id	sid	tid	token	lemma	pos
ejpam-6529	1	1	european	european	PROPN
ejpam-6529	1	2	journal	journal	PROPN
ejpam-6529	1	3	of	of	ADP
ejpam-6529	1	4	pure	pure	ADJ
ejpam-6529	1	5	and	and	CCONJ
ejpam-6529	1	6	applied	applied	ADJ
ejpam-6529	1	7	mathematics	mathematic	NOUN
ejpam-6529	1	8	2025	2025	NUM
ejpam-6529	1	9	,	,	PUNCT
ejpam-6529	1	10	vol	vol	NOUN
ejpam-6529	1	11	.	.	PROPN
ejpam-6529	1	12	18	18	NUM
ejpam-6529	1	13	,	,	PUNCT
ejpam-6529	1	14	issue	issue	NOUN
ejpam-6529	1	15	3	3	NUM
ejpam-6529	1	16	,	,	PUNCT
ejpam-6529	1	17	article	article	NOUN
ejpam-6529	1	18	number	number	NOUN
ejpam-6529	1	19	6529	6529	NUM
ejpam-6529	1	20	issn	issn	PROPN
ejpam-6529	1	21	1307	1307	NUM
ejpam-6529	1	22	-	-	SYM
ejpam-6529	1	23	5543	5543	NUM
ejpam-6529	1	24	–	–	PUNCT
ejpam-6529	1	25	ejpam.com	ejpam.com	X
ejpam-6529	1	26	published	publish	VERB
ejpam-6529	1	27	by	by	ADP
ejpam-6529	1	28	new	new	PROPN
ejpam-6529	1	29	york	york	PROPN
ejpam-6529	1	30	business	business	PROPN
ejpam-6529	1	31	global	global	ADJ
ejpam-6529	1	32	weak	weak	ADJ
ejpam-6529	1	33	filters	filter	NOUN
ejpam-6529	1	34	of	of	ADP
ejpam-6529	1	35	sheffer	sheffer	PROPN
ejpam-6529	1	36	stroke	stroke	PROPN
ejpam-6529	1	37	hilbert	hilbert	PROPN
ejpam-6529	1	38	algebras	algebras	PROPN
ejpam-6529	1	39	based	base	VERB
ejpam-6529	1	40	on	on	ADP
ejpam-6529	1	41	the	the	DET
ejpam-6529	1	42	intuitionistic	intuitionistic	ADJ
ejpam-6529	1	43	fuzzy	fuzzy	ADJ
ejpam-6529	1	44	set	set	VERB
ejpam-6529	1	45	sun	sun	NOUN
ejpam-6529	1	46	shin	shin	PROPN
ejpam-6529	1	47	ahn1,∗	ahn1,∗	PROPN
ejpam-6529	1	48	,	,	PUNCT
ejpam-6529	1	49	young	young	ADJ
ejpam-6529	1	50	joo	joo	NOUN
ejpam-6529	1	51	seo2	seo2	PROPN
ejpam-6529	1	52	,	,	PUNCT
ejpam-6529	1	53	young	young	ADJ
ejpam-6529	1	54	bae	bae	NOUN
ejpam-6529	1	55	jun3	jun3	PROPN
ejpam-6529	1	56	1	1	NUM
ejpam-6529	1	57	department	department	NOUN
ejpam-6529	1	58	of	of	ADP
ejpam-6529	1	59	mathematics	mathematics	PROPN
ejpam-6529	1	60	education	education	NOUN
ejpam-6529	1	61	,	,	PUNCT
ejpam-6529	1	62	dongguk	dongguk	PROPN
ejpam-6529	1	63	university	university	PROPN
ejpam-6529	1	64	,	,	PUNCT
ejpam-6529	1	65	seoul	seoul	PROPN
ejpam-6529	1	66	04620	04620	NUM
ejpam-6529	1	67	,	,	PUNCT
ejpam-6529	1	68	korea	korea	PROPN
ejpam-6529	1	69	2	2	NUM
ejpam-6529	1	70	research	research	NOUN
ejpam-6529	1	71	institute	institute	NOUN
ejpam-6529	1	72	for	for	ADP
ejpam-6529	1	73	natural	natural	ADJ
ejpam-6529	1	74	sciences	science	NOUN
ejpam-6529	1	75	,	,	PUNCT
ejpam-6529	1	76	department	department	NOUN
ejpam-6529	1	77	of	of	ADP
ejpam-6529	1	78	mathematics	mathematics	PROPN
ejpam-6529	1	79	,	,	PUNCT
ejpam-6529	1	80	hanyang	hanyang	PROPN
ejpam-6529	1	81	university	university	PROPN
ejpam-6529	1	82	,	,	PUNCT
ejpam-6529	1	83	seoul	seoul	PROPN
ejpam-6529	1	84	04763	04763	NUM
ejpam-6529	1	85	,	,	PUNCT
ejpam-6529	1	86	korea	korea	PROPN
ejpam-6529	1	87	3	3	NUM
ejpam-6529	1	88	department	department	PROPN
ejpam-6529	1	89	of	of	ADP
ejpam-6529	1	90	mathematics	mathematics	PROPN
ejpam-6529	1	91	education	education	NOUN
ejpam-6529	1	92	,	,	PUNCT
ejpam-6529	1	93	gyeongsang	gyeongsang	PROPN
ejpam-6529	1	94	national	national	PROPN
ejpam-6529	1	95	university	university	PROPN
ejpam-6529	1	96	,	,	PUNCT
ejpam-6529	1	97	jinju	jinju	NOUN
ejpam-6529	1	98	52828	52828	NUM
ejpam-6529	1	99	,	,	PUNCT
ejpam-6529	1	100	korea	korea	PROPN
ejpam-6529	1	101	abstract	abstract	NOUN
ejpam-6529	1	102	.	.	PUNCT
ejpam-6529	2	1	using	use	VERB
ejpam-6529	2	2	the	the	DET
ejpam-6529	2	3	concept	concept	NOUN
ejpam-6529	2	4	of	of	ADP
ejpam-6529	2	5	intuitionistic	intuitionistic	ADJ
ejpam-6529	2	6	fuzzy	fuzzy	ADJ
ejpam-6529	2	7	points	point	NOUN
ejpam-6529	2	8	,	,	PUNCT
ejpam-6529	2	9	the	the	DET
ejpam-6529	2	10	weak	weak	ADJ
ejpam-6529	2	11	filter	filter	NOUN
ejpam-6529	2	12	in	in	ADP
ejpam-6529	2	13	sheffer	sheffer	PROPN
ejpam-6529	2	14	stroke	stroke	PROPN
ejpam-6529	2	15	hilbert	hilbert	PROPN
ejpam-6529	2	16	algebras	algebras	PROPN
ejpam-6529	2	17	is	be	AUX
ejpam-6529	2	18	addressed	address	VERB
ejpam-6529	2	19	.	.	PUNCT
ejpam-6529	3	1	the	the	DET
ejpam-6529	3	2	notion	notion	NOUN
ejpam-6529	3	3	of	of	ADP
ejpam-6529	3	4	intuitionistic	intuitionistic	ADJ
ejpam-6529	3	5	fuzzy	fuzzy	ADJ
ejpam-6529	3	6	weak	weak	ADJ
ejpam-6529	3	7	filters	filter	NOUN
ejpam-6529	3	8	in	in	ADP
ejpam-6529	3	9	sheffer	sheffer	PROPN
ejpam-6529	3	10	stroke	stroke	PROPN
ejpam-6529	3	11	hilbert	hilbert	PROPN
ejpam-6529	3	12	algebras	algebras	PROPN
ejpam-6529	3	13	is	be	AUX
ejpam-6529	3	14	introduced	introduce	VERB
ejpam-6529	3	15	,	,	PUNCT
ejpam-6529	3	16	and	and	CCONJ
ejpam-6529	3	17	their	their	PRON
ejpam-6529	3	18	properties	property	NOUN
ejpam-6529	3	19	are	be	AUX
ejpam-6529	3	20	investigated	investigate	VERB
ejpam-6529	3	21	.	.	PUNCT
ejpam-6529	4	1	conditions	condition	NOUN
ejpam-6529	4	2	under	under	ADP
ejpam-6529	4	3	which	which	PRON
ejpam-6529	4	4	the	the	DET
ejpam-6529	4	5	intuitionistic	intuitionistic	ADJ
ejpam-6529	4	6	fuzzy	fuzzy	ADJ
ejpam-6529	4	7	set	set	NOUN
ejpam-6529	4	8	becomes	become	VERB
ejpam-6529	4	9	an	an	DET
ejpam-6529	4	10	intuitionistic	intuitionistic	ADJ
ejpam-6529	4	11	fuzzy	fuzzy	ADJ
ejpam-6529	4	12	weak	weak	ADJ
ejpam-6529	4	13	filter	filter	NOUN
ejpam-6529	4	14	are	be	AUX
ejpam-6529	4	15	examined	examine	VERB
ejpam-6529	4	16	.	.	PUNCT
ejpam-6529	5	1	characterizations	characterization	NOUN
ejpam-6529	5	2	of	of	ADP
ejpam-6529	5	3	intuitionistic	intuitionistic	ADJ
ejpam-6529	5	4	fuzzy	fuzzy	ADJ
ejpam-6529	5	5	weak	weak	ADJ
ejpam-6529	5	6	filters	filter	NOUN
ejpam-6529	5	7	are	be	AUX
ejpam-6529	5	8	considered	consider	VERB
ejpam-6529	5	9	,	,	PUNCT
ejpam-6529	5	10	and	and	CCONJ
ejpam-6529	5	11	conditions	condition	NOUN
ejpam-6529	5	12	under	under	ADP
ejpam-6529	5	13	which	which	PRON
ejpam-6529	5	14	the	the	DET
ejpam-6529	5	15	intuitionistic	intuitionistic	ADJ
ejpam-6529	5	16	fuzzy	fuzzy	ADJ
ejpam-6529	5	17	set	set	NOUN
ejpam-6529	5	18	becomes	become	VERB
ejpam-6529	5	19	an	an	DET
ejpam-6529	5	20	intuitionistic	intuitionistic	ADJ
ejpam-6529	5	21	fuzzy	fuzzy	ADJ
ejpam-6529	5	22	weak	weak	ADJ
ejpam-6529	5	23	filter	filter	NOUN
ejpam-6529	5	24	are	be	AUX
ejpam-6529	5	25	discussed	discuss	VERB
ejpam-6529	5	26	.	.	PUNCT
ejpam-6529	6	1	the	the	DET
ejpam-6529	6	2	(	(	PUNCT
ejpam-6529	6	3	0	0	NUM
ejpam-6529	6	4	,	,	PUNCT
ejpam-6529	6	5	1)-set	1)-set	NOUN
ejpam-6529	6	6	for	for	ADP
ejpam-6529	6	7	the	the	DET
ejpam-6529	6	8	intuitionistic	intuitionistic	ADJ
ejpam-6529	6	9	fuzzy	fuzzy	ADJ
ejpam-6529	6	10	set	set	NOUN
ejpam-6529	6	11	is	be	AUX
ejpam-6529	6	12	established	establish	VERB
ejpam-6529	6	13	,	,	PUNCT
ejpam-6529	6	14	and	and	CCONJ
ejpam-6529	6	15	the	the	DET
ejpam-6529	6	16	phases	phase	NOUN
ejpam-6529	6	17	in	in	ADP
ejpam-6529	6	18	which	which	PRON
ejpam-6529	6	19	it	it	PRON
ejpam-6529	6	20	can	can	AUX
ejpam-6529	6	21	be	be	AUX
ejpam-6529	6	22	a	a	DET
ejpam-6529	6	23	weak	weak	ADJ
ejpam-6529	6	24	filter	filter	NOUN
ejpam-6529	6	25	are	be	AUX
ejpam-6529	6	26	explored	explore	VERB
ejpam-6529	6	27	.	.	PUNCT
ejpam-6529	7	1	conditions	condition	NOUN
ejpam-6529	7	2	for	for	ADP
ejpam-6529	7	3	an	an	DET
ejpam-6529	7	4	intuitionistic	intuitionistic	ADJ
ejpam-6529	7	5	level	level	NOUN
ejpam-6529	7	6	set	set	NOUN
ejpam-6529	7	7	and	and	CCONJ
ejpam-6529	7	8	an	an	DET
ejpam-6529	7	9	intuitionistic	intuitionistic	ADJ
ejpam-6529	7	10	q	q	NOUN
ejpam-6529	7	11	-	-	PUNCT
ejpam-6529	7	12	set	set	NOUN
ejpam-6529	7	13	to	to	PART
ejpam-6529	7	14	be	be	AUX
ejpam-6529	7	15	weak	weak	ADJ
ejpam-6529	7	16	filters	filter	NOUN
ejpam-6529	7	17	are	be	AUX
ejpam-6529	7	18	provided	provide	VERB
ejpam-6529	7	19	.	.	PUNCT
ejpam-6529	8	1	2020	2020	NUM
ejpam-6529	8	2	mathematics	mathematic	NOUN
ejpam-6529	8	3	subject	subject	NOUN
ejpam-6529	8	4	classifications	classification	NOUN
ejpam-6529	8	5	:	:	PUNCT
ejpam-6529	8	6	03b05	03b05	NUM
ejpam-6529	8	7	,	,	PUNCT
ejpam-6529	8	8	03g25	03g25	NOUN
ejpam-6529	8	9	,	,	PUNCT
ejpam-6529	8	10	06f35	06f35	NUM
ejpam-6529	8	11	,	,	PUNCT
ejpam-6529	8	12	08a72	08a72	NOUN
ejpam-6529	8	13	key	key	ADJ
ejpam-6529	8	14	words	word	NOUN
ejpam-6529	8	15	and	and	CCONJ
ejpam-6529	8	16	phrases	phrase	NOUN
ejpam-6529	8	17	:	:	PUNCT
ejpam-6529	8	18	weak	weak	ADJ
ejpam-6529	8	19	filter	filter	NOUN
ejpam-6529	8	20	,	,	PUNCT
ejpam-6529	8	21	intuitionistic	intuitionistic	ADJ
ejpam-6529	8	22	fuzzy	fuzzy	ADJ
ejpam-6529	8	23	point	point	NOUN
ejpam-6529	8	24	,	,	PUNCT
ejpam-6529	8	25	intuitionistic	intuitionistic	ADJ
ejpam-6529	8	26	level	level	NOUN
ejpam-6529	8	27	set	set	NOUN
ejpam-6529	8	28	,	,	PUNCT
ejpam-6529	8	29	intuitionistic	intuitionistic	ADJ
ejpam-6529	8	30	q	q	NOUN
ejpam-6529	8	31	-	-	PUNCT
ejpam-6529	8	32	set	set	ADJ
ejpam-6529	8	33	,	,	PUNCT
ejpam-6529	8	34	(	(	PUNCT
ejpam-6529	8	35	0	0	NUM
ejpam-6529	8	36	,	,	PUNCT
ejpam-6529	8	37	1)-set	1)-set	NUM
ejpam-6529	8	38	,	,	PUNCT
ejpam-6529	8	39	intuitionistic	intuitionistic	ADJ
ejpam-6529	8	40	fuzzy	fuzzy	ADJ
ejpam-6529	8	41	weak	weak	ADJ
ejpam-6529	8	42	filter	filter	NOUN
ejpam-6529	8	43	1	1	NUM
ejpam-6529	8	44	.	.	PUNCT
ejpam-6529	8	45	introduction	introduction	NOUN
ejpam-6529	8	46	the	the	DET
ejpam-6529	8	47	sheffer	sheffer	NOUN
ejpam-6529	8	48	operation	operation	NOUN
ejpam-6529	8	49	(	(	PUNCT
ejpam-6529	8	50	or	or	CCONJ
ejpam-6529	8	51	,	,	PUNCT
ejpam-6529	8	52	sheffer	sheffer	NOUN
ejpam-6529	8	53	stroke	stroke	NOUN
ejpam-6529	8	54	)	)	PUNCT
ejpam-6529	8	55	is	be	AUX
ejpam-6529	8	56	a	a	DET
ejpam-6529	8	57	logical	logical	ADJ
ejpam-6529	8	58	operation	operation	NOUN
ejpam-6529	8	59	in	in	ADP
ejpam-6529	8	60	boolean	boolean	ADJ
ejpam-6529	8	61	algebra	algebra	NOUN
ejpam-6529	8	62	that	that	PRON
ejpam-6529	8	63	produces	produce	VERB
ejpam-6529	8	64	a	a	DET
ejpam-6529	8	65	false	false	ADJ
ejpam-6529	8	66	result	result	NOUN
ejpam-6529	8	67	only	only	ADV
ejpam-6529	8	68	when	when	SCONJ
ejpam-6529	8	69	both	both	PRON
ejpam-6529	8	70	of	of	ADP
ejpam-6529	8	71	its	its	PRON
ejpam-6529	8	72	inputs	input	NOUN
ejpam-6529	8	73	are	be	AUX
ejpam-6529	8	74	true	true	ADJ
ejpam-6529	8	75	.	.	PUNCT
ejpam-6529	9	1	it	it	PRON
ejpam-6529	9	2	is	be	AUX
ejpam-6529	9	3	also	also	ADV
ejpam-6529	9	4	known	know	VERB
ejpam-6529	9	5	as	as	ADP
ejpam-6529	9	6	the	the	DET
ejpam-6529	9	7	nand	nand	NOUN
ejpam-6529	9	8	operation	operation	NOUN
ejpam-6529	9	9	,	,	PUNCT
ejpam-6529	9	10	and	and	CCONJ
ejpam-6529	9	11	is	be	AUX
ejpam-6529	9	12	often	often	ADV
ejpam-6529	9	13	symbolized	symbolize	VERB
ejpam-6529	9	14	as	as	ADP
ejpam-6529	9	15	“	"	PUNCT
ejpam-6529	9	16	|	|	NOUN
ejpam-6529	9	17	”	"	PUNCT
ejpam-6529	9	18	or	or	CCONJ
ejpam-6529	9	19	sometimes	sometimes	ADV
ejpam-6529	9	20	as	as	ADP
ejpam-6529	9	21	“	"	PUNCT
ejpam-6529	9	22	↑	↑	NOUN
ejpam-6529	9	23	”	"	PUNCT
ejpam-6529	9	24	.	.	PUNCT
ejpam-6529	10	1	the	the	DET
ejpam-6529	10	2	sheffer	sheffer	NOUN
ejpam-6529	10	3	stroke	stroke	NOUN
ejpam-6529	10	4	has	have	AUX
ejpam-6529	10	5	been	be	AUX
ejpam-6529	10	6	applied	apply	VERB
ejpam-6529	10	7	to	to	ADP
ejpam-6529	10	8	several	several	ADJ
ejpam-6529	10	9	algebraic	algebraic	ADJ
ejpam-6529	10	10	structures	structure	NOUN
ejpam-6529	10	11	,	,	PUNCT
ejpam-6529	10	12	for	for	ADP
ejpam-6529	10	13	example	example	NOUN
ejpam-6529	10	14	,	,	PUNCT
ejpam-6529	10	15	boolean	boolean	ADJ
ejpam-6529	10	16	algebra	algebra	NOUN
ejpam-6529	10	17	,	,	PUNCT
ejpam-6529	10	18	bck	bck	NOUN
ejpam-6529	10	19	-	-	PUNCT
ejpam-6529	10	20	algebra	algebra	NOUN
ejpam-6529	10	21	,	,	PUNCT
ejpam-6529	10	22	mv	mv	PROPN
ejpam-6529	10	23	-	-	NOUN
ejpam-6529	10	24	algebra	algebra	NOUN
ejpam-6529	10	25	,	,	PUNCT
ejpam-6529	10	26	bl	bl	NOUN
ejpam-6529	10	27	-	-	PUNCT
ejpam-6529	10	28	algebra	algebra	NOUN
ejpam-6529	10	29	,	,	PUNCT
ejpam-6529	10	30	and	and	CCONJ
ejpam-6529	10	31	ortholattices	ortholattice	NOUN
ejpam-6529	10	32	,	,	PUNCT
ejpam-6529	10	33	etc	etc	X
ejpam-6529	10	34	.	.	X
ejpam-6529	10	35	,	,	PUNCT
ejpam-6529	10	36	and	and	CCONJ
ejpam-6529	10	37	it	it	PRON
ejpam-6529	10	38	is	be	AUX
ejpam-6529	10	39	also	also	ADV
ejpam-6529	10	40	being	be	AUX
ejpam-6529	10	41	dealt	deal	VERB
ejpam-6529	10	42	with	with	ADP
ejpam-6529	10	43	in	in	ADP
ejpam-6529	10	44	the	the	DET
ejpam-6529	10	45	fuzzy	fuzzy	ADJ
ejpam-6529	10	46	environment	environment	NOUN
ejpam-6529	10	47	(	(	PUNCT
ejpam-6529	10	48	see	see	VERB
ejpam-6529	10	49	[	[	X
ejpam-6529	10	50	1–11	1–11	X
ejpam-6529	10	51	]	]	PUNCT
ejpam-6529	10	52	)	)	PUNCT
ejpam-6529	10	53	.	.	PUNCT
ejpam-6529	11	1	in	in	ADP
ejpam-6529	11	2	2021	2021	NUM
ejpam-6529	11	3	,	,	PUNCT
ejpam-6529	11	4	oner	oner	NOUN
ejpam-6529	11	5	et	et	PROPN
ejpam-6529	11	6	al	al	PROPN
ejpam-6529	11	7	.	.	PUNCT
ejpam-6529	12	1	[	[	X
ejpam-6529	12	2	5	5	NUM
ejpam-6529	12	3	]	]	PUNCT
ejpam-6529	12	4	applied	apply	VERB
ejpam-6529	12	5	the	the	DET
ejpam-6529	12	6	sheffer	sheffer	NOUN
ejpam-6529	12	7	stroke	stroke	NOUN
ejpam-6529	12	8	to	to	ADP
ejpam-6529	12	9	hilbert	hilbert	PROPN
ejpam-6529	12	10	algebras	algebras	PROPN
ejpam-6529	12	11	.	.	PUNCT
ejpam-6529	13	1	they	they	PRON
ejpam-6529	13	2	introduced	introduce	VERB
ejpam-6529	13	3	sheffer	sheffer	NOUN
ejpam-6529	13	4	stroke	stroke	PROPN
ejpam-6529	13	5	hilbert	hilbert	PROPN
ejpam-6529	13	6	algebra	algebra	PROPN
ejpam-6529	13	7	and	and	CCONJ
ejpam-6529	13	8	investigated	investigate	VERB
ejpam-6529	13	9	several	several	ADJ
ejpam-6529	13	10	properties	property	NOUN
ejpam-6529	13	11	.	.	PUNCT
ejpam-6529	14	1	in	in	ADP
ejpam-6529	14	2	[	[	X
ejpam-6529	14	3	4	4	NUM
ejpam-6529	14	4	]	]	PUNCT
ejpam-6529	14	5	,	,	PUNCT
ejpam-6529	14	6	oner	oner	AUX
ejpam-6529	14	7	et	et	PROPN
ejpam-6529	14	8	al	al	PROPN
ejpam-6529	14	9	.	.	PROPN
ejpam-6529	14	10	introduced	introduce	VERB
ejpam-6529	14	11	the	the	DET
ejpam-6529	14	12	notion	notion	NOUN
ejpam-6529	14	13	of	of	ADP
ejpam-6529	14	14	deductive	deductive	ADJ
ejpam-6529	14	15	system	system	NOUN
ejpam-6529	14	16	and	and	CCONJ
ejpam-6529	14	17	filter	filter	NOUN
ejpam-6529	14	18	of	of	ADP
ejpam-6529	14	19	sheffer	sheffer	PROPN
ejpam-6529	14	20	stroke	stroke	PROPN
ejpam-6529	14	21	hilbert	hilbert	PROPN
ejpam-6529	14	22	algebras	algebras	PROPN
ejpam-6529	14	23	,	,	PUNCT
ejpam-6529	14	24	and	and	CCONJ
ejpam-6529	14	25	dealt	deal	VERB
ejpam-6529	14	26	with	with	ADP
ejpam-6529	14	27	their	their	PRON
ejpam-6529	14	28	fuzzification	fuzzification	NOUN
ejpam-6529	14	29	.	.	PUNCT
ejpam-6529	15	1	oner	oner	NOUN
ejpam-6529	15	2	et	et	PROPN
ejpam-6529	15	3	al	al	PROPN
ejpam-6529	15	4	.	.	PUNCT
ejpam-6529	16	1	[	[	X
ejpam-6529	16	2	5	5	NUM
ejpam-6529	16	3	]	]	PUNCT
ejpam-6529	16	4	∗corresponding	∗corresponde	VERB
ejpam-6529	16	5	author	author	NOUN
ejpam-6529	16	6	.	.	PUNCT
ejpam-6529	17	1	doi	doi	PROPN
ejpam-6529	17	2	:	:	PUNCT
ejpam-6529	17	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6529	https://doi.org/10.29020/nybg.ejpam.v18i3.6529	ADP
ejpam-6529	17	4	email	email	NOUN
ejpam-6529	17	5	addresses	address	NOUN
ejpam-6529	17	6	:	:	PUNCT
ejpam-6529	17	7	sunshine@dongguk.edu	sunshine@dongguk.edu	PROPN
ejpam-6529	17	8	(	(	PUNCT
ejpam-6529	17	9	s.	s.	PROPN
ejpam-6529	17	10	s.	s.	PROPN
ejpam-6529	17	11	ahn	ahn	PROPN
ejpam-6529	17	12	)	)	PUNCT
ejpam-6529	17	13	,	,	PUNCT
ejpam-6529	17	14	bejesus@hanyang.ac.kr	bejesus@hanyang.ac.kr	PROPN
ejpam-6529	17	15	(	(	PUNCT
ejpam-6529	17	16	y.	y.	PROPN
ejpam-6529	17	17	j.	j.	PROPN
ejpam-6529	17	18	seo	seo	PROPN
ejpam-6529	17	19	)	)	PUNCT
ejpam-6529	17	20	skywine@gmail.com	skywine@gmail.com	X
ejpam-6529	18	1	(	(	PUNCT
ejpam-6529	18	2	y.	y.	PROPN
ejpam-6529	18	3	b.	b.	PROPN
ejpam-6529	18	4	jun	jun	PROPN
ejpam-6529	18	5	)	)	PUNCT
ejpam-6529	18	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6529	19	1	1	1	NUM
ejpam-6529	19	2	copyright	copyright	NOUN
ejpam-6529	19	3	:	:	PUNCT
ejpam-6529	19	4	©	©	PROPN
ejpam-6529	19	5	2025	2025	NUM
ejpam-6529	19	6	the	the	DET
ejpam-6529	19	7	author(s	author(s	NOUN
ejpam-6529	19	8	)	)	PUNCT
ejpam-6529	19	9	.	.	PUNCT
ejpam-6529	20	1	(	(	PUNCT
ejpam-6529	20	2	cc	cc	NOUN
ejpam-6529	20	3	by	by	ADP
ejpam-6529	20	4	-	-	PUNCT
ejpam-6529	20	5	nc	nc	PROPN
ejpam-6529	20	6	4.0	4.0	NUM
ejpam-6529	20	7	)	)	PUNCT
ejpam-6529	20	8	s.	s.	PROPN
ejpam-6529	20	9	s.	s.	PROPN
ejpam-6529	20	10	ahn	ahn	PROPN
ejpam-6529	20	11	,	,	PUNCT
ejpam-6529	20	12	y.	y.	PROPN
ejpam-6529	20	13	j.	j.	PROPN
ejpam-6529	20	14	seo	seo	PROPN
ejpam-6529	20	15	,	,	PUNCT
ejpam-6529	20	16	y.	y.	PROPN
ejpam-6529	20	17	b.	b.	PROPN
ejpam-6529	20	18	jun	jun	PROPN
ejpam-6529	20	19	/	/	SYM
ejpam-6529	20	20	eur	eur	PROPN
ejpam-6529	20	21	.	.	PUNCT
ejpam-6529	21	1	j.	j.	PROPN
ejpam-6529	21	2	pure	pure	PROPN
ejpam-6529	21	3	appl	appl	PROPN
ejpam-6529	21	4	.	.	PROPN
ejpam-6529	21	5	math	math	PROPN
ejpam-6529	21	6	,	,	PUNCT
ejpam-6529	21	7	18	18	NUM
ejpam-6529	21	8	(	(	PUNCT
ejpam-6529	21	9	3	3	NUM
ejpam-6529	21	10	)	)	PUNCT
ejpam-6529	21	11	(	(	PUNCT
ejpam-6529	21	12	2025	2025	NUM
ejpam-6529	21	13	)	)	PUNCT
ejpam-6529	21	14	,	,	PUNCT
ejpam-6529	21	15	6529	6529	NUM
ejpam-6529	21	16	2	2	NUM
ejpam-6529	21	17	of	of	ADP
ejpam-6529	21	18	16	16	NUM
ejpam-6529	21	19	also	also	ADV
ejpam-6529	21	20	introduced	introduce	VERB
ejpam-6529	21	21	the	the	DET
ejpam-6529	21	22	concept	concept	NOUN
ejpam-6529	21	23	of	of	ADP
ejpam-6529	21	24	ideal	ideal	NOUN
ejpam-6529	21	25	and	and	CCONJ
ejpam-6529	21	26	examined	examine	VERB
ejpam-6529	21	27	its	its	PRON
ejpam-6529	21	28	properties	property	NOUN
ejpam-6529	21	29	in	in	ADP
ejpam-6529	21	30	sheffer	sheffer	PROPN
ejpam-6529	21	31	stroke	stroke	PROPN
ejpam-6529	21	32	hilbert	hilbert	PROPN
ejpam-6529	21	33	algebras	algebras	PROPN
ejpam-6529	21	34	.	.	PUNCT
ejpam-6529	22	1	the	the	DET
ejpam-6529	22	2	intuitionistic	intuitionistic	ADJ
ejpam-6529	22	3	fuzzy	fuzzy	ADJ
ejpam-6529	22	4	set	set	NOUN
ejpam-6529	22	5	,	,	PUNCT
ejpam-6529	22	6	which	which	PRON
ejpam-6529	22	7	is	be	AUX
ejpam-6529	22	8	a	a	DET
ejpam-6529	22	9	generalization	generalization	NOUN
ejpam-6529	22	10	of	of	ADP
ejpam-6529	22	11	fuzzy	fuzzy	ADJ
ejpam-6529	22	12	sets	set	NOUN
ejpam-6529	22	13	,	,	PUNCT
ejpam-6529	22	14	is	be	AUX
ejpam-6529	22	15	introduced	introduce	VERB
ejpam-6529	22	16	by	by	ADP
ejpam-6529	22	17	k.	k.	PROPN
ejpam-6529	22	18	athanasov	athanasov	PROPN
ejpam-6529	22	19	in	in	ADP
ejpam-6529	22	20	1986	1986	NUM
ejpam-6529	22	21	,	,	PUNCT
ejpam-6529	22	22	and	and	CCONJ
ejpam-6529	22	23	it	it	PRON
ejpam-6529	22	24	is	be	AUX
ejpam-6529	22	25	a	a	DET
ejpam-6529	22	26	useful	useful	ADJ
ejpam-6529	22	27	tool	tool	NOUN
ejpam-6529	22	28	for	for	ADP
ejpam-6529	22	29	better	well	ADJ
ejpam-6529	22	30	modeling	modeling	NOUN
ejpam-6529	22	31	uncertainties	uncertainty	NOUN
ejpam-6529	22	32	and	and	CCONJ
ejpam-6529	22	33	ambiguity	ambiguity	NOUN
ejpam-6529	22	34	.	.	PUNCT
ejpam-6529	23	1	the	the	DET
ejpam-6529	23	2	fuzzy	fuzzy	ADJ
ejpam-6529	23	3	set	set	NOUN
ejpam-6529	23	4	only	only	ADV
ejpam-6529	23	5	considers	consider	VERB
ejpam-6529	23	6	the	the	DET
ejpam-6529	23	7	degree	degree	NOUN
ejpam-6529	23	8	of	of	ADP
ejpam-6529	23	9	membership	membership	NOUN
ejpam-6529	23	10	of	of	ADP
ejpam-6529	23	11	the	the	DET
ejpam-6529	23	12	element	element	NOUN
ejpam-6529	23	13	,	,	PUNCT
ejpam-6529	23	14	while	while	SCONJ
ejpam-6529	23	15	the	the	DET
ejpam-6529	23	16	intuitionistic	intuitionistic	ADJ
ejpam-6529	23	17	fuzzy	fuzzy	ADJ
ejpam-6529	23	18	set	set	VERB
ejpam-6529	23	19	deals	deal	NOUN
ejpam-6529	23	20	with	with	ADP
ejpam-6529	23	21	membership	membership	NOUN
ejpam-6529	23	22	and	and	CCONJ
ejpam-6529	23	23	non	non	ADJ
ejpam-6529	23	24	-	-	NOUN
ejpam-6529	23	25	membership	membership	NOUN
ejpam-6529	23	26	simultaneously	simultaneously	ADV
ejpam-6529	23	27	,	,	PUNCT
ejpam-6529	23	28	along	along	ADP
ejpam-6529	23	29	with	with	ADP
ejpam-6529	23	30	the	the	DET
ejpam-6529	23	31	degree	degree	NOUN
ejpam-6529	23	32	of	of	ADP
ejpam-6529	23	33	hesitation	hesitation	NOUN
ejpam-6529	23	34	(	(	PUNCT
ejpam-6529	23	35	or	or	CCONJ
ejpam-6529	23	36	uncertainty	uncertainty	NOUN
ejpam-6529	23	37	)	)	PUNCT
ejpam-6529	23	38	about	about	ADP
ejpam-6529	23	39	the	the	DET
ejpam-6529	23	40	element	element	NOUN
ejpam-6529	23	41	.	.	PUNCT
ejpam-6529	24	1	an	an	DET
ejpam-6529	24	2	intuitionistic	intuitionistic	ADJ
ejpam-6529	24	3	fuzzy	fuzzy	ADJ
ejpam-6529	24	4	point	point	NOUN
ejpam-6529	24	5	(	(	PUNCT
ejpam-6529	24	6	see	see	VERB
ejpam-6529	24	7	[	[	X
ejpam-6529	24	8	12	12	NUM
ejpam-6529	24	9	]	]	PUNCT
ejpam-6529	24	10	)	)	PUNCT
ejpam-6529	24	11	is	be	AUX
ejpam-6529	24	12	an	an	DET
ejpam-6529	24	13	extension	extension	NOUN
ejpam-6529	24	14	of	of	ADP
ejpam-6529	24	15	the	the	DET
ejpam-6529	24	16	classical	classical	ADJ
ejpam-6529	24	17	concept	concept	NOUN
ejpam-6529	24	18	of	of	ADP
ejpam-6529	24	19	a	a	DET
ejpam-6529	24	20	point	point	NOUN
ejpam-6529	24	21	in	in	ADP
ejpam-6529	24	22	set	set	NOUN
ejpam-6529	24	23	theory	theory	NOUN
ejpam-6529	24	24	,	,	PUNCT
ejpam-6529	24	25	which	which	PRON
ejpam-6529	24	26	is	be	AUX
ejpam-6529	24	27	adapted	adapt	VERB
ejpam-6529	24	28	to	to	ADP
ejpam-6529	24	29	the	the	DET
ejpam-6529	24	30	framework	framework	NOUN
ejpam-6529	24	31	of	of	ADP
ejpam-6529	24	32	the	the	DET
ejpam-6529	24	33	intuitionistic	intuitionistic	ADJ
ejpam-6529	24	34	fuzzy	fuzzy	ADJ
ejpam-6529	24	35	set	set	NOUN
ejpam-6529	24	36	and	and	CCONJ
ejpam-6529	24	37	plays	play	VERB
ejpam-6529	24	38	an	an	DET
ejpam-6529	24	39	important	important	ADJ
ejpam-6529	24	40	role	role	NOUN
ejpam-6529	24	41	in	in	ADP
ejpam-6529	24	42	intuitionistic	intuitionistic	ADJ
ejpam-6529	24	43	fuzzy	fuzzy	ADJ
ejpam-6529	24	44	sets	set	NOUN
ejpam-6529	24	45	.	.	PUNCT
ejpam-6529	25	1	jun	jun	PROPN
ejpam-6529	25	2	et	et	PROPN
ejpam-6529	25	3	al	al	PROPN
ejpam-6529	25	4	.	.	PUNCT
ejpam-6529	26	1	[	[	X
ejpam-6529	26	2	13	13	NUM
ejpam-6529	26	3	]	]	PUNCT
ejpam-6529	26	4	introduced	introduce	VERB
ejpam-6529	26	5	the	the	DET
ejpam-6529	26	6	concept	concept	NOUN
ejpam-6529	26	7	of	of	ADP
ejpam-6529	26	8	weak	weak	ADJ
ejpam-6529	26	9	filters	filter	NOUN
ejpam-6529	26	10	that	that	PRON
ejpam-6529	26	11	have	have	AUX
ejpam-6529	26	12	weakened	weaken	VERB
ejpam-6529	26	13	the	the	DET
ejpam-6529	26	14	filter	filter	NOUN
ejpam-6529	26	15	conditions	condition	NOUN
ejpam-6529	26	16	in	in	ADP
ejpam-6529	26	17	the	the	DET
ejpam-6529	26	18	sheffer	sheffer	NOUN
ejpam-6529	26	19	stroke	stroke	NOUN
ejpam-6529	26	20	hilbert	hilbert	PROPN
ejpam-6529	26	21	algebra	algebra	PROPN
ejpam-6529	26	22	and	and	CCONJ
ejpam-6529	26	23	investigated	investigate	VERB
ejpam-6529	26	24	several	several	ADJ
ejpam-6529	26	25	properties	property	NOUN
ejpam-6529	26	26	.	.	PUNCT
ejpam-6529	27	1	they	they	PRON
ejpam-6529	27	2	presented	present	VERB
ejpam-6529	27	3	how	how	SCONJ
ejpam-6529	27	4	to	to	PART
ejpam-6529	27	5	make	make	VERB
ejpam-6529	27	6	weak	weak	ADJ
ejpam-6529	27	7	filters	filter	NOUN
ejpam-6529	27	8	using	use	VERB
ejpam-6529	27	9	ideals	ideal	NOUN
ejpam-6529	27	10	,	,	PUNCT
ejpam-6529	27	11	and	and	CCONJ
ejpam-6529	27	12	examined	examine	VERB
ejpam-6529	27	13	the	the	DET
ejpam-6529	27	14	shape	shape	NOUN
ejpam-6529	27	15	of	of	ADP
ejpam-6529	27	16	the	the	DET
ejpam-6529	27	17	weak	weak	ADJ
ejpam-6529	27	18	filter	filter	NOUN
ejpam-6529	27	19	in	in	ADP
ejpam-6529	27	20	the	the	DET
ejpam-6529	27	21	cartesian	cartesian	ADJ
ejpam-6529	27	22	product	product	NOUN
ejpam-6529	27	23	of	of	ADP
ejpam-6529	27	24	sheffer	sheffer	PROPN
ejpam-6529	27	25	stroke	stroke	PROPN
ejpam-6529	27	26	hilbert	hilbert	PROPN
ejpam-6529	27	27	algebras	algebras	PROPN
ejpam-6529	27	28	.	.	PUNCT
ejpam-6529	28	1	the	the	DET
ejpam-6529	28	2	purpose	purpose	NOUN
ejpam-6529	28	3	of	of	ADP
ejpam-6529	28	4	this	this	DET
ejpam-6529	28	5	paper	paper	NOUN
ejpam-6529	28	6	is	be	AUX
ejpam-6529	28	7	to	to	PART
ejpam-6529	28	8	study	study	VERB
ejpam-6529	28	9	weak	weak	ADJ
ejpam-6529	28	10	filters	filter	NOUN
ejpam-6529	28	11	in	in	ADP
ejpam-6529	28	12	sheffer	sheffer	PROPN
ejpam-6529	28	13	stroke	stroke	PROPN
ejpam-6529	28	14	hilbert	hilbert	PROPN
ejpam-6529	28	15	algebras	algebras	PROPN
ejpam-6529	28	16	using	use	VERB
ejpam-6529	28	17	the	the	DET
ejpam-6529	28	18	concept	concept	NOUN
ejpam-6529	28	19	of	of	ADP
ejpam-6529	28	20	intuitionistic	intuitionistic	ADJ
ejpam-6529	28	21	fuzzy	fuzzy	ADJ
ejpam-6529	28	22	points	point	NOUN
ejpam-6529	28	23	.	.	PUNCT
ejpam-6529	29	1	we	we	PRON
ejpam-6529	29	2	introduce	introduce	VERB
ejpam-6529	29	3	the	the	DET
ejpam-6529	29	4	notion	notion	NOUN
ejpam-6529	29	5	of	of	ADP
ejpam-6529	29	6	intuitionistic	intuitionistic	ADJ
ejpam-6529	29	7	fuzzy	fuzzy	ADJ
ejpam-6529	29	8	weak	weak	ADJ
ejpam-6529	29	9	filters	filter	NOUN
ejpam-6529	29	10	in	in	ADP
ejpam-6529	29	11	sheffer	sheffer	PROPN
ejpam-6529	29	12	stroke	stroke	PROPN
ejpam-6529	29	13	hilbert	hilbert	PROPN
ejpam-6529	29	14	algebras	algebras	PROPN
ejpam-6529	29	15	,	,	PUNCT
ejpam-6529	29	16	and	and	CCONJ
ejpam-6529	29	17	investigates	investigate	VERB
ejpam-6529	29	18	their	their	PRON
ejpam-6529	29	19	properties	property	NOUN
ejpam-6529	29	20	.	.	PUNCT
ejpam-6529	30	1	we	we	PRON
ejpam-6529	30	2	examine	examine	VERB
ejpam-6529	30	3	the	the	DET
ejpam-6529	30	4	conditions	condition	NOUN
ejpam-6529	30	5	under	under	ADP
ejpam-6529	30	6	which	which	PRON
ejpam-6529	30	7	the	the	DET
ejpam-6529	30	8	intuitionistic	intuitionistic	ADJ
ejpam-6529	30	9	fuzzy	fuzzy	ADJ
ejpam-6529	30	10	set	set	NOUN
ejpam-6529	30	11	becomes	become	VERB
ejpam-6529	30	12	an	an	DET
ejpam-6529	30	13	intuitionistic	intuitionistic	ADJ
ejpam-6529	30	14	fuzzy	fuzzy	ADJ
ejpam-6529	30	15	weak	weak	ADJ
ejpam-6529	30	16	filter	filter	NOUN
ejpam-6529	30	17	.	.	PUNCT
ejpam-6529	31	1	we	we	PRON
ejpam-6529	31	2	discuss	discuss	VERB
ejpam-6529	31	3	the	the	DET
ejpam-6529	31	4	characterization	characterization	NOUN
ejpam-6529	31	5	of	of	ADP
ejpam-6529	31	6	intuitionistic	intuitionistic	ADJ
ejpam-6529	31	7	fuzzy	fuzzy	ADJ
ejpam-6529	31	8	weak	weak	ADJ
ejpam-6529	31	9	filters	filter	NOUN
ejpam-6529	31	10	,	,	PUNCT
ejpam-6529	31	11	and	and	CCONJ
ejpam-6529	31	12	consider	consider	VERB
ejpam-6529	31	13	the	the	DET
ejpam-6529	31	14	conditions	condition	NOUN
ejpam-6529	31	15	under	under	ADP
ejpam-6529	31	16	which	which	PRON
ejpam-6529	31	17	the	the	DET
ejpam-6529	31	18	intuitionistic	intuitionistic	ADJ
ejpam-6529	31	19	fuzzy	fuzzy	ADJ
ejpam-6529	31	20	set	set	NOUN
ejpam-6529	31	21	becomes	become	VERB
ejpam-6529	31	22	an	an	DET
ejpam-6529	31	23	intuitionistic	intuitionistic	ADJ
ejpam-6529	31	24	fuzzy	fuzzy	ADJ
ejpam-6529	31	25	weak	weak	ADJ
ejpam-6529	31	26	filter	filter	NOUN
ejpam-6529	31	27	.	.	PUNCT
ejpam-6529	32	1	we	we	PRON
ejpam-6529	32	2	build	build	VERB
ejpam-6529	32	3	a	a	DET
ejpam-6529	32	4	(	(	PUNCT
ejpam-6529	32	5	0	0	NUM
ejpam-6529	32	6	,	,	PUNCT
ejpam-6529	32	7	1)-set	1)-set	NOUN
ejpam-6529	32	8	for	for	ADP
ejpam-6529	32	9	the	the	DET
ejpam-6529	32	10	intuitionistic	intuitionistic	ADJ
ejpam-6529	32	11	fuzzy	fuzzy	ADJ
ejpam-6529	32	12	set	set	NOUN
ejpam-6529	32	13	,	,	PUNCT
ejpam-6529	32	14	and	and	CCONJ
ejpam-6529	32	15	discuss	discuss	VERB
ejpam-6529	32	16	the	the	DET
ejpam-6529	32	17	phases	phase	NOUN
ejpam-6529	32	18	in	in	ADP
ejpam-6529	32	19	which	which	PRON
ejpam-6529	32	20	it	it	PRON
ejpam-6529	32	21	can	can	AUX
ejpam-6529	32	22	be	be	AUX
ejpam-6529	32	23	a	a	DET
ejpam-6529	32	24	weak	weak	ADJ
ejpam-6529	32	25	filter	filter	NOUN
ejpam-6529	32	26	.	.	PUNCT
ejpam-6529	33	1	it	it	PRON
ejpam-6529	33	2	provides	provide	VERB
ejpam-6529	33	3	conditions	condition	NOUN
ejpam-6529	33	4	for	for	SCONJ
ejpam-6529	33	5	an	an	DET
ejpam-6529	33	6	intuitionistic	intuitionistic	ADJ
ejpam-6529	33	7	level	level	NOUN
ejpam-6529	33	8	set	set	NOUN
ejpam-6529	33	9	and	and	CCONJ
ejpam-6529	33	10	an	an	DET
ejpam-6529	33	11	intuitionistic	intuitionistic	ADJ
ejpam-6529	33	12	q	q	NOUN
ejpam-6529	33	13	-	-	PUNCT
ejpam-6529	33	14	set	set	NOUN
ejpam-6529	33	15	to	to	PART
ejpam-6529	33	16	be	be	AUX
ejpam-6529	33	17	weak	weak	ADJ
ejpam-6529	33	18	filters	filter	NOUN
ejpam-6529	33	19	.	.	PUNCT
ejpam-6529	34	1	2	2	X
ejpam-6529	34	2	.	.	X
ejpam-6529	34	3	preliminaries	preliminary	NOUN
ejpam-6529	34	4	definition	definition	NOUN
ejpam-6529	34	5	1	1	NUM
ejpam-6529	34	6	(	(	PUNCT
ejpam-6529	34	7	[	[	X
ejpam-6529	34	8	14	14	NUM
ejpam-6529	34	9	]	]	NUM
ejpam-6529	34	10	)	)	PUNCT
ejpam-6529	34	11	.	.	PUNCT
ejpam-6529	35	1	let	let	VERB
ejpam-6529	35	2	b	b	X
ejpam-6529	35	3	:	:	PUNCT
ejpam-6529	35	4	=	=	SYM
ejpam-6529	35	5	(	(	PUNCT
ejpam-6529	35	6	b	b	NOUN
ejpam-6529	35	7	,	,	PUNCT
ejpam-6529	35	8	|	|	ADV
ejpam-6529	35	9	)	)	PUNCT
ejpam-6529	35	10	be	be	AUX
ejpam-6529	35	11	a	a	DET
ejpam-6529	35	12	groupoid	groupoid	NOUN
ejpam-6529	35	13	.	.	PUNCT
ejpam-6529	36	1	then	then	ADV
ejpam-6529	36	2	the	the	DET
ejpam-6529	36	3	operation	operation	NOUN
ejpam-6529	36	4	“	"	PUNCT
ejpam-6529	36	5	|	|	ADV
ejpam-6529	36	6	”	"	PUNCT
ejpam-6529	36	7	is	be	AUX
ejpam-6529	36	8	said	say	VERB
ejpam-6529	36	9	to	to	PART
ejpam-6529	36	10	be	be	AUX
ejpam-6529	36	11	sheffer	sheffer	NOUN
ejpam-6529	36	12	stroke	stroke	NOUN
ejpam-6529	36	13	or	or	CCONJ
ejpam-6529	36	14	sheffer	sheffer	VERB
ejpam-6529	36	15	operation	operation	NOUN
ejpam-6529	36	16	if	if	SCONJ
ejpam-6529	36	17	it	it	PRON
ejpam-6529	36	18	satisfies	satisfy	VERB
ejpam-6529	36	19	:	:	PUNCT
ejpam-6529	36	20	(	(	PUNCT
ejpam-6529	36	21	s1	s1	NOUN
ejpam-6529	36	22	)	)	PUNCT
ejpam-6529	36	23	(	(	PUNCT
ejpam-6529	36	24	∀a	∀a	X
ejpam-6529	36	25	,	,	PUNCT
ejpam-6529	36	26	b	b	PROPN
ejpam-6529	36	27	∈	∈	PROPN
ejpam-6529	36	28	b	b	NOUN
ejpam-6529	36	29	)	)	PUNCT
ejpam-6529	36	30	(	(	PUNCT
ejpam-6529	36	31	a|b	a|b	NOUN
ejpam-6529	36	32	=	=	SYM
ejpam-6529	36	33	b|a	b|a	NOUN
ejpam-6529	36	34	)	)	PUNCT
ejpam-6529	36	35	,	,	PUNCT
ejpam-6529	36	36	(	(	PUNCT
ejpam-6529	36	37	s2	s2	PROPN
ejpam-6529	36	38	)	)	PUNCT
ejpam-6529	36	39	(	(	PUNCT
ejpam-6529	36	40	∀a	∀a	X
ejpam-6529	36	41	,	,	PUNCT
ejpam-6529	36	42	b	b	PROPN
ejpam-6529	36	43	∈	∈	PROPN
ejpam-6529	36	44	b	b	NOUN
ejpam-6529	36	45	)	)	PUNCT
ejpam-6529	36	46	(	(	PUNCT
ejpam-6529	36	47	(	(	PUNCT
ejpam-6529	36	48	a|a)|(a|b	a|a)|(a|b	PROPN
ejpam-6529	36	49	)	)	PUNCT
ejpam-6529	36	50	=	=	SYM
ejpam-6529	37	1	a	a	NOUN
ejpam-6529	37	2	)	)	PUNCT
ejpam-6529	37	3	,	,	PUNCT
ejpam-6529	37	4	(	(	PUNCT
ejpam-6529	37	5	s3	s3	PROPN
ejpam-6529	37	6	)	)	PUNCT
ejpam-6529	37	7	(	(	PUNCT
ejpam-6529	37	8	∀a	∀a	X
ejpam-6529	37	9	,	,	PUNCT
ejpam-6529	37	10	b	b	NOUN
ejpam-6529	37	11	,	,	PUNCT
ejpam-6529	37	12	c	c	PROPN
ejpam-6529	37	13	∈	∈	PROPN
ejpam-6529	37	14	b	b	PROPN
ejpam-6529	37	15	)	)	PUNCT
ejpam-6529	37	16	(	(	PUNCT
ejpam-6529	37	17	a|((b|c)|(b|c	a|((b|c)|(b|c	NOUN
ejpam-6529	37	18	)	)	PUNCT
ejpam-6529	37	19	)	)	PUNCT
ejpam-6529	38	1	=	=	SYM
ejpam-6529	38	2	(	(	PUNCT
ejpam-6529	38	3	(	(	PUNCT
ejpam-6529	38	4	a|b)|(a|b))|c	a|b)|(a|b))|c	PROPN
ejpam-6529	38	5	)	)	PUNCT
ejpam-6529	38	6	,	,	PUNCT
ejpam-6529	38	7	(	(	PUNCT
ejpam-6529	38	8	s4	s4	PROPN
ejpam-6529	38	9	)	)	PUNCT
ejpam-6529	38	10	(	(	PUNCT
ejpam-6529	38	11	∀a	∀a	X
ejpam-6529	38	12	,	,	PUNCT
ejpam-6529	38	13	b	b	NOUN
ejpam-6529	38	14	,	,	PUNCT
ejpam-6529	38	15	c	c	PROPN
ejpam-6529	38	16	∈	∈	PROPN
ejpam-6529	38	17	b	b	X
ejpam-6529	38	18	)	)	PUNCT
ejpam-6529	38	19	(	(	PUNCT
ejpam-6529	38	20	(	(	PUNCT
ejpam-6529	38	21	a|((a|a)|(b|b)))|(a|((a|a)|(b|b	a|((a|a)|(b|b)))|(a|((a|a)|(b|b	NOUN
ejpam-6529	38	22	)	)	PUNCT
ejpam-6529	38	23	)	)	PUNCT
ejpam-6529	38	24	)	)	PUNCT
ejpam-6529	39	1	=	=	PUNCT
ejpam-6529	39	2	a	a	X
ejpam-6529	39	3	)	)	PUNCT
ejpam-6529	39	4	.	.	PUNCT
ejpam-6529	40	1	let	let	VERB
ejpam-6529	40	2	x	x	PRON
ejpam-6529	40	3	:	:	PUNCT
ejpam-6529	40	4	=	=	SYM
ejpam-6529	40	5	(	(	PUNCT
ejpam-6529	40	6	x	x	NOUN
ejpam-6529	40	7	,	,	PUNCT
ejpam-6529	40	8	|	|	ADV
ejpam-6529	40	9	)	)	PUNCT
ejpam-6529	40	10	be	be	AUX
ejpam-6529	40	11	a	a	DET
ejpam-6529	40	12	groupoid	groupoid	NOUN
ejpam-6529	40	13	.	.	PUNCT
ejpam-6529	41	1	for	for	ADP
ejpam-6529	41	2	every	every	DET
ejpam-6529	41	3	element	element	NOUN
ejpam-6529	41	4	a	a	DET
ejpam-6529	41	5	∈	∈	PROPN
ejpam-6529	41	6	x	x	NOUN
ejpam-6529	41	7	,	,	PUNCT
ejpam-6529	41	8	consider	consider	VERB
ejpam-6529	41	9	the	the	DET
ejpam-6529	41	10	following	follow	VERB
ejpam-6529	41	11	mapping	mapping	NOUN
ejpam-6529	41	12	:	:	PUNCT
ejpam-6529	41	13	ða	ða	INTJ
ejpam-6529	41	14	:	:	PUNCT
ejpam-6529	41	15	x	x	X
ejpam-6529	41	16	→	→	SYM
ejpam-6529	41	17	x	x	PROPN
ejpam-6529	41	18	,	,	PUNCT
ejpam-6529	41	19	b	b	PROPN
ejpam-6529	41	20	7→	7→	NUM
ejpam-6529	41	21	a|(b|b	a|(b|b	NOUN
ejpam-6529	41	22	)	)	PUNCT
ejpam-6529	41	23	.	.	PUNCT
ejpam-6529	42	1	definition	definition	NOUN
ejpam-6529	42	2	2	2	NUM
ejpam-6529	42	3	(	(	PUNCT
ejpam-6529	42	4	[	[	X
ejpam-6529	42	5	5	5	NUM
ejpam-6529	42	6	]	]	NUM
ejpam-6529	42	7	)	)	PUNCT
ejpam-6529	42	8	.	.	PUNCT
ejpam-6529	43	1	a	a	DET
ejpam-6529	43	2	sheffer	sheffer	NOUN
ejpam-6529	43	3	stroke	stroke	NOUN
ejpam-6529	43	4	hilbert	hilbert	PROPN
ejpam-6529	43	5	algebra	algebra	PROPN
ejpam-6529	43	6	is	be	AUX
ejpam-6529	43	7	a	a	DET
ejpam-6529	43	8	groupoid	groupoid	NOUN
ejpam-6529	43	9	x	x	X
ejpam-6529	43	10	:	:	PUNCT
ejpam-6529	43	11	=	=	SYM
ejpam-6529	43	12	(	(	PUNCT
ejpam-6529	43	13	x	x	NOUN
ejpam-6529	43	14	,	,	PUNCT
ejpam-6529	43	15	|	|	ADV
ejpam-6529	43	16	)	)	PUNCT
ejpam-6529	43	17	with	with	ADP
ejpam-6529	43	18	a	a	DET
ejpam-6529	43	19	sheffer	sheffer	NOUN
ejpam-6529	43	20	stroke	stroke	NOUN
ejpam-6529	43	21	“	"	PUNCT
ejpam-6529	43	22	|	|	ADV
ejpam-6529	43	23	”	"	PUNCT
ejpam-6529	43	24	that	that	PRON
ejpam-6529	43	25	satisfies	satisfy	VERB
ejpam-6529	43	26	:	:	PUNCT
ejpam-6529	43	27	(	(	PUNCT
ejpam-6529	43	28	sh1	sh1	PROPN
ejpam-6529	43	29	)	)	PUNCT
ejpam-6529	43	30	(	(	PUNCT
ejpam-6529	43	31	a|(ðb(c)|ðb(c)))|((ða(b)|(ða(c)|ða(c)))|(ða(b)|(ða(c)|ða(c	a|(ðb(c)|ðb(c)))|((ða(b)|(ða(c)|ða(c)))|(ða(b)|(ða(c)|ða(c	PROPN
ejpam-6529	43	32	)	)	PUNCT
ejpam-6529	43	33	)	)	PUNCT
ejpam-6529	43	34	)	)	PUNCT
ejpam-6529	43	35	)	)	PUNCT
ejpam-6529	44	1	=	=	SYM
ejpam-6529	44	2	ða(a	ða(a	PUNCT
ejpam-6529	44	3	)	)	PUNCT
ejpam-6529	44	4	,	,	PUNCT
ejpam-6529	44	5	(	(	PUNCT
ejpam-6529	44	6	sh2	sh2	PROPN
ejpam-6529	44	7	)	)	PUNCT
ejpam-6529	44	8	ða(b	ða(b	PUNCT
ejpam-6529	44	9	)	)	PUNCT
ejpam-6529	45	1	=	=	PUNCT
ejpam-6529	45	2	ðb(a	ðb(a	PUNCT
ejpam-6529	45	3	)	)	PUNCT
ejpam-6529	45	4	=	=	SYM
ejpam-6529	45	5	ða(a	ða(a	PUNCT
ejpam-6529	45	6	)	)	PUNCT
ejpam-6529	45	7	⇒	⇒	VERB
ejpam-6529	45	8	a	a	DET
ejpam-6529	45	9	=	=	SYM
ejpam-6529	45	10	b	b	PROPN
ejpam-6529	45	11	s.	s.	PROPN
ejpam-6529	45	12	s.	s.	PROPN
ejpam-6529	45	13	ahn	ahn	PROPN
ejpam-6529	45	14	,	,	PUNCT
ejpam-6529	45	15	y.	y.	PROPN
ejpam-6529	45	16	j.	j.	PROPN
ejpam-6529	45	17	seo	seo	PROPN
ejpam-6529	45	18	,	,	PUNCT
ejpam-6529	45	19	y.	y.	PROPN
ejpam-6529	45	20	b.	b.	PROPN
ejpam-6529	45	21	jun	jun	PROPN
ejpam-6529	45	22	/	/	SYM
ejpam-6529	45	23	eur	eur	PROPN
ejpam-6529	45	24	.	.	PUNCT
ejpam-6529	46	1	j.	j.	PROPN
ejpam-6529	46	2	pure	pure	PROPN
ejpam-6529	46	3	appl	appl	PROPN
ejpam-6529	46	4	.	.	PROPN
ejpam-6529	46	5	math	math	PROPN
ejpam-6529	46	6	,	,	PUNCT
ejpam-6529	46	7	18	18	NUM
ejpam-6529	46	8	(	(	PUNCT
ejpam-6529	46	9	3	3	NUM
ejpam-6529	46	10	)	)	PUNCT
ejpam-6529	46	11	(	(	PUNCT
ejpam-6529	46	12	2025	2025	NUM
ejpam-6529	46	13	)	)	PUNCT
ejpam-6529	46	14	,	,	PUNCT
ejpam-6529	46	15	6529	6529	NUM
ejpam-6529	46	16	3	3	NUM
ejpam-6529	46	17	of	of	ADP
ejpam-6529	46	18	16	16	NUM
ejpam-6529	46	19	for	for	ADP
ejpam-6529	46	20	all	all	DET
ejpam-6529	46	21	a	a	DET
ejpam-6529	46	22	,	,	PUNCT
ejpam-6529	46	23	b	b	NOUN
ejpam-6529	46	24	,	,	PUNCT
ejpam-6529	46	25	c	c	PROPN
ejpam-6529	46	26	∈	∈	PROPN
ejpam-6529	46	27	x.	x.	NOUN
ejpam-6529	46	28	recall	recall	VERB
ejpam-6529	46	29	that	that	SCONJ
ejpam-6529	46	30	every	every	DET
ejpam-6529	46	31	sheffer	sheffer	NOUN
ejpam-6529	46	32	stroke	stroke	NOUN
ejpam-6529	46	33	hilbert	hilbert	PROPN
ejpam-6529	46	34	algebra	algebra	PROPN
ejpam-6529	46	35	x	x	X
ejpam-6529	46	36	:	:	PUNCT
ejpam-6529	46	37	=	=	SYM
ejpam-6529	46	38	(	(	PUNCT
ejpam-6529	46	39	x	x	NOUN
ejpam-6529	46	40	,	,	PUNCT
ejpam-6529	46	41	|	|	ADV
ejpam-6529	46	42	)	)	PUNCT
ejpam-6529	46	43	satisfies	satisfie	NOUN
ejpam-6529	46	44	ða(a	ða(a	PUNCT
ejpam-6529	46	45	)	)	PUNCT
ejpam-6529	46	46	=	=	SYM
ejpam-6529	46	47	ðb(b	ðb(b	NOUN
ejpam-6529	46	48	)	)	PUNCT
ejpam-6529	46	49	for	for	ADP
ejpam-6529	46	50	all	all	DET
ejpam-6529	46	51	a	a	PRON
ejpam-6529	46	52	,	,	PUNCT
ejpam-6529	46	53	b	b	X
ejpam-6529	46	54	∈	∈	PROPN
ejpam-6529	46	55	x.	x.	NOUN
ejpam-6529	47	1	it	it	PRON
ejpam-6529	47	2	means	mean	VERB
ejpam-6529	47	3	that	that	SCONJ
ejpam-6529	47	4	x	x	X
ejpam-6529	47	5	:	:	PUNCT
ejpam-6529	47	6	=	=	SYM
ejpam-6529	47	7	(	(	PUNCT
ejpam-6529	47	8	x	x	NOUN
ejpam-6529	47	9	,	,	PUNCT
ejpam-6529	47	10	|	|	ADV
ejpam-6529	47	11	)	)	PUNCT
ejpam-6529	47	12	has	have	VERB
ejpam-6529	47	13	an	an	DET
ejpam-6529	47	14	algebraic	algebraic	ADJ
ejpam-6529	47	15	constant	constant	ADJ
ejpam-6529	47	16	which	which	PRON
ejpam-6529	47	17	is	be	AUX
ejpam-6529	47	18	denoted	denote	VERB
ejpam-6529	47	19	by	by	ADP
ejpam-6529	47	20	“	"	PUNCT
ejpam-6529	47	21	1	1	NUM
ejpam-6529	47	22	”	"	PUNCT
ejpam-6529	47	23	(	(	PUNCT
ejpam-6529	47	24	see	see	VERB
ejpam-6529	47	25	[	[	X
ejpam-6529	47	26	5	5	NUM
ejpam-6529	47	27	]	]	PUNCT
ejpam-6529	47	28	)	)	PUNCT
ejpam-6529	47	29	.	.	PUNCT
ejpam-6529	48	1	let	let	VERB
ejpam-6529	48	2	x	x	PRON
ejpam-6529	48	3	:	:	PUNCT
ejpam-6529	48	4	=	=	SYM
ejpam-6529	48	5	(	(	PUNCT
ejpam-6529	48	6	x	x	NOUN
ejpam-6529	48	7	,	,	PUNCT
ejpam-6529	48	8	|	|	ADV
ejpam-6529	48	9	)	)	PUNCT
ejpam-6529	48	10	be	be	AUX
ejpam-6529	48	11	a	a	DET
ejpam-6529	48	12	sheffer	sheffer	NOUN
ejpam-6529	48	13	stroke	stroke	NOUN
ejpam-6529	48	14	hilbert	hilbert	PROPN
ejpam-6529	48	15	algebra	algebra	PROPN
ejpam-6529	48	16	.	.	PUNCT
ejpam-6529	49	1	then	then	ADV
ejpam-6529	49	2	the	the	DET
ejpam-6529	49	3	order	order	NOUN
ejpam-6529	49	4	relation	relation	NOUN
ejpam-6529	49	5	“	"	PUNCT
ejpam-6529	49	6	⪯	⪯	NOUN
ejpam-6529	49	7	”	"	PUNCT
ejpam-6529	49	8	on	on	ADP
ejpam-6529	49	9	x	x	SYM
ejpam-6529	49	10	is	be	AUX
ejpam-6529	49	11	defined	define	VERB
ejpam-6529	49	12	as	as	SCONJ
ejpam-6529	49	13	follows	follow	VERB
ejpam-6529	49	14	:	:	PUNCT
ejpam-6529	49	15	(	(	PUNCT
ejpam-6529	49	16	∀a	∀a	X
ejpam-6529	49	17	,	,	PUNCT
ejpam-6529	49	18	b	b	PROPN
ejpam-6529	49	19	∈	∈	PROPN
ejpam-6529	49	20	x)(a	x)(a	PUNCT
ejpam-6529	50	1	⪯	⪯	PROPN
ejpam-6529	50	2	b	b	PROPN
ejpam-6529	50	3	⇔	⇔	PROPN
ejpam-6529	50	4	ða(b	ða(b	PUNCT
ejpam-6529	50	5	)	)	PUNCT
ejpam-6529	51	1	=	=	SYM
ejpam-6529	51	2	1	1	NUM
ejpam-6529	51	3	)	)	PUNCT
ejpam-6529	51	4	.	.	PUNCT
ejpam-6529	52	1	(	(	PUNCT
ejpam-6529	52	2	1	1	X
ejpam-6529	52	3	)	)	PUNCT
ejpam-6529	52	4	we	we	PRON
ejpam-6529	52	5	observe	observe	VERB
ejpam-6529	52	6	that	that	SCONJ
ejpam-6529	52	7	the	the	DET
ejpam-6529	52	8	relation	relation	NOUN
ejpam-6529	52	9	“	"	PUNCT
ejpam-6529	52	10	⪯	⪯	NOUN
ejpam-6529	52	11	”	"	PUNCT
ejpam-6529	52	12	is	be	AUX
ejpam-6529	52	13	a	a	DET
ejpam-6529	52	14	partial	partial	ADJ
ejpam-6529	52	15	order	order	NOUN
ejpam-6529	52	16	in	in	ADP
ejpam-6529	52	17	a	a	DET
ejpam-6529	52	18	sheffer	sheffer	NOUN
ejpam-6529	52	19	stroke	stroke	NOUN
ejpam-6529	52	20	hilbert	hilbert	PROPN
ejpam-6529	52	21	algebra	algebra	PROPN
ejpam-6529	52	22	x	x	X
ejpam-6529	52	23	:	:	PUNCT
ejpam-6529	52	24	=	=	SYM
ejpam-6529	52	25	(	(	PUNCT
ejpam-6529	52	26	x	x	NOUN
ejpam-6529	52	27	,	,	PUNCT
ejpam-6529	52	28	|	|	NOUN
ejpam-6529	52	29	)	)	PUNCT
ejpam-6529	52	30	(	(	PUNCT
ejpam-6529	52	31	see	see	VERB
ejpam-6529	52	32	[	[	X
ejpam-6529	52	33	5	5	NUM
ejpam-6529	52	34	]	]	NUM
ejpam-6529	52	35	)	)	PUNCT
ejpam-6529	52	36	.	.	PUNCT
ejpam-6529	53	1	proposition	proposition	NOUN
ejpam-6529	53	2	1	1	NUM
ejpam-6529	53	3	(	(	PUNCT
ejpam-6529	53	4	[	[	X
ejpam-6529	53	5	5	5	NUM
ejpam-6529	53	6	]	]	NUM
ejpam-6529	53	7	)	)	PUNCT
ejpam-6529	53	8	.	.	PUNCT
ejpam-6529	54	1	every	every	DET
ejpam-6529	54	2	sheffer	sheffer	NOUN
ejpam-6529	54	3	stroke	stroke	NOUN
ejpam-6529	54	4	hilbert	hilbert	PROPN
ejpam-6529	54	5	algebra	algebra	PROPN
ejpam-6529	54	6	x	x	X
ejpam-6529	54	7	:	:	PUNCT
ejpam-6529	54	8	=	=	SYM
ejpam-6529	54	9	(	(	PUNCT
ejpam-6529	54	10	x	x	NOUN
ejpam-6529	54	11	,	,	PUNCT
ejpam-6529	54	12	|	|	ADV
ejpam-6529	54	13	)	)	PUNCT
ejpam-6529	54	14	satisfies	satisfie	NOUN
ejpam-6529	54	15	:	:	PUNCT
ejpam-6529	54	16	ða(a	ða(a	PUNCT
ejpam-6529	54	17	)	)	PUNCT
ejpam-6529	54	18	=	=	SYM
ejpam-6529	54	19	1	1	NUM
ejpam-6529	54	20	,	,	PUNCT
ejpam-6529	54	21	ða(1	ða(1	NOUN
ejpam-6529	54	22	)	)	PUNCT
ejpam-6529	54	23	=	=	SYM
ejpam-6529	54	24	1	1	NUM
ejpam-6529	54	25	,	,	PUNCT
ejpam-6529	54	26	ð1(a	ð1(a	NUM
ejpam-6529	54	27	)	)	PUNCT
ejpam-6529	54	28	=	=	SYM
ejpam-6529	54	29	a	a	PRON
ejpam-6529	54	30	,	,	PUNCT
ejpam-6529	54	31	(	(	PUNCT
ejpam-6529	54	32	2	2	X
ejpam-6529	54	33	)	)	PUNCT
ejpam-6529	54	34	a	a	DET
ejpam-6529	54	35	⪯	⪯	NOUN
ejpam-6529	54	36	ðb(a	ðb(a	PUNCT
ejpam-6529	54	37	)	)	PUNCT
ejpam-6529	54	38	,	,	PUNCT
ejpam-6529	54	39	(	(	PUNCT
ejpam-6529	54	40	3	3	X
ejpam-6529	54	41	)	)	PUNCT
ejpam-6529	54	42	ða(b)|(b|b	ða(b)|(b|b	NOUN
ejpam-6529	54	43	)	)	PUNCT
ejpam-6529	54	44	=	=	SYM
ejpam-6529	54	45	ðb(a)|(a|a	ðb(a)|(a|a	NUM
ejpam-6529	54	46	)	)	PUNCT
ejpam-6529	54	47	,	,	PUNCT
ejpam-6529	54	48	(	(	PUNCT
ejpam-6529	54	49	4	4	X
ejpam-6529	54	50	)	)	PUNCT
ejpam-6529	54	51	(	(	PUNCT
ejpam-6529	54	52	ða(b)|(b|b))|(b|b	ða(b)|(b|b))|(b|b	NOUN
ejpam-6529	54	53	)	)	PUNCT
ejpam-6529	54	54	=	=	SYM
ejpam-6529	54	55	ða(b	ða(b	PUNCT
ejpam-6529	54	56	)	)	PUNCT
ejpam-6529	54	57	,	,	PUNCT
ejpam-6529	54	58	(	(	PUNCT
ejpam-6529	54	59	5	5	X
ejpam-6529	54	60	)	)	PUNCT
ejpam-6529	54	61	a|(ðb(c)|ðb(c	a|(ðb(c)|ðb(c	PROPN
ejpam-6529	54	62	)	)	PUNCT
ejpam-6529	54	63	)	)	PUNCT
ejpam-6529	55	1	=	=	SYM
ejpam-6529	55	2	b|(ða(c)|ða(c	b|(ða(c)|ða(c	NOUN
ejpam-6529	55	3	)	)	PUNCT
ejpam-6529	55	4	)	)	PUNCT
ejpam-6529	55	5	,	,	PUNCT
ejpam-6529	55	6	(	(	PUNCT
ejpam-6529	55	7	6	6	X
ejpam-6529	55	8	)	)	PUNCT
ejpam-6529	55	9	a	a	DET
ejpam-6529	55	10	⪯	⪯	NOUN
ejpam-6529	55	11	b	b	NOUN
ejpam-6529	55	12	⇒	⇒	PROPN
ejpam-6529	55	13	ðc(a	ðc(a	PRON
ejpam-6529	55	14	)	)	PUNCT
ejpam-6529	55	15	⪯	⪯	NOUN
ejpam-6529	55	16	ðc(b	ðc(b	NUM
ejpam-6529	55	17	)	)	PUNCT
ejpam-6529	55	18	,	,	PUNCT
ejpam-6529	55	19	ðb(c	ðb(c	PUNCT
ejpam-6529	55	20	)	)	PUNCT
ejpam-6529	55	21	⪯	⪯	NOUN
ejpam-6529	55	22	ða(c	ða(c	NOUN
ejpam-6529	55	23	)	)	PUNCT
ejpam-6529	55	24	,	,	PUNCT
ejpam-6529	55	25	(	(	PUNCT
ejpam-6529	55	26	7	7	X
ejpam-6529	55	27	)	)	PUNCT
ejpam-6529	55	28	a|(ðb(c)|ðb(c	a|(ðb(c)|ðb(c	PROPN
ejpam-6529	55	29	)	)	PUNCT
ejpam-6529	55	30	)	)	PUNCT
ejpam-6529	56	1	=	=	SYM
ejpam-6529	56	2	(	(	PUNCT
ejpam-6529	56	3	ða(b)|(ða(c)|ða(c	ða(b)|(ða(c)|ða(c	INTJ
ejpam-6529	56	4	)	)	PUNCT
ejpam-6529	56	5	)	)	PUNCT
ejpam-6529	56	6	,	,	PUNCT
ejpam-6529	56	7	(	(	PUNCT
ejpam-6529	56	8	8)	8)	NUM
ejpam-6529	56	9	for	for	ADP
ejpam-6529	56	10	all	all	DET
ejpam-6529	56	11	a	a	DET
ejpam-6529	56	12	,	,	PUNCT
ejpam-6529	56	13	b	b	NOUN
ejpam-6529	56	14	,	,	PUNCT
ejpam-6529	56	15	c	c	PROPN
ejpam-6529	56	16	∈	∈	PROPN
ejpam-6529	56	17	x.	x.	NOUN
ejpam-6529	56	18	by	by	ADP
ejpam-6529	56	19	(	(	PUNCT
ejpam-6529	56	20	2	2	NUM
ejpam-6529	56	21	)	)	PUNCT
ejpam-6529	56	22	,	,	PUNCT
ejpam-6529	56	23	we	we	PRON
ejpam-6529	56	24	know	know	VERB
ejpam-6529	56	25	that	that	SCONJ
ejpam-6529	56	26	the	the	DET
ejpam-6529	56	27	algebraic	algebraic	ADJ
ejpam-6529	56	28	constant	constant	ADJ
ejpam-6529	56	29	1	1	NUM
ejpam-6529	56	30	is	be	AUX
ejpam-6529	56	31	the	the	DET
ejpam-6529	56	32	greatest	great	ADJ
ejpam-6529	56	33	element	element	NOUN
ejpam-6529	56	34	in	in	ADP
ejpam-6529	56	35	x	x	X
ejpam-6529	56	36	:	:	PUNCT
ejpam-6529	56	37	=	=	SYM
ejpam-6529	56	38	(	(	PUNCT
ejpam-6529	56	39	x	x	NOUN
ejpam-6529	56	40	,	,	PUNCT
ejpam-6529	56	41	|	|	ADV
ejpam-6529	56	42	)	)	PUNCT
ejpam-6529	56	43	with	with	ADP
ejpam-6529	56	44	respect	respect	NOUN
ejpam-6529	56	45	to	to	ADP
ejpam-6529	56	46	the	the	DET
ejpam-6529	56	47	order	order	NOUN
ejpam-6529	56	48	⪯.	⪯.	VERB
ejpam-6529	56	49	proposition	proposition	NOUN
ejpam-6529	56	50	2	2	NUM
ejpam-6529	56	51	.	.	PUNCT
ejpam-6529	57	1	let	let	VERB
ejpam-6529	57	2	x	x	PRON
ejpam-6529	57	3	:	:	PUNCT
ejpam-6529	57	4	=	=	SYM
ejpam-6529	57	5	(	(	PUNCT
ejpam-6529	57	6	x	x	NOUN
ejpam-6529	57	7	,	,	PUNCT
ejpam-6529	57	8	|	|	ADV
ejpam-6529	57	9	)	)	PUNCT
ejpam-6529	57	10	be	be	AUX
ejpam-6529	57	11	a	a	DET
ejpam-6529	57	12	sheffer	sheffer	NOUN
ejpam-6529	57	13	stroke	stroke	NOUN
ejpam-6529	57	14	hilbert	hilbert	PROPN
ejpam-6529	57	15	algebra	algebra	PROPN
ejpam-6529	57	16	with	with	ADP
ejpam-6529	57	17	the	the	DET
ejpam-6529	57	18	smallest	small	ADJ
ejpam-6529	57	19	element	element	NOUN
ejpam-6529	57	20	0	0	NUM
ejpam-6529	57	21	.	.	PUNCT
ejpam-6529	58	1	then	then	ADV
ejpam-6529	58	2	0|0	0|0	NUM
ejpam-6529	58	3	=	=	SYM
ejpam-6529	58	4	1	1	NUM
ejpam-6529	58	5	,	,	PUNCT
ejpam-6529	58	6	1|1	1|1	NUM
ejpam-6529	58	7	=	=	SYM
ejpam-6529	58	8	0	0	NUM
ejpam-6529	58	9	,	,	PUNCT
ejpam-6529	58	10	(	(	PUNCT
ejpam-6529	58	11	9	9	X
ejpam-6529	58	12	)	)	PUNCT
ejpam-6529	58	13	ð1(0	ð1(0	PROPN
ejpam-6529	58	14	)	)	PUNCT
ejpam-6529	59	1	=	=	SYM
ejpam-6529	59	2	0	0	NUM
ejpam-6529	59	3	,	,	PUNCT
ejpam-6529	59	4	ð0(0	ð0(0	PROPN
ejpam-6529	59	5	)	)	PUNCT
ejpam-6529	59	6	=	=	SYM
ejpam-6529	60	1	1	1	X
ejpam-6529	60	2	.	.	PUNCT
ejpam-6529	60	3	(	(	PUNCT
ejpam-6529	60	4	10	10	NUM
ejpam-6529	60	5	)	)	PUNCT
ejpam-6529	60	6	definition	definition	NOUN
ejpam-6529	60	7	3	3	NUM
ejpam-6529	60	8	(	(	PUNCT
ejpam-6529	60	9	[	[	X
ejpam-6529	60	10	4	4	NUM
ejpam-6529	60	11	]	]	NUM
ejpam-6529	60	12	)	)	PUNCT
ejpam-6529	60	13	.	.	PUNCT
ejpam-6529	61	1	let	let	VERB
ejpam-6529	61	2	x	x	PRON
ejpam-6529	61	3	:	:	PUNCT
ejpam-6529	61	4	=	=	SYM
ejpam-6529	61	5	(	(	PUNCT
ejpam-6529	61	6	x	x	NOUN
ejpam-6529	61	7	,	,	PUNCT
ejpam-6529	61	8	|	|	ADV
ejpam-6529	61	9	)	)	PUNCT
ejpam-6529	61	10	be	be	AUX
ejpam-6529	61	11	a	a	DET
ejpam-6529	61	12	sheffer	sheffer	NOUN
ejpam-6529	61	13	stroke	stroke	NOUN
ejpam-6529	61	14	hilbert	hilbert	PROPN
ejpam-6529	61	15	algebra	algebra	PROPN
ejpam-6529	61	16	.	.	PUNCT
ejpam-6529	62	1	a	a	DET
ejpam-6529	62	2	subset	subset	NOUN
ejpam-6529	62	3	f	f	NOUN
ejpam-6529	62	4	of	of	ADP
ejpam-6529	62	5	x	x	PROPN
ejpam-6529	62	6	is	be	AUX
ejpam-6529	62	7	called	call	VERB
ejpam-6529	62	8	a	a	DET
ejpam-6529	62	9	filter	filter	NOUN
ejpam-6529	62	10	of	of	ADP
ejpam-6529	62	11	x	x	NOUN
ejpam-6529	62	12	:	:	PUNCT
ejpam-6529	62	13	=	=	SYM
ejpam-6529	62	14	(	(	PUNCT
ejpam-6529	62	15	x	x	NOUN
ejpam-6529	62	16	,	,	PUNCT
ejpam-6529	62	17	|	|	INTJ
ejpam-6529	62	18	)	)	PUNCT
ejpam-6529	62	19	if	if	SCONJ
ejpam-6529	62	20	it	it	PRON
ejpam-6529	62	21	satisfies	satisfy	VERB
ejpam-6529	62	22	:	:	PUNCT
ejpam-6529	62	23	1	1	NUM
ejpam-6529	62	24	∈	∈	NOUN
ejpam-6529	62	25	f	f	X
ejpam-6529	62	26	,	,	PUNCT
ejpam-6529	62	27	(	(	PUNCT
ejpam-6529	62	28	11	11	NUM
ejpam-6529	62	29	)	)	PUNCT
ejpam-6529	62	30	(	(	PUNCT
ejpam-6529	62	31	∀a	∀a	X
ejpam-6529	62	32	,	,	PUNCT
ejpam-6529	62	33	b	b	PROPN
ejpam-6529	62	34	∈	∈	PROPN
ejpam-6529	62	35	x)(b	x)(b	PROPN
ejpam-6529	62	36	∈	∈	PROPN
ejpam-6529	62	37	f	f	PROPN
ejpam-6529	62	38	⇒	⇒	PROPN
ejpam-6529	62	39	ða(b	ða(b	PUNCT
ejpam-6529	62	40	)	)	PUNCT
ejpam-6529	63	1	∈	∈	PROPN
ejpam-6529	63	2	f	f	PROPN
ejpam-6529	63	3	)	)	PUNCT
ejpam-6529	63	4	,	,	PUNCT
ejpam-6529	63	5	(	(	PUNCT
ejpam-6529	63	6	12	12	NUM
ejpam-6529	63	7	)	)	PUNCT
ejpam-6529	63	8	(	(	PUNCT
ejpam-6529	63	9	∀a	∀a	X
ejpam-6529	63	10	,	,	PUNCT
ejpam-6529	63	11	b	b	NOUN
ejpam-6529	63	12	,	,	PUNCT
ejpam-6529	63	13	c	c	PROPN
ejpam-6529	63	14	∈	∈	PROPN
ejpam-6529	63	15	x)(b	x)(b	PROPN
ejpam-6529	63	16	,	,	PUNCT
ejpam-6529	63	17	c	c	PROPN
ejpam-6529	63	18	∈	∈	PROPN
ejpam-6529	63	19	f	f	PROPN
ejpam-6529	63	20	⇒	⇒	PROPN
ejpam-6529	63	21	(	(	PUNCT
ejpam-6529	63	22	a|(b|c))|(b|c	a|(b|c))|(b|c	PROPN
ejpam-6529	63	23	)	)	PUNCT
ejpam-6529	63	24	∈	∈	PROPN
ejpam-6529	63	25	f	f	PROPN
ejpam-6529	63	26	)	)	PUNCT
ejpam-6529	63	27	.	.	PUNCT
ejpam-6529	64	1	(	(	PUNCT
ejpam-6529	64	2	13	13	X
ejpam-6529	64	3	)	)	PUNCT
ejpam-6529	64	4	let	let	VERB
ejpam-6529	64	5	x	x	PRON
ejpam-6529	64	6	:	:	PUNCT
ejpam-6529	64	7	=	=	SYM
ejpam-6529	64	8	(	(	PUNCT
ejpam-6529	64	9	x	x	NOUN
ejpam-6529	64	10	,	,	PUNCT
ejpam-6529	64	11	|	|	ADV
ejpam-6529	64	12	)	)	PUNCT
ejpam-6529	64	13	be	be	AUX
ejpam-6529	64	14	a	a	DET
ejpam-6529	64	15	sheffer	sheffer	NOUN
ejpam-6529	64	16	stroke	stroke	NOUN
ejpam-6529	64	17	hilbert	hilbert	PROPN
ejpam-6529	64	18	algebra	algebra	PROPN
ejpam-6529	64	19	.	.	PUNCT
ejpam-6529	65	1	if	if	SCONJ
ejpam-6529	65	2	a	a	DET
ejpam-6529	65	3	subset	subset	NOUN
ejpam-6529	65	4	f	f	X
ejpam-6529	65	5	of	of	ADP
ejpam-6529	65	6	x	x	PUNCT
ejpam-6529	65	7	satisfies	satisfie	NOUN
ejpam-6529	65	8	(	(	PUNCT
ejpam-6529	65	9	11	11	NUM
ejpam-6529	65	10	)	)	PUNCT
ejpam-6529	65	11	and	and	CCONJ
ejpam-6529	65	12	(	(	PUNCT
ejpam-6529	65	13	12	12	NUM
ejpam-6529	65	14	)	)	PUNCT
ejpam-6529	65	15	,	,	PUNCT
ejpam-6529	65	16	we	we	PRON
ejpam-6529	65	17	say	say	VERB
ejpam-6529	65	18	that	that	SCONJ
ejpam-6529	65	19	f	f	PROPN
ejpam-6529	65	20	is	be	AUX
ejpam-6529	65	21	a	a	DET
ejpam-6529	65	22	weak	weak	ADJ
ejpam-6529	65	23	filter	filter	NOUN
ejpam-6529	65	24	of	of	ADP
ejpam-6529	65	25	x	x	X
ejpam-6529	65	26	:	:	PUNCT
ejpam-6529	65	27	=	=	SYM
ejpam-6529	65	28	(	(	PUNCT
ejpam-6529	65	29	x	x	NOUN
ejpam-6529	65	30	,	,	PUNCT
ejpam-6529	65	31	|	|	NOUN
ejpam-6529	65	32	)	)	PUNCT
ejpam-6529	65	33	(	(	PUNCT
ejpam-6529	65	34	see	see	VERB
ejpam-6529	65	35	[	[	X
ejpam-6529	65	36	13	13	NUM
ejpam-6529	65	37	]	]	NUM
ejpam-6529	65	38	)	)	PUNCT
ejpam-6529	65	39	.	.	PUNCT
ejpam-6529	66	1	s.	s.	PROPN
ejpam-6529	66	2	s.	s.	PROPN
ejpam-6529	66	3	ahn	ahn	PROPN
ejpam-6529	66	4	,	,	PUNCT
ejpam-6529	66	5	y.	y.	PROPN
ejpam-6529	66	6	j.	j.	PROPN
ejpam-6529	66	7	seo	seo	PROPN
ejpam-6529	66	8	,	,	PUNCT
ejpam-6529	66	9	y.	y.	PROPN
ejpam-6529	66	10	b.	b.	PROPN
ejpam-6529	66	11	jun	jun	PROPN
ejpam-6529	66	12	/	/	SYM
ejpam-6529	66	13	eur	eur	PROPN
ejpam-6529	66	14	.	.	PUNCT
ejpam-6529	67	1	j.	j.	PROPN
ejpam-6529	67	2	pure	pure	PROPN
ejpam-6529	67	3	appl	appl	PROPN
ejpam-6529	67	4	.	.	PROPN
ejpam-6529	67	5	math	math	PROPN
ejpam-6529	67	6	,	,	PUNCT
ejpam-6529	67	7	18	18	NUM
ejpam-6529	67	8	(	(	PUNCT
ejpam-6529	67	9	3	3	NUM
ejpam-6529	67	10	)	)	PUNCT
ejpam-6529	67	11	(	(	PUNCT
ejpam-6529	67	12	2025	2025	NUM
ejpam-6529	67	13	)	)	PUNCT
ejpam-6529	67	14	,	,	PUNCT
ejpam-6529	67	15	6529	6529	NUM
ejpam-6529	67	16	4	4	NUM
ejpam-6529	67	17	of	of	ADP
ejpam-6529	67	18	16	16	NUM
ejpam-6529	67	19	let	let	VERB
ejpam-6529	67	20	x	x	PRON
ejpam-6529	67	21	be	be	AUX
ejpam-6529	67	22	a	a	DET
ejpam-6529	67	23	set	set	NOUN
ejpam-6529	67	24	.	.	PUNCT
ejpam-6529	68	1	an	an	DET
ejpam-6529	68	2	intuitionistic	intuitionistic	ADJ
ejpam-6529	68	3	fuzzy	fuzzy	ADJ
ejpam-6529	68	4	set	set	VERB
ejpam-6529	68	5	b∗	b∗	ADV
ejpam-6529	68	6	in	in	ADP
ejpam-6529	68	7	x	x	PART
ejpam-6529	68	8	(	(	PUNCT
ejpam-6529	68	9	see	see	VERB
ejpam-6529	68	10	[	[	X
ejpam-6529	68	11	15	15	NUM
ejpam-6529	68	12	]	]	PUNCT
ejpam-6529	68	13	)	)	PUNCT
ejpam-6529	68	14	is	be	AUX
ejpam-6529	68	15	an	an	DET
ejpam-6529	68	16	object	object	NOUN
ejpam-6529	68	17	having	have	VERB
ejpam-6529	68	18	the	the	DET
ejpam-6529	68	19	form	form	NOUN
ejpam-6529	68	20	b∗	b∗	ADJ
ejpam-6529	68	21	:	:	PUNCT
ejpam-6529	68	22	=	=	SYM
ejpam-6529	68	23	{	{	PUNCT
ejpam-6529	68	24	⟨a	⟨a	NOUN
ejpam-6529	68	25	,	,	PUNCT
ejpam-6529	68	26	fb(a	fb(a	NOUN
ejpam-6529	68	27	)	)	PUNCT
ejpam-6529	68	28	,	,	PUNCT
ejpam-6529	68	29	gb(a)⟩	gb(a)⟩	PROPN
ejpam-6529	68	30	|	|	ADV
ejpam-6529	68	31	fb(a	fb(a	PUNCT
ejpam-6529	68	32	)	)	PUNCT
ejpam-6529	68	33	+	+	CCONJ
ejpam-6529	69	1	gb(a	gb(a	NOUN
ejpam-6529	69	2	)	)	PUNCT
ejpam-6529	69	3	≤	≤	NUM
ejpam-6529	69	4	1	1	NUM
ejpam-6529	69	5	,	,	PUNCT
ejpam-6529	69	6	a	a	DET
ejpam-6529	69	7	∈	∈	NOUN
ejpam-6529	69	8	x	x	NOUN
ejpam-6529	69	9	}	}	PUNCT
ejpam-6529	69	10	,	,	PUNCT
ejpam-6529	69	11	which	which	PRON
ejpam-6529	69	12	is	be	AUX
ejpam-6529	69	13	simply	simply	ADV
ejpam-6529	69	14	denoted	denote	VERB
ejpam-6529	69	15	by	by	ADP
ejpam-6529	69	16	b∗	b∗	ADJ
ejpam-6529	69	17	:	:	PUNCT
ejpam-6529	69	18	=	=	SYM
ejpam-6529	69	19	(	(	PUNCT
ejpam-6529	69	20	x	x	X
ejpam-6529	69	21	;	;	PUNCT
ejpam-6529	69	22	fb	fb	INTJ
ejpam-6529	69	23	,	,	PUNCT
ejpam-6529	69	24	gb	gb	PROPN
ejpam-6529	69	25	)	)	PUNCT
ejpam-6529	69	26	where	where	SCONJ
ejpam-6529	69	27	fb	fb	INTJ
ejpam-6529	69	28	and	and	CCONJ
ejpam-6529	69	29	gb	gb	PRON
ejpam-6529	69	30	are	be	AUX
ejpam-6529	69	31	fuzzy	fuzzy	ADJ
ejpam-6529	69	32	sets	set	NOUN
ejpam-6529	69	33	in	in	ADP
ejpam-6529	69	34	x	x	PRON
ejpam-6529	69	35	,	,	PUNCT
ejpam-6529	69	36	the	the	DET
ejpam-6529	69	37	intuitionistic	intuitionistic	ADJ
ejpam-6529	69	38	fuzzy	fuzzy	ADJ
ejpam-6529	69	39	set	set	VERB
ejpam-6529	69	40	b∗	b∗	ADJ
ejpam-6529	69	41	:	:	PUNCT
ejpam-6529	69	42	=	=	SYM
ejpam-6529	69	43	(	(	PUNCT
ejpam-6529	69	44	x	x	X
ejpam-6529	69	45	;	;	PUNCT
ejpam-6529	69	46	fb	fb	INTJ
ejpam-6529	69	47	,	,	PUNCT
ejpam-6529	69	48	gb	gb	NOUN
ejpam-6529	69	49	)	)	PUNCT
ejpam-6529	69	50	in	in	ADP
ejpam-6529	69	51	x	x	PRON
ejpam-6529	69	52	can	can	AUX
ejpam-6529	69	53	be	be	AUX
ejpam-6529	69	54	represented	represent	VERB
ejpam-6529	69	55	as	as	SCONJ
ejpam-6529	69	56	follows	follow	VERB
ejpam-6529	69	57	:	:	PUNCT
ejpam-6529	69	58	b∗	b∗	ADJ
ejpam-6529	69	59	:	:	PUNCT
ejpam-6529	69	60	=	=	SYM
ejpam-6529	69	61	(	(	PUNCT
ejpam-6529	69	62	x	x	X
ejpam-6529	69	63	;	;	PUNCT
ejpam-6529	69	64	fb	fb	INTJ
ejpam-6529	69	65	,	,	PUNCT
ejpam-6529	69	66	gb	gb	PROPN
ejpam-6529	69	67	)	)	PUNCT
ejpam-6529	69	68	:	:	PUNCT
ejpam-6529	70	1	x	x	X
ejpam-6529	70	2	→	→	PUNCT
ejpam-6529	71	1	[	[	X
ejpam-6529	71	2	0	0	NUM
ejpam-6529	71	3	,	,	PUNCT
ejpam-6529	71	4	1]×	1]×	NUM
ejpam-6529	71	5	[	[	X
ejpam-6529	71	6	0	0	NUM
ejpam-6529	71	7	,	,	PUNCT
ejpam-6529	71	8	1	1	NUM
ejpam-6529	71	9	]	]	PUNCT
ejpam-6529	71	10	,	,	PUNCT
ejpam-6529	71	11	a	a	DET
ejpam-6529	71	12	7→	7→	NUM
ejpam-6529	71	13	(	(	PUNCT
ejpam-6529	71	14	fb(a	fb(a	NOUN
ejpam-6529	71	15	)	)	PUNCT
ejpam-6529	71	16	,	,	PUNCT
ejpam-6529	71	17	gb(a	gb(a	NOUN
ejpam-6529	71	18	)	)	PUNCT
ejpam-6529	71	19	)	)	PUNCT
ejpam-6529	72	1	such	such	ADJ
ejpam-6529	72	2	that	that	SCONJ
ejpam-6529	72	3	fb(a	fb(a	NUM
ejpam-6529	72	4	)	)	PUNCT
ejpam-6529	72	5	+	+	NUM
ejpam-6529	72	6	gb(a	gb(a	NOUN
ejpam-6529	72	7	)	)	PUNCT
ejpam-6529	72	8	≤	≤	NUM
ejpam-6529	72	9	1	1	NUM
ejpam-6529	72	10	.	.	PUNCT
ejpam-6529	72	11	an	an	DET
ejpam-6529	72	12	intuitionistic	intuitionistic	ADJ
ejpam-6529	72	13	fuzzy	fuzzy	ADJ
ejpam-6529	72	14	set	set	VERB
ejpam-6529	72	15	b∗	b∗	ADJ
ejpam-6529	72	16	:	:	PUNCT
ejpam-6529	72	17	=	=	SYM
ejpam-6529	72	18	(	(	PUNCT
ejpam-6529	72	19	x	x	X
ejpam-6529	72	20	;	;	PUNCT
ejpam-6529	72	21	fb	fb	INTJ
ejpam-6529	72	22	,	,	PUNCT
ejpam-6529	72	23	gb	gb	PROPN
ejpam-6529	72	24	)	)	PUNCT
ejpam-6529	72	25	in	in	ADP
ejpam-6529	72	26	a	a	DET
ejpam-6529	72	27	set	set	NOUN
ejpam-6529	72	28	x	x	X
ejpam-6529	72	29	of	of	ADP
ejpam-6529	72	30	the	the	DET
ejpam-6529	72	31	form	form	NOUN
ejpam-6529	72	32	b∗	b∗	ADJ
ejpam-6529	72	33	:	:	PUNCT
ejpam-6529	72	34	=	=	SYM
ejpam-6529	72	35	(	(	PUNCT
ejpam-6529	72	36	x	x	X
ejpam-6529	72	37	;	;	PUNCT
ejpam-6529	72	38	fb	fb	INTJ
ejpam-6529	72	39	,	,	PUNCT
ejpam-6529	72	40	gb	gb	PROPN
ejpam-6529	72	41	)	)	PUNCT
ejpam-6529	72	42	:	:	PUNCT
ejpam-6529	73	1	x	x	X
ejpam-6529	73	2	→	→	PUNCT
ejpam-6529	74	1	[	[	X
ejpam-6529	74	2	0	0	NUM
ejpam-6529	74	3	,	,	PUNCT
ejpam-6529	74	4	1]×	1]×	NUM
ejpam-6529	74	5	[	[	X
ejpam-6529	74	6	0	0	NUM
ejpam-6529	74	7	,	,	PUNCT
ejpam-6529	74	8	1	1	NUM
ejpam-6529	74	9	]	]	PUNCT
ejpam-6529	74	10	,	,	PUNCT
ejpam-6529	74	11	b	b	X
ejpam-6529	74	12	7→	7→	NUM
ejpam-6529	74	13	{	{	PUNCT
ejpam-6529	74	14	(	(	PUNCT
ejpam-6529	74	15	s	s	X
ejpam-6529	74	16	,	,	PUNCT
ejpam-6529	74	17	t	t	PROPN
ejpam-6529	74	18	)	)	PUNCT
ejpam-6529	74	19	∈	∈	PROPN
ejpam-6529	74	20	(	(	PUNCT
ejpam-6529	74	21	0	0	NUM
ejpam-6529	74	22	,	,	PUNCT
ejpam-6529	74	23	1]×	1]×	NUM
ejpam-6529	75	1	[	[	X
ejpam-6529	75	2	0	0	NUM
ejpam-6529	75	3	,	,	PUNCT
ejpam-6529	75	4	1	1	NUM
ejpam-6529	75	5	)	)	PUNCT
ejpam-6529	75	6	if	if	SCONJ
ejpam-6529	75	7	b	b	X
ejpam-6529	75	8	=	=	SYM
ejpam-6529	75	9	a	a	X
ejpam-6529	75	10	,	,	PUNCT
ejpam-6529	75	11	(	(	PUNCT
ejpam-6529	75	12	0	0	NUM
ejpam-6529	75	13	,	,	PUNCT
ejpam-6529	75	14	1	1	NUM
ejpam-6529	75	15	)	)	PUNCT
ejpam-6529	75	16	if	if	SCONJ
ejpam-6529	75	17	b	b	X
ejpam-6529	75	18	̸=	̸=	PROPN
ejpam-6529	75	19	a	a	PRON
ejpam-6529	75	20	,	,	PUNCT
ejpam-6529	75	21	is	be	AUX
ejpam-6529	75	22	said	say	VERB
ejpam-6529	75	23	to	to	PART
ejpam-6529	75	24	be	be	AUX
ejpam-6529	75	25	an	an	DET
ejpam-6529	75	26	intuitionistic	intuitionistic	ADJ
ejpam-6529	75	27	fuzzy	fuzzy	ADJ
ejpam-6529	75	28	point	point	NOUN
ejpam-6529	75	29	with	with	ADP
ejpam-6529	75	30	support	support	NOUN
ejpam-6529	75	31	a	a	PRON
ejpam-6529	75	32	and	and	CCONJ
ejpam-6529	75	33	value	value	NOUN
ejpam-6529	75	34	(	(	PUNCT
ejpam-6529	75	35	s	s	PROPN
ejpam-6529	75	36	,	,	PUNCT
ejpam-6529	75	37	t	t	PROPN
ejpam-6529	75	38	)	)	PUNCT
ejpam-6529	75	39	such	such	ADJ
ejpam-6529	75	40	that	that	SCONJ
ejpam-6529	75	41	s+t	s+t	PROPN
ejpam-6529	75	42	≤	≤	ADV
ejpam-6529	75	43	1	1	NUM
ejpam-6529	75	44	,	,	PUNCT
ejpam-6529	75	45	and	and	CCONJ
ejpam-6529	75	46	is	be	AUX
ejpam-6529	75	47	denoted	denote	VERB
ejpam-6529	75	48	by	by	ADP
ejpam-6529	75	49	a(s	a(s	PROPN
ejpam-6529	75	50	,	,	PUNCT
ejpam-6529	75	51	t	t	PROPN
ejpam-6529	75	52	)	)	PUNCT
ejpam-6529	75	53	.	.	PUNCT
ejpam-6529	76	1	given	give	VERB
ejpam-6529	76	2	an	an	DET
ejpam-6529	76	3	intuitionistic	intuitionistic	ADJ
ejpam-6529	76	4	fuzzy	fuzzy	ADJ
ejpam-6529	76	5	set	set	VERB
ejpam-6529	76	6	b∗	b∗	ADJ
ejpam-6529	76	7	:	:	PUNCT
ejpam-6529	76	8	=	=	SYM
ejpam-6529	76	9	(	(	PUNCT
ejpam-6529	76	10	x	x	X
ejpam-6529	76	11	;	;	PUNCT
ejpam-6529	76	12	fb	fb	INTJ
ejpam-6529	76	13	,	,	PUNCT
ejpam-6529	76	14	gb	gb	PROPN
ejpam-6529	76	15	)	)	PUNCT
ejpam-6529	76	16	and	and	CCONJ
ejpam-6529	76	17	intuitionistic	intuitionistic	ADJ
ejpam-6529	76	18	fuzzy	fuzzy	ADJ
ejpam-6529	76	19	point	point	NOUN
ejpam-6529	76	20	a(s	a(s	PROPN
ejpam-6529	76	21	,	,	PUNCT
ejpam-6529	76	22	t	t	PROPN
ejpam-6529	76	23	)	)	PUNCT
ejpam-6529	76	24	in	in	ADP
ejpam-6529	76	25	x	x	NOUN
ejpam-6529	76	26	,	,	PUNCT
ejpam-6529	76	27	we	we	PRON
ejpam-6529	76	28	say	say	VERB
ejpam-6529	76	29	a(s	a(s	PROPN
ejpam-6529	76	30	,	,	PUNCT
ejpam-6529	76	31	t	t	PROPN
ejpam-6529	76	32	)	)	PUNCT
ejpam-6529	76	33	∈	∈	NOUN
ejpam-6529	76	34	b∗	b∗	ADV
ejpam-6529	76	35	if	if	SCONJ
ejpam-6529	76	36	fb(a	fb(a	NOUN
ejpam-6529	76	37	)	)	PUNCT
ejpam-6529	76	38	≥	≥	NUM
ejpam-6529	76	39	s	s	NOUN
ejpam-6529	76	40	and	and	CCONJ
ejpam-6529	76	41	gb(a	gb(a	NOUN
ejpam-6529	76	42	)	)	PUNCT
ejpam-6529	76	43	≤	≤	NUM
ejpam-6529	76	44	t.	t.	NOUN
ejpam-6529	76	45	(	(	PUNCT
ejpam-6529	76	46	14	14	NUM
ejpam-6529	76	47	)	)	PUNCT
ejpam-6529	76	48	a(s	a(s	PROPN
ejpam-6529	76	49	,	,	PUNCT
ejpam-6529	76	50	t	t	PROPN
ejpam-6529	76	51	)	)	PUNCT
ejpam-6529	76	52	q	q	NOUN
ejpam-6529	77	1	b∗	b∗	ADV
ejpam-6529	77	2	if	if	SCONJ
ejpam-6529	77	3	fb(a	fb(a	NOUN
ejpam-6529	77	4	)	)	PUNCT
ejpam-6529	78	1	+	+	SYM
ejpam-6529	78	2	s	s	VERB
ejpam-6529	78	3	>	>	X
ejpam-6529	78	4	1	1	NUM
ejpam-6529	78	5	and	and	CCONJ
ejpam-6529	78	6	gb(a	gb(a	NUM
ejpam-6529	78	7	)	)	PUNCT
ejpam-6529	79	1	+	+	CCONJ
ejpam-6529	79	2	t	t	X
ejpam-6529	79	3	<	<	X
ejpam-6529	79	4	1	1	NUM
ejpam-6529	79	5	.	.	PUNCT
ejpam-6529	79	6	(	(	PUNCT
ejpam-6529	79	7	15	15	NUM
ejpam-6529	79	8	)	)	PUNCT
ejpam-6529	79	9	a(s	a(s	PROPN
ejpam-6529	79	10	,	,	PUNCT
ejpam-6529	79	11	t	t	PROPN
ejpam-6529	79	12	)	)	PUNCT
ejpam-6529	79	13	∈∨q	∈∨q	NOUN
ejpam-6529	79	14	b∗	b∗	ADV
ejpam-6529	79	15	if	if	SCONJ
ejpam-6529	79	16	a(s	a(s	PROPN
ejpam-6529	79	17	,	,	PUNCT
ejpam-6529	79	18	t	t	PROPN
ejpam-6529	79	19	)	)	PUNCT
ejpam-6529	79	20	∈	∈	PROPN
ejpam-6529	79	21	b∗	b∗	ADJ
ejpam-6529	79	22	or	or	CCONJ
ejpam-6529	79	23	a(s	a(s	PROPN
ejpam-6529	79	24	,	,	PUNCT
ejpam-6529	79	25	t	t	PROPN
ejpam-6529	79	26	)	)	PUNCT
ejpam-6529	80	1	q	q	NOUN
ejpam-6529	80	2	b∗.	b∗.	NOUN
ejpam-6529	80	3	(	(	PUNCT
ejpam-6529	80	4	16	16	NUM
ejpam-6529	80	5	)	)	PUNCT
ejpam-6529	80	6	given	give	VERB
ejpam-6529	80	7	(	(	PUNCT
ejpam-6529	80	8	s	s	PROPN
ejpam-6529	80	9	,	,	PUNCT
ejpam-6529	80	10	t	t	PROPN
ejpam-6529	80	11	)	)	PUNCT
ejpam-6529	80	12	∈	∈	PROPN
ejpam-6529	80	13	(	(	PUNCT
ejpam-6529	80	14	0	0	NUM
ejpam-6529	80	15	,	,	PUNCT
ejpam-6529	80	16	1	1	NUM
ejpam-6529	80	17	]	]	SYM
ejpam-6529	80	18	×	×	NOUN
ejpam-6529	81	1	[	[	X
ejpam-6529	81	2	0	0	NUM
ejpam-6529	81	3	,	,	PUNCT
ejpam-6529	81	4	1	1	NUM
ejpam-6529	81	5	)	)	PUNCT
ejpam-6529	81	6	and	and	CCONJ
ejpam-6529	81	7	an	an	DET
ejpam-6529	81	8	intuitionistic	intuitionistic	ADJ
ejpam-6529	81	9	fuzzy	fuzzy	ADJ
ejpam-6529	81	10	set	set	VERB
ejpam-6529	81	11	b∗	b∗	ADJ
ejpam-6529	81	12	:	:	PUNCT
ejpam-6529	81	13	=	=	SYM
ejpam-6529	81	14	(	(	PUNCT
ejpam-6529	81	15	x	x	X
ejpam-6529	81	16	;	;	PUNCT
ejpam-6529	81	17	fb	fb	INTJ
ejpam-6529	81	18	,	,	PUNCT
ejpam-6529	81	19	gb	gb	NOUN
ejpam-6529	81	20	)	)	PUNCT
ejpam-6529	81	21	in	in	ADP
ejpam-6529	81	22	x	x	X
ejpam-6529	81	23	,	,	PUNCT
ejpam-6529	81	24	consider	consider	VERB
ejpam-6529	81	25	the	the	DET
ejpam-6529	81	26	following	follow	VERB
ejpam-6529	81	27	sets	set	NOUN
ejpam-6529	81	28	:	:	PUNCT
ejpam-6529	81	29	(	(	PUNCT
ejpam-6529	81	30	fb	fb	INTJ
ejpam-6529	81	31	,	,	PUNCT
ejpam-6529	81	32	s)∈	s)∈	NUM
ejpam-6529	81	33	:	:	PUNCT
ejpam-6529	81	34	=	=	X
ejpam-6529	81	35	{	{	PUNCT
ejpam-6529	81	36	a	a	DET
ejpam-6529	81	37	∈	∈	NOUN
ejpam-6529	81	38	x	x	SYM
ejpam-6529	81	39	|	|	ADV
ejpam-6529	81	40	fb(a	fb(a	NOUN
ejpam-6529	81	41	)	)	PUNCT
ejpam-6529	81	42	≥	≥	PRON
ejpam-6529	81	43	s	s	X
ejpam-6529	81	44	}	}	PUNCT
ejpam-6529	81	45	,	,	PUNCT
ejpam-6529	81	46	(	(	PUNCT
ejpam-6529	81	47	gb	gb	NOUN
ejpam-6529	81	48	,	,	PUNCT
ejpam-6529	81	49	t)∈	t)∈	PROPN
ejpam-6529	81	50	:	:	PUNCT
ejpam-6529	81	51	=	=	X
ejpam-6529	81	52	{	{	PUNCT
ejpam-6529	81	53	a	a	DET
ejpam-6529	81	54	∈	∈	NOUN
ejpam-6529	81	55	x	x	X
ejpam-6529	81	56	|	|	NOUN
ejpam-6529	81	57	gb(a	gb(a	NOUN
ejpam-6529	81	58	)	)	PUNCT
ejpam-6529	81	59	≤	≤	NUM
ejpam-6529	81	60	t	t	PROPN
ejpam-6529	81	61	}	}	PUNCT
ejpam-6529	81	62	,	,	PUNCT
ejpam-6529	81	63	(	(	PUNCT
ejpam-6529	81	64	fb	fb	INTJ
ejpam-6529	81	65	,	,	PUNCT
ejpam-6529	81	66	s)q	s)q	PUNCT
ejpam-6529	81	67	:	:	PUNCT
ejpam-6529	81	68	=	=	X
ejpam-6529	81	69	{	{	PUNCT
ejpam-6529	81	70	a	a	DET
ejpam-6529	81	71	∈	∈	NOUN
ejpam-6529	81	72	x	x	SYM
ejpam-6529	81	73	|	|	ADV
ejpam-6529	81	74	fb(a	fb(a	PUNCT
ejpam-6529	81	75	)	)	PUNCT
ejpam-6529	82	1	+	+	CCONJ
ejpam-6529	82	2	s	s	VERB
ejpam-6529	82	3	>	>	X
ejpam-6529	82	4	1	1	NUM
ejpam-6529	82	5	}	}	PUNCT
ejpam-6529	82	6	,	,	PUNCT
ejpam-6529	82	7	(	(	PUNCT
ejpam-6529	82	8	gb	gb	ADP
ejpam-6529	82	9	,	,	PUNCT
ejpam-6529	82	10	t)q	t)q	PUNCT
ejpam-6529	82	11	:	:	PUNCT
ejpam-6529	82	12	=	=	X
ejpam-6529	82	13	{	{	PUNCT
ejpam-6529	82	14	a	a	DET
ejpam-6529	82	15	∈	∈	NOUN
ejpam-6529	82	16	x	x	X
ejpam-6529	82	17	|	|	ADV
ejpam-6529	82	18	gb(a	gb(a	PUNCT
ejpam-6529	82	19	)	)	PUNCT
ejpam-6529	83	1	+	+	CCONJ
ejpam-6529	83	2	t	t	X
ejpam-6529	83	3	<	<	X
ejpam-6529	83	4	1	1	NUM
ejpam-6529	83	5	}	}	PUNCT
ejpam-6529	83	6	.	.	PUNCT
ejpam-6529	84	1	(	(	PUNCT
ejpam-6529	84	2	fb	fb	INTJ
ejpam-6529	84	3	,	,	PUNCT
ejpam-6529	84	4	s)∈∨q	s)∈∨q	PROPN
ejpam-6529	84	5	:	:	PUNCT
ejpam-6529	85	1	=	=	X
ejpam-6529	85	2	{	{	PUNCT
ejpam-6529	85	3	a	a	DET
ejpam-6529	85	4	∈	∈	NOUN
ejpam-6529	85	5	x	x	SYM
ejpam-6529	85	6	|	|	ADV
ejpam-6529	85	7	fb(a	fb(a	NOUN
ejpam-6529	85	8	)	)	PUNCT
ejpam-6529	85	9	≥	≥	PRON
ejpam-6529	85	10	s	s	PART
ejpam-6529	85	11	or	or	CCONJ
ejpam-6529	85	12	fb(a	fb(a	NUM
ejpam-6529	85	13	)	)	PUNCT
ejpam-6529	86	1	+	+	PRON
ejpam-6529	86	2	s	s	VERB
ejpam-6529	86	3	>	>	X
ejpam-6529	86	4	1	1	NUM
ejpam-6529	86	5	}	}	PUNCT
ejpam-6529	86	6	.	.	PUNCT
ejpam-6529	87	1	(	(	PUNCT
ejpam-6529	87	2	gb	gb	NOUN
ejpam-6529	87	3	,	,	PUNCT
ejpam-6529	87	4	t)∈∨q	t)∈∨q	NOUN
ejpam-6529	87	5	:	:	PUNCT
ejpam-6529	87	6	=	=	SYM
ejpam-6529	87	7	{	{	PUNCT
ejpam-6529	87	8	a	a	DET
ejpam-6529	87	9	∈	∈	NOUN
ejpam-6529	87	10	x	x	X
ejpam-6529	87	11	|	|	NOUN
ejpam-6529	87	12	gb(a	gb(a	NOUN
ejpam-6529	87	13	)	)	PUNCT
ejpam-6529	87	14	≤	≤	NUM
ejpam-6529	87	15	t	t	NOUN
ejpam-6529	87	16	or	or	CCONJ
ejpam-6529	87	17	gb(a	gb(a	PUNCT
ejpam-6529	87	18	)	)	PUNCT
ejpam-6529	88	1	+	+	CCONJ
ejpam-6529	88	2	t	t	X
ejpam-6529	88	3	<	<	X
ejpam-6529	88	4	1	1	NUM
ejpam-6529	88	5	}	}	PUNCT
ejpam-6529	88	6	.	.	PUNCT
ejpam-6529	89	1	also	also	ADV
ejpam-6529	89	2	,	,	PUNCT
ejpam-6529	89	3	we	we	PRON
ejpam-6529	89	4	consider	consider	VERB
ejpam-6529	89	5	the	the	DET
ejpam-6529	89	6	sets	set	NOUN
ejpam-6529	89	7	below	below	ADV
ejpam-6529	89	8	.	.	PUNCT
ejpam-6529	90	1	(	(	PUNCT
ejpam-6529	90	2	b∗	b∗	ADJ
ejpam-6529	90	3	,	,	PUNCT
ejpam-6529	90	4	(	(	PUNCT
ejpam-6529	90	5	s	s	X
ejpam-6529	90	6	,	,	PUNCT
ejpam-6529	90	7	t))∈	t))∈	NOUN
ejpam-6529	90	8	:	:	PUNCT
ejpam-6529	90	9	=	=	SYM
ejpam-6529	90	10	(	(	PUNCT
ejpam-6529	90	11	fb	fb	INTJ
ejpam-6529	90	12	,	,	PUNCT
ejpam-6529	90	13	s)∈	s)∈	NUM
ejpam-6529	90	14	∩	∩	NOUN
ejpam-6529	90	15	(	(	PUNCT
ejpam-6529	90	16	gb	gb	NOUN
ejpam-6529	90	17	,	,	PUNCT
ejpam-6529	90	18	t)∈	t)∈	NUM
ejpam-6529	90	19	,	,	PUNCT
ejpam-6529	90	20	(	(	PUNCT
ejpam-6529	90	21	b∗	b∗	ADJ
ejpam-6529	90	22	,	,	PUNCT
ejpam-6529	90	23	(	(	PUNCT
ejpam-6529	90	24	s	s	X
ejpam-6529	90	25	,	,	PUNCT
ejpam-6529	90	26	t))q	t))q	NOUN
ejpam-6529	90	27	:	:	PUNCT
ejpam-6529	90	28	=	=	SYM
ejpam-6529	90	29	(	(	PUNCT
ejpam-6529	90	30	fb	fb	INTJ
ejpam-6529	90	31	,	,	PUNCT
ejpam-6529	90	32	s)q	s)q	PUNCT
ejpam-6529	90	33	∩	∩	NOUN
ejpam-6529	90	34	(	(	PUNCT
ejpam-6529	90	35	gb	gb	NOUN
ejpam-6529	90	36	,	,	PUNCT
ejpam-6529	90	37	t)q	t)q	NUM
ejpam-6529	90	38	,	,	PUNCT
ejpam-6529	90	39	(	(	PUNCT
ejpam-6529	90	40	b∗	b∗	ADJ
ejpam-6529	90	41	,	,	PUNCT
ejpam-6529	90	42	(	(	PUNCT
ejpam-6529	90	43	s	s	X
ejpam-6529	90	44	,	,	PUNCT
ejpam-6529	90	45	t))∈∨q	t))∈∨q	NOUN
ejpam-6529	90	46	:	:	PUNCT
ejpam-6529	90	47	=	=	SYM
ejpam-6529	90	48	(	(	PUNCT
ejpam-6529	90	49	fb	fb	INTJ
ejpam-6529	90	50	,	,	PUNCT
ejpam-6529	90	51	s)∈∨q	s)∈∨q	NOUN
ejpam-6529	90	52	∩	∩	NOUN
ejpam-6529	90	53	(	(	PUNCT
ejpam-6529	90	54	gb	gb	PROPN
ejpam-6529	90	55	,	,	PUNCT
ejpam-6529	90	56	t)∈∨q	t)∈∨q	PROPN
ejpam-6529	90	57	,	,	PUNCT
ejpam-6529	90	58	which	which	PRON
ejpam-6529	90	59	are	be	AUX
ejpam-6529	90	60	called	call	VERB
ejpam-6529	90	61	the	the	DET
ejpam-6529	90	62	intuitionistic	intuitionistic	ADJ
ejpam-6529	90	63	level	level	NOUN
ejpam-6529	90	64	set	set	NOUN
ejpam-6529	90	65	,	,	PUNCT
ejpam-6529	90	66	intuitionistic	intuitionistic	ADJ
ejpam-6529	90	67	q	q	NOUN
ejpam-6529	90	68	-	-	PUNCT
ejpam-6529	90	69	set	set	VERB
ejpam-6529	90	70	and	and	CCONJ
ejpam-6529	90	71	intuitionistic	intuitionistic	ADJ
ejpam-6529	90	72	∈∨q	∈∨q	NOUN
ejpam-6529	90	73	-	-	PUNCT
ejpam-6529	90	74	set	set	NOUN
ejpam-6529	90	75	of	of	ADP
ejpam-6529	90	76	b∗	b∗	ADJ
ejpam-6529	90	77	:	:	PUNCT
ejpam-6529	90	78	=	=	SYM
ejpam-6529	90	79	(	(	PUNCT
ejpam-6529	90	80	x	x	X
ejpam-6529	90	81	;	;	PUNCT
ejpam-6529	90	82	fb	fb	INTJ
ejpam-6529	90	83	,	,	PUNCT
ejpam-6529	90	84	gb	gb	PROPN
ejpam-6529	90	85	)	)	PUNCT
ejpam-6529	90	86	,	,	PUNCT
ejpam-6529	90	87	respectively	respectively	ADV
ejpam-6529	90	88	.	.	PUNCT
ejpam-6529	91	1	s.	s.	PROPN
ejpam-6529	91	2	s.	s.	PROPN
ejpam-6529	91	3	ahn	ahn	PROPN
ejpam-6529	91	4	,	,	PUNCT
ejpam-6529	91	5	y.	y.	PROPN
ejpam-6529	91	6	j.	j.	PROPN
ejpam-6529	91	7	seo	seo	PROPN
ejpam-6529	91	8	,	,	PUNCT
ejpam-6529	91	9	y.	y.	PROPN
ejpam-6529	91	10	b.	b.	PROPN
ejpam-6529	91	11	jun	jun	PROPN
ejpam-6529	91	12	/	/	SYM
ejpam-6529	91	13	eur	eur	PROPN
ejpam-6529	91	14	.	.	PUNCT
ejpam-6529	92	1	j.	j.	PROPN
ejpam-6529	92	2	pure	pure	PROPN
ejpam-6529	92	3	appl	appl	PROPN
ejpam-6529	92	4	.	.	PROPN
ejpam-6529	92	5	math	math	PROPN
ejpam-6529	92	6	,	,	PUNCT
ejpam-6529	92	7	18	18	NUM
ejpam-6529	92	8	(	(	PUNCT
ejpam-6529	92	9	3	3	NUM
ejpam-6529	92	10	)	)	PUNCT
ejpam-6529	92	11	(	(	PUNCT
ejpam-6529	92	12	2025	2025	NUM
ejpam-6529	92	13	)	)	PUNCT
ejpam-6529	92	14	,	,	PUNCT
ejpam-6529	92	15	6529	6529	NUM
ejpam-6529	92	16	5	5	NUM
ejpam-6529	92	17	of	of	ADP
ejpam-6529	92	18	16	16	NUM
ejpam-6529	92	19	definition	definition	NOUN
ejpam-6529	92	20	4	4	NUM
ejpam-6529	92	21	(	(	PUNCT
ejpam-6529	92	22	[	[	X
ejpam-6529	92	23	16	16	NUM
ejpam-6529	92	24	]	]	NUM
ejpam-6529	92	25	)	)	PUNCT
ejpam-6529	92	26	.	.	PUNCT
ejpam-6529	93	1	an	an	DET
ejpam-6529	93	2	intuitionistic	intuitionistic	ADJ
ejpam-6529	93	3	fuzzy	fuzzy	ADJ
ejpam-6529	93	4	set	set	VERB
ejpam-6529	93	5	b∗	b∗	ADJ
ejpam-6529	93	6	:	:	PUNCT
ejpam-6529	93	7	=	=	SYM
ejpam-6529	93	8	(	(	PUNCT
ejpam-6529	93	9	x	x	X
ejpam-6529	93	10	;	;	PUNCT
ejpam-6529	93	11	fb	fb	INTJ
ejpam-6529	93	12	,	,	PUNCT
ejpam-6529	93	13	gb	gb	PROPN
ejpam-6529	93	14	)	)	PUNCT
ejpam-6529	93	15	in	in	ADP
ejpam-6529	93	16	a	a	DET
ejpam-6529	93	17	sheffer	sheffer	NOUN
ejpam-6529	93	18	stroke	stroke	NOUN
ejpam-6529	93	19	hilbert	hilbert	PROPN
ejpam-6529	93	20	algebra	algebra	PROPN
ejpam-6529	93	21	x	x	X
ejpam-6529	93	22	:	:	PUNCT
ejpam-6529	93	23	=	=	SYM
ejpam-6529	93	24	(	(	PUNCT
ejpam-6529	93	25	x	x	NOUN
ejpam-6529	93	26	,	,	PUNCT
ejpam-6529	93	27	|	|	ADV
ejpam-6529	93	28	)	)	PUNCT
ejpam-6529	93	29	is	be	AUX
ejpam-6529	93	30	called	call	VERB
ejpam-6529	93	31	an	an	DET
ejpam-6529	93	32	intuitionistic	intuitionistic	ADJ
ejpam-6529	93	33	fuzzy	fuzzy	ADJ
ejpam-6529	93	34	filter	filter	NOUN
ejpam-6529	93	35	of	of	ADP
ejpam-6529	93	36	x	x	X
ejpam-6529	93	37	:	:	PUNCT
ejpam-6529	93	38	=	=	SYM
ejpam-6529	93	39	(	(	PUNCT
ejpam-6529	93	40	x	x	NOUN
ejpam-6529	93	41	,	,	PUNCT
ejpam-6529	93	42	|	|	INTJ
ejpam-6529	93	43	)	)	PUNCT
ejpam-6529	93	44	if	if	SCONJ
ejpam-6529	93	45	it	it	PRON
ejpam-6529	93	46	satisfies	satisfy	VERB
ejpam-6529	93	47	:	:	PUNCT
ejpam-6529	93	48	(	(	PUNCT
ejpam-6529	93	49	∀x	∀x	X
ejpam-6529	93	50	∈	∈	PROPN
ejpam-6529	93	51	x)(fb(1	x)(fb(1	PROPN
ejpam-6529	93	52	)	)	PUNCT
ejpam-6529	93	53	≥	≥	NOUN
ejpam-6529	93	54	fb(x	fb(x	NUM
ejpam-6529	93	55	)	)	PUNCT
ejpam-6529	93	56	,	,	PUNCT
ejpam-6529	93	57	gb(1	gb(1	PROPN
ejpam-6529	93	58	)	)	PUNCT
ejpam-6529	93	59	≤	≤	NOUN
ejpam-6529	93	60	gb(x	gb(x	NUM
ejpam-6529	93	61	)	)	PUNCT
ejpam-6529	93	62	)	)	PUNCT
ejpam-6529	93	63	,	,	PUNCT
ejpam-6529	93	64	(	(	PUNCT
ejpam-6529	93	65	17	17	NUM
ejpam-6529	93	66	)	)	PUNCT
ejpam-6529	93	67	(	(	PUNCT
ejpam-6529	93	68	∀x	∀x	X
ejpam-6529	93	69	,	,	PUNCT
ejpam-6529	93	70	y	y	PROPN
ejpam-6529	93	71	∈	∈	PROPN
ejpam-6529	93	72	x)(fb(ðx(y	x)(fb(ðx(y	PROPN
ejpam-6529	93	73	)	)	PUNCT
ejpam-6529	93	74	)	)	PUNCT
ejpam-6529	93	75	≥	≥	NOUN
ejpam-6529	93	76	fb(y	fb(y	NUM
ejpam-6529	93	77	)	)	PUNCT
ejpam-6529	93	78	,	,	PUNCT
ejpam-6529	93	79	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	93	80	)	)	PUNCT
ejpam-6529	93	81	)	)	PUNCT
ejpam-6529	93	82	≤	≤	NOUN
ejpam-6529	93	83	gb(y	gb(y	ADV
ejpam-6529	93	84	)	)	PUNCT
ejpam-6529	93	85	)	)	PUNCT
ejpam-6529	93	86	,	,	PUNCT
ejpam-6529	93	87	(	(	PUNCT
ejpam-6529	93	88	18	18	NUM
ejpam-6529	93	89	)	)	PUNCT
ejpam-6529	93	90	(	(	PUNCT
ejpam-6529	93	91	∀x	∀x	X
ejpam-6529	93	92	,	,	PUNCT
ejpam-6529	93	93	y	y	PROPN
ejpam-6529	93	94	,	,	PUNCT
ejpam-6529	93	95	z	z	NOUN
ejpam-6529	93	96	∈	∈	PROPN
ejpam-6529	93	97	x	x	X
ejpam-6529	93	98	)	)	PUNCT
ejpam-6529	93	99	(	(	PUNCT
ejpam-6529	93	100	fb((x|(y|z))|(y|z	fb((x|(y|z))|(y|z	NOUN
ejpam-6529	93	101	)	)	PUNCT
ejpam-6529	93	102	)	)	PUNCT
ejpam-6529	93	103	≥	≥	NOUN
ejpam-6529	93	104	min{fb(y	min{fb(y	NUM
ejpam-6529	93	105	)	)	PUNCT
ejpam-6529	93	106	,	,	PUNCT
ejpam-6529	93	107	fb(z	fb(z	NOUN
ejpam-6529	93	108	)	)	PUNCT
ejpam-6529	93	109	}	}	PUNCT
ejpam-6529	93	110	gb((x|(y|z))|(y|z	gb((x|(y|z))|(y|z	NOUN
ejpam-6529	93	111	)	)	PUNCT
ejpam-6529	93	112	)	)	PUNCT
ejpam-6529	93	113	≤	≤	NUM
ejpam-6529	93	114	max{gb(y	max{gb(y	PROPN
ejpam-6529	93	115	)	)	PUNCT
ejpam-6529	93	116	,	,	PUNCT
ejpam-6529	93	117	gb(z	gb(z	NOUN
ejpam-6529	93	118	)	)	PUNCT
ejpam-6529	93	119	}	}	PUNCT
ejpam-6529	93	120	)	)	PUNCT
ejpam-6529	93	121	.	.	PUNCT
ejpam-6529	94	1	(	(	PUNCT
ejpam-6529	94	2	19	19	NUM
ejpam-6529	94	3	)	)	PUNCT
ejpam-6529	94	4	3	3	NUM
ejpam-6529	94	5	.	.	PUNCT
ejpam-6529	94	6	intuitionistic	intuitionistic	ADJ
ejpam-6529	94	7	fuzzy	fuzzy	ADJ
ejpam-6529	94	8	weak	weak	ADJ
ejpam-6529	94	9	filters	filter	NOUN
ejpam-6529	94	10	in	in	ADP
ejpam-6529	94	11	what	what	PRON
ejpam-6529	94	12	follows	follow	VERB
ejpam-6529	94	13	,	,	PUNCT
ejpam-6529	94	14	x	x	PUNCT
ejpam-6529	94	15	:	:	PUNCT
ejpam-6529	94	16	=	=	SYM
ejpam-6529	94	17	(	(	PUNCT
ejpam-6529	94	18	x	x	NOUN
ejpam-6529	94	19	,	,	PUNCT
ejpam-6529	94	20	|	|	ADV
ejpam-6529	94	21	)	)	PUNCT
ejpam-6529	94	22	stands	stand	VERB
ejpam-6529	94	23	for	for	ADP
ejpam-6529	94	24	a	a	DET
ejpam-6529	94	25	sheffer	sheffer	NOUN
ejpam-6529	94	26	stroke	stroke	NOUN
ejpam-6529	94	27	hilbert	hilbert	PROPN
ejpam-6529	94	28	algebra	algebra	PROPN
ejpam-6529	94	29	,	,	PUNCT
ejpam-6529	94	30	unless	unless	SCONJ
ejpam-6529	94	31	otherwise	otherwise	ADV
ejpam-6529	94	32	stated	state	VERB
ejpam-6529	94	33	.	.	PUNCT
ejpam-6529	95	1	definition	definition	NOUN
ejpam-6529	95	2	5	5	NUM
ejpam-6529	95	3	.	.	PUNCT
ejpam-6529	96	1	an	an	DET
ejpam-6529	96	2	intuitionistic	intuitionistic	ADJ
ejpam-6529	96	3	fuzzy	fuzzy	ADJ
ejpam-6529	96	4	set	set	VERB
ejpam-6529	96	5	b∗	b∗	ADJ
ejpam-6529	96	6	:	:	PUNCT
ejpam-6529	96	7	=	=	SYM
ejpam-6529	96	8	(	(	PUNCT
ejpam-6529	96	9	x	x	X
ejpam-6529	96	10	;	;	PUNCT
ejpam-6529	96	11	fb	fb	INTJ
ejpam-6529	96	12	,	,	PUNCT
ejpam-6529	96	13	gb	gb	NOUN
ejpam-6529	96	14	)	)	PUNCT
ejpam-6529	96	15	in	in	ADP
ejpam-6529	96	16	x	x	PROPN
ejpam-6529	96	17	is	be	AUX
ejpam-6529	96	18	called	call	VERB
ejpam-6529	96	19	an	an	DET
ejpam-6529	96	20	intuitionistic	intuitionistic	ADJ
ejpam-6529	96	21	fuzzy	fuzzy	ADJ
ejpam-6529	96	22	weak	weak	ADJ
ejpam-6529	96	23	filter	filter	NOUN
ejpam-6529	96	24	of	of	ADP
ejpam-6529	96	25	x	x	X
ejpam-6529	96	26	:	:	PUNCT
ejpam-6529	96	27	=	=	SYM
ejpam-6529	96	28	(	(	PUNCT
ejpam-6529	96	29	x	x	NOUN
ejpam-6529	96	30	,	,	PUNCT
ejpam-6529	96	31	|	|	INTJ
ejpam-6529	96	32	)	)	PUNCT
ejpam-6529	96	33	if	if	SCONJ
ejpam-6529	96	34	it	it	PRON
ejpam-6529	96	35	satisfies	satisfy	VERB
ejpam-6529	96	36	:	:	PUNCT
ejpam-6529	96	37	(	(	PUNCT
ejpam-6529	96	38	∀x	∀x	X
ejpam-6529	96	39	∈	∈	PROPN
ejpam-6529	96	40	x)(∀(s	x)(∀(s	NOUN
ejpam-6529	96	41	,	,	PUNCT
ejpam-6529	96	42	t	t	PROPN
ejpam-6529	96	43	)	)	PUNCT
ejpam-6529	96	44	∈	∈	PROPN
ejpam-6529	96	45	(	(	PUNCT
ejpam-6529	96	46	0	0	NUM
ejpam-6529	96	47	,	,	PUNCT
ejpam-6529	96	48	1]×	1]×	NUM
ejpam-6529	96	49	[	[	X
ejpam-6529	96	50	0	0	NUM
ejpam-6529	96	51	,	,	PUNCT
ejpam-6529	96	52	1	1	NUM
ejpam-6529	96	53	)	)	PUNCT
ejpam-6529	96	54	)	)	PUNCT
ejpam-6529	96	55	(	(	PUNCT
ejpam-6529	96	56	x(s	x(s	PROPN
ejpam-6529	96	57	,	,	PUNCT
ejpam-6529	96	58	t	t	PROPN
ejpam-6529	96	59	)	)	PUNCT
ejpam-6529	96	60	∈	∈	PROPN
ejpam-6529	96	61	b∗	b∗	ADJ
ejpam-6529	96	62	⇒	⇒	NOUN
ejpam-6529	96	63	1(s	1(s	NUM
ejpam-6529	96	64	,	,	PUNCT
ejpam-6529	96	65	t	t	PROPN
ejpam-6529	96	66	)	)	PUNCT
ejpam-6529	96	67	∈	∈	PROPN
ejpam-6529	96	68	b∗	b∗	ADJ
ejpam-6529	96	69	)	)	PUNCT
ejpam-6529	96	70	,	,	PUNCT
ejpam-6529	96	71	(	(	PUNCT
ejpam-6529	96	72	20	20	NUM
ejpam-6529	96	73	)	)	PUNCT
ejpam-6529	96	74	(	(	PUNCT
ejpam-6529	96	75	∀x	∀x	X
ejpam-6529	96	76	,	,	PUNCT
ejpam-6529	96	77	y	y	PROPN
ejpam-6529	96	78	∈	∈	PROPN
ejpam-6529	96	79	x)(∀(s	x)(∀(s	NOUN
ejpam-6529	96	80	,	,	PUNCT
ejpam-6529	96	81	t	t	PROPN
ejpam-6529	96	82	)	)	PUNCT
ejpam-6529	96	83	∈	∈	PROPN
ejpam-6529	96	84	(	(	PUNCT
ejpam-6529	96	85	0	0	NUM
ejpam-6529	96	86	,	,	PUNCT
ejpam-6529	96	87	1]×	1]×	NUM
ejpam-6529	96	88	[	[	X
ejpam-6529	96	89	0	0	NUM
ejpam-6529	96	90	,	,	PUNCT
ejpam-6529	96	91	1	1	NUM
ejpam-6529	96	92	)	)	PUNCT
ejpam-6529	96	93	)	)	PUNCT
ejpam-6529	96	94	(	(	PUNCT
ejpam-6529	96	95	y(s	y(s	PROPN
ejpam-6529	96	96	,	,	PUNCT
ejpam-6529	96	97	t	t	PROPN
ejpam-6529	96	98	)	)	PUNCT
ejpam-6529	96	99	∈	∈	PROPN
ejpam-6529	96	100	b∗	b∗	ADJ
ejpam-6529	96	101	⇒	⇒	NOUN
ejpam-6529	96	102	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	96	103	,	,	PUNCT
ejpam-6529	96	104	t	t	PROPN
ejpam-6529	96	105	)	)	PUNCT
ejpam-6529	96	106	∈	∈	PROPN
ejpam-6529	96	107	b∗	b∗	ADJ
ejpam-6529	96	108	)	)	PUNCT
ejpam-6529	96	109	.	.	PUNCT
ejpam-6529	97	1	(	(	PUNCT
ejpam-6529	97	2	21	21	NUM
ejpam-6529	97	3	)	)	PUNCT
ejpam-6529	97	4	example	example	NOUN
ejpam-6529	98	1	1	1	NUM
ejpam-6529	98	2	.	.	PUNCT
ejpam-6529	98	3	let	let	VERB
ejpam-6529	98	4	x	x	PUNCT
ejpam-6529	98	5	=	=	PRON
ejpam-6529	98	6	{	{	PUNCT
ejpam-6529	98	7	c0	c0	NOUN
ejpam-6529	98	8	,	,	PUNCT
ejpam-6529	98	9	c1	c1	PROPN
ejpam-6529	98	10	,	,	PUNCT
ejpam-6529	98	11	c2	c2	PROPN
ejpam-6529	98	12	,	,	PUNCT
ejpam-6529	98	13	c3	c3	PROPN
ejpam-6529	98	14	,	,	PUNCT
ejpam-6529	98	15	c4	c4	NOUN
ejpam-6529	98	16	,	,	PUNCT
ejpam-6529	98	17	c5	c5	PROPN
ejpam-6529	98	18	,	,	PUNCT
ejpam-6529	98	19	c6	c6	PROPN
ejpam-6529	98	20	,	,	PUNCT
ejpam-6529	98	21	c7	c7	PROPN
ejpam-6529	98	22	}	}	PUNCT
ejpam-6529	98	23	be	be	AUX
ejpam-6529	98	24	a	a	DET
ejpam-6529	98	25	set	set	NOUN
ejpam-6529	98	26	with	with	ADP
ejpam-6529	98	27	the	the	DET
ejpam-6529	98	28	following	follow	VERB
ejpam-6529	98	29	hasse	hasse	PROPN
ejpam-6529	98	30	diagram	diagram	PROPN
ejpam-6529	98	31	:	:	PUNCT
ejpam-6529	98	32	rc3	rc3	PROPN
ejpam-6529	98	33	rc2	rc2	PROPN
ejpam-6529	98	34	r	r	PROPN
ejpam-6529	98	35	c0	c0	PROPN
ejpam-6529	98	36	rc4	rc4	PROPN
ejpam-6529	98	37	rc5	rc5	PROPN
ejpam-6529	98	38	rc6	rc6	NOUN
ejpam-6529	98	39	rc7	rc7	PROPN
ejpam-6529	98	40	rc1	rc1	PROPN
ejpam-6529	98	41	�	�	PROPN
ejpam-6529	98	42	�	�	PROPN
ejpam-6529	98	43	�	�	PROPN
ejpam-6529	98	44	�	�	PROPN
ejpam-6529	98	45	�	�	PROPN
ejpam-6529	98	46	hh	hh	PROPN
ejpam-6529	98	47	hhh	hhh	PROPN
ejpam-6529	98	48	�	�	PROPN
ejpam-6529	98	49	�	�	PROPN
ejpam-6529	98	50	�	�	PROPN
ejpam-6529	98	51	�	�	PROPN
ejpam-6529	98	52	�	�	PROPN
ejpam-6529	98	53	hhh	hhh	PROPN
ejpam-6529	98	54	hh	hh	PROPN
ejpam-6529	98	55	�	�	PROPN
ejpam-6529	98	56	�	�	PROPN
ejpam-6529	98	57	�	�	PROPN
ejpam-6529	98	58	�	�	PROPN
ejpam-6529	98	59	�	�	PROPN
ejpam-6529	98	60	�	�	PROPN
ejpam-6529	98	61	�	�	PROPN
ejpam-6529	98	62	�	�	PROPN
ejpam-6529	98	63	�	�	PROPN
ejpam-6529	98	64	�	�	PROPN
ejpam-6529	98	65	hhh	hhh	PROPN
ejpam-6529	98	66	hh	hh	PROPN
ejpam-6529	98	67	h	h	NOUN
ejpam-6529	98	68	hhh	hhh	PROPN
ejpam-6529	98	69	h	h	NOUN
ejpam-6529	98	70	define	define	VERB
ejpam-6529	98	71	a	a	DET
ejpam-6529	98	72	sheffer	sheffer	NOUN
ejpam-6529	98	73	stroke	stroke	NOUN
ejpam-6529	98	74	“	"	PUNCT
ejpam-6529	98	75	|	|	ADV
ejpam-6529	98	76	”	"	PUNCT
ejpam-6529	98	77	on	on	ADP
ejpam-6529	98	78	x	x	PUNCT
ejpam-6529	98	79	by	by	ADP
ejpam-6529	98	80	table	table	NOUN
ejpam-6529	98	81	1	1	NUM
ejpam-6529	98	82	then	then	ADV
ejpam-6529	98	83	x	x	X
ejpam-6529	98	84	:	:	PUNCT
ejpam-6529	98	85	=	=	SYM
ejpam-6529	98	86	(	(	PUNCT
ejpam-6529	98	87	x	x	NOUN
ejpam-6529	98	88	,	,	PUNCT
ejpam-6529	98	89	|	|	ADV
ejpam-6529	98	90	)	)	PUNCT
ejpam-6529	98	91	is	be	AUX
ejpam-6529	98	92	a	a	DET
ejpam-6529	98	93	sheffer	sheffer	NOUN
ejpam-6529	98	94	stroke	stroke	NOUN
ejpam-6529	98	95	hilbert	hilbert	PROPN
ejpam-6529	98	96	algebra	algebra	PROPN
ejpam-6529	98	97	where	where	SCONJ
ejpam-6529	98	98	the	the	DET
ejpam-6529	98	99	algebraic	algebraic	ADJ
ejpam-6529	98	100	constant	constant	ADJ
ejpam-6529	98	101	is	be	AUX
ejpam-6529	98	102	c1	c1	NOUN
ejpam-6529	98	103	(	(	PUNCT
ejpam-6529	98	104	see	see	VERB
ejpam-6529	98	105	[	[	X
ejpam-6529	98	106	5	5	NUM
ejpam-6529	98	107	]	]	PUNCT
ejpam-6529	98	108	)	)	PUNCT
ejpam-6529	98	109	.	.	PUNCT
ejpam-6529	99	1	let	let	VERB
ejpam-6529	99	2	b∗	b∗	ADV
ejpam-6529	99	3	:	:	PUNCT
ejpam-6529	99	4	=	=	SYM
ejpam-6529	99	5	(	(	PUNCT
ejpam-6529	99	6	x	x	X
ejpam-6529	99	7	;	;	PUNCT
ejpam-6529	99	8	fb	fb	INTJ
ejpam-6529	99	9	,	,	PUNCT
ejpam-6529	99	10	gb	gb	PROPN
ejpam-6529	99	11	)	)	PUNCT
ejpam-6529	99	12	be	be	VERB
ejpam-6529	99	13	an	an	DET
ejpam-6529	99	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	99	15	fuzzy	fuzzy	ADJ
ejpam-6529	99	16	set	set	NOUN
ejpam-6529	99	17	in	in	ADP
ejpam-6529	99	18	x	x	SYM
ejpam-6529	100	1	where	where	SCONJ
ejpam-6529	100	2	fb	fb	INTJ
ejpam-6529	100	3	:	:	PUNCT
ejpam-6529	100	4	x	x	X
ejpam-6529	100	5	→	→	SYM
ejpam-6529	101	1	[	[	X
ejpam-6529	101	2	0	0	NUM
ejpam-6529	101	3	,	,	PUNCT
ejpam-6529	101	4	1	1	NUM
ejpam-6529	101	5	]	]	PUNCT
ejpam-6529	101	6	,	,	PUNCT
ejpam-6529	101	7	x	x	PROPN
ejpam-6529	101	8	7→	7→	NUM
ejpam-6529	101	9			NUM
ejpam-6529	101	10	0.66	0.66	NUM
ejpam-6529	101	11	if	if	SCONJ
ejpam-6529	101	12	x	x	PROPN
ejpam-6529	101	13	=	=	SYM
ejpam-6529	101	14	c1	c1	PROPN
ejpam-6529	101	15	,	,	PUNCT
ejpam-6529	101	16	0.52	0.52	NUM
ejpam-6529	101	17	if	if	SCONJ
ejpam-6529	101	18	x	x	SYM
ejpam-6529	101	19	∈	∈	PROPN
ejpam-6529	101	20	{	{	PUNCT
ejpam-6529	101	21	c5	c5	PROPN
ejpam-6529	101	22	,	,	PUNCT
ejpam-6529	101	23	c6	c6	PROPN
ejpam-6529	101	24	}	}	PUNCT
ejpam-6529	101	25	,	,	PUNCT
ejpam-6529	101	26	0.44	0.44	NUM
ejpam-6529	101	27	if	if	SCONJ
ejpam-6529	101	28	x	x	PROPN
ejpam-6529	101	29	=	=	PROPN
ejpam-6529	101	30	c7	c7	PROPN
ejpam-6529	101	31	,	,	PUNCT
ejpam-6529	101	32	0.35	0.35	NUM
ejpam-6529	101	33	otherwise	otherwise	ADV
ejpam-6529	101	34	.	.	PUNCT
ejpam-6529	102	1	and	and	CCONJ
ejpam-6529	102	2	gb	gb	ADP
ejpam-6529	102	3	:	:	PUNCT
ejpam-6529	102	4	x	x	X
ejpam-6529	102	5	→	→	SYM
ejpam-6529	103	1	[	[	X
ejpam-6529	103	2	0	0	NUM
ejpam-6529	103	3	,	,	PUNCT
ejpam-6529	103	4	1	1	NUM
ejpam-6529	103	5	]	]	PUNCT
ejpam-6529	103	6	,	,	PUNCT
ejpam-6529	103	7	x	x	SYM
ejpam-6529	103	8	7→	7→	NUM
ejpam-6529	103	9			NUM
ejpam-6529	103	10	0.27	0.27	NUM
ejpam-6529	103	11	if	if	SCONJ
ejpam-6529	103	12	x	x	X
ejpam-6529	103	13	=	=	SYM
ejpam-6529	103	14	c1	c1	NOUN
ejpam-6529	103	15	,	,	PUNCT
ejpam-6529	103	16	0.32	0.32	NUM
ejpam-6529	103	17	if	if	SCONJ
ejpam-6529	103	18	x	x	SYM
ejpam-6529	103	19	∈	∈	PROPN
ejpam-6529	103	20	{	{	PUNCT
ejpam-6529	103	21	c6	c6	PROPN
ejpam-6529	103	22	,	,	PUNCT
ejpam-6529	103	23	c7	c7	PROPN
ejpam-6529	103	24	}	}	PUNCT
ejpam-6529	103	25	,	,	PUNCT
ejpam-6529	103	26	0.34	0.34	NUM
ejpam-6529	103	27	otherwise	otherwise	ADV
ejpam-6529	103	28	.	.	PUNCT
ejpam-6529	104	1	it	it	PRON
ejpam-6529	104	2	is	be	AUX
ejpam-6529	104	3	routine	routine	ADJ
ejpam-6529	104	4	to	to	PART
ejpam-6529	104	5	verify	verify	VERB
ejpam-6529	104	6	that	that	PRON
ejpam-6529	104	7	b∗	b∗	ADJ
ejpam-6529	104	8	:	:	PUNCT
ejpam-6529	104	9	=	=	SYM
ejpam-6529	104	10	(	(	PUNCT
ejpam-6529	104	11	x	x	X
ejpam-6529	104	12	;	;	PUNCT
ejpam-6529	104	13	fb	fb	INTJ
ejpam-6529	104	14	,	,	PUNCT
ejpam-6529	104	15	gb	gb	PROPN
ejpam-6529	104	16	)	)	PUNCT
ejpam-6529	104	17	is	be	AUX
ejpam-6529	104	18	an	an	DET
ejpam-6529	104	19	intuitionistic	intuitionistic	ADJ
ejpam-6529	104	20	fuzzy	fuzzy	ADJ
ejpam-6529	104	21	weak	weak	ADJ
ejpam-6529	104	22	filter	filter	NOUN
ejpam-6529	104	23	of	of	ADP
ejpam-6529	104	24	x	x	X
ejpam-6529	104	25	:	:	PUNCT
ejpam-6529	104	26	=	=	SYM
ejpam-6529	104	27	(	(	PUNCT
ejpam-6529	104	28	x	x	NOUN
ejpam-6529	104	29	,	,	PUNCT
ejpam-6529	104	30	|	|	NOUN
ejpam-6529	104	31	)	)	PUNCT
ejpam-6529	104	32	.	.	PUNCT
ejpam-6529	105	1	s.	s.	PROPN
ejpam-6529	105	2	s.	s.	PROPN
ejpam-6529	105	3	ahn	ahn	PROPN
ejpam-6529	105	4	,	,	PUNCT
ejpam-6529	105	5	y.	y.	PROPN
ejpam-6529	105	6	j.	j.	PROPN
ejpam-6529	105	7	seo	seo	PROPN
ejpam-6529	105	8	,	,	PUNCT
ejpam-6529	105	9	y.	y.	PROPN
ejpam-6529	105	10	b.	b.	PROPN
ejpam-6529	105	11	jun	jun	PROPN
ejpam-6529	105	12	/	/	SYM
ejpam-6529	105	13	eur	eur	PROPN
ejpam-6529	105	14	.	.	PUNCT
ejpam-6529	106	1	j.	j.	PROPN
ejpam-6529	106	2	pure	pure	PROPN
ejpam-6529	106	3	appl	appl	PROPN
ejpam-6529	106	4	.	.	PROPN
ejpam-6529	106	5	math	math	PROPN
ejpam-6529	106	6	,	,	PUNCT
ejpam-6529	106	7	18	18	NUM
ejpam-6529	106	8	(	(	PUNCT
ejpam-6529	106	9	3	3	NUM
ejpam-6529	106	10	)	)	PUNCT
ejpam-6529	106	11	(	(	PUNCT
ejpam-6529	106	12	2025	2025	NUM
ejpam-6529	106	13	)	)	PUNCT
ejpam-6529	106	14	,	,	PUNCT
ejpam-6529	106	15	6529	6529	NUM
ejpam-6529	106	16	6	6	NUM
ejpam-6529	106	17	of	of	ADP
ejpam-6529	106	18	16	16	NUM
ejpam-6529	106	19	table	table	NOUN
ejpam-6529	106	20	1	1	NUM
ejpam-6529	106	21	:	:	PUNCT
ejpam-6529	106	22	cayley	cayley	ADJ
ejpam-6529	106	23	table	table	NOUN
ejpam-6529	106	24	for	for	ADP
ejpam-6529	106	25	the	the	DET
ejpam-6529	106	26	sheffer	sheffer	NOUN
ejpam-6529	106	27	stroke	stroke	NOUN
ejpam-6529	106	28	“	"	PUNCT
ejpam-6529	106	29	|	|	ADV
ejpam-6529	106	30	”	"	PUNCT
ejpam-6529	106	31	|	|	ADV
ejpam-6529	106	32	c0	c0	PROPN
ejpam-6529	106	33	c2	c2	PROPN
ejpam-6529	106	34	c3	c3	PROPN
ejpam-6529	106	35	c4	c4	PROPN
ejpam-6529	106	36	c5	c5	PROPN
ejpam-6529	106	37	c6	c6	PROPN
ejpam-6529	106	38	c7	c7	PROPN
ejpam-6529	106	39	c1	c1	PROPN
ejpam-6529	106	40	c0	c0	PROPN
ejpam-6529	106	41	c1	c1	PROPN
ejpam-6529	106	42	c1	c1	PROPN
ejpam-6529	106	43	c1	c1	PROPN
ejpam-6529	106	44	c1	c1	PROPN
ejpam-6529	106	45	c1	c1	PROPN
ejpam-6529	106	46	c1	c1	PROPN
ejpam-6529	106	47	c1	c1	PROPN
ejpam-6529	106	48	c1	c1	PROPN
ejpam-6529	106	49	c2	c2	PROPN
ejpam-6529	106	50	c1	c1	PROPN
ejpam-6529	106	51	c7	c7	PROPN
ejpam-6529	106	52	c1	c1	PROPN
ejpam-6529	106	53	c1	c1	PROPN
ejpam-6529	106	54	c7	c7	PROPN
ejpam-6529	106	55	c7	c7	PROPN
ejpam-6529	106	56	c1	c1	PROPN
ejpam-6529	106	57	c7	c7	PROPN
ejpam-6529	106	58	c3	c3	PROPN
ejpam-6529	106	59	c1	c1	PROPN
ejpam-6529	106	60	c1	c1	PROPN
ejpam-6529	106	61	c6	c6	PROPN
ejpam-6529	106	62	c1	c1	PROPN
ejpam-6529	106	63	c6	c6	PROPN
ejpam-6529	106	64	c1	c1	PROPN
ejpam-6529	106	65	c6	c6	PROPN
ejpam-6529	106	66	c6	c6	PROPN
ejpam-6529	106	67	c4	c4	PROPN
ejpam-6529	106	68	c1	c1	PROPN
ejpam-6529	106	69	c1	c1	PROPN
ejpam-6529	106	70	c1	c1	PROPN
ejpam-6529	106	71	c5	c5	PROPN
ejpam-6529	106	72	c1	c1	PROPN
ejpam-6529	106	73	c5	c5	PROPN
ejpam-6529	106	74	c5	c5	PROPN
ejpam-6529	106	75	c5	c5	PROPN
ejpam-6529	106	76	c5	c5	PROPN
ejpam-6529	106	77	c1	c1	PROPN
ejpam-6529	106	78	c7	c7	PROPN
ejpam-6529	106	79	c6	c6	PROPN
ejpam-6529	106	80	c1	c1	PROPN
ejpam-6529	106	81	c4	c4	PROPN
ejpam-6529	106	82	c7	c7	PROPN
ejpam-6529	106	83	c6	c6	PROPN
ejpam-6529	106	84	c4	c4	PROPN
ejpam-6529	106	85	c6	c6	PROPN
ejpam-6529	106	86	c1	c1	PROPN
ejpam-6529	106	87	c7	c7	PROPN
ejpam-6529	106	88	c1	c1	PROPN
ejpam-6529	107	1	c5	c5	PROPN
ejpam-6529	107	2	c7	c7	PROPN
ejpam-6529	107	3	c3	c3	PROPN
ejpam-6529	107	4	c5	c5	PROPN
ejpam-6529	107	5	c3	c3	PROPN
ejpam-6529	107	6	c7	c7	PROPN
ejpam-6529	107	7	c1	c1	PROPN
ejpam-6529	107	8	c1	c1	PROPN
ejpam-6529	107	9	c6	c6	PROPN
ejpam-6529	107	10	c5	c5	PROPN
ejpam-6529	107	11	c6	c6	PROPN
ejpam-6529	107	12	c5	c5	PROPN
ejpam-6529	107	13	c2	c2	PROPN
ejpam-6529	107	14	c2	c2	PROPN
ejpam-6529	107	15	c1	c1	PROPN
ejpam-6529	107	16	c1	c1	PROPN
ejpam-6529	107	17	c7	c7	PROPN
ejpam-6529	107	18	c6	c6	PROPN
ejpam-6529	107	19	c5	c5	PROPN
ejpam-6529	107	20	c4	c4	PROPN
ejpam-6529	107	21	c3	c3	PROPN
ejpam-6529	107	22	c2	c2	PROPN
ejpam-6529	107	23	c0	c0	PROPN
ejpam-6529	107	24	it	it	PRON
ejpam-6529	107	25	is	be	AUX
ejpam-6529	107	26	obvious	obvious	ADJ
ejpam-6529	107	27	that	that	SCONJ
ejpam-6529	107	28	every	every	DET
ejpam-6529	107	29	intuitionistic	intuitionistic	ADJ
ejpam-6529	107	30	fuzzy	fuzzy	ADJ
ejpam-6529	107	31	filter	filter	NOUN
ejpam-6529	107	32	is	be	AUX
ejpam-6529	107	33	an	an	DET
ejpam-6529	107	34	intuitionistic	intuitionistic	ADJ
ejpam-6529	107	35	fuzzy	fuzzy	ADJ
ejpam-6529	107	36	weak	weak	ADJ
ejpam-6529	107	37	filter	filter	NOUN
ejpam-6529	107	38	,	,	PUNCT
ejpam-6529	107	39	but	but	CCONJ
ejpam-6529	107	40	the	the	DET
ejpam-6529	107	41	converse	converse	NOUN
ejpam-6529	107	42	may	may	AUX
ejpam-6529	107	43	not	not	PART
ejpam-6529	107	44	be	be	AUX
ejpam-6529	107	45	true	true	ADJ
ejpam-6529	107	46	.	.	PUNCT
ejpam-6529	108	1	in	in	ADP
ejpam-6529	108	2	fact	fact	NOUN
ejpam-6529	108	3	,	,	PUNCT
ejpam-6529	108	4	the	the	DET
ejpam-6529	108	5	intuitionistic	intuitionistic	ADJ
ejpam-6529	108	6	fuzzy	fuzzy	ADJ
ejpam-6529	108	7	weak	weak	ADJ
ejpam-6529	108	8	filter	filter	NOUN
ejpam-6529	108	9	b∗	b∗	ADJ
ejpam-6529	108	10	:	:	PUNCT
ejpam-6529	108	11	=	=	SYM
ejpam-6529	108	12	(	(	PUNCT
ejpam-6529	108	13	x	x	X
ejpam-6529	108	14	;	;	PUNCT
ejpam-6529	108	15	fb	fb	INTJ
ejpam-6529	108	16	,	,	PUNCT
ejpam-6529	108	17	gb	gb	PROPN
ejpam-6529	108	18	)	)	PUNCT
ejpam-6529	108	19	in	in	ADP
ejpam-6529	108	20	example	example	NOUN
ejpam-6529	108	21	1	1	NUM
ejpam-6529	108	22	is	be	AUX
ejpam-6529	108	23	not	not	PART
ejpam-6529	108	24	an	an	DET
ejpam-6529	108	25	intuitionistic	intuitionistic	ADJ
ejpam-6529	108	26	fuzzy	fuzzy	ADJ
ejpam-6529	108	27	filter	filter	NOUN
ejpam-6529	108	28	of	of	ADP
ejpam-6529	108	29	x	x	X
ejpam-6529	108	30	:	:	PUNCT
ejpam-6529	108	31	=	=	SYM
ejpam-6529	108	32	(	(	PUNCT
ejpam-6529	108	33	x	x	NOUN
ejpam-6529	108	34	,	,	PUNCT
ejpam-6529	108	35	|	|	ADV
ejpam-6529	108	36	)	)	PUNCT
ejpam-6529	108	37	because	because	SCONJ
ejpam-6529	108	38	of	of	ADP
ejpam-6529	108	39	gb((c4|(c6|c7))|(c6|c7	gb((c4|(c6|c7))|(c6|c7	NOUN
ejpam-6529	108	40	)	)	PUNCT
ejpam-6529	108	41	)	)	PUNCT
ejpam-6529	109	1	=	=	SYM
ejpam-6529	109	2	gb(c4	gb(c4	NOUN
ejpam-6529	109	3	)	)	PUNCT
ejpam-6529	109	4	=	=	SYM
ejpam-6529	110	1	0.34	0.34	NUM
ejpam-6529	110	2	≰	≰	PROPN
ejpam-6529	110	3	0.32	0.32	NUM
ejpam-6529	110	4	=	=	SYM
ejpam-6529	110	5	max{gb(c6	max{gb(c6	PROPN
ejpam-6529	110	6	)	)	PUNCT
ejpam-6529	110	7	,	,	PUNCT
ejpam-6529	110	8	gb(c7	gb(c7	NOUN
ejpam-6529	110	9	)	)	PUNCT
ejpam-6529	110	10	}	}	PUNCT
ejpam-6529	110	11	.	.	PUNCT
ejpam-6529	111	1	theorem	theorem	NOUN
ejpam-6529	111	2	1	1	NUM
ejpam-6529	111	3	.	.	PUNCT
ejpam-6529	112	1	an	an	DET
ejpam-6529	112	2	intuitionistic	intuitionistic	ADJ
ejpam-6529	112	3	fuzzy	fuzzy	ADJ
ejpam-6529	112	4	set	set	VERB
ejpam-6529	112	5	b∗	b∗	ADJ
ejpam-6529	112	6	:	:	PUNCT
ejpam-6529	112	7	=	=	SYM
ejpam-6529	112	8	(	(	PUNCT
ejpam-6529	112	9	x	x	X
ejpam-6529	112	10	;	;	PUNCT
ejpam-6529	112	11	fb	fb	INTJ
ejpam-6529	112	12	,	,	PUNCT
ejpam-6529	112	13	gb	gb	NOUN
ejpam-6529	112	14	)	)	PUNCT
ejpam-6529	112	15	in	in	ADP
ejpam-6529	112	16	x	x	PRON
ejpam-6529	112	17	is	be	AUX
ejpam-6529	112	18	an	an	DET
ejpam-6529	112	19	intuitionistic	intuitionistic	ADJ
ejpam-6529	112	20	fuzzy	fuzzy	ADJ
ejpam-6529	112	21	weak	weak	ADJ
ejpam-6529	112	22	filter	filter	NOUN
ejpam-6529	112	23	of	of	ADP
ejpam-6529	112	24	x	x	X
ejpam-6529	112	25	:	:	PUNCT
ejpam-6529	112	26	=	=	SYM
ejpam-6529	112	27	(	(	PUNCT
ejpam-6529	112	28	x	x	NOUN
ejpam-6529	112	29	,	,	PUNCT
ejpam-6529	112	30	|	|	INTJ
ejpam-6529	112	31	)	)	PUNCT
ejpam-6529	112	32	if	if	SCONJ
ejpam-6529	112	33	and	and	CCONJ
ejpam-6529	112	34	only	only	ADV
ejpam-6529	112	35	if	if	SCONJ
ejpam-6529	112	36	it	it	PRON
ejpam-6529	112	37	satisfies	satisfy	VERB
ejpam-6529	112	38	:	:	PUNCT
ejpam-6529	112	39	(	(	PUNCT
ejpam-6529	112	40	∀x	∀x	X
ejpam-6529	112	41	∈	∈	PROPN
ejpam-6529	112	42	x)(fb(1	x)(fb(1	PROPN
ejpam-6529	112	43	)	)	PUNCT
ejpam-6529	112	44	≥	≥	NOUN
ejpam-6529	112	45	fb(x	fb(x	NUM
ejpam-6529	112	46	)	)	PUNCT
ejpam-6529	112	47	,	,	PUNCT
ejpam-6529	112	48	gb(1	gb(1	PROPN
ejpam-6529	112	49	)	)	PUNCT
ejpam-6529	112	50	≤	≤	NOUN
ejpam-6529	112	51	gb(x	gb(x	NUM
ejpam-6529	112	52	)	)	PUNCT
ejpam-6529	112	53	)	)	PUNCT
ejpam-6529	112	54	,	,	PUNCT
ejpam-6529	112	55	(	(	PUNCT
ejpam-6529	112	56	22	22	NUM
ejpam-6529	112	57	)	)	PUNCT
ejpam-6529	112	58	(	(	PUNCT
ejpam-6529	112	59	∀x	∀x	X
ejpam-6529	112	60	,	,	PUNCT
ejpam-6529	112	61	y	y	PROPN
ejpam-6529	112	62	∈	∈	PROPN
ejpam-6529	112	63	x)(fb(ðx(y	x)(fb(ðx(y	PROPN
ejpam-6529	112	64	)	)	PUNCT
ejpam-6529	112	65	)	)	PUNCT
ejpam-6529	112	66	≥	≥	NOUN
ejpam-6529	112	67	fb(y	fb(y	NUM
ejpam-6529	112	68	)	)	PUNCT
ejpam-6529	112	69	,	,	PUNCT
ejpam-6529	112	70	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	112	71	)	)	PUNCT
ejpam-6529	112	72	)	)	PUNCT
ejpam-6529	112	73	≤	≤	NOUN
ejpam-6529	112	74	gb(y	gb(y	ADV
ejpam-6529	112	75	)	)	PUNCT
ejpam-6529	112	76	)	)	PUNCT
ejpam-6529	112	77	.	.	PUNCT
ejpam-6529	113	1	(	(	PUNCT
ejpam-6529	113	2	23	23	X
ejpam-6529	113	3	)	)	PUNCT
ejpam-6529	113	4	proof	proof	NOUN
ejpam-6529	113	5	.	.	PUNCT
ejpam-6529	114	1	assume	assume	VERB
ejpam-6529	114	2	that	that	SCONJ
ejpam-6529	114	3	b∗	b∗	ADJ
ejpam-6529	114	4	:	:	PUNCT
ejpam-6529	114	5	=	=	SYM
ejpam-6529	114	6	(	(	PUNCT
ejpam-6529	114	7	x	x	X
ejpam-6529	114	8	;	;	PUNCT
ejpam-6529	114	9	fb	fb	INTJ
ejpam-6529	114	10	,	,	PUNCT
ejpam-6529	114	11	gb	gb	NOUN
ejpam-6529	114	12	)	)	PUNCT
ejpam-6529	114	13	in	in	ADP
ejpam-6529	114	14	x	x	PRON
ejpam-6529	114	15	is	be	AUX
ejpam-6529	114	16	an	an	DET
ejpam-6529	114	17	intuitionistic	intuitionistic	ADJ
ejpam-6529	114	18	fuzzy	fuzzy	ADJ
ejpam-6529	114	19	weak	weak	ADJ
ejpam-6529	114	20	filter	filter	NOUN
ejpam-6529	114	21	of	of	ADP
ejpam-6529	114	22	x	x	X
ejpam-6529	114	23	:	:	PUNCT
ejpam-6529	114	24	=	=	SYM
ejpam-6529	114	25	(	(	PUNCT
ejpam-6529	114	26	x	x	NOUN
ejpam-6529	114	27	,	,	PUNCT
ejpam-6529	114	28	|	|	NOUN
ejpam-6529	114	29	)	)	PUNCT
ejpam-6529	114	30	.	.	PUNCT
ejpam-6529	115	1	since	since	SCONJ
ejpam-6529	115	2	x(s	x(s	PROPN
ejpam-6529	115	3	,	,	PUNCT
ejpam-6529	115	4	t	t	PROPN
ejpam-6529	115	5	)	)	PUNCT
ejpam-6529	115	6	∈	∈	NOUN
ejpam-6529	115	7	b∗	b∗	ADJ
ejpam-6529	115	8	for	for	ADP
ejpam-6529	115	9	s	s	NOUN
ejpam-6529	115	10	=	=	PUNCT
ejpam-6529	115	11	fb(x	fb(x	X
ejpam-6529	115	12	)	)	PUNCT
ejpam-6529	115	13	and	and	CCONJ
ejpam-6529	115	14	t	t	NOUN
ejpam-6529	115	15	=	=	PUNCT
ejpam-6529	115	16	gb(x	gb(x	NUM
ejpam-6529	115	17	)	)	PUNCT
ejpam-6529	115	18	,	,	PUNCT
ejpam-6529	115	19	we	we	PRON
ejpam-6529	115	20	have	have	VERB
ejpam-6529	115	21	1(s	1(s	NUM
ejpam-6529	115	22	,	,	PUNCT
ejpam-6529	115	23	t	t	PROPN
ejpam-6529	115	24	)	)	PUNCT
ejpam-6529	115	25	∈	∈	NOUN
ejpam-6529	115	26	b∗	b∗	ADV
ejpam-6529	115	27	by	by	ADP
ejpam-6529	115	28	(	(	PUNCT
ejpam-6529	115	29	20	20	NUM
ejpam-6529	115	30	)	)	PUNCT
ejpam-6529	115	31	.	.	PUNCT
ejpam-6529	116	1	hence	hence	ADV
ejpam-6529	116	2	fb(1	fb(1	PROPN
ejpam-6529	116	3	)	)	PUNCT
ejpam-6529	116	4	≥	≥	NOUN
ejpam-6529	116	5	s	s	NOUN
ejpam-6529	116	6	=	=	PUNCT
ejpam-6529	116	7	fb(x	fb(x	X
ejpam-6529	116	8	)	)	PUNCT
ejpam-6529	116	9	and	and	CCONJ
ejpam-6529	116	10	gb(1	gb(1	PROPN
ejpam-6529	116	11	)	)	PUNCT
ejpam-6529	116	12	≤	≤	NOUN
ejpam-6529	117	1	t	t	NOUN
ejpam-6529	117	2	=	=	PUNCT
ejpam-6529	117	3	gb(x	gb(x	NUM
ejpam-6529	117	4	)	)	PUNCT
ejpam-6529	117	5	,	,	PUNCT
ejpam-6529	117	6	i.e.	i.e.	X
ejpam-6529	117	7	,	,	PUNCT
ejpam-6529	117	8	(	(	PUNCT
ejpam-6529	117	9	22	22	NUM
ejpam-6529	117	10	)	)	PUNCT
ejpam-6529	117	11	is	be	AUX
ejpam-6529	117	12	valid	valid	ADJ
ejpam-6529	117	13	.	.	PUNCT
ejpam-6529	118	1	since	since	SCONJ
ejpam-6529	118	2	y(fb(y),gb(y	y(fb(y),gb(y	NOUN
ejpam-6529	118	3	)	)	PUNCT
ejpam-6529	118	4	)	)	PUNCT
ejpam-6529	119	1	∈	∈	PROPN
ejpam-6529	119	2	b∗	b∗	ADJ
ejpam-6529	119	3	for	for	ADP
ejpam-6529	119	4	all	all	DET
ejpam-6529	119	5	y	y	PROPN
ejpam-6529	119	6	∈	∈	PROPN
ejpam-6529	119	7	x	x	X
ejpam-6529	119	8	,	,	PUNCT
ejpam-6529	119	9	it	it	PRON
ejpam-6529	119	10	follows	follow	VERB
ejpam-6529	119	11	from	from	ADP
ejpam-6529	119	12	(	(	PUNCT
ejpam-6529	119	13	21	21	NUM
ejpam-6529	119	14	)	)	PUNCT
ejpam-6529	119	15	that	that	PRON
ejpam-6529	119	16	ðx(y)(fb(y),gb(y	ðx(y)(fb(y),gb(y	PROPN
ejpam-6529	119	17	)	)	PUNCT
ejpam-6529	119	18	)	)	PUNCT
ejpam-6529	120	1	∈	∈	NOUN
ejpam-6529	120	2	b∗	b∗	ADJ
ejpam-6529	120	3	for	for	ADP
ejpam-6529	120	4	all	all	DET
ejpam-6529	120	5	x	x	SYM
ejpam-6529	120	6	∈	∈	ADJ
ejpam-6529	120	7	x.	x.	NOUN
ejpam-6529	120	8	hence	hence	ADV
ejpam-6529	120	9	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	120	10	)	)	PUNCT
ejpam-6529	120	11	)	)	PUNCT
ejpam-6529	120	12	≥	≥	NOUN
ejpam-6529	120	13	fb(y	fb(y	NUM
ejpam-6529	120	14	)	)	PUNCT
ejpam-6529	120	15	and	and	CCONJ
ejpam-6529	120	16	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	120	17	)	)	PUNCT
ejpam-6529	120	18	)	)	PUNCT
ejpam-6529	120	19	≤	≤	NOUN
ejpam-6529	120	20	gb(y	gb(y	ADV
ejpam-6529	120	21	)	)	PUNCT
ejpam-6529	120	22	,	,	PUNCT
ejpam-6529	120	23	i.e.	i.e.	X
ejpam-6529	120	24	,	,	PUNCT
ejpam-6529	120	25	(	(	PUNCT
ejpam-6529	120	26	23	23	NUM
ejpam-6529	120	27	)	)	PUNCT
ejpam-6529	120	28	is	be	AUX
ejpam-6529	120	29	valid	valid	ADJ
ejpam-6529	120	30	.	.	PUNCT
ejpam-6529	121	1	conversely	conversely	ADV
ejpam-6529	121	2	,	,	PUNCT
ejpam-6529	121	3	let	let	VERB
ejpam-6529	121	4	b∗	b∗	ADV
ejpam-6529	121	5	:	:	PUNCT
ejpam-6529	121	6	=	=	SYM
ejpam-6529	121	7	(	(	PUNCT
ejpam-6529	121	8	x	x	X
ejpam-6529	121	9	;	;	PUNCT
ejpam-6529	121	10	fb	fb	INTJ
ejpam-6529	121	11	,	,	PUNCT
ejpam-6529	121	12	gb	gb	PROPN
ejpam-6529	121	13	)	)	PUNCT
ejpam-6529	121	14	be	be	VERB
ejpam-6529	121	15	an	an	DET
ejpam-6529	121	16	intuitionistic	intuitionistic	ADJ
ejpam-6529	121	17	fuzzy	fuzzy	ADJ
ejpam-6529	121	18	set	set	NOUN
ejpam-6529	121	19	in	in	ADP
ejpam-6529	121	20	x	x	PUNCT
ejpam-6529	121	21	that	that	SCONJ
ejpam-6529	121	22	satisfies	satisfie	NOUN
ejpam-6529	121	23	(	(	PUNCT
ejpam-6529	121	24	22	22	NUM
ejpam-6529	121	25	)	)	PUNCT
ejpam-6529	121	26	and	and	CCONJ
ejpam-6529	121	27	(	(	PUNCT
ejpam-6529	121	28	23	23	NUM
ejpam-6529	121	29	)	)	PUNCT
ejpam-6529	121	30	.	.	PUNCT
ejpam-6529	122	1	let	let	VERB
ejpam-6529	122	2	x	x	PUNCT
ejpam-6529	122	3	∈	∈	PROPN
ejpam-6529	122	4	x	x	X
ejpam-6529	122	5	and	and	CCONJ
ejpam-6529	122	6	(	(	PUNCT
ejpam-6529	122	7	s	s	PROPN
ejpam-6529	122	8	,	,	PUNCT
ejpam-6529	122	9	t	t	PROPN
ejpam-6529	122	10	)	)	PUNCT
ejpam-6529	122	11	∈	∈	PROPN
ejpam-6529	122	12	(	(	PUNCT
ejpam-6529	122	13	0	0	NUM
ejpam-6529	122	14	,	,	PUNCT
ejpam-6529	122	15	1	1	NUM
ejpam-6529	122	16	]	]	SYM
ejpam-6529	122	17	×	×	NOUN
ejpam-6529	123	1	[	[	X
ejpam-6529	123	2	0	0	NUM
ejpam-6529	123	3	,	,	PUNCT
ejpam-6529	123	4	1	1	NUM
ejpam-6529	123	5	)	)	PUNCT
ejpam-6529	123	6	be	be	AUX
ejpam-6529	123	7	such	such	ADJ
ejpam-6529	123	8	that	that	SCONJ
ejpam-6529	123	9	x(s	x(s	PROPN
ejpam-6529	123	10	,	,	PUNCT
ejpam-6529	123	11	t	t	PROPN
ejpam-6529	123	12	)	)	PUNCT
ejpam-6529	123	13	∈	∈	PROPN
ejpam-6529	123	14	b∗.	b∗.	NOUN
ejpam-6529	123	15	then	then	ADV
ejpam-6529	123	16	fb(x	fb(x	NOUN
ejpam-6529	123	17	)	)	PUNCT
ejpam-6529	123	18	≥	≥	NOUN
ejpam-6529	123	19	s	s	NOUN
ejpam-6529	123	20	and	and	CCONJ
ejpam-6529	123	21	gb(x	gb(x	NUM
ejpam-6529	123	22	)	)	PUNCT
ejpam-6529	123	23	≤	≤	NOUN
ejpam-6529	124	1	t.	t.	NOUN
ejpam-6529	125	1	if	if	SCONJ
ejpam-6529	125	2	1(s	1(s	NUM
ejpam-6529	125	3	,	,	PUNCT
ejpam-6529	125	4	t	t	PROPN
ejpam-6529	125	5	)	)	PUNCT
ejpam-6529	125	6	∈b∗	∈b∗	PROPN
ejpam-6529	125	7	,	,	PUNCT
ejpam-6529	125	8	then	then	ADV
ejpam-6529	125	9	fb(1	fb(1	PROPN
ejpam-6529	125	10	)	)	PUNCT
ejpam-6529	125	11	<	<	X
ejpam-6529	125	12	s	s	PART
ejpam-6529	125	13	≤	≤	NOUN
ejpam-6529	125	14	fb(x	fb(x	VERB
ejpam-6529	125	15	)	)	PUNCT
ejpam-6529	125	16	or	or	CCONJ
ejpam-6529	125	17	gb(1	gb(1	PROPN
ejpam-6529	125	18	)	)	PUNCT
ejpam-6529	125	19	>	>	X
ejpam-6529	125	20	t	t	PROPN
ejpam-6529	125	21	≥	≥	PROPN
ejpam-6529	125	22	gb(x	gb(x	PUNCT
ejpam-6529	125	23	)	)	PUNCT
ejpam-6529	125	24	which	which	PRON
ejpam-6529	125	25	is	be	AUX
ejpam-6529	125	26	a	a	DET
ejpam-6529	125	27	contradiction	contradiction	NOUN
ejpam-6529	125	28	.	.	PUNCT
ejpam-6529	126	1	thus	thus	ADV
ejpam-6529	126	2	1(s	1(s	NUM
ejpam-6529	126	3	,	,	PUNCT
ejpam-6529	126	4	t	t	PROPN
ejpam-6529	126	5	)	)	PUNCT
ejpam-6529	126	6	∈	∈	PROPN
ejpam-6529	126	7	b∗.	b∗.	NOUN
ejpam-6529	126	8	let	let	VERB
ejpam-6529	126	9	x	x	PRON
ejpam-6529	126	10	,	,	PUNCT
ejpam-6529	126	11	y	y	PROPN
ejpam-6529	126	12	∈	∈	PROPN
ejpam-6529	126	13	x	x	X
ejpam-6529	126	14	and	and	CCONJ
ejpam-6529	126	15	(	(	PUNCT
ejpam-6529	126	16	s	s	PROPN
ejpam-6529	126	17	,	,	PUNCT
ejpam-6529	126	18	t	t	PROPN
ejpam-6529	126	19	)	)	PUNCT
ejpam-6529	126	20	∈	∈	PROPN
ejpam-6529	126	21	(	(	PUNCT
ejpam-6529	126	22	0	0	NUM
ejpam-6529	126	23	,	,	PUNCT
ejpam-6529	126	24	1	1	NUM
ejpam-6529	126	25	]	]	SYM
ejpam-6529	126	26	×	×	NOUN
ejpam-6529	127	1	[	[	X
ejpam-6529	127	2	0	0	NUM
ejpam-6529	127	3	,	,	PUNCT
ejpam-6529	127	4	1	1	NUM
ejpam-6529	127	5	)	)	PUNCT
ejpam-6529	127	6	be	be	AUX
ejpam-6529	127	7	such	such	ADJ
ejpam-6529	127	8	that	that	SCONJ
ejpam-6529	127	9	y(s	y(s	PROPN
ejpam-6529	127	10	,	,	PUNCT
ejpam-6529	127	11	t	t	PROPN
ejpam-6529	127	12	)	)	PUNCT
ejpam-6529	127	13	∈	∈	PROPN
ejpam-6529	127	14	b∗.	b∗.	NOUN
ejpam-6529	127	15	then	then	ADV
ejpam-6529	127	16	fb(y	fb(y	X
ejpam-6529	127	17	)	)	PUNCT
ejpam-6529	127	18	≥	≥	PRON
ejpam-6529	127	19	s	s	PART
ejpam-6529	127	20	and	and	CCONJ
ejpam-6529	127	21	gb(y	gb(y	NUM
ejpam-6529	127	22	)	)	PUNCT
ejpam-6529	127	23	≤	≤	NOUN
ejpam-6529	127	24	t.	t.	NOUN
ejpam-6529	127	25	if	if	SCONJ
ejpam-6529	127	26	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	127	27	,	,	PUNCT
ejpam-6529	127	28	t	t	PROPN
ejpam-6529	127	29	)	)	PUNCT
ejpam-6529	127	30	∈b∗	∈b∗	PROPN
ejpam-6529	127	31	,	,	PUNCT
ejpam-6529	127	32	then	then	ADV
ejpam-6529	127	33	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	127	34	)	)	PUNCT
ejpam-6529	127	35	)	)	PUNCT
ejpam-6529	128	1	<	<	X
ejpam-6529	128	2	s	s	PART
ejpam-6529	128	3	≤	≤	NUM
ejpam-6529	128	4	fb(y	fb(y	NUM
ejpam-6529	128	5	)	)	PUNCT
ejpam-6529	128	6	or	or	CCONJ
ejpam-6529	128	7	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	128	8	)	)	PUNCT
ejpam-6529	128	9	)	)	PUNCT
ejpam-6529	129	1	>	>	X
ejpam-6529	129	2	t	t	PROPN
ejpam-6529	129	3	≥	≥	NOUN
ejpam-6529	129	4	gb(y	gb(y	ADV
ejpam-6529	129	5	)	)	PUNCT
ejpam-6529	129	6	which	which	PRON
ejpam-6529	129	7	is	be	AUX
ejpam-6529	129	8	a	a	DET
ejpam-6529	129	9	contradiction	contradiction	NOUN
ejpam-6529	129	10	.	.	PUNCT
ejpam-6529	130	1	thus	thus	ADV
ejpam-6529	130	2	ðx(y)(s	ðx(y)(s	NUM
ejpam-6529	130	3	,	,	PUNCT
ejpam-6529	130	4	t	t	X
ejpam-6529	130	5	)	)	PUNCT
ejpam-6529	130	6	∈	∈	PROPN
ejpam-6529	130	7	b∗.	b∗.	NOUN
ejpam-6529	130	8	therefore	therefore	ADV
ejpam-6529	130	9	b∗	b∗	ADJ
ejpam-6529	130	10	:	:	PUNCT
ejpam-6529	130	11	=	=	SYM
ejpam-6529	130	12	(	(	PUNCT
ejpam-6529	130	13	x	x	X
ejpam-6529	130	14	;	;	PUNCT
ejpam-6529	130	15	fb	fb	INTJ
ejpam-6529	130	16	,	,	PUNCT
ejpam-6529	130	17	gb	gb	PROPN
ejpam-6529	130	18	)	)	PUNCT
ejpam-6529	130	19	is	be	AUX
ejpam-6529	130	20	an	an	DET
ejpam-6529	130	21	intuitionistic	intuitionistic	ADJ
ejpam-6529	130	22	fuzzy	fuzzy	ADJ
ejpam-6529	130	23	weak	weak	ADJ
ejpam-6529	130	24	filter	filter	NOUN
ejpam-6529	130	25	of	of	ADP
ejpam-6529	130	26	x	x	X
ejpam-6529	130	27	:	:	PUNCT
ejpam-6529	130	28	=	=	SYM
ejpam-6529	130	29	(	(	PUNCT
ejpam-6529	130	30	x	x	NOUN
ejpam-6529	130	31	,	,	PUNCT
ejpam-6529	130	32	|	|	NOUN
ejpam-6529	130	33	)	)	PUNCT
ejpam-6529	130	34	.	.	PUNCT
ejpam-6529	131	1	theorem	theorem	NOUN
ejpam-6529	131	2	2	2	NUM
ejpam-6529	131	3	.	.	PUNCT
ejpam-6529	131	4	an	an	DET
ejpam-6529	131	5	intuitionistic	intuitionistic	ADJ
ejpam-6529	131	6	fuzzy	fuzzy	ADJ
ejpam-6529	131	7	set	set	VERB
ejpam-6529	131	8	b∗	b∗	ADJ
ejpam-6529	131	9	:	:	PUNCT
ejpam-6529	131	10	=	=	SYM
ejpam-6529	131	11	(	(	PUNCT
ejpam-6529	131	12	x	x	X
ejpam-6529	131	13	;	;	PUNCT
ejpam-6529	131	14	fb	fb	INTJ
ejpam-6529	131	15	,	,	PUNCT
ejpam-6529	131	16	gb	gb	NOUN
ejpam-6529	131	17	)	)	PUNCT
ejpam-6529	131	18	in	in	ADP
ejpam-6529	131	19	x	x	PRON
ejpam-6529	131	20	is	be	AUX
ejpam-6529	131	21	an	an	DET
ejpam-6529	131	22	intuitionistic	intuitionistic	ADJ
ejpam-6529	131	23	fuzzy	fuzzy	ADJ
ejpam-6529	131	24	weak	weak	ADJ
ejpam-6529	131	25	filter	filter	NOUN
ejpam-6529	131	26	of	of	ADP
ejpam-6529	131	27	x	x	X
ejpam-6529	131	28	:	:	PUNCT
ejpam-6529	131	29	=	=	SYM
ejpam-6529	131	30	(	(	PUNCT
ejpam-6529	131	31	x	x	NOUN
ejpam-6529	131	32	,	,	PUNCT
ejpam-6529	131	33	|	|	INTJ
ejpam-6529	131	34	)	)	PUNCT
ejpam-6529	131	35	if	if	SCONJ
ejpam-6529	131	36	and	and	CCONJ
ejpam-6529	131	37	only	only	ADV
ejpam-6529	131	38	if	if	SCONJ
ejpam-6529	131	39	the	the	DET
ejpam-6529	131	40	nonempty	nonempty	ADJ
ejpam-6529	131	41	sets	set	NOUN
ejpam-6529	131	42	(	(	PUNCT
ejpam-6529	131	43	fb	fb	INTJ
ejpam-6529	131	44	,	,	PUNCT
ejpam-6529	131	45	s)∈	s)∈	NUM
ejpam-6529	131	46	and	and	CCONJ
ejpam-6529	131	47	(	(	PUNCT
ejpam-6529	131	48	gb	gb	NOUN
ejpam-6529	131	49	,	,	PUNCT
ejpam-6529	131	50	t)∈	t)∈	NUM
ejpam-6529	131	51	are	be	AUX
ejpam-6529	131	52	weak	weak	ADJ
ejpam-6529	131	53	filters	filter	NOUN
ejpam-6529	131	54	of	of	ADP
ejpam-6529	131	55	x	x	PRON
ejpam-6529	131	56	:	:	PUNCT
ejpam-6529	131	57	=	=	SYM
ejpam-6529	131	58	(	(	PUNCT
ejpam-6529	131	59	x	x	NOUN
ejpam-6529	131	60	,	,	PUNCT
ejpam-6529	131	61	|	|	ADV
ejpam-6529	131	62	)	)	PUNCT
ejpam-6529	131	63	for	for	ADP
ejpam-6529	131	64	all	all	DET
ejpam-6529	131	65	(	(	PUNCT
ejpam-6529	131	66	s	s	PROPN
ejpam-6529	131	67	,	,	PUNCT
ejpam-6529	131	68	t	t	PROPN
ejpam-6529	131	69	)	)	PUNCT
ejpam-6529	131	70	∈	∈	PROPN
ejpam-6529	131	71	(	(	PUNCT
ejpam-6529	131	72	0	0	NUM
ejpam-6529	131	73	,	,	PUNCT
ejpam-6529	131	74	1]×	1]×	NUM
ejpam-6529	132	1	[	[	X
ejpam-6529	132	2	0	0	NUM
ejpam-6529	132	3	,	,	PUNCT
ejpam-6529	132	4	1	1	NUM
ejpam-6529	132	5	)	)	PUNCT
ejpam-6529	132	6	.	.	PUNCT
ejpam-6529	133	1	proof	proof	NOUN
ejpam-6529	133	2	.	.	PUNCT
ejpam-6529	134	1	assume	assume	VERB
ejpam-6529	134	2	that	that	SCONJ
ejpam-6529	134	3	b∗	b∗	ADJ
ejpam-6529	134	4	:	:	PUNCT
ejpam-6529	134	5	=	=	SYM
ejpam-6529	134	6	(	(	PUNCT
ejpam-6529	134	7	x	x	X
ejpam-6529	134	8	;	;	PUNCT
ejpam-6529	134	9	fb	fb	INTJ
ejpam-6529	134	10	,	,	PUNCT
ejpam-6529	134	11	gb	gb	PROPN
ejpam-6529	134	12	)	)	PUNCT
ejpam-6529	134	13	is	be	AUX
ejpam-6529	134	14	an	an	DET
ejpam-6529	134	15	intuitionistic	intuitionistic	ADJ
ejpam-6529	134	16	fuzzy	fuzzy	ADJ
ejpam-6529	134	17	weak	weak	ADJ
ejpam-6529	134	18	filter	filter	NOUN
ejpam-6529	134	19	of	of	ADP
ejpam-6529	134	20	x	x	X
ejpam-6529	134	21	:	:	PUNCT
ejpam-6529	134	22	=	=	SYM
ejpam-6529	134	23	(	(	PUNCT
ejpam-6529	134	24	x	x	NOUN
ejpam-6529	134	25	,	,	PUNCT
ejpam-6529	134	26	|	|	ADV
ejpam-6529	134	27	)	)	PUNCT
ejpam-6529	134	28	and	and	CCONJ
ejpam-6529	134	29	let	let	VERB
ejpam-6529	134	30	(	(	PUNCT
ejpam-6529	134	31	s	s	X
ejpam-6529	134	32	,	,	PUNCT
ejpam-6529	134	33	t	t	PROPN
ejpam-6529	134	34	)	)	PUNCT
ejpam-6529	134	35	∈	∈	PROPN
ejpam-6529	134	36	(	(	PUNCT
ejpam-6529	134	37	0	0	NUM
ejpam-6529	134	38	,	,	PUNCT
ejpam-6529	134	39	1	1	NUM
ejpam-6529	134	40	]	]	SYM
ejpam-6529	134	41	×	×	NOUN
ejpam-6529	135	1	[	[	X
ejpam-6529	135	2	0	0	NUM
ejpam-6529	135	3	,	,	PUNCT
ejpam-6529	135	4	1	1	NUM
ejpam-6529	135	5	)	)	PUNCT
ejpam-6529	135	6	be	be	AUX
ejpam-6529	135	7	such	such	ADJ
ejpam-6529	135	8	that	that	SCONJ
ejpam-6529	135	9	(	(	PUNCT
ejpam-6529	135	10	fb	fb	INTJ
ejpam-6529	135	11	,	,	PUNCT
ejpam-6529	135	12	s)∈	s)∈	NUM
ejpam-6529	135	13	̸=	̸=	PROPN
ejpam-6529	135	14	∅	∅	NOUN
ejpam-6529	135	15	̸=	̸=	PROPN
ejpam-6529	135	16	(	(	PUNCT
ejpam-6529	135	17	gb	gb	NOUN
ejpam-6529	135	18	,	,	PUNCT
ejpam-6529	135	19	t)∈	t)∈	NUM
ejpam-6529	135	20	,	,	PUNCT
ejpam-6529	135	21	say	say	VERB
ejpam-6529	135	22	x	x	X
ejpam-6529	135	23	∈	∈	PROPN
ejpam-6529	135	24	(	(	PUNCT
ejpam-6529	135	25	fb	fb	INTJ
ejpam-6529	135	26	,	,	PUNCT
ejpam-6529	135	27	s)∈	s)∈	NUM
ejpam-6529	135	28	and	and	CCONJ
ejpam-6529	135	29	s.	s.	PROPN
ejpam-6529	135	30	s.	s.	PROPN
ejpam-6529	135	31	ahn	ahn	PROPN
ejpam-6529	135	32	,	,	PUNCT
ejpam-6529	135	33	y.	y.	PROPN
ejpam-6529	135	34	j.	j.	PROPN
ejpam-6529	135	35	seo	seo	PROPN
ejpam-6529	135	36	,	,	PUNCT
ejpam-6529	135	37	y.	y.	PROPN
ejpam-6529	135	38	b.	b.	PROPN
ejpam-6529	135	39	jun	jun	PROPN
ejpam-6529	135	40	/	/	SYM
ejpam-6529	135	41	eur	eur	PROPN
ejpam-6529	135	42	.	.	PUNCT
ejpam-6529	136	1	j.	j.	PROPN
ejpam-6529	136	2	pure	pure	PROPN
ejpam-6529	136	3	appl	appl	PROPN
ejpam-6529	136	4	.	.	PROPN
ejpam-6529	136	5	math	math	PROPN
ejpam-6529	136	6	,	,	PUNCT
ejpam-6529	136	7	18	18	NUM
ejpam-6529	136	8	(	(	PUNCT
ejpam-6529	136	9	3	3	NUM
ejpam-6529	136	10	)	)	PUNCT
ejpam-6529	136	11	(	(	PUNCT
ejpam-6529	136	12	2025	2025	NUM
ejpam-6529	136	13	)	)	PUNCT
ejpam-6529	136	14	,	,	PUNCT
ejpam-6529	136	15	6529	6529	NUM
ejpam-6529	136	16	7	7	NUM
ejpam-6529	136	17	of	of	ADP
ejpam-6529	136	18	16	16	NUM
ejpam-6529	136	19	a	a	DET
ejpam-6529	136	20	∈	∈	PROPN
ejpam-6529	136	21	(	(	PUNCT
ejpam-6529	136	22	gb	gb	NOUN
ejpam-6529	136	23	,	,	PUNCT
ejpam-6529	136	24	t)∈.	t)∈.	PROPN
ejpam-6529	136	25	then	then	ADV
ejpam-6529	136	26	fb(1	fb(1	PROPN
ejpam-6529	136	27	)	)	PUNCT
ejpam-6529	136	28	≥	≥	NOUN
ejpam-6529	136	29	fb(x	fb(x	PUNCT
ejpam-6529	136	30	)	)	PUNCT
ejpam-6529	136	31	≥	≥	PRON
ejpam-6529	136	32	s	s	NOUN
ejpam-6529	136	33	and	and	CCONJ
ejpam-6529	136	34	gb(1	gb(1	PROPN
ejpam-6529	136	35	)	)	PUNCT
ejpam-6529	136	36	≤	≤	NOUN
ejpam-6529	136	37	gb(a	gb(a	NOUN
ejpam-6529	136	38	)	)	PUNCT
ejpam-6529	136	39	≤	≤	NUM
ejpam-6529	136	40	t	t	NOUN
ejpam-6529	136	41	by	by	ADP
ejpam-6529	136	42	(	(	PUNCT
ejpam-6529	136	43	22	22	NUM
ejpam-6529	136	44	)	)	PUNCT
ejpam-6529	136	45	.	.	PUNCT
ejpam-6529	137	1	hence	hence	ADV
ejpam-6529	137	2	1	1	NUM
ejpam-6529	137	3	∈	∈	NOUN
ejpam-6529	137	4	(	(	PUNCT
ejpam-6529	137	5	fb	fb	INTJ
ejpam-6529	137	6	,	,	PUNCT
ejpam-6529	137	7	s)∈	s)∈	NUM
ejpam-6529	137	8	and	and	CCONJ
ejpam-6529	137	9	1	1	NUM
ejpam-6529	137	10	∈	∈	NOUN
ejpam-6529	137	11	(	(	PUNCT
ejpam-6529	137	12	gb	gb	NOUN
ejpam-6529	137	13	,	,	PUNCT
ejpam-6529	137	14	t)∈.	t)∈.	PROPN
ejpam-6529	137	15	let	let	VERB
ejpam-6529	137	16	y	y	PROPN
ejpam-6529	137	17	∈	∈	PROPN
ejpam-6529	137	18	(	(	PUNCT
ejpam-6529	137	19	fb	fb	INTJ
ejpam-6529	137	20	,	,	PUNCT
ejpam-6529	137	21	s)∈	s)∈	NUM
ejpam-6529	137	22	and	and	CCONJ
ejpam-6529	137	23	b	b	X
ejpam-6529	137	24	∈	∈	PROPN
ejpam-6529	137	25	(	(	PUNCT
ejpam-6529	137	26	gb	gb	NOUN
ejpam-6529	137	27	,	,	PUNCT
ejpam-6529	137	28	t)∈.	t)∈.	PROPN
ejpam-6529	137	29	then	then	ADV
ejpam-6529	137	30	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	137	31	)	)	PUNCT
ejpam-6529	137	32	)	)	PUNCT
ejpam-6529	137	33	≥	≥	NOUN
ejpam-6529	137	34	fb(y	fb(y	NUM
ejpam-6529	137	35	)	)	PUNCT
ejpam-6529	137	36	≥	≥	NOUN
ejpam-6529	137	37	s	s	NOUN
ejpam-6529	137	38	and	and	CCONJ
ejpam-6529	137	39	ða(b	ða(b	NUM
ejpam-6529	137	40	)	)	PUNCT
ejpam-6529	137	41	≤	≤	NOUN
ejpam-6529	137	42	gb(b	gb(b	NOUN
ejpam-6529	137	43	)	)	PUNCT
ejpam-6529	137	44	≤	≤	NOUN
ejpam-6529	137	45	t	t	NOUN
ejpam-6529	137	46	for	for	ADP
ejpam-6529	137	47	all	all	DET
ejpam-6529	137	48	x	x	NOUN
ejpam-6529	137	49	,	,	PUNCT
ejpam-6529	137	50	a	a	DET
ejpam-6529	137	51	∈	∈	NOUN
ejpam-6529	137	52	x	x	PUNCT
ejpam-6529	137	53	by	by	ADP
ejpam-6529	137	54	(	(	PUNCT
ejpam-6529	137	55	23	23	NUM
ejpam-6529	137	56	)	)	PUNCT
ejpam-6529	137	57	.	.	PUNCT
ejpam-6529	138	1	it	it	PRON
ejpam-6529	138	2	follows	follow	VERB
ejpam-6529	138	3	that	that	PRON
ejpam-6529	138	4	ðx(y	ðx(y	PUNCT
ejpam-6529	139	1	)	)	PUNCT
ejpam-6529	139	2	∈	∈	PROPN
ejpam-6529	139	3	(	(	PUNCT
ejpam-6529	139	4	fb	fb	INTJ
ejpam-6529	139	5	,	,	PUNCT
ejpam-6529	139	6	s)∈	s)∈	NUM
ejpam-6529	139	7	and	and	CCONJ
ejpam-6529	139	8	ða(b	ða(b	NUM
ejpam-6529	139	9	)	)	PUNCT
ejpam-6529	140	1	∈	∈	PROPN
ejpam-6529	140	2	(	(	PUNCT
ejpam-6529	140	3	gb	gb	NOUN
ejpam-6529	140	4	,	,	PUNCT
ejpam-6529	140	5	t)∈.	t)∈.	PROPN
ejpam-6529	140	6	therefore	therefore	ADV
ejpam-6529	140	7	(	(	PUNCT
ejpam-6529	140	8	fb	fb	INTJ
ejpam-6529	140	9	,	,	PUNCT
ejpam-6529	140	10	s)∈	s)∈	NUM
ejpam-6529	140	11	and	and	CCONJ
ejpam-6529	140	12	(	(	PUNCT
ejpam-6529	140	13	gb	gb	NOUN
ejpam-6529	140	14	,	,	PUNCT
ejpam-6529	140	15	t)∈	t)∈	NUM
ejpam-6529	140	16	are	be	AUX
ejpam-6529	140	17	weak	weak	ADJ
ejpam-6529	140	18	filters	filter	NOUN
ejpam-6529	140	19	of	of	ADP
ejpam-6529	140	20	x	x	PRON
ejpam-6529	140	21	:	:	PUNCT
ejpam-6529	140	22	=	=	SYM
ejpam-6529	140	23	(	(	PUNCT
ejpam-6529	140	24	x	x	NOUN
ejpam-6529	140	25	,	,	PUNCT
ejpam-6529	140	26	|	|	NOUN
ejpam-6529	140	27	)	)	PUNCT
ejpam-6529	140	28	.	.	PUNCT
ejpam-6529	141	1	conversely	conversely	ADV
ejpam-6529	141	2	,	,	PUNCT
ejpam-6529	141	3	suppose	suppose	VERB
ejpam-6529	141	4	that	that	SCONJ
ejpam-6529	141	5	the	the	DET
ejpam-6529	141	6	nonempty	nonempty	ADJ
ejpam-6529	141	7	sets	set	NOUN
ejpam-6529	141	8	(	(	PUNCT
ejpam-6529	141	9	fb	fb	INTJ
ejpam-6529	141	10	,	,	PUNCT
ejpam-6529	141	11	s)∈	s)∈	NUM
ejpam-6529	141	12	and	and	CCONJ
ejpam-6529	141	13	(	(	PUNCT
ejpam-6529	141	14	gb	gb	NOUN
ejpam-6529	141	15	,	,	PUNCT
ejpam-6529	141	16	t)∈	t)∈	NUM
ejpam-6529	141	17	are	be	AUX
ejpam-6529	141	18	weak	weak	ADJ
ejpam-6529	141	19	filters	filter	NOUN
ejpam-6529	141	20	of	of	ADP
ejpam-6529	141	21	x	x	PRON
ejpam-6529	141	22	:	:	PUNCT
ejpam-6529	141	23	=	=	SYM
ejpam-6529	141	24	(	(	PUNCT
ejpam-6529	141	25	x	x	NOUN
ejpam-6529	141	26	,	,	PUNCT
ejpam-6529	141	27	|	|	ADV
ejpam-6529	141	28	)	)	PUNCT
ejpam-6529	141	29	for	for	ADP
ejpam-6529	141	30	all	all	DET
ejpam-6529	141	31	(	(	PUNCT
ejpam-6529	141	32	s	s	PROPN
ejpam-6529	141	33	,	,	PUNCT
ejpam-6529	141	34	t	t	PROPN
ejpam-6529	141	35	)	)	PUNCT
ejpam-6529	141	36	∈	∈	PROPN
ejpam-6529	141	37	(	(	PUNCT
ejpam-6529	141	38	0	0	NUM
ejpam-6529	141	39	,	,	PUNCT
ejpam-6529	141	40	1	1	NUM
ejpam-6529	141	41	]	]	SYM
ejpam-6529	141	42	×	×	NOUN
ejpam-6529	142	1	[	[	X
ejpam-6529	142	2	0	0	NUM
ejpam-6529	142	3	,	,	PUNCT
ejpam-6529	142	4	1	1	NUM
ejpam-6529	142	5	)	)	PUNCT
ejpam-6529	142	6	.	.	PUNCT
ejpam-6529	143	1	if	if	SCONJ
ejpam-6529	143	2	(	(	PUNCT
ejpam-6529	143	3	22	22	NUM
ejpam-6529	143	4	)	)	PUNCT
ejpam-6529	143	5	is	be	AUX
ejpam-6529	143	6	not	not	PART
ejpam-6529	143	7	valid	valid	ADJ
ejpam-6529	143	8	,	,	PUNCT
ejpam-6529	143	9	then	then	ADV
ejpam-6529	143	10	fb(1	fb(1	PROPN
ejpam-6529	143	11	)	)	PUNCT
ejpam-6529	143	12	<	<	X
ejpam-6529	143	13	fb(a	fb(a	NOUN
ejpam-6529	143	14	)	)	PUNCT
ejpam-6529	143	15	or	or	CCONJ
ejpam-6529	143	16	gb(1	gb(1	PROPN
ejpam-6529	143	17	)	)	PUNCT
ejpam-6529	143	18	>	>	X
ejpam-6529	143	19	gb(b	gb(b	X
ejpam-6529	143	20	)	)	PUNCT
ejpam-6529	143	21	for	for	ADP
ejpam-6529	143	22	some	some	PRON
ejpam-6529	143	23	a	a	PRON
ejpam-6529	143	24	,	,	PUNCT
ejpam-6529	143	25	b	b	X
ejpam-6529	143	26	∈	∈	PROPN
ejpam-6529	143	27	x.	x.	NOUN
ejpam-6529	144	1	it	it	PRON
ejpam-6529	144	2	follows	follow	VERB
ejpam-6529	144	3	that	that	SCONJ
ejpam-6529	144	4	1	1	NUM
ejpam-6529	144	5	/∈	/∈	PUNCT
ejpam-6529	144	6	(	(	PUNCT
ejpam-6529	144	7	fb	fb	INTJ
ejpam-6529	144	8	,	,	PUNCT
ejpam-6529	144	9	s)∈	s)∈	NUM
ejpam-6529	144	10	or	or	CCONJ
ejpam-6529	144	11	1	1	NUM
ejpam-6529	144	12	/∈	/∈	INTJ
ejpam-6529	144	13	(	(	PUNCT
ejpam-6529	144	14	gb	gb	NOUN
ejpam-6529	144	15	,	,	PUNCT
ejpam-6529	144	16	t)∈	t)∈	PROPN
ejpam-6529	144	17	where	where	SCONJ
ejpam-6529	144	18	s	s	VERB
ejpam-6529	144	19	:	:	PUNCT
ejpam-6529	144	20	=	=	NOUN
ejpam-6529	144	21	fb(a	fb(a	X
ejpam-6529	144	22	)	)	PUNCT
ejpam-6529	144	23	and	and	CCONJ
ejpam-6529	144	24	t	t	NOUN
ejpam-6529	144	25	:	:	PUNCT
ejpam-6529	144	26	=	=	SYM
ejpam-6529	144	27	gb(b	gb(b	X
ejpam-6529	144	28	)	)	PUNCT
ejpam-6529	144	29	.	.	PUNCT
ejpam-6529	145	1	this	this	PRON
ejpam-6529	145	2	is	be	AUX
ejpam-6529	145	3	a	a	DET
ejpam-6529	145	4	contradiction	contradiction	NOUN
ejpam-6529	145	5	,	,	PUNCT
ejpam-6529	145	6	and	and	CCONJ
ejpam-6529	145	7	so	so	ADV
ejpam-6529	145	8	(	(	PUNCT
ejpam-6529	145	9	22	22	NUM
ejpam-6529	145	10	)	)	PUNCT
ejpam-6529	145	11	is	be	AUX
ejpam-6529	145	12	valid	valid	ADJ
ejpam-6529	145	13	.	.	PUNCT
ejpam-6529	146	1	suppose	suppose	VERB
ejpam-6529	146	2	that	that	SCONJ
ejpam-6529	146	3	(	(	PUNCT
ejpam-6529	146	4	23	23	NUM
ejpam-6529	146	5	)	)	PUNCT
ejpam-6529	146	6	is	be	AUX
ejpam-6529	146	7	not	not	PART
ejpam-6529	146	8	valid	valid	ADJ
ejpam-6529	146	9	.	.	PUNCT
ejpam-6529	147	1	then	then	ADV
ejpam-6529	147	2	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	147	3	)	)	PUNCT
ejpam-6529	147	4	)	)	PUNCT
ejpam-6529	148	1	<	<	X
ejpam-6529	148	2	fb(y	fb(y	PUNCT
ejpam-6529	148	3	)	)	PUNCT
ejpam-6529	148	4	or	or	CCONJ
ejpam-6529	148	5	gb(ða(b	gb(ða(b	NOUN
ejpam-6529	148	6	)	)	PUNCT
ejpam-6529	148	7	)	)	PUNCT
ejpam-6529	149	1	>	>	X
ejpam-6529	149	2	gb(b	gb(b	NOUN
ejpam-6529	149	3	)	)	PUNCT
ejpam-6529	149	4	.	.	PUNCT
ejpam-6529	150	1	if	if	SCONJ
ejpam-6529	150	2	we	we	PRON
ejpam-6529	150	3	take	take	VERB
ejpam-6529	150	4	s	s	VERB
ejpam-6529	150	5	:	:	PUNCT
ejpam-6529	150	6	=	=	PUNCT
ejpam-6529	150	7	fb(y	fb(y	NUM
ejpam-6529	150	8	)	)	PUNCT
ejpam-6529	150	9	and	and	CCONJ
ejpam-6529	150	10	t	t	NOUN
ejpam-6529	150	11	:	:	PUNCT
ejpam-6529	150	12	=	=	SYM
ejpam-6529	150	13	gb(b	gb(b	X
ejpam-6529	150	14	)	)	PUNCT
ejpam-6529	150	15	,	,	PUNCT
ejpam-6529	150	16	then	then	ADV
ejpam-6529	150	17	ðx(y	ðx(y	PUNCT
ejpam-6529	150	18	)	)	PUNCT
ejpam-6529	150	19	/∈	/∈	PUNCT
ejpam-6529	151	1	(	(	PUNCT
ejpam-6529	151	2	fb	fb	INTJ
ejpam-6529	151	3	,	,	PUNCT
ejpam-6529	151	4	s)∈	s)∈	NUM
ejpam-6529	151	5	or	or	CCONJ
ejpam-6529	151	6	ða(b	ða(b	NUM
ejpam-6529	151	7	)	)	PUNCT
ejpam-6529	151	8	/∈	/∈	PUNCT
ejpam-6529	152	1	(	(	PUNCT
ejpam-6529	152	2	gb	gb	NOUN
ejpam-6529	152	3	,	,	PUNCT
ejpam-6529	152	4	t)∈	t)∈	PROPN
ejpam-6529	152	5	,	,	PUNCT
ejpam-6529	152	6	a	a	DET
ejpam-6529	152	7	contradiction	contradiction	NOUN
ejpam-6529	152	8	.	.	PUNCT
ejpam-6529	153	1	thus	thus	ADV
ejpam-6529	153	2	(	(	PUNCT
ejpam-6529	153	3	23	23	NUM
ejpam-6529	153	4	)	)	PUNCT
ejpam-6529	153	5	is	be	AUX
ejpam-6529	153	6	valid	valid	ADJ
ejpam-6529	153	7	.	.	PUNCT
ejpam-6529	154	1	consequently	consequently	ADV
ejpam-6529	154	2	,	,	PUNCT
ejpam-6529	154	3	b∗	b∗	ADJ
ejpam-6529	154	4	:	:	PUNCT
ejpam-6529	154	5	=	=	SYM
ejpam-6529	154	6	(	(	PUNCT
ejpam-6529	154	7	x	x	X
ejpam-6529	154	8	;	;	PUNCT
ejpam-6529	154	9	fb	fb	INTJ
ejpam-6529	154	10	,	,	PUNCT
ejpam-6529	154	11	gb	gb	PROPN
ejpam-6529	154	12	)	)	PUNCT
ejpam-6529	154	13	is	be	AUX
ejpam-6529	154	14	an	an	DET
ejpam-6529	154	15	intuitionistic	intuitionistic	ADJ
ejpam-6529	154	16	fuzzy	fuzzy	ADJ
ejpam-6529	154	17	weak	weak	ADJ
ejpam-6529	154	18	filter	filter	NOUN
ejpam-6529	154	19	of	of	ADP
ejpam-6529	154	20	x	x	X
ejpam-6529	154	21	:	:	PUNCT
ejpam-6529	154	22	=	=	SYM
ejpam-6529	154	23	(	(	PUNCT
ejpam-6529	154	24	x	x	NOUN
ejpam-6529	154	25	,	,	PUNCT
ejpam-6529	154	26	|	|	ADV
ejpam-6529	154	27	)	)	PUNCT
ejpam-6529	154	28	by	by	ADP
ejpam-6529	154	29	theorem	theorem	NOUN
ejpam-6529	154	30	1	1	NUM
ejpam-6529	154	31	.	.	PUNCT
ejpam-6529	154	32	corollary	corollary	ADJ
ejpam-6529	154	33	1	1	NUM
ejpam-6529	154	34	.	.	PUNCT
ejpam-6529	155	1	if	if	SCONJ
ejpam-6529	155	2	b∗	b∗	ADJ
ejpam-6529	155	3	:	:	PUNCT
ejpam-6529	155	4	=	=	SYM
ejpam-6529	155	5	(	(	PUNCT
ejpam-6529	155	6	x	x	X
ejpam-6529	155	7	;	;	PUNCT
ejpam-6529	155	8	fb	fb	INTJ
ejpam-6529	155	9	,	,	PUNCT
ejpam-6529	155	10	gb	gb	PROPN
ejpam-6529	155	11	)	)	PUNCT
ejpam-6529	155	12	is	be	AUX
ejpam-6529	155	13	an	an	DET
ejpam-6529	155	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	155	15	fuzzy	fuzzy	ADJ
ejpam-6529	155	16	weak	weak	ADJ
ejpam-6529	155	17	filter	filter	NOUN
ejpam-6529	155	18	of	of	ADP
ejpam-6529	155	19	x	x	X
ejpam-6529	155	20	:	:	PUNCT
ejpam-6529	155	21	=	=	SYM
ejpam-6529	155	22	(	(	PUNCT
ejpam-6529	155	23	x	x	NOUN
ejpam-6529	155	24	,	,	PUNCT
ejpam-6529	155	25	|	|	NOUN
ejpam-6529	155	26	)	)	PUNCT
ejpam-6529	155	27	,	,	PUNCT
ejpam-6529	155	28	then	then	ADV
ejpam-6529	155	29	its	its	PRON
ejpam-6529	155	30	nonempty	nonempty	ADV
ejpam-6529	155	31	intuitionistic	intuitionistic	ADJ
ejpam-6529	155	32	level	level	NOUN
ejpam-6529	155	33	set	set	NOUN
ejpam-6529	155	34	(	(	PUNCT
ejpam-6529	155	35	b∗	b∗	ADJ
ejpam-6529	155	36	,	,	PUNCT
ejpam-6529	155	37	(	(	PUNCT
ejpam-6529	155	38	s	s	X
ejpam-6529	155	39	,	,	PUNCT
ejpam-6529	155	40	t))∈	t))∈	NOUN
ejpam-6529	155	41	is	be	AUX
ejpam-6529	155	42	a	a	DET
ejpam-6529	155	43	weak	weak	ADJ
ejpam-6529	155	44	filter	filter	NOUN
ejpam-6529	155	45	of	of	ADP
ejpam-6529	155	46	x	x	X
ejpam-6529	155	47	:	:	PUNCT
ejpam-6529	155	48	=	=	SYM
ejpam-6529	155	49	(	(	PUNCT
ejpam-6529	155	50	x	x	NOUN
ejpam-6529	155	51	,	,	PUNCT
ejpam-6529	155	52	|	|	ADV
ejpam-6529	155	53	)	)	PUNCT
ejpam-6529	155	54	for	for	ADP
ejpam-6529	155	55	all	all	DET
ejpam-6529	155	56	(	(	PUNCT
ejpam-6529	155	57	s	s	PROPN
ejpam-6529	155	58	,	,	PUNCT
ejpam-6529	155	59	t	t	PROPN
ejpam-6529	155	60	)	)	PUNCT
ejpam-6529	155	61	∈	∈	PROPN
ejpam-6529	155	62	(	(	PUNCT
ejpam-6529	155	63	0	0	NUM
ejpam-6529	155	64	,	,	PUNCT
ejpam-6529	155	65	1]×	1]×	NUM
ejpam-6529	156	1	[	[	X
ejpam-6529	156	2	0	0	NUM
ejpam-6529	156	3	,	,	PUNCT
ejpam-6529	156	4	1	1	NUM
ejpam-6529	156	5	)	)	PUNCT
ejpam-6529	156	6	.	.	PUNCT
ejpam-6529	157	1	we	we	PRON
ejpam-6529	157	2	examine	examine	VERB
ejpam-6529	157	3	the	the	DET
ejpam-6529	157	4	conditions	condition	NOUN
ejpam-6529	157	5	under	under	ADP
ejpam-6529	157	6	which	which	PRON
ejpam-6529	157	7	the	the	DET
ejpam-6529	157	8	intuitionistic	intuitionistic	ADJ
ejpam-6529	157	9	fuzzy	fuzzy	ADJ
ejpam-6529	157	10	set	set	NOUN
ejpam-6529	157	11	becomes	become	VERB
ejpam-6529	157	12	an	an	DET
ejpam-6529	157	13	intuitionistic	intuitionistic	ADJ
ejpam-6529	157	14	fuzzy	fuzzy	ADJ
ejpam-6529	157	15	weak	weak	ADJ
ejpam-6529	157	16	filter	filter	NOUN
ejpam-6529	157	17	.	.	PUNCT
ejpam-6529	158	1	theorem	theorem	NOUN
ejpam-6529	158	2	3	3	NUM
ejpam-6529	158	3	.	.	PUNCT
ejpam-6529	159	1	if	if	SCONJ
ejpam-6529	159	2	an	an	DET
ejpam-6529	159	3	intuitionistic	intuitionistic	ADJ
ejpam-6529	159	4	fuzzy	fuzzy	ADJ
ejpam-6529	159	5	set	set	VERB
ejpam-6529	159	6	b∗	b∗	ADJ
ejpam-6529	159	7	:	:	PUNCT
ejpam-6529	159	8	=	=	SYM
ejpam-6529	159	9	(	(	PUNCT
ejpam-6529	159	10	x	x	X
ejpam-6529	159	11	;	;	PUNCT
ejpam-6529	159	12	fb	fb	INTJ
ejpam-6529	159	13	,	,	PUNCT
ejpam-6529	159	14	gb	gb	NOUN
ejpam-6529	159	15	)	)	PUNCT
ejpam-6529	159	16	in	in	ADP
ejpam-6529	159	17	x	x	X
ejpam-6529	159	18	satisfies	satisfie	NOUN
ejpam-6529	159	19	(	(	PUNCT
ejpam-6529	159	20	20	20	NUM
ejpam-6529	159	21	)	)	PUNCT
ejpam-6529	159	22	and	and	CCONJ
ejpam-6529	159	23	x(s1,t1	x(s1,t1	NOUN
ejpam-6529	159	24	)	)	PUNCT
ejpam-6529	159	25	∈	∈	PROPN
ejpam-6529	159	26	b∗	b∗	ADJ
ejpam-6529	159	27	,	,	PUNCT
ejpam-6529	159	28	ðx(y)(s2,t2	ðx(y)(s2,t2	ADJ
ejpam-6529	159	29	)	)	PUNCT
ejpam-6529	159	30	∈	∈	PROPN
ejpam-6529	159	31	b∗	b∗	ADJ
ejpam-6529	159	32	⇒	⇒	NOUN
ejpam-6529	159	33	y(min{s1,s2},max{t1,t2	y(min{s1,s2},max{t1,t2	NUM
ejpam-6529	159	34	}	}	PUNCT
ejpam-6529	159	35	)	)	PUNCT
ejpam-6529	160	1	∈	∈	PROPN
ejpam-6529	160	2	b∗	b∗	ADJ
ejpam-6529	160	3	(	(	PUNCT
ejpam-6529	160	4	24	24	NUM
ejpam-6529	160	5	)	)	PUNCT
ejpam-6529	160	6	for	for	ADP
ejpam-6529	160	7	all	all	DET
ejpam-6529	160	8	x	x	NOUN
ejpam-6529	160	9	,	,	PUNCT
ejpam-6529	160	10	y	y	PROPN
ejpam-6529	160	11	∈	∈	PROPN
ejpam-6529	160	12	x	x	X
ejpam-6529	160	13	and	and	CCONJ
ejpam-6529	160	14	(	(	PUNCT
ejpam-6529	160	15	s1	s1	NOUN
ejpam-6529	160	16	,	,	PUNCT
ejpam-6529	160	17	t1	t1	NOUN
ejpam-6529	160	18	)	)	PUNCT
ejpam-6529	160	19	,	,	PUNCT
ejpam-6529	160	20	(	(	PUNCT
ejpam-6529	160	21	s2	s2	PROPN
ejpam-6529	160	22	,	,	PUNCT
ejpam-6529	160	23	t2	t2	NOUN
ejpam-6529	160	24	)	)	PUNCT
ejpam-6529	160	25	∈	∈	PROPN
ejpam-6529	160	26	(	(	PUNCT
ejpam-6529	160	27	0	0	NUM
ejpam-6529	160	28	,	,	PUNCT
ejpam-6529	160	29	1]×	1]×	NUM
ejpam-6529	161	1	[	[	X
ejpam-6529	161	2	0	0	NUM
ejpam-6529	161	3	,	,	PUNCT
ejpam-6529	161	4	1	1	NUM
ejpam-6529	161	5	)	)	PUNCT
ejpam-6529	161	6	,	,	PUNCT
ejpam-6529	161	7	then	then	ADV
ejpam-6529	161	8	b∗	b∗	ADJ
ejpam-6529	161	9	:	:	PUNCT
ejpam-6529	161	10	=	=	SYM
ejpam-6529	161	11	(	(	PUNCT
ejpam-6529	161	12	x	x	X
ejpam-6529	161	13	;	;	PUNCT
ejpam-6529	161	14	fb	fb	INTJ
ejpam-6529	161	15	,	,	PUNCT
ejpam-6529	161	16	gb	gb	PROPN
ejpam-6529	161	17	)	)	PUNCT
ejpam-6529	161	18	is	be	AUX
ejpam-6529	161	19	an	an	DET
ejpam-6529	161	20	intuitionistic	intuitionistic	ADJ
ejpam-6529	161	21	fuzzy	fuzzy	ADJ
ejpam-6529	161	22	weak	weak	ADJ
ejpam-6529	161	23	filter	filter	NOUN
ejpam-6529	161	24	of	of	ADP
ejpam-6529	161	25	x	x	X
ejpam-6529	161	26	:	:	PUNCT
ejpam-6529	161	27	=	=	SYM
ejpam-6529	161	28	(	(	PUNCT
ejpam-6529	161	29	x	x	NOUN
ejpam-6529	161	30	,	,	PUNCT
ejpam-6529	161	31	|	|	NOUN
ejpam-6529	161	32	)	)	PUNCT
ejpam-6529	161	33	.	.	PUNCT
ejpam-6529	162	1	proof	proof	NOUN
ejpam-6529	162	2	.	.	PUNCT
ejpam-6529	163	1	let	let	VERB
ejpam-6529	163	2	b∗	b∗	ADV
ejpam-6529	163	3	:	:	PUNCT
ejpam-6529	163	4	=	=	SYM
ejpam-6529	163	5	(	(	PUNCT
ejpam-6529	163	6	x	x	X
ejpam-6529	163	7	;	;	PUNCT
ejpam-6529	163	8	fb	fb	INTJ
ejpam-6529	163	9	,	,	PUNCT
ejpam-6529	163	10	gb	gb	PROPN
ejpam-6529	163	11	)	)	PUNCT
ejpam-6529	163	12	be	be	VERB
ejpam-6529	163	13	an	an	DET
ejpam-6529	163	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	163	15	fuzzy	fuzzy	ADJ
ejpam-6529	163	16	set	set	NOUN
ejpam-6529	163	17	in	in	ADP
ejpam-6529	163	18	x	x	PUNCT
ejpam-6529	163	19	that	that	SCONJ
ejpam-6529	163	20	satisfies	satisfie	NOUN
ejpam-6529	163	21	(	(	PUNCT
ejpam-6529	163	22	20	20	NUM
ejpam-6529	163	23	)	)	PUNCT
ejpam-6529	163	24	and	and	CCONJ
ejpam-6529	163	25	(	(	PUNCT
ejpam-6529	163	26	24	24	NUM
ejpam-6529	163	27	)	)	PUNCT
ejpam-6529	163	28	.	.	PUNCT
ejpam-6529	164	1	we	we	PRON
ejpam-6529	164	2	first	first	ADV
ejpam-6529	164	3	show	show	VERB
ejpam-6529	164	4	that	that	SCONJ
ejpam-6529	164	5	the	the	DET
ejpam-6529	164	6	condition	condition	NOUN
ejpam-6529	164	7	(	(	PUNCT
ejpam-6529	164	8	24	24	NUM
ejpam-6529	164	9	)	)	PUNCT
ejpam-6529	164	10	is	be	AUX
ejpam-6529	164	11	equivalent	equivalent	ADJ
ejpam-6529	164	12	to	to	ADP
ejpam-6529	164	13	the	the	DET
ejpam-6529	164	14	following	follow	VERB
ejpam-6529	164	15	facts	fact	NOUN
ejpam-6529	164	16	.	.	PUNCT
ejpam-6529	165	1	(	(	PUNCT
ejpam-6529	165	2	∀x	∀x	X
ejpam-6529	165	3	,	,	PUNCT
ejpam-6529	165	4	y	y	PROPN
ejpam-6529	165	5	∈	∈	PROPN
ejpam-6529	165	6	x	x	X
ejpam-6529	165	7	)	)	PUNCT
ejpam-6529	165	8	(	(	PUNCT
ejpam-6529	165	9	fb(y	fb(y	CCONJ
ejpam-6529	165	10	)	)	PUNCT
ejpam-6529	165	11	≥	≥	NOUN
ejpam-6529	165	12	min{fb(x	min{fb(x	PROPN
ejpam-6529	165	13	)	)	PUNCT
ejpam-6529	165	14	,	,	PUNCT
ejpam-6529	165	15	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	165	16	)	)	PUNCT
ejpam-6529	165	17	)	)	PUNCT
ejpam-6529	165	18	}	}	PUNCT
ejpam-6529	165	19	gb(y	gb(y	ADV
ejpam-6529	165	20	)	)	PUNCT
ejpam-6529	165	21	≤	≤	NUM
ejpam-6529	165	22	max{gb(x	max{gb(x	PROPN
ejpam-6529	165	23	)	)	PUNCT
ejpam-6529	165	24	,	,	PUNCT
ejpam-6529	165	25	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	165	26	)	)	PUNCT
ejpam-6529	165	27	)	)	PUNCT
ejpam-6529	165	28	}	}	PUNCT
ejpam-6529	165	29	)	)	PUNCT
ejpam-6529	165	30	.	.	PUNCT
ejpam-6529	166	1	(	(	PUNCT
ejpam-6529	166	2	25	25	NUM
ejpam-6529	166	3	)	)	PUNCT
ejpam-6529	166	4	suppose	suppose	VERB
ejpam-6529	166	5	that	that	SCONJ
ejpam-6529	166	6	b∗	b∗	ADJ
ejpam-6529	166	7	:	:	PUNCT
ejpam-6529	166	8	=	=	SYM
ejpam-6529	166	9	(	(	PUNCT
ejpam-6529	166	10	x	x	X
ejpam-6529	166	11	;	;	PUNCT
ejpam-6529	166	12	fb	fb	INTJ
ejpam-6529	166	13	,	,	PUNCT
ejpam-6529	166	14	gb	gb	NOUN
ejpam-6529	166	15	)	)	PUNCT
ejpam-6529	166	16	satisfies	satisfie	NOUN
ejpam-6529	166	17	(	(	PUNCT
ejpam-6529	166	18	24	24	NUM
ejpam-6529	166	19	)	)	PUNCT
ejpam-6529	166	20	and	and	CCONJ
ejpam-6529	166	21	let	let	VERB
ejpam-6529	166	22	x	x	PRON
ejpam-6529	166	23	,	,	PUNCT
ejpam-6529	166	24	y	y	PROPN
ejpam-6529	166	25	∈	∈	PROPN
ejpam-6529	166	26	x.	x.	NOUN
ejpam-6529	167	1	if	if	SCONJ
ejpam-6529	167	2	we	we	PRON
ejpam-6529	167	3	take	take	VERB
ejpam-6529	167	4	(	(	PUNCT
ejpam-6529	167	5	s1	s1	NOUN
ejpam-6529	167	6	,	,	PUNCT
ejpam-6529	167	7	t1	t1	NOUN
ejpam-6529	167	8	)	)	PUNCT
ejpam-6529	167	9	=	=	SYM
ejpam-6529	167	10	(	(	PUNCT
ejpam-6529	167	11	fb(x	fb(x	NOUN
ejpam-6529	167	12	)	)	PUNCT
ejpam-6529	167	13	,	,	PUNCT
ejpam-6529	167	14	gb(x	gb(x	NUM
ejpam-6529	167	15	)	)	PUNCT
ejpam-6529	167	16	)	)	PUNCT
ejpam-6529	167	17	and	and	CCONJ
ejpam-6529	167	18	(	(	PUNCT
ejpam-6529	167	19	s2	s2	PROPN
ejpam-6529	167	20	,	,	PUNCT
ejpam-6529	167	21	t2	t2	NOUN
ejpam-6529	167	22	)	)	PUNCT
ejpam-6529	167	23	=	=	SYM
ejpam-6529	167	24	(	(	PUNCT
ejpam-6529	167	25	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	167	26	)	)	PUNCT
ejpam-6529	167	27	)	)	PUNCT
ejpam-6529	167	28	,	,	PUNCT
ejpam-6529	167	29	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	167	30	)	)	PUNCT
ejpam-6529	167	31	)	)	PUNCT
ejpam-6529	167	32	)	)	PUNCT
ejpam-6529	167	33	,	,	PUNCT
ejpam-6529	167	34	then	then	ADV
ejpam-6529	167	35	x(s1,t1	x(s1,t1	X
ejpam-6529	167	36	)	)	PUNCT
ejpam-6529	167	37	∈	∈	NOUN
ejpam-6529	167	38	b∗	b∗	ADJ
ejpam-6529	167	39	and	and	CCONJ
ejpam-6529	167	40	ðx(y)(s2,t2	ðx(y)(s2,t2	NUM
ejpam-6529	167	41	)	)	PUNCT
ejpam-6529	167	42	∈	∈	PROPN
ejpam-6529	167	43	b∗.	b∗.	NOUN
ejpam-6529	167	44	it	it	PRON
ejpam-6529	167	45	follows	follow	VERB
ejpam-6529	167	46	from	from	ADP
ejpam-6529	167	47	(	(	PUNCT
ejpam-6529	167	48	24	24	NUM
ejpam-6529	167	49	)	)	PUNCT
ejpam-6529	167	50	that	that	PRON
ejpam-6529	167	51	y(min{s1,s2},max{t1,t2	y(min{s1,s2},max{t1,t2	ADP
ejpam-6529	167	52	}	}	PUNCT
ejpam-6529	167	53	)	)	PUNCT
ejpam-6529	168	1	∈	∈	PROPN
ejpam-6529	168	2	b∗.	b∗.	NOUN
ejpam-6529	168	3	hence	hence	ADV
ejpam-6529	168	4	fb(y	fb(y	NUM
ejpam-6529	168	5	)	)	PUNCT
ejpam-6529	168	6	≥	≥	NOUN
ejpam-6529	168	7	min{s1	min{s1	NOUN
ejpam-6529	168	8	,	,	PUNCT
ejpam-6529	168	9	s2	s2	NOUN
ejpam-6529	168	10	}	}	PUNCT
ejpam-6529	168	11	=	=	SYM
ejpam-6529	168	12	min{fb(x	min{fb(x	PROPN
ejpam-6529	168	13	)	)	PUNCT
ejpam-6529	168	14	,	,	PUNCT
ejpam-6529	168	15	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	168	16	)	)	PUNCT
ejpam-6529	168	17	)	)	PUNCT
ejpam-6529	168	18	}	}	PUNCT
ejpam-6529	168	19	and	and	CCONJ
ejpam-6529	168	20	gb(y	gb(y	ADV
ejpam-6529	168	21	)	)	PUNCT
ejpam-6529	168	22	≤	≤	NOUN
ejpam-6529	168	23	max{t1	max{t1	NOUN
ejpam-6529	168	24	,	,	PUNCT
ejpam-6529	168	25	t2	t2	NOUN
ejpam-6529	168	26	}	}	PUNCT
ejpam-6529	168	27	=	=	SYM
ejpam-6529	168	28	max{gb(x	max{gb(x	PROPN
ejpam-6529	168	29	)	)	PUNCT
ejpam-6529	168	30	,	,	PUNCT
ejpam-6529	168	31	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	168	32	)	)	PUNCT
ejpam-6529	168	33	)	)	PUNCT
ejpam-6529	168	34	}	}	PUNCT
ejpam-6529	168	35	.	.	PUNCT
ejpam-6529	169	1	now	now	ADV
ejpam-6529	169	2	,	,	PUNCT
ejpam-6529	169	3	assume	assume	VERB
ejpam-6529	169	4	that	that	SCONJ
ejpam-6529	169	5	(	(	PUNCT
ejpam-6529	169	6	25	25	NUM
ejpam-6529	169	7	)	)	PUNCT
ejpam-6529	169	8	is	be	AUX
ejpam-6529	169	9	valid	valid	ADJ
ejpam-6529	169	10	and	and	CCONJ
ejpam-6529	169	11	let	let	VERB
ejpam-6529	169	12	x(s1,t1	x(s1,t1	PROPN
ejpam-6529	169	13	)	)	PUNCT
ejpam-6529	169	14	∈	∈	NOUN
ejpam-6529	170	1	b∗	b∗	ADJ
ejpam-6529	170	2	and	and	CCONJ
ejpam-6529	170	3	ðx(y)(s2,t2	ðx(y)(s2,t2	NUM
ejpam-6529	170	4	)	)	PUNCT
ejpam-6529	170	5	∈	∈	NOUN
ejpam-6529	170	6	b∗	b∗	ADJ
ejpam-6529	170	7	for	for	ADP
ejpam-6529	170	8	all	all	DET
ejpam-6529	170	9	(	(	PUNCT
ejpam-6529	170	10	s1	s1	PROPN
ejpam-6529	170	11	,	,	PUNCT
ejpam-6529	170	12	t1	t1	NOUN
ejpam-6529	170	13	)	)	PUNCT
ejpam-6529	170	14	,	,	PUNCT
ejpam-6529	170	15	(	(	PUNCT
ejpam-6529	170	16	s2	s2	PROPN
ejpam-6529	170	17	,	,	PUNCT
ejpam-6529	170	18	t2	t2	NOUN
ejpam-6529	170	19	)	)	PUNCT
ejpam-6529	170	20	∈	∈	PROPN
ejpam-6529	170	21	(	(	PUNCT
ejpam-6529	170	22	0	0	NUM
ejpam-6529	170	23	,	,	PUNCT
ejpam-6529	170	24	1	1	NUM
ejpam-6529	170	25	]	]	SYM
ejpam-6529	170	26	×	×	NOUN
ejpam-6529	171	1	[	[	X
ejpam-6529	171	2	0	0	NUM
ejpam-6529	171	3	,	,	PUNCT
ejpam-6529	171	4	1	1	NUM
ejpam-6529	171	5	)	)	PUNCT
ejpam-6529	171	6	.	.	PUNCT
ejpam-6529	172	1	then	then	ADV
ejpam-6529	172	2	fb(x	fb(x	NOUN
ejpam-6529	172	3	)	)	PUNCT
ejpam-6529	172	4	≥	≥	NOUN
ejpam-6529	172	5	s1	s1	NOUN
ejpam-6529	172	6	,	,	PUNCT
ejpam-6529	172	7	gb(x	gb(x	NUM
ejpam-6529	172	8	)	)	PUNCT
ejpam-6529	172	9	≤	≤	NOUN
ejpam-6529	172	10	t1	t1	PROPN
ejpam-6529	172	11	,	,	PUNCT
ejpam-6529	172	12	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	172	13	)	)	PUNCT
ejpam-6529	172	14	)	)	PUNCT
ejpam-6529	172	15	≥	≥	NUM
ejpam-6529	172	16	s2	s2	PROPN
ejpam-6529	172	17	,	,	PUNCT
ejpam-6529	172	18	and	and	CCONJ
ejpam-6529	172	19	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	172	20	)	)	PUNCT
ejpam-6529	172	21	)	)	PUNCT
ejpam-6529	172	22	≤	≤	NUM
ejpam-6529	172	23	t2	t2	NOUN
ejpam-6529	172	24	.	.	PUNCT
ejpam-6529	173	1	using	use	VERB
ejpam-6529	173	2	(	(	PUNCT
ejpam-6529	173	3	25	25	NUM
ejpam-6529	173	4	)	)	PUNCT
ejpam-6529	173	5	,	,	PUNCT
ejpam-6529	173	6	we	we	PRON
ejpam-6529	173	7	have	have	VERB
ejpam-6529	173	8	fb(y	fb(y	VERB
ejpam-6529	173	9	)	)	PUNCT
ejpam-6529	173	10	≥	≥	NOUN
ejpam-6529	173	11	min{fb(x	min{fb(x	PROPN
ejpam-6529	173	12	)	)	PUNCT
ejpam-6529	173	13	,	,	PUNCT
ejpam-6529	173	14	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	173	15	)	)	PUNCT
ejpam-6529	173	16	)	)	PUNCT
ejpam-6529	173	17	}	}	PUNCT
ejpam-6529	173	18	≥	≥	NOUN
ejpam-6529	173	19	min{s1	min{s1	NOUN
ejpam-6529	173	20	,	,	PUNCT
ejpam-6529	173	21	s2	s2	PROPN
ejpam-6529	173	22	}	}	PUNCT
ejpam-6529	173	23	s.	s.	PROPN
ejpam-6529	173	24	s.	s.	PROPN
ejpam-6529	173	25	ahn	ahn	PROPN
ejpam-6529	173	26	,	,	PUNCT
ejpam-6529	173	27	y.	y.	PROPN
ejpam-6529	173	28	j.	j.	PROPN
ejpam-6529	173	29	seo	seo	PROPN
ejpam-6529	173	30	,	,	PUNCT
ejpam-6529	173	31	y.	y.	PROPN
ejpam-6529	173	32	b.	b.	PROPN
ejpam-6529	173	33	jun	jun	PROPN
ejpam-6529	173	34	/	/	SYM
ejpam-6529	173	35	eur	eur	PROPN
ejpam-6529	173	36	.	.	PUNCT
ejpam-6529	174	1	j.	j.	PROPN
ejpam-6529	174	2	pure	pure	PROPN
ejpam-6529	174	3	appl	appl	PROPN
ejpam-6529	174	4	.	.	PROPN
ejpam-6529	174	5	math	math	PROPN
ejpam-6529	174	6	,	,	PUNCT
ejpam-6529	174	7	18	18	NUM
ejpam-6529	174	8	(	(	PUNCT
ejpam-6529	174	9	3	3	NUM
ejpam-6529	174	10	)	)	PUNCT
ejpam-6529	174	11	(	(	PUNCT
ejpam-6529	174	12	2025	2025	NUM
ejpam-6529	174	13	)	)	PUNCT
ejpam-6529	174	14	,	,	PUNCT
ejpam-6529	174	15	6529	6529	NUM
ejpam-6529	174	16	8	8	NUM
ejpam-6529	174	17	of	of	ADP
ejpam-6529	174	18	16	16	NUM
ejpam-6529	174	19	and	and	CCONJ
ejpam-6529	174	20	gb(y	gb(y	NOUN
ejpam-6529	174	21	)	)	PUNCT
ejpam-6529	174	22	≤	≤	NUM
ejpam-6529	174	23	max{gb(x	max{gb(x	PROPN
ejpam-6529	174	24	)	)	PUNCT
ejpam-6529	174	25	,	,	PUNCT
ejpam-6529	174	26	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	174	27	)	)	PUNCT
ejpam-6529	174	28	)	)	PUNCT
ejpam-6529	174	29	}	}	PUNCT
ejpam-6529	174	30	≤	≤	NUM
ejpam-6529	174	31	max{t1	max{t1	NOUN
ejpam-6529	174	32	,	,	PUNCT
ejpam-6529	174	33	t2	t2	NOUN
ejpam-6529	174	34	}	}	PUNCT
ejpam-6529	174	35	.	.	PUNCT
ejpam-6529	175	1	hence	hence	ADV
ejpam-6529	175	2	y(min{s1,s2},max{t1,t2	y(min{s1,s2},max{t1,t2	NUM
ejpam-6529	175	3	}	}	PUNCT
ejpam-6529	175	4	)	)	PUNCT
ejpam-6529	175	5	∈	∈	PROPN
ejpam-6529	176	1	b∗	b∗	ADJ
ejpam-6529	176	2	,	,	PUNCT
ejpam-6529	176	3	and	and	CCONJ
ejpam-6529	176	4	therefore	therefore	ADV
ejpam-6529	176	5	(	(	PUNCT
ejpam-6529	176	6	24	24	NUM
ejpam-6529	176	7	)	)	PUNCT
ejpam-6529	176	8	is	be	AUX
ejpam-6529	176	9	valid	valid	ADJ
ejpam-6529	176	10	.	.	PUNCT
ejpam-6529	177	1	the	the	DET
ejpam-6529	177	2	combination	combination	NOUN
ejpam-6529	177	3	of	of	ADP
ejpam-6529	177	4	(	(	PUNCT
ejpam-6529	177	5	1	1	NUM
ejpam-6529	177	6	)	)	PUNCT
ejpam-6529	177	7	and	and	CCONJ
ejpam-6529	177	8	(	(	PUNCT
ejpam-6529	177	9	3	3	X
ejpam-6529	177	10	)	)	PUNCT
ejpam-6529	177	11	induces	induce	VERB
ejpam-6529	177	12	y|(ðx(y)|ðx(y	y|(ðx(y)|ðx(y	PROPN
ejpam-6529	177	13	)	)	PUNCT
ejpam-6529	177	14	)	)	PUNCT
ejpam-6529	178	1	=	=	SYM
ejpam-6529	178	2	1	1	NUM
ejpam-6529	178	3	for	for	ADP
ejpam-6529	178	4	all	all	DET
ejpam-6529	178	5	x	x	NOUN
ejpam-6529	178	6	,	,	PUNCT
ejpam-6529	178	7	y	y	PROPN
ejpam-6529	178	8	∈	∈	PROPN
ejpam-6529	178	9	x.	x.	NOUN
ejpam-6529	179	1	it	it	PRON
ejpam-6529	179	2	follows	follow	VERB
ejpam-6529	179	3	from	from	ADP
ejpam-6529	179	4	(	(	PUNCT
ejpam-6529	179	5	22	22	NUM
ejpam-6529	179	6	)	)	PUNCT
ejpam-6529	179	7	and	and	CCONJ
ejpam-6529	179	8	(	(	PUNCT
ejpam-6529	179	9	25	25	NUM
ejpam-6529	179	10	)	)	PUNCT
ejpam-6529	179	11	that	that	DET
ejpam-6529	179	12	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	179	13	)	)	PUNCT
ejpam-6529	179	14	)	)	PUNCT
ejpam-6529	179	15	≥	≥	NOUN
ejpam-6529	179	16	min{fb(y	min{fb(y	NUM
ejpam-6529	179	17	)	)	PUNCT
ejpam-6529	179	18	,	,	PUNCT
ejpam-6529	179	19	fb(y|(ðx(y)|ðx(y	fb(y|(ðx(y)|ðx(y	NOUN
ejpam-6529	179	20	)	)	PUNCT
ejpam-6529	179	21	)	)	PUNCT
ejpam-6529	179	22	)	)	PUNCT
ejpam-6529	179	23	}	}	PUNCT
ejpam-6529	180	1	=	=	SYM
ejpam-6529	180	2	min{fb(y	min{fb(y	PROPN
ejpam-6529	180	3	)	)	PUNCT
ejpam-6529	180	4	,	,	PUNCT
ejpam-6529	180	5	fb(1	fb(1	PROPN
ejpam-6529	180	6	)	)	PUNCT
ejpam-6529	180	7	}	}	PUNCT
ejpam-6529	180	8	=	=	PUNCT
ejpam-6529	180	9	fb(y	fb(y	NUM
ejpam-6529	180	10	)	)	PUNCT
ejpam-6529	180	11	and	and	CCONJ
ejpam-6529	180	12	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	180	13	)	)	PUNCT
ejpam-6529	180	14	)	)	PUNCT
ejpam-6529	181	1	≤	≤	NUM
ejpam-6529	181	2	max{gb(y	max{gb(y	PROPN
ejpam-6529	181	3	)	)	PUNCT
ejpam-6529	181	4	,	,	PUNCT
ejpam-6529	181	5	gb(y|(ðx(y)|ðx(y	gb(y|(ðx(y)|ðx(y	NOUN
ejpam-6529	181	6	)	)	PUNCT
ejpam-6529	181	7	)	)	PUNCT
ejpam-6529	181	8	)	)	PUNCT
ejpam-6529	181	9	}	}	PUNCT
ejpam-6529	181	10	=	=	SYM
ejpam-6529	181	11	max{gb(y	max{gb(y	PROPN
ejpam-6529	181	12	)	)	PUNCT
ejpam-6529	181	13	,	,	PUNCT
ejpam-6529	181	14	gb(1	gb(1	PROPN
ejpam-6529	181	15	)	)	PUNCT
ejpam-6529	181	16	}	}	PUNCT
ejpam-6529	181	17	=	=	PUNCT
ejpam-6529	182	1	gb(y	gb(y	X
ejpam-6529	182	2	)	)	PUNCT
ejpam-6529	182	3	for	for	ADP
ejpam-6529	182	4	all	all	DET
ejpam-6529	182	5	x	x	NOUN
ejpam-6529	182	6	,	,	PUNCT
ejpam-6529	182	7	y	y	PROPN
ejpam-6529	182	8	∈	∈	PROPN
ejpam-6529	182	9	x.	x.	NOUN
ejpam-6529	182	10	therefore	therefore	ADV
ejpam-6529	182	11	b∗	b∗	ADJ
ejpam-6529	182	12	:	:	PUNCT
ejpam-6529	182	13	=	=	SYM
ejpam-6529	182	14	(	(	PUNCT
ejpam-6529	182	15	x	x	X
ejpam-6529	182	16	;	;	PUNCT
ejpam-6529	182	17	fb	fb	INTJ
ejpam-6529	182	18	,	,	PUNCT
ejpam-6529	182	19	gb	gb	PROPN
ejpam-6529	182	20	)	)	PUNCT
ejpam-6529	182	21	is	be	AUX
ejpam-6529	182	22	an	an	DET
ejpam-6529	182	23	intuitionistic	intuitionistic	ADJ
ejpam-6529	182	24	fuzzy	fuzzy	ADJ
ejpam-6529	182	25	weak	weak	ADJ
ejpam-6529	182	26	filter	filter	NOUN
ejpam-6529	182	27	of	of	ADP
ejpam-6529	182	28	x	x	X
ejpam-6529	182	29	:	:	PUNCT
ejpam-6529	182	30	=	=	SYM
ejpam-6529	182	31	(	(	PUNCT
ejpam-6529	182	32	x	x	NOUN
ejpam-6529	182	33	,	,	PUNCT
ejpam-6529	182	34	|	|	ADV
ejpam-6529	182	35	)	)	PUNCT
ejpam-6529	182	36	by	by	ADP
ejpam-6529	182	37	theorem	theorem	NOUN
ejpam-6529	182	38	1	1	NUM
ejpam-6529	182	39	.	.	PUNCT
ejpam-6529	183	1	in	in	ADP
ejpam-6529	183	2	the	the	DET
ejpam-6529	183	3	following	following	NOUN
ejpam-6529	183	4	theorem	theorem	NOUN
ejpam-6529	183	5	,	,	PUNCT
ejpam-6529	183	6	we	we	PRON
ejpam-6529	183	7	use	use	VERB
ejpam-6529	183	8	weak	weak	ADJ
ejpam-6529	183	9	filters	filter	NOUN
ejpam-6529	183	10	to	to	PART
ejpam-6529	183	11	form	form	VERB
ejpam-6529	183	12	intuitionistic	intuitionistic	ADJ
ejpam-6529	183	13	fuzzy	fuzzy	ADJ
ejpam-6529	183	14	weak	weak	ADJ
ejpam-6529	183	15	filters	filter	NOUN
ejpam-6529	183	16	.	.	PUNCT
ejpam-6529	184	1	theorem	theorem	ADJ
ejpam-6529	184	2	4	4	NUM
ejpam-6529	184	3	.	.	PUNCT
ejpam-6529	185	1	for	for	ADP
ejpam-6529	185	2	every	every	DET
ejpam-6529	185	3	nonempty	nonempty	NOUN
ejpam-6529	185	4	subset	subset	VERB
ejpam-6529	185	5	f	f	PROPN
ejpam-6529	185	6	of	of	ADP
ejpam-6529	185	7	x	x	PRON
ejpam-6529	185	8	,	,	PUNCT
ejpam-6529	185	9	consider	consider	VERB
ejpam-6529	185	10	an	an	DET
ejpam-6529	185	11	intuitionistic	intuitionistic	ADJ
ejpam-6529	185	12	fuzzy	fuzzy	ADJ
ejpam-6529	185	13	set	set	VERB
ejpam-6529	185	14	b∗	b∗	ADJ
ejpam-6529	185	15	f	f	X
ejpam-6529	186	1	:	:	PUNCT
ejpam-6529	186	2	=	=	SYM
ejpam-6529	186	3	(	(	PUNCT
ejpam-6529	186	4	x	x	X
ejpam-6529	186	5	;	;	PUNCT
ejpam-6529	186	6	ff	ff	PROPN
ejpam-6529	186	7	b	b	PROPN
ejpam-6529	186	8	,	,	PUNCT
ejpam-6529	186	9	gfb	gfb	PROPN
ejpam-6529	186	10	)	)	PUNCT
ejpam-6529	186	11	in	in	ADP
ejpam-6529	186	12	x	x	PUNCT
ejpam-6529	186	13	which	which	PRON
ejpam-6529	186	14	is	be	AUX
ejpam-6529	186	15	given	give	VERB
ejpam-6529	186	16	by	by	ADP
ejpam-6529	186	17	b∗	b∗	ADJ
ejpam-6529	186	18	f	f	NOUN
ejpam-6529	186	19	:	:	PUNCT
ejpam-6529	186	20	=	=	SYM
ejpam-6529	186	21	(	(	PUNCT
ejpam-6529	186	22	x	x	X
ejpam-6529	186	23	;	;	PUNCT
ejpam-6529	186	24	ff	ff	PROPN
ejpam-6529	186	25	b	b	PROPN
ejpam-6529	186	26	,	,	PUNCT
ejpam-6529	186	27	gfb	gfb	PROPN
ejpam-6529	186	28	)	)	PUNCT
ejpam-6529	186	29	:	:	PUNCT
ejpam-6529	187	1	x	x	X
ejpam-6529	187	2	→	→	PUNCT
ejpam-6529	188	1	[	[	X
ejpam-6529	188	2	0	0	NUM
ejpam-6529	188	3	,	,	PUNCT
ejpam-6529	188	4	1]×	1]×	NUM
ejpam-6529	188	5	[	[	X
ejpam-6529	188	6	0	0	NUM
ejpam-6529	188	7	,	,	PUNCT
ejpam-6529	188	8	1	1	NUM
ejpam-6529	188	9	]	]	PUNCT
ejpam-6529	188	10	,	,	PUNCT
ejpam-6529	188	11	x	x	SYM
ejpam-6529	188	12	7→	7→	NUM
ejpam-6529	188	13	{	{	PUNCT
ejpam-6529	188	14	(	(	PUNCT
ejpam-6529	188	15	s1	s1	NOUN
ejpam-6529	188	16	,	,	PUNCT
ejpam-6529	188	17	t1	t1	NOUN
ejpam-6529	188	18	)	)	PUNCT
ejpam-6529	188	19	if	if	SCONJ
ejpam-6529	188	20	x	x	SYM
ejpam-6529	188	21	∈	∈	PROPN
ejpam-6529	188	22	f	f	PROPN
ejpam-6529	188	23	,	,	PUNCT
ejpam-6529	188	24	(	(	PUNCT
ejpam-6529	188	25	s2	s2	PROPN
ejpam-6529	188	26	,	,	PUNCT
ejpam-6529	188	27	t2	t2	NOUN
ejpam-6529	188	28	)	)	PUNCT
ejpam-6529	188	29	otherwise	otherwise	ADV
ejpam-6529	188	30	where	where	SCONJ
ejpam-6529	188	31	(	(	PUNCT
ejpam-6529	188	32	s1	s1	NOUN
ejpam-6529	188	33	,	,	PUNCT
ejpam-6529	188	34	t1	t1	NOUN
ejpam-6529	188	35	)	)	PUNCT
ejpam-6529	188	36	,	,	PUNCT
ejpam-6529	188	37	(	(	PUNCT
ejpam-6529	188	38	s2	s2	PROPN
ejpam-6529	188	39	,	,	PUNCT
ejpam-6529	188	40	t2	t2	NOUN
ejpam-6529	188	41	)	)	PUNCT
ejpam-6529	188	42	∈	∈	PROPN
ejpam-6529	188	43	(	(	PUNCT
ejpam-6529	188	44	0	0	NUM
ejpam-6529	188	45	,	,	PUNCT
ejpam-6529	188	46	1	1	NUM
ejpam-6529	188	47	]	]	SYM
ejpam-6529	188	48	×	×	NOUN
ejpam-6529	188	49	[	[	X
ejpam-6529	188	50	0	0	NUM
ejpam-6529	188	51	,	,	PUNCT
ejpam-6529	188	52	1	1	NUM
ejpam-6529	188	53	)	)	PUNCT
ejpam-6529	188	54	with	with	ADP
ejpam-6529	188	55	s1	s1	PROPN
ejpam-6529	188	56	>	>	X
ejpam-6529	188	57	s2	s2	PROPN
ejpam-6529	188	58	and	and	CCONJ
ejpam-6529	188	59	t1	t1	VERB
ejpam-6529	188	60	<	<	X
ejpam-6529	188	61	t2	t2	PROPN
ejpam-6529	188	62	.	.	PUNCT
ejpam-6529	189	1	then	then	ADV
ejpam-6529	189	2	b∗	b∗	ADV
ejpam-6529	189	3	f	f	X
ejpam-6529	189	4	:	:	PUNCT
ejpam-6529	189	5	=	=	SYM
ejpam-6529	189	6	(	(	PUNCT
ejpam-6529	189	7	x	x	X
ejpam-6529	189	8	;	;	PUNCT
ejpam-6529	189	9	ff	ff	PROPN
ejpam-6529	189	10	b	b	PROPN
ejpam-6529	189	11	,	,	PUNCT
ejpam-6529	189	12	gfb	gfb	PROPN
ejpam-6529	189	13	)	)	PUNCT
ejpam-6529	189	14	is	be	AUX
ejpam-6529	189	15	an	an	DET
ejpam-6529	189	16	intuitionistic	intuitionistic	ADJ
ejpam-6529	189	17	fuzzy	fuzzy	ADJ
ejpam-6529	189	18	weak	weak	ADJ
ejpam-6529	189	19	filter	filter	NOUN
ejpam-6529	189	20	of	of	ADP
ejpam-6529	189	21	x	x	X
ejpam-6529	189	22	:	:	PUNCT
ejpam-6529	189	23	=	=	SYM
ejpam-6529	189	24	(	(	PUNCT
ejpam-6529	189	25	x	x	NOUN
ejpam-6529	189	26	,	,	PUNCT
ejpam-6529	189	27	|	|	INTJ
ejpam-6529	189	28	)	)	PUNCT
ejpam-6529	189	29	if	if	SCONJ
ejpam-6529	189	30	and	and	CCONJ
ejpam-6529	189	31	only	only	ADV
ejpam-6529	189	32	if	if	SCONJ
ejpam-6529	189	33	f	f	PROPN
ejpam-6529	189	34	is	be	AUX
ejpam-6529	189	35	a	a	DET
ejpam-6529	189	36	weak	weak	ADJ
ejpam-6529	189	37	filter	filter	NOUN
ejpam-6529	189	38	of	of	ADP
ejpam-6529	189	39	x	x	X
ejpam-6529	189	40	:	:	PUNCT
ejpam-6529	189	41	=	=	SYM
ejpam-6529	189	42	(	(	PUNCT
ejpam-6529	189	43	x	x	NOUN
ejpam-6529	189	44	,	,	PUNCT
ejpam-6529	189	45	|	|	NOUN
ejpam-6529	189	46	)	)	PUNCT
ejpam-6529	189	47	.	.	PUNCT
ejpam-6529	190	1	proof	proof	NOUN
ejpam-6529	190	2	.	.	PUNCT
ejpam-6529	191	1	let	let	VERB
ejpam-6529	191	2	(	(	PUNCT
ejpam-6529	191	3	s1	s1	NOUN
ejpam-6529	191	4	,	,	PUNCT
ejpam-6529	191	5	t1	t1	NOUN
ejpam-6529	191	6	)	)	PUNCT
ejpam-6529	191	7	,	,	PUNCT
ejpam-6529	191	8	(	(	PUNCT
ejpam-6529	191	9	s2	s2	PROPN
ejpam-6529	191	10	,	,	PUNCT
ejpam-6529	191	11	t2	t2	NOUN
ejpam-6529	191	12	)	)	PUNCT
ejpam-6529	191	13	∈	∈	PROPN
ejpam-6529	191	14	(	(	PUNCT
ejpam-6529	191	15	0	0	NUM
ejpam-6529	191	16	,	,	PUNCT
ejpam-6529	191	17	1]×[0	1]×[0	NUM
ejpam-6529	191	18	,	,	PUNCT
ejpam-6529	191	19	1	1	NUM
ejpam-6529	191	20	)	)	PUNCT
ejpam-6529	191	21	be	be	AUX
ejpam-6529	191	22	such	such	ADJ
ejpam-6529	191	23	that	that	SCONJ
ejpam-6529	191	24	s1	s1	PROPN
ejpam-6529	191	25	>	>	X
ejpam-6529	191	26	s2	s2	PROPN
ejpam-6529	191	27	and	and	CCONJ
ejpam-6529	191	28	t1	t1	VERB
ejpam-6529	191	29	<	<	X
ejpam-6529	191	30	t2	t2	PROPN
ejpam-6529	191	31	.	.	PUNCT
ejpam-6529	192	1	suppose	suppose	VERB
ejpam-6529	192	2	that	that	SCONJ
ejpam-6529	192	3	b∗	b∗	ADJ
ejpam-6529	192	4	f	f	X
ejpam-6529	193	1	:	:	PUNCT
ejpam-6529	193	2	=	=	SYM
ejpam-6529	193	3	(	(	PUNCT
ejpam-6529	193	4	x	x	X
ejpam-6529	193	5	;	;	PUNCT
ejpam-6529	193	6	ff	ff	PROPN
ejpam-6529	193	7	b	b	PROPN
ejpam-6529	193	8	,	,	PUNCT
ejpam-6529	193	9	gfb	gfb	PROPN
ejpam-6529	193	10	)	)	PUNCT
ejpam-6529	193	11	is	be	AUX
ejpam-6529	193	12	an	an	DET
ejpam-6529	193	13	intuitionistic	intuitionistic	ADJ
ejpam-6529	193	14	fuzzy	fuzzy	ADJ
ejpam-6529	193	15	weak	weak	ADJ
ejpam-6529	193	16	filter	filter	NOUN
ejpam-6529	193	17	of	of	ADP
ejpam-6529	193	18	x	x	X
ejpam-6529	193	19	:	:	PUNCT
ejpam-6529	193	20	=	=	SYM
ejpam-6529	193	21	(	(	PUNCT
ejpam-6529	193	22	x	x	NOUN
ejpam-6529	193	23	,	,	PUNCT
ejpam-6529	193	24	|	|	NOUN
ejpam-6529	193	25	)	)	PUNCT
ejpam-6529	193	26	.	.	PUNCT
ejpam-6529	194	1	since	since	SCONJ
ejpam-6529	194	2	fb(1	fb(1	PROPN
ejpam-6529	194	3	)	)	PUNCT
ejpam-6529	194	4	=	=	NOUN
ejpam-6529	194	5	s1	s1	PROPN
ejpam-6529	194	6	and	and	CCONJ
ejpam-6529	194	7	gb(1	gb(1	PROPN
ejpam-6529	194	8	)	)	PUNCT
ejpam-6529	194	9	=	=	PUNCT
ejpam-6529	194	10	t1	t1	NOUN
ejpam-6529	194	11	by	by	ADP
ejpam-6529	194	12	(	(	PUNCT
ejpam-6529	194	13	22	22	NUM
ejpam-6529	194	14	)	)	PUNCT
ejpam-6529	194	15	,	,	PUNCT
ejpam-6529	194	16	we	we	PRON
ejpam-6529	194	17	have	have	VERB
ejpam-6529	194	18	1	1	NUM
ejpam-6529	194	19	∈	∈	PROPN
ejpam-6529	194	20	f	f	NOUN
ejpam-6529	194	21	.	.	PUNCT
ejpam-6529	195	1	let	let	VERB
ejpam-6529	195	2	x	x	PUNCT
ejpam-6529	195	3	∈	∈	PROPN
ejpam-6529	195	4	x	x	X
ejpam-6529	195	5	and	and	CCONJ
ejpam-6529	195	6	y	y	PROPN
ejpam-6529	195	7	∈	∈	PROPN
ejpam-6529	195	8	f	f	X
ejpam-6529	195	9	.	.	PUNCT
ejpam-6529	196	1	using	use	VERB
ejpam-6529	196	2	(	(	PUNCT
ejpam-6529	196	3	23	23	NUM
ejpam-6529	196	4	)	)	PUNCT
ejpam-6529	196	5	,	,	PUNCT
ejpam-6529	196	6	we	we	PRON
ejpam-6529	196	7	have	have	VERB
ejpam-6529	196	8	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	196	9	)	)	PUNCT
ejpam-6529	196	10	)	)	PUNCT
ejpam-6529	196	11	≥	≥	NOUN
ejpam-6529	196	12	fb(y	fb(y	NUM
ejpam-6529	196	13	)	)	PUNCT
ejpam-6529	197	1	=	=	SYM
ejpam-6529	197	2	s1	s1	NOUN
ejpam-6529	197	3	and	and	CCONJ
ejpam-6529	197	4	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	197	5	)	)	PUNCT
ejpam-6529	197	6	)	)	PUNCT
ejpam-6529	197	7	≤	≤	NOUN
ejpam-6529	197	8	gb(y	gb(y	ADV
ejpam-6529	197	9	)	)	PUNCT
ejpam-6529	197	10	=	=	SYM
ejpam-6529	197	11	t1	t1	NOUN
ejpam-6529	197	12	.	.	PUNCT
ejpam-6529	198	1	thus	thus	ADV
ejpam-6529	198	2	fb(ðx(y	fb(ðx(y	X
ejpam-6529	198	3	)	)	PUNCT
ejpam-6529	198	4	)	)	PUNCT
ejpam-6529	199	1	=	=	SYM
ejpam-6529	199	2	s1	s1	NOUN
ejpam-6529	199	3	and	and	CCONJ
ejpam-6529	199	4	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	199	5	)	)	PUNCT
ejpam-6529	199	6	)	)	PUNCT
ejpam-6529	200	1	=	=	PUNCT
ejpam-6529	200	2	t1	t1	NOUN
ejpam-6529	200	3	which	which	PRON
ejpam-6529	200	4	shows	show	VERB
ejpam-6529	200	5	that	that	SCONJ
ejpam-6529	200	6	ðx(y	ðx(y	PUNCT
ejpam-6529	200	7	)	)	PUNCT
ejpam-6529	201	1	∈	∈	PROPN
ejpam-6529	201	2	f	f	X
ejpam-6529	201	3	.	.	PUNCT
ejpam-6529	202	1	hence	hence	ADV
ejpam-6529	202	2	f	f	PROPN
ejpam-6529	202	3	is	be	AUX
ejpam-6529	202	4	a	a	DET
ejpam-6529	202	5	weak	weak	ADJ
ejpam-6529	202	6	filter	filter	NOUN
ejpam-6529	202	7	of	of	ADP
ejpam-6529	202	8	x	x	X
ejpam-6529	202	9	:	:	PUNCT
ejpam-6529	202	10	=	=	SYM
ejpam-6529	202	11	(	(	PUNCT
ejpam-6529	202	12	x	x	NOUN
ejpam-6529	202	13	,	,	PUNCT
ejpam-6529	202	14	|	|	NOUN
ejpam-6529	202	15	)	)	PUNCT
ejpam-6529	202	16	.	.	PUNCT
ejpam-6529	203	1	conversely	conversely	ADV
ejpam-6529	203	2	,	,	PUNCT
ejpam-6529	203	3	assume	assume	VERB
ejpam-6529	203	4	that	that	SCONJ
ejpam-6529	203	5	f	f	PROPN
ejpam-6529	203	6	is	be	AUX
ejpam-6529	203	7	a	a	DET
ejpam-6529	203	8	weak	weak	ADJ
ejpam-6529	203	9	filter	filter	NOUN
ejpam-6529	203	10	of	of	ADP
ejpam-6529	203	11	x	x	X
ejpam-6529	203	12	:	:	PUNCT
ejpam-6529	203	13	=	=	SYM
ejpam-6529	203	14	(	(	PUNCT
ejpam-6529	203	15	x	x	NOUN
ejpam-6529	203	16	,	,	PUNCT
ejpam-6529	203	17	|	|	NOUN
ejpam-6529	203	18	)	)	PUNCT
ejpam-6529	203	19	.	.	PUNCT
ejpam-6529	204	1	then	then	ADV
ejpam-6529	204	2	1	1	NUM
ejpam-6529	204	3	∈	∈	NOUN
ejpam-6529	204	4	f	f	NOUN
ejpam-6529	204	5	,	,	PUNCT
ejpam-6529	204	6	and	and	CCONJ
ejpam-6529	204	7	so	so	ADV
ejpam-6529	204	8	fb(1	fb(1	PROPN
ejpam-6529	204	9	)	)	PUNCT
ejpam-6529	204	10	=	=	SYM
ejpam-6529	204	11	s1	s1	PROPN
ejpam-6529	204	12	≥	≥	NUM
ejpam-6529	204	13	fb(x	fb(x	PUNCT
ejpam-6529	204	14	)	)	PUNCT
ejpam-6529	204	15	and	and	CCONJ
ejpam-6529	204	16	gb(1	gb(1	PROPN
ejpam-6529	204	17	)	)	PUNCT
ejpam-6529	204	18	=	=	PUNCT
ejpam-6529	205	1	t1	t1	NOUN
ejpam-6529	205	2	≤	≤	NUM
ejpam-6529	205	3	gb(x	gb(x	PUNCT
ejpam-6529	205	4	)	)	PUNCT
ejpam-6529	205	5	for	for	ADP
ejpam-6529	205	6	all	all	PRON
ejpam-6529	205	7	x	x	SYM
ejpam-6529	205	8	∈	∈	NOUN
ejpam-6529	205	9	x.	x.	NOUN
ejpam-6529	205	10	let	let	VERB
ejpam-6529	205	11	x	x	PRON
ejpam-6529	205	12	,	,	PUNCT
ejpam-6529	205	13	y	y	PROPN
ejpam-6529	205	14	∈	∈	PROPN
ejpam-6529	205	15	x.	x.	NOUN
ejpam-6529	206	1	if	if	SCONJ
ejpam-6529	206	2	y	y	PROPN
ejpam-6529	206	3	/∈	/∈	PROPN
ejpam-6529	207	1	f	f	PROPN
ejpam-6529	207	2	,	,	PUNCT
ejpam-6529	207	3	then	then	ADV
ejpam-6529	207	4	fb(y	fb(y	X
ejpam-6529	207	5	)	)	PUNCT
ejpam-6529	207	6	=	=	SYM
ejpam-6529	207	7	s2	s2	VERB
ejpam-6529	207	8	≤	≤	ADJ
ejpam-6529	207	9	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	207	10	)	)	PUNCT
ejpam-6529	207	11	)	)	PUNCT
ejpam-6529	207	12	and	and	CCONJ
ejpam-6529	207	13	gb(y	gb(y	ADV
ejpam-6529	207	14	)	)	PUNCT
ejpam-6529	208	1	=	=	SYM
ejpam-6529	208	2	t2	t2	PROPN
ejpam-6529	208	3	≥	≥	NUM
ejpam-6529	208	4	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	208	5	)	)	PUNCT
ejpam-6529	208	6	)	)	PUNCT
ejpam-6529	208	7	.	.	PUNCT
ejpam-6529	209	1	if	if	SCONJ
ejpam-6529	209	2	y	y	PROPN
ejpam-6529	209	3	∈	∈	PROPN
ejpam-6529	209	4	f	f	PROPN
ejpam-6529	209	5	,	,	PUNCT
ejpam-6529	209	6	then	then	ADV
ejpam-6529	209	7	ðx(y	ðx(y	PUNCT
ejpam-6529	209	8	)	)	PUNCT
ejpam-6529	210	1	∈	∈	PROPN
ejpam-6529	210	2	f	f	X
ejpam-6529	210	3	,	,	PUNCT
ejpam-6529	210	4	and	and	CCONJ
ejpam-6529	210	5	thus	thus	ADV
ejpam-6529	210	6	fb(ðx(y	fb(ðx(y	NUM
ejpam-6529	210	7	)	)	PUNCT
ejpam-6529	210	8	)	)	PUNCT
ejpam-6529	211	1	=	=	SYM
ejpam-6529	211	2	s1	s1	PROPN
ejpam-6529	211	3	=	=	PUNCT
ejpam-6529	211	4	fb(y	fb(y	NUM
ejpam-6529	211	5	)	)	PUNCT
ejpam-6529	211	6	and	and	CCONJ
ejpam-6529	211	7	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	211	8	)	)	PUNCT
ejpam-6529	211	9	)	)	PUNCT
ejpam-6529	212	1	=	=	SYM
ejpam-6529	212	2	t1	t1	NOUN
ejpam-6529	212	3	=	=	PUNCT
ejpam-6529	212	4	gb(y	gb(y	ADV
ejpam-6529	212	5	)	)	PUNCT
ejpam-6529	212	6	.	.	PUNCT
ejpam-6529	213	1	it	it	PRON
ejpam-6529	213	2	follows	follow	VERB
ejpam-6529	213	3	from	from	ADP
ejpam-6529	213	4	theorem	theorem	ADJ
ejpam-6529	213	5	1	1	NUM
ejpam-6529	214	1	that	that	ADV
ejpam-6529	214	2	b∗	b∗	ADJ
ejpam-6529	214	3	f	f	X
ejpam-6529	214	4	:	:	PUNCT
ejpam-6529	214	5	=	=	SYM
ejpam-6529	214	6	(	(	PUNCT
ejpam-6529	214	7	x	x	X
ejpam-6529	214	8	;	;	PUNCT
ejpam-6529	214	9	ff	ff	PROPN
ejpam-6529	214	10	b	b	PROPN
ejpam-6529	214	11	,	,	PUNCT
ejpam-6529	214	12	gfb	gfb	PROPN
ejpam-6529	214	13	)	)	PUNCT
ejpam-6529	214	14	is	be	AUX
ejpam-6529	214	15	an	an	DET
ejpam-6529	214	16	intuitionistic	intuitionistic	ADJ
ejpam-6529	214	17	fuzzy	fuzzy	ADJ
ejpam-6529	214	18	weak	weak	ADJ
ejpam-6529	214	19	filter	filter	NOUN
ejpam-6529	214	20	of	of	ADP
ejpam-6529	214	21	x	x	X
ejpam-6529	214	22	:	:	PUNCT
ejpam-6529	214	23	=	=	SYM
ejpam-6529	214	24	(	(	PUNCT
ejpam-6529	214	25	x	x	NOUN
ejpam-6529	214	26	,	,	PUNCT
ejpam-6529	214	27	|	|	NOUN
ejpam-6529	214	28	)	)	PUNCT
ejpam-6529	214	29	.	.	PUNCT
ejpam-6529	215	1	the	the	DET
ejpam-6529	215	2	example	example	NOUN
ejpam-6529	215	3	below	below	ADP
ejpam-6529	215	4	illustrates	illustrate	NOUN
ejpam-6529	215	5	theorem	theorem	VERB
ejpam-6529	215	6	4	4	NUM
ejpam-6529	215	7	.	.	NOUN
ejpam-6529	215	8	example	example	NOUN
ejpam-6529	215	9	2	2	NUM
ejpam-6529	215	10	.	.	X
ejpam-6529	215	11	consider	consider	VERB
ejpam-6529	215	12	the	the	DET
ejpam-6529	215	13	sheffer	sheffer	NOUN
ejpam-6529	215	14	stroke	stroke	NOUN
ejpam-6529	215	15	hilbert	hilbert	PROPN
ejpam-6529	215	16	algebra	algebra	PROPN
ejpam-6529	215	17	x	x	X
ejpam-6529	215	18	:	:	PUNCT
ejpam-6529	215	19	=	=	SYM
ejpam-6529	215	20	(	(	PUNCT
ejpam-6529	215	21	x	x	NOUN
ejpam-6529	215	22	,	,	PUNCT
ejpam-6529	215	23	|	|	ADV
ejpam-6529	215	24	)	)	PUNCT
ejpam-6529	215	25	in	in	ADP
ejpam-6529	215	26	example	example	NOUN
ejpam-6529	216	1	1	1	X
ejpam-6529	216	2	.	.	PUNCT
ejpam-6529	217	1	we	we	PRON
ejpam-6529	217	2	can	can	AUX
ejpam-6529	217	3	observe	observe	VERB
ejpam-6529	217	4	that	that	SCONJ
ejpam-6529	217	5	f	f	X
ejpam-6529	217	6	:	:	PUNCT
ejpam-6529	217	7	=	=	SYM
ejpam-6529	217	8	{	{	PUNCT
ejpam-6529	217	9	c1	c1	PROPN
ejpam-6529	217	10	,	,	PUNCT
ejpam-6529	217	11	c5	c5	PROPN
ejpam-6529	217	12	,	,	PUNCT
ejpam-6529	217	13	c6	c6	PROPN
ejpam-6529	217	14	,	,	PUNCT
ejpam-6529	217	15	c7	c7	PROPN
ejpam-6529	217	16	}	}	PUNCT
ejpam-6529	217	17	is	be	AUX
ejpam-6529	217	18	a	a	DET
ejpam-6529	217	19	weak	weak	ADJ
ejpam-6529	217	20	filter	filter	NOUN
ejpam-6529	217	21	of	of	ADP
ejpam-6529	217	22	x	x	X
ejpam-6529	217	23	:	:	PUNCT
ejpam-6529	217	24	=	=	SYM
ejpam-6529	217	25	(	(	PUNCT
ejpam-6529	217	26	x	x	NOUN
ejpam-6529	217	27	,	,	PUNCT
ejpam-6529	217	28	|	|	NOUN
ejpam-6529	217	29	)	)	PUNCT
ejpam-6529	217	30	.	.	PUNCT
ejpam-6529	218	1	hence	hence	ADV
ejpam-6529	218	2	the	the	DET
ejpam-6529	218	3	intuitionistic	intuitionistic	ADJ
ejpam-6529	218	4	fuzzy	fuzzy	ADJ
ejpam-6529	218	5	set	set	VERB
ejpam-6529	218	6	b∗	b∗	ADJ
ejpam-6529	218	7	f	f	X
ejpam-6529	219	1	:	:	PUNCT
ejpam-6529	219	2	=	=	SYM
ejpam-6529	219	3	(	(	PUNCT
ejpam-6529	219	4	x	x	X
ejpam-6529	219	5	;	;	PUNCT
ejpam-6529	219	6	ff	ff	PROPN
ejpam-6529	219	7	b	b	PROPN
ejpam-6529	219	8	,	,	PUNCT
ejpam-6529	219	9	gfb	gfb	PROPN
ejpam-6529	219	10	)	)	PUNCT
ejpam-6529	219	11	given	give	VERB
ejpam-6529	219	12	by	by	ADP
ejpam-6529	219	13	b∗	b∗	ADJ
ejpam-6529	219	14	f	f	NOUN
ejpam-6529	219	15	:	:	PUNCT
ejpam-6529	219	16	=	=	SYM
ejpam-6529	219	17	(	(	PUNCT
ejpam-6529	219	18	x	x	X
ejpam-6529	219	19	;	;	PUNCT
ejpam-6529	219	20	ff	ff	PROPN
ejpam-6529	219	21	b	b	PROPN
ejpam-6529	219	22	,	,	PUNCT
ejpam-6529	219	23	gfb	gfb	PROPN
ejpam-6529	219	24	)	)	PUNCT
ejpam-6529	219	25	:	:	PUNCT
ejpam-6529	220	1	x	x	X
ejpam-6529	220	2	→	→	PUNCT
ejpam-6529	221	1	[	[	X
ejpam-6529	221	2	0	0	NUM
ejpam-6529	221	3	,	,	PUNCT
ejpam-6529	221	4	1]×	1]×	NUM
ejpam-6529	221	5	[	[	X
ejpam-6529	221	6	0	0	NUM
ejpam-6529	221	7	,	,	PUNCT
ejpam-6529	221	8	1	1	NUM
ejpam-6529	221	9	]	]	PUNCT
ejpam-6529	221	10	,	,	PUNCT
ejpam-6529	221	11	x	x	SYM
ejpam-6529	221	12	7→	7→	X
ejpam-6529	221	13	{	{	PUNCT
ejpam-6529	221	14	(	(	PUNCT
ejpam-6529	221	15	0.7n	0.7n	NOUN
ejpam-6529	221	16	,	,	PUNCT
ejpam-6529	221	17	0.52n	0.52n	NUM
ejpam-6529	221	18	)	)	PUNCT
ejpam-6529	222	1	if	if	SCONJ
ejpam-6529	222	2	x	x	SYM
ejpam-6529	222	3	∈	∈	PROPN
ejpam-6529	222	4	f	f	PROPN
ejpam-6529	222	5	,	,	PUNCT
ejpam-6529	222	6	(	(	PUNCT
ejpam-6529	222	7	0.72n	0.72n	NUM
ejpam-6529	222	8	,	,	PUNCT
ejpam-6529	222	9	0.5	0.5	NUM
ejpam-6529	222	10	n	n	CCONJ
ejpam-6529	222	11	)	)	PUNCT
ejpam-6529	222	12	otherwise	otherwise	ADV
ejpam-6529	222	13	,	,	PUNCT
ejpam-6529	222	14	where	where	SCONJ
ejpam-6529	222	15	n	n	PRON
ejpam-6529	222	16	is	be	AUX
ejpam-6529	222	17	a	a	DET
ejpam-6529	222	18	natural	natural	ADJ
ejpam-6529	222	19	number	number	NOUN
ejpam-6529	222	20	,	,	PUNCT
ejpam-6529	222	21	is	be	AUX
ejpam-6529	222	22	an	an	DET
ejpam-6529	222	23	intuitionistic	intuitionistic	ADJ
ejpam-6529	222	24	fuzzy	fuzzy	ADJ
ejpam-6529	222	25	weak	weak	ADJ
ejpam-6529	222	26	filter	filter	NOUN
ejpam-6529	222	27	of	of	ADP
ejpam-6529	222	28	x	x	X
ejpam-6529	222	29	:	:	PUNCT
ejpam-6529	222	30	=	=	SYM
ejpam-6529	222	31	(	(	PUNCT
ejpam-6529	222	32	x	x	NOUN
ejpam-6529	222	33	,	,	PUNCT
ejpam-6529	222	34	|	|	NOUN
ejpam-6529	222	35	)	)	PUNCT
ejpam-6529	222	36	.	.	PUNCT
ejpam-6529	223	1	s.	s.	PROPN
ejpam-6529	223	2	s.	s.	PROPN
ejpam-6529	223	3	ahn	ahn	PROPN
ejpam-6529	223	4	,	,	PUNCT
ejpam-6529	223	5	y.	y.	PROPN
ejpam-6529	223	6	j.	j.	PROPN
ejpam-6529	223	7	seo	seo	PROPN
ejpam-6529	223	8	,	,	PUNCT
ejpam-6529	223	9	y.	y.	PROPN
ejpam-6529	223	10	b.	b.	PROPN
ejpam-6529	223	11	jun	jun	PROPN
ejpam-6529	223	12	/	/	SYM
ejpam-6529	223	13	eur	eur	PROPN
ejpam-6529	223	14	.	.	PUNCT
ejpam-6529	224	1	j.	j.	PROPN
ejpam-6529	224	2	pure	pure	PROPN
ejpam-6529	224	3	appl	appl	PROPN
ejpam-6529	224	4	.	.	PROPN
ejpam-6529	224	5	math	math	PROPN
ejpam-6529	224	6	,	,	PUNCT
ejpam-6529	224	7	18	18	NUM
ejpam-6529	224	8	(	(	PUNCT
ejpam-6529	224	9	3	3	NUM
ejpam-6529	224	10	)	)	PUNCT
ejpam-6529	224	11	(	(	PUNCT
ejpam-6529	224	12	2025	2025	NUM
ejpam-6529	224	13	)	)	PUNCT
ejpam-6529	224	14	,	,	PUNCT
ejpam-6529	224	15	6529	6529	NUM
ejpam-6529	224	16	9	9	NUM
ejpam-6529	224	17	of	of	ADP
ejpam-6529	224	18	16	16	NUM
ejpam-6529	224	19	corollary	corollary	ADJ
ejpam-6529	224	20	2	2	NUM
ejpam-6529	224	21	.	.	PUNCT
ejpam-6529	225	1	for	for	ADP
ejpam-6529	225	2	every	every	DET
ejpam-6529	225	3	a	a	DET
ejpam-6529	225	4	∈	∈	NOUN
ejpam-6529	225	5	x	x	X
ejpam-6529	225	6	and	and	CCONJ
ejpam-6529	225	7	(	(	PUNCT
ejpam-6529	225	8	s1	s1	NOUN
ejpam-6529	225	9	,	,	PUNCT
ejpam-6529	225	10	t1	t1	NOUN
ejpam-6529	225	11	)	)	PUNCT
ejpam-6529	225	12	,	,	PUNCT
ejpam-6529	225	13	(	(	PUNCT
ejpam-6529	225	14	s2	s2	PROPN
ejpam-6529	225	15	,	,	PUNCT
ejpam-6529	225	16	t3	t3	PROPN
ejpam-6529	225	17	)	)	PUNCT
ejpam-6529	225	18	∈	∈	PROPN
ejpam-6529	225	19	(	(	PUNCT
ejpam-6529	225	20	0	0	NUM
ejpam-6529	225	21	,	,	PUNCT
ejpam-6529	225	22	1]×[0	1]×[0	NUM
ejpam-6529	225	23	,	,	PUNCT
ejpam-6529	225	24	1	1	NUM
ejpam-6529	225	25	)	)	PUNCT
ejpam-6529	225	26	with	with	ADP
ejpam-6529	225	27	s1	s1	PROPN
ejpam-6529	225	28	>	>	X
ejpam-6529	225	29	s2	s2	PROPN
ejpam-6529	225	30	and	and	CCONJ
ejpam-6529	225	31	t1	t1	VERB
ejpam-6529	225	32	<	<	X
ejpam-6529	225	33	t2	t2	PROPN
ejpam-6529	225	34	,	,	PUNCT
ejpam-6529	225	35	consider	consider	VERB
ejpam-6529	225	36	an	an	DET
ejpam-6529	225	37	intuitionistic	intuitionistic	ADJ
ejpam-6529	225	38	fuzzy	fuzzy	ADJ
ejpam-6529	225	39	set	set	VERB
ejpam-6529	225	40	b∗	b∗	ADJ
ejpam-6529	225	41	a⃗	a⃗	NOUN
ejpam-6529	225	42	:	:	PUNCT
ejpam-6529	225	43	=	=	SYM
ejpam-6529	225	44	(	(	PUNCT
ejpam-6529	225	45	x	x	X
ejpam-6529	225	46	;	;	PUNCT
ejpam-6529	225	47	f	f	PROPN
ejpam-6529	225	48	a⃗	a⃗	PROPN
ejpam-6529	225	49	b	b	PROPN
ejpam-6529	225	50	,	,	PUNCT
ejpam-6529	226	1	g	g	PROPN
ejpam-6529	226	2	a⃗	a⃗	PROPN
ejpam-6529	226	3	b	b	NUM
ejpam-6529	226	4	)	)	PUNCT
ejpam-6529	226	5	in	in	ADP
ejpam-6529	226	6	x	x	PUNCT
ejpam-6529	226	7	which	which	PRON
ejpam-6529	226	8	is	be	AUX
ejpam-6529	226	9	defined	define	VERB
ejpam-6529	226	10	by	by	ADP
ejpam-6529	226	11	b∗	b∗	ADJ
ejpam-6529	226	12	a⃗	a⃗	NOUN
ejpam-6529	226	13	:	:	PUNCT
ejpam-6529	226	14	=	=	SYM
ejpam-6529	226	15	(	(	PUNCT
ejpam-6529	226	16	x	x	X
ejpam-6529	226	17	;	;	PUNCT
ejpam-6529	226	18	f	f	PROPN
ejpam-6529	226	19	a⃗	a⃗	PROPN
ejpam-6529	226	20	b	b	PROPN
ejpam-6529	226	21	,	,	PUNCT
ejpam-6529	226	22	g	g	PROPN
ejpam-6529	226	23	a⃗	a⃗	PROPN
ejpam-6529	226	24	b	b	NUM
ejpam-6529	226	25	)	)	PUNCT
ejpam-6529	226	26	:	:	PUNCT
ejpam-6529	227	1	x	x	X
ejpam-6529	227	2	→	→	PUNCT
ejpam-6529	228	1	[	[	X
ejpam-6529	228	2	0	0	NUM
ejpam-6529	228	3	,	,	PUNCT
ejpam-6529	228	4	1]×	1]×	NUM
ejpam-6529	228	5	[	[	X
ejpam-6529	228	6	0	0	NUM
ejpam-6529	228	7	,	,	PUNCT
ejpam-6529	228	8	1	1	NUM
ejpam-6529	228	9	]	]	PUNCT
ejpam-6529	228	10	,	,	PUNCT
ejpam-6529	228	11	x	x	SYM
ejpam-6529	228	12	7→	7→	NUM
ejpam-6529	228	13	{	{	PUNCT
ejpam-6529	228	14	(	(	PUNCT
ejpam-6529	228	15	s1	s1	NOUN
ejpam-6529	228	16	,	,	PUNCT
ejpam-6529	228	17	t1	t1	NOUN
ejpam-6529	228	18	)	)	PUNCT
ejpam-6529	228	19	if	if	SCONJ
ejpam-6529	228	20	x	x	PROPN
ejpam-6529	228	21	∈	∈	PROPN
ejpam-6529	228	22	a⃗	a⃗	PROPN
ejpam-6529	228	23	,	,	PUNCT
ejpam-6529	228	24	(	(	PUNCT
ejpam-6529	228	25	s2	s2	PROPN
ejpam-6529	228	26	,	,	PUNCT
ejpam-6529	228	27	t2	t2	NOUN
ejpam-6529	228	28	)	)	PUNCT
ejpam-6529	228	29	otherwise	otherwise	ADV
ejpam-6529	228	30	is	be	AUX
ejpam-6529	228	31	an	an	DET
ejpam-6529	228	32	intuitionistic	intuitionistic	ADJ
ejpam-6529	228	33	fuzzy	fuzzy	ADJ
ejpam-6529	228	34	weak	weak	ADJ
ejpam-6529	228	35	filter	filter	NOUN
ejpam-6529	228	36	of	of	ADP
ejpam-6529	228	37	x	x	X
ejpam-6529	228	38	:	:	PUNCT
ejpam-6529	228	39	=	=	SYM
ejpam-6529	228	40	(	(	PUNCT
ejpam-6529	228	41	x	x	NOUN
ejpam-6529	228	42	,	,	PUNCT
ejpam-6529	228	43	|	|	NOUN
ejpam-6529	228	44	)	)	PUNCT
ejpam-6529	228	45	where	where	SCONJ
ejpam-6529	228	46	a⃗	a⃗	NOUN
ejpam-6529	228	47	:	:	PUNCT
ejpam-6529	228	48	=	=	SYM
ejpam-6529	228	49	{	{	PUNCT
ejpam-6529	228	50	x	x	PUNCT
ejpam-6529	228	51	∈	∈	PROPN
ejpam-6529	228	52	x	x	X
ejpam-6529	228	53	|	|	ADV
ejpam-6529	228	54	ða(x	ða(x	PUNCT
ejpam-6529	228	55	)	)	PUNCT
ejpam-6529	228	56	=	=	PUNCT
ejpam-6529	229	1	1	1	NUM
ejpam-6529	229	2	}	}	PUNCT
ejpam-6529	229	3	.	.	PUNCT
ejpam-6529	230	1	proof	proof	NOUN
ejpam-6529	230	2	.	.	PUNCT
ejpam-6529	231	1	since	since	SCONJ
ejpam-6529	231	2	a⃗	a⃗	NOUN
ejpam-6529	231	3	is	be	AUX
ejpam-6529	231	4	a	a	DET
ejpam-6529	231	5	weak	weak	ADJ
ejpam-6529	231	6	filter	filter	NOUN
ejpam-6529	231	7	of	of	ADP
ejpam-6529	231	8	x	x	X
ejpam-6529	231	9	:	:	PUNCT
ejpam-6529	231	10	=	=	SYM
ejpam-6529	231	11	(	(	PUNCT
ejpam-6529	231	12	x	x	NOUN
ejpam-6529	231	13	,	,	PUNCT
ejpam-6529	231	14	|	|	ADV
ejpam-6529	231	15	)	)	PUNCT
ejpam-6529	231	16	for	for	ADP
ejpam-6529	231	17	all	all	DET
ejpam-6529	231	18	a	a	DET
ejpam-6529	231	19	∈	∈	NOUN
ejpam-6529	231	20	x	x	PUNCT
ejpam-6529	231	21	(	(	PUNCT
ejpam-6529	231	22	see	see	VERB
ejpam-6529	231	23	[	[	X
ejpam-6529	231	24	13	13	NUM
ejpam-6529	231	25	]	]	NUM
ejpam-6529	231	26	)	)	PUNCT
ejpam-6529	231	27	,	,	PUNCT
ejpam-6529	231	28	it	it	PRON
ejpam-6529	231	29	follows	follow	VERB
ejpam-6529	231	30	from	from	ADP
ejpam-6529	231	31	theorem	theorem	ADJ
ejpam-6529	231	32	4	4	NUM
ejpam-6529	231	33	that	that	PRON
ejpam-6529	231	34	b∗	b∗	ADV
ejpam-6529	231	35	a⃗	a⃗	VERB
ejpam-6529	231	36	:	:	PUNCT
ejpam-6529	231	37	=	=	SYM
ejpam-6529	231	38	(	(	PUNCT
ejpam-6529	231	39	x	x	X
ejpam-6529	231	40	;	;	PUNCT
ejpam-6529	231	41	f	f	PROPN
ejpam-6529	231	42	a⃗	a⃗	PROPN
ejpam-6529	231	43	b	b	PROPN
ejpam-6529	231	44	,	,	PUNCT
ejpam-6529	231	45	g	g	PROPN
ejpam-6529	231	46	a⃗	a⃗	PROPN
ejpam-6529	231	47	b	b	NUM
ejpam-6529	231	48	)	)	PUNCT
ejpam-6529	231	49	is	be	AUX
ejpam-6529	231	50	an	an	DET
ejpam-6529	231	51	intuitionistic	intuitionistic	ADJ
ejpam-6529	231	52	fuzzy	fuzzy	ADJ
ejpam-6529	231	53	weak	weak	ADJ
ejpam-6529	231	54	filter	filter	NOUN
ejpam-6529	231	55	of	of	ADP
ejpam-6529	231	56	x	x	X
ejpam-6529	231	57	:	:	PUNCT
ejpam-6529	231	58	=	=	SYM
ejpam-6529	231	59	(	(	PUNCT
ejpam-6529	231	60	x	x	NOUN
ejpam-6529	231	61	,	,	PUNCT
ejpam-6529	231	62	|	|	ADV
ejpam-6529	231	63	)	)	PUNCT
ejpam-6529	231	64	for	for	ADP
ejpam-6529	231	65	all	all	DET
ejpam-6529	231	66	a	a	DET
ejpam-6529	231	67	∈	∈	PROPN
ejpam-6529	231	68	x.	x.	NOUN
ejpam-6529	231	69	corollary	corollary	NOUN
ejpam-6529	231	70	3	3	X
ejpam-6529	231	71	.	.	PUNCT
ejpam-6529	232	1	for	for	ADP
ejpam-6529	232	2	every	every	DET
ejpam-6529	232	3	b	b	PROPN
ejpam-6529	232	4	∈	∈	PROPN
ejpam-6529	232	5	x	x	X
ejpam-6529	232	6	and	and	CCONJ
ejpam-6529	232	7	(	(	PUNCT
ejpam-6529	232	8	s1	s1	NOUN
ejpam-6529	232	9	,	,	PUNCT
ejpam-6529	232	10	t1	t1	NOUN
ejpam-6529	232	11	)	)	PUNCT
ejpam-6529	232	12	,	,	PUNCT
ejpam-6529	232	13	(	(	PUNCT
ejpam-6529	232	14	s2	s2	PROPN
ejpam-6529	232	15	,	,	PUNCT
ejpam-6529	232	16	t3	t3	PROPN
ejpam-6529	232	17	)	)	PUNCT
ejpam-6529	232	18	∈	∈	PROPN
ejpam-6529	232	19	(	(	PUNCT
ejpam-6529	232	20	0	0	NUM
ejpam-6529	232	21	,	,	PUNCT
ejpam-6529	232	22	1]×[0	1]×[0	NUM
ejpam-6529	232	23	,	,	PUNCT
ejpam-6529	232	24	1	1	NUM
ejpam-6529	232	25	)	)	PUNCT
ejpam-6529	232	26	with	with	ADP
ejpam-6529	232	27	s1	s1	PROPN
ejpam-6529	232	28	>	>	X
ejpam-6529	232	29	s2	s2	PROPN
ejpam-6529	232	30	and	and	CCONJ
ejpam-6529	232	31	t1	t1	VERB
ejpam-6529	232	32	<	<	X
ejpam-6529	232	33	t2	t2	PROPN
ejpam-6529	232	34	,	,	PUNCT
ejpam-6529	232	35	consider	consider	VERB
ejpam-6529	232	36	an	an	DET
ejpam-6529	232	37	intuitionistic	intuitionistic	ADJ
ejpam-6529	232	38	fuzzy	fuzzy	ADJ
ejpam-6529	232	39	set	set	VERB
ejpam-6529	232	40	b∗	b∗	ADJ
ejpam-6529	232	41	xb	xb	X
ejpam-6529	233	1	:	:	PUNCT
ejpam-6529	233	2	=	=	SYM
ejpam-6529	233	3	(	(	PUNCT
ejpam-6529	233	4	x	x	X
ejpam-6529	233	5	;	;	PUNCT
ejpam-6529	233	6	fxb	fxb	PROPN
ejpam-6529	233	7	b	b	PROPN
ejpam-6529	233	8	,	,	PUNCT
ejpam-6529	233	9	gx	gx	PROPN
ejpam-6529	233	10	b	b	PROPN
ejpam-6529	233	11	b	b	PROPN
ejpam-6529	233	12	)	)	PUNCT
ejpam-6529	233	13	in	in	ADP
ejpam-6529	233	14	x	x	PUNCT
ejpam-6529	233	15	which	which	PRON
ejpam-6529	233	16	is	be	AUX
ejpam-6529	233	17	defined	define	VERB
ejpam-6529	233	18	by	by	ADP
ejpam-6529	233	19	b∗	b∗	ADJ
ejpam-6529	233	20	xb	xb	PROPN
ejpam-6529	234	1	:	:	PUNCT
ejpam-6529	234	2	=	=	SYM
ejpam-6529	234	3	(	(	PUNCT
ejpam-6529	234	4	x	x	X
ejpam-6529	234	5	;	;	PUNCT
ejpam-6529	234	6	fxb	fxb	PROPN
ejpam-6529	234	7	b	b	PROPN
ejpam-6529	234	8	,	,	PUNCT
ejpam-6529	234	9	gx	gx	PROPN
ejpam-6529	234	10	b	b	PROPN
ejpam-6529	234	11	b	b	PROPN
ejpam-6529	234	12	)	)	PUNCT
ejpam-6529	234	13	:	:	PUNCT
ejpam-6529	234	14	x	x	X
ejpam-6529	234	15	→	→	PUNCT
ejpam-6529	235	1	[	[	X
ejpam-6529	235	2	0	0	NUM
ejpam-6529	235	3	,	,	PUNCT
ejpam-6529	235	4	1]×	1]×	NUM
ejpam-6529	235	5	[	[	X
ejpam-6529	235	6	0	0	NUM
ejpam-6529	235	7	,	,	PUNCT
ejpam-6529	235	8	1	1	NUM
ejpam-6529	235	9	]	]	PUNCT
ejpam-6529	235	10	,	,	PUNCT
ejpam-6529	235	11	x	x	SYM
ejpam-6529	235	12	7→	7→	NUM
ejpam-6529	235	13	{	{	PUNCT
ejpam-6529	235	14	(	(	PUNCT
ejpam-6529	235	15	s1	s1	NOUN
ejpam-6529	235	16	,	,	PUNCT
ejpam-6529	235	17	t1	t1	NOUN
ejpam-6529	235	18	)	)	PUNCT
ejpam-6529	235	19	if	if	SCONJ
ejpam-6529	235	20	x	x	PROPN
ejpam-6529	235	21	∈	∈	PROPN
ejpam-6529	235	22	xb	xb	PROPN
ejpam-6529	235	23	,	,	PUNCT
ejpam-6529	235	24	(	(	PUNCT
ejpam-6529	235	25	s2	s2	PROPN
ejpam-6529	235	26	,	,	PUNCT
ejpam-6529	235	27	t2	t2	NOUN
ejpam-6529	235	28	)	)	PUNCT
ejpam-6529	235	29	otherwise	otherwise	ADV
ejpam-6529	235	30	is	be	AUX
ejpam-6529	235	31	an	an	DET
ejpam-6529	235	32	intuitionistic	intuitionistic	ADJ
ejpam-6529	235	33	fuzzy	fuzzy	ADJ
ejpam-6529	235	34	weak	weak	ADJ
ejpam-6529	235	35	filter	filter	NOUN
ejpam-6529	235	36	of	of	ADP
ejpam-6529	235	37	x	x	X
ejpam-6529	235	38	:	:	PUNCT
ejpam-6529	235	39	=	=	SYM
ejpam-6529	235	40	(	(	PUNCT
ejpam-6529	235	41	x	x	NOUN
ejpam-6529	235	42	,	,	PUNCT
ejpam-6529	235	43	|	|	NOUN
ejpam-6529	235	44	)	)	PUNCT
ejpam-6529	235	45	where	where	SCONJ
ejpam-6529	235	46	xb	xb	X
ejpam-6529	235	47	:	:	PUNCT
ejpam-6529	235	48	=	=	SYM
ejpam-6529	235	49	{	{	PUNCT
ejpam-6529	235	50	x	x	PUNCT
ejpam-6529	235	51	∈	∈	PROPN
ejpam-6529	235	52	x	x	X
ejpam-6529	235	53	|	|	ADV
ejpam-6529	235	54	ðb(x	ðb(x	PUNCT
ejpam-6529	235	55	)	)	PUNCT
ejpam-6529	235	56	=	=	SYM
ejpam-6529	236	1	x	x	X
ejpam-6529	236	2	}	}	PUNCT
ejpam-6529	236	3	.	.	PUNCT
ejpam-6529	237	1	proof	proof	NOUN
ejpam-6529	237	2	.	.	PUNCT
ejpam-6529	238	1	note	note	VERB
ejpam-6529	238	2	that	that	SCONJ
ejpam-6529	238	3	xb	xb	PROPN
ejpam-6529	238	4	is	be	AUX
ejpam-6529	238	5	a	a	DET
ejpam-6529	238	6	weak	weak	ADJ
ejpam-6529	238	7	filter	filter	NOUN
ejpam-6529	238	8	of	of	ADP
ejpam-6529	238	9	x	x	X
ejpam-6529	238	10	:	:	PUNCT
ejpam-6529	238	11	=	=	SYM
ejpam-6529	238	12	(	(	PUNCT
ejpam-6529	238	13	x	x	NOUN
ejpam-6529	238	14	,	,	PUNCT
ejpam-6529	238	15	|	|	ADV
ejpam-6529	238	16	)	)	PUNCT
ejpam-6529	238	17	for	for	ADP
ejpam-6529	238	18	all	all	DET
ejpam-6529	238	19	b	b	NOUN
ejpam-6529	238	20	∈	∈	NOUN
ejpam-6529	238	21	x	x	PUNCT
ejpam-6529	238	22	(	(	PUNCT
ejpam-6529	238	23	see	see	VERB
ejpam-6529	238	24	[	[	X
ejpam-6529	238	25	13	13	NUM
ejpam-6529	238	26	]	]	NUM
ejpam-6529	238	27	)	)	PUNCT
ejpam-6529	238	28	.	.	PUNCT
ejpam-6529	239	1	hence	hence	ADV
ejpam-6529	239	2	b∗	b∗	ADV
ejpam-6529	239	3	xb	xb	X
ejpam-6529	240	1	:	:	PUNCT
ejpam-6529	240	2	=	=	SYM
ejpam-6529	240	3	(	(	PUNCT
ejpam-6529	240	4	x	x	X
ejpam-6529	240	5	;	;	PUNCT
ejpam-6529	240	6	fxb	fxb	PROPN
ejpam-6529	240	7	b	b	PROPN
ejpam-6529	240	8	,	,	PUNCT
ejpam-6529	240	9	gx	gx	PROPN
ejpam-6529	240	10	b	b	PROPN
ejpam-6529	240	11	b	b	PROPN
ejpam-6529	240	12	)	)	PUNCT
ejpam-6529	240	13	is	be	AUX
ejpam-6529	240	14	an	an	DET
ejpam-6529	240	15	intuitionistic	intuitionistic	ADJ
ejpam-6529	240	16	fuzzy	fuzzy	ADJ
ejpam-6529	240	17	weak	weak	ADJ
ejpam-6529	240	18	filter	filter	NOUN
ejpam-6529	240	19	of	of	ADP
ejpam-6529	240	20	x	x	X
ejpam-6529	240	21	:	:	PUNCT
ejpam-6529	240	22	=	=	SYM
ejpam-6529	240	23	(	(	PUNCT
ejpam-6529	240	24	x	x	NOUN
ejpam-6529	240	25	,	,	PUNCT
ejpam-6529	240	26	|	|	ADV
ejpam-6529	240	27	)	)	PUNCT
ejpam-6529	240	28	for	for	ADP
ejpam-6529	240	29	all	all	DET
ejpam-6529	240	30	b	b	NOUN
ejpam-6529	240	31	∈	∈	PROPN
ejpam-6529	240	32	x	x	PUNCT
ejpam-6529	240	33	by	by	ADP
ejpam-6529	240	34	theorem	theorem	NOUN
ejpam-6529	240	35	4	4	NUM
ejpam-6529	240	36	.	.	PUNCT
ejpam-6529	240	37	corollary	corollary	ADJ
ejpam-6529	240	38	4	4	NUM
ejpam-6529	240	39	.	.	PUNCT
ejpam-6529	241	1	let	let	VERB
ejpam-6529	241	2	f	f	PRON
ejpam-6529	241	3	be	be	AUX
ejpam-6529	241	4	a	a	DET
ejpam-6529	241	5	subset	subset	NOUN
ejpam-6529	241	6	of	of	ADP
ejpam-6529	241	7	x.	x.	NOUN
ejpam-6529	241	8	for	for	ADP
ejpam-6529	241	9	every	every	DET
ejpam-6529	241	10	b	b	PROPN
ejpam-6529	241	11	∈	∈	PROPN
ejpam-6529	241	12	x	x	X
ejpam-6529	241	13	and	and	CCONJ
ejpam-6529	241	14	(	(	PUNCT
ejpam-6529	241	15	s1	s1	NOUN
ejpam-6529	241	16	,	,	PUNCT
ejpam-6529	241	17	t1	t1	NOUN
ejpam-6529	241	18	)	)	PUNCT
ejpam-6529	241	19	,	,	PUNCT
ejpam-6529	241	20	(	(	PUNCT
ejpam-6529	241	21	s2	s2	PROPN
ejpam-6529	241	22	,	,	PUNCT
ejpam-6529	241	23	t2	t2	NOUN
ejpam-6529	241	24	)	)	PUNCT
ejpam-6529	241	25	∈	∈	PROPN
ejpam-6529	241	26	(	(	PUNCT
ejpam-6529	241	27	0	0	NUM
ejpam-6529	241	28	,	,	PUNCT
ejpam-6529	241	29	1]×	1]×	NUM
ejpam-6529	242	1	[	[	X
ejpam-6529	242	2	0	0	NUM
ejpam-6529	242	3	,	,	PUNCT
ejpam-6529	242	4	1	1	NUM
ejpam-6529	242	5	)	)	PUNCT
ejpam-6529	242	6	with	with	ADP
ejpam-6529	242	7	s1	s1	PROPN
ejpam-6529	242	8	>	>	X
ejpam-6529	242	9	s2	s2	PROPN
ejpam-6529	242	10	and	and	CCONJ
ejpam-6529	242	11	t1	t1	VERB
ejpam-6529	242	12	<	<	X
ejpam-6529	242	13	t2	t2	PROPN
ejpam-6529	242	14	,	,	PUNCT
ejpam-6529	242	15	let	let	VERB
ejpam-6529	242	16	b∗	b∗	ADJ
ejpam-6529	243	1	fb	fb	INTJ
ejpam-6529	243	2	:	:	PUNCT
ejpam-6529	243	3	=	=	SYM
ejpam-6529	243	4	(	(	PUNCT
ejpam-6529	243	5	x	x	NOUN
ejpam-6529	243	6	;	;	PUNCT
ejpam-6529	243	7	ffb	ffb	PROPN
ejpam-6529	243	8	b	b	PROPN
ejpam-6529	243	9	,	,	PUNCT
ejpam-6529	243	10	gfb	gfb	PROPN
ejpam-6529	243	11	b	b	PROPN
ejpam-6529	243	12	)	)	PUNCT
ejpam-6529	243	13	be	be	AUX
ejpam-6529	243	14	an	an	DET
ejpam-6529	243	15	intuitionistic	intuitionistic	ADJ
ejpam-6529	243	16	fuzzy	fuzzy	ADJ
ejpam-6529	243	17	set	set	NOUN
ejpam-6529	243	18	in	in	ADP
ejpam-6529	243	19	x	x	PUNCT
ejpam-6529	243	20	which	which	PRON
ejpam-6529	243	21	is	be	AUX
ejpam-6529	243	22	defined	define	VERB
ejpam-6529	243	23	by	by	ADP
ejpam-6529	243	24	b∗	b∗	ADJ
ejpam-6529	243	25	fb	fb	NOUN
ejpam-6529	243	26	:	:	PUNCT
ejpam-6529	243	27	=	=	SYM
ejpam-6529	243	28	(	(	PUNCT
ejpam-6529	243	29	x	x	NOUN
ejpam-6529	243	30	;	;	PUNCT
ejpam-6529	243	31	ffb	ffb	PROPN
ejpam-6529	243	32	b	b	PROPN
ejpam-6529	243	33	,	,	PUNCT
ejpam-6529	243	34	gfb	gfb	PROPN
ejpam-6529	243	35	b	b	PROPN
ejpam-6529	243	36	)	)	PUNCT
ejpam-6529	243	37	:	:	PUNCT
ejpam-6529	244	1	x	x	X
ejpam-6529	244	2	→	→	PUNCT
ejpam-6529	245	1	[	[	X
ejpam-6529	245	2	0	0	NUM
ejpam-6529	245	3	,	,	PUNCT
ejpam-6529	245	4	1]×	1]×	NUM
ejpam-6529	245	5	[	[	X
ejpam-6529	245	6	0	0	NUM
ejpam-6529	245	7	,	,	PUNCT
ejpam-6529	245	8	1	1	NUM
ejpam-6529	245	9	]	]	PUNCT
ejpam-6529	245	10	,	,	PUNCT
ejpam-6529	245	11	x	x	SYM
ejpam-6529	245	12	7→	7→	NUM
ejpam-6529	245	13	{	{	PUNCT
ejpam-6529	245	14	(	(	PUNCT
ejpam-6529	245	15	s1	s1	NOUN
ejpam-6529	245	16	,	,	PUNCT
ejpam-6529	245	17	t1	t1	NOUN
ejpam-6529	245	18	)	)	PUNCT
ejpam-6529	245	19	if	if	SCONJ
ejpam-6529	245	20	x	x	SYM
ejpam-6529	245	21	∈	∈	PROPN
ejpam-6529	245	22	fb	fb	INTJ
ejpam-6529	245	23	,	,	PUNCT
ejpam-6529	245	24	(	(	PUNCT
ejpam-6529	245	25	s2	s2	PROPN
ejpam-6529	245	26	,	,	PUNCT
ejpam-6529	245	27	t2	t2	NOUN
ejpam-6529	245	28	)	)	PUNCT
ejpam-6529	245	29	otherwise	otherwise	ADV
ejpam-6529	245	30	where	where	SCONJ
ejpam-6529	245	31	fb	fb	INTJ
ejpam-6529	245	32	:	:	PUNCT
ejpam-6529	245	33	=	=	SYM
ejpam-6529	245	34	{	{	PUNCT
ejpam-6529	245	35	z	z	NOUN
ejpam-6529	245	36	∈	∈	PROPN
ejpam-6529	245	37	x	x	X
ejpam-6529	245	38	|	|	ADV
ejpam-6529	245	39	ðb(x	ðb(x	PUNCT
ejpam-6529	245	40	)	)	PUNCT
ejpam-6529	246	1	=	=	SYM
ejpam-6529	246	2	z	z	X
ejpam-6529	246	3	,	,	PUNCT
ejpam-6529	246	4	x	x	SYM
ejpam-6529	246	5	∈	∈	PROPN
ejpam-6529	246	6	f	f	X
ejpam-6529	246	7	}	}	PUNCT
ejpam-6529	246	8	.	.	PUNCT
ejpam-6529	247	1	if	if	SCONJ
ejpam-6529	247	2	f	f	PROPN
ejpam-6529	247	3	is	be	AUX
ejpam-6529	247	4	a	a	DET
ejpam-6529	247	5	weak	weak	ADJ
ejpam-6529	247	6	filter	filter	NOUN
ejpam-6529	247	7	of	of	ADP
ejpam-6529	247	8	x	x	X
ejpam-6529	247	9	:	:	PUNCT
ejpam-6529	247	10	=	=	SYM
ejpam-6529	247	11	(	(	PUNCT
ejpam-6529	247	12	x	x	NOUN
ejpam-6529	247	13	,	,	PUNCT
ejpam-6529	247	14	|	|	NOUN
ejpam-6529	247	15	)	)	PUNCT
ejpam-6529	247	16	,	,	PUNCT
ejpam-6529	247	17	then	then	ADV
ejpam-6529	247	18	b∗	b∗	ADV
ejpam-6529	247	19	fb	fb	INTJ
ejpam-6529	247	20	:	:	PUNCT
ejpam-6529	247	21	=	=	SYM
ejpam-6529	247	22	(	(	PUNCT
ejpam-6529	247	23	x	x	NOUN
ejpam-6529	247	24	;	;	PUNCT
ejpam-6529	247	25	ffb	ffb	PROPN
ejpam-6529	247	26	b	b	PROPN
ejpam-6529	247	27	,	,	PUNCT
ejpam-6529	247	28	gfb	gfb	PROPN
ejpam-6529	247	29	b	b	PROPN
ejpam-6529	247	30	)	)	PUNCT
ejpam-6529	247	31	is	be	AUX
ejpam-6529	247	32	an	an	DET
ejpam-6529	247	33	intuitionistic	intuitionistic	ADJ
ejpam-6529	247	34	fuzzy	fuzzy	ADJ
ejpam-6529	247	35	weak	weak	ADJ
ejpam-6529	247	36	filter	filter	NOUN
ejpam-6529	247	37	of	of	ADP
ejpam-6529	247	38	x	x	X
ejpam-6529	247	39	:	:	PUNCT
ejpam-6529	247	40	=	=	SYM
ejpam-6529	247	41	(	(	PUNCT
ejpam-6529	247	42	x	x	NOUN
ejpam-6529	247	43	,	,	PUNCT
ejpam-6529	247	44	|	|	NOUN
ejpam-6529	247	45	)	)	PUNCT
ejpam-6529	247	46	.	.	PUNCT
ejpam-6529	248	1	proof	proof	NOUN
ejpam-6529	248	2	.	.	PUNCT
ejpam-6529	249	1	if	if	SCONJ
ejpam-6529	249	2	f	f	PROPN
ejpam-6529	249	3	is	be	AUX
ejpam-6529	249	4	a	a	DET
ejpam-6529	249	5	weak	weak	ADJ
ejpam-6529	249	6	filter	filter	NOUN
ejpam-6529	249	7	of	of	ADP
ejpam-6529	249	8	x	x	X
ejpam-6529	249	9	:	:	PUNCT
ejpam-6529	249	10	=	=	SYM
ejpam-6529	249	11	(	(	PUNCT
ejpam-6529	249	12	x	x	NOUN
ejpam-6529	249	13	,	,	PUNCT
ejpam-6529	249	14	|	|	NOUN
ejpam-6529	249	15	)	)	PUNCT
ejpam-6529	249	16	,	,	PUNCT
ejpam-6529	249	17	then	then	ADV
ejpam-6529	249	18	fb	fb	INTJ
ejpam-6529	249	19	is	be	AUX
ejpam-6529	249	20	a	a	DET
ejpam-6529	249	21	weak	weak	ADJ
ejpam-6529	249	22	filter	filter	NOUN
ejpam-6529	249	23	of	of	ADP
ejpam-6529	249	24	x	x	X
ejpam-6529	249	25	:	:	PUNCT
ejpam-6529	249	26	=	=	SYM
ejpam-6529	249	27	(	(	PUNCT
ejpam-6529	249	28	x	x	NOUN
ejpam-6529	249	29	,	,	PUNCT
ejpam-6529	249	30	|	|	NOUN
ejpam-6529	249	31	)	)	PUNCT
ejpam-6529	249	32	(	(	PUNCT
ejpam-6529	249	33	see	see	VERB
ejpam-6529	249	34	[	[	X
ejpam-6529	249	35	13	13	NUM
ejpam-6529	249	36	]	]	NUM
ejpam-6529	249	37	)	)	PUNCT
ejpam-6529	249	38	.	.	PUNCT
ejpam-6529	250	1	thus	thus	ADV
ejpam-6529	250	2	b∗	b∗	ADJ
ejpam-6529	250	3	fb	fb	INTJ
ejpam-6529	250	4	:	:	PUNCT
ejpam-6529	250	5	=	=	SYM
ejpam-6529	250	6	(	(	PUNCT
ejpam-6529	250	7	x	x	NOUN
ejpam-6529	250	8	;	;	PUNCT
ejpam-6529	250	9	ffb	ffb	PROPN
ejpam-6529	250	10	b	b	PROPN
ejpam-6529	250	11	,	,	PUNCT
ejpam-6529	250	12	gfb	gfb	PROPN
ejpam-6529	250	13	b	b	PROPN
ejpam-6529	250	14	)	)	PUNCT
ejpam-6529	250	15	is	be	AUX
ejpam-6529	250	16	an	an	DET
ejpam-6529	250	17	intuitionistic	intuitionistic	ADJ
ejpam-6529	250	18	fuzzy	fuzzy	ADJ
ejpam-6529	250	19	weak	weak	ADJ
ejpam-6529	250	20	filter	filter	NOUN
ejpam-6529	250	21	of	of	ADP
ejpam-6529	250	22	x	x	X
ejpam-6529	250	23	:	:	PUNCT
ejpam-6529	250	24	=	=	SYM
ejpam-6529	250	25	(	(	PUNCT
ejpam-6529	250	26	x	x	NOUN
ejpam-6529	250	27	,	,	PUNCT
ejpam-6529	250	28	|	|	ADV
ejpam-6529	250	29	)	)	PUNCT
ejpam-6529	250	30	by	by	ADP
ejpam-6529	250	31	theorem	theorem	ADJ
ejpam-6529	250	32	4	4	NUM
ejpam-6529	250	33	.	.	PUNCT
ejpam-6529	250	34	corollary	corollary	ADJ
ejpam-6529	250	35	5	5	NUM
ejpam-6529	250	36	.	.	PUNCT
ejpam-6529	251	1	let	let	VERB
ejpam-6529	251	2	g	g	PRON
ejpam-6529	251	3	be	be	AUX
ejpam-6529	251	4	a	a	DET
ejpam-6529	251	5	subset	subset	NOUN
ejpam-6529	251	6	of	of	ADP
ejpam-6529	251	7	x.	x.	NOUN
ejpam-6529	251	8	for	for	ADP
ejpam-6529	251	9	every	every	DET
ejpam-6529	251	10	(	(	PUNCT
ejpam-6529	251	11	s1	s1	NOUN
ejpam-6529	251	12	,	,	PUNCT
ejpam-6529	251	13	t1	t1	NOUN
ejpam-6529	251	14	)	)	PUNCT
ejpam-6529	251	15	,	,	PUNCT
ejpam-6529	251	16	(	(	PUNCT
ejpam-6529	251	17	s2	s2	PROPN
ejpam-6529	251	18	,	,	PUNCT
ejpam-6529	251	19	t2	t2	NOUN
ejpam-6529	251	20	)	)	PUNCT
ejpam-6529	251	21	∈	∈	PROPN
ejpam-6529	251	22	(	(	PUNCT
ejpam-6529	251	23	0	0	NUM
ejpam-6529	251	24	,	,	PUNCT
ejpam-6529	251	25	1	1	NUM
ejpam-6529	251	26	]	]	SYM
ejpam-6529	251	27	×	×	NOUN
ejpam-6529	252	1	[	[	X
ejpam-6529	252	2	0	0	NUM
ejpam-6529	252	3	,	,	PUNCT
ejpam-6529	252	4	1	1	NUM
ejpam-6529	252	5	)	)	PUNCT
ejpam-6529	252	6	with	with	ADP
ejpam-6529	252	7	s1	s1	PROPN
ejpam-6529	252	8	>	>	X
ejpam-6529	252	9	s2	s2	PROPN
ejpam-6529	252	10	and	and	CCONJ
ejpam-6529	252	11	t1	t1	VERB
ejpam-6529	252	12	<	<	X
ejpam-6529	252	13	t2	t2	PROPN
ejpam-6529	252	14	,	,	PUNCT
ejpam-6529	252	15	let	let	VERB
ejpam-6529	252	16	b∗	b∗	ADJ
ejpam-6529	252	17	g	g	NOUN
ejpam-6529	252	18	:	:	PUNCT
ejpam-6529	252	19	=	=	SYM
ejpam-6529	252	20	(	(	PUNCT
ejpam-6529	252	21	x	x	X
ejpam-6529	252	22	;	;	PUNCT
ejpam-6529	252	23	fg	fg	PROPN
ejpam-6529	252	24	b	b	PROPN
ejpam-6529	252	25	,	,	PUNCT
ejpam-6529	252	26	ggb	ggb	PROPN
ejpam-6529	252	27	)	)	PUNCT
ejpam-6529	252	28	in	in	ADP
ejpam-6529	252	29	x	x	PUNCT
ejpam-6529	252	30	which	which	PRON
ejpam-6529	252	31	is	be	AUX
ejpam-6529	252	32	given	give	VERB
ejpam-6529	252	33	by	by	ADP
ejpam-6529	252	34	b∗	b∗	ADJ
ejpam-6529	252	35	g	g	NOUN
ejpam-6529	252	36	:	:	PUNCT
ejpam-6529	252	37	=	=	SYM
ejpam-6529	252	38	(	(	PUNCT
ejpam-6529	252	39	x	x	X
ejpam-6529	252	40	;	;	PUNCT
ejpam-6529	252	41	fg	fg	PROPN
ejpam-6529	252	42	b	b	PROPN
ejpam-6529	252	43	,	,	PUNCT
ejpam-6529	252	44	ggb	ggb	PROPN
ejpam-6529	252	45	)	)	PUNCT
ejpam-6529	252	46	:	:	PUNCT
ejpam-6529	253	1	x	x	X
ejpam-6529	253	2	→	→	PUNCT
ejpam-6529	254	1	[	[	X
ejpam-6529	254	2	0	0	NUM
ejpam-6529	254	3	,	,	PUNCT
ejpam-6529	254	4	1]×	1]×	NUM
ejpam-6529	254	5	[	[	X
ejpam-6529	254	6	0	0	NUM
ejpam-6529	254	7	,	,	PUNCT
ejpam-6529	254	8	1	1	NUM
ejpam-6529	254	9	]	]	PUNCT
ejpam-6529	254	10	,	,	PUNCT
ejpam-6529	254	11	x	x	SYM
ejpam-6529	254	12	7→	7→	NUM
ejpam-6529	254	13	{	{	PUNCT
ejpam-6529	254	14	(	(	PUNCT
ejpam-6529	254	15	s1	s1	NOUN
ejpam-6529	254	16	,	,	PUNCT
ejpam-6529	254	17	t1	t1	NOUN
ejpam-6529	254	18	)	)	PUNCT
ejpam-6529	254	19	if	if	SCONJ
ejpam-6529	254	20	x	x	PROPN
ejpam-6529	254	21	∈	∈	PROPN
ejpam-6529	254	22	g∗	g∗	PROPN
ejpam-6529	254	23	,	,	PUNCT
ejpam-6529	254	24	(	(	PUNCT
ejpam-6529	254	25	s2	s2	PROPN
ejpam-6529	254	26	,	,	PUNCT
ejpam-6529	254	27	t2	t2	NOUN
ejpam-6529	254	28	)	)	PUNCT
ejpam-6529	254	29	otherwise	otherwise	ADV
ejpam-6529	254	30	where	where	SCONJ
ejpam-6529	254	31	g∗	g∗	VERB
ejpam-6529	254	32	:	:	PUNCT
ejpam-6529	254	33	=	=	SYM
ejpam-6529	254	34	{	{	PUNCT
ejpam-6529	254	35	x	x	SYM
ejpam-6529	254	36	∈	∈	PROPN
ejpam-6529	254	37	x	x	SYM
ejpam-6529	254	38	|	|	ADV
ejpam-6529	254	39	(	(	PUNCT
ejpam-6529	254	40	∀y	∀y	PROPN
ejpam-6529	254	41	∈	∈	PROPN
ejpam-6529	254	42	g)(ðx(y	g)(ðx(y	NOUN
ejpam-6529	254	43	)	)	PUNCT
ejpam-6529	254	44	=	=	SYM
ejpam-6529	254	45	1	1	NUM
ejpam-6529	254	46	⇒	⇒	NOUN
ejpam-6529	254	47	y	y	PROPN
ejpam-6529	254	48	=	=	SYM
ejpam-6529	254	49	1	1	NUM
ejpam-6529	254	50	)	)	PUNCT
ejpam-6529	254	51	}	}	PUNCT
ejpam-6529	254	52	.	.	PUNCT
ejpam-6529	255	1	if	if	SCONJ
ejpam-6529	255	2	g	g	PROPN
ejpam-6529	255	3	is	be	AUX
ejpam-6529	255	4	a	a	DET
ejpam-6529	255	5	weak	weak	ADJ
ejpam-6529	255	6	filter	filter	NOUN
ejpam-6529	255	7	of	of	ADP
ejpam-6529	255	8	x	x	X
ejpam-6529	255	9	:	:	PUNCT
ejpam-6529	255	10	=	=	SYM
ejpam-6529	255	11	(	(	PUNCT
ejpam-6529	255	12	x	x	NOUN
ejpam-6529	255	13	,	,	PUNCT
ejpam-6529	255	14	|	|	NOUN
ejpam-6529	255	15	)	)	PUNCT
ejpam-6529	255	16	,	,	PUNCT
ejpam-6529	255	17	then	then	ADV
ejpam-6529	255	18	b∗	b∗	ADV
ejpam-6529	255	19	g	g	NOUN
ejpam-6529	255	20	:	:	PUNCT
ejpam-6529	255	21	=	=	SYM
ejpam-6529	255	22	(	(	PUNCT
ejpam-6529	255	23	x	x	X
ejpam-6529	255	24	;	;	PUNCT
ejpam-6529	255	25	fg	fg	PROPN
ejpam-6529	255	26	b	b	PROPN
ejpam-6529	255	27	,	,	PUNCT
ejpam-6529	255	28	ggb	ggb	PROPN
ejpam-6529	255	29	)	)	PUNCT
ejpam-6529	255	30	is	be	AUX
ejpam-6529	255	31	an	an	DET
ejpam-6529	255	32	intuitionistic	intuitionistic	ADJ
ejpam-6529	255	33	fuzzy	fuzzy	ADJ
ejpam-6529	255	34	weak	weak	ADJ
ejpam-6529	255	35	filter	filter	NOUN
ejpam-6529	255	36	of	of	ADP
ejpam-6529	255	37	x	x	X
ejpam-6529	255	38	:	:	PUNCT
ejpam-6529	255	39	=	=	SYM
ejpam-6529	255	40	(	(	PUNCT
ejpam-6529	255	41	x	x	NOUN
ejpam-6529	255	42	,	,	PUNCT
ejpam-6529	255	43	|	|	NOUN
ejpam-6529	255	44	)	)	PUNCT
ejpam-6529	255	45	.	.	PUNCT
ejpam-6529	256	1	s.	s.	PROPN
ejpam-6529	256	2	s.	s.	PROPN
ejpam-6529	256	3	ahn	ahn	PROPN
ejpam-6529	256	4	,	,	PUNCT
ejpam-6529	256	5	y.	y.	PROPN
ejpam-6529	256	6	j.	j.	PROPN
ejpam-6529	256	7	seo	seo	PROPN
ejpam-6529	256	8	,	,	PUNCT
ejpam-6529	256	9	y.	y.	PROPN
ejpam-6529	256	10	b.	b.	PROPN
ejpam-6529	256	11	jun	jun	PROPN
ejpam-6529	256	12	/	/	SYM
ejpam-6529	256	13	eur	eur	PROPN
ejpam-6529	256	14	.	.	PUNCT
ejpam-6529	257	1	j.	j.	PROPN
ejpam-6529	257	2	pure	pure	PROPN
ejpam-6529	257	3	appl	appl	PROPN
ejpam-6529	257	4	.	.	PROPN
ejpam-6529	257	5	math	math	PROPN
ejpam-6529	257	6	,	,	PUNCT
ejpam-6529	257	7	18	18	NUM
ejpam-6529	257	8	(	(	PUNCT
ejpam-6529	257	9	3	3	NUM
ejpam-6529	257	10	)	)	PUNCT
ejpam-6529	257	11	(	(	PUNCT
ejpam-6529	257	12	2025	2025	NUM
ejpam-6529	257	13	)	)	PUNCT
ejpam-6529	257	14	,	,	PUNCT
ejpam-6529	257	15	6529	6529	NUM
ejpam-6529	257	16	10	10	NUM
ejpam-6529	257	17	of	of	ADP
ejpam-6529	257	18	16	16	NUM
ejpam-6529	257	19	proof	proof	NOUN
ejpam-6529	257	20	.	.	PUNCT
ejpam-6529	258	1	if	if	SCONJ
ejpam-6529	258	2	g	g	PROPN
ejpam-6529	258	3	is	be	AUX
ejpam-6529	258	4	a	a	DET
ejpam-6529	258	5	weak	weak	ADJ
ejpam-6529	258	6	filter	filter	NOUN
ejpam-6529	258	7	of	of	ADP
ejpam-6529	258	8	x	x	X
ejpam-6529	258	9	:	:	PUNCT
ejpam-6529	258	10	=	=	SYM
ejpam-6529	258	11	(	(	PUNCT
ejpam-6529	258	12	x	x	NOUN
ejpam-6529	258	13	,	,	PUNCT
ejpam-6529	258	14	|	|	NOUN
ejpam-6529	258	15	)	)	PUNCT
ejpam-6529	258	16	,	,	PUNCT
ejpam-6529	258	17	then	then	ADV
ejpam-6529	258	18	g∗	g∗	VERB
ejpam-6529	258	19	is	be	AUX
ejpam-6529	258	20	a	a	DET
ejpam-6529	258	21	weak	weak	ADJ
ejpam-6529	258	22	filter	filter	NOUN
ejpam-6529	258	23	of	of	ADP
ejpam-6529	258	24	x	x	X
ejpam-6529	258	25	:	:	PUNCT
ejpam-6529	258	26	=	=	SYM
ejpam-6529	258	27	(	(	PUNCT
ejpam-6529	258	28	x	x	NOUN
ejpam-6529	258	29	,	,	PUNCT
ejpam-6529	258	30	|	|	NOUN
ejpam-6529	258	31	)	)	PUNCT
ejpam-6529	258	32	(	(	PUNCT
ejpam-6529	258	33	see	see	VERB
ejpam-6529	258	34	[	[	X
ejpam-6529	258	35	13	13	NUM
ejpam-6529	258	36	]	]	NUM
ejpam-6529	258	37	)	)	PUNCT
ejpam-6529	258	38	.	.	PUNCT
ejpam-6529	259	1	hence	hence	ADV
ejpam-6529	259	2	b∗	b∗	ADV
ejpam-6529	259	3	g	g	NOUN
ejpam-6529	259	4	:	:	PUNCT
ejpam-6529	259	5	=	=	SYM
ejpam-6529	259	6	(	(	PUNCT
ejpam-6529	259	7	x	x	X
ejpam-6529	259	8	;	;	PUNCT
ejpam-6529	259	9	fg	fg	PROPN
ejpam-6529	259	10	b	b	PROPN
ejpam-6529	259	11	,	,	PUNCT
ejpam-6529	259	12	ggb	ggb	PROPN
ejpam-6529	259	13	)	)	PUNCT
ejpam-6529	259	14	is	be	AUX
ejpam-6529	259	15	an	an	DET
ejpam-6529	259	16	intuitionistic	intuitionistic	ADJ
ejpam-6529	259	17	fuzzy	fuzzy	ADJ
ejpam-6529	259	18	weak	weak	ADJ
ejpam-6529	259	19	filter	filter	NOUN
ejpam-6529	259	20	of	of	ADP
ejpam-6529	259	21	x	x	X
ejpam-6529	259	22	:	:	PUNCT
ejpam-6529	259	23	=	=	SYM
ejpam-6529	259	24	(	(	PUNCT
ejpam-6529	259	25	x	x	NOUN
ejpam-6529	259	26	,	,	PUNCT
ejpam-6529	259	27	|	|	ADV
ejpam-6529	259	28	)	)	PUNCT
ejpam-6529	259	29	by	by	ADP
ejpam-6529	259	30	theorem	theorem	ADJ
ejpam-6529	259	31	4	4	NUM
ejpam-6529	259	32	.	.	PUNCT
ejpam-6529	259	33	theorem	theorem	NOUN
ejpam-6529	259	34	5	5	NUM
ejpam-6529	259	35	.	.	PUNCT
ejpam-6529	260	1	let	let	VERB
ejpam-6529	260	2	{	{	PUNCT
ejpam-6529	260	3	fi	fi	NOUN
ejpam-6529	260	4	|	|	INTJ
ejpam-6529	260	5	i	i	PRON
ejpam-6529	260	6	∈	∈	VERB
ejpam-6529	260	7	γ	γ	X
ejpam-6529	260	8	⊆	⊆	NUM
ejpam-6529	260	9	(	(	PUNCT
ejpam-6529	260	10	0	0	NUM
ejpam-6529	260	11	,	,	PUNCT
ejpam-6529	260	12	1	1	NUM
ejpam-6529	260	13	]	]	PUNCT
ejpam-6529	260	14	}	}	PUNCT
ejpam-6529	260	15	and	and	CCONJ
ejpam-6529	260	16	{	{	PUNCT
ejpam-6529	260	17	gi	gi	INTJ
ejpam-6529	261	1	|	|	ADV
ejpam-6529	262	1	i	i	PRON
ejpam-6529	262	2	∈	∈	VERB
ejpam-6529	263	1	λ	λ	NOUN
ejpam-6529	263	2	⊆	⊆	NUM
ejpam-6529	263	3	[	[	X
ejpam-6529	263	4	0	0	NUM
ejpam-6529	263	5	,	,	PUNCT
ejpam-6529	263	6	1	1	NUM
ejpam-6529	263	7	)	)	PUNCT
ejpam-6529	263	8	}	}	PUNCT
ejpam-6529	263	9	be	be	AUX
ejpam-6529	263	10	collections	collection	NOUN
ejpam-6529	263	11	of	of	ADP
ejpam-6529	263	12	weak	weak	ADJ
ejpam-6529	263	13	filters	filter	NOUN
ejpam-6529	263	14	of	of	ADP
ejpam-6529	263	15	x	x	X
ejpam-6529	263	16	:	:	PUNCT
ejpam-6529	263	17	=	=	SYM
ejpam-6529	263	18	(	(	PUNCT
ejpam-6529	263	19	x	x	NOUN
ejpam-6529	263	20	,	,	PUNCT
ejpam-6529	263	21	|	|	NOUN
ejpam-6529	263	22	)	)	PUNCT
ejpam-6529	263	23	that	that	PRON
ejpam-6529	263	24	satisfy	satisfy	VERB
ejpam-6529	263	25	⋃	⋃	NOUN
ejpam-6529	263	26	i∈γ	i∈γ	NOUN
ejpam-6529	263	27	fi	fi	NOUN
ejpam-6529	264	1	=	=	NOUN
ejpam-6529	264	2	x	x	SYM
ejpam-6529	264	3	=	=	PUNCT
ejpam-6529	264	4	⋃	⋃	NOUN
ejpam-6529	264	5	i∈λ	i∈λ	NOUN
ejpam-6529	264	6	gi	gi	NOUN
ejpam-6529	264	7	,	,	PUNCT
ejpam-6529	264	8	and	and	CCONJ
ejpam-6529	264	9	fj	fj	PROPN
ejpam-6529	264	10	⊂	⊂	PROPN
ejpam-6529	264	11	fi	fi	PROPN
ejpam-6529	265	1	⇔	⇔	PROPN
ejpam-6529	265	2	i	i	PROPN
ejpam-6529	265	3	<	<	X
ejpam-6529	265	4	j	j	PROPN
ejpam-6529	265	5	⇔	⇔	PROPN
ejpam-6529	265	6	gj	gj	PROPN
ejpam-6529	265	7	⊂	⊂	PROPN
ejpam-6529	265	8	gi	gi	VERB
ejpam-6529	265	9	for	for	ADP
ejpam-6529	265	10	all	all	DET
ejpam-6529	265	11	i	i	PRON
ejpam-6529	265	12	,	,	PUNCT
ejpam-6529	265	13	j	j	PROPN
ejpam-6529	265	14	∈	∈	PROPN
ejpam-6529	265	15	γ	γ	PROPN
ejpam-6529	265	16	∪	∪	X
ejpam-6529	265	17	λ	λ	PROPN
ejpam-6529	265	18	.	.	PUNCT
ejpam-6529	266	1	if	if	SCONJ
ejpam-6529	266	2	we	we	PRON
ejpam-6529	266	3	define	define	VERB
ejpam-6529	266	4	an	an	DET
ejpam-6529	266	5	intuitionistic	intuitionistic	ADJ
ejpam-6529	266	6	fuzzy	fuzzy	ADJ
ejpam-6529	266	7	set	set	VERB
ejpam-6529	266	8	b∗	b∗	ADJ
ejpam-6529	266	9	:	:	PUNCT
ejpam-6529	266	10	=	=	SYM
ejpam-6529	266	11	(	(	PUNCT
ejpam-6529	266	12	x	x	X
ejpam-6529	266	13	;	;	PUNCT
ejpam-6529	266	14	fb	fb	INTJ
ejpam-6529	266	15	,	,	PUNCT
ejpam-6529	266	16	gb	gb	NOUN
ejpam-6529	266	17	)	)	PUNCT
ejpam-6529	266	18	in	in	ADP
ejpam-6529	266	19	x	x	PUNCT
ejpam-6529	266	20	by	by	ADP
ejpam-6529	266	21	fb(x	fb(x	ADJ
ejpam-6529	266	22	)	)	PUNCT
ejpam-6529	266	23	=	=	PUNCT
ejpam-6529	266	24	sup{i	sup{i	PROPN
ejpam-6529	266	25	∈	∈	PROPN
ejpam-6529	266	26	γ	γ	X
ejpam-6529	266	27	|	|	NOUN
ejpam-6529	266	28	x	x	SYM
ejpam-6529	266	29	∈	∈	NOUN
ejpam-6529	266	30	fi	fi	NOUN
ejpam-6529	266	31	}	}	PUNCT
ejpam-6529	266	32	and	and	CCONJ
ejpam-6529	266	33	gb(x	gb(x	NUM
ejpam-6529	266	34	)	)	PUNCT
ejpam-6529	266	35	=	=	PUNCT
ejpam-6529	266	36	inf{i	inf{i	VERB
ejpam-6529	266	37	∈	∈	PROPN
ejpam-6529	266	38	λ	λ	NOUN
ejpam-6529	266	39	|	|	NOUN
ejpam-6529	266	40	x	x	X
ejpam-6529	266	41	∈	∈	PROPN
ejpam-6529	266	42	gi	gi	NOUN
ejpam-6529	266	43	}	}	PUNCT
ejpam-6529	266	44	for	for	ADP
ejpam-6529	266	45	all	all	DET
ejpam-6529	266	46	x	x	SYM
ejpam-6529	266	47	∈	∈	PROPN
ejpam-6529	266	48	x	x	NOUN
ejpam-6529	266	49	,	,	PUNCT
ejpam-6529	266	50	then	then	ADV
ejpam-6529	266	51	it	it	PRON
ejpam-6529	266	52	is	be	AUX
ejpam-6529	266	53	an	an	DET
ejpam-6529	266	54	intuitionistic	intuitionistic	ADJ
ejpam-6529	266	55	fuzzy	fuzzy	ADJ
ejpam-6529	266	56	weak	weak	ADJ
ejpam-6529	266	57	filter	filter	NOUN
ejpam-6529	266	58	of	of	ADP
ejpam-6529	266	59	x	x	X
ejpam-6529	266	60	:	:	PUNCT
ejpam-6529	266	61	=	=	SYM
ejpam-6529	266	62	(	(	PUNCT
ejpam-6529	266	63	x	x	NOUN
ejpam-6529	266	64	,	,	PUNCT
ejpam-6529	266	65	|	|	NOUN
ejpam-6529	266	66	)	)	PUNCT
ejpam-6529	266	67	.	.	PUNCT
ejpam-6529	267	1	proof	proof	NOUN
ejpam-6529	267	2	.	.	PUNCT
ejpam-6529	268	1	it	it	PRON
ejpam-6529	268	2	is	be	AUX
ejpam-6529	268	3	sufficient	sufficient	ADJ
ejpam-6529	268	4	to	to	PART
ejpam-6529	268	5	show	show	VERB
ejpam-6529	268	6	that	that	SCONJ
ejpam-6529	268	7	(	(	PUNCT
ejpam-6529	268	8	fb	fb	INTJ
ejpam-6529	268	9	,	,	PUNCT
ejpam-6529	268	10	s)∈	s)∈	NUM
ejpam-6529	268	11	and	and	CCONJ
ejpam-6529	268	12	(	(	PUNCT
ejpam-6529	268	13	gb	gb	NOUN
ejpam-6529	268	14	,	,	PUNCT
ejpam-6529	268	15	t)∈	t)∈	NUM
ejpam-6529	268	16	are	be	AUX
ejpam-6529	268	17	weak	weak	ADJ
ejpam-6529	268	18	filters	filter	NOUN
ejpam-6529	268	19	of	of	ADP
ejpam-6529	268	20	x	x	PRON
ejpam-6529	268	21	:	:	PUNCT
ejpam-6529	268	22	=	=	SYM
ejpam-6529	268	23	(	(	PUNCT
ejpam-6529	268	24	x	x	NOUN
ejpam-6529	268	25	,	,	PUNCT
ejpam-6529	268	26	|	|	ADV
ejpam-6529	268	27	)	)	PUNCT
ejpam-6529	268	28	for	for	ADP
ejpam-6529	268	29	all	all	DET
ejpam-6529	268	30	(	(	PUNCT
ejpam-6529	268	31	s	s	PROPN
ejpam-6529	268	32	,	,	PUNCT
ejpam-6529	268	33	t	t	PROPN
ejpam-6529	268	34	)	)	PUNCT
ejpam-6529	268	35	∈	∈	PROPN
ejpam-6529	268	36	(	(	PUNCT
ejpam-6529	268	37	0	0	NUM
ejpam-6529	268	38	,	,	PUNCT
ejpam-6529	268	39	f(1	f(1	PROPN
ejpam-6529	268	40	)	)	PUNCT
ejpam-6529	268	41	]	]	PUNCT
ejpam-6529	269	1	×	×	NOUN
ejpam-6529	269	2	[	[	X
ejpam-6529	269	3	gb(1	gb(1	PROPN
ejpam-6529	269	4	)	)	PUNCT
ejpam-6529	269	5	,	,	PUNCT
ejpam-6529	269	6	1	1	NUM
ejpam-6529	269	7	)	)	PUNCT
ejpam-6529	269	8	according	accord	VERB
ejpam-6529	269	9	to	to	ADP
ejpam-6529	269	10	theorem	theorem	NOUN
ejpam-6529	269	11	2	2	NUM
ejpam-6529	269	12	.	.	PUNCT
ejpam-6529	270	1	if	if	SCONJ
ejpam-6529	270	2	s	s	AUX
ejpam-6529	270	3	=	=	SYM
ejpam-6529	270	4	sup{sa	sup{sa	X
ejpam-6529	270	5	∈	∈	PROPN
ejpam-6529	270	6	γ	γ	PROPN
ejpam-6529	270	7	|	|	NOUN
ejpam-6529	270	8	sa	sa	NOUN
ejpam-6529	270	9	<	<	X
ejpam-6529	270	10	s	s	PROPN
ejpam-6529	270	11	}	}	PUNCT
ejpam-6529	270	12	,	,	PUNCT
ejpam-6529	270	13	then	then	ADV
ejpam-6529	270	14	x	x	SYM
ejpam-6529	270	15	∈	∈	PROPN
ejpam-6529	270	16	(	(	PUNCT
ejpam-6529	270	17	fb	fb	INTJ
ejpam-6529	270	18	,	,	PUNCT
ejpam-6529	270	19	s)∈	s)∈	PROPN
ejpam-6529	270	20	⇔	⇔	NOUN
ejpam-6529	270	21	(	(	PUNCT
ejpam-6529	270	22	∀sa	∀sa	NOUN
ejpam-6529	270	23	<	<	X
ejpam-6529	270	24	s)(x	s)(x	PROPN
ejpam-6529	270	25	∈	∈	PROPN
ejpam-6529	270	26	fsa	fsa	PROPN
ejpam-6529	270	27	)	)	PUNCT
ejpam-6529	270	28	⇔	⇔	PROPN
ejpam-6529	270	29	x	x	SYM
ejpam-6529	270	30	∈	∈	PROPN
ejpam-6529	270	31	⋂	⋂	PROPN
ejpam-6529	270	32	sa	sa	X
ejpam-6529	270	33	<	<	X
ejpam-6529	270	34	s	s	X
ejpam-6529	270	35	fsa	fsa	PROPN
ejpam-6529	270	36	.	.	PUNCT
ejpam-6529	271	1	hence	hence	ADV
ejpam-6529	271	2	(	(	PUNCT
ejpam-6529	271	3	fb	fb	INTJ
ejpam-6529	271	4	,	,	PUNCT
ejpam-6529	271	5	s)∈	s)∈	NUM
ejpam-6529	271	6	=	=	SYM
ejpam-6529	272	1	⋂	⋂	PROPN
ejpam-6529	272	2	sa	sa	X
ejpam-6529	272	3	<	<	X
ejpam-6529	272	4	s	s	X
ejpam-6529	272	5	fsa	fsa	PROPN
ejpam-6529	272	6	is	be	AUX
ejpam-6529	272	7	a	a	DET
ejpam-6529	272	8	weak	weak	ADJ
ejpam-6529	272	9	filter	filter	NOUN
ejpam-6529	272	10	of	of	ADP
ejpam-6529	272	11	x	x	X
ejpam-6529	272	12	:	:	PUNCT
ejpam-6529	272	13	=	=	SYM
ejpam-6529	272	14	(	(	PUNCT
ejpam-6529	272	15	x	x	NOUN
ejpam-6529	272	16	,	,	PUNCT
ejpam-6529	272	17	|	|	NOUN
ejpam-6529	272	18	)	)	PUNCT
ejpam-6529	272	19	.	.	PUNCT
ejpam-6529	273	1	suppose	suppose	VERB
ejpam-6529	273	2	that	that	SCONJ
ejpam-6529	273	3	s	s	AUX
ejpam-6529	273	4	̸=	̸=	PROPN
ejpam-6529	273	5	sup{sa	sup{sa	NOUN
ejpam-6529	273	6	∈	∈	PROPN
ejpam-6529	273	7	γ	γ	PROPN
ejpam-6529	273	8	|	|	NOUN
ejpam-6529	273	9	sa	sa	NOUN
ejpam-6529	273	10	<	<	X
ejpam-6529	273	11	s	s	PROPN
ejpam-6529	273	12	}	}	PUNCT
ejpam-6529	273	13	.	.	PUNCT
ejpam-6529	274	1	if	if	SCONJ
ejpam-6529	274	2	x	x	SYM
ejpam-6529	274	3	∈	∈	PROPN
ejpam-6529	274	4	⋃	⋃	PUNCT
ejpam-6529	274	5	sa≥s	sa≥s	NOUN
ejpam-6529	274	6	fsa	fsa	PROPN
ejpam-6529	274	7	,	,	PUNCT
ejpam-6529	274	8	then	then	ADV
ejpam-6529	274	9	x	x	PROPN
ejpam-6529	274	10	∈	∈	PROPN
ejpam-6529	274	11	fsa	fsa	PROPN
ejpam-6529	274	12	for	for	ADP
ejpam-6529	274	13	some	some	DET
ejpam-6529	274	14	sa	sa	PROPN
ejpam-6529	274	15	≥	≥	PROPN
ejpam-6529	274	16	s	s	PROPN
ejpam-6529	274	17	,	,	PUNCT
ejpam-6529	274	18	and	and	CCONJ
ejpam-6529	274	19	so	so	ADV
ejpam-6529	274	20	fb(x	fb(x	PUNCT
ejpam-6529	274	21	)	)	PUNCT
ejpam-6529	274	22	=	=	PUNCT
ejpam-6529	274	23	sup{s	sup{s	PROPN
ejpam-6529	274	24	∈	∈	PROPN
ejpam-6529	274	25	γ	γ	NOUN
ejpam-6529	274	26	|	|	NOUN
ejpam-6529	274	27	x	x	SYM
ejpam-6529	274	28	∈	∈	PROPN
ejpam-6529	274	29	fs	fs	PROPN
ejpam-6529	274	30	}	}	PUNCT
ejpam-6529	274	31	≥	≥	PROPN
ejpam-6529	274	32	sa	sa	PROPN
ejpam-6529	274	33	≥	≥	NOUN
ejpam-6529	274	34	s	s	PROPN
ejpam-6529	274	35	,	,	PUNCT
ejpam-6529	274	36	i.e.	i.e.	X
ejpam-6529	274	37	,	,	PUNCT
ejpam-6529	274	38	x	x	SYM
ejpam-6529	274	39	∈	∈	PROPN
ejpam-6529	274	40	(	(	PUNCT
ejpam-6529	274	41	fb	fb	INTJ
ejpam-6529	274	42	,	,	PUNCT
ejpam-6529	274	43	s)∈.	s)∈.	VERB
ejpam-6529	274	44	this	this	PRON
ejpam-6529	274	45	shows	show	VERB
ejpam-6529	274	46	that	that	SCONJ
ejpam-6529	274	47	⋃	⋃	PUNCT
ejpam-6529	274	48	sa≥s	sa≥s	PROPN
ejpam-6529	274	49	fsa	fsa	PROPN
ejpam-6529	274	50	⊆	⊆	NUM
ejpam-6529	274	51	(	(	PUNCT
ejpam-6529	274	52	fb	fb	INTJ
ejpam-6529	274	53	,	,	PUNCT
ejpam-6529	274	54	s)∈.	s)∈.	VERB
ejpam-6529	274	55	if	if	SCONJ
ejpam-6529	274	56	x	x	PRON
ejpam-6529	274	57	/∈	/∈	PUNCT
ejpam-6529	274	58	⋃	⋃	ADP
ejpam-6529	274	59	sa≥s	sa≥s	PROPN
ejpam-6529	274	60	fsa	fsa	PROPN
ejpam-6529	274	61	,	,	PUNCT
ejpam-6529	274	62	then	then	ADV
ejpam-6529	274	63	x	x	PROPN
ejpam-6529	274	64	/∈	/∈	PUNCT
ejpam-6529	274	65	fsa	fsa	PROPN
ejpam-6529	274	66	for	for	ADP
ejpam-6529	274	67	all	all	DET
ejpam-6529	274	68	sa	sa	PROPN
ejpam-6529	274	69	≥	≥	PROPN
ejpam-6529	274	70	s.	s.	PROPN
ejpam-6529	274	71	since	since	SCONJ
ejpam-6529	274	72	s	s	PROPN
ejpam-6529	274	73	̸=	̸=	PROPN
ejpam-6529	274	74	sup{sa	sup{sa	NOUN
ejpam-6529	274	75	∈	∈	PROPN
ejpam-6529	274	76	γ	γ	PROPN
ejpam-6529	274	77	|	|	NOUN
ejpam-6529	274	78	sa	sa	NOUN
ejpam-6529	274	79	<	<	X
ejpam-6529	274	80	s	s	PROPN
ejpam-6529	274	81	}	}	PUNCT
ejpam-6529	274	82	,	,	PUNCT
ejpam-6529	274	83	there	there	PRON
ejpam-6529	274	84	exists	exist	VERB
ejpam-6529	274	85	εa	εa	NOUN
ejpam-6529	274	86	>	>	X
ejpam-6529	274	87	0	0	NUM
ejpam-6529	274	88	such	such	ADJ
ejpam-6529	274	89	that	that	SCONJ
ejpam-6529	274	90	(	(	PUNCT
ejpam-6529	274	91	s	s	AUX
ejpam-6529	274	92	−	−	NOUN
ejpam-6529	274	93	εa	εa	PROPN
ejpam-6529	274	94	,	,	PUNCT
ejpam-6529	274	95	s	s	PART
ejpam-6529	274	96	)	)	PUNCT
ejpam-6529	274	97	∩	∩	NOUN
ejpam-6529	274	98	γ	γ	X
ejpam-6529	274	99	=	=	X
ejpam-6529	274	100	∅.	∅.	VERB
ejpam-6529	274	101	hence	hence	ADV
ejpam-6529	274	102	x	x	PROPN
ejpam-6529	274	103	/∈	/∈	PUNCT
ejpam-6529	274	104	fsa	fsa	PROPN
ejpam-6529	274	105	for	for	ADP
ejpam-6529	274	106	all	all	DET
ejpam-6529	274	107	sa	sa	PROPN
ejpam-6529	274	108	>	>	X
ejpam-6529	274	109	s	s	PROPN
ejpam-6529	274	110	−	−	NOUN
ejpam-6529	274	111	εa	εa	NOUN
ejpam-6529	274	112	,	,	PUNCT
ejpam-6529	274	113	and	and	CCONJ
ejpam-6529	274	114	so	so	ADV
ejpam-6529	274	115	if	if	SCONJ
ejpam-6529	274	116	x	x	PROPN
ejpam-6529	274	117	∈	∈	PROPN
ejpam-6529	274	118	fsa	fsa	PROPN
ejpam-6529	274	119	then	then	ADV
ejpam-6529	274	120	sa	sa	VERB
ejpam-6529	274	121	≤	≤	PROPN
ejpam-6529	274	122	s	s	PART
ejpam-6529	274	123	−	−	NOUN
ejpam-6529	274	124	εa	εa	NOUN
ejpam-6529	274	125	.	.	PUNCT
ejpam-6529	275	1	thus	thus	ADV
ejpam-6529	275	2	fb(x	fb(x	VERB
ejpam-6529	275	3	)	)	PUNCT
ejpam-6529	275	4	≤	≤	PROPN
ejpam-6529	275	5	s	s	PART
ejpam-6529	275	6	−	−	NOUN
ejpam-6529	275	7	εa	εa	NOUN
ejpam-6529	275	8	<	<	X
ejpam-6529	275	9	s	s	PROPN
ejpam-6529	275	10	,	,	PUNCT
ejpam-6529	275	11	that	that	ADV
ejpam-6529	275	12	is	is	ADV
ejpam-6529	275	13	,	,	PUNCT
ejpam-6529	275	14	x	x	X
ejpam-6529	275	15	/∈	/∈	PUNCT
ejpam-6529	275	16	(	(	PUNCT
ejpam-6529	275	17	fb	fb	INTJ
ejpam-6529	275	18	,	,	PUNCT
ejpam-6529	275	19	s)∈.	s)∈.	PROPN
ejpam-6529	275	20	therefore	therefore	ADV
ejpam-6529	275	21	(	(	PUNCT
ejpam-6529	275	22	fb	fb	INTJ
ejpam-6529	275	23	,	,	PUNCT
ejpam-6529	275	24	s)∈	s)∈	X
ejpam-6529	275	25	=	=	SYM
ejpam-6529	275	26	⋃	⋃	NOUN
ejpam-6529	275	27	sa≥s	sa≥s	X
ejpam-6529	275	28	fsa	fsa	PROPN
ejpam-6529	275	29	,	,	PUNCT
ejpam-6529	275	30	and	and	CCONJ
ejpam-6529	275	31	it	it	PRON
ejpam-6529	275	32	is	be	AUX
ejpam-6529	275	33	a	a	DET
ejpam-6529	275	34	weak	weak	ADJ
ejpam-6529	275	35	filter	filter	NOUN
ejpam-6529	275	36	of	of	ADP
ejpam-6529	275	37	x	x	X
ejpam-6529	275	38	:	:	PUNCT
ejpam-6529	275	39	=	=	SYM
ejpam-6529	275	40	(	(	PUNCT
ejpam-6529	275	41	x	x	NOUN
ejpam-6529	275	42	,	,	PUNCT
ejpam-6529	275	43	|	|	NOUN
ejpam-6529	275	44	)	)	PUNCT
ejpam-6529	275	45	.	.	PUNCT
ejpam-6529	276	1	in	in	ADP
ejpam-6529	276	2	order	order	NOUN
ejpam-6529	276	3	to	to	PART
ejpam-6529	276	4	show	show	VERB
ejpam-6529	276	5	that	that	SCONJ
ejpam-6529	276	6	(	(	PUNCT
ejpam-6529	276	7	gb	gb	NOUN
ejpam-6529	276	8	,	,	PUNCT
ejpam-6529	276	9	t)∈	t)∈	NUM
ejpam-6529	276	10	is	be	AUX
ejpam-6529	276	11	a	a	DET
ejpam-6529	276	12	weak	weak	ADJ
ejpam-6529	276	13	filter	filter	NOUN
ejpam-6529	276	14	of	of	ADP
ejpam-6529	276	15	x	x	X
ejpam-6529	276	16	:	:	PUNCT
ejpam-6529	276	17	=	=	SYM
ejpam-6529	276	18	(	(	PUNCT
ejpam-6529	276	19	x	x	NOUN
ejpam-6529	276	20	,	,	PUNCT
ejpam-6529	276	21	|	|	NOUN
ejpam-6529	276	22	)	)	PUNCT
ejpam-6529	276	23	,	,	PUNCT
ejpam-6529	276	24	we	we	PRON
ejpam-6529	276	25	need	need	VERB
ejpam-6529	276	26	to	to	PART
ejpam-6529	276	27	consider	consider	VERB
ejpam-6529	276	28	the	the	DET
ejpam-6529	276	29	following	follow	VERB
ejpam-6529	276	30	two	two	NUM
ejpam-6529	276	31	cases	case	NOUN
ejpam-6529	276	32	:	:	PUNCT
ejpam-6529	276	33	t	t	PROPN
ejpam-6529	276	34	̸=	̸=	PROPN
ejpam-6529	276	35	inf{tb	inf{tb	ADP
ejpam-6529	276	36	∈	∈	PROPN
ejpam-6529	276	37	λ	λ	NOUN
ejpam-6529	276	38	|	|	ADV
ejpam-6529	276	39	tb	tb	X
ejpam-6529	276	40	>	>	X
ejpam-6529	276	41	t	t	PROPN
ejpam-6529	276	42	}	}	PUNCT
ejpam-6529	276	43	and	and	CCONJ
ejpam-6529	276	44	t	t	NOUN
ejpam-6529	276	45	=	=	PUNCT
ejpam-6529	276	46	inf{tb	inf{tb	ADP
ejpam-6529	276	47	∈	∈	PROPN
ejpam-6529	276	48	λ	λ	NOUN
ejpam-6529	276	49	|	|	ADV
ejpam-6529	276	50	tb	tb	X
ejpam-6529	276	51	>	>	X
ejpam-6529	276	52	t	t	PROPN
ejpam-6529	276	53	}	}	PUNCT
ejpam-6529	276	54	.	.	PUNCT
ejpam-6529	277	1	if	if	SCONJ
ejpam-6529	277	2	the	the	DET
ejpam-6529	277	3	first	first	ADJ
ejpam-6529	277	4	case	case	NOUN
ejpam-6529	277	5	is	be	AUX
ejpam-6529	277	6	valid	valid	ADJ
ejpam-6529	277	7	,	,	PUNCT
ejpam-6529	277	8	then	then	ADV
ejpam-6529	277	9	(	(	PUNCT
ejpam-6529	277	10	t	t	PROPN
ejpam-6529	277	11	,	,	PUNCT
ejpam-6529	277	12	t+	t+	VERB
ejpam-6529	277	13	εb	εb	ADP
ejpam-6529	277	14	)	)	PUNCT
ejpam-6529	277	15	and	and	CCONJ
ejpam-6529	277	16	λ	λ	NOUN
ejpam-6529	277	17	are	be	AUX
ejpam-6529	277	18	disjoint	disjoint	ADJ
ejpam-6529	277	19	for	for	ADP
ejpam-6529	277	20	some	some	PRON
ejpam-6529	277	21	εb	εb	ADP
ejpam-6529	277	22	>	>	X
ejpam-6529	277	23	0	0	X
ejpam-6529	277	24	.	.	PUNCT
ejpam-6529	278	1	we	we	PRON
ejpam-6529	278	2	will	will	AUX
ejpam-6529	278	3	verify	verify	VERB
ejpam-6529	278	4	that	that	SCONJ
ejpam-6529	278	5	(	(	PUNCT
ejpam-6529	278	6	gb	gb	NOUN
ejpam-6529	278	7	,	,	PUNCT
ejpam-6529	278	8	t)∈	t)∈	PROPN
ejpam-6529	278	9	=	=	SYM
ejpam-6529	278	10	⋃	⋃	ADP
ejpam-6529	278	11	tb≤t	tb≤t	NOUN
ejpam-6529	278	12	gtb	gtb	NOUN
ejpam-6529	278	13	.	.	PUNCT
ejpam-6529	279	1	if	if	SCONJ
ejpam-6529	279	2	y	y	PROPN
ejpam-6529	279	3	∈	∈	PROPN
ejpam-6529	279	4	⋃	⋃	PUNCT
ejpam-6529	279	5	tb≤t	tb≤t	NOUN
ejpam-6529	279	6	gtb	gtb	NOUN
ejpam-6529	279	7	,	,	PUNCT
ejpam-6529	279	8	then	then	ADV
ejpam-6529	279	9	y	y	PROPN
ejpam-6529	279	10	∈	∈	PROPN
ejpam-6529	279	11	gtb	gtb	NOUN
ejpam-6529	279	12	for	for	ADP
ejpam-6529	279	13	some	some	DET
ejpam-6529	279	14	tb	tb	ADP
ejpam-6529	279	15	≤	≤	NOUN
ejpam-6529	279	16	t.	t.	NOUN
ejpam-6529	279	17	it	it	PRON
ejpam-6529	279	18	follows	follow	VERB
ejpam-6529	279	19	that	that	SCONJ
ejpam-6529	279	20	gb(y	gb(y	ADV
ejpam-6529	279	21	)	)	PUNCT
ejpam-6529	279	22	=	=	PUNCT
ejpam-6529	280	1	inf{t	inf{t	NOUN
ejpam-6529	280	2	∈	∈	PROPN
ejpam-6529	280	3	λ	λ	NOUN
ejpam-6529	280	4	|	|	NOUN
ejpam-6529	280	5	y	y	PROPN
ejpam-6529	280	6	∈	∈	PROPN
ejpam-6529	280	7	gt	gt	PROPN
ejpam-6529	280	8	}	}	PUNCT
ejpam-6529	280	9	≤	≤	NOUN
ejpam-6529	280	10	tb	tb	ADP
ejpam-6529	280	11	≤	≤	NUM
ejpam-6529	280	12	t	t	PROPN
ejpam-6529	280	13	,	,	PUNCT
ejpam-6529	280	14	i.e.	i.e.	X
ejpam-6529	280	15	,	,	PUNCT
ejpam-6529	280	16	y	y	PROPN
ejpam-6529	280	17	∈	∈	PROPN
ejpam-6529	280	18	(	(	PUNCT
ejpam-6529	280	19	gb	gb	NOUN
ejpam-6529	280	20	,	,	PUNCT
ejpam-6529	280	21	t)∈.	t)∈.	PROPN
ejpam-6529	280	22	if	if	SCONJ
ejpam-6529	280	23	y	y	PROPN
ejpam-6529	280	24	/∈	/∈	PUNCT
ejpam-6529	281	1	⋃	⋃	VERB
ejpam-6529	281	2	tb≤t	tb≤t	NOUN
ejpam-6529	281	3	gtb	gtb	NOUN
ejpam-6529	281	4	,	,	PUNCT
ejpam-6529	281	5	then	then	ADV
ejpam-6529	281	6	y	y	PROPN
ejpam-6529	281	7	/∈	/∈	PUNCT
ejpam-6529	281	8	gtb	gtb	NOUN
ejpam-6529	281	9	for	for	ADP
ejpam-6529	281	10	all	all	DET
ejpam-6529	281	11	tb	tb	ADP
ejpam-6529	281	12	≤	≤	NUM
ejpam-6529	281	13	t	t	NOUN
ejpam-6529	281	14	<	<	X
ejpam-6529	281	15	t+	t+	X
ejpam-6529	281	16	εb	εb	ADP
ejpam-6529	281	17	.	.	PUNCT
ejpam-6529	282	1	this	this	PRON
ejpam-6529	282	2	shows	show	VERB
ejpam-6529	282	3	that	that	SCONJ
ejpam-6529	282	4	if	if	SCONJ
ejpam-6529	282	5	y	y	PROPN
ejpam-6529	282	6	∈	∈	PROPN
ejpam-6529	282	7	gtb	gtb	NOUN
ejpam-6529	282	8	,	,	PUNCT
ejpam-6529	282	9	then	then	ADV
ejpam-6529	282	10	tb	tb	ADP
ejpam-6529	282	11	≥	≥	NOUN
ejpam-6529	282	12	t+	t+	VERB
ejpam-6529	282	13	εb	εb	ADP
ejpam-6529	282	14	>	>	X
ejpam-6529	282	15	t	t	PROPN
ejpam-6529	282	16	,	,	PUNCT
ejpam-6529	282	17	i.e.	i.e.	X
ejpam-6529	282	18	,	,	PUNCT
ejpam-6529	282	19	y	y	PROPN
ejpam-6529	282	20	/∈	/∈	PUNCT
ejpam-6529	282	21	(	(	PUNCT
ejpam-6529	282	22	gb	gb	ADP
ejpam-6529	282	23	,	,	PUNCT
ejpam-6529	282	24	t)∈.	t)∈.	PROPN
ejpam-6529	282	25	hence	hence	ADV
ejpam-6529	282	26	(	(	PUNCT
ejpam-6529	282	27	gb	gb	NOUN
ejpam-6529	282	28	,	,	PUNCT
ejpam-6529	282	29	t)∈	t)∈	PROPN
ejpam-6529	282	30	=	=	PUNCT
ejpam-6529	282	31	⋃	⋃	ADP
ejpam-6529	282	32	tb≤t	tb≤t	NOUN
ejpam-6529	282	33	gtb	gtb	NOUN
ejpam-6529	282	34	which	which	PRON
ejpam-6529	282	35	is	be	AUX
ejpam-6529	282	36	a	a	DET
ejpam-6529	282	37	weak	weak	ADJ
ejpam-6529	282	38	filter	filter	NOUN
ejpam-6529	282	39	of	of	ADP
ejpam-6529	282	40	x	x	X
ejpam-6529	282	41	:	:	PUNCT
ejpam-6529	282	42	=	=	SYM
ejpam-6529	282	43	(	(	PUNCT
ejpam-6529	282	44	x	x	NOUN
ejpam-6529	282	45	,	,	PUNCT
ejpam-6529	282	46	|	|	NOUN
ejpam-6529	282	47	)	)	PUNCT
ejpam-6529	282	48	.	.	PUNCT
ejpam-6529	283	1	for	for	ADP
ejpam-6529	283	2	the	the	DET
ejpam-6529	283	3	second	second	ADJ
ejpam-6529	283	4	case	case	NOUN
ejpam-6529	283	5	,	,	PUNCT
ejpam-6529	283	6	we	we	PRON
ejpam-6529	283	7	have	have	VERB
ejpam-6529	283	8	y	y	PROPN
ejpam-6529	283	9	∈	∈	PROPN
ejpam-6529	283	10	(	(	PUNCT
ejpam-6529	283	11	gb	gb	NOUN
ejpam-6529	283	12	,	,	PUNCT
ejpam-6529	283	13	t)∈	t)∈	PROPN
ejpam-6529	283	14	⇔	⇔	X
ejpam-6529	283	15	(	(	PUNCT
ejpam-6529	283	16	∀tb	∀tb	PROPN
ejpam-6529	283	17	>	>	X
ejpam-6529	283	18	t)(y	t)(y	PROPN
ejpam-6529	283	19	∈	∈	PROPN
ejpam-6529	283	20	gtb	gtb	PROPN
ejpam-6529	283	21	)	)	PUNCT
ejpam-6529	283	22	⇔	⇔	PROPN
ejpam-6529	283	23	y	y	PROPN
ejpam-6529	283	24	∈	∈	PROPN
ejpam-6529	283	25	⋂	⋂	PROPN
ejpam-6529	283	26	tb	tb	X
ejpam-6529	283	27	>	>	X
ejpam-6529	283	28	t	t	PROPN
ejpam-6529	283	29	gtb	gtb	NOUN
ejpam-6529	283	30	.	.	PUNCT
ejpam-6529	284	1	s.	s.	PROPN
ejpam-6529	284	2	s.	s.	PROPN
ejpam-6529	284	3	ahn	ahn	PROPN
ejpam-6529	284	4	,	,	PUNCT
ejpam-6529	284	5	y.	y.	PROPN
ejpam-6529	284	6	j.	j.	PROPN
ejpam-6529	284	7	seo	seo	PROPN
ejpam-6529	284	8	,	,	PUNCT
ejpam-6529	284	9	y.	y.	PROPN
ejpam-6529	284	10	b.	b.	PROPN
ejpam-6529	284	11	jun	jun	PROPN
ejpam-6529	284	12	/	/	SYM
ejpam-6529	284	13	eur	eur	PROPN
ejpam-6529	284	14	.	.	PUNCT
ejpam-6529	285	1	j.	j.	PROPN
ejpam-6529	285	2	pure	pure	PROPN
ejpam-6529	285	3	appl	appl	PROPN
ejpam-6529	285	4	.	.	PROPN
ejpam-6529	285	5	math	math	PROPN
ejpam-6529	285	6	,	,	PUNCT
ejpam-6529	285	7	18	18	NUM
ejpam-6529	285	8	(	(	PUNCT
ejpam-6529	285	9	3	3	NUM
ejpam-6529	285	10	)	)	PUNCT
ejpam-6529	285	11	(	(	PUNCT
ejpam-6529	285	12	2025	2025	NUM
ejpam-6529	285	13	)	)	PUNCT
ejpam-6529	285	14	,	,	PUNCT
ejpam-6529	285	15	6529	6529	NUM
ejpam-6529	285	16	11	11	NUM
ejpam-6529	285	17	of	of	ADP
ejpam-6529	285	18	16	16	NUM
ejpam-6529	285	19	hence	hence	ADV
ejpam-6529	285	20	(	(	PUNCT
ejpam-6529	285	21	gb	gb	NOUN
ejpam-6529	285	22	,	,	PUNCT
ejpam-6529	285	23	t)∈	t)∈	PROPN
ejpam-6529	285	24	=	=	SYM
ejpam-6529	285	25	⋂	⋂	PROPN
ejpam-6529	285	26	tb	tb	X
ejpam-6529	285	27	>	>	X
ejpam-6529	285	28	t	t	PROPN
ejpam-6529	285	29	gtb	gtb	NOUN
ejpam-6529	285	30	is	be	AUX
ejpam-6529	285	31	a	a	DET
ejpam-6529	285	32	weak	weak	ADJ
ejpam-6529	285	33	filter	filter	NOUN
ejpam-6529	285	34	of	of	ADP
ejpam-6529	285	35	x	x	X
ejpam-6529	285	36	:	:	PUNCT
ejpam-6529	285	37	=	=	SYM
ejpam-6529	285	38	(	(	PUNCT
ejpam-6529	285	39	x	x	NOUN
ejpam-6529	285	40	,	,	PUNCT
ejpam-6529	285	41	|	|	NOUN
ejpam-6529	285	42	)	)	PUNCT
ejpam-6529	285	43	.	.	PUNCT
ejpam-6529	286	1	this	this	PRON
ejpam-6529	286	2	completes	complete	VERB
ejpam-6529	286	3	the	the	DET
ejpam-6529	286	4	proof	proof	NOUN
ejpam-6529	286	5	.	.	PUNCT
ejpam-6529	287	1	given	give	VERB
ejpam-6529	287	2	an	an	DET
ejpam-6529	287	3	intuitionistic	intuitionistic	ADJ
ejpam-6529	287	4	fuzzy	fuzzy	ADJ
ejpam-6529	287	5	set	set	VERB
ejpam-6529	287	6	b∗	b∗	ADJ
ejpam-6529	287	7	:	:	PUNCT
ejpam-6529	287	8	=	=	SYM
ejpam-6529	287	9	(	(	PUNCT
ejpam-6529	287	10	x	x	X
ejpam-6529	287	11	;	;	PUNCT
ejpam-6529	287	12	fb	fb	INTJ
ejpam-6529	287	13	,	,	PUNCT
ejpam-6529	287	14	gb	gb	NOUN
ejpam-6529	287	15	)	)	PUNCT
ejpam-6529	287	16	in	in	ADP
ejpam-6529	287	17	x	x	X
ejpam-6529	287	18	,	,	PUNCT
ejpam-6529	287	19	consider	consider	VERB
ejpam-6529	287	20	the	the	DET
ejpam-6529	287	21	following	follow	VERB
ejpam-6529	287	22	set	set	NOUN
ejpam-6529	287	23	:	:	PUNCT
ejpam-6529	287	24	x(0,1	x(0,1	X
ejpam-6529	287	25	)	)	PUNCT
ejpam-6529	287	26	:	:	PUNCT
ejpam-6529	287	27	=	=	SYM
ejpam-6529	287	28	{	{	PUNCT
ejpam-6529	287	29	x	x	PUNCT
ejpam-6529	287	30	∈	∈	PROPN
ejpam-6529	287	31	x	x	X
ejpam-6529	287	32	|	|	ADV
ejpam-6529	287	33	fb(x	fb(x	PUNCT
ejpam-6529	287	34	)	)	PUNCT
ejpam-6529	287	35	̸=	̸=	PROPN
ejpam-6529	287	36	0	0	NUM
ejpam-6529	287	37	,	,	PUNCT
ejpam-6529	287	38	gb(x	gb(x	PUNCT
ejpam-6529	287	39	)	)	PUNCT
ejpam-6529	287	40	̸=	̸=	NOUN
ejpam-6529	287	41	1	1	NUM
ejpam-6529	287	42	}	}	PUNCT
ejpam-6529	287	43	which	which	PRON
ejpam-6529	287	44	is	be	AUX
ejpam-6529	287	45	called	call	VERB
ejpam-6529	287	46	the	the	DET
ejpam-6529	287	47	(	(	PUNCT
ejpam-6529	287	48	0	0	NUM
ejpam-6529	287	49	,	,	PUNCT
ejpam-6529	287	50	1)-set	1)-set	NOUN
ejpam-6529	287	51	of	of	ADP
ejpam-6529	287	52	b∗	b∗	ADJ
ejpam-6529	287	53	:	:	PUNCT
ejpam-6529	287	54	=	=	SYM
ejpam-6529	287	55	(	(	PUNCT
ejpam-6529	287	56	x	x	X
ejpam-6529	287	57	;	;	PUNCT
ejpam-6529	287	58	fb	fb	INTJ
ejpam-6529	287	59	,	,	PUNCT
ejpam-6529	287	60	gb	gb	NOUN
ejpam-6529	287	61	)	)	PUNCT
ejpam-6529	287	62	.	.	PUNCT
ejpam-6529	288	1	we	we	PRON
ejpam-6529	288	2	explore	explore	VERB
ejpam-6529	288	3	the	the	DET
ejpam-6529	288	4	conditions	condition	NOUN
ejpam-6529	288	5	under	under	ADP
ejpam-6529	288	6	which	which	PRON
ejpam-6529	288	7	the	the	DET
ejpam-6529	288	8	nonempty	nonempty	ADJ
ejpam-6529	288	9	(	(	PUNCT
ejpam-6529	288	10	0	0	NUM
ejpam-6529	288	11	,	,	PUNCT
ejpam-6529	288	12	1)-set	1)-set	NOUN
ejpam-6529	288	13	is	be	AUX
ejpam-6529	288	14	a	a	DET
ejpam-6529	288	15	weak	weak	ADJ
ejpam-6529	288	16	filter	filter	NOUN
ejpam-6529	288	17	.	.	PUNCT
ejpam-6529	289	1	theorem	theorem	ADJ
ejpam-6529	289	2	6	6	NUM
ejpam-6529	289	3	.	.	PUNCT
ejpam-6529	290	1	if	if	SCONJ
ejpam-6529	290	2	b∗	b∗	ADJ
ejpam-6529	290	3	:	:	PUNCT
ejpam-6529	290	4	=	=	SYM
ejpam-6529	290	5	(	(	PUNCT
ejpam-6529	290	6	x	x	X
ejpam-6529	290	7	;	;	PUNCT
ejpam-6529	290	8	fb	fb	INTJ
ejpam-6529	290	9	,	,	PUNCT
ejpam-6529	290	10	gb	gb	PROPN
ejpam-6529	290	11	)	)	PUNCT
ejpam-6529	290	12	is	be	AUX
ejpam-6529	290	13	an	an	DET
ejpam-6529	290	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	290	15	fuzzy	fuzzy	ADJ
ejpam-6529	290	16	weak	weak	ADJ
ejpam-6529	290	17	filter	filter	NOUN
ejpam-6529	290	18	of	of	ADP
ejpam-6529	290	19	x	x	X
ejpam-6529	290	20	:	:	PUNCT
ejpam-6529	290	21	=	=	SYM
ejpam-6529	290	22	(	(	PUNCT
ejpam-6529	290	23	x	x	NOUN
ejpam-6529	290	24	,	,	PUNCT
ejpam-6529	290	25	|	|	NOUN
ejpam-6529	290	26	)	)	PUNCT
ejpam-6529	290	27	,	,	PUNCT
ejpam-6529	290	28	then	then	ADV
ejpam-6529	290	29	its	its	PRON
ejpam-6529	290	30	nonempty	nonempty	ADJ
ejpam-6529	290	31	(	(	PUNCT
ejpam-6529	290	32	0	0	NUM
ejpam-6529	290	33	,	,	PUNCT
ejpam-6529	290	34	1)-set	1)-set	NOUN
ejpam-6529	290	35	is	be	AUX
ejpam-6529	290	36	a	a	DET
ejpam-6529	290	37	weak	weak	ADJ
ejpam-6529	290	38	filter	filter	NOUN
ejpam-6529	290	39	of	of	ADP
ejpam-6529	290	40	x	x	X
ejpam-6529	290	41	:	:	PUNCT
ejpam-6529	290	42	=	=	SYM
ejpam-6529	290	43	(	(	PUNCT
ejpam-6529	290	44	x	x	NOUN
ejpam-6529	290	45	,	,	PUNCT
ejpam-6529	290	46	|	|	NOUN
ejpam-6529	290	47	)	)	PUNCT
ejpam-6529	290	48	.	.	PUNCT
ejpam-6529	291	1	proof	proof	NOUN
ejpam-6529	291	2	.	.	PUNCT
ejpam-6529	292	1	let	let	VERB
ejpam-6529	292	2	b∗	b∗	ADV
ejpam-6529	292	3	:	:	PUNCT
ejpam-6529	292	4	=	=	SYM
ejpam-6529	292	5	(	(	PUNCT
ejpam-6529	292	6	x	x	X
ejpam-6529	292	7	;	;	PUNCT
ejpam-6529	292	8	fb	fb	INTJ
ejpam-6529	292	9	,	,	PUNCT
ejpam-6529	292	10	gb	gb	PROPN
ejpam-6529	292	11	)	)	PUNCT
ejpam-6529	292	12	be	be	AUX
ejpam-6529	292	13	an	an	DET
ejpam-6529	292	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	292	15	fuzzy	fuzzy	ADJ
ejpam-6529	292	16	weak	weak	ADJ
ejpam-6529	292	17	filter	filter	NOUN
ejpam-6529	292	18	of	of	ADP
ejpam-6529	292	19	x	x	X
ejpam-6529	292	20	:	:	PUNCT
ejpam-6529	292	21	=	=	SYM
ejpam-6529	292	22	(	(	PUNCT
ejpam-6529	292	23	x	x	NOUN
ejpam-6529	292	24	,	,	PUNCT
ejpam-6529	292	25	|	|	NOUN
ejpam-6529	292	26	)	)	PUNCT
ejpam-6529	292	27	.	.	PUNCT
ejpam-6529	293	1	suppose	suppose	VERB
ejpam-6529	293	2	x(0,1	x(0,1	X
ejpam-6529	293	3	)	)	PUNCT
ejpam-6529	293	4	̸=	̸=	NOUN
ejpam-6529	293	5	∅	∅	NOUN
ejpam-6529	293	6	,	,	PUNCT
ejpam-6529	293	7	say	say	VERB
ejpam-6529	293	8	x	x	X
ejpam-6529	293	9	∈	∈	PROPN
ejpam-6529	293	10	x(0,1	x(0,1	ADP
ejpam-6529	293	11	)	)	PUNCT
ejpam-6529	293	12	.	.	PUNCT
ejpam-6529	294	1	then	then	ADV
ejpam-6529	294	2	fb(1	fb(1	PROPN
ejpam-6529	294	3	)	)	PUNCT
ejpam-6529	294	4	≥	≥	NOUN
ejpam-6529	294	5	fb(x	fb(x	PUNCT
ejpam-6529	294	6	)	)	PUNCT
ejpam-6529	294	7	̸=	̸=	NOUN
ejpam-6529	294	8	0	0	NUM
ejpam-6529	294	9	and	and	CCONJ
ejpam-6529	294	10	gb(1	gb(1	PROPN
ejpam-6529	294	11	)	)	PUNCT
ejpam-6529	294	12	≤	≤	NOUN
ejpam-6529	294	13	gb(x	gb(x	PUNCT
ejpam-6529	294	14	)	)	PUNCT
ejpam-6529	294	15	̸=	̸=	PROPN
ejpam-6529	294	16	1	1	NUM
ejpam-6529	294	17	by	by	ADP
ejpam-6529	294	18	(	(	PUNCT
ejpam-6529	294	19	22	22	NUM
ejpam-6529	294	20	)	)	PUNCT
ejpam-6529	294	21	.	.	PUNCT
ejpam-6529	295	1	thus	thus	ADV
ejpam-6529	295	2	1	1	NUM
ejpam-6529	295	3	∈	∈	NOUN
ejpam-6529	295	4	x(0,1	x(0,1	ADP
ejpam-6529	295	5	)	)	PUNCT
ejpam-6529	295	6	.	.	PUNCT
ejpam-6529	296	1	let	let	VERB
ejpam-6529	296	2	x	x	PUNCT
ejpam-6529	296	3	∈	∈	PROPN
ejpam-6529	296	4	x	x	X
ejpam-6529	296	5	and	and	CCONJ
ejpam-6529	296	6	y	y	PROPN
ejpam-6529	296	7	∈	∈	PROPN
ejpam-6529	296	8	x(0,1	x(0,1	ADP
ejpam-6529	296	9	)	)	PUNCT
ejpam-6529	296	10	.	.	PUNCT
ejpam-6529	297	1	then	then	ADV
ejpam-6529	297	2	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	297	3	)	)	PUNCT
ejpam-6529	297	4	)	)	PUNCT
ejpam-6529	297	5	≥	≥	NOUN
ejpam-6529	297	6	fb(y	fb(y	NUM
ejpam-6529	297	7	)	)	PUNCT
ejpam-6529	298	1	̸=	̸=	PROPN
ejpam-6529	298	2	0	0	NUM
ejpam-6529	298	3	and	and	CCONJ
ejpam-6529	298	4	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	298	5	)	)	PUNCT
ejpam-6529	298	6	)	)	PUNCT
ejpam-6529	298	7	≤	≤	NOUN
ejpam-6529	298	8	gb(y	gb(y	ADV
ejpam-6529	298	9	)	)	PUNCT
ejpam-6529	298	10	̸=	̸=	PROPN
ejpam-6529	298	11	1	1	NUM
ejpam-6529	298	12	by	by	ADP
ejpam-6529	298	13	(	(	PUNCT
ejpam-6529	298	14	23	23	NUM
ejpam-6529	298	15	)	)	PUNCT
ejpam-6529	298	16	.	.	PUNCT
ejpam-6529	299	1	hence	hence	ADV
ejpam-6529	299	2	ðx(y	ðx(y	PUNCT
ejpam-6529	299	3	)	)	PUNCT
ejpam-6529	299	4	∈	∈	PROPN
ejpam-6529	299	5	x(0,1	x(0,1	ADP
ejpam-6529	299	6	)	)	PUNCT
ejpam-6529	299	7	,	,	PUNCT
ejpam-6529	299	8	and	and	CCONJ
ejpam-6529	299	9	therefore	therefore	ADV
ejpam-6529	299	10	x(0,1	x(0,1	ADV
ejpam-6529	299	11	)	)	PUNCT
ejpam-6529	299	12	is	be	AUX
ejpam-6529	299	13	a	a	DET
ejpam-6529	299	14	weak	weak	ADJ
ejpam-6529	299	15	filter	filter	NOUN
ejpam-6529	299	16	of	of	ADP
ejpam-6529	299	17	x	x	X
ejpam-6529	299	18	:	:	PUNCT
ejpam-6529	299	19	=	=	SYM
ejpam-6529	299	20	(	(	PUNCT
ejpam-6529	299	21	x	x	NOUN
ejpam-6529	299	22	,	,	PUNCT
ejpam-6529	299	23	|	|	NOUN
ejpam-6529	299	24	)	)	PUNCT
ejpam-6529	299	25	.	.	PUNCT
ejpam-6529	300	1	in	in	ADP
ejpam-6529	300	2	the	the	DET
ejpam-6529	300	3	following	follow	VERB
ejpam-6529	300	4	example	example	NOUN
ejpam-6529	300	5	,	,	PUNCT
ejpam-6529	300	6	we	we	PRON
ejpam-6529	300	7	can	can	AUX
ejpam-6529	300	8	observe	observe	VERB
ejpam-6529	300	9	that	that	SCONJ
ejpam-6529	300	10	the	the	DET
ejpam-6529	300	11	converse	converse	NOUN
ejpam-6529	300	12	of	of	ADP
ejpam-6529	300	13	theorem	theorem	NOUN
ejpam-6529	300	14	6	6	NUM
ejpam-6529	300	15	is	be	AUX
ejpam-6529	300	16	not	not	PART
ejpam-6529	300	17	true	true	ADJ
ejpam-6529	300	18	in	in	ADP
ejpam-6529	300	19	general	general	ADJ
ejpam-6529	300	20	.	.	PUNCT
ejpam-6529	301	1	example	example	NOUN
ejpam-6529	302	1	3	3	X
ejpam-6529	302	2	.	.	PUNCT
ejpam-6529	302	3	let	let	VERB
ejpam-6529	302	4	x	x	PRON
ejpam-6529	302	5	:	:	PUNCT
ejpam-6529	302	6	=	=	SYM
ejpam-6529	302	7	(	(	PUNCT
ejpam-6529	302	8	x	x	NOUN
ejpam-6529	302	9	,	,	PUNCT
ejpam-6529	302	10	|	|	ADV
ejpam-6529	302	11	)	)	PUNCT
ejpam-6529	302	12	be	be	AUX
ejpam-6529	302	13	the	the	DET
ejpam-6529	302	14	sheffer	sheffer	NOUN
ejpam-6529	302	15	stroke	stroke	NOUN
ejpam-6529	302	16	hilbert	hilbert	PROPN
ejpam-6529	302	17	algebra	algebra	PROPN
ejpam-6529	302	18	described	describe	VERB
ejpam-6529	302	19	in	in	ADP
ejpam-6529	302	20	example	example	NOUN
ejpam-6529	302	21	1	1	NUM
ejpam-6529	302	22	and	and	CCONJ
ejpam-6529	302	23	let	let	VERB
ejpam-6529	302	24	b∗	b∗	ADJ
ejpam-6529	302	25	:	:	PUNCT
ejpam-6529	302	26	=	=	SYM
ejpam-6529	302	27	(	(	PUNCT
ejpam-6529	302	28	x	x	X
ejpam-6529	302	29	;	;	PUNCT
ejpam-6529	302	30	fb	fb	INTJ
ejpam-6529	302	31	,	,	PUNCT
ejpam-6529	302	32	gb	gb	PROPN
ejpam-6529	302	33	)	)	PUNCT
ejpam-6529	302	34	be	be	VERB
ejpam-6529	302	35	an	an	DET
ejpam-6529	302	36	intuitionistic	intuitionistic	ADJ
ejpam-6529	302	37	fuzzy	fuzzy	ADJ
ejpam-6529	302	38	set	set	NOUN
ejpam-6529	302	39	in	in	ADP
ejpam-6529	302	40	x	x	PUNCT
ejpam-6529	302	41	given	give	VERB
ejpam-6529	302	42	as	as	SCONJ
ejpam-6529	302	43	follows	follow	VERB
ejpam-6529	302	44	:	:	PUNCT
ejpam-6529	302	45	b∗	b∗	ADJ
ejpam-6529	302	46	:	:	PUNCT
ejpam-6529	302	47	=	=	SYM
ejpam-6529	302	48	(	(	PUNCT
ejpam-6529	302	49	x	x	X
ejpam-6529	302	50	;	;	PUNCT
ejpam-6529	302	51	fb	fb	INTJ
ejpam-6529	302	52	,	,	PUNCT
ejpam-6529	302	53	gb	gb	PROPN
ejpam-6529	302	54	)	)	PUNCT
ejpam-6529	302	55	:x	:x	PUNCT
ejpam-6529	303	1	→	→	PUNCT
ejpam-6529	304	1	[	[	X
ejpam-6529	304	2	0	0	NUM
ejpam-6529	304	3	,	,	PUNCT
ejpam-6529	304	4	1]×	1]×	NUM
ejpam-6529	304	5	[	[	X
ejpam-6529	304	6	0	0	NUM
ejpam-6529	304	7	,	,	PUNCT
ejpam-6529	304	8	1	1	NUM
ejpam-6529	304	9	]	]	PUNCT
ejpam-6529	304	10	,	,	PUNCT
ejpam-6529	304	11	b	b	X
ejpam-6529	304	12	7→	7→	NUM
ejpam-6529	304	13			NUM
ejpam-6529	304	14	(	(	PUNCT
ejpam-6529	304	15	0.45	0.45	NUM
ejpam-6529	304	16	n	n	NOUN
ejpam-6529	304	17	,	,	PUNCT
ejpam-6529	304	18	0.872n	0.872n	PROPN
ejpam-6529	304	19	)	)	PUNCT
ejpam-6529	304	20	if	if	SCONJ
ejpam-6529	304	21	b	b	PROPN
ejpam-6529	304	22	=	=	PROPN
ejpam-6529	304	23	c1	c1	PROPN
ejpam-6529	304	24	,	,	PUNCT
ejpam-6529	304	25	(	(	PUNCT
ejpam-6529	304	26	0.69	0.69	NUM
ejpam-6529	304	27	n	n	NOUN
ejpam-6529	304	28	,	,	PUNCT
ejpam-6529	304	29	0.562n	0.562n	NOUN
ejpam-6529	304	30	)	)	PUNCT
ejpam-6529	305	1	if	if	SCONJ
ejpam-6529	305	2	b	b	X
ejpam-6529	305	3	∈	∈	PROPN
ejpam-6529	305	4	{	{	PUNCT
ejpam-6529	305	5	c5	c5	PROPN
ejpam-6529	305	6	,	,	PUNCT
ejpam-6529	305	7	c6	c6	PROPN
ejpam-6529	305	8	}	}	PUNCT
ejpam-6529	305	9	,	,	PUNCT
ejpam-6529	305	10	(	(	PUNCT
ejpam-6529	305	11	0.00	0.00	NUM
ejpam-6529	305	12	,	,	PUNCT
ejpam-6529	305	13	1.00	1.00	NUM
ejpam-6529	305	14	)	)	PUNCT
ejpam-6529	305	15	otherwise	otherwise	ADV
ejpam-6529	305	16	where	where	SCONJ
ejpam-6529	305	17	n	n	PRON
ejpam-6529	305	18	is	be	AUX
ejpam-6529	305	19	a	a	DET
ejpam-6529	305	20	natural	natural	ADJ
ejpam-6529	305	21	number	number	NOUN
ejpam-6529	305	22	.	.	PUNCT
ejpam-6529	306	1	then	then	ADV
ejpam-6529	306	2	x(0,1	x(0,1	X
ejpam-6529	306	3	)	)	PUNCT
ejpam-6529	306	4	=	=	PRON
ejpam-6529	306	5	{	{	PUNCT
ejpam-6529	306	6	c1	c1	PROPN
ejpam-6529	306	7	,	,	PUNCT
ejpam-6529	306	8	c5	c5	PROPN
ejpam-6529	306	9	,	,	PUNCT
ejpam-6529	306	10	c6	c6	PROPN
ejpam-6529	306	11	}	}	PUNCT
ejpam-6529	306	12	which	which	PRON
ejpam-6529	306	13	is	be	AUX
ejpam-6529	306	14	a	a	DET
ejpam-6529	306	15	weak	weak	ADJ
ejpam-6529	306	16	filter	filter	NOUN
ejpam-6529	306	17	of	of	ADP
ejpam-6529	306	18	x	x	X
ejpam-6529	306	19	:	:	PUNCT
ejpam-6529	306	20	=	=	SYM
ejpam-6529	306	21	(	(	PUNCT
ejpam-6529	306	22	x	x	NOUN
ejpam-6529	306	23	,	,	PUNCT
ejpam-6529	306	24	|	|	NOUN
ejpam-6529	306	25	)	)	PUNCT
ejpam-6529	306	26	.	.	PUNCT
ejpam-6529	307	1	we	we	PRON
ejpam-6529	307	2	can	can	AUX
ejpam-6529	307	3	observe	observe	VERB
ejpam-6529	307	4	that	that	SCONJ
ejpam-6529	307	5	fb(c1	fb(c1	NOUN
ejpam-6529	307	6	)	)	PUNCT
ejpam-6529	307	7	=	=	NOUN
ejpam-6529	307	8	0.45	0.45	NUM
ejpam-6529	307	9	n	n	CCONJ
ejpam-6529	307	10	<	<	X
ejpam-6529	307	11	0.69	0.69	NUM
ejpam-6529	307	12	n	n	NOUN
ejpam-6529	307	13	=	=	NUM
ejpam-6529	307	14	fb(c5	fb(c5	NOUN
ejpam-6529	307	15	)	)	PUNCT
ejpam-6529	307	16	and/or	and/or	CCONJ
ejpam-6529	307	17	gb(c1	gb(c1	PROPN
ejpam-6529	307	18	)	)	PUNCT
ejpam-6529	307	19	=	=	NUM
ejpam-6529	307	20	0.87	0.87	NUM
ejpam-6529	307	21	2n	2n	NUM
ejpam-6529	307	22	>	>	X
ejpam-6529	307	23	0.56	0.56	NUM
ejpam-6529	307	24	2n	2n	NUM
ejpam-6529	307	25	=	=	SYM
ejpam-6529	307	26	gb(c6	gb(c6	NOUN
ejpam-6529	307	27	)	)	PUNCT
ejpam-6529	307	28	,	,	PUNCT
ejpam-6529	307	29	that	that	ADV
ejpam-6529	307	30	is	is	ADV
ejpam-6529	307	31	,	,	PUNCT
ejpam-6529	307	32	(	(	PUNCT
ejpam-6529	307	33	22	22	NUM
ejpam-6529	307	34	)	)	PUNCT
ejpam-6529	307	35	is	be	AUX
ejpam-6529	307	36	not	not	PART
ejpam-6529	307	37	valid	valid	ADJ
ejpam-6529	307	38	.	.	PUNCT
ejpam-6529	308	1	hence	hence	ADV
ejpam-6529	308	2	b∗	b∗	ADV
ejpam-6529	308	3	:	:	PUNCT
ejpam-6529	308	4	=	=	SYM
ejpam-6529	308	5	(	(	PUNCT
ejpam-6529	308	6	x	x	X
ejpam-6529	308	7	;	;	PUNCT
ejpam-6529	308	8	fb	fb	INTJ
ejpam-6529	308	9	,	,	PUNCT
ejpam-6529	308	10	gb	gb	PROPN
ejpam-6529	308	11	)	)	PUNCT
ejpam-6529	308	12	is	be	AUX
ejpam-6529	308	13	not	not	PART
ejpam-6529	308	14	an	an	DET
ejpam-6529	308	15	intuitionistic	intuitionistic	ADJ
ejpam-6529	308	16	fuzzy	fuzzy	ADJ
ejpam-6529	308	17	weak	weak	ADJ
ejpam-6529	308	18	filter	filter	NOUN
ejpam-6529	308	19	of	of	ADP
ejpam-6529	308	20	x	x	X
ejpam-6529	308	21	:	:	PUNCT
ejpam-6529	308	22	=	=	SYM
ejpam-6529	308	23	(	(	PUNCT
ejpam-6529	308	24	x	x	NOUN
ejpam-6529	308	25	,	,	PUNCT
ejpam-6529	308	26	|	|	NOUN
ejpam-6529	308	27	)	)	PUNCT
ejpam-6529	308	28	.	.	PUNCT
ejpam-6529	309	1	theorem	theorem	VERB
ejpam-6529	309	2	7	7	NUM
ejpam-6529	309	3	.	.	PUNCT
ejpam-6529	310	1	if	if	SCONJ
ejpam-6529	310	2	an	an	DET
ejpam-6529	310	3	intuitionistic	intuitionistic	ADJ
ejpam-6529	310	4	fuzzy	fuzzy	ADJ
ejpam-6529	310	5	set	set	VERB
ejpam-6529	310	6	b∗	b∗	ADJ
ejpam-6529	310	7	:	:	PUNCT
ejpam-6529	310	8	=	=	SYM
ejpam-6529	310	9	(	(	PUNCT
ejpam-6529	310	10	x	x	X
ejpam-6529	310	11	;	;	PUNCT
ejpam-6529	310	12	fb	fb	INTJ
ejpam-6529	310	13	,	,	PUNCT
ejpam-6529	310	14	gb	gb	NOUN
ejpam-6529	310	15	)	)	PUNCT
ejpam-6529	310	16	in	in	ADP
ejpam-6529	310	17	x	x	X
ejpam-6529	310	18	satisfies	satisfie	NOUN
ejpam-6529	310	19	:	:	PUNCT
ejpam-6529	310	20	(	(	PUNCT
ejpam-6529	310	21	∀x	∀x	X
ejpam-6529	310	22	∈	∈	PROPN
ejpam-6529	310	23	x)(∀(s	x)(∀(s	NOUN
ejpam-6529	310	24	,	,	PUNCT
ejpam-6529	310	25	t	t	PROPN
ejpam-6529	310	26	)	)	PUNCT
ejpam-6529	310	27	∈	∈	PROPN
ejpam-6529	310	28	(	(	PUNCT
ejpam-6529	310	29	0	0	NUM
ejpam-6529	310	30	,	,	PUNCT
ejpam-6529	310	31	1]×	1]×	NUM
ejpam-6529	311	1	[	[	X
ejpam-6529	311	2	0	0	NUM
ejpam-6529	311	3	,	,	PUNCT
ejpam-6529	311	4	1	1	NUM
ejpam-6529	311	5	)	)	PUNCT
ejpam-6529	311	6	)	)	PUNCT
ejpam-6529	312	1	(	(	PUNCT
ejpam-6529	312	2	x(s	x(s	PROPN
ejpam-6529	312	3	,	,	PUNCT
ejpam-6529	312	4	t	t	PROPN
ejpam-6529	312	5	)	)	PUNCT
ejpam-6529	312	6	∈	∈	PROPN
ejpam-6529	312	7	b∗	b∗	ADJ
ejpam-6529	312	8	⇒	⇒	NOUN
ejpam-6529	312	9	1(s	1(s	NUM
ejpam-6529	312	10	,	,	PUNCT
ejpam-6529	312	11	t	t	PROPN
ejpam-6529	312	12	)	)	PUNCT
ejpam-6529	312	13	q	q	PROPN
ejpam-6529	313	1	b∗	b∗	ADJ
ejpam-6529	313	2	)	)	PUNCT
ejpam-6529	313	3	,	,	PUNCT
ejpam-6529	313	4	(	(	PUNCT
ejpam-6529	313	5	26	26	NUM
ejpam-6529	313	6	)	)	PUNCT
ejpam-6529	313	7	(	(	PUNCT
ejpam-6529	313	8	∀x	∀x	X
ejpam-6529	313	9	,	,	PUNCT
ejpam-6529	313	10	y	y	PROPN
ejpam-6529	313	11	∈	∈	PROPN
ejpam-6529	313	12	x)(∀(s	x)(∀(s	NOUN
ejpam-6529	313	13	,	,	PUNCT
ejpam-6529	313	14	t	t	PROPN
ejpam-6529	313	15	)	)	PUNCT
ejpam-6529	313	16	∈	∈	PROPN
ejpam-6529	313	17	(	(	PUNCT
ejpam-6529	313	18	0	0	NUM
ejpam-6529	313	19	,	,	PUNCT
ejpam-6529	313	20	1]×	1]×	NUM
ejpam-6529	314	1	[	[	X
ejpam-6529	314	2	0	0	NUM
ejpam-6529	314	3	,	,	PUNCT
ejpam-6529	314	4	1	1	NUM
ejpam-6529	314	5	)	)	PUNCT
ejpam-6529	314	6	)	)	PUNCT
ejpam-6529	315	1	(	(	PUNCT
ejpam-6529	315	2	y(s	y(s	PROPN
ejpam-6529	315	3	,	,	PUNCT
ejpam-6529	315	4	t	t	PROPN
ejpam-6529	315	5	)	)	PUNCT
ejpam-6529	315	6	∈	∈	PROPN
ejpam-6529	315	7	b∗	b∗	ADJ
ejpam-6529	315	8	⇒	⇒	NOUN
ejpam-6529	315	9	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	315	10	,	,	PUNCT
ejpam-6529	315	11	t	t	PROPN
ejpam-6529	315	12	)	)	PUNCT
ejpam-6529	315	13	q	q	PROPN
ejpam-6529	316	1	b∗	b∗	ADJ
ejpam-6529	316	2	)	)	PUNCT
ejpam-6529	316	3	,	,	PUNCT
ejpam-6529	316	4	(	(	PUNCT
ejpam-6529	316	5	27	27	NUM
ejpam-6529	316	6	)	)	PUNCT
ejpam-6529	316	7	then	then	ADV
ejpam-6529	316	8	its	its	PRON
ejpam-6529	316	9	nonempty	nonempty	ADJ
ejpam-6529	316	10	(	(	PUNCT
ejpam-6529	316	11	0	0	NUM
ejpam-6529	316	12	,	,	PUNCT
ejpam-6529	316	13	1)-set	1)-set	NOUN
ejpam-6529	316	14	is	be	AUX
ejpam-6529	316	15	a	a	DET
ejpam-6529	316	16	weak	weak	ADJ
ejpam-6529	316	17	filter	filter	NOUN
ejpam-6529	316	18	of	of	ADP
ejpam-6529	316	19	x	x	X
ejpam-6529	316	20	:	:	PUNCT
ejpam-6529	316	21	=	=	SYM
ejpam-6529	316	22	(	(	PUNCT
ejpam-6529	316	23	x	x	NOUN
ejpam-6529	316	24	,	,	PUNCT
ejpam-6529	316	25	|	|	NOUN
ejpam-6529	316	26	)	)	PUNCT
ejpam-6529	316	27	.	.	PUNCT
ejpam-6529	317	1	proof	proof	NOUN
ejpam-6529	317	2	.	.	PUNCT
ejpam-6529	318	1	let	let	VERB
ejpam-6529	318	2	b∗	b∗	ADV
ejpam-6529	318	3	:	:	PUNCT
ejpam-6529	318	4	=	=	SYM
ejpam-6529	318	5	(	(	PUNCT
ejpam-6529	318	6	x	x	X
ejpam-6529	318	7	;	;	PUNCT
ejpam-6529	318	8	fb	fb	INTJ
ejpam-6529	318	9	,	,	PUNCT
ejpam-6529	318	10	gb	gb	PROPN
ejpam-6529	318	11	)	)	PUNCT
ejpam-6529	318	12	be	be	VERB
ejpam-6529	318	13	an	an	DET
ejpam-6529	318	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	318	15	fuzzy	fuzzy	ADJ
ejpam-6529	318	16	set	set	NOUN
ejpam-6529	318	17	in	in	ADP
ejpam-6529	318	18	x	x	PUNCT
ejpam-6529	318	19	that	that	SCONJ
ejpam-6529	318	20	satisfies	satisfie	NOUN
ejpam-6529	318	21	(	(	PUNCT
ejpam-6529	318	22	26	26	NUM
ejpam-6529	318	23	)	)	PUNCT
ejpam-6529	318	24	and	and	CCONJ
ejpam-6529	318	25	(	(	PUNCT
ejpam-6529	318	26	27	27	NUM
ejpam-6529	318	27	)	)	PUNCT
ejpam-6529	318	28	.	.	PUNCT
ejpam-6529	319	1	suppose	suppose	VERB
ejpam-6529	319	2	that	that	SCONJ
ejpam-6529	319	3	x(0,1	x(0,1	NOUN
ejpam-6529	319	4	)	)	PUNCT
ejpam-6529	319	5	̸=	̸=	PROPN
ejpam-6529	319	6	∅	∅	NOUN
ejpam-6529	319	7	and	and	CCONJ
ejpam-6529	319	8	say	say	VERB
ejpam-6529	319	9	x	x	X
ejpam-6529	319	10	∈	∈	PROPN
ejpam-6529	319	11	x(0,1	x(0,1	ADP
ejpam-6529	319	12	)	)	PUNCT
ejpam-6529	319	13	.	.	PUNCT
ejpam-6529	320	1	then	then	ADV
ejpam-6529	320	2	fb(x	fb(x	NOUN
ejpam-6529	320	3	)	)	PUNCT
ejpam-6529	320	4	̸=	̸=	NOUN
ejpam-6529	320	5	0	0	NUM
ejpam-6529	320	6	and	and	CCONJ
ejpam-6529	320	7	gb(x	gb(x	NUM
ejpam-6529	320	8	)	)	PUNCT
ejpam-6529	320	9	̸=	̸=	PROPN
ejpam-6529	320	10	1	1	NUM
ejpam-6529	320	11	.	.	PUNCT
ejpam-6529	320	12	since	since	SCONJ
ejpam-6529	320	13	x(fb(x),gb(x	x(fb(x),gb(x	PROPN
ejpam-6529	320	14	)	)	PUNCT
ejpam-6529	320	15	)	)	PUNCT
ejpam-6529	320	16	∈	∈	PROPN
ejpam-6529	321	1	b∗	b∗	ADJ
ejpam-6529	321	2	,	,	PUNCT
ejpam-6529	321	3	we	we	PRON
ejpam-6529	321	4	have	have	VERB
ejpam-6529	321	5	1(fb(x),gb(x	1(fb(x),gb(x	NUM
ejpam-6529	321	6	)	)	PUNCT
ejpam-6529	321	7	)	)	PUNCT
ejpam-6529	322	1	∈	∈	PROPN
ejpam-6529	322	2	b∗	b∗	ADJ
ejpam-6529	322	3	by	by	ADP
ejpam-6529	322	4	(	(	PUNCT
ejpam-6529	322	5	26	26	NUM
ejpam-6529	322	6	)	)	PUNCT
ejpam-6529	322	7	.	.	PUNCT
ejpam-6529	323	1	hence	hence	ADV
ejpam-6529	323	2	fb(1	fb(1	PROPN
ejpam-6529	323	3	)	)	PUNCT
ejpam-6529	323	4	≥	≥	NOUN
ejpam-6529	323	5	fb(x	fb(x	PUNCT
ejpam-6529	323	6	)	)	PUNCT
ejpam-6529	324	1	̸=	̸=	NOUN
ejpam-6529	324	2	0	0	NUM
ejpam-6529	324	3	and	and	CCONJ
ejpam-6529	324	4	gb(1	gb(1	PROPN
ejpam-6529	324	5	)	)	PUNCT
ejpam-6529	324	6	≤	≤	NOUN
ejpam-6529	324	7	gb(x	gb(x	PUNCT
ejpam-6529	324	8	)	)	PUNCT
ejpam-6529	324	9	̸=	̸=	PROPN
ejpam-6529	324	10	1	1	NUM
ejpam-6529	324	11	,	,	PUNCT
ejpam-6529	324	12	and	and	CCONJ
ejpam-6529	324	13	so	so	ADV
ejpam-6529	324	14	1	1	NUM
ejpam-6529	324	15	∈	∈	NOUN
ejpam-6529	324	16	x(0,1	x(0,1	ADP
ejpam-6529	324	17	)	)	PUNCT
ejpam-6529	324	18	.	.	PUNCT
ejpam-6529	325	1	let	let	VERB
ejpam-6529	325	2	x	x	PUNCT
ejpam-6529	325	3	∈	∈	PROPN
ejpam-6529	325	4	x	x	X
ejpam-6529	325	5	and	and	CCONJ
ejpam-6529	325	6	y	y	PROPN
ejpam-6529	325	7	∈	∈	PROPN
ejpam-6529	325	8	x(0,1	x(0,1	ADP
ejpam-6529	325	9	)	)	PUNCT
ejpam-6529	325	10	.	.	PUNCT
ejpam-6529	326	1	then	then	ADV
ejpam-6529	326	2	fb(y	fb(y	PUNCT
ejpam-6529	326	3	)	)	PUNCT
ejpam-6529	326	4	̸=	̸=	PROPN
ejpam-6529	326	5	0	0	NUM
ejpam-6529	326	6	,	,	PUNCT
ejpam-6529	326	7	gb(y	gb(y	ADV
ejpam-6529	326	8	)	)	PUNCT
ejpam-6529	326	9	̸=	̸=	NOUN
ejpam-6529	326	10	1	1	NUM
ejpam-6529	326	11	and	and	CCONJ
ejpam-6529	326	12	y(fb(y),gb(y	y(fb(y),gb(y	NOUN
ejpam-6529	326	13	)	)	PUNCT
ejpam-6529	326	14	)	)	PUNCT
ejpam-6529	327	1	∈	∈	PROPN
ejpam-6529	327	2	b∗.	b∗.	NOUN
ejpam-6529	327	3	it	it	PRON
ejpam-6529	327	4	follows	follow	VERB
ejpam-6529	327	5	from	from	ADP
ejpam-6529	327	6	(	(	PUNCT
ejpam-6529	327	7	27	27	NUM
ejpam-6529	327	8	)	)	PUNCT
ejpam-6529	327	9	that	that	PRON
ejpam-6529	327	10	ðx(y)(fb(y),gb(y	ðx(y)(fb(y),gb(y	PROPN
ejpam-6529	327	11	)	)	PUNCT
ejpam-6529	327	12	)	)	PUNCT
ejpam-6529	328	1	∈	∈	PROPN
ejpam-6529	328	2	b∗.	b∗.	NOUN
ejpam-6529	328	3	thus	thus	ADV
ejpam-6529	328	4	fb(ðx(y	fb(ðx(y	X
ejpam-6529	328	5	)	)	PUNCT
ejpam-6529	328	6	)	)	PUNCT
ejpam-6529	328	7	≥	≥	NOUN
ejpam-6529	328	8	fb(y	fb(y	NUM
ejpam-6529	328	9	)	)	PUNCT
ejpam-6529	328	10	̸=	̸=	PROPN
ejpam-6529	328	11	0	0	NUM
ejpam-6529	328	12	and	and	CCONJ
ejpam-6529	328	13	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	328	14	)	)	PUNCT
ejpam-6529	328	15	)	)	PUNCT
ejpam-6529	328	16	≤	≤	NOUN
ejpam-6529	328	17	gb(y	gb(y	ADV
ejpam-6529	328	18	)	)	PUNCT
ejpam-6529	328	19	̸=	̸=	PROPN
ejpam-6529	328	20	1	1	NUM
ejpam-6529	328	21	which	which	PRON
ejpam-6529	328	22	imply	imply	VERB
ejpam-6529	328	23	that	that	PRON
ejpam-6529	328	24	ðx(y	ðx(y	PUNCT
ejpam-6529	328	25	)	)	PUNCT
ejpam-6529	328	26	∈	∈	PROPN
ejpam-6529	328	27	x(0,1	x(0,1	ADP
ejpam-6529	328	28	)	)	PUNCT
ejpam-6529	328	29	.	.	PUNCT
ejpam-6529	329	1	therefore	therefore	ADV
ejpam-6529	329	2	x(0,1	x(0,1	X
ejpam-6529	329	3	)	)	PUNCT
ejpam-6529	329	4	is	be	AUX
ejpam-6529	329	5	a	a	DET
ejpam-6529	329	6	weak	weak	ADJ
ejpam-6529	329	7	filter	filter	NOUN
ejpam-6529	329	8	of	of	ADP
ejpam-6529	329	9	x	x	X
ejpam-6529	329	10	:	:	PUNCT
ejpam-6529	329	11	=	=	SYM
ejpam-6529	329	12	(	(	PUNCT
ejpam-6529	329	13	x	x	NOUN
ejpam-6529	329	14	,	,	PUNCT
ejpam-6529	329	15	|	|	NOUN
ejpam-6529	329	16	)	)	PUNCT
ejpam-6529	329	17	.	.	PUNCT
ejpam-6529	330	1	s.	s.	PROPN
ejpam-6529	330	2	s.	s.	PROPN
ejpam-6529	330	3	ahn	ahn	PROPN
ejpam-6529	330	4	,	,	PUNCT
ejpam-6529	330	5	y.	y.	PROPN
ejpam-6529	330	6	j.	j.	PROPN
ejpam-6529	330	7	seo	seo	PROPN
ejpam-6529	330	8	,	,	PUNCT
ejpam-6529	330	9	y.	y.	PROPN
ejpam-6529	330	10	b.	b.	PROPN
ejpam-6529	330	11	jun	jun	PROPN
ejpam-6529	330	12	/	/	SYM
ejpam-6529	330	13	eur	eur	PROPN
ejpam-6529	330	14	.	.	PUNCT
ejpam-6529	331	1	j.	j.	PROPN
ejpam-6529	331	2	pure	pure	PROPN
ejpam-6529	331	3	appl	appl	PROPN
ejpam-6529	331	4	.	.	PROPN
ejpam-6529	331	5	math	math	PROPN
ejpam-6529	331	6	,	,	PUNCT
ejpam-6529	331	7	18	18	NUM
ejpam-6529	331	8	(	(	PUNCT
ejpam-6529	331	9	3	3	NUM
ejpam-6529	331	10	)	)	PUNCT
ejpam-6529	331	11	(	(	PUNCT
ejpam-6529	331	12	2025	2025	NUM
ejpam-6529	331	13	)	)	PUNCT
ejpam-6529	331	14	,	,	PUNCT
ejpam-6529	331	15	6529	6529	NUM
ejpam-6529	331	16	12	12	NUM
ejpam-6529	331	17	of	of	ADP
ejpam-6529	331	18	16	16	NUM
ejpam-6529	331	19	theorem	theorem	NOUN
ejpam-6529	331	20	8	8	NUM
ejpam-6529	331	21	.	.	PUNCT
ejpam-6529	332	1	if	if	SCONJ
ejpam-6529	332	2	an	an	DET
ejpam-6529	332	3	intuitionistic	intuitionistic	ADJ
ejpam-6529	332	4	fuzzy	fuzzy	ADJ
ejpam-6529	332	5	set	set	VERB
ejpam-6529	332	6	b∗	b∗	ADJ
ejpam-6529	332	7	:	:	PUNCT
ejpam-6529	332	8	=	=	SYM
ejpam-6529	332	9	(	(	PUNCT
ejpam-6529	332	10	x	x	X
ejpam-6529	332	11	;	;	PUNCT
ejpam-6529	332	12	fb	fb	INTJ
ejpam-6529	332	13	,	,	PUNCT
ejpam-6529	332	14	gb	gb	NOUN
ejpam-6529	332	15	)	)	PUNCT
ejpam-6529	332	16	in	in	ADP
ejpam-6529	332	17	x	x	X
ejpam-6529	332	18	satisfies	satisfie	NOUN
ejpam-6529	332	19	:	:	PUNCT
ejpam-6529	332	20	(	(	PUNCT
ejpam-6529	332	21	∀x	∀x	X
ejpam-6529	332	22	∈	∈	PROPN
ejpam-6529	332	23	x)(∀(s	x)(∀(s	NOUN
ejpam-6529	332	24	,	,	PUNCT
ejpam-6529	332	25	t	t	PROPN
ejpam-6529	332	26	)	)	PUNCT
ejpam-6529	332	27	∈	∈	PROPN
ejpam-6529	332	28	(	(	PUNCT
ejpam-6529	332	29	0	0	NUM
ejpam-6529	332	30	,	,	PUNCT
ejpam-6529	332	31	1]×	1]×	NUM
ejpam-6529	333	1	[	[	X
ejpam-6529	333	2	0	0	NUM
ejpam-6529	333	3	,	,	PUNCT
ejpam-6529	333	4	1	1	NUM
ejpam-6529	333	5	)	)	PUNCT
ejpam-6529	333	6	)	)	PUNCT
ejpam-6529	334	1	(	(	PUNCT
ejpam-6529	334	2	x(s	x(s	PROPN
ejpam-6529	334	3	,	,	PUNCT
ejpam-6529	334	4	t	t	PROPN
ejpam-6529	334	5	)	)	PUNCT
ejpam-6529	334	6	q	q	NOUN
ejpam-6529	334	7	b∗	b∗	ADJ
ejpam-6529	334	8	⇒	⇒	NOUN
ejpam-6529	334	9	1(s	1(s	NUM
ejpam-6529	334	10	,	,	PUNCT
ejpam-6529	334	11	t	t	PROPN
ejpam-6529	334	12	)	)	PUNCT
ejpam-6529	334	13	∈	∈	PROPN
ejpam-6529	334	14	b∗	b∗	ADJ
ejpam-6529	334	15	)	)	PUNCT
ejpam-6529	334	16	,	,	PUNCT
ejpam-6529	334	17	(	(	PUNCT
ejpam-6529	334	18	28	28	NUM
ejpam-6529	334	19	)	)	PUNCT
ejpam-6529	334	20	(	(	PUNCT
ejpam-6529	334	21	∀x	∀x	X
ejpam-6529	334	22	,	,	PUNCT
ejpam-6529	334	23	y	y	PROPN
ejpam-6529	334	24	∈	∈	PROPN
ejpam-6529	334	25	x)(∀(s	x)(∀(s	NOUN
ejpam-6529	334	26	,	,	PUNCT
ejpam-6529	334	27	t	t	PROPN
ejpam-6529	334	28	)	)	PUNCT
ejpam-6529	334	29	∈	∈	PROPN
ejpam-6529	334	30	(	(	PUNCT
ejpam-6529	334	31	0	0	NUM
ejpam-6529	334	32	,	,	PUNCT
ejpam-6529	334	33	1]×	1]×	NUM
ejpam-6529	335	1	[	[	X
ejpam-6529	335	2	0	0	NUM
ejpam-6529	335	3	,	,	PUNCT
ejpam-6529	335	4	1	1	NUM
ejpam-6529	335	5	)	)	PUNCT
ejpam-6529	335	6	)	)	PUNCT
ejpam-6529	336	1	(	(	PUNCT
ejpam-6529	336	2	y(s	y(s	PROPN
ejpam-6529	336	3	,	,	PUNCT
ejpam-6529	336	4	t	t	PROPN
ejpam-6529	336	5	)	)	PUNCT
ejpam-6529	336	6	q	q	NOUN
ejpam-6529	336	7	b∗	b∗	ADJ
ejpam-6529	336	8	⇒	⇒	NOUN
ejpam-6529	336	9	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	336	10	,	,	PUNCT
ejpam-6529	336	11	t	t	PROPN
ejpam-6529	336	12	)	)	PUNCT
ejpam-6529	336	13	∈	∈	PROPN
ejpam-6529	336	14	b∗	b∗	ADJ
ejpam-6529	336	15	)	)	PUNCT
ejpam-6529	336	16	,	,	PUNCT
ejpam-6529	336	17	(	(	PUNCT
ejpam-6529	336	18	29	29	NUM
ejpam-6529	336	19	)	)	PUNCT
ejpam-6529	336	20	then	then	ADV
ejpam-6529	336	21	its	its	PRON
ejpam-6529	336	22	nonempty	nonempty	ADJ
ejpam-6529	336	23	(	(	PUNCT
ejpam-6529	336	24	0	0	NUM
ejpam-6529	336	25	,	,	PUNCT
ejpam-6529	336	26	1)-set	1)-set	NOUN
ejpam-6529	336	27	is	be	AUX
ejpam-6529	336	28	a	a	DET
ejpam-6529	336	29	weak	weak	ADJ
ejpam-6529	336	30	filter	filter	NOUN
ejpam-6529	336	31	of	of	ADP
ejpam-6529	336	32	x	x	X
ejpam-6529	336	33	:	:	PUNCT
ejpam-6529	336	34	=	=	SYM
ejpam-6529	336	35	(	(	PUNCT
ejpam-6529	336	36	x	x	NOUN
ejpam-6529	336	37	,	,	PUNCT
ejpam-6529	336	38	|	|	NOUN
ejpam-6529	336	39	)	)	PUNCT
ejpam-6529	336	40	.	.	PUNCT
ejpam-6529	337	1	proof	proof	NOUN
ejpam-6529	337	2	.	.	PUNCT
ejpam-6529	338	1	let	let	VERB
ejpam-6529	338	2	b∗	b∗	ADV
ejpam-6529	338	3	:	:	PUNCT
ejpam-6529	338	4	=	=	SYM
ejpam-6529	338	5	(	(	PUNCT
ejpam-6529	338	6	x	x	X
ejpam-6529	338	7	;	;	PUNCT
ejpam-6529	338	8	fb	fb	INTJ
ejpam-6529	338	9	,	,	PUNCT
ejpam-6529	338	10	gb	gb	PROPN
ejpam-6529	338	11	)	)	PUNCT
ejpam-6529	338	12	be	be	VERB
ejpam-6529	338	13	an	an	DET
ejpam-6529	338	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	338	15	fuzzy	fuzzy	ADJ
ejpam-6529	338	16	set	set	NOUN
ejpam-6529	338	17	in	in	ADP
ejpam-6529	338	18	x	x	PUNCT
ejpam-6529	338	19	that	that	SCONJ
ejpam-6529	338	20	satisfies	satisfie	NOUN
ejpam-6529	338	21	(	(	PUNCT
ejpam-6529	338	22	28	28	NUM
ejpam-6529	338	23	)	)	PUNCT
ejpam-6529	338	24	and	and	CCONJ
ejpam-6529	338	25	(	(	PUNCT
ejpam-6529	338	26	29	29	NUM
ejpam-6529	338	27	)	)	PUNCT
ejpam-6529	338	28	.	.	PUNCT
ejpam-6529	339	1	suppose	suppose	VERB
ejpam-6529	339	2	that	that	SCONJ
ejpam-6529	339	3	x(0,1	x(0,1	NOUN
ejpam-6529	339	4	)	)	PUNCT
ejpam-6529	339	5	̸=	̸=	PROPN
ejpam-6529	339	6	∅	∅	NOUN
ejpam-6529	339	7	and	and	CCONJ
ejpam-6529	339	8	say	say	VERB
ejpam-6529	339	9	x	x	X
ejpam-6529	339	10	∈	∈	PROPN
ejpam-6529	339	11	x(0,1	x(0,1	ADP
ejpam-6529	339	12	)	)	PUNCT
ejpam-6529	339	13	.	.	PUNCT
ejpam-6529	340	1	then	then	ADV
ejpam-6529	340	2	fb(x	fb(x	NOUN
ejpam-6529	340	3	)	)	PUNCT
ejpam-6529	340	4	̸=	̸=	NOUN
ejpam-6529	340	5	0	0	NUM
ejpam-6529	340	6	and	and	CCONJ
ejpam-6529	340	7	gb(x	gb(x	NUM
ejpam-6529	340	8	)	)	PUNCT
ejpam-6529	340	9	̸=	̸=	PROPN
ejpam-6529	340	10	1	1	NUM
ejpam-6529	340	11	.	.	PUNCT
ejpam-6529	340	12	thus	thus	ADV
ejpam-6529	340	13	fb(x)+1	fb(x)+1	PROPN
ejpam-6529	340	14	>	>	SYM
ejpam-6529	340	15	1	1	NUM
ejpam-6529	340	16	and	and	CCONJ
ejpam-6529	340	17	gb(x)+0	gb(x)+0	PROPN
ejpam-6529	340	18	<	<	X
ejpam-6529	340	19	1	1	NUM
ejpam-6529	340	20	,	,	PUNCT
ejpam-6529	340	21	i.e.	i.e.	X
ejpam-6529	340	22	,	,	PUNCT
ejpam-6529	340	23	x(1,0	x(1,0	NUM
ejpam-6529	340	24	)	)	PUNCT
ejpam-6529	340	25	q	q	NOUN
ejpam-6529	340	26	b∗.	b∗.	NOUN
ejpam-6529	340	27	it	it	PRON
ejpam-6529	340	28	follows	follow	VERB
ejpam-6529	340	29	from	from	ADP
ejpam-6529	340	30	(	(	PUNCT
ejpam-6529	340	31	28	28	NUM
ejpam-6529	340	32	)	)	PUNCT
ejpam-6529	340	33	that	that	SCONJ
ejpam-6529	340	34	1(1,0	1(1,0	X
ejpam-6529	340	35	)	)	PUNCT
ejpam-6529	340	36	∈	∈	PROPN
ejpam-6529	341	1	b∗	b∗	ADJ
ejpam-6529	341	2	,	,	PUNCT
ejpam-6529	341	3	that	that	ADV
ejpam-6529	341	4	is	is	ADV
ejpam-6529	341	5	,	,	PUNCT
ejpam-6529	341	6	fb(1	fb(1	PROPN
ejpam-6529	341	7	)	)	PUNCT
ejpam-6529	341	8	≥	≥	NOUN
ejpam-6529	341	9	1	1	NUM
ejpam-6529	341	10	and	and	CCONJ
ejpam-6529	341	11	gb(1	gb(1	PROPN
ejpam-6529	341	12	)	)	PUNCT
ejpam-6529	341	13	≤	≤	NOUN
ejpam-6529	341	14	0	0	NUM
ejpam-6529	341	15	.	.	PUNCT
ejpam-6529	342	1	thus	thus	ADV
ejpam-6529	342	2	1	1	NUM
ejpam-6529	342	3	∈	∈	NOUN
ejpam-6529	342	4	x(0,1	x(0,1	ADP
ejpam-6529	342	5	)	)	PUNCT
ejpam-6529	342	6	.	.	PUNCT
ejpam-6529	343	1	if	if	SCONJ
ejpam-6529	343	2	x	x	SYM
ejpam-6529	343	3	∈	∈	PROPN
ejpam-6529	343	4	x	x	X
ejpam-6529	343	5	and	and	CCONJ
ejpam-6529	343	6	y	y	PROPN
ejpam-6529	343	7	∈	∈	PROPN
ejpam-6529	343	8	x(0,1	x(0,1	ADP
ejpam-6529	343	9	)	)	PUNCT
ejpam-6529	343	10	,	,	PUNCT
ejpam-6529	343	11	then	then	ADV
ejpam-6529	343	12	fb(y	fb(y	PUNCT
ejpam-6529	343	13	)	)	PUNCT
ejpam-6529	343	14	̸=	̸=	PROPN
ejpam-6529	343	15	0	0	NUM
ejpam-6529	343	16	and	and	CCONJ
ejpam-6529	343	17	gb(y	gb(y	ADV
ejpam-6529	343	18	)	)	PUNCT
ejpam-6529	343	19	̸=	̸=	PROPN
ejpam-6529	343	20	1	1	NUM
ejpam-6529	343	21	,	,	PUNCT
ejpam-6529	343	22	and	and	CCONJ
ejpam-6529	343	23	so	so	ADV
ejpam-6529	343	24	fb(y)+1	fb(y)+1	PROPN
ejpam-6529	343	25	>	>	X
ejpam-6529	343	26	1	1	NUM
ejpam-6529	343	27	and	and	CCONJ
ejpam-6529	343	28	gb(y)+0	gb(y)+0	NOUN
ejpam-6529	343	29	<	<	X
ejpam-6529	343	30	1	1	NUM
ejpam-6529	343	31	,	,	PUNCT
ejpam-6529	343	32	i.e.	i.e.	X
ejpam-6529	343	33	,	,	PUNCT
ejpam-6529	343	34	y(1,0	y(1,0	NUM
ejpam-6529	343	35	)	)	PUNCT
ejpam-6529	343	36	q	q	NOUN
ejpam-6529	343	37	b∗.	b∗.	NOUN
ejpam-6529	343	38	using	use	VERB
ejpam-6529	343	39	(	(	PUNCT
ejpam-6529	343	40	29	29	NUM
ejpam-6529	343	41	)	)	PUNCT
ejpam-6529	343	42	induces	induce	VERB
ejpam-6529	343	43	ðx(y)(1,0	ðx(y)(1,0	NOUN
ejpam-6529	343	44	)	)	PUNCT
ejpam-6529	343	45	∈	∈	PROPN
ejpam-6529	343	46	b∗.	b∗.	NOUN
ejpam-6529	343	47	hence	hence	ADV
ejpam-6529	343	48	fb(ðx(y	fb(ðx(y	PROPN
ejpam-6529	343	49	)	)	PUNCT
ejpam-6529	343	50	)	)	PUNCT
ejpam-6529	343	51	≥	≥	NOUN
ejpam-6529	343	52	1	1	NUM
ejpam-6529	343	53	and	and	CCONJ
ejpam-6529	343	54	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	343	55	)	)	PUNCT
ejpam-6529	343	56	)	)	PUNCT
ejpam-6529	343	57	≤	≤	NOUN
ejpam-6529	343	58	0	0	NUM
ejpam-6529	343	59	which	which	PRON
ejpam-6529	343	60	shows	show	VERB
ejpam-6529	343	61	that	that	SCONJ
ejpam-6529	343	62	ðx(y	ðx(y	PUNCT
ejpam-6529	343	63	)	)	PUNCT
ejpam-6529	343	64	∈	∈	PROPN
ejpam-6529	343	65	x(0,1	x(0,1	ADP
ejpam-6529	343	66	)	)	PUNCT
ejpam-6529	343	67	.	.	PUNCT
ejpam-6529	344	1	therefore	therefore	ADV
ejpam-6529	344	2	x(0,1	x(0,1	X
ejpam-6529	344	3	)	)	PUNCT
ejpam-6529	344	4	is	be	AUX
ejpam-6529	344	5	a	a	DET
ejpam-6529	344	6	weak	weak	ADJ
ejpam-6529	344	7	filter	filter	NOUN
ejpam-6529	344	8	of	of	ADP
ejpam-6529	344	9	x	x	X
ejpam-6529	344	10	:	:	PUNCT
ejpam-6529	344	11	=	=	SYM
ejpam-6529	344	12	(	(	PUNCT
ejpam-6529	344	13	x	x	NOUN
ejpam-6529	344	14	,	,	PUNCT
ejpam-6529	344	15	|	|	NOUN
ejpam-6529	344	16	)	)	PUNCT
ejpam-6529	344	17	.	.	PUNCT
ejpam-6529	345	1	theorem	theorem	VERB
ejpam-6529	345	2	9	9	NUM
ejpam-6529	345	3	.	.	PUNCT
ejpam-6529	346	1	if	if	SCONJ
ejpam-6529	346	2	an	an	DET
ejpam-6529	346	3	intuitionistic	intuitionistic	ADJ
ejpam-6529	346	4	fuzzy	fuzzy	ADJ
ejpam-6529	346	5	set	set	VERB
ejpam-6529	346	6	b∗	b∗	ADJ
ejpam-6529	346	7	:	:	PUNCT
ejpam-6529	346	8	=	=	SYM
ejpam-6529	346	9	(	(	PUNCT
ejpam-6529	346	10	x	x	X
ejpam-6529	346	11	;	;	PUNCT
ejpam-6529	346	12	fb	fb	INTJ
ejpam-6529	346	13	,	,	PUNCT
ejpam-6529	346	14	gb	gb	NOUN
ejpam-6529	346	15	)	)	PUNCT
ejpam-6529	346	16	in	in	ADP
ejpam-6529	346	17	x	x	X
ejpam-6529	346	18	satisfies	satisfie	NOUN
ejpam-6529	346	19	:	:	PUNCT
ejpam-6529	346	20	(	(	PUNCT
ejpam-6529	346	21	∀x	∀x	X
ejpam-6529	346	22	∈	∈	PROPN
ejpam-6529	346	23	x)(∀(s	x)(∀(s	NOUN
ejpam-6529	346	24	,	,	PUNCT
ejpam-6529	346	25	t	t	PROPN
ejpam-6529	346	26	)	)	PUNCT
ejpam-6529	346	27	∈	∈	PROPN
ejpam-6529	346	28	(	(	PUNCT
ejpam-6529	346	29	0	0	NUM
ejpam-6529	346	30	,	,	PUNCT
ejpam-6529	346	31	1]×	1]×	NUM
ejpam-6529	347	1	[	[	X
ejpam-6529	347	2	0	0	NUM
ejpam-6529	347	3	,	,	PUNCT
ejpam-6529	347	4	1	1	NUM
ejpam-6529	347	5	)	)	PUNCT
ejpam-6529	347	6	)	)	PUNCT
ejpam-6529	348	1	(	(	PUNCT
ejpam-6529	348	2	x(s	x(s	PROPN
ejpam-6529	348	3	,	,	PUNCT
ejpam-6529	348	4	t	t	PROPN
ejpam-6529	348	5	)	)	PUNCT
ejpam-6529	348	6	q	q	NOUN
ejpam-6529	348	7	b∗	b∗	ADJ
ejpam-6529	348	8	⇒	⇒	NOUN
ejpam-6529	348	9	1(s	1(s	NUM
ejpam-6529	348	10	,	,	PUNCT
ejpam-6529	348	11	t	t	PROPN
ejpam-6529	348	12	)	)	PUNCT
ejpam-6529	348	13	q	q	PROPN
ejpam-6529	349	1	b∗	b∗	ADJ
ejpam-6529	349	2	)	)	PUNCT
ejpam-6529	349	3	,	,	PUNCT
ejpam-6529	349	4	(	(	PUNCT
ejpam-6529	349	5	30	30	NUM
ejpam-6529	349	6	)	)	PUNCT
ejpam-6529	349	7	(	(	PUNCT
ejpam-6529	349	8	∀x	∀x	X
ejpam-6529	349	9	,	,	PUNCT
ejpam-6529	350	1	y	y	PROPN
ejpam-6529	350	2	∈	∈	PROPN
ejpam-6529	350	3	x)(∀(s	x)(∀(s	NOUN
ejpam-6529	350	4	,	,	PUNCT
ejpam-6529	350	5	t	t	PROPN
ejpam-6529	350	6	)	)	PUNCT
ejpam-6529	350	7	∈	∈	PROPN
ejpam-6529	350	8	(	(	PUNCT
ejpam-6529	350	9	0	0	NUM
ejpam-6529	350	10	,	,	PUNCT
ejpam-6529	350	11	1]×	1]×	NUM
ejpam-6529	350	12	[	[	X
ejpam-6529	350	13	0	0	NUM
ejpam-6529	350	14	,	,	PUNCT
ejpam-6529	350	15	1	1	NUM
ejpam-6529	350	16	)	)	PUNCT
ejpam-6529	350	17	)	)	PUNCT
ejpam-6529	351	1	(	(	PUNCT
ejpam-6529	351	2	y(s	y(s	PROPN
ejpam-6529	351	3	,	,	PUNCT
ejpam-6529	351	4	t	t	PROPN
ejpam-6529	351	5	)	)	PUNCT
ejpam-6529	351	6	q	q	NOUN
ejpam-6529	351	7	b∗	b∗	ADJ
ejpam-6529	351	8	⇒	⇒	NOUN
ejpam-6529	351	9	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	351	10	,	,	PUNCT
ejpam-6529	351	11	t	t	PROPN
ejpam-6529	351	12	)	)	PUNCT
ejpam-6529	351	13	q	q	PROPN
ejpam-6529	352	1	b∗	b∗	ADJ
ejpam-6529	352	2	)	)	PUNCT
ejpam-6529	352	3	,	,	PUNCT
ejpam-6529	352	4	(	(	PUNCT
ejpam-6529	352	5	31	31	NUM
ejpam-6529	352	6	)	)	PUNCT
ejpam-6529	352	7	then	then	ADV
ejpam-6529	352	8	its	its	PRON
ejpam-6529	352	9	nonempty	nonempty	ADJ
ejpam-6529	352	10	(	(	PUNCT
ejpam-6529	352	11	0	0	NUM
ejpam-6529	352	12	,	,	PUNCT
ejpam-6529	352	13	1)-set	1)-set	NOUN
ejpam-6529	352	14	is	be	AUX
ejpam-6529	352	15	a	a	DET
ejpam-6529	352	16	weak	weak	ADJ
ejpam-6529	352	17	filter	filter	NOUN
ejpam-6529	352	18	of	of	ADP
ejpam-6529	352	19	x	x	X
ejpam-6529	352	20	:	:	PUNCT
ejpam-6529	352	21	=	=	SYM
ejpam-6529	352	22	(	(	PUNCT
ejpam-6529	352	23	x	x	NOUN
ejpam-6529	352	24	,	,	PUNCT
ejpam-6529	352	25	|	|	NOUN
ejpam-6529	352	26	)	)	PUNCT
ejpam-6529	352	27	.	.	PUNCT
ejpam-6529	353	1	proof	proof	NOUN
ejpam-6529	353	2	.	.	PUNCT
ejpam-6529	354	1	let	let	VERB
ejpam-6529	354	2	b∗	b∗	ADV
ejpam-6529	354	3	:	:	PUNCT
ejpam-6529	354	4	=	=	SYM
ejpam-6529	354	5	(	(	PUNCT
ejpam-6529	354	6	x	x	X
ejpam-6529	354	7	;	;	PUNCT
ejpam-6529	354	8	fb	fb	INTJ
ejpam-6529	354	9	,	,	PUNCT
ejpam-6529	354	10	gb	gb	PROPN
ejpam-6529	354	11	)	)	PUNCT
ejpam-6529	354	12	be	be	VERB
ejpam-6529	354	13	an	an	DET
ejpam-6529	354	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	354	15	fuzzy	fuzzy	ADJ
ejpam-6529	354	16	set	set	NOUN
ejpam-6529	354	17	in	in	ADP
ejpam-6529	354	18	x	x	ADP
ejpam-6529	354	19	that	that	SCONJ
ejpam-6529	354	20	satisfies	satisfie	NOUN
ejpam-6529	354	21	(	(	PUNCT
ejpam-6529	354	22	30	30	NUM
ejpam-6529	354	23	)	)	PUNCT
ejpam-6529	354	24	and	and	CCONJ
ejpam-6529	354	25	(	(	PUNCT
ejpam-6529	354	26	31	31	NUM
ejpam-6529	354	27	)	)	PUNCT
ejpam-6529	354	28	.	.	PUNCT
ejpam-6529	355	1	suppose	suppose	VERB
ejpam-6529	355	2	that	that	SCONJ
ejpam-6529	355	3	x(0,1	x(0,1	NOUN
ejpam-6529	355	4	)	)	PUNCT
ejpam-6529	355	5	̸=	̸=	PROPN
ejpam-6529	355	6	∅	∅	NOUN
ejpam-6529	355	7	and	and	CCONJ
ejpam-6529	355	8	say	say	VERB
ejpam-6529	355	9	x	x	X
ejpam-6529	355	10	∈	∈	PROPN
ejpam-6529	355	11	x(0,1	x(0,1	ADP
ejpam-6529	355	12	)	)	PUNCT
ejpam-6529	355	13	.	.	PUNCT
ejpam-6529	356	1	then	then	ADV
ejpam-6529	356	2	fb(x	fb(x	NOUN
ejpam-6529	356	3	)	)	PUNCT
ejpam-6529	356	4	̸=	̸=	NOUN
ejpam-6529	356	5	0	0	NUM
ejpam-6529	356	6	and	and	CCONJ
ejpam-6529	356	7	gb(x	gb(x	NUM
ejpam-6529	356	8	)	)	PUNCT
ejpam-6529	356	9	̸=	̸=	PROPN
ejpam-6529	356	10	1	1	NUM
ejpam-6529	356	11	.	.	PUNCT
ejpam-6529	356	12	thus	thus	ADV
ejpam-6529	356	13	fb(x	fb(x	VERB
ejpam-6529	356	14	)	)	PUNCT
ejpam-6529	356	15	+	+	CCONJ
ejpam-6529	356	16	1	1	NUM
ejpam-6529	356	17	>	>	SYM
ejpam-6529	356	18	1	1	NUM
ejpam-6529	356	19	and	and	CCONJ
ejpam-6529	356	20	gb(x	gb(x	NUM
ejpam-6529	356	21	)	)	PUNCT
ejpam-6529	357	1	+	+	CCONJ
ejpam-6529	357	2	0	0	NUM
ejpam-6529	357	3	<	<	X
ejpam-6529	357	4	1	1	NUM
ejpam-6529	357	5	,	,	PUNCT
ejpam-6529	357	6	i.e.	i.e.	X
ejpam-6529	357	7	,	,	PUNCT
ejpam-6529	357	8	x(1,0	x(1,0	NUM
ejpam-6529	357	9	)	)	PUNCT
ejpam-6529	357	10	q	q	NOUN
ejpam-6529	357	11	b∗.	b∗.	NOUN
ejpam-6529	357	12	using	use	VERB
ejpam-6529	357	13	(	(	PUNCT
ejpam-6529	357	14	30	30	NUM
ejpam-6529	357	15	)	)	PUNCT
ejpam-6529	357	16	induces	induce	VERB
ejpam-6529	357	17	1(1,0	1(1,0	NUM
ejpam-6529	357	18	)	)	PUNCT
ejpam-6529	357	19	q	q	PUNCT
ejpam-6529	358	1	b∗	b∗	ADJ
ejpam-6529	358	2	,	,	PUNCT
ejpam-6529	358	3	that	that	ADV
ejpam-6529	358	4	is	is	ADV
ejpam-6529	358	5	,	,	PUNCT
ejpam-6529	358	6	fb(1)+	fb(1)+	PROPN
ejpam-6529	358	7	1	1	NUM
ejpam-6529	358	8	>	>	SYM
ejpam-6529	358	9	1	1	NUM
ejpam-6529	358	10	and	and	CCONJ
ejpam-6529	358	11	gb(1)+	gb(1)+	PROPN
ejpam-6529	358	12	0	0	PUNCT
ejpam-6529	359	1	<	<	X
ejpam-6529	359	2	1	1	NUM
ejpam-6529	359	3	.	.	PUNCT
ejpam-6529	359	4	thus	thus	ADV
ejpam-6529	359	5	fb(1	fb(1	PROPN
ejpam-6529	359	6	)	)	PUNCT
ejpam-6529	359	7	̸=	̸=	PROPN
ejpam-6529	359	8	0	0	NUM
ejpam-6529	359	9	and	and	CCONJ
ejpam-6529	359	10	gb(1	gb(1	PROPN
ejpam-6529	359	11	)	)	PUNCT
ejpam-6529	359	12	̸=	̸=	PROPN
ejpam-6529	359	13	1	1	NUM
ejpam-6529	359	14	,	,	PUNCT
ejpam-6529	359	15	i.e.	i.e.	X
ejpam-6529	359	16	,	,	PUNCT
ejpam-6529	359	17	1	1	NUM
ejpam-6529	359	18	∈	∈	PROPN
ejpam-6529	359	19	x(0,1	x(0,1	ADP
ejpam-6529	359	20	)	)	PUNCT
ejpam-6529	359	21	.	.	PUNCT
ejpam-6529	360	1	if	if	SCONJ
ejpam-6529	360	2	x	x	SYM
ejpam-6529	360	3	∈	∈	PROPN
ejpam-6529	360	4	x	x	X
ejpam-6529	360	5	and	and	CCONJ
ejpam-6529	360	6	y	y	PROPN
ejpam-6529	360	7	∈	∈	PROPN
ejpam-6529	360	8	x(0,1	x(0,1	ADP
ejpam-6529	360	9	)	)	PUNCT
ejpam-6529	360	10	,	,	PUNCT
ejpam-6529	360	11	then	then	ADV
ejpam-6529	360	12	fb(y	fb(y	PUNCT
ejpam-6529	360	13	)	)	PUNCT
ejpam-6529	360	14	̸=	̸=	PROPN
ejpam-6529	360	15	0	0	NUM
ejpam-6529	360	16	and	and	CCONJ
ejpam-6529	360	17	gb(y	gb(y	ADV
ejpam-6529	360	18	)	)	PUNCT
ejpam-6529	360	19	̸=	̸=	PROPN
ejpam-6529	360	20	1	1	NUM
ejpam-6529	360	21	,	,	PUNCT
ejpam-6529	360	22	and	and	CCONJ
ejpam-6529	360	23	so	so	ADV
ejpam-6529	360	24	fb(y	fb(y	NUM
ejpam-6529	360	25	)	)	PUNCT
ejpam-6529	360	26	+	+	CCONJ
ejpam-6529	360	27	1	1	NUM
ejpam-6529	360	28	>	>	SYM
ejpam-6529	360	29	1	1	NUM
ejpam-6529	360	30	and	and	CCONJ
ejpam-6529	360	31	gb(y	gb(y	NUM
ejpam-6529	360	32	)	)	PUNCT
ejpam-6529	361	1	+	+	CCONJ
ejpam-6529	361	2	0	0	NUM
ejpam-6529	361	3	<	<	X
ejpam-6529	361	4	1	1	NUM
ejpam-6529	361	5	,	,	PUNCT
ejpam-6529	361	6	i.e.	i.e.	X
ejpam-6529	361	7	,	,	PUNCT
ejpam-6529	361	8	y(1,0	y(1,0	NUM
ejpam-6529	361	9	)	)	PUNCT
ejpam-6529	361	10	q	q	NOUN
ejpam-6529	361	11	b∗.	b∗.	NOUN
ejpam-6529	362	1	it	it	PRON
ejpam-6529	362	2	follows	follow	VERB
ejpam-6529	362	3	from	from	ADP
ejpam-6529	362	4	(	(	PUNCT
ejpam-6529	362	5	31	31	NUM
ejpam-6529	362	6	)	)	PUNCT
ejpam-6529	362	7	that	that	SCONJ
ejpam-6529	362	8	ðx(y)(1,0	ðx(y)(1,0	VERB
ejpam-6529	362	9	)	)	PUNCT
ejpam-6529	362	10	q	q	NOUN
ejpam-6529	362	11	b∗.	b∗.	NOUN
ejpam-6529	362	12	hence	hence	ADV
ejpam-6529	362	13	fb(ðx(y	fb(ðx(y	PROPN
ejpam-6529	362	14	)	)	PUNCT
ejpam-6529	362	15	)	)	PUNCT
ejpam-6529	363	1	+	+	CCONJ
ejpam-6529	363	2	1	1	NUM
ejpam-6529	363	3	>	>	SYM
ejpam-6529	363	4	1	1	NUM
ejpam-6529	363	5	and	and	CCONJ
ejpam-6529	363	6	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	363	7	)	)	PUNCT
ejpam-6529	363	8	)	)	PUNCT
ejpam-6529	364	1	+	+	CCONJ
ejpam-6529	364	2	0	0	NUM
ejpam-6529	364	3	<	<	X
ejpam-6529	364	4	1	1	NUM
ejpam-6529	364	5	,	,	PUNCT
ejpam-6529	364	6	and	and	CCONJ
ejpam-6529	364	7	so	so	ADV
ejpam-6529	364	8	ðx(y	ðx(y	X
ejpam-6529	364	9	)	)	PUNCT
ejpam-6529	364	10	∈	∈	PROPN
ejpam-6529	364	11	x(0,1	x(0,1	ADP
ejpam-6529	364	12	)	)	PUNCT
ejpam-6529	364	13	.	.	PUNCT
ejpam-6529	365	1	therefore	therefore	ADV
ejpam-6529	365	2	x(0,1	x(0,1	X
ejpam-6529	365	3	)	)	PUNCT
ejpam-6529	365	4	is	be	AUX
ejpam-6529	365	5	a	a	DET
ejpam-6529	365	6	weak	weak	ADJ
ejpam-6529	365	7	filter	filter	NOUN
ejpam-6529	365	8	of	of	ADP
ejpam-6529	365	9	x	x	X
ejpam-6529	365	10	:	:	PUNCT
ejpam-6529	365	11	=	=	SYM
ejpam-6529	365	12	(	(	PUNCT
ejpam-6529	365	13	x	x	NOUN
ejpam-6529	365	14	,	,	PUNCT
ejpam-6529	365	15	|	|	NOUN
ejpam-6529	365	16	)	)	PUNCT
ejpam-6529	365	17	.	.	PUNCT
ejpam-6529	366	1	we	we	PRON
ejpam-6529	366	2	provide	provide	VERB
ejpam-6529	366	3	conditions	condition	NOUN
ejpam-6529	366	4	for	for	ADP
ejpam-6529	366	5	the	the	DET
ejpam-6529	366	6	intuitionistic	intuitionistic	ADJ
ejpam-6529	366	7	level	level	NOUN
ejpam-6529	366	8	set	set	VERB
ejpam-6529	366	9	and	and	CCONJ
ejpam-6529	366	10	intuitionistic	intuitionistic	ADJ
ejpam-6529	366	11	q	q	NOUN
ejpam-6529	366	12	-	-	PUNCT
ejpam-6529	366	13	set	set	NOUN
ejpam-6529	366	14	to	to	PART
ejpam-6529	366	15	be	be	AUX
ejpam-6529	366	16	weak	weak	ADJ
ejpam-6529	366	17	filters	filter	NOUN
ejpam-6529	366	18	.	.	PUNCT
ejpam-6529	367	1	theorem	theorem	VERB
ejpam-6529	367	2	10	10	NUM
ejpam-6529	367	3	.	.	PUNCT
ejpam-6529	368	1	if	if	SCONJ
ejpam-6529	368	2	an	an	DET
ejpam-6529	368	3	intuitionistic	intuitionistic	ADJ
ejpam-6529	368	4	fuzzy	fuzzy	ADJ
ejpam-6529	368	5	set	set	VERB
ejpam-6529	368	6	b∗	b∗	ADJ
ejpam-6529	368	7	:	:	PUNCT
ejpam-6529	368	8	=	=	SYM
ejpam-6529	368	9	(	(	PUNCT
ejpam-6529	368	10	x	x	X
ejpam-6529	368	11	;	;	PUNCT
ejpam-6529	368	12	fb	fb	INTJ
ejpam-6529	368	13	,	,	PUNCT
ejpam-6529	368	14	gb	gb	NOUN
ejpam-6529	368	15	)	)	PUNCT
ejpam-6529	368	16	in	in	ADP
ejpam-6529	368	17	x	x	PUNCT
ejpam-6529	368	18	satisfies	satisfie	NOUN
ejpam-6529	368	19	:	:	PUNCT
ejpam-6529	368	20	fb(x	fb(x	X
ejpam-6529	368	21	)	)	PUNCT
ejpam-6529	368	22	≤	≤	NOUN
ejpam-6529	368	23	max{fb(1	max{fb(1	PROPN
ejpam-6529	368	24	)	)	PUNCT
ejpam-6529	368	25	,	,	PUNCT
ejpam-6529	368	26	0.5	0.5	NUM
ejpam-6529	368	27	}	}	PUNCT
ejpam-6529	368	28	,	,	PUNCT
ejpam-6529	368	29	gb(x	gb(x	NUM
ejpam-6529	368	30	)	)	PUNCT
ejpam-6529	368	31	≥	≥	NUM
ejpam-6529	368	32	min{gb(1	min{gb(1	NOUN
ejpam-6529	368	33	)	)	PUNCT
ejpam-6529	368	34	,	,	PUNCT
ejpam-6529	368	35	0.5	0.5	NUM
ejpam-6529	368	36	}	}	PUNCT
ejpam-6529	368	37	,	,	PUNCT
ejpam-6529	368	38	(	(	PUNCT
ejpam-6529	368	39	32	32	NUM
ejpam-6529	368	40	)	)	PUNCT
ejpam-6529	368	41	fb(y	fb(y	NUM
ejpam-6529	368	42	)	)	PUNCT
ejpam-6529	368	43	≤	≤	NUM
ejpam-6529	368	44	max{fb(ðx(y	max{fb(ðx(y	NOUN
ejpam-6529	368	45	)	)	PUNCT
ejpam-6529	368	46	)	)	PUNCT
ejpam-6529	368	47	,	,	PUNCT
ejpam-6529	368	48	0.5	0.5	NUM
ejpam-6529	368	49	}	}	PUNCT
ejpam-6529	368	50	,	,	PUNCT
ejpam-6529	368	51	gb(y	gb(y	ADV
ejpam-6529	368	52	)	)	PUNCT
ejpam-6529	368	53	≥	≥	NOUN
ejpam-6529	368	54	min{gb(ðx(y	min{gb(ðx(y	PROPN
ejpam-6529	368	55	)	)	PUNCT
ejpam-6529	368	56	)	)	PUNCT
ejpam-6529	368	57	,	,	PUNCT
ejpam-6529	368	58	0.5	0.5	NUM
ejpam-6529	368	59	}	}	PUNCT
ejpam-6529	368	60	(	(	PUNCT
ejpam-6529	368	61	33	33	NUM
ejpam-6529	368	62	)	)	PUNCT
ejpam-6529	368	63	for	for	ADP
ejpam-6529	368	64	all	all	DET
ejpam-6529	368	65	x	x	NOUN
ejpam-6529	368	66	,	,	PUNCT
ejpam-6529	368	67	y	y	PROPN
ejpam-6529	368	68	∈	∈	PROPN
ejpam-6529	368	69	x	x	X
ejpam-6529	368	70	,	,	PUNCT
ejpam-6529	368	71	then	then	ADV
ejpam-6529	368	72	its	its	PRON
ejpam-6529	368	73	nonempty	nonempty	ADV
ejpam-6529	368	74	intuitionistic	intuitionistic	ADJ
ejpam-6529	368	75	level	level	NOUN
ejpam-6529	368	76	set	set	NOUN
ejpam-6529	368	77	(	(	PUNCT
ejpam-6529	368	78	b∗	b∗	ADJ
ejpam-6529	368	79	,	,	PUNCT
ejpam-6529	368	80	(	(	PUNCT
ejpam-6529	368	81	s	s	X
ejpam-6529	368	82	,	,	PUNCT
ejpam-6529	368	83	t))∈	t))∈	NOUN
ejpam-6529	368	84	is	be	AUX
ejpam-6529	368	85	a	a	DET
ejpam-6529	368	86	weak	weak	ADJ
ejpam-6529	368	87	filter	filter	NOUN
ejpam-6529	368	88	of	of	ADP
ejpam-6529	368	89	x	x	X
ejpam-6529	368	90	:	:	PUNCT
ejpam-6529	368	91	=	=	SYM
ejpam-6529	368	92	(	(	PUNCT
ejpam-6529	368	93	x	x	NOUN
ejpam-6529	368	94	,	,	PUNCT
ejpam-6529	368	95	|	|	ADV
ejpam-6529	368	96	)	)	PUNCT
ejpam-6529	368	97	for	for	ADP
ejpam-6529	368	98	all	all	DET
ejpam-6529	368	99	(	(	PUNCT
ejpam-6529	368	100	s	s	PROPN
ejpam-6529	368	101	,	,	PUNCT
ejpam-6529	368	102	t	t	PROPN
ejpam-6529	368	103	)	)	PUNCT
ejpam-6529	368	104	∈	∈	PROPN
ejpam-6529	368	105	(	(	PUNCT
ejpam-6529	368	106	0.5	0.5	NUM
ejpam-6529	368	107	,	,	PUNCT
ejpam-6529	368	108	1]×	1]×	NUM
ejpam-6529	368	109	[	[	X
ejpam-6529	368	110	0	0	NUM
ejpam-6529	368	111	,	,	PUNCT
ejpam-6529	368	112	0.5	0.5	NUM
ejpam-6529	368	113	)	)	PUNCT
ejpam-6529	368	114	.	.	PUNCT
ejpam-6529	369	1	proof	proof	NOUN
ejpam-6529	369	2	.	.	PUNCT
ejpam-6529	370	1	let	let	VERB
ejpam-6529	370	2	(	(	PUNCT
ejpam-6529	370	3	s	s	X
ejpam-6529	370	4	,	,	PUNCT
ejpam-6529	370	5	t	t	PROPN
ejpam-6529	370	6	)	)	PUNCT
ejpam-6529	370	7	∈	∈	PROPN
ejpam-6529	370	8	(	(	PUNCT
ejpam-6529	370	9	0.5	0.5	NUM
ejpam-6529	370	10	,	,	PUNCT
ejpam-6529	370	11	1]×	1]×	NUM
ejpam-6529	371	1	[	[	X
ejpam-6529	371	2	0	0	NUM
ejpam-6529	371	3	,	,	PUNCT
ejpam-6529	371	4	0.5	0.5	NUM
ejpam-6529	371	5	)	)	PUNCT
ejpam-6529	371	6	be	be	VERB
ejpam-6529	371	7	such	such	ADJ
ejpam-6529	371	8	that	that	SCONJ
ejpam-6529	371	9	(	(	PUNCT
ejpam-6529	371	10	b∗	b∗	ADJ
ejpam-6529	371	11	,	,	PUNCT
ejpam-6529	371	12	(	(	PUNCT
ejpam-6529	371	13	s	s	X
ejpam-6529	371	14	,	,	PUNCT
ejpam-6529	371	15	t))∈	t))∈	NOUN
ejpam-6529	371	16	̸=	̸=	PROPN
ejpam-6529	371	17	∅	∅	NOUN
ejpam-6529	371	18	,	,	PUNCT
ejpam-6529	371	19	say	say	VERB
ejpam-6529	371	20	x	x	X
ejpam-6529	371	21	∈	∈	PROPN
ejpam-6529	371	22	(	(	PUNCT
ejpam-6529	371	23	b∗	b∗	ADJ
ejpam-6529	371	24	,	,	PUNCT
ejpam-6529	371	25	(	(	PUNCT
ejpam-6529	371	26	s	s	X
ejpam-6529	371	27	,	,	PUNCT
ejpam-6529	371	28	t))∈.	t))∈.	NOUN
ejpam-6529	371	29	then	then	ADV
ejpam-6529	371	30	x	x	SYM
ejpam-6529	371	31	∈	∈	PROPN
ejpam-6529	371	32	(	(	PUNCT
ejpam-6529	371	33	fb	fb	INTJ
ejpam-6529	371	34	,	,	PUNCT
ejpam-6529	371	35	s)∈	s)∈	NUM
ejpam-6529	371	36	∩	∩	NOUN
ejpam-6529	371	37	(	(	PUNCT
ejpam-6529	371	38	gb	gb	NOUN
ejpam-6529	371	39	,	,	PUNCT
ejpam-6529	371	40	t)∈	t)∈	PROPN
ejpam-6529	371	41	,	,	PUNCT
ejpam-6529	371	42	which	which	PRON
ejpam-6529	371	43	implies	imply	VERB
ejpam-6529	371	44	from	from	ADP
ejpam-6529	371	45	(	(	PUNCT
ejpam-6529	371	46	32	32	NUM
ejpam-6529	371	47	)	)	PUNCT
ejpam-6529	371	48	that	that	PRON
ejpam-6529	371	49	max{fb(1	max{fb(1	PROPN
ejpam-6529	371	50	)	)	PUNCT
ejpam-6529	371	51	,	,	PUNCT
ejpam-6529	371	52	0.5	0.5	NUM
ejpam-6529	371	53	}	}	PUNCT
ejpam-6529	371	54	≥	≥	NUM
ejpam-6529	371	55	fb(x	fb(x	PUNCT
ejpam-6529	371	56	)	)	PUNCT
ejpam-6529	371	57	≥	≥	X
ejpam-6529	371	58	s	s	PART
ejpam-6529	371	59	>	>	X
ejpam-6529	371	60	0.5	0.5	NUM
ejpam-6529	371	61	s.	s.	PROPN
ejpam-6529	371	62	s.	s.	PROPN
ejpam-6529	371	63	ahn	ahn	PROPN
ejpam-6529	371	64	,	,	PUNCT
ejpam-6529	371	65	y.	y.	PROPN
ejpam-6529	371	66	j.	j.	PROPN
ejpam-6529	371	67	seo	seo	PROPN
ejpam-6529	371	68	,	,	PUNCT
ejpam-6529	371	69	y.	y.	PROPN
ejpam-6529	371	70	b.	b.	PROPN
ejpam-6529	371	71	jun	jun	PROPN
ejpam-6529	371	72	/	/	SYM
ejpam-6529	371	73	eur	eur	PROPN
ejpam-6529	371	74	.	.	PUNCT
ejpam-6529	372	1	j.	j.	PROPN
ejpam-6529	372	2	pure	pure	PROPN
ejpam-6529	372	3	appl	appl	PROPN
ejpam-6529	372	4	.	.	PROPN
ejpam-6529	372	5	math	math	PROPN
ejpam-6529	372	6	,	,	PUNCT
ejpam-6529	372	7	18	18	NUM
ejpam-6529	372	8	(	(	PUNCT
ejpam-6529	372	9	3	3	NUM
ejpam-6529	372	10	)	)	PUNCT
ejpam-6529	372	11	(	(	PUNCT
ejpam-6529	372	12	2025	2025	NUM
ejpam-6529	372	13	)	)	PUNCT
ejpam-6529	372	14	,	,	PUNCT
ejpam-6529	372	15	6529	6529	NUM
ejpam-6529	372	16	13	13	NUM
ejpam-6529	372	17	of	of	ADP
ejpam-6529	372	18	16	16	NUM
ejpam-6529	372	19	and	and	CCONJ
ejpam-6529	372	20	min{gb(1	min{gb(1	PROPN
ejpam-6529	372	21	)	)	PUNCT
ejpam-6529	372	22	,	,	PUNCT
ejpam-6529	372	23	0.5	0.5	NUM
ejpam-6529	372	24	}	}	PUNCT
ejpam-6529	372	25	≤	≤	NOUN
ejpam-6529	372	26	gb(x	gb(x	PUNCT
ejpam-6529	372	27	)	)	PUNCT
ejpam-6529	372	28	≤	≤	NOUN
ejpam-6529	373	1	t	t	PROPN
ejpam-6529	373	2	<	<	X
ejpam-6529	373	3	0.5	0.5	NUM
ejpam-6529	373	4	.	.	PUNCT
ejpam-6529	374	1	hence	hence	ADV
ejpam-6529	374	2	fb(1	fb(1	PROPN
ejpam-6529	374	3	)	)	PUNCT
ejpam-6529	374	4	≥	≥	NOUN
ejpam-6529	374	5	s	s	NOUN
ejpam-6529	374	6	and	and	CCONJ
ejpam-6529	374	7	gb(1	gb(1	PROPN
ejpam-6529	375	1	)	)	PUNCT
ejpam-6529	375	2	≤	≤	NOUN
ejpam-6529	375	3	t	t	PROPN
ejpam-6529	375	4	,	,	PUNCT
ejpam-6529	375	5	and	and	CCONJ
ejpam-6529	375	6	so	so	ADV
ejpam-6529	375	7	1	1	NUM
ejpam-6529	375	8	∈	∈	PROPN
ejpam-6529	375	9	(	(	PUNCT
ejpam-6529	375	10	fb	fb	INTJ
ejpam-6529	375	11	,	,	PUNCT
ejpam-6529	375	12	s)∈	s)∈	NUM
ejpam-6529	375	13	∩	∩	NOUN
ejpam-6529	375	14	(	(	PUNCT
ejpam-6529	375	15	gb	gb	NOUN
ejpam-6529	375	16	,	,	PUNCT
ejpam-6529	375	17	t)∈	t)∈	PROPN
ejpam-6529	375	18	=	=	SYM
ejpam-6529	375	19	(	(	PUNCT
ejpam-6529	375	20	b∗	b∗	ADJ
ejpam-6529	375	21	,	,	PUNCT
ejpam-6529	375	22	(	(	PUNCT
ejpam-6529	375	23	s	s	X
ejpam-6529	375	24	,	,	PUNCT
ejpam-6529	375	25	t))∈.	t))∈.	NOUN
ejpam-6529	375	26	if	if	SCONJ
ejpam-6529	375	27	x	x	SYM
ejpam-6529	375	28	∈	∈	PROPN
ejpam-6529	375	29	x	x	X
ejpam-6529	375	30	and	and	CCONJ
ejpam-6529	375	31	y	y	PROPN
ejpam-6529	375	32	∈	∈	PROPN
ejpam-6529	375	33	(	(	PUNCT
ejpam-6529	375	34	b∗	b∗	ADJ
ejpam-6529	375	35	,	,	PUNCT
ejpam-6529	375	36	(	(	PUNCT
ejpam-6529	375	37	s	s	X
ejpam-6529	375	38	,	,	PUNCT
ejpam-6529	375	39	t))∈	t))∈	NOUN
ejpam-6529	375	40	,	,	PUNCT
ejpam-6529	375	41	then	then	ADV
ejpam-6529	375	42	fb(y	fb(y	X
ejpam-6529	375	43	)	)	PUNCT
ejpam-6529	375	44	≥	≥	PRON
ejpam-6529	375	45	s	s	PART
ejpam-6529	375	46	and	and	CCONJ
ejpam-6529	375	47	gb(y	gb(y	NUM
ejpam-6529	375	48	)	)	PUNCT
ejpam-6529	375	49	≤	≤	PUNCT
ejpam-6529	376	1	t.	t.	NOUN
ejpam-6529	376	2	it	it	PRON
ejpam-6529	376	3	follows	follow	VERB
ejpam-6529	376	4	from	from	ADP
ejpam-6529	376	5	(	(	PUNCT
ejpam-6529	376	6	33	33	NUM
ejpam-6529	376	7	)	)	PUNCT
ejpam-6529	376	8	that	that	SCONJ
ejpam-6529	376	9	0.5	0.5	NUM
ejpam-6529	376	10	<	<	X
ejpam-6529	376	11	s	s	PART
ejpam-6529	376	12	≤	≤	NUM
ejpam-6529	376	13	fb(y	fb(y	NUM
ejpam-6529	376	14	)	)	PUNCT
ejpam-6529	376	15	≤	≤	NUM
ejpam-6529	376	16	max{fb(ðx(y	max{fb(ðx(y	NOUN
ejpam-6529	376	17	)	)	PUNCT
ejpam-6529	376	18	)	)	PUNCT
ejpam-6529	376	19	,	,	PUNCT
ejpam-6529	376	20	0.5	0.5	NUM
ejpam-6529	376	21	}	}	PUNCT
ejpam-6529	376	22	and	and	CCONJ
ejpam-6529	376	23	0.5	0.5	NUM
ejpam-6529	376	24	>	>	SYM
ejpam-6529	376	25	t	t	PROPN
ejpam-6529	376	26	≥	≥	NOUN
ejpam-6529	376	27	gb(y	gb(y	ADV
ejpam-6529	376	28	)	)	PUNCT
ejpam-6529	376	29	≥	≥	NOUN
ejpam-6529	376	30	min{gb(ðx(y	min{gb(ðx(y	PROPN
ejpam-6529	376	31	)	)	PUNCT
ejpam-6529	376	32	)	)	PUNCT
ejpam-6529	376	33	,	,	PUNCT
ejpam-6529	376	34	0.5	0.5	NUM
ejpam-6529	376	35	}	}	PUNCT
ejpam-6529	376	36	.	.	PUNCT
ejpam-6529	377	1	hence	hence	ADV
ejpam-6529	377	2	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	377	3	)	)	PUNCT
ejpam-6529	377	4	)	)	PUNCT
ejpam-6529	377	5	≥	≥	PROPN
ejpam-6529	377	6	s	s	NOUN
ejpam-6529	377	7	and	and	CCONJ
ejpam-6529	377	8	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	377	9	)	)	PUNCT
ejpam-6529	377	10	)	)	PUNCT
ejpam-6529	377	11	≤	≤	PROPN
ejpam-6529	377	12	t	t	PROPN
ejpam-6529	377	13	,	,	PUNCT
ejpam-6529	377	14	which	which	PRON
ejpam-6529	377	15	imply	imply	VERB
ejpam-6529	377	16	that	that	PRON
ejpam-6529	377	17	ðx(y	ðx(y	X
ejpam-6529	377	18	)	)	PUNCT
ejpam-6529	377	19	∈	∈	PROPN
ejpam-6529	377	20	(	(	PUNCT
ejpam-6529	377	21	fb	fb	INTJ
ejpam-6529	377	22	,	,	PUNCT
ejpam-6529	377	23	s)∈	s)∈	NUM
ejpam-6529	377	24	∩	∩	NOUN
ejpam-6529	377	25	(	(	PUNCT
ejpam-6529	377	26	gb	gb	NOUN
ejpam-6529	377	27	,	,	PUNCT
ejpam-6529	377	28	t)∈	t)∈	PROPN
ejpam-6529	377	29	=	=	SYM
ejpam-6529	377	30	(	(	PUNCT
ejpam-6529	377	31	b∗	b∗	ADJ
ejpam-6529	377	32	,	,	PUNCT
ejpam-6529	377	33	(	(	PUNCT
ejpam-6529	377	34	s	s	X
ejpam-6529	377	35	,	,	PUNCT
ejpam-6529	377	36	t))∈.	t))∈.	PROPN
ejpam-6529	377	37	therefore	therefore	ADV
ejpam-6529	377	38	(	(	PUNCT
ejpam-6529	377	39	b∗	b∗	ADJ
ejpam-6529	377	40	,	,	PUNCT
ejpam-6529	377	41	(	(	PUNCT
ejpam-6529	377	42	s	s	X
ejpam-6529	377	43	,	,	PUNCT
ejpam-6529	377	44	t))∈	t))∈	NOUN
ejpam-6529	377	45	is	be	AUX
ejpam-6529	377	46	a	a	DET
ejpam-6529	377	47	weak	weak	ADJ
ejpam-6529	377	48	filter	filter	NOUN
ejpam-6529	377	49	of	of	ADP
ejpam-6529	377	50	x	x	X
ejpam-6529	377	51	:	:	PUNCT
ejpam-6529	377	52	=	=	SYM
ejpam-6529	377	53	(	(	PUNCT
ejpam-6529	377	54	x	x	NOUN
ejpam-6529	377	55	,	,	PUNCT
ejpam-6529	377	56	|	|	NOUN
ejpam-6529	377	57	)	)	PUNCT
ejpam-6529	377	58	.	.	PUNCT
ejpam-6529	378	1	theorem	theorem	VERB
ejpam-6529	378	2	11	11	NUM
ejpam-6529	378	3	.	.	PUNCT
ejpam-6529	379	1	if	if	SCONJ
ejpam-6529	379	2	b∗	b∗	ADJ
ejpam-6529	379	3	:	:	PUNCT
ejpam-6529	379	4	=	=	SYM
ejpam-6529	379	5	(	(	PUNCT
ejpam-6529	379	6	x	x	X
ejpam-6529	379	7	;	;	PUNCT
ejpam-6529	379	8	fb	fb	INTJ
ejpam-6529	379	9	,	,	PUNCT
ejpam-6529	379	10	gb	gb	PROPN
ejpam-6529	379	11	)	)	PUNCT
ejpam-6529	379	12	is	be	AUX
ejpam-6529	379	13	an	an	DET
ejpam-6529	379	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	379	15	fuzzy	fuzzy	ADJ
ejpam-6529	379	16	weak	weak	ADJ
ejpam-6529	379	17	filter	filter	NOUN
ejpam-6529	379	18	of	of	ADP
ejpam-6529	379	19	x	x	X
ejpam-6529	379	20	:	:	PUNCT
ejpam-6529	379	21	=	=	SYM
ejpam-6529	379	22	(	(	PUNCT
ejpam-6529	379	23	x	x	NOUN
ejpam-6529	379	24	,	,	PUNCT
ejpam-6529	379	25	|	|	NOUN
ejpam-6529	379	26	)	)	PUNCT
ejpam-6529	379	27	,	,	PUNCT
ejpam-6529	379	28	then	then	ADV
ejpam-6529	379	29	its	its	PRON
ejpam-6529	379	30	nonempty	nonempty	ADJ
ejpam-6529	379	31	intuitionistic	intuitionistic	ADJ
ejpam-6529	379	32	q	q	NOUN
ejpam-6529	379	33	-	-	PUNCT
ejpam-6529	379	34	set	set	ADJ
ejpam-6529	379	35	(	(	PUNCT
ejpam-6529	379	36	b∗	b∗	ADJ
ejpam-6529	379	37	,	,	PUNCT
ejpam-6529	379	38	(	(	PUNCT
ejpam-6529	379	39	s	s	X
ejpam-6529	379	40	,	,	PUNCT
ejpam-6529	379	41	t))q	t))q	NOUN
ejpam-6529	379	42	is	be	AUX
ejpam-6529	379	43	a	a	DET
ejpam-6529	379	44	weak	weak	ADJ
ejpam-6529	379	45	filter	filter	NOUN
ejpam-6529	379	46	of	of	ADP
ejpam-6529	379	47	x	x	X
ejpam-6529	379	48	:	:	PUNCT
ejpam-6529	379	49	=	=	SYM
ejpam-6529	379	50	(	(	PUNCT
ejpam-6529	379	51	x	x	NOUN
ejpam-6529	379	52	,	,	PUNCT
ejpam-6529	379	53	|	|	ADV
ejpam-6529	379	54	)	)	PUNCT
ejpam-6529	379	55	for	for	ADP
ejpam-6529	379	56	all	all	DET
ejpam-6529	379	57	(	(	PUNCT
ejpam-6529	379	58	s	s	PROPN
ejpam-6529	379	59	,	,	PUNCT
ejpam-6529	379	60	t	t	PROPN
ejpam-6529	379	61	)	)	PUNCT
ejpam-6529	379	62	∈	∈	PROPN
ejpam-6529	379	63	(	(	PUNCT
ejpam-6529	379	64	0	0	NUM
ejpam-6529	379	65	,	,	PUNCT
ejpam-6529	379	66	1]×	1]×	NUM
ejpam-6529	379	67	[	[	X
ejpam-6529	379	68	0	0	NUM
ejpam-6529	379	69	,	,	PUNCT
ejpam-6529	379	70	1	1	NUM
ejpam-6529	379	71	)	)	PUNCT
ejpam-6529	379	72	.	.	PUNCT
ejpam-6529	380	1	proof	proof	NOUN
ejpam-6529	380	2	.	.	PUNCT
ejpam-6529	381	1	let	let	VERB
ejpam-6529	381	2	(	(	PUNCT
ejpam-6529	381	3	s	s	X
ejpam-6529	381	4	,	,	PUNCT
ejpam-6529	381	5	t	t	PROPN
ejpam-6529	381	6	)	)	PUNCT
ejpam-6529	381	7	∈	∈	PROPN
ejpam-6529	381	8	(	(	PUNCT
ejpam-6529	381	9	0	0	NUM
ejpam-6529	381	10	,	,	PUNCT
ejpam-6529	381	11	1	1	NUM
ejpam-6529	381	12	]	]	SYM
ejpam-6529	381	13	×	×	NOUN
ejpam-6529	382	1	[	[	X
ejpam-6529	382	2	0	0	NUM
ejpam-6529	382	3	,	,	PUNCT
ejpam-6529	382	4	1	1	NUM
ejpam-6529	382	5	)	)	PUNCT
ejpam-6529	382	6	be	be	AUX
ejpam-6529	382	7	such	such	ADJ
ejpam-6529	382	8	that	that	SCONJ
ejpam-6529	382	9	(	(	PUNCT
ejpam-6529	382	10	b∗	b∗	ADJ
ejpam-6529	382	11	,	,	PUNCT
ejpam-6529	382	12	(	(	PUNCT
ejpam-6529	382	13	s	s	X
ejpam-6529	382	14	,	,	PUNCT
ejpam-6529	382	15	t))q	t))q	NOUN
ejpam-6529	382	16	̸=	̸=	PROPN
ejpam-6529	382	17	∅.	∅.	NOUN
ejpam-6529	382	18	since	since	SCONJ
ejpam-6529	382	19	fb(1	fb(1	PROPN
ejpam-6529	382	20	)	)	PUNCT
ejpam-6529	382	21	≥	≥	NOUN
ejpam-6529	382	22	fb(x	fb(x	PUNCT
ejpam-6529	382	23	)	)	PUNCT
ejpam-6529	382	24	and	and	CCONJ
ejpam-6529	382	25	gb(1	gb(1	PROPN
ejpam-6529	382	26	)	)	PUNCT
ejpam-6529	382	27	≤	≤	NOUN
ejpam-6529	382	28	gb(x	gb(x	PUNCT
ejpam-6529	382	29	)	)	PUNCT
ejpam-6529	382	30	for	for	SCONJ
ejpam-6529	382	31	x	x	PROPN
ejpam-6529	382	32	∈	∈	PROPN
ejpam-6529	382	33	(	(	PUNCT
ejpam-6529	382	34	b∗	b∗	ADJ
ejpam-6529	382	35	,	,	PUNCT
ejpam-6529	382	36	(	(	PUNCT
ejpam-6529	382	37	s	s	X
ejpam-6529	382	38	,	,	PUNCT
ejpam-6529	382	39	t))q	t))q	NOUN
ejpam-6529	382	40	,	,	PUNCT
ejpam-6529	382	41	we	we	PRON
ejpam-6529	382	42	have	have	VERB
ejpam-6529	382	43	fb(1	fb(1	PROPN
ejpam-6529	382	44	)	)	PUNCT
ejpam-6529	382	45	≥	≥	NOUN
ejpam-6529	382	46	fb(x	fb(x	PUNCT
ejpam-6529	382	47	)	)	PUNCT
ejpam-6529	382	48	>	>	X
ejpam-6529	383	1	1	1	NUM
ejpam-6529	383	2	−	−	PROPN
ejpam-6529	383	3	s	s	PART
ejpam-6529	383	4	and	and	CCONJ
ejpam-6529	383	5	gb(1	gb(1	PROPN
ejpam-6529	383	6	)	)	PUNCT
ejpam-6529	383	7	≤	≤	NOUN
ejpam-6529	383	8	gb(x	gb(x	PUNCT
ejpam-6529	383	9	)	)	PUNCT
ejpam-6529	383	10	<	<	X
ejpam-6529	383	11	1	1	NUM
ejpam-6529	383	12	−	−	NOUN
ejpam-6529	383	13	t.	t.	NOUN
ejpam-6529	383	14	hence	hence	ADV
ejpam-6529	383	15	1	1	NUM
ejpam-6529	383	16	∈	∈	PROPN
ejpam-6529	383	17	(	(	PUNCT
ejpam-6529	383	18	fb	fb	INTJ
ejpam-6529	383	19	,	,	PUNCT
ejpam-6529	383	20	s)q	s)q	PUNCT
ejpam-6529	383	21	∩	∩	NOUN
ejpam-6529	383	22	(	(	PUNCT
ejpam-6529	383	23	gb	gb	NOUN
ejpam-6529	383	24	,	,	PUNCT
ejpam-6529	383	25	t)q	t)q	PUNCT
ejpam-6529	383	26	=	=	SYM
ejpam-6529	383	27	(	(	PUNCT
ejpam-6529	383	28	b∗	b∗	ADJ
ejpam-6529	383	29	,	,	PUNCT
ejpam-6529	383	30	(	(	PUNCT
ejpam-6529	383	31	s	s	X
ejpam-6529	383	32	,	,	PUNCT
ejpam-6529	383	33	t))q	t))q	NOUN
ejpam-6529	383	34	.	.	PUNCT
ejpam-6529	384	1	if	if	SCONJ
ejpam-6529	384	2	y	y	PROPN
ejpam-6529	384	3	∈	∈	PROPN
ejpam-6529	384	4	(	(	PUNCT
ejpam-6529	384	5	b∗	b∗	ADJ
ejpam-6529	384	6	,	,	PUNCT
ejpam-6529	384	7	(	(	PUNCT
ejpam-6529	384	8	s	s	X
ejpam-6529	384	9	,	,	PUNCT
ejpam-6529	384	10	t))q	t))q	NOUN
ejpam-6529	384	11	,	,	PUNCT
ejpam-6529	384	12	then	then	ADV
ejpam-6529	384	13	fb(ðx(y	fb(ðx(y	PROPN
ejpam-6529	384	14	)	)	PUNCT
ejpam-6529	384	15	)	)	PUNCT
ejpam-6529	384	16	≥	≥	NOUN
ejpam-6529	384	17	fb(y	fb(y	NUM
ejpam-6529	384	18	)	)	PUNCT
ejpam-6529	384	19	>	>	X
ejpam-6529	385	1	1	1	NUM
ejpam-6529	385	2	−	−	PROPN
ejpam-6529	385	3	s	s	NOUN
ejpam-6529	385	4	and	and	CCONJ
ejpam-6529	385	5	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	385	6	)	)	PUNCT
ejpam-6529	385	7	)	)	PUNCT
ejpam-6529	385	8	≤	≤	NOUN
ejpam-6529	385	9	gb(y	gb(y	ADV
ejpam-6529	385	10	)	)	PUNCT
ejpam-6529	385	11	<	<	X
ejpam-6529	385	12	1	1	NUM
ejpam-6529	385	13	−	−	PROPN
ejpam-6529	385	14	t	t	NOUN
ejpam-6529	385	15	for	for	ADP
ejpam-6529	385	16	all	all	DET
ejpam-6529	385	17	x	x	SYM
ejpam-6529	385	18	∈	∈	PROPN
ejpam-6529	385	19	x	x	PUNCT
ejpam-6529	385	20	by	by	ADP
ejpam-6529	385	21	(	(	PUNCT
ejpam-6529	385	22	23	23	NUM
ejpam-6529	385	23	)	)	PUNCT
ejpam-6529	385	24	.	.	PUNCT
ejpam-6529	386	1	thus	thus	ADV
ejpam-6529	386	2	ðx(y	ðx(y	X
ejpam-6529	386	3	)	)	PUNCT
ejpam-6529	386	4	∈	∈	PROPN
ejpam-6529	386	5	(	(	PUNCT
ejpam-6529	386	6	fb	fb	INTJ
ejpam-6529	386	7	,	,	PUNCT
ejpam-6529	386	8	s)q	s)q	PUNCT
ejpam-6529	386	9	∩	∩	NOUN
ejpam-6529	386	10	(	(	PUNCT
ejpam-6529	386	11	gb	gb	NOUN
ejpam-6529	386	12	,	,	PUNCT
ejpam-6529	386	13	t)q	t)q	PUNCT
ejpam-6529	386	14	=	=	SYM
ejpam-6529	386	15	(	(	PUNCT
ejpam-6529	386	16	b∗	b∗	ADJ
ejpam-6529	386	17	,	,	PUNCT
ejpam-6529	386	18	(	(	PUNCT
ejpam-6529	386	19	s	s	X
ejpam-6529	386	20	,	,	PUNCT
ejpam-6529	386	21	t))q	t))q	NOUN
ejpam-6529	386	22	.	.	PUNCT
ejpam-6529	387	1	therefore	therefore	ADV
ejpam-6529	387	2	(	(	PUNCT
ejpam-6529	387	3	b∗	b∗	ADJ
ejpam-6529	387	4	,	,	PUNCT
ejpam-6529	387	5	(	(	PUNCT
ejpam-6529	387	6	s	s	X
ejpam-6529	387	7	,	,	PUNCT
ejpam-6529	387	8	t))q	t))q	NOUN
ejpam-6529	387	9	is	be	AUX
ejpam-6529	387	10	a	a	DET
ejpam-6529	387	11	weak	weak	ADJ
ejpam-6529	387	12	filter	filter	NOUN
ejpam-6529	387	13	of	of	ADP
ejpam-6529	387	14	x	x	X
ejpam-6529	387	15	:	:	PUNCT
ejpam-6529	387	16	=	=	SYM
ejpam-6529	387	17	(	(	PUNCT
ejpam-6529	387	18	x	x	NOUN
ejpam-6529	387	19	,	,	PUNCT
ejpam-6529	387	20	|	|	NOUN
ejpam-6529	387	21	)	)	PUNCT
ejpam-6529	387	22	.	.	PUNCT
ejpam-6529	388	1	proposition	proposition	NOUN
ejpam-6529	388	2	3	3	X
ejpam-6529	388	3	.	.	PUNCT
ejpam-6529	389	1	let	let	VERB
ejpam-6529	389	2	b∗	b∗	ADV
ejpam-6529	389	3	:	:	PUNCT
ejpam-6529	389	4	=	=	SYM
ejpam-6529	389	5	(	(	PUNCT
ejpam-6529	389	6	x	x	X
ejpam-6529	389	7	;	;	PUNCT
ejpam-6529	389	8	fb	fb	INTJ
ejpam-6529	389	9	,	,	PUNCT
ejpam-6529	389	10	gb	gb	PROPN
ejpam-6529	389	11	)	)	PUNCT
ejpam-6529	389	12	be	be	VERB
ejpam-6529	389	13	an	an	DET
ejpam-6529	389	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	389	15	fuzzy	fuzzy	ADJ
ejpam-6529	389	16	set	set	NOUN
ejpam-6529	389	17	in	in	ADP
ejpam-6529	389	18	x.	x.	NOUN
ejpam-6529	389	19	if	if	SCONJ
ejpam-6529	389	20	its	its	PRON
ejpam-6529	389	21	intuitionistic	intuitionistic	ADJ
ejpam-6529	389	22	q	q	NOUN
ejpam-6529	389	23	-	-	PUNCT
ejpam-6529	389	24	set	set	ADJ
ejpam-6529	389	25	(	(	PUNCT
ejpam-6529	389	26	b∗	b∗	ADJ
ejpam-6529	389	27	,	,	PUNCT
ejpam-6529	389	28	(	(	PUNCT
ejpam-6529	389	29	s	s	X
ejpam-6529	389	30	,	,	PUNCT
ejpam-6529	389	31	t))q	t))q	NOUN
ejpam-6529	389	32	is	be	AUX
ejpam-6529	389	33	a	a	DET
ejpam-6529	389	34	weak	weak	ADJ
ejpam-6529	389	35	filter	filter	NOUN
ejpam-6529	389	36	of	of	ADP
ejpam-6529	389	37	x	x	X
ejpam-6529	389	38	:	:	PUNCT
ejpam-6529	389	39	=	=	SYM
ejpam-6529	389	40	(	(	PUNCT
ejpam-6529	389	41	x	x	NOUN
ejpam-6529	389	42	,	,	PUNCT
ejpam-6529	389	43	|	|	ADV
ejpam-6529	389	44	)	)	PUNCT
ejpam-6529	389	45	for	for	ADP
ejpam-6529	389	46	all	all	DET
ejpam-6529	389	47	(	(	PUNCT
ejpam-6529	389	48	s	s	PROPN
ejpam-6529	389	49	,	,	PUNCT
ejpam-6529	389	50	t	t	PROPN
ejpam-6529	389	51	)	)	PUNCT
ejpam-6529	389	52	∈	∈	PROPN
ejpam-6529	389	53	(	(	PUNCT
ejpam-6529	389	54	0	0	NUM
ejpam-6529	389	55	,	,	PUNCT
ejpam-6529	389	56	0.5	0.5	NUM
ejpam-6529	389	57	]	]	SYM
ejpam-6529	389	58	×	×	NOUN
ejpam-6529	390	1	[	[	X
ejpam-6529	390	2	0.5	0.5	NUM
ejpam-6529	390	3	,	,	PUNCT
ejpam-6529	390	4	1	1	NUM
ejpam-6529	390	5	)	)	PUNCT
ejpam-6529	390	6	,	,	PUNCT
ejpam-6529	390	7	then	then	ADV
ejpam-6529	390	8	1	1	NUM
ejpam-6529	390	9	∈	∈	NOUN
ejpam-6529	390	10	(	(	PUNCT
ejpam-6529	390	11	b∗	b∗	ADJ
ejpam-6529	390	12	,	,	PUNCT
ejpam-6529	390	13	(	(	PUNCT
ejpam-6529	390	14	s	s	X
ejpam-6529	390	15	,	,	PUNCT
ejpam-6529	390	16	t))∈	t))∈	NOUN
ejpam-6529	390	17	and	and	CCONJ
ejpam-6529	390	18	y	y	PROPN
ejpam-6529	390	19	∈	∈	PROPN
ejpam-6529	390	20	(	(	PUNCT
ejpam-6529	390	21	b∗	b∗	ADJ
ejpam-6529	390	22	,	,	PUNCT
ejpam-6529	390	23	(	(	PUNCT
ejpam-6529	390	24	s	s	X
ejpam-6529	390	25	,	,	PUNCT
ejpam-6529	390	26	t))q	t))q	ADJ
ejpam-6529	390	27	⇒	⇒	NOUN
ejpam-6529	390	28	ðx(y	ðx(y	PUNCT
ejpam-6529	390	29	)	)	PUNCT
ejpam-6529	390	30	∈	∈	PROPN
ejpam-6529	390	31	(	(	PUNCT
ejpam-6529	390	32	b∗	b∗	ADJ
ejpam-6529	390	33	,	,	PUNCT
ejpam-6529	390	34	(	(	PUNCT
ejpam-6529	390	35	s	s	X
ejpam-6529	390	36	,	,	PUNCT
ejpam-6529	390	37	t))∈	t))∈	NOUN
ejpam-6529	390	38	for	for	ADP
ejpam-6529	390	39	all	all	DET
ejpam-6529	390	40	x	x	NOUN
ejpam-6529	390	41	,	,	PUNCT
ejpam-6529	390	42	y	y	PROPN
ejpam-6529	390	43	∈	∈	PROPN
ejpam-6529	390	44	x	x	X
ejpam-6529	390	45	and	and	CCONJ
ejpam-6529	390	46	(	(	PUNCT
ejpam-6529	390	47	s	s	PROPN
ejpam-6529	390	48	,	,	PUNCT
ejpam-6529	390	49	t	t	PROPN
ejpam-6529	390	50	)	)	PUNCT
ejpam-6529	390	51	∈	∈	PROPN
ejpam-6529	390	52	(	(	PUNCT
ejpam-6529	390	53	0	0	NUM
ejpam-6529	390	54	,	,	PUNCT
ejpam-6529	390	55	0.5]×	0.5]×	NOUN
ejpam-6529	390	56	[	[	X
ejpam-6529	390	57	0.5	0.5	NUM
ejpam-6529	390	58	,	,	PUNCT
ejpam-6529	390	59	1	1	NUM
ejpam-6529	390	60	)	)	PUNCT
ejpam-6529	390	61	.	.	PUNCT
ejpam-6529	391	1	proof	proof	NOUN
ejpam-6529	391	2	.	.	PUNCT
ejpam-6529	392	1	let	let	VERB
ejpam-6529	392	2	x	x	PRON
ejpam-6529	392	3	,	,	PUNCT
ejpam-6529	392	4	y	y	PROPN
ejpam-6529	392	5	∈	∈	PROPN
ejpam-6529	392	6	x	x	X
ejpam-6529	392	7	and	and	CCONJ
ejpam-6529	392	8	(	(	PUNCT
ejpam-6529	392	9	s	s	PROPN
ejpam-6529	392	10	,	,	PUNCT
ejpam-6529	392	11	t	t	PROPN
ejpam-6529	392	12	)	)	PUNCT
ejpam-6529	392	13	∈	∈	PROPN
ejpam-6529	392	14	(	(	PUNCT
ejpam-6529	392	15	0	0	NUM
ejpam-6529	392	16	,	,	PUNCT
ejpam-6529	392	17	0.5	0.5	NUM
ejpam-6529	392	18	]	]	SYM
ejpam-6529	392	19	×	×	NOUN
ejpam-6529	392	20	[	[	X
ejpam-6529	392	21	0.5	0.5	NUM
ejpam-6529	392	22	,	,	PUNCT
ejpam-6529	392	23	1	1	NUM
ejpam-6529	392	24	)	)	PUNCT
ejpam-6529	392	25	.	.	PUNCT
ejpam-6529	393	1	assume	assume	VERB
ejpam-6529	393	2	that	that	SCONJ
ejpam-6529	393	3	(	(	PUNCT
ejpam-6529	393	4	b∗	b∗	ADJ
ejpam-6529	393	5	,	,	PUNCT
ejpam-6529	393	6	(	(	PUNCT
ejpam-6529	393	7	s	s	X
ejpam-6529	393	8	,	,	PUNCT
ejpam-6529	393	9	t))q	t))q	NOUN
ejpam-6529	393	10	is	be	AUX
ejpam-6529	393	11	a	a	DET
ejpam-6529	393	12	weak	weak	ADJ
ejpam-6529	393	13	filter	filter	NOUN
ejpam-6529	393	14	of	of	ADP
ejpam-6529	393	15	x	x	X
ejpam-6529	393	16	:	:	PUNCT
ejpam-6529	393	17	=	=	SYM
ejpam-6529	393	18	(	(	PUNCT
ejpam-6529	393	19	x	x	NOUN
ejpam-6529	393	20	,	,	PUNCT
ejpam-6529	393	21	|	|	NOUN
ejpam-6529	393	22	)	)	PUNCT
ejpam-6529	393	23	.	.	PUNCT
ejpam-6529	394	1	then	then	ADV
ejpam-6529	394	2	1	1	NUM
ejpam-6529	394	3	∈	∈	NOUN
ejpam-6529	394	4	(	(	PUNCT
ejpam-6529	394	5	b∗	b∗	ADJ
ejpam-6529	394	6	,	,	PUNCT
ejpam-6529	394	7	(	(	PUNCT
ejpam-6529	394	8	s	s	X
ejpam-6529	394	9	,	,	PUNCT
ejpam-6529	394	10	t))q	t))q	NOUN
ejpam-6529	394	11	and	and	CCONJ
ejpam-6529	394	12	so	so	ADV
ejpam-6529	394	13	fb(1	fb(1	PROPN
ejpam-6529	394	14	)	)	PUNCT
ejpam-6529	394	15	>	>	X
ejpam-6529	395	1	1−	1−	NUM
ejpam-6529	395	2	s	s	PART
ejpam-6529	395	3	≥	≥	NOUN
ejpam-6529	395	4	s	s	NOUN
ejpam-6529	395	5	and	and	CCONJ
ejpam-6529	395	6	gb(1	gb(1	PROPN
ejpam-6529	395	7	)	)	PUNCT
ejpam-6529	395	8	<	<	X
ejpam-6529	395	9	1−	1−	NUM
ejpam-6529	395	10	t	t	NOUN
ejpam-6529	395	11	≤	≤	NOUN
ejpam-6529	395	12	t.	t.	NOUN
ejpam-6529	395	13	hence	hence	ADV
ejpam-6529	395	14	1	1	NUM
ejpam-6529	395	15	∈	∈	NOUN
ejpam-6529	395	16	(	(	PUNCT
ejpam-6529	395	17	fb	fb	INTJ
ejpam-6529	395	18	,	,	PUNCT
ejpam-6529	395	19	s)∈	s)∈	NUM
ejpam-6529	395	20	∩	∩	NOUN
ejpam-6529	395	21	(	(	PUNCT
ejpam-6529	395	22	gb	gb	NOUN
ejpam-6529	395	23	,	,	PUNCT
ejpam-6529	395	24	t)∈	t)∈	PROPN
ejpam-6529	395	25	=	=	SYM
ejpam-6529	395	26	(	(	PUNCT
ejpam-6529	395	27	b∗	b∗	ADJ
ejpam-6529	395	28	,	,	PUNCT
ejpam-6529	395	29	(	(	PUNCT
ejpam-6529	395	30	s	s	X
ejpam-6529	395	31	,	,	PUNCT
ejpam-6529	395	32	t))∈.	t))∈.	NOUN
ejpam-6529	395	33	if	if	SCONJ
ejpam-6529	395	34	y	y	PROPN
ejpam-6529	395	35	∈	∈	PROPN
ejpam-6529	395	36	(	(	PUNCT
ejpam-6529	395	37	b∗	b∗	ADJ
ejpam-6529	395	38	,	,	PUNCT
ejpam-6529	395	39	(	(	PUNCT
ejpam-6529	395	40	s	s	X
ejpam-6529	395	41	,	,	PUNCT
ejpam-6529	395	42	t))q	t))q	NOUN
ejpam-6529	395	43	,	,	PUNCT
ejpam-6529	395	44	then	then	ADV
ejpam-6529	395	45	ðx(y	ðx(y	X
ejpam-6529	395	46	)	)	PUNCT
ejpam-6529	395	47	∈	∈	PROPN
ejpam-6529	395	48	(	(	PUNCT
ejpam-6529	395	49	b∗	b∗	ADJ
ejpam-6529	395	50	,	,	PUNCT
ejpam-6529	395	51	(	(	PUNCT
ejpam-6529	395	52	s	s	X
ejpam-6529	395	53	,	,	PUNCT
ejpam-6529	395	54	t))q	t))q	NOUN
ejpam-6529	395	55	.	.	PUNCT
ejpam-6529	396	1	it	it	PRON
ejpam-6529	396	2	follows	follow	VERB
ejpam-6529	396	3	that	that	PRON
ejpam-6529	396	4	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	396	5	)	)	PUNCT
ejpam-6529	396	6	)	)	PUNCT
ejpam-6529	397	1	>	>	X
ejpam-6529	398	1	1−	1−	NUM
ejpam-6529	398	2	s	s	PART
ejpam-6529	398	3	≥	≥	NOUN
ejpam-6529	398	4	s	s	NOUN
ejpam-6529	398	5	and	and	CCONJ
ejpam-6529	398	6	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	398	7	)	)	PUNCT
ejpam-6529	398	8	)	)	PUNCT
ejpam-6529	399	1	<	<	X
ejpam-6529	399	2	1−	1−	NUM
ejpam-6529	399	3	t	t	NOUN
ejpam-6529	399	4	≤	≤	NOUN
ejpam-6529	399	5	t.	t.	NOUN
ejpam-6529	399	6	thus	thus	ADV
ejpam-6529	399	7	ðx(y	ðx(y	PUNCT
ejpam-6529	399	8	)	)	PUNCT
ejpam-6529	400	1	∈	∈	PROPN
ejpam-6529	400	2	(	(	PUNCT
ejpam-6529	400	3	fb	fb	INTJ
ejpam-6529	400	4	,	,	PUNCT
ejpam-6529	400	5	s)∈	s)∈	NUM
ejpam-6529	400	6	∩	∩	NOUN
ejpam-6529	400	7	(	(	PUNCT
ejpam-6529	400	8	gb	gb	NOUN
ejpam-6529	400	9	,	,	PUNCT
ejpam-6529	400	10	t)∈	t)∈	PROPN
ejpam-6529	400	11	=	=	SYM
ejpam-6529	400	12	(	(	PUNCT
ejpam-6529	400	13	b∗	b∗	ADJ
ejpam-6529	400	14	,	,	PUNCT
ejpam-6529	400	15	(	(	PUNCT
ejpam-6529	400	16	s	s	X
ejpam-6529	400	17	,	,	PUNCT
ejpam-6529	400	18	t))∈.	t))∈.	NOUN
ejpam-6529	400	19	proposition	proposition	NOUN
ejpam-6529	400	20	4	4	NUM
ejpam-6529	400	21	.	.	PUNCT
ejpam-6529	400	22	given	give	VERB
ejpam-6529	400	23	an	an	DET
ejpam-6529	400	24	intuitionistic	intuitionistic	ADJ
ejpam-6529	400	25	fuzzy	fuzzy	ADJ
ejpam-6529	400	26	set	set	VERB
ejpam-6529	400	27	b∗	b∗	ADJ
ejpam-6529	400	28	:	:	PUNCT
ejpam-6529	400	29	=	=	SYM
ejpam-6529	400	30	(	(	PUNCT
ejpam-6529	400	31	x	x	X
ejpam-6529	400	32	;	;	PUNCT
ejpam-6529	400	33	fb	fb	INTJ
ejpam-6529	400	34	,	,	PUNCT
ejpam-6529	400	35	gb	gb	NOUN
ejpam-6529	400	36	)	)	PUNCT
ejpam-6529	400	37	in	in	ADP
ejpam-6529	400	38	x	x	SYM
ejpam-6529	400	39	,	,	PUNCT
ejpam-6529	400	40	if	if	SCONJ
ejpam-6529	400	41	its	its	PRON
ejpam-6529	400	42	intuitionistic	intuitionistic	ADJ
ejpam-6529	400	43	q	q	NOUN
ejpam-6529	400	44	-	-	PUNCT
ejpam-6529	400	45	set	set	ADJ
ejpam-6529	400	46	(	(	PUNCT
ejpam-6529	400	47	b∗	b∗	ADJ
ejpam-6529	400	48	,	,	PUNCT
ejpam-6529	400	49	(	(	PUNCT
ejpam-6529	400	50	s	s	X
ejpam-6529	400	51	,	,	PUNCT
ejpam-6529	400	52	t))q	t))q	NOUN
ejpam-6529	400	53	is	be	AUX
ejpam-6529	400	54	a	a	DET
ejpam-6529	400	55	weak	weak	ADJ
ejpam-6529	400	56	filter	filter	NOUN
ejpam-6529	400	57	of	of	ADP
ejpam-6529	400	58	x	x	X
ejpam-6529	400	59	:	:	PUNCT
ejpam-6529	400	60	=	=	SYM
ejpam-6529	400	61	(	(	PUNCT
ejpam-6529	400	62	x	x	NOUN
ejpam-6529	400	63	,	,	PUNCT
ejpam-6529	400	64	|	|	ADV
ejpam-6529	400	65	)	)	PUNCT
ejpam-6529	400	66	for	for	ADP
ejpam-6529	400	67	all	all	DET
ejpam-6529	400	68	(	(	PUNCT
ejpam-6529	400	69	s	s	PROPN
ejpam-6529	400	70	,	,	PUNCT
ejpam-6529	400	71	t	t	PROPN
ejpam-6529	400	72	)	)	PUNCT
ejpam-6529	400	73	∈	∈	PROPN
ejpam-6529	400	74	(	(	PUNCT
ejpam-6529	400	75	0.5	0.5	NUM
ejpam-6529	400	76	,	,	PUNCT
ejpam-6529	400	77	1	1	NUM
ejpam-6529	400	78	]	]	SYM
ejpam-6529	400	79	×	×	NOUN
ejpam-6529	401	1	[	[	X
ejpam-6529	401	2	0	0	NUM
ejpam-6529	401	3	,	,	PUNCT
ejpam-6529	401	4	0.5	0.5	NUM
ejpam-6529	401	5	)	)	PUNCT
ejpam-6529	401	6	,	,	PUNCT
ejpam-6529	401	7	then	then	ADV
ejpam-6529	401	8	the	the	DET
ejpam-6529	401	9	following	follow	VERB
ejpam-6529	401	10	is	be	AUX
ejpam-6529	401	11	valid	valid	ADJ
ejpam-6529	401	12	.	.	PUNCT
ejpam-6529	402	1	y	y	PROPN
ejpam-6529	402	2	∈	∈	PROPN
ejpam-6529	402	3	(	(	PUNCT
ejpam-6529	402	4	b∗	b∗	ADJ
ejpam-6529	402	5	,	,	PUNCT
ejpam-6529	402	6	(	(	PUNCT
ejpam-6529	402	7	s	s	X
ejpam-6529	402	8	,	,	PUNCT
ejpam-6529	402	9	t))∈	t))∈	NOUN
ejpam-6529	402	10	⇒	⇒	VERB
ejpam-6529	402	11	ðx(y	ðx(y	PUNCT
ejpam-6529	402	12	)	)	PUNCT
ejpam-6529	403	1	∈	∈	PROPN
ejpam-6529	403	2	(	(	PUNCT
ejpam-6529	403	3	b∗	b∗	ADJ
ejpam-6529	403	4	,	,	PUNCT
ejpam-6529	403	5	(	(	PUNCT
ejpam-6529	403	6	s	s	X
ejpam-6529	403	7	,	,	PUNCT
ejpam-6529	403	8	t))q	t))q	NOUN
ejpam-6529	403	9	for	for	ADP
ejpam-6529	403	10	all	all	DET
ejpam-6529	403	11	x	x	NOUN
ejpam-6529	403	12	,	,	PUNCT
ejpam-6529	403	13	y	y	PROPN
ejpam-6529	403	14	∈	∈	PROPN
ejpam-6529	403	15	x	x	X
ejpam-6529	403	16	and	and	CCONJ
ejpam-6529	403	17	(	(	PUNCT
ejpam-6529	403	18	s	s	PROPN
ejpam-6529	403	19	,	,	PUNCT
ejpam-6529	403	20	t	t	PROPN
ejpam-6529	403	21	)	)	PUNCT
ejpam-6529	403	22	∈	∈	PROPN
ejpam-6529	403	23	(	(	PUNCT
ejpam-6529	403	24	0.5	0.5	NUM
ejpam-6529	403	25	,	,	PUNCT
ejpam-6529	403	26	1]×	1]×	NUM
ejpam-6529	404	1	[	[	X
ejpam-6529	404	2	0	0	NUM
ejpam-6529	404	3	,	,	PUNCT
ejpam-6529	404	4	0.5	0.5	NUM
ejpam-6529	404	5	)	)	PUNCT
ejpam-6529	404	6	.	.	PUNCT
ejpam-6529	405	1	proof	proof	NOUN
ejpam-6529	405	2	.	.	PUNCT
ejpam-6529	406	1	let	let	VERB
ejpam-6529	406	2	x	x	PRON
ejpam-6529	406	3	,	,	PUNCT
ejpam-6529	406	4	y	y	PROPN
ejpam-6529	406	5	∈	∈	PROPN
ejpam-6529	406	6	x	x	X
ejpam-6529	406	7	and	and	CCONJ
ejpam-6529	406	8	(	(	PUNCT
ejpam-6529	406	9	s	s	PROPN
ejpam-6529	406	10	,	,	PUNCT
ejpam-6529	406	11	t	t	PROPN
ejpam-6529	406	12	)	)	PUNCT
ejpam-6529	406	13	∈	∈	PROPN
ejpam-6529	406	14	(	(	PUNCT
ejpam-6529	406	15	0.5	0.5	NUM
ejpam-6529	406	16	,	,	PUNCT
ejpam-6529	406	17	1	1	NUM
ejpam-6529	406	18	]	]	SYM
ejpam-6529	406	19	×	×	NOUN
ejpam-6529	407	1	[	[	X
ejpam-6529	407	2	0	0	NUM
ejpam-6529	407	3	,	,	PUNCT
ejpam-6529	407	4	0.5	0.5	NUM
ejpam-6529	407	5	)	)	PUNCT
ejpam-6529	407	6	.	.	PUNCT
ejpam-6529	408	1	if	if	SCONJ
ejpam-6529	408	2	y	y	PROPN
ejpam-6529	408	3	∈	∈	PROPN
ejpam-6529	408	4	(	(	PUNCT
ejpam-6529	408	5	b∗	b∗	ADJ
ejpam-6529	408	6	,	,	PUNCT
ejpam-6529	408	7	(	(	PUNCT
ejpam-6529	408	8	s	s	X
ejpam-6529	408	9	,	,	PUNCT
ejpam-6529	408	10	t))∈	t))∈	NOUN
ejpam-6529	408	11	,	,	PUNCT
ejpam-6529	408	12	then	then	ADV
ejpam-6529	408	13	fb(y	fb(y	X
ejpam-6529	408	14	)	)	PUNCT
ejpam-6529	408	15	≥	≥	PRON
ejpam-6529	408	16	s	s	NOUN
ejpam-6529	408	17	>	>	X
ejpam-6529	408	18	1	1	NUM
ejpam-6529	408	19	−	−	PROPN
ejpam-6529	408	20	s	s	PART
ejpam-6529	408	21	and	and	CCONJ
ejpam-6529	408	22	gb(y	gb(y	NUM
ejpam-6529	408	23	)	)	PUNCT
ejpam-6529	408	24	≤	≤	NOUN
ejpam-6529	408	25	t	t	NOUN
ejpam-6529	408	26	<	<	X
ejpam-6529	408	27	1	1	NUM
ejpam-6529	408	28	−	−	NOUN
ejpam-6529	408	29	t.	t.	NOUN
ejpam-6529	408	30	thus	thus	ADV
ejpam-6529	408	31	y	y	PROPN
ejpam-6529	408	32	∈	∈	PROPN
ejpam-6529	408	33	(	(	PUNCT
ejpam-6529	408	34	fb	fb	INTJ
ejpam-6529	408	35	,	,	PUNCT
ejpam-6529	408	36	s)q	s)q	PUNCT
ejpam-6529	408	37	∩	∩	NOUN
ejpam-6529	408	38	(	(	PUNCT
ejpam-6529	408	39	gb	gb	NOUN
ejpam-6529	408	40	,	,	PUNCT
ejpam-6529	408	41	t)q	t)q	PUNCT
ejpam-6529	408	42	=	=	SYM
ejpam-6529	408	43	(	(	PUNCT
ejpam-6529	408	44	b∗	b∗	ADJ
ejpam-6529	408	45	,	,	PUNCT
ejpam-6529	408	46	(	(	PUNCT
ejpam-6529	408	47	s	s	X
ejpam-6529	408	48	,	,	PUNCT
ejpam-6529	408	49	t))q	t))q	NOUN
ejpam-6529	408	50	,	,	PUNCT
ejpam-6529	408	51	and	and	CCONJ
ejpam-6529	408	52	so	so	ADV
ejpam-6529	408	53	ðx(y	ðx(y	X
ejpam-6529	408	54	)	)	PUNCT
ejpam-6529	409	1	∈	∈	PROPN
ejpam-6529	409	2	(	(	PUNCT
ejpam-6529	409	3	b∗	b∗	ADJ
ejpam-6529	409	4	,	,	PUNCT
ejpam-6529	409	5	(	(	PUNCT
ejpam-6529	409	6	s	s	X
ejpam-6529	409	7	,	,	PUNCT
ejpam-6529	409	8	t))q	t))q	NOUN
ejpam-6529	409	9	.	.	PUNCT
ejpam-6529	410	1	s.	s.	PROPN
ejpam-6529	410	2	s.	s.	PROPN
ejpam-6529	410	3	ahn	ahn	PROPN
ejpam-6529	410	4	,	,	PUNCT
ejpam-6529	410	5	y.	y.	PROPN
ejpam-6529	410	6	j.	j.	PROPN
ejpam-6529	410	7	seo	seo	PROPN
ejpam-6529	410	8	,	,	PUNCT
ejpam-6529	410	9	y.	y.	PROPN
ejpam-6529	410	10	b.	b.	PROPN
ejpam-6529	410	11	jun	jun	PROPN
ejpam-6529	410	12	/	/	SYM
ejpam-6529	410	13	eur	eur	PROPN
ejpam-6529	410	14	.	.	PUNCT
ejpam-6529	411	1	j.	j.	PROPN
ejpam-6529	411	2	pure	pure	PROPN
ejpam-6529	411	3	appl	appl	PROPN
ejpam-6529	411	4	.	.	PROPN
ejpam-6529	411	5	math	math	PROPN
ejpam-6529	411	6	,	,	PUNCT
ejpam-6529	411	7	18	18	NUM
ejpam-6529	411	8	(	(	PUNCT
ejpam-6529	411	9	3	3	NUM
ejpam-6529	411	10	)	)	PUNCT
ejpam-6529	411	11	(	(	PUNCT
ejpam-6529	411	12	2025	2025	NUM
ejpam-6529	411	13	)	)	PUNCT
ejpam-6529	411	14	,	,	PUNCT
ejpam-6529	411	15	6529	6529	NUM
ejpam-6529	411	16	14	14	NUM
ejpam-6529	411	17	of	of	ADP
ejpam-6529	411	18	16	16	NUM
ejpam-6529	411	19	theorem	theorem	NOUN
ejpam-6529	411	20	12	12	NUM
ejpam-6529	411	21	.	.	PUNCT
ejpam-6529	412	1	if	if	SCONJ
ejpam-6529	412	2	an	an	DET
ejpam-6529	412	3	intuitionistic	intuitionistic	ADJ
ejpam-6529	412	4	fuzzy	fuzzy	ADJ
ejpam-6529	412	5	set	set	VERB
ejpam-6529	412	6	b∗	b∗	ADJ
ejpam-6529	412	7	:	:	PUNCT
ejpam-6529	412	8	=	=	SYM
ejpam-6529	412	9	(	(	PUNCT
ejpam-6529	412	10	x	x	X
ejpam-6529	412	11	;	;	PUNCT
ejpam-6529	412	12	fb	fb	INTJ
ejpam-6529	412	13	,	,	PUNCT
ejpam-6529	412	14	gb	gb	NOUN
ejpam-6529	412	15	)	)	PUNCT
ejpam-6529	412	16	in	in	ADP
ejpam-6529	412	17	x	x	X
ejpam-6529	412	18	satisfies	satisfie	NOUN
ejpam-6529	412	19	:	:	PUNCT
ejpam-6529	412	20	x(s	x(s	PROPN
ejpam-6529	412	21	,	,	PUNCT
ejpam-6529	412	22	t	t	PROPN
ejpam-6529	412	23	)	)	PUNCT
ejpam-6529	412	24	q	q	NOUN
ejpam-6529	412	25	b∗	b∗	ADJ
ejpam-6529	412	26	⇒	⇒	NOUN
ejpam-6529	412	27	1(s	1(s	NUM
ejpam-6529	412	28	,	,	PUNCT
ejpam-6529	412	29	t	t	PROPN
ejpam-6529	412	30	)	)	PUNCT
ejpam-6529	412	31	∈∨q	∈∨q	NOUN
ejpam-6529	412	32	b∗	b∗	ADJ
ejpam-6529	412	33	,	,	PUNCT
ejpam-6529	412	34	(	(	PUNCT
ejpam-6529	412	35	34	34	NUM
ejpam-6529	412	36	)	)	PUNCT
ejpam-6529	412	37	y(s	y(s	PROPN
ejpam-6529	412	38	,	,	PUNCT
ejpam-6529	412	39	t	t	PROPN
ejpam-6529	412	40	)	)	PUNCT
ejpam-6529	412	41	q	q	NOUN
ejpam-6529	412	42	b∗	b∗	ADJ
ejpam-6529	412	43	⇒	⇒	NOUN
ejpam-6529	412	44	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	412	45	,	,	PUNCT
ejpam-6529	412	46	t	t	PROPN
ejpam-6529	412	47	)	)	PUNCT
ejpam-6529	412	48	∈∨q	∈∨q	NOUN
ejpam-6529	412	49	b∗	b∗	ADJ
ejpam-6529	412	50	,	,	PUNCT
ejpam-6529	412	51	(	(	PUNCT
ejpam-6529	412	52	35	35	NUM
ejpam-6529	412	53	)	)	PUNCT
ejpam-6529	412	54	for	for	ADP
ejpam-6529	412	55	all	all	DET
ejpam-6529	412	56	x	x	NOUN
ejpam-6529	412	57	,	,	PUNCT
ejpam-6529	412	58	y	y	PROPN
ejpam-6529	412	59	∈	∈	PROPN
ejpam-6529	412	60	x	x	X
ejpam-6529	412	61	and	and	CCONJ
ejpam-6529	412	62	(	(	PUNCT
ejpam-6529	412	63	s	s	PROPN
ejpam-6529	412	64	,	,	PUNCT
ejpam-6529	412	65	t	t	PROPN
ejpam-6529	412	66	)	)	PUNCT
ejpam-6529	412	67	∈	∈	PROPN
ejpam-6529	412	68	(	(	PUNCT
ejpam-6529	412	69	0.5	0.5	NUM
ejpam-6529	412	70	,	,	PUNCT
ejpam-6529	412	71	1	1	NUM
ejpam-6529	412	72	]	]	SYM
ejpam-6529	412	73	×	×	NOUN
ejpam-6529	413	1	[	[	X
ejpam-6529	413	2	0	0	NUM
ejpam-6529	413	3	,	,	PUNCT
ejpam-6529	413	4	0.5	0.5	NUM
ejpam-6529	413	5	)	)	PUNCT
ejpam-6529	413	6	,	,	PUNCT
ejpam-6529	413	7	then	then	ADV
ejpam-6529	413	8	its	its	PRON
ejpam-6529	413	9	nonempty	nonempty	ADJ
ejpam-6529	413	10	intuitionistic	intuitionistic	ADJ
ejpam-6529	413	11	q	q	NOUN
ejpam-6529	413	12	-	-	PUNCT
ejpam-6529	413	13	set	set	ADJ
ejpam-6529	413	14	(	(	PUNCT
ejpam-6529	413	15	b∗	b∗	ADJ
ejpam-6529	413	16	,	,	PUNCT
ejpam-6529	413	17	(	(	PUNCT
ejpam-6529	413	18	s	s	X
ejpam-6529	413	19	,	,	PUNCT
ejpam-6529	413	20	t))q	t))q	NOUN
ejpam-6529	413	21	is	be	AUX
ejpam-6529	413	22	a	a	DET
ejpam-6529	413	23	weak	weak	ADJ
ejpam-6529	413	24	filter	filter	NOUN
ejpam-6529	413	25	of	of	ADP
ejpam-6529	413	26	x	x	X
ejpam-6529	413	27	:	:	PUNCT
ejpam-6529	413	28	=	=	SYM
ejpam-6529	413	29	(	(	PUNCT
ejpam-6529	413	30	x	x	NOUN
ejpam-6529	413	31	,	,	PUNCT
ejpam-6529	413	32	|	|	ADV
ejpam-6529	413	33	)	)	PUNCT
ejpam-6529	413	34	for	for	ADP
ejpam-6529	413	35	all	all	DET
ejpam-6529	413	36	(	(	PUNCT
ejpam-6529	413	37	s	s	PROPN
ejpam-6529	413	38	,	,	PUNCT
ejpam-6529	413	39	t	t	PROPN
ejpam-6529	413	40	)	)	PUNCT
ejpam-6529	413	41	∈	∈	PROPN
ejpam-6529	413	42	(	(	PUNCT
ejpam-6529	413	43	0.5	0.5	NUM
ejpam-6529	413	44	,	,	PUNCT
ejpam-6529	413	45	1]×	1]×	NUM
ejpam-6529	413	46	[	[	X
ejpam-6529	413	47	0	0	NUM
ejpam-6529	413	48	,	,	PUNCT
ejpam-6529	413	49	0.5	0.5	NUM
ejpam-6529	413	50	)	)	PUNCT
ejpam-6529	413	51	proof	proof	NOUN
ejpam-6529	413	52	.	.	PUNCT
ejpam-6529	414	1	let	let	VERB
ejpam-6529	414	2	(	(	PUNCT
ejpam-6529	414	3	s	s	X
ejpam-6529	414	4	,	,	PUNCT
ejpam-6529	414	5	t	t	PROPN
ejpam-6529	414	6	)	)	PUNCT
ejpam-6529	414	7	∈	∈	PROPN
ejpam-6529	414	8	(	(	PUNCT
ejpam-6529	414	9	0.5	0.5	NUM
ejpam-6529	414	10	,	,	PUNCT
ejpam-6529	414	11	1]×	1]×	NUM
ejpam-6529	415	1	[	[	X
ejpam-6529	415	2	0	0	NUM
ejpam-6529	415	3	,	,	PUNCT
ejpam-6529	415	4	0.5	0.5	NUM
ejpam-6529	415	5	)	)	PUNCT
ejpam-6529	415	6	be	be	VERB
ejpam-6529	415	7	such	such	ADJ
ejpam-6529	415	8	that	that	SCONJ
ejpam-6529	415	9	(	(	PUNCT
ejpam-6529	415	10	b∗	b∗	ADJ
ejpam-6529	415	11	,	,	PUNCT
ejpam-6529	415	12	(	(	PUNCT
ejpam-6529	415	13	s	s	X
ejpam-6529	415	14	,	,	PUNCT
ejpam-6529	415	15	t))q	t))q	NOUN
ejpam-6529	415	16	̸=	̸=	PROPN
ejpam-6529	415	17	∅	∅	NOUN
ejpam-6529	415	18	,	,	PUNCT
ejpam-6529	415	19	say	say	VERB
ejpam-6529	415	20	x	x	X
ejpam-6529	415	21	∈	∈	PROPN
ejpam-6529	415	22	(	(	PUNCT
ejpam-6529	415	23	b∗	b∗	ADJ
ejpam-6529	415	24	,	,	PUNCT
ejpam-6529	415	25	(	(	PUNCT
ejpam-6529	415	26	s	s	X
ejpam-6529	415	27	,	,	PUNCT
ejpam-6529	415	28	t))q	t))q	NOUN
ejpam-6529	415	29	.	.	PUNCT
ejpam-6529	416	1	then	then	ADV
ejpam-6529	416	2	x(s	x(s	PROPN
ejpam-6529	416	3	,	,	PUNCT
ejpam-6529	416	4	t	t	PROPN
ejpam-6529	416	5	)	)	PUNCT
ejpam-6529	416	6	q	q	PROPN
ejpam-6529	416	7	b∗	b∗	ADJ
ejpam-6529	416	8	,	,	PUNCT
ejpam-6529	416	9	and	and	CCONJ
ejpam-6529	416	10	so	so	ADV
ejpam-6529	416	11	1(s	1(s	NUM
ejpam-6529	416	12	,	,	PUNCT
ejpam-6529	416	13	t	t	PROPN
ejpam-6529	416	14	)	)	PUNCT
ejpam-6529	416	15	∈	∈	PROPN
ejpam-6529	416	16	∨q	∨q	NOUN
ejpam-6529	416	17	b∗	b∗	ADV
ejpam-6529	416	18	by	by	ADP
ejpam-6529	416	19	(	(	PUNCT
ejpam-6529	416	20	34	34	NUM
ejpam-6529	416	21	)	)	PUNCT
ejpam-6529	416	22	,	,	PUNCT
ejpam-6529	416	23	i.e.	i.e.	X
ejpam-6529	416	24	,	,	PUNCT
ejpam-6529	416	25	1(s	1(s	NUM
ejpam-6529	416	26	,	,	PUNCT
ejpam-6529	416	27	t	t	PROPN
ejpam-6529	416	28	)	)	PUNCT
ejpam-6529	416	29	∈	∈	PROPN
ejpam-6529	416	30	b∗	b∗	ADJ
ejpam-6529	416	31	or	or	CCONJ
ejpam-6529	416	32	1(s	1(s	NUM
ejpam-6529	416	33	,	,	PUNCT
ejpam-6529	416	34	t	t	PROPN
ejpam-6529	416	35	)	)	PUNCT
ejpam-6529	416	36	q	q	NOUN
ejpam-6529	416	37	b∗.	b∗.	NOUN
ejpam-6529	416	38	if	if	SCONJ
ejpam-6529	416	39	1(s	1(s	NUM
ejpam-6529	416	40	,	,	PUNCT
ejpam-6529	416	41	t	t	PROPN
ejpam-6529	416	42	)	)	PUNCT
ejpam-6529	417	1	q	q	PUNCT
ejpam-6529	418	1	b∗	b∗	ADJ
ejpam-6529	418	2	,	,	PUNCT
ejpam-6529	418	3	then	then	ADV
ejpam-6529	418	4	1	1	NUM
ejpam-6529	418	5	∈	∈	NOUN
ejpam-6529	418	6	(	(	PUNCT
ejpam-6529	418	7	b∗	b∗	ADJ
ejpam-6529	418	8	,	,	PUNCT
ejpam-6529	418	9	(	(	PUNCT
ejpam-6529	418	10	s	s	X
ejpam-6529	418	11	,	,	PUNCT
ejpam-6529	418	12	t))q	t))q	NOUN
ejpam-6529	418	13	.	.	PUNCT
ejpam-6529	419	1	if	if	SCONJ
ejpam-6529	419	2	1(s	1(s	NUM
ejpam-6529	419	3	,	,	PUNCT
ejpam-6529	419	4	t	t	PROPN
ejpam-6529	419	5	)	)	PUNCT
ejpam-6529	419	6	∈	∈	PROPN
ejpam-6529	419	7	b∗	b∗	ADJ
ejpam-6529	419	8	,	,	PUNCT
ejpam-6529	419	9	then	then	ADV
ejpam-6529	419	10	fb(1	fb(1	PROPN
ejpam-6529	419	11	)	)	PUNCT
ejpam-6529	419	12	≥	≥	NOUN
ejpam-6529	419	13	s	s	NOUN
ejpam-6529	419	14	>	>	X
ejpam-6529	419	15	1	1	NUM
ejpam-6529	419	16	−	−	PROPN
ejpam-6529	419	17	s	s	PART
ejpam-6529	419	18	and	and	CCONJ
ejpam-6529	419	19	gb(1	gb(1	PROPN
ejpam-6529	419	20	)	)	PUNCT
ejpam-6529	419	21	≤	≤	NOUN
ejpam-6529	420	1	t	t	NOUN
ejpam-6529	420	2	<	<	X
ejpam-6529	420	3	1	1	NUM
ejpam-6529	420	4	−	−	NOUN
ejpam-6529	420	5	t.	t.	NOUN
ejpam-6529	420	6	hence	hence	ADV
ejpam-6529	420	7	1	1	NUM
ejpam-6529	420	8	∈	∈	PROPN
ejpam-6529	420	9	(	(	PUNCT
ejpam-6529	420	10	fb	fb	INTJ
ejpam-6529	420	11	,	,	PUNCT
ejpam-6529	420	12	s)q	s)q	PUNCT
ejpam-6529	420	13	∩	∩	NOUN
ejpam-6529	420	14	(	(	PUNCT
ejpam-6529	420	15	gb	gb	NOUN
ejpam-6529	420	16	,	,	PUNCT
ejpam-6529	420	17	t)q	t)q	PUNCT
ejpam-6529	420	18	=	=	SYM
ejpam-6529	420	19	(	(	PUNCT
ejpam-6529	420	20	b∗	b∗	ADJ
ejpam-6529	420	21	,	,	PUNCT
ejpam-6529	420	22	(	(	PUNCT
ejpam-6529	420	23	s	s	X
ejpam-6529	420	24	,	,	PUNCT
ejpam-6529	420	25	t))q	t))q	NOUN
ejpam-6529	420	26	.	.	PUNCT
ejpam-6529	421	1	let	let	VERB
ejpam-6529	421	2	y	y	PROPN
ejpam-6529	421	3	∈	∈	PROPN
ejpam-6529	421	4	(	(	PUNCT
ejpam-6529	421	5	b∗	b∗	ADJ
ejpam-6529	421	6	,	,	PUNCT
ejpam-6529	421	7	(	(	PUNCT
ejpam-6529	421	8	s	s	X
ejpam-6529	421	9	,	,	PUNCT
ejpam-6529	421	10	t))q	t))q	NOUN
ejpam-6529	421	11	.	.	PUNCT
ejpam-6529	422	1	then	then	ADV
ejpam-6529	422	2	y(s	y(s	PROPN
ejpam-6529	422	3	,	,	PUNCT
ejpam-6529	422	4	t	t	PROPN
ejpam-6529	422	5	)	)	PUNCT
ejpam-6529	422	6	q	q	PROPN
ejpam-6529	422	7	b∗	b∗	ADJ
ejpam-6529	422	8	,	,	PUNCT
ejpam-6529	422	9	and	and	CCONJ
ejpam-6529	422	10	so	so	ADV
ejpam-6529	422	11	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	422	12	,	,	PUNCT
ejpam-6529	422	13	t	t	PROPN
ejpam-6529	422	14	)	)	PUNCT
ejpam-6529	422	15	∈∨q	∈∨q	NOUN
ejpam-6529	422	16	b∗	b∗	ADV
ejpam-6529	422	17	by	by	ADP
ejpam-6529	422	18	(	(	PUNCT
ejpam-6529	422	19	35	35	NUM
ejpam-6529	422	20	)	)	PUNCT
ejpam-6529	422	21	,	,	PUNCT
ejpam-6529	422	22	that	that	ADV
ejpam-6529	422	23	is	is	ADV
ejpam-6529	422	24	,	,	PUNCT
ejpam-6529	422	25	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	422	26	,	,	PUNCT
ejpam-6529	422	27	t	t	PROPN
ejpam-6529	422	28	)	)	PUNCT
ejpam-6529	422	29	∈	∈	PROPN
ejpam-6529	422	30	b∗	b∗	ADJ
ejpam-6529	422	31	or	or	CCONJ
ejpam-6529	422	32	ðx(y)(s	ðx(y)(s	NUM
ejpam-6529	422	33	,	,	PUNCT
ejpam-6529	422	34	t	t	PROPN
ejpam-6529	422	35	)	)	PUNCT
ejpam-6529	423	1	q	q	NOUN
ejpam-6529	423	2	b∗.	b∗.	NOUN
ejpam-6529	423	3	if	if	SCONJ
ejpam-6529	423	4	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	423	5	,	,	PUNCT
ejpam-6529	423	6	t	t	PROPN
ejpam-6529	423	7	)	)	PUNCT
ejpam-6529	423	8	q	q	PUNCT
ejpam-6529	424	1	b∗	b∗	ADJ
ejpam-6529	424	2	,	,	PUNCT
ejpam-6529	424	3	then	then	ADV
ejpam-6529	424	4	ðx(y	ðx(y	X
ejpam-6529	424	5	)	)	PUNCT
ejpam-6529	424	6	∈	∈	PROPN
ejpam-6529	424	7	(	(	PUNCT
ejpam-6529	424	8	b∗	b∗	ADJ
ejpam-6529	424	9	,	,	PUNCT
ejpam-6529	424	10	(	(	PUNCT
ejpam-6529	424	11	s	s	X
ejpam-6529	424	12	,	,	PUNCT
ejpam-6529	424	13	t))q	t))q	NOUN
ejpam-6529	424	14	.	.	PUNCT
ejpam-6529	425	1	if	if	SCONJ
ejpam-6529	425	2	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	425	3	,	,	PUNCT
ejpam-6529	425	4	t	t	PROPN
ejpam-6529	425	5	)	)	PUNCT
ejpam-6529	425	6	∈	∈	PROPN
ejpam-6529	425	7	b∗	b∗	ADJ
ejpam-6529	425	8	,	,	PUNCT
ejpam-6529	425	9	then	then	ADV
ejpam-6529	425	10	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	425	11	)	)	PUNCT
ejpam-6529	425	12	)	)	PUNCT
ejpam-6529	426	1	≥	≥	PRON
ejpam-6529	426	2	s	s	NOUN
ejpam-6529	426	3	>	>	X
ejpam-6529	426	4	1	1	NUM
ejpam-6529	426	5	−	−	PROPN
ejpam-6529	426	6	s	s	NOUN
ejpam-6529	426	7	and	and	CCONJ
ejpam-6529	426	8	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	426	9	)	)	PUNCT
ejpam-6529	426	10	)	)	PUNCT
ejpam-6529	427	1	≤	≤	NUM
ejpam-6529	428	1	t	t	X
ejpam-6529	428	2	<	<	X
ejpam-6529	428	3	1−	1−	NUM
ejpam-6529	428	4	t.	t.	NOUN
ejpam-6529	428	5	hence	hence	ADV
ejpam-6529	428	6	ðx(y	ðx(y	PUNCT
ejpam-6529	428	7	)	)	PUNCT
ejpam-6529	429	1	∈	∈	PROPN
ejpam-6529	429	2	(	(	PUNCT
ejpam-6529	429	3	fb	fb	INTJ
ejpam-6529	429	4	,	,	PUNCT
ejpam-6529	429	5	s)q	s)q	PUNCT
ejpam-6529	429	6	∩	∩	NOUN
ejpam-6529	429	7	(	(	PUNCT
ejpam-6529	429	8	gb	gb	NOUN
ejpam-6529	429	9	,	,	PUNCT
ejpam-6529	429	10	t)q	t)q	PUNCT
ejpam-6529	429	11	=	=	SYM
ejpam-6529	429	12	(	(	PUNCT
ejpam-6529	429	13	b∗	b∗	ADJ
ejpam-6529	429	14	,	,	PUNCT
ejpam-6529	429	15	(	(	PUNCT
ejpam-6529	429	16	s	s	X
ejpam-6529	429	17	,	,	PUNCT
ejpam-6529	429	18	t))q	t))q	NOUN
ejpam-6529	429	19	.	.	PUNCT
ejpam-6529	430	1	consequently	consequently	ADV
ejpam-6529	430	2	,	,	PUNCT
ejpam-6529	430	3	(	(	PUNCT
ejpam-6529	430	4	b∗	b∗	ADJ
ejpam-6529	430	5	,	,	PUNCT
ejpam-6529	430	6	(	(	PUNCT
ejpam-6529	430	7	s	s	X
ejpam-6529	430	8	,	,	PUNCT
ejpam-6529	430	9	t))q	t))q	NOUN
ejpam-6529	430	10	is	be	AUX
ejpam-6529	430	11	a	a	DET
ejpam-6529	430	12	weak	weak	ADJ
ejpam-6529	430	13	filter	filter	NOUN
ejpam-6529	430	14	of	of	ADP
ejpam-6529	430	15	x	x	X
ejpam-6529	430	16	:	:	PUNCT
ejpam-6529	430	17	=	=	SYM
ejpam-6529	430	18	(	(	PUNCT
ejpam-6529	430	19	x	x	NOUN
ejpam-6529	430	20	,	,	PUNCT
ejpam-6529	430	21	|	|	NOUN
ejpam-6529	430	22	)	)	PUNCT
ejpam-6529	430	23	.	.	PUNCT
ejpam-6529	431	1	theorem	theorem	VERB
ejpam-6529	431	2	13	13	NUM
ejpam-6529	431	3	.	.	PUNCT
ejpam-6529	432	1	given	give	VERB
ejpam-6529	432	2	a	a	DET
ejpam-6529	432	3	weak	weak	ADJ
ejpam-6529	432	4	filter	filter	NOUN
ejpam-6529	432	5	f	f	NOUN
ejpam-6529	432	6	of	of	ADP
ejpam-6529	432	7	x	x	X
ejpam-6529	432	8	:	:	PUNCT
ejpam-6529	432	9	=	=	SYM
ejpam-6529	432	10	(	(	PUNCT
ejpam-6529	432	11	x	x	NOUN
ejpam-6529	432	12	,	,	PUNCT
ejpam-6529	432	13	|	|	ADV
ejpam-6529	432	14	)	)	PUNCT
ejpam-6529	432	15	,	,	PUNCT
ejpam-6529	432	16	if	if	SCONJ
ejpam-6529	432	17	an	an	DET
ejpam-6529	432	18	intuitionistic	intuitionistic	ADJ
ejpam-6529	432	19	fuzzy	fuzzy	ADJ
ejpam-6529	432	20	set	set	VERB
ejpam-6529	432	21	b∗	b∗	ADJ
ejpam-6529	432	22	:	:	PUNCT
ejpam-6529	432	23	=	=	SYM
ejpam-6529	432	24	(	(	PUNCT
ejpam-6529	432	25	x	x	X
ejpam-6529	432	26	;	;	PUNCT
ejpam-6529	432	27	fb	fb	INTJ
ejpam-6529	432	28	,	,	PUNCT
ejpam-6529	432	29	gb	gb	NOUN
ejpam-6529	432	30	)	)	PUNCT
ejpam-6529	432	31	in	in	ADP
ejpam-6529	432	32	x	x	X
ejpam-6529	432	33	satisfies	satisfie	NOUN
ejpam-6529	432	34	b∗(x	b∗(x	NOUN
ejpam-6529	432	35	)	)	PUNCT
ejpam-6529	432	36	=	=	PUNCT
ejpam-6529	432	37	(	(	PUNCT
ejpam-6529	432	38	0	0	NUM
ejpam-6529	432	39	,	,	PUNCT
ejpam-6529	432	40	1	1	NUM
ejpam-6529	432	41	)	)	PUNCT
ejpam-6529	432	42	,	,	PUNCT
ejpam-6529	432	43	i.e.	i.e.	X
ejpam-6529	432	44	,	,	PUNCT
ejpam-6529	432	45	fb(x	fb(x	ADJ
ejpam-6529	432	46	)	)	PUNCT
ejpam-6529	432	47	=	=	SYM
ejpam-6529	432	48	0	0	NUM
ejpam-6529	432	49	and	and	CCONJ
ejpam-6529	432	50	gb(x	gb(x	NUM
ejpam-6529	432	51	)	)	PUNCT
ejpam-6529	432	52	=	=	SYM
ejpam-6529	432	53	1	1	NUM
ejpam-6529	432	54	,	,	PUNCT
ejpam-6529	432	55	for	for	SCONJ
ejpam-6529	432	56	x	x	SYM
ejpam-6529	432	57	∈	∈	PROPN
ejpam-6529	432	58	x	x	PUNCT
ejpam-6529	432	59	\	\	PROPN
ejpam-6529	432	60	f	f	PROPN
ejpam-6529	432	61	and	and	CCONJ
ejpam-6529	432	62	x	x	PROPN
ejpam-6529	432	63	∈	∈	PROPN
ejpam-6529	432	64	(	(	PUNCT
ejpam-6529	432	65	b∗	b∗	ADJ
ejpam-6529	432	66	,	,	PUNCT
ejpam-6529	432	67	(	(	PUNCT
ejpam-6529	432	68	0.5	0.5	NUM
ejpam-6529	432	69	,	,	PUNCT
ejpam-6529	432	70	0.5))∈	0.5))∈	NUM
ejpam-6529	432	71	for	for	ADP
ejpam-6529	432	72	x	x	PROPN
ejpam-6529	432	73	∈	∈	PROPN
ejpam-6529	432	74	f	f	PROPN
ejpam-6529	432	75	,	,	PUNCT
ejpam-6529	432	76	then	then	ADV
ejpam-6529	432	77	its	its	PRON
ejpam-6529	432	78	nonempty	nonempty	ADJ
ejpam-6529	432	79	intuitionistic	intuitionistic	ADJ
ejpam-6529	432	80	q	q	NOUN
ejpam-6529	432	81	-	-	PUNCT
ejpam-6529	432	82	set	set	ADJ
ejpam-6529	432	83	(	(	PUNCT
ejpam-6529	432	84	b∗	b∗	ADJ
ejpam-6529	432	85	,	,	PUNCT
ejpam-6529	432	86	(	(	PUNCT
ejpam-6529	432	87	s	s	X
ejpam-6529	432	88	,	,	PUNCT
ejpam-6529	432	89	t))q	t))q	NOUN
ejpam-6529	432	90	is	be	AUX
ejpam-6529	432	91	a	a	DET
ejpam-6529	432	92	weak	weak	ADJ
ejpam-6529	432	93	filter	filter	NOUN
ejpam-6529	432	94	of	of	ADP
ejpam-6529	432	95	x	x	X
ejpam-6529	432	96	:	:	PUNCT
ejpam-6529	432	97	=	=	SYM
ejpam-6529	432	98	(	(	PUNCT
ejpam-6529	432	99	x	x	NOUN
ejpam-6529	432	100	,	,	PUNCT
ejpam-6529	432	101	|	|	ADV
ejpam-6529	432	102	)	)	PUNCT
ejpam-6529	432	103	for	for	ADP
ejpam-6529	432	104	all	all	DET
ejpam-6529	432	105	(	(	PUNCT
ejpam-6529	432	106	s	s	PROPN
ejpam-6529	432	107	,	,	PUNCT
ejpam-6529	432	108	t	t	PROPN
ejpam-6529	432	109	)	)	PUNCT
ejpam-6529	432	110	∈	∈	PROPN
ejpam-6529	432	111	(	(	PUNCT
ejpam-6529	432	112	0.5	0.5	NUM
ejpam-6529	432	113	,	,	PUNCT
ejpam-6529	432	114	1]×	1]×	NUM
ejpam-6529	432	115	[	[	X
ejpam-6529	432	116	0	0	NUM
ejpam-6529	432	117	,	,	PUNCT
ejpam-6529	432	118	0.5	0.5	NUM
ejpam-6529	432	119	)	)	PUNCT
ejpam-6529	432	120	.	.	PUNCT
ejpam-6529	433	1	proof	proof	NOUN
ejpam-6529	433	2	.	.	PUNCT
ejpam-6529	434	1	let	let	VERB
ejpam-6529	434	2	(	(	PUNCT
ejpam-6529	434	3	s	s	X
ejpam-6529	434	4	,	,	PUNCT
ejpam-6529	434	5	t	t	PROPN
ejpam-6529	434	6	)	)	PUNCT
ejpam-6529	434	7	∈	∈	PROPN
ejpam-6529	434	8	(	(	PUNCT
ejpam-6529	434	9	0.5	0.5	NUM
ejpam-6529	434	10	,	,	PUNCT
ejpam-6529	434	11	1]×	1]×	NUM
ejpam-6529	435	1	[	[	X
ejpam-6529	435	2	0	0	NUM
ejpam-6529	435	3	,	,	PUNCT
ejpam-6529	435	4	0.5	0.5	NUM
ejpam-6529	435	5	)	)	PUNCT
ejpam-6529	435	6	be	be	VERB
ejpam-6529	435	7	such	such	ADJ
ejpam-6529	435	8	that	that	SCONJ
ejpam-6529	435	9	(	(	PUNCT
ejpam-6529	435	10	b∗	b∗	ADJ
ejpam-6529	435	11	,	,	PUNCT
ejpam-6529	435	12	(	(	PUNCT
ejpam-6529	435	13	s	s	X
ejpam-6529	435	14	,	,	PUNCT
ejpam-6529	435	15	t))q	t))q	NOUN
ejpam-6529	435	16	̸=	̸=	PROPN
ejpam-6529	435	17	∅	∅	NOUN
ejpam-6529	435	18	,	,	PUNCT
ejpam-6529	435	19	say	say	VERB
ejpam-6529	435	20	y	y	PROPN
ejpam-6529	435	21	∈	∈	PROPN
ejpam-6529	435	22	(	(	PUNCT
ejpam-6529	435	23	b∗	b∗	ADJ
ejpam-6529	435	24	,	,	PUNCT
ejpam-6529	435	25	(	(	PUNCT
ejpam-6529	435	26	s	s	X
ejpam-6529	435	27	,	,	PUNCT
ejpam-6529	435	28	t))q	t))q	NOUN
ejpam-6529	435	29	.	.	PUNCT
ejpam-6529	436	1	then	then	ADV
ejpam-6529	436	2	y(s	y(s	PROPN
ejpam-6529	436	3	,	,	PUNCT
ejpam-6529	436	4	t	t	PROPN
ejpam-6529	436	5	)	)	PUNCT
ejpam-6529	436	6	q	q	PROPN
ejpam-6529	436	7	b∗	b∗	ADJ
ejpam-6529	436	8	,	,	PUNCT
ejpam-6529	436	9	and	and	CCONJ
ejpam-6529	436	10	so	so	ADV
ejpam-6529	436	11	fb(y	fb(y	NUM
ejpam-6529	436	12	)	)	PUNCT
ejpam-6529	437	1	+	+	PRON
ejpam-6529	437	2	s	s	VERB
ejpam-6529	437	3	>	>	X
ejpam-6529	437	4	1	1	NUM
ejpam-6529	437	5	and	and	CCONJ
ejpam-6529	437	6	gb(y	gb(y	NUM
ejpam-6529	437	7	)	)	PUNCT
ejpam-6529	438	1	+	+	CCONJ
ejpam-6529	438	2	t	t	X
ejpam-6529	438	3	<	<	X
ejpam-6529	438	4	1	1	NUM
ejpam-6529	438	5	.	.	PUNCT
ejpam-6529	439	1	if	if	SCONJ
ejpam-6529	439	2	y	y	PROPN
ejpam-6529	439	3	∈	∈	PROPN
ejpam-6529	439	4	x	x	PUNCT
ejpam-6529	439	5	\	\	PROPN
ejpam-6529	439	6	f	f	PROPN
ejpam-6529	439	7	,	,	PUNCT
ejpam-6529	439	8	then	then	ADV
ejpam-6529	439	9	1	1	NUM
ejpam-6529	439	10	<	<	X
ejpam-6529	439	11	fb(y	fb(y	PUNCT
ejpam-6529	439	12	)	)	PUNCT
ejpam-6529	440	1	+	+	PRON
ejpam-6529	440	2	s	s	X
ejpam-6529	440	3	=	=	SYM
ejpam-6529	440	4	0	0	PUNCT
ejpam-6529	440	5	+	+	NUM
ejpam-6529	440	6	s	s	X
ejpam-6529	440	7	=	=	X
ejpam-6529	440	8	s	s	X
ejpam-6529	440	9	and	and	CCONJ
ejpam-6529	440	10	1	1	NUM
ejpam-6529	440	11	>	>	PUNCT
ejpam-6529	440	12	gb(y	gb(y	PUNCT
ejpam-6529	440	13	)	)	PUNCT
ejpam-6529	441	1	+	+	CCONJ
ejpam-6529	441	2	t	t	X
ejpam-6529	441	3	=	=	SYM
ejpam-6529	441	4	1	1	NUM
ejpam-6529	441	5	+	+	SYM
ejpam-6529	441	6	s	s	VERB
ejpam-6529	441	7	which	which	PRON
ejpam-6529	441	8	is	be	AUX
ejpam-6529	441	9	a	a	DET
ejpam-6529	441	10	contradiction	contradiction	NOUN
ejpam-6529	441	11	.	.	PUNCT
ejpam-6529	442	1	hence	hence	ADV
ejpam-6529	442	2	y	y	PROPN
ejpam-6529	442	3	∈	∈	PROPN
ejpam-6529	442	4	f	f	X
ejpam-6529	442	5	,	,	PUNCT
ejpam-6529	442	6	and	and	CCONJ
ejpam-6529	442	7	thus	thus	ADV
ejpam-6529	442	8	y	y	PROPN
ejpam-6529	442	9	∈	∈	PROPN
ejpam-6529	442	10	(	(	PUNCT
ejpam-6529	442	11	b∗	b∗	ADJ
ejpam-6529	442	12	,	,	PUNCT
ejpam-6529	442	13	(	(	PUNCT
ejpam-6529	442	14	0.5	0.5	NUM
ejpam-6529	442	15	,	,	PUNCT
ejpam-6529	442	16	0.5))∈	0.5))∈	NUM
ejpam-6529	442	17	,	,	PUNCT
ejpam-6529	442	18	that	that	ADV
ejpam-6529	442	19	is	is	ADV
ejpam-6529	442	20	,	,	PUNCT
ejpam-6529	442	21	gb(y	gb(y	ADV
ejpam-6529	442	22	)	)	PUNCT
ejpam-6529	442	23	≤	≤	NUM
ejpam-6529	442	24	0.5	0.5	NUM
ejpam-6529	442	25	≤	≤	NUM
ejpam-6529	442	26	fb(y	fb(y	PUNCT
ejpam-6529	442	27	)	)	PUNCT
ejpam-6529	442	28	.	.	PUNCT
ejpam-6529	443	1	since	since	SCONJ
ejpam-6529	443	2	1	1	NUM
ejpam-6529	443	3	∈	∈	PROPN
ejpam-6529	443	4	f	f	NOUN
ejpam-6529	443	5	,	,	PUNCT
ejpam-6529	443	6	we	we	PRON
ejpam-6529	443	7	have	have	VERB
ejpam-6529	443	8	1	1	NUM
ejpam-6529	443	9	∈	∈	NOUN
ejpam-6529	443	10	(	(	PUNCT
ejpam-6529	443	11	b∗	b∗	ADJ
ejpam-6529	443	12	,	,	PUNCT
ejpam-6529	443	13	(	(	PUNCT
ejpam-6529	443	14	0.5	0.5	NUM
ejpam-6529	443	15	,	,	PUNCT
ejpam-6529	443	16	0.5))∈	0.5))∈	NUM
ejpam-6529	443	17	,	,	PUNCT
ejpam-6529	443	18	that	that	ADV
ejpam-6529	443	19	is	is	ADV
ejpam-6529	443	20	,	,	PUNCT
ejpam-6529	443	21	fb(1	fb(1	PROPN
ejpam-6529	443	22	)	)	PUNCT
ejpam-6529	443	23	≥	≥	NOUN
ejpam-6529	443	24	0.5	0.5	NUM
ejpam-6529	443	25	and	and	CCONJ
ejpam-6529	443	26	gb(1	gb(1	PROPN
ejpam-6529	443	27	)	)	PUNCT
ejpam-6529	443	28	≤	≤	NOUN
ejpam-6529	443	29	0.5	0.5	NUM
ejpam-6529	443	30	.	.	PUNCT
ejpam-6529	444	1	if	if	SCONJ
ejpam-6529	444	2	1(s	1(s	NUM
ejpam-6529	444	3	,	,	PUNCT
ejpam-6529	444	4	t	t	PROPN
ejpam-6529	444	5	)	)	PUNCT
ejpam-6529	444	6	∈b∗	∈b∗	PROPN
ejpam-6529	444	7	,	,	PUNCT
ejpam-6529	444	8	then	then	ADV
ejpam-6529	444	9	fb(1	fb(1	PROPN
ejpam-6529	444	10	)	)	PUNCT
ejpam-6529	444	11	<	<	X
ejpam-6529	444	12	s	s	X
ejpam-6529	444	13	or	or	CCONJ
ejpam-6529	444	14	gb(1	gb(1	PROPN
ejpam-6529	444	15	)	)	PUNCT
ejpam-6529	444	16	>	>	X
ejpam-6529	445	1	t.	t.	PROPN
ejpam-6529	445	2	at	at	ADP
ejpam-6529	445	3	this	this	DET
ejpam-6529	445	4	time	time	NOUN
ejpam-6529	445	5	,	,	PUNCT
ejpam-6529	445	6	the	the	DET
ejpam-6529	445	7	following	follow	VERB
ejpam-6529	445	8	three	three	NUM
ejpam-6529	445	9	cases	case	NOUN
ejpam-6529	445	10	should	should	AUX
ejpam-6529	445	11	be	be	AUX
ejpam-6529	445	12	considered	consider	VERB
ejpam-6529	445	13	.	.	PUNCT
ejpam-6529	446	1	(	(	PUNCT
ejpam-6529	446	2	i	i	NOUN
ejpam-6529	446	3	)	)	PUNCT
ejpam-6529	446	4	fb(1	fb(1	PROPN
ejpam-6529	446	5	)	)	PUNCT
ejpam-6529	446	6	<	<	X
ejpam-6529	446	7	s	s	X
ejpam-6529	446	8	and	and	CCONJ
ejpam-6529	446	9	gb(1	gb(1	PROPN
ejpam-6529	446	10	)	)	PUNCT
ejpam-6529	446	11	>	>	X
ejpam-6529	447	1	t.	t.	PROPN
ejpam-6529	447	2	(	(	PUNCT
ejpam-6529	447	3	ii	ii	PROPN
ejpam-6529	447	4	)	)	PUNCT
ejpam-6529	447	5	fb(1	fb(1	PROPN
ejpam-6529	447	6	)	)	PUNCT
ejpam-6529	447	7	<	<	X
ejpam-6529	447	8	s	s	X
ejpam-6529	447	9	and	and	CCONJ
ejpam-6529	447	10	gb(1	gb(1	PROPN
ejpam-6529	447	11	)	)	PUNCT
ejpam-6529	447	12	≤	≤	NOUN
ejpam-6529	447	13	t.	t.	NOUN
ejpam-6529	447	14	(	(	PUNCT
ejpam-6529	447	15	iii	iii	NOUN
ejpam-6529	447	16	)	)	PUNCT
ejpam-6529	447	17	fb(1	fb(1	PROPN
ejpam-6529	447	18	)	)	PUNCT
ejpam-6529	447	19	≥	≥	NOUN
ejpam-6529	447	20	s	s	NOUN
ejpam-6529	447	21	and	and	CCONJ
ejpam-6529	447	22	gb(1	gb(1	PROPN
ejpam-6529	447	23	)	)	PUNCT
ejpam-6529	447	24	>	>	X
ejpam-6529	448	1	t.	t.	X
ejpam-6529	448	2	the	the	DET
ejpam-6529	448	3	first	first	ADJ
ejpam-6529	448	4	case	case	NOUN
ejpam-6529	448	5	induces	induce	VERB
ejpam-6529	448	6	fb(1	fb(1	PROPN
ejpam-6529	448	7	)	)	PUNCT
ejpam-6529	448	8	+	+	PRON
ejpam-6529	448	9	s	s	VERB
ejpam-6529	448	10	>	>	X
ejpam-6529	448	11	2fb(1	2fb(1	PROPN
ejpam-6529	448	12	)	)	PUNCT
ejpam-6529	448	13	≥	≥	NOUN
ejpam-6529	448	14	1	1	NUM
ejpam-6529	448	15	and	and	CCONJ
ejpam-6529	448	16	gb(1	gb(1	PROPN
ejpam-6529	448	17	)	)	PUNCT
ejpam-6529	448	18	+	+	NUM
ejpam-6529	448	19	t	t	X
ejpam-6529	448	20	<	<	X
ejpam-6529	448	21	2gb(1	2gb(1	NUM
ejpam-6529	448	22	)	)	PUNCT
ejpam-6529	448	23	≤	≤	NUM
ejpam-6529	448	24	1	1	NUM
ejpam-6529	448	25	.	.	PUNCT
ejpam-6529	449	1	for	for	ADP
ejpam-6529	449	2	the	the	DET
ejpam-6529	449	3	case	case	NOUN
ejpam-6529	449	4	(	(	PUNCT
ejpam-6529	449	5	ii	ii	NOUN
ejpam-6529	449	6	)	)	PUNCT
ejpam-6529	449	7	,	,	PUNCT
ejpam-6529	449	8	we	we	PRON
ejpam-6529	449	9	get	get	VERB
ejpam-6529	449	10	fb(1	fb(1	NOUN
ejpam-6529	449	11	)	)	PUNCT
ejpam-6529	450	1	+	+	PRON
ejpam-6529	450	2	s	s	VERB
ejpam-6529	450	3	>	>	X
ejpam-6529	450	4	2fb(1	2fb(1	PROPN
ejpam-6529	450	5	)	)	PUNCT
ejpam-6529	450	6	≥	≥	NOUN
ejpam-6529	450	7	1	1	NUM
ejpam-6529	450	8	and	and	CCONJ
ejpam-6529	450	9	gb(1	gb(1	PROPN
ejpam-6529	450	10	)	)	PUNCT
ejpam-6529	450	11	+	+	NOUN
ejpam-6529	450	12	t	t	X
ejpam-6529	450	13	<	<	X
ejpam-6529	450	14	2	2	NUM
ejpam-6529	450	15	t	t	NOUN
ejpam-6529	450	16	≤	≤	NUM
ejpam-6529	450	17	1	1	NUM
ejpam-6529	450	18	.	.	PUNCT
ejpam-6529	451	1	the	the	DET
ejpam-6529	451	2	third	third	ADJ
ejpam-6529	451	3	case	case	NOUN
ejpam-6529	451	4	implies	imply	VERB
ejpam-6529	451	5	that	that	SCONJ
ejpam-6529	451	6	fb(1	fb(1	NOUN
ejpam-6529	451	7	)	)	PUNCT
ejpam-6529	451	8	+	+	PRON
ejpam-6529	451	9	s	s	VERB
ejpam-6529	451	10	>	>	X
ejpam-6529	451	11	2s	2s	NUM
ejpam-6529	451	12	≥	≥	NUM
ejpam-6529	451	13	1	1	NUM
ejpam-6529	451	14	and	and	CCONJ
ejpam-6529	451	15	gb(1	gb(1	PROPN
ejpam-6529	451	16	)	)	PUNCT
ejpam-6529	451	17	+	+	NUM
ejpam-6529	451	18	t	t	X
ejpam-6529	451	19	<	<	X
ejpam-6529	451	20	2gb(1	2gb(1	NUM
ejpam-6529	451	21	)	)	PUNCT
ejpam-6529	451	22	≤	≤	NUM
ejpam-6529	451	23	1	1	NUM
ejpam-6529	451	24	.	.	PUNCT
ejpam-6529	452	1	this	this	PRON
ejpam-6529	452	2	shows	show	VERB
ejpam-6529	452	3	that	that	SCONJ
ejpam-6529	452	4	1(s	1(s	NUM
ejpam-6529	452	5	,	,	PUNCT
ejpam-6529	452	6	t	t	PROPN
ejpam-6529	452	7	)	)	PUNCT
ejpam-6529	452	8	q	q	NOUN
ejpam-6529	453	1	b∗	b∗	ADJ
ejpam-6529	453	2	and	and	CCONJ
ejpam-6529	453	3	consequently	consequently	ADV
ejpam-6529	453	4	1(s	1(s	NUM
ejpam-6529	453	5	,	,	PUNCT
ejpam-6529	453	6	t	t	PROPN
ejpam-6529	453	7	)	)	PUNCT
ejpam-6529	453	8	∈∨q	∈∨q	NOUN
ejpam-6529	453	9	b∗.	b∗.	NOUN
ejpam-6529	453	10	since	since	SCONJ
ejpam-6529	453	11	y	y	PROPN
ejpam-6529	453	12	∈	∈	PROPN
ejpam-6529	453	13	f	f	PROPN
ejpam-6529	453	14	,	,	PUNCT
ejpam-6529	453	15	we	we	PRON
ejpam-6529	453	16	have	have	VERB
ejpam-6529	453	17	ðx(y	ðx(y	PUNCT
ejpam-6529	453	18	)	)	PUNCT
ejpam-6529	454	1	∈	∈	PROPN
ejpam-6529	454	2	f	f	PROPN
ejpam-6529	454	3	for	for	ADP
ejpam-6529	454	4	all	all	DET
ejpam-6529	454	5	x	x	SYM
ejpam-6529	454	6	∈	∈	PROPN
ejpam-6529	454	7	x	x	PUNCT
ejpam-6529	454	8	because	because	SCONJ
ejpam-6529	454	9	f	f	PROPN
ejpam-6529	454	10	is	be	AUX
ejpam-6529	454	11	a	a	DET
ejpam-6529	454	12	weak	weak	ADJ
ejpam-6529	454	13	filter	filter	NOUN
ejpam-6529	454	14	of	of	ADP
ejpam-6529	454	15	x	x	X
ejpam-6529	454	16	:	:	PUNCT
ejpam-6529	454	17	=	=	SYM
ejpam-6529	454	18	(	(	PUNCT
ejpam-6529	454	19	x	x	NOUN
ejpam-6529	454	20	,	,	PUNCT
ejpam-6529	454	21	|	|	NOUN
ejpam-6529	454	22	)	)	PUNCT
ejpam-6529	454	23	.	.	PUNCT
ejpam-6529	455	1	thus	thus	ADV
ejpam-6529	455	2	ðx(y	ðx(y	X
ejpam-6529	455	3	)	)	PUNCT
ejpam-6529	455	4	∈	∈	PROPN
ejpam-6529	455	5	(	(	PUNCT
ejpam-6529	455	6	b∗	b∗	ADJ
ejpam-6529	455	7	,	,	PUNCT
ejpam-6529	455	8	(	(	PUNCT
ejpam-6529	455	9	0.5	0.5	NUM
ejpam-6529	455	10	,	,	PUNCT
ejpam-6529	455	11	0.5))∈	0.5))∈	NUM
ejpam-6529	455	12	,	,	PUNCT
ejpam-6529	455	13	that	that	ADV
ejpam-6529	455	14	is	is	ADV
ejpam-6529	455	15	,	,	PUNCT
ejpam-6529	455	16	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	455	17	)	)	PUNCT
ejpam-6529	455	18	)	)	PUNCT
ejpam-6529	455	19	≥	≥	NOUN
ejpam-6529	455	20	0.5	0.5	NUM
ejpam-6529	455	21	and	and	CCONJ
ejpam-6529	455	22	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	455	23	)	)	PUNCT
ejpam-6529	455	24	)	)	PUNCT
ejpam-6529	455	25	≤	≤	NUM
ejpam-6529	455	26	0.5	0.5	NUM
ejpam-6529	455	27	.	.	PUNCT
ejpam-6529	456	1	if	if	SCONJ
ejpam-6529	456	2	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	456	3	,	,	PUNCT
ejpam-6529	456	4	t	t	PROPN
ejpam-6529	456	5	)	)	PUNCT
ejpam-6529	456	6	∈b∗	∈b∗	PROPN
ejpam-6529	456	7	,	,	PUNCT
ejpam-6529	456	8	then	then	ADV
ejpam-6529	456	9	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	456	10	)	)	PUNCT
ejpam-6529	456	11	)	)	PUNCT
ejpam-6529	457	1	<	<	X
ejpam-6529	457	2	s	s	X
ejpam-6529	457	3	or	or	CCONJ
ejpam-6529	457	4	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	457	5	)	)	PUNCT
ejpam-6529	457	6	)	)	PUNCT
ejpam-6529	458	1	>	>	X
ejpam-6529	459	1	t.	t.	PROPN
ejpam-6529	459	2	at	at	ADP
ejpam-6529	459	3	this	this	DET
ejpam-6529	459	4	time	time	NOUN
ejpam-6529	459	5	,	,	PUNCT
ejpam-6529	459	6	the	the	DET
ejpam-6529	459	7	following	follow	VERB
ejpam-6529	459	8	three	three	NUM
ejpam-6529	459	9	cases	case	NOUN
ejpam-6529	459	10	should	should	AUX
ejpam-6529	459	11	be	be	AUX
ejpam-6529	459	12	considered	consider	VERB
ejpam-6529	459	13	.	.	PUNCT
ejpam-6529	460	1	(	(	PUNCT
ejpam-6529	460	2	iv	iv	X
ejpam-6529	460	3	)	)	PUNCT
ejpam-6529	460	4	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	460	5	)	)	PUNCT
ejpam-6529	460	6	)	)	PUNCT
ejpam-6529	461	1	<	<	X
ejpam-6529	461	2	s	s	X
ejpam-6529	461	3	and	and	CCONJ
ejpam-6529	461	4	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	461	5	)	)	PUNCT
ejpam-6529	461	6	)	)	PUNCT
ejpam-6529	462	1	>	>	PUNCT
ejpam-6529	462	2	t.	t.	PROPN
ejpam-6529	462	3	(	(	PUNCT
ejpam-6529	462	4	v	v	NOUN
ejpam-6529	462	5	)	)	PUNCT
ejpam-6529	462	6	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	462	7	)	)	PUNCT
ejpam-6529	462	8	)	)	PUNCT
ejpam-6529	463	1	<	<	X
ejpam-6529	463	2	s	s	X
ejpam-6529	463	3	and	and	CCONJ
ejpam-6529	463	4	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	463	5	)	)	PUNCT
ejpam-6529	463	6	)	)	PUNCT
ejpam-6529	464	1	≤	≤	NOUN
ejpam-6529	464	2	t.	t.	PROPN
ejpam-6529	464	3	s.	s.	PROPN
ejpam-6529	464	4	s.	s.	PROPN
ejpam-6529	464	5	ahn	ahn	PROPN
ejpam-6529	464	6	,	,	PUNCT
ejpam-6529	464	7	y.	y.	PROPN
ejpam-6529	464	8	j.	j.	PROPN
ejpam-6529	464	9	seo	seo	PROPN
ejpam-6529	464	10	,	,	PUNCT
ejpam-6529	464	11	y.	y.	PROPN
ejpam-6529	464	12	b.	b.	PROPN
ejpam-6529	464	13	jun	jun	PROPN
ejpam-6529	464	14	/	/	SYM
ejpam-6529	464	15	eur	eur	PROPN
ejpam-6529	464	16	.	.	PUNCT
ejpam-6529	465	1	j.	j.	PROPN
ejpam-6529	465	2	pure	pure	PROPN
ejpam-6529	465	3	appl	appl	PROPN
ejpam-6529	465	4	.	.	PROPN
ejpam-6529	465	5	math	math	PROPN
ejpam-6529	465	6	,	,	PUNCT
ejpam-6529	465	7	18	18	NUM
ejpam-6529	465	8	(	(	PUNCT
ejpam-6529	465	9	3	3	NUM
ejpam-6529	465	10	)	)	PUNCT
ejpam-6529	465	11	(	(	PUNCT
ejpam-6529	465	12	2025	2025	NUM
ejpam-6529	465	13	)	)	PUNCT
ejpam-6529	465	14	,	,	PUNCT
ejpam-6529	465	15	6529	6529	NUM
ejpam-6529	465	16	15	15	NUM
ejpam-6529	465	17	of	of	ADP
ejpam-6529	465	18	16	16	NUM
ejpam-6529	465	19	(	(	PUNCT
ejpam-6529	465	20	vi	vi	NOUN
ejpam-6529	465	21	)	)	PUNCT
ejpam-6529	465	22	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	465	23	)	)	PUNCT
ejpam-6529	465	24	)	)	PUNCT
ejpam-6529	465	25	≥	≥	PROPN
ejpam-6529	465	26	s	s	NOUN
ejpam-6529	465	27	and	and	CCONJ
ejpam-6529	465	28	gb(ðx(y	gb(ðx(y	PROPN
ejpam-6529	465	29	)	)	PUNCT
ejpam-6529	465	30	)	)	PUNCT
ejpam-6529	465	31	>	>	PUNCT
ejpam-6529	466	1	t.	t.	NOUN
ejpam-6529	466	2	the	the	DET
ejpam-6529	466	3	case	case	NOUN
ejpam-6529	466	4	(	(	PUNCT
ejpam-6529	466	5	iv	iv	X
ejpam-6529	466	6	)	)	PUNCT
ejpam-6529	466	7	induces	induce	VERB
ejpam-6529	466	8	fb(ðx(y))+s	fb(ðx(y))+s	ADJ
ejpam-6529	466	9	>	>	X
ejpam-6529	466	10	2fb(ðx(y	2fb(ðx(y	PROPN
ejpam-6529	466	11	)	)	PUNCT
ejpam-6529	466	12	)	)	PUNCT
ejpam-6529	466	13	≥	≥	NOUN
ejpam-6529	466	14	1	1	NUM
ejpam-6529	466	15	and	and	CCONJ
ejpam-6529	466	16	gb(ðx(y))+t	gb(ðx(y))+t	NOUN
ejpam-6529	466	17	<	<	X
ejpam-6529	466	18	2gb(ðx(y	2gb(ðx(y	NUM
ejpam-6529	466	19	)	)	PUNCT
ejpam-6529	466	20	)	)	PUNCT
ejpam-6529	467	1	≤	≤	NUM
ejpam-6529	467	2	1	1	NUM
ejpam-6529	467	3	.	.	PUNCT
ejpam-6529	468	1	for	for	ADP
ejpam-6529	468	2	the	the	DET
ejpam-6529	468	3	case	case	NOUN
ejpam-6529	468	4	(	(	PUNCT
ejpam-6529	468	5	v	v	NOUN
ejpam-6529	468	6	)	)	PUNCT
ejpam-6529	468	7	,	,	PUNCT
ejpam-6529	468	8	we	we	PRON
ejpam-6529	468	9	hace	hace	VERB
ejpam-6529	468	10	fb(ðx(y))+s	fb(ðx(y))+s	PRON
ejpam-6529	468	11	>	>	X
ejpam-6529	468	12	2fb(ðx(y	2fb(ðx(y	PROPN
ejpam-6529	468	13	)	)	PUNCT
ejpam-6529	468	14	)	)	PUNCT
ejpam-6529	468	15	≥	≥	NOUN
ejpam-6529	468	16	1	1	NUM
ejpam-6529	468	17	and	and	CCONJ
ejpam-6529	468	18	gb(ðx(y))+	gb(ðx(y))+	NOUN
ejpam-6529	468	19	t	t	X
ejpam-6529	468	20	<	<	X
ejpam-6529	468	21	2	2	NUM
ejpam-6529	468	22	t	t	NOUN
ejpam-6529	468	23	≤	≤	NUM
ejpam-6529	468	24	1	1	NUM
ejpam-6529	468	25	.	.	PUNCT
ejpam-6529	469	1	the	the	DET
ejpam-6529	469	2	case	case	NOUN
ejpam-6529	469	3	(	(	PUNCT
ejpam-6529	469	4	vi	vi	NOUN
ejpam-6529	469	5	)	)	PUNCT
ejpam-6529	469	6	implies	imply	VERB
ejpam-6529	469	7	that	that	SCONJ
ejpam-6529	469	8	fb(ðx(y	fb(ðx(y	NOUN
ejpam-6529	469	9	)	)	PUNCT
ejpam-6529	469	10	)	)	PUNCT
ejpam-6529	470	1	+	+	CCONJ
ejpam-6529	470	2	s	s	VERB
ejpam-6529	470	3	>	>	X
ejpam-6529	470	4	2s	2s	NUM
ejpam-6529	470	5	≥	≥	NUM
ejpam-6529	470	6	1	1	NUM
ejpam-6529	470	7	and	and	CCONJ
ejpam-6529	470	8	gb(ðx(y	gb(ðx(y	NOUN
ejpam-6529	470	9	)	)	PUNCT
ejpam-6529	470	10	)	)	PUNCT
ejpam-6529	471	1	+	+	CCONJ
ejpam-6529	471	2	t	t	X
ejpam-6529	471	3	<	<	X
ejpam-6529	471	4	2gb(ðx(y	2gb(ðx(y	NUM
ejpam-6529	471	5	)	)	PUNCT
ejpam-6529	471	6	)	)	PUNCT
ejpam-6529	472	1	≤	≤	NUM
ejpam-6529	472	2	1	1	NUM
ejpam-6529	472	3	.	.	PUNCT
ejpam-6529	473	1	this	this	PRON
ejpam-6529	473	2	shows	show	VERB
ejpam-6529	473	3	that	that	SCONJ
ejpam-6529	473	4	ðx(y)(s	ðx(y)(s	PROPN
ejpam-6529	473	5	,	,	PUNCT
ejpam-6529	473	6	t	t	PROPN
ejpam-6529	473	7	)	)	PUNCT
ejpam-6529	473	8	q	q	NOUN
ejpam-6529	474	1	b∗	b∗	ADJ
ejpam-6529	474	2	and	and	CCONJ
ejpam-6529	474	3	consequently	consequently	ADV
ejpam-6529	474	4	ðx(y)(s	ðx(y)(s	NUM
ejpam-6529	474	5	,	,	PUNCT
ejpam-6529	474	6	t	t	PROPN
ejpam-6529	474	7	)	)	PUNCT
ejpam-6529	474	8	∈∨q	∈∨q	NOUN
ejpam-6529	474	9	b∗.	b∗.	VERB
ejpam-6529	474	10	it	it	PRON
ejpam-6529	474	11	follows	follow	VERB
ejpam-6529	474	12	from	from	ADP
ejpam-6529	474	13	theorem	theorem	ADJ
ejpam-6529	474	14	12	12	NUM
ejpam-6529	474	15	that	that	SCONJ
ejpam-6529	474	16	(	(	PUNCT
ejpam-6529	474	17	b∗	b∗	ADJ
ejpam-6529	474	18	,	,	PUNCT
ejpam-6529	474	19	(	(	PUNCT
ejpam-6529	474	20	s	s	X
ejpam-6529	474	21	,	,	PUNCT
ejpam-6529	474	22	t))q	t))q	NOUN
ejpam-6529	474	23	is	be	AUX
ejpam-6529	474	24	a	a	DET
ejpam-6529	474	25	weak	weak	ADJ
ejpam-6529	474	26	filter	filter	NOUN
ejpam-6529	474	27	of	of	ADP
ejpam-6529	474	28	x	x	X
ejpam-6529	474	29	:	:	PUNCT
ejpam-6529	474	30	=	=	SYM
ejpam-6529	474	31	(	(	PUNCT
ejpam-6529	474	32	x	x	NOUN
ejpam-6529	474	33	,	,	PUNCT
ejpam-6529	474	34	|	|	NOUN
ejpam-6529	474	35	)	)	PUNCT
ejpam-6529	474	36	.	.	PUNCT
ejpam-6529	475	1	4	4	X
ejpam-6529	475	2	.	.	X
ejpam-6529	475	3	conclusion	conclusion	NOUN
ejpam-6529	475	4	this	this	DET
ejpam-6529	475	5	work	work	NOUN
ejpam-6529	475	6	aims	aim	VERB
ejpam-6529	475	7	to	to	PART
ejpam-6529	475	8	advance	advance	VERB
ejpam-6529	475	9	the	the	DET
ejpam-6529	475	10	theoretical	theoretical	ADJ
ejpam-6529	475	11	framework	framework	NOUN
ejpam-6529	475	12	of	of	ADP
ejpam-6529	475	13	schaeffer	schaeffer	PROPN
ejpam-6529	475	14	stroke	stroke	PROPN
ejpam-6529	475	15	hilbert	hilbert	PROPN
ejpam-6529	475	16	algebras	algebras	PROPN
ejpam-6529	475	17	using	use	VERB
ejpam-6529	475	18	intuitionistic	intuitionistic	ADJ
ejpam-6529	475	19	fuzzy	fuzzy	ADJ
ejpam-6529	475	20	points	point	NOUN
ejpam-6529	475	21	to	to	PART
ejpam-6529	475	22	develop	develop	VERB
ejpam-6529	475	23	weak	weak	ADJ
ejpam-6529	475	24	filters	filter	NOUN
ejpam-6529	475	25	.	.	PUNCT
ejpam-6529	476	1	we	we	PRON
ejpam-6529	476	2	have	have	AUX
ejpam-6529	476	3	introduced	introduce	VERB
ejpam-6529	476	4	the	the	DET
ejpam-6529	476	5	concept	concept	NOUN
ejpam-6529	476	6	of	of	ADP
ejpam-6529	476	7	intuitionistic	intuitionistic	ADJ
ejpam-6529	476	8	fuzzy	fuzzy	ADJ
ejpam-6529	476	9	weak	weak	ADJ
ejpam-6529	476	10	filters	filter	NOUN
ejpam-6529	476	11	in	in	ADP
ejpam-6529	476	12	sheffer	sheffer	PROPN
ejpam-6529	476	13	stroke	stroke	PROPN
ejpam-6529	476	14	hilbert	hilbert	PROPN
ejpam-6529	476	15	algebras	algebras	PROPN
ejpam-6529	476	16	,	,	PUNCT
ejpam-6529	476	17	and	and	CCONJ
ejpam-6529	476	18	have	have	AUX
ejpam-6529	476	19	investigated	investigate	VERB
ejpam-6529	476	20	several	several	ADJ
ejpam-6529	476	21	properties	property	NOUN
ejpam-6529	476	22	.	.	PUNCT
ejpam-6529	477	1	we	we	PRON
ejpam-6529	477	2	have	have	AUX
ejpam-6529	477	3	explored	explore	VERB
ejpam-6529	477	4	the	the	DET
ejpam-6529	477	5	conditions	condition	NOUN
ejpam-6529	477	6	under	under	ADP
ejpam-6529	477	7	which	which	PRON
ejpam-6529	477	8	the	the	DET
ejpam-6529	477	9	intuitionistic	intuitionistic	ADJ
ejpam-6529	477	10	fuzzy	fuzzy	ADJ
ejpam-6529	477	11	set	set	NOUN
ejpam-6529	477	12	becomes	become	VERB
ejpam-6529	477	13	an	an	DET
ejpam-6529	477	14	intuitionistic	intuitionistic	ADJ
ejpam-6529	477	15	fuzzy	fuzzy	ADJ
ejpam-6529	477	16	weak	weak	ADJ
ejpam-6529	477	17	filter	filter	NOUN
ejpam-6529	477	18	.	.	PUNCT
ejpam-6529	478	1	we	we	PRON
ejpam-6529	478	2	have	have	AUX
ejpam-6529	478	3	discussed	discuss	VERB
ejpam-6529	478	4	the	the	DET
ejpam-6529	478	5	characterization	characterization	NOUN
ejpam-6529	478	6	of	of	ADP
ejpam-6529	478	7	intuitionistic	intuitionistic	ADJ
ejpam-6529	478	8	fuzzy	fuzzy	ADJ
ejpam-6529	478	9	weak	weak	ADJ
ejpam-6529	478	10	filters	filter	NOUN
ejpam-6529	478	11	.	.	PUNCT
ejpam-6529	479	1	forming	form	VERB
ejpam-6529	479	2	the	the	DET
ejpam-6529	479	3	(	(	PUNCT
ejpam-6529	479	4	0	0	NUM
ejpam-6529	479	5	;	;	PUNCT
ejpam-6529	479	6	1)-set	1)-set	NOUN
ejpam-6529	479	7	and	and	CCONJ
ejpam-6529	479	8	q	q	NOUN
ejpam-6529	479	9	-	-	PUNCT
ejpam-6529	479	10	set	set	NOUN
ejpam-6529	479	11	for	for	ADP
ejpam-6529	479	12	the	the	DET
ejpam-6529	479	13	intuitionistic	intuitionistic	ADJ
ejpam-6529	479	14	fuzzy	fuzzy	ADJ
ejpam-6529	479	15	set	set	NOUN
ejpam-6529	479	16	,	,	PUNCT
ejpam-6529	479	17	we	we	PRON
ejpam-6529	479	18	have	have	AUX
ejpam-6529	479	19	discussed	discuss	VERB
ejpam-6529	479	20	the	the	DET
ejpam-6529	479	21	phases	phase	NOUN
ejpam-6529	479	22	in	in	ADP
ejpam-6529	479	23	which	which	PRON
ejpam-6529	479	24	it	it	PRON
ejpam-6529	479	25	can	can	AUX
ejpam-6529	479	26	be	be	AUX
ejpam-6529	479	27	a	a	DET
ejpam-6529	479	28	weak	weak	ADJ
ejpam-6529	479	29	filter	filter	NOUN
ejpam-6529	479	30	.	.	PUNCT
ejpam-6529	480	1	based	base	VERB
ejpam-6529	480	2	on	on	ADP
ejpam-6529	480	3	the	the	DET
ejpam-6529	480	4	ideas	idea	NOUN
ejpam-6529	480	5	and	and	CCONJ
ejpam-6529	480	6	results	result	NOUN
ejpam-6529	480	7	of	of	ADP
ejpam-6529	480	8	this	this	DET
ejpam-6529	480	9	paper	paper	NOUN
ejpam-6529	480	10	,	,	PUNCT
ejpam-6529	480	11	we	we	PRON
ejpam-6529	480	12	will	will	AUX
ejpam-6529	480	13	study	study	VERB
ejpam-6529	480	14	the	the	DET
ejpam-6529	480	15	several	several	ADJ
ejpam-6529	480	16	types	type	NOUN
ejpam-6529	480	17	of	of	ADP
ejpam-6529	480	18	substructures	substructure	NOUN
ejpam-6529	480	19	using	use	VERB
ejpam-6529	480	20	intuitionistic	intuitionistic	ADJ
ejpam-6529	480	21	fuzzy	fuzzy	ADJ
ejpam-6529	480	22	points	point	NOUN
ejpam-6529	480	23	in	in	ADP
ejpam-6529	480	24	the	the	DET
ejpam-6529	480	25	study	study	NOUN
ejpam-6529	480	26	of	of	ADP
ejpam-6529	480	27	sheffer	sheffer	PROPN
ejpam-6529	480	28	stroke	stroke	NOUN
ejpam-6529	480	29	theory	theory	NOUN
ejpam-6529	480	30	for	for	ADP
ejpam-6529	480	31	various	various	ADJ
ejpam-6529	480	32	forms	form	NOUN
ejpam-6529	480	33	of	of	ADP
ejpam-6529	480	34	logical	logical	ADJ
ejpam-6529	480	35	algebras	algebra	NOUN
ejpam-6529	480	36	.	.	PUNCT
ejpam-6529	481	1	acknowledgments	acknowledgment	NOUN
ejpam-6529	481	2	the	the	DET
ejpam-6529	481	3	authors	author	NOUN
ejpam-6529	481	4	wish	wish	VERB
ejpam-6529	481	5	to	to	PART
ejpam-6529	481	6	thank	thank	VERB
ejpam-6529	481	7	the	the	DET
ejpam-6529	481	8	anonymous	anonymous	ADJ
ejpam-6529	481	9	reviewers	reviewer	NOUN
ejpam-6529	481	10	for	for	ADP
ejpam-6529	481	11	their	their	PRON
ejpam-6529	481	12	valuable	valuable	ADJ
ejpam-6529	481	13	suggestions	suggestion	NOUN
ejpam-6529	481	14	.	.	PUNCT
ejpam-6529	482	1	references	reference	NOUN
ejpam-6529	482	2	[	[	X
ejpam-6529	482	3	1	1	NUM
ejpam-6529	482	4	]	]	PUNCT
ejpam-6529	482	5	i.	i.	NOUN
ejpam-6529	482	6	chajad	chajad	PROPN
ejpam-6529	482	7	.	.	PUNCT
ejpam-6529	483	1	sheffer	sheffer	PROPN
ejpam-6529	483	2	operation	operation	NOUN
ejpam-6529	483	3	in	in	ADP
ejpam-6529	483	4	ortholattices	ortholattice	NOUN
ejpam-6529	483	5	.	.	PUNCT
ejpam-6529	484	1	acta	acta	PROPN
ejpam-6529	484	2	universitatis	universitatis	PROPN
ejpam-6529	484	3	palackianae	palackianae	VERB
ejpam-6529	484	4	olomucensis	olomucensis	NOUN
ejpam-6529	484	5	.	.	PUNCT
ejpam-6529	485	1	facultas	facultas	PROPN
ejpam-6529	485	2	rerum	rerum	PROPN
ejpam-6529	485	3	naturalium	naturalium	PROPN
ejpam-6529	485	4	.	.	PUNCT
ejpam-6529	486	1	mathematica	mathematica	PROPN
ejpam-6529	486	2	,	,	PUNCT
ejpam-6529	486	3	44(1):19–23	44(1):19–23	NUM
ejpam-6529	486	4	,	,	PUNCT
ejpam-6529	486	5	2005	2005	NUM
ejpam-6529	486	6	.	.	PUNCT
ejpam-6529	487	1	[	[	X
ejpam-6529	487	2	2	2	X
ejpam-6529	487	3	]	]	PUNCT
ejpam-6529	487	4	t.	t.	PROPN
ejpam-6529	487	5	katican	katican	PROPN
ejpam-6529	487	6	.	.	PUNCT
ejpam-6529	487	7	branchesm	branchesm	VERB
ejpam-6529	487	8	and	and	CCONJ
ejpam-6529	487	9	obstinate	obstinate	VERB
ejpam-6529	487	10	sbe	sbe	NOUN
ejpam-6529	487	11	-	-	PUNCT
ejpam-6529	487	12	filters	filter	NOUN
ejpam-6529	487	13	of	of	ADP
ejpam-6529	487	14	sheffer	sheffer	NOUN
ejpam-6529	487	15	stroke	stroke	NOUN
ejpam-6529	487	16	be	be	AUX
ejpam-6529	487	17	-	-	PUNCT
ejpam-6529	487	18	algebras	algebra	NOUN
ejpam-6529	487	19	.	.	PUNCT
ejpam-6529	488	1	bulletin	bulletin	NOUN
ejpam-6529	488	2	of	of	ADP
ejpam-6529	488	3	the	the	DET
ejpam-6529	488	4	international	international	ADJ
ejpam-6529	488	5	mathematical	mathematical	ADJ
ejpam-6529	488	6	virtual	virtual	PROPN
ejpam-6529	488	7	institute	institute	NOUN
ejpam-6529	488	8	,	,	PUNCT
ejpam-6529	488	9	12(1):41–50	12(1):41–50	NUM
ejpam-6529	488	10	,	,	PUNCT
ejpam-6529	488	11	2022	2022	NUM
ejpam-6529	488	12	.	.	PUNCT
ejpam-6529	489	1	[	[	X
ejpam-6529	489	2	3	3	X
ejpam-6529	489	3	]	]	PUNCT
ejpam-6529	489	4	v.	v.	CCONJ
ejpam-6529	489	5	kozarkiewicz	kozarkiewicz	PROPN
ejpam-6529	489	6	and	and	CCONJ
ejpam-6529	489	7	a.	a.	PROPN
ejpam-6529	489	8	grabowski	grabowski	PROPN
ejpam-6529	489	9	.	.	PUNCT
ejpam-6529	490	1	axiomatization	axiomatization	NOUN
ejpam-6529	490	2	of	of	ADP
ejpam-6529	490	3	boolean	boolean	ADJ
ejpam-6529	490	4	algebras	algebra	NOUN
ejpam-6529	490	5	based	base	VERB
ejpam-6529	490	6	on	on	ADP
ejpam-6529	490	7	sheffer	sheffer	PROPN
ejpam-6529	490	8	stroke	stroke	PROPN
ejpam-6529	490	9	.	.	PUNCT
ejpam-6529	491	1	formalized	formalize	VERB
ejpam-6529	491	2	mathematics	mathematic	NOUN
ejpam-6529	491	3	,	,	PUNCT
ejpam-6529	491	4	12(3):355–361	12(3):355–361	NUM
ejpam-6529	491	5	,	,	PUNCT
ejpam-6529	491	6	2004	2004	NUM
ejpam-6529	491	7	.	.	PUNCT
ejpam-6529	492	1	[	[	X
ejpam-6529	492	2	4	4	X
ejpam-6529	492	3	]	]	PUNCT
ejpam-6529	492	4	t.	t.	NOUN
ejpam-6529	492	5	oner	oner	NOUN
ejpam-6529	492	6	,	,	PUNCT
ejpam-6529	492	7	t.	t.	PROPN
ejpam-6529	492	8	katican	katican	PROPN
ejpam-6529	492	9	,	,	PUNCT
ejpam-6529	492	10	and	and	CCONJ
ejpam-6529	492	11	a.	a.	PROPN
ejpam-6529	492	12	borumand	borumand	PROPN
ejpam-6529	492	13	saeid	saeid	PROPN
ejpam-6529	492	14	.	.	PUNCT
ejpam-6529	493	1	fuzzy	fuzzy	ADJ
ejpam-6529	493	2	filters	filter	NOUN
ejpam-6529	493	3	of	of	ADP
ejpam-6529	493	4	sheffer	sheffer	PROPN
ejpam-6529	493	5	stroke	stroke	PROPN
ejpam-6529	493	6	hilbert	hilbert	PROPN
ejpam-6529	493	7	algebras	algebras	PROPN
ejpam-6529	493	8	.	.	PUNCT
ejpam-6529	494	1	journal	journal	PROPN
ejpam-6529	494	2	of	of	ADP
ejpam-6529	494	3	intelligent	intelligent	ADJ
ejpam-6529	494	4	&	&	CCONJ
ejpam-6529	494	5	fuzzy	fuzzy	ADJ
ejpam-6529	494	6	systems	system	NOUN
ejpam-6529	494	7	,	,	PUNCT
ejpam-6529	494	8	40(1):759–772	40(1):759–772	NOUN
ejpam-6529	494	9	,	,	PUNCT
ejpam-6529	494	10	2021	2021	NUM
ejpam-6529	494	11	.	.	PUNCT
ejpam-6529	495	1	[	[	X
ejpam-6529	495	2	5	5	X
ejpam-6529	495	3	]	]	PUNCT
ejpam-6529	495	4	t.	t.	NOUN
ejpam-6529	495	5	oner	oner	NOUN
ejpam-6529	495	6	,	,	PUNCT
ejpam-6529	495	7	t.	t.	PROPN
ejpam-6529	495	8	katican	katican	PROPN
ejpam-6529	495	9	,	,	PUNCT
ejpam-6529	495	10	and	and	CCONJ
ejpam-6529	495	11	a.	a.	PROPN
ejpam-6529	495	12	borumand	borumand	PROPN
ejpam-6529	495	13	saeid	saeid	PROPN
ejpam-6529	495	14	.	.	PUNCT
ejpam-6529	496	1	relation	relation	NOUN
ejpam-6529	496	2	between	between	ADP
ejpam-6529	496	3	sheffer	sheffer	PROPN
ejpam-6529	496	4	stroke	stroke	PROPN
ejpam-6529	496	5	and	and	CCONJ
ejpam-6529	496	6	hilbert	hilbert	PROPN
ejpam-6529	496	7	algebras	algebras	PROPN
ejpam-6529	496	8	.	.	PUNCT
ejpam-6529	496	9	categories	category	NOUN
ejpam-6529	496	10	and	and	CCONJ
ejpam-6529	496	11	general	general	ADJ
ejpam-6529	496	12	algebraic	algebraic	ADJ
ejpam-6529	496	13	structures	structure	NOUN
ejpam-6529	496	14	with	with	ADP
ejpam-6529	496	15	applications	application	NOUN
ejpam-6529	496	16	,	,	PUNCT
ejpam-6529	496	17	14(1):245–268	14(1):245–268	NUM
ejpam-6529	496	18	,	,	PUNCT
ejpam-6529	496	19	2021	2021	NUM
ejpam-6529	496	20	.	.	PUNCT
ejpam-6529	497	1	[	[	X
ejpam-6529	497	2	6	6	NUM
ejpam-6529	497	3	]	]	PUNCT
ejpam-6529	497	4	t.	t.	NOUN
ejpam-6529	497	5	oner	oner	NOUN
ejpam-6529	497	6	,	,	PUNCT
ejpam-6529	497	7	t.	t.	PROPN
ejpam-6529	497	8	katican	katican	PROPN
ejpam-6529	497	9	,	,	PUNCT
ejpam-6529	497	10	and	and	CCONJ
ejpam-6529	497	11	a.	a.	PROPN
ejpam-6529	497	12	borumand	borumand	PROPN
ejpam-6529	497	13	saeid	saeid	PROPN
ejpam-6529	497	14	.	.	PUNCT
ejpam-6529	497	15	bl	bl	VERB
ejpam-6529	497	16	-	-	PUNCT
ejpam-6529	497	17	algebras	algebras	PROPN
ejpam-6529	497	18	defined	define	VERB
ejpam-6529	497	19	by	by	ADP
ejpam-6529	497	20	an	an	DET
ejpam-6529	497	21	operator	operator	NOUN
ejpam-6529	497	22	.	.	PUNCT
ejpam-6529	498	1	honam	honam	PROPN
ejpam-6529	498	2	mathematical	mathematical	PROPN
ejpam-6529	498	3	journal	journal	PROPN
ejpam-6529	498	4	,	,	PUNCT
ejpam-6529	498	5	44(2):18–31	44(2):18–31	NUM
ejpam-6529	498	6	,	,	PUNCT
ejpam-6529	498	7	2022	2022	NUM
ejpam-6529	498	8	.	.	PUNCT
ejpam-6529	499	1	[	[	X
ejpam-6529	499	2	7	7	X
ejpam-6529	499	3	]	]	X
ejpam-6529	499	4	t.	t.	NOUN
ejpam-6529	499	5	oner	oner	NOUN
ejpam-6529	499	6	,	,	PUNCT
ejpam-6529	499	7	t.	t.	PROPN
ejpam-6529	499	8	katican	katican	PROPN
ejpam-6529	499	9	,	,	PUNCT
ejpam-6529	499	10	and	and	CCONJ
ejpam-6529	499	11	a.	a.	PROPN
ejpam-6529	499	12	borumand	borumand	PROPN
ejpam-6529	499	13	saeid	saeid	PROPN
ejpam-6529	499	14	.	.	PUNCT
ejpam-6529	500	1	class	class	NOUN
ejpam-6529	500	2	of	of	ADP
ejpam-6529	500	3	sheffer	sheffer	PROPN
ejpam-6529	500	4	stroke	stroke	NOUN
ejpam-6529	500	5	bck	bck	PROPN
ejpam-6529	500	6	-	-	PUNCT
ejpam-6529	500	7	algebras	algebras	PROPN
ejpam-6529	500	8	.	.	PUNCT
ejpam-6529	501	1	analele	analele	PROPN
ejpam-6529	501	2	s	s	PROPN
ejpam-6529	501	3	,	,	PUNCT
ejpam-6529	501	4	tiint	tiint	NOUN
ejpam-6529	501	5	,	,	PUNCT
ejpam-6529	501	6	ifice	ifice	ADJ
ejpam-6529	501	7	ale	ale	PROPN
ejpam-6529	501	8	universităt	universităt	PROPN
ejpam-6529	501	9	,	,	PUNCT
ejpam-6529	501	10	ii	ii	PROPN
ejpam-6529	501	11	“	"	PUNCT
ejpam-6529	501	12	ovidius	ovidius	NOUN
ejpam-6529	501	13	”	"	PUNCT
ejpam-6529	501	14	constant	constant	ADJ
ejpam-6529	501	15	,	,	PUNCT
ejpam-6529	501	16	a	a	DET
ejpam-6529	501	17	,	,	PUNCT
ejpam-6529	501	18	30(1):247–269	30(1):247–269	NOUN
ejpam-6529	501	19	,	,	PUNCT
ejpam-6529	501	20	2022	2022	NUM
ejpam-6529	501	21	.	.	PUNCT
ejpam-6529	502	1	s.	s.	PROPN
ejpam-6529	502	2	s.	s.	PROPN
ejpam-6529	502	3	ahn	ahn	PROPN
ejpam-6529	502	4	,	,	PUNCT
ejpam-6529	502	5	y.	y.	PROPN
ejpam-6529	502	6	j.	j.	PROPN
ejpam-6529	502	7	seo	seo	PROPN
ejpam-6529	502	8	,	,	PUNCT
ejpam-6529	502	9	y.	y.	PROPN
ejpam-6529	502	10	b.	b.	PROPN
ejpam-6529	502	11	jun	jun	PROPN
ejpam-6529	502	12	/	/	SYM
ejpam-6529	502	13	eur	eur	PROPN
ejpam-6529	502	14	.	.	PUNCT
ejpam-6529	503	1	j.	j.	PROPN
ejpam-6529	503	2	pure	pure	PROPN
ejpam-6529	503	3	appl	appl	PROPN
ejpam-6529	503	4	.	.	PROPN
ejpam-6529	503	5	math	math	PROPN
ejpam-6529	503	6	,	,	PUNCT
ejpam-6529	503	7	18	18	NUM
ejpam-6529	503	8	(	(	PUNCT
ejpam-6529	503	9	3	3	NUM
ejpam-6529	503	10	)	)	PUNCT
ejpam-6529	503	11	(	(	PUNCT
ejpam-6529	503	12	2025	2025	NUM
ejpam-6529	503	13	)	)	PUNCT
ejpam-6529	503	14	,	,	PUNCT
ejpam-6529	503	15	6529	6529	NUM
ejpam-6529	503	16	16	16	NUM
ejpam-6529	503	17	of	of	ADP
ejpam-6529	503	18	16	16	NUM
ejpam-6529	504	1	[	[	X
ejpam-6529	504	2	8	8	NUM
ejpam-6529	504	3	]	]	PUNCT
ejpam-6529	504	4	t.	t.	NOUN
ejpam-6529	504	5	oner	oner	NOUN
ejpam-6529	504	6	,	,	PUNCT
ejpam-6529	504	7	t.	t.	PROPN
ejpam-6529	504	8	katican	katican	PROPN
ejpam-6529	504	9	,	,	PUNCT
ejpam-6529	504	10	a.	a.	PROPN
ejpam-6529	504	11	borumand	borumand	PROPN
ejpam-6529	504	12	saeid	saeid	PROPN
ejpam-6529	504	13	,	,	PUNCT
ejpam-6529	504	14	and	and	CCONJ
ejpam-6529	504	15	m.	m.	NOUN
ejpam-6529	504	16	terziler	terziler	PROPN
ejpam-6529	504	17	.	.	PUNCT
ejpam-6529	505	1	filters	filter	NOUN
ejpam-6529	505	2	of	of	ADP
ejpam-6529	505	3	strong	strong	ADJ
ejpam-6529	505	4	sheffer	sheffer	NOUN
ejpam-6529	505	5	stroke	stroke	NOUN
ejpam-6529	505	6	non	non	ADJ
ejpam-6529	505	7	-	-	ADJ
ejpam-6529	505	8	associative	associative	ADJ
ejpam-6529	505	9	mv	mv	NOUN
ejpam-6529	505	10	-	-	PUNCT
ejpam-6529	505	11	algebras	algebras	X
ejpam-6529	505	12	.	.	PUNCT
ejpam-6529	506	1	analele	analele	PROPN
ejpam-6529	506	2	s	s	PROPN
ejpam-6529	506	3	,	,	PUNCT
ejpam-6529	506	4	tiint	tiint	NOUN
ejpam-6529	506	5	,	,	PUNCT
ejpam-6529	506	6	ifice	ifice	ADJ
ejpam-6529	506	7	ale	ale	PROPN
ejpam-6529	506	8	universităt	universităt	PROPN
ejpam-6529	506	9	,	,	PUNCT
ejpam-6529	506	10	ii	ii	PROPN
ejpam-6529	506	11	“	"	PUNCT
ejpam-6529	506	12	ovidius	ovidius	NOUN
ejpam-6529	506	13	”	"	PUNCT
ejpam-6529	506	14	constant	constant	ADJ
ejpam-6529	506	15	,	,	PUNCT
ejpam-6529	506	16	a	a	PRON
ejpam-6529	506	17	,	,	PUNCT
ejpam-6529	506	18	29(1):143–164	29(1):143–164	NOUN
ejpam-6529	506	19	,	,	PUNCT
ejpam-6529	506	20	2021	2021	NUM
ejpam-6529	506	21	.	.	PUNCT
ejpam-6529	507	1	[	[	X
ejpam-6529	507	2	9	9	NUM
ejpam-6529	507	3	]	]	PUNCT
ejpam-6529	507	4	t.	t.	NOUN
ejpam-6529	507	5	oner	oner	NOUN
ejpam-6529	507	6	,	,	PUNCT
ejpam-6529	507	7	n.	n.	PROPN
ejpam-6529	507	8	rajesh	rajesh	PROPN
ejpam-6529	507	9	,	,	PUNCT
ejpam-6529	507	10	a.	a.	NOUN
ejpam-6529	507	11	iampan	iampan	PROPN
ejpam-6529	507	12	,	,	PUNCT
ejpam-6529	507	13	and	and	CCONJ
ejpam-6529	507	14	a.	a.	PROPN
ejpam-6529	507	15	borumand	borumand	PROPN
ejpam-6529	507	16	saeid	saeid	PROPN
ejpam-6529	507	17	.	.	PUNCT
ejpam-6529	507	18	soft	soft	ADJ
ejpam-6529	507	19	subalgebras	subalgebra	NOUN
ejpam-6529	507	20	and	and	CCONJ
ejpam-6529	507	21	ideals	ideal	NOUN
ejpam-6529	507	22	of	of	ADP
ejpam-6529	507	23	sheffer	sheffer	PROPN
ejpam-6529	507	24	stroke	stroke	PROPN
ejpam-6529	507	25	hilbert	hilbert	PROPN
ejpam-6529	507	26	algebras	algebras	PROPN
ejpam-6529	507	27	based	base	VERB
ejpam-6529	507	28	on	on	ADP
ejpam-6529	507	29	n	n	CCONJ
ejpam-6529	507	30	-	-	PUNCT
ejpam-6529	507	31	structures	structure	NOUN
ejpam-6529	507	32	.	.	PUNCT
ejpam-6529	508	1	european	european	ADJ
ejpam-6529	508	2	journal	journal	PROPN
ejpam-6529	508	3	of	of	ADP
ejpam-6529	508	4	pure	pure	ADJ
ejpam-6529	508	5	and	and	CCONJ
ejpam-6529	508	6	applied	applied	ADJ
ejpam-6529	508	7	mathematics	mathematic	NOUN
ejpam-6529	508	8	,	,	PUNCT
ejpam-6529	508	9	18(2):6018	18(2):6018	NUM
ejpam-6529	508	10	,	,	PUNCT
ejpam-6529	508	11	2025	2025	NUM
ejpam-6529	508	12	.	.	PUNCT
ejpam-6529	509	1	[	[	X
ejpam-6529	509	2	10	10	NUM
ejpam-6529	509	3	]	]	X
ejpam-6529	509	4	n.	n.	PROPN
ejpam-6529	509	5	rajesh	rajesh	PROPN
ejpam-6529	509	6	,	,	PUNCT
ejpam-6529	509	7	t.	t.	PROPN
ejpam-6529	509	8	oner	oner	NOUN
ejpam-6529	509	9	,	,	PUNCT
ejpam-6529	509	10	a.	a.	NOUN
ejpam-6529	509	11	iampan	iampan	PROPN
ejpam-6529	509	12	,	,	PUNCT
ejpam-6529	509	13	and	and	CCONJ
ejpam-6529	509	14	a.	a.	NOUN
ejpam-6529	509	15	rezaei	rezaei	PROPN
ejpam-6529	509	16	.	.	PUNCT
ejpam-6529	510	1	investigating	investigate	VERB
ejpam-6529	510	2	length	length	NOUN
ejpam-6529	510	3	and	and	CCONJ
ejpam-6529	510	4	mean	mean	ADJ
ejpam-6529	510	5	-	-	PUNCT
ejpam-6529	510	6	fuzzy	fuzzy	ADJ
ejpam-6529	510	7	subalgebras	subalgebra	NOUN
ejpam-6529	510	8	in	in	ADP
ejpam-6529	510	9	sheffer	sheffer	PROPN
ejpam-6529	510	10	stroke	stroke	PROPN
ejpam-6529	510	11	hilbert	hilbert	PROPN
ejpam-6529	510	12	algebras	algebras	PROPN
ejpam-6529	510	13	.	.	PUNCT
ejpam-6529	511	1	european	european	PROPN
ejpam-6529	511	2	journal	journal	PROPN
ejpam-6529	511	3	of	of	ADP
ejpam-6529	511	4	pure	pure	ADJ
ejpam-6529	511	5	and	and	CCONJ
ejpam-6529	511	6	applied	applied	ADJ
ejpam-6529	511	7	mathematics	mathematic	NOUN
ejpam-6529	511	8	,	,	PUNCT
ejpam-6529	511	9	18(2):5914	18(2):5914	NUM
ejpam-6529	511	10	,	,	PUNCT
ejpam-6529	511	11	2025	2025	NUM
ejpam-6529	511	12	.	.	PUNCT
ejpam-6529	512	1	[	[	X
ejpam-6529	512	2	11	11	NUM
ejpam-6529	512	3	]	]	X
ejpam-6529	512	4	n.	n.	PROPN
ejpam-6529	512	5	rajesh	rajesh	PROPN
ejpam-6529	512	6	,	,	PUNCT
ejpam-6529	512	7	t.	t.	PROPN
ejpam-6529	512	8	oner	oner	NOUN
ejpam-6529	512	9	,	,	PUNCT
ejpam-6529	512	10	a.	a.	NOUN
ejpam-6529	512	11	iampan	iampan	PROPN
ejpam-6529	512	12	,	,	PUNCT
ejpam-6529	512	13	and	and	CCONJ
ejpam-6529	512	14	i.	i.	PROPN
ejpam-6529	512	15	senturk	senturk	PROPN
ejpam-6529	512	16	.	.	PUNCT
ejpam-6529	513	1	on	on	ADP
ejpam-6529	513	2	length	length	NOUN
ejpam-6529	513	3	and	and	CCONJ
ejpam-6529	513	4	mean	mean	VERB
ejpam-6529	513	5	fuzzy	fuzzy	ADJ
ejpam-6529	513	6	ideals	ideal	NOUN
ejpam-6529	513	7	of	of	ADP
ejpam-6529	513	8	sheffer	sheffer	PROPN
ejpam-6529	513	9	stroke	stroke	PROPN
ejpam-6529	513	10	hilbert	hilbert	PROPN
ejpam-6529	513	11	algebras	algebras	PROPN
ejpam-6529	513	12	.	.	PUNCT
ejpam-6529	514	1	european	european	PROPN
ejpam-6529	514	2	journal	journal	PROPN
ejpam-6529	514	3	of	of	ADP
ejpam-6529	514	4	pure	pure	ADJ
ejpam-6529	514	5	and	and	CCONJ
ejpam-6529	514	6	applied	applied	ADJ
ejpam-6529	514	7	mathematics	mathematic	NOUN
ejpam-6529	514	8	,	,	PUNCT
ejpam-6529	514	9	18(1):5779	18(1):5779	NUM
ejpam-6529	514	10	,	,	PUNCT
ejpam-6529	514	11	2025	2025	NUM
ejpam-6529	514	12	.	.	PUNCT
ejpam-6529	515	1	[	[	X
ejpam-6529	515	2	12	12	NUM
ejpam-6529	515	3	]	]	X
ejpam-6529	515	4	p.	p.	NOUN
ejpam-6529	515	5	m.	m.	NOUN
ejpam-6529	515	6	pu	pu	PROPN
ejpam-6529	515	7	and	and	CCONJ
ejpam-6529	515	8	y.	y.	PROPN
ejpam-6529	515	9	m.	m.	PROPN
ejpam-6529	515	10	liu	liu	PROPN
ejpam-6529	515	11	.	.	PROPN
ejpam-6529	516	1	fuzzy	fuzzy	ADJ
ejpam-6529	516	2	topology	topology	NOUN
ejpam-6529	516	3	i	i	PRON
ejpam-6529	516	4	,	,	PUNCT
ejpam-6529	516	5	neighborhood	neighborhood	NOUN
ejpam-6529	516	6	structure	structure	NOUN
ejpam-6529	516	7	of	of	ADP
ejpam-6529	516	8	a	a	DET
ejpam-6529	516	9	fuzzy	fuzzy	ADJ
ejpam-6529	516	10	point	point	NOUN
ejpam-6529	516	11	and	and	CCONJ
ejpam-6529	516	12	moore	moore	PROPN
ejpam-6529	516	13	-	-	PUNCT
ejpam-6529	516	14	smith	smith	PROPN
ejpam-6529	516	15	convergence	convergence	NOUN
ejpam-6529	516	16	.	.	PUNCT
ejpam-6529	517	1	journal	journal	PROPN
ejpam-6529	517	2	of	of	ADP
ejpam-6529	517	3	mathematical	mathematical	ADJ
ejpam-6529	517	4	analysis	analysis	NOUN
ejpam-6529	517	5	and	and	CCONJ
ejpam-6529	517	6	applications	application	NOUN
ejpam-6529	517	7	,	,	PUNCT
ejpam-6529	517	8	76:571–599	76:571–599	NUM
ejpam-6529	517	9	,	,	PUNCT
ejpam-6529	517	10	1980	1980	NUM
ejpam-6529	517	11	.	.	PUNCT
ejpam-6529	518	1	[	[	X
ejpam-6529	518	2	13	13	NUM
ejpam-6529	518	3	]	]	X
ejpam-6529	518	4	y.	y.	PROPN
ejpam-6529	518	5	b.	b.	PROPN
ejpam-6529	518	6	jun	jun	PROPN
ejpam-6529	518	7	and	and	CCONJ
ejpam-6529	518	8	t.	t.	PROPN
ejpam-6529	518	9	oner	oner	NOUN
ejpam-6529	518	10	.	.	PUNCT
ejpam-6529	519	1	weak	weak	ADJ
ejpam-6529	519	2	filters	filter	NOUN
ejpam-6529	519	3	and	and	CCONJ
ejpam-6529	519	4	multipliers	multiplier	NOUN
ejpam-6529	519	5	in	in	ADP
ejpam-6529	519	6	sheffer	sheffer	PROPN
ejpam-6529	519	7	stroke	stroke	PROPN
ejpam-6529	519	8	hilbert	hilbert	PROPN
ejpam-6529	519	9	algebras	algebras	PROPN
ejpam-6529	519	10	.	.	PUNCT
ejpam-6529	520	1	palestine	palestine	PROPN
ejpam-6529	520	2	journal	journal	PROPN
ejpam-6529	520	3	of	of	ADP
ejpam-6529	520	4	mathematics	mathematic	NOUN
ejpam-6529	520	5	,	,	PUNCT
ejpam-6529	520	6	14(2):749–761	14(2):749–761	PROPN
ejpam-6529	520	7	,	,	PUNCT
ejpam-6529	520	8	2025	2025	NUM
ejpam-6529	520	9	.	.	PUNCT
ejpam-6529	521	1	[	[	X
ejpam-6529	521	2	14	14	NUM
ejpam-6529	521	3	]	]	X
ejpam-6529	521	4	h.	h.	PROPN
ejpam-6529	521	5	m.	m.	PROPN
ejpam-6529	521	6	sheffer	sheffer	PROPN
ejpam-6529	521	7	.	.	PUNCT
ejpam-6529	522	1	a	a	DET
ejpam-6529	522	2	set	set	NOUN
ejpam-6529	522	3	of	of	ADP
ejpam-6529	522	4	five	five	NUM
ejpam-6529	522	5	independent	independent	ADJ
ejpam-6529	522	6	postulates	postulate	NOUN
ejpam-6529	522	7	for	for	ADP
ejpam-6529	522	8	boolean	boolean	ADJ
ejpam-6529	522	9	algebras	algebra	NOUN
ejpam-6529	522	10	.	.	PUNCT
ejpam-6529	523	1	transactions	transaction	NOUN
ejpam-6529	523	2	of	of	ADP
ejpam-6529	523	3	the	the	DET
ejpam-6529	523	4	american	american	PROPN
ejpam-6529	523	5	mathematical	mathematical	PROPN
ejpam-6529	523	6	society	society	NOUN
ejpam-6529	523	7	,	,	PUNCT
ejpam-6529	523	8	14(4):481–488	14(4):481–488	NUM
ejpam-6529	523	9	,	,	PUNCT
ejpam-6529	523	10	1913	1913	NUM
ejpam-6529	523	11	.	.	PUNCT
ejpam-6529	524	1	[	[	X
ejpam-6529	524	2	15	15	NUM
ejpam-6529	524	3	]	]	X
ejpam-6529	524	4	k.	k.	PROPN
ejpam-6529	524	5	t.	t.	PROPN
ejpam-6529	524	6	atanassov	atanassov	PROPN
ejpam-6529	524	7	.	.	PUNCT
ejpam-6529	525	1	intuitionistic	intuitionistic	ADJ
ejpam-6529	525	2	fuzzy	fuzzy	ADJ
ejpam-6529	525	3	sets	set	NOUN
ejpam-6529	525	4	.	.	PUNCT
ejpam-6529	526	1	fuzzy	fuzzy	ADJ
ejpam-6529	526	2	sets	set	NOUN
ejpam-6529	526	3	and	and	CCONJ
ejpam-6529	526	4	systems	system	NOUN
ejpam-6529	526	5	,	,	PUNCT
ejpam-6529	526	6	20(1):87–96	20(1):87–96	NUM
ejpam-6529	526	7	,	,	PUNCT
ejpam-6529	526	8	1986	1986	NUM
ejpam-6529	526	9	.	.	PUNCT
ejpam-6529	527	1	[	[	X
ejpam-6529	527	2	16	16	NUM
ejpam-6529	527	3	]	]	PUNCT
ejpam-6529	527	4	a.	a.	PROPN
ejpam-6529	527	5	borumand	borumand	PROPN
ejpam-6529	527	6	saeid	saeid	PROPN
ejpam-6529	527	7	,	,	PUNCT
ejpam-6529	527	8	t.	t.	PROPN
ejpam-6529	527	9	oner	oner	NOUN
ejpam-6529	527	10	,	,	PUNCT
ejpam-6529	527	11	and	and	CCONJ
ejpam-6529	527	12	y.	y.	PROPN
ejpam-6529	527	13	b.	b.	PROPN
ejpam-6529	527	14	jun	jun	PROPN
ejpam-6529	527	15	.	.	PROPN
ejpam-6529	528	1	intuitionistic	intuitionistic	ADJ
ejpam-6529	528	2	fuzzy	fuzzy	ADJ
ejpam-6529	528	3	filters	filter	NOUN
ejpam-6529	528	4	in	in	ADP
ejpam-6529	528	5	sheffer	sheffer	PROPN
ejpam-6529	528	6	stroke	stroke	PROPN
ejpam-6529	528	7	hilbert	hilbert	PROPN
ejpam-6529	528	8	algebras	algebras	PROPN
ejpam-6529	528	9	.	.	PUNCT
ejpam-6529	529	1	journal	journal	PROPN
ejpam-6529	529	2	of	of	ADP
ejpam-6529	529	3	mathematical	mathematical	ADJ
ejpam-6529	529	4	extension	extension	NOUN
ejpam-6529	529	5	,	,	PUNCT
ejpam-6529	529	6	18(10):1–20	18(10):1–20	NUM
ejpam-6529	529	7	,	,	PUNCT
ejpam-6529	529	8	2024	2024	NUM
ejpam-6529	529	9	.	.	PUNCT