	12	wsbg	wsbg	NOUN
ejpam-5894	468	13	-	-	PUNCT
ejpam-5894	468	14	algebra	algebra	NOUN
ejpam-5894	468	15	.	.	PUNCT
ejpam-5894	469	1	then	then	ADV
ejpam-5894	469	2	every	every	DET
ejpam-5894	469	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	469	4	fuzzy	fuzzy	NOUN
ejpam-5894	469	5	completely	completely	ADV
ejpam-5894	469	6	closed	close	VERB
ejpam-5894	469	7	wsbg	wsbg	ADV
ejpam-5894	469	8	-	-	PUNCT
ejpam-5894	469	9	ideal	ideal	NOUN
ejpam-5894	469	10	of	of	ADP
ejpam-5894	469	11	l	l	NOUN
ejpam-5894	469	12	is	be	AUX
ejpam-5894	469	13	an	an	DET
ejpam-5894	469	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	469	15	fuzzy	fuzzy	ADJ
ejpam-5894	469	16	implicative	implicative	ADJ
ejpam-5894	469	17	wsbg	wsbg	NOUN
ejpam-5894	469	18	-	-	PUNCT
ejpam-5894	469	19	ideal	ideal	NOUN
ejpam-5894	469	20	of	of	ADP
ejpam-5894	469	21	l.	l.	PROPN
ejpam-5894	469	22	definition	definition	NOUN
ejpam-5894	469	23	16	16	NUM
ejpam-5894	469	24	.	.	PUNCT
ejpam-5894	470	1	an	an	DET
ejpam-5894	470	2	intuitionistic	intuitionistic	ADJ
ejpam-5894	470	3	fuzzy	fuzzy	ADJ
ejpam-5894	470	4	set	set	NOUN
ejpam-5894	470	5	l	l	NOUN
ejpam-5894	470	6	=	=	SYM
ejpam-5894	470	7	(	(	PUNCT
ejpam-5894	470	8	l	l	NOUN
ejpam-5894	470	9	,	,	PUNCT
ejpam-5894	470	10	α	α	X
ejpam-5894	470	11	,	,	PUNCT
ejpam-5894	470	12	β	β	NOUN
ejpam-5894	470	13	)	)	PUNCT
ejpam-5894	470	14	of	of	ADP
ejpam-5894	470	15	a	a	DET
ejpam-5894	470	16	wsbg	wsbg	ADV
ejpam-5894	470	17	-	-	PUNCT
ejpam-5894	470	18	algebra	algebra	NOUN
ejpam-5894	470	19	l	l	NOUN
ejpam-5894	470	20	=	=	PUNCT
ejpam-5894	470	21	⟨l	⟨l	NOUN
ejpam-5894	470	22	;	;	PUNCT
ejpam-5894	470	23	|	|	ADV
ejpam-5894	470	24	,	,	PUNCT
ejpam-5894	470	25	0⟩	0⟩	PROPN
ejpam-5894	470	26	is	be	AUX
ejpam-5894	470	27	called	call	VERB
ejpam-5894	470	28	an	an	DET
ejpam-5894	470	29	intuitionistic	intuitionistic	ADJ
ejpam-5894	470	30	fuzzy	fuzzy	ADJ
ejpam-5894	470	31	p	p	NOUN
ejpam-5894	470	32	-	-	PUNCT
ejpam-5894	470	33	ideal	ideal	NOUN
ejpam-5894	470	34	of	of	ADP
ejpam-5894	470	35	l	l	NOUN
ejpam-5894	470	36	if	if	SCONJ
ejpam-5894	470	37	(	(	PUNCT
ejpam-5894	470	38	∀ζ	∀ζ	PROPN
ejpam-5894	470	39	,	,	PUNCT
ejpam-5894	470	40	η	η	PROPN
ejpam-5894	470	41	,	,	PUNCT
ejpam-5894	470	42	θ	θ	PROPN
ejpam-5894	470	43	∈	∈	PROPN
ejpam-5894	470	44	l	l	NOUN
ejpam-5894	470	45	)	)	PUNCT
ejpam-5894	470	46			NOUN
ejpam-5894	470	47	α(0	α(0	PROPN
ejpam-5894	470	48	)	)	PUNCT
ejpam-5894	470	49	≥	≥	NOUN
ejpam-5894	470	50	α(ζ	α(ζ	NOUN
ejpam-5894	470	51	)	)	PUNCT
ejpam-5894	470	52	,	,	PUNCT
ejpam-5894	470	53	β(0	β(0	PROPN
ejpam-5894	470	54	)	)	PUNCT
ejpam-5894	470	55	≤	≤	NOUN
ejpam-5894	470	56	β(ζ	β(ζ	PROPN
ejpam-5894	470	57	)	)	PUNCT
ejpam-5894	470	58	,	,	PUNCT
ejpam-5894	470	59	α(ζ	α(ζ	PROPN
ejpam-5894	470	60	)	)	PUNCT
ejpam-5894	470	61	≥	≥	NOUN
ejpam-5894	470	62	min{α(((((ζ|(θ|θ))|(ζ|(θ|θ)))|(η|(θ|θ)))|	min{α(((((ζ|(θ|θ))|(ζ|(θ|θ)))|(η|(θ|θ)))|	X
ejpam-5894	470	63	(	(	PUNCT
ejpam-5894	470	64	(	(	PUNCT
ejpam-5894	470	65	(	(	PUNCT
ejpam-5894	470	66	ζ|(θ|θ))|(ζ|(θ|θ)))|(η|(θ|θ	ζ|(θ|θ))|(ζ|(θ|θ)))|(η|(θ|θ	NOUN
ejpam-5894	470	67	)	)	PUNCT
ejpam-5894	470	68	)	)	PUNCT
ejpam-5894	470	69	)	)	PUNCT
ejpam-5894	470	70	)	)	PUNCT
ejpam-5894	470	71	)	)	PUNCT
ejpam-5894	470	72	,	,	PUNCT
ejpam-5894	470	73	α(η	α(η	PROPN
ejpam-5894	470	74	)	)	PUNCT
ejpam-5894	470	75	}	}	PUNCT
ejpam-5894	470	76	,	,	PUNCT
ejpam-5894	470	77	β(ζ	β(ζ	PROPN
ejpam-5894	470	78	)	)	PUNCT
ejpam-5894	470	79	≤	≤	NUM
ejpam-5894	470	80	max{β(((((ζ|(θ|θ))|(ζ|(θ|θ)))|(η|(θ|θ)))|	max{β(((((ζ|(θ|θ))|(ζ|(θ|θ)))|(η|(θ|θ)))|	NOUN
ejpam-5894	470	81	(	(	PUNCT
ejpam-5894	470	82	(	(	PUNCT
ejpam-5894	470	83	(	(	PUNCT
ejpam-5894	470	84	ζ|(θ|θ))|(ζ|(θ|θ)))|(η|(θ|θ	ζ|(θ|θ))|(ζ|(θ|θ)))|(η|(θ|θ	NOUN
ejpam-5894	470	85	)	)	PUNCT
ejpam-5894	470	86	)	)	PUNCT
ejpam-5894	470	87	)	)	PUNCT
ejpam-5894	470	88	)	)	PUNCT
ejpam-5894	470	89	)	)	PUNCT
ejpam-5894	470	90	,	,	PUNCT
ejpam-5894	470	91	β(η	β(η	PROPN
ejpam-5894	470	92	)	)	PUNCT
ejpam-5894	470	93	}	}	PUNCT
ejpam-5894	470	94			ADP
ejpam-5894	470	95	.	.	PUNCT
ejpam-5894	471	1	t.	t.	PROPN
ejpam-5894	471	2	oner	oner	PROPN
ejpam-5894	471	3	et	et	PROPN
ejpam-5894	471	4	al	al	PROPN
ejpam-5894	471	5	.	.	PUNCT
ejpam-5894	471	6	/	/	SYM
ejpam-5894	471	7	eur	eur	PROPN
ejpam-5894	471	8	.	.	PUNCT
ejpam-5894	472	1	j.	j.	PROPN
ejpam-5894	472	2	pure	pure	PROPN
ejpam-5894	472	3	appl	appl	PROPN
ejpam-5894	472	4	.	.	PROPN
ejpam-5894	472	5	math	math	PROPN
ejpam-5894	472	6	,	,	PUNCT
ejpam-5894	472	7	18	18	NUM
ejpam-5894	472	8	(	(	PUNCT
ejpam-5894	472	9	3	3	NUM
ejpam-5894	472	10	)	)	PUNCT
ejpam-5894	472	11	(	(	PUNCT
ejpam-5894	472	12	2025	2025	NUM
ejpam-5894	472	13	)	)	PUNCT
ejpam-5894	472	14	,	,	PUNCT
ejpam-5894	472	15	5894	5894	NUM
ejpam-5894	472	16	25	25	NUM
ejpam-5894	472	17	of	of	ADP
ejpam-5894	472	18	33	33	NUM
ejpam-5894	472	19	example	example	NOUN
ejpam-5894	472	20	17	17	NUM
ejpam-5894	472	21	.	.	PUNCT
ejpam-5894	473	1	consider	consider	VERB
ejpam-5894	473	2	the	the	DET
ejpam-5894	473	3	wsbg	wsbg	NOUN
ejpam-5894	473	4	-	-	PUNCT
ejpam-5894	473	5	algebra	algebra	NOUN
ejpam-5894	473	6	l	l	NOUN
ejpam-5894	473	7	=	=	PUNCT
ejpam-5894	473	8	⟨l	⟨l	NOUN
ejpam-5894	473	9	;	;	PUNCT
ejpam-5894	474	1	|	|	ADV
ejpam-5894	474	2	,	,	PUNCT
ejpam-5894	474	3	0⟩	0⟩	PROPN
ejpam-5894	474	4	where	where	SCONJ
ejpam-5894	474	5	l	l	NOUN
ejpam-5894	474	6	=	=	PUNCT
ejpam-5894	474	7	{	{	PUNCT
ejpam-5894	474	8	0	0	NUM
ejpam-5894	474	9	,	,	PUNCT
ejpam-5894	474	10	a	a	DET
ejpam-5894	474	11	,	,	PUNCT
ejpam-5894	474	12	b	b	NOUN
ejpam-5894	474	13	}	}	PUNCT
ejpam-5894	474	14	with	with	ADP
ejpam-5894	474	15	the	the	DET
ejpam-5894	474	16	following	follow	VERB
ejpam-5894	474	17	operation	operation	NOUN
ejpam-5894	474	18	table	table	NOUN
ejpam-5894	474	19	:	:	PUNCT
ejpam-5894	474	20	|	|	ADV
ejpam-5894	474	21	0	0	PUNCT
ejpam-5894	474	22	a	a	DET
ejpam-5894	474	23	b	b	NOUN
ejpam-5894	474	24	0	0	NUM
ejpam-5894	474	25	0	0	NUM
ejpam-5894	474	26	b	b	NOUN
ejpam-5894	474	27	a	a	PRON
ejpam-5894	474	28	a	a	DET
ejpam-5894	474	29	b	b	NOUN
ejpam-5894	474	30	a	a	PRON
ejpam-5894	474	31	0	0	NUM
ejpam-5894	474	32	b	b	NOUN
ejpam-5894	474	33	a	a	DET
ejpam-5894	474	34	0	0	NUM
ejpam-5894	474	35	b	b	NOUN
ejpam-5894	474	36	define	define	VERB
ejpam-5894	474	37	the	the	DET
ejpam-5894	474	38	intuitionistic	intuitionistic	ADJ
ejpam-5894	474	39	fuzzy	fuzzy	ADJ
ejpam-5894	474	40	set	set	NOUN
ejpam-5894	474	41	l	l	NOUN
ejpam-5894	474	42	=	=	SYM
ejpam-5894	474	43	(	(	PUNCT
ejpam-5894	474	44	l	l	NOUN
ejpam-5894	474	45	,	,	PUNCT
ejpam-5894	474	46	α	α	X
ejpam-5894	474	47	,	,	PUNCT
ejpam-5894	474	48	β	β	NOUN
ejpam-5894	474	49	)	)	PUNCT
ejpam-5894	474	50	by	by	ADP
ejpam-5894	474	51	:	:	PUNCT
ejpam-5894	474	52	α(0	α(0	NOUN
ejpam-5894	474	53	)	)	PUNCT
ejpam-5894	474	54	=	=	SYM
ejpam-5894	474	55	1	1	NUM
ejpam-5894	474	56	,	,	PUNCT
ejpam-5894	474	57	α(a	α(a	NOUN
ejpam-5894	474	58	)	)	PUNCT
ejpam-5894	474	59	=	=	SYM
ejpam-5894	474	60	0.5	0.5	NUM
ejpam-5894	474	61	,	,	PUNCT
ejpam-5894	474	62	α(b	α(b	NOUN
ejpam-5894	474	63	)	)	PUNCT
ejpam-5894	474	64	=	=	SYM
ejpam-5894	474	65	0.3	0.3	NUM
ejpam-5894	474	66	,	,	PUNCT
ejpam-5894	474	67	β(0	β(0	PROPN
ejpam-5894	474	68	)	)	PUNCT
ejpam-5894	474	69	=	=	SYM
ejpam-5894	474	70	0	0	NUM
ejpam-5894	474	71	,	,	PUNCT
ejpam-5894	474	72	β(a	β(a	PROPN
ejpam-5894	474	73	)	)	PUNCT
ejpam-5894	474	74	=	=	NUM
ejpam-5894	474	75	0.4	0.4	NUM
ejpam-5894	474	76	,	,	PUNCT
ejpam-5894	474	77	β(b	β(b	PUNCT
ejpam-5894	474	78	)	)	PUNCT
ejpam-5894	475	1	=	=	SYM
ejpam-5894	475	2	0.8	0.8	NUM
ejpam-5894	475	3	.	.	PUNCT
ejpam-5894	476	1	therefore	therefore	ADV
ejpam-5894	476	2	,	,	PUNCT
ejpam-5894	476	3	l	l	NOUN
ejpam-5894	476	4	=	=	SYM
ejpam-5894	476	5	(	(	PUNCT
ejpam-5894	476	6	l	l	NOUN
ejpam-5894	476	7	,	,	PUNCT
ejpam-5894	476	8	α	α	X
ejpam-5894	476	9	,	,	PUNCT
ejpam-5894	476	10	β	β	NOUN
ejpam-5894	476	11	)	)	PUNCT
ejpam-5894	476	12	is	be	AUX
ejpam-5894	476	13	an	an	DET
ejpam-5894	476	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	476	15	fuzzy	fuzzy	ADJ
ejpam-5894	476	16	p	p	NOUN
ejpam-5894	476	17	-	-	PUNCT
ejpam-5894	476	18	ideal	ideal	NOUN
ejpam-5894	476	19	of	of	ADP
ejpam-5894	476	20	l	l	NOUN
ejpam-5894	476	21	=	=	SYM
ejpam-5894	476	22	⟨l	⟨l	NOUN
ejpam-5894	476	23	;	;	PUNCT
ejpam-5894	476	24	|	|	ADV
ejpam-5894	476	25	,	,	PUNCT
ejpam-5894	476	26	0⟩.	0⟩.	PROPN
ejpam-5894	476	27	definition	definition	NOUN
ejpam-5894	476	28	17	17	NUM
ejpam-5894	476	29	.	.	PUNCT
ejpam-5894	477	1	let	let	VERB
ejpam-5894	477	2	l	l	NOUN
ejpam-5894	477	3	=	=	SYM
ejpam-5894	477	4	⟨l	⟨l	NOUN
ejpam-5894	477	5	;	;	PUNCT
ejpam-5894	477	6	|	|	ADV
ejpam-5894	477	7	,	,	PUNCT
ejpam-5894	477	8	0⟩	0⟩	PROPN
ejpam-5894	477	9	be	be	VERB
ejpam-5894	477	10	a	a	DET
ejpam-5894	477	11	wsbg	wsbg	ADV
ejpam-5894	477	12	-	-	PUNCT
ejpam-5894	477	13	algebra	algebra	NOUN
ejpam-5894	477	14	.	.	PUNCT
ejpam-5894	478	1	then	then	ADV
ejpam-5894	478	2	the	the	DET
ejpam-5894	478	3	set	set	NOUN
ejpam-5894	478	4	l+	l+	NOUN
ejpam-5894	478	5	=	=	PUNCT
ejpam-5894	478	6	{	{	PUNCT
ejpam-5894	478	7	ζ	ζ	NOUN
ejpam-5894	478	8	∈	∈	NOUN
ejpam-5894	478	9	l	l	NOUN
ejpam-5894	478	10	:	:	PUNCT
ejpam-5894	478	11	(	(	PUNCT
ejpam-5894	478	12	0|(ζ|ζ))|(0|(ζ|ζ	0|(ζ|ζ))|(0|(ζ|ζ	NOUN
ejpam-5894	478	13	)	)	PUNCT
ejpam-5894	478	14	)	)	PUNCT
ejpam-5894	479	1	=	=	PUNCT
ejpam-5894	479	2	0	0	X
ejpam-5894	479	3	}	}	PUNCT
ejpam-5894	479	4	is	be	AUX
ejpam-5894	479	5	called	call	VERB
ejpam-5894	479	6	the	the	DET
ejpam-5894	479	7	bca	bca	NOUN
ejpam-5894	479	8	-	-	PUNCT
ejpam-5894	479	9	part	part	NOUN
ejpam-5894	479	10	of	of	ADP
ejpam-5894	479	11	l.	l.	PROPN
ejpam-5894	479	12	proposition	proposition	PROPN
ejpam-5894	479	13	5	5	NUM
ejpam-5894	479	14	.	.	PUNCT
ejpam-5894	480	1	let	let	VERB
ejpam-5894	480	2	l	l	NOUN
ejpam-5894	480	3	=	=	SYM
ejpam-5894	480	4	⟨l	⟨l	NOUN
ejpam-5894	480	5	;	;	PUNCT
ejpam-5894	480	6	|	|	ADV
ejpam-5894	480	7	,	,	PUNCT
ejpam-5894	480	8	0⟩	0⟩	PROPN
ejpam-5894	480	9	be	be	VERB
ejpam-5894	480	10	a	a	DET
ejpam-5894	480	11	wsbg	wsbg	ADV
ejpam-5894	480	12	-	-	PUNCT
ejpam-5894	480	13	algebra	algebra	NOUN
ejpam-5894	480	14	.	.	PUNCT
ejpam-5894	481	1	then	then	ADV
ejpam-5894	481	2	l+	l+	PUNCT
ejpam-5894	481	3	is	be	AUX
ejpam-5894	481	4	a	a	DET
ejpam-5894	481	5	wsbg	wsbg	NOUN
ejpam-5894	481	6	-	-	PUNCT
ejpam-5894	481	7	subalgebra	subalgebra	NOUN
ejpam-5894	481	8	of	of	ADP
ejpam-5894	481	9	l.	l.	PROPN
ejpam-5894	481	10	proof	proof	NOUN
ejpam-5894	481	11	.	.	PUNCT
ejpam-5894	482	1	by	by	ADP
ejpam-5894	482	2	(	(	PUNCT
ejpam-5894	482	3	sbg1	sbg1	PROPN
ejpam-5894	482	4	)	)	PUNCT
ejpam-5894	482	5	,	,	PUNCT
ejpam-5894	482	6	(	(	PUNCT
ejpam-5894	482	7	0|(0|0))|(0|(0|0	0|(0|0))|(0|(0|0	NUM
ejpam-5894	482	8	)	)	PUNCT
ejpam-5894	482	9	)	)	PUNCT
ejpam-5894	482	10	=	=	PUNCT
ejpam-5894	483	1	0	0	X
ejpam-5894	483	2	.	.	PUNCT
ejpam-5894	484	1	then	then	ADV
ejpam-5894	484	2	0	0	NUM
ejpam-5894	484	3	∈	∈	NOUN
ejpam-5894	484	4	l+	l+	PUNCT
ejpam-5894	484	5	̸=	̸=	PROPN
ejpam-5894	484	6	∅.	∅.	ADV
ejpam-5894	484	7	let	let	VERB
ejpam-5894	484	8	a	a	DET
ejpam-5894	484	9	,	,	PUNCT
ejpam-5894	484	10	b	b	PROPN
ejpam-5894	484	11	∈	∈	PROPN
ejpam-5894	484	12	l+	l+	NOUN
ejpam-5894	484	13	.	.	PUNCT
ejpam-5894	485	1	then	then	ADV
ejpam-5894	485	2	(	(	PUNCT
ejpam-5894	485	3	0|(a|a))|(0|(a|a	0|(a|a))|(0|(a|a	NOUN
ejpam-5894	485	4	)	)	PUNCT
ejpam-5894	485	5	)	)	PUNCT
ejpam-5894	486	1	=	=	SYM
ejpam-5894	486	2	0	0	NUM
ejpam-5894	486	3	,	,	PUNCT
ejpam-5894	486	4	(	(	PUNCT
ejpam-5894	486	5	28	28	NUM
ejpam-5894	486	6	)	)	PUNCT
ejpam-5894	486	7	(	(	PUNCT
ejpam-5894	486	8	0|(b|b))|(0|(b|b	0|(b|b))|(0|(b|b	NOUN
ejpam-5894	486	9	)	)	PUNCT
ejpam-5894	486	10	)	)	PUNCT
ejpam-5894	487	1	=	=	PUNCT
ejpam-5894	487	2	0	0	X
ejpam-5894	487	3	.	.	PUNCT
ejpam-5894	488	1	(	(	PUNCT
ejpam-5894	488	2	29	29	NUM
ejpam-5894	488	3	)	)	PUNCT
ejpam-5894	488	4	assume	assume	VERB
ejpam-5894	488	5	that	that	SCONJ
ejpam-5894	488	6	(	(	PUNCT
ejpam-5894	488	7	0|(((a|(b|b))|(a|(b|b)))|((a|(b|b))|(a|(b|b)))))|	0|(((a|(b|b))|(a|(b|b)))|((a|(b|b))|(a|(b|b)))))|	NUM
ejpam-5894	488	8	(	(	PUNCT
ejpam-5894	488	9	0|(((a|(b|b))|(a|(b|b)))|((a|(b|b))|(a|(b|b	0|(((a|(b|b))|(a|(b|b)))|((a|(b|b))|(a|(b|b	NOUN
ejpam-5894	488	10	)	)	PUNCT
ejpam-5894	488	11	)	)	PUNCT
ejpam-5894	488	12	)	)	PUNCT
ejpam-5894	488	13	)	)	PUNCT
ejpam-5894	488	14	)	)	PUNCT
ejpam-5894	488	15	̸=	̸=	PROPN
ejpam-5894	488	16	0	0	NUM
ejpam-5894	488	17	.	.	PUNCT
ejpam-5894	489	1	(	(	PUNCT
ejpam-5894	489	2	30	30	NUM
ejpam-5894	489	3	)	)	PUNCT
ejpam-5894	489	4	by	by	ADP
ejpam-5894	489	5	(	(	PUNCT
ejpam-5894	489	6	sbg1	sbg1	PROPN
ejpam-5894	489	7	)	)	PUNCT
ejpam-5894	489	8	and	and	CCONJ
ejpam-5894	489	9	(	(	PUNCT
ejpam-5894	489	10	sbg2	sbg2	PROPN
ejpam-5894	489	11	)	)	PUNCT
ejpam-5894	489	12	,	,	PUNCT
ejpam-5894	489	13	we	we	PRON
ejpam-5894	489	14	have	have	VERB
ejpam-5894	489	15	(	(	PUNCT
ejpam-5894	489	16	0|(x|x))|0	0|(x|x))|0	NOUN
ejpam-5894	489	17	=	=	PUNCT
ejpam-5894	489	18	x|x	x|x	PROPN
ejpam-5894	489	19	.	.	PUNCT
ejpam-5894	490	1	(	(	PUNCT
ejpam-5894	490	2	31	31	NUM
ejpam-5894	490	3	)	)	PUNCT
ejpam-5894	490	4	by	by	ADP
ejpam-5894	490	5	(	(	PUNCT
ejpam-5894	490	6	sbg2	sbg2	ADJ
ejpam-5894	490	7	)	)	PUNCT
ejpam-5894	490	8	and	and	CCONJ
ejpam-5894	490	9	(	(	PUNCT
ejpam-5894	490	10	28	28	NUM
ejpam-5894	490	11	)	)	PUNCT
ejpam-5894	490	12	,	,	PUNCT
ejpam-5894	490	13	we	we	PRON
ejpam-5894	490	14	have	have	VERB
ejpam-5894	490	15	(	(	PUNCT
ejpam-5894	490	16	0|(a|a))|0	0|(a|a))|0	X
ejpam-5894	490	17	=	=	SYM
ejpam-5894	490	18	0|0	0|0	PROPN
ejpam-5894	490	19	.	.	PUNCT
ejpam-5894	491	1	(	(	PUNCT
ejpam-5894	491	2	32	32	NUM
ejpam-5894	491	3	)	)	PUNCT
ejpam-5894	491	4	combining	combine	VERB
ejpam-5894	491	5	(	(	PUNCT
ejpam-5894	491	6	31	31	NUM
ejpam-5894	491	7	)	)	PUNCT
ejpam-5894	491	8	and	and	CCONJ
ejpam-5894	491	9	(	(	PUNCT
ejpam-5894	491	10	32	32	NUM
ejpam-5894	491	11	)	)	PUNCT
ejpam-5894	491	12	,	,	PUNCT
ejpam-5894	491	13	we	we	PRON
ejpam-5894	491	14	have	have	VERB
ejpam-5894	491	15	a|a	a|a	NOUN
ejpam-5894	492	1	=	=	SYM
ejpam-5894	492	2	0|0	0|0	NUM
ejpam-5894	492	3	.	.	PUNCT
ejpam-5894	493	1	(	(	PUNCT
ejpam-5894	493	2	33	33	NUM
ejpam-5894	493	3	)	)	PUNCT
ejpam-5894	493	4	by	by	ADP
ejpam-5894	493	5	(	(	PUNCT
ejpam-5894	493	6	sbg2	sbg2	ADJ
ejpam-5894	493	7	)	)	PUNCT
ejpam-5894	493	8	and	and	CCONJ
ejpam-5894	493	9	(	(	PUNCT
ejpam-5894	493	10	29	29	NUM
ejpam-5894	493	11	)	)	PUNCT
ejpam-5894	493	12	,	,	PUNCT
ejpam-5894	493	13	we	we	PRON
ejpam-5894	493	14	have	have	VERB
ejpam-5894	493	15	(	(	PUNCT
ejpam-5894	493	16	0|(b|b))|0	0|(b|b))|0	NOUN
ejpam-5894	493	17	=	=	SYM
ejpam-5894	493	18	0|0	0|0	NUM
ejpam-5894	493	19	.	.	PUNCT
ejpam-5894	494	1	(	(	PUNCT
ejpam-5894	494	2	34	34	NUM
ejpam-5894	494	3	)	)	PUNCT
ejpam-5894	494	4	t.	t.	NOUN
ejpam-5894	494	5	oner	oner	NOUN
ejpam-5894	494	6	et	et	PROPN
ejpam-5894	494	7	al	al	PROPN
ejpam-5894	494	8	.	.	PUNCT
ejpam-5894	494	9	/	/	SYM
ejpam-5894	494	10	eur	eur	PROPN
ejpam-5894	494	11	.	.	PUNCT
ejpam-5894	495	1	j.	j.	PROPN
ejpam-5894	495	2	pure	pure	PROPN
ejpam-5894	495	3	appl	appl	PROPN
ejpam-5894	495	4	.	.	PROPN
ejpam-5894	495	5	math	math	PROPN
ejpam-5894	495	6	,	,	PUNCT
ejpam-5894	495	7	18	18	NUM
ejpam-5894	495	8	(	(	PUNCT
ejpam-5894	495	9	3	3	NUM
ejpam-5894	495	10	)	)	PUNCT
ejpam-5894	495	11	(	(	PUNCT
ejpam-5894	495	12	2025	2025	NUM
ejpam-5894	495	13	)	)	PUNCT
ejpam-5894	495	14	,	,	PUNCT
ejpam-5894	495	15	5894	5894	NUM
ejpam-5894	495	16	26	26	NUM
ejpam-5894	495	17	of	of	ADP
ejpam-5894	495	18	33	33	NUM
ejpam-5894	495	19	combining	combine	VERB
ejpam-5894	495	20	(	(	PUNCT
ejpam-5894	495	21	31	31	NUM
ejpam-5894	495	22	)	)	PUNCT
ejpam-5894	495	23	and	and	CCONJ
ejpam-5894	495	24	(	(	PUNCT
ejpam-5894	495	25	34	34	NUM
ejpam-5894	495	26	)	)	PUNCT
ejpam-5894	495	27	,	,	PUNCT
ejpam-5894	495	28	we	we	PRON
ejpam-5894	495	29	have	have	VERB
ejpam-5894	495	30	b|b	b|b	NOUN
ejpam-5894	495	31	=	=	SYM
ejpam-5894	495	32	0|0	0|0	PROPN
ejpam-5894	495	33	.	.	PUNCT
ejpam-5894	496	1	(	(	PUNCT
ejpam-5894	496	2	35	35	NUM
ejpam-5894	496	3	)	)	PUNCT
ejpam-5894	496	4	by	by	ADP
ejpam-5894	496	5	(	(	PUNCT
ejpam-5894	496	6	30	30	NUM
ejpam-5894	496	7	)	)	PUNCT
ejpam-5894	496	8	and	and	CCONJ
ejpam-5894	496	9	(	(	PUNCT
ejpam-5894	496	10	35	35	NUM
ejpam-5894	496	11	)	)	PUNCT
ejpam-5894	496	12	,	,	PUNCT
ejpam-5894	496	13	we	we	PRON
ejpam-5894	496	14	have	have	VERB
ejpam-5894	496	15	(	(	PUNCT
ejpam-5894	496	16	0|(((a|(0|0))|(a|(0|0)))|((a|(0|0))|(a|(0|0)))))|	0|(((a|(0|0))|(a|(0|0)))|((a|(0|0))|(a|(0|0)))))|	PROPN
ejpam-5894	496	17	(	(	PUNCT
ejpam-5894	496	18	0|(((a|(0|0))|(a|(0|0)))|((a|(0|0))|(a|(0|0	0|(((a|(0|0))|(a|(0|0)))|((a|(0|0))|(a|(0|0	NOUN
ejpam-5894	496	19	)	)	PUNCT
ejpam-5894	496	20	)	)	PUNCT
ejpam-5894	496	21	)	)	PUNCT
ejpam-5894	496	22	)	)	PUNCT
ejpam-5894	496	23	)	)	PUNCT
ejpam-5894	497	1	̸=	̸=	PROPN
ejpam-5894	497	2	0	0	NUM
ejpam-5894	497	3	.	.	PUNCT
ejpam-5894	498	1	(	(	PUNCT
ejpam-5894	498	2	36	36	NUM
ejpam-5894	498	3	)	)	PUNCT
ejpam-5894	498	4	by	by	ADP
ejpam-5894	498	5	(	(	PUNCT
ejpam-5894	498	6	33	33	NUM
ejpam-5894	498	7	)	)	PUNCT
ejpam-5894	498	8	and	and	CCONJ
ejpam-5894	498	9	(	(	PUNCT
ejpam-5894	498	10	sbg1	sbg1	PROPN
ejpam-5894	498	11	)	)	PUNCT
ejpam-5894	498	12	,	,	PUNCT
ejpam-5894	498	13	we	we	PRON
ejpam-5894	498	14	have	have	VERB
ejpam-5894	498	15	(	(	PUNCT
ejpam-5894	498	16	a|(0|0))|(a|(a|a	a|(0|0))|(a|(a|a	PROPN
ejpam-5894	498	17	)	)	PUNCT
ejpam-5894	498	18	)	)	PUNCT
ejpam-5894	499	1	=	=	PUNCT
ejpam-5894	499	2	0	0	X
ejpam-5894	499	3	.	.	PUNCT
ejpam-5894	500	1	(	(	PUNCT
ejpam-5894	500	2	37	37	NUM
ejpam-5894	500	3	)	)	PUNCT
ejpam-5894	500	4	by	by	ADP
ejpam-5894	500	5	(	(	PUNCT
ejpam-5894	500	6	33	33	NUM
ejpam-5894	500	7	)	)	PUNCT
ejpam-5894	500	8	and	and	CCONJ
ejpam-5894	500	9	(	(	PUNCT
ejpam-5894	500	10	37	37	NUM
ejpam-5894	500	11	)	)	PUNCT
ejpam-5894	500	12	,	,	PUNCT
ejpam-5894	500	13	we	we	PRON
ejpam-5894	500	14	have	have	VERB
ejpam-5894	500	15	(	(	PUNCT
ejpam-5894	500	16	a|(0|0))|(a|(0|0	a|(0|0))|(a|(0|0	PROPN
ejpam-5894	500	17	)	)	PUNCT
ejpam-5894	500	18	)	)	PUNCT
ejpam-5894	501	1	=	=	PUNCT
ejpam-5894	501	2	0	0	X
ejpam-5894	501	3	.	.	PUNCT
ejpam-5894	502	1	(	(	PUNCT
ejpam-5894	502	2	38	38	NUM
ejpam-5894	502	3	)	)	PUNCT
ejpam-5894	502	4	by	by	ADP
ejpam-5894	502	5	(	(	PUNCT
ejpam-5894	502	6	38	38	NUM
ejpam-5894	502	7	)	)	PUNCT
ejpam-5894	502	8	and	and	CCONJ
ejpam-5894	502	9	(	(	PUNCT
ejpam-5894	502	10	36	36	NUM
ejpam-5894	502	11	)	)	PUNCT
ejpam-5894	502	12	,	,	PUNCT
ejpam-5894	502	13	we	we	PRON
ejpam-5894	502	14	have	have	VERB
ejpam-5894	502	15	(	(	PUNCT
ejpam-5894	502	16	0|(0|((a|(0|0))|(a|(0|0)))))|	0|(0|((a|(0|0))|(a|(0|0)))))|	X
ejpam-5894	502	17	(	(	PUNCT
ejpam-5894	502	18	0|(((a|(0|0))|(a|(0|0)))|((a|(0|0))|(a|(0|0	0|(((a|(0|0))|(a|(0|0)))|((a|(0|0))|(a|(0|0	NOUN
ejpam-5894	502	19	)	)	PUNCT
ejpam-5894	502	20	)	)	PUNCT
ejpam-5894	502	21	)	)	PUNCT
ejpam-5894	502	22	)	)	PUNCT
ejpam-5894	502	23	)	)	PUNCT
ejpam-5894	503	1	̸=	̸=	PROPN
ejpam-5894	503	2	0	0	NUM
ejpam-5894	503	3	.	.	PUNCT
ejpam-5894	504	1	(	(	PUNCT
ejpam-5894	504	2	39	39	NUM
ejpam-5894	504	3	)	)	PUNCT
ejpam-5894	504	4	by	by	ADP
ejpam-5894	504	5	(	(	PUNCT
ejpam-5894	504	6	38	38	NUM
ejpam-5894	504	7	)	)	PUNCT
ejpam-5894	504	8	and	and	CCONJ
ejpam-5894	504	9	(	(	PUNCT
ejpam-5894	504	10	39	39	NUM
ejpam-5894	504	11	)	)	PUNCT
ejpam-5894	504	12	,	,	PUNCT
ejpam-5894	504	13	we	we	PRON
ejpam-5894	504	14	have	have	VERB
ejpam-5894	504	15	(	(	PUNCT
ejpam-5894	504	16	0|(0|0))|	0|(0|0))|	X
ejpam-5894	504	17	(	(	PUNCT
ejpam-5894	504	18	0|(((a|(0|0))|(a|(0|0)))|((a|(0|0))|(a|(0|0	0|(((a|(0|0))|(a|(0|0)))|((a|(0|0))|(a|(0|0	NOUN
ejpam-5894	504	19	)	)	PUNCT
ejpam-5894	504	20	)	)	PUNCT
ejpam-5894	504	21	)	)	PUNCT
ejpam-5894	504	22	)	)	PUNCT
ejpam-5894	504	23	)	)	PUNCT
ejpam-5894	505	1	̸=	̸=	PROPN
ejpam-5894	505	2	0	0	NUM
ejpam-5894	505	3	.	.	PUNCT
ejpam-5894	506	1	(	(	PUNCT
ejpam-5894	506	2	40	40	NUM
ejpam-5894	506	3	)	)	PUNCT
ejpam-5894	506	4	by	by	ADP
ejpam-5894	506	5	(	(	PUNCT
ejpam-5894	506	6	38	38	NUM
ejpam-5894	506	7	)	)	PUNCT
ejpam-5894	506	8	and	and	CCONJ
ejpam-5894	506	9	(	(	PUNCT
ejpam-5894	506	10	40	40	NUM
ejpam-5894	506	11	)	)	PUNCT
ejpam-5894	506	12	,	,	PUNCT
ejpam-5894	506	13	we	we	PRON
ejpam-5894	506	14	have	have	VERB
ejpam-5894	506	15	(	(	PUNCT
ejpam-5894	506	16	0|(0|0))|	0|(0|0))|	X
ejpam-5894	506	17	(	(	PUNCT
ejpam-5894	506	18	0|(0|((a|(0|0))|(a|(0|0	0|(0|((a|(0|0))|(a|(0|0	NOUN
ejpam-5894	506	19	)	)	PUNCT
ejpam-5894	506	20	)	)	PUNCT
ejpam-5894	506	21	)	)	PUNCT
ejpam-5894	506	22	)	)	PUNCT
ejpam-5894	506	23	)	)	PUNCT
ejpam-5894	507	1	̸=	̸=	PROPN
ejpam-5894	507	2	0	0	NUM
ejpam-5894	507	3	.	.	PUNCT
ejpam-5894	508	1	(	(	PUNCT
ejpam-5894	508	2	41	41	NUM
ejpam-5894	508	3	)	)	PUNCT
ejpam-5894	508	4	by	by	ADP
ejpam-5894	508	5	(	(	PUNCT
ejpam-5894	508	6	38	38	NUM
ejpam-5894	508	7	)	)	PUNCT
ejpam-5894	508	8	and	and	CCONJ
ejpam-5894	508	9	(	(	PUNCT
ejpam-5894	508	10	41	41	NUM
ejpam-5894	508	11	)	)	PUNCT
ejpam-5894	508	12	,	,	PUNCT
ejpam-5894	508	13	we	we	PRON
ejpam-5894	508	14	have	have	VERB
ejpam-5894	508	15	(	(	PUNCT
ejpam-5894	508	16	0|(0|0))|(0|(0|0	0|(0|0))|(0|(0|0	NUM
ejpam-5894	508	17	)	)	PUNCT
ejpam-5894	508	18	)	)	PUNCT
ejpam-5894	509	1	̸=	̸=	PROPN
ejpam-5894	509	2	0	0	NUM
ejpam-5894	509	3	.	.	PUNCT
ejpam-5894	510	1	(	(	PUNCT
ejpam-5894	510	2	42	42	NUM
ejpam-5894	510	3	)	)	PUNCT
ejpam-5894	510	4	by	by	ADP
ejpam-5894	510	5	(	(	PUNCT
ejpam-5894	510	6	42	42	NUM
ejpam-5894	510	7	)	)	PUNCT
ejpam-5894	510	8	and	and	CCONJ
ejpam-5894	510	9	(	(	PUNCT
ejpam-5894	510	10	sbg1	sbg1	PROPN
ejpam-5894	510	11	)	)	PUNCT
ejpam-5894	510	12	,	,	PUNCT
ejpam-5894	510	13	we	we	PRON
ejpam-5894	510	14	have	have	VERB
ejpam-5894	510	15	0	0	NUM
ejpam-5894	510	16	̸=	̸=	NOUN
ejpam-5894	510	17	0	0	NUM
ejpam-5894	510	18	,	,	PUNCT
ejpam-5894	510	19	which	which	PRON
ejpam-5894	510	20	is	be	AUX
ejpam-5894	510	21	a	a	DET
ejpam-5894	510	22	contradiction	contradiction	NOUN
ejpam-5894	510	23	.	.	PUNCT
ejpam-5894	511	1	so	so	ADV
ejpam-5894	511	2	,	,	PUNCT
ejpam-5894	511	3	(	(	PUNCT
ejpam-5894	511	4	0|(((a|(b|b))|(a|(b|b)))|((a|(b|b))|(a|(b|b)))))|	0|(((a|(b|b))|(a|(b|b)))|((a|(b|b))|(a|(b|b)))))|	NUM
ejpam-5894	511	5	(	(	PUNCT
ejpam-5894	511	6	0|(((a|(b|b))|(a|(b|b)))|((a|(b|b))|(a|(b|b	0|(((a|(b|b))|(a|(b|b)))|((a|(b|b))|(a|(b|b	NOUN
ejpam-5894	511	7	)	)	PUNCT
ejpam-5894	511	8	)	)	PUNCT
ejpam-5894	511	9	)	)	PUNCT
ejpam-5894	511	10	)	)	PUNCT
ejpam-5894	511	11	)	)	PUNCT
ejpam-5894	512	1	=	=	PUNCT
ejpam-5894	512	2	0	0	X
ejpam-5894	512	3	.	.	PUNCT
ejpam-5894	512	4	thus	thus	ADV
ejpam-5894	512	5	,	,	PUNCT
ejpam-5894	512	6	(	(	PUNCT
ejpam-5894	512	7	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5894	512	8	)	)	PUNCT
ejpam-5894	512	9	)	)	PUNCT
ejpam-5894	512	10	∈	∈	PROPN
ejpam-5894	512	11	l+	l+	NOUN
ejpam-5894	512	12	.	.	PUNCT
ejpam-5894	513	1	hence	hence	ADV
ejpam-5894	513	2	,	,	PUNCT
ejpam-5894	513	3	l+	l+	X
ejpam-5894	513	4	is	be	AUX
ejpam-5894	513	5	a	a	DET
ejpam-5894	513	6	wsbg	wsbg	NOUN
ejpam-5894	513	7	-	-	PUNCT
ejpam-5894	513	8	subalgebra	subalgebra	NOUN
ejpam-5894	513	9	of	of	ADP
ejpam-5894	513	10	l.	l.	PROPN
ejpam-5894	513	11	theorem	theorem	PROPN
ejpam-5894	513	12	11	11	NUM
ejpam-5894	513	13	.	.	PUNCT
ejpam-5894	514	1	let	let	VERB
ejpam-5894	514	2	l	l	NOUN
ejpam-5894	514	3	=	=	SYM
ejpam-5894	514	4	⟨l	⟨l	NOUN
ejpam-5894	514	5	;	;	PUNCT
ejpam-5894	514	6	|	|	ADV
ejpam-5894	514	7	,	,	PUNCT
ejpam-5894	514	8	0⟩	0⟩	PROPN
ejpam-5894	514	9	=	=	PRON
ejpam-5894	514	10	l+	l+	PUNCT
ejpam-5894	514	11	be	be	AUX
ejpam-5894	514	12	a	a	DET
ejpam-5894	514	13	wsbg	wsbg	ADV
ejpam-5894	514	14	-	-	PUNCT
ejpam-5894	514	15	algebra	algebra	NOUN
ejpam-5894	514	16	.	.	PUNCT
ejpam-5894	515	1	then	then	ADV
ejpam-5894	515	2	every	every	DET
ejpam-5894	515	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	515	4	fuzzy	fuzzy	ADJ
ejpam-5894	515	5	p	p	NOUN
ejpam-5894	515	6	-	-	PUNCT
ejpam-5894	515	7	ideal	ideal	NOUN
ejpam-5894	515	8	of	of	ADP
ejpam-5894	515	9	l	l	NOUN
ejpam-5894	515	10	is	be	AUX
ejpam-5894	515	11	an	an	DET
ejpam-5894	515	12	intuitionistic	intuitionistic	ADJ
ejpam-5894	515	13	fuzzy	fuzzy	ADJ
ejpam-5894	515	14	implicative	implicative	ADJ
ejpam-5894	515	15	wsbg	wsbg	NOUN
ejpam-5894	515	16	-	-	PUNCT
ejpam-5894	515	17	ideal	ideal	NOUN
ejpam-5894	515	18	of	of	ADP
ejpam-5894	515	19	l.	l.	PROPN
ejpam-5894	515	20	t.	t.	PROPN
ejpam-5894	515	21	oner	oner	PROPN
ejpam-5894	515	22	et	et	PROPN
ejpam-5894	515	23	al	al	PROPN
ejpam-5894	515	24	.	.	PUNCT
ejpam-5894	515	25	/	/	SYM
ejpam-5894	515	26	eur	eur	PROPN
ejpam-5894	515	27	.	.	PUNCT
ejpam-5894	516	1	j.	j.	PROPN
ejpam-5894	516	2	pure	pure	PROPN
ejpam-5894	516	3	appl	appl	PROPN
ejpam-5894	516	4	.	.	PROPN
ejpam-5894	516	5	math	math	PROPN
ejpam-5894	516	6	,	,	PUNCT
ejpam-5894	516	7	18	18	NUM
ejpam-5894	516	8	(	(	PUNCT
ejpam-5894	516	9	3	3	NUM
ejpam-5894	516	10	)	)	PUNCT
ejpam-5894	516	11	(	(	PUNCT
ejpam-5894	516	12	2025	2025	NUM
ejpam-5894	516	13	)	)	PUNCT
ejpam-5894	516	14	,	,	PUNCT
ejpam-5894	516	15	5894	5894	NUM
ejpam-5894	516	16	27	27	NUM
ejpam-5894	516	17	of	of	ADP
ejpam-5894	516	18	33	33	NUM
ejpam-5894	516	19	proof	proof	NOUN
ejpam-5894	516	20	.	.	PUNCT
ejpam-5894	517	1	let	let	VERB
ejpam-5894	517	2	l	l	NOUN
ejpam-5894	517	3	=	=	SYM
ejpam-5894	517	4	(	(	PUNCT
ejpam-5894	517	5	l	l	NOUN
ejpam-5894	517	6	,	,	PUNCT
ejpam-5894	517	7	α	α	X
ejpam-5894	517	8	,	,	PUNCT
ejpam-5894	517	9	β	β	NOUN
ejpam-5894	517	10	)	)	PUNCT
ejpam-5894	517	11	be	be	VERB
ejpam-5894	517	12	an	an	DET
ejpam-5894	517	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	517	14	fuzzy	fuzzy	ADJ
ejpam-5894	517	15	p	p	NOUN
ejpam-5894	517	16	-	-	PUNCT
ejpam-5894	517	17	ideal	ideal	NOUN
ejpam-5894	517	18	of	of	ADP
ejpam-5894	517	19	l	l	NOUN
ejpam-5894	517	20	=	=	SYM
ejpam-5894	517	21	⟨l	⟨l	NOUN
ejpam-5894	517	22	;	;	PUNCT
ejpam-5894	517	23	|	|	ADV
ejpam-5894	517	24	,	,	PUNCT
ejpam-5894	517	25	0⟩.	0⟩.	PROPN
ejpam-5894	517	26	then	then	ADV
ejpam-5894	517	27	α(ζ	α(ζ	PROPN
ejpam-5894	517	28	)	)	PUNCT
ejpam-5894	517	29	≥	≥	NOUN
ejpam-5894	517	30	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|(η|(ζ|ζ))))|	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|(η|(ζ|ζ))))|	X
ejpam-5894	517	31	(	(	PUNCT
ejpam-5894	517	32	(	(	PUNCT
ejpam-5894	517	33	(	(	PUNCT
ejpam-5894	517	34	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|(η|(ζ|ζ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|(η|(ζ|ζ	PROPN
ejpam-5894	517	35	)	)	PUNCT
ejpam-5894	517	36	)	)	PUNCT
ejpam-5894	517	37	)	)	PUNCT
ejpam-5894	517	38	)	)	PUNCT
ejpam-5894	517	39	)	)	PUNCT
ejpam-5894	517	40	)	)	PUNCT
ejpam-5894	517	41	,	,	PUNCT
ejpam-5894	517	42	α(0	α(0	NOUN
ejpam-5894	517	43	)	)	PUNCT
ejpam-5894	517	44	}	}	PUNCT
ejpam-5894	518	1	=	=	SYM
ejpam-5894	518	2	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0))|	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0))|	PROPN
ejpam-5894	518	3	(	(	PUNCT
ejpam-5894	518	4	(	(	PUNCT
ejpam-5894	518	5	(	(	PUNCT
ejpam-5894	518	6	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0	NOUN
ejpam-5894	518	7	)	)	PUNCT
ejpam-5894	518	8	)	)	PUNCT
ejpam-5894	518	9	)	)	PUNCT
ejpam-5894	518	10	)	)	PUNCT
ejpam-5894	518	11	,	,	PUNCT
ejpam-5894	518	12	α(0	α(0	NOUN
ejpam-5894	518	13	)	)	PUNCT
ejpam-5894	518	14	}	}	PUNCT
ejpam-5894	518	15	=	=	SYM
ejpam-5894	518	16	min{α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	min{α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	518	17	)	)	PUNCT
ejpam-5894	518	18	)	)	PUNCT
ejpam-5894	518	19	)	)	PUNCT
ejpam-5894	518	20	)	)	PUNCT
ejpam-5894	518	21	)	)	PUNCT
ejpam-5894	518	22	,	,	PUNCT
ejpam-5894	518	23	α(0	α(0	NOUN
ejpam-5894	518	24	)	)	PUNCT
ejpam-5894	518	25	}	}	PUNCT
ejpam-5894	518	26	=	=	SYM
ejpam-5894	518	27	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	α((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	518	28	)	)	PUNCT
ejpam-5894	518	29	)	)	PUNCT
ejpam-5894	518	30	)	)	PUNCT
ejpam-5894	518	31	)	)	PUNCT
ejpam-5894	518	32	and	and	CCONJ
ejpam-5894	518	33	β(ζ	β(ζ	NUM
ejpam-5894	518	34	)	)	PUNCT
ejpam-5894	518	35	≤	≤	NUM
ejpam-5894	519	1	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|(η|(ζ|ζ))))|	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|(η|(ζ|ζ))))|	NOUN
ejpam-5894	519	2	(	(	PUNCT
ejpam-5894	519	3	(	(	PUNCT
ejpam-5894	519	4	(	(	PUNCT
ejpam-5894	519	5	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|(η|(ζ|ζ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|(η|(ζ|ζ	PROPN
ejpam-5894	519	6	)	)	PUNCT
ejpam-5894	519	7	)	)	PUNCT
ejpam-5894	519	8	)	)	PUNCT
ejpam-5894	519	9	)	)	PUNCT
ejpam-5894	519	10	)	)	PUNCT
ejpam-5894	519	11	)	)	PUNCT
ejpam-5894	519	12	,	,	PUNCT
ejpam-5894	519	13	β(0	β(0	PROPN
ejpam-5894	519	14	)	)	PUNCT
ejpam-5894	519	15	}	}	PUNCT
ejpam-5894	519	16	=	=	SYM
ejpam-5894	520	1	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0))|	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0))|	NOUN
ejpam-5894	520	2	(	(	PUNCT
ejpam-5894	520	3	(	(	PUNCT
ejpam-5894	520	4	(	(	PUNCT
ejpam-5894	520	5	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(0|0	NOUN
ejpam-5894	520	6	)	)	PUNCT
ejpam-5894	520	7	)	)	PUNCT
ejpam-5894	520	8	)	)	PUNCT
ejpam-5894	520	9	)	)	PUNCT
ejpam-5894	520	10	,	,	PUNCT
ejpam-5894	520	11	β(0	β(0	PROPN
ejpam-5894	520	12	)	)	PUNCT
ejpam-5894	520	13	}	}	PUNCT
ejpam-5894	520	14	=	=	SYM
ejpam-5894	520	15	max{β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	max{β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	520	16	)	)	PUNCT
ejpam-5894	520	17	)	)	PUNCT
ejpam-5894	520	18	)	)	PUNCT
ejpam-5894	520	19	)	)	PUNCT
ejpam-5894	520	20	)	)	PUNCT
ejpam-5894	520	21	,	,	PUNCT
ejpam-5894	520	22	β(0	β(0	PROPN
ejpam-5894	520	23	)	)	PUNCT
ejpam-5894	520	24	}	}	PUNCT
ejpam-5894	520	25	=	=	PUNCT
ejpam-5894	520	26	β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	β((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	520	27	)	)	PUNCT
ejpam-5894	520	28	)	)	PUNCT
ejpam-5894	520	29	)	)	PUNCT
ejpam-5894	520	30	)	)	PUNCT
ejpam-5894	520	31	.	.	PUNCT
ejpam-5894	521	1	hence	hence	ADV
ejpam-5894	521	2	,	,	PUNCT
ejpam-5894	521	3	l	l	NOUN
ejpam-5894	521	4	=	=	SYM
ejpam-5894	521	5	(	(	PUNCT
ejpam-5894	521	6	l	l	NOUN
ejpam-5894	521	7	,	,	PUNCT
ejpam-5894	521	8	α	α	X
ejpam-5894	521	9	,	,	PUNCT
ejpam-5894	521	10	β	β	NOUN
ejpam-5894	521	11	)	)	PUNCT
ejpam-5894	521	12	is	be	AUX
ejpam-5894	521	13	an	an	DET
ejpam-5894	521	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	521	15	fuzzy	fuzzy	ADJ
ejpam-5894	521	16	implicative	implicative	ADJ
ejpam-5894	521	17	wsbg	wsbg	NOUN
ejpam-5894	521	18	-	-	PUNCT
ejpam-5894	521	19	ideal	ideal	NOUN
ejpam-5894	521	20	of	of	ADP
ejpam-5894	521	21	l.	l.	PROPN
ejpam-5894	521	22	example	example	PROPN
ejpam-5894	521	23	18	18	NUM
ejpam-5894	521	24	.	.	PUNCT
ejpam-5894	522	1	consider	consider	VERB
ejpam-5894	522	2	the	the	DET
ejpam-5894	522	3	wsbg	wsbg	NOUN
ejpam-5894	522	4	-	-	PUNCT
ejpam-5894	522	5	algebra	algebra	NOUN
ejpam-5894	522	6	l	l	NOUN
ejpam-5894	522	7	=	=	PUNCT
ejpam-5894	522	8	⟨l	⟨l	NOUN
ejpam-5894	522	9	;	;	PUNCT
ejpam-5894	523	1	|	|	ADV
ejpam-5894	523	2	,	,	PUNCT
ejpam-5894	523	3	0⟩	0⟩	PROPN
ejpam-5894	523	4	where	where	SCONJ
ejpam-5894	523	5	l	l	NOUN
ejpam-5894	523	6	=	=	PUNCT
ejpam-5894	523	7	{	{	PUNCT
ejpam-5894	523	8	0	0	NUM
ejpam-5894	523	9	,	,	PUNCT
ejpam-5894	523	10	a	a	DET
ejpam-5894	523	11	,	,	PUNCT
ejpam-5894	523	12	b	b	NOUN
ejpam-5894	523	13	,	,	PUNCT
ejpam-5894	523	14	c	c	NOUN
ejpam-5894	523	15	}	}	PUNCT
ejpam-5894	523	16	with	with	ADP
ejpam-5894	523	17	the	the	DET
ejpam-5894	523	18	following	follow	VERB
ejpam-5894	523	19	operation	operation	NOUN
ejpam-5894	523	20	table	table	NOUN
ejpam-5894	523	21	:	:	PUNCT
ejpam-5894	523	22	|	|	ADV
ejpam-5894	523	23	0	0	PUNCT
ejpam-5894	523	24	a	a	DET
ejpam-5894	523	25	b	b	NOUN
ejpam-5894	523	26	c	c	NOUN
ejpam-5894	523	27	0	0	NUM
ejpam-5894	523	28	0	0	NUM
ejpam-5894	523	29	c	c	PROPN
ejpam-5894	523	30	b	b	PROPN
ejpam-5894	523	31	a	a	DET
ejpam-5894	523	32	a	a	DET
ejpam-5894	523	33	c	c	NOUN
ejpam-5894	523	34	0	0	NUM
ejpam-5894	523	35	b	b	PROPN
ejpam-5894	523	36	b	b	PROPN
ejpam-5894	523	37	b	b	PROPN
ejpam-5894	523	38	b	b	PROPN
ejpam-5894	523	39	b	b	PROPN
ejpam-5894	523	40	0	0	NUM
ejpam-5894	523	41	0	0	NUM
ejpam-5894	523	42	c	c	PROPN
ejpam-5894	523	43	a	a	DET
ejpam-5894	523	44	b	b	PROPN
ejpam-5894	523	45	0	0	NUM
ejpam-5894	523	46	c	c	NOUN
ejpam-5894	523	47	thus	thus	ADV
ejpam-5894	523	48	,	,	PUNCT
ejpam-5894	523	49	l+	l+	X
ejpam-5894	523	50	=	=	PUNCT
ejpam-5894	523	51	{	{	PUNCT
ejpam-5894	523	52	0	0	NUM
ejpam-5894	523	53	,	,	PUNCT
ejpam-5894	523	54	a	a	DET
ejpam-5894	523	55	,	,	PUNCT
ejpam-5894	523	56	b	b	NOUN
ejpam-5894	523	57	}	}	PUNCT
ejpam-5894	523	58	=	=	ADJ
ejpam-5894	523	59	̸	̸	X
ejpam-5894	523	60	l.	l.	NOUN
ejpam-5894	523	61	define	define	VERB
ejpam-5894	523	62	the	the	DET
ejpam-5894	523	63	intuitionistic	intuitionistic	ADJ
ejpam-5894	523	64	fuzzy	fuzzy	ADJ
ejpam-5894	523	65	set	set	NOUN
ejpam-5894	523	66	l	l	NOUN
ejpam-5894	523	67	=	=	SYM
ejpam-5894	523	68	(	(	PUNCT
ejpam-5894	523	69	l	l	NOUN
ejpam-5894	523	70	,	,	PUNCT
ejpam-5894	523	71	α	α	X
ejpam-5894	523	72	,	,	PUNCT
ejpam-5894	523	73	β	β	NOUN
ejpam-5894	523	74	)	)	PUNCT
ejpam-5894	523	75	by	by	ADP
ejpam-5894	523	76	:	:	PUNCT
ejpam-5894	523	77	α(0	α(0	NOUN
ejpam-5894	523	78	)	)	PUNCT
ejpam-5894	523	79	=	=	SYM
ejpam-5894	523	80	1	1	NUM
ejpam-5894	523	81	,	,	PUNCT
ejpam-5894	523	82	α(a	α(a	NOUN
ejpam-5894	523	83	)	)	PUNCT
ejpam-5894	523	84	=	=	SYM
ejpam-5894	523	85	0.7	0.7	NUM
ejpam-5894	523	86	,	,	PUNCT
ejpam-5894	523	87	α(b	α(b	NOUN
ejpam-5894	523	88	)	)	PUNCT
ejpam-5894	523	89	=	=	SYM
ejpam-5894	523	90	0.6	0.6	NUM
ejpam-5894	523	91	,	,	PUNCT
ejpam-5894	523	92	α(c	α(c	PROPN
ejpam-5894	523	93	)	)	PUNCT
ejpam-5894	523	94	=	=	SYM
ejpam-5894	523	95	0.4	0.4	NUM
ejpam-5894	523	96	,	,	PUNCT
ejpam-5894	523	97	β(0	β(0	PROPN
ejpam-5894	523	98	)	)	PUNCT
ejpam-5894	523	99	=	=	SYM
ejpam-5894	523	100	0	0	NUM
ejpam-5894	523	101	,	,	PUNCT
ejpam-5894	523	102	β(a	β(a	PROPN
ejpam-5894	523	103	)	)	PUNCT
ejpam-5894	523	104	=	=	NUM
ejpam-5894	523	105	0.2	0.2	NUM
ejpam-5894	523	106	,	,	PUNCT
ejpam-5894	523	107	β(b	β(b	PUNCT
ejpam-5894	523	108	)	)	PUNCT
ejpam-5894	523	109	=	=	SYM
ejpam-5894	523	110	0.3	0.3	NUM
ejpam-5894	523	111	,	,	PUNCT
ejpam-5894	523	112	β(c	β(c	NUM
ejpam-5894	523	113	)	)	PUNCT
ejpam-5894	523	114	=	=	SYM
ejpam-5894	523	115	0.5	0.5	NUM
ejpam-5894	523	116	.	.	PUNCT
ejpam-5894	524	1	then	then	ADV
ejpam-5894	524	2	l	l	PROPN
ejpam-5894	524	3	is	be	AUX
ejpam-5894	524	4	an	an	DET
ejpam-5894	524	5	intuitionistic	intuitionistic	ADJ
ejpam-5894	524	6	fuzzy	fuzzy	ADJ
ejpam-5894	524	7	p	p	NOUN
ejpam-5894	524	8	-	-	PUNCT
ejpam-5894	524	9	ideal	ideal	NOUN
ejpam-5894	524	10	,	,	PUNCT
ejpam-5894	524	11	but	but	CCONJ
ejpam-5894	524	12	it	it	PRON
ejpam-5894	524	13	is	be	AUX
ejpam-5894	524	14	not	not	PART
ejpam-5894	524	15	an	an	DET
ejpam-5894	524	16	intuitionistic	intuitionistic	ADJ
ejpam-5894	524	17	fuzzy	fuzzy	ADJ
ejpam-5894	524	18	implicative	implicative	ADJ
ejpam-5894	524	19	wsbg	wsbg	NOUN
ejpam-5894	524	20	-	-	PUNCT
ejpam-5894	524	21	ideal	ideal	NOUN
ejpam-5894	524	22	of	of	ADP
ejpam-5894	524	23	l.	l.	PROPN
ejpam-5894	524	24	according	accord	VERB
ejpam-5894	524	25	to	to	ADP
ejpam-5894	524	26	definition	definition	NOUN
ejpam-5894	524	27	10	10	NUM
ejpam-5894	524	28	,	,	PUNCT
ejpam-5894	524	29	for	for	ADP
ejpam-5894	524	30	all	all	DET
ejpam-5894	524	31	ζ	ζ	NOUN
ejpam-5894	524	32	,	,	PUNCT
ejpam-5894	524	33	η	η	PROPN
ejpam-5894	524	34	,	,	PUNCT
ejpam-5894	524	35	θ	θ	PROPN
ejpam-5894	524	36	∈	∈	PROPN
ejpam-5894	524	37	l	l	NOUN
ejpam-5894	524	38	:	:	PUNCT
ejpam-5894	524	39	α(0	α(0	PROPN
ejpam-5894	524	40	)	)	PUNCT
ejpam-5894	524	41	≥	≥	NOUN
ejpam-5894	524	42	α(ζ	α(ζ	PROPN
ejpam-5894	524	43	)	)	PUNCT
ejpam-5894	524	44	≥	≥	NOUN
ejpam-5894	524	45	min{α(φ(ζ	min{α(φ(ζ	PROPN
ejpam-5894	524	46	,	,	PUNCT
ejpam-5894	524	47	η	η	PROPN
ejpam-5894	524	48	,	,	PUNCT
ejpam-5894	524	49	θ	θ	NOUN
ejpam-5894	524	50	)	)	PUNCT
ejpam-5894	524	51	)	)	PUNCT
ejpam-5894	524	52	,	,	PUNCT
ejpam-5894	524	53	α(θ	α(θ	NOUN
ejpam-5894	524	54	)	)	PUNCT
ejpam-5894	524	55	}	}	PUNCT
ejpam-5894	524	56	,	,	PUNCT
ejpam-5894	524	57	and	and	CCONJ
ejpam-5894	524	58	similarly	similarly	ADV
ejpam-5894	524	59	for	for	ADP
ejpam-5894	524	60	β	β	X
ejpam-5894	524	61	,	,	PUNCT
ejpam-5894	524	62	where	where	SCONJ
ejpam-5894	524	63	:	:	PUNCT
ejpam-5894	524	64	φ(ζ	φ(ζ	NOUN
ejpam-5894	524	65	,	,	PUNCT
ejpam-5894	524	66	η	η	NOUN
ejpam-5894	524	67	,	,	PUNCT
ejpam-5894	524	68	θ	θ	NOUN
ejpam-5894	524	69	)	)	PUNCT
ejpam-5894	525	1	=	=	SYM
ejpam-5894	525	2	(	(	PUNCT
ejpam-5894	525	3	(	(	PUNCT
ejpam-5894	525	4	(	(	PUNCT
ejpam-5894	525	5	(	(	PUNCT
ejpam-5894	525	6	(	(	PUNCT
ejpam-5894	525	7	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	525	8	)	)	PUNCT
ejpam-5894	525	9	)	)	PUNCT
ejpam-5894	525	10	)	)	PUNCT
ejpam-5894	525	11	.	.	PUNCT
ejpam-5894	526	1	however	however	ADV
ejpam-5894	526	2	,	,	PUNCT
ejpam-5894	526	3	this	this	DET
ejpam-5894	526	4	condition	condition	NOUN
ejpam-5894	526	5	fails	fail	VERB
ejpam-5894	526	6	at	at	ADP
ejpam-5894	526	7	ζ	ζ	NOUN
ejpam-5894	526	8	=	=	SYM
ejpam-5894	526	9	a	a	PROPN
ejpam-5894	526	10	,	,	PUNCT
ejpam-5894	526	11	η	η	PROPN
ejpam-5894	526	12	=	=	SYM
ejpam-5894	526	13	b	b	PROPN
ejpam-5894	526	14	,	,	PUNCT
ejpam-5894	526	15	θ	θ	PROPN
ejpam-5894	526	16	=	=	SYM
ejpam-5894	526	17	0	0	X
ejpam-5894	526	18	.	.	PUNCT
ejpam-5894	527	1	t.	t.	PROPN
ejpam-5894	527	2	oner	oner	PROPN
ejpam-5894	527	3	et	et	PROPN
ejpam-5894	527	4	al	al	PROPN
ejpam-5894	527	5	.	.	PUNCT
ejpam-5894	527	6	/	/	SYM
ejpam-5894	527	7	eur	eur	PROPN
ejpam-5894	527	8	.	.	PUNCT
ejpam-5894	528	1	j.	j.	PROPN
ejpam-5894	528	2	pure	pure	PROPN
ejpam-5894	528	3	appl	appl	PROPN
ejpam-5894	528	4	.	.	PROPN
ejpam-5894	528	5	math	math	PROPN
ejpam-5894	528	6	,	,	PUNCT
ejpam-5894	528	7	18	18	NUM
ejpam-5894	528	8	(	(	PUNCT
ejpam-5894	528	9	3	3	NUM
ejpam-5894	528	10	)	)	PUNCT
ejpam-5894	528	11	(	(	PUNCT
ejpam-5894	528	12	2025	2025	NUM
ejpam-5894	528	13	)	)	PUNCT
ejpam-5894	528	14	,	,	PUNCT
ejpam-5894	528	15	5894	5894	NUM
ejpam-5894	528	16	28	28	NUM
ejpam-5894	528	17	of	of	ADP
ejpam-5894	528	18	33	33	NUM
ejpam-5894	528	19	definition	definition	NOUN
ejpam-5894	528	20	18	18	NUM
ejpam-5894	528	21	.	.	PUNCT
ejpam-5894	529	1	let	let	VERB
ejpam-5894	529	2	l	l	NOUN
ejpam-5894	529	3	=	=	SYM
ejpam-5894	529	4	(	(	PUNCT
ejpam-5894	529	5	l	l	NOUN
ejpam-5894	529	6	,	,	PUNCT
ejpam-5894	529	7	α	α	X
ejpam-5894	529	8	,	,	PUNCT
ejpam-5894	529	9	β	β	NOUN
ejpam-5894	529	10	)	)	PUNCT
ejpam-5894	529	11	be	be	VERB
ejpam-5894	529	12	an	an	DET
ejpam-5894	529	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	529	14	fuzzy	fuzzy	ADJ
ejpam-5894	529	15	set	set	NOUN
ejpam-5894	529	16	on	on	ADP
ejpam-5894	529	17	a	a	DET
ejpam-5894	529	18	wsbg	wsbg	ADV
ejpam-5894	529	19	-	-	PUNCT
ejpam-5894	529	20	algebra	algebra	NOUN
ejpam-5894	529	21	l	l	NOUN
ejpam-5894	529	22	=	=	PUNCT
ejpam-5894	529	23	⟨l	⟨l	NOUN
ejpam-5894	529	24	;	;	PUNCT
ejpam-5894	529	25	|	|	ADV
ejpam-5894	529	26	,	,	PUNCT
ejpam-5894	529	27	0⟩.	0⟩.	PROPN
ejpam-5894	529	28	for	for	ADP
ejpam-5894	529	29	real	real	ADJ
ejpam-5894	529	30	numbers	number	NOUN
ejpam-5894	529	31	δ	δ	PROPN
ejpam-5894	529	32	,	,	PUNCT
ejpam-5894	529	33	γ	γ	PROPN
ejpam-5894	529	34	∈	∈	NOUN
ejpam-5894	529	35	r	r	NOUN
ejpam-5894	529	36	such	such	ADJ
ejpam-5894	529	37	that	that	PRON
ejpam-5894	529	38	:	:	PUNCT
ejpam-5894	529	39	δ	δ	PROPN
ejpam-5894	529	40	∈	∈	PROPN
ejpam-5894	530	1	[	[	X
ejpam-5894	530	2	±	±	NUM
ejpam-5894	530	3	,	,	PUNCT
ejpam-5894	530	4	0	0	NUM
ejpam-5894	530	5	]	]	PUNCT
ejpam-5894	530	6	:	:	PUNCT
ejpam-5894	530	7	=	=	PUNCT
ejpam-5894	531	1	[	[	X
ejpam-5894	531	2	−r	−r	ADJ
ejpam-5894	531	3	,	,	PUNCT
ejpam-5894	531	4	0	0	NUM
ejpam-5894	531	5	]	]	PUNCT
ejpam-5894	531	6	,	,	PUNCT
ejpam-5894	531	7	γ	γ	PROPN
ejpam-5894	531	8	∈	∈	PROPN
ejpam-5894	531	9	[	[	X
ejpam-5894	531	10	0,∓	0,∓	X
ejpam-5894	531	11	]	]	X
ejpam-5894	531	12	:	:	PUNCT
ejpam-5894	531	13	=	=	SYM
ejpam-5894	532	1	[	[	X
ejpam-5894	532	2	0	0	NUM
ejpam-5894	532	3	,	,	PUNCT
ejpam-5894	532	4	r	r	NOUN
ejpam-5894	532	5	]	]	PUNCT
ejpam-5894	532	6	for	for	ADP
ejpam-5894	532	7	some	some	DET
ejpam-5894	532	8	r	r	NOUN
ejpam-5894	532	9	>	>	X
ejpam-5894	532	10	0	0	NUM
ejpam-5894	532	11	,	,	PUNCT
ejpam-5894	532	12	we	we	PRON
ejpam-5894	532	13	define	define	VERB
ejpam-5894	532	14	the	the	DET
ejpam-5894	532	15	translated	translate	VERB
ejpam-5894	532	16	intuitionistic	intuitionistic	ADJ
ejpam-5894	532	17	fuzzy	fuzzy	ADJ
ejpam-5894	532	18	set	set	NOUN
ejpam-5894	532	19	:	:	PUNCT
ejpam-5894	532	20	lt	lt	PRON
ejpam-5894	532	21	(	(	PUNCT
ejpam-5894	532	22	δ	δ	PROPN
ejpam-5894	532	23	,	,	PUNCT
ejpam-5894	532	24	γ	γ	NOUN
ejpam-5894	532	25	)	)	PUNCT
ejpam-5894	532	26	=	=	SYM
ejpam-5894	532	27	(	(	PUNCT
ejpam-5894	532	28	l	l	NOUN
ejpam-5894	532	29	,	,	PUNCT
ejpam-5894	532	30	α(δ	α(δ	PROPN
ejpam-5894	532	31	,	,	PUNCT
ejpam-5894	532	32	t	t	NOUN
ejpam-5894	532	33	)	)	PUNCT
ejpam-5894	532	34	,	,	PUNCT
ejpam-5894	532	35	β(γ	β(γ	PROPN
ejpam-5894	532	36	,	,	PUNCT
ejpam-5894	532	37	t	t	NOUN
ejpam-5894	532	38	)	)	PUNCT
ejpam-5894	532	39	)	)	PUNCT
ejpam-5894	533	1	where	where	SCONJ
ejpam-5894	533	2	:	:	PUNCT
ejpam-5894	533	3	α(δ	α(δ	PROPN
ejpam-5894	533	4	,	,	PUNCT
ejpam-5894	533	5	t	t	NOUN
ejpam-5894	533	6	)	)	PUNCT
ejpam-5894	533	7	(	(	PUNCT
ejpam-5894	533	8	ζ	ζ	NOUN
ejpam-5894	533	9	)	)	PUNCT
ejpam-5894	533	10	:	:	PUNCT
ejpam-5894	533	11	=	=	PUNCT
ejpam-5894	533	12	α(ζ)−	α(ζ)−	PROPN
ejpam-5894	533	13	δ	δ	PROPN
ejpam-5894	533	14	,	,	PUNCT
ejpam-5894	533	15	β(γ	β(γ	PROPN
ejpam-5894	533	16	,	,	PUNCT
ejpam-5894	533	17	t	t	NOUN
ejpam-5894	533	18	)	)	PUNCT
ejpam-5894	533	19	(	(	PUNCT
ejpam-5894	533	20	ζ	ζ	NOUN
ejpam-5894	533	21	)	)	PUNCT
ejpam-5894	533	22	:	:	PUNCT
ejpam-5894	534	1	=	=	PUNCT
ejpam-5894	534	2	β(ζ)−	β(ζ)−	PUNCT
ejpam-5894	534	3	γ	γ	X
ejpam-5894	534	4	,	,	PUNCT
ejpam-5894	534	5	∀ζ	∀ζ	PROPN
ejpam-5894	534	6	∈	∈	PROPN
ejpam-5894	534	7	l.	l.	NOUN
ejpam-5894	534	8	here	here	ADV
ejpam-5894	534	9	,	,	PUNCT
ejpam-5894	534	10	the	the	DET
ejpam-5894	534	11	superscript	superscript	PROPN
ejpam-5894	534	12	t	t	PROPN
ejpam-5894	534	13	serves	serve	VERB
ejpam-5894	534	14	only	only	ADV
ejpam-5894	534	15	as	as	ADP
ejpam-5894	534	16	a	a	DET
ejpam-5894	534	17	label	label	NOUN
ejpam-5894	534	18	indicating	indicate	VERB
ejpam-5894	534	19	the	the	DET
ejpam-5894	534	20	form	form	NOUN
ejpam-5894	534	21	of	of	ADP
ejpam-5894	534	22	threshold	threshold	NOUN
ejpam-5894	534	23	transformation	transformation	NOUN
ejpam-5894	534	24	.	.	PUNCT
ejpam-5894	535	1	theorem	theorem	NOUN
ejpam-5894	535	2	12	12	NUM
ejpam-5894	535	3	.	.	PUNCT
ejpam-5894	536	1	if	if	SCONJ
ejpam-5894	536	2	an	an	DET
ejpam-5894	536	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	536	4	fuzzy	fuzzy	ADJ
ejpam-5894	536	5	set	set	NOUN
ejpam-5894	536	6	l	l	NOUN
ejpam-5894	536	7	=	=	SYM
ejpam-5894	536	8	(	(	PUNCT
ejpam-5894	536	9	l	l	NOUN
ejpam-5894	536	10	,	,	PUNCT
ejpam-5894	536	11	α	α	X
ejpam-5894	536	12	,	,	PUNCT
ejpam-5894	536	13	β	β	NOUN
ejpam-5894	536	14	)	)	PUNCT
ejpam-5894	536	15	in	in	ADP
ejpam-5894	536	16	a	a	DET
ejpam-5894	536	17	wsbg	wsbg	ADV
ejpam-5894	536	18	-	-	PUNCT
ejpam-5894	536	19	algebra	algebra	NOUN
ejpam-5894	536	20	l	l	NOUN
ejpam-5894	536	21	=	=	PUNCT
ejpam-5894	536	22	⟨l	⟨l	NOUN
ejpam-5894	536	23	;	;	PUNCT
ejpam-5894	536	24	|	|	ADV
ejpam-5894	536	25	,	,	PUNCT
ejpam-5894	536	26	0⟩	0⟩	PROPN
ejpam-5894	536	27	is	be	AUX
ejpam-5894	536	28	an	an	DET
ejpam-5894	536	29	intuitionistic	intuitionistic	ADJ
ejpam-5894	536	30	fuzzy	fuzzy	ADJ
ejpam-5894	536	31	implicative	implicative	ADJ
ejpam-5894	536	32	wsbg	wsbg	NOUN
ejpam-5894	536	33	-	-	PUNCT
ejpam-5894	536	34	ideal	ideal	NOUN
ejpam-5894	536	35	of	of	ADP
ejpam-5894	536	36	l	l	NOUN
ejpam-5894	536	37	,	,	PUNCT
ejpam-5894	536	38	then	then	ADV
ejpam-5894	536	39	for	for	ADP
ejpam-5894	536	40	all	all	DET
ejpam-5894	536	41	(	(	PUNCT
ejpam-5894	536	42	δ	δ	PROPN
ejpam-5894	536	43	,	,	PUNCT
ejpam-5894	536	44	γ	γ	NOUN
ejpam-5894	536	45	)	)	PUNCT
ejpam-5894	536	46	∈	∈	PROPN
ejpam-5894	537	1	[	[	X
ejpam-5894	537	2	±	±	NUM
ejpam-5894	537	3	,	,	PUNCT
ejpam-5894	537	4	0]×	0]×	NUM
ejpam-5894	538	1	[	[	X
ejpam-5894	538	2	0,∓	0,∓	NUM
ejpam-5894	538	3	]	]	X
ejpam-5894	538	4	,	,	PUNCT
ejpam-5894	538	5	an	an	DET
ejpam-5894	538	6	intuitionistic	intuitionistic	ADJ
ejpam-5894	538	7	fuzzy	fuzzy	ADJ
ejpam-5894	538	8	(	(	PUNCT
ejpam-5894	538	9	δ	δ	PROPN
ejpam-5894	538	10	,	,	PUNCT
ejpam-5894	538	11	γ)-translation	γ)-translation	VERB
ejpam-5894	538	12	lt	lt	PRON
ejpam-5894	538	13	(	(	PUNCT
ejpam-5894	538	14	δ	δ	PROPN
ejpam-5894	538	15	,	,	PUNCT
ejpam-5894	538	16	γ	γ	NOUN
ejpam-5894	538	17	)	)	PUNCT
ejpam-5894	538	18	=	=	SYM
ejpam-5894	538	19	(	(	PUNCT
ejpam-5894	538	20	l	l	NOUN
ejpam-5894	538	21	,	,	PUNCT
ejpam-5894	538	22	α(δ	α(δ	PROPN
ejpam-5894	538	23	,	,	PUNCT
ejpam-5894	538	24	t	t	NOUN
ejpam-5894	538	25	)	)	PUNCT
ejpam-5894	538	26	,	,	PUNCT
ejpam-5894	538	27	β(γ	β(γ	PROPN
ejpam-5894	538	28	,	,	PUNCT
ejpam-5894	538	29	t	t	NOUN
ejpam-5894	538	30	)	)	PUNCT
ejpam-5894	538	31	)	)	PUNCT
ejpam-5894	538	32	of	of	ADP
ejpam-5894	538	33	l	l	NOUN
ejpam-5894	538	34	=	=	SYM
ejpam-5894	538	35	(	(	PUNCT
ejpam-5894	538	36	l	l	NOUN
ejpam-5894	538	37	,	,	PUNCT
ejpam-5894	538	38	α	α	X
ejpam-5894	538	39	,	,	PUNCT
ejpam-5894	538	40	β	β	NOUN
ejpam-5894	538	41	)	)	PUNCT
ejpam-5894	538	42	is	be	AUX
ejpam-5894	538	43	an	an	DET
ejpam-5894	538	44	intuitionistic	intuitionistic	ADJ
ejpam-5894	538	45	fuzzy	fuzzy	ADJ
ejpam-5894	538	46	implicative	implicative	ADJ
ejpam-5894	538	47	wsbg	wsbg	NOUN
ejpam-5894	538	48	-	-	PUNCT
ejpam-5894	538	49	ideal	ideal	NOUN
ejpam-5894	538	50	of	of	ADP
ejpam-5894	538	51	l.	l.	PROPN
ejpam-5894	538	52	proof	proof	PROPN
ejpam-5894	538	53	.	.	PUNCT
ejpam-5894	539	1	assume	assume	VERB
ejpam-5894	539	2	that	that	SCONJ
ejpam-5894	539	3	l	l	NOUN
ejpam-5894	539	4	=	=	SYM
ejpam-5894	539	5	(	(	PUNCT
ejpam-5894	539	6	l	l	NOUN
ejpam-5894	539	7	,	,	PUNCT
ejpam-5894	539	8	α	α	X
ejpam-5894	539	9	,	,	PUNCT
ejpam-5894	539	10	β	β	NOUN
ejpam-5894	539	11	)	)	PUNCT
ejpam-5894	539	12	is	be	AUX
ejpam-5894	539	13	an	an	DET
ejpam-5894	539	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	539	15	fuzzy	fuzzy	ADJ
ejpam-5894	539	16	implicative	implicative	ADJ
ejpam-5894	539	17	wsbg	wsbg	NOUN
ejpam-5894	539	18	-	-	PUNCT
ejpam-5894	539	19	ideal	ideal	NOUN
ejpam-5894	539	20	of	of	ADP
ejpam-5894	539	21	l	l	NOUN
ejpam-5894	539	22	=	=	SYM
ejpam-5894	539	23	⟨l	⟨l	NOUN
ejpam-5894	539	24	;	;	PUNCT
ejpam-5894	539	25	|	|	ADV
ejpam-5894	539	26	,	,	PUNCT
ejpam-5894	539	27	0⟩.	0⟩.	PROPN
ejpam-5894	539	28	for	for	ADP
ejpam-5894	539	29	any	any	DET
ejpam-5894	539	30	(	(	PUNCT
ejpam-5894	539	31	δ	δ	PROPN
ejpam-5894	539	32	,	,	PUNCT
ejpam-5894	539	33	γ	γ	NOUN
ejpam-5894	539	34	)	)	PUNCT
ejpam-5894	539	35	∈	∈	PROPN
ejpam-5894	540	1	[	[	X
ejpam-5894	540	2	±	±	NUM
ejpam-5894	540	3	,	,	PUNCT
ejpam-5894	540	4	0	0	NUM
ejpam-5894	540	5	]	]	X
ejpam-5894	540	6	×	×	NOUN
ejpam-5894	541	1	[	[	X
ejpam-5894	541	2	0,∓	0,∓	X
ejpam-5894	541	3	]	]	X
ejpam-5894	541	4	and	and	CCONJ
ejpam-5894	541	5	for	for	ADP
ejpam-5894	541	6	all	all	DET
ejpam-5894	541	7	ζ	ζ	NOUN
ejpam-5894	541	8	∈	∈	PROPN
ejpam-5894	541	9	l	l	NOUN
ejpam-5894	541	10	,	,	PUNCT
ejpam-5894	541	11	we	we	PRON
ejpam-5894	541	12	have	have	VERB
ejpam-5894	541	13	α(0	α(0	PROPN
ejpam-5894	541	14	)	)	PUNCT
ejpam-5894	541	15	≥	≥	NOUN
ejpam-5894	541	16	α(ζ	α(ζ	PROPN
ejpam-5894	541	17	)	)	PUNCT
ejpam-5894	541	18	and	and	CCONJ
ejpam-5894	541	19	β(0	β(0	PROPN
ejpam-5894	541	20	)	)	PUNCT
ejpam-5894	541	21	≤	≤	NOUN
ejpam-5894	541	22	β(ζ	β(ζ	PROPN
ejpam-5894	541	23	)	)	PUNCT
ejpam-5894	541	24	.	.	PUNCT
ejpam-5894	542	1	also	also	ADV
ejpam-5894	542	2	,	,	PUNCT
ejpam-5894	542	3	α(δ	α(δ	PROPN
ejpam-5894	542	4	,	,	PUNCT
ejpam-5894	542	5	t	t	NOUN
ejpam-5894	542	6	)	)	PUNCT
ejpam-5894	542	7	(	(	PUNCT
ejpam-5894	542	8	0	0	NUM
ejpam-5894	542	9	)	)	PUNCT
ejpam-5894	542	10	=	=	SYM
ejpam-5894	542	11	α(0)−	α(0)−	NUM
ejpam-5894	542	12	δ	δ	PROPN
ejpam-5894	542	13	≥	≥	NOUN
ejpam-5894	542	14	α(ζ)−	α(ζ)−	PROPN
ejpam-5894	542	15	δ	δ	PROPN
ejpam-5894	542	16	=	=	SYM
ejpam-5894	542	17	α(δ	α(δ	PROPN
ejpam-5894	542	18	,	,	PUNCT
ejpam-5894	542	19	t	t	NOUN
ejpam-5894	542	20	)	)	PUNCT
ejpam-5894	542	21	(	(	PUNCT
ejpam-5894	542	22	ζ	ζ	NOUN
ejpam-5894	542	23	)	)	PUNCT
ejpam-5894	542	24	and	and	CCONJ
ejpam-5894	542	25	β(γ	β(γ	PROPN
ejpam-5894	542	26	,	,	PUNCT
ejpam-5894	542	27	t	t	NOUN
ejpam-5894	542	28	)	)	PUNCT
ejpam-5894	542	29	(	(	PUNCT
ejpam-5894	542	30	0	0	NUM
ejpam-5894	542	31	)	)	PUNCT
ejpam-5894	542	32	=	=	SYM
ejpam-5894	543	1	β(0)−	β(0)−	NUM
ejpam-5894	543	2	γ	γ	X
ejpam-5894	543	3	≤	≤	NOUN
ejpam-5894	543	4	β(ζ)−	β(ζ)−	PROPN
ejpam-5894	543	5	γ	γ	X
ejpam-5894	543	6	=	=	SYM
ejpam-5894	543	7	β(γ	β(γ	NOUN
ejpam-5894	543	8	,	,	PUNCT
ejpam-5894	543	9	t	t	NOUN
ejpam-5894	543	10	)	)	PUNCT
ejpam-5894	543	11	(	(	PUNCT
ejpam-5894	543	12	ζ	ζ	NOUN
ejpam-5894	543	13	)	)	PUNCT
ejpam-5894	543	14	.	.	PUNCT
ejpam-5894	544	1	next	next	ADV
ejpam-5894	544	2	,	,	PUNCT
ejpam-5894	544	3	let	let	VERB
ejpam-5894	544	4	ζ	ζ	NOUN
ejpam-5894	544	5	,	,	PUNCT
ejpam-5894	544	6	η	η	PROPN
ejpam-5894	544	7	,	,	PUNCT
ejpam-5894	544	8	θ	θ	PROPN
ejpam-5894	544	9	∈	∈	PROPN
ejpam-5894	544	10	l.	l.	PROPN
ejpam-5894	544	11	then	then	ADV
ejpam-5894	544	12	α(ζ	α(ζ	PROPN
ejpam-5894	544	13	)	)	PUNCT
ejpam-5894	544	14	≥	≥	NOUN
ejpam-5894	544	15	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NUM
ejpam-5894	544	16	)	)	PUNCT
ejpam-5894	544	17	)	)	PUNCT
ejpam-5894	544	18	)	)	PUNCT
ejpam-5894	544	19	)	)	PUNCT
ejpam-5894	544	20	,	,	PUNCT
ejpam-5894	544	21	α(θ	α(θ	NOUN
ejpam-5894	544	22	)	)	PUNCT
ejpam-5894	544	23	}	}	PUNCT
ejpam-5894	544	24	and	and	CCONJ
ejpam-5894	544	25	β(ζ	β(ζ	NUM
ejpam-5894	544	26	)	)	PUNCT
ejpam-5894	544	27	≤	≤	NOUN
ejpam-5894	544	28	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	544	29	)	)	PUNCT
ejpam-5894	544	30	)	)	PUNCT
ejpam-5894	544	31	)	)	PUNCT
ejpam-5894	544	32	)	)	PUNCT
ejpam-5894	544	33	,	,	PUNCT
ejpam-5894	544	34	β(θ	β(θ	NUM
ejpam-5894	544	35	)	)	PUNCT
ejpam-5894	544	36	}	}	PUNCT
ejpam-5894	544	37	.	.	PUNCT
ejpam-5894	545	1	therefore	therefore	ADV
ejpam-5894	545	2	,	,	PUNCT
ejpam-5894	545	3	α(δ	α(δ	PROPN
ejpam-5894	545	4	,	,	PUNCT
ejpam-5894	545	5	t	t	NOUN
ejpam-5894	545	6	)	)	PUNCT
ejpam-5894	545	7	(	(	PUNCT
ejpam-5894	545	8	ζ	ζ	NOUN
ejpam-5894	545	9	)	)	PUNCT
ejpam-5894	545	10	=	=	PUNCT
ejpam-5894	546	1	α(ζ)−	α(ζ)−	PROPN
ejpam-5894	546	2	δ	δ	PROPN
ejpam-5894	546	3	≥	≥	NOUN
ejpam-5894	546	4	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NUM
ejpam-5894	546	5	)	)	PUNCT
ejpam-5894	546	6	)	)	PUNCT
ejpam-5894	546	7	)	)	PUNCT
ejpam-5894	546	8	)	)	PUNCT
ejpam-5894	546	9	,	,	PUNCT
ejpam-5894	546	10	α(θ	α(θ	NOUN
ejpam-5894	546	11	)	)	PUNCT
ejpam-5894	546	12	}	}	PUNCT
ejpam-5894	546	13	−	−	PROPN
ejpam-5894	546	14	δ	δ	PROPN
ejpam-5894	546	15	=	=	SYM
ejpam-5894	546	16	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))))−	min{α(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))))−	PROPN
ejpam-5894	546	17	δ	δ	PROPN
ejpam-5894	546	18	,	,	PUNCT
ejpam-5894	546	19	α(θ)−	α(θ)−	PROPN
ejpam-5894	546	20	δ	δ	PROPN
ejpam-5894	546	21	}	}	PUNCT
ejpam-5894	546	22	=	=	SYM
ejpam-5894	546	23	min{α(δ	min{α(δ	PROPN
ejpam-5894	546	24	,	,	PUNCT
ejpam-5894	546	25	t	t	NOUN
ejpam-5894	546	26	)	)	PUNCT
ejpam-5894	546	27	(	(	PUNCT
ejpam-5894	546	28	(	(	PUNCT
ejpam-5894	546	29	(	(	PUNCT
ejpam-5894	546	30	(	(	PUNCT
ejpam-5894	546	31	(	(	PUNCT
ejpam-5894	546	32	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	546	33	)	)	PUNCT
ejpam-5894	546	34	)	)	PUNCT
ejpam-5894	546	35	)	)	PUNCT
ejpam-5894	546	36	)	)	PUNCT
ejpam-5894	546	37	,	,	PUNCT
ejpam-5894	546	38	α(δ	α(δ	PROPN
ejpam-5894	546	39	,	,	PUNCT
ejpam-5894	546	40	t	t	NOUN
ejpam-5894	546	41	)	)	PUNCT
ejpam-5894	546	42	(	(	PUNCT
ejpam-5894	546	43	θ	θ	NOUN
ejpam-5894	546	44	)	)	PUNCT
ejpam-5894	546	45	}	}	PUNCT
ejpam-5894	546	46	.	.	PUNCT
ejpam-5894	547	1	t.	t.	PROPN
ejpam-5894	547	2	oner	oner	PROPN
ejpam-5894	547	3	et	et	PROPN
ejpam-5894	547	4	al	al	PROPN
ejpam-5894	547	5	.	.	PUNCT
ejpam-5894	547	6	/	/	SYM
ejpam-5894	547	7	eur	eur	PROPN
ejpam-5894	547	8	.	.	PUNCT
ejpam-5894	548	1	j.	j.	PROPN
ejpam-5894	548	2	pure	pure	PROPN
ejpam-5894	548	3	appl	appl	PROPN
ejpam-5894	548	4	.	.	PROPN
ejpam-5894	548	5	math	math	PROPN
ejpam-5894	548	6	,	,	PUNCT
ejpam-5894	548	7	18	18	NUM
ejpam-5894	548	8	(	(	PUNCT
ejpam-5894	548	9	3	3	NUM
ejpam-5894	548	10	)	)	PUNCT
ejpam-5894	548	11	(	(	PUNCT
ejpam-5894	548	12	2025	2025	NUM
ejpam-5894	548	13	)	)	PUNCT
ejpam-5894	548	14	,	,	PUNCT
ejpam-5894	548	15	5894	5894	NUM
ejpam-5894	548	16	29	29	NUM
ejpam-5894	548	17	of	of	ADP
ejpam-5894	548	18	33	33	NUM
ejpam-5894	548	19	similarly	similarly	ADV
ejpam-5894	548	20	,	,	PUNCT
ejpam-5894	548	21	β(γ	β(γ	PROPN
ejpam-5894	548	22	,	,	PUNCT
ejpam-5894	548	23	t	t	NOUN
ejpam-5894	548	24	)	)	PUNCT
ejpam-5894	548	25	(	(	PUNCT
ejpam-5894	548	26	ζ	ζ	NOUN
ejpam-5894	548	27	)	)	PUNCT
ejpam-5894	548	28	=	=	PUNCT
ejpam-5894	549	1	β(ζ)−	β(ζ)−	PROPN
ejpam-5894	549	2	γ	γ	X
ejpam-5894	549	3	≤	≤	NOUN
ejpam-5894	549	4	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	549	5	)	)	PUNCT
ejpam-5894	549	6	)	)	PUNCT
ejpam-5894	549	7	)	)	PUNCT
ejpam-5894	549	8	)	)	PUNCT
ejpam-5894	549	9	,	,	PUNCT
ejpam-5894	549	10	β(θ	β(θ	NUM
ejpam-5894	549	11	)	)	PUNCT
ejpam-5894	549	12	}	}	PUNCT
ejpam-5894	549	13	−	−	ADP
ejpam-5894	549	14	γ	γ	PROPN
ejpam-5894	549	15	=	=	SYM
ejpam-5894	549	16	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))))−	max{β(((((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))))−	PROPN
ejpam-5894	549	17	γ	γ	PROPN
ejpam-5894	549	18	,	,	PUNCT
ejpam-5894	549	19	β(θ)−	β(θ)−	PROPN
ejpam-5894	549	20	γ	γ	PROPN
ejpam-5894	549	21	}	}	PUNCT
ejpam-5894	549	22	=	=	SYM
ejpam-5894	549	23	max{β(γ	max{β(γ	PROPN
ejpam-5894	549	24	,	,	PUNCT
ejpam-5894	549	25	t	t	NOUN
ejpam-5894	549	26	)	)	PUNCT
ejpam-5894	549	27	(	(	PUNCT
ejpam-5894	549	28	(	(	PUNCT
ejpam-5894	549	29	(	(	PUNCT
ejpam-5894	549	30	(	(	PUNCT
ejpam-5894	549	31	(	(	PUNCT
ejpam-5894	549	32	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	549	33	)	)	PUNCT
ejpam-5894	549	34	)	)	PUNCT
ejpam-5894	549	35	)	)	PUNCT
ejpam-5894	549	36	)	)	PUNCT
ejpam-5894	549	37	,	,	PUNCT
ejpam-5894	549	38	β(γ	β(γ	PROPN
ejpam-5894	549	39	,	,	PUNCT
ejpam-5894	549	40	t	t	NOUN
ejpam-5894	549	41	)	)	PUNCT
ejpam-5894	549	42	(	(	PUNCT
ejpam-5894	549	43	θ	θ	NOUN
ejpam-5894	549	44	)	)	PUNCT
ejpam-5894	549	45	}	}	PUNCT
ejpam-5894	549	46	.	.	PUNCT
ejpam-5894	550	1	hence	hence	ADV
ejpam-5894	550	2	,	,	PUNCT
ejpam-5894	550	3	lt	lt	PRON
ejpam-5894	550	4	(	(	PUNCT
ejpam-5894	550	5	δ	δ	PROPN
ejpam-5894	550	6	,	,	PUNCT
ejpam-5894	550	7	γ	γ	NOUN
ejpam-5894	550	8	)	)	PUNCT
ejpam-5894	550	9	=	=	SYM
ejpam-5894	550	10	(	(	PUNCT
ejpam-5894	550	11	l	l	NOUN
ejpam-5894	550	12	,	,	PUNCT
ejpam-5894	550	13	α(δ	α(δ	PROPN
ejpam-5894	550	14	,	,	PUNCT
ejpam-5894	550	15	t	t	NOUN
ejpam-5894	550	16	)	)	PUNCT
ejpam-5894	550	17	,	,	PUNCT
ejpam-5894	550	18	β(γ	β(γ	PROPN
ejpam-5894	550	19	,	,	PUNCT
ejpam-5894	550	20	t	t	NOUN
ejpam-5894	550	21	)	)	PUNCT
ejpam-5894	550	22	)	)	PUNCT
ejpam-5894	550	23	is	be	AUX
ejpam-5894	550	24	an	an	DET
ejpam-5894	550	25	intuitionistic	intuitionistic	ADJ
ejpam-5894	550	26	fuzzy	fuzzy	ADJ
ejpam-5894	550	27	implicative	implicative	ADJ
ejpam-5894	550	28	wsbg	wsbg	NOUN
ejpam-5894	550	29	-	-	PUNCT
ejpam-5894	550	30	ideal	ideal	NOUN
ejpam-5894	550	31	of	of	ADP
ejpam-5894	550	32	l.	l.	PROPN
ejpam-5894	550	33	theorem	theorem	VERB
ejpam-5894	550	34	13	13	NUM
ejpam-5894	550	35	.	.	PUNCT
ejpam-5894	551	1	if	if	SCONJ
ejpam-5894	551	2	there	there	PRON
ejpam-5894	551	3	exists	exist	VERB
ejpam-5894	551	4	(	(	PUNCT
ejpam-5894	551	5	δ	δ	PROPN
ejpam-5894	551	6	,	,	PUNCT
ejpam-5894	551	7	γ	γ	NOUN
ejpam-5894	551	8	)	)	PUNCT
ejpam-5894	551	9	∈	∈	PROPN
ejpam-5894	552	1	[	[	X
ejpam-5894	552	2	±	±	NUM
ejpam-5894	552	3	,	,	PUNCT
ejpam-5894	552	4	0]×	0]×	NUM
ejpam-5894	553	1	[	[	X
ejpam-5894	553	2	0,∓	0,∓	X
ejpam-5894	553	3	]	]	X
ejpam-5894	553	4	such	such	ADJ
ejpam-5894	553	5	that	that	SCONJ
ejpam-5894	553	6	the	the	DET
ejpam-5894	553	7	intuitionistic	intuitionistic	ADJ
ejpam-5894	553	8	fuzzy	fuzzy	ADJ
ejpam-5894	553	9	(	(	PUNCT
ejpam-5894	553	10	δ	δ	PROPN
ejpam-5894	553	11	,	,	PUNCT
ejpam-5894	553	12	γ)translation	γ)translation	NOUN
ejpam-5894	553	13	lt	lt	PRON
ejpam-5894	553	14	(	(	PUNCT
ejpam-5894	553	15	δ	δ	PROPN
ejpam-5894	553	16	,	,	PUNCT
ejpam-5894	553	17	γ	γ	NOUN
ejpam-5894	553	18	)	)	PUNCT
ejpam-5894	553	19	=	=	SYM
ejpam-5894	553	20	(	(	PUNCT
ejpam-5894	553	21	l	l	NOUN
ejpam-5894	553	22	,	,	PUNCT
ejpam-5894	553	23	α(δ	α(δ	PROPN
ejpam-5894	553	24	,	,	PUNCT
ejpam-5894	553	25	t	t	NOUN
ejpam-5894	553	26	)	)	PUNCT
ejpam-5894	553	27	,	,	PUNCT
ejpam-5894	553	28	β(γ	β(γ	PROPN
ejpam-5894	553	29	,	,	PUNCT
ejpam-5894	553	30	t	t	NOUN
ejpam-5894	553	31	)	)	PUNCT
ejpam-5894	553	32	)	)	PUNCT
ejpam-5894	553	33	of	of	ADP
ejpam-5894	553	34	l	l	NOUN
ejpam-5894	553	35	=	=	SYM
ejpam-5894	553	36	(	(	PUNCT
ejpam-5894	553	37	l	l	NOUN
ejpam-5894	553	38	,	,	PUNCT
ejpam-5894	553	39	α	α	X
ejpam-5894	553	40	,	,	PUNCT
ejpam-5894	553	41	β	β	NOUN
ejpam-5894	553	42	)	)	PUNCT
ejpam-5894	553	43	is	be	AUX
ejpam-5894	553	44	an	an	DET
ejpam-5894	553	45	intuitionistic	intuitionistic	ADJ
ejpam-5894	553	46	fuzzy	fuzzy	ADJ
ejpam-5894	553	47	implicative	implicative	ADJ
ejpam-5894	553	48	wsbg	wsbg	NOUN
ejpam-5894	553	49	-	-	PUNCT
ejpam-5894	553	50	ideal	ideal	NOUN
ejpam-5894	553	51	of	of	ADP
ejpam-5894	553	52	a	a	DET
ejpam-5894	553	53	wsbg	wsbg	ADV
ejpam-5894	553	54	-	-	PUNCT
ejpam-5894	553	55	algebra	algebra	NOUN
ejpam-5894	553	56	l	l	NOUN
ejpam-5894	553	57	=	=	PUNCT
ejpam-5894	553	58	⟨l	⟨l	NOUN
ejpam-5894	553	59	;	;	PUNCT
ejpam-5894	553	60	|	|	ADV
ejpam-5894	553	61	,	,	PUNCT
ejpam-5894	553	62	0⟩	0⟩	PROPN
ejpam-5894	553	63	,	,	PUNCT
ejpam-5894	553	64	then	then	ADV
ejpam-5894	553	65	l	l	NOUN
ejpam-5894	553	66	is	be	AUX
ejpam-5894	553	67	also	also	ADV
ejpam-5894	553	68	an	an	DET
ejpam-5894	553	69	intuitionistic	intuitionistic	ADJ
ejpam-5894	553	70	fuzzy	fuzzy	ADJ
ejpam-5894	553	71	implicative	implicative	ADJ
ejpam-5894	553	72	wsbg	wsbg	NOUN
ejpam-5894	553	73	-	-	PUNCT
ejpam-5894	553	74	ideal	ideal	NOUN
ejpam-5894	553	75	of	of	ADP
ejpam-5894	553	76	l.	l.	PROPN
ejpam-5894	553	77	proof	proof	PROPN
ejpam-5894	553	78	.	.	PUNCT
ejpam-5894	554	1	assume	assume	VERB
ejpam-5894	554	2	lt	lt	NOUN
ejpam-5894	554	3	(	(	PUNCT
ejpam-5894	554	4	δ	δ	PROPN
ejpam-5894	554	5	,	,	PUNCT
ejpam-5894	554	6	γ	γ	NOUN
ejpam-5894	554	7	)	)	PUNCT
ejpam-5894	554	8	=	=	SYM
ejpam-5894	554	9	(	(	PUNCT
ejpam-5894	554	10	l	l	NOUN
ejpam-5894	554	11	,	,	PUNCT
ejpam-5894	554	12	α(δ	α(δ	PROPN
ejpam-5894	554	13	,	,	PUNCT
ejpam-5894	554	14	t	t	NOUN
ejpam-5894	554	15	)	)	PUNCT
ejpam-5894	554	16	,	,	PUNCT
ejpam-5894	554	17	β(γ	β(γ	PROPN
ejpam-5894	554	18	,	,	PUNCT
ejpam-5894	554	19	t	t	NOUN
ejpam-5894	554	20	)	)	PUNCT
ejpam-5894	554	21	)	)	PUNCT
ejpam-5894	554	22	is	be	AUX
ejpam-5894	554	23	an	an	DET
ejpam-5894	554	24	intuitionistic	intuitionistic	ADJ
ejpam-5894	554	25	fuzzy	fuzzy	ADJ
ejpam-5894	554	26	implicative	implicative	ADJ
ejpam-5894	554	27	wsbgideal	wsbgideal	NOUN
ejpam-5894	554	28	of	of	ADP
ejpam-5894	554	29	l	l	NOUN
ejpam-5894	554	30	=	=	SYM
ejpam-5894	554	31	⟨l	⟨l	NOUN
ejpam-5894	554	32	;	;	PUNCT
ejpam-5894	554	33	|	|	ADV
ejpam-5894	554	34	,	,	PUNCT
ejpam-5894	554	35	0⟩.	0⟩.	PROPN
ejpam-5894	554	36	then	then	ADV
ejpam-5894	554	37	for	for	ADP
ejpam-5894	554	38	all	all	DET
ejpam-5894	554	39	ζ	ζ	NOUN
ejpam-5894	554	40	∈	∈	PROPN
ejpam-5894	554	41	l	l	NOUN
ejpam-5894	554	42	,	,	PUNCT
ejpam-5894	554	43	α(δ	α(δ	PROPN
ejpam-5894	554	44	,	,	PUNCT
ejpam-5894	554	45	t	t	NOUN
ejpam-5894	554	46	)	)	PUNCT
ejpam-5894	554	47	(	(	PUNCT
ejpam-5894	554	48	0	0	NUM
ejpam-5894	554	49	)	)	PUNCT
ejpam-5894	554	50	=	=	SYM
ejpam-5894	555	1	α(0)−	α(0)−	NUM
ejpam-5894	555	2	δ	δ	PROPN
ejpam-5894	555	3	≥	≥	NOUN
ejpam-5894	555	4	α(δ	α(δ	NUM
ejpam-5894	555	5	,	,	PUNCT
ejpam-5894	555	6	t	t	NOUN
ejpam-5894	555	7	)	)	PUNCT
ejpam-5894	555	8	(	(	PUNCT
ejpam-5894	555	9	ζ	ζ	NOUN
ejpam-5894	555	10	)	)	PUNCT
ejpam-5894	555	11	=	=	PUNCT
ejpam-5894	555	12	α(ζ)−	α(ζ)−	PROPN
ejpam-5894	555	13	δ	δ	PROPN
ejpam-5894	555	14	,	,	PUNCT
ejpam-5894	555	15	β(γ	β(γ	PROPN
ejpam-5894	555	16	,	,	PUNCT
ejpam-5894	555	17	t	t	NOUN
ejpam-5894	555	18	)	)	PUNCT
ejpam-5894	555	19	(	(	PUNCT
ejpam-5894	555	20	0	0	NUM
ejpam-5894	555	21	)	)	PUNCT
ejpam-5894	555	22	=	=	SYM
ejpam-5894	555	23	β(0)−	β(0)−	NUM
ejpam-5894	555	24	γ	γ	X
ejpam-5894	555	25	≤	≤	X
ejpam-5894	555	26	β(γ	β(γ	PROPN
ejpam-5894	555	27	,	,	PUNCT
ejpam-5894	555	28	t	t	NOUN
ejpam-5894	555	29	)	)	PUNCT
ejpam-5894	555	30	(	(	PUNCT
ejpam-5894	555	31	ζ	ζ	NOUN
ejpam-5894	555	32	)	)	PUNCT
ejpam-5894	555	33	=	=	PUNCT
ejpam-5894	555	34	β(ζ)−	β(ζ)−	PROPN
ejpam-5894	555	35	γ	γ	X
ejpam-5894	555	36	.	.	PROPN
ejpam-5894	555	37	for	for	ADP
ejpam-5894	555	38	ζ	ζ	PROPN
ejpam-5894	555	39	,	,	PUNCT
ejpam-5894	555	40	η	η	PROPN
ejpam-5894	555	41	,	,	PUNCT
ejpam-5894	555	42	θ	θ	PROPN
ejpam-5894	555	43	∈	∈	PROPN
ejpam-5894	555	44	l	l	NOUN
ejpam-5894	555	45	,	,	PUNCT
ejpam-5894	555	46	the	the	DET
ejpam-5894	555	47	implicative	implicative	ADJ
ejpam-5894	555	48	condition	condition	NOUN
ejpam-5894	555	49	for	for	ADP
ejpam-5894	555	50	lt	lt	DET
ejpam-5894	555	51	(	(	PUNCT
ejpam-5894	555	52	δ	δ	PROPN
ejpam-5894	555	53	,	,	PUNCT
ejpam-5894	555	54	γ	γ	PROPN
ejpam-5894	555	55	)	)	PUNCT
ejpam-5894	555	56	gives	give	VERB
ejpam-5894	555	57	α(δ	α(δ	PROPN
ejpam-5894	555	58	,	,	PUNCT
ejpam-5894	555	59	t	t	NOUN
ejpam-5894	555	60	)	)	PUNCT
ejpam-5894	555	61	(	(	PUNCT
ejpam-5894	555	62	ζ	ζ	NOUN
ejpam-5894	555	63	)	)	PUNCT
ejpam-5894	555	64	≥	≥	NOUN
ejpam-5894	555	65	min{α(δ	min{α(δ	PROPN
ejpam-5894	555	66	,	,	PUNCT
ejpam-5894	555	67	t	t	NOUN
ejpam-5894	555	68	)	)	PUNCT
ejpam-5894	555	69	(	(	PUNCT
ejpam-5894	555	70	f(ζ	f(ζ	PROPN
ejpam-5894	555	71	,	,	PUNCT
ejpam-5894	555	72	η	η	PROPN
ejpam-5894	555	73	,	,	PUNCT
ejpam-5894	555	74	θ	θ	NOUN
ejpam-5894	555	75	)	)	PUNCT
ejpam-5894	555	76	)	)	PUNCT
ejpam-5894	555	77	,	,	PUNCT
ejpam-5894	555	78	α(δ	α(δ	PROPN
ejpam-5894	555	79	,	,	PUNCT
ejpam-5894	555	80	t	t	NOUN
ejpam-5894	555	81	)	)	PUNCT
ejpam-5894	555	82	(	(	PUNCT
ejpam-5894	555	83	θ	θ	NOUN
ejpam-5894	555	84	)	)	PUNCT
ejpam-5894	555	85	}	}	PUNCT
ejpam-5894	555	86	,	,	PUNCT
ejpam-5894	555	87	where	where	SCONJ
ejpam-5894	555	88	f(ζ	f(ζ	PROPN
ejpam-5894	555	89	,	,	PUNCT
ejpam-5894	555	90	η	η	PROPN
ejpam-5894	555	91	,	,	PUNCT
ejpam-5894	555	92	θ	θ	NOUN
ejpam-5894	555	93	)	)	PUNCT
ejpam-5894	555	94	=	=	SYM
ejpam-5894	555	95	(	(	PUNCT
ejpam-5894	555	96	(	(	PUNCT
ejpam-5894	555	97	(	(	PUNCT
ejpam-5894	555	98	(	(	PUNCT
ejpam-5894	555	99	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|(((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ	NOUN
ejpam-5894	555	100	)	)	PUNCT
ejpam-5894	555	101	)	)	PUNCT
ejpam-5894	555	102	)	)	PUNCT
ejpam-5894	555	103	,	,	PUNCT
ejpam-5894	555	104	expanding	expand	VERB
ejpam-5894	555	105	α(ζ)−	α(ζ)−	PROPN
ejpam-5894	555	106	δ	δ	PROPN
ejpam-5894	555	107	≥	≥	PRON
ejpam-5894	555	108	min{α(f(ζ	min{α(f(ζ	NOUN
ejpam-5894	555	109	,	,	PUNCT
ejpam-5894	555	110	η	η	NOUN
ejpam-5894	555	111	,	,	PUNCT
ejpam-5894	555	112	θ))−	θ))−	VERB
ejpam-5894	555	113	δ	δ	PROPN
ejpam-5894	555	114	,	,	PUNCT
ejpam-5894	555	115	α(θ)−	α(θ)−	PROPN
ejpam-5894	555	116	δ	δ	PROPN
ejpam-5894	555	117	}	}	PUNCT
ejpam-5894	555	118	.	.	PUNCT
ejpam-5894	556	1	adding	add	VERB
ejpam-5894	556	2	δ	δ	PROPN
ejpam-5894	556	3	to	to	ADP
ejpam-5894	556	4	all	all	DET
ejpam-5894	556	5	terms	term	NOUN
ejpam-5894	556	6	,	,	PUNCT
ejpam-5894	556	7	α(ζ	α(ζ	PROPN
ejpam-5894	556	8	)	)	PUNCT
ejpam-5894	556	9	≥	≥	NOUN
ejpam-5894	556	10	min{α(f(ζ	min{α(f(ζ	NOUN
ejpam-5894	556	11	,	,	PUNCT
ejpam-5894	556	12	η	η	NOUN
ejpam-5894	556	13	,	,	PUNCT
ejpam-5894	556	14	θ	θ	NOUN
ejpam-5894	556	15	)	)	PUNCT
ejpam-5894	556	16	)	)	PUNCT
ejpam-5894	556	17	,	,	PUNCT
ejpam-5894	556	18	α(θ	α(θ	NOUN
ejpam-5894	556	19	)	)	PUNCT
ejpam-5894	556	20	}	}	PUNCT
ejpam-5894	556	21	.	.	PUNCT
ejpam-5894	557	1	similarly	similarly	ADV
ejpam-5894	557	2	,	,	PUNCT
ejpam-5894	557	3	for	for	ADP
ejpam-5894	557	4	β	β	X
ejpam-5894	557	5	,	,	PUNCT
ejpam-5894	557	6	β(γ	β(γ	PROPN
ejpam-5894	557	7	,	,	PUNCT
ejpam-5894	557	8	t	t	NOUN
ejpam-5894	557	9	)	)	PUNCT
ejpam-5894	557	10	(	(	PUNCT
ejpam-5894	557	11	ζ	ζ	NOUN
ejpam-5894	557	12	)	)	PUNCT
ejpam-5894	557	13	≤	≤	NOUN
ejpam-5894	557	14	max{β(γ	max{β(γ	PROPN
ejpam-5894	557	15	,	,	PUNCT
ejpam-5894	557	16	t	t	PROPN
ejpam-5894	557	17	)	)	PUNCT
ejpam-5894	557	18	(	(	PUNCT
ejpam-5894	557	19	f(ζ	f(ζ	PROPN
ejpam-5894	557	20	,	,	PUNCT
ejpam-5894	557	21	η	η	PROPN
ejpam-5894	557	22	,	,	PUNCT
ejpam-5894	557	23	θ	θ	NOUN
ejpam-5894	557	24	)	)	PUNCT
ejpam-5894	557	25	)	)	PUNCT
ejpam-5894	557	26	,	,	PUNCT
ejpam-5894	557	27	β(γ	β(γ	PROPN
ejpam-5894	557	28	,	,	PUNCT
ejpam-5894	557	29	t	t	NOUN
ejpam-5894	557	30	)	)	PUNCT
ejpam-5894	557	31	(	(	PUNCT
ejpam-5894	557	32	η	η	NOUN
ejpam-5894	557	33	)	)	PUNCT
ejpam-5894	557	34	}	}	PUNCT
ejpam-5894	557	35	,	,	PUNCT
ejpam-5894	557	36	expanding	expand	VERB
ejpam-5894	557	37	β(ζ)−	β(ζ)−	PRON
ejpam-5894	557	38	γ	γ	NOUN
ejpam-5894	557	39	≤	≤	PROPN
ejpam-5894	557	40	max{β(f(ζ	max{β(f(ζ	PROPN
ejpam-5894	557	41	,	,	PUNCT
ejpam-5894	557	42	η	η	PROPN
ejpam-5894	557	43	,	,	PUNCT
ejpam-5894	557	44	θ))−	θ))−	VERB
ejpam-5894	557	45	γ	γ	PROPN
ejpam-5894	557	46	,	,	PUNCT
ejpam-5894	557	47	β(η)−	β(η)−	PROPN
ejpam-5894	557	48	γ	γ	NOUN
ejpam-5894	557	49	}	}	PUNCT
ejpam-5894	557	50	.	.	PUNCT
ejpam-5894	557	51	adding	add	VERB
ejpam-5894	557	52	γ	γ	PRON
ejpam-5894	557	53	to	to	ADP
ejpam-5894	557	54	all	all	DET
ejpam-5894	557	55	terms	term	NOUN
ejpam-5894	557	56	,	,	PUNCT
ejpam-5894	557	57	β(ζ	β(ζ	NUM
ejpam-5894	557	58	)	)	PUNCT
ejpam-5894	557	59	≤	≤	NUM
ejpam-5894	557	60	max{β(f(ζ	max{β(f(ζ	PROPN
ejpam-5894	557	61	,	,	PUNCT
ejpam-5894	557	62	η	η	PROPN
ejpam-5894	557	63	,	,	PUNCT
ejpam-5894	557	64	θ	θ	NOUN
ejpam-5894	557	65	)	)	PUNCT
ejpam-5894	557	66	)	)	PUNCT
ejpam-5894	557	67	,	,	PUNCT
ejpam-5894	557	68	β(η	β(η	PROPN
ejpam-5894	557	69	)	)	PUNCT
ejpam-5894	557	70	}	}	PUNCT
ejpam-5894	557	71	.	.	PUNCT
ejpam-5894	558	1	thus	thus	ADV
ejpam-5894	558	2	,	,	PUNCT
ejpam-5894	558	3	l	l	NOUN
ejpam-5894	558	4	=	=	SYM
ejpam-5894	558	5	(	(	PUNCT
ejpam-5894	558	6	l	l	NOUN
ejpam-5894	558	7	,	,	PUNCT
ejpam-5894	558	8	α	α	X
ejpam-5894	558	9	,	,	PUNCT
ejpam-5894	558	10	β	β	NOUN
ejpam-5894	558	11	)	)	PUNCT
ejpam-5894	558	12	is	be	AUX
ejpam-5894	558	13	an	an	DET
ejpam-5894	558	14	intuitionistic	intuitionistic	ADJ
ejpam-5894	558	15	fuzzy	fuzzy	ADJ
ejpam-5894	558	16	implicative	implicative	ADJ
ejpam-5894	558	17	wsbg	wsbg	NOUN
ejpam-5894	558	18	-	-	PUNCT
ejpam-5894	558	19	ideal	ideal	NOUN
ejpam-5894	558	20	of	of	ADP
ejpam-5894	558	21	l.	l.	PROPN
ejpam-5894	558	22	t.	t.	PROPN
ejpam-5894	558	23	oner	oner	PROPN
ejpam-5894	558	24	et	et	PROPN
ejpam-5894	558	25	al	al	PROPN
ejpam-5894	558	26	.	.	PUNCT
ejpam-5894	558	27	/	/	SYM
ejpam-5894	558	28	eur	eur	PROPN
ejpam-5894	558	29	.	.	PUNCT
ejpam-5894	559	1	j.	j.	PROPN
ejpam-5894	559	2	pure	pure	PROPN
ejpam-5894	559	3	appl	appl	PROPN
ejpam-5894	559	4	.	.	PROPN
ejpam-5894	559	5	math	math	PROPN
ejpam-5894	559	6	,	,	PUNCT
ejpam-5894	559	7	18	18	NUM
ejpam-5894	559	8	(	(	PUNCT
ejpam-5894	559	9	3	3	NUM
ejpam-5894	559	10	)	)	PUNCT
ejpam-5894	559	11	(	(	PUNCT
ejpam-5894	559	12	2025	2025	NUM
ejpam-5894	559	13	)	)	PUNCT
ejpam-5894	559	14	,	,	PUNCT
ejpam-5894	559	15	5894	5894	NUM
ejpam-5894	559	16	30	30	NUM
ejpam-5894	559	17	of	of	ADP
ejpam-5894	559	18	33	33	NUM
ejpam-5894	559	19	theorem	theorem	NOUN
ejpam-5894	559	20	14	14	NUM
ejpam-5894	559	21	.	.	PUNCT
ejpam-5894	560	1	let	let	VERB
ejpam-5894	560	2	l	l	NOUN
ejpam-5894	560	3	=	=	SYM
ejpam-5894	560	4	(	(	PUNCT
ejpam-5894	560	5	l	l	NOUN
ejpam-5894	560	6	,	,	PUNCT
ejpam-5894	560	7	β	β	X
ejpam-5894	560	8	,	,	PUNCT
ejpam-5894	560	9	α	α	NOUN
ejpam-5894	560	10	)	)	PUNCT
ejpam-5894	560	11	be	be	VERB
ejpam-5894	560	12	an	an	DET
ejpam-5894	560	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	560	14	fuzzy	fuzzy	ADJ
ejpam-5894	560	15	set	set	NOUN
ejpam-5894	560	16	in	in	ADP
ejpam-5894	560	17	a	a	DET
ejpam-5894	560	18	wsbg	wsbg	ADV
ejpam-5894	560	19	-	-	PUNCT
ejpam-5894	560	20	algebra	algebra	NOUN
ejpam-5894	560	21	l	l	NOUN
ejpam-5894	560	22	=	=	PUNCT
ejpam-5894	560	23	⟨l	⟨l	NOUN
ejpam-5894	560	24	;	;	PUNCT
ejpam-5894	560	25	|	|	ADV
ejpam-5894	560	26	,	,	PUNCT
ejpam-5894	560	27	0⟩.	0⟩.	PROPN
ejpam-5894	560	28	then	then	ADV
ejpam-5894	560	29	l	l	PROPN
ejpam-5894	561	1	=	=	PUNCT
ejpam-5894	561	2	(	(	PUNCT
ejpam-5894	561	3	l	l	NOUN
ejpam-5894	561	4	,	,	PUNCT
ejpam-5894	561	5	α	α	X
ejpam-5894	561	6	,	,	PUNCT
ejpam-5894	561	7	β	β	NOUN
ejpam-5894	561	8	)	)	PUNCT
ejpam-5894	561	9	is	be	AUX
ejpam-5894	561	10	an	an	DET
ejpam-5894	561	11	intuitionistic	intuitionistic	ADJ
ejpam-5894	561	12	fuzzy	fuzzy	ADJ
ejpam-5894	561	13	implicative	implicative	ADJ
ejpam-5894	561	14	wsbg	wsbg	NOUN
ejpam-5894	561	15	-	-	PUNCT
ejpam-5894	561	16	ideal	ideal	NOUN
ejpam-5894	561	17	of	of	ADP
ejpam-5894	561	18	l	l	NOUN
ejpam-5894	561	19	if	if	SCONJ
ejpam-5894	561	20	and	and	CCONJ
ejpam-5894	561	21	only	only	ADV
ejpam-5894	561	22	if	if	SCONJ
ejpam-5894	561	23	for	for	ADP
ejpam-5894	561	24	all	all	DET
ejpam-5894	561	25	t	t	NOUN
ejpam-5894	561	26	,	,	PUNCT
ejpam-5894	561	27	s	s	PART
ejpam-5894	561	28	∈	∈	PROPN
ejpam-5894	562	1	[	[	X
ejpam-5894	562	2	0	0	NUM
ejpam-5894	562	3	,	,	PUNCT
ejpam-5894	562	4	1	1	NUM
ejpam-5894	562	5	]	]	PUNCT
ejpam-5894	562	6	,	,	PUNCT
ejpam-5894	562	7	u(β	u(β	PROPN
ejpam-5894	562	8	,	,	PUNCT
ejpam-5894	562	9	t	t	PROPN
ejpam-5894	562	10	)	)	PUNCT
ejpam-5894	562	11	and	and	CCONJ
ejpam-5894	562	12	l(α	l(α	PROPN
ejpam-5894	562	13	,	,	PUNCT
ejpam-5894	562	14	s	s	X
ejpam-5894	562	15	)	)	PUNCT
ejpam-5894	562	16	are	be	AUX
ejpam-5894	562	17	implicative	implicative	ADJ
ejpam-5894	562	18	wsbg	wsbg	NOUN
ejpam-5894	562	19	-	-	PUNCT
ejpam-5894	562	20	ideals	ideal	NOUN
ejpam-5894	562	21	of	of	ADP
ejpam-5894	562	22	l	l	NOUN
ejpam-5894	562	23	,	,	PUNCT
ejpam-5894	562	24	provided	provide	VERB
ejpam-5894	562	25	u(β	u(β	PROPN
ejpam-5894	562	26	,	,	PUNCT
ejpam-5894	562	27	t	t	PROPN
ejpam-5894	562	28	)	)	PUNCT
ejpam-5894	562	29	and	and	CCONJ
ejpam-5894	562	30	l(α	l(α	PROPN
ejpam-5894	562	31	,	,	PUNCT
ejpam-5894	562	32	s	s	X
ejpam-5894	562	33	)	)	PUNCT
ejpam-5894	562	34	are	be	AUX
ejpam-5894	562	35	nonempty	nonempty	ADJ
ejpam-5894	562	36	.	.	PUNCT
ejpam-5894	563	1	proof	proof	NOUN
ejpam-5894	563	2	.	.	PUNCT
ejpam-5894	564	1	assume	assume	VERB
ejpam-5894	564	2	l	l	NOUN
ejpam-5894	564	3	=	=	SYM
ejpam-5894	564	4	(	(	PUNCT
ejpam-5894	564	5	l	l	NOUN
ejpam-5894	564	6	,	,	PUNCT
ejpam-5894	564	7	β	β	X
ejpam-5894	564	8	,	,	PUNCT
ejpam-5894	564	9	α	α	X
ejpam-5894	564	10	)	)	PUNCT
ejpam-5894	564	11	is	be	AUX
ejpam-5894	564	12	an	an	DET
ejpam-5894	564	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	564	14	fuzzy	fuzzy	ADJ
ejpam-5894	564	15	implicative	implicative	ADJ
ejpam-5894	564	16	wsbg	wsbg	NOUN
ejpam-5894	564	17	-	-	PUNCT
ejpam-5894	564	18	ideal	ideal	NOUN
ejpam-5894	564	19	of	of	ADP
ejpam-5894	564	20	l	l	NOUN
ejpam-5894	564	21	=	=	SYM
ejpam-5894	564	22	⟨l	⟨l	NOUN
ejpam-5894	564	23	;	;	PUNCT
ejpam-5894	564	24	|	|	ADV
ejpam-5894	564	25	,	,	PUNCT
ejpam-5894	564	26	0⟩.	0⟩.	PROPN
ejpam-5894	564	27	let	let	VERB
ejpam-5894	564	28	t	t	PROPN
ejpam-5894	564	29	,	,	PUNCT
ejpam-5894	564	30	s	s	PART
ejpam-5894	564	31	∈	∈	PROPN
ejpam-5894	565	1	[	[	X
ejpam-5894	565	2	0	0	NUM
ejpam-5894	565	3	,	,	PUNCT
ejpam-5894	565	4	1	1	NUM
ejpam-5894	565	5	]	]	PUNCT
ejpam-5894	565	6	be	be	AUX
ejpam-5894	565	7	such	such	ADJ
ejpam-5894	565	8	that	that	SCONJ
ejpam-5894	565	9	u(β	u(β	PROPN
ejpam-5894	565	10	,	,	PUNCT
ejpam-5894	565	11	t	t	PROPN
ejpam-5894	565	12	)	)	PUNCT
ejpam-5894	565	13	and	and	CCONJ
ejpam-5894	565	14	l(α	l(α	PROPN
ejpam-5894	565	15	,	,	PUNCT
ejpam-5894	565	16	s	s	X
ejpam-5894	565	17	)	)	PUNCT
ejpam-5894	565	18	are	be	AUX
ejpam-5894	565	19	nonempty	nonempty	X
ejpam-5894	565	20	.	.	PUNCT
ejpam-5894	566	1	case	case	NOUN
ejpam-5894	566	2	1	1	NUM
ejpam-5894	566	3	:	:	PUNCT
ejpam-5894	566	4	u(β	u(β	ADV
ejpam-5894	566	5	,	,	PUNCT
ejpam-5894	566	6	t	t	PROPN
ejpam-5894	566	7	)	)	PUNCT
ejpam-5894	566	8	is	be	AUX
ejpam-5894	566	9	an	an	DET
ejpam-5894	566	10	implicative	implicative	ADJ
ejpam-5894	566	11	wsbg	wsbg	ADV
ejpam-5894	566	12	-	-	PUNCT
ejpam-5894	566	13	ideal	ideal	NOUN
ejpam-5894	566	14	of	of	ADP
ejpam-5894	566	15	l.	l.	PROPN
ejpam-5894	566	16	let	let	VERB
ejpam-5894	566	17	ζ	ζ	NOUN
ejpam-5894	566	18	∈	∈	PROPN
ejpam-5894	566	19	u(β	u(β	PROPN
ejpam-5894	566	20	,	,	PUNCT
ejpam-5894	566	21	t	t	PROPN
ejpam-5894	566	22	)	)	PUNCT
ejpam-5894	566	23	.	.	PUNCT
ejpam-5894	567	1	then	then	ADV
ejpam-5894	567	2	β(ζ	β(ζ	NUM
ejpam-5894	567	3	)	)	PUNCT
ejpam-5894	567	4	≥	≥	NOUN
ejpam-5894	567	5	t.	t.	NOUN
ejpam-5894	567	6	since	since	SCONJ
ejpam-5894	567	7	l	l	PROPN
ejpam-5894	567	8	is	be	AUX
ejpam-5894	567	9	an	an	DET
ejpam-5894	567	10	intuitionistic	intuitionistic	ADJ
ejpam-5894	567	11	fuzzy	fuzzy	ADJ
ejpam-5894	567	12	implicative	implicative	ADJ
ejpam-5894	567	13	wsbgideal	wsbgideal	NOUN
ejpam-5894	567	14	of	of	ADP
ejpam-5894	567	15	l	l	PROPN
ejpam-5894	567	16	,	,	PUNCT
ejpam-5894	567	17	we	we	PRON
ejpam-5894	567	18	have	have	VERB
ejpam-5894	567	19	β(0	β(0	NOUN
ejpam-5894	567	20	)	)	PUNCT
ejpam-5894	567	21	≤	≤	NOUN
ejpam-5894	567	22	β(ζ	β(ζ	PROPN
ejpam-5894	567	23	)	)	PUNCT
ejpam-5894	568	1	=	=	SYM
ejpam-5894	568	2	⇒	⇒	NOUN
ejpam-5894	568	3	1−	1−	NUM
ejpam-5894	568	4	β(0	β(0	PROPN
ejpam-5894	568	5	)	)	PUNCT
ejpam-5894	568	6	≤	≤	NOUN
ejpam-5894	568	7	1−	1−	NUM
ejpam-5894	568	8	β(ζ	β(ζ	NUM
ejpam-5894	568	9	)	)	PUNCT
ejpam-5894	569	1	=	=	VERB
ejpam-5894	569	2	⇒	⇒	NOUN
ejpam-5894	569	3	β(0	β(0	PROPN
ejpam-5894	569	4	)	)	PUNCT
ejpam-5894	569	5	≥	≥	NOUN
ejpam-5894	569	6	β(ζ	β(ζ	NUM
ejpam-5894	569	7	)	)	PUNCT
ejpam-5894	569	8	≥	≥	NOUN
ejpam-5894	569	9	t.	t.	NOUN
ejpam-5894	569	10	hence	hence	ADV
ejpam-5894	569	11	,	,	PUNCT
ejpam-5894	569	12	0	0	NUM
ejpam-5894	569	13	∈	∈	PROPN
ejpam-5894	569	14	u(β	u(β	PROPN
ejpam-5894	569	15	,	,	PUNCT
ejpam-5894	569	16	t	t	PROPN
ejpam-5894	569	17	)	)	PUNCT
ejpam-5894	569	18	.	.	PUNCT
ejpam-5894	570	1	next	next	ADV
ejpam-5894	570	2	,	,	PUNCT
ejpam-5894	570	3	for	for	ADP
ejpam-5894	570	4	ζ	ζ	NOUN
ejpam-5894	570	5	,	,	PUNCT
ejpam-5894	570	6	η	η	PROPN
ejpam-5894	570	7	,	,	PUNCT
ejpam-5894	570	8	θ	θ	PROPN
ejpam-5894	570	9	∈	∈	PROPN
ejpam-5894	570	10	l	l	NOUN
ejpam-5894	570	11	,	,	PUNCT
ejpam-5894	570	12	let	let	VERB
ejpam-5894	570	13	f(ζ	f(ζ	PROPN
ejpam-5894	570	14	,	,	PUNCT
ejpam-5894	570	15	η	η	PROPN
ejpam-5894	570	16	,	,	PUNCT
ejpam-5894	570	17	θ	θ	NOUN
ejpam-5894	570	18	)	)	PUNCT
ejpam-5894	570	19	denote	denote	VERB
ejpam-5894	570	20	the	the	DET
ejpam-5894	570	21	complex	complex	ADJ
ejpam-5894	570	22	expression	expression	NOUN
ejpam-5894	570	23	:	:	PUNCT
ejpam-5894	570	24	f(ζ	f(ζ	NOUN
ejpam-5894	570	25	,	,	PUNCT
ejpam-5894	570	26	η	η	PROPN
ejpam-5894	570	27	,	,	PUNCT
ejpam-5894	570	28	θ	θ	NOUN
ejpam-5894	570	29	)	)	PUNCT
ejpam-5894	570	30	=	=	SYM
ejpam-5894	570	31	(	(	PUNCT
ejpam-5894	570	32	(	(	PUNCT
ejpam-5894	570	33	(	(	PUNCT
ejpam-5894	570	34	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ))))|(θ|θ))|((ζ|(η|(ζ|ζ)))|(ζ|(η|(ζ|ζ	NOUN
ejpam-5894	570	35	)	)	PUNCT
ejpam-5894	570	36	)	)	PUNCT
ejpam-5894	570	37	)	)	PUNCT
ejpam-5894	570	38	)	)	PUNCT
ejpam-5894	570	39	.	.	PUNCT
ejpam-5894	571	1	if	if	SCONJ
ejpam-5894	571	2	θ	θ	PROPN
ejpam-5894	571	3	∈	∈	PROPN
ejpam-5894	571	4	u(β	u(β	PROPN
ejpam-5894	571	5	,	,	PUNCT
ejpam-5894	571	6	t	t	PROPN
ejpam-5894	571	7	)	)	PUNCT
ejpam-5894	571	8	,	,	PUNCT
ejpam-5894	571	9	then	then	ADV
ejpam-5894	571	10	β(f(ζ	β(f(ζ	PROPN
ejpam-5894	571	11	,	,	PUNCT
ejpam-5894	571	12	η	η	PROPN
ejpam-5894	571	13	,	,	PUNCT
ejpam-5894	571	14	θ	θ	NOUN
ejpam-5894	571	15	)	)	PUNCT
ejpam-5894	571	16	)	)	PUNCT
ejpam-5894	571	17	≥	≥	PROPN
ejpam-5894	571	18	t	t	NOUN
ejpam-5894	571	19	and	and	CCONJ
ejpam-5894	571	20	β(θ	β(θ	NUM
ejpam-5894	571	21	)	)	PUNCT
ejpam-5894	571	22	≥	≥	NOUN
ejpam-5894	571	23	t.	t.	NOUN
ejpam-5894	571	24	since	since	SCONJ
ejpam-5894	571	25	l	l	PROPN
ejpam-5894	571	26	is	be	AUX
ejpam-5894	571	27	an	an	DET
ejpam-5894	571	28	intuitionistic	intuitionistic	ADJ
ejpam-5894	571	29	fuzzy	fuzzy	ADJ
ejpam-5894	571	30	implicative	implicative	ADJ
ejpam-5894	571	31	wsbg	wsbg	NOUN
ejpam-5894	571	32	-	-	PUNCT
ejpam-5894	571	33	ideal	ideal	NOUN
ejpam-5894	571	34	of	of	ADP
ejpam-5894	571	35	l	l	NOUN
ejpam-5894	571	36	,	,	PUNCT
ejpam-5894	571	37	β(ζ	β(ζ	PROPN
ejpam-5894	571	38	)	)	PUNCT
ejpam-5894	571	39	≤	≤	NUM
ejpam-5894	571	40	max{β(f(ζ	max{β(f(ζ	PROPN
ejpam-5894	571	41	,	,	PUNCT
ejpam-5894	571	42	η	η	PROPN
ejpam-5894	571	43	,	,	PUNCT
ejpam-5894	571	44	θ	θ	NOUN
ejpam-5894	571	45	)	)	PUNCT
ejpam-5894	571	46	)	)	PUNCT
ejpam-5894	571	47	,	,	PUNCT
ejpam-5894	571	48	β(θ	β(θ	NUM
ejpam-5894	571	49	)	)	PUNCT
ejpam-5894	571	50	}	}	PUNCT
ejpam-5894	571	51	.	.	PUNCT
ejpam-5894	572	1	expanding	expand	VERB
ejpam-5894	572	2	this	this	DET
ejpam-5894	572	3	:	:	PUNCT
ejpam-5894	572	4	1−	1−	NUM
ejpam-5894	572	5	β(ζ	β(ζ	NUM
ejpam-5894	572	6	)	)	PUNCT
ejpam-5894	572	7	≤	≤	PUNCT
ejpam-5894	573	1	max{1−	max{1−	VERB
ejpam-5894	573	2	β(f(ζ	β(f(ζ	PROPN
ejpam-5894	573	3	,	,	PUNCT
ejpam-5894	573	4	η	η	PROPN
ejpam-5894	573	5	,	,	PUNCT
ejpam-5894	573	6	θ	θ	NOUN
ejpam-5894	573	7	)	)	PUNCT
ejpam-5894	573	8	)	)	PUNCT
ejpam-5894	573	9	,	,	PUNCT
ejpam-5894	573	10	1−	1−	NUM
ejpam-5894	573	11	β(θ	β(θ	NUM
ejpam-5894	573	12	)	)	PUNCT
ejpam-5894	573	13	}	}	PUNCT
ejpam-5894	573	14	.	.	PUNCT
ejpam-5894	574	1	simplifying	simplify	VERB
ejpam-5894	574	2	:	:	PUNCT
ejpam-5894	574	3	β(ζ	β(ζ	NUM
ejpam-5894	574	4	)	)	PUNCT
ejpam-5894	574	5	≥	≥	NOUN
ejpam-5894	574	6	min{β(f(ζ	min{β(f(ζ	PROPN
ejpam-5894	574	7	,	,	PUNCT
ejpam-5894	574	8	η	η	PROPN
ejpam-5894	574	9	,	,	PUNCT
ejpam-5894	574	10	θ	θ	NOUN
ejpam-5894	574	11	)	)	PUNCT
ejpam-5894	574	12	)	)	PUNCT
ejpam-5894	574	13	,	,	PUNCT
ejpam-5894	574	14	β(θ	β(θ	NUM
ejpam-5894	574	15	)	)	PUNCT
ejpam-5894	574	16	}	}	PUNCT
ejpam-5894	574	17	≥	≥	X
ejpam-5894	574	18	t.	t.	PROPN
ejpam-5894	575	1	thus	thus	ADV
ejpam-5894	575	2	,	,	PUNCT
ejpam-5894	575	3	ζ	ζ	PROPN
ejpam-5894	575	4	∈	∈	PROPN
ejpam-5894	575	5	u(β	u(β	PROPN
ejpam-5894	575	6	,	,	PUNCT
ejpam-5894	575	7	t	t	PROPN
ejpam-5894	575	8	)	)	PUNCT
ejpam-5894	575	9	,	,	PUNCT
ejpam-5894	575	10	proving	prove	VERB
ejpam-5894	575	11	u(β	u(β	PROPN
ejpam-5894	575	12	,	,	PUNCT
ejpam-5894	575	13	t	t	PROPN
ejpam-5894	575	14	)	)	PUNCT
ejpam-5894	575	15	is	be	AUX
ejpam-5894	575	16	an	an	DET
ejpam-5894	575	17	implicative	implicative	ADJ
ejpam-5894	575	18	wsbg	wsbg	ADV
ejpam-5894	575	19	-	-	PUNCT
ejpam-5894	575	20	ideal	ideal	NOUN
ejpam-5894	575	21	of	of	ADP
ejpam-5894	575	22	l.	l.	PROPN
ejpam-5894	575	23	case	case	PROPN
ejpam-5894	575	24	2	2	NUM
ejpam-5894	575	25	:	:	PUNCT
ejpam-5894	575	26	l(α	l(α	PROPN
ejpam-5894	575	27	,	,	PUNCT
ejpam-5894	575	28	s	s	AUX
ejpam-5894	575	29	)	)	PUNCT
ejpam-5894	575	30	is	be	AUX
ejpam-5894	575	31	an	an	DET
ejpam-5894	575	32	implicative	implicative	ADJ
ejpam-5894	575	33	wsbg	wsbg	ADV
ejpam-5894	575	34	-	-	PUNCT
ejpam-5894	575	35	ideal	ideal	NOUN
ejpam-5894	575	36	of	of	ADP
ejpam-5894	575	37	l.	l.	PROPN
ejpam-5894	575	38	let	let	VERB
ejpam-5894	575	39	ζ	ζ	NOUN
ejpam-5894	575	40	∈	∈	PROPN
ejpam-5894	575	41	l(α	l(α	PROPN
ejpam-5894	575	42	,	,	PUNCT
ejpam-5894	575	43	s	s	NOUN
ejpam-5894	575	44	)	)	PUNCT
ejpam-5894	575	45	.	.	PUNCT
ejpam-5894	576	1	then	then	ADV
ejpam-5894	576	2	α(ζ	α(ζ	PROPN
ejpam-5894	576	3	)	)	PUNCT
ejpam-5894	576	4	≥	≥	NOUN
ejpam-5894	576	5	s.	s.	PROPN
ejpam-5894	576	6	since	since	SCONJ
ejpam-5894	576	7	l	l	PROPN
ejpam-5894	576	8	is	be	AUX
ejpam-5894	576	9	an	an	DET
ejpam-5894	576	10	intuitionistic	intuitionistic	ADJ
ejpam-5894	576	11	fuzzy	fuzzy	ADJ
ejpam-5894	576	12	implicative	implicative	ADJ
ejpam-5894	576	13	wsbgideal	wsbgideal	NOUN
ejpam-5894	576	14	of	of	ADP
ejpam-5894	576	15	l	l	PROPN
ejpam-5894	576	16	,	,	PUNCT
ejpam-5894	576	17	α(0	α(0	PROPN
ejpam-5894	576	18	)	)	PUNCT
ejpam-5894	576	19	≥	≥	NOUN
ejpam-5894	576	20	α(ζ	α(ζ	NOUN
ejpam-5894	576	21	)	)	PUNCT
ejpam-5894	577	1	=	=	VERB
ejpam-5894	577	2	⇒	⇒	NOUN
ejpam-5894	577	3	1−	1−	NUM
ejpam-5894	577	4	α(0	α(0	NOUN
ejpam-5894	577	5	)	)	PUNCT
ejpam-5894	577	6	≥	≥	NOUN
ejpam-5894	577	7	1−	1−	NUM
ejpam-5894	577	8	α(ζ	α(ζ	NOUN
ejpam-5894	577	9	)	)	PUNCT
ejpam-5894	578	1	=	=	SYM
ejpam-5894	578	2	⇒	⇒	NOUN
ejpam-5894	578	3	α(0	α(0	PROPN
ejpam-5894	578	4	)	)	PUNCT
ejpam-5894	578	5	≤	≤	NUM
ejpam-5894	578	6	α(ζ	α(ζ	NOUN
ejpam-5894	578	7	)	)	PUNCT
ejpam-5894	578	8	≤	≤	PUNCT
ejpam-5894	578	9	s.	s.	PROPN
ejpam-5894	578	10	hence	hence	ADV
ejpam-5894	578	11	,	,	PUNCT
ejpam-5894	578	12	0	0	NUM
ejpam-5894	578	13	∈	∈	PROPN
ejpam-5894	578	14	l(α	l(α	PROPN
ejpam-5894	578	15	,	,	PUNCT
ejpam-5894	578	16	s	s	NOUN
ejpam-5894	578	17	)	)	PUNCT
ejpam-5894	578	18	.	.	PUNCT
ejpam-5894	579	1	for	for	ADP
ejpam-5894	579	2	ζ	ζ	PROPN
ejpam-5894	579	3	,	,	PUNCT
ejpam-5894	579	4	η	η	PROPN
ejpam-5894	579	5	,	,	PUNCT
ejpam-5894	579	6	θ	θ	PROPN
ejpam-5894	579	7	∈	∈	PROPN
ejpam-5894	579	8	l	l	NOUN
ejpam-5894	579	9	,	,	PUNCT
ejpam-5894	579	10	if	if	SCONJ
ejpam-5894	579	11	θ	θ	PROPN
ejpam-5894	579	12	∈	∈	PROPN
ejpam-5894	579	13	l(α	l(α	PROPN
ejpam-5894	579	14	,	,	PUNCT
ejpam-5894	579	15	s	s	X
ejpam-5894	579	16	)	)	PUNCT
ejpam-5894	579	17	,	,	PUNCT
ejpam-5894	579	18	then	then	ADV
ejpam-5894	579	19	α(f(ζ	α(f(ζ	NOUN
ejpam-5894	579	20	,	,	PUNCT
ejpam-5894	579	21	η	η	PROPN
ejpam-5894	579	22	,	,	PUNCT
ejpam-5894	579	23	θ	θ	NOUN
ejpam-5894	579	24	)	)	PUNCT
ejpam-5894	579	25	)	)	PUNCT
ejpam-5894	579	26	≥	≥	PROPN
ejpam-5894	579	27	s	s	NOUN
ejpam-5894	579	28	and	and	CCONJ
ejpam-5894	579	29	α(θ	α(θ	NOUN
ejpam-5894	579	30	)	)	PUNCT
ejpam-5894	579	31	≥	≥	NOUN
ejpam-5894	579	32	s.	s.	PROPN
ejpam-5894	579	33	since	since	SCONJ
ejpam-5894	579	34	l	l	PROPN
ejpam-5894	579	35	is	be	AUX
ejpam-5894	579	36	an	an	DET
ejpam-5894	579	37	intuitionistic	intuitionistic	ADJ
ejpam-5894	579	38	fuzzy	fuzzy	ADJ
ejpam-5894	579	39	implicative	implicative	ADJ
ejpam-5894	579	40	wsbg	wsbg	NOUN
ejpam-5894	579	41	-	-	PUNCT
ejpam-5894	579	42	ideal	ideal	NOUN
ejpam-5894	579	43	of	of	ADP
ejpam-5894	579	44	l	l	NOUN
ejpam-5894	579	45	,	,	PUNCT
ejpam-5894	579	46	α(ζ	α(ζ	NOUN
ejpam-5894	579	47	)	)	PUNCT
ejpam-5894	579	48	≤	≤	NOUN
ejpam-5894	579	49	max{α(f(ζ	max{α(f(ζ	PROPN
ejpam-5894	579	50	,	,	PUNCT
ejpam-5894	579	51	η	η	PROPN
ejpam-5894	579	52	,	,	PUNCT
ejpam-5894	579	53	θ	θ	NOUN
ejpam-5894	579	54	)	)	PUNCT
ejpam-5894	579	55	)	)	PUNCT
ejpam-5894	579	56	,	,	PUNCT
ejpam-5894	579	57	α(θ	α(θ	NOUN
ejpam-5894	579	58	)	)	PUNCT
ejpam-5894	579	59	}	}	PUNCT
ejpam-5894	579	60	.	.	PUNCT
ejpam-5894	580	1	expanding	expand	VERB
ejpam-5894	580	2	this	this	PRON
ejpam-5894	580	3	:	:	PUNCT
ejpam-5894	580	4	1−	1−	NUM
ejpam-5894	580	5	α(ζ	α(ζ	NOUN
ejpam-5894	580	6	)	)	PUNCT
ejpam-5894	580	7	≤	≤	NUM
ejpam-5894	580	8	max{1−	max{1−	PROPN
ejpam-5894	580	9	α(f(ζ	α(f(ζ	PROPN
ejpam-5894	580	10	,	,	PUNCT
ejpam-5894	580	11	η	η	PROPN
ejpam-5894	580	12	,	,	PUNCT
ejpam-5894	580	13	θ	θ	NOUN
ejpam-5894	580	14	)	)	PUNCT
ejpam-5894	580	15	)	)	PUNCT
ejpam-5894	580	16	,	,	PUNCT
ejpam-5894	580	17	1−	1−	NUM
ejpam-5894	580	18	α(θ	α(θ	NOUN
ejpam-5894	580	19	)	)	PUNCT
ejpam-5894	580	20	}	}	PUNCT
ejpam-5894	580	21	.	.	PUNCT
ejpam-5894	581	1	simplifying	simplify	VERB
ejpam-5894	581	2	:	:	PUNCT
ejpam-5894	581	3	α(ζ	α(ζ	NOUN
ejpam-5894	581	4	)	)	PUNCT
ejpam-5894	581	5	≥	≥	NOUN
ejpam-5894	581	6	min{α(f(ζ	min{α(f(ζ	NOUN
ejpam-5894	581	7	,	,	PUNCT
ejpam-5894	581	8	η	η	NOUN
ejpam-5894	581	9	,	,	PUNCT
ejpam-5894	581	10	θ	θ	NOUN
ejpam-5894	581	11	)	)	PUNCT
ejpam-5894	581	12	)	)	PUNCT
ejpam-5894	581	13	,	,	PUNCT
ejpam-5894	581	14	α(θ	α(θ	NOUN
ejpam-5894	581	15	)	)	PUNCT
ejpam-5894	581	16	}	}	PUNCT
ejpam-5894	581	17	≥	≥	PROPN
ejpam-5894	581	18	s.	s.	PROPN
ejpam-5894	581	19	t.	t.	PROPN
ejpam-5894	581	20	oner	oner	PROPN
ejpam-5894	581	21	et	et	PROPN
ejpam-5894	581	22	al	al	PROPN
ejpam-5894	581	23	.	.	PUNCT
ejpam-5894	581	24	/	/	SYM
ejpam-5894	581	25	eur	eur	PROPN
ejpam-5894	581	26	.	.	PUNCT
ejpam-5894	582	1	j.	j.	PROPN
ejpam-5894	582	2	pure	pure	PROPN
ejpam-5894	582	3	appl	appl	PROPN
ejpam-5894	582	4	.	.	PROPN
ejpam-5894	582	5	math	math	PROPN
ejpam-5894	582	6	,	,	PUNCT
ejpam-5894	582	7	18	18	NUM
ejpam-5894	582	8	(	(	PUNCT
ejpam-5894	582	9	3	3	NUM
ejpam-5894	582	10	)	)	PUNCT
ejpam-5894	582	11	(	(	PUNCT
ejpam-5894	582	12	2025	2025	NUM
ejpam-5894	582	13	)	)	PUNCT
ejpam-5894	582	14	,	,	PUNCT
ejpam-5894	582	15	5894	5894	NUM
ejpam-5894	582	16	31	31	NUM
ejpam-5894	582	17	of	of	ADP
ejpam-5894	582	18	33	33	NUM
ejpam-5894	582	19	thus	thus	ADV
ejpam-5894	582	20	,	,	PUNCT
ejpam-5894	582	21	ζ	ζ	PROPN
ejpam-5894	582	22	∈	∈	NOUN
ejpam-5894	582	23	l(α	l(α	PROPN
ejpam-5894	582	24	,	,	PUNCT
ejpam-5894	582	25	s	s	X
ejpam-5894	582	26	)	)	PUNCT
ejpam-5894	582	27	,	,	PUNCT
ejpam-5894	582	28	proving	prove	VERB
ejpam-5894	582	29	l(α	l(α	PROPN
ejpam-5894	582	30	,	,	PUNCT
ejpam-5894	582	31	s	s	AUX
ejpam-5894	582	32	)	)	PUNCT
ejpam-5894	582	33	is	be	AUX
ejpam-5894	582	34	an	an	DET
ejpam-5894	582	35	implicative	implicative	ADJ
ejpam-5894	582	36	wsbg	wsbg	ADV
ejpam-5894	582	37	-	-	PUNCT
ejpam-5894	582	38	ideal	ideal	NOUN
ejpam-5894	582	39	of	of	ADP
ejpam-5894	582	40	l.	l.	NOUN
ejpam-5894	582	41	conversely	conversely	ADV
ejpam-5894	582	42	,	,	PUNCT
ejpam-5894	582	43	assume	assume	VERB
ejpam-5894	582	44	u(β	u(β	PROPN
ejpam-5894	582	45	,	,	PUNCT
ejpam-5894	582	46	t	t	PROPN
ejpam-5894	582	47	)	)	PUNCT
ejpam-5894	582	48	and	and	CCONJ
ejpam-5894	582	49	l(α	l(α	PROPN
ejpam-5894	582	50	,	,	PUNCT
ejpam-5894	582	51	s	s	X
ejpam-5894	582	52	)	)	PUNCT
ejpam-5894	582	53	are	be	AUX
ejpam-5894	582	54	implicative	implicative	ADJ
ejpam-5894	582	55	wsbg	wsbg	NOUN
ejpam-5894	582	56	-	-	PUNCT
ejpam-5894	582	57	ideals	ideal	NOUN
ejpam-5894	582	58	of	of	ADP
ejpam-5894	582	59	a	a	DET
ejpam-5894	582	60	wsbgalgebra	wsbgalgebra	NOUN
ejpam-5894	582	61	l	l	NOUN
ejpam-5894	582	62	=	=	SYM
ejpam-5894	582	63	⟨l	⟨l	NOUN
ejpam-5894	582	64	;	;	PUNCT
ejpam-5894	582	65	|	|	ADV
ejpam-5894	582	66	,	,	PUNCT
ejpam-5894	582	67	0⟩	0⟩	PROPN
ejpam-5894	582	68	for	for	ADP
ejpam-5894	582	69	all	all	DET
ejpam-5894	582	70	t	t	PROPN
ejpam-5894	582	71	,	,	PUNCT
ejpam-5894	582	72	s	s	PART
ejpam-5894	582	73	∈	∈	PROPN
ejpam-5894	583	1	[	[	X
ejpam-5894	583	2	0	0	NUM
ejpam-5894	583	3	,	,	PUNCT
ejpam-5894	583	4	1	1	NUM
ejpam-5894	583	5	]	]	PUNCT
ejpam-5894	583	6	when	when	SCONJ
ejpam-5894	583	7	they	they	PRON
ejpam-5894	583	8	are	be	AUX
ejpam-5894	583	9	nonempty	nonempty	ADJ
ejpam-5894	583	10	.	.	PUNCT
ejpam-5894	584	1	for	for	ADP
ejpam-5894	584	2	any	any	DET
ejpam-5894	584	3	ζ	ζ	PROPN
ejpam-5894	584	4	∈	∈	PROPN
ejpam-5894	584	5	l	l	NOUN
ejpam-5894	584	6	,	,	PUNCT
ejpam-5894	584	7	let	let	VERB
ejpam-5894	584	8	t	t	NOUN
ejpam-5894	584	9	=	=	PUNCT
ejpam-5894	584	10	β(ζ	β(ζ	PROPN
ejpam-5894	584	11	)	)	PUNCT
ejpam-5894	584	12	.	.	PUNCT
ejpam-5894	585	1	then	then	ADV
ejpam-5894	585	2	0	0	NUM
ejpam-5894	585	3	∈	∈	PROPN
ejpam-5894	585	4	u(β	u(β	PROPN
ejpam-5894	585	5	,	,	PUNCT
ejpam-5894	585	6	t	t	PROPN
ejpam-5894	585	7	)	)	PUNCT
ejpam-5894	585	8	,	,	PUNCT
ejpam-5894	585	9	so	so	SCONJ
ejpam-5894	585	10	β(0	β(0	PROPN
ejpam-5894	585	11	)	)	PUNCT
ejpam-5894	585	12	≥	≥	NOUN
ejpam-5894	585	13	β(ζ	β(ζ	NUM
ejpam-5894	585	14	)	)	PUNCT
ejpam-5894	586	1	=	=	VERB
ejpam-5894	586	2	⇒	⇒	NOUN
ejpam-5894	586	3	β(0	β(0	PROPN
ejpam-5894	586	4	)	)	PUNCT
ejpam-5894	586	5	≤	≤	NOUN
ejpam-5894	586	6	β(ζ	β(ζ	PROPN
ejpam-5894	586	7	)	)	PUNCT
ejpam-5894	586	8	.	.	PUNCT
ejpam-5894	587	1	similarly	similarly	ADV
ejpam-5894	587	2	,	,	PUNCT
ejpam-5894	587	3	let	let	VERB
ejpam-5894	587	4	s	s	PRON
ejpam-5894	587	5	=	=	VERB
ejpam-5894	587	6	α(ζ	α(ζ	PROPN
ejpam-5894	587	7	)	)	PUNCT
ejpam-5894	587	8	.	.	PUNCT
ejpam-5894	588	1	then	then	ADV
ejpam-5894	588	2	0	0	NUM
ejpam-5894	588	3	∈	∈	PROPN
ejpam-5894	588	4	l(α	l(α	PROPN
ejpam-5894	588	5	,	,	PUNCT
ejpam-5894	588	6	s	s	NOUN
ejpam-5894	588	7	)	)	PUNCT
ejpam-5894	588	8	,	,	PUNCT
ejpam-5894	588	9	so	so	ADV
ejpam-5894	588	10	α(0	α(0	PROPN
ejpam-5894	588	11	)	)	PUNCT
ejpam-5894	588	12	≤	≤	NUM
ejpam-5894	588	13	α(ζ	α(ζ	NOUN
ejpam-5894	588	14	)	)	PUNCT
ejpam-5894	589	1	=	=	SYM
ejpam-5894	589	2	⇒	⇒	NOUN
ejpam-5894	589	3	α(0	α(0	PROPN
ejpam-5894	589	4	)	)	PUNCT
ejpam-5894	589	5	≥	≥	NOUN
ejpam-5894	589	6	α(ζ	α(ζ	NOUN
ejpam-5894	589	7	)	)	PUNCT
ejpam-5894	589	8	.	.	PUNCT
ejpam-5894	590	1	thus	thus	ADV
ejpam-5894	590	2	,	,	PUNCT
ejpam-5894	590	3	l	l	NOUN
ejpam-5894	590	4	is	be	AUX
ejpam-5894	590	5	an	an	DET
ejpam-5894	590	6	intuitionistic	intuitionistic	ADJ
ejpam-5894	590	7	fuzzy	fuzzy	ADJ
ejpam-5894	590	8	implicative	implicative	ADJ
ejpam-5894	590	9	wsbg	wsbg	NOUN
ejpam-5894	590	10	-	-	PUNCT
ejpam-5894	590	11	ideal	ideal	NOUN
ejpam-5894	590	12	of	of	ADP
ejpam-5894	590	13	l.	l.	PROPN
ejpam-5894	590	14	5	5	NUM
ejpam-5894	590	15	.	.	PUNCT
ejpam-5894	590	16	conclusion	conclusion	NOUN
ejpam-5894	590	17	this	this	DET
ejpam-5894	590	18	paper	paper	NOUN
ejpam-5894	590	19	presents	present	VERB
ejpam-5894	590	20	a	a	DET
ejpam-5894	590	21	detailed	detailed	ADJ
ejpam-5894	590	22	study	study	NOUN
ejpam-5894	590	23	of	of	ADP
ejpam-5894	590	24	intuitionistic	intuitionistic	ADJ
ejpam-5894	590	25	fuzzy	fuzzy	ADJ
ejpam-5894	590	26	wsbg	wsbg	NOUN
ejpam-5894	590	27	-	-	PUNCT
ejpam-5894	590	28	ideals	ideal	NOUN
ejpam-5894	590	29	and	and	CCONJ
ejpam-5894	590	30	intuitionistic	intuitionistic	ADJ
ejpam-5894	590	31	fuzzy	fuzzy	ADJ
ejpam-5894	590	32	implicative	implicative	ADJ
ejpam-5894	590	33	wsbg	wsbg	NOUN
ejpam-5894	590	34	-	-	PUNCT
ejpam-5894	590	35	ideals	ideal	NOUN
ejpam-5894	590	36	within	within	ADP
ejpam-5894	590	37	the	the	DET
ejpam-5894	590	38	framework	framework	NOUN
ejpam-5894	590	39	of	of	ADP
ejpam-5894	590	40	wsbg	wsbg	NOUN
ejpam-5894	590	41	-	-	PUNCT
ejpam-5894	590	42	algebras	algebras	X
ejpam-5894	590	43	.	.	PUNCT
ejpam-5894	591	1	by	by	ADP
ejpam-5894	591	2	combining	combine	VERB
ejpam-5894	591	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	591	4	fuzzy	fuzzy	ADJ
ejpam-5894	591	5	set	set	NOUN
ejpam-5894	591	6	theory	theory	NOUN
ejpam-5894	591	7	with	with	ADP
ejpam-5894	591	8	the	the	DET
ejpam-5894	591	9	sheffer	sheffer	NOUN
ejpam-5894	591	10	stroke	stroke	NOUN
ejpam-5894	591	11	operation	operation	NOUN
ejpam-5894	591	12	,	,	PUNCT
ejpam-5894	591	13	we	we	PRON
ejpam-5894	591	14	have	have	AUX
ejpam-5894	591	15	extended	extend	VERB
ejpam-5894	591	16	classical	classical	ADJ
ejpam-5894	591	17	algebraic	algebraic	ADJ
ejpam-5894	591	18	frameworks	framework	NOUN
ejpam-5894	591	19	to	to	PART
ejpam-5894	591	20	handle	handle	VERB
ejpam-5894	591	21	uncertainty	uncertainty	NOUN
ejpam-5894	591	22	and	and	CCONJ
ejpam-5894	591	23	vagueness	vagueness	NOUN
ejpam-5894	591	24	,	,	PUNCT
ejpam-5894	591	25	thereby	thereby	ADV
ejpam-5894	591	26	contributing	contribute	VERB
ejpam-5894	591	27	significantly	significantly	ADV
ejpam-5894	591	28	to	to	ADP
ejpam-5894	591	29	the	the	DET
ejpam-5894	591	30	development	development	NOUN
ejpam-5894	591	31	of	of	ADP
ejpam-5894	591	32	fuzzy	fuzzy	ADJ
ejpam-5894	591	33	algebraic	algebraic	ADJ
ejpam-5894	591	34	structures	structure	NOUN
ejpam-5894	591	35	.	.	PUNCT
ejpam-5894	592	1	a	a	DET
ejpam-5894	592	2	key	key	ADJ
ejpam-5894	592	3	result	result	NOUN
ejpam-5894	592	4	of	of	ADP
ejpam-5894	592	5	this	this	DET
ejpam-5894	592	6	work	work	NOUN
ejpam-5894	592	7	is	be	AUX
ejpam-5894	592	8	the	the	DET
ejpam-5894	592	9	establishment	establishment	NOUN
ejpam-5894	592	10	of	of	ADP
ejpam-5894	592	11	a	a	DET
ejpam-5894	592	12	structural	structural	ADJ
ejpam-5894	592	13	connection	connection	NOUN
ejpam-5894	592	14	between	between	ADP
ejpam-5894	592	15	intuitionistic	intuitionistic	ADJ
ejpam-5894	592	16	fuzzy	fuzzy	ADJ
ejpam-5894	592	17	implicative	implicative	ADJ
ejpam-5894	592	18	wsbg	wsbg	NOUN
ejpam-5894	592	19	-	-	PUNCT
ejpam-5894	592	20	ideals	ideal	NOUN
ejpam-5894	592	21	and	and	CCONJ
ejpam-5894	592	22	their	their	PRON
ejpam-5894	592	23	level	level	NOUN
ejpam-5894	592	24	sets	set	NOUN
ejpam-5894	592	25	,	,	PUNCT
ejpam-5894	592	26	demonstrating	demonstrate	VERB
ejpam-5894	592	27	that	that	SCONJ
ejpam-5894	592	28	every	every	DET
ejpam-5894	592	29	level	level	NOUN
ejpam-5894	592	30	set	set	VERB
ejpam-5894	592	31	corresponds	correspond	VERB
ejpam-5894	592	32	to	to	ADP
ejpam-5894	592	33	an	an	DET
ejpam-5894	592	34	implicative	implicative	ADJ
ejpam-5894	592	35	wsbg	wsbg	ADV
ejpam-5894	592	36	-	-	PUNCT
ejpam-5894	592	37	ideal	ideal	ADJ
ejpam-5894	592	38	and	and	CCONJ
ejpam-5894	592	39	vice	vice	ADV
ejpam-5894	592	40	versa	versa	ADV
ejpam-5894	592	41	.	.	PUNCT
ejpam-5894	593	1	this	this	DET
ejpam-5894	593	2	result	result	NOUN
ejpam-5894	593	3	provides	provide	VERB
ejpam-5894	593	4	a	a	DET
ejpam-5894	593	5	systematic	systematic	ADJ
ejpam-5894	593	6	approach	approach	NOUN
ejpam-5894	593	7	for	for	ADP
ejpam-5894	593	8	analyzing	analyze	VERB
ejpam-5894	593	9	these	these	DET
ejpam-5894	593	10	subalgebras	subalgebra	NOUN
ejpam-5894	593	11	,	,	PUNCT
ejpam-5894	593	12	enhancing	enhance	VERB
ejpam-5894	593	13	our	our	PRON
ejpam-5894	593	14	understanding	understanding	NOUN
ejpam-5894	593	15	of	of	ADP
ejpam-5894	593	16	their	their	PRON
ejpam-5894	593	17	role	role	NOUN
ejpam-5894	593	18	in	in	ADP
ejpam-5894	593	19	wsbg	wsbg	NOUN
ejpam-5894	593	20	-	-	PUNCT
ejpam-5894	593	21	algebras	algebras	X
ejpam-5894	593	22	.	.	PUNCT
ejpam-5894	594	1	additionally	additionally	ADV
ejpam-5894	594	2	,	,	PUNCT
ejpam-5894	594	3	we	we	PRON
ejpam-5894	594	4	explored	explore	VERB
ejpam-5894	594	5	the	the	DET
ejpam-5894	594	6	properties	property	NOUN
ejpam-5894	594	7	of	of	ADP
ejpam-5894	594	8	intuitionistic	intuitionistic	ADJ
ejpam-5894	594	9	fuzzy	fuzzy	ADJ
ejpam-5894	594	10	wsbg	wsbg	NOUN
ejpam-5894	594	11	-	-	PUNCT
ejpam-5894	594	12	ideals	ideal	NOUN
ejpam-5894	594	13	,	,	PUNCT
ejpam-5894	594	14	proving	prove	VERB
ejpam-5894	594	15	that	that	SCONJ
ejpam-5894	594	16	every	every	DET
ejpam-5894	594	17	intuitionistic	intuitionistic	ADJ
ejpam-5894	594	18	fuzzy	fuzzy	ADJ
ejpam-5894	594	19	implicative	implicative	ADJ
ejpam-5894	594	20	wsbg	wsbg	PROPN
ejpam-5894	594	21	-	-	PUNCT
ejpam-5894	594	22	ideal	ideal	NOUN
ejpam-5894	594	23	is	be	AUX
ejpam-5894	594	24	also	also	ADV
ejpam-5894	594	25	an	an	DET
ejpam-5894	594	26	intuitionistic	intuitionistic	ADJ
ejpam-5894	594	27	fuzzy	fuzzy	ADJ
ejpam-5894	594	28	wsbg	wsbg	NOUN
ejpam-5894	594	29	-	-	PUNCT
ejpam-5894	594	30	ideal	ideal	ADJ
ejpam-5894	594	31	.	.	PUNCT
ejpam-5894	595	1	however	however	ADV
ejpam-5894	595	2	,	,	PUNCT
ejpam-5894	595	3	the	the	DET
ejpam-5894	595	4	converse	converse	NOUN
ejpam-5894	595	5	does	do	AUX
ejpam-5894	595	6	not	not	PART
ejpam-5894	595	7	always	always	ADV
ejpam-5894	595	8	hold	hold	VERB
ejpam-5894	595	9	.	.	PUNCT
ejpam-5894	596	1	this	this	DET
ejpam-5894	596	2	distinction	distinction	NOUN
ejpam-5894	596	3	highlights	highlight	VERB
ejpam-5894	596	4	the	the	DET
ejpam-5894	596	5	unique	unique	ADJ
ejpam-5894	596	6	characteristics	characteristic	NOUN
ejpam-5894	596	7	of	of	ADP
ejpam-5894	596	8	wsbg	wsbg	NOUN
ejpam-5894	596	9	-	-	PUNCT
ejpam-5894	596	10	ideals	ideal	NOUN
ejpam-5894	596	11	and	and	CCONJ
ejpam-5894	596	12	their	their	PRON
ejpam-5894	596	13	importance	importance	NOUN
ejpam-5894	596	14	in	in	ADP
ejpam-5894	596	15	the	the	DET
ejpam-5894	596	16	algebraic	algebraic	ADJ
ejpam-5894	596	17	hierarchy	hierarchy	NOUN
ejpam-5894	596	18	.	.	PUNCT
ejpam-5894	597	1	the	the	DET
ejpam-5894	597	2	integration	integration	NOUN
ejpam-5894	597	3	of	of	ADP
ejpam-5894	597	4	intuitionistic	intuitionistic	ADJ
ejpam-5894	597	5	fuzzy	fuzzy	ADJ
ejpam-5894	597	6	sets	set	NOUN
ejpam-5894	597	7	with	with	ADP
ejpam-5894	597	8	wsbg	wsbg	NOUN
ejpam-5894	597	9	-	-	PUNCT
ejpam-5894	597	10	algebras	algebras	X
ejpam-5894	597	11	is	be	AUX
ejpam-5894	597	12	a	a	DET
ejpam-5894	597	13	novel	novel	ADJ
ejpam-5894	597	14	contribution	contribution	NOUN
ejpam-5894	597	15	,	,	PUNCT
ejpam-5894	597	16	offering	offer	VERB
ejpam-5894	597	17	a	a	DET
ejpam-5894	597	18	robust	robust	ADJ
ejpam-5894	597	19	framework	framework	NOUN
ejpam-5894	597	20	for	for	ADP
ejpam-5894	597	21	reasoning	reasoning	NOUN
ejpam-5894	597	22	under	under	ADP
ejpam-5894	597	23	uncertainty	uncertainty	NOUN
ejpam-5894	597	24	.	.	PUNCT
ejpam-5894	598	1	these	these	DET
ejpam-5894	598	2	findings	finding	NOUN
ejpam-5894	598	3	have	have	VERB
ejpam-5894	598	4	potential	potential	ADJ
ejpam-5894	598	5	applications	application	NOUN
ejpam-5894	598	6	in	in	ADP
ejpam-5894	598	7	areas	area	NOUN
ejpam-5894	598	8	such	such	ADJ
ejpam-5894	598	9	as	as	ADP
ejpam-5894	598	10	decision	decision	NOUN
ejpam-5894	598	11	-	-	PUNCT
ejpam-5894	598	12	making	making	NOUN
ejpam-5894	598	13	,	,	PUNCT
ejpam-5894	598	14	artificial	artificial	ADJ
ejpam-5894	598	15	intelligence	intelligence	NOUN
ejpam-5894	598	16	,	,	PUNCT
ejpam-5894	598	17	and	and	CCONJ
ejpam-5894	598	18	quantum	quantum	NOUN
ejpam-5894	598	19	computing	computing	NOUN
ejpam-5894	598	20	,	,	PUNCT
ejpam-5894	598	21	where	where	SCONJ
ejpam-5894	598	22	classical	classical	ADJ
ejpam-5894	598	23	logic	logic	NOUN
ejpam-5894	598	24	frameworks	framework	NOUN
ejpam-5894	598	25	often	often	ADV
ejpam-5894	598	26	fall	fall	VERB
ejpam-5894	598	27	short	short	ADJ
ejpam-5894	598	28	.	.	PUNCT
ejpam-5894	599	1	the	the	DET
ejpam-5894	599	2	results	result	NOUN
ejpam-5894	599	3	of	of	ADP
ejpam-5894	599	4	this	this	DET
ejpam-5894	599	5	study	study	NOUN
ejpam-5894	599	6	open	open	VERB
ejpam-5894	599	7	several	several	ADJ
ejpam-5894	599	8	promising	promising	ADJ
ejpam-5894	599	9	avenues	avenue	NOUN
ejpam-5894	599	10	for	for	ADP
ejpam-5894	599	11	future	future	ADJ
ejpam-5894	599	12	research	research	NOUN
ejpam-5894	599	13	.	.	PUNCT
ejpam-5894	600	1	these	these	PRON
ejpam-5894	600	2	include	include	VERB
ejpam-5894	600	3	extending	extend	VERB
ejpam-5894	600	4	the	the	DET
ejpam-5894	600	5	concepts	concept	NOUN
ejpam-5894	600	6	of	of	ADP
ejpam-5894	600	7	intuitionistic	intuitionistic	ADJ
ejpam-5894	600	8	fuzzy	fuzzy	ADJ
ejpam-5894	600	9	wsbg	wsbg	NOUN
ejpam-5894	600	10	-	-	PUNCT
ejpam-5894	600	11	algebras	algebras	ADJ
ejpam-5894	600	12	to	to	ADP
ejpam-5894	600	13	other	other	ADJ
ejpam-5894	600	14	algebraic	algebraic	ADJ
ejpam-5894	600	15	systems	system	NOUN
ejpam-5894	600	16	,	,	PUNCT
ejpam-5894	600	17	exploring	explore	VERB
ejpam-5894	600	18	their	their	PRON
ejpam-5894	600	19	dynamic	dynamic	ADJ
ejpam-5894	600	20	behavior	behavior	NOUN
ejpam-5894	600	21	in	in	ADP
ejpam-5894	600	22	evolving	evolving	NOUN
ejpam-5894	600	23	systems	system	NOUN
ejpam-5894	600	24	,	,	PUNCT
ejpam-5894	600	25	and	and	CCONJ
ejpam-5894	600	26	developing	develop	VERB
ejpam-5894	600	27	computational	computational	ADJ
ejpam-5894	600	28	tools	tool	NOUN
ejpam-5894	600	29	for	for	ADP
ejpam-5894	600	30	analyzing	analyze	VERB
ejpam-5894	600	31	large	large	ADJ
ejpam-5894	600	32	-	-	PUNCT
ejpam-5894	600	33	scale	scale	NOUN
ejpam-5894	600	34	structures	structure	NOUN
ejpam-5894	600	35	.	.	PUNCT
ejpam-5894	601	1	furthermore	furthermore	ADV
ejpam-5894	601	2	,	,	PUNCT
ejpam-5894	601	3	practical	practical	ADJ
ejpam-5894	601	4	applications	application	NOUN
ejpam-5894	601	5	in	in	ADP
ejpam-5894	601	6	fields	field	NOUN
ejpam-5894	601	7	such	such	ADJ
ejpam-5894	601	8	as	as	ADP
ejpam-5894	601	9	machine	machine	NOUN
ejpam-5894	601	10	learning	learning	NOUN
ejpam-5894	601	11	,	,	PUNCT
ejpam-5894	601	12	optimization	optimization	NOUN
ejpam-5894	601	13	,	,	PUNCT
ejpam-5894	601	14	and	and	CCONJ
ejpam-5894	601	15	fuzzy	fuzzy	ADJ
ejpam-5894	601	16	control	control	NOUN
ejpam-5894	601	17	systems	system	NOUN
ejpam-5894	601	18	could	could	AUX
ejpam-5894	601	19	benefit	benefit	VERB
ejpam-5894	601	20	from	from	ADP
ejpam-5894	601	21	these	these	DET
ejpam-5894	601	22	algebraic	algebraic	ADJ
ejpam-5894	601	23	tools	tool	NOUN
ejpam-5894	601	24	.	.	PUNCT
ejpam-5894	602	1	overall	overall	ADV
ejpam-5894	602	2	,	,	PUNCT
ejpam-5894	602	3	this	this	DET
ejpam-5894	602	4	work	work	NOUN
ejpam-5894	602	5	provides	provide	VERB
ejpam-5894	602	6	a	a	DET
ejpam-5894	602	7	solid	solid	ADJ
ejpam-5894	602	8	foundation	foundation	NOUN
ejpam-5894	602	9	for	for	ADP
ejpam-5894	602	10	the	the	DET
ejpam-5894	602	11	study	study	NOUN
ejpam-5894	602	12	of	of	ADP
ejpam-5894	602	13	intuitionistic	intuitionistic	ADJ
ejpam-5894	602	14	fuzzy	fuzzy	ADJ
ejpam-5894	602	15	algebraic	algebraic	ADJ
ejpam-5894	602	16	structures	structure	NOUN
ejpam-5894	602	17	and	and	CCONJ
ejpam-5894	602	18	their	their	PRON
ejpam-5894	602	19	applications	application	NOUN
ejpam-5894	602	20	in	in	ADP
ejpam-5894	602	21	addressing	address	VERB
ejpam-5894	602	22	complexity	complexity	NOUN
ejpam-5894	602	23	and	and	CCONJ
ejpam-5894	602	24	uncertainty	uncertainty	NOUN
ejpam-5894	602	25	in	in	ADP
ejpam-5894	602	26	mathematical	mathematical	ADJ
ejpam-5894	602	27	and	and	CCONJ
ejpam-5894	602	28	computational	computational	ADJ
ejpam-5894	602	29	models	model	NOUN
ejpam-5894	602	30	.	.	PUNCT
ejpam-5894	603	1	acknowledgements	acknowledgement	NOUN
ejpam-5894	603	2	this	this	DET
ejpam-5894	603	3	research	research	NOUN
ejpam-5894	603	4	was	be	AUX
ejpam-5894	603	5	supported	support	VERB
ejpam-5894	603	6	by	by	ADP
ejpam-5894	603	7	university	university	NOUN
ejpam-5894	603	8	of	of	ADP
ejpam-5894	603	9	phayao	phayao	NOUN
ejpam-5894	603	10	and	and	CCONJ
ejpam-5894	603	11	thailand	thailand	PROPN
ejpam-5894	603	12	science	science	PROPN
ejpam-5894	603	13	research	research	PROPN
ejpam-5894	603	14	and	and	CCONJ
ejpam-5894	603	15	innovation	innovation	NOUN
ejpam-5894	603	16	fund	fund	NOUN
ejpam-5894	603	17	(	(	PUNCT
ejpam-5894	603	18	fundamental	fundamental	ADJ
ejpam-5894	603	19	fund	fund	NOUN
ejpam-5894	603	20	2025	2025	NUM
ejpam-5894	603	21	,	,	PUNCT
ejpam-5894	603	22	grant	grant	VERB
ejpam-5894	603	23	no	no	NOUN
ejpam-5894	603	24	.	.	PROPN
ejpam-5894	604	1	5027/2567	5027/2567	NUM
ejpam-5894	604	2	)	)	PUNCT
ejpam-5894	604	3	.	.	PUNCT
ejpam-5894	605	1	t.	t.	PROPN
ejpam-5894	605	2	oner	oner	PROPN
ejpam-5894	605	3	et	et	PROPN
ejpam-5894	605	4	al	al	PROPN
ejpam-5894	605	5	.	.	PUNCT
ejpam-5894	605	6	/	/	SYM
ejpam-5894	605	7	eur	eur	PROPN
ejpam-5894	605	8	.	.	PUNCT
ejpam-5894	606	1	j.	j.	PROPN
ejpam-5894	606	2	pure	pure	PROPN
ejpam-5894	606	3	appl	appl	PROPN
ejpam-5894	606	4	.	.	PROPN
ejpam-5894	606	5	math	math	PROPN
ejpam-5894	606	6	,	,	PUNCT
ejpam-5894	606	7	18	18	NUM
ejpam-5894	606	8	(	(	PUNCT
ejpam-5894	606	9	3	3	NUM
ejpam-5894	606	10	)	)	PUNCT
ejpam-5894	606	11	(	(	PUNCT
ejpam-5894	606	12	2025	2025	NUM
ejpam-5894	606	13	)	)	PUNCT
ejpam-5894	606	14	,	,	PUNCT
ejpam-5894	606	15	5894	5894	NUM
ejpam-5894	606	16	32	32	NUM
ejpam-5894	606	17	of	of	ADP
ejpam-5894	606	18	33	33	NUM
ejpam-5894	606	19	references	reference	NOUN
ejpam-5894	606	20	[	[	X
ejpam-5894	606	21	1	1	NUM
ejpam-5894	606	22	]	]	PUNCT
ejpam-5894	606	23	c.	c.	PROPN
ejpam-5894	606	24	b.	b.	PROPN
ejpam-5894	606	25	kim	kim	PROPN
ejpam-5894	606	26	and	and	CCONJ
ejpam-5894	606	27	h.	h.	PROPN
ejpam-5894	606	28	s.	s.	PROPN
ejpam-5894	606	29	kim	kim	PROPN
ejpam-5894	606	30	.	.	PUNCT
ejpam-5894	607	1	on	on	ADP
ejpam-5894	607	2	bg	bg	PROPN
ejpam-5894	607	3	-	-	PUNCT
ejpam-5894	607	4	algebras	algebras	PROPN
ejpam-5894	607	5	.	.	PROPN
ejpam-5894	607	6	demonstratio	demonstratio	PROPN
ejpam-5894	607	7	mathematica	mathematica	PROPN
ejpam-5894	607	8	,	,	PUNCT
ejpam-5894	607	9	41(3):497	41(3):497	NOUN
ejpam-5894	607	10	–	–	PUNCT
ejpam-5894	607	11	506	506	NUM
ejpam-5894	607	12	,	,	PUNCT
ejpam-5894	607	13	2008	2008	NUM
ejpam-5894	607	14	.	.	PUNCT
ejpam-5894	608	1	[	[	X
ejpam-5894	608	2	2	2	X
ejpam-5894	608	3	]	]	X
ejpam-5894	608	4	t.	t.	NOUN
ejpam-5894	608	5	guntasow	guntasow	NOUN
ejpam-5894	608	6	,	,	PUNCT
ejpam-5894	608	7	s.	s.	PROPN
ejpam-5894	608	8	sajak	sajak	PROPN
ejpam-5894	608	9	,	,	PUNCT
ejpam-5894	608	10	a.	a.	PROPN
ejpam-5894	608	11	jomkham	jomkham	PROPN
ejpam-5894	608	12	,	,	PUNCT
ejpam-5894	608	13	and	and	CCONJ
ejpam-5894	608	14	a.	a.	NOUN
ejpam-5894	608	15	iampan	iampan	PROPN
ejpam-5894	608	16	.	.	PUNCT
ejpam-5894	609	1	fuzzy	fuzzy	ADJ
ejpam-5894	609	2	translation	translation	NOUN
ejpam-5894	609	3	of	of	ADP
ejpam-5894	609	4	a	a	DET
ejpam-5894	609	5	fuzzy	fuzzy	ADJ
ejpam-5894	609	6	set	set	NOUN
ejpam-5894	609	7	in	in	ADP
ejpam-5894	609	8	up	up	ADP
ejpam-5894	609	9	-	-	PUNCT
ejpam-5894	609	10	algebras	algebras	X
ejpam-5894	609	11	.	.	PUNCT
ejpam-5894	610	1	journal	journal	PROPN
ejpam-5894	610	2	of	of	ADP
ejpam-5894	610	3	the	the	DET
ejpam-5894	610	4	indonesian	indonesian	PROPN
ejpam-5894	610	5	mathematical	mathematical	ADJ
ejpam-5894	610	6	society	society	NOUN
ejpam-5894	610	7	,	,	PUNCT
ejpam-5894	610	8	23(2):1–19	23(2):1–19	NUM
ejpam-5894	610	9	,	,	PUNCT
ejpam-5894	610	10	2017	2017	NUM
ejpam-5894	610	11	.	.	PUNCT
ejpam-5894	611	1	[	[	X
ejpam-5894	611	2	3	3	X
ejpam-5894	611	3	]	]	X
ejpam-5894	611	4	n.	n.	NOUN
ejpam-5894	611	5	udten	udten	PROPN
ejpam-5894	611	6	,	,	PUNCT
ejpam-5894	611	7	n.	n.	PROPN
ejpam-5894	611	8	songseang	songseang	PROPN
ejpam-5894	611	9	,	,	PUNCT
ejpam-5894	611	10	and	and	CCONJ
ejpam-5894	611	11	a.	a.	NOUN
ejpam-5894	611	12	iampan	iampan	PROPN
ejpam-5894	611	13	.	.	PUNCT
ejpam-5894	612	1	translation	translation	NOUN
ejpam-5894	612	2	and	and	CCONJ
ejpam-5894	612	3	density	density	NOUN
ejpam-5894	612	4	of	of	ADP
ejpam-5894	612	5	an	an	DET
ejpam-5894	612	6	intuitionistic	intuitionistic	ADJ
ejpam-5894	612	7	fuzzy	fuzzy	ADJ
ejpam-5894	612	8	set	set	NOUN
ejpam-5894	612	9	in	in	ADP
ejpam-5894	612	10	up	up	ADJ
ejpam-5894	612	11	-	-	PUNCT
ejpam-5894	612	12	algebra	algebra	NOUN
ejpam-5894	612	13	.	.	PUNCT
ejpam-5894	613	1	italian	italian	ADJ
ejpam-5894	613	2	journal	journal	NOUN
ejpam-5894	613	3	of	of	ADP
ejpam-5894	613	4	pure	pure	ADJ
ejpam-5894	613	5	and	and	CCONJ
ejpam-5894	613	6	applied	applied	ADJ
ejpam-5894	613	7	mathematics	mathematic	NOUN
ejpam-5894	613	8	,	,	PUNCT
ejpam-5894	613	9	41:469	41:469	NUM
ejpam-5894	613	10	–	–	PUNCT
ejpam-5894	613	11	496	496	NUM
ejpam-5894	613	12	,	,	PUNCT
ejpam-5894	613	13	2019	2019	NUM
ejpam-5894	613	14	.	.	PUNCT
ejpam-5894	614	1	[	[	X
ejpam-5894	614	2	4	4	X
ejpam-5894	614	3	]	]	PUNCT
ejpam-5894	614	4	k.	k.	PROPN
ejpam-5894	614	5	j.	j.	PROPN
ejpam-5894	614	6	lee	lee	PROPN
ejpam-5894	614	7	,	,	PUNCT
ejpam-5894	614	8	y.	y.	PROPN
ejpam-5894	614	9	b.	b.	PROPN
ejpam-5894	614	10	jun	jun	PROPN
ejpam-5894	614	11	,	,	PUNCT
ejpam-5894	614	12	and	and	CCONJ
ejpam-5894	614	13	m.	m.	PROPN
ejpam-5894	614	14	i.	i.	PROPN
ejpam-5894	614	15	doh	doh	PROPN
ejpam-5894	614	16	.	.	PUNCT
ejpam-5894	614	17	fuzzy	fuzzy	ADJ
ejpam-5894	614	18	translations	translation	NOUN
ejpam-5894	614	19	and	and	CCONJ
ejpam-5894	614	20	fuzzy	fuzzy	ADJ
ejpam-5894	614	21	multiplications	multiplication	NOUN
ejpam-5894	614	22	of	of	ADP
ejpam-5894	614	23	bck	bck	PROPN
ejpam-5894	614	24	/	/	SYM
ejpam-5894	614	25	bci	bci	NOUN
ejpam-5894	614	26	-	-	PUNCT
ejpam-5894	614	27	algebras	algebra	NOUN
ejpam-5894	614	28	.	.	PUNCT
ejpam-5894	615	1	communications	communication	NOUN
ejpam-5894	615	2	of	of	ADP
ejpam-5894	615	3	the	the	DET
ejpam-5894	615	4	korean	korean	ADJ
ejpam-5894	615	5	mathematical	mathematical	ADJ
ejpam-5894	615	6	society	society	NOUN
ejpam-5894	615	7	,	,	PUNCT
ejpam-5894	615	8	24(3):353	24(3):353	NUM
ejpam-5894	615	9	–	–	PUNCT
ejpam-5894	615	10	360	360	NUM
ejpam-5894	615	11	,	,	PUNCT
ejpam-5894	615	12	2009	2009	NUM
ejpam-5894	615	13	.	.	PUNCT
ejpam-5894	616	1	[	[	X
ejpam-5894	616	2	5	5	NUM
ejpam-5894	616	3	]	]	PUNCT
ejpam-5894	616	4	m.	m.	NOUN
ejpam-5894	616	5	balamurugan	balamurugan	NOUN
ejpam-5894	616	6	,	,	PUNCT
ejpam-5894	616	7	g.	g.	PROPN
ejpam-5894	616	8	balasubramanian	balasubramanian	PROPN
ejpam-5894	616	9	,	,	PUNCT
ejpam-5894	616	10	and	and	CCONJ
ejpam-5894	616	11	c.	c.	PROPN
ejpam-5894	616	12	ragavan	ragavan	NOUN
ejpam-5894	616	13	.	.	PUNCT
ejpam-5894	617	1	translations	translation	NOUN
ejpam-5894	617	2	of	of	ADP
ejpam-5894	617	3	intuitionistic	intuitionistic	ADJ
ejpam-5894	617	4	fuzzy	fuzzy	ADJ
ejpam-5894	617	5	soft	soft	ADJ
ejpam-5894	617	6	structure	structure	NOUN
ejpam-5894	617	7	of	of	ADP
ejpam-5894	617	8	b	b	NOUN
ejpam-5894	617	9	-	-	PUNCT
ejpam-5894	617	10	algebras	algebras	PROPN
ejpam-5894	617	11	.	.	PUNCT
ejpam-5894	618	1	malaya	malaya	PROPN
ejpam-5894	618	2	journal	journal	PROPN
ejpam-5894	618	3	of	of	ADP
ejpam-5894	618	4	matematik	matematik	PROPN
ejpam-5894	618	5	,	,	PUNCT
ejpam-5894	618	6	6(3):685–700	6(3):685–700	NUM
ejpam-5894	618	7	,	,	PUNCT
ejpam-5894	618	8	2018	2018	NUM
ejpam-5894	618	9	.	.	PUNCT
ejpam-5894	619	1	[	[	X
ejpam-5894	619	2	6	6	NUM
ejpam-5894	619	3	]	]	X
ejpam-5894	619	4	h.	h.	PROPN
ejpam-5894	619	5	m.	m.	PROPN
ejpam-5894	619	6	sheffer	sheffer	PROPN
ejpam-5894	619	7	.	.	PUNCT
ejpam-5894	620	1	a	a	DET
ejpam-5894	620	2	set	set	NOUN
ejpam-5894	620	3	of	of	ADP
ejpam-5894	620	4	five	five	NUM
ejpam-5894	620	5	independent	independent	ADJ
ejpam-5894	620	6	postulates	postulate	NOUN
ejpam-5894	620	7	for	for	ADP
ejpam-5894	620	8	boolean	boolean	ADJ
ejpam-5894	620	9	algebras	algebra	NOUN
ejpam-5894	620	10	,	,	PUNCT
ejpam-5894	620	11	with	with	ADP
ejpam-5894	620	12	application	application	NOUN
ejpam-5894	620	13	to	to	ADP
ejpam-5894	620	14	logical	logical	ADJ
ejpam-5894	620	15	constants	constant	NOUN
ejpam-5894	620	16	.	.	PUNCT
ejpam-5894	621	1	transactions	transaction	NOUN
ejpam-5894	621	2	of	of	ADP
ejpam-5894	621	3	the	the	DET
ejpam-5894	621	4	american	american	PROPN
ejpam-5894	621	5	mathematical	mathematical	PROPN
ejpam-5894	621	6	society	society	NOUN
ejpam-5894	621	7	,	,	PUNCT
ejpam-5894	621	8	14(4):481–488	14(4):481–488	NUM
ejpam-5894	621	9	,	,	PUNCT
ejpam-5894	621	10	1913	1913	NUM
ejpam-5894	621	11	.	.	PUNCT
ejpam-5894	622	1	[	[	X
ejpam-5894	622	2	7	7	X
ejpam-5894	622	3	]	]	X
ejpam-5894	622	4	w.	w.	PROPN
ejpam-5894	622	5	mccune	mccune	PROPN
ejpam-5894	622	6	,	,	PUNCT
ejpam-5894	622	7	r.	r.	PROPN
ejpam-5894	622	8	veroff	veroff	PROPN
ejpam-5894	622	9	,	,	PUNCT
ejpam-5894	622	10	b.	b.	PROPN
ejpam-5894	622	11	fitelson	fitelson	PROPN
ejpam-5894	622	12	,	,	PUNCT
ejpam-5894	622	13	k.	k.	PROPN
ejpam-5894	622	14	harris	harris	PROPN
ejpam-5894	622	15	,	,	PUNCT
ejpam-5894	622	16	a.	a.	NOUN
ejpam-5894	622	17	feist	feist	PROPN
ejpam-5894	622	18	,	,	PUNCT
ejpam-5894	622	19	and	and	CCONJ
ejpam-5894	622	20	l.	l.	PROPN
ejpam-5894	622	21	wos	wos	PROPN
ejpam-5894	622	22	.	.	PUNCT
ejpam-5894	623	1	short	short	ADJ
ejpam-5894	623	2	single	single	ADJ
ejpam-5894	623	3	axioms	axiom	NOUN
ejpam-5894	623	4	for	for	ADP
ejpam-5894	623	5	boolean	boolean	ADJ
ejpam-5894	623	6	algebra	algebra	NOUN
ejpam-5894	623	7	.	.	PUNCT
ejpam-5894	624	1	journal	journal	NOUN
ejpam-5894	624	2	of	of	ADP
ejpam-5894	624	3	automated	automate	VERB
ejpam-5894	624	4	reasoning	reasoning	NOUN
ejpam-5894	624	5	,	,	PUNCT
ejpam-5894	624	6	29(1):1–16	29(1):1–16	PROPN
ejpam-5894	624	7	,	,	PUNCT
ejpam-5894	624	8	2002	2002	NUM
ejpam-5894	624	9	.	.	PUNCT
ejpam-5894	625	1	[	[	X
ejpam-5894	625	2	8	8	NUM
ejpam-5894	625	3	]	]	PUNCT
ejpam-5894	625	4	t.	t.	NOUN
ejpam-5894	625	5	oner	oner	NOUN
ejpam-5894	625	6	and	and	CCONJ
ejpam-5894	625	7	i.	i.	PROPN
ejpam-5894	625	8	senturk	senturk	PROPN
ejpam-5894	625	9	.	.	PUNCT
ejpam-5894	626	1	the	the	DET
ejpam-5894	626	2	sheffer	sheffer	PROPN
ejpam-5894	626	3	stroke	stroke	NOUN
ejpam-5894	626	4	operation	operation	NOUN
ejpam-5894	626	5	reducts	reduct	NOUN
ejpam-5894	626	6	of	of	ADP
ejpam-5894	626	7	basic	basic	ADJ
ejpam-5894	626	8	algebra	algebra	NOUN
ejpam-5894	626	9	.	.	PUNCT
ejpam-5894	627	1	open	open	ADJ
ejpam-5894	627	2	mathematics	mathematic	NOUN
ejpam-5894	627	3	,	,	PUNCT
ejpam-5894	627	4	15(1):926–935	15(1):926–935	PROPN
ejpam-5894	627	5	,	,	PUNCT
ejpam-5894	627	6	2017	2017	NUM
ejpam-5894	627	7	.	.	PUNCT
ejpam-5894	628	1	[	[	X
ejpam-5894	628	2	9	9	NUM
ejpam-5894	628	3	]	]	PUNCT
ejpam-5894	628	4	i.	i.	NOUN
ejpam-5894	628	5	senturk	senturk	PROPN
ejpam-5894	628	6	,	,	PUNCT
ejpam-5894	628	7	t.	t.	PROPN
ejpam-5894	628	8	oner	oner	NOUN
ejpam-5894	628	9	,	,	PUNCT
ejpam-5894	628	10	and	and	CCONJ
ejpam-5894	628	11	a.	a.	PROPN
ejpam-5894	628	12	b.	b.	PROPN
ejpam-5894	628	13	saeid	saeid	PROPN
ejpam-5894	628	14	.	.	PUNCT
ejpam-5894	629	1	congruences	congruence	NOUN
ejpam-5894	629	2	of	of	ADP
ejpam-5894	629	3	sheffer	sheffer	NOUN
ejpam-5894	629	4	stroke	stroke	NOUN
ejpam-5894	629	5	basic	basic	ADJ
ejpam-5894	629	6	algebras	algebra	NOUN
ejpam-5894	629	7	.	.	PUNCT
ejpam-5894	630	1	analele	analele	PROPN
ejpam-5894	630	2	stiintifice	stiintifice	PROPN
ejpam-5894	630	3	ale	ale	PROPN
ejpam-5894	630	4	universitatii	universitatii	PROPN
ejpam-5894	630	5	ovidius	ovidius	PROPN
ejpam-5894	630	6	constanta	constanta	PROPN
ejpam-5894	630	7	,	,	PUNCT
ejpam-5894	630	8	seria	seria	PROPN
ejpam-5894	630	9	matematica	matematica	PROPN
ejpam-5894	630	10	,	,	PUNCT
ejpam-5894	630	11	28(2):209	28(2):209	NOUN
ejpam-5894	630	12	–	–	PUNCT
ejpam-5894	630	13	228	228	NUM
ejpam-5894	630	14	,	,	PUNCT
ejpam-5894	630	15	2020	2020	NUM
ejpam-5894	630	16	.	.	PUNCT
ejpam-5894	631	1	[	[	X
ejpam-5894	631	2	10	10	NUM
ejpam-5894	631	3	]	]	X
ejpam-5894	631	4	i.	i.	NOUN
ejpam-5894	631	5	senturk	senturk	PROPN
ejpam-5894	631	6	and	and	CCONJ
ejpam-5894	631	7	t.	t.	PROPN
ejpam-5894	631	8	oner	oner	NOUN
ejpam-5894	631	9	.	.	PUNCT
ejpam-5894	632	1	a	a	DET
ejpam-5894	632	2	construction	construction	NOUN
ejpam-5894	632	3	of	of	ADP
ejpam-5894	632	4	very	very	ADV
ejpam-5894	632	5	true	true	ADJ
ejpam-5894	632	6	operator	operator	NOUN
ejpam-5894	632	7	on	on	ADP
ejpam-5894	632	8	sheffer	sheffer	PROPN
ejpam-5894	632	9	stroke	stroke	PROPN
ejpam-5894	632	10	mtlalgebras	mtlalgebras	PROPN
ejpam-5894	632	11	.	.	PUNCT
ejpam-5894	633	1	international	international	ADJ
ejpam-5894	633	2	journal	journal	PROPN
ejpam-5894	633	3	of	of	ADP
ejpam-5894	633	4	maps	map	NOUN
ejpam-5894	633	5	in	in	ADP
ejpam-5894	633	6	mathematics	mathematic	NOUN
ejpam-5894	633	7	,	,	PUNCT
ejpam-5894	633	8	4:93–106	4:93–106	NUM
ejpam-5894	633	9	,	,	PUNCT
ejpam-5894	633	10	2021	2021	NUM
ejpam-5894	633	11	.	.	PUNCT
ejpam-5894	634	1	[	[	X
ejpam-5894	634	2	11	11	NUM
ejpam-5894	634	3	]	]	PUNCT
ejpam-5894	634	4	i.	i.	NOUN
ejpam-5894	634	5	chajda	chajda	PROPN
ejpam-5894	634	6	.	.	PUNCT
ejpam-5894	635	1	sheffer	sheffer	PROPN
ejpam-5894	635	2	operation	operation	NOUN
ejpam-5894	635	3	in	in	ADP
ejpam-5894	635	4	ortholattices	ortholattice	NOUN
ejpam-5894	635	5	.	.	PUNCT
ejpam-5894	636	1	acta	acta	PROPN
ejpam-5894	636	2	universitatis	universitatis	PROPN
ejpam-5894	636	3	palackianae	palackianae	VERB
ejpam-5894	636	4	olomucensis	olomucensis	NOUN
ejpam-5894	636	5	.	.	PUNCT
ejpam-5894	637	1	facultas	facultas	PROPN
ejpam-5894	637	2	rerum	rerum	PROPN
ejpam-5894	637	3	naturalium	naturalium	PROPN
ejpam-5894	637	4	.	.	PUNCT
ejpam-5894	638	1	mathematica	mathematica	PROPN
ejpam-5894	638	2	,	,	PUNCT
ejpam-5894	638	3	44(1):19–23	44(1):19–23	NUM
ejpam-5894	638	4	,	,	PUNCT
ejpam-5894	638	5	2005	2005	NUM
ejpam-5894	638	6	.	.	PUNCT
ejpam-5894	639	1	[	[	X
ejpam-5894	639	2	12	12	NUM
ejpam-5894	639	3	]	]	X
ejpam-5894	639	4	i.	i.	NOUN
ejpam-5894	639	5	senturk	senturk	PROPN
ejpam-5894	639	6	.	.	PUNCT
ejpam-5894	640	1	a	a	DET
ejpam-5894	640	2	new	new	ADJ
ejpam-5894	640	3	on	on	ADP
ejpam-5894	640	4	state	state	NOUN
ejpam-5894	640	5	operators	operator	NOUN
ejpam-5894	640	6	in	in	ADP
ejpam-5894	640	7	sheffer	sheffer	PROPN
ejpam-5894	640	8	stroke	stroke	NOUN
ejpam-5894	640	9	basic	basic	ADJ
ejpam-5894	640	10	algebras	algebra	NOUN
ejpam-5894	640	11	.	.	PUNCT
ejpam-5894	640	12	soft	soft	ADJ
ejpam-5894	640	13	computing	computing	NOUN
ejpam-5894	640	14	,	,	PUNCT
ejpam-5894	640	15	25:11471–11484	25:11471–11484	NUM
ejpam-5894	640	16	,	,	PUNCT
ejpam-5894	640	17	2021	2021	NUM
ejpam-5894	640	18	.	.	PUNCT
ejpam-5894	641	1	[	[	X
ejpam-5894	641	2	13	13	NUM
ejpam-5894	641	3	]	]	PUNCT
ejpam-5894	641	4	i.	i.	NOUN
ejpam-5894	641	5	senturk	senturk	PROPN
ejpam-5894	641	6	.	.	PUNCT
ejpam-5894	642	1	riečan	riečan	NOUN
ejpam-5894	642	2	and	and	CCONJ
ejpam-5894	642	3	bosbach	bosbach	ADJ
ejpam-5894	642	4	state	state	NOUN
ejpam-5894	642	5	operators	operator	NOUN
ejpam-5894	642	6	on	on	ADP
ejpam-5894	642	7	sheffer	sheffer	PROPN
ejpam-5894	642	8	stroke	stroke	NOUN
ejpam-5894	642	9	mtl	mtl	PROPN
ejpam-5894	642	10	-	-	PUNCT
ejpam-5894	642	11	algebras	algebras	PROPN
ejpam-5894	642	12	.	.	PUNCT
ejpam-5894	643	1	bulletin	bulletin	NOUN
ejpam-5894	643	2	of	of	ADP
ejpam-5894	643	3	the	the	DET
ejpam-5894	643	4	international	international	ADJ
ejpam-5894	643	5	mathematical	mathematical	ADJ
ejpam-5894	643	6	virtual	virtual	PROPN
ejpam-5894	643	7	institute	institute	PROPN
ejpam-5894	643	8	,	,	PUNCT
ejpam-5894	643	9	12(1):181–193	12(1):181–193	PROPN
ejpam-5894	643	10	,	,	PUNCT
ejpam-5894	643	11	2022	2022	NUM
ejpam-5894	643	12	.	.	PUNCT
ejpam-5894	644	1	[	[	X
ejpam-5894	644	2	14	14	NUM
ejpam-5894	644	3	]	]	X
ejpam-5894	644	4	n.	n.	PROPN
ejpam-5894	644	5	chunsee	chunsee	PROPN
ejpam-5894	644	6	,	,	PUNCT
ejpam-5894	644	7	p.	p.	PROPN
ejpam-5894	644	8	julatha	julatha	PROPN
ejpam-5894	644	9	,	,	PUNCT
ejpam-5894	644	10	and	and	CCONJ
ejpam-5894	644	11	a.	a.	NOUN
ejpam-5894	644	12	iampan	iampan	PROPN
ejpam-5894	644	13	.	.	PUNCT
ejpam-5894	645	1	fuzzy	fuzzy	ADJ
ejpam-5894	645	2	set	set	VERB
ejpam-5894	645	3	approach	approach	NOUN
ejpam-5894	645	4	to	to	ADP
ejpam-5894	645	5	ideal	ideal	ADJ
ejpam-5894	645	6	theory	theory	NOUN
ejpam-5894	645	7	on	on	ADP
ejpam-5894	645	8	sheffer	sheffer	PROPN
ejpam-5894	645	9	stroke	stroke	NOUN
ejpam-5894	645	10	be	be	AUX
ejpam-5894	645	11	-	-	PUNCT
ejpam-5894	645	12	algebras	algebra	NOUN
ejpam-5894	645	13	.	.	PUNCT
ejpam-5894	646	1	journal	journal	PROPN
ejpam-5894	646	2	of	of	ADP
ejpam-5894	646	3	mathematics	mathematic	NOUN
ejpam-5894	646	4	and	and	CCONJ
ejpam-5894	646	5	computer	computer	NOUN
ejpam-5894	646	6	science	science	NOUN
ejpam-5894	646	7	,	,	PUNCT
ejpam-5894	646	8	34(3):283–294	34(3):283–294	NUM
ejpam-5894	646	9	,	,	PUNCT
ejpam-5894	646	10	2024	2024	NUM
ejpam-5894	646	11	.	.	PUNCT
ejpam-5894	647	1	[	[	X
ejpam-5894	647	2	15	15	NUM
ejpam-5894	647	3	]	]	X
ejpam-5894	647	4	t.	t.	NOUN
ejpam-5894	647	5	oner	oner	NOUN
ejpam-5894	647	6	,	,	PUNCT
ejpam-5894	647	7	t.	t.	PROPN
ejpam-5894	647	8	kalkan	kalkan	PROPN
ejpam-5894	647	9	,	,	PUNCT
ejpam-5894	647	10	and	and	CCONJ
ejpam-5894	647	11	n.	n.	PROPN
ejpam-5894	647	12	k.	k.	PROPN
ejpam-5894	647	13	gursoy	gursoy	PROPN
ejpam-5894	647	14	.	.	PUNCT
ejpam-5894	648	1	sheffer	sheffer	PROPN
ejpam-5894	648	2	stroke	stroke	PROPN
ejpam-5894	648	3	bg	bg	PROPN
ejpam-5894	648	4	-	-	PUNCT
ejpam-5894	648	5	algebras	algebras	PROPN
ejpam-5894	648	6	.	.	PUNCT
ejpam-5894	649	1	international	international	ADJ
ejpam-5894	649	2	journal	journal	PROPN
ejpam-5894	649	3	of	of	ADP
ejpam-5894	649	4	maps	map	NOUN
ejpam-5894	649	5	in	in	ADP
ejpam-5894	649	6	mathematics	mathematic	NOUN
ejpam-5894	649	7	,	,	PUNCT
ejpam-5894	649	8	4(1):27–39	4(1):27–39	NUM
ejpam-5894	649	9	,	,	PUNCT
ejpam-5894	649	10	2021	2021	NUM
ejpam-5894	649	11	.	.	PUNCT
ejpam-5894	650	1	[	[	X
ejpam-5894	650	2	16	16	NUM
ejpam-5894	650	3	]	]	PUNCT
ejpam-5894	650	4	k.	k.	PROPN
ejpam-5894	650	5	t.	t.	PROPN
ejpam-5894	650	6	atanassov	atanassov	PROPN
ejpam-5894	650	7	.	.	PUNCT
ejpam-5894	651	1	intuitionistic	intuitionistic	ADJ
ejpam-5894	651	2	fuzzy	fuzzy	ADJ
ejpam-5894	651	3	sets	set	NOUN
ejpam-5894	651	4	.	.	PUNCT
ejpam-5894	652	1	fuzzy	fuzzy	ADJ
ejpam-5894	652	2	sets	set	NOUN
ejpam-5894	652	3	and	and	CCONJ
ejpam-5894	652	4	systems	system	NOUN
ejpam-5894	652	5	,	,	PUNCT
ejpam-5894	652	6	20(1):87–96	20(1):87–96	NUM
ejpam-5894	652	7	,	,	PUNCT
ejpam-5894	652	8	1986	1986	NUM
ejpam-5894	652	9	.	.	PUNCT
ejpam-5894	653	1	[	[	X
ejpam-5894	653	2	17	17	NUM
ejpam-5894	653	3	]	]	PUNCT
ejpam-5894	653	4	t.	t.	PROPN
ejpam-5894	653	5	katican	katican	PROPN
ejpam-5894	653	6	,	,	PUNCT
ejpam-5894	653	7	t.	t.	PROPN
ejpam-5894	653	8	oner	oner	NOUN
ejpam-5894	653	9	,	,	PUNCT
ejpam-5894	653	10	and	and	CCONJ
ejpam-5894	653	11	a.	a.	PROPN
ejpam-5894	653	12	b.	b.	PROPN
ejpam-5894	653	13	saeid	saeid	PROPN
ejpam-5894	653	14	.	.	PUNCT
ejpam-5894	654	1	on	on	ADP
ejpam-5894	654	2	sheffer	sheffer	PROPN
ejpam-5894	654	3	stroke	stroke	NOUN
ejpam-5894	654	4	be	be	AUX
ejpam-5894	654	5	-	-	PUNCT
ejpam-5894	654	6	algebras	algebra	NOUN
ejpam-5894	654	7	.	.	PUNCT
ejpam-5894	655	1	discussiones	discussione	NOUN
ejpam-5894	655	2	mathematicae	mathematicae	VERB
ejpam-5894	655	3	general	general	ADJ
ejpam-5894	655	4	algebra	algebra	PROPN
ejpam-5894	655	5	and	and	CCONJ
ejpam-5894	655	6	applications	application	NOUN
ejpam-5894	655	7	,	,	PUNCT
ejpam-5894	655	8	42:293–314	42:293–314	PROPN
ejpam-5894	655	9	,	,	PUNCT
ejpam-5894	655	10	2022	2022	NUM
ejpam-5894	655	11	.	.	PUNCT
ejpam-5894	656	1	[	[	X
ejpam-5894	656	2	18	18	NUM
ejpam-5894	656	3	]	]	PUNCT
ejpam-5894	656	4	t.	t.	NOUN
ejpam-5894	656	5	oner	oner	NOUN
ejpam-5894	656	6	,	,	PUNCT
ejpam-5894	656	7	i.	i.	PROPN
ejpam-5894	656	8	senturk	senturk	PROPN
ejpam-5894	656	9	,	,	PUNCT
ejpam-5894	656	10	y.	y.	PROPN
ejpam-5894	656	11	b.	b.	PROPN
ejpam-5894	656	12	jun	jun	PROPN
ejpam-5894	656	13	,	,	PUNCT
ejpam-5894	656	14	and	and	CCONJ
ejpam-5894	656	15	a.	a.	PROPN
ejpam-5894	656	16	b.	b.	PROPN
ejpam-5894	656	17	saeid	saeid	PROPN
ejpam-5894	656	18	.	.	PUNCT
ejpam-5894	657	1	sheffer	sheffer	PROPN
ejpam-5894	657	2	stroke	stroke	PROPN
ejpam-5894	657	3	be	be	AUX
ejpam-5894	657	4	-	-	PUNCT
ejpam-5894	657	5	algebras	algebra	NOUN
ejpam-5894	657	6	based	base	VERB
ejpam-5894	657	7	on	on	ADP
ejpam-5894	657	8	the	the	DET
ejpam-5894	657	9	soft	soft	ADJ
ejpam-5894	657	10	environment	environment	NOUN
ejpam-5894	657	11	.	.	PUNCT
ejpam-5894	658	1	journal	journal	NOUN
ejpam-5894	658	2	of	of	ADP
ejpam-5894	658	3	algebraic	algebraic	PROPN
ejpam-5894	658	4	systems	system	NOUN
ejpam-5894	658	5	,	,	PUNCT
ejpam-5894	658	6	articles	article	NOUN
ejpam-5894	658	7	in	in	ADP
ejpam-5894	658	8	press	press	NOUN
ejpam-5894	658	9	.	.	PUNCT
ejpam-5894	659	1	[	[	X
ejpam-5894	659	2	19	19	NUM
ejpam-5894	659	3	]	]	PUNCT
ejpam-5894	659	4	t.	t.	NOUN
ejpam-5894	659	5	oner	oner	NOUN
ejpam-5894	659	6	and	and	CCONJ
ejpam-5894	659	7	y.	y.	PROPN
ejpam-5894	659	8	b.	b.	PROPN
ejpam-5894	659	9	jun	jun	PROPN
ejpam-5894	659	10	.	.	PROPN
ejpam-5894	659	11	ideals	ideal	NOUN
ejpam-5894	659	12	of	of	ADP
ejpam-5894	659	13	sheffer	sheffer	PROPN
ejpam-5894	659	14	stroke	stroke	PROPN
ejpam-5894	659	15	hilbert	hilbert	PROPN
ejpam-5894	659	16	algebras	algebras	PROPN
ejpam-5894	659	17	based	base	VERB
ejpam-5894	659	18	on	on	ADP
ejpam-5894	659	19	fuzzy	fuzzy	ADJ
ejpam-5894	659	20	points	point	NOUN
ejpam-5894	659	21	.	.	PUNCT
ejpam-5894	660	1	t.	t.	PROPN
ejpam-5894	660	2	oner	oner	PROPN
ejpam-5894	660	3	et	et	PROPN
ejpam-5894	660	4	al	al	PROPN
ejpam-5894	660	5	.	.	PUNCT
ejpam-5894	660	6	/	/	SYM
ejpam-5894	660	7	eur	eur	PROPN
ejpam-5894	660	8	.	.	PUNCT
ejpam-5894	661	1	j.	j.	PROPN
ejpam-5894	661	2	pure	pure	PROPN
ejpam-5894	661	3	appl	appl	PROPN
ejpam-5894	661	4	.	.	PROPN
ejpam-5894	661	5	math	math	PROPN
ejpam-5894	661	6	,	,	PUNCT
ejpam-5894	661	7	18	18	NUM
ejpam-5894	661	8	(	(	PUNCT
ejpam-5894	661	9	3	3	NUM
ejpam-5894	661	10	)	)	PUNCT
ejpam-5894	661	11	(	(	PUNCT
ejpam-5894	661	12	2025	2025	NUM
ejpam-5894	661	13	)	)	PUNCT
ejpam-5894	661	14	,	,	PUNCT
ejpam-5894	661	15	5894	5894	NUM
ejpam-5894	661	16	33	33	NUM
ejpam-5894	661	17	of	of	ADP
ejpam-5894	661	18	33	33	NUM
ejpam-5894	661	19	honam	honam	PROPN
ejpam-5894	661	20	mathematical	mathematical	ADJ
ejpam-5894	661	21	journal	journal	NOUN
ejpam-5894	661	22	,	,	PUNCT
ejpam-5894	661	23	46:82–100	46:82–100	NUM
ejpam-5894	661	24	,	,	PUNCT
ejpam-5894	661	25	2021	2021	NUM
ejpam-5894	661	26	.	.	PUNCT
ejpam-5894	662	1	[	[	X
ejpam-5894	662	2	20	20	NUM
ejpam-5894	662	3	]	]	X
ejpam-5894	662	4	n.	n.	PROPN
ejpam-5894	662	5	rajesh	rajesh	PROPN
ejpam-5894	662	6	,	,	PUNCT
ejpam-5894	662	7	t.	t.	PROPN
ejpam-5894	662	8	oner	oner	NOUN
ejpam-5894	662	9	,	,	PUNCT
ejpam-5894	662	10	a.	a.	NOUN
ejpam-5894	662	11	iampan	iampan	PROPN
ejpam-5894	662	12	,	,	PUNCT
ejpam-5894	662	13	and	and	CCONJ
ejpam-5894	662	14	i.	i.	PROPN
ejpam-5894	662	15	senturk	senturk	PROPN
ejpam-5894	662	16	.	.	PUNCT
ejpam-5894	663	1	on	on	ADP
ejpam-5894	663	2	length	length	NOUN
ejpam-5894	663	3	and	and	CCONJ
ejpam-5894	663	4	mean	mean	VERB
ejpam-5894	663	5	fuzzy	fuzzy	ADJ
ejpam-5894	663	6	ideals	ideal	NOUN
ejpam-5894	663	7	of	of	ADP
ejpam-5894	663	8	sheffer	sheffer	PROPN
ejpam-5894	663	9	stroke	stroke	PROPN
ejpam-5894	663	10	hilbert	hilbert	PROPN
ejpam-5894	663	11	algebras	algebras	PROPN
ejpam-5894	663	12	.	.	PUNCT
ejpam-5894	664	1	european	european	PROPN
ejpam-5894	664	2	journal	journal	PROPN
ejpam-5894	664	3	of	of	ADP
ejpam-5894	664	4	pure	pure	ADJ
ejpam-5894	664	5	and	and	CCONJ
ejpam-5894	664	6	applied	applied	ADJ
ejpam-5894	664	7	mathematics	mathematic	NOUN
ejpam-5894	664	8	,	,	PUNCT
ejpam-5894	664	9	18(1):5779	18(1):5779	NUM
ejpam-5894	664	10	,	,	PUNCT
ejpam-5894	664	11	2025	2025	NUM
ejpam-5894	664	12	.	.	PUNCT
ejpam-5894	665	1	[	[	X
ejpam-5894	665	2	21	21	NUM
ejpam-5894	665	3	]	]	X
ejpam-5894	665	4	t.	t.	NOUN
ejpam-5894	665	5	oner	oner	NOUN
ejpam-5894	665	6	,	,	PUNCT
ejpam-5894	665	7	n.	n.	PROPN
ejpam-5894	665	8	rajesh	rajesh	PROPN
ejpam-5894	665	9	,	,	PUNCT
ejpam-5894	665	10	a.	a.	NOUN
ejpam-5894	665	11	iampan	iampan	PROPN
ejpam-5894	665	12	,	,	PUNCT
ejpam-5894	665	13	and	and	CCONJ
ejpam-5894	665	14	a.	a.	PROPN
ejpam-5894	665	15	b.	b.	PROPN
ejpam-5894	665	16	saeid	saeid	PROPN
ejpam-5894	665	17	.	.	PUNCT
ejpam-5894	665	18	soft	soft	ADJ
ejpam-5894	665	19	subalgebras	subalgebra	NOUN
ejpam-5894	665	20	and	and	CCONJ
ejpam-5894	665	21	ideals	ideal	NOUN
ejpam-5894	665	22	of	of	ADP
ejpam-5894	665	23	sheffer	sheffer	PROPN
ejpam-5894	665	24	stroke	stroke	PROPN
ejpam-5894	665	25	hilbert	hilbert	PROPN
ejpam-5894	665	26	algebras	algebras	PROPN
ejpam-5894	665	27	based	base	VERB
ejpam-5894	665	28	on	on	ADP
ejpam-5894	665	29	n	n	DET
ejpam-5894	665	30	-structures	-structure	NOUN
ejpam-5894	665	31	.	.	PUNCT
ejpam-5894	666	1	european	european	ADJ
ejpam-5894	666	2	journal	journal	PROPN
ejpam-5894	666	3	of	of	ADP
ejpam-5894	666	4	pure	pure	ADJ
ejpam-5894	666	5	and	and	CCONJ
ejpam-5894	666	6	applied	applied	ADJ
ejpam-5894	666	7	mathematics	mathematic	NOUN
ejpam-5894	666	8	,	,	PUNCT
ejpam-5894	666	9	18(2):6018	18(2):6018	NUM
ejpam-5894	666	10	,	,	PUNCT
ejpam-5894	666	11	2025	2025	NUM
ejpam-5894	666	12	.	.	PUNCT
ejpam-5894	667	1	[	[	X
ejpam-5894	667	2	22	22	NUM
ejpam-5894	667	3	]	]	X
ejpam-5894	667	4	n.	n.	PROPN
ejpam-5894	667	5	rajesh	rajesh	PROPN
ejpam-5894	667	6	,	,	PUNCT
ejpam-5894	667	7	t.	t.	PROPN
ejpam-5894	667	8	oner	oner	NOUN
ejpam-5894	667	9	,	,	PUNCT
ejpam-5894	667	10	a.	a.	NOUN
ejpam-5894	667	11	iampan	iampan	PROPN
ejpam-5894	667	12	,	,	PUNCT
ejpam-5894	667	13	and	and	CCONJ
ejpam-5894	667	14	a.	a.	NOUN
ejpam-5894	667	15	rezaei	rezaei	PROPN
ejpam-5894	667	16	.	.	PUNCT
ejpam-5894	668	1	investigating	investigate	VERB
ejpam-5894	668	2	length	length	NOUN
ejpam-5894	668	3	and	and	CCONJ
ejpam-5894	668	4	mean	mean	ADJ
ejpam-5894	668	5	-	-	PUNCT
ejpam-5894	668	6	fuzzy	fuzzy	ADJ
ejpam-5894	668	7	subalgebras	subalgebra	NOUN
ejpam-5894	668	8	in	in	ADP
ejpam-5894	668	9	sheffer	sheffer	PROPN
ejpam-5894	668	10	stroke	stroke	PROPN
ejpam-5894	668	11	hilbert	hilbert	PROPN
ejpam-5894	668	12	algebras	algebras	PROPN
ejpam-5894	668	13	.	.	PUNCT
ejpam-5894	669	1	european	european	PROPN
ejpam-5894	669	2	journal	journal	PROPN
ejpam-5894	669	3	of	of	ADP
ejpam-5894	669	4	pure	pure	ADJ
ejpam-5894	669	5	and	and	CCONJ
ejpam-5894	669	6	applied	applied	ADJ
ejpam-5894	669	7	mathematics	mathematic	NOUN
ejpam-5894	669	8	,	,	PUNCT
ejpam-5894	669	9	18(2):5914	18(2):5914	NUM
ejpam-5894	669	10	,	,	PUNCT
ejpam-5894	669	11	2025	2025	NUM
ejpam-5894	669	12	.	.	PUNCT
ejpam-5894	670	1	[	[	X
ejpam-5894	670	2	23	23	NUM
ejpam-5894	670	3	]	]	PUNCT
ejpam-5894	670	4	t.	t.	NOUN
ejpam-5894	670	5	oner	oner	NOUN
ejpam-5894	670	6	,	,	PUNCT
ejpam-5894	670	7	y.	y.	PROPN
ejpam-5894	670	8	b.	b.	PROPN
ejpam-5894	670	9	jun	jun	PROPN
ejpam-5894	670	10	,	,	PUNCT
ejpam-5894	670	11	and	and	CCONJ
ejpam-5894	670	12	i.	i.	PROPN
ejpam-5894	670	13	senturk	senturk	PROPN
ejpam-5894	670	14	.	.	PUNCT
ejpam-5894	671	1	subalgebras	subalgebras	PROPN
ejpam-5894	671	2	of	of	ADP
ejpam-5894	671	3	sheffer	sheffer	PROPN
ejpam-5894	671	4	stroke	stroke	PROPN
ejpam-5894	671	5	bck	bck	PROPN
ejpam-5894	671	6	-	-	PUNCT
ejpam-5894	671	7	algebras	algebra	NOUN
ejpam-5894	671	8	illuminated	illuminate	VERB
ejpam-5894	671	9	by	by	ADP
ejpam-5894	671	10	the	the	DET
ejpam-5894	671	11	new	new	ADJ
ejpam-5894	671	12	fuzzy	fuzzy	ADJ
ejpam-5894	671	13	set	set	NOUN
ejpam-5894	671	14	environment	environment	NOUN
ejpam-5894	671	15	.	.	PUNCT
ejpam-5894	672	1	new	new	ADJ
ejpam-5894	672	2	mathematics	mathematic	NOUN
ejpam-5894	672	3	and	and	CCONJ
ejpam-5894	672	4	natural	natural	ADJ
ejpam-5894	672	5	computation	computation	NOUN
ejpam-5894	672	6	,	,	PUNCT
ejpam-5894	672	7	page	page	NOUN
ejpam-5894	672	8	1–16	1–16	NOUN
ejpam-5894	672	9	,	,	PUNCT
ejpam-5894	672	10	online	online	ADV
ejpam-5894	672	11	ready	ready	ADJ
ejpam-5894	672	12	.	.	PUNCT
ejpam-5894	673	1	[	[	X
ejpam-5894	673	2	24	24	NUM
ejpam-5894	673	3	]	]	PUNCT
ejpam-5894	673	4	t.	t.	NOUN
ejpam-5894	673	5	oner	oner	PROPN
ejpam-5894	673	6	,	,	PUNCT
ejpam-5894	673	7	i.	i.	PROPN
ejpam-5894	673	8	senturk	senturk	PROPN
ejpam-5894	673	9	,	,	PUNCT
ejpam-5894	673	10	and	and	CCONJ
ejpam-5894	673	11	a.	a.	NOUN
ejpam-5894	673	12	rezaei	rezaei	PROPN
ejpam-5894	673	13	.	.	PUNCT
ejpam-5894	674	1	a	a	DET
ejpam-5894	674	2	note	note	NOUN
ejpam-5894	674	3	on	on	ADP
ejpam-5894	674	4	translation	translation	NOUN
ejpam-5894	674	5	of	of	ADP
ejpam-5894	674	6	bipolar	bipolar	ADV
ejpam-5894	674	7	-	-	PUNCT
ejpam-5894	674	8	valued	value	VERB
ejpam-5894	674	9	fuzzy	fuzzy	ADJ
ejpam-5894	674	10	sets	set	NOUN
ejpam-5894	674	11	in	in	ADP
ejpam-5894	674	12	sheffer	sheffer	PROPN
ejpam-5894	674	13	stroke	stroke	NOUN
ejpam-5894	674	14	mtl	mtl	PROPN
ejpam-5894	674	15	-	-	PUNCT
ejpam-5894	674	16	algebras	algebras	PROPN
ejpam-5894	674	17	.	.	PUNCT
ejpam-5894	675	1	in	in	ADP
ejpam-5894	675	2	said	said	PROPN
ejpam-5894	675	3	broumi	broumi	PROPN
ejpam-5894	675	4	,	,	PUNCT
ejpam-5894	675	5	d.	d.	PROPN
ejpam-5894	675	6	nagarajan	nagarajan	PROPN
ejpam-5894	675	7	,	,	PUNCT
ejpam-5894	675	8	michael	michael	PROPN
ejpam-5894	675	9	gr	gr	PROPN
ejpam-5894	675	10	.	.	PROPN
ejpam-5894	675	11	voskoglou	voskoglou	PROPN
ejpam-5894	675	12	,	,	PUNCT
ejpam-5894	675	13	and	and	CCONJ
ejpam-5894	675	14	s.	s.	PROPN
ejpam-5894	675	15	a.	a.	PROPN
ejpam-5894	675	16	edalatpanah	edalatpanah	PROPN
ejpam-5894	675	17	,	,	PUNCT
ejpam-5894	675	18	editors	editor	NOUN
ejpam-5894	675	19	,	,	PUNCT
ejpam-5894	675	20	data	datum	NOUN
ejpam-5894	675	21	-	-	PUNCT
ejpam-5894	675	22	driven	drive	VERB
ejpam-5894	675	23	modelling	modelling	NOUN
ejpam-5894	675	24	with	with	ADP
ejpam-5894	675	25	fuzzy	fuzzy	ADJ
ejpam-5894	675	26	sets	set	NOUN
ejpam-5894	675	27	,	,	PUNCT
ejpam-5894	675	28	pages	page	NOUN
ejpam-5894	675	29	177–203	177–203	NUM
ejpam-5894	675	30	.	.	PUNCT
ejpam-5894	676	1	crc	crc	PROPN
ejpam-5894	676	2	press	press	PROPN
ejpam-5894	676	3	,	,	PUNCT
ejpam-5894	676	4	boca	boca	PROPN
ejpam-5894	676	5	raton	raton	PROPN
ejpam-5894	676	6	,	,	PUNCT
ejpam-5894	676	7	2024	2024	NUM
ejpam-5894	676	8	.	.	PUNCT
ejpam-5894	677	1	[	[	X
ejpam-5894	677	2	25	25	NUM
ejpam-5894	677	3	]	]	X
ejpam-5894	677	4	y.	y.	PROPN
ejpam-5894	677	5	b.	b.	PROPN
ejpam-5894	677	6	jun	jun	PROPN
ejpam-5894	677	7	,	,	PUNCT
ejpam-5894	677	8	t.	t.	PROPN
ejpam-5894	677	9	oner	oner	PROPN
ejpam-5894	677	10	,	,	PUNCT
ejpam-5894	677	11	d.	d.	PROPN
ejpam-5894	677	12	s.	s.	PROPN
ejpam-5894	677	13	turan	turan	PROPN
ejpam-5894	677	14	,	,	PUNCT
ejpam-5894	677	15	and	and	CCONJ
ejpam-5894	677	16	b.	b.	PROPN
ejpam-5894	677	17	ordin	ordin	PROPN
ejpam-5894	677	18	.	.	PUNCT
ejpam-5894	678	1	bipolar	bipolar	ADJ
ejpam-5894	678	2	-	-	PUNCT
ejpam-5894	678	3	valued	value	VERB
ejpam-5894	678	4	fuzzy	fuzzy	ADJ
ejpam-5894	678	5	filters	filter	NOUN
ejpam-5894	678	6	of	of	ADP
ejpam-5894	678	7	sheffer	sheffer	PROPN
ejpam-5894	678	8	stroke	stroke	PROPN
ejpam-5894	678	9	bl	bl	PROPN
ejpam-5894	678	10	-	-	PUNCT
ejpam-5894	678	11	algebras	algebras	PROPN
ejpam-5894	678	12	.	.	PUNCT
ejpam-5894	679	1	new	new	ADJ
ejpam-5894	679	2	mathematics	mathematic	NOUN
ejpam-5894	679	3	and	and	CCONJ
ejpam-5894	679	4	natural	natural	ADJ
ejpam-5894	679	5	computation	computation	NOUN
ejpam-5894	679	6	,	,	PUNCT
ejpam-5894	679	7	20(2):505–521	20(2):505–521	NOUN
ejpam-5894	679	8	,	,	PUNCT
ejpam-5894	679	9	2024	2024	NUM
ejpam-5894	679	10	.	.	PUNCT
ejpam-5894	680	1	[	[	X
ejpam-5894	680	2	26	26	NUM
ejpam-5894	680	3	]	]	X
ejpam-5894	680	4	i.	i.	NOUN
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ejpam-5894	680	6	,	,	PUNCT
ejpam-5894	680	7	t.	t.	PROPN
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ejpam-5894	680	9	,	,	PUNCT
ejpam-5894	680	10	y.	y.	PROPN
ejpam-5894	680	11	b.	b.	PROPN
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ejpam-5894	680	13	,	,	PUNCT
ejpam-5894	680	14	and	and	CCONJ
ejpam-5894	680	15	a.	a.	PROPN
ejpam-5894	680	16	b.	b.	PROPN
ejpam-5894	680	17	saeid	saeid	PROPN
ejpam-5894	680	18	.	.	PUNCT
ejpam-5894	681	1	exploring	explore	VERB
ejpam-5894	681	2	fuzzy	fuzzy	ADJ
ejpam-5894	681	3	filters	filter	NOUN
ejpam-5894	681	4	and	and	CCONJ
ejpam-5894	681	5	their	their	PRON
ejpam-5894	681	6	relationships	relationship	NOUN
ejpam-5894	681	7	on	on	ADP
ejpam-5894	681	8	sheffer	sheffer	PROPN
ejpam-5894	681	9	stroke	stroke	NOUN
ejpam-5894	681	10	basic	basic	ADJ
ejpam-5894	681	11	algebras	algebra	NOUN
ejpam-5894	681	12	.	.	PUNCT
ejpam-5894	681	13	soft	soft	ADJ
ejpam-5894	681	14	computing	computing	NOUN
ejpam-5894	681	15	,	,	PUNCT
ejpam-5894	681	16	28:12507–12520	28:12507–12520	NUM
ejpam-5894	681	17	,	,	PUNCT
ejpam-5894	681	18	2024	2024	NUM
ejpam-5894	681	19	.	.	PUNCT
ejpam-5894	682	1	[	[	X
ejpam-5894	682	2	27	27	NUM
ejpam-5894	682	3	]	]	PUNCT
ejpam-5894	682	4	t.	t.	NOUN
ejpam-5894	682	5	oner	oner	NOUN
ejpam-5894	682	6	,	,	PUNCT
ejpam-5894	682	7	t.	t.	PROPN
ejpam-5894	682	8	kalkan	kalkan	PROPN
ejpam-5894	682	9	,	,	PUNCT
ejpam-5894	682	10	and	and	CCONJ
ejpam-5894	682	11	m.	m.	NOUN
ejpam-5894	682	12	cakar	cakar	PROPN
ejpam-5894	682	13	.	.	PUNCT
ejpam-5894	683	1	sheffer	sheffer	PROPN
ejpam-5894	683	2	stroke	stroke	PROPN
ejpam-5894	683	3	bch	bch	PROPN
ejpam-5894	683	4	-	-	PUNCT
ejpam-5894	683	5	algebras	algebras	PROPN
ejpam-5894	683	6	.	.	PUNCT
ejpam-5894	683	7	journal	journal	PROPN
ejpam-5894	683	8	of	of	ADP
ejpam-5894	683	9	international	international	PROPN
ejpam-5894	683	10	mathematical	mathematical	ADJ
ejpam-5894	683	11	virtual	virtual	PROPN
ejpam-5894	683	12	institute	institute	NOUN
ejpam-5894	683	13	,	,	PUNCT
ejpam-5894	683	14	11(1):119–135	11(1):119–135	PROPN
ejpam-5894	683	15	,	,	PUNCT
ejpam-5894	683	16	2021	2021	NUM
ejpam-5894	683	17	.	.	PUNCT
ejpam-5894	684	1	[	[	X
ejpam-5894	684	2	28	28	NUM
ejpam-5894	684	3	]	]	X
ejpam-5894	684	4	t.	t.	NOUN
ejpam-5894	684	5	oner	oner	NOUN
ejpam-5894	684	6	,	,	PUNCT
ejpam-5894	684	7	t.	t.	PROPN
ejpam-5894	684	8	kalkan	kalkan	PROPN
ejpam-5894	684	9	,	,	PUNCT
ejpam-5894	684	10	and	and	CCONJ
ejpam-5894	684	11	a.	a.	PROPN
ejpam-5894	684	12	b.	b.	PROPN
ejpam-5894	684	13	saeid	saeid	PROPN
ejpam-5894	684	14	.	.	PUNCT
ejpam-5894	685	1	sheffer	sheffer	PROPN
ejpam-5894	685	2	stroke	stroke	PROPN
ejpam-5894	685	3	bh	bh	PROPN
ejpam-5894	685	4	-	-	PUNCT
ejpam-5894	685	5	algebras	algebras	PROPN
ejpam-5894	685	6	.	.	PUNCT
ejpam-5894	686	1	international	international	ADJ
ejpam-5894	686	2	journal	journal	PROPN
ejpam-5894	686	3	of	of	ADP
ejpam-5894	686	4	maps	map	NOUN
ejpam-5894	686	5	in	in	ADP
ejpam-5894	686	6	mathematics	mathematic	NOUN
ejpam-5894	686	7	,	,	PUNCT
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ejpam-5894	686	9	,	,	PUNCT
ejpam-5894	686	10	2024	2024	NUM
ejpam-5894	686	11	.	.	PUNCT
ejpam-5894	687	1	[	[	X
ejpam-5894	687	2	29	29	NUM
ejpam-5894	687	3	]	]	X
ejpam-5894	687	4	n.	n.	PROPN
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ejpam-5894	687	6	,	,	PUNCT
ejpam-5894	687	7	t.	t.	PROPN
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ejpam-5894	687	9	,	,	PUNCT
ejpam-5894	687	10	a.	a.	NOUN
ejpam-5894	687	11	iampan	iampan	PROPN
ejpam-5894	687	12	,	,	PUNCT
ejpam-5894	687	13	and	and	CCONJ
ejpam-5894	687	14	i.	i.	PROPN
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ejpam-5894	687	16	.	.	PUNCT
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ejpam-5894	688	2	fuzzy	fuzzy	ADJ
ejpam-5894	688	3	structures	structure	NOUN
ejpam-5894	688	4	on	on	ADP
ejpam-5894	688	5	sheffer	sheffer	NOUN
ejpam-5894	688	6	stroke	stroke	NOUN
ejpam-5894	688	7	up	up	ADP
ejpam-5894	688	8	-	-	PUNCT
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ejpam-5894	688	10	.	.	PUNCT
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ejpam-5894	689	2	journal	journal	PROPN
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ejpam-5894	689	4	pure	pure	ADJ
ejpam-5894	689	5	and	and	CCONJ
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ejpam-5894	689	7	mathematics	mathematic	NOUN
ejpam-5894	689	8	,	,	PUNCT
ejpam-5894	689	9	18(1):5627	18(1):5627	NUM
ejpam-5894	689	10	,	,	PUNCT
ejpam-5894	689	11	2025	2025	NUM
ejpam-5894	689	12	.	.	PUNCT
ejpam-5894	690	1	[	[	X
ejpam-5894	690	2	30	30	NUM
ejpam-5894	690	3	]	]	X
ejpam-5894	690	4	t.	t.	NOUN
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ejpam-5894	690	6	,	,	PUNCT
ejpam-5894	690	7	n.	n.	PROPN
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ejpam-5894	690	9	,	,	PUNCT
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ejpam-5894	691	1	semidetached	semidetache	VERB
ejpam-5894	691	2	sup	sup	NOUN
ejpam-5894	691	3	-	-	PUNCT
ejpam-5894	691	4	subalgebras	subalgebras	NOUN
ejpam-5894	691	5	of	of	ADP
ejpam-5894	691	6	sheffer	sheffer	PROPN
ejpam-5894	691	7	stroke	stroke	PROPN
ejpam-5894	691	8	up	up	ADP
ejpam-5894	691	9	-	-	PUNCT
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ejpam-5894	691	11	.	.	PUNCT
ejpam-5894	692	1	european	european	PROPN
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ejpam-5894	692	5	and	and	CCONJ
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ejpam-5894	692	8	,	,	PUNCT
ejpam-5894	692	9	18(2):5876	18(2):5876	NUM
ejpam-5894	692	10	,	,	PUNCT
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ejpam-5894	692	12	.	.	PUNCT