id	sid	tid	token	lemma	pos
ejpam-4467	1	1	european	european	PROPN
ejpam-4467	1	2	journal	journal	PROPN
ejpam-4467	1	3	of	of	ADP
ejpam-4467	1	4	pure	pure	ADJ
ejpam-4467	1	5	and	and	CCONJ
ejpam-4467	1	6	applied	apply	VERB
ejpam-4467	1	7	mathematics	mathematic	NOUN
ejpam-4467	1	8	vol	vol	NOUN
ejpam-4467	1	9	.	.	PROPN
ejpam-4467	2	1	15	15	NUM
ejpam-4467	2	2	,	,	PUNCT
ejpam-4467	2	3	no	no	INTJ
ejpam-4467	2	4	.	.	NOUN
ejpam-4467	2	5	3	3	NUM
ejpam-4467	2	6	,	,	PUNCT
ejpam-4467	2	7	2022	2022	NUM
ejpam-4467	2	8	,	,	PUNCT
ejpam-4467	2	9	1307	1307	NUM
ejpam-4467	2	10	-	-	SYM
ejpam-4467	2	11	1320	1320	NUM
ejpam-4467	2	12	issn	issn	PROPN
ejpam-4467	2	13	1307	1307	NUM
ejpam-4467	2	14	-	-	SYM
ejpam-4467	2	15	5543	5543	NUM
ejpam-4467	2	16	–	–	PUNCT
ejpam-4467	2	17	ejpam.com	ejpam.com	X
ejpam-4467	2	18	published	publish	VERB
ejpam-4467	2	19	by	by	ADP
ejpam-4467	2	20	new	new	PROPN
ejpam-4467	2	21	york	york	PROPN
ejpam-4467	2	22	business	business	PROPN
ejpam-4467	2	23	global	global	ADJ
ejpam-4467	2	24	ideals	ideal	NOUN
ejpam-4467	2	25	in	in	ADP
ejpam-4467	2	26	be	be	NOUN
ejpam-4467	2	27	-	-	PUNCT
ejpam-4467	2	28	algebras	algebra	NOUN
ejpam-4467	2	29	based	base	VERB
ejpam-4467	2	30	on	on	ADP
ejpam-4467	2	31	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	2	32	fuzzy	fuzzy	ADJ
ejpam-4467	2	33	set	set	VERB
ejpam-4467	2	34	sun	sun	NOUN
ejpam-4467	2	35	shin	shin	PROPN
ejpam-4467	2	36	ahn1,∗	ahn1,∗	PROPN
ejpam-4467	2	37	,	,	PUNCT
ejpam-4467	2	38	eun	eun	PROPN
ejpam-4467	2	39	hwan	hwan	PROPN
ejpam-4467	2	40	roh2	roh2	PROPN
ejpam-4467	2	41	,	,	PUNCT
ejpam-4467	2	42	young	young	ADJ
ejpam-4467	2	43	bae	bae	NOUN
ejpam-4467	2	44	jun3	jun3	PROPN
ejpam-4467	2	45	1	1	NUM
ejpam-4467	2	46	department	department	NOUN
ejpam-4467	2	47	of	of	ADP
ejpam-4467	2	48	mathematics	mathematics	PROPN
ejpam-4467	2	49	education	education	NOUN
ejpam-4467	2	50	,	,	PUNCT
ejpam-4467	2	51	dongguk	dongguk	PROPN
ejpam-4467	2	52	university	university	PROPN
ejpam-4467	2	53	,	,	PUNCT
ejpam-4467	2	54	seoul	seoul	PROPN
ejpam-4467	2	55	04620	04620	NUM
ejpam-4467	2	56	,	,	PUNCT
ejpam-4467	2	57	korea	korea	PROPN
ejpam-4467	2	58	2	2	NUM
ejpam-4467	2	59	department	department	NOUN
ejpam-4467	2	60	of	of	ADP
ejpam-4467	2	61	mathematics	mathematics	PROPN
ejpam-4467	2	62	education	education	NOUN
ejpam-4467	2	63	,	,	PUNCT
ejpam-4467	2	64	chinju	chinju	PROPN
ejpam-4467	2	65	national	national	PROPN
ejpam-4467	2	66	university	university	PROPN
ejpam-4467	2	67	of	of	ADP
ejpam-4467	2	68	education	education	NOUN
ejpam-4467	2	69	,	,	PUNCT
ejpam-4467	2	70	jinju	jinju	PROPN
ejpam-4467	2	71	52673	52673	NUM
ejpam-4467	2	72	,	,	PUNCT
ejpam-4467	2	73	korea	korea	PROPN
ejpam-4467	2	74	3	3	NUM
ejpam-4467	2	75	department	department	PROPN
ejpam-4467	2	76	of	of	ADP
ejpam-4467	2	77	mathematics	mathematics	PROPN
ejpam-4467	2	78	education	education	NOUN
ejpam-4467	2	79	,	,	PUNCT
ejpam-4467	2	80	gyeongsang	gyeongsang	PROPN
ejpam-4467	2	81	national	national	PROPN
ejpam-4467	2	82	university	university	PROPN
ejpam-4467	2	83	,	,	PUNCT
ejpam-4467	2	84	jinju	jinju	NOUN
ejpam-4467	2	85	52828	52828	NUM
ejpam-4467	2	86	,	,	PUNCT
ejpam-4467	2	87	korea	korea	PROPN
ejpam-4467	2	88	abstract	abstract	NOUN
ejpam-4467	2	89	.	.	PUNCT
ejpam-4467	3	1	for	for	ADP
ejpam-4467	3	2	the	the	DET
ejpam-4467	3	3	purpose	purpose	NOUN
ejpam-4467	3	4	of	of	ADP
ejpam-4467	3	5	applying	apply	VERB
ejpam-4467	3	6	the	the	DET
ejpam-4467	3	7	concept	concept	NOUN
ejpam-4467	3	8	of	of	ADP
ejpam-4467	3	9	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	3	10	fuzzy	fuzzy	ADJ
ejpam-4467	3	11	set	set	VERB
ejpam-4467	3	12	to	to	ADP
ejpam-4467	3	13	ideals	ideal	NOUN
ejpam-4467	3	14	in	in	ADP
ejpam-4467	3	15	bealgebras	bealgebras	ADJ
ejpam-4467	3	16	,	,	PUNCT
ejpam-4467	3	17	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	3	18	fuzzy	fuzzy	ADJ
ejpam-4467	3	19	ideal	ideal	NOUN
ejpam-4467	3	20	is	be	AUX
ejpam-4467	3	21	introduced	introduce	VERB
ejpam-4467	3	22	,	,	PUNCT
ejpam-4467	3	23	and	and	CCONJ
ejpam-4467	3	24	its	its	PRON
ejpam-4467	3	25	properties	property	NOUN
ejpam-4467	3	26	are	be	AUX
ejpam-4467	3	27	studied	study	VERB
ejpam-4467	3	28	.	.	PUNCT
ejpam-4467	4	1	the	the	DET
ejpam-4467	4	2	relationship	relationship	NOUN
ejpam-4467	4	3	between	between	ADP
ejpam-4467	4	4	fuzzy	fuzzy	ADJ
ejpam-4467	4	5	ideal	ideal	NOUN
ejpam-4467	4	6	and	and	CCONJ
ejpam-4467	4	7	lukasiewicz	lukasiewicz	VERB
ejpam-4467	4	8	fuzzy	fuzzy	ADJ
ejpam-4467	4	9	ideal	ideal	NOUN
ejpam-4467	4	10	is	be	AUX
ejpam-4467	4	11	discussed	discuss	VERB
ejpam-4467	4	12	.	.	PUNCT
ejpam-4467	5	1	conditions	condition	NOUN
ejpam-4467	5	2	for	for	ADP
ejpam-4467	5	3	the	the	DET
ejpam-4467	5	4	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	5	5	fuzzy	fuzzy	NOUN
ejpam-4467	5	6	set	set	VERB
ejpam-4467	5	7	to	to	PART
ejpam-4467	5	8	be	be	AUX
ejpam-4467	5	9	a	a	DET
ejpam-4467	5	10	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	5	11	fuzzy	fuzzy	ADJ
ejpam-4467	5	12	ideal	ideal	NOUN
ejpam-4467	5	13	are	be	AUX
ejpam-4467	5	14	provided	provide	VERB
ejpam-4467	5	15	,	,	PUNCT
ejpam-4467	5	16	and	and	CCONJ
ejpam-4467	5	17	characterizations	characterization	NOUN
ejpam-4467	5	18	of	of	ADP
ejpam-4467	5	19	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	5	20	fuzzy	fuzzy	ADJ
ejpam-4467	5	21	ideal	ideal	NOUN
ejpam-4467	5	22	are	be	AUX
ejpam-4467	5	23	displayed	display	VERB
ejpam-4467	5	24	.	.	PUNCT
ejpam-4467	6	1	conditions	condition	NOUN
ejpam-4467	6	2	in	in	ADP
ejpam-4467	6	3	which	which	PRON
ejpam-4467	6	4	three	three	NUM
ejpam-4467	6	5	subsets	subset	NOUN
ejpam-4467	6	6	,	,	PUNCT
ejpam-4467	6	7	called	call	VERB
ejpam-4467	6	8	∈-set	∈-set	NOUN
ejpam-4467	6	9	,	,	PUNCT
ejpam-4467	6	10	q	q	NOUN
ejpam-4467	6	11	-	-	PUNCT
ejpam-4467	6	12	set	set	VERB
ejpam-4467	6	13	and	and	CCONJ
ejpam-4467	6	14	o	o	NOUN
ejpam-4467	6	15	-	-	NOUN
ejpam-4467	6	16	set	set	ADJ
ejpam-4467	6	17	,	,	PUNCT
ejpam-4467	6	18	are	be	AUX
ejpam-4467	6	19	ideals	ideal	NOUN
ejpam-4467	6	20	are	be	AUX
ejpam-4467	6	21	explored	explore	VERB
ejpam-4467	6	22	.	.	PUNCT
ejpam-4467	7	1	2020	2020	NUM
ejpam-4467	7	2	mathematics	mathematics	PROPN
ejpam-4467	7	3	subject	subject	NOUN
ejpam-4467	7	4	classifications	classification	NOUN
ejpam-4467	7	5	:	:	PUNCT
ejpam-4467	7	6	2020	2020	NUM
ejpam-4467	7	7	mathematics	mathematic	NOUN
ejpam-4467	7	8	subject	subject	ADJ
ejpam-4467	7	9	classification	classification	NOUN
ejpam-4467	7	10	.	.	PUNCT
ejpam-4467	8	1	03g25	03g25	NOUN
ejpam-4467	8	2	,	,	PUNCT
ejpam-4467	8	3	06f35	06f35	NUM
ejpam-4467	8	4	,	,	PUNCT
ejpam-4467	8	5	08a72	08a72	NUM
ejpam-4467	8	6	.	.	PUNCT
ejpam-4467	9	1	key	key	ADJ
ejpam-4467	9	2	words	word	NOUN
ejpam-4467	9	3	and	and	CCONJ
ejpam-4467	9	4	phrases	phrase	NOUN
ejpam-4467	9	5	:	:	PUNCT
ejpam-4467	9	6	fuzzy	fuzzy	ADJ
ejpam-4467	9	7	ideal	ideal	NOUN
ejpam-4467	9	8	,	,	PUNCT
ejpam-4467	9	9	lukasiewicz	lukasiewicz	VERB
ejpam-4467	9	10	fuzzy	fuzzy	ADJ
ejpam-4467	9	11	ideal	ideal	NOUN
ejpam-4467	9	12	,	,	PUNCT
ejpam-4467	9	13	∈-set	∈-set	NOUN
ejpam-4467	9	14	,	,	PUNCT
ejpam-4467	9	15	q	q	NOUN
ejpam-4467	9	16	-	-	PUNCT
ejpam-4467	9	17	set	set	ADJ
ejpam-4467	9	18	,	,	PUNCT
ejpam-4467	9	19	o	o	NOUN
ejpam-4467	9	20	-	-	PUNCT
ejpam-4467	9	21	set	set	ADJ
ejpam-4467	9	22	.	.	PUNCT
ejpam-4467	10	1	1	1	X
ejpam-4467	10	2	.	.	X
ejpam-4467	10	3	introduction	introduction	NOUN
ejpam-4467	10	4	in	in	ADP
ejpam-4467	10	5	1966	1966	NUM
ejpam-4467	10	6	,	,	PUNCT
ejpam-4467	10	7	y.	y.	PROPN
ejpam-4467	10	8	imai	imai	PROPN
ejpam-4467	10	9	,	,	PUNCT
ejpam-4467	10	10	k.	k.	PROPN
ejpam-4467	10	11	iséki	iséki	PROPN
ejpam-4467	10	12	and	and	CCONJ
ejpam-4467	10	13	s.	s.	PROPN
ejpam-4467	10	14	tanaka	tanaka	PROPN
ejpam-4467	10	15	introduced	introduce	VERB
ejpam-4467	10	16	bck	bck	NOUN
ejpam-4467	10	17	-	-	PUNCT
ejpam-4467	10	18	algebra	algebra	PROPN
ejpam-4467	10	19	and	and	CCONJ
ejpam-4467	10	20	bci	bci	NOUN
ejpam-4467	10	21	-	-	NOUN
ejpam-4467	10	22	algebra	algebra	NOUN
ejpam-4467	10	23	as	as	ADP
ejpam-4467	10	24	algebraic	algebraic	ADJ
ejpam-4467	10	25	structures	structure	NOUN
ejpam-4467	10	26	of	of	ADP
ejpam-4467	10	27	universal	universal	ADJ
ejpam-4467	10	28	algebra	algebra	NOUN
ejpam-4467	10	29	which	which	PRON
ejpam-4467	10	30	describe	describe	VERB
ejpam-4467	10	31	fragments	fragment	NOUN
ejpam-4467	10	32	of	of	ADP
ejpam-4467	10	33	propositional	propositional	ADJ
ejpam-4467	10	34	calculus	calculus	NOUN
ejpam-4467	10	35	related	relate	VERB
ejpam-4467	10	36	to	to	ADP
ejpam-4467	10	37	implications	implication	NOUN
ejpam-4467	10	38	known	know	VERB
ejpam-4467	10	39	as	as	ADP
ejpam-4467	10	40	bck	bck	NOUN
ejpam-4467	10	41	and	and	CCONJ
ejpam-4467	10	42	bci	bci	NOUN
ejpam-4467	10	43	-	-	NOUN
ejpam-4467	10	44	logic	logic	NOUN
ejpam-4467	10	45	.	.	PUNCT
ejpam-4467	11	1	various	various	ADJ
ejpam-4467	11	2	generalizations	generalization	NOUN
ejpam-4467	11	3	were	be	AUX
ejpam-4467	11	4	then	then	ADV
ejpam-4467	11	5	attempted	attempt	VERB
ejpam-4467	11	6	,	,	PUNCT
ejpam-4467	11	7	and	and	CCONJ
ejpam-4467	11	8	bcc	bcc	PROPN
ejpam-4467	11	9	-	-	PUNCT
ejpam-4467	11	10	algebra	algebra	PROPN
ejpam-4467	11	11	,	,	PUNCT
ejpam-4467	11	12	bch	bch	NOUN
ejpam-4467	11	13	-	-	PUNCT
ejpam-4467	11	14	algebra	algebra	NOUN
ejpam-4467	11	15	,	,	PUNCT
ejpam-4467	11	16	be	be	NOUN
ejpam-4467	11	17	-	-	PUNCT
ejpam-4467	11	18	algebra	algebra	NOUN
ejpam-4467	11	19	,	,	PUNCT
ejpam-4467	11	20	bh	bh	NOUN
ejpam-4467	11	21	-	-	NOUN
ejpam-4467	11	22	algebra	algebra	NOUN
ejpam-4467	11	23	,	,	PUNCT
ejpam-4467	11	24	and	and	CCONJ
ejpam-4467	12	1	d	d	X
ejpam-4467	12	2	-	-	PUNCT
ejpam-4467	12	3	algebra	algebra	NOUN
ejpam-4467	12	4	etc	etc	X
ejpam-4467	12	5	.	.	X
ejpam-4467	12	6	appeared	appear	VERB
ejpam-4467	12	7	.	.	PUNCT
ejpam-4467	13	1	in	in	ADP
ejpam-4467	13	2	2008	2008	NUM
ejpam-4467	13	3	,	,	PUNCT
ejpam-4467	13	4	s.	s.	PROPN
ejpam-4467	13	5	s.	s.	PROPN
ejpam-4467	13	6	ahn	ahn	PROPN
ejpam-4467	13	7	and	and	CCONJ
ejpam-4467	13	8	k.	k.	PROPN
ejpam-4467	13	9	s.	s.	PROPN
ejpam-4467	14	1	so	so	ADV
ejpam-4467	14	2	studied	study	VERB
ejpam-4467	14	3	ideal	ideal	ADJ
ejpam-4467	14	4	theory	theory	NOUN
ejpam-4467	14	5	in	in	ADP
ejpam-4467	14	6	be	be	NOUN
ejpam-4467	14	7	-	-	PUNCT
ejpam-4467	14	8	algebras	algebras	X
ejpam-4467	14	9	(	(	PUNCT
ejpam-4467	14	10	see	see	VERB
ejpam-4467	14	11	[	[	X
ejpam-4467	14	12	1	1	NUM
ejpam-4467	14	13	]	]	NUM
ejpam-4467	14	14	)	)	PUNCT
ejpam-4467	14	15	,	,	PUNCT
ejpam-4467	14	16	and	and	CCONJ
ejpam-4467	14	17	its	its	PRON
ejpam-4467	14	18	fuzzy	fuzzy	ADJ
ejpam-4467	14	19	set	set	NOUN
ejpam-4467	14	20	theory	theory	NOUN
ejpam-4467	14	21	is	be	AUX
ejpam-4467	14	22	studied	study	VERB
ejpam-4467	14	23	by	by	ADP
ejpam-4467	14	24	y.	y.	PROPN
ejpam-4467	14	25	b.	b.	PROPN
ejpam-4467	14	26	jun	jun	PROPN
ejpam-4467	14	27	,	,	PUNCT
ejpam-4467	14	28	k.	k.	PROPN
ejpam-4467	14	29	j.	j.	PROPN
ejpam-4467	14	30	lee	lee	PROPN
ejpam-4467	14	31	and	and	CCONJ
ejpam-4467	14	32	s.	s.	PROPN
ejpam-4467	14	33	z.	z.	PROPN
ejpam-4467	14	34	song	song	PROPN
ejpam-4467	14	35	(	(	PUNCT
ejpam-4467	14	36	see	see	VERB
ejpam-4467	14	37	[	[	X
ejpam-4467	14	38	9	9	NUM
ejpam-4467	14	39	]	]	NUM
ejpam-4467	14	40	)	)	PUNCT
ejpam-4467	14	41	.	.	PUNCT
ejpam-4467	15	1	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	15	2	logic	logic	NOUN
ejpam-4467	15	3	,	,	PUNCT
ejpam-4467	15	4	which	which	PRON
ejpam-4467	15	5	is	be	AUX
ejpam-4467	15	6	the	the	DET
ejpam-4467	15	7	logic	logic	NOUN
ejpam-4467	15	8	of	of	ADP
ejpam-4467	15	9	the	the	DET
ejpam-4467	15	10	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	15	11	t	t	PROPN
ejpam-4467	15	12	-	-	PUNCT
ejpam-4467	15	13	norm	norm	NOUN
ejpam-4467	15	14	,	,	PUNCT
ejpam-4467	15	15	is	be	AUX
ejpam-4467	15	16	a	a	DET
ejpam-4467	15	17	non	non	ADJ
ejpam-4467	15	18	-	-	ADJ
ejpam-4467	15	19	classical	classical	ADJ
ejpam-4467	15	20	and	and	CCONJ
ejpam-4467	15	21	many	many	ADV
ejpam-4467	15	22	-	-	PUNCT
ejpam-4467	15	23	valued	value	VERB
ejpam-4467	15	24	logic	logic	NOUN
ejpam-4467	15	25	.	.	PUNCT
ejpam-4467	16	1	it	it	PRON
ejpam-4467	16	2	was	be	AUX
ejpam-4467	16	3	originally	originally	ADV
ejpam-4467	16	4	defined	define	VERB
ejpam-4467	16	5	in	in	ADP
ejpam-4467	16	6	the	the	DET
ejpam-4467	16	7	early	early	ADJ
ejpam-4467	16	8	20th	20th	ADJ
ejpam-4467	16	9	century	century	NOUN
ejpam-4467	16	10	by	by	ADP
ejpam-4467	16	11	jan	jan	PROPN
ejpam-4467	16	12	lukasiewicz	lukasiewicz	PROPN
ejpam-4467	16	13	as	as	ADP
ejpam-4467	16	14	a	a	DET
ejpam-4467	16	15	three	three	NUM
ejpam-4467	16	16	-	-	PUNCT
ejpam-4467	16	17	valued	value	VERB
ejpam-4467	16	18	logic	logic	NOUN
ejpam-4467	16	19	.	.	PUNCT
ejpam-4467	17	1	using	use	VERB
ejpam-4467	17	2	the	the	DET
ejpam-4467	17	3	idea	idea	NOUN
ejpam-4467	17	4	of	of	ADP
ejpam-4467	17	5	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	17	6	t	t	PROPN
ejpam-4467	17	7	-	-	PUNCT
ejpam-4467	17	8	norm	norm	NOUN
ejpam-4467	17	9	,	,	PUNCT
ejpam-4467	17	10	y.	y.	PROPN
ejpam-4467	17	11	b.	b.	PROPN
ejpam-4467	17	12	jun	jun	PROPN
ejpam-4467	18	1	[	[	X
ejpam-4467	18	2	3	3	NUM
ejpam-4467	18	3	]	]	PUNCT
ejpam-4467	18	4	constructed	construct	VERB
ejpam-4467	18	5	the	the	DET
ejpam-4467	18	6	concept	concept	NOUN
ejpam-4467	18	7	of	of	ADP
ejpam-4467	18	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	18	9	fuzzy	fuzzy	ADJ
ejpam-4467	18	10	sets	set	NOUN
ejpam-4467	18	11	based	base	VERB
ejpam-4467	18	12	on	on	ADP
ejpam-4467	18	13	a	a	DET
ejpam-4467	18	14	given	give	VERB
ejpam-4467	18	15	fuzzy	fuzzy	ADJ
ejpam-4467	18	16	set	set	NOUN
ejpam-4467	18	17	and	and	CCONJ
ejpam-4467	18	18	applied	apply	VERB
ejpam-4467	18	19	it	it	PRON
ejpam-4467	18	20	to	to	ADP
ejpam-4467	18	21	bckalgebras	bckalgebra	NOUN
ejpam-4467	18	22	and	and	CCONJ
ejpam-4467	18	23	bci	bci	NOUN
ejpam-4467	18	24	-	-	PUNCT
ejpam-4467	18	25	algebras	algebras	X
ejpam-4467	18	26	.	.	PUNCT
ejpam-4467	19	1	s.	s.	PROPN
ejpam-4467	19	2	s.	s.	PROPN
ejpam-4467	19	3	ahn	ahn	PROPN
ejpam-4467	19	4	et	et	PROPN
ejpam-4467	19	5	al	al	PROPN
ejpam-4467	19	6	.	.	PUNCT
ejpam-4467	20	1	[	[	X
ejpam-4467	20	2	8	8	NUM
ejpam-4467	20	3	]	]	PUNCT
ejpam-4467	20	4	,	,	PUNCT
ejpam-4467	20	5	and	and	CCONJ
ejpam-4467	20	6	a.	a.	NOUN
ejpam-4467	20	7	rezaei	rezaei	PROPN
ejpam-4467	20	8	and	and	CCONJ
ejpam-4467	20	9	a.	a.	PROPN
ejpam-4467	20	10	borumand	borumand	PROPN
ejpam-4467	20	11	saeid	saeid	PROPN
ejpam-4467	20	12	[	[	X
ejpam-4467	20	13	7	7	X
ejpam-4467	20	14	]	]	PUNCT
ejpam-4467	20	15	studied	study	VERB
ejpam-4467	20	16	fuzzy	fuzzy	ADJ
ejpam-4467	20	17	be	be	NOUN
ejpam-4467	20	18	-	-	PUNCT
ejpam-4467	20	19	algebras	algebra	NOUN
ejpam-4467	20	20	.	.	PUNCT
ejpam-4467	21	1	g.	g.	PROPN
ejpam-4467	21	2	dymek	dymek	PROPN
ejpam-4467	21	3	and	and	CCONJ
ejpam-4467	21	4	a.	a.	PROPN
ejpam-4467	21	5	walendziak	walendziak	PROPN
ejpam-4467	22	1	[	[	X
ejpam-4467	22	2	2	2	NUM
ejpam-4467	22	3	]	]	PUNCT
ejpam-4467	22	4	developed	develop	VERB
ejpam-4467	22	5	the	the	DET
ejpam-4467	22	6	theory	theory	NOUN
ejpam-4467	22	7	of	of	ADP
ejpam-4467	22	8	∗corresponding	∗corresponde	VERB
ejpam-4467	22	9	author	author	NOUN
ejpam-4467	22	10	.	.	PUNCT
ejpam-4467	23	1	doi	doi	NOUN
ejpam-4467	23	2	:	:	PUNCT
ejpam-4467	23	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4467	https://doi.org/10.29020/nybg.ejpam.v15i3.4467	PRON
ejpam-4467	23	4	email	email	NOUN
ejpam-4467	23	5	addresses	address	NOUN
ejpam-4467	23	6	:	:	PUNCT
ejpam-4467	23	7	sunshine@dongguk.edu	sunshine@dongguk.edu	PROPN
ejpam-4467	23	8	(	(	PUNCT
ejpam-4467	23	9	s.	s.	PROPN
ejpam-4467	23	10	s.	s.	PROPN
ejpam-4467	23	11	ahn	ahn	PROPN
ejpam-4467	23	12	)	)	PUNCT
ejpam-4467	23	13	,	,	PUNCT
ejpam-4467	23	14	ehroh9988@gmail.com	ehroh9988@gmail.com	X
ejpam-4467	24	1	(	(	PUNCT
ejpam-4467	24	2	e.	e.	PROPN
ejpam-4467	24	3	h.	h.	PROPN
ejpam-4467	24	4	roh	roh	PROPN
ejpam-4467	24	5	)	)	PUNCT
ejpam-4467	24	6	,	,	PUNCT
ejpam-4467	24	7	skywine@gmail.com	skywine@gmail.com	X
ejpam-4467	25	1	(	(	PUNCT
ejpam-4467	25	2	y.	y.	PROPN
ejpam-4467	25	3	b.	b.	PROPN
ejpam-4467	25	4	jun	jun	PROPN
ejpam-4467	25	5	)	)	PUNCT
ejpam-4467	25	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4467	25	7	1307	1307	NUM
ejpam-4467	26	1	©	©	PROPN
ejpam-4467	26	2	2022	2022	NUM
ejpam-4467	26	3	ejpam	ejpam	VERB
ejpam-4467	26	4	all	all	DET
ejpam-4467	26	5	rights	right	NOUN
ejpam-4467	26	6	reserved	reserve	VERB
ejpam-4467	26	7	.	.	PUNCT
ejpam-4467	27	1	s.	s.	PROPN
ejpam-4467	27	2	s.	s.	PROPN
ejpam-4467	27	3	ahn	ahn	PROPN
ejpam-4467	27	4	,	,	PUNCT
ejpam-4467	27	5	e.	e.	PROPN
ejpam-4467	27	6	h.	h.	PROPN
ejpam-4467	27	7	roh	roh	PROPN
ejpam-4467	27	8	and	and	CCONJ
ejpam-4467	27	9	y.	y.	PROPN
ejpam-4467	27	10	b.	b.	PROPN
ejpam-4467	27	11	jun	jun	PROPN
ejpam-4467	27	12	/	/	SYM
ejpam-4467	27	13	eur	eur	PROPN
ejpam-4467	27	14	.	.	PUNCT
ejpam-4467	28	1	j.	j.	PROPN
ejpam-4467	28	2	pure	pure	PROPN
ejpam-4467	28	3	appl	appl	PROPN
ejpam-4467	28	4	.	.	PROPN
ejpam-4467	28	5	math	math	PROPN
ejpam-4467	28	6	,	,	PUNCT
ejpam-4467	28	7	15	15	NUM
ejpam-4467	28	8	(	(	PUNCT
ejpam-4467	28	9	3	3	NUM
ejpam-4467	28	10	)	)	PUNCT
ejpam-4467	28	11	(	(	PUNCT
ejpam-4467	28	12	2022	2022	NUM
ejpam-4467	28	13	)	)	PUNCT
ejpam-4467	28	14	,	,	PUNCT
ejpam-4467	28	15	1307	1307	NUM
ejpam-4467	28	16	-	-	SYM
ejpam-4467	28	17	1320	1320	NUM
ejpam-4467	28	18	1308	1308	NUM
ejpam-4467	28	19	fuzzy	fuzzy	ADJ
ejpam-4467	28	20	filters	filter	NOUN
ejpam-4467	28	21	in	in	ADP
ejpam-4467	28	22	be	be	AUX
ejpam-4467	28	23	-	-	PUNCT
ejpam-4467	28	24	algebras	algebras	X
ejpam-4467	28	25	.	.	PUNCT
ejpam-4467	29	1	y.	y.	PROPN
ejpam-4467	29	2	b.	b.	PROPN
ejpam-4467	29	3	jun	jun	PROPN
ejpam-4467	29	4	and	and	CCONJ
ejpam-4467	29	5	s.	s.	PROPN
ejpam-4467	29	6	s.	s.	PROPN
ejpam-4467	29	7	ahn	ahn	PROPN
ejpam-4467	29	8	applied	apply	VERB
ejpam-4467	29	9	the	the	DET
ejpam-4467	29	10	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	29	11	fuzzy	fuzzy	NOUN
ejpam-4467	29	12	set	set	VERB
ejpam-4467	29	13	to	to	PART
ejpam-4467	29	14	be	be	AUX
ejpam-4467	29	15	-	-	PUNCT
ejpam-4467	29	16	filters	filter	NOUN
ejpam-4467	29	17	and	and	CCONJ
ejpam-4467	29	18	subalgebras	subalgebras	PROPN
ejpam-4467	29	19	(	(	PUNCT
ejpam-4467	29	20	see	see	VERB
ejpam-4467	29	21	[	[	X
ejpam-4467	29	22	4	4	NUM
ejpam-4467	29	23	]	]	NUM
ejpam-4467	29	24	)	)	PUNCT
ejpam-4467	29	25	.	.	PUNCT
ejpam-4467	30	1	the	the	DET
ejpam-4467	30	2	purpose	purpose	NOUN
ejpam-4467	30	3	of	of	ADP
ejpam-4467	30	4	this	this	DET
ejpam-4467	30	5	paper	paper	NOUN
ejpam-4467	30	6	is	be	AUX
ejpam-4467	30	7	to	to	PART
ejpam-4467	30	8	apply	apply	VERB
ejpam-4467	30	9	the	the	DET
ejpam-4467	30	10	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	30	11	fuzzy	fuzzy	ADJ
ejpam-4467	30	12	set	set	VERB
ejpam-4467	30	13	to	to	ADP
ejpam-4467	30	14	ideals	ideal	NOUN
ejpam-4467	30	15	in	in	ADP
ejpam-4467	30	16	bealgebras	bealgebras	ADJ
ejpam-4467	30	17	.	.	PUNCT
ejpam-4467	31	1	we	we	PRON
ejpam-4467	31	2	introduce	introduce	VERB
ejpam-4467	31	3	the	the	DET
ejpam-4467	31	4	notion	notion	NOUN
ejpam-4467	31	5	of	of	ADP
ejpam-4467	31	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	31	7	fuzzy	fuzzy	ADJ
ejpam-4467	31	8	ideal	ideal	NOUN
ejpam-4467	31	9	,	,	PUNCT
ejpam-4467	31	10	and	and	CCONJ
ejpam-4467	31	11	investigate	investigate	VERB
ejpam-4467	31	12	several	several	ADJ
ejpam-4467	31	13	properties	property	NOUN
ejpam-4467	31	14	.	.	PUNCT
ejpam-4467	32	1	we	we	PRON
ejpam-4467	32	2	discuss	discuss	VERB
ejpam-4467	32	3	the	the	DET
ejpam-4467	32	4	characterization	characterization	NOUN
ejpam-4467	32	5	of	of	ADP
ejpam-4467	32	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	32	7	fuzzy	fuzzy	ADJ
ejpam-4467	32	8	ideal	ideal	NOUN
ejpam-4467	32	9	.	.	PUNCT
ejpam-4467	33	1	we	we	PRON
ejpam-4467	33	2	consider	consider	VERB
ejpam-4467	33	3	the	the	DET
ejpam-4467	33	4	relationship	relationship	NOUN
ejpam-4467	33	5	between	between	ADP
ejpam-4467	33	6	fuzzy	fuzzy	ADJ
ejpam-4467	33	7	ideal	ideal	NOUN
ejpam-4467	33	8	and	and	CCONJ
ejpam-4467	33	9	lukasiewicz	lukasiewicz	VERB
ejpam-4467	33	10	fuzzy	fuzzy	ADJ
ejpam-4467	33	11	ideal	ideal	NOUN
ejpam-4467	33	12	.	.	PUNCT
ejpam-4467	34	1	we	we	PRON
ejpam-4467	34	2	provide	provide	VERB
ejpam-4467	34	3	conditions	condition	NOUN
ejpam-4467	34	4	for	for	ADP
ejpam-4467	34	5	the	the	DET
ejpam-4467	34	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	34	7	fuzzy	fuzzy	NOUN
ejpam-4467	34	8	set	set	VERB
ejpam-4467	34	9	to	to	PART
ejpam-4467	34	10	be	be	AUX
ejpam-4467	34	11	a	a	DET
ejpam-4467	34	12	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	34	13	fuzzy	fuzzy	ADJ
ejpam-4467	34	14	ideal	ideal	NOUN
ejpam-4467	34	15	.	.	PUNCT
ejpam-4467	35	1	we	we	PRON
ejpam-4467	35	2	explore	explore	VERB
ejpam-4467	35	3	the	the	DET
ejpam-4467	35	4	conditions	condition	NOUN
ejpam-4467	35	5	under	under	ADP
ejpam-4467	35	6	which	which	PRON
ejpam-4467	35	7	three	three	NUM
ejpam-4467	35	8	subsets	subset	NOUN
ejpam-4467	35	9	,	,	PUNCT
ejpam-4467	35	10	called	call	VERB
ejpam-4467	35	11	∈-set	∈-set	NOUN
ejpam-4467	35	12	,	,	PUNCT
ejpam-4467	35	13	q	q	NOUN
ejpam-4467	35	14	-	-	PUNCT
ejpam-4467	35	15	set	set	VERB
ejpam-4467	35	16	and	and	CCONJ
ejpam-4467	35	17	o	o	NOUN
ejpam-4467	35	18	-	-	NOUN
ejpam-4467	35	19	set	set	ADJ
ejpam-4467	35	20	,	,	PUNCT
ejpam-4467	35	21	will	will	AUX
ejpam-4467	35	22	become	become	VERB
ejpam-4467	35	23	ideals	ideal	NOUN
ejpam-4467	35	24	.	.	PUNCT
ejpam-4467	36	1	2	2	X
ejpam-4467	36	2	.	.	X
ejpam-4467	36	3	preliminaries	preliminary	NOUN
ejpam-4467	36	4	this	this	DET
ejpam-4467	36	5	section	section	NOUN
ejpam-4467	36	6	lists	list	VERB
ejpam-4467	36	7	the	the	DET
ejpam-4467	36	8	known	know	VERB
ejpam-4467	36	9	default	default	NOUN
ejpam-4467	36	10	content	content	NOUN
ejpam-4467	36	11	that	that	PRON
ejpam-4467	36	12	will	will	AUX
ejpam-4467	36	13	be	be	AUX
ejpam-4467	36	14	used	use	VERB
ejpam-4467	36	15	later	later	ADV
ejpam-4467	36	16	.	.	PUNCT
ejpam-4467	37	1	definition	definition	NOUN
ejpam-4467	37	2	1	1	NUM
ejpam-4467	37	3	(	(	PUNCT
ejpam-4467	37	4	[	[	X
ejpam-4467	37	5	5	5	NUM
ejpam-4467	37	6	]	]	NUM
ejpam-4467	37	7	)	)	PUNCT
ejpam-4467	37	8	.	.	PUNCT
ejpam-4467	38	1	a	a	DET
ejpam-4467	38	2	be	be	NOUN
ejpam-4467	38	3	-	-	PUNCT
ejpam-4467	38	4	algebra	algebra	NOUN
ejpam-4467	38	5	is	be	AUX
ejpam-4467	38	6	defined	define	VERB
ejpam-4467	38	7	to	to	PART
ejpam-4467	38	8	be	be	AUX
ejpam-4467	38	9	a	a	DET
ejpam-4467	38	10	set	set	NOUN
ejpam-4467	38	11	x	x	PUNCT
ejpam-4467	38	12	together	together	ADV
ejpam-4467	38	13	with	with	ADP
ejpam-4467	38	14	a	a	DET
ejpam-4467	38	15	binary	binary	ADJ
ejpam-4467	38	16	operation	operation	NOUN
ejpam-4467	38	17	“	"	PUNCT
ejpam-4467	38	18	∗	∗	NOUN
ejpam-4467	38	19	”	"	PUNCT
ejpam-4467	38	20	and	and	CCONJ
ejpam-4467	38	21	a	a	DET
ejpam-4467	38	22	special	special	ADJ
ejpam-4467	38	23	element	element	NOUN
ejpam-4467	38	24	“	"	PUNCT
ejpam-4467	38	25	1	1	NUM
ejpam-4467	38	26	”	"	PUNCT
ejpam-4467	38	27	satisfying	satisfy	VERB
ejpam-4467	38	28	the	the	DET
ejpam-4467	38	29	conditions	condition	NOUN
ejpam-4467	38	30	:	:	PUNCT
ejpam-4467	38	31	(	(	PUNCT
ejpam-4467	38	32	be1	be1	NOUN
ejpam-4467	38	33	)	)	PUNCT
ejpam-4467	38	34	(	(	PUNCT
ejpam-4467	39	1	∀a	∀a	NOUN
ejpam-4467	39	2	∈	∈	NOUN
ejpam-4467	39	3	x	x	NOUN
ejpam-4467	39	4	)	)	PUNCT
ejpam-4467	39	5	(	(	PUNCT
ejpam-4467	39	6	a	a	DET
ejpam-4467	39	7	∗	∗	NOUN
ejpam-4467	39	8	a	a	DET
ejpam-4467	39	9	=	=	NOUN
ejpam-4467	39	10	1	1	NUM
ejpam-4467	39	11	)	)	PUNCT
ejpam-4467	39	12	,	,	PUNCT
ejpam-4467	39	13	(	(	PUNCT
ejpam-4467	39	14	be2	be2	PROPN
ejpam-4467	39	15	)	)	PUNCT
ejpam-4467	39	16	(	(	PUNCT
ejpam-4467	39	17	∀a	∀a	NOUN
ejpam-4467	39	18	∈	∈	NOUN
ejpam-4467	39	19	x	x	NOUN
ejpam-4467	39	20	)	)	PUNCT
ejpam-4467	39	21	(	(	PUNCT
ejpam-4467	39	22	a	a	DET
ejpam-4467	39	23	∗	∗	NOUN
ejpam-4467	39	24	1	1	NUM
ejpam-4467	39	25	=	=	SYM
ejpam-4467	39	26	1	1	NUM
ejpam-4467	39	27	)	)	PUNCT
ejpam-4467	39	28	,	,	PUNCT
ejpam-4467	39	29	(	(	PUNCT
ejpam-4467	39	30	be3	be3	PROPN
ejpam-4467	39	31	)	)	PUNCT
ejpam-4467	39	32	(	(	PUNCT
ejpam-4467	39	33	∀a	∀a	NOUN
ejpam-4467	39	34	∈	∈	NOUN
ejpam-4467	39	35	x	x	NOUN
ejpam-4467	39	36	)	)	PUNCT
ejpam-4467	39	37	(	(	PUNCT
ejpam-4467	39	38	1	1	NUM
ejpam-4467	39	39	∗	∗	NOUN
ejpam-4467	39	40	a	a	DET
ejpam-4467	39	41	=	=	NOUN
ejpam-4467	39	42	a	a	NOUN
ejpam-4467	39	43	)	)	PUNCT
ejpam-4467	39	44	,	,	PUNCT
ejpam-4467	39	45	(	(	PUNCT
ejpam-4467	39	46	be4	be4	NOUN
ejpam-4467	39	47	)	)	PUNCT
ejpam-4467	39	48	(	(	PUNCT
ejpam-4467	39	49	∀a	∀a	X
ejpam-4467	39	50	,	,	PUNCT
ejpam-4467	39	51	y	y	PROPN
ejpam-4467	39	52	,	,	PUNCT
ejpam-4467	39	53	c	c	PROPN
ejpam-4467	39	54	∈	∈	PROPN
ejpam-4467	39	55	x	x	X
ejpam-4467	39	56	)	)	PUNCT
ejpam-4467	39	57	(	(	PUNCT
ejpam-4467	39	58	a	a	DET
ejpam-4467	39	59	∗	∗	X
ejpam-4467	39	60	(	(	PUNCT
ejpam-4467	39	61	y	y	NOUN
ejpam-4467	39	62	∗	∗	X
ejpam-4467	39	63	c	c	NOUN
ejpam-4467	39	64	)	)	PUNCT
ejpam-4467	39	65	=	=	SYM
ejpam-4467	39	66	y	y	PROPN
ejpam-4467	39	67	∗	∗	NOUN
ejpam-4467	39	68	(	(	PUNCT
ejpam-4467	39	69	a	a	DET
ejpam-4467	39	70	∗	∗	NOUN
ejpam-4467	39	71	c	c	NOUN
ejpam-4467	39	72	)	)	PUNCT
ejpam-4467	39	73	)	)	PUNCT
ejpam-4467	39	74	.	.	PUNCT
ejpam-4467	40	1	in	in	ADP
ejpam-4467	40	2	the	the	DET
ejpam-4467	40	3	following	following	NOUN
ejpam-4467	40	4	,	,	PUNCT
ejpam-4467	40	5	the	the	DET
ejpam-4467	40	6	be	be	NOUN
ejpam-4467	40	7	-	-	PUNCT
ejpam-4467	40	8	algebra	algebra	NOUN
ejpam-4467	40	9	is	be	AUX
ejpam-4467	40	10	expressed	express	VERB
ejpam-4467	40	11	as	as	ADP
ejpam-4467	40	12	(	(	PUNCT
ejpam-4467	40	13	x	x	X
ejpam-4467	40	14	,	,	PUNCT
ejpam-4467	40	15	1)∗.	1)∗.	PROPN
ejpam-4467	40	16	a	a	DET
ejpam-4467	40	17	relation	relation	NOUN
ejpam-4467	40	18	“	"	PUNCT
ejpam-4467	40	19	≤	≤	NUM
ejpam-4467	40	20	”	"	PUNCT
ejpam-4467	40	21	in	in	ADP
ejpam-4467	40	22	(	(	PUNCT
ejpam-4467	40	23	x	x	NOUN
ejpam-4467	40	24	,	,	PUNCT
ejpam-4467	40	25	1)∗	1)∗	NUM
ejpam-4467	40	26	is	be	AUX
ejpam-4467	40	27	defined	define	VERB
ejpam-4467	40	28	as	as	SCONJ
ejpam-4467	40	29	follows	follow	VERB
ejpam-4467	40	30	:	:	PUNCT
ejpam-4467	40	31	(	(	PUNCT
ejpam-4467	40	32	∀x	∀x	X
ejpam-4467	40	33	,	,	PUNCT
ejpam-4467	40	34	b	b	PROPN
ejpam-4467	40	35	∈	∈	PROPN
ejpam-4467	40	36	x)(x	x)(x	PROPN
ejpam-4467	41	1	≤	≤	PROPN
ejpam-4467	41	2	b	b	PROPN
ejpam-4467	41	3	⇔	⇔	X
ejpam-4467	41	4	x	x	PROPN
ejpam-4467	41	5	∗	∗	NOUN
ejpam-4467	41	6	b	b	NOUN
ejpam-4467	41	7	=	=	NOUN
ejpam-4467	41	8	1	1	NUM
ejpam-4467	41	9	)	)	PUNCT
ejpam-4467	41	10	.	.	PUNCT
ejpam-4467	42	1	(	(	PUNCT
ejpam-4467	42	2	1	1	X
ejpam-4467	42	3	)	)	PUNCT
ejpam-4467	42	4	definition	definition	NOUN
ejpam-4467	42	5	2	2	NUM
ejpam-4467	42	6	.	.	PUNCT
ejpam-4467	43	1	a	a	DET
ejpam-4467	43	2	subset	subset	NOUN
ejpam-4467	43	3	k	k	NOUN
ejpam-4467	43	4	of	of	ADP
ejpam-4467	43	5	x	x	PROPN
ejpam-4467	43	6	is	be	AUX
ejpam-4467	43	7	called	call	VERB
ejpam-4467	43	8	an	an	DET
ejpam-4467	43	9	ideal	ideal	NOUN
ejpam-4467	43	10	of	of	ADP
ejpam-4467	43	11	(	(	PUNCT
ejpam-4467	43	12	x	x	X
ejpam-4467	43	13	,	,	PUNCT
ejpam-4467	43	14	1)∗	1)∗	NUM
ejpam-4467	43	15	(	(	PUNCT
ejpam-4467	43	16	see	see	VERB
ejpam-4467	43	17	[	[	X
ejpam-4467	43	18	1	1	NUM
ejpam-4467	43	19	]	]	PUNCT
ejpam-4467	43	20	)	)	PUNCT
ejpam-4467	43	21	if	if	SCONJ
ejpam-4467	43	22	it	it	PRON
ejpam-4467	43	23	satisfies	satisfy	VERB
ejpam-4467	43	24	:	:	PUNCT
ejpam-4467	43	25	(	(	PUNCT
ejpam-4467	43	26	∀a	∀a	NOUN
ejpam-4467	43	27	,	,	PUNCT
ejpam-4467	43	28	b	b	PROPN
ejpam-4467	43	29	∈	∈	PROPN
ejpam-4467	43	30	x	x	X
ejpam-4467	43	31	)	)	PUNCT
ejpam-4467	43	32	(	(	PUNCT
ejpam-4467	43	33	b	b	X
ejpam-4467	43	34	∈	∈	PROPN
ejpam-4467	43	35	k	k	PROPN
ejpam-4467	43	36	⇒	⇒	VERB
ejpam-4467	43	37	a	a	DET
ejpam-4467	43	38	∗	∗	NOUN
ejpam-4467	43	39	b	b	NOUN
ejpam-4467	43	40	∈	∈	PROPN
ejpam-4467	43	41	k	k	NOUN
ejpam-4467	43	42	)	)	PUNCT
ejpam-4467	43	43	,	,	PUNCT
ejpam-4467	43	44	(	(	PUNCT
ejpam-4467	43	45	2	2	X
ejpam-4467	43	46	)	)	PUNCT
ejpam-4467	43	47	(	(	PUNCT
ejpam-4467	43	48	∀x	∀x	X
ejpam-4467	43	49	,	,	PUNCT
ejpam-4467	43	50	y	y	PROPN
ejpam-4467	43	51	,	,	PUNCT
ejpam-4467	43	52	a	a	DET
ejpam-4467	43	53	∈	∈	PROPN
ejpam-4467	43	54	x	x	X
ejpam-4467	43	55	)	)	PUNCT
ejpam-4467	43	56	(	(	PUNCT
ejpam-4467	43	57	x	x	X
ejpam-4467	43	58	,	,	PUNCT
ejpam-4467	43	59	y	y	PROPN
ejpam-4467	43	60	∈	∈	PROPN
ejpam-4467	43	61	k	k	PROPN
ejpam-4467	43	62	⇒	⇒	PROPN
ejpam-4467	43	63	(	(	PUNCT
ejpam-4467	43	64	x	x	SYM
ejpam-4467	43	65	∗	∗	NOUN
ejpam-4467	43	66	(	(	PUNCT
ejpam-4467	43	67	y	y	PROPN
ejpam-4467	43	68	∗	∗	PROPN
ejpam-4467	43	69	a	a	NOUN
ejpam-4467	43	70	)	)	PUNCT
ejpam-4467	43	71	)	)	PUNCT
ejpam-4467	43	72	∗	∗	VERB
ejpam-4467	43	73	a	a	DET
ejpam-4467	43	74	∈	∈	PROPN
ejpam-4467	43	75	k	k	NOUN
ejpam-4467	43	76	)	)	PUNCT
ejpam-4467	43	77	.	.	PUNCT
ejpam-4467	44	1	(	(	PUNCT
ejpam-4467	44	2	3	3	X
ejpam-4467	44	3	)	)	PUNCT
ejpam-4467	44	4	lemma	lemma	PROPN
ejpam-4467	44	5	1	1	NUM
ejpam-4467	44	6	(	(	PUNCT
ejpam-4467	44	7	[	[	X
ejpam-4467	44	8	9	9	NUM
ejpam-4467	44	9	]	]	NUM
ejpam-4467	44	10	)	)	PUNCT
ejpam-4467	44	11	.	.	PUNCT
ejpam-4467	45	1	a	a	DET
ejpam-4467	45	2	subset	subset	NOUN
ejpam-4467	45	3	k	k	NOUN
ejpam-4467	45	4	of	of	ADP
ejpam-4467	45	5	x	x	PROPN
ejpam-4467	45	6	is	be	AUX
ejpam-4467	45	7	an	an	DET
ejpam-4467	45	8	ideal	ideal	NOUN
ejpam-4467	45	9	of	of	ADP
ejpam-4467	45	10	(	(	PUNCT
ejpam-4467	45	11	x	x	NOUN
ejpam-4467	45	12	,	,	PUNCT
ejpam-4467	45	13	1)∗	1)∗	NOUN
ejpam-4467	45	14	if	if	SCONJ
ejpam-4467	45	15	and	and	CCONJ
ejpam-4467	45	16	only	only	ADV
ejpam-4467	45	17	if	if	SCONJ
ejpam-4467	45	18	it	it	PRON
ejpam-4467	45	19	satisfies	satisfy	VERB
ejpam-4467	45	20	:	:	PUNCT
ejpam-4467	45	21	1	1	NUM
ejpam-4467	45	22	∈	∈	PROPN
ejpam-4467	45	23	k	k	NOUN
ejpam-4467	45	24	,	,	PUNCT
ejpam-4467	45	25	(	(	PUNCT
ejpam-4467	45	26	4	4	NUM
ejpam-4467	45	27	)	)	PUNCT
ejpam-4467	45	28	(	(	PUNCT
ejpam-4467	45	29	∀a	∀a	X
ejpam-4467	45	30	,	,	PUNCT
ejpam-4467	45	31	b	b	NOUN
ejpam-4467	45	32	,	,	PUNCT
ejpam-4467	45	33	c	c	PROPN
ejpam-4467	45	34	∈	∈	PROPN
ejpam-4467	45	35	x)(a	x)(a	PUNCT
ejpam-4467	46	1	∗	∗	NOUN
ejpam-4467	46	2	(	(	PUNCT
ejpam-4467	46	3	b	b	NOUN
ejpam-4467	46	4	∗	∗	ADP
ejpam-4467	46	5	c	c	NOUN
ejpam-4467	46	6	)	)	PUNCT
ejpam-4467	46	7	∈	∈	PROPN
ejpam-4467	46	8	k	k	PROPN
ejpam-4467	46	9	,	,	PUNCT
ejpam-4467	46	10	b	b	X
ejpam-4467	46	11	∈	∈	PROPN
ejpam-4467	46	12	k	k	PROPN
ejpam-4467	46	13	⇒	⇒	VERB
ejpam-4467	46	14	a	a	DET
ejpam-4467	46	15	∗	∗	NOUN
ejpam-4467	46	16	c	c	NOUN
ejpam-4467	46	17	∈	∈	PROPN
ejpam-4467	46	18	k	k	NOUN
ejpam-4467	46	19	)	)	PUNCT
ejpam-4467	46	20	.	.	PUNCT
ejpam-4467	47	1	(	(	PUNCT
ejpam-4467	47	2	5	5	X
ejpam-4467	47	3	)	)	PUNCT
ejpam-4467	47	4	definition	definition	NOUN
ejpam-4467	47	5	3	3	NUM
ejpam-4467	47	6	.	.	PUNCT
ejpam-4467	48	1	a	a	DET
ejpam-4467	48	2	fuzzy	fuzzy	ADJ
ejpam-4467	48	3	set	set	NOUN
ejpam-4467	48	4	ψ	ψ	PRON
ejpam-4467	48	5	in	in	ADP
ejpam-4467	48	6	x	x	PROPN
ejpam-4467	48	7	is	be	AUX
ejpam-4467	48	8	called	call	VERB
ejpam-4467	48	9	a	a	DET
ejpam-4467	48	10	fuzzy	fuzzy	ADJ
ejpam-4467	48	11	ideal	ideal	NOUN
ejpam-4467	48	12	of	of	ADP
ejpam-4467	48	13	(	(	PUNCT
ejpam-4467	48	14	x	x	X
ejpam-4467	48	15	,	,	PUNCT
ejpam-4467	48	16	1)∗	1)∗	NUM
ejpam-4467	48	17	(	(	PUNCT
ejpam-4467	48	18	see	see	VERB
ejpam-4467	48	19	[	[	X
ejpam-4467	48	20	9	9	NUM
ejpam-4467	48	21	]	]	SYM
ejpam-4467	48	22	)	)	PUNCT
ejpam-4467	48	23	if	if	SCONJ
ejpam-4467	48	24	it	it	PRON
ejpam-4467	48	25	satisfies	satisfy	VERB
ejpam-4467	48	26	:	:	PUNCT
ejpam-4467	48	27	(	(	PUNCT
ejpam-4467	48	28	∀x	∀x	X
ejpam-4467	48	29	,	,	PUNCT
ejpam-4467	48	30	b	b	X
ejpam-4467	48	31	∈	∈	PROPN
ejpam-4467	48	32	x	x	X
ejpam-4467	48	33	)	)	PUNCT
ejpam-4467	48	34	(	(	PUNCT
ejpam-4467	48	35	ψ(x	ψ(x	NOUN
ejpam-4467	48	36	∗	∗	NOUN
ejpam-4467	48	37	b	b	NOUN
ejpam-4467	48	38	)	)	PUNCT
ejpam-4467	48	39	≥	≥	NOUN
ejpam-4467	48	40	ψ(b	ψ(b	PROPN
ejpam-4467	48	41	)	)	PUNCT
ejpam-4467	48	42	)	)	PUNCT
ejpam-4467	48	43	,	,	PUNCT
ejpam-4467	48	44	(	(	PUNCT
ejpam-4467	48	45	6	6	NUM
ejpam-4467	48	46	)	)	PUNCT
ejpam-4467	48	47	(	(	PUNCT
ejpam-4467	48	48	∀x	∀x	X
ejpam-4467	48	49	,	,	PUNCT
ejpam-4467	48	50	b	b	NOUN
ejpam-4467	48	51	,	,	PUNCT
ejpam-4467	48	52	c	c	PROPN
ejpam-4467	48	53	∈	∈	PROPN
ejpam-4467	48	54	x	x	X
ejpam-4467	48	55	)	)	PUNCT
ejpam-4467	48	56	(	(	PUNCT
ejpam-4467	48	57	ψ((b	ψ((b	NOUN
ejpam-4467	48	58	∗	∗	NOUN
ejpam-4467	48	59	(	(	PUNCT
ejpam-4467	48	60	c	c	NOUN
ejpam-4467	48	61	∗	∗	X
ejpam-4467	48	62	x	x	NOUN
ejpam-4467	48	63	)	)	PUNCT
ejpam-4467	48	64	)	)	PUNCT
ejpam-4467	48	65	∗	∗	NOUN
ejpam-4467	48	66	x	x	NOUN
ejpam-4467	48	67	)	)	PUNCT
ejpam-4467	48	68	≥	≥	NOUN
ejpam-4467	48	69	min{ψ(b	min{ψ(b	NOUN
ejpam-4467	48	70	)	)	PUNCT
ejpam-4467	48	71	,	,	PUNCT
ejpam-4467	48	72	ψ(c	ψ(c	PROPN
ejpam-4467	48	73	)	)	PUNCT
ejpam-4467	48	74	}	}	PUNCT
ejpam-4467	48	75	)	)	PUNCT
ejpam-4467	48	76	.	.	PUNCT
ejpam-4467	49	1	(	(	PUNCT
ejpam-4467	49	2	7	7	X
ejpam-4467	49	3	)	)	PUNCT
ejpam-4467	49	4	a	a	DET
ejpam-4467	49	5	fuzzy	fuzzy	ADJ
ejpam-4467	49	6	set	set	NOUN
ejpam-4467	49	7	ψ	ψ	NOUN
ejpam-4467	49	8	in	in	ADP
ejpam-4467	49	9	a	a	DET
ejpam-4467	49	10	set	set	NOUN
ejpam-4467	49	11	x	x	X
ejpam-4467	49	12	of	of	ADP
ejpam-4467	49	13	the	the	DET
ejpam-4467	49	14	form	form	NOUN
ejpam-4467	49	15	ψ(b	ψ(b	PROPN
ejpam-4467	49	16	)	)	PUNCT
ejpam-4467	49	17	:	:	PUNCT
ejpam-4467	50	1	=	=	X
ejpam-4467	50	2	{	{	PUNCT
ejpam-4467	50	3	t	t	PROPN
ejpam-4467	50	4	∈	∈	PROPN
ejpam-4467	50	5	(	(	PUNCT
ejpam-4467	50	6	0	0	NUM
ejpam-4467	50	7	,	,	PUNCT
ejpam-4467	50	8	1	1	NUM
ejpam-4467	50	9	]	]	PUNCT
ejpam-4467	50	10	if	if	SCONJ
ejpam-4467	50	11	b	b	X
ejpam-4467	50	12	=	=	SYM
ejpam-4467	50	13	a	a	PROPN
ejpam-4467	50	14	,	,	PUNCT
ejpam-4467	50	15	0	0	PUNCT
ejpam-4467	50	16	if	if	SCONJ
ejpam-4467	50	17	b	b	X
ejpam-4467	50	18	̸=	̸=	PROPN
ejpam-4467	50	19	a	a	PRON
ejpam-4467	50	20	,	,	PUNCT
ejpam-4467	50	21	is	be	AUX
ejpam-4467	50	22	said	say	VERB
ejpam-4467	50	23	to	to	PART
ejpam-4467	50	24	be	be	AUX
ejpam-4467	50	25	a	a	DET
ejpam-4467	50	26	fuzzy	fuzzy	ADJ
ejpam-4467	50	27	point	point	NOUN
ejpam-4467	50	28	with	with	ADP
ejpam-4467	50	29	support	support	NOUN
ejpam-4467	50	30	a	a	PRON
ejpam-4467	50	31	and	and	CCONJ
ejpam-4467	50	32	value	value	NOUN
ejpam-4467	50	33	t	t	NOUN
ejpam-4467	50	34	and	and	CCONJ
ejpam-4467	50	35	is	be	AUX
ejpam-4467	50	36	denoted	denote	VERB
ejpam-4467	50	37	by	by	ADP
ejpam-4467	50	38	⟨a	⟨a	PROPN
ejpam-4467	50	39	/	/	SYM
ejpam-4467	50	40	t⟩.	t⟩.	NOUN
ejpam-4467	50	41	for	for	ADP
ejpam-4467	50	42	a	a	DET
ejpam-4467	50	43	fuzzy	fuzzy	ADJ
ejpam-4467	50	44	set	set	NOUN
ejpam-4467	50	45	ψ	ψ	NOUN
ejpam-4467	50	46	in	in	ADP
ejpam-4467	50	47	a	a	DET
ejpam-4467	50	48	set	set	NOUN
ejpam-4467	50	49	x	x	NOUN
ejpam-4467	50	50	,	,	PUNCT
ejpam-4467	50	51	we	we	PRON
ejpam-4467	50	52	say	say	VERB
ejpam-4467	50	53	that	that	SCONJ
ejpam-4467	50	54	a	a	DET
ejpam-4467	50	55	fuzzy	fuzzy	ADJ
ejpam-4467	50	56	point	point	NOUN
ejpam-4467	50	57	⟨a	⟨a	PUNCT
ejpam-4467	50	58	/	/	SYM
ejpam-4467	50	59	t⟩	t⟩	PRON
ejpam-4467	50	60	is	be	AUX
ejpam-4467	50	61	s.	s.	PROPN
ejpam-4467	50	62	s.	s.	PROPN
ejpam-4467	50	63	ahn	ahn	PROPN
ejpam-4467	50	64	,	,	PUNCT
ejpam-4467	50	65	e.	e.	PROPN
ejpam-4467	50	66	h.	h.	PROPN
ejpam-4467	50	67	roh	roh	PROPN
ejpam-4467	50	68	and	and	CCONJ
ejpam-4467	50	69	y.	y.	PROPN
ejpam-4467	50	70	b.	b.	PROPN
ejpam-4467	50	71	jun	jun	PROPN
ejpam-4467	50	72	/	/	SYM
ejpam-4467	50	73	eur	eur	PROPN
ejpam-4467	50	74	.	.	PUNCT
ejpam-4467	51	1	j.	j.	PROPN
ejpam-4467	51	2	pure	pure	PROPN
ejpam-4467	51	3	appl	appl	PROPN
ejpam-4467	51	4	.	.	PROPN
ejpam-4467	51	5	math	math	PROPN
ejpam-4467	51	6	,	,	PUNCT
ejpam-4467	51	7	15	15	NUM
ejpam-4467	51	8	(	(	PUNCT
ejpam-4467	51	9	3	3	NUM
ejpam-4467	51	10	)	)	PUNCT
ejpam-4467	51	11	(	(	PUNCT
ejpam-4467	51	12	2022	2022	NUM
ejpam-4467	51	13	)	)	PUNCT
ejpam-4467	51	14	,	,	PUNCT
ejpam-4467	51	15	1307	1307	NUM
ejpam-4467	51	16	-	-	SYM
ejpam-4467	51	17	1320	1320	NUM
ejpam-4467	51	18	1309	1309	NUM
ejpam-4467	51	19	(	(	PUNCT
ejpam-4467	51	20	i	i	NOUN
ejpam-4467	51	21	)	)	PUNCT
ejpam-4467	51	22	contained	contain	VERB
ejpam-4467	51	23	in	in	ADP
ejpam-4467	51	24	ψ	ψ	NOUN
ejpam-4467	51	25	,	,	PUNCT
ejpam-4467	51	26	denoted	denote	VERB
ejpam-4467	51	27	by	by	ADP
ejpam-4467	51	28	⟨a	⟨a	NOUN
ejpam-4467	51	29	/	/	SYM
ejpam-4467	51	30	t⟩	t⟩	NOUN
ejpam-4467	51	31	∈	∈	NOUN
ejpam-4467	51	32	ψ	ψ	NOUN
ejpam-4467	51	33	,	,	PUNCT
ejpam-4467	51	34	(	(	PUNCT
ejpam-4467	51	35	[	[	X
ejpam-4467	51	36	6	6	NUM
ejpam-4467	51	37	]	]	SYM
ejpam-4467	51	38	)	)	PUNCT
ejpam-4467	51	39	if	if	SCONJ
ejpam-4467	51	40	ψ(a	ψ(a	PROPN
ejpam-4467	51	41	)	)	PUNCT
ejpam-4467	51	42	≥	≥	NOUN
ejpam-4467	51	43	t.	t.	PROPN
ejpam-4467	51	44	(	(	PUNCT
ejpam-4467	51	45	ii	ii	NOUN
ejpam-4467	51	46	)	)	PUNCT
ejpam-4467	51	47	quasi	quasi	NOUN
ejpam-4467	51	48	-	-	VERB
ejpam-4467	51	49	coincident	coincident	ADJ
ejpam-4467	51	50	with	with	ADP
ejpam-4467	51	51	ψ	ψ	NOUN
ejpam-4467	51	52	,	,	PUNCT
ejpam-4467	51	53	denoted	denote	VERB
ejpam-4467	51	54	by	by	ADP
ejpam-4467	51	55	⟨a	⟨a	NOUN
ejpam-4467	51	56	/	/	SYM
ejpam-4467	51	57	t⟩	t⟩	PRON
ejpam-4467	51	58	q	q	NOUN
ejpam-4467	51	59	ψ	ψ	NOUN
ejpam-4467	51	60	,	,	PUNCT
ejpam-4467	51	61	(	(	PUNCT
ejpam-4467	51	62	[	[	X
ejpam-4467	51	63	6	6	NUM
ejpam-4467	51	64	]	]	SYM
ejpam-4467	51	65	)	)	PUNCT
ejpam-4467	51	66	if	if	SCONJ
ejpam-4467	51	67	ψ(a	ψ(a	PROPN
ejpam-4467	51	68	)	)	PUNCT
ejpam-4467	52	1	+	+	CCONJ
ejpam-4467	52	2	t	t	X
ejpam-4467	52	3	>	>	X
ejpam-4467	52	4	1	1	X
ejpam-4467	52	5	.	.	PUNCT
ejpam-4467	52	6	definition	definition	NOUN
ejpam-4467	52	7	4	4	NUM
ejpam-4467	52	8	(	(	PUNCT
ejpam-4467	52	9	[	[	X
ejpam-4467	52	10	3	3	NUM
ejpam-4467	52	11	]	]	NUM
ejpam-4467	52	12	)	)	PUNCT
ejpam-4467	52	13	.	.	PUNCT
ejpam-4467	53	1	let	let	VERB
ejpam-4467	53	2	ψ	ψ	PART
ejpam-4467	53	3	be	be	AUX
ejpam-4467	53	4	a	a	DET
ejpam-4467	53	5	fuzzy	fuzzy	ADJ
ejpam-4467	53	6	set	set	NOUN
ejpam-4467	53	7	in	in	ADP
ejpam-4467	53	8	a	a	DET
ejpam-4467	53	9	set	set	NOUN
ejpam-4467	53	10	x	x	PUNCT
ejpam-4467	53	11	and	and	CCONJ
ejpam-4467	53	12	let	let	VERB
ejpam-4467	53	13	ε	ε	PROPN
ejpam-4467	53	14	∈	∈	PROPN
ejpam-4467	53	15	(	(	PUNCT
ejpam-4467	53	16	0	0	NUM
ejpam-4467	53	17	,	,	PUNCT
ejpam-4467	53	18	1	1	NUM
ejpam-4467	53	19	)	)	PUNCT
ejpam-4467	53	20	.	.	PUNCT
ejpam-4467	54	1	a	a	DET
ejpam-4467	54	2	function	function	NOUN
ejpam-4467	54	3	lεψ	lεψ	VERB
ejpam-4467	54	4	:	:	PUNCT
ejpam-4467	54	5	x	x	X
ejpam-4467	54	6	→	→	SYM
ejpam-4467	55	1	[	[	X
ejpam-4467	55	2	0	0	NUM
ejpam-4467	55	3	,	,	PUNCT
ejpam-4467	55	4	1	1	NUM
ejpam-4467	55	5	]	]	PUNCT
ejpam-4467	55	6	,	,	PUNCT
ejpam-4467	55	7	x	x	PROPN
ejpam-4467	55	8	7→	7→	NUM
ejpam-4467	55	9	max{0	max{0	NOUN
ejpam-4467	55	10	,	,	PUNCT
ejpam-4467	55	11	ψ(x	ψ(x	NOUN
ejpam-4467	55	12	)	)	PUNCT
ejpam-4467	56	1	+	+	CCONJ
ejpam-4467	56	2	ε−	ε−	PROPN
ejpam-4467	56	3	1	1	NUM
ejpam-4467	56	4	}	}	PUNCT
ejpam-4467	56	5	is	be	AUX
ejpam-4467	56	6	called	call	VERB
ejpam-4467	56	7	the	the	DET
ejpam-4467	56	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	56	9	fuzzy	fuzzy	ADJ
ejpam-4467	56	10	set	set	NOUN
ejpam-4467	56	11	(	(	PUNCT
ejpam-4467	56	12	of	of	ADP
ejpam-4467	56	13	ψ	ψ	NOUN
ejpam-4467	56	14	)	)	PUNCT
ejpam-4467	56	15	in	in	ADP
ejpam-4467	56	16	x.	x.	NOUN
ejpam-4467	56	17	for	for	SCONJ
ejpam-4467	56	18	the	the	DET
ejpam-4467	56	19	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	56	20	fuzzy	fuzzy	ADJ
ejpam-4467	56	21	set	set	VERB
ejpam-4467	56	22	lεψ	lεψ	ADJ
ejpam-4467	56	23	(	(	PUNCT
ejpam-4467	56	24	of	of	ADP
ejpam-4467	56	25	ψ	ψ	NOUN
ejpam-4467	56	26	)	)	PUNCT
ejpam-4467	56	27	in	in	ADP
ejpam-4467	56	28	x	x	PUNCT
ejpam-4467	56	29	and	and	CCONJ
ejpam-4467	56	30	t	t	PROPN
ejpam-4467	56	31	∈	∈	PROPN
ejpam-4467	56	32	(	(	PUNCT
ejpam-4467	56	33	0	0	NUM
ejpam-4467	56	34	,	,	PUNCT
ejpam-4467	56	35	1	1	NUM
ejpam-4467	56	36	]	]	PUNCT
ejpam-4467	56	37	,	,	PUNCT
ejpam-4467	56	38	consider	consider	VERB
ejpam-4467	56	39	the	the	DET
ejpam-4467	56	40	sets	set	NOUN
ejpam-4467	56	41	(	(	PUNCT
ejpam-4467	56	42	lεψ	lεψ	ADJ
ejpam-4467	56	43	,	,	PUNCT
ejpam-4467	56	44	t)∈	t)∈	PUNCT
ejpam-4467	56	45	:	:	PUNCT
ejpam-4467	56	46	=	=	SYM
ejpam-4467	56	47	{	{	PUNCT
ejpam-4467	56	48	x	x	PUNCT
ejpam-4467	56	49	∈	∈	PROPN
ejpam-4467	56	50	x	x	X
ejpam-4467	56	51	|	|	ADV
ejpam-4467	56	52	⟨x	⟨x	VERB
ejpam-4467	56	53	/	/	SYM
ejpam-4467	56	54	t⟩	t⟩	NOUN
ejpam-4467	56	55	∈	∈	PROPN
ejpam-4467	56	56	lεψ	lεψ	PROPN
ejpam-4467	56	57	}	}	PUNCT
ejpam-4467	56	58	,	,	PUNCT
ejpam-4467	56	59	(	(	PUNCT
ejpam-4467	56	60	lεψ	lεψ	ADJ
ejpam-4467	56	61	,	,	PUNCT
ejpam-4467	56	62	t)q	t)q	PUNCT
ejpam-4467	56	63	:	:	PUNCT
ejpam-4467	56	64	=	=	SYM
ejpam-4467	56	65	{	{	PUNCT
ejpam-4467	56	66	x	x	PUNCT
ejpam-4467	56	67	∈	∈	PROPN
ejpam-4467	56	68	x	x	X
ejpam-4467	56	69	|	|	ADV
ejpam-4467	56	70	⟨x	⟨x	VERB
ejpam-4467	56	71	/	/	SYM
ejpam-4467	56	72	t⟩	t⟩	PRON
ejpam-4467	56	73	q	q	X
ejpam-4467	56	74	lεψ	lεψ	PROPN
ejpam-4467	56	75	}	}	PUNCT
ejpam-4467	56	76	,	,	PUNCT
ejpam-4467	56	77	which	which	PRON
ejpam-4467	56	78	are	be	AUX
ejpam-4467	56	79	called	call	VERB
ejpam-4467	56	80	the	the	DET
ejpam-4467	56	81	∈-set	∈-set	NOUN
ejpam-4467	56	82	and	and	CCONJ
ejpam-4467	56	83	q	q	NOUN
ejpam-4467	56	84	-	-	PUNCT
ejpam-4467	56	85	set	set	VERB
ejpam-4467	56	86	,	,	PUNCT
ejpam-4467	56	87	respectively	respectively	ADV
ejpam-4467	56	88	,	,	PUNCT
ejpam-4467	56	89	of	of	ADP
ejpam-4467	56	90	lεψ	lεψ	PROPN
ejpam-4467	56	91	(	(	PUNCT
ejpam-4467	56	92	with	with	ADP
ejpam-4467	56	93	value	value	NOUN
ejpam-4467	56	94	t	t	PROPN
ejpam-4467	56	95	)	)	PUNCT
ejpam-4467	56	96	.	.	PUNCT
ejpam-4467	57	1	also	also	ADV
ejpam-4467	57	2	,	,	PUNCT
ejpam-4467	57	3	consider	consider	VERB
ejpam-4467	57	4	a	a	DET
ejpam-4467	57	5	set	set	NOUN
ejpam-4467	57	6	:	:	PUNCT
ejpam-4467	57	7	o	o	NOUN
ejpam-4467	57	8	(	(	PUNCT
ejpam-4467	57	9	lεψ	lεψ	PROPN
ejpam-4467	57	10	)	)	PUNCT
ejpam-4467	57	11	:	:	PUNCT
ejpam-4467	58	1	=	=	SYM
ejpam-4467	58	2	{	{	PUNCT
ejpam-4467	58	3	x	x	PUNCT
ejpam-4467	58	4	∈	∈	PROPN
ejpam-4467	58	5	x	x	INTJ
ejpam-4467	58	6	|	|	ADV
ejpam-4467	58	7	lεψ(x	lεψ(x	NOUN
ejpam-4467	58	8	)	)	PUNCT
ejpam-4467	58	9	>	>	X
ejpam-4467	58	10	0	0	X
ejpam-4467	58	11	}	}	PUNCT
ejpam-4467	58	12	(	(	PUNCT
ejpam-4467	58	13	8)	8)	NUM
ejpam-4467	58	14	which	which	PRON
ejpam-4467	58	15	is	be	AUX
ejpam-4467	58	16	called	call	VERB
ejpam-4467	58	17	an	an	DET
ejpam-4467	58	18	o	o	NOUN
ejpam-4467	58	19	-	-	NOUN
ejpam-4467	58	20	set	set	NOUN
ejpam-4467	58	21	of	of	ADP
ejpam-4467	58	22	lεψ	lεψ	ADJ
ejpam-4467	58	23	.	.	PUNCT
ejpam-4467	59	1	it	it	PRON
ejpam-4467	59	2	is	be	AUX
ejpam-4467	59	3	observed	observe	VERB
ejpam-4467	59	4	that	that	SCONJ
ejpam-4467	59	5	o	o	NOUN
ejpam-4467	59	6	(	(	PUNCT
ejpam-4467	59	7	lεψ	lεψ	ADJ
ejpam-4467	59	8	)	)	PUNCT
ejpam-4467	59	9	=	=	PRON
ejpam-4467	59	10	{	{	PUNCT
ejpam-4467	59	11	x	x	PUNCT
ejpam-4467	59	12	∈	∈	PROPN
ejpam-4467	59	13	x	x	X
ejpam-4467	59	14	|	|	NOUN
ejpam-4467	59	15	ψ(x	ψ(x	NOUN
ejpam-4467	59	16	)	)	PUNCT
ejpam-4467	60	1	+	+	CCONJ
ejpam-4467	60	2	ε−	ε−	PROPN
ejpam-4467	60	3	1	1	NUM
ejpam-4467	60	4	>	>	PUNCT
ejpam-4467	60	5	0	0	NUM
ejpam-4467	60	6	}	}	PUNCT
ejpam-4467	60	7	.	.	PUNCT
ejpam-4467	61	1	3	3	X
ejpam-4467	61	2	.	.	X
ejpam-4467	61	3	lukasiewicz	lukasiewicz	VERB
ejpam-4467	61	4	fuzzy	fuzzy	ADJ
ejpam-4467	61	5	ideals	ideal	NOUN
ejpam-4467	61	6	in	in	ADP
ejpam-4467	61	7	this	this	DET
ejpam-4467	61	8	section	section	NOUN
ejpam-4467	61	9	,	,	PUNCT
ejpam-4467	61	10	let	let	VERB
ejpam-4467	61	11	ψ	ψ	PRON
ejpam-4467	61	12	and	and	CCONJ
ejpam-4467	61	13	ε	ε	PROPN
ejpam-4467	61	14	be	be	VERB
ejpam-4467	61	15	a	a	DET
ejpam-4467	61	16	fuzzy	fuzzy	ADJ
ejpam-4467	61	17	set	set	NOUN
ejpam-4467	61	18	in	in	ADP
ejpam-4467	61	19	x	x	PUNCT
ejpam-4467	61	20	and	and	CCONJ
ejpam-4467	61	21	an	an	DET
ejpam-4467	61	22	element	element	NOUN
ejpam-4467	61	23	of	of	ADP
ejpam-4467	61	24	(	(	PUNCT
ejpam-4467	61	25	0	0	NUM
ejpam-4467	61	26	,	,	PUNCT
ejpam-4467	61	27	1	1	NUM
ejpam-4467	61	28	)	)	PUNCT
ejpam-4467	61	29	,	,	PUNCT
ejpam-4467	61	30	respectively	respectively	ADV
ejpam-4467	61	31	,	,	PUNCT
ejpam-4467	61	32	unless	unless	SCONJ
ejpam-4467	61	33	otherwise	otherwise	ADV
ejpam-4467	61	34	specified	specify	VERB
ejpam-4467	61	35	.	.	PUNCT
ejpam-4467	62	1	definition	definition	NOUN
ejpam-4467	62	2	5	5	NUM
ejpam-4467	62	3	.	.	PUNCT
ejpam-4467	63	1	a	a	DET
ejpam-4467	63	2	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	63	3	fuzzy	fuzzy	ADJ
ejpam-4467	63	4	set	set	VERB
ejpam-4467	63	5	lεψ	lεψ	VERB
ejpam-4467	63	6	in	in	ADP
ejpam-4467	63	7	x	x	PROPN
ejpam-4467	63	8	is	be	AUX
ejpam-4467	63	9	called	call	VERB
ejpam-4467	63	10	a	a	DET
ejpam-4467	63	11	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	63	12	fuzzy	fuzzy	ADJ
ejpam-4467	63	13	ideal	ideal	NOUN
ejpam-4467	63	14	of	of	ADP
ejpam-4467	63	15	(	(	PUNCT
ejpam-4467	63	16	x	x	X
ejpam-4467	63	17	,	,	PUNCT
ejpam-4467	63	18	1)∗	1)∗	NOUN
ejpam-4467	63	19	if	if	SCONJ
ejpam-4467	63	20	it	it	PRON
ejpam-4467	63	21	satisfies	satisfy	VERB
ejpam-4467	63	22	:	:	PUNCT
ejpam-4467	63	23	(	(	PUNCT
ejpam-4467	63	24	∀x	∀x	X
ejpam-4467	63	25	,	,	PUNCT
ejpam-4467	63	26	y	y	PROPN
ejpam-4467	63	27	∈	∈	PROPN
ejpam-4467	63	28	x)(∀t	x)(∀t	PROPN
ejpam-4467	63	29	∈	∈	PROPN
ejpam-4467	63	30	(	(	PUNCT
ejpam-4467	63	31	0	0	NUM
ejpam-4467	63	32	,	,	PUNCT
ejpam-4467	63	33	1	1	NUM
ejpam-4467	63	34	]	]	NUM
ejpam-4467	63	35	)	)	PUNCT
ejpam-4467	63	36	(	(	PUNCT
ejpam-4467	63	37	⟨y	⟨y	X
ejpam-4467	63	38	/	/	SYM
ejpam-4467	63	39	t⟩	t⟩	PRON
ejpam-4467	63	40	∈	∈	PROPN
ejpam-4467	63	41	lεψ	lεψ	ADJ
ejpam-4467	63	42	⇒	⇒	PROPN
ejpam-4467	63	43	⟨(x	⟨(x	PROPN
ejpam-4467	63	44	∗	∗	NOUN
ejpam-4467	63	45	y)/t⟩	y)/t⟩	PUNCT
ejpam-4467	64	1	∈	∈	PROPN
ejpam-4467	64	2	lεψ	lεψ	VERB
ejpam-4467	64	3	)	)	PUNCT
ejpam-4467	64	4	,	,	PUNCT
ejpam-4467	64	5	(	(	PUNCT
ejpam-4467	64	6	9	9	X
ejpam-4467	64	7	)	)	PUNCT
ejpam-4467	64	8	(	(	PUNCT
ejpam-4467	64	9	∀x	∀x	X
ejpam-4467	64	10	,	,	PUNCT
ejpam-4467	64	11	y	y	PROPN
ejpam-4467	64	12	,	,	PUNCT
ejpam-4467	64	13	z	z	PROPN
ejpam-4467	64	14	∈	∈	PROPN
ejpam-4467	64	15	x)(∀ta	x)(∀ta	NOUN
ejpam-4467	64	16	,	,	PUNCT
ejpam-4467	64	17	tb	tb	ADP
ejpam-4467	64	18	∈	∈	PROPN
ejpam-4467	64	19	(	(	PUNCT
ejpam-4467	64	20	0	0	NUM
ejpam-4467	64	21	,	,	PUNCT
ejpam-4467	64	22	1	1	NUM
ejpam-4467	64	23	]	]	NUM
ejpam-4467	64	24	)	)	PUNCT
ejpam-4467	64	25	(	(	PUNCT
ejpam-4467	64	26	⟨x	⟨x	VERB
ejpam-4467	64	27	/	/	SYM
ejpam-4467	64	28	ta⟩	ta⟩	CCONJ
ejpam-4467	64	29	∈	∈	PROPN
ejpam-4467	64	30	lεψ	lεψ	VERB
ejpam-4467	64	31	,	,	PUNCT
ejpam-4467	64	32	⟨y	⟨y	AUX
ejpam-4467	64	33	/	/	SYM
ejpam-4467	64	34	tb⟩	tb⟩	PROPN
ejpam-4467	64	35	∈	∈	PROPN
ejpam-4467	64	36	lεψ	lεψ	VERB
ejpam-4467	64	37	⇒	⇒	PROPN
ejpam-4467	64	38	⟨((x	⟨((x	PROPN
ejpam-4467	64	39	∗	∗	NOUN
ejpam-4467	64	40	(	(	PUNCT
ejpam-4467	64	41	y	y	PROPN
ejpam-4467	64	42	∗	∗	PROPN
ejpam-4467	64	43	z	z	NOUN
ejpam-4467	64	44	)	)	PUNCT
ejpam-4467	64	45	)	)	PUNCT
ejpam-4467	64	46	∗	∗	NOUN
ejpam-4467	64	47	z)/min{ta	z)/min{ta	PROPN
ejpam-4467	64	48	,	,	PUNCT
ejpam-4467	64	49	tb}⟩	tb}⟩	X
ejpam-4467	64	50	∈	∈	PROPN
ejpam-4467	64	51	lεψ	lεψ	VERB
ejpam-4467	64	52	)	)	PUNCT
ejpam-4467	64	53	.	.	PUNCT
ejpam-4467	65	1	(	(	PUNCT
ejpam-4467	65	2	10	10	NUM
ejpam-4467	65	3	)	)	PUNCT
ejpam-4467	65	4	example	example	NOUN
ejpam-4467	66	1	1	1	NUM
ejpam-4467	66	2	.	.	PUNCT
ejpam-4467	66	3	let	let	VERB
ejpam-4467	66	4	x	x	PUNCT
ejpam-4467	66	5	=	=	PRON
ejpam-4467	66	6	{	{	PUNCT
ejpam-4467	66	7	1	1	NUM
ejpam-4467	66	8	,	,	PUNCT
ejpam-4467	66	9	a	a	DET
ejpam-4467	66	10	,	,	PUNCT
ejpam-4467	66	11	b	b	NOUN
ejpam-4467	66	12	,	,	PUNCT
ejpam-4467	66	13	c	c	NOUN
ejpam-4467	66	14	,	,	PUNCT
ejpam-4467	66	15	d	d	NOUN
ejpam-4467	66	16	,	,	PUNCT
ejpam-4467	66	17	0	0	NUM
ejpam-4467	66	18	}	}	PUNCT
ejpam-4467	66	19	be	be	AUX
ejpam-4467	66	20	a	a	DET
ejpam-4467	66	21	set	set	NOUN
ejpam-4467	66	22	with	with	ADP
ejpam-4467	66	23	the	the	DET
ejpam-4467	66	24	binary	binary	PROPN
ejpam-4467	66	25	operation	operation	NOUN
ejpam-4467	66	26	“	"	PUNCT
ejpam-4467	66	27	∗	∗	NOUN
ejpam-4467	66	28	”	"	PUNCT
ejpam-4467	66	29	given	give	VERB
ejpam-4467	66	30	by	by	ADP
ejpam-4467	66	31	the	the	DET
ejpam-4467	66	32	following	follow	VERB
ejpam-4467	66	33	cayley	cayley	ADJ
ejpam-4467	66	34	table	table	NOUN
ejpam-4467	66	35	:	:	PUNCT
ejpam-4467	66	36	∗	∗	NOUN
ejpam-4467	66	37	1	1	NUM
ejpam-4467	66	38	a	a	DET
ejpam-4467	66	39	b	b	NOUN
ejpam-4467	66	40	c	c	NOUN
ejpam-4467	66	41	d	d	SYM
ejpam-4467	66	42	0	0	NUM
ejpam-4467	66	43	1	1	NUM
ejpam-4467	66	44	1	1	NUM
ejpam-4467	66	45	a	a	DET
ejpam-4467	66	46	b	b	NOUN
ejpam-4467	66	47	c	c	NOUN
ejpam-4467	66	48	d	d	NOUN
ejpam-4467	66	49	0	0	PUNCT
ejpam-4467	66	50	a	a	DET
ejpam-4467	66	51	1	1	NUM
ejpam-4467	66	52	1	1	NUM
ejpam-4467	66	53	a	a	DET
ejpam-4467	66	54	c	c	NOUN
ejpam-4467	66	55	c	c	NOUN
ejpam-4467	66	56	d	d	PROPN
ejpam-4467	66	57	b	b	PROPN
ejpam-4467	66	58	1	1	NUM
ejpam-4467	66	59	1	1	NUM
ejpam-4467	66	60	1	1	NUM
ejpam-4467	66	61	c	c	NOUN
ejpam-4467	66	62	c	c	NOUN
ejpam-4467	66	63	c	c	NOUN
ejpam-4467	66	64	c	c	PROPN
ejpam-4467	66	65	1	1	NUM
ejpam-4467	66	66	a	a	DET
ejpam-4467	66	67	b	b	PROPN
ejpam-4467	66	68	1	1	NUM
ejpam-4467	66	69	a	a	DET
ejpam-4467	66	70	b	b	PROPN
ejpam-4467	66	71	d	d	SYM
ejpam-4467	66	72	1	1	NUM
ejpam-4467	66	73	1	1	NUM
ejpam-4467	66	74	a	a	DET
ejpam-4467	66	75	1	1	NUM
ejpam-4467	66	76	1	1	NUM
ejpam-4467	66	77	a	a	DET
ejpam-4467	66	78	0	0	NUM
ejpam-4467	66	79	1	1	NUM
ejpam-4467	66	80	1	1	NUM
ejpam-4467	66	81	1	1	NUM
ejpam-4467	66	82	1	1	NUM
ejpam-4467	66	83	1	1	NUM
ejpam-4467	66	84	1	1	NUM
ejpam-4467	66	85	s.	s.	PROPN
ejpam-4467	66	86	s.	s.	PROPN
ejpam-4467	66	87	ahn	ahn	PROPN
ejpam-4467	66	88	,	,	PUNCT
ejpam-4467	66	89	e.	e.	PROPN
ejpam-4467	66	90	h.	h.	PROPN
ejpam-4467	66	91	roh	roh	PROPN
ejpam-4467	66	92	and	and	CCONJ
ejpam-4467	66	93	y.	y.	PROPN
ejpam-4467	66	94	b.	b.	PROPN
ejpam-4467	66	95	jun	jun	PROPN
ejpam-4467	66	96	/	/	SYM
ejpam-4467	66	97	eur	eur	PROPN
ejpam-4467	66	98	.	.	PUNCT
ejpam-4467	67	1	j.	j.	PROPN
ejpam-4467	67	2	pure	pure	PROPN
ejpam-4467	67	3	appl	appl	PROPN
ejpam-4467	67	4	.	.	PROPN
ejpam-4467	67	5	math	math	PROPN
ejpam-4467	67	6	,	,	PUNCT
ejpam-4467	67	7	15	15	NUM
ejpam-4467	67	8	(	(	PUNCT
ejpam-4467	67	9	3	3	NUM
ejpam-4467	67	10	)	)	PUNCT
ejpam-4467	67	11	(	(	PUNCT
ejpam-4467	67	12	2022	2022	NUM
ejpam-4467	67	13	)	)	PUNCT
ejpam-4467	67	14	,	,	PUNCT
ejpam-4467	67	15	1307	1307	NUM
ejpam-4467	67	16	-	-	SYM
ejpam-4467	67	17	1320	1320	NUM
ejpam-4467	67	18	1310	1310	NUM
ejpam-4467	67	19	then	then	ADV
ejpam-4467	67	20	(	(	PUNCT
ejpam-4467	67	21	x	x	X
ejpam-4467	67	22	,	,	PUNCT
ejpam-4467	67	23	1)∗	1)∗	NUM
ejpam-4467	67	24	is	be	AUX
ejpam-4467	67	25	a	a	DET
ejpam-4467	67	26	be	be	NOUN
ejpam-4467	67	27	-	-	PUNCT
ejpam-4467	67	28	algebra	algebra	NOUN
ejpam-4467	67	29	(	(	PUNCT
ejpam-4467	67	30	see	see	VERB
ejpam-4467	67	31	[	[	X
ejpam-4467	67	32	5	5	NUM
ejpam-4467	67	33	]	]	PUNCT
ejpam-4467	67	34	)	)	PUNCT
ejpam-4467	67	35	.	.	PUNCT
ejpam-4467	68	1	let	let	VERB
ejpam-4467	68	2	ψ	ψ	PART
ejpam-4467	68	3	be	be	AUX
ejpam-4467	68	4	a	a	DET
ejpam-4467	68	5	fuzzy	fuzzy	ADJ
ejpam-4467	68	6	set	set	NOUN
ejpam-4467	68	7	in	in	ADP
ejpam-4467	68	8	x	x	PUNCT
ejpam-4467	68	9	defined	define	VERB
ejpam-4467	68	10	as	as	SCONJ
ejpam-4467	68	11	follows	follow	VERB
ejpam-4467	68	12	.	.	PUNCT
ejpam-4467	69	1	ψ	ψ	X
ejpam-4467	69	2	:	:	PUNCT
ejpam-4467	69	3	x	x	X
ejpam-4467	69	4	→	→	SYM
ejpam-4467	70	1	[	[	X
ejpam-4467	70	2	0	0	NUM
ejpam-4467	70	3	,	,	PUNCT
ejpam-4467	70	4	1	1	NUM
ejpam-4467	70	5	]	]	PUNCT
ejpam-4467	70	6	,	,	PUNCT
ejpam-4467	70	7	x	x	PROPN
ejpam-4467	70	8	7→	7→	NUM
ejpam-4467	70	9			NUM
ejpam-4467	70	10	0.57	0.57	NUM
ejpam-4467	70	11	if	if	SCONJ
ejpam-4467	70	12	x	x	X
ejpam-4467	70	13	∈	∈	NOUN
ejpam-4467	70	14	{	{	PUNCT
ejpam-4467	70	15	1	1	NUM
ejpam-4467	70	16	,	,	PUNCT
ejpam-4467	70	17	a	a	DET
ejpam-4467	70	18	,	,	PUNCT
ejpam-4467	70	19	b	b	NOUN
ejpam-4467	70	20	}	}	PUNCT
ejpam-4467	70	21	,	,	PUNCT
ejpam-4467	70	22	0.14	0.14	NUM
ejpam-4467	70	23	if	if	SCONJ
ejpam-4467	70	24	x	x	PROPN
ejpam-4467	70	25	=	=	SYM
ejpam-4467	70	26	c	c	NOUN
ejpam-4467	70	27	,	,	PUNCT
ejpam-4467	70	28	0.33	0.33	NUM
ejpam-4467	70	29	if	if	SCONJ
ejpam-4467	70	30	x	x	X
ejpam-4467	70	31	=	=	SYM
ejpam-4467	70	32	d	d	PROPN
ejpam-4467	70	33	,	,	PUNCT
ejpam-4467	70	34	0.21	0.21	NUM
ejpam-4467	70	35	if	if	SCONJ
ejpam-4467	70	36	x	x	X
ejpam-4467	70	37	=	=	NOUN
ejpam-4467	70	38	0	0	X
ejpam-4467	70	39	.	.	PUNCT
ejpam-4467	71	1	for	for	ADP
ejpam-4467	71	2	ε	ε	PROPN
ejpam-4467	71	3	:	:	PUNCT
ejpam-4467	71	4	=	=	SYM
ejpam-4467	71	5	0.65	0.65	NUM
ejpam-4467	71	6	,	,	PUNCT
ejpam-4467	71	7	the	the	DET
ejpam-4467	71	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	71	9	fuzzy	fuzzy	ADJ
ejpam-4467	71	10	set	set	VERB
ejpam-4467	71	11	lεψ	lεψ	ADJ
ejpam-4467	71	12	of	of	ADP
ejpam-4467	71	13	ψ	ψ	PRON
ejpam-4467	71	14	in	in	ADP
ejpam-4467	71	15	x	x	PROPN
ejpam-4467	71	16	is	be	AUX
ejpam-4467	71	17	given	give	VERB
ejpam-4467	71	18	as	as	SCONJ
ejpam-4467	71	19	follows	follow	NOUN
ejpam-4467	71	20	.	.	PUNCT
ejpam-4467	72	1	lεψ	lεψ	VERB
ejpam-4467	72	2	:	:	PUNCT
ejpam-4467	72	3	x	x	X
ejpam-4467	72	4	→	→	SYM
ejpam-4467	73	1	[	[	X
ejpam-4467	73	2	0	0	NUM
ejpam-4467	73	3	,	,	PUNCT
ejpam-4467	73	4	1	1	NUM
ejpam-4467	73	5	]	]	PUNCT
ejpam-4467	73	6	,	,	PUNCT
ejpam-4467	73	7	y	y	PROPN
ejpam-4467	73	8	7→	7→	PROPN
ejpam-4467	73	9	{	{	PUNCT
ejpam-4467	73	10	0.22	0.22	NUM
ejpam-4467	73	11	if	if	SCONJ
ejpam-4467	73	12	y	y	PROPN
ejpam-4467	73	13	∈	∈	PROPN
ejpam-4467	73	14	{	{	PUNCT
ejpam-4467	73	15	1	1	NUM
ejpam-4467	73	16	,	,	PUNCT
ejpam-4467	73	17	a	a	DET
ejpam-4467	73	18	,	,	PUNCT
ejpam-4467	73	19	b	b	NOUN
ejpam-4467	73	20	}	}	PUNCT
ejpam-4467	73	21	,	,	PUNCT
ejpam-4467	73	22	0.00	0.00	NUM
ejpam-4467	73	23	if	if	SCONJ
ejpam-4467	73	24	y	y	PROPN
ejpam-4467	73	25	∈	∈	PROPN
ejpam-4467	73	26	{	{	PUNCT
ejpam-4467	73	27	c	c	NOUN
ejpam-4467	73	28	,	,	PUNCT
ejpam-4467	73	29	d	d	NOUN
ejpam-4467	73	30	,	,	PUNCT
ejpam-4467	73	31	0	0	NUM
ejpam-4467	73	32	}	}	PUNCT
ejpam-4467	73	33	.	.	PUNCT
ejpam-4467	74	1	it	it	PRON
ejpam-4467	74	2	is	be	AUX
ejpam-4467	74	3	routine	routine	ADJ
ejpam-4467	74	4	to	to	PART
ejpam-4467	74	5	verify	verify	VERB
ejpam-4467	74	6	that	that	SCONJ
ejpam-4467	74	7	lεψ	lεψ	ADJ
ejpam-4467	74	8	is	be	AUX
ejpam-4467	74	9	a	a	DET
ejpam-4467	74	10	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	74	11	fuzzy	fuzzy	ADJ
ejpam-4467	74	12	ideal	ideal	NOUN
ejpam-4467	74	13	of	of	ADP
ejpam-4467	74	14	(	(	PUNCT
ejpam-4467	74	15	x	x	X
ejpam-4467	74	16	,	,	PUNCT
ejpam-4467	74	17	1)∗.	1)∗.	PRON
ejpam-4467	74	18	theorem	theorem	VERB
ejpam-4467	74	19	1	1	NUM
ejpam-4467	74	20	.	.	PUNCT
ejpam-4467	75	1	a	a	DET
ejpam-4467	75	2	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	75	3	fuzzy	fuzzy	ADJ
ejpam-4467	75	4	set	set	VERB
ejpam-4467	75	5	lεψ	lεψ	VERB
ejpam-4467	75	6	in	in	ADP
ejpam-4467	75	7	x	x	PROPN
ejpam-4467	75	8	is	be	AUX
ejpam-4467	75	9	a	a	DET
ejpam-4467	75	10	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	75	11	fuzzy	fuzzy	ADJ
ejpam-4467	75	12	ideal	ideal	NOUN
ejpam-4467	75	13	of	of	ADP
ejpam-4467	75	14	(	(	PUNCT
ejpam-4467	75	15	x	x	NOUN
ejpam-4467	75	16	,	,	PUNCT
ejpam-4467	75	17	1)∗	1)∗	NOUN
ejpam-4467	75	18	if	if	SCONJ
ejpam-4467	75	19	and	and	CCONJ
ejpam-4467	75	20	only	only	ADV
ejpam-4467	75	21	if	if	SCONJ
ejpam-4467	75	22	it	it	PRON
ejpam-4467	75	23	satisfies	satisfy	VERB
ejpam-4467	75	24	:	:	PUNCT
ejpam-4467	75	25	(	(	PUNCT
ejpam-4467	75	26	∀x	∀x	X
ejpam-4467	75	27	,	,	PUNCT
ejpam-4467	75	28	y	y	PROPN
ejpam-4467	75	29	∈	∈	PROPN
ejpam-4467	75	30	x	x	X
ejpam-4467	75	31	)	)	PUNCT
ejpam-4467	75	32	(	(	PUNCT
ejpam-4467	75	33	lεψ(x	lεψ(x	PROPN
ejpam-4467	75	34	∗	∗	X
ejpam-4467	75	35	y	y	NOUN
ejpam-4467	75	36	)	)	PUNCT
ejpam-4467	75	37	≥	≥	NOUN
ejpam-4467	75	38	lεψ(y	lεψ(y	VERB
ejpam-4467	75	39	)	)	PUNCT
ejpam-4467	75	40	)	)	PUNCT
ejpam-4467	75	41	.	.	PUNCT
ejpam-4467	76	1	(	(	PUNCT
ejpam-4467	76	2	11	11	NUM
ejpam-4467	76	3	)	)	PUNCT
ejpam-4467	76	4	(	(	PUNCT
ejpam-4467	76	5	∀x	∀x	X
ejpam-4467	76	6	,	,	PUNCT
ejpam-4467	76	7	y	y	PROPN
ejpam-4467	76	8	,	,	PUNCT
ejpam-4467	76	9	z	z	NOUN
ejpam-4467	76	10	∈	∈	PROPN
ejpam-4467	76	11	x	x	X
ejpam-4467	76	12	)	)	PUNCT
ejpam-4467	76	13	(	(	PUNCT
ejpam-4467	76	14	lεψ((x	lεψ((x	NOUN
ejpam-4467	76	15	∗	∗	NOUN
ejpam-4467	76	16	(	(	PUNCT
ejpam-4467	76	17	y	y	PROPN
ejpam-4467	76	18	∗	∗	PROPN
ejpam-4467	76	19	z	z	NOUN
ejpam-4467	76	20	)	)	PUNCT
ejpam-4467	76	21	)	)	PUNCT
ejpam-4467	76	22	∗	∗	PROPN
ejpam-4467	76	23	z	z	NOUN
ejpam-4467	76	24	)	)	PUNCT
ejpam-4467	76	25	≥	≥	PROPN
ejpam-4467	76	26	min	min	NOUN
ejpam-4467	76	27	{	{	PUNCT
ejpam-4467	76	28	lεψ(x	lεψ(x	NOUN
ejpam-4467	76	29	)	)	PUNCT
ejpam-4467	76	30	,	,	PUNCT
ejpam-4467	76	31	lεψ(y	lεψ(y	PROPN
ejpam-4467	76	32	)	)	PUNCT
ejpam-4467	76	33	}	}	PUNCT
ejpam-4467	76	34	)	)	PUNCT
ejpam-4467	76	35	.	.	PUNCT
ejpam-4467	77	1	(	(	PUNCT
ejpam-4467	77	2	12	12	NUM
ejpam-4467	77	3	)	)	PUNCT
ejpam-4467	77	4	proof	proof	NOUN
ejpam-4467	77	5	.	.	PUNCT
ejpam-4467	78	1	assume	assume	VERB
ejpam-4467	78	2	that	that	SCONJ
ejpam-4467	78	3	lεψ	lεψ	ADJ
ejpam-4467	78	4	is	be	AUX
ejpam-4467	78	5	a	a	DET
ejpam-4467	78	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	78	7	fuzzy	fuzzy	ADJ
ejpam-4467	78	8	ideal	ideal	NOUN
ejpam-4467	78	9	of	of	ADP
ejpam-4467	78	10	(	(	PUNCT
ejpam-4467	78	11	x	x	X
ejpam-4467	78	12	,	,	PUNCT
ejpam-4467	78	13	1)∗.	1)∗.	PRON
ejpam-4467	78	14	let	let	VERB
ejpam-4467	78	15	x	x	PRON
ejpam-4467	78	16	,	,	PUNCT
ejpam-4467	78	17	y	y	PROPN
ejpam-4467	78	18	∈	∈	PROPN
ejpam-4467	78	19	x.	x.	NOUN
ejpam-4467	78	20	since	since	SCONJ
ejpam-4467	78	21	⟨y/	⟨y/	PROPN
ejpam-4467	78	22	lεψ(y)⟩	lεψ(y)⟩	PROPN
ejpam-4467	78	23	∈	∈	PROPN
ejpam-4467	78	24	lεψ	lεψ	PROPN
ejpam-4467	78	25	,	,	PUNCT
ejpam-4467	78	26	we	we	PRON
ejpam-4467	78	27	have	have	VERB
ejpam-4467	78	28	⟨(x	⟨(x	PROPN
ejpam-4467	78	29	∗	∗	NOUN
ejpam-4467	78	30	y)/	y)/	PROPN
ejpam-4467	78	31	lεψ(y)⟩	lεψ(y)⟩	PROPN
ejpam-4467	78	32	∈	∈	PROPN
ejpam-4467	78	33	lεψ	lεψ	VERB
ejpam-4467	78	34	by	by	ADP
ejpam-4467	78	35	(	(	PUNCT
ejpam-4467	78	36	9	9	NUM
ejpam-4467	78	37	)	)	PUNCT
ejpam-4467	78	38	,	,	PUNCT
ejpam-4467	78	39	and	and	CCONJ
ejpam-4467	78	40	so	so	ADV
ejpam-4467	78	41	lεψ(x	lεψ(x	PROPN
ejpam-4467	78	42	∗	∗	PROPN
ejpam-4467	78	43	y	y	NOUN
ejpam-4467	78	44	)	)	PUNCT
ejpam-4467	78	45	≥	≥	NOUN
ejpam-4467	78	46	lεψ(y	lεψ(y	VERB
ejpam-4467	78	47	)	)	PUNCT
ejpam-4467	78	48	.	.	PUNCT
ejpam-4467	79	1	note	note	VERB
ejpam-4467	79	2	that	that	SCONJ
ejpam-4467	79	3	⟨x/	⟨x/	PUNCT
ejpam-4467	80	1	lεψ(x)⟩	lεψ(x)⟩	PUNCT
ejpam-4467	81	1	∈	∈	NOUN
ejpam-4467	81	2	lεψ	lεψ	ADJ
ejpam-4467	81	3	and	and	CCONJ
ejpam-4467	81	4	⟨y/	⟨y/	NUM
ejpam-4467	81	5	lεψ(y)⟩	lεψ(y)⟩	PROPN
ejpam-4467	81	6	∈	∈	PROPN
ejpam-4467	81	7	lεψ	lεψ	VERB
ejpam-4467	81	8	for	for	ADP
ejpam-4467	81	9	all	all	DET
ejpam-4467	81	10	x	x	NOUN
ejpam-4467	81	11	,	,	PUNCT
ejpam-4467	81	12	y	y	PROPN
ejpam-4467	81	13	∈	∈	PROPN
ejpam-4467	81	14	x.	x.	NOUN
ejpam-4467	82	1	it	it	PRON
ejpam-4467	82	2	follows	follow	VERB
ejpam-4467	82	3	from	from	ADP
ejpam-4467	82	4	(	(	PUNCT
ejpam-4467	82	5	10	10	NUM
ejpam-4467	82	6	)	)	PUNCT
ejpam-4467	83	1	that	that	PRON
ejpam-4467	83	2	⟨((x	⟨((x	PROPN
ejpam-4467	83	3	∗	∗	NOUN
ejpam-4467	83	4	(	(	PUNCT
ejpam-4467	83	5	y	y	PROPN
ejpam-4467	83	6	∗	∗	PROPN
ejpam-4467	83	7	z	z	NOUN
ejpam-4467	83	8	)	)	PUNCT
ejpam-4467	83	9	)	)	PUNCT
ejpam-4467	83	10	∗	∗	NOUN
ejpam-4467	83	11	z)/min	z)/min	PROPN
ejpam-4467	83	12	{	{	PUNCT
ejpam-4467	83	13	lεψ(x	lεψ(x	NOUN
ejpam-4467	83	14	)	)	PUNCT
ejpam-4467	83	15	,	,	PUNCT
ejpam-4467	83	16	lεψ(y)}⟩	lεψ(y)}⟩	PROPN
ejpam-4467	83	17	∈	∈	PROPN
ejpam-4467	83	18	lεψ	lεψ	VERB
ejpam-4467	83	19	,	,	PUNCT
ejpam-4467	83	20	that	that	ADV
ejpam-4467	83	21	is	is	ADV
ejpam-4467	83	22	,	,	PUNCT
ejpam-4467	83	23	lεψ((x	lεψ((x	NOUN
ejpam-4467	83	24	∗	∗	NOUN
ejpam-4467	83	25	(	(	PUNCT
ejpam-4467	83	26	y	y	PROPN
ejpam-4467	83	27	∗	∗	PROPN
ejpam-4467	83	28	z	z	NOUN
ejpam-4467	83	29	)	)	PUNCT
ejpam-4467	83	30	)	)	PUNCT
ejpam-4467	84	1	∗	∗	PROPN
ejpam-4467	84	2	z	z	NOUN
ejpam-4467	84	3	)	)	PUNCT
ejpam-4467	84	4	≥	≥	PROPN
ejpam-4467	84	5	min	min	NOUN
ejpam-4467	84	6	{	{	PUNCT
ejpam-4467	84	7	lεψ(x	lεψ(x	NOUN
ejpam-4467	84	8	)	)	PUNCT
ejpam-4467	84	9	,	,	PUNCT
ejpam-4467	84	10	lεψ(y	lεψ(y	PROPN
ejpam-4467	84	11	)	)	PUNCT
ejpam-4467	84	12	}	}	PUNCT
ejpam-4467	84	13	for	for	ADP
ejpam-4467	84	14	all	all	DET
ejpam-4467	84	15	x	x	NOUN
ejpam-4467	84	16	,	,	PUNCT
ejpam-4467	84	17	y	y	PROPN
ejpam-4467	84	18	,	,	PUNCT
ejpam-4467	84	19	z	z	NOUN
ejpam-4467	84	20	∈	∈	NOUN
ejpam-4467	84	21	x.	x.	NOUN
ejpam-4467	84	22	conversely	conversely	ADV
ejpam-4467	84	23	,	,	PUNCT
ejpam-4467	84	24	let	let	VERB
ejpam-4467	84	25	lεψ	lεψ	ADJ
ejpam-4467	84	26	be	be	AUX
ejpam-4467	84	27	a	a	DET
ejpam-4467	84	28	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	84	29	fuzzy	fuzzy	ADJ
ejpam-4467	84	30	set	set	VERB
ejpam-4467	84	31	satisfying	satisfy	VERB
ejpam-4467	84	32	(	(	PUNCT
ejpam-4467	84	33	11	11	NUM
ejpam-4467	84	34	)	)	PUNCT
ejpam-4467	84	35	and	and	CCONJ
ejpam-4467	84	36	(	(	PUNCT
ejpam-4467	84	37	12	12	NUM
ejpam-4467	84	38	)	)	PUNCT
ejpam-4467	84	39	.	.	PUNCT
ejpam-4467	85	1	if	if	SCONJ
ejpam-4467	85	2	⟨y	⟨y	NOUN
ejpam-4467	85	3	/	/	SYM
ejpam-4467	85	4	t⟩	t⟩	PRON
ejpam-4467	85	5	∈	∈	PROPN
ejpam-4467	85	6	lεψ	lεψ	VERB
ejpam-4467	85	7	for	for	ADP
ejpam-4467	85	8	all	all	DET
ejpam-4467	85	9	y	y	PROPN
ejpam-4467	85	10	∈	∈	PROPN
ejpam-4467	85	11	x	x	X
ejpam-4467	85	12	and	and	CCONJ
ejpam-4467	85	13	t	t	PROPN
ejpam-4467	85	14	∈	∈	PROPN
ejpam-4467	85	15	(	(	PUNCT
ejpam-4467	85	16	0	0	NUM
ejpam-4467	85	17	,	,	PUNCT
ejpam-4467	85	18	1	1	NUM
ejpam-4467	85	19	]	]	PUNCT
ejpam-4467	85	20	,	,	PUNCT
ejpam-4467	85	21	then	then	ADV
ejpam-4467	85	22	lεψ(x	lεψ(x	PROPN
ejpam-4467	85	23	∗	∗	NOUN
ejpam-4467	85	24	y	y	PROPN
ejpam-4467	85	25	)	)	PUNCT
ejpam-4467	85	26	≥	≥	NOUN
ejpam-4467	85	27	lεψ(y	lεψ(y	PROPN
ejpam-4467	85	28	)	)	PUNCT
ejpam-4467	85	29	≥	≥	NOUN
ejpam-4467	85	30	t	t	NOUN
ejpam-4467	85	31	for	for	ADP
ejpam-4467	85	32	all	all	DET
ejpam-4467	85	33	x	x	SYM
ejpam-4467	85	34	∈	∈	PROPN
ejpam-4467	85	35	x	x	PUNCT
ejpam-4467	85	36	by	by	ADP
ejpam-4467	85	37	(	(	PUNCT
ejpam-4467	85	38	11	11	NUM
ejpam-4467	85	39	)	)	PUNCT
ejpam-4467	85	40	.	.	PUNCT
ejpam-4467	86	1	hence	hence	ADV
ejpam-4467	86	2	⟨(x∗y)/t⟩	⟨(x∗y)/t⟩	X
ejpam-4467	86	3	∈	∈	PROPN
ejpam-4467	86	4	lεψ	lεψ	PROPN
ejpam-4467	86	5	.	.	PUNCT
ejpam-4467	87	1	let	let	VERB
ejpam-4467	87	2	x	x	PRON
ejpam-4467	87	3	,	,	PUNCT
ejpam-4467	87	4	y	y	PROPN
ejpam-4467	87	5	,	,	PUNCT
ejpam-4467	87	6	z	z	NOUN
ejpam-4467	87	7	∈	∈	PROPN
ejpam-4467	87	8	x	x	X
ejpam-4467	87	9	and	and	CCONJ
ejpam-4467	87	10	ta	ta	PROPN
ejpam-4467	87	11	,	,	PUNCT
ejpam-4467	87	12	tb	tb	ADP
ejpam-4467	87	13	∈	∈	PROPN
ejpam-4467	87	14	(	(	PUNCT
ejpam-4467	87	15	0	0	NUM
ejpam-4467	87	16	,	,	PUNCT
ejpam-4467	87	17	1	1	NUM
ejpam-4467	87	18	]	]	PUNCT
ejpam-4467	87	19	be	be	AUX
ejpam-4467	87	20	such	such	ADJ
ejpam-4467	87	21	that	that	SCONJ
ejpam-4467	87	22	⟨x	⟨x	VERB
ejpam-4467	87	23	/	/	SYM
ejpam-4467	87	24	ta⟩	ta⟩	PUNCT
ejpam-4467	87	25	∈	∈	PROPN
ejpam-4467	87	26	lεψ	lεψ	VERB
ejpam-4467	87	27	and	and	CCONJ
ejpam-4467	87	28	⟨y	⟨y	NOUN
ejpam-4467	87	29	/	/	SYM
ejpam-4467	87	30	tb⟩	tb⟩	PROPN
ejpam-4467	87	31	∈	∈	PROPN
ejpam-4467	87	32	lεψ	lεψ	NOUN
ejpam-4467	87	33	.	.	PUNCT
ejpam-4467	88	1	then	then	ADV
ejpam-4467	88	2	lεψ(x	lεψ(x	PROPN
ejpam-4467	88	3	)	)	PUNCT
ejpam-4467	88	4	≥	≥	NOUN
ejpam-4467	88	5	ta	ta	ADP
ejpam-4467	88	6	and	and	CCONJ
ejpam-4467	88	7	lεψ(y	lεψ(y	PROPN
ejpam-4467	88	8	)	)	PUNCT
ejpam-4467	88	9	≥	≥	NOUN
ejpam-4467	88	10	tb	tb	NOUN
ejpam-4467	88	11	.	.	PUNCT
ejpam-4467	89	1	it	it	PRON
ejpam-4467	89	2	follows	follow	VERB
ejpam-4467	89	3	from	from	ADP
ejpam-4467	89	4	(	(	PUNCT
ejpam-4467	89	5	12	12	NUM
ejpam-4467	89	6	)	)	PUNCT
ejpam-4467	89	7	that	that	PRON
ejpam-4467	89	8	lεψ((x	lεψ((x	NOUN
ejpam-4467	89	9	∗	∗	NOUN
ejpam-4467	89	10	(	(	PUNCT
ejpam-4467	89	11	y	y	PROPN
ejpam-4467	89	12	∗	∗	PROPN
ejpam-4467	89	13	z	z	NOUN
ejpam-4467	89	14	)	)	PUNCT
ejpam-4467	89	15	)	)	PUNCT
ejpam-4467	89	16	∗	∗	PROPN
ejpam-4467	89	17	z	z	NOUN
ejpam-4467	89	18	)	)	PUNCT
ejpam-4467	89	19	≥	≥	PROPN
ejpam-4467	89	20	min	min	NOUN
ejpam-4467	89	21	{	{	PUNCT
ejpam-4467	89	22	lεψ(x	lεψ(x	NOUN
ejpam-4467	89	23	)	)	PUNCT
ejpam-4467	89	24	,	,	PUNCT
ejpam-4467	89	25	lεψ(y	lεψ(y	PROPN
ejpam-4467	89	26	)	)	PUNCT
ejpam-4467	89	27	}	}	PUNCT
ejpam-4467	89	28	≥	≥	NOUN
ejpam-4467	89	29	min{ta	min{ta	X
ejpam-4467	89	30	,	,	PUNCT
ejpam-4467	89	31	tb	tb	NOUN
ejpam-4467	89	32	}	}	PUNCT
ejpam-4467	89	33	.	.	PUNCT
ejpam-4467	90	1	hence	hence	ADV
ejpam-4467	90	2	⟨((x	⟨((x	PROPN
ejpam-4467	90	3	∗	∗	NOUN
ejpam-4467	90	4	(	(	PUNCT
ejpam-4467	90	5	y	y	PROPN
ejpam-4467	90	6	∗	∗	PROPN
ejpam-4467	90	7	z	z	NOUN
ejpam-4467	90	8	)	)	PUNCT
ejpam-4467	90	9	)	)	PUNCT
ejpam-4467	90	10	∗	∗	NOUN
ejpam-4467	90	11	z)/min{ta	z)/min{ta	PROPN
ejpam-4467	90	12	,	,	PUNCT
ejpam-4467	90	13	tb}⟩	tb}⟩	X
ejpam-4467	90	14	∈	∈	PROPN
ejpam-4467	90	15	lεψ	lεψ	VERB
ejpam-4467	90	16	,	,	PUNCT
ejpam-4467	90	17	and	and	CCONJ
ejpam-4467	90	18	therefore	therefore	ADV
ejpam-4467	90	19	lεψ	lεψ	ADJ
ejpam-4467	90	20	is	be	AUX
ejpam-4467	90	21	a	a	DET
ejpam-4467	90	22	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	90	23	fuzzy	fuzzy	ADJ
ejpam-4467	90	24	ideal	ideal	NOUN
ejpam-4467	90	25	of	of	ADP
ejpam-4467	90	26	(	(	PUNCT
ejpam-4467	90	27	x	x	X
ejpam-4467	90	28	,	,	PUNCT
ejpam-4467	90	29	1)∗.	1)∗.	PRON
ejpam-4467	90	30	proposition	proposition	NOUN
ejpam-4467	90	31	1	1	NUM
ejpam-4467	90	32	.	.	PUNCT
ejpam-4467	91	1	every	every	DET
ejpam-4467	91	2	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	91	3	fuzzy	fuzzy	ADJ
ejpam-4467	91	4	ideal	ideal	NOUN
ejpam-4467	91	5	lεψ	lεψ	VERB
ejpam-4467	91	6	of	of	ADP
ejpam-4467	91	7	(	(	PUNCT
ejpam-4467	91	8	x	x	NOUN
ejpam-4467	91	9	,	,	PUNCT
ejpam-4467	91	10	1)∗	1)∗	NUM
ejpam-4467	91	11	satisfies	satisfie	NOUN
ejpam-4467	91	12	:	:	PUNCT
ejpam-4467	91	13	(	(	PUNCT
ejpam-4467	91	14	∀x	∀x	X
ejpam-4467	91	15	∈	∈	PROPN
ejpam-4467	91	16	x)(∀t	x)(∀t	X
ejpam-4467	91	17	∈	∈	PROPN
ejpam-4467	91	18	(	(	PUNCT
ejpam-4467	91	19	0	0	NUM
ejpam-4467	91	20	,	,	PUNCT
ejpam-4467	91	21	1	1	NUM
ejpam-4467	91	22	]	]	NUM
ejpam-4467	91	23	)	)	PUNCT
ejpam-4467	91	24	(	(	PUNCT
ejpam-4467	91	25	⟨x	⟨x	VERB
ejpam-4467	91	26	/	/	SYM
ejpam-4467	91	27	t⟩	t⟩	NOUN
ejpam-4467	91	28	∈	∈	PROPN
ejpam-4467	91	29	lεψ	lεψ	VERB
ejpam-4467	91	30	⇒	⇒	PROPN
ejpam-4467	91	31	⟨1	⟨1	PROPN
ejpam-4467	91	32	/	/	SYM
ejpam-4467	91	33	t⟩	t⟩	PRON
ejpam-4467	91	34	∈	∈	PROPN
ejpam-4467	91	35	lεψ	lεψ	VERB
ejpam-4467	91	36	)	)	PUNCT
ejpam-4467	91	37	.	.	PUNCT
ejpam-4467	92	1	(	(	PUNCT
ejpam-4467	92	2	13	13	NUM
ejpam-4467	92	3	)	)	PUNCT
ejpam-4467	92	4	(	(	PUNCT
ejpam-4467	92	5	∀x	∀x	X
ejpam-4467	92	6	,	,	PUNCT
ejpam-4467	92	7	y	y	PROPN
ejpam-4467	92	8	∈	∈	PROPN
ejpam-4467	92	9	x)(∀t	x)(∀t	PROPN
ejpam-4467	92	10	∈	∈	PROPN
ejpam-4467	92	11	(	(	PUNCT
ejpam-4467	92	12	0	0	NUM
ejpam-4467	92	13	,	,	PUNCT
ejpam-4467	92	14	1	1	NUM
ejpam-4467	92	15	]	]	NUM
ejpam-4467	92	16	)	)	PUNCT
ejpam-4467	92	17	(	(	PUNCT
ejpam-4467	92	18	⟨x	⟨x	VERB
ejpam-4467	92	19	/	/	SYM
ejpam-4467	92	20	t⟩	t⟩	NOUN
ejpam-4467	92	21	∈	∈	PROPN
ejpam-4467	92	22	lεψ	lεψ	VERB
ejpam-4467	92	23	⇒	⇒	PROPN
ejpam-4467	92	24	⟨((x	⟨((x	PROPN
ejpam-4467	92	25	∗	∗	PROPN
ejpam-4467	92	26	y	y	NOUN
ejpam-4467	92	27	)	)	PUNCT
ejpam-4467	92	28	∗	∗	NOUN
ejpam-4467	92	29	y)/t⟩	y)/t⟩	PUNCT
ejpam-4467	93	1	∈	∈	PROPN
ejpam-4467	93	2	lεψ	lεψ	VERB
ejpam-4467	93	3	)	)	PUNCT
ejpam-4467	93	4	.	.	PUNCT
ejpam-4467	94	1	(	(	PUNCT
ejpam-4467	94	2	14	14	NUM
ejpam-4467	94	3	)	)	PUNCT
ejpam-4467	94	4	(	(	PUNCT
ejpam-4467	94	5	∀x	∀x	X
ejpam-4467	94	6	,	,	PUNCT
ejpam-4467	94	7	y	y	PROPN
ejpam-4467	94	8	∈	∈	PROPN
ejpam-4467	94	9	x)(∀t	x)(∀t	PROPN
ejpam-4467	94	10	∈	∈	PROPN
ejpam-4467	94	11	(	(	PUNCT
ejpam-4467	94	12	0	0	NUM
ejpam-4467	94	13	,	,	PUNCT
ejpam-4467	94	14	1	1	NUM
ejpam-4467	94	15	]	]	PUNCT
ejpam-4467	94	16	)	)	PUNCT
ejpam-4467	94	17	(	(	PUNCT
ejpam-4467	94	18	x	x	X
ejpam-4467	94	19	≤	≤	NUM
ejpam-4467	94	20	y	y	NOUN
ejpam-4467	94	21	,	,	PUNCT
ejpam-4467	94	22	⟨x	⟨x	VERB
ejpam-4467	94	23	/	/	SYM
ejpam-4467	94	24	t⟩	t⟩	NOUN
ejpam-4467	94	25	∈	∈	PROPN
ejpam-4467	94	26	lεψ	lεψ	ADJ
ejpam-4467	94	27	⇒	⇒	NOUN
ejpam-4467	94	28	⟨y	⟨y	NOUN
ejpam-4467	94	29	/	/	SYM
ejpam-4467	94	30	t⟩	t⟩	PRON
ejpam-4467	94	31	∈	∈	PROPN
ejpam-4467	94	32	lεψ	lεψ	VERB
ejpam-4467	94	33	)	)	PUNCT
ejpam-4467	94	34	.	.	PUNCT
ejpam-4467	95	1	(	(	PUNCT
ejpam-4467	95	2	15	15	NUM
ejpam-4467	95	3	)	)	PUNCT
ejpam-4467	95	4	(	(	PUNCT
ejpam-4467	95	5	∀x	∀x	X
ejpam-4467	95	6	,	,	PUNCT
ejpam-4467	95	7	y	y	PROPN
ejpam-4467	95	8	∈	∈	PROPN
ejpam-4467	95	9	x)(∀ta	x)(∀ta	NOUN
ejpam-4467	95	10	,	,	PUNCT
ejpam-4467	95	11	tb	tb	ADP
ejpam-4467	95	12	∈	∈	PROPN
ejpam-4467	95	13	(	(	PUNCT
ejpam-4467	95	14	0	0	NUM
ejpam-4467	95	15	,	,	PUNCT
ejpam-4467	95	16	1	1	NUM
ejpam-4467	95	17	]	]	NUM
ejpam-4467	95	18	)	)	PUNCT
ejpam-4467	95	19	(	(	PUNCT
ejpam-4467	95	20	⟨(x	⟨(x	NOUN
ejpam-4467	95	21	∗	∗	VERB
ejpam-4467	95	22	y)/tb⟩	y)/tb⟩	ADP
ejpam-4467	95	23	∈	∈	PROPN
ejpam-4467	95	24	lεψ	lεψ	VERB
ejpam-4467	95	25	,	,	PUNCT
ejpam-4467	95	26	⟨x	⟨x	VERB
ejpam-4467	95	27	/	/	SYM
ejpam-4467	95	28	ta⟩	ta⟩	PUNCT
ejpam-4467	95	29	∈	∈	PROPN
ejpam-4467	95	30	lεψ	lεψ	ADJ
ejpam-4467	95	31	⇒	⇒	NOUN
ejpam-4467	95	32	⟨y	⟨y	X
ejpam-4467	95	33	/	/	SYM
ejpam-4467	95	34	min{ta	min{ta	NUM
ejpam-4467	95	35	,	,	PUNCT
ejpam-4467	95	36	tb}⟩	tb}⟩	X
ejpam-4467	95	37	∈	∈	PROPN
ejpam-4467	95	38	lεψ	lεψ	PROPN
ejpam-4467	95	39	.	.	PUNCT
ejpam-4467	95	40	)	)	PUNCT
ejpam-4467	95	41	.	.	PUNCT
ejpam-4467	96	1	(	(	PUNCT
ejpam-4467	96	2	16	16	NUM
ejpam-4467	96	3	)	)	PUNCT
ejpam-4467	96	4	(	(	PUNCT
ejpam-4467	96	5	∀x	∀x	X
ejpam-4467	96	6	,	,	PUNCT
ejpam-4467	96	7	y	y	PROPN
ejpam-4467	96	8	,	,	PUNCT
ejpam-4467	96	9	z	z	PROPN
ejpam-4467	96	10	∈	∈	PROPN
ejpam-4467	96	11	x)(∀ta	x)(∀ta	NOUN
ejpam-4467	96	12	,	,	PUNCT
ejpam-4467	96	13	tb	tb	ADP
ejpam-4467	96	14	∈	∈	PROPN
ejpam-4467	96	15	(	(	PUNCT
ejpam-4467	96	16	0	0	NUM
ejpam-4467	96	17	,	,	PUNCT
ejpam-4467	96	18	1	1	NUM
ejpam-4467	96	19	]	]	NUM
ejpam-4467	96	20	)	)	PUNCT
ejpam-4467	96	21	(	(	PUNCT
ejpam-4467	96	22	⟨(x	⟨(x	NOUN
ejpam-4467	96	23	∗	∗	NOUN
ejpam-4467	96	24	(	(	PUNCT
ejpam-4467	96	25	y	y	PROPN
ejpam-4467	96	26	∗	∗	X
ejpam-4467	96	27	z))/ta⟩	z))/ta⟩	PROPN
ejpam-4467	96	28	∈	∈	PROPN
ejpam-4467	96	29	lεψ	lεψ	VERB
ejpam-4467	96	30	,	,	PUNCT
ejpam-4467	96	31	⟨y	⟨y	AUX
ejpam-4467	96	32	/	/	SYM
ejpam-4467	96	33	tb⟩	tb⟩	PROPN
ejpam-4467	96	34	∈	∈	PROPN
ejpam-4467	96	35	lεψ	lεψ	ADJ
ejpam-4467	96	36	⇒	⇒	PROPN
ejpam-4467	96	37	⟨(x	⟨(x	PROPN
ejpam-4467	96	38	∗	∗	PROPN
ejpam-4467	96	39	z)/min{ta	z)/min{ta	PROPN
ejpam-4467	96	40	,	,	PUNCT
ejpam-4467	96	41	tb}⟩	tb}⟩	X
ejpam-4467	96	42	∈	∈	PROPN
ejpam-4467	96	43	lεψ	lεψ	PROPN
ejpam-4467	96	44	.	.	PUNCT
ejpam-4467	96	45	)	)	PUNCT
ejpam-4467	96	46	.	.	PUNCT
ejpam-4467	97	1	(	(	PUNCT
ejpam-4467	97	2	17	17	NUM
ejpam-4467	97	3	)	)	PUNCT
ejpam-4467	97	4	s.	s.	PROPN
ejpam-4467	97	5	s.	s.	PROPN
ejpam-4467	97	6	ahn	ahn	PROPN
ejpam-4467	97	7	,	,	PUNCT
ejpam-4467	97	8	e.	e.	PROPN
ejpam-4467	97	9	h.	h.	PROPN
ejpam-4467	97	10	roh	roh	PROPN
ejpam-4467	97	11	and	and	CCONJ
ejpam-4467	97	12	y.	y.	PROPN
ejpam-4467	97	13	b.	b.	PROPN
ejpam-4467	97	14	jun	jun	PROPN
ejpam-4467	97	15	/	/	SYM
ejpam-4467	97	16	eur	eur	PROPN
ejpam-4467	97	17	.	.	PUNCT
ejpam-4467	98	1	j.	j.	PROPN
ejpam-4467	98	2	pure	pure	PROPN
ejpam-4467	98	3	appl	appl	PROPN
ejpam-4467	98	4	.	.	PROPN
ejpam-4467	98	5	math	math	PROPN
ejpam-4467	98	6	,	,	PUNCT
ejpam-4467	98	7	15	15	NUM
ejpam-4467	98	8	(	(	PUNCT
ejpam-4467	98	9	3	3	NUM
ejpam-4467	98	10	)	)	PUNCT
ejpam-4467	98	11	(	(	PUNCT
ejpam-4467	98	12	2022	2022	NUM
ejpam-4467	98	13	)	)	PUNCT
ejpam-4467	98	14	,	,	PUNCT
ejpam-4467	98	15	1307	1307	NUM
ejpam-4467	98	16	-	-	SYM
ejpam-4467	98	17	1320	1320	NUM
ejpam-4467	98	18	1311	1311	NUM
ejpam-4467	98	19	proof	proof	NOUN
ejpam-4467	98	20	.	.	PUNCT
ejpam-4467	99	1	the	the	DET
ejpam-4467	99	2	condition	condition	NOUN
ejpam-4467	99	3	(	(	PUNCT
ejpam-4467	99	4	13	13	NUM
ejpam-4467	99	5	)	)	PUNCT
ejpam-4467	99	6	is	be	AUX
ejpam-4467	99	7	derived	derive	VERB
ejpam-4467	99	8	from	from	ADP
ejpam-4467	99	9	the	the	DET
ejpam-4467	99	10	combination	combination	NOUN
ejpam-4467	99	11	of	of	ADP
ejpam-4467	99	12	(	(	PUNCT
ejpam-4467	99	13	be1	be1	NOUN
ejpam-4467	99	14	)	)	PUNCT
ejpam-4467	99	15	and	and	CCONJ
ejpam-4467	99	16	(	(	PUNCT
ejpam-4467	99	17	9	9	NUM
ejpam-4467	99	18	)	)	PUNCT
ejpam-4467	99	19	.	.	PUNCT
ejpam-4467	100	1	let	let	VERB
ejpam-4467	100	2	x	x	PUNCT
ejpam-4467	100	3	∈	∈	PROPN
ejpam-4467	100	4	x	x	X
ejpam-4467	100	5	and	and	CCONJ
ejpam-4467	100	6	t	t	PROPN
ejpam-4467	100	7	∈	∈	PROPN
ejpam-4467	100	8	(	(	PUNCT
ejpam-4467	100	9	0	0	NUM
ejpam-4467	100	10	,	,	PUNCT
ejpam-4467	100	11	1	1	NUM
ejpam-4467	100	12	]	]	PUNCT
ejpam-4467	100	13	be	be	AUX
ejpam-4467	100	14	such	such	ADJ
ejpam-4467	100	15	that	that	SCONJ
ejpam-4467	100	16	⟨x	⟨x	VERB
ejpam-4467	100	17	/	/	SYM
ejpam-4467	100	18	t⟩	t⟩	NOUN
ejpam-4467	100	19	∈	∈	PROPN
ejpam-4467	100	20	lεψ	lεψ	PROPN
ejpam-4467	100	21	.	.	PUNCT
ejpam-4467	101	1	then	then	ADV
ejpam-4467	101	2	⟨((x	⟨((x	PROPN
ejpam-4467	101	3	∗	∗	PROPN
ejpam-4467	101	4	y	y	NOUN
ejpam-4467	101	5	)	)	PUNCT
ejpam-4467	101	6	∗	∗	NOUN
ejpam-4467	101	7	y)/t⟩	y)/t⟩	PUNCT
ejpam-4467	102	1	=	=	PUNCT
ejpam-4467	102	2	⟨((x	⟨((x	PROPN
ejpam-4467	102	3	∗	∗	NOUN
ejpam-4467	102	4	(	(	PUNCT
ejpam-4467	102	5	1	1	NUM
ejpam-4467	102	6	∗	∗	NOUN
ejpam-4467	102	7	y	y	NOUN
ejpam-4467	102	8	)	)	PUNCT
ejpam-4467	102	9	)	)	PUNCT
ejpam-4467	102	10	∗	∗	NOUN
ejpam-4467	102	11	y)/t⟩	y)/t⟩	PUNCT
ejpam-4467	103	1	=	=	PUNCT
ejpam-4467	103	2	⟨((x	⟨((x	PROPN
ejpam-4467	103	3	∗	∗	NOUN
ejpam-4467	103	4	(	(	PUNCT
ejpam-4467	103	5	1	1	NUM
ejpam-4467	103	6	∗	∗	NOUN
ejpam-4467	103	7	y	y	NOUN
ejpam-4467	103	8	)	)	PUNCT
ejpam-4467	103	9	)	)	PUNCT
ejpam-4467	103	10	∗	∗	NOUN
ejpam-4467	103	11	y)/min{t	y)/min{t	PROPN
ejpam-4467	103	12	,	,	PUNCT
ejpam-4467	103	13	t}⟩	t}⟩	PROPN
ejpam-4467	103	14	∈	∈	PROPN
ejpam-4467	103	15	lεψ	lεψ	VERB
ejpam-4467	103	16	by	by	ADP
ejpam-4467	103	17	(	(	PUNCT
ejpam-4467	103	18	be3	be3	PROPN
ejpam-4467	103	19	)	)	PUNCT
ejpam-4467	103	20	,	,	PUNCT
ejpam-4467	103	21	(	(	PUNCT
ejpam-4467	103	22	10	10	NUM
ejpam-4467	103	23	)	)	PUNCT
ejpam-4467	103	24	and	and	CCONJ
ejpam-4467	103	25	(	(	PUNCT
ejpam-4467	103	26	13	13	NUM
ejpam-4467	103	27	)	)	PUNCT
ejpam-4467	103	28	.	.	PUNCT
ejpam-4467	104	1	the	the	DET
ejpam-4467	104	2	combination	combination	NOUN
ejpam-4467	104	3	of	of	ADP
ejpam-4467	104	4	(	(	PUNCT
ejpam-4467	104	5	be3	be3	PROPN
ejpam-4467	104	6	)	)	PUNCT
ejpam-4467	104	7	,	,	PUNCT
ejpam-4467	104	8	(	(	PUNCT
ejpam-4467	104	9	1	1	X
ejpam-4467	104	10	)	)	PUNCT
ejpam-4467	104	11	and	and	CCONJ
ejpam-4467	104	12	(	(	PUNCT
ejpam-4467	104	13	14	14	NUM
ejpam-4467	104	14	)	)	PUNCT
ejpam-4467	104	15	induces	induce	NOUN
ejpam-4467	104	16	(	(	PUNCT
ejpam-4467	104	17	15	15	NUM
ejpam-4467	104	18	)	)	PUNCT
ejpam-4467	104	19	.	.	PUNCT
ejpam-4467	105	1	let	let	VERB
ejpam-4467	105	2	x	x	PRON
ejpam-4467	105	3	,	,	PUNCT
ejpam-4467	105	4	y	y	PROPN
ejpam-4467	105	5	∈	∈	PROPN
ejpam-4467	105	6	x	x	X
ejpam-4467	105	7	and	and	CCONJ
ejpam-4467	105	8	ta	ta	PROPN
ejpam-4467	105	9	,	,	PUNCT
ejpam-4467	105	10	tb	tb	ADP
ejpam-4467	105	11	∈	∈	PROPN
ejpam-4467	105	12	(	(	PUNCT
ejpam-4467	105	13	0	0	NUM
ejpam-4467	105	14	,	,	PUNCT
ejpam-4467	105	15	1	1	NUM
ejpam-4467	105	16	]	]	PUNCT
ejpam-4467	105	17	be	be	AUX
ejpam-4467	105	18	such	such	ADJ
ejpam-4467	105	19	that	that	SCONJ
ejpam-4467	105	20	⟨(x	⟨(x	PROPN
ejpam-4467	105	21	∗	∗	VERB
ejpam-4467	105	22	y)/tb⟩	y)/tb⟩	ADP
ejpam-4467	106	1	∈	∈	PROPN
ejpam-4467	106	2	lεψ	lεψ	ADJ
ejpam-4467	106	3	and	and	CCONJ
ejpam-4467	106	4	⟨x	⟨x	NUM
ejpam-4467	106	5	/	/	SYM
ejpam-4467	106	6	ta⟩	ta⟩	CCONJ
ejpam-4467	106	7	∈	∈	PROPN
ejpam-4467	106	8	lεψ	lεψ	PROPN
ejpam-4467	106	9	.	.	PUNCT
ejpam-4467	107	1	then	then	ADV
ejpam-4467	107	2	⟨y	⟨y	X
ejpam-4467	107	3	/	/	SYM
ejpam-4467	107	4	min{ta	min{ta	X
ejpam-4467	107	5	,	,	PUNCT
ejpam-4467	107	6	tb}⟩	tb}⟩	X
ejpam-4467	107	7	=	=	SYM
ejpam-4467	107	8	⟨(1	⟨(1	NOUN
ejpam-4467	107	9	∗	∗	NOUN
ejpam-4467	107	10	y)/min{ta	y)/min{ta	NOUN
ejpam-4467	107	11	,	,	PUNCT
ejpam-4467	107	12	tb}⟩	tb}⟩	X
ejpam-4467	107	13	=	=	SYM
ejpam-4467	107	14	⟨(((x	⟨(((x	NOUN
ejpam-4467	107	15	∗	∗	X
ejpam-4467	107	16	y	y	NOUN
ejpam-4467	107	17	)	)	PUNCT
ejpam-4467	107	18	∗	∗	NOUN
ejpam-4467	107	19	(	(	PUNCT
ejpam-4467	107	20	x	x	X
ejpam-4467	107	21	∗	∗	PROPN
ejpam-4467	107	22	y	y	PROPN
ejpam-4467	107	23	)	)	PUNCT
ejpam-4467	107	24	)	)	PUNCT
ejpam-4467	108	1	∗	∗	NOUN
ejpam-4467	108	2	y)/min{ta	y)/min{ta	PROPN
ejpam-4467	108	3	,	,	PUNCT
ejpam-4467	108	4	tb}⟩	tb}⟩	X
ejpam-4467	108	5	∈	∈	PROPN
ejpam-4467	108	6	lεψ	lεψ	VERB
ejpam-4467	108	7	by	by	ADP
ejpam-4467	108	8	(	(	PUNCT
ejpam-4467	108	9	be1	be1	NOUN
ejpam-4467	108	10	)	)	PUNCT
ejpam-4467	108	11	,	,	PUNCT
ejpam-4467	108	12	(	(	PUNCT
ejpam-4467	108	13	be3	be3	PROPN
ejpam-4467	108	14	)	)	PUNCT
ejpam-4467	108	15	and	and	CCONJ
ejpam-4467	108	16	(	(	PUNCT
ejpam-4467	108	17	10	10	NUM
ejpam-4467	108	18	)	)	PUNCT
ejpam-4467	108	19	,	,	PUNCT
ejpam-4467	108	20	which	which	PRON
ejpam-4467	108	21	proves	prove	VERB
ejpam-4467	108	22	(	(	PUNCT
ejpam-4467	108	23	16	16	NUM
ejpam-4467	108	24	)	)	PUNCT
ejpam-4467	108	25	.	.	PUNCT
ejpam-4467	109	1	the	the	DET
ejpam-4467	109	2	condition	condition	NOUN
ejpam-4467	109	3	(	(	PUNCT
ejpam-4467	109	4	17	17	NUM
ejpam-4467	109	5	)	)	PUNCT
ejpam-4467	109	6	is	be	AUX
ejpam-4467	109	7	derived	derive	VERB
ejpam-4467	109	8	from	from	ADP
ejpam-4467	109	9	the	the	DET
ejpam-4467	109	10	combination	combination	NOUN
ejpam-4467	109	11	of	of	ADP
ejpam-4467	109	12	(	(	PUNCT
ejpam-4467	109	13	be4	be4	NOUN
ejpam-4467	109	14	)	)	PUNCT
ejpam-4467	109	15	and	and	CCONJ
ejpam-4467	109	16	(	(	PUNCT
ejpam-4467	109	17	16	16	NUM
ejpam-4467	109	18	)	)	PUNCT
ejpam-4467	109	19	.	.	PUNCT
ejpam-4467	110	1	we	we	PRON
ejpam-4467	110	2	provide	provide	VERB
ejpam-4467	110	3	conditions	condition	NOUN
ejpam-4467	110	4	for	for	ADP
ejpam-4467	110	5	the	the	DET
ejpam-4467	110	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	110	7	fuzzy	fuzzy	NOUN
ejpam-4467	110	8	set	set	VERB
ejpam-4467	110	9	to	to	PART
ejpam-4467	110	10	be	be	AUX
ejpam-4467	110	11	a	a	DET
ejpam-4467	110	12	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	110	13	fuzzy	fuzzy	ADJ
ejpam-4467	110	14	ideal	ideal	NOUN
ejpam-4467	110	15	.	.	PUNCT
ejpam-4467	111	1	theorem	theorem	NOUN
ejpam-4467	111	2	2	2	NUM
ejpam-4467	111	3	.	.	PUNCT
ejpam-4467	112	1	if	if	SCONJ
ejpam-4467	112	2	a	a	DET
ejpam-4467	112	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	112	4	fuzzy	fuzzy	ADJ
ejpam-4467	112	5	set	set	VERB
ejpam-4467	112	6	lεψ	lεψ	VERB
ejpam-4467	112	7	in	in	ADP
ejpam-4467	112	8	x	x	PART
ejpam-4467	112	9	satisfies	satisfie	NOUN
ejpam-4467	112	10	conditions	condition	NOUN
ejpam-4467	112	11	(	(	PUNCT
ejpam-4467	112	12	13	13	NUM
ejpam-4467	112	13	)	)	PUNCT
ejpam-4467	112	14	and	and	CCONJ
ejpam-4467	112	15	(	(	PUNCT
ejpam-4467	112	16	17	17	NUM
ejpam-4467	112	17	)	)	PUNCT
ejpam-4467	112	18	,	,	PUNCT
ejpam-4467	112	19	then	then	ADV
ejpam-4467	112	20	it	it	PRON
ejpam-4467	112	21	is	be	AUX
ejpam-4467	112	22	a	a	DET
ejpam-4467	112	23	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	112	24	fuzzy	fuzzy	ADJ
ejpam-4467	112	25	ideal	ideal	NOUN
ejpam-4467	112	26	of	of	ADP
ejpam-4467	112	27	(	(	PUNCT
ejpam-4467	112	28	x	x	X
ejpam-4467	112	29	,	,	PUNCT
ejpam-4467	112	30	1)∗.	1)∗.	PRON
ejpam-4467	112	31	proof	proof	NOUN
ejpam-4467	112	32	.	.	PUNCT
ejpam-4467	113	1	assume	assume	VERB
ejpam-4467	113	2	that	that	SCONJ
ejpam-4467	113	3	lεψ	lεψ	ADJ
ejpam-4467	113	4	satisfies	satisfie	NOUN
ejpam-4467	113	5	conditions	condition	NOUN
ejpam-4467	113	6	(	(	PUNCT
ejpam-4467	113	7	13	13	NUM
ejpam-4467	113	8	)	)	PUNCT
ejpam-4467	113	9	and	and	CCONJ
ejpam-4467	113	10	(	(	PUNCT
ejpam-4467	113	11	17	17	NUM
ejpam-4467	113	12	)	)	PUNCT
ejpam-4467	113	13	.	.	PUNCT
ejpam-4467	114	1	let	let	VERB
ejpam-4467	114	2	y	y	PROPN
ejpam-4467	114	3	∈	∈	PROPN
ejpam-4467	114	4	x	x	X
ejpam-4467	114	5	and	and	CCONJ
ejpam-4467	114	6	t	t	PROPN
ejpam-4467	114	7	∈	∈	PROPN
ejpam-4467	114	8	(	(	PUNCT
ejpam-4467	114	9	0	0	NUM
ejpam-4467	114	10	,	,	PUNCT
ejpam-4467	114	11	1	1	NUM
ejpam-4467	114	12	]	]	PUNCT
ejpam-4467	114	13	be	be	AUX
ejpam-4467	114	14	such	such	ADJ
ejpam-4467	114	15	that	that	SCONJ
ejpam-4467	114	16	⟨y	⟨y	NOUN
ejpam-4467	114	17	/	/	SYM
ejpam-4467	114	18	t⟩	t⟩	PRON
ejpam-4467	114	19	∈	∈	PROPN
ejpam-4467	114	20	lεψ	lεψ	PROPN
ejpam-4467	114	21	.	.	PUNCT
ejpam-4467	115	1	then	then	ADV
ejpam-4467	115	2	⟨(x	⟨(x	VERB
ejpam-4467	115	3	∗	∗	NOUN
ejpam-4467	115	4	(	(	PUNCT
ejpam-4467	115	5	y	y	NOUN
ejpam-4467	115	6	∗	∗	NOUN
ejpam-4467	115	7	y))/t⟩	y))/t⟩	PROPN
ejpam-4467	115	8	=	=	PUNCT
ejpam-4467	115	9	⟨(x	⟨(x	PROPN
ejpam-4467	115	10	∗	∗	NOUN
ejpam-4467	115	11	1)/t⟩	1)/t⟩	NUM
ejpam-4467	116	1	=	=	PUNCT
ejpam-4467	117	1	⟨1	⟨1	PROPN
ejpam-4467	117	2	/	/	SYM
ejpam-4467	117	3	t⟩	t⟩	PRON
ejpam-4467	117	4	∈	∈	PROPN
ejpam-4467	117	5	lεψ	lεψ	VERB
ejpam-4467	117	6	for	for	ADP
ejpam-4467	117	7	all	all	DET
ejpam-4467	117	8	x	x	SYM
ejpam-4467	117	9	∈	∈	PROPN
ejpam-4467	117	10	x	x	PUNCT
ejpam-4467	117	11	by	by	ADP
ejpam-4467	117	12	(	(	PUNCT
ejpam-4467	117	13	be1	be1	NOUN
ejpam-4467	117	14	)	)	PUNCT
ejpam-4467	117	15	,	,	PUNCT
ejpam-4467	117	16	(	(	PUNCT
ejpam-4467	117	17	be2	be2	PROPN
ejpam-4467	117	18	)	)	PUNCT
ejpam-4467	117	19	and	and	CCONJ
ejpam-4467	117	20	(	(	PUNCT
ejpam-4467	117	21	13	13	NUM
ejpam-4467	117	22	)	)	PUNCT
ejpam-4467	117	23	.	.	PUNCT
ejpam-4467	118	1	it	it	PRON
ejpam-4467	118	2	follows	follow	VERB
ejpam-4467	118	3	from	from	ADP
ejpam-4467	118	4	(	(	PUNCT
ejpam-4467	118	5	17	17	NUM
ejpam-4467	118	6	)	)	PUNCT
ejpam-4467	118	7	that	that	PRON
ejpam-4467	118	8	⟨(x	⟨(x	PROPN
ejpam-4467	118	9	∗	∗	NOUN
ejpam-4467	118	10	y)/t⟩	y)/t⟩	PUNCT
ejpam-4467	119	1	∈	∈	PROPN
ejpam-4467	119	2	lεψ	lεψ	VERB
ejpam-4467	119	3	.	.	PUNCT
ejpam-4467	120	1	let	let	VERB
ejpam-4467	120	2	x	x	PRON
ejpam-4467	120	3	,	,	PUNCT
ejpam-4467	120	4	y	y	PROPN
ejpam-4467	120	5	∈	∈	PROPN
ejpam-4467	120	6	x	x	X
ejpam-4467	120	7	and	and	CCONJ
ejpam-4467	120	8	ta	ta	PROPN
ejpam-4467	120	9	,	,	PUNCT
ejpam-4467	120	10	tb	tb	ADP
ejpam-4467	120	11	∈	∈	PROPN
ejpam-4467	120	12	(	(	PUNCT
ejpam-4467	120	13	0	0	NUM
ejpam-4467	120	14	,	,	PUNCT
ejpam-4467	120	15	1	1	NUM
ejpam-4467	120	16	]	]	PUNCT
ejpam-4467	120	17	be	be	AUX
ejpam-4467	120	18	such	such	ADJ
ejpam-4467	120	19	that	that	SCONJ
ejpam-4467	120	20	⟨x	⟨x	VERB
ejpam-4467	120	21	/	/	SYM
ejpam-4467	120	22	ta⟩	ta⟩	PUNCT
ejpam-4467	120	23	∈	∈	PROPN
ejpam-4467	120	24	lεψ	lεψ	VERB
ejpam-4467	120	25	and	and	CCONJ
ejpam-4467	120	26	⟨y	⟨y	NOUN
ejpam-4467	120	27	/	/	SYM
ejpam-4467	120	28	tb⟩	tb⟩	PROPN
ejpam-4467	120	29	∈	∈	PROPN
ejpam-4467	120	30	lεψ	lεψ	PROPN
ejpam-4467	120	31	.	.	PUNCT
ejpam-4467	121	1	then	then	ADV
ejpam-4467	121	2	⟨((x	⟨((x	PROPN
ejpam-4467	121	3	∗	∗	PROPN
ejpam-4467	121	4	z	z	NOUN
ejpam-4467	121	5	)	)	PUNCT
ejpam-4467	121	6	∗	∗	NOUN
ejpam-4467	121	7	(	(	PUNCT
ejpam-4467	121	8	x	x	X
ejpam-4467	121	9	∗	∗	NOUN
ejpam-4467	121	10	z))/tb⟩	z))/tb⟩	PROPN
ejpam-4467	121	11	=	=	SYM
ejpam-4467	121	12	⟨1	⟨1	PROPN
ejpam-4467	121	13	/	/	SYM
ejpam-4467	121	14	tb⟩	tb⟩	PROPN
ejpam-4467	121	15	∈	∈	PROPN
ejpam-4467	121	16	lεψ	lεψ	VERB
ejpam-4467	121	17	and	and	CCONJ
ejpam-4467	121	18	so	so	ADV
ejpam-4467	121	19	⟨((x	⟨((x	PROPN
ejpam-4467	121	20	∗	∗	PROPN
ejpam-4467	121	21	z	z	NOUN
ejpam-4467	121	22	)	)	PUNCT
ejpam-4467	121	23	∗	∗	NOUN
ejpam-4467	121	24	z)/min{ta	z)/min{ta	PROPN
ejpam-4467	121	25	,	,	PUNCT
ejpam-4467	121	26	tb}⟩	tb}⟩	X
ejpam-4467	121	27	∈	∈	PROPN
ejpam-4467	121	28	lεψ	lεψ	VERB
ejpam-4467	121	29	for	for	ADP
ejpam-4467	121	30	all	all	DET
ejpam-4467	121	31	z	z	NOUN
ejpam-4467	121	32	∈	∈	NOUN
ejpam-4467	121	33	x	x	PUNCT
ejpam-4467	121	34	by	by	ADP
ejpam-4467	121	35	(	(	PUNCT
ejpam-4467	121	36	17	17	NUM
ejpam-4467	121	37	)	)	PUNCT
ejpam-4467	121	38	.	.	PUNCT
ejpam-4467	122	1	in	in	ADP
ejpam-4467	122	2	particular	particular	ADJ
ejpam-4467	122	3	,	,	PUNCT
ejpam-4467	122	4	⟨((x	⟨((x	PROPN
ejpam-4467	122	5	∗	∗	NOUN
ejpam-4467	122	6	(	(	PUNCT
ejpam-4467	122	7	y	y	PROPN
ejpam-4467	122	8	∗	∗	PROPN
ejpam-4467	122	9	z	z	NOUN
ejpam-4467	122	10	)	)	PUNCT
ejpam-4467	122	11	)	)	PUNCT
ejpam-4467	122	12	∗	∗	NOUN
ejpam-4467	122	13	(	(	PUNCT
ejpam-4467	122	14	y	y	PROPN
ejpam-4467	122	15	∗	∗	PROPN
ejpam-4467	122	16	z))/min{ta	z))/min{ta	NUM
ejpam-4467	122	17	,	,	PUNCT
ejpam-4467	122	18	tb}⟩	tb}⟩	X
ejpam-4467	122	19	∈	∈	PROPN
ejpam-4467	122	20	lεψ	lεψ	PROPN
ejpam-4467	122	21	,	,	PUNCT
ejpam-4467	122	22	which	which	PRON
ejpam-4467	122	23	implies	imply	VERB
ejpam-4467	122	24	from	from	ADP
ejpam-4467	122	25	(	(	PUNCT
ejpam-4467	122	26	17	17	NUM
ejpam-4467	122	27	)	)	PUNCT
ejpam-4467	123	1	that	that	PRON
ejpam-4467	123	2	⟨((x	⟨((x	PROPN
ejpam-4467	123	3	∗	∗	NOUN
ejpam-4467	123	4	(	(	PUNCT
ejpam-4467	123	5	y	y	PROPN
ejpam-4467	123	6	∗	∗	PROPN
ejpam-4467	123	7	z	z	NOUN
ejpam-4467	123	8	)	)	PUNCT
ejpam-4467	123	9	)	)	PUNCT
ejpam-4467	123	10	∗	∗	NOUN
ejpam-4467	123	11	z)/min{ta	z)/min{ta	PROPN
ejpam-4467	123	12	,	,	PUNCT
ejpam-4467	123	13	tb}⟩	tb}⟩	X
ejpam-4467	123	14	∈	∈	PROPN
ejpam-4467	123	15	lεψ	lεψ	VERB
ejpam-4467	123	16	for	for	ADP
ejpam-4467	123	17	all	all	DET
ejpam-4467	123	18	z	z	NOUN
ejpam-4467	123	19	∈	∈	NOUN
ejpam-4467	123	20	x.	x.	NOUN
ejpam-4467	123	21	hence	hence	ADV
ejpam-4467	123	22	lεψ	lεψ	VERB
ejpam-4467	123	23	is	be	AUX
ejpam-4467	123	24	a	a	DET
ejpam-4467	123	25	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	123	26	fuzzy	fuzzy	ADJ
ejpam-4467	123	27	ideal	ideal	NOUN
ejpam-4467	123	28	of	of	ADP
ejpam-4467	123	29	(	(	PUNCT
ejpam-4467	123	30	x	x	X
ejpam-4467	123	31	,	,	PUNCT
ejpam-4467	123	32	1)∗.	1)∗.	PRON
ejpam-4467	123	33	corollary	corollary	ADJ
ejpam-4467	123	34	1	1	X
ejpam-4467	123	35	.	.	PUNCT
ejpam-4467	124	1	if	if	SCONJ
ejpam-4467	124	2	a	a	DET
ejpam-4467	124	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	124	4	fuzzy	fuzzy	ADJ
ejpam-4467	124	5	set	set	VERB
ejpam-4467	124	6	lεψ	lεψ	VERB
ejpam-4467	124	7	in	in	ADP
ejpam-4467	124	8	x	x	X
ejpam-4467	124	9	satisfies	satisfie	NOUN
ejpam-4467	124	10	(	(	PUNCT
ejpam-4467	124	11	13	13	NUM
ejpam-4467	124	12	)	)	PUNCT
ejpam-4467	124	13	and	and	CCONJ
ejpam-4467	124	14	(	(	PUNCT
ejpam-4467	124	15	17	17	NUM
ejpam-4467	124	16	)	)	PUNCT
ejpam-4467	124	17	,	,	PUNCT
ejpam-4467	124	18	then	then	ADV
ejpam-4467	124	19	it	it	PRON
ejpam-4467	124	20	satisfies	satisfy	VERB
ejpam-4467	124	21	the	the	DET
ejpam-4467	124	22	conditions	condition	NOUN
ejpam-4467	124	23	(	(	PUNCT
ejpam-4467	124	24	14	14	NUM
ejpam-4467	124	25	)	)	PUNCT
ejpam-4467	124	26	,	,	PUNCT
ejpam-4467	124	27	(	(	PUNCT
ejpam-4467	124	28	15	15	NUM
ejpam-4467	124	29	)	)	PUNCT
ejpam-4467	124	30	and	and	CCONJ
ejpam-4467	124	31	(	(	PUNCT
ejpam-4467	124	32	16	16	NUM
ejpam-4467	124	33	)	)	PUNCT
ejpam-4467	124	34	.	.	PUNCT
ejpam-4467	125	1	we	we	PRON
ejpam-4467	125	2	discuss	discuss	VERB
ejpam-4467	125	3	the	the	DET
ejpam-4467	125	4	relationship	relationship	NOUN
ejpam-4467	125	5	between	between	ADP
ejpam-4467	125	6	fuzzy	fuzzy	ADJ
ejpam-4467	125	7	ideal	ideal	NOUN
ejpam-4467	125	8	and	and	CCONJ
ejpam-4467	125	9	lukasiewicz	lukasiewicz	VERB
ejpam-4467	125	10	fuzzy	fuzzy	ADJ
ejpam-4467	125	11	ideal	ideal	NOUN
ejpam-4467	125	12	.	.	PUNCT
ejpam-4467	126	1	theorem	theorem	VERB
ejpam-4467	126	2	3	3	X
ejpam-4467	126	3	.	.	PUNCT
ejpam-4467	127	1	if	if	SCONJ
ejpam-4467	127	2	ψ	ψ	NOUN
ejpam-4467	127	3	is	be	AUX
ejpam-4467	127	4	a	a	DET
ejpam-4467	127	5	fuzzy	fuzzy	ADJ
ejpam-4467	127	6	ideal	ideal	NOUN
ejpam-4467	127	7	of	of	ADP
ejpam-4467	127	8	(	(	PUNCT
ejpam-4467	127	9	x	x	X
ejpam-4467	127	10	,	,	PUNCT
ejpam-4467	127	11	1)∗	1)∗	NUM
ejpam-4467	127	12	,	,	PUNCT
ejpam-4467	127	13	then	then	ADV
ejpam-4467	127	14	lεψ	lεψ	ADJ
ejpam-4467	127	15	is	be	AUX
ejpam-4467	127	16	a	a	DET
ejpam-4467	127	17	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	127	18	fuzzy	fuzzy	ADJ
ejpam-4467	127	19	ideal	ideal	NOUN
ejpam-4467	127	20	of	of	ADP
ejpam-4467	127	21	(	(	PUNCT
ejpam-4467	127	22	x	x	X
ejpam-4467	127	23	,	,	PUNCT
ejpam-4467	127	24	1)∗.	1)∗.	PRON
ejpam-4467	127	25	proof	proof	NOUN
ejpam-4467	127	26	.	.	PUNCT
ejpam-4467	128	1	let	let	VERB
ejpam-4467	128	2	y	y	PROPN
ejpam-4467	128	3	∈	∈	PROPN
ejpam-4467	128	4	x	x	X
ejpam-4467	128	5	and	and	CCONJ
ejpam-4467	128	6	t	t	PROPN
ejpam-4467	128	7	∈	∈	PROPN
ejpam-4467	128	8	(	(	PUNCT
ejpam-4467	128	9	0	0	NUM
ejpam-4467	128	10	,	,	PUNCT
ejpam-4467	128	11	1	1	NUM
ejpam-4467	128	12	]	]	PUNCT
ejpam-4467	128	13	be	be	AUX
ejpam-4467	128	14	such	such	ADJ
ejpam-4467	128	15	that	that	SCONJ
ejpam-4467	128	16	⟨y	⟨y	NOUN
ejpam-4467	128	17	/	/	SYM
ejpam-4467	128	18	t⟩	t⟩	PRON
ejpam-4467	128	19	∈	∈	PROPN
ejpam-4467	128	20	lεψ	lεψ	PROPN
ejpam-4467	128	21	.	.	PUNCT
ejpam-4467	129	1	then	then	ADV
ejpam-4467	129	2	lεψ(y	lεψ(y	PROPN
ejpam-4467	129	3	)	)	PUNCT
ejpam-4467	129	4	≥	≥	NOUN
ejpam-4467	129	5	t	t	PROPN
ejpam-4467	129	6	,	,	PUNCT
ejpam-4467	129	7	and	and	CCONJ
ejpam-4467	129	8	so	so	ADV
ejpam-4467	129	9	lεψ(x	lεψ(x	PROPN
ejpam-4467	129	10	∗	∗	NOUN
ejpam-4467	129	11	y	y	NOUN
ejpam-4467	129	12	)	)	PUNCT
ejpam-4467	130	1	=	=	SYM
ejpam-4467	130	2	max{0	max{0	PROPN
ejpam-4467	130	3	,	,	PUNCT
ejpam-4467	130	4	ψ(x	ψ(x	NOUN
ejpam-4467	130	5	∗	∗	NOUN
ejpam-4467	130	6	y	y	NOUN
ejpam-4467	130	7	)	)	PUNCT
ejpam-4467	131	1	+	+	CCONJ
ejpam-4467	131	2	ε−	ε−	PROPN
ejpam-4467	131	3	1	1	NUM
ejpam-4467	131	4	}	}	PUNCT
ejpam-4467	131	5	≥	≥	NUM
ejpam-4467	131	6	max{0	max{0	NUM
ejpam-4467	131	7	,	,	PUNCT
ejpam-4467	131	8	ψ(y	ψ(y	PROPN
ejpam-4467	131	9	)	)	PUNCT
ejpam-4467	131	10	+	+	CCONJ
ejpam-4467	131	11	ε−	ε−	PROPN
ejpam-4467	131	12	1	1	NUM
ejpam-4467	131	13	}	}	PUNCT
ejpam-4467	131	14	=	=	SYM
ejpam-4467	131	15	lεψ(y	lεψ(y	PROPN
ejpam-4467	131	16	)	)	PUNCT
ejpam-4467	131	17	≥	≥	NOUN
ejpam-4467	131	18	t	t	NOUN
ejpam-4467	131	19	for	for	ADP
ejpam-4467	131	20	all	all	PRON
ejpam-4467	131	21	x	x	SYM
ejpam-4467	131	22	∈	∈	ADJ
ejpam-4467	131	23	x.	x.	NOUN
ejpam-4467	131	24	hence	hence	ADV
ejpam-4467	131	25	⟨(x	⟨(x	PROPN
ejpam-4467	131	26	∗	∗	NOUN
ejpam-4467	131	27	y)/t⟩	y)/t⟩	PUNCT
ejpam-4467	132	1	∈	∈	PROPN
ejpam-4467	132	2	lεψ	lεψ	VERB
ejpam-4467	132	3	for	for	ADP
ejpam-4467	132	4	all	all	DET
ejpam-4467	132	5	x	x	SYM
ejpam-4467	132	6	∈	∈	NOUN
ejpam-4467	132	7	x.	x.	NOUN
ejpam-4467	132	8	let	let	VERB
ejpam-4467	132	9	x	x	PRON
ejpam-4467	132	10	,	,	PUNCT
ejpam-4467	132	11	y	y	PROPN
ejpam-4467	132	12	∈	∈	PROPN
ejpam-4467	132	13	x	x	X
ejpam-4467	132	14	and	and	CCONJ
ejpam-4467	132	15	ta	ta	PROPN
ejpam-4467	132	16	,	,	PUNCT
ejpam-4467	132	17	tb	tb	ADP
ejpam-4467	132	18	∈	∈	PROPN
ejpam-4467	132	19	(	(	PUNCT
ejpam-4467	132	20	0	0	NUM
ejpam-4467	132	21	,	,	PUNCT
ejpam-4467	132	22	1	1	NUM
ejpam-4467	132	23	]	]	PUNCT
ejpam-4467	132	24	be	be	AUX
ejpam-4467	132	25	such	such	ADJ
ejpam-4467	132	26	that	that	SCONJ
ejpam-4467	132	27	⟨x	⟨x	VERB
ejpam-4467	132	28	/	/	SYM
ejpam-4467	132	29	ta⟩	ta⟩	PUNCT
ejpam-4467	132	30	∈	∈	PROPN
ejpam-4467	132	31	lεψ	lεψ	VERB
ejpam-4467	132	32	and	and	CCONJ
ejpam-4467	132	33	⟨y	⟨y	NOUN
ejpam-4467	132	34	/	/	SYM
ejpam-4467	132	35	tb⟩	tb⟩	PROPN
ejpam-4467	132	36	∈	∈	PROPN
ejpam-4467	132	37	lεψ	lεψ	NOUN
ejpam-4467	132	38	.	.	PUNCT
ejpam-4467	133	1	then	then	ADV
ejpam-4467	133	2	lεψ(x	lεψ(x	PROPN
ejpam-4467	133	3	)	)	PUNCT
ejpam-4467	133	4	≥	≥	NOUN
ejpam-4467	133	5	ta	ta	ADP
ejpam-4467	133	6	and	and	CCONJ
ejpam-4467	133	7	lεψ(y	lεψ(y	PROPN
ejpam-4467	133	8	)	)	PUNCT
ejpam-4467	133	9	≥	≥	NOUN
ejpam-4467	133	10	tb	tb	NOUN
ejpam-4467	133	11	.	.	PUNCT
ejpam-4467	134	1	it	it	PRON
ejpam-4467	134	2	follows	follow	VERB
ejpam-4467	134	3	that	that	SCONJ
ejpam-4467	134	4	lεψ((x	lεψ((x	NOUN
ejpam-4467	134	5	∗	∗	NOUN
ejpam-4467	134	6	(	(	PUNCT
ejpam-4467	134	7	y	y	PROPN
ejpam-4467	134	8	∗	∗	PROPN
ejpam-4467	134	9	z	z	NOUN
ejpam-4467	134	10	)	)	PUNCT
ejpam-4467	134	11	)	)	PUNCT
ejpam-4467	134	12	∗	∗	PROPN
ejpam-4467	135	1	z	z	NOUN
ejpam-4467	135	2	)	)	PUNCT
ejpam-4467	135	3	=	=	SYM
ejpam-4467	135	4	max{0	max{0	PROPN
ejpam-4467	135	5	,	,	PUNCT
ejpam-4467	135	6	ψ((x	ψ((x	PUNCT
ejpam-4467	135	7	∗	∗	NOUN
ejpam-4467	135	8	(	(	PUNCT
ejpam-4467	135	9	y	y	PROPN
ejpam-4467	135	10	∗	∗	PROPN
ejpam-4467	135	11	z	z	NOUN
ejpam-4467	135	12	)	)	PUNCT
ejpam-4467	135	13	)	)	PUNCT
ejpam-4467	135	14	∗	∗	PROPN
ejpam-4467	135	15	z	z	NOUN
ejpam-4467	135	16	)	)	PUNCT
ejpam-4467	136	1	+	+	CCONJ
ejpam-4467	136	2	ε−	ε−	PROPN
ejpam-4467	136	3	1	1	NUM
ejpam-4467	136	4	}	}	PUNCT
ejpam-4467	136	5	≥	≥	NOUN
ejpam-4467	136	6	max{0,min{ψ(x	max{0,min{ψ(x	NOUN
ejpam-4467	136	7	)	)	PUNCT
ejpam-4467	136	8	,	,	PUNCT
ejpam-4467	136	9	ψ(y	ψ(y	NOUN
ejpam-4467	136	10	)	)	PUNCT
ejpam-4467	136	11	}	}	PUNCT
ejpam-4467	136	12	+	+	CCONJ
ejpam-4467	137	1	ε−	ε−	PROPN
ejpam-4467	137	2	1	1	NUM
ejpam-4467	137	3	}	}	PUNCT
ejpam-4467	137	4	=	=	SYM
ejpam-4467	137	5	max{0,min{ψ(x	max{0,min{ψ(x	NOUN
ejpam-4467	137	6	)	)	PUNCT
ejpam-4467	137	7	+	+	CCONJ
ejpam-4467	137	8	ε−	ε−	PROPN
ejpam-4467	137	9	1	1	NUM
ejpam-4467	137	10	,	,	PUNCT
ejpam-4467	137	11	ψ(y	ψ(y	NOUN
ejpam-4467	137	12	)	)	PUNCT
ejpam-4467	137	13	+	+	CCONJ
ejpam-4467	137	14	ε−	ε−	PROPN
ejpam-4467	137	15	1	1	NUM
ejpam-4467	137	16	}	}	PUNCT
ejpam-4467	137	17	}	}	PUNCT
ejpam-4467	137	18	=	=	SYM
ejpam-4467	137	19	min{max{0	min{max{0	X
ejpam-4467	137	20	,	,	PUNCT
ejpam-4467	137	21	ψ(x	ψ(x	NOUN
ejpam-4467	137	22	)	)	PUNCT
ejpam-4467	137	23	+	+	CCONJ
ejpam-4467	137	24	ε−	ε−	PROPN
ejpam-4467	137	25	1},max{0	1},max{0	NUM
ejpam-4467	137	26	,	,	PUNCT
ejpam-4467	137	27	ψ(y	ψ(y	PROPN
ejpam-4467	137	28	)	)	PUNCT
ejpam-4467	137	29	+	+	CCONJ
ejpam-4467	137	30	ε−	ε−	PROPN
ejpam-4467	137	31	1	1	NUM
ejpam-4467	137	32	}	}	PUNCT
ejpam-4467	137	33	}	}	PUNCT
ejpam-4467	137	34	s.	s.	PROPN
ejpam-4467	137	35	s.	s.	PROPN
ejpam-4467	137	36	ahn	ahn	PROPN
ejpam-4467	137	37	,	,	PUNCT
ejpam-4467	137	38	e.	e.	PROPN
ejpam-4467	137	39	h.	h.	PROPN
ejpam-4467	137	40	roh	roh	PROPN
ejpam-4467	137	41	and	and	CCONJ
ejpam-4467	137	42	y.	y.	PROPN
ejpam-4467	137	43	b.	b.	PROPN
ejpam-4467	137	44	jun	jun	PROPN
ejpam-4467	137	45	/	/	SYM
ejpam-4467	137	46	eur	eur	PROPN
ejpam-4467	137	47	.	.	PUNCT
ejpam-4467	138	1	j.	j.	PROPN
ejpam-4467	138	2	pure	pure	PROPN
ejpam-4467	138	3	appl	appl	PROPN
ejpam-4467	138	4	.	.	PROPN
ejpam-4467	138	5	math	math	PROPN
ejpam-4467	138	6	,	,	PUNCT
ejpam-4467	138	7	15	15	NUM
ejpam-4467	138	8	(	(	PUNCT
ejpam-4467	138	9	3	3	NUM
ejpam-4467	138	10	)	)	PUNCT
ejpam-4467	138	11	(	(	PUNCT
ejpam-4467	138	12	2022	2022	NUM
ejpam-4467	138	13	)	)	PUNCT
ejpam-4467	138	14	,	,	PUNCT
ejpam-4467	138	15	1307	1307	NUM
ejpam-4467	138	16	-	-	SYM
ejpam-4467	138	17	1320	1320	NUM
ejpam-4467	138	18	1312	1312	NUM
ejpam-4467	138	19	=	=	SYM
ejpam-4467	138	20	min	min	PROPN
ejpam-4467	138	21	{	{	PUNCT
ejpam-4467	138	22	lεψ(x	lεψ(x	NOUN
ejpam-4467	138	23	)	)	PUNCT
ejpam-4467	138	24	,	,	PUNCT
ejpam-4467	138	25	lεψ(y	lεψ(y	PROPN
ejpam-4467	138	26	)	)	PUNCT
ejpam-4467	138	27	}	}	PUNCT
ejpam-4467	138	28	≥	≥	NOUN
ejpam-4467	138	29	min{ta	min{ta	X
ejpam-4467	138	30	,	,	PUNCT
ejpam-4467	138	31	tb	tb	NOUN
ejpam-4467	138	32	}	}	PUNCT
ejpam-4467	138	33	for	for	ADP
ejpam-4467	138	34	all	all	DET
ejpam-4467	138	35	z	z	NOUN
ejpam-4467	138	36	∈	∈	NOUN
ejpam-4467	138	37	x.	x.	NOUN
ejpam-4467	139	1	thus	thus	ADV
ejpam-4467	139	2	⟨((x	⟨((x	PROPN
ejpam-4467	139	3	∗	∗	NOUN
ejpam-4467	139	4	(	(	PUNCT
ejpam-4467	139	5	y	y	PROPN
ejpam-4467	139	6	∗	∗	PROPN
ejpam-4467	139	7	z	z	NOUN
ejpam-4467	139	8	)	)	PUNCT
ejpam-4467	139	9	)	)	PUNCT
ejpam-4467	139	10	∗	∗	NOUN
ejpam-4467	139	11	z)/min{ta	z)/min{ta	PROPN
ejpam-4467	139	12	,	,	PUNCT
ejpam-4467	139	13	tb}⟩	tb}⟩	X
ejpam-4467	139	14	∈	∈	PROPN
ejpam-4467	139	15	lεψ	lεψ	VERB
ejpam-4467	139	16	for	for	ADP
ejpam-4467	139	17	all	all	DET
ejpam-4467	139	18	z	z	NOUN
ejpam-4467	139	19	∈	∈	NOUN
ejpam-4467	139	20	x.	x.	NOUN
ejpam-4467	139	21	therefore	therefore	ADV
ejpam-4467	139	22	lεψ	lεψ	PROPN
ejpam-4467	139	23	is	be	AUX
ejpam-4467	139	24	a	a	DET
ejpam-4467	139	25	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	139	26	fuzzy	fuzzy	ADJ
ejpam-4467	139	27	ideal	ideal	NOUN
ejpam-4467	139	28	of	of	ADP
ejpam-4467	139	29	(	(	PUNCT
ejpam-4467	139	30	x	x	X
ejpam-4467	139	31	,	,	PUNCT
ejpam-4467	139	32	1)∗.	1)∗.	NUM
ejpam-4467	139	33	in	in	ADP
ejpam-4467	139	34	example	example	NOUN
ejpam-4467	139	35	1	1	NUM
ejpam-4467	139	36	,	,	PUNCT
ejpam-4467	139	37	lεψ	lεψ	ADJ
ejpam-4467	139	38	is	be	AUX
ejpam-4467	139	39	a	a	DET
ejpam-4467	139	40	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	139	41	fuzzy	fuzzy	ADJ
ejpam-4467	139	42	ideal	ideal	NOUN
ejpam-4467	139	43	of	of	ADP
ejpam-4467	139	44	(	(	PUNCT
ejpam-4467	139	45	x	x	X
ejpam-4467	139	46	,	,	PUNCT
ejpam-4467	139	47	1)∗.	1)∗.	NUM
ejpam-4467	139	48	but	but	CCONJ
ejpam-4467	139	49	ψ	ψ	NOUN
ejpam-4467	139	50	is	be	AUX
ejpam-4467	139	51	not	not	PART
ejpam-4467	139	52	a	a	DET
ejpam-4467	139	53	fuzzy	fuzzy	ADJ
ejpam-4467	139	54	ideal	ideal	NOUN
ejpam-4467	139	55	of	of	ADP
ejpam-4467	139	56	(	(	PUNCT
ejpam-4467	139	57	x	x	NOUN
ejpam-4467	139	58	,	,	PUNCT
ejpam-4467	139	59	1)∗	1)∗	NOUN
ejpam-4467	139	60	since	since	SCONJ
ejpam-4467	139	61	ψ(b	ψ(b	PROPN
ejpam-4467	139	62	∗	∗	NOUN
ejpam-4467	139	63	0	0	NUM
ejpam-4467	139	64	)	)	PUNCT
ejpam-4467	139	65	=	=	SYM
ejpam-4467	139	66	ψ(c	ψ(c	PROPN
ejpam-4467	139	67	)	)	PUNCT
ejpam-4467	139	68	=	=	PUNCT
ejpam-4467	140	1	0.14	0.14	NUM
ejpam-4467	140	2	≱	≱	PROPN
ejpam-4467	140	3	0.21	0.21	NUM
ejpam-4467	140	4	=	=	PUNCT
ejpam-4467	140	5	ψ(0	ψ(0	PROPN
ejpam-4467	140	6	)	)	PUNCT
ejpam-4467	140	7	.	.	PUNCT
ejpam-4467	141	1	therefore	therefore	ADV
ejpam-4467	141	2	,	,	PUNCT
ejpam-4467	141	3	the	the	DET
ejpam-4467	141	4	converse	converse	NOUN
ejpam-4467	141	5	of	of	ADP
ejpam-4467	141	6	theorem	theorem	NOUN
ejpam-4467	141	7	3	3	NUM
ejpam-4467	141	8	may	may	AUX
ejpam-4467	141	9	not	not	PART
ejpam-4467	141	10	be	be	AUX
ejpam-4467	141	11	true	true	ADJ
ejpam-4467	141	12	.	.	PUNCT
ejpam-4467	142	1	in	in	ADP
ejpam-4467	142	2	the	the	DET
ejpam-4467	142	3	sense	sense	NOUN
ejpam-4467	142	4	of	of	ADP
ejpam-4467	142	5	theorem	theorem	NOUN
ejpam-4467	142	6	3	3	NUM
ejpam-4467	142	7	,	,	PUNCT
ejpam-4467	142	8	we	we	PRON
ejpam-4467	142	9	can	can	AUX
ejpam-4467	142	10	say	say	VERB
ejpam-4467	142	11	that	that	DET
ejpam-4467	142	12	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	142	13	fuzzy	fuzzy	ADJ
ejpam-4467	142	14	ideal	ideal	NOUN
ejpam-4467	142	15	is	be	AUX
ejpam-4467	142	16	a	a	DET
ejpam-4467	142	17	generalization	generalization	NOUN
ejpam-4467	142	18	of	of	ADP
ejpam-4467	142	19	fuzzy	fuzzy	ADJ
ejpam-4467	142	20	ideal	ideal	NOUN
ejpam-4467	142	21	.	.	PUNCT
ejpam-4467	143	1	we	we	PRON
ejpam-4467	143	2	explore	explore	VERB
ejpam-4467	143	3	the	the	DET
ejpam-4467	143	4	conditions	condition	NOUN
ejpam-4467	143	5	under	under	ADP
ejpam-4467	143	6	which	which	PRON
ejpam-4467	143	7	∈-set	∈-set	NOUN
ejpam-4467	143	8	and	and	CCONJ
ejpam-4467	143	9	q	q	NOUN
ejpam-4467	143	10	-	-	PUNCT
ejpam-4467	143	11	set	set	NOUN
ejpam-4467	143	12	of	of	ADP
ejpam-4467	143	13	the	the	DET
ejpam-4467	143	14	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	143	15	fuzzy	fuzzy	ADJ
ejpam-4467	143	16	set	set	NOUN
ejpam-4467	143	17	can	can	AUX
ejpam-4467	143	18	be	be	AUX
ejpam-4467	143	19	ideal	ideal	ADJ
ejpam-4467	143	20	.	.	PUNCT
ejpam-4467	144	1	theorem	theorem	ADJ
ejpam-4467	144	2	4	4	NUM
ejpam-4467	144	3	.	.	PUNCT
ejpam-4467	145	1	let	let	VERB
ejpam-4467	145	2	lεψ	lεψ	ADJ
ejpam-4467	145	3	be	be	AUX
ejpam-4467	145	4	a	a	DET
ejpam-4467	145	5	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	145	6	fuzzy	fuzzy	ADJ
ejpam-4467	145	7	set	set	VERB
ejpam-4467	145	8	in	in	ADP
ejpam-4467	145	9	x.	x.	NOUN
ejpam-4467	145	10	then	then	ADV
ejpam-4467	145	11	the	the	DET
ejpam-4467	145	12	∈-set	∈-set	NOUN
ejpam-4467	145	13	(	(	PUNCT
ejpam-4467	145	14	lεψ	lεψ	ADJ
ejpam-4467	145	15	,	,	PUNCT
ejpam-4467	145	16	t)∈	t)∈	PROPN
ejpam-4467	145	17	of	of	ADP
ejpam-4467	145	18	lεψ	lεψ	VERB
ejpam-4467	145	19	with	with	ADP
ejpam-4467	145	20	value	value	NOUN
ejpam-4467	145	21	t	t	X
ejpam-4467	145	22	∈	∈	PROPN
ejpam-4467	145	23	(	(	PUNCT
ejpam-4467	145	24	0.5	0.5	NUM
ejpam-4467	145	25	,	,	PUNCT
ejpam-4467	145	26	1	1	NUM
ejpam-4467	145	27	]	]	PUNCT
ejpam-4467	145	28	is	be	AUX
ejpam-4467	145	29	an	an	DET
ejpam-4467	145	30	ideal	ideal	NOUN
ejpam-4467	145	31	of	of	ADP
ejpam-4467	145	32	(	(	PUNCT
ejpam-4467	145	33	x	x	NOUN
ejpam-4467	145	34	,	,	PUNCT
ejpam-4467	145	35	1)∗	1)∗	NOUN
ejpam-4467	145	36	if	if	SCONJ
ejpam-4467	145	37	and	and	CCONJ
ejpam-4467	145	38	only	only	ADV
ejpam-4467	145	39	if	if	SCONJ
ejpam-4467	145	40	lεψ	lεψ	ADJ
ejpam-4467	145	41	satisfies	satisfie	NOUN
ejpam-4467	145	42	:	:	PUNCT
ejpam-4467	145	43	(	(	PUNCT
ejpam-4467	145	44	∀x	∀x	X
ejpam-4467	145	45	,	,	PUNCT
ejpam-4467	145	46	y	y	PROPN
ejpam-4467	145	47	∈	∈	PROPN
ejpam-4467	145	48	x	x	X
ejpam-4467	145	49	)	)	PUNCT
ejpam-4467	145	50	(	(	PUNCT
ejpam-4467	145	51	lεψ(y	lεψ(y	PROPN
ejpam-4467	145	52	)	)	PUNCT
ejpam-4467	145	53	≤	≤	NUM
ejpam-4467	145	54	max	max	PROPN
ejpam-4467	145	55	{	{	PUNCT
ejpam-4467	145	56	lεψ(x	lεψ(x	PROPN
ejpam-4467	145	57	∗	∗	PROPN
ejpam-4467	145	58	y	y	PROPN
ejpam-4467	145	59	)	)	PUNCT
ejpam-4467	145	60	,	,	PUNCT
ejpam-4467	145	61	0.5	0.5	NUM
ejpam-4467	145	62	}	}	PUNCT
ejpam-4467	145	63	)	)	PUNCT
ejpam-4467	145	64	,	,	PUNCT
ejpam-4467	145	65	(	(	PUNCT
ejpam-4467	145	66	18	18	NUM
ejpam-4467	145	67	)	)	PUNCT
ejpam-4467	145	68	(	(	PUNCT
ejpam-4467	145	69	∀x	∀x	X
ejpam-4467	145	70	,	,	PUNCT
ejpam-4467	145	71	y	y	PROPN
ejpam-4467	145	72	,	,	PUNCT
ejpam-4467	145	73	z	z	NOUN
ejpam-4467	145	74	∈	∈	PROPN
ejpam-4467	145	75	x	x	X
ejpam-4467	145	76	)	)	PUNCT
ejpam-4467	145	77	(	(	PUNCT
ejpam-4467	145	78	min	min	NOUN
ejpam-4467	145	79	{	{	PUNCT
ejpam-4467	145	80	lεψ(x	lεψ(x	NOUN
ejpam-4467	145	81	)	)	PUNCT
ejpam-4467	145	82	,	,	PUNCT
ejpam-4467	145	83	lεψ(y	lεψ(y	PROPN
ejpam-4467	145	84	)	)	PUNCT
ejpam-4467	145	85	}	}	PUNCT
ejpam-4467	145	86	≤	≤	NUM
ejpam-4467	145	87	max	max	PROPN
ejpam-4467	145	88	{	{	PUNCT
ejpam-4467	145	89	lεψ((x	lεψ((x	NOUN
ejpam-4467	145	90	∗	∗	NOUN
ejpam-4467	145	91	(	(	PUNCT
ejpam-4467	145	92	y	y	PROPN
ejpam-4467	145	93	∗	∗	PROPN
ejpam-4467	145	94	z	z	NOUN
ejpam-4467	145	95	)	)	PUNCT
ejpam-4467	145	96	)	)	PUNCT
ejpam-4467	145	97	∗	∗	PROPN
ejpam-4467	145	98	z	z	PROPN
ejpam-4467	145	99	)	)	PUNCT
ejpam-4467	145	100	,	,	PUNCT
ejpam-4467	145	101	0.5	0.5	NUM
ejpam-4467	145	102	}	}	PUNCT
ejpam-4467	145	103	)	)	PUNCT
ejpam-4467	145	104	.	.	PUNCT
ejpam-4467	146	1	(	(	PUNCT
ejpam-4467	146	2	19	19	NUM
ejpam-4467	146	3	)	)	PUNCT
ejpam-4467	146	4	proof	proof	NOUN
ejpam-4467	146	5	.	.	PUNCT
ejpam-4467	147	1	assume	assume	VERB
ejpam-4467	147	2	that	that	SCONJ
ejpam-4467	147	3	(	(	PUNCT
ejpam-4467	147	4	lεψ	lεψ	ADJ
ejpam-4467	147	5	,	,	PUNCT
ejpam-4467	147	6	t)∈	t)∈	NUM
ejpam-4467	147	7	is	be	AUX
ejpam-4467	147	8	an	an	DET
ejpam-4467	147	9	ideal	ideal	NOUN
ejpam-4467	147	10	of	of	ADP
ejpam-4467	147	11	(	(	PUNCT
ejpam-4467	147	12	x	x	X
ejpam-4467	147	13	,	,	PUNCT
ejpam-4467	147	14	1)∗	1)∗	NUM
ejpam-4467	147	15	for	for	ADP
ejpam-4467	147	16	t	t	PROPN
ejpam-4467	147	17	∈	∈	PROPN
ejpam-4467	147	18	(	(	PUNCT
ejpam-4467	147	19	0.5	0.5	NUM
ejpam-4467	147	20	,	,	PUNCT
ejpam-4467	147	21	1	1	NUM
ejpam-4467	147	22	]	]	PUNCT
ejpam-4467	147	23	.	.	PUNCT
ejpam-4467	148	1	if	if	SCONJ
ejpam-4467	148	2	there	there	PRON
ejpam-4467	148	3	exist	exist	VERB
ejpam-4467	148	4	a	a	DET
ejpam-4467	148	5	,	,	PUNCT
ejpam-4467	148	6	b	b	X
ejpam-4467	148	7	∈	∈	PROPN
ejpam-4467	148	8	x	x	PUNCT
ejpam-4467	148	9	such	such	ADJ
ejpam-4467	148	10	that	that	DET
ejpam-4467	148	11	lεψ(b	lεψ(b	NOUN
ejpam-4467	148	12	)	)	PUNCT
ejpam-4467	148	13	>	>	X
ejpam-4467	148	14	max	max	PROPN
ejpam-4467	148	15	{	{	PUNCT
ejpam-4467	148	16	lεψ(a	lεψ(a	PROPN
ejpam-4467	148	17	∗	∗	NOUN
ejpam-4467	148	18	b	b	NOUN
ejpam-4467	148	19	)	)	PUNCT
ejpam-4467	148	20	,	,	PUNCT
ejpam-4467	148	21	0.5	0.5	NUM
ejpam-4467	148	22	}	}	PUNCT
ejpam-4467	148	23	,	,	PUNCT
ejpam-4467	148	24	then	then	ADV
ejpam-4467	148	25	lεψ(b	lεψ(b	PROPN
ejpam-4467	148	26	)	)	PUNCT
ejpam-4467	148	27	∈	∈	PROPN
ejpam-4467	148	28	(	(	PUNCT
ejpam-4467	148	29	0.5	0.5	NUM
ejpam-4467	148	30	,	,	PUNCT
ejpam-4467	148	31	1	1	NUM
ejpam-4467	148	32	]	]	PUNCT
ejpam-4467	148	33	and	and	CCONJ
ejpam-4467	148	34	lεψ(a	lεψ(a	PROPN
ejpam-4467	148	35	∗	∗	NOUN
ejpam-4467	148	36	b	b	NOUN
ejpam-4467	148	37	)	)	PUNCT
ejpam-4467	148	38	<	<	X
ejpam-4467	148	39	lεψ(b	lεψ(b	PROPN
ejpam-4467	148	40	)	)	PUNCT
ejpam-4467	148	41	.	.	PUNCT
ejpam-4467	149	1	hence	hence	ADV
ejpam-4467	149	2	⟨b/	⟨b/	PUNCT
ejpam-4467	150	1	lεψ(b)⟩	lεψ(b)⟩	PROPN
ejpam-4467	150	2	∈	∈	PROPN
ejpam-4467	150	3	lεψ	lεψ	ADJ
ejpam-4467	150	4	,	,	PUNCT
ejpam-4467	150	5	and	and	CCONJ
ejpam-4467	150	6	so	so	ADV
ejpam-4467	150	7	b	b	PROPN
ejpam-4467	150	8	∈	∈	PROPN
ejpam-4467	150	9	(	(	PUNCT
ejpam-4467	150	10	lεψ	lεψ	ADJ
ejpam-4467	150	11	,	,	PUNCT
ejpam-4467	150	12	l	l	PROPN
ejpam-4467	150	13	ε	ε	PROPN
ejpam-4467	150	14	ψ(b))∈	ψ(b))∈	NOUN
ejpam-4467	150	15	,	,	PUNCT
ejpam-4467	150	16	but	but	CCONJ
ejpam-4467	150	17	a	a	DET
ejpam-4467	150	18	∗	∗	NOUN
ejpam-4467	150	19	b	b	NOUN
ejpam-4467	150	20	/∈	/∈	PUNCT
ejpam-4467	150	21	(	(	PUNCT
ejpam-4467	150	22	lεψ	lεψ	ADJ
ejpam-4467	150	23	,	,	PUNCT
ejpam-4467	150	24	l	l	PROPN
ejpam-4467	150	25	ε	ε	PROPN
ejpam-4467	150	26	ψ(b))∈.	ψ(b))∈.	VERB
ejpam-4467	150	27	this	this	PRON
ejpam-4467	150	28	is	be	AUX
ejpam-4467	150	29	a	a	DET
ejpam-4467	150	30	contradiction	contradiction	NOUN
ejpam-4467	150	31	,	,	PUNCT
ejpam-4467	150	32	and	and	CCONJ
ejpam-4467	150	33	thus	thus	ADV
ejpam-4467	150	34	lεψ(y	lεψ(y	ADJ
ejpam-4467	150	35	)	)	PUNCT
ejpam-4467	150	36	≤	≤	NUM
ejpam-4467	150	37	max	max	PROPN
ejpam-4467	150	38	{	{	PUNCT
ejpam-4467	150	39	lεψ(x	lεψ(x	PROPN
ejpam-4467	150	40	∗	∗	PROPN
ejpam-4467	150	41	y	y	PROPN
ejpam-4467	150	42	)	)	PUNCT
ejpam-4467	150	43	,	,	PUNCT
ejpam-4467	150	44	0.5	0.5	NUM
ejpam-4467	150	45	}	}	PUNCT
ejpam-4467	150	46	for	for	ADP
ejpam-4467	150	47	all	all	DET
ejpam-4467	150	48	x	x	NOUN
ejpam-4467	150	49	,	,	PUNCT
ejpam-4467	150	50	y	y	PROPN
ejpam-4467	150	51	∈	∈	PROPN
ejpam-4467	150	52	x.	x.	NOUN
ejpam-4467	151	1	if	if	SCONJ
ejpam-4467	151	2	the	the	DET
ejpam-4467	151	3	condition	condition	NOUN
ejpam-4467	151	4	(	(	PUNCT
ejpam-4467	151	5	19	19	NUM
ejpam-4467	151	6	)	)	PUNCT
ejpam-4467	151	7	is	be	AUX
ejpam-4467	151	8	not	not	PART
ejpam-4467	151	9	valid	valid	ADJ
ejpam-4467	151	10	,	,	PUNCT
ejpam-4467	151	11	then	then	ADV
ejpam-4467	151	12	there	there	PRON
ejpam-4467	151	13	exist	exist	VERB
ejpam-4467	151	14	a	a	DET
ejpam-4467	151	15	,	,	PUNCT
ejpam-4467	151	16	b	b	NOUN
ejpam-4467	151	17	,	,	PUNCT
ejpam-4467	151	18	c	c	PROPN
ejpam-4467	151	19	∈	∈	PROPN
ejpam-4467	151	20	x	x	PUNCT
ejpam-4467	151	21	such	such	ADJ
ejpam-4467	151	22	that	that	DET
ejpam-4467	151	23	min	min	NOUN
ejpam-4467	151	24	{	{	PUNCT
ejpam-4467	151	25	lεψ(a	lεψ(a	PROPN
ejpam-4467	151	26	)	)	PUNCT
ejpam-4467	151	27	,	,	PUNCT
ejpam-4467	151	28	lεψ(b	lεψ(b	NOUN
ejpam-4467	151	29	)	)	PUNCT
ejpam-4467	151	30	}	}	PUNCT
ejpam-4467	151	31	>	>	X
ejpam-4467	151	32	max	max	PROPN
ejpam-4467	151	33	{	{	PUNCT
ejpam-4467	151	34	lεψ((a	lεψ((a	PROPN
ejpam-4467	151	35	∗	∗	NOUN
ejpam-4467	151	36	(	(	PUNCT
ejpam-4467	151	37	b	b	NOUN
ejpam-4467	151	38	∗	∗	NOUN
ejpam-4467	151	39	c	c	NOUN
ejpam-4467	151	40	)	)	PUNCT
ejpam-4467	151	41	)	)	PUNCT
ejpam-4467	151	42	∗	∗	NOUN
ejpam-4467	151	43	c	c	NOUN
ejpam-4467	151	44	)	)	PUNCT
ejpam-4467	151	45	,	,	PUNCT
ejpam-4467	151	46	0.5	0.5	NUM
ejpam-4467	151	47	}	}	PUNCT
ejpam-4467	151	48	.	.	PUNCT
ejpam-4467	152	1	if	if	SCONJ
ejpam-4467	152	2	we	we	PRON
ejpam-4467	152	3	take	take	VERB
ejpam-4467	152	4	t	t	NOUN
ejpam-4467	152	5	:	:	PUNCT
ejpam-4467	152	6	=	=	SYM
ejpam-4467	152	7	min	min	X
ejpam-4467	152	8	{	{	PUNCT
ejpam-4467	152	9	lεψ(a	lεψ(a	PROPN
ejpam-4467	152	10	)	)	PUNCT
ejpam-4467	152	11	,	,	PUNCT
ejpam-4467	152	12	lεψ(b	lεψ(b	NOUN
ejpam-4467	152	13	)	)	PUNCT
ejpam-4467	152	14	}	}	PUNCT
ejpam-4467	152	15	,	,	PUNCT
ejpam-4467	152	16	then	then	ADV
ejpam-4467	152	17	t	t	PROPN
ejpam-4467	152	18	∈	∈	PROPN
ejpam-4467	152	19	(	(	PUNCT
ejpam-4467	152	20	0.5	0.5	NUM
ejpam-4467	152	21	,	,	PUNCT
ejpam-4467	152	22	1	1	NUM
ejpam-4467	152	23	]	]	PUNCT
ejpam-4467	152	24	,	,	PUNCT
ejpam-4467	152	25	⟨a	⟨a	NOUN
ejpam-4467	152	26	/	/	SYM
ejpam-4467	152	27	t⟩	t⟩	PRON
ejpam-4467	152	28	∈	∈	PROPN
ejpam-4467	152	29	lεψ	lεψ	VERB
ejpam-4467	152	30	and	and	CCONJ
ejpam-4467	152	31	⟨b	⟨b	NOUN
ejpam-4467	152	32	/	/	SYM
ejpam-4467	152	33	t⟩	t⟩	NOUN
ejpam-4467	152	34	∈	∈	PROPN
ejpam-4467	152	35	lεψ	lεψ	ADJ
ejpam-4467	152	36	,	,	PUNCT
ejpam-4467	152	37	but	but	CCONJ
ejpam-4467	152	38	⟨((a∗(b∗c))∗c)/t⟩	⟨((a∗(b∗c))∗c)/t⟩	NUM
ejpam-4467	152	39	∈	∈	PROPN
ejpam-4467	152	40	lεψ	lεψ	PROPN
ejpam-4467	152	41	,	,	PUNCT
ejpam-4467	152	42	that	that	ADV
ejpam-4467	152	43	is	is	ADV
ejpam-4467	152	44	,	,	PUNCT
ejpam-4467	152	45	a	a	DET
ejpam-4467	152	46	∈	∈	PROPN
ejpam-4467	152	47	(	(	PUNCT
ejpam-4467	152	48	lεψ	lεψ	ADJ
ejpam-4467	152	49	,	,	PUNCT
ejpam-4467	152	50	t)∈	t)∈	NUM
ejpam-4467	152	51	and	and	CCONJ
ejpam-4467	152	52	b	b	X
ejpam-4467	152	53	∈	∈	PROPN
ejpam-4467	152	54	(	(	PUNCT
ejpam-4467	152	55	lεψ	lεψ	ADJ
ejpam-4467	152	56	,	,	PUNCT
ejpam-4467	152	57	t)∈	t)∈	NUM
ejpam-4467	152	58	,	,	PUNCT
ejpam-4467	152	59	but	but	CCONJ
ejpam-4467	152	60	(	(	PUNCT
ejpam-4467	152	61	a∗(b∗c))∗c	a∗(b∗c))∗c	PROPN
ejpam-4467	152	62	/∈	/∈	PUNCT
ejpam-4467	153	1	(	(	PUNCT
ejpam-4467	153	2	lεψ	lεψ	ADJ
ejpam-4467	153	3	,	,	PUNCT
ejpam-4467	153	4	t)∈.	t)∈.	PROPN
ejpam-4467	153	5	this	this	PRON
ejpam-4467	153	6	is	be	AUX
ejpam-4467	153	7	a	a	DET
ejpam-4467	153	8	contradiction	contradiction	NOUN
ejpam-4467	153	9	,	,	PUNCT
ejpam-4467	153	10	and	and	CCONJ
ejpam-4467	153	11	thus	thus	ADV
ejpam-4467	153	12	(	(	PUNCT
ejpam-4467	153	13	19	19	NUM
ejpam-4467	153	14	)	)	PUNCT
ejpam-4467	153	15	is	be	AUX
ejpam-4467	153	16	valid	valid	ADJ
ejpam-4467	153	17	.	.	PUNCT
ejpam-4467	154	1	conversely	conversely	ADV
ejpam-4467	154	2	,	,	PUNCT
ejpam-4467	154	3	suppose	suppose	VERB
ejpam-4467	154	4	that	that	SCONJ
ejpam-4467	154	5	lεψ	lεψ	ADJ
ejpam-4467	154	6	satisfies	satisfie	NOUN
ejpam-4467	154	7	(	(	PUNCT
ejpam-4467	154	8	18	18	NUM
ejpam-4467	154	9	)	)	PUNCT
ejpam-4467	154	10	and	and	CCONJ
ejpam-4467	154	11	(	(	PUNCT
ejpam-4467	154	12	19	19	NUM
ejpam-4467	154	13	)	)	PUNCT
ejpam-4467	154	14	,	,	PUNCT
ejpam-4467	154	15	and	and	CCONJ
ejpam-4467	154	16	let	let	VERB
ejpam-4467	154	17	y	y	PROPN
ejpam-4467	154	18	∈	∈	PROPN
ejpam-4467	154	19	(	(	PUNCT
ejpam-4467	154	20	lεψ	lεψ	ADJ
ejpam-4467	154	21	,	,	PUNCT
ejpam-4467	154	22	t)∈	t)∈	PROPN
ejpam-4467	154	23	for	for	ADP
ejpam-4467	154	24	t	t	PROPN
ejpam-4467	154	25	∈	∈	PROPN
ejpam-4467	154	26	(	(	PUNCT
ejpam-4467	154	27	0.5	0.5	NUM
ejpam-4467	154	28	,	,	PUNCT
ejpam-4467	154	29	1	1	NUM
ejpam-4467	154	30	]	]	PUNCT
ejpam-4467	154	31	.	.	PUNCT
ejpam-4467	155	1	then	then	ADV
ejpam-4467	155	2	t	t	X
ejpam-4467	155	3	≤	≤	PROPN
ejpam-4467	155	4	lεψ(y	lεψ(y	PROPN
ejpam-4467	155	5	)	)	PUNCT
ejpam-4467	155	6	≤	≤	NUM
ejpam-4467	155	7	max	max	PROPN
ejpam-4467	155	8	{	{	PUNCT
ejpam-4467	155	9	lεψ(x∗y	lεψ(x∗y	PROPN
ejpam-4467	155	10	)	)	PUNCT
ejpam-4467	155	11	,	,	PUNCT
ejpam-4467	155	12	0.5	0.5	NUM
ejpam-4467	155	13	}	}	PUNCT
ejpam-4467	155	14	by	by	ADP
ejpam-4467	155	15	(	(	PUNCT
ejpam-4467	155	16	18	18	NUM
ejpam-4467	155	17	)	)	PUNCT
ejpam-4467	155	18	.	.	PUNCT
ejpam-4467	156	1	hence	hence	ADV
ejpam-4467	156	2	lεψ(x∗y	lεψ(x∗y	X
ejpam-4467	156	3	)	)	PUNCT
ejpam-4467	156	4	≥	≥	PROPN
ejpam-4467	156	5	t	t	PROPN
ejpam-4467	156	6	,	,	PUNCT
ejpam-4467	156	7	and	and	CCONJ
ejpam-4467	156	8	so	so	ADV
ejpam-4467	156	9	x∗y	x∗y	PUNCT
ejpam-4467	156	10	∈	∈	PROPN
ejpam-4467	156	11	(	(	PUNCT
ejpam-4467	156	12	lεψ	lεψ	ADJ
ejpam-4467	156	13	,	,	PUNCT
ejpam-4467	156	14	t)∈.	t)∈.	PROPN
ejpam-4467	156	15	let	let	VERB
ejpam-4467	156	16	x	x	PRON
ejpam-4467	156	17	,	,	PUNCT
ejpam-4467	156	18	y	y	PROPN
ejpam-4467	156	19	∈	∈	PROPN
ejpam-4467	156	20	x	x	X
ejpam-4467	156	21	and	and	CCONJ
ejpam-4467	156	22	t	t	PROPN
ejpam-4467	156	23	∈	∈	PROPN
ejpam-4467	156	24	(	(	PUNCT
ejpam-4467	156	25	0.5	0.5	NUM
ejpam-4467	156	26	,	,	PUNCT
ejpam-4467	156	27	1	1	NUM
ejpam-4467	156	28	]	]	PUNCT
ejpam-4467	156	29	be	be	AUX
ejpam-4467	156	30	such	such	ADJ
ejpam-4467	156	31	that	that	SCONJ
ejpam-4467	156	32	x	x	SYM
ejpam-4467	156	33	∈	∈	PROPN
ejpam-4467	156	34	(	(	PUNCT
ejpam-4467	156	35	lεψ	lεψ	ADJ
ejpam-4467	156	36	,	,	PUNCT
ejpam-4467	156	37	t)∈	t)∈	PROPN
ejpam-4467	156	38	and	and	CCONJ
ejpam-4467	156	39	y	y	PROPN
ejpam-4467	156	40	∈	∈	PROPN
ejpam-4467	156	41	(	(	PUNCT
ejpam-4467	156	42	lεψ	lεψ	PROPN
ejpam-4467	156	43	,	,	PUNCT
ejpam-4467	156	44	t)∈.	t)∈.	PROPN
ejpam-4467	156	45	then	then	ADV
ejpam-4467	156	46	lεψ(x	lεψ(x	PROPN
ejpam-4467	156	47	)	)	PUNCT
ejpam-4467	156	48	≥	≥	NOUN
ejpam-4467	156	49	t	t	NOUN
ejpam-4467	156	50	and	and	CCONJ
ejpam-4467	156	51	lεψ(y	lεψ(y	PROPN
ejpam-4467	156	52	)	)	PUNCT
ejpam-4467	156	53	≥	≥	NOUN
ejpam-4467	156	54	t	t	PROPN
ejpam-4467	156	55	,	,	PUNCT
ejpam-4467	156	56	which	which	PRON
ejpam-4467	156	57	imply	imply	VERB
ejpam-4467	156	58	from	from	ADP
ejpam-4467	156	59	(	(	PUNCT
ejpam-4467	156	60	19	19	NUM
ejpam-4467	156	61	)	)	PUNCT
ejpam-4467	156	62	that	that	PRON
ejpam-4467	156	63	0.5	0.5	NUM
ejpam-4467	156	64	<	<	X
ejpam-4467	156	65	t	t	PROPN
ejpam-4467	156	66	≤	≤	NUM
ejpam-4467	156	67	min	min	PROPN
ejpam-4467	156	68	{	{	PUNCT
ejpam-4467	156	69	lεψ(x	lεψ(x	NOUN
ejpam-4467	156	70	)	)	PUNCT
ejpam-4467	156	71	,	,	PUNCT
ejpam-4467	156	72	lεψ(y	lεψ(y	PROPN
ejpam-4467	156	73	)	)	PUNCT
ejpam-4467	156	74	}	}	PUNCT
ejpam-4467	156	75	≤	≤	NUM
ejpam-4467	156	76	max	max	PROPN
ejpam-4467	156	77	{	{	PUNCT
ejpam-4467	156	78	lεψ((x	lεψ((x	NOUN
ejpam-4467	156	79	∗	∗	NOUN
ejpam-4467	156	80	(	(	PUNCT
ejpam-4467	156	81	y	y	PROPN
ejpam-4467	156	82	∗	∗	PROPN
ejpam-4467	156	83	z	z	NOUN
ejpam-4467	156	84	)	)	PUNCT
ejpam-4467	156	85	)	)	PUNCT
ejpam-4467	156	86	∗	∗	PROPN
ejpam-4467	156	87	z	z	PROPN
ejpam-4467	156	88	)	)	PUNCT
ejpam-4467	156	89	,	,	PUNCT
ejpam-4467	156	90	0.5	0.5	NUM
ejpam-4467	156	91	}	}	PUNCT
ejpam-4467	156	92	for	for	ADP
ejpam-4467	156	93	all	all	DET
ejpam-4467	156	94	z	z	NOUN
ejpam-4467	156	95	∈	∈	NOUN
ejpam-4467	156	96	x.	x.	NOUN
ejpam-4467	156	97	hence	hence	ADV
ejpam-4467	156	98	⟨((x∗(y∗z))∗z)/t⟩	⟨((x∗(y∗z))∗z)/t⟩	X
ejpam-4467	156	99	∈	∈	PROPN
ejpam-4467	156	100	lεψ	lεψ	VERB
ejpam-4467	156	101	,	,	PUNCT
ejpam-4467	156	102	that	that	ADV
ejpam-4467	156	103	is	is	ADV
ejpam-4467	156	104	,	,	PUNCT
ejpam-4467	156	105	(	(	PUNCT
ejpam-4467	156	106	x∗(y∗z))∗z	x∗(y∗z))∗z	PROPN
ejpam-4467	156	107	∈	∈	PROPN
ejpam-4467	156	108	(	(	PUNCT
ejpam-4467	156	109	lεψ	lεψ	PROPN
ejpam-4467	156	110	,	,	PUNCT
ejpam-4467	156	111	t)∈.	t)∈.	PROPN
ejpam-4467	156	112	therefore	therefore	ADV
ejpam-4467	156	113	(	(	PUNCT
ejpam-4467	156	114	lεψ	lεψ	ADJ
ejpam-4467	156	115	,	,	PUNCT
ejpam-4467	156	116	t)∈	t)∈	NUM
ejpam-4467	156	117	is	be	AUX
ejpam-4467	156	118	an	an	DET
ejpam-4467	156	119	ideal	ideal	NOUN
ejpam-4467	156	120	of	of	ADP
ejpam-4467	156	121	(	(	PUNCT
ejpam-4467	156	122	x	x	X
ejpam-4467	156	123	,	,	PUNCT
ejpam-4467	156	124	1)∗	1)∗	NUM
ejpam-4467	156	125	for	for	ADP
ejpam-4467	156	126	t	t	PROPN
ejpam-4467	156	127	∈	∈	PROPN
ejpam-4467	156	128	(	(	PUNCT
ejpam-4467	156	129	0.5	0.5	NUM
ejpam-4467	156	130	,	,	PUNCT
ejpam-4467	156	131	1	1	NUM
ejpam-4467	156	132	]	]	PUNCT
ejpam-4467	156	133	.	.	PUNCT
ejpam-4467	157	1	theorem	theorem	NOUN
ejpam-4467	157	2	5	5	NUM
ejpam-4467	157	3	.	.	PUNCT
ejpam-4467	158	1	let	let	VERB
ejpam-4467	158	2	lεψ	lεψ	ADJ
ejpam-4467	158	3	be	be	AUX
ejpam-4467	158	4	a	a	DET
ejpam-4467	158	5	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	158	6	fuzzy	fuzzy	ADJ
ejpam-4467	158	7	set	set	VERB
ejpam-4467	158	8	in	in	ADP
ejpam-4467	158	9	x.	x.	NOUN
ejpam-4467	158	10	then	then	ADV
ejpam-4467	158	11	the	the	DET
ejpam-4467	158	12	∈-set	∈-set	NOUN
ejpam-4467	158	13	(	(	PUNCT
ejpam-4467	158	14	lεψ	lεψ	ADJ
ejpam-4467	158	15	,	,	PUNCT
ejpam-4467	158	16	t)∈	t)∈	PROPN
ejpam-4467	158	17	of	of	ADP
ejpam-4467	158	18	lεψ	lεψ	VERB
ejpam-4467	158	19	with	with	ADP
ejpam-4467	158	20	value	value	NOUN
ejpam-4467	158	21	t	t	X
ejpam-4467	158	22	∈	∈	PROPN
ejpam-4467	158	23	(	(	PUNCT
ejpam-4467	158	24	0.5	0.5	NUM
ejpam-4467	158	25	,	,	PUNCT
ejpam-4467	158	26	1	1	NUM
ejpam-4467	158	27	]	]	PUNCT
ejpam-4467	158	28	is	be	AUX
ejpam-4467	158	29	an	an	DET
ejpam-4467	158	30	ideal	ideal	NOUN
ejpam-4467	158	31	of	of	ADP
ejpam-4467	158	32	(	(	PUNCT
ejpam-4467	158	33	x	x	NOUN
ejpam-4467	158	34	,	,	PUNCT
ejpam-4467	158	35	1)∗	1)∗	NOUN
ejpam-4467	158	36	if	if	SCONJ
ejpam-4467	158	37	and	and	CCONJ
ejpam-4467	158	38	only	only	ADV
ejpam-4467	158	39	if	if	SCONJ
ejpam-4467	158	40	lεψ	lεψ	ADJ
ejpam-4467	158	41	satisfies	satisfie	NOUN
ejpam-4467	158	42	:	:	PUNCT
ejpam-4467	158	43	(	(	PUNCT
ejpam-4467	158	44	∀x	∀x	X
ejpam-4467	158	45	∈	∈	PROPN
ejpam-4467	158	46	x	x	NOUN
ejpam-4467	158	47	)	)	PUNCT
ejpam-4467	158	48	(	(	PUNCT
ejpam-4467	158	49	lεψ(x	lεψ(x	NOUN
ejpam-4467	158	50	)	)	PUNCT
ejpam-4467	158	51	≤	≤	NUM
ejpam-4467	158	52	max	max	PROPN
ejpam-4467	158	53	{	{	PUNCT
ejpam-4467	158	54	lεψ(1	lεψ(1	ADJ
ejpam-4467	158	55	)	)	PUNCT
ejpam-4467	158	56	,	,	PUNCT
ejpam-4467	158	57	0.5	0.5	NUM
ejpam-4467	158	58	}	}	PUNCT
ejpam-4467	158	59	)	)	PUNCT
ejpam-4467	158	60	,	,	PUNCT
ejpam-4467	158	61	(	(	PUNCT
ejpam-4467	158	62	20	20	NUM
ejpam-4467	158	63	)	)	PUNCT
ejpam-4467	158	64	(	(	PUNCT
ejpam-4467	158	65	∀x	∀x	X
ejpam-4467	158	66	,	,	PUNCT
ejpam-4467	158	67	y	y	PROPN
ejpam-4467	158	68	,	,	PUNCT
ejpam-4467	158	69	z	z	NOUN
ejpam-4467	158	70	∈	∈	PROPN
ejpam-4467	158	71	x	x	X
ejpam-4467	158	72	)	)	PUNCT
ejpam-4467	158	73	(	(	PUNCT
ejpam-4467	158	74	min	min	NOUN
ejpam-4467	158	75	{	{	PUNCT
ejpam-4467	158	76	lεψ(x	lεψ(x	ADJ
ejpam-4467	158	77	∗	∗	NOUN
ejpam-4467	158	78	(	(	PUNCT
ejpam-4467	158	79	y	y	PROPN
ejpam-4467	158	80	∗	∗	PROPN
ejpam-4467	158	81	z	z	PROPN
ejpam-4467	158	82	)	)	PUNCT
ejpam-4467	158	83	)	)	PUNCT
ejpam-4467	158	84	,	,	PUNCT
ejpam-4467	158	85	lεψ(y	lεψ(y	PROPN
ejpam-4467	158	86	)	)	PUNCT
ejpam-4467	158	87	}	}	PUNCT
ejpam-4467	158	88	≤	≤	NUM
ejpam-4467	159	1	max	max	PROPN
ejpam-4467	159	2	{	{	PUNCT
ejpam-4467	159	3	lεψ(x	lεψ(x	PROPN
ejpam-4467	159	4	∗	∗	PROPN
ejpam-4467	159	5	z	z	NOUN
ejpam-4467	159	6	)	)	PUNCT
ejpam-4467	159	7	,	,	PUNCT
ejpam-4467	159	8	0.5	0.5	NUM
ejpam-4467	159	9	}	}	PUNCT
ejpam-4467	159	10	)	)	PUNCT
ejpam-4467	159	11	.	.	PUNCT
ejpam-4467	160	1	(	(	PUNCT
ejpam-4467	160	2	21	21	NUM
ejpam-4467	160	3	)	)	PUNCT
ejpam-4467	160	4	s.	s.	PROPN
ejpam-4467	160	5	s.	s.	PROPN
ejpam-4467	160	6	ahn	ahn	PROPN
ejpam-4467	160	7	,	,	PUNCT
ejpam-4467	160	8	e.	e.	PROPN
ejpam-4467	160	9	h.	h.	PROPN
ejpam-4467	160	10	roh	roh	PROPN
ejpam-4467	160	11	and	and	CCONJ
ejpam-4467	160	12	y.	y.	PROPN
ejpam-4467	160	13	b.	b.	PROPN
ejpam-4467	160	14	jun	jun	PROPN
ejpam-4467	160	15	/	/	SYM
ejpam-4467	160	16	eur	eur	PROPN
ejpam-4467	160	17	.	.	PUNCT
ejpam-4467	161	1	j.	j.	PROPN
ejpam-4467	161	2	pure	pure	PROPN
ejpam-4467	161	3	appl	appl	PROPN
ejpam-4467	161	4	.	.	PROPN
ejpam-4467	161	5	math	math	PROPN
ejpam-4467	161	6	,	,	PUNCT
ejpam-4467	161	7	15	15	NUM
ejpam-4467	161	8	(	(	PUNCT
ejpam-4467	161	9	3	3	NUM
ejpam-4467	161	10	)	)	PUNCT
ejpam-4467	161	11	(	(	PUNCT
ejpam-4467	161	12	2022	2022	NUM
ejpam-4467	161	13	)	)	PUNCT
ejpam-4467	161	14	,	,	PUNCT
ejpam-4467	161	15	1307	1307	NUM
ejpam-4467	161	16	-	-	SYM
ejpam-4467	161	17	1320	1320	NUM
ejpam-4467	161	18	1313	1313	NUM
ejpam-4467	161	19	proof	proof	NOUN
ejpam-4467	161	20	.	.	PUNCT
ejpam-4467	162	1	assume	assume	VERB
ejpam-4467	162	2	that	that	SCONJ
ejpam-4467	162	3	(	(	PUNCT
ejpam-4467	162	4	lεψ	lεψ	ADJ
ejpam-4467	162	5	,	,	PUNCT
ejpam-4467	162	6	t)∈	t)∈	NUM
ejpam-4467	162	7	is	be	AUX
ejpam-4467	162	8	an	an	DET
ejpam-4467	162	9	ideal	ideal	NOUN
ejpam-4467	162	10	of	of	ADP
ejpam-4467	162	11	(	(	PUNCT
ejpam-4467	162	12	x	x	X
ejpam-4467	162	13	,	,	PUNCT
ejpam-4467	162	14	1)∗	1)∗	NUM
ejpam-4467	162	15	for	for	ADP
ejpam-4467	162	16	t	t	PROPN
ejpam-4467	162	17	∈	∈	PROPN
ejpam-4467	162	18	(	(	PUNCT
ejpam-4467	162	19	0.5	0.5	NUM
ejpam-4467	162	20	,	,	PUNCT
ejpam-4467	162	21	1	1	NUM
ejpam-4467	162	22	]	]	PUNCT
ejpam-4467	162	23	.	.	PUNCT
ejpam-4467	163	1	if	if	SCONJ
ejpam-4467	163	2	there	there	PRON
ejpam-4467	163	3	exist	exist	VERB
ejpam-4467	163	4	a	a	DET
ejpam-4467	163	5	∈	∈	NOUN
ejpam-4467	163	6	x	x	PUNCT
ejpam-4467	163	7	such	such	ADJ
ejpam-4467	163	8	that	that	SCONJ
ejpam-4467	163	9	lεψ(a	lεψ(a	PROPN
ejpam-4467	163	10	)	)	PUNCT
ejpam-4467	163	11	>	>	X
ejpam-4467	163	12	max	max	PROPN
ejpam-4467	163	13	{	{	PUNCT
ejpam-4467	163	14	lεψ(1	lεψ(1	ADJ
ejpam-4467	163	15	)	)	PUNCT
ejpam-4467	163	16	,	,	PUNCT
ejpam-4467	163	17	0.5	0.5	NUM
ejpam-4467	163	18	}	}	PUNCT
ejpam-4467	163	19	,	,	PUNCT
ejpam-4467	163	20	then	then	ADV
ejpam-4467	163	21	lεψ(a	lεψ(a	PROPN
ejpam-4467	163	22	)	)	PUNCT
ejpam-4467	163	23	∈	∈	PROPN
ejpam-4467	163	24	(	(	PUNCT
ejpam-4467	163	25	0.5	0.5	NUM
ejpam-4467	163	26	,	,	PUNCT
ejpam-4467	163	27	1	1	NUM
ejpam-4467	163	28	]	]	PUNCT
ejpam-4467	163	29	and	and	CCONJ
ejpam-4467	163	30	lεψ(1	lεψ(1	ADJ
ejpam-4467	163	31	)	)	PUNCT
ejpam-4467	163	32	<	<	X
ejpam-4467	163	33	lεψ(a	lεψ(a	PROPN
ejpam-4467	163	34	)	)	PUNCT
ejpam-4467	163	35	.	.	PUNCT
ejpam-4467	164	1	hence	hence	ADV
ejpam-4467	164	2	⟨a/	⟨a/	ADJ
ejpam-4467	165	1	lεψ(a)⟩	lεψ(a)⟩	PRON
ejpam-4467	165	2	∈	∈	PROPN
ejpam-4467	165	3	lεψ	lεψ	ADJ
ejpam-4467	165	4	,	,	PUNCT
ejpam-4467	165	5	and	and	CCONJ
ejpam-4467	165	6	so	so	ADV
ejpam-4467	165	7	a	a	DET
ejpam-4467	165	8	∈	∈	PROPN
ejpam-4467	165	9	(	(	PUNCT
ejpam-4467	165	10	lεψ	lεψ	ADJ
ejpam-4467	165	11	,	,	PUNCT
ejpam-4467	165	12	l	l	PROPN
ejpam-4467	165	13	ε	ε	PROPN
ejpam-4467	165	14	ψ(a))∈	ψ(a))∈	NOUN
ejpam-4467	165	15	,	,	PUNCT
ejpam-4467	165	16	but	but	CCONJ
ejpam-4467	165	17	1	1	X
ejpam-4467	165	18	/∈	/∈	INTJ
ejpam-4467	165	19	(	(	PUNCT
ejpam-4467	165	20	lεψ	lεψ	ADJ
ejpam-4467	165	21	,	,	PUNCT
ejpam-4467	165	22	l	l	PROPN
ejpam-4467	165	23	ε	ε	PROPN
ejpam-4467	165	24	ψ(a))∈.	ψ(a))∈.	VERB
ejpam-4467	165	25	this	this	PRON
ejpam-4467	165	26	is	be	AUX
ejpam-4467	165	27	a	a	DET
ejpam-4467	165	28	contradiction	contradiction	NOUN
ejpam-4467	165	29	,	,	PUNCT
ejpam-4467	165	30	and	and	CCONJ
ejpam-4467	165	31	thus	thus	ADV
ejpam-4467	165	32	lεψ(x	lεψ(x	NOUN
ejpam-4467	165	33	)	)	PUNCT
ejpam-4467	165	34	≤	≤	NUM
ejpam-4467	165	35	max	max	PROPN
ejpam-4467	165	36	{	{	PUNCT
ejpam-4467	165	37	lεψ(1	lεψ(1	ADJ
ejpam-4467	165	38	)	)	PUNCT
ejpam-4467	165	39	,	,	PUNCT
ejpam-4467	165	40	0.5	0.5	NUM
ejpam-4467	165	41	}	}	PUNCT
ejpam-4467	165	42	for	for	ADP
ejpam-4467	165	43	all	all	DET
ejpam-4467	165	44	x	x	SYM
ejpam-4467	165	45	∈	∈	PROPN
ejpam-4467	165	46	x.	x.	NOUN
ejpam-4467	166	1	if	if	SCONJ
ejpam-4467	166	2	the	the	DET
ejpam-4467	166	3	condition	condition	NOUN
ejpam-4467	166	4	(	(	PUNCT
ejpam-4467	166	5	21	21	NUM
ejpam-4467	166	6	)	)	PUNCT
ejpam-4467	166	7	is	be	AUX
ejpam-4467	166	8	not	not	PART
ejpam-4467	166	9	valid	valid	ADJ
ejpam-4467	166	10	,	,	PUNCT
ejpam-4467	166	11	then	then	ADV
ejpam-4467	166	12	there	there	PRON
ejpam-4467	166	13	exist	exist	VERB
ejpam-4467	166	14	a	a	DET
ejpam-4467	166	15	,	,	PUNCT
ejpam-4467	166	16	b	b	NOUN
ejpam-4467	166	17	,	,	PUNCT
ejpam-4467	166	18	c	c	PROPN
ejpam-4467	166	19	∈	∈	PROPN
ejpam-4467	166	20	x	x	PUNCT
ejpam-4467	166	21	such	such	ADJ
ejpam-4467	166	22	that	that	DET
ejpam-4467	166	23	min	min	NOUN
ejpam-4467	166	24	{	{	PUNCT
ejpam-4467	166	25	lεψ(a	lεψ(a	PROPN
ejpam-4467	166	26	∗	∗	NOUN
ejpam-4467	166	27	(	(	PUNCT
ejpam-4467	166	28	b	b	NOUN
ejpam-4467	166	29	∗	∗	NOUN
ejpam-4467	166	30	c	c	NOUN
ejpam-4467	166	31	)	)	PUNCT
ejpam-4467	166	32	)	)	PUNCT
ejpam-4467	166	33	,	,	PUNCT
ejpam-4467	166	34	lεψ(b	lεψ(b	NOUN
ejpam-4467	166	35	)	)	PUNCT
ejpam-4467	166	36	}	}	PUNCT
ejpam-4467	166	37	>	>	X
ejpam-4467	166	38	max	max	PROPN
ejpam-4467	166	39	{	{	PUNCT
ejpam-4467	166	40	lεψ(a	lεψ(a	PROPN
ejpam-4467	166	41	∗	∗	NOUN
ejpam-4467	166	42	c	c	NOUN
ejpam-4467	166	43	)	)	PUNCT
ejpam-4467	166	44	,	,	PUNCT
ejpam-4467	166	45	0.5	0.5	NUM
ejpam-4467	166	46	}	}	PUNCT
ejpam-4467	166	47	.	.	PUNCT
ejpam-4467	167	1	if	if	SCONJ
ejpam-4467	167	2	we	we	PRON
ejpam-4467	167	3	take	take	VERB
ejpam-4467	167	4	t	t	NOUN
ejpam-4467	167	5	:	:	PUNCT
ejpam-4467	167	6	=	=	SYM
ejpam-4467	167	7	min	min	X
ejpam-4467	167	8	{	{	PUNCT
ejpam-4467	167	9	lεψ(a	lεψ(a	PROPN
ejpam-4467	167	10	∗	∗	NOUN
ejpam-4467	167	11	(	(	PUNCT
ejpam-4467	167	12	b	b	NOUN
ejpam-4467	167	13	∗	∗	NOUN
ejpam-4467	167	14	c	c	NOUN
ejpam-4467	167	15	)	)	PUNCT
ejpam-4467	167	16	)	)	PUNCT
ejpam-4467	167	17	,	,	PUNCT
ejpam-4467	167	18	lεψ(b	lεψ(b	NOUN
ejpam-4467	167	19	)	)	PUNCT
ejpam-4467	167	20	}	}	PUNCT
ejpam-4467	167	21	,	,	PUNCT
ejpam-4467	167	22	then	then	ADV
ejpam-4467	167	23	t	t	PROPN
ejpam-4467	167	24	∈	∈	PROPN
ejpam-4467	167	25	(	(	PUNCT
ejpam-4467	167	26	0.5	0.5	NUM
ejpam-4467	167	27	,	,	PUNCT
ejpam-4467	167	28	1	1	NUM
ejpam-4467	167	29	]	]	PUNCT
ejpam-4467	167	30	,	,	PUNCT
ejpam-4467	167	31	⟨(a	⟨(a	ADP
ejpam-4467	167	32	∗	∗	NOUN
ejpam-4467	167	33	(	(	PUNCT
ejpam-4467	167	34	b	b	NOUN
ejpam-4467	167	35	∗	∗	NOUN
ejpam-4467	167	36	c))/t⟩	c))/t⟩	NOUN
ejpam-4467	167	37	∈	∈	PROPN
ejpam-4467	167	38	lεψ	lεψ	VERB
ejpam-4467	167	39	and	and	CCONJ
ejpam-4467	167	40	⟨b	⟨b	NOUN
ejpam-4467	167	41	/	/	SYM
ejpam-4467	167	42	t⟩	t⟩	NOUN
ejpam-4467	167	43	∈	∈	PROPN
ejpam-4467	167	44	lεψ	lεψ	ADJ
ejpam-4467	167	45	,	,	PUNCT
ejpam-4467	167	46	but	but	CCONJ
ejpam-4467	167	47	⟨(a	⟨(a	NOUN
ejpam-4467	167	48	∗	∗	NOUN
ejpam-4467	167	49	c)/t⟩	c)/t⟩	PROPN
ejpam-4467	167	50	∈	∈	PROPN
ejpam-4467	167	51	lεψ	lεψ	PROPN
ejpam-4467	167	52	,	,	PUNCT
ejpam-4467	167	53	that	that	ADV
ejpam-4467	167	54	is	is	ADV
ejpam-4467	167	55	,	,	PUNCT
ejpam-4467	167	56	a	a	DET
ejpam-4467	167	57	∗	∗	NOUN
ejpam-4467	167	58	(	(	PUNCT
ejpam-4467	167	59	b	b	NOUN
ejpam-4467	167	60	∗	∗	ADP
ejpam-4467	167	61	c	c	NOUN
ejpam-4467	167	62	)	)	PUNCT
ejpam-4467	167	63	∈	∈	PROPN
ejpam-4467	167	64	(	(	PUNCT
ejpam-4467	167	65	lεψ	lεψ	ADJ
ejpam-4467	167	66	,	,	PUNCT
ejpam-4467	167	67	t)∈	t)∈	NUM
ejpam-4467	167	68	and	and	CCONJ
ejpam-4467	167	69	b	b	X
ejpam-4467	167	70	∈	∈	PROPN
ejpam-4467	167	71	(	(	PUNCT
ejpam-4467	167	72	lεψ	lεψ	ADJ
ejpam-4467	167	73	,	,	PUNCT
ejpam-4467	167	74	t)∈	t)∈	NUM
ejpam-4467	167	75	,	,	PUNCT
ejpam-4467	167	76	but	but	CCONJ
ejpam-4467	167	77	a	a	DET
ejpam-4467	167	78	∗	∗	NOUN
ejpam-4467	167	79	c	c	NOUN
ejpam-4467	167	80	/∈	/∈	PUNCT
ejpam-4467	168	1	(	(	PUNCT
ejpam-4467	168	2	lεψ	lεψ	ADJ
ejpam-4467	168	3	,	,	PUNCT
ejpam-4467	168	4	t)∈.	t)∈.	PROPN
ejpam-4467	168	5	this	this	PRON
ejpam-4467	168	6	is	be	AUX
ejpam-4467	168	7	a	a	DET
ejpam-4467	168	8	contradiction	contradiction	NOUN
ejpam-4467	168	9	,	,	PUNCT
ejpam-4467	168	10	and	and	CCONJ
ejpam-4467	168	11	thus	thus	ADV
ejpam-4467	168	12	(	(	PUNCT
ejpam-4467	168	13	21	21	NUM
ejpam-4467	168	14	)	)	PUNCT
ejpam-4467	168	15	is	be	AUX
ejpam-4467	168	16	valid	valid	ADJ
ejpam-4467	168	17	.	.	PUNCT
ejpam-4467	169	1	conversely	conversely	ADV
ejpam-4467	169	2	,	,	PUNCT
ejpam-4467	169	3	suppose	suppose	VERB
ejpam-4467	169	4	that	that	SCONJ
ejpam-4467	169	5	lεψ	lεψ	ADJ
ejpam-4467	169	6	satisfies	satisfie	NOUN
ejpam-4467	169	7	(	(	PUNCT
ejpam-4467	169	8	20	20	NUM
ejpam-4467	169	9	)	)	PUNCT
ejpam-4467	169	10	and	and	CCONJ
ejpam-4467	169	11	(	(	PUNCT
ejpam-4467	169	12	21	21	NUM
ejpam-4467	169	13	)	)	PUNCT
ejpam-4467	169	14	,	,	PUNCT
ejpam-4467	169	15	and	and	CCONJ
ejpam-4467	169	16	let	let	VERB
ejpam-4467	169	17	t	t	PROPN
ejpam-4467	169	18	∈	∈	PROPN
ejpam-4467	169	19	(	(	PUNCT
ejpam-4467	169	20	0.5	0.5	NUM
ejpam-4467	169	21	,	,	PUNCT
ejpam-4467	169	22	1	1	NUM
ejpam-4467	169	23	]	]	PUNCT
ejpam-4467	169	24	.	.	PUNCT
ejpam-4467	170	1	for	for	ADP
ejpam-4467	170	2	every	every	DET
ejpam-4467	170	3	x	x	SYM
ejpam-4467	170	4	∈	∈	PROPN
ejpam-4467	170	5	(	(	PUNCT
ejpam-4467	170	6	lεψ	lεψ	ADJ
ejpam-4467	170	7	,	,	PUNCT
ejpam-4467	170	8	t)∈	t)∈	NUM
ejpam-4467	170	9	,	,	PUNCT
ejpam-4467	170	10	we	we	PRON
ejpam-4467	170	11	have	have	VERB
ejpam-4467	170	12	t	t	NOUN
ejpam-4467	170	13	≤	≤	NUM
ejpam-4467	170	14	lεψ(x	lεψ(x	NOUN
ejpam-4467	170	15	)	)	PUNCT
ejpam-4467	170	16	≤	≤	NUM
ejpam-4467	170	17	max	max	PROPN
ejpam-4467	170	18	{	{	PUNCT
ejpam-4467	170	19	lεψ(1	lεψ(1	ADJ
ejpam-4467	170	20	)	)	PUNCT
ejpam-4467	170	21	,	,	PUNCT
ejpam-4467	170	22	0.5	0.5	NUM
ejpam-4467	170	23	}	}	PUNCT
ejpam-4467	170	24	by	by	ADP
ejpam-4467	170	25	(	(	PUNCT
ejpam-4467	170	26	20	20	NUM
ejpam-4467	170	27	)	)	PUNCT
ejpam-4467	170	28	.	.	PUNCT
ejpam-4467	171	1	hence	hence	ADV
ejpam-4467	171	2	lεψ(1	lεψ(1	ADV
ejpam-4467	171	3	)	)	PUNCT
ejpam-4467	171	4	≥	≥	NOUN
ejpam-4467	171	5	t	t	PROPN
ejpam-4467	171	6	,	,	PUNCT
ejpam-4467	171	7	and	and	CCONJ
ejpam-4467	171	8	so	so	ADV
ejpam-4467	171	9	1	1	NUM
ejpam-4467	171	10	∈	∈	PROPN
ejpam-4467	171	11	(	(	PUNCT
ejpam-4467	171	12	lεψ	lεψ	ADJ
ejpam-4467	171	13	,	,	PUNCT
ejpam-4467	171	14	t)∈.	t)∈.	PROPN
ejpam-4467	171	15	let	let	VERB
ejpam-4467	171	16	x	x	PRON
ejpam-4467	171	17	,	,	PUNCT
ejpam-4467	171	18	y	y	PROPN
ejpam-4467	171	19	,	,	PUNCT
ejpam-4467	171	20	z	z	NOUN
ejpam-4467	171	21	∈	∈	PROPN
ejpam-4467	171	22	x	x	X
ejpam-4467	171	23	and	and	CCONJ
ejpam-4467	171	24	t	t	PROPN
ejpam-4467	171	25	∈	∈	PROPN
ejpam-4467	171	26	(	(	PUNCT
ejpam-4467	171	27	0.5	0.5	NUM
ejpam-4467	171	28	,	,	PUNCT
ejpam-4467	171	29	1	1	NUM
ejpam-4467	171	30	]	]	PUNCT
ejpam-4467	171	31	be	be	AUX
ejpam-4467	171	32	such	such	ADJ
ejpam-4467	172	1	that	that	SCONJ
ejpam-4467	172	2	x	x	SYM
ejpam-4467	172	3	∗	∗	NOUN
ejpam-4467	172	4	(	(	PUNCT
ejpam-4467	172	5	y	y	PROPN
ejpam-4467	172	6	∗	∗	PROPN
ejpam-4467	172	7	z	z	NOUN
ejpam-4467	172	8	)	)	PUNCT
ejpam-4467	172	9	∈	∈	PROPN
ejpam-4467	172	10	(	(	PUNCT
ejpam-4467	172	11	lεψ	lεψ	ADJ
ejpam-4467	172	12	,	,	PUNCT
ejpam-4467	172	13	t)∈	t)∈	PROPN
ejpam-4467	172	14	and	and	CCONJ
ejpam-4467	172	15	y	y	PROPN
ejpam-4467	172	16	∈	∈	PROPN
ejpam-4467	172	17	(	(	PUNCT
ejpam-4467	172	18	lεψ	lεψ	PROPN
ejpam-4467	172	19	,	,	PUNCT
ejpam-4467	172	20	t)∈.	t)∈.	PROPN
ejpam-4467	172	21	then	then	ADV
ejpam-4467	172	22	lεψ(x	lεψ(x	ADJ
ejpam-4467	172	23	∗	∗	NOUN
ejpam-4467	172	24	(	(	PUNCT
ejpam-4467	172	25	y	y	PROPN
ejpam-4467	172	26	∗	∗	PROPN
ejpam-4467	172	27	z	z	NOUN
ejpam-4467	172	28	)	)	PUNCT
ejpam-4467	172	29	)	)	PUNCT
ejpam-4467	172	30	≥	≥	PROPN
ejpam-4467	172	31	t	t	NOUN
ejpam-4467	172	32	and	and	CCONJ
ejpam-4467	172	33	lεψ(y	lεψ(y	PROPN
ejpam-4467	172	34	)	)	PUNCT
ejpam-4467	172	35	≥	≥	NOUN
ejpam-4467	172	36	t	t	PROPN
ejpam-4467	172	37	,	,	PUNCT
ejpam-4467	172	38	which	which	PRON
ejpam-4467	172	39	imply	imply	VERB
ejpam-4467	172	40	from	from	ADP
ejpam-4467	172	41	(	(	PUNCT
ejpam-4467	172	42	21	21	NUM
ejpam-4467	172	43	)	)	PUNCT
ejpam-4467	172	44	that	that	PRON
ejpam-4467	172	45	0.5	0.5	NUM
ejpam-4467	172	46	<	<	X
ejpam-4467	172	47	t	t	PROPN
ejpam-4467	172	48	≤	≤	NUM
ejpam-4467	172	49	min	min	PROPN
ejpam-4467	172	50	{	{	PUNCT
ejpam-4467	172	51	lεψ(x	lεψ(x	ADJ
ejpam-4467	172	52	∗	∗	NOUN
ejpam-4467	172	53	(	(	PUNCT
ejpam-4467	172	54	y	y	PROPN
ejpam-4467	172	55	∗	∗	PROPN
ejpam-4467	172	56	z	z	PROPN
ejpam-4467	172	57	)	)	PUNCT
ejpam-4467	172	58	)	)	PUNCT
ejpam-4467	172	59	,	,	PUNCT
ejpam-4467	172	60	lεψ(y	lεψ(y	PROPN
ejpam-4467	172	61	)	)	PUNCT
ejpam-4467	172	62	}	}	PUNCT
ejpam-4467	173	1	≤	≤	NUM
ejpam-4467	174	1	max	max	PROPN
ejpam-4467	174	2	{	{	PUNCT
ejpam-4467	174	3	lεψ(x	lεψ(x	PROPN
ejpam-4467	174	4	∗	∗	PROPN
ejpam-4467	174	5	z	z	NOUN
ejpam-4467	174	6	)	)	PUNCT
ejpam-4467	174	7	,	,	PUNCT
ejpam-4467	174	8	0.5	0.5	NUM
ejpam-4467	174	9	}	}	PUNCT
ejpam-4467	174	10	.	.	PUNCT
ejpam-4467	175	1	hence	hence	ADV
ejpam-4467	175	2	⟨(x	⟨(x	PROPN
ejpam-4467	175	3	∗	∗	NOUN
ejpam-4467	175	4	z)/t⟩	z)/t⟩	PROPN
ejpam-4467	175	5	∈	∈	PROPN
ejpam-4467	175	6	lεψ	lεψ	PROPN
ejpam-4467	175	7	,	,	PUNCT
ejpam-4467	175	8	that	that	ADV
ejpam-4467	175	9	is	is	ADV
ejpam-4467	175	10	,	,	PUNCT
ejpam-4467	175	11	x	x	X
ejpam-4467	175	12	∗	∗	NOUN
ejpam-4467	175	13	z	z	NOUN
ejpam-4467	175	14	∈	∈	PROPN
ejpam-4467	175	15	(	(	PUNCT
ejpam-4467	175	16	lεψ	lεψ	ADJ
ejpam-4467	175	17	,	,	PUNCT
ejpam-4467	175	18	t)∈.	t)∈.	PROPN
ejpam-4467	175	19	therefore	therefore	ADV
ejpam-4467	175	20	(	(	PUNCT
ejpam-4467	175	21	lεψ	lεψ	ADJ
ejpam-4467	175	22	,	,	PUNCT
ejpam-4467	175	23	t)∈	t)∈	NUM
ejpam-4467	175	24	is	be	AUX
ejpam-4467	175	25	an	an	DET
ejpam-4467	175	26	ideal	ideal	NOUN
ejpam-4467	175	27	of	of	ADP
ejpam-4467	175	28	(	(	PUNCT
ejpam-4467	175	29	x	x	X
ejpam-4467	175	30	,	,	PUNCT
ejpam-4467	175	31	1)∗	1)∗	NUM
ejpam-4467	175	32	for	for	ADP
ejpam-4467	175	33	t	t	PROPN
ejpam-4467	175	34	∈	∈	PROPN
ejpam-4467	175	35	(	(	PUNCT
ejpam-4467	175	36	0.5	0.5	NUM
ejpam-4467	175	37	,	,	PUNCT
ejpam-4467	175	38	1	1	NUM
ejpam-4467	175	39	]	]	PUNCT
ejpam-4467	175	40	by	by	ADP
ejpam-4467	175	41	lemma	lemma	PROPN
ejpam-4467	175	42	1	1	NUM
ejpam-4467	175	43	.	.	PUNCT
ejpam-4467	175	44	remark	remark	PROPN
ejpam-4467	175	45	1	1	NUM
ejpam-4467	175	46	.	.	PUNCT
ejpam-4467	176	1	in	in	ADP
ejpam-4467	176	2	theorems	theorem	NOUN
ejpam-4467	176	3	4	4	NUM
ejpam-4467	176	4	and	and	CCONJ
ejpam-4467	176	5	5	5	NUM
ejpam-4467	176	6	,	,	PUNCT
ejpam-4467	176	7	if	if	SCONJ
ejpam-4467	176	8	t	t	PROPN
ejpam-4467	176	9	/∈	/∈	PUNCT
ejpam-4467	176	10	(	(	PUNCT
ejpam-4467	176	11	0.5	0.5	NUM
ejpam-4467	176	12	,	,	PUNCT
ejpam-4467	176	13	1	1	NUM
ejpam-4467	176	14	]	]	PUNCT
ejpam-4467	176	15	,	,	PUNCT
ejpam-4467	176	16	that	that	ADV
ejpam-4467	176	17	is	is	ADV
ejpam-4467	176	18	,	,	PUNCT
ejpam-4467	176	19	there	there	PRON
ejpam-4467	176	20	exists	exist	VERB
ejpam-4467	176	21	at	at	ADP
ejpam-4467	176	22	least	least	ADV
ejpam-4467	176	23	one	one	NUM
ejpam-4467	176	24	t	t	NOUN
ejpam-4467	176	25	≤	≤	NUM
ejpam-4467	176	26	0.5	0.5	NUM
ejpam-4467	176	27	,	,	PUNCT
ejpam-4467	176	28	then	then	ADV
ejpam-4467	176	29	theorems	theorem	VERB
ejpam-4467	176	30	4	4	NUM
ejpam-4467	176	31	and	and	CCONJ
ejpam-4467	176	32	5	5	NUM
ejpam-4467	176	33	are	be	AUX
ejpam-4467	176	34	incorrect	incorrect	ADJ
ejpam-4467	176	35	as	as	SCONJ
ejpam-4467	176	36	shown	show	VERB
ejpam-4467	176	37	in	in	ADP
ejpam-4467	176	38	the	the	DET
ejpam-4467	176	39	following	follow	VERB
ejpam-4467	176	40	example	example	NOUN
ejpam-4467	176	41	.	.	PUNCT
ejpam-4467	177	1	example	example	NOUN
ejpam-4467	178	1	2	2	NUM
ejpam-4467	178	2	.	.	X
ejpam-4467	178	3	consider	consider	VERB
ejpam-4467	178	4	the	the	DET
ejpam-4467	178	5	be	be	NOUN
ejpam-4467	178	6	-	-	PUNCT
ejpam-4467	178	7	algebra	algebra	NOUN
ejpam-4467	178	8	(	(	PUNCT
ejpam-4467	178	9	x	x	X
ejpam-4467	178	10	,	,	PUNCT
ejpam-4467	178	11	1)∗	1)∗	NUM
ejpam-4467	178	12	in	in	ADP
ejpam-4467	178	13	example	example	NOUN
ejpam-4467	178	14	1	1	NUM
ejpam-4467	178	15	and	and	CCONJ
ejpam-4467	178	16	let	let	VERB
ejpam-4467	178	17	ψ	ψ	PART
ejpam-4467	178	18	be	be	AUX
ejpam-4467	178	19	a	a	DET
ejpam-4467	178	20	fuzzy	fuzzy	ADJ
ejpam-4467	178	21	set	set	NOUN
ejpam-4467	178	22	in	in	ADP
ejpam-4467	178	23	x	x	PUNCT
ejpam-4467	178	24	defined	define	VERB
ejpam-4467	178	25	as	as	SCONJ
ejpam-4467	178	26	follows	follow	VERB
ejpam-4467	178	27	.	.	PUNCT
ejpam-4467	179	1	ψ	ψ	X
ejpam-4467	179	2	:	:	PUNCT
ejpam-4467	179	3	x	x	X
ejpam-4467	179	4	→	→	SYM
ejpam-4467	180	1	[	[	X
ejpam-4467	180	2	0	0	NUM
ejpam-4467	180	3	,	,	PUNCT
ejpam-4467	180	4	1	1	NUM
ejpam-4467	180	5	]	]	PUNCT
ejpam-4467	180	6	,	,	PUNCT
ejpam-4467	180	7	x	x	SYM
ejpam-4467	180	8	7→	7→	X
ejpam-4467	180	9			NUM
ejpam-4467	180	10	0.92	0.92	NUM
ejpam-4467	180	11	if	if	SCONJ
ejpam-4467	180	12	x	x	PROPN
ejpam-4467	180	13	=	=	SYM
ejpam-4467	180	14	1	1	NUM
ejpam-4467	180	15	,	,	PUNCT
ejpam-4467	180	16	0.66	0.66	NUM
ejpam-4467	180	17	if	if	SCONJ
ejpam-4467	180	18	x	x	PROPN
ejpam-4467	180	19	=	=	SYM
ejpam-4467	180	20	a	a	NOUN
ejpam-4467	180	21	,	,	PUNCT
ejpam-4467	180	22	0.66	0.66	NUM
ejpam-4467	180	23	if	if	SCONJ
ejpam-4467	180	24	x	x	PROPN
ejpam-4467	180	25	=	=	SYM
ejpam-4467	180	26	b	b	PROPN
ejpam-4467	180	27	,	,	PUNCT
ejpam-4467	180	28	0.77	0.77	NUM
ejpam-4467	180	29	if	if	SCONJ
ejpam-4467	180	30	x	x	PROPN
ejpam-4467	180	31	=	=	SYM
ejpam-4467	180	32	c	c	NOUN
ejpam-4467	180	33	,	,	PUNCT
ejpam-4467	180	34	0.81	0.81	NUM
ejpam-4467	180	35	if	if	SCONJ
ejpam-4467	180	36	x	x	PROPN
ejpam-4467	180	37	=	=	SYM
ejpam-4467	180	38	d	d	PROPN
ejpam-4467	180	39	,	,	PUNCT
ejpam-4467	180	40	0.95	0.95	NUM
ejpam-4467	180	41	if	if	SCONJ
ejpam-4467	180	42	x	x	X
ejpam-4467	180	43	=	=	NOUN
ejpam-4467	180	44	0	0	X
ejpam-4467	180	45	.	.	PUNCT
ejpam-4467	181	1	for	for	ADP
ejpam-4467	181	2	ε	ε	PROPN
ejpam-4467	181	3	:	:	PUNCT
ejpam-4467	181	4	=	=	SYM
ejpam-4467	181	5	0.61	0.61	NUM
ejpam-4467	181	6	,	,	PUNCT
ejpam-4467	181	7	the	the	DET
ejpam-4467	181	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	181	9	fuzzy	fuzzy	ADJ
ejpam-4467	181	10	set	set	VERB
ejpam-4467	181	11	lεψ	lεψ	ADJ
ejpam-4467	181	12	of	of	ADP
ejpam-4467	181	13	ψ	ψ	PRON
ejpam-4467	181	14	in	in	ADP
ejpam-4467	181	15	x	x	PROPN
ejpam-4467	181	16	is	be	AUX
ejpam-4467	181	17	given	give	VERB
ejpam-4467	181	18	as	as	SCONJ
ejpam-4467	181	19	follows	follow	NOUN
ejpam-4467	181	20	.	.	PUNCT
ejpam-4467	182	1	lεψ	lεψ	VERB
ejpam-4467	182	2	:	:	PUNCT
ejpam-4467	182	3	x	x	X
ejpam-4467	182	4	→	→	SYM
ejpam-4467	183	1	[	[	X
ejpam-4467	183	2	0	0	NUM
ejpam-4467	183	3	,	,	PUNCT
ejpam-4467	183	4	1	1	NUM
ejpam-4467	183	5	]	]	PUNCT
ejpam-4467	183	6	,	,	PUNCT
ejpam-4467	183	7	y	y	PROPN
ejpam-4467	183	8	7→	7→	PROPN
ejpam-4467	183	9			VERB
ejpam-4467	183	10	0.53	0.53	NUM
ejpam-4467	184	1	if	if	SCONJ
ejpam-4467	184	2	y	y	PROPN
ejpam-4467	184	3	=	=	SYM
ejpam-4467	184	4	1	1	NUM
ejpam-4467	184	5	,	,	PUNCT
ejpam-4467	184	6	0.27	0.27	NUM
ejpam-4467	184	7	if	if	SCONJ
ejpam-4467	184	8	y	y	PROPN
ejpam-4467	184	9	∈	∈	PROPN
ejpam-4467	184	10	{	{	PUNCT
ejpam-4467	184	11	a	a	PROPN
ejpam-4467	184	12	,	,	PUNCT
ejpam-4467	184	13	b	b	NOUN
ejpam-4467	184	14	}	}	PUNCT
ejpam-4467	184	15	,	,	PUNCT
ejpam-4467	184	16	0.38	0.38	NUM
ejpam-4467	184	17	if	if	SCONJ
ejpam-4467	184	18	y	y	PROPN
ejpam-4467	184	19	=	=	SYM
ejpam-4467	184	20	c	c	PROPN
ejpam-4467	184	21	,	,	PUNCT
ejpam-4467	184	22	0.42	0.42	NUM
ejpam-4467	185	1	if	if	SCONJ
ejpam-4467	185	2	y	y	PROPN
ejpam-4467	185	3	=	=	SYM
ejpam-4467	185	4	d	d	PROPN
ejpam-4467	185	5	,	,	PUNCT
ejpam-4467	185	6	0.56	0.56	NUM
ejpam-4467	185	7	if	if	SCONJ
ejpam-4467	185	8	y	y	PROPN
ejpam-4467	185	9	=	=	NOUN
ejpam-4467	185	10	0	0	PROPN
ejpam-4467	185	11	.	.	PUNCT
ejpam-4467	186	1	then	then	ADV
ejpam-4467	186	2	(	(	PUNCT
ejpam-4467	186	3	lεψ	lεψ	ADJ
ejpam-4467	186	4	,	,	PUNCT
ejpam-4467	186	5	0.41)∈	0.41)∈	NUM
ejpam-4467	186	6	=	=	SYM
ejpam-4467	186	7	{	{	PUNCT
ejpam-4467	186	8	1	1	NUM
ejpam-4467	186	9	,	,	PUNCT
ejpam-4467	186	10	d	d	NOUN
ejpam-4467	186	11	,	,	PUNCT
ejpam-4467	186	12	0	0	NUM
ejpam-4467	186	13	}	}	PUNCT
ejpam-4467	186	14	is	be	AUX
ejpam-4467	186	15	not	not	PART
ejpam-4467	186	16	an	an	DET
ejpam-4467	186	17	ideal	ideal	NOUN
ejpam-4467	186	18	of	of	ADP
ejpam-4467	186	19	(	(	PUNCT
ejpam-4467	186	20	x	x	X
ejpam-4467	186	21	,	,	PUNCT
ejpam-4467	186	22	1)∗	1)∗	NOUN
ejpam-4467	186	23	because	because	SCONJ
ejpam-4467	186	24	of	of	ADP
ejpam-4467	186	25	b∗0	b∗0	NOUN
ejpam-4467	186	26	=	=	PUNCT
ejpam-4467	186	27	c	c	NOUN
ejpam-4467	186	28	/∈	/∈	PUNCT
ejpam-4467	186	29	(	(	PUNCT
ejpam-4467	186	30	lεψ	lεψ	ADJ
ejpam-4467	186	31	,	,	PUNCT
ejpam-4467	186	32	0.41)∈.	0.41)∈.	NOUN
ejpam-4467	186	33	in	in	ADP
ejpam-4467	186	34	this	this	DET
ejpam-4467	186	35	case	case	NOUN
ejpam-4467	186	36	,	,	PUNCT
ejpam-4467	186	37	we	we	PRON
ejpam-4467	186	38	know	know	VERB
ejpam-4467	186	39	that	that	PRON
ejpam-4467	186	40	lεψ(0	lεψ(0	PROPN
ejpam-4467	186	41	)	)	PUNCT
ejpam-4467	187	1	=	=	PUNCT
ejpam-4467	187	2	0.56	0.56	NUM
ejpam-4467	187	3	≰	≰	PROPN
ejpam-4467	187	4	0.5	0.5	NUM
ejpam-4467	187	5	=	=	SYM
ejpam-4467	187	6	max	max	PROPN
ejpam-4467	187	7	{	{	PUNCT
ejpam-4467	187	8	lεψ(b	lεψ(b	NOUN
ejpam-4467	187	9	∗	∗	NOUN
ejpam-4467	187	10	0	0	NUM
ejpam-4467	187	11	)	)	PUNCT
ejpam-4467	187	12	,	,	PUNCT
ejpam-4467	187	13	0.5	0.5	NUM
ejpam-4467	187	14	}	}	PUNCT
ejpam-4467	187	15	and	and	CCONJ
ejpam-4467	187	16	lεψ(0	lεψ(0	ADJ
ejpam-4467	187	17	)	)	PUNCT
ejpam-4467	187	18	=	=	PUNCT
ejpam-4467	188	1	0.56	0.56	NUM
ejpam-4467	188	2	≰	≰	PROPN
ejpam-4467	188	3	0.53	0.53	NUM
ejpam-4467	188	4	=	=	SYM
ejpam-4467	188	5	max	max	PROPN
ejpam-4467	188	6	{	{	PUNCT
ejpam-4467	188	7	lεψ(1	lεψ(1	ADJ
ejpam-4467	188	8	)	)	PUNCT
ejpam-4467	188	9	,	,	PUNCT
ejpam-4467	188	10	0.5	0.5	NUM
ejpam-4467	188	11	}	}	PUNCT
ejpam-4467	188	12	.	.	PUNCT
ejpam-4467	189	1	s.	s.	PROPN
ejpam-4467	189	2	s.	s.	PROPN
ejpam-4467	189	3	ahn	ahn	PROPN
ejpam-4467	189	4	,	,	PUNCT
ejpam-4467	189	5	e.	e.	PROPN
ejpam-4467	189	6	h.	h.	PROPN
ejpam-4467	189	7	roh	roh	PROPN
ejpam-4467	189	8	and	and	CCONJ
ejpam-4467	189	9	y.	y.	PROPN
ejpam-4467	189	10	b.	b.	PROPN
ejpam-4467	189	11	jun	jun	PROPN
ejpam-4467	189	12	/	/	SYM
ejpam-4467	189	13	eur	eur	PROPN
ejpam-4467	189	14	.	.	PUNCT
ejpam-4467	190	1	j.	j.	PROPN
ejpam-4467	190	2	pure	pure	PROPN
ejpam-4467	190	3	appl	appl	PROPN
ejpam-4467	190	4	.	.	PROPN
ejpam-4467	190	5	math	math	PROPN
ejpam-4467	190	6	,	,	PUNCT
ejpam-4467	190	7	15	15	NUM
ejpam-4467	190	8	(	(	PUNCT
ejpam-4467	190	9	3	3	NUM
ejpam-4467	190	10	)	)	PUNCT
ejpam-4467	190	11	(	(	PUNCT
ejpam-4467	190	12	2022	2022	NUM
ejpam-4467	190	13	)	)	PUNCT
ejpam-4467	190	14	,	,	PUNCT
ejpam-4467	190	15	1307	1307	NUM
ejpam-4467	190	16	-	-	SYM
ejpam-4467	190	17	1320	1320	NUM
ejpam-4467	190	18	1314	1314	NUM
ejpam-4467	190	19	theorem	theorem	VERB
ejpam-4467	190	20	6	6	NUM
ejpam-4467	190	21	.	.	PUNCT
ejpam-4467	191	1	if	if	SCONJ
ejpam-4467	191	2	a	a	DET
ejpam-4467	191	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	191	4	fuzzy	fuzzy	ADJ
ejpam-4467	191	5	set	set	VERB
ejpam-4467	191	6	lεψ	lεψ	VERB
ejpam-4467	191	7	in	in	ADP
ejpam-4467	191	8	x	x	X
ejpam-4467	191	9	satisfies	satisfie	NOUN
ejpam-4467	191	10	:	:	PUNCT
ejpam-4467	191	11	(	(	PUNCT
ejpam-4467	191	12	∀x	∀x	X
ejpam-4467	191	13	∈	∈	PROPN
ejpam-4467	191	14	x)(∀t	x)(∀t	PROPN
ejpam-4467	191	15	∈	∈	PROPN
ejpam-4467	191	16	(	(	PUNCT
ejpam-4467	191	17	0.5	0.5	NUM
ejpam-4467	191	18	,	,	PUNCT
ejpam-4467	191	19	1	1	NUM
ejpam-4467	191	20	]	]	NUM
ejpam-4467	191	21	)	)	PUNCT
ejpam-4467	191	22	(	(	PUNCT
ejpam-4467	191	23	⟨x	⟨x	VERB
ejpam-4467	191	24	/	/	SYM
ejpam-4467	191	25	t⟩	t⟩	PRON
ejpam-4467	191	26	q	q	X
ejpam-4467	191	27	lεψ	lεψ	ADJ
ejpam-4467	191	28	⇒	⇒	PROPN
ejpam-4467	191	29	⟨1	⟨1	PROPN
ejpam-4467	191	30	/	/	SYM
ejpam-4467	191	31	t⟩	t⟩	PRON
ejpam-4467	191	32	∈	∈	PROPN
ejpam-4467	191	33	lεψ	lεψ	VERB
ejpam-4467	191	34	)	)	PUNCT
ejpam-4467	191	35	,	,	PUNCT
ejpam-4467	191	36	(	(	PUNCT
ejpam-4467	191	37	22	22	NUM
ejpam-4467	191	38	)	)	PUNCT
ejpam-4467	191	39	(	(	PUNCT
ejpam-4467	191	40	∀x	∀x	X
ejpam-4467	191	41	,	,	PUNCT
ejpam-4467	191	42	y	y	PROPN
ejpam-4467	191	43	,	,	PUNCT
ejpam-4467	191	44	z	z	PROPN
ejpam-4467	191	45	∈	∈	PROPN
ejpam-4467	191	46	x)(∀ta	x)(∀ta	NOUN
ejpam-4467	191	47	,	,	PUNCT
ejpam-4467	191	48	tb	tb	ADP
ejpam-4467	191	49	∈	∈	PROPN
ejpam-4467	191	50	(	(	PUNCT
ejpam-4467	191	51	0.5	0.5	NUM
ejpam-4467	191	52	,	,	PUNCT
ejpam-4467	191	53	1	1	NUM
ejpam-4467	191	54	]	]	PUNCT
ejpam-4467	191	55	)	)	PUNCT
ejpam-4467	191	56	(	(	PUNCT
ejpam-4467	191	57	⟨(x	⟨(x	NOUN
ejpam-4467	191	58	∗	∗	NOUN
ejpam-4467	191	59	(	(	PUNCT
ejpam-4467	191	60	y	y	PROPN
ejpam-4467	191	61	∗	∗	X
ejpam-4467	191	62	z))/ta⟩	z))/ta⟩	PROPN
ejpam-4467	192	1	q	q	PROPN
ejpam-4467	192	2	lεψ	lεψ	ADJ
ejpam-4467	192	3	,	,	PUNCT
ejpam-4467	192	4	⟨y	⟨y	AUX
ejpam-4467	192	5	/	/	SYM
ejpam-4467	192	6	tb⟩	tb⟩	PROPN
ejpam-4467	192	7	q	q	ADJ
ejpam-4467	192	8	lεψ	lεψ	ADJ
ejpam-4467	192	9	⇒	⇒	PROPN
ejpam-4467	192	10	⟨(x	⟨(x	PROPN
ejpam-4467	192	11	∗	∗	PROPN
ejpam-4467	192	12	z)/max{ta	z)/max{ta	PROPN
ejpam-4467	192	13	,	,	PUNCT
ejpam-4467	192	14	tb}⟩	tb}⟩	X
ejpam-4467	192	15	∈	∈	PROPN
ejpam-4467	192	16	lεψ	lεψ	VERB
ejpam-4467	192	17	)	)	PUNCT
ejpam-4467	192	18	,	,	PUNCT
ejpam-4467	192	19	(	(	PUNCT
ejpam-4467	192	20	23	23	NUM
ejpam-4467	192	21	)	)	PUNCT
ejpam-4467	192	22	then	then	ADV
ejpam-4467	192	23	the	the	DET
ejpam-4467	192	24	non	non	ADJ
ejpam-4467	192	25	-	-	ADJ
ejpam-4467	192	26	empty	empty	ADJ
ejpam-4467	192	27	∈-set	∈-set	NOUN
ejpam-4467	192	28	(	(	PUNCT
ejpam-4467	192	29	lεψ	lεψ	ADJ
ejpam-4467	192	30	,	,	PUNCT
ejpam-4467	192	31	max{ta	max{ta	NUM
ejpam-4467	192	32	,	,	PUNCT
ejpam-4467	192	33	tb})∈	tb})∈	PROPN
ejpam-4467	192	34	of	of	ADP
ejpam-4467	192	35	lεψ	lεψ	PROPN
ejpam-4467	192	36	is	be	AUX
ejpam-4467	192	37	an	an	DET
ejpam-4467	192	38	ideal	ideal	NOUN
ejpam-4467	192	39	of	of	ADP
ejpam-4467	192	40	(	(	PUNCT
ejpam-4467	192	41	x	x	X
ejpam-4467	192	42	,	,	PUNCT
ejpam-4467	192	43	1)∗	1)∗	NUM
ejpam-4467	192	44	for	for	ADP
ejpam-4467	192	45	all	all	DET
ejpam-4467	192	46	ta	ta	PROPN
ejpam-4467	192	47	,	,	PUNCT
ejpam-4467	192	48	tb	tb	ADP
ejpam-4467	192	49	∈	∈	PROPN
ejpam-4467	192	50	(	(	PUNCT
ejpam-4467	192	51	0.5	0.5	NUM
ejpam-4467	192	52	,	,	PUNCT
ejpam-4467	192	53	1	1	NUM
ejpam-4467	192	54	]	]	PUNCT
ejpam-4467	192	55	.	.	PUNCT
ejpam-4467	193	1	proof	proof	NOUN
ejpam-4467	193	2	.	.	PUNCT
ejpam-4467	194	1	let	let	VERB
ejpam-4467	194	2	ta	ta	PART
ejpam-4467	194	3	,	,	PUNCT
ejpam-4467	194	4	tb	tb	ADP
ejpam-4467	194	5	∈	∈	PROPN
ejpam-4467	194	6	(	(	PUNCT
ejpam-4467	194	7	0.5	0.5	NUM
ejpam-4467	194	8	,	,	PUNCT
ejpam-4467	194	9	1	1	NUM
ejpam-4467	194	10	]	]	PUNCT
ejpam-4467	194	11	and	and	CCONJ
ejpam-4467	194	12	assume	assume	VERB
ejpam-4467	194	13	that	that	SCONJ
ejpam-4467	194	14	the	the	DET
ejpam-4467	194	15	∈-set	∈-set	NOUN
ejpam-4467	194	16	(	(	PUNCT
ejpam-4467	194	17	lεψ	lεψ	ADJ
ejpam-4467	194	18	,	,	PUNCT
ejpam-4467	194	19	max{ta	max{ta	NUM
ejpam-4467	194	20	,	,	PUNCT
ejpam-4467	194	21	tb})∈	tb})∈	PROPN
ejpam-4467	194	22	of	of	ADP
ejpam-4467	194	23	lεψ	lεψ	PROPN
ejpam-4467	194	24	is	be	AUX
ejpam-4467	194	25	non	non	ADJ
ejpam-4467	194	26	-	-	ADJ
ejpam-4467	194	27	empty	empty	ADJ
ejpam-4467	194	28	.	.	PUNCT
ejpam-4467	195	1	then	then	ADV
ejpam-4467	195	2	there	there	PRON
ejpam-4467	195	3	exists	exist	VERB
ejpam-4467	195	4	x	x	X
ejpam-4467	195	5	∈	∈	PROPN
ejpam-4467	195	6	(	(	PUNCT
ejpam-4467	195	7	lεψ	lεψ	ADJ
ejpam-4467	195	8	,	,	PUNCT
ejpam-4467	195	9	max{ta	max{ta	NOUN
ejpam-4467	195	10	,	,	PUNCT
ejpam-4467	195	11	tb})∈	tb})∈	ADJ
ejpam-4467	195	12	,	,	PUNCT
ejpam-4467	195	13	and	and	CCONJ
ejpam-4467	195	14	so	so	ADV
ejpam-4467	195	15	lεψ(x	lεψ(x	PROPN
ejpam-4467	195	16	)	)	PUNCT
ejpam-4467	195	17	≥	≥	NOUN
ejpam-4467	195	18	max{ta	max{ta	VERB
ejpam-4467	195	19	,	,	PUNCT
ejpam-4467	195	20	tb	tb	NOUN
ejpam-4467	195	21	}	}	PUNCT
ejpam-4467	195	22	>	>	X
ejpam-4467	195	23	1	1	NUM
ejpam-4467	195	24	−	−	NOUN
ejpam-4467	195	25	max{ta	max{ta	NOUN
ejpam-4467	195	26	,	,	PUNCT
ejpam-4467	195	27	tb	tb	NOUN
ejpam-4467	195	28	}	}	PUNCT
ejpam-4467	195	29	,	,	PUNCT
ejpam-4467	195	30	i.e.	i.e.	X
ejpam-4467	195	31	,	,	PUNCT
ejpam-4467	195	32	⟨x	⟨x	VERB
ejpam-4467	195	33	/	/	SYM
ejpam-4467	195	34	max{ta	max{ta	NOUN
ejpam-4467	195	35	,	,	PUNCT
ejpam-4467	195	36	tb}⟩	tb}⟩	X
ejpam-4467	195	37	q	q	VERB
ejpam-4467	195	38	lεψ	lεψ	ADJ
ejpam-4467	195	39	.	.	PUNCT
ejpam-4467	196	1	hence	hence	ADV
ejpam-4467	196	2	⟨1	⟨1	PROPN
ejpam-4467	196	3	/	/	SYM
ejpam-4467	196	4	max{ta	max{ta	NUM
ejpam-4467	196	5	,	,	PUNCT
ejpam-4467	196	6	tb}⟩	tb}⟩	X
ejpam-4467	196	7	∈	∈	NOUN
ejpam-4467	196	8	lεψ	lεψ	VERB
ejpam-4467	196	9	by	by	ADP
ejpam-4467	196	10	(	(	PUNCT
ejpam-4467	196	11	22	22	NUM
ejpam-4467	196	12	)	)	PUNCT
ejpam-4467	196	13	,	,	PUNCT
ejpam-4467	196	14	and	and	CCONJ
ejpam-4467	196	15	thus	thus	ADV
ejpam-4467	196	16	1	1	NUM
ejpam-4467	196	17	∈	∈	PROPN
ejpam-4467	196	18	(	(	PUNCT
ejpam-4467	196	19	lεψ	lεψ	ADJ
ejpam-4467	196	20	,	,	PUNCT
ejpam-4467	196	21	max{ta	max{ta	NOUN
ejpam-4467	196	22	,	,	PUNCT
ejpam-4467	196	23	tb})∈.	tb})∈.	NUM
ejpam-4467	196	24	let	let	VERB
ejpam-4467	196	25	x	x	PRON
ejpam-4467	196	26	,	,	PUNCT
ejpam-4467	196	27	y	y	PROPN
ejpam-4467	196	28	,	,	PUNCT
ejpam-4467	196	29	z	z	NOUN
ejpam-4467	196	30	∈	∈	PROPN
ejpam-4467	196	31	x	x	AUX
ejpam-4467	196	32	be	be	AUX
ejpam-4467	196	33	such	such	ADJ
ejpam-4467	196	34	that	that	SCONJ
ejpam-4467	196	35	x	x	SYM
ejpam-4467	196	36	∗	∗	NOUN
ejpam-4467	196	37	(	(	PUNCT
ejpam-4467	196	38	y	y	PROPN
ejpam-4467	196	39	∗	∗	PROPN
ejpam-4467	196	40	z	z	NOUN
ejpam-4467	196	41	)	)	PUNCT
ejpam-4467	196	42	∈	∈	PROPN
ejpam-4467	196	43	(	(	PUNCT
ejpam-4467	196	44	lεψ	lεψ	ADJ
ejpam-4467	196	45	,	,	PUNCT
ejpam-4467	196	46	max{ta	max{ta	NOUN
ejpam-4467	196	47	,	,	PUNCT
ejpam-4467	196	48	tb})∈	tb})∈	ADJ
ejpam-4467	196	49	and	and	CCONJ
ejpam-4467	196	50	y	y	PROPN
ejpam-4467	196	51	∈	∈	PROPN
ejpam-4467	196	52	(	(	PUNCT
ejpam-4467	196	53	lεψ	lεψ	ADJ
ejpam-4467	196	54	,	,	PUNCT
ejpam-4467	196	55	max{ta	max{ta	NOUN
ejpam-4467	196	56	,	,	PUNCT
ejpam-4467	196	57	tb})∈.	tb})∈.	ADJ
ejpam-4467	196	58	then	then	ADV
ejpam-4467	196	59	lεψ(x	lεψ(x	ADJ
ejpam-4467	196	60	∗	∗	NOUN
ejpam-4467	196	61	(	(	PUNCT
ejpam-4467	196	62	y	y	PROPN
ejpam-4467	196	63	∗	∗	PROPN
ejpam-4467	196	64	z	z	PROPN
ejpam-4467	196	65	)	)	PUNCT
ejpam-4467	196	66	)	)	PUNCT
ejpam-4467	196	67	≥	≥	NOUN
ejpam-4467	196	68	max{ta	max{ta	NOUN
ejpam-4467	196	69	,	,	PUNCT
ejpam-4467	196	70	tb	tb	NOUN
ejpam-4467	196	71	}	}	PUNCT
ejpam-4467	196	72	>	>	X
ejpam-4467	196	73	1	1	NUM
ejpam-4467	196	74	−	−	NOUN
ejpam-4467	196	75	max{ta	max{ta	NOUN
ejpam-4467	196	76	,	,	PUNCT
ejpam-4467	196	77	tb	tb	NOUN
ejpam-4467	196	78	}	}	PUNCT
ejpam-4467	196	79	and	and	CCONJ
ejpam-4467	196	80	lεψ(y	lεψ(y	PROPN
ejpam-4467	196	81	)	)	PUNCT
ejpam-4467	196	82	≥	≥	NOUN
ejpam-4467	196	83	max{ta	max{ta	NOUN
ejpam-4467	196	84	,	,	PUNCT
ejpam-4467	196	85	tb	tb	NOUN
ejpam-4467	196	86	}	}	PUNCT
ejpam-4467	196	87	>	>	X
ejpam-4467	196	88	1	1	NUM
ejpam-4467	196	89	−	−	NOUN
ejpam-4467	196	90	max{ta	max{ta	NOUN
ejpam-4467	196	91	,	,	PUNCT
ejpam-4467	196	92	tb	tb	NOUN
ejpam-4467	196	93	}	}	PUNCT
ejpam-4467	196	94	,	,	PUNCT
ejpam-4467	196	95	that	that	ADV
ejpam-4467	196	96	is	is	ADV
ejpam-4467	196	97	,	,	PUNCT
ejpam-4467	196	98	⟨(x	⟨(x	PROPN
ejpam-4467	196	99	∗	∗	NOUN
ejpam-4467	196	100	(	(	PUNCT
ejpam-4467	196	101	y	y	PROPN
ejpam-4467	196	102	∗	∗	NOUN
ejpam-4467	196	103	z))/max{ta	z))/max{ta	NUM
ejpam-4467	196	104	,	,	PUNCT
ejpam-4467	196	105	tb}⟩	tb}⟩	X
ejpam-4467	196	106	q	q	NOUN
ejpam-4467	196	107	lεψ	lεψ	ADJ
ejpam-4467	196	108	and	and	CCONJ
ejpam-4467	196	109	⟨y	⟨y	NOUN
ejpam-4467	196	110	/	/	SYM
ejpam-4467	196	111	max{ta	max{ta	NOUN
ejpam-4467	196	112	,	,	PUNCT
ejpam-4467	196	113	tb}⟩	tb}⟩	X
ejpam-4467	196	114	q	q	VERB
ejpam-4467	196	115	lεψ	lεψ	ADJ
ejpam-4467	196	116	.	.	PUNCT
ejpam-4467	197	1	it	it	PRON
ejpam-4467	197	2	follows	follow	VERB
ejpam-4467	197	3	from	from	ADP
ejpam-4467	197	4	(	(	PUNCT
ejpam-4467	197	5	23	23	NUM
ejpam-4467	197	6	)	)	PUNCT
ejpam-4467	197	7	that	that	PRON
ejpam-4467	197	8	⟨(x	⟨(x	PROPN
ejpam-4467	197	9	∗	∗	NOUN
ejpam-4467	197	10	z)/max{ta	z)/max{ta	PROPN
ejpam-4467	197	11	,	,	PUNCT
ejpam-4467	197	12	tb}⟩	tb}⟩	X
ejpam-4467	197	13	∈	∈	PROPN
ejpam-4467	197	14	lεψ	lεψ	VERB
ejpam-4467	197	15	.	.	PUNCT
ejpam-4467	198	1	hence	hence	ADV
ejpam-4467	198	2	x	x	X
ejpam-4467	198	3	∗	∗	NOUN
ejpam-4467	198	4	z	z	NOUN
ejpam-4467	198	5	∈	∈	PROPN
ejpam-4467	198	6	(	(	PUNCT
ejpam-4467	198	7	lεψ	lεψ	ADJ
ejpam-4467	198	8	,	,	PUNCT
ejpam-4467	198	9	max{ta	max{ta	NOUN
ejpam-4467	198	10	,	,	PUNCT
ejpam-4467	198	11	tb})∈	tb})∈	ADJ
ejpam-4467	198	12	,	,	PUNCT
ejpam-4467	198	13	and	and	CCONJ
ejpam-4467	198	14	therefore	therefore	ADV
ejpam-4467	198	15	(	(	PUNCT
ejpam-4467	198	16	lεψ	lεψ	ADJ
ejpam-4467	198	17	,	,	PUNCT
ejpam-4467	198	18	max{ta	max{ta	NUM
ejpam-4467	198	19	,	,	PUNCT
ejpam-4467	198	20	tb})∈	tb})∈	PROPN
ejpam-4467	198	21	is	be	AUX
ejpam-4467	198	22	an	an	DET
ejpam-4467	198	23	ideal	ideal	NOUN
ejpam-4467	198	24	of	of	ADP
ejpam-4467	198	25	(	(	PUNCT
ejpam-4467	198	26	x	x	X
ejpam-4467	198	27	,	,	PUNCT
ejpam-4467	198	28	1)∗	1)∗	NUM
ejpam-4467	198	29	for	for	ADP
ejpam-4467	198	30	all	all	DET
ejpam-4467	198	31	ta	ta	PROPN
ejpam-4467	198	32	,	,	PUNCT
ejpam-4467	198	33	tb	tb	ADP
ejpam-4467	198	34	∈	∈	PROPN
ejpam-4467	198	35	(	(	PUNCT
ejpam-4467	198	36	0.5	0.5	NUM
ejpam-4467	198	37	,	,	PUNCT
ejpam-4467	198	38	1	1	NUM
ejpam-4467	198	39	]	]	PUNCT
ejpam-4467	198	40	by	by	ADP
ejpam-4467	198	41	lemma	lemma	PROPN
ejpam-4467	198	42	1	1	NUM
ejpam-4467	198	43	.	.	PUNCT
ejpam-4467	198	44	theorem	theorem	VERB
ejpam-4467	198	45	7	7	NUM
ejpam-4467	198	46	.	.	PUNCT
ejpam-4467	199	1	if	if	SCONJ
ejpam-4467	199	2	a	a	DET
ejpam-4467	199	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	199	4	fuzzy	fuzzy	ADJ
ejpam-4467	199	5	set	set	VERB
ejpam-4467	199	6	lεψ	lεψ	VERB
ejpam-4467	199	7	in	in	ADP
ejpam-4467	199	8	x	x	X
ejpam-4467	199	9	satisfies	satisfie	NOUN
ejpam-4467	199	10	(	(	PUNCT
ejpam-4467	199	11	22	22	NUM
ejpam-4467	199	12	)	)	PUNCT
ejpam-4467	199	13	and	and	CCONJ
ejpam-4467	199	14	(	(	PUNCT
ejpam-4467	199	15	∀x	∀x	NUM
ejpam-4467	199	16	,	,	PUNCT
ejpam-4467	199	17	y	y	PROPN
ejpam-4467	199	18	,	,	PUNCT
ejpam-4467	199	19	z	z	PROPN
ejpam-4467	199	20	∈	∈	PROPN
ejpam-4467	199	21	x)(∀ta	x)(∀ta	NOUN
ejpam-4467	199	22	,	,	PUNCT
ejpam-4467	199	23	tb	tb	ADP
ejpam-4467	199	24	∈	∈	PROPN
ejpam-4467	199	25	(	(	PUNCT
ejpam-4467	199	26	0.5	0.5	NUM
ejpam-4467	199	27	,	,	PUNCT
ejpam-4467	199	28	1	1	NUM
ejpam-4467	199	29	]	]	PUNCT
ejpam-4467	199	30	)	)	PUNCT
ejpam-4467	199	31	(	(	PUNCT
ejpam-4467	199	32	⟨(x	⟨(x	NOUN
ejpam-4467	199	33	∗	∗	NOUN
ejpam-4467	199	34	(	(	PUNCT
ejpam-4467	199	35	y	y	PROPN
ejpam-4467	199	36	∗	∗	X
ejpam-4467	199	37	z))/ta⟩	z))/ta⟩	PROPN
ejpam-4467	200	1	q	q	PROPN
ejpam-4467	200	2	lεψ	lεψ	ADJ
ejpam-4467	200	3	,	,	PUNCT
ejpam-4467	200	4	⟨y	⟨y	AUX
ejpam-4467	200	5	/	/	SYM
ejpam-4467	200	6	tb⟩	tb⟩	PROPN
ejpam-4467	200	7	q	q	ADJ
ejpam-4467	200	8	lεψ	lεψ	ADJ
ejpam-4467	200	9	⇒	⇒	PROPN
ejpam-4467	200	10	⟨(x	⟨(x	PROPN
ejpam-4467	200	11	∗	∗	PROPN
ejpam-4467	200	12	z)/min{ta	z)/min{ta	PROPN
ejpam-4467	200	13	,	,	PUNCT
ejpam-4467	200	14	tb}⟩	tb}⟩	X
ejpam-4467	200	15	∈	∈	PROPN
ejpam-4467	200	16	lεψ	lεψ	VERB
ejpam-4467	200	17	)	)	PUNCT
ejpam-4467	200	18	,	,	PUNCT
ejpam-4467	200	19	(	(	PUNCT
ejpam-4467	200	20	24	24	NUM
ejpam-4467	200	21	)	)	PUNCT
ejpam-4467	200	22	then	then	ADV
ejpam-4467	200	23	the	the	DET
ejpam-4467	200	24	non	non	ADJ
ejpam-4467	200	25	-	-	ADJ
ejpam-4467	200	26	empty	empty	ADJ
ejpam-4467	200	27	∈-set	∈-set	NOUN
ejpam-4467	200	28	(	(	PUNCT
ejpam-4467	200	29	lεψ	lεψ	ADJ
ejpam-4467	200	30	,	,	PUNCT
ejpam-4467	200	31	min{ta	min{ta	X
ejpam-4467	200	32	,	,	PUNCT
ejpam-4467	200	33	tb})∈	tb})∈	PROPN
ejpam-4467	200	34	of	of	ADP
ejpam-4467	200	35	lεψ	lεψ	PROPN
ejpam-4467	200	36	is	be	AUX
ejpam-4467	200	37	an	an	DET
ejpam-4467	200	38	ideal	ideal	NOUN
ejpam-4467	200	39	of	of	ADP
ejpam-4467	200	40	(	(	PUNCT
ejpam-4467	200	41	x	x	X
ejpam-4467	200	42	,	,	PUNCT
ejpam-4467	200	43	1)∗	1)∗	NUM
ejpam-4467	200	44	for	for	ADP
ejpam-4467	200	45	all	all	DET
ejpam-4467	200	46	ta	ta	PROPN
ejpam-4467	200	47	,	,	PUNCT
ejpam-4467	200	48	tb	tb	ADP
ejpam-4467	200	49	∈	∈	PROPN
ejpam-4467	200	50	(	(	PUNCT
ejpam-4467	200	51	0.5	0.5	NUM
ejpam-4467	200	52	,	,	PUNCT
ejpam-4467	200	53	1	1	NUM
ejpam-4467	200	54	]	]	PUNCT
ejpam-4467	200	55	.	.	PUNCT
ejpam-4467	201	1	proof	proof	NOUN
ejpam-4467	201	2	.	.	PUNCT
ejpam-4467	202	1	it	it	PRON
ejpam-4467	202	2	can	can	AUX
ejpam-4467	202	3	be	be	AUX
ejpam-4467	202	4	verified	verify	VERB
ejpam-4467	202	5	through	through	ADP
ejpam-4467	202	6	a	a	DET
ejpam-4467	202	7	process	process	NOUN
ejpam-4467	202	8	similar	similar	ADJ
ejpam-4467	202	9	to	to	ADP
ejpam-4467	202	10	the	the	DET
ejpam-4467	202	11	proof	proof	NOUN
ejpam-4467	202	12	in	in	ADP
ejpam-4467	202	13	theorem	theorem	ADJ
ejpam-4467	202	14	6	6	NUM
ejpam-4467	202	15	.	.	PUNCT
ejpam-4467	202	16	theorem	theorem	NOUN
ejpam-4467	202	17	8	8	NUM
ejpam-4467	202	18	.	.	PUNCT
ejpam-4467	203	1	if	if	SCONJ
ejpam-4467	203	2	a	a	DET
ejpam-4467	203	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	203	4	fuzzy	fuzzy	ADJ
ejpam-4467	203	5	set	set	VERB
ejpam-4467	203	6	lεψ	lεψ	VERB
ejpam-4467	203	7	in	in	ADP
ejpam-4467	203	8	x	x	X
ejpam-4467	203	9	satisfies	satisfie	NOUN
ejpam-4467	203	10	:	:	PUNCT
ejpam-4467	203	11	(	(	PUNCT
ejpam-4467	203	12	∀x	∀x	X
ejpam-4467	203	13	,	,	PUNCT
ejpam-4467	203	14	y	y	PROPN
ejpam-4467	203	15	∈	∈	PROPN
ejpam-4467	203	16	x)(∀t	x)(∀t	PROPN
ejpam-4467	203	17	∈	∈	PROPN
ejpam-4467	203	18	(	(	PUNCT
ejpam-4467	203	19	0.5	0.5	NUM
ejpam-4467	203	20	,	,	PUNCT
ejpam-4467	203	21	1	1	NUM
ejpam-4467	203	22	]	]	NUM
ejpam-4467	203	23	)	)	PUNCT
ejpam-4467	203	24	(	(	PUNCT
ejpam-4467	203	25	⟨y	⟨y	X
ejpam-4467	203	26	/	/	SYM
ejpam-4467	203	27	t⟩	t⟩	PRON
ejpam-4467	203	28	q	q	X
ejpam-4467	203	29	lεψ	lεψ	ADJ
ejpam-4467	203	30	⇒	⇒	PROPN
ejpam-4467	203	31	⟨(x	⟨(x	PROPN
ejpam-4467	203	32	∗	∗	NOUN
ejpam-4467	203	33	y)/t⟩	y)/t⟩	PUNCT
ejpam-4467	204	1	∈	∈	PROPN
ejpam-4467	204	2	lεψ	lεψ	VERB
ejpam-4467	204	3	)	)	PUNCT
ejpam-4467	204	4	,	,	PUNCT
ejpam-4467	204	5	(	(	PUNCT
ejpam-4467	204	6	25	25	NUM
ejpam-4467	204	7	)	)	PUNCT
ejpam-4467	204	8	and	and	CCONJ
ejpam-4467	204	9	⟨x	⟨x	VERB
ejpam-4467	204	10	/	/	SYM
ejpam-4467	204	11	ta⟩	ta⟩	PROPN
ejpam-4467	204	12	q	q	PROPN
ejpam-4467	204	13	lεψ	lεψ	PROPN
ejpam-4467	204	14	,	,	PUNCT
ejpam-4467	204	15	⟨y	⟨y	AUX
ejpam-4467	204	16	/	/	SYM
ejpam-4467	204	17	tb⟩	tb⟩	PROPN
ejpam-4467	204	18	q	q	NOUN
ejpam-4467	204	19	lεψ	lεψ	ADJ
ejpam-4467	204	20	⇒	⇒	PROPN
ejpam-4467	204	21	⟨((x	⟨((x	PROPN
ejpam-4467	204	22	∗	∗	NOUN
ejpam-4467	204	23	(	(	PUNCT
ejpam-4467	204	24	y	y	PROPN
ejpam-4467	204	25	∗	∗	PROPN
ejpam-4467	204	26	z	z	NOUN
ejpam-4467	204	27	)	)	PUNCT
ejpam-4467	204	28	)	)	PUNCT
ejpam-4467	204	29	∗	∗	NOUN
ejpam-4467	204	30	z)/max{ta	z)/max{ta	PROPN
ejpam-4467	204	31	,	,	PUNCT
ejpam-4467	204	32	tb}⟩	tb}⟩	X
ejpam-4467	204	33	∈	∈	PROPN
ejpam-4467	204	34	lεψ	lεψ	VERB
ejpam-4467	204	35	,	,	PUNCT
ejpam-4467	204	36	(	(	PUNCT
ejpam-4467	204	37	26	26	NUM
ejpam-4467	204	38	)	)	PUNCT
ejpam-4467	204	39	for	for	ADP
ejpam-4467	204	40	all	all	DET
ejpam-4467	204	41	x	x	NOUN
ejpam-4467	204	42	,	,	PUNCT
ejpam-4467	204	43	y	y	PROPN
ejpam-4467	204	44	,	,	PUNCT
ejpam-4467	204	45	z	z	NOUN
ejpam-4467	204	46	∈	∈	PROPN
ejpam-4467	204	47	x	x	X
ejpam-4467	204	48	and	and	CCONJ
ejpam-4467	204	49	ta	ta	PROPN
ejpam-4467	204	50	,	,	PUNCT
ejpam-4467	204	51	tb	tb	ADP
ejpam-4467	204	52	∈	∈	PROPN
ejpam-4467	204	53	(	(	PUNCT
ejpam-4467	204	54	0.5	0.5	NUM
ejpam-4467	204	55	,	,	PUNCT
ejpam-4467	204	56	1	1	NUM
ejpam-4467	204	57	]	]	PUNCT
ejpam-4467	204	58	,	,	PUNCT
ejpam-4467	204	59	then	then	ADV
ejpam-4467	204	60	the	the	DET
ejpam-4467	204	61	non	non	ADJ
ejpam-4467	204	62	-	-	ADJ
ejpam-4467	204	63	empty	empty	ADJ
ejpam-4467	204	64	∈-set	∈-set	NOUN
ejpam-4467	204	65	(	(	PUNCT
ejpam-4467	204	66	lεψ	lεψ	ADJ
ejpam-4467	204	67	,	,	PUNCT
ejpam-4467	204	68	max{ta	max{ta	NUM
ejpam-4467	204	69	,	,	PUNCT
ejpam-4467	204	70	tb})∈	tb})∈	PROPN
ejpam-4467	204	71	of	of	ADP
ejpam-4467	204	72	lεψ	lεψ	PROPN
ejpam-4467	204	73	is	be	AUX
ejpam-4467	204	74	an	an	DET
ejpam-4467	204	75	ideal	ideal	NOUN
ejpam-4467	204	76	of	of	ADP
ejpam-4467	204	77	(	(	PUNCT
ejpam-4467	204	78	x	x	X
ejpam-4467	204	79	,	,	PUNCT
ejpam-4467	204	80	1)∗	1)∗	NUM
ejpam-4467	204	81	for	for	ADP
ejpam-4467	204	82	all	all	DET
ejpam-4467	204	83	ta	ta	PROPN
ejpam-4467	204	84	,	,	PUNCT
ejpam-4467	204	85	tb	tb	ADP
ejpam-4467	204	86	∈	∈	PROPN
ejpam-4467	204	87	(	(	PUNCT
ejpam-4467	204	88	0.5	0.5	NUM
ejpam-4467	204	89	,	,	PUNCT
ejpam-4467	204	90	1	1	NUM
ejpam-4467	204	91	]	]	PUNCT
ejpam-4467	204	92	.	.	PUNCT
ejpam-4467	205	1	proof	proof	NOUN
ejpam-4467	205	2	.	.	PUNCT
ejpam-4467	206	1	let	let	VERB
ejpam-4467	206	2	y	y	PROPN
ejpam-4467	206	3	∈	∈	PROPN
ejpam-4467	206	4	(	(	PUNCT
ejpam-4467	206	5	lεψ	lεψ	ADJ
ejpam-4467	206	6	,	,	PUNCT
ejpam-4467	206	7	max{ta	max{ta	NOUN
ejpam-4467	206	8	,	,	PUNCT
ejpam-4467	206	9	tb})∈	tb})∈	ADJ
ejpam-4467	206	10	for	for	ADP
ejpam-4467	206	11	ta	ta	PROPN
ejpam-4467	206	12	,	,	PUNCT
ejpam-4467	206	13	tb	tb	ADP
ejpam-4467	206	14	∈	∈	PROPN
ejpam-4467	206	15	(	(	PUNCT
ejpam-4467	206	16	0.5	0.5	NUM
ejpam-4467	206	17	,	,	PUNCT
ejpam-4467	206	18	1	1	NUM
ejpam-4467	206	19	]	]	PUNCT
ejpam-4467	206	20	.	.	PUNCT
ejpam-4467	207	1	then	then	ADV
ejpam-4467	207	2	lεψ(y	lεψ(y	PROPN
ejpam-4467	207	3	)	)	PUNCT
ejpam-4467	207	4	≥	≥	NOUN
ejpam-4467	207	5	max{ta	max{ta	NOUN
ejpam-4467	207	6	,	,	PUNCT
ejpam-4467	207	7	tb	tb	NOUN
ejpam-4467	207	8	}	}	PUNCT
ejpam-4467	207	9	>	>	X
ejpam-4467	207	10	1	1	NUM
ejpam-4467	207	11	−	−	NOUN
ejpam-4467	207	12	max{ta	max{ta	NOUN
ejpam-4467	207	13	,	,	PUNCT
ejpam-4467	207	14	tb	tb	NOUN
ejpam-4467	207	15	}	}	PUNCT
ejpam-4467	207	16	,	,	PUNCT
ejpam-4467	207	17	and	and	CCONJ
ejpam-4467	207	18	so	so	ADV
ejpam-4467	207	19	⟨y	⟨y	NOUN
ejpam-4467	207	20	/	/	SYM
ejpam-4467	207	21	max{ta	max{ta	NOUN
ejpam-4467	207	22	,	,	PUNCT
ejpam-4467	207	23	tb}⟩	tb}⟩	X
ejpam-4467	207	24	q	q	VERB
ejpam-4467	207	25	lεψ	lεψ	ADJ
ejpam-4467	207	26	.	.	PUNCT
ejpam-4467	208	1	hence	hence	ADV
ejpam-4467	208	2	⟨(x	⟨(x	PROPN
ejpam-4467	208	3	∗	∗	NOUN
ejpam-4467	208	4	y)/max{ta	y)/max{ta	PROPN
ejpam-4467	208	5	,	,	PUNCT
ejpam-4467	208	6	tb}⟩	tb}⟩	X
ejpam-4467	208	7	∈	∈	PROPN
ejpam-4467	208	8	lεψ	lεψ	VERB
ejpam-4467	208	9	for	for	ADP
ejpam-4467	208	10	all	all	DET
ejpam-4467	208	11	x	x	SYM
ejpam-4467	208	12	∈	∈	PROPN
ejpam-4467	208	13	x	x	PUNCT
ejpam-4467	208	14	by	by	ADP
ejpam-4467	208	15	(	(	PUNCT
ejpam-4467	208	16	25	25	NUM
ejpam-4467	208	17	)	)	PUNCT
ejpam-4467	208	18	,	,	PUNCT
ejpam-4467	208	19	which	which	PRON
ejpam-4467	208	20	implies	imply	VERB
ejpam-4467	208	21	that	that	SCONJ
ejpam-4467	208	22	x	x	SYM
ejpam-4467	208	23	∗	∗	VERB
ejpam-4467	208	24	y	y	PROPN
ejpam-4467	208	25	∈	∈	PROPN
ejpam-4467	208	26	(	(	PUNCT
ejpam-4467	208	27	lεψ	lεψ	ADJ
ejpam-4467	208	28	,	,	PUNCT
ejpam-4467	208	29	max{ta	max{ta	NOUN
ejpam-4467	208	30	,	,	PUNCT
ejpam-4467	208	31	tb})∈	tb})∈	ADJ
ejpam-4467	208	32	for	for	ADP
ejpam-4467	208	33	all	all	DET
ejpam-4467	208	34	x	x	SYM
ejpam-4467	208	35	∈	∈	NOUN
ejpam-4467	208	36	x.	x.	NOUN
ejpam-4467	208	37	let	let	VERB
ejpam-4467	208	38	x	x	PRON
ejpam-4467	208	39	,	,	PUNCT
ejpam-4467	208	40	y	y	PROPN
ejpam-4467	208	41	∈	∈	PROPN
ejpam-4467	208	42	(	(	PUNCT
ejpam-4467	208	43	lεψ	lεψ	ADJ
ejpam-4467	208	44	,	,	PUNCT
ejpam-4467	208	45	max{ta	max{ta	NOUN
ejpam-4467	208	46	,	,	PUNCT
ejpam-4467	208	47	tb})∈	tb})∈	ADJ
ejpam-4467	208	48	for	for	ADP
ejpam-4467	208	49	ta	ta	PROPN
ejpam-4467	208	50	,	,	PUNCT
ejpam-4467	208	51	tb	tb	ADP
ejpam-4467	208	52	∈	∈	PROPN
ejpam-4467	208	53	(	(	PUNCT
ejpam-4467	208	54	0.5	0.5	NUM
ejpam-4467	208	55	,	,	PUNCT
ejpam-4467	208	56	1	1	NUM
ejpam-4467	208	57	]	]	PUNCT
ejpam-4467	208	58	.	.	PUNCT
ejpam-4467	209	1	then	then	ADV
ejpam-4467	209	2	lεψ(x	lεψ(x	PROPN
ejpam-4467	209	3	)	)	PUNCT
ejpam-4467	209	4	≥	≥	NOUN
ejpam-4467	209	5	max{ta	max{ta	VERB
ejpam-4467	209	6	,	,	PUNCT
ejpam-4467	209	7	tb	tb	NOUN
ejpam-4467	209	8	}	}	PUNCT
ejpam-4467	209	9	>	>	X
ejpam-4467	209	10	1	1	NUM
ejpam-4467	209	11	−	−	NOUN
ejpam-4467	209	12	max{ta	max{ta	NOUN
ejpam-4467	209	13	,	,	PUNCT
ejpam-4467	209	14	tb	tb	NOUN
ejpam-4467	209	15	}	}	PUNCT
ejpam-4467	209	16	and	and	CCONJ
ejpam-4467	209	17	lεψ(y	lεψ(y	PROPN
ejpam-4467	209	18	)	)	PUNCT
ejpam-4467	209	19	≥	≥	NOUN
ejpam-4467	209	20	max{ta	max{ta	NOUN
ejpam-4467	209	21	,	,	PUNCT
ejpam-4467	209	22	tb	tb	ADP
ejpam-4467	209	23	}	}	PUNCT
ejpam-4467	209	24	>	>	X
ejpam-4467	209	25	1−max{ta	1−max{ta	PROPN
ejpam-4467	209	26	,	,	PUNCT
ejpam-4467	209	27	tb	tb	NOUN
ejpam-4467	209	28	}	}	PUNCT
ejpam-4467	209	29	,	,	PUNCT
ejpam-4467	209	30	that	that	ADV
ejpam-4467	209	31	is	is	ADV
ejpam-4467	209	32	,	,	PUNCT
ejpam-4467	209	33	⟨x	⟨x	VERB
ejpam-4467	209	34	/	/	SYM
ejpam-4467	209	35	max{ta	max{ta	NOUN
ejpam-4467	209	36	,	,	PUNCT
ejpam-4467	209	37	tb}⟩	tb}⟩	X
ejpam-4467	209	38	q	q	X
ejpam-4467	209	39	lεψ	lεψ	ADJ
ejpam-4467	209	40	and	and	CCONJ
ejpam-4467	209	41	⟨y	⟨y	NOUN
ejpam-4467	209	42	/	/	SYM
ejpam-4467	209	43	max{ta	max{ta	NOUN
ejpam-4467	209	44	,	,	PUNCT
ejpam-4467	209	45	tb}⟩	tb}⟩	X
ejpam-4467	209	46	q	q	VERB
ejpam-4467	209	47	lεψ	lεψ	ADJ
ejpam-4467	209	48	.	.	PUNCT
ejpam-4467	210	1	it	it	PRON
ejpam-4467	210	2	follows	follow	VERB
ejpam-4467	210	3	from	from	ADP
ejpam-4467	210	4	(	(	PUNCT
ejpam-4467	210	5	26	26	NUM
ejpam-4467	210	6	)	)	PUNCT
ejpam-4467	210	7	that	that	PRON
ejpam-4467	210	8	⟨((x	⟨((x	PROPN
ejpam-4467	210	9	∗	∗	NOUN
ejpam-4467	210	10	(	(	PUNCT
ejpam-4467	210	11	y	y	PROPN
ejpam-4467	210	12	∗	∗	PROPN
ejpam-4467	210	13	z	z	NOUN
ejpam-4467	210	14	)	)	PUNCT
ejpam-4467	210	15	)	)	PUNCT
ejpam-4467	210	16	∗	∗	NOUN
ejpam-4467	210	17	z)/max{ta	z)/max{ta	PROPN
ejpam-4467	210	18	,	,	PUNCT
ejpam-4467	210	19	tb}⟩	tb}⟩	X
ejpam-4467	210	20	∈	∈	PROPN
ejpam-4467	210	21	lεψ	lεψ	VERB
ejpam-4467	210	22	for	for	ADP
ejpam-4467	210	23	all	all	DET
ejpam-4467	210	24	z	z	NOUN
ejpam-4467	210	25	∈	∈	NOUN
ejpam-4467	210	26	x.	x.	NOUN
ejpam-4467	210	27	hence	hence	ADV
ejpam-4467	210	28	(	(	PUNCT
ejpam-4467	210	29	x	x	SYM
ejpam-4467	210	30	∗	∗	NOUN
ejpam-4467	210	31	(	(	PUNCT
ejpam-4467	210	32	y	y	PROPN
ejpam-4467	210	33	∗	∗	PROPN
ejpam-4467	210	34	z	z	NOUN
ejpam-4467	210	35	)	)	PUNCT
ejpam-4467	210	36	)	)	PUNCT
ejpam-4467	211	1	∗	∗	NOUN
ejpam-4467	211	2	z	z	NOUN
ejpam-4467	211	3	∈	∈	PROPN
ejpam-4467	211	4	(	(	PUNCT
ejpam-4467	211	5	lεψ	lεψ	ADJ
ejpam-4467	211	6	,	,	PUNCT
ejpam-4467	211	7	max{ta	max{ta	NOUN
ejpam-4467	211	8	,	,	PUNCT
ejpam-4467	211	9	tb})∈	tb})∈	ADJ
ejpam-4467	211	10	for	for	ADP
ejpam-4467	211	11	all	all	DET
ejpam-4467	211	12	z	z	NOUN
ejpam-4467	211	13	∈	∈	NOUN
ejpam-4467	211	14	x.	x.	NOUN
ejpam-4467	211	15	therefore	therefore	ADV
ejpam-4467	211	16	(	(	PUNCT
ejpam-4467	211	17	lεψ	lεψ	ADJ
ejpam-4467	211	18	,	,	PUNCT
ejpam-4467	211	19	max{ta	max{ta	NUM
ejpam-4467	211	20	,	,	PUNCT
ejpam-4467	211	21	tb})∈	tb})∈	PROPN
ejpam-4467	211	22	of	of	ADP
ejpam-4467	211	23	lεψ	lεψ	PROPN
ejpam-4467	211	24	is	be	AUX
ejpam-4467	211	25	an	an	DET
ejpam-4467	211	26	ideal	ideal	NOUN
ejpam-4467	211	27	of	of	ADP
ejpam-4467	211	28	(	(	PUNCT
ejpam-4467	211	29	x	x	X
ejpam-4467	211	30	,	,	PUNCT
ejpam-4467	211	31	1)∗	1)∗	NUM
ejpam-4467	211	32	for	for	ADP
ejpam-4467	211	33	all	all	DET
ejpam-4467	211	34	ta	ta	PROPN
ejpam-4467	211	35	,	,	PUNCT
ejpam-4467	211	36	tb	tb	ADP
ejpam-4467	211	37	∈	∈	PROPN
ejpam-4467	211	38	(	(	PUNCT
ejpam-4467	211	39	0.5	0.5	NUM
ejpam-4467	211	40	,	,	PUNCT
ejpam-4467	211	41	1	1	NUM
ejpam-4467	211	42	]	]	PUNCT
ejpam-4467	211	43	.	.	PUNCT
ejpam-4467	212	1	s.	s.	PROPN
ejpam-4467	212	2	s.	s.	PROPN
ejpam-4467	212	3	ahn	ahn	PROPN
ejpam-4467	212	4	,	,	PUNCT
ejpam-4467	212	5	e.	e.	PROPN
ejpam-4467	212	6	h.	h.	PROPN
ejpam-4467	212	7	roh	roh	PROPN
ejpam-4467	212	8	and	and	CCONJ
ejpam-4467	212	9	y.	y.	PROPN
ejpam-4467	212	10	b.	b.	PROPN
ejpam-4467	212	11	jun	jun	PROPN
ejpam-4467	212	12	/	/	SYM
ejpam-4467	212	13	eur	eur	PROPN
ejpam-4467	212	14	.	.	PUNCT
ejpam-4467	213	1	j.	j.	PROPN
ejpam-4467	213	2	pure	pure	PROPN
ejpam-4467	213	3	appl	appl	PROPN
ejpam-4467	213	4	.	.	PROPN
ejpam-4467	213	5	math	math	PROPN
ejpam-4467	213	6	,	,	PUNCT
ejpam-4467	213	7	15	15	NUM
ejpam-4467	213	8	(	(	PUNCT
ejpam-4467	213	9	3	3	NUM
ejpam-4467	213	10	)	)	PUNCT
ejpam-4467	213	11	(	(	PUNCT
ejpam-4467	213	12	2022	2022	NUM
ejpam-4467	213	13	)	)	PUNCT
ejpam-4467	213	14	,	,	PUNCT
ejpam-4467	213	15	1307	1307	NUM
ejpam-4467	213	16	-	-	SYM
ejpam-4467	213	17	1320	1320	NUM
ejpam-4467	213	18	1315	1315	NUM
ejpam-4467	213	19	lemma	lemma	PROPN
ejpam-4467	213	20	2	2	X
ejpam-4467	213	21	.	.	PUNCT
ejpam-4467	214	1	every	every	DET
ejpam-4467	214	2	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	214	3	fuzzy	fuzzy	ADJ
ejpam-4467	214	4	ideal	ideal	NOUN
ejpam-4467	214	5	lεψ	lεψ	VERB
ejpam-4467	214	6	of	of	ADP
ejpam-4467	214	7	(	(	PUNCT
ejpam-4467	214	8	x	x	NOUN
ejpam-4467	214	9	,	,	PUNCT
ejpam-4467	214	10	1)∗	1)∗	NUM
ejpam-4467	214	11	satisfies	satisfie	NOUN
ejpam-4467	214	12	:	:	PUNCT
ejpam-4467	214	13	(	(	PUNCT
ejpam-4467	214	14	∀x	∀x	X
ejpam-4467	214	15	,	,	PUNCT
ejpam-4467	214	16	y	y	PROPN
ejpam-4467	214	17	,	,	PUNCT
ejpam-4467	214	18	z	z	NOUN
ejpam-4467	214	19	∈	∈	PROPN
ejpam-4467	214	20	x	x	X
ejpam-4467	214	21	)	)	PUNCT
ejpam-4467	214	22	(	(	PUNCT
ejpam-4467	214	23	lεψ(x	lεψ(x	NOUN
ejpam-4467	214	24	∗	∗	X
ejpam-4467	214	25	z	z	NOUN
ejpam-4467	214	26	)	)	PUNCT
ejpam-4467	214	27	≥	≥	PROPN
ejpam-4467	214	28	max	max	PROPN
ejpam-4467	214	29	{	{	PUNCT
ejpam-4467	214	30	lεψ(x	lεψ(x	PROPN
ejpam-4467	214	31	∗	∗	NOUN
ejpam-4467	214	32	(	(	PUNCT
ejpam-4467	214	33	y	y	PROPN
ejpam-4467	214	34	∗	∗	PROPN
ejpam-4467	214	35	z	z	PROPN
ejpam-4467	214	36	)	)	PUNCT
ejpam-4467	214	37	)	)	PUNCT
ejpam-4467	214	38	,	,	PUNCT
ejpam-4467	214	39	lεψ(y	lεψ(y	PROPN
ejpam-4467	214	40	)	)	PUNCT
ejpam-4467	214	41	}	}	PUNCT
ejpam-4467	214	42	)	)	PUNCT
ejpam-4467	214	43	.	.	PUNCT
ejpam-4467	215	1	proof	proof	NOUN
ejpam-4467	215	2	.	.	PUNCT
ejpam-4467	216	1	note	note	VERB
ejpam-4467	216	2	that	that	SCONJ
ejpam-4467	216	3	⟨(x	⟨(x	PROPN
ejpam-4467	216	4	∗	∗	NOUN
ejpam-4467	216	5	(	(	PUNCT
ejpam-4467	216	6	y	y	NOUN
ejpam-4467	216	7	∗	∗	NOUN
ejpam-4467	216	8	z))/	z))/	PROPN
ejpam-4467	217	1	lεψ(x	lεψ(x	PROPN
ejpam-4467	217	2	∗	∗	NOUN
ejpam-4467	217	3	(	(	PUNCT
ejpam-4467	217	4	y	y	NOUN
ejpam-4467	217	5	∗	∗	X
ejpam-4467	217	6	z))⟩	z))⟩	PROPN
ejpam-4467	217	7	∈	∈	PROPN
ejpam-4467	217	8	lεψ	lεψ	PROPN
ejpam-4467	217	9	and	and	CCONJ
ejpam-4467	217	10	⟨y/	⟨y/	PROPN
ejpam-4467	217	11	lεψ(y)⟩	lεψ(y)⟩	PROPN
ejpam-4467	217	12	∈	∈	PROPN
ejpam-4467	217	13	lεψ	lεψ	VERB
ejpam-4467	217	14	for	for	ADP
ejpam-4467	217	15	all	all	DET
ejpam-4467	217	16	x	x	NOUN
ejpam-4467	217	17	,	,	PUNCT
ejpam-4467	217	18	y	y	PROPN
ejpam-4467	217	19	,	,	PUNCT
ejpam-4467	217	20	z	z	NOUN
ejpam-4467	217	21	∈	∈	PROPN
ejpam-4467	217	22	x.	x.	NOUN
ejpam-4467	218	1	it	it	PRON
ejpam-4467	218	2	follows	follow	VERB
ejpam-4467	218	3	from	from	ADP
ejpam-4467	218	4	(	(	PUNCT
ejpam-4467	218	5	17	17	NUM
ejpam-4467	218	6	)	)	PUNCT
ejpam-4467	218	7	that	that	PRON
ejpam-4467	218	8	⟨(x	⟨(x	VERB
ejpam-4467	218	9	∗	∗	NOUN
ejpam-4467	218	10	z)/min	z)/min	PROPN
ejpam-4467	218	11	{	{	PUNCT
ejpam-4467	218	12	lεψ(x	lεψ(x	PROPN
ejpam-4467	218	13	∗	∗	NOUN
ejpam-4467	218	14	(	(	PUNCT
ejpam-4467	218	15	y	y	PROPN
ejpam-4467	218	16	∗	∗	PROPN
ejpam-4467	218	17	z	z	PROPN
ejpam-4467	218	18	)	)	PUNCT
ejpam-4467	218	19	)	)	PUNCT
ejpam-4467	218	20	,	,	PUNCT
ejpam-4467	218	21	lεψ(y)}⟩	lεψ(y)}⟩	PROPN
ejpam-4467	218	22	∈	∈	PROPN
ejpam-4467	218	23	lεψ	lεψ	VERB
ejpam-4467	218	24	,	,	PUNCT
ejpam-4467	218	25	that	that	ADV
ejpam-4467	218	26	is	is	ADV
ejpam-4467	218	27	,	,	PUNCT
ejpam-4467	218	28	lεψ(x	lεψ(x	PROPN
ejpam-4467	218	29	∗	∗	NOUN
ejpam-4467	218	30	z	z	NOUN
ejpam-4467	218	31	)	)	PUNCT
ejpam-4467	218	32	≥	≥	NOUN
ejpam-4467	218	33	min	min	PROPN
ejpam-4467	218	34	{	{	PUNCT
ejpam-4467	218	35	lεψ(x	lεψ(x	ADJ
ejpam-4467	218	36	∗	∗	NOUN
ejpam-4467	218	37	(	(	PUNCT
ejpam-4467	218	38	y	y	PROPN
ejpam-4467	218	39	∗	∗	PROPN
ejpam-4467	218	40	z	z	PROPN
ejpam-4467	218	41	)	)	PUNCT
ejpam-4467	218	42	)	)	PUNCT
ejpam-4467	218	43	,	,	PUNCT
ejpam-4467	218	44	lεψ(y	lεψ(y	PROPN
ejpam-4467	218	45	)	)	PUNCT
ejpam-4467	218	46	}	}	PUNCT
ejpam-4467	218	47	for	for	ADP
ejpam-4467	218	48	all	all	DET
ejpam-4467	218	49	x	x	NOUN
ejpam-4467	218	50	,	,	PUNCT
ejpam-4467	218	51	y	y	PROPN
ejpam-4467	218	52	,	,	PUNCT
ejpam-4467	218	53	z	z	PROPN
ejpam-4467	218	54	∈	∈	PROPN
ejpam-4467	218	55	x.	x.	NOUN
ejpam-4467	218	56	theorem	theorem	VERB
ejpam-4467	218	57	9	9	NUM
ejpam-4467	218	58	.	.	PUNCT
ejpam-4467	219	1	if	if	SCONJ
ejpam-4467	219	2	lεψ	lεψ	ADJ
ejpam-4467	219	3	is	be	AUX
ejpam-4467	219	4	a	a	DET
ejpam-4467	219	5	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	219	6	fuzzy	fuzzy	ADJ
ejpam-4467	219	7	ideal	ideal	NOUN
ejpam-4467	219	8	of	of	ADP
ejpam-4467	219	9	(	(	PUNCT
ejpam-4467	219	10	x	x	X
ejpam-4467	219	11	,	,	PUNCT
ejpam-4467	219	12	1)∗	1)∗	NUM
ejpam-4467	219	13	,	,	PUNCT
ejpam-4467	219	14	then	then	ADV
ejpam-4467	219	15	its	its	PRON
ejpam-4467	219	16	q	q	NOUN
ejpam-4467	219	17	-	-	PUNCT
ejpam-4467	219	18	set	set	ADJ
ejpam-4467	219	19	(	(	PUNCT
ejpam-4467	219	20	lεψ	lεψ	ADJ
ejpam-4467	219	21	,	,	PUNCT
ejpam-4467	219	22	t)q	t)q	PRON
ejpam-4467	219	23	is	be	AUX
ejpam-4467	219	24	an	an	DET
ejpam-4467	219	25	ideal	ideal	NOUN
ejpam-4467	219	26	of	of	ADP
ejpam-4467	219	27	(	(	PUNCT
ejpam-4467	219	28	x	x	X
ejpam-4467	219	29	,	,	PUNCT
ejpam-4467	219	30	1)∗	1)∗	NUM
ejpam-4467	219	31	for	for	ADP
ejpam-4467	219	32	all	all	DET
ejpam-4467	219	33	t	t	NOUN
ejpam-4467	219	34	∈	∈	PROPN
ejpam-4467	219	35	(	(	PUNCT
ejpam-4467	219	36	0	0	NUM
ejpam-4467	219	37	,	,	PUNCT
ejpam-4467	219	38	1	1	NUM
ejpam-4467	219	39	]	]	PUNCT
ejpam-4467	219	40	.	.	PUNCT
ejpam-4467	220	1	proof	proof	NOUN
ejpam-4467	220	2	.	.	PUNCT
ejpam-4467	221	1	let	let	VERB
ejpam-4467	221	2	lεψ	lεψ	ADJ
ejpam-4467	221	3	be	be	AUX
ejpam-4467	221	4	a	a	DET
ejpam-4467	221	5	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	221	6	fuzzy	fuzzy	ADJ
ejpam-4467	221	7	ideal	ideal	NOUN
ejpam-4467	221	8	of	of	ADP
ejpam-4467	221	9	(	(	PUNCT
ejpam-4467	221	10	x	x	NOUN
ejpam-4467	221	11	,	,	PUNCT
ejpam-4467	221	12	1)∗	1)∗	NUM
ejpam-4467	221	13	and	and	CCONJ
ejpam-4467	221	14	let	let	VERB
ejpam-4467	221	15	t	t	PROPN
ejpam-4467	221	16	∈	∈	PROPN
ejpam-4467	221	17	(	(	PUNCT
ejpam-4467	221	18	0	0	NUM
ejpam-4467	221	19	,	,	PUNCT
ejpam-4467	221	20	1	1	NUM
ejpam-4467	221	21	]	]	PUNCT
ejpam-4467	221	22	.	.	PUNCT
ejpam-4467	222	1	if	if	SCONJ
ejpam-4467	222	2	1	1	NUM
ejpam-4467	222	3	/∈	/∈	INTJ
ejpam-4467	222	4	(	(	PUNCT
ejpam-4467	222	5	lεψ	lεψ	ADJ
ejpam-4467	222	6	,	,	PUNCT
ejpam-4467	222	7	t)q	t)q	NUM
ejpam-4467	222	8	,	,	PUNCT
ejpam-4467	222	9	then	then	ADV
ejpam-4467	222	10	⟨1	⟨1	PROPN
ejpam-4467	222	11	/	/	SYM
ejpam-4467	222	12	t⟩	t⟩	PRON
ejpam-4467	222	13	q	q	X
ejpam-4467	222	14	lεψ	lεψ	ADJ
ejpam-4467	222	15	,	,	PUNCT
ejpam-4467	222	16	i.e.	i.e.	X
ejpam-4467	222	17	,	,	PUNCT
ejpam-4467	222	18	lεψ(1	lεψ(1	ADJ
ejpam-4467	222	19	)	)	PUNCT
ejpam-4467	222	20	+	+	NUM
ejpam-4467	222	21	t	t	X
ejpam-4467	222	22	≤	≤	NUM
ejpam-4467	222	23	1	1	NUM
ejpam-4467	222	24	.	.	PUNCT
ejpam-4467	223	1	since	since	SCONJ
ejpam-4467	223	2	⟨x/	⟨x/	NUM
ejpam-4467	223	3	lεψ(x)⟩	lεψ(x)⟩	X
ejpam-4467	223	4	∈	∈	NOUN
ejpam-4467	223	5	lεψ	lεψ	VERB
ejpam-4467	223	6	for	for	ADP
ejpam-4467	223	7	all	all	DET
ejpam-4467	223	8	x	x	SYM
ejpam-4467	223	9	∈	∈	PROPN
ejpam-4467	223	10	x	x	X
ejpam-4467	223	11	,	,	PUNCT
ejpam-4467	223	12	we	we	PRON
ejpam-4467	223	13	get	get	VERB
ejpam-4467	223	14	⟨1/	⟨1/	PRON
ejpam-4467	223	15	lεψ(x)⟩	lεψ(x)⟩	X
ejpam-4467	224	1	∈	∈	NOUN
ejpam-4467	225	1	lεψ	lεψ	VERB
ejpam-4467	225	2	for	for	ADP
ejpam-4467	225	3	all	all	DET
ejpam-4467	225	4	x	x	SYM
ejpam-4467	225	5	∈	∈	PROPN
ejpam-4467	225	6	x	x	PUNCT
ejpam-4467	225	7	by	by	ADP
ejpam-4467	225	8	(	(	PUNCT
ejpam-4467	225	9	13	13	NUM
ejpam-4467	225	10	)	)	PUNCT
ejpam-4467	225	11	.	.	PUNCT
ejpam-4467	226	1	hence	hence	ADV
ejpam-4467	226	2	lεψ(1	lεψ(1	ADJ
ejpam-4467	226	3	)	)	PUNCT
ejpam-4467	226	4	≥	≥	NOUN
ejpam-4467	226	5	lεψ(x	lεψ(x	NOUN
ejpam-4467	226	6	)	)	PUNCT
ejpam-4467	226	7	for	for	ADP
ejpam-4467	226	8	x	x	PROPN
ejpam-4467	226	9	∈	∈	PROPN
ejpam-4467	226	10	(	(	PUNCT
ejpam-4467	226	11	lεψ	lεψ	ADJ
ejpam-4467	226	12	,	,	PUNCT
ejpam-4467	226	13	t)q	t)q	ADV
ejpam-4467	226	14	,	,	PUNCT
ejpam-4467	226	15	and	and	CCONJ
ejpam-4467	226	16	so	so	ADV
ejpam-4467	226	17	1	1	NUM
ejpam-4467	226	18	−	−	PROPN
ejpam-4467	226	19	t	t	PROPN
ejpam-4467	226	20	≥	≥	NOUN
ejpam-4467	226	21	lεψ(1	lεψ(1	ADJ
ejpam-4467	226	22	)	)	PUNCT
ejpam-4467	226	23	≥	≥	NOUN
ejpam-4467	226	24	lεψ(x	lεψ(x	NOUN
ejpam-4467	226	25	)	)	PUNCT
ejpam-4467	226	26	.	.	PUNCT
ejpam-4467	227	1	this	this	PRON
ejpam-4467	227	2	shows	show	VERB
ejpam-4467	227	3	that	that	SCONJ
ejpam-4467	227	4	⟨x	⟨x	VERB
ejpam-4467	227	5	/	/	SYM
ejpam-4467	227	6	t⟩	t⟩	PRON
ejpam-4467	227	7	q	q	X
ejpam-4467	227	8	lεψ	lεψ	ADJ
ejpam-4467	227	9	,	,	PUNCT
ejpam-4467	227	10	that	that	ADV
ejpam-4467	227	11	is	is	ADV
ejpam-4467	227	12	,	,	PUNCT
ejpam-4467	227	13	x	x	X
ejpam-4467	227	14	/∈	/∈	PUNCT
ejpam-4467	228	1	(	(	PUNCT
ejpam-4467	228	2	lεψ	lεψ	ADJ
ejpam-4467	228	3	,	,	PUNCT
ejpam-4467	228	4	t)q	t)q	NUM
ejpam-4467	228	5	,	,	PUNCT
ejpam-4467	228	6	a	a	DET
ejpam-4467	228	7	contradiction	contradiction	NOUN
ejpam-4467	228	8	.	.	PUNCT
ejpam-4467	229	1	thus	thus	ADV
ejpam-4467	229	2	1	1	NUM
ejpam-4467	229	3	∈	∈	PROPN
ejpam-4467	229	4	(	(	PUNCT
ejpam-4467	229	5	lεψ	lεψ	ADJ
ejpam-4467	229	6	,	,	PUNCT
ejpam-4467	229	7	t)q	t)q	PUNCT
ejpam-4467	229	8	.	.	PUNCT
ejpam-4467	230	1	let	let	VERB
ejpam-4467	230	2	x	x	PRON
ejpam-4467	230	3	,	,	PUNCT
ejpam-4467	230	4	y	y	PROPN
ejpam-4467	230	5	,	,	PUNCT
ejpam-4467	230	6	z	z	NOUN
ejpam-4467	230	7	∈	∈	PROPN
ejpam-4467	230	8	x	x	AUX
ejpam-4467	230	9	be	be	AUX
ejpam-4467	230	10	such	such	ADJ
ejpam-4467	230	11	that	that	DET
ejpam-4467	230	12	x∗	x∗	PROPN
ejpam-4467	230	13	(	(	PUNCT
ejpam-4467	230	14	y	y	PROPN
ejpam-4467	230	15	∗	∗	PROPN
ejpam-4467	230	16	z	z	NOUN
ejpam-4467	230	17	)	)	PUNCT
ejpam-4467	230	18	∈	∈	PROPN
ejpam-4467	230	19	(	(	PUNCT
ejpam-4467	230	20	lεψ	lεψ	ADJ
ejpam-4467	230	21	,	,	PUNCT
ejpam-4467	230	22	t)q	t)q	PUNCT
ejpam-4467	230	23	and	and	CCONJ
ejpam-4467	230	24	y	y	PROPN
ejpam-4467	230	25	∈	∈	PROPN
ejpam-4467	230	26	(	(	PUNCT
ejpam-4467	230	27	lεψ	lεψ	ADJ
ejpam-4467	230	28	,	,	PUNCT
ejpam-4467	230	29	t)q	t)q	PUNCT
ejpam-4467	230	30	.	.	PUNCT
ejpam-4467	231	1	then	then	ADV
ejpam-4467	231	2	⟨(x	⟨(x	VERB
ejpam-4467	231	3	∗	∗	NOUN
ejpam-4467	231	4	(	(	PUNCT
ejpam-4467	231	5	y	y	NOUN
ejpam-4467	231	6	∗	∗	NOUN
ejpam-4467	231	7	z))/t⟩	z))/t⟩	PROPN
ejpam-4467	231	8	q	q	PUNCT
ejpam-4467	231	9	lεψ	lεψ	ADJ
ejpam-4467	231	10	and	and	CCONJ
ejpam-4467	231	11	⟨y	⟨y	NOUN
ejpam-4467	231	12	/	/	SYM
ejpam-4467	231	13	t⟩	t⟩	PRON
ejpam-4467	231	14	q	q	X
ejpam-4467	231	15	lεψ	lεψ	ADJ
ejpam-4467	231	16	,	,	PUNCT
ejpam-4467	231	17	that	that	ADV
ejpam-4467	231	18	is	is	ADV
ejpam-4467	231	19	,	,	PUNCT
ejpam-4467	231	20	lεψ(x	lεψ(x	ADJ
ejpam-4467	231	21	∗	∗	NOUN
ejpam-4467	231	22	(	(	PUNCT
ejpam-4467	231	23	y	y	PROPN
ejpam-4467	231	24	∗	∗	PROPN
ejpam-4467	231	25	z	z	PROPN
ejpam-4467	231	26	)	)	PUNCT
ejpam-4467	231	27	)	)	PUNCT
ejpam-4467	231	28	>	>	X
ejpam-4467	232	1	1	1	NUM
ejpam-4467	232	2	−	−	PROPN
ejpam-4467	232	3	t	t	PROPN
ejpam-4467	232	4	and	and	CCONJ
ejpam-4467	232	5	lεψ(y	lεψ(y	PROPN
ejpam-4467	232	6	)	)	PUNCT
ejpam-4467	232	7	>	>	X
ejpam-4467	232	8	1	1	NUM
ejpam-4467	232	9	−	−	NOUN
ejpam-4467	232	10	t.	t.	NOUN
ejpam-4467	232	11	it	it	PRON
ejpam-4467	232	12	follows	follow	VERB
ejpam-4467	232	13	from	from	ADP
ejpam-4467	232	14	lemma	lemma	PROPN
ejpam-4467	232	15	2	2	NUM
ejpam-4467	232	16	that	that	PRON
ejpam-4467	232	17	lεψ(x	lεψ(x	PROPN
ejpam-4467	232	18	∗	∗	NOUN
ejpam-4467	232	19	z	z	NOUN
ejpam-4467	232	20	)	)	PUNCT
ejpam-4467	232	21	≥	≥	PROPN
ejpam-4467	232	22	max	max	PROPN
ejpam-4467	232	23	{	{	PUNCT
ejpam-4467	232	24	lεψ(x	lεψ(x	PROPN
ejpam-4467	232	25	∗	∗	NOUN
ejpam-4467	232	26	(	(	PUNCT
ejpam-4467	232	27	y	y	PROPN
ejpam-4467	232	28	∗	∗	PROPN
ejpam-4467	232	29	z	z	PROPN
ejpam-4467	232	30	)	)	PUNCT
ejpam-4467	232	31	)	)	PUNCT
ejpam-4467	232	32	,	,	PUNCT
ejpam-4467	232	33	lεψ(y	lεψ(y	PROPN
ejpam-4467	232	34	)	)	PUNCT
ejpam-4467	232	35	}	}	PUNCT
ejpam-4467	232	36	>	>	X
ejpam-4467	233	1	1	1	NUM
ejpam-4467	233	2	−	−	NOUN
ejpam-4467	233	3	t.	t.	NOUN
ejpam-4467	233	4	hence	hence	ADV
ejpam-4467	233	5	⟨(x	⟨(x	PROPN
ejpam-4467	233	6	∗	∗	PROPN
ejpam-4467	233	7	z)/t⟩	z)/t⟩	PROPN
ejpam-4467	233	8	q	q	PROPN
ejpam-4467	233	9	lεψ	lεψ	ADJ
ejpam-4467	233	10	,	,	PUNCT
ejpam-4467	233	11	and	and	CCONJ
ejpam-4467	233	12	so	so	ADV
ejpam-4467	233	13	x	x	SYM
ejpam-4467	233	14	∗	∗	NOUN
ejpam-4467	233	15	z	z	NOUN
ejpam-4467	233	16	∈	∈	PROPN
ejpam-4467	233	17	(	(	PUNCT
ejpam-4467	233	18	lεψ	lεψ	ADJ
ejpam-4467	233	19	,	,	PUNCT
ejpam-4467	233	20	t)q	t)q	PUNCT
ejpam-4467	233	21	.	.	PUNCT
ejpam-4467	234	1	therefore	therefore	ADV
ejpam-4467	234	2	(	(	PUNCT
ejpam-4467	234	3	lεψ	lεψ	ADJ
ejpam-4467	234	4	,	,	PUNCT
ejpam-4467	234	5	t)q	t)q	PRON
ejpam-4467	234	6	is	be	AUX
ejpam-4467	234	7	an	an	DET
ejpam-4467	234	8	ideal	ideal	NOUN
ejpam-4467	234	9	of	of	ADP
ejpam-4467	234	10	(	(	PUNCT
ejpam-4467	234	11	x	x	X
ejpam-4467	234	12	,	,	PUNCT
ejpam-4467	234	13	1)∗	1)∗	NUM
ejpam-4467	234	14	by	by	ADP
ejpam-4467	234	15	lemma	lemma	PROPN
ejpam-4467	234	16	1	1	NUM
ejpam-4467	234	17	.	.	PUNCT
ejpam-4467	234	18	corollary	corollary	ADJ
ejpam-4467	234	19	2	2	NUM
ejpam-4467	234	20	.	.	PUNCT
ejpam-4467	235	1	if	if	SCONJ
ejpam-4467	235	2	ψ	ψ	NOUN
ejpam-4467	235	3	is	be	AUX
ejpam-4467	235	4	a	a	DET
ejpam-4467	235	5	fuzzy	fuzzy	ADJ
ejpam-4467	235	6	ideal	ideal	NOUN
ejpam-4467	235	7	of	of	ADP
ejpam-4467	235	8	(	(	PUNCT
ejpam-4467	235	9	x	x	X
ejpam-4467	235	10	,	,	PUNCT
ejpam-4467	235	11	1)∗	1)∗	NUM
ejpam-4467	235	12	,	,	PUNCT
ejpam-4467	235	13	then	then	ADV
ejpam-4467	235	14	the	the	DET
ejpam-4467	235	15	q	q	NOUN
ejpam-4467	235	16	-	-	PUNCT
ejpam-4467	235	17	set	set	NOUN
ejpam-4467	235	18	of	of	ADP
ejpam-4467	235	19	lεψ	lεψ	PROPN
ejpam-4467	235	20	is	be	AUX
ejpam-4467	235	21	an	an	DET
ejpam-4467	235	22	ideal	ideal	NOUN
ejpam-4467	235	23	of	of	ADP
ejpam-4467	235	24	(	(	PUNCT
ejpam-4467	235	25	x	x	X
ejpam-4467	235	26	,	,	PUNCT
ejpam-4467	235	27	1)∗.	1)∗.	PRON
ejpam-4467	235	28	proposition	proposition	NOUN
ejpam-4467	235	29	2	2	NUM
ejpam-4467	235	30	.	.	X
ejpam-4467	236	1	for	for	SCONJ
ejpam-4467	236	2	the	the	DET
ejpam-4467	236	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	236	4	fuzzy	fuzzy	ADJ
ejpam-4467	236	5	set	set	VERB
ejpam-4467	236	6	lεψ	lεψ	VERB
ejpam-4467	236	7	in	in	ADP
ejpam-4467	236	8	x	x	PRON
ejpam-4467	236	9	,	,	PUNCT
ejpam-4467	236	10	if	if	SCONJ
ejpam-4467	236	11	the	the	DET
ejpam-4467	236	12	q	q	NOUN
ejpam-4467	236	13	-	-	PUNCT
ejpam-4467	236	14	set	set	NOUN
ejpam-4467	236	15	of	of	ADP
ejpam-4467	236	16	lεψ	lεψ	PROPN
ejpam-4467	236	17	is	be	AUX
ejpam-4467	236	18	an	an	DET
ejpam-4467	236	19	ideal	ideal	NOUN
ejpam-4467	236	20	of	of	ADP
ejpam-4467	236	21	(	(	PUNCT
ejpam-4467	236	22	x	x	X
ejpam-4467	236	23	,	,	PUNCT
ejpam-4467	236	24	1)∗	1)∗	NUM
ejpam-4467	236	25	,	,	PUNCT
ejpam-4467	236	26	then	then	ADV
ejpam-4467	236	27	the	the	DET
ejpam-4467	236	28	following	follow	VERB
ejpam-4467	236	29	arguments	argument	NOUN
ejpam-4467	236	30	are	be	AUX
ejpam-4467	236	31	satisfied	satisfied	ADJ
ejpam-4467	236	32	.	.	PUNCT
ejpam-4467	237	1	1	1	NUM
ejpam-4467	237	2	∈	∈	PROPN
ejpam-4467	237	3	(	(	PUNCT
ejpam-4467	237	4	lεψ	lεψ	ADJ
ejpam-4467	237	5	,	,	PUNCT
ejpam-4467	237	6	t)∈	t)∈	NUM
ejpam-4467	237	7	,	,	PUNCT
ejpam-4467	237	8	(	(	PUNCT
ejpam-4467	237	9	27	27	NUM
ejpam-4467	237	10	)	)	PUNCT
ejpam-4467	237	11	⟨x	⟨x	NUM
ejpam-4467	237	12	/	/	SYM
ejpam-4467	237	13	ta⟩	ta⟩	PROPN
ejpam-4467	237	14	q	q	PROPN
ejpam-4467	237	15	lεψ	lεψ	PROPN
ejpam-4467	237	16	,	,	PUNCT
ejpam-4467	237	17	⟨y	⟨y	AUX
ejpam-4467	237	18	/	/	SYM
ejpam-4467	237	19	tb⟩	tb⟩	PROPN
ejpam-4467	237	20	q	q	ADJ
ejpam-4467	237	21	lεψ	lεψ	ADJ
ejpam-4467	237	22	⇒	⇒	NOUN
ejpam-4467	237	23	(	(	PUNCT
ejpam-4467	237	24	x	x	SYM
ejpam-4467	237	25	∗	∗	NOUN
ejpam-4467	237	26	(	(	PUNCT
ejpam-4467	237	27	y	y	PROPN
ejpam-4467	237	28	∗	∗	PROPN
ejpam-4467	237	29	z	z	NOUN
ejpam-4467	237	30	)	)	PUNCT
ejpam-4467	237	31	)	)	PUNCT
ejpam-4467	237	32	∗	∗	NOUN
ejpam-4467	237	33	z	z	NOUN
ejpam-4467	237	34	∈	∈	PROPN
ejpam-4467	237	35	(	(	PUNCT
ejpam-4467	237	36	lεψ	lεψ	ADJ
ejpam-4467	237	37	,	,	PUNCT
ejpam-4467	237	38	max{ta	max{ta	NOUN
ejpam-4467	237	39	,	,	PUNCT
ejpam-4467	237	40	tb})∈	tb})∈	ADJ
ejpam-4467	237	41	,	,	PUNCT
ejpam-4467	237	42	(	(	PUNCT
ejpam-4467	237	43	28	28	NUM
ejpam-4467	237	44	)	)	PUNCT
ejpam-4467	237	45	⟨(x	⟨(x	NOUN
ejpam-4467	238	1	∗	∗	NOUN
ejpam-4467	238	2	(	(	PUNCT
ejpam-4467	238	3	y	y	PROPN
ejpam-4467	238	4	∗	∗	X
ejpam-4467	238	5	z))/ta⟩	z))/ta⟩	PROPN
ejpam-4467	238	6	q	q	PROPN
ejpam-4467	238	7	lεψ	lεψ	ADJ
ejpam-4467	238	8	,	,	PUNCT
ejpam-4467	238	9	⟨y	⟨y	AUX
ejpam-4467	238	10	/	/	SYM
ejpam-4467	238	11	tb⟩	tb⟩	PROPN
ejpam-4467	238	12	q	q	NOUN
ejpam-4467	238	13	lεψ	lεψ	ADJ
ejpam-4467	238	14	⇒	⇒	NOUN
ejpam-4467	238	15	x	x	PROPN
ejpam-4467	238	16	∗	∗	PROPN
ejpam-4467	238	17	z	z	NOUN
ejpam-4467	238	18	∈	∈	PROPN
ejpam-4467	238	19	(	(	PUNCT
ejpam-4467	238	20	lεψ	lεψ	ADJ
ejpam-4467	238	21	,	,	PUNCT
ejpam-4467	238	22	max{ta	max{ta	NUM
ejpam-4467	238	23	,	,	PUNCT
ejpam-4467	238	24	tb})∈	tb})∈	X
ejpam-4467	238	25	(	(	PUNCT
ejpam-4467	238	26	29	29	NUM
ejpam-4467	238	27	)	)	PUNCT
ejpam-4467	238	28	for	for	ADP
ejpam-4467	238	29	all	all	DET
ejpam-4467	238	30	x	x	NOUN
ejpam-4467	238	31	,	,	PUNCT
ejpam-4467	238	32	y	y	PROPN
ejpam-4467	238	33	,	,	PUNCT
ejpam-4467	238	34	z	z	NOUN
ejpam-4467	238	35	∈	∈	PROPN
ejpam-4467	238	36	x	x	X
ejpam-4467	238	37	and	and	CCONJ
ejpam-4467	238	38	t	t	PROPN
ejpam-4467	238	39	,	,	PUNCT
ejpam-4467	238	40	ta	ta	X
ejpam-4467	238	41	,	,	PUNCT
ejpam-4467	238	42	tb	tb	ADP
ejpam-4467	238	43	∈	∈	PROPN
ejpam-4467	238	44	(	(	PUNCT
ejpam-4467	238	45	0	0	NUM
ejpam-4467	238	46	,	,	PUNCT
ejpam-4467	238	47	0.5	0.5	NUM
ejpam-4467	238	48	]	]	PUNCT
ejpam-4467	238	49	.	.	PUNCT
ejpam-4467	239	1	proof	proof	NOUN
ejpam-4467	239	2	.	.	PUNCT
ejpam-4467	240	1	assume	assume	VERB
ejpam-4467	240	2	that	that	SCONJ
ejpam-4467	240	3	the	the	DET
ejpam-4467	240	4	q	q	NOUN
ejpam-4467	240	5	-	-	PUNCT
ejpam-4467	240	6	set	set	VERB
ejpam-4467	240	7	(	(	PUNCT
ejpam-4467	240	8	lεψ	lεψ	ADJ
ejpam-4467	240	9	,	,	PUNCT
ejpam-4467	240	10	t)q	t)q	PRON
ejpam-4467	240	11	of	of	ADP
ejpam-4467	240	12	lεψ	lεψ	ADJ
ejpam-4467	240	13	is	be	AUX
ejpam-4467	240	14	an	an	DET
ejpam-4467	240	15	ideal	ideal	NOUN
ejpam-4467	240	16	of	of	ADP
ejpam-4467	240	17	(	(	PUNCT
ejpam-4467	240	18	x	x	X
ejpam-4467	240	19	,	,	PUNCT
ejpam-4467	240	20	1)∗.	1)∗.	NUM
ejpam-4467	240	21	then	then	ADV
ejpam-4467	240	22	1	1	NUM
ejpam-4467	240	23	∈	∈	PROPN
ejpam-4467	240	24	(	(	PUNCT
ejpam-4467	240	25	lεψ	lεψ	ADJ
ejpam-4467	240	26	,	,	PUNCT
ejpam-4467	240	27	t)q	t)q	PUNCT
ejpam-4467	240	28	by	by	ADP
ejpam-4467	240	29	lemma	lemma	PROPN
ejpam-4467	240	30	1	1	NUM
ejpam-4467	240	31	.	.	PUNCT
ejpam-4467	241	1	if	if	SCONJ
ejpam-4467	241	2	1	1	NUM
ejpam-4467	241	3	/∈	/∈	INTJ
ejpam-4467	241	4	(	(	PUNCT
ejpam-4467	241	5	lεψ	lεψ	ADJ
ejpam-4467	241	6	,	,	PUNCT
ejpam-4467	241	7	t)∈	t)∈	NUM
ejpam-4467	241	8	for	for	ADP
ejpam-4467	241	9	some	some	DET
ejpam-4467	241	10	t	t	NOUN
ejpam-4467	241	11	∈	∈	PROPN
ejpam-4467	241	12	(	(	PUNCT
ejpam-4467	241	13	0	0	NUM
ejpam-4467	241	14	,	,	PUNCT
ejpam-4467	241	15	0.5	0.5	NUM
ejpam-4467	241	16	]	]	PUNCT
ejpam-4467	241	17	,	,	PUNCT
ejpam-4467	241	18	then	then	ADV
ejpam-4467	241	19	⟨1	⟨1	PROPN
ejpam-4467	241	20	/	/	SYM
ejpam-4467	241	21	t⟩	t⟩	PRON
ejpam-4467	241	22	∈	∈	PROPN
ejpam-4467	241	23	lεψ	lεψ	PROPN
ejpam-4467	241	24	.	.	PUNCT
ejpam-4467	242	1	hence	hence	ADV
ejpam-4467	242	2	lεψ(1	lεψ(1	ADV
ejpam-4467	242	3	)	)	PUNCT
ejpam-4467	242	4	<	<	X
ejpam-4467	242	5	t	t	X
ejpam-4467	242	6	≤	≤	NUM
ejpam-4467	243	1	1	1	NUM
ejpam-4467	243	2	−	−	PROPN
ejpam-4467	243	3	t	t	PROPN
ejpam-4467	243	4	since	since	SCONJ
ejpam-4467	243	5	t	t	PROPN
ejpam-4467	243	6	∈	∈	PROPN
ejpam-4467	243	7	(	(	PUNCT
ejpam-4467	243	8	0	0	NUM
ejpam-4467	243	9	,	,	PUNCT
ejpam-4467	243	10	0.5	0.5	NUM
ejpam-4467	243	11	]	]	PUNCT
ejpam-4467	243	12	,	,	PUNCT
ejpam-4467	243	13	and	and	CCONJ
ejpam-4467	243	14	so	so	ADV
ejpam-4467	243	15	⟨1	⟨1	PROPN
ejpam-4467	243	16	/	/	SYM
ejpam-4467	243	17	t⟩	t⟩	PRON
ejpam-4467	243	18	q	q	X
ejpam-4467	243	19	lεψ	lεψ	ADJ
ejpam-4467	243	20	,	,	PUNCT
ejpam-4467	243	21	i.e.	i.e.	X
ejpam-4467	243	22	,	,	PUNCT
ejpam-4467	243	23	1	1	NUM
ejpam-4467	243	24	/∈	/∈	PUNCT
ejpam-4467	243	25	(	(	PUNCT
ejpam-4467	243	26	lεψ	lεψ	ADJ
ejpam-4467	243	27	,	,	PUNCT
ejpam-4467	243	28	t)q	t)q	PUNCT
ejpam-4467	243	29	.	.	PUNCT
ejpam-4467	244	1	this	this	PRON
ejpam-4467	244	2	is	be	AUX
ejpam-4467	244	3	a	a	DET
ejpam-4467	244	4	conradiction	conradiction	NOUN
ejpam-4467	244	5	,	,	PUNCT
ejpam-4467	244	6	and	and	CCONJ
ejpam-4467	244	7	thus	thus	ADV
ejpam-4467	244	8	1	1	NUM
ejpam-4467	244	9	∈	∈	PROPN
ejpam-4467	244	10	(	(	PUNCT
ejpam-4467	244	11	lεψ	lεψ	ADJ
ejpam-4467	244	12	,	,	PUNCT
ejpam-4467	244	13	t)∈.	t)∈.	PROPN
ejpam-4467	244	14	let	let	VERB
ejpam-4467	244	15	x	x	PRON
ejpam-4467	244	16	,	,	PUNCT
ejpam-4467	244	17	y	y	PROPN
ejpam-4467	244	18	∈	∈	PROPN
ejpam-4467	244	19	x	x	X
ejpam-4467	244	20	and	and	CCONJ
ejpam-4467	244	21	ta	ta	PROPN
ejpam-4467	244	22	,	,	PUNCT
ejpam-4467	244	23	tb	tb	ADP
ejpam-4467	244	24	∈	∈	PROPN
ejpam-4467	244	25	(	(	PUNCT
ejpam-4467	244	26	0	0	NUM
ejpam-4467	244	27	,	,	PUNCT
ejpam-4467	244	28	0.5	0.5	NUM
ejpam-4467	244	29	]	]	PUNCT
ejpam-4467	244	30	be	be	VERB
ejpam-4467	244	31	such	such	ADJ
ejpam-4467	244	32	that	that	SCONJ
ejpam-4467	244	33	⟨x	⟨x	VERB
ejpam-4467	244	34	/	/	SYM
ejpam-4467	244	35	ta⟩	ta⟩	PROPN
ejpam-4467	244	36	q	q	PROPN
ejpam-4467	244	37	lεψ	lεψ	ADJ
ejpam-4467	244	38	and	and	CCONJ
ejpam-4467	244	39	⟨y	⟨y	NOUN
ejpam-4467	244	40	/	/	SYM
ejpam-4467	244	41	tb⟩	tb⟩	PROPN
ejpam-4467	244	42	q	q	PUNCT
ejpam-4467	244	43	lεψ	lεψ	PROPN
ejpam-4467	244	44	.	.	PUNCT
ejpam-4467	245	1	then	then	ADV
ejpam-4467	245	2	x	x	SYM
ejpam-4467	245	3	∈	∈	PROPN
ejpam-4467	245	4	(	(	PUNCT
ejpam-4467	245	5	lεψ	lεψ	ADJ
ejpam-4467	245	6	,	,	PUNCT
ejpam-4467	245	7	ta)q	ta)q	NOUN
ejpam-4467	245	8	⊆	⊆	NUM
ejpam-4467	245	9	(	(	PUNCT
ejpam-4467	245	10	lεψ	lεψ	ADJ
ejpam-4467	245	11	,	,	PUNCT
ejpam-4467	245	12	max{ta	max{ta	NOUN
ejpam-4467	245	13	,	,	PUNCT
ejpam-4467	245	14	tb})q	tb})q	PROPN
ejpam-4467	245	15	and	and	CCONJ
ejpam-4467	245	16	y	y	PROPN
ejpam-4467	245	17	∈	∈	PROPN
ejpam-4467	245	18	(	(	PUNCT
ejpam-4467	245	19	lεψ	lεψ	PROPN
ejpam-4467	245	20	,	,	PUNCT
ejpam-4467	245	21	tb)q	tb)q	PROPN
ejpam-4467	245	22	⊆	⊆	NUM
ejpam-4467	245	23	(	(	PUNCT
ejpam-4467	245	24	lεψ	lεψ	ADJ
ejpam-4467	245	25	,	,	PUNCT
ejpam-4467	245	26	max{ta	max{ta	NOUN
ejpam-4467	245	27	,	,	PUNCT
ejpam-4467	245	28	tb})q	tb})q	NOUN
ejpam-4467	245	29	,	,	PUNCT
ejpam-4467	245	30	from	from	ADP
ejpam-4467	245	31	which	which	PRON
ejpam-4467	245	32	(	(	PUNCT
ejpam-4467	245	33	x	x	SYM
ejpam-4467	245	34	∗	∗	NOUN
ejpam-4467	245	35	(	(	PUNCT
ejpam-4467	245	36	y	y	PROPN
ejpam-4467	245	37	∗	∗	PROPN
ejpam-4467	245	38	z	z	NOUN
ejpam-4467	245	39	)	)	PUNCT
ejpam-4467	245	40	)	)	PUNCT
ejpam-4467	245	41	∗	∗	NOUN
ejpam-4467	245	42	z	z	NOUN
ejpam-4467	245	43	∈	∈	PROPN
ejpam-4467	245	44	(	(	PUNCT
ejpam-4467	245	45	lεψ	lεψ	ADJ
ejpam-4467	245	46	,	,	PUNCT
ejpam-4467	245	47	max{ta	max{ta	NUM
ejpam-4467	245	48	,	,	PUNCT
ejpam-4467	245	49	tb})q	tb})q	PROPN
ejpam-4467	245	50	is	be	AUX
ejpam-4467	245	51	derived	derive	VERB
ejpam-4467	245	52	.	.	PUNCT
ejpam-4467	246	1	hence	hence	ADV
ejpam-4467	246	2	lεψ((x	lεψ((x	NOUN
ejpam-4467	246	3	∗	∗	NOUN
ejpam-4467	246	4	(	(	PUNCT
ejpam-4467	246	5	y	y	PROPN
ejpam-4467	246	6	∗	∗	PROPN
ejpam-4467	246	7	z	z	NOUN
ejpam-4467	246	8	)	)	PUNCT
ejpam-4467	246	9	)	)	PUNCT
ejpam-4467	247	1	∗	∗	PROPN
ejpam-4467	247	2	z	z	PROPN
ejpam-4467	247	3	)	)	PUNCT
ejpam-4467	247	4	>	>	X
ejpam-4467	247	5	1	1	NUM
ejpam-4467	247	6	−	−	NOUN
ejpam-4467	247	7	max{ta	max{ta	NOUN
ejpam-4467	247	8	,	,	PUNCT
ejpam-4467	247	9	tb	tb	NOUN
ejpam-4467	247	10	}	}	PUNCT
ejpam-4467	247	11	≥	≥	X
ejpam-4467	247	12	max{ta	max{ta	NOUN
ejpam-4467	247	13	,	,	PUNCT
ejpam-4467	247	14	tb	tb	NOUN
ejpam-4467	247	15	}	}	PUNCT
ejpam-4467	247	16	,	,	PUNCT
ejpam-4467	247	17	s.	s.	PROPN
ejpam-4467	247	18	s.	s.	PROPN
ejpam-4467	247	19	ahn	ahn	PROPN
ejpam-4467	247	20	,	,	PUNCT
ejpam-4467	247	21	e.	e.	PROPN
ejpam-4467	247	22	h.	h.	PROPN
ejpam-4467	247	23	roh	roh	PROPN
ejpam-4467	247	24	and	and	CCONJ
ejpam-4467	247	25	y.	y.	PROPN
ejpam-4467	247	26	b.	b.	PROPN
ejpam-4467	247	27	jun	jun	PROPN
ejpam-4467	247	28	/	/	SYM
ejpam-4467	247	29	eur	eur	PROPN
ejpam-4467	247	30	.	.	PUNCT
ejpam-4467	248	1	j.	j.	PROPN
ejpam-4467	248	2	pure	pure	PROPN
ejpam-4467	248	3	appl	appl	PROPN
ejpam-4467	248	4	.	.	PROPN
ejpam-4467	248	5	math	math	PROPN
ejpam-4467	248	6	,	,	PUNCT
ejpam-4467	248	7	15	15	NUM
ejpam-4467	248	8	(	(	PUNCT
ejpam-4467	248	9	3	3	NUM
ejpam-4467	248	10	)	)	PUNCT
ejpam-4467	248	11	(	(	PUNCT
ejpam-4467	248	12	2022	2022	NUM
ejpam-4467	248	13	)	)	PUNCT
ejpam-4467	248	14	,	,	PUNCT
ejpam-4467	248	15	1307	1307	NUM
ejpam-4467	248	16	-	-	SYM
ejpam-4467	248	17	1320	1320	NUM
ejpam-4467	248	18	1316	1316	NUM
ejpam-4467	248	19	i.e.	i.e.	X
ejpam-4467	248	20	,	,	PUNCT
ejpam-4467	248	21	⟨((x	⟨((x	PROPN
ejpam-4467	248	22	∗	∗	NOUN
ejpam-4467	248	23	(	(	PUNCT
ejpam-4467	248	24	y	y	PROPN
ejpam-4467	248	25	∗	∗	PROPN
ejpam-4467	248	26	z	z	NOUN
ejpam-4467	248	27	)	)	PUNCT
ejpam-4467	248	28	)	)	PUNCT
ejpam-4467	248	29	∗	∗	NOUN
ejpam-4467	248	30	z)/max{ta	z)/max{ta	PROPN
ejpam-4467	248	31	,	,	PUNCT
ejpam-4467	248	32	tb}⟩	tb}⟩	X
ejpam-4467	248	33	∈	∈	PROPN
ejpam-4467	248	34	lεψ	lεψ	VERB
ejpam-4467	248	35	.	.	PUNCT
ejpam-4467	249	1	hence	hence	ADV
ejpam-4467	249	2	(	(	PUNCT
ejpam-4467	249	3	x	x	SYM
ejpam-4467	249	4	∗	∗	NOUN
ejpam-4467	249	5	(	(	PUNCT
ejpam-4467	249	6	y	y	PROPN
ejpam-4467	249	7	∗	∗	PROPN
ejpam-4467	249	8	z	z	NOUN
ejpam-4467	249	9	)	)	PUNCT
ejpam-4467	249	10	)	)	PUNCT
ejpam-4467	249	11	∗	∗	NOUN
ejpam-4467	249	12	z	z	NOUN
ejpam-4467	249	13	∈	∈	PROPN
ejpam-4467	249	14	(	(	PUNCT
ejpam-4467	249	15	lεψ	lεψ	ADJ
ejpam-4467	249	16	,	,	PUNCT
ejpam-4467	249	17	max{ta	max{ta	NOUN
ejpam-4467	249	18	,	,	PUNCT
ejpam-4467	249	19	tb})∈.	tb})∈.	NUM
ejpam-4467	249	20	let	let	VERB
ejpam-4467	249	21	x	x	PRON
ejpam-4467	249	22	,	,	PUNCT
ejpam-4467	249	23	y	y	PROPN
ejpam-4467	249	24	,	,	PUNCT
ejpam-4467	249	25	z	z	NOUN
ejpam-4467	249	26	∈	∈	PROPN
ejpam-4467	249	27	x	x	X
ejpam-4467	249	28	and	and	CCONJ
ejpam-4467	249	29	ta	ta	PROPN
ejpam-4467	249	30	,	,	PUNCT
ejpam-4467	249	31	tb	tb	ADP
ejpam-4467	249	32	∈	∈	PROPN
ejpam-4467	249	33	(	(	PUNCT
ejpam-4467	249	34	0	0	NUM
ejpam-4467	249	35	,	,	PUNCT
ejpam-4467	249	36	0.5	0.5	NUM
ejpam-4467	249	37	]	]	PUNCT
ejpam-4467	249	38	be	be	VERB
ejpam-4467	249	39	such	such	ADJ
ejpam-4467	249	40	that	that	SCONJ
ejpam-4467	249	41	⟨(x	⟨(x	PROPN
ejpam-4467	249	42	∗	∗	NOUN
ejpam-4467	249	43	(	(	PUNCT
ejpam-4467	249	44	y	y	PROPN
ejpam-4467	249	45	∗	∗	X
ejpam-4467	249	46	z))/ta⟩	z))/ta⟩	PROPN
ejpam-4467	249	47	q	q	PROPN
ejpam-4467	249	48	lεψ	lεψ	ADJ
ejpam-4467	249	49	and	and	CCONJ
ejpam-4467	249	50	⟨y	⟨y	NOUN
ejpam-4467	249	51	/	/	SYM
ejpam-4467	249	52	tb⟩	tb⟩	PROPN
ejpam-4467	249	53	q	q	PUNCT
ejpam-4467	249	54	lεψ	lεψ	PROPN
ejpam-4467	249	55	.	.	PUNCT
ejpam-4467	250	1	then	then	ADV
ejpam-4467	250	2	x	x	X
ejpam-4467	250	3	∗	∗	NOUN
ejpam-4467	250	4	(	(	PUNCT
ejpam-4467	250	5	y	y	PROPN
ejpam-4467	250	6	∗	∗	PROPN
ejpam-4467	250	7	z	z	NOUN
ejpam-4467	250	8	)	)	PUNCT
ejpam-4467	250	9	∈	∈	PROPN
ejpam-4467	250	10	(	(	PUNCT
ejpam-4467	250	11	lεψ	lεψ	ADJ
ejpam-4467	250	12	,	,	PUNCT
ejpam-4467	250	13	ta)q	ta)q	NOUN
ejpam-4467	250	14	⊆	⊆	NUM
ejpam-4467	250	15	(	(	PUNCT
ejpam-4467	250	16	lεψ	lεψ	ADJ
ejpam-4467	250	17	,	,	PUNCT
ejpam-4467	250	18	max{ta	max{ta	NOUN
ejpam-4467	250	19	,	,	PUNCT
ejpam-4467	250	20	tb})q	tb})q	PROPN
ejpam-4467	250	21	and	and	CCONJ
ejpam-4467	250	22	y	y	PROPN
ejpam-4467	250	23	∈	∈	PROPN
ejpam-4467	250	24	(	(	PUNCT
ejpam-4467	250	25	lεψ	lεψ	PROPN
ejpam-4467	250	26	,	,	PUNCT
ejpam-4467	250	27	tb)q	tb)q	PROPN
ejpam-4467	250	28	⊆	⊆	NUM
ejpam-4467	250	29	(	(	PUNCT
ejpam-4467	250	30	lεψ	lεψ	ADJ
ejpam-4467	250	31	,	,	PUNCT
ejpam-4467	250	32	max{ta	max{ta	NOUN
ejpam-4467	250	33	,	,	PUNCT
ejpam-4467	250	34	tb})q	tb})q	NOUN
ejpam-4467	250	35	,	,	PUNCT
ejpam-4467	250	36	from	from	ADP
ejpam-4467	250	37	which	which	PRON
ejpam-4467	250	38	x	x	SYM
ejpam-4467	250	39	∗	∗	NOUN
ejpam-4467	250	40	z	z	NOUN
ejpam-4467	250	41	∈	∈	PROPN
ejpam-4467	250	42	(	(	PUNCT
ejpam-4467	250	43	lεψ	lεψ	ADJ
ejpam-4467	250	44	,	,	PUNCT
ejpam-4467	250	45	max{ta	max{ta	NUM
ejpam-4467	250	46	,	,	PUNCT
ejpam-4467	250	47	tb})q	tb})q	PROPN
ejpam-4467	250	48	is	be	AUX
ejpam-4467	250	49	derived	derive	VERB
ejpam-4467	250	50	by	by	ADP
ejpam-4467	250	51	lemma	lemma	PROPN
ejpam-4467	250	52	1	1	NUM
ejpam-4467	250	53	.	.	PUNCT
ejpam-4467	250	54	hence	hence	ADV
ejpam-4467	250	55	lεψ(x	lεψ(x	PROPN
ejpam-4467	250	56	∗	∗	NOUN
ejpam-4467	250	57	z	z	NOUN
ejpam-4467	250	58	)	)	PUNCT
ejpam-4467	250	59	>	>	X
ejpam-4467	250	60	1	1	NUM
ejpam-4467	250	61	−	−	NOUN
ejpam-4467	250	62	max{ta	max{ta	NOUN
ejpam-4467	250	63	,	,	PUNCT
ejpam-4467	250	64	tb	tb	NOUN
ejpam-4467	250	65	}	}	PUNCT
ejpam-4467	250	66	≥	≥	X
ejpam-4467	250	67	max{ta	max{ta	NOUN
ejpam-4467	250	68	,	,	PUNCT
ejpam-4467	250	69	tb	tb	NOUN
ejpam-4467	250	70	}	}	PUNCT
ejpam-4467	250	71	,	,	PUNCT
ejpam-4467	250	72	i.e.	i.e.	X
ejpam-4467	250	73	,	,	PUNCT
ejpam-4467	250	74	⟨(x	⟨(x	PROPN
ejpam-4467	250	75	∗	∗	NOUN
ejpam-4467	250	76	z)/max{ta	z)/max{ta	PROPN
ejpam-4467	250	77	,	,	PUNCT
ejpam-4467	250	78	tb}⟩	tb}⟩	X
ejpam-4467	250	79	∈	∈	PROPN
ejpam-4467	250	80	lεψ	lεψ	VERB
ejpam-4467	250	81	.	.	PUNCT
ejpam-4467	251	1	therefore	therefore	ADV
ejpam-4467	251	2	x	x	X
ejpam-4467	251	3	∗	∗	PROPN
ejpam-4467	251	4	z	z	NOUN
ejpam-4467	251	5	∈	∈	PROPN
ejpam-4467	251	6	(	(	PUNCT
ejpam-4467	251	7	lεψ	lεψ	ADJ
ejpam-4467	251	8	,	,	PUNCT
ejpam-4467	251	9	max{ta	max{ta	NOUN
ejpam-4467	251	10	,	,	PUNCT
ejpam-4467	251	11	tb})∈.	tb})∈.	NUM
ejpam-4467	251	12	theorem	theorem	VERB
ejpam-4467	251	13	10	10	NUM
ejpam-4467	251	14	.	.	PUNCT
ejpam-4467	252	1	if	if	SCONJ
ejpam-4467	252	2	a	a	DET
ejpam-4467	252	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	252	4	fuzzy	fuzzy	ADJ
ejpam-4467	252	5	set	set	VERB
ejpam-4467	252	6	lεψ	lεψ	VERB
ejpam-4467	252	7	in	in	ADP
ejpam-4467	252	8	x	x	X
ejpam-4467	252	9	satisfies	satisfie	NOUN
ejpam-4467	252	10	(	(	PUNCT
ejpam-4467	252	11	∀x	∀x	X
ejpam-4467	252	12	,	,	PUNCT
ejpam-4467	252	13	y	y	PROPN
ejpam-4467	252	14	∈	∈	PROPN
ejpam-4467	252	15	x)(∀t	x)(∀t	PROPN
ejpam-4467	252	16	∈	∈	PROPN
ejpam-4467	252	17	(	(	PUNCT
ejpam-4467	252	18	0	0	NUM
ejpam-4467	252	19	,	,	PUNCT
ejpam-4467	252	20	1	1	NUM
ejpam-4467	252	21	]	]	NUM
ejpam-4467	252	22	)	)	PUNCT
ejpam-4467	252	23	(	(	PUNCT
ejpam-4467	252	24	⟨y	⟨y	X
ejpam-4467	252	25	/	/	SYM
ejpam-4467	252	26	t⟩	t⟩	PRON
ejpam-4467	252	27	∈	∈	PROPN
ejpam-4467	252	28	lεψ	lεψ	ADJ
ejpam-4467	252	29	⇒	⇒	PROPN
ejpam-4467	252	30	⟨(x	⟨(x	PROPN
ejpam-4467	252	31	∗	∗	NOUN
ejpam-4467	252	32	y)/t⟩	y)/t⟩	PROPN
ejpam-4467	253	1	q	q	PROPN
ejpam-4467	253	2	lεψ	lεψ	ADJ
ejpam-4467	253	3	)	)	PUNCT
ejpam-4467	253	4	,	,	PUNCT
ejpam-4467	253	5	(	(	PUNCT
ejpam-4467	253	6	30	30	NUM
ejpam-4467	253	7	)	)	PUNCT
ejpam-4467	253	8	and	and	CCONJ
ejpam-4467	253	9	⟨x	⟨x	VERB
ejpam-4467	253	10	/	/	SYM
ejpam-4467	253	11	ta⟩	ta⟩	CCONJ
ejpam-4467	253	12	∈	∈	PROPN
ejpam-4467	253	13	lεψ	lεψ	VERB
ejpam-4467	253	14	,	,	PUNCT
ejpam-4467	253	15	⟨y	⟨y	AUX
ejpam-4467	253	16	/	/	SYM
ejpam-4467	253	17	tb⟩	tb⟩	PROPN
ejpam-4467	253	18	∈	∈	PROPN
ejpam-4467	253	19	lεψ	lεψ	VERB
ejpam-4467	253	20	⇒	⇒	PROPN
ejpam-4467	253	21	⟨((x	⟨((x	PROPN
ejpam-4467	253	22	∗	∗	NOUN
ejpam-4467	253	23	(	(	PUNCT
ejpam-4467	253	24	y	y	PROPN
ejpam-4467	253	25	∗	∗	PROPN
ejpam-4467	253	26	z	z	NOUN
ejpam-4467	253	27	)	)	PUNCT
ejpam-4467	253	28	)	)	PUNCT
ejpam-4467	254	1	∗	∗	NOUN
ejpam-4467	254	2	z)/min{ta	z)/min{ta	PROPN
ejpam-4467	254	3	,	,	PUNCT
ejpam-4467	254	4	tb}⟩	tb}⟩	X
ejpam-4467	254	5	q	q	X
ejpam-4467	254	6	lεψ	lεψ	ADJ
ejpam-4467	254	7	(	(	PUNCT
ejpam-4467	254	8	31	31	NUM
ejpam-4467	254	9	)	)	PUNCT
ejpam-4467	254	10	for	for	ADP
ejpam-4467	254	11	all	all	DET
ejpam-4467	254	12	x	x	NOUN
ejpam-4467	254	13	,	,	PUNCT
ejpam-4467	254	14	y	y	PROPN
ejpam-4467	254	15	,	,	PUNCT
ejpam-4467	254	16	z	z	NOUN
ejpam-4467	254	17	∈	∈	PROPN
ejpam-4467	254	18	x	x	X
ejpam-4467	254	19	and	and	CCONJ
ejpam-4467	254	20	ta	ta	PROPN
ejpam-4467	254	21	,	,	PUNCT
ejpam-4467	254	22	tb	tb	ADP
ejpam-4467	254	23	∈	∈	PROPN
ejpam-4467	254	24	(	(	PUNCT
ejpam-4467	254	25	0	0	NUM
ejpam-4467	254	26	,	,	PUNCT
ejpam-4467	254	27	1	1	NUM
ejpam-4467	254	28	]	]	PUNCT
ejpam-4467	254	29	,	,	PUNCT
ejpam-4467	254	30	then	then	ADV
ejpam-4467	254	31	the	the	DET
ejpam-4467	254	32	q	q	NOUN
ejpam-4467	254	33	-	-	PUNCT
ejpam-4467	254	34	set	set	ADJ
ejpam-4467	254	35	(	(	PUNCT
ejpam-4467	254	36	lεψ	lεψ	ADJ
ejpam-4467	254	37	,	,	PUNCT
ejpam-4467	254	38	min{ta	min{ta	X
ejpam-4467	254	39	,	,	PUNCT
ejpam-4467	254	40	tb})q	tb})q	PROPN
ejpam-4467	254	41	of	of	ADP
ejpam-4467	254	42	lεψ	lεψ	PROPN
ejpam-4467	254	43	is	be	AUX
ejpam-4467	254	44	an	an	DET
ejpam-4467	254	45	ideal	ideal	NOUN
ejpam-4467	254	46	of	of	ADP
ejpam-4467	254	47	(	(	PUNCT
ejpam-4467	254	48	x	x	X
ejpam-4467	254	49	,	,	PUNCT
ejpam-4467	254	50	1)∗	1)∗	NUM
ejpam-4467	254	51	for	for	ADP
ejpam-4467	254	52	all	all	DET
ejpam-4467	254	53	ta	ta	PROPN
ejpam-4467	254	54	,	,	PUNCT
ejpam-4467	254	55	tb	tb	ADP
ejpam-4467	254	56	∈	∈	PROPN
ejpam-4467	254	57	(	(	PUNCT
ejpam-4467	254	58	0	0	NUM
ejpam-4467	254	59	,	,	PUNCT
ejpam-4467	254	60	0.5	0.5	NUM
ejpam-4467	254	61	]	]	PUNCT
ejpam-4467	254	62	.	.	PUNCT
ejpam-4467	255	1	proof	proof	NOUN
ejpam-4467	255	2	.	.	PUNCT
ejpam-4467	256	1	let	let	VERB
ejpam-4467	256	2	t	t	NOUN
ejpam-4467	256	3	:	:	PUNCT
ejpam-4467	256	4	=	=	SYM
ejpam-4467	256	5	min{ta	min{ta	X
ejpam-4467	256	6	,	,	PUNCT
ejpam-4467	256	7	tb	tb	NOUN
ejpam-4467	256	8	}	}	PUNCT
ejpam-4467	256	9	for	for	ADP
ejpam-4467	256	10	all	all	DET
ejpam-4467	256	11	ta	ta	NOUN
ejpam-4467	256	12	,	,	PUNCT
ejpam-4467	256	13	tb	tb	ADP
ejpam-4467	256	14	∈	∈	PROPN
ejpam-4467	256	15	(	(	PUNCT
ejpam-4467	256	16	0	0	NUM
ejpam-4467	256	17	,	,	PUNCT
ejpam-4467	256	18	0.5	0.5	NUM
ejpam-4467	256	19	]	]	PUNCT
ejpam-4467	256	20	.	.	PUNCT
ejpam-4467	257	1	if	if	SCONJ
ejpam-4467	257	2	y	y	PROPN
ejpam-4467	257	3	∈	∈	PROPN
ejpam-4467	257	4	(	(	PUNCT
ejpam-4467	257	5	lεψ	lεψ	ADJ
ejpam-4467	257	6	,	,	PUNCT
ejpam-4467	257	7	t)q	t)q	NUM
ejpam-4467	257	8	,	,	PUNCT
ejpam-4467	257	9	then	then	ADV
ejpam-4467	257	10	lεψ(y	lεψ(y	PROPN
ejpam-4467	257	11	)	)	PUNCT
ejpam-4467	257	12	>	>	X
ejpam-4467	257	13	1−	1−	NUM
ejpam-4467	257	14	t	t	PROPN
ejpam-4467	257	15	≥	≥	PROPN
ejpam-4467	257	16	t	t	PROPN
ejpam-4467	257	17	since	since	SCONJ
ejpam-4467	257	18	t	t	PROPN
ejpam-4467	257	19	≤	≤	NUM
ejpam-4467	257	20	0.5	0.5	NUM
ejpam-4467	257	21	,	,	PUNCT
ejpam-4467	257	22	and	and	CCONJ
ejpam-4467	257	23	so	so	ADV
ejpam-4467	257	24	⟨y	⟨y	NOUN
ejpam-4467	257	25	/	/	SYM
ejpam-4467	257	26	t⟩	t⟩	PRON
ejpam-4467	257	27	∈	∈	PROPN
ejpam-4467	257	28	lεψ	lεψ	PROPN
ejpam-4467	257	29	.	.	PUNCT
ejpam-4467	258	1	thus	thus	ADV
ejpam-4467	258	2	⟨(x	⟨(x	VERB
ejpam-4467	258	3	∗	∗	NOUN
ejpam-4467	258	4	y)/t⟩	y)/t⟩	PROPN
ejpam-4467	259	1	q	q	PROPN
ejpam-4467	259	2	lεψ	lεψ	VERB
ejpam-4467	259	3	by	by	ADP
ejpam-4467	259	4	(	(	PUNCT
ejpam-4467	259	5	30	30	NUM
ejpam-4467	259	6	)	)	PUNCT
ejpam-4467	259	7	,	,	PUNCT
ejpam-4467	259	8	that	that	ADV
ejpam-4467	259	9	is	is	ADV
ejpam-4467	259	10	,	,	PUNCT
ejpam-4467	259	11	x	x	SYM
ejpam-4467	259	12	∗	∗	NOUN
ejpam-4467	259	13	y	y	PROPN
ejpam-4467	259	14	∈	∈	PROPN
ejpam-4467	259	15	(	(	PUNCT
ejpam-4467	259	16	lεψ	lεψ	ADJ
ejpam-4467	259	17	,	,	PUNCT
ejpam-4467	259	18	t)q	t)q	PUNCT
ejpam-4467	259	19	=	=	SYM
ejpam-4467	259	20	(	(	PUNCT
ejpam-4467	259	21	lεψ	lεψ	ADJ
ejpam-4467	259	22	,	,	PUNCT
ejpam-4467	259	23	min{ta	min{ta	X
ejpam-4467	259	24	,	,	PUNCT
ejpam-4467	259	25	tb})q	tb})q	PROPN
ejpam-4467	259	26	for	for	ADP
ejpam-4467	259	27	all	all	PRON
ejpam-4467	259	28	x	x	SYM
ejpam-4467	259	29	∈	∈	NOUN
ejpam-4467	259	30	x.	x.	NOUN
ejpam-4467	259	31	let	let	VERB
ejpam-4467	259	32	x	x	PRON
ejpam-4467	259	33	,	,	PUNCT
ejpam-4467	259	34	y	y	PROPN
ejpam-4467	259	35	∈	∈	PROPN
ejpam-4467	259	36	x	x	AUX
ejpam-4467	259	37	be	be	AUX
ejpam-4467	259	38	such	such	ADJ
ejpam-4467	259	39	that	that	SCONJ
ejpam-4467	259	40	x	x	NOUN
ejpam-4467	259	41	,	,	PUNCT
ejpam-4467	259	42	y	y	PROPN
ejpam-4467	259	43	∈	∈	PROPN
ejpam-4467	259	44	(	(	PUNCT
ejpam-4467	259	45	lεψ	lεψ	ADJ
ejpam-4467	259	46	,	,	PUNCT
ejpam-4467	259	47	min{ta	min{ta	X
ejpam-4467	259	48	,	,	PUNCT
ejpam-4467	259	49	tb})q	tb})q	PROPN
ejpam-4467	259	50	.	.	PUNCT
ejpam-4467	260	1	then	then	ADV
ejpam-4467	260	2	lεψ(x	lεψ(x	NOUN
ejpam-4467	260	3	)	)	PUNCT
ejpam-4467	261	1	+	+	NUM
ejpam-4467	261	2	ta	ta	X
ejpam-4467	261	3	≥	≥	NOUN
ejpam-4467	261	4	lεψ(x	lεψ(x	PROPN
ejpam-4467	261	5	)	)	PUNCT
ejpam-4467	262	1	+	+	X
ejpam-4467	262	2	min{ta	min{ta	X
ejpam-4467	262	3	,	,	PUNCT
ejpam-4467	262	4	tb	tb	NOUN
ejpam-4467	262	5	}	}	PUNCT
ejpam-4467	262	6	>	>	X
ejpam-4467	262	7	1	1	NUM
ejpam-4467	262	8	and	and	CCONJ
ejpam-4467	262	9	lεψ(y	lεψ(y	PROPN
ejpam-4467	262	10	)	)	PUNCT
ejpam-4467	262	11	+	+	X
ejpam-4467	262	12	tb	tb	ADP
ejpam-4467	262	13	≥	≥	NOUN
ejpam-4467	262	14	lεψ(y	lεψ(y	PROPN
ejpam-4467	262	15	)	)	PUNCT
ejpam-4467	262	16	+	+	X
ejpam-4467	262	17	min{ta	min{ta	NUM
ejpam-4467	262	18	,	,	PUNCT
ejpam-4467	262	19	tb	tb	NOUN
ejpam-4467	262	20	}	}	PUNCT
ejpam-4467	262	21	>	>	X
ejpam-4467	262	22	1	1	NUM
ejpam-4467	262	23	,	,	PUNCT
ejpam-4467	262	24	which	which	PRON
ejpam-4467	262	25	implies	imply	VERB
ejpam-4467	262	26	that	that	DET
ejpam-4467	262	27	lεψ(x	lεψ(x	NOUN
ejpam-4467	262	28	)	)	PUNCT
ejpam-4467	262	29	>	>	X
ejpam-4467	263	1	1	1	NUM
ejpam-4467	263	2	−	−	PART
ejpam-4467	263	3	ta	ta	PART
ejpam-4467	263	4	≥	≥	X
ejpam-4467	263	5	ta	ta	PROPN
ejpam-4467	263	6	and	and	CCONJ
ejpam-4467	263	7	lεψ(y	lεψ(y	PROPN
ejpam-4467	263	8	)	)	PUNCT
ejpam-4467	263	9	>	>	X
ejpam-4467	263	10	1	1	NUM
ejpam-4467	263	11	−	−	NOUN
ejpam-4467	263	12	tb	tb	ADP
ejpam-4467	263	13	≥	≥	NOUN
ejpam-4467	263	14	tb	tb	NOUN
ejpam-4467	263	15	,	,	PUNCT
ejpam-4467	263	16	that	that	ADV
ejpam-4467	263	17	is	is	ADV
ejpam-4467	263	18	,	,	PUNCT
ejpam-4467	263	19	⟨x	⟨x	VERB
ejpam-4467	263	20	/	/	SYM
ejpam-4467	263	21	ta⟩	ta⟩	PROPN
ejpam-4467	263	22	∈	∈	PROPN
ejpam-4467	263	23	lεψ	lεψ	VERB
ejpam-4467	263	24	and	and	CCONJ
ejpam-4467	263	25	⟨y	⟨y	NOUN
ejpam-4467	263	26	/	/	SYM
ejpam-4467	263	27	tb⟩	tb⟩	PROPN
ejpam-4467	263	28	∈	∈	PROPN
ejpam-4467	263	29	lεψ	lεψ	ADJ
ejpam-4467	263	30	.	.	PUNCT
ejpam-4467	264	1	it	it	PRON
ejpam-4467	264	2	follows	follow	VERB
ejpam-4467	264	3	from	from	ADP
ejpam-4467	264	4	(	(	PUNCT
ejpam-4467	264	5	31	31	NUM
ejpam-4467	264	6	)	)	PUNCT
ejpam-4467	265	1	that	that	PRON
ejpam-4467	265	2	⟨((x	⟨((x	PROPN
ejpam-4467	265	3	∗	∗	NOUN
ejpam-4467	265	4	(	(	PUNCT
ejpam-4467	265	5	y	y	PROPN
ejpam-4467	265	6	∗	∗	PROPN
ejpam-4467	265	7	z	z	NOUN
ejpam-4467	265	8	)	)	PUNCT
ejpam-4467	265	9	)	)	PUNCT
ejpam-4467	265	10	∗	∗	NOUN
ejpam-4467	265	11	z)/min{ta	z)/min{ta	PROPN
ejpam-4467	265	12	,	,	PUNCT
ejpam-4467	265	13	tb}⟩	tb}⟩	X
ejpam-4467	265	14	q	q	PUNCT
ejpam-4467	265	15	lεψ	lεψ	VERB
ejpam-4467	265	16	for	for	ADP
ejpam-4467	265	17	all	all	DET
ejpam-4467	265	18	z	z	NOUN
ejpam-4467	265	19	∈	∈	NOUN
ejpam-4467	265	20	x.	x.	NOUN
ejpam-4467	265	21	hence	hence	ADV
ejpam-4467	265	22	(	(	PUNCT
ejpam-4467	265	23	x	x	SYM
ejpam-4467	265	24	∗	∗	NOUN
ejpam-4467	265	25	(	(	PUNCT
ejpam-4467	265	26	y	y	PROPN
ejpam-4467	265	27	∗	∗	PROPN
ejpam-4467	265	28	z	z	NOUN
ejpam-4467	265	29	)	)	PUNCT
ejpam-4467	265	30	)	)	PUNCT
ejpam-4467	265	31	∗	∗	NOUN
ejpam-4467	265	32	z	z	NOUN
ejpam-4467	265	33	∈	∈	PROPN
ejpam-4467	265	34	(	(	PUNCT
ejpam-4467	265	35	lεψ	lεψ	ADJ
ejpam-4467	265	36	,	,	PUNCT
ejpam-4467	265	37	min{ta	min{ta	X
ejpam-4467	265	38	,	,	PUNCT
ejpam-4467	265	39	tb})q	tb})q	PROPN
ejpam-4467	265	40	for	for	ADP
ejpam-4467	265	41	all	all	DET
ejpam-4467	265	42	z	z	NOUN
ejpam-4467	265	43	∈	∈	NOUN
ejpam-4467	265	44	x.	x.	NOUN
ejpam-4467	265	45	therefore	therefore	ADV
ejpam-4467	265	46	(	(	PUNCT
ejpam-4467	265	47	lεψ	lεψ	ADJ
ejpam-4467	265	48	,	,	PUNCT
ejpam-4467	265	49	min{ta	min{ta	X
ejpam-4467	265	50	,	,	PUNCT
ejpam-4467	265	51	tb})q	tb})q	PROPN
ejpam-4467	265	52	is	be	AUX
ejpam-4467	265	53	an	an	DET
ejpam-4467	265	54	ideal	ideal	NOUN
ejpam-4467	265	55	of	of	ADP
ejpam-4467	265	56	(	(	PUNCT
ejpam-4467	265	57	x	x	X
ejpam-4467	265	58	,	,	PUNCT
ejpam-4467	265	59	1)∗	1)∗	NUM
ejpam-4467	265	60	for	for	ADP
ejpam-4467	265	61	all	all	DET
ejpam-4467	265	62	ta	ta	PROPN
ejpam-4467	265	63	,	,	PUNCT
ejpam-4467	265	64	tb	tb	ADP
ejpam-4467	265	65	∈	∈	PROPN
ejpam-4467	265	66	(	(	PUNCT
ejpam-4467	265	67	0	0	NUM
ejpam-4467	265	68	,	,	PUNCT
ejpam-4467	265	69	0.5	0.5	NUM
ejpam-4467	265	70	]	]	PUNCT
ejpam-4467	265	71	.	.	PUNCT
ejpam-4467	266	1	theorem	theorem	VERB
ejpam-4467	266	2	11	11	NUM
ejpam-4467	266	3	.	.	PUNCT
ejpam-4467	267	1	if	if	SCONJ
ejpam-4467	267	2	a	a	DET
ejpam-4467	267	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	267	4	fuzzy	fuzzy	ADJ
ejpam-4467	267	5	set	set	VERB
ejpam-4467	267	6	lεψ	lεψ	VERB
ejpam-4467	267	7	in	in	ADP
ejpam-4467	267	8	x	x	X
ejpam-4467	267	9	satisfies	satisfie	NOUN
ejpam-4467	267	10	:	:	PUNCT
ejpam-4467	267	11	(	(	PUNCT
ejpam-4467	267	12	∀x	∀x	X
ejpam-4467	267	13	∈	∈	PROPN
ejpam-4467	267	14	x)(∀t	x)(∀t	X
ejpam-4467	267	15	∈	∈	PROPN
ejpam-4467	267	16	(	(	PUNCT
ejpam-4467	267	17	0	0	NUM
ejpam-4467	267	18	,	,	PUNCT
ejpam-4467	267	19	1	1	NUM
ejpam-4467	267	20	]	]	NUM
ejpam-4467	267	21	)	)	PUNCT
ejpam-4467	267	22	(	(	PUNCT
ejpam-4467	267	23	⟨x	⟨x	VERB
ejpam-4467	267	24	/	/	SYM
ejpam-4467	267	25	t⟩	t⟩	NOUN
ejpam-4467	267	26	∈	∈	PROPN
ejpam-4467	267	27	lεψ	lεψ	VERB
ejpam-4467	267	28	⇒	⇒	PROPN
ejpam-4467	267	29	⟨1	⟨1	PROPN
ejpam-4467	267	30	/	/	SYM
ejpam-4467	267	31	t⟩	t⟩	PRON
ejpam-4467	267	32	q	q	NOUN
ejpam-4467	267	33	lεψ	lεψ	ADJ
ejpam-4467	267	34	)	)	PUNCT
ejpam-4467	267	35	,	,	PUNCT
ejpam-4467	267	36	(	(	PUNCT
ejpam-4467	267	37	32	32	NUM
ejpam-4467	267	38	)	)	PUNCT
ejpam-4467	267	39	and	and	CCONJ
ejpam-4467	267	40	⟨(x	⟨(x	PROPN
ejpam-4467	267	41	∗	∗	NOUN
ejpam-4467	267	42	(	(	PUNCT
ejpam-4467	267	43	y	y	PROPN
ejpam-4467	267	44	∗	∗	X
ejpam-4467	267	45	z))/ta⟩	z))/ta⟩	PROPN
ejpam-4467	267	46	∈	∈	PROPN
ejpam-4467	267	47	lεψ	lεψ	VERB
ejpam-4467	267	48	,	,	PUNCT
ejpam-4467	267	49	⟨y	⟨y	AUX
ejpam-4467	267	50	/	/	SYM
ejpam-4467	267	51	tb⟩	tb⟩	PROPN
ejpam-4467	267	52	∈	∈	PROPN
ejpam-4467	267	53	lεψ	lεψ	ADJ
ejpam-4467	267	54	⇒	⇒	PROPN
ejpam-4467	267	55	⟨(x	⟨(x	PROPN
ejpam-4467	267	56	∗	∗	PROPN
ejpam-4467	267	57	z)/min{ta	z)/min{ta	PROPN
ejpam-4467	267	58	,	,	PUNCT
ejpam-4467	267	59	tb}⟩	tb}⟩	X
ejpam-4467	267	60	q	q	X
ejpam-4467	267	61	lεψ	lεψ	ADJ
ejpam-4467	267	62	(	(	PUNCT
ejpam-4467	267	63	33	33	NUM
ejpam-4467	267	64	)	)	PUNCT
ejpam-4467	267	65	for	for	ADP
ejpam-4467	267	66	all	all	DET
ejpam-4467	267	67	x	x	NOUN
ejpam-4467	267	68	,	,	PUNCT
ejpam-4467	267	69	y	y	PROPN
ejpam-4467	267	70	,	,	PUNCT
ejpam-4467	267	71	z	z	NOUN
ejpam-4467	267	72	∈	∈	PROPN
ejpam-4467	267	73	x	x	X
ejpam-4467	267	74	and	and	CCONJ
ejpam-4467	267	75	ta	ta	PROPN
ejpam-4467	267	76	,	,	PUNCT
ejpam-4467	267	77	tb	tb	ADP
ejpam-4467	267	78	∈	∈	PROPN
ejpam-4467	267	79	(	(	PUNCT
ejpam-4467	267	80	0	0	NUM
ejpam-4467	267	81	,	,	PUNCT
ejpam-4467	267	82	1	1	NUM
ejpam-4467	267	83	]	]	PUNCT
ejpam-4467	267	84	,	,	PUNCT
ejpam-4467	267	85	then	then	ADV
ejpam-4467	267	86	the	the	DET
ejpam-4467	267	87	non	non	ADJ
ejpam-4467	267	88	-	-	ADJ
ejpam-4467	267	89	empty	empty	ADJ
ejpam-4467	267	90	q	q	NOUN
ejpam-4467	267	91	-	-	PUNCT
ejpam-4467	267	92	set	set	ADJ
ejpam-4467	267	93	(	(	PUNCT
ejpam-4467	267	94	lεψ	lεψ	ADJ
ejpam-4467	267	95	,	,	PUNCT
ejpam-4467	267	96	min{ta	min{ta	X
ejpam-4467	267	97	,	,	PUNCT
ejpam-4467	267	98	tb})q	tb})q	PROPN
ejpam-4467	267	99	of	of	ADP
ejpam-4467	267	100	lεψ	lεψ	PROPN
ejpam-4467	267	101	is	be	AUX
ejpam-4467	267	102	an	an	DET
ejpam-4467	267	103	ideal	ideal	NOUN
ejpam-4467	267	104	of	of	ADP
ejpam-4467	267	105	(	(	PUNCT
ejpam-4467	267	106	x	x	X
ejpam-4467	267	107	,	,	PUNCT
ejpam-4467	267	108	1)∗	1)∗	NUM
ejpam-4467	267	109	for	for	ADP
ejpam-4467	267	110	all	all	DET
ejpam-4467	267	111	ta	ta	PROPN
ejpam-4467	267	112	,	,	PUNCT
ejpam-4467	267	113	tb	tb	ADP
ejpam-4467	267	114	∈	∈	PROPN
ejpam-4467	267	115	(	(	PUNCT
ejpam-4467	267	116	0	0	NUM
ejpam-4467	267	117	,	,	PUNCT
ejpam-4467	267	118	0.5	0.5	NUM
ejpam-4467	267	119	]	]	PUNCT
ejpam-4467	267	120	.	.	PUNCT
ejpam-4467	268	1	s.	s.	PROPN
ejpam-4467	268	2	s.	s.	PROPN
ejpam-4467	268	3	ahn	ahn	PROPN
ejpam-4467	268	4	,	,	PUNCT
ejpam-4467	268	5	e.	e.	PROPN
ejpam-4467	268	6	h.	h.	PROPN
ejpam-4467	268	7	roh	roh	PROPN
ejpam-4467	268	8	and	and	CCONJ
ejpam-4467	268	9	y.	y.	PROPN
ejpam-4467	268	10	b.	b.	PROPN
ejpam-4467	268	11	jun	jun	PROPN
ejpam-4467	268	12	/	/	SYM
ejpam-4467	268	13	eur	eur	PROPN
ejpam-4467	268	14	.	.	PUNCT
ejpam-4467	269	1	j.	j.	PROPN
ejpam-4467	269	2	pure	pure	PROPN
ejpam-4467	269	3	appl	appl	PROPN
ejpam-4467	269	4	.	.	PROPN
ejpam-4467	269	5	math	math	PROPN
ejpam-4467	269	6	,	,	PUNCT
ejpam-4467	269	7	15	15	NUM
ejpam-4467	269	8	(	(	PUNCT
ejpam-4467	269	9	3	3	NUM
ejpam-4467	269	10	)	)	PUNCT
ejpam-4467	269	11	(	(	PUNCT
ejpam-4467	269	12	2022	2022	NUM
ejpam-4467	269	13	)	)	PUNCT
ejpam-4467	269	14	,	,	PUNCT
ejpam-4467	269	15	1307	1307	NUM
ejpam-4467	269	16	-	-	SYM
ejpam-4467	269	17	1320	1320	NUM
ejpam-4467	269	18	1317	1317	NUM
ejpam-4467	269	19	proof	proof	NOUN
ejpam-4467	269	20	.	.	PUNCT
ejpam-4467	270	1	let	let	VERB
ejpam-4467	270	2	ta	ta	PART
ejpam-4467	270	3	,	,	PUNCT
ejpam-4467	270	4	tb	tb	ADP
ejpam-4467	270	5	∈	∈	PROPN
ejpam-4467	270	6	(	(	PUNCT
ejpam-4467	270	7	0	0	NUM
ejpam-4467	270	8	,	,	PUNCT
ejpam-4467	270	9	0.5	0.5	NUM
ejpam-4467	270	10	]	]	PUNCT
ejpam-4467	270	11	.	.	PUNCT
ejpam-4467	271	1	if	if	SCONJ
ejpam-4467	271	2	(	(	PUNCT
ejpam-4467	271	3	lεψ	lεψ	ADJ
ejpam-4467	271	4	,	,	PUNCT
ejpam-4467	271	5	min{ta	min{ta	X
ejpam-4467	271	6	,	,	PUNCT
ejpam-4467	271	7	tb})q	tb})q	PROPN
ejpam-4467	271	8	is	be	AUX
ejpam-4467	271	9	non	non	ADJ
ejpam-4467	271	10	-	-	ADJ
ejpam-4467	271	11	empty	empty	ADJ
ejpam-4467	271	12	,	,	PUNCT
ejpam-4467	271	13	then	then	ADV
ejpam-4467	271	14	there	there	PRON
ejpam-4467	271	15	exists	exist	VERB
ejpam-4467	271	16	x	x	X
ejpam-4467	271	17	∈	∈	PROPN
ejpam-4467	271	18	(	(	PUNCT
ejpam-4467	271	19	lεψ	lεψ	ADJ
ejpam-4467	271	20	,	,	PUNCT
ejpam-4467	271	21	min{ta	min{ta	X
ejpam-4467	271	22	,	,	PUNCT
ejpam-4467	271	23	tb})q	tb})q	PROPN
ejpam-4467	271	24	.	.	PUNCT
ejpam-4467	272	1	hence	hence	ADV
ejpam-4467	272	2	lεψ(x	lεψ(x	NOUN
ejpam-4467	272	3	)	)	PUNCT
ejpam-4467	272	4	>	>	X
ejpam-4467	273	1	1	1	NUM
ejpam-4467	273	2	−	−	NOUN
ejpam-4467	273	3	min{ta	min{ta	NOUN
ejpam-4467	273	4	,	,	PUNCT
ejpam-4467	273	5	tb	tb	ADP
ejpam-4467	273	6	}	}	PUNCT
ejpam-4467	273	7	≥	≥	X
ejpam-4467	273	8	min{ta	min{ta	NOUN
ejpam-4467	273	9	,	,	PUNCT
ejpam-4467	273	10	tb	tb	NOUN
ejpam-4467	273	11	}	}	PUNCT
ejpam-4467	273	12	,	,	PUNCT
ejpam-4467	273	13	which	which	PRON
ejpam-4467	273	14	shows	show	VERB
ejpam-4467	273	15	that	that	SCONJ
ejpam-4467	273	16	⟨x	⟨x	VERB
ejpam-4467	273	17	/	/	SYM
ejpam-4467	273	18	min{ta	min{ta	NUM
ejpam-4467	273	19	,	,	PUNCT
ejpam-4467	273	20	tb}⟩	tb}⟩	X
ejpam-4467	273	21	∈	∈	PROPN
ejpam-4467	273	22	lεψ	lεψ	ADJ
ejpam-4467	273	23	.	.	PUNCT
ejpam-4467	274	1	it	it	PRON
ejpam-4467	274	2	follows	follow	VERB
ejpam-4467	274	3	from	from	ADP
ejpam-4467	274	4	(	(	PUNCT
ejpam-4467	274	5	32	32	NUM
ejpam-4467	274	6	)	)	PUNCT
ejpam-4467	274	7	that	that	PRON
ejpam-4467	274	8	⟨1	⟨1	PROPN
ejpam-4467	274	9	/	/	SYM
ejpam-4467	274	10	min{ta	min{ta	PROPN
ejpam-4467	274	11	,	,	PUNCT
ejpam-4467	274	12	tb}⟩	tb}⟩	X
ejpam-4467	274	13	q	q	VERB
ejpam-4467	274	14	lεψ	lεψ	VERB
ejpam-4467	274	15	.	.	PUNCT
ejpam-4467	275	1	thus	thus	ADV
ejpam-4467	275	2	1	1	NUM
ejpam-4467	275	3	∈	∈	PROPN
ejpam-4467	275	4	(	(	PUNCT
ejpam-4467	275	5	lεψ	lεψ	ADJ
ejpam-4467	275	6	,	,	PUNCT
ejpam-4467	275	7	min{ta	min{ta	X
ejpam-4467	275	8	,	,	PUNCT
ejpam-4467	275	9	tb})q	tb})q	PROPN
ejpam-4467	275	10	.	.	PUNCT
ejpam-4467	276	1	let	let	VERB
ejpam-4467	276	2	x	x	PRON
ejpam-4467	276	3	,	,	PUNCT
ejpam-4467	276	4	y	y	PROPN
ejpam-4467	276	5	,	,	PUNCT
ejpam-4467	276	6	z	z	NOUN
ejpam-4467	276	7	∈	∈	PROPN
ejpam-4467	276	8	x	x	AUX
ejpam-4467	276	9	be	be	AUX
ejpam-4467	276	10	such	such	ADJ
ejpam-4467	276	11	that	that	SCONJ
ejpam-4467	276	12	x	x	SYM
ejpam-4467	276	13	∗	∗	NOUN
ejpam-4467	276	14	(	(	PUNCT
ejpam-4467	276	15	y	y	PROPN
ejpam-4467	276	16	∗	∗	PROPN
ejpam-4467	276	17	z	z	NOUN
ejpam-4467	276	18	)	)	PUNCT
ejpam-4467	276	19	∈	∈	PROPN
ejpam-4467	276	20	(	(	PUNCT
ejpam-4467	276	21	lεψ	lεψ	ADJ
ejpam-4467	276	22	,	,	PUNCT
ejpam-4467	276	23	min{ta	min{ta	X
ejpam-4467	276	24	,	,	PUNCT
ejpam-4467	276	25	tb})q	tb})q	PROPN
ejpam-4467	276	26	and	and	CCONJ
ejpam-4467	276	27	y	y	PROPN
ejpam-4467	276	28	∈	∈	PROPN
ejpam-4467	276	29	(	(	PUNCT
ejpam-4467	276	30	lεψ	lεψ	ADJ
ejpam-4467	276	31	,	,	PUNCT
ejpam-4467	276	32	min{ta	min{ta	X
ejpam-4467	276	33	,	,	PUNCT
ejpam-4467	276	34	tb})q	tb})q	PROPN
ejpam-4467	276	35	.	.	PUNCT
ejpam-4467	277	1	then	then	ADV
ejpam-4467	277	2	lεψ(x	lεψ(x	PROPN
ejpam-4467	277	3	∗	∗	NOUN
ejpam-4467	277	4	(	(	PUNCT
ejpam-4467	277	5	y	y	PROPN
ejpam-4467	277	6	∗	∗	PROPN
ejpam-4467	277	7	z	z	PROPN
ejpam-4467	277	8	)	)	PUNCT
ejpam-4467	277	9	)	)	PUNCT
ejpam-4467	277	10	>	>	X
ejpam-4467	278	1	1	1	NUM
ejpam-4467	278	2	−	−	NOUN
ejpam-4467	278	3	min{ta	min{ta	NOUN
ejpam-4467	278	4	,	,	PUNCT
ejpam-4467	278	5	tb	tb	ADP
ejpam-4467	278	6	}	}	PUNCT
ejpam-4467	278	7	≥	≥	X
ejpam-4467	278	8	min{ta	min{ta	NOUN
ejpam-4467	278	9	,	,	PUNCT
ejpam-4467	278	10	tb	tb	NOUN
ejpam-4467	278	11	}	}	PUNCT
ejpam-4467	278	12	and	and	CCONJ
ejpam-4467	278	13	lεψ(y	lεψ(y	PROPN
ejpam-4467	278	14	)	)	PUNCT
ejpam-4467	278	15	>	>	X
ejpam-4467	278	16	1−min{ta	1−min{ta	NUM
ejpam-4467	278	17	,	,	PUNCT
ejpam-4467	278	18	tb	tb	NOUN
ejpam-4467	278	19	}	}	PUNCT
ejpam-4467	278	20	≥	≥	X
ejpam-4467	278	21	min{ta	min{ta	NOUN
ejpam-4467	278	22	,	,	PUNCT
ejpam-4467	278	23	tb	tb	NOUN
ejpam-4467	278	24	}	}	PUNCT
ejpam-4467	278	25	.	.	PUNCT
ejpam-4467	279	1	thus	thus	ADV
ejpam-4467	279	2	⟨(x∗(y∗z))/min{ta	⟨(x∗(y∗z))/min{ta	VERB
ejpam-4467	279	3	,	,	PUNCT
ejpam-4467	279	4	tb}⟩	tb}⟩	X
ejpam-4467	279	5	∈	∈	PROPN
ejpam-4467	279	6	lεψ	lεψ	ADJ
ejpam-4467	279	7	and	and	CCONJ
ejpam-4467	279	8	⟨y	⟨y	NOUN
ejpam-4467	279	9	/	/	SYM
ejpam-4467	279	10	min{ta	min{ta	NUM
ejpam-4467	279	11	,	,	PUNCT
ejpam-4467	279	12	tb}⟩	tb}⟩	X
ejpam-4467	279	13	∈	∈	PROPN
ejpam-4467	279	14	lεψ	lεψ	ADJ
ejpam-4467	279	15	.	.	PUNCT
ejpam-4467	280	1	it	it	PRON
ejpam-4467	280	2	follows	follow	VERB
ejpam-4467	280	3	from	from	ADP
ejpam-4467	280	4	(	(	PUNCT
ejpam-4467	280	5	33	33	NUM
ejpam-4467	280	6	)	)	PUNCT
ejpam-4467	280	7	that	that	PRON
ejpam-4467	280	8	⟨(x∗z)/min{ta	⟨(x∗z)/min{ta	PROPN
ejpam-4467	280	9	,	,	PUNCT
ejpam-4467	280	10	tb}⟩	tb}⟩	X
ejpam-4467	280	11	q	q	VERB
ejpam-4467	280	12	lεψ	lεψ	ADJ
ejpam-4467	280	13	,	,	PUNCT
ejpam-4467	280	14	i.e.	i.e.	X
ejpam-4467	280	15	,	,	PUNCT
ejpam-4467	280	16	x∗z	x∗z	PUNCT
ejpam-4467	280	17	∈	∈	PROPN
ejpam-4467	280	18	(	(	PUNCT
ejpam-4467	280	19	lεψ	lεψ	ADJ
ejpam-4467	280	20	,	,	PUNCT
ejpam-4467	280	21	min{ta	min{ta	X
ejpam-4467	280	22	,	,	PUNCT
ejpam-4467	280	23	tb})q	tb})q	PROPN
ejpam-4467	280	24	.	.	PUNCT
ejpam-4467	281	1	therefore	therefore	ADV
ejpam-4467	281	2	(	(	PUNCT
ejpam-4467	281	3	lεψ	lεψ	ADJ
ejpam-4467	281	4	,	,	PUNCT
ejpam-4467	281	5	min{ta	min{ta	X
ejpam-4467	281	6	,	,	PUNCT
ejpam-4467	281	7	tb})q	tb})q	PROPN
ejpam-4467	281	8	is	be	AUX
ejpam-4467	281	9	an	an	DET
ejpam-4467	281	10	ideal	ideal	NOUN
ejpam-4467	281	11	of	of	ADP
ejpam-4467	281	12	(	(	PUNCT
ejpam-4467	281	13	x	x	X
ejpam-4467	281	14	,	,	PUNCT
ejpam-4467	281	15	1)∗	1)∗	NUM
ejpam-4467	281	16	by	by	ADP
ejpam-4467	281	17	lemma	lemma	PROPN
ejpam-4467	281	18	1	1	NUM
ejpam-4467	281	19	.	.	PUNCT
ejpam-4467	281	20	theorem	theorem	NOUN
ejpam-4467	281	21	12	12	NUM
ejpam-4467	281	22	.	.	PUNCT
ejpam-4467	282	1	if	if	SCONJ
ejpam-4467	282	2	a	a	DET
ejpam-4467	282	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	282	4	fuzzy	fuzzy	ADJ
ejpam-4467	282	5	set	set	VERB
ejpam-4467	282	6	lεψ	lεψ	VERB
ejpam-4467	282	7	in	in	ADP
ejpam-4467	282	8	x	x	X
ejpam-4467	282	9	satisfies	satisfie	NOUN
ejpam-4467	282	10	(	(	PUNCT
ejpam-4467	282	11	27	27	NUM
ejpam-4467	282	12	)	)	PUNCT
ejpam-4467	282	13	and	and	CCONJ
ejpam-4467	282	14	(	(	PUNCT
ejpam-4467	282	15	29	29	NUM
ejpam-4467	282	16	)	)	PUNCT
ejpam-4467	282	17	for	for	ADP
ejpam-4467	282	18	all	all	DET
ejpam-4467	282	19	x	x	NOUN
ejpam-4467	282	20	,	,	PUNCT
ejpam-4467	282	21	y	y	PROPN
ejpam-4467	282	22	,	,	PUNCT
ejpam-4467	282	23	z	z	NOUN
ejpam-4467	282	24	∈	∈	PROPN
ejpam-4467	282	25	x	x	X
ejpam-4467	282	26	and	and	CCONJ
ejpam-4467	282	27	t	t	PROPN
ejpam-4467	282	28	,	,	PUNCT
ejpam-4467	282	29	ta	ta	X
ejpam-4467	282	30	,	,	PUNCT
ejpam-4467	282	31	tb	tb	ADP
ejpam-4467	282	32	∈	∈	PROPN
ejpam-4467	282	33	(	(	PUNCT
ejpam-4467	282	34	0.5	0.5	NUM
ejpam-4467	282	35	,	,	PUNCT
ejpam-4467	282	36	1	1	NUM
ejpam-4467	282	37	]	]	PUNCT
ejpam-4467	282	38	,	,	PUNCT
ejpam-4467	282	39	then	then	ADV
ejpam-4467	282	40	the	the	DET
ejpam-4467	282	41	q	q	NOUN
ejpam-4467	282	42	-	-	PUNCT
ejpam-4467	282	43	set	set	ADJ
ejpam-4467	282	44	(	(	PUNCT
ejpam-4467	282	45	lεψ	lεψ	ADJ
ejpam-4467	282	46	,	,	PUNCT
ejpam-4467	282	47	t)q	t)q	PRON
ejpam-4467	282	48	of	of	ADP
ejpam-4467	282	49	lεψ	lεψ	ADJ
ejpam-4467	282	50	is	be	AUX
ejpam-4467	282	51	an	an	DET
ejpam-4467	282	52	ideal	ideal	NOUN
ejpam-4467	282	53	of	of	ADP
ejpam-4467	282	54	(	(	PUNCT
ejpam-4467	282	55	x	x	X
ejpam-4467	282	56	,	,	PUNCT
ejpam-4467	282	57	1)∗	1)∗	NUM
ejpam-4467	282	58	for	for	ADP
ejpam-4467	282	59	all	all	DET
ejpam-4467	282	60	t	t	NOUN
ejpam-4467	282	61	∈	∈	PROPN
ejpam-4467	282	62	(	(	PUNCT
ejpam-4467	282	63	0.5	0.5	NUM
ejpam-4467	282	64	,	,	PUNCT
ejpam-4467	282	65	1	1	NUM
ejpam-4467	282	66	]	]	PUNCT
ejpam-4467	282	67	.	.	PUNCT
ejpam-4467	283	1	proof	proof	NOUN
ejpam-4467	283	2	.	.	PUNCT
ejpam-4467	284	1	assume	assume	VERB
ejpam-4467	284	2	that	that	SCONJ
ejpam-4467	284	3	lεψ	lεψ	ADJ
ejpam-4467	284	4	satisfies	satisfie	NOUN
ejpam-4467	284	5	(	(	PUNCT
ejpam-4467	284	6	27	27	NUM
ejpam-4467	284	7	)	)	PUNCT
ejpam-4467	284	8	and	and	CCONJ
ejpam-4467	284	9	(	(	PUNCT
ejpam-4467	284	10	29	29	NUM
ejpam-4467	284	11	)	)	PUNCT
ejpam-4467	284	12	for	for	ADP
ejpam-4467	284	13	all	all	DET
ejpam-4467	284	14	x	x	NOUN
ejpam-4467	284	15	,	,	PUNCT
ejpam-4467	284	16	y	y	PROPN
ejpam-4467	284	17	,	,	PUNCT
ejpam-4467	284	18	z	z	NOUN
ejpam-4467	284	19	∈	∈	PROPN
ejpam-4467	284	20	x	x	X
ejpam-4467	284	21	and	and	CCONJ
ejpam-4467	284	22	t	t	PROPN
ejpam-4467	284	23	,	,	PUNCT
ejpam-4467	284	24	ta	ta	X
ejpam-4467	284	25	,	,	PUNCT
ejpam-4467	284	26	tb	tb	ADP
ejpam-4467	284	27	∈	∈	PROPN
ejpam-4467	284	28	(	(	PUNCT
ejpam-4467	284	29	0.5	0.5	NUM
ejpam-4467	284	30	,	,	PUNCT
ejpam-4467	284	31	1	1	NUM
ejpam-4467	284	32	]	]	PUNCT
ejpam-4467	284	33	.	.	PUNCT
ejpam-4467	285	1	the	the	DET
ejpam-4467	285	2	condition	condition	NOUN
ejpam-4467	285	3	(	(	PUNCT
ejpam-4467	285	4	27	27	NUM
ejpam-4467	285	5	)	)	PUNCT
ejpam-4467	285	6	induces	induce	VERB
ejpam-4467	285	7	lψ(1	lψ(1	NOUN
ejpam-4467	285	8	)	)	PUNCT
ejpam-4467	285	9	+	+	NOUN
ejpam-4467	285	10	t	t	PROPN
ejpam-4467	285	11	≥	≥	NUM
ejpam-4467	285	12	2	2	NUM
ejpam-4467	285	13	t	t	NOUN
ejpam-4467	285	14	>	>	X
ejpam-4467	285	15	1	1	NUM
ejpam-4467	285	16	,	,	PUNCT
ejpam-4467	285	17	i.e.	i.e.	X
ejpam-4467	285	18	,	,	PUNCT
ejpam-4467	285	19	⟨1	⟨1	PROPN
ejpam-4467	285	20	/	/	SYM
ejpam-4467	285	21	t⟩	t⟩	PRON
ejpam-4467	285	22	q	q	X
ejpam-4467	285	23	lεψ	lεψ	ADJ
ejpam-4467	285	24	.	.	PUNCT
ejpam-4467	286	1	hence	hence	ADV
ejpam-4467	286	2	1	1	NUM
ejpam-4467	286	3	∈	∈	PROPN
ejpam-4467	286	4	(	(	PUNCT
ejpam-4467	286	5	lεψ	lεψ	ADJ
ejpam-4467	286	6	,	,	PUNCT
ejpam-4467	286	7	t)q	t)q	PUNCT
ejpam-4467	286	8	.	.	PUNCT
ejpam-4467	287	1	let	let	VERB
ejpam-4467	287	2	x	x	PRON
ejpam-4467	287	3	,	,	PUNCT
ejpam-4467	287	4	y	y	PROPN
ejpam-4467	287	5	,	,	PUNCT
ejpam-4467	287	6	z	z	NOUN
ejpam-4467	287	7	∈	∈	PROPN
ejpam-4467	287	8	x	x	AUX
ejpam-4467	287	9	be	be	AUX
ejpam-4467	287	10	such	such	ADJ
ejpam-4467	287	11	that	that	SCONJ
ejpam-4467	287	12	x	x	SYM
ejpam-4467	287	13	∗	∗	NOUN
ejpam-4467	287	14	(	(	PUNCT
ejpam-4467	287	15	y	y	PROPN
ejpam-4467	287	16	∗	∗	PROPN
ejpam-4467	287	17	z	z	NOUN
ejpam-4467	287	18	)	)	PUNCT
ejpam-4467	287	19	∈	∈	PROPN
ejpam-4467	287	20	(	(	PUNCT
ejpam-4467	287	21	lεψ	lεψ	ADJ
ejpam-4467	287	22	,	,	PUNCT
ejpam-4467	287	23	t)q	t)q	PUNCT
ejpam-4467	287	24	and	and	CCONJ
ejpam-4467	287	25	y	y	PROPN
ejpam-4467	287	26	∈	∈	PROPN
ejpam-4467	287	27	(	(	PUNCT
ejpam-4467	287	28	lεψ	lεψ	ADJ
ejpam-4467	287	29	,	,	PUNCT
ejpam-4467	287	30	t)q	t)q	PUNCT
ejpam-4467	287	31	.	.	PUNCT
ejpam-4467	288	1	then	then	ADV
ejpam-4467	288	2	⟨(x	⟨(x	VERB
ejpam-4467	288	3	∗	∗	NOUN
ejpam-4467	288	4	(	(	PUNCT
ejpam-4467	288	5	y	y	NOUN
ejpam-4467	288	6	∗	∗	NOUN
ejpam-4467	288	7	z))/t⟩	z))/t⟩	PROPN
ejpam-4467	288	8	q	q	PUNCT
ejpam-4467	288	9	lεψ	lεψ	ADJ
ejpam-4467	288	10	and	and	CCONJ
ejpam-4467	288	11	⟨y	⟨y	NOUN
ejpam-4467	288	12	/	/	SYM
ejpam-4467	288	13	t⟩	t⟩	PRON
ejpam-4467	288	14	q	q	X
ejpam-4467	288	15	lεψ	lεψ	ADJ
ejpam-4467	288	16	.	.	PUNCT
ejpam-4467	289	1	it	it	PRON
ejpam-4467	289	2	follows	follow	VERB
ejpam-4467	289	3	from	from	ADP
ejpam-4467	289	4	(	(	PUNCT
ejpam-4467	289	5	29	29	NUM
ejpam-4467	289	6	)	)	PUNCT
ejpam-4467	289	7	that	that	PRON
ejpam-4467	289	8	x	x	X
ejpam-4467	289	9	∗	∗	NOUN
ejpam-4467	289	10	z	z	NOUN
ejpam-4467	289	11	∈	∈	PROPN
ejpam-4467	289	12	(	(	PUNCT
ejpam-4467	289	13	lεψ	lεψ	PROPN
ejpam-4467	289	14	,	,	PUNCT
ejpam-4467	289	15	min{t	min{t	PROPN
ejpam-4467	289	16	,	,	PUNCT
ejpam-4467	289	17	t})∈	t})∈	NOUN
ejpam-4467	289	18	=	=	PUNCT
ejpam-4467	289	19	(	(	PUNCT
ejpam-4467	289	20	lεψ	lεψ	ADJ
ejpam-4467	289	21	,	,	PUNCT
ejpam-4467	289	22	t)∈.	t)∈.	PROPN
ejpam-4467	289	23	hence	hence	ADV
ejpam-4467	289	24	lεψ(x	lεψ(x	PROPN
ejpam-4467	289	25	∗	∗	NOUN
ejpam-4467	289	26	z	z	NOUN
ejpam-4467	289	27	)	)	PUNCT
ejpam-4467	289	28	≥	≥	PROPN
ejpam-4467	289	29	t	t	X
ejpam-4467	289	30	>	>	X
ejpam-4467	289	31	1	1	NUM
ejpam-4467	289	32	−	−	PROPN
ejpam-4467	289	33	t	t	PROPN
ejpam-4467	289	34	,	,	PUNCT
ejpam-4467	289	35	that	that	ADV
ejpam-4467	289	36	is	is	ADV
ejpam-4467	289	37	,	,	PUNCT
ejpam-4467	289	38	x	x	X
ejpam-4467	289	39	∗	∗	NOUN
ejpam-4467	289	40	z	z	NOUN
ejpam-4467	289	41	∈	∈	PROPN
ejpam-4467	289	42	(	(	PUNCT
ejpam-4467	289	43	lεψ	lεψ	ADJ
ejpam-4467	289	44	,	,	PUNCT
ejpam-4467	289	45	t)q	t)q	PUNCT
ejpam-4467	289	46	.	.	PUNCT
ejpam-4467	290	1	therefore	therefore	ADV
ejpam-4467	290	2	(	(	PUNCT
ejpam-4467	290	3	lεψ	lεψ	ADJ
ejpam-4467	290	4	,	,	PUNCT
ejpam-4467	290	5	t)q	t)q	PRON
ejpam-4467	290	6	is	be	AUX
ejpam-4467	290	7	an	an	DET
ejpam-4467	290	8	ideal	ideal	NOUN
ejpam-4467	290	9	of	of	ADP
ejpam-4467	290	10	(	(	PUNCT
ejpam-4467	290	11	x	x	X
ejpam-4467	290	12	,	,	PUNCT
ejpam-4467	290	13	1)∗	1)∗	NUM
ejpam-4467	290	14	for	for	ADP
ejpam-4467	290	15	all	all	DET
ejpam-4467	290	16	t	t	NOUN
ejpam-4467	290	17	∈	∈	PROPN
ejpam-4467	290	18	(	(	PUNCT
ejpam-4467	290	19	0.5	0.5	NUM
ejpam-4467	290	20	,	,	PUNCT
ejpam-4467	290	21	1	1	NUM
ejpam-4467	290	22	]	]	PUNCT
ejpam-4467	290	23	by	by	ADP
ejpam-4467	290	24	lemma	lemma	PROPN
ejpam-4467	290	25	1	1	NUM
ejpam-4467	290	26	.	.	PUNCT
ejpam-4467	290	27	theorem	theorem	VERB
ejpam-4467	290	28	13	13	NUM
ejpam-4467	290	29	.	.	PUNCT
ejpam-4467	291	1	if	if	SCONJ
ejpam-4467	291	2	a	a	DET
ejpam-4467	291	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	291	4	fuzzy	fuzzy	ADJ
ejpam-4467	291	5	set	set	VERB
ejpam-4467	291	6	lεψ	lεψ	VERB
ejpam-4467	291	7	in	in	ADP
ejpam-4467	291	8	x	x	X
ejpam-4467	291	9	satisfies	satisfie	NOUN
ejpam-4467	291	10	(	(	PUNCT
ejpam-4467	291	11	28	28	NUM
ejpam-4467	291	12	)	)	PUNCT
ejpam-4467	291	13	for	for	ADP
ejpam-4467	291	14	all	all	DET
ejpam-4467	291	15	x	x	NOUN
ejpam-4467	291	16	,	,	PUNCT
ejpam-4467	291	17	y	y	PROPN
ejpam-4467	291	18	,	,	PUNCT
ejpam-4467	291	19	z	z	NOUN
ejpam-4467	291	20	∈	∈	PROPN
ejpam-4467	291	21	x	x	X
ejpam-4467	291	22	and	and	CCONJ
ejpam-4467	291	23	ta	ta	PROPN
ejpam-4467	291	24	,	,	PUNCT
ejpam-4467	291	25	tb	tb	ADP
ejpam-4467	291	26	∈	∈	PROPN
ejpam-4467	291	27	(	(	PUNCT
ejpam-4467	291	28	0.5	0.5	NUM
ejpam-4467	291	29	,	,	PUNCT
ejpam-4467	291	30	1	1	NUM
ejpam-4467	291	31	]	]	PUNCT
ejpam-4467	291	32	,	,	PUNCT
ejpam-4467	291	33	and	and	CCONJ
ejpam-4467	291	34	(	(	PUNCT
ejpam-4467	291	35	∀x	∀x	X
ejpam-4467	291	36	,	,	PUNCT
ejpam-4467	291	37	y	y	PROPN
ejpam-4467	291	38	∈	∈	PROPN
ejpam-4467	291	39	x)(∀t	x)(∀t	PROPN
ejpam-4467	291	40	∈	∈	PROPN
ejpam-4467	291	41	(	(	PUNCT
ejpam-4467	291	42	0.5	0.5	NUM
ejpam-4467	291	43	,	,	PUNCT
ejpam-4467	291	44	1	1	NUM
ejpam-4467	291	45	]	]	NUM
ejpam-4467	291	46	)	)	PUNCT
ejpam-4467	291	47	(	(	PUNCT
ejpam-4467	291	48	⟨y	⟨y	X
ejpam-4467	291	49	/	/	SYM
ejpam-4467	291	50	t⟩	t⟩	PRON
ejpam-4467	291	51	q	q	X
ejpam-4467	291	52	lεψ	lεψ	ADJ
ejpam-4467	291	53	⇒	⇒	PROPN
ejpam-4467	291	54	⟨(x	⟨(x	PROPN
ejpam-4467	291	55	∗	∗	NOUN
ejpam-4467	291	56	y)/t⟩	y)/t⟩	PUNCT
ejpam-4467	292	1	∈	∈	PROPN
ejpam-4467	292	2	lεψ	lεψ	VERB
ejpam-4467	292	3	)	)	PUNCT
ejpam-4467	292	4	,	,	PUNCT
ejpam-4467	292	5	(	(	PUNCT
ejpam-4467	292	6	34	34	NUM
ejpam-4467	292	7	)	)	PUNCT
ejpam-4467	292	8	then	then	ADV
ejpam-4467	292	9	the	the	DET
ejpam-4467	292	10	q	q	NOUN
ejpam-4467	292	11	-	-	PUNCT
ejpam-4467	292	12	set	set	ADJ
ejpam-4467	292	13	(	(	PUNCT
ejpam-4467	292	14	lεψ	lεψ	ADJ
ejpam-4467	292	15	,	,	PUNCT
ejpam-4467	292	16	t)q	t)q	PRON
ejpam-4467	292	17	of	of	ADP
ejpam-4467	292	18	lεψ	lεψ	ADJ
ejpam-4467	292	19	is	be	AUX
ejpam-4467	292	20	an	an	DET
ejpam-4467	292	21	ideal	ideal	NOUN
ejpam-4467	292	22	of	of	ADP
ejpam-4467	292	23	(	(	PUNCT
ejpam-4467	292	24	x	x	X
ejpam-4467	292	25	,	,	PUNCT
ejpam-4467	292	26	1)∗	1)∗	NUM
ejpam-4467	292	27	for	for	ADP
ejpam-4467	292	28	all	all	DET
ejpam-4467	292	29	t	t	NOUN
ejpam-4467	292	30	∈	∈	PROPN
ejpam-4467	292	31	(	(	PUNCT
ejpam-4467	292	32	0.5	0.5	NUM
ejpam-4467	292	33	,	,	PUNCT
ejpam-4467	292	34	1	1	NUM
ejpam-4467	292	35	]	]	PUNCT
ejpam-4467	292	36	.	.	PUNCT
ejpam-4467	293	1	proof	proof	NOUN
ejpam-4467	293	2	.	.	PUNCT
ejpam-4467	294	1	let	let	VERB
ejpam-4467	294	2	x	x	PRON
ejpam-4467	294	3	,	,	PUNCT
ejpam-4467	294	4	y	y	PROPN
ejpam-4467	294	5	∈	∈	PROPN
ejpam-4467	294	6	x	x	X
ejpam-4467	294	7	and	and	CCONJ
ejpam-4467	294	8	t	t	PROPN
ejpam-4467	294	9	∈	∈	PROPN
ejpam-4467	294	10	(	(	PUNCT
ejpam-4467	294	11	0.5	0.5	NUM
ejpam-4467	294	12	,	,	PUNCT
ejpam-4467	294	13	1	1	NUM
ejpam-4467	294	14	]	]	PUNCT
ejpam-4467	294	15	be	be	AUX
ejpam-4467	294	16	such	such	ADJ
ejpam-4467	294	17	that	that	SCONJ
ejpam-4467	294	18	y	y	PROPN
ejpam-4467	294	19	∈	∈	PROPN
ejpam-4467	294	20	(	(	PUNCT
ejpam-4467	294	21	lεψ	lεψ	ADJ
ejpam-4467	294	22	,	,	PUNCT
ejpam-4467	294	23	t)q	t)q	PUNCT
ejpam-4467	294	24	.	.	PUNCT
ejpam-4467	295	1	then	then	ADV
ejpam-4467	295	2	⟨y	⟨y	NOUN
ejpam-4467	295	3	/	/	SYM
ejpam-4467	295	4	t⟩	t⟩	PRON
ejpam-4467	295	5	q	q	X
ejpam-4467	295	6	lεψ	lεψ	ADJ
ejpam-4467	295	7	,	,	PUNCT
ejpam-4467	295	8	and	and	CCONJ
ejpam-4467	295	9	so	so	ADV
ejpam-4467	295	10	⟨(x	⟨(x	NOUN
ejpam-4467	295	11	∗	∗	NOUN
ejpam-4467	295	12	y)/t⟩	y)/t⟩	PUNCT
ejpam-4467	296	1	∈	∈	PROPN
ejpam-4467	296	2	lεψ	lεψ	VERB
ejpam-4467	296	3	by	by	ADP
ejpam-4467	296	4	(	(	PUNCT
ejpam-4467	296	5	34	34	NUM
ejpam-4467	296	6	)	)	PUNCT
ejpam-4467	296	7	.	.	PUNCT
ejpam-4467	297	1	thus	thus	ADV
ejpam-4467	297	2	lεψ(x	lεψ(x	PROPN
ejpam-4467	297	3	∗	∗	NOUN
ejpam-4467	297	4	y	y	PROPN
ejpam-4467	297	5	)	)	PUNCT
ejpam-4467	297	6	≥	≥	PROPN
ejpam-4467	297	7	t	t	X
ejpam-4467	297	8	>	>	X
ejpam-4467	297	9	1	1	NUM
ejpam-4467	297	10	−	−	PROPN
ejpam-4467	297	11	t	t	PROPN
ejpam-4467	297	12	,	,	PUNCT
ejpam-4467	297	13	that	that	ADV
ejpam-4467	297	14	is	is	ADV
ejpam-4467	297	15	,	,	PUNCT
ejpam-4467	297	16	⟨(x	⟨(x	PROPN
ejpam-4467	297	17	∗	∗	NOUN
ejpam-4467	297	18	y)/t⟩	y)/t⟩	PROPN
ejpam-4467	298	1	q	q	PROPN
ejpam-4467	298	2	lεψ	lεψ	ADJ
ejpam-4467	298	3	.	.	PUNCT
ejpam-4467	299	1	hence	hence	ADV
ejpam-4467	299	2	x	x	X
ejpam-4467	299	3	∗	∗	VERB
ejpam-4467	299	4	y	y	PROPN
ejpam-4467	299	5	∈	∈	PROPN
ejpam-4467	299	6	(	(	PUNCT
ejpam-4467	299	7	lεψ	lεψ	ADJ
ejpam-4467	299	8	,	,	PUNCT
ejpam-4467	299	9	t)q	t)q	PUNCT
ejpam-4467	299	10	.	.	PUNCT
ejpam-4467	300	1	let	let	VERB
ejpam-4467	300	2	x	x	PRON
ejpam-4467	300	3	,	,	PUNCT
ejpam-4467	300	4	y	y	PROPN
ejpam-4467	300	5	∈	∈	PROPN
ejpam-4467	300	6	x	x	X
ejpam-4467	300	7	and	and	CCONJ
ejpam-4467	300	8	t	t	PROPN
ejpam-4467	300	9	∈	∈	PROPN
ejpam-4467	300	10	(	(	PUNCT
ejpam-4467	300	11	0.5	0.5	NUM
ejpam-4467	300	12	,	,	PUNCT
ejpam-4467	300	13	1	1	NUM
ejpam-4467	300	14	]	]	PUNCT
ejpam-4467	300	15	be	be	AUX
ejpam-4467	300	16	such	such	ADJ
ejpam-4467	300	17	that	that	SCONJ
ejpam-4467	300	18	x	x	SYM
ejpam-4467	300	19	∈	∈	PROPN
ejpam-4467	300	20	(	(	PUNCT
ejpam-4467	300	21	lεψ	lεψ	ADJ
ejpam-4467	300	22	,	,	PUNCT
ejpam-4467	300	23	t)q	t)q	PUNCT
ejpam-4467	300	24	and	and	CCONJ
ejpam-4467	300	25	y	y	PROPN
ejpam-4467	300	26	∈	∈	PROPN
ejpam-4467	300	27	(	(	PUNCT
ejpam-4467	300	28	lεψ	lεψ	ADJ
ejpam-4467	300	29	,	,	PUNCT
ejpam-4467	300	30	t)q	t)q	PUNCT
ejpam-4467	300	31	.	.	PUNCT
ejpam-4467	301	1	then	then	ADV
ejpam-4467	301	2	lεψ(x	lεψ(x	PROPN
ejpam-4467	301	3	)	)	PUNCT
ejpam-4467	301	4	≥	≥	PROPN
ejpam-4467	302	1	t	t	X
ejpam-4467	302	2	>	>	X
ejpam-4467	302	3	1	1	NUM
ejpam-4467	302	4	−	−	PROPN
ejpam-4467	302	5	t	t	PROPN
ejpam-4467	302	6	and	and	CCONJ
ejpam-4467	302	7	lεψ(y	lεψ(y	PROPN
ejpam-4467	302	8	)	)	PUNCT
ejpam-4467	302	9	≥	≥	NOUN
ejpam-4467	302	10	t	t	X
ejpam-4467	302	11	>	>	X
ejpam-4467	302	12	1	1	NUM
ejpam-4467	302	13	−	−	PROPN
ejpam-4467	302	14	t	t	PROPN
ejpam-4467	302	15	,	,	PUNCT
ejpam-4467	302	16	i.e.	i.e.	X
ejpam-4467	302	17	,	,	PUNCT
ejpam-4467	302	18	⟨x	⟨x	VERB
ejpam-4467	302	19	/	/	SYM
ejpam-4467	302	20	t⟩	t⟩	PRON
ejpam-4467	302	21	q	q	NOUN
ejpam-4467	302	22	lεψ	lεψ	ADJ
ejpam-4467	302	23	and	and	CCONJ
ejpam-4467	302	24	⟨y	⟨y	NOUN
ejpam-4467	302	25	/	/	SYM
ejpam-4467	302	26	t⟩	t⟩	PRON
ejpam-4467	302	27	q	q	X
ejpam-4467	302	28	lεψ	lεψ	ADJ
ejpam-4467	302	29	.	.	PUNCT
ejpam-4467	303	1	it	it	PRON
ejpam-4467	303	2	follows	follow	VERB
ejpam-4467	303	3	from	from	ADP
ejpam-4467	303	4	(	(	PUNCT
ejpam-4467	303	5	28	28	NUM
ejpam-4467	303	6	)	)	PUNCT
ejpam-4467	303	7	that	that	PRON
ejpam-4467	303	8	⟨((x	⟨((x	PROPN
ejpam-4467	303	9	∗	∗	NOUN
ejpam-4467	303	10	(	(	PUNCT
ejpam-4467	303	11	y	y	PROPN
ejpam-4467	303	12	∗	∗	PROPN
ejpam-4467	303	13	z	z	NOUN
ejpam-4467	303	14	)	)	PUNCT
ejpam-4467	303	15	)	)	PUNCT
ejpam-4467	303	16	∗	∗	NOUN
ejpam-4467	303	17	z)/t⟩	z)/t⟩	NOUN
ejpam-4467	304	1	=	=	SYM
ejpam-4467	305	1	⟨((x	⟨((x	PROPN
ejpam-4467	305	2	∗	∗	NOUN
ejpam-4467	305	3	(	(	PUNCT
ejpam-4467	305	4	y	y	PROPN
ejpam-4467	305	5	∗	∗	PROPN
ejpam-4467	305	6	z	z	NOUN
ejpam-4467	305	7	)	)	PUNCT
ejpam-4467	305	8	)	)	PUNCT
ejpam-4467	305	9	∗	∗	NOUN
ejpam-4467	305	10	z)/min{t	z)/min{t	PROPN
ejpam-4467	305	11	,	,	PUNCT
ejpam-4467	305	12	t}⟩	t}⟩	PROPN
ejpam-4467	305	13	q	q	PUNCT
ejpam-4467	305	14	lεψ	lεψ	ADJ
ejpam-4467	305	15	.	.	PUNCT
ejpam-4467	306	1	this	this	PRON
ejpam-4467	306	2	shows	show	VERB
ejpam-4467	306	3	that	that	SCONJ
ejpam-4467	306	4	(	(	PUNCT
ejpam-4467	306	5	x	x	SYM
ejpam-4467	306	6	∗	∗	NOUN
ejpam-4467	306	7	(	(	PUNCT
ejpam-4467	306	8	y	y	PROPN
ejpam-4467	306	9	∗	∗	PROPN
ejpam-4467	306	10	z	z	NOUN
ejpam-4467	306	11	)	)	PUNCT
ejpam-4467	306	12	)	)	PUNCT
ejpam-4467	306	13	∗	∗	NOUN
ejpam-4467	306	14	z	z	NOUN
ejpam-4467	306	15	∈	∈	PROPN
ejpam-4467	306	16	(	(	PUNCT
ejpam-4467	306	17	lεψ	lεψ	ADJ
ejpam-4467	306	18	,	,	PUNCT
ejpam-4467	306	19	t)q	t)q	PUNCT
ejpam-4467	306	20	.	.	PUNCT
ejpam-4467	307	1	therefore	therefore	ADV
ejpam-4467	307	2	the	the	DET
ejpam-4467	307	3	q	q	NOUN
ejpam-4467	307	4	-	-	PUNCT
ejpam-4467	307	5	set	set	ADJ
ejpam-4467	307	6	(	(	PUNCT
ejpam-4467	307	7	lεψ	lεψ	ADJ
ejpam-4467	307	8	,	,	PUNCT
ejpam-4467	307	9	t)q	t)q	PRON
ejpam-4467	307	10	of	of	ADP
ejpam-4467	307	11	lεψ	lεψ	ADJ
ejpam-4467	307	12	is	be	AUX
ejpam-4467	307	13	an	an	DET
ejpam-4467	307	14	ideal	ideal	NOUN
ejpam-4467	307	15	of	of	ADP
ejpam-4467	307	16	(	(	PUNCT
ejpam-4467	307	17	x	x	X
ejpam-4467	307	18	,	,	PUNCT
ejpam-4467	307	19	1)∗	1)∗	NUM
ejpam-4467	307	20	for	for	ADP
ejpam-4467	307	21	all	all	DET
ejpam-4467	307	22	t	t	NOUN
ejpam-4467	307	23	∈	∈	PROPN
ejpam-4467	307	24	(	(	PUNCT
ejpam-4467	307	25	0.5	0.5	NUM
ejpam-4467	307	26	,	,	PUNCT
ejpam-4467	307	27	1	1	NUM
ejpam-4467	307	28	]	]	PUNCT
ejpam-4467	307	29	.	.	PUNCT
ejpam-4467	308	1	theorem	theorem	PROPN
ejpam-4467	308	2	14	14	NUM
ejpam-4467	308	3	.	.	PUNCT
ejpam-4467	309	1	if	if	SCONJ
ejpam-4467	309	2	ψ	ψ	NOUN
ejpam-4467	309	3	is	be	AUX
ejpam-4467	309	4	a	a	DET
ejpam-4467	309	5	fuzzy	fuzzy	ADJ
ejpam-4467	309	6	ideal	ideal	NOUN
ejpam-4467	309	7	of	of	ADP
ejpam-4467	309	8	(	(	PUNCT
ejpam-4467	309	9	x	x	X
ejpam-4467	309	10	,	,	PUNCT
ejpam-4467	309	11	1)∗	1)∗	NUM
ejpam-4467	309	12	,	,	PUNCT
ejpam-4467	309	13	then	then	ADV
ejpam-4467	309	14	the	the	DET
ejpam-4467	309	15	non	non	ADJ
ejpam-4467	309	16	-	-	ADJ
ejpam-4467	309	17	empty	empty	ADJ
ejpam-4467	309	18	o	o	NOUN
ejpam-4467	309	19	-	-	NOUN
ejpam-4467	309	20	set	set	NOUN
ejpam-4467	309	21	of	of	ADP
ejpam-4467	309	22	lεψ	lεψ	PROPN
ejpam-4467	309	23	is	be	AUX
ejpam-4467	309	24	an	an	DET
ejpam-4467	309	25	ideal	ideal	NOUN
ejpam-4467	309	26	of	of	ADP
ejpam-4467	309	27	(	(	PUNCT
ejpam-4467	309	28	x	x	X
ejpam-4467	309	29	,	,	PUNCT
ejpam-4467	309	30	1)∗.	1)∗.	PRON
ejpam-4467	309	31	proof	proof	NOUN
ejpam-4467	309	32	.	.	PUNCT
ejpam-4467	310	1	if	if	SCONJ
ejpam-4467	310	2	ψ	ψ	NOUN
ejpam-4467	310	3	is	be	AUX
ejpam-4467	310	4	a	a	DET
ejpam-4467	310	5	fuzzy	fuzzy	ADJ
ejpam-4467	310	6	ideal	ideal	NOUN
ejpam-4467	310	7	of	of	ADP
ejpam-4467	310	8	(	(	PUNCT
ejpam-4467	310	9	x	x	X
ejpam-4467	310	10	,	,	PUNCT
ejpam-4467	310	11	1)∗	1)∗	NUM
ejpam-4467	310	12	,	,	PUNCT
ejpam-4467	310	13	then	then	ADV
ejpam-4467	310	14	lεψ	lεψ	ADJ
ejpam-4467	310	15	is	be	AUX
ejpam-4467	310	16	a	a	DET
ejpam-4467	310	17	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	310	18	fuzzy	fuzzy	ADJ
ejpam-4467	310	19	ideal	ideal	NOUN
ejpam-4467	310	20	of	of	ADP
ejpam-4467	310	21	(	(	PUNCT
ejpam-4467	310	22	x	x	X
ejpam-4467	310	23	,	,	PUNCT
ejpam-4467	310	24	1)∗	1)∗	NUM
ejpam-4467	310	25	(	(	PUNCT
ejpam-4467	310	26	see	see	VERB
ejpam-4467	310	27	theorem	theorem	NOUN
ejpam-4467	310	28	3	3	NUM
ejpam-4467	310	29	)	)	PUNCT
ejpam-4467	310	30	.	.	PUNCT
ejpam-4467	311	1	it	it	PRON
ejpam-4467	311	2	is	be	AUX
ejpam-4467	311	3	clear	clear	ADJ
ejpam-4467	311	4	that	that	SCONJ
ejpam-4467	311	5	1	1	NUM
ejpam-4467	311	6	∈	∈	NOUN
ejpam-4467	311	7	o	o	NOUN
ejpam-4467	311	8	(	(	PUNCT
ejpam-4467	311	9	lεψ	lεψ	ADJ
ejpam-4467	311	10	)	)	PUNCT
ejpam-4467	311	11	.	.	PUNCT
ejpam-4467	312	1	let	let	VERB
ejpam-4467	312	2	x	x	PRON
ejpam-4467	312	3	,	,	PUNCT
ejpam-4467	312	4	y	y	PROPN
ejpam-4467	312	5	,	,	PUNCT
ejpam-4467	312	6	z	z	NOUN
ejpam-4467	312	7	∈	∈	PROPN
ejpam-4467	312	8	x	x	AUX
ejpam-4467	312	9	be	be	AUX
ejpam-4467	312	10	such	such	ADJ
ejpam-4467	312	11	that	that	SCONJ
ejpam-4467	312	12	y	y	PROPN
ejpam-4467	312	13	∈	∈	PROPN
ejpam-4467	312	14	o	o	NOUN
ejpam-4467	312	15	(	(	PUNCT
ejpam-4467	312	16	lεψ	lεψ	ADJ
ejpam-4467	312	17	)	)	PUNCT
ejpam-4467	312	18	and	and	CCONJ
ejpam-4467	312	19	x	x	SYM
ejpam-4467	312	20	∗	∗	NOUN
ejpam-4467	312	21	(	(	PUNCT
ejpam-4467	312	22	y	y	PROPN
ejpam-4467	312	23	∗	∗	PROPN
ejpam-4467	312	24	z	z	PROPN
ejpam-4467	312	25	)	)	PUNCT
ejpam-4467	312	26	∈	∈	PROPN
ejpam-4467	312	27	o	o	NOUN
ejpam-4467	312	28	(	(	PUNCT
ejpam-4467	312	29	lεψ	lεψ	ADJ
ejpam-4467	312	30	)	)	PUNCT
ejpam-4467	312	31	.	.	PUNCT
ejpam-4467	313	1	then	then	ADV
ejpam-4467	313	2	lεψ(x	lεψ(x	PROPN
ejpam-4467	313	3	∗	∗	NOUN
ejpam-4467	313	4	(	(	PUNCT
ejpam-4467	313	5	y	y	PROPN
ejpam-4467	313	6	∗	∗	PROPN
ejpam-4467	313	7	z	z	PROPN
ejpam-4467	313	8	)	)	PUNCT
ejpam-4467	313	9	)	)	PUNCT
ejpam-4467	313	10	>	>	X
ejpam-4467	313	11	0	0	PUNCT
ejpam-4467	313	12	and	and	CCONJ
ejpam-4467	313	13	lεψ(y	lεψ(y	PROPN
ejpam-4467	313	14	)	)	PUNCT
ejpam-4467	313	15	>	>	X
ejpam-4467	313	16	0	0	X
ejpam-4467	313	17	.	.	PUNCT
ejpam-4467	314	1	since	since	SCONJ
ejpam-4467	314	2	⟨(x	⟨(x	PROPN
ejpam-4467	314	3	∗	∗	NOUN
ejpam-4467	314	4	(	(	PUNCT
ejpam-4467	314	5	y	y	NOUN
ejpam-4467	314	6	∗	∗	NOUN
ejpam-4467	314	7	z))/	z))/	PROPN
ejpam-4467	314	8	lεψ(x	lεψ(x	PROPN
ejpam-4467	314	9	∗	∗	NOUN
ejpam-4467	314	10	(	(	PUNCT
ejpam-4467	314	11	y	y	NOUN
ejpam-4467	314	12	∗	∗	X
ejpam-4467	314	13	z))⟩	z))⟩	PROPN
ejpam-4467	314	14	∈	∈	PROPN
ejpam-4467	314	15	lεψ	lεψ	PROPN
ejpam-4467	314	16	and	and	CCONJ
ejpam-4467	314	17	⟨y/	⟨y/	NUM
ejpam-4467	314	18	lεψ(y)⟩	lεψ(y)⟩	PROPN
ejpam-4467	314	19	∈	∈	PROPN
ejpam-4467	314	20	lεψ	lεψ	PROPN
ejpam-4467	314	21	,	,	PUNCT
ejpam-4467	314	22	we	we	PRON
ejpam-4467	314	23	have	have	VERB
ejpam-4467	314	24	⟨(x	⟨(x	PROPN
ejpam-4467	314	25	∗	∗	NOUN
ejpam-4467	314	26	z)/min	z)/min	PROPN
ejpam-4467	314	27	{	{	PUNCT
ejpam-4467	314	28	lεψ(x	lεψ(x	PROPN
ejpam-4467	314	29	∗	∗	NOUN
ejpam-4467	314	30	(	(	PUNCT
ejpam-4467	314	31	y	y	PROPN
ejpam-4467	314	32	∗	∗	PROPN
ejpam-4467	314	33	z	z	PROPN
ejpam-4467	314	34	)	)	PUNCT
ejpam-4467	314	35	)	)	PUNCT
ejpam-4467	314	36	,	,	PUNCT
ejpam-4467	314	37	lεψ(y	lεψ(y	PROPN
ejpam-4467	314	38	)	)	PUNCT
ejpam-4467	314	39	}	}	PUNCT
ejpam-4467	314	40	⟩	⟩	NOUN
ejpam-4467	314	41	∈	∈	PROPN
ejpam-4467	314	42	lεψ	lεψ	VERB
ejpam-4467	314	43	by	by	ADP
ejpam-4467	314	44	(	(	PUNCT
ejpam-4467	314	45	17	17	NUM
ejpam-4467	314	46	)	)	PUNCT
ejpam-4467	314	47	.	.	PUNCT
ejpam-4467	315	1	it	it	PRON
ejpam-4467	315	2	follows	follow	VERB
ejpam-4467	315	3	that	that	SCONJ
ejpam-4467	315	4	lεψ(x	lεψ(x	ADJ
ejpam-4467	315	5	∗	∗	NOUN
ejpam-4467	315	6	z	z	NOUN
ejpam-4467	315	7	)	)	PUNCT
ejpam-4467	315	8	≥	≥	PROPN
ejpam-4467	315	9	min	min	NOUN
ejpam-4467	315	10	{	{	PUNCT
ejpam-4467	315	11	lεψ(x	lεψ(x	NOUN
ejpam-4467	315	12	∗	∗	NOUN
ejpam-4467	315	13	(	(	PUNCT
ejpam-4467	315	14	y	y	PROPN
ejpam-4467	315	15	∗	∗	PROPN
ejpam-4467	315	16	z	z	PROPN
ejpam-4467	315	17	)	)	PUNCT
ejpam-4467	315	18	)	)	PUNCT
ejpam-4467	315	19	,	,	PUNCT
ejpam-4467	315	20	lεψ(y	lεψ(y	PROPN
ejpam-4467	315	21	)	)	PUNCT
ejpam-4467	315	22	}	}	PUNCT
ejpam-4467	315	23	>	>	X
ejpam-4467	316	1	0	0	X
ejpam-4467	316	2	.	.	PUNCT
ejpam-4467	316	3	s.	s.	PROPN
ejpam-4467	316	4	s.	s.	PROPN
ejpam-4467	316	5	ahn	ahn	PROPN
ejpam-4467	316	6	,	,	PUNCT
ejpam-4467	316	7	e.	e.	PROPN
ejpam-4467	316	8	h.	h.	PROPN
ejpam-4467	316	9	roh	roh	PROPN
ejpam-4467	316	10	and	and	CCONJ
ejpam-4467	316	11	y.	y.	PROPN
ejpam-4467	316	12	b.	b.	PROPN
ejpam-4467	316	13	jun	jun	PROPN
ejpam-4467	316	14	/	/	SYM
ejpam-4467	316	15	eur	eur	PROPN
ejpam-4467	316	16	.	.	PUNCT
ejpam-4467	317	1	j.	j.	PROPN
ejpam-4467	317	2	pure	pure	PROPN
ejpam-4467	317	3	appl	appl	PROPN
ejpam-4467	317	4	.	.	PROPN
ejpam-4467	317	5	math	math	PROPN
ejpam-4467	317	6	,	,	PUNCT
ejpam-4467	317	7	15	15	NUM
ejpam-4467	317	8	(	(	PUNCT
ejpam-4467	317	9	3	3	NUM
ejpam-4467	317	10	)	)	PUNCT
ejpam-4467	317	11	(	(	PUNCT
ejpam-4467	317	12	2022	2022	NUM
ejpam-4467	317	13	)	)	PUNCT
ejpam-4467	317	14	,	,	PUNCT
ejpam-4467	317	15	1307	1307	NUM
ejpam-4467	317	16	-	-	SYM
ejpam-4467	317	17	1320	1320	NUM
ejpam-4467	317	18	1318	1318	NUM
ejpam-4467	317	19	hence	hence	ADV
ejpam-4467	317	20	x	x	X
ejpam-4467	317	21	∗	∗	NOUN
ejpam-4467	317	22	z	z	NOUN
ejpam-4467	317	23	∈	∈	PROPN
ejpam-4467	317	24	o	o	NOUN
ejpam-4467	317	25	(	(	PUNCT
ejpam-4467	317	26	lεψ	lεψ	ADJ
ejpam-4467	317	27	)	)	PUNCT
ejpam-4467	317	28	,	,	PUNCT
ejpam-4467	317	29	and	and	CCONJ
ejpam-4467	317	30	therefore	therefore	ADV
ejpam-4467	317	31	o	o	X
ejpam-4467	317	32	(	(	PUNCT
ejpam-4467	317	33	lεψ	lεψ	ADJ
ejpam-4467	317	34	)	)	PUNCT
ejpam-4467	317	35	is	be	AUX
ejpam-4467	317	36	an	an	DET
ejpam-4467	317	37	ideal	ideal	NOUN
ejpam-4467	317	38	of	of	ADP
ejpam-4467	317	39	(	(	PUNCT
ejpam-4467	317	40	x	x	X
ejpam-4467	317	41	,	,	PUNCT
ejpam-4467	317	42	1)∗	1)∗	NUM
ejpam-4467	317	43	by	by	ADP
ejpam-4467	317	44	lemma	lemma	PROPN
ejpam-4467	317	45	1	1	NUM
ejpam-4467	317	46	.	.	PUNCT
ejpam-4467	317	47	theorem	theorem	VERB
ejpam-4467	317	48	15	15	NUM
ejpam-4467	317	49	.	.	PUNCT
ejpam-4467	318	1	if	if	SCONJ
ejpam-4467	318	2	a	a	DET
ejpam-4467	318	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	318	4	fuzzy	fuzzy	ADJ
ejpam-4467	318	5	set	set	VERB
ejpam-4467	318	6	lεψ	lεψ	VERB
ejpam-4467	318	7	in	in	ADP
ejpam-4467	318	8	x	x	X
ejpam-4467	318	9	satisfies	satisfie	NOUN
ejpam-4467	318	10	(	(	PUNCT
ejpam-4467	318	11	13	13	NUM
ejpam-4467	318	12	)	)	PUNCT
ejpam-4467	318	13	and	and	CCONJ
ejpam-4467	318	14	(	(	PUNCT
ejpam-4467	318	15	∀x	∀x	NUM
ejpam-4467	318	16	,	,	PUNCT
ejpam-4467	318	17	y	y	PROPN
ejpam-4467	318	18	,	,	PUNCT
ejpam-4467	318	19	z	z	PROPN
ejpam-4467	318	20	∈	∈	PROPN
ejpam-4467	318	21	x)(∀ta	x)(∀ta	NOUN
ejpam-4467	318	22	,	,	PUNCT
ejpam-4467	318	23	tb	tb	ADP
ejpam-4467	318	24	∈	∈	PROPN
ejpam-4467	318	25	(	(	PUNCT
ejpam-4467	318	26	0	0	NUM
ejpam-4467	318	27	,	,	PUNCT
ejpam-4467	318	28	1	1	NUM
ejpam-4467	318	29	]	]	NUM
ejpam-4467	318	30	)	)	PUNCT
ejpam-4467	318	31	(	(	PUNCT
ejpam-4467	318	32	⟨(x	⟨(x	NOUN
ejpam-4467	318	33	∗	∗	NOUN
ejpam-4467	318	34	(	(	PUNCT
ejpam-4467	318	35	y	y	PROPN
ejpam-4467	318	36	∗	∗	X
ejpam-4467	318	37	z))/ta⟩	z))/ta⟩	PROPN
ejpam-4467	318	38	∈	∈	PROPN
ejpam-4467	318	39	lεψ	lεψ	VERB
ejpam-4467	318	40	,	,	PUNCT
ejpam-4467	318	41	⟨y	⟨y	AUX
ejpam-4467	318	42	/	/	SYM
ejpam-4467	318	43	tb⟩	tb⟩	PROPN
ejpam-4467	318	44	∈	∈	PROPN
ejpam-4467	318	45	lεψ	lεψ	ADJ
ejpam-4467	318	46	⇒	⇒	PROPN
ejpam-4467	318	47	⟨(x	⟨(x	PROPN
ejpam-4467	318	48	∗	∗	PROPN
ejpam-4467	318	49	z)/max{ta	z)/max{ta	PROPN
ejpam-4467	318	50	,	,	PUNCT
ejpam-4467	318	51	tb}⟩	tb}⟩	X
ejpam-4467	318	52	q	q	PUNCT
ejpam-4467	318	53	lεψ	lεψ	ADJ
ejpam-4467	318	54	)	)	PUNCT
ejpam-4467	318	55	.	.	PUNCT
ejpam-4467	319	1	(	(	PUNCT
ejpam-4467	319	2	35	35	NUM
ejpam-4467	319	3	)	)	PUNCT
ejpam-4467	319	4	then	then	ADV
ejpam-4467	319	5	the	the	DET
ejpam-4467	319	6	non	non	ADJ
ejpam-4467	319	7	-	-	ADJ
ejpam-4467	319	8	empty	empty	ADJ
ejpam-4467	319	9	o	o	NOUN
ejpam-4467	319	10	-	-	NOUN
ejpam-4467	319	11	set	set	NOUN
ejpam-4467	319	12	of	of	ADP
ejpam-4467	319	13	lεψ	lεψ	PROPN
ejpam-4467	319	14	is	be	AUX
ejpam-4467	319	15	an	an	DET
ejpam-4467	319	16	ideal	ideal	NOUN
ejpam-4467	319	17	of	of	ADP
ejpam-4467	319	18	(	(	PUNCT
ejpam-4467	319	19	x	x	X
ejpam-4467	319	20	,	,	PUNCT
ejpam-4467	319	21	1)∗.	1)∗.	PRON
ejpam-4467	319	22	proof	proof	NOUN
ejpam-4467	319	23	.	.	PUNCT
ejpam-4467	320	1	let	let	VERB
ejpam-4467	320	2	o	o	INTJ
ejpam-4467	320	3	(	(	PUNCT
ejpam-4467	320	4	lεψ	lεψ	ADJ
ejpam-4467	320	5	)	)	PUNCT
ejpam-4467	320	6	be	be	AUX
ejpam-4467	320	7	a	a	DET
ejpam-4467	320	8	non	non	ADJ
ejpam-4467	320	9	-	-	ADJ
ejpam-4467	320	10	empty	empty	ADJ
ejpam-4467	320	11	o	o	NOUN
ejpam-4467	320	12	-	-	NOUN
ejpam-4467	320	13	set	set	NOUN
ejpam-4467	320	14	of	of	ADP
ejpam-4467	320	15	lεψ	lεψ	ADJ
ejpam-4467	320	16	.	.	PUNCT
ejpam-4467	321	1	then	then	ADV
ejpam-4467	321	2	there	there	PRON
ejpam-4467	321	3	exists	exist	VERB
ejpam-4467	321	4	x	x	X
ejpam-4467	321	5	∈	∈	PRON
ejpam-4467	321	6	o	o	NOUN
ejpam-4467	321	7	(	(	PUNCT
ejpam-4467	321	8	lεψ	lεψ	ADJ
ejpam-4467	321	9	)	)	PUNCT
ejpam-4467	321	10	,	,	PUNCT
ejpam-4467	321	11	and	and	CCONJ
ejpam-4467	321	12	so	so	ADV
ejpam-4467	321	13	t	t	X
ejpam-4467	321	14	:	:	PUNCT
ejpam-4467	321	15	=	=	SYM
ejpam-4467	321	16	lεψ(x	lεψ(x	NOUN
ejpam-4467	321	17	)	)	PUNCT
ejpam-4467	321	18	>	>	X
ejpam-4467	321	19	0	0	NUM
ejpam-4467	321	20	,	,	PUNCT
ejpam-4467	321	21	i.e.	i.e.	X
ejpam-4467	321	22	,	,	PUNCT
ejpam-4467	321	23	⟨x	⟨x	VERB
ejpam-4467	321	24	/	/	SYM
ejpam-4467	321	25	t⟩	t⟩	SYM
ejpam-4467	321	26	∈	∈	PROPN
ejpam-4467	321	27	lεψ	lεψ	VERB
ejpam-4467	321	28	for	for	ADP
ejpam-4467	321	29	t	t	PROPN
ejpam-4467	321	30	>	>	X
ejpam-4467	321	31	0	0	X
ejpam-4467	321	32	.	.	PUNCT
ejpam-4467	322	1	hence	hence	ADV
ejpam-4467	322	2	⟨1	⟨1	PROPN
ejpam-4467	322	3	/	/	SYM
ejpam-4467	322	4	t⟩	t⟩	PRON
ejpam-4467	322	5	∈	∈	PROPN
ejpam-4467	322	6	lεψ	lεψ	VERB
ejpam-4467	322	7	by	by	ADP
ejpam-4467	322	8	(	(	PUNCT
ejpam-4467	322	9	13	13	NUM
ejpam-4467	322	10	)	)	PUNCT
ejpam-4467	322	11	,	,	PUNCT
ejpam-4467	322	12	and	and	CCONJ
ejpam-4467	322	13	thus	thus	ADV
ejpam-4467	322	14	lεψ(1	lεψ(1	ADJ
ejpam-4467	322	15	)	)	PUNCT
ejpam-4467	322	16	≥	≥	PROPN
ejpam-4467	322	17	t	t	X
ejpam-4467	322	18	>	>	X
ejpam-4467	322	19	0	0	X
ejpam-4467	322	20	.	.	PUNCT
ejpam-4467	323	1	thus	thus	ADV
ejpam-4467	323	2	1	1	NUM
ejpam-4467	323	3	∈	∈	NOUN
ejpam-4467	323	4	o	o	NOUN
ejpam-4467	323	5	(	(	PUNCT
ejpam-4467	323	6	lεψ	lεψ	ADJ
ejpam-4467	323	7	)	)	PUNCT
ejpam-4467	323	8	.	.	PUNCT
ejpam-4467	324	1	let	let	VERB
ejpam-4467	324	2	x	x	PRON
ejpam-4467	324	3	,	,	PUNCT
ejpam-4467	324	4	y	y	PROPN
ejpam-4467	324	5	,	,	PUNCT
ejpam-4467	324	6	z	z	NOUN
ejpam-4467	324	7	∈	∈	PROPN
ejpam-4467	324	8	x	x	AUX
ejpam-4467	324	9	be	be	AUX
ejpam-4467	324	10	such	such	ADJ
ejpam-4467	324	11	that	that	SCONJ
ejpam-4467	324	12	x	x	SYM
ejpam-4467	324	13	∗	∗	NOUN
ejpam-4467	324	14	(	(	PUNCT
ejpam-4467	324	15	y	y	PROPN
ejpam-4467	324	16	∗	∗	PROPN
ejpam-4467	324	17	z	z	PROPN
ejpam-4467	324	18	)	)	PUNCT
ejpam-4467	324	19	∈	∈	PROPN
ejpam-4467	324	20	o	o	NOUN
ejpam-4467	324	21	(	(	PUNCT
ejpam-4467	324	22	lεψ	lεψ	ADJ
ejpam-4467	324	23	)	)	PUNCT
ejpam-4467	324	24	and	and	CCONJ
ejpam-4467	324	25	y	y	PROPN
ejpam-4467	324	26	∈	∈	PROPN
ejpam-4467	325	1	o	o	NOUN
ejpam-4467	325	2	(	(	PUNCT
ejpam-4467	325	3	lεψ	lεψ	ADJ
ejpam-4467	325	4	)	)	PUNCT
ejpam-4467	325	5	.	.	PUNCT
ejpam-4467	326	1	then	then	ADV
ejpam-4467	326	2	ψ(x	ψ(x	NOUN
ejpam-4467	326	3	∗	∗	NOUN
ejpam-4467	326	4	(	(	PUNCT
ejpam-4467	326	5	y	y	PROPN
ejpam-4467	326	6	∗	∗	PROPN
ejpam-4467	326	7	z	z	PROPN
ejpam-4467	326	8	)	)	PUNCT
ejpam-4467	326	9	)	)	PUNCT
ejpam-4467	327	1	+	+	CCONJ
ejpam-4467	327	2	ε	ε	X
ejpam-4467	327	3	>	>	SYM
ejpam-4467	327	4	1	1	NUM
ejpam-4467	327	5	and	and	CCONJ
ejpam-4467	327	6	ψ(y	ψ(y	NOUN
ejpam-4467	327	7	)	)	PUNCT
ejpam-4467	328	1	+	+	CCONJ
ejpam-4467	328	2	ε	ε	PROPN
ejpam-4467	328	3	>	>	X
ejpam-4467	328	4	1	1	X
ejpam-4467	328	5	.	.	PUNCT
ejpam-4467	329	1	since	since	SCONJ
ejpam-4467	329	2	⟨(x	⟨(x	PROPN
ejpam-4467	329	3	∗	∗	NOUN
ejpam-4467	329	4	(	(	PUNCT
ejpam-4467	329	5	y	y	NOUN
ejpam-4467	329	6	∗	∗	NOUN
ejpam-4467	329	7	z))/	z))/	PROPN
ejpam-4467	329	8	lεψ(x	lεψ(x	PROPN
ejpam-4467	329	9	∗	∗	NOUN
ejpam-4467	329	10	(	(	PUNCT
ejpam-4467	329	11	y	y	NOUN
ejpam-4467	329	12	∗	∗	X
ejpam-4467	329	13	z))⟩	z))⟩	PROPN
ejpam-4467	329	14	∈	∈	PROPN
ejpam-4467	329	15	lεψ	lεψ	PROPN
ejpam-4467	329	16	and	and	CCONJ
ejpam-4467	329	17	⟨y/	⟨y/	NUM
ejpam-4467	329	18	lεψ(y)⟩	lεψ(y)⟩	PROPN
ejpam-4467	329	19	∈	∈	PROPN
ejpam-4467	329	20	lεψ	lεψ	VERB
ejpam-4467	329	21	,	,	PUNCT
ejpam-4467	329	22	it	it	PRON
ejpam-4467	329	23	follows	follow	VERB
ejpam-4467	329	24	from	from	ADP
ejpam-4467	329	25	(	(	PUNCT
ejpam-4467	329	26	35	35	NUM
ejpam-4467	329	27	)	)	PUNCT
ejpam-4467	330	1	that	that	PRON
ejpam-4467	330	2	⟨(x	⟨(x	VERB
ejpam-4467	330	3	∗	∗	PROPN
ejpam-4467	330	4	z)/max	z)/max	PROPN
ejpam-4467	330	5	{	{	PUNCT
ejpam-4467	330	6	lεψ(x	lεψ(x	PROPN
ejpam-4467	330	7	∗	∗	NOUN
ejpam-4467	330	8	(	(	PUNCT
ejpam-4467	330	9	y	y	PROPN
ejpam-4467	330	10	∗	∗	PROPN
ejpam-4467	330	11	z	z	PROPN
ejpam-4467	330	12	)	)	PUNCT
ejpam-4467	330	13	)	)	PUNCT
ejpam-4467	330	14	,	,	PUNCT
ejpam-4467	330	15	lεψ(y)}⟩	lεψ(y)}⟩	PROPN
ejpam-4467	330	16	q	q	PROPN
ejpam-4467	330	17	lεψ	lεψ	ADJ
ejpam-4467	330	18	.	.	PUNCT
ejpam-4467	331	1	if	if	SCONJ
ejpam-4467	331	2	x	x	PROPN
ejpam-4467	331	3	∗	∗	NOUN
ejpam-4467	331	4	z	z	NOUN
ejpam-4467	331	5	/∈	/∈	PUNCT
ejpam-4467	332	1	o	o	NOUN
ejpam-4467	332	2	(	(	PUNCT
ejpam-4467	332	3	lεψ	lεψ	PROPN
ejpam-4467	332	4	)	)	PUNCT
ejpam-4467	332	5	,	,	PUNCT
ejpam-4467	333	1	then	then	ADV
ejpam-4467	333	2	lεψ(x	lεψ(x	PROPN
ejpam-4467	333	3	∗	∗	X
ejpam-4467	333	4	z	z	NOUN
ejpam-4467	333	5	)	)	PUNCT
ejpam-4467	333	6	=	=	SYM
ejpam-4467	333	7	0	0	NUM
ejpam-4467	333	8	,	,	PUNCT
ejpam-4467	333	9	and	and	CCONJ
ejpam-4467	333	10	so	so	ADV
ejpam-4467	333	11	lεψ(x	lεψ(x	ADJ
ejpam-4467	333	12	∗	∗	PROPN
ejpam-4467	333	13	z	z	NOUN
ejpam-4467	333	14	)	)	PUNCT
ejpam-4467	334	1	+	+	CCONJ
ejpam-4467	334	2	max	max	PROPN
ejpam-4467	334	3	{	{	PUNCT
ejpam-4467	334	4	lεψ(x	lεψ(x	PROPN
ejpam-4467	334	5	∗	∗	NOUN
ejpam-4467	334	6	(	(	PUNCT
ejpam-4467	334	7	y	y	PROPN
ejpam-4467	334	8	∗	∗	PROPN
ejpam-4467	334	9	z	z	PROPN
ejpam-4467	334	10	)	)	PUNCT
ejpam-4467	334	11	)	)	PUNCT
ejpam-4467	334	12	,	,	PUNCT
ejpam-4467	334	13	lεψ(y	lεψ(y	PROPN
ejpam-4467	334	14	)	)	PUNCT
ejpam-4467	334	15	}	}	PUNCT
ejpam-4467	334	16	=	=	SYM
ejpam-4467	334	17	max	max	PROPN
ejpam-4467	334	18	{	{	PUNCT
ejpam-4467	334	19	lεψ(x	lεψ(x	PROPN
ejpam-4467	334	20	∗	∗	NOUN
ejpam-4467	334	21	(	(	PUNCT
ejpam-4467	334	22	y	y	PROPN
ejpam-4467	334	23	∗	∗	PROPN
ejpam-4467	334	24	z	z	PROPN
ejpam-4467	334	25	)	)	PUNCT
ejpam-4467	334	26	)	)	PUNCT
ejpam-4467	334	27	,	,	PUNCT
ejpam-4467	334	28	lεψ(y	lεψ(y	PROPN
ejpam-4467	334	29	)	)	PUNCT
ejpam-4467	334	30	}	}	PUNCT
ejpam-4467	334	31	=	=	SYM
ejpam-4467	334	32	max{max{0	max{max{0	X
ejpam-4467	334	33	,	,	PUNCT
ejpam-4467	334	34	ψ(x	ψ(x	NOUN
ejpam-4467	334	35	∗	∗	NOUN
ejpam-4467	334	36	(	(	PUNCT
ejpam-4467	334	37	y	y	PROPN
ejpam-4467	334	38	∗	∗	PROPN
ejpam-4467	334	39	z	z	PROPN
ejpam-4467	334	40	)	)	PUNCT
ejpam-4467	334	41	)	)	PUNCT
ejpam-4467	335	1	+	+	CCONJ
ejpam-4467	335	2	ε−	ε−	PROPN
ejpam-4467	335	3	1	1	NUM
ejpam-4467	335	4	}	}	PUNCT
ejpam-4467	335	5	,	,	PUNCT
ejpam-4467	335	6	max{0	max{0	PROPN
ejpam-4467	335	7	,	,	PUNCT
ejpam-4467	335	8	ψ(y	ψ(y	PROPN
ejpam-4467	335	9	)	)	PUNCT
ejpam-4467	335	10	+	+	CCONJ
ejpam-4467	335	11	ε−	ε−	PROPN
ejpam-4467	335	12	1	1	NUM
ejpam-4467	335	13	}	}	PUNCT
ejpam-4467	335	14	}	}	PUNCT
ejpam-4467	335	15	=	=	SYM
ejpam-4467	335	16	max{ψ(x	max{ψ(x	PROPN
ejpam-4467	335	17	∗	∗	NOUN
ejpam-4467	335	18	(	(	PUNCT
ejpam-4467	335	19	y	y	PROPN
ejpam-4467	335	20	∗	∗	PROPN
ejpam-4467	335	21	z	z	PROPN
ejpam-4467	335	22	)	)	PUNCT
ejpam-4467	335	23	)	)	PUNCT
ejpam-4467	336	1	+	+	CCONJ
ejpam-4467	336	2	ε−	ε−	PROPN
ejpam-4467	336	3	1	1	NUM
ejpam-4467	336	4	,	,	PUNCT
ejpam-4467	336	5	ψ(y	ψ(y	NOUN
ejpam-4467	336	6	)	)	PUNCT
ejpam-4467	336	7	+	+	CCONJ
ejpam-4467	337	1	ε−	ε−	PROPN
ejpam-4467	337	2	1	1	NUM
ejpam-4467	337	3	}	}	PUNCT
ejpam-4467	337	4	=	=	SYM
ejpam-4467	337	5	max{ψ(x	max{ψ(x	PROPN
ejpam-4467	337	6	∗	∗	NOUN
ejpam-4467	337	7	(	(	PUNCT
ejpam-4467	337	8	y	y	PROPN
ejpam-4467	337	9	∗	∗	PROPN
ejpam-4467	337	10	z	z	PROPN
ejpam-4467	337	11	)	)	PUNCT
ejpam-4467	337	12	)	)	PUNCT
ejpam-4467	337	13	,	,	PUNCT
ejpam-4467	337	14	ψ(y	ψ(y	NOUN
ejpam-4467	337	15	)	)	PUNCT
ejpam-4467	337	16	}	}	PUNCT
ejpam-4467	337	17	+	+	CCONJ
ejpam-4467	337	18	ε−	ε−	PROPN
ejpam-4467	337	19	1	1	NUM
ejpam-4467	337	20	≤	≤	NUM
ejpam-4467	337	21	1	1	NUM
ejpam-4467	337	22	+	+	CCONJ
ejpam-4467	337	23	ε−	ε−	PROPN
ejpam-4467	337	24	1	1	NUM
ejpam-4467	337	25	≤	≤	NUM
ejpam-4467	337	26	1	1	NUM
ejpam-4467	337	27	.	.	PUNCT
ejpam-4467	338	1	hence	hence	ADV
ejpam-4467	338	2	⟨(x	⟨(x	PUNCT
ejpam-4467	338	3	∗	∗	PROPN
ejpam-4467	338	4	z)/max	z)/max	PROPN
ejpam-4467	338	5	{	{	PUNCT
ejpam-4467	338	6	lεψ(x	lεψ(x	PROPN
ejpam-4467	338	7	∗	∗	NOUN
ejpam-4467	338	8	(	(	PUNCT
ejpam-4467	338	9	y	y	PROPN
ejpam-4467	338	10	∗	∗	PROPN
ejpam-4467	338	11	z	z	PROPN
ejpam-4467	338	12	)	)	PUNCT
ejpam-4467	338	13	)	)	PUNCT
ejpam-4467	338	14	,	,	PUNCT
ejpam-4467	338	15	lεψ(y)}⟩	lεψ(y)}⟩	PROPN
ejpam-4467	338	16	q	q	PROPN
ejpam-4467	338	17	lεψ	lεψ	PROPN
ejpam-4467	338	18	,	,	PUNCT
ejpam-4467	338	19	a	a	DET
ejpam-4467	338	20	contradiction	contradiction	NOUN
ejpam-4467	338	21	.	.	PUNCT
ejpam-4467	339	1	thus	thus	ADV
ejpam-4467	339	2	x	x	X
ejpam-4467	339	3	∗	∗	NOUN
ejpam-4467	339	4	z	z	NOUN
ejpam-4467	339	5	∈	∈	PROPN
ejpam-4467	339	6	o	o	NOUN
ejpam-4467	339	7	(	(	PUNCT
ejpam-4467	339	8	lεψ	lεψ	ADJ
ejpam-4467	339	9	)	)	PUNCT
ejpam-4467	339	10	,	,	PUNCT
ejpam-4467	339	11	and	and	CCONJ
ejpam-4467	339	12	therefore	therefore	ADV
ejpam-4467	339	13	o	o	X
ejpam-4467	339	14	(	(	PUNCT
ejpam-4467	339	15	lεψ	lεψ	ADJ
ejpam-4467	339	16	)	)	PUNCT
ejpam-4467	339	17	is	be	AUX
ejpam-4467	339	18	an	an	DET
ejpam-4467	339	19	ideal	ideal	NOUN
ejpam-4467	339	20	of	of	ADP
ejpam-4467	339	21	(	(	PUNCT
ejpam-4467	339	22	x	x	X
ejpam-4467	339	23	,	,	PUNCT
ejpam-4467	339	24	1)∗	1)∗	NUM
ejpam-4467	339	25	by	by	ADP
ejpam-4467	339	26	lemma	lemma	PROPN
ejpam-4467	339	27	1	1	NUM
ejpam-4467	339	28	.	.	PUNCT
ejpam-4467	339	29	theorem	theorem	VERB
ejpam-4467	339	30	16	16	NUM
ejpam-4467	339	31	.	.	PUNCT
ejpam-4467	340	1	if	if	SCONJ
ejpam-4467	340	2	a	a	DET
ejpam-4467	340	3	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	340	4	fuzzy	fuzzy	ADJ
ejpam-4467	340	5	set	set	VERB
ejpam-4467	340	6	lεψ	lεψ	VERB
ejpam-4467	340	7	in	in	ADP
ejpam-4467	340	8	x	x	X
ejpam-4467	340	9	satisfies	satisfie	NOUN
ejpam-4467	340	10	(	(	PUNCT
ejpam-4467	340	11	∀x	∀x	X
ejpam-4467	340	12	,	,	PUNCT
ejpam-4467	340	13	y	y	PROPN
ejpam-4467	340	14	∈	∈	PROPN
ejpam-4467	340	15	x)(∀t	x)(∀t	PROPN
ejpam-4467	340	16	∈	∈	PROPN
ejpam-4467	340	17	(	(	PUNCT
ejpam-4467	340	18	0	0	NUM
ejpam-4467	340	19	,	,	PUNCT
ejpam-4467	340	20	1	1	NUM
ejpam-4467	340	21	]	]	NUM
ejpam-4467	340	22	)	)	PUNCT
ejpam-4467	340	23	(	(	PUNCT
ejpam-4467	340	24	⟨y	⟨y	X
ejpam-4467	340	25	/	/	SYM
ejpam-4467	340	26	t⟩	t⟩	NOUN
ejpam-4467	340	27	∈	∈	NOUN
ejpam-4467	340	28	ψ	ψ	ADP
ejpam-4467	340	29	⇒	⇒	PROPN
ejpam-4467	340	30	⟨(x	⟨(x	PROPN
ejpam-4467	340	31	∗	∗	NOUN
ejpam-4467	340	32	y)/t⟩	y)/t⟩	PROPN
ejpam-4467	341	1	q	q	PROPN
ejpam-4467	341	2	lεψ	lεψ	ADJ
ejpam-4467	341	3	)	)	PUNCT
ejpam-4467	341	4	,	,	PUNCT
ejpam-4467	341	5	(	(	PUNCT
ejpam-4467	341	6	36	36	NUM
ejpam-4467	341	7	)	)	PUNCT
ejpam-4467	341	8	and	and	CCONJ
ejpam-4467	341	9	⟨x	⟨x	VERB
ejpam-4467	341	10	/	/	SYM
ejpam-4467	341	11	ta⟩	ta⟩	CCONJ
ejpam-4467	341	12	∈	∈	PROPN
ejpam-4467	341	13	ψ	ψ	PROPN
ejpam-4467	341	14	,	,	PUNCT
ejpam-4467	341	15	⟨y	⟨y	X
ejpam-4467	341	16	/	/	SYM
ejpam-4467	341	17	tb⟩	tb⟩	PROPN
ejpam-4467	341	18	∈	∈	PROPN
ejpam-4467	341	19	ψ	ψ	ADP
ejpam-4467	341	20	⇒	⇒	PROPN
ejpam-4467	341	21	⟨((x	⟨((x	PROPN
ejpam-4467	341	22	∗	∗	VERB
ejpam-4467	341	23	(	(	PUNCT
ejpam-4467	341	24	y	y	PROPN
ejpam-4467	341	25	∗	∗	PROPN
ejpam-4467	341	26	z	z	NOUN
ejpam-4467	341	27	)	)	PUNCT
ejpam-4467	341	28	)	)	PUNCT
ejpam-4467	341	29	∗	∗	NOUN
ejpam-4467	341	30	z)/max{ta	z)/max{ta	PROPN
ejpam-4467	341	31	,	,	PUNCT
ejpam-4467	341	32	tb}⟩	tb}⟩	X
ejpam-4467	341	33	q	q	X
ejpam-4467	341	34	lεψ	lεψ	ADJ
ejpam-4467	341	35	(	(	PUNCT
ejpam-4467	341	36	37	37	NUM
ejpam-4467	341	37	)	)	PUNCT
ejpam-4467	341	38	for	for	ADP
ejpam-4467	341	39	all	all	DET
ejpam-4467	341	40	x	x	NOUN
ejpam-4467	341	41	,	,	PUNCT
ejpam-4467	341	42	y	y	PROPN
ejpam-4467	341	43	,	,	PUNCT
ejpam-4467	341	44	z	z	NOUN
ejpam-4467	341	45	∈	∈	PROPN
ejpam-4467	341	46	x	x	X
ejpam-4467	341	47	and	and	CCONJ
ejpam-4467	341	48	ta	ta	PROPN
ejpam-4467	341	49	,	,	PUNCT
ejpam-4467	341	50	tb	tb	ADP
ejpam-4467	341	51	∈	∈	PROPN
ejpam-4467	341	52	(	(	PUNCT
ejpam-4467	341	53	0	0	NUM
ejpam-4467	341	54	,	,	PUNCT
ejpam-4467	341	55	1	1	NUM
ejpam-4467	341	56	]	]	PUNCT
ejpam-4467	341	57	,	,	PUNCT
ejpam-4467	341	58	then	then	ADV
ejpam-4467	341	59	the	the	DET
ejpam-4467	341	60	o	o	NOUN
ejpam-4467	341	61	-	-	NOUN
ejpam-4467	341	62	set	set	NOUN
ejpam-4467	341	63	of	of	ADP
ejpam-4467	341	64	lεψ	lεψ	PROPN
ejpam-4467	341	65	is	be	AUX
ejpam-4467	341	66	an	an	DET
ejpam-4467	341	67	ideal	ideal	NOUN
ejpam-4467	341	68	of	of	ADP
ejpam-4467	341	69	(	(	PUNCT
ejpam-4467	341	70	x	x	X
ejpam-4467	341	71	,	,	PUNCT
ejpam-4467	341	72	1)∗.	1)∗.	PRON
ejpam-4467	341	73	proof	proof	NOUN
ejpam-4467	341	74	.	.	PUNCT
ejpam-4467	342	1	if	if	SCONJ
ejpam-4467	342	2	y	y	PROPN
ejpam-4467	342	3	∈	∈	PROPN
ejpam-4467	342	4	o	o	NOUN
ejpam-4467	342	5	(	(	PUNCT
ejpam-4467	342	6	lεψ	lεψ	PROPN
ejpam-4467	342	7	)	)	PUNCT
ejpam-4467	342	8	,	,	PUNCT
ejpam-4467	342	9	then	then	ADV
ejpam-4467	342	10	ψ(y	ψ(y	NOUN
ejpam-4467	342	11	)	)	PUNCT
ejpam-4467	342	12	>	>	X
ejpam-4467	342	13	1−ε	1−ε	NUM
ejpam-4467	342	14	,	,	PUNCT
ejpam-4467	342	15	i.e.	i.e.	X
ejpam-4467	342	16	,	,	PUNCT
ejpam-4467	342	17	⟨y/(1−ε)⟩	⟨y/(1−ε)⟩	PROPN
ejpam-4467	342	18	∈	∈	PROPN
ejpam-4467	342	19	ψ	ψ	NOUN
ejpam-4467	342	20	.	.	PUNCT
ejpam-4467	342	21	hence	hence	ADV
ejpam-4467	342	22	⟨(x∗y)/(1	⟨(x∗y)/(1	PROPN
ejpam-4467	342	23	−	−	PROPN
ejpam-4467	342	24	ε)⟩	ε)⟩	NOUN
ejpam-4467	342	25	q	q	PROPN
ejpam-4467	342	26	lεψ	lεψ	VERB
ejpam-4467	342	27	for	for	ADP
ejpam-4467	342	28	all	all	DET
ejpam-4467	342	29	x	x	SYM
ejpam-4467	342	30	∈	∈	PROPN
ejpam-4467	342	31	x	x	PUNCT
ejpam-4467	342	32	by	by	ADP
ejpam-4467	342	33	(	(	PUNCT
ejpam-4467	342	34	36	36	NUM
ejpam-4467	342	35	)	)	PUNCT
ejpam-4467	342	36	,	,	PUNCT
ejpam-4467	342	37	and	and	CCONJ
ejpam-4467	342	38	thus	thus	ADV
ejpam-4467	342	39	lεψ(x	lεψ(x	PROPN
ejpam-4467	342	40	∗	∗	NOUN
ejpam-4467	342	41	y	y	NOUN
ejpam-4467	342	42	)	)	PUNCT
ejpam-4467	342	43	+	+	CCONJ
ejpam-4467	342	44	1	1	NUM
ejpam-4467	342	45	−	−	NOUN
ejpam-4467	342	46	ε	ε	PROPN
ejpam-4467	342	47	>	>	X
ejpam-4467	342	48	1	1	NUM
ejpam-4467	342	49	.	.	PUNCT
ejpam-4467	342	50	thus	thus	ADV
ejpam-4467	342	51	lεψ(x	lεψ(x	PROPN
ejpam-4467	342	52	∗	∗	NOUN
ejpam-4467	342	53	y	y	NOUN
ejpam-4467	342	54	)	)	PUNCT
ejpam-4467	342	55	>	>	PUNCT
ejpam-4467	342	56	ε	ε	PROPN
ejpam-4467	342	57	>	>	X
ejpam-4467	342	58	0	0	PROPN
ejpam-4467	342	59	,	,	PUNCT
ejpam-4467	342	60	which	which	PRON
ejpam-4467	342	61	shows	show	VERB
ejpam-4467	342	62	that	that	SCONJ
ejpam-4467	342	63	x	x	PROPN
ejpam-4467	342	64	∗	∗	VERB
ejpam-4467	342	65	y	y	PROPN
ejpam-4467	342	66	∈	∈	PROPN
ejpam-4467	342	67	o	o	NOUN
ejpam-4467	342	68	(	(	PUNCT
ejpam-4467	342	69	lεψ	lεψ	ADJ
ejpam-4467	342	70	)	)	PUNCT
ejpam-4467	342	71	for	for	ADP
ejpam-4467	342	72	all	all	PRON
ejpam-4467	342	73	x	x	SYM
ejpam-4467	342	74	∈	∈	NOUN
ejpam-4467	342	75	x.	x.	NOUN
ejpam-4467	342	76	let	let	VERB
ejpam-4467	342	77	x	x	PRON
ejpam-4467	342	78	,	,	PUNCT
ejpam-4467	342	79	y	y	PROPN
ejpam-4467	342	80	,	,	PUNCT
ejpam-4467	342	81	z	z	NOUN
ejpam-4467	342	82	∈	∈	PROPN
ejpam-4467	342	83	x	x	AUX
ejpam-4467	342	84	be	be	AUX
ejpam-4467	342	85	such	such	ADJ
ejpam-4467	342	86	that	that	SCONJ
ejpam-4467	342	87	x	x	NOUN
ejpam-4467	342	88	,	,	PUNCT
ejpam-4467	342	89	y	y	PROPN
ejpam-4467	342	90	∈	∈	PROPN
ejpam-4467	342	91	o	o	NOUN
ejpam-4467	342	92	(	(	PUNCT
ejpam-4467	342	93	lεψ	lεψ	ADJ
ejpam-4467	342	94	)	)	PUNCT
ejpam-4467	342	95	.	.	PUNCT
ejpam-4467	343	1	then	then	ADV
ejpam-4467	343	2	ψ(x	ψ(x	NUM
ejpam-4467	343	3	)	)	PUNCT
ejpam-4467	343	4	>	>	X
ejpam-4467	343	5	1	1	NUM
ejpam-4467	343	6	−	−	PROPN
ejpam-4467	343	7	ε	ε	PROPN
ejpam-4467	343	8	and	and	CCONJ
ejpam-4467	343	9	ψ(y	ψ(y	PROPN
ejpam-4467	343	10	)	)	PUNCT
ejpam-4467	343	11	>	>	X
ejpam-4467	343	12	1	1	NUM
ejpam-4467	343	13	−	−	ADP
ejpam-4467	343	14	ε	ε	PROPN
ejpam-4467	343	15	,	,	PUNCT
ejpam-4467	343	16	that	that	ADV
ejpam-4467	343	17	is	is	ADV
ejpam-4467	343	18	,	,	PUNCT
ejpam-4467	343	19	⟨x/(1	⟨x/(1	NUM
ejpam-4467	343	20	−	−	PROPN
ejpam-4467	343	21	ε)⟩	ε)⟩	NUM
ejpam-4467	343	22	∈	∈	NOUN
ejpam-4467	343	23	ψ	ψ	NOUN
ejpam-4467	343	24	and	and	CCONJ
ejpam-4467	343	25	⟨y/(1	⟨y/(1	NUM
ejpam-4467	343	26	−	−	PROPN
ejpam-4467	343	27	ε)⟩	ε)⟩	PROPN
ejpam-4467	343	28	∈	∈	PROPN
ejpam-4467	343	29	ψ	ψ	NOUN
ejpam-4467	343	30	.	.	PUNCT
ejpam-4467	344	1	it	it	PRON
ejpam-4467	344	2	follows	follow	VERB
ejpam-4467	344	3	from	from	ADP
ejpam-4467	344	4	(	(	PUNCT
ejpam-4467	344	5	37	37	NUM
ejpam-4467	344	6	)	)	PUNCT
ejpam-4467	344	7	that	that	PRON
ejpam-4467	344	8	⟨((x	⟨((x	PROPN
ejpam-4467	344	9	∗	∗	NOUN
ejpam-4467	344	10	(	(	PUNCT
ejpam-4467	344	11	y	y	PROPN
ejpam-4467	344	12	∗	∗	PROPN
ejpam-4467	344	13	z	z	NOUN
ejpam-4467	344	14	)	)	PUNCT
ejpam-4467	344	15	)	)	PUNCT
ejpam-4467	344	16	∗	∗	NOUN
ejpam-4467	344	17	z)/(1	z)/(1	NUM
ejpam-4467	344	18	−	−	PROPN
ejpam-4467	344	19	ε)⟩	ε)⟩	PROPN
ejpam-4467	344	20	=	=	SYM
ejpam-4467	344	21	⟨((x	⟨((x	PROPN
ejpam-4467	344	22	∗	∗	NOUN
ejpam-4467	344	23	(	(	PUNCT
ejpam-4467	344	24	y	y	PROPN
ejpam-4467	344	25	∗	∗	PROPN
ejpam-4467	344	26	z	z	NOUN
ejpam-4467	344	27	)	)	PUNCT
ejpam-4467	344	28	)	)	PUNCT
ejpam-4467	344	29	∗	∗	NOUN
ejpam-4467	344	30	z)/max{1	z)/max{1	PROPN
ejpam-4467	344	31	−	−	ADP
ejpam-4467	344	32	ε	ε	PROPN
ejpam-4467	344	33	,	,	PUNCT
ejpam-4467	344	34	1	1	NUM
ejpam-4467	344	35	−	−	PROPN
ejpam-4467	344	36	ε}⟩	ε}⟩	PROPN
ejpam-4467	344	37	q	q	PROPN
ejpam-4467	344	38	lεψ	lεψ	ADJ
ejpam-4467	344	39	.	.	PUNCT
ejpam-4467	345	1	thus	thus	ADV
ejpam-4467	345	2	lεψ((x	lεψ((x	NOUN
ejpam-4467	345	3	∗	∗	NOUN
ejpam-4467	345	4	(	(	PUNCT
ejpam-4467	345	5	y	y	PROPN
ejpam-4467	345	6	∗	∗	PROPN
ejpam-4467	345	7	z	z	NOUN
ejpam-4467	345	8	)	)	PUNCT
ejpam-4467	345	9	)	)	PUNCT
ejpam-4467	345	10	∗	∗	PROPN
ejpam-4467	345	11	z	z	NOUN
ejpam-4467	345	12	)	)	PUNCT
ejpam-4467	346	1	+	+	CCONJ
ejpam-4467	346	2	1	1	NUM
ejpam-4467	346	3	−	−	NOUN
ejpam-4467	346	4	ε	ε	PROPN
ejpam-4467	346	5	>	>	X
ejpam-4467	346	6	1	1	NUM
ejpam-4467	346	7	,	,	PUNCT
ejpam-4467	346	8	and	and	CCONJ
ejpam-4467	346	9	so	so	ADV
ejpam-4467	346	10	lεψ((x	lεψ((x	NOUN
ejpam-4467	346	11	∗	∗	NOUN
ejpam-4467	346	12	(	(	PUNCT
ejpam-4467	346	13	y	y	PROPN
ejpam-4467	346	14	∗	∗	PROPN
ejpam-4467	346	15	z	z	NOUN
ejpam-4467	346	16	)	)	PUNCT
ejpam-4467	346	17	)	)	PUNCT
ejpam-4467	346	18	∗	∗	PROPN
ejpam-4467	346	19	z	z	PROPN
ejpam-4467	346	20	)	)	PUNCT
ejpam-4467	346	21	>	>	PUNCT
ejpam-4467	346	22	ε	ε	PROPN
ejpam-4467	346	23	>	>	X
ejpam-4467	346	24	0	0	PROPN
ejpam-4467	346	25	.	.	PUNCT
ejpam-4467	347	1	hence	hence	ADV
ejpam-4467	347	2	(	(	PUNCT
ejpam-4467	347	3	x	x	SYM
ejpam-4467	347	4	∗	∗	NOUN
ejpam-4467	347	5	(	(	PUNCT
ejpam-4467	347	6	y	y	PROPN
ejpam-4467	347	7	∗	∗	PROPN
ejpam-4467	347	8	z	z	NOUN
ejpam-4467	347	9	)	)	PUNCT
ejpam-4467	347	10	)	)	PUNCT
ejpam-4467	347	11	∗	∗	NOUN
ejpam-4467	347	12	z	z	X
ejpam-4467	347	13	∈	∈	PROPN
ejpam-4467	348	1	o	o	NOUN
ejpam-4467	348	2	(	(	PUNCT
ejpam-4467	348	3	lεψ	lεψ	ADJ
ejpam-4467	348	4	)	)	PUNCT
ejpam-4467	348	5	,	,	PUNCT
ejpam-4467	348	6	and	and	CCONJ
ejpam-4467	348	7	therefore	therefore	ADV
ejpam-4467	348	8	o	o	X
ejpam-4467	348	9	(	(	PUNCT
ejpam-4467	348	10	lεψ	lεψ	ADJ
ejpam-4467	348	11	)	)	PUNCT
ejpam-4467	348	12	is	be	AUX
ejpam-4467	348	13	an	an	DET
ejpam-4467	348	14	ideal	ideal	NOUN
ejpam-4467	348	15	of	of	ADP
ejpam-4467	348	16	(	(	PUNCT
ejpam-4467	348	17	x	x	X
ejpam-4467	348	18	,	,	PUNCT
ejpam-4467	348	19	1)∗.	1)∗.	PROPN
ejpam-4467	348	20	s.	s.	PROPN
ejpam-4467	348	21	s.	s.	PROPN
ejpam-4467	348	22	ahn	ahn	PROPN
ejpam-4467	348	23	,	,	PUNCT
ejpam-4467	348	24	e.	e.	PROPN
ejpam-4467	348	25	h.	h.	PROPN
ejpam-4467	348	26	roh	roh	PROPN
ejpam-4467	348	27	and	and	CCONJ
ejpam-4467	348	28	y.	y.	PROPN
ejpam-4467	348	29	b.	b.	PROPN
ejpam-4467	348	30	jun	jun	PROPN
ejpam-4467	348	31	/	/	SYM
ejpam-4467	348	32	eur	eur	PROPN
ejpam-4467	348	33	.	.	PUNCT
ejpam-4467	349	1	j.	j.	PROPN
ejpam-4467	349	2	pure	pure	PROPN
ejpam-4467	349	3	appl	appl	PROPN
ejpam-4467	349	4	.	.	PROPN
ejpam-4467	349	5	math	math	PROPN
ejpam-4467	349	6	,	,	PUNCT
ejpam-4467	349	7	15	15	NUM
ejpam-4467	349	8	(	(	PUNCT
ejpam-4467	349	9	3	3	NUM
ejpam-4467	349	10	)	)	PUNCT
ejpam-4467	349	11	(	(	PUNCT
ejpam-4467	349	12	2022	2022	NUM
ejpam-4467	349	13	)	)	PUNCT
ejpam-4467	349	14	,	,	PUNCT
ejpam-4467	349	15	1307	1307	NUM
ejpam-4467	349	16	-	-	SYM
ejpam-4467	349	17	1320	1320	NUM
ejpam-4467	349	18	1319	1319	NUM
ejpam-4467	349	19	theorem	theorem	NOUN
ejpam-4467	349	20	17	17	NUM
ejpam-4467	349	21	.	.	PUNCT
ejpam-4467	350	1	let	let	VERB
ejpam-4467	350	2	lεψ	lεψ	ADJ
ejpam-4467	350	3	be	be	AUX
ejpam-4467	350	4	a	a	DET
ejpam-4467	350	5	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	350	6	fuzzy	fuzzy	ADJ
ejpam-4467	350	7	set	set	VERB
ejpam-4467	350	8	in	in	ADP
ejpam-4467	350	9	x	x	PUNCT
ejpam-4467	350	10	that	that	PRON
ejpam-4467	350	11	satisfies	satisfy	VERB
ejpam-4467	350	12	⟨1	⟨1	PROPN
ejpam-4467	350	13	/	/	SYM
ejpam-4467	350	14	ε⟩	ε⟩	NOUN
ejpam-4467	350	15	q	q	NOUN
ejpam-4467	350	16	ψ	ψ	NOUN
ejpam-4467	350	17	and	and	CCONJ
ejpam-4467	350	18	(	(	PUNCT
ejpam-4467	350	19	∀x	∀x	NUM
ejpam-4467	350	20	,	,	PUNCT
ejpam-4467	350	21	y	y	PROPN
ejpam-4467	350	22	,	,	PUNCT
ejpam-4467	350	23	z	z	NOUN
ejpam-4467	350	24	∈	∈	PROPN
ejpam-4467	350	25	x	x	X
ejpam-4467	350	26	)	)	PUNCT
ejpam-4467	350	27	(	(	PUNCT
ejpam-4467	350	28	⟨(x	⟨(x	PROPN
ejpam-4467	350	29	∗	∗	NOUN
ejpam-4467	350	30	(	(	PUNCT
ejpam-4467	350	31	y	y	PROPN
ejpam-4467	350	32	∗	∗	PROPN
ejpam-4467	350	33	z))/ε⟩	z))/ε⟩	PROPN
ejpam-4467	350	34	q	q	PROPN
ejpam-4467	350	35	ψ	ψ	NOUN
ejpam-4467	350	36	,	,	PUNCT
ejpam-4467	350	37	⟨y	⟨y	X
ejpam-4467	350	38	/	/	SYM
ejpam-4467	350	39	ε⟩	ε⟩	NOUN
ejpam-4467	350	40	q	q	X
ejpam-4467	350	41	ψ	ψ	NOUN
ejpam-4467	350	42	⇒	⇒	PROPN
ejpam-4467	350	43	⟨(x	⟨(x	PROPN
ejpam-4467	351	1	∗	∗	NOUN
ejpam-4467	351	2	z)/ε⟩	z)/ε⟩	PUNCT
ejpam-4467	352	1	∈	∈	PROPN
ejpam-4467	352	2	lεψ	lεψ	VERB
ejpam-4467	352	3	)	)	PUNCT
ejpam-4467	352	4	.	.	PUNCT
ejpam-4467	353	1	(	(	PUNCT
ejpam-4467	353	2	38	38	NUM
ejpam-4467	353	3	)	)	PUNCT
ejpam-4467	353	4	then	then	ADV
ejpam-4467	353	5	the	the	DET
ejpam-4467	353	6	o	o	NOUN
ejpam-4467	353	7	-	-	NOUN
ejpam-4467	353	8	set	set	NOUN
ejpam-4467	353	9	of	of	ADP
ejpam-4467	353	10	lεψ	lεψ	PROPN
ejpam-4467	353	11	is	be	AUX
ejpam-4467	353	12	an	an	DET
ejpam-4467	353	13	ideal	ideal	NOUN
ejpam-4467	353	14	of	of	ADP
ejpam-4467	353	15	(	(	PUNCT
ejpam-4467	353	16	x	x	X
ejpam-4467	353	17	,	,	PUNCT
ejpam-4467	353	18	1)∗.	1)∗.	PRON
ejpam-4467	353	19	proof	proof	NOUN
ejpam-4467	353	20	.	.	PUNCT
ejpam-4467	354	1	let	let	VERB
ejpam-4467	354	2	o	o	INTJ
ejpam-4467	354	3	(	(	PUNCT
ejpam-4467	354	4	lεψ	lεψ	ADJ
ejpam-4467	354	5	)	)	PUNCT
ejpam-4467	354	6	be	be	AUX
ejpam-4467	354	7	the	the	DET
ejpam-4467	354	8	o	o	NOUN
ejpam-4467	354	9	-	-	NOUN
ejpam-4467	354	10	set	set	NOUN
ejpam-4467	354	11	of	of	ADP
ejpam-4467	354	12	lεψ	lεψ	ADJ
ejpam-4467	354	13	.	.	PUNCT
ejpam-4467	355	1	if	if	SCONJ
ejpam-4467	355	2	⟨1	⟨1	PROPN
ejpam-4467	355	3	/	/	SYM
ejpam-4467	355	4	ε⟩	ε⟩	NOUN
ejpam-4467	355	5	q	q	X
ejpam-4467	355	6	ψ	ψ	NOUN
ejpam-4467	355	7	,	,	PUNCT
ejpam-4467	355	8	then	then	ADV
ejpam-4467	355	9	ψ(1	ψ(1	PROPN
ejpam-4467	355	10	)	)	PUNCT
ejpam-4467	356	1	+	+	CCONJ
ejpam-4467	356	2	ε	ε	PROPN
ejpam-4467	356	3	>	>	X
ejpam-4467	356	4	1	1	NUM
ejpam-4467	356	5	and	and	CCONJ
ejpam-4467	356	6	so	so	ADV
ejpam-4467	356	7	lεψ(1	lεψ(1	ADJ
ejpam-4467	356	8	)	)	PUNCT
ejpam-4467	356	9	=	=	SYM
ejpam-4467	356	10	max{0	max{0	PROPN
ejpam-4467	356	11	,	,	PUNCT
ejpam-4467	356	12	ψ(1	ψ(1	PROPN
ejpam-4467	356	13	)	)	PUNCT
ejpam-4467	356	14	+	+	CCONJ
ejpam-4467	356	15	ε−	ε−	PROPN
ejpam-4467	356	16	1	1	NUM
ejpam-4467	356	17	}	}	PUNCT
ejpam-4467	356	18	=	=	SYM
ejpam-4467	356	19	ψ(1	ψ(1	PROPN
ejpam-4467	356	20	)	)	PUNCT
ejpam-4467	356	21	+	+	CCONJ
ejpam-4467	356	22	ε−	ε−	PROPN
ejpam-4467	356	23	1	1	NUM
ejpam-4467	356	24	>	>	SYM
ejpam-4467	356	25	0	0	NUM
ejpam-4467	356	26	.	.	PUNCT
ejpam-4467	357	1	hence	hence	ADV
ejpam-4467	357	2	1	1	NUM
ejpam-4467	357	3	∈	∈	NOUN
ejpam-4467	357	4	o	o	NOUN
ejpam-4467	357	5	(	(	PUNCT
ejpam-4467	357	6	lεψ	lεψ	ADJ
ejpam-4467	357	7	)	)	PUNCT
ejpam-4467	357	8	.	.	PUNCT
ejpam-4467	358	1	let	let	VERB
ejpam-4467	358	2	x	x	PRON
ejpam-4467	358	3	,	,	PUNCT
ejpam-4467	358	4	y	y	PROPN
ejpam-4467	358	5	,	,	PUNCT
ejpam-4467	358	6	z	z	NOUN
ejpam-4467	358	7	∈	∈	PROPN
ejpam-4467	358	8	x	x	AUX
ejpam-4467	358	9	be	be	AUX
ejpam-4467	358	10	such	such	ADJ
ejpam-4467	358	11	that	that	SCONJ
ejpam-4467	358	12	x	x	SYM
ejpam-4467	358	13	∗	∗	NOUN
ejpam-4467	358	14	(	(	PUNCT
ejpam-4467	358	15	y	y	PROPN
ejpam-4467	358	16	∗	∗	PROPN
ejpam-4467	358	17	z	z	PROPN
ejpam-4467	358	18	)	)	PUNCT
ejpam-4467	358	19	∈	∈	PROPN
ejpam-4467	358	20	o	o	NOUN
ejpam-4467	358	21	(	(	PUNCT
ejpam-4467	358	22	lεψ	lεψ	ADJ
ejpam-4467	358	23	)	)	PUNCT
ejpam-4467	358	24	and	and	CCONJ
ejpam-4467	358	25	y	y	PROPN
ejpam-4467	358	26	∈	∈	PROPN
ejpam-4467	359	1	o	o	NOUN
ejpam-4467	359	2	(	(	PUNCT
ejpam-4467	359	3	lεψ	lεψ	ADJ
ejpam-4467	359	4	)	)	PUNCT
ejpam-4467	359	5	.	.	PUNCT
ejpam-4467	360	1	then	then	ADV
ejpam-4467	360	2	ψ(x	ψ(x	NOUN
ejpam-4467	360	3	∗	∗	NOUN
ejpam-4467	360	4	(	(	PUNCT
ejpam-4467	360	5	y	y	PROPN
ejpam-4467	360	6	∗	∗	PROPN
ejpam-4467	360	7	z	z	PROPN
ejpam-4467	360	8	)	)	PUNCT
ejpam-4467	360	9	)	)	PUNCT
ejpam-4467	361	1	+	+	CCONJ
ejpam-4467	361	2	ε	ε	X
ejpam-4467	361	3	>	>	SYM
ejpam-4467	361	4	1	1	NUM
ejpam-4467	361	5	and	and	CCONJ
ejpam-4467	361	6	ψ(y	ψ(y	NOUN
ejpam-4467	361	7	)	)	PUNCT
ejpam-4467	362	1	+	+	CCONJ
ejpam-4467	362	2	ε	ε	PROPN
ejpam-4467	362	3	>	>	X
ejpam-4467	362	4	1	1	NUM
ejpam-4467	362	5	,	,	PUNCT
ejpam-4467	362	6	i.e.	i.e.	X
ejpam-4467	362	7	,	,	PUNCT
ejpam-4467	362	8	⟨(x	⟨(x	NOUN
ejpam-4467	362	9	∗	∗	NOUN
ejpam-4467	362	10	(	(	PUNCT
ejpam-4467	362	11	y	y	PROPN
ejpam-4467	362	12	∗	∗	PROPN
ejpam-4467	362	13	z))/ε⟩	z))/ε⟩	PROPN
ejpam-4467	362	14	q	q	X
ejpam-4467	362	15	ψ	ψ	NOUN
ejpam-4467	362	16	and	and	CCONJ
ejpam-4467	362	17	⟨y	⟨y	NOUN
ejpam-4467	362	18	/	/	SYM
ejpam-4467	362	19	ε⟩	ε⟩	NOUN
ejpam-4467	362	20	q	q	X
ejpam-4467	362	21	ψ	ψ	X
ejpam-4467	362	22	.	.	PUNCT
ejpam-4467	363	1	it	it	PRON
ejpam-4467	363	2	follows	follow	VERB
ejpam-4467	363	3	from	from	ADP
ejpam-4467	363	4	(	(	PUNCT
ejpam-4467	363	5	38	38	NUM
ejpam-4467	363	6	)	)	PUNCT
ejpam-4467	363	7	that	that	PRON
ejpam-4467	363	8	⟨(x	⟨(x	PROPN
ejpam-4467	364	1	∗	∗	NOUN
ejpam-4467	364	2	z)/ε⟩	z)/ε⟩	PUNCT
ejpam-4467	364	3	∈	∈	PROPN
ejpam-4467	364	4	lεψ	lεψ	PROPN
ejpam-4467	364	5	,	,	PUNCT
ejpam-4467	364	6	which	which	PRON
ejpam-4467	364	7	shows	show	VERB
ejpam-4467	364	8	lεψ(x	lεψ(x	PROPN
ejpam-4467	364	9	∗	∗	PROPN
ejpam-4467	364	10	z	z	NOUN
ejpam-4467	364	11	)	)	PUNCT
ejpam-4467	364	12	≥	≥	X
ejpam-4467	364	13	ε	ε	PROPN
ejpam-4467	364	14	>	>	X
ejpam-4467	364	15	0	0	X
ejpam-4467	364	16	.	.	PUNCT
ejpam-4467	365	1	hence	hence	ADV
ejpam-4467	365	2	x	x	X
ejpam-4467	365	3	∗	∗	NOUN
ejpam-4467	365	4	z	z	NOUN
ejpam-4467	365	5	∈	∈	PROPN
ejpam-4467	365	6	o	o	NOUN
ejpam-4467	365	7	(	(	PUNCT
ejpam-4467	365	8	lεψ	lεψ	ADJ
ejpam-4467	365	9	)	)	PUNCT
ejpam-4467	365	10	,	,	PUNCT
ejpam-4467	365	11	and	and	CCONJ
ejpam-4467	365	12	therefore	therefore	ADV
ejpam-4467	365	13	o	o	X
ejpam-4467	365	14	(	(	PUNCT
ejpam-4467	365	15	lεψ	lεψ	ADJ
ejpam-4467	365	16	)	)	PUNCT
ejpam-4467	365	17	is	be	AUX
ejpam-4467	365	18	an	an	DET
ejpam-4467	365	19	ideal	ideal	NOUN
ejpam-4467	365	20	of	of	ADP
ejpam-4467	365	21	(	(	PUNCT
ejpam-4467	365	22	x	x	X
ejpam-4467	365	23	,	,	PUNCT
ejpam-4467	365	24	1)∗	1)∗	NUM
ejpam-4467	365	25	by	by	ADP
ejpam-4467	365	26	lemma	lemma	PROPN
ejpam-4467	365	27	1	1	NUM
ejpam-4467	365	28	.	.	PUNCT
ejpam-4467	365	29	theorem	theorem	NOUN
ejpam-4467	365	30	18	18	NUM
ejpam-4467	365	31	.	.	PUNCT
ejpam-4467	366	1	let	let	VERB
ejpam-4467	366	2	lεψ	lεψ	ADJ
ejpam-4467	366	3	be	be	AUX
ejpam-4467	366	4	a	a	DET
ejpam-4467	366	5	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	366	6	fuzzy	fuzzy	ADJ
ejpam-4467	366	7	set	set	VERB
ejpam-4467	366	8	in	in	ADP
ejpam-4467	366	9	x	x	PUNCT
ejpam-4467	366	10	that	that	PRON
ejpam-4467	366	11	satisfies	satisfy	VERB
ejpam-4467	366	12	:	:	PUNCT
ejpam-4467	366	13	(	(	PUNCT
ejpam-4467	366	14	∀x	∀x	X
ejpam-4467	366	15	,	,	PUNCT
ejpam-4467	366	16	y	y	PROPN
ejpam-4467	366	17	∈	∈	PROPN
ejpam-4467	367	1	x)(∀t	x)(∀t	PUNCT
ejpam-4467	367	2	∈	∈	PROPN
ejpam-4467	367	3	[	[	X
ejpam-4467	367	4	ε	ε	PROPN
ejpam-4467	367	5	,	,	PUNCT
ejpam-4467	367	6	1	1	NUM
ejpam-4467	367	7	]	]	PUNCT
ejpam-4467	367	8	)	)	PUNCT
ejpam-4467	367	9	(	(	PUNCT
ejpam-4467	367	10	⟨y	⟨y	X
ejpam-4467	367	11	/	/	SYM
ejpam-4467	367	12	t⟩	t⟩	NOUN
ejpam-4467	367	13	q	q	X
ejpam-4467	367	14	ψ	ψ	NOUN
ejpam-4467	367	15	⇒	⇒	PROPN
ejpam-4467	367	16	⟨(x	⟨(x	PROPN
ejpam-4467	367	17	∗	∗	NOUN
ejpam-4467	367	18	y)/ε⟩	y)/ε⟩	PROPN
ejpam-4467	367	19	∈	∈	PROPN
ejpam-4467	367	20	lεψ	lεψ	VERB
ejpam-4467	367	21	)	)	PUNCT
ejpam-4467	367	22	,	,	PUNCT
ejpam-4467	367	23	(	(	PUNCT
ejpam-4467	367	24	39	39	NUM
ejpam-4467	367	25	)	)	PUNCT
ejpam-4467	367	26	(	(	PUNCT
ejpam-4467	367	27	∀x	∀x	X
ejpam-4467	367	28	,	,	PUNCT
ejpam-4467	367	29	y	y	PROPN
ejpam-4467	367	30	,	,	PUNCT
ejpam-4467	367	31	z	z	PROPN
ejpam-4467	367	32	∈	∈	PROPN
ejpam-4467	367	33	x)(∀ta	x)(∀ta	NOUN
ejpam-4467	367	34	,	,	PUNCT
ejpam-4467	367	35	tb	tb	ADP
ejpam-4467	367	36	∈	∈	PROPN
ejpam-4467	367	37	[	[	X
ejpam-4467	367	38	ε	ε	PROPN
ejpam-4467	367	39	,	,	PUNCT
ejpam-4467	367	40	1	1	NUM
ejpam-4467	367	41	]	]	PUNCT
ejpam-4467	367	42	)	)	PUNCT
ejpam-4467	367	43	(	(	PUNCT
ejpam-4467	367	44	⟨x	⟨x	VERB
ejpam-4467	367	45	/	/	SYM
ejpam-4467	367	46	ta⟩	ta⟩	ADJ
ejpam-4467	367	47	q	q	PROPN
ejpam-4467	367	48	ψ	ψ	PROPN
ejpam-4467	367	49	,	,	PUNCT
ejpam-4467	367	50	⟨y	⟨y	X
ejpam-4467	367	51	/	/	SYM
ejpam-4467	367	52	tb⟩	tb⟩	PROPN
ejpam-4467	367	53	q	q	NOUN
ejpam-4467	367	54	ψ	ψ	NOUN
ejpam-4467	367	55	⇒	⇒	NOUN
ejpam-4467	367	56	(	(	PUNCT
ejpam-4467	367	57	x	x	SYM
ejpam-4467	367	58	∗	∗	NOUN
ejpam-4467	367	59	(	(	PUNCT
ejpam-4467	367	60	y	y	PROPN
ejpam-4467	367	61	∗	∗	PROPN
ejpam-4467	367	62	z	z	NOUN
ejpam-4467	367	63	)	)	PUNCT
ejpam-4467	367	64	)	)	PUNCT
ejpam-4467	367	65	∗	∗	NOUN
ejpam-4467	367	66	z	z	NOUN
ejpam-4467	367	67	∈	∈	PROPN
ejpam-4467	367	68	(	(	PUNCT
ejpam-4467	367	69	lεψ	lεψ	ADJ
ejpam-4467	367	70	,	,	PUNCT
ejpam-4467	367	71	ε)∈	ε)∈	PROPN
ejpam-4467	367	72	)	)	PUNCT
ejpam-4467	367	73	.	.	PUNCT
ejpam-4467	368	1	(	(	PUNCT
ejpam-4467	368	2	40	40	NUM
ejpam-4467	368	3	)	)	PUNCT
ejpam-4467	368	4	then	then	ADV
ejpam-4467	368	5	the	the	DET
ejpam-4467	368	6	o	o	NOUN
ejpam-4467	368	7	-	-	NOUN
ejpam-4467	368	8	set	set	NOUN
ejpam-4467	368	9	of	of	ADP
ejpam-4467	368	10	lεψ	lεψ	PROPN
ejpam-4467	368	11	is	be	AUX
ejpam-4467	368	12	an	an	DET
ejpam-4467	368	13	ideal	ideal	NOUN
ejpam-4467	368	14	of	of	ADP
ejpam-4467	368	15	(	(	PUNCT
ejpam-4467	368	16	x	x	X
ejpam-4467	368	17	,	,	PUNCT
ejpam-4467	368	18	1)∗.	1)∗.	PRON
ejpam-4467	368	19	proof	proof	NOUN
ejpam-4467	368	20	.	.	PUNCT
ejpam-4467	369	1	let	let	VERB
ejpam-4467	369	2	t	t	PROPN
ejpam-4467	369	3	∈	∈	PROPN
ejpam-4467	370	1	[	[	X
ejpam-4467	370	2	ε	ε	PROPN
ejpam-4467	370	3	,	,	PUNCT
ejpam-4467	370	4	1	1	NUM
ejpam-4467	370	5	]	]	PUNCT
ejpam-4467	370	6	,	,	PUNCT
ejpam-4467	370	7	x	x	SYM
ejpam-4467	370	8	∈	∈	PROPN
ejpam-4467	370	9	x	x	X
ejpam-4467	370	10	and	and	CCONJ
ejpam-4467	370	11	y	y	PROPN
ejpam-4467	370	12	∈	∈	PROPN
ejpam-4467	370	13	o	o	NOUN
ejpam-4467	370	14	(	(	PUNCT
ejpam-4467	370	15	lεψ	lεψ	ADJ
ejpam-4467	370	16	)	)	PUNCT
ejpam-4467	370	17	.	.	PUNCT
ejpam-4467	371	1	then	then	ADV
ejpam-4467	371	2	ψ(y	ψ(y	NOUN
ejpam-4467	371	3	)	)	PUNCT
ejpam-4467	371	4	+	+	NUM
ejpam-4467	371	5	t	t	PROPN
ejpam-4467	371	6	≥	≥	PROPN
ejpam-4467	371	7	ψ(y	ψ(y	PROPN
ejpam-4467	371	8	)	)	PUNCT
ejpam-4467	372	1	+	+	CCONJ
ejpam-4467	372	2	ε	ε	PROPN
ejpam-4467	372	3	>	>	X
ejpam-4467	372	4	1	1	NUM
ejpam-4467	372	5	,	,	PUNCT
ejpam-4467	372	6	and	and	CCONJ
ejpam-4467	372	7	so	so	ADV
ejpam-4467	372	8	⟨y	⟨y	NOUN
ejpam-4467	372	9	/	/	SYM
ejpam-4467	372	10	t⟩	t⟩	PRON
ejpam-4467	372	11	q	q	X
ejpam-4467	373	1	ψ	ψ	NOUN
ejpam-4467	373	2	,	,	PUNCT
ejpam-4467	373	3	which	which	PRON
ejpam-4467	373	4	implies	imply	VERB
ejpam-4467	373	5	that	that	SCONJ
ejpam-4467	373	6	⟨(x	⟨(x	PROPN
ejpam-4467	373	7	∗	∗	NOUN
ejpam-4467	373	8	y)/ε⟩	y)/ε⟩	PROPN
ejpam-4467	373	9	∈	∈	PROPN
ejpam-4467	373	10	lεψ	lεψ	VERB
ejpam-4467	373	11	by	by	ADP
ejpam-4467	373	12	(	(	PUNCT
ejpam-4467	373	13	39	39	NUM
ejpam-4467	373	14	)	)	PUNCT
ejpam-4467	373	15	.	.	PUNCT
ejpam-4467	374	1	hence	hence	ADV
ejpam-4467	374	2	lεψ(x	lεψ(x	PROPN
ejpam-4467	374	3	∗	∗	NOUN
ejpam-4467	374	4	y	y	PROPN
ejpam-4467	374	5	)	)	PUNCT
ejpam-4467	374	6	≥	≥	X
ejpam-4467	374	7	ε	ε	PROPN
ejpam-4467	374	8	>	>	X
ejpam-4467	374	9	0	0	NUM
ejpam-4467	374	10	,	,	PUNCT
ejpam-4467	374	11	i.e.	i.e.	X
ejpam-4467	374	12	,	,	PUNCT
ejpam-4467	374	13	x	x	X
ejpam-4467	374	14	∗	∗	NOUN
ejpam-4467	374	15	y	y	PROPN
ejpam-4467	374	16	∈	∈	PROPN
ejpam-4467	375	1	o	o	NOUN
ejpam-4467	375	2	(	(	PUNCT
ejpam-4467	375	3	lεψ	lεψ	PROPN
ejpam-4467	375	4	)	)	PUNCT
ejpam-4467	375	5	.	.	PUNCT
ejpam-4467	376	1	let	let	VERB
ejpam-4467	376	2	ta	ta	PART
ejpam-4467	376	3	,	,	PUNCT
ejpam-4467	376	4	tb	tb	ADP
ejpam-4467	376	5	∈	∈	PROPN
ejpam-4467	376	6	[	[	X
ejpam-4467	376	7	ε	ε	PROPN
ejpam-4467	376	8	,	,	PUNCT
ejpam-4467	376	9	1	1	NUM
ejpam-4467	376	10	]	]	PUNCT
ejpam-4467	376	11	and	and	CCONJ
ejpam-4467	376	12	x	x	NOUN
ejpam-4467	376	13	,	,	PUNCT
ejpam-4467	376	14	y	y	PROPN
ejpam-4467	376	15	,	,	PUNCT
ejpam-4467	376	16	z	z	NOUN
ejpam-4467	376	17	∈	∈	PROPN
ejpam-4467	376	18	x	x	AUX
ejpam-4467	376	19	be	be	AUX
ejpam-4467	376	20	such	such	ADJ
ejpam-4467	376	21	that	that	SCONJ
ejpam-4467	376	22	x	x	SYM
ejpam-4467	376	23	∈	∈	PRON
ejpam-4467	376	24	o	o	NOUN
ejpam-4467	376	25	(	(	PUNCT
ejpam-4467	376	26	lεψ	lεψ	ADJ
ejpam-4467	376	27	)	)	PUNCT
ejpam-4467	376	28	and	and	CCONJ
ejpam-4467	376	29	y	y	PROPN
ejpam-4467	376	30	∈	∈	PROPN
ejpam-4467	377	1	o	o	NOUN
ejpam-4467	377	2	(	(	PUNCT
ejpam-4467	377	3	lεψ	lεψ	ADJ
ejpam-4467	377	4	)	)	PUNCT
ejpam-4467	377	5	.	.	PUNCT
ejpam-4467	378	1	then	then	ADV
ejpam-4467	378	2	ψ(x)+ta	ψ(x)+ta	PROPN
ejpam-4467	378	3	≥	≥	PRON
ejpam-4467	378	4	ψ(x)+ε	ψ(x)+ε	X
ejpam-4467	378	5	>	>	X
ejpam-4467	378	6	1	1	NUM
ejpam-4467	378	7	and	and	CCONJ
ejpam-4467	378	8	ψ(y)+tb	ψ(y)+tb	VERB
ejpam-4467	378	9	≥	≥	PROPN
ejpam-4467	378	10	ψ(y)+ε	ψ(y)+ε	X
ejpam-4467	378	11	>	>	X
ejpam-4467	379	1	1	1	X
ejpam-4467	379	2	.	.	PUNCT
ejpam-4467	379	3	thus	thus	ADV
ejpam-4467	379	4	⟨x	⟨x	VERB
ejpam-4467	379	5	/	/	SYM
ejpam-4467	379	6	ta⟩	ta⟩	ADJ
ejpam-4467	379	7	q	q	NOUN
ejpam-4467	379	8	ψ	ψ	PROPN
ejpam-4467	379	9	and	and	CCONJ
ejpam-4467	379	10	⟨y	⟨y	NOUN
ejpam-4467	379	11	/	/	SYM
ejpam-4467	379	12	tb⟩	tb⟩	PROPN
ejpam-4467	379	13	q	q	NOUN
ejpam-4467	379	14	ψ	ψ	ADP
ejpam-4467	379	15	using	use	VERB
ejpam-4467	379	16	(	(	PUNCT
ejpam-4467	379	17	40	40	NUM
ejpam-4467	379	18	)	)	PUNCT
ejpam-4467	379	19	leads	lead	VERB
ejpam-4467	379	20	to	to	ADP
ejpam-4467	379	21	(	(	PUNCT
ejpam-4467	379	22	x	x	X
ejpam-4467	379	23	∗	∗	NOUN
ejpam-4467	379	24	(	(	PUNCT
ejpam-4467	379	25	y	y	PROPN
ejpam-4467	379	26	∗	∗	PROPN
ejpam-4467	379	27	z	z	NOUN
ejpam-4467	379	28	)	)	PUNCT
ejpam-4467	379	29	)	)	PUNCT
ejpam-4467	380	1	∗	∗	NOUN
ejpam-4467	380	2	z	z	NOUN
ejpam-4467	380	3	∈	∈	PROPN
ejpam-4467	380	4	(	(	PUNCT
ejpam-4467	380	5	lεψ	lεψ	ADJ
ejpam-4467	380	6	,	,	PUNCT
ejpam-4467	380	7	ε)∈.	ε)∈.	NOUN
ejpam-4467	380	8	hence	hence	ADV
ejpam-4467	380	9	lεψ((x	lεψ((x	NOUN
ejpam-4467	380	10	∗	∗	NOUN
ejpam-4467	380	11	(	(	PUNCT
ejpam-4467	380	12	y	y	PROPN
ejpam-4467	380	13	∗	∗	PROPN
ejpam-4467	380	14	z	z	NOUN
ejpam-4467	380	15	)	)	PUNCT
ejpam-4467	380	16	)	)	PUNCT
ejpam-4467	380	17	∗	∗	PROPN
ejpam-4467	380	18	z	z	NOUN
ejpam-4467	380	19	)	)	PUNCT
ejpam-4467	380	20	≥	≥	X
ejpam-4467	380	21	ε	ε	PROPN
ejpam-4467	380	22	>	>	X
ejpam-4467	380	23	0	0	PROPN
ejpam-4467	380	24	,	,	PUNCT
ejpam-4467	380	25	and	and	CCONJ
ejpam-4467	380	26	so	so	ADV
ejpam-4467	380	27	(	(	PUNCT
ejpam-4467	380	28	x	x	SYM
ejpam-4467	380	29	∗	∗	NOUN
ejpam-4467	380	30	(	(	PUNCT
ejpam-4467	380	31	y	y	PROPN
ejpam-4467	380	32	∗	∗	PROPN
ejpam-4467	380	33	z	z	NOUN
ejpam-4467	380	34	)	)	PUNCT
ejpam-4467	380	35	)	)	PUNCT
ejpam-4467	381	1	∗	∗	NOUN
ejpam-4467	381	2	z	z	X
ejpam-4467	381	3	∈	∈	PROPN
ejpam-4467	382	1	o	o	NOUN
ejpam-4467	382	2	(	(	PUNCT
ejpam-4467	382	3	lεψ	lεψ	PROPN
ejpam-4467	382	4	)	)	PUNCT
ejpam-4467	382	5	.	.	PUNCT
ejpam-4467	383	1	consequently	consequently	ADV
ejpam-4467	383	2	,	,	PUNCT
ejpam-4467	383	3	o	o	X
ejpam-4467	383	4	(	(	PUNCT
ejpam-4467	383	5	lεψ	lεψ	ADJ
ejpam-4467	383	6	)	)	PUNCT
ejpam-4467	383	7	is	be	AUX
ejpam-4467	383	8	an	an	DET
ejpam-4467	383	9	ideal	ideal	NOUN
ejpam-4467	383	10	of	of	ADP
ejpam-4467	383	11	(	(	PUNCT
ejpam-4467	383	12	x	x	X
ejpam-4467	383	13	,	,	PUNCT
ejpam-4467	383	14	1)∗.	1)∗.	PRON
ejpam-4467	383	15	corollary	corollary	ADJ
ejpam-4467	383	16	3	3	X
ejpam-4467	383	17	.	.	PUNCT
ejpam-4467	384	1	let	let	VERB
ejpam-4467	384	2	lεψ	lεψ	ADJ
ejpam-4467	384	3	be	be	AUX
ejpam-4467	384	4	a	a	DET
ejpam-4467	384	5	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	384	6	fuzzy	fuzzy	ADJ
ejpam-4467	384	7	set	set	VERB
ejpam-4467	384	8	in	in	ADP
ejpam-4467	384	9	x	x	PUNCT
ejpam-4467	384	10	that	that	PRON
ejpam-4467	384	11	satisfies	satisfy	VERB
ejpam-4467	384	12	:	:	PUNCT
ejpam-4467	384	13	(	(	PUNCT
ejpam-4467	384	14	∀x	∀x	X
ejpam-4467	384	15	,	,	PUNCT
ejpam-4467	384	16	y	y	PROPN
ejpam-4467	384	17	∈	∈	PROPN
ejpam-4467	384	18	x	x	X
ejpam-4467	384	19	)	)	PUNCT
ejpam-4467	384	20	(	(	PUNCT
ejpam-4467	384	21	⟨y	⟨y	X
ejpam-4467	384	22	/	/	SYM
ejpam-4467	384	23	ε⟩	ε⟩	NOUN
ejpam-4467	384	24	q	q	X
ejpam-4467	384	25	ψ	ψ	NOUN
ejpam-4467	384	26	⇒	⇒	PROPN
ejpam-4467	384	27	⟨(x	⟨(x	PROPN
ejpam-4467	384	28	∗	∗	NOUN
ejpam-4467	384	29	y)/ε⟩	y)/ε⟩	PROPN
ejpam-4467	384	30	∈	∈	PROPN
ejpam-4467	384	31	lεψ	lεψ	VERB
ejpam-4467	384	32	)	)	PUNCT
ejpam-4467	384	33	,	,	PUNCT
ejpam-4467	384	34	(	(	PUNCT
ejpam-4467	384	35	41	41	NUM
ejpam-4467	384	36	)	)	PUNCT
ejpam-4467	384	37	(	(	PUNCT
ejpam-4467	384	38	∀x	∀x	X
ejpam-4467	384	39	,	,	PUNCT
ejpam-4467	384	40	y	y	PROPN
ejpam-4467	384	41	,	,	PUNCT
ejpam-4467	384	42	z	z	NOUN
ejpam-4467	384	43	∈	∈	PROPN
ejpam-4467	384	44	x	x	X
ejpam-4467	384	45	)	)	PUNCT
ejpam-4467	384	46	(	(	PUNCT
ejpam-4467	384	47	⟨x	⟨x	VERB
ejpam-4467	384	48	/	/	SYM
ejpam-4467	384	49	ε⟩	ε⟩	NOUN
ejpam-4467	384	50	q	q	ADJ
ejpam-4467	384	51	ψ	ψ	NOUN
ejpam-4467	384	52	,	,	PUNCT
ejpam-4467	384	53	⟨y	⟨y	X
ejpam-4467	384	54	/	/	SYM
ejpam-4467	384	55	ε⟩	ε⟩	NOUN
ejpam-4467	384	56	q	q	X
ejpam-4467	384	57	ψ	ψ	NOUN
ejpam-4467	384	58	⇒	⇒	NOUN
ejpam-4467	384	59	(	(	PUNCT
ejpam-4467	384	60	x	x	SYM
ejpam-4467	384	61	∗	∗	NOUN
ejpam-4467	384	62	(	(	PUNCT
ejpam-4467	384	63	y	y	PROPN
ejpam-4467	384	64	∗	∗	PROPN
ejpam-4467	384	65	z	z	NOUN
ejpam-4467	384	66	)	)	PUNCT
ejpam-4467	384	67	)	)	PUNCT
ejpam-4467	385	1	∗	∗	NOUN
ejpam-4467	385	2	z	z	NOUN
ejpam-4467	385	3	∈	∈	PROPN
ejpam-4467	385	4	(	(	PUNCT
ejpam-4467	385	5	lεψ	lεψ	ADJ
ejpam-4467	385	6	,	,	PUNCT
ejpam-4467	385	7	ε)∈	ε)∈	PROPN
ejpam-4467	385	8	)	)	PUNCT
ejpam-4467	385	9	.	.	PUNCT
ejpam-4467	386	1	(	(	PUNCT
ejpam-4467	386	2	42	42	NUM
ejpam-4467	386	3	)	)	PUNCT
ejpam-4467	386	4	then	then	ADV
ejpam-4467	386	5	the	the	DET
ejpam-4467	386	6	o	o	NOUN
ejpam-4467	386	7	-	-	NOUN
ejpam-4467	386	8	set	set	NOUN
ejpam-4467	386	9	of	of	ADP
ejpam-4467	386	10	lεψ	lεψ	PROPN
ejpam-4467	386	11	is	be	AUX
ejpam-4467	386	12	an	an	DET
ejpam-4467	386	13	ideal	ideal	NOUN
ejpam-4467	386	14	of	of	ADP
ejpam-4467	386	15	(	(	PUNCT
ejpam-4467	386	16	x	x	X
ejpam-4467	386	17	,	,	PUNCT
ejpam-4467	386	18	1)∗.	1)∗.	PROPN
ejpam-4467	386	19	4	4	NUM
ejpam-4467	386	20	.	.	PUNCT
ejpam-4467	386	21	conclusions	conclusion	NOUN
ejpam-4467	386	22	and	and	CCONJ
ejpam-4467	386	23	future	future	ADJ
ejpam-4467	386	24	work	work	NOUN
ejpam-4467	386	25	the	the	DET
ejpam-4467	386	26	concept	concept	NOUN
ejpam-4467	386	27	of	of	ADP
ejpam-4467	386	28	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	386	29	fuzzy	fuzzy	ADJ
ejpam-4467	386	30	sets	set	NOUN
ejpam-4467	386	31	using	use	VERB
ejpam-4467	386	32	lukasiewicz	lukasiewicz	PROPN
ejpam-4467	386	33	t	t	PROPN
ejpam-4467	386	34	-	-	PUNCT
ejpam-4467	386	35	norm	norm	NOUN
ejpam-4467	386	36	was	be	AUX
ejpam-4467	386	37	introduced	introduce	VERB
ejpam-4467	386	38	by	by	ADP
ejpam-4467	386	39	y.	y.	PROPN
ejpam-4467	386	40	b.	b.	PROPN
ejpam-4467	386	41	jun	jun	PROPN
ejpam-4467	386	42	.	.	PROPN
ejpam-4467	387	1	in	in	ADP
ejpam-4467	387	2	this	this	DET
ejpam-4467	387	3	paper	paper	NOUN
ejpam-4467	387	4	,	,	PUNCT
ejpam-4467	387	5	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	387	6	fuzzy	fuzzy	ADJ
ejpam-4467	387	7	set	set	NOUN
ejpam-4467	387	8	has	have	AUX
ejpam-4467	387	9	been	be	AUX
ejpam-4467	387	10	applied	apply	VERB
ejpam-4467	387	11	to	to	ADP
ejpam-4467	387	12	the	the	DET
ejpam-4467	387	13	ideal	ideal	NOUN
ejpam-4467	387	14	in	in	ADP
ejpam-4467	387	15	bealgebra	bealgebra	NOUN
ejpam-4467	387	16	,	,	PUNCT
ejpam-4467	387	17	and	and	CCONJ
ejpam-4467	387	18	introducing	introduce	VERB
ejpam-4467	387	19	the	the	DET
ejpam-4467	387	20	concept	concept	NOUN
ejpam-4467	387	21	of	of	ADP
ejpam-4467	387	22	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	387	23	fuzzy	fuzzy	ADJ
ejpam-4467	387	24	ideal	ideal	NOUN
ejpam-4467	387	25	and	and	CCONJ
ejpam-4467	387	26	examining	examine	VERB
ejpam-4467	387	27	several	several	ADJ
ejpam-4467	387	28	properties	property	NOUN
ejpam-4467	387	29	.	.	PUNCT
ejpam-4467	388	1	we	we	PRON
ejpam-4467	388	2	discussed	discuss	VERB
ejpam-4467	388	3	the	the	DET
ejpam-4467	388	4	characterization	characterization	NOUN
ejpam-4467	388	5	of	of	ADP
ejpam-4467	388	6	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	388	7	fuzzy	fuzzy	ADJ
ejpam-4467	388	8	ideal	ideal	NOUN
ejpam-4467	388	9	and	and	CCONJ
ejpam-4467	388	10	considered	consider	VERB
ejpam-4467	388	11	the	the	DET
ejpam-4467	388	12	relationship	relationship	NOUN
ejpam-4467	388	13	between	between	ADP
ejpam-4467	388	14	fuzzy	fuzzy	ADJ
ejpam-4467	388	15	ideal	ideal	NOUN
ejpam-4467	388	16	and	and	CCONJ
ejpam-4467	388	17	lukasiewicz	lukasiewicz	VERB
ejpam-4467	388	18	fuzzy	fuzzy	ADJ
ejpam-4467	388	19	ideal	ideal	NOUN
ejpam-4467	388	20	.	.	PUNCT
ejpam-4467	389	1	we	we	PRON
ejpam-4467	389	2	provided	provide	VERB
ejpam-4467	389	3	conditions	condition	NOUN
ejpam-4467	389	4	references	reference	NOUN
ejpam-4467	389	5	1320	1320	NUM
ejpam-4467	389	6	under	under	ADP
ejpam-4467	389	7	which	which	PRON
ejpam-4467	389	8	lukasiewicz	lukasiewicz	ADJ
ejpam-4467	389	9	fuzzy	fuzzy	ADJ
ejpam-4467	389	10	set	set	NOUN
ejpam-4467	389	11	can	can	AUX
ejpam-4467	389	12	be	be	AUX
ejpam-4467	389	13	lukasiewicz	lukasiewicz	VERB
ejpam-4467	389	14	fuzzy	fuzzy	ADJ
ejpam-4467	389	15	ideal	ideal	NOUN
ejpam-4467	389	16	,	,	PUNCT
ejpam-4467	389	17	and	and	CCONJ
ejpam-4467	389	18	further	far	ADV
ejpam-4467	389	19	explored	explore	VERB
ejpam-4467	389	20	conditions	condition	NOUN
ejpam-4467	389	21	under	under	ADP
ejpam-4467	389	22	which	which	PRON
ejpam-4467	389	23	three	three	NUM
ejpam-4467	389	24	subsets	subset	NOUN
ejpam-4467	389	25	,	,	PUNCT
ejpam-4467	389	26	∈-set	∈-set	NOUN
ejpam-4467	389	27	,	,	PUNCT
ejpam-4467	389	28	q	q	NOUN
ejpam-4467	389	29	-	-	PUNCT
ejpam-4467	389	30	set	set	NOUN
ejpam-4467	389	31	,	,	PUNCT
ejpam-4467	389	32	and	and	CCONJ
ejpam-4467	389	33	o	o	X
ejpam-4467	389	34	-	-	NOUN
ejpam-4467	389	35	set	set	ADJ
ejpam-4467	389	36	,	,	PUNCT
ejpam-4467	389	37	will	will	AUX
ejpam-4467	389	38	be	be	AUX
ejpam-4467	389	39	ideal	ideal	ADJ
ejpam-4467	389	40	the	the	DET
ejpam-4467	389	41	ideas	idea	NOUN
ejpam-4467	389	42	and	and	CCONJ
ejpam-4467	389	43	results	result	NOUN
ejpam-4467	389	44	obtained	obtain	VERB
ejpam-4467	389	45	in	in	ADP
ejpam-4467	389	46	this	this	DET
ejpam-4467	389	47	paper	paper	NOUN
ejpam-4467	389	48	will	will	AUX
ejpam-4467	389	49	be	be	AUX
ejpam-4467	389	50	applied	apply	VERB
ejpam-4467	389	51	to	to	ADP
ejpam-4467	389	52	the	the	DET
ejpam-4467	389	53	relevant	relevant	ADJ
ejpam-4467	389	54	algebraic	algebraic	ADJ
ejpam-4467	389	55	systems	system	NOUN
ejpam-4467	389	56	in	in	ADP
ejpam-4467	389	57	the	the	DET
ejpam-4467	389	58	future	future	NOUN
ejpam-4467	389	59	,	,	PUNCT
ejpam-4467	389	60	further	far	ADV
ejpam-4467	389	61	examining	examine	VERB
ejpam-4467	389	62	their	their	PRON
ejpam-4467	389	63	usability	usability	NOUN
ejpam-4467	389	64	as	as	ADP
ejpam-4467	389	65	a	a	DET
ejpam-4467	389	66	mathematical	mathematical	ADJ
ejpam-4467	389	67	tool	tool	NOUN
ejpam-4467	389	68	applicable	applicable	ADJ
ejpam-4467	389	69	to	to	ADP
ejpam-4467	389	70	decision	decision	NOUN
ejpam-4467	389	71	theory	theory	NOUN
ejpam-4467	389	72	,	,	PUNCT
ejpam-4467	389	73	medical	medical	ADJ
ejpam-4467	389	74	diagnosis	diagnosis	NOUN
ejpam-4467	389	75	systems	system	NOUN
ejpam-4467	389	76	,	,	PUNCT
ejpam-4467	389	77	and	and	CCONJ
ejpam-4467	389	78	automation	automation	NOUN
ejpam-4467	389	79	systems	system	NOUN
ejpam-4467	389	80	etc	etc	X
ejpam-4467	389	81	.	.	X
ejpam-4467	390	1	acknowledgements	acknowledgement	VERB
ejpam-4467	390	2	the	the	DET
ejpam-4467	390	3	authors	author	NOUN
ejpam-4467	390	4	are	be	AUX
ejpam-4467	390	5	very	very	ADV
ejpam-4467	390	6	grateful	grateful	ADJ
ejpam-4467	390	7	to	to	ADP
ejpam-4467	390	8	anonymous	anonymous	ADJ
ejpam-4467	390	9	reviewers	reviewer	NOUN
ejpam-4467	390	10	for	for	ADP
ejpam-4467	390	11	their	their	PRON
ejpam-4467	390	12	valuable	valuable	ADJ
ejpam-4467	390	13	comments	comment	NOUN
ejpam-4467	390	14	.	.	PUNCT
ejpam-4467	391	1	references	reference	NOUN
ejpam-4467	391	2	[	[	X
ejpam-4467	391	3	1	1	X
ejpam-4467	391	4	]	]	PUNCT
ejpam-4467	391	5	s.	s.	PROPN
ejpam-4467	391	6	s.	s.	PROPN
ejpam-4467	391	7	ahn	ahn	PROPN
ejpam-4467	391	8	and	and	CCONJ
ejpam-4467	391	9	k.	k.	PROPN
ejpam-4467	391	10	s.	s.	PROPN
ejpam-4467	392	1	so	so	ADV
ejpam-4467	392	2	.	.	PUNCT
ejpam-4467	393	1	on	on	ADP
ejpam-4467	393	2	ideals	ideal	NOUN
ejpam-4467	393	3	and	and	CCONJ
ejpam-4467	393	4	upper	upper	ADJ
ejpam-4467	393	5	sets	set	NOUN
ejpam-4467	393	6	in	in	ADP
ejpam-4467	393	7	be	be	NOUN
ejpam-4467	393	8	-	-	PUNCT
ejpam-4467	393	9	algebras	algebra	NOUN
ejpam-4467	393	10	.	.	PUNCT
ejpam-4467	394	1	sci	sci	PROPN
ejpam-4467	394	2	.	.	PROPN
ejpam-4467	394	3	math	math	PROPN
ejpam-4467	394	4	.	.	PUNCT
ejpam-4467	395	1	jpn	jpn	PROPN
ejpam-4467	395	2	.	.	PROPN
ejpam-4467	395	3	,	,	PUNCT
ejpam-4467	395	4	68(2	68(2	NOUN
ejpam-4467	395	5	)	)	PUNCT
ejpam-4467	395	6	,	,	PUNCT
ejpam-4467	395	7	2008	2008	NUM
ejpam-4467	395	8	.	.	PUNCT
ejpam-4467	396	1	[	[	X
ejpam-4467	396	2	2	2	NUM
ejpam-4467	396	3	]	]	SYM
ejpam-4467	396	4	g.dymek	g.dymek	NOUN
ejpam-4467	396	5	and	and	CCONJ
ejpam-4467	396	6	a.	a.	PROPN
ejpam-4467	396	7	walendiziak	walendiziak	PROPN
ejpam-4467	396	8	.	.	PUNCT
ejpam-4467	397	1	fuzzy	fuzzy	ADJ
ejpam-4467	397	2	filters	filter	NOUN
ejpam-4467	397	3	of	of	ADP
ejpam-4467	397	4	be	be	NOUN
ejpam-4467	397	5	-	-	PUNCT
ejpam-4467	397	6	algebras	algebra	NOUN
ejpam-4467	397	7	.	.	PUNCT
ejpam-4467	398	1	math	math	NOUN
ejpam-4467	398	2	.	.	PUNCT
ejpam-4467	399	1	slovaca	slovaca	PROPN
ejpam-4467	399	2	,	,	PUNCT
ejpam-4467	399	3	63:935–946	63:935–946	PROPN
ejpam-4467	399	4	,	,	PUNCT
ejpam-4467	399	5	2013	2013	NUM
ejpam-4467	399	6	.	.	PUNCT
ejpam-4467	400	1	[	[	X
ejpam-4467	400	2	3	3	X
ejpam-4467	400	3	]	]	X
ejpam-4467	400	4	y.	y.	PROPN
ejpam-4467	400	5	b.	b.	PROPN
ejpam-4467	400	6	jun	jun	PROPN
ejpam-4467	400	7	.	.	PROPN
ejpam-4467	400	8	lukasiewicz	lukasiewicz	PROPN
ejpam-4467	400	9	fuzzy	fuzzy	ADJ
ejpam-4467	400	10	subalgebrs	subalgebrs	ADJ
ejpam-4467	400	11	in	in	ADP
ejpam-4467	400	12	bck	bck	PROPN
ejpam-4467	400	13	-	-	PUNCT
ejpam-4467	400	14	algebras	algebras	PROPN
ejpam-4467	400	15	and	and	CCONJ
ejpam-4467	400	16	bci	bci	NOUN
ejpam-4467	400	17	-	-	PUNCT
ejpam-4467	400	18	algebras	algebras	PROPN
ejpam-4467	400	19	.	.	PUNCT
ejpam-4467	401	1	ann	ann	PROPN
ejpam-4467	401	2	.	.	PUNCT
ejpam-4467	401	3	fuzzy	fuzzy	ADJ
ejpam-4467	401	4	math	math	NOUN
ejpam-4467	401	5	.	.	PUNCT
ejpam-4467	402	1	inform	inform	NOUN
ejpam-4467	402	2	.	.	PUNCT
ejpam-4467	402	3	,	,	PUNCT
ejpam-4467	402	4	23(2):213–223	23(2):213–223	NOUN
ejpam-4467	402	5	,	,	PUNCT
ejpam-4467	402	6	2022	2022	NUM
ejpam-4467	402	7	.	.	PUNCT
ejpam-4467	403	1	[	[	X
ejpam-4467	403	2	4	4	X
ejpam-4467	403	3	]	]	X
ejpam-4467	403	4	y.	y.	PROPN
ejpam-4467	403	5	b.	b.	PROPN
ejpam-4467	403	6	jun	jun	PROPN
ejpam-4467	403	7	and	and	CCONJ
ejpam-4467	403	8	s.	s.	PROPN
ejpam-4467	403	9	s.	s.	PROPN
ejpam-4467	403	10	ahn	ahn	PROPN
ejpam-4467	403	11	.	.	PROPN
ejpam-4467	403	12	lukasiewicz	lukasiewicz	PROPN
ejpam-4467	403	13	fuzzy	fuzzy	ADJ
ejpam-4467	403	14	be	be	NOUN
ejpam-4467	403	15	-	-	PUNCT
ejpam-4467	403	16	algegbras	algegbra	NOUN
ejpam-4467	403	17	and	and	CCONJ
ejpam-4467	403	18	be	be	NOUN
ejpam-4467	403	19	-	-	PUNCT
ejpam-4467	403	20	filters	filter	NOUN
ejpam-4467	403	21	.	.	PUNCT
ejpam-4467	404	1	eur	eur	PROPN
ejpam-4467	404	2	.	.	PUNCT
ejpam-4467	405	1	j.	j.	PROPN
ejpam-4467	405	2	pure	pure	PROPN
ejpam-4467	405	3	appl	appl	PROPN
ejpam-4467	405	4	.	.	PUNCT
ejpam-4467	405	5	math	math	NOUN
ejpam-4467	405	6	.	.	PUNCT
ejpam-4467	406	1	[	[	X
ejpam-4467	406	2	5	5	X
ejpam-4467	406	3	]	]	PUNCT
ejpam-4467	406	4	h.	h.	PROPN
ejpam-4467	406	5	s.	s.	PROPN
ejpam-4467	406	6	kim	kim	PROPN
ejpam-4467	406	7	and	and	CCONJ
ejpam-4467	406	8	y.	y.	PROPN
ejpam-4467	406	9	h.	h.	PROPN
ejpam-4467	406	10	kim	kim	PROPN
ejpam-4467	406	11	.	.	PUNCT
ejpam-4467	407	1	on	on	ADP
ejpam-4467	407	2	be	be	AUX
ejpam-4467	407	3	-	-	PUNCT
ejpam-4467	407	4	algebras	algebra	NOUN
ejpam-4467	407	5	.	.	PUNCT
ejpam-4467	407	6	sci	sci	PROPN
ejpam-4467	407	7	.	.	PROPN
ejpam-4467	407	8	math	math	PROPN
ejpam-4467	407	9	.	.	PUNCT
ejpam-4467	408	1	jpn	jpn	PROPN
ejpam-4467	408	2	.	.	PROPN
ejpam-4467	408	3	,	,	PUNCT
ejpam-4467	408	4	66:113–116	66:113–116	PROPN
ejpam-4467	408	5	,	,	PUNCT
ejpam-4467	408	6	2007	2007	NUM
ejpam-4467	408	7	.	.	PUNCT
ejpam-4467	409	1	[	[	X
ejpam-4467	409	2	6	6	NUM
ejpam-4467	409	3	]	]	PUNCT
ejpam-4467	409	4	p.	p.	NOUN
ejpam-4467	409	5	m.	m.	NOUN
ejpam-4467	409	6	pu	pu	PROPN
ejpam-4467	409	7	and	and	CCONJ
ejpam-4467	409	8	y.	y.	PROPN
ejpam-4467	409	9	m.	m.	PROPN
ejpam-4467	409	10	liu	liu	PROPN
ejpam-4467	409	11	.	.	PROPN
ejpam-4467	410	1	fuzzy	fuzzy	ADJ
ejpam-4467	410	2	topology	topology	NOUN
ejpam-4467	410	3	i	i	PRON
ejpam-4467	410	4	,	,	PUNCT
ejpam-4467	410	5	neighborhood	neighborhood	NOUN
ejpam-4467	410	6	structure	structure	NOUN
ejpam-4467	410	7	of	of	ADP
ejpam-4467	410	8	a	a	DET
ejpam-4467	410	9	fuzzy	fuzzy	ADJ
ejpam-4467	410	10	point	point	NOUN
ejpam-4467	410	11	and	and	CCONJ
ejpam-4467	410	12	moore	moore	PROPN
ejpam-4467	410	13	-	-	PUNCT
ejpam-4467	410	14	smith	smith	PROPN
ejpam-4467	410	15	convergence	convergence	NOUN
ejpam-4467	410	16	.	.	PUNCT
ejpam-4467	411	1	j.	j.	PROPN
ejpam-4467	411	2	math	math	PROPN
ejpam-4467	411	3	.	.	PUNCT
ejpam-4467	412	1	anal	anal	PROPN
ejpam-4467	412	2	.	.	PUNCT
ejpam-4467	413	1	appl	appl	PROPN
ejpam-4467	413	2	.	.	PROPN
ejpam-4467	413	3	,	,	PUNCT
ejpam-4467	414	1	76:571–599	76:571–599	NUM
ejpam-4467	414	2	,	,	PUNCT
ejpam-4467	414	3	1980	1980	NUM
ejpam-4467	414	4	.	.	PUNCT
ejpam-4467	415	1	[	[	X
ejpam-4467	415	2	7	7	X
ejpam-4467	415	3	]	]	PUNCT
ejpam-4467	415	4	a.	a.	NOUN
ejpam-4467	415	5	rezaei	rezaei	NOUN
ejpam-4467	415	6	and	and	CCONJ
ejpam-4467	415	7	a.	a.	PROPN
ejpam-4467	415	8	borumand	borumand	PROPN
ejpam-4467	415	9	saeid	saeid	PROPN
ejpam-4467	415	10	.	.	PUNCT
ejpam-4467	416	1	on	on	ADP
ejpam-4467	416	2	fuzzy	fuzzy	ADJ
ejpam-4467	416	3	subalgebras	subalgebra	NOUN
ejpam-4467	416	4	of	of	ADP
ejpam-4467	416	5	be	be	AUX
ejpam-4467	416	6	-	-	PUNCT
ejpam-4467	416	7	algebras	algebra	NOUN
ejpam-4467	416	8	.	.	PUNCT
ejpam-4467	416	9	afr	afr	PROPN
ejpam-4467	416	10	.	.	PUNCT
ejpam-4467	417	1	mat	mat	PROPN
ejpam-4467	417	2	.	.	PROPN
ejpam-4467	417	3	,	,	PUNCT
ejpam-4467	417	4	22:115–127	22:115–127	PROPN
ejpam-4467	417	5	,	,	PUNCT
ejpam-4467	417	6	2011	2011	NUM
ejpam-4467	417	7	.	.	PUNCT
ejpam-4467	418	1	[	[	X
ejpam-4467	418	2	8	8	X
ejpam-4467	418	3	]	]	X
ejpam-4467	418	4	y.	y.	PROPN
ejpam-4467	418	5	h.	h.	PROPN
ejpam-4467	418	6	kim	kim	PROPN
ejpam-4467	418	7	s.	s.	PROPN
ejpam-4467	418	8	s.	s.	PROPN
ejpam-4467	418	9	ahn	ahn	PROPN
ejpam-4467	418	10	and	and	CCONJ
ejpam-4467	418	11	k.	k.	PROPN
ejpam-4467	418	12	s.	s.	PROPN
ejpam-4467	419	1	so	so	ADV
ejpam-4467	419	2	.	.	PUNCT
ejpam-4467	420	1	fuzzy	fuzzy	ADJ
ejpam-4467	420	2	be	be	AUX
ejpam-4467	420	3	-	-	PUNCT
ejpam-4467	420	4	algebras	algebras	X
ejpam-4467	420	5	.	.	PUNCT
ejpam-4467	421	1	j.	j.	PROPN
ejpam-4467	421	2	appl	appl	PROPN
ejpam-4467	421	3	.	.	PROPN
ejpam-4467	421	4	math	math	PROPN
ejpam-4467	421	5	.	.	PUNCT
ejpam-4467	422	1	informatics	informatic	NOUN
ejpam-4467	422	2	,	,	PUNCT
ejpam-4467	422	3	29:1049–1057	29:1049–1057	PROPN
ejpam-4467	422	4	,	,	PUNCT
ejpam-4467	422	5	2011	2011	NUM
ejpam-4467	422	6	.	.	PUNCT
ejpam-4467	423	1	[	[	X
ejpam-4467	423	2	9	9	NUM
ejpam-4467	423	3	]	]	PUNCT
ejpam-4467	423	4	k.	k.	PROPN
ejpam-4467	423	5	j.	j.	PROPN
ejpam-4467	423	6	lee	lee	PROPN
ejpam-4467	423	7	y.	y.	PROPN
ejpam-4467	423	8	b.	b.	PROPN
ejpam-4467	423	9	jun	jun	PROPN
ejpam-4467	423	10	and	and	CCONJ
ejpam-4467	423	11	s.	s.	PROPN
ejpam-4467	423	12	z.	z.	PROPN
ejpam-4467	423	13	song	song	PROPN
ejpam-4467	423	14	.	.	PUNCT
ejpam-4467	424	1	fuzzy	fuzzy	ADJ
ejpam-4467	424	2	ideals	ideal	NOUN
ejpam-4467	424	3	in	in	ADP
ejpam-4467	424	4	be	be	NOUN
ejpam-4467	424	5	-	-	PUNCT
ejpam-4467	424	6	algebra	algebra	NOUN
ejpam-4467	424	7	.	.	PUNCT
ejpam-4467	425	1	bull	bull	NOUN
ejpam-4467	425	2	.	.	PUNCT
ejpam-4467	426	1	malays	malays	PROPN
ejpam-4467	426	2	.	.	PUNCT
ejpam-4467	427	1	math	math	NOUN
ejpam-4467	427	2	.	.	PUNCT
ejpam-4467	428	1	sci	sci	PROPN
ejpam-4467	428	2	.	.	PROPN
ejpam-4467	428	3	soc	soc	PROPN
ejpam-4467	428	4	.	.	PUNCT
ejpam-4467	428	5	,	,	PUNCT
ejpam-4467	428	6	33:147–153	33:147–153	NUM
ejpam-4467	428	7	,	,	PUNCT
ejpam-4467	428	8	2010	2010	NUM
ejpam-4467	428	9	.	.	PUNCT