id	sid	tid	token	lemma	pos
ejpam-5876	1	1	european	european	PROPN
ejpam-5876	1	2	journal	journal	PROPN
ejpam-5876	1	3	of	of	ADP
ejpam-5876	1	4	pure	pure	ADJ
ejpam-5876	1	5	and	and	CCONJ
ejpam-5876	1	6	applied	applied	ADJ
ejpam-5876	1	7	mathematics	mathematic	NOUN
ejpam-5876	1	8	2025	2025	NUM
ejpam-5876	1	9	,	,	PUNCT
ejpam-5876	1	10	vol	vol	NOUN
ejpam-5876	1	11	.	.	PROPN
ejpam-5876	1	12	18	18	NUM
ejpam-5876	1	13	,	,	PUNCT
ejpam-5876	1	14	issue	issue	NOUN
ejpam-5876	1	15	2	2	NUM
ejpam-5876	1	16	,	,	PUNCT
ejpam-5876	1	17	article	article	NOUN
ejpam-5876	1	18	number	number	NOUN
ejpam-5876	1	19	5876	5876	NUM
ejpam-5876	1	20	issn	issn	PROPN
ejpam-5876	1	21	1307	1307	NUM
ejpam-5876	1	22	-	-	SYM
ejpam-5876	1	23	5543	5543	NUM
ejpam-5876	1	24	–	–	PUNCT
ejpam-5876	1	25	ejpam.com	ejpam.com	X
ejpam-5876	1	26	published	publish	VERB
ejpam-5876	1	27	by	by	ADP
ejpam-5876	1	28	new	new	PROPN
ejpam-5876	1	29	york	york	PROPN
ejpam-5876	1	30	business	business	PROPN
ejpam-5876	1	31	global	global	ADJ
ejpam-5876	1	32	semidetached	semidetache	VERB
ejpam-5876	1	33	sup	sup	NOUN
ejpam-5876	1	34	-	-	PUNCT
ejpam-5876	1	35	subalgebras	subalgebras	NOUN
ejpam-5876	1	36	of	of	ADP
ejpam-5876	1	37	sheffer	sheffer	PROPN
ejpam-5876	1	38	stroke	stroke	PROPN
ejpam-5876	1	39	up	up	ADP
ejpam-5876	1	40	-	-	PUNCT
ejpam-5876	1	41	algebras	algebras	NOUN
ejpam-5876	1	42	tahsin	tahsin	PROPN
ejpam-5876	1	43	oner1	oner1	PROPN
ejpam-5876	1	44	,	,	PUNCT
ejpam-5876	1	45	neelamegarajan	neelamegarajan	NOUN
ejpam-5876	1	46	rajesh2	rajesh2	PROPN
ejpam-5876	1	47	,	,	PUNCT
ejpam-5876	1	48	aiyared	aiyare	VERB
ejpam-5876	1	49	iampan3,∗	iampan3,∗	ADJ
ejpam-5876	1	50	,	,	PUNCT
ejpam-5876	1	51	ibrahim	ibrahim	PROPN
ejpam-5876	1	52	senturk1	senturk1	X
ejpam-5876	2	1	1	1	NUM
ejpam-5876	2	2	department	department	NOUN
ejpam-5876	2	3	of	of	ADP
ejpam-5876	2	4	mathematics	mathematic	NOUN
ejpam-5876	2	5	,	,	PUNCT
ejpam-5876	2	6	faculty	faculty	NOUN
ejpam-5876	2	7	of	of	ADP
ejpam-5876	2	8	science	science	NOUN
ejpam-5876	2	9	,	,	PUNCT
ejpam-5876	2	10	ege	ege	PROPN
ejpam-5876	2	11	university	university	NOUN
ejpam-5876	2	12	,	,	PUNCT
ejpam-5876	2	13	35100	35100	NUM
ejpam-5876	2	14	izmir	izmir	PROPN
ejpam-5876	2	15	,	,	PUNCT
ejpam-5876	2	16	turkey	turkey	PROPN
ejpam-5876	2	17	2	2	NUM
ejpam-5876	2	18	department	department	NOUN
ejpam-5876	2	19	of	of	ADP
ejpam-5876	2	20	mathematics	mathematic	NOUN
ejpam-5876	2	21	,	,	PUNCT
ejpam-5876	2	22	rajah	rajah	NOUN
ejpam-5876	2	23	serfoji	serfoji	ADJ
ejpam-5876	2	24	government	government	NOUN
ejpam-5876	2	25	college	college	NOUN
ejpam-5876	2	26	,	,	PUNCT
ejpam-5876	2	27	thanjavur-613005	thanjavur-613005	NOUN
ejpam-5876	2	28	,	,	PUNCT
ejpam-5876	2	29	tamil	tamil	PROPN
ejpam-5876	2	30	nadu	nadu	NOUN
ejpam-5876	2	31	,	,	PUNCT
ejpam-5876	2	32	india	india	PROPN
ejpam-5876	2	33	3	3	NUM
ejpam-5876	2	34	department	department	PROPN
ejpam-5876	2	35	of	of	ADP
ejpam-5876	2	36	mathematics	mathematic	NOUN
ejpam-5876	2	37	,	,	PUNCT
ejpam-5876	2	38	school	school	NOUN
ejpam-5876	2	39	of	of	ADP
ejpam-5876	2	40	science	science	NOUN
ejpam-5876	2	41	,	,	PUNCT
ejpam-5876	2	42	university	university	NOUN
ejpam-5876	2	43	of	of	ADP
ejpam-5876	2	44	phayao	phayao	NOUN
ejpam-5876	2	45	,	,	PUNCT
ejpam-5876	2	46	mae	mae	PROPN
ejpam-5876	2	47	ka	ka	PROPN
ejpam-5876	2	48	,	,	PUNCT
ejpam-5876	2	49	mueang	mueang	PROPN
ejpam-5876	2	50	,	,	PUNCT
ejpam-5876	2	51	phayao	phayao	NOUN
ejpam-5876	2	52	56000	56000	NUM
ejpam-5876	2	53	,	,	PUNCT
ejpam-5876	2	54	thailand	thailand	PROPN
ejpam-5876	2	55	abstract	abstract	NOUN
ejpam-5876	2	56	.	.	PUNCT
ejpam-5876	3	1	the	the	DET
ejpam-5876	3	2	notion	notion	NOUN
ejpam-5876	3	3	of	of	ADP
ejpam-5876	3	4	semidetached	semidetache	VERB
ejpam-5876	3	5	sheffer	sheffer	NOUN
ejpam-5876	3	6	stroke	stroke	NOUN
ejpam-5876	3	7	up	up	ADP
ejpam-5876	3	8	-	-	PUNCT
ejpam-5876	3	9	algebras	algebras	PROPN
ejpam-5876	3	10	is	be	AUX
ejpam-5876	3	11	introduced	introduce	VERB
ejpam-5876	3	12	,	,	PUNCT
ejpam-5876	3	13	and	and	CCONJ
ejpam-5876	3	14	their	their	PRON
ejpam-5876	3	15	properties	property	NOUN
ejpam-5876	3	16	are	be	AUX
ejpam-5876	3	17	investigated	investigate	VERB
ejpam-5876	3	18	.	.	PUNCT
ejpam-5876	4	1	several	several	ADJ
ejpam-5876	4	2	conditions	condition	NOUN
ejpam-5876	4	3	for	for	ADP
ejpam-5876	4	4	a	a	DET
ejpam-5876	4	5	semidetached	semidetache	VERB
ejpam-5876	4	6	structure	structure	NOUN
ejpam-5876	4	7	in	in	ADP
ejpam-5876	4	8	sheffer	sheffer	PROPN
ejpam-5876	4	9	stroke	stroke	NOUN
ejpam-5876	4	10	up	up	ADP
ejpam-5876	4	11	-	-	PUNCT
ejpam-5876	4	12	algebras	algebra	NOUN
ejpam-5876	4	13	to	to	PART
ejpam-5876	4	14	be	be	AUX
ejpam-5876	4	15	a	a	DET
ejpam-5876	4	16	semidetached	semidetache	VERB
ejpam-5876	4	17	sup	sup	NOUN
ejpam-5876	4	18	-	-	PUNCT
ejpam-5876	4	19	subalgebra	subalgebra	NOUN
ejpam-5876	4	20	are	be	AUX
ejpam-5876	4	21	provided	provide	VERB
ejpam-5876	4	22	.	.	PUNCT
ejpam-5876	5	1	the	the	DET
ejpam-5876	5	2	concepts	concept	NOUN
ejpam-5876	5	3	of	of	ADP
ejpam-5876	5	4	(	(	PUNCT
ejpam-5876	5	5	∈,∈	∈,∈	X
ejpam-5876	5	6	∨	∨	NUM
ejpam-5876	5	7	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	5	8	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	5	9	,	,	PUNCT
ejpam-5876	5	10	k	k	NOUN
ejpam-5876	5	11	-	-	ADJ
ejpam-5876	5	12	left	left	ADJ
ejpam-5876	5	13	(	(	PUNCT
ejpam-5876	5	14	k	k	NOUN
ejpam-5876	5	15	-	-	NOUN
ejpam-5876	5	16	right	right	NOUN
ejpam-5876	5	17	)	)	PUNCT
ejpam-5876	5	18	(	(	PUNCT
ejpam-5876	5	19	qk,∈	qk,∈	PROPN
ejpam-5876	5	20	∨	∨	NUM
ejpam-5876	5	21	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	5	22	sup	sup	NOUN
ejpam-5876	5	23	-	-	PUNCT
ejpam-5876	5	24	subalgebra	subalgebra	NOUN
ejpam-5876	5	25	,	,	PUNCT
ejpam-5876	5	26	(	(	PUNCT
ejpam-5876	5	27	qk,∈	qk,∈	PROPN
ejpam-5876	5	28	∨	∨	NUM
ejpam-5876	5	29	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	5	30	sup	sup	NOUN
ejpam-5876	5	31	-	-	PUNCT
ejpam-5876	5	32	subalgebra	subalgebra	NOUN
ejpam-5876	5	33	and	and	CCONJ
ejpam-5876	5	34	(	(	PUNCT
ejpam-5876	5	35	∈∨	∈∨	PROPN
ejpam-5876	5	36	qk,∈∨	qk,∈∨	PUNCT
ejpam-5876	5	37	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	5	38	sup	sup	NOUN
ejpam-5876	5	39	-	-	PUNCT
ejpam-5876	5	40	subalgebra	subalgebra	NOUN
ejpam-5876	5	41	are	be	AUX
ejpam-5876	5	42	introduced	introduce	VERB
ejpam-5876	5	43	,	,	PUNCT
ejpam-5876	5	44	and	and	CCONJ
ejpam-5876	5	45	relative	relative	ADJ
ejpam-5876	5	46	relations	relation	NOUN
ejpam-5876	5	47	and	and	CCONJ
ejpam-5876	5	48	properties	property	NOUN
ejpam-5876	5	49	are	be	AUX
ejpam-5876	5	50	discussed	discuss	VERB
ejpam-5876	5	51	.	.	PUNCT
ejpam-5876	6	1	2020	2020	NUM
ejpam-5876	6	2	mathematics	mathematic	NOUN
ejpam-5876	6	3	subject	subject	NOUN
ejpam-5876	6	4	classifications	classification	NOUN
ejpam-5876	6	5	:	:	PUNCT
ejpam-5876	6	6	03g25	03g25	NUM
ejpam-5876	6	7	,	,	PUNCT
ejpam-5876	6	8	06f35	06f35	NUM
ejpam-5876	6	9	,	,	PUNCT
ejpam-5876	6	10	08a72	08a72	NOUN
ejpam-5876	6	11	key	key	ADJ
ejpam-5876	6	12	words	word	NOUN
ejpam-5876	6	13	and	and	CCONJ
ejpam-5876	6	14	phrases	phrase	NOUN
ejpam-5876	6	15	:	:	PUNCT
ejpam-5876	6	16	sheffer	sheffer	VERB
ejpam-5876	6	17	stroke	stroke	NOUN
ejpam-5876	6	18	up	up	ADP
ejpam-5876	6	19	-	-	PUNCT
ejpam-5876	6	20	algebra	algebra	NOUN
ejpam-5876	6	21	,	,	PUNCT
ejpam-5876	6	22	(	(	PUNCT
ejpam-5876	6	23	∈,∈	∈,∈	X
ejpam-5876	6	24	∨	∨	NUM
ejpam-5876	6	25	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	6	26	sup	sup	NOUN
ejpam-5876	6	27	-	-	PUNCT
ejpam-5876	6	28	subalgebra	subalgebra	NOUN
ejpam-5876	6	29	,	,	PUNCT
ejpam-5876	6	30	k	k	NOUN
ejpam-5876	6	31	-	-	ADJ
ejpam-5876	6	32	left	left	ADJ
ejpam-5876	6	33	(	(	PUNCT
ejpam-5876	6	34	k	k	NOUN
ejpam-5876	6	35	-	-	NOUN
ejpam-5876	6	36	right	right	NOUN
ejpam-5876	6	37	)	)	PUNCT
ejpam-5876	6	38	(	(	PUNCT
ejpam-5876	6	39	qk,∈	qk,∈	PROPN
ejpam-5876	6	40	∨	∨	NUM
ejpam-5876	6	41	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	6	42	sup	sup	NOUN
ejpam-5876	6	43	-	-	PUNCT
ejpam-5876	6	44	subalgebra	subalgebra	NOUN
ejpam-5876	6	45	,	,	PUNCT
ejpam-5876	6	46	(	(	PUNCT
ejpam-5876	6	47	∈	∈	PROPN
ejpam-5876	6	48	∨	∨	NUM
ejpam-5876	6	49	qk,∈	qk,∈	PROPN
ejpam-5876	6	50	∨	∨	NUM
ejpam-5876	6	51	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	6	52	sup	sup	NOUN
ejpam-5876	6	53	-	-	PUNCT
ejpam-5876	6	54	subalgebra	subalgebra	NOUN
ejpam-5876	6	55	,	,	PUNCT
ejpam-5876	6	56	semidetached	semidetache	VERB
ejpam-5876	6	57	sup	sup	NOUN
ejpam-5876	6	58	-	-	PUNCT
ejpam-5876	6	59	subalgebra	subalgebra	NOUN
ejpam-5876	6	60	1	1	NUM
ejpam-5876	6	61	.	.	X
ejpam-5876	6	62	introduction	introduction	NOUN
ejpam-5876	6	63	the	the	DET
ejpam-5876	6	64	sheffer	sheffer	NOUN
ejpam-5876	6	65	operation	operation	NOUN
ejpam-5876	6	66	,	,	PUNCT
ejpam-5876	6	67	commonly	commonly	ADV
ejpam-5876	6	68	referred	refer	VERB
ejpam-5876	6	69	to	to	ADP
ejpam-5876	6	70	as	as	ADP
ejpam-5876	6	71	the	the	DET
ejpam-5876	6	72	sheffer	sheffer	NOUN
ejpam-5876	6	73	stroke	stroke	NOUN
ejpam-5876	6	74	or	or	CCONJ
ejpam-5876	6	75	nand	nand	NOUN
ejpam-5876	6	76	operator	operator	NOUN
ejpam-5876	6	77	,	,	PUNCT
ejpam-5876	6	78	was	be	AUX
ejpam-5876	6	79	first	first	ADV
ejpam-5876	6	80	introduced	introduce	VERB
ejpam-5876	6	81	by	by	ADP
ejpam-5876	6	82	sheffer	sheffer	NOUN
ejpam-5876	7	1	[	[	X
ejpam-5876	7	2	1	1	NUM
ejpam-5876	7	3	]	]	PUNCT
ejpam-5876	7	4	.	.	PUNCT
ejpam-5876	8	1	this	this	DET
ejpam-5876	8	2	operation	operation	NOUN
ejpam-5876	8	3	is	be	AUX
ejpam-5876	8	4	particularly	particularly	ADV
ejpam-5876	8	5	notable	notable	ADJ
ejpam-5876	8	6	for	for	ADP
ejpam-5876	8	7	its	its	PRON
ejpam-5876	8	8	ability	ability	NOUN
ejpam-5876	8	9	to	to	PART
ejpam-5876	8	10	form	form	VERB
ejpam-5876	8	11	a	a	DET
ejpam-5876	8	12	complete	complete	ADJ
ejpam-5876	8	13	logical	logical	ADJ
ejpam-5876	8	14	system	system	NOUN
ejpam-5876	8	15	on	on	ADP
ejpam-5876	8	16	its	its	PRON
ejpam-5876	8	17	own	own	ADJ
ejpam-5876	8	18	,	,	PUNCT
ejpam-5876	8	19	without	without	ADP
ejpam-5876	8	20	relying	rely	VERB
ejpam-5876	8	21	on	on	ADP
ejpam-5876	8	22	any	any	DET
ejpam-5876	8	23	other	other	ADJ
ejpam-5876	8	24	logical	logical	ADJ
ejpam-5876	8	25	connectives	connective	NOUN
ejpam-5876	8	26	.	.	PUNCT
ejpam-5876	9	1	in	in	ADP
ejpam-5876	9	2	fact	fact	NOUN
ejpam-5876	9	3	,	,	PUNCT
ejpam-5876	9	4	any	any	DET
ejpam-5876	9	5	logical	logical	ADJ
ejpam-5876	9	6	axiom	axiom	NOUN
ejpam-5876	9	7	can	can	AUX
ejpam-5876	9	8	be	be	AUX
ejpam-5876	9	9	expressed	express	VERB
ejpam-5876	9	10	using	use	VERB
ejpam-5876	9	11	only	only	ADV
ejpam-5876	9	12	the	the	DET
ejpam-5876	9	13	sheffer	sheffer	NOUN
ejpam-5876	9	14	stroke	stroke	NOUN
ejpam-5876	9	15	,	,	PUNCT
ejpam-5876	9	16	which	which	PRON
ejpam-5876	9	17	simplifies	simplify	VERB
ejpam-5876	9	18	the	the	DET
ejpam-5876	9	19	manipulation	manipulation	NOUN
ejpam-5876	9	20	and	and	CCONJ
ejpam-5876	9	21	analysis	analysis	NOUN
ejpam-5876	9	22	of	of	ADP
ejpam-5876	9	23	logical	logical	ADJ
ejpam-5876	9	24	systems	system	NOUN
ejpam-5876	9	25	.	.	PUNCT
ejpam-5876	10	1	moreover	moreover	ADV
ejpam-5876	10	2	,	,	PUNCT
ejpam-5876	10	3	all	all	DET
ejpam-5876	10	4	the	the	DET
ejpam-5876	10	5	axioms	axiom	NOUN
ejpam-5876	10	6	of	of	ADP
ejpam-5876	10	7	boolean	boolean	ADJ
ejpam-5876	10	8	algebra	algebra	NOUN
ejpam-5876	10	9	,	,	PUNCT
ejpam-5876	10	10	the	the	DET
ejpam-5876	10	11	algebraic	algebraic	ADJ
ejpam-5876	10	12	foundation	foundation	NOUN
ejpam-5876	10	13	of	of	ADP
ejpam-5876	10	14	classical	classical	ADJ
ejpam-5876	10	15	propositional	propositional	ADJ
ejpam-5876	10	16	logic	logic	NOUN
ejpam-5876	10	17	,	,	PUNCT
ejpam-5876	10	18	can	can	AUX
ejpam-5876	10	19	also	also	ADV
ejpam-5876	10	20	be	be	AUX
ejpam-5876	10	21	expressed	express	VERB
ejpam-5876	10	22	exclusively	exclusively	ADV
ejpam-5876	10	23	with	with	ADP
ejpam-5876	10	24	the	the	DET
ejpam-5876	10	25	sheffer	sheffer	NOUN
ejpam-5876	10	26	operation	operation	NOUN
ejpam-5876	10	27	.	.	PUNCT
ejpam-5876	11	1	this	this	PRON
ejpam-5876	11	2	underscores	underscore	VERB
ejpam-5876	11	3	the	the	DET
ejpam-5876	11	4	fundamental	fundamental	ADJ
ejpam-5876	11	5	role	role	NOUN
ejpam-5876	11	6	of	of	ADP
ejpam-5876	11	7	the	the	DET
ejpam-5876	11	8	sheffer	sheffer	NOUN
ejpam-5876	11	9	stroke	stroke	NOUN
ejpam-5876	11	10	in	in	ADP
ejpam-5876	11	11	both	both	CCONJ
ejpam-5876	11	12	logic	logic	NOUN
ejpam-5876	11	13	and	and	CCONJ
ejpam-5876	11	14	algebra	algebra	NOUN
ejpam-5876	11	15	,	,	PUNCT
ejpam-5876	11	16	showcasing	showcase	VERB
ejpam-5876	11	17	its	its	PRON
ejpam-5876	11	18	power	power	NOUN
ejpam-5876	11	19	and	and	CCONJ
ejpam-5876	11	20	flexibility	flexibility	NOUN
ejpam-5876	11	21	in	in	ADP
ejpam-5876	11	22	constructing	construct	VERB
ejpam-5876	11	23	and	and	CCONJ
ejpam-5876	11	24	understanding	understand	VERB
ejpam-5876	11	25	logical	logical	ADJ
ejpam-5876	11	26	frameworks	framework	NOUN
ejpam-5876	11	27	.	.	PUNCT
ejpam-5876	12	1	∗corresponding	∗corresponde	VERB
ejpam-5876	12	2	author	author	NOUN
ejpam-5876	12	3	.	.	PUNCT
ejpam-5876	13	1	doi	doi	NOUN
ejpam-5876	13	2	:	:	PUNCT
ejpam-5876	13	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5876	https://doi.org/10.29020/nybg.ejpam.v18i2.5876	VERB
ejpam-5876	13	4	email	email	NOUN
ejpam-5876	13	5	addresses	address	NOUN
ejpam-5876	13	6	:	:	PUNCT
ejpam-5876	13	7	tahsin.oner@ege.edu.tr	tahsin.oner@ege.edu.tr	NOUN
ejpam-5876	13	8	(	(	PUNCT
ejpam-5876	13	9	t.	t.	NOUN
ejpam-5876	13	10	oner	oner	PROPN
ejpam-5876	13	11	)	)	PUNCT
ejpam-5876	13	12	,	,	PUNCT
ejpam-5876	13	13	nrajesh	nrajesh	PROPN
ejpam-5876	13	14	topology@yahoo.co.in	topology@yahoo.co.in	PROPN
ejpam-5876	13	15	(	(	PUNCT
ejpam-5876	13	16	n.	n.	PROPN
ejpam-5876	13	17	rajesh	rajesh	PROPN
ejpam-5876	13	18	)	)	PUNCT
ejpam-5876	13	19	,	,	PUNCT
ejpam-5876	13	20	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-5876	13	21	(	(	PUNCT
ejpam-5876	13	22	a.	a.	NOUN
ejpam-5876	13	23	iampan	iampan	PROPN
ejpam-5876	13	24	)	)	PUNCT
ejpam-5876	13	25	,	,	PUNCT
ejpam-5876	13	26	ibrahim.senturk@ege.edu.tr	ibrahim.senturk@ege.edu.tr	PROPN
ejpam-5876	13	27	(	(	PUNCT
ejpam-5876	13	28	i.	i.	PROPN
ejpam-5876	13	29	senturk	senturk	PROPN
ejpam-5876	13	30	)	)	PUNCT
ejpam-5876	13	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5876	14	1	1	1	NUM
ejpam-5876	14	2	copyright	copyright	NOUN
ejpam-5876	14	3	:	:	PUNCT
ejpam-5876	14	4	©	©	PROPN
ejpam-5876	14	5	2025	2025	NUM
ejpam-5876	14	6	the	the	DET
ejpam-5876	14	7	author(s	author(s	NOUN
ejpam-5876	14	8	)	)	PUNCT
ejpam-5876	14	9	.	.	PUNCT
ejpam-5876	15	1	(	(	PUNCT
ejpam-5876	15	2	cc	cc	NOUN
ejpam-5876	15	3	by	by	ADP
ejpam-5876	15	4	-	-	PUNCT
ejpam-5876	15	5	nc	nc	PROPN
ejpam-5876	15	6	4.0	4.0	NUM
ejpam-5876	15	7	)	)	PUNCT
ejpam-5876	15	8	t.	t.	NOUN
ejpam-5876	15	9	oner	oner	NOUN
ejpam-5876	15	10	et	et	PROPN
ejpam-5876	15	11	al	al	PROPN
ejpam-5876	15	12	.	.	PUNCT
ejpam-5876	15	13	/	/	SYM
ejpam-5876	15	14	eur	eur	PROPN
ejpam-5876	15	15	.	.	PUNCT
ejpam-5876	16	1	j.	j.	PROPN
ejpam-5876	16	2	pure	pure	PROPN
ejpam-5876	16	3	appl	appl	PROPN
ejpam-5876	16	4	.	.	PROPN
ejpam-5876	16	5	math	math	PROPN
ejpam-5876	16	6	,	,	PUNCT
ejpam-5876	16	7	18	18	NUM
ejpam-5876	16	8	(	(	PUNCT
ejpam-5876	16	9	2	2	NUM
ejpam-5876	16	10	)	)	PUNCT
ejpam-5876	16	11	(	(	PUNCT
ejpam-5876	16	12	2025	2025	NUM
ejpam-5876	16	13	)	)	PUNCT
ejpam-5876	16	14	,	,	PUNCT
ejpam-5876	16	15	5876	5876	NUM
ejpam-5876	16	16	2	2	NUM
ejpam-5876	16	17	of	of	ADP
ejpam-5876	16	18	16	16	NUM
ejpam-5876	16	19	building	build	VERB
ejpam-5876	16	20	upon	upon	SCONJ
ejpam-5876	16	21	this	this	DET
ejpam-5876	16	22	foundational	foundational	ADJ
ejpam-5876	16	23	framework	framework	NOUN
ejpam-5876	16	24	,	,	PUNCT
ejpam-5876	16	25	sheffer	sheffer	NOUN
ejpam-5876	16	26	stroke	stroke	NOUN
ejpam-5876	16	27	up	up	ADP
ejpam-5876	16	28	-	-	PUNCT
ejpam-5876	16	29	algebras	algebras	X
ejpam-5876	16	30	establish	establish	VERB
ejpam-5876	16	31	a	a	DET
ejpam-5876	16	32	distinctive	distinctive	ADJ
ejpam-5876	16	33	algebraic	algebraic	ADJ
ejpam-5876	16	34	structure	structure	NOUN
ejpam-5876	16	35	that	that	PRON
ejpam-5876	16	36	seamlessly	seamlessly	ADV
ejpam-5876	16	37	integrates	integrate	VERB
ejpam-5876	16	38	logical	logical	ADJ
ejpam-5876	16	39	and	and	CCONJ
ejpam-5876	16	40	algebraic	algebraic	ADJ
ejpam-5876	16	41	principles	principle	NOUN
ejpam-5876	16	42	.	.	PUNCT
ejpam-5876	17	1	as	as	SCONJ
ejpam-5876	17	2	elaborated	elaborate	VERB
ejpam-5876	17	3	by	by	ADP
ejpam-5876	17	4	iampan	iampan	NOUN
ejpam-5876	17	5	[	[	X
ejpam-5876	17	6	2	2	X
ejpam-5876	17	7	]	]	PUNCT
ejpam-5876	17	8	in	in	ADP
ejpam-5876	17	9	2017	2017	NUM
ejpam-5876	17	10	,	,	PUNCT
ejpam-5876	17	11	up	up	ADP
ejpam-5876	17	12	-	-	PUNCT
ejpam-5876	17	13	algebras	algebras	NOUN
ejpam-5876	17	14	mark	mark	VERB
ejpam-5876	17	15	a	a	DET
ejpam-5876	17	16	significant	significant	ADJ
ejpam-5876	17	17	advancement	advancement	NOUN
ejpam-5876	17	18	in	in	ADP
ejpam-5876	17	19	the	the	DET
ejpam-5876	17	20	field	field	NOUN
ejpam-5876	17	21	of	of	ADP
ejpam-5876	17	22	logical	logical	ADJ
ejpam-5876	17	23	algebra	algebra	NOUN
ejpam-5876	17	24	,	,	PUNCT
ejpam-5876	17	25	introducing	introduce	VERB
ejpam-5876	17	26	a	a	DET
ejpam-5876	17	27	versatile	versatile	ADJ
ejpam-5876	17	28	paradigm	paradigm	NOUN
ejpam-5876	17	29	for	for	ADP
ejpam-5876	17	30	analyzing	analyze	VERB
ejpam-5876	17	31	algebraic	algebraic	ADJ
ejpam-5876	17	32	systems	system	NOUN
ejpam-5876	17	33	enriched	enrich	VERB
ejpam-5876	17	34	with	with	ADP
ejpam-5876	17	35	sophisticated	sophisticated	ADJ
ejpam-5876	17	36	logical	logical	ADJ
ejpam-5876	17	37	constructs	construct	NOUN
ejpam-5876	17	38	.	.	PUNCT
ejpam-5876	18	1	this	this	DET
ejpam-5876	18	2	innovative	innovative	ADJ
ejpam-5876	18	3	approach	approach	NOUN
ejpam-5876	18	4	not	not	PART
ejpam-5876	18	5	only	only	ADV
ejpam-5876	18	6	deepens	deepen	VERB
ejpam-5876	18	7	our	our	PRON
ejpam-5876	18	8	comprehension	comprehension	NOUN
ejpam-5876	18	9	of	of	ADP
ejpam-5876	18	10	the	the	DET
ejpam-5876	18	11	interplay	interplay	NOUN
ejpam-5876	18	12	between	between	ADP
ejpam-5876	18	13	logical	logical	ADJ
ejpam-5876	18	14	operations	operation	NOUN
ejpam-5876	18	15	and	and	CCONJ
ejpam-5876	18	16	their	their	PRON
ejpam-5876	18	17	algebraic	algebraic	ADJ
ejpam-5876	18	18	counterparts	counterpart	NOUN
ejpam-5876	18	19	but	but	CCONJ
ejpam-5876	18	20	also	also	ADV
ejpam-5876	18	21	unlocks	unlock	VERB
ejpam-5876	18	22	potential	potential	ADJ
ejpam-5876	18	23	applications	application	NOUN
ejpam-5876	18	24	across	across	ADP
ejpam-5876	18	25	diverse	diverse	ADJ
ejpam-5876	18	26	disciplines	discipline	NOUN
ejpam-5876	18	27	,	,	PUNCT
ejpam-5876	18	28	including	include	VERB
ejpam-5876	18	29	decision	decision	NOUN
ejpam-5876	18	30	theory	theory	NOUN
ejpam-5876	18	31	and	and	CCONJ
ejpam-5876	18	32	computational	computational	ADJ
ejpam-5876	18	33	logic	logic	NOUN
ejpam-5876	18	34	.	.	PUNCT
ejpam-5876	19	1	by	by	ADP
ejpam-5876	19	2	bridging	bridge	VERB
ejpam-5876	19	3	these	these	DET
ejpam-5876	19	4	domains	domain	NOUN
ejpam-5876	19	5	,	,	PUNCT
ejpam-5876	19	6	sheffer	sheffer	NOUN
ejpam-5876	19	7	stroke	stroke	NOUN
ejpam-5876	19	8	up	up	ADP
ejpam-5876	19	9	-	-	PUNCT
ejpam-5876	19	10	algebras	algebra	NOUN
ejpam-5876	19	11	demonstrate	demonstrate	VERB
ejpam-5876	19	12	their	their	PRON
ejpam-5876	19	13	capacity	capacity	NOUN
ejpam-5876	19	14	to	to	PART
ejpam-5876	19	15	contribute	contribute	VERB
ejpam-5876	19	16	to	to	ADP
ejpam-5876	19	17	both	both	CCONJ
ejpam-5876	19	18	theoretical	theoretical	ADJ
ejpam-5876	19	19	exploration	exploration	NOUN
ejpam-5876	19	20	and	and	CCONJ
ejpam-5876	19	21	practical	practical	ADJ
ejpam-5876	19	22	problem	problem	NOUN
ejpam-5876	19	23	-	-	PUNCT
ejpam-5876	19	24	solving	solving	NOUN
ejpam-5876	19	25	.	.	PUNCT
ejpam-5876	20	1	sheffer	sheffer	PROPN
ejpam-5876	20	2	stroke	stroke	PROPN
ejpam-5876	20	3	up	up	ADP
ejpam-5876	20	4	-	-	PUNCT
ejpam-5876	20	5	algebras	algebras	ADV
ejpam-5876	20	6	lie	lie	NOUN
ejpam-5876	20	7	at	at	ADP
ejpam-5876	20	8	the	the	DET
ejpam-5876	20	9	crossroads	crossroad	NOUN
ejpam-5876	20	10	of	of	ADP
ejpam-5876	20	11	logic	logic	NOUN
ejpam-5876	20	12	,	,	PUNCT
ejpam-5876	20	13	algebra	algebra	NOUN
ejpam-5876	20	14	,	,	PUNCT
ejpam-5876	20	15	and	and	CCONJ
ejpam-5876	20	16	analysis	analysis	NOUN
ejpam-5876	20	17	,	,	PUNCT
ejpam-5876	20	18	providing	provide	VERB
ejpam-5876	20	19	a	a	DET
ejpam-5876	20	20	unique	unique	ADJ
ejpam-5876	20	21	framework	framework	NOUN
ejpam-5876	20	22	for	for	ADP
ejpam-5876	20	23	exploration	exploration	NOUN
ejpam-5876	20	24	.	.	PUNCT
ejpam-5876	21	1	these	these	DET
ejpam-5876	21	2	algebras	algebra	NOUN
ejpam-5876	21	3	are	be	AUX
ejpam-5876	21	4	pre	pre	ADJ
ejpam-5876	21	5	-	-	ADJ
ejpam-5876	21	6	normed	normed	ADJ
ejpam-5876	21	7	structures	structure	NOUN
ejpam-5876	21	8	where	where	SCONJ
ejpam-5876	21	9	the	the	DET
ejpam-5876	21	10	primary	primary	ADJ
ejpam-5876	21	11	operation	operation	NOUN
ejpam-5876	21	12	is	be	AUX
ejpam-5876	21	13	the	the	DET
ejpam-5876	21	14	sheffer	sheffer	NOUN
ejpam-5876	21	15	stroke	stroke	NOUN
ejpam-5876	21	16	logic	logic	NOUN
ejpam-5876	21	17	,	,	PUNCT
ejpam-5876	21	18	and	and	CCONJ
ejpam-5876	21	19	they	they	PRON
ejpam-5876	21	20	possess	possess	VERB
ejpam-5876	21	21	a	a	DET
ejpam-5876	21	22	multiplicative	multiplicative	ADJ
ejpam-5876	21	23	identity	identity	NOUN
ejpam-5876	21	24	element	element	NOUN
ejpam-5876	21	25	.	.	PUNCT
ejpam-5876	22	1	they	they	PRON
ejpam-5876	22	2	serve	serve	VERB
ejpam-5876	22	3	as	as	ADP
ejpam-5876	22	4	a	a	DET
ejpam-5876	22	5	useful	useful	ADJ
ejpam-5876	22	6	tool	tool	NOUN
ejpam-5876	22	7	for	for	ADP
ejpam-5876	22	8	investigating	investigate	VERB
ejpam-5876	22	9	logical	logical	ADJ
ejpam-5876	22	10	systems	system	NOUN
ejpam-5876	22	11	within	within	ADP
ejpam-5876	22	12	an	an	DET
ejpam-5876	22	13	algebraic	algebraic	ADJ
ejpam-5876	22	14	context	context	NOUN
ejpam-5876	22	15	,	,	PUNCT
ejpam-5876	22	16	with	with	ADP
ejpam-5876	22	17	potential	potential	ADJ
ejpam-5876	22	18	applications	application	NOUN
ejpam-5876	22	19	in	in	ADP
ejpam-5876	22	20	areas	area	NOUN
ejpam-5876	22	21	such	such	ADJ
ejpam-5876	22	22	as	as	ADP
ejpam-5876	22	23	functional	functional	ADJ
ejpam-5876	22	24	analysis	analysis	NOUN
ejpam-5876	22	25	,	,	PUNCT
ejpam-5876	22	26	operator	operator	NOUN
ejpam-5876	22	27	theory	theory	NOUN
ejpam-5876	22	28	,	,	PUNCT
ejpam-5876	22	29	and	and	CCONJ
ejpam-5876	22	30	the	the	DET
ejpam-5876	22	31	algebraic	algebraic	ADJ
ejpam-5876	22	32	study	study	NOUN
ejpam-5876	22	33	of	of	ADP
ejpam-5876	22	34	logic	logic	NOUN
ejpam-5876	22	35	.	.	PUNCT
ejpam-5876	23	1	by	by	ADP
ejpam-5876	23	2	incorporating	incorporate	VERB
ejpam-5876	23	3	the	the	DET
ejpam-5876	23	4	sheffer	sheffer	NOUN
ejpam-5876	23	5	stroke	stroke	NOUN
ejpam-5876	23	6	as	as	ADP
ejpam-5876	23	7	a	a	DET
ejpam-5876	23	8	core	core	NOUN
ejpam-5876	23	9	operation	operation	NOUN
ejpam-5876	23	10	,	,	PUNCT
ejpam-5876	23	11	these	these	DET
ejpam-5876	23	12	algebras	algebra	NOUN
ejpam-5876	23	13	extend	extend	VERB
ejpam-5876	23	14	the	the	DET
ejpam-5876	23	15	concept	concept	NOUN
ejpam-5876	23	16	of	of	ADP
ejpam-5876	23	17	boolean	boolean	ADJ
ejpam-5876	23	18	algebras	algebra	NOUN
ejpam-5876	23	19	,	,	PUNCT
ejpam-5876	23	20	offering	offer	VERB
ejpam-5876	23	21	a	a	DET
ejpam-5876	23	22	broader	broad	ADJ
ejpam-5876	23	23	perspective	perspective	NOUN
ejpam-5876	23	24	on	on	ADP
ejpam-5876	23	25	logical	logical	ADJ
ejpam-5876	23	26	and	and	CCONJ
ejpam-5876	23	27	algebraic	algebraic	ADJ
ejpam-5876	23	28	interactions	interaction	NOUN
ejpam-5876	23	29	.	.	PUNCT
ejpam-5876	24	1	recent	recent	ADJ
ejpam-5876	24	2	works	work	NOUN
ejpam-5876	24	3	have	have	AUX
ejpam-5876	24	4	highlighted	highlight	VERB
ejpam-5876	24	5	this	this	DET
ejpam-5876	24	6	richness	richness	NOUN
ejpam-5876	24	7	:	:	PUNCT
ejpam-5876	24	8	rajesh	rajesh	PROPN
ejpam-5876	24	9	et	et	PROPN
ejpam-5876	24	10	al	al	PROPN
ejpam-5876	24	11	.	.	PUNCT
ejpam-5876	25	1	[	[	X
ejpam-5876	25	2	3	3	X
ejpam-5876	25	3	]	]	PUNCT
ejpam-5876	25	4	introduced	introduce	VERB
ejpam-5876	25	5	the	the	DET
ejpam-5876	25	6	notion	notion	NOUN
ejpam-5876	25	7	of	of	ADP
ejpam-5876	25	8	intuitionistic	intuitionistic	ADJ
ejpam-5876	25	9	fuzzy	fuzzy	ADJ
ejpam-5876	25	10	subalgebras	subalgebra	NOUN
ejpam-5876	25	11	in	in	ADP
ejpam-5876	25	12	sheffer	sheffer	PROPN
ejpam-5876	25	13	stroke	stroke	NOUN
ejpam-5876	25	14	up	up	ADP
ejpam-5876	25	15	-	-	PUNCT
ejpam-5876	25	16	algebras	algebra	VERB
ejpam-5876	25	17	and	and	CCONJ
ejpam-5876	25	18	established	establish	VERB
ejpam-5876	25	19	important	important	ADJ
ejpam-5876	25	20	structural	structural	ADJ
ejpam-5876	25	21	properties	property	NOUN
ejpam-5876	25	22	of	of	ADP
ejpam-5876	25	23	their	their	PRON
ejpam-5876	25	24	level	level	NOUN
ejpam-5876	25	25	sets	set	NOUN
ejpam-5876	25	26	,	,	PUNCT
ejpam-5876	25	27	while	while	SCONJ
ejpam-5876	25	28	vidhya	vidhya	PROPN
ejpam-5876	25	29	et	et	PROPN
ejpam-5876	25	30	al	al	PROPN
ejpam-5876	25	31	.	.	PUNCT
ejpam-5876	26	1	[	[	X
ejpam-5876	26	2	4	4	NUM
ejpam-5876	26	3	]	]	PUNCT
ejpam-5876	26	4	further	far	ADV
ejpam-5876	26	5	extended	extend	VERB
ejpam-5876	26	6	this	this	DET
ejpam-5876	26	7	framework	framework	NOUN
ejpam-5876	26	8	by	by	ADP
ejpam-5876	26	9	exploring	explore	VERB
ejpam-5876	26	10	neutrosophic	neutrosophic	ADJ
ejpam-5876	26	11	n	n	CCONJ
ejpam-5876	26	12	-	-	PUNCT
ejpam-5876	26	13	subalgebras	subalgebras	PROPN
ejpam-5876	26	14	and	and	CCONJ
ejpam-5876	26	15	their	their	PRON
ejpam-5876	26	16	corresponding	corresponding	ADJ
ejpam-5876	26	17	lattice	lattice	NOUN
ejpam-5876	26	18	-	-	PUNCT
ejpam-5876	26	19	theoretic	theoretic	NOUN
ejpam-5876	26	20	characterizations	characterization	NOUN
ejpam-5876	26	21	.	.	PUNCT
ejpam-5876	27	1	these	these	DET
ejpam-5876	27	2	studies	study	NOUN
ejpam-5876	27	3	emphasize	emphasize	VERB
ejpam-5876	27	4	the	the	DET
ejpam-5876	27	5	growing	grow	VERB
ejpam-5876	27	6	relevance	relevance	NOUN
ejpam-5876	27	7	of	of	ADP
ejpam-5876	27	8	fuzzy	fuzzy	ADJ
ejpam-5876	27	9	and	and	CCONJ
ejpam-5876	27	10	neutrosophic	neutrosophic	ADJ
ejpam-5876	27	11	perspectives	perspective	NOUN
ejpam-5876	27	12	in	in	ADP
ejpam-5876	27	13	the	the	DET
ejpam-5876	27	14	theory	theory	NOUN
ejpam-5876	27	15	of	of	ADP
ejpam-5876	27	16	sheffer	sheffer	PROPN
ejpam-5876	27	17	stroke	stroke	PROPN
ejpam-5876	27	18	up	up	ADP
ejpam-5876	27	19	-	-	PUNCT
ejpam-5876	27	20	algebras	algebras	X
ejpam-5876	27	21	,	,	PUNCT
ejpam-5876	27	22	paving	pave	VERB
ejpam-5876	27	23	the	the	DET
ejpam-5876	27	24	way	way	NOUN
ejpam-5876	27	25	for	for	ADP
ejpam-5876	27	26	deeper	deep	ADJ
ejpam-5876	27	27	investigations	investigation	NOUN
ejpam-5876	27	28	into	into	ADP
ejpam-5876	27	29	generalized	generalized	ADJ
ejpam-5876	27	30	substructures	substructure	NOUN
ejpam-5876	27	31	,	,	PUNCT
ejpam-5876	27	32	such	such	ADJ
ejpam-5876	27	33	as	as	ADP
ejpam-5876	27	34	the	the	DET
ejpam-5876	27	35	semidetached	semidetached	ADJ
ejpam-5876	27	36	forms	form	NOUN
ejpam-5876	27	37	explored	explore	VERB
ejpam-5876	27	38	in	in	ADP
ejpam-5876	27	39	this	this	DET
ejpam-5876	27	40	paper	paper	NOUN
ejpam-5876	27	41	.	.	PUNCT
ejpam-5876	28	1	the	the	DET
ejpam-5876	28	2	concept	concept	NOUN
ejpam-5876	28	3	of	of	ADP
ejpam-5876	28	4	the	the	DET
ejpam-5876	28	5	quasi	quasi	NOUN
ejpam-5876	28	6	-	-	NOUN
ejpam-5876	28	7	coincidence	coincidence	NOUN
ejpam-5876	28	8	of	of	ADP
ejpam-5876	28	9	a	a	DET
ejpam-5876	28	10	fuzzy	fuzzy	ADJ
ejpam-5876	28	11	point	point	NOUN
ejpam-5876	28	12	with	with	ADP
ejpam-5876	28	13	a	a	DET
ejpam-5876	28	14	fuzzy	fuzzy	ADJ
ejpam-5876	28	15	set	set	NOUN
ejpam-5876	28	16	,	,	PUNCT
ejpam-5876	28	17	as	as	SCONJ
ejpam-5876	28	18	discussed	discuss	VERB
ejpam-5876	28	19	in	in	ADP
ejpam-5876	28	20	bhakat	bhakat	NOUN
ejpam-5876	28	21	and	and	CCONJ
ejpam-5876	28	22	das	das	PROPN
ejpam-5876	28	23	’s	’s	PART
ejpam-5876	28	24	pioneering	pioneer	VERB
ejpam-5876	28	25	work	work	NOUN
ejpam-5876	28	26	[	[	X
ejpam-5876	28	27	5	5	NUM
ejpam-5876	28	28	]	]	PUNCT
ejpam-5876	28	29	,	,	PUNCT
ejpam-5876	28	30	has	have	AUX
ejpam-5876	28	31	been	be	AUX
ejpam-5876	28	32	instrumental	instrumental	ADJ
ejpam-5876	28	33	in	in	ADP
ejpam-5876	28	34	shaping	shape	VERB
ejpam-5876	28	35	the	the	DET
ejpam-5876	28	36	development	development	NOUN
ejpam-5876	28	37	of	of	ADP
ejpam-5876	28	38	various	various	ADJ
ejpam-5876	28	39	classifications	classification	NOUN
ejpam-5876	28	40	of	of	ADP
ejpam-5876	28	41	fuzzy	fuzzy	ADJ
ejpam-5876	28	42	subgroups	subgroup	NOUN
ejpam-5876	28	43	.	.	PUNCT
ejpam-5876	29	1	this	this	DET
ejpam-5876	29	2	innovative	innovative	ADJ
ejpam-5876	29	3	approach	approach	NOUN
ejpam-5876	29	4	extends	extend	VERB
ejpam-5876	29	5	traditional	traditional	ADJ
ejpam-5876	29	6	notions	notion	NOUN
ejpam-5876	29	7	,	,	PUNCT
ejpam-5876	29	8	enabling	enable	VERB
ejpam-5876	29	9	the	the	DET
ejpam-5876	29	10	formulation	formulation	NOUN
ejpam-5876	29	11	of	of	ADP
ejpam-5876	29	12	new	new	ADJ
ejpam-5876	29	13	types	type	NOUN
ejpam-5876	29	14	of	of	ADP
ejpam-5876	29	15	fuzzy	fuzzy	ADJ
ejpam-5876	29	16	subgroups	subgroup	NOUN
ejpam-5876	29	17	that	that	PRON
ejpam-5876	29	18	have	have	AUX
ejpam-5876	29	19	broadened	broaden	VERB
ejpam-5876	29	20	the	the	DET
ejpam-5876	29	21	scope	scope	NOUN
ejpam-5876	29	22	of	of	ADP
ejpam-5876	29	23	algebraic	algebraic	ADJ
ejpam-5876	29	24	studies	study	NOUN
ejpam-5876	29	25	in	in	ADP
ejpam-5876	29	26	this	this	DET
ejpam-5876	29	27	domain	domain	NOUN
ejpam-5876	29	28	.	.	PUNCT
ejpam-5876	30	1	notably	notably	ADV
ejpam-5876	30	2	,	,	PUNCT
ejpam-5876	30	3	the	the	DET
ejpam-5876	30	4	(	(	PUNCT
ejpam-5876	30	5	∈,∈	∈,∈	X
ejpam-5876	30	6	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	30	7	subgroup	subgroup	NOUN
ejpam-5876	30	8	represents	represent	VERB
ejpam-5876	30	9	a	a	DET
ejpam-5876	30	10	significant	significant	ADJ
ejpam-5876	30	11	and	and	CCONJ
ejpam-5876	30	12	practical	practical	ADJ
ejpam-5876	30	13	generalization	generalization	NOUN
ejpam-5876	30	14	of	of	ADP
ejpam-5876	30	15	rosenfeld	rosenfeld	PROPN
ejpam-5876	30	16	’s	’s	PART
ejpam-5876	30	17	foundational	foundational	ADJ
ejpam-5876	30	18	concept	concept	NOUN
ejpam-5876	30	19	of	of	ADP
ejpam-5876	30	20	fuzzy	fuzzy	ADJ
ejpam-5876	30	21	subgroups	subgroup	NOUN
ejpam-5876	30	22	[	[	X
ejpam-5876	30	23	6	6	NUM
ejpam-5876	30	24	]	]	PUNCT
ejpam-5876	30	25	,	,	PUNCT
ejpam-5876	30	26	thereby	thereby	ADV
ejpam-5876	30	27	offering	offer	VERB
ejpam-5876	30	28	a	a	DET
ejpam-5876	30	29	more	more	ADV
ejpam-5876	30	30	flexible	flexible	ADJ
ejpam-5876	30	31	framework	framework	NOUN
ejpam-5876	30	32	for	for	ADP
ejpam-5876	30	33	understanding	understand	VERB
ejpam-5876	30	34	the	the	DET
ejpam-5876	30	35	structural	structural	ADJ
ejpam-5876	30	36	relationships	relationship	NOUN
ejpam-5876	30	37	in	in	ADP
ejpam-5876	30	38	fuzzy	fuzzy	ADJ
ejpam-5876	30	39	algebra	algebra	NOUN
ejpam-5876	30	40	.	.	PUNCT
ejpam-5876	31	1	the	the	DET
ejpam-5876	31	2	motivation	motivation	NOUN
ejpam-5876	31	3	for	for	ADP
ejpam-5876	31	4	studying	study	VERB
ejpam-5876	31	5	semidetached	semidetache	VERB
ejpam-5876	31	6	sup	sup	NOUN
ejpam-5876	31	7	-	-	PUNCT
ejpam-5876	31	8	subalgebras	subalgebras	PROPN
ejpam-5876	31	9	arises	arise	VERB
ejpam-5876	31	10	from	from	ADP
ejpam-5876	31	11	the	the	DET
ejpam-5876	31	12	need	need	NOUN
ejpam-5876	31	13	to	to	PART
ejpam-5876	31	14	extend	extend	VERB
ejpam-5876	31	15	the	the	DET
ejpam-5876	31	16	algebraic	algebraic	ADJ
ejpam-5876	31	17	understanding	understanding	NOUN
ejpam-5876	31	18	of	of	ADP
ejpam-5876	31	19	sheffer	sheffer	NOUN
ejpam-5876	31	20	stroke	stroke	NOUN
ejpam-5876	31	21	-	-	PUNCT
ejpam-5876	31	22	based	base	VERB
ejpam-5876	31	23	logical	logical	ADJ
ejpam-5876	31	24	systems	system	NOUN
ejpam-5876	31	25	under	under	ADP
ejpam-5876	31	26	uncertainty	uncertainty	NOUN
ejpam-5876	31	27	.	.	PUNCT
ejpam-5876	32	1	by	by	ADP
ejpam-5876	32	2	incorporating	incorporate	VERB
ejpam-5876	32	3	fuzzy	fuzzy	ADJ
ejpam-5876	32	4	sets	set	NOUN
ejpam-5876	32	5	and	and	CCONJ
ejpam-5876	32	6	semidetached	semidetache	VERB
ejpam-5876	32	7	structures	structure	NOUN
ejpam-5876	32	8	into	into	ADP
ejpam-5876	32	9	sup	sup	NOUN
ejpam-5876	32	10	-	-	PUNCT
ejpam-5876	32	11	algebras	algebra	NOUN
ejpam-5876	32	12	,	,	PUNCT
ejpam-5876	32	13	the	the	DET
ejpam-5876	32	14	framework	framework	NOUN
ejpam-5876	32	15	becomes	become	VERB
ejpam-5876	32	16	more	more	ADV
ejpam-5876	32	17	flexible	flexible	ADJ
ejpam-5876	32	18	and	and	CCONJ
ejpam-5876	32	19	applicable	applicable	ADJ
ejpam-5876	32	20	to	to	ADP
ejpam-5876	32	21	real	real	ADJ
ejpam-5876	32	22	-	-	PUNCT
ejpam-5876	32	23	world	world	NOUN
ejpam-5876	32	24	scenarios	scenario	NOUN
ejpam-5876	32	25	involving	involve	VERB
ejpam-5876	32	26	partial	partial	ADJ
ejpam-5876	32	27	truth	truth	NOUN
ejpam-5876	32	28	or	or	CCONJ
ejpam-5876	32	29	threshold	threshold	NOUN
ejpam-5876	32	30	reasoning	reasoning	NOUN
ejpam-5876	32	31	.	.	PUNCT
ejpam-5876	33	1	these	these	DET
ejpam-5876	33	2	structures	structure	NOUN
ejpam-5876	33	3	have	have	VERB
ejpam-5876	33	4	potential	potential	ADJ
ejpam-5876	33	5	applications	application	NOUN
ejpam-5876	33	6	in	in	ADP
ejpam-5876	33	7	areas	area	NOUN
ejpam-5876	33	8	such	such	ADJ
ejpam-5876	33	9	as	as	ADP
ejpam-5876	33	10	fuzzy	fuzzy	ADJ
ejpam-5876	33	11	decision	decision	NOUN
ejpam-5876	33	12	-	-	PUNCT
ejpam-5876	33	13	making	making	NOUN
ejpam-5876	33	14	,	,	PUNCT
ejpam-5876	33	15	knowledge	knowledge	NOUN
ejpam-5876	33	16	representation	representation	NOUN
ejpam-5876	33	17	in	in	ADP
ejpam-5876	33	18	ai	ai	NOUN
ejpam-5876	33	19	,	,	PUNCT
ejpam-5876	33	20	and	and	CCONJ
ejpam-5876	33	21	logical	logical	ADJ
ejpam-5876	33	22	circuit	circuit	NOUN
ejpam-5876	33	23	design	design	NOUN
ejpam-5876	33	24	,	,	PUNCT
ejpam-5876	33	25	particularly	particularly	ADV
ejpam-5876	33	26	where	where	SCONJ
ejpam-5876	33	27	nand	nand	NOUN
ejpam-5876	33	28	logic	logic	NOUN
ejpam-5876	33	29	and	and	CCONJ
ejpam-5876	33	30	graded	grade	VERB
ejpam-5876	33	31	membership	membership	NOUN
ejpam-5876	33	32	play	play	VERB
ejpam-5876	33	33	a	a	DET
ejpam-5876	33	34	central	central	ADJ
ejpam-5876	33	35	role	role	NOUN
ejpam-5876	33	36	.	.	PUNCT
ejpam-5876	34	1	in	in	ADP
ejpam-5876	34	2	this	this	DET
ejpam-5876	34	3	paper	paper	NOUN
ejpam-5876	34	4	,	,	PUNCT
ejpam-5876	34	5	we	we	PRON
ejpam-5876	34	6	introduce	introduce	VERB
ejpam-5876	34	7	the	the	DET
ejpam-5876	34	8	concepts	concept	NOUN
ejpam-5876	34	9	of	of	ADP
ejpam-5876	34	10	(	(	PUNCT
ejpam-5876	34	11	∈,∈	∈,∈	X
ejpam-5876	34	12	∨	∨	NUM
ejpam-5876	34	13	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	34	14	sup	sup	PROPN
ejpam-5876	34	15	-	-	PUNCT
ejpam-5876	34	16	subalgebras	subalgebras	PROPN
ejpam-5876	34	17	,	,	PUNCT
ejpam-5876	34	18	kleft	kleft	PROPN
ejpam-5876	34	19	(	(	PUNCT
ejpam-5876	34	20	k	k	NOUN
ejpam-5876	34	21	-	-	NOUN
ejpam-5876	34	22	right	right	NOUN
ejpam-5876	34	23	)	)	PUNCT
ejpam-5876	35	1	(	(	PUNCT
ejpam-5876	35	2	qk,∈	qk,∈	PROPN
ejpam-5876	35	3	∨	∨	NUM
ejpam-5876	36	1	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	36	2	sup	sup	NOUN
ejpam-5876	36	3	-	-	PUNCT
ejpam-5876	36	4	subalgebras	subalgebras	X
ejpam-5876	36	5	,	,	PUNCT
ejpam-5876	36	6	(	(	PUNCT
ejpam-5876	36	7	qk,∈	qk,∈	PROPN
ejpam-5876	36	8	∨	∨	NUM
ejpam-5876	36	9	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	36	10	sup	sup	PROPN
ejpam-5876	36	11	-	-	PUNCT
ejpam-5876	36	12	subalgebras	subalgebras	X
ejpam-5876	36	13	,	,	PUNCT
ejpam-5876	36	14	and	and	CCONJ
ejpam-5876	36	15	(	(	PUNCT
ejpam-5876	36	16	∈	∈	PROPN
ejpam-5876	36	17	∨	∨	NUM
ejpam-5876	36	18	qk,∈	qk,∈	PROPN
ejpam-5876	36	19	∨	∨	NUM
ejpam-5876	36	20	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	36	21	sup	sup	PROPN
ejpam-5876	36	22	-	-	PUNCT
ejpam-5876	36	23	subalgebras	subalgebras	X
ejpam-5876	36	24	,	,	PUNCT
ejpam-5876	36	25	and	and	CCONJ
ejpam-5876	36	26	investigate	investigate	VERB
ejpam-5876	36	27	relative	relative	ADJ
ejpam-5876	36	28	relations	relation	NOUN
ejpam-5876	36	29	and	and	CCONJ
ejpam-5876	36	30	properties	property	NOUN
ejpam-5876	36	31	.	.	PUNCT
ejpam-5876	37	1	t.	t.	PROPN
ejpam-5876	37	2	oner	oner	PROPN
ejpam-5876	37	3	et	et	PROPN
ejpam-5876	37	4	al	al	PROPN
ejpam-5876	37	5	.	.	PUNCT
ejpam-5876	37	6	/	/	SYM
ejpam-5876	37	7	eur	eur	PROPN
ejpam-5876	37	8	.	.	PUNCT
ejpam-5876	38	1	j.	j.	PROPN
ejpam-5876	38	2	pure	pure	PROPN
ejpam-5876	38	3	appl	appl	PROPN
ejpam-5876	38	4	.	.	PROPN
ejpam-5876	38	5	math	math	PROPN
ejpam-5876	38	6	,	,	PUNCT
ejpam-5876	38	7	18	18	NUM
ejpam-5876	38	8	(	(	PUNCT
ejpam-5876	38	9	2	2	NUM
ejpam-5876	38	10	)	)	PUNCT
ejpam-5876	38	11	(	(	PUNCT
ejpam-5876	38	12	2025	2025	NUM
ejpam-5876	38	13	)	)	PUNCT
ejpam-5876	38	14	,	,	PUNCT
ejpam-5876	38	15	5876	5876	NUM
ejpam-5876	38	16	3	3	NUM
ejpam-5876	38	17	of	of	ADP
ejpam-5876	38	18	16	16	NUM
ejpam-5876	38	19	we	we	PRON
ejpam-5876	38	20	provide	provide	VERB
ejpam-5876	38	21	several	several	ADJ
ejpam-5876	38	22	conditions	condition	NOUN
ejpam-5876	38	23	for	for	ADP
ejpam-5876	38	24	a	a	DET
ejpam-5876	38	25	semidetached	semidetache	VERB
ejpam-5876	38	26	structure	structure	NOUN
ejpam-5876	38	27	in	in	ADP
ejpam-5876	38	28	sup	sup	NOUN
ejpam-5876	38	29	-	-	PUNCT
ejpam-5876	38	30	algebras	algebras	NOUN
ejpam-5876	38	31	to	to	PART
ejpam-5876	38	32	be	be	AUX
ejpam-5876	38	33	a	a	DET
ejpam-5876	38	34	semidetached	semidetache	VERB
ejpam-5876	38	35	sup	sup	NOUN
ejpam-5876	38	36	-	-	PUNCT
ejpam-5876	38	37	subalgebra	subalgebra	NOUN
ejpam-5876	38	38	.	.	PUNCT
ejpam-5876	39	1	2	2	X
ejpam-5876	39	2	.	.	X
ejpam-5876	39	3	preliminaries	preliminary	NOUN
ejpam-5876	39	4	sheffer	sheffer	VERB
ejpam-5876	39	5	stroke	stroke	NOUN
ejpam-5876	39	6	up	up	ADP
ejpam-5876	39	7	-	-	PUNCT
ejpam-5876	39	8	algebras	algebras	NOUN
ejpam-5876	39	9	epitomize	epitomize	VERB
ejpam-5876	39	10	a	a	DET
ejpam-5876	39	11	fascinating	fascinating	ADJ
ejpam-5876	39	12	convergence	convergence	NOUN
ejpam-5876	39	13	of	of	ADP
ejpam-5876	39	14	algebraic	algebraic	ADJ
ejpam-5876	39	15	theory	theory	NOUN
ejpam-5876	39	16	and	and	CCONJ
ejpam-5876	39	17	logical	logical	ADJ
ejpam-5876	39	18	principles	principle	NOUN
ejpam-5876	39	19	,	,	PUNCT
ejpam-5876	39	20	distinguished	distinguish	VERB
ejpam-5876	39	21	by	by	ADP
ejpam-5876	39	22	the	the	DET
ejpam-5876	39	23	sheffer	sheffer	PROPN
ejpam-5876	39	24	stroke	stroke	NOUN
ejpam-5876	39	25	operation	operation	NOUN
ejpam-5876	39	26	,	,	PUNCT
ejpam-5876	39	27	which	which	PRON
ejpam-5876	39	28	serves	serve	VERB
ejpam-5876	39	29	as	as	ADP
ejpam-5876	39	30	a	a	DET
ejpam-5876	39	31	fundamental	fundamental	ADJ
ejpam-5876	39	32	connective	connective	NOUN
ejpam-5876	39	33	within	within	ADP
ejpam-5876	39	34	the	the	DET
ejpam-5876	39	35	realm	realm	NOUN
ejpam-5876	39	36	of	of	ADP
ejpam-5876	39	37	propositional	propositional	ADJ
ejpam-5876	39	38	calculus	calculus	NOUN
ejpam-5876	39	39	.	.	PUNCT
ejpam-5876	40	1	this	this	DET
ejpam-5876	40	2	particular	particular	ADJ
ejpam-5876	40	3	algebraic	algebraic	NOUN
ejpam-5876	40	4	construct	construct	NOUN
ejpam-5876	40	5	not	not	PART
ejpam-5876	40	6	only	only	ADV
ejpam-5876	40	7	augments	augment	VERB
ejpam-5876	40	8	our	our	PRON
ejpam-5876	40	9	comprehension	comprehension	NOUN
ejpam-5876	40	10	of	of	ADP
ejpam-5876	40	11	logical	logical	ADJ
ejpam-5876	40	12	operations	operation	NOUN
ejpam-5876	40	13	but	but	CCONJ
ejpam-5876	40	14	also	also	ADV
ejpam-5876	40	15	bears	bear	VERB
ejpam-5876	40	16	considerable	considerable	ADJ
ejpam-5876	40	17	ramifications	ramification	NOUN
ejpam-5876	40	18	in	in	ADP
ejpam-5876	40	19	disciplines	discipline	NOUN
ejpam-5876	40	20	such	such	ADJ
ejpam-5876	40	21	as	as	ADP
ejpam-5876	40	22	computer	computer	NOUN
ejpam-5876	40	23	science	science	NOUN
ejpam-5876	40	24	and	and	CCONJ
ejpam-5876	40	25	decision	decision	NOUN
ejpam-5876	40	26	theory	theory	NOUN
ejpam-5876	40	27	.	.	PUNCT
ejpam-5876	41	1	the	the	DET
ejpam-5876	41	2	present	present	ADJ
ejpam-5876	41	3	article	article	NOUN
ejpam-5876	41	4	will	will	AUX
ejpam-5876	41	5	explore	explore	VERB
ejpam-5876	41	6	the	the	DET
ejpam-5876	41	7	definitions	definition	NOUN
ejpam-5876	41	8	and	and	CCONJ
ejpam-5876	41	9	foundational	foundational	ADJ
ejpam-5876	41	10	elements	element	NOUN
ejpam-5876	41	11	of	of	ADP
ejpam-5876	41	12	sheffer	sheffer	PROPN
ejpam-5876	41	13	stroke	stroke	PROPN
ejpam-5876	41	14	up	up	ADP
ejpam-5876	41	15	-	-	PUNCT
ejpam-5876	41	16	algebras	algebras	ADV
ejpam-5876	41	17	,	,	PUNCT
ejpam-5876	41	18	underscoring	underscore	VERB
ejpam-5876	41	19	their	their	PRON
ejpam-5876	41	20	significance	significance	NOUN
ejpam-5876	41	21	within	within	ADP
ejpam-5876	41	22	the	the	DET
ejpam-5876	41	23	context	context	NOUN
ejpam-5876	41	24	of	of	ADP
ejpam-5876	41	25	algebraic	algebraic	ADJ
ejpam-5876	41	26	theory	theory	NOUN
ejpam-5876	41	27	.	.	PUNCT
ejpam-5876	42	1	definition	definition	NOUN
ejpam-5876	42	2	1	1	NUM
ejpam-5876	42	3	.	.	PUNCT
ejpam-5876	43	1	[	[	X
ejpam-5876	43	2	1	1	X
ejpam-5876	43	3	]	]	PUNCT
ejpam-5876	43	4	let	let	VERB
ejpam-5876	43	5	⟨x	⟨x	VERB
ejpam-5876	43	6	,	,	PUNCT
ejpam-5876	43	7	|⟩	|⟩	PROPN
ejpam-5876	43	8	be	be	AUX
ejpam-5876	43	9	a	a	DET
ejpam-5876	43	10	groupoid	groupoid	NOUN
ejpam-5876	43	11	.	.	PUNCT
ejpam-5876	44	1	the	the	DET
ejpam-5876	44	2	operation	operation	NOUN
ejpam-5876	44	3	|	|	ADV
ejpam-5876	44	4	is	be	AUX
ejpam-5876	44	5	said	say	VERB
ejpam-5876	44	6	to	to	PART
ejpam-5876	44	7	be	be	AUX
ejpam-5876	44	8	a	a	DET
ejpam-5876	44	9	sheffer	sheffer	NOUN
ejpam-5876	44	10	stroke	stroke	NOUN
ejpam-5876	44	11	operation	operation	NOUN
ejpam-5876	44	12	if	if	SCONJ
ejpam-5876	44	13	it	it	PRON
ejpam-5876	44	14	satisfies	satisfy	VERB
ejpam-5876	44	15	the	the	DET
ejpam-5876	44	16	following	follow	VERB
ejpam-5876	44	17	conditions	condition	NOUN
ejpam-5876	44	18	:	:	PUNCT
ejpam-5876	44	19	for	for	ADP
ejpam-5876	44	20	all	all	DET
ejpam-5876	44	21	x	x	NOUN
ejpam-5876	44	22	,	,	PUNCT
ejpam-5876	44	23	y	y	PROPN
ejpam-5876	44	24	,	,	PUNCT
ejpam-5876	44	25	z	z	PROPN
ejpam-5876	44	26	∈	∈	PROPN
ejpam-5876	44	27	x	x	X
ejpam-5876	44	28	,	,	PUNCT
ejpam-5876	44	29	(	(	PUNCT
ejpam-5876	44	30	s1	s1	NOUN
ejpam-5876	44	31	)	)	PUNCT
ejpam-5876	44	32	x|y	x|y	PUNCT
ejpam-5876	45	1	=	=	PUNCT
ejpam-5876	45	2	y|x	y|x	NOUN
ejpam-5876	45	3	(	(	PUNCT
ejpam-5876	45	4	s2	s2	PROPN
ejpam-5876	45	5	)	)	PUNCT
ejpam-5876	45	6	(	(	PUNCT
ejpam-5876	45	7	x|x)|(x|y	x|x)|(x|y	PROPN
ejpam-5876	45	8	)	)	PUNCT
ejpam-5876	46	1	=	=	SYM
ejpam-5876	46	2	x	x	X
ejpam-5876	46	3	(	(	PUNCT
ejpam-5876	46	4	s3	s3	PROPN
ejpam-5876	46	5	)	)	PUNCT
ejpam-5876	46	6	x|((y|z)|(y|z	x|((y|z)|(y|z	NUM
ejpam-5876	46	7	)	)	PUNCT
ejpam-5876	46	8	)	)	PUNCT
ejpam-5876	47	1	=	=	SYM
ejpam-5876	47	2	(	(	PUNCT
ejpam-5876	47	3	(	(	PUNCT
ejpam-5876	47	4	x|y)|(x|y))|z	x|y)|(x|y))|z	PROPN
ejpam-5876	47	5	(	(	PUNCT
ejpam-5876	47	6	s4	s4	PROPN
ejpam-5876	47	7	)	)	PUNCT
ejpam-5876	47	8	(	(	PUNCT
ejpam-5876	47	9	x|((x|x)|(y|y)))|(x|((x|x)|(y|y	x|((x|x)|(y|y)))|(x|((x|x)|(y|y	NUM
ejpam-5876	47	10	)	)	PUNCT
ejpam-5876	47	11	)	)	PUNCT
ejpam-5876	47	12	)	)	PUNCT
ejpam-5876	47	13	=	=	PUNCT
ejpam-5876	48	1	x.	x.	NOUN
ejpam-5876	48	2	definition	definition	NOUN
ejpam-5876	48	3	2	2	NUM
ejpam-5876	48	4	.	.	PUNCT
ejpam-5876	49	1	[	[	X
ejpam-5876	49	2	7	7	X
ejpam-5876	49	3	]	]	X
ejpam-5876	49	4	a	a	DET
ejpam-5876	49	5	sheffer	sheffer	NOUN
ejpam-5876	49	6	stroke	stroke	NOUN
ejpam-5876	49	7	up	up	ADP
ejpam-5876	49	8	-	-	PUNCT
ejpam-5876	49	9	algebra	algebra	NOUN
ejpam-5876	49	10	(	(	PUNCT
ejpam-5876	49	11	briefly	briefly	ADV
ejpam-5876	49	12	,	,	PUNCT
ejpam-5876	49	13	sup	sup	NOUN
ejpam-5876	49	14	-	-	PUNCT
ejpam-5876	49	15	algebra	algebra	NOUN
ejpam-5876	49	16	)	)	PUNCT
ejpam-5876	49	17	is	be	AUX
ejpam-5876	49	18	a	a	DET
ejpam-5876	49	19	structure	structure	NOUN
ejpam-5876	49	20	⟨x	⟨x	VERB
ejpam-5876	49	21	,	,	PUNCT
ejpam-5876	49	22	|	|	INTJ
ejpam-5876	49	23	,	,	PUNCT
ejpam-5876	49	24	0⟩	0⟩	PROPN
ejpam-5876	49	25	of	of	ADP
ejpam-5876	49	26	type	type	NOUN
ejpam-5876	49	27	(	(	PUNCT
ejpam-5876	49	28	2	2	NUM
ejpam-5876	49	29	,	,	PUNCT
ejpam-5876	49	30	0	0	NUM
ejpam-5876	49	31	)	)	PUNCT
ejpam-5876	49	32	such	such	ADJ
ejpam-5876	49	33	that	that	DET
ejpam-5876	49	34	0	0	NUM
ejpam-5876	49	35	is	be	AUX
ejpam-5876	49	36	the	the	DET
ejpam-5876	49	37	fixed	fix	VERB
ejpam-5876	49	38	element	element	NOUN
ejpam-5876	49	39	in	in	ADP
ejpam-5876	49	40	x	x	X
ejpam-5876	49	41	and	and	CCONJ
ejpam-5876	49	42	the	the	DET
ejpam-5876	49	43	following	follow	VERB
ejpam-5876	49	44	conditions	condition	NOUN
ejpam-5876	49	45	are	be	AUX
ejpam-5876	49	46	satisfied	satisfied	ADJ
ejpam-5876	49	47	for	for	ADP
ejpam-5876	49	48	all	all	DET
ejpam-5876	49	49	x	x	NOUN
ejpam-5876	49	50	,	,	PUNCT
ejpam-5876	49	51	y	y	PROPN
ejpam-5876	49	52	,	,	PUNCT
ejpam-5876	49	53	z	z	PROPN
ejpam-5876	49	54	∈	∈	PROPN
ejpam-5876	49	55	x	x	X
ejpam-5876	49	56	,	,	PUNCT
ejpam-5876	49	57	(	(	PUNCT
ejpam-5876	49	58	sup-1	sup-1	NOUN
ejpam-5876	49	59	)	)	PUNCT
ejpam-5876	49	60	(	(	PUNCT
ejpam-5876	49	61	(	(	PUNCT
ejpam-5876	49	62	(	(	PUNCT
ejpam-5876	49	63	z|(x|x))|(z|(x|x)))|(((y|(x|x))|(z|(y|y)))|((y|(x|x))|	z|(x|x))|(z|(x|x)))|(((y|(x|x))|(z|(y|y)))|((y|(x|x))|	X
ejpam-5876	49	64	(	(	PUNCT
ejpam-5876	49	65	z|(y|y)))))|(((z|(x|x))|(z|(x|x)))|(((y|(x|x))|(z|(y|y)))|	z|(y|y)))))|(((z|(x|x))|(z|(x|x)))|(((y|(x|x))|(z|(y|y)))|	X
ejpam-5876	49	66	(	(	PUNCT
ejpam-5876	49	67	(	(	PUNCT
ejpam-5876	49	68	y|(x|x))|(z|(y|y	y|(x|x))|(z|(y|y	PROPN
ejpam-5876	49	69	)	)	PUNCT
ejpam-5876	49	70	)	)	PUNCT
ejpam-5876	49	71	)	)	PUNCT
ejpam-5876	49	72	)	)	PUNCT
ejpam-5876	49	73	)	)	PUNCT
ejpam-5876	50	1	=	=	SYM
ejpam-5876	50	2	0	0	PUNCT
ejpam-5876	50	3	(	(	PUNCT
ejpam-5876	50	4	sup-2	sup-2	NOUN
ejpam-5876	50	5	)	)	PUNCT
ejpam-5876	50	6	x|x	x|x	PUNCT
ejpam-5876	51	1	=	=	PUNCT
ejpam-5876	51	2	x|(0|0	x|(0|0	NUM
ejpam-5876	51	3	)	)	PUNCT
ejpam-5876	51	4	(	(	PUNCT
ejpam-5876	51	5	sup-3	sup-3	NOUN
ejpam-5876	51	6	)	)	PUNCT
ejpam-5876	51	7	(	(	PUNCT
ejpam-5876	51	8	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	PROPN
ejpam-5876	51	9	)	)	PUNCT
ejpam-5876	51	10	)	)	PUNCT
ejpam-5876	52	1	=	=	SYM
ejpam-5876	52	2	0	0	NUM
ejpam-5876	53	1	and	and	CCONJ
ejpam-5876	53	2	(	(	PUNCT
ejpam-5876	53	3	y|(x|x))|(y|(x|x	y|(x|x))|(y|(x|x	PROPN
ejpam-5876	53	4	)	)	PUNCT
ejpam-5876	53	5	)	)	PUNCT
ejpam-5876	54	1	=	=	SYM
ejpam-5876	54	2	0	0	NUM
ejpam-5876	54	3	⇒	⇒	NOUN
ejpam-5876	54	4	x	x	PUNCT
ejpam-5876	55	1	=	=	PUNCT
ejpam-5876	55	2	y.	y.	NOUN
ejpam-5876	55	3	proposition	proposition	NOUN
ejpam-5876	55	4	1	1	NUM
ejpam-5876	55	5	.	.	PUNCT
ejpam-5876	56	1	[	[	X
ejpam-5876	56	2	7	7	X
ejpam-5876	56	3	]	]	PUNCT
ejpam-5876	56	4	let	let	VERB
ejpam-5876	56	5	⟨x	⟨x	VERB
ejpam-5876	56	6	,	,	PUNCT
ejpam-5876	56	7	|	|	ADV
ejpam-5876	56	8	,	,	PUNCT
ejpam-5876	56	9	0⟩	0⟩	PROPN
ejpam-5876	56	10	be	be	VERB
ejpam-5876	56	11	an	an	DET
ejpam-5876	56	12	sup	sup	NOUN
ejpam-5876	56	13	-	-	PUNCT
ejpam-5876	56	14	algebra	algebra	NOUN
ejpam-5876	56	15	.	.	PUNCT
ejpam-5876	57	1	then	then	ADV
ejpam-5876	57	2	the	the	DET
ejpam-5876	57	3	binary	binary	PROPN
ejpam-5876	57	4	relation	relation	PROPN
ejpam-5876	57	5	x	x	SYM
ejpam-5876	57	6	≤	≤	ADJ
ejpam-5876	57	7	y	y	NOUN
ejpam-5876	57	8	if	if	SCONJ
ejpam-5876	58	1	and	and	CCONJ
ejpam-5876	58	2	only	only	ADV
ejpam-5876	58	3	if	if	SCONJ
ejpam-5876	58	4	(	(	PUNCT
ejpam-5876	58	5	y|(x|x))|(y|(x|x	y|(x|x))|(y|(x|x	NOUN
ejpam-5876	58	6	)	)	PUNCT
ejpam-5876	58	7	)	)	PUNCT
ejpam-5876	59	1	=	=	SYM
ejpam-5876	59	2	0	0	NUM
ejpam-5876	59	3	is	be	AUX
ejpam-5876	59	4	a	a	DET
ejpam-5876	59	5	partial	partial	ADJ
ejpam-5876	59	6	order	order	NOUN
ejpam-5876	59	7	on	on	ADP
ejpam-5876	59	8	x.	x.	NOUN
ejpam-5876	59	9	definition	definition	NOUN
ejpam-5876	59	10	3	3	NUM
ejpam-5876	59	11	.	.	PUNCT
ejpam-5876	60	1	[	[	X
ejpam-5876	60	2	7	7	X
ejpam-5876	60	3	]	]	X
ejpam-5876	60	4	a	a	DET
ejpam-5876	60	5	nonempty	nonempty	NOUN
ejpam-5876	60	6	subset	subset	VERB
ejpam-5876	60	7	g	g	NOUN
ejpam-5876	60	8	of	of	ADP
ejpam-5876	60	9	an	an	DET
ejpam-5876	60	10	sup	sup	NOUN
ejpam-5876	60	11	-	-	PUNCT
ejpam-5876	60	12	algebra	algebra	NOUN
ejpam-5876	60	13	⟨x	⟨x	VERB
ejpam-5876	60	14	,	,	PUNCT
ejpam-5876	60	15	|	|	INTJ
ejpam-5876	60	16	,	,	PUNCT
ejpam-5876	60	17	0⟩	0⟩	PROPN
ejpam-5876	60	18	is	be	AUX
ejpam-5876	60	19	called	call	VERB
ejpam-5876	60	20	an	an	DET
ejpam-5876	60	21	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	60	22	of	of	ADP
ejpam-5876	60	23	x	x	PUNCT
ejpam-5876	60	24	if	if	SCONJ
ejpam-5876	60	25	(	(	PUNCT
ejpam-5876	60	26	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	60	27	)	)	PUNCT
ejpam-5876	60	28	)	)	PUNCT
ejpam-5876	61	1	∈	∈	PROPN
ejpam-5876	61	2	g	g	NOUN
ejpam-5876	61	3	for	for	ADP
ejpam-5876	61	4	all	all	DET
ejpam-5876	61	5	x	x	NOUN
ejpam-5876	61	6	,	,	PUNCT
ejpam-5876	61	7	y	y	PROPN
ejpam-5876	61	8	∈	∈	PROPN
ejpam-5876	61	9	g.	g.	PROPN
ejpam-5876	61	10	lemma	lemma	PROPN
ejpam-5876	61	11	1	1	X
ejpam-5876	61	12	.	.	PUNCT
ejpam-5876	62	1	[	[	X
ejpam-5876	62	2	7	7	X
ejpam-5876	62	3	]	]	PUNCT
ejpam-5876	62	4	let	let	VERB
ejpam-5876	62	5	⟨x	⟨x	VERB
ejpam-5876	62	6	,	,	PUNCT
ejpam-5876	62	7	|	|	ADV
ejpam-5876	62	8	,	,	PUNCT
ejpam-5876	62	9	0⟩	0⟩	PROPN
ejpam-5876	62	10	be	be	VERB
ejpam-5876	62	11	an	an	DET
ejpam-5876	62	12	sup	sup	NOUN
ejpam-5876	62	13	-	-	PUNCT
ejpam-5876	62	14	algebra	algebra	NOUN
ejpam-5876	62	15	.	.	PUNCT
ejpam-5876	63	1	then	then	ADV
ejpam-5876	63	2	for	for	ADP
ejpam-5876	63	3	all	all	DET
ejpam-5876	63	4	x	x	NOUN
ejpam-5876	63	5	,	,	PUNCT
ejpam-5876	63	6	y	y	PROPN
ejpam-5876	63	7	,	,	PUNCT
ejpam-5876	63	8	z	z	PROPN
ejpam-5876	63	9	∈	∈	PROPN
ejpam-5876	63	10	x	x	X
ejpam-5876	63	11	,	,	PUNCT
ejpam-5876	63	12	we	we	PRON
ejpam-5876	63	13	have	have	VERB
ejpam-5876	63	14	(	(	PUNCT
ejpam-5876	63	15	1	1	X
ejpam-5876	63	16	)	)	PUNCT
ejpam-5876	63	17	x	x	PUNCT
ejpam-5876	63	18	≤	≤	X
ejpam-5876	63	19	y	y	PROPN
ejpam-5876	63	20	⇒	⇒	NOUN
ejpam-5876	63	21	y|(z|z	y|(z|z	PROPN
ejpam-5876	63	22	)	)	PUNCT
ejpam-5876	63	23	≤	≤	NOUN
ejpam-5876	64	1	x|(z|z	x|(z|z	PROPN
ejpam-5876	64	2	)	)	PUNCT
ejpam-5876	64	3	and	and	CCONJ
ejpam-5876	64	4	z|(x|x	z|(x|x	PROPN
ejpam-5876	64	5	)	)	PUNCT
ejpam-5876	64	6	≤	≤	NOUN
ejpam-5876	65	1	z|(y|y	z|(y|y	PROPN
ejpam-5876	65	2	)	)	PUNCT
ejpam-5876	65	3	(	(	PUNCT
ejpam-5876	65	4	2	2	X
ejpam-5876	65	5	)	)	PUNCT
ejpam-5876	65	6	x	x	PUNCT
ejpam-5876	65	7	≤	≤	PROPN
ejpam-5876	65	8	y	y	PROPN
ejpam-5876	65	9	⇔	⇔	PROPN
ejpam-5876	65	10	y|y	y|y	PROPN
ejpam-5876	65	11	≤	≤	PROPN
ejpam-5876	65	12	x|x	x|x	PUNCT
ejpam-5876	66	1	(	(	PUNCT
ejpam-5876	66	2	3	3	X
ejpam-5876	66	3	)	)	PUNCT
ejpam-5876	66	4	y|(x|x	y|(x|x	PROPN
ejpam-5876	66	5	)	)	PUNCT
ejpam-5876	66	6	≤	≤	NUM
ejpam-5876	66	7	x	x	SYM
ejpam-5876	66	8	(	(	PUNCT
ejpam-5876	66	9	4	4	X
ejpam-5876	66	10	)	)	PUNCT
ejpam-5876	66	11	y	y	PROPN
ejpam-5876	66	12	≤	≤	PROPN
ejpam-5876	66	13	(	(	PUNCT
ejpam-5876	66	14	y|(x|x))|(y|(x|x	y|(x|x))|(y|(x|x	NOUN
ejpam-5876	66	15	)	)	PUNCT
ejpam-5876	66	16	)	)	PUNCT
ejpam-5876	67	1	t.	t.	NOUN
ejpam-5876	67	2	oner	oner	NOUN
ejpam-5876	67	3	et	et	PROPN
ejpam-5876	67	4	al	al	PROPN
ejpam-5876	67	5	.	.	PUNCT
ejpam-5876	67	6	/	/	SYM
ejpam-5876	67	7	eur	eur	PROPN
ejpam-5876	67	8	.	.	PUNCT
ejpam-5876	68	1	j.	j.	PROPN
ejpam-5876	68	2	pure	pure	PROPN
ejpam-5876	68	3	appl	appl	PROPN
ejpam-5876	68	4	.	.	PROPN
ejpam-5876	68	5	math	math	PROPN
ejpam-5876	68	6	,	,	PUNCT
ejpam-5876	68	7	18	18	NUM
ejpam-5876	68	8	(	(	PUNCT
ejpam-5876	68	9	2	2	NUM
ejpam-5876	68	10	)	)	PUNCT
ejpam-5876	68	11	(	(	PUNCT
ejpam-5876	68	12	2025	2025	NUM
ejpam-5876	68	13	)	)	PUNCT
ejpam-5876	68	14	,	,	PUNCT
ejpam-5876	68	15	5876	5876	NUM
ejpam-5876	68	16	4	4	NUM
ejpam-5876	68	17	of	of	ADP
ejpam-5876	68	18	16	16	NUM
ejpam-5876	68	19	(	(	PUNCT
ejpam-5876	68	20	5	5	NUM
ejpam-5876	68	21	)	)	PUNCT
ejpam-5876	68	22	x	x	PUNCT
ejpam-5876	68	23	≤	≤	X
ejpam-5876	68	24	y	y	PROPN
ejpam-5876	68	25	⇒	⇒	NOUN
ejpam-5876	68	26	x	x	X
ejpam-5876	68	27	≤	≤	X
ejpam-5876	68	28	(	(	PUNCT
ejpam-5876	68	29	y|(z|z))|(y|(z|z	y|(z|z))|(y|(z|z	NOUN
ejpam-5876	68	30	)	)	PUNCT
ejpam-5876	68	31	)	)	PUNCT
ejpam-5876	68	32	(	(	PUNCT
ejpam-5876	68	33	6	6	NUM
ejpam-5876	68	34	)	)	PUNCT
ejpam-5876	68	35	z|(y|y	z|(y|y	NUM
ejpam-5876	68	36	)	)	PUNCT
ejpam-5876	68	37	≤	≤	NOUN
ejpam-5876	68	38	z|(y|(x|x	z|(y|(x|x	NOUN
ejpam-5876	68	39	)	)	PUNCT
ejpam-5876	68	40	)	)	PUNCT
ejpam-5876	68	41	(	(	PUNCT
ejpam-5876	68	42	7	7	X
ejpam-5876	68	43	)	)	PUNCT
ejpam-5876	68	44	(	(	PUNCT
ejpam-5876	68	45	(	(	PUNCT
ejpam-5876	68	46	z|(y|y))|(z|(y|y)))|(x|x	z|(y|y))|(z|(y|y)))|(x|x	NOUN
ejpam-5876	68	47	)	)	PUNCT
ejpam-5876	68	48	≤	≤	NOUN
ejpam-5876	68	49	z|(y|(x|x	z|(y|(x|x	NOUN
ejpam-5876	68	50	)	)	PUNCT
ejpam-5876	68	51	)	)	PUNCT
ejpam-5876	68	52	(	(	PUNCT
ejpam-5876	68	53	8)	8)	NUM
ejpam-5876	68	54	x|((y|(z|z))|(y|(z|z	x|((y|(z|z))|(y|(z|z	NUM
ejpam-5876	68	55	)	)	PUNCT
ejpam-5876	68	56	)	)	PUNCT
ejpam-5876	68	57	)	)	PUNCT
ejpam-5876	69	1	≤	≤	NUM
ejpam-5876	69	2	(	(	PUNCT
ejpam-5876	69	3	x|(y|y))|((x|(z|z))|(x|(z|z	x|(y|y))|((x|(z|z))|(x|(z|z	PROPN
ejpam-5876	69	4	)	)	PUNCT
ejpam-5876	69	5	)	)	PUNCT
ejpam-5876	69	6	)	)	PUNCT
ejpam-5876	69	7	.	.	PUNCT
ejpam-5876	70	1	definition	definition	NOUN
ejpam-5876	70	2	4	4	NUM
ejpam-5876	70	3	.	.	PUNCT
ejpam-5876	71	1	a	a	DET
ejpam-5876	71	2	fuzzy	fuzzy	ADJ
ejpam-5876	71	3	set	set	VERB
ejpam-5876	71	4	µ	µ	NOUN
ejpam-5876	71	5	in	in	ADP
ejpam-5876	71	6	an	an	DET
ejpam-5876	71	7	sup	sup	NOUN
ejpam-5876	71	8	-	-	PUNCT
ejpam-5876	71	9	algebra	algebra	NOUN
ejpam-5876	71	10	⟨x	⟨x	VERB
ejpam-5876	71	11	,	,	PUNCT
ejpam-5876	71	12	|	|	INTJ
ejpam-5876	71	13	,	,	PUNCT
ejpam-5876	71	14	0⟩	0⟩	PROPN
ejpam-5876	71	15	is	be	AUX
ejpam-5876	71	16	called	call	VERB
ejpam-5876	71	17	a	a	DET
ejpam-5876	71	18	fuzzy	fuzzy	ADJ
ejpam-5876	71	19	sup	sup	NOUN
ejpam-5876	71	20	-	-	PUNCT
ejpam-5876	71	21	subalgebra	subalgebra	NOUN
ejpam-5876	71	22	of	of	ADP
ejpam-5876	71	23	x	x	PRON
ejpam-5876	71	24	if	if	SCONJ
ejpam-5876	71	25	it	it	PRON
ejpam-5876	71	26	satisfies	satisfy	VERB
ejpam-5876	71	27	the	the	DET
ejpam-5876	71	28	following	following	NOUN
ejpam-5876	71	29	:	:	PUNCT
ejpam-5876	71	30	(	(	PUNCT
ejpam-5876	71	31	∀x	∀x	X
ejpam-5876	71	32	,	,	PUNCT
ejpam-5876	71	33	y	y	PROPN
ejpam-5876	71	34	∈	∈	PROPN
ejpam-5876	71	35	x)(µ((x|(y|y))|(x|(y|y	x)(µ((x|(y|y))|(x|(y|y	PROPN
ejpam-5876	71	36	)	)	PUNCT
ejpam-5876	71	37	)	)	PUNCT
ejpam-5876	71	38	)	)	PUNCT
ejpam-5876	71	39	≥	≥	NOUN
ejpam-5876	71	40	min{µ(x	min{µ(x	NOUN
ejpam-5876	71	41	)	)	PUNCT
ejpam-5876	71	42	,	,	PUNCT
ejpam-5876	71	43	µ(y	µ(y	PROPN
ejpam-5876	71	44	)	)	PUNCT
ejpam-5876	71	45	}	}	PUNCT
ejpam-5876	71	46	)	)	PUNCT
ejpam-5876	71	47	.	.	PUNCT
ejpam-5876	72	1	definition	definition	NOUN
ejpam-5876	72	2	5	5	NUM
ejpam-5876	72	3	.	.	PUNCT
ejpam-5876	73	1	a	a	DET
ejpam-5876	73	2	fuzzy	fuzzy	ADJ
ejpam-5876	73	3	set	set	VERB
ejpam-5876	73	4	µ	µ	NOUN
ejpam-5876	73	5	in	in	ADP
ejpam-5876	73	6	an	an	DET
ejpam-5876	73	7	sup	sup	NOUN
ejpam-5876	73	8	-	-	PUNCT
ejpam-5876	73	9	algebra	algebra	NOUN
ejpam-5876	73	10	⟨x	⟨x	VERB
ejpam-5876	73	11	,	,	PUNCT
ejpam-5876	73	12	|	|	INTJ
ejpam-5876	73	13	,	,	PUNCT
ejpam-5876	73	14	0⟩	0⟩	PROPN
ejpam-5876	73	15	is	be	AUX
ejpam-5876	73	16	called	call	VERB
ejpam-5876	73	17	an	an	DET
ejpam-5876	73	18	(	(	PUNCT
ejpam-5876	73	19	∈,∈	∈,∈	X
ejpam-5876	73	20	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	73	21	sup	sup	ADJ
ejpam-5876	73	22	-	-	PUNCT
ejpam-5876	73	23	subalgebra	subalgebra	NOUN
ejpam-5876	73	24	of	of	ADP
ejpam-5876	73	25	x	x	PRON
ejpam-5876	73	26	if	if	SCONJ
ejpam-5876	73	27	it	it	PRON
ejpam-5876	73	28	satisfies	satisfy	VERB
ejpam-5876	73	29	the	the	DET
ejpam-5876	73	30	following	following	NOUN
ejpam-5876	73	31	:	:	PUNCT
ejpam-5876	73	32	(	(	PUNCT
ejpam-5876	73	33	∀x	∀x	X
ejpam-5876	73	34	,	,	PUNCT
ejpam-5876	73	35	y	y	PROPN
ejpam-5876	73	36	∈	∈	PROPN
ejpam-5876	73	37	x)(∀t	x)(∀t	PROPN
ejpam-5876	73	38	,	,	PUNCT
ejpam-5876	73	39	r	r	NOUN
ejpam-5876	73	40	∈	∈	PROPN
ejpam-5876	73	41	(	(	PUNCT
ejpam-5876	73	42	0	0	NUM
ejpam-5876	73	43	,	,	PUNCT
ejpam-5876	73	44	1])(xt	1])(xt	NUM
ejpam-5876	73	45	∈	∈	NOUN
ejpam-5876	73	46	µ	µ	NOUN
ejpam-5876	73	47	,	,	PUNCT
ejpam-5876	73	48	yr	yr	PROPN
ejpam-5876	73	49	∈	∈	PROPN
ejpam-5876	73	50	µ	µ	PRON
ejpam-5876	73	51	⇒	⇒	NOUN
ejpam-5876	73	52	(	(	PUNCT
ejpam-5876	73	53	(	(	PUNCT
ejpam-5876	73	54	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	73	55	,	,	PUNCT
ejpam-5876	73	56	r	r	NOUN
ejpam-5876	73	57	}	}	PUNCT
ejpam-5876	73	58	∈	∈	PROPN
ejpam-5876	73	59	∨qkµ	∨qkµ	PROPN
ejpam-5876	73	60	)	)	PUNCT
ejpam-5876	73	61	.	.	PUNCT
ejpam-5876	74	1	(	(	PUNCT
ejpam-5876	74	2	1	1	X
ejpam-5876	74	3	)	)	PUNCT
ejpam-5876	74	4	definition	definition	NOUN
ejpam-5876	74	5	6	6	NUM
ejpam-5876	74	6	.	.	PUNCT
ejpam-5876	75	1	[	[	X
ejpam-5876	75	2	8	8	NUM
ejpam-5876	75	3	]	]	X
ejpam-5876	75	4	a	a	DET
ejpam-5876	75	5	fuzzy	fuzzy	ADJ
ejpam-5876	75	6	set	set	VERB
ejpam-5876	75	7	µ	µ	NOUN
ejpam-5876	75	8	in	in	ADP
ejpam-5876	75	9	a	a	DET
ejpam-5876	75	10	set	set	NOUN
ejpam-5876	75	11	x	x	X
ejpam-5876	75	12	of	of	ADP
ejpam-5876	75	13	the	the	DET
ejpam-5876	75	14	form	form	NOUN
ejpam-5876	75	15	µ(y	µ(y	NUM
ejpam-5876	75	16	)	)	PUNCT
ejpam-5876	75	17	=	=	PRON
ejpam-5876	75	18	{	{	PUNCT
ejpam-5876	75	19	t	t	PROPN
ejpam-5876	75	20	∈	∈	PROPN
ejpam-5876	75	21	(	(	PUNCT
ejpam-5876	75	22	0	0	NUM
ejpam-5876	75	23	,	,	PUNCT
ejpam-5876	75	24	1	1	NUM
ejpam-5876	75	25	]	]	PUNCT
ejpam-5876	75	26	if	if	SCONJ
ejpam-5876	75	27	y	y	PROPN
ejpam-5876	75	28	=	=	PUNCT
ejpam-5876	75	29	x	x	SYM
ejpam-5876	75	30	0	0	NUM
ejpam-5876	75	31	otherwise	otherwise	ADV
ejpam-5876	75	32	is	be	AUX
ejpam-5876	75	33	said	say	VERB
ejpam-5876	75	34	to	to	PART
ejpam-5876	75	35	be	be	AUX
ejpam-5876	75	36	a	a	DET
ejpam-5876	75	37	fuzzy	fuzzy	ADJ
ejpam-5876	75	38	point	point	NOUN
ejpam-5876	75	39	with	with	ADP
ejpam-5876	75	40	support	support	NOUN
ejpam-5876	75	41	x	x	PUNCT
ejpam-5876	75	42	and	and	CCONJ
ejpam-5876	75	43	value	value	NOUN
ejpam-5876	75	44	t	t	PROPN
ejpam-5876	75	45	and	and	CCONJ
ejpam-5876	75	46	is	be	AUX
ejpam-5876	75	47	denoted	denote	VERB
ejpam-5876	75	48	by	by	ADP
ejpam-5876	75	49	xt	xt	PROPN
ejpam-5876	75	50	.	.	PUNCT
ejpam-5876	76	1	the	the	DET
ejpam-5876	76	2	general	general	ADJ
ejpam-5876	76	3	form	form	NOUN
ejpam-5876	76	4	of	of	ADP
ejpam-5876	76	5	the	the	DET
ejpam-5876	76	6	symbol	symbol	NOUN
ejpam-5876	76	7	xtqµ	xtqµ	NOUN
ejpam-5876	76	8	as	as	SCONJ
ejpam-5876	76	9	follows	follow	VERB
ejpam-5876	76	10	:	:	PUNCT
ejpam-5876	76	11	for	for	ADP
ejpam-5876	76	12	an	an	DET
ejpam-5876	76	13	arbitrary	arbitrary	ADJ
ejpam-5876	76	14	element	element	NOUN
ejpam-5876	76	15	k	k	PROPN
ejpam-5876	76	16	∈	∈	PROPN
ejpam-5876	77	1	[	[	X
ejpam-5876	77	2	0	0	NUM
ejpam-5876	77	3	,	,	PUNCT
ejpam-5876	77	4	1	1	NUM
ejpam-5876	77	5	)	)	PUNCT
ejpam-5876	77	6	,	,	PUNCT
ejpam-5876	77	7	we	we	PRON
ejpam-5876	77	8	say	say	VERB
ejpam-5876	77	9	that	that	SCONJ
ejpam-5876	77	10	•	•	NUM
ejpam-5876	77	11	xtqkµ	xtqkµ	NOUN
ejpam-5876	77	12	if	if	SCONJ
ejpam-5876	77	13	µ(x	µ(x	VERB
ejpam-5876	77	14	)	)	PUNCT
ejpam-5876	77	15	+	+	CCONJ
ejpam-5876	77	16	t+	t+	VERB
ejpam-5876	77	17	k	k	X
ejpam-5876	77	18	>	>	X
ejpam-5876	77	19	1	1	NUM
ejpam-5876	77	20	.	.	NUM
ejpam-5876	77	21	•	•	NUM
ejpam-5876	77	22	xt	xt	ADP
ejpam-5876	77	23	∈	∈	PROPN
ejpam-5876	77	24	∨qkµ	∨qkµ	PROPN
ejpam-5876	77	25	if	if	SCONJ
ejpam-5876	77	26	xt	xt	PROPN
ejpam-5876	77	27	∈	∈	PROPN
ejpam-5876	77	28	µ	µ	X
ejpam-5876	77	29	or	or	CCONJ
ejpam-5876	77	30	xtqkµ.	xtqkµ.	NOUN
ejpam-5876	77	31	definition	definition	NOUN
ejpam-5876	77	32	7	7	NUM
ejpam-5876	77	33	.	.	X
ejpam-5876	78	1	for	for	ADP
ejpam-5876	78	2	any	any	DET
ejpam-5876	78	3	fuzzy	fuzzy	ADJ
ejpam-5876	78	4	set	set	VERB
ejpam-5876	78	5	µ	µ	NOUN
ejpam-5876	78	6	in	in	ADP
ejpam-5876	78	7	a	a	DET
ejpam-5876	78	8	set	set	NOUN
ejpam-5876	78	9	x	x	PUNCT
ejpam-5876	78	10	and	and	CCONJ
ejpam-5876	78	11	any	any	DET
ejpam-5876	78	12	t	t	NOUN
ejpam-5876	78	13	∈	∈	PROPN
ejpam-5876	79	1	[	[	X
ejpam-5876	79	2	0	0	NUM
ejpam-5876	79	3	,	,	PUNCT
ejpam-5876	79	4	1	1	NUM
ejpam-5876	79	5	]	]	PUNCT
ejpam-5876	79	6	,	,	PUNCT
ejpam-5876	79	7	the	the	DET
ejpam-5876	79	8	set	set	NOUN
ejpam-5876	79	9	u(µ	u(µ	PROPN
ejpam-5876	79	10	,	,	PUNCT
ejpam-5876	79	11	t	t	PROPN
ejpam-5876	79	12	)	)	PUNCT
ejpam-5876	79	13	=	=	PRON
ejpam-5876	79	14	{	{	PUNCT
ejpam-5876	79	15	x	x	PUNCT
ejpam-5876	79	16	∈	∈	NOUN
ejpam-5876	79	17	x	x	X
ejpam-5876	79	18	:	:	PUNCT
ejpam-5876	79	19	µ(x	µ(x	NUM
ejpam-5876	79	20	)	)	PUNCT
ejpam-5876	79	21	≥	≥	NOUN
ejpam-5876	79	22	t	t	PROPN
ejpam-5876	79	23	}	}	PUNCT
ejpam-5876	79	24	is	be	AUX
ejpam-5876	79	25	called	call	VERB
ejpam-5876	79	26	a	a	DET
ejpam-5876	79	27	level	level	NOUN
ejpam-5876	79	28	subset	subset	NOUN
ejpam-5876	79	29	of	of	ADP
ejpam-5876	79	30	µ.	µ.	NOUN
ejpam-5876	79	31	3	3	NUM
ejpam-5876	79	32	.	.	PUNCT
ejpam-5876	79	33	foundational	foundational	ADJ
ejpam-5876	79	34	results	result	NOUN
ejpam-5876	79	35	on	on	ADP
ejpam-5876	79	36	semidetached	semidetache	VERB
ejpam-5876	79	37	sup	sup	NOUN
ejpam-5876	79	38	-	-	PUNCT
ejpam-5876	79	39	subalgebras	subalgebras	NOUN
ejpam-5876	79	40	before	before	ADP
ejpam-5876	79	41	delving	delve	VERB
ejpam-5876	79	42	into	into	ADP
ejpam-5876	79	43	the	the	DET
ejpam-5876	79	44	concept	concept	NOUN
ejpam-5876	79	45	of	of	ADP
ejpam-5876	79	46	semidetached	semidetache	VERB
ejpam-5876	79	47	sup	sup	NOUN
ejpam-5876	79	48	-	-	PUNCT
ejpam-5876	79	49	subalgebras	subalgebras	PROPN
ejpam-5876	79	50	,	,	PUNCT
ejpam-5876	79	51	it	it	PRON
ejpam-5876	79	52	is	be	AUX
ejpam-5876	79	53	essential	essential	ADJ
ejpam-5876	79	54	to	to	PART
ejpam-5876	79	55	recognize	recognize	VERB
ejpam-5876	79	56	the	the	DET
ejpam-5876	79	57	foundational	foundational	ADJ
ejpam-5876	79	58	framework	framework	NOUN
ejpam-5876	79	59	of	of	ADP
ejpam-5876	79	60	sup	sup	NOUN
ejpam-5876	79	61	-	-	PUNCT
ejpam-5876	79	62	algebras	algebras	NOUN
ejpam-5876	79	63	as	as	ADP
ejpam-5876	79	64	a	a	DET
ejpam-5876	79	65	unique	unique	ADJ
ejpam-5876	79	66	algebraic	algebraic	ADJ
ejpam-5876	79	67	structure	structure	NOUN
ejpam-5876	79	68	that	that	PRON
ejpam-5876	79	69	integrates	integrate	VERB
ejpam-5876	79	70	logical	logical	ADJ
ejpam-5876	79	71	operations	operation	NOUN
ejpam-5876	79	72	through	through	ADP
ejpam-5876	79	73	the	the	DET
ejpam-5876	79	74	sheffer	sheffer	NOUN
ejpam-5876	79	75	stroke	stroke	NOUN
ejpam-5876	79	76	.	.	PUNCT
ejpam-5876	80	1	this	this	DET
ejpam-5876	80	2	section	section	NOUN
ejpam-5876	80	3	explores	explore	VERB
ejpam-5876	80	4	how	how	SCONJ
ejpam-5876	80	5	semidetached	semidetache	VERB
ejpam-5876	80	6	structures	structure	NOUN
ejpam-5876	80	7	can	can	AUX
ejpam-5876	80	8	emerge	emerge	VERB
ejpam-5876	80	9	within	within	ADP
ejpam-5876	80	10	sup	sup	NOUN
ejpam-5876	80	11	-	-	PUNCT
ejpam-5876	80	12	algebras	algebra	NOUN
ejpam-5876	80	13	,	,	PUNCT
ejpam-5876	80	14	emphasizing	emphasize	VERB
ejpam-5876	80	15	their	their	PRON
ejpam-5876	80	16	significance	significance	NOUN
ejpam-5876	80	17	in	in	ADP
ejpam-5876	80	18	the	the	DET
ejpam-5876	80	19	broader	broad	ADJ
ejpam-5876	80	20	context	context	NOUN
ejpam-5876	80	21	of	of	ADP
ejpam-5876	80	22	fuzzy	fuzzy	ADJ
ejpam-5876	80	23	subalgebra	subalgebra	NOUN
ejpam-5876	80	24	theory	theory	NOUN
ejpam-5876	80	25	.	.	PUNCT
ejpam-5876	81	1	by	by	ADP
ejpam-5876	81	2	establishing	establish	VERB
ejpam-5876	81	3	a	a	DET
ejpam-5876	81	4	robust	robust	ADJ
ejpam-5876	81	5	theoretical	theoretical	ADJ
ejpam-5876	81	6	basis	basis	NOUN
ejpam-5876	81	7	,	,	PUNCT
ejpam-5876	81	8	we	we	PRON
ejpam-5876	81	9	aim	aim	VERB
ejpam-5876	81	10	to	to	PART
ejpam-5876	81	11	illustrate	illustrate	VERB
ejpam-5876	81	12	the	the	DET
ejpam-5876	81	13	intricate	intricate	ADJ
ejpam-5876	81	14	relationships	relationship	NOUN
ejpam-5876	81	15	and	and	CCONJ
ejpam-5876	81	16	conditions	condition	NOUN
ejpam-5876	81	17	that	that	PRON
ejpam-5876	81	18	govern	govern	VERB
ejpam-5876	81	19	these	these	DET
ejpam-5876	81	20	semidetached	semidetache	VERB
ejpam-5876	81	21	structures	structure	NOUN
ejpam-5876	81	22	.	.	PUNCT
ejpam-5876	82	1	in	in	ADP
ejpam-5876	82	2	what	what	PRON
ejpam-5876	82	3	follows	follow	VERB
ejpam-5876	82	4	,	,	PUNCT
ejpam-5876	82	5	let	let	VERB
ejpam-5876	82	6	x	x	X
ejpam-5876	82	7	=	=	PUNCT
ejpam-5876	82	8	⟨x	⟨x	VERB
ejpam-5876	82	9	,	,	PUNCT
ejpam-5876	82	10	|	|	ADV
ejpam-5876	82	11	,	,	PUNCT
ejpam-5876	82	12	0⟩	0⟩	PROPN
ejpam-5876	82	13	denote	denote	VERB
ejpam-5876	82	14	an	an	DET
ejpam-5876	82	15	sup	sup	NOUN
ejpam-5876	82	16	-	-	PUNCT
ejpam-5876	82	17	algebra	algebra	NOUN
ejpam-5876	82	18	unless	unless	SCONJ
ejpam-5876	82	19	otherwise	otherwise	ADV
ejpam-5876	82	20	specified	specify	VERB
ejpam-5876	82	21	.	.	PUNCT
ejpam-5876	83	1	given	give	VERB
ejpam-5876	83	2	a	a	DET
ejpam-5876	83	3	set	set	NOUN
ejpam-5876	83	4	x	x	PUNCT
ejpam-5876	83	5	and	and	CCONJ
ejpam-5876	83	6	a	a	DET
ejpam-5876	83	7	subinterval	subinterval	NOUN
ejpam-5876	83	8	ω	ω	NOUN
ejpam-5876	83	9	of	of	ADP
ejpam-5876	83	10	[	[	X
ejpam-5876	83	11	0	0	NUM
ejpam-5876	83	12	,	,	PUNCT
ejpam-5876	83	13	1	1	NUM
ejpam-5876	83	14	]	]	PUNCT
ejpam-5876	83	15	,	,	PUNCT
ejpam-5876	83	16	a	a	DET
ejpam-5876	83	17	semidetached	semidetache	VERB
ejpam-5876	83	18	structure	structure	NOUN
ejpam-5876	83	19	over	over	ADP
ejpam-5876	83	20	ω	ω	PROPN
ejpam-5876	83	21	is	be	AUX
ejpam-5876	83	22	defined	define	VERB
ejpam-5876	83	23	to	to	PART
ejpam-5876	83	24	be	be	AUX
ejpam-5876	83	25	a	a	DET
ejpam-5876	83	26	pair	pair	NOUN
ejpam-5876	83	27	(	(	PUNCT
ejpam-5876	83	28	x	x	NOUN
ejpam-5876	83	29	,	,	PUNCT
ejpam-5876	83	30	f	f	PROPN
ejpam-5876	83	31	)	)	PUNCT
ejpam-5876	83	32	,	,	PUNCT
ejpam-5876	83	33	where	where	SCONJ
ejpam-5876	83	34	f	f	X
ejpam-5876	83	35	:	:	PUNCT
ejpam-5876	83	36	ω	ω	PROPN
ejpam-5876	83	37	→	→	SYM
ejpam-5876	83	38	p	p	X
ejpam-5876	83	39	(	(	PUNCT
ejpam-5876	83	40	x	x	X
ejpam-5876	83	41	)	)	PUNCT
ejpam-5876	83	42	is	be	AUX
ejpam-5876	83	43	a	a	DET
ejpam-5876	83	44	mapping	mapping	NOUN
ejpam-5876	83	45	when	when	SCONJ
ejpam-5876	83	46	p	p	PROPN
ejpam-5876	83	47	(	(	PUNCT
ejpam-5876	83	48	x	x	X
ejpam-5876	83	49	)	)	PUNCT
ejpam-5876	83	50	is	be	AUX
ejpam-5876	83	51	represented	represent	VERB
ejpam-5876	83	52	as	as	ADP
ejpam-5876	83	53	the	the	DET
ejpam-5876	83	54	power	power	NOUN
ejpam-5876	83	55	set	set	NOUN
ejpam-5876	83	56	of	of	ADP
ejpam-5876	83	57	x.	x.	PROPN
ejpam-5876	83	58	t.	t.	PROPN
ejpam-5876	83	59	oner	oner	PROPN
ejpam-5876	83	60	et	et	PROPN
ejpam-5876	83	61	al	al	PROPN
ejpam-5876	83	62	.	.	PUNCT
ejpam-5876	83	63	/	/	SYM
ejpam-5876	83	64	eur	eur	PROPN
ejpam-5876	83	65	.	.	PUNCT
ejpam-5876	84	1	j.	j.	PROPN
ejpam-5876	84	2	pure	pure	PROPN
ejpam-5876	84	3	appl	appl	PROPN
ejpam-5876	84	4	.	.	PROPN
ejpam-5876	84	5	math	math	PROPN
ejpam-5876	84	6	,	,	PUNCT
ejpam-5876	84	7	18	18	NUM
ejpam-5876	84	8	(	(	PUNCT
ejpam-5876	84	9	2	2	NUM
ejpam-5876	84	10	)	)	PUNCT
ejpam-5876	84	11	(	(	PUNCT
ejpam-5876	84	12	2025	2025	NUM
ejpam-5876	84	13	)	)	PUNCT
ejpam-5876	84	14	,	,	PUNCT
ejpam-5876	84	15	5876	5876	NUM
ejpam-5876	84	16	5	5	NUM
ejpam-5876	84	17	of	of	ADP
ejpam-5876	84	18	16	16	NUM
ejpam-5876	84	19	definition	definition	NOUN
ejpam-5876	84	20	8	8	NUM
ejpam-5876	84	21	.	.	PUNCT
ejpam-5876	85	1	a	a	DET
ejpam-5876	85	2	semidetached	semidetache	VERB
ejpam-5876	85	3	structure	structure	NOUN
ejpam-5876	85	4	(	(	PUNCT
ejpam-5876	85	5	x	x	NOUN
ejpam-5876	85	6	,	,	PUNCT
ejpam-5876	85	7	f	f	NOUN
ejpam-5876	85	8	)	)	PUNCT
ejpam-5876	85	9	over	over	ADP
ejpam-5876	85	10	ω	ω	PROPN
ejpam-5876	85	11	is	be	AUX
ejpam-5876	85	12	called	call	VERB
ejpam-5876	85	13	a	a	DET
ejpam-5876	85	14	semidetached	semidetached	NOUN
ejpam-5876	85	15	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	85	16	over	over	ADP
ejpam-5876	85	17	ω	ω	PROPN
ejpam-5876	85	18	with	with	ADP
ejpam-5876	85	19	respect	respect	NOUN
ejpam-5876	85	20	to	to	ADP
ejpam-5876	85	21	t	t	PROPN
ejpam-5876	85	22	∈	∈	PROPN
ejpam-5876	85	23	ω	ω	PROPN
ejpam-5876	85	24	(	(	PUNCT
ejpam-5876	85	25	briefly	briefly	ADV
ejpam-5876	85	26	,	,	PUNCT
ejpam-5876	85	27	t	t	NOUN
ejpam-5876	85	28	-	-	PUNCT
ejpam-5876	85	29	semidetached	semidetache	VERB
ejpam-5876	85	30	sup	sup	NOUN
ejpam-5876	85	31	-	-	PUNCT
ejpam-5876	85	32	subalgebra	subalgebra	NOUN
ejpam-5876	85	33	)	)	PUNCT
ejpam-5876	85	34	if	if	SCONJ
ejpam-5876	85	35	f(t	f(t	NOUN
ejpam-5876	85	36	)	)	PUNCT
ejpam-5876	85	37	is	be	AUX
ejpam-5876	85	38	an	an	DET
ejpam-5876	85	39	sup	sup	ADJ
ejpam-5876	85	40	-	-	PUNCT
ejpam-5876	85	41	subalgebra	subalgebra	NOUN
ejpam-5876	85	42	of	of	ADP
ejpam-5876	85	43	x.	x.	NOUN
ejpam-5876	85	44	we	we	PRON
ejpam-5876	85	45	say	say	VERB
ejpam-5876	85	46	that	that	SCONJ
ejpam-5876	85	47	(	(	PUNCT
ejpam-5876	85	48	x	x	X
ejpam-5876	85	49	,	,	PUNCT
ejpam-5876	85	50	f	f	X
ejpam-5876	85	51	)	)	PUNCT
ejpam-5876	85	52	is	be	AUX
ejpam-5876	85	53	a	a	DET
ejpam-5876	85	54	semidetached	semidetache	VERB
ejpam-5876	85	55	sup	sup	NOUN
ejpam-5876	85	56	-	-	PUNCT
ejpam-5876	85	57	subalgebra	subalgebra	NOUN
ejpam-5876	85	58	over	over	ADP
ejpam-5876	85	59	ω	ω	NUM
ejpam-5876	85	60	if	if	SCONJ
ejpam-5876	85	61	it	it	PRON
ejpam-5876	85	62	is	be	AUX
ejpam-5876	85	63	a	a	DET
ejpam-5876	85	64	t	t	NOUN
ejpam-5876	85	65	-	-	PUNCT
ejpam-5876	85	66	semidetached	semidetache	VERB
ejpam-5876	85	67	sup	sup	NOUN
ejpam-5876	85	68	-	-	PUNCT
ejpam-5876	85	69	subalgebra	subalgebra	NOUN
ejpam-5876	85	70	with	with	ADP
ejpam-5876	85	71	respect	respect	NOUN
ejpam-5876	85	72	to	to	ADP
ejpam-5876	85	73	all	all	PRON
ejpam-5876	85	74	t	t	NOUN
ejpam-5876	85	75	∈	∈	PROPN
ejpam-5876	85	76	ω	ω	PROPN
ejpam-5876	85	77	.	.	PUNCT
ejpam-5876	86	1	given	give	VERB
ejpam-5876	86	2	a	a	DET
ejpam-5876	86	3	fuzzy	fuzzy	ADJ
ejpam-5876	86	4	set	set	VERB
ejpam-5876	86	5	µ	µ	NOUN
ejpam-5876	86	6	in	in	ADP
ejpam-5876	86	7	x	x	X
ejpam-5876	86	8	,	,	PUNCT
ejpam-5876	86	9	consider	consider	VERB
ejpam-5876	86	10	the	the	DET
ejpam-5876	86	11	following	follow	VERB
ejpam-5876	86	12	mappings	mapping	NOUN
ejpam-5876	86	13	:	:	PUNCT
ejpam-5876	86	14	ℓµu	ℓµu	NOUN
ejpam-5876	86	15	:	:	PUNCT
ejpam-5876	86	16	ω	ω	X
ejpam-5876	86	17	→	→	SYM
ejpam-5876	86	18	p	p	X
ejpam-5876	86	19	(	(	PUNCT
ejpam-5876	86	20	x	x	NOUN
ejpam-5876	86	21	)	)	PUNCT
ejpam-5876	86	22	;	;	PUNCT
ejpam-5876	86	23	t	t	PROPN
ejpam-5876	86	24	7→	7→	NUM
ejpam-5876	86	25	u(µ	u(µ	PROPN
ejpam-5876	86	26	,	,	PUNCT
ejpam-5876	86	27	t	t	PROPN
ejpam-5876	86	28	)	)	PUNCT
ejpam-5876	86	29	(	(	PUNCT
ejpam-5876	86	30	2	2	X
ejpam-5876	86	31	)	)	PUNCT
ejpam-5876	86	32	ℓµqk	ℓµqk	ADJ
ejpam-5876	86	33	:	:	PUNCT
ejpam-5876	86	34	ω	ω	X
ejpam-5876	86	35	→	→	SYM
ejpam-5876	86	36	p	p	X
ejpam-5876	86	37	(	(	PUNCT
ejpam-5876	86	38	x	x	NOUN
ejpam-5876	86	39	)	)	PUNCT
ejpam-5876	86	40	;	;	PUNCT
ejpam-5876	86	41	t	t	PROPN
ejpam-5876	86	42	7→	7→	NUM
ejpam-5876	86	43	qk(µ	qk(µ	NUM
ejpam-5876	86	44	,	,	PUNCT
ejpam-5876	86	45	t	t	PROPN
ejpam-5876	86	46	)	)	PUNCT
ejpam-5876	86	47	(	(	PUNCT
ejpam-5876	86	48	3	3	X
ejpam-5876	86	49	)	)	PUNCT
ejpam-5876	86	50	ℓµek	ℓµek	NOUN
ejpam-5876	86	51	:	:	PUNCT
ejpam-5876	87	1	ω	ω	X
ejpam-5876	87	2	→	→	SYM
ejpam-5876	87	3	p	p	X
ejpam-5876	87	4	(	(	PUNCT
ejpam-5876	87	5	x	x	NOUN
ejpam-5876	87	6	)	)	PUNCT
ejpam-5876	87	7	;	;	PUNCT
ejpam-5876	87	8	t	t	PROPN
ejpam-5876	87	9	7→	7→	NUM
ejpam-5876	87	10	ek(µ	ek(µ	NUM
ejpam-5876	87	11	,	,	PUNCT
ejpam-5876	87	12	t	t	PROPN
ejpam-5876	87	13	)	)	PUNCT
ejpam-5876	87	14	(	(	PUNCT
ejpam-5876	87	15	4	4	X
ejpam-5876	87	16	)	)	PUNCT
ejpam-5876	88	1	where	where	SCONJ
ejpam-5876	88	2	qk(µ	qk(µ	NUM
ejpam-5876	88	3	,	,	PUNCT
ejpam-5876	88	4	t	t	PROPN
ejpam-5876	88	5	)	)	PUNCT
ejpam-5876	88	6	=	=	PRON
ejpam-5876	88	7	{	{	PUNCT
ejpam-5876	88	8	x	x	PUNCT
ejpam-5876	88	9	∈	∈	PROPN
ejpam-5876	88	10	x	x	X
ejpam-5876	88	11	:	:	PUNCT
ejpam-5876	88	12	xtqkµ	xtqkµ	NOUN
ejpam-5876	88	13	}	}	PUNCT
ejpam-5876	88	14	and	and	CCONJ
ejpam-5876	88	15	ek(µ	ek(µ	NUM
ejpam-5876	88	16	,	,	PUNCT
ejpam-5876	88	17	t	t	PROPN
ejpam-5876	88	18	)	)	PUNCT
ejpam-5876	88	19	=	=	PRON
ejpam-5876	88	20	{	{	PUNCT
ejpam-5876	88	21	x	x	PUNCT
ejpam-5876	88	22	∈	∈	PROPN
ejpam-5876	88	23	x	x	X
ejpam-5876	88	24	:	:	PUNCT
ejpam-5876	88	25	xt	xt	PROPN
ejpam-5876	88	26	∈	∈	PROPN
ejpam-5876	88	27	∨qkµ	∨qkµ	PROPN
ejpam-5876	88	28	}	}	PUNCT
ejpam-5876	88	29	,	,	PUNCT
ejpam-5876	88	30	which	which	PRON
ejpam-5876	88	31	are	be	AUX
ejpam-5876	88	32	called	call	VERB
ejpam-5876	88	33	the	the	DET
ejpam-5876	88	34	qk	qk	NOUN
ejpam-5876	88	35	-	-	PUNCT
ejpam-5876	88	36	set	set	VERB
ejpam-5876	88	37	and	and	CCONJ
ejpam-5876	88	38	∈	∈	NOUN
ejpam-5876	88	39	∨qk	∨qk	NOUN
ejpam-5876	88	40	-	-	NOUN
ejpam-5876	88	41	set	set	VERB
ejpam-5876	88	42	with	with	ADP
ejpam-5876	88	43	respect	respect	NOUN
ejpam-5876	88	44	to	to	ADP
ejpam-5876	88	45	t	t	PROPN
ejpam-5876	88	46	(	(	PUNCT
ejpam-5876	88	47	briefly	briefly	ADV
ejpam-5876	88	48	,	,	PUNCT
ejpam-5876	88	49	t	t	PROPN
ejpam-5876	88	50	-	-	PUNCT
ejpam-5876	88	51	qk	qk	NOUN
ejpam-5876	88	52	-	-	PUNCT
ejpam-5876	88	53	set	set	VERB
ejpam-5876	88	54	and	and	CCONJ
ejpam-5876	88	55	t-∈	t-∈	NOUN
ejpam-5876	88	56	∨qk	∨qk	NOUN
ejpam-5876	88	57	-	-	NOUN
ejpam-5876	88	58	set	set	NOUN
ejpam-5876	88	59	)	)	PUNCT
ejpam-5876	88	60	,	,	PUNCT
ejpam-5876	88	61	respectively	respectively	ADV
ejpam-5876	88	62	,	,	PUNCT
ejpam-5876	88	63	of	of	ADP
ejpam-5876	88	64	µ.	µ.	PROPN
ejpam-5876	88	65	a	a	DET
ejpam-5876	88	66	t	t	PROPN
ejpam-5876	88	67	-	-	PUNCT
ejpam-5876	88	68	qk	qk	NOUN
ejpam-5876	88	69	-	-	PUNCT
ejpam-5876	88	70	set	set	NOUN
ejpam-5876	88	71	with	with	ADP
ejpam-5876	88	72	k	k	PROPN
ejpam-5876	88	73	=	=	SYM
ejpam-5876	88	74	0	0	NUM
ejpam-5876	88	75	is	be	AUX
ejpam-5876	88	76	called	call	VERB
ejpam-5876	88	77	a	a	DET
ejpam-5876	88	78	t	t	PROPN
ejpam-5876	88	79	-	-	PUNCT
ejpam-5876	88	80	q	q	NOUN
ejpam-5876	88	81	-	-	PUNCT
ejpam-5876	88	82	set	set	VERB
ejpam-5876	88	83	and	and	CCONJ
ejpam-5876	88	84	is	be	AUX
ejpam-5876	88	85	denoted	denote	VERB
ejpam-5876	88	86	by	by	ADP
ejpam-5876	88	87	q(µ	q(µ	NOUN
ejpam-5876	88	88	,	,	PUNCT
ejpam-5876	88	89	t	t	PROPN
ejpam-5876	88	90	)	)	PUNCT
ejpam-5876	88	91	.	.	PUNCT
ejpam-5876	89	1	a	a	DET
ejpam-5876	89	2	t-∈	t-∈	NUM
ejpam-5876	89	3	∨qk	∨qk	NOUN
ejpam-5876	89	4	-	-	NOUN
ejpam-5876	89	5	set	set	NOUN
ejpam-5876	89	6	with	with	ADP
ejpam-5876	89	7	k	k	PROPN
ejpam-5876	89	8	=	=	SYM
ejpam-5876	89	9	0	0	NUM
ejpam-5876	89	10	is	be	AUX
ejpam-5876	89	11	called	call	VERB
ejpam-5876	89	12	a	a	DET
ejpam-5876	89	13	t-∈	t-∈	PUNCT
ejpam-5876	89	14	∨q	∨q	NOUN
ejpam-5876	89	15	-	-	PUNCT
ejpam-5876	89	16	set	set	VERB
ejpam-5876	89	17	and	and	CCONJ
ejpam-5876	89	18	is	be	AUX
ejpam-5876	89	19	denoted	denote	VERB
ejpam-5876	89	20	by	by	ADP
ejpam-5876	89	21	e	e	PROPN
ejpam-5876	89	22	(	(	PUNCT
ejpam-5876	89	23	µ	µ	X
ejpam-5876	89	24	,	,	PUNCT
ejpam-5876	89	25	t	t	PROPN
ejpam-5876	89	26	)	)	PUNCT
ejpam-5876	89	27	.	.	PUNCT
ejpam-5876	90	1	note	note	VERB
ejpam-5876	90	2	that	that	SCONJ
ejpam-5876	90	3	,	,	PUNCT
ejpam-5876	90	4	for	for	ADP
ejpam-5876	90	5	any	any	DET
ejpam-5876	90	6	t	t	NOUN
ejpam-5876	90	7	,	,	PUNCT
ejpam-5876	90	8	r	r	NOUN
ejpam-5876	90	9	∈	∈	PROPN
ejpam-5876	90	10	(	(	PUNCT
ejpam-5876	90	11	0	0	NUM
ejpam-5876	90	12	,	,	PUNCT
ejpam-5876	90	13	1	1	NUM
ejpam-5876	90	14	]	]	PUNCT
ejpam-5876	90	15	,	,	PUNCT
ejpam-5876	90	16	if	if	SCONJ
ejpam-5876	90	17	t	t	PROPN
ejpam-5876	90	18	≥	≥	NOUN
ejpam-5876	90	19	r	r	NOUN
ejpam-5876	90	20	,	,	PUNCT
ejpam-5876	90	21	then	then	ADV
ejpam-5876	90	22	every	every	DET
ejpam-5876	90	23	r	r	NOUN
ejpam-5876	90	24	-	-	PUNCT
ejpam-5876	90	25	qk	qk	NOUN
ejpam-5876	90	26	-	-	PUNCT
ejpam-5876	90	27	set	set	NOUN
ejpam-5876	90	28	is	be	AUX
ejpam-5876	90	29	contained	contain	VERB
ejpam-5876	90	30	in	in	ADP
ejpam-5876	90	31	the	the	DET
ejpam-5876	90	32	t	t	PROPN
ejpam-5876	90	33	-	-	PUNCT
ejpam-5876	90	34	qk	qk	NOUN
ejpam-5876	90	35	-	-	PUNCT
ejpam-5876	90	36	set	set	NOUN
ejpam-5876	90	37	,	,	PUNCT
ejpam-5876	90	38	that	that	ADV
ejpam-5876	90	39	is	is	ADV
ejpam-5876	90	40	,	,	PUNCT
ejpam-5876	90	41	qk(µ	qk(µ	ADV
ejpam-5876	90	42	,	,	PUNCT
ejpam-5876	90	43	r	r	NOUN
ejpam-5876	90	44	)	)	PUNCT
ejpam-5876	90	45	⊆	⊆	NUM
ejpam-5876	90	46	qk(µ	qk(µ	NUM
ejpam-5876	90	47	,	,	PUNCT
ejpam-5876	90	48	t	t	PROPN
ejpam-5876	90	49	)	)	PUNCT
ejpam-5876	90	50	.	.	PUNCT
ejpam-5876	91	1	obviously	obviously	ADV
ejpam-5876	91	2	,	,	PUNCT
ejpam-5876	91	3	ek(µ	ek(µ	PROPN
ejpam-5876	91	4	,	,	PUNCT
ejpam-5876	91	5	t	t	PROPN
ejpam-5876	91	6	)	)	PUNCT
ejpam-5876	91	7	=	=	SYM
ejpam-5876	91	8	u(µ	u(µ	PROPN
ejpam-5876	91	9	,	,	PUNCT
ejpam-5876	91	10	t	t	PROPN
ejpam-5876	91	11	)	)	PUNCT
ejpam-5876	91	12	∪qk(µ	∪qk(µ	PROPN
ejpam-5876	91	13	,	,	PUNCT
ejpam-5876	91	14	t	t	PROPN
ejpam-5876	91	15	)	)	PUNCT
ejpam-5876	91	16	.	.	PUNCT
ejpam-5876	92	1	lemma	lemma	PROPN
ejpam-5876	92	2	2	2	NUM
ejpam-5876	92	3	.	.	PUNCT
ejpam-5876	93	1	[	[	X
ejpam-5876	93	2	9	9	NUM
ejpam-5876	93	3	]	]	PUNCT
ejpam-5876	93	4	a	a	DET
ejpam-5876	93	5	fuzzy	fuzzy	ADJ
ejpam-5876	93	6	set	set	NOUN
ejpam-5876	93	7	µ	µ	NOUN
ejpam-5876	93	8	is	be	AUX
ejpam-5876	93	9	a	a	DET
ejpam-5876	93	10	fuzzy	fuzzy	ADJ
ejpam-5876	93	11	sup	sup	ADJ
ejpam-5876	93	12	-	-	PUNCT
ejpam-5876	93	13	subalgebra	subalgebra	NOUN
ejpam-5876	93	14	of	of	ADP
ejpam-5876	93	15	x	x	PRON
ejpam-5876	93	16	if	if	SCONJ
ejpam-5876	93	17	and	and	CCONJ
ejpam-5876	93	18	only	only	ADV
ejpam-5876	93	19	if	if	SCONJ
ejpam-5876	93	20	u(µ	u(µ	NOUN
ejpam-5876	93	21	,	,	PUNCT
ejpam-5876	93	22	t	t	PROPN
ejpam-5876	93	23	)	)	PUNCT
ejpam-5876	93	24	is	be	AUX
ejpam-5876	93	25	a	a	DET
ejpam-5876	93	26	sup	sup	ADJ
ejpam-5876	93	27	-	-	PUNCT
ejpam-5876	93	28	subalgebra	subalgebra	NOUN
ejpam-5876	93	29	of	of	ADP
ejpam-5876	93	30	x	x	PUNCT
ejpam-5876	93	31	for	for	ADP
ejpam-5876	93	32	all	all	DET
ejpam-5876	93	33	t	t	NOUN
ejpam-5876	93	34	∈	∈	PROPN
ejpam-5876	93	35	(	(	PUNCT
ejpam-5876	93	36	0	0	NUM
ejpam-5876	93	37	,	,	PUNCT
ejpam-5876	93	38	1	1	NUM
ejpam-5876	93	39	]	]	PUNCT
ejpam-5876	93	40	.	.	PUNCT
ejpam-5876	94	1	theorem	theorem	NOUN
ejpam-5876	94	2	1	1	NUM
ejpam-5876	94	3	.	.	PUNCT
ejpam-5876	94	4	a	a	DET
ejpam-5876	94	5	semidetached	semidetache	VERB
ejpam-5876	94	6	structure	structure	NOUN
ejpam-5876	94	7	(	(	PUNCT
ejpam-5876	94	8	x	x	NOUN
ejpam-5876	94	9	,	,	PUNCT
ejpam-5876	94	10	ℓµu	ℓµu	NOUN
ejpam-5876	94	11	)	)	PUNCT
ejpam-5876	94	12	is	be	AUX
ejpam-5876	94	13	a	a	DET
ejpam-5876	94	14	semidetached	semidetache	VERB
ejpam-5876	94	15	sup	sup	NOUN
ejpam-5876	94	16	-	-	PUNCT
ejpam-5876	94	17	subalgebra	subalgebra	NOUN
ejpam-5876	94	18	over	over	ADP
ejpam-5876	94	19	ω	ω	NUM
ejpam-5876	94	20	=	=	SYM
ejpam-5876	94	21	(	(	PUNCT
ejpam-5876	94	22	0	0	NUM
ejpam-5876	94	23	,	,	PUNCT
ejpam-5876	94	24	1	1	NUM
ejpam-5876	94	25	]	]	PUNCT
ejpam-5876	94	26	if	if	SCONJ
ejpam-5876	95	1	and	and	CCONJ
ejpam-5876	95	2	only	only	ADV
ejpam-5876	95	3	if	if	SCONJ
ejpam-5876	95	4	µ	µ	NOUN
ejpam-5876	95	5	is	be	AUX
ejpam-5876	95	6	a	a	DET
ejpam-5876	95	7	fuzzy	fuzzy	ADJ
ejpam-5876	95	8	sup	sup	ADJ
ejpam-5876	95	9	-	-	PUNCT
ejpam-5876	95	10	subalgebra	subalgebra	NOUN
ejpam-5876	95	11	of	of	ADP
ejpam-5876	95	12	x.	x.	NOUN
ejpam-5876	95	13	proof	proof	NOUN
ejpam-5876	95	14	.	.	PUNCT
ejpam-5876	96	1	straightforward	straightforward	ADJ
ejpam-5876	96	2	from	from	ADP
ejpam-5876	96	3	lemma	lemma	PROPN
ejpam-5876	96	4	2	2	NUM
ejpam-5876	96	5	.	.	PUNCT
ejpam-5876	96	6	theorem	theorem	NOUN
ejpam-5876	96	7	2	2	NUM
ejpam-5876	96	8	.	.	PUNCT
ejpam-5876	97	1	if	if	SCONJ
ejpam-5876	97	2	µ	µ	NOUN
ejpam-5876	97	3	is	be	AUX
ejpam-5876	97	4	an	an	DET
ejpam-5876	97	5	(	(	PUNCT
ejpam-5876	97	6	∈,∈)-fuzzy	∈,∈)-fuzzy	ADJ
ejpam-5876	97	7	sup	sup	NOUN
ejpam-5876	97	8	-	-	PUNCT
ejpam-5876	97	9	subalgebra	subalgebra	NOUN
ejpam-5876	97	10	(	(	PUNCT
ejpam-5876	97	11	or	or	CCONJ
ejpam-5876	97	12	equivalently	equivalently	ADV
ejpam-5876	97	13	,	,	PUNCT
ejpam-5876	97	14	µ	µ	PRON
ejpam-5876	97	15	is	be	AUX
ejpam-5876	97	16	a	a	DET
ejpam-5876	97	17	fuzzy	fuzzy	ADJ
ejpam-5876	97	18	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	97	19	)	)	PUNCT
ejpam-5876	97	20	of	of	ADP
ejpam-5876	97	21	x	x	PRON
ejpam-5876	97	22	,	,	PUNCT
ejpam-5876	97	23	then	then	ADV
ejpam-5876	97	24	a	a	DET
ejpam-5876	97	25	semidetached	semidetached	ADJ
ejpam-5876	97	26	structure	structure	NOUN
ejpam-5876	97	27	(	(	PUNCT
ejpam-5876	97	28	x	x	NOUN
ejpam-5876	97	29	,	,	PUNCT
ejpam-5876	97	30	ℓµqk	ℓµqk	PROPN
ejpam-5876	97	31	)	)	PUNCT
ejpam-5876	97	32	is	be	AUX
ejpam-5876	97	33	a	a	DET
ejpam-5876	97	34	semidetached	semidetache	VERB
ejpam-5876	97	35	sup	sup	NOUN
ejpam-5876	97	36	-	-	PUNCT
ejpam-5876	97	37	subalgebra	subalgebra	NOUN
ejpam-5876	97	38	over	over	ADP
ejpam-5876	97	39	ω	ω	NUM
ejpam-5876	97	40	=	=	SYM
ejpam-5876	97	41	(	(	PUNCT
ejpam-5876	97	42	0	0	NUM
ejpam-5876	97	43	,	,	PUNCT
ejpam-5876	97	44	1	1	NUM
ejpam-5876	97	45	]	]	PUNCT
ejpam-5876	97	46	.	.	PUNCT
ejpam-5876	98	1	proof	proof	NOUN
ejpam-5876	98	2	.	.	PUNCT
ejpam-5876	99	1	let	let	VERB
ejpam-5876	99	2	x	x	PRON
ejpam-5876	99	3	,	,	PUNCT
ejpam-5876	99	4	y	y	PROPN
ejpam-5876	99	5	∈	∈	PROPN
ejpam-5876	99	6	ℓµqk	ℓµqk	PROPN
ejpam-5876	99	7	(	(	PUNCT
ejpam-5876	99	8	t	t	NOUN
ejpam-5876	99	9	)	)	PUNCT
ejpam-5876	99	10	for	for	ADP
ejpam-5876	99	11	t	t	PROPN
ejpam-5876	99	12	∈	∈	PROPN
ejpam-5876	99	13	ω	ω	PROPN
ejpam-5876	99	14	=	=	SYM
ejpam-5876	99	15	(	(	PUNCT
ejpam-5876	99	16	0	0	NUM
ejpam-5876	99	17	,	,	PUNCT
ejpam-5876	99	18	1	1	NUM
ejpam-5876	99	19	]	]	PUNCT
ejpam-5876	99	20	.	.	PUNCT
ejpam-5876	100	1	then	then	ADV
ejpam-5876	100	2	xtqkµ	xtqkµ	PROPN
ejpam-5876	100	3	and	and	CCONJ
ejpam-5876	100	4	ytqkµ	ytqkµ	PROPN
ejpam-5876	100	5	,	,	PUNCT
ejpam-5876	100	6	that	that	ADV
ejpam-5876	100	7	is	is	ADV
ejpam-5876	100	8	,	,	PUNCT
ejpam-5876	100	9	µ(x)+t+k	µ(x)+t+k	PROPN
ejpam-5876	100	10	>	>	X
ejpam-5876	100	11	1	1	NUM
ejpam-5876	100	12	and	and	CCONJ
ejpam-5876	100	13	µ(y	µ(y	NUM
ejpam-5876	100	14	)	)	PUNCT
ejpam-5876	100	15	+	+	NUM
ejpam-5876	100	16	t	t	NOUN
ejpam-5876	100	17	+	+	CCONJ
ejpam-5876	100	18	k	k	X
ejpam-5876	100	19	>	>	X
ejpam-5876	100	20	1	1	X
ejpam-5876	100	21	.	.	PUNCT
ejpam-5876	100	22	then	then	ADV
ejpam-5876	100	23	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	100	24	)	)	PUNCT
ejpam-5876	100	25	)	)	PUNCT
ejpam-5876	100	26	)	)	PUNCT
ejpam-5876	101	1	+	+	CCONJ
ejpam-5876	101	2	t	t	NOUN
ejpam-5876	101	3	+	+	CCONJ
ejpam-5876	101	4	k	k	PROPN
ejpam-5876	101	5	≥	≥	NOUN
ejpam-5876	101	6	min{µ(x	min{µ(x	PROPN
ejpam-5876	101	7	)	)	PUNCT
ejpam-5876	101	8	,	,	PUNCT
ejpam-5876	101	9	µ(y	µ(y	PROPN
ejpam-5876	101	10	)	)	PUNCT
ejpam-5876	101	11	}	}	PUNCT
ejpam-5876	102	1	+	+	NUM
ejpam-5876	102	2	t	t	X
ejpam-5876	102	3	+	+	CCONJ
ejpam-5876	102	4	k	k	PROPN
ejpam-5876	102	5	=	=	SYM
ejpam-5876	102	6	min{µ(x	min{µ(x	PROPN
ejpam-5876	102	7	)	)	PUNCT
ejpam-5876	103	1	+	+	NUM
ejpam-5876	103	2	t	t	NOUN
ejpam-5876	103	3	+	+	CCONJ
ejpam-5876	103	4	k	k	PROPN
ejpam-5876	103	5	,	,	PUNCT
ejpam-5876	103	6	µ(y	µ(y	PROPN
ejpam-5876	103	7	)	)	PUNCT
ejpam-5876	104	1	+	+	NUM
ejpam-5876	104	2	t	t	NOUN
ejpam-5876	104	3	+	+	CCONJ
ejpam-5876	104	4	k	k	X
ejpam-5876	104	5	}	}	PUNCT
ejpam-5876	104	6	>	>	X
ejpam-5876	104	7	1	1	X
ejpam-5876	104	8	.	.	PUNCT
ejpam-5876	105	1	hence	hence	ADV
ejpam-5876	105	2	,	,	PUNCT
ejpam-5876	105	3	(	(	PUNCT
ejpam-5876	105	4	(	(	PUNCT
ejpam-5876	105	5	x|(y|y))|(x|(y|y)))t	x|(y|y))|(x|(y|y)))t	PROPN
ejpam-5876	105	6	∈	∈	PROPN
ejpam-5876	105	7	∨qkµ	∨qkµ	PROPN
ejpam-5876	105	8	,	,	PUNCT
ejpam-5876	105	9	and	and	CCONJ
ejpam-5876	105	10	so	so	ADV
ejpam-5876	105	11	(	(	PUNCT
ejpam-5876	105	12	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	105	13	)	)	PUNCT
ejpam-5876	105	14	)	)	PUNCT
ejpam-5876	106	1	∈	∈	PROPN
ejpam-5876	106	2	ℓµqk	ℓµqk	NOUN
ejpam-5876	106	3	(	(	PUNCT
ejpam-5876	106	4	t	t	PROPN
ejpam-5876	106	5	)	)	PUNCT
ejpam-5876	106	6	.	.	PUNCT
ejpam-5876	107	1	therefore	therefore	ADV
ejpam-5876	107	2	,	,	PUNCT
ejpam-5876	107	3	ℓµqk	ℓµqk	PROPN
ejpam-5876	107	4	(	(	PUNCT
ejpam-5876	107	5	t	t	NOUN
ejpam-5876	107	6	)	)	PUNCT
ejpam-5876	107	7	is	be	AUX
ejpam-5876	107	8	an	an	DET
ejpam-5876	107	9	sup	sup	ADJ
ejpam-5876	107	10	-	-	PUNCT
ejpam-5876	107	11	subalgebra	subalgebra	NOUN
ejpam-5876	107	12	of	of	ADP
ejpam-5876	107	13	x.	x.	NOUN
ejpam-5876	107	14	consequently	consequently	ADV
ejpam-5876	107	15	,	,	PUNCT
ejpam-5876	107	16	(	(	PUNCT
ejpam-5876	107	17	x	x	X
ejpam-5876	107	18	,	,	PUNCT
ejpam-5876	107	19	ℓµqk	ℓµqk	PROPN
ejpam-5876	107	20	)	)	PUNCT
ejpam-5876	107	21	is	be	AUX
ejpam-5876	107	22	a	a	DET
ejpam-5876	107	23	semidetached	semidetache	VERB
ejpam-5876	107	24	sup	sup	NOUN
ejpam-5876	107	25	-	-	PUNCT
ejpam-5876	107	26	subalgebra	subalgebra	NOUN
ejpam-5876	107	27	over	over	ADP
ejpam-5876	107	28	ω	ω	NUM
ejpam-5876	107	29	=	=	SYM
ejpam-5876	107	30	(	(	PUNCT
ejpam-5876	107	31	0	0	NUM
ejpam-5876	107	32	,	,	PUNCT
ejpam-5876	107	33	1	1	NUM
ejpam-5876	107	34	]	]	PUNCT
ejpam-5876	107	35	.	.	PUNCT
ejpam-5876	108	1	corollary	corollary	ADJ
ejpam-5876	108	2	1	1	NUM
ejpam-5876	108	3	is	be	AUX
ejpam-5876	108	4	a	a	DET
ejpam-5876	108	5	direct	direct	ADJ
ejpam-5876	108	6	consequence	consequence	NOUN
ejpam-5876	108	7	of	of	ADP
ejpam-5876	108	8	theorem	theorem	NOUN
ejpam-5876	108	9	1	1	NUM
ejpam-5876	108	10	.	.	PUNCT
ejpam-5876	108	11	specifically	specifically	ADV
ejpam-5876	108	12	,	,	PUNCT
ejpam-5876	108	13	theorem	theorem	VERB
ejpam-5876	108	14	1	1	NUM
ejpam-5876	108	15	states	state	NOUN
ejpam-5876	108	16	that	that	SCONJ
ejpam-5876	108	17	a	a	DET
ejpam-5876	108	18	semidetached	semidetache	VERB
ejpam-5876	108	19	structure	structure	NOUN
ejpam-5876	108	20	(	(	PUNCT
ejpam-5876	108	21	x	x	NOUN
ejpam-5876	108	22	,	,	PUNCT
ejpam-5876	108	23	ℓuµ	ℓuµ	NOUN
ejpam-5876	108	24	)	)	PUNCT
ejpam-5876	108	25	over	over	ADP
ejpam-5876	108	26	ω	ω	NUM
ejpam-5876	108	27	=	=	SYM
ejpam-5876	108	28	(	(	PUNCT
ejpam-5876	108	29	0	0	NUM
ejpam-5876	108	30	,	,	PUNCT
ejpam-5876	108	31	1	1	NUM
ejpam-5876	108	32	]	]	PUNCT
ejpam-5876	108	33	exists	exist	VERB
ejpam-5876	108	34	if	if	SCONJ
ejpam-5876	108	35	and	and	CCONJ
ejpam-5876	108	36	only	only	ADV
ejpam-5876	108	37	if	if	SCONJ
ejpam-5876	108	38	µ	µ	NOUN
ejpam-5876	108	39	is	be	AUX
ejpam-5876	108	40	a	a	DET
ejpam-5876	108	41	fuzzy	fuzzy	ADJ
ejpam-5876	108	42	sup	sup	ADJ
ejpam-5876	108	43	-	-	PUNCT
ejpam-5876	108	44	subalgebra	subalgebra	NOUN
ejpam-5876	108	45	of	of	ADP
ejpam-5876	108	46	x.	x.	NOUN
ejpam-5876	108	47	since	since	SCONJ
ejpam-5876	108	48	an	an	PRON
ejpam-5876	108	49	(	(	PUNCT
ejpam-5876	108	50	∈,∈)-fuzzy	∈,∈)-fuzzy	ADJ
ejpam-5876	108	51	sup	sup	NOUN
ejpam-5876	108	52	-	-	PUNCT
ejpam-5876	108	53	subalgebra	subalgebra	NOUN
ejpam-5876	108	54	is	be	AUX
ejpam-5876	108	55	equivalent	equivalent	ADJ
ejpam-5876	108	56	to	to	ADP
ejpam-5876	108	57	a	a	DET
ejpam-5876	108	58	fuzzy	fuzzy	ADJ
ejpam-5876	108	59	sup	sup	NOUN
ejpam-5876	108	60	-	-	PUNCT
ejpam-5876	108	61	subalgebra	subalgebra	NOUN
ejpam-5876	108	62	,	,	PUNCT
ejpam-5876	108	63	the	the	DET
ejpam-5876	108	64	condition	condition	NOUN
ejpam-5876	108	65	in	in	ADP
ejpam-5876	108	66	corollary	corollary	ADJ
ejpam-5876	108	67	1	1	NUM
ejpam-5876	108	68	is	be	AUX
ejpam-5876	108	69	satisfied	satisfied	ADJ
ejpam-5876	108	70	,	,	PUNCT
ejpam-5876	108	71	and	and	CCONJ
ejpam-5876	108	72	the	the	DET
ejpam-5876	108	73	semidetached	semidetache	VERB
ejpam-5876	108	74	property	property	NOUN
ejpam-5876	108	75	follows	follow	VERB
ejpam-5876	108	76	immediately	immediately	ADV
ejpam-5876	108	77	.	.	PUNCT
ejpam-5876	109	1	corollary	corollary	ADJ
ejpam-5876	109	2	1	1	NUM
ejpam-5876	109	3	.	.	PUNCT
ejpam-5876	110	1	if	if	SCONJ
ejpam-5876	110	2	µ	µ	NOUN
ejpam-5876	110	3	is	be	AUX
ejpam-5876	110	4	an	an	DET
ejpam-5876	110	5	(	(	PUNCT
ejpam-5876	110	6	∈,∈)-fuzzy	∈,∈)-fuzzy	ADJ
ejpam-5876	110	7	sup	sup	NOUN
ejpam-5876	110	8	-	-	PUNCT
ejpam-5876	110	9	subalgebra	subalgebra	NOUN
ejpam-5876	110	10	(	(	PUNCT
ejpam-5876	110	11	or	or	CCONJ
ejpam-5876	110	12	equivalently	equivalently	ADV
ejpam-5876	110	13	,	,	PUNCT
ejpam-5876	110	14	µ	µ	PRON
ejpam-5876	110	15	is	be	AUX
ejpam-5876	110	16	a	a	DET
ejpam-5876	110	17	fuzzy	fuzzy	ADJ
ejpam-5876	110	18	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	110	19	)	)	PUNCT
ejpam-5876	110	20	of	of	ADP
ejpam-5876	110	21	x	x	PRON
ejpam-5876	110	22	,	,	PUNCT
ejpam-5876	110	23	then	then	ADV
ejpam-5876	110	24	a	a	DET
ejpam-5876	110	25	semidetached	semidetached	ADJ
ejpam-5876	110	26	structure	structure	NOUN
ejpam-5876	110	27	(	(	PUNCT
ejpam-5876	110	28	x	x	NOUN
ejpam-5876	110	29	,	,	PUNCT
ejpam-5876	110	30	ℓµu	ℓµu	NOUN
ejpam-5876	110	31	)	)	PUNCT
ejpam-5876	110	32	is	be	AUX
ejpam-5876	110	33	a	a	DET
ejpam-5876	110	34	semidetached	semidetache	VERB
ejpam-5876	110	35	sup	sup	NOUN
ejpam-5876	110	36	-	-	PUNCT
ejpam-5876	110	37	subalgebra	subalgebra	NOUN
ejpam-5876	110	38	over	over	ADP
ejpam-5876	110	39	ω	ω	NUM
ejpam-5876	110	40	=	=	SYM
ejpam-5876	110	41	(	(	PUNCT
ejpam-5876	110	42	0	0	NUM
ejpam-5876	110	43	,	,	PUNCT
ejpam-5876	110	44	1	1	NUM
ejpam-5876	110	45	]	]	PUNCT
ejpam-5876	110	46	.	.	PUNCT
ejpam-5876	111	1	t.	t.	PROPN
ejpam-5876	111	2	oner	oner	PROPN
ejpam-5876	111	3	et	et	PROPN
ejpam-5876	111	4	al	al	PROPN
ejpam-5876	111	5	.	.	PUNCT
ejpam-5876	111	6	/	/	SYM
ejpam-5876	111	7	eur	eur	PROPN
ejpam-5876	111	8	.	.	PUNCT
ejpam-5876	112	1	j.	j.	PROPN
ejpam-5876	112	2	pure	pure	PROPN
ejpam-5876	112	3	appl	appl	PROPN
ejpam-5876	112	4	.	.	PROPN
ejpam-5876	112	5	math	math	PROPN
ejpam-5876	112	6	,	,	PUNCT
ejpam-5876	112	7	18	18	NUM
ejpam-5876	112	8	(	(	PUNCT
ejpam-5876	112	9	2	2	NUM
ejpam-5876	112	10	)	)	PUNCT
ejpam-5876	112	11	(	(	PUNCT
ejpam-5876	112	12	2025	2025	NUM
ejpam-5876	112	13	)	)	PUNCT
ejpam-5876	112	14	,	,	PUNCT
ejpam-5876	112	15	5876	5876	NUM
ejpam-5876	112	16	6	6	NUM
ejpam-5876	112	17	of	of	ADP
ejpam-5876	112	18	16	16	NUM
ejpam-5876	112	19	given	give	VERB
ejpam-5876	112	20	a	a	DET
ejpam-5876	112	21	fuzzy	fuzzy	ADJ
ejpam-5876	112	22	set	set	VERB
ejpam-5876	112	23	µ	µ	NOUN
ejpam-5876	112	24	in	in	ADP
ejpam-5876	112	25	x	x	X
ejpam-5876	112	26	and	and	CCONJ
ejpam-5876	112	27	k	k	PROPN
ejpam-5876	112	28	∈	∈	PROPN
ejpam-5876	113	1	[	[	X
ejpam-5876	113	2	0	0	NUM
ejpam-5876	113	3	,	,	PUNCT
ejpam-5876	113	4	1	1	NUM
ejpam-5876	113	5	)	)	PUNCT
ejpam-5876	113	6	,	,	PUNCT
ejpam-5876	113	7	we	we	PRON
ejpam-5876	113	8	consider	consider	VERB
ejpam-5876	113	9	the	the	DET
ejpam-5876	113	10	following	follow	VERB
ejpam-5876	113	11	condition	condition	NOUN
ejpam-5876	113	12	:	:	PUNCT
ejpam-5876	113	13	(	(	PUNCT
ejpam-5876	113	14	∀x	∀x	X
ejpam-5876	113	15	,	,	PUNCT
ejpam-5876	113	16	y	y	PROPN
ejpam-5876	113	17	∈	∈	PROPN
ejpam-5876	113	18	x)(∀t	x)(∀t	PROPN
ejpam-5876	113	19	,	,	PUNCT
ejpam-5876	113	20	r	r	NOUN
ejpam-5876	113	21	∈	∈	PROPN
ejpam-5876	114	1	[	[	X
ejpam-5876	114	2	0	0	NUM
ejpam-5876	114	3	,	,	PUNCT
ejpam-5876	114	4	1])(xtqkµ	1])(xtqkµ	NUM
ejpam-5876	114	5	,	,	PUNCT
ejpam-5876	114	6	yrqkµ	yrqkµ	NOUN
ejpam-5876	114	7	⇒	⇒	NOUN
ejpam-5876	114	8	(	(	PUNCT
ejpam-5876	114	9	(	(	PUNCT
ejpam-5876	114	10	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	114	11	,	,	PUNCT
ejpam-5876	114	12	r	r	NOUN
ejpam-5876	114	13	}	}	PUNCT
ejpam-5876	114	14	∈	∈	PROPN
ejpam-5876	114	15	∨qkµ	∨qkµ	PROPN
ejpam-5876	114	16	)	)	PUNCT
ejpam-5876	114	17	.	.	PUNCT
ejpam-5876	115	1	(	(	PUNCT
ejpam-5876	115	2	5	5	X
ejpam-5876	115	3	)	)	PUNCT
ejpam-5876	115	4	definition	definition	NOUN
ejpam-5876	115	5	9	9	NUM
ejpam-5876	115	6	.	.	PUNCT
ejpam-5876	116	1	a	a	DET
ejpam-5876	116	2	fuzzy	fuzzy	ADJ
ejpam-5876	116	3	set	set	VERB
ejpam-5876	116	4	µ	µ	NOUN
ejpam-5876	116	5	in	in	ADP
ejpam-5876	116	6	x	x	AUX
ejpam-5876	116	7	is	be	AUX
ejpam-5876	116	8	called	call	VERB
ejpam-5876	116	9	a	a	DET
ejpam-5876	116	10	k	k	NOUN
ejpam-5876	116	11	-	-	ADJ
ejpam-5876	116	12	left	left	ADJ
ejpam-5876	116	13	(	(	PUNCT
ejpam-5876	116	14	resp	resp	NOUN
ejpam-5876	116	15	.	.	PUNCT
ejpam-5876	116	16	,	,	PUNCT
ejpam-5876	117	1	k	k	X
ejpam-5876	117	2	-	-	NOUN
ejpam-5876	117	3	right	right	NOUN
ejpam-5876	117	4	)	)	PUNCT
ejpam-5876	118	1	(	(	PUNCT
ejpam-5876	118	2	qk,∈	qk,∈	INTJ
ejpam-5876	118	3	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	118	4	subalgebra	subalgebra	NOUN
ejpam-5876	118	5	of	of	ADP
ejpam-5876	118	6	x	x	PRON
ejpam-5876	118	7	if	if	SCONJ
ejpam-5876	118	8	it	it	PRON
ejpam-5876	118	9	satisfies	satisfy	VERB
ejpam-5876	118	10	the	the	DET
ejpam-5876	118	11	condition	condition	NOUN
ejpam-5876	118	12	(	(	PUNCT
ejpam-5876	118	13	5	5	NUM
ejpam-5876	118	14	)	)	PUNCT
ejpam-5876	118	15	for	for	ADP
ejpam-5876	118	16	all	all	DET
ejpam-5876	118	17	x	x	NOUN
ejpam-5876	118	18	,	,	PUNCT
ejpam-5876	118	19	y	y	PROPN
ejpam-5876	118	20	∈	∈	PROPN
ejpam-5876	118	21	x	x	X
ejpam-5876	118	22	and	and	CCONJ
ejpam-5876	118	23	t	t	PROPN
ejpam-5876	118	24	,	,	PUNCT
ejpam-5876	118	25	r	r	NOUN
ejpam-5876	118	26	∈	∈	PROPN
ejpam-5876	118	27	(	(	PUNCT
ejpam-5876	118	28	0	0	NUM
ejpam-5876	118	29	,	,	PUNCT
ejpam-5876	118	30	1−k	1−k	NUM
ejpam-5876	118	31	2	2	NUM
ejpam-5876	118	32	]	]	PUNCT
ejpam-5876	118	33	(	(	PUNCT
ejpam-5876	118	34	resp	resp	NOUN
ejpam-5876	118	35	.	.	PUNCT
ejpam-5876	118	36	,	,	PUNCT
ejpam-5876	118	37	t	t	PROPN
ejpam-5876	118	38	,	,	PUNCT
ejpam-5876	118	39	r	r	NOUN
ejpam-5876	118	40	∈	∈	PROPN
ejpam-5876	118	41	(	(	PUNCT
ejpam-5876	118	42	1−k	1−k	NUM
ejpam-5876	118	43	2	2	NUM
ejpam-5876	118	44	,	,	PUNCT
ejpam-5876	118	45	1	1	NUM
ejpam-5876	118	46	]	]	NUM
ejpam-5876	118	47	)	)	PUNCT
ejpam-5876	118	48	.	.	PUNCT
ejpam-5876	119	1	theorem	theorem	NOUN
ejpam-5876	119	2	3	3	NUM
ejpam-5876	119	3	.	.	PUNCT
ejpam-5876	120	1	every	every	DET
ejpam-5876	120	2	k	k	NOUN
ejpam-5876	120	3	-	-	PROPN
ejpam-5876	120	4	right	right	ADJ
ejpam-5876	120	5	(	(	PUNCT
ejpam-5876	120	6	qk,∈	qk,∈	X
ejpam-5876	120	7	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	120	8	sup	sup	ADJ
ejpam-5876	120	9	-	-	PUNCT
ejpam-5876	120	10	subalgebra	subalgebra	NOUN
ejpam-5876	120	11	is	be	AUX
ejpam-5876	120	12	an	an	DET
ejpam-5876	120	13	(	(	PUNCT
ejpam-5876	120	14	∈,∈	∈,∈	X
ejpam-5876	120	15	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	120	16	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	120	17	.	.	PUNCT
ejpam-5876	121	1	proof	proof	NOUN
ejpam-5876	121	2	.	.	PUNCT
ejpam-5876	122	1	let	let	VERB
ejpam-5876	122	2	µ	µ	X
ejpam-5876	122	3	be	be	AUX
ejpam-5876	122	4	a	a	DET
ejpam-5876	122	5	k	k	NOUN
ejpam-5876	122	6	-	-	NOUN
ejpam-5876	122	7	right	right	NOUN
ejpam-5876	122	8	(	(	PUNCT
ejpam-5876	122	9	qk,∈	qk,∈	X
ejpam-5876	122	10	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	122	11	sup	sup	NOUN
ejpam-5876	122	12	-	-	PUNCT
ejpam-5876	122	13	subalgebra	subalgebra	NOUN
ejpam-5876	122	14	of	of	ADP
ejpam-5876	122	15	x.	x.	NOUN
ejpam-5876	122	16	let	let	VERB
ejpam-5876	122	17	x	x	PRON
ejpam-5876	122	18	,	,	PUNCT
ejpam-5876	122	19	y	y	PROPN
ejpam-5876	122	20	∈	∈	PROPN
ejpam-5876	122	21	x	x	X
ejpam-5876	122	22	and	and	CCONJ
ejpam-5876	122	23	t	t	PROPN
ejpam-5876	122	24	,	,	PUNCT
ejpam-5876	122	25	r	r	NOUN
ejpam-5876	122	26	∈	∈	PROPN
ejpam-5876	122	27	(	(	PUNCT
ejpam-5876	122	28	0	0	NUM
ejpam-5876	122	29	,	,	PUNCT
ejpam-5876	122	30	1	1	NUM
ejpam-5876	122	31	]	]	PUNCT
ejpam-5876	122	32	be	be	AUX
ejpam-5876	122	33	such	such	ADJ
ejpam-5876	122	34	that	that	SCONJ
ejpam-5876	122	35	xt	xt	PROPN
ejpam-5876	122	36	∈	∈	PROPN
ejpam-5876	122	37	µ	µ	X
ejpam-5876	122	38	and	and	CCONJ
ejpam-5876	122	39	yr	yr	NOUN
ejpam-5876	122	40	∈	∈	PROPN
ejpam-5876	122	41	µ.	µ.	NOUN
ejpam-5876	122	42	then	then	ADV
ejpam-5876	122	43	µ(x	µ(x	NOUN
ejpam-5876	122	44	)	)	PUNCT
ejpam-5876	122	45	≥	≥	NOUN
ejpam-5876	122	46	t	t	NOUN
ejpam-5876	122	47	and	and	CCONJ
ejpam-5876	122	48	µ(y	µ(y	PROPN
ejpam-5876	122	49	)	)	PUNCT
ejpam-5876	122	50	≥	≥	PROPN
ejpam-5876	122	51	r.	r.	PROPN
ejpam-5876	122	52	suppose	suppose	VERB
ejpam-5876	122	53	that	that	SCONJ
ejpam-5876	122	54	(	(	PUNCT
ejpam-5876	122	55	(	(	PUNCT
ejpam-5876	122	56	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	122	57	,	,	PUNCT
ejpam-5876	122	58	r}∈	r}∈	NOUN
ejpam-5876	122	59	qkµ.	qkµ.	VERB
ejpam-5876	122	60	then	then	ADV
ejpam-5876	122	61	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	122	62	)	)	PUNCT
ejpam-5876	122	63	)	)	PUNCT
ejpam-5876	122	64	)	)	PUNCT
ejpam-5876	123	1	<	<	X
ejpam-5876	123	2	min{t	min{t	PROPN
ejpam-5876	123	3	,	,	PUNCT
ejpam-5876	123	4	r	r	NOUN
ejpam-5876	123	5	}	}	PUNCT
ejpam-5876	123	6	and	and	CCONJ
ejpam-5876	123	7	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	123	8	)	)	PUNCT
ejpam-5876	123	9	)	)	PUNCT
ejpam-5876	123	10	)	)	PUNCT
ejpam-5876	124	1	+	+	CCONJ
ejpam-5876	124	2	min{t	min{t	PROPN
ejpam-5876	124	3	,	,	PUNCT
ejpam-5876	124	4	r	r	NOUN
ejpam-5876	124	5	}	}	PUNCT
ejpam-5876	124	6	+	+	CCONJ
ejpam-5876	124	7	k	k	X
ejpam-5876	124	8	≤	≤	ADJ
ejpam-5876	124	9	1	1	NUM
ejpam-5876	124	10	.	.	PUNCT
ejpam-5876	125	1	it	it	PRON
ejpam-5876	125	2	follows	follow	VERB
ejpam-5876	125	3	that	that	SCONJ
ejpam-5876	125	4	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	VERB
ejpam-5876	125	5	)	)	PUNCT
ejpam-5876	125	6	)	)	PUNCT
ejpam-5876	125	7	)	)	PUNCT
ejpam-5876	126	1	<	<	X
ejpam-5876	126	2	1−k	1−k	NUM
ejpam-5876	126	3	2	2	NUM
ejpam-5876	126	4	,	,	PUNCT
ejpam-5876	126	5	and	and	CCONJ
ejpam-5876	126	6	so	so	SCONJ
ejpam-5876	126	7	that	that	SCONJ
ejpam-5876	126	8	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	126	9	)	)	PUNCT
ejpam-5876	126	10	)	)	PUNCT
ejpam-5876	126	11	)	)	PUNCT
ejpam-5876	126	12	<	<	X
ejpam-5876	126	13	min{t	min{t	PROPN
ejpam-5876	126	14	,	,	PUNCT
ejpam-5876	126	15	r	r	NOUN
ejpam-5876	126	16	,	,	PUNCT
ejpam-5876	126	17	1−k	1−k	NUM
ejpam-5876	126	18	2	2	NUM
ejpam-5876	126	19	}	}	PUNCT
ejpam-5876	126	20	.	.	PUNCT
ejpam-5876	127	1	hence	hence	ADV
ejpam-5876	127	2	,	,	PUNCT
ejpam-5876	127	3	1−k−µ((x|(y|y))|(x|(y|y	1−k−µ((x|(y|y))|(x|(y|y	NUM
ejpam-5876	127	4	)	)	PUNCT
ejpam-5876	127	5	)	)	PUNCT
ejpam-5876	127	6	)	)	PUNCT
ejpam-5876	128	1	>	>	PUNCT
ejpam-5876	129	1	1	1	NUM
ejpam-5876	129	2	−	−	NOUN
ejpam-5876	129	3	k	k	X
ejpam-5876	129	4	−min{t	−min{t	PROPN
ejpam-5876	129	5	,	,	PUNCT
ejpam-5876	129	6	r	r	NOUN
ejpam-5876	129	7	,	,	PUNCT
ejpam-5876	129	8	1−k	1−k	NUM
ejpam-5876	129	9	2	2	NUM
ejpam-5876	129	10	}	}	PUNCT
ejpam-5876	129	11	=	=	SYM
ejpam-5876	129	12	max{1	max{1	NOUN
ejpam-5876	129	13	−	−	PROPN
ejpam-5876	129	14	k	k	PROPN
ejpam-5876	129	15	−	−	PROPN
ejpam-5876	129	16	t	t	PROPN
ejpam-5876	129	17	,	,	PUNCT
ejpam-5876	129	18	1	1	NUM
ejpam-5876	129	19	−	−	NOUN
ejpam-5876	129	20	k	k	NOUN
ejpam-5876	129	21	−	−	NOUN
ejpam-5876	129	22	r	r	NOUN
ejpam-5876	129	23	,	,	PUNCT
ejpam-5876	129	24	1	1	NUM
ejpam-5876	129	25	−	−	NOUN
ejpam-5876	129	26	k	k	NOUN
ejpam-5876	129	27	−	−	NOUN
ejpam-5876	129	28	1−k	1−k	NUM
ejpam-5876	129	29	2	2	NUM
ejpam-5876	129	30	}	}	PUNCT
ejpam-5876	129	31	≥	≥	NOUN
ejpam-5876	129	32	max{1	max{1	NOUN
ejpam-5876	129	33	−	−	NOUN
ejpam-5876	129	34	k	k	NOUN
ejpam-5876	129	35	−	−	PROPN
ejpam-5876	129	36	µ(x	µ(x	NOUN
ejpam-5876	129	37	)	)	PUNCT
ejpam-5876	129	38	,	,	PUNCT
ejpam-5876	129	39	1	1	NUM
ejpam-5876	129	40	−	−	NOUN
ejpam-5876	129	41	k	k	NOUN
ejpam-5876	129	42	−	−	PROPN
ejpam-5876	129	43	µ(y	µ(y	PROPN
ejpam-5876	129	44	)	)	PUNCT
ejpam-5876	129	45	,	,	PUNCT
ejpam-5876	129	46	1−k	1−k	NUM
ejpam-5876	129	47	2	2	NUM
ejpam-5876	129	48	}	}	PUNCT
ejpam-5876	129	49	,	,	PUNCT
ejpam-5876	129	50	and	and	CCONJ
ejpam-5876	129	51	so	so	ADV
ejpam-5876	129	52	there	there	PRON
ejpam-5876	129	53	exists	exist	VERB
ejpam-5876	129	54	δ	δ	PROPN
ejpam-5876	129	55	∈	∈	PROPN
ejpam-5876	129	56	(	(	PUNCT
ejpam-5876	129	57	0	0	NUM
ejpam-5876	129	58	,	,	PUNCT
ejpam-5876	129	59	1	1	NUM
ejpam-5876	129	60	]	]	PUNCT
ejpam-5876	129	61	such	such	ADJ
ejpam-5876	129	62	that	that	SCONJ
ejpam-5876	129	63	1	1	NUM
ejpam-5876	129	64	−	−	NOUN
ejpam-5876	129	65	k	k	NOUN
ejpam-5876	129	66	−	−	PROPN
ejpam-5876	129	67	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	129	68	)	)	PUNCT
ejpam-5876	129	69	)	)	PUNCT
ejpam-5876	129	70	)	)	PUNCT
ejpam-5876	129	71	≥	≥	X
ejpam-5876	129	72	δ	δ	X
ejpam-5876	129	73	>	>	X
ejpam-5876	129	74	max{1	max{1	PROPN
ejpam-5876	129	75	−	−	PROPN
ejpam-5876	129	76	k	k	NOUN
ejpam-5876	129	77	−	−	PROPN
ejpam-5876	129	78	µ(x	µ(x	NOUN
ejpam-5876	129	79	)	)	PUNCT
ejpam-5876	129	80	,	,	PUNCT
ejpam-5876	129	81	1	1	NUM
ejpam-5876	129	82	−	−	NOUN
ejpam-5876	129	83	k	k	NOUN
ejpam-5876	129	84	−	−	PROPN
ejpam-5876	129	85	µ(y	µ(y	PROPN
ejpam-5876	129	86	)	)	PUNCT
ejpam-5876	129	87	,	,	PUNCT
ejpam-5876	129	88	1−k	1−k	NUM
ejpam-5876	129	89	2	2	NUM
ejpam-5876	129	90	}	}	PUNCT
ejpam-5876	129	91	.	.	PUNCT
ejpam-5876	130	1	then	then	ADV
ejpam-5876	130	2	δ	δ	PROPN
ejpam-5876	130	3	∈	∈	PROPN
ejpam-5876	130	4	(	(	PUNCT
ejpam-5876	130	5	1−k	1−k	NUM
ejpam-5876	130	6	2	2	NUM
ejpam-5876	130	7	,	,	PUNCT
ejpam-5876	130	8	1	1	NUM
ejpam-5876	130	9	]	]	PUNCT
ejpam-5876	130	10	,	,	PUNCT
ejpam-5876	130	11	µ(x	µ(x	X
ejpam-5876	130	12	)	)	PUNCT
ejpam-5876	130	13	+	+	NUM
ejpam-5876	130	14	δ	δ	PROPN
ejpam-5876	131	1	+	+	X
ejpam-5876	131	2	k	k	X
ejpam-5876	131	3	>	>	X
ejpam-5876	131	4	1	1	NUM
ejpam-5876	131	5	and	and	CCONJ
ejpam-5876	131	6	µ(y	µ(y	NUM
ejpam-5876	131	7	)	)	PUNCT
ejpam-5876	132	1	+	+	NUM
ejpam-5876	132	2	δ	δ	PROPN
ejpam-5876	132	3	+	+	X
ejpam-5876	132	4	k	k	X
ejpam-5876	132	5	>	>	X
ejpam-5876	132	6	1	1	NUM
ejpam-5876	132	7	,	,	PUNCT
ejpam-5876	132	8	that	that	ADV
ejpam-5876	132	9	is	is	ADV
ejpam-5876	132	10	,	,	PUNCT
ejpam-5876	132	11	xδqkµ	xδqkµ	PROPN
ejpam-5876	132	12	and	and	CCONJ
ejpam-5876	132	13	yδqkµ.	yδqkµ.	NOUN
ejpam-5876	132	14	since	since	SCONJ
ejpam-5876	132	15	µ	µ	NOUN
ejpam-5876	132	16	is	be	AUX
ejpam-5876	132	17	a	a	DET
ejpam-5876	132	18	k	k	NOUN
ejpam-5876	132	19	-	-	NOUN
ejpam-5876	132	20	right	right	NOUN
ejpam-5876	132	21	(	(	PUNCT
ejpam-5876	132	22	qk,∈	qk,∈	X
ejpam-5876	132	23	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	132	24	sup	sup	ADJ
ejpam-5876	132	25	-	-	PUNCT
ejpam-5876	132	26	subalgebra	subalgebra	NOUN
ejpam-5876	132	27	of	of	ADP
ejpam-5876	132	28	x	x	PRON
ejpam-5876	132	29	,	,	PUNCT
ejpam-5876	132	30	it	it	PRON
ejpam-5876	132	31	follows	follow	VERB
ejpam-5876	132	32	that	that	SCONJ
ejpam-5876	132	33	(	(	PUNCT
ejpam-5876	132	34	(	(	PUNCT
ejpam-5876	132	35	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	132	36	)	)	PUNCT
ejpam-5876	132	37	)	)	PUNCT
ejpam-5876	132	38	,	,	PUNCT
ejpam-5876	132	39	δ	δ	PROPN
ejpam-5876	132	40	)	)	PUNCT
ejpam-5876	132	41	∈	∈	PROPN
ejpam-5876	132	42	∨qkµ.	∨qkµ.	VERB
ejpam-5876	132	43	on	on	ADP
ejpam-5876	132	44	the	the	DET
ejpam-5876	132	45	other	other	ADJ
ejpam-5876	132	46	hand	hand	NOUN
ejpam-5876	132	47	,	,	PUNCT
ejpam-5876	132	48	1	1	NUM
ejpam-5876	132	49	−	−	PROPN
ejpam-5876	132	50	k	k	NOUN
ejpam-5876	132	51	−	−	PROPN
ejpam-5876	132	52	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	132	53	)	)	PUNCT
ejpam-5876	132	54	)	)	PUNCT
ejpam-5876	132	55	)	)	PUNCT
ejpam-5876	133	1	≥	≥	PROPN
ejpam-5876	133	2	δ	δ	PROPN
ejpam-5876	133	3	implies	imply	VERB
ejpam-5876	133	4	that	that	SCONJ
ejpam-5876	133	5	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	VERB
ejpam-5876	133	6	)	)	PUNCT
ejpam-5876	133	7	)	)	PUNCT
ejpam-5876	133	8	)	)	PUNCT
ejpam-5876	134	1	+	+	CCONJ
ejpam-5876	135	1	δ	δ	PROPN
ejpam-5876	135	2	+	+	CCONJ
ejpam-5876	135	3	k	k	X
ejpam-5876	135	4	≤	≤	NUM
ejpam-5876	135	5	1	1	NUM
ejpam-5876	135	6	,	,	PUNCT
ejpam-5876	135	7	that	that	ADV
ejpam-5876	135	8	is	is	ADV
ejpam-5876	135	9	,	,	PUNCT
ejpam-5876	135	10	(	(	PUNCT
ejpam-5876	135	11	(	(	PUNCT
ejpam-5876	135	12	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	135	13	)	)	PUNCT
ejpam-5876	135	14	)	)	PUNCT
ejpam-5876	135	15	,	,	PUNCT
ejpam-5876	135	16	δ)qkµ	δ)qkµ	NOUN
ejpam-5876	135	17	,	,	PUNCT
ejpam-5876	135	18	and	and	CCONJ
ejpam-5876	135	19	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	135	20	)	)	PUNCT
ejpam-5876	135	21	)	)	PUNCT
ejpam-5876	135	22	)	)	PUNCT
ejpam-5876	135	23	≤	≤	NOUN
ejpam-5876	136	1	1−	1−	NUM
ejpam-5876	136	2	δ−	δ−	PROPN
ejpam-5876	137	1	k	k	PROPN
ejpam-5876	137	2	<	<	X
ejpam-5876	137	3	1−	1−	NUM
ejpam-5876	137	4	k−	k−	PROPN
ejpam-5876	137	5	1−k	1−k	NUM
ejpam-5876	137	6	2	2	NUM
ejpam-5876	137	7	=	=	SYM
ejpam-5876	137	8	1−k	1−k	NUM
ejpam-5876	137	9	2	2	NUM
ejpam-5876	137	10	<	<	X
ejpam-5876	137	11	δ	δ	PROPN
ejpam-5876	137	12	,	,	PUNCT
ejpam-5876	137	13	that	that	ADV
ejpam-5876	137	14	is	is	ADV
ejpam-5876	137	15	,	,	PUNCT
ejpam-5876	137	16	(	(	PUNCT
ejpam-5876	137	17	(	(	PUNCT
ejpam-5876	137	18	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	137	19	)	)	PUNCT
ejpam-5876	137	20	)	)	PUNCT
ejpam-5876	137	21	,	,	PUNCT
ejpam-5876	137	22	δ)∈µ.	δ)∈µ.	X
ejpam-5876	137	23	hence	hence	ADV
ejpam-5876	137	24	,	,	PUNCT
ejpam-5876	137	25	(	(	PUNCT
ejpam-5876	137	26	(	(	PUNCT
ejpam-5876	137	27	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	137	28	)	)	PUNCT
ejpam-5876	137	29	)	)	PUNCT
ejpam-5876	137	30	,	,	PUNCT
ejpam-5876	137	31	δ)∈	δ)∈	PROPN
ejpam-5876	137	32	∨qkµ	∨qkµ	PROPN
ejpam-5876	137	33	,	,	PUNCT
ejpam-5876	137	34	which	which	PRON
ejpam-5876	137	35	is	be	AUX
ejpam-5876	137	36	a	a	DET
ejpam-5876	137	37	contradiction	contradiction	NOUN
ejpam-5876	137	38	.	.	PUNCT
ejpam-5876	138	1	therefore	therefore	ADV
ejpam-5876	138	2	,	,	PUNCT
ejpam-5876	138	3	(	(	PUNCT
ejpam-5876	138	4	(	(	PUNCT
ejpam-5876	138	5	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	138	6	,	,	PUNCT
ejpam-5876	138	7	r	r	NOUN
ejpam-5876	138	8	}	}	PUNCT
ejpam-5876	138	9	∈	∈	PROPN
ejpam-5876	138	10	∨qkµ	∨qkµ	PROPN
ejpam-5876	138	11	,	,	PUNCT
ejpam-5876	138	12	and	and	CCONJ
ejpam-5876	138	13	thus	thus	ADV
ejpam-5876	138	14	µ	µ	PRON
ejpam-5876	138	15	is	be	AUX
ejpam-5876	138	16	an	an	DET
ejpam-5876	138	17	(	(	PUNCT
ejpam-5876	138	18	∈,∈	∈,∈	X
ejpam-5876	138	19	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	138	20	sup	sup	ADJ
ejpam-5876	138	21	-	-	PUNCT
ejpam-5876	138	22	subalgebra	subalgebra	NOUN
ejpam-5876	138	23	of	of	ADP
ejpam-5876	138	24	x.	x.	PROPN
ejpam-5876	138	25	corollary	corollary	PROPN
ejpam-5876	138	26	2	2	NUM
ejpam-5876	138	27	is	be	AUX
ejpam-5876	138	28	an	an	DET
ejpam-5876	138	29	immediate	immediate	ADJ
ejpam-5876	138	30	consequence	consequence	NOUN
ejpam-5876	138	31	of	of	ADP
ejpam-5876	138	32	theorem	theorem	NOUN
ejpam-5876	138	33	3	3	NUM
ejpam-5876	138	34	by	by	ADP
ejpam-5876	138	35	setting	set	VERB
ejpam-5876	138	36	k	k	PROPN
ejpam-5876	138	37	=	=	PUNCT
ejpam-5876	138	38	0	0	X
ejpam-5876	138	39	.	.	PUNCT
ejpam-5876	139	1	specifically	specifically	ADV
ejpam-5876	139	2	,	,	PUNCT
ejpam-5876	139	3	a	a	DET
ejpam-5876	139	4	0	0	NUM
ejpam-5876	139	5	-	-	PUNCT
ejpam-5876	139	6	right	right	NOUN
ejpam-5876	139	7	(	(	PUNCT
ejpam-5876	139	8	q,∈	q,∈	NOUN
ejpam-5876	139	9	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	139	10	sup	sup	ADJ
ejpam-5876	139	11	-	-	PUNCT
ejpam-5876	139	12	subalgebra	subalgebra	NOUN
ejpam-5876	139	13	satisfies	satisfie	NOUN
ejpam-5876	139	14	all	all	DET
ejpam-5876	139	15	the	the	DET
ejpam-5876	139	16	conditions	condition	NOUN
ejpam-5876	139	17	required	require	VERB
ejpam-5876	139	18	by	by	ADP
ejpam-5876	139	19	theorem	theorem	NOUN
ejpam-5876	139	20	3	3	NUM
ejpam-5876	139	21	,	,	PUNCT
ejpam-5876	139	22	and	and	CCONJ
ejpam-5876	139	23	hence	hence	ADV
ejpam-5876	139	24	it	it	PRON
ejpam-5876	139	25	is	be	AUX
ejpam-5876	139	26	also	also	ADV
ejpam-5876	139	27	an	an	DET
ejpam-5876	139	28	(	(	PUNCT
ejpam-5876	139	29	∈,∈	∈,∈	X
ejpam-5876	139	30	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	139	31	sup	sup	NOUN
ejpam-5876	139	32	-	-	PUNCT
ejpam-5876	139	33	subalgebra	subalgebra	NOUN
ejpam-5876	139	34	.	.	PUNCT
ejpam-5876	140	1	corollary	corollary	ADJ
ejpam-5876	140	2	2	2	NUM
ejpam-5876	140	3	.	.	PUNCT
ejpam-5876	141	1	every	every	DET
ejpam-5876	141	2	0	0	NUM
ejpam-5876	141	3	-	-	PUNCT
ejpam-5876	141	4	right	right	NOUN
ejpam-5876	141	5	(	(	PUNCT
ejpam-5876	141	6	q,∈	q,∈	NOUN
ejpam-5876	141	7	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	141	8	sup	sup	ADJ
ejpam-5876	141	9	-	-	PUNCT
ejpam-5876	141	10	subalgebra	subalgebra	NOUN
ejpam-5876	141	11	is	be	AUX
ejpam-5876	141	12	an	an	DET
ejpam-5876	141	13	(	(	PUNCT
ejpam-5876	141	14	∈,∈	∈,∈	X
ejpam-5876	141	15	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	141	16	subalgebra	subalgebra	NOUN
ejpam-5876	141	17	.	.	PUNCT
ejpam-5876	142	1	theorem	theorem	NOUN
ejpam-5876	142	2	4	4	NUM
ejpam-5876	142	3	.	.	PUNCT
ejpam-5876	143	1	if	if	SCONJ
ejpam-5876	143	2	every	every	DET
ejpam-5876	143	3	fuzzy	fuzzy	ADJ
ejpam-5876	143	4	point	point	NOUN
ejpam-5876	143	5	has	have	VERB
ejpam-5876	143	6	the	the	DET
ejpam-5876	143	7	value	value	NOUN
ejpam-5876	143	8	t	t	NOUN
ejpam-5876	143	9	in	in	ADP
ejpam-5876	143	10	(	(	PUNCT
ejpam-5876	143	11	0	0	NUM
ejpam-5876	143	12	,	,	PUNCT
ejpam-5876	143	13	1−k	1−k	NUM
ejpam-5876	143	14	2	2	NUM
ejpam-5876	143	15	]	]	PUNCT
ejpam-5876	143	16	,	,	PUNCT
ejpam-5876	143	17	then	then	ADV
ejpam-5876	143	18	every	every	DET
ejpam-5876	143	19	(	(	PUNCT
ejpam-5876	143	20	∈,∈	∈,∈	X
ejpam-5876	143	21	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	143	22	subalgebra	subalgebra	NOUN
ejpam-5876	143	23	is	be	AUX
ejpam-5876	143	24	a	a	DET
ejpam-5876	143	25	k	k	NOUN
ejpam-5876	143	26	-	-	ADJ
ejpam-5876	143	27	left	left	ADJ
ejpam-5876	143	28	(	(	PUNCT
ejpam-5876	143	29	qk,∈	qk,∈	X
ejpam-5876	143	30	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	143	31	sup	sup	NOUN
ejpam-5876	143	32	-	-	PUNCT
ejpam-5876	143	33	subalgebra	subalgebra	NOUN
ejpam-5876	143	34	.	.	PUNCT
ejpam-5876	144	1	proof	proof	NOUN
ejpam-5876	144	2	.	.	PUNCT
ejpam-5876	145	1	let	let	VERB
ejpam-5876	145	2	µ	µ	X
ejpam-5876	145	3	be	be	AUX
ejpam-5876	145	4	an	an	DET
ejpam-5876	145	5	(	(	PUNCT
ejpam-5876	145	6	∈,∈	∈,∈	X
ejpam-5876	145	7	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	145	8	sup	sup	ADJ
ejpam-5876	145	9	-	-	PUNCT
ejpam-5876	145	10	subalgebra	subalgebra	NOUN
ejpam-5876	145	11	of	of	ADP
ejpam-5876	145	12	x.	x.	NOUN
ejpam-5876	145	13	let	let	VERB
ejpam-5876	145	14	x	x	PRON
ejpam-5876	145	15	,	,	PUNCT
ejpam-5876	145	16	y	y	PROPN
ejpam-5876	145	17	∈	∈	PROPN
ejpam-5876	145	18	x	x	X
ejpam-5876	145	19	and	and	CCONJ
ejpam-5876	145	20	t	t	PROPN
ejpam-5876	145	21	,	,	PUNCT
ejpam-5876	145	22	r	r	NOUN
ejpam-5876	145	23	∈	∈	PROPN
ejpam-5876	145	24	(	(	PUNCT
ejpam-5876	145	25	0	0	NUM
ejpam-5876	145	26	,	,	PUNCT
ejpam-5876	145	27	1−k	1−k	NUM
ejpam-5876	145	28	2	2	NUM
ejpam-5876	145	29	]	]	PUNCT
ejpam-5876	145	30	be	be	AUX
ejpam-5876	145	31	such	such	ADJ
ejpam-5876	145	32	that	that	DET
ejpam-5876	145	33	xtqkµ	xtqkµ	NOUN
ejpam-5876	145	34	and	and	CCONJ
ejpam-5876	145	35	yrqkµ.	yrqkµ.	NOUN
ejpam-5876	145	36	then	then	ADV
ejpam-5876	145	37	µ(x	µ(x	VERB
ejpam-5876	145	38	)	)	PUNCT
ejpam-5876	146	1	+	+	CCONJ
ejpam-5876	146	2	t+	t+	VERB
ejpam-5876	146	3	k	k	X
ejpam-5876	146	4	>	>	X
ejpam-5876	146	5	1	1	NUM
ejpam-5876	146	6	and	and	CCONJ
ejpam-5876	146	7	µ(y	µ(y	NUM
ejpam-5876	146	8	)	)	PUNCT
ejpam-5876	146	9	+	+	NUM
ejpam-5876	146	10	r+	r+	PUNCT
ejpam-5876	146	11	k	k	X
ejpam-5876	146	12	>	>	X
ejpam-5876	146	13	1	1	X
ejpam-5876	146	14	.	.	PUNCT
ejpam-5876	146	15	since	since	SCONJ
ejpam-5876	146	16	t	t	PROPN
ejpam-5876	146	17	,	,	PUNCT
ejpam-5876	146	18	r	r	NOUN
ejpam-5876	146	19	∈	∈	PROPN
ejpam-5876	146	20	(	(	PUNCT
ejpam-5876	146	21	0	0	NUM
ejpam-5876	146	22	,	,	PUNCT
ejpam-5876	146	23	1−k	1−k	NUM
ejpam-5876	146	24	2	2	NUM
ejpam-5876	146	25	]	]	PUNCT
ejpam-5876	146	26	,	,	PUNCT
ejpam-5876	146	27	we	we	PRON
ejpam-5876	146	28	have	have	VERB
ejpam-5876	146	29	µ(x	µ(x	NOUN
ejpam-5876	146	30	)	)	PUNCT
ejpam-5876	146	31	>	>	X
ejpam-5876	146	32	1	1	NUM
ejpam-5876	146	33	−	−	NOUN
ejpam-5876	146	34	t	t	NOUN
ejpam-5876	146	35	−	−	PROPN
ejpam-5876	147	1	k	k	PROPN
ejpam-5876	147	2	≥	≥	NUM
ejpam-5876	147	3	1−k	1−k	NUM
ejpam-5876	147	4	2	2	NUM
ejpam-5876	147	5	≥	≥	NOUN
ejpam-5876	147	6	t	t	NOUN
ejpam-5876	147	7	and	and	CCONJ
ejpam-5876	147	8	µ(y	µ(y	PROPN
ejpam-5876	147	9	)	)	PUNCT
ejpam-5876	147	10	>	>	X
ejpam-5876	147	11	1	1	NUM
ejpam-5876	148	1	−	−	NOUN
ejpam-5876	148	2	r	r	NOUN
ejpam-5876	148	3	−	−	PROPN
ejpam-5876	148	4	k	k	X
ejpam-5876	148	5	≥	≥	NUM
ejpam-5876	148	6	1−k	1−k	NUM
ejpam-5876	148	7	2	2	NUM
ejpam-5876	148	8	≥	≥	NOUN
ejpam-5876	148	9	r	r	NOUN
ejpam-5876	148	10	,	,	PUNCT
ejpam-5876	148	11	that	that	ADV
ejpam-5876	148	12	is	is	ADV
ejpam-5876	148	13	,	,	PUNCT
ejpam-5876	148	14	xt	xt	PROPN
ejpam-5876	148	15	∈	∈	PROPN
ejpam-5876	148	16	µ	µ	X
ejpam-5876	148	17	and	and	CCONJ
ejpam-5876	148	18	yr	yr	NOUN
ejpam-5876	148	19	∈	∈	PROPN
ejpam-5876	148	20	µ.	µ.	NOUN
ejpam-5876	148	21	then	then	ADV
ejpam-5876	148	22	(	(	PUNCT
ejpam-5876	148	23	(	(	PUNCT
ejpam-5876	148	24	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	148	25	,	,	PUNCT
ejpam-5876	148	26	r	r	NOUN
ejpam-5876	148	27	}	}	PUNCT
ejpam-5876	148	28	∈	∈	NOUN
ejpam-5876	148	29	∨qkµ.	∨qkµ.	NOUN
ejpam-5876	148	30	hence	hence	ADV
ejpam-5876	148	31	,	,	PUNCT
ejpam-5876	148	32	µ	µ	X
ejpam-5876	148	33	is	be	AUX
ejpam-5876	148	34	a	a	DET
ejpam-5876	148	35	k	k	NOUN
ejpam-5876	148	36	-	-	ADJ
ejpam-5876	148	37	left	left	ADJ
ejpam-5876	148	38	(	(	PUNCT
ejpam-5876	148	39	qk,∈	qk,∈	X
ejpam-5876	148	40	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	148	41	sup	sup	ADJ
ejpam-5876	148	42	-	-	PUNCT
ejpam-5876	148	43	subalgebra	subalgebra	NOUN
ejpam-5876	148	44	of	of	ADP
ejpam-5876	148	45	x.	x.	PROPN
ejpam-5876	148	46	corollary	corollary	PROPN
ejpam-5876	148	47	3	3	NUM
ejpam-5876	148	48	is	be	AUX
ejpam-5876	148	49	a	a	DET
ejpam-5876	148	50	direct	direct	ADJ
ejpam-5876	148	51	consequence	consequence	NOUN
ejpam-5876	148	52	of	of	ADP
ejpam-5876	148	53	theorem	theorem	NOUN
ejpam-5876	148	54	4	4	NUM
ejpam-5876	148	55	by	by	ADP
ejpam-5876	148	56	setting	set	VERB
ejpam-5876	148	57	k	k	PROPN
ejpam-5876	148	58	=	=	PUNCT
ejpam-5876	148	59	0	0	X
ejpam-5876	148	60	.	.	PUNCT
ejpam-5876	149	1	in	in	ADP
ejpam-5876	149	2	this	this	DET
ejpam-5876	149	3	case	case	NOUN
ejpam-5876	149	4	,	,	PUNCT
ejpam-5876	149	5	the	the	DET
ejpam-5876	149	6	interval	interval	NOUN
ejpam-5876	149	7	(	(	PUNCT
ejpam-5876	149	8	0	0	NUM
ejpam-5876	149	9	,	,	PUNCT
ejpam-5876	149	10	1−k	1−k	NUM
ejpam-5876	149	11	2	2	NUM
ejpam-5876	149	12	]	]	PUNCT
ejpam-5876	149	13	becomes	become	VERB
ejpam-5876	149	14	(	(	PUNCT
ejpam-5876	149	15	0	0	NUM
ejpam-5876	149	16	,	,	PUNCT
ejpam-5876	149	17	0.5	0.5	NUM
ejpam-5876	149	18	]	]	PUNCT
ejpam-5876	149	19	,	,	PUNCT
ejpam-5876	149	20	and	and	CCONJ
ejpam-5876	149	21	the	the	DET
ejpam-5876	149	22	(	(	PUNCT
ejpam-5876	149	23	∈,∈	∈,∈	X
ejpam-5876	149	24	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	149	25	sup	sup	ADJ
ejpam-5876	149	26	-	-	PUNCT
ejpam-5876	149	27	subalgebra	subalgebra	NOUN
ejpam-5876	149	28	reduces	reduce	VERB
ejpam-5876	149	29	to	to	ADP
ejpam-5876	149	30	the	the	DET
ejpam-5876	149	31	(	(	PUNCT
ejpam-5876	149	32	∈,∈	∈,∈	X
ejpam-5876	149	33	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	149	34	case	case	NOUN
ejpam-5876	149	35	.	.	PUNCT
ejpam-5876	150	1	theorem	theorem	VERB
ejpam-5876	150	2	4	4	NUM
ejpam-5876	150	3	guarantees	guarantee	VERB
ejpam-5876	150	4	that	that	SCONJ
ejpam-5876	150	5	under	under	ADP
ejpam-5876	150	6	these	these	DET
ejpam-5876	150	7	conditions	condition	NOUN
ejpam-5876	150	8	,	,	PUNCT
ejpam-5876	150	9	every	every	DET
ejpam-5876	150	10	(	(	PUNCT
ejpam-5876	150	11	∈,∈	∈,∈	X
ejpam-5876	150	12	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	150	13	sup	sup	NOUN
ejpam-5876	150	14	-	-	PUNCT
ejpam-5876	150	15	subalgebra	subalgebra	NOUN
ejpam-5876	150	16	is	be	AUX
ejpam-5876	150	17	a	a	DET
ejpam-5876	150	18	0	0	ADV
ejpam-5876	150	19	-	-	PUNCT
ejpam-5876	150	20	left	left	ADJ
ejpam-5876	150	21	(	(	PUNCT
ejpam-5876	150	22	q,∈	q,∈	NOUN
ejpam-5876	150	23	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	150	24	sup	sup	ADJ
ejpam-5876	150	25	-	-	PUNCT
ejpam-5876	150	26	subalgebra	subalgebra	NOUN
ejpam-5876	150	27	,	,	PUNCT
ejpam-5876	150	28	which	which	PRON
ejpam-5876	150	29	proves	prove	VERB
ejpam-5876	150	30	the	the	DET
ejpam-5876	150	31	corollary	corollary	NOUN
ejpam-5876	150	32	.	.	PUNCT
ejpam-5876	151	1	t.	t.	PROPN
ejpam-5876	151	2	oner	oner	PROPN
ejpam-5876	151	3	et	et	PROPN
ejpam-5876	151	4	al	al	PROPN
ejpam-5876	151	5	.	.	PUNCT
ejpam-5876	151	6	/	/	SYM
ejpam-5876	151	7	eur	eur	PROPN
ejpam-5876	151	8	.	.	PUNCT
ejpam-5876	152	1	j.	j.	PROPN
ejpam-5876	152	2	pure	pure	PROPN
ejpam-5876	152	3	appl	appl	PROPN
ejpam-5876	152	4	.	.	PROPN
ejpam-5876	152	5	math	math	PROPN
ejpam-5876	152	6	,	,	PUNCT
ejpam-5876	152	7	18	18	NUM
ejpam-5876	152	8	(	(	PUNCT
ejpam-5876	152	9	2	2	NUM
ejpam-5876	152	10	)	)	PUNCT
ejpam-5876	152	11	(	(	PUNCT
ejpam-5876	152	12	2025	2025	NUM
ejpam-5876	152	13	)	)	PUNCT
ejpam-5876	152	14	,	,	PUNCT
ejpam-5876	152	15	5876	5876	NUM
ejpam-5876	152	16	7	7	NUM
ejpam-5876	152	17	of	of	ADP
ejpam-5876	152	18	16	16	NUM
ejpam-5876	152	19	corollary	corollary	ADJ
ejpam-5876	152	20	3	3	NUM
ejpam-5876	152	21	.	.	PUNCT
ejpam-5876	153	1	if	if	SCONJ
ejpam-5876	153	2	every	every	DET
ejpam-5876	153	3	fuzzy	fuzzy	ADJ
ejpam-5876	153	4	point	point	NOUN
ejpam-5876	153	5	has	have	VERB
ejpam-5876	153	6	the	the	DET
ejpam-5876	153	7	value	value	NOUN
ejpam-5876	153	8	t	t	NOUN
ejpam-5876	153	9	in	in	ADP
ejpam-5876	153	10	(	(	PUNCT
ejpam-5876	153	11	0	0	NUM
ejpam-5876	153	12	,	,	PUNCT
ejpam-5876	153	13	0.5	0.5	NUM
ejpam-5876	153	14	]	]	PUNCT
ejpam-5876	153	15	,	,	PUNCT
ejpam-5876	153	16	then	then	ADV
ejpam-5876	153	17	every	every	DET
ejpam-5876	153	18	(	(	PUNCT
ejpam-5876	153	19	∈,∈	∈,∈	X
ejpam-5876	153	20	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	153	21	sup	sup	NOUN
ejpam-5876	153	22	-	-	PUNCT
ejpam-5876	153	23	subalgebra	subalgebra	NOUN
ejpam-5876	153	24	is	be	AUX
ejpam-5876	153	25	a	a	DET
ejpam-5876	153	26	0	0	ADV
ejpam-5876	153	27	-	-	PUNCT
ejpam-5876	153	28	left	left	ADJ
ejpam-5876	153	29	(	(	PUNCT
ejpam-5876	153	30	q,∈	q,∈	NOUN
ejpam-5876	153	31	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	153	32	sup	sup	ADJ
ejpam-5876	153	33	-	-	PUNCT
ejpam-5876	153	34	subalgebra	subalgebra	NOUN
ejpam-5876	153	35	.	.	PUNCT
ejpam-5876	154	1	proposition	proposition	NOUN
ejpam-5876	154	2	2	2	NUM
ejpam-5876	154	3	.	.	PUNCT
ejpam-5876	155	1	if	if	SCONJ
ejpam-5876	155	2	(	(	PUNCT
ejpam-5876	155	3	x	x	NOUN
ejpam-5876	155	4	,	,	PUNCT
ejpam-5876	155	5	ℓµqk	ℓµqk	PROPN
ejpam-5876	155	6	)	)	PUNCT
ejpam-5876	155	7	is	be	AUX
ejpam-5876	155	8	a	a	DET
ejpam-5876	155	9	semidetached	semidetache	VERB
ejpam-5876	155	10	sup	sup	NOUN
ejpam-5876	155	11	-	-	PUNCT
ejpam-5876	155	12	subalgebra	subalgebra	NOUN
ejpam-5876	155	13	over	over	ADP
ejpam-5876	155	14	ω	ω	NUM
ejpam-5876	155	15	=	=	SYM
ejpam-5876	155	16	(	(	PUNCT
ejpam-5876	155	17	1−k	1−k	NUM
ejpam-5876	155	18	2	2	NUM
ejpam-5876	155	19	,	,	PUNCT
ejpam-5876	155	20	1	1	NUM
ejpam-5876	155	21	]	]	PUNCT
ejpam-5876	155	22	,	,	PUNCT
ejpam-5876	155	23	then	then	ADV
ejpam-5876	155	24	µ	µ	X
ejpam-5876	155	25	satisfies	satisfie	NOUN
ejpam-5876	155	26	:	:	PUNCT
ejpam-5876	155	27	(	(	PUNCT
ejpam-5876	155	28	∀x	∀x	X
ejpam-5876	155	29	,	,	PUNCT
ejpam-5876	155	30	y	y	PROPN
ejpam-5876	155	31	∈	∈	PROPN
ejpam-5876	155	32	x)(∀t	x)(∀t	PROPN
ejpam-5876	155	33	,	,	PUNCT
ejpam-5876	155	34	r	r	NOUN
ejpam-5876	155	35	∈	∈	PROPN
ejpam-5876	155	36	ω)(xt	ω)(xt	NUM
ejpam-5876	155	37	∈	∈	PROPN
ejpam-5876	155	38	µ	µ	NOUN
ejpam-5876	155	39	,	,	PUNCT
ejpam-5876	155	40	yr	yr	PROPN
ejpam-5876	155	41	∈	∈	PROPN
ejpam-5876	155	42	µ	µ	PRON
ejpam-5876	155	43	⇒	⇒	NOUN
ejpam-5876	155	44	(	(	PUNCT
ejpam-5876	155	45	(	(	PUNCT
ejpam-5876	155	46	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	155	47	,	,	PUNCT
ejpam-5876	155	48	r}qkµ	r}qkµ	NOUN
ejpam-5876	155	49	)	)	PUNCT
ejpam-5876	155	50	.	.	PUNCT
ejpam-5876	156	1	(	(	PUNCT
ejpam-5876	156	2	6	6	X
ejpam-5876	156	3	)	)	PUNCT
ejpam-5876	156	4	proof	proof	NOUN
ejpam-5876	156	5	.	.	PUNCT
ejpam-5876	157	1	let	let	VERB
ejpam-5876	157	2	x	x	PRON
ejpam-5876	157	3	,	,	PUNCT
ejpam-5876	157	4	y	y	PROPN
ejpam-5876	157	5	∈	∈	PROPN
ejpam-5876	157	6	x	x	X
ejpam-5876	157	7	and	and	CCONJ
ejpam-5876	157	8	t	t	PROPN
ejpam-5876	157	9	,	,	PUNCT
ejpam-5876	157	10	r	r	NOUN
ejpam-5876	157	11	∈	∈	PROPN
ejpam-5876	157	12	ω	ω	NUM
ejpam-5876	157	13	=	=	SYM
ejpam-5876	157	14	(	(	PUNCT
ejpam-5876	157	15	1−k	1−k	NUM
ejpam-5876	157	16	2	2	NUM
ejpam-5876	157	17	,	,	PUNCT
ejpam-5876	157	18	1	1	NUM
ejpam-5876	157	19	]	]	PUNCT
ejpam-5876	157	20	be	be	AUX
ejpam-5876	157	21	such	such	ADJ
ejpam-5876	157	22	that	that	SCONJ
ejpam-5876	157	23	xt	xt	PROPN
ejpam-5876	157	24	∈	∈	PROPN
ejpam-5876	157	25	µ	µ	X
ejpam-5876	157	26	and	and	CCONJ
ejpam-5876	157	27	yr	yr	NOUN
ejpam-5876	157	28	∈	∈	PROPN
ejpam-5876	157	29	µ.	µ.	NOUN
ejpam-5876	157	30	then	then	ADV
ejpam-5876	157	31	µ(x	µ(x	NOUN
ejpam-5876	157	32	)	)	PUNCT
ejpam-5876	157	33	≥	≥	NOUN
ejpam-5876	157	34	t	t	PROPN
ejpam-5876	157	35	>	>	X
ejpam-5876	157	36	1−k	1−k	NUM
ejpam-5876	157	37	2	2	NUM
ejpam-5876	157	38	and	and	CCONJ
ejpam-5876	157	39	µ(y	µ(y	NUM
ejpam-5876	157	40	)	)	PUNCT
ejpam-5876	157	41	≥	≥	NOUN
ejpam-5876	158	1	r	r	NOUN
ejpam-5876	158	2	>	>	X
ejpam-5876	158	3	1−k	1−k	NUM
ejpam-5876	158	4	2	2	NUM
ejpam-5876	158	5	,	,	PUNCT
ejpam-5876	158	6	which	which	PRON
ejpam-5876	158	7	imply	imply	VERB
ejpam-5876	158	8	that	that	SCONJ
ejpam-5876	158	9	µ(x	µ(x	VERB
ejpam-5876	158	10	)	)	PUNCT
ejpam-5876	158	11	+	+	NUM
ejpam-5876	158	12	t	t	NOUN
ejpam-5876	158	13	+	+	CCONJ
ejpam-5876	158	14	k	k	X
ejpam-5876	158	15	>	>	X
ejpam-5876	158	16	1	1	NUM
ejpam-5876	158	17	and	and	CCONJ
ejpam-5876	158	18	µ(y	µ(y	NUM
ejpam-5876	158	19	)	)	PUNCT
ejpam-5876	159	1	+	+	CCONJ
ejpam-5876	159	2	r	r	NOUN
ejpam-5876	159	3	+	+	X
ejpam-5876	159	4	k	k	X
ejpam-5876	159	5	>	>	X
ejpam-5876	159	6	1	1	NUM
ejpam-5876	159	7	,	,	PUNCT
ejpam-5876	159	8	that	that	ADV
ejpam-5876	159	9	is	is	ADV
ejpam-5876	159	10	,	,	PUNCT
ejpam-5876	159	11	xtqkµ	xtqkµ	PROPN
ejpam-5876	159	12	and	and	CCONJ
ejpam-5876	159	13	yrqkµ.	yrqkµ.	NOUN
ejpam-5876	159	14	it	it	PRON
ejpam-5876	159	15	follows	follow	VERB
ejpam-5876	159	16	that	that	SCONJ
ejpam-5876	159	17	x	x	SYM
ejpam-5876	159	18	,	,	PUNCT
ejpam-5876	159	19	y	y	PROPN
ejpam-5876	159	20	∈	∈	PROPN
ejpam-5876	159	21	ℓµqk	ℓµqk	NOUN
ejpam-5876	159	22	(	(	PUNCT
ejpam-5876	159	23	max{t	max{t	NOUN
ejpam-5876	159	24	,	,	PUNCT
ejpam-5876	159	25	r	r	NOUN
ejpam-5876	159	26	}	}	PUNCT
ejpam-5876	159	27	)	)	PUNCT
ejpam-5876	159	28	and	and	CCONJ
ejpam-5876	159	29	max{t	max{t	NOUN
ejpam-5876	159	30	,	,	PUNCT
ejpam-5876	159	31	r	r	NOUN
ejpam-5876	159	32	}	}	PUNCT
ejpam-5876	159	33	∈	∈	PROPN
ejpam-5876	159	34	(	(	PUNCT
ejpam-5876	159	35	1−k	1−k	NUM
ejpam-5876	159	36	2	2	NUM
ejpam-5876	159	37	,	,	PUNCT
ejpam-5876	159	38	1	1	NUM
ejpam-5876	159	39	]	]	PUNCT
ejpam-5876	159	40	.	.	PUNCT
ejpam-5876	160	1	since	since	SCONJ
ejpam-5876	160	2	ℓµqk	ℓµqk	PROPN
ejpam-5876	160	3	(	(	PUNCT
ejpam-5876	160	4	max{t	max{t	NOUN
ejpam-5876	160	5	,	,	PUNCT
ejpam-5876	160	6	r	r	NOUN
ejpam-5876	160	7	}	}	PUNCT
ejpam-5876	160	8	)	)	PUNCT
ejpam-5876	160	9	is	be	AUX
ejpam-5876	160	10	an	an	DET
ejpam-5876	160	11	sup	sup	ADJ
ejpam-5876	160	12	-	-	PUNCT
ejpam-5876	160	13	subalgebra	subalgebra	NOUN
ejpam-5876	160	14	of	of	ADP
ejpam-5876	160	15	x	x	PRON
ejpam-5876	160	16	,	,	PUNCT
ejpam-5876	160	17	we	we	PRON
ejpam-5876	160	18	have	have	VERB
ejpam-5876	160	19	(	(	PUNCT
ejpam-5876	160	20	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	160	21	)	)	PUNCT
ejpam-5876	160	22	)	)	PUNCT
ejpam-5876	161	1	∈	∈	PROPN
ejpam-5876	161	2	ℓµqk	ℓµqk	NOUN
ejpam-5876	161	3	(	(	PUNCT
ejpam-5876	161	4	max{t	max{t	NOUN
ejpam-5876	161	5	,	,	PUNCT
ejpam-5876	161	6	r	r	NOUN
ejpam-5876	161	7	}	}	PUNCT
ejpam-5876	161	8	)	)	PUNCT
ejpam-5876	161	9	,	,	PUNCT
ejpam-5876	161	10	and	and	CCONJ
ejpam-5876	161	11	so	so	ADV
ejpam-5876	161	12	(	(	PUNCT
ejpam-5876	161	13	(	(	PUNCT
ejpam-5876	161	14	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	161	15	,	,	PUNCT
ejpam-5876	161	16	r}qkµ.	r}qkµ.	PROPN
ejpam-5876	161	17	corollary	corollary	ADJ
ejpam-5876	161	18	4	4	NUM
ejpam-5876	161	19	is	be	AUX
ejpam-5876	161	20	a	a	DET
ejpam-5876	161	21	direct	direct	ADJ
ejpam-5876	161	22	consequence	consequence	NOUN
ejpam-5876	161	23	of	of	ADP
ejpam-5876	161	24	proposition	proposition	NOUN
ejpam-5876	161	25	2	2	NUM
ejpam-5876	161	26	by	by	ADP
ejpam-5876	161	27	taking	take	VERB
ejpam-5876	161	28	k	k	PROPN
ejpam-5876	161	29	=	=	PUNCT
ejpam-5876	161	30	0	0	PROPN
ejpam-5876	161	31	,	,	PUNCT
ejpam-5876	161	32	which	which	PRON
ejpam-5876	161	33	leads	lead	VERB
ejpam-5876	161	34	to	to	ADP
ejpam-5876	161	35	ω	ω	PROPN
ejpam-5876	161	36	=	=	SYM
ejpam-5876	161	37	(	(	PUNCT
ejpam-5876	161	38	0.5	0.5	NUM
ejpam-5876	161	39	,	,	PUNCT
ejpam-5876	161	40	1	1	NUM
ejpam-5876	161	41	]	]	PUNCT
ejpam-5876	161	42	and	and	CCONJ
ejpam-5876	161	43	the	the	DET
ejpam-5876	161	44	standard	standard	ADJ
ejpam-5876	161	45	quasi	quasi	ADJ
ejpam-5876	161	46	-	-	ADJ
ejpam-5876	161	47	coincidence	coincidence	NOUN
ejpam-5876	161	48	operator	operator	NOUN
ejpam-5876	161	49	q.	q.	NOUN
ejpam-5876	161	50	the	the	DET
ejpam-5876	161	51	proposition	proposition	NOUN
ejpam-5876	161	52	ensures	ensure	VERB
ejpam-5876	161	53	that	that	SCONJ
ejpam-5876	161	54	under	under	ADP
ejpam-5876	161	55	the	the	DET
ejpam-5876	161	56	semidetached	semidetache	VERB
ejpam-5876	161	57	structure	structure	NOUN
ejpam-5876	161	58	condition	condition	NOUN
ejpam-5876	161	59	,	,	PUNCT
ejpam-5876	161	60	the	the	DET
ejpam-5876	161	61	image	image	NOUN
ejpam-5876	161	62	of	of	ADP
ejpam-5876	161	63	the	the	DET
ejpam-5876	161	64	sheffer	sheffer	NOUN
ejpam-5876	161	65	stroke	stroke	NOUN
ejpam-5876	161	66	operation	operation	NOUN
ejpam-5876	161	67	remains	remain	VERB
ejpam-5876	161	68	within	within	ADP
ejpam-5876	161	69	the	the	DET
ejpam-5876	161	70	fuzzy	fuzzy	ADJ
ejpam-5876	161	71	quasi	quasi	NOUN
ejpam-5876	161	72	-	-	NOUN
ejpam-5876	161	73	coincidence	coincidence	NOUN
ejpam-5876	161	74	set	set	NOUN
ejpam-5876	161	75	,	,	PUNCT
ejpam-5876	161	76	establishing	establish	VERB
ejpam-5876	161	77	the	the	DET
ejpam-5876	161	78	desired	desire	VERB
ejpam-5876	161	79	inclusion	inclusion	NOUN
ejpam-5876	161	80	.	.	PUNCT
ejpam-5876	162	1	corollary	corollary	ADJ
ejpam-5876	162	2	4	4	NUM
ejpam-5876	162	3	.	.	PUNCT
ejpam-5876	163	1	if	if	SCONJ
ejpam-5876	163	2	(	(	PUNCT
ejpam-5876	163	3	x	x	NOUN
ejpam-5876	163	4	,	,	PUNCT
ejpam-5876	163	5	ℓµqk	ℓµqk	PROPN
ejpam-5876	163	6	)	)	PUNCT
ejpam-5876	163	7	is	be	AUX
ejpam-5876	163	8	a	a	DET
ejpam-5876	163	9	semidetached	semidetache	VERB
ejpam-5876	163	10	sup	sup	NOUN
ejpam-5876	163	11	-	-	PUNCT
ejpam-5876	163	12	subalgebra	subalgebra	NOUN
ejpam-5876	163	13	over	over	ADP
ejpam-5876	163	14	ω	ω	NUM
ejpam-5876	163	15	=	=	SYM
ejpam-5876	163	16	(	(	PUNCT
ejpam-5876	163	17	0.5	0.5	NUM
ejpam-5876	163	18	,	,	PUNCT
ejpam-5876	163	19	1	1	NUM
ejpam-5876	163	20	]	]	PUNCT
ejpam-5876	163	21	,	,	PUNCT
ejpam-5876	163	22	then	then	ADV
ejpam-5876	163	23	µ	µ	X
ejpam-5876	163	24	satisfies	satisfie	NOUN
ejpam-5876	163	25	:	:	PUNCT
ejpam-5876	163	26	(	(	PUNCT
ejpam-5876	163	27	∀x	∀x	X
ejpam-5876	163	28	,	,	PUNCT
ejpam-5876	163	29	y	y	PROPN
ejpam-5876	163	30	∈	∈	PROPN
ejpam-5876	163	31	x)(∀t	x)(∀t	PROPN
ejpam-5876	163	32	,	,	PUNCT
ejpam-5876	163	33	r	r	NOUN
ejpam-5876	163	34	∈	∈	PROPN
ejpam-5876	163	35	ω)(xt	ω)(xt	NUM
ejpam-5876	163	36	∈	∈	PROPN
ejpam-5876	163	37	µ	µ	NOUN
ejpam-5876	163	38	,	,	PUNCT
ejpam-5876	163	39	yr	yr	PROPN
ejpam-5876	163	40	∈	∈	PROPN
ejpam-5876	163	41	µ	µ	PRON
ejpam-5876	163	42	⇒	⇒	NOUN
ejpam-5876	163	43	(	(	PUNCT
ejpam-5876	163	44	(	(	PUNCT
ejpam-5876	163	45	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	163	46	,	,	PUNCT
ejpam-5876	163	47	r}qµ	r}qµ	PROPN
ejpam-5876	163	48	)	)	PUNCT
ejpam-5876	163	49	.	.	PUNCT
ejpam-5876	164	1	(	(	PUNCT
ejpam-5876	164	2	7	7	X
ejpam-5876	164	3	)	)	PUNCT
ejpam-5876	164	4	proposition	proposition	NOUN
ejpam-5876	164	5	3	3	NUM
ejpam-5876	164	6	.	.	PUNCT
ejpam-5876	165	1	if	if	SCONJ
ejpam-5876	165	2	(	(	PUNCT
ejpam-5876	165	3	x	x	NOUN
ejpam-5876	165	4	,	,	PUNCT
ejpam-5876	165	5	ℓµqk	ℓµqk	PROPN
ejpam-5876	165	6	)	)	PUNCT
ejpam-5876	165	7	is	be	AUX
ejpam-5876	165	8	a	a	DET
ejpam-5876	165	9	semidetached	semidetache	VERB
ejpam-5876	165	10	sup	sup	NOUN
ejpam-5876	165	11	-	-	PUNCT
ejpam-5876	165	12	subalgebra	subalgebra	NOUN
ejpam-5876	165	13	over	over	ADP
ejpam-5876	165	14	ω	ω	NUM
ejpam-5876	165	15	=	=	SYM
ejpam-5876	165	16	(	(	PUNCT
ejpam-5876	165	17	0	0	NUM
ejpam-5876	165	18	,	,	PUNCT
ejpam-5876	165	19	1−k	1−k	NUM
ejpam-5876	165	20	2	2	NUM
ejpam-5876	165	21	]	]	PUNCT
ejpam-5876	165	22	,	,	PUNCT
ejpam-5876	165	23	then	then	ADV
ejpam-5876	165	24	µ	µ	X
ejpam-5876	165	25	satisfies	satisfie	NOUN
ejpam-5876	165	26	:	:	PUNCT
ejpam-5876	165	27	(	(	PUNCT
ejpam-5876	165	28	∀x	∀x	X
ejpam-5876	165	29	,	,	PUNCT
ejpam-5876	165	30	y	y	PROPN
ejpam-5876	165	31	∈	∈	PROPN
ejpam-5876	165	32	x)(∀t	x)(∀t	PROPN
ejpam-5876	165	33	,	,	PUNCT
ejpam-5876	165	34	r	r	PROPN
ejpam-5876	165	35	∈	∈	PROPN
ejpam-5876	165	36	ω)(xtqkµ	ω)(xtqkµ	NUM
ejpam-5876	165	37	,	,	PUNCT
ejpam-5876	165	38	yrqkµ	yrqkµ	NOUN
ejpam-5876	165	39	)	)	PUNCT
ejpam-5876	165	40	⇒	⇒	NOUN
ejpam-5876	165	41	(	(	PUNCT
ejpam-5876	165	42	(	(	PUNCT
ejpam-5876	165	43	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	165	44	,	,	PUNCT
ejpam-5876	165	45	r	r	NOUN
ejpam-5876	165	46	}	}	PUNCT
ejpam-5876	165	47	∈	∈	PROPN
ejpam-5876	165	48	µ	µ	NUM
ejpam-5876	165	49	)	)	PUNCT
ejpam-5876	165	50	.	.	PUNCT
ejpam-5876	166	1	(	(	PUNCT
ejpam-5876	166	2	8)	8)	NUM
ejpam-5876	166	3	proof	proof	NOUN
ejpam-5876	166	4	.	.	PUNCT
ejpam-5876	167	1	let	let	VERB
ejpam-5876	167	2	x	x	PRON
ejpam-5876	167	3	,	,	PUNCT
ejpam-5876	167	4	y	y	PROPN
ejpam-5876	167	5	∈	∈	PROPN
ejpam-5876	167	6	x	x	X
ejpam-5876	167	7	and	and	CCONJ
ejpam-5876	167	8	t	t	PROPN
ejpam-5876	167	9	,	,	PUNCT
ejpam-5876	167	10	r	r	NOUN
ejpam-5876	167	11	∈	∈	PROPN
ejpam-5876	167	12	ω	ω	NUM
ejpam-5876	167	13	=	=	SYM
ejpam-5876	167	14	(	(	PUNCT
ejpam-5876	167	15	0	0	NUM
ejpam-5876	167	16	,	,	PUNCT
ejpam-5876	167	17	1−k	1−k	NUM
ejpam-5876	167	18	2	2	NUM
ejpam-5876	167	19	]	]	PUNCT
ejpam-5876	167	20	be	be	AUX
ejpam-5876	167	21	such	such	ADJ
ejpam-5876	167	22	that	that	DET
ejpam-5876	167	23	xtqkµ	xtqkµ	NOUN
ejpam-5876	167	24	and	and	CCONJ
ejpam-5876	167	25	yrqkµ.	yrqkµ.	NOUN
ejpam-5876	168	1	then	then	ADV
ejpam-5876	168	2	x	x	SYM
ejpam-5876	168	3	∈	∈	PROPN
ejpam-5876	168	4	ℓµqk	ℓµqk	NOUN
ejpam-5876	168	5	(	(	PUNCT
ejpam-5876	168	6	t	t	PROPN
ejpam-5876	168	7	)	)	PUNCT
ejpam-5876	168	8	and	and	CCONJ
ejpam-5876	168	9	y	y	PROPN
ejpam-5876	168	10	∈	∈	PROPN
ejpam-5876	168	11	ℓµqk	ℓµqk	NOUN
ejpam-5876	168	12	(	(	PUNCT
ejpam-5876	168	13	r	r	NOUN
ejpam-5876	168	14	)	)	PUNCT
ejpam-5876	168	15	.	.	PUNCT
ejpam-5876	169	1	it	it	PRON
ejpam-5876	169	2	follows	follow	VERB
ejpam-5876	169	3	that	that	SCONJ
ejpam-5876	169	4	x	x	SYM
ejpam-5876	169	5	,	,	PUNCT
ejpam-5876	169	6	y	y	PROPN
ejpam-5876	169	7	∈	∈	PROPN
ejpam-5876	169	8	ℓµqk	ℓµqk	NOUN
ejpam-5876	169	9	(	(	PUNCT
ejpam-5876	169	10	max{t	max{t	NOUN
ejpam-5876	169	11	,	,	PUNCT
ejpam-5876	169	12	r	r	NOUN
ejpam-5876	169	13	}	}	PUNCT
ejpam-5876	169	14	)	)	PUNCT
ejpam-5876	169	15	and	and	CCONJ
ejpam-5876	169	16	max{t	max{t	NOUN
ejpam-5876	169	17	,	,	PUNCT
ejpam-5876	169	18	r	r	NOUN
ejpam-5876	169	19	}	}	PUNCT
ejpam-5876	169	20	∈	∈	PROPN
ejpam-5876	169	21	(	(	PUNCT
ejpam-5876	169	22	0	0	NUM
ejpam-5876	169	23	,	,	PUNCT
ejpam-5876	169	24	1−k	1−k	NUM
ejpam-5876	169	25	2	2	NUM
ejpam-5876	169	26	]	]	PUNCT
ejpam-5876	169	27	.	.	PUNCT
ejpam-5876	170	1	thus	thus	ADV
ejpam-5876	170	2	,	,	PUNCT
ejpam-5876	170	3	(	(	PUNCT
ejpam-5876	170	4	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	170	5	)	)	PUNCT
ejpam-5876	170	6	)	)	PUNCT
ejpam-5876	171	1	∈	∈	PROPN
ejpam-5876	171	2	ℓµqk	ℓµqk	NOUN
ejpam-5876	171	3	(	(	PUNCT
ejpam-5876	171	4	max{t	max{t	NOUN
ejpam-5876	171	5	,	,	PUNCT
ejpam-5876	171	6	r	r	NOUN
ejpam-5876	171	7	}	}	PUNCT
ejpam-5876	171	8	)	)	PUNCT
ejpam-5876	171	9	since	since	SCONJ
ejpam-5876	171	10	ℓµqk	ℓµqk	PROPN
ejpam-5876	171	11	(	(	PUNCT
ejpam-5876	171	12	max{t	max{t	NOUN
ejpam-5876	171	13	,	,	PUNCT
ejpam-5876	171	14	r	r	NOUN
ejpam-5876	171	15	}	}	PUNCT
ejpam-5876	171	16	)	)	PUNCT
ejpam-5876	171	17	is	be	AUX
ejpam-5876	171	18	an	an	DET
ejpam-5876	171	19	sup	sup	ADJ
ejpam-5876	171	20	-	-	PUNCT
ejpam-5876	171	21	subalgebra	subalgebra	NOUN
ejpam-5876	171	22	of	of	ADP
ejpam-5876	171	23	x.	x.	NOUN
ejpam-5876	171	24	hence	hence	ADV
ejpam-5876	171	25	,	,	PUNCT
ejpam-5876	171	26	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	171	27	)	)	PUNCT
ejpam-5876	171	28	)	)	PUNCT
ejpam-5876	171	29	)	)	PUNCT
ejpam-5876	172	1	+	+	CCONJ
ejpam-5876	173	1	k	k	X
ejpam-5876	173	2	+	+	NUM
ejpam-5876	173	3	max{t	max{t	NOUN
ejpam-5876	173	4	,	,	PUNCT
ejpam-5876	173	5	r	r	NOUN
ejpam-5876	173	6	}	}	PUNCT
ejpam-5876	173	7	>	>	X
ejpam-5876	173	8	1	1	NUM
ejpam-5876	173	9	,	,	PUNCT
ejpam-5876	173	10	and	and	CCONJ
ejpam-5876	173	11	so	so	ADV
ejpam-5876	173	12	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	173	13	)	)	PUNCT
ejpam-5876	173	14	)	)	PUNCT
ejpam-5876	173	15	)	)	PUNCT
ejpam-5876	173	16	>	>	PUNCT
ejpam-5876	174	1	1	1	NUM
ejpam-5876	174	2	−	−	NOUN
ejpam-5876	174	3	k	k	NOUN
ejpam-5876	174	4	−	−	PROPN
ejpam-5876	174	5	max{t	max{t	NOUN
ejpam-5876	174	6	,	,	PUNCT
ejpam-5876	174	7	r	r	NOUN
ejpam-5876	174	8	}	}	PUNCT
ejpam-5876	174	9	≥	≥	NUM
ejpam-5876	174	10	1−k	1−k	NUM
ejpam-5876	174	11	2	2	NUM
ejpam-5876	174	12	≥	≥	NOUN
ejpam-5876	174	13	max{t	max{t	NOUN
ejpam-5876	174	14	,	,	PUNCT
ejpam-5876	174	15	r	r	NOUN
ejpam-5876	174	16	}	}	PUNCT
ejpam-5876	174	17	.	.	PUNCT
ejpam-5876	175	1	thus	thus	ADV
ejpam-5876	175	2	,	,	PUNCT
ejpam-5876	175	3	(	(	PUNCT
ejpam-5876	175	4	(	(	PUNCT
ejpam-5876	175	5	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	175	6	,	,	PUNCT
ejpam-5876	175	7	r	r	NOUN
ejpam-5876	175	8	}	}	PUNCT
ejpam-5876	175	9	∈	∈	PROPN
ejpam-5876	175	10	µ	µ	X
ejpam-5876	175	11	and	and	CCONJ
ejpam-5876	175	12	(	(	PUNCT
ejpam-5876	175	13	8)	8)	NUM
ejpam-5876	175	14	is	be	AUX
ejpam-5876	175	15	valid	valid	ADJ
ejpam-5876	175	16	.	.	PUNCT
ejpam-5876	176	1	corollary	corollary	ADJ
ejpam-5876	176	2	5	5	NUM
ejpam-5876	176	3	follows	follow	VERB
ejpam-5876	176	4	directly	directly	ADV
ejpam-5876	176	5	from	from	ADP
ejpam-5876	176	6	proposition	proposition	NOUN
ejpam-5876	176	7	3	3	NUM
ejpam-5876	176	8	by	by	ADP
ejpam-5876	176	9	setting	set	VERB
ejpam-5876	176	10	k	k	PROPN
ejpam-5876	176	11	=	=	SYM
ejpam-5876	176	12	0	0	PROPN
ejpam-5876	176	13	,	,	PUNCT
ejpam-5876	176	14	which	which	PRON
ejpam-5876	176	15	implies	imply	VERB
ejpam-5876	176	16	ω	ω	PROPN
ejpam-5876	176	17	=	=	SYM
ejpam-5876	176	18	(	(	PUNCT
ejpam-5876	176	19	0	0	NUM
ejpam-5876	176	20	,	,	PUNCT
ejpam-5876	176	21	0.5	0.5	NUM
ejpam-5876	176	22	]	]	PUNCT
ejpam-5876	176	23	and	and	CCONJ
ejpam-5876	176	24	uses	use	VERB
ejpam-5876	176	25	the	the	DET
ejpam-5876	176	26	standard	standard	ADJ
ejpam-5876	176	27	quasi	quasi	ADJ
ejpam-5876	176	28	-	-	ADJ
ejpam-5876	176	29	coincidence	coincidence	NOUN
ejpam-5876	176	30	operator	operator	NOUN
ejpam-5876	176	31	q.	q.	NOUN
ejpam-5876	176	32	proposition	proposition	NOUN
ejpam-5876	176	33	3	3	NUM
ejpam-5876	176	34	establishes	establish	VERB
ejpam-5876	176	35	that	that	SCONJ
ejpam-5876	176	36	when	when	SCONJ
ejpam-5876	176	37	the	the	DET
ejpam-5876	176	38	fuzzy	fuzzy	ADJ
ejpam-5876	176	39	elements	element	NOUN
ejpam-5876	176	40	xt	xt	X
ejpam-5876	176	41	and	and	CCONJ
ejpam-5876	176	42	yr	yr	VERB
ejpam-5876	176	43	quasi	quasi	NOUN
ejpam-5876	176	44	-	-	NOUN
ejpam-5876	176	45	coincide	coincide	NOUN
ejpam-5876	176	46	with	with	ADP
ejpam-5876	176	47	µ	µ	NOUN
ejpam-5876	176	48	,	,	PUNCT
ejpam-5876	176	49	their	their	PRON
ejpam-5876	176	50	sheffer	sheffer	NOUN
ejpam-5876	176	51	stroke	stroke	NOUN
ejpam-5876	176	52	combination	combination	NOUN
ejpam-5876	176	53	also	also	ADV
ejpam-5876	176	54	satisfies	satisfy	VERB
ejpam-5876	176	55	the	the	DET
ejpam-5876	176	56	membership	membership	NOUN
ejpam-5876	176	57	condition	condition	NOUN
ejpam-5876	176	58	in	in	ADP
ejpam-5876	176	59	µ	µ	NUM
ejpam-5876	176	60	,	,	PUNCT
ejpam-5876	176	61	as	as	SCONJ
ejpam-5876	176	62	required	require	VERB
ejpam-5876	176	63	.	.	PUNCT
ejpam-5876	177	1	corollary	corollary	ADJ
ejpam-5876	177	2	5	5	NUM
ejpam-5876	177	3	.	.	PUNCT
ejpam-5876	178	1	if	if	SCONJ
ejpam-5876	178	2	(	(	PUNCT
ejpam-5876	178	3	x	x	NOUN
ejpam-5876	178	4	,	,	PUNCT
ejpam-5876	178	5	ℓµqk	ℓµqk	PROPN
ejpam-5876	178	6	)	)	PUNCT
ejpam-5876	178	7	is	be	AUX
ejpam-5876	178	8	a	a	DET
ejpam-5876	178	9	semidetached	semidetache	VERB
ejpam-5876	178	10	sup	sup	NOUN
ejpam-5876	178	11	-	-	PUNCT
ejpam-5876	178	12	subalgebra	subalgebra	NOUN
ejpam-5876	178	13	over	over	ADP
ejpam-5876	178	14	ω	ω	NUM
ejpam-5876	178	15	=	=	SYM
ejpam-5876	178	16	(	(	PUNCT
ejpam-5876	178	17	0	0	NUM
ejpam-5876	178	18	,	,	PUNCT
ejpam-5876	178	19	0.5	0.5	NUM
ejpam-5876	178	20	]	]	PUNCT
ejpam-5876	178	21	,	,	PUNCT
ejpam-5876	178	22	then	then	ADV
ejpam-5876	178	23	µ	µ	X
ejpam-5876	178	24	satisfies	satisfie	NOUN
ejpam-5876	178	25	:	:	PUNCT
ejpam-5876	178	26	(	(	PUNCT
ejpam-5876	178	27	∀x	∀x	X
ejpam-5876	178	28	,	,	PUNCT
ejpam-5876	178	29	y	y	PROPN
ejpam-5876	178	30	∈	∈	PROPN
ejpam-5876	178	31	x)(∀t	x)(∀t	PROPN
ejpam-5876	178	32	,	,	PUNCT
ejpam-5876	178	33	r	r	NOUN
ejpam-5876	178	34	∈)(xtqµ	∈)(xtqµ	PROPN
ejpam-5876	178	35	,	,	PUNCT
ejpam-5876	178	36	yrqµ	yrqµ	PROPN
ejpam-5876	178	37	⇒	⇒	PROPN
ejpam-5876	178	38	(	(	PUNCT
ejpam-5876	178	39	(	(	PUNCT
ejpam-5876	178	40	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	178	41	,	,	PUNCT
ejpam-5876	178	42	r	r	NOUN
ejpam-5876	178	43	}	}	PUNCT
ejpam-5876	178	44	∈	∈	PROPN
ejpam-5876	178	45	µ	µ	NUM
ejpam-5876	178	46	)	)	PUNCT
ejpam-5876	178	47	.	.	PUNCT
ejpam-5876	179	1	(	(	PUNCT
ejpam-5876	179	2	9	9	X
ejpam-5876	179	3	)	)	PUNCT
ejpam-5876	179	4	t.	t.	NOUN
ejpam-5876	179	5	oner	oner	NOUN
ejpam-5876	179	6	et	et	PROPN
ejpam-5876	179	7	al	al	PROPN
ejpam-5876	179	8	.	.	PUNCT
ejpam-5876	179	9	/	/	SYM
ejpam-5876	179	10	eur	eur	PROPN
ejpam-5876	179	11	.	.	PUNCT
ejpam-5876	180	1	j.	j.	PROPN
ejpam-5876	180	2	pure	pure	PROPN
ejpam-5876	180	3	appl	appl	PROPN
ejpam-5876	180	4	.	.	PROPN
ejpam-5876	180	5	math	math	PROPN
ejpam-5876	180	6	,	,	PUNCT
ejpam-5876	180	7	18	18	NUM
ejpam-5876	180	8	(	(	PUNCT
ejpam-5876	180	9	2	2	NUM
ejpam-5876	180	10	)	)	PUNCT
ejpam-5876	180	11	(	(	PUNCT
ejpam-5876	180	12	2025	2025	NUM
ejpam-5876	180	13	)	)	PUNCT
ejpam-5876	180	14	,	,	PUNCT
ejpam-5876	180	15	5876	5876	NUM
ejpam-5876	180	16	8	8	NUM
ejpam-5876	180	17	of	of	ADP
ejpam-5876	180	18	16	16	NUM
ejpam-5876	180	19	theorem	theorem	NOUN
ejpam-5876	180	20	5	5	NUM
ejpam-5876	180	21	.	.	PUNCT
ejpam-5876	181	1	if	if	SCONJ
ejpam-5876	181	2	µ	µ	NOUN
ejpam-5876	181	3	is	be	AUX
ejpam-5876	181	4	a	a	DET
ejpam-5876	181	5	k	k	NOUN
ejpam-5876	181	6	-	-	NOUN
ejpam-5876	181	7	right	right	NOUN
ejpam-5876	181	8	(	(	PUNCT
ejpam-5876	181	9	qk,∈	qk,∈	X
ejpam-5876	181	10	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	181	11	sup	sup	ADJ
ejpam-5876	181	12	-	-	PUNCT
ejpam-5876	181	13	subalgebra	subalgebra	NOUN
ejpam-5876	181	14	of	of	ADP
ejpam-5876	181	15	x	x	PRON
ejpam-5876	181	16	,	,	PUNCT
ejpam-5876	181	17	then	then	ADV
ejpam-5876	181	18	(	(	PUNCT
ejpam-5876	181	19	x	x	X
ejpam-5876	181	20	,	,	PUNCT
ejpam-5876	181	21	ℓµqk	ℓµqk	PROPN
ejpam-5876	181	22	)	)	PUNCT
ejpam-5876	181	23	is	be	AUX
ejpam-5876	181	24	a	a	DET
ejpam-5876	181	25	semidetached	semidetache	VERB
ejpam-5876	181	26	sup	sup	NOUN
ejpam-5876	181	27	-	-	PUNCT
ejpam-5876	181	28	subalgebra	subalgebra	NOUN
ejpam-5876	181	29	over	over	ADP
ejpam-5876	181	30	ω	ω	NUM
ejpam-5876	181	31	=	=	SYM
ejpam-5876	181	32	(	(	PUNCT
ejpam-5876	181	33	1−k	1−k	NUM
ejpam-5876	181	34	2	2	NUM
ejpam-5876	181	35	,	,	PUNCT
ejpam-5876	181	36	1	1	NUM
ejpam-5876	181	37	]	]	PUNCT
ejpam-5876	181	38	.	.	PUNCT
ejpam-5876	182	1	proof	proof	NOUN
ejpam-5876	182	2	.	.	PUNCT
ejpam-5876	183	1	let	let	VERB
ejpam-5876	183	2	x	x	PRON
ejpam-5876	183	3	,	,	PUNCT
ejpam-5876	183	4	y	y	PROPN
ejpam-5876	183	5	∈	∈	PROPN
ejpam-5876	183	6	ℓµqk	ℓµqk	PROPN
ejpam-5876	183	7	(	(	PUNCT
ejpam-5876	183	8	t	t	NOUN
ejpam-5876	183	9	)	)	PUNCT
ejpam-5876	183	10	for	for	ADP
ejpam-5876	183	11	t	t	PROPN
ejpam-5876	183	12	∈	∈	PROPN
ejpam-5876	183	13	(	(	PUNCT
ejpam-5876	183	14	1−k	1−k	NUM
ejpam-5876	183	15	2	2	NUM
ejpam-5876	183	16	,	,	PUNCT
ejpam-5876	183	17	1	1	NUM
ejpam-5876	183	18	]	]	PUNCT
ejpam-5876	183	19	.	.	PUNCT
ejpam-5876	184	1	then	then	ADV
ejpam-5876	184	2	xtqkµ	xtqkµ	PROPN
ejpam-5876	184	3	and	and	CCONJ
ejpam-5876	184	4	ytqkµ.	ytqkµ.	NOUN
ejpam-5876	184	5	since	since	SCONJ
ejpam-5876	184	6	µ	µ	NOUN
ejpam-5876	184	7	is	be	AUX
ejpam-5876	184	8	a	a	DET
ejpam-5876	184	9	k	k	NOUN
ejpam-5876	184	10	-	-	NOUN
ejpam-5876	184	11	right	right	NOUN
ejpam-5876	184	12	(	(	PUNCT
ejpam-5876	184	13	qk,∈	qk,∈	X
ejpam-5876	184	14	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	184	15	sup	sup	ADJ
ejpam-5876	184	16	-	-	PUNCT
ejpam-5876	184	17	subalgebra	subalgebra	NOUN
ejpam-5876	184	18	of	of	ADP
ejpam-5876	184	19	x	x	PRON
ejpam-5876	184	20	,	,	PUNCT
ejpam-5876	184	21	we	we	PRON
ejpam-5876	184	22	have	have	VERB
ejpam-5876	184	23	(	(	PUNCT
ejpam-5876	184	24	(	(	PUNCT
ejpam-5876	184	25	x|(y|y))|(x|(y|y)))t	x|(y|y))|(x|(y|y)))t	PROPN
ejpam-5876	184	26	∈	∈	PROPN
ejpam-5876	184	27	∨qkµ	∨qkµ	PROPN
ejpam-5876	184	28	,	,	PUNCT
ejpam-5876	184	29	that	that	ADV
ejpam-5876	184	30	is	is	ADV
ejpam-5876	184	31	,	,	PUNCT
ejpam-5876	184	32	(	(	PUNCT
ejpam-5876	184	33	(	(	PUNCT
ejpam-5876	184	34	x|(y|y))|(x|(y|y)))t	x|(y|y))|(x|(y|y)))t	PROPN
ejpam-5876	184	35	∈	∈	PROPN
ejpam-5876	184	36	µ	µ	X
ejpam-5876	184	37	or	or	CCONJ
ejpam-5876	184	38	(	(	PUNCT
ejpam-5876	184	39	(	(	PUNCT
ejpam-5876	184	40	x|(y|y))|(x|(y|y)))tqkµ.	x|(y|y))|(x|(y|y)))tqkµ.	PUNCT
ejpam-5876	184	41	if	if	SCONJ
ejpam-5876	184	42	(	(	PUNCT
ejpam-5876	184	43	(	(	PUNCT
ejpam-5876	184	44	x|(y|y))|(x|(y|y)))t	x|(y|y))|(x|(y|y)))t	PROPN
ejpam-5876	184	45	∈	∈	PROPN
ejpam-5876	184	46	µ	µ	NOUN
ejpam-5876	184	47	,	,	PUNCT
ejpam-5876	184	48	then	then	ADV
ejpam-5876	184	49	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	184	50	)	)	PUNCT
ejpam-5876	184	51	)	)	PUNCT
ejpam-5876	184	52	)	)	PUNCT
ejpam-5876	185	1	≥	≥	PROPN
ejpam-5876	186	1	t	t	X
ejpam-5876	186	2	>	>	X
ejpam-5876	186	3	1−k	1−k	NUM
ejpam-5876	186	4	2	2	NUM
ejpam-5876	186	5	>	>	SYM
ejpam-5876	186	6	1−	1−	NUM
ejpam-5876	186	7	t−	t−	PROPN
ejpam-5876	186	8	k	k	PROPN
ejpam-5876	186	9	,	,	PUNCT
ejpam-5876	186	10	and	and	CCONJ
ejpam-5876	186	11	so	so	ADV
ejpam-5876	186	12	µ((x|(y|y))|(x|(y|y)))+	µ((x|(y|y))|(x|(y|y)))+	PUNCT
ejpam-5876	186	13	t+	t+	VERB
ejpam-5876	186	14	k	k	PROPN
ejpam-5876	186	15	>	>	X
ejpam-5876	186	16	1	1	NUM
ejpam-5876	186	17	,	,	PUNCT
ejpam-5876	186	18	that	that	ADV
ejpam-5876	186	19	is	is	ADV
ejpam-5876	186	20	,	,	PUNCT
ejpam-5876	186	21	(	(	PUNCT
ejpam-5876	186	22	(	(	PUNCT
ejpam-5876	186	23	x|(y|y))|(x|(y|y)))tqkµ.	x|(y|y))|(x|(y|y)))tqkµ.	X
ejpam-5876	186	24	hence	hence	ADV
ejpam-5876	186	25	,	,	PUNCT
ejpam-5876	186	26	(	(	PUNCT
ejpam-5876	186	27	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	186	28	)	)	PUNCT
ejpam-5876	186	29	)	)	PUNCT
ejpam-5876	187	1	∈	∈	PROPN
ejpam-5876	187	2	ℓµqk	ℓµqk	VERB
ejpam-5876	187	3	.	.	PUNCT
ejpam-5876	188	1	if	if	SCONJ
ejpam-5876	188	2	(	(	PUNCT
ejpam-5876	188	3	(	(	PUNCT
ejpam-5876	188	4	x|(y|y))|(x|(y|y)))tqkµ	x|(y|y))|(x|(y|y)))tqkµ	INTJ
ejpam-5876	188	5	,	,	PUNCT
ejpam-5876	188	6	then	then	ADV
ejpam-5876	188	7	(	(	PUNCT
ejpam-5876	188	8	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	188	9	)	)	PUNCT
ejpam-5876	188	10	)	)	PUNCT
ejpam-5876	188	11	∈	∈	PROPN
ejpam-5876	188	12	ℓµqk	ℓµqk	NOUN
ejpam-5876	188	13	(	(	PUNCT
ejpam-5876	188	14	t	t	PROPN
ejpam-5876	188	15	)	)	PUNCT
ejpam-5876	188	16	.	.	PUNCT
ejpam-5876	189	1	therefore	therefore	ADV
ejpam-5876	189	2	,	,	PUNCT
ejpam-5876	189	3	ℓµqk	ℓµqk	PROPN
ejpam-5876	189	4	(	(	PUNCT
ejpam-5876	189	5	t	t	NOUN
ejpam-5876	189	6	)	)	PUNCT
ejpam-5876	189	7	is	be	AUX
ejpam-5876	189	8	an	an	DET
ejpam-5876	189	9	sup	sup	ADJ
ejpam-5876	189	10	-	-	PUNCT
ejpam-5876	189	11	subalgebra	subalgebra	NOUN
ejpam-5876	189	12	of	of	ADP
ejpam-5876	189	13	x	x	NOUN
ejpam-5876	189	14	,	,	PUNCT
ejpam-5876	189	15	and	and	CCONJ
ejpam-5876	189	16	consequently	consequently	ADV
ejpam-5876	189	17	,	,	PUNCT
ejpam-5876	189	18	(	(	PUNCT
ejpam-5876	189	19	x	x	X
ejpam-5876	189	20	,	,	PUNCT
ejpam-5876	189	21	ℓµqk	ℓµqk	PROPN
ejpam-5876	189	22	)	)	PUNCT
ejpam-5876	189	23	is	be	AUX
ejpam-5876	189	24	a	a	DET
ejpam-5876	189	25	semidetached	semidetache	VERB
ejpam-5876	189	26	sup	sup	NOUN
ejpam-5876	189	27	-	-	PUNCT
ejpam-5876	189	28	subalgebra	subalgebra	NOUN
ejpam-5876	189	29	over	over	ADP
ejpam-5876	189	30	ω	ω	NUM
ejpam-5876	189	31	=	=	SYM
ejpam-5876	189	32	(	(	PUNCT
ejpam-5876	189	33	1−k	1−k	NUM
ejpam-5876	189	34	2	2	NUM
ejpam-5876	189	35	,	,	PUNCT
ejpam-5876	189	36	1	1	NUM
ejpam-5876	189	37	]	]	PUNCT
ejpam-5876	189	38	.	.	PUNCT
ejpam-5876	190	1	corollary	corollary	ADJ
ejpam-5876	190	2	6	6	NUM
ejpam-5876	190	3	is	be	AUX
ejpam-5876	190	4	a	a	DET
ejpam-5876	190	5	direct	direct	ADJ
ejpam-5876	190	6	consequence	consequence	NOUN
ejpam-5876	190	7	of	of	ADP
ejpam-5876	190	8	theorem	theorem	NOUN
ejpam-5876	190	9	5	5	NUM
ejpam-5876	190	10	by	by	ADP
ejpam-5876	190	11	taking	take	VERB
ejpam-5876	190	12	k	k	PROPN
ejpam-5876	190	13	=	=	PUNCT
ejpam-5876	190	14	0	0	PROPN
ejpam-5876	190	15	,	,	PUNCT
ejpam-5876	190	16	which	which	PRON
ejpam-5876	190	17	yields	yield	VERB
ejpam-5876	190	18	the	the	DET
ejpam-5876	190	19	interval	interval	NOUN
ejpam-5876	190	20	ω	ω	PROPN
ejpam-5876	190	21	=	=	SYM
ejpam-5876	190	22	(	(	PUNCT
ejpam-5876	190	23	0.5	0.5	NUM
ejpam-5876	190	24	,	,	PUNCT
ejpam-5876	190	25	1	1	NUM
ejpam-5876	190	26	]	]	PUNCT
ejpam-5876	190	27	and	and	CCONJ
ejpam-5876	190	28	replaces	replace	VERB
ejpam-5876	190	29	qk	qk	NOUN
ejpam-5876	190	30	with	with	ADP
ejpam-5876	190	31	the	the	DET
ejpam-5876	190	32	standard	standard	PROPN
ejpam-5876	190	33	q.	q.	PROPN
ejpam-5876	190	34	since	since	SCONJ
ejpam-5876	190	35	theorem	theorem	VERB
ejpam-5876	190	36	5	5	NUM
ejpam-5876	190	37	ensures	ensure	VERB
ejpam-5876	190	38	that	that	SCONJ
ejpam-5876	190	39	a	a	DET
ejpam-5876	190	40	k	k	NOUN
ejpam-5876	190	41	-	-	NOUN
ejpam-5876	190	42	right	right	NOUN
ejpam-5876	190	43	(	(	PUNCT
ejpam-5876	190	44	qk,∈	qk,∈	X
ejpam-5876	190	45	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	190	46	sup	sup	ADJ
ejpam-5876	190	47	-	-	PUNCT
ejpam-5876	190	48	subalgebra	subalgebra	NOUN
ejpam-5876	190	49	induces	induce	VERB
ejpam-5876	190	50	a	a	DET
ejpam-5876	190	51	semidetached	semidetache	VERB
ejpam-5876	190	52	structure	structure	NOUN
ejpam-5876	190	53	,	,	PUNCT
ejpam-5876	190	54	it	it	PRON
ejpam-5876	190	55	follows	follow	VERB
ejpam-5876	190	56	that	that	SCONJ
ejpam-5876	190	57	a	a	DET
ejpam-5876	190	58	0	0	NUM
ejpam-5876	190	59	-	-	PUNCT
ejpam-5876	190	60	right	right	NOUN
ejpam-5876	190	61	(	(	PUNCT
ejpam-5876	190	62	q,∈	q,∈	NOUN
ejpam-5876	190	63	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	190	64	sup	sup	ADJ
ejpam-5876	190	65	-	-	PUNCT
ejpam-5876	190	66	subalgebra	subalgebra	NOUN
ejpam-5876	190	67	also	also	ADV
ejpam-5876	190	68	generates	generate	VERB
ejpam-5876	190	69	a	a	DET
ejpam-5876	190	70	semidetached	semidetache	VERB
ejpam-5876	190	71	sup	sup	NOUN
ejpam-5876	190	72	-	-	PUNCT
ejpam-5876	190	73	subalgebra	subalgebra	NOUN
ejpam-5876	190	74	over	over	ADP
ejpam-5876	190	75	this	this	DET
ejpam-5876	190	76	interval	interval	NOUN
ejpam-5876	190	77	.	.	PUNCT
ejpam-5876	191	1	corollary	corollary	ADJ
ejpam-5876	191	2	6	6	NUM
ejpam-5876	191	3	.	.	PUNCT
ejpam-5876	192	1	if	if	SCONJ
ejpam-5876	192	2	µ	µ	NOUN
ejpam-5876	192	3	is	be	AUX
ejpam-5876	192	4	a	a	DET
ejpam-5876	192	5	0	0	NUM
ejpam-5876	192	6	-	-	PUNCT
ejpam-5876	192	7	right	right	NOUN
ejpam-5876	192	8	(	(	PUNCT
ejpam-5876	192	9	q,∈	q,∈	NOUN
ejpam-5876	192	10	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	192	11	sup	sup	ADJ
ejpam-5876	192	12	-	-	PUNCT
ejpam-5876	192	13	subalgebra	subalgebra	NOUN
ejpam-5876	192	14	of	of	ADP
ejpam-5876	192	15	x	x	PRON
ejpam-5876	192	16	,	,	PUNCT
ejpam-5876	192	17	then	then	ADV
ejpam-5876	192	18	(	(	PUNCT
ejpam-5876	192	19	x	x	X
ejpam-5876	192	20	,	,	PUNCT
ejpam-5876	192	21	ℓµqk	ℓµqk	PROPN
ejpam-5876	192	22	)	)	PUNCT
ejpam-5876	192	23	is	be	AUX
ejpam-5876	192	24	a	a	DET
ejpam-5876	192	25	semidetached	semidetache	VERB
ejpam-5876	192	26	sup	sup	NOUN
ejpam-5876	192	27	-	-	PUNCT
ejpam-5876	192	28	subalgebra	subalgebra	NOUN
ejpam-5876	192	29	over	over	ADP
ejpam-5876	192	30	ω	ω	NUM
ejpam-5876	192	31	=	=	SYM
ejpam-5876	192	32	(	(	PUNCT
ejpam-5876	192	33	0.5	0.5	NUM
ejpam-5876	192	34	,	,	PUNCT
ejpam-5876	192	35	1	1	NUM
ejpam-5876	192	36	]	]	PUNCT
ejpam-5876	192	37	.	.	PUNCT
ejpam-5876	193	1	4	4	X
ejpam-5876	193	2	.	.	NUM
ejpam-5876	193	3	equivalences	equivalence	NOUN
ejpam-5876	193	4	and	and	CCONJ
ejpam-5876	193	5	characterizations	characterization	NOUN
ejpam-5876	193	6	of	of	ADP
ejpam-5876	193	7	fuzzy	fuzzy	ADJ
ejpam-5876	193	8	sup	sup	NOUN
ejpam-5876	193	9	-	-	PUNCT
ejpam-5876	193	10	subalgebras	subalgebra	NOUN
ejpam-5876	193	11	this	this	DET
ejpam-5876	193	12	section	section	NOUN
ejpam-5876	193	13	is	be	AUX
ejpam-5876	193	14	devoted	devote	VERB
ejpam-5876	193	15	to	to	ADP
ejpam-5876	193	16	a	a	DET
ejpam-5876	193	17	deeper	deep	ADJ
ejpam-5876	193	18	exploration	exploration	NOUN
ejpam-5876	193	19	of	of	ADP
ejpam-5876	193	20	the	the	DET
ejpam-5876	193	21	relationships	relationship	NOUN
ejpam-5876	193	22	between	between	ADP
ejpam-5876	193	23	various	various	ADJ
ejpam-5876	193	24	classes	class	NOUN
ejpam-5876	193	25	of	of	ADP
ejpam-5876	193	26	fuzzy	fuzzy	ADJ
ejpam-5876	193	27	sup	sup	NOUN
ejpam-5876	193	28	-	-	PUNCT
ejpam-5876	193	29	subalgebras	subalgebras	PROPN
ejpam-5876	193	30	and	and	CCONJ
ejpam-5876	193	31	their	their	PRON
ejpam-5876	193	32	role	role	NOUN
ejpam-5876	193	33	in	in	ADP
ejpam-5876	193	34	generating	generate	VERB
ejpam-5876	193	35	semidetached	semidetache	VERB
ejpam-5876	193	36	structures	structure	NOUN
ejpam-5876	193	37	within	within	ADP
ejpam-5876	193	38	sheffer	sheffer	PROPN
ejpam-5876	193	39	stroke	stroke	NOUN
ejpam-5876	193	40	up	up	ADP
ejpam-5876	193	41	-	-	PUNCT
ejpam-5876	193	42	algebras	algebras	X
ejpam-5876	193	43	.	.	PUNCT
ejpam-5876	194	1	building	build	VERB
ejpam-5876	194	2	upon	upon	SCONJ
ejpam-5876	194	3	the	the	DET
ejpam-5876	194	4	foundational	foundational	ADJ
ejpam-5876	194	5	results	result	NOUN
ejpam-5876	194	6	established	establish	VERB
ejpam-5876	194	7	in	in	ADP
ejpam-5876	194	8	the	the	DET
ejpam-5876	194	9	previous	previous	ADJ
ejpam-5876	194	10	section	section	NOUN
ejpam-5876	194	11	,	,	PUNCT
ejpam-5876	194	12	we	we	PRON
ejpam-5876	194	13	present	present	VERB
ejpam-5876	194	14	a	a	DET
ejpam-5876	194	15	series	series	NOUN
ejpam-5876	194	16	of	of	ADP
ejpam-5876	194	17	theorems	theorem	NOUN
ejpam-5876	194	18	and	and	CCONJ
ejpam-5876	194	19	corollaries	corollary	NOUN
ejpam-5876	194	20	that	that	PRON
ejpam-5876	194	21	provide	provide	VERB
ejpam-5876	194	22	necessary	necessary	ADJ
ejpam-5876	194	23	and	and	CCONJ
ejpam-5876	194	24	sufficient	sufficient	ADJ
ejpam-5876	194	25	conditions	condition	NOUN
ejpam-5876	194	26	for	for	ADP
ejpam-5876	194	27	a	a	DET
ejpam-5876	194	28	fuzzy	fuzzy	ADJ
ejpam-5876	194	29	set	set	NOUN
ejpam-5876	194	30	to	to	PART
ejpam-5876	194	31	induce	induce	VERB
ejpam-5876	194	32	a	a	DET
ejpam-5876	194	33	semidetached	semidetache	VERB
ejpam-5876	194	34	sup	sup	NOUN
ejpam-5876	194	35	-	-	PUNCT
ejpam-5876	194	36	subalgebra	subalgebra	NOUN
ejpam-5876	194	37	over	over	ADP
ejpam-5876	194	38	specified	specified	ADJ
ejpam-5876	194	39	subintervals	subinterval	NOUN
ejpam-5876	194	40	of	of	ADP
ejpam-5876	194	41	(	(	PUNCT
ejpam-5876	194	42	0	0	NUM
ejpam-5876	194	43	,	,	PUNCT
ejpam-5876	194	44	1	1	NUM
ejpam-5876	194	45	]	]	PUNCT
ejpam-5876	194	46	.	.	PUNCT
ejpam-5876	195	1	particular	particular	ADJ
ejpam-5876	195	2	emphasis	emphasis	NOUN
ejpam-5876	195	3	is	be	AUX
ejpam-5876	195	4	placed	place	VERB
ejpam-5876	195	5	on	on	ADP
ejpam-5876	195	6	the	the	DET
ejpam-5876	195	7	structural	structural	ADJ
ejpam-5876	195	8	implications	implication	NOUN
ejpam-5876	195	9	of	of	ADP
ejpam-5876	195	10	(	(	PUNCT
ejpam-5876	195	11	∈,∈	∈,∈	X
ejpam-5876	195	12	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	195	13	,	,	PUNCT
ejpam-5876	195	14	k	k	NOUN
ejpam-5876	195	15	-	-	ADJ
ejpam-5876	195	16	left	left	ADJ
ejpam-5876	195	17	,	,	PUNCT
ejpam-5876	195	18	k	k	NOUN
ejpam-5876	195	19	-	-	NOUN
ejpam-5876	195	20	right	right	ADJ
ejpam-5876	195	21	,	,	PUNCT
ejpam-5876	195	22	and	and	CCONJ
ejpam-5876	195	23	(	(	PUNCT
ejpam-5876	195	24	qk,∈	qk,∈	INTJ
ejpam-5876	195	25	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	195	26	sup	sup	NOUN
ejpam-5876	195	27	-	-	PUNCT
ejpam-5876	195	28	subalgebras	subalgebra	NOUN
ejpam-5876	195	29	,	,	PUNCT
ejpam-5876	195	30	along	along	ADP
ejpam-5876	195	31	with	with	ADP
ejpam-5876	195	32	their	their	PRON
ejpam-5876	195	33	interrelationships	interrelationship	NOUN
ejpam-5876	195	34	and	and	CCONJ
ejpam-5876	195	35	equivalences	equivalence	NOUN
ejpam-5876	195	36	.	.	PUNCT
ejpam-5876	196	1	these	these	DET
ejpam-5876	196	2	characterizations	characterization	NOUN
ejpam-5876	196	3	not	not	PART
ejpam-5876	196	4	only	only	ADV
ejpam-5876	196	5	unify	unify	VERB
ejpam-5876	196	6	various	various	ADJ
ejpam-5876	196	7	fuzzy	fuzzy	ADJ
ejpam-5876	196	8	concepts	concept	NOUN
ejpam-5876	196	9	under	under	ADP
ejpam-5876	196	10	a	a	DET
ejpam-5876	196	11	common	common	ADJ
ejpam-5876	196	12	algebraic	algebraic	ADJ
ejpam-5876	196	13	framework	framework	NOUN
ejpam-5876	196	14	but	but	CCONJ
ejpam-5876	196	15	also	also	ADV
ejpam-5876	196	16	demonstrate	demonstrate	VERB
ejpam-5876	196	17	how	how	SCONJ
ejpam-5876	196	18	logical	logical	ADJ
ejpam-5876	196	19	fuzziness	fuzziness	NOUN
ejpam-5876	196	20	can	can	AUX
ejpam-5876	196	21	precisely	precisely	ADV
ejpam-5876	196	22	determine	determine	VERB
ejpam-5876	196	23	the	the	DET
ejpam-5876	196	24	formation	formation	NOUN
ejpam-5876	196	25	of	of	ADP
ejpam-5876	196	26	algebraic	algebraic	ADJ
ejpam-5876	196	27	substructures	substructure	NOUN
ejpam-5876	196	28	.	.	PUNCT
ejpam-5876	197	1	the	the	DET
ejpam-5876	197	2	results	result	NOUN
ejpam-5876	197	3	in	in	ADP
ejpam-5876	197	4	this	this	DET
ejpam-5876	197	5	section	section	NOUN
ejpam-5876	197	6	contribute	contribute	VERB
ejpam-5876	197	7	to	to	ADP
ejpam-5876	197	8	a	a	DET
ejpam-5876	197	9	comprehensive	comprehensive	ADJ
ejpam-5876	197	10	theoretical	theoretical	ADJ
ejpam-5876	197	11	foundation	foundation	NOUN
ejpam-5876	197	12	for	for	ADP
ejpam-5876	197	13	fuzzy	fuzzy	ADJ
ejpam-5876	197	14	logic	logic	NOUN
ejpam-5876	197	15	integration	integration	NOUN
ejpam-5876	197	16	in	in	ADP
ejpam-5876	197	17	algebraic	algebraic	PROPN
ejpam-5876	197	18	systems	system	NOUN
ejpam-5876	197	19	based	base	VERB
ejpam-5876	197	20	on	on	ADP
ejpam-5876	197	21	sheffer	sheffer	NOUN
ejpam-5876	197	22	stroke	stroke	NOUN
ejpam-5876	197	23	operations	operation	NOUN
ejpam-5876	197	24	.	.	PUNCT
ejpam-5876	198	1	theorem	theorem	VERB
ejpam-5876	198	2	6	6	NUM
ejpam-5876	198	3	.	.	PUNCT
ejpam-5876	199	1	for	for	ADP
ejpam-5876	199	2	an	an	DET
ejpam-5876	199	3	sup	sup	ADJ
ejpam-5876	199	4	-	-	PUNCT
ejpam-5876	199	5	subalgebra	subalgebra	NOUN
ejpam-5876	199	6	a	a	PRON
ejpam-5876	199	7	of	of	ADP
ejpam-5876	199	8	x	x	PRON
ejpam-5876	199	9	,	,	PUNCT
ejpam-5876	199	10	let	let	VERB
ejpam-5876	199	11	µ	µ	X
ejpam-5876	199	12	be	be	AUX
ejpam-5876	199	13	a	a	DET
ejpam-5876	199	14	fuzzy	fuzzy	ADJ
ejpam-5876	199	15	set	set	NOUN
ejpam-5876	199	16	in	in	ADP
ejpam-5876	199	17	x	x	INTJ
ejpam-5876	199	18	such	such	ADJ
ejpam-5876	199	19	that	that	SCONJ
ejpam-5876	199	20	(	(	PUNCT
ejpam-5876	199	21	1	1	NUM
ejpam-5876	199	22	)	)	PUNCT
ejpam-5876	199	23	µ(x	µ(x	NOUN
ejpam-5876	199	24	)	)	PUNCT
ejpam-5876	199	25	≥	≥	NOUN
ejpam-5876	199	26	1−k	1−k	NUM
ejpam-5876	199	27	2	2	NUM
ejpam-5876	199	28	for	for	ADP
ejpam-5876	199	29	all	all	DET
ejpam-5876	199	30	x	x	SYM
ejpam-5876	199	31	∈	∈	PROPN
ejpam-5876	199	32	a	a	DET
ejpam-5876	199	33	,	,	PUNCT
ejpam-5876	199	34	(	(	PUNCT
ejpam-5876	199	35	2	2	NUM
ejpam-5876	199	36	)	)	PUNCT
ejpam-5876	199	37	µ(x	µ(x	NOUN
ejpam-5876	199	38	)	)	PUNCT
ejpam-5876	199	39	=	=	SYM
ejpam-5876	199	40	0	0	NUM
ejpam-5876	199	41	for	for	ADP
ejpam-5876	199	42	all	all	DET
ejpam-5876	199	43	x	x	NOUN
ejpam-5876	199	44	∈	∈	PROPN
ejpam-5876	199	45	x\a	x\a	PROPN
ejpam-5876	199	46	.	.	PUNCT
ejpam-5876	200	1	then	then	ADV
ejpam-5876	200	2	µ	µ	X
ejpam-5876	200	3	is	be	AUX
ejpam-5876	200	4	a	a	DET
ejpam-5876	200	5	k	k	NOUN
ejpam-5876	200	6	-	-	ADJ
ejpam-5876	200	7	left	left	ADJ
ejpam-5876	200	8	(	(	PUNCT
ejpam-5876	200	9	qk,∈	qk,∈	X
ejpam-5876	200	10	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	200	11	sup	sup	ADJ
ejpam-5876	200	12	-	-	PUNCT
ejpam-5876	200	13	subalgebra	subalgebra	NOUN
ejpam-5876	200	14	of	of	ADP
ejpam-5876	200	15	x.	x.	NOUN
ejpam-5876	200	16	proof	proof	NOUN
ejpam-5876	200	17	.	.	PUNCT
ejpam-5876	201	1	let	let	VERB
ejpam-5876	201	2	x	x	PRON
ejpam-5876	201	3	,	,	PUNCT
ejpam-5876	201	4	y	y	PROPN
ejpam-5876	201	5	∈	∈	PROPN
ejpam-5876	201	6	x	x	X
ejpam-5876	201	7	and	and	CCONJ
ejpam-5876	201	8	t	t	PROPN
ejpam-5876	201	9	,	,	PUNCT
ejpam-5876	201	10	r	r	NOUN
ejpam-5876	201	11	∈	∈	PROPN
ejpam-5876	201	12	(	(	PUNCT
ejpam-5876	201	13	0	0	NUM
ejpam-5876	201	14	,	,	PUNCT
ejpam-5876	201	15	1−k	1−k	NUM
ejpam-5876	201	16	2	2	NUM
ejpam-5876	201	17	]	]	PUNCT
ejpam-5876	201	18	be	be	AUX
ejpam-5876	201	19	such	such	ADJ
ejpam-5876	201	20	that	that	DET
ejpam-5876	201	21	xtqkµ	xtqkµ	NOUN
ejpam-5876	201	22	and	and	CCONJ
ejpam-5876	201	23	yrqkµ.	yrqkµ.	NOUN
ejpam-5876	201	24	then	then	ADV
ejpam-5876	201	25	µ(x	µ(x	VERB
ejpam-5876	201	26	)	)	PUNCT
ejpam-5876	201	27	+	+	NUM
ejpam-5876	201	28	t	t	NOUN
ejpam-5876	201	29	+	+	CCONJ
ejpam-5876	201	30	k	k	X
ejpam-5876	201	31	>	>	X
ejpam-5876	201	32	1	1	NUM
ejpam-5876	201	33	and	and	CCONJ
ejpam-5876	201	34	µ(y	µ(y	NUM
ejpam-5876	201	35	)	)	PUNCT
ejpam-5876	202	1	+	+	CCONJ
ejpam-5876	202	2	r	r	NOUN
ejpam-5876	202	3	+	+	X
ejpam-5876	202	4	k	k	X
ejpam-5876	202	5	>	>	X
ejpam-5876	202	6	1	1	NUM
ejpam-5876	202	7	,	,	PUNCT
ejpam-5876	202	8	which	which	PRON
ejpam-5876	202	9	imply	imply	VERB
ejpam-5876	202	10	that	that	SCONJ
ejpam-5876	202	11	µ(x	µ(x	VERB
ejpam-5876	202	12	)	)	PUNCT
ejpam-5876	202	13	>	>	X
ejpam-5876	202	14	1	1	NUM
ejpam-5876	202	15	−	−	NOUN
ejpam-5876	202	16	t	t	NOUN
ejpam-5876	202	17	−	−	PROPN
ejpam-5876	202	18	k	k	PROPN
ejpam-5876	202	19	≥	≥	NUM
ejpam-5876	202	20	1−k	1−k	NUM
ejpam-5876	202	21	2	2	NUM
ejpam-5876	202	22	and	and	CCONJ
ejpam-5876	202	23	µ(y	µ(y	NUM
ejpam-5876	202	24	)	)	PUNCT
ejpam-5876	202	25	>	>	X
ejpam-5876	203	1	1	1	NUM
ejpam-5876	203	2	−	−	NOUN
ejpam-5876	203	3	r	r	NOUN
ejpam-5876	203	4	−	−	PROPN
ejpam-5876	203	5	k	k	X
ejpam-5876	203	6	≥	≥	NUM
ejpam-5876	203	7	1−k	1−k	NUM
ejpam-5876	203	8	2	2	NUM
ejpam-5876	203	9	.	.	PUNCT
ejpam-5876	204	1	hence	hence	ADV
ejpam-5876	204	2	,	,	PUNCT
ejpam-5876	204	3	x	x	PUNCT
ejpam-5876	204	4	∈	∈	PROPN
ejpam-5876	204	5	a	a	PRON
ejpam-5876	204	6	and	and	CCONJ
ejpam-5876	204	7	y	y	PROPN
ejpam-5876	204	8	∈	∈	PROPN
ejpam-5876	204	9	a.	a.	NOUN
ejpam-5876	204	10	since	since	SCONJ
ejpam-5876	204	11	a	a	PRON
ejpam-5876	204	12	is	be	AUX
ejpam-5876	204	13	an	an	DET
ejpam-5876	204	14	sup	sup	ADJ
ejpam-5876	204	15	-	-	PUNCT
ejpam-5876	204	16	subalgebra	subalgebra	NOUN
ejpam-5876	204	17	of	of	ADP
ejpam-5876	204	18	x	x	PRON
ejpam-5876	204	19	,	,	PUNCT
ejpam-5876	204	20	t.	t.	PROPN
ejpam-5876	204	21	oner	oner	NOUN
ejpam-5876	204	22	et	et	PROPN
ejpam-5876	204	23	al	al	PROPN
ejpam-5876	204	24	.	.	PUNCT
ejpam-5876	204	25	/	/	SYM
ejpam-5876	204	26	eur	eur	PROPN
ejpam-5876	204	27	.	.	PUNCT
ejpam-5876	205	1	j.	j.	PROPN
ejpam-5876	205	2	pure	pure	PROPN
ejpam-5876	205	3	appl	appl	PROPN
ejpam-5876	205	4	.	.	PROPN
ejpam-5876	205	5	math	math	PROPN
ejpam-5876	205	6	,	,	PUNCT
ejpam-5876	205	7	18	18	NUM
ejpam-5876	205	8	(	(	PUNCT
ejpam-5876	205	9	2	2	NUM
ejpam-5876	205	10	)	)	PUNCT
ejpam-5876	205	11	(	(	PUNCT
ejpam-5876	205	12	2025	2025	NUM
ejpam-5876	205	13	)	)	PUNCT
ejpam-5876	205	14	,	,	PUNCT
ejpam-5876	205	15	5876	5876	NUM
ejpam-5876	205	16	9	9	NUM
ejpam-5876	205	17	of	of	ADP
ejpam-5876	205	18	16	16	NUM
ejpam-5876	205	19	we	we	PRON
ejpam-5876	205	20	get	get	VERB
ejpam-5876	205	21	(	(	PUNCT
ejpam-5876	205	22	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	205	23	)	)	PUNCT
ejpam-5876	205	24	)	)	PUNCT
ejpam-5876	206	1	∈	∈	PROPN
ejpam-5876	206	2	a	a	PRON
ejpam-5876	206	3	,	,	PUNCT
ejpam-5876	206	4	and	and	CCONJ
ejpam-5876	206	5	so	so	ADV
ejpam-5876	206	6	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	206	7	)	)	PUNCT
ejpam-5876	206	8	)	)	PUNCT
ejpam-5876	206	9	)	)	PUNCT
ejpam-5876	206	10	≥	≥	NOUN
ejpam-5876	206	11	1−k	1−k	NUM
ejpam-5876	206	12	2	2	NUM
ejpam-5876	206	13	≥	≥	NOUN
ejpam-5876	206	14	max{t	max{t	NOUN
ejpam-5876	206	15	,	,	PUNCT
ejpam-5876	206	16	r	r	NOUN
ejpam-5876	206	17	}	}	PUNCT
ejpam-5876	206	18	.	.	PUNCT
ejpam-5876	207	1	thus	thus	ADV
ejpam-5876	207	2	,	,	PUNCT
ejpam-5876	207	3	(	(	PUNCT
ejpam-5876	207	4	(	(	PUNCT
ejpam-5876	207	5	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	207	6	,	,	PUNCT
ejpam-5876	207	7	r	r	NOUN
ejpam-5876	207	8	}	}	PUNCT
ejpam-5876	207	9	∈	∈	PROPN
ejpam-5876	207	10	µ	µ	NOUN
ejpam-5876	207	11	,	,	PUNCT
ejpam-5876	207	12	and	and	CCONJ
ejpam-5876	207	13	so	so	ADV
ejpam-5876	207	14	(	(	PUNCT
ejpam-5876	207	15	(	(	PUNCT
ejpam-5876	207	16	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	207	17	,	,	PUNCT
ejpam-5876	207	18	r	r	NOUN
ejpam-5876	207	19	}	}	PUNCT
ejpam-5876	207	20	∈	∈	NOUN
ejpam-5876	207	21	∨qkµ.	∨qkµ.	VERB
ejpam-5876	207	22	therefore	therefore	ADV
ejpam-5876	207	23	,	,	PUNCT
ejpam-5876	207	24	µ	µ	X
ejpam-5876	207	25	is	be	AUX
ejpam-5876	207	26	a	a	DET
ejpam-5876	207	27	k	k	NOUN
ejpam-5876	207	28	-	-	ADJ
ejpam-5876	207	29	left	left	ADJ
ejpam-5876	207	30	(	(	PUNCT
ejpam-5876	207	31	qk,∈	qk,∈	X
ejpam-5876	207	32	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	207	33	sup	sup	ADJ
ejpam-5876	207	34	-	-	PUNCT
ejpam-5876	207	35	subalgebra	subalgebra	NOUN
ejpam-5876	207	36	of	of	ADP
ejpam-5876	207	37	x.	x.	PROPN
ejpam-5876	207	38	corollary	corollary	PROPN
ejpam-5876	207	39	7	7	NUM
ejpam-5876	207	40	is	be	AUX
ejpam-5876	207	41	a	a	DET
ejpam-5876	207	42	special	special	ADJ
ejpam-5876	207	43	case	case	NOUN
ejpam-5876	207	44	of	of	ADP
ejpam-5876	207	45	theorem	theorem	NOUN
ejpam-5876	207	46	6	6	NUM
ejpam-5876	207	47	by	by	ADP
ejpam-5876	207	48	setting	set	VERB
ejpam-5876	207	49	k	k	PROPN
ejpam-5876	207	50	=	=	PUNCT
ejpam-5876	207	51	0	0	X
ejpam-5876	207	52	.	.	PUNCT
ejpam-5876	208	1	in	in	ADP
ejpam-5876	208	2	this	this	DET
ejpam-5876	208	3	case	case	NOUN
ejpam-5876	208	4	,	,	PUNCT
ejpam-5876	208	5	the	the	DET
ejpam-5876	208	6	threshold	threshold	NOUN
ejpam-5876	208	7	1−k	1−k	NUM
ejpam-5876	208	8	2	2	NUM
ejpam-5876	208	9	becomes	become	VERB
ejpam-5876	208	10	0.5	0.5	NUM
ejpam-5876	208	11	,	,	PUNCT
ejpam-5876	208	12	and	and	CCONJ
ejpam-5876	208	13	the	the	DET
ejpam-5876	208	14	conditions	condition	NOUN
ejpam-5876	208	15	in	in	ADP
ejpam-5876	208	16	corollary	corollary	ADJ
ejpam-5876	208	17	7	7	NUM
ejpam-5876	208	18	match	match	NOUN
ejpam-5876	208	19	exactly	exactly	ADV
ejpam-5876	208	20	the	the	DET
ejpam-5876	208	21	assumptions	assumption	NOUN
ejpam-5876	208	22	of	of	ADP
ejpam-5876	208	23	theorem	theorem	NOUN
ejpam-5876	208	24	6	6	NUM
ejpam-5876	208	25	.	.	PUNCT
ejpam-5876	209	1	therefore	therefore	ADV
ejpam-5876	209	2	,	,	PUNCT
ejpam-5876	209	3	the	the	DET
ejpam-5876	209	4	fuzzy	fuzzy	ADJ
ejpam-5876	209	5	set	set	VERB
ejpam-5876	209	6	µ	µ	NOUN
ejpam-5876	209	7	constructed	construct	VERB
ejpam-5876	209	8	as	as	ADP
ejpam-5876	209	9	described	describe	VERB
ejpam-5876	209	10	satisfies	satisfie	NOUN
ejpam-5876	209	11	the	the	DET
ejpam-5876	209	12	definition	definition	NOUN
ejpam-5876	209	13	of	of	ADP
ejpam-5876	209	14	a	a	DET
ejpam-5876	209	15	0	0	ADV
ejpam-5876	209	16	-	-	PUNCT
ejpam-5876	209	17	left	left	ADJ
ejpam-5876	209	18	(	(	PUNCT
ejpam-5876	209	19	q,∈	q,∈	NOUN
ejpam-5876	209	20	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	209	21	sup	sup	ADJ
ejpam-5876	209	22	-	-	PUNCT
ejpam-5876	209	23	subalgebra	subalgebra	NOUN
ejpam-5876	209	24	of	of	ADP
ejpam-5876	209	25	x.	x.	PROPN
ejpam-5876	209	26	corollary	corollary	PROPN
ejpam-5876	209	27	7	7	NUM
ejpam-5876	209	28	.	.	PUNCT
ejpam-5876	209	29	for	for	ADP
ejpam-5876	209	30	an	an	DET
ejpam-5876	209	31	sup	sup	ADJ
ejpam-5876	209	32	-	-	PUNCT
ejpam-5876	209	33	subalgebra	subalgebra	NOUN
ejpam-5876	209	34	a	a	PRON
ejpam-5876	209	35	of	of	ADP
ejpam-5876	209	36	x	x	PRON
ejpam-5876	209	37	,	,	PUNCT
ejpam-5876	209	38	let	let	VERB
ejpam-5876	209	39	µ	µ	X
ejpam-5876	209	40	be	be	AUX
ejpam-5876	209	41	a	a	DET
ejpam-5876	209	42	fuzzy	fuzzy	ADJ
ejpam-5876	209	43	set	set	NOUN
ejpam-5876	209	44	in	in	ADP
ejpam-5876	209	45	x	x	INTJ
ejpam-5876	209	46	such	such	ADJ
ejpam-5876	209	47	that	that	SCONJ
ejpam-5876	209	48	(	(	PUNCT
ejpam-5876	209	49	1	1	NUM
ejpam-5876	209	50	)	)	PUNCT
ejpam-5876	209	51	µ(x	µ(x	NOUN
ejpam-5876	209	52	)	)	PUNCT
ejpam-5876	209	53	≥	≥	NOUN
ejpam-5876	209	54	0.5	0.5	NUM
ejpam-5876	209	55	for	for	ADP
ejpam-5876	209	56	all	all	DET
ejpam-5876	209	57	x	x	PART
ejpam-5876	209	58	∈	∈	PROPN
ejpam-5876	209	59	a	a	DET
ejpam-5876	209	60	,	,	PUNCT
ejpam-5876	209	61	(	(	PUNCT
ejpam-5876	209	62	2	2	NUM
ejpam-5876	209	63	)	)	PUNCT
ejpam-5876	209	64	µ(x	µ(x	NOUN
ejpam-5876	209	65	)	)	PUNCT
ejpam-5876	209	66	=	=	SYM
ejpam-5876	209	67	0	0	NUM
ejpam-5876	209	68	for	for	ADP
ejpam-5876	209	69	all	all	DET
ejpam-5876	209	70	x	x	NOUN
ejpam-5876	209	71	∈	∈	PROPN
ejpam-5876	209	72	x\a	x\a	PROPN
ejpam-5876	209	73	.	.	PUNCT
ejpam-5876	210	1	then	then	ADV
ejpam-5876	210	2	µ	µ	X
ejpam-5876	210	3	is	be	AUX
ejpam-5876	210	4	a	a	DET
ejpam-5876	210	5	0	0	ADV
ejpam-5876	210	6	-	-	PUNCT
ejpam-5876	210	7	left	left	ADJ
ejpam-5876	210	8	(	(	PUNCT
ejpam-5876	210	9	q,∈	q,∈	NOUN
ejpam-5876	210	10	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	210	11	sup	sup	ADJ
ejpam-5876	210	12	-	-	PUNCT
ejpam-5876	210	13	subalgebra	subalgebra	NOUN
ejpam-5876	210	14	of	of	ADP
ejpam-5876	210	15	x.	x.	NOUN
ejpam-5876	210	16	proposition	proposition	NOUN
ejpam-5876	210	17	4	4	NUM
ejpam-5876	210	18	.	.	PUNCT
ejpam-5876	211	1	if	if	SCONJ
ejpam-5876	211	2	(	(	PUNCT
ejpam-5876	211	3	x	x	NOUN
ejpam-5876	211	4	,	,	PUNCT
ejpam-5876	211	5	ℓµek	ℓµek	NOUN
ejpam-5876	211	6	)	)	PUNCT
ejpam-5876	211	7	is	be	AUX
ejpam-5876	211	8	a	a	DET
ejpam-5876	211	9	semidetached	semidetache	VERB
ejpam-5876	211	10	sup	sup	NOUN
ejpam-5876	211	11	-	-	PUNCT
ejpam-5876	211	12	subalgebra	subalgebra	NOUN
ejpam-5876	211	13	over	over	ADP
ejpam-5876	211	14	ω	ω	NUM
ejpam-5876	211	15	=	=	SYM
ejpam-5876	211	16	(	(	PUNCT
ejpam-5876	211	17	1−k	1−k	NUM
ejpam-5876	211	18	2	2	NUM
ejpam-5876	211	19	,	,	PUNCT
ejpam-5876	211	20	1	1	NUM
ejpam-5876	211	21	]	]	PUNCT
ejpam-5876	211	22	,	,	PUNCT
ejpam-5876	211	23	then	then	ADV
ejpam-5876	211	24	µ	µ	X
ejpam-5876	211	25	satisfies	satisfie	NOUN
ejpam-5876	211	26	:	:	PUNCT
ejpam-5876	211	27	(	(	PUNCT
ejpam-5876	211	28	∀x	∀x	X
ejpam-5876	211	29	,	,	PUNCT
ejpam-5876	211	30	y	y	PROPN
ejpam-5876	211	31	∈	∈	PROPN
ejpam-5876	211	32	x)(∀t	x)(∀t	PROPN
ejpam-5876	211	33	,	,	PUNCT
ejpam-5876	211	34	r	r	PROPN
ejpam-5876	211	35	∈	∈	PROPN
ejpam-5876	211	36	ω)(xtqkµ	ω)(xtqkµ	NUM
ejpam-5876	211	37	,	,	PUNCT
ejpam-5876	211	38	yrqkµ	yrqkµ	NOUN
ejpam-5876	211	39	⇒	⇒	NOUN
ejpam-5876	211	40	(	(	PUNCT
ejpam-5876	211	41	(	(	PUNCT
ejpam-5876	211	42	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	211	43	,	,	PUNCT
ejpam-5876	211	44	r	r	NOUN
ejpam-5876	211	45	}	}	PUNCT
ejpam-5876	211	46	∈	∈	PROPN
ejpam-5876	211	47	∨qkµ	∨qkµ	PROPN
ejpam-5876	211	48	)	)	PUNCT
ejpam-5876	211	49	.	.	PUNCT
ejpam-5876	212	1	(	(	PUNCT
ejpam-5876	212	2	10	10	NUM
ejpam-5876	212	3	)	)	PUNCT
ejpam-5876	212	4	proof	proof	NOUN
ejpam-5876	212	5	.	.	PUNCT
ejpam-5876	213	1	let	let	VERB
ejpam-5876	213	2	x	x	PRON
ejpam-5876	213	3	,	,	PUNCT
ejpam-5876	213	4	y	y	PROPN
ejpam-5876	213	5	∈	∈	PROPN
ejpam-5876	213	6	x	x	X
ejpam-5876	213	7	and	and	CCONJ
ejpam-5876	213	8	t	t	PROPN
ejpam-5876	213	9	,	,	PUNCT
ejpam-5876	213	10	r	r	NOUN
ejpam-5876	213	11	∈	∈	PROPN
ejpam-5876	213	12	ω	ω	NUM
ejpam-5876	213	13	=	=	SYM
ejpam-5876	213	14	(	(	PUNCT
ejpam-5876	213	15	0	0	NUM
ejpam-5876	213	16	,	,	PUNCT
ejpam-5876	213	17	1	1	NUM
ejpam-5876	213	18	]	]	PUNCT
ejpam-5876	213	19	be	be	AUX
ejpam-5876	213	20	such	such	ADJ
ejpam-5876	213	21	that	that	DET
ejpam-5876	213	22	xtqkµ	xtqkµ	NOUN
ejpam-5876	213	23	and	and	CCONJ
ejpam-5876	213	24	yrqkµ.	yrqkµ.	NOUN
ejpam-5876	214	1	then	then	ADV
ejpam-5876	214	2	x	x	SYM
ejpam-5876	214	3	∈	∈	PROPN
ejpam-5876	214	4	ℓµqk	ℓµqk	NOUN
ejpam-5876	214	5	(	(	PUNCT
ejpam-5876	214	6	t	t	PROPN
ejpam-5876	214	7	)	)	PUNCT
ejpam-5876	214	8	⊆	⊆	NUM
ejpam-5876	214	9	ℓµek	ℓµek	NOUN
ejpam-5876	214	10	(	(	PUNCT
ejpam-5876	214	11	t	t	PROPN
ejpam-5876	214	12	)	)	PUNCT
ejpam-5876	214	13	and	and	CCONJ
ejpam-5876	214	14	y	y	PROPN
ejpam-5876	214	15	∈	∈	PROPN
ejpam-5876	214	16	ℓµqk	ℓµqk	NOUN
ejpam-5876	214	17	(	(	PUNCT
ejpam-5876	214	18	r	r	NOUN
ejpam-5876	214	19	)	)	PUNCT
ejpam-5876	214	20	⊆	⊆	NUM
ejpam-5876	214	21	ℓµek	ℓµek	NOUN
ejpam-5876	214	22	(	(	PUNCT
ejpam-5876	214	23	r	r	NOUN
ejpam-5876	214	24	)	)	PUNCT
ejpam-5876	214	25	.	.	PUNCT
ejpam-5876	215	1	it	it	PRON
ejpam-5876	215	2	follows	follow	VERB
ejpam-5876	215	3	that	that	SCONJ
ejpam-5876	215	4	x	x	SYM
ejpam-5876	215	5	,	,	PUNCT
ejpam-5876	215	6	y	y	PROPN
ejpam-5876	215	7	∈	∈	PROPN
ejpam-5876	215	8	ℓµek	ℓµek	NOUN
ejpam-5876	215	9	(	(	PUNCT
ejpam-5876	215	10	max{t	max{t	NOUN
ejpam-5876	215	11	,	,	PUNCT
ejpam-5876	215	12	r	r	NOUN
ejpam-5876	215	13	}	}	PUNCT
ejpam-5876	215	14	)	)	PUNCT
ejpam-5876	215	15	,	,	PUNCT
ejpam-5876	215	16	and	and	CCONJ
ejpam-5876	215	17	so	so	ADV
ejpam-5876	215	18	from	from	ADP
ejpam-5876	215	19	the	the	DET
ejpam-5876	215	20	hypothesis	hypothesis	NOUN
ejpam-5876	216	1	that	that	SCONJ
ejpam-5876	216	2	(	(	PUNCT
ejpam-5876	216	3	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	216	4	)	)	PUNCT
ejpam-5876	216	5	)	)	PUNCT
ejpam-5876	217	1	∈	∈	PROPN
ejpam-5876	217	2	ℓµek	ℓµek	NOUN
ejpam-5876	217	3	(	(	PUNCT
ejpam-5876	217	4	max{t	max{t	NOUN
ejpam-5876	217	5	,	,	PUNCT
ejpam-5876	217	6	r	r	NOUN
ejpam-5876	217	7	}	}	PUNCT
ejpam-5876	217	8	)	)	PUNCT
ejpam-5876	217	9	.	.	PUNCT
ejpam-5876	218	1	hence	hence	ADV
ejpam-5876	218	2	,	,	PUNCT
ejpam-5876	218	3	(	(	PUNCT
ejpam-5876	218	4	(	(	PUNCT
ejpam-5876	218	5	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	218	6	,	,	PUNCT
ejpam-5876	218	7	r	r	NOUN
ejpam-5876	218	8	}	}	PUNCT
ejpam-5876	218	9	∈	∈	PROPN
ejpam-5876	218	10	∨qkµ	∨qkµ	PROPN
ejpam-5876	218	11	,	,	PUNCT
ejpam-5876	218	12	and	and	CCONJ
ejpam-5876	218	13	consequently	consequently	ADV
ejpam-5876	218	14	,	,	PUNCT
ejpam-5876	218	15	(	(	PUNCT
ejpam-5876	218	16	10	10	NUM
ejpam-5876	218	17	)	)	PUNCT
ejpam-5876	218	18	is	be	AUX
ejpam-5876	218	19	valid	valid	ADJ
ejpam-5876	218	20	.	.	PUNCT
ejpam-5876	219	1	corollary	corollary	ADJ
ejpam-5876	219	2	8	8	NUM
ejpam-5876	219	3	follows	follow	VERB
ejpam-5876	219	4	directly	directly	ADV
ejpam-5876	219	5	from	from	ADP
ejpam-5876	219	6	proposition	proposition	NOUN
ejpam-5876	219	7	4	4	NUM
ejpam-5876	219	8	by	by	ADP
ejpam-5876	219	9	taking	take	VERB
ejpam-5876	219	10	k	k	PROPN
ejpam-5876	219	11	=	=	PUNCT
ejpam-5876	219	12	0	0	PROPN
ejpam-5876	219	13	,	,	PUNCT
ejpam-5876	219	14	which	which	PRON
ejpam-5876	219	15	implies	imply	VERB
ejpam-5876	219	16	that	that	SCONJ
ejpam-5876	219	17	ω	ω	PROPN
ejpam-5876	219	18	=	=	SYM
ejpam-5876	219	19	(	(	PUNCT
ejpam-5876	219	20	0.5	0.5	NUM
ejpam-5876	219	21	,	,	PUNCT
ejpam-5876	219	22	1	1	NUM
ejpam-5876	219	23	]	]	PUNCT
ejpam-5876	219	24	and	and	CCONJ
ejpam-5876	219	25	the	the	DET
ejpam-5876	219	26	fuzzy	fuzzy	ADJ
ejpam-5876	219	27	quasi	quasi	ADJ
ejpam-5876	219	28	-	-	ADJ
ejpam-5876	219	29	coincidence	coincidence	NOUN
ejpam-5876	219	30	operator	operator	NOUN
ejpam-5876	219	31	qk	qk	NOUN
ejpam-5876	219	32	becomes	become	VERB
ejpam-5876	219	33	the	the	DET
ejpam-5876	219	34	standard	standard	ADJ
ejpam-5876	219	35	q.	q.	NOUN
ejpam-5876	219	36	corollary	corollary	NOUN
ejpam-5876	219	37	8	8	NUM
ejpam-5876	219	38	.	.	PUNCT
ejpam-5876	220	1	if	if	SCONJ
ejpam-5876	220	2	(	(	PUNCT
ejpam-5876	220	3	x	x	NOUN
ejpam-5876	220	4	,	,	PUNCT
ejpam-5876	220	5	ℓµqk	ℓµqk	PROPN
ejpam-5876	220	6	)	)	PUNCT
ejpam-5876	220	7	is	be	AUX
ejpam-5876	220	8	a	a	DET
ejpam-5876	220	9	semidetached	semidetache	VERB
ejpam-5876	220	10	sup	sup	NOUN
ejpam-5876	220	11	-	-	PUNCT
ejpam-5876	220	12	subalgebra	subalgebra	NOUN
ejpam-5876	220	13	over	over	ADP
ejpam-5876	220	14	ω	ω	NUM
ejpam-5876	220	15	=	=	SYM
ejpam-5876	220	16	(	(	PUNCT
ejpam-5876	220	17	1−k	1−k	NUM
ejpam-5876	220	18	2	2	NUM
ejpam-5876	220	19	,	,	PUNCT
ejpam-5876	220	20	1	1	NUM
ejpam-5876	220	21	]	]	PUNCT
ejpam-5876	220	22	,	,	PUNCT
ejpam-5876	220	23	then	then	ADV
ejpam-5876	220	24	µ	µ	X
ejpam-5876	220	25	satisfies	satisfie	NOUN
ejpam-5876	220	26	:	:	PUNCT
ejpam-5876	220	27	(	(	PUNCT
ejpam-5876	220	28	∀x	∀x	X
ejpam-5876	220	29	,	,	PUNCT
ejpam-5876	220	30	y	y	PROPN
ejpam-5876	220	31	∈	∈	PROPN
ejpam-5876	220	32	x)(∀t	x)(∀t	PROPN
ejpam-5876	220	33	,	,	PUNCT
ejpam-5876	220	34	r	r	NOUN
ejpam-5876	220	35	∈	∈	PROPN
ejpam-5876	220	36	ω)(xtqµ	ω)(xtqµ	NUM
ejpam-5876	220	37	,	,	PUNCT
ejpam-5876	220	38	yrqµ	yrqµ	PROPN
ejpam-5876	220	39	⇒	⇒	NOUN
ejpam-5876	220	40	(	(	PUNCT
ejpam-5876	220	41	(	(	PUNCT
ejpam-5876	220	42	x|(y|y))|(x|(y|y)))max{t	x|(y|y))|(x|(y|y)))max{t	NOUN
ejpam-5876	220	43	,	,	PUNCT
ejpam-5876	220	44	r	r	NOUN
ejpam-5876	220	45	}	}	PUNCT
ejpam-5876	220	46	∈	∈	PROPN
ejpam-5876	220	47	∨qµ	∨qµ	NOUN
ejpam-5876	220	48	)	)	PUNCT
ejpam-5876	220	49	.	.	PUNCT
ejpam-5876	221	1	(	(	PUNCT
ejpam-5876	221	2	11	11	NUM
ejpam-5876	221	3	)	)	PUNCT
ejpam-5876	221	4	the	the	DET
ejpam-5876	221	5	following	follow	VERB
ejpam-5876	221	6	lemma	lemma	PROPN
ejpam-5876	221	7	is	be	AUX
ejpam-5876	221	8	directly	directly	ADV
ejpam-5876	221	9	proved	prove	VERB
ejpam-5876	221	10	by	by	ADP
ejpam-5876	221	11	definition	definition	NOUN
ejpam-5876	221	12	5	5	NUM
ejpam-5876	221	13	.	.	PUNCT
ejpam-5876	222	1	lemma	lemma	PROPN
ejpam-5876	222	2	3	3	NUM
ejpam-5876	222	3	.	.	PUNCT
ejpam-5876	223	1	a	a	DET
ejpam-5876	223	2	fuzzy	fuzzy	ADJ
ejpam-5876	223	3	set	set	VERB
ejpam-5876	223	4	µ	µ	NOUN
ejpam-5876	223	5	in	in	ADP
ejpam-5876	223	6	x	x	VERB
ejpam-5876	223	7	is	be	AUX
ejpam-5876	223	8	an	an	DET
ejpam-5876	223	9	(	(	PUNCT
ejpam-5876	223	10	∈,∈	∈,∈	X
ejpam-5876	223	11	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	223	12	sup	sup	ADJ
ejpam-5876	223	13	-	-	PUNCT
ejpam-5876	223	14	subalgebra	subalgebra	NOUN
ejpam-5876	223	15	of	of	ADP
ejpam-5876	223	16	x	x	PRON
ejpam-5876	223	17	if	if	SCONJ
ejpam-5876	223	18	and	and	CCONJ
ejpam-5876	223	19	only	only	ADV
ejpam-5876	223	20	if	if	SCONJ
ejpam-5876	223	21	it	it	PRON
ejpam-5876	223	22	satisfies	satisfy	VERB
ejpam-5876	223	23	the	the	DET
ejpam-5876	223	24	following	following	NOUN
ejpam-5876	223	25	:	:	PUNCT
ejpam-5876	223	26	(	(	PUNCT
ejpam-5876	223	27	∀x	∀x	X
ejpam-5876	223	28	,	,	PUNCT
ejpam-5876	223	29	y	y	PROPN
ejpam-5876	223	30	∈	∈	PROPN
ejpam-5876	223	31	x)(µ((x|(y|y))|(x|(y|y	x)(µ((x|(y|y))|(x|(y|y	PROPN
ejpam-5876	223	32	)	)	PUNCT
ejpam-5876	223	33	)	)	PUNCT
ejpam-5876	223	34	)	)	PUNCT
ejpam-5876	223	35	≥	≥	NOUN
ejpam-5876	224	1	min{µ(x	min{µ(x	NOUN
ejpam-5876	224	2	)	)	PUNCT
ejpam-5876	224	3	,	,	PUNCT
ejpam-5876	224	4	µ(y	µ(y	PROPN
ejpam-5876	224	5	)	)	PUNCT
ejpam-5876	224	6	,	,	PUNCT
ejpam-5876	224	7	1−	1−	NUM
ejpam-5876	224	8	k	k	NOUN
ejpam-5876	224	9	2	2	NUM
ejpam-5876	224	10	}	}	PUNCT
ejpam-5876	224	11	)	)	PUNCT
ejpam-5876	224	12	.	.	PUNCT
ejpam-5876	225	1	(	(	PUNCT
ejpam-5876	225	2	12	12	NUM
ejpam-5876	225	3	)	)	PUNCT
ejpam-5876	225	4	theorem	theorem	NOUN
ejpam-5876	225	5	7	7	NUM
ejpam-5876	225	6	.	.	PUNCT
ejpam-5876	226	1	if	if	SCONJ
ejpam-5876	226	2	µ	µ	NOUN
ejpam-5876	226	3	is	be	AUX
ejpam-5876	226	4	an	an	DET
ejpam-5876	226	5	(	(	PUNCT
ejpam-5876	226	6	∈,∈	∈,∈	X
ejpam-5876	226	7	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	226	8	sup	sup	ADJ
ejpam-5876	226	9	-	-	PUNCT
ejpam-5876	226	10	subalgebra	subalgebra	NOUN
ejpam-5876	226	11	of	of	ADP
ejpam-5876	226	12	x	x	PRON
ejpam-5876	226	13	,	,	PUNCT
ejpam-5876	226	14	then	then	ADV
ejpam-5876	226	15	(	(	PUNCT
ejpam-5876	226	16	x	x	X
ejpam-5876	226	17	,	,	PUNCT
ejpam-5876	226	18	ℓµqk	ℓµqk	PROPN
ejpam-5876	226	19	)	)	PUNCT
ejpam-5876	226	20	is	be	AUX
ejpam-5876	226	21	a	a	DET
ejpam-5876	226	22	semidetached	semidetache	VERB
ejpam-5876	226	23	sup	sup	NOUN
ejpam-5876	226	24	-	-	PUNCT
ejpam-5876	226	25	subalgebra	subalgebra	NOUN
ejpam-5876	226	26	over	over	ADP
ejpam-5876	226	27	ω	ω	NUM
ejpam-5876	226	28	=	=	SYM
ejpam-5876	226	29	(	(	PUNCT
ejpam-5876	226	30	1−k	1−k	NUM
ejpam-5876	226	31	2	2	NUM
ejpam-5876	226	32	,	,	PUNCT
ejpam-5876	226	33	1	1	NUM
ejpam-5876	226	34	]	]	PUNCT
ejpam-5876	226	35	.	.	PUNCT
ejpam-5876	227	1	t.	t.	PROPN
ejpam-5876	227	2	oner	oner	PROPN
ejpam-5876	227	3	et	et	PROPN
ejpam-5876	227	4	al	al	PROPN
ejpam-5876	227	5	.	.	PUNCT
ejpam-5876	227	6	/	/	SYM
ejpam-5876	227	7	eur	eur	PROPN
ejpam-5876	227	8	.	.	PUNCT
ejpam-5876	228	1	j.	j.	PROPN
ejpam-5876	228	2	pure	pure	PROPN
ejpam-5876	228	3	appl	appl	PROPN
ejpam-5876	228	4	.	.	PROPN
ejpam-5876	228	5	math	math	PROPN
ejpam-5876	228	6	,	,	PUNCT
ejpam-5876	228	7	18	18	NUM
ejpam-5876	228	8	(	(	PUNCT
ejpam-5876	228	9	2	2	NUM
ejpam-5876	228	10	)	)	PUNCT
ejpam-5876	228	11	(	(	PUNCT
ejpam-5876	228	12	2025	2025	NUM
ejpam-5876	228	13	)	)	PUNCT
ejpam-5876	228	14	,	,	PUNCT
ejpam-5876	228	15	5876	5876	NUM
ejpam-5876	228	16	10	10	NUM
ejpam-5876	228	17	of	of	ADP
ejpam-5876	228	18	16	16	NUM
ejpam-5876	228	19	proof	proof	NOUN
ejpam-5876	228	20	.	.	PUNCT
ejpam-5876	229	1	let	let	VERB
ejpam-5876	229	2	x	x	PRON
ejpam-5876	229	3	,	,	PUNCT
ejpam-5876	229	4	y	y	PROPN
ejpam-5876	229	5	∈	∈	PROPN
ejpam-5876	229	6	ℓµqk	ℓµqk	PROPN
ejpam-5876	229	7	(	(	PUNCT
ejpam-5876	229	8	t	t	NOUN
ejpam-5876	229	9	)	)	PUNCT
ejpam-5876	229	10	for	for	ADP
ejpam-5876	229	11	t	t	PROPN
ejpam-5876	229	12	∈	∈	PROPN
ejpam-5876	229	13	ω	ω	PROPN
ejpam-5876	229	14	=	=	SYM
ejpam-5876	229	15	(	(	PUNCT
ejpam-5876	229	16	1−k	1−k	NUM
ejpam-5876	229	17	2	2	NUM
ejpam-5876	229	18	,	,	PUNCT
ejpam-5876	229	19	1	1	NUM
ejpam-5876	229	20	]	]	PUNCT
ejpam-5876	229	21	.	.	PUNCT
ejpam-5876	230	1	then	then	ADV
ejpam-5876	230	2	xtqkµ	xtqkµ	PROPN
ejpam-5876	230	3	and	and	CCONJ
ejpam-5876	230	4	ytqkµ	ytqkµ	PROPN
ejpam-5876	230	5	,	,	PUNCT
ejpam-5876	230	6	that	that	ADV
ejpam-5876	230	7	is	is	ADV
ejpam-5876	230	8	,	,	PUNCT
ejpam-5876	230	9	µ(x)+	µ(x)+	ADP
ejpam-5876	230	10	t+	t+	NOUN
ejpam-5876	230	11	k	k	PROPN
ejpam-5876	230	12	>	>	X
ejpam-5876	230	13	1	1	NUM
ejpam-5876	230	14	and	and	CCONJ
ejpam-5876	230	15	µ(y	µ(y	NUM
ejpam-5876	230	16	)	)	PUNCT
ejpam-5876	230	17	+	+	CCONJ
ejpam-5876	230	18	t+	t+	VERB
ejpam-5876	230	19	k	k	X
ejpam-5876	230	20	>	>	X
ejpam-5876	230	21	1	1	X
ejpam-5876	230	22	.	.	PUNCT
ejpam-5876	231	1	it	it	PRON
ejpam-5876	231	2	follows	follow	VERB
ejpam-5876	231	3	from	from	ADP
ejpam-5876	231	4	lemma	lemma	PROPN
ejpam-5876	231	5	3	3	NUM
ejpam-5876	231	6	that	that	SCONJ
ejpam-5876	231	7	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	VERB
ejpam-5876	231	8	)	)	PUNCT
ejpam-5876	231	9	)	)	PUNCT
ejpam-5876	231	10	)	)	PUNCT
ejpam-5876	232	1	+	+	CCONJ
ejpam-5876	232	2	t+	t+	VERB
ejpam-5876	232	3	k	k	X
ejpam-5876	232	4	≥	≥	NOUN
ejpam-5876	232	5	min{µ(x	min{µ(x	PROPN
ejpam-5876	232	6	)	)	PUNCT
ejpam-5876	232	7	,	,	PUNCT
ejpam-5876	232	8	µ(y	µ(y	PROPN
ejpam-5876	232	9	)	)	PUNCT
ejpam-5876	232	10	,	,	PUNCT
ejpam-5876	232	11	1−k	1−k	NUM
ejpam-5876	232	12	2	2	NUM
ejpam-5876	232	13	}	}	PUNCT
ejpam-5876	232	14	+	+	NUM
ejpam-5876	232	15	t	t	NOUN
ejpam-5876	232	16	+	+	CCONJ
ejpam-5876	232	17	k	k	PROPN
ejpam-5876	232	18	=	=	SYM
ejpam-5876	232	19	min{µ(x	min{µ(x	PROPN
ejpam-5876	232	20	)	)	PUNCT
ejpam-5876	233	1	+	+	NUM
ejpam-5876	233	2	t	t	NOUN
ejpam-5876	233	3	+	+	CCONJ
ejpam-5876	233	4	k	k	PROPN
ejpam-5876	233	5	,	,	PUNCT
ejpam-5876	233	6	µ(y	µ(y	PROPN
ejpam-5876	233	7	)	)	PUNCT
ejpam-5876	234	1	+	+	NUM
ejpam-5876	234	2	t	t	NOUN
ejpam-5876	234	3	+	+	CCONJ
ejpam-5876	234	4	k	k	PROPN
ejpam-5876	234	5	,	,	PUNCT
ejpam-5876	234	6	1−k	1−k	NUM
ejpam-5876	234	7	2	2	NUM
ejpam-5876	234	8	+	+	NUM
ejpam-5876	234	9	t	t	NOUN
ejpam-5876	234	10	+	+	CCONJ
ejpam-5876	234	11	k	k	X
ejpam-5876	234	12	}	}	PUNCT
ejpam-5876	234	13	>	>	X
ejpam-5876	234	14	1	1	X
ejpam-5876	234	15	.	.	PUNCT
ejpam-5876	235	1	hence	hence	ADV
ejpam-5876	235	2	,	,	PUNCT
ejpam-5876	235	3	(	(	PUNCT
ejpam-5876	235	4	(	(	PUNCT
ejpam-5876	235	5	x|(y|y))|(x|(y|y)))tqkµ	x|(y|y))|(x|(y|y)))tqkµ	INTJ
ejpam-5876	235	6	,	,	PUNCT
ejpam-5876	235	7	and	and	CCONJ
ejpam-5876	235	8	so	so	ADV
ejpam-5876	235	9	(	(	PUNCT
ejpam-5876	235	10	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	235	11	)	)	PUNCT
ejpam-5876	235	12	)	)	PUNCT
ejpam-5876	235	13	∈	∈	PROPN
ejpam-5876	235	14	ℓµqk	ℓµqk	NOUN
ejpam-5876	235	15	(	(	PUNCT
ejpam-5876	235	16	t	t	PROPN
ejpam-5876	235	17	)	)	PUNCT
ejpam-5876	235	18	.	.	PUNCT
ejpam-5876	236	1	therefore	therefore	ADV
ejpam-5876	236	2	,	,	PUNCT
ejpam-5876	236	3	ℓµqk	ℓµqk	PROPN
ejpam-5876	236	4	(	(	PUNCT
ejpam-5876	236	5	t	t	NOUN
ejpam-5876	236	6	)	)	PUNCT
ejpam-5876	236	7	is	be	AUX
ejpam-5876	236	8	an	an	DET
ejpam-5876	236	9	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	236	10	of	of	ADP
ejpam-5876	236	11	x	x	PUNCT
ejpam-5876	236	12	for	for	ADP
ejpam-5876	236	13	all	all	DET
ejpam-5876	236	14	t	t	NOUN
ejpam-5876	236	15	∈	∈	PROPN
ejpam-5876	236	16	(	(	PUNCT
ejpam-5876	236	17	1−k	1−k	NUM
ejpam-5876	236	18	2	2	NUM
ejpam-5876	236	19	,	,	PUNCT
ejpam-5876	236	20	1	1	NUM
ejpam-5876	236	21	]	]	PUNCT
ejpam-5876	236	22	,	,	PUNCT
ejpam-5876	236	23	and	and	CCONJ
ejpam-5876	236	24	consequently	consequently	ADV
ejpam-5876	236	25	,	,	PUNCT
ejpam-5876	236	26	(	(	PUNCT
ejpam-5876	236	27	x	x	X
ejpam-5876	236	28	,	,	PUNCT
ejpam-5876	236	29	ℓµqk	ℓµqk	PROPN
ejpam-5876	236	30	)	)	PUNCT
ejpam-5876	236	31	is	be	AUX
ejpam-5876	236	32	a	a	DET
ejpam-5876	236	33	semidetached	semidetached	ADJ
ejpam-5876	236	34	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	236	35	over	over	ADP
ejpam-5876	236	36	ω	ω	PROPN
ejpam-5876	236	37	=	=	SYM
ejpam-5876	236	38	(	(	PUNCT
ejpam-5876	236	39	1−k	1−k	NUM
ejpam-5876	236	40	2	2	NUM
ejpam-5876	236	41	,	,	PUNCT
ejpam-5876	236	42	1	1	NUM
ejpam-5876	236	43	]	]	PUNCT
ejpam-5876	236	44	.	.	PUNCT
ejpam-5876	237	1	corollary	corollary	ADJ
ejpam-5876	237	2	9	9	NUM
ejpam-5876	237	3	is	be	AUX
ejpam-5876	237	4	a	a	DET
ejpam-5876	237	5	special	special	ADJ
ejpam-5876	237	6	case	case	NOUN
ejpam-5876	237	7	of	of	ADP
ejpam-5876	237	8	theorem	theorem	NOUN
ejpam-5876	237	9	7	7	NUM
ejpam-5876	237	10	by	by	ADP
ejpam-5876	237	11	setting	set	VERB
ejpam-5876	237	12	k	k	PROPN
ejpam-5876	237	13	=	=	SYM
ejpam-5876	237	14	0	0	PROPN
ejpam-5876	237	15	,	,	PUNCT
ejpam-5876	237	16	which	which	PRON
ejpam-5876	237	17	leads	lead	VERB
ejpam-5876	237	18	to	to	ADP
ejpam-5876	237	19	the	the	DET
ejpam-5876	237	20	interval	interval	NOUN
ejpam-5876	237	21	ω	ω	PROPN
ejpam-5876	237	22	=	=	SYM
ejpam-5876	237	23	(	(	PUNCT
ejpam-5876	237	24	0.5	0.5	NUM
ejpam-5876	237	25	,	,	PUNCT
ejpam-5876	237	26	1	1	NUM
ejpam-5876	237	27	]	]	PUNCT
ejpam-5876	237	28	.	.	PUNCT
ejpam-5876	238	1	the	the	DET
ejpam-5876	238	2	assumption	assumption	NOUN
ejpam-5876	238	3	that	that	SCONJ
ejpam-5876	238	4	µ	µ	NOUN
ejpam-5876	238	5	is	be	AUX
ejpam-5876	238	6	an	an	DET
ejpam-5876	238	7	(	(	PUNCT
ejpam-5876	238	8	∈,∈	∈,∈	X
ejpam-5876	238	9	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	238	10	sup	sup	ADJ
ejpam-5876	238	11	-	-	PUNCT
ejpam-5876	238	12	subalgebra	subalgebra	NOUN
ejpam-5876	238	13	guarantees	guarantee	NOUN
ejpam-5876	238	14	,	,	PUNCT
ejpam-5876	238	15	via	via	ADP
ejpam-5876	238	16	theorem	theorem	NOUN
ejpam-5876	238	17	7	7	NUM
ejpam-5876	238	18	,	,	PUNCT
ejpam-5876	238	19	that	that	SCONJ
ejpam-5876	238	20	the	the	DET
ejpam-5876	238	21	level	level	NOUN
ejpam-5876	238	22	sets	set	VERB
ejpam-5876	238	23	ℓqµ	ℓqµ	NOUN
ejpam-5876	238	24	(	(	PUNCT
ejpam-5876	238	25	t	t	NOUN
ejpam-5876	238	26	)	)	PUNCT
ejpam-5876	238	27	are	be	AUX
ejpam-5876	238	28	sup	sup	NOUN
ejpam-5876	238	29	-	-	PUNCT
ejpam-5876	238	30	subalgebras	subalgebras	NOUN
ejpam-5876	238	31	for	for	ADP
ejpam-5876	238	32	all	all	DET
ejpam-5876	238	33	t	t	NOUN
ejpam-5876	238	34	∈	∈	PROPN
ejpam-5876	238	35	ω	ω	PROPN
ejpam-5876	238	36	,	,	PUNCT
ejpam-5876	238	37	and	and	CCONJ
ejpam-5876	238	38	thus	thus	ADV
ejpam-5876	238	39	(	(	PUNCT
ejpam-5876	238	40	x	x	X
ejpam-5876	238	41	,	,	PUNCT
ejpam-5876	238	42	ℓqµ	ℓqµ	NOUN
ejpam-5876	238	43	)	)	PUNCT
ejpam-5876	238	44	is	be	AUX
ejpam-5876	238	45	a	a	DET
ejpam-5876	238	46	semidetached	semidetache	VERB
ejpam-5876	238	47	sup	sup	NOUN
ejpam-5876	238	48	-	-	PUNCT
ejpam-5876	238	49	subalgebra	subalgebra	NOUN
ejpam-5876	238	50	over	over	ADP
ejpam-5876	238	51	this	this	DET
ejpam-5876	238	52	interval	interval	NOUN
ejpam-5876	238	53	.	.	PUNCT
ejpam-5876	239	1	corollary	corollary	ADJ
ejpam-5876	239	2	9	9	NUM
ejpam-5876	239	3	.	.	PUNCT
ejpam-5876	240	1	if	if	SCONJ
ejpam-5876	240	2	µ	µ	NOUN
ejpam-5876	240	3	is	be	AUX
ejpam-5876	240	4	an	an	DET
ejpam-5876	240	5	(	(	PUNCT
ejpam-5876	240	6	∈,∈	∈,∈	X
ejpam-5876	240	7	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	240	8	sup	sup	NOUN
ejpam-5876	240	9	-	-	PUNCT
ejpam-5876	240	10	subalgebra	subalgebra	NOUN
ejpam-5876	240	11	of	of	ADP
ejpam-5876	240	12	x	x	PRON
ejpam-5876	240	13	,	,	PUNCT
ejpam-5876	240	14	then	then	ADV
ejpam-5876	240	15	µ	µ	NOUN
ejpam-5876	240	16	is	be	AUX
ejpam-5876	240	17	a	a	DET
ejpam-5876	240	18	semidetached	semidetache	VERB
ejpam-5876	240	19	sup	sup	NOUN
ejpam-5876	240	20	-	-	PUNCT
ejpam-5876	240	21	subalgebra	subalgebra	NOUN
ejpam-5876	240	22	over	over	ADP
ejpam-5876	240	23	ω	ω	NUM
ejpam-5876	240	24	=	=	SYM
ejpam-5876	240	25	(	(	PUNCT
ejpam-5876	240	26	0.5	0.5	NUM
ejpam-5876	240	27	,	,	PUNCT
ejpam-5876	240	28	1	1	NUM
ejpam-5876	240	29	]	]	PUNCT
ejpam-5876	240	30	.	.	PUNCT
ejpam-5876	241	1	theorem	theorem	ADJ
ejpam-5876	241	2	8	8	NUM
ejpam-5876	241	3	.	.	PUNCT
ejpam-5876	242	1	if	if	SCONJ
ejpam-5876	242	2	µ	µ	NOUN
ejpam-5876	242	3	is	be	AUX
ejpam-5876	242	4	a	a	DET
ejpam-5876	242	5	semidetached	semidetache	VERB
ejpam-5876	242	6	sup	sup	NOUN
ejpam-5876	242	7	-	-	PUNCT
ejpam-5876	242	8	subalgebra	subalgebra	NOUN
ejpam-5876	242	9	over	over	ADP
ejpam-5876	242	10	ω	ω	NUM
ejpam-5876	242	11	=	=	SYM
ejpam-5876	242	12	(	(	PUNCT
ejpam-5876	242	13	1−k	1−k	NUM
ejpam-5876	242	14	2	2	NUM
ejpam-5876	242	15	,	,	PUNCT
ejpam-5876	242	16	1	1	NUM
ejpam-5876	242	17	]	]	PUNCT
ejpam-5876	242	18	,	,	PUNCT
ejpam-5876	242	19	then	then	ADV
ejpam-5876	242	20	µ	µ	NOUN
ejpam-5876	242	21	is	be	AUX
ejpam-5876	242	22	an	an	DET
ejpam-5876	242	23	(	(	PUNCT
ejpam-5876	242	24	∈,∈	∈,∈	X
ejpam-5876	242	25	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	242	26	sup	sup	ADJ
ejpam-5876	242	27	-	-	PUNCT
ejpam-5876	242	28	subalgebra	subalgebra	NOUN
ejpam-5876	242	29	of	of	ADP
ejpam-5876	242	30	x.	x.	NOUN
ejpam-5876	242	31	proof	proof	NOUN
ejpam-5876	242	32	.	.	PUNCT
ejpam-5876	243	1	for	for	ADP
ejpam-5876	243	2	a	a	DET
ejpam-5876	243	3	semidetached	semidetache	VERB
ejpam-5876	243	4	sup	sup	NOUN
ejpam-5876	243	5	-	-	PUNCT
ejpam-5876	243	6	subalgebra	subalgebra	NOUN
ejpam-5876	243	7	µ	µ	NOUN
ejpam-5876	243	8	over	over	ADP
ejpam-5876	243	9	ω	ω	PROPN
ejpam-5876	243	10	=	=	SYM
ejpam-5876	243	11	(	(	PUNCT
ejpam-5876	243	12	1−k	1−k	NUM
ejpam-5876	243	13	2	2	NUM
ejpam-5876	243	14	,	,	PUNCT
ejpam-5876	243	15	1	1	NUM
ejpam-5876	243	16	]	]	PUNCT
ejpam-5876	243	17	,	,	PUNCT
ejpam-5876	243	18	assume	assume	VERB
ejpam-5876	243	19	that	that	SCONJ
ejpam-5876	243	20	there	there	PRON
ejpam-5876	243	21	exist	exist	VERB
ejpam-5876	243	22	a	a	DET
ejpam-5876	243	23	,	,	PUNCT
ejpam-5876	243	24	b	b	X
ejpam-5876	243	25	∈	∈	PROPN
ejpam-5876	243	26	x	x	PUNCT
ejpam-5876	243	27	such	such	ADJ
ejpam-5876	243	28	that	that	DET
ejpam-5876	243	29	µ((a|(b|b))|(a|(b|b	µ((a|(b|b))|(a|(b|b	NOUN
ejpam-5876	243	30	)	)	PUNCT
ejpam-5876	243	31	)	)	PUNCT
ejpam-5876	243	32	)	)	PUNCT
ejpam-5876	244	1	<	<	X
ejpam-5876	244	2	min{µ(a	min{µ(a	PROPN
ejpam-5876	244	3	)	)	PUNCT
ejpam-5876	244	4	,	,	PUNCT
ejpam-5876	244	5	µ(b	µ(b	PROPN
ejpam-5876	244	6	)	)	PUNCT
ejpam-5876	244	7	,	,	PUNCT
ejpam-5876	244	8	1−k	1−k	NUM
ejpam-5876	244	9	2	2	NUM
ejpam-5876	244	10	}	}	PUNCT
ejpam-5876	244	11	=	=	SYM
ejpam-5876	244	12	t0	t0	PROPN
ejpam-5876	244	13	.	.	PUNCT
ejpam-5876	245	1	then	then	ADV
ejpam-5876	245	2	t0	t0	PROPN
ejpam-5876	245	3	∈	∈	PROPN
ejpam-5876	245	4	(	(	PUNCT
ejpam-5876	245	5	0	0	NUM
ejpam-5876	245	6	,	,	PUNCT
ejpam-5876	245	7	1−k	1−k	NUM
ejpam-5876	245	8	2	2	NUM
ejpam-5876	245	9	]	]	PUNCT
ejpam-5876	245	10	,	,	PUNCT
ejpam-5876	245	11	a	a	PRON
ejpam-5876	245	12	,	,	PUNCT
ejpam-5876	245	13	b	b	PROPN
ejpam-5876	245	14	∈	∈	PROPN
ejpam-5876	245	15	u(µ	u(µ	PROPN
ejpam-5876	245	16	,	,	PUNCT
ejpam-5876	245	17	t0	t0	PROPN
ejpam-5876	245	18	)	)	PUNCT
ejpam-5876	245	19	⊆	⊆	NUM
ejpam-5876	245	20	ℓµek	ℓµek	NOUN
ejpam-5876	245	21	(	(	PUNCT
ejpam-5876	245	22	t0	t0	PROPN
ejpam-5876	245	23	)	)	PUNCT
ejpam-5876	245	24	,	,	PUNCT
ejpam-5876	245	25	which	which	PRON
ejpam-5876	245	26	implies	imply	VERB
ejpam-5876	245	27	that	that	SCONJ
ejpam-5876	245	28	(	(	PUNCT
ejpam-5876	245	29	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5876	245	30	)	)	PUNCT
ejpam-5876	245	31	)	)	PUNCT
ejpam-5876	245	32	∈	∈	PROPN
ejpam-5876	245	33	ℓµek	ℓµek	NOUN
ejpam-5876	245	34	(	(	PUNCT
ejpam-5876	245	35	t0	t0	NOUN
ejpam-5876	245	36	)	)	PUNCT
ejpam-5876	245	37	.	.	PUNCT
ejpam-5876	246	1	hence	hence	ADV
ejpam-5876	246	2	µ((a|(b|b))|(a|(b|b	µ((a|(b|b))|(a|(b|b	NOUN
ejpam-5876	246	3	)	)	PUNCT
ejpam-5876	246	4	)	)	PUNCT
ejpam-5876	246	5	)	)	PUNCT
ejpam-5876	247	1	≥	≥	NUM
ejpam-5876	247	2	t0	t0	PROPN
ejpam-5876	247	3	or	or	CCONJ
ejpam-5876	247	4	µ((a|(b|b))|(a|(b|b)))+t0+k	µ((a|(b|b))|(a|(b|b)))+t0+k	X
ejpam-5876	247	5	>	>	X
ejpam-5876	247	6	1	1	X
ejpam-5876	247	7	.	.	PUNCT
ejpam-5876	248	1	this	this	PRON
ejpam-5876	248	2	is	be	AUX
ejpam-5876	248	3	a	a	DET
ejpam-5876	248	4	contradiction	contradiction	NOUN
ejpam-5876	248	5	.	.	PUNCT
ejpam-5876	249	1	thus	thus	ADV
ejpam-5876	249	2	,	,	PUNCT
ejpam-5876	249	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	249	4	)	)	PUNCT
ejpam-5876	249	5	)	)	PUNCT
ejpam-5876	249	6	)	)	PUNCT
ejpam-5876	249	7	≥	≥	NOUN
ejpam-5876	250	1	min{µ(x	min{µ(x	NOUN
ejpam-5876	250	2	)	)	PUNCT
ejpam-5876	250	3	,	,	PUNCT
ejpam-5876	250	4	µ(y	µ(y	PROPN
ejpam-5876	250	5	)	)	PUNCT
ejpam-5876	250	6	,	,	PUNCT
ejpam-5876	250	7	1−k	1−k	NUM
ejpam-5876	250	8	2	2	NUM
ejpam-5876	250	9	}	}	PUNCT
ejpam-5876	250	10	for	for	ADP
ejpam-5876	250	11	all	all	DET
ejpam-5876	250	12	x	x	NOUN
ejpam-5876	250	13	,	,	PUNCT
ejpam-5876	250	14	y	y	PROPN
ejpam-5876	250	15	∈	∈	PROPN
ejpam-5876	250	16	x.	x.	NOUN
ejpam-5876	251	1	it	it	PRON
ejpam-5876	251	2	follows	follow	VERB
ejpam-5876	251	3	from	from	ADP
ejpam-5876	251	4	lemma	lemma	PROPN
ejpam-5876	251	5	3	3	NUM
ejpam-5876	251	6	that	that	PRON
ejpam-5876	251	7	µ	µ	NOUN
ejpam-5876	251	8	is	be	AUX
ejpam-5876	251	9	an	an	DET
ejpam-5876	251	10	(	(	PUNCT
ejpam-5876	251	11	∈,∈	∈,∈	X
ejpam-5876	251	12	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	251	13	sup	sup	ADJ
ejpam-5876	251	14	-	-	PUNCT
ejpam-5876	251	15	subalgebra	subalgebra	NOUN
ejpam-5876	251	16	of	of	ADP
ejpam-5876	251	17	x.	x.	PROPN
ejpam-5876	251	18	corollary	corollary	PROPN
ejpam-5876	251	19	10	10	NUM
ejpam-5876	251	20	follows	follow	VERB
ejpam-5876	251	21	immediately	immediately	ADV
ejpam-5876	251	22	from	from	ADP
ejpam-5876	251	23	theorem	theorem	ADJ
ejpam-5876	251	24	8	8	NUM
ejpam-5876	251	25	,	,	PUNCT
ejpam-5876	251	26	which	which	PRON
ejpam-5876	251	27	shows	show	VERB
ejpam-5876	251	28	that	that	SCONJ
ejpam-5876	251	29	if	if	SCONJ
ejpam-5876	251	30	(	(	PUNCT
ejpam-5876	251	31	x	x	X
ejpam-5876	251	32	,	,	PUNCT
ejpam-5876	251	33	ℓqk	ℓqk	NOUN
ejpam-5876	251	34	µ	µ	NOUN
ejpam-5876	251	35	)	)	PUNCT
ejpam-5876	251	36	is	be	AUX
ejpam-5876	251	37	a	a	DET
ejpam-5876	251	38	semidetached	semidetache	VERB
ejpam-5876	251	39	sup	sup	NOUN
ejpam-5876	251	40	-	-	PUNCT
ejpam-5876	251	41	subalgebra	subalgebra	NOUN
ejpam-5876	251	42	over	over	ADP
ejpam-5876	251	43	ω	ω	NUM
ejpam-5876	251	44	=	=	SYM
ejpam-5876	251	45	(	(	PUNCT
ejpam-5876	251	46	1−k	1−k	NUM
ejpam-5876	251	47	2	2	NUM
ejpam-5876	251	48	,	,	PUNCT
ejpam-5876	251	49	1	1	NUM
ejpam-5876	251	50	]	]	PUNCT
ejpam-5876	251	51	,	,	PUNCT
ejpam-5876	251	52	then	then	ADV
ejpam-5876	251	53	µ	µ	X
ejpam-5876	251	54	must	must	AUX
ejpam-5876	251	55	be	be	AUX
ejpam-5876	251	56	an	an	DET
ejpam-5876	251	57	(	(	PUNCT
ejpam-5876	251	58	∈,∈	∈,∈	X
ejpam-5876	251	59	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	251	60	sup	sup	ADJ
ejpam-5876	251	61	-	-	PUNCT
ejpam-5876	251	62	subalgebra	subalgebra	NOUN
ejpam-5876	251	63	.	.	PUNCT
ejpam-5876	252	1	by	by	ADP
ejpam-5876	252	2	applying	apply	VERB
ejpam-5876	252	3	theorem	theorem	NOUN
ejpam-5876	252	4	7	7	NUM
ejpam-5876	252	5	,	,	PUNCT
ejpam-5876	252	6	it	it	PRON
ejpam-5876	252	7	follows	follow	VERB
ejpam-5876	252	8	that	that	SCONJ
ejpam-5876	252	9	(	(	PUNCT
ejpam-5876	252	10	x	x	X
ejpam-5876	252	11	,	,	PUNCT
ejpam-5876	252	12	ℓqk	ℓqk	NOUN
ejpam-5876	252	13	µ	µ	NOUN
ejpam-5876	252	14	)	)	PUNCT
ejpam-5876	252	15	is	be	AUX
ejpam-5876	252	16	again	again	ADV
ejpam-5876	252	17	a	a	DET
ejpam-5876	252	18	semidetached	semidetache	VERB
ejpam-5876	252	19	sup	sup	NOUN
ejpam-5876	252	20	-	-	PUNCT
ejpam-5876	252	21	subalgebra	subalgebra	NOUN
ejpam-5876	252	22	over	over	ADP
ejpam-5876	252	23	the	the	DET
ejpam-5876	252	24	same	same	ADJ
ejpam-5876	252	25	interval	interval	NOUN
ejpam-5876	252	26	.	.	PUNCT
ejpam-5876	253	1	thus	thus	ADV
ejpam-5876	253	2	,	,	PUNCT
ejpam-5876	253	3	the	the	DET
ejpam-5876	253	4	conclusion	conclusion	NOUN
ejpam-5876	253	5	reconfirms	reconfirm	VERB
ejpam-5876	253	6	the	the	DET
ejpam-5876	253	7	consistency	consistency	NOUN
ejpam-5876	253	8	of	of	ADP
ejpam-5876	253	9	the	the	DET
ejpam-5876	253	10	structure	structure	NOUN
ejpam-5876	253	11	.	.	PUNCT
ejpam-5876	254	1	corollary	corollary	ADJ
ejpam-5876	254	2	10	10	NUM
ejpam-5876	254	3	.	.	PUNCT
ejpam-5876	255	1	if	if	SCONJ
ejpam-5876	255	2	(	(	PUNCT
ejpam-5876	255	3	x	x	NOUN
ejpam-5876	255	4	,	,	PUNCT
ejpam-5876	255	5	ℓµqk	ℓµqk	PROPN
ejpam-5876	255	6	)	)	PUNCT
ejpam-5876	255	7	is	be	AUX
ejpam-5876	255	8	a	a	DET
ejpam-5876	255	9	semidetached	semidetache	VERB
ejpam-5876	255	10	sup	sup	NOUN
ejpam-5876	255	11	-	-	PUNCT
ejpam-5876	255	12	subalgebra	subalgebra	NOUN
ejpam-5876	255	13	over	over	ADP
ejpam-5876	255	14	ω	ω	NUM
ejpam-5876	255	15	=	=	SYM
ejpam-5876	255	16	(	(	PUNCT
ejpam-5876	255	17	1−k	1−k	NUM
ejpam-5876	255	18	2	2	NUM
ejpam-5876	255	19	,	,	PUNCT
ejpam-5876	255	20	1	1	NUM
ejpam-5876	255	21	]	]	PUNCT
ejpam-5876	255	22	,	,	PUNCT
ejpam-5876	255	23	then	then	ADV
ejpam-5876	255	24	(	(	PUNCT
ejpam-5876	255	25	x	x	X
ejpam-5876	255	26	,	,	PUNCT
ejpam-5876	255	27	ℓµqk	ℓµqk	PROPN
ejpam-5876	255	28	)	)	PUNCT
ejpam-5876	255	29	is	be	AUX
ejpam-5876	255	30	a	a	DET
ejpam-5876	255	31	semidetached	semidetache	VERB
ejpam-5876	255	32	sup	sup	NOUN
ejpam-5876	255	33	-	-	PUNCT
ejpam-5876	255	34	subalgebra	subalgebra	NOUN
ejpam-5876	255	35	over	over	ADP
ejpam-5876	255	36	ω	ω	NUM
ejpam-5876	255	37	=	=	SYM
ejpam-5876	255	38	(	(	PUNCT
ejpam-5876	255	39	1−k	1−k	NUM
ejpam-5876	255	40	2	2	NUM
ejpam-5876	255	41	,	,	PUNCT
ejpam-5876	255	42	1	1	NUM
ejpam-5876	255	43	]	]	PUNCT
ejpam-5876	255	44	.	.	PUNCT
ejpam-5876	256	1	theorem	theorem	VERB
ejpam-5876	256	2	9	9	NUM
ejpam-5876	256	3	.	.	PUNCT
ejpam-5876	257	1	if	if	SCONJ
ejpam-5876	257	2	µ	µ	NOUN
ejpam-5876	257	3	is	be	AUX
ejpam-5876	257	4	an	an	DET
ejpam-5876	257	5	(	(	PUNCT
ejpam-5876	257	6	∈,∈	∈,∈	X
ejpam-5876	257	7	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	257	8	sup	sup	ADJ
ejpam-5876	257	9	-	-	PUNCT
ejpam-5876	257	10	subalgebra	subalgebra	NOUN
ejpam-5876	257	11	of	of	ADP
ejpam-5876	257	12	x	x	PRON
ejpam-5876	257	13	,	,	PUNCT
ejpam-5876	257	14	then	then	ADV
ejpam-5876	257	15	(	(	PUNCT
ejpam-5876	257	16	x	x	X
ejpam-5876	257	17	,	,	PUNCT
ejpam-5876	257	18	ℓµqk	ℓµqk	PROPN
ejpam-5876	257	19	)	)	PUNCT
ejpam-5876	257	20	is	be	AUX
ejpam-5876	257	21	a	a	DET
ejpam-5876	257	22	semidetached	semidetache	VERB
ejpam-5876	257	23	sup	sup	NOUN
ejpam-5876	257	24	-	-	PUNCT
ejpam-5876	257	25	subalgebra	subalgebra	NOUN
ejpam-5876	257	26	over	over	ADP
ejpam-5876	257	27	ω	ω	NUM
ejpam-5876	257	28	=	=	SYM
ejpam-5876	257	29	(	(	PUNCT
ejpam-5876	257	30	1−k	1−k	NUM
ejpam-5876	257	31	2	2	NUM
ejpam-5876	257	32	,	,	PUNCT
ejpam-5876	257	33	1	1	NUM
ejpam-5876	257	34	]	]	PUNCT
ejpam-5876	257	35	.	.	PUNCT
ejpam-5876	258	1	proof	proof	NOUN
ejpam-5876	258	2	.	.	PUNCT
ejpam-5876	259	1	let	let	VERB
ejpam-5876	259	2	x	x	PRON
ejpam-5876	259	3	,	,	PUNCT
ejpam-5876	259	4	y	y	PROPN
ejpam-5876	259	5	∈	∈	PROPN
ejpam-5876	259	6	ℓµek	ℓµek	NOUN
ejpam-5876	259	7	(	(	PUNCT
ejpam-5876	259	8	t	t	PROPN
ejpam-5876	259	9	)	)	PUNCT
ejpam-5876	259	10	for	for	ADP
ejpam-5876	259	11	t	t	PROPN
ejpam-5876	259	12	∈	∈	PROPN
ejpam-5876	259	13	ω	ω	PROPN
ejpam-5876	259	14	=	=	SYM
ejpam-5876	259	15	(	(	PUNCT
ejpam-5876	259	16	0	0	NUM
ejpam-5876	259	17	,	,	PUNCT
ejpam-5876	259	18	1−k	1−k	NUM
ejpam-5876	259	19	2	2	NUM
ejpam-5876	259	20	]	]	PUNCT
ejpam-5876	259	21	.	.	PUNCT
ejpam-5876	260	1	then	then	ADV
ejpam-5876	260	2	xt	xt	PROPN
ejpam-5876	260	3	∈	∈	PROPN
ejpam-5876	260	4	∨qkµ	∨qkµ	PROPN
ejpam-5876	260	5	and	and	CCONJ
ejpam-5876	260	6	yt	yt	PROPN
ejpam-5876	260	7	∈	∈	PROPN
ejpam-5876	260	8	∨qkµ.	∨qkµ.	VERB
ejpam-5876	260	9	hence	hence	ADV
ejpam-5876	260	10	,	,	PUNCT
ejpam-5876	260	11	we	we	PRON
ejpam-5876	260	12	have	have	VERB
ejpam-5876	260	13	the	the	DET
ejpam-5876	260	14	following	follow	VERB
ejpam-5876	260	15	four	four	NUM
ejpam-5876	260	16	cases	case	NOUN
ejpam-5876	260	17	:	:	PUNCT
ejpam-5876	260	18	(	(	PUNCT
ejpam-5876	260	19	1	1	X
ejpam-5876	260	20	)	)	PUNCT
ejpam-5876	260	21	xt	xt	ADP
ejpam-5876	261	1	∈	∈	PROPN
ejpam-5876	261	2	µ	µ	X
ejpam-5876	261	3	and	and	CCONJ
ejpam-5876	261	4	yt	yt	PROPN
ejpam-5876	261	5	∈	∈	PROPN
ejpam-5876	261	6	µ	µ	PROPN
ejpam-5876	261	7	,	,	PUNCT
ejpam-5876	261	8	(	(	PUNCT
ejpam-5876	261	9	2	2	NUM
ejpam-5876	261	10	)	)	PUNCT
ejpam-5876	261	11	xt	xt	ADP
ejpam-5876	262	1	∈	∈	PROPN
ejpam-5876	262	2	µ	µ	X
ejpam-5876	262	3	and	and	CCONJ
ejpam-5876	262	4	ytqkµ	ytqkµ	NOUN
ejpam-5876	262	5	,	,	PUNCT
ejpam-5876	262	6	(	(	PUNCT
ejpam-5876	262	7	3	3	X
ejpam-5876	262	8	)	)	PUNCT
ejpam-5876	262	9	xtqkµ	xtqkµ	NOUN
ejpam-5876	262	10	and	and	CCONJ
ejpam-5876	262	11	yt	yt	PROPN
ejpam-5876	262	12	∈	∈	PROPN
ejpam-5876	262	13	µ	µ	PROPN
ejpam-5876	262	14	,	,	PUNCT
ejpam-5876	262	15	(	(	PUNCT
ejpam-5876	262	16	4	4	X
ejpam-5876	262	17	)	)	PUNCT
ejpam-5876	262	18	xtqkµ	xtqkµ	NOUN
ejpam-5876	262	19	and	and	CCONJ
ejpam-5876	262	20	ytqkµ.	ytqkµ.	ADJ
ejpam-5876	262	21	t.	t.	PROPN
ejpam-5876	262	22	oner	oner	PROPN
ejpam-5876	262	23	et	et	PROPN
ejpam-5876	262	24	al	al	PROPN
ejpam-5876	262	25	.	.	PUNCT
ejpam-5876	262	26	/	/	SYM
ejpam-5876	262	27	eur	eur	PROPN
ejpam-5876	262	28	.	.	PUNCT
ejpam-5876	263	1	j.	j.	PROPN
ejpam-5876	263	2	pure	pure	PROPN
ejpam-5876	263	3	appl	appl	PROPN
ejpam-5876	263	4	.	.	PROPN
ejpam-5876	263	5	math	math	PROPN
ejpam-5876	263	6	,	,	PUNCT
ejpam-5876	263	7	18	18	NUM
ejpam-5876	263	8	(	(	PUNCT
ejpam-5876	263	9	2	2	NUM
ejpam-5876	263	10	)	)	PUNCT
ejpam-5876	263	11	(	(	PUNCT
ejpam-5876	263	12	2025	2025	NUM
ejpam-5876	263	13	)	)	PUNCT
ejpam-5876	263	14	,	,	PUNCT
ejpam-5876	263	15	5876	5876	NUM
ejpam-5876	263	16	11	11	NUM
ejpam-5876	263	17	of	of	ADP
ejpam-5876	263	18	16	16	NUM
ejpam-5876	263	19	the	the	DET
ejpam-5876	263	20	first	first	ADJ
ejpam-5876	263	21	case	case	NOUN
ejpam-5876	263	22	implies	imply	VERB
ejpam-5876	263	23	that	that	SCONJ
ejpam-5876	263	24	(	(	PUNCT
ejpam-5876	263	25	(	(	PUNCT
ejpam-5876	263	26	x|(y|y))|(x|(y|y)))t	x|(y|y))|(x|(y|y)))t	PROPN
ejpam-5876	263	27	∈	∈	PROPN
ejpam-5876	263	28	∨qkµ	∨qkµ	PROPN
ejpam-5876	263	29	,	,	PUNCT
ejpam-5876	263	30	and	and	CCONJ
ejpam-5876	263	31	so	so	ADV
ejpam-5876	263	32	(	(	PUNCT
ejpam-5876	263	33	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	263	34	)	)	PUNCT
ejpam-5876	263	35	)	)	PUNCT
ejpam-5876	263	36	∈	∈	PROPN
ejpam-5876	263	37	ℓµek	ℓµek	NOUN
ejpam-5876	263	38	(	(	PUNCT
ejpam-5876	263	39	t	t	PROPN
ejpam-5876	263	40	)	)	PUNCT
ejpam-5876	263	41	.	.	PUNCT
ejpam-5876	264	1	for	for	ADP
ejpam-5876	264	2	the	the	DET
ejpam-5876	264	3	second	second	ADJ
ejpam-5876	264	4	case	case	NOUN
ejpam-5876	264	5	,	,	PUNCT
ejpam-5876	264	6	ytqkµ	ytqkµ	NOUN
ejpam-5876	264	7	induces	induce	VERB
ejpam-5876	264	8	µ(y	µ(y	PROPN
ejpam-5876	264	9	)	)	PUNCT
ejpam-5876	264	10	>	>	X
ejpam-5876	265	1	1	1	NUM
ejpam-5876	265	2	−	−	NOUN
ejpam-5876	265	3	t	t	NOUN
ejpam-5876	265	4	−	−	PROPN
ejpam-5876	266	1	k	k	PROPN
ejpam-5876	266	2	≥	≥	NUM
ejpam-5876	266	3	t	t	PROPN
ejpam-5876	266	4	,	,	PUNCT
ejpam-5876	266	5	that	that	ADV
ejpam-5876	266	6	is	is	ADV
ejpam-5876	266	7	,	,	PUNCT
ejpam-5876	266	8	yt	yt	PROPN
ejpam-5876	266	9	∈	∈	PROPN
ejpam-5876	266	10	µ.	µ.	NOUN
ejpam-5876	266	11	hence	hence	ADV
ejpam-5876	266	12	,	,	PUNCT
ejpam-5876	266	13	(	(	PUNCT
ejpam-5876	266	14	(	(	PUNCT
ejpam-5876	266	15	x|(y|y))|(x|(y|y)))t	x|(y|y))|(x|(y|y)))t	PROPN
ejpam-5876	266	16	∈	∈	PROPN
ejpam-5876	266	17	∨qkµ	∨qkµ	PROPN
ejpam-5876	266	18	,	,	PUNCT
ejpam-5876	266	19	and	and	CCONJ
ejpam-5876	266	20	so	so	ADV
ejpam-5876	266	21	(	(	PUNCT
ejpam-5876	266	22	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	266	23	)	)	PUNCT
ejpam-5876	266	24	)	)	PUNCT
ejpam-5876	267	1	∈	∈	PROPN
ejpam-5876	267	2	ℓµek	ℓµek	NOUN
ejpam-5876	267	3	(	(	PUNCT
ejpam-5876	267	4	t	t	PROPN
ejpam-5876	267	5	)	)	PUNCT
ejpam-5876	267	6	.	.	PUNCT
ejpam-5876	268	1	similarly	similarly	ADV
ejpam-5876	268	2	,	,	PUNCT
ejpam-5876	268	3	the	the	DET
ejpam-5876	268	4	third	third	ADJ
ejpam-5876	268	5	case	case	NOUN
ejpam-5876	268	6	implies	imply	VERB
ejpam-5876	268	7	(	(	PUNCT
ejpam-5876	268	8	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	NUM
ejpam-5876	268	9	)	)	PUNCT
ejpam-5876	268	10	)	)	PUNCT
ejpam-5876	269	1	∈	∈	PROPN
ejpam-5876	269	2	ℓµek	ℓµek	NOUN
ejpam-5876	269	3	(	(	PUNCT
ejpam-5876	269	4	t	t	PROPN
ejpam-5876	269	5	)	)	PUNCT
ejpam-5876	269	6	.	.	PUNCT
ejpam-5876	270	1	the	the	DET
ejpam-5876	270	2	last	last	ADJ
ejpam-5876	270	3	case	case	NOUN
ejpam-5876	270	4	induces	induce	VERB
ejpam-5876	270	5	µ(x	µ(x	NOUN
ejpam-5876	270	6	)	)	PUNCT
ejpam-5876	270	7	>	>	X
ejpam-5876	270	8	1	1	NUM
ejpam-5876	270	9	−	−	NOUN
ejpam-5876	270	10	t	t	NOUN
ejpam-5876	270	11	−	−	PROPN
ejpam-5876	270	12	k	k	PROPN
ejpam-5876	270	13	≥	≥	PROPN
ejpam-5876	270	14	t	t	PROPN
ejpam-5876	270	15	and	and	CCONJ
ejpam-5876	270	16	µ(y	µ(y	NUM
ejpam-5876	270	17	)	)	PUNCT
ejpam-5876	270	18	>	>	X
ejpam-5876	270	19	1−t−k	1−t−k	PROPN
ejpam-5876	270	20	≥	≥	PROPN
ejpam-5876	270	21	t	t	PROPN
ejpam-5876	270	22	,	,	PUNCT
ejpam-5876	270	23	that	that	ADV
ejpam-5876	270	24	is	is	ADV
ejpam-5876	270	25	,	,	PUNCT
ejpam-5876	270	26	xt	xt	PROPN
ejpam-5876	270	27	∈	∈	PROPN
ejpam-5876	270	28	µ	µ	X
ejpam-5876	270	29	and	and	CCONJ
ejpam-5876	270	30	yt	yt	PROPN
ejpam-5876	270	31	∈	∈	PROPN
ejpam-5876	270	32	µ.	µ.	NOUN
ejpam-5876	270	33	it	it	PRON
ejpam-5876	270	34	follows	follow	VERB
ejpam-5876	270	35	that	that	SCONJ
ejpam-5876	270	36	(	(	PUNCT
ejpam-5876	270	37	(	(	PUNCT
ejpam-5876	270	38	x|(y|y))|(x|(y|y)))t	x|(y|y))|(x|(y|y)))t	PROPN
ejpam-5876	270	39	∈	∈	PROPN
ejpam-5876	270	40	∨qkµ	∨qkµ	PROPN
ejpam-5876	270	41	and	and	CCONJ
ejpam-5876	270	42	so	so	SCONJ
ejpam-5876	270	43	that	that	SCONJ
ejpam-5876	270	44	(	(	PUNCT
ejpam-5876	270	45	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	270	46	)	)	PUNCT
ejpam-5876	270	47	)	)	PUNCT
ejpam-5876	270	48	∈	∈	PROPN
ejpam-5876	270	49	ℓµek	ℓµek	NOUN
ejpam-5876	270	50	(	(	PUNCT
ejpam-5876	270	51	t	t	PROPN
ejpam-5876	270	52	)	)	PUNCT
ejpam-5876	270	53	.	.	PUNCT
ejpam-5876	271	1	therefore	therefore	ADV
ejpam-5876	271	2	,	,	PUNCT
ejpam-5876	271	3	ℓµek	ℓµek	PROPN
ejpam-5876	271	4	(	(	PUNCT
ejpam-5876	271	5	t	t	PROPN
ejpam-5876	271	6	)	)	PUNCT
ejpam-5876	271	7	is	be	AUX
ejpam-5876	271	8	an	an	DET
ejpam-5876	271	9	sup	sup	ADJ
ejpam-5876	271	10	-	-	PUNCT
ejpam-5876	271	11	subalgebra	subalgebra	NOUN
ejpam-5876	271	12	of	of	ADP
ejpam-5876	271	13	x	x	PUNCT
ejpam-5876	271	14	for	for	ADP
ejpam-5876	271	15	all	all	DET
ejpam-5876	271	16	t	t	NOUN
ejpam-5876	271	17	∈	∈	PROPN
ejpam-5876	271	18	0	0	NUM
ejpam-5876	271	19	,	,	PUNCT
ejpam-5876	271	20	1−k	1−k	NUM
ejpam-5876	271	21	2	2	NUM
ejpam-5876	271	22	.	.	PUNCT
ejpam-5876	272	1	hence	hence	ADV
ejpam-5876	272	2	,	,	PUNCT
ejpam-5876	272	3	(	(	PUNCT
ejpam-5876	272	4	x	x	X
ejpam-5876	272	5	,	,	PUNCT
ejpam-5876	272	6	ℓµqk	ℓµqk	PROPN
ejpam-5876	272	7	)	)	PUNCT
ejpam-5876	272	8	is	be	AUX
ejpam-5876	272	9	a	a	DET
ejpam-5876	272	10	semidetached	semidetache	VERB
ejpam-5876	272	11	sup	sup	NOUN
ejpam-5876	272	12	-	-	PUNCT
ejpam-5876	272	13	subalgebra	subalgebra	NOUN
ejpam-5876	272	14	over	over	ADP
ejpam-5876	272	15	ω	ω	NUM
ejpam-5876	272	16	=	=	SYM
ejpam-5876	272	17	(	(	PUNCT
ejpam-5876	272	18	1−k	1−k	NUM
ejpam-5876	272	19	2	2	NUM
ejpam-5876	272	20	,	,	PUNCT
ejpam-5876	272	21	1	1	NUM
ejpam-5876	272	22	]	]	PUNCT
ejpam-5876	272	23	.	.	PUNCT
ejpam-5876	273	1	corollary	corollary	ADJ
ejpam-5876	273	2	11	11	NUM
ejpam-5876	273	3	is	be	AUX
ejpam-5876	273	4	a	a	DET
ejpam-5876	273	5	direct	direct	ADJ
ejpam-5876	273	6	consequence	consequence	NOUN
ejpam-5876	273	7	of	of	ADP
ejpam-5876	273	8	theorem	theorem	NOUN
ejpam-5876	273	9	9	9	NUM
ejpam-5876	273	10	by	by	ADP
ejpam-5876	273	11	setting	set	VERB
ejpam-5876	273	12	k	k	PROPN
ejpam-5876	273	13	=	=	PUNCT
ejpam-5876	273	14	0	0	PROPN
ejpam-5876	273	15	.	.	PUNCT
ejpam-5876	274	1	when	when	SCONJ
ejpam-5876	274	2	k	k	PROPN
ejpam-5876	274	3	=	=	SYM
ejpam-5876	274	4	0	0	PROPN
ejpam-5876	274	5	,	,	PUNCT
ejpam-5876	274	6	the	the	DET
ejpam-5876	274	7	interval	interval	NOUN
ejpam-5876	274	8	ω	ω	PROPN
ejpam-5876	274	9	=	=	SYM
ejpam-5876	274	10	(	(	PUNCT
ejpam-5876	274	11	0	0	NUM
ejpam-5876	274	12	,	,	PUNCT
ejpam-5876	274	13	1−k	1−k	NUM
ejpam-5876	274	14	2	2	NUM
ejpam-5876	274	15	]	]	PUNCT
ejpam-5876	274	16	becomes	become	VERB
ejpam-5876	274	17	(	(	PUNCT
ejpam-5876	274	18	0	0	NUM
ejpam-5876	274	19	,	,	PUNCT
ejpam-5876	274	20	0.5	0.5	NUM
ejpam-5876	274	21	]	]	PUNCT
ejpam-5876	274	22	,	,	PUNCT
ejpam-5876	274	23	and	and	CCONJ
ejpam-5876	274	24	the	the	DET
ejpam-5876	274	25	operator	operator	NOUN
ejpam-5876	274	26	qk	qk	NOUN
ejpam-5876	274	27	becomes	become	VERB
ejpam-5876	274	28	the	the	DET
ejpam-5876	274	29	standard	standard	ADJ
ejpam-5876	274	30	quasicoincidence	quasicoincidence	NOUN
ejpam-5876	274	31	operator	operator	NOUN
ejpam-5876	274	32	q.	q.	PROPN
ejpam-5876	274	33	theorem	theorem	VERB
ejpam-5876	274	34	9	9	NUM
ejpam-5876	274	35	ensures	ensure	VERB
ejpam-5876	274	36	that	that	SCONJ
ejpam-5876	274	37	if	if	SCONJ
ejpam-5876	274	38	µ	µ	NOUN
ejpam-5876	274	39	is	be	AUX
ejpam-5876	274	40	an	an	DET
ejpam-5876	274	41	(	(	PUNCT
ejpam-5876	274	42	∈,∈	∈,∈	X
ejpam-5876	274	43	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	274	44	sup	sup	NOUN
ejpam-5876	274	45	-	-	PUNCT
ejpam-5876	274	46	subalgebra	subalgebra	NOUN
ejpam-5876	274	47	,	,	PUNCT
ejpam-5876	274	48	then	then	ADV
ejpam-5876	274	49	the	the	DET
ejpam-5876	274	50	structure	structure	NOUN
ejpam-5876	274	51	(	(	PUNCT
ejpam-5876	274	52	x	x	X
ejpam-5876	274	53	,	,	PUNCT
ejpam-5876	274	54	ℓeµ	ℓeµ	ADV
ejpam-5876	274	55	)	)	PUNCT
ejpam-5876	274	56	forms	form	VERB
ejpam-5876	274	57	a	a	DET
ejpam-5876	274	58	semidetached	semidetache	VERB
ejpam-5876	274	59	sup	sup	NOUN
ejpam-5876	274	60	-	-	PUNCT
ejpam-5876	274	61	subalgebra	subalgebra	NOUN
ejpam-5876	274	62	over	over	ADP
ejpam-5876	274	63	this	this	DET
ejpam-5876	274	64	interval	interval	NOUN
ejpam-5876	274	65	.	.	PUNCT
ejpam-5876	275	1	corollary	corollary	ADJ
ejpam-5876	275	2	11	11	NUM
ejpam-5876	275	3	.	.	PUNCT
ejpam-5876	276	1	if	if	SCONJ
ejpam-5876	276	2	µ	µ	NOUN
ejpam-5876	276	3	is	be	AUX
ejpam-5876	276	4	an	an	DET
ejpam-5876	276	5	(	(	PUNCT
ejpam-5876	276	6	∈,∈	∈,∈	X
ejpam-5876	276	7	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	276	8	sup	sup	NOUN
ejpam-5876	276	9	-	-	PUNCT
ejpam-5876	276	10	subalgebra	subalgebra	NOUN
ejpam-5876	276	11	of	of	ADP
ejpam-5876	276	12	x	x	PRON
ejpam-5876	276	13	,	,	PUNCT
ejpam-5876	276	14	then	then	ADV
ejpam-5876	276	15	(	(	PUNCT
ejpam-5876	276	16	x	x	X
ejpam-5876	276	17	,	,	PUNCT
ejpam-5876	276	18	ℓµek	ℓµek	NOUN
ejpam-5876	276	19	)	)	PUNCT
ejpam-5876	276	20	is	be	AUX
ejpam-5876	276	21	a	a	DET
ejpam-5876	276	22	semidetached	semidetache	VERB
ejpam-5876	276	23	sup	sup	NOUN
ejpam-5876	276	24	-	-	PUNCT
ejpam-5876	276	25	subalgebra	subalgebra	NOUN
ejpam-5876	276	26	over	over	ADP
ejpam-5876	276	27	ω	ω	NUM
ejpam-5876	276	28	=	=	SYM
ejpam-5876	276	29	(	(	PUNCT
ejpam-5876	276	30	0	0	NUM
ejpam-5876	276	31	,	,	PUNCT
ejpam-5876	276	32	0.5	0.5	NUM
ejpam-5876	276	33	]	]	PUNCT
ejpam-5876	276	34	.	.	PUNCT
ejpam-5876	277	1	theorem	theorem	ADJ
ejpam-5876	277	2	10	10	NUM
ejpam-5876	277	3	.	.	PUNCT
ejpam-5876	278	1	if	if	SCONJ
ejpam-5876	278	2	µ	µ	NOUN
ejpam-5876	278	3	is	be	AUX
ejpam-5876	278	4	a	a	DET
ejpam-5876	278	5	(	(	PUNCT
ejpam-5876	278	6	qk,∈	qk,∈	INTJ
ejpam-5876	278	7	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	278	8	sup	sup	NOUN
ejpam-5876	278	9	-	-	PUNCT
ejpam-5876	278	10	subalgebra	subalgebra	NOUN
ejpam-5876	278	11	of	of	ADP
ejpam-5876	278	12	x	x	PRON
ejpam-5876	278	13	,	,	PUNCT
ejpam-5876	278	14	then	then	ADV
ejpam-5876	278	15	(	(	PUNCT
ejpam-5876	278	16	x	x	X
ejpam-5876	278	17	,	,	PUNCT
ejpam-5876	278	18	ℓµek	ℓµek	NOUN
ejpam-5876	278	19	)	)	PUNCT
ejpam-5876	278	20	is	be	AUX
ejpam-5876	278	21	a	a	DET
ejpam-5876	278	22	semidetached	semidetache	VERB
ejpam-5876	278	23	sup	sup	NOUN
ejpam-5876	278	24	-	-	PUNCT
ejpam-5876	278	25	subalgebra	subalgebra	NOUN
ejpam-5876	278	26	over	over	ADP
ejpam-5876	278	27	ω	ω	NUM
ejpam-5876	278	28	=	=	SYM
ejpam-5876	278	29	(	(	PUNCT
ejpam-5876	278	30	1−k	1−k	NUM
ejpam-5876	278	31	2	2	NUM
ejpam-5876	278	32	,	,	PUNCT
ejpam-5876	278	33	1	1	NUM
ejpam-5876	278	34	]	]	PUNCT
ejpam-5876	278	35	.	.	PUNCT
ejpam-5876	279	1	proof	proof	NOUN
ejpam-5876	279	2	.	.	PUNCT
ejpam-5876	280	1	let	let	VERB
ejpam-5876	280	2	x	x	PRON
ejpam-5876	280	3	,	,	PUNCT
ejpam-5876	280	4	y	y	PROPN
ejpam-5876	280	5	∈	∈	PROPN
ejpam-5876	280	6	ℓµek	ℓµek	NOUN
ejpam-5876	280	7	(	(	PUNCT
ejpam-5876	280	8	t	t	PROPN
ejpam-5876	280	9	)	)	PUNCT
ejpam-5876	280	10	for	for	ADP
ejpam-5876	280	11	t	t	PROPN
ejpam-5876	280	12	∈	∈	PROPN
ejpam-5876	280	13	ω	ω	PROPN
ejpam-5876	280	14	=	=	SYM
ejpam-5876	280	15	(	(	PUNCT
ejpam-5876	280	16	1−k	1−k	NUM
ejpam-5876	280	17	2	2	NUM
ejpam-5876	280	18	,	,	PUNCT
ejpam-5876	280	19	1	1	NUM
ejpam-5876	280	20	]	]	PUNCT
ejpam-5876	280	21	.	.	PUNCT
ejpam-5876	281	1	then	then	ADV
ejpam-5876	281	2	xt	xt	PROPN
ejpam-5876	281	3	∈	∈	PROPN
ejpam-5876	281	4	∨qkµ	∨qkµ	PROPN
ejpam-5876	281	5	and	and	CCONJ
ejpam-5876	281	6	yt	yt	PROPN
ejpam-5876	281	7	∈	∈	PROPN
ejpam-5876	281	8	∨qkµ.	∨qkµ.	VERB
ejpam-5876	281	9	hence	hence	ADV
ejpam-5876	281	10	,	,	PUNCT
ejpam-5876	281	11	we	we	PRON
ejpam-5876	281	12	have	have	VERB
ejpam-5876	281	13	the	the	DET
ejpam-5876	281	14	following	follow	VERB
ejpam-5876	281	15	four	four	NUM
ejpam-5876	281	16	cases	case	NOUN
ejpam-5876	281	17	:	:	PUNCT
ejpam-5876	281	18	(	(	PUNCT
ejpam-5876	281	19	1	1	X
ejpam-5876	281	20	)	)	PUNCT
ejpam-5876	281	21	xt	xt	ADP
ejpam-5876	282	1	∈	∈	PROPN
ejpam-5876	282	2	µ	µ	X
ejpam-5876	282	3	and	and	CCONJ
ejpam-5876	282	4	yt	yt	PROPN
ejpam-5876	282	5	∈	∈	PROPN
ejpam-5876	282	6	µ	µ	PROPN
ejpam-5876	282	7	,	,	PUNCT
ejpam-5876	282	8	(	(	PUNCT
ejpam-5876	282	9	2	2	NUM
ejpam-5876	282	10	)	)	PUNCT
ejpam-5876	282	11	xt	xt	ADP
ejpam-5876	283	1	∈	∈	PROPN
ejpam-5876	283	2	µ	µ	X
ejpam-5876	283	3	and	and	CCONJ
ejpam-5876	283	4	ytqkµ	ytqkµ	NOUN
ejpam-5876	283	5	,	,	PUNCT
ejpam-5876	283	6	(	(	PUNCT
ejpam-5876	283	7	3	3	X
ejpam-5876	283	8	)	)	PUNCT
ejpam-5876	283	9	xtqkµ	xtqkµ	NOUN
ejpam-5876	283	10	and	and	CCONJ
ejpam-5876	283	11	yt	yt	PROPN
ejpam-5876	283	12	∈	∈	PROPN
ejpam-5876	283	13	µ	µ	PROPN
ejpam-5876	283	14	,	,	PUNCT
ejpam-5876	283	15	(	(	PUNCT
ejpam-5876	283	16	4	4	X
ejpam-5876	283	17	)	)	PUNCT
ejpam-5876	283	18	xtqkµ	xtqkµ	NOUN
ejpam-5876	283	19	and	and	CCONJ
ejpam-5876	283	20	ytqkµ.	ytqkµ.	NOUN
ejpam-5876	283	21	for	for	ADP
ejpam-5876	283	22	the	the	DET
ejpam-5876	283	23	first	first	ADJ
ejpam-5876	283	24	case	case	NOUN
ejpam-5876	283	25	,	,	PUNCT
ejpam-5876	283	26	we	we	PRON
ejpam-5876	283	27	have	have	VERB
ejpam-5876	283	28	µ(x)+	µ(x)+	ADP
ejpam-5876	283	29	t+	t+	VERB
ejpam-5876	283	30	k	k	PROPN
ejpam-5876	283	31	≥	≥	NUM
ejpam-5876	283	32	2t+	2t+	NUM
ejpam-5876	283	33	k	k	X
ejpam-5876	283	34	>	>	X
ejpam-5876	283	35	1	1	NUM
ejpam-5876	283	36	and	and	CCONJ
ejpam-5876	283	37	µ(y)+	µ(y)+	INTJ
ejpam-5876	283	38	t+	t+	PUNCT
ejpam-5876	283	39	k	k	PROPN
ejpam-5876	283	40	≥	≥	NUM
ejpam-5876	283	41	2t+	2t+	NUM
ejpam-5876	283	42	k	k	X
ejpam-5876	283	43	>	>	X
ejpam-5876	283	44	1	1	NUM
ejpam-5876	283	45	,	,	PUNCT
ejpam-5876	283	46	that	that	ADV
ejpam-5876	283	47	is	is	ADV
ejpam-5876	283	48	,	,	PUNCT
ejpam-5876	283	49	xtqkµ	xtqkµ	NOUN
ejpam-5876	283	50	and	and	CCONJ
ejpam-5876	283	51	ytqkµ.	ytqkµ.	PROPN
ejpam-5876	283	52	hence	hence	ADV
ejpam-5876	283	53	,	,	PUNCT
ejpam-5876	283	54	(	(	PUNCT
ejpam-5876	283	55	(	(	PUNCT
ejpam-5876	283	56	x|(y|y))|(x|(y|y)))t	x|(y|y))|(x|(y|y)))t	PROPN
ejpam-5876	283	57	∈	∈	PROPN
ejpam-5876	283	58	∨qkµ	∨qkµ	PROPN
ejpam-5876	283	59	,	,	PUNCT
ejpam-5876	283	60	and	and	CCONJ
ejpam-5876	284	1	so	so	ADV
ejpam-5876	284	2	(	(	PUNCT
ejpam-5876	284	3	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	284	4	)	)	PUNCT
ejpam-5876	284	5	)	)	PUNCT
ejpam-5876	285	1	∈	∈	PROPN
ejpam-5876	285	2	ℓµek	ℓµek	NOUN
ejpam-5876	285	3	(	(	PUNCT
ejpam-5876	285	4	t	t	PROPN
ejpam-5876	285	5	)	)	PUNCT
ejpam-5876	285	6	.	.	PUNCT
ejpam-5876	286	1	in	in	ADP
ejpam-5876	286	2	the	the	DET
ejpam-5876	286	3	second	second	ADJ
ejpam-5876	286	4	case	case	NOUN
ejpam-5876	286	5	,	,	PUNCT
ejpam-5876	286	6	xt	xt	ADP
ejpam-5876	286	7	∈	∈	PROPN
ejpam-5876	286	8	µ	µ	NOUN
ejpam-5876	286	9	implies	imply	VERB
ejpam-5876	286	10	µ(x	µ(x	NOUN
ejpam-5876	286	11	)	)	PUNCT
ejpam-5876	286	12	+	+	NUM
ejpam-5876	286	13	t	t	NOUN
ejpam-5876	286	14	+	+	CCONJ
ejpam-5876	286	15	k	k	PROPN
ejpam-5876	286	16	≥	≥	NUM
ejpam-5876	286	17	2	2	NUM
ejpam-5876	286	18	t	t	NOUN
ejpam-5876	286	19	+	+	CCONJ
ejpam-5876	286	20	k	k	X
ejpam-5876	286	21	>	>	X
ejpam-5876	286	22	1	1	NUM
ejpam-5876	286	23	,	,	PUNCT
ejpam-5876	286	24	that	that	ADV
ejpam-5876	286	25	is	is	ADV
ejpam-5876	286	26	,	,	PUNCT
ejpam-5876	286	27	xtqkµ.	xtqkµ.	PROPN
ejpam-5876	286	28	hence	hence	ADV
ejpam-5876	286	29	,	,	PUNCT
ejpam-5876	286	30	(	(	PUNCT
ejpam-5876	286	31	(	(	PUNCT
ejpam-5876	286	32	x|(y|y))|(x|(y|y)))t	x|(y|y))|(x|(y|y)))t	PROPN
ejpam-5876	286	33	∈	∈	PROPN
ejpam-5876	286	34	∨qkµ	∨qkµ	PROPN
ejpam-5876	286	35	,	,	PUNCT
ejpam-5876	286	36	and	and	CCONJ
ejpam-5876	286	37	so	so	ADV
ejpam-5876	286	38	(	(	PUNCT
ejpam-5876	286	39	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	286	40	)	)	PUNCT
ejpam-5876	286	41	)	)	PUNCT
ejpam-5876	287	1	∈	∈	PROPN
ejpam-5876	287	2	ℓµek	ℓµek	NOUN
ejpam-5876	287	3	(	(	PUNCT
ejpam-5876	287	4	t	t	PROPN
ejpam-5876	287	5	)	)	PUNCT
ejpam-5876	287	6	.	.	PUNCT
ejpam-5876	288	1	similarly	similarly	ADV
ejpam-5876	288	2	,	,	PUNCT
ejpam-5876	288	3	the	the	DET
ejpam-5876	288	4	third	third	ADJ
ejpam-5876	288	5	case	case	NOUN
ejpam-5876	288	6	implies	imply	VERB
ejpam-5876	288	7	(	(	PUNCT
ejpam-5876	288	8	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	NUM
ejpam-5876	288	9	)	)	PUNCT
ejpam-5876	288	10	)	)	PUNCT
ejpam-5876	289	1	∈	∈	PROPN
ejpam-5876	289	2	ℓµek	ℓµek	NOUN
ejpam-5876	289	3	(	(	PUNCT
ejpam-5876	289	4	t	t	PROPN
ejpam-5876	289	5	)	)	PUNCT
ejpam-5876	289	6	.	.	PUNCT
ejpam-5876	290	1	for	for	ADP
ejpam-5876	290	2	the	the	DET
ejpam-5876	290	3	last	last	ADJ
ejpam-5876	290	4	case	case	NOUN
ejpam-5876	290	5	,	,	PUNCT
ejpam-5876	290	6	we	we	PRON
ejpam-5876	290	7	have	have	VERB
ejpam-5876	290	8	(	(	PUNCT
ejpam-5876	290	9	(	(	PUNCT
ejpam-5876	290	10	x|(y|y))|(x|(y|y)))t	x|(y|y))|(x|(y|y)))t	PROPN
ejpam-5876	290	11	∈	∈	PROPN
ejpam-5876	290	12	∨qkµ	∨qkµ	PROPN
ejpam-5876	290	13	,	,	PUNCT
ejpam-5876	290	14	and	and	CCONJ
ejpam-5876	291	1	so	so	ADV
ejpam-5876	291	2	(	(	PUNCT
ejpam-5876	291	3	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	291	4	)	)	PUNCT
ejpam-5876	291	5	)	)	PUNCT
ejpam-5876	292	1	∈	∈	PROPN
ejpam-5876	292	2	ℓµek	ℓµek	NOUN
ejpam-5876	292	3	(	(	PUNCT
ejpam-5876	292	4	t	t	PROPN
ejpam-5876	292	5	)	)	PUNCT
ejpam-5876	292	6	.	.	PUNCT
ejpam-5876	293	1	consequently	consequently	ADV
ejpam-5876	293	2	,	,	PUNCT
ejpam-5876	293	3	ℓµek	ℓµek	PROPN
ejpam-5876	293	4	(	(	PUNCT
ejpam-5876	293	5	t	t	PROPN
ejpam-5876	293	6	)	)	PUNCT
ejpam-5876	293	7	is	be	AUX
ejpam-5876	293	8	an	an	DET
ejpam-5876	293	9	sup	sup	ADJ
ejpam-5876	293	10	-	-	PUNCT
ejpam-5876	293	11	subalgebra	subalgebra	NOUN
ejpam-5876	293	12	of	of	ADP
ejpam-5876	293	13	x	x	PUNCT
ejpam-5876	293	14	for	for	ADP
ejpam-5876	293	15	all	all	DET
ejpam-5876	293	16	t	t	NOUN
ejpam-5876	293	17	∈	∈	PROPN
ejpam-5876	293	18	ω	ω	PROPN
ejpam-5876	293	19	=	=	SYM
ejpam-5876	293	20	(	(	PUNCT
ejpam-5876	293	21	1−k	1−k	NUM
ejpam-5876	293	22	2	2	NUM
ejpam-5876	293	23	,	,	PUNCT
ejpam-5876	293	24	1	1	NUM
ejpam-5876	293	25	]	]	PUNCT
ejpam-5876	293	26	.	.	PUNCT
ejpam-5876	294	1	therefore	therefore	ADV
ejpam-5876	294	2	,	,	PUNCT
ejpam-5876	294	3	(	(	PUNCT
ejpam-5876	294	4	x	x	X
ejpam-5876	294	5	,	,	PUNCT
ejpam-5876	294	6	ℓµek	ℓµek	NOUN
ejpam-5876	294	7	)	)	PUNCT
ejpam-5876	294	8	is	be	AUX
ejpam-5876	294	9	a	a	DET
ejpam-5876	294	10	semidetached	semidetache	VERB
ejpam-5876	294	11	sup	sup	NOUN
ejpam-5876	294	12	-	-	PUNCT
ejpam-5876	294	13	subalgebra	subalgebra	NOUN
ejpam-5876	294	14	over	over	ADP
ejpam-5876	294	15	ω	ω	NUM
ejpam-5876	294	16	=	=	SYM
ejpam-5876	294	17	(	(	PUNCT
ejpam-5876	294	18	1−k	1−k	NUM
ejpam-5876	294	19	2	2	NUM
ejpam-5876	294	20	,	,	PUNCT
ejpam-5876	294	21	1	1	NUM
ejpam-5876	294	22	]	]	PUNCT
ejpam-5876	294	23	.	.	PUNCT
ejpam-5876	295	1	corollary	corollary	ADJ
ejpam-5876	295	2	12	12	NUM
ejpam-5876	295	3	is	be	AUX
ejpam-5876	295	4	derived	derive	VERB
ejpam-5876	295	5	from	from	ADP
ejpam-5876	295	6	theorem	theorem	NOUN
ejpam-5876	295	7	10	10	NUM
ejpam-5876	295	8	by	by	ADP
ejpam-5876	295	9	taking	take	VERB
ejpam-5876	295	10	k	k	PROPN
ejpam-5876	295	11	=	=	PUNCT
ejpam-5876	295	12	0	0	PROPN
ejpam-5876	295	13	,	,	PUNCT
ejpam-5876	295	14	which	which	PRON
ejpam-5876	295	15	yields	yield	VERB
ejpam-5876	295	16	the	the	DET
ejpam-5876	295	17	interval	interval	NOUN
ejpam-5876	295	18	ω	ω	PROPN
ejpam-5876	295	19	=	=	SYM
ejpam-5876	295	20	(	(	PUNCT
ejpam-5876	295	21	0.5	0.5	NUM
ejpam-5876	295	22	,	,	PUNCT
ejpam-5876	295	23	1	1	NUM
ejpam-5876	295	24	]	]	PUNCT
ejpam-5876	295	25	and	and	CCONJ
ejpam-5876	295	26	converts	convert	VERB
ejpam-5876	295	27	the	the	DET
ejpam-5876	295	28	generalized	generalized	ADJ
ejpam-5876	295	29	operator	operator	NOUN
ejpam-5876	295	30	qk	qk	NOUN
ejpam-5876	295	31	into	into	ADP
ejpam-5876	295	32	the	the	DET
ejpam-5876	295	33	standard	standard	ADJ
ejpam-5876	295	34	quasi	quasi	ADJ
ejpam-5876	295	35	-	-	ADJ
ejpam-5876	295	36	coincidence	coincidence	NOUN
ejpam-5876	295	37	operator	operator	NOUN
ejpam-5876	295	38	q.	q.	NOUN
ejpam-5876	295	39	theorem	theorem	VERB
ejpam-5876	295	40	10	10	NUM
ejpam-5876	295	41	proves	prove	VERB
ejpam-5876	295	42	that	that	SCONJ
ejpam-5876	295	43	if	if	SCONJ
ejpam-5876	295	44	µ	µ	NOUN
ejpam-5876	295	45	is	be	AUX
ejpam-5876	295	46	a	a	DET
ejpam-5876	295	47	(	(	PUNCT
ejpam-5876	295	48	qk,∈	qk,∈	INTJ
ejpam-5876	295	49	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	295	50	sup	sup	NOUN
ejpam-5876	295	51	-	-	PUNCT
ejpam-5876	295	52	subalgebra	subalgebra	NOUN
ejpam-5876	295	53	,	,	PUNCT
ejpam-5876	295	54	then	then	ADV
ejpam-5876	295	55	the	the	DET
ejpam-5876	295	56	structure	structure	NOUN
ejpam-5876	295	57	(	(	PUNCT
ejpam-5876	295	58	x	x	X
ejpam-5876	295	59	,	,	PUNCT
ejpam-5876	295	60	ℓeµ	ℓeµ	ADV
ejpam-5876	295	61	)	)	PUNCT
ejpam-5876	295	62	forms	form	VERB
ejpam-5876	295	63	a	a	DET
ejpam-5876	295	64	semidetached	semidetache	VERB
ejpam-5876	295	65	sup	sup	NOUN
ejpam-5876	295	66	-	-	PUNCT
ejpam-5876	295	67	subalgebra	subalgebra	NOUN
ejpam-5876	295	68	over	over	ADP
ejpam-5876	295	69	ω	ω	NUM
ejpam-5876	295	70	=	=	SYM
ejpam-5876	295	71	(	(	PUNCT
ejpam-5876	295	72	1−k	1−k	NUM
ejpam-5876	295	73	2	2	NUM
ejpam-5876	295	74	,	,	PUNCT
ejpam-5876	295	75	1	1	NUM
ejpam-5876	295	76	]	]	PUNCT
ejpam-5876	295	77	.	.	PUNCT
ejpam-5876	296	1	substituting	substitute	VERB
ejpam-5876	296	2	k	k	PROPN
ejpam-5876	296	3	=	=	SYM
ejpam-5876	296	4	0	0	NUM
ejpam-5876	296	5	confirms	confirm	VERB
ejpam-5876	296	6	the	the	DET
ejpam-5876	296	7	conclusion	conclusion	NOUN
ejpam-5876	296	8	for	for	ADP
ejpam-5876	296	9	the	the	DET
ejpam-5876	296	10	(	(	PUNCT
ejpam-5876	296	11	q,∈	q,∈	PROPN
ejpam-5876	296	12	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	296	13	case	case	NOUN
ejpam-5876	296	14	.	.	PUNCT
ejpam-5876	297	1	corollary	corollary	ADJ
ejpam-5876	297	2	12	12	NUM
ejpam-5876	297	3	.	.	PUNCT
ejpam-5876	298	1	if	if	SCONJ
ejpam-5876	298	2	µ	µ	NOUN
ejpam-5876	298	3	is	be	AUX
ejpam-5876	298	4	a	a	DET
ejpam-5876	298	5	(	(	PUNCT
ejpam-5876	298	6	q,∈	q,∈	PROPN
ejpam-5876	298	7	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	298	8	sup	sup	ADJ
ejpam-5876	298	9	-	-	PUNCT
ejpam-5876	298	10	subalgebra	subalgebra	NOUN
ejpam-5876	298	11	of	of	ADP
ejpam-5876	298	12	x	x	PRON
ejpam-5876	298	13	,	,	PUNCT
ejpam-5876	298	14	then	then	ADV
ejpam-5876	298	15	(	(	PUNCT
ejpam-5876	298	16	x	x	X
ejpam-5876	298	17	,	,	PUNCT
ejpam-5876	298	18	ℓµek	ℓµek	NOUN
ejpam-5876	298	19	)	)	PUNCT
ejpam-5876	298	20	is	be	AUX
ejpam-5876	298	21	a	a	DET
ejpam-5876	298	22	semidetached	semidetache	VERB
ejpam-5876	298	23	sup	sup	NOUN
ejpam-5876	298	24	-	-	PUNCT
ejpam-5876	298	25	subalgebra	subalgebra	NOUN
ejpam-5876	298	26	over	over	ADP
ejpam-5876	298	27	ω	ω	NUM
ejpam-5876	298	28	=	=	SYM
ejpam-5876	298	29	(	(	PUNCT
ejpam-5876	298	30	0.5	0.5	NUM
ejpam-5876	298	31	,	,	PUNCT
ejpam-5876	298	32	1	1	NUM
ejpam-5876	298	33	]	]	PUNCT
ejpam-5876	298	34	.	.	PUNCT
ejpam-5876	299	1	t.	t.	PROPN
ejpam-5876	299	2	oner	oner	PROPN
ejpam-5876	299	3	et	et	PROPN
ejpam-5876	299	4	al	al	PROPN
ejpam-5876	299	5	.	.	PUNCT
ejpam-5876	299	6	/	/	SYM
ejpam-5876	299	7	eur	eur	PROPN
ejpam-5876	299	8	.	.	PUNCT
ejpam-5876	300	1	j.	j.	PROPN
ejpam-5876	300	2	pure	pure	PROPN
ejpam-5876	300	3	appl	appl	PROPN
ejpam-5876	300	4	.	.	PROPN
ejpam-5876	300	5	math	math	PROPN
ejpam-5876	300	6	,	,	PUNCT
ejpam-5876	300	7	18	18	NUM
ejpam-5876	300	8	(	(	PUNCT
ejpam-5876	300	9	2	2	NUM
ejpam-5876	300	10	)	)	PUNCT
ejpam-5876	300	11	(	(	PUNCT
ejpam-5876	300	12	2025	2025	NUM
ejpam-5876	300	13	)	)	PUNCT
ejpam-5876	300	14	,	,	PUNCT
ejpam-5876	300	15	5876	5876	NUM
ejpam-5876	300	16	12	12	NUM
ejpam-5876	300	17	of	of	ADP
ejpam-5876	300	18	16	16	NUM
ejpam-5876	300	19	for	for	ADP
ejpam-5876	300	20	α	α	PRON
ejpam-5876	300	21	∈	∈	PROPN
ejpam-5876	300	22	{	{	PUNCT
ejpam-5876	300	23	∈	∈	PROPN
ejpam-5876	300	24	,	,	PUNCT
ejpam-5876	300	25	qk	qk	NOUN
ejpam-5876	300	26	}	}	PUNCT
ejpam-5876	300	27	and	and	CCONJ
ejpam-5876	300	28	t	t	PROPN
ejpam-5876	300	29	∈	∈	PROPN
ejpam-5876	300	30	(	(	PUNCT
ejpam-5876	300	31	0	0	NUM
ejpam-5876	300	32	,	,	PUNCT
ejpam-5876	300	33	1	1	NUM
ejpam-5876	300	34	]	]	PUNCT
ejpam-5876	301	1	,	,	PUNCT
ejpam-5876	301	2	we	we	PRON
ejpam-5876	301	3	say	say	VERB
ejpam-5876	301	4	that	that	PRON
ejpam-5876	301	5	xtαµ	xtαµ	PROPN
ejpam-5876	301	6	if	if	SCONJ
ejpam-5876	301	7	xtαµ	xtαµ	PROPN
ejpam-5876	301	8	does	do	AUX
ejpam-5876	301	9	not	not	PART
ejpam-5876	301	10	hold	hold	VERB
ejpam-5876	301	11	.	.	PUNCT
ejpam-5876	302	1	definition	definition	NOUN
ejpam-5876	302	2	10	10	NUM
ejpam-5876	302	3	.	.	PUNCT
ejpam-5876	303	1	a	a	DET
ejpam-5876	303	2	fuzzy	fuzzy	ADJ
ejpam-5876	303	3	set	set	VERB
ejpam-5876	303	4	µ	µ	NOUN
ejpam-5876	303	5	in	in	ADP
ejpam-5876	303	6	x	x	AUX
ejpam-5876	303	7	is	be	AUX
ejpam-5876	303	8	called	call	VERB
ejpam-5876	303	9	an	an	DET
ejpam-5876	303	10	(	(	PUNCT
ejpam-5876	303	11	∈,∈	∈,∈	X
ejpam-5876	303	12	∨	∨	NUM
ejpam-5876	303	13	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	303	14	sup	sup	NOUN
ejpam-5876	303	15	-	-	PUNCT
ejpam-5876	303	16	subalgebra	subalgebra	NOUN
ejpam-5876	303	17	of	of	ADP
ejpam-5876	303	18	x	x	PRON
ejpam-5876	303	19	if	if	SCONJ
ejpam-5876	303	20	it	it	PRON
ejpam-5876	303	21	satisfies	satisfy	VERB
ejpam-5876	303	22	the	the	DET
ejpam-5876	303	23	following	following	NOUN
ejpam-5876	303	24	:	:	PUNCT
ejpam-5876	303	25	(	(	PUNCT
ejpam-5876	303	26	∀x	∀x	X
ejpam-5876	303	27	,	,	PUNCT
ejpam-5876	303	28	y	y	PROPN
ejpam-5876	303	29	∈	∈	PROPN
ejpam-5876	303	30	x)(∀t	x)(∀t	PROPN
ejpam-5876	303	31	,	,	PUNCT
ejpam-5876	303	32	r	r	NOUN
ejpam-5876	303	33	∈	∈	PROPN
ejpam-5876	303	34	(	(	PUNCT
ejpam-5876	303	35	0	0	NUM
ejpam-5876	303	36	,	,	PUNCT
ejpam-5876	303	37	1])(((x|(y|y))|(x|(y|y)))min{t	1])(((x|(y|y))|(x|(y|y)))min{t	NUM
ejpam-5876	303	38	,	,	PUNCT
ejpam-5876	303	39	r}∈µ	r}∈µ	ADP
ejpam-5876	303	40	⇒	⇒	PROPN
ejpam-5876	303	41	xt∈	xt∈	PROPN
ejpam-5876	303	42	∨	∨	NUM
ejpam-5876	303	43	qkµ	qkµ	NOUN
ejpam-5876	303	44	or	or	CCONJ
ejpam-5876	303	45	yr∈	yr∈	PROPN
ejpam-5876	303	46	∨	∨	PROPN
ejpam-5876	303	47	qkµ	qkµ	PROPN
ejpam-5876	303	48	)	)	PUNCT
ejpam-5876	303	49	.	.	PUNCT
ejpam-5876	304	1	(	(	PUNCT
ejpam-5876	304	2	13	13	NUM
ejpam-5876	304	3	)	)	PUNCT
ejpam-5876	304	4	an	an	DET
ejpam-5876	304	5	(	(	PUNCT
ejpam-5876	304	6	∈,∈	∈,∈	X
ejpam-5876	304	7	∨	∨	NUM
ejpam-5876	304	8	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	304	9	sup	sup	NOUN
ejpam-5876	304	10	-	-	PUNCT
ejpam-5876	304	11	subalgebra	subalgebra	NOUN
ejpam-5876	304	12	with	with	ADP
ejpam-5876	304	13	k	k	PROPN
ejpam-5876	304	14	=	=	SYM
ejpam-5876	304	15	0	0	NUM
ejpam-5876	304	16	is	be	AUX
ejpam-5876	304	17	called	call	VERB
ejpam-5876	304	18	an	an	DET
ejpam-5876	304	19	(	(	PUNCT
ejpam-5876	304	20	∈,∈	∈,∈	X
ejpam-5876	304	21	∨	∨	NUM
ejpam-5876	304	22	q)-fuzzy	q)-fuzzy	PUNCT
ejpam-5876	304	23	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	304	24	.	.	PUNCT
ejpam-5876	305	1	theorem	theorem	VERB
ejpam-5876	305	2	11	11	NUM
ejpam-5876	305	3	.	.	PUNCT
ejpam-5876	306	1	a	a	DET
ejpam-5876	306	2	fuzzy	fuzzy	ADJ
ejpam-5876	306	3	set	set	VERB
ejpam-5876	306	4	µ	µ	NOUN
ejpam-5876	306	5	in	in	ADP
ejpam-5876	306	6	x	x	VERB
ejpam-5876	306	7	is	be	AUX
ejpam-5876	306	8	an	an	DET
ejpam-5876	306	9	(	(	PUNCT
ejpam-5876	306	10	∈,∈∨	∈,∈∨	PROPN
ejpam-5876	306	11	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	306	12	sup	sup	NOUN
ejpam-5876	306	13	-	-	PUNCT
ejpam-5876	306	14	subalgebra	subalgebra	NOUN
ejpam-5876	306	15	of	of	ADP
ejpam-5876	306	16	x	x	PRON
ejpam-5876	306	17	if	if	SCONJ
ejpam-5876	306	18	and	and	CCONJ
ejpam-5876	306	19	only	only	ADV
ejpam-5876	306	20	if	if	SCONJ
ejpam-5876	306	21	the	the	DET
ejpam-5876	306	22	following	follow	VERB
ejpam-5876	306	23	inequality	inequality	NOUN
ejpam-5876	306	24	is	be	AUX
ejpam-5876	306	25	valid	valid	ADJ
ejpam-5876	306	26	:	:	PUNCT
ejpam-5876	306	27	(	(	PUNCT
ejpam-5876	306	28	∀x	∀x	X
ejpam-5876	306	29	,	,	PUNCT
ejpam-5876	306	30	y	y	PROPN
ejpam-5876	306	31	∈	∈	PROPN
ejpam-5876	306	32	x)(max{µ((x|(y|y))|(x|(y|y	x)(max{µ((x|(y|y))|(x|(y|y	PROPN
ejpam-5876	306	33	)	)	PUNCT
ejpam-5876	306	34	)	)	PUNCT
ejpam-5876	306	35	)	)	PUNCT
ejpam-5876	306	36	,	,	PUNCT
ejpam-5876	306	37	1−	1−	NUM
ejpam-5876	306	38	k	k	NOUN
ejpam-5876	306	39	2	2	NUM
ejpam-5876	306	40	}	}	PUNCT
ejpam-5876	306	41	≥	≥	NOUN
ejpam-5876	306	42	min{µ(x	min{µ(x	NOUN
ejpam-5876	306	43	)	)	PUNCT
ejpam-5876	306	44	,	,	PUNCT
ejpam-5876	306	45	µ(y	µ(y	PROPN
ejpam-5876	306	46	)	)	PUNCT
ejpam-5876	306	47	}	}	PUNCT
ejpam-5876	306	48	)	)	PUNCT
ejpam-5876	306	49	.	.	PUNCT
ejpam-5876	307	1	(	(	PUNCT
ejpam-5876	307	2	14	14	NUM
ejpam-5876	307	3	)	)	PUNCT
ejpam-5876	307	4	proof	proof	NOUN
ejpam-5876	307	5	.	.	PUNCT
ejpam-5876	308	1	let	let	VERB
ejpam-5876	308	2	µ	µ	X
ejpam-5876	308	3	be	be	AUX
ejpam-5876	308	4	an	an	DET
ejpam-5876	308	5	(	(	PUNCT
ejpam-5876	308	6	∈,∈	∈,∈	X
ejpam-5876	308	7	∨	∨	NUM
ejpam-5876	308	8	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	308	9	sup	sup	NOUN
ejpam-5876	308	10	-	-	PUNCT
ejpam-5876	308	11	subalgebra	subalgebra	NOUN
ejpam-5876	308	12	of	of	ADP
ejpam-5876	308	13	x.	x.	NOUN
ejpam-5876	308	14	assume	assume	VERB
ejpam-5876	308	15	that	that	SCONJ
ejpam-5876	308	16	(	(	PUNCT
ejpam-5876	308	17	14	14	NUM
ejpam-5876	308	18	)	)	PUNCT
ejpam-5876	308	19	is	be	AUX
ejpam-5876	308	20	not	not	PART
ejpam-5876	308	21	valid	valid	ADJ
ejpam-5876	308	22	.	.	PUNCT
ejpam-5876	309	1	then	then	ADV
ejpam-5876	309	2	there	there	PRON
ejpam-5876	309	3	exist	exist	VERB
ejpam-5876	309	4	a	a	DET
ejpam-5876	309	5	,	,	PUNCT
ejpam-5876	309	6	b	b	X
ejpam-5876	309	7	∈	∈	PROPN
ejpam-5876	309	8	x	x	PUNCT
ejpam-5876	309	9	such	such	ADJ
ejpam-5876	309	10	that	that	DET
ejpam-5876	309	11	max{µ((a|(b|b))|(a|(b|b	max{µ((a|(b|b))|(a|(b|b	NOUN
ejpam-5876	309	12	)	)	PUNCT
ejpam-5876	309	13	)	)	PUNCT
ejpam-5876	309	14	)	)	PUNCT
ejpam-5876	309	15	,	,	PUNCT
ejpam-5876	309	16	1−k	1−k	NUM
ejpam-5876	309	17	2	2	NUM
ejpam-5876	309	18	}	}	PUNCT
ejpam-5876	309	19	<	<	X
ejpam-5876	309	20	min{µ(a	min{µ(a	PROPN
ejpam-5876	309	21	)	)	PUNCT
ejpam-5876	309	22	,	,	PUNCT
ejpam-5876	309	23	µ(b	µ(b	PROPN
ejpam-5876	309	24	)	)	PUNCT
ejpam-5876	309	25	}	}	PUNCT
ejpam-5876	309	26	=	=	SYM
ejpam-5876	310	1	t.	t.	NOUN
ejpam-5876	310	2	then	then	ADV
ejpam-5876	310	3	1−k	1−k	NUM
ejpam-5876	310	4	2	2	NUM
ejpam-5876	310	5	<	<	X
ejpam-5876	310	6	t	t	X
ejpam-5876	310	7	≤	≤	NUM
ejpam-5876	310	8	1	1	NUM
ejpam-5876	310	9	,	,	PUNCT
ejpam-5876	310	10	at	at	ADP
ejpam-5876	310	11	∈	∈	PROPN
ejpam-5876	310	12	µ	µ	NUM
ejpam-5876	310	13	,	,	PUNCT
ejpam-5876	310	14	bt	bt	PROPN
ejpam-5876	310	15	∈	∈	PROPN
ejpam-5876	310	16	µ	µ	X
ejpam-5876	310	17	and	and	CCONJ
ejpam-5876	310	18	(	(	PUNCT
ejpam-5876	310	19	(	(	PUNCT
ejpam-5876	310	20	a|(b|b))|(a|(b|b)))t∈µ.	a|(b|b))|(a|(b|b)))t∈µ.	NOUN
ejpam-5876	310	21	it	it	PRON
ejpam-5876	310	22	follows	follow	VERB
ejpam-5876	310	23	from	from	ADP
ejpam-5876	310	24	(	(	PUNCT
ejpam-5876	310	25	13	13	NUM
ejpam-5876	310	26	)	)	PUNCT
ejpam-5876	310	27	that	that	PRON
ejpam-5876	310	28	atqkµ	atqkµ	VERB
ejpam-5876	310	29	or	or	CCONJ
ejpam-5876	310	30	btqkµ.	btqkµ.	NOUN
ejpam-5876	310	31	hence	hence	ADV
ejpam-5876	310	32	,	,	PUNCT
ejpam-5876	310	33	µ(a	µ(a	PROPN
ejpam-5876	310	34	)	)	PUNCT
ejpam-5876	310	35	≥	≥	NOUN
ejpam-5876	310	36	t	t	NOUN
ejpam-5876	310	37	and	and	CCONJ
ejpam-5876	310	38	µ(a	µ(a	PROPN
ejpam-5876	310	39	)	)	PUNCT
ejpam-5876	311	1	+	+	NUM
ejpam-5876	311	2	t	t	NOUN
ejpam-5876	311	3	+	+	CCONJ
ejpam-5876	311	4	k	k	PROPN
ejpam-5876	311	5	≤	≤	ADV
ejpam-5876	311	6	1	1	NUM
ejpam-5876	311	7	or	or	CCONJ
ejpam-5876	311	8	µ(b	µ(b	NOUN
ejpam-5876	311	9	)	)	PUNCT
ejpam-5876	311	10	≥	≥	NOUN
ejpam-5876	311	11	t	t	NOUN
ejpam-5876	311	12	and	and	CCONJ
ejpam-5876	311	13	µ(b	µ(b	NOUN
ejpam-5876	311	14	)	)	PUNCT
ejpam-5876	312	1	+	+	NUM
ejpam-5876	312	2	t	t	NOUN
ejpam-5876	312	3	+	+	CCONJ
ejpam-5876	312	4	k	k	PROPN
ejpam-5876	312	5	≤	≤	ADV
ejpam-5876	312	6	1	1	NUM
ejpam-5876	312	7	.	.	PUNCT
ejpam-5876	313	1	in	in	ADP
ejpam-5876	313	2	either	either	DET
ejpam-5876	313	3	case	case	NOUN
ejpam-5876	313	4	,	,	PUNCT
ejpam-5876	313	5	we	we	PRON
ejpam-5876	313	6	have	have	VERB
ejpam-5876	313	7	t	t	NOUN
ejpam-5876	313	8	≤	≤	NUM
ejpam-5876	313	9	1−k	1−k	NUM
ejpam-5876	313	10	2	2	NUM
ejpam-5876	313	11	,	,	PUNCT
ejpam-5876	313	12	which	which	PRON
ejpam-5876	313	13	is	be	AUX
ejpam-5876	313	14	a	a	DET
ejpam-5876	313	15	contradiction	contradiction	NOUN
ejpam-5876	313	16	.	.	PUNCT
ejpam-5876	314	1	therefore	therefore	ADV
ejpam-5876	314	2	,	,	PUNCT
ejpam-5876	314	3	max{µ((x|(y|y))|(x|(y|y	max{µ((x|(y|y))|(x|(y|y	PROPN
ejpam-5876	314	4	)	)	PUNCT
ejpam-5876	314	5	)	)	PUNCT
ejpam-5876	314	6	)	)	PUNCT
ejpam-5876	314	7	,	,	PUNCT
ejpam-5876	314	8	1−k	1−k	NUM
ejpam-5876	314	9	2	2	NUM
ejpam-5876	314	10	}	}	PUNCT
ejpam-5876	314	11	≥	≥	NOUN
ejpam-5876	314	12	min{µ(x	min{µ(x	NOUN
ejpam-5876	314	13	)	)	PUNCT
ejpam-5876	314	14	,	,	PUNCT
ejpam-5876	314	15	µ(y	µ(y	PROPN
ejpam-5876	314	16	)	)	PUNCT
ejpam-5876	314	17	}	}	PUNCT
ejpam-5876	314	18	for	for	ADP
ejpam-5876	314	19	all	all	DET
ejpam-5876	314	20	x	x	NOUN
ejpam-5876	314	21	,	,	PUNCT
ejpam-5876	314	22	y	y	PROPN
ejpam-5876	314	23	∈	∈	PROPN
ejpam-5876	314	24	x.	x.	NOUN
ejpam-5876	314	25	conversely	conversely	ADV
ejpam-5876	314	26	,	,	PUNCT
ejpam-5876	314	27	suppose	suppose	VERB
ejpam-5876	314	28	that	that	SCONJ
ejpam-5876	314	29	(	(	PUNCT
ejpam-5876	314	30	14	14	NUM
ejpam-5876	314	31	)	)	PUNCT
ejpam-5876	314	32	is	be	AUX
ejpam-5876	314	33	valid	valid	ADJ
ejpam-5876	314	34	.	.	PUNCT
ejpam-5876	315	1	let	let	VERB
ejpam-5876	315	2	(	(	PUNCT
ejpam-5876	315	3	(	(	PUNCT
ejpam-5876	315	4	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	315	5	,	,	PUNCT
ejpam-5876	315	6	r}∈µ	r}∈µ	ADP
ejpam-5876	315	7	for	for	ADP
ejpam-5876	315	8	all	all	DET
ejpam-5876	315	9	x	x	NOUN
ejpam-5876	315	10	,	,	PUNCT
ejpam-5876	315	11	y	y	PROPN
ejpam-5876	315	12	∈	∈	PROPN
ejpam-5876	315	13	x	x	X
ejpam-5876	315	14	and	and	CCONJ
ejpam-5876	315	15	t	t	PROPN
ejpam-5876	315	16	,	,	PUNCT
ejpam-5876	315	17	r	r	NOUN
ejpam-5876	315	18	∈	∈	PROPN
ejpam-5876	315	19	(	(	PUNCT
ejpam-5876	315	20	0	0	NUM
ejpam-5876	315	21	,	,	PUNCT
ejpam-5876	315	22	1	1	NUM
ejpam-5876	315	23	]	]	PUNCT
ejpam-5876	315	24	.	.	PUNCT
ejpam-5876	316	1	then	then	ADV
ejpam-5876	316	2	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	316	3	)	)	PUNCT
ejpam-5876	316	4	)	)	PUNCT
ejpam-5876	316	5	)	)	PUNCT
ejpam-5876	317	1	<	<	X
ejpam-5876	317	2	min{t	min{t	PROPN
ejpam-5876	317	3	,	,	PUNCT
ejpam-5876	317	4	r	r	NOUN
ejpam-5876	317	5	}	}	PUNCT
ejpam-5876	317	6	.	.	PUNCT
ejpam-5876	318	1	if	if	SCONJ
ejpam-5876	318	2	max{µ((x|(y|y))|(x|(y|y	max{µ((x|(y|y))|(x|(y|y	PROPN
ejpam-5876	318	3	)	)	PUNCT
ejpam-5876	318	4	)	)	PUNCT
ejpam-5876	318	5	)	)	PUNCT
ejpam-5876	318	6	,	,	PUNCT
ejpam-5876	318	7	1−k	1−k	NUM
ejpam-5876	318	8	2	2	NUM
ejpam-5876	318	9	}	}	PUNCT
ejpam-5876	318	10	=	=	SYM
ejpam-5876	318	11	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	318	12	)	)	PUNCT
ejpam-5876	318	13	)	)	PUNCT
ejpam-5876	318	14	)	)	PUNCT
ejpam-5876	318	15	,	,	PUNCT
ejpam-5876	318	16	then	then	ADV
ejpam-5876	318	17	min{t	min{t	PROPN
ejpam-5876	318	18	,	,	PUNCT
ejpam-5876	318	19	r	r	NOUN
ejpam-5876	318	20	}	}	PUNCT
ejpam-5876	318	21	>	>	X
ejpam-5876	318	22	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	318	23	)	)	PUNCT
ejpam-5876	318	24	)	)	PUNCT
ejpam-5876	318	25	)	)	PUNCT
ejpam-5876	318	26	≥	≥	NOUN
ejpam-5876	319	1	min{µ(x	min{µ(x	NOUN
ejpam-5876	319	2	)	)	PUNCT
ejpam-5876	319	3	,	,	PUNCT
ejpam-5876	319	4	µ(y	µ(y	PROPN
ejpam-5876	319	5	)	)	PUNCT
ejpam-5876	319	6	}	}	PUNCT
ejpam-5876	319	7	,	,	PUNCT
ejpam-5876	319	8	and	and	CCONJ
ejpam-5876	319	9	so	so	ADV
ejpam-5876	319	10	µ(x	µ(x	NOUN
ejpam-5876	319	11	)	)	PUNCT
ejpam-5876	319	12	<	<	X
ejpam-5876	319	13	t	t	PROPN
ejpam-5876	319	14	or	or	CCONJ
ejpam-5876	319	15	µ(y	µ(y	NUM
ejpam-5876	319	16	)	)	PUNCT
ejpam-5876	319	17	<	<	X
ejpam-5876	319	18	r.	r.	PROPN
ejpam-5876	319	19	thus	thus	ADV
ejpam-5876	319	20	,	,	PUNCT
ejpam-5876	319	21	xt∈µ	xt∈µ	PROPN
ejpam-5876	319	22	or	or	CCONJ
ejpam-5876	319	23	yr∈µ	yr∈µ	NOUN
ejpam-5876	319	24	,	,	PUNCT
ejpam-5876	319	25	which	which	PRON
ejpam-5876	319	26	implies	imply	VERB
ejpam-5876	319	27	that	that	SCONJ
ejpam-5876	319	28	xt∈∨qkµ	xt∈∨qkµ	PROPN
ejpam-5876	319	29	or	or	CCONJ
ejpam-5876	319	30	yr∈∨qkµ.	yr∈∨qkµ.	PRON
ejpam-5876	319	31	if	if	SCONJ
ejpam-5876	319	32	max{µ((x|(y|y))|(x|(y|y	max{µ((x|(y|y))|(x|(y|y	PROPN
ejpam-5876	319	33	)	)	PUNCT
ejpam-5876	319	34	)	)	PUNCT
ejpam-5876	319	35	)	)	PUNCT
ejpam-5876	319	36	,	,	PUNCT
ejpam-5876	319	37	1−k	1−k	NUM
ejpam-5876	319	38	2	2	NUM
ejpam-5876	319	39	}	}	PUNCT
ejpam-5876	319	40	=	=	PUNCT
ejpam-5876	320	1	1−k	1−k	NUM
ejpam-5876	320	2	2	2	NUM
ejpam-5876	320	3	,	,	PUNCT
ejpam-5876	320	4	then	then	ADV
ejpam-5876	320	5	min{µ(x	min{µ(x	PROPN
ejpam-5876	320	6	)	)	PUNCT
ejpam-5876	320	7	,	,	PUNCT
ejpam-5876	320	8	µ(y	µ(y	PROPN
ejpam-5876	320	9	)	)	PUNCT
ejpam-5876	320	10	}	}	PUNCT
ejpam-5876	320	11	≤	≤	NOUN
ejpam-5876	320	12	1−k	1−k	NUM
ejpam-5876	320	13	2	2	NUM
ejpam-5876	320	14	.	.	PUNCT
ejpam-5876	320	15	suppose	suppose	VERB
ejpam-5876	320	16	xt	xt	PROPN
ejpam-5876	320	17	∈	∈	PROPN
ejpam-5876	320	18	µ	µ	PROPN
ejpam-5876	320	19	or	or	CCONJ
ejpam-5876	320	20	yr	yr	NOUN
ejpam-5876	320	21	∈	∈	PROPN
ejpam-5876	320	22	µ.	µ.	NOUN
ejpam-5876	320	23	then	then	ADV
ejpam-5876	320	24	t	t	X
ejpam-5876	320	25	≤	≤	NUM
ejpam-5876	320	26	µ(x	µ(x	NOUN
ejpam-5876	320	27	)	)	PUNCT
ejpam-5876	320	28	≤	≤	NOUN
ejpam-5876	320	29	1−k	1−k	NUM
ejpam-5876	320	30	2	2	NUM
ejpam-5876	320	31	or	or	CCONJ
ejpam-5876	320	32	r	r	NOUN
ejpam-5876	320	33	≤	≤	NUM
ejpam-5876	320	34	µ(y	µ(y	NOUN
ejpam-5876	320	35	)	)	PUNCT
ejpam-5876	320	36	≤	≤	NOUN
ejpam-5876	320	37	1−k	1−k	NUM
ejpam-5876	320	38	2	2	NUM
ejpam-5876	320	39	,	,	PUNCT
ejpam-5876	320	40	and	and	CCONJ
ejpam-5876	320	41	so	so	ADV
ejpam-5876	320	42	µ(x)+t+k	µ(x)+t+k	ADJ
ejpam-5876	320	43	≤	≤	NUM
ejpam-5876	320	44	1−k	1−k	NUM
ejpam-5876	320	45	2	2	NUM
ejpam-5876	321	1	+	+	CCONJ
ejpam-5876	321	2	1−k	1−k	NUM
ejpam-5876	321	3	2	2	NUM
ejpam-5876	322	1	+	+	NOUN
ejpam-5876	322	2	k	k	NOUN
ejpam-5876	322	3	=	=	SYM
ejpam-5876	322	4	1	1	NUM
ejpam-5876	322	5	or	or	CCONJ
ejpam-5876	322	6	µ(y	µ(y	NUM
ejpam-5876	322	7	)	)	PUNCT
ejpam-5876	323	1	+	+	CCONJ
ejpam-5876	323	2	r	r	NOUN
ejpam-5876	323	3	+	+	CCONJ
ejpam-5876	323	4	k	k	PROPN
ejpam-5876	323	5	≤	≤	NUM
ejpam-5876	323	6	1−k	1−k	NUM
ejpam-5876	323	7	2	2	NUM
ejpam-5876	323	8	+	+	CCONJ
ejpam-5876	323	9	1−k	1−k	NUM
ejpam-5876	323	10	2	2	NUM
ejpam-5876	323	11	+	+	CCONJ
ejpam-5876	323	12	k	k	NOUN
ejpam-5876	323	13	=	=	SYM
ejpam-5876	323	14	1	1	X
ejpam-5876	323	15	.	.	PUNCT
ejpam-5876	324	1	hence	hence	ADV
ejpam-5876	324	2	,	,	PUNCT
ejpam-5876	324	3	xtqkµ	xtqkµ	PROPN
ejpam-5876	324	4	or	or	CCONJ
ejpam-5876	324	5	yrqkµ.	yrqkµ.	NOUN
ejpam-5876	324	6	therefore	therefore	ADV
ejpam-5876	324	7	,	,	PUNCT
ejpam-5876	324	8	xt∈	xt∈	PROPN
ejpam-5876	324	9	∨	∨	NUM
ejpam-5876	324	10	qkµ	qkµ	NOUN
ejpam-5876	324	11	or	or	CCONJ
ejpam-5876	324	12	yr∈	yr∈	PROPN
ejpam-5876	324	13	∨	∨	PROPN
ejpam-5876	324	14	qkµ.	qkµ.	NOUN
ejpam-5876	324	15	this	this	PRON
ejpam-5876	324	16	shows	show	VERB
ejpam-5876	324	17	that	that	SCONJ
ejpam-5876	324	18	µ	µ	NOUN
ejpam-5876	324	19	is	be	AUX
ejpam-5876	324	20	an	an	DET
ejpam-5876	324	21	(	(	PUNCT
ejpam-5876	324	22	∈,∈	∈,∈	X
ejpam-5876	324	23	∨	∨	NUM
ejpam-5876	324	24	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	324	25	sup	sup	NOUN
ejpam-5876	324	26	-	-	PUNCT
ejpam-5876	324	27	subalgebra	subalgebra	NOUN
ejpam-5876	324	28	of	of	ADP
ejpam-5876	324	29	x.	x.	PROPN
ejpam-5876	324	30	corollary	corollary	PROPN
ejpam-5876	324	31	13	13	NUM
ejpam-5876	324	32	follows	follow	VERB
ejpam-5876	324	33	directly	directly	ADV
ejpam-5876	324	34	from	from	ADP
ejpam-5876	324	35	theorem	theorem	NOUN
ejpam-5876	324	36	11	11	NUM
ejpam-5876	324	37	by	by	ADP
ejpam-5876	324	38	setting	set	VERB
ejpam-5876	324	39	k	k	PROPN
ejpam-5876	324	40	=	=	PUNCT
ejpam-5876	324	41	0	0	X
ejpam-5876	324	42	.	.	PUNCT
ejpam-5876	325	1	in	in	ADP
ejpam-5876	325	2	this	this	DET
ejpam-5876	325	3	case	case	NOUN
ejpam-5876	325	4	,	,	PUNCT
ejpam-5876	325	5	the	the	DET
ejpam-5876	325	6	inequality	inequality	NOUN
ejpam-5876	325	7	given	give	VERB
ejpam-5876	325	8	in	in	ADP
ejpam-5876	325	9	theorem	theorem	ADJ
ejpam-5876	325	10	11	11	NUM
ejpam-5876	325	11	simplifies	simplifie	NOUN
ejpam-5876	325	12	to	to	ADP
ejpam-5876	325	13	max{µ((x|(y|y))|(x|(y|y	max{µ((x|(y|y))|(x|(y|y	NOUN
ejpam-5876	325	14	)	)	PUNCT
ejpam-5876	325	15	)	)	PUNCT
ejpam-5876	325	16	)	)	PUNCT
ejpam-5876	325	17	,	,	PUNCT
ejpam-5876	325	18	0.5	0.5	NUM
ejpam-5876	325	19	}	}	PUNCT
ejpam-5876	325	20	≥	≥	NOUN
ejpam-5876	325	21	min{µ(x	min{µ(x	NOUN
ejpam-5876	325	22	)	)	PUNCT
ejpam-5876	325	23	,	,	PUNCT
ejpam-5876	325	24	µ(y	µ(y	PROPN
ejpam-5876	325	25	)	)	PUNCT
ejpam-5876	325	26	}	}	PUNCT
ejpam-5876	325	27	,	,	PUNCT
ejpam-5876	325	28	which	which	PRON
ejpam-5876	325	29	is	be	AUX
ejpam-5876	325	30	exactly	exactly	ADV
ejpam-5876	325	31	the	the	DET
ejpam-5876	325	32	condition	condition	NOUN
ejpam-5876	325	33	stated	state	VERB
ejpam-5876	325	34	in	in	ADP
ejpam-5876	325	35	corollary	corollary	ADJ
ejpam-5876	325	36	13	13	NUM
ejpam-5876	325	37	.	.	PUNCT
ejpam-5876	326	1	hence	hence	ADV
ejpam-5876	326	2	,	,	PUNCT
ejpam-5876	326	3	the	the	DET
ejpam-5876	326	4	result	result	NOUN
ejpam-5876	326	5	is	be	AUX
ejpam-5876	326	6	an	an	DET
ejpam-5876	326	7	immediate	immediate	ADJ
ejpam-5876	326	8	specialization	specialization	NOUN
ejpam-5876	326	9	of	of	ADP
ejpam-5876	326	10	the	the	DET
ejpam-5876	326	11	general	general	ADJ
ejpam-5876	326	12	case	case	NOUN
ejpam-5876	326	13	when	when	SCONJ
ejpam-5876	326	14	k	k	PROPN
ejpam-5876	326	15	=	=	SYM
ejpam-5876	326	16	0	0	X
ejpam-5876	326	17	.	.	PUNCT
ejpam-5876	326	18	corollary	corollary	ADJ
ejpam-5876	326	19	13	13	NUM
ejpam-5876	326	20	.	.	PUNCT
ejpam-5876	327	1	a	a	DET
ejpam-5876	327	2	fuzzy	fuzzy	ADJ
ejpam-5876	327	3	set	set	VERB
ejpam-5876	327	4	µ	µ	NOUN
ejpam-5876	327	5	in	in	ADP
ejpam-5876	327	6	x	x	VERB
ejpam-5876	327	7	is	be	AUX
ejpam-5876	327	8	an	an	DET
ejpam-5876	327	9	(	(	PUNCT
ejpam-5876	327	10	∈,∈∨	∈,∈∨	PROPN
ejpam-5876	327	11	q)-fuzzy	q)-fuzzy	PUNCT
ejpam-5876	327	12	sup	sup	NOUN
ejpam-5876	327	13	-	-	PUNCT
ejpam-5876	327	14	subalgebra	subalgebra	NOUN
ejpam-5876	327	15	of	of	ADP
ejpam-5876	327	16	x	x	PRON
ejpam-5876	327	17	if	if	SCONJ
ejpam-5876	327	18	and	and	CCONJ
ejpam-5876	327	19	only	only	ADV
ejpam-5876	327	20	if	if	SCONJ
ejpam-5876	327	21	the	the	DET
ejpam-5876	327	22	following	follow	VERB
ejpam-5876	327	23	inequality	inequality	NOUN
ejpam-5876	327	24	is	be	AUX
ejpam-5876	327	25	valid	valid	ADJ
ejpam-5876	327	26	:	:	PUNCT
ejpam-5876	327	27	(	(	PUNCT
ejpam-5876	327	28	∀x	∀x	X
ejpam-5876	327	29	,	,	PUNCT
ejpam-5876	327	30	y	y	PROPN
ejpam-5876	327	31	∈	∈	PROPN
ejpam-5876	327	32	x)(max{µ((x|(y|y))|(x|(y|y	x)(max{µ((x|(y|y))|(x|(y|y	PROPN
ejpam-5876	327	33	)	)	PUNCT
ejpam-5876	327	34	)	)	PUNCT
ejpam-5876	327	35	)	)	PUNCT
ejpam-5876	327	36	,	,	PUNCT
ejpam-5876	327	37	0.5	0.5	NUM
ejpam-5876	327	38	}	}	PUNCT
ejpam-5876	327	39	≥	≥	NOUN
ejpam-5876	327	40	min{µ(x	min{µ(x	NOUN
ejpam-5876	327	41	)	)	PUNCT
ejpam-5876	327	42	,	,	PUNCT
ejpam-5876	327	43	µ(y	µ(y	PROPN
ejpam-5876	327	44	)	)	PUNCT
ejpam-5876	327	45	}	}	PUNCT
ejpam-5876	327	46	)	)	PUNCT
ejpam-5876	327	47	.	.	PUNCT
ejpam-5876	328	1	(	(	PUNCT
ejpam-5876	328	2	15	15	NUM
ejpam-5876	328	3	)	)	PUNCT
ejpam-5876	328	4	theorem	theorem	NOUN
ejpam-5876	328	5	12	12	NUM
ejpam-5876	328	6	.	.	PUNCT
ejpam-5876	329	1	a	a	DET
ejpam-5876	329	2	fuzzy	fuzzy	ADJ
ejpam-5876	329	3	set	set	VERB
ejpam-5876	329	4	µ	µ	NOUN
ejpam-5876	329	5	in	in	ADP
ejpam-5876	329	6	x	x	VERB
ejpam-5876	329	7	is	be	AUX
ejpam-5876	329	8	an	an	DET
ejpam-5876	329	9	(	(	PUNCT
ejpam-5876	329	10	∈,∈∨	∈,∈∨	PROPN
ejpam-5876	329	11	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	329	12	sup	sup	NOUN
ejpam-5876	329	13	-	-	PUNCT
ejpam-5876	329	14	subalgebra	subalgebra	NOUN
ejpam-5876	329	15	of	of	ADP
ejpam-5876	329	16	x	x	PRON
ejpam-5876	329	17	if	if	SCONJ
ejpam-5876	329	18	and	and	CCONJ
ejpam-5876	329	19	only	only	ADV
ejpam-5876	329	20	if	if	SCONJ
ejpam-5876	329	21	(	(	PUNCT
ejpam-5876	329	22	x	x	NOUN
ejpam-5876	329	23	,	,	PUNCT
ejpam-5876	329	24	ℓµu	ℓµu	NOUN
ejpam-5876	329	25	)	)	PUNCT
ejpam-5876	329	26	is	be	AUX
ejpam-5876	329	27	a	a	DET
ejpam-5876	329	28	semidetached	semidetache	VERB
ejpam-5876	329	29	sup	sup	NOUN
ejpam-5876	329	30	-	-	PUNCT
ejpam-5876	329	31	subalgebra	subalgebra	NOUN
ejpam-5876	329	32	over	over	ADP
ejpam-5876	329	33	ω	ω	NUM
ejpam-5876	329	34	=	=	SYM
ejpam-5876	329	35	(	(	PUNCT
ejpam-5876	329	36	1−k	1−k	NUM
ejpam-5876	329	37	2	2	NUM
ejpam-5876	329	38	,	,	PUNCT
ejpam-5876	329	39	1	1	NUM
ejpam-5876	329	40	]	]	PUNCT
ejpam-5876	329	41	.	.	PUNCT
ejpam-5876	330	1	t.	t.	PROPN
ejpam-5876	330	2	oner	oner	PROPN
ejpam-5876	330	3	et	et	PROPN
ejpam-5876	330	4	al	al	PROPN
ejpam-5876	330	5	.	.	PUNCT
ejpam-5876	330	6	/	/	SYM
ejpam-5876	330	7	eur	eur	PROPN
ejpam-5876	330	8	.	.	PUNCT
ejpam-5876	331	1	j.	j.	PROPN
ejpam-5876	331	2	pure	pure	PROPN
ejpam-5876	331	3	appl	appl	PROPN
ejpam-5876	331	4	.	.	PROPN
ejpam-5876	331	5	math	math	PROPN
ejpam-5876	331	6	,	,	PUNCT
ejpam-5876	331	7	18	18	NUM
ejpam-5876	331	8	(	(	PUNCT
ejpam-5876	331	9	2	2	NUM
ejpam-5876	331	10	)	)	PUNCT
ejpam-5876	331	11	(	(	PUNCT
ejpam-5876	331	12	2025	2025	NUM
ejpam-5876	331	13	)	)	PUNCT
ejpam-5876	331	14	,	,	PUNCT
ejpam-5876	331	15	5876	5876	NUM
ejpam-5876	331	16	13	13	NUM
ejpam-5876	331	17	of	of	ADP
ejpam-5876	331	18	16	16	NUM
ejpam-5876	331	19	proof	proof	NOUN
ejpam-5876	331	20	.	.	PUNCT
ejpam-5876	332	1	assume	assume	VERB
ejpam-5876	332	2	that	that	SCONJ
ejpam-5876	332	3	µ	µ	NOUN
ejpam-5876	332	4	is	be	AUX
ejpam-5876	332	5	an	an	DET
ejpam-5876	332	6	(	(	PUNCT
ejpam-5876	332	7	∈,∈	∈,∈	X
ejpam-5876	332	8	∨	∨	NUM
ejpam-5876	332	9	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	332	10	sup	sup	NOUN
ejpam-5876	332	11	-	-	PUNCT
ejpam-5876	332	12	subalgebra	subalgebra	NOUN
ejpam-5876	332	13	of	of	ADP
ejpam-5876	332	14	x.	x.	NOUN
ejpam-5876	332	15	let	let	VERB
ejpam-5876	332	16	x	x	PRON
ejpam-5876	332	17	,	,	PUNCT
ejpam-5876	332	18	y	y	PROPN
ejpam-5876	332	19	∈	∈	PROPN
ejpam-5876	332	20	ℓµu	ℓµu	NOUN
ejpam-5876	332	21	(	(	PUNCT
ejpam-5876	332	22	t	t	NOUN
ejpam-5876	332	23	)	)	PUNCT
ejpam-5876	332	24	for	for	ADP
ejpam-5876	332	25	t	t	PROPN
ejpam-5876	332	26	∈	∈	PROPN
ejpam-5876	332	27	ω	ω	PROPN
ejpam-5876	332	28	=	=	SYM
ejpam-5876	332	29	(	(	PUNCT
ejpam-5876	332	30	1−k	1−k	NUM
ejpam-5876	332	31	2	2	NUM
ejpam-5876	332	32	,	,	PUNCT
ejpam-5876	332	33	1	1	NUM
ejpam-5876	332	34	]	]	PUNCT
ejpam-5876	332	35	.	.	PUNCT
ejpam-5876	333	1	then	then	ADV
ejpam-5876	333	2	µ(x	µ(x	NOUN
ejpam-5876	333	3	)	)	PUNCT
ejpam-5876	333	4	≥	≥	NOUN
ejpam-5876	333	5	t	t	NOUN
ejpam-5876	333	6	and	and	CCONJ
ejpam-5876	333	7	µ(y	µ(y	PROPN
ejpam-5876	333	8	)	)	PUNCT
ejpam-5876	333	9	≥	≥	NOUN
ejpam-5876	333	10	t.	t.	NOUN
ejpam-5876	333	11	it	it	PRON
ejpam-5876	333	12	follows	follow	VERB
ejpam-5876	333	13	from	from	ADP
ejpam-5876	333	14	(	(	PUNCT
ejpam-5876	333	15	14	14	NUM
ejpam-5876	333	16	)	)	PUNCT
ejpam-5876	333	17	that	that	PRON
ejpam-5876	333	18	max{µ((x|(y|y))|(x|(y|y	max{µ((x|(y|y))|(x|(y|y	PROPN
ejpam-5876	333	19	)	)	PUNCT
ejpam-5876	333	20	)	)	PUNCT
ejpam-5876	333	21	)	)	PUNCT
ejpam-5876	333	22	,	,	PUNCT
ejpam-5876	333	23	1−k	1−k	NUM
ejpam-5876	333	24	2	2	NUM
ejpam-5876	333	25	}	}	PUNCT
ejpam-5876	333	26	≥	≥	NOUN
ejpam-5876	333	27	min{µ(x	min{µ(x	NOUN
ejpam-5876	333	28	)	)	PUNCT
ejpam-5876	333	29	,	,	PUNCT
ejpam-5876	333	30	µ(y	µ(y	PROPN
ejpam-5876	333	31	)	)	PUNCT
ejpam-5876	333	32	}	}	PUNCT
ejpam-5876	333	33	≥	≥	NOUN
ejpam-5876	333	34	t.	t.	NOUN
ejpam-5876	333	35	since	since	SCONJ
ejpam-5876	333	36	t	t	PROPN
ejpam-5876	333	37	>	>	X
ejpam-5876	333	38	1−k	1−k	NUM
ejpam-5876	333	39	2	2	NUM
ejpam-5876	333	40	,	,	PUNCT
ejpam-5876	333	41	it	it	PRON
ejpam-5876	333	42	follows	follow	VERB
ejpam-5876	333	43	that	that	SCONJ
ejpam-5876	333	44	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	VERB
ejpam-5876	333	45	)	)	PUNCT
ejpam-5876	333	46	)	)	PUNCT
ejpam-5876	333	47	)	)	PUNCT
ejpam-5876	333	48	≥	≥	PROPN
ejpam-5876	333	49	t	t	PROPN
ejpam-5876	333	50	,	,	PUNCT
ejpam-5876	333	51	and	and	CCONJ
ejpam-5876	334	1	so	so	SCONJ
ejpam-5876	334	2	that	that	SCONJ
ejpam-5876	334	3	(	(	PUNCT
ejpam-5876	334	4	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	NUM
ejpam-5876	334	5	)	)	PUNCT
ejpam-5876	334	6	)	)	PUNCT
ejpam-5876	335	1	∈	∈	NOUN
ejpam-5876	335	2	ℓµu	ℓµu	NOUN
ejpam-5876	335	3	(	(	PUNCT
ejpam-5876	335	4	t	t	NOUN
ejpam-5876	335	5	)	)	PUNCT
ejpam-5876	335	6	.	.	PUNCT
ejpam-5876	336	1	thus	thus	ADV
ejpam-5876	336	2	,	,	PUNCT
ejpam-5876	336	3	ℓµu	ℓµu	NOUN
ejpam-5876	336	4	(	(	PUNCT
ejpam-5876	336	5	t	t	NOUN
ejpam-5876	336	6	)	)	PUNCT
ejpam-5876	336	7	is	be	AUX
ejpam-5876	336	8	an	an	DET
ejpam-5876	336	9	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	336	10	of	of	ADP
ejpam-5876	336	11	x	x	PRON
ejpam-5876	336	12	,	,	PUNCT
ejpam-5876	336	13	and	and	CCONJ
ejpam-5876	336	14	(	(	PUNCT
ejpam-5876	336	15	x	x	X
ejpam-5876	336	16	,	,	PUNCT
ejpam-5876	336	17	ℓµu	ℓµu	NOUN
ejpam-5876	336	18	)	)	PUNCT
ejpam-5876	336	19	is	be	AUX
ejpam-5876	336	20	a	a	DET
ejpam-5876	336	21	semidetached	semidetache	VERB
ejpam-5876	336	22	sup	sup	NOUN
ejpam-5876	336	23	-	-	PUNCT
ejpam-5876	336	24	subalgebra	subalgebra	NOUN
ejpam-5876	336	25	over	over	ADP
ejpam-5876	336	26	ω	ω	NUM
ejpam-5876	336	27	=	=	SYM
ejpam-5876	336	28	(	(	PUNCT
ejpam-5876	336	29	1−k	1−k	NUM
ejpam-5876	336	30	2	2	NUM
ejpam-5876	336	31	,	,	PUNCT
ejpam-5876	336	32	1	1	NUM
ejpam-5876	336	33	]	]	PUNCT
ejpam-5876	336	34	.	.	PUNCT
ejpam-5876	337	1	conversely	conversely	ADV
ejpam-5876	337	2	,	,	PUNCT
ejpam-5876	337	3	suppose	suppose	VERB
ejpam-5876	337	4	that	that	SCONJ
ejpam-5876	337	5	(	(	PUNCT
ejpam-5876	337	6	x	x	X
ejpam-5876	337	7	,	,	PUNCT
ejpam-5876	337	8	ℓµu	ℓµu	NOUN
ejpam-5876	337	9	)	)	PUNCT
ejpam-5876	337	10	is	be	AUX
ejpam-5876	337	11	a	a	DET
ejpam-5876	337	12	semidetached	semidetache	VERB
ejpam-5876	337	13	sup	sup	NOUN
ejpam-5876	337	14	-	-	PUNCT
ejpam-5876	337	15	subalgebra	subalgebra	NOUN
ejpam-5876	337	16	over	over	ADP
ejpam-5876	337	17	ω	ω	NUM
ejpam-5876	337	18	=	=	SYM
ejpam-5876	337	19	(	(	PUNCT
ejpam-5876	337	20	1−k	1−k	NUM
ejpam-5876	337	21	2	2	NUM
ejpam-5876	337	22	,	,	PUNCT
ejpam-5876	337	23	1	1	NUM
ejpam-5876	337	24	]	]	PUNCT
ejpam-5876	337	25	.	.	PUNCT
ejpam-5876	338	1	if	if	SCONJ
ejpam-5876	338	2	(	(	PUNCT
ejpam-5876	338	3	14	14	NUM
ejpam-5876	338	4	)	)	PUNCT
ejpam-5876	338	5	is	be	AUX
ejpam-5876	338	6	not	not	PART
ejpam-5876	338	7	valid	valid	ADJ
ejpam-5876	338	8	,	,	PUNCT
ejpam-5876	338	9	then	then	ADV
ejpam-5876	338	10	there	there	PRON
ejpam-5876	338	11	exist	exist	VERB
ejpam-5876	338	12	a	a	DET
ejpam-5876	338	13	,	,	PUNCT
ejpam-5876	338	14	b	b	X
ejpam-5876	338	15	∈	∈	PROPN
ejpam-5876	338	16	x	x	PUNCT
ejpam-5876	338	17	such	such	ADJ
ejpam-5876	338	18	that	that	DET
ejpam-5876	338	19	max{µ((a|(b|b))|(a|(b|b	max{µ((a|(b|b))|(a|(b|b	NOUN
ejpam-5876	338	20	)	)	PUNCT
ejpam-5876	338	21	)	)	PUNCT
ejpam-5876	338	22	)	)	PUNCT
ejpam-5876	338	23	,	,	PUNCT
ejpam-5876	338	24	1−k	1−k	NUM
ejpam-5876	338	25	2	2	NUM
ejpam-5876	338	26	}	}	PUNCT
ejpam-5876	338	27	<	<	X
ejpam-5876	338	28	min{µ(a	min{µ(a	PROPN
ejpam-5876	338	29	)	)	PUNCT
ejpam-5876	338	30	,	,	PUNCT
ejpam-5876	338	31	µ(b	µ(b	PROPN
ejpam-5876	338	32	)	)	PUNCT
ejpam-5876	338	33	}	}	PUNCT
ejpam-5876	339	1	=	=	SYM
ejpam-5876	339	2	t.	t.	NOUN
ejpam-5876	339	3	then	then	ADV
ejpam-5876	339	4	t	t	PROPN
ejpam-5876	339	5	∈	∈	PROPN
ejpam-5876	339	6	(	(	PUNCT
ejpam-5876	339	7	1−k	1−k	NUM
ejpam-5876	339	8	2	2	NUM
ejpam-5876	339	9	,	,	PUNCT
ejpam-5876	339	10	1	1	NUM
ejpam-5876	339	11	]	]	PUNCT
ejpam-5876	339	12	,	,	PUNCT
ejpam-5876	339	13	a	a	PRON
ejpam-5876	339	14	,	,	PUNCT
ejpam-5876	339	15	b	b	PROPN
ejpam-5876	339	16	∈	∈	PROPN
ejpam-5876	339	17	ℓµu	ℓµu	NOUN
ejpam-5876	339	18	(	(	PUNCT
ejpam-5876	339	19	t	t	NOUN
ejpam-5876	339	20	)	)	PUNCT
ejpam-5876	339	21	and	and	CCONJ
ejpam-5876	339	22	(	(	PUNCT
ejpam-5876	339	23	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5876	339	24	)	)	PUNCT
ejpam-5876	339	25	)	)	PUNCT
ejpam-5876	339	26	/∈	/∈	PUNCT
ejpam-5876	340	1	ℓµu	ℓµu	NOUN
ejpam-5876	340	2	(	(	PUNCT
ejpam-5876	340	3	t	t	NOUN
ejpam-5876	340	4	)	)	PUNCT
ejpam-5876	340	5	.	.	PUNCT
ejpam-5876	341	1	this	this	PRON
ejpam-5876	341	2	is	be	AUX
ejpam-5876	341	3	a	a	DET
ejpam-5876	341	4	contradiction	contradiction	NOUN
ejpam-5876	341	5	,	,	PUNCT
ejpam-5876	341	6	and	and	CCONJ
ejpam-5876	341	7	so	so	ADV
ejpam-5876	341	8	(	(	PUNCT
ejpam-5876	341	9	14	14	NUM
ejpam-5876	341	10	)	)	PUNCT
ejpam-5876	341	11	is	be	AUX
ejpam-5876	341	12	valid	valid	ADJ
ejpam-5876	341	13	.	.	PUNCT
ejpam-5876	342	1	using	use	VERB
ejpam-5876	342	2	theorem	theorem	NOUN
ejpam-5876	342	3	11	11	NUM
ejpam-5876	342	4	,	,	PUNCT
ejpam-5876	342	5	we	we	PRON
ejpam-5876	342	6	know	know	VERB
ejpam-5876	342	7	that	that	SCONJ
ejpam-5876	342	8	µ	µ	NOUN
ejpam-5876	342	9	is	be	AUX
ejpam-5876	342	10	an	an	DET
ejpam-5876	342	11	(	(	PUNCT
ejpam-5876	342	12	∈,∈∨	∈,∈∨	PROPN
ejpam-5876	342	13	qk)fuzzy	qk)fuzzy	ADJ
ejpam-5876	342	14	sup	sup	NOUN
ejpam-5876	342	15	-	-	PUNCT
ejpam-5876	342	16	subalgebra	subalgebra	NOUN
ejpam-5876	342	17	of	of	ADP
ejpam-5876	342	18	x.	x.	PROPN
ejpam-5876	342	19	corollary	corollary	PROPN
ejpam-5876	342	20	14	14	NUM
ejpam-5876	342	21	is	be	AUX
ejpam-5876	342	22	a	a	DET
ejpam-5876	342	23	direct	direct	ADJ
ejpam-5876	342	24	consequence	consequence	NOUN
ejpam-5876	342	25	of	of	ADP
ejpam-5876	342	26	theorem	theorem	NOUN
ejpam-5876	342	27	12	12	NUM
ejpam-5876	342	28	by	by	ADP
ejpam-5876	342	29	setting	set	VERB
ejpam-5876	342	30	k	k	PROPN
ejpam-5876	342	31	=	=	PUNCT
ejpam-5876	342	32	0	0	PROPN
ejpam-5876	342	33	.	.	PUNCT
ejpam-5876	343	1	when	when	SCONJ
ejpam-5876	343	2	k	k	PROPN
ejpam-5876	343	3	=	=	SYM
ejpam-5876	343	4	0	0	PROPN
ejpam-5876	343	5	,	,	PUNCT
ejpam-5876	343	6	the	the	DET
ejpam-5876	343	7	interval	interval	NOUN
ejpam-5876	343	8	ω	ω	PROPN
ejpam-5876	343	9	=	=	SYM
ejpam-5876	343	10	(	(	PUNCT
ejpam-5876	343	11	1−k	1−k	NUM
ejpam-5876	343	12	2	2	NUM
ejpam-5876	343	13	,	,	PUNCT
ejpam-5876	343	14	1	1	NUM
ejpam-5876	343	15	]	]	PUNCT
ejpam-5876	343	16	becomes	become	VERB
ejpam-5876	343	17	(	(	PUNCT
ejpam-5876	343	18	0.5	0.5	NUM
ejpam-5876	343	19	,	,	PUNCT
ejpam-5876	343	20	1	1	NUM
ejpam-5876	343	21	]	]	PUNCT
ejpam-5876	343	22	,	,	PUNCT
ejpam-5876	343	23	and	and	CCONJ
ejpam-5876	343	24	the	the	DET
ejpam-5876	343	25	condition	condition	NOUN
ejpam-5876	343	26	in	in	ADP
ejpam-5876	343	27	theorem	theorem	ADJ
ejpam-5876	343	28	3.33	3.33	NUM
ejpam-5876	343	29	simplifies	simplifie	NOUN
ejpam-5876	343	30	accordingly	accordingly	ADV
ejpam-5876	343	31	.	.	PUNCT
ejpam-5876	344	1	thus	thus	ADV
ejpam-5876	344	2	,	,	PUNCT
ejpam-5876	344	3	an	an	PRON
ejpam-5876	344	4	(	(	PUNCT
ejpam-5876	344	5	∈,∈	∈,∈	X
ejpam-5876	344	6	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	344	7	sup	sup	ADJ
ejpam-5876	344	8	-	-	PUNCT
ejpam-5876	344	9	subalgebra	subalgebra	NOUN
ejpam-5876	344	10	ofx	ofx	NOUN
ejpam-5876	344	11	is	be	AUX
ejpam-5876	344	12	equivalent	equivalent	ADJ
ejpam-5876	344	13	to	to	ADP
ejpam-5876	344	14	a	a	DET
ejpam-5876	344	15	semidetached	semidetache	VERB
ejpam-5876	344	16	sup	sup	NOUN
ejpam-5876	344	17	-	-	PUNCT
ejpam-5876	344	18	subalgebra	subalgebra	NOUN
ejpam-5876	344	19	over	over	ADP
ejpam-5876	344	20	(	(	PUNCT
ejpam-5876	344	21	0.5	0.5	NUM
ejpam-5876	344	22	,	,	PUNCT
ejpam-5876	344	23	1	1	NUM
ejpam-5876	344	24	]	]	PUNCT
ejpam-5876	344	25	,	,	PUNCT
ejpam-5876	344	26	establishing	establish	VERB
ejpam-5876	344	27	the	the	DET
ejpam-5876	344	28	result	result	NOUN
ejpam-5876	344	29	.	.	PUNCT
ejpam-5876	345	1	corollary	corollary	ADJ
ejpam-5876	345	2	14	14	NUM
ejpam-5876	345	3	.	.	PUNCT
ejpam-5876	346	1	a	a	DET
ejpam-5876	346	2	fuzzy	fuzzy	ADJ
ejpam-5876	346	3	set	set	VERB
ejpam-5876	346	4	µ	µ	NOUN
ejpam-5876	346	5	in	in	ADP
ejpam-5876	346	6	x	x	VERB
ejpam-5876	346	7	is	be	AUX
ejpam-5876	346	8	an	an	DET
ejpam-5876	346	9	(	(	PUNCT
ejpam-5876	346	10	∈,∈∨	∈,∈∨	PROPN
ejpam-5876	346	11	q)-fuzzy	q)-fuzzy	PUNCT
ejpam-5876	346	12	sup	sup	NOUN
ejpam-5876	346	13	-	-	PUNCT
ejpam-5876	346	14	subalgebra	subalgebra	NOUN
ejpam-5876	346	15	of	of	ADP
ejpam-5876	346	16	x	x	PRON
ejpam-5876	346	17	if	if	SCONJ
ejpam-5876	346	18	and	and	CCONJ
ejpam-5876	346	19	only	only	ADV
ejpam-5876	346	20	if	if	SCONJ
ejpam-5876	346	21	µ	µ	NOUN
ejpam-5876	346	22	is	be	AUX
ejpam-5876	346	23	a	a	DET
ejpam-5876	346	24	semidetached	semidetache	VERB
ejpam-5876	346	25	sup	sup	NOUN
ejpam-5876	346	26	-	-	PUNCT
ejpam-5876	346	27	subalgebra	subalgebra	NOUN
ejpam-5876	346	28	over	over	ADP
ejpam-5876	346	29	ω	ω	NUM
ejpam-5876	346	30	=	=	SYM
ejpam-5876	346	31	(	(	PUNCT
ejpam-5876	346	32	0.5	0.5	NUM
ejpam-5876	346	33	,	,	PUNCT
ejpam-5876	346	34	1	1	NUM
ejpam-5876	346	35	]	]	PUNCT
ejpam-5876	346	36	.	.	PUNCT
ejpam-5876	347	1	theorem	theorem	VERB
ejpam-5876	347	2	13	13	NUM
ejpam-5876	347	3	.	.	PUNCT
ejpam-5876	348	1	a	a	DET
ejpam-5876	348	2	fuzzy	fuzzy	ADJ
ejpam-5876	348	3	set	set	VERB
ejpam-5876	348	4	µ	µ	NOUN
ejpam-5876	348	5	in	in	ADP
ejpam-5876	348	6	x	x	VERB
ejpam-5876	348	7	is	be	AUX
ejpam-5876	348	8	an	an	DET
ejpam-5876	348	9	(	(	PUNCT
ejpam-5876	348	10	∈,∈∨	∈,∈∨	PROPN
ejpam-5876	348	11	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	348	12	sup	sup	NOUN
ejpam-5876	348	13	-	-	PUNCT
ejpam-5876	348	14	subalgebra	subalgebra	NOUN
ejpam-5876	348	15	of	of	ADP
ejpam-5876	348	16	x	x	PRON
ejpam-5876	348	17	if	if	SCONJ
ejpam-5876	348	18	and	and	CCONJ
ejpam-5876	348	19	only	only	ADV
ejpam-5876	348	20	if	if	SCONJ
ejpam-5876	348	21	(	(	PUNCT
ejpam-5876	348	22	x	x	NOUN
ejpam-5876	348	23	,	,	PUNCT
ejpam-5876	348	24	ℓµqk	ℓµqk	PROPN
ejpam-5876	348	25	)	)	PUNCT
ejpam-5876	348	26	is	be	AUX
ejpam-5876	348	27	a	a	DET
ejpam-5876	348	28	semidetached	semidetache	VERB
ejpam-5876	348	29	sup	sup	NOUN
ejpam-5876	348	30	-	-	PUNCT
ejpam-5876	348	31	subalgebra	subalgebra	NOUN
ejpam-5876	348	32	over	over	ADP
ejpam-5876	348	33	ω	ω	NUM
ejpam-5876	348	34	=	=	SYM
ejpam-5876	348	35	(	(	PUNCT
ejpam-5876	348	36	0	0	NUM
ejpam-5876	348	37	,	,	PUNCT
ejpam-5876	348	38	1−k	1−k	NUM
ejpam-5876	348	39	2	2	NUM
ejpam-5876	348	40	]	]	PUNCT
ejpam-5876	348	41	.	.	PUNCT
ejpam-5876	349	1	proof	proof	NOUN
ejpam-5876	349	2	.	.	PUNCT
ejpam-5876	350	1	assume	assume	VERB
ejpam-5876	350	2	that	that	SCONJ
ejpam-5876	350	3	(	(	PUNCT
ejpam-5876	350	4	x	x	X
ejpam-5876	350	5	,	,	PUNCT
ejpam-5876	350	6	ℓµu	ℓµu	NOUN
ejpam-5876	350	7	)	)	PUNCT
ejpam-5876	350	8	is	be	AUX
ejpam-5876	350	9	a	a	DET
ejpam-5876	350	10	semidetached	semidetache	VERB
ejpam-5876	350	11	sup	sup	NOUN
ejpam-5876	350	12	-	-	PUNCT
ejpam-5876	350	13	subalgebra	subalgebra	NOUN
ejpam-5876	350	14	over	over	ADP
ejpam-5876	350	15	ω	ω	NUM
ejpam-5876	350	16	=	=	SYM
ejpam-5876	350	17	(	(	PUNCT
ejpam-5876	350	18	0	0	NUM
ejpam-5876	350	19	,	,	PUNCT
ejpam-5876	350	20	1−k	1−k	NUM
ejpam-5876	350	21	2	2	NUM
ejpam-5876	350	22	]	]	PUNCT
ejpam-5876	350	23	.	.	PUNCT
ejpam-5876	351	1	if	if	SCONJ
ejpam-5876	351	2	(	(	PUNCT
ejpam-5876	351	3	14	14	NUM
ejpam-5876	351	4	)	)	PUNCT
ejpam-5876	351	5	is	be	AUX
ejpam-5876	351	6	not	not	PART
ejpam-5876	351	7	valid	valid	ADJ
ejpam-5876	351	8	,	,	PUNCT
ejpam-5876	351	9	then	then	ADV
ejpam-5876	351	10	there	there	PRON
ejpam-5876	351	11	exist	exist	VERB
ejpam-5876	351	12	a	a	PRON
ejpam-5876	351	13	,	,	PUNCT
ejpam-5876	351	14	b	b	PROPN
ejpam-5876	351	15	∈	∈	PROPN
ejpam-5876	351	16	x	x	NOUN
ejpam-5876	351	17	,	,	PUNCT
ejpam-5876	351	18	t	t	PROPN
ejpam-5876	351	19	∈	∈	PROPN
ejpam-5876	351	20	(	(	PUNCT
ejpam-5876	351	21	0	0	NUM
ejpam-5876	351	22	,	,	PUNCT
ejpam-5876	351	23	1	1	NUM
ejpam-5876	351	24	]	]	PUNCT
ejpam-5876	351	25	and	and	CCONJ
ejpam-5876	351	26	k	k	PROPN
ejpam-5876	351	27	∈	∈	PROPN
ejpam-5876	352	1	[	[	X
ejpam-5876	352	2	0	0	NUM
ejpam-5876	352	3	,	,	PUNCT
ejpam-5876	352	4	1	1	NUM
ejpam-5876	352	5	)	)	PUNCT
ejpam-5876	352	6	such	such	ADJ
ejpam-5876	352	7	that	that	DET
ejpam-5876	352	8	max{µ((a|(b|b))|(a|(b|b	max{µ((a|(b|b))|(a|(b|b	NOUN
ejpam-5876	352	9	)	)	PUNCT
ejpam-5876	352	10	)	)	PUNCT
ejpam-5876	352	11	)	)	PUNCT
ejpam-5876	352	12	,	,	PUNCT
ejpam-5876	352	13	1−k	1−k	NUM
ejpam-5876	352	14	2	2	NUM
ejpam-5876	352	15	}	}	PUNCT
ejpam-5876	352	16	+	+	NUM
ejpam-5876	352	17	t+k	t+k	NUM
ejpam-5876	352	18	≤	≤	NUM
ejpam-5876	352	19	1	1	NUM
ejpam-5876	352	20	<	<	X
ejpam-5876	352	21	min{µ(a	min{µ(a	PROPN
ejpam-5876	352	22	)	)	PUNCT
ejpam-5876	352	23	,	,	PUNCT
ejpam-5876	352	24	µ(b)}+	µ(b)}+	NUM
ejpam-5876	352	25	t+k	t+k	NUM
ejpam-5876	352	26	.	.	PUNCT
ejpam-5876	353	1	it	it	PRON
ejpam-5876	353	2	follows	follow	VERB
ejpam-5876	353	3	that	that	SCONJ
ejpam-5876	353	4	atqkµ	atqkµ	NOUN
ejpam-5876	353	5	and	and	CCONJ
ejpam-5876	353	6	btqkµ	btqkµ	NOUN
ejpam-5876	353	7	,	,	PUNCT
ejpam-5876	353	8	that	that	ADV
ejpam-5876	353	9	is	is	ADV
ejpam-5876	353	10	,	,	PUNCT
ejpam-5876	353	11	a	a	PRON
ejpam-5876	353	12	,	,	PUNCT
ejpam-5876	353	13	b	b	PROPN
ejpam-5876	353	14	∈	∈	PROPN
ejpam-5876	353	15	ℓµqk	ℓµqk	NOUN
ejpam-5876	353	16	(	(	PUNCT
ejpam-5876	353	17	t	t	PROPN
ejpam-5876	353	18	)	)	PUNCT
ejpam-5876	353	19	,	,	PUNCT
ejpam-5876	353	20	but	but	CCONJ
ejpam-5876	353	21	(	(	PUNCT
ejpam-5876	353	22	(	(	PUNCT
ejpam-5876	353	23	a|(b|b))|(a|(b|b)))tqkµ	a|(b|b))|(a|(b|b)))tqkµ	INTJ
ejpam-5876	353	24	,	,	PUNCT
ejpam-5876	353	25	that	that	ADV
ejpam-5876	353	26	is	is	ADV
ejpam-5876	353	27	,	,	PUNCT
ejpam-5876	353	28	(	(	PUNCT
ejpam-5876	353	29	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5876	353	30	)	)	PUNCT
ejpam-5876	353	31	)	)	PUNCT
ejpam-5876	353	32	/∈	/∈	PUNCT
ejpam-5876	354	1	ℓµqk	ℓµqk	ADJ
ejpam-5876	354	2	.	.	PUNCT
ejpam-5876	355	1	this	this	PRON
ejpam-5876	355	2	is	be	AUX
ejpam-5876	355	3	a	a	DET
ejpam-5876	355	4	contradiction	contradiction	NOUN
ejpam-5876	355	5	,	,	PUNCT
ejpam-5876	355	6	and	and	CCONJ
ejpam-5876	355	7	so	so	ADV
ejpam-5876	355	8	(	(	PUNCT
ejpam-5876	355	9	14	14	NUM
ejpam-5876	355	10	)	)	PUNCT
ejpam-5876	355	11	is	be	AUX
ejpam-5876	355	12	valid	valid	ADJ
ejpam-5876	355	13	.	.	PUNCT
ejpam-5876	356	1	using	use	VERB
ejpam-5876	356	2	theorem	theorem	NOUN
ejpam-5876	356	3	11	11	NUM
ejpam-5876	356	4	,	,	PUNCT
ejpam-5876	356	5	we	we	PRON
ejpam-5876	356	6	have	have	VERB
ejpam-5876	356	7	µ	µ	NOUN
ejpam-5876	356	8	is	be	AUX
ejpam-5876	356	9	an	an	DET
ejpam-5876	356	10	(	(	PUNCT
ejpam-5876	356	11	∈,∈	∈,∈	X
ejpam-5876	356	12	∨	∨	NUM
ejpam-5876	356	13	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	356	14	sup	sup	NOUN
ejpam-5876	356	15	-	-	PUNCT
ejpam-5876	356	16	subalgebra	subalgebra	NOUN
ejpam-5876	356	17	of	of	ADP
ejpam-5876	356	18	x.	x.	NOUN
ejpam-5876	356	19	conversely	conversely	ADV
ejpam-5876	356	20	,	,	PUNCT
ejpam-5876	356	21	suppose	suppose	VERB
ejpam-5876	356	22	that	that	SCONJ
ejpam-5876	356	23	µ	µ	NOUN
ejpam-5876	356	24	is	be	AUX
ejpam-5876	356	25	an	an	DET
ejpam-5876	356	26	(	(	PUNCT
ejpam-5876	356	27	∈,∈	∈,∈	X
ejpam-5876	356	28	∨	∨	NUM
ejpam-5876	356	29	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	356	30	sup	sup	NOUN
ejpam-5876	356	31	-	-	PUNCT
ejpam-5876	356	32	subalgebra	subalgebra	NOUN
ejpam-5876	356	33	of	of	ADP
ejpam-5876	356	34	x.	x.	NOUN
ejpam-5876	356	35	let	let	VERB
ejpam-5876	356	36	x	x	PRON
ejpam-5876	356	37	,	,	PUNCT
ejpam-5876	356	38	y	y	PROPN
ejpam-5876	356	39	∈	∈	PROPN
ejpam-5876	356	40	ℓµqk	ℓµqk	PROPN
ejpam-5876	356	41	(	(	PUNCT
ejpam-5876	356	42	t	t	NOUN
ejpam-5876	356	43	)	)	PUNCT
ejpam-5876	356	44	for	for	ADP
ejpam-5876	356	45	t	t	PROPN
ejpam-5876	356	46	∈	∈	PROPN
ejpam-5876	356	47	ω	ω	PROPN
ejpam-5876	356	48	=	=	SYM
ejpam-5876	356	49	(	(	PUNCT
ejpam-5876	356	50	0	0	NUM
ejpam-5876	356	51	,	,	PUNCT
ejpam-5876	356	52	1−k	1−k	NUM
ejpam-5876	356	53	2	2	NUM
ejpam-5876	356	54	]	]	PUNCT
ejpam-5876	356	55	.	.	PUNCT
ejpam-5876	357	1	then	then	ADV
ejpam-5876	357	2	xtqkµ	xtqkµ	PROPN
ejpam-5876	357	3	and	and	CCONJ
ejpam-5876	357	4	ytqkµ	ytqkµ	PROPN
ejpam-5876	357	5	,	,	PUNCT
ejpam-5876	357	6	that	that	ADV
ejpam-5876	357	7	is	is	ADV
ejpam-5876	357	8	,	,	PUNCT
ejpam-5876	357	9	µ(x	µ(x	ADJ
ejpam-5876	357	10	)	)	PUNCT
ejpam-5876	357	11	+	+	NUM
ejpam-5876	357	12	t	t	NOUN
ejpam-5876	357	13	+	+	CCONJ
ejpam-5876	357	14	k	k	X
ejpam-5876	357	15	>	>	X
ejpam-5876	357	16	1	1	NUM
ejpam-5876	357	17	and	and	CCONJ
ejpam-5876	357	18	µ(y	µ(y	NUM
ejpam-5876	357	19	)	)	PUNCT
ejpam-5876	358	1	+	+	CCONJ
ejpam-5876	358	2	t+	t+	VERB
ejpam-5876	358	3	k	k	X
ejpam-5876	358	4	>	>	X
ejpam-5876	358	5	1	1	X
ejpam-5876	358	6	.	.	PUNCT
ejpam-5876	359	1	it	it	PRON
ejpam-5876	359	2	follows	follow	VERB
ejpam-5876	359	3	from	from	ADP
ejpam-5876	359	4	(	(	PUNCT
ejpam-5876	359	5	14	14	NUM
ejpam-5876	359	6	)	)	PUNCT
ejpam-5876	359	7	that	that	PRON
ejpam-5876	359	8	max{µ((x|(y|y))|(x|(y|y	max{µ((x|(y|y))|(x|(y|y	PROPN
ejpam-5876	359	9	)	)	PUNCT
ejpam-5876	359	10	)	)	PUNCT
ejpam-5876	359	11	)	)	PUNCT
ejpam-5876	359	12	,	,	PUNCT
ejpam-5876	359	13	1−k	1−k	NUM
ejpam-5876	359	14	2	2	NUM
ejpam-5876	359	15	}	}	PUNCT
ejpam-5876	359	16	≥	≥	NOUN
ejpam-5876	359	17	min{µ(x	min{µ(x	NOUN
ejpam-5876	359	18	)	)	PUNCT
ejpam-5876	359	19	,	,	PUNCT
ejpam-5876	359	20	µ(y	µ(y	PROPN
ejpam-5876	359	21	)	)	PUNCT
ejpam-5876	359	22	}	}	PUNCT
ejpam-5876	359	23	>	>	X
ejpam-5876	359	24	1−	1−	NUM
ejpam-5876	359	25	t−	t−	PROPN
ejpam-5876	359	26	k	k	PROPN
ejpam-5876	359	27	≥	≥	NUM
ejpam-5876	359	28	1−k	1−k	NUM
ejpam-5876	359	29	2	2	NUM
ejpam-5876	360	1	and	and	CCONJ
ejpam-5876	360	2	so	so	SCONJ
ejpam-5876	360	3	that	that	SCONJ
ejpam-5876	360	4	µ((x|(y|y))|(x|(y|y)))+	µ((x|(y|y))|(x|(y|y)))+	PUNCT
ejpam-5876	360	5	t+	t+	VERB
ejpam-5876	360	6	k	k	PROPN
ejpam-5876	360	7	>	>	X
ejpam-5876	360	8	1	1	NUM
ejpam-5876	360	9	,	,	PUNCT
ejpam-5876	360	10	that	that	ADV
ejpam-5876	360	11	is	is	ADV
ejpam-5876	360	12	,	,	PUNCT
ejpam-5876	360	13	(	(	PUNCT
ejpam-5876	360	14	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5876	360	15	)	)	PUNCT
ejpam-5876	360	16	)	)	PUNCT
ejpam-5876	360	17	∈	∈	PROPN
ejpam-5876	360	18	µ.	µ.	NOUN
ejpam-5876	360	19	therefore	therefore	ADV
ejpam-5876	360	20	,	,	PUNCT
ejpam-5876	360	21	ℓµqk	ℓµqk	PROPN
ejpam-5876	360	22	(	(	PUNCT
ejpam-5876	360	23	t	t	NOUN
ejpam-5876	360	24	)	)	PUNCT
ejpam-5876	360	25	is	be	AUX
ejpam-5876	360	26	an	an	DET
ejpam-5876	360	27	sup	sup	ADJ
ejpam-5876	360	28	-	-	PUNCT
ejpam-5876	360	29	subalgebra	subalgebra	NOUN
ejpam-5876	360	30	of	of	ADP
ejpam-5876	360	31	x	x	PRON
ejpam-5876	360	32	,	,	PUNCT
ejpam-5876	360	33	and	and	CCONJ
ejpam-5876	360	34	(	(	PUNCT
ejpam-5876	360	35	x	x	X
ejpam-5876	360	36	,	,	PUNCT
ejpam-5876	360	37	ℓµqk	ℓµqk	PROPN
ejpam-5876	360	38	)	)	PUNCT
ejpam-5876	360	39	is	be	AUX
ejpam-5876	360	40	a	a	DET
ejpam-5876	360	41	semidetached	semidetached	ADJ
ejpam-5876	360	42	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	360	43	over	over	ADP
ejpam-5876	360	44	ω	ω	PROPN
ejpam-5876	360	45	=	=	SYM
ejpam-5876	360	46	(	(	PUNCT
ejpam-5876	360	47	0	0	NUM
ejpam-5876	360	48	,	,	PUNCT
ejpam-5876	360	49	1−k	1−k	NUM
ejpam-5876	360	50	2	2	NUM
ejpam-5876	360	51	]	]	PUNCT
ejpam-5876	360	52	.	.	PUNCT
ejpam-5876	361	1	corollary	corollary	ADJ
ejpam-5876	361	2	15	15	NUM
ejpam-5876	361	3	follows	follow	VERB
ejpam-5876	361	4	directly	directly	ADV
ejpam-5876	361	5	from	from	ADP
ejpam-5876	361	6	theorems	theorem	NOUN
ejpam-5876	361	7	12	12	NUM
ejpam-5876	361	8	and	and	CCONJ
ejpam-5876	361	9	13	13	NUM
ejpam-5876	361	10	.	.	PUNCT
ejpam-5876	361	11	theorem	theorem	VERB
ejpam-5876	361	12	12	12	NUM
ejpam-5876	361	13	states	state	NOUN
ejpam-5876	361	14	that	that	SCONJ
ejpam-5876	361	15	(	(	PUNCT
ejpam-5876	361	16	x	x	X
ejpam-5876	361	17	,	,	PUNCT
ejpam-5876	361	18	ℓuµ	ℓuµ	PROPN
ejpam-5876	361	19	)	)	PUNCT
ejpam-5876	361	20	is	be	AUX
ejpam-5876	361	21	a	a	DET
ejpam-5876	361	22	semidetached	semidetache	VERB
ejpam-5876	361	23	sup	sup	NOUN
ejpam-5876	361	24	-	-	PUNCT
ejpam-5876	361	25	subalgebra	subalgebra	NOUN
ejpam-5876	361	26	over	over	ADP
ejpam-5876	361	27	ω	ω	NUM
ejpam-5876	361	28	=	=	SYM
ejpam-5876	361	29	(	(	PUNCT
ejpam-5876	361	30	1−k	1−k	NUM
ejpam-5876	361	31	2	2	NUM
ejpam-5876	361	32	,	,	PUNCT
ejpam-5876	361	33	1	1	NUM
ejpam-5876	361	34	]	]	PUNCT
ejpam-5876	361	35	if	if	SCONJ
ejpam-5876	361	36	and	and	CCONJ
ejpam-5876	361	37	only	only	ADV
ejpam-5876	361	38	if	if	SCONJ
ejpam-5876	361	39	µ	µ	NOUN
ejpam-5876	361	40	is	be	AUX
ejpam-5876	361	41	an	an	DET
ejpam-5876	361	42	(	(	PUNCT
ejpam-5876	361	43	∈,∈	∈,∈	X
ejpam-5876	361	44	∨qk)fuzzy	∨qk)fuzzy	ADJ
ejpam-5876	361	45	sup	sup	NOUN
ejpam-5876	361	46	-	-	PUNCT
ejpam-5876	361	47	subalgebra	subalgebra	NOUN
ejpam-5876	361	48	.	.	PUNCT
ejpam-5876	362	1	similarly	similarly	ADV
ejpam-5876	362	2	,	,	PUNCT
ejpam-5876	362	3	theorem	theorem	VERB
ejpam-5876	362	4	13	13	NUM
ejpam-5876	362	5	establishes	establish	VERB
ejpam-5876	362	6	that	that	SCONJ
ejpam-5876	362	7	(	(	PUNCT
ejpam-5876	362	8	x	x	X
ejpam-5876	362	9	,	,	PUNCT
ejpam-5876	362	10	ℓqk	ℓqk	NOUN
ejpam-5876	362	11	µ	µ	NOUN
ejpam-5876	362	12	)	)	PUNCT
ejpam-5876	362	13	is	be	AUX
ejpam-5876	362	14	a	a	DET
ejpam-5876	362	15	semidetached	semidetache	VERB
ejpam-5876	362	16	sup	sup	NOUN
ejpam-5876	362	17	-	-	PUNCT
ejpam-5876	362	18	subalgebra	subalgebra	NOUN
ejpam-5876	362	19	over	over	ADP
ejpam-5876	362	20	ω	ω	NUM
ejpam-5876	362	21	=	=	SYM
ejpam-5876	362	22	(	(	PUNCT
ejpam-5876	362	23	0	0	NUM
ejpam-5876	362	24	,	,	PUNCT
ejpam-5876	362	25	1−k	1−k	NUM
ejpam-5876	362	26	2	2	NUM
ejpam-5876	362	27	]	]	PUNCT
ejpam-5876	362	28	under	under	ADP
ejpam-5876	362	29	the	the	DET
ejpam-5876	362	30	same	same	ADJ
ejpam-5876	362	31	condition	condition	NOUN
ejpam-5876	362	32	.	.	PUNCT
ejpam-5876	363	1	therefore	therefore	ADV
ejpam-5876	363	2	,	,	PUNCT
ejpam-5876	363	3	the	the	DET
ejpam-5876	363	4	equivalence	equivalence	NOUN
ejpam-5876	363	5	between	between	ADP
ejpam-5876	363	6	the	the	DET
ejpam-5876	363	7	two	two	NUM
ejpam-5876	363	8	semidetached	semidetache	VERB
ejpam-5876	363	9	structures	structure	NOUN
ejpam-5876	363	10	directly	directly	ADV
ejpam-5876	363	11	follows	follow	VERB
ejpam-5876	363	12	.	.	PUNCT
ejpam-5876	364	1	corollary	corollary	ADJ
ejpam-5876	364	2	15	15	NUM
ejpam-5876	364	3	.	.	PUNCT
ejpam-5876	365	1	for	for	ADP
ejpam-5876	365	2	a	a	DET
ejpam-5876	365	3	fuzzy	fuzzy	ADJ
ejpam-5876	365	4	set	set	VERB
ejpam-5876	365	5	µ	µ	NOUN
ejpam-5876	365	6	in	in	ADP
ejpam-5876	365	7	x	x	PRON
ejpam-5876	365	8	,	,	PUNCT
ejpam-5876	365	9	the	the	DET
ejpam-5876	365	10	following	follow	VERB
ejpam-5876	365	11	are	be	AUX
ejpam-5876	365	12	equivalent	equivalent	ADJ
ejpam-5876	365	13	.	.	PUNCT
ejpam-5876	366	1	(	(	PUNCT
ejpam-5876	366	2	1	1	NUM
ejpam-5876	366	3	)	)	PUNCT
ejpam-5876	366	4	(	(	PUNCT
ejpam-5876	366	5	x	x	X
ejpam-5876	366	6	,	,	PUNCT
ejpam-5876	366	7	ℓµu	ℓµu	NOUN
ejpam-5876	366	8	)	)	PUNCT
ejpam-5876	366	9	is	be	AUX
ejpam-5876	366	10	a	a	DET
ejpam-5876	366	11	semidetached	semidetache	VERB
ejpam-5876	366	12	sup	sup	NOUN
ejpam-5876	366	13	-	-	PUNCT
ejpam-5876	366	14	subalgebra	subalgebra	NOUN
ejpam-5876	366	15	over	over	ADP
ejpam-5876	366	16	ω	ω	NUM
ejpam-5876	366	17	=	=	SYM
ejpam-5876	366	18	(	(	PUNCT
ejpam-5876	366	19	1−k	1−k	NUM
ejpam-5876	366	20	2	2	NUM
ejpam-5876	366	21	,	,	PUNCT
ejpam-5876	366	22	1	1	NUM
ejpam-5876	366	23	]	]	PUNCT
ejpam-5876	366	24	,	,	PUNCT
ejpam-5876	366	25	(	(	PUNCT
ejpam-5876	366	26	2	2	NUM
ejpam-5876	366	27	)	)	PUNCT
ejpam-5876	366	28	(	(	PUNCT
ejpam-5876	366	29	x	x	X
ejpam-5876	366	30	,	,	PUNCT
ejpam-5876	366	31	ℓµqk	ℓµqk	PROPN
ejpam-5876	366	32	)	)	PUNCT
ejpam-5876	366	33	is	be	AUX
ejpam-5876	366	34	a	a	DET
ejpam-5876	366	35	semidetached	semidetache	VERB
ejpam-5876	366	36	sup	sup	NOUN
ejpam-5876	366	37	-	-	PUNCT
ejpam-5876	366	38	subalgebra	subalgebra	NOUN
ejpam-5876	366	39	over	over	ADP
ejpam-5876	366	40	ω	ω	NUM
ejpam-5876	366	41	=	=	SYM
ejpam-5876	366	42	(	(	PUNCT
ejpam-5876	366	43	0	0	NUM
ejpam-5876	366	44	,	,	PUNCT
ejpam-5876	366	45	1−k	1−k	NUM
ejpam-5876	366	46	2	2	NUM
ejpam-5876	366	47	]	]	PUNCT
ejpam-5876	366	48	.	.	PUNCT
ejpam-5876	367	1	t.	t.	PROPN
ejpam-5876	367	2	oner	oner	PROPN
ejpam-5876	367	3	et	et	PROPN
ejpam-5876	367	4	al	al	PROPN
ejpam-5876	367	5	.	.	PUNCT
ejpam-5876	367	6	/	/	SYM
ejpam-5876	367	7	eur	eur	PROPN
ejpam-5876	367	8	.	.	PUNCT
ejpam-5876	368	1	j.	j.	PROPN
ejpam-5876	368	2	pure	pure	PROPN
ejpam-5876	368	3	appl	appl	PROPN
ejpam-5876	368	4	.	.	PROPN
ejpam-5876	368	5	math	math	PROPN
ejpam-5876	368	6	,	,	PUNCT
ejpam-5876	368	7	18	18	NUM
ejpam-5876	368	8	(	(	PUNCT
ejpam-5876	368	9	2	2	NUM
ejpam-5876	368	10	)	)	PUNCT
ejpam-5876	368	11	(	(	PUNCT
ejpam-5876	368	12	2025	2025	NUM
ejpam-5876	368	13	)	)	PUNCT
ejpam-5876	368	14	,	,	PUNCT
ejpam-5876	368	15	5876	5876	NUM
ejpam-5876	368	16	14	14	NUM
ejpam-5876	368	17	of	of	ADP
ejpam-5876	368	18	16	16	NUM
ejpam-5876	368	19	definition	definition	NOUN
ejpam-5876	368	20	11	11	NUM
ejpam-5876	368	21	.	.	PUNCT
ejpam-5876	369	1	a	a	DET
ejpam-5876	369	2	fuzzy	fuzzy	ADJ
ejpam-5876	369	3	set	set	VERB
ejpam-5876	369	4	µ	µ	NOUN
ejpam-5876	369	5	in	in	ADP
ejpam-5876	369	6	x	x	AUX
ejpam-5876	369	7	is	be	AUX
ejpam-5876	369	8	called	call	VERB
ejpam-5876	369	9	an	an	DET
ejpam-5876	369	10	(	(	PUNCT
ejpam-5876	369	11	∈	∈	PROPN
ejpam-5876	369	12	∨	∨	NUM
ejpam-5876	369	13	qk,∈	qk,∈	PROPN
ejpam-5876	370	1	∨	∨	NUM
ejpam-5876	370	2	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	370	3	sup	sup	NOUN
ejpam-5876	370	4	-	-	PUNCT
ejpam-5876	370	5	subalgebra	subalgebra	NOUN
ejpam-5876	370	6	of	of	ADP
ejpam-5876	370	7	x	x	PRON
ejpam-5876	370	8	if	if	SCONJ
ejpam-5876	370	9	it	it	PRON
ejpam-5876	370	10	satisfies	satisfy	VERB
ejpam-5876	370	11	the	the	DET
ejpam-5876	370	12	following	following	NOUN
ejpam-5876	370	13	:	:	PUNCT
ejpam-5876	370	14	(	(	PUNCT
ejpam-5876	370	15	∀x	∀x	X
ejpam-5876	370	16	,	,	PUNCT
ejpam-5876	370	17	y	y	PROPN
ejpam-5876	370	18	∈	∈	PROPN
ejpam-5876	370	19	x)(∀t	x)(∀t	PROPN
ejpam-5876	370	20	,	,	PUNCT
ejpam-5876	370	21	r	r	NOUN
ejpam-5876	370	22	∈	∈	PROPN
ejpam-5876	370	23	(	(	PUNCT
ejpam-5876	370	24	0	0	NUM
ejpam-5876	370	25	,	,	PUNCT
ejpam-5876	370	26	1])(((x|(y|y))|(x|(y|y)))min{t	1])(((x|(y|y))|(x|(y|y)))min{t	NUM
ejpam-5876	370	27	,	,	PUNCT
ejpam-5876	370	28	r}∈	r}∈	VERB
ejpam-5876	370	29	∨	∨	NUM
ejpam-5876	370	30	qkµ	qkµ	NOUN
ejpam-5876	370	31	⇒	⇒	PROPN
ejpam-5876	370	32	xt∈	xt∈	PROPN
ejpam-5876	370	33	∨	∨	NUM
ejpam-5876	370	34	qkµ	qkµ	NOUN
ejpam-5876	370	35	or	or	CCONJ
ejpam-5876	370	36	yr∈	yr∈	PROPN
ejpam-5876	370	37	∨	∨	PROPN
ejpam-5876	370	38	qkµ	qkµ	PROPN
ejpam-5876	370	39	)	)	PUNCT
ejpam-5876	370	40	.	.	PUNCT
ejpam-5876	371	1	(	(	PUNCT
ejpam-5876	371	2	16	16	NUM
ejpam-5876	371	3	)	)	PUNCT
ejpam-5876	371	4	theorem	theorem	VERB
ejpam-5876	371	5	14	14	NUM
ejpam-5876	371	6	.	.	PUNCT
ejpam-5876	372	1	every	every	DET
ejpam-5876	372	2	(	(	PUNCT
ejpam-5876	372	3	∈	∈	PROPN
ejpam-5876	372	4	∨	∨	NUM
ejpam-5876	372	5	qk,∈	qk,∈	PROPN
ejpam-5876	372	6	∨	∨	NUM
ejpam-5876	372	7	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	372	8	sup	sup	NOUN
ejpam-5876	372	9	-	-	PUNCT
ejpam-5876	372	10	subalgebra	subalgebra	NOUN
ejpam-5876	372	11	is	be	AUX
ejpam-5876	372	12	an	an	DET
ejpam-5876	372	13	(	(	PUNCT
ejpam-5876	372	14	∈,∈	∈,∈	X
ejpam-5876	372	15	∨	∨	NUM
ejpam-5876	372	16	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	372	17	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	372	18	.	.	PUNCT
ejpam-5876	373	1	proof	proof	NOUN
ejpam-5876	373	2	.	.	PUNCT
ejpam-5876	374	1	let	let	VERB
ejpam-5876	374	2	x	x	PRON
ejpam-5876	374	3	,	,	PUNCT
ejpam-5876	374	4	y	y	PROPN
ejpam-5876	374	5	∈	∈	PROPN
ejpam-5876	374	6	x	x	X
ejpam-5876	374	7	and	and	CCONJ
ejpam-5876	374	8	t	t	PROPN
ejpam-5876	374	9	,	,	PUNCT
ejpam-5876	374	10	r	r	NOUN
ejpam-5876	374	11	∈	∈	PROPN
ejpam-5876	374	12	(	(	PUNCT
ejpam-5876	374	13	0	0	NUM
ejpam-5876	374	14	,	,	PUNCT
ejpam-5876	374	15	1	1	NUM
ejpam-5876	374	16	]	]	PUNCT
ejpam-5876	374	17	be	be	AUX
ejpam-5876	374	18	such	such	ADJ
ejpam-5876	374	19	that	that	SCONJ
ejpam-5876	374	20	(	(	PUNCT
ejpam-5876	374	21	(	(	PUNCT
ejpam-5876	374	22	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	374	23	,	,	PUNCT
ejpam-5876	374	24	r}∈µ.	r}∈µ.	PROPN
ejpam-5876	374	25	then	then	ADV
ejpam-5876	374	26	(	(	PUNCT
ejpam-5876	374	27	(	(	PUNCT
ejpam-5876	374	28	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	374	29	,	,	PUNCT
ejpam-5876	374	30	r}∈	r}∈	VERB
ejpam-5876	374	31	∨	∨	NUM
ejpam-5876	374	32	qkµ	qkµ	PROPN
ejpam-5876	374	33	,	,	PUNCT
ejpam-5876	374	34	and	and	CCONJ
ejpam-5876	374	35	so	so	ADV
ejpam-5876	374	36	xt∈	xt∈	PROPN
ejpam-5876	374	37	∨	∨	NUM
ejpam-5876	374	38	qkµ	qkµ	NOUN
ejpam-5876	374	39	or	or	CCONJ
ejpam-5876	374	40	yr∈	yr∈	PROPN
ejpam-5876	374	41	∨	∨	PROPN
ejpam-5876	374	42	qkµ	qkµ	NOUN
ejpam-5876	374	43	by	by	ADP
ejpam-5876	374	44	(	(	PUNCT
ejpam-5876	374	45	16	16	NUM
ejpam-5876	374	46	)	)	PUNCT
ejpam-5876	374	47	.	.	PUNCT
ejpam-5876	375	1	therefore	therefore	ADV
ejpam-5876	375	2	,	,	PUNCT
ejpam-5876	375	3	µ	µ	X
ejpam-5876	375	4	is	be	AUX
ejpam-5876	375	5	an	an	DET
ejpam-5876	375	6	(	(	PUNCT
ejpam-5876	375	7	∈,∈	∈,∈	X
ejpam-5876	375	8	∨	∨	NUM
ejpam-5876	375	9	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	375	10	sup	sup	NOUN
ejpam-5876	375	11	-	-	PUNCT
ejpam-5876	375	12	subalgebra	subalgebra	NOUN
ejpam-5876	375	13	of	of	ADP
ejpam-5876	375	14	x.	x.	PROPN
ejpam-5876	375	15	corollary	corollary	PROPN
ejpam-5876	375	16	16	16	NUM
ejpam-5876	375	17	is	be	AUX
ejpam-5876	375	18	an	an	DET
ejpam-5876	375	19	immediate	immediate	ADJ
ejpam-5876	375	20	consequence	consequence	NOUN
ejpam-5876	375	21	of	of	ADP
ejpam-5876	375	22	theorem	theorem	NOUN
ejpam-5876	375	23	14	14	NUM
ejpam-5876	375	24	,	,	PUNCT
ejpam-5876	375	25	which	which	PRON
ejpam-5876	375	26	states	state	VERB
ejpam-5876	375	27	that	that	SCONJ
ejpam-5876	375	28	every	every	DET
ejpam-5876	375	29	(	(	PUNCT
ejpam-5876	375	30	∈	∈	PROPN
ejpam-5876	375	31	∨qk,∈	∨qk,∈	NOUN
ejpam-5876	375	32	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	375	33	sup	sup	ADJ
ejpam-5876	375	34	-	-	PUNCT
ejpam-5876	375	35	subalgebra	subalgebra	NOUN
ejpam-5876	375	36	is	be	AUX
ejpam-5876	375	37	also	also	ADV
ejpam-5876	375	38	an	an	DET
ejpam-5876	375	39	(	(	PUNCT
ejpam-5876	375	40	∈,∈	∈,∈	X
ejpam-5876	375	41	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	375	42	sup	sup	ADJ
ejpam-5876	375	43	-	-	PUNCT
ejpam-5876	375	44	subalgebra	subalgebra	NOUN
ejpam-5876	375	45	.	.	PUNCT
ejpam-5876	376	1	from	from	ADP
ejpam-5876	376	2	this	this	PRON
ejpam-5876	376	3	,	,	PUNCT
ejpam-5876	376	4	properties	property	NOUN
ejpam-5876	376	5	(	(	PUNCT
ejpam-5876	376	6	2	2	NUM
ejpam-5876	376	7	)	)	PUNCT
ejpam-5876	376	8	,	,	PUNCT
ejpam-5876	376	9	(	(	PUNCT
ejpam-5876	376	10	3	3	NUM
ejpam-5876	376	11	)	)	PUNCT
ejpam-5876	376	12	,	,	PUNCT
ejpam-5876	376	13	and	and	CCONJ
ejpam-5876	376	14	(	(	PUNCT
ejpam-5876	376	15	4	4	X
ejpam-5876	376	16	)	)	PUNCT
ejpam-5876	376	17	follow	follow	VERB
ejpam-5876	376	18	directly	directly	ADV
ejpam-5876	376	19	by	by	ADP
ejpam-5876	376	20	invoking	invoke	VERB
ejpam-5876	376	21	theorems	theorem	NOUN
ejpam-5876	376	22	11	11	NUM
ejpam-5876	376	23	,	,	PUNCT
ejpam-5876	376	24	12	12	NUM
ejpam-5876	376	25	,	,	PUNCT
ejpam-5876	376	26	and	and	CCONJ
ejpam-5876	376	27	13	13	NUM
ejpam-5876	376	28	,	,	PUNCT
ejpam-5876	376	29	respectively	respectively	ADV
ejpam-5876	376	30	.	.	PUNCT
ejpam-5876	377	1	thus	thus	ADV
ejpam-5876	377	2	,	,	PUNCT
ejpam-5876	377	3	the	the	DET
ejpam-5876	377	4	corollary	corollary	ADJ
ejpam-5876	377	5	summarizes	summarize	NOUN
ejpam-5876	377	6	the	the	DET
ejpam-5876	377	7	logical	logical	ADJ
ejpam-5876	377	8	implications	implication	NOUN
ejpam-5876	377	9	of	of	ADP
ejpam-5876	377	10	theorem	theorem	ADJ
ejpam-5876	377	11	14	14	NUM
ejpam-5876	377	12	and	and	CCONJ
ejpam-5876	377	13	the	the	DET
ejpam-5876	377	14	previously	previously	ADV
ejpam-5876	377	15	established	establish	VERB
ejpam-5876	377	16	equivalences	equivalence	NOUN
ejpam-5876	377	17	.	.	PUNCT
ejpam-5876	378	1	corollary	corollary	ADJ
ejpam-5876	378	2	16	16	NUM
ejpam-5876	378	3	.	.	PUNCT
ejpam-5876	379	1	if	if	SCONJ
ejpam-5876	379	2	µ	µ	NOUN
ejpam-5876	379	3	is	be	AUX
ejpam-5876	379	4	an	an	DET
ejpam-5876	379	5	(	(	PUNCT
ejpam-5876	379	6	∈	∈	PROPN
ejpam-5876	379	7	∨	∨	NUM
ejpam-5876	379	8	qk,∈	qk,∈	PROPN
ejpam-5876	379	9	∨	∨	NUM
ejpam-5876	379	10	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	379	11	sup	sup	NOUN
ejpam-5876	379	12	-	-	PUNCT
ejpam-5876	379	13	subalgebra	subalgebra	NOUN
ejpam-5876	379	14	of	of	ADP
ejpam-5876	379	15	x	x	PRON
ejpam-5876	379	16	,	,	PUNCT
ejpam-5876	379	17	then	then	ADV
ejpam-5876	379	18	(	(	PUNCT
ejpam-5876	379	19	1	1	X
ejpam-5876	379	20	)	)	PUNCT
ejpam-5876	379	21	µ	µ	X
ejpam-5876	379	22	is	be	AUX
ejpam-5876	379	23	an	an	DET
ejpam-5876	379	24	(	(	PUNCT
ejpam-5876	379	25	∈,∈	∈,∈	X
ejpam-5876	379	26	∨	∨	NUM
ejpam-5876	379	27	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	379	28	sup	sup	NOUN
ejpam-5876	379	29	-	-	PUNCT
ejpam-5876	379	30	subalgebra	subalgebra	NOUN
ejpam-5876	379	31	,	,	PUNCT
ejpam-5876	379	32	(	(	PUNCT
ejpam-5876	379	33	2	2	X
ejpam-5876	379	34	)	)	PUNCT
ejpam-5876	379	35	µ	µ	PRON
ejpam-5876	379	36	satisfies	satisfie	NOUN
ejpam-5876	379	37	the	the	DET
ejpam-5876	379	38	condition	condition	NOUN
ejpam-5876	379	39	(	(	PUNCT
ejpam-5876	379	40	14	14	NUM
ejpam-5876	379	41	)	)	PUNCT
ejpam-5876	379	42	,	,	PUNCT
ejpam-5876	379	43	(	(	PUNCT
ejpam-5876	379	44	3	3	X
ejpam-5876	379	45	)	)	PUNCT
ejpam-5876	379	46	(	(	PUNCT
ejpam-5876	379	47	x	x	X
ejpam-5876	379	48	,	,	PUNCT
ejpam-5876	379	49	ℓµu	ℓµu	NOUN
ejpam-5876	379	50	)	)	PUNCT
ejpam-5876	379	51	is	be	AUX
ejpam-5876	379	52	a	a	DET
ejpam-5876	379	53	semidetached	semidetache	VERB
ejpam-5876	379	54	sup	sup	NOUN
ejpam-5876	379	55	-	-	PUNCT
ejpam-5876	379	56	subalgebra	subalgebra	NOUN
ejpam-5876	379	57	over	over	ADP
ejpam-5876	379	58	ω	ω	NUM
ejpam-5876	379	59	=	=	SYM
ejpam-5876	379	60	(	(	PUNCT
ejpam-5876	379	61	1−k	1−k	NUM
ejpam-5876	379	62	2	2	NUM
ejpam-5876	379	63	,	,	PUNCT
ejpam-5876	379	64	1	1	NUM
ejpam-5876	379	65	]	]	PUNCT
ejpam-5876	379	66	,	,	PUNCT
ejpam-5876	379	67	(	(	PUNCT
ejpam-5876	379	68	4	4	NUM
ejpam-5876	379	69	)	)	PUNCT
ejpam-5876	379	70	(	(	PUNCT
ejpam-5876	379	71	x	x	X
ejpam-5876	379	72	,	,	PUNCT
ejpam-5876	379	73	ℓµqk	ℓµqk	PROPN
ejpam-5876	379	74	)	)	PUNCT
ejpam-5876	379	75	is	be	AUX
ejpam-5876	379	76	a	a	DET
ejpam-5876	379	77	semidetached	semidetache	VERB
ejpam-5876	379	78	sup	sup	NOUN
ejpam-5876	379	79	-	-	PUNCT
ejpam-5876	379	80	subalgebra	subalgebra	NOUN
ejpam-5876	379	81	over	over	ADP
ejpam-5876	379	82	ω	ω	NUM
ejpam-5876	379	83	=	=	SYM
ejpam-5876	379	84	(	(	PUNCT
ejpam-5876	379	85	0	0	NUM
ejpam-5876	379	86	,	,	PUNCT
ejpam-5876	379	87	1−k	1−k	NUM
ejpam-5876	379	88	2	2	NUM
ejpam-5876	379	89	]	]	PUNCT
ejpam-5876	379	90	.	.	PUNCT
ejpam-5876	380	1	definition	definition	NOUN
ejpam-5876	380	2	12	12	NUM
ejpam-5876	380	3	.	.	PUNCT
ejpam-5876	381	1	a	a	DET
ejpam-5876	381	2	fuzzy	fuzzy	ADJ
ejpam-5876	381	3	set	set	VERB
ejpam-5876	381	4	µ	µ	NOUN
ejpam-5876	381	5	in	in	ADP
ejpam-5876	381	6	x	x	AUX
ejpam-5876	381	7	is	be	AUX
ejpam-5876	381	8	called	call	VERB
ejpam-5876	381	9	a	a	DET
ejpam-5876	381	10	(	(	PUNCT
ejpam-5876	381	11	qk,∈∨	qk,∈∨	NUM
ejpam-5876	381	12	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	381	13	sup	sup	NOUN
ejpam-5876	381	14	-	-	PUNCT
ejpam-5876	381	15	subalgebra	subalgebra	NOUN
ejpam-5876	381	16	of	of	ADP
ejpam-5876	381	17	x	x	SYM
ejpam-5876	381	18	if	if	SCONJ
ejpam-5876	381	19	if	if	SCONJ
ejpam-5876	381	20	it	it	PRON
ejpam-5876	381	21	satisfies	satisfy	VERB
ejpam-5876	381	22	the	the	DET
ejpam-5876	381	23	following	following	NOUN
ejpam-5876	381	24	:	:	PUNCT
ejpam-5876	381	25	(	(	PUNCT
ejpam-5876	381	26	∀x	∀x	X
ejpam-5876	381	27	,	,	PUNCT
ejpam-5876	381	28	y	y	PROPN
ejpam-5876	381	29	∈	∈	PROPN
ejpam-5876	381	30	x)(∀t	x)(∀t	PROPN
ejpam-5876	381	31	,	,	PUNCT
ejpam-5876	381	32	r	r	NOUN
ejpam-5876	381	33	∈	∈	PROPN
ejpam-5876	381	34	(	(	PUNCT
ejpam-5876	381	35	0	0	NUM
ejpam-5876	381	36	,	,	PUNCT
ejpam-5876	381	37	1])(((x|(y|y))|(x|(y|y)))min{t	1])(((x|(y|y))|(x|(y|y)))min{t	NUM
ejpam-5876	381	38	,	,	PUNCT
ejpam-5876	381	39	r}qkµ	r}qkµ	NOUN
ejpam-5876	381	40	⇒	⇒	VERB
ejpam-5876	381	41	xt∈	xt∈	PROPN
ejpam-5876	381	42	∨	∨	NUM
ejpam-5876	381	43	qkµ	qkµ	NOUN
ejpam-5876	381	44	or	or	CCONJ
ejpam-5876	381	45	yr∈	yr∈	PROPN
ejpam-5876	381	46	∨	∨	PROPN
ejpam-5876	381	47	qkµ	qkµ	PROPN
ejpam-5876	381	48	)	)	PUNCT
ejpam-5876	381	49	.	.	PUNCT
ejpam-5876	382	1	(	(	PUNCT
ejpam-5876	382	2	17	17	NUM
ejpam-5876	382	3	)	)	PUNCT
ejpam-5876	382	4	theorem	theorem	NOUN
ejpam-5876	382	5	15	15	NUM
ejpam-5876	382	6	.	.	PUNCT
ejpam-5876	383	1	assume	assume	VERB
ejpam-5876	383	2	that	that	SCONJ
ejpam-5876	383	3	min{t	min{t	PROPN
ejpam-5876	383	4	,	,	PUNCT
ejpam-5876	383	5	r	r	NOUN
ejpam-5876	383	6	}	}	PUNCT
ejpam-5876	383	7	≤	≤	NOUN
ejpam-5876	383	8	1−k	1−k	NUM
ejpam-5876	383	9	2	2	NUM
ejpam-5876	383	10	for	for	ADP
ejpam-5876	383	11	any	any	DET
ejpam-5876	383	12	t	t	NOUN
ejpam-5876	383	13	,	,	PUNCT
ejpam-5876	383	14	r	r	NOUN
ejpam-5876	383	15	∈	∈	PROPN
ejpam-5876	383	16	(	(	PUNCT
ejpam-5876	383	17	0	0	NUM
ejpam-5876	383	18	,	,	PUNCT
ejpam-5876	383	19	1	1	NUM
ejpam-5876	383	20	]	]	PUNCT
ejpam-5876	383	21	.	.	PUNCT
ejpam-5876	384	1	then	then	ADV
ejpam-5876	384	2	every	every	DET
ejpam-5876	384	3	(	(	PUNCT
ejpam-5876	384	4	qk,∈∨	qk,∈∨	NUM
ejpam-5876	384	5	qk)fuzzy	qk)fuzzy	ADJ
ejpam-5876	384	6	sup	sup	NOUN
ejpam-5876	384	7	-	-	PUNCT
ejpam-5876	384	8	subalgebra	subalgebra	NOUN
ejpam-5876	384	9	is	be	AUX
ejpam-5876	384	10	an	an	DET
ejpam-5876	384	11	(	(	PUNCT
ejpam-5876	384	12	∈,∈	∈,∈	X
ejpam-5876	384	13	∨	∨	NUM
ejpam-5876	384	14	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	384	15	sup	sup	NOUN
ejpam-5876	384	16	-	-	PUNCT
ejpam-5876	384	17	subalgebra	subalgebra	NOUN
ejpam-5876	384	18	.	.	PUNCT
ejpam-5876	385	1	proof	proof	NOUN
ejpam-5876	385	2	.	.	PUNCT
ejpam-5876	386	1	let	let	VERB
ejpam-5876	386	2	µ	µ	X
ejpam-5876	386	3	be	be	AUX
ejpam-5876	386	4	an	an	DET
ejpam-5876	386	5	(	(	PUNCT
ejpam-5876	386	6	qk,∈	qk,∈	PROPN
ejpam-5876	386	7	∨	∨	NUM
ejpam-5876	386	8	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	386	9	sup	sup	NOUN
ejpam-5876	386	10	-	-	PUNCT
ejpam-5876	386	11	subalgebra	subalgebra	NOUN
ejpam-5876	386	12	of	of	ADP
ejpam-5876	386	13	x.	x.	NOUN
ejpam-5876	386	14	assume	assume	VERB
ejpam-5876	386	15	that	that	SCONJ
ejpam-5876	386	16	(	(	PUNCT
ejpam-5876	386	17	(	(	PUNCT
ejpam-5876	386	18	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	386	19	,	,	PUNCT
ejpam-5876	386	20	r}∈µ	r}∈µ	X
ejpam-5876	386	21	for	for	ADP
ejpam-5876	386	22	x	x	X
ejpam-5876	386	23	,	,	PUNCT
ejpam-5876	386	24	y	y	PROPN
ejpam-5876	386	25	∈	∈	PROPN
ejpam-5876	386	26	x	x	X
ejpam-5876	386	27	and	and	CCONJ
ejpam-5876	386	28	t	t	PROPN
ejpam-5876	386	29	,	,	PUNCT
ejpam-5876	386	30	r	r	NOUN
ejpam-5876	386	31	∈	∈	PROPN
ejpam-5876	386	32	(	(	PUNCT
ejpam-5876	386	33	0	0	NUM
ejpam-5876	386	34	,	,	PUNCT
ejpam-5876	386	35	1	1	NUM
ejpam-5876	386	36	]	]	PUNCT
ejpam-5876	386	37	with	with	ADP
ejpam-5876	386	38	min{t	min{t	PROPN
ejpam-5876	386	39	,	,	PUNCT
ejpam-5876	386	40	r	r	NOUN
ejpam-5876	386	41	}	}	PUNCT
ejpam-5876	386	42	≤	≤	NOUN
ejpam-5876	386	43	1−k	1−k	NUM
ejpam-5876	386	44	2	2	NUM
ejpam-5876	386	45	.	.	PUNCT
ejpam-5876	387	1	then	then	ADV
ejpam-5876	387	2	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	387	3	)	)	PUNCT
ejpam-5876	387	4	)	)	PUNCT
ejpam-5876	387	5	)	)	PUNCT
ejpam-5876	388	1	<	<	X
ejpam-5876	388	2	min{t	min{t	PROPN
ejpam-5876	388	3	,	,	PUNCT
ejpam-5876	388	4	r	r	NOUN
ejpam-5876	388	5	}	}	PUNCT
ejpam-5876	388	6	≤	≤	NOUN
ejpam-5876	388	7	1−k	1−k	NUM
ejpam-5876	388	8	2	2	NUM
ejpam-5876	388	9	,	,	PUNCT
ejpam-5876	388	10	and	and	CCONJ
ejpam-5876	388	11	so	so	ADV
ejpam-5876	388	12	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	388	13	)	)	PUNCT
ejpam-5876	388	14	)	)	PUNCT
ejpam-5876	388	15	)	)	PUNCT
ejpam-5876	389	1	+	+	CCONJ
ejpam-5876	389	2	k	k	PROPN
ejpam-5876	389	3	+	+	PUNCT
ejpam-5876	389	4	min{t	min{t	PROPN
ejpam-5876	389	5	,	,	PUNCT
ejpam-5876	389	6	r	r	NOUN
ejpam-5876	389	7	}	}	PUNCT
ejpam-5876	389	8	<	<	X
ejpam-5876	389	9	1−k	1−k	NUM
ejpam-5876	389	10	2	2	NUM
ejpam-5876	389	11	+	+	CCONJ
ejpam-5876	389	12	1−k	1−k	NUM
ejpam-5876	389	13	2	2	NUM
ejpam-5876	390	1	+	+	CCONJ
ejpam-5876	390	2	k	k	NOUN
ejpam-5876	390	3	=	=	SYM
ejpam-5876	390	4	1	1	NUM
ejpam-5876	390	5	,	,	PUNCT
ejpam-5876	390	6	that	that	ADV
ejpam-5876	390	7	is	is	ADV
ejpam-5876	390	8	,	,	PUNCT
ejpam-5876	390	9	(	(	PUNCT
ejpam-5876	390	10	(	(	PUNCT
ejpam-5876	390	11	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	390	12	,	,	PUNCT
ejpam-5876	390	13	r}qkµ.	r}qkµ.	VERB
ejpam-5876	390	14	it	it	PRON
ejpam-5876	390	15	follows	follow	VERB
ejpam-5876	390	16	from	from	ADP
ejpam-5876	390	17	(	(	PUNCT
ejpam-5876	390	18	17	17	NUM
ejpam-5876	390	19	)	)	PUNCT
ejpam-5876	390	20	that	that	PRON
ejpam-5876	390	21	xt∈	xt∈	PROPN
ejpam-5876	390	22	∨	∨	NUM
ejpam-5876	390	23	qkµ	qkµ	NOUN
ejpam-5876	390	24	or	or	CCONJ
ejpam-5876	390	25	yr∈	yr∈	PROPN
ejpam-5876	390	26	∨	∨	PROPN
ejpam-5876	390	27	qkµ.	qkµ.	X
ejpam-5876	390	28	therefore	therefore	ADV
ejpam-5876	390	29	,	,	PUNCT
ejpam-5876	390	30	µ	µ	X
ejpam-5876	390	31	is	be	AUX
ejpam-5876	390	32	an	an	DET
ejpam-5876	390	33	(	(	PUNCT
ejpam-5876	390	34	∈,∈	∈,∈	X
ejpam-5876	390	35	∨	∨	NUM
ejpam-5876	390	36	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	390	37	sup	sup	NOUN
ejpam-5876	390	38	-	-	PUNCT
ejpam-5876	390	39	subalgebra	subalgebra	NOUN
ejpam-5876	390	40	of	of	ADP
ejpam-5876	390	41	x.	x.	PROPN
ejpam-5876	390	42	corollary	corollary	PROPN
ejpam-5876	390	43	17	17	NUM
ejpam-5876	390	44	directly	directly	ADV
ejpam-5876	390	45	follows	follow	VERB
ejpam-5876	390	46	from	from	ADP
ejpam-5876	390	47	theorem	theorem	NOUN
ejpam-5876	390	48	15	15	NUM
ejpam-5876	390	49	by	by	ADP
ejpam-5876	390	50	setting	set	VERB
ejpam-5876	390	51	k	k	PROPN
ejpam-5876	390	52	=	=	PUNCT
ejpam-5876	390	53	0	0	X
ejpam-5876	390	54	.	.	PUNCT
ejpam-5876	391	1	in	in	ADP
ejpam-5876	391	2	this	this	DET
ejpam-5876	391	3	case	case	NOUN
ejpam-5876	391	4	,	,	PUNCT
ejpam-5876	391	5	the	the	DET
ejpam-5876	391	6	condition	condition	NOUN
ejpam-5876	391	7	min{t	min{t	PROPN
ejpam-5876	391	8	,	,	PUNCT
ejpam-5876	391	9	r	r	NOUN
ejpam-5876	391	10	}	}	PUNCT
ejpam-5876	391	11	≤	≤	NOUN
ejpam-5876	391	12	1−k	1−k	NUM
ejpam-5876	391	13	2	2	NUM
ejpam-5876	391	14	becomes	become	VERB
ejpam-5876	391	15	min{t	min{t	PROPN
ejpam-5876	391	16	,	,	PUNCT
ejpam-5876	391	17	r	r	NOUN
ejpam-5876	391	18	}	}	PUNCT
ejpam-5876	391	19	≤	≤	NUM
ejpam-5876	391	20	0.5	0.5	NUM
ejpam-5876	391	21	.	.	PUNCT
ejpam-5876	392	1	theorem	theorem	VERB
ejpam-5876	392	2	15	15	NUM
ejpam-5876	392	3	ensures	ensure	VERB
ejpam-5876	392	4	that	that	SCONJ
ejpam-5876	392	5	under	under	ADP
ejpam-5876	392	6	t.	t.	PROPN
ejpam-5876	392	7	oner	oner	NOUN
ejpam-5876	392	8	et	et	PROPN
ejpam-5876	392	9	al	al	PROPN
ejpam-5876	392	10	.	.	PUNCT
ejpam-5876	392	11	/	/	SYM
ejpam-5876	392	12	eur	eur	PROPN
ejpam-5876	392	13	.	.	PUNCT
ejpam-5876	393	1	j.	j.	PROPN
ejpam-5876	393	2	pure	pure	PROPN
ejpam-5876	393	3	appl	appl	PROPN
ejpam-5876	393	4	.	.	PROPN
ejpam-5876	393	5	math	math	PROPN
ejpam-5876	393	6	,	,	PUNCT
ejpam-5876	393	7	18	18	NUM
ejpam-5876	393	8	(	(	PUNCT
ejpam-5876	393	9	2	2	NUM
ejpam-5876	393	10	)	)	PUNCT
ejpam-5876	393	11	(	(	PUNCT
ejpam-5876	393	12	2025	2025	NUM
ejpam-5876	393	13	)	)	PUNCT
ejpam-5876	393	14	,	,	PUNCT
ejpam-5876	393	15	5876	5876	NUM
ejpam-5876	393	16	15	15	NUM
ejpam-5876	393	17	of	of	ADP
ejpam-5876	393	18	16	16	NUM
ejpam-5876	393	19	this	this	DET
ejpam-5876	393	20	condition	condition	NOUN
ejpam-5876	393	21	,	,	PUNCT
ejpam-5876	393	22	every	every	DET
ejpam-5876	393	23	(	(	PUNCT
ejpam-5876	393	24	qk,∈	qk,∈	X
ejpam-5876	393	25	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	393	26	sup	sup	ADJ
ejpam-5876	393	27	-	-	PUNCT
ejpam-5876	393	28	subalgebra	subalgebra	NOUN
ejpam-5876	393	29	is	be	AUX
ejpam-5876	393	30	also	also	ADV
ejpam-5876	393	31	an	an	DET
ejpam-5876	393	32	(	(	PUNCT
ejpam-5876	393	33	∈,∈	∈,∈	X
ejpam-5876	393	34	∨qk)-fuzzy	∨qk)-fuzzy	ADJ
ejpam-5876	393	35	supsubalgebra	supsubalgebra	NOUN
ejpam-5876	393	36	.	.	PUNCT
ejpam-5876	394	1	therefore	therefore	ADV
ejpam-5876	394	2	,	,	PUNCT
ejpam-5876	394	3	for	for	ADP
ejpam-5876	394	4	k	k	PROPN
ejpam-5876	394	5	=	=	SYM
ejpam-5876	394	6	0	0	PROPN
ejpam-5876	394	7	,	,	PUNCT
ejpam-5876	394	8	every	every	DET
ejpam-5876	394	9	(	(	PUNCT
ejpam-5876	394	10	q,∈	q,∈	PROPN
ejpam-5876	394	11	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	394	12	sup	sup	ADJ
ejpam-5876	394	13	-	-	PUNCT
ejpam-5876	394	14	subalgebra	subalgebra	NOUN
ejpam-5876	394	15	becomes	become	VERB
ejpam-5876	394	16	an	an	DET
ejpam-5876	394	17	(	(	PUNCT
ejpam-5876	394	18	∈,∈	∈,∈	X
ejpam-5876	394	19	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	394	20	sup	sup	NOUN
ejpam-5876	394	21	-	-	PUNCT
ejpam-5876	394	22	subalgebra	subalgebra	NOUN
ejpam-5876	394	23	.	.	PUNCT
ejpam-5876	395	1	corollary	corollary	ADJ
ejpam-5876	395	2	17	17	NUM
ejpam-5876	395	3	.	.	PUNCT
ejpam-5876	396	1	assume	assume	VERB
ejpam-5876	396	2	that	that	SCONJ
ejpam-5876	396	3	min{t	min{t	PROPN
ejpam-5876	396	4	,	,	PUNCT
ejpam-5876	396	5	r	r	NOUN
ejpam-5876	396	6	}	}	PUNCT
ejpam-5876	396	7	≤	≤	NUM
ejpam-5876	396	8	0.5	0.5	NUM
ejpam-5876	396	9	for	for	ADP
ejpam-5876	396	10	any	any	DET
ejpam-5876	396	11	t	t	NOUN
ejpam-5876	396	12	,	,	PUNCT
ejpam-5876	396	13	r	r	NOUN
ejpam-5876	396	14	∈	∈	PROPN
ejpam-5876	396	15	(	(	PUNCT
ejpam-5876	396	16	0	0	NUM
ejpam-5876	396	17	,	,	PUNCT
ejpam-5876	396	18	1	1	NUM
ejpam-5876	396	19	]	]	PUNCT
ejpam-5876	396	20	.	.	PUNCT
ejpam-5876	397	1	then	then	ADV
ejpam-5876	397	2	every	every	PRON
ejpam-5876	397	3	(	(	PUNCT
ejpam-5876	397	4	q,∈	q,∈	PROPN
ejpam-5876	397	5	∨	∨	NOUN
ejpam-5876	397	6	q)fuzzy	q)fuzzy	PROPN
ejpam-5876	397	7	sup	sup	ADJ
ejpam-5876	397	8	-	-	PUNCT
ejpam-5876	397	9	subalgebra	subalgebra	NOUN
ejpam-5876	397	10	is	be	AUX
ejpam-5876	397	11	an	an	DET
ejpam-5876	397	12	(	(	PUNCT
ejpam-5876	397	13	∈,∈	∈,∈	X
ejpam-5876	397	14	∨	∨	NUM
ejpam-5876	397	15	q)-fuzzy	q)-fuzzy	PUNCT
ejpam-5876	397	16	sup	sup	NOUN
ejpam-5876	397	17	-	-	PUNCT
ejpam-5876	397	18	subalgebra	subalgebra	NOUN
ejpam-5876	397	19	.	.	PUNCT
ejpam-5876	398	1	theorem	theorem	NOUN
ejpam-5876	398	2	16	16	NUM
ejpam-5876	398	3	.	.	PUNCT
ejpam-5876	399	1	assume	assume	VERB
ejpam-5876	399	2	that	that	SCONJ
ejpam-5876	399	3	min{t	min{t	PROPN
ejpam-5876	399	4	,	,	PUNCT
ejpam-5876	399	5	r	r	NOUN
ejpam-5876	399	6	}	}	PUNCT
ejpam-5876	399	7	>	>	X
ejpam-5876	399	8	1−k	1−k	NUM
ejpam-5876	399	9	2	2	NUM
ejpam-5876	399	10	for	for	ADP
ejpam-5876	399	11	any	any	DET
ejpam-5876	399	12	t	t	NOUN
ejpam-5876	399	13	,	,	PUNCT
ejpam-5876	399	14	r	r	NOUN
ejpam-5876	399	15	∈	∈	PROPN
ejpam-5876	399	16	(	(	PUNCT
ejpam-5876	399	17	0	0	NUM
ejpam-5876	399	18	,	,	PUNCT
ejpam-5876	399	19	1	1	NUM
ejpam-5876	399	20	]	]	PUNCT
ejpam-5876	399	21	.	.	PUNCT
ejpam-5876	400	1	then	then	ADV
ejpam-5876	400	2	every	every	DET
ejpam-5876	400	3	(	(	PUNCT
ejpam-5876	400	4	∈,∈	∈,∈	X
ejpam-5876	400	5	∨	∨	ADJ
ejpam-5876	400	6	qk)fuzzy	qk)fuzzy	ADJ
ejpam-5876	400	7	sup	sup	NOUN
ejpam-5876	400	8	-	-	PUNCT
ejpam-5876	400	9	subalgebra	subalgebra	NOUN
ejpam-5876	400	10	is	be	AUX
ejpam-5876	400	11	a	a	DET
ejpam-5876	400	12	(	(	PUNCT
ejpam-5876	400	13	qk,∈	qk,∈	PROPN
ejpam-5876	400	14	∨	∨	NUM
ejpam-5876	400	15	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	400	16	sup	sup	NOUN
ejpam-5876	400	17	-	-	PUNCT
ejpam-5876	400	18	subalgebra	subalgebra	NOUN
ejpam-5876	400	19	.	.	PUNCT
ejpam-5876	401	1	proof	proof	NOUN
ejpam-5876	401	2	.	.	PUNCT
ejpam-5876	402	1	let	let	VERB
ejpam-5876	402	2	µ	µ	X
ejpam-5876	402	3	be	be	AUX
ejpam-5876	402	4	an	an	DET
ejpam-5876	402	5	(	(	PUNCT
ejpam-5876	402	6	∈,∈	∈,∈	X
ejpam-5876	402	7	∨	∨	NUM
ejpam-5876	402	8	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	402	9	sup	sup	NOUN
ejpam-5876	402	10	-	-	PUNCT
ejpam-5876	402	11	subalgebra	subalgebra	NOUN
ejpam-5876	402	12	of	of	ADP
ejpam-5876	402	13	x.	x.	NOUN
ejpam-5876	402	14	assume	assume	VERB
ejpam-5876	402	15	that	that	SCONJ
ejpam-5876	402	16	(	(	PUNCT
ejpam-5876	402	17	(	(	PUNCT
ejpam-5876	402	18	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	402	19	,	,	PUNCT
ejpam-5876	402	20	r}qkµ	r}qkµ	NOUN
ejpam-5876	402	21	for	for	ADP
ejpam-5876	402	22	x	x	PROPN
ejpam-5876	402	23	,	,	PUNCT
ejpam-5876	402	24	y	y	PROPN
ejpam-5876	402	25	∈	∈	PROPN
ejpam-5876	402	26	x	x	X
ejpam-5876	402	27	and	and	CCONJ
ejpam-5876	402	28	t	t	PROPN
ejpam-5876	402	29	,	,	PUNCT
ejpam-5876	402	30	r	r	NOUN
ejpam-5876	402	31	∈	∈	PROPN
ejpam-5876	402	32	(	(	PUNCT
ejpam-5876	402	33	0	0	NUM
ejpam-5876	402	34	,	,	PUNCT
ejpam-5876	402	35	1	1	NUM
ejpam-5876	402	36	]	]	PUNCT
ejpam-5876	402	37	with	with	ADP
ejpam-5876	402	38	min{t	min{t	PROPN
ejpam-5876	402	39	,	,	PUNCT
ejpam-5876	402	40	r	r	NOUN
ejpam-5876	402	41	}	}	PUNCT
ejpam-5876	402	42	>	>	X
ejpam-5876	402	43	1−k	1−k	NUM
ejpam-5876	402	44	2	2	NUM
ejpam-5876	402	45	.	.	PUNCT
ejpam-5876	403	1	if	if	SCONJ
ejpam-5876	403	2	(	(	PUNCT
ejpam-5876	403	3	(	(	PUNCT
ejpam-5876	403	4	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	403	5	,	,	PUNCT
ejpam-5876	403	6	r	r	NOUN
ejpam-5876	403	7	}	}	PUNCT
ejpam-5876	403	8	∈	∈	PROPN
ejpam-5876	403	9	µ	µ	NOUN
ejpam-5876	403	10	,	,	PUNCT
ejpam-5876	403	11	then	then	ADV
ejpam-5876	403	12	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	403	13	)	)	PUNCT
ejpam-5876	403	14	)	)	PUNCT
ejpam-5876	403	15	)	)	PUNCT
ejpam-5876	403	16	≥	≥	NOUN
ejpam-5876	403	17	min{t	min{t	PROPN
ejpam-5876	403	18	,	,	PUNCT
ejpam-5876	403	19	r	r	NOUN
ejpam-5876	403	20	}	}	PUNCT
ejpam-5876	403	21	,	,	PUNCT
ejpam-5876	403	22	and	and	CCONJ
ejpam-5876	403	23	so	so	ADV
ejpam-5876	403	24	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5876	403	25	)	)	PUNCT
ejpam-5876	403	26	)	)	PUNCT
ejpam-5876	403	27	)	)	PUNCT
ejpam-5876	404	1	+	+	CCONJ
ejpam-5876	404	2	k	k	PROPN
ejpam-5876	404	3	+	+	PUNCT
ejpam-5876	404	4	min{t	min{t	PROPN
ejpam-5876	404	5	,	,	PUNCT
ejpam-5876	404	6	r	r	NOUN
ejpam-5876	404	7	}	}	PUNCT
ejpam-5876	404	8	>	>	X
ejpam-5876	404	9	1−k	1−k	NUM
ejpam-5876	404	10	2	2	NUM
ejpam-5876	404	11	+	+	CCONJ
ejpam-5876	404	12	1−k	1−k	NUM
ejpam-5876	404	13	2	2	NUM
ejpam-5876	405	1	+	+	CCONJ
ejpam-5876	405	2	k	k	NOUN
ejpam-5876	405	3	=	=	SYM
ejpam-5876	405	4	1	1	X
ejpam-5876	405	5	.	.	PUNCT
ejpam-5876	406	1	hence	hence	ADV
ejpam-5876	406	2	,	,	PUNCT
ejpam-5876	406	3	(	(	PUNCT
ejpam-5876	406	4	(	(	PUNCT
ejpam-5876	406	5	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	406	6	,	,	PUNCT
ejpam-5876	406	7	r}qkµ	r}qkµ	PROPN
ejpam-5876	406	8	,	,	PUNCT
ejpam-5876	406	9	a	a	DET
ejpam-5876	406	10	contradiction	contradiction	NOUN
ejpam-5876	406	11	.	.	PUNCT
ejpam-5876	407	1	thus	thus	ADV
ejpam-5876	407	2	,	,	PUNCT
ejpam-5876	407	3	(	(	PUNCT
ejpam-5876	407	4	(	(	PUNCT
ejpam-5876	407	5	x|(y|y))|(x|(y|y)))min{t	x|(y|y))|(x|(y|y)))min{t	PROPN
ejpam-5876	407	6	,	,	PUNCT
ejpam-5876	407	7	r}∈µ	r}∈µ	NOUN
ejpam-5876	407	8	,	,	PUNCT
ejpam-5876	407	9	which	which	PRON
ejpam-5876	407	10	implies	imply	VERB
ejpam-5876	407	11	from	from	ADP
ejpam-5876	407	12	(	(	PUNCT
ejpam-5876	407	13	13	13	NUM
ejpam-5876	407	14	)	)	PUNCT
ejpam-5876	407	15	that	that	PRON
ejpam-5876	407	16	xt∈	xt∈	PROPN
ejpam-5876	407	17	∨	∨	NUM
ejpam-5876	407	18	qkµ	qkµ	NOUN
ejpam-5876	407	19	or	or	CCONJ
ejpam-5876	407	20	yr∈	yr∈	PROPN
ejpam-5876	407	21	∨	∨	PROPN
ejpam-5876	407	22	qkµ.	qkµ.	X
ejpam-5876	407	23	therefore	therefore	ADV
ejpam-5876	407	24	,	,	PUNCT
ejpam-5876	407	25	µ	µ	X
ejpam-5876	407	26	is	be	AUX
ejpam-5876	407	27	a	a	DET
ejpam-5876	407	28	(	(	PUNCT
ejpam-5876	407	29	qk,∈	qk,∈	PROPN
ejpam-5876	407	30	∨	∨	NUM
ejpam-5876	407	31	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	407	32	sup	sup	NOUN
ejpam-5876	407	33	-	-	PUNCT
ejpam-5876	407	34	subalgebra	subalgebra	NOUN
ejpam-5876	407	35	of	of	ADP
ejpam-5876	407	36	x.	x.	PROPN
ejpam-5876	407	37	corollary	corollary	PROPN
ejpam-5876	407	38	18	18	NUM
ejpam-5876	407	39	.	.	PUNCT
ejpam-5876	407	40	assume	assume	VERB
ejpam-5876	407	41	that	that	SCONJ
ejpam-5876	407	42	min{t	min{t	PROPN
ejpam-5876	407	43	,	,	PUNCT
ejpam-5876	407	44	r	r	NOUN
ejpam-5876	407	45	}	}	PUNCT
ejpam-5876	407	46	>	>	X
ejpam-5876	407	47	0.5	0.5	NUM
ejpam-5876	407	48	for	for	ADP
ejpam-5876	407	49	any	any	DET
ejpam-5876	407	50	t	t	NOUN
ejpam-5876	407	51	,	,	PUNCT
ejpam-5876	407	52	r	r	NOUN
ejpam-5876	407	53	∈	∈	PROPN
ejpam-5876	407	54	(	(	PUNCT
ejpam-5876	407	55	0	0	NUM
ejpam-5876	407	56	,	,	PUNCT
ejpam-5876	407	57	1	1	NUM
ejpam-5876	407	58	]	]	PUNCT
ejpam-5876	407	59	.	.	PUNCT
ejpam-5876	408	1	then	then	ADV
ejpam-5876	408	2	every	every	PRON
ejpam-5876	408	3	(	(	PUNCT
ejpam-5876	408	4	∈,∈	∈,∈	X
ejpam-5876	408	5	∨	∨	NUM
ejpam-5876	408	6	q)fuzzy	q)fuzzy	PROPN
ejpam-5876	408	7	sup	sup	ADJ
ejpam-5876	408	8	-	-	PUNCT
ejpam-5876	408	9	subalgebra	subalgebra	NOUN
ejpam-5876	408	10	is	be	AUX
ejpam-5876	408	11	a	a	DET
ejpam-5876	408	12	(	(	PUNCT
ejpam-5876	408	13	q,∈	q,∈	PROPN
ejpam-5876	408	14	∨	∨	NOUN
ejpam-5876	408	15	q)-fuzzy	q)-fuzzy	PUNCT
ejpam-5876	408	16	sup	sup	NOUN
ejpam-5876	408	17	-	-	PUNCT
ejpam-5876	408	18	subalgebra	subalgebra	NOUN
ejpam-5876	408	19	.	.	PUNCT
ejpam-5876	409	1	5	5	X
ejpam-5876	409	2	.	.	X
ejpam-5876	409	3	conclusion	conclusion	NOUN
ejpam-5876	409	4	in	in	ADP
ejpam-5876	409	5	this	this	DET
ejpam-5876	409	6	paper	paper	NOUN
ejpam-5876	409	7	,	,	PUNCT
ejpam-5876	409	8	we	we	PRON
ejpam-5876	409	9	have	have	AUX
ejpam-5876	409	10	introduced	introduce	VERB
ejpam-5876	409	11	the	the	DET
ejpam-5876	409	12	concept	concept	NOUN
ejpam-5876	409	13	of	of	ADP
ejpam-5876	409	14	semidetached	semidetache	VERB
ejpam-5876	409	15	sup	sup	NOUN
ejpam-5876	409	16	-	-	PUNCT
ejpam-5876	409	17	algebras	algebras	NOUN
ejpam-5876	409	18	and	and	CCONJ
ejpam-5876	409	19	explored	explore	VERB
ejpam-5876	409	20	their	their	PRON
ejpam-5876	409	21	fundamental	fundamental	ADJ
ejpam-5876	409	22	properties	property	NOUN
ejpam-5876	409	23	.	.	PUNCT
ejpam-5876	410	1	the	the	DET
ejpam-5876	410	2	investigation	investigation	NOUN
ejpam-5876	410	3	into	into	ADP
ejpam-5876	410	4	these	these	DET
ejpam-5876	410	5	algebraic	algebraic	ADJ
ejpam-5876	410	6	structures	structure	NOUN
ejpam-5876	410	7	has	have	AUX
ejpam-5876	410	8	revealed	reveal	VERB
ejpam-5876	410	9	several	several	ADJ
ejpam-5876	410	10	significant	significant	ADJ
ejpam-5876	410	11	findings	finding	NOUN
ejpam-5876	410	12	.	.	PUNCT
ejpam-5876	411	1	the	the	DET
ejpam-5876	411	2	notion	notion	NOUN
ejpam-5876	411	3	of	of	ADP
ejpam-5876	411	4	semidetached	semidetache	VERB
ejpam-5876	411	5	sup	sup	NOUN
ejpam-5876	411	6	-	-	PUNCT
ejpam-5876	411	7	subalgebras	subalgebras	PROPN
ejpam-5876	411	8	has	have	AUX
ejpam-5876	411	9	been	be	AUX
ejpam-5876	411	10	clearly	clearly	ADV
ejpam-5876	411	11	defined	define	VERB
ejpam-5876	411	12	,	,	PUNCT
ejpam-5876	411	13	providing	provide	VERB
ejpam-5876	411	14	a	a	DET
ejpam-5876	411	15	new	new	ADJ
ejpam-5876	411	16	perspective	perspective	NOUN
ejpam-5876	411	17	on	on	ADP
ejpam-5876	411	18	the	the	DET
ejpam-5876	411	19	relationships	relationship	NOUN
ejpam-5876	411	20	within	within	ADP
ejpam-5876	411	21	sup	sup	NOUN
ejpam-5876	411	22	-	-	PUNCT
ejpam-5876	411	23	algebras	algebras	NOUN
ejpam-5876	411	24	.	.	PUNCT
ejpam-5876	412	1	this	this	PRON
ejpam-5876	412	2	contributes	contribute	VERB
ejpam-5876	412	3	to	to	ADP
ejpam-5876	412	4	a	a	DET
ejpam-5876	412	5	deeper	deep	ADJ
ejpam-5876	412	6	understanding	understanding	NOUN
ejpam-5876	412	7	of	of	ADP
ejpam-5876	412	8	their	their	PRON
ejpam-5876	412	9	algebraic	algebraic	ADJ
ejpam-5876	412	10	properties	property	NOUN
ejpam-5876	412	11	and	and	CCONJ
ejpam-5876	412	12	potential	potential	ADJ
ejpam-5876	412	13	applications	application	NOUN
ejpam-5876	412	14	in	in	ADP
ejpam-5876	412	15	various	various	ADJ
ejpam-5876	412	16	fields	field	NOUN
ejpam-5876	412	17	of	of	ADP
ejpam-5876	412	18	study	study	NOUN
ejpam-5876	412	19	,	,	PUNCT
ejpam-5876	412	20	including	include	VERB
ejpam-5876	412	21	logic	logic	NOUN
ejpam-5876	412	22	and	and	CCONJ
ejpam-5876	412	23	functional	functional	ADJ
ejpam-5876	412	24	analysis	analysis	NOUN
ejpam-5876	412	25	.	.	PUNCT
ejpam-5876	413	1	additionally	additionally	ADV
ejpam-5876	413	2	,	,	PUNCT
ejpam-5876	413	3	we	we	PRON
ejpam-5876	413	4	have	have	AUX
ejpam-5876	413	5	discussed	discuss	VERB
ejpam-5876	413	6	various	various	ADJ
ejpam-5876	413	7	types	type	NOUN
ejpam-5876	413	8	of	of	ADP
ejpam-5876	413	9	fuzzy	fuzzy	ADJ
ejpam-5876	413	10	sup	sup	NOUN
ejpam-5876	413	11	-	-	PUNCT
ejpam-5876	413	12	subalgebras	subalgebra	NOUN
ejpam-5876	413	13	,	,	PUNCT
ejpam-5876	413	14	including	include	VERB
ejpam-5876	413	15	(	(	PUNCT
ejpam-5876	413	16	∈,∈∨qk)-fuzzy	∈,∈∨qk)-fuzzy	ADJ
ejpam-5876	413	17	supsubalgebras	supsubalgebras	NOUN
ejpam-5876	413	18	and	and	CCONJ
ejpam-5876	413	19	k	k	VERB
ejpam-5876	413	20	-	-	ADJ
ejpam-5876	413	21	left	left	ADJ
ejpam-5876	413	22	(	(	PUNCT
ejpam-5876	413	23	k	k	NOUN
ejpam-5876	413	24	-	-	NOUN
ejpam-5876	413	25	right	right	NOUN
ejpam-5876	413	26	)	)	PUNCT
ejpam-5876	413	27	(	(	PUNCT
ejpam-5876	413	28	qk,∈	qk,∈	PROPN
ejpam-5876	413	29	∨	∨	NUM
ejpam-5876	413	30	qk)-fuzzy	qk)-fuzzy	ADJ
ejpam-5876	413	31	sup	sup	NOUN
ejpam-5876	413	32	-	-	PUNCT
ejpam-5876	413	33	subalgebras	subalgebras	PROPN
ejpam-5876	413	34	.	.	PUNCT
ejpam-5876	414	1	these	these	DET
ejpam-5876	414	2	classifications	classification	NOUN
ejpam-5876	414	3	are	be	AUX
ejpam-5876	414	4	crucial	crucial	ADJ
ejpam-5876	414	5	for	for	ADP
ejpam-5876	414	6	establishing	establish	VERB
ejpam-5876	414	7	the	the	DET
ejpam-5876	414	8	framework	framework	NOUN
ejpam-5876	414	9	necessary	necessary	ADJ
ejpam-5876	414	10	for	for	ADP
ejpam-5876	414	11	further	further	ADJ
ejpam-5876	414	12	research	research	NOUN
ejpam-5876	414	13	and	and	CCONJ
ejpam-5876	414	14	applications	application	NOUN
ejpam-5876	414	15	of	of	ADP
ejpam-5876	414	16	these	these	DET
ejpam-5876	414	17	algebraic	algebraic	ADJ
ejpam-5876	414	18	structures	structure	NOUN
ejpam-5876	414	19	.	.	PUNCT
ejpam-5876	415	1	the	the	DET
ejpam-5876	415	2	paper	paper	NOUN
ejpam-5876	415	3	has	have	AUX
ejpam-5876	415	4	provided	provide	VERB
ejpam-5876	415	5	several	several	ADJ
ejpam-5876	415	6	conditions	condition	NOUN
ejpam-5876	415	7	under	under	ADP
ejpam-5876	415	8	which	which	PRON
ejpam-5876	415	9	a	a	DET
ejpam-5876	415	10	semidetached	semidetache	VERB
ejpam-5876	415	11	structure	structure	NOUN
ejpam-5876	415	12	can	can	AUX
ejpam-5876	415	13	be	be	AUX
ejpam-5876	415	14	classified	classify	VERB
ejpam-5876	415	15	as	as	ADP
ejpam-5876	415	16	a	a	DET
ejpam-5876	415	17	semidetached	semidetache	VERB
ejpam-5876	415	18	sup	sup	NOUN
ejpam-5876	415	19	-	-	PUNCT
ejpam-5876	415	20	subalgebra	subalgebra	NOUN
ejpam-5876	415	21	.	.	PUNCT
ejpam-5876	416	1	this	this	PRON
ejpam-5876	416	2	is	be	AUX
ejpam-5876	416	3	essential	essential	ADJ
ejpam-5876	416	4	for	for	ADP
ejpam-5876	416	5	validating	validate	VERB
ejpam-5876	416	6	the	the	DET
ejpam-5876	416	7	theoretical	theoretical	ADJ
ejpam-5876	416	8	framework	framework	NOUN
ejpam-5876	416	9	and	and	CCONJ
ejpam-5876	416	10	ensuring	ensure	VERB
ejpam-5876	416	11	that	that	SCONJ
ejpam-5876	416	12	the	the	DET
ejpam-5876	416	13	properties	property	NOUN
ejpam-5876	416	14	discussed	discuss	VERB
ejpam-5876	416	15	are	be	AUX
ejpam-5876	416	16	applicable	applicable	ADJ
ejpam-5876	416	17	in	in	ADP
ejpam-5876	416	18	practical	practical	ADJ
ejpam-5876	416	19	scenarios	scenario	NOUN
ejpam-5876	416	20	.	.	PUNCT
ejpam-5876	417	1	the	the	DET
ejpam-5876	417	2	findings	finding	NOUN
ejpam-5876	417	3	of	of	ADP
ejpam-5876	417	4	this	this	DET
ejpam-5876	417	5	study	study	NOUN
ejpam-5876	417	6	open	open	ADJ
ejpam-5876	417	7	avenues	avenue	NOUN
ejpam-5876	417	8	for	for	ADP
ejpam-5876	417	9	future	future	ADJ
ejpam-5876	417	10	research	research	NOUN
ejpam-5876	417	11	,	,	PUNCT
ejpam-5876	417	12	particularly	particularly	ADV
ejpam-5876	417	13	in	in	ADP
ejpam-5876	417	14	exploring	explore	VERB
ejpam-5876	417	15	the	the	DET
ejpam-5876	417	16	applications	application	NOUN
ejpam-5876	417	17	of	of	ADP
ejpam-5876	417	18	semidetached	semidetache	VERB
ejpam-5876	417	19	sup	sup	NOUN
ejpam-5876	417	20	-	-	PUNCT
ejpam-5876	417	21	algebras	algebras	NOUN
ejpam-5876	417	22	in	in	ADP
ejpam-5876	417	23	logical	logical	ADJ
ejpam-5876	417	24	systems	system	NOUN
ejpam-5876	417	25	and	and	CCONJ
ejpam-5876	417	26	operator	operator	NOUN
ejpam-5876	417	27	theory	theory	NOUN
ejpam-5876	417	28	.	.	PUNCT
ejpam-5876	418	1	the	the	DET
ejpam-5876	418	2	flexibility	flexibility	NOUN
ejpam-5876	418	3	and	and	CCONJ
ejpam-5876	418	4	completeness	completeness	NOUN
ejpam-5876	418	5	of	of	ADP
ejpam-5876	418	6	the	the	DET
ejpam-5876	418	7	sheffer	sheffer	NOUN
ejpam-5876	418	8	stroke	stroke	NOUN
ejpam-5876	418	9	as	as	ADP
ejpam-5876	418	10	a	a	DET
ejpam-5876	418	11	logical	logical	ADJ
ejpam-5876	418	12	operator	operator	NOUN
ejpam-5876	418	13	suggest	suggest	VERB
ejpam-5876	418	14	that	that	SCONJ
ejpam-5876	418	15	further	further	ADJ
ejpam-5876	418	16	investigations	investigation	NOUN
ejpam-5876	418	17	could	could	AUX
ejpam-5876	418	18	yield	yield	VERB
ejpam-5876	418	19	valuable	valuable	ADJ
ejpam-5876	418	20	insights	insight	NOUN
ejpam-5876	418	21	into	into	ADP
ejpam-5876	418	22	both	both	CCONJ
ejpam-5876	418	23	algebraic	algebraic	ADJ
ejpam-5876	418	24	and	and	CCONJ
ejpam-5876	418	25	logical	logical	ADJ
ejpam-5876	418	26	frameworks	framework	NOUN
ejpam-5876	418	27	.	.	PUNCT
ejpam-5876	419	1	in	in	ADP
ejpam-5876	419	2	t.	t.	PROPN
ejpam-5876	419	3	oner	oner	NOUN
ejpam-5876	419	4	et	et	PROPN
ejpam-5876	419	5	al	al	PROPN
ejpam-5876	419	6	.	.	PUNCT
ejpam-5876	419	7	/	/	SYM
ejpam-5876	419	8	eur	eur	PROPN
ejpam-5876	419	9	.	.	PUNCT
ejpam-5876	420	1	j.	j.	PROPN
ejpam-5876	420	2	pure	pure	PROPN
ejpam-5876	420	3	appl	appl	PROPN
ejpam-5876	420	4	.	.	PROPN
ejpam-5876	420	5	math	math	PROPN
ejpam-5876	420	6	,	,	PUNCT
ejpam-5876	420	7	18	18	NUM
ejpam-5876	420	8	(	(	PUNCT
ejpam-5876	420	9	2	2	NUM
ejpam-5876	420	10	)	)	PUNCT
ejpam-5876	420	11	(	(	PUNCT
ejpam-5876	420	12	2025	2025	NUM
ejpam-5876	420	13	)	)	PUNCT
ejpam-5876	420	14	,	,	PUNCT
ejpam-5876	420	15	5876	5876	NUM
ejpam-5876	420	16	16	16	NUM
ejpam-5876	420	17	of	of	ADP
ejpam-5876	420	18	16	16	NUM
ejpam-5876	420	19	conclusion	conclusion	NOUN
ejpam-5876	421	1	,	,	PUNCT
ejpam-5876	421	2	the	the	DET
ejpam-5876	421	3	exploration	exploration	NOUN
ejpam-5876	421	4	of	of	ADP
ejpam-5876	421	5	semidetached	semidetache	VERB
ejpam-5876	421	6	sup	sup	NOUN
ejpam-5876	421	7	-	-	PUNCT
ejpam-5876	421	8	subalgebras	subalgebras	NOUN
ejpam-5876	421	9	in	in	ADP
ejpam-5876	421	10	sup	sup	NOUN
ejpam-5876	421	11	-	-	PUNCT
ejpam-5876	421	12	algebras	algebras	ADJ
ejpam-5876	421	13	not	not	PART
ejpam-5876	421	14	only	only	ADV
ejpam-5876	421	15	enhances	enhance	VERB
ejpam-5876	421	16	our	our	PRON
ejpam-5876	421	17	understanding	understanding	NOUN
ejpam-5876	421	18	of	of	ADP
ejpam-5876	421	19	these	these	DET
ejpam-5876	421	20	structures	structure	NOUN
ejpam-5876	421	21	but	but	CCONJ
ejpam-5876	421	22	also	also	ADV
ejpam-5876	421	23	sets	set	VERB
ejpam-5876	421	24	the	the	DET
ejpam-5876	421	25	stage	stage	NOUN
ejpam-5876	421	26	for	for	ADP
ejpam-5876	421	27	future	future	ADJ
ejpam-5876	421	28	research	research	NOUN
ejpam-5876	421	29	that	that	PRON
ejpam-5876	421	30	could	could	AUX
ejpam-5876	421	31	bridge	bridge	VERB
ejpam-5876	421	32	the	the	DET
ejpam-5876	421	33	gap	gap	NOUN
ejpam-5876	421	34	between	between	ADP
ejpam-5876	421	35	algebra	algebra	NOUN
ejpam-5876	421	36	,	,	PUNCT
ejpam-5876	421	37	logic	logic	NOUN
ejpam-5876	421	38	,	,	PUNCT
ejpam-5876	421	39	and	and	CCONJ
ejpam-5876	421	40	analysis	analysis	NOUN
ejpam-5876	421	41	.	.	PUNCT
ejpam-5876	422	1	the	the	DET
ejpam-5876	422	2	potential	potential	ADJ
ejpam-5876	422	3	applications	application	NOUN
ejpam-5876	422	4	of	of	ADP
ejpam-5876	422	5	these	these	DET
ejpam-5876	422	6	findings	finding	NOUN
ejpam-5876	422	7	are	be	AUX
ejpam-5876	422	8	vast	vast	ADJ
ejpam-5876	422	9	,	,	PUNCT
ejpam-5876	422	10	and	and	CCONJ
ejpam-5876	422	11	we	we	PRON
ejpam-5876	422	12	encourage	encourage	VERB
ejpam-5876	422	13	further	further	ADJ
ejpam-5876	422	14	exploration	exploration	NOUN
ejpam-5876	422	15	in	in	ADP
ejpam-5876	422	16	this	this	DET
ejpam-5876	422	17	promising	promising	ADJ
ejpam-5876	422	18	area	area	NOUN
ejpam-5876	422	19	of	of	ADP
ejpam-5876	422	20	study	study	NOUN
ejpam-5876	422	21	.	.	PUNCT
ejpam-5876	423	1	acknowledgements	acknowledgement	NOUN
ejpam-5876	423	2	this	this	DET
ejpam-5876	423	3	research	research	NOUN
ejpam-5876	423	4	was	be	AUX
ejpam-5876	423	5	supported	support	VERB
ejpam-5876	423	6	by	by	ADP
ejpam-5876	423	7	university	university	NOUN
ejpam-5876	423	8	of	of	ADP
ejpam-5876	423	9	phayao	phayao	NOUN
ejpam-5876	423	10	and	and	CCONJ
ejpam-5876	423	11	thailand	thailand	PROPN
ejpam-5876	423	12	science	science	PROPN
ejpam-5876	423	13	research	research	PROPN
ejpam-5876	423	14	and	and	CCONJ
ejpam-5876	423	15	innovation	innovation	NOUN
ejpam-5876	423	16	fund	fund	NOUN
ejpam-5876	423	17	(	(	PUNCT
ejpam-5876	423	18	fundamental	fundamental	ADJ
ejpam-5876	423	19	fund	fund	NOUN
ejpam-5876	423	20	2025	2025	NUM
ejpam-5876	423	21	,	,	PUNCT
ejpam-5876	423	22	grant	grant	VERB
ejpam-5876	423	23	no	no	NOUN
ejpam-5876	423	24	.	.	PROPN
ejpam-5876	424	1	5027/2567	5027/2567	NUM
ejpam-5876	424	2	)	)	PUNCT
ejpam-5876	424	3	.	.	PUNCT
ejpam-5876	425	1	references	reference	NOUN
ejpam-5876	425	2	[	[	X
ejpam-5876	425	3	1	1	NUM
ejpam-5876	425	4	]	]	PUNCT
ejpam-5876	425	5	h.	h.	PROPN
ejpam-5876	425	6	m.	m.	PROPN
ejpam-5876	425	7	sheffer	sheffer	PROPN
ejpam-5876	425	8	.	.	PUNCT
ejpam-5876	426	1	a	a	DET
ejpam-5876	426	2	set	set	NOUN
ejpam-5876	426	3	of	of	ADP
ejpam-5876	426	4	five	five	NUM
ejpam-5876	426	5	independent	independent	ADJ
ejpam-5876	426	6	postulates	postulate	NOUN
ejpam-5876	426	7	for	for	ADP
ejpam-5876	426	8	boolean	boolean	ADJ
ejpam-5876	426	9	algebras	algebra	NOUN
ejpam-5876	426	10	,	,	PUNCT
ejpam-5876	426	11	with	with	ADP
ejpam-5876	426	12	application	application	NOUN
ejpam-5876	426	13	to	to	ADP
ejpam-5876	426	14	logical	logical	ADJ
ejpam-5876	426	15	constants	constant	NOUN
ejpam-5876	426	16	.	.	PUNCT
ejpam-5876	427	1	trans	trans	AUX
ejpam-5876	427	2	.	.	PUNCT
ejpam-5876	427	3	am	be	AUX
ejpam-5876	427	4	.	.	PUNCT
ejpam-5876	428	1	math	math	NOUN
ejpam-5876	428	2	.	.	PUNCT
ejpam-5876	429	1	soc	soc	PROPN
ejpam-5876	429	2	.	.	PUNCT
ejpam-5876	429	3	,	,	PUNCT
ejpam-5876	429	4	14(4):481–488	14(4):481–488	NUM
ejpam-5876	429	5	,	,	PUNCT
ejpam-5876	429	6	1913	1913	NUM
ejpam-5876	429	7	.	.	PUNCT
ejpam-5876	430	1	[	[	X
ejpam-5876	430	2	2	2	NUM
ejpam-5876	430	3	]	]	PUNCT
ejpam-5876	430	4	a.	a.	NOUN
ejpam-5876	430	5	iampan	iampan	PROPN
ejpam-5876	430	6	.	.	PUNCT
ejpam-5876	431	1	a	a	DET
ejpam-5876	431	2	new	new	ADJ
ejpam-5876	431	3	branch	branch	NOUN
ejpam-5876	431	4	of	of	ADP
ejpam-5876	431	5	the	the	DET
ejpam-5876	431	6	logical	logical	ADJ
ejpam-5876	431	7	algebra	algebra	NOUN
ejpam-5876	431	8	:	:	PUNCT
ejpam-5876	431	9	up	up	ADP
ejpam-5876	431	10	-	-	PUNCT
ejpam-5876	431	11	algebras	algebras	X
ejpam-5876	431	12	.	.	PUNCT
ejpam-5876	432	1	j.	j.	PROPN
ejpam-5876	432	2	algebra	algebra	PROPN
ejpam-5876	432	3	relat	relat	PROPN
ejpam-5876	432	4	.	.	PUNCT
ejpam-5876	433	1	top	top	PROPN
ejpam-5876	433	2	.	.	PROPN
ejpam-5876	433	3	,	,	PUNCT
ejpam-5876	433	4	5(1):35–54	5(1):35–54	NUM
ejpam-5876	433	5	,	,	PUNCT
ejpam-5876	433	6	2017	2017	NUM
ejpam-5876	433	7	.	.	PUNCT
ejpam-5876	434	1	[	[	X
ejpam-5876	434	2	3	3	X
ejpam-5876	434	3	]	]	X
ejpam-5876	434	4	n.	n.	PROPN
ejpam-5876	434	5	rajesh	rajesh	PROPN
ejpam-5876	434	6	,	,	PUNCT
ejpam-5876	434	7	t.	t.	PROPN
ejpam-5876	434	8	oner	oner	NOUN
ejpam-5876	434	9	,	,	PUNCT
ejpam-5876	434	10	a.	a.	NOUN
ejpam-5876	434	11	iampan	iampan	PROPN
ejpam-5876	434	12	,	,	PUNCT
ejpam-5876	434	13	and	and	CCONJ
ejpam-5876	434	14	i.	i.	PROPN
ejpam-5876	434	15	senturk	senturk	PROPN
ejpam-5876	434	16	.	.	PUNCT
ejpam-5876	435	1	intuitionistic	intuitionistic	ADJ
ejpam-5876	435	2	fuzzy	fuzzy	ADJ
ejpam-5876	435	3	structures	structure	NOUN
ejpam-5876	435	4	on	on	ADP
ejpam-5876	435	5	sheffer	sheffer	NOUN
ejpam-5876	435	6	stroke	stroke	NOUN
ejpam-5876	435	7	up	up	ADP
ejpam-5876	435	8	-	-	PUNCT
ejpam-5876	435	9	algebras	algebras	X
ejpam-5876	435	10	.	.	PUNCT
ejpam-5876	436	1	eur	eur	PROPN
ejpam-5876	436	2	.	.	PUNCT
ejpam-5876	437	1	j.	j.	PROPN
ejpam-5876	437	2	pure	pure	PROPN
ejpam-5876	437	3	appl	appl	PROPN
ejpam-5876	437	4	.	.	PUNCT
ejpam-5876	437	5	math	math	PROPN
ejpam-5876	437	6	.	.	PUNCT
ejpam-5876	437	7	,	,	PUNCT
ejpam-5876	438	1	18(1):5627	18(1):5627	NUM
ejpam-5876	438	2	,	,	PUNCT
ejpam-5876	438	3	2025	2025	NUM
ejpam-5876	438	4	.	.	PUNCT
ejpam-5876	439	1	[	[	X
ejpam-5876	439	2	4	4	X
ejpam-5876	439	3	]	]	PUNCT
ejpam-5876	439	4	s.	s.	PROPN
ejpam-5876	439	5	r.	r.	PROPN
ejpam-5876	439	6	vidhya	vidhya	PROPN
ejpam-5876	439	7	,	,	PUNCT
ejpam-5876	439	8	a.	a.	NOUN
ejpam-5876	439	9	iampan	iampan	PROPN
ejpam-5876	439	10	,	,	PUNCT
ejpam-5876	439	11	and	and	CCONJ
ejpam-5876	439	12	n.	n.	PROPN
ejpam-5876	439	13	rajesh	rajesh	PROPN
ejpam-5876	439	14	.	.	PUNCT
ejpam-5876	440	1	neutrosophic	neutrosophic	PROPN
ejpam-5876	440	2	n	n	PRON
ejpam-5876	440	3	-structures	-structure	NOUN
ejpam-5876	440	4	on	on	ADP
ejpam-5876	440	5	sheffer	sheffer	NOUN
ejpam-5876	440	6	stroke	stroke	NOUN
ejpam-5876	440	7	up	up	ADP
ejpam-5876	440	8	-	-	PUNCT
ejpam-5876	440	9	algebras	algebras	PROPN
ejpam-5876	440	10	.	.	PUNCT
ejpam-5876	441	1	int	int	NOUN
ejpam-5876	441	2	.	.	PUNCT
ejpam-5876	442	1	j.	j.	PROPN
ejpam-5876	442	2	neutrosophic	neutrosophic	PROPN
ejpam-5876	442	3	sci	sci	PROPN
ejpam-5876	442	4	.	.	PROPN
ejpam-5876	442	5	,	,	PUNCT
ejpam-5876	442	6	25(4):433–443	25(4):433–443	PROPN
ejpam-5876	442	7	,	,	PUNCT
ejpam-5876	442	8	2025	2025	NUM
ejpam-5876	442	9	.	.	PUNCT
ejpam-5876	443	1	[	[	X
ejpam-5876	443	2	5	5	X
ejpam-5876	443	3	]	]	PUNCT
ejpam-5876	443	4	s.	s.	PROPN
ejpam-5876	443	5	k.	k.	PROPN
ejpam-5876	443	6	bhakat	bhakat	PROPN
ejpam-5876	443	7	and	and	CCONJ
ejpam-5876	443	8	p.	p.	PROPN
ejpam-5876	443	9	das	das	PROPN
ejpam-5876	443	10	.	.	PUNCT
ejpam-5876	444	1	(	(	PUNCT
ejpam-5876	444	2	∈,∈	∈,∈	X
ejpam-5876	444	3	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-5876	444	4	subgroup	subgroup	NOUN
ejpam-5876	444	5	.	.	PUNCT
ejpam-5876	445	1	fuzzy	fuzzy	ADJ
ejpam-5876	445	2	sets	set	VERB
ejpam-5876	445	3	syst	syst	PROPN
ejpam-5876	445	4	.	.	PUNCT
ejpam-5876	445	5	,	,	PUNCT
ejpam-5876	445	6	80(3):359–368	80(3):359–368	NUM
ejpam-5876	445	7	,	,	PUNCT
ejpam-5876	445	8	1996	1996	NUM
ejpam-5876	445	9	.	.	PUNCT
ejpam-5876	446	1	[	[	X
ejpam-5876	446	2	6	6	NUM
ejpam-5876	446	3	]	]	PUNCT
ejpam-5876	446	4	a.	a.	NOUN
ejpam-5876	446	5	rosenfeld	rosenfeld	PROPN
ejpam-5876	446	6	.	.	PUNCT
ejpam-5876	447	1	fuzzy	fuzzy	ADJ
ejpam-5876	447	2	groups	group	NOUN
ejpam-5876	447	3	.	.	PUNCT
ejpam-5876	448	1	j.	j.	PROPN
ejpam-5876	448	2	math	math	PROPN
ejpam-5876	448	3	.	.	PUNCT
ejpam-5876	449	1	anal	anal	PROPN
ejpam-5876	449	2	.	.	PUNCT
ejpam-5876	450	1	appl	appl	PROPN
ejpam-5876	450	2	.	.	PROPN
ejpam-5876	451	1	,	,	PUNCT
ejpam-5876	451	2	35(3):512–517	35(3):512–517	PROPN
ejpam-5876	451	3	,	,	PUNCT
ejpam-5876	451	4	1971	1971	NUM
ejpam-5876	451	5	.	.	PUNCT
ejpam-5876	452	1	[	[	X
ejpam-5876	452	2	7	7	X
ejpam-5876	452	3	]	]	X
ejpam-5876	452	4	t.	t.	NOUN
ejpam-5876	452	5	oner	oner	NOUN
ejpam-5876	452	6	,	,	PUNCT
ejpam-5876	452	7	t.	t.	PROPN
ejpam-5876	452	8	katican	katican	PROPN
ejpam-5876	452	9	,	,	PUNCT
ejpam-5876	452	10	and	and	CCONJ
ejpam-5876	452	11	a.	a.	PROPN
ejpam-5876	452	12	borumand	borumand	PROPN
ejpam-5876	452	13	saeid	saeid	PROPN
ejpam-5876	452	14	.	.	PUNCT
ejpam-5876	453	1	on	on	ADP
ejpam-5876	453	2	sheffer	sheffer	PROPN
ejpam-5876	453	3	stroke	stroke	PROPN
ejpam-5876	453	4	up	up	ADP
ejpam-5876	453	5	-	-	PUNCT
ejpam-5876	453	6	algebras	algebras	X
ejpam-5876	453	7	.	.	PUNCT
ejpam-5876	454	1	discuss	discuss	PROPN
ejpam-5876	454	2	.	.	PUNCT
ejpam-5876	454	3	math	math	PROPN
ejpam-5876	454	4	.	.	PUNCT
ejpam-5876	454	5	,	,	PUNCT
ejpam-5876	455	1	gen	gen	PROPN
ejpam-5876	455	2	.	.	PROPN
ejpam-5876	455	3	algebra	algebra	PROPN
ejpam-5876	455	4	appl	appl	PROPN
ejpam-5876	455	5	.	.	PROPN
ejpam-5876	455	6	,	,	PUNCT
ejpam-5876	455	7	41(2):381–394	41(2):381–394	NOUN
ejpam-5876	455	8	,	,	PUNCT
ejpam-5876	455	9	2021	2021	NUM
ejpam-5876	455	10	.	.	PUNCT
ejpam-5876	456	1	[	[	X
ejpam-5876	456	2	8	8	NUM
ejpam-5876	456	3	]	]	X
ejpam-5876	456	4	p.	p.	NOUN
ejpam-5876	456	5	m.	m.	NOUN
ejpam-5876	456	6	pu	pu	PROPN
ejpam-5876	456	7	and	and	CCONJ
ejpam-5876	456	8	y.	y.	PROPN
ejpam-5876	456	9	m.	m.	PROPN
ejpam-5876	456	10	liu	liu	PROPN
ejpam-5876	456	11	.	.	PROPN
ejpam-5876	457	1	fuzzy	fuzzy	ADJ
ejpam-5876	457	2	topology	topology	NOUN
ejpam-5876	457	3	i	i	PRON
ejpam-5876	457	4	,	,	PUNCT
ejpam-5876	457	5	neighborhood	neighborhood	NOUN
ejpam-5876	457	6	structure	structure	NOUN
ejpam-5876	457	7	of	of	ADP
ejpam-5876	457	8	a	a	DET
ejpam-5876	457	9	fuzzy	fuzzy	ADJ
ejpam-5876	457	10	point	point	NOUN
ejpam-5876	457	11	and	and	CCONJ
ejpam-5876	457	12	moore	moore	PROPN
ejpam-5876	457	13	-	-	PUNCT
ejpam-5876	457	14	smith	smith	PROPN
ejpam-5876	457	15	convergence	convergence	NOUN
ejpam-5876	457	16	.	.	PUNCT
ejpam-5876	458	1	j.	j.	PROPN
ejpam-5876	458	2	math	math	PROPN
ejpam-5876	458	3	.	.	PUNCT
ejpam-5876	459	1	anal	anal	PROPN
ejpam-5876	459	2	.	.	PUNCT
ejpam-5876	460	1	appl	appl	PROPN
ejpam-5876	460	2	.	.	PROPN
ejpam-5876	460	3	,	,	PUNCT
ejpam-5876	461	1	76:571–599	76:571–599	NUM
ejpam-5876	461	2	,	,	PUNCT
ejpam-5876	461	3	1980	1980	NUM
ejpam-5876	461	4	.	.	PUNCT
ejpam-5876	462	1	[	[	X
ejpam-5876	462	2	9	9	NUM
ejpam-5876	462	3	]	]	PUNCT
ejpam-5876	462	4	t.	t.	NOUN
ejpam-5876	462	5	oner	oner	NOUN
ejpam-5876	462	6	,	,	PUNCT
ejpam-5876	462	7	t.	t.	PROPN
ejpam-5876	462	8	katican	katican	PROPN
ejpam-5876	462	9	,	,	PUNCT
ejpam-5876	462	10	and	and	CCONJ
ejpam-5876	462	11	a.	a.	PROPN
ejpam-5876	462	12	borumand	borumand	PROPN
ejpam-5876	462	13	saeid	saeid	PROPN
ejpam-5876	462	14	.	.	PUNCT
ejpam-5876	463	1	(	(	PUNCT
ejpam-5876	463	2	hesitant	hesitant	ADJ
ejpam-5876	463	3	)	)	PUNCT
ejpam-5876	463	4	fuzzy	fuzzy	ADJ
ejpam-5876	463	5	sets	set	NOUN
ejpam-5876	463	6	on	on	ADP
ejpam-5876	463	7	sheffer	sheffer	PROPN
ejpam-5876	463	8	stroke	stroke	NOUN
ejpam-5876	463	9	up	up	ADP
ejpam-5876	463	10	-	-	PUNCT
ejpam-5876	463	11	algebras	algebras	X
ejpam-5876	463	12	.	.	PUNCT
ejpam-5876	464	1	j.	j.	PROPN
ejpam-5876	464	2	interdiscip	interdiscip	PROPN
ejpam-5876	464	3	.	.	PUNCT
ejpam-5876	465	1	math	math	NOUN
ejpam-5876	465	2	.	.	PUNCT
ejpam-5876	465	3	,	,	PUNCT
ejpam-5876	466	1	25(5):1221–1236	25(5):1221–1236	NUM
ejpam-5876	466	2	,	,	PUNCT
ejpam-5876	466	3	2022	2022	NUM
ejpam-5876	466	4	.	.	PUNCT