id	sid	tid	token	lemma	pos
ejpam-4446	1	1	european	european	PROPN
ejpam-4446	1	2	journal	journal	PROPN
ejpam-4446	1	3	of	of	ADP
ejpam-4446	1	4	pure	pure	ADJ
ejpam-4446	1	5	and	and	CCONJ
ejpam-4446	1	6	applied	apply	VERB
ejpam-4446	1	7	mathematics	mathematic	NOUN
ejpam-4446	1	8	vol	vol	NOUN
ejpam-4446	1	9	.	.	PROPN
ejpam-4446	2	1	15	15	NUM
ejpam-4446	2	2	,	,	PUNCT
ejpam-4446	2	3	no	no	INTJ
ejpam-4446	2	4	.	.	NOUN
ejpam-4446	2	5	3	3	NUM
ejpam-4446	2	6	,	,	PUNCT
ejpam-4446	2	7	2022	2022	NUM
ejpam-4446	2	8	,	,	PUNCT
ejpam-4446	2	9	924	924	NUM
ejpam-4446	2	10	-	-	SYM
ejpam-4446	2	11	937	937	NUM
ejpam-4446	2	12	issn	issn	PROPN
ejpam-4446	2	13	1307	1307	NUM
ejpam-4446	2	14	-	-	SYM
ejpam-4446	2	15	5543	5543	NUM
ejpam-4446	2	16	–	–	PUNCT
ejpam-4446	2	17	ejpam.com	ejpam.com	X
ejpam-4446	2	18	published	publish	VERB
ejpam-4446	2	19	by	by	ADP
ejpam-4446	2	20	new	new	PROPN
ejpam-4446	2	21	york	york	PROPN
ejpam-4446	2	22	business	business	PROPN
ejpam-4446	2	23	global	global	PROPN
ejpam-4446	2	24	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	2	25	fuzzy	fuzzy	ADJ
ejpam-4446	2	26	be	be	AUX
ejpam-4446	2	27	-	-	PUNCT
ejpam-4446	2	28	algebras	algebra	VERB
ejpam-4446	2	29	and	and	CCONJ
ejpam-4446	2	30	be	be	NOUN
ejpam-4446	2	31	-	-	PUNCT
ejpam-4446	2	32	filters	filter	NOUN
ejpam-4446	2	33	young	young	ADJ
ejpam-4446	2	34	bae	bae	PROPN
ejpam-4446	2	35	jun1	jun1	PROPN
ejpam-4446	2	36	,	,	PUNCT
ejpam-4446	2	37	sun	sun	PROPN
ejpam-4446	2	38	shin	shin	NOUN
ejpam-4446	2	39	ahn2,∗	ahn2,∗	PROPN
ejpam-4446	2	40	1	1	NUM
ejpam-4446	2	41	department	department	NOUN
ejpam-4446	2	42	of	of	ADP
ejpam-4446	2	43	mathematics	mathematics	PROPN
ejpam-4446	2	44	education	education	NOUN
ejpam-4446	2	45	,	,	PUNCT
ejpam-4446	2	46	gyeongsang	gyeongsang	PROPN
ejpam-4446	2	47	national	national	PROPN
ejpam-4446	2	48	university	university	PROPN
ejpam-4446	2	49	,	,	PUNCT
ejpam-4446	2	50	jinju	jinju	NOUN
ejpam-4446	2	51	52828	52828	NUM
ejpam-4446	2	52	,	,	PUNCT
ejpam-4446	2	53	korea	korea	PROPN
ejpam-4446	2	54	2	2	NUM
ejpam-4446	2	55	department	department	NOUN
ejpam-4446	2	56	of	of	ADP
ejpam-4446	2	57	mathematics	mathematics	PROPN
ejpam-4446	2	58	education	education	NOUN
ejpam-4446	2	59	,	,	PUNCT
ejpam-4446	2	60	dongguk	dongguk	PROPN
ejpam-4446	2	61	university	university	PROPN
ejpam-4446	2	62	,	,	PUNCT
ejpam-4446	2	63	seoul	seoul	PROPN
ejpam-4446	2	64	04620	04620	NUM
ejpam-4446	2	65	,	,	PUNCT
ejpam-4446	2	66	korea	korea	PROPN
ejpam-4446	2	67	abstract	abstract	NOUN
ejpam-4446	2	68	.	.	PUNCT
ejpam-4446	3	1	by	by	ADP
ejpam-4446	3	2	applying	apply	VERB
ejpam-4446	3	3	the	the	DET
ejpam-4446	3	4	concept	concept	NOUN
ejpam-4446	3	5	of	of	ADP
ejpam-4446	3	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	3	7	fuzzy	fuzzy	ADJ
ejpam-4446	3	8	set	set	VERB
ejpam-4446	3	9	to	to	PART
ejpam-4446	3	10	be	be	AUX
ejpam-4446	3	11	-	-	PUNCT
ejpam-4446	3	12	algebras	algebra	NOUN
ejpam-4446	3	13	,	,	PUNCT
ejpam-4446	3	14	the	the	DET
ejpam-4446	3	15	notions	notion	NOUN
ejpam-4446	3	16	of	of	ADP
ejpam-4446	3	17	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	3	18	fuzzy	fuzzy	ADJ
ejpam-4446	3	19	be	be	NOUN
ejpam-4446	3	20	-	-	PUNCT
ejpam-4446	3	21	algebra	algebra	NOUN
ejpam-4446	3	22	and	and	CCONJ
ejpam-4446	3	23	lukasiewicz	lukasiewicz	VERB
ejpam-4446	3	24	fuzzy	fuzzy	ADJ
ejpam-4446	3	25	be	be	NOUN
ejpam-4446	3	26	-	-	PUNCT
ejpam-4446	3	27	filter	filter	NOUN
ejpam-4446	3	28	are	be	AUX
ejpam-4446	3	29	introduced	introduce	VERB
ejpam-4446	3	30	,	,	PUNCT
ejpam-4446	3	31	and	and	CCONJ
ejpam-4446	3	32	their	their	PRON
ejpam-4446	3	33	properties	property	NOUN
ejpam-4446	3	34	are	be	AUX
ejpam-4446	3	35	investigated	investigate	VERB
ejpam-4446	3	36	.	.	PUNCT
ejpam-4446	4	1	characterizations	characterization	NOUN
ejpam-4446	4	2	of	of	ADP
ejpam-4446	4	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	4	4	fuzzy	fuzzy	ADJ
ejpam-4446	4	5	be	be	NOUN
ejpam-4446	4	6	-	-	PUNCT
ejpam-4446	4	7	algebra	algebra	NOUN
ejpam-4446	4	8	and	and	CCONJ
ejpam-4446	4	9	lukasiewicz	lukasiewicz	VERB
ejpam-4446	4	10	fuzzy	fuzzy	ADJ
ejpam-4446	4	11	be	be	NOUN
ejpam-4446	4	12	-	-	PUNCT
ejpam-4446	4	13	filter	filter	NOUN
ejpam-4446	4	14	are	be	AUX
ejpam-4446	4	15	discussed	discuss	VERB
ejpam-4446	4	16	,	,	PUNCT
ejpam-4446	4	17	and	and	CCONJ
ejpam-4446	4	18	the	the	DET
ejpam-4446	4	19	relationship	relationship	NOUN
ejpam-4446	4	20	between	between	ADP
ejpam-4446	4	21	fuzzy	fuzzy	ADJ
ejpam-4446	4	22	be	be	NOUN
ejpam-4446	4	23	-	-	PUNCT
ejpam-4446	4	24	algebra	algebra	NOUN
ejpam-4446	4	25	(	(	PUNCT
ejpam-4446	4	26	resp	resp	NOUN
ejpam-4446	4	27	.	.	PUNCT
ejpam-4446	4	28	,	,	PUNCT
ejpam-4446	4	29	fuzzy	fuzzy	ADJ
ejpam-4446	4	30	be	be	NOUN
ejpam-4446	4	31	-	-	PUNCT
ejpam-4446	4	32	filter	filter	NOUN
ejpam-4446	4	33	)	)	PUNCT
ejpam-4446	4	34	and	and	CCONJ
ejpam-4446	4	35	lukasiewicz	lukasiewicz	VERB
ejpam-4446	4	36	fuzzy	fuzzy	ADJ
ejpam-4446	4	37	be	be	NOUN
ejpam-4446	4	38	-	-	PUNCT
ejpam-4446	4	39	algebra	algebra	NOUN
ejpam-4446	4	40	(	(	PUNCT
ejpam-4446	4	41	resp	resp	NOUN
ejpam-4446	4	42	.	.	PUNCT
ejpam-4446	4	43	,	,	PUNCT
ejpam-4446	4	44	lukasiewicz	lukasiewicz	VERB
ejpam-4446	4	45	fuzzy	fuzzy	ADJ
ejpam-4446	4	46	be	be	NOUN
ejpam-4446	4	47	-	-	PUNCT
ejpam-4446	4	48	filter	filter	NOUN
ejpam-4446	4	49	)	)	PUNCT
ejpam-4446	4	50	is	be	AUX
ejpam-4446	4	51	established	establish	VERB
ejpam-4446	4	52	.	.	PUNCT
ejpam-4446	5	1	the	the	DET
ejpam-4446	5	2	conditions	condition	NOUN
ejpam-4446	5	3	for	for	ADP
ejpam-4446	5	4	the	the	DET
ejpam-4446	5	5	∈-set	∈-set	NOUN
ejpam-4446	5	6	,	,	PUNCT
ejpam-4446	5	7	q	q	NOUN
ejpam-4446	5	8	-	-	PUNCT
ejpam-4446	5	9	set	set	VERB
ejpam-4446	5	10	and	and	CCONJ
ejpam-4446	5	11	o	o	NOUN
ejpam-4446	5	12	-	-	PUNCT
ejpam-4446	5	13	set	set	NOUN
ejpam-4446	5	14	of	of	ADP
ejpam-4446	5	15	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	5	16	fuzzy	fuzzy	ADJ
ejpam-4446	5	17	set	set	VERB
ejpam-4446	5	18	to	to	PART
ejpam-4446	5	19	be	be	AUX
ejpam-4446	5	20	be	be	AUX
ejpam-4446	5	21	-	-	PUNCT
ejpam-4446	5	22	subalgebras	subalgebra	NOUN
ejpam-4446	5	23	are	be	AUX
ejpam-4446	5	24	explored	explore	VERB
ejpam-4446	5	25	.	.	PUNCT
ejpam-4446	6	1	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	6	2	fuzzy	fuzzy	ADJ
ejpam-4446	6	3	be	be	NOUN
ejpam-4446	6	4	-	-	PUNCT
ejpam-4446	6	5	filter	filter	NOUN
ejpam-4446	6	6	is	be	AUX
ejpam-4446	6	7	created	create	VERB
ejpam-4446	6	8	by	by	ADP
ejpam-4446	6	9	using	use	VERB
ejpam-4446	6	10	be	be	NOUN
ejpam-4446	6	11	-	-	PUNCT
ejpam-4446	6	12	filter	filter	NOUN
ejpam-4446	6	13	.	.	PUNCT
ejpam-4446	7	1	2020	2020	NUM
ejpam-4446	7	2	mathematics	mathematic	NOUN
ejpam-4446	7	3	subject	subject	NOUN
ejpam-4446	7	4	classifications	classification	NOUN
ejpam-4446	7	5	:	:	PUNCT
ejpam-4446	7	6	03g25	03g25	NUM
ejpam-4446	7	7	,	,	PUNCT
ejpam-4446	7	8	06f35	06f35	NUM
ejpam-4446	7	9	,	,	PUNCT
ejpam-4446	7	10	08a72	08a72	NOUN
ejpam-4446	7	11	key	key	ADJ
ejpam-4446	7	12	words	word	NOUN
ejpam-4446	7	13	and	and	CCONJ
ejpam-4446	7	14	phrases	phrase	NOUN
ejpam-4446	7	15	:	:	PUNCT
ejpam-4446	7	16	lukasiewicz	lukasiewicz	VERB
ejpam-4446	7	17	fuzzy	fuzzy	ADJ
ejpam-4446	7	18	be	be	NOUN
ejpam-4446	7	19	-	-	PUNCT
ejpam-4446	7	20	algebra	algebra	NOUN
ejpam-4446	7	21	,	,	PUNCT
ejpam-4446	7	22	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	7	23	fuzzy	fuzzy	ADJ
ejpam-4446	7	24	be	be	NOUN
ejpam-4446	7	25	-	-	PUNCT
ejpam-4446	7	26	filter	filter	NOUN
ejpam-4446	7	27	,	,	PUNCT
ejpam-4446	7	28	∈-set	∈-set	NOUN
ejpam-4446	7	29	,	,	PUNCT
ejpam-4446	7	30	q	q	NOUN
ejpam-4446	7	31	-	-	PUNCT
ejpam-4446	7	32	set	set	ADJ
ejpam-4446	7	33	,	,	PUNCT
ejpam-4446	7	34	o	o	NOUN
ejpam-4446	7	35	-	-	PUNCT
ejpam-4446	7	36	set	set	ADJ
ejpam-4446	7	37	.	.	PUNCT
ejpam-4446	8	1	1	1	X
ejpam-4446	8	2	.	.	X
ejpam-4446	8	3	introduction	introduction	NOUN
ejpam-4446	8	4	bck	bck	NOUN
ejpam-4446	8	5	-	-	PUNCT
ejpam-4446	8	6	algebra	algebra	PROPN
ejpam-4446	8	7	and	and	CCONJ
ejpam-4446	8	8	bci	bci	NOUN
ejpam-4446	8	9	-	-	NOUN
ejpam-4446	8	10	algebra	algebra	NOUN
ejpam-4446	8	11	,	,	PUNCT
ejpam-4446	8	12	introduced	introduce	VERB
ejpam-4446	8	13	by	by	ADP
ejpam-4446	8	14	y.	y.	PROPN
ejpam-4446	8	15	imai	imai	PROPN
ejpam-4446	8	16	,	,	PUNCT
ejpam-4446	8	17	k.	k.	PROPN
ejpam-4446	8	18	iséki	iséki	PROPN
ejpam-4446	8	19	and	and	CCONJ
ejpam-4446	8	20	s.	s.	PROPN
ejpam-4446	8	21	tanaka	tanaka	PROPN
ejpam-4446	8	22	in	in	ADP
ejpam-4446	8	23	1966	1966	NUM
ejpam-4446	8	24	,	,	PUNCT
ejpam-4446	8	25	are	be	AUX
ejpam-4446	8	26	algebraic	algebraic	ADJ
ejpam-4446	8	27	structures	structure	NOUN
ejpam-4446	8	28	of	of	ADP
ejpam-4446	8	29	universal	universal	ADJ
ejpam-4446	8	30	algebra	algebra	NOUN
ejpam-4446	8	31	which	which	PRON
ejpam-4446	8	32	describe	describe	VERB
ejpam-4446	8	33	fragments	fragment	NOUN
ejpam-4446	8	34	of	of	ADP
ejpam-4446	8	35	propositional	propositional	ADJ
ejpam-4446	8	36	calculus	calculus	NOUN
ejpam-4446	8	37	related	relate	VERB
ejpam-4446	8	38	to	to	ADP
ejpam-4446	8	39	implications	implication	NOUN
ejpam-4446	8	40	known	know	VERB
ejpam-4446	8	41	as	as	ADP
ejpam-4446	8	42	bck	bck	NOUN
ejpam-4446	8	43	and	and	CCONJ
ejpam-4446	8	44	bci	bci	NOUN
ejpam-4446	8	45	-	-	NOUN
ejpam-4446	8	46	logic	logic	NOUN
ejpam-4446	8	47	.	.	PUNCT
ejpam-4446	9	1	after	after	ADP
ejpam-4446	9	2	that	that	PRON
ejpam-4446	9	3	,	,	PUNCT
ejpam-4446	9	4	various	various	ADJ
ejpam-4446	9	5	generalizations	generalization	NOUN
ejpam-4446	9	6	were	be	AUX
ejpam-4446	9	7	attempted	attempt	VERB
ejpam-4446	9	8	,	,	PUNCT
ejpam-4446	9	9	and	and	CCONJ
ejpam-4446	9	10	bcc	bcc	PROPN
ejpam-4446	9	11	-	-	PUNCT
ejpam-4446	9	12	algebras	algebras	PROPN
ejpam-4446	9	13	,	,	PUNCT
ejpam-4446	9	14	bch	bch	PROPN
ejpam-4446	9	15	-	-	PUNCT
ejpam-4446	9	16	algebras	algebras	PROPN
ejpam-4446	9	17	,	,	PUNCT
ejpam-4446	9	18	bh	bh	NOUN
ejpam-4446	9	19	-	-	PUNCT
ejpam-4446	9	20	algebras	algebras	PROPN
ejpam-4446	9	21	,	,	PUNCT
ejpam-4446	9	22	d	d	X
ejpam-4446	9	23	-	-	PUNCT
ejpam-4446	9	24	algebras	algebras	X
ejpam-4446	9	25	etc	etc	X
ejpam-4446	9	26	.	.	X
ejpam-4446	9	27	appeared	appear	VERB
ejpam-4446	9	28	.	.	PUNCT
ejpam-4446	10	1	in	in	ADP
ejpam-4446	10	2	2007	2007	NUM
ejpam-4446	10	3	,	,	PUNCT
ejpam-4446	10	4	h.	h.	PROPN
ejpam-4446	10	5	s.	s.	PROPN
ejpam-4446	10	6	kim	kim	PROPN
ejpam-4446	10	7	and	and	CCONJ
ejpam-4446	10	8	y.	y.	PROPN
ejpam-4446	10	9	h.	h.	PROPN
ejpam-4446	10	10	kim	kim	PROPN
ejpam-4446	11	1	[	[	X
ejpam-4446	11	2	3	3	NUM
ejpam-4446	11	3	]	]	PUNCT
ejpam-4446	11	4	introduced	introduce	VERB
ejpam-4446	11	5	the	the	DET
ejpam-4446	11	6	notion	notion	NOUN
ejpam-4446	11	7	of	of	ADP
ejpam-4446	11	8	a	a	DET
ejpam-4446	11	9	be	be	NOUN
ejpam-4446	11	10	-	-	PUNCT
ejpam-4446	11	11	algebra	algebra	NOUN
ejpam-4446	11	12	as	as	ADP
ejpam-4446	11	13	a	a	DET
ejpam-4446	11	14	dualization	dualization	NOUN
ejpam-4446	11	15	of	of	ADP
ejpam-4446	11	16	a	a	DET
ejpam-4446	11	17	generalization	generalization	NOUN
ejpam-4446	11	18	of	of	ADP
ejpam-4446	11	19	a	a	DET
ejpam-4446	11	20	bck	bck	NOUN
ejpam-4446	11	21	-	-	PUNCT
ejpam-4446	11	22	algebra	algebra	NOUN
ejpam-4446	11	23	.	.	PUNCT
ejpam-4446	12	1	they	they	PRON
ejpam-4446	12	2	defined	define	VERB
ejpam-4446	12	3	and	and	CCONJ
ejpam-4446	12	4	studied	study	VERB
ejpam-4446	12	5	the	the	DET
ejpam-4446	12	6	concept	concept	NOUN
ejpam-4446	12	7	of	of	ADP
ejpam-4446	12	8	a	a	DET
ejpam-4446	12	9	filter	filter	NOUN
ejpam-4446	12	10	in	in	ADP
ejpam-4446	12	11	be	be	NOUN
ejpam-4446	12	12	-	-	PUNCT
ejpam-4446	12	13	algebras	algebra	NOUN
ejpam-4446	12	14	.	.	PUNCT
ejpam-4446	13	1	in	in	ADP
ejpam-4446	13	2	[	[	X
ejpam-4446	13	3	7	7	NUM
ejpam-4446	13	4	]	]	PUNCT
ejpam-4446	13	5	and	and	CCONJ
ejpam-4446	13	6	[	[	X
ejpam-4446	13	7	6	6	NUM
ejpam-4446	13	8	]	]	PUNCT
ejpam-4446	13	9	,	,	PUNCT
ejpam-4446	13	10	s.	s.	PROPN
ejpam-4446	13	11	s.	s.	PROPN
ejpam-4446	13	12	ahn	ahn	PROPN
ejpam-4446	13	13	et	et	PROPN
ejpam-4446	13	14	al	al	PROPN
ejpam-4446	13	15	.	.	PROPN
ejpam-4446	13	16	and	and	CCONJ
ejpam-4446	13	17	a.	a.	PROPN
ejpam-4446	13	18	rezaei	rezaei	PROPN
ejpam-4446	13	19	et	et	PROPN
ejpam-4446	13	20	al	al	PROPN
ejpam-4446	13	21	.	.	PROPN
ejpam-4446	13	22	studied	study	VERB
ejpam-4446	13	23	fuzzy	fuzzy	ADJ
ejpam-4446	13	24	be	be	NOUN
ejpam-4446	13	25	-	-	PUNCT
ejpam-4446	13	26	algebras	algebra	NOUN
ejpam-4446	13	27	.	.	PUNCT
ejpam-4446	14	1	g.	g.	PROPN
ejpam-4446	14	2	dymek	dymek	PROPN
ejpam-4446	14	3	and	and	CCONJ
ejpam-4446	14	4	a.	a.	PROPN
ejpam-4446	14	5	walendziak	walendziak	PROPN
ejpam-4446	15	1	[	[	X
ejpam-4446	15	2	1	1	NUM
ejpam-4446	15	3	]	]	PUNCT
ejpam-4446	15	4	developed	develop	VERB
ejpam-4446	15	5	the	the	DET
ejpam-4446	15	6	theory	theory	NOUN
ejpam-4446	15	7	of	of	ADP
ejpam-4446	15	8	fuzzy	fuzzy	ADJ
ejpam-4446	15	9	filters	filter	NOUN
ejpam-4446	15	10	in	in	ADP
ejpam-4446	15	11	be	be	AUX
ejpam-4446	15	12	-	-	PUNCT
ejpam-4446	15	13	algebras	algebra	NOUN
ejpam-4446	15	14	.	.	PUNCT
ejpam-4446	16	1	in	in	ADP
ejpam-4446	16	2	the	the	DET
ejpam-4446	16	3	website	website	NOUN
ejpam-4446	16	4	https://plato.stanford.edu/entries/lukasiewicz/	https://plato.stanford.edu/entries/lukasiewicz/	PROPN
ejpam-4446	16	5	,	,	PUNCT
ejpam-4446	16	6	we	we	PRON
ejpam-4446	16	7	can	can	AUX
ejpam-4446	16	8	see	see	VERB
ejpam-4446	16	9	that	that	DET
ejpam-4446	16	10	jan	jan	PROPN
ejpam-4446	16	11	lukasiewicz	lukasiewicz	PROPN
ejpam-4446	16	12	(	(	PUNCT
ejpam-4446	16	13	1878–1956	1878–1956	NUM
ejpam-4446	16	14	)	)	PUNCT
ejpam-4446	16	15	was	be	AUX
ejpam-4446	16	16	a	a	DET
ejpam-4446	16	17	polish	polish	ADJ
ejpam-4446	16	18	logician	logician	NOUN
ejpam-4446	16	19	and	and	CCONJ
ejpam-4446	16	20	philosopher	philosopher	NOUN
ejpam-4446	16	21	who	who	PRON
ejpam-4446	16	22	introduced	introduce	VERB
ejpam-4446	16	23	mathematical	mathematical	ADJ
ejpam-4446	16	24	logic	logic	NOUN
ejpam-4446	16	25	into	into	ADP
ejpam-4446	16	26	poland	poland	PROPN
ejpam-4446	16	27	,	,	PUNCT
ejpam-4446	16	28	became	become	VERB
ejpam-4446	16	29	the	the	DET
ejpam-4446	16	30	earliest	early	ADJ
ejpam-4446	16	31	founder	founder	NOUN
ejpam-4446	16	32	of	of	ADP
ejpam-4446	16	33	the	the	DET
ejpam-4446	16	34	warsaw	warsaw	PROPN
ejpam-4446	16	35	school	school	NOUN
ejpam-4446	16	36	of	of	ADP
ejpam-4446	16	37	logic	logic	NOUN
ejpam-4446	16	38	,	,	PUNCT
ejpam-4446	16	39	and	and	CCONJ
ejpam-4446	16	40	one	one	NUM
ejpam-4446	16	41	of	of	ADP
ejpam-4446	16	42	the	the	DET
ejpam-4446	16	43	principal	principal	ADJ
ejpam-4446	16	44	architects	architect	NOUN
ejpam-4446	16	45	and	and	CCONJ
ejpam-4446	16	46	teachers	teacher	NOUN
ejpam-4446	16	47	of	of	ADP
ejpam-4446	16	48	that	that	DET
ejpam-4446	16	49	school	school	NOUN
ejpam-4446	16	50	.	.	PUNCT
ejpam-4446	17	1	his	his	PRON
ejpam-4446	17	2	most	most	ADV
ejpam-4446	17	3	famous	famous	ADJ
ejpam-4446	17	4	achievement	achievement	NOUN
ejpam-4446	17	5	was	be	AUX
ejpam-4446	17	6	to	to	PART
ejpam-4446	17	7	give	give	VERB
ejpam-4446	17	8	the	the	DET
ejpam-4446	17	9	first	first	ADJ
ejpam-4446	17	10	rigorous	rigorous	ADJ
ejpam-4446	17	11	formulation	formulation	NOUN
ejpam-4446	17	12	of	of	ADP
ejpam-4446	17	13	many	many	ADV
ejpam-4446	17	14	-	-	PUNCT
ejpam-4446	17	15	valued	value	VERB
ejpam-4446	17	16	logic	logic	NOUN
ejpam-4446	17	17	.	.	PUNCT
ejpam-4446	18	1	he	he	PRON
ejpam-4446	18	2	introduced	introduce	VERB
ejpam-4446	18	3	many	many	ADJ
ejpam-4446	18	4	improvements	improvement	NOUN
ejpam-4446	18	5	in	in	ADP
ejpam-4446	18	6	propositional	propositional	ADJ
ejpam-4446	18	7	logic	logic	NOUN
ejpam-4446	18	8	,	,	PUNCT
ejpam-4446	18	9	and	and	CCONJ
ejpam-4446	18	10	became	become	VERB
ejpam-4446	18	11	the	the	DET
ejpam-4446	18	12	first	first	ADJ
ejpam-4446	18	13	historian	historian	NOUN
ejpam-4446	18	14	of	of	ADP
ejpam-4446	18	15	logic	logic	NOUN
ejpam-4446	18	16	to	to	PART
ejpam-4446	18	17	treat	treat	VERB
ejpam-4446	18	18	the	the	DET
ejpam-4446	18	19	∗corresponding	∗corresponding	NOUN
ejpam-4446	18	20	author	author	NOUN
ejpam-4446	18	21	.	.	PUNCT
ejpam-4446	19	1	doi	doi	NOUN
ejpam-4446	19	2	:	:	PUNCT
ejpam-4446	19	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4446	https://doi.org/10.29020/nybg.ejpam.v15i3.4446	NOUN
ejpam-4446	19	4	email	email	NOUN
ejpam-4446	19	5	addresses	address	VERB
ejpam-4446	19	6	:	:	PUNCT
ejpam-4446	19	7	skywine@gmail.com	skywine@gmail.com	X
ejpam-4446	19	8	(	(	PUNCT
ejpam-4446	19	9	y.	y.	PROPN
ejpam-4446	19	10	b.	b.	PROPN
ejpam-4446	19	11	jun	jun	PROPN
ejpam-4446	19	12	)	)	PUNCT
ejpam-4446	19	13	,	,	PUNCT
ejpam-4446	19	14	sunshine@dongguk.edu	sunshine@dongguk.edu	PROPN
ejpam-4446	19	15	(	(	PUNCT
ejpam-4446	19	16	s.	s.	PROPN
ejpam-4446	19	17	s.	s.	PROPN
ejpam-4446	19	18	ahn	ahn	PROPN
ejpam-4446	19	19	)	)	PUNCT
ejpam-4446	19	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4446	20	1	924	924	NUM
ejpam-4446	20	2	©	©	ADP
ejpam-4446	20	3	2022	2022	NUM
ejpam-4446	20	4	ejpam	ejpam	VERB
ejpam-4446	20	5	all	all	DET
ejpam-4446	20	6	rights	right	NOUN
ejpam-4446	20	7	reserved	reserve	VERB
ejpam-4446	20	8	.	.	PUNCT
ejpam-4446	21	1	y.	y.	PROPN
ejpam-4446	21	2	b.	b.	PROPN
ejpam-4446	21	3	jun	jun	PROPN
ejpam-4446	21	4	,	,	PUNCT
ejpam-4446	21	5	s.	s.	PROPN
ejpam-4446	21	6	s.	s.	PROPN
ejpam-4446	21	7	ahn	ahn	PROPN
ejpam-4446	21	8	/	/	SYM
ejpam-4446	21	9	eur	eur	PROPN
ejpam-4446	21	10	.	.	PUNCT
ejpam-4446	22	1	j.	j.	PROPN
ejpam-4446	22	2	pure	pure	PROPN
ejpam-4446	22	3	appl	appl	PROPN
ejpam-4446	22	4	.	.	PROPN
ejpam-4446	22	5	math	math	PROPN
ejpam-4446	22	6	,	,	PUNCT
ejpam-4446	22	7	15	15	NUM
ejpam-4446	22	8	(	(	PUNCT
ejpam-4446	22	9	3	3	NUM
ejpam-4446	22	10	)	)	PUNCT
ejpam-4446	22	11	(	(	PUNCT
ejpam-4446	22	12	2022	2022	NUM
ejpam-4446	22	13	)	)	PUNCT
ejpam-4446	22	14	,	,	PUNCT
ejpam-4446	22	15	924	924	NUM
ejpam-4446	22	16	-	-	SYM
ejpam-4446	22	17	937	937	NUM
ejpam-4446	22	18	925	925	NUM
ejpam-4446	22	19	subject	subject	NOUN
ejpam-4446	22	20	’s	’s	PART
ejpam-4446	22	21	history	history	NOUN
ejpam-4446	22	22	from	from	ADP
ejpam-4446	22	23	the	the	DET
ejpam-4446	22	24	standpoint	standpoint	NOUN
ejpam-4446	22	25	of	of	ADP
ejpam-4446	22	26	modern	modern	ADJ
ejpam-4446	22	27	formal	formal	ADJ
ejpam-4446	22	28	logic	logic	NOUN
ejpam-4446	22	29	.	.	PUNCT
ejpam-4446	23	1	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	23	2	logic	logic	NOUN
ejpam-4446	23	3	,	,	PUNCT
ejpam-4446	23	4	which	which	PRON
ejpam-4446	23	5	is	be	AUX
ejpam-4446	23	6	the	the	DET
ejpam-4446	23	7	logic	logic	NOUN
ejpam-4446	23	8	of	of	ADP
ejpam-4446	23	9	the	the	DET
ejpam-4446	23	10	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	23	11	t	t	PROPN
ejpam-4446	23	12	-	-	PUNCT
ejpam-4446	23	13	norm	norm	NOUN
ejpam-4446	23	14	,	,	PUNCT
ejpam-4446	23	15	is	be	AUX
ejpam-4446	23	16	a	a	DET
ejpam-4446	23	17	non	non	ADJ
ejpam-4446	23	18	-	-	ADJ
ejpam-4446	23	19	classical	classical	ADJ
ejpam-4446	23	20	and	and	CCONJ
ejpam-4446	23	21	many	many	ADV
ejpam-4446	23	22	-	-	PUNCT
ejpam-4446	23	23	valued	value	VERB
ejpam-4446	23	24	logic	logic	NOUN
ejpam-4446	23	25	.	.	PUNCT
ejpam-4446	24	1	it	it	PRON
ejpam-4446	24	2	was	be	AUX
ejpam-4446	24	3	originally	originally	ADV
ejpam-4446	24	4	defined	define	VERB
ejpam-4446	24	5	in	in	ADP
ejpam-4446	24	6	the	the	DET
ejpam-4446	24	7	early	early	ADJ
ejpam-4446	24	8	20th	20th	ADJ
ejpam-4446	24	9	century	century	NOUN
ejpam-4446	24	10	by	by	ADP
ejpam-4446	24	11	jan	jan	PROPN
ejpam-4446	24	12	lukasiewicz	lukasiewicz	PROPN
ejpam-4446	24	13	as	as	ADP
ejpam-4446	24	14	a	a	DET
ejpam-4446	24	15	three	three	NUM
ejpam-4446	24	16	-	-	PUNCT
ejpam-4446	24	17	valued	value	VERB
ejpam-4446	24	18	logic	logic	NOUN
ejpam-4446	24	19	.	.	PUNCT
ejpam-4446	25	1	using	use	VERB
ejpam-4446	25	2	the	the	DET
ejpam-4446	25	3	idea	idea	NOUN
ejpam-4446	25	4	of	of	ADP
ejpam-4446	25	5	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	25	6	t	t	PROPN
ejpam-4446	25	7	-	-	PUNCT
ejpam-4446	25	8	norm	norm	NOUN
ejpam-4446	25	9	,	,	PUNCT
ejpam-4446	25	10	y.	y.	PROPN
ejpam-4446	25	11	b.	b.	PROPN
ejpam-4446	25	12	jun	jun	PROPN
ejpam-4446	26	1	[	[	X
ejpam-4446	26	2	2	2	NUM
ejpam-4446	26	3	]	]	PUNCT
ejpam-4446	26	4	constructed	construct	VERB
ejpam-4446	26	5	the	the	DET
ejpam-4446	26	6	concept	concept	NOUN
ejpam-4446	26	7	of	of	ADP
ejpam-4446	26	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	26	9	fuzzy	fuzzy	ADJ
ejpam-4446	26	10	sets	set	NOUN
ejpam-4446	26	11	based	base	VERB
ejpam-4446	26	12	on	on	ADP
ejpam-4446	26	13	a	a	DET
ejpam-4446	26	14	given	give	VERB
ejpam-4446	26	15	fuzzy	fuzzy	ADJ
ejpam-4446	26	16	set	set	NOUN
ejpam-4446	26	17	and	and	CCONJ
ejpam-4446	26	18	applied	apply	VERB
ejpam-4446	26	19	it	it	PRON
ejpam-4446	26	20	to	to	PART
ejpam-4446	26	21	bck	bck	VERB
ejpam-4446	26	22	-	-	PUNCT
ejpam-4446	26	23	algebras	algebras	PROPN
ejpam-4446	26	24	and	and	CCONJ
ejpam-4446	26	25	bci	bci	NOUN
ejpam-4446	26	26	-	-	PUNCT
ejpam-4446	26	27	algebras	algebras	X
ejpam-4446	26	28	.	.	PUNCT
ejpam-4446	27	1	in	in	ADP
ejpam-4446	27	2	this	this	DET
ejpam-4446	27	3	paper	paper	NOUN
ejpam-4446	27	4	,	,	PUNCT
ejpam-4446	27	5	we	we	PRON
ejpam-4446	27	6	apply	apply	VERB
ejpam-4446	27	7	the	the	DET
ejpam-4446	27	8	concept	concept	NOUN
ejpam-4446	27	9	of	of	ADP
ejpam-4446	27	10	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	27	11	fuzzy	fuzzy	ADJ
ejpam-4446	27	12	set	set	VERB
ejpam-4446	27	13	to	to	PART
ejpam-4446	27	14	be	be	AUX
ejpam-4446	27	15	-	-	PUNCT
ejpam-4446	27	16	algebras	algebras	X
ejpam-4446	27	17	.	.	PUNCT
ejpam-4446	28	1	we	we	PRON
ejpam-4446	28	2	introduce	introduce	VERB
ejpam-4446	28	3	the	the	DET
ejpam-4446	28	4	notion	notion	NOUN
ejpam-4446	28	5	of	of	ADP
ejpam-4446	28	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	28	7	fuzzy	fuzzy	ADJ
ejpam-4446	28	8	be	be	NOUN
ejpam-4446	28	9	-	-	PUNCT
ejpam-4446	28	10	algebra	algebra	NOUN
ejpam-4446	28	11	and	and	CCONJ
ejpam-4446	28	12	lukasiewicz	lukasiewicz	VERB
ejpam-4446	28	13	fuzzy	fuzzy	ADJ
ejpam-4446	28	14	be	be	NOUN
ejpam-4446	28	15	-	-	PUNCT
ejpam-4446	28	16	filter	filter	NOUN
ejpam-4446	28	17	,	,	PUNCT
ejpam-4446	28	18	and	and	CCONJ
ejpam-4446	28	19	investigate	investigate	VERB
ejpam-4446	28	20	several	several	ADJ
ejpam-4446	28	21	properties	property	NOUN
ejpam-4446	28	22	.	.	PUNCT
ejpam-4446	29	1	we	we	PRON
ejpam-4446	29	2	discuss	discuss	VERB
ejpam-4446	29	3	the	the	DET
ejpam-4446	29	4	characterization	characterization	NOUN
ejpam-4446	29	5	of	of	ADP
ejpam-4446	29	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	29	7	fuzzy	fuzzy	ADJ
ejpam-4446	29	8	be	be	NOUN
ejpam-4446	29	9	-	-	PUNCT
ejpam-4446	29	10	algebra	algebra	NOUN
ejpam-4446	29	11	and	and	CCONJ
ejpam-4446	29	12	lukasiewicz	lukasiewicz	VERB
ejpam-4446	29	13	fuzzy	fuzzy	ADJ
ejpam-4446	29	14	be	be	NOUN
ejpam-4446	29	15	-	-	PUNCT
ejpam-4446	29	16	filter	filter	NOUN
ejpam-4446	29	17	.	.	PUNCT
ejpam-4446	30	1	we	we	PRON
ejpam-4446	30	2	conside	conside	VERB
ejpam-4446	30	3	the	the	DET
ejpam-4446	30	4	relationship	relationship	NOUN
ejpam-4446	30	5	between	between	ADP
ejpam-4446	30	6	fuzzy	fuzzy	ADJ
ejpam-4446	30	7	be	be	NOUN
ejpam-4446	30	8	-	-	PUNCT
ejpam-4446	30	9	algebra	algebra	NOUN
ejpam-4446	30	10	(	(	PUNCT
ejpam-4446	30	11	resp	resp	NOUN
ejpam-4446	30	12	.	.	PUNCT
ejpam-4446	30	13	,	,	PUNCT
ejpam-4446	30	14	fuzzy	fuzzy	ADJ
ejpam-4446	30	15	be	be	NOUN
ejpam-4446	30	16	-	-	PUNCT
ejpam-4446	30	17	filter	filter	NOUN
ejpam-4446	30	18	)	)	PUNCT
ejpam-4446	30	19	and	and	CCONJ
ejpam-4446	30	20	lukasiewicz	lukasiewicz	VERB
ejpam-4446	30	21	fuzzy	fuzzy	ADJ
ejpam-4446	30	22	be	be	NOUN
ejpam-4446	30	23	-	-	PUNCT
ejpam-4446	30	24	algebra	algebra	NOUN
ejpam-4446	30	25	(	(	PUNCT
ejpam-4446	30	26	resp	resp	NOUN
ejpam-4446	30	27	.	.	PUNCT
ejpam-4446	30	28	,	,	PUNCT
ejpam-4446	30	29	lukasiewicz	lukasiewicz	VERB
ejpam-4446	30	30	fuzzy	fuzzy	ADJ
ejpam-4446	30	31	be	be	NOUN
ejpam-4446	30	32	-	-	PUNCT
ejpam-4446	30	33	filter	filter	NOUN
ejpam-4446	30	34	)	)	PUNCT
ejpam-4446	30	35	.	.	PUNCT
ejpam-4446	31	1	we	we	PRON
ejpam-4446	31	2	explore	explore	VERB
ejpam-4446	31	3	the	the	DET
ejpam-4446	31	4	conditions	condition	NOUN
ejpam-4446	31	5	for	for	ADP
ejpam-4446	31	6	the	the	DET
ejpam-4446	31	7	∈-set	∈-set	NOUN
ejpam-4446	31	8	,	,	PUNCT
ejpam-4446	31	9	q	q	NOUN
ejpam-4446	31	10	-	-	PUNCT
ejpam-4446	31	11	set	set	VERB
ejpam-4446	31	12	and	and	CCONJ
ejpam-4446	31	13	o	o	NOUN
ejpam-4446	31	14	-	-	PUNCT
ejpam-4446	31	15	set	set	NOUN
ejpam-4446	31	16	of	of	ADP
ejpam-4446	31	17	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	31	18	fuzzy	fuzzy	ADJ
ejpam-4446	31	19	set	set	VERB
ejpam-4446	31	20	to	to	PART
ejpam-4446	31	21	be	be	AUX
ejpam-4446	31	22	be	be	AUX
ejpam-4446	31	23	-	-	PUNCT
ejpam-4446	31	24	subalgebras	subalgebras	X
ejpam-4446	31	25	.	.	PUNCT
ejpam-4446	32	1	we	we	PRON
ejpam-4446	32	2	use	use	VERB
ejpam-4446	32	3	be	be	NOUN
ejpam-4446	32	4	-	-	PUNCT
ejpam-4446	32	5	filter	filter	NOUN
ejpam-4446	32	6	to	to	PART
ejpam-4446	32	7	create	create	VERB
ejpam-4446	32	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	32	9	fuzzy	fuzzy	ADJ
ejpam-4446	32	10	be	be	NOUN
ejpam-4446	32	11	-	-	PUNCT
ejpam-4446	32	12	filter	filter	NOUN
ejpam-4446	32	13	.	.	PUNCT
ejpam-4446	33	1	2	2	X
ejpam-4446	33	2	.	.	X
ejpam-4446	33	3	preliminary	preliminary	ADJ
ejpam-4446	33	4	a	a	DET
ejpam-4446	33	5	be	be	NOUN
ejpam-4446	33	6	-	-	PUNCT
ejpam-4446	33	7	algebra	algebra	NOUN
ejpam-4446	33	8	(	(	PUNCT
ejpam-4446	33	9	see	see	VERB
ejpam-4446	33	10	[	[	X
ejpam-4446	33	11	3	3	NUM
ejpam-4446	33	12	]	]	PUNCT
ejpam-4446	33	13	)	)	PUNCT
ejpam-4446	33	14	is	be	AUX
ejpam-4446	33	15	defined	define	VERB
ejpam-4446	33	16	to	to	PART
ejpam-4446	33	17	be	be	AUX
ejpam-4446	33	18	a	a	DET
ejpam-4446	33	19	set	set	NOUN
ejpam-4446	33	20	x	x	PUNCT
ejpam-4446	33	21	together	together	ADV
ejpam-4446	33	22	with	with	ADP
ejpam-4446	33	23	a	a	DET
ejpam-4446	33	24	binary	binary	ADJ
ejpam-4446	33	25	operation	operation	NOUN
ejpam-4446	33	26	“	"	PUNCT
ejpam-4446	33	27	∗	∗	NOUN
ejpam-4446	33	28	”	"	PUNCT
ejpam-4446	33	29	and	and	CCONJ
ejpam-4446	33	30	a	a	DET
ejpam-4446	33	31	special	special	ADJ
ejpam-4446	33	32	element	element	NOUN
ejpam-4446	33	33	“	"	PUNCT
ejpam-4446	33	34	1	1	NUM
ejpam-4446	33	35	”	"	PUNCT
ejpam-4446	33	36	satisfying	satisfy	VERB
ejpam-4446	33	37	the	the	DET
ejpam-4446	33	38	conditions	condition	NOUN
ejpam-4446	33	39	:	:	PUNCT
ejpam-4446	33	40	(	(	PUNCT
ejpam-4446	33	41	be1	be1	NOUN
ejpam-4446	33	42	)	)	PUNCT
ejpam-4446	33	43	(	(	PUNCT
ejpam-4446	33	44	∀a	∀a	NOUN
ejpam-4446	33	45	∈	∈	NOUN
ejpam-4446	33	46	x	x	NOUN
ejpam-4446	33	47	)	)	PUNCT
ejpam-4446	33	48	(	(	PUNCT
ejpam-4446	33	49	a	a	DET
ejpam-4446	33	50	∗	∗	NOUN
ejpam-4446	33	51	a	a	DET
ejpam-4446	33	52	=	=	NOUN
ejpam-4446	33	53	1	1	NUM
ejpam-4446	33	54	)	)	PUNCT
ejpam-4446	33	55	,	,	PUNCT
ejpam-4446	33	56	(	(	PUNCT
ejpam-4446	33	57	be2	be2	PROPN
ejpam-4446	33	58	)	)	PUNCT
ejpam-4446	33	59	(	(	PUNCT
ejpam-4446	33	60	∀a	∀a	NOUN
ejpam-4446	33	61	∈	∈	NOUN
ejpam-4446	33	62	x	x	NOUN
ejpam-4446	33	63	)	)	PUNCT
ejpam-4446	33	64	(	(	PUNCT
ejpam-4446	33	65	a	a	DET
ejpam-4446	33	66	∗	∗	NOUN
ejpam-4446	33	67	1	1	NUM
ejpam-4446	33	68	=	=	SYM
ejpam-4446	33	69	1	1	NUM
ejpam-4446	33	70	)	)	PUNCT
ejpam-4446	33	71	,	,	PUNCT
ejpam-4446	33	72	(	(	PUNCT
ejpam-4446	33	73	be3	be3	PROPN
ejpam-4446	33	74	)	)	PUNCT
ejpam-4446	33	75	(	(	PUNCT
ejpam-4446	33	76	∀a	∀a	NOUN
ejpam-4446	33	77	∈	∈	NOUN
ejpam-4446	33	78	x	x	NOUN
ejpam-4446	33	79	)	)	PUNCT
ejpam-4446	33	80	(	(	PUNCT
ejpam-4446	33	81	1	1	NUM
ejpam-4446	33	82	∗	∗	NOUN
ejpam-4446	33	83	a	a	DET
ejpam-4446	33	84	=	=	NOUN
ejpam-4446	33	85	a	a	NOUN
ejpam-4446	33	86	)	)	PUNCT
ejpam-4446	33	87	,	,	PUNCT
ejpam-4446	33	88	(	(	PUNCT
ejpam-4446	33	89	be4	be4	NOUN
ejpam-4446	33	90	)	)	PUNCT
ejpam-4446	33	91	(	(	PUNCT
ejpam-4446	33	92	∀a	∀a	X
ejpam-4446	33	93	,	,	PUNCT
ejpam-4446	33	94	b	b	NOUN
ejpam-4446	33	95	,	,	PUNCT
ejpam-4446	33	96	c	c	PROPN
ejpam-4446	33	97	∈	∈	PROPN
ejpam-4446	33	98	x	x	X
ejpam-4446	33	99	)	)	PUNCT
ejpam-4446	33	100	(	(	PUNCT
ejpam-4446	33	101	a	a	DET
ejpam-4446	33	102	∗	∗	NOUN
ejpam-4446	33	103	(	(	PUNCT
ejpam-4446	33	104	b	b	NOUN
ejpam-4446	33	105	∗	∗	NOUN
ejpam-4446	33	106	c	c	NOUN
ejpam-4446	33	107	)	)	PUNCT
ejpam-4446	33	108	=	=	SYM
ejpam-4446	33	109	b	b	NOUN
ejpam-4446	33	110	∗	∗	NOUN
ejpam-4446	33	111	(	(	PUNCT
ejpam-4446	33	112	a	a	DET
ejpam-4446	33	113	∗	∗	NOUN
ejpam-4446	33	114	c	c	NOUN
ejpam-4446	33	115	)	)	PUNCT
ejpam-4446	33	116	)	)	PUNCT
ejpam-4446	33	117	.	.	PUNCT
ejpam-4446	34	1	the	the	DET
ejpam-4446	34	2	order	order	NOUN
ejpam-4446	34	3	relation	relation	NOUN
ejpam-4446	34	4	“	"	PUNCT
ejpam-4446	34	5	≤	≤	NUM
ejpam-4446	34	6	”	"	PUNCT
ejpam-4446	34	7	in	in	ADP
ejpam-4446	34	8	a	a	DET
ejpam-4446	34	9	be	be	NOUN
ejpam-4446	34	10	-	-	PUNCT
ejpam-4446	34	11	algebra	algebra	NOUN
ejpam-4446	34	12	x	x	PUNCT
ejpam-4446	34	13	is	be	AUX
ejpam-4446	34	14	defined	define	VERB
ejpam-4446	34	15	as	as	SCONJ
ejpam-4446	34	16	follows	follow	VERB
ejpam-4446	34	17	:	:	PUNCT
ejpam-4446	34	18	(	(	PUNCT
ejpam-4446	34	19	∀a	∀a	X
ejpam-4446	34	20	,	,	PUNCT
ejpam-4446	34	21	b	b	PROPN
ejpam-4446	34	22	∈	∈	PROPN
ejpam-4446	34	23	x)(a	x)(a	PUNCT
ejpam-4446	35	1	≤	≤	PROPN
ejpam-4446	35	2	b	b	X
ejpam-4446	35	3	⇔	⇔	X
ejpam-4446	35	4	a	a	DET
ejpam-4446	35	5	∗	∗	NOUN
ejpam-4446	35	6	b	b	NOUN
ejpam-4446	35	7	=	=	SYM
ejpam-4446	35	8	1	1	NUM
ejpam-4446	35	9	)	)	PUNCT
ejpam-4446	35	10	.	.	PUNCT
ejpam-4446	36	1	(	(	PUNCT
ejpam-4446	36	2	1	1	X
ejpam-4446	36	3	)	)	PUNCT
ejpam-4446	36	4	every	every	DET
ejpam-4446	36	5	be	be	NOUN
ejpam-4446	36	6	-	-	PUNCT
ejpam-4446	36	7	algebra	algebra	NOUN
ejpam-4446	36	8	x	x	PRON
ejpam-4446	36	9	satisfies	satisfy	VERB
ejpam-4446	36	10	the	the	DET
ejpam-4446	36	11	following	follow	VERB
ejpam-4446	36	12	conditions	condition	NOUN
ejpam-4446	36	13	(	(	PUNCT
ejpam-4446	36	14	see	see	VERB
ejpam-4446	36	15	[	[	X
ejpam-4446	36	16	3	3	NUM
ejpam-4446	36	17	]	]	NUM
ejpam-4446	36	18	):	):	PUNCT
ejpam-4446	36	19	(	(	PUNCT
ejpam-4446	36	20	∀a	∀a	NOUN
ejpam-4446	36	21	,	,	PUNCT
ejpam-4446	36	22	b	b	PROPN
ejpam-4446	36	23	∈	∈	PROPN
ejpam-4446	36	24	x	x	X
ejpam-4446	36	25	)	)	PUNCT
ejpam-4446	36	26	(	(	PUNCT
ejpam-4446	36	27	a	a	DET
ejpam-4446	36	28	∗	∗	NOUN
ejpam-4446	36	29	(	(	PUNCT
ejpam-4446	36	30	b	b	NOUN
ejpam-4446	36	31	∗	∗	X
ejpam-4446	36	32	a	a	NOUN
ejpam-4446	36	33	)	)	PUNCT
ejpam-4446	36	34	=	=	SYM
ejpam-4446	36	35	1	1	NUM
ejpam-4446	36	36	)	)	PUNCT
ejpam-4446	36	37	.	.	PUNCT
ejpam-4446	37	1	(	(	PUNCT
ejpam-4446	37	2	2	2	X
ejpam-4446	37	3	)	)	PUNCT
ejpam-4446	37	4	(	(	PUNCT
ejpam-4446	37	5	∀a	∀a	X
ejpam-4446	37	6	,	,	PUNCT
ejpam-4446	37	7	b	b	PROPN
ejpam-4446	37	8	∈	∈	PROPN
ejpam-4446	37	9	x	x	X
ejpam-4446	37	10	)	)	PUNCT
ejpam-4446	37	11	(	(	PUNCT
ejpam-4446	37	12	a	a	DET
ejpam-4446	37	13	∗	∗	NOUN
ejpam-4446	37	14	(	(	PUNCT
ejpam-4446	37	15	(	(	PUNCT
ejpam-4446	37	16	a	a	DET
ejpam-4446	37	17	∗	∗	NOUN
ejpam-4446	37	18	b	b	NOUN
ejpam-4446	37	19	)	)	PUNCT
ejpam-4446	37	20	∗	∗	PROPN
ejpam-4446	37	21	b	b	NOUN
ejpam-4446	37	22	)	)	PUNCT
ejpam-4446	37	23	=	=	SYM
ejpam-4446	37	24	1	1	NUM
ejpam-4446	37	25	)	)	PUNCT
ejpam-4446	37	26	.	.	PUNCT
ejpam-4446	38	1	(	(	PUNCT
ejpam-4446	38	2	3	3	X
ejpam-4446	38	3	)	)	PUNCT
ejpam-4446	38	4	a	a	DET
ejpam-4446	38	5	subset	subset	NOUN
ejpam-4446	38	6	a	a	PRON
ejpam-4446	38	7	of	of	ADP
ejpam-4446	38	8	a	a	DET
ejpam-4446	38	9	be	be	NOUN
ejpam-4446	38	10	-	-	PUNCT
ejpam-4446	38	11	algebra	algebra	NOUN
ejpam-4446	38	12	x	x	PUNCT
ejpam-4446	38	13	is	be	AUX
ejpam-4446	38	14	called	call	VERB
ejpam-4446	38	15	•	•	ADP
ejpam-4446	38	16	a	a	DET
ejpam-4446	38	17	be	be	NOUN
ejpam-4446	38	18	-	-	PUNCT
ejpam-4446	38	19	subalgebra	subalgebra	NOUN
ejpam-4446	38	20	of	of	ADP
ejpam-4446	38	21	x	x	PRON
ejpam-4446	38	22	if	if	SCONJ
ejpam-4446	38	23	it	it	PRON
ejpam-4446	38	24	satisfies	satisfy	VERB
ejpam-4446	38	25	:	:	PUNCT
ejpam-4446	38	26	(	(	PUNCT
ejpam-4446	38	27	∀a	∀a	NOUN
ejpam-4446	38	28	,	,	PUNCT
ejpam-4446	38	29	b	b	PROPN
ejpam-4446	38	30	∈	∈	PROPN
ejpam-4446	38	31	a)(a	a)(a	NOUN
ejpam-4446	38	32	∗	∗	NOUN
ejpam-4446	38	33	b	b	PROPN
ejpam-4446	38	34	∈	∈	PROPN
ejpam-4446	38	35	a	a	PRON
ejpam-4446	38	36	)	)	PUNCT
ejpam-4446	38	37	,	,	PUNCT
ejpam-4446	38	38	(	(	PUNCT
ejpam-4446	38	39	4	4	X
ejpam-4446	38	40	)	)	PUNCT
ejpam-4446	38	41	•	•	NOUN
ejpam-4446	38	42	a	a	DET
ejpam-4446	38	43	be	be	NOUN
ejpam-4446	38	44	-	-	PUNCT
ejpam-4446	38	45	filter	filter	NOUN
ejpam-4446	38	46	of	of	ADP
ejpam-4446	38	47	x	x	PUNCT
ejpam-4446	38	48	(	(	PUNCT
ejpam-4446	38	49	see	see	VERB
ejpam-4446	38	50	[	[	X
ejpam-4446	38	51	3	3	NUM
ejpam-4446	38	52	]	]	PUNCT
ejpam-4446	38	53	)	)	PUNCT
ejpam-4446	38	54	if	if	SCONJ
ejpam-4446	38	55	it	it	PRON
ejpam-4446	38	56	satisfies	satisfy	VERB
ejpam-4446	38	57	:	:	PUNCT
ejpam-4446	38	58	1	1	NUM
ejpam-4446	38	59	∈	∈	PROPN
ejpam-4446	38	60	a	a	PRON
ejpam-4446	38	61	,	,	PUNCT
ejpam-4446	38	62	(	(	PUNCT
ejpam-4446	38	63	5	5	NUM
ejpam-4446	38	64	)	)	PUNCT
ejpam-4446	38	65	(	(	PUNCT
ejpam-4446	38	66	∀a	∀a	X
ejpam-4446	38	67	,	,	PUNCT
ejpam-4446	38	68	b	b	PROPN
ejpam-4446	38	69	∈	∈	PROPN
ejpam-4446	38	70	x)(a	x)(a	PUNCT
ejpam-4446	39	1	∗	∗	NOUN
ejpam-4446	39	2	b	b	X
ejpam-4446	39	3	∈	∈	PROPN
ejpam-4446	39	4	a	a	PRON
ejpam-4446	39	5	,	,	PUNCT
ejpam-4446	39	6	a	a	DET
ejpam-4446	39	7	∈	∈	PROPN
ejpam-4446	39	8	a	a	DET
ejpam-4446	39	9	⇒	⇒	NOUN
ejpam-4446	39	10	b	b	X
ejpam-4446	39	11	∈	∈	PROPN
ejpam-4446	39	12	a	a	PRON
ejpam-4446	39	13	)	)	PUNCT
ejpam-4446	39	14	.	.	PUNCT
ejpam-4446	40	1	(	(	PUNCT
ejpam-4446	40	2	6	6	X
ejpam-4446	40	3	)	)	PUNCT
ejpam-4446	40	4	a	a	DET
ejpam-4446	40	5	fuzzy	fuzzy	ADJ
ejpam-4446	40	6	set	set	NOUN
ejpam-4446	40	7	ξ	ξ	PROPN
ejpam-4446	40	8	in	in	ADP
ejpam-4446	40	9	a	a	DET
ejpam-4446	40	10	be	be	NOUN
ejpam-4446	40	11	-	-	PUNCT
ejpam-4446	40	12	algebra	algebra	NOUN
ejpam-4446	40	13	x	x	PUNCT
ejpam-4446	40	14	is	be	AUX
ejpam-4446	40	15	called	call	VERB
ejpam-4446	40	16	•	•	ADP
ejpam-4446	40	17	a	a	DET
ejpam-4446	40	18	fuzzy	fuzzy	ADJ
ejpam-4446	40	19	be	be	NOUN
ejpam-4446	40	20	-	-	PUNCT
ejpam-4446	40	21	algebra	algebra	NOUN
ejpam-4446	40	22	of	of	ADP
ejpam-4446	40	23	x	x	PUNCT
ejpam-4446	40	24	(	(	PUNCT
ejpam-4446	40	25	see	see	VERB
ejpam-4446	40	26	[	[	X
ejpam-4446	40	27	7	7	NUM
ejpam-4446	40	28	]	]	PUNCT
ejpam-4446	40	29	)	)	PUNCT
ejpam-4446	40	30	if	if	SCONJ
ejpam-4446	40	31	it	it	PRON
ejpam-4446	40	32	satisfies	satisfy	VERB
ejpam-4446	40	33	:	:	PUNCT
ejpam-4446	40	34	(	(	PUNCT
ejpam-4446	40	35	∀a	∀a	NOUN
ejpam-4446	40	36	,	,	PUNCT
ejpam-4446	41	1	b	b	PROPN
ejpam-4446	41	2	∈	∈	PROPN
ejpam-4446	41	3	x)(ξ(a	x)(ξ(a	PUNCT
ejpam-4446	41	4	∗	∗	PROPN
ejpam-4446	41	5	b	b	NOUN
ejpam-4446	41	6	)	)	PUNCT
ejpam-4446	41	7	≥	≥	NOUN
ejpam-4446	41	8	min{ξ(a	min{ξ(a	NUM
ejpam-4446	41	9	)	)	PUNCT
ejpam-4446	41	10	,	,	PUNCT
ejpam-4446	41	11	ξ(b	ξ(b	NOUN
ejpam-4446	41	12	)	)	PUNCT
ejpam-4446	41	13	}	}	PUNCT
ejpam-4446	41	14	)	)	PUNCT
ejpam-4446	41	15	.	.	PUNCT
ejpam-4446	42	1	(	(	PUNCT
ejpam-4446	42	2	7	7	X
ejpam-4446	42	3	)	)	PUNCT
ejpam-4446	42	4	y.	y.	PROPN
ejpam-4446	42	5	b.	b.	PROPN
ejpam-4446	42	6	jun	jun	PROPN
ejpam-4446	42	7	,	,	PUNCT
ejpam-4446	42	8	s.	s.	PROPN
ejpam-4446	42	9	s.	s.	PROPN
ejpam-4446	42	10	ahn	ahn	PROPN
ejpam-4446	42	11	/	/	SYM
ejpam-4446	42	12	eur	eur	PROPN
ejpam-4446	42	13	.	.	PUNCT
ejpam-4446	43	1	j.	j.	PROPN
ejpam-4446	43	2	pure	pure	PROPN
ejpam-4446	43	3	appl	appl	PROPN
ejpam-4446	43	4	.	.	PROPN
ejpam-4446	43	5	math	math	PROPN
ejpam-4446	43	6	,	,	PUNCT
ejpam-4446	43	7	15	15	NUM
ejpam-4446	43	8	(	(	PUNCT
ejpam-4446	43	9	3	3	NUM
ejpam-4446	43	10	)	)	PUNCT
ejpam-4446	43	11	(	(	PUNCT
ejpam-4446	43	12	2022	2022	NUM
ejpam-4446	43	13	)	)	PUNCT
ejpam-4446	43	14	,	,	PUNCT
ejpam-4446	43	15	924	924	NUM
ejpam-4446	43	16	-	-	SYM
ejpam-4446	43	17	937	937	NUM
ejpam-4446	43	18	926	926	NUM
ejpam-4446	43	19	•	•	NOUN
ejpam-4446	43	20	a	a	DET
ejpam-4446	43	21	fuzzy	fuzzy	ADJ
ejpam-4446	43	22	be	be	NOUN
ejpam-4446	43	23	-	-	PUNCT
ejpam-4446	43	24	filter	filter	NOUN
ejpam-4446	43	25	of	of	ADP
ejpam-4446	43	26	x	x	PUNCT
ejpam-4446	43	27	(	(	PUNCT
ejpam-4446	43	28	see	see	VERB
ejpam-4446	43	29	[	[	X
ejpam-4446	43	30	1	1	NUM
ejpam-4446	43	31	]	]	PUNCT
ejpam-4446	43	32	)	)	PUNCT
ejpam-4446	43	33	if	if	SCONJ
ejpam-4446	43	34	it	it	PRON
ejpam-4446	43	35	satisfies	satisfy	VERB
ejpam-4446	43	36	:	:	PUNCT
ejpam-4446	43	37	(	(	PUNCT
ejpam-4446	43	38	∀a	∀a	NOUN
ejpam-4446	43	39	∈	∈	PROPN
ejpam-4446	43	40	x)(ξ(1	x)(ξ(1	PROPN
ejpam-4446	43	41	)	)	PUNCT
ejpam-4446	43	42	≥	≥	NOUN
ejpam-4446	43	43	ξ(a	ξ(a	NUM
ejpam-4446	43	44	)	)	PUNCT
ejpam-4446	43	45	)	)	PUNCT
ejpam-4446	43	46	,	,	PUNCT
ejpam-4446	43	47	(	(	PUNCT
ejpam-4446	43	48	8)	8)	NUM
ejpam-4446	43	49	(	(	PUNCT
ejpam-4446	43	50	∀a	∀a	NOUN
ejpam-4446	43	51	,	,	PUNCT
ejpam-4446	43	52	b	b	PROPN
ejpam-4446	43	53	∈	∈	PROPN
ejpam-4446	43	54	x)(ξ(b	x)(ξ(b	NOUN
ejpam-4446	43	55	)	)	PUNCT
ejpam-4446	43	56	≥	≥	NOUN
ejpam-4446	44	1	min{ξ(a	min{ξ(a	PROPN
ejpam-4446	44	2	∗	∗	NOUN
ejpam-4446	44	3	b	b	NOUN
ejpam-4446	44	4	)	)	PUNCT
ejpam-4446	44	5	,	,	PUNCT
ejpam-4446	44	6	ξ(a	ξ(a	NOUN
ejpam-4446	44	7	)	)	PUNCT
ejpam-4446	44	8	}	}	PUNCT
ejpam-4446	44	9	)	)	PUNCT
ejpam-4446	44	10	.	.	PUNCT
ejpam-4446	45	1	(	(	PUNCT
ejpam-4446	45	2	9	9	X
ejpam-4446	45	3	)	)	PUNCT
ejpam-4446	45	4	a	a	DET
ejpam-4446	45	5	fuzzy	fuzzy	ADJ
ejpam-4446	45	6	set	set	NOUN
ejpam-4446	45	7	ξ	ξ	PROPN
ejpam-4446	45	8	in	in	ADP
ejpam-4446	45	9	a	a	DET
ejpam-4446	45	10	set	set	NOUN
ejpam-4446	45	11	x	x	X
ejpam-4446	45	12	of	of	ADP
ejpam-4446	45	13	the	the	DET
ejpam-4446	45	14	form	form	NOUN
ejpam-4446	45	15	ξ(b	ξ(b	NOUN
ejpam-4446	45	16	)	)	PUNCT
ejpam-4446	45	17	:	:	PUNCT
ejpam-4446	46	1	=	=	X
ejpam-4446	46	2	{	{	PUNCT
ejpam-4446	46	3	t	t	PROPN
ejpam-4446	46	4	∈	∈	PROPN
ejpam-4446	46	5	(	(	PUNCT
ejpam-4446	46	6	0	0	NUM
ejpam-4446	46	7	,	,	PUNCT
ejpam-4446	46	8	1	1	NUM
ejpam-4446	46	9	]	]	PUNCT
ejpam-4446	46	10	if	if	SCONJ
ejpam-4446	46	11	b	b	X
ejpam-4446	46	12	=	=	SYM
ejpam-4446	46	13	a	a	PROPN
ejpam-4446	46	14	,	,	PUNCT
ejpam-4446	46	15	0	0	PUNCT
ejpam-4446	46	16	if	if	SCONJ
ejpam-4446	46	17	b	b	X
ejpam-4446	46	18	̸=	̸=	PROPN
ejpam-4446	46	19	a	a	PRON
ejpam-4446	46	20	,	,	PUNCT
ejpam-4446	46	21	is	be	AUX
ejpam-4446	46	22	said	say	VERB
ejpam-4446	46	23	to	to	PART
ejpam-4446	46	24	be	be	AUX
ejpam-4446	46	25	a	a	DET
ejpam-4446	46	26	fuzzy	fuzzy	ADJ
ejpam-4446	46	27	point	point	NOUN
ejpam-4446	46	28	with	with	ADP
ejpam-4446	46	29	support	support	NOUN
ejpam-4446	46	30	a	a	PRON
ejpam-4446	46	31	and	and	CCONJ
ejpam-4446	46	32	value	value	NOUN
ejpam-4446	46	33	t	t	NOUN
ejpam-4446	46	34	and	and	CCONJ
ejpam-4446	46	35	is	be	AUX
ejpam-4446	46	36	denoted	denote	VERB
ejpam-4446	46	37	by	by	ADP
ejpam-4446	46	38	[	[	PUNCT
ejpam-4446	46	39	a	a	X
ejpam-4446	46	40	/	/	SYM
ejpam-4446	46	41	t	t	NOUN
ejpam-4446	46	42	]	]	PUNCT
ejpam-4446	46	43	.	.	PUNCT
ejpam-4446	47	1	for	for	ADP
ejpam-4446	47	2	a	a	DET
ejpam-4446	47	3	fuzzy	fuzzy	ADJ
ejpam-4446	47	4	set	set	NOUN
ejpam-4446	47	5	ξ	ξ	PROPN
ejpam-4446	47	6	in	in	ADP
ejpam-4446	47	7	a	a	DET
ejpam-4446	47	8	set	set	NOUN
ejpam-4446	47	9	x	x	NOUN
ejpam-4446	47	10	,	,	PUNCT
ejpam-4446	47	11	we	we	PRON
ejpam-4446	47	12	say	say	VERB
ejpam-4446	47	13	that	that	SCONJ
ejpam-4446	47	14	a	a	DET
ejpam-4446	47	15	fuzzy	fuzzy	ADJ
ejpam-4446	47	16	point	point	NOUN
ejpam-4446	47	17	[	[	X
ejpam-4446	47	18	a	a	X
ejpam-4446	47	19	/	/	SYM
ejpam-4446	47	20	t	t	NOUN
ejpam-4446	47	21	]	]	PUNCT
ejpam-4446	47	22	is	be	AUX
ejpam-4446	47	23	(	(	PUNCT
ejpam-4446	47	24	i	i	NOUN
ejpam-4446	47	25	)	)	PUNCT
ejpam-4446	47	26	contained	contain	VERB
ejpam-4446	47	27	in	in	ADP
ejpam-4446	47	28	ξ	ξ	PROPN
ejpam-4446	47	29	,	,	PUNCT
ejpam-4446	47	30	denoted	denote	VERB
ejpam-4446	47	31	by	by	ADP
ejpam-4446	47	32	[	[	PUNCT
ejpam-4446	47	33	a	a	X
ejpam-4446	47	34	/	/	SYM
ejpam-4446	47	35	t	t	NOUN
ejpam-4446	47	36	]	]	PUNCT
ejpam-4446	47	37	∈	∈	PROPN
ejpam-4446	47	38	ξ	ξ	PROPN
ejpam-4446	47	39	,	,	PUNCT
ejpam-4446	47	40	(	(	PUNCT
ejpam-4446	47	41	see	see	VERB
ejpam-4446	47	42	[	[	X
ejpam-4446	47	43	5	5	NUM
ejpam-4446	47	44	]	]	SYM
ejpam-4446	47	45	)	)	PUNCT
ejpam-4446	47	46	if	if	SCONJ
ejpam-4446	47	47	ξ(a	ξ(a	NUM
ejpam-4446	47	48	)	)	PUNCT
ejpam-4446	47	49	≥	≥	NOUN
ejpam-4446	47	50	t.	t.	PROPN
ejpam-4446	47	51	(	(	PUNCT
ejpam-4446	47	52	ii	ii	NOUN
ejpam-4446	47	53	)	)	PUNCT
ejpam-4446	47	54	quasi	quasi	NOUN
ejpam-4446	47	55	-	-	VERB
ejpam-4446	47	56	coincident	coincident	ADJ
ejpam-4446	47	57	with	with	ADP
ejpam-4446	47	58	ξ	ξ	PROPN
ejpam-4446	47	59	,	,	PUNCT
ejpam-4446	47	60	denoted	denote	VERB
ejpam-4446	47	61	by	by	ADP
ejpam-4446	47	62	[	[	PUNCT
ejpam-4446	47	63	a	a	X
ejpam-4446	47	64	/	/	SYM
ejpam-4446	47	65	t	t	NOUN
ejpam-4446	47	66	]	]	X
ejpam-4446	47	67	q	q	X
ejpam-4446	47	68	ξ	ξ	PROPN
ejpam-4446	47	69	,	,	PUNCT
ejpam-4446	47	70	(	(	PUNCT
ejpam-4446	47	71	see	see	VERB
ejpam-4446	47	72	[	[	X
ejpam-4446	47	73	5	5	NUM
ejpam-4446	47	74	]	]	SYM
ejpam-4446	47	75	)	)	PUNCT
ejpam-4446	47	76	if	if	SCONJ
ejpam-4446	47	77	ξ(a	ξ(a	NUM
ejpam-4446	47	78	)	)	PUNCT
ejpam-4446	48	1	+	+	CCONJ
ejpam-4446	48	2	t	t	X
ejpam-4446	48	3	>	>	X
ejpam-4446	48	4	1	1	X
ejpam-4446	48	5	.	.	PUNCT
ejpam-4446	49	1	if	if	SCONJ
ejpam-4446	49	2	[	[	X
ejpam-4446	49	3	a	a	X
ejpam-4446	49	4	/	/	SYM
ejpam-4446	49	5	t]α	t]α	NOUN
ejpam-4446	49	6	ξ	ξ	NOUN
ejpam-4446	49	7	is	be	AUX
ejpam-4446	49	8	not	not	PART
ejpam-4446	49	9	established	establish	VERB
ejpam-4446	49	10	for	for	ADP
ejpam-4446	49	11	α	α	PRON
ejpam-4446	49	12	∈	∈	PROPN
ejpam-4446	49	13	{	{	PUNCT
ejpam-4446	49	14	∈	∈	PROPN
ejpam-4446	49	15	,	,	PUNCT
ejpam-4446	49	16	q	q	NOUN
ejpam-4446	49	17	}	}	PUNCT
ejpam-4446	49	18	,	,	PUNCT
ejpam-4446	49	19	it	it	PRON
ejpam-4446	49	20	is	be	AUX
ejpam-4446	49	21	denoted	denote	VERB
ejpam-4446	49	22	by	by	ADP
ejpam-4446	49	23	[	[	PUNCT
ejpam-4446	49	24	a	a	PRON
ejpam-4446	49	25	/	/	SYM
ejpam-4446	49	26	t]α	t]α	NOUN
ejpam-4446	49	27	ξ	ξ	X
ejpam-4446	49	28	.	.	PUNCT
ejpam-4446	50	1	let	let	VERB
ejpam-4446	50	2	ξ	ξ	X
ejpam-4446	50	3	be	be	AUX
ejpam-4446	50	4	a	a	DET
ejpam-4446	50	5	fuzzy	fuzzy	ADJ
ejpam-4446	50	6	set	set	NOUN
ejpam-4446	50	7	in	in	ADP
ejpam-4446	50	8	a	a	DET
ejpam-4446	50	9	set	set	NOUN
ejpam-4446	50	10	x	x	PUNCT
ejpam-4446	50	11	and	and	CCONJ
ejpam-4446	50	12	let	let	VERB
ejpam-4446	50	13	ε	ε	PROPN
ejpam-4446	50	14	∈	∈	PROPN
ejpam-4446	50	15	(	(	PUNCT
ejpam-4446	50	16	0	0	NUM
ejpam-4446	50	17	,	,	PUNCT
ejpam-4446	50	18	1	1	NUM
ejpam-4446	50	19	)	)	PUNCT
ejpam-4446	50	20	.	.	PUNCT
ejpam-4446	51	1	a	a	DET
ejpam-4446	51	2	function	function	NOUN
ejpam-4446	51	3	lε	lε	ADP
ejpam-4446	51	4	ξ	ξ	NOUN
ejpam-4446	51	5	:	:	PUNCT
ejpam-4446	51	6	x	x	SYM
ejpam-4446	51	7	→	→	SYM
ejpam-4446	52	1	[	[	X
ejpam-4446	52	2	0	0	NUM
ejpam-4446	52	3	,	,	PUNCT
ejpam-4446	52	4	1	1	NUM
ejpam-4446	52	5	]	]	PUNCT
ejpam-4446	52	6	,	,	PUNCT
ejpam-4446	52	7	x	x	PROPN
ejpam-4446	52	8	7→	7→	NUM
ejpam-4446	52	9	max{0	max{0	NOUN
ejpam-4446	52	10	,	,	PUNCT
ejpam-4446	52	11	ξ(x	ξ(x	NOUN
ejpam-4446	52	12	)	)	PUNCT
ejpam-4446	53	1	+	+	CCONJ
ejpam-4446	53	2	ε−	ε−	PROPN
ejpam-4446	53	3	1	1	NUM
ejpam-4446	53	4	}	}	PUNCT
ejpam-4446	53	5	is	be	AUX
ejpam-4446	53	6	called	call	VERB
ejpam-4446	53	7	the	the	DET
ejpam-4446	53	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	53	9	fuzzy	fuzzy	ADJ
ejpam-4446	53	10	set	set	NOUN
ejpam-4446	53	11	of	of	ADP
ejpam-4446	53	12	ξ	ξ	PROPN
ejpam-4446	53	13	in	in	ADP
ejpam-4446	53	14	x.	x.	NOUN
ejpam-4446	53	15	for	for	ADP
ejpam-4446	53	16	the	the	DET
ejpam-4446	53	17	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	53	18	fuzzy	fuzzy	NOUN
ejpam-4446	53	19	set	set	VERB
ejpam-4446	53	20	lε	lε	ADP
ejpam-4446	53	21	ξ	ξ	PROPN
ejpam-4446	53	22	of	of	ADP
ejpam-4446	53	23	ξ	ξ	PROPN
ejpam-4446	53	24	in	in	ADP
ejpam-4446	53	25	x	x	X
ejpam-4446	53	26	and	and	CCONJ
ejpam-4446	53	27	t	t	PROPN
ejpam-4446	53	28	∈	∈	PROPN
ejpam-4446	53	29	(	(	PUNCT
ejpam-4446	53	30	0	0	NUM
ejpam-4446	53	31	,	,	PUNCT
ejpam-4446	53	32	1	1	NUM
ejpam-4446	53	33	]	]	PUNCT
ejpam-4446	53	34	,	,	PUNCT
ejpam-4446	53	35	consider	consider	VERB
ejpam-4446	53	36	the	the	DET
ejpam-4446	53	37	sets	set	NOUN
ejpam-4446	53	38	(	(	PUNCT
ejpam-4446	53	39	lε	lε	X
ejpam-4446	53	40	ξ	ξ	PROPN
ejpam-4446	53	41	,	,	PUNCT
ejpam-4446	53	42	t)∈	t)∈	NUM
ejpam-4446	53	43	:	:	PUNCT
ejpam-4446	53	44	=	=	SYM
ejpam-4446	53	45	{	{	PUNCT
ejpam-4446	53	46	x	x	SYM
ejpam-4446	53	47	∈	∈	PROPN
ejpam-4446	53	48	x	x	PUNCT
ejpam-4446	54	1	|	|	NOUN
ejpam-4446	54	2	[	[	X
ejpam-4446	54	3	x	x	X
ejpam-4446	54	4	/	/	SYM
ejpam-4446	54	5	t	t	PROPN
ejpam-4446	54	6	]	]	X
ejpam-4446	54	7	∈	∈	PROPN
ejpam-4446	54	8	lε	lε	X
ejpam-4446	54	9	ξ	ξ	X
ejpam-4446	54	10	}	}	PUNCT
ejpam-4446	54	11	,	,	PUNCT
ejpam-4446	54	12	(	(	PUNCT
ejpam-4446	54	13	lε	lε	X
ejpam-4446	54	14	ξ	ξ	PROPN
ejpam-4446	54	15	,	,	PUNCT
ejpam-4446	54	16	t)q	t)q	PUNCT
ejpam-4446	54	17	:	:	PUNCT
ejpam-4446	54	18	=	=	SYM
ejpam-4446	54	19	{	{	PUNCT
ejpam-4446	54	20	x	x	SYM
ejpam-4446	54	21	∈	∈	PROPN
ejpam-4446	54	22	x	x	PUNCT
ejpam-4446	55	1	|	|	NOUN
ejpam-4446	55	2	[	[	X
ejpam-4446	55	3	x	x	X
ejpam-4446	55	4	/	/	SYM
ejpam-4446	55	5	t	t	PROPN
ejpam-4446	55	6	]	]	X
ejpam-4446	55	7	q	q	X
ejpam-4446	55	8	lε	lε	X
ejpam-4446	55	9	ξ	ξ	PROPN
ejpam-4446	55	10	}	}	PUNCT
ejpam-4446	55	11	,	,	PUNCT
ejpam-4446	55	12	which	which	PRON
ejpam-4446	55	13	are	be	AUX
ejpam-4446	55	14	called	call	VERB
ejpam-4446	55	15	the	the	DET
ejpam-4446	55	16	∈-set	∈-set	NOUN
ejpam-4446	55	17	and	and	CCONJ
ejpam-4446	55	18	q	q	NOUN
ejpam-4446	55	19	-	-	PUNCT
ejpam-4446	55	20	set	set	VERB
ejpam-4446	55	21	,	,	PUNCT
ejpam-4446	55	22	respectively	respectively	ADV
ejpam-4446	55	23	,	,	PUNCT
ejpam-4446	55	24	of	of	ADP
ejpam-4446	55	25	lε	lε	ADP
ejpam-4446	55	26	ξ	ξ	PROPN
ejpam-4446	55	27	(	(	PUNCT
ejpam-4446	55	28	with	with	ADP
ejpam-4446	55	29	value	value	NOUN
ejpam-4446	55	30	t	t	PROPN
ejpam-4446	55	31	)	)	PUNCT
ejpam-4446	55	32	.	.	PUNCT
ejpam-4446	56	1	also	also	ADV
ejpam-4446	56	2	,	,	PUNCT
ejpam-4446	56	3	consider	consider	VERB
ejpam-4446	56	4	a	a	DET
ejpam-4446	56	5	set	set	NOUN
ejpam-4446	56	6	:	:	PUNCT
ejpam-4446	56	7	o	o	NOUN
ejpam-4446	56	8	(	(	PUNCT
ejpam-4446	56	9	lε	lε	X
ejpam-4446	56	10	ξ	ξ	PROPN
ejpam-4446	56	11	)	)	PUNCT
ejpam-4446	56	12	:	:	PUNCT
ejpam-4446	56	13	=	=	SYM
ejpam-4446	56	14	{	{	PUNCT
ejpam-4446	56	15	x	x	SYM
ejpam-4446	56	16	∈	∈	NOUN
ejpam-4446	56	17	x	x	INTJ
ejpam-4446	56	18	|	|	ADV
ejpam-4446	56	19	lε	lε	ADP
ejpam-4446	56	20	ξ(x	ξ(x	NOUN
ejpam-4446	56	21	)	)	PUNCT
ejpam-4446	56	22	>	>	X
ejpam-4446	56	23	0	0	NUM
ejpam-4446	56	24	}	}	PUNCT
ejpam-4446	56	25	(	(	PUNCT
ejpam-4446	56	26	10	10	NUM
ejpam-4446	56	27	)	)	PUNCT
ejpam-4446	56	28	which	which	PRON
ejpam-4446	56	29	is	be	AUX
ejpam-4446	56	30	called	call	VERB
ejpam-4446	56	31	an	an	DET
ejpam-4446	56	32	o	o	NOUN
ejpam-4446	56	33	-	-	NOUN
ejpam-4446	56	34	set	set	NOUN
ejpam-4446	56	35	of	of	ADP
ejpam-4446	56	36	lε	lε	PART
ejpam-4446	56	37	ξ	ξ	PROPN
ejpam-4446	56	38	.	.	PUNCT
ejpam-4446	57	1	it	it	PRON
ejpam-4446	57	2	is	be	AUX
ejpam-4446	57	3	observed	observe	VERB
ejpam-4446	57	4	that	that	SCONJ
ejpam-4446	58	1	o	o	NOUN
ejpam-4446	58	2	(	(	PUNCT
ejpam-4446	58	3	lε	lε	INTJ
ejpam-4446	58	4	ξ	ξ	X
ejpam-4446	58	5	)	)	PUNCT
ejpam-4446	58	6	=	=	PRON
ejpam-4446	58	7	{	{	PUNCT
ejpam-4446	58	8	x	x	PUNCT
ejpam-4446	58	9	∈	∈	PROPN
ejpam-4446	58	10	x	x	X
ejpam-4446	58	11	|	|	NOUN
ejpam-4446	58	12	ξ(x	ξ(x	NOUN
ejpam-4446	58	13	)	)	PUNCT
ejpam-4446	58	14	+	+	CCONJ
ejpam-4446	58	15	ε−	ε−	PROPN
ejpam-4446	58	16	1	1	NUM
ejpam-4446	58	17	>	>	PUNCT
ejpam-4446	58	18	0	0	NUM
ejpam-4446	58	19	}	}	PUNCT
ejpam-4446	58	20	.	.	PUNCT
ejpam-4446	59	1	3	3	X
ejpam-4446	59	2	.	.	X
ejpam-4446	59	3	lukasiewicz	lukasiewicz	VERB
ejpam-4446	59	4	fuzzy	fuzzy	ADJ
ejpam-4446	59	5	be	be	AUX
ejpam-4446	59	6	-	-	PUNCT
ejpam-4446	59	7	algebras	algebras	ADJ
ejpam-4446	59	8	in	in	ADP
ejpam-4446	59	9	what	what	PRON
ejpam-4446	59	10	follows	follow	VERB
ejpam-4446	59	11	,	,	PUNCT
ejpam-4446	59	12	let	let	VERB
ejpam-4446	59	13	x	x	PRON
ejpam-4446	59	14	and	and	CCONJ
ejpam-4446	59	15	ξ	ξ	PROPN
ejpam-4446	59	16	be	be	AUX
ejpam-4446	59	17	a	a	DET
ejpam-4446	59	18	be	be	NOUN
ejpam-4446	59	19	-	-	PUNCT
ejpam-4446	59	20	algebra	algebra	NOUN
ejpam-4446	59	21	and	and	CCONJ
ejpam-4446	59	22	a	a	DET
ejpam-4446	59	23	fuzzy	fuzzy	ADJ
ejpam-4446	59	24	set	set	NOUN
ejpam-4446	59	25	in	in	ADP
ejpam-4446	59	26	x	x	PUNCT
ejpam-4446	59	27	respectively	respectively	ADV
ejpam-4446	59	28	,	,	PUNCT
ejpam-4446	59	29	and	and	CCONJ
ejpam-4446	59	30	ε	ε	PROPN
ejpam-4446	59	31	is	be	AUX
ejpam-4446	59	32	an	an	DET
ejpam-4446	59	33	element	element	NOUN
ejpam-4446	59	34	of	of	ADP
ejpam-4446	59	35	(	(	PUNCT
ejpam-4446	59	36	0	0	NUM
ejpam-4446	59	37	,	,	PUNCT
ejpam-4446	59	38	1	1	NUM
ejpam-4446	59	39	)	)	PUNCT
ejpam-4446	59	40	unless	unless	SCONJ
ejpam-4446	59	41	otherwise	otherwise	ADV
ejpam-4446	59	42	specified	specify	VERB
ejpam-4446	59	43	.	.	PUNCT
ejpam-4446	60	1	definition	definition	NOUN
ejpam-4446	60	2	1	1	NUM
ejpam-4446	60	3	.	.	PUNCT
ejpam-4446	61	1	the	the	DET
ejpam-4446	61	2	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	61	3	fuzzy	fuzzy	NOUN
ejpam-4446	61	4	set	set	VERB
ejpam-4446	61	5	lε	lε	ADP
ejpam-4446	61	6	ξ	ξ	PROPN
ejpam-4446	61	7	of	of	ADP
ejpam-4446	61	8	ξ	ξ	PROPN
ejpam-4446	61	9	in	in	ADP
ejpam-4446	61	10	x	x	PROPN
ejpam-4446	61	11	is	be	AUX
ejpam-4446	61	12	called	call	VERB
ejpam-4446	61	13	a	a	DET
ejpam-4446	61	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	61	15	fuzzy	fuzzy	ADJ
ejpam-4446	61	16	bealgebra	bealgebra	NOUN
ejpam-4446	61	17	of	of	ADP
ejpam-4446	61	18	x	x	PRON
ejpam-4446	61	19	if	if	SCONJ
ejpam-4446	61	20	it	it	PRON
ejpam-4446	61	21	satisfies	satisfy	VERB
ejpam-4446	61	22	:	:	PUNCT
ejpam-4446	62	1	[	[	X
ejpam-4446	62	2	x	x	X
ejpam-4446	62	3	/	/	SYM
ejpam-4446	62	4	ta	ta	X
ejpam-4446	62	5	]	]	X
ejpam-4446	62	6	∈	∈	PROPN
ejpam-4446	62	7	lε	lε	X
ejpam-4446	62	8	ξ	ξ	X
ejpam-4446	62	9	,	,	PUNCT
ejpam-4446	62	10	[	[	X
ejpam-4446	62	11	y	y	X
ejpam-4446	62	12	/	/	SYM
ejpam-4446	62	13	tb	tb	NOUN
ejpam-4446	62	14	]	]	PUNCT
ejpam-4446	62	15	∈	∈	PROPN
ejpam-4446	62	16	lε	lε	X
ejpam-4446	62	17	ξ	ξ	X
ejpam-4446	62	18	⇒	⇒	NOUN
ejpam-4446	62	19	[	[	X
ejpam-4446	62	20	(	(	PUNCT
ejpam-4446	62	21	x	x	X
ejpam-4446	62	22	∗	∗	NOUN
ejpam-4446	62	23	y)/min{ta	y)/min{ta	NOUN
ejpam-4446	62	24	,	,	PUNCT
ejpam-4446	62	25	tb	tb	NOUN
ejpam-4446	62	26	}	}	PUNCT
ejpam-4446	62	27	]	]	PUNCT
ejpam-4446	62	28	∈	∈	PROPN
ejpam-4446	62	29	lε	lε	X
ejpam-4446	62	30	ξ	ξ	X
ejpam-4446	62	31	(	(	PUNCT
ejpam-4446	62	32	11	11	NUM
ejpam-4446	62	33	)	)	PUNCT
ejpam-4446	62	34	for	for	ADP
ejpam-4446	62	35	all	all	DET
ejpam-4446	62	36	x	x	NOUN
ejpam-4446	62	37	,	,	PUNCT
ejpam-4446	62	38	y	y	PROPN
ejpam-4446	62	39	∈	∈	PROPN
ejpam-4446	62	40	x	x	X
ejpam-4446	62	41	and	and	CCONJ
ejpam-4446	62	42	ta	ta	PROPN
ejpam-4446	62	43	,	,	PUNCT
ejpam-4446	62	44	tb	tb	ADP
ejpam-4446	62	45	∈	∈	PROPN
ejpam-4446	62	46	(	(	PUNCT
ejpam-4446	62	47	0	0	NUM
ejpam-4446	62	48	,	,	PUNCT
ejpam-4446	62	49	1	1	NUM
ejpam-4446	62	50	]	]	PUNCT
ejpam-4446	62	51	.	.	PUNCT
ejpam-4446	63	1	y.	y.	PROPN
ejpam-4446	63	2	b.	b.	PROPN
ejpam-4446	63	3	jun	jun	PROPN
ejpam-4446	63	4	,	,	PUNCT
ejpam-4446	63	5	s.	s.	PROPN
ejpam-4446	63	6	s.	s.	PROPN
ejpam-4446	63	7	ahn	ahn	PROPN
ejpam-4446	63	8	/	/	SYM
ejpam-4446	63	9	eur	eur	PROPN
ejpam-4446	63	10	.	.	PUNCT
ejpam-4446	64	1	j.	j.	PROPN
ejpam-4446	64	2	pure	pure	PROPN
ejpam-4446	64	3	appl	appl	PROPN
ejpam-4446	64	4	.	.	PROPN
ejpam-4446	64	5	math	math	PROPN
ejpam-4446	64	6	,	,	PUNCT
ejpam-4446	64	7	15	15	NUM
ejpam-4446	64	8	(	(	PUNCT
ejpam-4446	64	9	3	3	NUM
ejpam-4446	64	10	)	)	PUNCT
ejpam-4446	64	11	(	(	PUNCT
ejpam-4446	64	12	2022	2022	NUM
ejpam-4446	64	13	)	)	PUNCT
ejpam-4446	64	14	,	,	PUNCT
ejpam-4446	64	15	924	924	NUM
ejpam-4446	64	16	-	-	SYM
ejpam-4446	64	17	937	937	NUM
ejpam-4446	64	18	927	927	NUM
ejpam-4446	64	19	example	example	NOUN
ejpam-4446	64	20	1	1	NUM
ejpam-4446	64	21	.	.	X
ejpam-4446	64	22	consider	consider	VERB
ejpam-4446	64	23	a	a	DET
ejpam-4446	64	24	set	set	NOUN
ejpam-4446	64	25	x	x	X
ejpam-4446	64	26	=	=	SYM
ejpam-4446	64	27	{	{	PUNCT
ejpam-4446	64	28	1	1	NUM
ejpam-4446	64	29	,	,	PUNCT
ejpam-4446	64	30	b1	b1	NOUN
ejpam-4446	64	31	,	,	PUNCT
ejpam-4446	64	32	b2	b2	NOUN
ejpam-4446	64	33	,	,	PUNCT
ejpam-4446	64	34	b3	b3	PROPN
ejpam-4446	64	35	,	,	PUNCT
ejpam-4446	64	36	b4	b4	NOUN
ejpam-4446	64	37	,	,	PUNCT
ejpam-4446	64	38	b5	b5	PROPN
ejpam-4446	64	39	}	}	PUNCT
ejpam-4446	64	40	with	with	ADP
ejpam-4446	64	41	a	a	DET
ejpam-4446	64	42	binary	binary	ADJ
ejpam-4446	64	43	operation	operation	NOUN
ejpam-4446	64	44	“	"	PUNCT
ejpam-4446	64	45	∗	∗	NOUN
ejpam-4446	64	46	”	"	PUNCT
ejpam-4446	64	47	given	give	VERB
ejpam-4446	64	48	in	in	ADP
ejpam-4446	64	49	the	the	DET
ejpam-4446	64	50	table	table	NOUN
ejpam-4446	64	51	below	below	ADV
ejpam-4446	64	52	.	.	PUNCT
ejpam-4446	65	1	∗	∗	NOUN
ejpam-4446	65	2	1	1	NUM
ejpam-4446	65	3	b1	b1	NOUN
ejpam-4446	65	4	b2	b2	NOUN
ejpam-4446	65	5	b3	b3	PROPN
ejpam-4446	65	6	b4	b4	NOUN
ejpam-4446	65	7	b5	b5	PROPN
ejpam-4446	65	8	1	1	NUM
ejpam-4446	65	9	1	1	NUM
ejpam-4446	65	10	b1	b1	NOUN
ejpam-4446	65	11	b2	b2	NOUN
ejpam-4446	65	12	b3	b3	PROPN
ejpam-4446	65	13	b4	b4	PROPN
ejpam-4446	65	14	b5	b5	PROPN
ejpam-4446	65	15	b1	b1	NOUN
ejpam-4446	65	16	1	1	NUM
ejpam-4446	65	17	1	1	NUM
ejpam-4446	65	18	b1	b1	NOUN
ejpam-4446	65	19	b3	b3	PROPN
ejpam-4446	65	20	b3	b3	PROPN
ejpam-4446	65	21	b4	b4	PROPN
ejpam-4446	65	22	b2	b2	NOUN
ejpam-4446	65	23	1	1	NUM
ejpam-4446	65	24	1	1	NUM
ejpam-4446	65	25	1	1	NUM
ejpam-4446	65	26	b3	b3	PROPN
ejpam-4446	65	27	b3	b3	PROPN
ejpam-4446	65	28	b3	b3	PROPN
ejpam-4446	65	29	b3	b3	PROPN
ejpam-4446	65	30	1	1	NUM
ejpam-4446	65	31	b1	b1	NOUN
ejpam-4446	65	32	b2	b2	NOUN
ejpam-4446	65	33	1	1	NUM
ejpam-4446	65	34	b1	b1	NOUN
ejpam-4446	65	35	b2	b2	NOUN
ejpam-4446	65	36	b4	b4	NOUN
ejpam-4446	65	37	1	1	NUM
ejpam-4446	65	38	1	1	NUM
ejpam-4446	65	39	b1	b1	NOUN
ejpam-4446	65	40	1	1	NUM
ejpam-4446	65	41	1	1	NUM
ejpam-4446	65	42	b1	b1	NOUN
ejpam-4446	65	43	b5	b5	PROPN
ejpam-4446	65	44	1	1	NUM
ejpam-4446	65	45	1	1	NUM
ejpam-4446	65	46	1	1	NUM
ejpam-4446	65	47	1	1	NUM
ejpam-4446	65	48	1	1	NUM
ejpam-4446	65	49	1	1	NUM
ejpam-4446	65	50	then	then	ADV
ejpam-4446	65	51	(	(	PUNCT
ejpam-4446	65	52	x	x	X
ejpam-4446	65	53	,	,	PUNCT
ejpam-4446	65	54	∗	∗	NOUN
ejpam-4446	65	55	,	,	PUNCT
ejpam-4446	65	56	1	1	NUM
ejpam-4446	65	57	)	)	PUNCT
ejpam-4446	65	58	is	be	AUX
ejpam-4446	65	59	a	a	DET
ejpam-4446	65	60	be	be	NOUN
ejpam-4446	65	61	-	-	PUNCT
ejpam-4446	65	62	algebra	algebra	NOUN
ejpam-4446	65	63	(	(	PUNCT
ejpam-4446	65	64	see	see	VERB
ejpam-4446	65	65	[	[	X
ejpam-4446	65	66	7	7	NUM
ejpam-4446	65	67	]	]	NUM
ejpam-4446	65	68	)	)	PUNCT
ejpam-4446	65	69	.	.	PUNCT
ejpam-4446	66	1	define	define	VERB
ejpam-4446	66	2	a	a	DET
ejpam-4446	66	3	fuzzy	fuzzy	ADJ
ejpam-4446	66	4	set	set	NOUN
ejpam-4446	66	5	ξ	ξ	PROPN
ejpam-4446	66	6	in	in	ADP
ejpam-4446	66	7	x	x	PUNCT
ejpam-4446	66	8	as	as	SCONJ
ejpam-4446	66	9	follows	follow	VERB
ejpam-4446	66	10	:	:	PUNCT
ejpam-4446	66	11	ξ	ξ	X
ejpam-4446	66	12	:	:	PUNCT
ejpam-4446	66	13	x	x	SYM
ejpam-4446	66	14	→	→	SYM
ejpam-4446	67	1	[	[	X
ejpam-4446	67	2	0	0	NUM
ejpam-4446	67	3	,	,	PUNCT
ejpam-4446	67	4	1	1	NUM
ejpam-4446	67	5	]	]	PUNCT
ejpam-4446	67	6	,	,	PUNCT
ejpam-4446	67	7	x	x	SYM
ejpam-4446	67	8	7→	7→	NUM
ejpam-4446	67	9	{	{	PUNCT
ejpam-4446	67	10	0.76	0.76	NUM
ejpam-4446	67	11	if	if	SCONJ
ejpam-4446	67	12	x	x	X
ejpam-4446	67	13	∈	∈	PROPN
ejpam-4446	67	14	{	{	PUNCT
ejpam-4446	67	15	1	1	NUM
ejpam-4446	67	16	,	,	PUNCT
ejpam-4446	67	17	b1	b1	NOUN
ejpam-4446	67	18	,	,	PUNCT
ejpam-4446	67	19	b2	b2	NOUN
ejpam-4446	67	20	}	}	PUNCT
ejpam-4446	67	21	,	,	PUNCT
ejpam-4446	67	22	0.52	0.52	NUM
ejpam-4446	67	23	otherwise	otherwise	ADV
ejpam-4446	67	24	.	.	PUNCT
ejpam-4446	68	1	given	give	VERB
ejpam-4446	68	2	ε	ε	PROPN
ejpam-4446	68	3	:	:	PUNCT
ejpam-4446	68	4	=	=	NOUN
ejpam-4446	68	5	0.67	0.67	NUM
ejpam-4446	68	6	,	,	PUNCT
ejpam-4446	68	7	the	the	DET
ejpam-4446	68	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	68	9	fuzzy	fuzzy	NOUN
ejpam-4446	68	10	set	set	VERB
ejpam-4446	68	11	lε	lε	ADP
ejpam-4446	68	12	ξ	ξ	PROPN
ejpam-4446	68	13	of	of	ADP
ejpam-4446	68	14	ξ	ξ	PROPN
ejpam-4446	68	15	in	in	ADP
ejpam-4446	68	16	x	x	AUX
ejpam-4446	68	17	is	be	AUX
ejpam-4446	68	18	given	give	VERB
ejpam-4446	68	19	as	as	SCONJ
ejpam-4446	68	20	follows	follow	VERB
ejpam-4446	68	21	:	:	PUNCT
ejpam-4446	68	22	lε	lε	ADP
ejpam-4446	68	23	ξ	ξ	X
ejpam-4446	68	24	:	:	PUNCT
ejpam-4446	68	25	x	x	SYM
ejpam-4446	68	26	→	→	SYM
ejpam-4446	69	1	[	[	X
ejpam-4446	69	2	0	0	NUM
ejpam-4446	69	3	,	,	PUNCT
ejpam-4446	69	4	1	1	NUM
ejpam-4446	69	5	]	]	PUNCT
ejpam-4446	69	6	,	,	PUNCT
ejpam-4446	69	7	x	x	SYM
ejpam-4446	69	8	7→	7→	NUM
ejpam-4446	69	9	{	{	PUNCT
ejpam-4446	69	10	0.43	0.43	NUM
ejpam-4446	69	11	if	if	SCONJ
ejpam-4446	69	12	x	x	SYM
ejpam-4446	69	13	∈	∈	PROPN
ejpam-4446	69	14	{	{	PUNCT
ejpam-4446	69	15	1	1	NUM
ejpam-4446	69	16	,	,	PUNCT
ejpam-4446	69	17	b1	b1	NOUN
ejpam-4446	69	18	,	,	PUNCT
ejpam-4446	69	19	b2	b2	NOUN
ejpam-4446	69	20	}	}	PUNCT
ejpam-4446	69	21	,	,	PUNCT
ejpam-4446	69	22	0.19	0.19	NUM
ejpam-4446	69	23	otherwise	otherwise	ADV
ejpam-4446	69	24	.	.	PUNCT
ejpam-4446	70	1	it	it	PRON
ejpam-4446	70	2	is	be	AUX
ejpam-4446	70	3	routine	routine	ADJ
ejpam-4446	70	4	to	to	PART
ejpam-4446	70	5	verify	verify	VERB
ejpam-4446	70	6	that	that	SCONJ
ejpam-4446	70	7	lε	lε	ADP
ejpam-4446	70	8	ξ	ξ	PROPN
ejpam-4446	70	9	is	be	AUX
ejpam-4446	70	10	a	a	DET
ejpam-4446	70	11	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	70	12	fuzzy	fuzzy	ADJ
ejpam-4446	70	13	be	be	NOUN
ejpam-4446	70	14	-	-	PUNCT
ejpam-4446	70	15	algebra	algebra	NOUN
ejpam-4446	70	16	of	of	ADP
ejpam-4446	70	17	x.	x.	NOUN
ejpam-4446	70	18	we	we	PRON
ejpam-4446	70	19	provide	provide	VERB
ejpam-4446	70	20	a	a	DET
ejpam-4446	70	21	characterization	characterization	NOUN
ejpam-4446	70	22	of	of	ADP
ejpam-4446	70	23	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	70	24	fuzzy	fuzzy	ADJ
ejpam-4446	70	25	be	be	NOUN
ejpam-4446	70	26	-	-	PUNCT
ejpam-4446	70	27	algebra	algebra	NOUN
ejpam-4446	70	28	.	.	PUNCT
ejpam-4446	71	1	theorem	theorem	NOUN
ejpam-4446	71	2	1	1	NUM
ejpam-4446	71	3	.	.	PUNCT
ejpam-4446	72	1	given	give	VERB
ejpam-4446	72	2	the	the	DET
ejpam-4446	72	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	72	4	fuzzy	fuzzy	NOUN
ejpam-4446	72	5	set	set	VERB
ejpam-4446	72	6	lε	lε	ADP
ejpam-4446	72	7	ξ	ξ	PROPN
ejpam-4446	72	8	of	of	ADP
ejpam-4446	72	9	ξ	ξ	PROPN
ejpam-4446	72	10	in	in	ADP
ejpam-4446	72	11	x	x	PROPN
ejpam-4446	72	12	,	,	PUNCT
ejpam-4446	72	13	the	the	DET
ejpam-4446	72	14	following	follow	VERB
ejpam-4446	72	15	assertions	assertion	NOUN
ejpam-4446	72	16	are	be	AUX
ejpam-4446	72	17	equivalent	equivalent	ADJ
ejpam-4446	72	18	.	.	PUNCT
ejpam-4446	73	1	(	(	PUNCT
ejpam-4446	73	2	i	i	NOUN
ejpam-4446	73	3	)	)	PUNCT
ejpam-4446	73	4	lε	lε	ADP
ejpam-4446	73	5	ξ	ξ	X
ejpam-4446	73	6	satisfies	satisfie	NOUN
ejpam-4446	73	7	lε	lε	ADP
ejpam-4446	73	8	ξ(x	ξ(x	PROPN
ejpam-4446	73	9	∗	∗	X
ejpam-4446	73	10	y	y	PROPN
ejpam-4446	73	11	)	)	PUNCT
ejpam-4446	73	12	≥	≥	PROPN
ejpam-4446	73	13	min	min	PROPN
ejpam-4446	73	14	{	{	PUNCT
ejpam-4446	73	15	lε	lε	ADP
ejpam-4446	73	16	ξ(x	ξ(x	PROPN
ejpam-4446	73	17	)	)	PUNCT
ejpam-4446	73	18	,	,	PUNCT
ejpam-4446	73	19	lε	lε	ADP
ejpam-4446	73	20	ξ(y	ξ(y	PROPN
ejpam-4446	73	21	)	)	PUNCT
ejpam-4446	73	22	}	}	PUNCT
ejpam-4446	73	23	for	for	ADP
ejpam-4446	73	24	all	all	DET
ejpam-4446	73	25	x	x	NOUN
ejpam-4446	73	26	,	,	PUNCT
ejpam-4446	73	27	y	y	PROPN
ejpam-4446	73	28	∈	∈	PROPN
ejpam-4446	73	29	x.	x.	NOUN
ejpam-4446	73	30	(	(	PUNCT
ejpam-4446	73	31	ii	ii	NOUN
ejpam-4446	73	32	)	)	PUNCT
ejpam-4446	73	33	lε	lε	ADP
ejpam-4446	73	34	ξ	ξ	X
ejpam-4446	73	35	is	be	AUX
ejpam-4446	73	36	a	a	DET
ejpam-4446	73	37	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	73	38	fuzzy	fuzzy	ADJ
ejpam-4446	73	39	be	be	NOUN
ejpam-4446	73	40	-	-	PUNCT
ejpam-4446	73	41	algebra	algebra	NOUN
ejpam-4446	73	42	of	of	ADP
ejpam-4446	73	43	x.	x.	NOUN
ejpam-4446	73	44	proof	proof	NOUN
ejpam-4446	73	45	.	.	PUNCT
ejpam-4446	74	1	(	(	PUNCT
ejpam-4446	74	2	i	i	NOUN
ejpam-4446	74	3	)	)	PUNCT
ejpam-4446	74	4	⇒	⇒	PROPN
ejpam-4446	74	5	(	(	PUNCT
ejpam-4446	74	6	ii	ii	NOUN
ejpam-4446	74	7	)	)	PUNCT
ejpam-4446	74	8	.	.	PUNCT
ejpam-4446	75	1	let	let	VERB
ejpam-4446	75	2	x	x	PRON
ejpam-4446	75	3	,	,	PUNCT
ejpam-4446	75	4	y	y	PROPN
ejpam-4446	75	5	∈	∈	PROPN
ejpam-4446	75	6	x	x	X
ejpam-4446	75	7	and	and	CCONJ
ejpam-4446	75	8	ta	ta	PROPN
ejpam-4446	75	9	,	,	PUNCT
ejpam-4446	75	10	tb	tb	ADP
ejpam-4446	75	11	∈	∈	PROPN
ejpam-4446	75	12	(	(	PUNCT
ejpam-4446	75	13	0	0	NUM
ejpam-4446	75	14	,	,	PUNCT
ejpam-4446	75	15	1	1	NUM
ejpam-4446	75	16	]	]	PUNCT
ejpam-4446	75	17	be	be	AUX
ejpam-4446	75	18	such	such	ADJ
ejpam-4446	75	19	that	that	SCONJ
ejpam-4446	75	20	[	[	X
ejpam-4446	75	21	x	x	X
ejpam-4446	75	22	/	/	SYM
ejpam-4446	75	23	ta	ta	X
ejpam-4446	75	24	]	]	X
ejpam-4446	75	25	∈	∈	PROPN
ejpam-4446	75	26	lε	lε	X
ejpam-4446	75	27	ξ	ξ	PROPN
ejpam-4446	75	28	and	and	CCONJ
ejpam-4446	75	29	[	[	X
ejpam-4446	75	30	y	y	X
ejpam-4446	75	31	/	/	SYM
ejpam-4446	75	32	tb	tb	NOUN
ejpam-4446	75	33	]	]	PUNCT
ejpam-4446	75	34	∈	∈	PROPN
ejpam-4446	75	35	lε	lε	X
ejpam-4446	75	36	ξ	ξ	X
ejpam-4446	75	37	.	.	PUNCT
ejpam-4446	76	1	then	then	ADV
ejpam-4446	76	2	lε	lε	ADP
ejpam-4446	76	3	ξ(x	ξ(x	NOUN
ejpam-4446	76	4	)	)	PUNCT
ejpam-4446	76	5	≥	≥	NOUN
ejpam-4446	76	6	ta	ta	X
ejpam-4446	76	7	and	and	CCONJ
ejpam-4446	76	8	lε	lε	ADP
ejpam-4446	76	9	ξ(y	ξ(y	PROPN
ejpam-4446	76	10	)	)	PUNCT
ejpam-4446	76	11	≥	≥	NOUN
ejpam-4446	76	12	tb	tb	NOUN
ejpam-4446	76	13	,	,	PUNCT
ejpam-4446	76	14	which	which	PRON
ejpam-4446	76	15	implis	impli	VERB
ejpam-4446	76	16	that	that	SCONJ
ejpam-4446	76	17	lε	lε	ADP
ejpam-4446	76	18	ξ(x	ξ(x	PROPN
ejpam-4446	76	19	∗	∗	X
ejpam-4446	76	20	y	y	PROPN
ejpam-4446	76	21	)	)	PUNCT
ejpam-4446	76	22	≥	≥	PROPN
ejpam-4446	76	23	min	min	PROPN
ejpam-4446	76	24	{	{	PUNCT
ejpam-4446	76	25	lε	lε	ADP
ejpam-4446	76	26	ξ(x	ξ(x	PROPN
ejpam-4446	76	27	)	)	PUNCT
ejpam-4446	76	28	,	,	PUNCT
ejpam-4446	76	29	lε	lε	ADP
ejpam-4446	76	30	ξ(y	ξ(y	PROPN
ejpam-4446	76	31	)	)	PUNCT
ejpam-4446	76	32	}	}	PUNCT
ejpam-4446	76	33	≥	≥	NUM
ejpam-4446	76	34	min{ta	min{ta	X
ejpam-4446	76	35	,	,	PUNCT
ejpam-4446	76	36	tb	tb	NOUN
ejpam-4446	76	37	}	}	PUNCT
ejpam-4446	76	38	.	.	PUNCT
ejpam-4446	77	1	therefore	therefore	ADV
ejpam-4446	77	2	[	[	X
ejpam-4446	77	3	(	(	PUNCT
ejpam-4446	77	4	x	x	SYM
ejpam-4446	77	5	∗	∗	NOUN
ejpam-4446	77	6	y)min{tb	y)min{tb	NOUN
ejpam-4446	77	7	,	,	PUNCT
ejpam-4446	77	8	tb	tb	NOUN
ejpam-4446	77	9	}	}	PUNCT
ejpam-4446	77	10	]	]	PUNCT
ejpam-4446	77	11	∈	∈	PROPN
ejpam-4446	77	12	lε	lε	X
ejpam-4446	77	13	ξ	ξ	PROPN
ejpam-4446	77	14	,	,	PUNCT
ejpam-4446	77	15	and	and	CCONJ
ejpam-4446	77	16	consequently	consequently	ADV
ejpam-4446	77	17	lε	lε	SCONJ
ejpam-4446	77	18	ξ	ξ	PROPN
ejpam-4446	77	19	is	be	AUX
ejpam-4446	77	20	a	a	DET
ejpam-4446	77	21	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	77	22	fuzzy	fuzzy	ADJ
ejpam-4446	77	23	be	be	NOUN
ejpam-4446	77	24	-	-	PUNCT
ejpam-4446	77	25	algebra	algebra	NOUN
ejpam-4446	77	26	of	of	ADP
ejpam-4446	77	27	x.	x.	PROPN
ejpam-4446	77	28	(	(	PUNCT
ejpam-4446	77	29	ii	ii	NOUN
ejpam-4446	77	30	)	)	PUNCT
ejpam-4446	77	31	⇒	⇒	NOUN
ejpam-4446	77	32	(	(	PUNCT
ejpam-4446	77	33	i	i	NOUN
ejpam-4446	77	34	)	)	PUNCT
ejpam-4446	77	35	.	.	PUNCT
ejpam-4446	78	1	let	let	VERB
ejpam-4446	78	2	x	x	PRON
ejpam-4446	78	3	,	,	PUNCT
ejpam-4446	78	4	y	y	PROPN
ejpam-4446	78	5	∈	∈	PROPN
ejpam-4446	78	6	x.	x.	NOUN
ejpam-4446	79	1	it	it	PRON
ejpam-4446	79	2	is	be	AUX
ejpam-4446	79	3	clear	clear	ADJ
ejpam-4446	79	4	that	that	SCONJ
ejpam-4446	79	5	[	[	X
ejpam-4446	79	6	x/	x/	X
ejpam-4446	79	7	lε	lε	X
ejpam-4446	79	8	ξ(x	ξ(x	NOUN
ejpam-4446	79	9	)	)	PUNCT
ejpam-4446	79	10	]	]	PUNCT
ejpam-4446	80	1	∈	∈	PROPN
ejpam-4446	80	2	lε	lε	X
ejpam-4446	80	3	ξ	ξ	PROPN
ejpam-4446	80	4	and	and	CCONJ
ejpam-4446	80	5	[	[	X
ejpam-4446	80	6	y/	y/	NOUN
ejpam-4446	80	7	lε	lε	ADP
ejpam-4446	80	8	ξ(y	ξ(y	PROPN
ejpam-4446	80	9	)	)	PUNCT
ejpam-4446	80	10	]	]	PUNCT
ejpam-4446	81	1	∈	∈	PROPN
ejpam-4446	81	2	lε	lε	X
ejpam-4446	81	3	ξ	ξ	X
ejpam-4446	81	4	.	.	PUNCT
ejpam-4446	82	1	hence	hence	ADV
ejpam-4446	82	2	[	[	X
ejpam-4446	82	3	(	(	PUNCT
ejpam-4446	82	4	x	x	SYM
ejpam-4446	82	5	∗	∗	NOUN
ejpam-4446	82	6	y)/min	y)/min	NOUN
ejpam-4446	82	7	{	{	PUNCT
ejpam-4446	82	8	lε	lε	ADP
ejpam-4446	82	9	ξ(x	ξ(x	PROPN
ejpam-4446	82	10	)	)	PUNCT
ejpam-4446	82	11	,	,	PUNCT
ejpam-4446	82	12	lε	lε	ADP
ejpam-4446	82	13	ξ(y	ξ(y	PROPN
ejpam-4446	82	14	)	)	PUNCT
ejpam-4446	82	15	}	}	PUNCT
ejpam-4446	82	16	]	]	PUNCT
ejpam-4446	83	1	∈	∈	NOUN
ejpam-4446	83	2	lε	lε	X
ejpam-4446	83	3	ξ	ξ	X
ejpam-4446	83	4	by	by	ADP
ejpam-4446	83	5	(	(	PUNCT
ejpam-4446	83	6	11	11	NUM
ejpam-4446	83	7	)	)	PUNCT
ejpam-4446	83	8	,	,	PUNCT
ejpam-4446	83	9	that	that	ADV
ejpam-4446	83	10	is	is	ADV
ejpam-4446	83	11	,	,	PUNCT
ejpam-4446	83	12	lε	lε	ADP
ejpam-4446	83	13	ξ(x	ξ(x	PROPN
ejpam-4446	83	14	∗	∗	X
ejpam-4446	83	15	y	y	PROPN
ejpam-4446	83	16	)	)	PUNCT
ejpam-4446	83	17	≥	≥	PROPN
ejpam-4446	83	18	min	min	PROPN
ejpam-4446	83	19	{	{	PUNCT
ejpam-4446	83	20	lε	lε	ADP
ejpam-4446	83	21	ξ(x	ξ(x	PROPN
ejpam-4446	83	22	)	)	PUNCT
ejpam-4446	83	23	,	,	PUNCT
ejpam-4446	83	24	lε	lε	ADP
ejpam-4446	83	25	ξ(y	ξ(y	PROPN
ejpam-4446	83	26	)	)	PUNCT
ejpam-4446	83	27	}	}	PUNCT
ejpam-4446	83	28	.	.	PUNCT
ejpam-4446	84	1	proposition	proposition	NOUN
ejpam-4446	84	2	1	1	NUM
ejpam-4446	84	3	.	.	PUNCT
ejpam-4446	85	1	if	if	SCONJ
ejpam-4446	85	2	ξ	ξ	PROPN
ejpam-4446	85	3	is	be	AUX
ejpam-4446	85	4	order	order	NOUN
ejpam-4446	85	5	preserving	preserve	VERB
ejpam-4446	85	6	or	or	CCONJ
ejpam-4446	85	7	order	order	NOUN
ejpam-4446	85	8	reversing	reverse	VERB
ejpam-4446	85	9	in	in	ADP
ejpam-4446	85	10	x	x	NOUN
ejpam-4446	85	11	,	,	PUNCT
ejpam-4446	85	12	then	then	ADV
ejpam-4446	85	13	its	its	PRON
ejpam-4446	85	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	85	15	fuzzy	fuzzy	NOUN
ejpam-4446	85	16	set	set	VERB
ejpam-4446	85	17	lε	lε	AUX
ejpam-4446	85	18	ξ	ξ	X
ejpam-4446	85	19	is	be	AUX
ejpam-4446	85	20	also	also	ADV
ejpam-4446	85	21	order	order	NOUN
ejpam-4446	85	22	preserving	preserve	VERB
ejpam-4446	85	23	or	or	CCONJ
ejpam-4446	85	24	order	order	NOUN
ejpam-4446	85	25	reversing	reverse	VERB
ejpam-4446	85	26	in	in	ADP
ejpam-4446	85	27	x.	x.	NOUN
ejpam-4446	85	28	proof	proof	NOUN
ejpam-4446	85	29	.	.	PUNCT
ejpam-4446	86	1	straightforward	straightforward	ADJ
ejpam-4446	86	2	.	.	PUNCT
ejpam-4446	87	1	in	in	ADP
ejpam-4446	87	2	poposition	poposition	NOUN
ejpam-4446	87	3	1	1	NUM
ejpam-4446	87	4	,	,	PUNCT
ejpam-4446	87	5	the	the	DET
ejpam-4446	87	6	converse	converse	NOUN
ejpam-4446	87	7	may	may	AUX
ejpam-4446	87	8	not	not	PART
ejpam-4446	87	9	be	be	AUX
ejpam-4446	87	10	true	true	ADJ
ejpam-4446	87	11	as	as	SCONJ
ejpam-4446	87	12	seen	see	VERB
ejpam-4446	87	13	in	in	ADP
ejpam-4446	87	14	the	the	DET
ejpam-4446	87	15	following	follow	VERB
ejpam-4446	87	16	example	example	NOUN
ejpam-4446	87	17	.	.	PUNCT
ejpam-4446	88	1	y.	y.	PROPN
ejpam-4446	88	2	b.	b.	PROPN
ejpam-4446	88	3	jun	jun	PROPN
ejpam-4446	88	4	,	,	PUNCT
ejpam-4446	88	5	s.	s.	PROPN
ejpam-4446	88	6	s.	s.	PROPN
ejpam-4446	88	7	ahn	ahn	PROPN
ejpam-4446	88	8	/	/	SYM
ejpam-4446	88	9	eur	eur	PROPN
ejpam-4446	88	10	.	.	PUNCT
ejpam-4446	89	1	j.	j.	PROPN
ejpam-4446	89	2	pure	pure	PROPN
ejpam-4446	89	3	appl	appl	PROPN
ejpam-4446	89	4	.	.	PROPN
ejpam-4446	89	5	math	math	PROPN
ejpam-4446	89	6	,	,	PUNCT
ejpam-4446	89	7	15	15	NUM
ejpam-4446	89	8	(	(	PUNCT
ejpam-4446	89	9	3	3	NUM
ejpam-4446	89	10	)	)	PUNCT
ejpam-4446	89	11	(	(	PUNCT
ejpam-4446	89	12	2022	2022	NUM
ejpam-4446	89	13	)	)	PUNCT
ejpam-4446	89	14	,	,	PUNCT
ejpam-4446	89	15	924	924	NUM
ejpam-4446	89	16	-	-	SYM
ejpam-4446	89	17	937	937	NUM
ejpam-4446	89	18	928	928	NUM
ejpam-4446	89	19	example	example	NOUN
ejpam-4446	89	20	2	2	NUM
ejpam-4446	89	21	.	.	X
ejpam-4446	89	22	consider	consider	VERB
ejpam-4446	89	23	the	the	DET
ejpam-4446	89	24	be	be	NOUN
ejpam-4446	89	25	-	-	PUNCT
ejpam-4446	89	26	algebra	algebra	NOUN
ejpam-4446	89	27	x	x	PUNCT
ejpam-4446	89	28	given	give	VERB
ejpam-4446	89	29	in	in	ADP
ejpam-4446	89	30	example	example	NOUN
ejpam-4446	89	31	1	1	X
ejpam-4446	89	32	.	.	PUNCT
ejpam-4446	90	1	its	its	PRON
ejpam-4446	90	2	hasse	hasse	ADJ
ejpam-4446	90	3	diagram	diagram	NOUN
ejpam-4446	90	4	is	be	AUX
ejpam-4446	90	5	given	give	VERB
ejpam-4446	90	6	as	as	SCONJ
ejpam-4446	90	7	follows	follow	VERB
ejpam-4446	90	8	:	:	PUNCT
ejpam-4446	90	9	r	r	NOUN
ejpam-4446	90	10	b5	b5	PROPN
ejpam-4446	90	11	jj	jj	PROPN
ejpam-4446	90	12	rb2	rb2	PROPN
ejpam-4446	90	13	rz	rz	NOUN
ejpam-4446	90	14	z	z	PROPN
ejpam-4446	90	15	b4	b4	PROPN
ejpam-4446	90	16	rjj	rjj	PROPN
ejpam-4446	90	17	b3r	b3r	PROPN
ejpam-4446	90	18	b1	b1	PROPN
ejpam-4446	90	19	r1	r1	PROPN
ejpam-4446	90	20	(	(	PUNCT
ejpam-4446	90	21	1	1	X
ejpam-4446	90	22	)	)	PUNCT
ejpam-4446	90	23	let	let	VERB
ejpam-4446	90	24	ξ	ξ	X
ejpam-4446	90	25	be	be	AUX
ejpam-4446	90	26	a	a	DET
ejpam-4446	90	27	fuzzy	fuzzy	ADJ
ejpam-4446	90	28	set	set	NOUN
ejpam-4446	90	29	in	in	ADP
ejpam-4446	90	30	x	x	PUNCT
ejpam-4446	90	31	defined	define	VERB
ejpam-4446	90	32	as	as	SCONJ
ejpam-4446	90	33	follows	follow	VERB
ejpam-4446	90	34	:	:	PUNCT
ejpam-4446	90	35	ξ	ξ	X
ejpam-4446	90	36	:	:	PUNCT
ejpam-4446	90	37	x	x	SYM
ejpam-4446	90	38	→	→	SYM
ejpam-4446	91	1	[	[	X
ejpam-4446	91	2	0	0	NUM
ejpam-4446	91	3	,	,	PUNCT
ejpam-4446	91	4	1	1	NUM
ejpam-4446	91	5	]	]	PUNCT
ejpam-4446	91	6	,	,	PUNCT
ejpam-4446	91	7	x	x	SYM
ejpam-4446	91	8	7→	7→	NUM
ejpam-4446	91	9			NUM
ejpam-4446	91	10	0.88	0.88	NUM
ejpam-4446	91	11	if	if	SCONJ
ejpam-4446	91	12	x	x	NOUN
ejpam-4446	91	13	=	=	SYM
ejpam-4446	91	14	1	1	NUM
ejpam-4446	91	15	,	,	PUNCT
ejpam-4446	91	16	0.78	0.78	NUM
ejpam-4446	91	17	if	if	SCONJ
ejpam-4446	91	18	x	x	NOUN
ejpam-4446	91	19	=	=	SYM
ejpam-4446	91	20	b1	b1	NOUN
ejpam-4446	91	21	,	,	PUNCT
ejpam-4446	91	22	0.63	0.63	NUM
ejpam-4446	91	23	if	if	SCONJ
ejpam-4446	91	24	x	x	PART
ejpam-4446	91	25	=	=	SYM
ejpam-4446	91	26	b2	b2	NOUN
ejpam-4446	91	27	,	,	PUNCT
ejpam-4446	91	28	0.48	0.48	NUM
ejpam-4446	92	1	if	if	SCONJ
ejpam-4446	92	2	x	x	NOUN
ejpam-4446	92	3	=	=	SYM
ejpam-4446	92	4	b3	b3	PROPN
ejpam-4446	92	5	,	,	PUNCT
ejpam-4446	92	6	0.55	0.55	NUM
ejpam-4446	92	7	if	if	SCONJ
ejpam-4446	92	8	x	x	NOUN
ejpam-4446	92	9	=	=	SYM
ejpam-4446	92	10	b4	b4	NOUN
ejpam-4446	92	11	,	,	PUNCT
ejpam-4446	92	12	0.47	0.47	NUM
ejpam-4446	92	13	if	if	SCONJ
ejpam-4446	92	14	x	x	PROPN
ejpam-4446	92	15	=	=	SYM
ejpam-4446	92	16	b5	b5	PROPN
ejpam-4446	92	17	.	.	PUNCT
ejpam-4446	93	1	given	give	VERB
ejpam-4446	93	2	ε	ε	PROPN
ejpam-4446	93	3	:	:	PUNCT
ejpam-4446	93	4	=	=	SYM
ejpam-4446	93	5	0.43	0.43	NUM
ejpam-4446	93	6	,	,	PUNCT
ejpam-4446	93	7	the	the	DET
ejpam-4446	93	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	93	9	fuzzy	fuzzy	NOUN
ejpam-4446	93	10	set	set	VERB
ejpam-4446	93	11	lε	lε	ADP
ejpam-4446	93	12	ξ	ξ	PROPN
ejpam-4446	93	13	of	of	ADP
ejpam-4446	93	14	ξ	ξ	PROPN
ejpam-4446	93	15	in	in	ADP
ejpam-4446	93	16	x	x	AUX
ejpam-4446	93	17	is	be	AUX
ejpam-4446	93	18	given	give	VERB
ejpam-4446	93	19	as	as	SCONJ
ejpam-4446	93	20	follows	follow	VERB
ejpam-4446	93	21	:	:	PUNCT
ejpam-4446	93	22	lε	lε	ADP
ejpam-4446	93	23	ξ	ξ	X
ejpam-4446	93	24	:	:	PUNCT
ejpam-4446	93	25	x	x	SYM
ejpam-4446	93	26	→	→	SYM
ejpam-4446	94	1	[	[	X
ejpam-4446	94	2	0	0	NUM
ejpam-4446	94	3	,	,	PUNCT
ejpam-4446	94	4	1	1	NUM
ejpam-4446	94	5	]	]	PUNCT
ejpam-4446	94	6	,	,	PUNCT
ejpam-4446	94	7	x	x	SYM
ejpam-4446	94	8	7→	7→	NUM
ejpam-4446	94	9			NUM
ejpam-4446	94	10	0.31	0.31	NUM
ejpam-4446	95	1	if	if	SCONJ
ejpam-4446	95	2	x	x	NOUN
ejpam-4446	95	3	=	=	SYM
ejpam-4446	95	4	1	1	NUM
ejpam-4446	95	5	,	,	PUNCT
ejpam-4446	95	6	0.21	0.21	NUM
ejpam-4446	95	7	if	if	SCONJ
ejpam-4446	95	8	x	x	X
ejpam-4446	95	9	=	=	SYM
ejpam-4446	95	10	b1	b1	NOUN
ejpam-4446	95	11	,	,	PUNCT
ejpam-4446	95	12	0.06	0.06	PUNCT
ejpam-4446	95	13	if	if	SCONJ
ejpam-4446	95	14	x	x	NOUN
ejpam-4446	95	15	=	=	SYM
ejpam-4446	95	16	b2	b2	NOUN
ejpam-4446	95	17	,	,	PUNCT
ejpam-4446	95	18	0.00	0.00	NUM
ejpam-4446	95	19	if	if	SCONJ
ejpam-4446	95	20	x	x	NOUN
ejpam-4446	95	21	=	=	SYM
ejpam-4446	95	22	b3	b3	PROPN
ejpam-4446	95	23	,	,	PUNCT
ejpam-4446	95	24	0.00	0.00	NUM
ejpam-4446	95	25	if	if	SCONJ
ejpam-4446	95	26	x	x	NOUN
ejpam-4446	95	27	=	=	SYM
ejpam-4446	95	28	b4	b4	NOUN
ejpam-4446	95	29	,	,	PUNCT
ejpam-4446	95	30	0.00	0.00	NUM
ejpam-4446	95	31	if	if	SCONJ
ejpam-4446	95	32	x	x	X
ejpam-4446	95	33	=	=	SYM
ejpam-4446	95	34	b5	b5	PROPN
ejpam-4446	95	35	.	.	PUNCT
ejpam-4446	96	1	then	then	ADV
ejpam-4446	96	2	lε	lε	X
ejpam-4446	96	3	ξ	ξ	PROPN
ejpam-4446	96	4	is	be	AUX
ejpam-4446	96	5	order	order	NOUN
ejpam-4446	96	6	preversing	preverse	VERB
ejpam-4446	96	7	in	in	ADP
ejpam-4446	96	8	x	x	NOUN
ejpam-4446	96	9	,	,	PUNCT
ejpam-4446	96	10	but	but	CCONJ
ejpam-4446	96	11	ξ	ξ	PROPN
ejpam-4446	96	12	is	be	AUX
ejpam-4446	96	13	not	not	PART
ejpam-4446	96	14	order	order	NOUN
ejpam-4446	96	15	preserving	preserve	VERB
ejpam-4446	96	16	in	in	ADP
ejpam-4446	96	17	x	x	PUNCT
ejpam-4446	96	18	since	since	SCONJ
ejpam-4446	96	19	b4	b4	NOUN
ejpam-4446	96	20	≤	≤	PROPN
ejpam-4446	96	21	b3	b3	PROPN
ejpam-4446	96	22	and	and	CCONJ
ejpam-4446	96	23	ξ(b4	ξ(b4	NOUN
ejpam-4446	96	24	)	)	PUNCT
ejpam-4446	96	25	≥	≥	NOUN
ejpam-4446	96	26	ξ(b3	ξ(b3	NOUN
ejpam-4446	96	27	)	)	PUNCT
ejpam-4446	96	28	.	.	PUNCT
ejpam-4446	97	1	(	(	PUNCT
ejpam-4446	97	2	2	2	X
ejpam-4446	97	3	)	)	PUNCT
ejpam-4446	97	4	let	let	VERB
ejpam-4446	97	5	ζ	ζ	NOUN
ejpam-4446	97	6	be	be	AUX
ejpam-4446	97	7	a	a	DET
ejpam-4446	97	8	fuzzy	fuzzy	ADJ
ejpam-4446	97	9	set	set	NOUN
ejpam-4446	97	10	in	in	ADP
ejpam-4446	97	11	x	x	PUNCT
ejpam-4446	97	12	defined	define	VERB
ejpam-4446	97	13	as	as	SCONJ
ejpam-4446	97	14	follows	follow	VERB
ejpam-4446	97	15	:	:	PUNCT
ejpam-4446	97	16	ζ	ζ	NOUN
ejpam-4446	97	17	:	:	PUNCT
ejpam-4446	97	18	x	x	X
ejpam-4446	97	19	→	→	SYM
ejpam-4446	98	1	[	[	X
ejpam-4446	98	2	0	0	NUM
ejpam-4446	98	3	,	,	PUNCT
ejpam-4446	98	4	1	1	NUM
ejpam-4446	98	5	]	]	PUNCT
ejpam-4446	98	6	,	,	PUNCT
ejpam-4446	98	7	x	x	SYM
ejpam-4446	98	8	7→	7→	NUM
ejpam-4446	98	9			NUM
ejpam-4446	98	10	0.34	0.34	NUM
ejpam-4446	99	1	if	if	SCONJ
ejpam-4446	99	2	x	x	X
ejpam-4446	99	3	=	=	SYM
ejpam-4446	99	4	1	1	NUM
ejpam-4446	99	5	,	,	PUNCT
ejpam-4446	99	6	0.31	0.31	NUM
ejpam-4446	99	7	if	if	SCONJ
ejpam-4446	99	8	x	x	NOUN
ejpam-4446	99	9	=	=	SYM
ejpam-4446	99	10	b1	b1	NOUN
ejpam-4446	99	11	,	,	PUNCT
ejpam-4446	99	12	0.55	0.55	NUM
ejpam-4446	99	13	if	if	SCONJ
ejpam-4446	99	14	x	x	NOUN
ejpam-4446	99	15	=	=	SYM
ejpam-4446	99	16	b2	b2	NOUN
ejpam-4446	99	17	,	,	PUNCT
ejpam-4446	99	18	0.48	0.48	NUM
ejpam-4446	100	1	if	if	SCONJ
ejpam-4446	100	2	x	x	NOUN
ejpam-4446	100	3	=	=	SYM
ejpam-4446	100	4	b3	b3	PROPN
ejpam-4446	100	5	,	,	PUNCT
ejpam-4446	100	6	0.53	0.53	NUM
ejpam-4446	100	7	if	if	SCONJ
ejpam-4446	100	8	x	x	X
ejpam-4446	100	9	=	=	SYM
ejpam-4446	100	10	b4	b4	NOUN
ejpam-4446	100	11	,	,	PUNCT
ejpam-4446	100	12	0.63	0.63	NUM
ejpam-4446	100	13	if	if	SCONJ
ejpam-4446	100	14	x	x	X
ejpam-4446	100	15	=	=	SYM
ejpam-4446	100	16	b5	b5	PROPN
ejpam-4446	100	17	.	.	PUNCT
ejpam-4446	100	18	given	give	VERB
ejpam-4446	100	19	δ	δ	PROPN
ejpam-4446	100	20	:	:	PUNCT
ejpam-4446	100	21	=	=	SYM
ejpam-4446	100	22	0.62	0.62	NUM
ejpam-4446	100	23	,	,	PUNCT
ejpam-4446	100	24	the	the	DET
ejpam-4446	100	25	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	100	26	fuzzy	fuzzy	ADJ
ejpam-4446	100	27	set	set	VERB
ejpam-4446	100	28	lδ	lδ	NOUN
ejpam-4446	100	29	ζ	ζ	NOUN
ejpam-4446	100	30	of	of	ADP
ejpam-4446	100	31	ζ	ζ	NOUN
ejpam-4446	100	32	in	in	ADP
ejpam-4446	100	33	x	x	AUX
ejpam-4446	100	34	is	be	AUX
ejpam-4446	100	35	given	give	VERB
ejpam-4446	100	36	as	as	SCONJ
ejpam-4446	100	37	follows	follow	VERB
ejpam-4446	100	38	:	:	PUNCT
ejpam-4446	100	39	lδ	lδ	VERB
ejpam-4446	100	40	ζ	ζ	NOUN
ejpam-4446	100	41	:	:	PUNCT
ejpam-4446	100	42	x	x	X
ejpam-4446	100	43	→	→	SYM
ejpam-4446	101	1	[	[	X
ejpam-4446	101	2	0	0	NUM
ejpam-4446	101	3	,	,	PUNCT
ejpam-4446	101	4	1	1	NUM
ejpam-4446	101	5	]	]	PUNCT
ejpam-4446	101	6	,	,	PUNCT
ejpam-4446	101	7	x	x	SYM
ejpam-4446	101	8	7→	7→	NUM
ejpam-4446	101	9			NUM
ejpam-4446	101	10	0.00	0.00	NUM
ejpam-4446	101	11	if	if	SCONJ
ejpam-4446	101	12	x	x	SYM
ejpam-4446	101	13	=	=	SYM
ejpam-4446	101	14	1	1	NUM
ejpam-4446	101	15	,	,	PUNCT
ejpam-4446	101	16	0.00	0.00	NUM
ejpam-4446	101	17	if	if	SCONJ
ejpam-4446	101	18	x	x	X
ejpam-4446	101	19	=	=	SYM
ejpam-4446	101	20	b1	b1	NOUN
ejpam-4446	101	21	,	,	PUNCT
ejpam-4446	101	22	0.17	0.17	NUM
ejpam-4446	101	23	if	if	SCONJ
ejpam-4446	101	24	x	x	NOUN
ejpam-4446	101	25	=	=	SYM
ejpam-4446	101	26	b2	b2	NOUN
ejpam-4446	101	27	,	,	PUNCT
ejpam-4446	101	28	0.10	0.10	NUM
ejpam-4446	101	29	if	if	SCONJ
ejpam-4446	101	30	x	x	NOUN
ejpam-4446	101	31	=	=	SYM
ejpam-4446	101	32	b3	b3	PROPN
ejpam-4446	101	33	,	,	PUNCT
ejpam-4446	101	34	0.15	0.15	NUM
ejpam-4446	101	35	if	if	SCONJ
ejpam-4446	101	36	x	x	X
ejpam-4446	101	37	=	=	SYM
ejpam-4446	101	38	b4	b4	NOUN
ejpam-4446	101	39	,	,	PUNCT
ejpam-4446	101	40	0.25	0.25	NUM
ejpam-4446	101	41	if	if	SCONJ
ejpam-4446	101	42	x	x	NOUN
ejpam-4446	101	43	=	=	SYM
ejpam-4446	101	44	b5	b5	PROPN
ejpam-4446	101	45	.	.	PUNCT
ejpam-4446	102	1	then	then	ADV
ejpam-4446	102	2	lε	lε	X
ejpam-4446	102	3	ξ	ξ	PROPN
ejpam-4446	102	4	is	be	AUX
ejpam-4446	102	5	order	order	NOUN
ejpam-4446	102	6	reversing	reverse	VERB
ejpam-4446	102	7	in	in	ADP
ejpam-4446	102	8	x	x	NOUN
ejpam-4446	102	9	,	,	PUNCT
ejpam-4446	102	10	but	but	CCONJ
ejpam-4446	102	11	ζ	ζ	NOUN
ejpam-4446	102	12	is	be	AUX
ejpam-4446	102	13	not	not	PART
ejpam-4446	102	14	order	order	NOUN
ejpam-4446	102	15	reversing	reverse	VERB
ejpam-4446	102	16	in	in	ADP
ejpam-4446	102	17	x	x	PUNCT
ejpam-4446	102	18	since	since	SCONJ
ejpam-4446	102	19	b1	b1	NOUN
ejpam-4446	102	20	≤	≤	NUM
ejpam-4446	102	21	1	1	NUM
ejpam-4446	102	22	and	and	CCONJ
ejpam-4446	102	23	ζ(b1	ζ(b1	VERB
ejpam-4446	102	24	)	)	PUNCT
ejpam-4446	102	25	≤	≤	NOUN
ejpam-4446	102	26	ζ(1	ζ(1	PROPN
ejpam-4446	102	27	)	)	PUNCT
ejpam-4446	102	28	.	.	PUNCT
ejpam-4446	103	1	y.	y.	PROPN
ejpam-4446	103	2	b.	b.	PROPN
ejpam-4446	103	3	jun	jun	PROPN
ejpam-4446	103	4	,	,	PUNCT
ejpam-4446	103	5	s.	s.	PROPN
ejpam-4446	103	6	s.	s.	PROPN
ejpam-4446	103	7	ahn	ahn	PROPN
ejpam-4446	103	8	/	/	SYM
ejpam-4446	103	9	eur	eur	PROPN
ejpam-4446	103	10	.	.	PUNCT
ejpam-4446	104	1	j.	j.	PROPN
ejpam-4446	104	2	pure	pure	PROPN
ejpam-4446	104	3	appl	appl	PROPN
ejpam-4446	104	4	.	.	PROPN
ejpam-4446	104	5	math	math	PROPN
ejpam-4446	104	6	,	,	PUNCT
ejpam-4446	104	7	15	15	NUM
ejpam-4446	104	8	(	(	PUNCT
ejpam-4446	104	9	3	3	NUM
ejpam-4446	104	10	)	)	PUNCT
ejpam-4446	104	11	(	(	PUNCT
ejpam-4446	104	12	2022	2022	NUM
ejpam-4446	104	13	)	)	PUNCT
ejpam-4446	104	14	,	,	PUNCT
ejpam-4446	104	15	924	924	NUM
ejpam-4446	104	16	-	-	SYM
ejpam-4446	104	17	937	937	NUM
ejpam-4446	104	18	929	929	NUM
ejpam-4446	104	19	lemma	lemma	PROPN
ejpam-4446	104	20	1	1	NUM
ejpam-4446	104	21	.	.	PUNCT
ejpam-4446	105	1	if	if	SCONJ
ejpam-4446	105	2	lε	lε	PRON
ejpam-4446	105	3	ξ	ξ	PROPN
ejpam-4446	105	4	is	be	AUX
ejpam-4446	105	5	a	a	DET
ejpam-4446	105	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	105	7	fuzzy	fuzzy	ADJ
ejpam-4446	105	8	be	be	NOUN
ejpam-4446	105	9	-	-	PUNCT
ejpam-4446	105	10	algebra	algebra	NOUN
ejpam-4446	105	11	of	of	ADP
ejpam-4446	105	12	x	x	NOUN
ejpam-4446	105	13	,	,	PUNCT
ejpam-4446	105	14	then	then	ADV
ejpam-4446	105	15	lε	lε	PROPN
ejpam-4446	105	16	ξ(1	ξ(1	PROPN
ejpam-4446	105	17	)	)	PUNCT
ejpam-4446	105	18	≥	≥	NOUN
ejpam-4446	105	19	lε	lε	ADP
ejpam-4446	105	20	ξ(x	ξ(x	PROPN
ejpam-4446	105	21	)	)	PUNCT
ejpam-4446	105	22	for	for	ADP
ejpam-4446	105	23	all	all	DET
ejpam-4446	105	24	x	x	SYM
ejpam-4446	105	25	∈	∈	ADJ
ejpam-4446	105	26	x.	x.	NOUN
ejpam-4446	105	27	proof	proof	NOUN
ejpam-4446	105	28	.	.	PUNCT
ejpam-4446	106	1	it	it	PRON
ejpam-4446	106	2	can	can	AUX
ejpam-4446	106	3	be	be	AUX
ejpam-4446	106	4	induced	induce	VERB
ejpam-4446	106	5	by	by	ADP
ejpam-4446	106	6	(	(	PUNCT
ejpam-4446	106	7	be1	be1	NOUN
ejpam-4446	106	8	)	)	PUNCT
ejpam-4446	106	9	and	and	CCONJ
ejpam-4446	106	10	theorem	theorem	VERB
ejpam-4446	106	11	1	1	NUM
ejpam-4446	106	12	.	.	PUNCT
ejpam-4446	106	13	proposition	proposition	NOUN
ejpam-4446	106	14	2	2	NUM
ejpam-4446	106	15	.	.	PUNCT
ejpam-4446	107	1	if	if	SCONJ
ejpam-4446	107	2	a	a	DET
ejpam-4446	107	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	107	4	fuzzy	fuzzy	ADJ
ejpam-4446	107	5	be	be	NOUN
ejpam-4446	107	6	-	-	PUNCT
ejpam-4446	107	7	algebra	algebra	NOUN
ejpam-4446	107	8	lε	lε	X
ejpam-4446	107	9	ξ	ξ	PROPN
ejpam-4446	107	10	of	of	ADP
ejpam-4446	107	11	ξ	ξ	PROPN
ejpam-4446	107	12	is	be	AUX
ejpam-4446	107	13	order	order	NOUN
ejpam-4446	107	14	reversing	reverse	VERB
ejpam-4446	107	15	in	in	ADP
ejpam-4446	107	16	x	x	NOUN
ejpam-4446	107	17	,	,	PUNCT
ejpam-4446	107	18	then	then	ADV
ejpam-4446	107	19	it	it	PRON
ejpam-4446	107	20	is	be	AUX
ejpam-4446	107	21	constant	constant	ADJ
ejpam-4446	107	22	.	.	PUNCT
ejpam-4446	108	1	proof	proof	NOUN
ejpam-4446	108	2	.	.	PUNCT
ejpam-4446	109	1	let	let	VERB
ejpam-4446	109	2	lε	lε	PRON
ejpam-4446	109	3	ξ	ξ	X
ejpam-4446	109	4	be	be	AUX
ejpam-4446	109	5	a	a	DET
ejpam-4446	109	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	109	7	fuzzy	fuzzy	ADJ
ejpam-4446	109	8	be	be	NOUN
ejpam-4446	109	9	-	-	PUNCT
ejpam-4446	109	10	algebra	algebra	NOUN
ejpam-4446	109	11	of	of	ADP
ejpam-4446	109	12	x	x	PUNCT
ejpam-4446	109	13	which	which	PRON
ejpam-4446	109	14	is	be	AUX
ejpam-4446	109	15	order	order	NOUN
ejpam-4446	109	16	reversing	reverse	VERB
ejpam-4446	109	17	.	.	PUNCT
ejpam-4446	110	1	since	since	SCONJ
ejpam-4446	110	2	x	x	PROPN
ejpam-4446	110	3	≤	≤	X
ejpam-4446	110	4	1	1	NUM
ejpam-4446	110	5	for	for	ADP
ejpam-4446	110	6	all	all	PRON
ejpam-4446	110	7	x	x	SYM
ejpam-4446	110	8	∈	∈	PROPN
ejpam-4446	110	9	x	x	NOUN
ejpam-4446	110	10	,	,	PUNCT
ejpam-4446	110	11	we	we	PRON
ejpam-4446	110	12	have	have	VERB
ejpam-4446	110	13	lε	lε	ADP
ejpam-4446	110	14	ξ(x	ξ(x	NOUN
ejpam-4446	110	15	)	)	PUNCT
ejpam-4446	110	16	≥	≥	NOUN
ejpam-4446	110	17	lε	lε	X
ejpam-4446	110	18	ξ(1	ξ(1	PROPN
ejpam-4446	110	19	)	)	PUNCT
ejpam-4446	110	20	for	for	ADP
ejpam-4446	110	21	all	all	PRON
ejpam-4446	110	22	x	x	SYM
ejpam-4446	110	23	∈	∈	NOUN
ejpam-4446	110	24	x.	x.	NOUN
ejpam-4446	111	1	the	the	DET
ejpam-4446	111	2	combination	combination	NOUN
ejpam-4446	111	3	of	of	ADP
ejpam-4446	111	4	this	this	PRON
ejpam-4446	111	5	and	and	CCONJ
ejpam-4446	111	6	lemma	lemma	PROPN
ejpam-4446	111	7	1	1	NUM
ejpam-4446	111	8	induces	induce	VERB
ejpam-4446	111	9	lε	lε	ADP
ejpam-4446	111	10	ξ(x	ξ(x	NOUN
ejpam-4446	111	11	)	)	PUNCT
ejpam-4446	112	1	=	=	PRON
ejpam-4446	112	2	lε	lε	X
ejpam-4446	112	3	ξ(1	ξ(1	PROPN
ejpam-4446	112	4	)	)	PUNCT
ejpam-4446	112	5	for	for	ADP
ejpam-4446	112	6	all	all	PRON
ejpam-4446	112	7	x	x	SYM
ejpam-4446	112	8	∈	∈	ADJ
ejpam-4446	112	9	x.	x.	NOUN
ejpam-4446	112	10	hence	hence	ADV
ejpam-4446	112	11	lε	lε	PROPN
ejpam-4446	112	12	ξ	ξ	PROPN
ejpam-4446	112	13	is	be	AUX
ejpam-4446	112	14	a	a	DET
ejpam-4446	112	15	constant	constant	ADJ
ejpam-4446	112	16	on	on	ADP
ejpam-4446	112	17	x.	x.	NOUN
ejpam-4446	112	18	theorem	theorem	VERB
ejpam-4446	112	19	2	2	NUM
ejpam-4446	112	20	.	.	PUNCT
ejpam-4446	113	1	if	if	SCONJ
ejpam-4446	113	2	ξ	ξ	PROPN
ejpam-4446	113	3	is	be	AUX
ejpam-4446	113	4	a	a	DET
ejpam-4446	113	5	fuzzy	fuzzy	ADJ
ejpam-4446	113	6	be	be	NOUN
ejpam-4446	113	7	-	-	PUNCT
ejpam-4446	113	8	algebra	algebra	NOUN
ejpam-4446	113	9	of	of	ADP
ejpam-4446	113	10	x	x	NOUN
ejpam-4446	113	11	,	,	PUNCT
ejpam-4446	113	12	then	then	ADV
ejpam-4446	113	13	its	its	PRON
ejpam-4446	113	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	113	15	fuzzy	fuzzy	NOUN
ejpam-4446	113	16	set	set	VERB
ejpam-4446	113	17	lε	lε	AUX
ejpam-4446	113	18	ξ	ξ	X
ejpam-4446	113	19	is	be	AUX
ejpam-4446	113	20	a	a	DET
ejpam-4446	113	21	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	113	22	fuzzy	fuzzy	ADJ
ejpam-4446	113	23	be	be	NOUN
ejpam-4446	113	24	-	-	PUNCT
ejpam-4446	113	25	algebra	algebra	NOUN
ejpam-4446	113	26	of	of	ADP
ejpam-4446	113	27	x.	x.	NOUN
ejpam-4446	113	28	proof	proof	PROPN
ejpam-4446	113	29	.	.	PUNCT
ejpam-4446	114	1	assume	assume	VERB
ejpam-4446	114	2	that	that	SCONJ
ejpam-4446	114	3	ξ	ξ	PROPN
ejpam-4446	114	4	is	be	AUX
ejpam-4446	114	5	a	a	DET
ejpam-4446	114	6	fuzzy	fuzzy	ADJ
ejpam-4446	114	7	be	be	NOUN
ejpam-4446	114	8	-	-	PUNCT
ejpam-4446	114	9	algebra	algebra	NOUN
ejpam-4446	114	10	of	of	ADP
ejpam-4446	114	11	x.	x.	NOUN
ejpam-4446	114	12	let	let	VERB
ejpam-4446	114	13	x	x	PRON
ejpam-4446	114	14	,	,	PUNCT
ejpam-4446	114	15	y	y	PROPN
ejpam-4446	114	16	∈	∈	PROPN
ejpam-4446	114	17	x	x	X
ejpam-4446	114	18	and	and	CCONJ
ejpam-4446	114	19	ta	ta	PROPN
ejpam-4446	114	20	,	,	PUNCT
ejpam-4446	114	21	tb	tb	ADP
ejpam-4446	114	22	∈	∈	PROPN
ejpam-4446	114	23	(	(	PUNCT
ejpam-4446	114	24	0	0	NUM
ejpam-4446	114	25	,	,	PUNCT
ejpam-4446	114	26	1	1	NUM
ejpam-4446	114	27	]	]	PUNCT
ejpam-4446	114	28	be	be	AUX
ejpam-4446	114	29	such	such	ADJ
ejpam-4446	114	30	that	that	SCONJ
ejpam-4446	114	31	[	[	X
ejpam-4446	114	32	x	x	X
ejpam-4446	114	33	/	/	SYM
ejpam-4446	114	34	ta	ta	X
ejpam-4446	114	35	]	]	X
ejpam-4446	114	36	∈	∈	PROPN
ejpam-4446	114	37	lε	lε	X
ejpam-4446	114	38	ξ	ξ	PROPN
ejpam-4446	114	39	and	and	CCONJ
ejpam-4446	114	40	[	[	X
ejpam-4446	114	41	y	y	X
ejpam-4446	114	42	/	/	SYM
ejpam-4446	114	43	tb	tb	NOUN
ejpam-4446	114	44	]	]	PUNCT
ejpam-4446	114	45	∈	∈	PROPN
ejpam-4446	114	46	lε	lε	X
ejpam-4446	114	47	ξ	ξ	X
ejpam-4446	114	48	.	.	PUNCT
ejpam-4446	115	1	then	then	ADV
ejpam-4446	115	2	lε	lε	ADP
ejpam-4446	115	3	ξ(x	ξ(x	NOUN
ejpam-4446	115	4	)	)	PUNCT
ejpam-4446	115	5	≥	≥	NOUN
ejpam-4446	115	6	ta	ta	X
ejpam-4446	115	7	and	and	CCONJ
ejpam-4446	115	8	lε	lε	ADP
ejpam-4446	115	9	ξ(y	ξ(y	PROPN
ejpam-4446	115	10	)	)	PUNCT
ejpam-4446	115	11	≥	≥	NOUN
ejpam-4446	115	12	tb	tb	NOUN
ejpam-4446	115	13	,	,	PUNCT
ejpam-4446	115	14	so	so	ADV
ejpam-4446	115	15	lε	lε	ADP
ejpam-4446	115	16	ξ(x	ξ(x	PROPN
ejpam-4446	115	17	∗	∗	X
ejpam-4446	115	18	y	y	NOUN
ejpam-4446	115	19	)	)	PUNCT
ejpam-4446	115	20	=	=	SYM
ejpam-4446	115	21	max{0	max{0	PROPN
ejpam-4446	115	22	,	,	PUNCT
ejpam-4446	115	23	ξ(x	ξ(x	PROPN
ejpam-4446	115	24	∗	∗	NOUN
ejpam-4446	115	25	y	y	NOUN
ejpam-4446	115	26	)	)	PUNCT
ejpam-4446	116	1	+	+	CCONJ
ejpam-4446	116	2	ε−	ε−	PROPN
ejpam-4446	116	3	1	1	NUM
ejpam-4446	116	4	}	}	PUNCT
ejpam-4446	116	5	≥	≥	NOUN
ejpam-4446	116	6	max{0,min{ξ(x	max{0,min{ξ(x	NOUN
ejpam-4446	116	7	)	)	PUNCT
ejpam-4446	116	8	,	,	PUNCT
ejpam-4446	116	9	ξ(y	ξ(y	PROPN
ejpam-4446	116	10	)	)	PUNCT
ejpam-4446	116	11	}	}	PUNCT
ejpam-4446	117	1	+	+	CCONJ
ejpam-4446	117	2	ε−	ε−	PROPN
ejpam-4446	117	3	1	1	NUM
ejpam-4446	117	4	}	}	PUNCT
ejpam-4446	117	5	=	=	SYM
ejpam-4446	117	6	max{0,min{ξ(x	max{0,min{ξ(x	NOUN
ejpam-4446	117	7	)	)	PUNCT
ejpam-4446	118	1	+	+	CCONJ
ejpam-4446	118	2	ε−	ε−	PROPN
ejpam-4446	118	3	1	1	NUM
ejpam-4446	118	4	,	,	PUNCT
ejpam-4446	118	5	ξ(y	ξ(y	PROPN
ejpam-4446	118	6	)	)	PUNCT
ejpam-4446	119	1	+	+	CCONJ
ejpam-4446	119	2	ε−	ε−	PROPN
ejpam-4446	119	3	1	1	NUM
ejpam-4446	119	4	}	}	PUNCT
ejpam-4446	119	5	}	}	PUNCT
ejpam-4446	119	6	=	=	SYM
ejpam-4446	119	7	min{max{0	min{max{0	X
ejpam-4446	119	8	,	,	PUNCT
ejpam-4446	119	9	ξ(x	ξ(x	NOUN
ejpam-4446	119	10	)	)	PUNCT
ejpam-4446	119	11	+	+	CCONJ
ejpam-4446	119	12	ε−	ε−	PROPN
ejpam-4446	119	13	1},max{0	1},max{0	NUM
ejpam-4446	119	14	,	,	PUNCT
ejpam-4446	119	15	ξ(y	ξ(y	PROPN
ejpam-4446	119	16	)	)	PUNCT
ejpam-4446	120	1	+	+	CCONJ
ejpam-4446	120	2	ε−	ε−	PROPN
ejpam-4446	120	3	1	1	NUM
ejpam-4446	120	4	}	}	PUNCT
ejpam-4446	120	5	}	}	PUNCT
ejpam-4446	120	6	=	=	SYM
ejpam-4446	120	7	min	min	NOUN
ejpam-4446	120	8	{	{	PUNCT
ejpam-4446	120	9	lε	lε	ADP
ejpam-4446	120	10	ξ(x	ξ(x	PROPN
ejpam-4446	120	11	)	)	PUNCT
ejpam-4446	120	12	,	,	PUNCT
ejpam-4446	120	13	lε	lε	ADP
ejpam-4446	120	14	ξ(y	ξ(y	PROPN
ejpam-4446	120	15	)	)	PUNCT
ejpam-4446	120	16	}	}	PUNCT
ejpam-4446	120	17	≥	≥	NUM
ejpam-4446	120	18	min{ta	min{ta	X
ejpam-4446	120	19	,	,	PUNCT
ejpam-4446	120	20	tb	tb	NOUN
ejpam-4446	120	21	}	}	PUNCT
ejpam-4446	120	22	.	.	PUNCT
ejpam-4446	121	1	hence	hence	ADV
ejpam-4446	121	2	[	[	X
ejpam-4446	121	3	(	(	PUNCT
ejpam-4446	121	4	x∗y)/min{ta	x∗y)/min{ta	ADJ
ejpam-4446	121	5	,	,	PUNCT
ejpam-4446	121	6	tb	tb	X
ejpam-4446	121	7	}	}	PUNCT
ejpam-4446	121	8	]	]	PUNCT
ejpam-4446	121	9	∈	∈	PROPN
ejpam-4446	121	10	lε	lε	X
ejpam-4446	121	11	ξ	ξ	PROPN
ejpam-4446	121	12	,	,	PUNCT
ejpam-4446	121	13	and	and	CCONJ
ejpam-4446	121	14	therefore	therefore	ADV
ejpam-4446	121	15	lε	lε	X
ejpam-4446	121	16	ξ	ξ	PROPN
ejpam-4446	121	17	is	be	AUX
ejpam-4446	121	18	a	a	DET
ejpam-4446	121	19	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	121	20	fuzzy	fuzzy	ADJ
ejpam-4446	121	21	be	be	NOUN
ejpam-4446	121	22	-	-	PUNCT
ejpam-4446	121	23	algebra	algebra	NOUN
ejpam-4446	121	24	of	of	ADP
ejpam-4446	121	25	x.	x.	NOUN
ejpam-4446	121	26	the	the	DET
ejpam-4446	121	27	converse	converse	NOUN
ejpam-4446	121	28	of	of	ADP
ejpam-4446	121	29	theorem	theorem	ADJ
ejpam-4446	121	30	2	2	NUM
ejpam-4446	121	31	may	may	AUX
ejpam-4446	121	32	not	not	PART
ejpam-4446	121	33	be	be	AUX
ejpam-4446	121	34	true	true	ADJ
ejpam-4446	121	35	as	as	SCONJ
ejpam-4446	121	36	shown	show	VERB
ejpam-4446	121	37	in	in	ADP
ejpam-4446	121	38	the	the	DET
ejpam-4446	121	39	following	follow	VERB
ejpam-4446	121	40	example	example	NOUN
ejpam-4446	121	41	.	.	PUNCT
ejpam-4446	122	1	example	example	NOUN
ejpam-4446	123	1	3	3	X
ejpam-4446	123	2	.	.	X
ejpam-4446	123	3	consider	consider	VERB
ejpam-4446	123	4	a	a	DET
ejpam-4446	123	5	set	set	NOUN
ejpam-4446	123	6	x	x	X
ejpam-4446	123	7	=	=	SYM
ejpam-4446	123	8	{	{	PUNCT
ejpam-4446	123	9	1	1	NUM
ejpam-4446	123	10	,	,	PUNCT
ejpam-4446	123	11	b1	b1	NOUN
ejpam-4446	123	12	,	,	PUNCT
ejpam-4446	123	13	b2	b2	NOUN
ejpam-4446	123	14	,	,	PUNCT
ejpam-4446	123	15	b3	b3	NOUN
ejpam-4446	123	16	,	,	PUNCT
ejpam-4446	123	17	b4	b4	NOUN
ejpam-4446	123	18	}	}	PUNCT
ejpam-4446	123	19	with	with	ADP
ejpam-4446	123	20	a	a	DET
ejpam-4446	123	21	binary	binary	ADJ
ejpam-4446	123	22	operation	operation	NOUN
ejpam-4446	123	23	“	"	PUNCT
ejpam-4446	123	24	∗	∗	NOUN
ejpam-4446	123	25	”	"	PUNCT
ejpam-4446	123	26	given	give	VERB
ejpam-4446	123	27	in	in	ADP
ejpam-4446	123	28	the	the	DET
ejpam-4446	123	29	table	table	NOUN
ejpam-4446	123	30	below	below	ADV
ejpam-4446	123	31	.	.	PUNCT
ejpam-4446	124	1	∗	∗	NOUN
ejpam-4446	124	2	1	1	NUM
ejpam-4446	124	3	b1	b1	NOUN
ejpam-4446	124	4	b2	b2	NOUN
ejpam-4446	124	5	b3	b3	PROPN
ejpam-4446	124	6	b4	b4	NOUN
ejpam-4446	124	7	1	1	NUM
ejpam-4446	124	8	1	1	NUM
ejpam-4446	124	9	b1	b1	NOUN
ejpam-4446	124	10	b2	b2	NOUN
ejpam-4446	124	11	b3	b3	PROPN
ejpam-4446	124	12	b4	b4	NOUN
ejpam-4446	124	13	b1	b1	VERB
ejpam-4446	124	14	1	1	NUM
ejpam-4446	124	15	1	1	NUM
ejpam-4446	124	16	b2	b2	NOUN
ejpam-4446	124	17	b3	b3	PROPN
ejpam-4446	124	18	b4	b4	PROPN
ejpam-4446	124	19	b2	b2	NOUN
ejpam-4446	124	20	1	1	NUM
ejpam-4446	124	21	b1	b1	NOUN
ejpam-4446	124	22	1	1	NUM
ejpam-4446	124	23	b3	b3	PROPN
ejpam-4446	124	24	b3	b3	PROPN
ejpam-4446	124	25	b3	b3	PROPN
ejpam-4446	124	26	1	1	NUM
ejpam-4446	124	27	1	1	NUM
ejpam-4446	124	28	b2	b2	NOUN
ejpam-4446	124	29	1	1	NUM
ejpam-4446	124	30	b2	b2	NOUN
ejpam-4446	124	31	b4	b4	NOUN
ejpam-4446	124	32	1	1	NUM
ejpam-4446	124	33	1	1	NUM
ejpam-4446	124	34	1	1	NUM
ejpam-4446	124	35	1	1	NUM
ejpam-4446	124	36	1	1	NUM
ejpam-4446	124	37	then	then	ADV
ejpam-4446	124	38	(	(	PUNCT
ejpam-4446	124	39	x	x	X
ejpam-4446	124	40	,	,	PUNCT
ejpam-4446	124	41	∗	∗	NOUN
ejpam-4446	124	42	,	,	PUNCT
ejpam-4446	124	43	1	1	NUM
ejpam-4446	124	44	)	)	PUNCT
ejpam-4446	124	45	is	be	AUX
ejpam-4446	124	46	a	a	DET
ejpam-4446	124	47	be	be	NOUN
ejpam-4446	124	48	-	-	PUNCT
ejpam-4446	124	49	algebra	algebra	NOUN
ejpam-4446	124	50	(	(	PUNCT
ejpam-4446	124	51	see	see	VERB
ejpam-4446	124	52	[	[	X
ejpam-4446	124	53	7	7	NUM
ejpam-4446	124	54	]	]	NUM
ejpam-4446	124	55	)	)	PUNCT
ejpam-4446	124	56	.	.	PUNCT
ejpam-4446	125	1	define	define	VERB
ejpam-4446	125	2	a	a	DET
ejpam-4446	125	3	fuzzy	fuzzy	ADJ
ejpam-4446	125	4	set	set	NOUN
ejpam-4446	125	5	ξ	ξ	PROPN
ejpam-4446	125	6	in	in	ADP
ejpam-4446	125	7	x	x	PUNCT
ejpam-4446	125	8	as	as	SCONJ
ejpam-4446	125	9	follows	follow	VERB
ejpam-4446	125	10	:	:	PUNCT
ejpam-4446	125	11	ξ	ξ	X
ejpam-4446	125	12	:	:	PUNCT
ejpam-4446	125	13	x	x	SYM
ejpam-4446	125	14	→	→	SYM
ejpam-4446	126	1	[	[	X
ejpam-4446	126	2	0	0	NUM
ejpam-4446	126	3	,	,	PUNCT
ejpam-4446	126	4	1	1	NUM
ejpam-4446	126	5	]	]	PUNCT
ejpam-4446	126	6	,	,	PUNCT
ejpam-4446	126	7	x	x	X
ejpam-4446	126	8	7→	7→	NOUN
ejpam-4446	126	9			NOUN
ejpam-4446	126	10	0.73	0.73	NUM
ejpam-4446	126	11	if	if	SCONJ
ejpam-4446	126	12	x	x	NOUN
ejpam-4446	126	13	=	=	SYM
ejpam-4446	126	14	1	1	NUM
ejpam-4446	126	15	,	,	PUNCT
ejpam-4446	126	16	0.42	0.42	NUM
ejpam-4446	126	17	if	if	SCONJ
ejpam-4446	126	18	x	x	X
ejpam-4446	126	19	=	=	SYM
ejpam-4446	126	20	b1	b1	NOUN
ejpam-4446	126	21	,	,	PUNCT
ejpam-4446	126	22	0.59	0.59	NUM
ejpam-4446	126	23	if	if	SCONJ
ejpam-4446	126	24	x	x	NOUN
ejpam-4446	126	25	=	=	SYM
ejpam-4446	126	26	b2	b2	NOUN
ejpam-4446	126	27	,	,	PUNCT
ejpam-4446	126	28	0.46	0.46	NUM
ejpam-4446	126	29	if	if	SCONJ
ejpam-4446	126	30	x	x	NOUN
ejpam-4446	126	31	=	=	SYM
ejpam-4446	126	32	b3	b3	PROPN
ejpam-4446	126	33	,	,	PUNCT
ejpam-4446	126	34	0.68	0.68	NUM
ejpam-4446	126	35	if	if	SCONJ
ejpam-4446	126	36	x	x	NOUN
ejpam-4446	126	37	=	=	NOUN
ejpam-4446	126	38	b4	b4	NOUN
ejpam-4446	126	39	.	.	PUNCT
ejpam-4446	127	1	y.	y.	PROPN
ejpam-4446	127	2	b.	b.	PROPN
ejpam-4446	127	3	jun	jun	PROPN
ejpam-4446	127	4	,	,	PUNCT
ejpam-4446	127	5	s.	s.	PROPN
ejpam-4446	127	6	s.	s.	PROPN
ejpam-4446	127	7	ahn	ahn	PROPN
ejpam-4446	127	8	/	/	SYM
ejpam-4446	127	9	eur	eur	PROPN
ejpam-4446	127	10	.	.	PUNCT
ejpam-4446	128	1	j.	j.	PROPN
ejpam-4446	128	2	pure	pure	PROPN
ejpam-4446	128	3	appl	appl	PROPN
ejpam-4446	128	4	.	.	PROPN
ejpam-4446	128	5	math	math	PROPN
ejpam-4446	128	6	,	,	PUNCT
ejpam-4446	128	7	15	15	NUM
ejpam-4446	128	8	(	(	PUNCT
ejpam-4446	128	9	3	3	NUM
ejpam-4446	128	10	)	)	PUNCT
ejpam-4446	128	11	(	(	PUNCT
ejpam-4446	128	12	2022	2022	NUM
ejpam-4446	128	13	)	)	PUNCT
ejpam-4446	128	14	,	,	PUNCT
ejpam-4446	128	15	924	924	NUM
ejpam-4446	128	16	-	-	SYM
ejpam-4446	128	17	937	937	NUM
ejpam-4446	128	18	930	930	NUM
ejpam-4446	128	19	given	give	VERB
ejpam-4446	128	20	ε	ε	PROPN
ejpam-4446	128	21	:	:	PUNCT
ejpam-4446	128	22	=	=	NOUN
ejpam-4446	128	23	0.41	0.41	NUM
ejpam-4446	128	24	,	,	PUNCT
ejpam-4446	128	25	the	the	DET
ejpam-4446	128	26	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	128	27	fuzzy	fuzzy	NOUN
ejpam-4446	128	28	set	set	VERB
ejpam-4446	128	29	lε	lε	ADP
ejpam-4446	128	30	ξ	ξ	PROPN
ejpam-4446	128	31	of	of	ADP
ejpam-4446	128	32	ξ	ξ	PROPN
ejpam-4446	128	33	in	in	ADP
ejpam-4446	128	34	x	x	AUX
ejpam-4446	128	35	is	be	AUX
ejpam-4446	128	36	given	give	VERB
ejpam-4446	128	37	as	as	SCONJ
ejpam-4446	128	38	follows	follow	VERB
ejpam-4446	128	39	:	:	PUNCT
ejpam-4446	128	40	lε	lε	ADP
ejpam-4446	128	41	ξ	ξ	X
ejpam-4446	128	42	:	:	PUNCT
ejpam-4446	128	43	x	x	SYM
ejpam-4446	128	44	→	→	SYM
ejpam-4446	128	45	[	[	X
ejpam-4446	128	46	0	0	NUM
ejpam-4446	128	47	,	,	PUNCT
ejpam-4446	128	48	1	1	NUM
ejpam-4446	128	49	]	]	PUNCT
ejpam-4446	128	50	,	,	PUNCT
ejpam-4446	128	51	x	x	PUNCT
ejpam-4446	128	52	7→	7→	NOUN
ejpam-4446	128	53			NOUN
ejpam-4446	128	54	0.14	0.14	NUM
ejpam-4446	128	55	if	if	SCONJ
ejpam-4446	128	56	x	x	PROPN
ejpam-4446	128	57	=	=	SYM
ejpam-4446	128	58	1	1	NUM
ejpam-4446	128	59	,	,	PUNCT
ejpam-4446	128	60	0.00	0.00	NUM
ejpam-4446	128	61	if	if	SCONJ
ejpam-4446	128	62	x	x	X
ejpam-4446	128	63	=	=	SYM
ejpam-4446	128	64	b1	b1	NOUN
ejpam-4446	128	65	,	,	PUNCT
ejpam-4446	128	66	0.00	0.00	NUM
ejpam-4446	128	67	if	if	SCONJ
ejpam-4446	128	68	x	x	PRON
ejpam-4446	128	69	=	=	SYM
ejpam-4446	128	70	b2	b2	NOUN
ejpam-4446	128	71	,	,	PUNCT
ejpam-4446	128	72	0.00	0.00	NUM
ejpam-4446	128	73	if	if	SCONJ
ejpam-4446	128	74	x	x	NOUN
ejpam-4446	128	75	=	=	SYM
ejpam-4446	128	76	b3	b3	PROPN
ejpam-4446	128	77	,	,	PUNCT
ejpam-4446	128	78	0.09	0.09	NUM
ejpam-4446	128	79	if	if	SCONJ
ejpam-4446	128	80	x	x	X
ejpam-4446	128	81	=	=	NOUN
ejpam-4446	128	82	b4	b4	NOUN
ejpam-4446	128	83	.	.	PUNCT
ejpam-4446	129	1	it	it	PRON
ejpam-4446	129	2	is	be	AUX
ejpam-4446	129	3	routine	routine	ADJ
ejpam-4446	129	4	to	to	PART
ejpam-4446	129	5	verify	verify	VERB
ejpam-4446	129	6	that	that	SCONJ
ejpam-4446	129	7	lε	lε	ADP
ejpam-4446	129	8	ξ	ξ	PROPN
ejpam-4446	129	9	is	be	AUX
ejpam-4446	129	10	a	a	DET
ejpam-4446	129	11	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	129	12	fuzzy	fuzzy	ADJ
ejpam-4446	129	13	be	be	NOUN
ejpam-4446	129	14	-	-	PUNCT
ejpam-4446	129	15	algebra	algebra	NOUN
ejpam-4446	129	16	of	of	ADP
ejpam-4446	129	17	x.	x.	PROPN
ejpam-4446	129	18	but	but	CCONJ
ejpam-4446	129	19	ξ	ξ	PROPN
ejpam-4446	129	20	is	be	AUX
ejpam-4446	129	21	not	not	PART
ejpam-4446	129	22	a	a	DET
ejpam-4446	129	23	fuzzy	fuzzy	ADJ
ejpam-4446	129	24	be	be	NOUN
ejpam-4446	129	25	-	-	PUNCT
ejpam-4446	129	26	algebra	algebra	NOUN
ejpam-4446	129	27	of	of	ADP
ejpam-4446	129	28	x	x	PRON
ejpam-4446	129	29	because	because	SCONJ
ejpam-4446	129	30	of	of	ADP
ejpam-4446	129	31	ξ(b2	ξ(b2	NOUN
ejpam-4446	129	32	∗	∗	NOUN
ejpam-4446	129	33	b4	b4	NOUN
ejpam-4446	129	34	)	)	PUNCT
ejpam-4446	129	35	=	=	SYM
ejpam-4446	129	36	ξ(b3	ξ(b3	X
ejpam-4446	129	37	)	)	PUNCT
ejpam-4446	129	38	=	=	SYM
ejpam-4446	130	1	0.46	0.46	NUM
ejpam-4446	130	2	≱	≱	PROPN
ejpam-4446	130	3	0.59	0.59	NUM
ejpam-4446	130	4	=	=	SYM
ejpam-4446	130	5	min{ξ(b2	min{ξ(b2	NOUN
ejpam-4446	130	6	)	)	PUNCT
ejpam-4446	130	7	,	,	PUNCT
ejpam-4446	130	8	ξ(b4	ξ(b4	NOUN
ejpam-4446	130	9	)	)	PUNCT
ejpam-4446	130	10	}	}	PUNCT
ejpam-4446	130	11	.	.	PUNCT
ejpam-4446	131	1	theorem	theorem	NOUN
ejpam-4446	131	2	3	3	NUM
ejpam-4446	131	3	.	.	PUNCT
ejpam-4446	131	4	given	give	VERB
ejpam-4446	131	5	a	a	DET
ejpam-4446	131	6	be	be	NOUN
ejpam-4446	131	7	-	-	PUNCT
ejpam-4446	131	8	subalgebra	subalgebra	ADJ
ejpam-4446	131	9	f	f	PROPN
ejpam-4446	131	10	of	of	ADP
ejpam-4446	131	11	x	x	PRON
ejpam-4446	131	12	,	,	PUNCT
ejpam-4446	131	13	define	define	VERB
ejpam-4446	131	14	a	a	DET
ejpam-4446	131	15	fuzzy	fuzzy	ADJ
ejpam-4446	131	16	set	set	NOUN
ejpam-4446	131	17	ξ	ξ	PROPN
ejpam-4446	131	18	in	in	ADP
ejpam-4446	131	19	x	x	PUNCT
ejpam-4446	131	20	as	as	SCONJ
ejpam-4446	131	21	follows	follow	VERB
ejpam-4446	131	22	:	:	PUNCT
ejpam-4446	131	23	ξ	ξ	X
ejpam-4446	131	24	:	:	PUNCT
ejpam-4446	131	25	x	x	SYM
ejpam-4446	131	26	→	→	SYM
ejpam-4446	132	1	[	[	X
ejpam-4446	132	2	0	0	NUM
ejpam-4446	132	3	,	,	PUNCT
ejpam-4446	132	4	1	1	NUM
ejpam-4446	132	5	]	]	PUNCT
ejpam-4446	132	6	,	,	PUNCT
ejpam-4446	132	7	x	x	SYM
ejpam-4446	132	8	7→	7→	X
ejpam-4446	132	9	{	{	PUNCT
ejpam-4446	132	10	t0	t0	NOUN
ejpam-4446	132	11	if	if	SCONJ
ejpam-4446	132	12	x	x	PROPN
ejpam-4446	132	13	∈	∈	PROPN
ejpam-4446	132	14	f	f	PROPN
ejpam-4446	132	15	,	,	PUNCT
ejpam-4446	132	16	t1	t1	VERB
ejpam-4446	132	17	if	if	SCONJ
ejpam-4446	132	18	x	x	PROPN
ejpam-4446	132	19	/∈	/∈	PROPN
ejpam-4446	133	1	f	f	PROPN
ejpam-4446	133	2	(	(	PUNCT
ejpam-4446	133	3	12	12	NUM
ejpam-4446	133	4	)	)	PUNCT
ejpam-4446	133	5	where	where	SCONJ
ejpam-4446	133	6	t0	t0	PROPN
ejpam-4446	133	7	>	>	X
ejpam-4446	134	1	t1	t1	VERB
ejpam-4446	134	2	in	in	ADP
ejpam-4446	134	3	[	[	X
ejpam-4446	134	4	0	0	NUM
ejpam-4446	134	5	,	,	PUNCT
ejpam-4446	134	6	1	1	NUM
ejpam-4446	134	7	]	]	PUNCT
ejpam-4446	134	8	.	.	PUNCT
ejpam-4446	135	1	then	then	ADV
ejpam-4446	135	2	the	the	DET
ejpam-4446	135	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	135	4	fuzzy	fuzzy	NOUN
ejpam-4446	135	5	set	set	VERB
ejpam-4446	135	6	lε	lε	ADP
ejpam-4446	135	7	ξ	ξ	PROPN
ejpam-4446	135	8	of	of	ADP
ejpam-4446	135	9	ξ	ξ	PROPN
ejpam-4446	135	10	is	be	AUX
ejpam-4446	135	11	a	a	DET
ejpam-4446	135	12	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	135	13	fuzzy	fuzzy	ADJ
ejpam-4446	135	14	be	be	NOUN
ejpam-4446	135	15	-	-	PUNCT
ejpam-4446	135	16	algebra	algebra	NOUN
ejpam-4446	135	17	of	of	ADP
ejpam-4446	135	18	x.	x.	NOUN
ejpam-4446	135	19	proof	proof	NOUN
ejpam-4446	135	20	.	.	PUNCT
ejpam-4446	136	1	it	it	PRON
ejpam-4446	136	2	is	be	AUX
ejpam-4446	136	3	easy	easy	ADJ
ejpam-4446	136	4	to	to	PART
ejpam-4446	136	5	verify	verify	VERB
ejpam-4446	136	6	that	that	SCONJ
ejpam-4446	136	7	the	the	DET
ejpam-4446	136	8	fuzzy	fuzzy	ADJ
ejpam-4446	136	9	set	set	VERB
ejpam-4446	136	10	ξ	ξ	PROPN
ejpam-4446	136	11	given	give	VERB
ejpam-4446	136	12	in	in	ADP
ejpam-4446	136	13	(	(	PUNCT
ejpam-4446	136	14	12	12	NUM
ejpam-4446	136	15	)	)	PUNCT
ejpam-4446	136	16	is	be	AUX
ejpam-4446	136	17	a	a	DET
ejpam-4446	136	18	fuzzy	fuzzy	ADJ
ejpam-4446	136	19	be	be	NOUN
ejpam-4446	136	20	-	-	PUNCT
ejpam-4446	136	21	algebra	algebra	NOUN
ejpam-4446	136	22	of	of	ADP
ejpam-4446	136	23	x.	x.	NOUN
ejpam-4446	136	24	hence	hence	ADV
ejpam-4446	136	25	the	the	DET
ejpam-4446	136	26	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	136	27	fuzzy	fuzzy	NOUN
ejpam-4446	136	28	set	set	VERB
ejpam-4446	136	29	lε	lε	ADP
ejpam-4446	136	30	ξ	ξ	PROPN
ejpam-4446	136	31	of	of	ADP
ejpam-4446	136	32	ξ	ξ	PROPN
ejpam-4446	136	33	is	be	AUX
ejpam-4446	136	34	a	a	DET
ejpam-4446	136	35	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	136	36	fuzzy	fuzzy	ADJ
ejpam-4446	136	37	be	be	NOUN
ejpam-4446	136	38	-	-	PUNCT
ejpam-4446	136	39	algebra	algebra	NOUN
ejpam-4446	136	40	of	of	ADP
ejpam-4446	136	41	x	x	PUNCT
ejpam-4446	136	42	by	by	ADP
ejpam-4446	136	43	theorem	theorem	NOUN
ejpam-4446	136	44	2	2	NUM
ejpam-4446	136	45	.	.	PUNCT
ejpam-4446	136	46	proposition	proposition	NOUN
ejpam-4446	136	47	3	3	X
ejpam-4446	136	48	.	.	PUNCT
ejpam-4446	137	1	if	if	SCONJ
ejpam-4446	137	2	ξ	ξ	PROPN
ejpam-4446	137	3	is	be	AUX
ejpam-4446	137	4	a	a	DET
ejpam-4446	137	5	fuzzy	fuzzy	ADJ
ejpam-4446	137	6	be	be	NOUN
ejpam-4446	137	7	-	-	PUNCT
ejpam-4446	137	8	algebra	algebra	NOUN
ejpam-4446	137	9	of	of	ADP
ejpam-4446	137	10	x	x	NOUN
ejpam-4446	137	11	,	,	PUNCT
ejpam-4446	137	12	then	then	ADV
ejpam-4446	137	13	its	its	PRON
ejpam-4446	137	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	137	15	fuzzy	fuzzy	NOUN
ejpam-4446	137	16	set	set	VERB
ejpam-4446	137	17	lε	lε	AUX
ejpam-4446	137	18	ξ	ξ	X
ejpam-4446	137	19	satisfies	satisfie	NOUN
ejpam-4446	137	20	:	:	PUNCT
ejpam-4446	137	21	(	(	PUNCT
ejpam-4446	137	22	∀x	∀x	X
ejpam-4446	137	23	,	,	PUNCT
ejpam-4446	137	24	y	y	PROPN
ejpam-4446	137	25	∈	∈	PROPN
ejpam-4446	137	26	x	x	X
ejpam-4446	137	27	)	)	PUNCT
ejpam-4446	137	28	(	(	PUNCT
ejpam-4446	137	29	lε	lε	ADP
ejpam-4446	137	30	ξ(y	ξ(y	PROPN
ejpam-4446	137	31	)	)	PUNCT
ejpam-4446	137	32	=	=	PRON
ejpam-4446	137	33	lε	lε	PROPN
ejpam-4446	137	34	ξ(1	ξ(1	PROPN
ejpam-4446	137	35	)	)	PUNCT
ejpam-4446	137	36	⇔	⇔	PROPN
ejpam-4446	137	37	lε	lε	CCONJ
ejpam-4446	137	38	ξ(x	ξ(x	PROPN
ejpam-4446	137	39	)	)	PUNCT
ejpam-4446	137	40	≤	≤	NUM
ejpam-4446	137	41	lε	lε	ADP
ejpam-4446	137	42	ξ(x	ξ(x	PROPN
ejpam-4446	137	43	∗	∗	X
ejpam-4446	137	44	y	y	NOUN
ejpam-4446	137	45	)	)	PUNCT
ejpam-4446	137	46	)	)	PUNCT
ejpam-4446	137	47	.	.	PUNCT
ejpam-4446	138	1	(	(	PUNCT
ejpam-4446	138	2	13	13	X
ejpam-4446	138	3	)	)	PUNCT
ejpam-4446	138	4	proof	proof	NOUN
ejpam-4446	138	5	.	.	PUNCT
ejpam-4446	139	1	if	if	SCONJ
ejpam-4446	139	2	ξ	ξ	PROPN
ejpam-4446	139	3	is	be	AUX
ejpam-4446	139	4	a	a	DET
ejpam-4446	139	5	fuzzy	fuzzy	ADJ
ejpam-4446	139	6	be	be	NOUN
ejpam-4446	139	7	-	-	PUNCT
ejpam-4446	139	8	algebra	algebra	NOUN
ejpam-4446	139	9	of	of	ADP
ejpam-4446	139	10	x	x	NOUN
ejpam-4446	139	11	,	,	PUNCT
ejpam-4446	139	12	then	then	ADV
ejpam-4446	139	13	its	its	PRON
ejpam-4446	139	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	139	15	fuzzy	fuzzy	NOUN
ejpam-4446	139	16	set	set	VERB
ejpam-4446	139	17	lε	lε	AUX
ejpam-4446	139	18	ξ	ξ	X
ejpam-4446	139	19	is	be	AUX
ejpam-4446	139	20	a	a	DET
ejpam-4446	139	21	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	139	22	fuzzy	fuzzy	ADJ
ejpam-4446	139	23	be	be	NOUN
ejpam-4446	139	24	-	-	PUNCT
ejpam-4446	139	25	algebra	algebra	NOUN
ejpam-4446	139	26	of	of	ADP
ejpam-4446	139	27	x	x	PUNCT
ejpam-4446	139	28	(	(	PUNCT
ejpam-4446	139	29	see	see	VERB
ejpam-4446	139	30	theoem	theoem	NOUN
ejpam-4446	139	31	2	2	NUM
ejpam-4446	139	32	)	)	PUNCT
ejpam-4446	139	33	.	.	PUNCT
ejpam-4446	140	1	assume	assume	VERB
ejpam-4446	140	2	that	that	SCONJ
ejpam-4446	140	3	lε	lε	ADP
ejpam-4446	140	4	ξ(y	ξ(y	PROPN
ejpam-4446	140	5	)	)	PUNCT
ejpam-4446	140	6	=	=	PRON
ejpam-4446	140	7	lε	lε	X
ejpam-4446	140	8	ξ(1	ξ(1	PROPN
ejpam-4446	140	9	)	)	PUNCT
ejpam-4446	140	10	for	for	ADP
ejpam-4446	140	11	all	all	DET
ejpam-4446	140	12	y	y	PROPN
ejpam-4446	140	13	∈	∈	PROPN
ejpam-4446	140	14	x.	x.	NOUN
ejpam-4446	141	1	then	then	ADV
ejpam-4446	141	2	lε	lε	ADP
ejpam-4446	141	3	ξ(x	ξ(x	NOUN
ejpam-4446	141	4	)	)	PUNCT
ejpam-4446	141	5	=	=	SYM
ejpam-4446	141	6	min	min	NOUN
ejpam-4446	141	7	{	{	PUNCT
ejpam-4446	141	8	lε	lε	ADP
ejpam-4446	141	9	ξ(x	ξ(x	PROPN
ejpam-4446	141	10	)	)	PUNCT
ejpam-4446	141	11	,	,	PUNCT
ejpam-4446	141	12	lε	lε	X
ejpam-4446	141	13	ξ(1	ξ(1	PROPN
ejpam-4446	141	14	)	)	PUNCT
ejpam-4446	141	15	}	}	PUNCT
ejpam-4446	141	16	=	=	SYM
ejpam-4446	141	17	min	min	X
ejpam-4446	141	18	{	{	PUNCT
ejpam-4446	141	19	lε	lε	ADP
ejpam-4446	141	20	ξ(x	ξ(x	PROPN
ejpam-4446	141	21	)	)	PUNCT
ejpam-4446	141	22	,	,	PUNCT
ejpam-4446	141	23	lε	lε	ADP
ejpam-4446	141	24	ξ(y	ξ(y	PROPN
ejpam-4446	141	25	)	)	PUNCT
ejpam-4446	141	26	}	}	PUNCT
ejpam-4446	141	27	≤	≤	NUM
ejpam-4446	141	28	lε	lε	ADP
ejpam-4446	141	29	ξ(x	ξ(x	PROPN
ejpam-4446	141	30	∗	∗	X
ejpam-4446	141	31	y	y	NOUN
ejpam-4446	141	32	)	)	PUNCT
ejpam-4446	141	33	for	for	ADP
ejpam-4446	141	34	all	all	DET
ejpam-4446	141	35	x	x	NOUN
ejpam-4446	141	36	,	,	PUNCT
ejpam-4446	141	37	y	y	PROPN
ejpam-4446	141	38	∈	∈	PROPN
ejpam-4446	141	39	x	x	PUNCT
ejpam-4446	141	40	by	by	ADP
ejpam-4446	141	41	theorem	theorem	NOUN
ejpam-4446	141	42	1	1	NUM
ejpam-4446	141	43	and	and	CCONJ
ejpam-4446	141	44	lemma	lemma	PROPN
ejpam-4446	141	45	1	1	NUM
ejpam-4446	141	46	.	.	PUNCT
ejpam-4446	142	1	conversely	conversely	ADV
ejpam-4446	142	2	,	,	PUNCT
ejpam-4446	142	3	suppose	suppose	VERB
ejpam-4446	142	4	that	that	SCONJ
ejpam-4446	142	5	lε	lε	ADP
ejpam-4446	142	6	ξ(x	ξ(x	PROPN
ejpam-4446	142	7	)	)	PUNCT
ejpam-4446	142	8	≤	≤	NUM
ejpam-4446	142	9	lε	lε	ADP
ejpam-4446	142	10	ξ(x	ξ(x	PROPN
ejpam-4446	142	11	∗	∗	X
ejpam-4446	142	12	y	y	NOUN
ejpam-4446	142	13	)	)	PUNCT
ejpam-4446	142	14	for	for	ADP
ejpam-4446	142	15	all	all	DET
ejpam-4446	142	16	x	x	NOUN
ejpam-4446	142	17	,	,	PUNCT
ejpam-4446	142	18	y	y	PROPN
ejpam-4446	142	19	∈	∈	PROPN
ejpam-4446	142	20	x.	x.	NOUN
ejpam-4446	142	21	then	then	ADV
ejpam-4446	142	22	lε	lε	ADP
ejpam-4446	142	23	ξ(y	ξ(y	PROPN
ejpam-4446	142	24	)	)	PUNCT
ejpam-4446	143	1	=	=	PRON
ejpam-4446	144	1	lε	lε	PRON
ejpam-4446	144	2	ξ(1	ξ(1	PROPN
ejpam-4446	144	3	∗	∗	PROPN
ejpam-4446	144	4	y	y	PROPN
ejpam-4446	144	5	)	)	PUNCT
ejpam-4446	144	6	≥	≥	NOUN
ejpam-4446	144	7	lε	lε	X
ejpam-4446	144	8	ξ(1	ξ(1	PROPN
ejpam-4446	144	9	)	)	PUNCT
ejpam-4446	144	10	by	by	ADP
ejpam-4446	144	11	(	(	PUNCT
ejpam-4446	144	12	be3	be3	PROPN
ejpam-4446	144	13	)	)	PUNCT
ejpam-4446	144	14	,	,	PUNCT
ejpam-4446	144	15	and	and	CCONJ
ejpam-4446	144	16	so	so	ADV
ejpam-4446	144	17	lε	lε	ADP
ejpam-4446	144	18	ξ(y	ξ(y	PROPN
ejpam-4446	144	19	)	)	PUNCT
ejpam-4446	144	20	=	=	PRON
ejpam-4446	144	21	lε	lε	X
ejpam-4446	144	22	ξ(1	ξ(1	PROPN
ejpam-4446	144	23	)	)	PUNCT
ejpam-4446	144	24	for	for	SCONJ
ejpam-4446	144	25	all	all	DET
ejpam-4446	144	26	y	y	PROPN
ejpam-4446	144	27	∈	∈	PROPN
ejpam-4446	144	28	x.	x.	NOUN
ejpam-4446	144	29	theorem	theorem	VERB
ejpam-4446	144	30	4	4	NUM
ejpam-4446	144	31	.	.	PUNCT
ejpam-4446	145	1	if	if	SCONJ
ejpam-4446	145	2	the	the	DET
ejpam-4446	145	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	145	4	fuzzy	fuzzy	NOUN
ejpam-4446	145	5	set	set	VERB
ejpam-4446	145	6	lε	lε	ADP
ejpam-4446	145	7	ξ	ξ	PROPN
ejpam-4446	145	8	of	of	ADP
ejpam-4446	145	9	ξ	ξ	PROPN
ejpam-4446	145	10	in	in	ADP
ejpam-4446	145	11	x	x	X
ejpam-4446	145	12	satisfies	satisfie	NOUN
ejpam-4446	145	13	:	:	PUNCT
ejpam-4446	145	14	[	[	X
ejpam-4446	145	15	x	x	X
ejpam-4446	145	16	/	/	SYM
ejpam-4446	145	17	ta	ta	X
ejpam-4446	145	18	]	]	X
ejpam-4446	145	19	∈	∈	PROPN
ejpam-4446	145	20	lε	lε	X
ejpam-4446	145	21	ξ	ξ	X
ejpam-4446	145	22	,	,	PUNCT
ejpam-4446	145	23	[	[	X
ejpam-4446	145	24	z	z	X
ejpam-4446	145	25	/	/	SYM
ejpam-4446	145	26	tc	tc	NOUN
ejpam-4446	145	27	]	]	X
ejpam-4446	145	28	∈	∈	X
ejpam-4446	145	29	lε	lε	X
ejpam-4446	145	30	ξ	ξ	X
ejpam-4446	145	31	⇒	⇒	NOUN
ejpam-4446	145	32	[	[	X
ejpam-4446	145	33	(	(	PUNCT
ejpam-4446	145	34	x	x	X
ejpam-4446	145	35	∗	∗	NOUN
ejpam-4446	145	36	y)/min{ta	y)/min{ta	NOUN
ejpam-4446	145	37	,	,	PUNCT
ejpam-4446	145	38	tc	tc	NOUN
ejpam-4446	145	39	}	}	PUNCT
ejpam-4446	145	40	]	]	PUNCT
ejpam-4446	145	41	∈	∈	PROPN
ejpam-4446	146	1	lε	lε	X
ejpam-4446	146	2	ξ	ξ	PROPN
ejpam-4446	146	3	(	(	PUNCT
ejpam-4446	146	4	14	14	NUM
ejpam-4446	146	5	)	)	PUNCT
ejpam-4446	146	6	for	for	ADP
ejpam-4446	146	7	all	all	DET
ejpam-4446	146	8	ta	ta	PROPN
ejpam-4446	146	9	,	,	PUNCT
ejpam-4446	146	10	tc	tc	PROPN
ejpam-4446	146	11	∈	∈	PROPN
ejpam-4446	146	12	(	(	PUNCT
ejpam-4446	146	13	0	0	NUM
ejpam-4446	146	14	,	,	PUNCT
ejpam-4446	146	15	1	1	NUM
ejpam-4446	146	16	]	]	PUNCT
ejpam-4446	146	17	and	and	CCONJ
ejpam-4446	146	18	x	x	NOUN
ejpam-4446	146	19	,	,	PUNCT
ejpam-4446	146	20	y	y	PROPN
ejpam-4446	146	21	,	,	PUNCT
ejpam-4446	146	22	z	z	NOUN
ejpam-4446	146	23	∈	∈	PROPN
ejpam-4446	146	24	x	x	PUNCT
ejpam-4446	146	25	with	with	ADP
ejpam-4446	146	26	z	z	NOUN
ejpam-4446	146	27	≤	≤	NOUN
ejpam-4446	146	28	y	y	PROPN
ejpam-4446	146	29	,	,	PUNCT
ejpam-4446	146	30	then	then	ADV
ejpam-4446	146	31	lε	lε	X
ejpam-4446	146	32	ξ	ξ	PROPN
ejpam-4446	146	33	is	be	AUX
ejpam-4446	146	34	a	a	DET
ejpam-4446	146	35	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	146	36	fuzzy	fuzzy	ADJ
ejpam-4446	146	37	be	be	NOUN
ejpam-4446	146	38	-	-	PUNCT
ejpam-4446	146	39	algebra	algebra	NOUN
ejpam-4446	146	40	of	of	ADP
ejpam-4446	146	41	x.	x.	NOUN
ejpam-4446	146	42	proof	proof	NOUN
ejpam-4446	146	43	.	.	PUNCT
ejpam-4446	147	1	let	let	VERB
ejpam-4446	147	2	x	x	PRON
ejpam-4446	147	3	,	,	PUNCT
ejpam-4446	147	4	y	y	PROPN
ejpam-4446	147	5	∈	∈	PROPN
ejpam-4446	147	6	x	x	X
ejpam-4446	147	7	and	and	CCONJ
ejpam-4446	147	8	ta	ta	PROPN
ejpam-4446	147	9	,	,	PUNCT
ejpam-4446	147	10	tb	tb	ADP
ejpam-4446	147	11	∈	∈	PROPN
ejpam-4446	147	12	(	(	PUNCT
ejpam-4446	147	13	0	0	NUM
ejpam-4446	147	14	,	,	PUNCT
ejpam-4446	147	15	1	1	NUM
ejpam-4446	147	16	]	]	PUNCT
ejpam-4446	147	17	be	be	AUX
ejpam-4446	147	18	such	such	ADJ
ejpam-4446	147	19	that	that	SCONJ
ejpam-4446	147	20	[	[	X
ejpam-4446	147	21	x	x	X
ejpam-4446	147	22	/	/	SYM
ejpam-4446	147	23	ta	ta	X
ejpam-4446	147	24	]	]	X
ejpam-4446	147	25	∈	∈	PROPN
ejpam-4446	147	26	lε	lε	X
ejpam-4446	147	27	ξ	ξ	PROPN
ejpam-4446	147	28	and	and	CCONJ
ejpam-4446	147	29	[	[	X
ejpam-4446	147	30	y	y	X
ejpam-4446	147	31	/	/	SYM
ejpam-4446	147	32	tb	tb	NOUN
ejpam-4446	147	33	]	]	PUNCT
ejpam-4446	147	34	∈	∈	PROPN
ejpam-4446	147	35	lε	lε	X
ejpam-4446	147	36	ξ	ξ	PROPN
ejpam-4446	147	37	.	.	PUNCT
ejpam-4446	148	1	since	since	SCONJ
ejpam-4446	148	2	y	y	PROPN
ejpam-4446	148	3	≤	≤	PROPN
ejpam-4446	148	4	y	y	PROPN
ejpam-4446	148	5	for	for	ADP
ejpam-4446	148	6	all	all	DET
ejpam-4446	148	7	y	y	PROPN
ejpam-4446	148	8	∈	∈	PROPN
ejpam-4446	148	9	x	x	X
ejpam-4446	148	10	,	,	PUNCT
ejpam-4446	148	11	it	it	PRON
ejpam-4446	148	12	follows	follow	VERB
ejpam-4446	148	13	from	from	ADP
ejpam-4446	148	14	(	(	PUNCT
ejpam-4446	148	15	14	14	NUM
ejpam-4446	148	16	)	)	PUNCT
ejpam-4446	148	17	that	that	SCONJ
ejpam-4446	149	1	[	[	X
ejpam-4446	149	2	(	(	PUNCT
ejpam-4446	149	3	x	x	X
ejpam-4446	149	4	∗	∗	NOUN
ejpam-4446	149	5	y)/min{ta	y)/min{ta	NOUN
ejpam-4446	149	6	,	,	PUNCT
ejpam-4446	149	7	tb	tb	NOUN
ejpam-4446	149	8	}	}	PUNCT
ejpam-4446	149	9	]	]	PUNCT
ejpam-4446	149	10	∈	∈	PROPN
ejpam-4446	149	11	lε	lε	X
ejpam-4446	149	12	ξ	ξ	PROPN
ejpam-4446	149	13	.	.	PUNCT
ejpam-4446	149	14	hence	hence	ADV
ejpam-4446	149	15	lε	lε	PROPN
ejpam-4446	149	16	ξ	ξ	PROPN
ejpam-4446	149	17	is	be	AUX
ejpam-4446	149	18	a	a	DET
ejpam-4446	149	19	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	149	20	fuzzy	fuzzy	ADJ
ejpam-4446	149	21	be	be	NOUN
ejpam-4446	149	22	-	-	PUNCT
ejpam-4446	149	23	algebra	algebra	NOUN
ejpam-4446	149	24	of	of	ADP
ejpam-4446	149	25	x.	x.	NOUN
ejpam-4446	149	26	we	we	PRON
ejpam-4446	149	27	consider	consider	VERB
ejpam-4446	149	28	the	the	DET
ejpam-4446	149	29	conditions	condition	NOUN
ejpam-4446	149	30	for	for	ADP
ejpam-4446	149	31	the	the	DET
ejpam-4446	149	32	∈-set	∈-set	NOUN
ejpam-4446	149	33	and	and	CCONJ
ejpam-4446	149	34	q	q	NOUN
ejpam-4446	149	35	-	-	PUNCT
ejpam-4446	149	36	set	set	NOUN
ejpam-4446	149	37	of	of	ADP
ejpam-4446	149	38	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	149	39	fuzzy	fuzzy	ADJ
ejpam-4446	149	40	set	set	VERB
ejpam-4446	149	41	to	to	PART
ejpam-4446	149	42	be	be	AUX
ejpam-4446	149	43	be	be	AUX
ejpam-4446	149	44	-	-	PUNCT
ejpam-4446	149	45	subalgebras	subalgebras	X
ejpam-4446	149	46	.	.	PUNCT
ejpam-4446	150	1	y.	y.	PROPN
ejpam-4446	150	2	b.	b.	PROPN
ejpam-4446	150	3	jun	jun	PROPN
ejpam-4446	150	4	,	,	PUNCT
ejpam-4446	150	5	s.	s.	PROPN
ejpam-4446	150	6	s.	s.	PROPN
ejpam-4446	150	7	ahn	ahn	PROPN
ejpam-4446	150	8	/	/	SYM
ejpam-4446	150	9	eur	eur	PROPN
ejpam-4446	150	10	.	.	PUNCT
ejpam-4446	151	1	j.	j.	PROPN
ejpam-4446	151	2	pure	pure	PROPN
ejpam-4446	151	3	appl	appl	PROPN
ejpam-4446	151	4	.	.	PROPN
ejpam-4446	151	5	math	math	PROPN
ejpam-4446	151	6	,	,	PUNCT
ejpam-4446	151	7	15	15	NUM
ejpam-4446	151	8	(	(	PUNCT
ejpam-4446	151	9	3	3	NUM
ejpam-4446	151	10	)	)	PUNCT
ejpam-4446	151	11	(	(	PUNCT
ejpam-4446	151	12	2022	2022	NUM
ejpam-4446	151	13	)	)	PUNCT
ejpam-4446	151	14	,	,	PUNCT
ejpam-4446	151	15	924	924	NUM
ejpam-4446	151	16	-	-	SYM
ejpam-4446	151	17	937	937	NUM
ejpam-4446	151	18	931	931	NUM
ejpam-4446	151	19	theorem	theorem	NOUN
ejpam-4446	151	20	5	5	NUM
ejpam-4446	151	21	.	.	PUNCT
ejpam-4446	152	1	if	if	SCONJ
ejpam-4446	152	2	lε	lε	PRON
ejpam-4446	152	3	ξ	ξ	PROPN
ejpam-4446	152	4	is	be	AUX
ejpam-4446	152	5	the	the	DET
ejpam-4446	152	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	152	7	fuzzy	fuzzy	ADJ
ejpam-4446	152	8	set	set	NOUN
ejpam-4446	152	9	of	of	ADP
ejpam-4446	152	10	ξ	ξ	PROPN
ejpam-4446	152	11	in	in	ADP
ejpam-4446	152	12	x	x	PUNCT
ejpam-4446	152	13	which	which	PRON
ejpam-4446	152	14	satisfies	satisfy	VERB
ejpam-4446	152	15	:	:	PUNCT
ejpam-4446	152	16	(	(	PUNCT
ejpam-4446	152	17	∀x	∀x	X
ejpam-4446	152	18	,	,	PUNCT
ejpam-4446	152	19	y	y	PROPN
ejpam-4446	152	20	∈	∈	PROPN
ejpam-4446	152	21	x	x	X
ejpam-4446	152	22	)	)	PUNCT
ejpam-4446	152	23	(	(	PUNCT
ejpam-4446	152	24	min	min	NOUN
ejpam-4446	152	25	{	{	PUNCT
ejpam-4446	152	26	lε	lε	ADP
ejpam-4446	152	27	ξ(x	ξ(x	PROPN
ejpam-4446	152	28	)	)	PUNCT
ejpam-4446	152	29	,	,	PUNCT
ejpam-4446	152	30	lε	lε	ADP
ejpam-4446	152	31	ξ(y	ξ(y	PROPN
ejpam-4446	152	32	)	)	PUNCT
ejpam-4446	152	33	}	}	PUNCT
ejpam-4446	152	34	≤	≤	NUM
ejpam-4446	152	35	max	max	PROPN
ejpam-4446	152	36	{	{	PUNCT
ejpam-4446	152	37	lε	lε	ADP
ejpam-4446	152	38	ξ(x	ξ(x	PROPN
ejpam-4446	152	39	∗	∗	X
ejpam-4446	152	40	y	y	PROPN
ejpam-4446	152	41	)	)	PUNCT
ejpam-4446	152	42	,	,	PUNCT
ejpam-4446	152	43	0.5	0.5	NUM
ejpam-4446	152	44	}	}	PUNCT
ejpam-4446	152	45	)	)	PUNCT
ejpam-4446	152	46	,	,	PUNCT
ejpam-4446	152	47	(	(	PUNCT
ejpam-4446	152	48	15	15	NUM
ejpam-4446	152	49	)	)	PUNCT
ejpam-4446	152	50	then	then	ADV
ejpam-4446	152	51	the	the	DET
ejpam-4446	152	52	∈-set	∈-set	NOUN
ejpam-4446	152	53	(	(	PUNCT
ejpam-4446	152	54	lε	lε	X
ejpam-4446	152	55	ξ	ξ	PROPN
ejpam-4446	152	56	,	,	PUNCT
ejpam-4446	152	57	t)∈	t)∈	NUM
ejpam-4446	152	58	of	of	ADP
ejpam-4446	152	59	lε	lε	PRON
ejpam-4446	152	60	ξ	ξ	PROPN
ejpam-4446	152	61	is	be	AUX
ejpam-4446	152	62	a	a	DET
ejpam-4446	152	63	be	be	NOUN
ejpam-4446	152	64	-	-	PUNCT
ejpam-4446	152	65	subalgebra	subalgebra	NOUN
ejpam-4446	152	66	of	of	ADP
ejpam-4446	152	67	x	x	PUNCT
ejpam-4446	152	68	for	for	ADP
ejpam-4446	152	69	the	the	DET
ejpam-4446	152	70	value	value	NOUN
ejpam-4446	152	71	t	t	PROPN
ejpam-4446	152	72	∈	∈	PROPN
ejpam-4446	152	73	(	(	PUNCT
ejpam-4446	152	74	0.5	0.5	NUM
ejpam-4446	152	75	,	,	PUNCT
ejpam-4446	152	76	1	1	NUM
ejpam-4446	152	77	]	]	PUNCT
ejpam-4446	152	78	.	.	PUNCT
ejpam-4446	153	1	proof	proof	NOUN
ejpam-4446	153	2	.	.	PUNCT
ejpam-4446	154	1	assume	assume	VERB
ejpam-4446	154	2	that	that	SCONJ
ejpam-4446	154	3	lε	lε	PRON
ejpam-4446	154	4	ξ	ξ	X
ejpam-4446	154	5	satisfies	satisfy	VERB
ejpam-4446	154	6	the	the	DET
ejpam-4446	154	7	condition	condition	NOUN
ejpam-4446	154	8	(	(	PUNCT
ejpam-4446	154	9	15	15	NUM
ejpam-4446	154	10	)	)	PUNCT
ejpam-4446	154	11	and	and	CCONJ
ejpam-4446	154	12	let	let	VERB
ejpam-4446	154	13	x	x	PRON
ejpam-4446	154	14	,	,	PUNCT
ejpam-4446	154	15	y	y	PROPN
ejpam-4446	154	16	∈	∈	PROPN
ejpam-4446	154	17	x	x	AUX
ejpam-4446	154	18	be	be	AUX
ejpam-4446	154	19	such	such	ADJ
ejpam-4446	154	20	that	that	SCONJ
ejpam-4446	154	21	x	x	NOUN
ejpam-4446	154	22	,	,	PUNCT
ejpam-4446	154	23	y	y	PROPN
ejpam-4446	154	24	∈	∈	PROPN
ejpam-4446	154	25	(	(	PUNCT
ejpam-4446	154	26	lε	lε	X
ejpam-4446	154	27	ξ	ξ	PROPN
ejpam-4446	154	28	,	,	PUNCT
ejpam-4446	154	29	t)∈	t)∈	VERB
ejpam-4446	154	30	for	for	ADP
ejpam-4446	154	31	t	t	PROPN
ejpam-4446	154	32	∈	∈	PROPN
ejpam-4446	154	33	(	(	PUNCT
ejpam-4446	154	34	0.5	0.5	NUM
ejpam-4446	154	35	,	,	PUNCT
ejpam-4446	154	36	1	1	NUM
ejpam-4446	154	37	]	]	PUNCT
ejpam-4446	154	38	.	.	PUNCT
ejpam-4446	155	1	then	then	ADV
ejpam-4446	155	2	lε	lε	ADP
ejpam-4446	155	3	ξ(x	ξ(x	NOUN
ejpam-4446	155	4	)	)	PUNCT
ejpam-4446	155	5	≥	≥	NOUN
ejpam-4446	155	6	t	t	NOUN
ejpam-4446	155	7	and	and	CCONJ
ejpam-4446	155	8	lε	lε	ADP
ejpam-4446	155	9	ξ(y	ξ(y	PROPN
ejpam-4446	155	10	)	)	PUNCT
ejpam-4446	155	11	≥	≥	PROPN
ejpam-4446	155	12	t	t	PROPN
ejpam-4446	155	13	,	,	PUNCT
ejpam-4446	155	14	which	which	PRON
ejpam-4446	155	15	imply	imply	VERB
ejpam-4446	155	16	from	from	ADP
ejpam-4446	155	17	(	(	PUNCT
ejpam-4446	155	18	15	15	NUM
ejpam-4446	155	19	)	)	PUNCT
ejpam-4446	155	20	that	that	DET
ejpam-4446	155	21	max	max	PROPN
ejpam-4446	155	22	{	{	PUNCT
ejpam-4446	155	23	lε	lε	ADP
ejpam-4446	155	24	ξ(x	ξ(x	PROPN
ejpam-4446	155	25	∗	∗	X
ejpam-4446	155	26	y	y	PROPN
ejpam-4446	155	27	)	)	PUNCT
ejpam-4446	155	28	,	,	PUNCT
ejpam-4446	155	29	0.5	0.5	NUM
ejpam-4446	155	30	}	}	PUNCT
ejpam-4446	155	31	≥	≥	NUM
ejpam-4446	155	32	min	min	PROPN
ejpam-4446	155	33	{	{	PUNCT
ejpam-4446	155	34	lε	lε	ADP
ejpam-4446	155	35	ξ(x	ξ(x	PROPN
ejpam-4446	155	36	)	)	PUNCT
ejpam-4446	155	37	,	,	PUNCT
ejpam-4446	155	38	lε	lε	ADP
ejpam-4446	155	39	ξ(y	ξ(y	PROPN
ejpam-4446	155	40	)	)	PUNCT
ejpam-4446	155	41	}	}	PUNCT
ejpam-4446	155	42	≥	≥	AUX
ejpam-4446	155	43	t	t	X
ejpam-4446	155	44	>	>	X
ejpam-4446	155	45	0.5	0.5	NUM
ejpam-4446	155	46	.	.	PUNCT
ejpam-4446	156	1	hense	hense	NOUN
ejpam-4446	156	2	[	[	X
ejpam-4446	156	3	(	(	PUNCT
ejpam-4446	156	4	x	x	SYM
ejpam-4446	156	5	∗	∗	PROPN
ejpam-4446	156	6	y)/t	y)/t	NOUN
ejpam-4446	156	7	]	]	X
ejpam-4446	156	8	∈	∈	PROPN
ejpam-4446	156	9	lε	lε	X
ejpam-4446	156	10	ξ	ξ	X
ejpam-4446	156	11	,	,	PUNCT
ejpam-4446	156	12	i.e.	i.e.	X
ejpam-4446	156	13	,	,	PUNCT
ejpam-4446	156	14	x	x	PUNCT
ejpam-4446	156	15	∗	∗	NOUN
ejpam-4446	156	16	y	y	PROPN
ejpam-4446	156	17	∈	∈	PROPN
ejpam-4446	156	18	(	(	PUNCT
ejpam-4446	156	19	lε	lε	X
ejpam-4446	156	20	ξ	ξ	PROPN
ejpam-4446	156	21	,	,	PUNCT
ejpam-4446	156	22	t)∈	t)∈	NUM
ejpam-4446	156	23	,	,	PUNCT
ejpam-4446	156	24	and	and	CCONJ
ejpam-4446	156	25	therefore	therefore	ADV
ejpam-4446	156	26	(	(	PUNCT
ejpam-4446	156	27	lε	lε	X
ejpam-4446	156	28	ξ	ξ	PROPN
ejpam-4446	156	29	,	,	PUNCT
ejpam-4446	156	30	t)∈	t)∈	NUM
ejpam-4446	156	31	is	be	AUX
ejpam-4446	156	32	a	a	DET
ejpam-4446	156	33	be	be	NOUN
ejpam-4446	156	34	-	-	PUNCT
ejpam-4446	156	35	subalgebra	subalgebra	NOUN
ejpam-4446	156	36	of	of	ADP
ejpam-4446	156	37	x	x	PUNCT
ejpam-4446	156	38	for	for	ADP
ejpam-4446	156	39	t	t	PROPN
ejpam-4446	156	40	∈	∈	PROPN
ejpam-4446	156	41	(	(	PUNCT
ejpam-4446	156	42	0.5	0.5	NUM
ejpam-4446	156	43	,	,	PUNCT
ejpam-4446	156	44	1	1	NUM
ejpam-4446	156	45	]	]	PUNCT
ejpam-4446	156	46	.	.	PUNCT
ejpam-4446	157	1	theorem	theorem	ADJ
ejpam-4446	157	2	6	6	NUM
ejpam-4446	157	3	.	.	PUNCT
ejpam-4446	158	1	for	for	ADP
ejpam-4446	158	2	the	the	DET
ejpam-4446	158	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	158	4	fuzzy	fuzzy	NOUN
ejpam-4446	158	5	set	set	VERB
ejpam-4446	158	6	lε	lε	ADP
ejpam-4446	158	7	ξ	ξ	PROPN
ejpam-4446	158	8	of	of	ADP
ejpam-4446	158	9	ξ	ξ	PROPN
ejpam-4446	158	10	in	in	ADP
ejpam-4446	158	11	x	x	SYM
ejpam-4446	158	12	,	,	PUNCT
ejpam-4446	158	13	if	if	SCONJ
ejpam-4446	158	14	its	its	PRON
ejpam-4446	158	15	∈-set	∈-set	NOUN
ejpam-4446	158	16	(	(	PUNCT
ejpam-4446	158	17	lε	lε	X
ejpam-4446	158	18	ξ	ξ	PROPN
ejpam-4446	158	19	,	,	PUNCT
ejpam-4446	158	20	t)∈	t)∈	NUM
ejpam-4446	158	21	is	be	AUX
ejpam-4446	158	22	a	a	DET
ejpam-4446	158	23	besubalgebra	besubalgebra	NOUN
ejpam-4446	158	24	of	of	ADP
ejpam-4446	158	25	x	x	PUNCT
ejpam-4446	158	26	for	for	ADP
ejpam-4446	158	27	the	the	DET
ejpam-4446	158	28	value	value	NOUN
ejpam-4446	158	29	t	t	PROPN
ejpam-4446	158	30	∈	∈	PROPN
ejpam-4446	158	31	(	(	PUNCT
ejpam-4446	158	32	0.5	0.5	NUM
ejpam-4446	158	33	,	,	PUNCT
ejpam-4446	158	34	1	1	NUM
ejpam-4446	158	35	]	]	PUNCT
ejpam-4446	158	36	,	,	PUNCT
ejpam-4446	158	37	then	then	ADV
ejpam-4446	158	38	lε	lε	X
ejpam-4446	158	39	ξ	ξ	PROPN
ejpam-4446	158	40	satisfies	satisfy	VERB
ejpam-4446	158	41	the	the	DET
ejpam-4446	158	42	condition	condition	NOUN
ejpam-4446	158	43	(	(	PUNCT
ejpam-4446	158	44	15	15	NUM
ejpam-4446	158	45	)	)	PUNCT
ejpam-4446	158	46	.	.	PUNCT
ejpam-4446	159	1	proof	proof	NOUN
ejpam-4446	159	2	.	.	PUNCT
ejpam-4446	160	1	assume	assume	VERB
ejpam-4446	160	2	that	that	SCONJ
ejpam-4446	160	3	lε	lε	PROPN
ejpam-4446	160	4	ξ	ξ	PROPN
ejpam-4446	160	5	does	do	AUX
ejpam-4446	160	6	not	not	PART
ejpam-4446	160	7	satisfy	satisfy	VERB
ejpam-4446	160	8	the	the	DET
ejpam-4446	160	9	condition	condition	NOUN
ejpam-4446	160	10	(	(	PUNCT
ejpam-4446	160	11	15	15	NUM
ejpam-4446	160	12	)	)	PUNCT
ejpam-4446	160	13	.	.	PUNCT
ejpam-4446	161	1	then	then	ADV
ejpam-4446	161	2	min	min	PROPN
ejpam-4446	161	3	{	{	PUNCT
ejpam-4446	161	4	lε	lε	X
ejpam-4446	161	5	ξ(a	ξ(a	NUM
ejpam-4446	161	6	)	)	PUNCT
ejpam-4446	161	7	,	,	PUNCT
ejpam-4446	161	8	lε	lε	X
ejpam-4446	161	9	ξ(b	ξ(b	NOUN
ejpam-4446	161	10	)	)	PUNCT
ejpam-4446	161	11	}	}	PUNCT
ejpam-4446	161	12	>	>	X
ejpam-4446	161	13	max	max	PROPN
ejpam-4446	161	14	{	{	PUNCT
ejpam-4446	161	15	lε	lε	ADP
ejpam-4446	161	16	ξ(a	ξ(a	PROPN
ejpam-4446	161	17	∗	∗	PROPN
ejpam-4446	161	18	b	b	NOUN
ejpam-4446	161	19	)	)	PUNCT
ejpam-4446	161	20	,	,	PUNCT
ejpam-4446	161	21	0.5	0.5	NUM
ejpam-4446	161	22	}	}	PUNCT
ejpam-4446	161	23	for	for	ADP
ejpam-4446	161	24	some	some	PRON
ejpam-4446	161	25	a	a	PRON
ejpam-4446	161	26	,	,	PUNCT
ejpam-4446	161	27	b	b	PROPN
ejpam-4446	161	28	∈	∈	PROPN
ejpam-4446	161	29	x	x	NOUN
ejpam-4446	161	30	,	,	PUNCT
ejpam-4446	161	31	and	and	CCONJ
ejpam-4446	161	32	so	so	ADV
ejpam-4446	161	33	s	s	X
ejpam-4446	161	34	∈	∈	PROPN
ejpam-4446	161	35	(	(	PUNCT
ejpam-4446	161	36	0.5	0.5	NUM
ejpam-4446	161	37	,	,	PUNCT
ejpam-4446	161	38	1	1	NUM
ejpam-4446	161	39	]	]	PUNCT
ejpam-4446	161	40	and	and	CCONJ
ejpam-4446	161	41	[	[	X
ejpam-4446	161	42	a	a	X
ejpam-4446	161	43	/	/	SYM
ejpam-4446	161	44	s	s	NOUN
ejpam-4446	161	45	]	]	X
ejpam-4446	161	46	,	,	PUNCT
ejpam-4446	161	47	[	[	X
ejpam-4446	161	48	b	b	X
ejpam-4446	161	49	/	/	SYM
ejpam-4446	161	50	s	s	NOUN
ejpam-4446	161	51	]	]	X
ejpam-4446	161	52	∈	∈	PROPN
ejpam-4446	161	53	lε	lε	X
ejpam-4446	161	54	ξ	ξ	X
ejpam-4446	161	55	,	,	PUNCT
ejpam-4446	161	56	i.e.	i.e.	X
ejpam-4446	161	57	,	,	PUNCT
ejpam-4446	161	58	a	a	PRON
ejpam-4446	161	59	,	,	PUNCT
ejpam-4446	161	60	b	b	X
ejpam-4446	161	61	∈	∈	PROPN
ejpam-4446	161	62	(	(	PUNCT
ejpam-4446	161	63	lε	lε	X
ejpam-4446	161	64	ξ	ξ	PROPN
ejpam-4446	161	65	,	,	PUNCT
ejpam-4446	161	66	s)∈	s)∈	NUM
ejpam-4446	161	67	where	where	SCONJ
ejpam-4446	161	68	s	s	X
ejpam-4446	161	69	:	:	PUNCT
ejpam-4446	161	70	=	=	SYM
ejpam-4446	161	71	min	min	NOUN
ejpam-4446	161	72	{	{	PUNCT
ejpam-4446	161	73	lε	lε	X
ejpam-4446	161	74	ξ(a	ξ(a	NUM
ejpam-4446	161	75	)	)	PUNCT
ejpam-4446	161	76	,	,	PUNCT
ejpam-4446	161	77	lε	lε	X
ejpam-4446	161	78	ξ(b	ξ(b	NOUN
ejpam-4446	161	79	)	)	PUNCT
ejpam-4446	161	80	}	}	PUNCT
ejpam-4446	161	81	.	.	PUNCT
ejpam-4446	162	1	since	since	SCONJ
ejpam-4446	162	2	(	(	PUNCT
ejpam-4446	162	3	lε	lε	X
ejpam-4446	162	4	ξ	ξ	PROPN
ejpam-4446	162	5	,	,	PUNCT
ejpam-4446	162	6	s)∈	s)∈	NUM
ejpam-4446	162	7	is	be	AUX
ejpam-4446	162	8	a	a	DET
ejpam-4446	162	9	be	be	NOUN
ejpam-4446	162	10	-	-	PUNCT
ejpam-4446	162	11	subalgebra	subalgebra	NOUN
ejpam-4446	162	12	of	of	ADP
ejpam-4446	162	13	x	x	PUNCT
ejpam-4446	162	14	by	by	ADP
ejpam-4446	162	15	assumption	assumption	NOUN
ejpam-4446	162	16	,	,	PUNCT
ejpam-4446	162	17	we	we	PRON
ejpam-4446	162	18	have	have	VERB
ejpam-4446	162	19	a	a	DET
ejpam-4446	162	20	∗	∗	NOUN
ejpam-4446	162	21	b	b	NOUN
ejpam-4446	162	22	∈	∈	PROPN
ejpam-4446	162	23	(	(	PUNCT
ejpam-4446	162	24	lε	lε	X
ejpam-4446	162	25	ξ	ξ	PROPN
ejpam-4446	162	26	,	,	PUNCT
ejpam-4446	162	27	s)∈	s)∈	NUM
ejpam-4446	162	28	and	and	CCONJ
ejpam-4446	162	29	hence	hence	ADV
ejpam-4446	162	30	[	[	X
ejpam-4446	162	31	(	(	PUNCT
ejpam-4446	162	32	a	a	DET
ejpam-4446	162	33	∗	∗	NOUN
ejpam-4446	162	34	b)//s	b)//	NOUN
ejpam-4446	162	35	]	]	X
ejpam-4446	162	36	∈	∈	PROPN
ejpam-4446	162	37	lε	lε	X
ejpam-4446	162	38	ξ	ξ	X
ejpam-4446	162	39	,	,	PUNCT
ejpam-4446	162	40	i.e.	i.e.	X
ejpam-4446	162	41	,	,	PUNCT
ejpam-4446	162	42	lε	lε	ADP
ejpam-4446	162	43	ξ(a	ξ(a	PROPN
ejpam-4446	162	44	∗	∗	NOUN
ejpam-4446	162	45	b	b	NOUN
ejpam-4446	162	46	)	)	PUNCT
ejpam-4446	162	47	≥	≥	NOUN
ejpam-4446	162	48	s	s	NOUN
ejpam-4446	162	49	=	=	SYM
ejpam-4446	162	50	min	min	PROPN
ejpam-4446	162	51	{	{	PUNCT
ejpam-4446	162	52	lε	lε	X
ejpam-4446	162	53	ξ(a	ξ(a	NUM
ejpam-4446	162	54	)	)	PUNCT
ejpam-4446	162	55	,	,	PUNCT
ejpam-4446	162	56	lε	lε	X
ejpam-4446	162	57	ξ(b	ξ(b	NOUN
ejpam-4446	162	58	)	)	PUNCT
ejpam-4446	162	59	}	}	PUNCT
ejpam-4446	162	60	.	.	PUNCT
ejpam-4446	163	1	this	this	PRON
ejpam-4446	163	2	is	be	AUX
ejpam-4446	163	3	a	a	DET
ejpam-4446	163	4	contradiction	contradiction	NOUN
ejpam-4446	163	5	.	.	PUNCT
ejpam-4446	164	1	hence	hence	ADV
ejpam-4446	164	2	min	min	PROPN
ejpam-4446	164	3	{	{	PUNCT
ejpam-4446	164	4	lε	lε	ADP
ejpam-4446	164	5	ξ(x	ξ(x	PROPN
ejpam-4446	164	6	)	)	PUNCT
ejpam-4446	164	7	,	,	PUNCT
ejpam-4446	164	8	lε	lε	ADP
ejpam-4446	164	9	ξ(y	ξ(y	PROPN
ejpam-4446	164	10	)	)	PUNCT
ejpam-4446	164	11	}	}	PUNCT
ejpam-4446	164	12	≤	≤	NUM
ejpam-4446	164	13	max	max	PROPN
ejpam-4446	164	14	{	{	PUNCT
ejpam-4446	164	15	lε	lε	ADP
ejpam-4446	164	16	ξ(x	ξ(x	PROPN
ejpam-4446	164	17	∗	∗	X
ejpam-4446	164	18	y	y	PROPN
ejpam-4446	164	19	)	)	PUNCT
ejpam-4446	164	20	,	,	PUNCT
ejpam-4446	164	21	0.5	0.5	NUM
ejpam-4446	164	22	}	}	PUNCT
ejpam-4446	164	23	for	for	ADP
ejpam-4446	164	24	all	all	DET
ejpam-4446	164	25	x	x	NOUN
ejpam-4446	164	26	,	,	PUNCT
ejpam-4446	164	27	y	y	PROPN
ejpam-4446	164	28	∈	∈	PROPN
ejpam-4446	164	29	x	x	PRON
ejpam-4446	164	30	,	,	PUNCT
ejpam-4446	164	31	that	that	ADV
ejpam-4446	164	32	is	is	ADV
ejpam-4446	164	33	,	,	PUNCT
ejpam-4446	164	34	lε	lε	PRON
ejpam-4446	164	35	ξ	ξ	X
ejpam-4446	164	36	satisfies	satisfy	VERB
ejpam-4446	164	37	the	the	DET
ejpam-4446	164	38	condition	condition	NOUN
ejpam-4446	164	39	(	(	PUNCT
ejpam-4446	164	40	15	15	NUM
ejpam-4446	164	41	)	)	PUNCT
ejpam-4446	164	42	.	.	PUNCT
ejpam-4446	165	1	theorem	theorem	VERB
ejpam-4446	165	2	7	7	NUM
ejpam-4446	165	3	.	.	PUNCT
ejpam-4446	166	1	if	if	SCONJ
ejpam-4446	166	2	the	the	DET
ejpam-4446	166	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	166	4	fuzzy	fuzzy	NOUN
ejpam-4446	166	5	set	set	VERB
ejpam-4446	166	6	lε	lε	ADP
ejpam-4446	166	7	ξ	ξ	PROPN
ejpam-4446	166	8	of	of	ADP
ejpam-4446	166	9	ξ	ξ	PROPN
ejpam-4446	166	10	in	in	ADP
ejpam-4446	166	11	x	x	PROPN
ejpam-4446	166	12	is	be	AUX
ejpam-4446	166	13	a	a	DET
ejpam-4446	166	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	166	15	fuzzy	fuzzy	ADJ
ejpam-4446	166	16	be	be	NOUN
ejpam-4446	166	17	-	-	PUNCT
ejpam-4446	166	18	algebra	algebra	NOUN
ejpam-4446	166	19	of	of	ADP
ejpam-4446	166	20	x	x	NOUN
ejpam-4446	166	21	,	,	PUNCT
ejpam-4446	166	22	then	then	ADV
ejpam-4446	166	23	its	its	PRON
ejpam-4446	166	24	q	q	NOUN
ejpam-4446	166	25	-	-	PUNCT
ejpam-4446	166	26	set	set	ADJ
ejpam-4446	166	27	(	(	PUNCT
ejpam-4446	166	28	lε	lε	X
ejpam-4446	166	29	ξ	ξ	PROPN
ejpam-4446	166	30	,	,	PUNCT
ejpam-4446	166	31	t)q	t)q	PUNCT
ejpam-4446	166	32	is	be	AUX
ejpam-4446	166	33	a	a	DET
ejpam-4446	166	34	be	be	NOUN
ejpam-4446	166	35	-	-	PUNCT
ejpam-4446	166	36	subalgebra	subalgebra	NOUN
ejpam-4446	166	37	of	of	ADP
ejpam-4446	166	38	x	x	PUNCT
ejpam-4446	166	39	for	for	ADP
ejpam-4446	166	40	the	the	DET
ejpam-4446	166	41	value	value	NOUN
ejpam-4446	166	42	t	t	PROPN
ejpam-4446	166	43	∈	∈	PROPN
ejpam-4446	166	44	(	(	PUNCT
ejpam-4446	166	45	0	0	NUM
ejpam-4446	166	46	,	,	PUNCT
ejpam-4446	166	47	1	1	NUM
ejpam-4446	166	48	]	]	PUNCT
ejpam-4446	166	49	.	.	PUNCT
ejpam-4446	167	1	proof	proof	NOUN
ejpam-4446	167	2	.	.	PUNCT
ejpam-4446	168	1	let	let	VERB
ejpam-4446	168	2	t	t	PROPN
ejpam-4446	168	3	∈	∈	PROPN
ejpam-4446	168	4	(	(	PUNCT
ejpam-4446	168	5	0	0	NUM
ejpam-4446	168	6	,	,	PUNCT
ejpam-4446	168	7	1	1	NUM
ejpam-4446	168	8	]	]	PUNCT
ejpam-4446	168	9	and	and	CCONJ
ejpam-4446	168	10	x	x	X
ejpam-4446	168	11	,	,	PUNCT
ejpam-4446	168	12	y	y	PROPN
ejpam-4446	168	13	∈	∈	PROPN
ejpam-4446	168	14	(	(	PUNCT
ejpam-4446	168	15	lε	lε	X
ejpam-4446	168	16	ξ	ξ	PROPN
ejpam-4446	168	17	,	,	PUNCT
ejpam-4446	168	18	t)q	t)q	PUNCT
ejpam-4446	168	19	.	.	PUNCT
ejpam-4446	169	1	then	then	ADV
ejpam-4446	169	2	[	[	X
ejpam-4446	169	3	x	x	X
ejpam-4446	169	4	/	/	SYM
ejpam-4446	169	5	t	t	PROPN
ejpam-4446	169	6	]	]	X
ejpam-4446	169	7	q	q	X
ejpam-4446	169	8	lε	lε	X
ejpam-4446	169	9	ξ	ξ	PROPN
ejpam-4446	169	10	and	and	CCONJ
ejpam-4446	169	11	[	[	X
ejpam-4446	169	12	y	y	PROPN
ejpam-4446	169	13	/	/	SYM
ejpam-4446	169	14	t	t	PROPN
ejpam-4446	169	15	]	]	X
ejpam-4446	169	16	q	q	X
ejpam-4446	169	17	lε	lε	X
ejpam-4446	169	18	ξ	ξ	PROPN
ejpam-4446	169	19	,	,	PUNCT
ejpam-4446	169	20	that	that	ADV
ejpam-4446	169	21	is	is	ADV
ejpam-4446	169	22	,	,	PUNCT
ejpam-4446	169	23	lε	lε	ADP
ejpam-4446	169	24	ξ(x	ξ(x	NOUN
ejpam-4446	169	25	)	)	PUNCT
ejpam-4446	170	1	+	+	CCONJ
ejpam-4446	170	2	t	t	X
ejpam-4446	170	3	>	>	X
ejpam-4446	170	4	1	1	NUM
ejpam-4446	170	5	and	and	CCONJ
ejpam-4446	170	6	lε	lε	ADP
ejpam-4446	170	7	ξ(y	ξ(y	PROPN
ejpam-4446	170	8	)	)	PUNCT
ejpam-4446	171	1	+	+	CCONJ
ejpam-4446	171	2	t	t	X
ejpam-4446	171	3	>	>	X
ejpam-4446	171	4	1	1	X
ejpam-4446	171	5	.	.	PUNCT
ejpam-4446	172	1	it	it	PRON
ejpam-4446	172	2	follows	follow	VERB
ejpam-4446	172	3	from	from	ADP
ejpam-4446	172	4	theorem	theorem	ADJ
ejpam-4446	172	5	1	1	NUM
ejpam-4446	173	1	that	that	PRON
ejpam-4446	173	2	lε	lε	ADP
ejpam-4446	173	3	ξ(x	ξ(x	PROPN
ejpam-4446	173	4	∗	∗	X
ejpam-4446	173	5	y	y	NOUN
ejpam-4446	173	6	)	)	PUNCT
ejpam-4446	174	1	+	+	CCONJ
ejpam-4446	174	2	t	t	PROPN
ejpam-4446	174	3	≥	≥	NOUN
ejpam-4446	174	4	min	min	PROPN
ejpam-4446	174	5	{	{	PUNCT
ejpam-4446	174	6	lε	lε	ADP
ejpam-4446	174	7	ξ(x	ξ(x	PROPN
ejpam-4446	174	8	)	)	PUNCT
ejpam-4446	174	9	,	,	PUNCT
ejpam-4446	174	10	lε	lε	ADP
ejpam-4446	174	11	ξ(y	ξ(y	PROPN
ejpam-4446	174	12	)	)	PUNCT
ejpam-4446	174	13	}	}	PUNCT
ejpam-4446	175	1	+	+	NUM
ejpam-4446	175	2	t	t	NOUN
ejpam-4446	175	3	=	=	SYM
ejpam-4446	175	4	min	min	PROPN
ejpam-4446	175	5	{	{	PUNCT
ejpam-4446	175	6	lε	lε	X
ejpam-4446	175	7	ξ(x	ξ(x	NOUN
ejpam-4446	175	8	)	)	PUNCT
ejpam-4446	175	9	+	+	SYM
ejpam-4446	175	10	t	t	PROPN
ejpam-4446	175	11	,	,	PUNCT
ejpam-4446	175	12	lε	lε	ADP
ejpam-4446	175	13	ξ(y	ξ(y	PROPN
ejpam-4446	175	14	)	)	PUNCT
ejpam-4446	175	15	+	+	CCONJ
ejpam-4446	175	16	t	t	X
ejpam-4446	175	17	}	}	PUNCT
ejpam-4446	175	18	>	>	X
ejpam-4446	175	19	1	1	NUM
ejpam-4446	175	20	.	.	PUNCT
ejpam-4446	176	1	thus	thus	ADV
ejpam-4446	176	2	[	[	X
ejpam-4446	176	3	(	(	PUNCT
ejpam-4446	176	4	x	x	SYM
ejpam-4446	176	5	∗	∗	PROPN
ejpam-4446	176	6	y)/t	y)/t	NOUN
ejpam-4446	176	7	]	]	X
ejpam-4446	176	8	q	q	X
ejpam-4446	176	9	lε	lε	X
ejpam-4446	176	10	ξ	ξ	PROPN
ejpam-4446	176	11	,	,	PUNCT
ejpam-4446	176	12	i.e.	i.e.	X
ejpam-4446	176	13	,	,	PUNCT
ejpam-4446	176	14	x	x	PUNCT
ejpam-4446	176	15	∗	∗	NOUN
ejpam-4446	176	16	y	y	PROPN
ejpam-4446	176	17	∈	∈	PROPN
ejpam-4446	176	18	(	(	PUNCT
ejpam-4446	176	19	lε	lε	X
ejpam-4446	176	20	ξ	ξ	PROPN
ejpam-4446	176	21	,	,	PUNCT
ejpam-4446	176	22	t)q	t)q	PUNCT
ejpam-4446	176	23	.	.	PUNCT
ejpam-4446	177	1	hence	hence	ADV
ejpam-4446	177	2	(	(	PUNCT
ejpam-4446	177	3	lε	lε	X
ejpam-4446	177	4	ξ	ξ	PROPN
ejpam-4446	177	5	,	,	PUNCT
ejpam-4446	177	6	t)q	t)q	PUNCT
ejpam-4446	177	7	is	be	AUX
ejpam-4446	177	8	a	a	DET
ejpam-4446	177	9	be	be	NOUN
ejpam-4446	177	10	-	-	PUNCT
ejpam-4446	177	11	subalgebra	subalgebra	NOUN
ejpam-4446	177	12	of	of	ADP
ejpam-4446	177	13	x.	x.	PROPN
ejpam-4446	177	14	corollary	corollary	NOUN
ejpam-4446	178	1	1	1	X
ejpam-4446	178	2	.	.	PUNCT
ejpam-4446	179	1	if	if	SCONJ
ejpam-4446	179	2	ξ	ξ	PROPN
ejpam-4446	179	3	is	be	AUX
ejpam-4446	179	4	a	a	DET
ejpam-4446	179	5	fuzzy	fuzzy	ADJ
ejpam-4446	179	6	be	be	NOUN
ejpam-4446	179	7	-	-	PUNCT
ejpam-4446	179	8	algebra	algebra	NOUN
ejpam-4446	179	9	of	of	ADP
ejpam-4446	179	10	x	x	NOUN
ejpam-4446	179	11	,	,	PUNCT
ejpam-4446	179	12	then	then	ADV
ejpam-4446	179	13	the	the	DET
ejpam-4446	179	14	q	q	NOUN
ejpam-4446	179	15	-	-	PUNCT
ejpam-4446	179	16	set	set	ADJ
ejpam-4446	179	17	(	(	PUNCT
ejpam-4446	179	18	lε	lε	X
ejpam-4446	179	19	ξ	ξ	PROPN
ejpam-4446	179	20	,	,	PUNCT
ejpam-4446	179	21	t)q	t)q	PRON
ejpam-4446	179	22	of	of	ADP
ejpam-4446	179	23	lε	lε	ADP
ejpam-4446	179	24	ξ	ξ	PROPN
ejpam-4446	179	25	is	be	AUX
ejpam-4446	179	26	a	a	DET
ejpam-4446	179	27	besubalgebra	besubalgebra	NOUN
ejpam-4446	179	28	of	of	ADP
ejpam-4446	179	29	x	x	PUNCT
ejpam-4446	179	30	for	for	ADP
ejpam-4446	179	31	the	the	DET
ejpam-4446	179	32	value	value	NOUN
ejpam-4446	179	33	t	t	PROPN
ejpam-4446	179	34	∈	∈	PROPN
ejpam-4446	179	35	(	(	PUNCT
ejpam-4446	179	36	0	0	NUM
ejpam-4446	179	37	,	,	PUNCT
ejpam-4446	179	38	1	1	NUM
ejpam-4446	179	39	]	]	PUNCT
ejpam-4446	179	40	.	.	PUNCT
ejpam-4446	180	1	theorem	theorem	ADJ
ejpam-4446	180	2	8	8	NUM
ejpam-4446	180	3	.	.	PUNCT
ejpam-4446	181	1	for	for	ADP
ejpam-4446	181	2	the	the	DET
ejpam-4446	181	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	181	4	fuzzy	fuzzy	NOUN
ejpam-4446	181	5	set	set	VERB
ejpam-4446	181	6	lε	lε	ADP
ejpam-4446	181	7	ξ	ξ	PROPN
ejpam-4446	181	8	of	of	ADP
ejpam-4446	181	9	ξ	ξ	PROPN
ejpam-4446	181	10	in	in	ADP
ejpam-4446	181	11	x	x	SYM
ejpam-4446	181	12	,	,	PUNCT
ejpam-4446	181	13	if	if	SCONJ
ejpam-4446	181	14	the	the	DET
ejpam-4446	181	15	q	q	NOUN
ejpam-4446	181	16	-	-	PUNCT
ejpam-4446	181	17	set	set	ADJ
ejpam-4446	181	18	(	(	PUNCT
ejpam-4446	181	19	lε	lε	X
ejpam-4446	181	20	ξ	ξ	PROPN
ejpam-4446	181	21	,	,	PUNCT
ejpam-4446	181	22	t)q	t)q	PUNCT
ejpam-4446	181	23	is	be	AUX
ejpam-4446	181	24	a	a	DET
ejpam-4446	181	25	besubalgebra	besubalgebra	NOUN
ejpam-4446	181	26	of	of	ADP
ejpam-4446	181	27	x	x	NOUN
ejpam-4446	181	28	,	,	PUNCT
ejpam-4446	181	29	then	then	ADV
ejpam-4446	181	30	lε	lε	X
ejpam-4446	181	31	ξ	ξ	X
ejpam-4446	181	32	satisfies	satisfie	NOUN
ejpam-4446	181	33	:	:	PUNCT
ejpam-4446	181	34	x	x	SYM
ejpam-4446	181	35	∈	∈	PROPN
ejpam-4446	181	36	(	(	PUNCT
ejpam-4446	181	37	lε	lε	X
ejpam-4446	181	38	ξ	ξ	PROPN
ejpam-4446	181	39	,	,	PUNCT
ejpam-4446	181	40	ta)q	ta)q	INTJ
ejpam-4446	181	41	,	,	PUNCT
ejpam-4446	181	42	y	y	PROPN
ejpam-4446	181	43	∈	∈	PROPN
ejpam-4446	181	44	(	(	PUNCT
ejpam-4446	181	45	lε	lε	PART
ejpam-4446	181	46	ξ	ξ	PROPN
ejpam-4446	181	47	,	,	PUNCT
ejpam-4446	181	48	tb)q	tb)q	DET
ejpam-4446	181	49	⇒	⇒	NOUN
ejpam-4446	181	50	x	x	PUNCT
ejpam-4446	181	51	∗	∗	VERB
ejpam-4446	181	52	y	y	PROPN
ejpam-4446	181	53	∈	∈	PROPN
ejpam-4446	181	54	(	(	PUNCT
ejpam-4446	181	55	lε	lε	ADP
ejpam-4446	181	56	ξ	ξ	PROPN
ejpam-4446	181	57	,	,	PUNCT
ejpam-4446	181	58	max{ta	max{ta	NUM
ejpam-4446	181	59	,	,	PUNCT
ejpam-4446	181	60	tb})∈	tb})∈	X
ejpam-4446	181	61	(	(	PUNCT
ejpam-4446	181	62	16	16	NUM
ejpam-4446	181	63	)	)	PUNCT
ejpam-4446	181	64	for	for	ADP
ejpam-4446	181	65	all	all	DET
ejpam-4446	181	66	x	x	NOUN
ejpam-4446	181	67	,	,	PUNCT
ejpam-4446	181	68	y	y	PROPN
ejpam-4446	181	69	∈	∈	PROPN
ejpam-4446	181	70	x	x	X
ejpam-4446	181	71	and	and	CCONJ
ejpam-4446	181	72	ta	ta	PROPN
ejpam-4446	181	73	,	,	PUNCT
ejpam-4446	181	74	tb	tb	ADP
ejpam-4446	181	75	∈	∈	PROPN
ejpam-4446	181	76	(	(	PUNCT
ejpam-4446	181	77	0	0	NUM
ejpam-4446	181	78	,	,	PUNCT
ejpam-4446	181	79	0.5	0.5	NUM
ejpam-4446	181	80	]	]	PUNCT
ejpam-4446	181	81	.	.	PUNCT
ejpam-4446	182	1	y.	y.	PROPN
ejpam-4446	182	2	b.	b.	PROPN
ejpam-4446	182	3	jun	jun	PROPN
ejpam-4446	182	4	,	,	PUNCT
ejpam-4446	182	5	s.	s.	PROPN
ejpam-4446	182	6	s.	s.	PROPN
ejpam-4446	182	7	ahn	ahn	PROPN
ejpam-4446	182	8	/	/	SYM
ejpam-4446	182	9	eur	eur	PROPN
ejpam-4446	182	10	.	.	PUNCT
ejpam-4446	183	1	j.	j.	PROPN
ejpam-4446	183	2	pure	pure	PROPN
ejpam-4446	183	3	appl	appl	PROPN
ejpam-4446	183	4	.	.	PROPN
ejpam-4446	183	5	math	math	PROPN
ejpam-4446	183	6	,	,	PUNCT
ejpam-4446	183	7	15	15	NUM
ejpam-4446	183	8	(	(	PUNCT
ejpam-4446	183	9	3	3	NUM
ejpam-4446	183	10	)	)	PUNCT
ejpam-4446	183	11	(	(	PUNCT
ejpam-4446	183	12	2022	2022	NUM
ejpam-4446	183	13	)	)	PUNCT
ejpam-4446	183	14	,	,	PUNCT
ejpam-4446	183	15	924	924	NUM
ejpam-4446	183	16	-	-	SYM
ejpam-4446	183	17	937	937	NUM
ejpam-4446	183	18	932	932	NUM
ejpam-4446	183	19	proof	proof	NOUN
ejpam-4446	183	20	.	.	PUNCT
ejpam-4446	184	1	assume	assume	VERB
ejpam-4446	184	2	that	that	SCONJ
ejpam-4446	184	3	the	the	DET
ejpam-4446	184	4	q	q	NOUN
ejpam-4446	184	5	-	-	PUNCT
ejpam-4446	184	6	set	set	ADJ
ejpam-4446	184	7	(	(	PUNCT
ejpam-4446	184	8	lε	lε	X
ejpam-4446	184	9	ξ	ξ	PROPN
ejpam-4446	184	10	,	,	PUNCT
ejpam-4446	184	11	t)q	t)q	PUNCT
ejpam-4446	184	12	is	be	AUX
ejpam-4446	184	13	a	a	DET
ejpam-4446	184	14	be	be	NOUN
ejpam-4446	184	15	-	-	PUNCT
ejpam-4446	184	16	subalgebra	subalgebra	NOUN
ejpam-4446	184	17	of	of	ADP
ejpam-4446	184	18	x.	x.	NOUN
ejpam-4446	184	19	let	let	VERB
ejpam-4446	184	20	x	x	PRON
ejpam-4446	184	21	,	,	PUNCT
ejpam-4446	184	22	y	y	PROPN
ejpam-4446	184	23	∈	∈	PROPN
ejpam-4446	184	24	x	x	X
ejpam-4446	184	25	and	and	CCONJ
ejpam-4446	184	26	ta	ta	PROPN
ejpam-4446	184	27	,	,	PUNCT
ejpam-4446	184	28	tb	tb	ADP
ejpam-4446	184	29	∈	∈	PROPN
ejpam-4446	184	30	(	(	PUNCT
ejpam-4446	184	31	0	0	NUM
ejpam-4446	184	32	,	,	PUNCT
ejpam-4446	184	33	0.5	0.5	NUM
ejpam-4446	184	34	]	]	PUNCT
ejpam-4446	184	35	be	be	VERB
ejpam-4446	184	36	such	such	ADJ
ejpam-4446	184	37	that	that	SCONJ
ejpam-4446	184	38	x	x	SYM
ejpam-4446	184	39	∈	∈	PROPN
ejpam-4446	184	40	(	(	PUNCT
ejpam-4446	184	41	lε	lε	X
ejpam-4446	184	42	ξ	ξ	PROPN
ejpam-4446	184	43	,	,	PUNCT
ejpam-4446	184	44	ta)q	ta)q	NOUN
ejpam-4446	184	45	and	and	CCONJ
ejpam-4446	184	46	y	y	PROPN
ejpam-4446	184	47	∈	∈	PROPN
ejpam-4446	184	48	(	(	PUNCT
ejpam-4446	184	49	lε	lε	ADP
ejpam-4446	184	50	ξ	ξ	PROPN
ejpam-4446	184	51	,	,	PUNCT
ejpam-4446	184	52	tb)q	tb)q	PROPN
ejpam-4446	184	53	.	.	PUNCT
ejpam-4446	185	1	then	then	ADV
ejpam-4446	185	2	x	x	X
ejpam-4446	185	3	,	,	PUNCT
ejpam-4446	185	4	y	y	PROPN
ejpam-4446	185	5	∈	∈	PROPN
ejpam-4446	185	6	(	(	PUNCT
ejpam-4446	185	7	lε	lε	ADP
ejpam-4446	185	8	ξ	ξ	PROPN
ejpam-4446	185	9	,	,	PUNCT
ejpam-4446	185	10	max{ta	max{ta	NOUN
ejpam-4446	185	11	,	,	PUNCT
ejpam-4446	185	12	tb})q	tb})q	NOUN
ejpam-4446	185	13	,	,	PUNCT
ejpam-4446	185	14	and	and	CCONJ
ejpam-4446	185	15	hence	hence	ADV
ejpam-4446	185	16	x	x	ADP
ejpam-4446	185	17	∗	∗	VERB
ejpam-4446	185	18	y	y	PROPN
ejpam-4446	185	19	∈	∈	PROPN
ejpam-4446	185	20	(	(	PUNCT
ejpam-4446	185	21	lε	lε	ADP
ejpam-4446	185	22	ξ	ξ	PROPN
ejpam-4446	185	23	,	,	PUNCT
ejpam-4446	185	24	max{ta	max{ta	NUM
ejpam-4446	185	25	,	,	PUNCT
ejpam-4446	185	26	tb})q	tb})q	NOUN
ejpam-4446	185	27	by	by	ADP
ejpam-4446	185	28	hypothesis	hypothesis	NOUN
ejpam-4446	185	29	.	.	PUNCT
ejpam-4446	186	1	it	it	PRON
ejpam-4446	186	2	follows	follow	VERB
ejpam-4446	186	3	that	that	SCONJ
ejpam-4446	186	4	lε	lε	ADP
ejpam-4446	186	5	ξ(x	ξ(x	PROPN
ejpam-4446	186	6	∗	∗	X
ejpam-4446	186	7	y	y	PROPN
ejpam-4446	186	8	)	)	PUNCT
ejpam-4446	186	9	>	>	X
ejpam-4446	186	10	1	1	NUM
ejpam-4446	186	11	−	−	NOUN
ejpam-4446	186	12	max{ta	max{ta	NOUN
ejpam-4446	186	13	,	,	PUNCT
ejpam-4446	186	14	tb	tb	NOUN
ejpam-4446	186	15	}	}	PUNCT
ejpam-4446	186	16	≥	≥	X
ejpam-4446	186	17	max{ta	max{ta	NOUN
ejpam-4446	186	18	,	,	PUNCT
ejpam-4446	186	19	tb	tb	NOUN
ejpam-4446	186	20	}	}	PUNCT
ejpam-4446	186	21	since	since	SCONJ
ejpam-4446	186	22	max{ta	max{ta	NOUN
ejpam-4446	186	23	,	,	PUNCT
ejpam-4446	186	24	tb	tb	NOUN
ejpam-4446	186	25	}	}	PUNCT
ejpam-4446	186	26	≤	≤	NUM
ejpam-4446	186	27	0.5	0.5	NUM
ejpam-4446	186	28	.	.	PUNCT
ejpam-4446	187	1	therefore	therefore	ADV
ejpam-4446	187	2	[	[	X
ejpam-4446	187	3	(	(	PUNCT
ejpam-4446	187	4	x∗y)/max{ta	x∗y)/max{ta	VERB
ejpam-4446	187	5	,	,	PUNCT
ejpam-4446	187	6	tb	tb	NOUN
ejpam-4446	187	7	}	}	PUNCT
ejpam-4446	187	8	]	]	PUNCT
ejpam-4446	187	9	∈	∈	PROPN
ejpam-4446	187	10	lε	lε	X
ejpam-4446	187	11	ξ	ξ	PROPN
ejpam-4446	187	12	,	,	PUNCT
ejpam-4446	187	13	that	that	ADV
ejpam-4446	187	14	is	is	ADV
ejpam-4446	187	15	,	,	PUNCT
ejpam-4446	187	16	x∗y	x∗y	PUNCT
ejpam-4446	187	17	∈	∈	PROPN
ejpam-4446	187	18	(	(	PUNCT
ejpam-4446	187	19	lε	lε	ADP
ejpam-4446	187	20	ξ	ξ	PROPN
ejpam-4446	187	21	,	,	PUNCT
ejpam-4446	187	22	max{ta	max{ta	X
ejpam-4446	187	23	,	,	PUNCT
ejpam-4446	187	24	tb})∈.	tb})∈.	NUM
ejpam-4446	187	25	theorem	theorem	VERB
ejpam-4446	187	26	9	9	NUM
ejpam-4446	187	27	.	.	PUNCT
ejpam-4446	188	1	if	if	SCONJ
ejpam-4446	188	2	the	the	DET
ejpam-4446	188	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	188	4	fuzzy	fuzzy	NOUN
ejpam-4446	188	5	set	set	VERB
ejpam-4446	188	6	lε	lε	ADP
ejpam-4446	188	7	ξ	ξ	PROPN
ejpam-4446	188	8	of	of	ADP
ejpam-4446	188	9	ξ	ξ	PROPN
ejpam-4446	188	10	is	be	AUX
ejpam-4446	188	11	a	a	DET
ejpam-4446	188	12	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	188	13	fuzzy	fuzzy	ADJ
ejpam-4446	188	14	be	be	NOUN
ejpam-4446	188	15	-	-	PUNCT
ejpam-4446	188	16	algebra	algebra	NOUN
ejpam-4446	188	17	of	of	ADP
ejpam-4446	188	18	x	x	NOUN
ejpam-4446	188	19	,	,	PUNCT
ejpam-4446	188	20	then	then	ADV
ejpam-4446	188	21	its	its	PRON
ejpam-4446	188	22	o	o	NOUN
ejpam-4446	188	23	-	-	ADJ
ejpam-4446	188	24	set	set	VERB
ejpam-4446	188	25	o	o	NOUN
ejpam-4446	188	26	(	(	PUNCT
ejpam-4446	188	27	lε	lε	X
ejpam-4446	188	28	ξ	ξ	X
ejpam-4446	188	29	)	)	PUNCT
ejpam-4446	188	30	is	be	AUX
ejpam-4446	188	31	a	a	DET
ejpam-4446	188	32	be	be	NOUN
ejpam-4446	188	33	-	-	PUNCT
ejpam-4446	188	34	subalgebra	subalgebra	NOUN
ejpam-4446	188	35	of	of	ADP
ejpam-4446	188	36	x.	x.	NOUN
ejpam-4446	188	37	proof	proof	PROPN
ejpam-4446	188	38	.	.	PUNCT
ejpam-4446	189	1	assume	assume	VERB
ejpam-4446	189	2	that	that	SCONJ
ejpam-4446	189	3	lε	lε	X
ejpam-4446	189	4	ξ	ξ	PROPN
ejpam-4446	189	5	is	be	AUX
ejpam-4446	189	6	a	a	DET
ejpam-4446	189	7	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	189	8	fuzzy	fuzzy	ADJ
ejpam-4446	189	9	be	be	NOUN
ejpam-4446	189	10	-	-	PUNCT
ejpam-4446	189	11	algebra	algebra	NOUN
ejpam-4446	189	12	of	of	ADP
ejpam-4446	189	13	x	x	PUNCT
ejpam-4446	189	14	and	and	CCONJ
ejpam-4446	189	15	let	let	VERB
ejpam-4446	189	16	x	x	PRON
ejpam-4446	189	17	,	,	PUNCT
ejpam-4446	189	18	y	y	PROPN
ejpam-4446	189	19	∈	∈	PROPN
ejpam-4446	190	1	o	o	NOUN
ejpam-4446	190	2	(	(	PUNCT
ejpam-4446	190	3	lε	lε	INTJ
ejpam-4446	190	4	ξ	ξ	NUM
ejpam-4446	190	5	)	)	PUNCT
ejpam-4446	190	6	.	.	PUNCT
ejpam-4446	191	1	then	then	ADV
ejpam-4446	191	2	ξ(x	ξ(x	NOUN
ejpam-4446	191	3	)	)	PUNCT
ejpam-4446	192	1	+	+	CCONJ
ejpam-4446	192	2	ε−	ε−	PROPN
ejpam-4446	192	3	1	1	NUM
ejpam-4446	192	4	>	>	SYM
ejpam-4446	192	5	0	0	NUM
ejpam-4446	192	6	and	and	CCONJ
ejpam-4446	192	7	ξ(y	ξ(y	PROPN
ejpam-4446	192	8	)	)	PUNCT
ejpam-4446	193	1	+	+	CCONJ
ejpam-4446	193	2	ε−	ε−	PROPN
ejpam-4446	193	3	1	1	NUM
ejpam-4446	193	4	>	>	SYM
ejpam-4446	193	5	0	0	NUM
ejpam-4446	194	1	which	which	PRON
ejpam-4446	194	2	implies	imply	VERB
ejpam-4446	194	3	that	that	SCONJ
ejpam-4446	194	4	lε	lε	ADP
ejpam-4446	194	5	ξ(x	ξ(x	PROPN
ejpam-4446	194	6	∗	∗	X
ejpam-4446	194	7	y	y	PROPN
ejpam-4446	194	8	)	)	PUNCT
ejpam-4446	194	9	≥	≥	PROPN
ejpam-4446	194	10	min	min	PROPN
ejpam-4446	194	11	{	{	PUNCT
ejpam-4446	194	12	lε	lε	ADP
ejpam-4446	194	13	ξ(x	ξ(x	PROPN
ejpam-4446	194	14	)	)	PUNCT
ejpam-4446	194	15	,	,	PUNCT
ejpam-4446	194	16	lε	lε	ADP
ejpam-4446	194	17	ξ(y	ξ(y	PROPN
ejpam-4446	194	18	)	)	PUNCT
ejpam-4446	194	19	}	}	PUNCT
ejpam-4446	194	20	=	=	SYM
ejpam-4446	194	21	min{ξ(x	min{ξ(x	NOUN
ejpam-4446	194	22	)	)	PUNCT
ejpam-4446	195	1	+	+	CCONJ
ejpam-4446	195	2	ε−	ε−	PROPN
ejpam-4446	195	3	1	1	NUM
ejpam-4446	195	4	,	,	PUNCT
ejpam-4446	195	5	ξ(y	ξ(y	PROPN
ejpam-4446	195	6	)	)	PUNCT
ejpam-4446	196	1	+	+	CCONJ
ejpam-4446	196	2	ε−	ε−	PROPN
ejpam-4446	196	3	1	1	NUM
ejpam-4446	196	4	}	}	PUNCT
ejpam-4446	196	5	>	>	X
ejpam-4446	196	6	0	0	PUNCT
ejpam-4446	196	7	by	by	ADP
ejpam-4446	196	8	theoem	theoem	NOUN
ejpam-4446	196	9	1	1	NUM
ejpam-4446	196	10	.	.	PUNCT
ejpam-4446	197	1	hence	hence	ADV
ejpam-4446	197	2	x	x	X
ejpam-4446	197	3	∗	∗	NOUN
ejpam-4446	197	4	y	y	PROPN
ejpam-4446	197	5	∈	∈	PROPN
ejpam-4446	198	1	o	o	NOUN
ejpam-4446	198	2	(	(	PUNCT
ejpam-4446	198	3	lε	lε	INTJ
ejpam-4446	198	4	ξ	ξ	PROPN
ejpam-4446	198	5	)	)	PUNCT
ejpam-4446	198	6	,	,	PUNCT
ejpam-4446	198	7	and	and	CCONJ
ejpam-4446	198	8	therefore	therefore	ADV
ejpam-4446	198	9	o	o	X
ejpam-4446	198	10	(	(	PUNCT
ejpam-4446	198	11	lε	lε	X
ejpam-4446	198	12	ξ	ξ	X
ejpam-4446	198	13	)	)	PUNCT
ejpam-4446	198	14	is	be	AUX
ejpam-4446	198	15	a	a	DET
ejpam-4446	198	16	be	be	NOUN
ejpam-4446	198	17	-	-	PUNCT
ejpam-4446	198	18	subalgebra	subalgebra	NOUN
ejpam-4446	198	19	of	of	ADP
ejpam-4446	198	20	x.	x.	PROPN
ejpam-4446	198	21	corollary	corollary	PROPN
ejpam-4446	199	1	2	2	X
ejpam-4446	199	2	.	.	PUNCT
ejpam-4446	200	1	if	if	SCONJ
ejpam-4446	200	2	ξ	ξ	PROPN
ejpam-4446	200	3	is	be	AUX
ejpam-4446	200	4	a	a	DET
ejpam-4446	200	5	fuzzy	fuzzy	ADJ
ejpam-4446	200	6	be	be	NOUN
ejpam-4446	200	7	-	-	PUNCT
ejpam-4446	200	8	algebra	algebra	NOUN
ejpam-4446	200	9	of	of	ADP
ejpam-4446	200	10	x	x	NOUN
ejpam-4446	200	11	,	,	PUNCT
ejpam-4446	200	12	then	then	ADV
ejpam-4446	200	13	the	the	DET
ejpam-4446	200	14	o	o	NOUN
ejpam-4446	200	15	-	-	ADJ
ejpam-4446	200	16	set	set	VERB
ejpam-4446	200	17	o	o	NOUN
ejpam-4446	200	18	(	(	PUNCT
ejpam-4446	200	19	lε	lε	X
ejpam-4446	200	20	ξ	ξ	NOUN
ejpam-4446	200	21	)	)	PUNCT
ejpam-4446	200	22	of	of	ADP
ejpam-4446	200	23	lε	lε	PRON
ejpam-4446	200	24	ξ	ξ	PROPN
ejpam-4446	200	25	is	be	AUX
ejpam-4446	200	26	a	a	DET
ejpam-4446	200	27	besubalgebra	besubalgebra	NOUN
ejpam-4446	200	28	of	of	ADP
ejpam-4446	200	29	x.	x.	PROPN
ejpam-4446	200	30	theorem	theorem	VERB
ejpam-4446	200	31	10	10	NUM
ejpam-4446	200	32	.	.	PUNCT
ejpam-4446	201	1	if	if	SCONJ
ejpam-4446	201	2	the	the	DET
ejpam-4446	201	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	201	4	fuzzy	fuzzy	NOUN
ejpam-4446	201	5	set	set	VERB
ejpam-4446	201	6	lε	lε	ADP
ejpam-4446	201	7	ξ	ξ	PROPN
ejpam-4446	201	8	of	of	ADP
ejpam-4446	201	9	ξ	ξ	PROPN
ejpam-4446	201	10	in	in	ADP
ejpam-4446	201	11	x	x	X
ejpam-4446	201	12	satisfies	satisfie	NOUN
ejpam-4446	201	13	:	:	PUNCT
ejpam-4446	201	14	x	x	SYM
ejpam-4446	201	15	∈	∈	PROPN
ejpam-4446	201	16	(	(	PUNCT
ejpam-4446	201	17	lε	lε	PART
ejpam-4446	201	18	ξ	ξ	PROPN
ejpam-4446	201	19	,	,	PUNCT
ejpam-4446	201	20	ta)∈	ta)∈	PROPN
ejpam-4446	201	21	,	,	PUNCT
ejpam-4446	201	22	y	y	PROPN
ejpam-4446	201	23	∈	∈	PROPN
ejpam-4446	201	24	(	(	PUNCT
ejpam-4446	201	25	lε	lε	PART
ejpam-4446	201	26	ξ	ξ	PROPN
ejpam-4446	201	27	,	,	PUNCT
ejpam-4446	201	28	tb)∈	tb)∈	PROPN
ejpam-4446	201	29	⇒	⇒	VERB
ejpam-4446	201	30	x	x	X
ejpam-4446	201	31	∗	∗	NOUN
ejpam-4446	201	32	y	y	PROPN
ejpam-4446	201	33	∈	∈	PROPN
ejpam-4446	201	34	(	(	PUNCT
ejpam-4446	201	35	lε	lε	ADP
ejpam-4446	201	36	ξ	ξ	PROPN
ejpam-4446	201	37	,	,	PUNCT
ejpam-4446	201	38	max{ta	max{ta	NUM
ejpam-4446	201	39	,	,	PUNCT
ejpam-4446	201	40	tb})q	tb})q	PROPN
ejpam-4446	201	41	(	(	PUNCT
ejpam-4446	201	42	17	17	NUM
ejpam-4446	201	43	)	)	PUNCT
ejpam-4446	201	44	for	for	ADP
ejpam-4446	201	45	all	all	DET
ejpam-4446	201	46	x	x	NOUN
ejpam-4446	201	47	,	,	PUNCT
ejpam-4446	201	48	y	y	PROPN
ejpam-4446	201	49	∈	∈	PROPN
ejpam-4446	201	50	x	x	X
ejpam-4446	201	51	and	and	CCONJ
ejpam-4446	201	52	ta	ta	PROPN
ejpam-4446	201	53	,	,	PUNCT
ejpam-4446	201	54	tb	tb	ADP
ejpam-4446	201	55	∈	∈	PROPN
ejpam-4446	201	56	(	(	PUNCT
ejpam-4446	201	57	0	0	NUM
ejpam-4446	201	58	,	,	PUNCT
ejpam-4446	201	59	1	1	NUM
ejpam-4446	201	60	]	]	PUNCT
ejpam-4446	201	61	,	,	PUNCT
ejpam-4446	201	62	then	then	ADV
ejpam-4446	201	63	its	its	PRON
ejpam-4446	201	64	o	o	NOUN
ejpam-4446	201	65	-	-	ADJ
ejpam-4446	201	66	set	set	VERB
ejpam-4446	201	67	o	o	NOUN
ejpam-4446	201	68	(	(	PUNCT
ejpam-4446	201	69	lε	lε	X
ejpam-4446	201	70	ξ	ξ	X
ejpam-4446	201	71	)	)	PUNCT
ejpam-4446	201	72	is	be	AUX
ejpam-4446	201	73	a	a	DET
ejpam-4446	201	74	be	be	NOUN
ejpam-4446	201	75	-	-	PUNCT
ejpam-4446	201	76	subalgebra	subalgebra	NOUN
ejpam-4446	201	77	of	of	ADP
ejpam-4446	201	78	x.	x.	NOUN
ejpam-4446	201	79	proof	proof	PROPN
ejpam-4446	201	80	.	.	PUNCT
ejpam-4446	202	1	assume	assume	VERB
ejpam-4446	202	2	that	that	SCONJ
ejpam-4446	202	3	lε	lε	PRON
ejpam-4446	202	4	ξ	ξ	X
ejpam-4446	202	5	satisfies	satisfy	VERB
ejpam-4446	202	6	the	the	DET
ejpam-4446	202	7	condition	condition	NOUN
ejpam-4446	202	8	(	(	PUNCT
ejpam-4446	202	9	17	17	NUM
ejpam-4446	202	10	)	)	PUNCT
ejpam-4446	202	11	for	for	ADP
ejpam-4446	202	12	all	all	DET
ejpam-4446	202	13	x	x	NOUN
ejpam-4446	202	14	,	,	PUNCT
ejpam-4446	202	15	y	y	PROPN
ejpam-4446	202	16	∈	∈	PROPN
ejpam-4446	202	17	x	x	X
ejpam-4446	202	18	and	and	CCONJ
ejpam-4446	202	19	ta	ta	PROPN
ejpam-4446	202	20	,	,	PUNCT
ejpam-4446	202	21	tb	tb	ADP
ejpam-4446	202	22	∈	∈	PROPN
ejpam-4446	202	23	(	(	PUNCT
ejpam-4446	202	24	0	0	NUM
ejpam-4446	202	25	,	,	PUNCT
ejpam-4446	202	26	1	1	NUM
ejpam-4446	202	27	]	]	PUNCT
ejpam-4446	202	28	.	.	PUNCT
ejpam-4446	203	1	let	let	VERB
ejpam-4446	203	2	x	x	PRON
ejpam-4446	203	3	,	,	PUNCT
ejpam-4446	203	4	y	y	PROPN
ejpam-4446	203	5	∈	∈	PROPN
ejpam-4446	203	6	o	o	NOUN
ejpam-4446	203	7	(	(	PUNCT
ejpam-4446	203	8	lε	lε	INTJ
ejpam-4446	203	9	ξ	ξ	NUM
ejpam-4446	203	10	)	)	PUNCT
ejpam-4446	203	11	.	.	PUNCT
ejpam-4446	204	1	then	then	ADV
ejpam-4446	204	2	ξ(x	ξ(x	NOUN
ejpam-4446	204	3	)	)	PUNCT
ejpam-4446	205	1	+	+	CCONJ
ejpam-4446	205	2	ε−	ε−	PROPN
ejpam-4446	205	3	1	1	NUM
ejpam-4446	205	4	>	>	SYM
ejpam-4446	205	5	0	0	NUM
ejpam-4446	205	6	and	and	CCONJ
ejpam-4446	205	7	ξ(y	ξ(y	PROPN
ejpam-4446	205	8	)	)	PUNCT
ejpam-4446	206	1	+	+	CCONJ
ejpam-4446	206	2	ε−	ε−	PROPN
ejpam-4446	206	3	1	1	NUM
ejpam-4446	206	4	>	>	X
ejpam-4446	206	5	0	0	X
ejpam-4446	206	6	.	.	PUNCT
ejpam-4446	207	1	since	since	SCONJ
ejpam-4446	207	2	x	x	PROPN
ejpam-4446	207	3	∈	∈	PROPN
ejpam-4446	207	4	(	(	PUNCT
ejpam-4446	207	5	lε	lε	X
ejpam-4446	207	6	ξ	ξ	PROPN
ejpam-4446	207	7	,	,	PUNCT
ejpam-4446	207	8	lε	lε	X
ejpam-4446	207	9	ξ(x))∈	ξ(x))∈	NOUN
ejpam-4446	207	10	and	and	CCONJ
ejpam-4446	207	11	y	y	PROPN
ejpam-4446	207	12	∈	∈	PROPN
ejpam-4446	207	13	(	(	PUNCT
ejpam-4446	207	14	lε	lε	X
ejpam-4446	207	15	ξ	ξ	PROPN
ejpam-4446	207	16	,	,	PUNCT
ejpam-4446	207	17	lε	lε	ADP
ejpam-4446	207	18	ξ(y))∈	ξ(y))∈	NOUN
ejpam-4446	207	19	,	,	PUNCT
ejpam-4446	207	20	it	it	PRON
ejpam-4446	207	21	follows	follow	VERB
ejpam-4446	207	22	from	from	ADP
ejpam-4446	207	23	(	(	PUNCT
ejpam-4446	207	24	17	17	NUM
ejpam-4446	207	25	)	)	PUNCT
ejpam-4446	207	26	that	that	PRON
ejpam-4446	207	27	x	x	PUNCT
ejpam-4446	207	28	∗	∗	VERB
ejpam-4446	207	29	y	y	PROPN
ejpam-4446	207	30	∈	∈	PROPN
ejpam-4446	207	31	(	(	PUNCT
ejpam-4446	207	32	lε	lε	PART
ejpam-4446	207	33	ξ	ξ	PROPN
ejpam-4446	207	34	,	,	PUNCT
ejpam-4446	207	35	max	max	PROPN
ejpam-4446	207	36	{	{	PUNCT
ejpam-4446	207	37	lε	lε	ADP
ejpam-4446	207	38	ξ(x	ξ(x	PROPN
ejpam-4446	207	39	)	)	PUNCT
ejpam-4446	207	40	,	,	PUNCT
ejpam-4446	207	41	lε	lε	ADP
ejpam-4446	207	42	ξ(y)})q	ξ(y)})q	ADJ
ejpam-4446	207	43	.	.	PUNCT
ejpam-4446	208	1	(	(	PUNCT
ejpam-4446	208	2	18	18	NUM
ejpam-4446	208	3	)	)	PUNCT
ejpam-4446	208	4	if	if	SCONJ
ejpam-4446	208	5	x	x	PROPN
ejpam-4446	208	6	∗	∗	VERB
ejpam-4446	208	7	y	y	PROPN
ejpam-4446	208	8	/∈	/∈	PUNCT
ejpam-4446	209	1	o	o	NOUN
ejpam-4446	209	2	(	(	PUNCT
ejpam-4446	209	3	lε	lε	INTJ
ejpam-4446	209	4	ξ	ξ	X
ejpam-4446	209	5	)	)	PUNCT
ejpam-4446	209	6	,	,	PUNCT
ejpam-4446	209	7	then	then	ADV
ejpam-4446	209	8	lε	lε	ADP
ejpam-4446	209	9	ξ(x	ξ(x	PROPN
ejpam-4446	209	10	∗	∗	X
ejpam-4446	209	11	y	y	NOUN
ejpam-4446	209	12	)	)	PUNCT
ejpam-4446	210	1	=	=	SYM
ejpam-4446	210	2	0	0	PUNCT
ejpam-4446	211	1	and	and	CCONJ
ejpam-4446	211	2	so	so	ADV
ejpam-4446	211	3	lε	lε	ADP
ejpam-4446	211	4	ξ(x	ξ(x	PROPN
ejpam-4446	211	5	∗	∗	X
ejpam-4446	211	6	y	y	NOUN
ejpam-4446	211	7	)	)	PUNCT
ejpam-4446	212	1	+	+	CCONJ
ejpam-4446	212	2	max	max	PROPN
ejpam-4446	212	3	{	{	PUNCT
ejpam-4446	212	4	lε	lε	X
ejpam-4446	212	5	ξ(x	ξ(x	PROPN
ejpam-4446	212	6	)	)	PUNCT
ejpam-4446	212	7	,	,	PUNCT
ejpam-4446	212	8	lε	lε	ADP
ejpam-4446	212	9	ξ(y	ξ(y	PROPN
ejpam-4446	212	10	)	)	PUNCT
ejpam-4446	212	11	}	}	PUNCT
ejpam-4446	212	12	=	=	SYM
ejpam-4446	212	13	max	max	X
ejpam-4446	212	14	{	{	PUNCT
ejpam-4446	212	15	lε	lε	X
ejpam-4446	212	16	ξ(x	ξ(x	PROPN
ejpam-4446	212	17	)	)	PUNCT
ejpam-4446	212	18	,	,	PUNCT
ejpam-4446	212	19	lε	lε	ADP
ejpam-4446	212	20	ξ(y	ξ(y	PROPN
ejpam-4446	212	21	)	)	PUNCT
ejpam-4446	212	22	}	}	PUNCT
ejpam-4446	212	23	=	=	SYM
ejpam-4446	212	24	max{max{0	max{max{0	NOUN
ejpam-4446	212	25	,	,	PUNCT
ejpam-4446	212	26	ξ(x	ξ(x	NOUN
ejpam-4446	212	27	)	)	PUNCT
ejpam-4446	212	28	+	+	CCONJ
ejpam-4446	212	29	ε−	ε−	PROPN
ejpam-4446	212	30	1},max{0	1},max{0	NUM
ejpam-4446	212	31	,	,	PUNCT
ejpam-4446	212	32	ξ(y	ξ(y	PROPN
ejpam-4446	212	33	)	)	PUNCT
ejpam-4446	212	34	+	+	CCONJ
ejpam-4446	212	35	ε−	ε−	PROPN
ejpam-4446	212	36	1	1	NUM
ejpam-4446	212	37	}	}	PUNCT
ejpam-4446	212	38	}	}	PUNCT
ejpam-4446	212	39	=	=	SYM
ejpam-4446	212	40	max{ξ(x	max{ξ(x	PROPN
ejpam-4446	212	41	)	)	PUNCT
ejpam-4446	212	42	+	+	CCONJ
ejpam-4446	212	43	ε−	ε−	PROPN
ejpam-4446	212	44	1	1	NUM
ejpam-4446	212	45	,	,	PUNCT
ejpam-4446	212	46	ξ(y	ξ(y	PROPN
ejpam-4446	212	47	)	)	PUNCT
ejpam-4446	212	48	+	+	CCONJ
ejpam-4446	212	49	ε−	ε−	PROPN
ejpam-4446	212	50	1	1	NUM
ejpam-4446	212	51	}	}	PUNCT
ejpam-4446	212	52	=	=	SYM
ejpam-4446	212	53	max{ξ(x	max{ξ(x	PROPN
ejpam-4446	212	54	)	)	PUNCT
ejpam-4446	212	55	,	,	PUNCT
ejpam-4446	212	56	ξ(y	ξ(y	PROPN
ejpam-4446	212	57	)	)	PUNCT
ejpam-4446	212	58	}	}	PUNCT
ejpam-4446	213	1	+	+	CCONJ
ejpam-4446	213	2	ε−	ε−	PROPN
ejpam-4446	213	3	1	1	NUM
ejpam-4446	213	4	≤	≤	NUM
ejpam-4446	213	5	1	1	NUM
ejpam-4446	213	6	+	+	CCONJ
ejpam-4446	213	7	ε−	ε−	PROPN
ejpam-4446	213	8	1	1	NUM
ejpam-4446	213	9	=	=	SYM
ejpam-4446	213	10	ε	ε	PROPN
ejpam-4446	213	11	≤	≤	ADJ
ejpam-4446	213	12	1	1	NUM
ejpam-4446	213	13	,	,	PUNCT
ejpam-4446	213	14	that	that	ADV
ejpam-4446	213	15	is	is	ADV
ejpam-4446	213	16	,	,	PUNCT
ejpam-4446	213	17	[	[	X
ejpam-4446	213	18	(	(	PUNCT
ejpam-4446	213	19	x	x	SYM
ejpam-4446	213	20	∗	∗	NOUN
ejpam-4446	213	21	y)/max	y)/max	ADJ
ejpam-4446	213	22	{	{	PUNCT
ejpam-4446	213	23	lε	lε	ADP
ejpam-4446	213	24	ξ(x	ξ(x	PROPN
ejpam-4446	213	25	)	)	PUNCT
ejpam-4446	213	26	,	,	PUNCT
ejpam-4446	213	27	lε	lε	ADP
ejpam-4446	213	28	ξ(y	ξ(y	PROPN
ejpam-4446	213	29	)	)	PUNCT
ejpam-4446	213	30	}	}	PUNCT
ejpam-4446	213	31	]	]	PUNCT
ejpam-4446	213	32	q	q	X
ejpam-4446	213	33	lε	lε	X
ejpam-4446	213	34	ξ	ξ	X
ejpam-4446	213	35	which	which	PRON
ejpam-4446	213	36	shows	show	VERB
ejpam-4446	213	37	that	that	SCONJ
ejpam-4446	213	38	(	(	PUNCT
ejpam-4446	213	39	18	18	NUM
ejpam-4446	213	40	)	)	PUNCT
ejpam-4446	213	41	is	be	AUX
ejpam-4446	213	42	not	not	PART
ejpam-4446	213	43	valid	valid	ADJ
ejpam-4446	213	44	.	.	PUNCT
ejpam-4446	214	1	this	this	PRON
ejpam-4446	214	2	is	be	AUX
ejpam-4446	214	3	a	a	DET
ejpam-4446	214	4	contradiction	contradiction	NOUN
ejpam-4446	214	5	,	,	PUNCT
ejpam-4446	214	6	and	and	CCONJ
ejpam-4446	214	7	thus	thus	ADV
ejpam-4446	214	8	x	x	ADP
ejpam-4446	214	9	∗	∗	NOUN
ejpam-4446	214	10	y	y	PROPN
ejpam-4446	214	11	∈	∈	PROPN
ejpam-4446	214	12	o	o	NOUN
ejpam-4446	214	13	(	(	PUNCT
ejpam-4446	214	14	lε	lε	INTJ
ejpam-4446	214	15	ξ	ξ	NUM
ejpam-4446	214	16	)	)	PUNCT
ejpam-4446	214	17	.	.	PUNCT
ejpam-4446	215	1	hence	hence	ADV
ejpam-4446	215	2	o	o	INTJ
ejpam-4446	215	3	(	(	PUNCT
ejpam-4446	215	4	lε	lε	X
ejpam-4446	215	5	ξ	ξ	X
ejpam-4446	215	6	)	)	PUNCT
ejpam-4446	215	7	is	be	AUX
ejpam-4446	215	8	a	a	DET
ejpam-4446	215	9	be	be	NOUN
ejpam-4446	215	10	-	-	PUNCT
ejpam-4446	215	11	subalgebra	subalgebra	NOUN
ejpam-4446	215	12	of	of	ADP
ejpam-4446	215	13	x.	x.	PROPN
ejpam-4446	215	14	y.	y.	PROPN
ejpam-4446	215	15	b.	b.	PROPN
ejpam-4446	215	16	jun	jun	PROPN
ejpam-4446	215	17	,	,	PUNCT
ejpam-4446	215	18	s.	s.	PROPN
ejpam-4446	215	19	s.	s.	PROPN
ejpam-4446	215	20	ahn	ahn	PROPN
ejpam-4446	215	21	/	/	SYM
ejpam-4446	215	22	eur	eur	PROPN
ejpam-4446	215	23	.	.	PUNCT
ejpam-4446	216	1	j.	j.	PROPN
ejpam-4446	216	2	pure	pure	PROPN
ejpam-4446	216	3	appl	appl	PROPN
ejpam-4446	216	4	.	.	PROPN
ejpam-4446	216	5	math	math	PROPN
ejpam-4446	216	6	,	,	PUNCT
ejpam-4446	216	7	15	15	NUM
ejpam-4446	216	8	(	(	PUNCT
ejpam-4446	216	9	3	3	NUM
ejpam-4446	216	10	)	)	PUNCT
ejpam-4446	216	11	(	(	PUNCT
ejpam-4446	216	12	2022	2022	NUM
ejpam-4446	216	13	)	)	PUNCT
ejpam-4446	216	14	,	,	PUNCT
ejpam-4446	216	15	924	924	NUM
ejpam-4446	216	16	-	-	SYM
ejpam-4446	216	17	937	937	NUM
ejpam-4446	216	18	933	933	NUM
ejpam-4446	216	19	theorem	theorem	VERB
ejpam-4446	216	20	11	11	NUM
ejpam-4446	216	21	.	.	PUNCT
ejpam-4446	217	1	if	if	SCONJ
ejpam-4446	217	2	the	the	DET
ejpam-4446	217	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	217	4	fuzzy	fuzzy	NOUN
ejpam-4446	217	5	set	set	VERB
ejpam-4446	217	6	lε	lε	ADP
ejpam-4446	217	7	ξ	ξ	PROPN
ejpam-4446	217	8	of	of	ADP
ejpam-4446	217	9	ξ	ξ	PROPN
ejpam-4446	217	10	in	in	ADP
ejpam-4446	217	11	x	x	X
ejpam-4446	217	12	satisfies	satisfie	NOUN
ejpam-4446	217	13	the	the	DET
ejpam-4446	217	14	condition	condition	NOUN
ejpam-4446	217	15	(	(	PUNCT
ejpam-4446	217	16	16	16	NUM
ejpam-4446	217	17	)	)	PUNCT
ejpam-4446	217	18	for	for	ADP
ejpam-4446	217	19	all	all	DET
ejpam-4446	217	20	x	x	NOUN
ejpam-4446	217	21	,	,	PUNCT
ejpam-4446	217	22	y	y	PROPN
ejpam-4446	217	23	∈	∈	PROPN
ejpam-4446	217	24	x	x	X
ejpam-4446	217	25	and	and	CCONJ
ejpam-4446	217	26	ta	ta	PROPN
ejpam-4446	217	27	,	,	PUNCT
ejpam-4446	217	28	tb	tb	ADP
ejpam-4446	217	29	∈	∈	PROPN
ejpam-4446	217	30	(	(	PUNCT
ejpam-4446	217	31	0	0	NUM
ejpam-4446	217	32	,	,	PUNCT
ejpam-4446	217	33	1	1	NUM
ejpam-4446	217	34	]	]	PUNCT
ejpam-4446	217	35	,	,	PUNCT
ejpam-4446	217	36	then	then	ADV
ejpam-4446	217	37	its	its	PRON
ejpam-4446	217	38	o	o	NOUN
ejpam-4446	217	39	-	-	ADJ
ejpam-4446	217	40	set	set	VERB
ejpam-4446	217	41	o	o	NOUN
ejpam-4446	217	42	(	(	PUNCT
ejpam-4446	217	43	lε	lε	X
ejpam-4446	217	44	ξ	ξ	X
ejpam-4446	217	45	)	)	PUNCT
ejpam-4446	217	46	is	be	AUX
ejpam-4446	217	47	a	a	DET
ejpam-4446	217	48	be	be	NOUN
ejpam-4446	217	49	-	-	PUNCT
ejpam-4446	217	50	subalgebra	subalgebra	NOUN
ejpam-4446	217	51	of	of	ADP
ejpam-4446	217	52	x.	x.	NOUN
ejpam-4446	217	53	proof	proof	NOUN
ejpam-4446	217	54	.	.	PUNCT
ejpam-4446	218	1	let	let	VERB
ejpam-4446	218	2	x	x	PRON
ejpam-4446	218	3	,	,	PUNCT
ejpam-4446	218	4	y	y	PROPN
ejpam-4446	218	5	∈	∈	PROPN
ejpam-4446	218	6	o	o	NOUN
ejpam-4446	218	7	(	(	PUNCT
ejpam-4446	218	8	lε	lε	INTJ
ejpam-4446	218	9	ξ	ξ	NUM
ejpam-4446	218	10	)	)	PUNCT
ejpam-4446	218	11	.	.	PUNCT
ejpam-4446	219	1	then	then	ADV
ejpam-4446	219	2	ξ(x	ξ(x	NOUN
ejpam-4446	219	3	)	)	PUNCT
ejpam-4446	220	1	+	+	CCONJ
ejpam-4446	220	2	ε−	ε−	PROPN
ejpam-4446	220	3	1	1	NUM
ejpam-4446	220	4	>	>	SYM
ejpam-4446	220	5	0	0	NUM
ejpam-4446	220	6	and	and	CCONJ
ejpam-4446	220	7	ξ(y	ξ(y	PROPN
ejpam-4446	220	8	)	)	PUNCT
ejpam-4446	221	1	+	+	CCONJ
ejpam-4446	221	2	ε−	ε−	PROPN
ejpam-4446	221	3	1	1	NUM
ejpam-4446	221	4	>	>	SYM
ejpam-4446	221	5	0	0	NUM
ejpam-4446	221	6	.	.	PUNCT
ejpam-4446	222	1	hence	hence	ADV
ejpam-4446	222	2	lε	lε	ADP
ejpam-4446	222	3	ξ(x	ξ(x	NOUN
ejpam-4446	222	4	)	)	PUNCT
ejpam-4446	222	5	+	+	CCONJ
ejpam-4446	222	6	1	1	NUM
ejpam-4446	222	7	=	=	SYM
ejpam-4446	222	8	max{0	max{0	PROPN
ejpam-4446	222	9	,	,	PUNCT
ejpam-4446	222	10	ξ(x	ξ(x	NOUN
ejpam-4446	222	11	)	)	PUNCT
ejpam-4446	223	1	+	+	CCONJ
ejpam-4446	223	2	ε−	ε−	PROPN
ejpam-4446	223	3	1	1	NUM
ejpam-4446	223	4	}	}	PUNCT
ejpam-4446	223	5	+	+	CCONJ
ejpam-4446	223	6	1	1	NUM
ejpam-4446	223	7	=	=	SYM
ejpam-4446	223	8	ξ(x	ξ(x	NOUN
ejpam-4446	223	9	)	)	PUNCT
ejpam-4446	223	10	+	+	CCONJ
ejpam-4446	223	11	ε−	ε−	PROPN
ejpam-4446	223	12	1	1	NUM
ejpam-4446	223	13	+	+	NUM
ejpam-4446	223	14	1	1	NUM
ejpam-4446	223	15	=	=	SYM
ejpam-4446	223	16	ξ(x	ξ(x	NOUN
ejpam-4446	223	17	)	)	PUNCT
ejpam-4446	224	1	+	+	CCONJ
ejpam-4446	224	2	ε	ε	X
ejpam-4446	224	3	>	>	X
ejpam-4446	224	4	1	1	NUM
ejpam-4446	224	5	and	and	CCONJ
ejpam-4446	224	6	lε	lε	ADP
ejpam-4446	224	7	ξ(y	ξ(y	PROPN
ejpam-4446	224	8	)	)	PUNCT
ejpam-4446	225	1	+	+	CCONJ
ejpam-4446	225	2	1	1	NUM
ejpam-4446	225	3	=	=	SYM
ejpam-4446	225	4	max{0	max{0	PROPN
ejpam-4446	225	5	,	,	PUNCT
ejpam-4446	225	6	ξ(y	ξ(y	PROPN
ejpam-4446	225	7	)	)	PUNCT
ejpam-4446	225	8	+	+	CCONJ
ejpam-4446	225	9	ε−	ε−	PROPN
ejpam-4446	225	10	1	1	NUM
ejpam-4446	225	11	}	}	PUNCT
ejpam-4446	225	12	+	+	CCONJ
ejpam-4446	225	13	1	1	NUM
ejpam-4446	225	14	=	=	SYM
ejpam-4446	225	15	ξ(y	ξ(y	PROPN
ejpam-4446	225	16	)	)	PUNCT
ejpam-4446	225	17	+	+	CCONJ
ejpam-4446	225	18	ε−	ε−	PROPN
ejpam-4446	225	19	1	1	NUM
ejpam-4446	225	20	+	+	SYM
ejpam-4446	225	21	1	1	NUM
ejpam-4446	225	22	=	=	SYM
ejpam-4446	225	23	ξ(y	ξ(y	PROPN
ejpam-4446	225	24	)	)	PUNCT
ejpam-4446	226	1	+	+	CCONJ
ejpam-4446	226	2	ε	ε	PROPN
ejpam-4446	226	3	>	>	X
ejpam-4446	226	4	1	1	NUM
ejpam-4446	226	5	,	,	PUNCT
ejpam-4446	226	6	that	that	ADV
ejpam-4446	226	7	is	is	ADV
ejpam-4446	226	8	,	,	PUNCT
ejpam-4446	226	9	x	x	SYM
ejpam-4446	226	10	∈	∈	PROPN
ejpam-4446	226	11	(	(	PUNCT
ejpam-4446	226	12	lε	lε	X
ejpam-4446	226	13	ξ	ξ	PROPN
ejpam-4446	226	14	,	,	PUNCT
ejpam-4446	226	15	1)q	1)q	NOUN
ejpam-4446	226	16	and	and	CCONJ
ejpam-4446	226	17	y	y	PROPN
ejpam-4446	226	18	∈	∈	PROPN
ejpam-4446	226	19	(	(	PUNCT
ejpam-4446	226	20	lε	lε	X
ejpam-4446	226	21	ξ	ξ	PROPN
ejpam-4446	226	22	,	,	PUNCT
ejpam-4446	226	23	1)q	1)q	PROPN
ejpam-4446	226	24	.	.	PUNCT
ejpam-4446	227	1	it	it	PRON
ejpam-4446	227	2	follows	follow	VERB
ejpam-4446	227	3	from	from	ADP
ejpam-4446	227	4	(	(	PUNCT
ejpam-4446	227	5	16	16	NUM
ejpam-4446	227	6	)	)	PUNCT
ejpam-4446	227	7	that	that	PRON
ejpam-4446	227	8	x	x	PUNCT
ejpam-4446	227	9	∗	∗	VERB
ejpam-4446	227	10	y	y	PROPN
ejpam-4446	227	11	∈	∈	PROPN
ejpam-4446	227	12	(	(	PUNCT
ejpam-4446	227	13	lε	lε	ADP
ejpam-4446	227	14	ξ	ξ	PROPN
ejpam-4446	227	15	,	,	PUNCT
ejpam-4446	227	16	max{1	max{1	NOUN
ejpam-4446	227	17	,	,	PUNCT
ejpam-4446	227	18	1})∈	1})∈	NUM
ejpam-4446	227	19	=	=	SYM
ejpam-4446	227	20	(	(	PUNCT
ejpam-4446	227	21	lε	lε	PART
ejpam-4446	227	22	ξ	ξ	PROPN
ejpam-4446	227	23	,	,	PUNCT
ejpam-4446	227	24	1)∈.	1)∈.	NUM
ejpam-4446	227	25	thus	thus	ADV
ejpam-4446	227	26	lε	lε	ADP
ejpam-4446	227	27	ξ(x	ξ(x	PROPN
ejpam-4446	227	28	∗	∗	X
ejpam-4446	227	29	y	y	NOUN
ejpam-4446	227	30	)	)	PUNCT
ejpam-4446	228	1	+	+	CCONJ
ejpam-4446	228	2	1	1	NUM
ejpam-4446	228	3	>	>	SYM
ejpam-4446	228	4	1	1	NUM
ejpam-4446	228	5	,	,	PUNCT
ejpam-4446	228	6	and	and	CCONJ
ejpam-4446	228	7	so	so	ADV
ejpam-4446	228	8	lε	lε	ADP
ejpam-4446	228	9	ξ(x	ξ(x	PROPN
ejpam-4446	228	10	∗	∗	X
ejpam-4446	228	11	y	y	NOUN
ejpam-4446	228	12	)	)	PUNCT
ejpam-4446	228	13	>	>	X
ejpam-4446	229	1	0	0	NUM
ejpam-4446	229	2	,	,	PUNCT
ejpam-4446	229	3	i.e.	i.e.	X
ejpam-4446	229	4	,	,	PUNCT
ejpam-4446	229	5	x	x	X
ejpam-4446	229	6	∗	∗	NOUN
ejpam-4446	229	7	y	y	PROPN
ejpam-4446	229	8	∈	∈	PROPN
ejpam-4446	229	9	o	o	NOUN
ejpam-4446	229	10	(	(	PUNCT
ejpam-4446	229	11	lε	lε	INTJ
ejpam-4446	229	12	ξ	ξ	NUM
ejpam-4446	229	13	)	)	PUNCT
ejpam-4446	229	14	.	.	PUNCT
ejpam-4446	230	1	therefore	therefore	ADV
ejpam-4446	230	2	o	o	X
ejpam-4446	230	3	(	(	PUNCT
ejpam-4446	230	4	lε	lε	X
ejpam-4446	230	5	ξ	ξ	X
ejpam-4446	230	6	)	)	PUNCT
ejpam-4446	230	7	is	be	AUX
ejpam-4446	230	8	a	a	DET
ejpam-4446	230	9	be	be	NOUN
ejpam-4446	230	10	-	-	PUNCT
ejpam-4446	230	11	subalgebra	subalgebra	NOUN
ejpam-4446	230	12	of	of	ADP
ejpam-4446	230	13	x.	x.	NOUN
ejpam-4446	230	14	4	4	NUM
ejpam-4446	230	15	.	.	X
ejpam-4446	230	16	lukasiewicz	lukasiewicz	VERB
ejpam-4446	230	17	fuzzy	fuzzy	ADJ
ejpam-4446	230	18	be	be	AUX
ejpam-4446	230	19	-	-	PUNCT
ejpam-4446	230	20	filters	filter	NOUN
ejpam-4446	230	21	definition	definition	NOUN
ejpam-4446	230	22	2	2	NUM
ejpam-4446	230	23	.	.	PUNCT
ejpam-4446	231	1	the	the	DET
ejpam-4446	231	2	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	231	3	fuzzy	fuzzy	NOUN
ejpam-4446	231	4	set	set	VERB
ejpam-4446	231	5	lε	lε	ADP
ejpam-4446	231	6	ξ	ξ	PROPN
ejpam-4446	231	7	of	of	ADP
ejpam-4446	231	8	ξ	ξ	PROPN
ejpam-4446	231	9	in	in	ADP
ejpam-4446	231	10	x	x	PROPN
ejpam-4446	231	11	is	be	AUX
ejpam-4446	231	12	called	call	VERB
ejpam-4446	231	13	a	a	DET
ejpam-4446	231	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	231	15	fuzzy	fuzzy	ADJ
ejpam-4446	231	16	befilter	befilter	NOUN
ejpam-4446	231	17	of	of	ADP
ejpam-4446	231	18	x	x	PRON
ejpam-4446	231	19	if	if	SCONJ
ejpam-4446	231	20	it	it	PRON
ejpam-4446	231	21	satisfies	satisfy	VERB
ejpam-4446	231	22	:	:	PUNCT
ejpam-4446	231	23	x	x	SYM
ejpam-4446	231	24	∈	∈	PROPN
ejpam-4446	231	25	(	(	PUNCT
ejpam-4446	231	26	lε	lε	X
ejpam-4446	231	27	ξ	ξ	PROPN
ejpam-4446	231	28	,	,	PUNCT
ejpam-4446	231	29	ta)∈	ta)∈	PROPN
ejpam-4446	231	30	⇒	⇒	VERB
ejpam-4446	231	31	1	1	NUM
ejpam-4446	231	32	∈	∈	PROPN
ejpam-4446	231	33	(	(	PUNCT
ejpam-4446	231	34	lε	lε	PART
ejpam-4446	231	35	ξ	ξ	PROPN
ejpam-4446	231	36	,	,	PUNCT
ejpam-4446	231	37	ta)∈	ta)∈	PROPN
ejpam-4446	231	38	,	,	PUNCT
ejpam-4446	231	39	(	(	PUNCT
ejpam-4446	231	40	19	19	NUM
ejpam-4446	231	41	)	)	PUNCT
ejpam-4446	231	42	x	x	NOUN
ejpam-4446	231	43	∗	∗	NOUN
ejpam-4446	231	44	y	y	PROPN
ejpam-4446	231	45	∈	∈	PROPN
ejpam-4446	231	46	(	(	PUNCT
ejpam-4446	231	47	lε	lε	ADP
ejpam-4446	231	48	ξ	ξ	PROPN
ejpam-4446	231	49	,	,	PUNCT
ejpam-4446	231	50	ta)∈	ta)∈	PROPN
ejpam-4446	231	51	,	,	PUNCT
ejpam-4446	231	52	x	x	SYM
ejpam-4446	231	53	∈	∈	PROPN
ejpam-4446	231	54	(	(	PUNCT
ejpam-4446	231	55	lε	lε	PART
ejpam-4446	231	56	ξ	ξ	PROPN
ejpam-4446	231	57	,	,	PUNCT
ejpam-4446	231	58	tb)∈	tb)∈	PROPN
ejpam-4446	231	59	⇒	⇒	VERB
ejpam-4446	231	60	y	y	PROPN
ejpam-4446	231	61	∈	∈	PROPN
ejpam-4446	231	62	(	(	PUNCT
ejpam-4446	231	63	lε	lε	PART
ejpam-4446	231	64	ξ	ξ	PROPN
ejpam-4446	231	65	,	,	PUNCT
ejpam-4446	231	66	min{ta	min{ta	X
ejpam-4446	231	67	,	,	PUNCT
ejpam-4446	231	68	tb})∈	tb})∈	X
ejpam-4446	231	69	(	(	PUNCT
ejpam-4446	231	70	20	20	NUM
ejpam-4446	231	71	)	)	PUNCT
ejpam-4446	231	72	for	for	ADP
ejpam-4446	231	73	all	all	DET
ejpam-4446	231	74	x	x	NOUN
ejpam-4446	231	75	,	,	PUNCT
ejpam-4446	231	76	y	y	PROPN
ejpam-4446	231	77	∈	∈	PROPN
ejpam-4446	231	78	x	x	X
ejpam-4446	231	79	and	and	CCONJ
ejpam-4446	231	80	ta	ta	PROPN
ejpam-4446	231	81	,	,	PUNCT
ejpam-4446	231	82	tb	tb	ADP
ejpam-4446	231	83	∈	∈	PROPN
ejpam-4446	231	84	(	(	PUNCT
ejpam-4446	231	85	0	0	NUM
ejpam-4446	231	86	,	,	PUNCT
ejpam-4446	231	87	1	1	NUM
ejpam-4446	231	88	]	]	PUNCT
ejpam-4446	231	89	.	.	PUNCT
ejpam-4446	231	90	example	example	NOUN
ejpam-4446	232	1	4	4	X
ejpam-4446	232	2	.	.	X
ejpam-4446	232	3	consider	consider	VERB
ejpam-4446	232	4	a	a	DET
ejpam-4446	232	5	set	set	NOUN
ejpam-4446	232	6	x	x	X
ejpam-4446	232	7	=	=	SYM
ejpam-4446	232	8	{	{	PUNCT
ejpam-4446	232	9	1	1	NUM
ejpam-4446	232	10	,	,	PUNCT
ejpam-4446	232	11	b1	b1	NOUN
ejpam-4446	232	12	,	,	PUNCT
ejpam-4446	232	13	b2	b2	NOUN
ejpam-4446	232	14	,	,	PUNCT
ejpam-4446	232	15	b3	b3	PROPN
ejpam-4446	232	16	}	}	PUNCT
ejpam-4446	232	17	with	with	ADP
ejpam-4446	232	18	a	a	DET
ejpam-4446	232	19	binary	binary	ADJ
ejpam-4446	232	20	operation	operation	NOUN
ejpam-4446	232	21	“	"	PUNCT
ejpam-4446	232	22	∗	∗	NOUN
ejpam-4446	232	23	”	"	PUNCT
ejpam-4446	232	24	given	give	VERB
ejpam-4446	232	25	in	in	ADP
ejpam-4446	232	26	the	the	DET
ejpam-4446	232	27	table	table	NOUN
ejpam-4446	232	28	below	below	ADV
ejpam-4446	232	29	.	.	PUNCT
ejpam-4446	233	1	∗	∗	NOUN
ejpam-4446	233	2	1	1	NUM
ejpam-4446	233	3	b1	b1	NOUN
ejpam-4446	233	4	b2	b2	NOUN
ejpam-4446	233	5	b3	b3	NOUN
ejpam-4446	233	6	1	1	NUM
ejpam-4446	233	7	1	1	NUM
ejpam-4446	233	8	b1	b1	NOUN
ejpam-4446	233	9	b2	b2	NOUN
ejpam-4446	233	10	b3	b3	PROPN
ejpam-4446	233	11	b1	b1	NOUN
ejpam-4446	233	12	1	1	NUM
ejpam-4446	233	13	1	1	NUM
ejpam-4446	233	14	b2	b2	NOUN
ejpam-4446	233	15	b2	b2	NOUN
ejpam-4446	233	16	b2	b2	NOUN
ejpam-4446	233	17	1	1	NUM
ejpam-4446	233	18	b1	b1	NOUN
ejpam-4446	233	19	1	1	NUM
ejpam-4446	233	20	b1	b1	NOUN
ejpam-4446	233	21	b3	b3	NOUN
ejpam-4446	233	22	1	1	NUM
ejpam-4446	233	23	1	1	NUM
ejpam-4446	233	24	1	1	NUM
ejpam-4446	233	25	1	1	NUM
ejpam-4446	233	26	then	then	ADV
ejpam-4446	233	27	(	(	PUNCT
ejpam-4446	233	28	x	x	X
ejpam-4446	233	29	,	,	PUNCT
ejpam-4446	233	30	∗	∗	NOUN
ejpam-4446	233	31	,	,	PUNCT
ejpam-4446	233	32	1	1	NUM
ejpam-4446	233	33	)	)	PUNCT
ejpam-4446	233	34	is	be	AUX
ejpam-4446	233	35	a	a	DET
ejpam-4446	233	36	be	be	NOUN
ejpam-4446	233	37	-	-	PUNCT
ejpam-4446	233	38	algebra	algebra	NOUN
ejpam-4446	233	39	(	(	PUNCT
ejpam-4446	233	40	see	see	VERB
ejpam-4446	233	41	[	[	X
ejpam-4446	233	42	4	4	NUM
ejpam-4446	233	43	]	]	NUM
ejpam-4446	233	44	)	)	PUNCT
ejpam-4446	233	45	.	.	PUNCT
ejpam-4446	234	1	define	define	VERB
ejpam-4446	234	2	a	a	DET
ejpam-4446	234	3	fuzzy	fuzzy	ADJ
ejpam-4446	234	4	set	set	NOUN
ejpam-4446	234	5	ξ	ξ	PROPN
ejpam-4446	234	6	in	in	ADP
ejpam-4446	234	7	x	x	PUNCT
ejpam-4446	234	8	as	as	SCONJ
ejpam-4446	234	9	follows	follow	VERB
ejpam-4446	234	10	:	:	PUNCT
ejpam-4446	234	11	ξ	ξ	X
ejpam-4446	234	12	:	:	PUNCT
ejpam-4446	234	13	x	x	SYM
ejpam-4446	234	14	→	→	SYM
ejpam-4446	234	15	[	[	X
ejpam-4446	234	16	0	0	NUM
ejpam-4446	234	17	,	,	PUNCT
ejpam-4446	234	18	1	1	NUM
ejpam-4446	234	19	]	]	PUNCT
ejpam-4446	234	20	,	,	PUNCT
ejpam-4446	234	21	x	x	SYM
ejpam-4446	234	22	7→	7→	NUM
ejpam-4446	234	23			NUM
ejpam-4446	234	24	0.73	0.73	NUM
ejpam-4446	234	25	if	if	SCONJ
ejpam-4446	234	26	x	x	NOUN
ejpam-4446	234	27	=	=	SYM
ejpam-4446	234	28	1	1	NUM
ejpam-4446	234	29	,	,	PUNCT
ejpam-4446	234	30	0.62	0.62	NUM
ejpam-4446	234	31	if	if	SCONJ
ejpam-4446	234	32	x	x	NOUN
ejpam-4446	234	33	=	=	SYM
ejpam-4446	234	34	b1	b1	NOUN
ejpam-4446	234	35	,	,	PUNCT
ejpam-4446	234	36	0.48	0.48	NUM
ejpam-4446	234	37	if	if	SCONJ
ejpam-4446	234	38	x	x	SYM
ejpam-4446	234	39	∈	∈	PROPN
ejpam-4446	234	40	{	{	PUNCT
ejpam-4446	234	41	b2	b2	NOUN
ejpam-4446	234	42	,	,	PUNCT
ejpam-4446	234	43	b3	b3	PROPN
ejpam-4446	234	44	}	}	PUNCT
ejpam-4446	234	45	.	.	PUNCT
ejpam-4446	235	1	given	give	VERB
ejpam-4446	235	2	ε	ε	AUX
ejpam-4446	235	3	:	:	PUNCT
ejpam-4446	235	4	=	=	NOUN
ejpam-4446	235	5	0.62	0.62	NUM
ejpam-4446	235	6	,	,	PUNCT
ejpam-4446	235	7	the	the	DET
ejpam-4446	235	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	235	9	fuzzy	fuzzy	NOUN
ejpam-4446	235	10	set	set	VERB
ejpam-4446	235	11	lε	lε	ADP
ejpam-4446	235	12	ξ	ξ	PROPN
ejpam-4446	235	13	of	of	ADP
ejpam-4446	235	14	ξ	ξ	PROPN
ejpam-4446	235	15	in	in	ADP
ejpam-4446	235	16	x	x	AUX
ejpam-4446	235	17	is	be	AUX
ejpam-4446	235	18	given	give	VERB
ejpam-4446	235	19	as	as	SCONJ
ejpam-4446	235	20	follows	follow	VERB
ejpam-4446	235	21	:	:	PUNCT
ejpam-4446	235	22	lε	lε	ADP
ejpam-4446	235	23	ξ	ξ	X
ejpam-4446	235	24	:	:	PUNCT
ejpam-4446	235	25	x	x	SYM
ejpam-4446	235	26	→	→	SYM
ejpam-4446	236	1	[	[	X
ejpam-4446	236	2	0	0	NUM
ejpam-4446	236	3	,	,	PUNCT
ejpam-4446	236	4	1	1	NUM
ejpam-4446	236	5	]	]	PUNCT
ejpam-4446	236	6	,	,	PUNCT
ejpam-4446	236	7	x	x	SYM
ejpam-4446	236	8	7→	7→	NUM
ejpam-4446	236	9			NUM
ejpam-4446	236	10	0.35	0.35	NUM
ejpam-4446	236	11	if	if	SCONJ
ejpam-4446	236	12	x	x	PROPN
ejpam-4446	236	13	=	=	SYM
ejpam-4446	236	14	1	1	NUM
ejpam-4446	236	15	,	,	PUNCT
ejpam-4446	236	16	0.24	0.24	NUM
ejpam-4446	236	17	if	if	SCONJ
ejpam-4446	236	18	x	x	NOUN
ejpam-4446	236	19	=	=	SYM
ejpam-4446	236	20	b1	b1	NOUN
ejpam-4446	236	21	,	,	PUNCT
ejpam-4446	236	22	0.10	0.10	NUM
ejpam-4446	236	23	if	if	SCONJ
ejpam-4446	236	24	x	x	SYM
ejpam-4446	236	25	∈	∈	PROPN
ejpam-4446	236	26	{	{	PUNCT
ejpam-4446	236	27	b2	b2	NOUN
ejpam-4446	236	28	,	,	PUNCT
ejpam-4446	236	29	b3	b3	PROPN
ejpam-4446	236	30	}	}	PUNCT
ejpam-4446	236	31	.	.	PUNCT
ejpam-4446	237	1	it	it	PRON
ejpam-4446	237	2	is	be	AUX
ejpam-4446	237	3	routine	routine	ADJ
ejpam-4446	237	4	to	to	PART
ejpam-4446	237	5	verify	verify	VERB
ejpam-4446	237	6	that	that	SCONJ
ejpam-4446	237	7	lε	lε	ADP
ejpam-4446	237	8	ξ	ξ	PROPN
ejpam-4446	237	9	is	be	AUX
ejpam-4446	237	10	a	a	DET
ejpam-4446	237	11	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	237	12	fuzzy	fuzzy	ADJ
ejpam-4446	237	13	be	be	NOUN
ejpam-4446	237	14	-	-	PUNCT
ejpam-4446	237	15	filter	filter	NOUN
ejpam-4446	237	16	of	of	ADP
ejpam-4446	237	17	x.	x.	PROPN
ejpam-4446	237	18	y.	y.	PROPN
ejpam-4446	237	19	b.	b.	PROPN
ejpam-4446	237	20	jun	jun	PROPN
ejpam-4446	237	21	,	,	PUNCT
ejpam-4446	237	22	s.	s.	PROPN
ejpam-4446	237	23	s.	s.	PROPN
ejpam-4446	237	24	ahn	ahn	PROPN
ejpam-4446	237	25	/	/	SYM
ejpam-4446	237	26	eur	eur	PROPN
ejpam-4446	237	27	.	.	PUNCT
ejpam-4446	238	1	j.	j.	PROPN
ejpam-4446	238	2	pure	pure	PROPN
ejpam-4446	238	3	appl	appl	PROPN
ejpam-4446	238	4	.	.	PROPN
ejpam-4446	238	5	math	math	PROPN
ejpam-4446	238	6	,	,	PUNCT
ejpam-4446	238	7	15	15	NUM
ejpam-4446	238	8	(	(	PUNCT
ejpam-4446	238	9	3	3	NUM
ejpam-4446	238	10	)	)	PUNCT
ejpam-4446	238	11	(	(	PUNCT
ejpam-4446	238	12	2022	2022	NUM
ejpam-4446	238	13	)	)	PUNCT
ejpam-4446	238	14	,	,	PUNCT
ejpam-4446	238	15	924	924	NUM
ejpam-4446	238	16	-	-	SYM
ejpam-4446	238	17	937	937	NUM
ejpam-4446	238	18	934	934	NUM
ejpam-4446	238	19	we	we	PRON
ejpam-4446	238	20	discuss	discuss	VERB
ejpam-4446	238	21	relationship	relationship	NOUN
ejpam-4446	238	22	between	between	ADP
ejpam-4446	238	23	fuzzy	fuzzy	ADJ
ejpam-4446	238	24	be	be	NOUN
ejpam-4446	238	25	-	-	PUNCT
ejpam-4446	238	26	filter	filter	NOUN
ejpam-4446	238	27	and	and	CCONJ
ejpam-4446	238	28	lukasiewicz	lukasiewicz	VERB
ejpam-4446	238	29	fuzzy	fuzzy	ADJ
ejpam-4446	238	30	be	be	NOUN
ejpam-4446	238	31	-	-	PUNCT
ejpam-4446	238	32	filter	filter	NOUN
ejpam-4446	238	33	.	.	PUNCT
ejpam-4446	239	1	theorem	theorem	NOUN
ejpam-4446	239	2	12	12	NUM
ejpam-4446	239	3	.	.	PUNCT
ejpam-4446	240	1	if	if	SCONJ
ejpam-4446	240	2	ξ	ξ	PROPN
ejpam-4446	240	3	is	be	AUX
ejpam-4446	240	4	a	a	DET
ejpam-4446	240	5	fuzzy	fuzzy	ADJ
ejpam-4446	240	6	be	be	NOUN
ejpam-4446	240	7	-	-	PUNCT
ejpam-4446	240	8	filter	filter	NOUN
ejpam-4446	240	9	of	of	ADP
ejpam-4446	240	10	x	x	NOUN
ejpam-4446	240	11	,	,	PUNCT
ejpam-4446	240	12	then	then	ADV
ejpam-4446	240	13	its	its	PRON
ejpam-4446	240	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	240	15	fuzzy	fuzzy	NOUN
ejpam-4446	240	16	set	set	VERB
ejpam-4446	240	17	lε	lε	AUX
ejpam-4446	240	18	ξ	ξ	X
ejpam-4446	240	19	is	be	AUX
ejpam-4446	240	20	a	a	DET
ejpam-4446	240	21	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	240	22	fuzzy	fuzzy	ADJ
ejpam-4446	240	23	be	be	NOUN
ejpam-4446	240	24	-	-	PUNCT
ejpam-4446	240	25	filter	filter	NOUN
ejpam-4446	240	26	of	of	ADP
ejpam-4446	240	27	x.	x.	NOUN
ejpam-4446	240	28	proof	proof	PROPN
ejpam-4446	240	29	.	.	PUNCT
ejpam-4446	241	1	assume	assume	VERB
ejpam-4446	241	2	that	that	SCONJ
ejpam-4446	241	3	ξ	ξ	PROPN
ejpam-4446	241	4	is	be	AUX
ejpam-4446	241	5	a	a	DET
ejpam-4446	241	6	fuzzy	fuzzy	ADJ
ejpam-4446	241	7	be	be	NOUN
ejpam-4446	241	8	-	-	PUNCT
ejpam-4446	241	9	filter	filter	NOUN
ejpam-4446	241	10	of	of	ADP
ejpam-4446	241	11	x	x	PUNCT
ejpam-4446	241	12	and	and	CCONJ
ejpam-4446	241	13	let	let	VERB
ejpam-4446	241	14	lε	lε	PRON
ejpam-4446	241	15	ξ	ξ	X
ejpam-4446	241	16	be	be	AUX
ejpam-4446	241	17	its	its	PRON
ejpam-4446	241	18	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	241	19	fuzzy	fuzzy	ADJ
ejpam-4446	241	20	set	set	VERB
ejpam-4446	241	21	in	in	ADP
ejpam-4446	241	22	x.	x.	NOUN
ejpam-4446	241	23	let	let	VERB
ejpam-4446	242	1	x	x	X
ejpam-4446	242	2	∈	∈	PROPN
ejpam-4446	242	3	x	x	X
ejpam-4446	242	4	and	and	CCONJ
ejpam-4446	242	5	ta	ta	ADP
ejpam-4446	242	6	∈	∈	PROPN
ejpam-4446	242	7	(	(	PUNCT
ejpam-4446	242	8	0	0	NUM
ejpam-4446	242	9	,	,	PUNCT
ejpam-4446	242	10	1	1	NUM
ejpam-4446	242	11	]	]	PUNCT
ejpam-4446	242	12	be	be	AUX
ejpam-4446	242	13	such	such	ADJ
ejpam-4446	242	14	that	that	SCONJ
ejpam-4446	242	15	x	x	SYM
ejpam-4446	242	16	∈	∈	PROPN
ejpam-4446	242	17	(	(	PUNCT
ejpam-4446	242	18	lε	lε	X
ejpam-4446	242	19	ξ	ξ	PROPN
ejpam-4446	242	20	,	,	PUNCT
ejpam-4446	242	21	ta)∈.	ta)∈.	ADP
ejpam-4446	242	22	then	then	ADV
ejpam-4446	242	23	lε	lε	PROPN
ejpam-4446	242	24	ξ(1	ξ(1	PROPN
ejpam-4446	242	25	)	)	PUNCT
ejpam-4446	242	26	=	=	SYM
ejpam-4446	242	27	max{0	max{0	PROPN
ejpam-4446	242	28	,	,	PUNCT
ejpam-4446	242	29	ξ(1	ξ(1	PROPN
ejpam-4446	242	30	)	)	PUNCT
ejpam-4446	242	31	+	+	CCONJ
ejpam-4446	242	32	ε−	ε−	PROPN
ejpam-4446	242	33	1	1	NUM
ejpam-4446	242	34	}	}	PUNCT
ejpam-4446	242	35	≥	≥	X
ejpam-4446	242	36	max{0	max{0	NUM
ejpam-4446	242	37	,	,	PUNCT
ejpam-4446	242	38	ξ(x	ξ(x	NOUN
ejpam-4446	242	39	)	)	PUNCT
ejpam-4446	242	40	+	+	CCONJ
ejpam-4446	242	41	ε−	ε−	PROPN
ejpam-4446	242	42	1	1	NUM
ejpam-4446	242	43	}	}	PUNCT
ejpam-4446	242	44	=	=	PUNCT
ejpam-4446	242	45	lε	lε	PRON
ejpam-4446	242	46	ξ(x	ξ(x	NOUN
ejpam-4446	242	47	)	)	PUNCT
ejpam-4446	242	48	≥	≥	NOUN
ejpam-4446	242	49	ta	ta	ADP
ejpam-4446	242	50	,	,	PUNCT
ejpam-4446	242	51	and	and	CCONJ
ejpam-4446	242	52	so	so	ADV
ejpam-4446	242	53	1	1	NUM
ejpam-4446	242	54	∈	∈	NOUN
ejpam-4446	242	55	(	(	PUNCT
ejpam-4446	242	56	lε	lε	X
ejpam-4446	242	57	ξ	ξ	PROPN
ejpam-4446	242	58	,	,	PUNCT
ejpam-4446	242	59	ta)∈.	ta)∈.	VERB
ejpam-4446	242	60	let	let	VERB
ejpam-4446	242	61	x	x	PRON
ejpam-4446	242	62	,	,	PUNCT
ejpam-4446	242	63	y	y	PROPN
ejpam-4446	242	64	∈	∈	PROPN
ejpam-4446	242	65	x	x	X
ejpam-4446	242	66	and	and	CCONJ
ejpam-4446	242	67	ta	ta	PROPN
ejpam-4446	242	68	,	,	PUNCT
ejpam-4446	242	69	tb	tb	ADP
ejpam-4446	242	70	∈	∈	PROPN
ejpam-4446	242	71	(	(	PUNCT
ejpam-4446	242	72	0	0	NUM
ejpam-4446	242	73	,	,	PUNCT
ejpam-4446	242	74	1	1	NUM
ejpam-4446	242	75	]	]	PUNCT
ejpam-4446	242	76	be	be	AUX
ejpam-4446	242	77	such	such	ADJ
ejpam-4446	242	78	that	that	SCONJ
ejpam-4446	242	79	x	x	PUNCT
ejpam-4446	242	80	∗	∗	NOUN
ejpam-4446	242	81	y	y	PROPN
ejpam-4446	242	82	∈	∈	PROPN
ejpam-4446	242	83	(	(	PUNCT
ejpam-4446	242	84	lε	lε	X
ejpam-4446	242	85	ξ	ξ	PROPN
ejpam-4446	242	86	,	,	PUNCT
ejpam-4446	242	87	ta)∈	ta)∈	PROPN
ejpam-4446	242	88	and	and	CCONJ
ejpam-4446	242	89	x	x	SYM
ejpam-4446	242	90	∈	∈	PROPN
ejpam-4446	242	91	(	(	PUNCT
ejpam-4446	242	92	lε	lε	X
ejpam-4446	242	93	ξ	ξ	PROPN
ejpam-4446	242	94	,	,	PUNCT
ejpam-4446	242	95	tb)∈.	tb)∈.	PUNCT
ejpam-4446	242	96	then	then	ADV
ejpam-4446	242	97	lε	lε	ADP
ejpam-4446	242	98	ξ(x	ξ(x	PROPN
ejpam-4446	242	99	∗	∗	X
ejpam-4446	242	100	y	y	PROPN
ejpam-4446	242	101	)	)	PUNCT
ejpam-4446	242	102	≥	≥	NOUN
ejpam-4446	242	103	ta	ta	NOUN
ejpam-4446	242	104	and	and	CCONJ
ejpam-4446	242	105	lε	lε	ADP
ejpam-4446	242	106	ξ(x	ξ(x	PROPN
ejpam-4446	242	107	)	)	PUNCT
ejpam-4446	242	108	≥	≥	NOUN
ejpam-4446	242	109	tb	tb	NOUN
ejpam-4446	242	110	,	,	PUNCT
ejpam-4446	242	111	which	which	PRON
ejpam-4446	242	112	imply	imply	VERB
ejpam-4446	242	113	that	that	SCONJ
ejpam-4446	242	114	lε	lε	ADP
ejpam-4446	242	115	ξ(y	ξ(y	PROPN
ejpam-4446	242	116	)	)	PUNCT
ejpam-4446	242	117	=	=	SYM
ejpam-4446	242	118	max{0	max{0	PROPN
ejpam-4446	242	119	,	,	PUNCT
ejpam-4446	242	120	ξ(y	ξ(y	PROPN
ejpam-4446	242	121	)	)	PUNCT
ejpam-4446	242	122	+	+	CCONJ
ejpam-4446	242	123	ε−	ε−	PROPN
ejpam-4446	242	124	1	1	NUM
ejpam-4446	242	125	}	}	PUNCT
ejpam-4446	242	126	≥	≥	NOUN
ejpam-4446	242	127	max{0,min{ξ(x	max{0,min{ξ(x	NOUN
ejpam-4446	242	128	∗	∗	NOUN
ejpam-4446	242	129	y	y	PROPN
ejpam-4446	242	130	)	)	PUNCT
ejpam-4446	242	131	,	,	PUNCT
ejpam-4446	242	132	ξ(x	ξ(x	NOUN
ejpam-4446	242	133	)	)	PUNCT
ejpam-4446	242	134	}	}	PUNCT
ejpam-4446	242	135	+	+	CCONJ
ejpam-4446	242	136	ε−	ε−	PROPN
ejpam-4446	242	137	1	1	NUM
ejpam-4446	242	138	}	}	PUNCT
ejpam-4446	242	139	=	=	SYM
ejpam-4446	242	140	max{0,min{ξ(x	max{0,min{ξ(x	NOUN
ejpam-4446	242	141	∗	∗	NOUN
ejpam-4446	242	142	y	y	PROPN
ejpam-4446	242	143	)	)	PUNCT
ejpam-4446	242	144	+	+	CCONJ
ejpam-4446	242	145	ε−	ε−	PROPN
ejpam-4446	242	146	1	1	NUM
ejpam-4446	242	147	,	,	PUNCT
ejpam-4446	242	148	ξ(x	ξ(x	NOUN
ejpam-4446	242	149	)	)	PUNCT
ejpam-4446	242	150	+	+	CCONJ
ejpam-4446	242	151	ε−	ε−	PROPN
ejpam-4446	242	152	1	1	NUM
ejpam-4446	242	153	}	}	PUNCT
ejpam-4446	242	154	}	}	PUNCT
ejpam-4446	242	155	=	=	SYM
ejpam-4446	242	156	min{max{0	min{max{0	X
ejpam-4446	242	157	,	,	PUNCT
ejpam-4446	242	158	ξ(x	ξ(x	NOUN
ejpam-4446	242	159	∗	∗	NOUN
ejpam-4446	242	160	y	y	NOUN
ejpam-4446	242	161	)	)	PUNCT
ejpam-4446	243	1	+	+	CCONJ
ejpam-4446	243	2	ε−	ε−	PROPN
ejpam-4446	243	3	1},max{0	1},max{0	NUM
ejpam-4446	243	4	,	,	PUNCT
ejpam-4446	243	5	ξ(x	ξ(x	NOUN
ejpam-4446	243	6	)	)	PUNCT
ejpam-4446	243	7	+	+	CCONJ
ejpam-4446	243	8	ε−	ε−	PROPN
ejpam-4446	243	9	1	1	NUM
ejpam-4446	243	10	}	}	PUNCT
ejpam-4446	243	11	}	}	PUNCT
ejpam-4446	243	12	}	}	PUNCT
ejpam-4446	243	13	=	=	SYM
ejpam-4446	243	14	min	min	X
ejpam-4446	243	15	{	{	PUNCT
ejpam-4446	243	16	lε	lε	ADP
ejpam-4446	243	17	ξ(x	ξ(x	PROPN
ejpam-4446	243	18	∗	∗	X
ejpam-4446	243	19	y	y	PROPN
ejpam-4446	243	20	)	)	PUNCT
ejpam-4446	243	21	,	,	PUNCT
ejpam-4446	243	22	lε	lε	ADP
ejpam-4446	243	23	ξ(x	ξ(x	NOUN
ejpam-4446	243	24	)	)	PUNCT
ejpam-4446	243	25	}	}	PUNCT
ejpam-4446	243	26	≥	≥	NOUN
ejpam-4446	243	27	min{ta	min{ta	X
ejpam-4446	243	28	,	,	PUNCT
ejpam-4446	243	29	tb	tb	NOUN
ejpam-4446	243	30	}	}	PUNCT
ejpam-4446	243	31	.	.	PUNCT
ejpam-4446	244	1	hence	hence	ADV
ejpam-4446	244	2	[	[	X
ejpam-4446	244	3	y	y	X
ejpam-4446	244	4	/	/	SYM
ejpam-4446	244	5	min{ta	min{ta	NUM
ejpam-4446	244	6	,	,	PUNCT
ejpam-4446	244	7	tb	tb	NOUN
ejpam-4446	244	8	}	}	PUNCT
ejpam-4446	244	9	]	]	PUNCT
ejpam-4446	244	10	∈	∈	PROPN
ejpam-4446	244	11	lε	lε	X
ejpam-4446	244	12	ξ	ξ	PROPN
ejpam-4446	244	13	,	,	PUNCT
ejpam-4446	244	14	that	that	ADV
ejpam-4446	244	15	is	is	ADV
ejpam-4446	244	16	,	,	PUNCT
ejpam-4446	244	17	y	y	PROPN
ejpam-4446	244	18	∈	∈	PROPN
ejpam-4446	244	19	(	(	PUNCT
ejpam-4446	244	20	lε	lε	PART
ejpam-4446	244	21	ξ	ξ	PROPN
ejpam-4446	244	22	,	,	PUNCT
ejpam-4446	244	23	min{ta	min{ta	X
ejpam-4446	244	24	,	,	PUNCT
ejpam-4446	244	25	tb})∈.	tb})∈.	ADJ
ejpam-4446	244	26	therefore	therefore	ADV
ejpam-4446	244	27	lε	lε	X
ejpam-4446	244	28	ξ	ξ	PROPN
ejpam-4446	244	29	is	be	AUX
ejpam-4446	244	30	a	a	DET
ejpam-4446	244	31	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	244	32	fuzzy	fuzzy	ADJ
ejpam-4446	244	33	be	be	NOUN
ejpam-4446	244	34	-	-	PUNCT
ejpam-4446	244	35	filter	filter	NOUN
ejpam-4446	244	36	of	of	ADP
ejpam-4446	244	37	x.	x.	NOUN
ejpam-4446	244	38	in	in	ADP
ejpam-4446	244	39	theorem	theorem	PROPN
ejpam-4446	244	40	12	12	NUM
ejpam-4446	244	41	,	,	PUNCT
ejpam-4446	244	42	the	the	DET
ejpam-4446	244	43	converse	converse	NOUN
ejpam-4446	244	44	may	may	AUX
ejpam-4446	244	45	not	not	PART
ejpam-4446	244	46	be	be	AUX
ejpam-4446	244	47	true	true	ADJ
ejpam-4446	244	48	as	as	SCONJ
ejpam-4446	244	49	shown	show	VERB
ejpam-4446	244	50	in	in	ADP
ejpam-4446	244	51	the	the	DET
ejpam-4446	244	52	following	follow	VERB
ejpam-4446	244	53	example	example	NOUN
ejpam-4446	244	54	.	.	PUNCT
ejpam-4446	245	1	example	example	NOUN
ejpam-4446	245	2	5	5	NUM
ejpam-4446	245	3	.	.	X
ejpam-4446	246	1	consider	consider	VERB
ejpam-4446	246	2	the	the	DET
ejpam-4446	246	3	be	be	NOUN
ejpam-4446	246	4	-	-	PUNCT
ejpam-4446	246	5	algebra	algebra	NOUN
ejpam-4446	246	6	(	(	PUNCT
ejpam-4446	246	7	x	x	X
ejpam-4446	246	8	,	,	PUNCT
ejpam-4446	246	9	∗	∗	NOUN
ejpam-4446	246	10	,	,	PUNCT
ejpam-4446	246	11	1	1	NUM
ejpam-4446	246	12	)	)	PUNCT
ejpam-4446	246	13	in	in	ADP
ejpam-4446	246	14	example	example	NOUN
ejpam-4446	246	15	4	4	NUM
ejpam-4446	246	16	and	and	CCONJ
ejpam-4446	246	17	let	let	VERB
ejpam-4446	246	18	ξ	ξ	X
ejpam-4446	246	19	be	be	AUX
ejpam-4446	246	20	a	a	DET
ejpam-4446	246	21	fuzzy	fuzzy	ADJ
ejpam-4446	246	22	set	set	NOUN
ejpam-4446	246	23	in	in	ADP
ejpam-4446	246	24	x	x	PUNCT
ejpam-4446	246	25	defined	define	VERB
ejpam-4446	246	26	by	by	ADP
ejpam-4446	246	27	ξ	ξ	PROPN
ejpam-4446	246	28	:	:	PUNCT
ejpam-4446	246	29	x	x	SYM
ejpam-4446	246	30	→	→	SYM
ejpam-4446	247	1	[	[	X
ejpam-4446	247	2	0	0	NUM
ejpam-4446	247	3	,	,	PUNCT
ejpam-4446	247	4	1	1	NUM
ejpam-4446	247	5	]	]	PUNCT
ejpam-4446	247	6	,	,	PUNCT
ejpam-4446	247	7	x	x	PROPN
ejpam-4446	247	8	7→	7→	NUM
ejpam-4446	247	9			NUM
ejpam-4446	247	10	0.73	0.73	NUM
ejpam-4446	247	11	if	if	SCONJ
ejpam-4446	247	12	x	x	NOUN
ejpam-4446	247	13	=	=	SYM
ejpam-4446	247	14	1	1	NUM
ejpam-4446	247	15	,	,	PUNCT
ejpam-4446	247	16	0.51	0.51	NUM
ejpam-4446	247	17	if	if	SCONJ
ejpam-4446	247	18	x	x	X
ejpam-4446	247	19	=	=	SYM
ejpam-4446	247	20	b1	b1	NOUN
ejpam-4446	247	21	,	,	PUNCT
ejpam-4446	247	22	0.62	0.62	NUM
ejpam-4446	247	23	if	if	SCONJ
ejpam-4446	247	24	x	x	NOUN
ejpam-4446	247	25	=	=	SYM
ejpam-4446	247	26	b2	b2	NOUN
ejpam-4446	247	27	,	,	PUNCT
ejpam-4446	247	28	0.47	0.47	NUM
ejpam-4446	247	29	if	if	SCONJ
ejpam-4446	247	30	x	x	NOUN
ejpam-4446	247	31	=	=	SYM
ejpam-4446	247	32	b3	b3	PROPN
ejpam-4446	247	33	.	.	PUNCT
ejpam-4446	248	1	then	then	ADV
ejpam-4446	248	2	ξ	ξ	PROPN
ejpam-4446	248	3	is	be	AUX
ejpam-4446	248	4	not	not	PART
ejpam-4446	248	5	a	a	DET
ejpam-4446	248	6	fuzzy	fuzzy	ADJ
ejpam-4446	248	7	be	be	NOUN
ejpam-4446	248	8	-	-	PUNCT
ejpam-4446	248	9	filter	filter	NOUN
ejpam-4446	248	10	of	of	ADP
ejpam-4446	248	11	x	x	PRON
ejpam-4446	248	12	since	since	SCONJ
ejpam-4446	248	13	ξ(b3	ξ(b3	ADJ
ejpam-4446	248	14	)	)	PUNCT
ejpam-4446	248	15	=	=	PUNCT
ejpam-4446	249	1	0.47	0.47	NUM
ejpam-4446	249	2	≱	≱	PROPN
ejpam-4446	249	3	0.51	0.51	NUM
ejpam-4446	249	4	=	=	PUNCT
ejpam-4446	249	5	min{ξ(b1	min{ξ(b1	NOUN
ejpam-4446	249	6	∗	∗	NOUN
ejpam-4446	249	7	b3	b3	NOUN
ejpam-4446	249	8	)	)	PUNCT
ejpam-4446	249	9	,	,	PUNCT
ejpam-4446	249	10	ξ(b1	ξ(b1	NOUN
ejpam-4446	249	11	)	)	PUNCT
ejpam-4446	249	12	}	}	PUNCT
ejpam-4446	249	13	.	.	PUNCT
ejpam-4446	250	1	given	give	VERB
ejpam-4446	250	2	ε	ε	AUX
ejpam-4446	250	3	:	:	PUNCT
ejpam-4446	250	4	=	=	SYM
ejpam-4446	250	5	0.49	0.49	NUM
ejpam-4446	250	6	,	,	PUNCT
ejpam-4446	250	7	the	the	DET
ejpam-4446	250	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	250	9	fuzzy	fuzzy	NOUN
ejpam-4446	250	10	set	set	VERB
ejpam-4446	250	11	lε	lε	ADP
ejpam-4446	250	12	ξ	ξ	PROPN
ejpam-4446	250	13	of	of	ADP
ejpam-4446	250	14	ξ	ξ	PROPN
ejpam-4446	250	15	in	in	ADP
ejpam-4446	250	16	x	x	PROPN
ejpam-4446	250	17	is	be	AUX
ejpam-4446	250	18	calculated	calculate	VERB
ejpam-4446	250	19	as	as	SCONJ
ejpam-4446	250	20	follows	follow	VERB
ejpam-4446	250	21	:	:	PUNCT
ejpam-4446	250	22	lε	lε	ADP
ejpam-4446	250	23	ξ	ξ	X
ejpam-4446	250	24	:	:	PUNCT
ejpam-4446	250	25	x	x	SYM
ejpam-4446	250	26	→	→	SYM
ejpam-4446	251	1	[	[	X
ejpam-4446	251	2	0	0	NUM
ejpam-4446	251	3	,	,	PUNCT
ejpam-4446	251	4	1	1	NUM
ejpam-4446	251	5	]	]	PUNCT
ejpam-4446	251	6	,	,	PUNCT
ejpam-4446	251	7	x	x	PROPN
ejpam-4446	251	8	7→	7→	NUM
ejpam-4446	251	9			NUM
ejpam-4446	251	10	0.22	0.22	NUM
ejpam-4446	251	11	if	if	SCONJ
ejpam-4446	251	12	x	x	NOUN
ejpam-4446	251	13	=	=	SYM
ejpam-4446	251	14	1	1	NUM
ejpam-4446	251	15	,	,	PUNCT
ejpam-4446	251	16	0.00	0.00	NUM
ejpam-4446	251	17	if	if	SCONJ
ejpam-4446	251	18	x	x	X
ejpam-4446	251	19	=	=	SYM
ejpam-4446	251	20	b1	b1	NOUN
ejpam-4446	251	21	,	,	PUNCT
ejpam-4446	251	22	0.11	0.11	NUM
ejpam-4446	251	23	if	if	SCONJ
ejpam-4446	251	24	x	x	NOUN
ejpam-4446	251	25	=	=	SYM
ejpam-4446	251	26	b2	b2	NOUN
ejpam-4446	251	27	,	,	PUNCT
ejpam-4446	251	28	0.00	0.00	NUM
ejpam-4446	251	29	if	if	SCONJ
ejpam-4446	251	30	x	x	NOUN
ejpam-4446	251	31	=	=	SYM
ejpam-4446	251	32	b3	b3	PROPN
ejpam-4446	251	33	,	,	PUNCT
ejpam-4446	251	34	and	and	CCONJ
ejpam-4446	251	35	it	it	PRON
ejpam-4446	251	36	is	be	AUX
ejpam-4446	251	37	a	a	DET
ejpam-4446	251	38	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	251	39	fuzzy	fuzzy	ADJ
ejpam-4446	251	40	be	be	NOUN
ejpam-4446	251	41	-	-	PUNCT
ejpam-4446	251	42	filter	filter	NOUN
ejpam-4446	251	43	of	of	ADP
ejpam-4446	251	44	x.	x.	PROPN
ejpam-4446	251	45	theorem	theorem	VERB
ejpam-4446	251	46	13	13	NUM
ejpam-4446	251	47	.	.	PUNCT
ejpam-4446	252	1	the	the	DET
ejpam-4446	252	2	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	252	3	fuzzy	fuzzy	NOUN
ejpam-4446	252	4	set	set	VERB
ejpam-4446	252	5	lε	lε	ADP
ejpam-4446	252	6	ξ	ξ	PROPN
ejpam-4446	252	7	of	of	ADP
ejpam-4446	252	8	ξ	ξ	PROPN
ejpam-4446	252	9	is	be	AUX
ejpam-4446	252	10	a	a	DET
ejpam-4446	252	11	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	252	12	fuzzy	fuzzy	ADJ
ejpam-4446	252	13	be	be	NOUN
ejpam-4446	252	14	-	-	PUNCT
ejpam-4446	252	15	filter	filter	NOUN
ejpam-4446	252	16	of	of	ADP
ejpam-4446	252	17	x	x	SYM
ejpam-4446	252	18	if	if	SCONJ
ejpam-4446	252	19	and	and	CCONJ
ejpam-4446	252	20	only	only	ADV
ejpam-4446	252	21	if	if	SCONJ
ejpam-4446	252	22	it	it	PRON
ejpam-4446	252	23	satisfies	satisfy	VERB
ejpam-4446	252	24	:	:	PUNCT
ejpam-4446	252	25	lε	lε	PROPN
ejpam-4446	252	26	ξ(1	ξ(1	PROPN
ejpam-4446	252	27	)	)	PUNCT
ejpam-4446	252	28	is	be	AUX
ejpam-4446	252	29	an	an	DET
ejpam-4446	252	30	upper	upper	ADJ
ejpam-4446	252	31	bound	bind	VERB
ejpam-4446	252	32	of	of	ADP
ejpam-4446	252	33	{	{	PUNCT
ejpam-4446	252	34	lε	lε	X
ejpam-4446	252	35	ξ(x	ξ(x	NOUN
ejpam-4446	252	36	)	)	PUNCT
ejpam-4446	253	1	|	|	ADV
ejpam-4446	253	2	x	x	SYM
ejpam-4446	253	3	∈	∈	NOUN
ejpam-4446	253	4	x	x	X
ejpam-4446	253	5	}	}	PUNCT
ejpam-4446	253	6	,	,	PUNCT
ejpam-4446	253	7	(	(	PUNCT
ejpam-4446	253	8	21	21	NUM
ejpam-4446	253	9	)	)	PUNCT
ejpam-4446	253	10	(	(	PUNCT
ejpam-4446	253	11	∀x	∀x	X
ejpam-4446	253	12	,	,	PUNCT
ejpam-4446	253	13	y	y	PROPN
ejpam-4446	253	14	∈	∈	PROPN
ejpam-4446	253	15	x	x	X
ejpam-4446	253	16	)	)	PUNCT
ejpam-4446	253	17	(	(	PUNCT
ejpam-4446	253	18	lε	lε	ADP
ejpam-4446	253	19	ξ(y	ξ(y	PROPN
ejpam-4446	253	20	)	)	PUNCT
ejpam-4446	253	21	≥	≥	NOUN
ejpam-4446	253	22	min	min	PROPN
ejpam-4446	253	23	{	{	PUNCT
ejpam-4446	253	24	lε	lε	ADP
ejpam-4446	253	25	ξ(x	ξ(x	PROPN
ejpam-4446	253	26	∗	∗	X
ejpam-4446	253	27	y	y	PROPN
ejpam-4446	253	28	)	)	PUNCT
ejpam-4446	253	29	,	,	PUNCT
ejpam-4446	253	30	lε	lε	ADP
ejpam-4446	253	31	ξ(x	ξ(x	NOUN
ejpam-4446	253	32	)	)	PUNCT
ejpam-4446	253	33	}	}	PUNCT
ejpam-4446	253	34	)	)	PUNCT
ejpam-4446	253	35	.	.	PUNCT
ejpam-4446	254	1	(	(	PUNCT
ejpam-4446	254	2	22	22	X
ejpam-4446	254	3	)	)	PUNCT
ejpam-4446	254	4	y.	y.	PROPN
ejpam-4446	254	5	b.	b.	PROPN
ejpam-4446	254	6	jun	jun	PROPN
ejpam-4446	254	7	,	,	PUNCT
ejpam-4446	254	8	s.	s.	PROPN
ejpam-4446	254	9	s.	s.	PROPN
ejpam-4446	254	10	ahn	ahn	PROPN
ejpam-4446	254	11	/	/	SYM
ejpam-4446	254	12	eur	eur	PROPN
ejpam-4446	254	13	.	.	PUNCT
ejpam-4446	255	1	j.	j.	PROPN
ejpam-4446	255	2	pure	pure	PROPN
ejpam-4446	255	3	appl	appl	PROPN
ejpam-4446	255	4	.	.	PROPN
ejpam-4446	255	5	math	math	PROPN
ejpam-4446	255	6	,	,	PUNCT
ejpam-4446	255	7	15	15	NUM
ejpam-4446	255	8	(	(	PUNCT
ejpam-4446	255	9	3	3	NUM
ejpam-4446	255	10	)	)	PUNCT
ejpam-4446	255	11	(	(	PUNCT
ejpam-4446	255	12	2022	2022	NUM
ejpam-4446	255	13	)	)	PUNCT
ejpam-4446	255	14	,	,	PUNCT
ejpam-4446	255	15	924	924	NUM
ejpam-4446	255	16	-	-	SYM
ejpam-4446	255	17	937	937	NUM
ejpam-4446	255	18	935	935	NUM
ejpam-4446	255	19	proof	proof	NOUN
ejpam-4446	255	20	.	.	PUNCT
ejpam-4446	256	1	assume	assume	VERB
ejpam-4446	256	2	that	that	SCONJ
ejpam-4446	256	3	lε	lε	X
ejpam-4446	256	4	ξ	ξ	PROPN
ejpam-4446	256	5	is	be	AUX
ejpam-4446	256	6	a	a	DET
ejpam-4446	256	7	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	256	8	fuzzy	fuzzy	ADJ
ejpam-4446	256	9	be	be	NOUN
ejpam-4446	256	10	-	-	PUNCT
ejpam-4446	256	11	filter	filter	NOUN
ejpam-4446	256	12	of	of	ADP
ejpam-4446	256	13	x.	x.	NOUN
ejpam-4446	256	14	since	since	SCONJ
ejpam-4446	256	15	x	x	PROPN
ejpam-4446	256	16	∈	∈	PROPN
ejpam-4446	256	17	(	(	PUNCT
ejpam-4446	256	18	lε	lε	X
ejpam-4446	256	19	ξ	ξ	PROPN
ejpam-4446	256	20	,	,	PUNCT
ejpam-4446	256	21	lε	lε	X
ejpam-4446	256	22	ξ(x))∈	ξ(x))∈	NOUN
ejpam-4446	256	23	for	for	ADP
ejpam-4446	256	24	all	all	DET
ejpam-4446	256	25	x	x	SYM
ejpam-4446	256	26	∈	∈	NOUN
ejpam-4446	256	27	x	x	X
ejpam-4446	256	28	,	,	PUNCT
ejpam-4446	256	29	it	it	PRON
ejpam-4446	256	30	follows	follow	VERB
ejpam-4446	256	31	from	from	ADP
ejpam-4446	256	32	(	(	PUNCT
ejpam-4446	256	33	19	19	NUM
ejpam-4446	256	34	)	)	PUNCT
ejpam-4446	257	1	that	that	SCONJ
ejpam-4446	257	2	1	1	NUM
ejpam-4446	257	3	∈	∈	NOUN
ejpam-4446	257	4	(	(	PUNCT
ejpam-4446	257	5	lε	lε	PART
ejpam-4446	257	6	ξ	ξ	PROPN
ejpam-4446	257	7	,	,	PUNCT
ejpam-4446	257	8	lε	lε	VERB
ejpam-4446	257	9	ξ(x))∈.	ξ(x))∈.	ADV
ejpam-4446	257	10	hence	hence	ADV
ejpam-4446	257	11	lε	lε	PROPN
ejpam-4446	257	12	ξ(1	ξ(1	PROPN
ejpam-4446	257	13	)	)	PUNCT
ejpam-4446	257	14	≥	≥	NOUN
ejpam-4446	257	15	lε	lε	ADP
ejpam-4446	257	16	ξ(x	ξ(x	PROPN
ejpam-4446	257	17	)	)	PUNCT
ejpam-4446	257	18	for	for	ADP
ejpam-4446	257	19	all	all	DET
ejpam-4446	257	20	x	x	SYM
ejpam-4446	257	21	∈	∈	PROPN
ejpam-4446	257	22	x	x	NOUN
ejpam-4446	257	23	,	,	PUNCT
ejpam-4446	257	24	and	and	CCONJ
ejpam-4446	257	25	thus	thus	ADV
ejpam-4446	257	26	(	(	PUNCT
ejpam-4446	257	27	21	21	NUM
ejpam-4446	257	28	)	)	PUNCT
ejpam-4446	257	29	is	be	AUX
ejpam-4446	257	30	valid	valid	ADJ
ejpam-4446	257	31	.	.	PUNCT
ejpam-4446	258	1	since	since	SCONJ
ejpam-4446	258	2	x	x	PROPN
ejpam-4446	258	3	∗	∗	VERB
ejpam-4446	258	4	y	y	PROPN
ejpam-4446	258	5	∈	∈	PROPN
ejpam-4446	258	6	(	(	PUNCT
ejpam-4446	258	7	lε	lε	PART
ejpam-4446	258	8	ξ	ξ	PROPN
ejpam-4446	258	9	,	,	PUNCT
ejpam-4446	258	10	lε	lε	ADP
ejpam-4446	258	11	ξ(x	ξ(x	NOUN
ejpam-4446	258	12	∗	∗	NOUN
ejpam-4446	258	13	y))∈	y))∈	PROPN
ejpam-4446	258	14	and	and	CCONJ
ejpam-4446	258	15	x	x	PUNCT
ejpam-4446	258	16	∈	∈	PROPN
ejpam-4446	258	17	(	(	PUNCT
ejpam-4446	258	18	lε	lε	X
ejpam-4446	258	19	ξ	ξ	PROPN
ejpam-4446	258	20	,	,	PUNCT
ejpam-4446	258	21	lε	lε	X
ejpam-4446	258	22	ξ(x))∈	ξ(x))∈	NOUN
ejpam-4446	258	23	for	for	ADP
ejpam-4446	258	24	all	all	DET
ejpam-4446	258	25	x	x	NOUN
ejpam-4446	258	26	,	,	PUNCT
ejpam-4446	258	27	y	y	PROPN
ejpam-4446	258	28	∈	∈	PROPN
ejpam-4446	258	29	x	x	X
ejpam-4446	258	30	,	,	PUNCT
ejpam-4446	258	31	we	we	PRON
ejpam-4446	258	32	have	have	VERB
ejpam-4446	258	33	y	y	PROPN
ejpam-4446	258	34	∈	∈	PROPN
ejpam-4446	258	35	(	(	PUNCT
ejpam-4446	258	36	lε	lε	PART
ejpam-4446	258	37	ξ	ξ	PROPN
ejpam-4446	258	38	,	,	PUNCT
ejpam-4446	258	39	min	min	NOUN
ejpam-4446	258	40	{	{	PUNCT
ejpam-4446	258	41	lε	lε	ADP
ejpam-4446	258	42	ξ(x	ξ(x	PROPN
ejpam-4446	258	43	∗	∗	X
ejpam-4446	258	44	y	y	PROPN
ejpam-4446	258	45	)	)	PUNCT
ejpam-4446	258	46	,	,	PUNCT
ejpam-4446	258	47	lε	lε	AUX
ejpam-4446	258	48	ξ(x)})∈	ξ(x)})∈	VERB
ejpam-4446	258	49	by	by	ADP
ejpam-4446	258	50	(	(	PUNCT
ejpam-4446	258	51	20	20	NUM
ejpam-4446	258	52	)	)	PUNCT
ejpam-4446	258	53	.	.	PUNCT
ejpam-4446	259	1	hence	hence	ADV
ejpam-4446	259	2	lε	lε	ADP
ejpam-4446	259	3	ξ(y	ξ(y	PROPN
ejpam-4446	259	4	)	)	PUNCT
ejpam-4446	259	5	≥	≥	NOUN
ejpam-4446	259	6	min	min	PROPN
ejpam-4446	259	7	{	{	PUNCT
ejpam-4446	259	8	lε	lε	ADP
ejpam-4446	259	9	ξ(x	ξ(x	PROPN
ejpam-4446	259	10	∗	∗	X
ejpam-4446	259	11	y	y	PROPN
ejpam-4446	259	12	)	)	PUNCT
ejpam-4446	259	13	,	,	PUNCT
ejpam-4446	259	14	lε	lε	ADP
ejpam-4446	259	15	ξ(x	ξ(x	NOUN
ejpam-4446	259	16	)	)	PUNCT
ejpam-4446	259	17	}	}	PUNCT
ejpam-4446	259	18	for	for	ADP
ejpam-4446	259	19	all	all	DET
ejpam-4446	259	20	x	x	NOUN
ejpam-4446	259	21	,	,	PUNCT
ejpam-4446	259	22	y	y	PROPN
ejpam-4446	259	23	∈	∈	PROPN
ejpam-4446	259	24	x.	x.	NOUN
ejpam-4446	259	25	conversely	conversely	ADV
ejpam-4446	259	26	,	,	PUNCT
ejpam-4446	259	27	suppose	suppose	VERB
ejpam-4446	259	28	that	that	SCONJ
ejpam-4446	259	29	lε	lε	PROPN
ejpam-4446	259	30	ξ	ξ	X
ejpam-4446	259	31	satisfies	satisfie	NOUN
ejpam-4446	259	32	(	(	PUNCT
ejpam-4446	259	33	21	21	NUM
ejpam-4446	259	34	)	)	PUNCT
ejpam-4446	259	35	and	and	CCONJ
ejpam-4446	259	36	(	(	PUNCT
ejpam-4446	259	37	22	22	NUM
ejpam-4446	259	38	)	)	PUNCT
ejpam-4446	259	39	.	.	PUNCT
ejpam-4446	260	1	let	let	VERB
ejpam-4446	260	2	x	x	PRON
ejpam-4446	260	3	,	,	PUNCT
ejpam-4446	260	4	y	y	PROPN
ejpam-4446	260	5	∈	∈	PROPN
ejpam-4446	260	6	x	x	X
ejpam-4446	260	7	and	and	CCONJ
ejpam-4446	260	8	ta	ta	PROPN
ejpam-4446	260	9	,	,	PUNCT
ejpam-4446	260	10	tb	tb	ADP
ejpam-4446	260	11	∈	∈	PROPN
ejpam-4446	260	12	(	(	PUNCT
ejpam-4446	260	13	0	0	NUM
ejpam-4446	260	14	,	,	PUNCT
ejpam-4446	260	15	1	1	NUM
ejpam-4446	260	16	]	]	PUNCT
ejpam-4446	260	17	.	.	PUNCT
ejpam-4446	261	1	if	if	SCONJ
ejpam-4446	261	2	x	x	SYM
ejpam-4446	261	3	∈	∈	PROPN
ejpam-4446	261	4	(	(	PUNCT
ejpam-4446	261	5	lε	lε	PART
ejpam-4446	261	6	ξ	ξ	PROPN
ejpam-4446	261	7	,	,	PUNCT
ejpam-4446	261	8	ta)∈	ta)∈	PROPN
ejpam-4446	261	9	,	,	PUNCT
ejpam-4446	261	10	then	then	ADV
ejpam-4446	261	11	lε	lε	PROPN
ejpam-4446	261	12	ξ(1	ξ(1	PROPN
ejpam-4446	261	13	)	)	PUNCT
ejpam-4446	261	14	≥	≥	NOUN
ejpam-4446	261	15	lε	lε	ADP
ejpam-4446	261	16	ξ(x	ξ(x	PROPN
ejpam-4446	261	17	)	)	PUNCT
ejpam-4446	261	18	≥	≥	NOUN
ejpam-4446	261	19	ta	ta	NOUN
ejpam-4446	261	20	and	and	CCONJ
ejpam-4446	261	21	so	so	ADV
ejpam-4446	261	22	1	1	NUM
ejpam-4446	261	23	∈	∈	PROPN
ejpam-4446	261	24	(	(	PUNCT
ejpam-4446	261	25	lε	lε	PART
ejpam-4446	261	26	ξ	ξ	PROPN
ejpam-4446	261	27	,	,	PUNCT
ejpam-4446	261	28	ta)∈.	ta)∈.	PART
ejpam-4446	261	29	assume	assume	VERB
ejpam-4446	261	30	that	that	SCONJ
ejpam-4446	261	31	x	x	PROPN
ejpam-4446	261	32	∗	∗	VERB
ejpam-4446	261	33	y	y	PROPN
ejpam-4446	261	34	∈	∈	PROPN
ejpam-4446	261	35	(	(	PUNCT
ejpam-4446	261	36	lε	lε	X
ejpam-4446	261	37	ξ	ξ	PROPN
ejpam-4446	261	38	,	,	PUNCT
ejpam-4446	261	39	ta)∈	ta)∈	PROPN
ejpam-4446	261	40	and	and	CCONJ
ejpam-4446	261	41	x	x	SYM
ejpam-4446	261	42	∈	∈	PROPN
ejpam-4446	261	43	(	(	PUNCT
ejpam-4446	261	44	lε	lε	X
ejpam-4446	261	45	ξ	ξ	PROPN
ejpam-4446	261	46	,	,	PUNCT
ejpam-4446	261	47	tb)∈.	tb)∈.	PUNCT
ejpam-4446	261	48	then	then	ADV
ejpam-4446	261	49	lε	lε	ADP
ejpam-4446	261	50	ξ(x	ξ(x	PROPN
ejpam-4446	261	51	∗	∗	X
ejpam-4446	261	52	y	y	PROPN
ejpam-4446	261	53	)	)	PUNCT
ejpam-4446	261	54	≥	≥	NOUN
ejpam-4446	261	55	ta	ta	NOUN
ejpam-4446	261	56	and	and	CCONJ
ejpam-4446	261	57	lε	lε	ADP
ejpam-4446	261	58	ξ(x	ξ(x	PROPN
ejpam-4446	261	59	)	)	PUNCT
ejpam-4446	261	60	≥	≥	NOUN
ejpam-4446	261	61	tb	tb	ADP
ejpam-4446	261	62	it	it	PRON
ejpam-4446	261	63	follows	follow	VERB
ejpam-4446	261	64	from	from	ADP
ejpam-4446	261	65	(	(	PUNCT
ejpam-4446	261	66	22	22	NUM
ejpam-4446	261	67	)	)	PUNCT
ejpam-4446	261	68	that	that	PRON
ejpam-4446	261	69	lε	lε	ADP
ejpam-4446	261	70	ξ(y	ξ(y	PROPN
ejpam-4446	261	71	)	)	PUNCT
ejpam-4446	261	72	≥	≥	NOUN
ejpam-4446	261	73	min	min	PROPN
ejpam-4446	261	74	{	{	PUNCT
ejpam-4446	261	75	lε	lε	X
ejpam-4446	261	76	ξ(x∗y	ξ(x∗y	PROPN
ejpam-4446	261	77	)	)	PUNCT
ejpam-4446	261	78	,	,	PUNCT
ejpam-4446	261	79	lε	lε	ADP
ejpam-4446	261	80	ξ(x	ξ(x	NOUN
ejpam-4446	261	81	)	)	PUNCT
ejpam-4446	261	82	}	}	PUNCT
ejpam-4446	261	83	≥	≥	NOUN
ejpam-4446	261	84	min{ta	min{ta	X
ejpam-4446	261	85	,	,	PUNCT
ejpam-4446	261	86	tb	tb	NOUN
ejpam-4446	261	87	}	}	PUNCT
ejpam-4446	261	88	,	,	PUNCT
ejpam-4446	261	89	i.e.	i.e.	X
ejpam-4446	261	90	,	,	PUNCT
ejpam-4446	261	91	[	[	X
ejpam-4446	261	92	y	y	X
ejpam-4446	261	93	/	/	SYM
ejpam-4446	261	94	min{ta	min{ta	NUM
ejpam-4446	261	95	,	,	PUNCT
ejpam-4446	261	96	tb	tb	NOUN
ejpam-4446	261	97	}	}	PUNCT
ejpam-4446	261	98	]	]	PUNCT
ejpam-4446	261	99	∈	∈	PROPN
ejpam-4446	261	100	lε	lε	X
ejpam-4446	261	101	ξ	ξ	X
ejpam-4446	261	102	.	.	PUNCT
ejpam-4446	262	1	hence	hence	ADV
ejpam-4446	262	2	y	y	PROPN
ejpam-4446	262	3	∈	∈	PROPN
ejpam-4446	262	4	(	(	PUNCT
ejpam-4446	262	5	lε	lε	PART
ejpam-4446	262	6	ξ	ξ	PROPN
ejpam-4446	262	7	,	,	PUNCT
ejpam-4446	262	8	min{ta	min{ta	X
ejpam-4446	262	9	,	,	PUNCT
ejpam-4446	262	10	tb})∈.	tb})∈.	ADJ
ejpam-4446	262	11	therefore	therefore	ADV
ejpam-4446	262	12	lε	lε	X
ejpam-4446	262	13	ξ	ξ	PROPN
ejpam-4446	262	14	is	be	AUX
ejpam-4446	262	15	a	a	DET
ejpam-4446	262	16	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	262	17	fuzzy	fuzzy	ADJ
ejpam-4446	262	18	be	be	NOUN
ejpam-4446	262	19	-	-	PUNCT
ejpam-4446	262	20	filter	filter	NOUN
ejpam-4446	262	21	of	of	ADP
ejpam-4446	262	22	x.	x.	NOUN
ejpam-4446	262	23	corollary	corollary	PROPN
ejpam-4446	263	1	3	3	X
ejpam-4446	263	2	.	.	PUNCT
ejpam-4446	264	1	if	if	SCONJ
ejpam-4446	264	2	ξ	ξ	PROPN
ejpam-4446	264	3	is	be	AUX
ejpam-4446	264	4	a	a	DET
ejpam-4446	264	5	fuzzy	fuzzy	ADJ
ejpam-4446	264	6	be	be	NOUN
ejpam-4446	264	7	-	-	PUNCT
ejpam-4446	264	8	filter	filter	NOUN
ejpam-4446	264	9	of	of	ADP
ejpam-4446	264	10	x	x	NOUN
ejpam-4446	264	11	,	,	PUNCT
ejpam-4446	264	12	then	then	ADV
ejpam-4446	264	13	its	its	PRON
ejpam-4446	264	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	264	15	fuzzy	fuzzy	NOUN
ejpam-4446	264	16	set	set	VERB
ejpam-4446	264	17	lε	lε	AUX
ejpam-4446	264	18	ξ	ξ	X
ejpam-4446	264	19	satisfies	satisfie	NOUN
ejpam-4446	264	20	(	(	PUNCT
ejpam-4446	264	21	21	21	NUM
ejpam-4446	264	22	)	)	PUNCT
ejpam-4446	264	23	and	and	CCONJ
ejpam-4446	264	24	(	(	PUNCT
ejpam-4446	264	25	22	22	NUM
ejpam-4446	264	26	)	)	PUNCT
ejpam-4446	264	27	.	.	PUNCT
ejpam-4446	265	1	theorem	theorem	VERB
ejpam-4446	265	2	14	14	NUM
ejpam-4446	265	3	.	.	PUNCT
ejpam-4446	266	1	the	the	DET
ejpam-4446	266	2	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	266	3	fuzzy	fuzzy	NOUN
ejpam-4446	266	4	set	set	VERB
ejpam-4446	266	5	lε	lε	ADP
ejpam-4446	266	6	ξ	ξ	PROPN
ejpam-4446	266	7	of	of	ADP
ejpam-4446	266	8	ξ	ξ	PROPN
ejpam-4446	266	9	is	be	AUX
ejpam-4446	266	10	a	a	DET
ejpam-4446	266	11	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	266	12	fuzzy	fuzzy	ADJ
ejpam-4446	266	13	be	be	NOUN
ejpam-4446	266	14	-	-	PUNCT
ejpam-4446	266	15	filter	filter	NOUN
ejpam-4446	266	16	of	of	ADP
ejpam-4446	266	17	x	x	SYM
ejpam-4446	266	18	if	if	SCONJ
ejpam-4446	266	19	and	and	CCONJ
ejpam-4446	266	20	only	only	ADV
ejpam-4446	266	21	if	if	SCONJ
ejpam-4446	266	22	it	it	PRON
ejpam-4446	266	23	satisfies	satisfy	VERB
ejpam-4446	266	24	the	the	DET
ejpam-4446	266	25	condition	condition	NOUN
ejpam-4446	266	26	(	(	PUNCT
ejpam-4446	266	27	21	21	NUM
ejpam-4446	266	28	)	)	PUNCT
ejpam-4446	266	29	and	and	CCONJ
ejpam-4446	266	30	(	(	PUNCT
ejpam-4446	266	31	∀x	∀x	NUM
ejpam-4446	266	32	,	,	PUNCT
ejpam-4446	266	33	y	y	PROPN
ejpam-4446	266	34	,	,	PUNCT
ejpam-4446	266	35	z	z	NOUN
ejpam-4446	266	36	∈	∈	PROPN
ejpam-4446	266	37	x	x	X
ejpam-4446	266	38	)	)	PUNCT
ejpam-4446	266	39	(	(	PUNCT
ejpam-4446	266	40	lε	lε	ADP
ejpam-4446	266	41	ξ(x	ξ(x	PROPN
ejpam-4446	266	42	∗	∗	X
ejpam-4446	266	43	z	z	PROPN
ejpam-4446	266	44	)	)	PUNCT
ejpam-4446	266	45	≥	≥	PROPN
ejpam-4446	266	46	min	min	PROPN
ejpam-4446	266	47	{	{	PUNCT
ejpam-4446	266	48	lε	lε	ADP
ejpam-4446	266	49	ξ(x	ξ(x	NOUN
ejpam-4446	266	50	∗	∗	NOUN
ejpam-4446	266	51	(	(	PUNCT
ejpam-4446	266	52	y	y	PROPN
ejpam-4446	266	53	∗	∗	PROPN
ejpam-4446	266	54	z	z	PROPN
ejpam-4446	266	55	)	)	PUNCT
ejpam-4446	266	56	)	)	PUNCT
ejpam-4446	266	57	,	,	PUNCT
ejpam-4446	266	58	lε	lε	ADP
ejpam-4446	266	59	ξ(y	ξ(y	PROPN
ejpam-4446	266	60	)	)	PUNCT
ejpam-4446	266	61	}	}	PUNCT
ejpam-4446	266	62	)	)	PUNCT
ejpam-4446	266	63	.	.	PUNCT
ejpam-4446	267	1	(	(	PUNCT
ejpam-4446	267	2	23	23	X
ejpam-4446	267	3	)	)	PUNCT
ejpam-4446	267	4	proof	proof	NOUN
ejpam-4446	267	5	.	.	PUNCT
ejpam-4446	268	1	assume	assume	VERB
ejpam-4446	268	2	that	that	SCONJ
ejpam-4446	268	3	lε	lε	X
ejpam-4446	268	4	ξ	ξ	PROPN
ejpam-4446	268	5	is	be	AUX
ejpam-4446	268	6	a	a	DET
ejpam-4446	268	7	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	268	8	fuzzy	fuzzy	ADJ
ejpam-4446	268	9	be	be	NOUN
ejpam-4446	268	10	-	-	PUNCT
ejpam-4446	268	11	filter	filter	NOUN
ejpam-4446	268	12	of	of	ADP
ejpam-4446	268	13	x.	x.	NOUN
ejpam-4446	268	14	the	the	DET
ejpam-4446	268	15	condition	condition	NOUN
ejpam-4446	268	16	(	(	PUNCT
ejpam-4446	268	17	21	21	NUM
ejpam-4446	268	18	)	)	PUNCT
ejpam-4446	268	19	was	be	AUX
ejpam-4446	268	20	verified	verify	VERB
ejpam-4446	268	21	by	by	ADP
ejpam-4446	268	22	the	the	DET
ejpam-4446	268	23	proof	proof	NOUN
ejpam-4446	268	24	of	of	ADP
ejpam-4446	268	25	theorem	theorem	ADJ
ejpam-4446	268	26	13	13	NUM
ejpam-4446	268	27	.	.	PUNCT
ejpam-4446	269	1	using	use	VERB
ejpam-4446	269	2	(	(	PUNCT
ejpam-4446	269	3	be4	be4	NOUN
ejpam-4446	269	4	)	)	PUNCT
ejpam-4446	269	5	and	and	CCONJ
ejpam-4446	269	6	(	(	PUNCT
ejpam-4446	269	7	22	22	NUM
ejpam-4446	269	8	)	)	PUNCT
ejpam-4446	269	9	,	,	PUNCT
ejpam-4446	269	10	we	we	PRON
ejpam-4446	269	11	get	get	VERB
ejpam-4446	269	12	lε	lε	ADP
ejpam-4446	269	13	ξ(x	ξ(x	NOUN
ejpam-4446	269	14	∗	∗	X
ejpam-4446	269	15	z	z	NOUN
ejpam-4446	269	16	)	)	PUNCT
ejpam-4446	269	17	≥	≥	PROPN
ejpam-4446	269	18	min	min	NOUN
ejpam-4446	269	19	{	{	PUNCT
ejpam-4446	269	20	lε	lε	ADP
ejpam-4446	269	21	ξ(y	ξ(y	PROPN
ejpam-4446	269	22	∗	∗	NOUN
ejpam-4446	269	23	(	(	PUNCT
ejpam-4446	269	24	x	x	X
ejpam-4446	269	25	∗	∗	PROPN
ejpam-4446	269	26	z	z	NOUN
ejpam-4446	269	27	)	)	PUNCT
ejpam-4446	269	28	)	)	PUNCT
ejpam-4446	269	29	,	,	PUNCT
ejpam-4446	269	30	lε	lε	ADP
ejpam-4446	269	31	ξ(y	ξ(y	PROPN
ejpam-4446	269	32	)	)	PUNCT
ejpam-4446	269	33	}	}	PUNCT
ejpam-4446	270	1	=	=	SYM
ejpam-4446	270	2	min	min	X
ejpam-4446	270	3	{	{	PUNCT
ejpam-4446	270	4	lε	lε	ADP
ejpam-4446	270	5	ξ(x	ξ(x	NOUN
ejpam-4446	270	6	∗	∗	NOUN
ejpam-4446	270	7	(	(	PUNCT
ejpam-4446	270	8	y	y	PROPN
ejpam-4446	270	9	∗	∗	PROPN
ejpam-4446	270	10	z	z	PROPN
ejpam-4446	270	11	)	)	PUNCT
ejpam-4446	270	12	)	)	PUNCT
ejpam-4446	270	13	,	,	PUNCT
ejpam-4446	270	14	lε	lε	ADP
ejpam-4446	270	15	ξ(y	ξ(y	PROPN
ejpam-4446	270	16	)	)	PUNCT
ejpam-4446	270	17	}	}	PUNCT
ejpam-4446	270	18	.	.	PUNCT
ejpam-4446	271	1	conversely	conversely	ADV
ejpam-4446	271	2	,	,	PUNCT
ejpam-4446	271	3	suppose	suppose	VERB
ejpam-4446	271	4	that	that	SCONJ
ejpam-4446	271	5	lε	lε	PROPN
ejpam-4446	271	6	ξ	ξ	X
ejpam-4446	271	7	satisfies	satisfy	VERB
ejpam-4446	271	8	the	the	DET
ejpam-4446	271	9	conditions	condition	NOUN
ejpam-4446	271	10	(	(	PUNCT
ejpam-4446	271	11	21	21	NUM
ejpam-4446	271	12	)	)	PUNCT
ejpam-4446	271	13	and	and	CCONJ
ejpam-4446	271	14	(	(	PUNCT
ejpam-4446	271	15	23	23	NUM
ejpam-4446	271	16	)	)	PUNCT
ejpam-4446	271	17	.	.	PUNCT
ejpam-4446	272	1	if	if	SCONJ
ejpam-4446	272	2	we	we	PRON
ejpam-4446	272	3	take	take	VERB
ejpam-4446	272	4	x	x	PUNCT
ejpam-4446	272	5	:	:	PUNCT
ejpam-4446	272	6	=	=	SYM
ejpam-4446	272	7	1	1	NUM
ejpam-4446	272	8	in	in	ADP
ejpam-4446	272	9	(	(	PUNCT
ejpam-4446	272	10	23	23	NUM
ejpam-4446	272	11	)	)	PUNCT
ejpam-4446	272	12	and	and	CCONJ
ejpam-4446	272	13	use	use	NOUN
ejpam-4446	272	14	(	(	PUNCT
ejpam-4446	272	15	be3	be3	PROPN
ejpam-4446	272	16	)	)	PUNCT
ejpam-4446	272	17	,	,	PUNCT
ejpam-4446	272	18	then	then	ADV
ejpam-4446	272	19	lε	lε	ADP
ejpam-4446	272	20	ξ(z	ξ(z	PROPN
ejpam-4446	272	21	)	)	PUNCT
ejpam-4446	272	22	=	=	PRON
ejpam-4446	272	23	lε	lε	PRON
ejpam-4446	272	24	ξ(1	ξ(1	PROPN
ejpam-4446	272	25	∗	∗	PROPN
ejpam-4446	272	26	z	z	PROPN
ejpam-4446	272	27	)	)	PUNCT
ejpam-4446	272	28	≥	≥	PROPN
ejpam-4446	272	29	min	min	PROPN
ejpam-4446	272	30	{	{	PUNCT
ejpam-4446	272	31	lε	lε	PROPN
ejpam-4446	272	32	ξ(1	ξ(1	PROPN
ejpam-4446	272	33	∗	∗	NOUN
ejpam-4446	272	34	(	(	PUNCT
ejpam-4446	272	35	y	y	PROPN
ejpam-4446	272	36	∗	∗	PROPN
ejpam-4446	272	37	z	z	PROPN
ejpam-4446	272	38	)	)	PUNCT
ejpam-4446	272	39	)	)	PUNCT
ejpam-4446	272	40	,	,	PUNCT
ejpam-4446	272	41	lε	lε	ADP
ejpam-4446	272	42	ξ(y	ξ(y	PROPN
ejpam-4446	272	43	)	)	PUNCT
ejpam-4446	272	44	}	}	PUNCT
ejpam-4446	272	45	=	=	SYM
ejpam-4446	272	46	min	min	X
ejpam-4446	272	47	{	{	PUNCT
ejpam-4446	272	48	lε	lε	ADP
ejpam-4446	272	49	ξ(y	ξ(y	PROPN
ejpam-4446	272	50	∗	∗	NOUN
ejpam-4446	272	51	z	z	PROPN
ejpam-4446	272	52	)	)	PUNCT
ejpam-4446	272	53	,	,	PUNCT
ejpam-4446	272	54	lε	lε	ADP
ejpam-4446	272	55	ξ(y	ξ(y	PROPN
ejpam-4446	272	56	)	)	PUNCT
ejpam-4446	272	57	}	}	PUNCT
ejpam-4446	272	58	for	for	ADP
ejpam-4446	272	59	all	all	DET
ejpam-4446	272	60	y	y	PROPN
ejpam-4446	272	61	,	,	PUNCT
ejpam-4446	272	62	z	z	PROPN
ejpam-4446	272	63	∈	∈	PROPN
ejpam-4446	272	64	x.	x.	NOUN
ejpam-4446	272	65	therefore	therefore	ADV
ejpam-4446	272	66	lε	lε	X
ejpam-4446	272	67	ξ	ξ	PROPN
ejpam-4446	272	68	is	be	AUX
ejpam-4446	272	69	a	a	DET
ejpam-4446	272	70	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	272	71	fuzzy	fuzzy	ADJ
ejpam-4446	272	72	be	be	NOUN
ejpam-4446	272	73	-	-	PUNCT
ejpam-4446	272	74	filter	filter	NOUN
ejpam-4446	272	75	of	of	ADP
ejpam-4446	272	76	x	x	PUNCT
ejpam-4446	272	77	by	by	ADP
ejpam-4446	272	78	theorem	theorem	NOUN
ejpam-4446	272	79	13	13	NUM
ejpam-4446	272	80	.	.	PUNCT
ejpam-4446	272	81	corollary	corollary	ADJ
ejpam-4446	272	82	4	4	NUM
ejpam-4446	272	83	.	.	PUNCT
ejpam-4446	273	1	if	if	SCONJ
ejpam-4446	273	2	ξ	ξ	PROPN
ejpam-4446	273	3	is	be	AUX
ejpam-4446	273	4	a	a	DET
ejpam-4446	273	5	fuzzy	fuzzy	ADJ
ejpam-4446	273	6	be	be	NOUN
ejpam-4446	273	7	-	-	PUNCT
ejpam-4446	273	8	filter	filter	NOUN
ejpam-4446	273	9	of	of	ADP
ejpam-4446	273	10	x	x	NOUN
ejpam-4446	273	11	,	,	PUNCT
ejpam-4446	273	12	then	then	ADV
ejpam-4446	273	13	its	its	PRON
ejpam-4446	273	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	273	15	fuzzy	fuzzy	NOUN
ejpam-4446	273	16	set	set	VERB
ejpam-4446	273	17	lε	lε	AUX
ejpam-4446	273	18	ξ	ξ	X
ejpam-4446	273	19	satisfies	satisfie	NOUN
ejpam-4446	273	20	(	(	PUNCT
ejpam-4446	273	21	23	23	NUM
ejpam-4446	273	22	)	)	PUNCT
ejpam-4446	273	23	.	.	PUNCT
ejpam-4446	274	1	theorem	theorem	VERB
ejpam-4446	274	2	15	15	NUM
ejpam-4446	274	3	.	.	PUNCT
ejpam-4446	275	1	the	the	DET
ejpam-4446	275	2	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	275	3	fuzzy	fuzzy	NOUN
ejpam-4446	275	4	set	set	VERB
ejpam-4446	275	5	lε	lε	ADP
ejpam-4446	275	6	ξ	ξ	PROPN
ejpam-4446	275	7	of	of	ADP
ejpam-4446	275	8	ξ	ξ	PROPN
ejpam-4446	275	9	is	be	AUX
ejpam-4446	275	10	a	a	DET
ejpam-4446	275	11	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	275	12	fuzzy	fuzzy	ADJ
ejpam-4446	275	13	be	be	NOUN
ejpam-4446	275	14	-	-	PUNCT
ejpam-4446	275	15	filter	filter	NOUN
ejpam-4446	275	16	of	of	ADP
ejpam-4446	275	17	x	x	SYM
ejpam-4446	275	18	if	if	SCONJ
ejpam-4446	275	19	and	and	CCONJ
ejpam-4446	275	20	only	only	ADV
ejpam-4446	275	21	if	if	SCONJ
ejpam-4446	275	22	it	it	PRON
ejpam-4446	275	23	satisfies	satisfy	VERB
ejpam-4446	275	24	:	:	PUNCT
ejpam-4446	275	25	(	(	PUNCT
ejpam-4446	275	26	∀x	∀x	X
ejpam-4446	275	27	,	,	PUNCT
ejpam-4446	275	28	y	y	PROPN
ejpam-4446	275	29	∈	∈	PROPN
ejpam-4446	275	30	x	x	X
ejpam-4446	275	31	)	)	PUNCT
ejpam-4446	275	32	(	(	PUNCT
ejpam-4446	275	33	lε	lε	ADP
ejpam-4446	275	34	ξ(x	ξ(x	PROPN
ejpam-4446	275	35	∗	∗	X
ejpam-4446	275	36	y	y	PROPN
ejpam-4446	275	37	)	)	PUNCT
ejpam-4446	275	38	≥	≥	NOUN
ejpam-4446	275	39	lε	lε	ADP
ejpam-4446	275	40	ξ(y	ξ(y	PROPN
ejpam-4446	275	41	)	)	PUNCT
ejpam-4446	275	42	)	)	PUNCT
ejpam-4446	275	43	,	,	PUNCT
ejpam-4446	275	44	(	(	PUNCT
ejpam-4446	275	45	24	24	NUM
ejpam-4446	275	46	)	)	PUNCT
ejpam-4446	275	47	(	(	PUNCT
ejpam-4446	275	48	∀x	∀x	X
ejpam-4446	275	49	,	,	PUNCT
ejpam-4446	275	50	y	y	PROPN
ejpam-4446	275	51	,	,	PUNCT
ejpam-4446	275	52	z	z	NOUN
ejpam-4446	275	53	∈	∈	PROPN
ejpam-4446	275	54	x	x	X
ejpam-4446	275	55	)	)	PUNCT
ejpam-4446	275	56	(	(	PUNCT
ejpam-4446	275	57	lε	lε	AUX
ejpam-4446	275	58	ξ((x	ξ((x	VERB
ejpam-4446	275	59	∗	∗	NOUN
ejpam-4446	275	60	(	(	PUNCT
ejpam-4446	275	61	y	y	PROPN
ejpam-4446	275	62	∗	∗	PROPN
ejpam-4446	275	63	z	z	NOUN
ejpam-4446	275	64	)	)	PUNCT
ejpam-4446	275	65	)	)	PUNCT
ejpam-4446	275	66	∗	∗	PROPN
ejpam-4446	275	67	z	z	NOUN
ejpam-4446	275	68	)	)	PUNCT
ejpam-4446	275	69	≥	≥	PROPN
ejpam-4446	275	70	min	min	PROPN
ejpam-4446	275	71	{	{	PUNCT
ejpam-4446	275	72	lε	lε	ADP
ejpam-4446	275	73	ξ(x	ξ(x	PROPN
ejpam-4446	275	74	)	)	PUNCT
ejpam-4446	275	75	,	,	PUNCT
ejpam-4446	275	76	lε	lε	ADP
ejpam-4446	275	77	ξ(y	ξ(y	PROPN
ejpam-4446	275	78	)	)	PUNCT
ejpam-4446	275	79	}	}	PUNCT
ejpam-4446	275	80	)	)	PUNCT
ejpam-4446	275	81	.	.	PUNCT
ejpam-4446	276	1	(	(	PUNCT
ejpam-4446	276	2	25	25	NUM
ejpam-4446	276	3	)	)	PUNCT
ejpam-4446	276	4	proof	proof	NOUN
ejpam-4446	276	5	.	.	PUNCT
ejpam-4446	277	1	assume	assume	VERB
ejpam-4446	277	2	that	that	SCONJ
ejpam-4446	277	3	lε	lε	X
ejpam-4446	277	4	ξ	ξ	PROPN
ejpam-4446	277	5	is	be	AUX
ejpam-4446	277	6	a	a	DET
ejpam-4446	277	7	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	277	8	fuzzy	fuzzy	ADJ
ejpam-4446	277	9	be	be	NOUN
ejpam-4446	277	10	-	-	PUNCT
ejpam-4446	277	11	filter	filter	NOUN
ejpam-4446	277	12	of	of	ADP
ejpam-4446	277	13	x	x	PUNCT
ejpam-4446	277	14	and	and	CCONJ
ejpam-4446	277	15	let	let	VERB
ejpam-4446	277	16	x	x	PRON
ejpam-4446	277	17	,	,	PUNCT
ejpam-4446	277	18	y	y	PROPN
ejpam-4446	277	19	,	,	PUNCT
ejpam-4446	277	20	z	z	PROPN
ejpam-4446	277	21	∈	∈	PROPN
ejpam-4446	277	22	x.	x.	NOUN
ejpam-4446	278	1	then	then	ADV
ejpam-4446	278	2	lε	lε	ADP
ejpam-4446	278	3	ξ(x	ξ(x	PROPN
ejpam-4446	278	4	∗	∗	X
ejpam-4446	278	5	y	y	PROPN
ejpam-4446	278	6	)	)	PUNCT
ejpam-4446	278	7	≥	≥	PROPN
ejpam-4446	278	8	min	min	PROPN
ejpam-4446	278	9	{	{	PUNCT
ejpam-4446	278	10	lε	lε	ADP
ejpam-4446	278	11	ξ(y	ξ(y	PROPN
ejpam-4446	278	12	∗	∗	NOUN
ejpam-4446	278	13	(	(	PUNCT
ejpam-4446	278	14	x	x	X
ejpam-4446	278	15	∗	∗	PROPN
ejpam-4446	278	16	y	y	PROPN
ejpam-4446	278	17	)	)	PUNCT
ejpam-4446	278	18	)	)	PUNCT
ejpam-4446	278	19	,	,	PUNCT
ejpam-4446	278	20	lε	lε	ADP
ejpam-4446	278	21	ξ(y	ξ(y	PROPN
ejpam-4446	278	22	)	)	PUNCT
ejpam-4446	278	23	}	}	PUNCT
ejpam-4446	278	24	=	=	SYM
ejpam-4446	278	25	min	min	X
ejpam-4446	278	26	{	{	PUNCT
ejpam-4446	278	27	lε	lε	ADP
ejpam-4446	278	28	ξ(x	ξ(x	NOUN
ejpam-4446	278	29	∗	∗	NOUN
ejpam-4446	278	30	(	(	PUNCT
ejpam-4446	278	31	y	y	PROPN
ejpam-4446	278	32	∗	∗	PROPN
ejpam-4446	278	33	y	y	PROPN
ejpam-4446	278	34	)	)	PUNCT
ejpam-4446	278	35	)	)	PUNCT
ejpam-4446	278	36	,	,	PUNCT
ejpam-4446	278	37	lε	lε	ADP
ejpam-4446	278	38	ξ(y	ξ(y	PROPN
ejpam-4446	278	39	)	)	PUNCT
ejpam-4446	278	40	}	}	PUNCT
ejpam-4446	278	41	=	=	SYM
ejpam-4446	278	42	min	min	X
ejpam-4446	278	43	{	{	PUNCT
ejpam-4446	278	44	lε	lε	ADP
ejpam-4446	278	45	ξ(x	ξ(x	NOUN
ejpam-4446	278	46	∗	∗	NOUN
ejpam-4446	278	47	1	1	NUM
ejpam-4446	278	48	)	)	PUNCT
ejpam-4446	278	49	,	,	PUNCT
ejpam-4446	278	50	lε	lε	ADP
ejpam-4446	278	51	ξ(y	ξ(y	PROPN
ejpam-4446	278	52	)	)	PUNCT
ejpam-4446	278	53	}	}	PUNCT
ejpam-4446	278	54	=	=	SYM
ejpam-4446	278	55	min	min	X
ejpam-4446	278	56	{	{	PUNCT
ejpam-4446	278	57	lε	lε	X
ejpam-4446	278	58	ξ(1	ξ(1	PROPN
ejpam-4446	278	59	)	)	PUNCT
ejpam-4446	278	60	,	,	PUNCT
ejpam-4446	278	61	lε	lε	ADP
ejpam-4446	278	62	ξ(y	ξ(y	PROPN
ejpam-4446	278	63	)	)	PUNCT
ejpam-4446	278	64	}	}	PUNCT
ejpam-4446	278	65	=	=	PUNCT
ejpam-4446	278	66	lε	lε	ADP
ejpam-4446	279	1	ξ(y	ξ(y	PROPN
ejpam-4446	279	2	)	)	PUNCT
ejpam-4446	279	3	y.	y.	PROPN
ejpam-4446	279	4	b.	b.	PROPN
ejpam-4446	279	5	jun	jun	PROPN
ejpam-4446	279	6	,	,	PUNCT
ejpam-4446	279	7	s.	s.	PROPN
ejpam-4446	279	8	s.	s.	PROPN
ejpam-4446	279	9	ahn	ahn	PROPN
ejpam-4446	279	10	/	/	SYM
ejpam-4446	279	11	eur	eur	PROPN
ejpam-4446	279	12	.	.	PUNCT
ejpam-4446	280	1	j.	j.	PROPN
ejpam-4446	280	2	pure	pure	PROPN
ejpam-4446	280	3	appl	appl	PROPN
ejpam-4446	280	4	.	.	PROPN
ejpam-4446	280	5	math	math	PROPN
ejpam-4446	280	6	,	,	PUNCT
ejpam-4446	280	7	15	15	NUM
ejpam-4446	280	8	(	(	PUNCT
ejpam-4446	280	9	3	3	NUM
ejpam-4446	280	10	)	)	PUNCT
ejpam-4446	280	11	(	(	PUNCT
ejpam-4446	280	12	2022	2022	NUM
ejpam-4446	280	13	)	)	PUNCT
ejpam-4446	280	14	,	,	PUNCT
ejpam-4446	280	15	924	924	NUM
ejpam-4446	280	16	-	-	SYM
ejpam-4446	280	17	937	937	NUM
ejpam-4446	280	18	936	936	NUM
ejpam-4446	280	19	by	by	ADP
ejpam-4446	280	20	(	(	PUNCT
ejpam-4446	280	21	be1	be1	NOUN
ejpam-4446	280	22	)	)	PUNCT
ejpam-4446	280	23	,	,	PUNCT
ejpam-4446	280	24	(	(	PUNCT
ejpam-4446	280	25	be2	be2	PROPN
ejpam-4446	280	26	)	)	PUNCT
ejpam-4446	280	27	,	,	PUNCT
ejpam-4446	280	28	(	(	PUNCT
ejpam-4446	280	29	be4	be4	NOUN
ejpam-4446	280	30	)	)	PUNCT
ejpam-4446	280	31	and	and	CCONJ
ejpam-4446	280	32	theorem	theorem	VERB
ejpam-4446	280	33	13	13	NUM
ejpam-4446	280	34	.	.	PUNCT
ejpam-4446	281	1	also	also	ADV
ejpam-4446	281	2	,	,	PUNCT
ejpam-4446	281	3	we	we	PRON
ejpam-4446	281	4	have	have	AUX
ejpam-4446	281	5	lε	lε	AUX
ejpam-4446	281	6	ξ((x	ξ((x	VERB
ejpam-4446	281	7	∗	∗	NOUN
ejpam-4446	281	8	(	(	PUNCT
ejpam-4446	281	9	y	y	PROPN
ejpam-4446	281	10	∗	∗	PROPN
ejpam-4446	281	11	z	z	NOUN
ejpam-4446	281	12	)	)	PUNCT
ejpam-4446	281	13	)	)	PUNCT
ejpam-4446	281	14	∗	∗	PROPN
ejpam-4446	281	15	z	z	NOUN
ejpam-4446	281	16	)	)	PUNCT
ejpam-4446	281	17	≥	≥	PROPN
ejpam-4446	281	18	min	min	PROPN
ejpam-4446	281	19	{	{	PUNCT
ejpam-4446	281	20	lε	lε	PART
ejpam-4446	281	21	ξ((x	ξ((x	VERB
ejpam-4446	281	22	∗	∗	NOUN
ejpam-4446	281	23	(	(	PUNCT
ejpam-4446	281	24	y	y	PROPN
ejpam-4446	281	25	∗	∗	PROPN
ejpam-4446	281	26	z	z	NOUN
ejpam-4446	281	27	)	)	PUNCT
ejpam-4446	281	28	)	)	PUNCT
ejpam-4446	281	29	∗	∗	NOUN
ejpam-4446	281	30	(	(	PUNCT
ejpam-4446	281	31	y	y	PROPN
ejpam-4446	281	32	∗	∗	PROPN
ejpam-4446	281	33	z	z	PROPN
ejpam-4446	281	34	)	)	PUNCT
ejpam-4446	281	35	)	)	PUNCT
ejpam-4446	281	36	,	,	PUNCT
ejpam-4446	281	37	lε	lε	ADP
ejpam-4446	281	38	ξ(y	ξ(y	PROPN
ejpam-4446	281	39	)	)	PUNCT
ejpam-4446	281	40	}	}	PUNCT
ejpam-4446	281	41	≥	≥	X
ejpam-4446	281	42	min{min	min{min	NOUN
ejpam-4446	281	43	{	{	PUNCT
ejpam-4446	281	44	lε	lε	ADP
ejpam-4446	281	45	ξ(x	ξ(x	NOUN
ejpam-4446	281	46	∗	∗	NOUN
ejpam-4446	281	47	(	(	PUNCT
ejpam-4446	281	48	(	(	PUNCT
ejpam-4446	281	49	x	x	SYM
ejpam-4446	281	50	∗	∗	NOUN
ejpam-4446	281	51	(	(	PUNCT
ejpam-4446	281	52	y	y	PROPN
ejpam-4446	281	53	∗	∗	PROPN
ejpam-4446	281	54	z	z	NOUN
ejpam-4446	281	55	)	)	PUNCT
ejpam-4446	281	56	)	)	PUNCT
ejpam-4446	282	1	∗	∗	NOUN
ejpam-4446	282	2	(	(	PUNCT
ejpam-4446	282	3	y	y	PROPN
ejpam-4446	282	4	∗	∗	PROPN
ejpam-4446	282	5	z	z	PROPN
ejpam-4446	282	6	)	)	PUNCT
ejpam-4446	282	7	)	)	PUNCT
ejpam-4446	282	8	,	,	PUNCT
ejpam-4446	282	9	lε	lε	ADP
ejpam-4446	282	10	ξ(x	ξ(x	NOUN
ejpam-4446	282	11	)	)	PUNCT
ejpam-4446	282	12	)	)	PUNCT
ejpam-4446	282	13	}	}	PUNCT
ejpam-4446	282	14	,	,	PUNCT
ejpam-4446	282	15	lε	lε	ADP
ejpam-4446	282	16	ξ(y	ξ(y	PROPN
ejpam-4446	282	17	)	)	PUNCT
ejpam-4446	282	18	}	}	PUNCT
ejpam-4446	283	1	=	=	SYM
ejpam-4446	283	2	min{min	min{min	ADJ
ejpam-4446	283	3	{	{	PUNCT
ejpam-4446	283	4	lε	lε	PROPN
ejpam-4446	283	5	ξ(1	ξ(1	PROPN
ejpam-4446	283	6	)	)	PUNCT
ejpam-4446	283	7	,	,	PUNCT
ejpam-4446	283	8	lε	lε	ADP
ejpam-4446	283	9	ξ(x	ξ(x	NOUN
ejpam-4446	283	10	)	)	PUNCT
ejpam-4446	283	11	}	}	PUNCT
ejpam-4446	283	12	,	,	PUNCT
ejpam-4446	283	13	lε	lε	ADP
ejpam-4446	283	14	ξ(y	ξ(y	PROPN
ejpam-4446	283	15	)	)	PUNCT
ejpam-4446	283	16	}	}	PUNCT
ejpam-4446	283	17	=	=	SYM
ejpam-4446	283	18	min	min	X
ejpam-4446	283	19	{	{	PUNCT
ejpam-4446	283	20	lε	lε	ADP
ejpam-4446	283	21	ξ(x	ξ(x	PROPN
ejpam-4446	283	22	)	)	PUNCT
ejpam-4446	283	23	,	,	PUNCT
ejpam-4446	283	24	lε	lε	ADP
ejpam-4446	283	25	ξ(y	ξ(y	PROPN
ejpam-4446	283	26	)	)	PUNCT
ejpam-4446	283	27	}	}	PUNCT
ejpam-4446	283	28	by	by	ADP
ejpam-4446	283	29	(	(	PUNCT
ejpam-4446	283	30	3	3	NUM
ejpam-4446	283	31	)	)	PUNCT
ejpam-4446	283	32	,	,	PUNCT
ejpam-4446	283	33	theorem	theorem	VERB
ejpam-4446	283	34	13	13	NUM
ejpam-4446	283	35	and	and	CCONJ
ejpam-4446	283	36	theorem	theorem	VERB
ejpam-4446	283	37	14	14	NUM
ejpam-4446	283	38	.	.	PUNCT
ejpam-4446	284	1	conversely	conversely	ADV
ejpam-4446	284	2	,	,	PUNCT
ejpam-4446	284	3	suppose	suppose	VERB
ejpam-4446	284	4	that	that	SCONJ
ejpam-4446	284	5	lε	lε	PROPN
ejpam-4446	284	6	ξ	ξ	X
ejpam-4446	284	7	satisfies	satisfie	NOUN
ejpam-4446	284	8	(	(	PUNCT
ejpam-4446	284	9	24	24	NUM
ejpam-4446	284	10	)	)	PUNCT
ejpam-4446	284	11	and	and	CCONJ
ejpam-4446	284	12	(	(	PUNCT
ejpam-4446	284	13	25	25	NUM
ejpam-4446	284	14	)	)	PUNCT
ejpam-4446	284	15	.	.	PUNCT
ejpam-4446	285	1	if	if	SCONJ
ejpam-4446	285	2	we	we	PRON
ejpam-4446	285	3	take	take	VERB
ejpam-4446	285	4	y	y	NOUN
ejpam-4446	285	5	=	=	PUNCT
ejpam-4446	286	1	x	x	PROPN
ejpam-4446	286	2	in	in	ADP
ejpam-4446	286	3	(	(	PUNCT
ejpam-4446	286	4	24	24	NUM
ejpam-4446	286	5	)	)	PUNCT
ejpam-4446	286	6	and	and	CCONJ
ejpam-4446	286	7	use	use	NOUN
ejpam-4446	286	8	(	(	PUNCT
ejpam-4446	286	9	be1	be1	NOUN
ejpam-4446	286	10	)	)	PUNCT
ejpam-4446	286	11	,	,	PUNCT
ejpam-4446	286	12	then	then	ADV
ejpam-4446	286	13	lε	lε	ADP
ejpam-4446	286	14	ξ(1	ξ(1	PROPN
ejpam-4446	286	15	)	)	PUNCT
ejpam-4446	286	16	=	=	PRON
ejpam-4446	286	17	lε	lε	ADP
ejpam-4446	286	18	ξ(x	ξ(x	PROPN
ejpam-4446	286	19	∗	∗	NOUN
ejpam-4446	286	20	x	x	NOUN
ejpam-4446	286	21	)	)	PUNCT
ejpam-4446	286	22	≥	≥	NOUN
ejpam-4446	286	23	lε	lε	ADP
ejpam-4446	286	24	ξ(x	ξ(x	PROPN
ejpam-4446	286	25	)	)	PUNCT
ejpam-4446	286	26	for	for	ADP
ejpam-4446	286	27	all	all	DET
ejpam-4446	286	28	x	x	SYM
ejpam-4446	286	29	∈	∈	PROPN
ejpam-4446	286	30	x	x	NOUN
ejpam-4446	286	31	,	,	PUNCT
ejpam-4446	286	32	that	that	ADV
ejpam-4446	286	33	is	is	ADV
ejpam-4446	286	34	,	,	PUNCT
ejpam-4446	286	35	lε	lε	X
ejpam-4446	286	36	ξ(1	ξ(1	PROPN
ejpam-4446	286	37	)	)	PUNCT
ejpam-4446	286	38	is	be	AUX
ejpam-4446	286	39	an	an	DET
ejpam-4446	286	40	upper	upper	ADJ
ejpam-4446	286	41	bound	bind	VERB
ejpam-4446	286	42	of	of	ADP
ejpam-4446	286	43	{	{	PUNCT
ejpam-4446	286	44	lε	lε	X
ejpam-4446	286	45	ξ(x	ξ(x	NOUN
ejpam-4446	286	46	)	)	PUNCT
ejpam-4446	287	1	|	|	ADV
ejpam-4446	287	2	x	x	SYM
ejpam-4446	287	3	∈	∈	NOUN
ejpam-4446	287	4	x	x	X
ejpam-4446	287	5	}	}	PUNCT
ejpam-4446	287	6	.	.	PUNCT
ejpam-4446	288	1	the	the	DET
ejpam-4446	288	2	combination	combination	NOUN
ejpam-4446	288	3	of	of	ADP
ejpam-4446	288	4	(	(	PUNCT
ejpam-4446	288	5	be1	be1	NOUN
ejpam-4446	288	6	)	)	PUNCT
ejpam-4446	288	7	,	,	PUNCT
ejpam-4446	288	8	(	(	PUNCT
ejpam-4446	288	9	be3	be3	PROPN
ejpam-4446	288	10	)	)	PUNCT
ejpam-4446	288	11	and	and	CCONJ
ejpam-4446	288	12	(	(	PUNCT
ejpam-4446	288	13	25	25	NUM
ejpam-4446	288	14	)	)	PUNCT
ejpam-4446	288	15	induces	induce	VERB
ejpam-4446	288	16	lε	lε	ADP
ejpam-4446	288	17	ξ(y	ξ(y	PROPN
ejpam-4446	288	18	)	)	PUNCT
ejpam-4446	289	1	=	=	PRON
ejpam-4446	289	2	lε	lε	PRON
ejpam-4446	289	3	ξ(1	ξ(1	PROPN
ejpam-4446	289	4	∗	∗	PROPN
ejpam-4446	289	5	y	y	PROPN
ejpam-4446	289	6	)	)	PUNCT
ejpam-4446	290	1	=	=	NOUN
ejpam-4446	290	2	lε	lε	X
ejpam-4446	290	3	ξ(((x	ξ(((x	PROPN
ejpam-4446	290	4	∗	∗	NOUN
ejpam-4446	290	5	y	y	NOUN
ejpam-4446	290	6	)	)	PUNCT
ejpam-4446	290	7	∗	∗	NOUN
ejpam-4446	290	8	(	(	PUNCT
ejpam-4446	290	9	x	x	X
ejpam-4446	290	10	∗	∗	PROPN
ejpam-4446	290	11	y	y	PROPN
ejpam-4446	290	12	)	)	PUNCT
ejpam-4446	290	13	)	)	PUNCT
ejpam-4446	290	14	∗	∗	PROPN
ejpam-4446	290	15	y	y	PROPN
ejpam-4446	290	16	)	)	PUNCT
ejpam-4446	290	17	≥	≥	PROPN
ejpam-4446	290	18	min	min	PROPN
ejpam-4446	290	19	{	{	PUNCT
ejpam-4446	290	20	lε	lε	ADP
ejpam-4446	290	21	ξ(x	ξ(x	PROPN
ejpam-4446	290	22	∗	∗	X
ejpam-4446	290	23	y	y	PROPN
ejpam-4446	290	24	)	)	PUNCT
ejpam-4446	290	25	,	,	PUNCT
ejpam-4446	290	26	lε	lε	ADP
ejpam-4446	290	27	ξ(x	ξ(x	NOUN
ejpam-4446	290	28	)	)	PUNCT
ejpam-4446	290	29	}	}	PUNCT
ejpam-4446	290	30	for	for	ADP
ejpam-4446	290	31	all	all	DET
ejpam-4446	290	32	x	x	NOUN
ejpam-4446	290	33	,	,	PUNCT
ejpam-4446	290	34	y	y	PROPN
ejpam-4446	290	35	∈	∈	PROPN
ejpam-4446	290	36	x.	x.	NOUN
ejpam-4446	291	1	it	it	PRON
ejpam-4446	291	2	follows	follow	VERB
ejpam-4446	291	3	from	from	ADP
ejpam-4446	291	4	theorem	theorem	ADJ
ejpam-4446	291	5	13	13	NUM
ejpam-4446	291	6	that	that	PRON
ejpam-4446	291	7	lε	lε	ADP
ejpam-4446	291	8	ξ	ξ	PROPN
ejpam-4446	291	9	is	be	AUX
ejpam-4446	291	10	a	a	DET
ejpam-4446	291	11	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	291	12	fuzzy	fuzzy	ADJ
ejpam-4446	291	13	be	be	NOUN
ejpam-4446	291	14	-	-	PUNCT
ejpam-4446	291	15	filter	filter	NOUN
ejpam-4446	291	16	of	of	ADP
ejpam-4446	291	17	x.	x.	NOUN
ejpam-4446	291	18	corollary	corollary	PROPN
ejpam-4446	291	19	5	5	NUM
ejpam-4446	291	20	.	.	PUNCT
ejpam-4446	292	1	if	if	SCONJ
ejpam-4446	292	2	ξ	ξ	PROPN
ejpam-4446	292	3	is	be	AUX
ejpam-4446	292	4	a	a	DET
ejpam-4446	292	5	fuzzy	fuzzy	ADJ
ejpam-4446	292	6	be	be	NOUN
ejpam-4446	292	7	-	-	PUNCT
ejpam-4446	292	8	filter	filter	NOUN
ejpam-4446	292	9	of	of	ADP
ejpam-4446	292	10	x	x	NOUN
ejpam-4446	292	11	,	,	PUNCT
ejpam-4446	292	12	then	then	ADV
ejpam-4446	292	13	its	its	PRON
ejpam-4446	292	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	292	15	fuzzy	fuzzy	NOUN
ejpam-4446	292	16	set	set	VERB
ejpam-4446	292	17	lε	lε	AUX
ejpam-4446	292	18	ξ	ξ	X
ejpam-4446	292	19	satisfies	satisfie	NOUN
ejpam-4446	292	20	(	(	PUNCT
ejpam-4446	292	21	24	24	NUM
ejpam-4446	292	22	)	)	PUNCT
ejpam-4446	292	23	and	and	CCONJ
ejpam-4446	292	24	(	(	PUNCT
ejpam-4446	292	25	25	25	NUM
ejpam-4446	292	26	)	)	PUNCT
ejpam-4446	292	27	.	.	PUNCT
ejpam-4446	293	1	theorem	theorem	VERB
ejpam-4446	293	2	16	16	NUM
ejpam-4446	293	3	.	.	PUNCT
ejpam-4446	294	1	the	the	DET
ejpam-4446	294	2	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	294	3	fuzzy	fuzzy	NOUN
ejpam-4446	294	4	set	set	VERB
ejpam-4446	294	5	lε	lε	ADP
ejpam-4446	294	6	ξ	ξ	PROPN
ejpam-4446	294	7	of	of	ADP
ejpam-4446	294	8	ξ	ξ	PROPN
ejpam-4446	294	9	is	be	AUX
ejpam-4446	294	10	a	a	DET
ejpam-4446	294	11	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	294	12	fuzzy	fuzzy	ADJ
ejpam-4446	294	13	be	be	NOUN
ejpam-4446	294	14	-	-	PUNCT
ejpam-4446	294	15	filter	filter	NOUN
ejpam-4446	294	16	of	of	ADP
ejpam-4446	294	17	x	x	SYM
ejpam-4446	294	18	if	if	SCONJ
ejpam-4446	294	19	and	and	CCONJ
ejpam-4446	294	20	only	only	ADV
ejpam-4446	294	21	if	if	SCONJ
ejpam-4446	294	22	it	it	PRON
ejpam-4446	294	23	satisfies	satisfy	VERB
ejpam-4446	294	24	the	the	DET
ejpam-4446	294	25	condition	condition	NOUN
ejpam-4446	294	26	(	(	PUNCT
ejpam-4446	294	27	21	21	NUM
ejpam-4446	294	28	)	)	PUNCT
ejpam-4446	294	29	and	and	CCONJ
ejpam-4446	294	30	(	(	PUNCT
ejpam-4446	294	31	∀x	∀x	NUM
ejpam-4446	294	32	,	,	PUNCT
ejpam-4446	294	33	y	y	PROPN
ejpam-4446	294	34	,	,	PUNCT
ejpam-4446	294	35	z	z	NOUN
ejpam-4446	294	36	∈	∈	PROPN
ejpam-4446	294	37	x	x	X
ejpam-4446	294	38	)	)	PUNCT
ejpam-4446	294	39	(	(	PUNCT
ejpam-4446	294	40	x	x	SYM
ejpam-4446	294	41	∗	∗	NOUN
ejpam-4446	294	42	(	(	PUNCT
ejpam-4446	294	43	y	y	PROPN
ejpam-4446	294	44	∗	∗	PROPN
ejpam-4446	294	45	z	z	NOUN
ejpam-4446	294	46	)	)	PUNCT
ejpam-4446	294	47	=	=	SYM
ejpam-4446	294	48	1	1	NUM
ejpam-4446	294	49	⇒	⇒	NOUN
ejpam-4446	294	50	lε	lε	ADP
ejpam-4446	294	51	ξ(z	ξ(z	PROPN
ejpam-4446	294	52	)	)	PUNCT
ejpam-4446	294	53	≥	≥	NOUN
ejpam-4446	294	54	min	min	PROPN
ejpam-4446	294	55	{	{	PUNCT
ejpam-4446	294	56	lε	lε	ADP
ejpam-4446	294	57	ξ(x	ξ(x	PROPN
ejpam-4446	294	58	)	)	PUNCT
ejpam-4446	294	59	,	,	PUNCT
ejpam-4446	294	60	lε	lε	ADP
ejpam-4446	294	61	ξ(y	ξ(y	PROPN
ejpam-4446	294	62	)	)	PUNCT
ejpam-4446	294	63	}	}	PUNCT
ejpam-4446	294	64	)	)	PUNCT
ejpam-4446	294	65	.	.	PUNCT
ejpam-4446	295	1	(	(	PUNCT
ejpam-4446	295	2	26	26	NUM
ejpam-4446	295	3	)	)	PUNCT
ejpam-4446	295	4	proof	proof	NOUN
ejpam-4446	295	5	.	.	PUNCT
ejpam-4446	296	1	assume	assume	VERB
ejpam-4446	296	2	that	that	SCONJ
ejpam-4446	296	3	lε	lε	X
ejpam-4446	296	4	ξ	ξ	PROPN
ejpam-4446	296	5	is	be	AUX
ejpam-4446	296	6	a	a	DET
ejpam-4446	296	7	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	296	8	fuzzy	fuzzy	ADJ
ejpam-4446	296	9	be	be	NOUN
ejpam-4446	296	10	-	-	PUNCT
ejpam-4446	296	11	filter	filter	NOUN
ejpam-4446	296	12	of	of	ADP
ejpam-4446	296	13	x.	x.	NOUN
ejpam-4446	296	14	the	the	DET
ejpam-4446	296	15	condition	condition	NOUN
ejpam-4446	296	16	(	(	PUNCT
ejpam-4446	296	17	21	21	NUM
ejpam-4446	296	18	)	)	PUNCT
ejpam-4446	296	19	was	be	AUX
ejpam-4446	296	20	verified	verify	VERB
ejpam-4446	296	21	by	by	ADP
ejpam-4446	296	22	the	the	DET
ejpam-4446	296	23	proof	proof	NOUN
ejpam-4446	296	24	of	of	ADP
ejpam-4446	296	25	theorem	theorem	NOUN
ejpam-4446	296	26	13	13	NUM
ejpam-4446	296	27	.	.	PUNCT
ejpam-4446	297	1	let	let	VERB
ejpam-4446	297	2	x	x	PRON
ejpam-4446	297	3	,	,	PUNCT
ejpam-4446	297	4	y	y	PROPN
ejpam-4446	297	5	,	,	PUNCT
ejpam-4446	297	6	z	z	NOUN
ejpam-4446	297	7	∈	∈	PROPN
ejpam-4446	297	8	x	x	AUX
ejpam-4446	297	9	be	be	AUX
ejpam-4446	297	10	such	such	ADJ
ejpam-4446	297	11	that	that	SCONJ
ejpam-4446	297	12	x	x	SYM
ejpam-4446	297	13	∗	∗	NOUN
ejpam-4446	297	14	(	(	PUNCT
ejpam-4446	297	15	y	y	PROPN
ejpam-4446	297	16	∗	∗	PROPN
ejpam-4446	297	17	z	z	NOUN
ejpam-4446	297	18	)	)	PUNCT
ejpam-4446	297	19	=	=	SYM
ejpam-4446	298	1	1	1	X
ejpam-4446	298	2	.	.	X
ejpam-4446	298	3	using	use	VERB
ejpam-4446	298	4	theorem	theorem	NOUN
ejpam-4446	298	5	13	13	NUM
ejpam-4446	298	6	,	,	PUNCT
ejpam-4446	298	7	we	we	PRON
ejpam-4446	298	8	have	have	VERB
ejpam-4446	298	9	lε	lε	ADP
ejpam-4446	298	10	ξ(y	ξ(y	PROPN
ejpam-4446	298	11	∗	∗	NOUN
ejpam-4446	298	12	z	z	PROPN
ejpam-4446	298	13	)	)	PUNCT
ejpam-4446	298	14	≥	≥	PROPN
ejpam-4446	298	15	min	min	PROPN
ejpam-4446	298	16	{	{	PUNCT
ejpam-4446	298	17	lε	lε	ADP
ejpam-4446	298	18	ξ(x	ξ(x	NOUN
ejpam-4446	298	19	∗	∗	NOUN
ejpam-4446	298	20	(	(	PUNCT
ejpam-4446	298	21	y	y	PROPN
ejpam-4446	298	22	∗	∗	PROPN
ejpam-4446	298	23	z	z	PROPN
ejpam-4446	298	24	)	)	PUNCT
ejpam-4446	298	25	)	)	PUNCT
ejpam-4446	298	26	,	,	PUNCT
ejpam-4446	298	27	lε	lε	ADP
ejpam-4446	298	28	ξ(x	ξ(x	NOUN
ejpam-4446	298	29	)	)	PUNCT
ejpam-4446	298	30	}	}	PUNCT
ejpam-4446	298	31	=	=	SYM
ejpam-4446	298	32	min	min	X
ejpam-4446	298	33	{	{	PUNCT
ejpam-4446	298	34	lε	lε	X
ejpam-4446	298	35	ξ(1	ξ(1	PROPN
ejpam-4446	298	36	)	)	PUNCT
ejpam-4446	298	37	,	,	PUNCT
ejpam-4446	298	38	lε	lε	ADP
ejpam-4446	298	39	ξ(x	ξ(x	NOUN
ejpam-4446	298	40	)	)	PUNCT
ejpam-4446	298	41	}	}	PUNCT
ejpam-4446	298	42	=	=	PUNCT
ejpam-4446	298	43	lε	lε	PRON
ejpam-4446	298	44	ξ(x	ξ(x	NOUN
ejpam-4446	298	45	)	)	PUNCT
ejpam-4446	298	46	and	and	CCONJ
ejpam-4446	298	47	so	so	ADV
ejpam-4446	298	48	lε	lε	ADP
ejpam-4446	298	49	ξ(z	ξ(z	PROPN
ejpam-4446	298	50	)	)	PUNCT
ejpam-4446	298	51	≥	≥	NOUN
ejpam-4446	298	52	min	min	NOUN
ejpam-4446	298	53	{	{	PUNCT
ejpam-4446	298	54	lε	lε	ADP
ejpam-4446	298	55	ξ(y	ξ(y	PROPN
ejpam-4446	298	56	∗	∗	NOUN
ejpam-4446	298	57	z	z	PROPN
ejpam-4446	298	58	)	)	PUNCT
ejpam-4446	298	59	,	,	PUNCT
ejpam-4446	298	60	lε	lε	ADP
ejpam-4446	298	61	ξ(y	ξ(y	PROPN
ejpam-4446	298	62	)	)	PUNCT
ejpam-4446	298	63	}	}	PUNCT
ejpam-4446	298	64	≥	≥	PROPN
ejpam-4446	298	65	min	min	NOUN
ejpam-4446	298	66	{	{	PUNCT
ejpam-4446	298	67	lε	lε	ADP
ejpam-4446	298	68	ξ(x	ξ(x	PROPN
ejpam-4446	298	69	)	)	PUNCT
ejpam-4446	298	70	,	,	PUNCT
ejpam-4446	298	71	lε	lε	ADP
ejpam-4446	298	72	ξ(y	ξ(y	PROPN
ejpam-4446	298	73	)	)	PUNCT
ejpam-4446	298	74	}	}	PUNCT
ejpam-4446	298	75	.	.	PUNCT
ejpam-4446	299	1	conversely	conversely	ADV
ejpam-4446	299	2	,	,	PUNCT
ejpam-4446	299	3	suppose	suppose	VERB
ejpam-4446	299	4	that	that	SCONJ
ejpam-4446	299	5	lε	lε	PROPN
ejpam-4446	299	6	ξ	ξ	X
ejpam-4446	299	7	satisfies	satisfy	VERB
ejpam-4446	299	8	the	the	DET
ejpam-4446	299	9	condition	condition	NOUN
ejpam-4446	299	10	(	(	PUNCT
ejpam-4446	299	11	21	21	NUM
ejpam-4446	299	12	)	)	PUNCT
ejpam-4446	299	13	and	and	CCONJ
ejpam-4446	299	14	(	(	PUNCT
ejpam-4446	299	15	26	26	NUM
ejpam-4446	299	16	)	)	PUNCT
ejpam-4446	299	17	.	.	PUNCT
ejpam-4446	300	1	since	since	SCONJ
ejpam-4446	300	2	(	(	PUNCT
ejpam-4446	300	3	x∗y)∗(x∗y	x∗y)∗(x∗y	PROPN
ejpam-4446	300	4	)	)	PUNCT
ejpam-4446	300	5	=	=	SYM
ejpam-4446	300	6	1	1	NUM
ejpam-4446	300	7	for	for	ADP
ejpam-4446	300	8	all	all	DET
ejpam-4446	300	9	x	x	NOUN
ejpam-4446	300	10	,	,	PUNCT
ejpam-4446	300	11	y	y	PROPN
ejpam-4446	300	12	∈	∈	PROPN
ejpam-4446	300	13	x	x	X
ejpam-4446	300	14	,	,	PUNCT
ejpam-4446	300	15	we	we	PRON
ejpam-4446	300	16	have	have	VERB
ejpam-4446	300	17	lε	lε	ADP
ejpam-4446	300	18	ξ(y	ξ(y	PROPN
ejpam-4446	300	19	)	)	PUNCT
ejpam-4446	300	20	≥	≥	NOUN
ejpam-4446	300	21	min	min	PROPN
ejpam-4446	300	22	{	{	PUNCT
ejpam-4446	300	23	lε	lε	ADP
ejpam-4446	300	24	ξ(x	ξ(x	PROPN
ejpam-4446	300	25	∗	∗	X
ejpam-4446	300	26	y	y	PROPN
ejpam-4446	300	27	)	)	PUNCT
ejpam-4446	300	28	,	,	PUNCT
ejpam-4446	300	29	lε	lε	ADP
ejpam-4446	300	30	ξ(x	ξ(x	NOUN
ejpam-4446	300	31	)	)	PUNCT
ejpam-4446	300	32	}	}	PUNCT
ejpam-4446	300	33	for	for	ADP
ejpam-4446	300	34	all	all	DET
ejpam-4446	300	35	x	x	NOUN
ejpam-4446	300	36	,	,	PUNCT
ejpam-4446	300	37	y	y	PROPN
ejpam-4446	300	38	∈	∈	PROPN
ejpam-4446	300	39	x.	x.	NOUN
ejpam-4446	301	1	it	it	PRON
ejpam-4446	301	2	follows	follow	VERB
ejpam-4446	301	3	from	from	ADP
ejpam-4446	301	4	theorem	theorem	ADJ
ejpam-4446	301	5	13	13	NUM
ejpam-4446	301	6	that	that	PRON
ejpam-4446	301	7	lε	lε	ADP
ejpam-4446	301	8	ξ	ξ	PROPN
ejpam-4446	301	9	is	be	AUX
ejpam-4446	301	10	a	a	DET
ejpam-4446	301	11	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	301	12	fuzzy	fuzzy	ADJ
ejpam-4446	301	13	be	be	NOUN
ejpam-4446	301	14	-	-	PUNCT
ejpam-4446	301	15	filter	filter	NOUN
ejpam-4446	301	16	of	of	ADP
ejpam-4446	301	17	x.	x.	NOUN
ejpam-4446	301	18	corollary	corollary	PROPN
ejpam-4446	301	19	6	6	NUM
ejpam-4446	301	20	.	.	PUNCT
ejpam-4446	302	1	if	if	SCONJ
ejpam-4446	302	2	ξ	ξ	PROPN
ejpam-4446	302	3	is	be	AUX
ejpam-4446	302	4	a	a	DET
ejpam-4446	302	5	fuzzy	fuzzy	ADJ
ejpam-4446	302	6	be	be	NOUN
ejpam-4446	302	7	-	-	PUNCT
ejpam-4446	302	8	filter	filter	NOUN
ejpam-4446	302	9	of	of	ADP
ejpam-4446	302	10	x	x	NOUN
ejpam-4446	302	11	,	,	PUNCT
ejpam-4446	302	12	then	then	ADV
ejpam-4446	302	13	its	its	PRON
ejpam-4446	302	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	302	15	fuzzy	fuzzy	NOUN
ejpam-4446	302	16	set	set	VERB
ejpam-4446	302	17	lε	lε	AUX
ejpam-4446	302	18	ξ	ξ	X
ejpam-4446	302	19	satisfies	satisfie	NOUN
ejpam-4446	302	20	(	(	PUNCT
ejpam-4446	302	21	26	26	NUM
ejpam-4446	302	22	)	)	PUNCT
ejpam-4446	302	23	.	.	PUNCT
ejpam-4446	303	1	we	we	PRON
ejpam-4446	303	2	use	use	VERB
ejpam-4446	303	3	be	be	NOUN
ejpam-4446	303	4	-	-	PUNCT
ejpam-4446	303	5	filter	filter	NOUN
ejpam-4446	303	6	to	to	PART
ejpam-4446	303	7	create	create	VERB
ejpam-4446	303	8	a	a	DET
ejpam-4446	303	9	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	303	10	fuzzy	fuzzy	ADJ
ejpam-4446	303	11	be	be	NOUN
ejpam-4446	303	12	-	-	PUNCT
ejpam-4446	303	13	filter	filter	NOUN
ejpam-4446	303	14	.	.	PUNCT
ejpam-4446	304	1	theorem	theorem	NOUN
ejpam-4446	304	2	17	17	NUM
ejpam-4446	304	3	.	.	PUNCT
ejpam-4446	305	1	let	let	VERB
ejpam-4446	305	2	f	f	PRON
ejpam-4446	305	3	be	be	AUX
ejpam-4446	305	4	a	a	DET
ejpam-4446	305	5	be	be	NOUN
ejpam-4446	305	6	-	-	PUNCT
ejpam-4446	305	7	filter	filter	NOUN
ejpam-4446	305	8	of	of	ADP
ejpam-4446	305	9	x	x	PUNCT
ejpam-4446	305	10	and	and	CCONJ
ejpam-4446	305	11	let	let	VERB
ejpam-4446	305	12	α	α	PRON
ejpam-4446	305	13	,	,	PUNCT
ejpam-4446	305	14	β	β	X
ejpam-4446	305	15	∈	∈	PROPN
ejpam-4446	305	16	(	(	PUNCT
ejpam-4446	305	17	0	0	NUM
ejpam-4446	305	18	,	,	PUNCT
ejpam-4446	305	19	1	1	NUM
ejpam-4446	305	20	]	]	PUNCT
ejpam-4446	305	21	with	with	ADP
ejpam-4446	305	22	α	α	PROPN
ejpam-4446	305	23	≥	≥	NOUN
ejpam-4446	305	24	β	β	X
ejpam-4446	305	25	.	.	PUNCT
ejpam-4446	306	1	for	for	ADP
ejpam-4446	306	2	every	every	DET
ejpam-4446	306	3	ε	ε	PROPN
ejpam-4446	306	4	,	,	PUNCT
ejpam-4446	306	5	define	define	VERB
ejpam-4446	306	6	the	the	DET
ejpam-4446	306	7	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	306	8	fuzzy	fuzzy	NOUN
ejpam-4446	306	9	set	set	VERB
ejpam-4446	306	10	lε	lε	ADP
ejpam-4446	306	11	ξ	ξ	PROPN
ejpam-4446	306	12	of	of	ADP
ejpam-4446	306	13	ξ	ξ	PROPN
ejpam-4446	306	14	in	in	ADP
ejpam-4446	306	15	x	x	PUNCT
ejpam-4446	306	16	as	as	SCONJ
ejpam-4446	306	17	follows	follow	VERB
ejpam-4446	306	18	:	:	PUNCT
ejpam-4446	306	19	lε	lε	ADP
ejpam-4446	306	20	ξ	ξ	X
ejpam-4446	306	21	:	:	PUNCT
ejpam-4446	306	22	x	x	SYM
ejpam-4446	306	23	→	→	SYM
ejpam-4446	307	1	[	[	X
ejpam-4446	307	2	0	0	NUM
ejpam-4446	307	3	,	,	PUNCT
ejpam-4446	307	4	1	1	NUM
ejpam-4446	307	5	]	]	PUNCT
ejpam-4446	307	6	,	,	PUNCT
ejpam-4446	307	7	x	x	SYM
ejpam-4446	307	8	7→	7→	X
ejpam-4446	307	9	{	{	PUNCT
ejpam-4446	307	10	α	α	NOUN
ejpam-4446	307	11	if	if	SCONJ
ejpam-4446	307	12	x	x	PROPN
ejpam-4446	307	13	∈	∈	PROPN
ejpam-4446	307	14	f	f	PROPN
ejpam-4446	307	15	,	,	PUNCT
ejpam-4446	307	16	β	β	X
ejpam-4446	307	17	otherwise	otherwise	ADV
ejpam-4446	307	18	.	.	PUNCT
ejpam-4446	308	1	then	then	ADV
ejpam-4446	308	2	lε	lε	X
ejpam-4446	308	3	ξ	ξ	PROPN
ejpam-4446	308	4	is	be	AUX
ejpam-4446	308	5	a	a	DET
ejpam-4446	308	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	308	7	fuzzy	fuzzy	ADJ
ejpam-4446	308	8	be	be	NOUN
ejpam-4446	308	9	-	-	PUNCT
ejpam-4446	308	10	filter	filter	NOUN
ejpam-4446	308	11	of	of	ADP
ejpam-4446	308	12	x.	x.	NOUN
ejpam-4446	308	13	references	reference	NOUN
ejpam-4446	308	14	937	937	NUM
ejpam-4446	308	15	proof	proof	NOUN
ejpam-4446	308	16	.	.	PUNCT
ejpam-4446	309	1	since	since	SCONJ
ejpam-4446	309	2	1	1	NUM
ejpam-4446	309	3	∈	∈	PROPN
ejpam-4446	309	4	f	f	NOUN
ejpam-4446	309	5	,	,	PUNCT
ejpam-4446	309	6	we	we	PRON
ejpam-4446	309	7	have	have	AUX
ejpam-4446	309	8	lε	lε	VERB
ejpam-4446	309	9	ξ(1	ξ(1	PROPN
ejpam-4446	309	10	)	)	PUNCT
ejpam-4446	310	1	=	=	PUNCT
ejpam-4446	310	2	α	α	PRON
ejpam-4446	310	3	≥	≥	X
ejpam-4446	310	4	lε	lε	ADP
ejpam-4446	310	5	ξ(x	ξ(x	PROPN
ejpam-4446	310	6	)	)	PUNCT
ejpam-4446	310	7	for	for	ADP
ejpam-4446	310	8	all	all	PRON
ejpam-4446	310	9	x	x	SYM
ejpam-4446	310	10	∈	∈	NOUN
ejpam-4446	310	11	x.	x.	NOUN
ejpam-4446	310	12	hence	hence	ADV
ejpam-4446	310	13	lε	lε	PROPN
ejpam-4446	310	14	ξ(1	ξ(1	PROPN
ejpam-4446	310	15	)	)	PUNCT
ejpam-4446	310	16	is	be	AUX
ejpam-4446	310	17	an	an	DET
ejpam-4446	310	18	upper	upper	ADJ
ejpam-4446	310	19	bound	bind	VERB
ejpam-4446	310	20	of	of	ADP
ejpam-4446	310	21	{	{	PUNCT
ejpam-4446	310	22	lε	lε	X
ejpam-4446	310	23	ξ(x	ξ(x	NOUN
ejpam-4446	310	24	)	)	PUNCT
ejpam-4446	311	1	|	|	ADV
ejpam-4446	311	2	x	x	SYM
ejpam-4446	311	3	∈	∈	NOUN
ejpam-4446	311	4	x	x	X
ejpam-4446	311	5	}	}	PUNCT
ejpam-4446	311	6	.	.	PUNCT
ejpam-4446	312	1	let	let	VERB
ejpam-4446	312	2	x	x	PRON
ejpam-4446	312	3	,	,	PUNCT
ejpam-4446	312	4	y	y	PROPN
ejpam-4446	312	5	∈	∈	PROPN
ejpam-4446	312	6	x.	x.	NOUN
ejpam-4446	313	1	if	if	SCONJ
ejpam-4446	313	2	y	y	PROPN
ejpam-4446	313	3	∈	∈	PROPN
ejpam-4446	313	4	f	f	PROPN
ejpam-4446	313	5	,	,	PUNCT
ejpam-4446	313	6	then	then	ADV
ejpam-4446	313	7	lε	lε	ADP
ejpam-4446	313	8	ξ(y	ξ(y	PROPN
ejpam-4446	313	9	)	)	PUNCT
ejpam-4446	313	10	=	=	PUNCT
ejpam-4446	314	1	α	α	PRON
ejpam-4446	314	2	≥	≥	NOUN
ejpam-4446	314	3	min	min	NOUN
ejpam-4446	314	4	{	{	PUNCT
ejpam-4446	314	5	lε	lε	X
ejpam-4446	314	6	ξ(x∗y	ξ(x∗y	PROPN
ejpam-4446	314	7	)	)	PUNCT
ejpam-4446	314	8	,	,	PUNCT
ejpam-4446	314	9	lε	lε	ADP
ejpam-4446	314	10	ξ(x	ξ(x	NOUN
ejpam-4446	314	11	)	)	PUNCT
ejpam-4446	314	12	}	}	PUNCT
ejpam-4446	314	13	.	.	PUNCT
ejpam-4446	315	1	if	if	SCONJ
ejpam-4446	315	2	y	y	PROPN
ejpam-4446	315	3	/∈	/∈	PROPN
ejpam-4446	316	1	f	f	PROPN
ejpam-4446	316	2	,	,	PUNCT
ejpam-4446	316	3	then	then	ADV
ejpam-4446	316	4	x	x	X
ejpam-4446	316	5	∗	∗	NOUN
ejpam-4446	316	6	y	y	PROPN
ejpam-4446	316	7	/∈	/∈	PUNCT
ejpam-4446	317	1	f	f	PROPN
ejpam-4446	317	2	or	or	CCONJ
ejpam-4446	317	3	x	x	PROPN
ejpam-4446	317	4	/∈	/∈	PROPN
ejpam-4446	318	1	f	f	PROPN
ejpam-4446	318	2	.	.	PUNCT
ejpam-4446	319	1	hence	hence	ADV
ejpam-4446	319	2	min	min	PROPN
ejpam-4446	319	3	{	{	PUNCT
ejpam-4446	319	4	lε	lε	ADP
ejpam-4446	319	5	ξ(x	ξ(x	PROPN
ejpam-4446	319	6	∗	∗	X
ejpam-4446	319	7	y	y	PROPN
ejpam-4446	319	8	)	)	PUNCT
ejpam-4446	319	9	,	,	PUNCT
ejpam-4446	319	10	lε	lε	ADP
ejpam-4446	319	11	ξ(x	ξ(x	NOUN
ejpam-4446	319	12	)	)	PUNCT
ejpam-4446	319	13	}	}	PUNCT
ejpam-4446	320	1	=	=	PUNCT
ejpam-4446	320	2	β	β	X
ejpam-4446	320	3	=	=	PUNCT
ejpam-4446	320	4	lε	lε	PROPN
ejpam-4446	320	5	ξ(y	ξ(y	PROPN
ejpam-4446	320	6	)	)	PUNCT
ejpam-4446	320	7	.	.	PUNCT
ejpam-4446	321	1	therefore	therefore	ADV
ejpam-4446	321	2	lε	lε	X
ejpam-4446	321	3	ξ	ξ	PROPN
ejpam-4446	321	4	is	be	AUX
ejpam-4446	321	5	a	a	DET
ejpam-4446	321	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4446	321	7	fuzzy	fuzzy	ADJ
ejpam-4446	321	8	be	be	NOUN
ejpam-4446	321	9	-	-	PUNCT
ejpam-4446	321	10	filter	filter	NOUN
ejpam-4446	321	11	of	of	ADP
ejpam-4446	321	12	x	x	PUNCT
ejpam-4446	321	13	by	by	ADP
ejpam-4446	321	14	theorem	theorem	NOUN
ejpam-4446	321	15	13	13	NUM
ejpam-4446	321	16	.	.	PUNCT
ejpam-4446	322	1	acknowledgements	acknowledgement	NOUN
ejpam-4446	322	2	the	the	DET
ejpam-4446	322	3	authors	author	NOUN
ejpam-4446	322	4	wish	wish	VERB
ejpam-4446	322	5	to	to	PART
ejpam-4446	322	6	thank	thank	VERB
ejpam-4446	322	7	the	the	DET
ejpam-4446	322	8	anonymous	anonymous	ADJ
ejpam-4446	322	9	reviewers	reviewer	NOUN
ejpam-4446	322	10	for	for	ADP
ejpam-4446	322	11	their	their	PRON
ejpam-4446	322	12	valuable	valuable	ADJ
ejpam-4446	322	13	suggestions	suggestion	NOUN
ejpam-4446	322	14	.	.	PUNCT
ejpam-4446	323	1	references	reference	NOUN
ejpam-4446	323	2	[	[	X
ejpam-4446	323	3	1	1	NUM
ejpam-4446	323	4	]	]	SYM
ejpam-4446	323	5	g.dymek	g.dymek	NOUN
ejpam-4446	323	6	and	and	CCONJ
ejpam-4446	323	7	a.	a.	PROPN
ejpam-4446	323	8	walendiziak	walendiziak	PROPN
ejpam-4446	323	9	.	.	PUNCT
ejpam-4446	324	1	fuzzy	fuzzy	ADJ
ejpam-4446	324	2	filters	filter	NOUN
ejpam-4446	324	3	of	of	ADP
ejpam-4446	324	4	be	be	NOUN
ejpam-4446	324	5	-	-	PUNCT
ejpam-4446	324	6	algebras	algebra	NOUN
ejpam-4446	324	7	.	.	PUNCT
ejpam-4446	325	1	math	math	NOUN
ejpam-4446	325	2	.	.	PUNCT
ejpam-4446	326	1	slovaca	slovaca	PROPN
ejpam-4446	326	2	,	,	PUNCT
ejpam-4446	326	3	63:935–946	63:935–946	PROPN
ejpam-4446	326	4	,	,	PUNCT
ejpam-4446	326	5	2013	2013	NUM
ejpam-4446	326	6	.	.	PUNCT
ejpam-4446	327	1	[	[	X
ejpam-4446	327	2	2	2	X
ejpam-4446	327	3	]	]	X
ejpam-4446	327	4	y.	y.	PROPN
ejpam-4446	327	5	b.	b.	PROPN
ejpam-4446	327	6	jun	jun	PROPN
ejpam-4446	327	7	.	.	PROPN
ejpam-4446	327	8	lukasiewicz	lukasiewicz	PROPN
ejpam-4446	327	9	fuzzy	fuzzy	ADJ
ejpam-4446	327	10	subalgebrs	subalgebrs	ADJ
ejpam-4446	327	11	in	in	ADP
ejpam-4446	327	12	bck	bck	PROPN
ejpam-4446	327	13	-	-	PUNCT
ejpam-4446	327	14	algebras	algebras	PROPN
ejpam-4446	327	15	and	and	CCONJ
ejpam-4446	327	16	bci	bci	NOUN
ejpam-4446	327	17	-	-	PUNCT
ejpam-4446	327	18	algebras	algebras	PROPN
ejpam-4446	327	19	.	.	PUNCT
ejpam-4446	328	1	ann	ann	PROPN
ejpam-4446	328	2	.	.	PUNCT
ejpam-4446	328	3	fuzzy	fuzzy	ADJ
ejpam-4446	328	4	math	math	NOUN
ejpam-4446	328	5	.	.	PUNCT
ejpam-4446	329	1	inform	inform	NOUN
ejpam-4446	329	2	.	.	PUNCT
ejpam-4446	329	3	,	,	PUNCT
ejpam-4446	329	4	23(2):213–223	23(2):213–223	NOUN
ejpam-4446	329	5	,	,	PUNCT
ejpam-4446	329	6	2022	2022	NUM
ejpam-4446	329	7	.	.	PUNCT
ejpam-4446	330	1	[	[	X
ejpam-4446	330	2	3	3	X
ejpam-4446	330	3	]	]	PUNCT
ejpam-4446	330	4	h.	h.	PROPN
ejpam-4446	330	5	s.	s.	PROPN
ejpam-4446	330	6	kim	kim	PROPN
ejpam-4446	330	7	and	and	CCONJ
ejpam-4446	330	8	y.	y.	PROPN
ejpam-4446	330	9	h.	h.	PROPN
ejpam-4446	330	10	kim	kim	PROPN
ejpam-4446	330	11	.	.	PUNCT
ejpam-4446	331	1	on	on	ADP
ejpam-4446	331	2	be	be	AUX
ejpam-4446	331	3	-	-	PUNCT
ejpam-4446	331	4	algebras	algebra	NOUN
ejpam-4446	331	5	.	.	PUNCT
ejpam-4446	331	6	sci	sci	PROPN
ejpam-4446	331	7	.	.	PROPN
ejpam-4446	331	8	math	math	PROPN
ejpam-4446	331	9	.	.	PUNCT
ejpam-4446	332	1	jpn	jpn	PROPN
ejpam-4446	332	2	.	.	PROPN
ejpam-4446	332	3	,	,	PUNCT
ejpam-4446	332	4	66:113–116	66:113–116	PROPN
ejpam-4446	332	5	,	,	PUNCT
ejpam-4446	332	6	2007	2007	NUM
ejpam-4446	332	7	.	.	PUNCT
ejpam-4446	333	1	[	[	X
ejpam-4446	333	2	4	4	X
ejpam-4446	333	3	]	]	PUNCT
ejpam-4446	333	4	h.	h.	PROPN
ejpam-4446	333	5	s.	s.	PROPN
ejpam-4446	333	6	kim	kim	PROPN
ejpam-4446	333	7	and	and	CCONJ
ejpam-4446	333	8	k.	k.	PROPN
ejpam-4446	333	9	j.	j.	PROPN
ejpam-4446	333	10	lee	lee	PROPN
ejpam-4446	333	11	.	.	PROPN
ejpam-4446	333	12	extended	extend	VERB
ejpam-4446	333	13	upper	upper	ADJ
ejpam-4446	333	14	sets	set	NOUN
ejpam-4446	333	15	in	in	ADP
ejpam-4446	333	16	be	be	NOUN
ejpam-4446	333	17	-	-	PUNCT
ejpam-4446	333	18	algebras	algebra	NOUN
ejpam-4446	333	19	.	.	PUNCT
ejpam-4446	334	1	bull	bull	NOUN
ejpam-4446	334	2	.	.	PUNCT
ejpam-4446	335	1	malays	malays	PROPN
ejpam-4446	335	2	.	.	PUNCT
ejpam-4446	336	1	math	math	NOUN
ejpam-4446	336	2	.	.	PUNCT
ejpam-4446	337	1	sci	sci	PROPN
ejpam-4446	337	2	.	.	PROPN
ejpam-4446	337	3	soc	soc	PROPN
ejpam-4446	337	4	.	.	PUNCT
ejpam-4446	337	5	,	,	PUNCT
ejpam-4446	338	1	34:511–520	34:511–520	PROPN
ejpam-4446	338	2	,	,	PUNCT
ejpam-4446	338	3	2011	2011	NUM
ejpam-4446	338	4	.	.	PUNCT
ejpam-4446	339	1	[	[	X
ejpam-4446	339	2	5	5	X
ejpam-4446	339	3	]	]	PUNCT
ejpam-4446	339	4	p.	p.	NOUN
ejpam-4446	339	5	m.	m.	NOUN
ejpam-4446	339	6	pu	pu	PROPN
ejpam-4446	339	7	and	and	CCONJ
ejpam-4446	339	8	y.	y.	PROPN
ejpam-4446	339	9	m.	m.	PROPN
ejpam-4446	339	10	liu	liu	PROPN
ejpam-4446	339	11	.	.	PROPN
ejpam-4446	340	1	fuzzy	fuzzy	ADJ
ejpam-4446	340	2	topology	topology	NOUN
ejpam-4446	340	3	i	i	PRON
ejpam-4446	340	4	,	,	PUNCT
ejpam-4446	340	5	neighborhood	neighborhood	NOUN
ejpam-4446	340	6	structure	structure	NOUN
ejpam-4446	340	7	of	of	ADP
ejpam-4446	340	8	a	a	DET
ejpam-4446	340	9	fuzzy	fuzzy	ADJ
ejpam-4446	340	10	point	point	NOUN
ejpam-4446	340	11	and	and	CCONJ
ejpam-4446	340	12	moore	moore	PROPN
ejpam-4446	340	13	-	-	PUNCT
ejpam-4446	340	14	smith	smith	PROPN
ejpam-4446	340	15	convergence	convergence	NOUN
ejpam-4446	340	16	.	.	PUNCT
ejpam-4446	341	1	j.	j.	PROPN
ejpam-4446	341	2	math	math	PROPN
ejpam-4446	341	3	.	.	PUNCT
ejpam-4446	342	1	anal	anal	PROPN
ejpam-4446	342	2	.	.	PUNCT
ejpam-4446	343	1	appl	appl	PROPN
ejpam-4446	343	2	.	.	PROPN
ejpam-4446	343	3	,	,	PUNCT
ejpam-4446	344	1	76:571–599	76:571–599	NUM
ejpam-4446	344	2	,	,	PUNCT
ejpam-4446	344	3	1980	1980	NUM
ejpam-4446	344	4	.	.	PUNCT
ejpam-4446	345	1	[	[	X
ejpam-4446	345	2	6	6	NUM
ejpam-4446	345	3	]	]	PUNCT
ejpam-4446	345	4	a.	a.	NOUN
ejpam-4446	345	5	rezaei	rezaei	NOUN
ejpam-4446	345	6	and	and	CCONJ
ejpam-4446	345	7	a.	a.	PROPN
ejpam-4446	345	8	borumand	borumand	PROPN
ejpam-4446	345	9	saeid	saeid	PROPN
ejpam-4446	345	10	.	.	PUNCT
ejpam-4446	346	1	on	on	ADP
ejpam-4446	346	2	fuzzy	fuzzy	ADJ
ejpam-4446	346	3	subalgebras	subalgebra	NOUN
ejpam-4446	346	4	of	of	ADP
ejpam-4446	346	5	be	be	AUX
ejpam-4446	346	6	-	-	PUNCT
ejpam-4446	346	7	algebras	algebra	NOUN
ejpam-4446	346	8	.	.	PUNCT
ejpam-4446	346	9	afr	afr	PROPN
ejpam-4446	346	10	.	.	PUNCT
ejpam-4446	347	1	mat	mat	PROPN
ejpam-4446	347	2	.	.	PROPN
ejpam-4446	347	3	,	,	PUNCT
ejpam-4446	347	4	22:115–127	22:115–127	PROPN
ejpam-4446	347	5	,	,	PUNCT
ejpam-4446	347	6	2011	2011	NUM
ejpam-4446	347	7	.	.	PUNCT
ejpam-4446	348	1	[	[	X
ejpam-4446	348	2	7	7	X
ejpam-4446	348	3	]	]	X
ejpam-4446	348	4	y.	y.	PROPN
ejpam-4446	348	5	h.	h.	PROPN
ejpam-4446	348	6	kim	kim	PROPN
ejpam-4446	348	7	s.	s.	PROPN
ejpam-4446	348	8	s.	s.	PROPN
ejpam-4446	348	9	ahn	ahn	PROPN
ejpam-4446	348	10	and	and	CCONJ
ejpam-4446	348	11	k.	k.	PROPN
ejpam-4446	348	12	s.	s.	PROPN
ejpam-4446	349	1	so	so	ADV
ejpam-4446	349	2	.	.	PUNCT
ejpam-4446	350	1	fuzzy	fuzzy	ADJ
ejpam-4446	350	2	be	be	AUX
ejpam-4446	350	3	-	-	PUNCT
ejpam-4446	350	4	algebras	algebra	NOUN
ejpam-4446	350	5	.	.	PROPN
ejpam-4446	350	6	,	,	PUNCT
ejpam-4446	350	7	2011	2011	NUM
ejpam-4446	350	8	.	.	PUNCT