id	sid	tid	token	lemma	pos
ejpam-6500	1	1	european	european	PROPN
ejpam-6500	1	2	journal	journal	PROPN
ejpam-6500	1	3	of	of	ADP
ejpam-6500	1	4	pure	pure	ADJ
ejpam-6500	1	5	and	and	CCONJ
ejpam-6500	1	6	applied	applied	ADJ
ejpam-6500	1	7	mathematics	mathematic	NOUN
ejpam-6500	1	8	2025	2025	NUM
ejpam-6500	1	9	,	,	PUNCT
ejpam-6500	1	10	vol	vol	NOUN
ejpam-6500	1	11	.	.	PROPN
ejpam-6500	1	12	18	18	NUM
ejpam-6500	1	13	,	,	PUNCT
ejpam-6500	1	14	issue	issue	NOUN
ejpam-6500	1	15	3	3	NUM
ejpam-6500	1	16	,	,	PUNCT
ejpam-6500	1	17	article	article	NOUN
ejpam-6500	1	18	number	number	NOUN
ejpam-6500	1	19	6500	6500	NUM
ejpam-6500	1	20	issn	issn	PROPN
ejpam-6500	1	21	1307	1307	NUM
ejpam-6500	1	22	-	-	SYM
ejpam-6500	1	23	5543	5543	NUM
ejpam-6500	1	24	–	–	PUNCT
ejpam-6500	1	25	ejpam.com	ejpam.com	X
ejpam-6500	1	26	published	publish	VERB
ejpam-6500	1	27	by	by	ADP
ejpam-6500	1	28	new	new	PROPN
ejpam-6500	1	29	york	york	PROPN
ejpam-6500	1	30	business	business	PROPN
ejpam-6500	1	31	global	global	ADJ
ejpam-6500	1	32	generalized	generalize	VERB
ejpam-6500	1	33	fuzzy	fuzzy	ADJ
ejpam-6500	1	34	subalgebras	subalgebra	NOUN
ejpam-6500	1	35	of	of	ADP
ejpam-6500	1	36	sheffer	sheffer	PROPN
ejpam-6500	1	37	stroke	stroke	PROPN
ejpam-6500	1	38	hilbert	hilbert	PROPN
ejpam-6500	1	39	algebras	algebras	PROPN
ejpam-6500	1	40	neelamegarajan	neelamegarajan	PROPN
ejpam-6500	1	41	rajesh1	rajesh1	PROPN
ejpam-6500	1	42	,	,	PUNCT
ejpam-6500	1	43	aiyared	aiyare	VERB
ejpam-6500	1	44	iampan2,∗	iampan2,∗	PROPN
ejpam-6500	1	45	,	,	PUNCT
ejpam-6500	1	46	tahsin	tahsin	VERB
ejpam-6500	1	47	oner3	oner3	PROPN
ejpam-6500	1	48	,	,	PUNCT
ejpam-6500	1	49	arsham	arsham	PROPN
ejpam-6500	2	1	borumand	borumand	INTJ
ejpam-6500	2	2	saeid1	saeid1	PROPN
ejpam-6500	2	3	1	1	NUM
ejpam-6500	2	4	department	department	NOUN
ejpam-6500	2	5	of	of	ADP
ejpam-6500	2	6	mathematics	mathematic	NOUN
ejpam-6500	2	7	,	,	PUNCT
ejpam-6500	2	8	rajah	rajah	NOUN
ejpam-6500	2	9	serfoji	serfoji	ADJ
ejpam-6500	2	10	government	government	NOUN
ejpam-6500	2	11	college	college	NOUN
ejpam-6500	2	12	,	,	PUNCT
ejpam-6500	2	13	thanjavur-613005	thanjavur-613005	NOUN
ejpam-6500	2	14	,	,	PUNCT
ejpam-6500	2	15	tamil	tamil	PROPN
ejpam-6500	2	16	nadu	nadu	NOUN
ejpam-6500	2	17	,	,	PUNCT
ejpam-6500	2	18	india	india	PROPN
ejpam-6500	2	19	2	2	NUM
ejpam-6500	2	20	department	department	NOUN
ejpam-6500	2	21	of	of	ADP
ejpam-6500	2	22	mathematics	mathematic	NOUN
ejpam-6500	2	23	,	,	PUNCT
ejpam-6500	2	24	school	school	NOUN
ejpam-6500	2	25	of	of	ADP
ejpam-6500	2	26	science	science	NOUN
ejpam-6500	2	27	,	,	PUNCT
ejpam-6500	2	28	university	university	NOUN
ejpam-6500	2	29	of	of	ADP
ejpam-6500	2	30	phayao	phayao	NOUN
ejpam-6500	2	31	,	,	PUNCT
ejpam-6500	2	32	mae	mae	PROPN
ejpam-6500	2	33	ka	ka	PROPN
ejpam-6500	2	34	,	,	PUNCT
ejpam-6500	2	35	mueang	mueang	PROPN
ejpam-6500	2	36	,	,	PUNCT
ejpam-6500	2	37	phayao	phayao	NOUN
ejpam-6500	2	38	56000	56000	NUM
ejpam-6500	2	39	,	,	PUNCT
ejpam-6500	2	40	thailand	thailand	PROPN
ejpam-6500	2	41	3	3	NUM
ejpam-6500	2	42	department	department	NOUN
ejpam-6500	2	43	of	of	ADP
ejpam-6500	2	44	mathematics	mathematic	NOUN
ejpam-6500	2	45	,	,	PUNCT
ejpam-6500	2	46	faculty	faculty	NOUN
ejpam-6500	2	47	of	of	ADP
ejpam-6500	2	48	science	science	NOUN
ejpam-6500	2	49	,	,	PUNCT
ejpam-6500	2	50	ege	ege	PROPN
ejpam-6500	2	51	university	university	NOUN
ejpam-6500	2	52	,	,	PUNCT
ejpam-6500	2	53	35100	35100	NUM
ejpam-6500	2	54	izmir	izmir	PROPN
ejpam-6500	2	55	,	,	PUNCT
ejpam-6500	2	56	turkey	turkey	PROPN
ejpam-6500	2	57	4	4	NUM
ejpam-6500	2	58	department	department	NOUN
ejpam-6500	2	59	of	of	ADP
ejpam-6500	2	60	mathematics	mathematic	NOUN
ejpam-6500	2	61	,	,	PUNCT
ejpam-6500	2	62	faculty	faculty	NOUN
ejpam-6500	2	63	of	of	ADP
ejpam-6500	2	64	mathematics	mathematic	NOUN
ejpam-6500	2	65	and	and	CCONJ
ejpam-6500	2	66	computer	computer	NOUN
ejpam-6500	2	67	,	,	PUNCT
ejpam-6500	2	68	shahid	shahid	PROPN
ejpam-6500	2	69	bahonar	bahonar	VERB
ejpam-6500	2	70	university	university	PROPN
ejpam-6500	2	71	of	of	ADP
ejpam-6500	2	72	kerman	kerman	PROPN
ejpam-6500	2	73	,	,	PUNCT
ejpam-6500	2	74	kerman	kerman	PROPN
ejpam-6500	2	75	,	,	PUNCT
ejpam-6500	2	76	iran	iran	PROPN
ejpam-6500	2	77	abstract	abstract	ADJ
ejpam-6500	2	78	.	.	PUNCT
ejpam-6500	3	1	this	this	DET
ejpam-6500	3	2	paper	paper	NOUN
ejpam-6500	3	3	introduces	introduce	VERB
ejpam-6500	3	4	new	new	ADJ
ejpam-6500	3	5	generalized	generalized	ADJ
ejpam-6500	3	6	fuzzy	fuzzy	ADJ
ejpam-6500	3	7	subalgebras	subalgebra	NOUN
ejpam-6500	3	8	and	and	CCONJ
ejpam-6500	3	9	investigates	investigate	VERB
ejpam-6500	3	10	their	their	PRON
ejpam-6500	3	11	important	important	ADJ
ejpam-6500	3	12	properties	property	NOUN
ejpam-6500	3	13	within	within	ADP
ejpam-6500	3	14	the	the	DET
ejpam-6500	3	15	framework	framework	NOUN
ejpam-6500	3	16	of	of	ADP
ejpam-6500	3	17	sheffer	sheffer	PROPN
ejpam-6500	3	18	stroke	stroke	PROPN
ejpam-6500	3	19	hilbert	hilbert	PROPN
ejpam-6500	3	20	algebras	algebras	PROPN
ejpam-6500	3	21	.	.	PUNCT
ejpam-6500	4	1	we	we	PRON
ejpam-6500	4	2	characterize	characterize	VERB
ejpam-6500	4	3	these	these	DET
ejpam-6500	4	4	generalized	generalize	VERB
ejpam-6500	4	5	subalgebras	subalgebra	NOUN
ejpam-6500	4	6	through	through	ADP
ejpam-6500	4	7	their	their	PRON
ejpam-6500	4	8	level	level	NOUN
ejpam-6500	4	9	subsets	subset	NOUN
ejpam-6500	4	10	and	and	CCONJ
ejpam-6500	4	11	establish	establish	VERB
ejpam-6500	4	12	key	key	ADJ
ejpam-6500	4	13	properties	property	NOUN
ejpam-6500	4	14	that	that	PRON
ejpam-6500	4	15	define	define	VERB
ejpam-6500	4	16	their	their	PRON
ejpam-6500	4	17	structure	structure	NOUN
ejpam-6500	4	18	.	.	PUNCT
ejpam-6500	5	1	the	the	DET
ejpam-6500	5	2	sheffer	sheffer	PROPN
ejpam-6500	5	3	stroke	stroke	NOUN
ejpam-6500	5	4	operation	operation	NOUN
ejpam-6500	5	5	,	,	PUNCT
ejpam-6500	5	6	known	know	VERB
ejpam-6500	5	7	for	for	ADP
ejpam-6500	5	8	its	its	PRON
ejpam-6500	5	9	ability	ability	NOUN
ejpam-6500	5	10	to	to	PART
ejpam-6500	5	11	construct	construct	VERB
ejpam-6500	5	12	logical	logical	ADJ
ejpam-6500	5	13	systems	system	NOUN
ejpam-6500	5	14	independently	independently	ADV
ejpam-6500	5	15	of	of	ADP
ejpam-6500	5	16	other	other	ADJ
ejpam-6500	5	17	operators	operator	NOUN
ejpam-6500	5	18	,	,	PUNCT
ejpam-6500	5	19	plays	play	VERB
ejpam-6500	5	20	a	a	DET
ejpam-6500	5	21	central	central	ADJ
ejpam-6500	5	22	role	role	NOUN
ejpam-6500	5	23	in	in	ADP
ejpam-6500	5	24	our	our	PRON
ejpam-6500	5	25	study	study	NOUN
ejpam-6500	5	26	.	.	PUNCT
ejpam-6500	6	1	using	use	VERB
ejpam-6500	6	2	fuzzy	fuzzy	ADJ
ejpam-6500	6	3	set	set	NOUN
ejpam-6500	6	4	theory	theory	NOUN
ejpam-6500	6	5	,	,	PUNCT
ejpam-6500	6	6	we	we	PRON
ejpam-6500	6	7	adapt	adapt	VERB
ejpam-6500	6	8	the	the	DET
ejpam-6500	6	9	traditional	traditional	ADJ
ejpam-6500	6	10	ideas	idea	NOUN
ejpam-6500	6	11	of	of	ADP
ejpam-6500	6	12	subalgebras	subalgebras	PROPN
ejpam-6500	6	13	to	to	PART
ejpam-6500	6	14	fit	fit	VERB
ejpam-6500	6	15	fuzzy	fuzzy	ADJ
ejpam-6500	6	16	contexts	contexts	NOUN
ejpam-6500	6	17	,	,	PUNCT
ejpam-6500	6	18	giving	give	VERB
ejpam-6500	6	19	a	a	DET
ejpam-6500	6	20	detailed	detailed	ADJ
ejpam-6500	6	21	look	look	NOUN
ejpam-6500	6	22	at	at	ADP
ejpam-6500	6	23	(	(	PUNCT
ejpam-6500	6	24	∈,∈	∈,∈	INTJ
ejpam-6500	6	25	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	6	26	subalgebras	subalgebras	PROPN
ejpam-6500	6	27	.	.	PUNCT
ejpam-6500	7	1	our	our	PRON
ejpam-6500	7	2	results	result	NOUN
ejpam-6500	7	3	include	include	VERB
ejpam-6500	7	4	necessary	necessary	ADJ
ejpam-6500	7	5	and	and	CCONJ
ejpam-6500	7	6	sufficient	sufficient	ADJ
ejpam-6500	7	7	conditions	condition	NOUN
ejpam-6500	7	8	for	for	ADP
ejpam-6500	7	9	a	a	DET
ejpam-6500	7	10	fuzzy	fuzzy	ADJ
ejpam-6500	7	11	set	set	NOUN
ejpam-6500	7	12	to	to	PART
ejpam-6500	7	13	qualify	qualify	VERB
ejpam-6500	7	14	as	as	ADP
ejpam-6500	7	15	such	such	DET
ejpam-6500	7	16	a	a	DET
ejpam-6500	7	17	subalgebra	subalgebra	NOUN
ejpam-6500	7	18	,	,	PUNCT
ejpam-6500	7	19	along	along	ADP
ejpam-6500	7	20	with	with	ADP
ejpam-6500	7	21	theorems	theorem	NOUN
ejpam-6500	7	22	addressing	address	VERB
ejpam-6500	7	23	their	their	PRON
ejpam-6500	7	24	intersections	intersection	NOUN
ejpam-6500	7	25	,	,	PUNCT
ejpam-6500	7	26	unions	union	NOUN
ejpam-6500	7	27	,	,	PUNCT
ejpam-6500	7	28	and	and	CCONJ
ejpam-6500	7	29	homomorphic	homomorphic	ADJ
ejpam-6500	7	30	invariance	invariance	NOUN
ejpam-6500	7	31	.	.	PUNCT
ejpam-6500	8	1	this	this	DET
ejpam-6500	8	2	work	work	NOUN
ejpam-6500	8	3	contributes	contribute	VERB
ejpam-6500	8	4	to	to	ADP
ejpam-6500	8	5	the	the	DET
ejpam-6500	8	6	broader	broad	ADJ
ejpam-6500	8	7	understanding	understanding	NOUN
ejpam-6500	8	8	of	of	ADP
ejpam-6500	8	9	algebraic	algebraic	ADJ
ejpam-6500	8	10	structures	structure	NOUN
ejpam-6500	8	11	in	in	ADP
ejpam-6500	8	12	fuzzy	fuzzy	ADJ
ejpam-6500	8	13	logic	logic	NOUN
ejpam-6500	8	14	and	and	CCONJ
ejpam-6500	8	15	their	their	PRON
ejpam-6500	8	16	applications	application	NOUN
ejpam-6500	8	17	in	in	ADP
ejpam-6500	8	18	logical	logical	ADJ
ejpam-6500	8	19	systems	system	NOUN
ejpam-6500	8	20	.	.	PUNCT
ejpam-6500	9	1	2020	2020	NUM
ejpam-6500	9	2	mathematics	mathematic	NOUN
ejpam-6500	9	3	subject	subject	NOUN
ejpam-6500	9	4	classifications	classification	NOUN
ejpam-6500	9	5	:	:	PUNCT
ejpam-6500	9	6	03g25	03g25	NUM
ejpam-6500	9	7	,	,	PUNCT
ejpam-6500	9	8	03e72	03e72	AUX
ejpam-6500	9	9	key	key	ADJ
ejpam-6500	9	10	words	word	NOUN
ejpam-6500	9	11	and	and	CCONJ
ejpam-6500	9	12	phrases	phrase	NOUN
ejpam-6500	9	13	:	:	PUNCT
ejpam-6500	9	14	sheffer	sheffer	NOUN
ejpam-6500	9	15	stroke	stroke	PROPN
ejpam-6500	9	16	hilbert	hilbert	PROPN
ejpam-6500	9	17	algebra	algebra	PROPN
ejpam-6500	9	18	,	,	PUNCT
ejpam-6500	9	19	subalgebra	subalgebra	NOUN
ejpam-6500	9	20	,	,	PUNCT
ejpam-6500	9	21	fuzzy	fuzzy	ADJ
ejpam-6500	9	22	set	set	NOUN
ejpam-6500	9	23	,	,	PUNCT
ejpam-6500	9	24	fuzzy	fuzzy	ADJ
ejpam-6500	9	25	subalgebra	subalgebra	NOUN
ejpam-6500	9	26	1	1	X
ejpam-6500	9	27	.	.	X
ejpam-6500	10	1	introduction	introduction	NOUN
ejpam-6500	10	2	the	the	DET
ejpam-6500	10	3	study	study	NOUN
ejpam-6500	10	4	of	of	ADP
ejpam-6500	10	5	algebraic	algebraic	ADJ
ejpam-6500	10	6	structures	structure	NOUN
ejpam-6500	10	7	in	in	ADP
ejpam-6500	10	8	logic	logic	NOUN
ejpam-6500	10	9	has	have	AUX
ejpam-6500	10	10	been	be	AUX
ejpam-6500	10	11	profoundly	profoundly	ADV
ejpam-6500	10	12	influenced	influence	VERB
ejpam-6500	10	13	by	by	ADP
ejpam-6500	10	14	the	the	DET
ejpam-6500	10	15	discovery	discovery	NOUN
ejpam-6500	10	16	of	of	ADP
ejpam-6500	10	17	universal	universal	ADJ
ejpam-6500	10	18	operations	operation	NOUN
ejpam-6500	10	19	,	,	PUNCT
ejpam-6500	10	20	among	among	ADP
ejpam-6500	10	21	which	which	PRON
ejpam-6500	10	22	the	the	DET
ejpam-6500	10	23	sheffer	sheffer	NOUN
ejpam-6500	10	24	stroke	stroke	NOUN
ejpam-6500	10	25	(	(	PUNCT
ejpam-6500	10	26	also	also	ADV
ejpam-6500	10	27	known	know	VERB
ejpam-6500	10	28	as	as	ADP
ejpam-6500	10	29	the	the	DET
ejpam-6500	10	30	nand	nand	NOUN
ejpam-6500	10	31	operator	operator	NOUN
ejpam-6500	10	32	)	)	PUNCT
ejpam-6500	10	33	stands	stand	VERB
ejpam-6500	10	34	out	out	ADP
ejpam-6500	10	35	as	as	ADP
ejpam-6500	10	36	a	a	DET
ejpam-6500	10	37	cornerstone	cornerstone	NOUN
ejpam-6500	10	38	.	.	PUNCT
ejpam-6500	11	1	introduced	introduce	VERB
ejpam-6500	11	2	by	by	ADP
ejpam-6500	11	3	sheffer	sheffer	NOUN
ejpam-6500	11	4	in	in	ADP
ejpam-6500	11	5	1913	1913	NUM
ejpam-6500	12	1	[	[	X
ejpam-6500	12	2	1	1	NUM
ejpam-6500	12	3	]	]	PUNCT
ejpam-6500	12	4	,	,	PUNCT
ejpam-6500	12	5	this	this	DET
ejpam-6500	12	6	operation	operation	NOUN
ejpam-6500	12	7	possesses	possess	VERB
ejpam-6500	12	8	the	the	DET
ejpam-6500	12	9	remarkable	remarkable	ADJ
ejpam-6500	12	10	property	property	NOUN
ejpam-6500	12	11	of	of	ADP
ejpam-6500	12	12	functional	functional	ADJ
ejpam-6500	12	13	completeness	completeness	NOUN
ejpam-6500	12	14	:	:	PUNCT
ejpam-6500	12	15	it	it	PRON
ejpam-6500	12	16	can	can	AUX
ejpam-6500	12	17	express	express	VERB
ejpam-6500	12	18	all	all	DET
ejpam-6500	12	19	other	other	ADJ
ejpam-6500	12	20	logical	logical	ADJ
ejpam-6500	12	21	connectives	connective	NOUN
ejpam-6500	12	22	independently	independently	ADV
ejpam-6500	12	23	,	,	PUNCT
ejpam-6500	12	24	thereby	thereby	ADV
ejpam-6500	12	25	simplifying	simplify	VERB
ejpam-6500	12	26	the	the	DET
ejpam-6500	12	27	axiomatization	axiomatization	NOUN
ejpam-6500	12	28	of	of	ADP
ejpam-6500	12	29	logical	logical	ADJ
ejpam-6500	12	30	systems	system	NOUN
ejpam-6500	12	31	.	.	PUNCT
ejpam-6500	13	1	∗corresponding	∗corresponde	VERB
ejpam-6500	13	2	author	author	NOUN
ejpam-6500	13	3	.	.	PUNCT
ejpam-6500	14	1	doi	doi	NOUN
ejpam-6500	14	2	:	:	PUNCT
ejpam-6500	14	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6500	https://doi.org/10.29020/nybg.ejpam.v18i3.6500	NOUN
ejpam-6500	14	4	email	email	NOUN
ejpam-6500	14	5	addresses	address	NOUN
ejpam-6500	14	6	:	:	PUNCT
ejpam-6500	14	7	nrajesh	nrajesh	PROPN
ejpam-6500	14	8	topology@yahoo.co.in	topology@yahoo.co.in	PROPN
ejpam-6500	14	9	(	(	PUNCT
ejpam-6500	14	10	n.	n.	PROPN
ejpam-6500	14	11	rajesh	rajesh	PROPN
ejpam-6500	14	12	)	)	PUNCT
ejpam-6500	14	13	,	,	PUNCT
ejpam-6500	14	14	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-6500	14	15	(	(	PUNCT
ejpam-6500	14	16	a.	a.	NOUN
ejpam-6500	14	17	iampan	iampan	PROPN
ejpam-6500	14	18	)	)	PUNCT
ejpam-6500	14	19	,	,	PUNCT
ejpam-6500	14	20	tahsin.oner@ege.edu.tr	tahsin.oner@ege.edu.tr	NOUN
ejpam-6500	14	21	(	(	PUNCT
ejpam-6500	14	22	t.	t.	NOUN
ejpam-6500	14	23	oner	oner	PROPN
ejpam-6500	14	24	)	)	PUNCT
ejpam-6500	14	25	,	,	PUNCT
ejpam-6500	14	26	arsham@uk.ac.ir	arsham@uk.ac.ir	PROPN
ejpam-6500	14	27	(	(	PUNCT
ejpam-6500	14	28	a.	a.	PROPN
ejpam-6500	14	29	b.	b.	PROPN
ejpam-6500	14	30	saeid	saeid	PROPN
ejpam-6500	14	31	)	)	PUNCT
ejpam-6500	14	32	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6500	14	33	1	1	NUM
ejpam-6500	14	34	copyright	copyright	NOUN
ejpam-6500	14	35	:	:	PUNCT
ejpam-6500	15	1	©	©	PROPN
ejpam-6500	15	2	2025	2025	NUM
ejpam-6500	15	3	the	the	DET
ejpam-6500	15	4	author(s	author(s	NOUN
ejpam-6500	15	5	)	)	PUNCT
ejpam-6500	15	6	.	.	PUNCT
ejpam-6500	16	1	(	(	PUNCT
ejpam-6500	16	2	cc	cc	NOUN
ejpam-6500	16	3	by	by	ADP
ejpam-6500	16	4	-	-	PUNCT
ejpam-6500	16	5	nc	nc	PROPN
ejpam-6500	16	6	4.0	4.0	NUM
ejpam-6500	16	7	)	)	PUNCT
ejpam-6500	16	8	t.	t.	NOUN
ejpam-6500	16	9	oner	oner	NOUN
ejpam-6500	16	10	et	et	PROPN
ejpam-6500	16	11	al	al	PROPN
ejpam-6500	16	12	.	.	PUNCT
ejpam-6500	16	13	/	/	SYM
ejpam-6500	16	14	eur	eur	PROPN
ejpam-6500	16	15	.	.	PUNCT
ejpam-6500	17	1	j.	j.	PROPN
ejpam-6500	17	2	pure	pure	PROPN
ejpam-6500	17	3	appl	appl	PROPN
ejpam-6500	17	4	.	.	PROPN
ejpam-6500	17	5	math	math	PROPN
ejpam-6500	17	6	,	,	PUNCT
ejpam-6500	17	7	18	18	NUM
ejpam-6500	17	8	(	(	PUNCT
ejpam-6500	17	9	3	3	NUM
ejpam-6500	17	10	)	)	PUNCT
ejpam-6500	17	11	(	(	PUNCT
ejpam-6500	17	12	2025	2025	NUM
ejpam-6500	17	13	)	)	PUNCT
ejpam-6500	17	14	,	,	PUNCT
ejpam-6500	17	15	6500	6500	NUM
ejpam-6500	17	16	2	2	NUM
ejpam-6500	17	17	of	of	ADP
ejpam-6500	17	18	13	13	NUM
ejpam-6500	17	19	this	this	DET
ejpam-6500	17	20	universality	universality	NOUN
ejpam-6500	17	21	extends	extend	VERB
ejpam-6500	17	22	to	to	ADP
ejpam-6500	17	23	boolean	boolean	ADJ
ejpam-6500	17	24	algebras	algebra	NOUN
ejpam-6500	17	25	,	,	PUNCT
ejpam-6500	17	26	where	where	SCONJ
ejpam-6500	17	27	the	the	DET
ejpam-6500	17	28	sheffer	sheffer	NOUN
ejpam-6500	17	29	stroke	stroke	NOUN
ejpam-6500	17	30	alone	alone	ADV
ejpam-6500	17	31	suffices	suffice	VERB
ejpam-6500	17	32	to	to	PART
ejpam-6500	17	33	formulate	formulate	VERB
ejpam-6500	17	34	their	their	PRON
ejpam-6500	17	35	axioms	axiom	NOUN
ejpam-6500	17	36	,	,	PUNCT
ejpam-6500	17	37	offering	offer	VERB
ejpam-6500	17	38	a	a	DET
ejpam-6500	17	39	minimalist	minimalist	NOUN
ejpam-6500	17	40	yet	yet	CCONJ
ejpam-6500	17	41	powerful	powerful	ADJ
ejpam-6500	17	42	framework	framework	NOUN
ejpam-6500	17	43	for	for	ADP
ejpam-6500	17	44	algebraic	algebraic	ADJ
ejpam-6500	17	45	and	and	CCONJ
ejpam-6500	17	46	logical	logical	ADJ
ejpam-6500	17	47	investigations	investigation	NOUN
ejpam-6500	17	48	[	[	X
ejpam-6500	17	49	2	2	NUM
ejpam-6500	17	50	]	]	PUNCT
ejpam-6500	17	51	.	.	PUNCT
ejpam-6500	18	1	inspired	inspire	VERB
ejpam-6500	18	2	by	by	ADP
ejpam-6500	18	3	its	its	PRON
ejpam-6500	18	4	efficiency	efficiency	NOUN
ejpam-6500	18	5	and	and	CCONJ
ejpam-6500	18	6	expressive	expressive	ADJ
ejpam-6500	18	7	power	power	NOUN
ejpam-6500	18	8	,	,	PUNCT
ejpam-6500	18	9	recent	recent	ADJ
ejpam-6500	18	10	studies	study	NOUN
ejpam-6500	18	11	by	by	ADP
ejpam-6500	18	12	oner	oner	NOUN
ejpam-6500	18	13	et	et	PROPN
ejpam-6500	18	14	al	al	PROPN
ejpam-6500	18	15	.	.	PUNCT
ejpam-6500	19	1	[	[	X
ejpam-6500	19	2	3	3	NUM
ejpam-6500	19	3	]	]	PUNCT
ejpam-6500	19	4	introduced	introduce	VERB
ejpam-6500	19	5	sheffer	sheffer	PROPN
ejpam-6500	19	6	stroke	stroke	PROPN
ejpam-6500	19	7	hilbert	hilbert	PROPN
ejpam-6500	19	8	algebras	algebras	PROPN
ejpam-6500	19	9	,	,	PUNCT
ejpam-6500	19	10	merging	merge	VERB
ejpam-6500	19	11	the	the	DET
ejpam-6500	19	12	conceptual	conceptual	ADJ
ejpam-6500	19	13	simplicity	simplicity	NOUN
ejpam-6500	19	14	of	of	ADP
ejpam-6500	19	15	the	the	DET
ejpam-6500	19	16	nand	nand	NOUN
ejpam-6500	19	17	operation	operation	NOUN
ejpam-6500	19	18	with	with	ADP
ejpam-6500	19	19	the	the	DET
ejpam-6500	19	20	structured	structured	ADJ
ejpam-6500	19	21	implications	implication	NOUN
ejpam-6500	19	22	of	of	ADP
ejpam-6500	19	23	hilbert	hilbert	PROPN
ejpam-6500	19	24	algebras	algebras	PROPN
ejpam-6500	19	25	.	.	PUNCT
ejpam-6500	20	1	their	their	PRON
ejpam-6500	20	2	work	work	NOUN
ejpam-6500	20	3	revealed	reveal	VERB
ejpam-6500	20	4	new	new	ADJ
ejpam-6500	20	5	algebraic	algebraic	ADJ
ejpam-6500	20	6	properties	property	NOUN
ejpam-6500	20	7	and	and	CCONJ
ejpam-6500	20	8	paved	pave	VERB
ejpam-6500	20	9	the	the	DET
ejpam-6500	20	10	way	way	NOUN
ejpam-6500	20	11	for	for	ADP
ejpam-6500	20	12	exploring	explore	VERB
ejpam-6500	20	13	substructures	substructure	NOUN
ejpam-6500	20	14	within	within	ADP
ejpam-6500	20	15	these	these	DET
ejpam-6500	20	16	algebras	algebra	NOUN
ejpam-6500	20	17	,	,	PUNCT
ejpam-6500	20	18	particularly	particularly	ADV
ejpam-6500	20	19	in	in	ADP
ejpam-6500	20	20	fuzzy	fuzzy	ADJ
ejpam-6500	20	21	settings	setting	NOUN
ejpam-6500	20	22	.	.	PUNCT
ejpam-6500	21	1	in	in	ADP
ejpam-6500	21	2	parallel	parallel	NOUN
ejpam-6500	21	3	,	,	PUNCT
ejpam-6500	21	4	hilbert	hilbert	PROPN
ejpam-6500	21	5	algebras	algebras	PROPN
ejpam-6500	21	6	—	—	PUNCT
ejpam-6500	21	7	initially	initially	ADV
ejpam-6500	21	8	studied	study	VERB
ejpam-6500	21	9	in	in	ADP
ejpam-6500	21	10	the	the	DET
ejpam-6500	21	11	1930s	1930	NOUN
ejpam-6500	21	12	as	as	ADP
ejpam-6500	21	13	algebraic	algebraic	ADJ
ejpam-6500	21	14	models	model	NOUN
ejpam-6500	21	15	for	for	ADP
ejpam-6500	21	16	the	the	DET
ejpam-6500	21	17	implicative	implicative	ADJ
ejpam-6500	21	18	fragment	fragment	NOUN
ejpam-6500	21	19	of	of	ADP
ejpam-6500	21	20	intuitionistic	intuitionistic	ADJ
ejpam-6500	21	21	logic	logic	NOUN
ejpam-6500	21	22	[	[	X
ejpam-6500	21	23	4–7]—emerged	4–7]—emerge	VERB
ejpam-6500	21	24	as	as	ADP
ejpam-6500	21	25	pivotal	pivotal	ADJ
ejpam-6500	21	26	objects	object	NOUN
ejpam-6500	21	27	in	in	ADP
ejpam-6500	21	28	algebraic	algebraic	ADJ
ejpam-6500	21	29	logic	logic	NOUN
ejpam-6500	21	30	due	due	ADP
ejpam-6500	21	31	to	to	ADP
ejpam-6500	21	32	their	their	PRON
ejpam-6500	21	33	ability	ability	NOUN
ejpam-6500	21	34	to	to	PART
ejpam-6500	21	35	model	model	VERB
ejpam-6500	21	36	logical	logical	ADJ
ejpam-6500	21	37	implication	implication	NOUN
ejpam-6500	21	38	in	in	ADP
ejpam-6500	21	39	a	a	DET
ejpam-6500	21	40	purely	purely	ADV
ejpam-6500	21	41	algebraic	algebraic	ADJ
ejpam-6500	21	42	setting	setting	NOUN
ejpam-6500	21	43	.	.	PUNCT
ejpam-6500	22	1	over	over	ADP
ejpam-6500	22	2	time	time	NOUN
ejpam-6500	22	3	,	,	PUNCT
ejpam-6500	22	4	researchers	researcher	NOUN
ejpam-6500	22	5	have	have	AUX
ejpam-6500	22	6	extended	extend	VERB
ejpam-6500	22	7	hilbert	hilbert	NOUN
ejpam-6500	22	8	algebras	algebra	NOUN
ejpam-6500	22	9	to	to	ADP
ejpam-6500	22	10	enriched	enrich	VERB
ejpam-6500	22	11	systems	system	NOUN
ejpam-6500	22	12	,	,	PUNCT
ejpam-6500	22	13	incorporating	incorporate	VERB
ejpam-6500	22	14	operations	operation	NOUN
ejpam-6500	22	15	such	such	ADJ
ejpam-6500	22	16	as	as	ADP
ejpam-6500	22	17	infimum	infimum	ADJ
ejpam-6500	22	18	and	and	CCONJ
ejpam-6500	22	19	supremum	supremum	ADJ
ejpam-6500	22	20	to	to	PART
ejpam-6500	22	21	enhance	enhance	VERB
ejpam-6500	22	22	their	their	PRON
ejpam-6500	22	23	expressive	expressive	ADJ
ejpam-6500	22	24	power	power	NOUN
ejpam-6500	22	25	[	[	X
ejpam-6500	22	26	7	7	NUM
ejpam-6500	22	27	]	]	PUNCT
ejpam-6500	22	28	.	.	PUNCT
ejpam-6500	23	1	however	however	ADV
ejpam-6500	23	2	,	,	PUNCT
ejpam-6500	23	3	it	it	PRON
ejpam-6500	23	4	was	be	AUX
ejpam-6500	23	5	not	not	PART
ejpam-6500	23	6	until	until	ADP
ejpam-6500	23	7	the	the	DET
ejpam-6500	23	8	synthesis	synthesis	NOUN
ejpam-6500	23	9	with	with	ADP
ejpam-6500	23	10	sheffer	sheffer	NOUN
ejpam-6500	23	11	stroke	stroke	NOUN
ejpam-6500	23	12	operations	operation	NOUN
ejpam-6500	23	13	that	that	SCONJ
ejpam-6500	23	14	a	a	DET
ejpam-6500	23	15	minimalist	minimalist	NOUN
ejpam-6500	23	16	yet	yet	CCONJ
ejpam-6500	23	17	expressive	expressive	ADJ
ejpam-6500	23	18	representation	representation	NOUN
ejpam-6500	23	19	of	of	ADP
ejpam-6500	23	20	logical	logical	ADJ
ejpam-6500	23	21	structures	structure	NOUN
ejpam-6500	23	22	was	be	AUX
ejpam-6500	23	23	achieved	achieve	VERB
ejpam-6500	23	24	[	[	PUNCT
ejpam-6500	23	25	3	3	NUM
ejpam-6500	23	26	]	]	PUNCT
ejpam-6500	23	27	.	.	PUNCT
ejpam-6500	24	1	the	the	DET
ejpam-6500	24	2	introduction	introduction	NOUN
ejpam-6500	24	3	of	of	ADP
ejpam-6500	24	4	fuzzy	fuzzy	ADJ
ejpam-6500	24	5	set	set	NOUN
ejpam-6500	24	6	theory	theory	NOUN
ejpam-6500	24	7	by	by	ADP
ejpam-6500	24	8	zadeh	zadeh	PROPN
ejpam-6500	24	9	in	in	ADP
ejpam-6500	24	10	1965	1965	NUM
ejpam-6500	24	11	[	[	X
ejpam-6500	24	12	8	8	NUM
ejpam-6500	24	13	]	]	PUNCT
ejpam-6500	24	14	revolutionized	revolutionize	VERB
ejpam-6500	24	15	the	the	DET
ejpam-6500	24	16	modeling	modeling	NOUN
ejpam-6500	24	17	of	of	ADP
ejpam-6500	24	18	vagueness	vagueness	NOUN
ejpam-6500	24	19	and	and	CCONJ
ejpam-6500	24	20	imprecision	imprecision	NOUN
ejpam-6500	24	21	in	in	ADP
ejpam-6500	24	22	mathematical	mathematical	ADJ
ejpam-6500	24	23	systems	system	NOUN
ejpam-6500	24	24	.	.	PUNCT
ejpam-6500	25	1	this	this	DET
ejpam-6500	25	2	extension	extension	NOUN
ejpam-6500	25	3	inspired	inspire	VERB
ejpam-6500	25	4	the	the	DET
ejpam-6500	25	5	fuzzification	fuzzification	NOUN
ejpam-6500	25	6	of	of	ADP
ejpam-6500	25	7	various	various	ADJ
ejpam-6500	25	8	algebraic	algebraic	ADJ
ejpam-6500	25	9	structures	structure	NOUN
ejpam-6500	25	10	,	,	PUNCT
ejpam-6500	25	11	beginning	begin	VERB
ejpam-6500	25	12	with	with	ADP
ejpam-6500	25	13	fuzzy	fuzzy	ADJ
ejpam-6500	25	14	subgroups	subgroup	NOUN
ejpam-6500	25	15	[	[	X
ejpam-6500	25	16	9	9	NUM
ejpam-6500	25	17	]	]	PUNCT
ejpam-6500	25	18	and	and	CCONJ
ejpam-6500	25	19	evolving	evolve	VERB
ejpam-6500	25	20	into	into	ADP
ejpam-6500	25	21	fuzzy	fuzzy	ADJ
ejpam-6500	25	22	ideals	ideal	NOUN
ejpam-6500	25	23	in	in	ADP
ejpam-6500	25	24	rings	ring	NOUN
ejpam-6500	25	25	[	[	X
ejpam-6500	25	26	10	10	NUM
ejpam-6500	25	27	]	]	PUNCT
ejpam-6500	25	28	.	.	PUNCT
ejpam-6500	26	1	building	build	VERB
ejpam-6500	26	2	on	on	ADP
ejpam-6500	26	3	these	these	DET
ejpam-6500	26	4	foundations	foundation	NOUN
ejpam-6500	26	5	,	,	PUNCT
ejpam-6500	26	6	dudek	dudek	PROPN
ejpam-6500	26	7	and	and	CCONJ
ejpam-6500	26	8	jun	jun	PROPN
ejpam-6500	27	1	[	[	X
ejpam-6500	27	2	11	11	NUM
ejpam-6500	27	3	]	]	PUNCT
ejpam-6500	27	4	extended	extend	VERB
ejpam-6500	27	5	the	the	DET
ejpam-6500	27	6	concept	concept	NOUN
ejpam-6500	27	7	of	of	ADP
ejpam-6500	27	8	ideals	ideal	NOUN
ejpam-6500	27	9	in	in	ADP
ejpam-6500	27	10	hilbert	hilbert	PROPN
ejpam-6500	27	11	algebras	algebras	PROPN
ejpam-6500	27	12	to	to	ADP
ejpam-6500	27	13	fuzzy	fuzzy	ADJ
ejpam-6500	27	14	ideals	ideal	NOUN
ejpam-6500	27	15	,	,	PUNCT
ejpam-6500	27	16	introducing	introduce	VERB
ejpam-6500	27	17	foundational	foundational	ADJ
ejpam-6500	27	18	results	result	NOUN
ejpam-6500	27	19	on	on	ADP
ejpam-6500	27	20	closure	closure	NOUN
ejpam-6500	27	21	properties	property	NOUN
ejpam-6500	27	22	and	and	CCONJ
ejpam-6500	27	23	their	their	PRON
ejpam-6500	27	24	connections	connection	NOUN
ejpam-6500	27	25	to	to	ADP
ejpam-6500	27	26	deductive	deductive	ADJ
ejpam-6500	27	27	systems	system	NOUN
ejpam-6500	27	28	.	.	PUNCT
ejpam-6500	28	1	borzooei	borzooei	PROPN
ejpam-6500	28	2	et	et	PROPN
ejpam-6500	28	3	al	al	PROPN
ejpam-6500	28	4	.	.	PUNCT
ejpam-6500	29	1	[	[	X
ejpam-6500	29	2	12	12	NUM
ejpam-6500	29	3	]	]	PUNCT
ejpam-6500	29	4	introduced	introduce	VERB
ejpam-6500	29	5	fuzzy	fuzzy	ADJ
ejpam-6500	29	6	weak	weak	ADJ
ejpam-6500	29	7	filters	filter	NOUN
ejpam-6500	29	8	in	in	ADP
ejpam-6500	29	9	sheffer	sheffer	PROPN
ejpam-6500	29	10	stroke	stroke	PROPN
ejpam-6500	29	11	hilbert	hilbert	PROPN
ejpam-6500	29	12	algebras	algebras	PROPN
ejpam-6500	29	13	,	,	PUNCT
ejpam-6500	29	14	exploring	explore	VERB
ejpam-6500	29	15	their	their	PRON
ejpam-6500	29	16	definitions	definition	NOUN
ejpam-6500	29	17	and	and	CCONJ
ejpam-6500	29	18	key	key	ADJ
ejpam-6500	29	19	properties	property	NOUN
ejpam-6500	29	20	.	.	PUNCT
ejpam-6500	30	1	the	the	DET
ejpam-6500	30	2	recent	recent	ADJ
ejpam-6500	30	3	incorporation	incorporation	NOUN
ejpam-6500	30	4	of	of	ADP
ejpam-6500	30	5	fuzzy	fuzzy	ADJ
ejpam-6500	30	6	principles	principle	NOUN
ejpam-6500	30	7	into	into	ADP
ejpam-6500	30	8	sheffer	sheffer	PROPN
ejpam-6500	30	9	stroke	stroke	PROPN
ejpam-6500	30	10	hilbert	hilbert	PROPN
ejpam-6500	30	11	algebras	algebras	PROPN
ejpam-6500	30	12	by	by	ADP
ejpam-6500	30	13	oner	oner	NOUN
ejpam-6500	30	14	et	et	PROPN
ejpam-6500	30	15	al	al	PROPN
ejpam-6500	30	16	.	.	PUNCT
ejpam-6500	31	1	[	[	X
ejpam-6500	31	2	3	3	X
ejpam-6500	31	3	]	]	PUNCT
ejpam-6500	31	4	marks	mark	VERB
ejpam-6500	31	5	a	a	DET
ejpam-6500	31	6	critical	critical	ADJ
ejpam-6500	31	7	step	step	NOUN
ejpam-6500	31	8	forward	forward	ADV
ejpam-6500	31	9	,	,	PUNCT
ejpam-6500	31	10	demonstrating	demonstrate	VERB
ejpam-6500	31	11	that	that	SCONJ
ejpam-6500	31	12	the	the	DET
ejpam-6500	31	13	sheffer	sheffer	NOUN
ejpam-6500	31	14	stroke	stroke	NOUN
ejpam-6500	31	15	’s	’s	PART
ejpam-6500	31	16	functional	functional	ADJ
ejpam-6500	31	17	completeness	completeness	NOUN
ejpam-6500	31	18	persists	persist	VERB
ejpam-6500	31	19	even	even	ADV
ejpam-6500	31	20	in	in	ADP
ejpam-6500	31	21	fuzzy	fuzzy	ADJ
ejpam-6500	31	22	settings	setting	NOUN
ejpam-6500	31	23	.	.	PUNCT
ejpam-6500	32	1	despite	despite	SCONJ
ejpam-6500	32	2	these	these	DET
ejpam-6500	32	3	advancements	advancement	NOUN
ejpam-6500	32	4	,	,	PUNCT
ejpam-6500	32	5	the	the	DET
ejpam-6500	32	6	study	study	NOUN
ejpam-6500	32	7	of	of	ADP
ejpam-6500	32	8	fuzzy	fuzzy	ADJ
ejpam-6500	32	9	subalgebras	subalgebras	PROPN
ejpam-6500	32	10	within	within	ADP
ejpam-6500	32	11	sheffer	sheffer	PROPN
ejpam-6500	32	12	stroke	stroke	PROPN
ejpam-6500	32	13	hilbert	hilbert	PROPN
ejpam-6500	32	14	algebras	algebras	PROPN
ejpam-6500	32	15	,	,	PUNCT
ejpam-6500	32	16	particularly	particularly	ADV
ejpam-6500	32	17	those	those	PRON
ejpam-6500	32	18	characterized	characterize	VERB
ejpam-6500	32	19	by	by	ADP
ejpam-6500	32	20	(	(	PUNCT
ejpam-6500	32	21	∈,∈	∈,∈	X
ejpam-6500	32	22	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	32	23	substructures	substructure	NOUN
ejpam-6500	32	24	,	,	PUNCT
ejpam-6500	32	25	remains	remain	VERB
ejpam-6500	32	26	largely	largely	ADV
ejpam-6500	32	27	uncharted	uncharted	ADJ
ejpam-6500	32	28	.	.	PUNCT
ejpam-6500	33	1	the	the	DET
ejpam-6500	33	2	generalization	generalization	NOUN
ejpam-6500	33	3	of	of	ADP
ejpam-6500	33	4	subalgebras	subalgebras	PROPN
ejpam-6500	33	5	to	to	ADP
ejpam-6500	33	6	fuzzy	fuzzy	ADJ
ejpam-6500	33	7	contexts	context	NOUN
ejpam-6500	33	8	introduces	introduce	NOUN
ejpam-6500	33	9	graded	grade	VERB
ejpam-6500	33	10	membership	membership	NOUN
ejpam-6500	33	11	,	,	PUNCT
ejpam-6500	33	12	which	which	PRON
ejpam-6500	33	13	allows	allow	VERB
ejpam-6500	33	14	for	for	ADP
ejpam-6500	33	15	varying	vary	VERB
ejpam-6500	33	16	degrees	degree	NOUN
ejpam-6500	33	17	of	of	ADP
ejpam-6500	33	18	inclusion	inclusion	NOUN
ejpam-6500	33	19	,	,	PUNCT
ejpam-6500	33	20	thereby	thereby	ADV
ejpam-6500	33	21	reflecting	reflect	VERB
ejpam-6500	33	22	realworld	realworld	PROPN
ejpam-6500	33	23	imprecision	imprecision	NOUN
ejpam-6500	33	24	more	more	ADV
ejpam-6500	33	25	effectively	effectively	ADV
ejpam-6500	33	26	.	.	PUNCT
ejpam-6500	34	1	this	this	DET
ejpam-6500	34	2	gap	gap	NOUN
ejpam-6500	34	3	presents	present	VERB
ejpam-6500	34	4	a	a	DET
ejpam-6500	34	5	promising	promising	ADJ
ejpam-6500	34	6	opportunity	opportunity	NOUN
ejpam-6500	34	7	for	for	ADP
ejpam-6500	34	8	deepening	deepen	VERB
ejpam-6500	34	9	the	the	DET
ejpam-6500	34	10	theoretical	theoretical	ADJ
ejpam-6500	34	11	understanding	understanding	NOUN
ejpam-6500	34	12	of	of	ADP
ejpam-6500	34	13	fuzzy	fuzzy	ADJ
ejpam-6500	34	14	algebraic	algebraic	ADJ
ejpam-6500	34	15	systems	system	NOUN
ejpam-6500	34	16	and	and	CCONJ
ejpam-6500	34	17	expanding	expand	VERB
ejpam-6500	34	18	their	their	PRON
ejpam-6500	34	19	applications	application	NOUN
ejpam-6500	34	20	in	in	ADP
ejpam-6500	34	21	logic	logic	NOUN
ejpam-6500	34	22	and	and	CCONJ
ejpam-6500	34	23	information	information	NOUN
ejpam-6500	34	24	processing	processing	NOUN
ejpam-6500	34	25	.	.	PUNCT
ejpam-6500	35	1	the	the	DET
ejpam-6500	35	2	exploration	exploration	NOUN
ejpam-6500	35	3	of	of	ADP
ejpam-6500	35	4	sheffer	sheffer	PROPN
ejpam-6500	35	5	stroke	stroke	PROPN
ejpam-6500	35	6	hilbert	hilbert	PROPN
ejpam-6500	35	7	algebras	algebras	PROPN
ejpam-6500	35	8	has	have	AUX
ejpam-6500	35	9	witnessed	witness	VERB
ejpam-6500	35	10	increasing	increase	VERB
ejpam-6500	35	11	depth	depth	NOUN
ejpam-6500	35	12	and	and	CCONJ
ejpam-6500	35	13	diversity	diversity	NOUN
ejpam-6500	35	14	,	,	PUNCT
ejpam-6500	35	15	highlighting	highlight	VERB
ejpam-6500	35	16	their	their	PRON
ejpam-6500	35	17	central	central	ADJ
ejpam-6500	35	18	role	role	NOUN
ejpam-6500	35	19	in	in	ADP
ejpam-6500	35	20	algebraic	algebraic	ADJ
ejpam-6500	35	21	logic	logic	NOUN
ejpam-6500	35	22	and	and	CCONJ
ejpam-6500	35	23	fuzzy	fuzzy	ADJ
ejpam-6500	35	24	systems	system	NOUN
ejpam-6500	35	25	.	.	PUNCT
ejpam-6500	36	1	foundational	foundational	ADJ
ejpam-6500	36	2	work	work	NOUN
ejpam-6500	36	3	has	have	AUX
ejpam-6500	36	4	addressed	address	VERB
ejpam-6500	36	5	the	the	DET
ejpam-6500	36	6	algebraic	algebraic	ADJ
ejpam-6500	36	7	basis	basis	NOUN
ejpam-6500	36	8	of	of	ADP
ejpam-6500	36	9	these	these	DET
ejpam-6500	36	10	structures	structure	NOUN
ejpam-6500	36	11	,	,	PUNCT
ejpam-6500	36	12	particularly	particularly	ADV
ejpam-6500	36	13	the	the	DET
ejpam-6500	36	14	interplay	interplay	NOUN
ejpam-6500	36	15	between	between	ADP
ejpam-6500	36	16	sheffer	sheffer	PROPN
ejpam-6500	36	17	stroke	stroke	PROPN
ejpam-6500	36	18	and	and	CCONJ
ejpam-6500	36	19	hilbert	hilbert	PROPN
ejpam-6500	36	20	algebras	algebras	PROPN
ejpam-6500	37	1	[	[	X
ejpam-6500	37	2	3	3	NUM
ejpam-6500	37	3	]	]	PUNCT
ejpam-6500	37	4	,	,	PUNCT
ejpam-6500	37	5	and	and	CCONJ
ejpam-6500	37	6	has	have	AUX
ejpam-6500	37	7	been	be	AUX
ejpam-6500	37	8	extended	extend	VERB
ejpam-6500	37	9	through	through	ADP
ejpam-6500	37	10	the	the	DET
ejpam-6500	37	11	study	study	NOUN
ejpam-6500	37	12	of	of	ADP
ejpam-6500	37	13	fuzzy	fuzzy	ADJ
ejpam-6500	37	14	ideals	ideal	NOUN
ejpam-6500	37	15	[	[	X
ejpam-6500	37	16	13	13	NUM
ejpam-6500	37	17	]	]	PUNCT
ejpam-6500	37	18	and	and	CCONJ
ejpam-6500	37	19	fuzzy	fuzzy	ADJ
ejpam-6500	37	20	filters	filter	NOUN
ejpam-6500	37	21	[	[	X
ejpam-6500	37	22	14	14	NUM
ejpam-6500	37	23	]	]	PUNCT
ejpam-6500	37	24	.	.	PUNCT
ejpam-6500	38	1	the	the	DET
ejpam-6500	38	2	introduction	introduction	NOUN
ejpam-6500	38	3	of	of	ADP
ejpam-6500	38	4	fuzzy	fuzzy	ADJ
ejpam-6500	38	5	weak	weak	ADJ
ejpam-6500	38	6	filters	filter	NOUN
ejpam-6500	38	7	[	[	X
ejpam-6500	38	8	12	12	NUM
ejpam-6500	38	9	]	]	PUNCT
ejpam-6500	38	10	and	and	CCONJ
ejpam-6500	38	11	bipolar	bipolar	ADV
ejpam-6500	38	12	-	-	PUNCT
ejpam-6500	38	13	valued	value	VERB
ejpam-6500	38	14	fuzzy	fuzzy	ADJ
ejpam-6500	38	15	deductive	deductive	ADJ
ejpam-6500	38	16	systems	system	NOUN
ejpam-6500	38	17	[	[	X
ejpam-6500	38	18	15	15	NUM
ejpam-6500	38	19	]	]	X
ejpam-6500	38	20	further	far	ADV
ejpam-6500	38	21	enriched	enrich	VERB
ejpam-6500	38	22	the	the	DET
ejpam-6500	38	23	theoretical	theoretical	ADJ
ejpam-6500	38	24	framework	framework	NOUN
ejpam-6500	38	25	,	,	PUNCT
ejpam-6500	38	26	allowing	allow	VERB
ejpam-6500	38	27	nuanced	nuanced	ADJ
ejpam-6500	38	28	treatment	treatment	NOUN
ejpam-6500	38	29	of	of	ADP
ejpam-6500	38	30	uncertainty	uncertainty	NOUN
ejpam-6500	38	31	and	and	CCONJ
ejpam-6500	38	32	graded	grade	VERB
ejpam-6500	38	33	reasoning	reasoning	NOUN
ejpam-6500	38	34	.	.	PUNCT
ejpam-6500	39	1	more	more	ADV
ejpam-6500	39	2	recent	recent	ADJ
ejpam-6500	39	3	developments	development	NOUN
ejpam-6500	39	4	have	have	AUX
ejpam-6500	39	5	focused	focus	VERB
ejpam-6500	39	6	on	on	ADP
ejpam-6500	39	7	structural	structural	ADJ
ejpam-6500	39	8	generalizations	generalization	NOUN
ejpam-6500	39	9	,	,	PUNCT
ejpam-6500	39	10	such	such	ADJ
ejpam-6500	39	11	as	as	ADP
ejpam-6500	39	12	the	the	DET
ejpam-6500	39	13	incorporation	incorporation	NOUN
ejpam-6500	39	14	of	of	ADP
ejpam-6500	39	15	n	n	CCONJ
ejpam-6500	39	16	-based	-based	ADJ
ejpam-6500	39	17	soft	soft	ADJ
ejpam-6500	39	18	subalgebras	subalgebra	NOUN
ejpam-6500	39	19	and	and	CCONJ
ejpam-6500	39	20	ideals	ideal	NOUN
ejpam-6500	39	21	[	[	X
ejpam-6500	39	22	16	16	NUM
ejpam-6500	39	23	]	]	PUNCT
ejpam-6500	39	24	,	,	PUNCT
ejpam-6500	39	25	and	and	CCONJ
ejpam-6500	39	26	the	the	DET
ejpam-6500	39	27	formulation	formulation	NOUN
ejpam-6500	39	28	of	of	ADP
ejpam-6500	39	29	length	length	NOUN
ejpam-6500	39	30	and	and	CCONJ
ejpam-6500	39	31	mean	mean	ADJ
ejpam-6500	39	32	-	-	PUNCT
ejpam-6500	39	33	fuzzy	fuzzy	ADJ
ejpam-6500	39	34	ideals	ideal	NOUN
ejpam-6500	39	35	[	[	X
ejpam-6500	39	36	17	17	NUM
ejpam-6500	39	37	]	]	PUNCT
ejpam-6500	39	38	and	and	CCONJ
ejpam-6500	39	39	subalgebras	subalgebras	PROPN
ejpam-6500	40	1	[	[	X
ejpam-6500	40	2	18	18	NUM
ejpam-6500	40	3	]	]	PUNCT
ejpam-6500	40	4	,	,	PUNCT
ejpam-6500	40	5	revealing	reveal	VERB
ejpam-6500	40	6	new	new	ADJ
ejpam-6500	40	7	perspectives	perspective	NOUN
ejpam-6500	40	8	on	on	ADP
ejpam-6500	40	9	the	the	DET
ejpam-6500	40	10	quantitative	quantitative	ADJ
ejpam-6500	40	11	dimensions	dimension	NOUN
ejpam-6500	40	12	of	of	ADP
ejpam-6500	40	13	fuzzy	fuzzy	ADJ
ejpam-6500	40	14	membership	membership	NOUN
ejpam-6500	40	15	.	.	PUNCT
ejpam-6500	41	1	building	build	VERB
ejpam-6500	41	2	upon	upon	SCONJ
ejpam-6500	41	3	this	this	DET
ejpam-6500	41	4	progression	progression	NOUN
ejpam-6500	41	5	,	,	PUNCT
ejpam-6500	41	6	the	the	DET
ejpam-6500	41	7	present	present	ADJ
ejpam-6500	41	8	paper	paper	NOUN
ejpam-6500	41	9	introduces	introduce	VERB
ejpam-6500	41	10	a	a	DET
ejpam-6500	41	11	new	new	ADJ
ejpam-6500	41	12	class	class	NOUN
ejpam-6500	41	13	of	of	ADP
ejpam-6500	41	14	fuzzy	fuzzy	ADJ
ejpam-6500	41	15	subt	subt	NOUN
ejpam-6500	41	16	.	.	PUNCT
ejpam-6500	42	1	oner	oner	NOUN
ejpam-6500	42	2	et	et	PROPN
ejpam-6500	42	3	al	al	PROPN
ejpam-6500	42	4	.	.	PUNCT
ejpam-6500	42	5	/	/	SYM
ejpam-6500	42	6	eur	eur	PROPN
ejpam-6500	42	7	.	.	PUNCT
ejpam-6500	43	1	j.	j.	PROPN
ejpam-6500	43	2	pure	pure	PROPN
ejpam-6500	43	3	appl	appl	PROPN
ejpam-6500	43	4	.	.	PROPN
ejpam-6500	43	5	math	math	PROPN
ejpam-6500	43	6	,	,	PUNCT
ejpam-6500	43	7	18	18	NUM
ejpam-6500	43	8	(	(	PUNCT
ejpam-6500	43	9	3	3	NUM
ejpam-6500	43	10	)	)	PUNCT
ejpam-6500	43	11	(	(	PUNCT
ejpam-6500	43	12	2025	2025	NUM
ejpam-6500	43	13	)	)	PUNCT
ejpam-6500	43	14	,	,	PUNCT
ejpam-6500	43	15	6500	6500	NUM
ejpam-6500	43	16	3	3	NUM
ejpam-6500	43	17	of	of	ADP
ejpam-6500	43	18	13	13	NUM
ejpam-6500	43	19	structures	structure	NOUN
ejpam-6500	43	20	—	—	PUNCT
ejpam-6500	43	21	namely	namely	ADV
ejpam-6500	43	22	,	,	PUNCT
ejpam-6500	43	23	(	(	PUNCT
ejpam-6500	43	24	∈,∈	∈,∈	X
ejpam-6500	43	25	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	43	26	subalgebras	subalgebra	NOUN
ejpam-6500	43	27	—	—	PUNCT
ejpam-6500	43	28	within	within	ADP
ejpam-6500	43	29	sheffer	sheffer	PROPN
ejpam-6500	43	30	stroke	stroke	PROPN
ejpam-6500	43	31	hilbert	hilbert	PROPN
ejpam-6500	43	32	algebras	algebras	PROPN
ejpam-6500	43	33	.	.	PUNCT
ejpam-6500	44	1	these	these	DET
ejpam-6500	44	2	subalgebras	subalgebra	NOUN
ejpam-6500	44	3	extend	extend	VERB
ejpam-6500	44	4	existing	exist	VERB
ejpam-6500	44	5	frameworks	framework	NOUN
ejpam-6500	44	6	by	by	ADP
ejpam-6500	44	7	incorporating	incorporate	VERB
ejpam-6500	44	8	graded	grade	VERB
ejpam-6500	44	9	membership	membership	NOUN
ejpam-6500	44	10	with	with	ADP
ejpam-6500	44	11	tolerance	tolerance	NOUN
ejpam-6500	44	12	for	for	ADP
ejpam-6500	44	13	ambiguity	ambiguity	NOUN
ejpam-6500	44	14	,	,	PUNCT
ejpam-6500	44	15	providing	provide	VERB
ejpam-6500	44	16	refined	refined	ADJ
ejpam-6500	44	17	algebraic	algebraic	ADJ
ejpam-6500	44	18	tools	tool	NOUN
ejpam-6500	44	19	to	to	PART
ejpam-6500	44	20	model	model	VERB
ejpam-6500	44	21	fuzzy	fuzzy	ADJ
ejpam-6500	44	22	logic	logic	NOUN
ejpam-6500	44	23	under	under	ADP
ejpam-6500	44	24	sheffer	sheffer	NOUN
ejpam-6500	44	25	stroke	stroke	NOUN
ejpam-6500	44	26	operations	operation	NOUN
ejpam-6500	44	27	.	.	PUNCT
ejpam-6500	45	1	our	our	PRON
ejpam-6500	45	2	investigation	investigation	NOUN
ejpam-6500	45	3	establishes	establish	VERB
ejpam-6500	45	4	necessary	necessary	ADJ
ejpam-6500	45	5	and	and	CCONJ
ejpam-6500	45	6	sufficient	sufficient	ADJ
ejpam-6500	45	7	conditions	condition	NOUN
ejpam-6500	45	8	,	,	PUNCT
ejpam-6500	45	9	level	level	NOUN
ejpam-6500	45	10	set	set	NOUN
ejpam-6500	45	11	characterizations	characterization	NOUN
ejpam-6500	45	12	,	,	PUNCT
ejpam-6500	45	13	and	and	CCONJ
ejpam-6500	45	14	structural	structural	ADJ
ejpam-6500	45	15	invariance	invariance	NOUN
ejpam-6500	45	16	under	under	ADP
ejpam-6500	45	17	algebraic	algebraic	ADJ
ejpam-6500	45	18	operations	operation	NOUN
ejpam-6500	45	19	and	and	CCONJ
ejpam-6500	45	20	homomorphisms	homomorphism	NOUN
ejpam-6500	45	21	,	,	PUNCT
ejpam-6500	45	22	thereby	thereby	ADV
ejpam-6500	45	23	contributing	contribute	VERB
ejpam-6500	45	24	to	to	ADP
ejpam-6500	45	25	the	the	DET
ejpam-6500	45	26	ongoing	ongoing	ADJ
ejpam-6500	45	27	evolution	evolution	NOUN
ejpam-6500	45	28	of	of	ADP
ejpam-6500	45	29	fuzzy	fuzzy	ADJ
ejpam-6500	45	30	algebraic	algebraic	ADJ
ejpam-6500	45	31	theory	theory	NOUN
ejpam-6500	45	32	.	.	PUNCT
ejpam-6500	46	1	in	in	ADP
ejpam-6500	46	2	this	this	DET
ejpam-6500	46	3	paper	paper	NOUN
ejpam-6500	46	4	,	,	PUNCT
ejpam-6500	46	5	we	we	PRON
ejpam-6500	46	6	leverage	leverage	VERB
ejpam-6500	46	7	this	this	DET
ejpam-6500	46	8	interaction	interaction	NOUN
ejpam-6500	46	9	to	to	PART
ejpam-6500	46	10	introduce	introduce	VERB
ejpam-6500	46	11	generalized	generalized	ADJ
ejpam-6500	46	12	fuzzy	fuzzy	ADJ
ejpam-6500	46	13	subalgebras	subalgebra	NOUN
ejpam-6500	46	14	within	within	ADP
ejpam-6500	46	15	sheffer	sheffer	PROPN
ejpam-6500	46	16	stroke	stroke	PROPN
ejpam-6500	46	17	hilbert	hilbert	PROPN
ejpam-6500	46	18	algebras	algebras	PROPN
ejpam-6500	46	19	.	.	PUNCT
ejpam-6500	47	1	specifically	specifically	ADV
ejpam-6500	47	2	,	,	PUNCT
ejpam-6500	47	3	we	we	PRON
ejpam-6500	47	4	define	define	VERB
ejpam-6500	47	5	and	and	CCONJ
ejpam-6500	47	6	analyze	analyze	VERB
ejpam-6500	47	7	(	(	PUNCT
ejpam-6500	47	8	∈,∈	∈,∈	X
ejpam-6500	47	9	∨qm)fuzzy	∨qm)fuzzy	X
ejpam-6500	47	10	subalgebras	subalgebras	PROPN
ejpam-6500	47	11	,	,	PUNCT
ejpam-6500	47	12	a	a	DET
ejpam-6500	47	13	class	class	NOUN
ejpam-6500	47	14	of	of	ADP
ejpam-6500	47	15	fuzzy	fuzzy	ADJ
ejpam-6500	47	16	substructures	substructure	NOUN
ejpam-6500	47	17	that	that	PRON
ejpam-6500	47	18	extend	extend	VERB
ejpam-6500	47	19	traditional	traditional	ADJ
ejpam-6500	47	20	subalgebras	subalgebra	NOUN
ejpam-6500	47	21	by	by	ADP
ejpam-6500	47	22	incorporating	incorporate	VERB
ejpam-6500	47	23	graded	grade	VERB
ejpam-6500	47	24	membership	membership	NOUN
ejpam-6500	47	25	and	and	CCONJ
ejpam-6500	47	26	tolerance	tolerance	NOUN
ejpam-6500	47	27	for	for	ADP
ejpam-6500	47	28	ambiguity	ambiguity	NOUN
ejpam-6500	47	29	.	.	PUNCT
ejpam-6500	48	1	these	these	DET
ejpam-6500	48	2	subalgebras	subalgebra	NOUN
ejpam-6500	48	3	are	be	AUX
ejpam-6500	48	4	characterized	characterize	VERB
ejpam-6500	48	5	by	by	ADP
ejpam-6500	48	6	their	their	PRON
ejpam-6500	48	7	interaction	interaction	NOUN
ejpam-6500	48	8	with	with	ADP
ejpam-6500	48	9	level	level	NOUN
ejpam-6500	48	10	subsets	subset	NOUN
ejpam-6500	48	11	and	and	CCONJ
ejpam-6500	48	12	their	their	PRON
ejpam-6500	48	13	behavior	behavior	NOUN
ejpam-6500	48	14	under	under	ADP
ejpam-6500	48	15	algebraic	algebraic	ADJ
ejpam-6500	48	16	operations	operation	NOUN
ejpam-6500	48	17	,	,	PUNCT
ejpam-6500	48	18	offering	offer	VERB
ejpam-6500	48	19	a	a	DET
ejpam-6500	48	20	nuanced	nuanced	ADJ
ejpam-6500	48	21	perspective	perspective	NOUN
ejpam-6500	48	22	on	on	ADP
ejpam-6500	48	23	the	the	DET
ejpam-6500	48	24	interplay	interplay	NOUN
ejpam-6500	48	25	between	between	ADP
ejpam-6500	48	26	logic	logic	NOUN
ejpam-6500	48	27	and	and	CCONJ
ejpam-6500	48	28	fuzziness	fuzziness	NOUN
ejpam-6500	48	29	.	.	PUNCT
ejpam-6500	49	1	the	the	DET
ejpam-6500	49	2	primary	primary	ADJ
ejpam-6500	49	3	contributions	contribution	NOUN
ejpam-6500	49	4	of	of	ADP
ejpam-6500	49	5	this	this	DET
ejpam-6500	49	6	paper	paper	NOUN
ejpam-6500	49	7	include	include	VERB
ejpam-6500	49	8	:	:	PUNCT
ejpam-6500	49	9	•	•	ADP
ejpam-6500	49	10	the	the	DET
ejpam-6500	49	11	definition	definition	NOUN
ejpam-6500	49	12	and	and	CCONJ
ejpam-6500	49	13	characterization	characterization	NOUN
ejpam-6500	49	14	of	of	ADP
ejpam-6500	49	15	(	(	PUNCT
ejpam-6500	49	16	∈,∈	∈,∈	X
ejpam-6500	49	17	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	49	18	subalgebras	subalgebras	PROPN
ejpam-6500	49	19	in	in	ADP
ejpam-6500	49	20	sheffer	sheffer	PROPN
ejpam-6500	49	21	stroke	stroke	PROPN
ejpam-6500	49	22	hilbert	hilbert	PROPN
ejpam-6500	49	23	algebras	algebras	PROPN
ejpam-6500	49	24	.	.	PUNCT
ejpam-6500	50	1	•	•	NUM
ejpam-6500	50	2	the	the	DET
ejpam-6500	50	3	establishment	establishment	NOUN
ejpam-6500	50	4	of	of	ADP
ejpam-6500	50	5	necessary	necessary	ADJ
ejpam-6500	50	6	and	and	CCONJ
ejpam-6500	50	7	sufficient	sufficient	ADJ
ejpam-6500	50	8	conditions	condition	NOUN
ejpam-6500	50	9	for	for	ADP
ejpam-6500	50	10	a	a	DET
ejpam-6500	50	11	fuzzy	fuzzy	ADJ
ejpam-6500	50	12	set	set	NOUN
ejpam-6500	50	13	to	to	PART
ejpam-6500	50	14	be	be	AUX
ejpam-6500	50	15	an	an	DET
ejpam-6500	50	16	(	(	PUNCT
ejpam-6500	50	17	∈,∈	∈,∈	INTJ
ejpam-6500	50	18	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	50	19	subalgebra	subalgebra	NOUN
ejpam-6500	50	20	.	.	PUNCT
ejpam-6500	51	1	•	•	NUM
ejpam-6500	51	2	the	the	DET
ejpam-6500	51	3	investigation	investigation	NOUN
ejpam-6500	51	4	of	of	ADP
ejpam-6500	51	5	level	level	NOUN
ejpam-6500	51	6	subsets	subset	NOUN
ejpam-6500	51	7	and	and	CCONJ
ejpam-6500	51	8	their	their	PRON
ejpam-6500	51	9	role	role	NOUN
ejpam-6500	51	10	in	in	ADP
ejpam-6500	51	11	characterizing	characterize	VERB
ejpam-6500	51	12	these	these	DET
ejpam-6500	51	13	subalgebras	subalgebra	NOUN
ejpam-6500	51	14	.	.	PUNCT
ejpam-6500	52	1	•	•	NUM
ejpam-6500	52	2	the	the	DET
ejpam-6500	52	3	study	study	NOUN
ejpam-6500	52	4	of	of	ADP
ejpam-6500	52	5	algebraic	algebraic	ADJ
ejpam-6500	52	6	properties	property	NOUN
ejpam-6500	52	7	such	such	ADJ
ejpam-6500	52	8	as	as	ADP
ejpam-6500	52	9	intersections	intersection	NOUN
ejpam-6500	52	10	,	,	PUNCT
ejpam-6500	52	11	unions	union	NOUN
ejpam-6500	52	12	,	,	PUNCT
ejpam-6500	52	13	and	and	CCONJ
ejpam-6500	52	14	homomorphic	homomorphic	ADJ
ejpam-6500	52	15	invariance	invariance	NOUN
ejpam-6500	52	16	in	in	ADP
ejpam-6500	52	17	the	the	DET
ejpam-6500	52	18	context	context	NOUN
ejpam-6500	52	19	of	of	ADP
ejpam-6500	52	20	fuzzy	fuzzy	ADJ
ejpam-6500	52	21	subalgebras	subalgebra	NOUN
ejpam-6500	52	22	.	.	PUNCT
ejpam-6500	53	1	our	our	PRON
ejpam-6500	53	2	results	result	NOUN
ejpam-6500	53	3	not	not	PART
ejpam-6500	53	4	only	only	ADV
ejpam-6500	53	5	extend	extend	VERB
ejpam-6500	53	6	the	the	DET
ejpam-6500	53	7	theoretical	theoretical	ADJ
ejpam-6500	53	8	understanding	understanding	NOUN
ejpam-6500	53	9	of	of	ADP
ejpam-6500	53	10	sheffer	sheffer	PROPN
ejpam-6500	53	11	stroke	stroke	PROPN
ejpam-6500	53	12	hilbert	hilbert	PROPN
ejpam-6500	53	13	algebras	algebras	PROPN
ejpam-6500	53	14	but	but	CCONJ
ejpam-6500	53	15	also	also	ADV
ejpam-6500	53	16	provide	provide	VERB
ejpam-6500	53	17	a	a	DET
ejpam-6500	53	18	foundation	foundation	NOUN
ejpam-6500	53	19	for	for	ADP
ejpam-6500	53	20	future	future	ADJ
ejpam-6500	53	21	applications	application	NOUN
ejpam-6500	53	22	in	in	ADP
ejpam-6500	53	23	fuzzy	fuzzy	ADJ
ejpam-6500	53	24	logic	logic	NOUN
ejpam-6500	53	25	and	and	CCONJ
ejpam-6500	53	26	algebraic	algebraic	ADJ
ejpam-6500	53	27	structures	structure	NOUN
ejpam-6500	53	28	.	.	PUNCT
ejpam-6500	54	1	2	2	X
ejpam-6500	54	2	.	.	X
ejpam-6500	54	3	preliminaries	preliminary	NOUN
ejpam-6500	54	4	sheffer	sheffer	VERB
ejpam-6500	54	5	stroke	stroke	PROPN
ejpam-6500	54	6	hilbert	hilbert	PROPN
ejpam-6500	54	7	algebras	algebras	PROPN
ejpam-6500	54	8	form	form	VERB
ejpam-6500	54	9	a	a	DET
ejpam-6500	54	10	significant	significant	ADJ
ejpam-6500	54	11	algebraic	algebraic	ADJ
ejpam-6500	54	12	system	system	NOUN
ejpam-6500	54	13	bridging	bridge	VERB
ejpam-6500	54	14	logic	logic	NOUN
ejpam-6500	54	15	and	and	CCONJ
ejpam-6500	54	16	lattice	lattice	PROPN
ejpam-6500	54	17	theory	theory	NOUN
ejpam-6500	54	18	.	.	PUNCT
ejpam-6500	55	1	these	these	DET
ejpam-6500	55	2	structures	structure	NOUN
ejpam-6500	55	3	incorporate	incorporate	VERB
ejpam-6500	55	4	the	the	DET
ejpam-6500	55	5	sheffer	sheffer	NOUN
ejpam-6500	55	6	stroke	stroke	NOUN
ejpam-6500	55	7	(	(	PUNCT
ejpam-6500	55	8	nand	nand	NOUN
ejpam-6500	55	9	)	)	PUNCT
ejpam-6500	55	10	operation	operation	NOUN
ejpam-6500	55	11	—	—	PUNCT
ejpam-6500	55	12	an	an	DET
ejpam-6500	55	13	essential	essential	ADJ
ejpam-6500	55	14	logical	logical	ADJ
ejpam-6500	55	15	connective	connective	NOUN
ejpam-6500	55	16	in	in	ADP
ejpam-6500	55	17	boolean	boolean	ADJ
ejpam-6500	55	18	algebra	algebra	NOUN
ejpam-6500	55	19	—	—	PUNCT
ejpam-6500	55	20	into	into	ADP
ejpam-6500	55	21	the	the	DET
ejpam-6500	55	22	classical	classical	ADJ
ejpam-6500	55	23	hilbert	hilbert	NOUN
ejpam-6500	55	24	algebra	algebra	NOUN
ejpam-6500	55	25	framework	framework	NOUN
ejpam-6500	55	26	.	.	PUNCT
ejpam-6500	56	1	by	by	ADP
ejpam-6500	56	2	extending	extend	VERB
ejpam-6500	56	3	hilbert	hilbert	NOUN
ejpam-6500	56	4	algebras	algebra	NOUN
ejpam-6500	56	5	with	with	ADP
ejpam-6500	56	6	this	this	DET
ejpam-6500	56	7	operation	operation	NOUN
ejpam-6500	56	8	,	,	PUNCT
ejpam-6500	56	9	they	they	PRON
ejpam-6500	56	10	provide	provide	VERB
ejpam-6500	56	11	a	a	DET
ejpam-6500	56	12	robust	robust	ADJ
ejpam-6500	56	13	tool	tool	NOUN
ejpam-6500	56	14	for	for	ADP
ejpam-6500	56	15	analyzing	analyze	VERB
ejpam-6500	56	16	logical	logical	ADJ
ejpam-6500	56	17	structures	structure	NOUN
ejpam-6500	56	18	and	and	CCONJ
ejpam-6500	56	19	addressing	address	VERB
ejpam-6500	56	20	applications	application	NOUN
ejpam-6500	56	21	in	in	ADP
ejpam-6500	56	22	fuzzy	fuzzy	ADJ
ejpam-6500	56	23	logic	logic	NOUN
ejpam-6500	56	24	,	,	PUNCT
ejpam-6500	56	25	decision	decision	NOUN
ejpam-6500	56	26	-	-	PUNCT
ejpam-6500	56	27	making	making	NOUN
ejpam-6500	56	28	,	,	PUNCT
ejpam-6500	56	29	and	and	CCONJ
ejpam-6500	56	30	computational	computational	ADJ
ejpam-6500	56	31	frameworks	framework	NOUN
ejpam-6500	56	32	.	.	PUNCT
ejpam-6500	57	1	their	their	PRON
ejpam-6500	57	2	study	study	NOUN
ejpam-6500	57	3	deepens	deepen	VERB
ejpam-6500	57	4	the	the	DET
ejpam-6500	57	5	theoretical	theoretical	ADJ
ejpam-6500	57	6	foundation	foundation	NOUN
ejpam-6500	57	7	of	of	ADP
ejpam-6500	57	8	algebraic	algebraic	PROPN
ejpam-6500	57	9	systems	system	NOUN
ejpam-6500	57	10	and	and	CCONJ
ejpam-6500	57	11	offers	offer	VERB
ejpam-6500	57	12	practical	practical	ADJ
ejpam-6500	57	13	models	model	NOUN
ejpam-6500	57	14	for	for	ADP
ejpam-6500	57	15	uncertainty	uncertainty	NOUN
ejpam-6500	57	16	and	and	CCONJ
ejpam-6500	57	17	vagueness	vagueness	NOUN
ejpam-6500	57	18	.	.	PUNCT
ejpam-6500	58	1	definition	definition	NOUN
ejpam-6500	58	2	1	1	NUM
ejpam-6500	58	3	.	.	PUNCT
ejpam-6500	59	1	[	[	X
ejpam-6500	59	2	1	1	X
ejpam-6500	59	3	]	]	PUNCT
ejpam-6500	59	4	let	let	NOUN
ejpam-6500	59	5	h	h	NOUN
ejpam-6500	59	6	=	=	SYM
ejpam-6500	59	7	⟨h	⟨h	PROPN
ejpam-6500	59	8	,	,	PUNCT
ejpam-6500	59	9	|⟩	|⟩	PROPN
ejpam-6500	59	10	be	be	VERB
ejpam-6500	59	11	a	a	DET
ejpam-6500	59	12	groupoid	groupoid	NOUN
ejpam-6500	59	13	.	.	PUNCT
ejpam-6500	60	1	the	the	DET
ejpam-6500	60	2	operation	operation	NOUN
ejpam-6500	60	3	|	|	ADV
ejpam-6500	60	4	is	be	AUX
ejpam-6500	60	5	said	say	VERB
ejpam-6500	60	6	to	to	PART
ejpam-6500	60	7	be	be	AUX
ejpam-6500	60	8	a	a	DET
ejpam-6500	60	9	sheffer	sheffer	NOUN
ejpam-6500	60	10	stroke	stroke	NOUN
ejpam-6500	60	11	operation	operation	NOUN
ejpam-6500	60	12	if	if	SCONJ
ejpam-6500	60	13	it	it	PRON
ejpam-6500	60	14	satisfies	satisfy	VERB
ejpam-6500	60	15	the	the	DET
ejpam-6500	60	16	following	follow	VERB
ejpam-6500	60	17	conditions	condition	NOUN
ejpam-6500	60	18	:	:	PUNCT
ejpam-6500	60	19	(	(	PUNCT
ejpam-6500	60	20	s1	s1	NOUN
ejpam-6500	60	21	)	)	PUNCT
ejpam-6500	60	22	(	(	PUNCT
ejpam-6500	60	23	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	PROPN
ejpam-6500	60	24	)	)	PUNCT
ejpam-6500	60	25	)	)	PUNCT
ejpam-6500	61	1	=	=	SYM
ejpam-6500	61	2	y|x	y|x	NOUN
ejpam-6500	61	3	(	(	PUNCT
ejpam-6500	61	4	s2	s2	PROPN
ejpam-6500	61	5	)	)	PUNCT
ejpam-6500	61	6	(	(	PUNCT
ejpam-6500	61	7	x|x)|((x|(y|y))|(x|(y|y	x|x)|((x|(y|y))|(x|(y|y	PROPN
ejpam-6500	61	8	)	)	PUNCT
ejpam-6500	61	9	)	)	PUNCT
ejpam-6500	61	10	)	)	PUNCT
ejpam-6500	62	1	=	=	PUNCT
ejpam-6500	62	2	x	x	X
ejpam-6500	62	3	(	(	PUNCT
ejpam-6500	62	4	s3	s3	PROPN
ejpam-6500	62	5	)	)	PUNCT
ejpam-6500	62	6	x|((y|z)|(y|z	x|((y|z)|(y|z	NUM
ejpam-6500	62	7	)	)	PUNCT
ejpam-6500	62	8	)	)	PUNCT
ejpam-6500	63	1	=	=	PUNCT
ejpam-6500	63	2	(	(	PUNCT
ejpam-6500	63	3	(	(	PUNCT
ejpam-6500	63	4	(	(	PUNCT
ejpam-6500	63	5	(	(	PUNCT
ejpam-6500	63	6	x|(y|y))|(x|(y|y))))|((x|(y|y))|(x|(y|y))))|z	x|(y|y))|(x|(y|y))))|((x|(y|y))|(x|(y|y))))|z	PROPN
ejpam-6500	63	7	(	(	PUNCT
ejpam-6500	63	8	s4	s4	PROPN
ejpam-6500	63	9	)	)	PUNCT
ejpam-6500	63	10	(	(	PUNCT
ejpam-6500	63	11	x|((x|x)|(y|y)))|(x|((x|x)|(y|y	x|((x|x)|(y|y)))|(x|((x|x)|(y|y	NUM
ejpam-6500	63	12	)	)	PUNCT
ejpam-6500	63	13	)	)	PUNCT
ejpam-6500	63	14	)	)	PUNCT
ejpam-6500	63	15	=	=	PUNCT
ejpam-6500	64	1	x.	x.	NOUN
ejpam-6500	64	2	t.	t.	PROPN
ejpam-6500	64	3	oner	oner	PROPN
ejpam-6500	64	4	et	et	PROPN
ejpam-6500	64	5	al	al	PROPN
ejpam-6500	64	6	.	.	PUNCT
ejpam-6500	64	7	/	/	SYM
ejpam-6500	64	8	eur	eur	PROPN
ejpam-6500	64	9	.	.	PUNCT
ejpam-6500	65	1	j.	j.	PROPN
ejpam-6500	65	2	pure	pure	PROPN
ejpam-6500	65	3	appl	appl	PROPN
ejpam-6500	65	4	.	.	PROPN
ejpam-6500	65	5	math	math	PROPN
ejpam-6500	65	6	,	,	PUNCT
ejpam-6500	65	7	18	18	NUM
ejpam-6500	65	8	(	(	PUNCT
ejpam-6500	65	9	3	3	NUM
ejpam-6500	65	10	)	)	PUNCT
ejpam-6500	65	11	(	(	PUNCT
ejpam-6500	65	12	2025	2025	NUM
ejpam-6500	65	13	)	)	PUNCT
ejpam-6500	65	14	,	,	PUNCT
ejpam-6500	65	15	6500	6500	NUM
ejpam-6500	65	16	4	4	NUM
ejpam-6500	65	17	of	of	ADP
ejpam-6500	65	18	13	13	NUM
ejpam-6500	65	19	definition	definition	NOUN
ejpam-6500	65	20	2	2	NUM
ejpam-6500	65	21	.	.	PUNCT
ejpam-6500	66	1	[	[	X
ejpam-6500	66	2	3	3	X
ejpam-6500	66	3	]	]	X
ejpam-6500	66	4	a	a	DET
ejpam-6500	66	5	sheffer	sheffer	NOUN
ejpam-6500	66	6	stroke	stroke	NOUN
ejpam-6500	66	7	hilbert	hilbert	PROPN
ejpam-6500	66	8	algebra	algebra	PROPN
ejpam-6500	66	9	is	be	AUX
ejpam-6500	66	10	a	a	DET
ejpam-6500	66	11	structure	structure	NOUN
ejpam-6500	66	12	h	h	NOUN
ejpam-6500	66	13	=	=	SYM
ejpam-6500	66	14	⟨h	⟨h	PROPN
ejpam-6500	66	15	,	,	PUNCT
ejpam-6500	66	16	|	|	ADV
ejpam-6500	66	17	,	,	PUNCT
ejpam-6500	66	18	0⟩	0⟩	PROPN
ejpam-6500	66	19	of	of	ADP
ejpam-6500	66	20	type	type	NOUN
ejpam-6500	66	21	(	(	PUNCT
ejpam-6500	66	22	2	2	NUM
ejpam-6500	66	23	,	,	PUNCT
ejpam-6500	66	24	0	0	NUM
ejpam-6500	66	25	)	)	PUNCT
ejpam-6500	66	26	,	,	PUNCT
ejpam-6500	66	27	in	in	ADP
ejpam-6500	66	28	which	which	PRON
ejpam-6500	66	29	h	h	NOUN
ejpam-6500	66	30	is	be	AUX
ejpam-6500	66	31	a	a	DET
ejpam-6500	66	32	non	non	ADJ
ejpam-6500	66	33	-	-	ADJ
ejpam-6500	66	34	empty	empty	ADJ
ejpam-6500	66	35	set	set	NOUN
ejpam-6500	66	36	,	,	PUNCT
ejpam-6500	66	37	|	|	ADV
ejpam-6500	66	38	is	be	AUX
ejpam-6500	66	39	a	a	DET
ejpam-6500	66	40	sheffer	sheffer	NOUN
ejpam-6500	66	41	stroke	stroke	NOUN
ejpam-6500	66	42	operation	operation	NOUN
ejpam-6500	66	43	on	on	ADP
ejpam-6500	66	44	h	h	NOUN
ejpam-6500	66	45	,	,	PUNCT
ejpam-6500	66	46	and	and	CCONJ
ejpam-6500	66	47	0	0	NUM
ejpam-6500	66	48	is	be	AUX
ejpam-6500	66	49	the	the	DET
ejpam-6500	66	50	fixed	fix	VERB
ejpam-6500	66	51	element	element	NOUN
ejpam-6500	66	52	in	in	ADP
ejpam-6500	66	53	h	h	NOUN
ejpam-6500	66	54	such	such	ADJ
ejpam-6500	66	55	that	that	SCONJ
ejpam-6500	66	56	the	the	DET
ejpam-6500	66	57	following	follow	VERB
ejpam-6500	66	58	identities	identity	NOUN
ejpam-6500	66	59	are	be	AUX
ejpam-6500	66	60	satisfied	satisfied	ADJ
ejpam-6500	66	61	for	for	ADP
ejpam-6500	66	62	all	all	DET
ejpam-6500	66	63	x	x	NOUN
ejpam-6500	66	64	,	,	PUNCT
ejpam-6500	66	65	y	y	PROPN
ejpam-6500	66	66	,	,	PUNCT
ejpam-6500	66	67	z	z	PROPN
ejpam-6500	66	68	∈	∈	PROPN
ejpam-6500	66	69	h	h	NOUN
ejpam-6500	66	70	:	:	PUNCT
ejpam-6500	66	71	(	(	PUNCT
ejpam-6500	66	72	1	1	X
ejpam-6500	66	73	)	)	PUNCT
ejpam-6500	66	74	(	(	PUNCT
ejpam-6500	66	75	x|((y|(z|z))|(y|(z|z))))|(((x|(y|y))|((x|(z|z))|(x|(z|z))))|	x|((y|(z|z))|(y|(z|z))))|(((x|(y|y))|((x|(z|z))|(x|(z|z))))|	X
ejpam-6500	66	76	(	(	PUNCT
ejpam-6500	66	77	(	(	PUNCT
ejpam-6500	66	78	x|(y|y))|((x|(z|z))|(x|(z|z	x|(y|y))|((x|(z|z))|(x|(z|z	NOUN
ejpam-6500	66	79	)	)	PUNCT
ejpam-6500	66	80	)	)	PUNCT
ejpam-6500	66	81	)	)	PUNCT
ejpam-6500	66	82	)	)	PUNCT
ejpam-6500	66	83	)	)	PUNCT
ejpam-6500	67	1	=	=	SYM
ejpam-6500	67	2	x|(x|x	x|(x|x	PROPN
ejpam-6500	67	3	)	)	PUNCT
ejpam-6500	67	4	(	(	PUNCT
ejpam-6500	67	5	2	2	X
ejpam-6500	67	6	)	)	PUNCT
ejpam-6500	67	7	x|(y|y	x|(y|y	NUM
ejpam-6500	67	8	)	)	PUNCT
ejpam-6500	67	9	=	=	SYM
ejpam-6500	67	10	y|(x|x	y|(x|x	PROPN
ejpam-6500	67	11	)	)	PUNCT
ejpam-6500	67	12	⇒	⇒	NOUN
ejpam-6500	67	13	x	x	PUNCT
ejpam-6500	68	1	=	=	PUNCT
ejpam-6500	68	2	y.	y.	NOUN
ejpam-6500	68	3	proposition	proposition	NOUN
ejpam-6500	68	4	1	1	NUM
ejpam-6500	68	5	.	.	PUNCT
ejpam-6500	69	1	[	[	X
ejpam-6500	69	2	3	3	X
ejpam-6500	69	3	]	]	X
ejpam-6500	69	4	let	let	NOUN
ejpam-6500	69	5	h	h	NOUN
ejpam-6500	69	6	=	=	SYM
ejpam-6500	69	7	⟨h	⟨h	PROPN
ejpam-6500	69	8	,	,	PUNCT
ejpam-6500	69	9	|	|	ADV
ejpam-6500	69	10	,	,	PUNCT
ejpam-6500	69	11	0⟩	0⟩	PROPN
ejpam-6500	69	12	be	be	VERB
ejpam-6500	69	13	a	a	DET
ejpam-6500	69	14	sheffer	sheffer	NOUN
ejpam-6500	69	15	stroke	stroke	NOUN
ejpam-6500	69	16	hilbert	hilbert	PROPN
ejpam-6500	69	17	algebra	algebra	PROPN
ejpam-6500	69	18	.	.	PUNCT
ejpam-6500	70	1	then	then	ADV
ejpam-6500	70	2	the	the	DET
ejpam-6500	70	3	binary	binary	PROPN
ejpam-6500	70	4	relation	relation	PROPN
ejpam-6500	70	5	x	x	SYM
ejpam-6500	70	6	≤	≤	ADJ
ejpam-6500	70	7	y	y	NOUN
ejpam-6500	70	8	if	if	SCONJ
ejpam-6500	71	1	and	and	CCONJ
ejpam-6500	71	2	only	only	ADV
ejpam-6500	71	3	if	if	SCONJ
ejpam-6500	71	4	(	(	PUNCT
ejpam-6500	71	5	x|(y|y	x|(y|y	PROPN
ejpam-6500	71	6	)	)	PUNCT
ejpam-6500	71	7	)	)	PUNCT
ejpam-6500	72	1	=	=	SYM
ejpam-6500	72	2	0	0	NUM
ejpam-6500	72	3	is	be	AUX
ejpam-6500	72	4	a	a	DET
ejpam-6500	72	5	partial	partial	ADJ
ejpam-6500	72	6	order	order	NOUN
ejpam-6500	72	7	on	on	ADP
ejpam-6500	72	8	h.	h.	PROPN
ejpam-6500	72	9	definition	definition	NOUN
ejpam-6500	72	10	3	3	NUM
ejpam-6500	72	11	.	.	PUNCT
ejpam-6500	73	1	[	[	X
ejpam-6500	73	2	3	3	X
ejpam-6500	73	3	]	]	PUNCT
ejpam-6500	73	4	a	a	DET
ejpam-6500	73	5	nonempty	nonempty	NOUN
ejpam-6500	73	6	subset	subset	VERB
ejpam-6500	73	7	g	g	NOUN
ejpam-6500	73	8	of	of	ADP
ejpam-6500	73	9	a	a	DET
ejpam-6500	73	10	sheffer	sheffer	NOUN
ejpam-6500	73	11	stroke	stroke	NOUN
ejpam-6500	73	12	hilbert	hilbert	PROPN
ejpam-6500	73	13	algebra	algebra	PROPN
ejpam-6500	73	14	h	h	PROPN
ejpam-6500	73	15	=	=	SYM
ejpam-6500	73	16	⟨h	⟨h	PROPN
ejpam-6500	73	17	,	,	PUNCT
ejpam-6500	73	18	|	|	ADV
ejpam-6500	73	19	,	,	PUNCT
ejpam-6500	73	20	0⟩	0⟩	PROPN
ejpam-6500	73	21	is	be	AUX
ejpam-6500	73	22	called	call	VERB
ejpam-6500	73	23	a	a	DET
ejpam-6500	73	24	subalgebra	subalgebra	NOUN
ejpam-6500	73	25	of	of	ADP
ejpam-6500	73	26	h	h	NOUN
ejpam-6500	73	27	if	if	SCONJ
ejpam-6500	73	28	(	(	PUNCT
ejpam-6500	73	29	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	73	30	)	)	PUNCT
ejpam-6500	73	31	)	)	PUNCT
ejpam-6500	74	1	∈	∈	PROPN
ejpam-6500	74	2	g	g	NOUN
ejpam-6500	74	3	for	for	ADP
ejpam-6500	74	4	all	all	DET
ejpam-6500	74	5	x	x	NOUN
ejpam-6500	74	6	,	,	PUNCT
ejpam-6500	74	7	y	y	PROPN
ejpam-6500	74	8	∈	∈	PROPN
ejpam-6500	74	9	g.	g.	NOUN
ejpam-6500	74	10	definition	definition	NOUN
ejpam-6500	74	11	4	4	NUM
ejpam-6500	74	12	.	.	PUNCT
ejpam-6500	75	1	a	a	DET
ejpam-6500	75	2	fuzzy	fuzzy	ADJ
ejpam-6500	75	3	set	set	VERB
ejpam-6500	75	4	µ	µ	NOUN
ejpam-6500	75	5	in	in	ADP
ejpam-6500	75	6	a	a	DET
ejpam-6500	75	7	non	non	ADJ
ejpam-6500	75	8	-	-	ADJ
ejpam-6500	75	9	empty	empty	ADJ
ejpam-6500	75	10	set	set	NOUN
ejpam-6500	75	11	x	x	PUNCT
ejpam-6500	75	12	of	of	ADP
ejpam-6500	75	13	the	the	DET
ejpam-6500	75	14	form	form	NOUN
ejpam-6500	75	15	µ	µ	X
ejpam-6500	75	16	=	=	PUNCT
ejpam-6500	75	17	{	{	PUNCT
ejpam-6500	75	18	t	t	PROPN
ejpam-6500	75	19	∈	∈	PROPN
ejpam-6500	75	20	(	(	PUNCT
ejpam-6500	75	21	0	0	NUM
ejpam-6500	75	22	,	,	PUNCT
ejpam-6500	75	23	1	1	NUM
ejpam-6500	75	24	]	]	PUNCT
ejpam-6500	75	25	if	if	SCONJ
ejpam-6500	75	26	y	y	PROPN
ejpam-6500	75	27	=	=	PUNCT
ejpam-6500	75	28	x	x	SYM
ejpam-6500	75	29	0	0	PUNCT
ejpam-6500	75	30	if	if	SCONJ
ejpam-6500	75	31	y	y	PROPN
ejpam-6500	75	32	̸=	̸=	PROPN
ejpam-6500	75	33	x	x	NUM
ejpam-6500	75	34	is	be	AUX
ejpam-6500	75	35	said	say	VERB
ejpam-6500	75	36	to	to	PART
ejpam-6500	75	37	be	be	AUX
ejpam-6500	75	38	a	a	DET
ejpam-6500	75	39	fuzzy	fuzzy	ADJ
ejpam-6500	75	40	point	point	NOUN
ejpam-6500	75	41	with	with	ADP
ejpam-6500	75	42	support	support	NOUN
ejpam-6500	75	43	x	x	PUNCT
ejpam-6500	75	44	and	and	CCONJ
ejpam-6500	75	45	value	value	NOUN
ejpam-6500	75	46	t	t	PROPN
ejpam-6500	75	47	and	and	CCONJ
ejpam-6500	75	48	is	be	AUX
ejpam-6500	75	49	denoted	denote	VERB
ejpam-6500	75	50	by	by	ADP
ejpam-6500	75	51	xt	xt	PROPN
ejpam-6500	75	52	.	.	PUNCT
ejpam-6500	76	1	the	the	DET
ejpam-6500	76	2	general	general	ADJ
ejpam-6500	76	3	form	form	NOUN
ejpam-6500	76	4	of	of	ADP
ejpam-6500	76	5	the	the	DET
ejpam-6500	76	6	symbol	symbol	NOUN
ejpam-6500	76	7	xt	xt	PUNCT
ejpam-6500	76	8	q	q	PROPN
ejpam-6500	76	9	λ	λ	PROPN
ejpam-6500	76	10	as	as	SCONJ
ejpam-6500	76	11	follows	follow	VERB
ejpam-6500	76	12	:	:	PUNCT
ejpam-6500	76	13	for	for	ADP
ejpam-6500	76	14	an	an	DET
ejpam-6500	76	15	arbitrary	arbitrary	ADJ
ejpam-6500	76	16	element	element	NOUN
ejpam-6500	76	17	k	k	NOUN
ejpam-6500	76	18	of	of	ADP
ejpam-6500	76	19	[	[	X
ejpam-6500	76	20	0	0	NUM
ejpam-6500	76	21	,	,	PUNCT
ejpam-6500	76	22	1	1	NUM
ejpam-6500	76	23	)	)	PUNCT
ejpam-6500	76	24	,	,	PUNCT
ejpam-6500	76	25	we	we	PRON
ejpam-6500	76	26	say	say	VERB
ejpam-6500	76	27	that	that	SCONJ
ejpam-6500	76	28	•	•	NUM
ejpam-6500	76	29	xt	xt	ADP
ejpam-6500	76	30	qk	qk	NOUN
ejpam-6500	76	31	λ	λ	PROPN
ejpam-6500	76	32	if	if	SCONJ
ejpam-6500	76	33	λ(x	λ(x	PROPN
ejpam-6500	76	34	)	)	PUNCT
ejpam-6500	77	1	+	+	CCONJ
ejpam-6500	77	2	t+	t+	VERB
ejpam-6500	77	3	k	k	X
ejpam-6500	77	4	>	>	X
ejpam-6500	77	5	1	1	NUM
ejpam-6500	77	6	.	.	NUM
ejpam-6500	77	7	•	•	NUM
ejpam-6500	77	8	xt	xt	X
ejpam-6500	77	9	∈	∈	PROPN
ejpam-6500	77	10	∨qkλ	∨qkλ	NOUN
ejpam-6500	77	11	if	if	SCONJ
ejpam-6500	77	12	xt	xt	ADP
ejpam-6500	77	13	∈	∈	PROPN
ejpam-6500	77	14	λ	λ	PROPN
ejpam-6500	77	15	or	or	CCONJ
ejpam-6500	77	16	xtqkλ	xtqkλ	ADJ
ejpam-6500	77	17	.	.	PUNCT
ejpam-6500	78	1	3	3	X
ejpam-6500	78	2	.	.	X
ejpam-6500	78	3	new	new	ADJ
ejpam-6500	78	4	fuzzy	fuzzy	ADJ
ejpam-6500	78	5	subalgebras	subalgebra	NOUN
ejpam-6500	78	6	of	of	ADP
ejpam-6500	78	7	sheffer	sheffer	PROPN
ejpam-6500	78	8	stroke	stroke	PROPN
ejpam-6500	78	9	hilbert	hilbert	PROPN
ejpam-6500	78	10	algebras	algebras	PROPN
ejpam-6500	78	11	in	in	ADP
ejpam-6500	78	12	this	this	DET
ejpam-6500	78	13	section	section	NOUN
ejpam-6500	78	14	,	,	PUNCT
ejpam-6500	78	15	let	let	VERB
ejpam-6500	78	16	h	h	NOUN
ejpam-6500	78	17	=	=	SYM
ejpam-6500	78	18	⟨h	⟨h	PROPN
ejpam-6500	78	19	,	,	PUNCT
ejpam-6500	78	20	|	|	ADV
ejpam-6500	78	21	,	,	PUNCT
ejpam-6500	78	22	0⟩	0⟩	PROPN
ejpam-6500	78	23	denote	denote	VERB
ejpam-6500	78	24	the	the	DET
ejpam-6500	78	25	sheffer	sheffer	NOUN
ejpam-6500	78	26	stroke	stroke	NOUN
ejpam-6500	78	27	hilbert	hilbert	PROPN
ejpam-6500	78	28	algebra	algebra	PROPN
ejpam-6500	78	29	unless	unless	SCONJ
ejpam-6500	78	30	otherwise	otherwise	ADV
ejpam-6500	78	31	specified	specify	VERB
ejpam-6500	78	32	.	.	PUNCT
ejpam-6500	79	1	definition	definition	NOUN
ejpam-6500	79	2	5	5	NUM
ejpam-6500	79	3	.	.	PUNCT
ejpam-6500	80	1	a	a	DET
ejpam-6500	80	2	fuzzy	fuzzy	ADJ
ejpam-6500	80	3	set	set	VERB
ejpam-6500	80	4	µ	µ	NOUN
ejpam-6500	80	5	in	in	ADP
ejpam-6500	80	6	h	h	NOUN
ejpam-6500	80	7	is	be	AUX
ejpam-6500	80	8	called	call	VERB
ejpam-6500	80	9	an	an	DET
ejpam-6500	80	10	(	(	PUNCT
ejpam-6500	80	11	∈,∈	∈,∈	X
ejpam-6500	80	12	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-6500	80	13	subalgebra	subalgebra	NOUN
ejpam-6500	80	14	of	of	ADP
ejpam-6500	80	15	h	h	NOUN
ejpam-6500	80	16	=	=	SYM
ejpam-6500	80	17	⟨h	⟨h	PROPN
ejpam-6500	80	18	,	,	PUNCT
ejpam-6500	80	19	|	|	ADV
ejpam-6500	80	20	,	,	PUNCT
ejpam-6500	80	21	0⟩	0⟩	PROPN
ejpam-6500	80	22	,	,	PUNCT
ejpam-6500	80	23	if	if	SCONJ
ejpam-6500	80	24	it	it	PRON
ejpam-6500	80	25	satisfies	satisfy	VERB
ejpam-6500	80	26	(	(	PUNCT
ejpam-6500	80	27	∀x	∀x	X
ejpam-6500	80	28	,	,	PUNCT
ejpam-6500	80	29	y	y	PROPN
ejpam-6500	80	30	∈	∈	PROPN
ejpam-6500	80	31	h	h	NOUN
ejpam-6500	80	32	,	,	PUNCT
ejpam-6500	80	33	t1	t1	PROPN
ejpam-6500	80	34	,	,	PUNCT
ejpam-6500	80	35	t2	t2	NOUN
ejpam-6500	80	36	∈	∈	PROPN
ejpam-6500	80	37	(	(	PUNCT
ejpam-6500	80	38	0	0	NUM
ejpam-6500	80	39	,	,	PUNCT
ejpam-6500	80	40	1])(xt1	1])(xt1	NOUN
ejpam-6500	80	41	,	,	PUNCT
ejpam-6500	80	42	yt2	yt2	PROPN
ejpam-6500	80	43	∈	∈	PROPN
ejpam-6500	80	44	µ	µ	PRON
ejpam-6500	80	45	⇒	⇒	X
ejpam-6500	80	46	(	(	PUNCT
ejpam-6500	80	47	(	(	PUNCT
ejpam-6500	80	48	x|(y|y))|(x|(y|y)))min{t1,t2	x|(y|y))|(x|(y|y)))min{t1,t2	NOUN
ejpam-6500	80	49	}	}	PUNCT
ejpam-6500	80	50	∈	∈	PROPN
ejpam-6500	80	51	∨qµ	∨qµ	NOUN
ejpam-6500	80	52	)	)	PUNCT
ejpam-6500	80	53	.	.	PUNCT
ejpam-6500	81	1	(	(	PUNCT
ejpam-6500	81	2	1	1	X
ejpam-6500	81	3	)	)	PUNCT
ejpam-6500	81	4	remark	remark	NOUN
ejpam-6500	81	5	1	1	NUM
ejpam-6500	81	6	.	.	PUNCT
ejpam-6500	82	1	let	let	VERB
ejpam-6500	82	2	m	m	PRON
ejpam-6500	82	3	be	be	AUX
ejpam-6500	82	4	an	an	DET
ejpam-6500	82	5	element	element	NOUN
ejpam-6500	82	6	of	of	ADP
ejpam-6500	82	7	[	[	X
ejpam-6500	82	8	0	0	NUM
ejpam-6500	82	9	,	,	PUNCT
ejpam-6500	82	10	1	1	NUM
ejpam-6500	82	11	)	)	PUNCT
ejpam-6500	82	12	unless	unless	SCONJ
ejpam-6500	82	13	otherwise	otherwise	ADV
ejpam-6500	82	14	specified	specify	VERB
ejpam-6500	82	15	.	.	PUNCT
ejpam-6500	83	1	by	by	ADP
ejpam-6500	83	2	xtqmµ	xtqmµ	PROPN
ejpam-6500	83	3	,	,	PUNCT
ejpam-6500	83	4	we	we	PRON
ejpam-6500	83	5	mean	mean	VERB
ejpam-6500	83	6	µ(x	µ(x	X
ejpam-6500	83	7	)	)	PUNCT
ejpam-6500	84	1	+	+	CCONJ
ejpam-6500	85	1	t+m	t+m	PRON
ejpam-6500	85	2	>	>	SYM
ejpam-6500	85	3	1	1	NUM
ejpam-6500	85	4	,	,	PUNCT
ejpam-6500	85	5	t	t	PROPN
ejpam-6500	85	6	∈	∈	PROPN
ejpam-6500	85	7	(	(	PUNCT
ejpam-6500	85	8	0	0	NUM
ejpam-6500	85	9	,	,	PUNCT
ejpam-6500	85	10	1−m	1−m	NUM
ejpam-6500	85	11	2	2	NUM
ejpam-6500	85	12	]	]	PUNCT
ejpam-6500	85	13	.	.	PUNCT
ejpam-6500	86	1	the	the	DET
ejpam-6500	86	2	notation	notation	NOUN
ejpam-6500	86	3	xt	xt	PROPN
ejpam-6500	86	4	∈	∈	PROPN
ejpam-6500	86	5	∨qmµ	∨qmµ	PROPN
ejpam-6500	86	6	means	mean	VERB
ejpam-6500	86	7	that	that	SCONJ
ejpam-6500	86	8	xt	xt	PROPN
ejpam-6500	86	9	∈	∈	PROPN
ejpam-6500	86	10	µ	µ	X
ejpam-6500	86	11	or	or	CCONJ
ejpam-6500	86	12	xtqmµ.	xtqmµ.	NOUN
ejpam-6500	86	13	definition	definition	NOUN
ejpam-6500	86	14	6	6	NUM
ejpam-6500	86	15	.	.	PUNCT
ejpam-6500	87	1	a	a	DET
ejpam-6500	87	2	fuzzy	fuzzy	ADJ
ejpam-6500	87	3	set	set	VERB
ejpam-6500	87	4	µ	µ	NOUN
ejpam-6500	87	5	in	in	ADP
ejpam-6500	87	6	h	h	NOUN
ejpam-6500	87	7	is	be	AUX
ejpam-6500	87	8	called	call	VERB
ejpam-6500	87	9	an	an	DET
ejpam-6500	87	10	(	(	PUNCT
ejpam-6500	87	11	∈,∈	∈,∈	X
ejpam-6500	87	12	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	87	13	subalgebra	subalgebra	NOUN
ejpam-6500	87	14	of	of	ADP
ejpam-6500	87	15	h	h	NOUN
ejpam-6500	87	16	if	if	SCONJ
ejpam-6500	87	17	(	(	PUNCT
ejpam-6500	87	18	∀x	∀x	X
ejpam-6500	87	19	,	,	PUNCT
ejpam-6500	87	20	y	y	PROPN
ejpam-6500	87	21	∈	∈	PROPN
ejpam-6500	87	22	h	h	NOUN
ejpam-6500	87	23	,	,	PUNCT
ejpam-6500	87	24	t1	t1	PROPN
ejpam-6500	87	25	,	,	PUNCT
ejpam-6500	87	26	t2	t2	NOUN
ejpam-6500	87	27	∈	∈	PROPN
ejpam-6500	87	28	(	(	PUNCT
ejpam-6500	87	29	0	0	NUM
ejpam-6500	87	30	,	,	PUNCT
ejpam-6500	87	31	1])(xt1	1])(xt1	NOUN
ejpam-6500	87	32	,	,	PUNCT
ejpam-6500	87	33	yt2	yt2	PROPN
ejpam-6500	87	34	∈	∈	PROPN
ejpam-6500	87	35	µ	µ	PRON
ejpam-6500	87	36	⇒	⇒	X
ejpam-6500	87	37	(	(	PUNCT
ejpam-6500	87	38	(	(	PUNCT
ejpam-6500	87	39	x|(y|y))|(x|(y|y)))min{t1,t2	x|(y|y))|(x|(y|y)))min{t1,t2	NOUN
ejpam-6500	87	40	}	}	PUNCT
ejpam-6500	87	41	∈	∈	PROPN
ejpam-6500	87	42	∨qmµ	∨qmµ	PROPN
ejpam-6500	87	43	)	)	PUNCT
ejpam-6500	87	44	.	.	PUNCT
ejpam-6500	88	1	(	(	PUNCT
ejpam-6500	88	2	2	2	X
ejpam-6500	88	3	)	)	PUNCT
ejpam-6500	88	4	we	we	PRON
ejpam-6500	88	5	note	note	VERB
ejpam-6500	88	6	that	that	SCONJ
ejpam-6500	88	7	different	different	ADJ
ejpam-6500	88	8	types	type	NOUN
ejpam-6500	88	9	of	of	ADP
ejpam-6500	88	10	fuzzy	fuzzy	ADJ
ejpam-6500	88	11	subalgebras	subalgebras	PROPN
ejpam-6500	88	12	can	can	AUX
ejpam-6500	88	13	be	be	AUX
ejpam-6500	88	14	constructed	construct	VERB
ejpam-6500	88	15	for	for	ADP
ejpam-6500	88	16	different	different	ADJ
ejpam-6500	88	17	values	value	NOUN
ejpam-6500	88	18	of	of	ADP
ejpam-6500	88	19	m	m	PROPN
ejpam-6500	88	20	∈	∈	PROPN
ejpam-6500	89	1	[	[	X
ejpam-6500	89	2	0	0	NUM
ejpam-6500	89	3	,	,	PUNCT
ejpam-6500	89	4	1	1	NUM
ejpam-6500	89	5	)	)	PUNCT
ejpam-6500	89	6	.	.	PUNCT
ejpam-6500	90	1	hence	hence	ADV
ejpam-6500	90	2	,	,	PUNCT
ejpam-6500	90	3	an	an	DET
ejpam-6500	90	4	(	(	PUNCT
ejpam-6500	90	5	∈,∈	∈,∈	X
ejpam-6500	90	6	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	90	7	subalgebra	subalgebra	NOUN
ejpam-6500	90	8	with	with	ADP
ejpam-6500	90	9	m	m	PROPN
ejpam-6500	90	10	=	=	SYM
ejpam-6500	90	11	0	0	NUM
ejpam-6500	90	12	is	be	AUX
ejpam-6500	90	13	called	call	VERB
ejpam-6500	90	14	an	an	DET
ejpam-6500	90	15	(	(	PUNCT
ejpam-6500	90	16	∈,∈	∈,∈	X
ejpam-6500	90	17	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-6500	90	18	subalgebra	subalgebra	NOUN
ejpam-6500	90	19	.	.	PUNCT
ejpam-6500	91	1	t.	t.	PROPN
ejpam-6500	91	2	oner	oner	PROPN
ejpam-6500	91	3	et	et	PROPN
ejpam-6500	91	4	al	al	PROPN
ejpam-6500	91	5	.	.	PUNCT
ejpam-6500	91	6	/	/	SYM
ejpam-6500	91	7	eur	eur	PROPN
ejpam-6500	91	8	.	.	PUNCT
ejpam-6500	92	1	j.	j.	PROPN
ejpam-6500	92	2	pure	pure	PROPN
ejpam-6500	92	3	appl	appl	PROPN
ejpam-6500	92	4	.	.	PROPN
ejpam-6500	92	5	math	math	PROPN
ejpam-6500	92	6	,	,	PUNCT
ejpam-6500	92	7	18	18	NUM
ejpam-6500	92	8	(	(	PUNCT
ejpam-6500	92	9	3	3	NUM
ejpam-6500	92	10	)	)	PUNCT
ejpam-6500	92	11	(	(	PUNCT
ejpam-6500	92	12	2025	2025	NUM
ejpam-6500	92	13	)	)	PUNCT
ejpam-6500	92	14	,	,	PUNCT
ejpam-6500	92	15	6500	6500	NUM
ejpam-6500	92	16	5	5	NUM
ejpam-6500	92	17	of	of	ADP
ejpam-6500	92	18	13	13	NUM
ejpam-6500	92	19	proposition	proposition	NOUN
ejpam-6500	92	20	2	2	NUM
ejpam-6500	92	21	.	.	PUNCT
ejpam-6500	93	1	every	every	PRON
ejpam-6500	93	2	(	(	PUNCT
ejpam-6500	93	3	∈,∈)-fuzzy	∈,∈)-fuzzy	ADJ
ejpam-6500	93	4	subalgebra	subalgebra	NOUN
ejpam-6500	93	5	is	be	AUX
ejpam-6500	93	6	an	an	DET
ejpam-6500	93	7	(	(	PUNCT
ejpam-6500	93	8	∈,∈	∈,∈	INTJ
ejpam-6500	93	9	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	93	10	subalgebra	subalgebra	NOUN
ejpam-6500	93	11	.	.	PUNCT
ejpam-6500	94	1	proof	proof	NOUN
ejpam-6500	94	2	.	.	PUNCT
ejpam-6500	95	1	straightforward	straightforward	ADJ
ejpam-6500	95	2	.	.	PUNCT
ejpam-6500	96	1	theorem	theorem	NOUN
ejpam-6500	96	2	1	1	NUM
ejpam-6500	96	3	.	.	PUNCT
ejpam-6500	97	1	a	a	DET
ejpam-6500	97	2	fuzzy	fuzzy	ADJ
ejpam-6500	97	3	set	set	VERB
ejpam-6500	97	4	µ	µ	NOUN
ejpam-6500	97	5	in	in	ADP
ejpam-6500	97	6	h	h	NOUN
ejpam-6500	97	7	is	be	AUX
ejpam-6500	97	8	an	an	DET
ejpam-6500	97	9	(	(	PUNCT
ejpam-6500	97	10	∈,∈	∈,∈	INTJ
ejpam-6500	97	11	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	97	12	subalgebra	subalgebra	NOUN
ejpam-6500	97	13	of	of	ADP
ejpam-6500	97	14	h	h	NOUN
ejpam-6500	97	15	if	if	SCONJ
ejpam-6500	97	16	and	and	CCONJ
ejpam-6500	97	17	only	only	ADV
ejpam-6500	97	18	if	if	SCONJ
ejpam-6500	97	19	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	97	20	)	)	PUNCT
ejpam-6500	97	21	)	)	PUNCT
ejpam-6500	97	22	)	)	PUNCT
ejpam-6500	97	23	≥	≥	NOUN
ejpam-6500	98	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	98	2	)	)	PUNCT
ejpam-6500	98	3	,	,	PUNCT
ejpam-6500	98	4	µ(y	µ(y	PROPN
ejpam-6500	98	5	)	)	PUNCT
ejpam-6500	98	6	,	,	PUNCT
ejpam-6500	98	7	1−m	1−m	NUM
ejpam-6500	98	8	2	2	NUM
ejpam-6500	98	9	}	}	PUNCT
ejpam-6500	98	10	holds	hold	VERB
ejpam-6500	98	11	for	for	ADP
ejpam-6500	98	12	all	all	DET
ejpam-6500	98	13	x	x	NOUN
ejpam-6500	98	14	,	,	PUNCT
ejpam-6500	98	15	y	y	PROPN
ejpam-6500	98	16	∈	∈	PROPN
ejpam-6500	98	17	h.	h.	NOUN
ejpam-6500	98	18	proof	proof	NOUN
ejpam-6500	98	19	.	.	PUNCT
ejpam-6500	99	1	let	let	VERB
ejpam-6500	99	2	µ	µ	X
ejpam-6500	99	3	be	be	AUX
ejpam-6500	99	4	an	an	DET
ejpam-6500	99	5	(	(	PUNCT
ejpam-6500	99	6	∈,∈	∈,∈	INTJ
ejpam-6500	99	7	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	99	8	subalgebra	subalgebra	NOUN
ejpam-6500	99	9	of	of	ADP
ejpam-6500	99	10	h.	h.	PROPN
ejpam-6500	99	11	assume	assume	VERB
ejpam-6500	99	12	that	that	SCONJ
ejpam-6500	99	13	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	VERB
ejpam-6500	99	14	)	)	PUNCT
ejpam-6500	99	15	)	)	PUNCT
ejpam-6500	99	16	)	)	PUNCT
ejpam-6500	99	17	≥	≥	NOUN
ejpam-6500	100	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	100	2	)	)	PUNCT
ejpam-6500	100	3	,	,	PUNCT
ejpam-6500	100	4	µ(y	µ(y	PROPN
ejpam-6500	100	5	)	)	PUNCT
ejpam-6500	100	6	,	,	PUNCT
ejpam-6500	100	7	1−m	1−m	NUM
ejpam-6500	100	8	2	2	NUM
ejpam-6500	100	9	}	}	PUNCT
ejpam-6500	100	10	is	be	AUX
ejpam-6500	100	11	not	not	PART
ejpam-6500	100	12	true	true	ADJ
ejpam-6500	100	13	.	.	PUNCT
ejpam-6500	101	1	then	then	ADV
ejpam-6500	101	2	there	there	PRON
ejpam-6500	101	3	exist	exist	VERB
ejpam-6500	101	4	x′	x′	NUM
ejpam-6500	101	5	,	,	PUNCT
ejpam-6500	101	6	y′	y′	NOUN
ejpam-6500	101	7	∈	∈	PROPN
ejpam-6500	101	8	h	h	NOUN
ejpam-6500	101	9	such	such	ADJ
ejpam-6500	102	1	that	that	SCONJ
ejpam-6500	102	2	µ((x′|(y′|y′))|(x′|(y′|y′	µ((x′|(y′|y′))|(x′|(y′|y′	NUM
ejpam-6500	102	3	)	)	PUNCT
ejpam-6500	102	4	)	)	PUNCT
ejpam-6500	102	5	)	)	PUNCT
ejpam-6500	103	1	<	<	X
ejpam-6500	103	2	min{µ(x′	min{µ(x′	PROPN
ejpam-6500	103	3	)	)	PUNCT
ejpam-6500	103	4	,	,	PUNCT
ejpam-6500	103	5	µ(y′	µ(y′	NUM
ejpam-6500	103	6	)	)	PUNCT
ejpam-6500	103	7	,	,	PUNCT
ejpam-6500	103	8	1−m	1−m	NUM
ejpam-6500	103	9	2	2	NUM
ejpam-6500	103	10	}	}	PUNCT
ejpam-6500	103	11	.	.	PUNCT
ejpam-6500	104	1	if	if	SCONJ
ejpam-6500	104	2	min{µ(x′	min{µ(x′	NOUN
ejpam-6500	104	3	)	)	PUNCT
ejpam-6500	104	4	,	,	PUNCT
ejpam-6500	104	5	µ(y′	µ(y′	ADV
ejpam-6500	104	6	)	)	PUNCT
ejpam-6500	104	7	}	}	PUNCT
ejpam-6500	104	8	<	<	X
ejpam-6500	104	9	1−m	1−m	NUM
ejpam-6500	104	10	2	2	NUM
ejpam-6500	104	11	,	,	PUNCT
ejpam-6500	104	12	then	then	ADV
ejpam-6500	104	13	µ((x′|(y′|y′))|(x′|(y′|y′	µ((x′|(y′|y′))|(x′|(y′|y′	NUM
ejpam-6500	104	14	)	)	PUNCT
ejpam-6500	104	15	)	)	PUNCT
ejpam-6500	104	16	)	)	PUNCT
ejpam-6500	105	1	<	<	X
ejpam-6500	105	2	min{µ(x′	min{µ(x′	PROPN
ejpam-6500	105	3	)	)	PUNCT
ejpam-6500	105	4	,	,	PUNCT
ejpam-6500	105	5	µ(y′	µ(y′	ADV
ejpam-6500	105	6	)	)	PUNCT
ejpam-6500	105	7	}	}	PUNCT
ejpam-6500	105	8	.	.	PUNCT
ejpam-6500	106	1	thus	thus	ADV
ejpam-6500	106	2	,	,	PUNCT
ejpam-6500	106	3	µ((x′|(y′|y′))|(x′|(y′|y′	µ((x′|(y′|y′))|(x′|(y′|y′	NUM
ejpam-6500	106	4	)	)	PUNCT
ejpam-6500	106	5	)	)	PUNCT
ejpam-6500	106	6	)	)	PUNCT
ejpam-6500	107	1	<	<	X
ejpam-6500	107	2	t	t	X
ejpam-6500	107	3	≤	≤	NUM
ejpam-6500	107	4	min{µ(x′	min{µ(x′	NOUN
ejpam-6500	107	5	)	)	PUNCT
ejpam-6500	107	6	,	,	PUNCT
ejpam-6500	107	7	µ(y′	µ(y′	ADV
ejpam-6500	107	8	)	)	PUNCT
ejpam-6500	107	9	}	}	PUNCT
ejpam-6500	107	10	for	for	ADP
ejpam-6500	107	11	some	some	DET
ejpam-6500	107	12	t	t	NOUN
ejpam-6500	107	13	∈	∈	PROPN
ejpam-6500	107	14	(	(	PUNCT
ejpam-6500	107	15	0	0	NUM
ejpam-6500	107	16	,	,	PUNCT
ejpam-6500	107	17	1	1	NUM
ejpam-6500	107	18	]	]	PUNCT
ejpam-6500	107	19	.	.	PUNCT
ejpam-6500	108	1	it	it	PRON
ejpam-6500	108	2	follows	follow	VERB
ejpam-6500	108	3	that	that	SCONJ
ejpam-6500	108	4	x′t	x′t	PROPN
ejpam-6500	108	5	∈	∈	PROPN
ejpam-6500	108	6	µ	µ	PROPN
ejpam-6500	108	7	and	and	CCONJ
ejpam-6500	108	8	y′t	y′t	PROPN
ejpam-6500	108	9	∈	∈	PROPN
ejpam-6500	108	10	µ	µ	NOUN
ejpam-6500	108	11	,	,	PUNCT
ejpam-6500	108	12	but	but	CCONJ
ejpam-6500	108	13	(	(	PUNCT
ejpam-6500	108	14	(	(	PUNCT
ejpam-6500	108	15	x′|(y′|y′))|(x′|(y′|y′)))∈µ	x′|(y′|y′))|(x′|(y′|y′)))∈µ	PROPN
ejpam-6500	108	16	,	,	PUNCT
ejpam-6500	108	17	a	a	DET
ejpam-6500	108	18	contradiction	contradiction	NOUN
ejpam-6500	108	19	.	.	PUNCT
ejpam-6500	109	1	moreover	moreover	ADV
ejpam-6500	109	2	,	,	PUNCT
ejpam-6500	109	3	µ((x′|(y′|y′))|(x′|(y′|y′	µ((x′|(y′|y′))|(x′|(y′|y′	NUM
ejpam-6500	109	4	)	)	PUNCT
ejpam-6500	109	5	)	)	PUNCT
ejpam-6500	109	6	)	)	PUNCT
ejpam-6500	110	1	+	+	CCONJ
ejpam-6500	110	2	t	t	X
ejpam-6500	110	3	<	<	X
ejpam-6500	110	4	2	2	NUM
ejpam-6500	110	5	t	t	NOUN
ejpam-6500	110	6	<	<	X
ejpam-6500	110	7	1−m	1−m	NUM
ejpam-6500	110	8	,	,	PUNCT
ejpam-6500	110	9	and	and	CCONJ
ejpam-6500	110	10	so	so	ADV
ejpam-6500	110	11	(	(	PUNCT
ejpam-6500	110	12	(	(	PUNCT
ejpam-6500	110	13	x′|(y′|y′))|(x′|(y′|y′)))tqmµ.	x′|(y′|y′))|(x′|(y′|y′)))tqmµ.	PROPN
ejpam-6500	110	14	hence	hence	ADV
ejpam-6500	110	15	,	,	PUNCT
ejpam-6500	110	16	(	(	PUNCT
ejpam-6500	110	17	(	(	PUNCT
ejpam-6500	110	18	x′|(y′|y′))|(x′|(y′|y′)))t∈	x′|(y′|y′))|(x′|(y′|y′)))t∈	PROPN
ejpam-6500	110	19	∨qmµ	∨qmµ	PROPN
ejpam-6500	110	20	,	,	PUNCT
ejpam-6500	110	21	a	a	DET
ejpam-6500	110	22	contradiction	contradiction	NOUN
ejpam-6500	110	23	.	.	PUNCT
ejpam-6500	111	1	on	on	ADP
ejpam-6500	111	2	the	the	DET
ejpam-6500	111	3	other	other	ADJ
ejpam-6500	111	4	hand	hand	NOUN
ejpam-6500	111	5	,	,	PUNCT
ejpam-6500	111	6	if	if	SCONJ
ejpam-6500	111	7	min{µ(x′	min{µ(x′	NOUN
ejpam-6500	111	8	)	)	PUNCT
ejpam-6500	111	9	,	,	PUNCT
ejpam-6500	111	10	µ(y′	µ(y′	ADV
ejpam-6500	111	11	)	)	PUNCT
ejpam-6500	111	12	}	}	PUNCT
ejpam-6500	111	13	≥	≥	NUM
ejpam-6500	111	14	1−m	1−m	NUM
ejpam-6500	111	15	2	2	NUM
ejpam-6500	111	16	,	,	PUNCT
ejpam-6500	111	17	then	then	ADV
ejpam-6500	111	18	µ(x′	µ(x′	PROPN
ejpam-6500	111	19	)	)	PUNCT
ejpam-6500	111	20	≥	≥	NOUN
ejpam-6500	111	21	1−m	1−m	NUM
ejpam-6500	111	22	2	2	NUM
ejpam-6500	111	23	,	,	PUNCT
ejpam-6500	111	24	µ(y′	µ(y′	NUM
ejpam-6500	111	25	)	)	PUNCT
ejpam-6500	111	26	≥	≥	NOUN
ejpam-6500	111	27	1−m	1−m	NUM
ejpam-6500	111	28	2	2	NUM
ejpam-6500	111	29	and	and	CCONJ
ejpam-6500	111	30	µ((x′|(y′|y′))|(x′|(y′|y′	µ((x′|(y′|y′))|(x′|(y′|y′	NUM
ejpam-6500	111	31	)	)	PUNCT
ejpam-6500	111	32	)	)	PUNCT
ejpam-6500	111	33	)	)	PUNCT
ejpam-6500	112	1	<	<	X
ejpam-6500	112	2	1−m	1−m	NUM
ejpam-6500	112	3	2	2	NUM
ejpam-6500	112	4	.	.	PUNCT
ejpam-6500	113	1	thus	thus	ADV
ejpam-6500	113	2	,	,	PUNCT
ejpam-6500	113	3	x′1−m	x′1−m	ADJ
ejpam-6500	113	4	2	2	NUM
ejpam-6500	113	5	∈	∈	PROPN
ejpam-6500	113	6	µ	µ	NOUN
ejpam-6500	113	7	and	and	CCONJ
ejpam-6500	113	8	y′1−m	y′1−m	NUM
ejpam-6500	113	9	2	2	NUM
ejpam-6500	113	10	∈	∈	PROPN
ejpam-6500	113	11	µ	µ	NOUN
ejpam-6500	113	12	,	,	PUNCT
ejpam-6500	113	13	but	but	CCONJ
ejpam-6500	113	14	(	(	PUNCT
ejpam-6500	113	15	(	(	PUNCT
ejpam-6500	113	16	x′|(y′|y′))|(x′|(y′|y′	x′|(y′|y′))|(x′|(y′|y′	PROPN
ejpam-6500	113	17	)	)	PUNCT
ejpam-6500	113	18	)	)	PUNCT
ejpam-6500	113	19	)	)	PUNCT
ejpam-6500	114	1	1−m	1−m	NUM
ejpam-6500	114	2	2	2	NUM
ejpam-6500	114	3	∈µ.	∈µ.	NOUN
ejpam-6500	114	4	also	also	ADV
ejpam-6500	114	5	,	,	PUNCT
ejpam-6500	114	6	µ((x′|(y′|y′))|(x′|(y′|y′	µ((x′|(y′|y′))|(x′|(y′|y′	NUM
ejpam-6500	114	7	)	)	PUNCT
ejpam-6500	114	8	)	)	PUNCT
ejpam-6500	114	9	)	)	PUNCT
ejpam-6500	115	1	+	+	CCONJ
ejpam-6500	116	1	1−m	1−m	NUM
ejpam-6500	116	2	2	2	NUM
ejpam-6500	116	3	<	<	X
ejpam-6500	116	4	1−m	1−m	NUM
ejpam-6500	116	5	2	2	NUM
ejpam-6500	116	6	+	+	SYM
ejpam-6500	116	7	1−m	1−m	NUM
ejpam-6500	116	8	2	2	NUM
ejpam-6500	116	9	=	=	SYM
ejpam-6500	116	10	1−m	1−m	NUM
ejpam-6500	116	11	,	,	PUNCT
ejpam-6500	116	12	that	that	ADV
ejpam-6500	116	13	is	is	ADV
ejpam-6500	116	14	,	,	PUNCT
ejpam-6500	116	15	(	(	PUNCT
ejpam-6500	116	16	(	(	PUNCT
ejpam-6500	116	17	x′|(y′|y′))|(x′|(y′|y′	x′|(y′|y′))|(x′|(y′|y′	PROPN
ejpam-6500	116	18	)	)	PUNCT
ejpam-6500	116	19	)	)	PUNCT
ejpam-6500	116	20	)	)	PUNCT
ejpam-6500	117	1	1−m	1−m	NUM
ejpam-6500	117	2	2	2	NUM
ejpam-6500	117	3	qmµ.	qmµ.	NOUN
ejpam-6500	117	4	hence	hence	ADV
ejpam-6500	117	5	,	,	PUNCT
ejpam-6500	117	6	(	(	PUNCT
ejpam-6500	117	7	(	(	PUNCT
ejpam-6500	117	8	x′|(y′|y′))|(x′|(y′|y′	x′|(y′|y′))|(x′|(y′|y′	PROPN
ejpam-6500	117	9	)	)	PUNCT
ejpam-6500	117	10	)	)	PUNCT
ejpam-6500	117	11	)	)	PUNCT
ejpam-6500	118	1	1−m	1−m	NUM
ejpam-6500	118	2	2	2	NUM
ejpam-6500	118	3	∈	∈	PROPN
ejpam-6500	118	4	∨qmµ	∨qmµ	PROPN
ejpam-6500	118	5	,	,	PUNCT
ejpam-6500	118	6	a	a	DET
ejpam-6500	118	7	contradiction	contradiction	NOUN
ejpam-6500	118	8	.	.	PUNCT
ejpam-6500	119	1	hence	hence	ADV
ejpam-6500	119	2	,	,	PUNCT
ejpam-6500	119	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	119	4	)	)	PUNCT
ejpam-6500	119	5	)	)	PUNCT
ejpam-6500	119	6	)	)	PUNCT
ejpam-6500	119	7	≥	≥	NOUN
ejpam-6500	120	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	120	2	)	)	PUNCT
ejpam-6500	120	3	,	,	PUNCT
ejpam-6500	120	4	µ(y	µ(y	PROPN
ejpam-6500	120	5	)	)	PUNCT
ejpam-6500	120	6	,	,	PUNCT
ejpam-6500	120	7	1−m	1−m	NUM
ejpam-6500	120	8	2	2	NUM
ejpam-6500	120	9	}	}	PUNCT
ejpam-6500	120	10	holds	hold	VERB
ejpam-6500	120	11	for	for	ADP
ejpam-6500	120	12	all	all	DET
ejpam-6500	120	13	x	x	NOUN
ejpam-6500	120	14	,	,	PUNCT
ejpam-6500	120	15	y	y	PROPN
ejpam-6500	120	16	∈	∈	PROPN
ejpam-6500	120	17	h.	h.	NOUN
ejpam-6500	120	18	conversely	conversely	ADV
ejpam-6500	120	19	,	,	PUNCT
ejpam-6500	120	20	assume	assume	VERB
ejpam-6500	120	21	that	that	SCONJ
ejpam-6500	120	22	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	VERB
ejpam-6500	120	23	)	)	PUNCT
ejpam-6500	120	24	)	)	PUNCT
ejpam-6500	120	25	)	)	PUNCT
ejpam-6500	120	26	≥	≥	NOUN
ejpam-6500	121	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	121	2	)	)	PUNCT
ejpam-6500	121	3	,	,	PUNCT
ejpam-6500	121	4	µ(y	µ(y	PROPN
ejpam-6500	121	5	)	)	PUNCT
ejpam-6500	121	6	,	,	PUNCT
ejpam-6500	121	7	1−m	1−m	NUM
ejpam-6500	121	8	2	2	NUM
ejpam-6500	121	9	}	}	PUNCT
ejpam-6500	121	10	holds	hold	VERB
ejpam-6500	121	11	for	for	ADP
ejpam-6500	121	12	all	all	DET
ejpam-6500	121	13	x	x	NOUN
ejpam-6500	121	14	,	,	PUNCT
ejpam-6500	121	15	y	y	PROPN
ejpam-6500	121	16	∈	∈	PROPN
ejpam-6500	121	17	h.	h.	PROPN
ejpam-6500	121	18	let	let	VERB
ejpam-6500	121	19	x	x	PRON
ejpam-6500	121	20	,	,	PUNCT
ejpam-6500	121	21	y	y	PROPN
ejpam-6500	121	22	∈	∈	PROPN
ejpam-6500	121	23	h	h	NOUN
ejpam-6500	121	24	and	and	CCONJ
ejpam-6500	121	25	t1	t1	PROPN
ejpam-6500	121	26	,	,	PUNCT
ejpam-6500	121	27	t2	t2	PROPN
ejpam-6500	121	28	∈	∈	PROPN
ejpam-6500	121	29	(	(	PUNCT
ejpam-6500	121	30	0	0	NUM
ejpam-6500	121	31	,	,	PUNCT
ejpam-6500	121	32	1	1	NUM
ejpam-6500	121	33	]	]	PUNCT
ejpam-6500	121	34	be	be	AUX
ejpam-6500	121	35	such	such	ADJ
ejpam-6500	121	36	that	that	SCONJ
ejpam-6500	121	37	xt1	xt1	PROPN
ejpam-6500	121	38	∈	∈	PROPN
ejpam-6500	121	39	µ	µ	PROPN
ejpam-6500	122	1	and	and	CCONJ
ejpam-6500	122	2	yt2	yt2	PROPN
ejpam-6500	122	3	∈	∈	PROPN
ejpam-6500	122	4	µ.	µ.	NOUN
ejpam-6500	122	5	then	then	ADV
ejpam-6500	122	6	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	122	7	)	)	PUNCT
ejpam-6500	122	8	)	)	PUNCT
ejpam-6500	122	9	)	)	PUNCT
ejpam-6500	122	10	≥	≥	NOUN
ejpam-6500	123	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	123	2	)	)	PUNCT
ejpam-6500	123	3	,	,	PUNCT
ejpam-6500	123	4	µ(y	µ(y	PROPN
ejpam-6500	123	5	)	)	PUNCT
ejpam-6500	123	6	,	,	PUNCT
ejpam-6500	123	7	1−m	1−m	NUM
ejpam-6500	123	8	2	2	NUM
ejpam-6500	123	9	}	}	PUNCT
ejpam-6500	123	10	≥	≥	NOUN
ejpam-6500	123	11	min{t1	min{t1	NOUN
ejpam-6500	123	12	,	,	PUNCT
ejpam-6500	123	13	t2	t2	NOUN
ejpam-6500	123	14	,	,	PUNCT
ejpam-6500	123	15	1−m	1−m	NUM
ejpam-6500	123	16	2	2	NUM
ejpam-6500	123	17	}	}	PUNCT
ejpam-6500	123	18	.	.	PUNCT
ejpam-6500	124	1	assume	assume	VERB
ejpam-6500	124	2	that	that	SCONJ
ejpam-6500	124	3	t1	t1	VERB
ejpam-6500	124	4	≤	≤	NUM
ejpam-6500	124	5	1−m	1−m	NUM
ejpam-6500	124	6	2	2	NUM
ejpam-6500	124	7	or	or	CCONJ
ejpam-6500	124	8	t2	t2	NOUN
ejpam-6500	124	9	≤	≤	NUM
ejpam-6500	124	10	1−m	1−m	NUM
ejpam-6500	124	11	2	2	NUM
ejpam-6500	124	12	.	.	PUNCT
ejpam-6500	125	1	then	then	ADV
ejpam-6500	125	2	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	125	3	)	)	PUNCT
ejpam-6500	125	4	)	)	PUNCT
ejpam-6500	125	5	)	)	PUNCT
ejpam-6500	126	1	≥	≥	NOUN
ejpam-6500	126	2	min{t1	min{t1	NOUN
ejpam-6500	126	3	,	,	PUNCT
ejpam-6500	126	4	t2	t2	NOUN
ejpam-6500	126	5	}	}	PUNCT
ejpam-6500	126	6	,	,	PUNCT
ejpam-6500	126	7	which	which	PRON
ejpam-6500	126	8	implies	imply	VERB
ejpam-6500	126	9	that	that	SCONJ
ejpam-6500	126	10	(	(	PUNCT
ejpam-6500	126	11	(	(	PUNCT
ejpam-6500	126	12	x|(y|y))|(x|(y|y)))min{t1,t2	x|(y|y))|(x|(y|y)))min{t1,t2	NOUN
ejpam-6500	126	13	}	}	PUNCT
ejpam-6500	126	14	∈	∈	PROPN
ejpam-6500	126	15	µ.	µ.	NOUN
ejpam-6500	126	16	now	now	ADV
ejpam-6500	126	17	,	,	PUNCT
ejpam-6500	126	18	suppose	suppose	VERB
ejpam-6500	126	19	that	that	SCONJ
ejpam-6500	126	20	t1	t1	PROPN
ejpam-6500	126	21	>	>	X
ejpam-6500	126	22	1−m	1−m	NUM
ejpam-6500	126	23	2	2	NUM
ejpam-6500	126	24	and	and	CCONJ
ejpam-6500	126	25	t2	t2	PROPN
ejpam-6500	126	26	>	>	X
ejpam-6500	126	27	1−m	1−m	NUM
ejpam-6500	126	28	2	2	NUM
ejpam-6500	126	29	.	.	PUNCT
ejpam-6500	127	1	then	then	ADV
ejpam-6500	127	2	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	127	3	)	)	PUNCT
ejpam-6500	127	4	)	)	PUNCT
ejpam-6500	127	5	)	)	PUNCT
ejpam-6500	128	1	≥	≥	NOUN
ejpam-6500	128	2	1−m	1−m	NUM
ejpam-6500	128	3	2	2	NUM
ejpam-6500	128	4	,	,	PUNCT
ejpam-6500	128	5	and	and	CCONJ
ejpam-6500	128	6	thus	thus	ADV
ejpam-6500	128	7	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	128	8	)	)	PUNCT
ejpam-6500	128	9	)	)	PUNCT
ejpam-6500	128	10	)	)	PUNCT
ejpam-6500	129	1	+	+	CCONJ
ejpam-6500	129	2	min{t1	min{t1	NOUN
ejpam-6500	129	3	,	,	PUNCT
ejpam-6500	129	4	t2	t2	NOUN
ejpam-6500	129	5	}	}	PUNCT
ejpam-6500	129	6	>	>	X
ejpam-6500	129	7	1−m	1−m	NUM
ejpam-6500	129	8	2	2	NUM
ejpam-6500	129	9	+	+	SYM
ejpam-6500	129	10	1−m	1−m	NUM
ejpam-6500	129	11	2	2	NUM
ejpam-6500	129	12	=	=	SYM
ejpam-6500	129	13	1−m	1−m	NUM
ejpam-6500	129	14	,	,	PUNCT
ejpam-6500	129	15	that	that	ADV
ejpam-6500	129	16	is	is	ADV
ejpam-6500	129	17	,	,	PUNCT
ejpam-6500	129	18	(	(	PUNCT
ejpam-6500	129	19	(	(	PUNCT
ejpam-6500	129	20	x|(y|y))|(x|(y|y)))min{t1,t2}qmµ.	x|(y|y))|(x|(y|y)))min{t1,t2}qmµ.	PROPN
ejpam-6500	129	21	hence	hence	ADV
ejpam-6500	129	22	,	,	PUNCT
ejpam-6500	129	23	(	(	PUNCT
ejpam-6500	129	24	(	(	PUNCT
ejpam-6500	129	25	x|(y|y))|(x|(y|y)))min{t1,t2	x|(y|y))|(x|(y|y)))min{t1,t2	NOUN
ejpam-6500	129	26	}	}	PUNCT
ejpam-6500	129	27	∈	∈	PROPN
ejpam-6500	129	28	∨qmµ	∨qmµ	PROPN
ejpam-6500	129	29	,	,	PUNCT
ejpam-6500	129	30	and	and	CCONJ
ejpam-6500	129	31	consequently	consequently	ADV
ejpam-6500	129	32	,	,	PUNCT
ejpam-6500	129	33	µ	µ	X
ejpam-6500	129	34	is	be	AUX
ejpam-6500	129	35	an	an	DET
ejpam-6500	129	36	(	(	PUNCT
ejpam-6500	129	37	∈,∈	∈,∈	INTJ
ejpam-6500	129	38	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	129	39	subalgebra	subalgebra	NOUN
ejpam-6500	129	40	of	of	ADP
ejpam-6500	129	41	h.	h.	PROPN
ejpam-6500	129	42	t.	t.	PROPN
ejpam-6500	129	43	oner	oner	PROPN
ejpam-6500	129	44	et	et	PROPN
ejpam-6500	129	45	al	al	PROPN
ejpam-6500	129	46	.	.	PUNCT
ejpam-6500	129	47	/	/	SYM
ejpam-6500	129	48	eur	eur	PROPN
ejpam-6500	129	49	.	.	PUNCT
ejpam-6500	130	1	j.	j.	PROPN
ejpam-6500	130	2	pure	pure	PROPN
ejpam-6500	130	3	appl	appl	PROPN
ejpam-6500	130	4	.	.	PROPN
ejpam-6500	130	5	math	math	PROPN
ejpam-6500	130	6	,	,	PUNCT
ejpam-6500	130	7	18	18	NUM
ejpam-6500	130	8	(	(	PUNCT
ejpam-6500	130	9	3	3	NUM
ejpam-6500	130	10	)	)	PUNCT
ejpam-6500	130	11	(	(	PUNCT
ejpam-6500	130	12	2025	2025	NUM
ejpam-6500	130	13	)	)	PUNCT
ejpam-6500	130	14	,	,	PUNCT
ejpam-6500	130	15	6500	6500	NUM
ejpam-6500	130	16	6	6	NUM
ejpam-6500	130	17	of	of	ADP
ejpam-6500	130	18	13	13	NUM
ejpam-6500	130	19	theorem	theorem	NOUN
ejpam-6500	130	20	2	2	NUM
ejpam-6500	130	21	.	.	PUNCT
ejpam-6500	131	1	a	a	DET
ejpam-6500	131	2	fuzzy	fuzzy	ADJ
ejpam-6500	131	3	set	set	VERB
ejpam-6500	131	4	µ	µ	PROPN
ejpam-6500	131	5	of	of	ADP
ejpam-6500	131	6	h	h	NOUN
ejpam-6500	131	7	is	be	AUX
ejpam-6500	131	8	an	an	DET
ejpam-6500	131	9	(	(	PUNCT
ejpam-6500	131	10	∈,∈	∈,∈	INTJ
ejpam-6500	131	11	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	131	12	subalgebra	subalgebra	NOUN
ejpam-6500	131	13	of	of	ADP
ejpam-6500	131	14	h	h	NOUN
ejpam-6500	131	15	if	if	SCONJ
ejpam-6500	132	1	and	and	CCONJ
ejpam-6500	132	2	only	only	ADV
ejpam-6500	132	3	if	if	SCONJ
ejpam-6500	132	4	each	each	DET
ejpam-6500	132	5	nonempty	nonempty	ADJ
ejpam-6500	132	6	level	level	NOUN
ejpam-6500	132	7	set	set	VERB
ejpam-6500	132	8	u(µ	u(µ	PROPN
ejpam-6500	132	9	,	,	PUNCT
ejpam-6500	132	10	t	t	PROPN
ejpam-6500	132	11	)	)	PUNCT
ejpam-6500	132	12	=	=	PRON
ejpam-6500	133	1	{	{	PUNCT
ejpam-6500	133	2	x	x	PUNCT
ejpam-6500	133	3	∈	∈	PROPN
ejpam-6500	133	4	h	h	NOUN
ejpam-6500	133	5	:	:	PUNCT
ejpam-6500	133	6	µ(x	µ(x	X
ejpam-6500	133	7	)	)	PUNCT
ejpam-6500	133	8	≥	≥	NOUN
ejpam-6500	133	9	t	t	PROPN
ejpam-6500	133	10	}	}	PUNCT
ejpam-6500	133	11	,	,	PUNCT
ejpam-6500	133	12	t	t	PROPN
ejpam-6500	133	13	∈	∈	PROPN
ejpam-6500	133	14	(	(	PUNCT
ejpam-6500	133	15	0	0	NUM
ejpam-6500	133	16	,	,	PUNCT
ejpam-6500	133	17	1−m	1−m	NUM
ejpam-6500	133	18	2	2	NUM
ejpam-6500	133	19	]	]	PUNCT
ejpam-6500	133	20	,	,	PUNCT
ejpam-6500	133	21	is	be	AUX
ejpam-6500	133	22	a	a	DET
ejpam-6500	133	23	subalgebra	subalgebra	NOUN
ejpam-6500	133	24	of	of	ADP
ejpam-6500	133	25	x.	x.	NOUN
ejpam-6500	133	26	proof	proof	PROPN
ejpam-6500	133	27	.	.	PUNCT
ejpam-6500	134	1	assume	assume	VERB
ejpam-6500	134	2	that	that	SCONJ
ejpam-6500	134	3	a	a	DET
ejpam-6500	134	4	fuzzy	fuzzy	ADJ
ejpam-6500	134	5	set	set	NOUN
ejpam-6500	134	6	µ	µ	NOUN
ejpam-6500	134	7	is	be	AUX
ejpam-6500	134	8	an	an	DET
ejpam-6500	134	9	(	(	PUNCT
ejpam-6500	134	10	∈,∈	∈,∈	X
ejpam-6500	134	11	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-6500	134	12	subalgebra	subalgebra	NOUN
ejpam-6500	134	13	of	of	ADP
ejpam-6500	134	14	h.	h.	NOUN
ejpam-6500	134	15	let	let	VERB
ejpam-6500	134	16	t	t	PROPN
ejpam-6500	134	17	∈	∈	PROPN
ejpam-6500	134	18	(	(	PUNCT
ejpam-6500	134	19	0	0	NUM
ejpam-6500	134	20	,	,	PUNCT
ejpam-6500	134	21	1−m	1−m	NUM
ejpam-6500	134	22	2	2	NUM
ejpam-6500	134	23	]	]	PUNCT
ejpam-6500	134	24	and	and	CCONJ
ejpam-6500	134	25	x	x	X
ejpam-6500	134	26	,	,	PUNCT
ejpam-6500	134	27	y	y	PROPN
ejpam-6500	134	28	∈	∈	PROPN
ejpam-6500	134	29	u(µ	u(µ	PROPN
ejpam-6500	134	30	,	,	PUNCT
ejpam-6500	134	31	t	t	PROPN
ejpam-6500	134	32	)	)	PUNCT
ejpam-6500	134	33	.	.	PUNCT
ejpam-6500	135	1	then	then	ADV
ejpam-6500	135	2	µ(x	µ(x	NOUN
ejpam-6500	135	3	)	)	PUNCT
ejpam-6500	135	4	≥	≥	NOUN
ejpam-6500	135	5	t	t	NOUN
ejpam-6500	135	6	and	and	CCONJ
ejpam-6500	135	7	µ(y	µ(y	PROPN
ejpam-6500	135	8	)	)	PUNCT
ejpam-6500	135	9	≥	≥	NOUN
ejpam-6500	135	10	t.	t.	NOUN
ejpam-6500	135	11	it	it	PRON
ejpam-6500	135	12	follows	follow	VERB
ejpam-6500	135	13	from	from	ADP
ejpam-6500	135	14	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	135	15	)	)	PUNCT
ejpam-6500	135	16	)	)	PUNCT
ejpam-6500	135	17	)	)	PUNCT
ejpam-6500	135	18	≥	≥	NOUN
ejpam-6500	136	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	136	2	)	)	PUNCT
ejpam-6500	136	3	,	,	PUNCT
ejpam-6500	136	4	µ(y	µ(y	PROPN
ejpam-6500	136	5	)	)	PUNCT
ejpam-6500	136	6	,	,	PUNCT
ejpam-6500	136	7	1−m	1−m	NUM
ejpam-6500	136	8	2	2	NUM
ejpam-6500	136	9	}	}	PUNCT
ejpam-6500	136	10	holds	hold	VERB
ejpam-6500	136	11	for	for	ADP
ejpam-6500	136	12	all	all	DET
ejpam-6500	136	13	x	x	NOUN
ejpam-6500	136	14	,	,	PUNCT
ejpam-6500	136	15	y	y	PROPN
ejpam-6500	136	16	∈	∈	PROPN
ejpam-6500	136	17	h	h	NOUN
ejpam-6500	136	18	that	that	PRON
ejpam-6500	136	19	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	VERB
ejpam-6500	136	20	)	)	PUNCT
ejpam-6500	136	21	)	)	PUNCT
ejpam-6500	136	22	)	)	PUNCT
ejpam-6500	136	23	≥	≥	NOUN
ejpam-6500	137	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	137	2	)	)	PUNCT
ejpam-6500	137	3	,	,	PUNCT
ejpam-6500	137	4	µ(y	µ(y	PROPN
ejpam-6500	137	5	)	)	PUNCT
ejpam-6500	137	6	,	,	PUNCT
ejpam-6500	137	7	1−m	1−m	NUM
ejpam-6500	137	8	2	2	NUM
ejpam-6500	137	9	}	}	PUNCT
ejpam-6500	137	10	≥	≥	NOUN
ejpam-6500	137	11	min{t	min{t	PROPN
ejpam-6500	137	12	,	,	PUNCT
ejpam-6500	137	13	1−m	1−m	NUM
ejpam-6500	137	14	2	2	NUM
ejpam-6500	137	15	}	}	PUNCT
ejpam-6500	137	16	=	=	SYM
ejpam-6500	137	17	t	t	PROPN
ejpam-6500	137	18	,	,	PUNCT
ejpam-6500	137	19	so	so	SCONJ
ejpam-6500	137	20	that	that	SCONJ
ejpam-6500	137	21	(	(	PUNCT
ejpam-6500	137	22	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	137	23	)	)	PUNCT
ejpam-6500	137	24	)	)	PUNCT
ejpam-6500	137	25	∈	∈	PROPN
ejpam-6500	137	26	u(µ	u(µ	PROPN
ejpam-6500	137	27	,	,	PUNCT
ejpam-6500	137	28	t	t	PROPN
ejpam-6500	137	29	)	)	PUNCT
ejpam-6500	137	30	.	.	PUNCT
ejpam-6500	138	1	hence	hence	ADV
ejpam-6500	138	2	,	,	PUNCT
ejpam-6500	138	3	u(µ	u(µ	PROPN
ejpam-6500	138	4	,	,	PUNCT
ejpam-6500	138	5	t	t	PROPN
ejpam-6500	138	6	)	)	PUNCT
ejpam-6500	138	7	is	be	AUX
ejpam-6500	138	8	an	an	DET
ejpam-6500	138	9	(	(	PUNCT
ejpam-6500	138	10	∈,∈	∈,∈	INTJ
ejpam-6500	138	11	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	138	12	subalgebra	subalgebra	NOUN
ejpam-6500	138	13	of	of	ADP
ejpam-6500	138	14	h.	h.	NOUN
ejpam-6500	138	15	conversely	conversely	ADV
ejpam-6500	138	16	,	,	PUNCT
ejpam-6500	138	17	suppose	suppose	VERB
ejpam-6500	138	18	that	that	SCONJ
ejpam-6500	138	19	the	the	DET
ejpam-6500	138	20	nonempty	nonempty	ADJ
ejpam-6500	138	21	set	set	VERB
ejpam-6500	138	22	u(µ	u(µ	PROPN
ejpam-6500	138	23	,	,	PUNCT
ejpam-6500	138	24	t	t	PROPN
ejpam-6500	138	25	)	)	PUNCT
ejpam-6500	138	26	is	be	AUX
ejpam-6500	138	27	a	a	DET
ejpam-6500	138	28	subalgebra	subalgebra	NOUN
ejpam-6500	138	29	of	of	ADP
ejpam-6500	138	30	h	h	NOUN
ejpam-6500	138	31	for	for	ADP
ejpam-6500	138	32	all	all	DET
ejpam-6500	138	33	t	t	NOUN
ejpam-6500	138	34	∈	∈	PROPN
ejpam-6500	138	35	(	(	PUNCT
ejpam-6500	138	36	0	0	NUM
ejpam-6500	138	37	,	,	PUNCT
ejpam-6500	138	38	1−m	1−m	NUM
ejpam-6500	138	39	2	2	NUM
ejpam-6500	138	40	]	]	PUNCT
ejpam-6500	138	41	.	.	PUNCT
ejpam-6500	139	1	if	if	SCONJ
ejpam-6500	139	2	the	the	DET
ejpam-6500	139	3	condition	condition	NOUN
ejpam-6500	139	4	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	139	5	)	)	PUNCT
ejpam-6500	139	6	)	)	PUNCT
ejpam-6500	139	7	)	)	PUNCT
ejpam-6500	139	8	≥	≥	NOUN
ejpam-6500	140	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	140	2	)	)	PUNCT
ejpam-6500	140	3	,	,	PUNCT
ejpam-6500	140	4	µ(y	µ(y	PROPN
ejpam-6500	140	5	)	)	PUNCT
ejpam-6500	140	6	,	,	PUNCT
ejpam-6500	140	7	1−m	1−m	NUM
ejpam-6500	140	8	2	2	NUM
ejpam-6500	140	9	}	}	PUNCT
ejpam-6500	140	10	holds	hold	VERB
ejpam-6500	140	11	for	for	ADP
ejpam-6500	140	12	all	all	DET
ejpam-6500	140	13	x	x	NOUN
ejpam-6500	140	14	,	,	PUNCT
ejpam-6500	140	15	y	y	PROPN
ejpam-6500	140	16	∈	∈	PROPN
ejpam-6500	140	17	h	h	NOUN
ejpam-6500	140	18	is	be	AUX
ejpam-6500	140	19	not	not	PART
ejpam-6500	140	20	true	true	ADJ
ejpam-6500	140	21	,	,	PUNCT
ejpam-6500	140	22	then	then	ADV
ejpam-6500	140	23	there	there	PRON
ejpam-6500	140	24	exist	exist	VERB
ejpam-6500	140	25	a	a	DET
ejpam-6500	140	26	,	,	PUNCT
ejpam-6500	140	27	b	b	X
ejpam-6500	140	28	∈	∈	ADJ
ejpam-6500	140	29	h	h	NOUN
ejpam-6500	140	30	such	such	ADJ
ejpam-6500	140	31	that	that	DET
ejpam-6500	140	32	µ((a|(b|b))|(a|(b|b	µ((a|(b|b))|(a|(b|b	NOUN
ejpam-6500	140	33	)	)	PUNCT
ejpam-6500	140	34	)	)	PUNCT
ejpam-6500	140	35	)	)	PUNCT
ejpam-6500	141	1	<	<	X
ejpam-6500	141	2	min{µ(a	min{µ(a	PROPN
ejpam-6500	141	3	)	)	PUNCT
ejpam-6500	141	4	,	,	PUNCT
ejpam-6500	141	5	µ(b	µ(b	PROPN
ejpam-6500	141	6	)	)	PUNCT
ejpam-6500	141	7	,	,	PUNCT
ejpam-6500	141	8	1−m	1−m	NUM
ejpam-6500	141	9	2	2	NUM
ejpam-6500	141	10	}	}	PUNCT
ejpam-6500	141	11	.	.	PUNCT
ejpam-6500	142	1	hence	hence	ADV
ejpam-6500	142	2	,	,	PUNCT
ejpam-6500	142	3	we	we	PRON
ejpam-6500	142	4	can	can	AUX
ejpam-6500	142	5	take	take	VERB
ejpam-6500	142	6	t	t	X
ejpam-6500	142	7	∈	∈	PROPN
ejpam-6500	142	8	(	(	PUNCT
ejpam-6500	142	9	0	0	NUM
ejpam-6500	142	10	,	,	PUNCT
ejpam-6500	142	11	1	1	NUM
ejpam-6500	142	12	]	]	PUNCT
ejpam-6500	142	13	such	such	ADJ
ejpam-6500	142	14	that	that	DET
ejpam-6500	142	15	µ((a|(b|b))|(a|(b|b	µ((a|(b|b))|(a|(b|b	NOUN
ejpam-6500	142	16	)	)	PUNCT
ejpam-6500	142	17	)	)	PUNCT
ejpam-6500	142	18	)	)	PUNCT
ejpam-6500	143	1	<	<	X
ejpam-6500	143	2	t1	t1	X
ejpam-6500	143	3	<	<	X
ejpam-6500	143	4	min{µ(a	min{µ(a	PROPN
ejpam-6500	143	5	)	)	PUNCT
ejpam-6500	143	6	,	,	PUNCT
ejpam-6500	143	7	µ(b	µ(b	PROPN
ejpam-6500	143	8	)	)	PUNCT
ejpam-6500	143	9	,	,	PUNCT
ejpam-6500	143	10	1−m	1−m	NUM
ejpam-6500	143	11	2	2	NUM
ejpam-6500	143	12	}	}	PUNCT
ejpam-6500	143	13	.	.	PUNCT
ejpam-6500	144	1	then	then	ADV
ejpam-6500	144	2	t	t	PROPN
ejpam-6500	144	3	∈	∈	PROPN
ejpam-6500	144	4	(	(	PUNCT
ejpam-6500	144	5	0	0	NUM
ejpam-6500	144	6	,	,	PUNCT
ejpam-6500	144	7	1−m	1−m	NUM
ejpam-6500	144	8	2	2	NUM
ejpam-6500	144	9	]	]	PUNCT
ejpam-6500	144	10	and	and	CCONJ
ejpam-6500	144	11	a	a	PRON
ejpam-6500	144	12	,	,	PUNCT
ejpam-6500	144	13	b	b	PROPN
ejpam-6500	144	14	∈	∈	PROPN
ejpam-6500	144	15	u(µ	u(µ	PROPN
ejpam-6500	144	16	,	,	PUNCT
ejpam-6500	144	17	t	t	PROPN
ejpam-6500	144	18	)	)	PUNCT
ejpam-6500	144	19	.	.	PUNCT
ejpam-6500	145	1	since	since	SCONJ
ejpam-6500	145	2	u(µ	u(µ	PROPN
ejpam-6500	145	3	,	,	PUNCT
ejpam-6500	145	4	t	t	PROPN
ejpam-6500	145	5	)	)	PUNCT
ejpam-6500	145	6	is	be	AUX
ejpam-6500	145	7	a	a	DET
ejpam-6500	145	8	subalgebra	subalgebra	NOUN
ejpam-6500	145	9	of	of	ADP
ejpam-6500	145	10	h	h	NOUN
ejpam-6500	145	11	,	,	PUNCT
ejpam-6500	145	12	we	we	PRON
ejpam-6500	145	13	have	have	VERB
ejpam-6500	145	14	(	(	PUNCT
ejpam-6500	145	15	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-6500	145	16	)	)	PUNCT
ejpam-6500	145	17	)	)	PUNCT
ejpam-6500	146	1	∈	∈	PROPN
ejpam-6500	146	2	u(µ	u(µ	PROPN
ejpam-6500	146	3	,	,	PUNCT
ejpam-6500	146	4	t	t	PROPN
ejpam-6500	146	5	)	)	PUNCT
ejpam-6500	146	6	,	,	PUNCT
ejpam-6500	146	7	so	so	ADV
ejpam-6500	146	8	µ((a|(b|b))|(a|(b|b	µ((a|(b|b))|(a|(b|b	NOUN
ejpam-6500	146	9	)	)	PUNCT
ejpam-6500	146	10	)	)	PUNCT
ejpam-6500	146	11	)	)	PUNCT
ejpam-6500	146	12	≥	≥	PROPN
ejpam-6500	147	1	t.	t.	NOUN
ejpam-6500	147	2	this	this	PRON
ejpam-6500	147	3	is	be	AUX
ejpam-6500	147	4	a	a	DET
ejpam-6500	147	5	contradiction	contradiction	NOUN
ejpam-6500	147	6	.	.	PUNCT
ejpam-6500	148	1	therefore	therefore	ADV
ejpam-6500	148	2	,	,	PUNCT
ejpam-6500	148	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	148	4	)	)	PUNCT
ejpam-6500	148	5	)	)	PUNCT
ejpam-6500	148	6	)	)	PUNCT
ejpam-6500	148	7	≥	≥	NOUN
ejpam-6500	149	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	149	2	)	)	PUNCT
ejpam-6500	149	3	,	,	PUNCT
ejpam-6500	149	4	µ(y	µ(y	PROPN
ejpam-6500	149	5	)	)	PUNCT
ejpam-6500	149	6	,	,	PUNCT
ejpam-6500	149	7	1−m	1−m	NUM
ejpam-6500	149	8	2	2	NUM
ejpam-6500	149	9	}	}	PUNCT
ejpam-6500	149	10	holds	hold	VERB
ejpam-6500	149	11	for	for	ADP
ejpam-6500	149	12	all	all	DET
ejpam-6500	149	13	x	x	NOUN
ejpam-6500	149	14	,	,	PUNCT
ejpam-6500	149	15	y	y	PROPN
ejpam-6500	149	16	∈	∈	PROPN
ejpam-6500	149	17	h	h	NOUN
ejpam-6500	149	18	,	,	PUNCT
ejpam-6500	149	19	and	and	CCONJ
ejpam-6500	149	20	so	so	ADV
ejpam-6500	149	21	µ	µ	PRON
ejpam-6500	149	22	is	be	AUX
ejpam-6500	149	23	an	an	DET
ejpam-6500	149	24	(	(	PUNCT
ejpam-6500	149	25	∈,∈	∈,∈	INTJ
ejpam-6500	149	26	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	149	27	subalgebra	subalgebra	NOUN
ejpam-6500	149	28	of	of	ADP
ejpam-6500	149	29	h.	h.	PROPN
ejpam-6500	149	30	theorem	theorem	PROPN
ejpam-6500	149	31	3	3	X
ejpam-6500	149	32	.	.	PUNCT
ejpam-6500	150	1	let	let	VERB
ejpam-6500	150	2	µ	µ	X
ejpam-6500	150	3	be	be	AUX
ejpam-6500	150	4	a	a	DET
ejpam-6500	150	5	fuzzy	fuzzy	ADJ
ejpam-6500	150	6	set	set	NOUN
ejpam-6500	150	7	of	of	ADP
ejpam-6500	150	8	h.	h.	PROPN
ejpam-6500	150	9	then	then	ADV
ejpam-6500	150	10	the	the	DET
ejpam-6500	150	11	nonempty	nonempty	ADJ
ejpam-6500	150	12	level	level	NOUN
ejpam-6500	150	13	set	set	VERB
ejpam-6500	150	14	u(µ	u(µ	PROPN
ejpam-6500	150	15	,	,	PUNCT
ejpam-6500	150	16	t	t	PROPN
ejpam-6500	150	17	)	)	PUNCT
ejpam-6500	150	18	is	be	AUX
ejpam-6500	150	19	a	a	DET
ejpam-6500	150	20	subalgebra	subalgebra	NOUN
ejpam-6500	150	21	of	of	ADP
ejpam-6500	150	22	h	h	NOUN
ejpam-6500	150	23	for	for	ADP
ejpam-6500	150	24	all	all	DET
ejpam-6500	150	25	t	t	NOUN
ejpam-6500	150	26	∈	∈	PROPN
ejpam-6500	150	27	(	(	PUNCT
ejpam-6500	150	28	1−m	1−m	NUM
ejpam-6500	150	29	2	2	NUM
ejpam-6500	150	30	,	,	PUNCT
ejpam-6500	150	31	1	1	NUM
ejpam-6500	150	32	]	]	PUNCT
ejpam-6500	151	1	if	if	SCONJ
ejpam-6500	151	2	and	and	CCONJ
ejpam-6500	151	3	only	only	ADV
ejpam-6500	151	4	if	if	SCONJ
ejpam-6500	151	5	max{µ((x|(y|y))|(x|(y|y	max{µ((x|(y|y))|(x|(y|y	PROPN
ejpam-6500	151	6	)	)	PUNCT
ejpam-6500	151	7	)	)	PUNCT
ejpam-6500	151	8	)	)	PUNCT
ejpam-6500	151	9	,	,	PUNCT
ejpam-6500	151	10	1−m	1−m	NUM
ejpam-6500	151	11	2	2	NUM
ejpam-6500	151	12	}	}	PUNCT
ejpam-6500	151	13	≥	≥	NOUN
ejpam-6500	151	14	min{µ(x	min{µ(x	NOUN
ejpam-6500	151	15	)	)	PUNCT
ejpam-6500	151	16	,	,	PUNCT
ejpam-6500	151	17	µ(y	µ(y	PROPN
ejpam-6500	151	18	)	)	PUNCT
ejpam-6500	151	19	}	}	PUNCT
ejpam-6500	151	20	for	for	ADP
ejpam-6500	151	21	all	all	DET
ejpam-6500	151	22	x	x	NOUN
ejpam-6500	151	23	,	,	PUNCT
ejpam-6500	151	24	y	y	PROPN
ejpam-6500	151	25	∈	∈	PROPN
ejpam-6500	151	26	h.	h.	PROPN
ejpam-6500	151	27	proof	proof	NOUN
ejpam-6500	151	28	.	.	PUNCT
ejpam-6500	151	29	suppose	suppose	VERB
ejpam-6500	151	30	that	that	SCONJ
ejpam-6500	151	31	u(µ	u(µ	PROPN
ejpam-6500	151	32	,	,	PUNCT
ejpam-6500	151	33	t	t	PROPN
ejpam-6500	151	34	)	)	PUNCT
ejpam-6500	151	35	̸=	̸=	PROPN
ejpam-6500	151	36	∅	∅	NOUN
ejpam-6500	151	37	is	be	AUX
ejpam-6500	151	38	a	a	DET
ejpam-6500	151	39	subalgebra	subalgebra	NOUN
ejpam-6500	151	40	of	of	ADP
ejpam-6500	151	41	h.	h.	PROPN
ejpam-6500	151	42	assume	assume	VERB
ejpam-6500	151	43	that	that	SCONJ
ejpam-6500	151	44	max{µ((x|(y|y))|(x|(y|y	max{µ((x|(y|y))|(x|(y|y	PROPN
ejpam-6500	151	45	)	)	PUNCT
ejpam-6500	151	46	)	)	PUNCT
ejpam-6500	151	47	)	)	PUNCT
ejpam-6500	151	48	,	,	PUNCT
ejpam-6500	151	49	1−m	1−m	NUM
ejpam-6500	151	50	2	2	NUM
ejpam-6500	151	51	}	}	PUNCT
ejpam-6500	151	52	<	<	X
ejpam-6500	151	53	min{µ(x	min{µ(x	PROPN
ejpam-6500	151	54	)	)	PUNCT
ejpam-6500	151	55	,	,	PUNCT
ejpam-6500	151	56	µ(y	µ(y	PROPN
ejpam-6500	151	57	)	)	PUNCT
ejpam-6500	151	58	}	}	PUNCT
ejpam-6500	151	59	=	=	SYM
ejpam-6500	151	60	t	t	NOUN
ejpam-6500	151	61	for	for	ADP
ejpam-6500	151	62	some	some	DET
ejpam-6500	151	63	x	x	NOUN
ejpam-6500	151	64	,	,	PUNCT
ejpam-6500	151	65	y	y	PROPN
ejpam-6500	151	66	∈	∈	PROPN
ejpam-6500	151	67	h.	h.	PROPN
ejpam-6500	151	68	then	then	ADV
ejpam-6500	151	69	t	t	PROPN
ejpam-6500	151	70	∈	∈	PROPN
ejpam-6500	151	71	(	(	PUNCT
ejpam-6500	151	72	1−m	1−m	NUM
ejpam-6500	151	73	2	2	NUM
ejpam-6500	151	74	,	,	PUNCT
ejpam-6500	151	75	1	1	NUM
ejpam-6500	151	76	]	]	PUNCT
ejpam-6500	151	77	,	,	PUNCT
ejpam-6500	151	78	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	151	79	)	)	PUNCT
ejpam-6500	151	80	)	)	PUNCT
ejpam-6500	151	81	)	)	PUNCT
ejpam-6500	152	1	<	<	X
ejpam-6500	152	2	t	t	PROPN
ejpam-6500	152	3	,	,	PUNCT
ejpam-6500	152	4	x	x	X
ejpam-6500	152	5	∈	∈	PROPN
ejpam-6500	152	6	u(µ	u(µ	PROPN
ejpam-6500	152	7	,	,	PUNCT
ejpam-6500	152	8	t	t	PROPN
ejpam-6500	152	9	)	)	PUNCT
ejpam-6500	152	10	and	and	CCONJ
ejpam-6500	152	11	y	y	PROPN
ejpam-6500	152	12	∈	∈	PROPN
ejpam-6500	152	13	u(µ	u(µ	PROPN
ejpam-6500	152	14	,	,	PUNCT
ejpam-6500	152	15	t	t	PROPN
ejpam-6500	152	16	)	)	PUNCT
ejpam-6500	152	17	.	.	PUNCT
ejpam-6500	153	1	since	since	SCONJ
ejpam-6500	153	2	x	x	X
ejpam-6500	153	3	,	,	PUNCT
ejpam-6500	153	4	y	y	PROPN
ejpam-6500	153	5	∈	∈	PROPN
ejpam-6500	153	6	u(µ	u(µ	PROPN
ejpam-6500	153	7	,	,	PUNCT
ejpam-6500	153	8	t	t	PROPN
ejpam-6500	153	9	)	)	PUNCT
ejpam-6500	153	10	,	,	PUNCT
ejpam-6500	153	11	we	we	PRON
ejpam-6500	153	12	have	have	VERB
ejpam-6500	153	13	u(µ	u(µ	NOUN
ejpam-6500	153	14	,	,	PUNCT
ejpam-6500	153	15	t	t	PROPN
ejpam-6500	153	16	)	)	PUNCT
ejpam-6500	153	17	is	be	AUX
ejpam-6500	153	18	a	a	DET
ejpam-6500	153	19	subalgebra	subalgebra	NOUN
ejpam-6500	153	20	of	of	ADP
ejpam-6500	153	21	h	h	NOUN
ejpam-6500	153	22	,	,	PUNCT
ejpam-6500	153	23	so	so	CCONJ
ejpam-6500	153	24	(	(	PUNCT
ejpam-6500	153	25	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	153	26	)	)	PUNCT
ejpam-6500	153	27	)	)	PUNCT
ejpam-6500	154	1	∈	∈	PROPN
ejpam-6500	154	2	u(µ	u(µ	PROPN
ejpam-6500	154	3	,	,	PUNCT
ejpam-6500	154	4	t	t	PROPN
ejpam-6500	154	5	)	)	PUNCT
ejpam-6500	154	6	,	,	PUNCT
ejpam-6500	154	7	a	a	DET
ejpam-6500	154	8	contradiction	contradiction	NOUN
ejpam-6500	154	9	.	.	PUNCT
ejpam-6500	155	1	the	the	DET
ejpam-6500	155	2	proof	proof	NOUN
ejpam-6500	155	3	of	of	ADP
ejpam-6500	155	4	the	the	DET
ejpam-6500	155	5	second	second	ADJ
ejpam-6500	155	6	part	part	NOUN
ejpam-6500	155	7	of	of	ADP
ejpam-6500	155	8	the	the	DET
ejpam-6500	155	9	theorem	theorem	NOUN
ejpam-6500	155	10	is	be	AUX
ejpam-6500	155	11	straightforward	straightforward	ADJ
ejpam-6500	155	12	.	.	PUNCT
ejpam-6500	156	1	theorem	theorem	ADJ
ejpam-6500	156	2	4	4	NUM
ejpam-6500	156	3	.	.	PUNCT
ejpam-6500	157	1	let	let	VERB
ejpam-6500	157	2	µ	µ	X
ejpam-6500	157	3	be	be	AUX
ejpam-6500	157	4	an	an	DET
ejpam-6500	157	5	(	(	PUNCT
ejpam-6500	157	6	∈,∈	∈,∈	INTJ
ejpam-6500	157	7	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	157	8	subalgebra	subalgebra	NOUN
ejpam-6500	157	9	of	of	ADP
ejpam-6500	157	10	h.	h.	PROPN
ejpam-6500	157	11	if	if	SCONJ
ejpam-6500	157	12	it	it	PRON
ejpam-6500	157	13	satisfies	satisfy	VERB
ejpam-6500	157	14	µ(x	µ(x	NOUN
ejpam-6500	157	15	)	)	PUNCT
ejpam-6500	157	16	<	<	X
ejpam-6500	157	17	1−m	1−m	NUM
ejpam-6500	157	18	2	2	NUM
ejpam-6500	157	19	for	for	ADP
ejpam-6500	157	20	all	all	DET
ejpam-6500	157	21	x	x	SYM
ejpam-6500	157	22	∈	∈	PROPN
ejpam-6500	157	23	h	h	NOUN
ejpam-6500	157	24	,	,	PUNCT
ejpam-6500	157	25	then	then	ADV
ejpam-6500	157	26	it	it	PRON
ejpam-6500	157	27	is	be	AUX
ejpam-6500	157	28	a	a	DET
ejpam-6500	157	29	fuzzy	fuzzy	ADJ
ejpam-6500	157	30	subalgebra	subalgebra	NOUN
ejpam-6500	157	31	of	of	ADP
ejpam-6500	157	32	h.	h.	NOUN
ejpam-6500	157	33	proof	proof	NOUN
ejpam-6500	157	34	.	.	PUNCT
ejpam-6500	158	1	let	let	VERB
ejpam-6500	158	2	x	x	PRON
ejpam-6500	158	3	,	,	PUNCT
ejpam-6500	158	4	y	y	PROPN
ejpam-6500	158	5	∈	∈	PROPN
ejpam-6500	158	6	h	h	NOUN
ejpam-6500	158	7	and	and	CCONJ
ejpam-6500	158	8	t1	t1	PROPN
ejpam-6500	158	9	,	,	PUNCT
ejpam-6500	158	10	t2	t2	PROPN
ejpam-6500	158	11	∈	∈	PROPN
ejpam-6500	158	12	(	(	PUNCT
ejpam-6500	158	13	0	0	NUM
ejpam-6500	158	14	,	,	PUNCT
ejpam-6500	158	15	1	1	NUM
ejpam-6500	158	16	]	]	PUNCT
ejpam-6500	158	17	be	be	AUX
ejpam-6500	158	18	such	such	ADJ
ejpam-6500	158	19	that	that	SCONJ
ejpam-6500	158	20	xt1	xt1	PROPN
ejpam-6500	158	21	∈	∈	PROPN
ejpam-6500	158	22	µ	µ	PROPN
ejpam-6500	159	1	and	and	CCONJ
ejpam-6500	159	2	yt2	yt2	PROPN
ejpam-6500	159	3	∈	∈	PROPN
ejpam-6500	159	4	µ.	µ.	NOUN
ejpam-6500	159	5	then	then	ADV
ejpam-6500	159	6	µ(x	µ(x	NOUN
ejpam-6500	159	7	)	)	PUNCT
ejpam-6500	159	8	≥	≥	NOUN
ejpam-6500	159	9	t1	t1	NOUN
ejpam-6500	159	10	and	and	CCONJ
ejpam-6500	159	11	µ(y	µ(y	PROPN
ejpam-6500	159	12	)	)	PUNCT
ejpam-6500	159	13	≥	≥	NOUN
ejpam-6500	159	14	t2	t2	NOUN
ejpam-6500	159	15	.	.	PUNCT
ejpam-6500	160	1	it	it	PRON
ejpam-6500	160	2	follows	follow	VERB
ejpam-6500	160	3	from	from	ADP
ejpam-6500	160	4	theorem	theorem	ADJ
ejpam-6500	160	5	1	1	NUM
ejpam-6500	160	6	that	that	SCONJ
ejpam-6500	160	7	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	VERB
ejpam-6500	160	8	)	)	PUNCT
ejpam-6500	160	9	)	)	PUNCT
ejpam-6500	160	10	)	)	PUNCT
ejpam-6500	160	11	>	>	X
ejpam-6500	161	1	min{µ(x	min{µ(x	PROPN
ejpam-6500	161	2	)	)	PUNCT
ejpam-6500	161	3	,	,	PUNCT
ejpam-6500	161	4	µ(y	µ(y	PROPN
ejpam-6500	161	5	)	)	PUNCT
ejpam-6500	161	6	,	,	PUNCT
ejpam-6500	161	7	1−m	1−m	NUM
ejpam-6500	161	8	2	2	NUM
ejpam-6500	161	9	}	}	PUNCT
ejpam-6500	161	10	=	=	SYM
ejpam-6500	161	11	min{µ(x	min{µ(x	NOUN
ejpam-6500	161	12	)	)	PUNCT
ejpam-6500	161	13	,	,	PUNCT
ejpam-6500	161	14	µ(y	µ(y	PROPN
ejpam-6500	161	15	)	)	PUNCT
ejpam-6500	161	16	}	}	PUNCT
ejpam-6500	161	17	=	=	SYM
ejpam-6500	161	18	min{t1	min{t1	NOUN
ejpam-6500	161	19	,	,	PUNCT
ejpam-6500	161	20	t2	t2	NOUN
ejpam-6500	161	21	}	}	PUNCT
ejpam-6500	161	22	,	,	PUNCT
ejpam-6500	161	23	so	so	CCONJ
ejpam-6500	161	24	(	(	PUNCT
ejpam-6500	161	25	(	(	PUNCT
ejpam-6500	161	26	x|(y|y))|(x|(y|y)))min{t1,t2	x|(y|y))|(x|(y|y)))min{t1,t2	NOUN
ejpam-6500	161	27	}	}	PUNCT
ejpam-6500	161	28	∈	∈	PROPN
ejpam-6500	161	29	µ.	µ.	NOUN
ejpam-6500	161	30	hence	hence	ADV
ejpam-6500	161	31	,	,	PUNCT
ejpam-6500	161	32	µ	µ	X
ejpam-6500	161	33	is	be	AUX
ejpam-6500	161	34	a	a	DET
ejpam-6500	161	35	fuzzy	fuzzy	ADJ
ejpam-6500	161	36	subalgebra	subalgebra	NOUN
ejpam-6500	161	37	of	of	ADP
ejpam-6500	161	38	h.	h.	PROPN
ejpam-6500	161	39	t.	t.	PROPN
ejpam-6500	161	40	oner	oner	PROPN
ejpam-6500	161	41	et	et	PROPN
ejpam-6500	161	42	al	al	PROPN
ejpam-6500	161	43	.	.	PUNCT
ejpam-6500	161	44	/	/	SYM
ejpam-6500	161	45	eur	eur	PROPN
ejpam-6500	161	46	.	.	PUNCT
ejpam-6500	162	1	j.	j.	PROPN
ejpam-6500	162	2	pure	pure	PROPN
ejpam-6500	162	3	appl	appl	PROPN
ejpam-6500	162	4	.	.	PROPN
ejpam-6500	162	5	math	math	PROPN
ejpam-6500	162	6	,	,	PUNCT
ejpam-6500	162	7	18	18	NUM
ejpam-6500	162	8	(	(	PUNCT
ejpam-6500	162	9	3	3	NUM
ejpam-6500	162	10	)	)	PUNCT
ejpam-6500	162	11	(	(	PUNCT
ejpam-6500	162	12	2025	2025	NUM
ejpam-6500	162	13	)	)	PUNCT
ejpam-6500	162	14	,	,	PUNCT
ejpam-6500	162	15	6500	6500	NUM
ejpam-6500	162	16	7	7	NUM
ejpam-6500	162	17	of	of	ADP
ejpam-6500	162	18	13	13	NUM
ejpam-6500	162	19	theorem	theorem	NOUN
ejpam-6500	162	20	5	5	NUM
ejpam-6500	162	21	.	.	PUNCT
ejpam-6500	163	1	if	if	SCONJ
ejpam-6500	163	2	0	0	NUM
ejpam-6500	163	3	≤	≤	NUM
ejpam-6500	163	4	m	m	VERB
ejpam-6500	163	5	<	<	X
ejpam-6500	163	6	n	n	X
ejpam-6500	163	7	<	<	X
ejpam-6500	163	8	1	1	NUM
ejpam-6500	164	1	,	,	PUNCT
ejpam-6500	164	2	then	then	ADV
ejpam-6500	164	3	each	each	DET
ejpam-6500	164	4	(	(	PUNCT
ejpam-6500	164	5	∈,∈	∈,∈	X
ejpam-6500	164	6	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	164	7	subalgebra	subalgebra	NOUN
ejpam-6500	164	8	of	of	ADP
ejpam-6500	164	9	h	h	NOUN
ejpam-6500	164	10	is	be	AUX
ejpam-6500	164	11	an	an	DET
ejpam-6500	164	12	(	(	PUNCT
ejpam-6500	164	13	∈,∈	∈,∈	INTJ
ejpam-6500	164	14	∨qn)-fuzzy	∨qn)-fuzzy	ADJ
ejpam-6500	164	15	subalgebra	subalgebra	NOUN
ejpam-6500	164	16	of	of	ADP
ejpam-6500	164	17	h.	h.	NOUN
ejpam-6500	164	18	proof	proof	NOUN
ejpam-6500	164	19	.	.	PUNCT
ejpam-6500	165	1	let	let	VERB
ejpam-6500	165	2	µ	µ	X
ejpam-6500	165	3	be	be	AUX
ejpam-6500	165	4	an	an	DET
ejpam-6500	165	5	(	(	PUNCT
ejpam-6500	165	6	∈,∈	∈,∈	INTJ
ejpam-6500	165	7	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	165	8	subalgebra	subalgebra	NOUN
ejpam-6500	165	9	of	of	ADP
ejpam-6500	165	10	h	h	NOUN
ejpam-6500	165	11	and	and	CCONJ
ejpam-6500	165	12	let	let	VERB
ejpam-6500	165	13	x	x	PRON
ejpam-6500	165	14	,	,	PUNCT
ejpam-6500	165	15	y	y	PROPN
ejpam-6500	165	16	∈	∈	PROPN
ejpam-6500	165	17	h.	h.	PROPN
ejpam-6500	165	18	then	then	ADV
ejpam-6500	165	19	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	165	20	)	)	PUNCT
ejpam-6500	165	21	)	)	PUNCT
ejpam-6500	165	22	)	)	PUNCT
ejpam-6500	166	1	>	>	X
ejpam-6500	167	1	min{µ(x	min{µ(x	PROPN
ejpam-6500	167	2	)	)	PUNCT
ejpam-6500	167	3	,	,	PUNCT
ejpam-6500	167	4	µ(y	µ(y	PROPN
ejpam-6500	167	5	)	)	PUNCT
ejpam-6500	167	6	,	,	PUNCT
ejpam-6500	167	7	1−m	1−m	NUM
ejpam-6500	167	8	2	2	NUM
ejpam-6500	167	9	}	}	PUNCT
ejpam-6500	167	10	≥	≥	NOUN
ejpam-6500	167	11	min{µ(x	min{µ(x	NOUN
ejpam-6500	167	12	)	)	PUNCT
ejpam-6500	167	13	,	,	PUNCT
ejpam-6500	167	14	µ(y	µ(y	PROPN
ejpam-6500	167	15	)	)	PUNCT
ejpam-6500	167	16	,	,	PUNCT
ejpam-6500	167	17	1−n	1−n	NUM
ejpam-6500	167	18	2	2	NUM
ejpam-6500	167	19	}	}	PUNCT
ejpam-6500	167	20	.	.	PUNCT
ejpam-6500	168	1	thus	thus	ADV
ejpam-6500	168	2	,	,	PUNCT
ejpam-6500	168	3	from	from	ADP
ejpam-6500	168	4	theorem	theorem	NOUN
ejpam-6500	168	5	1	1	NUM
ejpam-6500	168	6	,	,	PUNCT
ejpam-6500	168	7	we	we	PRON
ejpam-6500	168	8	have	have	VERB
ejpam-6500	168	9	µ	µ	NOUN
ejpam-6500	168	10	is	be	AUX
ejpam-6500	168	11	an	an	DET
ejpam-6500	168	12	(	(	PUNCT
ejpam-6500	168	13	∈,∈	∈,∈	INTJ
ejpam-6500	168	14	∨qn)-fuzzy	∨qn)-fuzzy	ADJ
ejpam-6500	168	15	subalgebra	subalgebra	NOUN
ejpam-6500	168	16	of	of	ADP
ejpam-6500	168	17	h.	h.	PROPN
ejpam-6500	168	18	note	note	VERB
ejpam-6500	168	19	that	that	SCONJ
ejpam-6500	168	20	an	an	DET
ejpam-6500	168	21	(	(	PUNCT
ejpam-6500	168	22	∈,∈	∈,∈	X
ejpam-6500	168	23	∨qn)-fuzzy	∨qn)-fuzzy	ADJ
ejpam-6500	168	24	subalgebra	subalgebra	NOUN
ejpam-6500	168	25	may	may	AUX
ejpam-6500	168	26	not	not	PART
ejpam-6500	168	27	be	be	AUX
ejpam-6500	168	28	an	an	DET
ejpam-6500	168	29	(	(	PUNCT
ejpam-6500	168	30	∈,∈	∈,∈	INTJ
ejpam-6500	168	31	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	168	32	subalgebra	subalgebra	NOUN
ejpam-6500	168	33	for	for	ADP
ejpam-6500	168	34	0	0	NUM
ejpam-6500	168	35	≤	≤	NUM
ejpam-6500	168	36	m	m	VERB
ejpam-6500	168	37	<	<	X
ejpam-6500	168	38	n	n	X
ejpam-6500	168	39	<	<	X
ejpam-6500	168	40	1	1	NUM
ejpam-6500	168	41	.	.	PUNCT
ejpam-6500	168	42	theorem	theorem	NOUN
ejpam-6500	168	43	6	6	NUM
ejpam-6500	168	44	.	.	PUNCT
ejpam-6500	169	1	a	a	DET
ejpam-6500	169	2	nonempty	nonempty	NOUN
ejpam-6500	169	3	subset	subset	VERB
ejpam-6500	169	4	m	m	NOUN
ejpam-6500	169	5	of	of	ADP
ejpam-6500	169	6	h	h	NOUN
ejpam-6500	169	7	is	be	AUX
ejpam-6500	169	8	a	a	DET
ejpam-6500	169	9	subalgebra	subalgebra	NOUN
ejpam-6500	169	10	of	of	ADP
ejpam-6500	169	11	h	h	NOUN
ejpam-6500	169	12	if	if	SCONJ
ejpam-6500	170	1	and	and	CCONJ
ejpam-6500	170	2	only	only	ADV
ejpam-6500	170	3	if	if	SCONJ
ejpam-6500	170	4	its	its	PRON
ejpam-6500	170	5	characteristic	characteristic	ADJ
ejpam-6500	170	6	function	function	NOUN
ejpam-6500	170	7	is	be	AUX
ejpam-6500	170	8	an	an	DET
ejpam-6500	170	9	(	(	PUNCT
ejpam-6500	170	10	∈,∈	∈,∈	INTJ
ejpam-6500	170	11	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	170	12	subalgebra	subalgebra	NOUN
ejpam-6500	170	13	of	of	ADP
ejpam-6500	170	14	h.	h.	NOUN
ejpam-6500	170	15	proof	proof	NOUN
ejpam-6500	170	16	.	.	PUNCT
ejpam-6500	171	1	let	let	VERB
ejpam-6500	171	2	m	m	PRON
ejpam-6500	171	3	be	be	AUX
ejpam-6500	171	4	a	a	DET
ejpam-6500	171	5	subalgebra	subalgebra	NOUN
ejpam-6500	171	6	of	of	ADP
ejpam-6500	171	7	h.	h.	PROPN
ejpam-6500	171	8	then	then	ADV
ejpam-6500	171	9	χm	χm	VERB
ejpam-6500	171	10	(	(	PUNCT
ejpam-6500	171	11	x	x	X
ejpam-6500	171	12	)	)	PUNCT
ejpam-6500	171	13	=	=	SYM
ejpam-6500	171	14	1	1	NUM
ejpam-6500	171	15	for	for	ADP
ejpam-6500	171	16	x	x	PROPN
ejpam-6500	171	17	∈	∈	PROPN
ejpam-6500	171	18	m	m	PROPN
ejpam-6500	171	19	and	and	CCONJ
ejpam-6500	171	20	χm	χm	PROPN
ejpam-6500	171	21	(	(	PUNCT
ejpam-6500	171	22	x	x	NOUN
ejpam-6500	171	23	)	)	PUNCT
ejpam-6500	171	24	=	=	SYM
ejpam-6500	171	25	0	0	NUM
ejpam-6500	172	1	for	for	ADP
ejpam-6500	172	2	x	x	PROPN
ejpam-6500	172	3	/∈	/∈	PROPN
ejpam-6500	172	4	m	m	VERB
ejpam-6500	172	5	.	.	PUNCT
ejpam-6500	173	1	thus	thus	ADV
ejpam-6500	173	2	,	,	PUNCT
ejpam-6500	173	3	u(µm	u(µm	PROPN
ejpam-6500	173	4	,	,	PUNCT
ejpam-6500	173	5	t	t	PROPN
ejpam-6500	173	6	)	)	PUNCT
ejpam-6500	173	7	=	=	SYM
ejpam-6500	173	8	m	m	VERB
ejpam-6500	173	9	for	for	ADP
ejpam-6500	173	10	all	all	DET
ejpam-6500	173	11	t	t	NOUN
ejpam-6500	173	12	∈	∈	PROPN
ejpam-6500	173	13	(	(	PUNCT
ejpam-6500	173	14	0	0	NUM
ejpam-6500	173	15	,	,	PUNCT
ejpam-6500	173	16	1−m	1−m	NUM
ejpam-6500	173	17	2	2	NUM
ejpam-6500	173	18	]	]	PUNCT
ejpam-6500	173	19	.	.	PUNCT
ejpam-6500	174	1	hence	hence	ADV
ejpam-6500	174	2	,	,	PUNCT
ejpam-6500	174	3	by	by	ADP
ejpam-6500	174	4	theorem	theorem	NOUN
ejpam-6500	174	5	2	2	NUM
ejpam-6500	174	6	,	,	PUNCT
ejpam-6500	174	7	we	we	PRON
ejpam-6500	174	8	have	have	VERB
ejpam-6500	174	9	χm	χm	PROPN
ejpam-6500	174	10	is	be	AUX
ejpam-6500	174	11	an	an	DET
ejpam-6500	174	12	(	(	PUNCT
ejpam-6500	174	13	∈,∈	∈,∈	INTJ
ejpam-6500	174	14	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	174	15	subalgebra	subalgebra	NOUN
ejpam-6500	174	16	of	of	ADP
ejpam-6500	174	17	h.	h.	NOUN
ejpam-6500	174	18	conversely	conversely	ADV
ejpam-6500	174	19	,	,	PUNCT
ejpam-6500	174	20	suppose	suppose	VERB
ejpam-6500	174	21	that	that	SCONJ
ejpam-6500	174	22	µm	µm	NOUN
ejpam-6500	174	23	is	be	AUX
ejpam-6500	174	24	an	an	DET
ejpam-6500	174	25	(	(	PUNCT
ejpam-6500	174	26	∈,∈	∈,∈	INTJ
ejpam-6500	174	27	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	174	28	subalgebra	subalgebra	NOUN
ejpam-6500	174	29	of	of	ADP
ejpam-6500	174	30	h.	h.	PROPN
ejpam-6500	174	31	then	then	ADV
ejpam-6500	174	32	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	174	33	)	)	PUNCT
ejpam-6500	174	34	)	)	PUNCT
ejpam-6500	174	35	)	)	PUNCT
ejpam-6500	175	1	>	>	PUNCT
ejpam-6500	175	2	min{χm	min{χm	NOUN
ejpam-6500	175	3	(	(	PUNCT
ejpam-6500	175	4	x	x	NOUN
ejpam-6500	175	5	)	)	PUNCT
ejpam-6500	175	6	,	,	PUNCT
ejpam-6500	175	7	χm	χm	PROPN
ejpam-6500	175	8	(	(	PUNCT
ejpam-6500	175	9	y	y	NOUN
ejpam-6500	175	10	)	)	PUNCT
ejpam-6500	175	11	,	,	PUNCT
ejpam-6500	175	12	1−m	1−m	NUM
ejpam-6500	175	13	2	2	NUM
ejpam-6500	175	14	}	}	PUNCT
ejpam-6500	175	15	=	=	SYM
ejpam-6500	175	16	min{1	min{1	PROPN
ejpam-6500	175	17	,	,	PUNCT
ejpam-6500	175	18	1−m	1−m	NUM
ejpam-6500	175	19	2	2	NUM
ejpam-6500	175	20	}	}	PUNCT
ejpam-6500	175	21	=	=	SYM
ejpam-6500	176	1	1−m	1−m	NUM
ejpam-6500	176	2	2	2	NUM
ejpam-6500	176	3	for	for	ADP
ejpam-6500	176	4	all	all	DET
ejpam-6500	176	5	x	x	NOUN
ejpam-6500	176	6	,	,	PUNCT
ejpam-6500	176	7	y	y	PROPN
ejpam-6500	176	8	∈	∈	PROPN
ejpam-6500	176	9	h.	h.	PROPN
ejpam-6500	176	10	since	since	SCONJ
ejpam-6500	176	11	m	m	PROPN
ejpam-6500	176	12	∈	∈	PROPN
ejpam-6500	177	1	[	[	X
ejpam-6500	177	2	0	0	NUM
ejpam-6500	177	3	,	,	PUNCT
ejpam-6500	177	4	1	1	NUM
ejpam-6500	177	5	)	)	PUNCT
ejpam-6500	177	6	,	,	PUNCT
ejpam-6500	177	7	χm	χm	PROPN
ejpam-6500	177	8	(	(	PUNCT
ejpam-6500	177	9	(	(	PUNCT
ejpam-6500	177	10	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	177	11	)	)	PUNCT
ejpam-6500	177	12	)	)	PUNCT
ejpam-6500	177	13	)	)	PUNCT
ejpam-6500	178	1	=	=	PUNCT
ejpam-6500	178	2	1	1	NUM
ejpam-6500	178	3	,	,	PUNCT
ejpam-6500	178	4	so	so	CCONJ
ejpam-6500	178	5	(	(	PUNCT
ejpam-6500	178	6	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	178	7	)	)	PUNCT
ejpam-6500	178	8	)	)	PUNCT
ejpam-6500	179	1	∈	∈	PROPN
ejpam-6500	179	2	m	m	VERB
ejpam-6500	179	3	.	.	PUNCT
ejpam-6500	180	1	hence	hence	ADV
ejpam-6500	180	2	,	,	PUNCT
ejpam-6500	180	3	m	m	VERB
ejpam-6500	180	4	is	be	AUX
ejpam-6500	180	5	a	a	DET
ejpam-6500	180	6	subalgebra	subalgebra	NOUN
ejpam-6500	180	7	of	of	ADP
ejpam-6500	180	8	h.	h.	PROPN
ejpam-6500	180	9	theorem	theorem	PROPN
ejpam-6500	180	10	7	7	NUM
ejpam-6500	180	11	.	.	X
ejpam-6500	180	12	for	for	ADP
ejpam-6500	180	13	every	every	DET
ejpam-6500	180	14	subalgebra	subalgebra	NOUN
ejpam-6500	180	15	m	m	VERB
ejpam-6500	180	16	of	of	ADP
ejpam-6500	180	17	h	h	NOUN
ejpam-6500	180	18	and	and	CCONJ
ejpam-6500	180	19	every	every	DET
ejpam-6500	180	20	t	t	NOUN
ejpam-6500	180	21	∈	∈	PROPN
ejpam-6500	180	22	(	(	PUNCT
ejpam-6500	180	23	0	0	NUM
ejpam-6500	180	24	,	,	PUNCT
ejpam-6500	180	25	1−m	1−m	NUM
ejpam-6500	180	26	2	2	NUM
ejpam-6500	180	27	]	]	PUNCT
ejpam-6500	180	28	there	there	PRON
ejpam-6500	180	29	exists	exist	VERB
ejpam-6500	180	30	an	an	DET
ejpam-6500	180	31	(	(	PUNCT
ejpam-6500	180	32	∈,∈	∈,∈	X
ejpam-6500	180	33	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	180	34	subalgebra	subalgebra	PROPN
ejpam-6500	180	35	µ	µ	X
ejpam-6500	180	36	of	of	ADP
ejpam-6500	180	37	h	h	NOUN
ejpam-6500	180	38	such	such	ADJ
ejpam-6500	180	39	that	that	SCONJ
ejpam-6500	180	40	u(µ	u(µ	NOUN
ejpam-6500	180	41	,	,	PUNCT
ejpam-6500	180	42	t	t	PROPN
ejpam-6500	180	43	)	)	PUNCT
ejpam-6500	180	44	=	=	NOUN
ejpam-6500	180	45	m	m	NOUN
ejpam-6500	180	46	.	.	PUNCT
ejpam-6500	181	1	proof	proof	NOUN
ejpam-6500	181	2	.	.	PUNCT
ejpam-6500	182	1	let	let	VERB
ejpam-6500	182	2	µ	µ	X
ejpam-6500	182	3	be	be	AUX
ejpam-6500	182	4	a	a	DET
ejpam-6500	182	5	fuzzy	fuzzy	ADJ
ejpam-6500	182	6	set	set	NOUN
ejpam-6500	182	7	in	in	ADP
ejpam-6500	182	8	h	h	NOUN
ejpam-6500	182	9	defined	define	VERB
ejpam-6500	182	10	by	by	ADP
ejpam-6500	182	11	µ(x	µ(x	NOUN
ejpam-6500	182	12	)	)	PUNCT
ejpam-6500	182	13	=	=	PRON
ejpam-6500	182	14	{	{	PUNCT
ejpam-6500	182	15	t	t	X
ejpam-6500	182	16	if	if	SCONJ
ejpam-6500	182	17	x	x	PROPN
ejpam-6500	182	18	∈	∈	PROPN
ejpam-6500	182	19	m	m	VERB
ejpam-6500	182	20	0	0	NUM
ejpam-6500	182	21	otherwise	otherwise	ADV
ejpam-6500	182	22	,	,	PUNCT
ejpam-6500	182	23	where	where	SCONJ
ejpam-6500	182	24	t	t	PROPN
ejpam-6500	182	25	∈	∈	PROPN
ejpam-6500	182	26	(	(	PUNCT
ejpam-6500	182	27	0	0	NUM
ejpam-6500	182	28	,	,	PUNCT
ejpam-6500	182	29	1−m	1−m	NUM
ejpam-6500	182	30	2	2	NUM
ejpam-6500	182	31	]	]	PUNCT
ejpam-6500	182	32	.	.	PUNCT
ejpam-6500	183	1	obviously	obviously	ADV
ejpam-6500	183	2	,	,	PUNCT
ejpam-6500	183	3	u(µ	u(µ	PROPN
ejpam-6500	183	4	,	,	PUNCT
ejpam-6500	183	5	t	t	PROPN
ejpam-6500	183	6	)	)	PUNCT
ejpam-6500	183	7	=	=	PUNCT
ejpam-6500	184	1	m	m	PROPN
ejpam-6500	184	2	.	.	PUNCT
ejpam-6500	185	1	assume	assume	VERB
ejpam-6500	185	2	that	that	SCONJ
ejpam-6500	185	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	VERB
ejpam-6500	185	4	)	)	PUNCT
ejpam-6500	185	5	)	)	PUNCT
ejpam-6500	185	6	)	)	PUNCT
ejpam-6500	186	1	<	<	X
ejpam-6500	186	2	min{µ(x	min{µ(x	PROPN
ejpam-6500	186	3	)	)	PUNCT
ejpam-6500	186	4	,	,	PUNCT
ejpam-6500	186	5	µ(y	µ(y	PROPN
ejpam-6500	186	6	)	)	PUNCT
ejpam-6500	186	7	,	,	PUNCT
ejpam-6500	186	8	1−m	1−m	NUM
ejpam-6500	186	9	2	2	NUM
ejpam-6500	186	10	}	}	PUNCT
ejpam-6500	186	11	for	for	ADP
ejpam-6500	186	12	some	some	DET
ejpam-6500	186	13	x	x	NOUN
ejpam-6500	186	14	,	,	PUNCT
ejpam-6500	186	15	y	y	PROPN
ejpam-6500	186	16	∈	∈	PROPN
ejpam-6500	186	17	h.	h.	PROPN
ejpam-6500	186	18	since	since	SCONJ
ejpam-6500	186	19	|im(µ)|	|im(µ)|	PROPN
ejpam-6500	186	20	=	=	SYM
ejpam-6500	186	21	2	2	NUM
ejpam-6500	186	22	,	,	PUNCT
ejpam-6500	186	23	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	186	24	)	)	PUNCT
ejpam-6500	186	25	)	)	PUNCT
ejpam-6500	186	26	)	)	PUNCT
ejpam-6500	187	1	=	=	SYM
ejpam-6500	187	2	0	0	NUM
ejpam-6500	187	3	and	and	CCONJ
ejpam-6500	187	4	min{µ(x	min{µ(x	PROPN
ejpam-6500	187	5	)	)	PUNCT
ejpam-6500	187	6	,	,	PUNCT
ejpam-6500	187	7	µ(y	µ(y	PROPN
ejpam-6500	187	8	)	)	PUNCT
ejpam-6500	187	9	,	,	PUNCT
ejpam-6500	187	10	1−m	1−m	NUM
ejpam-6500	187	11	2	2	NUM
ejpam-6500	187	12	}	}	PUNCT
ejpam-6500	187	13	=	=	PUNCT
ejpam-6500	187	14	t.	t.	NOUN
ejpam-6500	187	15	hence	hence	ADV
ejpam-6500	187	16	,	,	PUNCT
ejpam-6500	187	17	µ(x	µ(x	X
ejpam-6500	187	18	)	)	PUNCT
ejpam-6500	187	19	=	=	SYM
ejpam-6500	187	20	µ(y	µ(y	PROPN
ejpam-6500	187	21	)	)	PUNCT
ejpam-6500	187	22	=	=	SYM
ejpam-6500	187	23	t	t	PROPN
ejpam-6500	187	24	,	,	PUNCT
ejpam-6500	187	25	and	and	CCONJ
ejpam-6500	187	26	so	so	ADV
ejpam-6500	187	27	x	x	NOUN
ejpam-6500	187	28	,	,	PUNCT
ejpam-6500	187	29	y	y	PROPN
ejpam-6500	187	30	∈	∈	PROPN
ejpam-6500	187	31	m	m	VERB
ejpam-6500	187	32	.	.	PUNCT
ejpam-6500	188	1	since	since	SCONJ
ejpam-6500	188	2	m	m	PROPN
ejpam-6500	188	3	is	be	AUX
ejpam-6500	188	4	a	a	DET
ejpam-6500	188	5	subalgebra	subalgebra	NOUN
ejpam-6500	188	6	of	of	ADP
ejpam-6500	188	7	h	h	NOUN
ejpam-6500	188	8	,	,	PUNCT
ejpam-6500	188	9	(	(	PUNCT
ejpam-6500	188	10	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	188	11	)	)	PUNCT
ejpam-6500	188	12	)	)	PUNCT
ejpam-6500	189	1	∈	∈	PROPN
ejpam-6500	189	2	m	m	VERB
ejpam-6500	189	3	.	.	PUNCT
ejpam-6500	190	1	thus	thus	ADV
ejpam-6500	190	2	,	,	PUNCT
ejpam-6500	190	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	190	4	)	)	PUNCT
ejpam-6500	190	5	)	)	PUNCT
ejpam-6500	190	6	)	)	PUNCT
ejpam-6500	191	1	=	=	SYM
ejpam-6500	191	2	t	t	PROPN
ejpam-6500	191	3	,	,	PUNCT
ejpam-6500	191	4	which	which	PRON
ejpam-6500	191	5	is	be	AUX
ejpam-6500	191	6	a	a	DET
ejpam-6500	191	7	contradiction	contradiction	NOUN
ejpam-6500	191	8	.	.	PUNCT
ejpam-6500	192	1	therefore	therefore	ADV
ejpam-6500	192	2	,	,	PUNCT
ejpam-6500	192	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	192	4	)	)	PUNCT
ejpam-6500	192	5	)	)	PUNCT
ejpam-6500	192	6	)	)	PUNCT
ejpam-6500	192	7	≥	≥	NOUN
ejpam-6500	193	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	193	2	)	)	PUNCT
ejpam-6500	193	3	,	,	PUNCT
ejpam-6500	193	4	µ(y	µ(y	PROPN
ejpam-6500	193	5	)	)	PUNCT
ejpam-6500	193	6	,	,	PUNCT
ejpam-6500	193	7	1−m	1−m	NUM
ejpam-6500	193	8	2	2	NUM
ejpam-6500	193	9	}	}	PUNCT
ejpam-6500	193	10	for	for	ADP
ejpam-6500	193	11	all	all	DET
ejpam-6500	193	12	x	x	NOUN
ejpam-6500	193	13	,	,	PUNCT
ejpam-6500	193	14	y	y	PROPN
ejpam-6500	193	15	∈	∈	PROPN
ejpam-6500	193	16	h.	h.	PROPN
ejpam-6500	193	17	by	by	ADP
ejpam-6500	193	18	theorem	theorem	NOUN
ejpam-6500	193	19	1	1	NUM
ejpam-6500	193	20	,	,	PUNCT
ejpam-6500	193	21	we	we	PRON
ejpam-6500	193	22	have	have	VERB
ejpam-6500	193	23	µ	µ	NOUN
ejpam-6500	193	24	is	be	AUX
ejpam-6500	193	25	an	an	DET
ejpam-6500	193	26	(	(	PUNCT
ejpam-6500	193	27	∈,∈	∈,∈	INTJ
ejpam-6500	193	28	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	193	29	subalgebra	subalgebra	NOUN
ejpam-6500	193	30	of	of	ADP
ejpam-6500	193	31	h.	h.	PROPN
ejpam-6500	193	32	theorem	theorem	PROPN
ejpam-6500	193	33	8	8	NUM
ejpam-6500	193	34	.	.	PUNCT
ejpam-6500	194	1	the	the	DET
ejpam-6500	194	2	intersection	intersection	NOUN
ejpam-6500	194	3	of	of	ADP
ejpam-6500	194	4	any	any	DET
ejpam-6500	194	5	family	family	NOUN
ejpam-6500	194	6	of	of	ADP
ejpam-6500	194	7	(	(	PUNCT
ejpam-6500	194	8	∈,∈	∈,∈	X
ejpam-6500	194	9	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	194	10	subalgebras	subalgebras	PROPN
ejpam-6500	194	11	of	of	ADP
ejpam-6500	194	12	h	h	PROPN
ejpam-6500	194	13	is	be	AUX
ejpam-6500	194	14	an	an	DET
ejpam-6500	194	15	(	(	PUNCT
ejpam-6500	194	16	∈,∈	∈,∈	INTJ
ejpam-6500	194	17	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	194	18	subalgebra	subalgebra	NOUN
ejpam-6500	194	19	of	of	ADP
ejpam-6500	194	20	h.	h.	PROPN
ejpam-6500	194	21	t.	t.	PROPN
ejpam-6500	194	22	oner	oner	PROPN
ejpam-6500	194	23	et	et	PROPN
ejpam-6500	194	24	al	al	PROPN
ejpam-6500	194	25	.	.	PUNCT
ejpam-6500	194	26	/	/	SYM
ejpam-6500	194	27	eur	eur	PROPN
ejpam-6500	194	28	.	.	PUNCT
ejpam-6500	195	1	j.	j.	PROPN
ejpam-6500	195	2	pure	pure	PROPN
ejpam-6500	195	3	appl	appl	PROPN
ejpam-6500	195	4	.	.	PROPN
ejpam-6500	195	5	math	math	PROPN
ejpam-6500	195	6	,	,	PUNCT
ejpam-6500	195	7	18	18	NUM
ejpam-6500	195	8	(	(	PUNCT
ejpam-6500	195	9	3	3	NUM
ejpam-6500	195	10	)	)	PUNCT
ejpam-6500	195	11	(	(	PUNCT
ejpam-6500	195	12	2025	2025	NUM
ejpam-6500	195	13	)	)	PUNCT
ejpam-6500	195	14	,	,	PUNCT
ejpam-6500	195	15	6500	6500	NUM
ejpam-6500	195	16	8	8	NUM
ejpam-6500	195	17	of	of	ADP
ejpam-6500	195	18	13	13	NUM
ejpam-6500	195	19	proof	proof	NOUN
ejpam-6500	195	20	.	.	PUNCT
ejpam-6500	196	1	let	let	VERB
ejpam-6500	196	2	µ	µ	X
ejpam-6500	196	3	=	=	SYM
ejpam-6500	196	4	⋂	⋂	PROPN
ejpam-6500	196	5	i∈∆	i∈∆	NOUN
ejpam-6500	196	6	µi	µi	PROPN
ejpam-6500	196	7	,	,	PUNCT
ejpam-6500	196	8	where	where	SCONJ
ejpam-6500	196	9	µi	µi	PROPN
ejpam-6500	196	10	is	be	AUX
ejpam-6500	196	11	an	an	DET
ejpam-6500	196	12	(	(	PUNCT
ejpam-6500	196	13	∈,∈	∈,∈	X
ejpam-6500	196	14	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	196	15	subalgebras	subalgebras	PROPN
ejpam-6500	196	16	of	of	ADP
ejpam-6500	196	17	h.	h.	PROPN
ejpam-6500	196	18	then	then	ADV
ejpam-6500	196	19	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	196	20	)	)	PUNCT
ejpam-6500	196	21	)	)	PUNCT
ejpam-6500	196	22	)	)	PUNCT
ejpam-6500	197	1	=	=	PRON
ejpam-6500	197	2	inf	inf	PROPN
ejpam-6500	197	3	i∈∆	i∈∆	PROPN
ejpam-6500	197	4	µi((x|(y|y))|(x|(y|y	µi((x|(y|y))|(x|(y|y	PROPN
ejpam-6500	197	5	)	)	PUNCT
ejpam-6500	197	6	)	)	PUNCT
ejpam-6500	197	7	)	)	PUNCT
ejpam-6500	197	8	≥	≥	PROPN
ejpam-6500	197	9	inf	inf	PROPN
ejpam-6500	197	10	i∈∆	i∈∆	PROPN
ejpam-6500	197	11	min{µi(x	min{µi(x	NUM
ejpam-6500	197	12	)	)	PUNCT
ejpam-6500	197	13	,	,	PUNCT
ejpam-6500	197	14	µi(y	µi(y	NOUN
ejpam-6500	197	15	)	)	PUNCT
ejpam-6500	197	16	,	,	PUNCT
ejpam-6500	197	17	1−m	1−m	NUM
ejpam-6500	197	18	2	2	NUM
ejpam-6500	197	19	}	}	PUNCT
ejpam-6500	197	20	≥	≥	NOUN
ejpam-6500	197	21	min	min	PROPN
ejpam-6500	197	22	{	{	PUNCT
ejpam-6500	197	23	inf	inf	NOUN
ejpam-6500	197	24	i∈∆	i∈∆	PROPN
ejpam-6500	197	25	µi(x	µi(x	NUM
ejpam-6500	197	26	)	)	PUNCT
ejpam-6500	197	27	,	,	PUNCT
ejpam-6500	197	28	inf	inf	NOUN
ejpam-6500	197	29	i∈∆	i∈∆	PROPN
ejpam-6500	197	30	µi(y	µi(y	NOUN
ejpam-6500	197	31	)	)	PUNCT
ejpam-6500	197	32	,	,	PUNCT
ejpam-6500	197	33	1−m	1−m	NUM
ejpam-6500	197	34	2	2	NUM
ejpam-6500	197	35	}	}	PUNCT
ejpam-6500	197	36	=	=	SYM
ejpam-6500	197	37	min	min	NOUN
ejpam-6500	197	38	{	{	PUNCT
ejpam-6500	197	39	⋂	⋂	PROPN
ejpam-6500	197	40	i∈∆	i∈∆	PROPN
ejpam-6500	197	41	µi(x	µi(x	NUM
ejpam-6500	197	42	)	)	PUNCT
ejpam-6500	197	43	,	,	PUNCT
ejpam-6500	197	44	⋂	⋂	PROPN
ejpam-6500	197	45	i∈∆	i∈∆	PROPN
ejpam-6500	197	46	µi(y	µi(y	NOUN
ejpam-6500	197	47	)	)	PUNCT
ejpam-6500	197	48	,	,	PUNCT
ejpam-6500	197	49	1−m	1−m	NUM
ejpam-6500	197	50	2	2	NUM
ejpam-6500	197	51	}	}	PUNCT
ejpam-6500	197	52	=	=	SYM
ejpam-6500	197	53	min{µ(x	min{µ(x	NOUN
ejpam-6500	197	54	)	)	PUNCT
ejpam-6500	197	55	,	,	PUNCT
ejpam-6500	197	56	µ(y	µ(y	PROPN
ejpam-6500	197	57	)	)	PUNCT
ejpam-6500	197	58	,	,	PUNCT
ejpam-6500	197	59	1−m	1−m	NUM
ejpam-6500	197	60	2	2	NUM
ejpam-6500	197	61	}	}	PUNCT
ejpam-6500	197	62	.	.	PUNCT
ejpam-6500	198	1	hence	hence	ADV
ejpam-6500	198	2	,	,	PUNCT
ejpam-6500	198	3	by	by	ADP
ejpam-6500	198	4	theorem	theorem	NOUN
ejpam-6500	198	5	1	1	NUM
ejpam-6500	198	6	,	,	PUNCT
ejpam-6500	198	7	we	we	PRON
ejpam-6500	198	8	have	have	VERB
ejpam-6500	198	9	µ	µ	NOUN
ejpam-6500	198	10	is	be	AUX
ejpam-6500	198	11	an	an	DET
ejpam-6500	198	12	(	(	PUNCT
ejpam-6500	198	13	∈,∈	∈,∈	INTJ
ejpam-6500	198	14	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	198	15	subalgebra	subalgebra	NOUN
ejpam-6500	198	16	of	of	ADP
ejpam-6500	198	17	h.	h.	PROPN
ejpam-6500	198	18	theorem	theorem	PROPN
ejpam-6500	198	19	9	9	NUM
ejpam-6500	198	20	.	.	X
ejpam-6500	199	1	for	for	ADP
ejpam-6500	199	2	any	any	DET
ejpam-6500	199	3	finite	finite	NOUN
ejpam-6500	199	4	strictly	strictly	ADV
ejpam-6500	199	5	increasing	increase	VERB
ejpam-6500	199	6	chain	chain	NOUN
ejpam-6500	199	7	of	of	ADP
ejpam-6500	199	8	subalgebras	subalgebras	PROPN
ejpam-6500	199	9	of	of	ADP
ejpam-6500	199	10	h	h	NOUN
ejpam-6500	199	11	there	there	PRON
ejpam-6500	199	12	exists	exist	VERB
ejpam-6500	199	13	an	an	DET
ejpam-6500	199	14	(	(	PUNCT
ejpam-6500	199	15	∈,∈	∈,∈	X
ejpam-6500	199	16	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	199	17	subalgebra	subalgebra	PROPN
ejpam-6500	199	18	µ	µ	X
ejpam-6500	199	19	of	of	ADP
ejpam-6500	199	20	h	h	PRON
ejpam-6500	199	21	whose	whose	DET
ejpam-6500	199	22	level	level	NOUN
ejpam-6500	199	23	subalgebras	subalgebra	NOUN
ejpam-6500	199	24	are	be	AUX
ejpam-6500	199	25	precisely	precisely	ADV
ejpam-6500	199	26	the	the	DET
ejpam-6500	199	27	members	member	NOUN
ejpam-6500	199	28	of	of	ADP
ejpam-6500	199	29	the	the	DET
ejpam-6500	199	30	chain	chain	NOUN
ejpam-6500	199	31	with	with	ADP
ejpam-6500	199	32	µ	µ	PROPN
ejpam-6500	199	33	1−m	1−m	NUM
ejpam-6500	199	34	2	2	NUM
ejpam-6500	199	35	=	=	SYM
ejpam-6500	199	36	h0	h0	PROPN
ejpam-6500	199	37	⊂	⊂	PROPN
ejpam-6500	199	38	h1	h1	PROPN
ejpam-6500	199	39	⊂	⊂	PROPN
ejpam-6500	199	40	.	.	PUNCT
ejpam-6500	199	41	.	.	PUNCT
ejpam-6500	199	42	.	.	PUNCT
ejpam-6500	200	1	⊂	⊂	PROPN
ejpam-6500	200	2	hn	hn	PROPN
ejpam-6500	201	1	=	=	NOUN
ejpam-6500	201	2	h.	h.	PROPN
ejpam-6500	201	3	proof	proof	NOUN
ejpam-6500	201	4	.	.	PUNCT
ejpam-6500	202	1	let	let	VERB
ejpam-6500	202	2	{	{	PUNCT
ejpam-6500	202	3	ti	ti	NOUN
ejpam-6500	202	4	:	:	PUNCT
ejpam-6500	202	5	ti	ti	PROPN
ejpam-6500	202	6	∈	∈	PROPN
ejpam-6500	202	7	(	(	PUNCT
ejpam-6500	202	8	0	0	NUM
ejpam-6500	202	9	,	,	PUNCT
ejpam-6500	202	10	1−m	1−m	NUM
ejpam-6500	202	11	2	2	NUM
ejpam-6500	202	12	]	]	PUNCT
ejpam-6500	202	13	,	,	PUNCT
ejpam-6500	202	14	i	i	PRON
ejpam-6500	202	15	=	=	NOUN
ejpam-6500	202	16	1	1	NUM
ejpam-6500	202	17	,	,	PUNCT
ejpam-6500	202	18	2	2	NUM
ejpam-6500	202	19	,	,	PUNCT
ejpam-6500	202	20	.	.	PUNCT
ejpam-6500	202	21	.	.	PUNCT
ejpam-6500	203	1	.	.	PUNCT
ejpam-6500	204	1	,	,	PUNCT
ejpam-6500	204	2	n	n	CCONJ
ejpam-6500	204	3	}	}	PUNCT
ejpam-6500	204	4	be	be	AUX
ejpam-6500	204	5	such	such	ADJ
ejpam-6500	204	6	that	that	DET
ejpam-6500	204	7	1−m	1−m	NUM
ejpam-6500	204	8	2	2	NUM
ejpam-6500	204	9	>	>	SYM
ejpam-6500	204	10	t1	t1	NOUN
ejpam-6500	204	11	>	>	X
ejpam-6500	204	12	t2	t2	PROPN
ejpam-6500	204	13	>	>	X
ejpam-6500	204	14	t3	t3	PROPN
ejpam-6500	204	15	>	>	X
ejpam-6500	204	16	.	.	PUNCT
ejpam-6500	204	17	.	.	PUNCT
ejpam-6500	205	1	.	.	PUNCT
ejpam-6500	206	1	>	>	X
ejpam-6500	206	2	tn	tn	PROPN
ejpam-6500	206	3	.	.	PUNCT
ejpam-6500	207	1	consider	consider	VERB
ejpam-6500	207	2	the	the	DET
ejpam-6500	207	3	fuzzy	fuzzy	ADJ
ejpam-6500	207	4	set	set	NOUN
ejpam-6500	207	5	µ	µ	PRON
ejpam-6500	207	6	defined	define	VERB
ejpam-6500	207	7	by	by	ADP
ejpam-6500	207	8	µ(x	µ(x	NOUN
ejpam-6500	207	9	)	)	PUNCT
ejpam-6500	207	10	=	=	SYM
ejpam-6500	207	11	{	{	PUNCT
ejpam-6500	207	12	1−m	1−m	NUM
ejpam-6500	207	13	2	2	NUM
ejpam-6500	207	14	if	if	SCONJ
ejpam-6500	207	15	x	x	PROPN
ejpam-6500	207	16	∈	∈	PROPN
ejpam-6500	207	17	h0	h0	NOUN
ejpam-6500	207	18	tk	tk	PROPN
ejpam-6500	207	19	if	if	SCONJ
ejpam-6500	207	20	x	x	PROPN
ejpam-6500	207	21	∈	∈	PROPN
ejpam-6500	207	22	hk\hk−1	hk\hk−1	NOUN
ejpam-6500	207	23	,	,	PUNCT
ejpam-6500	207	24	k	k	NOUN
ejpam-6500	207	25	=	=	SYM
ejpam-6500	207	26	1	1	NUM
ejpam-6500	207	27	,	,	PUNCT
ejpam-6500	207	28	2	2	NUM
ejpam-6500	207	29	,	,	PUNCT
ejpam-6500	207	30	.	.	PUNCT
ejpam-6500	207	31	.	.	PUNCT
ejpam-6500	208	1	.	.	PUNCT
ejpam-6500	209	1	,	,	PUNCT
ejpam-6500	209	2	n.	n.	PROPN
ejpam-6500	209	3	let	let	VERB
ejpam-6500	209	4	x	x	PRON
ejpam-6500	209	5	,	,	PUNCT
ejpam-6500	209	6	y	y	PROPN
ejpam-6500	209	7	∈	∈	PROPN
ejpam-6500	209	8	h	h	NOUN
ejpam-6500	209	9	be	be	AUX
ejpam-6500	209	10	such	such	ADJ
ejpam-6500	209	11	that	that	SCONJ
ejpam-6500	209	12	x	x	SYM
ejpam-6500	209	13	∈	∈	PROPN
ejpam-6500	209	14	hi\hi−1	hi\hi−1	PROPN
ejpam-6500	209	15	and	and	CCONJ
ejpam-6500	209	16	y	y	PROPN
ejpam-6500	209	17	∈	∈	PROPN
ejpam-6500	209	18	hj\hj−1	hj\hj−1	NOUN
ejpam-6500	209	19	,	,	PUNCT
ejpam-6500	210	1	where	where	SCONJ
ejpam-6500	210	2	1	1	NUM
ejpam-6500	210	3	≤	≤	PUNCT
ejpam-6500	210	4	i	i	PRON
ejpam-6500	210	5	,	,	PUNCT
ejpam-6500	210	6	j	j	PROPN
ejpam-6500	210	7	≤	≤	PROPN
ejpam-6500	210	8	n.	n.	NOUN
ejpam-6500	210	9	if	if	SCONJ
ejpam-6500	210	10	i	i	PRON
ejpam-6500	210	11	≥	≥	VERB
ejpam-6500	210	12	j	j	NOUN
ejpam-6500	210	13	,	,	PUNCT
ejpam-6500	210	14	then	then	ADV
ejpam-6500	210	15	x	x	SYM
ejpam-6500	210	16	∈	∈	PROPN
ejpam-6500	210	17	hi	hi	INTJ
ejpam-6500	210	18	and	and	CCONJ
ejpam-6500	210	19	y	y	PROPN
ejpam-6500	210	20	∈	∈	PROPN
ejpam-6500	210	21	hi	hi	INTJ
ejpam-6500	210	22	,	,	PUNCT
ejpam-6500	210	23	so	so	CCONJ
ejpam-6500	210	24	(	(	PUNCT
ejpam-6500	210	25	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	210	26	)	)	PUNCT
ejpam-6500	210	27	)	)	PUNCT
ejpam-6500	211	1	∈	∈	PROPN
ejpam-6500	212	1	hi	hi	INTJ
ejpam-6500	212	2	.	.	PUNCT
ejpam-6500	213	1	thus	thus	ADV
ejpam-6500	213	2	,	,	PUNCT
ejpam-6500	213	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	213	4	)	)	PUNCT
ejpam-6500	213	5	)	)	PUNCT
ejpam-6500	213	6	)	)	PUNCT
ejpam-6500	214	1	≥	≥	X
ejpam-6500	214	2	ti	ti	NOUN
ejpam-6500	214	3	=	=	SYM
ejpam-6500	214	4	min{ti	min{ti	X
ejpam-6500	214	5	,	,	PUNCT
ejpam-6500	214	6	tj	tj	NOUN
ejpam-6500	214	7	}	}	PUNCT
ejpam-6500	214	8	=	=	SYM
ejpam-6500	214	9	min{µ(x	min{µ(x	NOUN
ejpam-6500	214	10	)	)	PUNCT
ejpam-6500	214	11	,	,	PUNCT
ejpam-6500	214	12	µ(y	µ(y	PROPN
ejpam-6500	214	13	)	)	PUNCT
ejpam-6500	214	14	,	,	PUNCT
ejpam-6500	214	15	1−m	1−m	NUM
ejpam-6500	214	16	2	2	NUM
ejpam-6500	214	17	}	}	PUNCT
ejpam-6500	214	18	.	.	PUNCT
ejpam-6500	215	1	if	if	SCONJ
ejpam-6500	215	2	i	i	PRON
ejpam-6500	215	3	<	<	X
ejpam-6500	215	4	j	j	PROPN
ejpam-6500	215	5	,	,	PUNCT
ejpam-6500	215	6	then	then	ADV
ejpam-6500	215	7	x	x	SYM
ejpam-6500	215	8	∈	∈	PROPN
ejpam-6500	215	9	hj	hj	PROPN
ejpam-6500	215	10	and	and	CCONJ
ejpam-6500	215	11	y	y	PROPN
ejpam-6500	215	12	∈	∈	PROPN
ejpam-6500	215	13	hj	hj	PROPN
ejpam-6500	215	14	,	,	PUNCT
ejpam-6500	215	15	so	so	CCONJ
ejpam-6500	215	16	(	(	PUNCT
ejpam-6500	215	17	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	215	18	)	)	PUNCT
ejpam-6500	215	19	)	)	PUNCT
ejpam-6500	216	1	∈	∈	PROPN
ejpam-6500	216	2	hj	hj	PROPN
ejpam-6500	216	3	.	.	PUNCT
ejpam-6500	217	1	thus	thus	ADV
ejpam-6500	217	2	,	,	PUNCT
ejpam-6500	217	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	217	4	)	)	PUNCT
ejpam-6500	217	5	)	)	PUNCT
ejpam-6500	217	6	)	)	PUNCT
ejpam-6500	218	1	≤	≤	NUM
ejpam-6500	218	2	tj	tj	X
ejpam-6500	218	3	=	=	SYM
ejpam-6500	218	4	min{ti	min{ti	PROPN
ejpam-6500	218	5	,	,	PUNCT
ejpam-6500	218	6	tj	tj	NOUN
ejpam-6500	218	7	}	}	PUNCT
ejpam-6500	218	8	=	=	SYM
ejpam-6500	218	9	min{µ(x	min{µ(x	NOUN
ejpam-6500	218	10	)	)	PUNCT
ejpam-6500	218	11	,	,	PUNCT
ejpam-6500	218	12	µ(y	µ(y	PROPN
ejpam-6500	218	13	)	)	PUNCT
ejpam-6500	218	14	,	,	PUNCT
ejpam-6500	218	15	1−m	1−m	NUM
ejpam-6500	218	16	2	2	NUM
ejpam-6500	218	17	}	}	PUNCT
ejpam-6500	218	18	.	.	PUNCT
ejpam-6500	219	1	hence	hence	ADV
ejpam-6500	219	2	,	,	PUNCT
ejpam-6500	219	3	µ	µ	X
ejpam-6500	219	4	is	be	AUX
ejpam-6500	219	5	an	an	DET
ejpam-6500	219	6	(	(	PUNCT
ejpam-6500	219	7	∈,∈	∈,∈	INTJ
ejpam-6500	219	8	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	219	9	subalgebra	subalgebra	NOUN
ejpam-6500	219	10	of	of	ADP
ejpam-6500	219	11	h.	h.	PROPN
ejpam-6500	219	12	definition	definition	NOUN
ejpam-6500	219	13	7	7	NUM
ejpam-6500	219	14	.	.	PUNCT
ejpam-6500	220	1	for	for	ADP
ejpam-6500	220	2	any	any	DET
ejpam-6500	220	3	fuzzy	fuzzy	ADJ
ejpam-6500	220	4	set	set	VERB
ejpam-6500	220	5	µ	µ	NOUN
ejpam-6500	220	6	in	in	ADP
ejpam-6500	220	7	h	h	PROPN
ejpam-6500	220	8	and	and	CCONJ
ejpam-6500	220	9	t	t	PROPN
ejpam-6500	220	10	∈	∈	PROPN
ejpam-6500	220	11	(	(	PUNCT
ejpam-6500	220	12	0	0	NUM
ejpam-6500	220	13	,	,	PUNCT
ejpam-6500	220	14	1	1	NUM
ejpam-6500	220	15	]	]	PUNCT
ejpam-6500	220	16	,	,	PUNCT
ejpam-6500	220	17	we	we	PRON
ejpam-6500	220	18	define	define	VERB
ejpam-6500	220	19	the	the	DET
ejpam-6500	220	20	sets	set	NOUN
ejpam-6500	220	21	[	[	X
ejpam-6500	220	22	µ]t	µ]t	X
ejpam-6500	220	23	=	=	SYM
ejpam-6500	220	24	{	{	PUNCT
ejpam-6500	220	25	x	x	PUNCT
ejpam-6500	220	26	∈	∈	PROPN
ejpam-6500	220	27	h	h	NOUN
ejpam-6500	220	28	:	:	PUNCT
ejpam-6500	220	29	xt	xt	PROPN
ejpam-6500	220	30	∈	∈	PROPN
ejpam-6500	220	31	∨qmµ	∨qmµ	PROPN
ejpam-6500	220	32	}	}	PUNCT
ejpam-6500	220	33	and	and	CCONJ
ejpam-6500	220	34	q(µ	q(µ	PROPN
ejpam-6500	220	35	,	,	PUNCT
ejpam-6500	220	36	t	t	PROPN
ejpam-6500	220	37	)	)	PUNCT
ejpam-6500	220	38	=	=	PRON
ejpam-6500	221	1	{	{	PUNCT
ejpam-6500	221	2	x	x	PUNCT
ejpam-6500	221	3	∈	∈	PROPN
ejpam-6500	221	4	h	h	NOUN
ejpam-6500	221	5	:	:	PUNCT
ejpam-6500	221	6	xtqmµ	xtqmµ	PROPN
ejpam-6500	221	7	}	}	PUNCT
ejpam-6500	221	8	.	.	PUNCT
ejpam-6500	222	1	it	it	PRON
ejpam-6500	222	2	is	be	AUX
ejpam-6500	222	3	clear	clear	ADJ
ejpam-6500	222	4	that	that	SCONJ
ejpam-6500	222	5	[	[	X
ejpam-6500	222	6	µ]t	µ]t	X
ejpam-6500	222	7	=	=	SYM
ejpam-6500	222	8	u(µ	u(µ	PROPN
ejpam-6500	222	9	,	,	PUNCT
ejpam-6500	222	10	t	t	PROPN
ejpam-6500	222	11	)	)	PUNCT
ejpam-6500	222	12	∪q(µ	∪q(µ	NOUN
ejpam-6500	222	13	,	,	PUNCT
ejpam-6500	222	14	t	t	PROPN
ejpam-6500	222	15	)	)	PUNCT
ejpam-6500	222	16	.	.	PUNCT
ejpam-6500	223	1	theorem	theorem	ADJ
ejpam-6500	223	2	10	10	NUM
ejpam-6500	223	3	.	.	PUNCT
ejpam-6500	224	1	let	let	VERB
ejpam-6500	224	2	µ	µ	X
ejpam-6500	224	3	be	be	AUX
ejpam-6500	224	4	a	a	DET
ejpam-6500	224	5	fuzzy	fuzzy	ADJ
ejpam-6500	224	6	set	set	NOUN
ejpam-6500	224	7	in	in	ADP
ejpam-6500	224	8	h.	h.	PROPN
ejpam-6500	224	9	then	then	ADV
ejpam-6500	224	10	µ	µ	PROPN
ejpam-6500	224	11	is	be	AUX
ejpam-6500	224	12	an	an	DET
ejpam-6500	224	13	(	(	PUNCT
ejpam-6500	224	14	∈,∈	∈,∈	INTJ
ejpam-6500	224	15	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	224	16	subalgebra	subalgebra	NOUN
ejpam-6500	224	17	of	of	ADP
ejpam-6500	224	18	h	h	NOUN
ejpam-6500	224	19	if	if	SCONJ
ejpam-6500	225	1	and	and	CCONJ
ejpam-6500	225	2	only	only	ADV
ejpam-6500	225	3	if	if	SCONJ
ejpam-6500	225	4	[	[	X
ejpam-6500	225	5	µ]t	µ]t	NOUN
ejpam-6500	225	6	is	be	AUX
ejpam-6500	225	7	a	a	DET
ejpam-6500	225	8	subalgebra	subalgebra	NOUN
ejpam-6500	225	9	of	of	ADP
ejpam-6500	225	10	h	h	NOUN
ejpam-6500	225	11	for	for	ADP
ejpam-6500	225	12	all	all	DET
ejpam-6500	225	13	t	t	NOUN
ejpam-6500	225	14	∈	∈	PROPN
ejpam-6500	225	15	(	(	PUNCT
ejpam-6500	225	16	0	0	NUM
ejpam-6500	225	17	,	,	PUNCT
ejpam-6500	225	18	1	1	NUM
ejpam-6500	225	19	]	]	PUNCT
ejpam-6500	225	20	.	.	PUNCT
ejpam-6500	226	1	we	we	PRON
ejpam-6500	226	2	call	call	VERB
ejpam-6500	226	3	[	[	X
ejpam-6500	226	4	µ]t	µ]t	ADJ
ejpam-6500	226	5	an	an	DET
ejpam-6500	226	6	(	(	PUNCT
ejpam-6500	226	7	∈	∈	NOUN
ejpam-6500	226	8	∨qm)-level	∨qm)-level	NOUN
ejpam-6500	226	9	subalgebra	subalgebra	NOUN
ejpam-6500	226	10	of	of	ADP
ejpam-6500	226	11	µ.	µ.	NOUN
ejpam-6500	226	12	proof	proof	NOUN
ejpam-6500	226	13	.	.	PUNCT
ejpam-6500	227	1	assume	assume	VERB
ejpam-6500	227	2	that	that	SCONJ
ejpam-6500	227	3	µ	µ	NOUN
ejpam-6500	227	4	is	be	AUX
ejpam-6500	227	5	an	an	DET
ejpam-6500	227	6	(	(	PUNCT
ejpam-6500	227	7	∈,∈	∈,∈	INTJ
ejpam-6500	227	8	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	227	9	subalgebra	subalgebra	NOUN
ejpam-6500	227	10	of	of	ADP
ejpam-6500	227	11	hand	hand	NOUN
ejpam-6500	227	12	let	let	VERB
ejpam-6500	227	13	x	x	PRON
ejpam-6500	227	14	,	,	PUNCT
ejpam-6500	227	15	y	y	PROPN
ejpam-6500	227	16	∈	∈	PROPN
ejpam-6500	228	1	[	[	X
ejpam-6500	228	2	µ]t	µ]t	NOUN
ejpam-6500	228	3	for	for	ADP
ejpam-6500	228	4	t	t	PROPN
ejpam-6500	228	5	∈	∈	PROPN
ejpam-6500	228	6	(	(	PUNCT
ejpam-6500	228	7	0	0	NUM
ejpam-6500	228	8	,	,	PUNCT
ejpam-6500	228	9	1	1	NUM
ejpam-6500	228	10	]	]	PUNCT
ejpam-6500	228	11	.	.	PUNCT
ejpam-6500	229	1	then	then	ADV
ejpam-6500	229	2	(	(	PUNCT
ejpam-6500	229	3	x	x	X
ejpam-6500	229	4	,	,	PUNCT
ejpam-6500	229	5	t	t	PROPN
ejpam-6500	229	6	)	)	PUNCT
ejpam-6500	229	7	∈	∈	PROPN
ejpam-6500	229	8	∨qmµ	∨qmµ	PROPN
ejpam-6500	229	9	and	and	CCONJ
ejpam-6500	229	10	(	(	PUNCT
ejpam-6500	229	11	y	y	PROPN
ejpam-6500	229	12	,	,	PUNCT
ejpam-6500	229	13	t	t	PROPN
ejpam-6500	229	14	)	)	PUNCT
ejpam-6500	229	15	∈	∈	PROPN
ejpam-6500	229	16	∨qmµ	∨qmµ	PROPN
ejpam-6500	229	17	,	,	PUNCT
ejpam-6500	229	18	that	that	ADV
ejpam-6500	229	19	is	is	ADV
ejpam-6500	229	20	,	,	PUNCT
ejpam-6500	229	21	µ(x	µ(x	X
ejpam-6500	229	22	)	)	PUNCT
ejpam-6500	229	23	>	>	SYM
ejpam-6500	229	24	1	1	NUM
ejpam-6500	229	25	or	or	CCONJ
ejpam-6500	229	26	µ(x	µ(x	NOUN
ejpam-6500	229	27	)	)	PUNCT
ejpam-6500	230	1	+	+	NUM
ejpam-6500	230	2	t	t	X
ejpam-6500	230	3	>	>	X
ejpam-6500	230	4	1	1	NUM
ejpam-6500	230	5	−m	−m	NOUN
ejpam-6500	230	6	,	,	PUNCT
ejpam-6500	230	7	and	and	CCONJ
ejpam-6500	230	8	µ(y	µ(y	NUM
ejpam-6500	230	9	)	)	PUNCT
ejpam-6500	230	10	>	>	X
ejpam-6500	230	11	1	1	NUM
ejpam-6500	230	12	or	or	CCONJ
ejpam-6500	230	13	µ(y	µ(y	NUM
ejpam-6500	230	14	)	)	PUNCT
ejpam-6500	231	1	+	+	NUM
ejpam-6500	231	2	t	t	X
ejpam-6500	231	3	>	>	X
ejpam-6500	231	4	1	1	NUM
ejpam-6500	231	5	−	−	NOUN
ejpam-6500	231	6	m.	m.	NOUN
ejpam-6500	231	7	by	by	ADP
ejpam-6500	231	8	theorem	theorem	NOUN
ejpam-6500	231	9	1	1	NUM
ejpam-6500	231	10	,	,	PUNCT
ejpam-6500	231	11	we	we	PRON
ejpam-6500	231	12	have	have	AUX
ejpam-6500	231	13	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	VERB
ejpam-6500	231	14	)	)	PUNCT
ejpam-6500	231	15	)	)	PUNCT
ejpam-6500	231	16	)	)	PUNCT
ejpam-6500	231	17	≥	≥	NOUN
ejpam-6500	232	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	232	2	)	)	PUNCT
ejpam-6500	232	3	,	,	PUNCT
ejpam-6500	232	4	µ(y	µ(y	PROPN
ejpam-6500	232	5	)	)	PUNCT
ejpam-6500	232	6	,	,	PUNCT
ejpam-6500	232	7	1−m	1−m	NUM
ejpam-6500	232	8	2	2	NUM
ejpam-6500	232	9	}	}	PUNCT
ejpam-6500	232	10	.	.	PUNCT
ejpam-6500	233	1	t.	t.	PROPN
ejpam-6500	233	2	oner	oner	PROPN
ejpam-6500	233	3	et	et	PROPN
ejpam-6500	233	4	al	al	PROPN
ejpam-6500	233	5	.	.	PUNCT
ejpam-6500	233	6	/	/	SYM
ejpam-6500	233	7	eur	eur	PROPN
ejpam-6500	233	8	.	.	PUNCT
ejpam-6500	234	1	j.	j.	PROPN
ejpam-6500	234	2	pure	pure	PROPN
ejpam-6500	234	3	appl	appl	PROPN
ejpam-6500	234	4	.	.	PROPN
ejpam-6500	234	5	math	math	PROPN
ejpam-6500	234	6	,	,	PUNCT
ejpam-6500	234	7	18	18	NUM
ejpam-6500	234	8	(	(	PUNCT
ejpam-6500	234	9	3	3	NUM
ejpam-6500	234	10	)	)	PUNCT
ejpam-6500	234	11	(	(	PUNCT
ejpam-6500	234	12	2025	2025	NUM
ejpam-6500	234	13	)	)	PUNCT
ejpam-6500	234	14	,	,	PUNCT
ejpam-6500	234	15	6500	6500	NUM
ejpam-6500	234	16	9	9	NUM
ejpam-6500	234	17	of	of	ADP
ejpam-6500	234	18	13	13	NUM
ejpam-6500	234	19	case	case	NOUN
ejpam-6500	234	20	1	1	NUM
ejpam-6500	234	21	:	:	PUNCT
ejpam-6500	234	22	if	if	SCONJ
ejpam-6500	234	23	µ(x	µ(x	NOUN
ejpam-6500	234	24	)	)	PUNCT
ejpam-6500	234	25	≥	≥	NOUN
ejpam-6500	234	26	t	t	NOUN
ejpam-6500	234	27	and	and	CCONJ
ejpam-6500	234	28	µ(y	µ(y	PROPN
ejpam-6500	234	29	)	)	PUNCT
ejpam-6500	234	30	≥	≥	NOUN
ejpam-6500	234	31	t	t	PROPN
ejpam-6500	234	32	,	,	PUNCT
ejpam-6500	234	33	then	then	ADV
ejpam-6500	234	34	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	234	35	)	)	PUNCT
ejpam-6500	234	36	)	)	PUNCT
ejpam-6500	234	37	)	)	PUNCT
ejpam-6500	234	38	≥	≥	NOUN
ejpam-6500	235	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	235	2	)	)	PUNCT
ejpam-6500	235	3	,	,	PUNCT
ejpam-6500	235	4	µ(y	µ(y	PROPN
ejpam-6500	235	5	)	)	PUNCT
ejpam-6500	235	6	,	,	PUNCT
ejpam-6500	235	7	1−m	1−m	NUM
ejpam-6500	235	8	2	2	NUM
ejpam-6500	235	9	}	}	PUNCT
ejpam-6500	235	10	=	=	SYM
ejpam-6500	235	11	1−m	1−m	NUM
ejpam-6500	235	12	2	2	NUM
ejpam-6500	235	13	.	.	PUNCT
ejpam-6500	236	1	hence	hence	ADV
ejpam-6500	236	2	,	,	PUNCT
ejpam-6500	236	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	236	4	)	)	PUNCT
ejpam-6500	236	5	)	)	PUNCT
ejpam-6500	236	6	)	)	PUNCT
ejpam-6500	237	1	+	+	CCONJ
ejpam-6500	237	2	t	t	X
ejpam-6500	237	3	>	>	X
ejpam-6500	237	4	1−m	1−m	NUM
ejpam-6500	237	5	2	2	NUM
ejpam-6500	237	6	+	+	SYM
ejpam-6500	237	7	1−m	1−m	NUM
ejpam-6500	237	8	2	2	NUM
ejpam-6500	237	9	=	=	SYM
ejpam-6500	237	10	1−m	1−m	NUM
ejpam-6500	237	11	,	,	PUNCT
ejpam-6500	237	12	and	and	CCONJ
ejpam-6500	237	13	so	so	ADV
ejpam-6500	237	14	(	(	PUNCT
ejpam-6500	237	15	(	(	PUNCT
ejpam-6500	237	16	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	237	17	)	)	PUNCT
ejpam-6500	237	18	)	)	PUNCT
ejpam-6500	237	19	,	,	PUNCT
ejpam-6500	237	20	t)qmµ.	t)qmµ.	INTJ
ejpam-6500	237	21	if	if	SCONJ
ejpam-6500	237	22	t	t	NOUN
ejpam-6500	237	23	≤	≤	NUM
ejpam-6500	237	24	1−m	1−m	NUM
ejpam-6500	237	25	2	2	NUM
ejpam-6500	237	26	,	,	PUNCT
ejpam-6500	237	27	then	then	ADV
ejpam-6500	237	28	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	237	29	)	)	PUNCT
ejpam-6500	237	30	)	)	PUNCT
ejpam-6500	237	31	)	)	PUNCT
ejpam-6500	237	32	≥	≥	NOUN
ejpam-6500	238	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	238	2	)	)	PUNCT
ejpam-6500	238	3	,	,	PUNCT
ejpam-6500	238	4	µ(y	µ(y	PROPN
ejpam-6500	238	5	)	)	PUNCT
ejpam-6500	238	6	,	,	PUNCT
ejpam-6500	238	7	1−m	1−m	NUM
ejpam-6500	238	8	2	2	NUM
ejpam-6500	238	9	}	}	PUNCT
ejpam-6500	238	10	=	=	SYM
ejpam-6500	238	11	1−m	1−m	NUM
ejpam-6500	238	12	2	2	NUM
ejpam-6500	238	13	≥	≥	NOUN
ejpam-6500	238	14	t	t	NOUN
ejpam-6500	238	15	,	,	PUNCT
ejpam-6500	238	16	and	and	CCONJ
ejpam-6500	238	17	thus	thus	ADV
ejpam-6500	238	18	(	(	PUNCT
ejpam-6500	238	19	(	(	PUNCT
ejpam-6500	238	20	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	238	21	)	)	PUNCT
ejpam-6500	238	22	)	)	PUNCT
ejpam-6500	238	23	,	,	PUNCT
ejpam-6500	238	24	t	t	X
ejpam-6500	238	25	)	)	PUNCT
ejpam-6500	238	26	∈	∈	PROPN
ejpam-6500	238	27	µ.	µ.	NOUN
ejpam-6500	238	28	hence	hence	ADV
ejpam-6500	238	29	,	,	PUNCT
ejpam-6500	238	30	(	(	PUNCT
ejpam-6500	238	31	(	(	PUNCT
ejpam-6500	238	32	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	238	33	)	)	PUNCT
ejpam-6500	238	34	)	)	PUNCT
ejpam-6500	238	35	,	,	PUNCT
ejpam-6500	238	36	t	t	X
ejpam-6500	238	37	)	)	PUNCT
ejpam-6500	238	38	∈	∈	PROPN
ejpam-6500	238	39	∨qmµ.	∨qmµ.	PUNCT
ejpam-6500	238	40	therefore	therefore	ADV
ejpam-6500	238	41	,	,	PUNCT
ejpam-6500	238	42	(	(	PUNCT
ejpam-6500	238	43	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	238	44	)	)	PUNCT
ejpam-6500	238	45	)	)	PUNCT
ejpam-6500	239	1	∈	∈	PROPN
ejpam-6500	240	1	[	[	X
ejpam-6500	240	2	µ]t	µ]t	NOUN
ejpam-6500	240	3	.	.	PUNCT
ejpam-6500	241	1	case	case	NOUN
ejpam-6500	242	1	2	2	NUM
ejpam-6500	242	2	:	:	PUNCT
ejpam-6500	242	3	if	if	SCONJ
ejpam-6500	242	4	µ(x	µ(x	NOUN
ejpam-6500	242	5	)	)	PUNCT
ejpam-6500	242	6	≥	≥	NOUN
ejpam-6500	242	7	t	t	NOUN
ejpam-6500	242	8	and	and	CCONJ
ejpam-6500	242	9	µ(y	µ(y	NUM
ejpam-6500	242	10	)	)	PUNCT
ejpam-6500	243	1	+	+	NUM
ejpam-6500	243	2	t	t	X
ejpam-6500	243	3	>	>	X
ejpam-6500	243	4	1	1	NUM
ejpam-6500	243	5	−m	−m	NOUN
ejpam-6500	243	6	.	.	PUNCT
ejpam-6500	244	1	if	if	SCONJ
ejpam-6500	244	2	t	t	PROPN
ejpam-6500	244	3	>	>	X
ejpam-6500	244	4	1−m	1−m	NUM
ejpam-6500	244	5	2	2	NUM
ejpam-6500	244	6	,	,	PUNCT
ejpam-6500	244	7	then	then	ADV
ejpam-6500	244	8	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	244	9	)	)	PUNCT
ejpam-6500	244	10	)	)	PUNCT
ejpam-6500	244	11	)	)	PUNCT
ejpam-6500	244	12	≥	≥	NOUN
ejpam-6500	245	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	245	2	)	)	PUNCT
ejpam-6500	245	3	,	,	PUNCT
ejpam-6500	245	4	µ(y	µ(y	PROPN
ejpam-6500	245	5	)	)	PUNCT
ejpam-6500	245	6	,	,	PUNCT
ejpam-6500	245	7	1−m	1−m	NUM
ejpam-6500	245	8	2	2	NUM
ejpam-6500	245	9	}	}	PUNCT
ejpam-6500	245	10	=	=	SYM
ejpam-6500	245	11	µ(y	µ(y	PROPN
ejpam-6500	245	12	)	)	PUNCT
ejpam-6500	245	13	∧	∧	NOUN
ejpam-6500	245	14	1−m	1−m	NUM
ejpam-6500	245	15	2	2	NUM
ejpam-6500	245	16	>	>	X
ejpam-6500	245	17	(	(	PUNCT
ejpam-6500	245	18	1−m−	1−m−	NUM
ejpam-6500	245	19	t	t	PROPN
ejpam-6500	245	20	)	)	PUNCT
ejpam-6500	245	21	∧	∧	PROPN
ejpam-6500	245	22	1−m	1−m	NUM
ejpam-6500	245	23	2	2	NUM
ejpam-6500	245	24	=	=	SYM
ejpam-6500	245	25	1−m−	1−m−	NUM
ejpam-6500	245	26	t	t	PROPN
ejpam-6500	245	27	,	,	PUNCT
ejpam-6500	245	28	and	and	CCONJ
ejpam-6500	245	29	so	so	ADV
ejpam-6500	245	30	(	(	PUNCT
ejpam-6500	245	31	(	(	PUNCT
ejpam-6500	245	32	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	245	33	)	)	PUNCT
ejpam-6500	245	34	)	)	PUNCT
ejpam-6500	245	35	,	,	PUNCT
ejpam-6500	246	1	t)qmµ.	t)qmµ.	INTJ
ejpam-6500	246	2	if	if	SCONJ
ejpam-6500	246	3	t	t	NOUN
ejpam-6500	246	4	≤	≤	NUM
ejpam-6500	246	5	1−m	1−m	NUM
ejpam-6500	246	6	2	2	NUM
ejpam-6500	246	7	,	,	PUNCT
ejpam-6500	246	8	then	then	ADV
ejpam-6500	246	9	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	246	10	)	)	PUNCT
ejpam-6500	246	11	)	)	PUNCT
ejpam-6500	246	12	)	)	PUNCT
ejpam-6500	246	13	≥	≥	NOUN
ejpam-6500	247	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	247	2	)	)	PUNCT
ejpam-6500	247	3	,	,	PUNCT
ejpam-6500	247	4	µ(y	µ(y	PROPN
ejpam-6500	247	5	)	)	PUNCT
ejpam-6500	247	6	,	,	PUNCT
ejpam-6500	247	7	1−m	1−m	NUM
ejpam-6500	247	8	2	2	NUM
ejpam-6500	247	9	}	}	PUNCT
ejpam-6500	247	10	≥	≥	NOUN
ejpam-6500	247	11	min{t	min{t	PROPN
ejpam-6500	247	12	,	,	PUNCT
ejpam-6500	247	13	1−m−t	1−m−t	NUM
ejpam-6500	247	14	,	,	PUNCT
ejpam-6500	247	15	1−m	1−m	NUM
ejpam-6500	247	16	2	2	NUM
ejpam-6500	247	17	}	}	PUNCT
ejpam-6500	247	18	=	=	PUNCT
ejpam-6500	247	19	t.	t.	NOUN
ejpam-6500	247	20	hence	hence	ADV
ejpam-6500	247	21	,	,	PUNCT
ejpam-6500	247	22	(	(	PUNCT
ejpam-6500	247	23	(	(	PUNCT
ejpam-6500	247	24	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	247	25	)	)	PUNCT
ejpam-6500	247	26	)	)	PUNCT
ejpam-6500	247	27	,	,	PUNCT
ejpam-6500	247	28	t	t	X
ejpam-6500	247	29	)	)	PUNCT
ejpam-6500	247	30	∈	∈	PROPN
ejpam-6500	247	31	µ	µ	NOUN
ejpam-6500	247	32	,	,	PUNCT
ejpam-6500	247	33	and	and	CCONJ
ejpam-6500	247	34	hence	hence	ADV
ejpam-6500	247	35	(	(	PUNCT
ejpam-6500	247	36	(	(	PUNCT
ejpam-6500	247	37	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	247	38	)	)	PUNCT
ejpam-6500	247	39	)	)	PUNCT
ejpam-6500	247	40	,	,	PUNCT
ejpam-6500	247	41	t	t	X
ejpam-6500	247	42	)	)	PUNCT
ejpam-6500	247	43	∈	∈	PROPN
ejpam-6500	247	44	∨qmµ.	∨qmµ.	PUNCT
ejpam-6500	247	45	therefore	therefore	ADV
ejpam-6500	247	46	,	,	PUNCT
ejpam-6500	247	47	(	(	PUNCT
ejpam-6500	247	48	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	247	49	)	)	PUNCT
ejpam-6500	247	50	)	)	PUNCT
ejpam-6500	248	1	∈	∈	PROPN
ejpam-6500	249	1	[	[	X
ejpam-6500	249	2	µ]t	µ]t	NOUN
ejpam-6500	249	3	.	.	PUNCT
ejpam-6500	250	1	case	case	NOUN
ejpam-6500	251	1	3	3	NUM
ejpam-6500	251	2	:	:	PUNCT
ejpam-6500	251	3	if	if	SCONJ
ejpam-6500	251	4	µ(x	µ(x	VERB
ejpam-6500	251	5	)	)	PUNCT
ejpam-6500	251	6	+	+	NUM
ejpam-6500	251	7	t	t	X
ejpam-6500	251	8	>	>	X
ejpam-6500	251	9	1	1	NUM
ejpam-6500	251	10	−m	−m	NOUN
ejpam-6500	251	11	and	and	CCONJ
ejpam-6500	251	12	µ(y	µ(y	PROPN
ejpam-6500	251	13	)	)	PUNCT
ejpam-6500	251	14	≥	≥	NOUN
ejpam-6500	251	15	t.	t.	NOUN
ejpam-6500	252	1	if	if	SCONJ
ejpam-6500	252	2	t	t	PROPN
ejpam-6500	252	3	>	>	X
ejpam-6500	252	4	1−m	1−m	NUM
ejpam-6500	252	5	2	2	NUM
ejpam-6500	252	6	,	,	PUNCT
ejpam-6500	252	7	then	then	ADV
ejpam-6500	252	8	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	252	9	)	)	PUNCT
ejpam-6500	252	10	)	)	PUNCT
ejpam-6500	252	11	)	)	PUNCT
ejpam-6500	252	12	≥	≥	NOUN
ejpam-6500	253	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	253	2	)	)	PUNCT
ejpam-6500	253	3	,	,	PUNCT
ejpam-6500	253	4	µ(y	µ(y	PROPN
ejpam-6500	253	5	)	)	PUNCT
ejpam-6500	253	6	,	,	PUNCT
ejpam-6500	253	7	1−m	1−m	NUM
ejpam-6500	253	8	2	2	NUM
ejpam-6500	253	9	}	}	PUNCT
ejpam-6500	253	10	=	=	SYM
ejpam-6500	253	11	µ(x	µ(x	X
ejpam-6500	253	12	)	)	PUNCT
ejpam-6500	253	13	∧	∧	NOUN
ejpam-6500	253	14	1−m	1−m	NUM
ejpam-6500	253	15	2	2	NUM
ejpam-6500	253	16	>	>	X
ejpam-6500	253	17	(	(	PUNCT
ejpam-6500	253	18	1−m−	1−m−	NUM
ejpam-6500	253	19	t	t	PROPN
ejpam-6500	253	20	)	)	PUNCT
ejpam-6500	253	21	∧	∧	PROPN
ejpam-6500	253	22	1−m	1−m	NUM
ejpam-6500	253	23	2	2	NUM
ejpam-6500	253	24	=	=	SYM
ejpam-6500	253	25	1−m−	1−m−	NUM
ejpam-6500	253	26	t	t	PROPN
ejpam-6500	253	27	,	,	PUNCT
ejpam-6500	253	28	and	and	CCONJ
ejpam-6500	253	29	so	so	ADV
ejpam-6500	253	30	(	(	PUNCT
ejpam-6500	253	31	(	(	PUNCT
ejpam-6500	253	32	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	253	33	)	)	PUNCT
ejpam-6500	253	34	)	)	PUNCT
ejpam-6500	253	35	,	,	PUNCT
ejpam-6500	254	1	t)qmµ.	t)qmµ.	INTJ
ejpam-6500	254	2	if	if	SCONJ
ejpam-6500	254	3	t	t	NOUN
ejpam-6500	254	4	≤	≤	NUM
ejpam-6500	254	5	1−m	1−m	NUM
ejpam-6500	254	6	2	2	NUM
ejpam-6500	254	7	,	,	PUNCT
ejpam-6500	254	8	then	then	ADV
ejpam-6500	254	9	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	254	10	)	)	PUNCT
ejpam-6500	254	11	)	)	PUNCT
ejpam-6500	254	12	)	)	PUNCT
ejpam-6500	254	13	≥	≥	NOUN
ejpam-6500	255	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	255	2	)	)	PUNCT
ejpam-6500	255	3	,	,	PUNCT
ejpam-6500	255	4	µ(y	µ(y	PROPN
ejpam-6500	255	5	)	)	PUNCT
ejpam-6500	255	6	,	,	PUNCT
ejpam-6500	255	7	1−m	1−m	NUM
ejpam-6500	255	8	2	2	NUM
ejpam-6500	255	9	}	}	PUNCT
ejpam-6500	255	10	≥	≥	NOUN
ejpam-6500	255	11	min{1−m−t	min{1−m−t	PROPN
ejpam-6500	255	12	,	,	PUNCT
ejpam-6500	255	13	t	t	PROPN
ejpam-6500	255	14	,	,	PUNCT
ejpam-6500	255	15	1−m	1−m	NUM
ejpam-6500	255	16	2	2	NUM
ejpam-6500	255	17	}	}	PUNCT
ejpam-6500	255	18	=	=	PUNCT
ejpam-6500	255	19	t.	t.	NOUN
ejpam-6500	255	20	hence	hence	ADV
ejpam-6500	255	21	,	,	PUNCT
ejpam-6500	255	22	(	(	PUNCT
ejpam-6500	255	23	(	(	PUNCT
ejpam-6500	255	24	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	255	25	)	)	PUNCT
ejpam-6500	255	26	)	)	PUNCT
ejpam-6500	255	27	,	,	PUNCT
ejpam-6500	255	28	t	t	X
ejpam-6500	255	29	)	)	PUNCT
ejpam-6500	255	30	∈	∈	PROPN
ejpam-6500	255	31	µ	µ	NOUN
ejpam-6500	255	32	,	,	PUNCT
ejpam-6500	255	33	and	and	CCONJ
ejpam-6500	255	34	hence	hence	ADV
ejpam-6500	255	35	(	(	PUNCT
ejpam-6500	255	36	(	(	PUNCT
ejpam-6500	255	37	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	255	38	)	)	PUNCT
ejpam-6500	255	39	)	)	PUNCT
ejpam-6500	255	40	,	,	PUNCT
ejpam-6500	255	41	t	t	X
ejpam-6500	255	42	)	)	PUNCT
ejpam-6500	255	43	∈	∈	PROPN
ejpam-6500	255	44	∨qmµ.	∨qmµ.	PUNCT
ejpam-6500	255	45	therefore	therefore	ADV
ejpam-6500	255	46	,	,	PUNCT
ejpam-6500	255	47	(	(	PUNCT
ejpam-6500	255	48	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	255	49	)	)	PUNCT
ejpam-6500	255	50	)	)	PUNCT
ejpam-6500	256	1	∈	∈	PROPN
ejpam-6500	257	1	[	[	X
ejpam-6500	257	2	µ]t	µ]t	NOUN
ejpam-6500	257	3	.	.	PUNCT
ejpam-6500	258	1	case	case	NOUN
ejpam-6500	258	2	4	4	NUM
ejpam-6500	258	3	:	:	PUNCT
ejpam-6500	258	4	if	if	SCONJ
ejpam-6500	258	5	µ(x)+t	µ(x)+t	X
ejpam-6500	258	6	>	>	X
ejpam-6500	258	7	1−m	1−m	NUM
ejpam-6500	259	1	and	and	CCONJ
ejpam-6500	259	2	µ(y)+t	µ(y)+t	NOUN
ejpam-6500	259	3	>	>	X
ejpam-6500	259	4	1−m	1−m	NUM
ejpam-6500	259	5	.	.	PUNCT
ejpam-6500	260	1	if	if	SCONJ
ejpam-6500	260	2	t	t	PROPN
ejpam-6500	260	3	>	>	X
ejpam-6500	260	4	1−m	1−m	NUM
ejpam-6500	260	5	2	2	NUM
ejpam-6500	260	6	,	,	PUNCT
ejpam-6500	260	7	then	then	ADV
ejpam-6500	260	8	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	260	9	)	)	PUNCT
ejpam-6500	260	10	)	)	PUNCT
ejpam-6500	260	11	)	)	PUNCT
ejpam-6500	260	12	≥	≥	NOUN
ejpam-6500	261	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	261	2	)	)	PUNCT
ejpam-6500	261	3	,	,	PUNCT
ejpam-6500	261	4	µ(y	µ(y	PROPN
ejpam-6500	261	5	)	)	PUNCT
ejpam-6500	261	6	,	,	PUNCT
ejpam-6500	261	7	1−m	1−m	NUM
ejpam-6500	261	8	2	2	NUM
ejpam-6500	261	9	}	}	PUNCT
ejpam-6500	261	10	>	>	X
ejpam-6500	261	11	(	(	PUNCT
ejpam-6500	261	12	1−m−	1−m−	NUM
ejpam-6500	261	13	t	t	PROPN
ejpam-6500	261	14	)	)	PUNCT
ejpam-6500	261	15	∧	∧	PROPN
ejpam-6500	261	16	1−m	1−m	NUM
ejpam-6500	261	17	2	2	NUM
ejpam-6500	261	18	=	=	SYM
ejpam-6500	261	19	1−m−	1−m−	NUM
ejpam-6500	261	20	t	t	PROPN
ejpam-6500	261	21	,	,	PUNCT
ejpam-6500	261	22	and	and	CCONJ
ejpam-6500	261	23	so	so	ADV
ejpam-6500	261	24	(	(	PUNCT
ejpam-6500	261	25	(	(	PUNCT
ejpam-6500	261	26	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	261	27	)	)	PUNCT
ejpam-6500	261	28	)	)	PUNCT
ejpam-6500	261	29	,	,	PUNCT
ejpam-6500	262	1	t)qmµ.	t)qmµ.	INTJ
ejpam-6500	262	2	if	if	SCONJ
ejpam-6500	262	3	t	t	NOUN
ejpam-6500	262	4	≤	≤	NUM
ejpam-6500	262	5	1−m	1−m	NUM
ejpam-6500	262	6	2	2	NUM
ejpam-6500	262	7	,	,	PUNCT
ejpam-6500	262	8	then	then	ADV
ejpam-6500	262	9	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	262	10	)	)	PUNCT
ejpam-6500	262	11	)	)	PUNCT
ejpam-6500	262	12	)	)	PUNCT
ejpam-6500	262	13	≥	≥	NOUN
ejpam-6500	263	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	263	2	)	)	PUNCT
ejpam-6500	263	3	,	,	PUNCT
ejpam-6500	263	4	µ(y	µ(y	PROPN
ejpam-6500	263	5	)	)	PUNCT
ejpam-6500	263	6	,	,	PUNCT
ejpam-6500	263	7	1−m	1−m	NUM
ejpam-6500	263	8	2	2	NUM
ejpam-6500	263	9	}	}	PUNCT
ejpam-6500	263	10	≥	≥	NOUN
ejpam-6500	263	11	min{1−m−t	min{1−m−t	PROPN
ejpam-6500	263	12	,	,	PUNCT
ejpam-6500	263	13	t	t	PROPN
ejpam-6500	263	14	,	,	PUNCT
ejpam-6500	263	15	1−m	1−m	NUM
ejpam-6500	263	16	2	2	NUM
ejpam-6500	263	17	}	}	PUNCT
ejpam-6500	263	18	≥	≥	NUM
ejpam-6500	263	19	(	(	PUNCT
ejpam-6500	263	20	1−m−	1−m−	NUM
ejpam-6500	263	21	t	t	NOUN
ejpam-6500	263	22	)	)	PUNCT
ejpam-6500	263	23	∧	∧	PROPN
ejpam-6500	263	24	1−m	1−m	NUM
ejpam-6500	263	25	2	2	NUM
ejpam-6500	263	26	=	=	SYM
ejpam-6500	263	27	1−m	1−m	NUM
ejpam-6500	263	28	2	2	NUM
ejpam-6500	263	29	≥	≥	NOUN
ejpam-6500	263	30	t.	t.	NOUN
ejpam-6500	263	31	hence	hence	ADV
ejpam-6500	263	32	,	,	PUNCT
ejpam-6500	263	33	(	(	PUNCT
ejpam-6500	263	34	(	(	PUNCT
ejpam-6500	263	35	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	263	36	)	)	PUNCT
ejpam-6500	263	37	)	)	PUNCT
ejpam-6500	263	38	,	,	PUNCT
ejpam-6500	263	39	t	t	X
ejpam-6500	263	40	)	)	PUNCT
ejpam-6500	263	41	∈	∈	PROPN
ejpam-6500	263	42	µ	µ	NOUN
ejpam-6500	263	43	,	,	PUNCT
ejpam-6500	263	44	and	and	CCONJ
ejpam-6500	263	45	hence	hence	ADV
ejpam-6500	263	46	(	(	PUNCT
ejpam-6500	263	47	(	(	PUNCT
ejpam-6500	263	48	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	263	49	)	)	PUNCT
ejpam-6500	263	50	)	)	PUNCT
ejpam-6500	263	51	,	,	PUNCT
ejpam-6500	263	52	t	t	X
ejpam-6500	263	53	)	)	PUNCT
ejpam-6500	263	54	∈	∈	PROPN
ejpam-6500	263	55	∨qmµ.	∨qmµ.	PUNCT
ejpam-6500	263	56	therefore	therefore	ADV
ejpam-6500	263	57	,	,	PUNCT
ejpam-6500	263	58	(	(	PUNCT
ejpam-6500	263	59	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	263	60	)	)	PUNCT
ejpam-6500	263	61	)	)	PUNCT
ejpam-6500	264	1	∈	∈	PROPN
ejpam-6500	265	1	[	[	X
ejpam-6500	265	2	µ]t	µ]t	NOUN
ejpam-6500	265	3	.	.	PUNCT
ejpam-6500	266	1	consequently	consequently	ADV
ejpam-6500	266	2	,	,	PUNCT
ejpam-6500	266	3	[	[	X
ejpam-6500	266	4	µ]t	µ]t	ADJ
ejpam-6500	266	5	is	be	AUX
ejpam-6500	266	6	a	a	DET
ejpam-6500	266	7	subalgebra	subalgebra	NOUN
ejpam-6500	266	8	of	of	ADP
ejpam-6500	266	9	h.	h.	NOUN
ejpam-6500	266	10	conversely	conversely	ADV
ejpam-6500	266	11	,	,	PUNCT
ejpam-6500	266	12	let	let	VERB
ejpam-6500	266	13	µ	µ	X
ejpam-6500	266	14	be	be	AUX
ejpam-6500	266	15	a	a	DET
ejpam-6500	266	16	fuzzy	fuzzy	ADJ
ejpam-6500	266	17	set	set	NOUN
ejpam-6500	266	18	in	in	ADP
ejpam-6500	266	19	h	h	NOUN
ejpam-6500	266	20	and	and	CCONJ
ejpam-6500	266	21	t	t	PROPN
ejpam-6500	266	22	∈	∈	PROPN
ejpam-6500	266	23	(	(	PUNCT
ejpam-6500	266	24	0	0	NUM
ejpam-6500	266	25	,	,	PUNCT
ejpam-6500	266	26	1	1	NUM
ejpam-6500	266	27	]	]	PUNCT
ejpam-6500	266	28	be	be	AUX
ejpam-6500	266	29	such	such	ADJ
ejpam-6500	266	30	that	that	SCONJ
ejpam-6500	266	31	[	[	X
ejpam-6500	266	32	µ]t	µ]t	PROPN
ejpam-6500	266	33	is	be	AUX
ejpam-6500	266	34	a	a	DET
ejpam-6500	266	35	subalgebra	subalgebra	NOUN
ejpam-6500	266	36	of	of	ADP
ejpam-6500	266	37	h.	h.	NOUN
ejpam-6500	266	38	if	if	SCONJ
ejpam-6500	266	39	it	it	PRON
ejpam-6500	266	40	is	be	AUX
ejpam-6500	266	41	possible	possible	ADJ
ejpam-6500	266	42	,	,	PUNCT
ejpam-6500	266	43	let	let	VERB
ejpam-6500	266	44	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	266	45	)	)	PUNCT
ejpam-6500	266	46	)	)	PUNCT
ejpam-6500	266	47	)	)	PUNCT
ejpam-6500	267	1	<	<	X
ejpam-6500	267	2	t	t	X
ejpam-6500	267	3	≤	≤	NOUN
ejpam-6500	267	4	min{µ(x	min{µ(x	PROPN
ejpam-6500	267	5	)	)	PUNCT
ejpam-6500	267	6	,	,	PUNCT
ejpam-6500	267	7	µ(y	µ(y	PROPN
ejpam-6500	267	8	)	)	PUNCT
ejpam-6500	267	9	,	,	PUNCT
ejpam-6500	267	10	1−m	1−m	NUM
ejpam-6500	267	11	2	2	NUM
ejpam-6500	267	12	}	}	PUNCT
ejpam-6500	267	13	for	for	ADP
ejpam-6500	267	14	some	some	DET
ejpam-6500	267	15	t	t	NOUN
ejpam-6500	267	16	∈	∈	PROPN
ejpam-6500	267	17	(	(	PUNCT
ejpam-6500	267	18	0	0	NUM
ejpam-6500	267	19	,	,	PUNCT
ejpam-6500	267	20	1	1	NUM
ejpam-6500	267	21	)	)	PUNCT
ejpam-6500	267	22	.	.	PUNCT
ejpam-6500	268	1	then	then	ADV
ejpam-6500	268	2	x	x	X
ejpam-6500	268	3	,	,	PUNCT
ejpam-6500	268	4	y	y	PROPN
ejpam-6500	268	5	∈	∈	PROPN
ejpam-6500	268	6	u(µ	u(µ	PROPN
ejpam-6500	268	7	,	,	PUNCT
ejpam-6500	268	8	t	t	PROPN
ejpam-6500	268	9	)	)	PUNCT
ejpam-6500	268	10	⊆	⊆	NUM
ejpam-6500	268	11	[	[	X
ejpam-6500	268	12	µ]t	µ]t	NOUN
ejpam-6500	268	13	,	,	PUNCT
ejpam-6500	268	14	which	which	PRON
ejpam-6500	268	15	implies	imply	VERB
ejpam-6500	268	16	that	that	SCONJ
ejpam-6500	268	17	(	(	PUNCT
ejpam-6500	268	18	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-6500	268	19	)	)	PUNCT
ejpam-6500	268	20	)	)	PUNCT
ejpam-6500	268	21	∈	∈	PROPN
ejpam-6500	269	1	[	[	X
ejpam-6500	269	2	µ]t	µ]t	NOUN
ejpam-6500	269	3	.	.	PUNCT
ejpam-6500	270	1	hence	hence	ADV
ejpam-6500	270	2	,	,	PUNCT
ejpam-6500	270	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	270	4	)	)	PUNCT
ejpam-6500	270	5	)	)	PUNCT
ejpam-6500	270	6	)	)	PUNCT
ejpam-6500	271	1	∈	∈	PROPN
ejpam-6500	272	1	[	[	X
ejpam-6500	272	2	µ]t	µ]t	ADJ
ejpam-6500	272	3	or	or	CCONJ
ejpam-6500	272	4	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	272	5	)	)	PUNCT
ejpam-6500	272	6	)	)	PUNCT
ejpam-6500	272	7	)	)	PUNCT
ejpam-6500	273	1	+	+	CCONJ
ejpam-6500	273	2	t+m	t+m	PRON
ejpam-6500	273	3	>	>	SYM
ejpam-6500	273	4	1	1	NUM
ejpam-6500	273	5	,	,	PUNCT
ejpam-6500	273	6	a	a	DET
ejpam-6500	273	7	contradiction	contradiction	NOUN
ejpam-6500	273	8	.	.	PUNCT
ejpam-6500	274	1	therefore	therefore	ADV
ejpam-6500	274	2	,	,	PUNCT
ejpam-6500	274	3	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-6500	274	4	)	)	PUNCT
ejpam-6500	274	5	)	)	PUNCT
ejpam-6500	274	6	)	)	PUNCT
ejpam-6500	274	7	≥	≥	NOUN
ejpam-6500	275	1	min{µ(x	min{µ(x	NOUN
ejpam-6500	275	2	)	)	PUNCT
ejpam-6500	275	3	,	,	PUNCT
ejpam-6500	275	4	µ(y	µ(y	PROPN
ejpam-6500	275	5	)	)	PUNCT
ejpam-6500	275	6	,	,	PUNCT
ejpam-6500	275	7	1−m	1−m	NUM
ejpam-6500	275	8	2	2	NUM
ejpam-6500	275	9	}	}	PUNCT
ejpam-6500	275	10	for	for	ADP
ejpam-6500	275	11	all	all	DET
ejpam-6500	275	12	x	x	NOUN
ejpam-6500	275	13	,	,	PUNCT
ejpam-6500	275	14	y	y	PROPN
ejpam-6500	275	15	∈	∈	PROPN
ejpam-6500	275	16	h.	h.	PROPN
ejpam-6500	275	17	by	by	ADP
ejpam-6500	275	18	theorem	theorem	NOUN
ejpam-6500	275	19	1	1	NUM
ejpam-6500	275	20	,	,	PUNCT
ejpam-6500	275	21	we	we	PRON
ejpam-6500	275	22	conclude	conclude	VERB
ejpam-6500	275	23	that	that	SCONJ
ejpam-6500	275	24	µ	µ	NOUN
ejpam-6500	275	25	is	be	AUX
ejpam-6500	275	26	an	an	DET
ejpam-6500	275	27	(	(	PUNCT
ejpam-6500	275	28	∈,∈	∈,∈	INTJ
ejpam-6500	275	29	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	275	30	subalgebra	subalgebra	NOUN
ejpam-6500	275	31	of	of	ADP
ejpam-6500	275	32	h.	h.	PROPN
ejpam-6500	275	33	t.	t.	PROPN
ejpam-6500	275	34	oner	oner	PROPN
ejpam-6500	275	35	et	et	PROPN
ejpam-6500	275	36	al	al	PROPN
ejpam-6500	275	37	.	.	PUNCT
ejpam-6500	275	38	/	/	SYM
ejpam-6500	275	39	eur	eur	PROPN
ejpam-6500	275	40	.	.	PUNCT
ejpam-6500	276	1	j.	j.	PROPN
ejpam-6500	276	2	pure	pure	PROPN
ejpam-6500	276	3	appl	appl	PROPN
ejpam-6500	276	4	.	.	PROPN
ejpam-6500	276	5	math	math	PROPN
ejpam-6500	276	6	,	,	PUNCT
ejpam-6500	276	7	18	18	NUM
ejpam-6500	276	8	(	(	PUNCT
ejpam-6500	276	9	3	3	NUM
ejpam-6500	276	10	)	)	PUNCT
ejpam-6500	276	11	(	(	PUNCT
ejpam-6500	276	12	2025	2025	NUM
ejpam-6500	276	13	)	)	PUNCT
ejpam-6500	276	14	,	,	PUNCT
ejpam-6500	276	15	6500	6500	NUM
ejpam-6500	276	16	10	10	NUM
ejpam-6500	276	17	of	of	ADP
ejpam-6500	276	18	13	13	NUM
ejpam-6500	276	19	theorem	theorem	NOUN
ejpam-6500	276	20	11	11	NUM
ejpam-6500	276	21	.	.	PUNCT
ejpam-6500	277	1	let	let	VERB
ejpam-6500	277	2	µ	µ	X
ejpam-6500	277	3	be	be	AUX
ejpam-6500	277	4	a	a	DET
ejpam-6500	277	5	proper	proper	ADJ
ejpam-6500	277	6	(	(	PUNCT
ejpam-6500	277	7	∈,∈	∈,∈	X
ejpam-6500	277	8	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	277	9	subalgebra	subalgebra	NOUN
ejpam-6500	277	10	of	of	ADP
ejpam-6500	277	11	h	h	NOUN
ejpam-6500	277	12	having	have	VERB
ejpam-6500	277	13	at	at	ADV
ejpam-6500	277	14	least	least	ADV
ejpam-6500	277	15	two	two	NUM
ejpam-6500	277	16	values	value	NOUN
ejpam-6500	277	17	t1	t1	PROPN
ejpam-6500	277	18	,	,	PUNCT
ejpam-6500	277	19	t2	t2	NOUN
ejpam-6500	277	20	<	<	X
ejpam-6500	277	21	1−m	1−m	NUM
ejpam-6500	277	22	2	2	NUM
ejpam-6500	277	23	.	.	PUNCT
ejpam-6500	278	1	if	if	SCONJ
ejpam-6500	278	2	all	all	PRON
ejpam-6500	278	3	[	[	X
ejpam-6500	278	4	µ]t	µ]t	ADJ
ejpam-6500	278	5	,	,	PUNCT
ejpam-6500	278	6	t	t	PROPN
ejpam-6500	278	7	∈	∈	PROPN
ejpam-6500	278	8	(	(	PUNCT
ejpam-6500	278	9	0	0	NUM
ejpam-6500	278	10	,	,	PUNCT
ejpam-6500	278	11	1−m	1−m	NUM
ejpam-6500	278	12	2	2	NUM
ejpam-6500	278	13	]	]	PUNCT
ejpam-6500	278	14	,	,	PUNCT
ejpam-6500	278	15	are	be	AUX
ejpam-6500	278	16	subalgebras	subalgebra	NOUN
ejpam-6500	278	17	,	,	PUNCT
ejpam-6500	278	18	then	then	ADV
ejpam-6500	278	19	µ	µ	X
ejpam-6500	278	20	can	can	AUX
ejpam-6500	278	21	be	be	AUX
ejpam-6500	278	22	decomposed	decompose	VERB
ejpam-6500	278	23	into	into	ADP
ejpam-6500	278	24	the	the	DET
ejpam-6500	278	25	union	union	NOUN
ejpam-6500	278	26	of	of	ADP
ejpam-6500	278	27	two	two	NUM
ejpam-6500	278	28	proper	proper	ADJ
ejpam-6500	278	29	nonequivalent	nonequivalent	NOUN
ejpam-6500	278	30	(	(	PUNCT
ejpam-6500	278	31	∈,∈	∈,∈	X
ejpam-6500	278	32	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	278	33	subalgebras	subalgebras	PROPN
ejpam-6500	278	34	of	of	ADP
ejpam-6500	278	35	h.	h.	PROPN
ejpam-6500	278	36	proof	proof	PROPN
ejpam-6500	278	37	.	.	PUNCT
ejpam-6500	279	1	let	let	VERB
ejpam-6500	279	2	µ	µ	X
ejpam-6500	279	3	be	be	AUX
ejpam-6500	279	4	a	a	DET
ejpam-6500	279	5	proper	proper	ADJ
ejpam-6500	279	6	(	(	PUNCT
ejpam-6500	279	7	∈,∈	∈,∈	X
ejpam-6500	279	8	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	279	9	subalgebra	subalgebra	NOUN
ejpam-6500	279	10	of	of	ADP
ejpam-6500	279	11	h	h	NOUN
ejpam-6500	279	12	with	with	ADP
ejpam-6500	279	13	values	value	NOUN
ejpam-6500	279	14	1−m	1−m	NUM
ejpam-6500	279	15	2	2	NUM
ejpam-6500	279	16	>	>	SYM
ejpam-6500	279	17	t1	t1	NOUN
ejpam-6500	279	18	>	>	X
ejpam-6500	279	19	t2	t2	PROPN
ejpam-6500	279	20	>	>	X
ejpam-6500	279	21	.	.	PUNCT
ejpam-6500	279	22	.	.	PUNCT
ejpam-6500	280	1	.	.	PUNCT
ejpam-6500	281	1	>	>	X
ejpam-6500	281	2	tn	tn	PROPN
ejpam-6500	281	3	,	,	PUNCT
ejpam-6500	281	4	where	where	SCONJ
ejpam-6500	281	5	n	n	X
ejpam-6500	281	6	>	>	X
ejpam-6500	281	7	2	2	X
ejpam-6500	281	8	.	.	PUNCT
ejpam-6500	282	1	let	let	VERB
ejpam-6500	282	2	h0	h0	PROPN
ejpam-6500	282	3	=	=	PUNCT
ejpam-6500	283	1	[	[	X
ejpam-6500	283	2	µ	µ	X
ejpam-6500	283	3	]	]	X
ejpam-6500	283	4	1−m	1−m	NUM
ejpam-6500	283	5	2	2	NUM
ejpam-6500	283	6	and	and	CCONJ
ejpam-6500	283	7	hk	hk	NOUN
ejpam-6500	284	1	=	=	PUNCT
ejpam-6500	285	1	[	[	X
ejpam-6500	285	2	µ]tk	µ]tk	X
ejpam-6500	285	3	for	for	ADP
ejpam-6500	285	4	k	k	PROPN
ejpam-6500	285	5	=	=	SYM
ejpam-6500	285	6	1	1	NUM
ejpam-6500	285	7	,	,	PUNCT
ejpam-6500	285	8	2	2	NUM
ejpam-6500	285	9	,	,	PUNCT
ejpam-6500	285	10	.	.	PUNCT
ejpam-6500	285	11	.	.	PUNCT
ejpam-6500	285	12	.	.	PUNCT
ejpam-6500	286	1	,	,	PUNCT
ejpam-6500	286	2	n.	n.	PROPN
ejpam-6500	286	3	then	then	ADV
ejpam-6500	286	4	µ	µ	X
ejpam-6500	286	5	1−m	1−m	NUM
ejpam-6500	286	6	2	2	NUM
ejpam-6500	286	7	=	=	SYM
ejpam-6500	286	8	h0	h0	PROPN
ejpam-6500	286	9	⊂	⊂	PROPN
ejpam-6500	286	10	h1	h1	PROPN
ejpam-6500	286	11	⊂	⊂	PROPN
ejpam-6500	286	12	.	.	PUNCT
ejpam-6500	286	13	.	.	PUNCT
ejpam-6500	286	14	.	.	PUNCT
ejpam-6500	287	1	⊂	⊂	PROPN
ejpam-6500	287	2	hn	hn	X
ejpam-6500	288	1	=	=	PUNCT
ejpam-6500	288	2	h	h	NOUN
ejpam-6500	288	3	is	be	AUX
ejpam-6500	288	4	the	the	DET
ejpam-6500	288	5	chain	chain	NOUN
ejpam-6500	288	6	of	of	ADP
ejpam-6500	288	7	(	(	PUNCT
ejpam-6500	288	8	∈,∈	∈,∈	X
ejpam-6500	288	9	∨qm)-subalgebras	∨qm)-subalgebras	PROPN
ejpam-6500	288	10	of	of	ADP
ejpam-6500	288	11	h.	h.	PROPN
ejpam-6500	288	12	consider	consider	VERB
ejpam-6500	288	13	the	the	DET
ejpam-6500	288	14	fuzzy	fuzzy	ADJ
ejpam-6500	288	15	sets	set	NOUN
ejpam-6500	288	16	λ1	λ1	ADJ
ejpam-6500	288	17	,	,	PUNCT
ejpam-6500	288	18	λ2	λ2	NOUN
ejpam-6500	288	19	≤	≤	NOUN
ejpam-6500	288	20	µ	µ	PRON
ejpam-6500	288	21	defined	define	VERB
ejpam-6500	288	22	by	by	ADP
ejpam-6500	288	23	λ1(x	λ1(x	NOUN
ejpam-6500	288	24	)	)	PUNCT
ejpam-6500	288	25	=	=	PRON
ejpam-6500	288	26	{	{	PUNCT
ejpam-6500	288	27	t1	t1	VERB
ejpam-6500	288	28	if	if	SCONJ
ejpam-6500	288	29	x	x	PROPN
ejpam-6500	288	30	∈	∈	PROPN
ejpam-6500	288	31	h1	h1	AUX
ejpam-6500	288	32	tk	tk	PROPN
ejpam-6500	288	33	if	if	SCONJ
ejpam-6500	288	34	x	x	PROPN
ejpam-6500	288	35	∈	∈	PROPN
ejpam-6500	288	36	hk\hk−1	hk\hk−1	NOUN
ejpam-6500	288	37	,	,	PUNCT
ejpam-6500	288	38	k	k	PROPN
ejpam-6500	288	39	=	=	SYM
ejpam-6500	288	40	2	2	NUM
ejpam-6500	288	41	,	,	PUNCT
ejpam-6500	288	42	.	.	PUNCT
ejpam-6500	288	43	.	.	PUNCT
ejpam-6500	289	1	.	.	PUNCT
ejpam-6500	290	1	,	,	PUNCT
ejpam-6500	290	2	n	n	CCONJ
ejpam-6500	290	3	,	,	PUNCT
ejpam-6500	290	4	λ2(x	λ2(x	NOUN
ejpam-6500	290	5	)	)	PUNCT
ejpam-6500	290	6	=	=	PUNCT
ejpam-6500	290	7			PUNCT
ejpam-6500	290	8	µ(x	µ(x	X
ejpam-6500	290	9	)	)	PUNCT
ejpam-6500	290	10	if	if	SCONJ
ejpam-6500	290	11	x	x	PROPN
ejpam-6500	290	12	∈	∈	PROPN
ejpam-6500	290	13	h0	h0	NOUN
ejpam-6500	290	14	t2	t2	PROPN
ejpam-6500	290	15	if	if	SCONJ
ejpam-6500	290	16	x	x	PROPN
ejpam-6500	290	17	∈	∈	PROPN
ejpam-6500	290	18	h2\h0	h2\h0	NOUN
ejpam-6500	290	19	tk	tk	NOUN
ejpam-6500	290	20	if	if	SCONJ
ejpam-6500	290	21	x	x	PROPN
ejpam-6500	290	22	∈	∈	PROPN
ejpam-6500	290	23	hk\hk−1	hk\hk−1	NOUN
ejpam-6500	290	24	,	,	PUNCT
ejpam-6500	290	25	k	k	PROPN
ejpam-6500	290	26	=	=	SYM
ejpam-6500	290	27	3	3	NUM
ejpam-6500	290	28	,	,	PUNCT
ejpam-6500	290	29	.	.	PUNCT
ejpam-6500	290	30	.	.	PUNCT
ejpam-6500	291	1	.	.	PUNCT
ejpam-6500	292	1	,	,	PUNCT
ejpam-6500	292	2	n.	n.	PROPN
ejpam-6500	292	3	then	then	ADV
ejpam-6500	292	4	λ1	λ1	PROPN
ejpam-6500	292	5	and	and	CCONJ
ejpam-6500	292	6	λ2	λ2	NOUN
ejpam-6500	292	7	are	be	AUX
ejpam-6500	292	8	(	(	PUNCT
ejpam-6500	292	9	∈,∈	∈,∈	X
ejpam-6500	292	10	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	292	11	subalgebras	subalgebras	PROPN
ejpam-6500	292	12	of	of	ADP
ejpam-6500	292	13	h	h	PROPN
ejpam-6500	292	14	with	with	ADP
ejpam-6500	292	15	h0	h0	PROPN
ejpam-6500	292	16	⊂	⊂	PROPN
ejpam-6500	292	17	h1	h1	PROPN
ejpam-6500	292	18	⊂	⊂	PROPN
ejpam-6500	292	19	.	.	PUNCT
ejpam-6500	292	20	.	.	PUNCT
ejpam-6500	292	21	.	.	PUNCT
ejpam-6500	293	1	⊂	⊂	PROPN
ejpam-6500	293	2	hn	hn	PROPN
ejpam-6500	293	3	and	and	CCONJ
ejpam-6500	293	4	h0	h0	PROPN
ejpam-6500	293	5	⊂	⊂	PROPN
ejpam-6500	293	6	h1	h1	PROPN
ejpam-6500	293	7	⊂	⊂	PROPN
ejpam-6500	293	8	.	.	PUNCT
ejpam-6500	293	9	.	.	PUNCT
ejpam-6500	293	10	.	.	PUNCT
ejpam-6500	294	1	⊂	⊂	PROPN
ejpam-6500	295	1	hn	hn	PRON
ejpam-6500	295	2	being	be	AUX
ejpam-6500	295	3	respectively	respectively	ADV
ejpam-6500	295	4	chains	chain	NOUN
ejpam-6500	295	5	of	of	ADP
ejpam-6500	295	6	(	(	PUNCT
ejpam-6500	295	7	∈,∈	∈,∈	X
ejpam-6500	295	8	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	295	9	subalgebras	subalgebras	PROPN
ejpam-6500	295	10	of	of	ADP
ejpam-6500	295	11	h.	h.	PROPN
ejpam-6500	295	12	obviously	obviously	ADV
ejpam-6500	295	13	,	,	PUNCT
ejpam-6500	295	14	µ	µ	X
ejpam-6500	295	15	=	=	SYM
ejpam-6500	295	16	λ1	λ1	PROPN
ejpam-6500	295	17	∨	∨	NUM
ejpam-6500	295	18	λ2	λ2	NOUN
ejpam-6500	295	19	.	.	PUNCT
ejpam-6500	296	1	moreover	moreover	ADV
ejpam-6500	296	2	,	,	PUNCT
ejpam-6500	296	3	λ1	λ1	ADJ
ejpam-6500	296	4	and	and	CCONJ
ejpam-6500	296	5	λ2	λ2	NOUN
ejpam-6500	296	6	are	be	AUX
ejpam-6500	296	7	non	non	ADJ
ejpam-6500	296	8	-	-	ADJ
ejpam-6500	296	9	equivalent	equivalent	ADJ
ejpam-6500	296	10	since	since	SCONJ
ejpam-6500	296	11	h0	h0	PROPN
ejpam-6500	296	12	̸=	̸=	PROPN
ejpam-6500	296	13	h1	h1	PROPN
ejpam-6500	296	14	.	.	PUNCT
ejpam-6500	297	1	definition	definition	NOUN
ejpam-6500	297	2	8	8	NUM
ejpam-6500	297	3	.	.	PUNCT
ejpam-6500	298	1	let	let	VERB
ejpam-6500	298	2	⟨a	⟨a	NOUN
ejpam-6500	298	3	,	,	PUNCT
ejpam-6500	298	4	|a	|a	NOUN
ejpam-6500	298	5	,	,	PUNCT
ejpam-6500	298	6	0a⟩	0a⟩	NUM
ejpam-6500	298	7	and	and	CCONJ
ejpam-6500	298	8	⟨b	⟨b	PROPN
ejpam-6500	298	9	,	,	PUNCT
ejpam-6500	298	10	|b	|b	PROPN
ejpam-6500	298	11	,	,	PUNCT
ejpam-6500	298	12	0b⟩	0b⟩	NUM
ejpam-6500	298	13	be	be	AUX
ejpam-6500	298	14	sheffer	sheffer	NOUN
ejpam-6500	298	15	stroke	stroke	PROPN
ejpam-6500	298	16	hilbert	hilbert	PROPN
ejpam-6500	298	17	algebras	algebras	PROPN
ejpam-6500	298	18	.	.	PUNCT
ejpam-6500	299	1	then	then	ADV
ejpam-6500	299	2	a	a	DET
ejpam-6500	299	3	mapping	mapping	NOUN
ejpam-6500	299	4	f	f	NOUN
ejpam-6500	299	5	:	:	PUNCT
ejpam-6500	299	6	a	a	DET
ejpam-6500	299	7	→	→	SYM
ejpam-6500	299	8	b	b	PROPN
ejpam-6500	299	9	is	be	AUX
ejpam-6500	299	10	called	call	VERB
ejpam-6500	299	11	a	a	DET
ejpam-6500	299	12	homomorphism	homomorphism	NOUN
ejpam-6500	299	13	if	if	SCONJ
ejpam-6500	299	14	f(x|ay	f(x|ay	ADJ
ejpam-6500	299	15	)	)	PUNCT
ejpam-6500	299	16	=	=	SYM
ejpam-6500	299	17	f(x)|bf(y	f(x)|bf(y	NOUN
ejpam-6500	299	18	)	)	PUNCT
ejpam-6500	299	19	for	for	ADP
ejpam-6500	299	20	all	all	DET
ejpam-6500	299	21	x	x	NOUN
ejpam-6500	299	22	,	,	PUNCT
ejpam-6500	299	23	y	y	PROPN
ejpam-6500	299	24	∈	∈	PROPN
ejpam-6500	299	25	a	a	PRON
ejpam-6500	299	26	and	and	CCONJ
ejpam-6500	299	27	f(0a	f(0a	NOUN
ejpam-6500	299	28	)	)	PUNCT
ejpam-6500	299	29	=	=	SYM
ejpam-6500	299	30	0b	0b	NOUN
ejpam-6500	299	31	.	.	PUNCT
ejpam-6500	300	1	theorem	theorem	NOUN
ejpam-6500	300	2	12	12	NUM
ejpam-6500	300	3	.	.	PUNCT
ejpam-6500	301	1	let	let	VERB
ejpam-6500	301	2	a	a	DET
ejpam-6500	301	3	=	=	SYM
ejpam-6500	301	4	⟨a	⟨a	NOUN
ejpam-6500	301	5	,	,	PUNCT
ejpam-6500	301	6	|a	|a	NOUN
ejpam-6500	301	7	,	,	PUNCT
ejpam-6500	301	8	0a⟩	0a⟩	NUM
ejpam-6500	301	9	and	and	CCONJ
ejpam-6500	301	10	b	b	X
ejpam-6500	301	11	=	=	SYM
ejpam-6500	301	12	⟨b	⟨b	PROPN
ejpam-6500	301	13	,	,	PUNCT
ejpam-6500	301	14	|b	|b	PROPN
ejpam-6500	301	15	,	,	PUNCT
ejpam-6500	301	16	0b⟩	0b⟩	NUM
ejpam-6500	301	17	be	be	AUX
ejpam-6500	301	18	sheffer	sheffer	NOUN
ejpam-6500	301	19	stroke	stroke	PROPN
ejpam-6500	301	20	hilbert	hilbert	PROPN
ejpam-6500	301	21	algebras	algebras	PROPN
ejpam-6500	301	22	,	,	PUNCT
ejpam-6500	301	23	f	f	X
ejpam-6500	301	24	:	:	PUNCT
ejpam-6500	301	25	a	a	DET
ejpam-6500	301	26	→	→	SYM
ejpam-6500	301	27	b	b	X
ejpam-6500	301	28	be	be	AUX
ejpam-6500	301	29	a	a	DET
ejpam-6500	301	30	surjective	surjective	ADJ
ejpam-6500	301	31	homomorphism	homomorphism	NOUN
ejpam-6500	301	32	.	.	PUNCT
ejpam-6500	302	1	if	if	SCONJ
ejpam-6500	302	2	µ	µ	NOUN
ejpam-6500	302	3	is	be	AUX
ejpam-6500	302	4	an	an	DET
ejpam-6500	302	5	(	(	PUNCT
ejpam-6500	302	6	∈,∈	∈,∈	INTJ
ejpam-6500	302	7	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	302	8	subalgebra	subalgebra	NOUN
ejpam-6500	302	9	of	of	ADP
ejpam-6500	302	10	b	b	PROPN
ejpam-6500	302	11	for	for	ADP
ejpam-6500	302	12	m	m	PROPN
ejpam-6500	302	13	∈	∈	PROPN
ejpam-6500	302	14	(	(	PUNCT
ejpam-6500	302	15	0	0	NUM
ejpam-6500	302	16	,	,	PUNCT
ejpam-6500	302	17	1	1	NUM
ejpam-6500	302	18	)	)	PUNCT
ejpam-6500	302	19	,	,	PUNCT
ejpam-6500	302	20	then	then	ADV
ejpam-6500	302	21	f−1(b	f−1(b	PROPN
ejpam-6500	302	22	)	)	PUNCT
ejpam-6500	302	23	is	be	AUX
ejpam-6500	302	24	an	an	DET
ejpam-6500	302	25	(	(	PUNCT
ejpam-6500	302	26	∈,∈	∈,∈	INTJ
ejpam-6500	302	27	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	302	28	subalgebra	subalgebra	NOUN
ejpam-6500	302	29	of	of	ADP
ejpam-6500	302	30	a.	a.	NOUN
ejpam-6500	302	31	proof	proof	NOUN
ejpam-6500	302	32	.	.	PUNCT
ejpam-6500	303	1	let	let	VERB
ejpam-6500	303	2	µ	µ	X
ejpam-6500	303	3	be	be	AUX
ejpam-6500	303	4	an	an	DET
ejpam-6500	303	5	(	(	PUNCT
ejpam-6500	303	6	∈,∈	∈,∈	INTJ
ejpam-6500	303	7	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	303	8	subalgebra	subalgebra	NOUN
ejpam-6500	303	9	of	of	ADP
ejpam-6500	303	10	b	b	PROPN
ejpam-6500	303	11	for	for	ADP
ejpam-6500	303	12	m	m	PROPN
ejpam-6500	303	13	∈	∈	PROPN
ejpam-6500	303	14	(	(	PUNCT
ejpam-6500	303	15	0	0	NUM
ejpam-6500	303	16	,	,	PUNCT
ejpam-6500	303	17	1	1	NUM
ejpam-6500	303	18	)	)	PUNCT
ejpam-6500	303	19	and	and	CCONJ
ejpam-6500	303	20	x	x	X
ejpam-6500	303	21	,	,	PUNCT
ejpam-6500	303	22	y	y	PROPN
ejpam-6500	303	23	∈	∈	PROPN
ejpam-6500	303	24	a.	a.	NOUN
ejpam-6500	303	25	then	then	ADV
ejpam-6500	303	26	f−1(µ)((x|a(y|ay))|a(x|a(y|ay	f−1(µ)((x|a(y|ay))|a(x|a(y|ay	NOUN
ejpam-6500	303	27	)	)	PUNCT
ejpam-6500	303	28	)	)	PUNCT
ejpam-6500	303	29	)	)	PUNCT
ejpam-6500	304	1	=	=	PUNCT
ejpam-6500	304	2	µ(f((x|a(y|ay))|a(x|a(y|ay	µ(f((x|a(y|ay))|a(x|a(y|ay	PROPN
ejpam-6500	304	3	)	)	PUNCT
ejpam-6500	304	4	)	)	PUNCT
ejpam-6500	304	5	)	)	PUNCT
ejpam-6500	304	6	)	)	PUNCT
ejpam-6500	305	1	=	=	SYM
ejpam-6500	305	2	µ((f(x)|b(f(y)|bf(y)))|b(f(x)|b(f(y)|bf(y	µ((f(x)|b(f(y)|bf(y)))|b(f(x)|b(f(y)|bf(y	NOUN
ejpam-6500	305	3	)	)	PUNCT
ejpam-6500	305	4	)	)	PUNCT
ejpam-6500	305	5	)	)	PUNCT
ejpam-6500	305	6	)	)	PUNCT
ejpam-6500	305	7	≥	≥	PROPN
ejpam-6500	305	8	min{µ(f(x	min{µ(f(x	PROPN
ejpam-6500	305	9	)	)	PUNCT
ejpam-6500	305	10	)	)	PUNCT
ejpam-6500	305	11	,	,	PUNCT
ejpam-6500	305	12	µ(f(y	µ(f(y	PROPN
ejpam-6500	305	13	)	)	PUNCT
ejpam-6500	305	14	)	)	PUNCT
ejpam-6500	305	15	,	,	PUNCT
ejpam-6500	305	16	1−m	1−m	NUM
ejpam-6500	305	17	2	2	NUM
ejpam-6500	305	18	}	}	PUNCT
ejpam-6500	305	19	=	=	SYM
ejpam-6500	305	20	min{f−1(µ(x	min{f−1(µ(x	NOUN
ejpam-6500	305	21	)	)	PUNCT
ejpam-6500	305	22	)	)	PUNCT
ejpam-6500	305	23	,	,	PUNCT
ejpam-6500	305	24	f−1(µ(y	f−1(µ(y	PROPN
ejpam-6500	305	25	)	)	PUNCT
ejpam-6500	305	26	)	)	PUNCT
ejpam-6500	305	27	,	,	PUNCT
ejpam-6500	305	28	1−m	1−m	NUM
ejpam-6500	305	29	2	2	NUM
ejpam-6500	305	30	}	}	PUNCT
ejpam-6500	305	31	.	.	PUNCT
ejpam-6500	306	1	hence	hence	ADV
ejpam-6500	306	2	,	,	PUNCT
ejpam-6500	306	3	f−1(µ	f−1(µ	PROPN
ejpam-6500	306	4	)	)	PUNCT
ejpam-6500	306	5	is	be	AUX
ejpam-6500	306	6	an	an	DET
ejpam-6500	306	7	(	(	PUNCT
ejpam-6500	306	8	∈,∈	∈,∈	INTJ
ejpam-6500	306	9	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	306	10	subalgebra	subalgebra	NOUN
ejpam-6500	306	11	of	of	ADP
ejpam-6500	306	12	a.	a.	NOUN
ejpam-6500	306	13	definition	definition	NOUN
ejpam-6500	306	14	9	9	NUM
ejpam-6500	306	15	.	.	PUNCT
ejpam-6500	307	1	let	let	VERB
ejpam-6500	307	2	f	f	NOUN
ejpam-6500	307	3	:	:	PUNCT
ejpam-6500	307	4	x	x	X
ejpam-6500	307	5	→	→	SYM
ejpam-6500	307	6	y	y	X
ejpam-6500	307	7	be	be	AUX
ejpam-6500	307	8	a	a	DET
ejpam-6500	307	9	function	function	NOUN
ejpam-6500	307	10	.	.	PUNCT
ejpam-6500	308	1	an	an	PRON
ejpam-6500	308	2	(	(	PUNCT
ejpam-6500	308	3	∈,∈	∈,∈	X
ejpam-6500	308	4	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	308	5	subalgebra	subalgebra	NOUN
ejpam-6500	308	6	µ	µ	NOUN
ejpam-6500	308	7	is	be	AUX
ejpam-6500	308	8	said	say	VERB
ejpam-6500	308	9	to	to	PART
ejpam-6500	308	10	be	be	AUX
ejpam-6500	308	11	f	f	PROPN
ejpam-6500	308	12	-invariant	-invariant	ADJ
ejpam-6500	308	13	if	if	SCONJ
ejpam-6500	308	14	f(x	f(x	PROPN
ejpam-6500	308	15	)	)	PUNCT
ejpam-6500	309	1	=	=	SYM
ejpam-6500	309	2	f(y	f(y	NOUN
ejpam-6500	309	3	)	)	PUNCT
ejpam-6500	309	4	implies	imply	VERB
ejpam-6500	309	5	that	that	SCONJ
ejpam-6500	309	6	µ(x	µ(x	VERB
ejpam-6500	309	7	)	)	PUNCT
ejpam-6500	309	8	=	=	SYM
ejpam-6500	309	9	µ(y	µ(y	NOUN
ejpam-6500	309	10	)	)	PUNCT
ejpam-6500	309	11	for	for	ADP
ejpam-6500	309	12	all	all	DET
ejpam-6500	309	13	x	x	NOUN
ejpam-6500	309	14	,	,	PUNCT
ejpam-6500	309	15	y	y	PROPN
ejpam-6500	309	16	∈	∈	PROPN
ejpam-6500	309	17	x.	x.	NOUN
ejpam-6500	309	18	theorem	theorem	VERB
ejpam-6500	309	19	13	13	NUM
ejpam-6500	309	20	.	.	PUNCT
ejpam-6500	310	1	let	let	VERB
ejpam-6500	310	2	a	a	DET
ejpam-6500	310	3	=	=	SYM
ejpam-6500	310	4	⟨a	⟨a	NOUN
ejpam-6500	310	5	,	,	PUNCT
ejpam-6500	310	6	|a	|a	NOUN
ejpam-6500	310	7	,	,	PUNCT
ejpam-6500	310	8	0a⟩	0a⟩	NUM
ejpam-6500	310	9	and	and	CCONJ
ejpam-6500	310	10	b	b	X
ejpam-6500	310	11	=	=	SYM
ejpam-6500	310	12	⟨b	⟨b	PROPN
ejpam-6500	310	13	,	,	PUNCT
ejpam-6500	310	14	|b	|b	PROPN
ejpam-6500	310	15	,	,	PUNCT
ejpam-6500	310	16	0b⟩	0b⟩	NUM
ejpam-6500	310	17	be	be	AUX
ejpam-6500	310	18	sheffer	sheffer	NOUN
ejpam-6500	310	19	stroke	stroke	PROPN
ejpam-6500	310	20	hilbert	hilbert	PROPN
ejpam-6500	310	21	algebras	algebras	PROPN
ejpam-6500	310	22	,	,	PUNCT
ejpam-6500	310	23	f	f	X
ejpam-6500	310	24	:	:	PUNCT
ejpam-6500	310	25	a	a	DET
ejpam-6500	310	26	→	→	SYM
ejpam-6500	310	27	b	b	X
ejpam-6500	310	28	be	be	AUX
ejpam-6500	310	29	a	a	DET
ejpam-6500	310	30	homomorphism	homomorphism	NOUN
ejpam-6500	310	31	and	and	CCONJ
ejpam-6500	310	32	µ	µ	DET
ejpam-6500	310	33	an	an	DET
ejpam-6500	310	34	(	(	PUNCT
ejpam-6500	310	35	∈,∈	∈,∈	X
ejpam-6500	310	36	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	310	37	subalgebra	subalgebra	NOUN
ejpam-6500	310	38	of	of	ADP
ejpam-6500	310	39	a.	a.	NOUN
ejpam-6500	310	40	if	if	SCONJ
ejpam-6500	310	41	µ	µ	X
ejpam-6500	310	42	is	be	AUX
ejpam-6500	310	43	f	f	PROPN
ejpam-6500	310	44	-invariant	-invariant	PROPN
ejpam-6500	310	45	,	,	PUNCT
ejpam-6500	310	46	then	then	ADV
ejpam-6500	310	47	f(µ	f(µ	NOUN
ejpam-6500	310	48	)	)	PUNCT
ejpam-6500	310	49	is	be	AUX
ejpam-6500	310	50	an	an	DET
ejpam-6500	310	51	(	(	PUNCT
ejpam-6500	310	52	∈,∈	∈,∈	INTJ
ejpam-6500	310	53	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	310	54	subalgebra	subalgebra	NOUN
ejpam-6500	310	55	of	of	ADP
ejpam-6500	310	56	b	b	NOUN
ejpam-6500	310	57	,	,	PUNCT
ejpam-6500	310	58	where	where	SCONJ
ejpam-6500	310	59	f(µ)(x	f(µ)(x	NOUN
ejpam-6500	310	60	)	)	PUNCT
ejpam-6500	311	1	=	=	PRON
ejpam-6500	311	2	{	{	PUNCT
ejpam-6500	311	3	sup	sup	NOUN
ejpam-6500	311	4	x∈f−1(y	x∈f−1(y	NOUN
ejpam-6500	311	5	)	)	PUNCT
ejpam-6500	311	6	µ(x	µ(x	NOUN
ejpam-6500	311	7	)	)	PUNCT
ejpam-6500	311	8	if	if	SCONJ
ejpam-6500	311	9	f−1(y	f−1(y	PROPN
ejpam-6500	311	10	)	)	PUNCT
ejpam-6500	311	11	̸=	̸=	PROPN
ejpam-6500	311	12	∅	∅	NOUN
ejpam-6500	311	13	0	0	NUM
ejpam-6500	311	14	otherwise	otherwise	ADV
ejpam-6500	311	15	.	.	PUNCT
ejpam-6500	312	1	t.	t.	PROPN
ejpam-6500	312	2	oner	oner	PROPN
ejpam-6500	312	3	et	et	PROPN
ejpam-6500	312	4	al	al	PROPN
ejpam-6500	312	5	.	.	PUNCT
ejpam-6500	312	6	/	/	SYM
ejpam-6500	312	7	eur	eur	PROPN
ejpam-6500	312	8	.	.	PUNCT
ejpam-6500	313	1	j.	j.	PROPN
ejpam-6500	313	2	pure	pure	PROPN
ejpam-6500	313	3	appl	appl	PROPN
ejpam-6500	313	4	.	.	PROPN
ejpam-6500	313	5	math	math	PROPN
ejpam-6500	313	6	,	,	PUNCT
ejpam-6500	313	7	18	18	NUM
ejpam-6500	313	8	(	(	PUNCT
ejpam-6500	313	9	3	3	NUM
ejpam-6500	313	10	)	)	PUNCT
ejpam-6500	313	11	(	(	PUNCT
ejpam-6500	313	12	2025	2025	NUM
ejpam-6500	313	13	)	)	PUNCT
ejpam-6500	313	14	,	,	PUNCT
ejpam-6500	313	15	6500	6500	NUM
ejpam-6500	313	16	11	11	NUM
ejpam-6500	313	17	of	of	ADP
ejpam-6500	313	18	13	13	NUM
ejpam-6500	313	19	proof	proof	NOUN
ejpam-6500	313	20	.	.	PUNCT
ejpam-6500	314	1	let	let	VERB
ejpam-6500	314	2	y1	y1	INTJ
ejpam-6500	314	3	,	,	PUNCT
ejpam-6500	314	4	y2	y2	PROPN
ejpam-6500	314	5	∈	∈	PROPN
ejpam-6500	314	6	b.	b.	PROPN
ejpam-6500	315	1	if	if	SCONJ
ejpam-6500	315	2	f−1(y1	f−1(y1	NOUN
ejpam-6500	315	3	)	)	PUNCT
ejpam-6500	315	4	=	=	NOUN
ejpam-6500	315	5	∅	∅	NOUN
ejpam-6500	315	6	or	or	CCONJ
ejpam-6500	315	7	f−1(y2	f−1(y2	VERB
ejpam-6500	315	8	)	)	PUNCT
ejpam-6500	315	9	=	=	SYM
ejpam-6500	315	10	∅	∅	NOUN
ejpam-6500	315	11	,	,	PUNCT
ejpam-6500	315	12	then	then	ADV
ejpam-6500	315	13	the	the	DET
ejpam-6500	315	14	proof	proof	NOUN
ejpam-6500	315	15	is	be	AUX
ejpam-6500	315	16	obvious	obvious	ADJ
ejpam-6500	315	17	.	.	PUNCT
ejpam-6500	316	1	otherwise	otherwise	ADV
ejpam-6500	316	2	,	,	PUNCT
ejpam-6500	316	3	let	let	VERB
ejpam-6500	316	4	f−1(y1	f−1(y1	NOUN
ejpam-6500	316	5	)	)	PUNCT
ejpam-6500	316	6	̸=	̸=	PROPN
ejpam-6500	316	7	∅	∅	NOUN
ejpam-6500	316	8	or	or	CCONJ
ejpam-6500	316	9	f−1(y2	f−1(y2	NOUN
ejpam-6500	316	10	)	)	PUNCT
ejpam-6500	316	11	̸=	̸=	PROPN
ejpam-6500	316	12	∅.	∅.	ADV
ejpam-6500	316	13	then	then	ADV
ejpam-6500	316	14	there	there	PRON
ejpam-6500	316	15	exist	exist	VERB
ejpam-6500	316	16	x1	x1	PROPN
ejpam-6500	316	17	,	,	PUNCT
ejpam-6500	316	18	x2	x2	PROPN
ejpam-6500	316	19	∈	∈	PROPN
ejpam-6500	316	20	a	a	DET
ejpam-6500	316	21	such	such	ADJ
ejpam-6500	316	22	that	that	PRON
ejpam-6500	316	23	and	and	CCONJ
ejpam-6500	316	24	f(x1	f(x1	ADJ
ejpam-6500	316	25	)	)	PUNCT
ejpam-6500	317	1	=	=	SYM
ejpam-6500	317	2	y1	y1	NOUN
ejpam-6500	317	3	and	and	CCONJ
ejpam-6500	317	4	f(x2	f(x2	NOUN
ejpam-6500	317	5	)	)	PUNCT
ejpam-6500	318	1	=	=	VERB
ejpam-6500	318	2	y2	y2	PROPN
ejpam-6500	318	3	.	.	PUNCT
ejpam-6500	319	1	thus	thus	ADV
ejpam-6500	319	2	,	,	PUNCT
ejpam-6500	319	3	f(µ)((y1|b(y2|by2))|b(y1|b(y2|by2	f(µ)((y1|b(y2|by2))|b(y1|b(y2|by2	NOUN
ejpam-6500	319	4	)	)	PUNCT
ejpam-6500	319	5	)	)	PUNCT
ejpam-6500	319	6	)	)	PUNCT
ejpam-6500	320	1	=	=	SYM
ejpam-6500	320	2	sup	sup	NOUN
ejpam-6500	320	3	x∈f−1((y1|b(y2|by2))|b(y1|b(y2|by2	x∈f−1((y1|b(y2|by2))|b(y1|b(y2|by2	NUM
ejpam-6500	320	4	)	)	PUNCT
ejpam-6500	320	5	)	)	PUNCT
ejpam-6500	320	6	)	)	PUNCT
ejpam-6500	321	1	µ(x	µ(x	VERB
ejpam-6500	321	2	)	)	PUNCT
ejpam-6500	321	3	=	=	SYM
ejpam-6500	321	4	sup	sup	NOUN
ejpam-6500	321	5	x∈f−1((f(x1)|b(f(x2)|bf(x2)))|b(f(x1)|b(f(x2)|bf(x2	x∈f−1((f(x1)|b(f(x2)|bf(x2)))|b(f(x1)|b(f(x2)|bf(x2	PROPN
ejpam-6500	321	6	)	)	PUNCT
ejpam-6500	321	7	)	)	PUNCT
ejpam-6500	321	8	)	)	PUNCT
ejpam-6500	321	9	)	)	PUNCT
ejpam-6500	322	1	µ(x	µ(x	VERB
ejpam-6500	322	2	)	)	PUNCT
ejpam-6500	322	3	=	=	SYM
ejpam-6500	322	4	sup	sup	NOUN
ejpam-6500	322	5	x∈f−1(f((x1|a(x2|ax2))|a(x1|a(x2|ax2	x∈f−1(f((x1|a(x2|ax2))|a(x1|a(x2|ax2	PROPN
ejpam-6500	322	6	)	)	PUNCT
ejpam-6500	322	7	)	)	PUNCT
ejpam-6500	322	8	)	)	PUNCT
ejpam-6500	322	9	)	)	PUNCT
ejpam-6500	323	1	µ(x	µ(x	VERB
ejpam-6500	323	2	)	)	PUNCT
ejpam-6500	323	3	=	=	SYM
ejpam-6500	323	4	µ((x1|a(x2|ax2))|a(x1|a(x2|ax2	µ((x1|a(x2|ax2))|a(x1|a(x2|ax2	NOUN
ejpam-6500	323	5	)	)	PUNCT
ejpam-6500	323	6	)	)	PUNCT
ejpam-6500	323	7	)	)	PUNCT
ejpam-6500	323	8	≥	≥	NOUN
ejpam-6500	323	9	min{µ(x1	min{µ(x1	NOUN
ejpam-6500	323	10	)	)	PUNCT
ejpam-6500	323	11	,	,	PUNCT
ejpam-6500	323	12	µ(x2	µ(x2	NOUN
ejpam-6500	323	13	)	)	PUNCT
ejpam-6500	323	14	,	,	PUNCT
ejpam-6500	323	15	1−m	1−m	NUM
ejpam-6500	323	16	2	2	NUM
ejpam-6500	323	17	}	}	PUNCT
ejpam-6500	323	18	=	=	SYM
ejpam-6500	323	19	min	min	NOUN
ejpam-6500	323	20	{	{	PUNCT
ejpam-6500	323	21	sup	sup	NOUN
ejpam-6500	323	22	x∈f−1(f(x1	x∈f−1(f(x1	PROPN
ejpam-6500	323	23	)	)	PUNCT
ejpam-6500	323	24	)	)	PUNCT
ejpam-6500	324	1	µ(x	µ(x	NUM
ejpam-6500	324	2	)	)	PUNCT
ejpam-6500	324	3	,	,	PUNCT
ejpam-6500	324	4	sup	sup	NOUN
ejpam-6500	324	5	x∈f−1(f(x2	x∈f−1(f(x2	NOUN
ejpam-6500	324	6	)	)	PUNCT
ejpam-6500	324	7	)	)	PUNCT
ejpam-6500	325	1	µ(x	µ(x	PROPN
ejpam-6500	325	2	)	)	PUNCT
ejpam-6500	325	3	,	,	PUNCT
ejpam-6500	325	4	1−m	1−m	NUM
ejpam-6500	325	5	2	2	NUM
ejpam-6500	325	6	}	}	PUNCT
ejpam-6500	325	7	=	=	SYM
ejpam-6500	325	8	min	min	NOUN
ejpam-6500	325	9	{	{	PUNCT
ejpam-6500	325	10	sup	sup	NOUN
ejpam-6500	325	11	x∈f−1(y1	x∈f−1(y1	NUM
ejpam-6500	325	12	)	)	PUNCT
ejpam-6500	325	13	µ(x	µ(x	NUM
ejpam-6500	325	14	)	)	PUNCT
ejpam-6500	325	15	,	,	PUNCT
ejpam-6500	325	16	sup	sup	NOUN
ejpam-6500	325	17	x∈f−1(y2	x∈f−1(y2	NUM
ejpam-6500	325	18	)	)	PUNCT
ejpam-6500	325	19	µ(x	µ(x	NUM
ejpam-6500	325	20	)	)	PUNCT
ejpam-6500	325	21	,	,	PUNCT
ejpam-6500	325	22	1−m	1−m	NUM
ejpam-6500	325	23	2	2	NUM
ejpam-6500	325	24	}	}	PUNCT
ejpam-6500	325	25	=	=	SYM
ejpam-6500	325	26	min	min	NOUN
ejpam-6500	325	27	{	{	PUNCT
ejpam-6500	325	28	f(µ)(y1	f(µ)(y1	PROPN
ejpam-6500	325	29	)	)	PUNCT
ejpam-6500	325	30	,	,	PUNCT
ejpam-6500	325	31	f(µ)(y2	f(µ)(y2	NOUN
ejpam-6500	325	32	)	)	PUNCT
ejpam-6500	325	33	,	,	PUNCT
ejpam-6500	325	34	1−m	1−m	NUM
ejpam-6500	325	35	2	2	NUM
ejpam-6500	325	36	}	}	PUNCT
ejpam-6500	325	37	.	.	PUNCT
ejpam-6500	326	1	hence	hence	ADV
ejpam-6500	326	2	,	,	PUNCT
ejpam-6500	326	3	f(µ	f(µ	PROPN
ejpam-6500	326	4	)	)	PUNCT
ejpam-6500	326	5	is	be	AUX
ejpam-6500	326	6	an	an	DET
ejpam-6500	326	7	(	(	PUNCT
ejpam-6500	326	8	∈,∈	∈,∈	INTJ
ejpam-6500	326	9	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	326	10	subalgebra	subalgebra	NOUN
ejpam-6500	326	11	of	of	ADP
ejpam-6500	326	12	b.	b.	PROPN
ejpam-6500	326	13	remark	remark	PROPN
ejpam-6500	326	14	2	2	NUM
ejpam-6500	326	15	.	.	PUNCT
ejpam-6500	327	1	let	let	VERB
ejpam-6500	327	2	a	a	DET
ejpam-6500	327	3	=	=	SYM
ejpam-6500	327	4	⟨a	⟨a	NOUN
ejpam-6500	327	5	,	,	PUNCT
ejpam-6500	327	6	|a	|a	NOUN
ejpam-6500	327	7	,	,	PUNCT
ejpam-6500	327	8	0a⟩	0a⟩	NUM
ejpam-6500	327	9	and	and	CCONJ
ejpam-6500	327	10	b	b	X
ejpam-6500	327	11	=	=	SYM
ejpam-6500	327	12	⟨b	⟨b	PROPN
ejpam-6500	327	13	,	,	PUNCT
ejpam-6500	327	14	|b	|b	PROPN
ejpam-6500	327	15	,	,	PUNCT
ejpam-6500	327	16	0b⟩	0b⟩	NUM
ejpam-6500	327	17	be	be	AUX
ejpam-6500	327	18	sheffer	sheffer	NOUN
ejpam-6500	327	19	stroke	stroke	PROPN
ejpam-6500	327	20	hilbert	hilbert	PROPN
ejpam-6500	327	21	algebras	algebras	PROPN
ejpam-6500	327	22	.	.	PUNCT
ejpam-6500	328	1	then	then	ADV
ejpam-6500	328	2	a×b	a×b	PUNCT
ejpam-6500	328	3	=	=	SYM
ejpam-6500	328	4	⟨a×b	⟨a×b	ADJ
ejpam-6500	328	5	,	,	PUNCT
ejpam-6500	328	6	|a×b	|a×b	PROPN
ejpam-6500	328	7	,	,	PUNCT
ejpam-6500	328	8	0a×b⟩	0a×b⟩	PROPN
ejpam-6500	328	9	is	be	AUX
ejpam-6500	328	10	a	a	DET
ejpam-6500	328	11	sheffer	sheffer	NOUN
ejpam-6500	328	12	stroke	stroke	NOUN
ejpam-6500	328	13	hilbert	hilbert	PROPN
ejpam-6500	328	14	algebra	algebra	PROPN
ejpam-6500	328	15	,	,	PUNCT
ejpam-6500	328	16	where	where	SCONJ
ejpam-6500	328	17	the	the	DET
ejpam-6500	328	18	set	set	NOUN
ejpam-6500	328	19	a×b	a×b	PROPN
ejpam-6500	328	20	is	be	AUX
ejpam-6500	328	21	the	the	DET
ejpam-6500	328	22	cartesian	cartesian	ADJ
ejpam-6500	328	23	product	product	NOUN
ejpam-6500	328	24	of	of	ADP
ejpam-6500	328	25	a	a	PRON
ejpam-6500	328	26	and	and	CCONJ
ejpam-6500	328	27	b	b	NOUN
ejpam-6500	328	28	and	and	CCONJ
ejpam-6500	328	29	the	the	DET
ejpam-6500	328	30	operation	operation	NOUN
ejpam-6500	328	31	|a×b	|a×b	PROPN
ejpam-6500	328	32	on	on	ADP
ejpam-6500	328	33	this	this	DET
ejpam-6500	328	34	set	set	NOUN
ejpam-6500	328	35	is	be	AUX
ejpam-6500	328	36	defined	define	VERB
ejpam-6500	328	37	by	by	ADP
ejpam-6500	328	38	(	(	PUNCT
ejpam-6500	328	39	a1	a1	NOUN
ejpam-6500	328	40	,	,	PUNCT
ejpam-6500	328	41	b1)|a×b(a2	b1)|a×b(a2	NUM
ejpam-6500	328	42	,	,	PUNCT
ejpam-6500	328	43	b2	b2	NOUN
ejpam-6500	328	44	)	)	PUNCT
ejpam-6500	328	45	=	=	SYM
ejpam-6500	328	46	(	(	PUNCT
ejpam-6500	328	47	a1|aa2	a1|aa2	PROPN
ejpam-6500	328	48	,	,	PUNCT
ejpam-6500	328	49	b1|bb2	b1|bb2	NOUN
ejpam-6500	328	50	)	)	PUNCT
ejpam-6500	328	51	,	,	PUNCT
ejpam-6500	328	52	and	and	CCONJ
ejpam-6500	328	53	the	the	DET
ejpam-6500	328	54	fixed	fix	VERB
ejpam-6500	328	55	element	element	NOUN
ejpam-6500	328	56	is	be	AUX
ejpam-6500	328	57	0a×b	0a×b	PUNCT
ejpam-6500	329	1	=	=	PUNCT
ejpam-6500	329	2	(	(	PUNCT
ejpam-6500	329	3	0a	0a	PROPN
ejpam-6500	329	4	,	,	PUNCT
ejpam-6500	329	5	0b	0b	NUM
ejpam-6500	329	6	)	)	PUNCT
ejpam-6500	329	7	.	.	PUNCT
ejpam-6500	330	1	let	let	VERB
ejpam-6500	330	2	µa	µa	NOUN
ejpam-6500	330	3	and	and	CCONJ
ejpam-6500	330	4	µb	µb	AUX
ejpam-6500	330	5	be	be	AUX
ejpam-6500	330	6	(	(	PUNCT
ejpam-6500	330	7	∈,∈	∈,∈	X
ejpam-6500	330	8	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	330	9	subalgebras	subalgebras	PROPN
ejpam-6500	330	10	of	of	ADP
ejpam-6500	330	11	sheffer	sheffer	PROPN
ejpam-6500	330	12	stroke	stroke	PROPN
ejpam-6500	330	13	hilbert	hilbert	PROPN
ejpam-6500	330	14	algebras	algebra	VERB
ejpam-6500	330	15	a	a	DET
ejpam-6500	330	16	=	=	SYM
ejpam-6500	330	17	⟨a	⟨a	PROPN
ejpam-6500	330	18	,	,	PUNCT
ejpam-6500	330	19	|a	|a	NOUN
ejpam-6500	330	20	,	,	PUNCT
ejpam-6500	330	21	0a⟩	0a⟩	NUM
ejpam-6500	330	22	and	and	CCONJ
ejpam-6500	330	23	b	b	X
ejpam-6500	330	24	=	=	SYM
ejpam-6500	330	25	⟨b	⟨b	PROPN
ejpam-6500	330	26	,	,	PUNCT
ejpam-6500	330	27	|b	|b	ADJ
ejpam-6500	330	28	,	,	PUNCT
ejpam-6500	330	29	0b⟩	0b⟩	NUM
ejpam-6500	330	30	,	,	PUNCT
ejpam-6500	330	31	respectively	respectively	ADV
ejpam-6500	330	32	,	,	PUNCT
ejpam-6500	330	33	for	for	ADP
ejpam-6500	330	34	m	m	PROPN
ejpam-6500	330	35	∈	∈	NOUN
ejpam-6500	330	36	(	(	PUNCT
ejpam-6500	330	37	0	0	NUM
ejpam-6500	330	38	,	,	PUNCT
ejpam-6500	330	39	1	1	NUM
ejpam-6500	330	40	)	)	PUNCT
ejpam-6500	330	41	.	.	PUNCT
ejpam-6500	331	1	the	the	DET
ejpam-6500	331	2	cartesian	cartesian	ADJ
ejpam-6500	331	3	product	product	NOUN
ejpam-6500	331	4	of	of	ADP
ejpam-6500	331	5	µa	µa	NOUN
ejpam-6500	331	6	and	and	CCONJ
ejpam-6500	331	7	µb	µb	PROPN
ejpam-6500	331	8	is	be	AUX
ejpam-6500	331	9	defined	define	VERB
ejpam-6500	331	10	by	by	ADP
ejpam-6500	331	11	µ	µ	NOUN
ejpam-6500	331	12	=	=	SYM
ejpam-6500	331	13	µa	µa	PROPN
ejpam-6500	331	14	×	×	PROPN
ejpam-6500	331	15	µb	µb	NOUN
ejpam-6500	331	16	,	,	PUNCT
ejpam-6500	331	17	where	where	SCONJ
ejpam-6500	331	18	µ(x	µ(x	VERB
ejpam-6500	331	19	,	,	PUNCT
ejpam-6500	331	20	y	y	NOUN
ejpam-6500	331	21	)	)	PUNCT
ejpam-6500	331	22	=	=	SYM
ejpam-6500	331	23	min{µa(x	min{µa(x	NOUN
ejpam-6500	331	24	)	)	PUNCT
ejpam-6500	331	25	,	,	PUNCT
ejpam-6500	331	26	µb(y	µb(y	NUM
ejpam-6500	331	27	)	)	PUNCT
ejpam-6500	331	28	}	}	PUNCT
ejpam-6500	331	29	.	.	PUNCT
ejpam-6500	332	1	theorem	theorem	VERB
ejpam-6500	332	2	14	14	NUM
ejpam-6500	332	3	.	.	PUNCT
ejpam-6500	333	1	if	if	SCONJ
ejpam-6500	333	2	µa	µa	NOUN
ejpam-6500	333	3	and	and	CCONJ
ejpam-6500	333	4	µb	µb	NOUN
ejpam-6500	333	5	are	be	AUX
ejpam-6500	333	6	(	(	PUNCT
ejpam-6500	333	7	∈,∈	∈,∈	X
ejpam-6500	333	8	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	333	9	subalgebras	subalgebras	PROPN
ejpam-6500	333	10	of	of	ADP
ejpam-6500	333	11	sheffer	sheffer	PROPN
ejpam-6500	333	12	stroke	stroke	PROPN
ejpam-6500	333	13	hilbert	hilbert	PROPN
ejpam-6500	333	14	algebras	algebra	VERB
ejpam-6500	333	15	a	a	DET
ejpam-6500	333	16	=	=	SYM
ejpam-6500	333	17	⟨a	⟨a	PROPN
ejpam-6500	333	18	,	,	PUNCT
ejpam-6500	333	19	|a	|a	NOUN
ejpam-6500	333	20	,	,	PUNCT
ejpam-6500	333	21	0a⟩	0a⟩	NUM
ejpam-6500	333	22	and	and	CCONJ
ejpam-6500	333	23	b	b	X
ejpam-6500	333	24	=	=	SYM
ejpam-6500	333	25	⟨b	⟨b	PROPN
ejpam-6500	333	26	,	,	PUNCT
ejpam-6500	333	27	|b	|b	ADJ
ejpam-6500	333	28	,	,	PUNCT
ejpam-6500	333	29	0b⟩	0b⟩	NUM
ejpam-6500	333	30	,	,	PUNCT
ejpam-6500	333	31	respectively	respectively	ADV
ejpam-6500	333	32	,	,	PUNCT
ejpam-6500	333	33	then	then	ADV
ejpam-6500	333	34	µ	µ	NOUN
ejpam-6500	333	35	is	be	AUX
ejpam-6500	333	36	an	an	DET
ejpam-6500	333	37	(	(	PUNCT
ejpam-6500	333	38	∈,∈	∈,∈	INTJ
ejpam-6500	333	39	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	333	40	subalgebra	subalgebra	NOUN
ejpam-6500	333	41	of	of	ADP
ejpam-6500	333	42	a×b	a×b	PROPN
ejpam-6500	333	43	=	=	SYM
ejpam-6500	333	44	⟨a×b	⟨a×b	ADJ
ejpam-6500	333	45	,	,	PUNCT
ejpam-6500	333	46	|a×b	|a×b	PROPN
ejpam-6500	333	47	,	,	PUNCT
ejpam-6500	333	48	0a×b⟩.	0a×b⟩.	NOUN
ejpam-6500	333	49	proof	proof	NOUN
ejpam-6500	333	50	.	.	PUNCT
ejpam-6500	334	1	for	for	ADP
ejpam-6500	334	2	any	any	DET
ejpam-6500	334	3	(	(	PUNCT
ejpam-6500	334	4	x1	x1	PROPN
ejpam-6500	334	5	,	,	PUNCT
ejpam-6500	334	6	y1	y1	PROPN
ejpam-6500	334	7	)	)	PUNCT
ejpam-6500	334	8	,	,	PUNCT
ejpam-6500	334	9	(	(	PUNCT
ejpam-6500	334	10	x2	x2	PROPN
ejpam-6500	334	11	,	,	PUNCT
ejpam-6500	334	12	y2	y2	PROPN
ejpam-6500	334	13	)	)	PUNCT
ejpam-6500	334	14	∈	∈	PROPN
ejpam-6500	334	15	a×b	a×b	PROPN
ejpam-6500	334	16	,	,	PUNCT
ejpam-6500	334	17	we	we	PRON
ejpam-6500	334	18	have	have	VERB
ejpam-6500	334	19	µ(((x1	µ(((x1	NOUN
ejpam-6500	334	20	,	,	PUNCT
ejpam-6500	334	21	y1)|a×b((x2	y1)|a×b((x2	NOUN
ejpam-6500	334	22	,	,	PUNCT
ejpam-6500	334	23	y2)|a×b(x2	y2)|a×b(x2	PROPN
ejpam-6500	334	24	,	,	PUNCT
ejpam-6500	334	25	y2)))|a×b((x1	y2)))|a×b((x1	PROPN
ejpam-6500	334	26	,	,	PUNCT
ejpam-6500	334	27	y1)|a×b((x2	y1)|a×b((x2	NOUN
ejpam-6500	334	28	,	,	PUNCT
ejpam-6500	334	29	y2)|a×b(x2	y2)|a×b(x2	X
ejpam-6500	334	30	,	,	PUNCT
ejpam-6500	334	31	y2	y2	NOUN
ejpam-6500	334	32	)	)	PUNCT
ejpam-6500	334	33	)	)	PUNCT
ejpam-6500	334	34	)	)	PUNCT
ejpam-6500	334	35	)	)	PUNCT
ejpam-6500	335	1	=	=	SYM
ejpam-6500	335	2	µ((x1|a(x2|ax2))|a(x1|a(x2|ax2	µ((x1|a(x2|ax2))|a(x1|a(x2|ax2	ADJ
ejpam-6500	335	3	)	)	PUNCT
ejpam-6500	335	4	)	)	PUNCT
ejpam-6500	335	5	,	,	PUNCT
ejpam-6500	335	6	(	(	PUNCT
ejpam-6500	335	7	y1|b(y2|by2))|b(y1|b(y2|by2	y1|b(y2|by2))|b(y1|b(y2|by2	NOUN
ejpam-6500	335	8	)	)	PUNCT
ejpam-6500	335	9	)	)	PUNCT
ejpam-6500	335	10	)	)	PUNCT
ejpam-6500	336	1	=	=	SYM
ejpam-6500	336	2	min{µa((x1|a(x2|ax2))|a(x1|a(x2|ax2	min{µa((x1|a(x2|ax2))|a(x1|a(x2|ax2	NOUN
ejpam-6500	336	3	)	)	PUNCT
ejpam-6500	336	4	)	)	PUNCT
ejpam-6500	336	5	)	)	PUNCT
ejpam-6500	336	6	,	,	PUNCT
ejpam-6500	336	7	µb((y1|b(y2|by2))|b(y1|b(y2|by2	µb((y1|b(y2|by2))|b(y1|b(y2|by2	NUM
ejpam-6500	336	8	)	)	PUNCT
ejpam-6500	336	9	)	)	PUNCT
ejpam-6500	336	10	)	)	PUNCT
ejpam-6500	336	11	}	}	PUNCT
ejpam-6500	336	12	≥	≥	PROPN
ejpam-6500	336	13	min	min	PROPN
ejpam-6500	336	14	{	{	PUNCT
ejpam-6500	336	15	min	min	PROPN
ejpam-6500	336	16	{	{	PUNCT
ejpam-6500	336	17	µa(x1	µa(x1	NOUN
ejpam-6500	336	18	)	)	PUNCT
ejpam-6500	336	19	,	,	PUNCT
ejpam-6500	336	20	µa(x2	µa(x2	PROPN
ejpam-6500	336	21	)	)	PUNCT
ejpam-6500	336	22	,	,	PUNCT
ejpam-6500	336	23	1−m	1−m	NUM
ejpam-6500	336	24	2	2	NUM
ejpam-6500	336	25	}	}	PUNCT
ejpam-6500	336	26	,	,	PUNCT
ejpam-6500	336	27	min	min	PROPN
ejpam-6500	336	28	{	{	PUNCT
ejpam-6500	336	29	µb(y1	µb(y1	NUM
ejpam-6500	336	30	)	)	PUNCT
ejpam-6500	336	31	,	,	PUNCT
ejpam-6500	336	32	µb(y2	µb(y2	NOUN
ejpam-6500	336	33	)	)	PUNCT
ejpam-6500	336	34	,	,	PUNCT
ejpam-6500	336	35	1−m	1−m	NUM
ejpam-6500	336	36	2	2	NUM
ejpam-6500	336	37	}	}	PUNCT
ejpam-6500	336	38	}	}	PUNCT
ejpam-6500	336	39	=	=	SYM
ejpam-6500	336	40	min	min	PROPN
ejpam-6500	336	41	{	{	PUNCT
ejpam-6500	336	42	min	min	PROPN
ejpam-6500	336	43	{	{	PUNCT
ejpam-6500	336	44	µa(x1	µa(x1	NOUN
ejpam-6500	336	45	)	)	PUNCT
ejpam-6500	336	46	,	,	PUNCT
ejpam-6500	336	47	µb(y1	µb(y1	NOUN
ejpam-6500	336	48	)	)	PUNCT
ejpam-6500	336	49	,	,	PUNCT
ejpam-6500	336	50	1−m	1−m	NUM
ejpam-6500	336	51	2	2	NUM
ejpam-6500	336	52	}	}	PUNCT
ejpam-6500	336	53	,	,	PUNCT
ejpam-6500	336	54	min	min	PROPN
ejpam-6500	336	55	{	{	PUNCT
ejpam-6500	336	56	µa(x2	µa(x2	NOUN
ejpam-6500	336	57	)	)	PUNCT
ejpam-6500	336	58	,	,	PUNCT
ejpam-6500	336	59	µb(y2	µb(y2	NOUN
ejpam-6500	336	60	)	)	PUNCT
ejpam-6500	336	61	,	,	PUNCT
ejpam-6500	336	62	1−m	1−m	NUM
ejpam-6500	336	63	2	2	NUM
ejpam-6500	336	64	}	}	PUNCT
ejpam-6500	336	65	}	}	PUNCT
ejpam-6500	336	66	=	=	SYM
ejpam-6500	336	67	min	min	NOUN
ejpam-6500	336	68	{	{	PUNCT
ejpam-6500	336	69	µ(x1	µ(x1	ADJ
ejpam-6500	336	70	,	,	PUNCT
ejpam-6500	336	71	y1	y1	NOUN
ejpam-6500	336	72	)	)	PUNCT
ejpam-6500	336	73	,	,	PUNCT
ejpam-6500	336	74	µ(x2	µ(x2	NOUN
ejpam-6500	336	75	,	,	PUNCT
ejpam-6500	336	76	y2	y2	PROPN
ejpam-6500	336	77	)	)	PUNCT
ejpam-6500	336	78	,	,	PUNCT
ejpam-6500	336	79	1−m	1−m	NUM
ejpam-6500	336	80	2	2	NUM
ejpam-6500	336	81	}	}	PUNCT
ejpam-6500	336	82	.	.	PUNCT
ejpam-6500	337	1	hence	hence	ADV
ejpam-6500	337	2	,	,	PUNCT
ejpam-6500	337	3	⟨a×b	⟨a×b	PROPN
ejpam-6500	337	4	,	,	PUNCT
ejpam-6500	337	5	|a×b⟩	|a×b⟩	PROPN
ejpam-6500	337	6	is	be	AUX
ejpam-6500	337	7	an	an	DET
ejpam-6500	337	8	(	(	PUNCT
ejpam-6500	337	9	∈,∈	∈,∈	INTJ
ejpam-6500	337	10	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	337	11	subalgebra	subalgebra	NOUN
ejpam-6500	337	12	of	of	ADP
ejpam-6500	337	13	a×b	a×b	PROPN
ejpam-6500	337	14	.	.	PUNCT
ejpam-6500	338	1	t.	t.	PROPN
ejpam-6500	338	2	oner	oner	PROPN
ejpam-6500	338	3	et	et	PROPN
ejpam-6500	338	4	al	al	PROPN
ejpam-6500	338	5	.	.	PUNCT
ejpam-6500	338	6	/	/	SYM
ejpam-6500	338	7	eur	eur	PROPN
ejpam-6500	338	8	.	.	PUNCT
ejpam-6500	339	1	j.	j.	PROPN
ejpam-6500	339	2	pure	pure	PROPN
ejpam-6500	339	3	appl	appl	PROPN
ejpam-6500	339	4	.	.	PROPN
ejpam-6500	339	5	math	math	PROPN
ejpam-6500	339	6	,	,	PUNCT
ejpam-6500	339	7	18	18	NUM
ejpam-6500	339	8	(	(	PUNCT
ejpam-6500	339	9	3	3	NUM
ejpam-6500	339	10	)	)	PUNCT
ejpam-6500	339	11	(	(	PUNCT
ejpam-6500	339	12	2025	2025	NUM
ejpam-6500	339	13	)	)	PUNCT
ejpam-6500	339	14	,	,	PUNCT
ejpam-6500	339	15	6500	6500	NUM
ejpam-6500	339	16	12	12	NUM
ejpam-6500	339	17	of	of	ADP
ejpam-6500	339	18	13	13	NUM
ejpam-6500	339	19	4	4	NUM
ejpam-6500	339	20	.	.	PUNCT
ejpam-6500	340	1	conclusion	conclusion	NOUN
ejpam-6500	340	2	in	in	ADP
ejpam-6500	340	3	this	this	DET
ejpam-6500	340	4	paper	paper	NOUN
ejpam-6500	340	5	,	,	PUNCT
ejpam-6500	340	6	we	we	PRON
ejpam-6500	340	7	introduce	introduce	VERB
ejpam-6500	340	8	and	and	CCONJ
ejpam-6500	340	9	study	study	VERB
ejpam-6500	340	10	generalized	generalize	VERB
ejpam-6500	340	11	fuzzy	fuzzy	ADJ
ejpam-6500	340	12	subalgebras	subalgebra	NOUN
ejpam-6500	340	13	within	within	ADP
ejpam-6500	340	14	the	the	DET
ejpam-6500	340	15	framework	framework	NOUN
ejpam-6500	340	16	of	of	ADP
ejpam-6500	340	17	sheffer	sheffer	PROPN
ejpam-6500	340	18	stroke	stroke	PROPN
ejpam-6500	340	19	hilbert	hilbert	PROPN
ejpam-6500	340	20	algebras	algebras	PROPN
ejpam-6500	340	21	.	.	PUNCT
ejpam-6500	341	1	by	by	ADP
ejpam-6500	341	2	defining	define	VERB
ejpam-6500	341	3	(	(	PUNCT
ejpam-6500	341	4	∈,∈	∈,∈	X
ejpam-6500	341	5	∨qm)-fuzzy	∨qm)-fuzzy	ADJ
ejpam-6500	341	6	subalgebras	subalgebras	PROPN
ejpam-6500	341	7	,	,	PUNCT
ejpam-6500	341	8	we	we	PRON
ejpam-6500	341	9	have	have	AUX
ejpam-6500	341	10	extended	extend	VERB
ejpam-6500	341	11	classical	classical	ADJ
ejpam-6500	341	12	subalgebra	subalgebra	NOUN
ejpam-6500	341	13	concepts	concept	NOUN
ejpam-6500	341	14	to	to	ADP
ejpam-6500	341	15	the	the	DET
ejpam-6500	341	16	fuzzy	fuzzy	ADJ
ejpam-6500	341	17	setting	setting	NOUN
ejpam-6500	341	18	,	,	PUNCT
ejpam-6500	341	19	providing	provide	VERB
ejpam-6500	341	20	a	a	DET
ejpam-6500	341	21	robust	robust	ADJ
ejpam-6500	341	22	theoretical	theoretical	ADJ
ejpam-6500	341	23	foundation	foundation	NOUN
ejpam-6500	341	24	for	for	ADP
ejpam-6500	341	25	further	further	ADJ
ejpam-6500	341	26	research	research	NOUN
ejpam-6500	341	27	.	.	PUNCT
ejpam-6500	342	1	our	our	PRON
ejpam-6500	342	2	key	key	ADJ
ejpam-6500	342	3	results	result	NOUN
ejpam-6500	342	4	include	include	VERB
ejpam-6500	342	5	the	the	DET
ejpam-6500	342	6	characterization	characterization	NOUN
ejpam-6500	342	7	of	of	ADP
ejpam-6500	342	8	these	these	DET
ejpam-6500	342	9	subalgebras	subalgebra	NOUN
ejpam-6500	342	10	through	through	ADP
ejpam-6500	342	11	their	their	PRON
ejpam-6500	342	12	level	level	NOUN
ejpam-6500	342	13	subsets	subset	NOUN
ejpam-6500	342	14	,	,	PUNCT
ejpam-6500	342	15	as	as	ADV
ejpam-6500	342	16	well	well	ADV
ejpam-6500	342	17	as	as	ADP
ejpam-6500	342	18	necessary	necessary	ADJ
ejpam-6500	342	19	and	and	CCONJ
ejpam-6500	342	20	sufficient	sufficient	ADJ
ejpam-6500	342	21	conditions	condition	NOUN
ejpam-6500	342	22	for	for	ADP
ejpam-6500	342	23	their	their	PRON
ejpam-6500	342	24	existence	existence	NOUN
ejpam-6500	342	25	.	.	PUNCT
ejpam-6500	343	1	additionally	additionally	ADV
ejpam-6500	343	2	,	,	PUNCT
ejpam-6500	343	3	we	we	PRON
ejpam-6500	343	4	have	have	AUX
ejpam-6500	343	5	demonstrated	demonstrate	VERB
ejpam-6500	343	6	the	the	DET
ejpam-6500	343	7	algebraic	algebraic	ADJ
ejpam-6500	343	8	properties	property	NOUN
ejpam-6500	343	9	of	of	ADP
ejpam-6500	343	10	these	these	DET
ejpam-6500	343	11	subalgebras	subalgebra	NOUN
ejpam-6500	343	12	,	,	PUNCT
ejpam-6500	343	13	including	include	VERB
ejpam-6500	343	14	their	their	PRON
ejpam-6500	343	15	behavior	behavior	NOUN
ejpam-6500	343	16	under	under	ADP
ejpam-6500	343	17	intersection	intersection	NOUN
ejpam-6500	343	18	,	,	PUNCT
ejpam-6500	343	19	union	union	NOUN
ejpam-6500	343	20	,	,	PUNCT
ejpam-6500	343	21	and	and	CCONJ
ejpam-6500	343	22	homomorphism	homomorphism	NOUN
ejpam-6500	343	23	.	.	PUNCT
ejpam-6500	344	1	the	the	DET
ejpam-6500	344	2	implications	implication	NOUN
ejpam-6500	344	3	of	of	ADP
ejpam-6500	344	4	this	this	DET
ejpam-6500	344	5	work	work	NOUN
ejpam-6500	344	6	are	be	AUX
ejpam-6500	344	7	twofold	twofold	ADJ
ejpam-6500	344	8	.	.	PUNCT
ejpam-6500	345	1	first	first	ADV
ejpam-6500	345	2	,	,	PUNCT
ejpam-6500	345	3	it	it	PRON
ejpam-6500	345	4	enriches	enrich	VERB
ejpam-6500	345	5	the	the	DET
ejpam-6500	345	6	theoretical	theoretical	ADJ
ejpam-6500	345	7	understanding	understanding	NOUN
ejpam-6500	345	8	of	of	ADP
ejpam-6500	345	9	sheffer	sheffer	PROPN
ejpam-6500	345	10	stroke	stroke	PROPN
ejpam-6500	345	11	hilbert	hilbert	PROPN
ejpam-6500	345	12	algebras	algebras	PROPN
ejpam-6500	345	13	by	by	ADP
ejpam-6500	345	14	incorporating	incorporate	VERB
ejpam-6500	345	15	fuzzy	fuzzy	ADJ
ejpam-6500	345	16	set	set	NOUN
ejpam-6500	345	17	theory	theory	NOUN
ejpam-6500	345	18	.	.	PUNCT
ejpam-6500	346	1	second	second	ADJ
ejpam-6500	346	2	,	,	PUNCT
ejpam-6500	346	3	it	it	PRON
ejpam-6500	346	4	opens	open	VERB
ejpam-6500	346	5	new	new	ADJ
ejpam-6500	346	6	avenues	avenue	NOUN
ejpam-6500	346	7	for	for	ADP
ejpam-6500	346	8	applications	application	NOUN
ejpam-6500	346	9	in	in	ADP
ejpam-6500	346	10	logical	logical	ADJ
ejpam-6500	346	11	systems	system	NOUN
ejpam-6500	346	12	and	and	CCONJ
ejpam-6500	346	13	algebraic	algebraic	ADJ
ejpam-6500	346	14	structures	structure	NOUN
ejpam-6500	346	15	where	where	SCONJ
ejpam-6500	346	16	uncertainty	uncertainty	NOUN
ejpam-6500	346	17	and	and	CCONJ
ejpam-6500	346	18	vagueness	vagueness	NOUN
ejpam-6500	346	19	are	be	AUX
ejpam-6500	346	20	inherent	inherent	ADJ
ejpam-6500	346	21	.	.	PUNCT
ejpam-6500	347	1	future	future	ADJ
ejpam-6500	347	2	research	research	NOUN
ejpam-6500	347	3	directions	direction	NOUN
ejpam-6500	347	4	could	could	AUX
ejpam-6500	347	5	explore	explore	VERB
ejpam-6500	347	6	the	the	DET
ejpam-6500	347	7	applications	application	NOUN
ejpam-6500	347	8	of	of	ADP
ejpam-6500	347	9	these	these	DET
ejpam-6500	347	10	generalized	generalize	VERB
ejpam-6500	347	11	fuzzy	fuzzy	ADJ
ejpam-6500	347	12	subalgebras	subalgebra	NOUN
ejpam-6500	347	13	in	in	ADP
ejpam-6500	347	14	automated	automate	VERB
ejpam-6500	347	15	reasoning	reasoning	NOUN
ejpam-6500	347	16	,	,	PUNCT
ejpam-6500	347	17	artificial	artificial	ADJ
ejpam-6500	347	18	intelligence	intelligence	NOUN
ejpam-6500	347	19	,	,	PUNCT
ejpam-6500	347	20	and	and	CCONJ
ejpam-6500	347	21	other	other	ADJ
ejpam-6500	347	22	areas	area	NOUN
ejpam-6500	347	23	of	of	ADP
ejpam-6500	347	24	computer	computer	NOUN
ejpam-6500	347	25	science	science	NOUN
ejpam-6500	347	26	.	.	PUNCT
ejpam-6500	348	1	acknowledgements	acknowledgement	NOUN
ejpam-6500	348	2	this	this	DET
ejpam-6500	348	3	work	work	NOUN
ejpam-6500	348	4	was	be	AUX
ejpam-6500	348	5	supported	support	VERB
ejpam-6500	348	6	by	by	ADP
ejpam-6500	348	7	the	the	DET
ejpam-6500	348	8	revenue	revenue	NOUN
ejpam-6500	348	9	budget	budget	NOUN
ejpam-6500	348	10	in	in	ADP
ejpam-6500	348	11	2025	2025	NUM
ejpam-6500	348	12	,	,	PUNCT
ejpam-6500	348	13	school	school	NOUN
ejpam-6500	348	14	of	of	ADP
ejpam-6500	348	15	science	science	NOUN
ejpam-6500	348	16	,	,	PUNCT
ejpam-6500	348	17	university	university	NOUN
ejpam-6500	348	18	of	of	ADP
ejpam-6500	348	19	phayao	phayao	NOUN
ejpam-6500	348	20	(	(	PUNCT
ejpam-6500	348	21	grant	grant	VERB
ejpam-6500	348	22	no	no	INTJ
ejpam-6500	348	23	.	.	PUNCT
ejpam-6500	348	24	pbtsc68018	pbtsc68018	NOUN
ejpam-6500	348	25	)	)	PUNCT
ejpam-6500	348	26	.	.	PUNCT
ejpam-6500	349	1	references	reference	NOUN
ejpam-6500	349	2	[	[	X
ejpam-6500	349	3	1	1	NUM
ejpam-6500	349	4	]	]	PUNCT
ejpam-6500	349	5	h.	h.	PROPN
ejpam-6500	349	6	m.	m.	PROPN
ejpam-6500	349	7	sheffer	sheffer	PROPN
ejpam-6500	349	8	.	.	PUNCT
ejpam-6500	350	1	a	a	DET
ejpam-6500	350	2	set	set	NOUN
ejpam-6500	350	3	of	of	ADP
ejpam-6500	350	4	five	five	NUM
ejpam-6500	350	5	independent	independent	ADJ
ejpam-6500	350	6	postulates	postulate	NOUN
ejpam-6500	350	7	for	for	ADP
ejpam-6500	350	8	boolean	boolean	ADJ
ejpam-6500	350	9	algebras	algebra	NOUN
ejpam-6500	350	10	,	,	PUNCT
ejpam-6500	350	11	with	with	ADP
ejpam-6500	350	12	application	application	NOUN
ejpam-6500	350	13	to	to	ADP
ejpam-6500	350	14	logical	logical	ADJ
ejpam-6500	350	15	constants	constant	NOUN
ejpam-6500	350	16	.	.	PUNCT
ejpam-6500	351	1	transactions	transaction	NOUN
ejpam-6500	351	2	of	of	ADP
ejpam-6500	351	3	the	the	DET
ejpam-6500	351	4	american	american	PROPN
ejpam-6500	351	5	mathematical	mathematical	PROPN
ejpam-6500	351	6	society	society	NOUN
ejpam-6500	351	7	,	,	PUNCT
ejpam-6500	351	8	14(4):481–488	14(4):481–488	NUM
ejpam-6500	351	9	,	,	PUNCT
ejpam-6500	351	10	1913	1913	NUM
ejpam-6500	351	11	.	.	PUNCT
ejpam-6500	352	1	[	[	X
ejpam-6500	352	2	2	2	NUM
ejpam-6500	352	3	]	]	PUNCT
ejpam-6500	352	4	w.	w.	PROPN
ejpam-6500	352	5	mccune	mccune	PROPN
ejpam-6500	352	6	.	.	PUNCT
ejpam-6500	353	1	sheffer	sheffer	PROPN
ejpam-6500	353	2	stroke	stroke	NOUN
ejpam-6500	353	3	bases	basis	NOUN
ejpam-6500	353	4	for	for	ADP
ejpam-6500	353	5	boolean	boolean	ADJ
ejpam-6500	353	6	algebras	algebra	NOUN
ejpam-6500	353	7	.	.	PUNCT
ejpam-6500	353	8	journal	journal	PROPN
ejpam-6500	353	9	of	of	ADP
ejpam-6500	353	10	automated	automate	VERB
ejpam-6500	353	11	reasoning	reasoning	NOUN
ejpam-6500	353	12	,	,	PUNCT
ejpam-6500	353	13	38:1–10	38:1–10	NOUN
ejpam-6500	353	14	,	,	PUNCT
ejpam-6500	353	15	2007	2007	NUM
ejpam-6500	353	16	.	.	PUNCT
ejpam-6500	354	1	[	[	X
ejpam-6500	354	2	3	3	X
ejpam-6500	354	3	]	]	PUNCT
ejpam-6500	354	4	t.	t.	NOUN
ejpam-6500	354	5	oner	oner	NOUN
ejpam-6500	354	6	,	,	PUNCT
ejpam-6500	354	7	t.	t.	PROPN
ejpam-6500	354	8	katican	katican	PROPN
ejpam-6500	354	9	,	,	PUNCT
ejpam-6500	354	10	and	and	CCONJ
ejpam-6500	354	11	a.	a.	PROPN
ejpam-6500	354	12	b.	b.	PROPN
ejpam-6500	354	13	saeid	saeid	PROPN
ejpam-6500	354	14	.	.	PUNCT
ejpam-6500	355	1	relation	relation	NOUN
ejpam-6500	355	2	between	between	ADP
ejpam-6500	355	3	sheffer	sheffer	PROPN
ejpam-6500	355	4	stroke	stroke	PROPN
ejpam-6500	355	5	and	and	CCONJ
ejpam-6500	355	6	hilbert	hilbert	PROPN
ejpam-6500	355	7	algebras	algebras	PROPN
ejpam-6500	355	8	.	.	PUNCT
ejpam-6500	355	9	categories	category	NOUN
ejpam-6500	355	10	and	and	CCONJ
ejpam-6500	355	11	general	general	ADJ
ejpam-6500	355	12	algebraic	algebraic	ADJ
ejpam-6500	355	13	structures	structure	NOUN
ejpam-6500	355	14	with	with	ADP
ejpam-6500	355	15	applications	application	NOUN
ejpam-6500	355	16	,	,	PUNCT
ejpam-6500	355	17	14(1):245	14(1):245	NUM
ejpam-6500	355	18	–	–	PUNCT
ejpam-6500	355	19	268	268	NUM
ejpam-6500	355	20	,	,	PUNCT
ejpam-6500	355	21	2021	2021	NUM
ejpam-6500	355	22	.	.	PUNCT
ejpam-6500	356	1	[	[	X
ejpam-6500	356	2	4	4	NUM
ejpam-6500	356	3	]	]	PUNCT
ejpam-6500	356	4	a.	a.	NOUN
ejpam-6500	356	5	diego	diego	PROPN
ejpam-6500	356	6	.	.	PUNCT
ejpam-6500	357	1	sur	sur	PROPN
ejpam-6500	357	2	les	les	PROPN
ejpam-6500	357	3	algèbres	algèbre	NOUN
ejpam-6500	357	4	de	de	X
ejpam-6500	357	5	hilbert	hilbert	NOUN
ejpam-6500	357	6	,	,	PUNCT
ejpam-6500	357	7	volume	volume	NOUN
ejpam-6500	357	8	21	21	NUM
ejpam-6500	357	9	of	of	ADP
ejpam-6500	357	10	collection	collection	NOUN
ejpam-6500	357	11	de	de	X
ejpam-6500	357	12	logique	logique	X
ejpam-6500	357	13	mathematique	mathematique	NOUN
ejpam-6500	357	14	,	,	PUNCT
ejpam-6500	357	15	serie	serie	PROPN
ejpam-6500	357	16	a.	a.	PROPN
ejpam-6500	357	17	gauthier	gauthier	PROPN
ejpam-6500	357	18	-	-	PUNCT
ejpam-6500	357	19	villars	villars	PROPN
ejpam-6500	357	20	,	,	PUNCT
ejpam-6500	357	21	paris	paris	PROPN
ejpam-6500	357	22	,	,	PUNCT
ejpam-6500	357	23	1966	1966	NUM
ejpam-6500	357	24	.	.	PUNCT
ejpam-6500	358	1	[	[	X
ejpam-6500	358	2	5	5	X
ejpam-6500	358	3	]	]	PUNCT
ejpam-6500	358	4	j.	j.	PROPN
ejpam-6500	358	5	porte	porte	PROPN
ejpam-6500	358	6	.	.	PUNCT
ejpam-6500	359	1	recherches	recherche	NOUN
ejpam-6500	359	2	sur	sur	PROPN
ejpam-6500	359	3	la	la	X
ejpam-6500	359	4	théorie	théorie	PROPN
ejpam-6500	359	5	des	des	PROPN
ejpam-6500	359	6	structures	structure	NOUN
ejpam-6500	359	7	algébriques	algébrique	NOUN
ejpam-6500	359	8	ordonnées	ordonnée	NOUN
ejpam-6500	359	9	.	.	PUNCT
ejpam-6500	360	1	phd	phd	NOUN
ejpam-6500	360	2	thesis	thesis	NOUN
ejpam-6500	360	3	,	,	PUNCT
ejpam-6500	360	4	université	université	ADJ
ejpam-6500	360	5	de	de	X
ejpam-6500	360	6	paris	paris	PROPN
ejpam-6500	360	7	,	,	PUNCT
ejpam-6500	360	8	1979	1979	NUM
ejpam-6500	360	9	.	.	PUNCT
ejpam-6500	361	1	[	[	X
ejpam-6500	361	2	6	6	NUM
ejpam-6500	361	3	]	]	X
ejpam-6500	361	4	d.	d.	PROPN
ejpam-6500	361	5	buşneag	buşneag	PROPN
ejpam-6500	361	6	.	.	PUNCT
ejpam-6500	362	1	hilbert	hilbert	PROPN
ejpam-6500	362	2	algebras	algebras	PROPN
ejpam-6500	362	3	with	with	ADP
ejpam-6500	362	4	supremum	supremum	ADJ
ejpam-6500	362	5	.	.	PUNCT
ejpam-6500	363	1	analele	analele	PROPN
ejpam-6500	363	2	universitatii	universitatii	PROPN
ejpam-6500	363	3	din	din	PROPN
ejpam-6500	363	4	craiova	craiova	PROPN
ejpam-6500	363	5	.	.	PUNCT
ejpam-6500	364	1	seria	seria	PROPN
ejpam-6500	364	2	matematica	matematica	PROPN
ejpam-6500	364	3	informatica	informatica	PROPN
ejpam-6500	364	4	,	,	PUNCT
ejpam-6500	364	5	12:33–40	12:33–40	NUM
ejpam-6500	364	6	,	,	PUNCT
ejpam-6500	364	7	1985	1985	NUM
ejpam-6500	364	8	.	.	PUNCT
ejpam-6500	365	1	[	[	X
ejpam-6500	365	2	7	7	NUM
ejpam-6500	365	3	]	]	X
ejpam-6500	365	4	i.	i.	NOUN
ejpam-6500	365	5	chajda	chajda	PROPN
ejpam-6500	365	6	.	.	PUNCT
ejpam-6500	366	1	hilbert	hilbert	PROPN
ejpam-6500	366	2	algebras	algebras	PROPN
ejpam-6500	366	3	with	with	ADP
ejpam-6500	366	4	infimum	infimum	PROPN
ejpam-6500	366	5	.	.	PUNCT
ejpam-6500	367	1	mathematica	mathematica	PROPN
ejpam-6500	367	2	bohemica	bohemica	PROPN
ejpam-6500	367	3	,	,	PUNCT
ejpam-6500	367	4	128:15–22	128:15–22	NUM
ejpam-6500	367	5	,	,	PUNCT
ejpam-6500	367	6	2003	2003	NUM
ejpam-6500	367	7	.	.	PUNCT
ejpam-6500	368	1	[	[	X
ejpam-6500	368	2	8	8	NUM
ejpam-6500	368	3	]	]	X
ejpam-6500	368	4	l.	l.	PROPN
ejpam-6500	368	5	a.	a.	PROPN
ejpam-6500	368	6	zadeh	zadeh	PROPN
ejpam-6500	368	7	.	.	PUNCT
ejpam-6500	368	8	fuzzy	fuzzy	ADJ
ejpam-6500	368	9	sets	set	NOUN
ejpam-6500	368	10	.	.	PUNCT
ejpam-6500	369	1	information	information	NOUN
ejpam-6500	369	2	and	and	CCONJ
ejpam-6500	369	3	control	control	NOUN
ejpam-6500	369	4	,	,	PUNCT
ejpam-6500	369	5	8(3):338–353	8(3):338–353	NUM
ejpam-6500	369	6	,	,	PUNCT
ejpam-6500	369	7	1965	1965	NUM
ejpam-6500	369	8	.	.	PUNCT
ejpam-6500	370	1	[	[	X
ejpam-6500	370	2	9	9	NUM
ejpam-6500	370	3	]	]	PUNCT
ejpam-6500	370	4	a.	a.	NOUN
ejpam-6500	370	5	rosenfeld	rosenfeld	PROPN
ejpam-6500	370	6	.	.	PUNCT
ejpam-6500	371	1	fuzzy	fuzzy	ADJ
ejpam-6500	371	2	groups	group	NOUN
ejpam-6500	371	3	.	.	PUNCT
ejpam-6500	372	1	journal	journal	PROPN
ejpam-6500	372	2	of	of	ADP
ejpam-6500	372	3	mathematical	mathematical	ADJ
ejpam-6500	372	4	analysis	analysis	NOUN
ejpam-6500	372	5	and	and	CCONJ
ejpam-6500	372	6	applications	application	NOUN
ejpam-6500	372	7	,	,	PUNCT
ejpam-6500	372	8	35(3):512–517	35(3):512–517	PROPN
ejpam-6500	372	9	,	,	PUNCT
ejpam-6500	372	10	1971	1971	NUM
ejpam-6500	372	11	.	.	PUNCT
ejpam-6500	373	1	[	[	X
ejpam-6500	373	2	10	10	NUM
ejpam-6500	373	3	]	]	PUNCT
ejpam-6500	373	4	w.-j	w.-j	PROPN
ejpam-6500	373	5	.	.	PUNCT
ejpam-6500	374	1	liu	liu	PROPN
ejpam-6500	374	2	.	.	PUNCT
ejpam-6500	374	3	fuzzy	fuzzy	ADJ
ejpam-6500	374	4	invariant	invariant	ADJ
ejpam-6500	374	5	subgroups	subgroup	NOUN
ejpam-6500	374	6	and	and	CCONJ
ejpam-6500	374	7	fuzzy	fuzzy	ADJ
ejpam-6500	374	8	ideals	ideal	NOUN
ejpam-6500	374	9	.	.	PUNCT
ejpam-6500	375	1	fuzzy	fuzzy	ADJ
ejpam-6500	375	2	sets	set	NOUN
ejpam-6500	375	3	and	and	CCONJ
ejpam-6500	375	4	systems	system	NOUN
ejpam-6500	375	5	,	,	PUNCT
ejpam-6500	375	6	8(2):133–139	8(2):133–139	NUM
ejpam-6500	375	7	,	,	PUNCT
ejpam-6500	375	8	1982	1982	NUM
ejpam-6500	375	9	.	.	PUNCT
ejpam-6500	376	1	t.	t.	PROPN
ejpam-6500	376	2	oner	oner	PROPN
ejpam-6500	376	3	et	et	PROPN
ejpam-6500	376	4	al	al	PROPN
ejpam-6500	376	5	.	.	PUNCT
ejpam-6500	376	6	/	/	SYM
ejpam-6500	376	7	eur	eur	PROPN
ejpam-6500	376	8	.	.	PUNCT
ejpam-6500	377	1	j.	j.	PROPN
ejpam-6500	377	2	pure	pure	PROPN
ejpam-6500	377	3	appl	appl	PROPN
ejpam-6500	377	4	.	.	PROPN
ejpam-6500	377	5	math	math	PROPN
ejpam-6500	377	6	,	,	PUNCT
ejpam-6500	377	7	18	18	NUM
ejpam-6500	377	8	(	(	PUNCT
ejpam-6500	377	9	3	3	NUM
ejpam-6500	377	10	)	)	PUNCT
ejpam-6500	377	11	(	(	PUNCT
ejpam-6500	377	12	2025	2025	NUM
ejpam-6500	377	13	)	)	PUNCT
ejpam-6500	377	14	,	,	PUNCT
ejpam-6500	377	15	6500	6500	NUM
ejpam-6500	377	16	13	13	NUM
ejpam-6500	377	17	of	of	ADP
ejpam-6500	377	18	13	13	NUM
ejpam-6500	377	19	[	[	X
ejpam-6500	377	20	11	11	NUM
ejpam-6500	377	21	]	]	PUNCT
ejpam-6500	377	22	w.	w.	PROPN
ejpam-6500	377	23	a.	a.	PROPN
ejpam-6500	377	24	dudek	dudek	PROPN
ejpam-6500	377	25	and	and	CCONJ
ejpam-6500	377	26	y.	y.	PROPN
ejpam-6500	377	27	b.	b.	PROPN
ejpam-6500	377	28	jun	jun	PROPN
ejpam-6500	377	29	.	.	PROPN
ejpam-6500	378	1	on	on	ADP
ejpam-6500	378	2	fuzzy	fuzzy	ADJ
ejpam-6500	378	3	ideals	ideal	NOUN
ejpam-6500	378	4	in	in	ADP
ejpam-6500	378	5	hilbert	hilbert	PROPN
ejpam-6500	378	6	algebras	algebras	PROPN
ejpam-6500	378	7	.	.	PUNCT
ejpam-6500	379	1	novi	novi	PROPN
ejpam-6500	379	2	sad	sad	PROPN
ejpam-6500	379	3	journal	journal	PROPN
ejpam-6500	379	4	of	of	ADP
ejpam-6500	379	5	mathematics	mathematic	NOUN
ejpam-6500	379	6	,	,	PUNCT
ejpam-6500	379	7	29(2):193–207	29(2):193–207	PROPN
ejpam-6500	379	8	,	,	PUNCT
ejpam-6500	379	9	1999	1999	NUM
ejpam-6500	379	10	.	.	PUNCT
ejpam-6500	380	1	[	[	X
ejpam-6500	380	2	12	12	NUM
ejpam-6500	380	3	]	]	X
ejpam-6500	380	4	r.	r.	PROPN
ejpam-6500	380	5	a.	a.	PROPN
ejpam-6500	380	6	borzooei	borzooei	PROPN
ejpam-6500	380	7	,	,	PUNCT
ejpam-6500	380	8	g.	g.	PROPN
ejpam-6500	380	9	r.	r.	PROPN
ejpam-6500	380	10	rezaei	rezaei	PROPN
ejpam-6500	380	11	,	,	PUNCT
ejpam-6500	380	12	and	and	CCONJ
ejpam-6500	381	1	y.	y.	PROPN
ejpam-6500	381	2	b.	b.	PROPN
ejpam-6500	381	3	jun	jun	PROPN
ejpam-6500	381	4	.	.	PROPN
ejpam-6500	382	1	fuzzy	fuzzy	ADJ
ejpam-6500	382	2	weak	weak	ADJ
ejpam-6500	382	3	filters	filter	NOUN
ejpam-6500	382	4	of	of	ADP
ejpam-6500	382	5	sheffer	sheffer	PROPN
ejpam-6500	382	6	stroke	stroke	PROPN
ejpam-6500	382	7	hilbert	hilbert	PROPN
ejpam-6500	382	8	algebras	algebras	PROPN
ejpam-6500	382	9	.	.	PUNCT
ejpam-6500	383	1	annales	annales	PROPN
ejpam-6500	383	2	mathematicae	mathematicae	PROPN
ejpam-6500	383	3	silesianae	silesianae	PROPN
ejpam-6500	383	4	,	,	PUNCT
ejpam-6500	383	5	37(2):185–203	37(2):185–203	PROPN
ejpam-6500	383	6	,	,	PUNCT
ejpam-6500	383	7	2023	2023	NUM
ejpam-6500	383	8	.	.	PUNCT
ejpam-6500	384	1	[	[	X
ejpam-6500	384	2	13	13	NUM
ejpam-6500	384	3	]	]	PUNCT
ejpam-6500	384	4	t.	t.	NOUN
ejpam-6500	384	5	oner	oner	NOUN
ejpam-6500	384	6	,	,	PUNCT
ejpam-6500	384	7	t.	t.	PROPN
ejpam-6500	384	8	katican	katican	PROPN
ejpam-6500	384	9	,	,	PUNCT
ejpam-6500	384	10	and	and	CCONJ
ejpam-6500	384	11	a.	a.	PROPN
ejpam-6500	384	12	b.	b.	PROPN
ejpam-6500	384	13	saeid	saeid	PROPN
ejpam-6500	384	14	.	.	PUNCT
ejpam-6500	385	1	fuzzy	fuzzy	ADJ
ejpam-6500	385	2	ideals	ideal	NOUN
ejpam-6500	385	3	of	of	ADP
ejpam-6500	385	4	sheffer	sheffer	PROPN
ejpam-6500	385	5	stroke	stroke	PROPN
ejpam-6500	385	6	hilbert	hilbert	PROPN
ejpam-6500	385	7	algebras	algebras	PROPN
ejpam-6500	385	8	.	.	PUNCT
ejpam-6500	386	1	proceedings	proceeding	NOUN
ejpam-6500	386	2	of	of	ADP
ejpam-6500	386	3	the	the	DET
ejpam-6500	386	4	national	national	PROPN
ejpam-6500	386	5	academy	academy	PROPN
ejpam-6500	386	6	of	of	ADP
ejpam-6500	386	7	sciences	sciences	PROPN
ejpam-6500	386	8	,	,	PUNCT
ejpam-6500	386	9	india	india	PROPN
ejpam-6500	386	10	section	section	PROPN
ejpam-6500	386	11	a	a	PRON
ejpam-6500	386	12	:	:	PUNCT
ejpam-6500	386	13	physical	physical	ADJ
ejpam-6500	386	14	sciences	science	NOUN
ejpam-6500	386	15	,	,	PUNCT
ejpam-6500	386	16	93:85–94	93:85–94	NUM
ejpam-6500	386	17	,	,	PUNCT
ejpam-6500	386	18	2023	2023	NUM
ejpam-6500	386	19	.	.	PUNCT
ejpam-6500	387	1	[	[	X
ejpam-6500	387	2	14	14	NUM
ejpam-6500	387	3	]	]	X
ejpam-6500	387	4	t.	t.	NOUN
ejpam-6500	387	5	oner	oner	NOUN
ejpam-6500	387	6	,	,	PUNCT
ejpam-6500	387	7	t.	t.	PROPN
ejpam-6500	387	8	katican	katican	PROPN
ejpam-6500	387	9	,	,	PUNCT
ejpam-6500	387	10	and	and	CCONJ
ejpam-6500	387	11	a.	a.	PROPN
ejpam-6500	387	12	b.	b.	PROPN
ejpam-6500	387	13	saeid	saeid	PROPN
ejpam-6500	387	14	.	.	PUNCT
ejpam-6500	388	1	fuzzy	fuzzy	ADJ
ejpam-6500	388	2	filters	filter	NOUN
ejpam-6500	388	3	of	of	ADP
ejpam-6500	388	4	sheffer	sheffer	PROPN
ejpam-6500	388	5	stroke	stroke	PROPN
ejpam-6500	388	6	hilbert	hilbert	PROPN
ejpam-6500	388	7	algebras	algebras	PROPN
ejpam-6500	388	8	.	.	PUNCT
ejpam-6500	389	1	journal	journal	PROPN
ejpam-6500	389	2	of	of	ADP
ejpam-6500	389	3	intelligent	intelligent	ADJ
ejpam-6500	389	4	and	and	CCONJ
ejpam-6500	389	5	fuzzy	fuzzy	ADJ
ejpam-6500	389	6	systems	system	NOUN
ejpam-6500	389	7	,	,	PUNCT
ejpam-6500	389	8	40(1):759–772	40(1):759–772	NOUN
ejpam-6500	389	9	,	,	PUNCT
ejpam-6500	389	10	2021	2021	NUM
ejpam-6500	389	11	.	.	PUNCT
ejpam-6500	390	1	[	[	X
ejpam-6500	390	2	15	15	NUM
ejpam-6500	390	3	]	]	X
ejpam-6500	390	4	h.	h.	PROPN
ejpam-6500	390	5	s.	s.	PROPN
ejpam-6500	390	6	kim	kim	PROPN
ejpam-6500	390	7	,	,	PUNCT
ejpam-6500	390	8	s.	s.	PROPN
ejpam-6500	390	9	z.	z.	PROPN
ejpam-6500	390	10	song	song	PROPN
ejpam-6500	390	11	,	,	PUNCT
ejpam-6500	390	12	s.	s.	PROPN
ejpam-6500	390	13	s.	s.	PROPN
ejpam-6500	390	14	ahn	ahn	PROPN
ejpam-6500	390	15	,	,	PUNCT
ejpam-6500	390	16	and	and	CCONJ
ejpam-6500	390	17	y.	y.	PROPN
ejpam-6500	390	18	b.	b.	PROPN
ejpam-6500	390	19	jun	jun	PROPN
ejpam-6500	390	20	.	.	PROPN
ejpam-6500	390	21	deductive	deductive	ADJ
ejpam-6500	390	22	systems	system	NOUN
ejpam-6500	390	23	and	and	CCONJ
ejpam-6500	390	24	filters	filter	NOUN
ejpam-6500	390	25	of	of	ADP
ejpam-6500	390	26	sheffer	sheffer	PROPN
ejpam-6500	390	27	stroke	stroke	PROPN
ejpam-6500	390	28	hilbert	hilbert	PROPN
ejpam-6500	390	29	algebras	algebras	PROPN
ejpam-6500	390	30	based	base	VERB
ejpam-6500	390	31	on	on	ADP
ejpam-6500	390	32	the	the	DET
ejpam-6500	390	33	bipolar	bipolar	ADV
ejpam-6500	390	34	-	-	PUNCT
ejpam-6500	390	35	valued	value	VERB
ejpam-6500	390	36	fuzzy	fuzzy	ADJ
ejpam-6500	390	37	set	set	NOUN
ejpam-6500	390	38	environment	environment	NOUN
ejpam-6500	390	39	.	.	PUNCT
ejpam-6500	391	1	journal	journal	PROPN
ejpam-6500	391	2	of	of	ADP
ejpam-6500	391	3	computational	computational	ADJ
ejpam-6500	391	4	analysis	analysis	NOUN
ejpam-6500	391	5	and	and	CCONJ
ejpam-6500	391	6	applications	application	NOUN
ejpam-6500	391	7	,	,	PUNCT
ejpam-6500	391	8	32(1):192–210	32(1):192–210	NUM
ejpam-6500	391	9	,	,	PUNCT
ejpam-6500	391	10	2024	2024	NUM
ejpam-6500	391	11	.	.	PUNCT
ejpam-6500	392	1	[	[	X
ejpam-6500	392	2	16	16	NUM
ejpam-6500	392	3	]	]	PUNCT
ejpam-6500	392	4	t.	t.	NOUN
ejpam-6500	392	5	oner	oner	NOUN
ejpam-6500	392	6	,	,	PUNCT
ejpam-6500	392	7	n.	n.	PROPN
ejpam-6500	392	8	rajesh	rajesh	PROPN
ejpam-6500	392	9	,	,	PUNCT
ejpam-6500	392	10	a.	a.	NOUN
ejpam-6500	392	11	iampan	iampan	PROPN
ejpam-6500	392	12	,	,	PUNCT
ejpam-6500	392	13	and	and	CCONJ
ejpam-6500	392	14	a.	a.	PROPN
ejpam-6500	392	15	b.	b.	PROPN
ejpam-6500	392	16	saeid	saeid	PROPN
ejpam-6500	392	17	.	.	PUNCT
ejpam-6500	393	1	soft	soft	ADJ
ejpam-6500	393	2	subalgebras	subalgebra	NOUN
ejpam-6500	393	3	and	and	CCONJ
ejpam-6500	393	4	ideals	ideal	NOUN
ejpam-6500	393	5	of	of	ADP
ejpam-6500	393	6	sheffer	sheffer	PROPN
ejpam-6500	393	7	stroke	stroke	PROPN
ejpam-6500	393	8	hilbert	hilbert	PROPN
ejpam-6500	393	9	algebras	algebras	PROPN
ejpam-6500	393	10	based	base	VERB
ejpam-6500	393	11	on	on	ADP
ejpam-6500	393	12	n	n	DET
ejpam-6500	393	13	-structures	-structure	NOUN
ejpam-6500	393	14	.	.	PUNCT
ejpam-6500	394	1	european	european	ADJ
ejpam-6500	394	2	journal	journal	PROPN
ejpam-6500	394	3	of	of	ADP
ejpam-6500	394	4	pure	pure	ADJ
ejpam-6500	394	5	and	and	CCONJ
ejpam-6500	394	6	applied	applied	ADJ
ejpam-6500	394	7	mathematics	mathematic	NOUN
ejpam-6500	394	8	,	,	PUNCT
ejpam-6500	394	9	18(2):6018	18(2):6018	NUM
ejpam-6500	394	10	,	,	PUNCT
ejpam-6500	394	11	2025	2025	NUM
ejpam-6500	394	12	.	.	PUNCT
ejpam-6500	395	1	[	[	X
ejpam-6500	395	2	17	17	NUM
ejpam-6500	395	3	]	]	X
ejpam-6500	395	4	n.	n.	PROPN
ejpam-6500	395	5	rajesh	rajesh	PROPN
ejpam-6500	395	6	,	,	PUNCT
ejpam-6500	395	7	t.	t.	PROPN
ejpam-6500	395	8	oner	oner	NOUN
ejpam-6500	395	9	,	,	PUNCT
ejpam-6500	395	10	a.	a.	NOUN
ejpam-6500	395	11	iampan	iampan	PROPN
ejpam-6500	395	12	,	,	PUNCT
ejpam-6500	395	13	and	and	CCONJ
ejpam-6500	395	14	i.	i.	PROPN
ejpam-6500	395	15	senturk	senturk	PROPN
ejpam-6500	395	16	.	.	PUNCT
ejpam-6500	396	1	on	on	ADP
ejpam-6500	396	2	length	length	NOUN
ejpam-6500	396	3	and	and	CCONJ
ejpam-6500	396	4	mean	mean	VERB
ejpam-6500	396	5	fuzzy	fuzzy	ADJ
ejpam-6500	396	6	ideals	ideal	NOUN
ejpam-6500	396	7	of	of	ADP
ejpam-6500	396	8	sheffer	sheffer	PROPN
ejpam-6500	396	9	stroke	stroke	PROPN
ejpam-6500	396	10	hilbert	hilbert	PROPN
ejpam-6500	396	11	algebras	algebras	PROPN
ejpam-6500	396	12	.	.	PUNCT
ejpam-6500	397	1	european	european	PROPN
ejpam-6500	397	2	journal	journal	PROPN
ejpam-6500	397	3	of	of	ADP
ejpam-6500	397	4	pure	pure	ADJ
ejpam-6500	397	5	and	and	CCONJ
ejpam-6500	397	6	applied	applied	ADJ
ejpam-6500	397	7	mathematics	mathematic	NOUN
ejpam-6500	397	8	,	,	PUNCT
ejpam-6500	397	9	18(1):5779	18(1):5779	NUM
ejpam-6500	397	10	,	,	PUNCT
ejpam-6500	397	11	2025	2025	NUM
ejpam-6500	397	12	.	.	PUNCT
ejpam-6500	398	1	[	[	X
ejpam-6500	398	2	18	18	NUM
ejpam-6500	398	3	]	]	X
ejpam-6500	398	4	n.	n.	PROPN
ejpam-6500	398	5	rajesh	rajesh	PROPN
ejpam-6500	398	6	,	,	PUNCT
ejpam-6500	398	7	t.	t.	PROPN
ejpam-6500	398	8	oner	oner	NOUN
ejpam-6500	398	9	,	,	PUNCT
ejpam-6500	398	10	a.	a.	NOUN
ejpam-6500	398	11	iampan	iampan	PROPN
ejpam-6500	398	12	,	,	PUNCT
ejpam-6500	398	13	and	and	CCONJ
ejpam-6500	398	14	a.	a.	NOUN
ejpam-6500	398	15	rezaei	rezaei	PROPN
ejpam-6500	398	16	.	.	PUNCT
ejpam-6500	399	1	investigating	investigate	VERB
ejpam-6500	399	2	length	length	NOUN
ejpam-6500	399	3	and	and	CCONJ
ejpam-6500	399	4	mean	mean	ADJ
ejpam-6500	399	5	-	-	PUNCT
ejpam-6500	399	6	fuzzy	fuzzy	ADJ
ejpam-6500	399	7	subalgebras	subalgebra	NOUN
ejpam-6500	399	8	in	in	ADP
ejpam-6500	399	9	sheffer	sheffer	PROPN
ejpam-6500	399	10	stroke	stroke	PROPN
ejpam-6500	399	11	hilbert	hilbert	PROPN
ejpam-6500	399	12	algebras	algebras	PROPN
ejpam-6500	399	13	.	.	PUNCT
ejpam-6500	400	1	european	european	PROPN
ejpam-6500	400	2	journal	journal	PROPN
ejpam-6500	400	3	of	of	ADP
ejpam-6500	400	4	pure	pure	ADJ
ejpam-6500	400	5	and	and	CCONJ
ejpam-6500	400	6	applied	applied	ADJ
ejpam-6500	400	7	mathematics	mathematic	NOUN
ejpam-6500	400	8	,	,	PUNCT
ejpam-6500	400	9	18(2):5914	18(2):5914	NUM
ejpam-6500	400	10	,	,	PUNCT
ejpam-6500	400	11	2025	2025	NUM
ejpam-6500	400	12	.	.	PUNCT