id	sid	tid	token	lemma	pos
ejpam-7074	1	1	european	european	PROPN
ejpam-7074	1	2	journal	journal	PROPN
ejpam-7074	1	3	of	of	ADP
ejpam-7074	1	4	pure	pure	ADJ
ejpam-7074	1	5	and	and	CCONJ
ejpam-7074	1	6	applied	applied	ADJ
ejpam-7074	1	7	mathematics	mathematic	NOUN
ejpam-7074	1	8	2025	2025	NUM
ejpam-7074	1	9	,	,	PUNCT
ejpam-7074	1	10	vol	vol	NOUN
ejpam-7074	1	11	.	.	PROPN
ejpam-7074	1	12	18	18	NUM
ejpam-7074	1	13	,	,	PUNCT
ejpam-7074	1	14	issue	issue	NOUN
ejpam-7074	1	15	4	4	NUM
ejpam-7074	1	16	,	,	PUNCT
ejpam-7074	1	17	article	article	NOUN
ejpam-7074	1	18	number	number	NOUN
ejpam-7074	1	19	7074	7074	NUM
ejpam-7074	1	20	issn	issn	PROPN
ejpam-7074	1	21	1307	1307	NUM
ejpam-7074	1	22	-	-	SYM
ejpam-7074	1	23	5543	5543	NUM
ejpam-7074	1	24	–	–	PUNCT
ejpam-7074	1	25	ejpam.com	ejpam.com	X
ejpam-7074	1	26	published	publish	VERB
ejpam-7074	1	27	by	by	ADP
ejpam-7074	1	28	new	new	PROPN
ejpam-7074	1	29	york	york	PROPN
ejpam-7074	1	30	business	business	PROPN
ejpam-7074	1	31	global	global	ADJ
ejpam-7074	1	32	on	on	ADP
ejpam-7074	1	33	interval	interval	NOUN
ejpam-7074	1	34	-	-	PUNCT
ejpam-7074	1	35	valued	value	VERB
ejpam-7074	1	36	intuitionistic	intuitionistic	ADJ
ejpam-7074	1	37	fuzzy	fuzzy	ADJ
ejpam-7074	1	38	subalgebras	subalgebra	NOUN
ejpam-7074	1	39	of	of	ADP
ejpam-7074	1	40	sheffer	sheffer	PROPN
ejpam-7074	1	41	stroke	stroke	PROPN
ejpam-7074	1	42	hilbert	hilbert	PROPN
ejpam-7074	1	43	algebras	algebras	PROPN
ejpam-7074	1	44	aiyared	aiyare	VERB
ejpam-7074	1	45	iampan1,∗	iampan1,∗	NOUN
ejpam-7074	1	46	,	,	PUNCT
ejpam-7074	1	47	neelamegarajan	neelamegarajan	NOUN
ejpam-7074	1	48	rajesh2	rajesh2	PROPN
ejpam-7074	1	49	,	,	PUNCT
ejpam-7074	1	50	tahsin	tahsin	VERB
ejpam-7074	1	51	oner3	oner3	PROPN
ejpam-7074	1	52	,	,	PUNCT
ejpam-7074	1	53	firat	firat	PROPN
ejpam-7074	1	54	ates4	ates4	PROPN
ejpam-7074	1	55	,	,	PUNCT
ejpam-7074	1	56	kannan	kannan	PROPN
ejpam-7074	1	57	geetha2	geetha2	PROPN
ejpam-7074	1	58	,	,	PUNCT
ejpam-7074	2	1	arsham	arsham	PROPN
ejpam-7074	2	2	borumand	borumand	PROPN
ejpam-7074	2	3	saeid5	saeid5	PROPN
ejpam-7074	2	4	1	1	NUM
ejpam-7074	2	5	department	department	NOUN
ejpam-7074	2	6	of	of	ADP
ejpam-7074	2	7	mathematics	mathematic	NOUN
ejpam-7074	2	8	,	,	PUNCT
ejpam-7074	2	9	school	school	NOUN
ejpam-7074	2	10	of	of	ADP
ejpam-7074	2	11	science	science	NOUN
ejpam-7074	2	12	,	,	PUNCT
ejpam-7074	2	13	university	university	NOUN
ejpam-7074	2	14	of	of	ADP
ejpam-7074	2	15	phayao	phayao	NOUN
ejpam-7074	2	16	,	,	PUNCT
ejpam-7074	2	17	mae	mae	PROPN
ejpam-7074	2	18	ka	ka	PROPN
ejpam-7074	2	19	,	,	PUNCT
ejpam-7074	2	20	mueang	mueang	PROPN
ejpam-7074	2	21	,	,	PUNCT
ejpam-7074	2	22	phayao	phayao	NOUN
ejpam-7074	2	23	56000	56000	NUM
ejpam-7074	2	24	,	,	PUNCT
ejpam-7074	2	25	thailand	thailand	PROPN
ejpam-7074	2	26	2	2	NUM
ejpam-7074	2	27	department	department	NOUN
ejpam-7074	2	28	of	of	ADP
ejpam-7074	2	29	mathematics	mathematic	NOUN
ejpam-7074	2	30	,	,	PUNCT
ejpam-7074	2	31	rajah	rajah	NOUN
ejpam-7074	2	32	serfoji	serfoji	ADJ
ejpam-7074	2	33	government	government	NOUN
ejpam-7074	2	34	college	college	NOUN
ejpam-7074	2	35	,	,	PUNCT
ejpam-7074	2	36	thanjavur-613005	thanjavur-613005	NOUN
ejpam-7074	2	37	,	,	PUNCT
ejpam-7074	2	38	tamil	tamil	PROPN
ejpam-7074	2	39	nadu	nadu	NOUN
ejpam-7074	2	40	,	,	PUNCT
ejpam-7074	2	41	india	india	PROPN
ejpam-7074	2	42	3	3	NUM
ejpam-7074	2	43	department	department	NOUN
ejpam-7074	2	44	of	of	ADP
ejpam-7074	2	45	mathematics	mathematic	NOUN
ejpam-7074	2	46	,	,	PUNCT
ejpam-7074	2	47	faculty	faculty	NOUN
ejpam-7074	2	48	of	of	ADP
ejpam-7074	2	49	science	science	NOUN
ejpam-7074	2	50	,	,	PUNCT
ejpam-7074	2	51	ege	ege	PROPN
ejpam-7074	2	52	university	university	NOUN
ejpam-7074	2	53	,	,	PUNCT
ejpam-7074	2	54	35100	35100	NUM
ejpam-7074	2	55	izmir	izmir	PROPN
ejpam-7074	2	56	,	,	PUNCT
ejpam-7074	2	57	turkey	turkey	PROPN
ejpam-7074	2	58	4	4	NUM
ejpam-7074	2	59	department	department	NOUN
ejpam-7074	2	60	of	of	ADP
ejpam-7074	2	61	mathematics	mathematic	NOUN
ejpam-7074	2	62	,	,	PUNCT
ejpam-7074	2	63	balıkesir	balıkesir	NOUN
ejpam-7074	2	64	university	university	NOUN
ejpam-7074	2	65	,	,	PUNCT
ejpam-7074	2	66	balıkesir	balıkesir	NOUN
ejpam-7074	2	67	,	,	PUNCT
ejpam-7074	2	68	turkey	turkey	PROPN
ejpam-7074	2	69	5	5	NUM
ejpam-7074	2	70	department	department	NOUN
ejpam-7074	2	71	of	of	ADP
ejpam-7074	2	72	pure	pure	ADJ
ejpam-7074	2	73	mathematics	mathematic	NOUN
ejpam-7074	2	74	,	,	PUNCT
ejpam-7074	2	75	faculty	faculty	NOUN
ejpam-7074	2	76	of	of	ADP
ejpam-7074	2	77	mathematics	mathematic	NOUN
ejpam-7074	2	78	and	and	CCONJ
ejpam-7074	2	79	computer	computer	NOUN
ejpam-7074	2	80	,	,	PUNCT
ejpam-7074	2	81	shahid	shahid	PROPN
ejpam-7074	2	82	bahonar	bahonar	VERB
ejpam-7074	2	83	university	university	PROPN
ejpam-7074	2	84	of	of	ADP
ejpam-7074	2	85	kerman	kerman	PROPN
ejpam-7074	2	86	,	,	PUNCT
ejpam-7074	2	87	kerman	kerman	PROPN
ejpam-7074	2	88	,	,	PUNCT
ejpam-7074	2	89	iran	iran	PROPN
ejpam-7074	2	90	abstract	abstract	ADJ
ejpam-7074	2	91	.	.	PUNCT
ejpam-7074	3	1	this	this	DET
ejpam-7074	3	2	paper	paper	NOUN
ejpam-7074	3	3	explores	explore	VERB
ejpam-7074	3	4	the	the	DET
ejpam-7074	3	5	structure	structure	NOUN
ejpam-7074	3	6	of	of	ADP
ejpam-7074	3	7	interval	interval	NOUN
ejpam-7074	3	8	-	-	PUNCT
ejpam-7074	3	9	valued	value	VERB
ejpam-7074	3	10	intuitionistic	intuitionistic	ADJ
ejpam-7074	3	11	fuzzy	fuzzy	ADJ
ejpam-7074	3	12	(	(	PUNCT
ejpam-7074	3	13	ivif	ivif	NOUN
ejpam-7074	3	14	)	)	PUNCT
ejpam-7074	3	15	subsets	subset	NOUN
ejpam-7074	3	16	within	within	ADP
ejpam-7074	3	17	the	the	DET
ejpam-7074	3	18	framework	framework	NOUN
ejpam-7074	3	19	of	of	ADP
ejpam-7074	3	20	sheffer	sheffer	PROPN
ejpam-7074	3	21	stroke	stroke	PROPN
ejpam-7074	3	22	hilbert	hilbert	PROPN
ejpam-7074	3	23	algebras	algebras	PROPN
ejpam-7074	3	24	(	(	PUNCT
ejpam-7074	3	25	sshas	ssha	NOUN
ejpam-7074	3	26	)	)	PUNCT
ejpam-7074	3	27	.	.	PUNCT
ejpam-7074	4	1	after	after	ADP
ejpam-7074	4	2	establishing	establish	VERB
ejpam-7074	4	3	the	the	DET
ejpam-7074	4	4	foundational	foundational	ADJ
ejpam-7074	4	5	definitions	definition	NOUN
ejpam-7074	4	6	of	of	ADP
ejpam-7074	4	7	interval	interval	NOUN
ejpam-7074	4	8	-	-	PUNCT
ejpam-7074	4	9	valued	value	VERB
ejpam-7074	4	10	intuitionistic	intuitionistic	ADJ
ejpam-7074	4	11	fuzzy	fuzzy	ADJ
ejpam-7074	4	12	sheffer	sheffer	NOUN
ejpam-7074	4	13	stroke	stroke	NOUN
ejpam-7074	4	14	subalgebras	subalgebras	PROPN
ejpam-7074	4	15	(	(	PUNCT
ejpam-7074	4	16	ivifsssubalgebras	ivifsssubalgebras	PROPN
ejpam-7074	4	17	)	)	PUNCT
ejpam-7074	4	18	,	,	PUNCT
ejpam-7074	4	19	we	we	PRON
ejpam-7074	4	20	investigate	investigate	VERB
ejpam-7074	4	21	their	their	PRON
ejpam-7074	4	22	algebraic	algebraic	ADJ
ejpam-7074	4	23	properties	property	NOUN
ejpam-7074	4	24	,	,	PUNCT
ejpam-7074	4	25	closure	closure	NOUN
ejpam-7074	4	26	under	under	ADP
ejpam-7074	4	27	sheffer	sheffer	NOUN
ejpam-7074	4	28	stroke	stroke	NOUN
ejpam-7074	4	29	operations	operation	NOUN
ejpam-7074	4	30	,	,	PUNCT
ejpam-7074	4	31	and	and	CCONJ
ejpam-7074	4	32	stability	stability	NOUN
ejpam-7074	4	33	under	under	ADP
ejpam-7074	4	34	set	set	NOUN
ejpam-7074	4	35	-	-	PUNCT
ejpam-7074	4	36	theoretic	theoretic	NOUN
ejpam-7074	4	37	intersections	intersection	NOUN
ejpam-7074	4	38	and	and	CCONJ
ejpam-7074	4	39	unions	union	NOUN
ejpam-7074	4	40	.	.	PUNCT
ejpam-7074	5	1	a	a	DET
ejpam-7074	5	2	key	key	ADJ
ejpam-7074	5	3	result	result	NOUN
ejpam-7074	5	4	characterizes	characterize	VERB
ejpam-7074	5	5	ivifsssubalgebras	ivifsssubalgebras	NOUN
ejpam-7074	5	6	through	through	ADP
ejpam-7074	5	7	a	a	DET
ejpam-7074	5	8	pair	pair	NOUN
ejpam-7074	5	9	of	of	ADP
ejpam-7074	5	10	membership	membership	NOUN
ejpam-7074	5	11	conditions	condition	NOUN
ejpam-7074	5	12	,	,	PUNCT
ejpam-7074	5	13	and	and	CCONJ
ejpam-7074	5	14	it	it	PRON
ejpam-7074	5	15	is	be	AUX
ejpam-7074	5	16	further	far	ADV
ejpam-7074	5	17	shown	show	VERB
ejpam-7074	5	18	that	that	SCONJ
ejpam-7074	5	19	the	the	DET
ejpam-7074	5	20	level	level	NOUN
ejpam-7074	5	21	subsets	subset	NOUN
ejpam-7074	5	22	corresponding	correspond	VERB
ejpam-7074	5	23	to	to	ADP
ejpam-7074	5	24	ivif	ivif	NOUN
ejpam-7074	5	25	-	-	PUNCT
ejpam-7074	5	26	degrees	degree	NOUN
ejpam-7074	5	27	form	form	NOUN
ejpam-7074	5	28	classical	classical	ADJ
ejpam-7074	5	29	subalgebras	subalgebra	NOUN
ejpam-7074	5	30	in	in	ADP
ejpam-7074	5	31	the	the	DET
ejpam-7074	5	32	crisp	crisp	ADJ
ejpam-7074	5	33	setting	setting	NOUN
ejpam-7074	5	34	.	.	PUNCT
ejpam-7074	6	1	these	these	DET
ejpam-7074	6	2	findings	finding	NOUN
ejpam-7074	6	3	demonstrate	demonstrate	VERB
ejpam-7074	6	4	that	that	SCONJ
ejpam-7074	6	5	ivif	ivif	VERB
ejpam-7074	6	6	extensions	extension	NOUN
ejpam-7074	6	7	preserve	preserve	VERB
ejpam-7074	6	8	core	core	NOUN
ejpam-7074	6	9	algebraic	algebraic	ADJ
ejpam-7074	6	10	behaviors	behavior	NOUN
ejpam-7074	6	11	while	while	SCONJ
ejpam-7074	6	12	offering	offer	VERB
ejpam-7074	6	13	a	a	DET
ejpam-7074	6	14	robust	robust	ADJ
ejpam-7074	6	15	model	model	NOUN
ejpam-7074	6	16	for	for	ADP
ejpam-7074	6	17	uncertainty	uncertainty	NOUN
ejpam-7074	6	18	.	.	PUNCT
ejpam-7074	7	1	the	the	DET
ejpam-7074	7	2	results	result	NOUN
ejpam-7074	7	3	contribute	contribute	VERB
ejpam-7074	7	4	to	to	ADP
ejpam-7074	7	5	the	the	DET
ejpam-7074	7	6	ongoing	ongoing	ADJ
ejpam-7074	7	7	generalization	generalization	NOUN
ejpam-7074	7	8	of	of	ADP
ejpam-7074	7	9	fuzzy	fuzzy	ADJ
ejpam-7074	7	10	algebraic	algebraic	ADJ
ejpam-7074	7	11	systems	system	NOUN
ejpam-7074	7	12	and	and	CCONJ
ejpam-7074	7	13	lay	lie	VERB
ejpam-7074	7	14	the	the	DET
ejpam-7074	7	15	groundwork	groundwork	NOUN
ejpam-7074	7	16	for	for	ADP
ejpam-7074	7	17	further	further	ADJ
ejpam-7074	7	18	developments	development	NOUN
ejpam-7074	7	19	involving	involve	VERB
ejpam-7074	7	20	fuzzy	fuzzy	ADJ
ejpam-7074	7	21	ideals	ideal	NOUN
ejpam-7074	7	22	and	and	CCONJ
ejpam-7074	7	23	logical	logical	ADJ
ejpam-7074	7	24	applications	application	NOUN
ejpam-7074	7	25	.	.	PUNCT
ejpam-7074	8	1	2020	2020	NUM
ejpam-7074	8	2	mathematics	mathematic	NOUN
ejpam-7074	8	3	subject	subject	NOUN
ejpam-7074	8	4	classifications	classification	NOUN
ejpam-7074	8	5	:	:	PUNCT
ejpam-7074	8	6	20n05	20n05	NUM
ejpam-7074	8	7	,	,	PUNCT
ejpam-7074	8	8	94d05	94d05	NUM
ejpam-7074	8	9	,	,	PUNCT
ejpam-7074	8	10	03e72	03e72	X
ejpam-7074	8	11	key	key	ADJ
ejpam-7074	8	12	words	word	NOUN
ejpam-7074	8	13	and	and	CCONJ
ejpam-7074	8	14	phrases	phrase	NOUN
ejpam-7074	8	15	:	:	PUNCT
ejpam-7074	8	16	sheffer	sheffer	NOUN
ejpam-7074	8	17	stroke	stroke	PROPN
ejpam-7074	8	18	hilbert	hilbert	PROPN
ejpam-7074	8	19	algebra	algebra	PROPN
ejpam-7074	8	20	,	,	PUNCT
ejpam-7074	8	21	interval	interval	NOUN
ejpam-7074	8	22	-	-	PUNCT
ejpam-7074	8	23	valued	value	VERB
ejpam-7074	8	24	intuitionistic	intuitionistic	ADJ
ejpam-7074	8	25	fuzzy	fuzzy	ADJ
ejpam-7074	8	26	set	set	NOUN
ejpam-7074	8	27	,	,	PUNCT
ejpam-7074	8	28	interval	interval	NOUN
ejpam-7074	8	29	-	-	PUNCT
ejpam-7074	8	30	valued	value	VERB
ejpam-7074	8	31	intuitionistic	intuitionistic	ADJ
ejpam-7074	8	32	fuzzy	fuzzy	ADJ
ejpam-7074	8	33	sheffer	sheffer	NOUN
ejpam-7074	8	34	stroke	stroke	NOUN
ejpam-7074	8	35	subalgebra	subalgebra	PROPN
ejpam-7074	8	36	1	1	NUM
ejpam-7074	8	37	.	.	PUNCT
ejpam-7074	8	38	introduction	introduction	NOUN
ejpam-7074	8	39	sheffer	sheffer	PROPN
ejpam-7074	8	40	stroke	stroke	PROPN
ejpam-7074	8	41	hilbert	hilbert	PROPN
ejpam-7074	8	42	algebras	algebras	PROPN
ejpam-7074	8	43	(	(	PUNCT
ejpam-7074	8	44	sshas	ssha	NOUN
ejpam-7074	8	45	)	)	PUNCT
ejpam-7074	8	46	are	be	AUX
ejpam-7074	8	47	essential	essential	ADJ
ejpam-7074	8	48	algebraic	algebraic	ADJ
ejpam-7074	8	49	structures	structure	NOUN
ejpam-7074	8	50	that	that	PRON
ejpam-7074	8	51	play	play	VERB
ejpam-7074	8	52	a	a	DET
ejpam-7074	8	53	significant	significant	ADJ
ejpam-7074	8	54	role	role	NOUN
ejpam-7074	8	55	in	in	ADP
ejpam-7074	8	56	logical	logical	ADJ
ejpam-7074	8	57	systems	system	NOUN
ejpam-7074	8	58	and	and	CCONJ
ejpam-7074	8	59	boolean	boolean	ADJ
ejpam-7074	8	60	algebras	algebra	NOUN
ejpam-7074	8	61	.	.	PUNCT
ejpam-7074	9	1	they	they	PRON
ejpam-7074	9	2	serve	serve	VERB
ejpam-7074	9	3	as	as	ADP
ejpam-7074	9	4	a	a	DET
ejpam-7074	9	5	foundation	foundation	NOUN
ejpam-7074	9	6	∗corresponding	∗corresponde	VERB
ejpam-7074	9	7	author	author	NOUN
ejpam-7074	9	8	.	.	PUNCT
ejpam-7074	10	1	doi	doi	NOUN
ejpam-7074	10	2	:	:	PUNCT
ejpam-7074	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7074	https://doi.org/10.29020/nybg.ejpam.v18i4.7074	PROPN
ejpam-7074	10	4	email	email	NOUN
ejpam-7074	10	5	addresses	address	NOUN
ejpam-7074	10	6	:	:	PUNCT
ejpam-7074	10	7	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-7074	10	8	(	(	PUNCT
ejpam-7074	10	9	a.	a.	NOUN
ejpam-7074	10	10	iampan	iampan	PROPN
ejpam-7074	10	11	)	)	PUNCT
ejpam-7074	10	12	,	,	PUNCT
ejpam-7074	10	13	nrajesh	nrajesh	PROPN
ejpam-7074	10	14	topology@yahoo.co.in	topology@yahoo.co.in	PROPN
ejpam-7074	10	15	(	(	PUNCT
ejpam-7074	10	16	n.	n.	PROPN
ejpam-7074	10	17	rajesh	rajesh	PROPN
ejpam-7074	10	18	)	)	PUNCT
ejpam-7074	10	19	,	,	PUNCT
ejpam-7074	10	20	tahsin.oner@ege.edu.tr	tahsin.oner@ege.edu.tr	NOUN
ejpam-7074	10	21	(	(	PUNCT
ejpam-7074	10	22	t.	t.	NOUN
ejpam-7074	10	23	oner	oner	PROPN
ejpam-7074	10	24	)	)	PUNCT
ejpam-7074	10	25	,	,	PUNCT
ejpam-7074	10	26	firat@balikesir.edu.tr	firat@balikesir.edu.tr	PROPN
ejpam-7074	10	27	(	(	PUNCT
ejpam-7074	10	28	f.	f.	PROPN
ejpam-7074	10	29	ates	ates	PROPN
ejpam-7074	10	30	)	)	PUNCT
ejpam-7074	10	31	,	,	PUNCT
ejpam-7074	10	32	geeethaak@gmail.com	geeethaak@gmail.com	X
ejpam-7074	10	33	(	(	PUNCT
ejpam-7074	10	34	k.	k.	NOUN
ejpam-7074	10	35	geetha	geetha	PROPN
ejpam-7074	10	36	)	)	PUNCT
ejpam-7074	10	37	,	,	PUNCT
ejpam-7074	10	38	arsham@uk.ac.ir	arsham@uk.ac.ir	PROPN
ejpam-7074	10	39	(	(	PUNCT
ejpam-7074	10	40	a.	a.	PROPN
ejpam-7074	10	41	borumand	borumand	PROPN
ejpam-7074	10	42	saeid	saeid	PROPN
ejpam-7074	10	43	)	)	PUNCT
ejpam-7074	10	44	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7074	11	1	1	1	NUM
ejpam-7074	11	2	copyright	copyright	NOUN
ejpam-7074	11	3	:	:	PUNCT
ejpam-7074	11	4	©	©	PROPN
ejpam-7074	11	5	2025	2025	NUM
ejpam-7074	11	6	the	the	DET
ejpam-7074	11	7	author(s	author(s	NOUN
ejpam-7074	11	8	)	)	PUNCT
ejpam-7074	11	9	.	.	PUNCT
ejpam-7074	12	1	(	(	PUNCT
ejpam-7074	12	2	cc	cc	NOUN
ejpam-7074	12	3	by	by	ADP
ejpam-7074	12	4	-	-	PUNCT
ejpam-7074	12	5	nc	nc	PROPN
ejpam-7074	12	6	4.0	4.0	NUM
ejpam-7074	12	7	)	)	PUNCT
ejpam-7074	12	8	a.	a.	NOUN
ejpam-7074	12	9	iampan	iampan	NOUN
ejpam-7074	12	10	et	et	PROPN
ejpam-7074	12	11	al	al	PROPN
ejpam-7074	12	12	.	.	PUNCT
ejpam-7074	12	13	/	/	SYM
ejpam-7074	12	14	eur	eur	PROPN
ejpam-7074	12	15	.	.	PUNCT
ejpam-7074	13	1	j.	j.	PROPN
ejpam-7074	13	2	pure	pure	PROPN
ejpam-7074	13	3	appl	appl	PROPN
ejpam-7074	13	4	.	.	PROPN
ejpam-7074	13	5	math	math	PROPN
ejpam-7074	13	6	,	,	PUNCT
ejpam-7074	13	7	18	18	NUM
ejpam-7074	13	8	(	(	PUNCT
ejpam-7074	13	9	4	4	NUM
ejpam-7074	13	10	)	)	PUNCT
ejpam-7074	13	11	(	(	PUNCT
ejpam-7074	13	12	2025	2025	NUM
ejpam-7074	13	13	)	)	PUNCT
ejpam-7074	13	14	,	,	PUNCT
ejpam-7074	13	15	7074	7074	NUM
ejpam-7074	13	16	2	2	NUM
ejpam-7074	13	17	of	of	ADP
ejpam-7074	13	18	14	14	NUM
ejpam-7074	13	19	for	for	ADP
ejpam-7074	13	20	representing	represent	VERB
ejpam-7074	13	21	logical	logical	ADJ
ejpam-7074	13	22	operations	operation	NOUN
ejpam-7074	13	23	and	and	CCONJ
ejpam-7074	13	24	have	have	VERB
ejpam-7074	13	25	broad	broad	ADJ
ejpam-7074	13	26	applications	application	NOUN
ejpam-7074	13	27	across	across	ADP
ejpam-7074	13	28	fields	field	NOUN
ejpam-7074	13	29	like	like	ADP
ejpam-7074	13	30	formal	formal	ADJ
ejpam-7074	13	31	logic	logic	NOUN
ejpam-7074	13	32	,	,	PUNCT
ejpam-7074	13	33	artificial	artificial	ADJ
ejpam-7074	13	34	intelligence	intelligence	NOUN
ejpam-7074	13	35	,	,	PUNCT
ejpam-7074	13	36	and	and	CCONJ
ejpam-7074	13	37	quantum	quantum	NOUN
ejpam-7074	13	38	computing	computing	NOUN
ejpam-7074	13	39	.	.	PUNCT
ejpam-7074	14	1	the	the	DET
ejpam-7074	14	2	sheffer	sheffer	PROPN
ejpam-7074	14	3	stroke	stroke	NOUN
ejpam-7074	14	4	operation	operation	NOUN
ejpam-7074	14	5	,	,	PUNCT
ejpam-7074	14	6	typically	typically	ADV
ejpam-7074	14	7	defined	define	VERB
ejpam-7074	14	8	by	by	ADP
ejpam-7074	14	9	the	the	DET
ejpam-7074	14	10	nand	nand	PROPN
ejpam-7074	14	11	operation	operation	NOUN
ejpam-7074	14	12	,	,	PUNCT
ejpam-7074	14	13	is	be	AUX
ejpam-7074	14	14	central	central	ADJ
ejpam-7074	14	15	to	to	ADP
ejpam-7074	14	16	these	these	DET
ejpam-7074	14	17	algebras	algebra	NOUN
ejpam-7074	14	18	and	and	CCONJ
ejpam-7074	14	19	is	be	AUX
ejpam-7074	14	20	fundamental	fundamental	ADJ
ejpam-7074	14	21	in	in	ADP
ejpam-7074	14	22	constructing	construct	VERB
ejpam-7074	14	23	more	more	ADV
ejpam-7074	14	24	advanced	advanced	ADJ
ejpam-7074	14	25	logical	logical	ADJ
ejpam-7074	14	26	systems	system	NOUN
ejpam-7074	14	27	.	.	PUNCT
ejpam-7074	15	1	the	the	DET
ejpam-7074	15	2	application	application	NOUN
ejpam-7074	15	3	of	of	ADP
ejpam-7074	15	4	the	the	DET
ejpam-7074	15	5	sheffer	sheffer	NOUN
ejpam-7074	15	6	stroke	stroke	NOUN
ejpam-7074	15	7	in	in	ADP
ejpam-7074	15	8	various	various	ADJ
ejpam-7074	15	9	algebraic	algebraic	ADJ
ejpam-7074	15	10	structures	structure	NOUN
ejpam-7074	15	11	has	have	AUX
ejpam-7074	15	12	been	be	AUX
ejpam-7074	15	13	thoroughly	thoroughly	ADV
ejpam-7074	15	14	explored	explore	VERB
ejpam-7074	15	15	,	,	PUNCT
ejpam-7074	15	16	making	make	VERB
ejpam-7074	15	17	significant	significant	ADJ
ejpam-7074	15	18	contributions	contribution	NOUN
ejpam-7074	15	19	to	to	ADP
ejpam-7074	15	20	multiple	multiple	ADJ
ejpam-7074	15	21	fields	field	NOUN
ejpam-7074	15	22	of	of	ADP
ejpam-7074	15	23	study	study	NOUN
ejpam-7074	15	24	.	.	PUNCT
ejpam-7074	16	1	research	research	NOUN
ejpam-7074	16	2	has	have	AUX
ejpam-7074	16	3	focused	focus	VERB
ejpam-7074	16	4	on	on	ADP
ejpam-7074	16	5	sheffer	sheffer	NOUN
ejpam-7074	16	6	stroke	stroke	NOUN
ejpam-7074	16	7	reducts	reduct	NOUN
ejpam-7074	16	8	within	within	ADP
ejpam-7074	16	9	basic	basic	ADJ
ejpam-7074	16	10	algebras	algebra	NOUN
ejpam-7074	17	1	[	[	X
ejpam-7074	17	2	1	1	NUM
ejpam-7074	17	3	,	,	PUNCT
ejpam-7074	17	4	2	2	NUM
ejpam-7074	17	5	]	]	PUNCT
ejpam-7074	17	6	,	,	PUNCT
ejpam-7074	17	7	sheffer	sheffer	PROPN
ejpam-7074	17	8	stroke	stroke	NOUN
ejpam-7074	17	9	mtl	mtl	PROPN
ejpam-7074	17	10	-	-	PUNCT
ejpam-7074	17	11	algebras	algebras	X
ejpam-7074	18	1	[	[	X
ejpam-7074	18	2	3	3	NUM
ejpam-7074	18	3	]	]	PUNCT
ejpam-7074	18	4	,	,	PUNCT
ejpam-7074	18	5	and	and	CCONJ
ejpam-7074	18	6	ortholattices	ortholattice	VERB
ejpam-7074	19	1	[	[	X
ejpam-7074	19	2	4	4	NUM
ejpam-7074	19	3	]	]	PUNCT
ejpam-7074	19	4	.	.	PUNCT
ejpam-7074	20	1	additionally	additionally	ADV
ejpam-7074	20	2	,	,	PUNCT
ejpam-7074	20	3	the	the	DET
ejpam-7074	20	4	role	role	NOUN
ejpam-7074	20	5	of	of	ADP
ejpam-7074	20	6	fuzzy	fuzzy	ADJ
ejpam-7074	20	7	sets	set	NOUN
ejpam-7074	20	8	in	in	ADP
ejpam-7074	20	9	sheffer	sheffer	NOUN
ejpam-7074	20	10	stroke	stroke	NOUN
ejpam-7074	20	11	be	be	AUX
ejpam-7074	20	12	-	-	PUNCT
ejpam-7074	20	13	algebras	algebras	X
ejpam-7074	20	14	[	[	X
ejpam-7074	20	15	5	5	NUM
ejpam-7074	20	16	]	]	PUNCT
ejpam-7074	20	17	has	have	AUX
ejpam-7074	20	18	been	be	AUX
ejpam-7074	20	19	investigated	investigate	VERB
ejpam-7074	20	20	,	,	PUNCT
ejpam-7074	20	21	underscoring	underscore	VERB
ejpam-7074	20	22	the	the	DET
ejpam-7074	20	23	far	far	ADV
ejpam-7074	20	24	-	-	PUNCT
ejpam-7074	20	25	reaching	reach	VERB
ejpam-7074	20	26	effects	effect	NOUN
ejpam-7074	20	27	of	of	ADP
ejpam-7074	20	28	the	the	DET
ejpam-7074	20	29	sheffer	sheffer	NOUN
ejpam-7074	20	30	stroke	stroke	NOUN
ejpam-7074	20	31	operation	operation	NOUN
ejpam-7074	20	32	across	across	ADP
ejpam-7074	20	33	diverse	diverse	ADJ
ejpam-7074	20	34	algebraic	algebraic	ADJ
ejpam-7074	20	35	systems	system	NOUN
ejpam-7074	20	36	.	.	PUNCT
ejpam-7074	21	1	the	the	DET
ejpam-7074	21	2	concept	concept	NOUN
ejpam-7074	21	3	of	of	ADP
ejpam-7074	21	4	fuzzy	fuzzy	ADJ
ejpam-7074	21	5	sets	set	NOUN
ejpam-7074	21	6	,	,	PUNCT
ejpam-7074	21	7	proposed	propose	VERB
ejpam-7074	21	8	by	by	ADP
ejpam-7074	21	9	zadeh	zadeh	PROPN
ejpam-7074	21	10	[	[	X
ejpam-7074	21	11	6	6	NUM
ejpam-7074	21	12	]	]	PUNCT
ejpam-7074	21	13	,	,	PUNCT
ejpam-7074	21	14	revolutionized	revolutionize	VERB
ejpam-7074	21	15	the	the	DET
ejpam-7074	21	16	study	study	NOUN
ejpam-7074	21	17	of	of	ADP
ejpam-7074	21	18	uncertainty	uncertainty	NOUN
ejpam-7074	21	19	and	and	CCONJ
ejpam-7074	21	20	vagueness	vagueness	NOUN
ejpam-7074	21	21	,	,	PUNCT
ejpam-7074	21	22	providing	provide	VERB
ejpam-7074	21	23	a	a	DET
ejpam-7074	21	24	powerful	powerful	ADJ
ejpam-7074	21	25	tool	tool	NOUN
ejpam-7074	21	26	for	for	ADP
ejpam-7074	21	27	modeling	model	VERB
ejpam-7074	21	28	imprecision	imprecision	NOUN
ejpam-7074	21	29	.	.	PUNCT
ejpam-7074	22	1	fuzzy	fuzzy	ADJ
ejpam-7074	22	2	set	set	NOUN
ejpam-7074	22	3	theory	theory	NOUN
ejpam-7074	22	4	has	have	AUX
ejpam-7074	22	5	since	since	ADV
ejpam-7074	22	6	been	be	AUX
ejpam-7074	22	7	applied	apply	VERB
ejpam-7074	22	8	in	in	ADP
ejpam-7074	22	9	a	a	DET
ejpam-7074	22	10	variety	variety	NOUN
ejpam-7074	22	11	of	of	ADP
ejpam-7074	22	12	real	real	ADJ
ejpam-7074	22	13	-	-	PUNCT
ejpam-7074	22	14	world	world	NOUN
ejpam-7074	22	15	contexts	contexts	NOUN
ejpam-7074	22	16	,	,	PUNCT
ejpam-7074	22	17	sparking	spark	VERB
ejpam-7074	22	18	considerable	considerable	ADJ
ejpam-7074	22	19	research	research	NOUN
ejpam-7074	22	20	into	into	ADP
ejpam-7074	22	21	its	its	PRON
ejpam-7074	22	22	expansion	expansion	NOUN
ejpam-7074	22	23	.	.	PUNCT
ejpam-7074	23	1	following	follow	VERB
ejpam-7074	23	2	the	the	DET
ejpam-7074	23	3	introduction	introduction	NOUN
ejpam-7074	23	4	of	of	ADP
ejpam-7074	23	5	fuzzy	fuzzy	ADJ
ejpam-7074	23	6	sets	set	NOUN
ejpam-7074	23	7	,	,	PUNCT
ejpam-7074	23	8	numerous	numerous	ADJ
ejpam-7074	23	9	studies	study	NOUN
ejpam-7074	23	10	focused	focus	VERB
ejpam-7074	23	11	on	on	ADP
ejpam-7074	23	12	generalizing	generalize	VERB
ejpam-7074	23	13	the	the	DET
ejpam-7074	23	14	theory	theory	NOUN
ejpam-7074	23	15	.	.	PUNCT
ejpam-7074	24	1	one	one	NUM
ejpam-7074	24	2	key	key	ADJ
ejpam-7074	24	3	direction	direction	NOUN
ejpam-7074	24	4	has	have	AUX
ejpam-7074	24	5	been	be	AUX
ejpam-7074	24	6	the	the	DET
ejpam-7074	24	7	integration	integration	NOUN
ejpam-7074	24	8	of	of	ADP
ejpam-7074	24	9	fuzzy	fuzzy	ADJ
ejpam-7074	24	10	sets	set	NOUN
ejpam-7074	24	11	with	with	ADP
ejpam-7074	24	12	other	other	ADJ
ejpam-7074	24	13	uncertainty	uncertainty	NOUN
ejpam-7074	24	14	models	model	NOUN
ejpam-7074	24	15	,	,	PUNCT
ejpam-7074	24	16	such	such	ADJ
ejpam-7074	24	17	as	as	ADP
ejpam-7074	24	18	soft	soft	ADJ
ejpam-7074	24	19	sets	set	NOUN
ejpam-7074	24	20	and	and	CCONJ
ejpam-7074	24	21	rough	rough	ADJ
ejpam-7074	24	22	sets	set	NOUN
ejpam-7074	24	23	,	,	PUNCT
ejpam-7074	24	24	as	as	SCONJ
ejpam-7074	24	25	explored	explore	VERB
ejpam-7074	24	26	in	in	ADP
ejpam-7074	24	27	various	various	ADJ
ejpam-7074	24	28	works	work	NOUN
ejpam-7074	24	29	[	[	X
ejpam-7074	24	30	7–9	7–9	NOUN
ejpam-7074	24	31	]	]	X
ejpam-7074	24	32	.	.	PUNCT
ejpam-7074	25	1	another	another	DET
ejpam-7074	25	2	significant	significant	ADJ
ejpam-7074	25	3	extension	extension	NOUN
ejpam-7074	25	4	of	of	ADP
ejpam-7074	25	5	fuzzy	fuzzy	ADJ
ejpam-7074	25	6	sets	set	NOUN
ejpam-7074	25	7	is	be	AUX
ejpam-7074	25	8	the	the	DET
ejpam-7074	25	9	notion	notion	NOUN
ejpam-7074	25	10	of	of	ADP
ejpam-7074	25	11	intuitionistic	intuitionistic	ADJ
ejpam-7074	25	12	fuzzy	fuzzy	ADJ
ejpam-7074	25	13	sets	set	NOUN
ejpam-7074	25	14	,	,	PUNCT
ejpam-7074	25	15	introduced	introduce	VERB
ejpam-7074	25	16	by	by	ADP
ejpam-7074	25	17	atanassov	atanassov	NOUN
ejpam-7074	25	18	[	[	X
ejpam-7074	25	19	10	10	NUM
ejpam-7074	25	20	]	]	PUNCT
ejpam-7074	25	21	.	.	PUNCT
ejpam-7074	26	1	these	these	DET
ejpam-7074	26	2	sets	set	NOUN
ejpam-7074	26	3	enhance	enhance	VERB
ejpam-7074	26	4	the	the	DET
ejpam-7074	26	5	applicability	applicability	NOUN
ejpam-7074	26	6	of	of	ADP
ejpam-7074	26	7	fuzzy	fuzzy	ADJ
ejpam-7074	26	8	sets	set	NOUN
ejpam-7074	26	9	by	by	ADP
ejpam-7074	26	10	incorporating	incorporate	VERB
ejpam-7074	26	11	both	both	CCONJ
ejpam-7074	26	12	membership	membership	NOUN
ejpam-7074	26	13	and	and	CCONJ
ejpam-7074	26	14	non	non	ADJ
ejpam-7074	26	15	-	-	ADJ
ejpam-7074	26	16	membership	membership	ADJ
ejpam-7074	26	17	degrees	degree	NOUN
ejpam-7074	26	18	,	,	PUNCT
ejpam-7074	26	19	making	make	VERB
ejpam-7074	26	20	them	they	PRON
ejpam-7074	26	21	suitable	suitable	ADJ
ejpam-7074	26	22	for	for	ADP
ejpam-7074	26	23	situations	situation	NOUN
ejpam-7074	26	24	involving	involve	VERB
ejpam-7074	26	25	incomplete	incomplete	ADJ
ejpam-7074	26	26	information	information	NOUN
ejpam-7074	26	27	or	or	CCONJ
ejpam-7074	26	28	uncertainty	uncertainty	NOUN
ejpam-7074	26	29	.	.	PUNCT
ejpam-7074	27	1	intuitionistic	intuitionistic	ADJ
ejpam-7074	27	2	fuzzy	fuzzy	ADJ
ejpam-7074	27	3	sets	set	NOUN
ejpam-7074	27	4	have	have	AUX
ejpam-7074	27	5	been	be	AUX
ejpam-7074	27	6	widely	widely	ADV
ejpam-7074	27	7	applied	apply	VERB
ejpam-7074	27	8	in	in	ADP
ejpam-7074	27	9	domains	domain	NOUN
ejpam-7074	27	10	such	such	ADJ
ejpam-7074	27	11	as	as	ADP
ejpam-7074	27	12	medical	medical	ADJ
ejpam-7074	27	13	diagnostics	diagnostic	NOUN
ejpam-7074	27	14	,	,	PUNCT
ejpam-7074	27	15	optimization	optimization	NOUN
ejpam-7074	27	16	,	,	PUNCT
ejpam-7074	27	17	and	and	CCONJ
ejpam-7074	27	18	multi	multi	ADJ
ejpam-7074	27	19	-	-	NOUN
ejpam-7074	27	20	criteria	criterion	NOUN
ejpam-7074	27	21	decision	decision	NOUN
ejpam-7074	27	22	-	-	PUNCT
ejpam-7074	27	23	making	making	NOUN
ejpam-7074	27	24	[	[	X
ejpam-7074	27	25	11–13	11–13	NUM
ejpam-7074	27	26	]	]	X
ejpam-7074	27	27	.	.	PUNCT
ejpam-7074	28	1	hilbert	hilbert	PROPN
ejpam-7074	28	2	algebras	algebras	PROPN
ejpam-7074	28	3	were	be	AUX
ejpam-7074	28	4	initially	initially	ADV
ejpam-7074	28	5	introduced	introduce	VERB
ejpam-7074	28	6	in	in	ADP
ejpam-7074	28	7	the	the	DET
ejpam-7074	28	8	1950s	1950	NOUN
ejpam-7074	28	9	by	by	ADP
ejpam-7074	28	10	henkin	henkin	PROPN
ejpam-7074	28	11	[	[	X
ejpam-7074	28	12	14	14	NUM
ejpam-7074	28	13	]	]	PUNCT
ejpam-7074	28	14	as	as	ADP
ejpam-7074	28	15	a	a	DET
ejpam-7074	28	16	means	means	NOUN
ejpam-7074	28	17	to	to	PART
ejpam-7074	28	18	investigate	investigate	VERB
ejpam-7074	28	19	implications	implication	NOUN
ejpam-7074	28	20	within	within	ADP
ejpam-7074	28	21	intuitionistic	intuitionistic	ADJ
ejpam-7074	28	22	and	and	CCONJ
ejpam-7074	28	23	other	other	ADJ
ejpam-7074	28	24	non	non	ADJ
ejpam-7074	28	25	-	-	ADJ
ejpam-7074	28	26	classical	classical	ADJ
ejpam-7074	28	27	logics	logic	NOUN
ejpam-7074	28	28	.	.	PUNCT
ejpam-7074	29	1	in	in	ADP
ejpam-7074	29	2	the	the	DET
ejpam-7074	29	3	1960s	1960	NOUN
ejpam-7074	29	4	,	,	PUNCT
ejpam-7074	29	5	scholars	scholar	NOUN
ejpam-7074	29	6	such	such	ADJ
ejpam-7074	29	7	as	as	ADP
ejpam-7074	29	8	horn	horn	NOUN
ejpam-7074	29	9	and	and	CCONJ
ejpam-7074	29	10	diego	diego	PROPN
ejpam-7074	29	11	further	far	ADV
ejpam-7074	29	12	developed	develop	VERB
ejpam-7074	29	13	these	these	DET
ejpam-7074	29	14	algebras	algebra	NOUN
ejpam-7074	29	15	from	from	ADP
ejpam-7074	29	16	an	an	DET
ejpam-7074	29	17	algebraic	algebraic	ADJ
ejpam-7074	29	18	standpoint	standpoint	NOUN
ejpam-7074	29	19	.	.	PUNCT
ejpam-7074	30	1	diego	diego	PROPN
ejpam-7074	30	2	demonstrated	demonstrate	VERB
ejpam-7074	30	3	that	that	SCONJ
ejpam-7074	30	4	hilbert	hilbert	PROPN
ejpam-7074	30	5	algebras	algebras	PROPN
ejpam-7074	30	6	form	form	VERB
ejpam-7074	30	7	a	a	DET
ejpam-7074	30	8	locally	locally	ADV
ejpam-7074	30	9	finite	finite	ADJ
ejpam-7074	30	10	variety	variety	NOUN
ejpam-7074	31	1	[	[	X
ejpam-7074	31	2	15	15	NUM
ejpam-7074	31	3	]	]	PUNCT
ejpam-7074	31	4	.	.	PUNCT
ejpam-7074	32	1	researchers	researcher	NOUN
ejpam-7074	32	2	such	such	ADJ
ejpam-7074	32	3	as	as	ADP
ejpam-7074	32	4	busneag	busneag	NOUN
ejpam-7074	32	5	[	[	X
ejpam-7074	32	6	16	16	NUM
ejpam-7074	32	7	,	,	PUNCT
ejpam-7074	32	8	17	17	NUM
ejpam-7074	32	9	]	]	PUNCT
ejpam-7074	32	10	and	and	CCONJ
ejpam-7074	32	11	jun	jun	PROPN
ejpam-7074	32	12	[	[	X
ejpam-7074	32	13	18	18	NUM
ejpam-7074	32	14	]	]	PUNCT
ejpam-7074	32	15	also	also	ADV
ejpam-7074	32	16	contributed	contribute	VERB
ejpam-7074	32	17	to	to	ADP
ejpam-7074	32	18	the	the	DET
ejpam-7074	32	19	study	study	NOUN
ejpam-7074	32	20	of	of	ADP
ejpam-7074	32	21	hilbert	hilbert	PROPN
ejpam-7074	32	22	algebras	algebras	PROPN
ejpam-7074	32	23	,	,	PUNCT
ejpam-7074	32	24	focusing	focus	VERB
ejpam-7074	32	25	on	on	ADP
ejpam-7074	32	26	the	the	DET
ejpam-7074	32	27	role	role	NOUN
ejpam-7074	32	28	of	of	ADP
ejpam-7074	32	29	their	their	PRON
ejpam-7074	32	30	filters	filter	NOUN
ejpam-7074	32	31	in	in	ADP
ejpam-7074	32	32	forming	form	VERB
ejpam-7074	32	33	deductive	deductive	ADJ
ejpam-7074	32	34	systems	system	NOUN
ejpam-7074	32	35	.	.	PUNCT
ejpam-7074	33	1	in	in	ADP
ejpam-7074	33	2	the	the	DET
ejpam-7074	33	3	context	context	NOUN
ejpam-7074	33	4	of	of	ADP
ejpam-7074	33	5	fuzzy	fuzzy	ADJ
ejpam-7074	33	6	logic	logic	NOUN
ejpam-7074	33	7	,	,	PUNCT
ejpam-7074	33	8	dudek	dudek	PROPN
ejpam-7074	34	1	[	[	X
ejpam-7074	34	2	19	19	NUM
ejpam-7074	34	3	]	]	PUNCT
ejpam-7074	34	4	explored	explore	VERB
ejpam-7074	34	5	the	the	DET
ejpam-7074	34	6	fuzzification	fuzzification	NOUN
ejpam-7074	34	7	of	of	ADP
ejpam-7074	34	8	subalgebras	subalgebras	PROPN
ejpam-7074	34	9	and	and	CCONJ
ejpam-7074	34	10	deductive	deductive	ADJ
ejpam-7074	34	11	systems	system	NOUN
ejpam-7074	34	12	in	in	ADP
ejpam-7074	34	13	hilbert	hilbert	PROPN
ejpam-7074	34	14	algebras	algebras	PROPN
ejpam-7074	34	15	,	,	PUNCT
ejpam-7074	34	16	adding	add	VERB
ejpam-7074	34	17	a	a	DET
ejpam-7074	34	18	new	new	ADJ
ejpam-7074	34	19	layer	layer	NOUN
ejpam-7074	34	20	of	of	ADP
ejpam-7074	34	21	complexity	complexity	NOUN
ejpam-7074	34	22	to	to	ADP
ejpam-7074	34	23	these	these	DET
ejpam-7074	34	24	structures	structure	NOUN
ejpam-7074	34	25	.	.	PUNCT
ejpam-7074	35	1	the	the	DET
ejpam-7074	35	2	algebraic	algebraic	ADJ
ejpam-7074	35	3	framework	framework	NOUN
ejpam-7074	35	4	of	of	ADP
ejpam-7074	35	5	sshas	ssha	NOUN
ejpam-7074	35	6	has	have	AUX
ejpam-7074	35	7	evolved	evolve	VERB
ejpam-7074	35	8	considerably	considerably	ADV
ejpam-7074	35	9	over	over	ADP
ejpam-7074	35	10	the	the	DET
ejpam-7074	35	11	past	past	ADJ
ejpam-7074	35	12	few	few	ADJ
ejpam-7074	35	13	years	year	NOUN
ejpam-7074	35	14	,	,	PUNCT
ejpam-7074	35	15	establishing	establish	VERB
ejpam-7074	35	16	itself	itself	PRON
ejpam-7074	35	17	as	as	ADP
ejpam-7074	35	18	a	a	DET
ejpam-7074	35	19	fertile	fertile	ADJ
ejpam-7074	35	20	ground	ground	NOUN
ejpam-7074	35	21	for	for	ADP
ejpam-7074	35	22	generalizations	generalization	NOUN
ejpam-7074	35	23	in	in	ADP
ejpam-7074	35	24	fuzzy	fuzzy	ADJ
ejpam-7074	35	25	and	and	CCONJ
ejpam-7074	35	26	soft	soft	ADJ
ejpam-7074	35	27	logic	logic	NOUN
ejpam-7074	35	28	.	.	PUNCT
ejpam-7074	36	1	the	the	DET
ejpam-7074	36	2	foundational	foundational	ADJ
ejpam-7074	36	3	connection	connection	NOUN
ejpam-7074	36	4	between	between	ADP
ejpam-7074	36	5	sheffer	sheffer	PROPN
ejpam-7074	36	6	stroke	stroke	NOUN
ejpam-7074	36	7	operations	operation	NOUN
ejpam-7074	36	8	and	and	CCONJ
ejpam-7074	36	9	hilbert	hilbert	PROPN
ejpam-7074	36	10	algebras	algebras	PROPN
ejpam-7074	36	11	was	be	AUX
ejpam-7074	36	12	rigorously	rigorously	ADV
ejpam-7074	36	13	explored	explore	VERB
ejpam-7074	36	14	by	by	ADP
ejpam-7074	36	15	oner	oner	NOUN
ejpam-7074	36	16	et	et	PROPN
ejpam-7074	36	17	al	al	PROPN
ejpam-7074	36	18	.	.	PUNCT
ejpam-7074	37	1	[	[	X
ejpam-7074	37	2	20	20	NUM
ejpam-7074	37	3	]	]	PUNCT
ejpam-7074	37	4	,	,	PUNCT
ejpam-7074	37	5	leading	lead	VERB
ejpam-7074	37	6	to	to	ADP
ejpam-7074	37	7	a	a	DET
ejpam-7074	37	8	formal	formal	ADJ
ejpam-7074	37	9	algebraic	algebraic	ADJ
ejpam-7074	37	10	structure	structure	NOUN
ejpam-7074	37	11	that	that	PRON
ejpam-7074	37	12	integrates	integrate	VERB
ejpam-7074	37	13	logical	logical	ADJ
ejpam-7074	37	14	minimalism	minimalism	NOUN
ejpam-7074	37	15	with	with	ADP
ejpam-7074	37	16	algebraic	algebraic	ADJ
ejpam-7074	37	17	expressiveness	expressiveness	NOUN
ejpam-7074	37	18	.	.	PUNCT
ejpam-7074	38	1	this	this	DET
ejpam-7074	38	2	foundation	foundation	NOUN
ejpam-7074	38	3	has	have	AUX
ejpam-7074	38	4	since	since	ADV
ejpam-7074	38	5	been	be	AUX
ejpam-7074	38	6	extended	extend	VERB
ejpam-7074	38	7	in	in	ADP
ejpam-7074	38	8	several	several	ADJ
ejpam-7074	38	9	directions	direction	NOUN
ejpam-7074	38	10	.	.	PUNCT
ejpam-7074	39	1	for	for	ADP
ejpam-7074	39	2	instance	instance	NOUN
ejpam-7074	39	3	,	,	PUNCT
ejpam-7074	39	4	stabilization	stabilization	NOUN
ejpam-7074	39	5	properties	property	NOUN
ejpam-7074	39	6	via	via	ADP
ejpam-7074	39	7	ideals	ideal	NOUN
ejpam-7074	39	8	have	have	AUX
ejpam-7074	39	9	been	be	AUX
ejpam-7074	39	10	analyzed	analyze	VERB
ejpam-7074	39	11	in	in	ADP
ejpam-7074	39	12	[	[	X
ejpam-7074	39	13	21	21	NUM
ejpam-7074	39	14	]	]	PUNCT
ejpam-7074	39	15	to	to	PART
ejpam-7074	39	16	explore	explore	VERB
ejpam-7074	39	17	internal	internal	ADJ
ejpam-7074	39	18	algebraic	algebraic	ADJ
ejpam-7074	39	19	regularities	regularity	NOUN
ejpam-7074	39	20	.	.	PUNCT
ejpam-7074	40	1	the	the	DET
ejpam-7074	40	2	incorporation	incorporation	NOUN
ejpam-7074	40	3	of	of	ADP
ejpam-7074	40	4	fuzzy	fuzzy	ADJ
ejpam-7074	40	5	logic	logic	NOUN
ejpam-7074	40	6	began	begin	VERB
ejpam-7074	40	7	with	with	ADP
ejpam-7074	40	8	fuzzy	fuzzy	ADJ
ejpam-7074	40	9	filters	filter	NOUN
ejpam-7074	40	10	[	[	X
ejpam-7074	40	11	22	22	NUM
ejpam-7074	40	12	]	]	PUNCT
ejpam-7074	40	13	,	,	PUNCT
ejpam-7074	40	14	followed	follow	VERB
ejpam-7074	40	15	by	by	ADP
ejpam-7074	40	16	the	the	DET
ejpam-7074	40	17	introduction	introduction	NOUN
ejpam-7074	40	18	of	of	ADP
ejpam-7074	40	19	fuzzy	fuzzy	ADJ
ejpam-7074	40	20	ideals	ideal	NOUN
ejpam-7074	40	21	[	[	X
ejpam-7074	40	22	23	23	NUM
ejpam-7074	40	23	]	]	PUNCT
ejpam-7074	40	24	,	,	PUNCT
ejpam-7074	40	25	and	and	CCONJ
ejpam-7074	40	26	then	then	ADV
ejpam-7074	40	27	generalized	generalize	VERB
ejpam-7074	40	28	fuzzy	fuzzy	ADJ
ejpam-7074	40	29	subalgebras	subalgebra	NOUN
ejpam-7074	40	30	[	[	X
ejpam-7074	40	31	24	24	NUM
ejpam-7074	40	32	]	]	PUNCT
ejpam-7074	40	33	.	.	PUNCT
ejpam-7074	41	1	parallel	parallel	ADJ
ejpam-7074	41	2	developments	development	NOUN
ejpam-7074	41	3	include	include	VERB
ejpam-7074	41	4	investigations	investigation	NOUN
ejpam-7074	41	5	into	into	ADP
ejpam-7074	41	6	length	length	NOUN
ejpam-7074	41	7	-	-	PUNCT
ejpam-7074	41	8	based	base	VERB
ejpam-7074	41	9	and	and	CCONJ
ejpam-7074	41	10	mean	mean	ADJ
ejpam-7074	41	11	-	-	PUNCT
ejpam-7074	41	12	fuzzy	fuzzy	ADJ
ejpam-7074	41	13	structures	structure	NOUN
ejpam-7074	41	14	[	[	X
ejpam-7074	41	15	25	25	NUM
ejpam-7074	41	16	,	,	PUNCT
ejpam-7074	41	17	26	26	NUM
ejpam-7074	41	18	]	]	PUNCT
ejpam-7074	41	19	,	,	PUNCT
ejpam-7074	41	20	as	as	ADV
ejpam-7074	41	21	well	well	ADV
ejpam-7074	41	22	as	as	ADP
ejpam-7074	41	23	soft	soft	ADJ
ejpam-7074	41	24	set	set	NOUN
ejpam-7074	41	25	extensions	extension	NOUN
ejpam-7074	41	26	using	use	VERB
ejpam-7074	41	27	n	n	CCONJ
ejpam-7074	41	28	-	-	PUNCT
ejpam-7074	41	29	structures	structure	NOUN
ejpam-7074	41	30	[	[	X
ejpam-7074	41	31	27	27	NUM
ejpam-7074	41	32	]	]	PUNCT
ejpam-7074	41	33	.	.	PUNCT
ejpam-7074	42	1	collectively	collectively	ADV
ejpam-7074	42	2	,	,	PUNCT
ejpam-7074	42	3	these	these	DET
ejpam-7074	42	4	contributions	contribution	NOUN
ejpam-7074	42	5	not	not	PART
ejpam-7074	42	6	only	only	ADV
ejpam-7074	42	7	demonstrate	demonstrate	VERB
ejpam-7074	42	8	the	the	DET
ejpam-7074	42	9	flexibility	flexibility	NOUN
ejpam-7074	42	10	of	of	ADP
ejpam-7074	42	11	the	the	DET
ejpam-7074	42	12	ssha	ssha	PROPN
ejpam-7074	42	13	model	model	NOUN
ejpam-7074	42	14	but	but	CCONJ
ejpam-7074	42	15	also	also	ADV
ejpam-7074	42	16	set	set	VERB
ejpam-7074	42	17	the	the	DET
ejpam-7074	42	18	stage	stage	NOUN
ejpam-7074	42	19	for	for	ADP
ejpam-7074	42	20	more	more	ADV
ejpam-7074	42	21	refined	refined	ADJ
ejpam-7074	42	22	fuzzy	fuzzy	ADJ
ejpam-7074	42	23	generalizations	generalization	NOUN
ejpam-7074	42	24	,	,	PUNCT
ejpam-7074	42	25	such	such	ADJ
ejpam-7074	42	26	as	as	ADP
ejpam-7074	42	27	those	those	PRON
ejpam-7074	42	28	based	base	VERB
ejpam-7074	42	29	on	on	ADP
ejpam-7074	42	30	intuitionistic	intuitionistic	ADJ
ejpam-7074	42	31	and	and	CCONJ
ejpam-7074	42	32	interval	interval	NOUN
ejpam-7074	42	33	-	-	PUNCT
ejpam-7074	42	34	valued	value	VERB
ejpam-7074	42	35	constructs	construct	NOUN
ejpam-7074	42	36	.	.	PUNCT
ejpam-7074	43	1	a.	a.	NOUN
ejpam-7074	43	2	iampan	iampan	PROPN
ejpam-7074	43	3	et	et	PROPN
ejpam-7074	43	4	al	al	PROPN
ejpam-7074	43	5	.	.	PUNCT
ejpam-7074	43	6	/	/	SYM
ejpam-7074	43	7	eur	eur	PROPN
ejpam-7074	43	8	.	.	PUNCT
ejpam-7074	44	1	j.	j.	PROPN
ejpam-7074	44	2	pure	pure	PROPN
ejpam-7074	44	3	appl	appl	PROPN
ejpam-7074	44	4	.	.	PROPN
ejpam-7074	44	5	math	math	PROPN
ejpam-7074	44	6	,	,	PUNCT
ejpam-7074	44	7	18	18	NUM
ejpam-7074	44	8	(	(	PUNCT
ejpam-7074	44	9	4	4	NUM
ejpam-7074	44	10	)	)	PUNCT
ejpam-7074	44	11	(	(	PUNCT
ejpam-7074	44	12	2025	2025	NUM
ejpam-7074	44	13	)	)	PUNCT
ejpam-7074	44	14	,	,	PUNCT
ejpam-7074	44	15	7074	7074	NUM
ejpam-7074	44	16	3	3	NUM
ejpam-7074	44	17	of	of	ADP
ejpam-7074	44	18	14	14	NUM
ejpam-7074	44	19	despite	despite	SCONJ
ejpam-7074	44	20	the	the	DET
ejpam-7074	44	21	broad	broad	ADJ
ejpam-7074	44	22	utilization	utilization	NOUN
ejpam-7074	44	23	of	of	ADP
ejpam-7074	44	24	sshas	ssha	NOUN
ejpam-7074	44	25	,	,	PUNCT
ejpam-7074	44	26	their	their	PRON
ejpam-7074	44	27	connection	connection	NOUN
ejpam-7074	44	28	with	with	ADP
ejpam-7074	44	29	fuzzy	fuzzy	ADJ
ejpam-7074	44	30	logic	logic	NOUN
ejpam-7074	44	31	and	and	CCONJ
ejpam-7074	44	32	intuitionistic	intuitionistic	ADJ
ejpam-7074	44	33	fuzzy	fuzzy	ADJ
ejpam-7074	44	34	set	set	NOUN
ejpam-7074	44	35	theory	theory	NOUN
ejpam-7074	44	36	remains	remain	VERB
ejpam-7074	44	37	largely	largely	ADV
ejpam-7074	44	38	unexplored	unexplored	ADJ
ejpam-7074	44	39	.	.	PUNCT
ejpam-7074	45	1	the	the	DET
ejpam-7074	45	2	introduction	introduction	NOUN
ejpam-7074	45	3	of	of	ADP
ejpam-7074	45	4	interval	interval	NOUN
ejpam-7074	45	5	-	-	PUNCT
ejpam-7074	45	6	valued	value	VERB
ejpam-7074	45	7	intuitionistic	intuitionistic	ADJ
ejpam-7074	45	8	fuzzy	fuzzy	ADJ
ejpam-7074	45	9	sets	set	NOUN
ejpam-7074	45	10	(	(	PUNCT
ejpam-7074	45	11	ivifss	ivifss	INTJ
ejpam-7074	45	12	)	)	PUNCT
ejpam-7074	45	13	offers	offer	VERB
ejpam-7074	45	14	a	a	DET
ejpam-7074	45	15	novel	novel	ADJ
ejpam-7074	45	16	approach	approach	NOUN
ejpam-7074	45	17	to	to	ADP
ejpam-7074	45	18	representing	represent	VERB
ejpam-7074	45	19	uncertainty	uncertainty	NOUN
ejpam-7074	45	20	and	and	CCONJ
ejpam-7074	45	21	partial	partial	ADJ
ejpam-7074	45	22	membership	membership	NOUN
ejpam-7074	45	23	in	in	ADP
ejpam-7074	45	24	algebraic	algebraic	ADJ
ejpam-7074	45	25	structures	structure	NOUN
ejpam-7074	45	26	.	.	PUNCT
ejpam-7074	46	1	by	by	ADP
ejpam-7074	46	2	replacing	replace	VERB
ejpam-7074	46	3	fixed	fix	VERB
ejpam-7074	46	4	values	value	NOUN
ejpam-7074	46	5	with	with	ADP
ejpam-7074	46	6	intervals	interval	NOUN
ejpam-7074	46	7	to	to	PART
ejpam-7074	46	8	denote	denote	VERB
ejpam-7074	46	9	membership	membership	NOUN
ejpam-7074	46	10	and	and	CCONJ
ejpam-7074	46	11	non	non	ADJ
ejpam-7074	46	12	-	-	ADJ
ejpam-7074	46	13	membership	membership	ADJ
ejpam-7074	46	14	degrees	degree	NOUN
ejpam-7074	46	15	,	,	PUNCT
ejpam-7074	46	16	ivifs	ivif	NOUN
ejpam-7074	46	17	provide	provide	VERB
ejpam-7074	46	18	a	a	DET
ejpam-7074	46	19	more	more	ADV
ejpam-7074	46	20	flexible	flexible	ADJ
ejpam-7074	46	21	approach	approach	NOUN
ejpam-7074	46	22	to	to	ADP
ejpam-7074	46	23	dealing	deal	VERB
ejpam-7074	46	24	with	with	ADP
ejpam-7074	46	25	vagueness	vagueness	NOUN
ejpam-7074	46	26	and	and	CCONJ
ejpam-7074	46	27	uncertainty	uncertainty	NOUN
ejpam-7074	46	28	.	.	PUNCT
ejpam-7074	47	1	the	the	DET
ejpam-7074	47	2	paper	paper	NOUN
ejpam-7074	47	3	introduces	introduce	VERB
ejpam-7074	47	4	the	the	DET
ejpam-7074	47	5	concept	concept	NOUN
ejpam-7074	47	6	of	of	ADP
ejpam-7074	47	7	fuzzy	fuzzy	ADJ
ejpam-7074	47	8	and	and	CCONJ
ejpam-7074	47	9	intuitionistic	intuitionistic	ADJ
ejpam-7074	47	10	fuzzy	fuzzy	ADJ
ejpam-7074	47	11	sets	set	NOUN
ejpam-7074	47	12	in	in	ADP
ejpam-7074	47	13	algebraic	algebraic	ADJ
ejpam-7074	47	14	structures	structure	NOUN
ejpam-7074	47	15	,	,	PUNCT
ejpam-7074	47	16	particularly	particularly	ADV
ejpam-7074	47	17	within	within	ADP
ejpam-7074	47	18	the	the	DET
ejpam-7074	47	19	context	context	NOUN
ejpam-7074	47	20	of	of	ADP
ejpam-7074	47	21	sheffer	sheffer	NOUN
ejpam-7074	47	22	-	-	PUNCT
ejpam-7074	47	23	styled	style	VERB
ejpam-7074	47	24	hilbert	hilbert	NOUN
ejpam-7074	47	25	algebras	algebra	NOUN
ejpam-7074	47	26	.	.	PUNCT
ejpam-7074	48	1	it	it	PRON
ejpam-7074	48	2	emphasizes	emphasize	VERB
ejpam-7074	48	3	the	the	DET
ejpam-7074	48	4	importance	importance	NOUN
ejpam-7074	48	5	of	of	ADP
ejpam-7074	48	6	fuzzy	fuzzy	ADJ
ejpam-7074	48	7	subsets	subset	NOUN
ejpam-7074	48	8	in	in	ADP
ejpam-7074	48	9	capturing	capture	VERB
ejpam-7074	48	10	uncertainty	uncertainty	NOUN
ejpam-7074	48	11	and	and	CCONJ
ejpam-7074	48	12	partial	partial	ADJ
ejpam-7074	48	13	membership	membership	NOUN
ejpam-7074	48	14	in	in	ADP
ejpam-7074	48	15	algebraic	algebraic	PROPN
ejpam-7074	48	16	systems	system	NOUN
ejpam-7074	48	17	.	.	PUNCT
ejpam-7074	49	1	the	the	DET
ejpam-7074	49	2	study	study	NOUN
ejpam-7074	49	3	then	then	ADV
ejpam-7074	49	4	focuses	focus	VERB
ejpam-7074	49	5	explicitly	explicitly	ADV
ejpam-7074	49	6	on	on	ADP
ejpam-7074	49	7	interval	interval	NOUN
ejpam-7074	49	8	-	-	PUNCT
ejpam-7074	49	9	valued	value	VERB
ejpam-7074	49	10	intuitionistic	intuitionistic	ADJ
ejpam-7074	49	11	fuzzy	fuzzy	ADJ
ejpam-7074	49	12	(	(	PUNCT
ejpam-7074	49	13	ivif	ivif	NOUN
ejpam-7074	49	14	)	)	PUNCT
ejpam-7074	49	15	subsets	subset	NOUN
ejpam-7074	49	16	,	,	PUNCT
ejpam-7074	49	17	providing	provide	VERB
ejpam-7074	49	18	fundamental	fundamental	ADJ
ejpam-7074	49	19	definitions	definition	NOUN
ejpam-7074	49	20	and	and	CCONJ
ejpam-7074	49	21	properties	property	NOUN
ejpam-7074	49	22	.	.	PUNCT
ejpam-7074	50	1	section	section	NOUN
ejpam-7074	50	2	3	3	NUM
ejpam-7074	50	3	elaborates	elaborate	VERB
ejpam-7074	50	4	on	on	ADP
ejpam-7074	50	5	these	these	DET
ejpam-7074	50	6	ivif	ivif	NOUN
ejpam-7074	50	7	subsets	subset	NOUN
ejpam-7074	50	8	,	,	PUNCT
ejpam-7074	50	9	examining	examine	VERB
ejpam-7074	50	10	how	how	SCONJ
ejpam-7074	50	11	they	they	PRON
ejpam-7074	50	12	can	can	AUX
ejpam-7074	50	13	be	be	AUX
ejpam-7074	50	14	characterized	characterize	VERB
ejpam-7074	50	15	as	as	ADP
ejpam-7074	50	16	subalgebras	subalgebra	NOUN
ejpam-7074	50	17	and	and	CCONJ
ejpam-7074	50	18	their	their	PRON
ejpam-7074	50	19	behavior	behavior	NOUN
ejpam-7074	50	20	under	under	ADP
ejpam-7074	50	21	various	various	ADJ
ejpam-7074	50	22	set	set	ADJ
ejpam-7074	50	23	operations	operation	NOUN
ejpam-7074	50	24	.	.	PUNCT
ejpam-7074	51	1	the	the	DET
ejpam-7074	51	2	section	section	NOUN
ejpam-7074	51	3	aims	aim	VERB
ejpam-7074	51	4	to	to	PART
ejpam-7074	51	5	establish	establish	VERB
ejpam-7074	51	6	a	a	DET
ejpam-7074	51	7	solid	solid	ADJ
ejpam-7074	51	8	theoretical	theoretical	ADJ
ejpam-7074	51	9	foundation	foundation	NOUN
ejpam-7074	51	10	for	for	ADP
ejpam-7074	51	11	integrating	integrate	VERB
ejpam-7074	51	12	fuzzy	fuzzy	ADJ
ejpam-7074	51	13	logic	logic	NOUN
ejpam-7074	51	14	principles	principle	NOUN
ejpam-7074	51	15	into	into	ADP
ejpam-7074	51	16	algebraic	algebraic	ADJ
ejpam-7074	51	17	structures	structure	NOUN
ejpam-7074	51	18	,	,	PUNCT
ejpam-7074	51	19	thereby	thereby	ADV
ejpam-7074	51	20	paving	pave	VERB
ejpam-7074	51	21	the	the	DET
ejpam-7074	51	22	way	way	NOUN
ejpam-7074	51	23	for	for	ADP
ejpam-7074	51	24	future	future	ADJ
ejpam-7074	51	25	research	research	NOUN
ejpam-7074	51	26	and	and	CCONJ
ejpam-7074	51	27	applications	application	NOUN
ejpam-7074	51	28	.	.	PUNCT
ejpam-7074	52	1	the	the	DET
ejpam-7074	52	2	list	list	NOUN
ejpam-7074	52	3	of	of	ADP
ejpam-7074	52	4	acronyms	acronym	NOUN
ejpam-7074	52	5	is	be	AUX
ejpam-7074	52	6	given	give	VERB
ejpam-7074	52	7	in	in	ADP
ejpam-7074	52	8	table	table	NOUN
ejpam-7074	52	9	1	1	NUM
ejpam-7074	52	10	.	.	PUNCT
ejpam-7074	52	11	table	table	NOUN
ejpam-7074	52	12	1	1	NUM
ejpam-7074	52	13	:	:	PUNCT
ejpam-7074	52	14	list	list	NOUN
ejpam-7074	52	15	of	of	ADP
ejpam-7074	52	16	acronyms	acronym	NOUN
ejpam-7074	52	17	acronyms	acronyms	PROPN
ejpam-7074	52	18	representation	representation	NOUN
ejpam-7074	52	19	ssha	ssha	PROPN
ejpam-7074	52	20	sheffer	sheffer	PROPN
ejpam-7074	52	21	stroke	stroke	PROPN
ejpam-7074	52	22	hilbert	hilbert	PROPN
ejpam-7074	52	23	algebra	algebra	PROPN
ejpam-7074	52	24	ifs	ifs	PROPN
ejpam-7074	52	25	intuitionistic	intuitionistic	ADJ
ejpam-7074	52	26	fuzzy	fuzzy	ADJ
ejpam-7074	52	27	set	set	VERB
ejpam-7074	52	28	ivifs	ivifs	PROPN
ejpam-7074	52	29	interval	interval	NOUN
ejpam-7074	52	30	-	-	PUNCT
ejpam-7074	52	31	valued	value	VERB
ejpam-7074	52	32	intuitionistic	intuitionistic	ADJ
ejpam-7074	52	33	fuzzy	fuzzy	ADJ
ejpam-7074	52	34	set	set	VERB
ejpam-7074	52	35	ivifss	ivifss	ADJ
ejpam-7074	52	36	-	-	PUNCT
ejpam-7074	52	37	subalgebra	subalgebra	ADJ
ejpam-7074	52	38	interval	interval	NOUN
ejpam-7074	52	39	-	-	PUNCT
ejpam-7074	52	40	valued	value	VERB
ejpam-7074	52	41	intuitionistic	intuitionistic	ADJ
ejpam-7074	52	42	fuzzy	fuzzy	ADJ
ejpam-7074	52	43	sheffer	sheffer	NOUN
ejpam-7074	52	44	stroke	stroke	NOUN
ejpam-7074	52	45	subalgebra	subalgebra	NOUN
ejpam-7074	52	46	2	2	NUM
ejpam-7074	52	47	.	.	PUNCT
ejpam-7074	52	48	preliminaries	preliminary	NOUN
ejpam-7074	52	49	in	in	ADP
ejpam-7074	52	50	this	this	DET
ejpam-7074	52	51	section	section	NOUN
ejpam-7074	52	52	,	,	PUNCT
ejpam-7074	52	53	to	to	PART
ejpam-7074	52	54	deepen	deepen	VERB
ejpam-7074	52	55	the	the	DET
ejpam-7074	52	56	understanding	understanding	NOUN
ejpam-7074	52	57	of	of	ADP
ejpam-7074	52	58	the	the	DET
ejpam-7074	52	59	foundational	foundational	ADJ
ejpam-7074	52	60	structures	structure	NOUN
ejpam-7074	52	61	introduced	introduce	VERB
ejpam-7074	52	62	earlier	early	ADV
ejpam-7074	52	63	,	,	PUNCT
ejpam-7074	52	64	we	we	PRON
ejpam-7074	52	65	will	will	AUX
ejpam-7074	52	66	elaborate	elaborate	VERB
ejpam-7074	52	67	on	on	ADP
ejpam-7074	52	68	the	the	DET
ejpam-7074	52	69	key	key	ADJ
ejpam-7074	52	70	properties	property	NOUN
ejpam-7074	52	71	and	and	CCONJ
ejpam-7074	52	72	relationships	relationship	NOUN
ejpam-7074	52	73	of	of	ADP
ejpam-7074	52	74	the	the	DET
ejpam-7074	52	75	relevant	relevant	ADJ
ejpam-7074	52	76	algebraic	algebraic	ADJ
ejpam-7074	52	77	and	and	CCONJ
ejpam-7074	52	78	fuzzy	fuzzy	ADJ
ejpam-7074	52	79	constructs	construct	NOUN
ejpam-7074	52	80	.	.	PUNCT
ejpam-7074	53	1	specifically	specifically	ADV
ejpam-7074	53	2	,	,	PUNCT
ejpam-7074	53	3	we	we	PRON
ejpam-7074	53	4	will	will	AUX
ejpam-7074	53	5	define	define	VERB
ejpam-7074	53	6	certain	certain	ADJ
ejpam-7074	53	7	operations	operation	NOUN
ejpam-7074	53	8	and	and	CCONJ
ejpam-7074	53	9	structures	structure	NOUN
ejpam-7074	53	10	,	,	PUNCT
ejpam-7074	53	11	and	and	CCONJ
ejpam-7074	53	12	examine	examine	VERB
ejpam-7074	53	13	their	their	PRON
ejpam-7074	53	14	characteristics	characteristic	NOUN
ejpam-7074	53	15	and	and	CCONJ
ejpam-7074	53	16	interconnections	interconnection	NOUN
ejpam-7074	53	17	.	.	PUNCT
ejpam-7074	54	1	this	this	DET
ejpam-7074	54	2	groundwork	groundwork	NOUN
ejpam-7074	54	3	will	will	AUX
ejpam-7074	54	4	ensure	ensure	VERB
ejpam-7074	54	5	clarity	clarity	NOUN
ejpam-7074	54	6	and	and	CCONJ
ejpam-7074	54	7	provide	provide	VERB
ejpam-7074	54	8	a	a	DET
ejpam-7074	54	9	solid	solid	ADJ
ejpam-7074	54	10	theoretical	theoretical	ADJ
ejpam-7074	54	11	basis	basis	NOUN
ejpam-7074	54	12	for	for	ADP
ejpam-7074	54	13	the	the	DET
ejpam-7074	54	14	subsequent	subsequent	ADJ
ejpam-7074	54	15	sections	section	NOUN
ejpam-7074	54	16	.	.	PUNCT
ejpam-7074	55	1	our	our	PRON
ejpam-7074	55	2	aim	aim	NOUN
ejpam-7074	55	3	is	be	AUX
ejpam-7074	55	4	to	to	PART
ejpam-7074	55	5	present	present	VERB
ejpam-7074	55	6	these	these	DET
ejpam-7074	55	7	fundamental	fundamental	ADJ
ejpam-7074	55	8	concepts	concept	NOUN
ejpam-7074	55	9	and	and	CCONJ
ejpam-7074	55	10	structures	structure	NOUN
ejpam-7074	55	11	in	in	ADP
ejpam-7074	55	12	a	a	DET
ejpam-7074	55	13	clear	clear	ADJ
ejpam-7074	55	14	and	and	CCONJ
ejpam-7074	55	15	precise	precise	ADJ
ejpam-7074	55	16	manner	manner	NOUN
ejpam-7074	55	17	,	,	PUNCT
ejpam-7074	55	18	establishing	establish	VERB
ejpam-7074	55	19	the	the	DET
ejpam-7074	55	20	essential	essential	ADJ
ejpam-7074	55	21	building	building	NOUN
ejpam-7074	55	22	blocks	block	NOUN
ejpam-7074	55	23	for	for	ADP
ejpam-7074	55	24	the	the	DET
ejpam-7074	55	25	developments	development	NOUN
ejpam-7074	55	26	that	that	PRON
ejpam-7074	55	27	follow	follow	VERB
ejpam-7074	55	28	.	.	PUNCT
ejpam-7074	56	1	definition	definition	NOUN
ejpam-7074	56	2	1	1	NUM
ejpam-7074	56	3	.	.	PUNCT
ejpam-7074	57	1	[	[	X
ejpam-7074	57	2	28	28	NUM
ejpam-7074	57	3	]	]	PUNCT
ejpam-7074	57	4	let	let	VERB
ejpam-7074	57	5	a	a	PRON
ejpam-7074	57	6	:	:	PUNCT
ejpam-7074	57	7	=	=	SYM
ejpam-7074	57	8	(	(	PUNCT
ejpam-7074	57	9	a	a	PRON
ejpam-7074	57	10	,	,	PUNCT
ejpam-7074	57	11	|	|	NOUN
ejpam-7074	57	12	)	)	PUNCT
ejpam-7074	57	13	be	be	AUX
ejpam-7074	57	14	a	a	DET
ejpam-7074	57	15	groupoid	groupoid	NOUN
ejpam-7074	57	16	.	.	PUNCT
ejpam-7074	58	1	then	then	ADV
ejpam-7074	58	2	the	the	DET
ejpam-7074	58	3	operation	operation	NOUN
ejpam-7074	58	4	|	|	ADV
ejpam-7074	58	5	is	be	AUX
ejpam-7074	58	6	said	say	VERB
ejpam-7074	58	7	to	to	PART
ejpam-7074	58	8	be	be	AUX
ejpam-7074	58	9	sheffer	sheffer	NOUN
ejpam-7074	58	10	stroke	stroke	NOUN
ejpam-7074	58	11	or	or	CCONJ
ejpam-7074	58	12	sheffer	sheffer	VERB
ejpam-7074	58	13	operation	operation	NOUN
ejpam-7074	58	14	if	if	SCONJ
ejpam-7074	58	15	it	it	PRON
ejpam-7074	58	16	satisfies	satisfy	VERB
ejpam-7074	58	17	:	:	PUNCT
ejpam-7074	58	18	(	(	PUNCT
ejpam-7074	58	19	s1	s1	NOUN
ejpam-7074	58	20	)	)	PUNCT
ejpam-7074	58	21	(	(	PUNCT
ejpam-7074	58	22	∀d	∀d	PROPN
ejpam-7074	58	23	,	,	PUNCT
ejpam-7074	58	24	g	g	PROPN
ejpam-7074	58	25	∈	∈	PROPN
ejpam-7074	58	26	a	a	NOUN
ejpam-7074	58	27	)	)	PUNCT
ejpam-7074	58	28	(	(	PUNCT
ejpam-7074	59	1	d	d	X
ejpam-7074	59	2	|	|	ADV
ejpam-7074	59	3	g	g	PROPN
ejpam-7074	59	4	=	=	SYM
ejpam-7074	59	5	g	g	PROPN
ejpam-7074	59	6	|	|	NOUN
ejpam-7074	59	7	d	d	NOUN
ejpam-7074	59	8	)	)	PUNCT
ejpam-7074	59	9	,	,	PUNCT
ejpam-7074	59	10	(	(	PUNCT
ejpam-7074	59	11	s2	s2	PROPN
ejpam-7074	59	12	)	)	PUNCT
ejpam-7074	59	13	(	(	PUNCT
ejpam-7074	59	14	∀d	∀d	PROPN
ejpam-7074	59	15	,	,	PUNCT
ejpam-7074	59	16	g	g	PROPN
ejpam-7074	59	17	∈	∈	PROPN
ejpam-7074	59	18	a	a	NOUN
ejpam-7074	59	19	)	)	PUNCT
ejpam-7074	59	20	(	(	PUNCT
ejpam-7074	59	21	(	(	PUNCT
ejpam-7074	59	22	d	d	X
ejpam-7074	59	23	|	|	NOUN
ejpam-7074	59	24	d	d	NOUN
ejpam-7074	59	25	)	)	PUNCT
ejpam-7074	60	1	|	|	ADV
ejpam-7074	60	2	(	(	PUNCT
ejpam-7074	60	3	d	d	NOUN
ejpam-7074	60	4	|	|	ADV
ejpam-7074	60	5	g	g	NOUN
ejpam-7074	60	6	)	)	PUNCT
ejpam-7074	60	7	=	=	SYM
ejpam-7074	61	1	d	d	NOUN
ejpam-7074	61	2	)	)	PUNCT
ejpam-7074	61	3	,	,	PUNCT
ejpam-7074	61	4	(	(	PUNCT
ejpam-7074	61	5	s3	s3	PROPN
ejpam-7074	61	6	)	)	PUNCT
ejpam-7074	61	7	(	(	PUNCT
ejpam-7074	61	8	∀d	∀d	PROPN
ejpam-7074	61	9	,	,	PUNCT
ejpam-7074	61	10	g	g	PROPN
ejpam-7074	61	11	,	,	PUNCT
ejpam-7074	61	12	w	w	PROPN
ejpam-7074	61	13	∈	∈	PROPN
ejpam-7074	61	14	a	a	NOUN
ejpam-7074	61	15	)	)	PUNCT
ejpam-7074	61	16	(	(	PUNCT
ejpam-7074	62	1	d	d	X
ejpam-7074	62	2	|	|	ADV
ejpam-7074	62	3	(	(	PUNCT
ejpam-7074	62	4	(	(	PUNCT
ejpam-7074	62	5	g	g	PROPN
ejpam-7074	62	6	|	|	ADV
ejpam-7074	62	7	w	w	PROPN
ejpam-7074	62	8	)	)	PUNCT
ejpam-7074	63	1	|	|	ADV
ejpam-7074	63	2	(	(	PUNCT
ejpam-7074	63	3	g	g	PROPN
ejpam-7074	63	4	|	|	ADV
ejpam-7074	63	5	w	w	NOUN
ejpam-7074	63	6	)	)	PUNCT
ejpam-7074	63	7	)	)	PUNCT
ejpam-7074	64	1	=	=	PUNCT
ejpam-7074	64	2	(	(	PUNCT
ejpam-7074	64	3	(	(	PUNCT
ejpam-7074	64	4	d	d	NOUN
ejpam-7074	64	5	|	|	ADV
ejpam-7074	64	6	g	g	NOUN
ejpam-7074	64	7	)	)	PUNCT
ejpam-7074	65	1	|	|	ADV
ejpam-7074	65	2	(	(	PUNCT
ejpam-7074	65	3	d	d	NOUN
ejpam-7074	65	4	|	|	ADV
ejpam-7074	65	5	g	g	NOUN
ejpam-7074	65	6	)	)	PUNCT
ejpam-7074	65	7	)	)	PUNCT
ejpam-7074	66	1	|	|	ADV
ejpam-7074	66	2	w	w	NOUN
ejpam-7074	66	3	)	)	PUNCT
ejpam-7074	66	4	,	,	PUNCT
ejpam-7074	66	5	a.	a.	NOUN
ejpam-7074	66	6	iampan	iampan	NOUN
ejpam-7074	66	7	et	et	PROPN
ejpam-7074	66	8	al	al	PROPN
ejpam-7074	66	9	.	.	PUNCT
ejpam-7074	66	10	/	/	SYM
ejpam-7074	66	11	eur	eur	PROPN
ejpam-7074	66	12	.	.	PUNCT
ejpam-7074	67	1	j.	j.	PROPN
ejpam-7074	67	2	pure	pure	PROPN
ejpam-7074	67	3	appl	appl	PROPN
ejpam-7074	67	4	.	.	PROPN
ejpam-7074	67	5	math	math	PROPN
ejpam-7074	67	6	,	,	PUNCT
ejpam-7074	67	7	18	18	NUM
ejpam-7074	67	8	(	(	PUNCT
ejpam-7074	67	9	4	4	NUM
ejpam-7074	67	10	)	)	PUNCT
ejpam-7074	67	11	(	(	PUNCT
ejpam-7074	67	12	2025	2025	NUM
ejpam-7074	67	13	)	)	PUNCT
ejpam-7074	67	14	,	,	PUNCT
ejpam-7074	67	15	7074	7074	NUM
ejpam-7074	67	16	4	4	NUM
ejpam-7074	67	17	of	of	ADP
ejpam-7074	67	18	14	14	NUM
ejpam-7074	67	19	(	(	PUNCT
ejpam-7074	67	20	s4	s4	PROPN
ejpam-7074	67	21	)	)	PUNCT
ejpam-7074	67	22	(	(	PUNCT
ejpam-7074	67	23	∀d	∀d	PROPN
ejpam-7074	67	24	,	,	PUNCT
ejpam-7074	67	25	g	g	PROPN
ejpam-7074	67	26	,	,	PUNCT
ejpam-7074	67	27	w	w	PROPN
ejpam-7074	67	28	∈	∈	PROPN
ejpam-7074	67	29	a	a	NOUN
ejpam-7074	67	30	)	)	PUNCT
ejpam-7074	67	31	(	(	PUNCT
ejpam-7074	67	32	(	(	PUNCT
ejpam-7074	68	1	d	d	X
ejpam-7074	68	2	|	|	ADV
ejpam-7074	68	3	(	(	PUNCT
ejpam-7074	68	4	(	(	PUNCT
ejpam-7074	68	5	d	d	X
ejpam-7074	68	6	|	|	NOUN
ejpam-7074	68	7	d	d	NOUN
ejpam-7074	68	8	)	)	PUNCT
ejpam-7074	69	1	|	|	ADV
ejpam-7074	69	2	(	(	PUNCT
ejpam-7074	69	3	g	g	NOUN
ejpam-7074	69	4	|	|	ADV
ejpam-7074	69	5	g	g	NOUN
ejpam-7074	69	6	)	)	PUNCT
ejpam-7074	69	7	)	)	PUNCT
ejpam-7074	69	8	)	)	PUNCT
ejpam-7074	70	1	|	|	ADV
ejpam-7074	70	2	(	(	PUNCT
ejpam-7074	70	3	d	d	NOUN
ejpam-7074	70	4	|	|	ADV
ejpam-7074	70	5	(	(	PUNCT
ejpam-7074	70	6	(	(	PUNCT
ejpam-7074	70	7	d	d	X
ejpam-7074	70	8	|	|	NOUN
ejpam-7074	70	9	d	d	NOUN
ejpam-7074	70	10	)	)	PUNCT
ejpam-7074	71	1	|	|	ADV
ejpam-7074	71	2	(	(	PUNCT
ejpam-7074	71	3	g	g	NOUN
ejpam-7074	71	4	|	|	ADV
ejpam-7074	71	5	g	g	NOUN
ejpam-7074	71	6	)	)	PUNCT
ejpam-7074	71	7	)	)	PUNCT
ejpam-7074	71	8	)	)	PUNCT
ejpam-7074	72	1	=	=	PUNCT
ejpam-7074	72	2	d	d	NOUN
ejpam-7074	72	3	)	)	PUNCT
ejpam-7074	72	4	.	.	PUNCT
ejpam-7074	73	1	to	to	PART
ejpam-7074	73	2	improve	improve	VERB
ejpam-7074	73	3	the	the	DET
ejpam-7074	73	4	clarity	clarity	NOUN
ejpam-7074	73	5	of	of	ADP
ejpam-7074	73	6	this	this	DET
ejpam-7074	73	7	manuscript	manuscript	NOUN
ejpam-7074	73	8	,	,	PUNCT
ejpam-7074	73	9	we	we	PRON
ejpam-7074	73	10	introduce	introduce	VERB
ejpam-7074	73	11	the	the	DET
ejpam-7074	73	12	following	following	ADJ
ejpam-7074	73	13	notation	notation	NOUN
ejpam-7074	73	14	,	,	PUNCT
ejpam-7074	73	15	which	which	PRON
ejpam-7074	73	16	will	will	AUX
ejpam-7074	73	17	be	be	AUX
ejpam-7074	73	18	used	use	VERB
ejpam-7074	73	19	consistently	consistently	ADV
ejpam-7074	73	20	throughout	throughout	ADP
ejpam-7074	73	21	the	the	DET
ejpam-7074	73	22	text	text	NOUN
ejpam-7074	73	23	:	:	PUNCT
ejpam-7074	74	1	w	w	X
ejpam-7074	75	1	|	|	ADV
ejpam-7074	76	1	(	(	PUNCT
ejpam-7074	76	2	g	g	NOUN
ejpam-7074	76	3	|	|	ADV
ejpam-7074	76	4	g	g	NOUN
ejpam-7074	76	5	)	)	PUNCT
ejpam-7074	76	6	:	:	PUNCT
ejpam-7074	76	7	=	=	PUNCT
ejpam-7074	76	8	wg	wg	PROPN
ejpam-7074	76	9	.	.	PUNCT
ejpam-7074	77	1	definition	definition	NOUN
ejpam-7074	77	2	2	2	NUM
ejpam-7074	77	3	.	.	PUNCT
ejpam-7074	78	1	[	[	X
ejpam-7074	78	2	20	20	NUM
ejpam-7074	78	3	]	]	PUNCT
ejpam-7074	78	4	a	a	DET
ejpam-7074	78	5	sheffer	sheffer	NOUN
ejpam-7074	78	6	stroke	stroke	NOUN
ejpam-7074	78	7	hilbert	hilbert	PROPN
ejpam-7074	78	8	algebra	algebra	PROPN
ejpam-7074	78	9	(	(	PUNCT
ejpam-7074	78	10	ssha	ssha	PROPN
ejpam-7074	78	11	)	)	PUNCT
ejpam-7074	78	12	is	be	AUX
ejpam-7074	78	13	a	a	DET
ejpam-7074	78	14	groupoid	groupoid	NOUN
ejpam-7074	78	15	sh	sh	INTJ
ejpam-7074	78	16	:	:	PUNCT
ejpam-7074	78	17	=	=	SYM
ejpam-7074	78	18	(	(	PUNCT
ejpam-7074	78	19	sh	sh	INTJ
ejpam-7074	78	20	,	,	PUNCT
ejpam-7074	78	21	|	|	ADV
ejpam-7074	78	22	,	,	PUNCT
ejpam-7074	78	23	0	0	NUM
ejpam-7074	78	24	)	)	PUNCT
ejpam-7074	78	25	equipped	equip	VERB
ejpam-7074	78	26	with	with	ADP
ejpam-7074	78	27	a	a	DET
ejpam-7074	78	28	sheffer	sheffer	NOUN
ejpam-7074	78	29	stroke	stroke	NOUN
ejpam-7074	78	30	operation	operation	NOUN
ejpam-7074	78	31	that	that	PRON
ejpam-7074	78	32	satisfies	satisfy	VERB
ejpam-7074	78	33	specific	specific	ADJ
ejpam-7074	78	34	conditions	condition	NOUN
ejpam-7074	78	35	:	:	PUNCT
ejpam-7074	78	36	(	(	PUNCT
ejpam-7074	78	37	sh1	sh1	PROPN
ejpam-7074	78	38	)	)	PUNCT
ejpam-7074	78	39	(	(	PUNCT
ejpam-7074	79	1	d	d	X
ejpam-7074	79	2	|	|	ADV
ejpam-7074	79	3	(	(	PUNCT
ejpam-7074	79	4	gw	gw	PROPN
ejpam-7074	79	5	|	|	NOUN
ejpam-7074	79	6	gw	gw	PROPN
ejpam-7074	79	7	)	)	PUNCT
ejpam-7074	79	8	)	)	PUNCT
ejpam-7074	80	1	|	|	ADV
ejpam-7074	80	2	(	(	PUNCT
ejpam-7074	80	3	(	(	PUNCT
ejpam-7074	80	4	dg	dg	INTJ
ejpam-7074	80	5	|	|	ADV
ejpam-7074	80	6	(	(	PUNCT
ejpam-7074	80	7	dw	dw	NOUN
ejpam-7074	80	8	|	|	PROPN
ejpam-7074	80	9	dw	dw	PROPN
ejpam-7074	80	10	)	)	PUNCT
ejpam-7074	80	11	)	)	PUNCT
ejpam-7074	81	1	|	|	ADV
ejpam-7074	81	2	(	(	PUNCT
ejpam-7074	81	3	dg	dg	NOUN
ejpam-7074	81	4	|	|	ADV
ejpam-7074	81	5	(	(	PUNCT
ejpam-7074	81	6	dw	dw	NOUN
ejpam-7074	81	7	|	|	PROPN
ejpam-7074	81	8	dw	dw	PROPN
ejpam-7074	81	9	)	)	PUNCT
ejpam-7074	81	10	)	)	PUNCT
ejpam-7074	81	11	)	)	PUNCT
ejpam-7074	82	1	=	=	PUNCT
ejpam-7074	82	2	dd	dd	PROPN
ejpam-7074	82	3	,	,	PUNCT
ejpam-7074	82	4	(	(	PUNCT
ejpam-7074	82	5	sh2	sh2	NOUN
ejpam-7074	82	6	)	)	PUNCT
ejpam-7074	82	7	dg	dg	PROPN
ejpam-7074	82	8	=	=	SYM
ejpam-7074	82	9	gd	gd	NOUN
ejpam-7074	82	10	=	=	PUNCT
ejpam-7074	82	11	dd	dd	NOUN
ejpam-7074	82	12	⇒	⇒	NOUN
ejpam-7074	83	1	d	d	NOUN
ejpam-7074	83	2	=	=	SYM
ejpam-7074	83	3	g	g	PROPN
ejpam-7074	83	4	for	for	ADP
ejpam-7074	83	5	all	all	PRON
ejpam-7074	83	6	d	d	PROPN
ejpam-7074	83	7	,	,	PUNCT
ejpam-7074	83	8	g	g	NOUN
ejpam-7074	83	9	,	,	PUNCT
ejpam-7074	83	10	w	w	PROPN
ejpam-7074	83	11	∈	∈	PROPN
ejpam-7074	83	12	sh	sh	INTJ
ejpam-7074	83	13	.	.	PUNCT
ejpam-7074	84	1	proposition	proposition	NOUN
ejpam-7074	84	2	1	1	NUM
ejpam-7074	84	3	.	.	PUNCT
ejpam-7074	85	1	[	[	X
ejpam-7074	85	2	20	20	NUM
ejpam-7074	85	3	]	]	PUNCT
ejpam-7074	85	4	let	let	VERB
ejpam-7074	85	5	sh	sh	INTJ
ejpam-7074	85	6	:	:	PUNCT
ejpam-7074	85	7	=	=	SYM
ejpam-7074	85	8	(	(	PUNCT
ejpam-7074	85	9	sh	sh	INTJ
ejpam-7074	85	10	,	,	PUNCT
ejpam-7074	85	11	|	|	ADV
ejpam-7074	85	12	,	,	PUNCT
ejpam-7074	85	13	0	0	NUM
ejpam-7074	85	14	)	)	PUNCT
ejpam-7074	85	15	be	be	AUX
ejpam-7074	85	16	an	an	DET
ejpam-7074	85	17	ssha	ssha	NOUN
ejpam-7074	85	18	.	.	PUNCT
ejpam-7074	86	1	then	then	ADV
ejpam-7074	86	2	the	the	DET
ejpam-7074	86	3	binary	binary	PROPN
ejpam-7074	86	4	relation	relation	PROPN
ejpam-7074	86	5	d	d	PROPN
ejpam-7074	86	6	≤	≤	NOUN
ejpam-7074	86	7	g	g	PROPN
ejpam-7074	86	8	⇔	⇔	X
ejpam-7074	86	9	dg	dg	PROPN
ejpam-7074	86	10	=	=	SYM
ejpam-7074	86	11	0	0	NUM
ejpam-7074	86	12	is	be	AUX
ejpam-7074	86	13	a	a	DET
ejpam-7074	86	14	partial	partial	ADJ
ejpam-7074	86	15	order	order	NOUN
ejpam-7074	86	16	on	on	ADP
ejpam-7074	86	17	sh	sh	PROPN
ejpam-7074	86	18	.	.	PUNCT
ejpam-7074	87	1	definition	definition	NOUN
ejpam-7074	87	2	3	3	NUM
ejpam-7074	87	3	.	.	PUNCT
ejpam-7074	88	1	[	[	X
ejpam-7074	88	2	20	20	NUM
ejpam-7074	88	3	]	]	PUNCT
ejpam-7074	88	4	let	let	VERB
ejpam-7074	88	5	sh	sh	INTJ
ejpam-7074	88	6	:	:	PUNCT
ejpam-7074	88	7	=	=	SYM
ejpam-7074	88	8	(	(	PUNCT
ejpam-7074	88	9	sh	sh	INTJ
ejpam-7074	88	10	,	,	PUNCT
ejpam-7074	88	11	|	|	ADV
ejpam-7074	88	12	,	,	PUNCT
ejpam-7074	88	13	0	0	NUM
ejpam-7074	88	14	)	)	PUNCT
ejpam-7074	88	15	be	be	AUX
ejpam-7074	88	16	an	an	DET
ejpam-7074	88	17	ssha	ssha	NOUN
ejpam-7074	88	18	.	.	PUNCT
ejpam-7074	89	1	a	a	DET
ejpam-7074	89	2	nonempty	nonempty	NOUN
ejpam-7074	89	3	subset	subset	VERB
ejpam-7074	89	4	a	a	PRON
ejpam-7074	89	5	of	of	ADP
ejpam-7074	89	6	sh	sh	PROPN
ejpam-7074	89	7	is	be	AUX
ejpam-7074	89	8	called	call	VERB
ejpam-7074	89	9	a	a	DET
ejpam-7074	89	10	subalgebra	subalgebra	NOUN
ejpam-7074	89	11	of	of	ADP
ejpam-7074	89	12	sh	sh	PRON
ejpam-7074	89	13	if	if	SCONJ
ejpam-7074	89	14	dg	dg	PROPN
ejpam-7074	89	15	|	|	ADV
ejpam-7074	89	16	dg	dg	VERB
ejpam-7074	89	17	∈	∈	PROPN
ejpam-7074	89	18	a	a	PRON
ejpam-7074	89	19	for	for	ADP
ejpam-7074	89	20	all	all	DET
ejpam-7074	89	21	d	d	NOUN
ejpam-7074	89	22	,	,	PUNCT
ejpam-7074	89	23	g	g	PROPN
ejpam-7074	89	24	∈	∈	PROPN
ejpam-7074	89	25	a.	a.	NOUN
ejpam-7074	89	26	definition	definition	NOUN
ejpam-7074	89	27	4	4	NUM
ejpam-7074	89	28	.	.	PUNCT
ejpam-7074	90	1	[	[	X
ejpam-7074	90	2	10	10	NUM
ejpam-7074	90	3	]	]	PUNCT
ejpam-7074	90	4	let	let	VERB
ejpam-7074	90	5	x	x	PRON
ejpam-7074	90	6	be	be	AUX
ejpam-7074	90	7	a	a	DET
ejpam-7074	90	8	nonempty	nonempty	ADV
ejpam-7074	90	9	set	set	VERB
ejpam-7074	90	10	.	.	PUNCT
ejpam-7074	91	1	the	the	DET
ejpam-7074	91	2	intuitionistic	intuitionistic	ADJ
ejpam-7074	91	3	fuzzy	fuzzy	ADJ
ejpam-7074	91	4	set	set	NOUN
ejpam-7074	91	5	(	(	PUNCT
ejpam-7074	91	6	ifs	ifs	PROPN
ejpam-7074	91	7	)	)	PUNCT
ejpam-7074	91	8	on	on	ADP
ejpam-7074	91	9	x	x	VERB
ejpam-7074	91	10	is	be	AUX
ejpam-7074	91	11	defined	define	VERB
ejpam-7074	91	12	as	as	ADP
ejpam-7074	91	13	a	a	DET
ejpam-7074	91	14	structure	structure	NOUN
ejpam-7074	91	15	a	a	PRON
ejpam-7074	91	16	:	:	PUNCT
ejpam-7074	91	17	=	=	SYM
ejpam-7074	91	18	{	{	PUNCT
ejpam-7074	91	19	⟨d	⟨d	PROPN
ejpam-7074	91	20	,	,	PUNCT
ejpam-7074	91	21	µa(d	µa(d	PUNCT
ejpam-7074	91	22	)	)	PUNCT
ejpam-7074	91	23	,	,	PUNCT
ejpam-7074	91	24	γa(d)⟩	γa(d)⟩	PROPN
ejpam-7074	92	1	|	|	NOUN
ejpam-7074	92	2	d	d	PROPN
ejpam-7074	92	3	∈	∈	PROPN
ejpam-7074	92	4	x	x	X
ejpam-7074	92	5	}	}	PUNCT
ejpam-7074	92	6	,	,	PUNCT
ejpam-7074	92	7	(	(	PUNCT
ejpam-7074	92	8	1	1	X
ejpam-7074	92	9	)	)	PUNCT
ejpam-7074	92	10	where	where	SCONJ
ejpam-7074	92	11	µa	µa	ADV
ejpam-7074	92	12	:	:	PUNCT
ejpam-7074	92	13	x	x	X
ejpam-7074	92	14	→	→	SYM
ejpam-7074	93	1	[	[	X
ejpam-7074	93	2	0	0	NUM
ejpam-7074	93	3	,	,	PUNCT
ejpam-7074	93	4	1	1	NUM
ejpam-7074	93	5	]	]	PUNCT
ejpam-7074	93	6	represents	represent	VERB
ejpam-7074	93	7	the	the	DET
ejpam-7074	93	8	degree	degree	NOUN
ejpam-7074	93	9	of	of	ADP
ejpam-7074	93	10	membership	membership	NOUN
ejpam-7074	93	11	of	of	ADP
ejpam-7074	93	12	d	d	PROPN
ejpam-7074	93	13	in	in	ADP
ejpam-7074	93	14	a	a	PRON
ejpam-7074	93	15	,	,	PUNCT
ejpam-7074	93	16	and	and	CCONJ
ejpam-7074	93	17	γa	γa	PRON
ejpam-7074	93	18	:	:	PUNCT
ejpam-7074	93	19	x	x	X
ejpam-7074	93	20	→	→	PUNCT
ejpam-7074	94	1	[	[	X
ejpam-7074	94	2	0	0	NUM
ejpam-7074	94	3	,	,	PUNCT
ejpam-7074	94	4	1	1	NUM
ejpam-7074	94	5	]	]	PUNCT
ejpam-7074	94	6	represents	represent	VERB
ejpam-7074	94	7	the	the	DET
ejpam-7074	94	8	degree	degree	NOUN
ejpam-7074	94	9	of	of	ADP
ejpam-7074	94	10	non	non	ADJ
ejpam-7074	94	11	-	-	NOUN
ejpam-7074	94	12	membership	membership	NOUN
ejpam-7074	94	13	of	of	ADP
ejpam-7074	94	14	d	d	PROPN
ejpam-7074	94	15	in	in	ADP
ejpam-7074	94	16	a	a	DET
ejpam-7074	94	17	such	such	ADJ
ejpam-7074	94	18	that	that	SCONJ
ejpam-7074	94	19	0	0	NUM
ejpam-7074	94	20	≤	≤	NOUN
ejpam-7074	94	21	µa(d	µa(d	PUNCT
ejpam-7074	94	22	)	)	PUNCT
ejpam-7074	94	23	+	+	CCONJ
ejpam-7074	94	24	γa(d	γa(d	X
ejpam-7074	94	25	)	)	PUNCT
ejpam-7074	94	26	≤	≤	NUM
ejpam-7074	94	27	1	1	NUM
ejpam-7074	94	28	.	.	PUNCT
ejpam-7074	95	1	the	the	DET
ejpam-7074	95	2	ifs	ifs	PROPN
ejpam-7074	95	3	in	in	ADP
ejpam-7074	95	4	(	(	PUNCT
ejpam-7074	95	5	1	1	NUM
ejpam-7074	95	6	)	)	PUNCT
ejpam-7074	95	7	is	be	AUX
ejpam-7074	95	8	simply	simply	ADV
ejpam-7074	95	9	denoted	denote	VERB
ejpam-7074	95	10	by	by	ADP
ejpam-7074	95	11	a	a	DET
ejpam-7074	95	12	=	=	SYM
ejpam-7074	95	13	(	(	PUNCT
ejpam-7074	95	14	µa	µa	PROPN
ejpam-7074	95	15	,	,	PUNCT
ejpam-7074	95	16	γa	γa	PROPN
ejpam-7074	95	17	)	)	PUNCT
ejpam-7074	95	18	.	.	PUNCT
ejpam-7074	96	1	let	let	VERB
ejpam-7074	97	1	d	d	X
ejpam-7074	97	2	[	[	X
ejpam-7074	97	3	0	0	NUM
ejpam-7074	97	4	,	,	PUNCT
ejpam-7074	97	5	1	1	NUM
ejpam-7074	97	6	]	]	PUNCT
ejpam-7074	97	7	be	be	AUX
ejpam-7074	97	8	the	the	DET
ejpam-7074	97	9	set	set	NOUN
ejpam-7074	97	10	of	of	ADP
ejpam-7074	97	11	all	all	DET
ejpam-7074	97	12	closed	closed	ADJ
ejpam-7074	97	13	subintervals	subinterval	NOUN
ejpam-7074	97	14	of	of	ADP
ejpam-7074	97	15	the	the	DET
ejpam-7074	97	16	interval	interval	NOUN
ejpam-7074	97	17	[	[	X
ejpam-7074	97	18	0	0	NUM
ejpam-7074	97	19	,	,	PUNCT
ejpam-7074	97	20	1	1	NUM
ejpam-7074	97	21	]	]	PUNCT
ejpam-7074	97	22	.	.	PUNCT
ejpam-7074	98	1	consider	consider	VERB
ejpam-7074	98	2	i1	i1	PROPN
ejpam-7074	98	3	,	,	PUNCT
ejpam-7074	98	4	i2	i2	PROPN
ejpam-7074	98	5	∈	∈	PROPN
ejpam-7074	99	1	d	d	X
ejpam-7074	100	1	[	[	X
ejpam-7074	100	2	0	0	NUM
ejpam-7074	100	3	,	,	PUNCT
ejpam-7074	100	4	1	1	NUM
ejpam-7074	100	5	]	]	PUNCT
ejpam-7074	100	6	.	.	PUNCT
ejpam-7074	101	1	if	if	SCONJ
ejpam-7074	101	2	i1	i1	PROPN
ejpam-7074	101	3	=	=	PROPN
ejpam-7074	102	1	[	[	X
ejpam-7074	102	2	m1	m1	NOUN
ejpam-7074	102	3	,	,	PUNCT
ejpam-7074	102	4	n1	n1	PROPN
ejpam-7074	102	5	]	]	PUNCT
ejpam-7074	102	6	and	and	CCONJ
ejpam-7074	102	7	i2	i2	PROPN
ejpam-7074	102	8	=	=	PUNCT
ejpam-7074	103	1	[	[	X
ejpam-7074	103	2	m2	m2	PROPN
ejpam-7074	103	3	,	,	PUNCT
ejpam-7074	103	4	n2	n2	NOUN
ejpam-7074	103	5	]	]	PUNCT
ejpam-7074	103	6	,	,	PUNCT
ejpam-7074	103	7	then	then	ADV
ejpam-7074	103	8	rmin{i1	rmin{i1	NOUN
ejpam-7074	103	9	,	,	PUNCT
ejpam-7074	103	10	i2	i2	NOUN
ejpam-7074	103	11	}	}	PUNCT
ejpam-7074	103	12	=	=	PUNCT
ejpam-7074	104	1	[	[	X
ejpam-7074	104	2	min{m1,m2},min{n1	min{m1,m2},min{n1	PROPN
ejpam-7074	104	3	,	,	PUNCT
ejpam-7074	104	4	n2	n2	ADJ
ejpam-7074	104	5	}	}	PUNCT
ejpam-7074	104	6	]	]	PUNCT
ejpam-7074	104	7	and	and	CCONJ
ejpam-7074	104	8	rmax{i1	rmax{i1	NOUN
ejpam-7074	104	9	,	,	PUNCT
ejpam-7074	104	10	i2	i2	NOUN
ejpam-7074	104	11	}	}	PUNCT
ejpam-7074	104	12	=	=	PUNCT
ejpam-7074	105	1	[	[	X
ejpam-7074	105	2	max{m1,m2},max{n1	max{m1,m2},max{n1	PROPN
ejpam-7074	105	3	,	,	PUNCT
ejpam-7074	105	4	n2	n2	ADJ
ejpam-7074	105	5	}	}	PUNCT
ejpam-7074	105	6	]	]	PUNCT
ejpam-7074	105	7	.	.	PUNCT
ejpam-7074	106	1	thus	thus	ADV
ejpam-7074	106	2	,	,	PUNCT
ejpam-7074	106	3	if	if	SCONJ
ejpam-7074	106	4	ii	ii	X
ejpam-7074	106	5	=	=	PUNCT
ejpam-7074	107	1	[	[	X
ejpam-7074	107	2	mi	mi	PROPN
ejpam-7074	107	3	,	,	PUNCT
ejpam-7074	107	4	ni	ni	PROPN
ejpam-7074	107	5	]	]	X
ejpam-7074	107	6	∈	∈	PROPN
ejpam-7074	108	1	d	d	X
ejpam-7074	109	1	[	[	X
ejpam-7074	109	2	0	0	NUM
ejpam-7074	109	3	,	,	PUNCT
ejpam-7074	109	4	1	1	NUM
ejpam-7074	109	5	]	]	PUNCT
ejpam-7074	109	6	for	for	ADP
ejpam-7074	109	7	i	i	PROPN
ejpam-7074	109	8	=	=	NOUN
ejpam-7074	109	9	1	1	NUM
ejpam-7074	109	10	,	,	PUNCT
ejpam-7074	109	11	2	2	NUM
ejpam-7074	109	12	,	,	PUNCT
ejpam-7074	109	13	.	.	PUNCT
ejpam-7074	109	14	.	.	PUNCT
ejpam-7074	110	1	.	.	PUNCT
ejpam-7074	111	1	,	,	PUNCT
ejpam-7074	111	2	then	then	ADV
ejpam-7074	111	3	we	we	PRON
ejpam-7074	111	4	define	define	VERB
ejpam-7074	111	5	rsupi{ii	rsupi{ii	NOUN
ejpam-7074	111	6	}	}	PUNCT
ejpam-7074	111	7	=	=	PUNCT
ejpam-7074	112	1	[	[	X
ejpam-7074	112	2	sup	sup	NOUN
ejpam-7074	112	3	i	i	PRON
ejpam-7074	112	4	{	{	PUNCT
ejpam-7074	112	5	mi	mi	PROPN
ejpam-7074	112	6	}	}	PUNCT
ejpam-7074	112	7	,	,	PUNCT
ejpam-7074	112	8	sup	sup	VERB
ejpam-7074	112	9	i	i	PRON
ejpam-7074	112	10	{	{	PUNCT
ejpam-7074	112	11	ni	ni	PROPN
ejpam-7074	112	12	}	}	PUNCT
ejpam-7074	112	13	]	]	PUNCT
ejpam-7074	112	14	and	and	CCONJ
ejpam-7074	112	15	rinf	rinf	ADJ
ejpam-7074	112	16	i{ii	i{ii	PROPN
ejpam-7074	112	17	}	}	PUNCT
ejpam-7074	112	18	=	=	PUNCT
ejpam-7074	113	1	[	[	X
ejpam-7074	113	2	inf	inf	NOUN
ejpam-7074	113	3	i	i	PRON
ejpam-7074	113	4	{	{	PUNCT
ejpam-7074	113	5	mi	mi	PROPN
ejpam-7074	113	6	}	}	PUNCT
ejpam-7074	113	7	,	,	PUNCT
ejpam-7074	113	8	inf	inf	PROPN
ejpam-7074	113	9	i	i	PRON
ejpam-7074	113	10	{	{	PUNCT
ejpam-7074	113	11	ni	ni	PROPN
ejpam-7074	113	12	}	}	PUNCT
ejpam-7074	113	13	]	]	PUNCT
ejpam-7074	113	14	.	.	PUNCT
ejpam-7074	114	1	now	now	ADV
ejpam-7074	114	2	,	,	PUNCT
ejpam-7074	114	3	we	we	PRON
ejpam-7074	114	4	call	call	VERB
ejpam-7074	114	5	i1	i1	PROPN
ejpam-7074	114	6	≥	≥	PROPN
ejpam-7074	114	7	i2	i2	PROPN
ejpam-7074	114	8	if	if	SCONJ
ejpam-7074	115	1	and	and	CCONJ
ejpam-7074	115	2	only	only	ADV
ejpam-7074	115	3	if	if	SCONJ
ejpam-7074	115	4	m1	m1	PROPN
ejpam-7074	115	5	≥	≥	NUM
ejpam-7074	115	6	m2	m2	PROPN
ejpam-7074	115	7	and	and	CCONJ
ejpam-7074	115	8	n1	n1	PROPN
ejpam-7074	115	9	≤	≤	PROPN
ejpam-7074	115	10	n2	n2	NOUN
ejpam-7074	115	11	.	.	PUNCT
ejpam-7074	115	12	similarly	similarly	ADV
ejpam-7074	115	13	,	,	PUNCT
ejpam-7074	115	14	the	the	DET
ejpam-7074	115	15	relations	relation	NOUN
ejpam-7074	115	16	i1	i1	PROPN
ejpam-7074	115	17	≤	≤	PROPN
ejpam-7074	115	18	i2	i2	PROPN
ejpam-7074	115	19	and	and	CCONJ
ejpam-7074	115	20	i1	i1	PROPN
ejpam-7074	115	21	=	=	PROPN
ejpam-7074	115	22	i2	i2	PROPN
ejpam-7074	115	23	are	be	AUX
ejpam-7074	115	24	defined	define	VERB
ejpam-7074	115	25	.	.	PUNCT
ejpam-7074	116	1	a.	a.	PROPN
ejpam-7074	116	2	iampan	iampan	PROPN
ejpam-7074	116	3	et	et	PROPN
ejpam-7074	116	4	al	al	PROPN
ejpam-7074	116	5	.	.	PUNCT
ejpam-7074	116	6	/	/	SYM
ejpam-7074	116	7	eur	eur	PROPN
ejpam-7074	116	8	.	.	PUNCT
ejpam-7074	117	1	j.	j.	PROPN
ejpam-7074	117	2	pure	pure	PROPN
ejpam-7074	117	3	appl	appl	PROPN
ejpam-7074	117	4	.	.	PROPN
ejpam-7074	117	5	math	math	PROPN
ejpam-7074	117	6	,	,	PUNCT
ejpam-7074	117	7	18	18	NUM
ejpam-7074	117	8	(	(	PUNCT
ejpam-7074	117	9	4	4	NUM
ejpam-7074	117	10	)	)	PUNCT
ejpam-7074	117	11	(	(	PUNCT
ejpam-7074	117	12	2025	2025	NUM
ejpam-7074	117	13	)	)	PUNCT
ejpam-7074	117	14	,	,	PUNCT
ejpam-7074	117	15	7074	7074	NUM
ejpam-7074	117	16	5	5	NUM
ejpam-7074	117	17	of	of	ADP
ejpam-7074	117	18	14	14	NUM
ejpam-7074	117	19	definition	definition	NOUN
ejpam-7074	117	20	5	5	NUM
ejpam-7074	117	21	.	.	PUNCT
ejpam-7074	118	1	an	an	DET
ejpam-7074	118	2	interval	interval	NOUN
ejpam-7074	118	3	-	-	PUNCT
ejpam-7074	118	4	valued	value	VERB
ejpam-7074	118	5	intuitionistic	intuitionistic	ADJ
ejpam-7074	118	6	fuzzy	fuzzy	ADJ
ejpam-7074	118	7	set	set	NOUN
ejpam-7074	118	8	(	(	PUNCT
ejpam-7074	118	9	ivifs	ivifs	PROPN
ejpam-7074	118	10	)	)	PUNCT
ejpam-7074	118	11	a	a	PRON
ejpam-7074	118	12	over	over	ADP
ejpam-7074	118	13	a	a	DET
ejpam-7074	118	14	universe	universe	NOUN
ejpam-7074	118	15	x	x	PUNCT
ejpam-7074	118	16	is	be	AUX
ejpam-7074	118	17	defined	define	VERB
ejpam-7074	118	18	as	as	ADP
ejpam-7074	118	19	an	an	DET
ejpam-7074	118	20	object	object	NOUN
ejpam-7074	118	21	of	of	ADP
ejpam-7074	118	22	the	the	DET
ejpam-7074	118	23	form	form	NOUN
ejpam-7074	118	24	a	a	X
ejpam-7074	118	25	=	=	SYM
ejpam-7074	118	26	{	{	PUNCT
ejpam-7074	118	27	⟨d	⟨d	PROPN
ejpam-7074	118	28	,	,	PUNCT
ejpam-7074	118	29	µa(d	µa(d	PUNCT
ejpam-7074	118	30	)	)	PUNCT
ejpam-7074	118	31	,	,	PUNCT
ejpam-7074	118	32	γa(d)⟩	γa(d)⟩	PROPN
ejpam-7074	119	1	|	|	NOUN
ejpam-7074	119	2	d	d	PROPN
ejpam-7074	119	3	∈	∈	PROPN
ejpam-7074	119	4	x	x	X
ejpam-7074	119	5	}	}	PUNCT
ejpam-7074	119	6	,	,	PUNCT
ejpam-7074	119	7	where	where	SCONJ
ejpam-7074	119	8	µa(d	µa(d	PUNCT
ejpam-7074	119	9	)	)	PUNCT
ejpam-7074	119	10	:	:	PUNCT
ejpam-7074	120	1	x	x	X
ejpam-7074	120	2	→	→	PUNCT
ejpam-7074	120	3	d	d	X
ejpam-7074	120	4	[	[	X
ejpam-7074	120	5	0	0	NUM
ejpam-7074	120	6	,	,	PUNCT
ejpam-7074	120	7	1	1	NUM
ejpam-7074	120	8	]	]	PUNCT
ejpam-7074	120	9	and	and	CCONJ
ejpam-7074	120	10	γa(d	γa(d	NUM
ejpam-7074	120	11	)	)	PUNCT
ejpam-7074	120	12	:	:	PUNCT
ejpam-7074	121	1	x	x	X
ejpam-7074	121	2	→	→	PUNCT
ejpam-7074	121	3	d	d	X
ejpam-7074	121	4	[	[	X
ejpam-7074	121	5	0	0	NUM
ejpam-7074	121	6	,	,	PUNCT
ejpam-7074	121	7	1	1	NUM
ejpam-7074	121	8	]	]	PUNCT
ejpam-7074	121	9	.	.	PUNCT
ejpam-7074	122	1	the	the	DET
ejpam-7074	122	2	functions	function	NOUN
ejpam-7074	122	3	µa(d	µa(d	PUNCT
ejpam-7074	122	4	)	)	PUNCT
ejpam-7074	122	5	and	and	CCONJ
ejpam-7074	122	6	γa(d	γa(d	NUM
ejpam-7074	122	7	)	)	PUNCT
ejpam-7074	122	8	represent	represent	VERB
ejpam-7074	122	9	the	the	DET
ejpam-7074	122	10	intervals	interval	NOUN
ejpam-7074	122	11	of	of	ADP
ejpam-7074	122	12	the	the	DET
ejpam-7074	122	13	degree	degree	NOUN
ejpam-7074	122	14	of	of	ADP
ejpam-7074	122	15	membership	membership	NOUN
ejpam-7074	122	16	and	and	CCONJ
ejpam-7074	122	17	non	non	ADJ
ejpam-7074	122	18	-	-	NOUN
ejpam-7074	122	19	membership	membership	NOUN
ejpam-7074	122	20	of	of	ADP
ejpam-7074	122	21	the	the	DET
ejpam-7074	122	22	element	element	NOUN
ejpam-7074	122	23	d	d	PROPN
ejpam-7074	122	24	in	in	ADP
ejpam-7074	122	25	a	a	DET
ejpam-7074	122	26	,	,	PUNCT
ejpam-7074	122	27	respectively	respectively	ADV
ejpam-7074	122	28	,	,	PUNCT
ejpam-7074	122	29	where	where	SCONJ
ejpam-7074	122	30	µa(d	µa(d	PUNCT
ejpam-7074	122	31	)	)	PUNCT
ejpam-7074	122	32	=	=	PUNCT
ejpam-7074	123	1	[	[	X
ejpam-7074	123	2	µl	µl	ADP
ejpam-7074	123	3	a(d	a(d	NOUN
ejpam-7074	123	4	)	)	PUNCT
ejpam-7074	123	5	,	,	PUNCT
ejpam-7074	123	6	µ	µ	X
ejpam-7074	123	7	u	u	PRON
ejpam-7074	123	8	a(d	a(d	PROPN
ejpam-7074	123	9	)	)	PUNCT
ejpam-7074	123	10	]	]	PUNCT
ejpam-7074	123	11	and	and	CCONJ
ejpam-7074	123	12	γa(d	γa(d	NUM
ejpam-7074	123	13	)	)	PUNCT
ejpam-7074	123	14	=	=	PUNCT
ejpam-7074	124	1	[	[	X
ejpam-7074	124	2	γla(d	γla(d	NOUN
ejpam-7074	124	3	)	)	PUNCT
ejpam-7074	124	4	,	,	PUNCT
ejpam-7074	124	5	γ	γ	X
ejpam-7074	124	6	u	u	NOUN
ejpam-7074	124	7	a(d	a(d	PROPN
ejpam-7074	124	8	)	)	PUNCT
ejpam-7074	124	9	]	]	PUNCT
ejpam-7074	124	10	for	for	ADP
ejpam-7074	124	11	all	all	DET
ejpam-7074	124	12	d	d	PROPN
ejpam-7074	124	13	∈	∈	PROPN
ejpam-7074	124	14	x	x	NOUN
ejpam-7074	124	15	,	,	PUNCT
ejpam-7074	124	16	subject	subject	ADJ
ejpam-7074	124	17	to	to	ADP
ejpam-7074	124	18	condition	condition	NOUN
ejpam-7074	124	19	0	0	NUM
ejpam-7074	124	20	≤	≤	NOUN
ejpam-7074	124	21	µl	µl	ADP
ejpam-7074	124	22	a(d	a(d	PROPN
ejpam-7074	124	23	)	)	PUNCT
ejpam-7074	124	24	+	+	NUM
ejpam-7074	124	25	γua(d	γua(d	X
ejpam-7074	124	26	)	)	PUNCT
ejpam-7074	124	27	≤	≤	NOUN
ejpam-7074	124	28	1	1	NUM
ejpam-7074	124	29	.	.	X
ejpam-7074	125	1	for	for	ADP
ejpam-7074	125	2	simplicity	simplicity	NOUN
ejpam-7074	125	3	,	,	PUNCT
ejpam-7074	125	4	we	we	PRON
ejpam-7074	125	5	denote	denote	VERB
ejpam-7074	125	6	the	the	DET
ejpam-7074	125	7	ivifs	ivif	NOUN
ejpam-7074	125	8	a	a	PRON
ejpam-7074	125	9	as	as	ADP
ejpam-7074	125	10	a	a	PRON
ejpam-7074	125	11	=	=	SYM
ejpam-7074	125	12	(	(	PUNCT
ejpam-7074	125	13	µa	µa	PROPN
ejpam-7074	125	14	,	,	PUNCT
ejpam-7074	125	15	γa	γa	PROPN
ejpam-7074	125	16	)	)	PUNCT
ejpam-7074	125	17	,	,	PUNCT
ejpam-7074	125	18	where	where	SCONJ
ejpam-7074	125	19	a	a	DET
ejpam-7074	125	20	=	=	SYM
ejpam-7074	125	21	{	{	PUNCT
ejpam-7074	125	22	⟨d	⟨d	PROPN
ejpam-7074	125	23	,	,	PUNCT
ejpam-7074	125	24	µa(d	µa(d	PUNCT
ejpam-7074	125	25	)	)	PUNCT
ejpam-7074	125	26	,	,	PUNCT
ejpam-7074	125	27	γa(d)⟩	γa(d)⟩	PROPN
ejpam-7074	125	28	|	|	NOUN
ejpam-7074	125	29	d	d	PROPN
ejpam-7074	125	30	∈	∈	PROPN
ejpam-7074	125	31	x	x	X
ejpam-7074	125	32	}	}	PUNCT
ejpam-7074	125	33	.	.	PUNCT
ejpam-7074	126	1	additionally	additionally	ADV
ejpam-7074	126	2	,	,	PUNCT
ejpam-7074	126	3	the	the	DET
ejpam-7074	126	4	complements	complement	NOUN
ejpam-7074	126	5	of	of	ADP
ejpam-7074	126	6	µa	µa	NOUN
ejpam-7074	126	7	and	and	CCONJ
ejpam-7074	126	8	γa	γa	PROPN
ejpam-7074	126	9	are	be	AUX
ejpam-7074	126	10	given	give	VERB
ejpam-7074	126	11	by	by	ADP
ejpam-7074	126	12	µa(d	µa(d	PUNCT
ejpam-7074	126	13	)	)	PUNCT
ejpam-7074	126	14	=	=	PUNCT
ejpam-7074	127	1	[	[	X
ejpam-7074	127	2	1−µu	1−µu	NUM
ejpam-7074	127	3	a(d	a(d	NOUN
ejpam-7074	127	4	)	)	PUNCT
ejpam-7074	127	5	,	,	PUNCT
ejpam-7074	127	6	1−µl	1−µl	NUM
ejpam-7074	127	7	a(d	a(d	NOUN
ejpam-7074	127	8	)	)	PUNCT
ejpam-7074	127	9	]	]	PUNCT
ejpam-7074	127	10	and	and	CCONJ
ejpam-7074	127	11	γa(d	γa(d	NUM
ejpam-7074	127	12	)	)	PUNCT
ejpam-7074	127	13	=	=	PUNCT
ejpam-7074	128	1	[	[	X
ejpam-7074	128	2	1−	1−	NUM
ejpam-7074	128	3	γua(d	γua(d	NUM
ejpam-7074	128	4	)	)	PUNCT
ejpam-7074	128	5	,	,	PUNCT
ejpam-7074	128	6	1−	1−	NUM
ejpam-7074	128	7	γla(d	γla(d	NUM
ejpam-7074	128	8	)	)	PUNCT
ejpam-7074	128	9	]	]	PUNCT
ejpam-7074	128	10	,	,	PUNCT
ejpam-7074	128	11	where	where	SCONJ
ejpam-7074	128	12	[	[	X
ejpam-7074	128	13	µa(d	µa(d	PUNCT
ejpam-7074	128	14	)	)	PUNCT
ejpam-7074	128	15	,	,	PUNCT
ejpam-7074	128	16	γa(d	γa(d	NUM
ejpam-7074	128	17	)	)	PUNCT
ejpam-7074	128	18	]	]	PUNCT
ejpam-7074	128	19	,	,	PUNCT
ejpam-7074	128	20	represents	represent	VERB
ejpam-7074	128	21	the	the	DET
ejpam-7074	128	22	complement	complement	NOUN
ejpam-7074	128	23	of	of	ADP
ejpam-7074	128	24	d	d	PROPN
ejpam-7074	128	25	in	in	ADP
ejpam-7074	128	26	a.	a.	NOUN
ejpam-7074	128	27	3	3	NUM
ejpam-7074	128	28	.	.	PUNCT
ejpam-7074	128	29	interval	interval	NOUN
ejpam-7074	128	30	-	-	PUNCT
ejpam-7074	128	31	valued	value	VERB
ejpam-7074	128	32	intuitionistic	intuitionistic	ADJ
ejpam-7074	128	33	fuzzy	fuzzy	ADJ
ejpam-7074	128	34	sheffer	sheffer	NOUN
ejpam-7074	128	35	stroke	stroke	NOUN
ejpam-7074	128	36	subalgebras	subalgebras	PROPN
ejpam-7074	128	37	the	the	DET
ejpam-7074	128	38	integration	integration	NOUN
ejpam-7074	128	39	of	of	ADP
ejpam-7074	128	40	ivifss	ivifss	ADV
ejpam-7074	128	41	with	with	ADP
ejpam-7074	128	42	sshas	ssha	NOUN
ejpam-7074	128	43	provides	provide	VERB
ejpam-7074	128	44	a	a	DET
ejpam-7074	128	45	fertile	fertile	ADJ
ejpam-7074	128	46	ground	ground	NOUN
ejpam-7074	128	47	for	for	ADP
ejpam-7074	128	48	generalizing	generalize	VERB
ejpam-7074	128	49	classical	classical	ADJ
ejpam-7074	128	50	algebraic	algebraic	ADJ
ejpam-7074	128	51	structures	structure	NOUN
ejpam-7074	128	52	under	under	ADP
ejpam-7074	128	53	uncertainty	uncertainty	NOUN
ejpam-7074	128	54	.	.	PUNCT
ejpam-7074	129	1	while	while	SCONJ
ejpam-7074	129	2	intuitionistic	intuitionistic	ADJ
ejpam-7074	129	3	fuzzy	fuzzy	ADJ
ejpam-7074	129	4	frameworks	framework	NOUN
ejpam-7074	129	5	have	have	AUX
ejpam-7074	129	6	been	be	AUX
ejpam-7074	129	7	extensively	extensively	ADV
ejpam-7074	129	8	applied	apply	VERB
ejpam-7074	129	9	to	to	ADP
ejpam-7074	129	10	various	various	ADJ
ejpam-7074	129	11	algebraic	algebraic	ADJ
ejpam-7074	129	12	systems	system	NOUN
ejpam-7074	129	13	,	,	PUNCT
ejpam-7074	129	14	their	their	PRON
ejpam-7074	129	15	interval	interval	NOUN
ejpam-7074	129	16	-	-	PUNCT
ejpam-7074	129	17	valued	value	VERB
ejpam-7074	129	18	extensions	extension	NOUN
ejpam-7074	129	19	remain	remain	VERB
ejpam-7074	129	20	relatively	relatively	ADV
ejpam-7074	129	21	underexplored	underexplored	ADJ
ejpam-7074	129	22	within	within	ADP
ejpam-7074	129	23	the	the	DET
ejpam-7074	129	24	context	context	NOUN
ejpam-7074	129	25	of	of	ADP
ejpam-7074	129	26	ssha	ssha	PROPN
ejpam-7074	129	27	.	.	PUNCT
ejpam-7074	130	1	this	this	PRON
ejpam-7074	130	2	motivates	motivate	VERB
ejpam-7074	130	3	a	a	DET
ejpam-7074	130	4	deeper	deep	ADJ
ejpam-7074	130	5	investigation	investigation	NOUN
ejpam-7074	130	6	into	into	ADP
ejpam-7074	130	7	the	the	DET
ejpam-7074	130	8	algebraic	algebraic	ADJ
ejpam-7074	130	9	behavior	behavior	NOUN
ejpam-7074	130	10	of	of	ADP
ejpam-7074	130	11	such	such	ADJ
ejpam-7074	130	12	fuzzy	fuzzy	ADJ
ejpam-7074	130	13	structures	structure	NOUN
ejpam-7074	130	14	.	.	PUNCT
ejpam-7074	131	1	in	in	ADP
ejpam-7074	131	2	this	this	DET
ejpam-7074	131	3	section	section	NOUN
ejpam-7074	131	4	,	,	PUNCT
ejpam-7074	131	5	we	we	PRON
ejpam-7074	131	6	introduce	introduce	VERB
ejpam-7074	131	7	the	the	DET
ejpam-7074	131	8	concept	concept	NOUN
ejpam-7074	131	9	of	of	ADP
ejpam-7074	131	10	interval	interval	NOUN
ejpam-7074	131	11	-	-	PUNCT
ejpam-7074	131	12	valued	value	VERB
ejpam-7074	131	13	intuitionistic	intuitionistic	ADJ
ejpam-7074	131	14	fuzzy	fuzzy	ADJ
ejpam-7074	131	15	sheffer	sheffer	NOUN
ejpam-7074	131	16	stroke	stroke	NOUN
ejpam-7074	131	17	subalgebras	subalgebras	PROPN
ejpam-7074	131	18	(	(	PUNCT
ejpam-7074	131	19	ivifss	ivifss	NOUN
ejpam-7074	131	20	-	-	PUNCT
ejpam-7074	131	21	subalgebras	subalgebras	X
ejpam-7074	131	22	)	)	PUNCT
ejpam-7074	131	23	and	and	CCONJ
ejpam-7074	131	24	examine	examine	VERB
ejpam-7074	131	25	their	their	PRON
ejpam-7074	131	26	fundamental	fundamental	ADJ
ejpam-7074	131	27	properties	property	NOUN
ejpam-7074	131	28	.	.	PUNCT
ejpam-7074	132	1	the	the	DET
ejpam-7074	132	2	aim	aim	NOUN
ejpam-7074	132	3	is	be	AUX
ejpam-7074	132	4	to	to	PART
ejpam-7074	132	5	establish	establish	VERB
ejpam-7074	132	6	criteria	criterion	NOUN
ejpam-7074	132	7	under	under	ADP
ejpam-7074	132	8	which	which	PRON
ejpam-7074	132	9	ivif	ivif	VERB
ejpam-7074	132	10	subsets	subset	NOUN
ejpam-7074	132	11	of	of	ADP
ejpam-7074	132	12	an	an	DET
ejpam-7074	132	13	ssha	ssha	NOUN
ejpam-7074	132	14	preserve	preserve	VERB
ejpam-7074	132	15	subalgebraic	subalgebraic	ADJ
ejpam-7074	132	16	structure	structure	NOUN
ejpam-7074	132	17	with	with	ADP
ejpam-7074	132	18	respect	respect	NOUN
ejpam-7074	132	19	to	to	ADP
ejpam-7074	132	20	the	the	DET
ejpam-7074	132	21	sheffer	sheffer	NOUN
ejpam-7074	132	22	operation	operation	NOUN
ejpam-7074	132	23	.	.	PUNCT
ejpam-7074	133	1	special	special	ADJ
ejpam-7074	133	2	attention	attention	NOUN
ejpam-7074	133	3	is	be	AUX
ejpam-7074	133	4	given	give	VERB
ejpam-7074	133	5	to	to	ADP
ejpam-7074	133	6	their	their	PRON
ejpam-7074	133	7	closure	closure	NOUN
ejpam-7074	133	8	properties	property	NOUN
ejpam-7074	133	9	,	,	PUNCT
ejpam-7074	133	10	interaction	interaction	NOUN
ejpam-7074	133	11	under	under	ADP
ejpam-7074	133	12	set	set	NOUN
ejpam-7074	133	13	-	-	PUNCT
ejpam-7074	133	14	theoretic	theoretic	NOUN
ejpam-7074	133	15	operations	operation	NOUN
ejpam-7074	133	16	,	,	PUNCT
ejpam-7074	133	17	and	and	CCONJ
ejpam-7074	133	18	logical	logical	ADJ
ejpam-7074	133	19	coherence	coherence	NOUN
ejpam-7074	133	20	.	.	PUNCT
ejpam-7074	134	1	these	these	DET
ejpam-7074	134	2	results	result	VERB
ejpam-7074	134	3	not	not	PART
ejpam-7074	134	4	only	only	ADV
ejpam-7074	134	5	enrich	enrich	VERB
ejpam-7074	134	6	the	the	DET
ejpam-7074	134	7	theory	theory	NOUN
ejpam-7074	134	8	of	of	ADP
ejpam-7074	134	9	fuzzy	fuzzy	ADJ
ejpam-7074	134	10	algebraic	algebraic	ADJ
ejpam-7074	134	11	systems	system	NOUN
ejpam-7074	134	12	but	but	CCONJ
ejpam-7074	134	13	also	also	ADV
ejpam-7074	134	14	offer	offer	VERB
ejpam-7074	134	15	tools	tool	NOUN
ejpam-7074	134	16	for	for	ADP
ejpam-7074	134	17	modeling	model	VERB
ejpam-7074	134	18	imprecise	imprecise	ADJ
ejpam-7074	134	19	reasoning	reasoning	NOUN
ejpam-7074	134	20	in	in	ADP
ejpam-7074	134	21	logic	logic	NOUN
ejpam-7074	134	22	and	and	CCONJ
ejpam-7074	134	23	computational	computational	ADJ
ejpam-7074	134	24	intelligence	intelligence	NOUN
ejpam-7074	134	25	.	.	PUNCT
ejpam-7074	135	1	definition	definition	NOUN
ejpam-7074	135	2	6	6	NUM
ejpam-7074	135	3	.	.	PUNCT
ejpam-7074	136	1	let	let	VERB
ejpam-7074	136	2	sh	sh	NOUN
ejpam-7074	136	3	:	:	PUNCT
ejpam-7074	136	4	=	=	SYM
ejpam-7074	136	5	(	(	PUNCT
ejpam-7074	136	6	sh	sh	INTJ
ejpam-7074	136	7	,	,	PUNCT
ejpam-7074	136	8	|	|	ADV
ejpam-7074	136	9	,	,	PUNCT
ejpam-7074	136	10	0	0	NUM
ejpam-7074	136	11	)	)	PUNCT
ejpam-7074	136	12	be	be	AUX
ejpam-7074	136	13	an	an	DET
ejpam-7074	136	14	ssha	ssha	NOUN
ejpam-7074	136	15	.	.	PUNCT
ejpam-7074	137	1	an	an	DET
ejpam-7074	137	2	ivifs	ivifs	PROPN
ejpam-7074	137	3	a	a	PRON
ejpam-7074	137	4	=	=	X
ejpam-7074	137	5	(	(	PUNCT
ejpam-7074	137	6	µa	µa	PROPN
ejpam-7074	137	7	,	,	PUNCT
ejpam-7074	137	8	γa	γa	NOUN
ejpam-7074	137	9	)	)	PUNCT
ejpam-7074	137	10	in	in	ADP
ejpam-7074	137	11	sh	sh	PROPN
ejpam-7074	137	12	is	be	AUX
ejpam-7074	137	13	called	call	VERB
ejpam-7074	137	14	an	an	DET
ejpam-7074	137	15	interval	interval	NOUN
ejpam-7074	137	16	-	-	PUNCT
ejpam-7074	137	17	valued	value	VERB
ejpam-7074	137	18	intuitionistic	intuitionistic	ADJ
ejpam-7074	137	19	fuzzy	fuzzy	ADJ
ejpam-7074	137	20	sheffer	sheffer	NOUN
ejpam-7074	137	21	stroke	stroke	NOUN
ejpam-7074	137	22	subalgebra	subalgebra	NOUN
ejpam-7074	137	23	(	(	PUNCT
ejpam-7074	137	24	ivifss	ivifss	NOUN
ejpam-7074	137	25	-	-	PUNCT
ejpam-7074	137	26	subalgebra	subalgebra	NOUN
ejpam-7074	137	27	)	)	PUNCT
ejpam-7074	137	28	of	of	ADP
ejpam-7074	137	29	sh	sh	PRON
ejpam-7074	137	30	if	if	SCONJ
ejpam-7074	137	31	(	(	PUNCT
ejpam-7074	137	32	∀d	∀d	PROPN
ejpam-7074	137	33	,	,	PUNCT
ejpam-7074	137	34	g	g	PROPN
ejpam-7074	137	35	∈	∈	PROPN
ejpam-7074	137	36	sh	sh	PROPN
ejpam-7074	137	37	)	)	PUNCT
ejpam-7074	137	38	(	(	PUNCT
ejpam-7074	137	39	µa(d	µa(d	PUNCT
ejpam-7074	137	40	g	g	NOUN
ejpam-7074	137	41	|	|	NOUN
ejpam-7074	137	42	dg	dg	PROPN
ejpam-7074	137	43	)	)	PUNCT
ejpam-7074	137	44	≥	≥	NOUN
ejpam-7074	137	45	rmin{µa(d	rmin{µa(d	ADV
ejpam-7074	137	46	)	)	PUNCT
ejpam-7074	137	47	,	,	PUNCT
ejpam-7074	137	48	µa(g	µa(g	NOUN
ejpam-7074	137	49	)	)	PUNCT
ejpam-7074	137	50	}	}	PUNCT
ejpam-7074	137	51	γa(d	γa(d	NUM
ejpam-7074	137	52	g	g	PROPN
ejpam-7074	137	53	|	|	ADV
ejpam-7074	137	54	dg	dg	PROPN
ejpam-7074	137	55	)	)	PUNCT
ejpam-7074	137	56	≤	≤	NUM
ejpam-7074	137	57	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	137	58	)	)	PUNCT
ejpam-7074	137	59	,	,	PUNCT
ejpam-7074	137	60	γa(g	γa(g	ADP
ejpam-7074	137	61	)	)	PUNCT
ejpam-7074	137	62	}	}	PUNCT
ejpam-7074	137	63	)	)	PUNCT
ejpam-7074	137	64	.	.	PUNCT
ejpam-7074	138	1	(	(	PUNCT
ejpam-7074	138	2	2	2	X
ejpam-7074	138	3	)	)	PUNCT
ejpam-7074	138	4	proposition	proposition	NOUN
ejpam-7074	138	5	2	2	NUM
ejpam-7074	138	6	.	.	PUNCT
ejpam-7074	139	1	let	let	VERB
ejpam-7074	139	2	sh	sh	NOUN
ejpam-7074	139	3	:	:	PUNCT
ejpam-7074	139	4	=	=	SYM
ejpam-7074	139	5	(	(	PUNCT
ejpam-7074	139	6	sh	sh	INTJ
ejpam-7074	139	7	,	,	PUNCT
ejpam-7074	139	8	|	|	ADV
ejpam-7074	139	9	,	,	PUNCT
ejpam-7074	139	10	0	0	NUM
ejpam-7074	139	11	)	)	PUNCT
ejpam-7074	139	12	be	be	AUX
ejpam-7074	139	13	an	an	DET
ejpam-7074	139	14	ssha	ssha	NOUN
ejpam-7074	139	15	.	.	PUNCT
ejpam-7074	140	1	every	every	DET
ejpam-7074	140	2	ivifss	ivifss	ADJ
ejpam-7074	140	3	-	-	PUNCT
ejpam-7074	140	4	subalgebra	subalgebra	VERB
ejpam-7074	140	5	a	a	PRON
ejpam-7074	140	6	=	=	SYM
ejpam-7074	140	7	(	(	PUNCT
ejpam-7074	140	8	µa	µa	PROPN
ejpam-7074	140	9	,	,	PUNCT
ejpam-7074	140	10	γa	γa	PROPN
ejpam-7074	140	11	)	)	PUNCT
ejpam-7074	140	12	of	of	ADP
ejpam-7074	140	13	sh	sh	PROPN
ejpam-7074	140	14	satisfies	satisfie	NOUN
ejpam-7074	140	15	(	(	PUNCT
ejpam-7074	140	16	∀d	∀d	X
ejpam-7074	140	17	∈	∈	PROPN
ejpam-7074	140	18	sh	sh	PROPN
ejpam-7074	140	19	)	)	PUNCT
ejpam-7074	140	20	(	(	PUNCT
ejpam-7074	140	21	µa(0	µa(0	NOUN
ejpam-7074	140	22	)	)	PUNCT
ejpam-7074	140	23	≥	≥	NOUN
ejpam-7074	140	24	µa(d	µa(d	PUNCT
ejpam-7074	140	25	)	)	PUNCT
ejpam-7074	140	26	γa(0	γa(0	NOUN
ejpam-7074	140	27	)	)	PUNCT
ejpam-7074	140	28	≤	≤	NOUN
ejpam-7074	140	29	γa(d	γa(d	NUM
ejpam-7074	140	30	)	)	PUNCT
ejpam-7074	140	31	)	)	PUNCT
ejpam-7074	140	32	.	.	PUNCT
ejpam-7074	141	1	(	(	PUNCT
ejpam-7074	141	2	3	3	X
ejpam-7074	141	3	)	)	PUNCT
ejpam-7074	141	4	proof	proof	NOUN
ejpam-7074	141	5	.	.	PUNCT
ejpam-7074	142	1	for	for	ADP
ejpam-7074	142	2	any	any	DET
ejpam-7074	142	3	d	d	PROPN
ejpam-7074	142	4	∈	∈	PROPN
ejpam-7074	142	5	sh	sh	INTJ
ejpam-7074	142	6	,	,	PUNCT
ejpam-7074	142	7	we	we	PRON
ejpam-7074	142	8	have	have	VERB
ejpam-7074	142	9	µa(0	µa(0	NOUN
ejpam-7074	142	10	)	)	PUNCT
ejpam-7074	142	11	=	=	SYM
ejpam-7074	142	12	µa(d	µa(d	PUNCT
ejpam-7074	143	1	d	d	NOUN
ejpam-7074	143	2	|	|	ADV
ejpam-7074	143	3	dd	dd	NOUN
ejpam-7074	143	4	)	)	PUNCT
ejpam-7074	143	5	≥	≥	NOUN
ejpam-7074	143	6	rmin{µa(d	rmin{µa(d	ADV
ejpam-7074	143	7	)	)	PUNCT
ejpam-7074	143	8	,	,	PUNCT
ejpam-7074	143	9	µa(d	µa(d	PUNCT
ejpam-7074	143	10	)	)	PUNCT
ejpam-7074	143	11	}	}	PUNCT
ejpam-7074	143	12	=	=	SYM
ejpam-7074	144	1	rmin{[µl	rmin{[µl	PROPN
ejpam-7074	144	2	a(d	a(d	PROPN
ejpam-7074	144	3	)	)	PUNCT
ejpam-7074	144	4	,	,	PUNCT
ejpam-7074	144	5	µ	µ	X
ejpam-7074	144	6	u	u	PRON
ejpam-7074	144	7	a(d	a(d	PROPN
ejpam-7074	144	8	)	)	PUNCT
ejpam-7074	144	9	]	]	PUNCT
ejpam-7074	144	10	,	,	PUNCT
ejpam-7074	145	1	[	[	X
ejpam-7074	145	2	µ	µ	X
ejpam-7074	145	3	l	l	NOUN
ejpam-7074	145	4	a(d	a(d	PROPN
ejpam-7074	145	5	)	)	PUNCT
ejpam-7074	145	6	,	,	PUNCT
ejpam-7074	145	7	µ	µ	X
ejpam-7074	145	8	u	u	PRON
ejpam-7074	145	9	a(d	a(d	PROPN
ejpam-7074	145	10	)	)	PUNCT
ejpam-7074	146	1	]	]	PUNCT
ejpam-7074	146	2	}	}	PUNCT
ejpam-7074	146	3	=	=	PUNCT
ejpam-7074	147	1	[	[	X
ejpam-7074	147	2	µl	µl	ADP
ejpam-7074	147	3	a(d	a(d	NOUN
ejpam-7074	147	4	)	)	PUNCT
ejpam-7074	147	5	,	,	PUNCT
ejpam-7074	147	6	µ	µ	X
ejpam-7074	147	7	u	u	PRON
ejpam-7074	147	8	a(d	a(d	NOUN
ejpam-7074	147	9	)	)	PUNCT
ejpam-7074	147	10	]	]	PUNCT
ejpam-7074	147	11	=	=	SYM
ejpam-7074	147	12	µa(d	µa(d	X
ejpam-7074	147	13	)	)	PUNCT
ejpam-7074	147	14	a.	a.	NOUN
ejpam-7074	147	15	iampan	iampan	NOUN
ejpam-7074	147	16	et	et	PROPN
ejpam-7074	147	17	al	al	PROPN
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ejpam-7074	147	19	/	/	SYM
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ejpam-7074	148	2	pure	pure	PROPN
ejpam-7074	148	3	appl	appl	PROPN
ejpam-7074	148	4	.	.	PROPN
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ejpam-7074	148	6	,	,	PUNCT
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ejpam-7074	148	8	(	(	PUNCT
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ejpam-7074	148	10	)	)	PUNCT
ejpam-7074	148	11	(	(	PUNCT
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ejpam-7074	148	14	,	,	PUNCT
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ejpam-7074	148	21	)	)	PUNCT
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ejpam-7074	148	30	)	)	PUNCT
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ejpam-7074	148	33	)	)	PUNCT
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ejpam-7074	148	37	)	)	PUNCT
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ejpam-7074	148	42	,	,	PUNCT
ejpam-7074	149	1	[	[	X
ejpam-7074	149	2	γla(d	γla(d	NOUN
ejpam-7074	149	3	)	)	PUNCT
ejpam-7074	149	4	,	,	PUNCT
ejpam-7074	149	5	γua(d	γua(d	PROPN
ejpam-7074	149	6	)	)	PUNCT
ejpam-7074	149	7	]	]	PUNCT
ejpam-7074	149	8	}	}	PUNCT
ejpam-7074	149	9	=	=	PUNCT
ejpam-7074	150	1	[	[	X
ejpam-7074	150	2	γla(d	γla(d	NUM
ejpam-7074	150	3	)	)	PUNCT
ejpam-7074	150	4	,	,	PUNCT
ejpam-7074	150	5	γ	γ	X
ejpam-7074	150	6	u	u	NOUN
ejpam-7074	150	7	a(d	a(d	PROPN
ejpam-7074	150	8	)	)	PUNCT
ejpam-7074	150	9	]	]	PUNCT
ejpam-7074	151	1	=	=	SYM
ejpam-7074	151	2	γa(d	γa(d	X
ejpam-7074	151	3	)	)	PUNCT
ejpam-7074	151	4	.	.	PUNCT
ejpam-7074	152	1	proposition	proposition	NOUN
ejpam-7074	152	2	3	3	X
ejpam-7074	152	3	.	.	PUNCT
ejpam-7074	153	1	let	let	VERB
ejpam-7074	153	2	sh	sh	NOUN
ejpam-7074	153	3	:	:	PUNCT
ejpam-7074	153	4	=	=	SYM
ejpam-7074	153	5	(	(	PUNCT
ejpam-7074	153	6	sh	sh	INTJ
ejpam-7074	153	7	,	,	PUNCT
ejpam-7074	153	8	|	|	ADV
ejpam-7074	153	9	,	,	PUNCT
ejpam-7074	153	10	0	0	NUM
ejpam-7074	153	11	)	)	PUNCT
ejpam-7074	153	12	be	be	AUX
ejpam-7074	153	13	an	an	DET
ejpam-7074	153	14	ssha	ssha	NOUN
ejpam-7074	153	15	.	.	PUNCT
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ejpam-7074	154	2	ivifss	ivifss	ADJ
ejpam-7074	154	3	-	-	PUNCT
ejpam-7074	154	4	subalgebra	subalgebra	VERB
ejpam-7074	154	5	a	a	PRON
ejpam-7074	154	6	=	=	SYM
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ejpam-7074	154	8	µa	µa	PROPN
ejpam-7074	154	9	,	,	PUNCT
ejpam-7074	154	10	γa	γa	PROPN
ejpam-7074	154	11	)	)	PUNCT
ejpam-7074	154	12	of	of	ADP
ejpam-7074	154	13	sh	sh	PROPN
ejpam-7074	154	14	satisfies	satisfy	VERB
ejpam-7074	154	15	the	the	DET
ejpam-7074	154	16	following	following	NOUN
ejpam-7074	154	17	:	:	PUNCT
ejpam-7074	154	18	(	(	PUNCT
ejpam-7074	154	19	∀d	∀d	PROPN
ejpam-7074	154	20	,	,	PUNCT
ejpam-7074	154	21	g	g	PROPN
ejpam-7074	154	22	∈	∈	PROPN
ejpam-7074	154	23	sh	sh	PROPN
ejpam-7074	154	24	)	)	PUNCT
ejpam-7074	154	25	(	(	PUNCT
ejpam-7074	154	26	µa(d	µa(d	PUNCT
ejpam-7074	154	27	g	g	NOUN
ejpam-7074	154	28	|	|	NOUN
ejpam-7074	154	29	dg	dg	PROPN
ejpam-7074	154	30	)	)	PUNCT
ejpam-7074	154	31	≥	≥	NOUN
ejpam-7074	154	32	µa(g	µa(g	PUNCT
ejpam-7074	154	33	)	)	PUNCT
ejpam-7074	154	34	γa(d	γa(d	X
ejpam-7074	154	35	g	g	PROPN
ejpam-7074	154	36	|	|	ADV
ejpam-7074	154	37	dg	dg	PROPN
ejpam-7074	154	38	)	)	PUNCT
ejpam-7074	154	39	≤	≤	NOUN
ejpam-7074	154	40	γa(g	γa(g	ADP
ejpam-7074	154	41	)	)	PUNCT
ejpam-7074	154	42	)	)	PUNCT
ejpam-7074	155	1	(	(	PUNCT
ejpam-7074	155	2	4	4	X
ejpam-7074	155	3	)	)	PUNCT
ejpam-7074	155	4	if	if	SCONJ
ejpam-7074	155	5	and	and	CCONJ
ejpam-7074	155	6	only	only	ADV
ejpam-7074	155	7	if	if	SCONJ
ejpam-7074	155	8	µa(0	µa(0	NOUN
ejpam-7074	155	9	)	)	PUNCT
ejpam-7074	155	10	=	=	NOUN
ejpam-7074	155	11	µa(d	µa(d	X
ejpam-7074	155	12	)	)	PUNCT
ejpam-7074	155	13	and	and	CCONJ
ejpam-7074	155	14	γa(0	γa(0	NOUN
ejpam-7074	155	15	)	)	PUNCT
ejpam-7074	155	16	=	=	NOUN
ejpam-7074	155	17	γa(d	γa(d	X
ejpam-7074	155	18	)	)	PUNCT
ejpam-7074	155	19	for	for	ADP
ejpam-7074	155	20	all	all	DET
ejpam-7074	155	21	d	d	PROPN
ejpam-7074	155	22	∈	∈	PROPN
ejpam-7074	155	23	sh	sh	INTJ
ejpam-7074	155	24	.	.	PUNCT
ejpam-7074	156	1	proof	proof	NOUN
ejpam-7074	156	2	.	.	PUNCT
ejpam-7074	157	1	let	let	VERB
ejpam-7074	158	1	d	d	X
ejpam-7074	158	2	∈	∈	PROPN
ejpam-7074	158	3	sh	sh	INTJ
ejpam-7074	158	4	.	.	PUNCT
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ejpam-7074	159	2	µa(d	µa(d	PUNCT
ejpam-7074	159	3	)	)	PUNCT
ejpam-7074	159	4	=	=	PUNCT
ejpam-7074	159	5	µa((d|0)|(d|0	µa((d|0)|(d|0	NUM
ejpam-7074	159	6	)	)	PUNCT
ejpam-7074	159	7	)	)	PUNCT
ejpam-7074	160	1	=	=	SYM
ejpam-7074	160	2	µa(d	µa(d	X
ejpam-7074	160	3	0	0	NUM
ejpam-7074	160	4	|	|	CCONJ
ejpam-7074	160	5	d0	d0	NOUN
ejpam-7074	160	6	)	)	PUNCT
ejpam-7074	160	7	≥	≥	NOUN
ejpam-7074	160	8	µa(0	µa(0	NOUN
ejpam-7074	160	9	)	)	PUNCT
ejpam-7074	160	10	and	and	CCONJ
ejpam-7074	160	11	γa(d	γa(d	NUM
ejpam-7074	160	12	)	)	PUNCT
ejpam-7074	161	1	=	=	PUNCT
ejpam-7074	161	2	γa((d|0)|(d|0	γa((d|0)|(d|0	PROPN
ejpam-7074	161	3	)	)	PUNCT
ejpam-7074	161	4	)	)	PUNCT
ejpam-7074	162	1	=	=	SYM
ejpam-7074	162	2	γa(d	γa(d	PUNCT
ejpam-7074	162	3	0	0	NUM
ejpam-7074	162	4	|	|	CCONJ
ejpam-7074	162	5	d0	d0	NOUN
ejpam-7074	162	6	)	)	PUNCT
ejpam-7074	162	7	≤	≤	NUM
ejpam-7074	162	8	γa(0	γa(0	NOUN
ejpam-7074	162	9	)	)	PUNCT
ejpam-7074	162	10	.	.	PUNCT
ejpam-7074	163	1	then	then	ADV
ejpam-7074	163	2	by	by	ADP
ejpam-7074	163	3	proposition	proposition	NOUN
ejpam-7074	163	4	2	2	NUM
ejpam-7074	163	5	,	,	PUNCT
ejpam-7074	163	6	µa(0	µa(0	NOUN
ejpam-7074	163	7	)	)	PUNCT
ejpam-7074	163	8	=	=	NOUN
ejpam-7074	163	9	µa(d	µa(d	X
ejpam-7074	163	10	)	)	PUNCT
ejpam-7074	163	11	and	and	CCONJ
ejpam-7074	163	12	γa(0	γa(0	NOUN
ejpam-7074	163	13	)	)	PUNCT
ejpam-7074	163	14	=	=	NOUN
ejpam-7074	163	15	γa(d	γa(d	X
ejpam-7074	163	16	)	)	PUNCT
ejpam-7074	163	17	.	.	PUNCT
ejpam-7074	164	1	the	the	DET
ejpam-7074	164	2	converse	converse	NOUN
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ejpam-7074	164	4	clear	clear	ADJ
ejpam-7074	164	5	.	.	PUNCT
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ejpam-7074	165	2	1	1	X
ejpam-7074	165	3	.	.	PUNCT
ejpam-7074	166	1	let	let	VERB
ejpam-7074	166	2	sh	sh	NOUN
ejpam-7074	166	3	:	:	PUNCT
ejpam-7074	166	4	=	=	SYM
ejpam-7074	166	5	(	(	PUNCT
ejpam-7074	166	6	sh	sh	INTJ
ejpam-7074	166	7	,	,	PUNCT
ejpam-7074	166	8	|	|	ADV
ejpam-7074	166	9	,	,	PUNCT
ejpam-7074	166	10	0	0	NUM
ejpam-7074	166	11	)	)	PUNCT
ejpam-7074	166	12	be	be	AUX
ejpam-7074	166	13	an	an	DET
ejpam-7074	166	14	ssha	ssha	NOUN
ejpam-7074	166	15	.	.	PUNCT
ejpam-7074	167	1	an	an	DET
ejpam-7074	167	2	ivifs	ivifs	PROPN
ejpam-7074	167	3	a	a	PRON
ejpam-7074	167	4	=	=	X
ejpam-7074	167	5	(	(	PUNCT
ejpam-7074	167	6	[	[	X
ejpam-7074	167	7	µl	µl	ADP
ejpam-7074	167	8	a	a	PRON
ejpam-7074	167	9	,	,	PUNCT
ejpam-7074	167	10	µ	µ	X
ejpam-7074	167	11	u	u	NOUN
ejpam-7074	167	12	a	a	X
ejpam-7074	167	13	]	]	X
ejpam-7074	167	14	,	,	PUNCT
ejpam-7074	167	15	[	[	X
ejpam-7074	167	16	γ	γ	X
ejpam-7074	167	17	l	l	NOUN
ejpam-7074	167	18	a	a	X
ejpam-7074	167	19	,	,	PUNCT
ejpam-7074	167	20	γ	γ	X
ejpam-7074	167	21	u	u	NOUN
ejpam-7074	167	22	a	a	X
ejpam-7074	167	23	]	]	X
ejpam-7074	167	24	)	)	PUNCT
ejpam-7074	167	25	in	in	ADP
ejpam-7074	167	26	sh	sh	PROPN
ejpam-7074	167	27	is	be	AUX
ejpam-7074	167	28	an	an	DET
ejpam-7074	167	29	ivifss	ivifss	ADJ
ejpam-7074	167	30	-	-	PUNCT
ejpam-7074	167	31	subalgebra	subalgebra	NOUN
ejpam-7074	167	32	of	of	ADP
ejpam-7074	167	33	sh	sh	PRON
ejpam-7074	167	34	if	if	SCONJ
ejpam-7074	168	1	and	and	CCONJ
ejpam-7074	168	2	only	only	ADV
ejpam-7074	168	3	if	if	SCONJ
ejpam-7074	168	4	µl	µl	ADP
ejpam-7074	168	5	a	a	DET
ejpam-7074	168	6	,	,	PUNCT
ejpam-7074	168	7	µ	µ	X
ejpam-7074	168	8	u	u	NOUN
ejpam-7074	168	9	a	a	NOUN
ejpam-7074	168	10	,	,	PUNCT
ejpam-7074	168	11	γ	γ	X
ejpam-7074	168	12	l	l	NOUN
ejpam-7074	168	13	a	a	NOUN
ejpam-7074	168	14	and	and	CCONJ
ejpam-7074	168	15	γua	γua	NOUN
ejpam-7074	168	16	are	be	AUX
ejpam-7074	168	17	fuzzy	fuzzy	ADJ
ejpam-7074	168	18	subalgebras	subalgebra	NOUN
ejpam-7074	168	19	of	of	ADP
ejpam-7074	168	20	sh	sh	PROPN
ejpam-7074	168	21	.	.	PUNCT
ejpam-7074	169	1	proof	proof	NOUN
ejpam-7074	169	2	.	.	PUNCT
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ejpam-7074	170	2	µl	µl	ADP
ejpam-7074	170	3	a	a	PRON
ejpam-7074	170	4	and	and	CCONJ
ejpam-7074	170	5	µu	µu	AUX
ejpam-7074	170	6	a	a	PRON
ejpam-7074	170	7	be	be	AUX
ejpam-7074	170	8	fuzzy	fuzzy	ADJ
ejpam-7074	170	9	subalgebras	subalgebra	NOUN
ejpam-7074	170	10	of	of	ADP
ejpam-7074	170	11	sh	sh	PROPN
ejpam-7074	170	12	and	and	CCONJ
ejpam-7074	170	13	d	d	PROPN
ejpam-7074	170	14	,	,	PUNCT
ejpam-7074	170	15	g	g	PROPN
ejpam-7074	170	16	∈	∈	PROPN
ejpam-7074	171	1	sh	sh	INTJ
ejpam-7074	171	2	.	.	PUNCT
ejpam-7074	172	1	then	then	ADV
ejpam-7074	172	2	µl	µl	ADP
ejpam-7074	172	3	a(d	a(d	PROPN
ejpam-7074	172	4	g	g	PROPN
ejpam-7074	172	5	|	|	ADV
ejpam-7074	172	6	dg	dg	PROPN
ejpam-7074	172	7	)	)	PUNCT
ejpam-7074	172	8	≥	≥	PROPN
ejpam-7074	172	9	min{µl	min{µl	NOUN
ejpam-7074	172	10	a(d	a(d	PROPN
ejpam-7074	172	11	)	)	PUNCT
ejpam-7074	172	12	,	,	PUNCT
ejpam-7074	172	13	µ	µ	X
ejpam-7074	172	14	l	l	NOUN
ejpam-7074	172	15	a(g	a(g	PROPN
ejpam-7074	172	16	)	)	PUNCT
ejpam-7074	172	17	}	}	PUNCT
ejpam-7074	172	18	and	and	CCONJ
ejpam-7074	172	19	µu	µu	ADP
ejpam-7074	172	20	a(d	a(d	PROPN
ejpam-7074	172	21	g	g	PROPN
ejpam-7074	172	22	|	|	NOUN
ejpam-7074	172	23	dg	dg	PROPN
ejpam-7074	172	24	)	)	PUNCT
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ejpam-7074	172	26	min{µu	min{µu	PUNCT
ejpam-7074	172	27	a(d	a(d	PROPN
ejpam-7074	172	28	)	)	PUNCT
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ejpam-7074	172	32	a(g	a(g	PROPN
ejpam-7074	172	33	)	)	PUNCT
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ejpam-7074	172	35	.	.	PUNCT
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ejpam-7074	173	4	g	g	NOUN
ejpam-7074	173	5	|	|	NOUN
ejpam-7074	173	6	dg	dg	PRON
ejpam-7074	173	7	)	)	PUNCT
ejpam-7074	173	8	=	=	PUNCT
ejpam-7074	174	1	[	[	X
ejpam-7074	174	2	µl	µl	ADP
ejpam-7074	174	3	a(d	a(d	PROPN
ejpam-7074	174	4	g	g	PROPN
ejpam-7074	174	5	|	|	ADV
ejpam-7074	174	6	dg	dg	PROPN
ejpam-7074	174	7	)	)	PUNCT
ejpam-7074	174	8	,	,	PUNCT
ejpam-7074	174	9	µu	µu	ADP
ejpam-7074	174	10	a(d	a(d	PROPN
ejpam-7074	174	11	g	g	PROPN
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ejpam-7074	174	17	[	[	X
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ejpam-7074	174	19	a(d	a(d	NOUN
ejpam-7074	174	20	)	)	PUNCT
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ejpam-7074	174	25	a(d	a(d	PROPN
ejpam-7074	174	26	)	)	PUNCT
ejpam-7074	174	27	,	,	PUNCT
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ejpam-7074	174	29	u	u	NOUN
ejpam-7074	174	30	a(g	a(g	PROPN
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ejpam-7074	175	4	)	)	PUNCT
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ejpam-7074	175	9	)	)	PUNCT
ejpam-7074	175	10	]	]	PUNCT
ejpam-7074	175	11	,	,	PUNCT
ejpam-7074	176	1	[	[	X
ejpam-7074	176	2	µ	µ	X
ejpam-7074	176	3	l	l	NOUN
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ejpam-7074	176	5	)	)	PUNCT
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ejpam-7074	176	7	µ	µ	X
ejpam-7074	176	8	u	u	NOUN
ejpam-7074	176	9	a(g	a(g	PROPN
ejpam-7074	176	10	)	)	PUNCT
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ejpam-7074	176	12	}	}	PUNCT
ejpam-7074	176	13	=	=	PUNCT
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ejpam-7074	176	15	)	)	PUNCT
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ejpam-7074	176	17	µa(g	µa(g	NOUN
ejpam-7074	176	18	)	)	PUNCT
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ejpam-7074	178	3	appl	appl	PROPN
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ejpam-7074	178	8	(	(	PUNCT
ejpam-7074	178	9	4	4	NUM
ejpam-7074	178	10	)	)	PUNCT
ejpam-7074	178	11	(	(	PUNCT
ejpam-7074	178	12	2025	2025	NUM
ejpam-7074	178	13	)	)	PUNCT
ejpam-7074	178	14	,	,	PUNCT
ejpam-7074	178	15	7074	7074	NUM
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ejpam-7074	178	18	14	14	NUM
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ejpam-7074	180	4	|	|	NOUN
ejpam-7074	180	5	dg	dg	PROPN
ejpam-7074	180	6	)	)	PUNCT
ejpam-7074	180	7	≤	≤	NOUN
ejpam-7074	180	8	max{γla(d	max{γla(d	PROPN
ejpam-7074	180	9	)	)	PUNCT
ejpam-7074	180	10	,	,	PUNCT
ejpam-7074	180	11	γla(g	γla(g	PROPN
ejpam-7074	180	12	)	)	PUNCT
ejpam-7074	180	13	}	}	PUNCT
ejpam-7074	180	14	and	and	CCONJ
ejpam-7074	180	15	γua(d	γua(d	PROPN
ejpam-7074	181	1	g	g	NOUN
ejpam-7074	181	2	|	|	NOUN
ejpam-7074	181	3	dg	dg	PROPN
ejpam-7074	181	4	)	)	PUNCT
ejpam-7074	181	5	≤	≤	PROPN
ejpam-7074	181	6	max{γua(d	max{γua(d	PROPN
ejpam-7074	181	7	)	)	PUNCT
ejpam-7074	181	8	,	,	PUNCT
ejpam-7074	181	9	γua(g	γua(g	PROPN
ejpam-7074	181	10	)	)	PUNCT
ejpam-7074	181	11	}	}	PUNCT
ejpam-7074	181	12	.	.	PUNCT
ejpam-7074	182	1	now	now	ADV
ejpam-7074	182	2	,	,	PUNCT
ejpam-7074	182	3	γa(d	γa(d	PROPN
ejpam-7074	182	4	g	g	PROPN
ejpam-7074	182	5	|	|	ADV
ejpam-7074	182	6	dg	dg	PROPN
ejpam-7074	182	7	)	)	PUNCT
ejpam-7074	182	8	=	=	PUNCT
ejpam-7074	183	1	[	[	PUNCT
ejpam-7074	183	2	γla(d	γla(d	NUM
ejpam-7074	183	3	g	g	NOUN
ejpam-7074	183	4	|	|	ADV
ejpam-7074	183	5	dg	dg	PROPN
ejpam-7074	183	6	)	)	PUNCT
ejpam-7074	183	7	,	,	PUNCT
ejpam-7074	183	8	γua(dg	γua(dg	PROPN
ejpam-7074	183	9	|	|	ADV
ejpam-7074	183	10	dg	dg	VERB
ejpam-7074	183	11	)	)	PUNCT
ejpam-7074	183	12	]	]	PUNCT
ejpam-7074	184	1	≤	≤	NOUN
ejpam-7074	185	1	[	[	X
ejpam-7074	185	2	max{γla(d	max{γla(d	PROPN
ejpam-7074	185	3	)	)	PUNCT
ejpam-7074	185	4	,	,	PUNCT
ejpam-7074	185	5	γla(g)},max{γua(d	γla(g)},max{γua(d	PROPN
ejpam-7074	185	6	)	)	PUNCT
ejpam-7074	185	7	,	,	PUNCT
ejpam-7074	185	8	γua(g	γua(g	PROPN
ejpam-7074	185	9	)	)	PUNCT
ejpam-7074	185	10	}	}	PUNCT
ejpam-7074	185	11	]	]	PUNCT
ejpam-7074	185	12	=	=	PUNCT
ejpam-7074	185	13	rmax{[γla(d	rmax{[γla(d	PROPN
ejpam-7074	185	14	)	)	PUNCT
ejpam-7074	185	15	,	,	PUNCT
ejpam-7074	185	16	γua(d	γua(d	PROPN
ejpam-7074	185	17	)	)	PUNCT
ejpam-7074	185	18	]	]	PUNCT
ejpam-7074	185	19	,	,	PUNCT
ejpam-7074	186	1	[	[	X
ejpam-7074	186	2	γla(g	γla(g	PROPN
ejpam-7074	186	3	)	)	PUNCT
ejpam-7074	186	4	,	,	PUNCT
ejpam-7074	186	5	γua(g	γua(g	PROPN
ejpam-7074	186	6	)	)	PUNCT
ejpam-7074	186	7	]	]	PUNCT
ejpam-7074	186	8	}	}	PUNCT
ejpam-7074	186	9	=	=	SYM
ejpam-7074	186	10	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	186	11	)	)	PUNCT
ejpam-7074	186	12	,	,	PUNCT
ejpam-7074	186	13	γa(g	γa(g	ADP
ejpam-7074	186	14	)	)	PUNCT
ejpam-7074	186	15	}	}	PUNCT
ejpam-7074	186	16	.	.	PUNCT
ejpam-7074	187	1	hence	hence	ADV
ejpam-7074	187	2	,	,	PUNCT
ejpam-7074	187	3	a	a	DET
ejpam-7074	187	4	=	=	X
ejpam-7074	187	5	(	(	PUNCT
ejpam-7074	187	6	[	[	X
ejpam-7074	187	7	µl	µl	ADP
ejpam-7074	187	8	a	a	PRON
ejpam-7074	187	9	,	,	PUNCT
ejpam-7074	187	10	µ	µ	X
ejpam-7074	187	11	u	u	NOUN
ejpam-7074	187	12	a	a	X
ejpam-7074	187	13	]	]	X
ejpam-7074	187	14	,	,	PUNCT
ejpam-7074	187	15	[	[	X
ejpam-7074	187	16	γ	γ	X
ejpam-7074	187	17	l	l	NOUN
ejpam-7074	187	18	a	a	X
ejpam-7074	187	19	,	,	PUNCT
ejpam-7074	187	20	γ	γ	X
ejpam-7074	187	21	u	u	NOUN
ejpam-7074	187	22	a	a	X
ejpam-7074	187	23	]	]	X
ejpam-7074	187	24	)	)	PUNCT
ejpam-7074	187	25	is	be	AUX
ejpam-7074	187	26	an	an	DET
ejpam-7074	187	27	ivifss	ivifss	ADJ
ejpam-7074	187	28	-	-	PUNCT
ejpam-7074	187	29	subalgebra	subalgebra	NOUN
ejpam-7074	187	30	of	of	ADP
ejpam-7074	187	31	sh	sh	PROPN
ejpam-7074	187	32	.	.	PUNCT
ejpam-7074	188	1	conversely	conversely	ADV
ejpam-7074	188	2	,	,	PUNCT
ejpam-7074	188	3	assume	assume	VERB
ejpam-7074	188	4	that	that	SCONJ
ejpam-7074	188	5	a	a	PRON
ejpam-7074	188	6	=	=	X
ejpam-7074	188	7	(	(	PUNCT
ejpam-7074	188	8	[	[	X
ejpam-7074	188	9	µl	µl	ADP
ejpam-7074	188	10	a	a	PRON
ejpam-7074	188	11	,	,	PUNCT
ejpam-7074	188	12	µ	µ	X
ejpam-7074	188	13	u	u	NOUN
ejpam-7074	188	14	a	a	X
ejpam-7074	188	15	]	]	X
ejpam-7074	188	16	,	,	PUNCT
ejpam-7074	188	17	[	[	X
ejpam-7074	188	18	γ	γ	X
ejpam-7074	188	19	l	l	NOUN
ejpam-7074	188	20	a	a	X
ejpam-7074	188	21	,	,	PUNCT
ejpam-7074	188	22	γ	γ	X
ejpam-7074	188	23	u	u	NOUN
ejpam-7074	188	24	a	a	X
ejpam-7074	188	25	]	]	X
ejpam-7074	188	26	)	)	PUNCT
ejpam-7074	188	27	is	be	AUX
ejpam-7074	188	28	an	an	DET
ejpam-7074	188	29	ivifss	ivifss	ADJ
ejpam-7074	188	30	-	-	PUNCT
ejpam-7074	188	31	subalgebra	subalgebra	NOUN
ejpam-7074	188	32	of	of	ADP
ejpam-7074	188	33	sh	sh	PROPN
ejpam-7074	188	34	.	.	PUNCT
ejpam-7074	189	1	for	for	ADP
ejpam-7074	189	2	any	any	DET
ejpam-7074	189	3	d	d	NOUN
ejpam-7074	189	4	,	,	PUNCT
ejpam-7074	189	5	g	g	PROPN
ejpam-7074	189	6	∈	∈	PROPN
ejpam-7074	189	7	sh	sh	INTJ
ejpam-7074	189	8	,	,	PUNCT
ejpam-7074	189	9	[	[	X
ejpam-7074	189	10	µl	µl	ADP
ejpam-7074	189	11	a(d	a(d	PROPN
ejpam-7074	189	12	g	g	PROPN
ejpam-7074	189	13	|	|	ADV
ejpam-7074	189	14	dg	dg	PROPN
ejpam-7074	189	15	)	)	PUNCT
ejpam-7074	189	16	,	,	PUNCT
ejpam-7074	189	17	µu	µu	ADP
ejpam-7074	189	18	a(d	a(d	PROPN
ejpam-7074	189	19	g	g	PROPN
ejpam-7074	189	20	|	|	ADV
ejpam-7074	189	21	dg	dg	PROPN
ejpam-7074	189	22	)	)	PUNCT
ejpam-7074	189	23	]	]	PUNCT
ejpam-7074	190	1	=	=	SYM
ejpam-7074	190	2	µa(d	µa(d	PUNCT
ejpam-7074	190	3	g	g	PROPN
ejpam-7074	190	4	|	|	NOUN
ejpam-7074	190	5	dg	dg	PROPN
ejpam-7074	190	6	)	)	PUNCT
ejpam-7074	190	7	≥	≥	NOUN
ejpam-7074	190	8	rmin{µa(d	rmin{µa(d	ADV
ejpam-7074	190	9	)	)	PUNCT
ejpam-7074	190	10	,	,	PUNCT
ejpam-7074	190	11	µa(g	µa(g	NOUN
ejpam-7074	190	12	)	)	PUNCT
ejpam-7074	190	13	}	}	PUNCT
ejpam-7074	190	14	=	=	SYM
ejpam-7074	191	1	rmin{[µl	rmin{[µl	PROPN
ejpam-7074	191	2	a(d	a(d	PROPN
ejpam-7074	191	3	)	)	PUNCT
ejpam-7074	191	4	,	,	PUNCT
ejpam-7074	191	5	µ	µ	X
ejpam-7074	191	6	u	u	PRON
ejpam-7074	191	7	a(d	a(d	PROPN
ejpam-7074	191	8	)	)	PUNCT
ejpam-7074	191	9	]	]	PUNCT
ejpam-7074	191	10	,	,	PUNCT
ejpam-7074	192	1	[	[	X
ejpam-7074	192	2	µ	µ	X
ejpam-7074	192	3	l	l	NOUN
ejpam-7074	192	4	a(g	a(g	PROPN
ejpam-7074	192	5	)	)	PUNCT
ejpam-7074	192	6	,	,	PUNCT
ejpam-7074	192	7	µ	µ	X
ejpam-7074	192	8	u	u	NOUN
ejpam-7074	192	9	a(g	a(g	PROPN
ejpam-7074	192	10	)	)	PUNCT
ejpam-7074	192	11	]	]	PUNCT
ejpam-7074	192	12	}	}	PUNCT
ejpam-7074	192	13	=	=	PUNCT
ejpam-7074	193	1	[	[	X
ejpam-7074	193	2	min{µl	min{µl	NOUN
ejpam-7074	193	3	a(d	a(d	NOUN
ejpam-7074	193	4	)	)	PUNCT
ejpam-7074	193	5	,	,	PUNCT
ejpam-7074	193	6	µ	µ	X
ejpam-7074	193	7	l	l	NOUN
ejpam-7074	193	8	a(g)},min{µu	a(g)},min{µu	PROPN
ejpam-7074	193	9	a(d	a(d	PROPN
ejpam-7074	193	10	)	)	PUNCT
ejpam-7074	193	11	,	,	PUNCT
ejpam-7074	193	12	µ	µ	X
ejpam-7074	193	13	u	u	NOUN
ejpam-7074	193	14	a(g	a(g	PROPN
ejpam-7074	193	15	)	)	PUNCT
ejpam-7074	193	16	}	}	PUNCT
ejpam-7074	193	17	]	]	PUNCT
ejpam-7074	193	18	,	,	PUNCT
ejpam-7074	193	19	and	and	CCONJ
ejpam-7074	193	20	[	[	X
ejpam-7074	193	21	γla(d	γla(d	NUM
ejpam-7074	193	22	g	g	NOUN
ejpam-7074	193	23	|	|	ADV
ejpam-7074	193	24	dg	dg	PROPN
ejpam-7074	193	25	)	)	PUNCT
ejpam-7074	193	26	,	,	PUNCT
ejpam-7074	193	27	γua(dg	γua(dg	PROPN
ejpam-7074	193	28	|	|	ADV
ejpam-7074	193	29	dg	dg	VERB
ejpam-7074	193	30	)	)	PUNCT
ejpam-7074	193	31	]	]	PUNCT
ejpam-7074	194	1	=	=	SYM
ejpam-7074	194	2	γa(d	γa(d	PUNCT
ejpam-7074	194	3	g	g	PROPN
ejpam-7074	194	4	|	|	ADV
ejpam-7074	194	5	dg	dg	PROPN
ejpam-7074	194	6	)	)	PUNCT
ejpam-7074	194	7	≤	≤	NUM
ejpam-7074	194	8	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	194	9	)	)	PUNCT
ejpam-7074	194	10	,	,	PUNCT
ejpam-7074	194	11	γa(g	γa(g	ADP
ejpam-7074	194	12	)	)	PUNCT
ejpam-7074	194	13	}	}	PUNCT
ejpam-7074	194	14	=	=	SYM
ejpam-7074	194	15	rmax{[γla(d	rmax{[γla(d	NUM
ejpam-7074	194	16	)	)	PUNCT
ejpam-7074	194	17	,	,	PUNCT
ejpam-7074	194	18	γua(d	γua(d	PROPN
ejpam-7074	194	19	)	)	PUNCT
ejpam-7074	194	20	]	]	PUNCT
ejpam-7074	194	21	,	,	PUNCT
ejpam-7074	194	22	[	[	X
ejpam-7074	194	23	γla(g	γla(g	PROPN
ejpam-7074	194	24	)	)	PUNCT
ejpam-7074	194	25	,	,	PUNCT
ejpam-7074	194	26	γua(g	γua(g	PROPN
ejpam-7074	194	27	)	)	PUNCT
ejpam-7074	194	28	]	]	PUNCT
ejpam-7074	194	29	}	}	PUNCT
ejpam-7074	194	30	=	=	PUNCT
ejpam-7074	195	1	[	[	X
ejpam-7074	195	2	max{γla(d	max{γla(d	PROPN
ejpam-7074	195	3	)	)	PUNCT
ejpam-7074	195	4	,	,	PUNCT
ejpam-7074	195	5	γla(g)},max{γua(d	γla(g)},max{γua(d	PROPN
ejpam-7074	195	6	)	)	PUNCT
ejpam-7074	195	7	,	,	PUNCT
ejpam-7074	195	8	γua(g	γua(g	PROPN
ejpam-7074	195	9	)	)	PUNCT
ejpam-7074	195	10	}	}	PUNCT
ejpam-7074	195	11	]	]	PUNCT
ejpam-7074	195	12	.	.	PUNCT
ejpam-7074	196	1	thus	thus	ADV
ejpam-7074	196	2	,	,	PUNCT
ejpam-7074	196	3	µl	µl	ADP
ejpam-7074	196	4	a(d	a(d	PROPN
ejpam-7074	196	5	g	g	PROPN
ejpam-7074	196	6	|	|	NOUN
ejpam-7074	196	7	dg	dg	PROPN
ejpam-7074	196	8	)	)	PUNCT
ejpam-7074	196	9	≥	≥	PROPN
ejpam-7074	196	10	min{µl	min{µl	NOUN
ejpam-7074	196	11	a(d	a(d	PROPN
ejpam-7074	196	12	)	)	PUNCT
ejpam-7074	196	13	,	,	PUNCT
ejpam-7074	196	14	µ	µ	X
ejpam-7074	196	15	l	l	NOUN
ejpam-7074	196	16	a(g	a(g	PROPN
ejpam-7074	196	17	)	)	PUNCT
ejpam-7074	196	18	}	}	PUNCT
ejpam-7074	196	19	,	,	PUNCT
ejpam-7074	196	20	µu	µu	ADP
ejpam-7074	196	21	a(d	a(d	PROPN
ejpam-7074	196	22	g	g	PROPN
ejpam-7074	196	23	|	|	NOUN
ejpam-7074	196	24	dg	dg	PROPN
ejpam-7074	196	25	)	)	PUNCT
ejpam-7074	196	26	≥	≥	PROPN
ejpam-7074	196	27	min{µu	min{µu	PROPN
ejpam-7074	196	28	a(d	a(d	PROPN
ejpam-7074	196	29	)	)	PUNCT
ejpam-7074	196	30	,	,	PUNCT
ejpam-7074	196	31	µ	µ	X
ejpam-7074	196	32	u	u	NOUN
ejpam-7074	196	33	a(g	a(g	PROPN
ejpam-7074	196	34	)	)	PUNCT
ejpam-7074	196	35	}	}	PUNCT
ejpam-7074	196	36	,	,	PUNCT
ejpam-7074	196	37	γla(dg	γla(dg	NUM
ejpam-7074	196	38	|	|	ADV
ejpam-7074	196	39	dg	dg	PROPN
ejpam-7074	196	40	)	)	PUNCT
ejpam-7074	196	41	≤	≤	PROPN
ejpam-7074	196	42	max{γla(d	max{γla(d	PROPN
ejpam-7074	196	43	)	)	PUNCT
ejpam-7074	196	44	,	,	PUNCT
ejpam-7074	196	45	γla(g	γla(g	PROPN
ejpam-7074	196	46	)	)	PUNCT
ejpam-7074	196	47	}	}	PUNCT
ejpam-7074	196	48	and	and	CCONJ
ejpam-7074	196	49	γua(d	γua(d	PROPN
ejpam-7074	197	1	g	g	NOUN
ejpam-7074	197	2	|	|	NOUN
ejpam-7074	197	3	dg	dg	PROPN
ejpam-7074	197	4	)	)	PUNCT
ejpam-7074	197	5	≤	≤	PROPN
ejpam-7074	197	6	max{γua(d	max{γua(d	PROPN
ejpam-7074	197	7	)	)	PUNCT
ejpam-7074	197	8	,	,	PUNCT
ejpam-7074	197	9	γua(g	γua(g	PROPN
ejpam-7074	197	10	)	)	PUNCT
ejpam-7074	197	11	}	}	PUNCT
ejpam-7074	197	12	.	.	PUNCT
ejpam-7074	198	1	therefore	therefore	ADV
ejpam-7074	198	2	,	,	PUNCT
ejpam-7074	198	3	µl	µl	ADP
ejpam-7074	198	4	a	a	DET
ejpam-7074	198	5	,	,	PUNCT
ejpam-7074	198	6	µ	µ	X
ejpam-7074	198	7	u	u	NOUN
ejpam-7074	198	8	a	a	NOUN
ejpam-7074	198	9	,	,	PUNCT
ejpam-7074	198	10	γ	γ	X
ejpam-7074	198	11	l	l	NOUN
ejpam-7074	198	12	a	a	NOUN
ejpam-7074	198	13	and	and	CCONJ
ejpam-7074	198	14	γua	γua	NOUN
ejpam-7074	198	15	are	be	AUX
ejpam-7074	198	16	fuzzy	fuzzy	ADJ
ejpam-7074	198	17	subalgebras	subalgebra	NOUN
ejpam-7074	198	18	of	of	ADP
ejpam-7074	198	19	sh	sh	PROPN
ejpam-7074	198	20	.	.	PUNCT
ejpam-7074	199	1	theorem	theorem	NOUN
ejpam-7074	199	2	2	2	NUM
ejpam-7074	199	3	.	.	PUNCT
ejpam-7074	200	1	let	let	VERB
ejpam-7074	200	2	sh	sh	NOUN
ejpam-7074	200	3	:	:	PUNCT
ejpam-7074	200	4	=	=	SYM
ejpam-7074	200	5	(	(	PUNCT
ejpam-7074	200	6	sh	sh	INTJ
ejpam-7074	200	7	,	,	PUNCT
ejpam-7074	200	8	|	|	ADV
ejpam-7074	200	9	,	,	PUNCT
ejpam-7074	200	10	0	0	NUM
ejpam-7074	200	11	)	)	PUNCT
ejpam-7074	200	12	be	be	AUX
ejpam-7074	200	13	an	an	DET
ejpam-7074	200	14	ssha	ssha	NOUN
ejpam-7074	200	15	.	.	PUNCT
ejpam-7074	201	1	if	if	SCONJ
ejpam-7074	201	2	a	a	PRON
ejpam-7074	201	3	=	=	X
ejpam-7074	201	4	(	(	PUNCT
ejpam-7074	201	5	µa	µa	PROPN
ejpam-7074	201	6	,	,	PUNCT
ejpam-7074	201	7	γa	γa	PROPN
ejpam-7074	201	8	)	)	PUNCT
ejpam-7074	201	9	and	and	CCONJ
ejpam-7074	201	10	b	b	X
ejpam-7074	201	11	=	=	SYM
ejpam-7074	201	12	(	(	PUNCT
ejpam-7074	201	13	µb	µb	PROPN
ejpam-7074	201	14	,	,	PUNCT
ejpam-7074	201	15	γb	γb	PROPN
ejpam-7074	201	16	)	)	PUNCT
ejpam-7074	201	17	are	be	AUX
ejpam-7074	201	18	ivifss	ivifss	ADJ
ejpam-7074	201	19	-	-	PUNCT
ejpam-7074	201	20	subalgebras	subalgebras	PROPN
ejpam-7074	201	21	of	of	ADP
ejpam-7074	201	22	sh	sh	PROPN
ejpam-7074	201	23	,	,	PUNCT
ejpam-7074	201	24	then	then	ADV
ejpam-7074	201	25	a	a	DET
ejpam-7074	201	26	∩b	∩b	NOUN
ejpam-7074	201	27	=	=	PUNCT
ejpam-7074	201	28	(	(	PUNCT
ejpam-7074	201	29	µa∩b	µa∩b	PROPN
ejpam-7074	201	30	,	,	PUNCT
ejpam-7074	201	31	γa∪b	γa∪b	ADJ
ejpam-7074	201	32	)	)	PUNCT
ejpam-7074	201	33	is	be	AUX
ejpam-7074	201	34	an	an	DET
ejpam-7074	201	35	ivifss	ivifss	ADJ
ejpam-7074	201	36	-	-	PUNCT
ejpam-7074	201	37	subalgebra	subalgebra	NOUN
ejpam-7074	201	38	of	of	ADP
ejpam-7074	201	39	sh	sh	PROPN
ejpam-7074	201	40	.	.	PUNCT
ejpam-7074	202	1	proof	proof	NOUN
ejpam-7074	202	2	.	.	PUNCT
ejpam-7074	203	1	let	let	VERB
ejpam-7074	203	2	d	d	X
ejpam-7074	203	3	,	,	PUNCT
ejpam-7074	203	4	g	g	PROPN
ejpam-7074	203	5	∈	∈	PROPN
ejpam-7074	203	6	a∩b	a∩b	PROPN
ejpam-7074	203	7	.	.	PUNCT
ejpam-7074	204	1	since	since	SCONJ
ejpam-7074	204	2	a	a	DET
ejpam-7074	204	3	=	=	SYM
ejpam-7074	204	4	(	(	PUNCT
ejpam-7074	204	5	µa	µa	PROPN
ejpam-7074	204	6	,	,	PUNCT
ejpam-7074	204	7	γa	γa	PROPN
ejpam-7074	204	8	)	)	PUNCT
ejpam-7074	204	9	and	and	CCONJ
ejpam-7074	204	10	b	b	X
ejpam-7074	204	11	=	=	SYM
ejpam-7074	204	12	(	(	PUNCT
ejpam-7074	204	13	µb	µb	PROPN
ejpam-7074	204	14	,	,	PUNCT
ejpam-7074	204	15	γb	γb	PROPN
ejpam-7074	204	16	)	)	PUNCT
ejpam-7074	204	17	are	be	AUX
ejpam-7074	204	18	ivifss	ivifss	ADJ
ejpam-7074	204	19	-	-	PUNCT
ejpam-7074	204	20	subalgebras	subalgebras	PROPN
ejpam-7074	204	21	of	of	ADP
ejpam-7074	204	22	sh	sh	PROPN
ejpam-7074	204	23	,	,	PUNCT
ejpam-7074	204	24	µa∩b(d	µa∩b(d	PROPN
ejpam-7074	204	25	g	g	PROPN
ejpam-7074	204	26	|	|	NOUN
ejpam-7074	204	27	dg	dg	PART
ejpam-7074	204	28	)	)	PUNCT
ejpam-7074	205	1	=	=	PUNCT
ejpam-7074	206	1	[	[	X
ejpam-7074	206	2	µl	µl	ADP
ejpam-7074	206	3	a∩b(d	a∩b(d	PROPN
ejpam-7074	206	4	g	g	ADP
ejpam-7074	206	5	|	|	ADV
ejpam-7074	206	6	dg	dg	PROPN
ejpam-7074	206	7	)	)	PUNCT
ejpam-7074	206	8	,	,	PUNCT
ejpam-7074	206	9	µu	µu	SCONJ
ejpam-7074	206	10	a∩b(d	a∩b(d	NOUN
ejpam-7074	206	11	g	g	ADP
ejpam-7074	206	12	|	|	ADV
ejpam-7074	206	13	dg	dg	PROPN
ejpam-7074	206	14	)	)	PUNCT
ejpam-7074	206	15	]	]	PUNCT
ejpam-7074	207	1	=	=	PUNCT
ejpam-7074	208	1	[	[	X
ejpam-7074	208	2	min{µl	min{µl	NOUN
ejpam-7074	208	3	a(d	a(d	PROPN
ejpam-7074	208	4	g	g	PROPN
ejpam-7074	208	5	|	|	ADV
ejpam-7074	208	6	dg	dg	PROPN
ejpam-7074	208	7	)	)	PUNCT
ejpam-7074	208	8	,	,	PUNCT
ejpam-7074	208	9	µl	µl	ADP
ejpam-7074	208	10	b(d	b(d	PROPN
ejpam-7074	208	11	g	g	NOUN
ejpam-7074	208	12	|	|	ADV
ejpam-7074	208	13	dg)},min{µu	dg)},min{µu	PROPN
ejpam-7074	208	14	a(d	a(d	PROPN
ejpam-7074	208	15	g	g	PROPN
ejpam-7074	208	16	|	|	ADV
ejpam-7074	208	17	dg	dg	PROPN
ejpam-7074	208	18	)	)	PUNCT
ejpam-7074	208	19	,	,	PUNCT
ejpam-7074	208	20	µu	µu	SCONJ
ejpam-7074	208	21	b(d	b(d	PROPN
ejpam-7074	208	22	g	g	PROPN
ejpam-7074	208	23	|	|	ADV
ejpam-7074	208	24	dg	dg	PROPN
ejpam-7074	208	25	)	)	PUNCT
ejpam-7074	208	26	}	}	PUNCT
ejpam-7074	208	27	]	]	PUNCT
ejpam-7074	208	28	≥	≥	X
ejpam-7074	208	29	[	[	X
ejpam-7074	208	30	min{µl	min{µl	NOUN
ejpam-7074	208	31	a∩b(d	a∩b(d	NOUN
ejpam-7074	208	32	)	)	PUNCT
ejpam-7074	208	33	,	,	PUNCT
ejpam-7074	208	34	µ	µ	X
ejpam-7074	208	35	l	l	NOUN
ejpam-7074	208	36	a∩b(g))},min{µu	a∩b(g))},min{µu	NUM
ejpam-7074	208	37	a∩b(d	a∩b(d	PROPN
ejpam-7074	208	38	)	)	PUNCT
ejpam-7074	208	39	,	,	PUNCT
ejpam-7074	208	40	µ	µ	X
ejpam-7074	208	41	u	u	NOUN
ejpam-7074	208	42	a∩b(g	a∩b(g	NOUN
ejpam-7074	208	43	)	)	PUNCT
ejpam-7074	208	44	)	)	PUNCT
ejpam-7074	208	45	}	}	PUNCT
ejpam-7074	208	46	]	]	PUNCT
ejpam-7074	209	1	=	=	PUNCT
ejpam-7074	209	2	rmin{µa∩b(d	rmin{µa∩b(d	NOUN
ejpam-7074	209	3	)	)	PUNCT
ejpam-7074	209	4	,	,	PUNCT
ejpam-7074	209	5	µa∩b(g	µa∩b(g	PROPN
ejpam-7074	209	6	)	)	PUNCT
ejpam-7074	209	7	}	}	PUNCT
ejpam-7074	209	8	and	and	CCONJ
ejpam-7074	209	9	γa∪b(d	γa∪b(d	PROPN
ejpam-7074	209	10	g	g	PROPN
ejpam-7074	209	11	|	|	ADV
ejpam-7074	209	12	dg	dg	PART
ejpam-7074	209	13	)	)	PUNCT
ejpam-7074	210	1	=	=	PUNCT
ejpam-7074	211	1	[	[	X
ejpam-7074	211	2	γla∪b(d	γla∪b(d	X
ejpam-7074	211	3	g	g	PROPN
ejpam-7074	211	4	|	|	ADV
ejpam-7074	211	5	dg	dg	PROPN
ejpam-7074	211	6	)	)	PUNCT
ejpam-7074	211	7	,	,	PUNCT
ejpam-7074	211	8	γua∪b(d	γua∪b(d	PROPN
ejpam-7074	211	9	g	g	ADP
ejpam-7074	211	10	|	|	ADV
ejpam-7074	211	11	dg	dg	PROPN
ejpam-7074	211	12	)	)	PUNCT
ejpam-7074	211	13	]	]	PUNCT
ejpam-7074	212	1	=	=	PUNCT
ejpam-7074	213	1	[	[	X
ejpam-7074	213	2	max{γla(dg	max{γla(dg	X
ejpam-7074	213	3	|	|	ADV
ejpam-7074	213	4	dg	dg	PROPN
ejpam-7074	213	5	)	)	PUNCT
ejpam-7074	213	6	,	,	PUNCT
ejpam-7074	213	7	γlb(dg	γlb(dg	PROPN
ejpam-7074	213	8	|	|	ADV
ejpam-7074	213	9	dg)},max{γua(dg	dg)},max{γua(dg	PROPN
ejpam-7074	213	10	|	|	ADV
ejpam-7074	213	11	dg	dg	VERB
ejpam-7074	213	12	)	)	PUNCT
ejpam-7074	213	13	,	,	PUNCT
ejpam-7074	213	14	γub(dg	γub(dg	PROPN
ejpam-7074	213	15	|	|	ADV
ejpam-7074	213	16	dg	dg	VERB
ejpam-7074	213	17	)	)	PUNCT
ejpam-7074	213	18	}	}	PUNCT
ejpam-7074	213	19	]	]	PUNCT
ejpam-7074	214	1	≤	≤	NOUN
ejpam-7074	215	1	[	[	X
ejpam-7074	215	2	max{γla∪b(d	max{γla∪b(d	NUM
ejpam-7074	215	3	)	)	PUNCT
ejpam-7074	215	4	,	,	PUNCT
ejpam-7074	215	5	γ	γ	PROPN
ejpam-7074	215	6	l	l	PROPN
ejpam-7074	215	7	a∪b(g)},max{γua∪b(d	a∪b(g)},max{γua∪b(d	PROPN
ejpam-7074	215	8	)	)	PUNCT
ejpam-7074	215	9	,	,	PUNCT
ejpam-7074	215	10	γ	γ	X
ejpam-7074	215	11	u	u	NOUN
ejpam-7074	215	12	a∪b(g	a∪b(g	NOUN
ejpam-7074	215	13	)	)	PUNCT
ejpam-7074	215	14	}	}	PUNCT
ejpam-7074	215	15	]	]	PUNCT
ejpam-7074	215	16	=	=	SYM
ejpam-7074	215	17	rmax{γa∪b(d	rmax{γa∪b(d	PROPN
ejpam-7074	215	18	)	)	PUNCT
ejpam-7074	215	19	,	,	PUNCT
ejpam-7074	215	20	γa∪b(g	γa∪b(g	NOUN
ejpam-7074	215	21	)	)	PUNCT
ejpam-7074	215	22	}	}	PUNCT
ejpam-7074	215	23	.	.	PUNCT
ejpam-7074	216	1	hence	hence	ADV
ejpam-7074	216	2	,	,	PUNCT
ejpam-7074	216	3	a	a	DET
ejpam-7074	216	4	∩b	∩b	NOUN
ejpam-7074	216	5	=	=	PUNCT
ejpam-7074	216	6	(	(	PUNCT
ejpam-7074	216	7	µa∩b	µa∩b	PROPN
ejpam-7074	216	8	,	,	PUNCT
ejpam-7074	216	9	γa∪b	γa∪b	ADJ
ejpam-7074	216	10	)	)	PUNCT
ejpam-7074	216	11	is	be	AUX
ejpam-7074	216	12	an	an	DET
ejpam-7074	216	13	ivifss	ivifss	ADJ
ejpam-7074	216	14	-	-	PUNCT
ejpam-7074	216	15	subalgebra	subalgebra	NOUN
ejpam-7074	216	16	of	of	ADP
ejpam-7074	216	17	sh	sh	PROPN
ejpam-7074	216	18	.	.	PUNCT
ejpam-7074	217	1	a.	a.	PROPN
ejpam-7074	217	2	iampan	iampan	PROPN
ejpam-7074	217	3	et	et	PROPN
ejpam-7074	217	4	al	al	PROPN
ejpam-7074	217	5	.	.	PUNCT
ejpam-7074	217	6	/	/	SYM
ejpam-7074	217	7	eur	eur	PROPN
ejpam-7074	217	8	.	.	PUNCT
ejpam-7074	218	1	j.	j.	PROPN
ejpam-7074	218	2	pure	pure	PROPN
ejpam-7074	218	3	appl	appl	PROPN
ejpam-7074	218	4	.	.	PROPN
ejpam-7074	218	5	math	math	PROPN
ejpam-7074	218	6	,	,	PUNCT
ejpam-7074	218	7	18	18	NUM
ejpam-7074	218	8	(	(	PUNCT
ejpam-7074	218	9	4	4	NUM
ejpam-7074	218	10	)	)	PUNCT
ejpam-7074	218	11	(	(	PUNCT
ejpam-7074	218	12	2025	2025	NUM
ejpam-7074	218	13	)	)	PUNCT
ejpam-7074	218	14	,	,	PUNCT
ejpam-7074	218	15	7074	7074	NUM
ejpam-7074	218	16	8	8	NUM
ejpam-7074	218	17	of	of	ADP
ejpam-7074	218	18	14	14	NUM
ejpam-7074	218	19	definition	definition	NOUN
ejpam-7074	218	20	7	7	NUM
ejpam-7074	218	21	.	.	PUNCT
ejpam-7074	219	1	let	let	VERB
ejpam-7074	219	2	sh	sh	NOUN
ejpam-7074	219	3	:	:	PUNCT
ejpam-7074	219	4	=	=	SYM
ejpam-7074	219	5	(	(	PUNCT
ejpam-7074	219	6	sh	sh	INTJ
ejpam-7074	219	7	,	,	PUNCT
ejpam-7074	219	8	|	|	ADV
ejpam-7074	219	9	,	,	PUNCT
ejpam-7074	219	10	0	0	NUM
ejpam-7074	219	11	)	)	PUNCT
ejpam-7074	219	12	be	be	AUX
ejpam-7074	219	13	an	an	DET
ejpam-7074	219	14	ssha	ssha	NOUN
ejpam-7074	219	15	.	.	PUNCT
ejpam-7074	220	1	let	let	VERB
ejpam-7074	220	2	a	a	PRON
ejpam-7074	220	3	=	=	SYM
ejpam-7074	220	4	(	(	PUNCT
ejpam-7074	220	5	µa	µa	PROPN
ejpam-7074	220	6	,	,	PUNCT
ejpam-7074	220	7	γa	γa	PROPN
ejpam-7074	220	8	)	)	PUNCT
ejpam-7074	220	9	be	be	VERB
ejpam-7074	220	10	an	an	DET
ejpam-7074	220	11	ivifs	ivif	NOUN
ejpam-7074	220	12	defined	define	VERB
ejpam-7074	220	13	on	on	ADP
ejpam-7074	220	14	sh	sh	PROPN
ejpam-7074	220	15	.	.	PUNCT
ejpam-7074	221	1	the	the	DET
ejpam-7074	221	2	operators	operator	NOUN
ejpam-7074	221	3	⊕a	⊕a	PROPN
ejpam-7074	221	4	and	and	CCONJ
ejpam-7074	221	5	⊗a	⊗a	PROPN
ejpam-7074	221	6	are	be	AUX
ejpam-7074	221	7	defined	define	VERB
ejpam-7074	221	8	as	as	ADP
ejpam-7074	221	9	⊕a	⊕a	NOUN
ejpam-7074	221	10	=	=	SYM
ejpam-7074	221	11	{	{	PUNCT
ejpam-7074	221	12	⟨d	⟨d	PROPN
ejpam-7074	221	13	,	,	PUNCT
ejpam-7074	221	14	µa(d	µa(d	PUNCT
ejpam-7074	221	15	)	)	PUNCT
ejpam-7074	221	16	,	,	PUNCT
ejpam-7074	221	17	µa(d)⟩	µa(d)⟩	PROPN
ejpam-7074	221	18	|	|	ADV
ejpam-7074	221	19	d	d	PROPN
ejpam-7074	221	20	∈	∈	PROPN
ejpam-7074	221	21	sh	sh	PROPN
ejpam-7074	221	22	}	}	PUNCT
ejpam-7074	221	23	and	and	CCONJ
ejpam-7074	221	24	⊗a	⊗a	NOUN
ejpam-7074	221	25	=	=	SYM
ejpam-7074	221	26	{	{	PUNCT
ejpam-7074	221	27	⟨d	⟨d	PROPN
ejpam-7074	221	28	,	,	PUNCT
ejpam-7074	221	29	γa(d	γa(d	NUM
ejpam-7074	221	30	)	)	PUNCT
ejpam-7074	221	31	,	,	PUNCT
ejpam-7074	221	32	γa(d)⟩	γa(d)⟩	PROPN
ejpam-7074	222	1	|	|	NOUN
ejpam-7074	222	2	d	d	PROPN
ejpam-7074	222	3	∈	∈	PROPN
ejpam-7074	222	4	sh	sh	PROPN
ejpam-7074	222	5	}	}	PUNCT
ejpam-7074	222	6	.	.	PUNCT
ejpam-7074	223	1	theorem	theorem	NOUN
ejpam-7074	223	2	3	3	X
ejpam-7074	223	3	.	.	PUNCT
ejpam-7074	224	1	let	let	VERB
ejpam-7074	224	2	sh	sh	NOUN
ejpam-7074	224	3	:	:	PUNCT
ejpam-7074	224	4	=	=	SYM
ejpam-7074	224	5	(	(	PUNCT
ejpam-7074	224	6	sh	sh	INTJ
ejpam-7074	224	7	,	,	PUNCT
ejpam-7074	224	8	|	|	ADV
ejpam-7074	224	9	,	,	PUNCT
ejpam-7074	224	10	0	0	NUM
ejpam-7074	224	11	)	)	PUNCT
ejpam-7074	224	12	be	be	AUX
ejpam-7074	224	13	an	an	DET
ejpam-7074	224	14	ssha	ssha	NOUN
ejpam-7074	224	15	.	.	PUNCT
ejpam-7074	225	1	if	if	SCONJ
ejpam-7074	225	2	a	a	DET
ejpam-7074	225	3	=	=	X
ejpam-7074	225	4	(	(	PUNCT
ejpam-7074	225	5	µa	µa	PROPN
ejpam-7074	225	6	,	,	PUNCT
ejpam-7074	225	7	γa	γa	PROPN
ejpam-7074	225	8	)	)	PUNCT
ejpam-7074	225	9	is	be	AUX
ejpam-7074	225	10	an	an	DET
ejpam-7074	225	11	ivifss	ivifss	ADJ
ejpam-7074	225	12	-	-	PUNCT
ejpam-7074	225	13	subalgebra	subalgebra	NOUN
ejpam-7074	225	14	of	of	ADP
ejpam-7074	225	15	sh	sh	INTJ
ejpam-7074	225	16	,	,	PUNCT
ejpam-7074	225	17	then	then	ADV
ejpam-7074	225	18	⊕a	⊕a	PROPN
ejpam-7074	225	19	and	and	CCONJ
ejpam-7074	225	20	⊗a	⊗a	PROPN
ejpam-7074	225	21	are	be	AUX
ejpam-7074	225	22	both	both	PRON
ejpam-7074	225	23	ivifss	ivifss	NOUN
ejpam-7074	225	24	-	-	PUNCT
ejpam-7074	225	25	subalgebras	subalgebras	PROPN
ejpam-7074	225	26	.	.	PUNCT
ejpam-7074	226	1	proof	proof	NOUN
ejpam-7074	226	2	.	.	PUNCT
ejpam-7074	227	1	let	let	VERB
ejpam-7074	227	2	d	d	X
ejpam-7074	227	3	,	,	PUNCT
ejpam-7074	227	4	g	g	PROPN
ejpam-7074	227	5	∈	∈	PROPN
ejpam-7074	227	6	sh	sh	INTJ
ejpam-7074	227	7	.	.	PUNCT
ejpam-7074	228	1	then	then	ADV
ejpam-7074	228	2	µa(d	µa(d	PUNCT
ejpam-7074	228	3	g	g	NOUN
ejpam-7074	228	4	|	|	NOUN
ejpam-7074	228	5	dg	dg	PRON
ejpam-7074	228	6	)	)	PUNCT
ejpam-7074	228	7	=	=	PUNCT
ejpam-7074	229	1	[	[	X
ejpam-7074	229	2	1	1	NUM
ejpam-7074	229	3	,	,	PUNCT
ejpam-7074	229	4	1]−	1]−	NUM
ejpam-7074	229	5	µa(d	µa(d	PUNCT
ejpam-7074	229	6	g	g	NOUN
ejpam-7074	229	7	|	|	NOUN
ejpam-7074	229	8	dg	dg	PROPN
ejpam-7074	229	9	)	)	PUNCT
ejpam-7074	229	10	≤	≤	NOUN
ejpam-7074	230	1	[	[	X
ejpam-7074	230	2	1	1	NUM
ejpam-7074	230	3	,	,	PUNCT
ejpam-7074	230	4	1]−	1]−	NUM
ejpam-7074	230	5	rmin{µa(d	rmin{µa(d	ADJ
ejpam-7074	230	6	)	)	PUNCT
ejpam-7074	230	7	,	,	PUNCT
ejpam-7074	230	8	µa(g	µa(g	NOUN
ejpam-7074	230	9	)	)	PUNCT
ejpam-7074	230	10	}	}	PUNCT
ejpam-7074	230	11	=	=	SYM
ejpam-7074	230	12	rmax{1−	rmax{1−	X
ejpam-7074	230	13	µa(d	µa(d	PUNCT
ejpam-7074	230	14	)	)	PUNCT
ejpam-7074	230	15	,	,	PUNCT
ejpam-7074	230	16	1−	1−	NUM
ejpam-7074	230	17	µa(g	µa(g	NOUN
ejpam-7074	230	18	)	)	PUNCT
ejpam-7074	230	19	}	}	PUNCT
ejpam-7074	230	20	=	=	SYM
ejpam-7074	230	21	rmax{µa(d	rmax{µa(d	NOUN
ejpam-7074	230	22	)	)	PUNCT
ejpam-7074	230	23	,	,	PUNCT
ejpam-7074	230	24	µa(g	µa(g	NOUN
ejpam-7074	230	25	)	)	PUNCT
ejpam-7074	230	26	}	}	PUNCT
ejpam-7074	230	27	.	.	PUNCT
ejpam-7074	231	1	hence	hence	ADV
ejpam-7074	231	2	,	,	PUNCT
ejpam-7074	231	3	⊕a	⊕a	PROPN
ejpam-7074	231	4	is	be	AUX
ejpam-7074	231	5	an	an	DET
ejpam-7074	231	6	ivifss	ivifss	ADJ
ejpam-7074	231	7	-	-	PUNCT
ejpam-7074	231	8	subalgebra	subalgebra	NOUN
ejpam-7074	231	9	of	of	ADP
ejpam-7074	231	10	sh	sh	PROPN
ejpam-7074	231	11	.	.	PUNCT
ejpam-7074	232	1	let	let	VERB
ejpam-7074	232	2	d	d	X
ejpam-7074	232	3	,	,	PUNCT
ejpam-7074	232	4	g	g	PROPN
ejpam-7074	232	5	∈	∈	PROPN
ejpam-7074	232	6	sh	sh	INTJ
ejpam-7074	232	7	.	.	PUNCT
ejpam-7074	233	1	then	then	ADV
ejpam-7074	233	2	γa(d	γa(d	NUM
ejpam-7074	233	3	g	g	PROPN
ejpam-7074	233	4	|	|	ADV
ejpam-7074	233	5	dg	dg	PROPN
ejpam-7074	233	6	)	)	PUNCT
ejpam-7074	233	7	=	=	PUNCT
ejpam-7074	234	1	[	[	X
ejpam-7074	234	2	1	1	NUM
ejpam-7074	234	3	,	,	PUNCT
ejpam-7074	234	4	1]−	1]−	NUM
ejpam-7074	234	5	γa(d	γa(d	NUM
ejpam-7074	234	6	g	g	PROPN
ejpam-7074	234	7	|	|	ADV
ejpam-7074	234	8	dg	dg	PROPN
ejpam-7074	234	9	)	)	PUNCT
ejpam-7074	234	10	≥	≥	NOUN
ejpam-7074	235	1	[	[	X
ejpam-7074	235	2	1	1	NUM
ejpam-7074	235	3	,	,	PUNCT
ejpam-7074	235	4	1]−	1]−	NUM
ejpam-7074	235	5	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	235	6	)	)	PUNCT
ejpam-7074	235	7	,	,	PUNCT
ejpam-7074	235	8	γa(g	γa(g	ADP
ejpam-7074	235	9	)	)	PUNCT
ejpam-7074	235	10	}	}	PUNCT
ejpam-7074	235	11	=	=	PUNCT
ejpam-7074	235	12	rmin{1−	rmin{1−	X
ejpam-7074	235	13	γa(d	γa(d	NOUN
ejpam-7074	235	14	)	)	PUNCT
ejpam-7074	235	15	,	,	PUNCT
ejpam-7074	235	16	1−	1−	NUM
ejpam-7074	235	17	γa(g	γa(g	NOUN
ejpam-7074	235	18	)	)	PUNCT
ejpam-7074	235	19	}	}	PUNCT
ejpam-7074	235	20	=	=	SYM
ejpam-7074	235	21	rmin{γa(d	rmin{γa(d	NOUN
ejpam-7074	235	22	)	)	PUNCT
ejpam-7074	235	23	,	,	PUNCT
ejpam-7074	235	24	γa(g	γa(g	ADP
ejpam-7074	235	25	)	)	PUNCT
ejpam-7074	235	26	}	}	PUNCT
ejpam-7074	235	27	.	.	PUNCT
ejpam-7074	236	1	hence	hence	ADV
ejpam-7074	236	2	,	,	PUNCT
ejpam-7074	236	3	⊗a	⊗a	PROPN
ejpam-7074	236	4	is	be	AUX
ejpam-7074	236	5	an	an	DET
ejpam-7074	236	6	ivifss	ivifss	ADJ
ejpam-7074	236	7	-	-	PUNCT
ejpam-7074	236	8	subalgebra	subalgebra	NOUN
ejpam-7074	236	9	of	of	ADP
ejpam-7074	236	10	sh	sh	PROPN
ejpam-7074	236	11	.	.	PUNCT
ejpam-7074	237	1	the	the	DET
ejpam-7074	237	2	sets	set	NOUN
ejpam-7074	237	3	{	{	PUNCT
ejpam-7074	237	4	d	d	X
ejpam-7074	237	5	∈	∈	PROPN
ejpam-7074	237	6	sh	sh	INTJ
ejpam-7074	237	7	|	|	ADV
ejpam-7074	237	8	µa(d	µa(d	PUNCT
ejpam-7074	237	9	)	)	PUNCT
ejpam-7074	237	10	=	=	SYM
ejpam-7074	237	11	µa(0	µa(0	NOUN
ejpam-7074	237	12	)	)	PUNCT
ejpam-7074	237	13	}	}	PUNCT
ejpam-7074	237	14	and	and	CCONJ
ejpam-7074	237	15	{	{	PUNCT
ejpam-7074	237	16	d	d	X
ejpam-7074	237	17	∈	∈	PROPN
ejpam-7074	237	18	sh	sh	INTJ
ejpam-7074	237	19	|	|	ADV
ejpam-7074	237	20	γa(d	γa(d	PUNCT
ejpam-7074	237	21	)	)	PUNCT
ejpam-7074	237	22	=	=	PUNCT
ejpam-7074	237	23	γa(0	γa(0	NOUN
ejpam-7074	237	24	)	)	PUNCT
ejpam-7074	237	25	}	}	PUNCT
ejpam-7074	237	26	are	be	AUX
ejpam-7074	237	27	denoted	denote	VERB
ejpam-7074	237	28	by	by	ADP
ejpam-7074	237	29	µ∗	µ∗	VERB
ejpam-7074	237	30	a	a	PRON
ejpam-7074	237	31	and	and	CCONJ
ejpam-7074	237	32	γ∗a	γ∗a	NUM
ejpam-7074	237	33	,	,	PUNCT
ejpam-7074	237	34	respectively	respectively	ADV
ejpam-7074	237	35	.	.	PUNCT
ejpam-7074	238	1	theorem	theorem	ADJ
ejpam-7074	238	2	4	4	NUM
ejpam-7074	238	3	.	.	PUNCT
ejpam-7074	239	1	let	let	VERB
ejpam-7074	239	2	sh	sh	NOUN
ejpam-7074	239	3	:	:	PUNCT
ejpam-7074	239	4	=	=	SYM
ejpam-7074	239	5	(	(	PUNCT
ejpam-7074	239	6	sh	sh	INTJ
ejpam-7074	239	7	,	,	PUNCT
ejpam-7074	239	8	|	|	ADV
ejpam-7074	239	9	,	,	PUNCT
ejpam-7074	239	10	0	0	NUM
ejpam-7074	239	11	)	)	PUNCT
ejpam-7074	239	12	be	be	AUX
ejpam-7074	239	13	an	an	DET
ejpam-7074	239	14	ssha	ssha	NOUN
ejpam-7074	239	15	.	.	PUNCT
ejpam-7074	240	1	let	let	VERB
ejpam-7074	240	2	a	a	PRON
ejpam-7074	240	3	=	=	SYM
ejpam-7074	240	4	(	(	PUNCT
ejpam-7074	240	5	µa	µa	PROPN
ejpam-7074	240	6	,	,	PUNCT
ejpam-7074	240	7	γa	γa	PROPN
ejpam-7074	240	8	)	)	PUNCT
ejpam-7074	240	9	be	be	AUX
ejpam-7074	240	10	an	an	DET
ejpam-7074	240	11	ivifss	ivifss	ADJ
ejpam-7074	240	12	-	-	PUNCT
ejpam-7074	240	13	subalgebra	subalgebra	NOUN
ejpam-7074	240	14	of	of	ADP
ejpam-7074	240	15	sh	sh	PROPN
ejpam-7074	240	16	,	,	PUNCT
ejpam-7074	240	17	then	then	ADV
ejpam-7074	240	18	the	the	DET
ejpam-7074	240	19	sets	set	NOUN
ejpam-7074	240	20	µ∗	µ∗	VERB
ejpam-7074	240	21	a	a	PRON
ejpam-7074	240	22	and	and	CCONJ
ejpam-7074	240	23	γ∗a	γ∗a	NUM
ejpam-7074	240	24	are	be	AUX
ejpam-7074	240	25	subalgebras	subalgebra	NOUN
ejpam-7074	240	26	of	of	ADP
ejpam-7074	240	27	sh	sh	PROPN
ejpam-7074	240	28	.	.	PUNCT
ejpam-7074	241	1	proof	proof	NOUN
ejpam-7074	241	2	.	.	PUNCT
ejpam-7074	242	1	let	let	VERB
ejpam-7074	242	2	d	d	X
ejpam-7074	242	3	,	,	PUNCT
ejpam-7074	242	4	g	g	PROPN
ejpam-7074	242	5	∈	∈	PROPN
ejpam-7074	242	6	µ∗	µ∗	PROPN
ejpam-7074	242	7	a.	a.	NOUN
ejpam-7074	242	8	then	then	ADV
ejpam-7074	242	9	µa(d	µa(d	PUNCT
ejpam-7074	242	10	)	)	PUNCT
ejpam-7074	242	11	=	=	SYM
ejpam-7074	242	12	µa(0	µa(0	NOUN
ejpam-7074	242	13	)	)	PUNCT
ejpam-7074	242	14	=	=	NOUN
ejpam-7074	242	15	µa(g	µa(g	NOUN
ejpam-7074	242	16	)	)	PUNCT
ejpam-7074	242	17	and	and	CCONJ
ejpam-7074	242	18	so	so	ADV
ejpam-7074	242	19	µa(d	µa(d	PUNCT
ejpam-7074	242	20	g	g	NOUN
ejpam-7074	242	21	|	|	NOUN
ejpam-7074	242	22	dg	dg	PROPN
ejpam-7074	242	23	)	)	PUNCT
ejpam-7074	242	24	≤	≤	NOUN
ejpam-7074	242	25	rmin{µa(d	rmin{µa(d	ADV
ejpam-7074	242	26	)	)	PUNCT
ejpam-7074	242	27	,	,	PUNCT
ejpam-7074	242	28	µa(g	µa(g	NOUN
ejpam-7074	242	29	)	)	PUNCT
ejpam-7074	242	30	}	}	PUNCT
ejpam-7074	243	1	=	=	SYM
ejpam-7074	243	2	µa(0	µa(0	NOUN
ejpam-7074	243	3	)	)	PUNCT
ejpam-7074	243	4	.	.	PUNCT
ejpam-7074	244	1	by	by	ADP
ejpam-7074	244	2	using	use	VERB
ejpam-7074	244	3	proposition	proposition	NOUN
ejpam-7074	244	4	2	2	NUM
ejpam-7074	244	5	,	,	PUNCT
ejpam-7074	244	6	we	we	PRON
ejpam-7074	244	7	have	have	VERB
ejpam-7074	244	8	µa(d	µa(d	PUNCT
ejpam-7074	244	9	g	g	NOUN
ejpam-7074	244	10	|	|	ADV
ejpam-7074	244	11	dg	dg	PROPN
ejpam-7074	244	12	)	)	PUNCT
ejpam-7074	245	1	=	=	SYM
ejpam-7074	245	2	µa(0	µa(0	NOUN
ejpam-7074	245	3	)	)	PUNCT
ejpam-7074	245	4	and	and	CCONJ
ejpam-7074	245	5	hence	hence	ADV
ejpam-7074	245	6	dg	dg	VERB
ejpam-7074	246	1	|	|	ADV
ejpam-7074	246	2	dg	dg	VERB
ejpam-7074	246	3	∈	∈	PROPN
ejpam-7074	246	4	µ∗	µ∗	VERB
ejpam-7074	246	5	a.	a.	NOUN
ejpam-7074	246	6	again	again	ADV
ejpam-7074	246	7	,	,	PUNCT
ejpam-7074	246	8	let	let	VERB
ejpam-7074	246	9	d	d	INTJ
ejpam-7074	246	10	,	,	PUNCT
ejpam-7074	246	11	g	g	PROPN
ejpam-7074	246	12	∈	∈	PROPN
ejpam-7074	246	13	γ∗a	γ∗a	NUM
ejpam-7074	246	14	.	.	PUNCT
ejpam-7074	247	1	then	then	ADV
ejpam-7074	247	2	γa(d	γa(d	PUNCT
ejpam-7074	247	3	)	)	PUNCT
ejpam-7074	247	4	=	=	PUNCT
ejpam-7074	247	5	γa(0	γa(0	NOUN
ejpam-7074	247	6	)	)	PUNCT
ejpam-7074	247	7	=	=	NOUN
ejpam-7074	247	8	γa(g	γa(g	NOUN
ejpam-7074	247	9	)	)	PUNCT
ejpam-7074	247	10	and	and	CCONJ
ejpam-7074	247	11	so	so	ADV
ejpam-7074	247	12	γa(d	γa(d	PUNCT
ejpam-7074	247	13	g	g	PROPN
ejpam-7074	247	14	|	|	ADV
ejpam-7074	247	15	dg	dg	PROPN
ejpam-7074	247	16	)	)	PUNCT
ejpam-7074	247	17	≤	≤	NUM
ejpam-7074	247	18	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	247	19	)	)	PUNCT
ejpam-7074	247	20	,	,	PUNCT
ejpam-7074	247	21	γa(g	γa(g	ADP
ejpam-7074	247	22	)	)	PUNCT
ejpam-7074	247	23	}	}	PUNCT
ejpam-7074	247	24	=	=	SYM
ejpam-7074	247	25	γa(0	γa(0	NOUN
ejpam-7074	247	26	)	)	PUNCT
ejpam-7074	247	27	.	.	PUNCT
ejpam-7074	248	1	again	again	ADV
ejpam-7074	248	2	,	,	PUNCT
ejpam-7074	248	3	by	by	ADP
ejpam-7074	248	4	proposition	proposition	NOUN
ejpam-7074	248	5	2	2	NUM
ejpam-7074	248	6	,	,	PUNCT
ejpam-7074	248	7	we	we	PRON
ejpam-7074	248	8	hece	hece	VERB
ejpam-7074	248	9	γa(x	γa(x	NUM
ejpam-7074	248	10	g	g	PROPN
ejpam-7074	248	11	|	|	ADV
ejpam-7074	248	12	dg	dg	PROPN
ejpam-7074	248	13	)	)	PUNCT
ejpam-7074	248	14	=	=	PUNCT
ejpam-7074	249	1	γa(0	γa(0	NOUN
ejpam-7074	249	2	)	)	PUNCT
ejpam-7074	249	3	;	;	PUNCT
ejpam-7074	249	4	hence	hence	ADV
ejpam-7074	249	5	dg	dg	VERB
ejpam-7074	249	6	|	|	ADV
ejpam-7074	249	7	dg	dg	VERB
ejpam-7074	249	8	∈	∈	NOUN
ejpam-7074	249	9	γ∗a	γ∗a	NUM
ejpam-7074	249	10	.	.	PUNCT
ejpam-7074	250	1	therefore	therefore	ADV
ejpam-7074	250	2	,	,	PUNCT
ejpam-7074	250	3	the	the	DET
ejpam-7074	250	4	sets	set	NOUN
ejpam-7074	250	5	µ∗	µ∗	VERB
ejpam-7074	250	6	a	a	PRON
ejpam-7074	250	7	and	and	CCONJ
ejpam-7074	250	8	γ∗a	γ∗a	NUM
ejpam-7074	250	9	are	be	AUX
ejpam-7074	250	10	subalgebras	subalgebra	NOUN
ejpam-7074	250	11	of	of	ADP
ejpam-7074	250	12	sh	sh	PROPN
ejpam-7074	250	13	.	.	PUNCT
ejpam-7074	251	1	theorem	theorem	ADJ
ejpam-7074	251	2	5	5	NUM
ejpam-7074	251	3	.	.	PUNCT
ejpam-7074	252	1	let	let	VERB
ejpam-7074	252	2	sh	sh	NOUN
ejpam-7074	252	3	:	:	PUNCT
ejpam-7074	252	4	=	=	SYM
ejpam-7074	252	5	(	(	PUNCT
ejpam-7074	252	6	sh	sh	INTJ
ejpam-7074	252	7	,	,	PUNCT
ejpam-7074	252	8	|	|	ADV
ejpam-7074	252	9	,	,	PUNCT
ejpam-7074	252	10	0	0	NUM
ejpam-7074	252	11	)	)	PUNCT
ejpam-7074	252	12	be	be	AUX
ejpam-7074	252	13	an	an	DET
ejpam-7074	252	14	ssha	ssha	NOUN
ejpam-7074	252	15	.	.	PUNCT
ejpam-7074	253	1	let	let	VERB
ejpam-7074	253	2	b	b	X
ejpam-7074	253	3	be	be	AUX
ejpam-7074	253	4	a	a	DET
ejpam-7074	253	5	nonempty	nonempty	ADJ
ejpam-7074	253	6	subset	subset	NOUN
ejpam-7074	253	7	of	of	ADP
ejpam-7074	253	8	sh	sh	PROPN
ejpam-7074	253	9	and	and	CCONJ
ejpam-7074	253	10	a	a	DET
ejpam-7074	253	11	=	=	X
ejpam-7074	253	12	(	(	PUNCT
ejpam-7074	253	13	µa	µa	PROPN
ejpam-7074	253	14	,	,	PUNCT
ejpam-7074	253	15	γa	γa	PROPN
ejpam-7074	253	16	)	)	PUNCT
ejpam-7074	253	17	be	be	VERB
ejpam-7074	253	18	an	an	DET
ejpam-7074	253	19	ivifs	ivif	NOUN
ejpam-7074	253	20	in	in	ADP
ejpam-7074	253	21	sh	sh	PROPN
ejpam-7074	253	22	defined	define	VERB
ejpam-7074	253	23	by	by	ADP
ejpam-7074	253	24	µa(d	µa(d	PUNCT
ejpam-7074	253	25	)	)	PUNCT
ejpam-7074	253	26	=	=	PRON
ejpam-7074	253	27	{	{	PUNCT
ejpam-7074	254	1	[	[	X
ejpam-7074	254	2	ϑ1	ϑ1	NOUN
ejpam-7074	254	3	,	,	PUNCT
ejpam-7074	254	4	ϑ2	ϑ2	PROPN
ejpam-7074	254	5	]	]	PUNCT
ejpam-7074	255	1	if	if	SCONJ
ejpam-7074	255	2	d	d	PROPN
ejpam-7074	255	3	∈	∈	PROPN
ejpam-7074	255	4	b	b	PROPN
ejpam-7074	256	1	[	[	X
ejpam-7074	256	2	η1	η1	NOUN
ejpam-7074	256	3	,	,	PUNCT
ejpam-7074	256	4	η2	η2	PROPN
ejpam-7074	256	5	]	]	PUNCT
ejpam-7074	256	6	otherwise	otherwise	ADV
ejpam-7074	256	7	and	and	CCONJ
ejpam-7074	256	8	γa(d	γa(d	PRON
ejpam-7074	256	9	)	)	PUNCT
ejpam-7074	256	10	=	=	PRON
ejpam-7074	256	11	{	{	PUNCT
ejpam-7074	257	1	[	[	X
ejpam-7074	257	2	ϖ1	ϖ1	ADJ
ejpam-7074	257	3	,	,	PUNCT
ejpam-7074	257	4	ϖ2	ϖ2	NOUN
ejpam-7074	257	5	]	]	PUNCT
ejpam-7074	258	1	if	if	SCONJ
ejpam-7074	258	2	d	d	PROPN
ejpam-7074	258	3	∈	∈	PROPN
ejpam-7074	258	4	b	b	NOUN
ejpam-7074	259	1	[	[	X
ejpam-7074	259	2	ς1	ς1	NOUN
ejpam-7074	259	3	,	,	PUNCT
ejpam-7074	259	4	ς2	ς2	PROPN
ejpam-7074	259	5	]	]	PUNCT
ejpam-7074	259	6	otherwise	otherwise	ADV
ejpam-7074	259	7	for	for	ADP
ejpam-7074	259	8	all	all	DET
ejpam-7074	259	9	[	[	X
ejpam-7074	259	10	ϑ1	ϑ1	NOUN
ejpam-7074	259	11	,	,	PUNCT
ejpam-7074	259	12	ϑ2	ϑ2	PROPN
ejpam-7074	259	13	]	]	PUNCT
ejpam-7074	259	14	,	,	PUNCT
ejpam-7074	259	15	[	[	X
ejpam-7074	259	16	η1	η1	NOUN
ejpam-7074	259	17	,	,	PUNCT
ejpam-7074	259	18	η2	η2	PROPN
ejpam-7074	259	19	]	]	PUNCT
ejpam-7074	259	20	,	,	PUNCT
ejpam-7074	259	21	[	[	X
ejpam-7074	259	22	ϖ1	ϖ1	ADJ
ejpam-7074	259	23	,	,	PUNCT
ejpam-7074	259	24	ϖ2	ϖ2	NOUN
ejpam-7074	259	25	]	]	PUNCT
ejpam-7074	259	26	,	,	PUNCT
ejpam-7074	259	27	[	[	X
ejpam-7074	259	28	δ1	δ1	NOUN
ejpam-7074	259	29	,	,	PUNCT
ejpam-7074	259	30	δ2	δ2	VERB
ejpam-7074	259	31	]	]	PUNCT
ejpam-7074	259	32	∈	∈	PROPN
ejpam-7074	260	1	d	d	X
ejpam-7074	261	1	[	[	X
ejpam-7074	261	2	0	0	NUM
ejpam-7074	261	3	,	,	PUNCT
ejpam-7074	261	4	1	1	NUM
ejpam-7074	261	5	]	]	PUNCT
ejpam-7074	261	6	with	with	ADP
ejpam-7074	261	7	[	[	X
ejpam-7074	261	8	ϑ1	ϑ1	NOUN
ejpam-7074	261	9	,	,	PUNCT
ejpam-7074	261	10	ϑ2	ϑ2	PROPN
ejpam-7074	261	11	]	]	PUNCT
ejpam-7074	261	12	≥	≥	NOUN
ejpam-7074	261	13	[	[	X
ejpam-7074	261	14	η1	η1	NOUN
ejpam-7074	261	15	,	,	PUNCT
ejpam-7074	261	16	η2	η2	PROPN
ejpam-7074	261	17	]	]	PUNCT
ejpam-7074	261	18	and	and	CCONJ
ejpam-7074	261	19	[	[	X
ejpam-7074	261	20	ϖ1	ϖ1	ADJ
ejpam-7074	261	21	,	,	PUNCT
ejpam-7074	261	22	ϖ2	ϖ2	NOUN
ejpam-7074	261	23	]	]	PUNCT
ejpam-7074	261	24	≤	≤	NOUN
ejpam-7074	262	1	[	[	X
ejpam-7074	262	2	ς1	ς1	NOUN
ejpam-7074	262	3	,	,	PUNCT
ejpam-7074	262	4	ς2	ς2	PROPN
ejpam-7074	262	5	]	]	PUNCT
ejpam-7074	262	6	and	and	CCONJ
ejpam-7074	262	7	ϑ2	ϑ2	PROPN
ejpam-7074	262	8	+	+	CCONJ
ejpam-7074	262	9	ϖ2	ϖ2	ADJ
ejpam-7074	262	10	≤	≤	NOUN
ejpam-7074	262	11	1	1	NUM
ejpam-7074	262	12	and	and	CCONJ
ejpam-7074	262	13	η2	η2	VERB
ejpam-7074	262	14	+	+	CCONJ
ejpam-7074	262	15	δ2	δ2	VERB
ejpam-7074	262	16	≤	≤	NOUN
ejpam-7074	262	17	1	1	NUM
ejpam-7074	262	18	.	.	PUNCT
ejpam-7074	263	1	then	then	ADV
ejpam-7074	263	2	a	a	DET
ejpam-7074	263	3	=	=	SYM
ejpam-7074	263	4	(	(	PUNCT
ejpam-7074	263	5	µa	µa	PROPN
ejpam-7074	263	6	,	,	PUNCT
ejpam-7074	263	7	γa	γa	PROPN
ejpam-7074	263	8	)	)	PUNCT
ejpam-7074	263	9	is	be	AUX
ejpam-7074	263	10	an	an	DET
ejpam-7074	263	11	ivifss	ivifss	ADJ
ejpam-7074	263	12	-	-	PUNCT
ejpam-7074	263	13	subalgebra	subalgebra	NOUN
ejpam-7074	263	14	of	of	ADP
ejpam-7074	263	15	sh	sh	PRON
ejpam-7074	263	16	if	if	SCONJ
ejpam-7074	264	1	and	and	CCONJ
ejpam-7074	264	2	only	only	ADV
ejpam-7074	264	3	if	if	SCONJ
ejpam-7074	264	4	b	b	NOUN
ejpam-7074	264	5	is	be	AUX
ejpam-7074	264	6	a	a	DET
ejpam-7074	264	7	subalgebra	subalgebra	NOUN
ejpam-7074	264	8	of	of	ADP
ejpam-7074	264	9	sh	sh	PROPN
ejpam-7074	264	10	.	.	PUNCT
ejpam-7074	265	1	moreover	moreover	ADV
ejpam-7074	265	2	,	,	PUNCT
ejpam-7074	265	3	µ∗	µ∗	VERB
ejpam-7074	265	4	a	a	DET
ejpam-7074	265	5	=	=	SYM
ejpam-7074	265	6	b	b	NOUN
ejpam-7074	265	7	=	=	SYM
ejpam-7074	265	8	γ∗a	γ∗a	PROPN
ejpam-7074	265	9	.	.	PUNCT
ejpam-7074	266	1	a.	a.	PROPN
ejpam-7074	266	2	iampan	iampan	PROPN
ejpam-7074	266	3	et	et	PROPN
ejpam-7074	266	4	al	al	PROPN
ejpam-7074	266	5	.	.	PUNCT
ejpam-7074	266	6	/	/	SYM
ejpam-7074	266	7	eur	eur	PROPN
ejpam-7074	266	8	.	.	PUNCT
ejpam-7074	267	1	j.	j.	PROPN
ejpam-7074	267	2	pure	pure	PROPN
ejpam-7074	267	3	appl	appl	PROPN
ejpam-7074	267	4	.	.	PROPN
ejpam-7074	267	5	math	math	PROPN
ejpam-7074	267	6	,	,	PUNCT
ejpam-7074	267	7	18	18	NUM
ejpam-7074	267	8	(	(	PUNCT
ejpam-7074	267	9	4	4	NUM
ejpam-7074	267	10	)	)	PUNCT
ejpam-7074	267	11	(	(	PUNCT
ejpam-7074	267	12	2025	2025	NUM
ejpam-7074	267	13	)	)	PUNCT
ejpam-7074	267	14	,	,	PUNCT
ejpam-7074	267	15	7074	7074	NUM
ejpam-7074	267	16	9	9	NUM
ejpam-7074	267	17	of	of	ADP
ejpam-7074	267	18	14	14	NUM
ejpam-7074	267	19	proof	proof	NOUN
ejpam-7074	267	20	.	.	PUNCT
ejpam-7074	268	1	let	let	VERB
ejpam-7074	268	2	a	a	DET
ejpam-7074	268	3	=	=	SYM
ejpam-7074	268	4	(	(	PUNCT
ejpam-7074	268	5	µa	µa	PROPN
ejpam-7074	268	6	,	,	PUNCT
ejpam-7074	268	7	γa	γa	PROPN
ejpam-7074	268	8	)	)	PUNCT
ejpam-7074	268	9	be	be	AUX
ejpam-7074	268	10	an	an	DET
ejpam-7074	268	11	ivifss	ivifss	ADJ
ejpam-7074	268	12	-	-	PUNCT
ejpam-7074	268	13	subalgebra	subalgebra	NOUN
ejpam-7074	268	14	of	of	ADP
ejpam-7074	268	15	sh	sh	PROPN
ejpam-7074	268	16	.	.	PUNCT
ejpam-7074	269	1	let	let	VERB
ejpam-7074	269	2	d	d	X
ejpam-7074	269	3	,	,	PUNCT
ejpam-7074	269	4	g	g	PROPN
ejpam-7074	269	5	∈	∈	PROPN
ejpam-7074	269	6	sh	sh	INTJ
ejpam-7074	269	7	be	be	AUX
ejpam-7074	269	8	such	such	ADJ
ejpam-7074	269	9	that	that	SCONJ
ejpam-7074	269	10	d	d	NOUN
ejpam-7074	269	11	,	,	PUNCT
ejpam-7074	269	12	g	g	PROPN
ejpam-7074	269	13	∈	∈	PROPN
ejpam-7074	269	14	b.	b.	PROPN
ejpam-7074	270	1	then	then	ADV
ejpam-7074	270	2	µa(d	µa(d	PUNCT
ejpam-7074	270	3	g	g	NOUN
ejpam-7074	270	4	|	|	NOUN
ejpam-7074	270	5	dg	dg	PROPN
ejpam-7074	270	6	)	)	PUNCT
ejpam-7074	270	7	≥	≥	NOUN
ejpam-7074	270	8	rmin{µa(d	rmin{µa(d	ADV
ejpam-7074	270	9	)	)	PUNCT
ejpam-7074	270	10	,	,	PUNCT
ejpam-7074	270	11	µa(g	µa(g	NOUN
ejpam-7074	270	12	)	)	PUNCT
ejpam-7074	270	13	}	}	PUNCT
ejpam-7074	270	14	=	=	SYM
ejpam-7074	270	15	rmin{[ϑ1	rmin{[ϑ1	NOUN
ejpam-7074	270	16	,	,	PUNCT
ejpam-7074	270	17	ϑ2	ϑ2	NOUN
ejpam-7074	270	18	]	]	PUNCT
ejpam-7074	270	19	,	,	PUNCT
ejpam-7074	271	1	[	[	X
ejpam-7074	271	2	ϑ1	ϑ1	NOUN
ejpam-7074	271	3	,	,	PUNCT
ejpam-7074	271	4	ϑ2	ϑ2	NOUN
ejpam-7074	271	5	]	]	PUNCT
ejpam-7074	271	6	}	}	PUNCT
ejpam-7074	271	7	=	=	PUNCT
ejpam-7074	272	1	[	[	X
ejpam-7074	272	2	ϑ1	ϑ1	NOUN
ejpam-7074	272	3	,	,	PUNCT
ejpam-7074	272	4	ϑ2	ϑ2	PROPN
ejpam-7074	272	5	]	]	PUNCT
ejpam-7074	272	6	and	and	CCONJ
ejpam-7074	272	7	γa(d	γa(d	NUM
ejpam-7074	272	8	g	g	PROPN
ejpam-7074	272	9	|	|	NOUN
ejpam-7074	272	10	dg	dg	PROPN
ejpam-7074	272	11	)	)	PUNCT
ejpam-7074	272	12	≤	≤	NUM
ejpam-7074	272	13	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	272	14	)	)	PUNCT
ejpam-7074	272	15	,	,	PUNCT
ejpam-7074	272	16	γa(g	γa(g	ADP
ejpam-7074	272	17	)	)	PUNCT
ejpam-7074	272	18	}	}	PUNCT
ejpam-7074	272	19	=	=	SYM
ejpam-7074	272	20	rmax{[ϑ1	rmax{[ϑ1	NOUN
ejpam-7074	272	21	,	,	PUNCT
ejpam-7074	272	22	ϑ2	ϑ2	PROPN
ejpam-7074	272	23	]	]	PUNCT
ejpam-7074	272	24	,	,	PUNCT
ejpam-7074	272	25	[	[	X
ejpam-7074	272	26	ϑ1	ϑ1	NOUN
ejpam-7074	272	27	,	,	PUNCT
ejpam-7074	272	28	ϑ2	ϑ2	NOUN
ejpam-7074	272	29	]	]	PUNCT
ejpam-7074	272	30	}	}	PUNCT
ejpam-7074	272	31	=	=	PUNCT
ejpam-7074	273	1	[	[	X
ejpam-7074	273	2	ϑ1	ϑ1	NOUN
ejpam-7074	273	3	,	,	PUNCT
ejpam-7074	273	4	ϑ2	ϑ2	PROPN
ejpam-7074	273	5	]	]	PUNCT
ejpam-7074	273	6	.	.	PUNCT
ejpam-7074	274	1	so	so	ADV
ejpam-7074	274	2	,	,	PUNCT
ejpam-7074	274	3	dg	dg	VERB
ejpam-7074	274	4	|	|	ADV
ejpam-7074	274	5	dg	dg	VERB
ejpam-7074	274	6	∈	∈	PROPN
ejpam-7074	274	7	b.	b.	PROPN
ejpam-7074	274	8	hence	hence	ADV
ejpam-7074	274	9	,	,	PUNCT
ejpam-7074	274	10	b	b	PROPN
ejpam-7074	274	11	is	be	AUX
ejpam-7074	274	12	a	a	DET
ejpam-7074	274	13	subalgebra	subalgebra	NOUN
ejpam-7074	274	14	of	of	ADP
ejpam-7074	274	15	sh	sh	PROPN
ejpam-7074	274	16	.	.	PUNCT
ejpam-7074	275	1	conversely	conversely	ADV
ejpam-7074	275	2	,	,	PUNCT
ejpam-7074	275	3	suppose	suppose	VERB
ejpam-7074	275	4	that	that	SCONJ
ejpam-7074	275	5	b	b	PROPN
ejpam-7074	275	6	is	be	AUX
ejpam-7074	275	7	a	a	DET
ejpam-7074	275	8	subalgebra	subalgebra	NOUN
ejpam-7074	275	9	of	of	ADP
ejpam-7074	275	10	sh	sh	PROPN
ejpam-7074	275	11	.	.	PUNCT
ejpam-7074	276	1	let	let	VERB
ejpam-7074	276	2	d	d	X
ejpam-7074	276	3	,	,	PUNCT
ejpam-7074	276	4	g	g	PROPN
ejpam-7074	276	5	∈	∈	PROPN
ejpam-7074	276	6	sh	sh	INTJ
ejpam-7074	276	7	.	.	PUNCT
ejpam-7074	277	1	consider	consider	VERB
ejpam-7074	277	2	two	two	NUM
ejpam-7074	277	3	cases	case	NOUN
ejpam-7074	277	4	:	:	PUNCT
ejpam-7074	277	5	case	case	NOUN
ejpam-7074	277	6	(	(	PUNCT
ejpam-7074	277	7	i	i	NOUN
ejpam-7074	277	8	):	):	PUNCT
ejpam-7074	277	9	if	if	SCONJ
ejpam-7074	277	10	d	d	X
ejpam-7074	277	11	,	,	PUNCT
ejpam-7074	277	12	g	g	PROPN
ejpam-7074	277	13	∈	∈	PROPN
ejpam-7074	277	14	b	b	PROPN
ejpam-7074	277	15	,	,	PUNCT
ejpam-7074	277	16	then	then	ADV
ejpam-7074	277	17	dg	dg	VERB
ejpam-7074	277	18	|	|	ADV
ejpam-7074	277	19	dg	dg	ADP
ejpam-7074	277	20	∈	∈	PROPN
ejpam-7074	277	21	b.	b.	PROPN
ejpam-7074	278	1	thus	thus	ADV
ejpam-7074	278	2	,	,	PUNCT
ejpam-7074	278	3	µa(d	µa(d	PUNCT
ejpam-7074	278	4	g	g	NOUN
ejpam-7074	278	5	|	|	NOUN
ejpam-7074	278	6	dg	dg	PRON
ejpam-7074	278	7	)	)	PUNCT
ejpam-7074	278	8	=	=	PUNCT
ejpam-7074	279	1	[	[	X
ejpam-7074	279	2	ϖ1	ϖ1	ADJ
ejpam-7074	279	3	,	,	PUNCT
ejpam-7074	279	4	ϖ2	ϖ2	NOUN
ejpam-7074	279	5	]	]	X
ejpam-7074	279	6	=	=	PUNCT
ejpam-7074	279	7	rmin{µa(d	rmin{µa(d	ADJ
ejpam-7074	279	8	)	)	PUNCT
ejpam-7074	279	9	,	,	PUNCT
ejpam-7074	279	10	µa(g	µa(g	NOUN
ejpam-7074	279	11	)	)	PUNCT
ejpam-7074	279	12	}	}	PUNCT
ejpam-7074	279	13	and	and	CCONJ
ejpam-7074	279	14	γa(d	γa(d	NUM
ejpam-7074	280	1	g	g	PROPN
ejpam-7074	280	2	|	|	ADV
ejpam-7074	280	3	dg	dg	PROPN
ejpam-7074	280	4	)	)	PUNCT
ejpam-7074	280	5	=	=	PUNCT
ejpam-7074	281	1	[	[	X
ejpam-7074	281	2	θ1	θ1	NOUN
ejpam-7074	281	3	,	,	PUNCT
ejpam-7074	281	4	θ2	θ2	PROPN
ejpam-7074	281	5	]	]	PUNCT
ejpam-7074	281	6	=	=	SYM
ejpam-7074	281	7	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	281	8	)	)	PUNCT
ejpam-7074	281	9	,	,	PUNCT
ejpam-7074	281	10	γa(g	γa(g	ADP
ejpam-7074	281	11	)	)	PUNCT
ejpam-7074	281	12	}	}	PUNCT
ejpam-7074	281	13	.	.	PUNCT
ejpam-7074	282	1	case	case	NOUN
ejpam-7074	282	2	(	(	PUNCT
ejpam-7074	282	3	ii	ii	NOUN
ejpam-7074	282	4	):	):	PUNCT
ejpam-7074	282	5	if	if	SCONJ
ejpam-7074	282	6	d	d	PROPN
ejpam-7074	282	7	/∈	/∈	PROPN
ejpam-7074	282	8	b	b	NOUN
ejpam-7074	282	9	or	or	CCONJ
ejpam-7074	282	10	g	g	PROPN
ejpam-7074	282	11	/∈	/∈	PUNCT
ejpam-7074	283	1	b	b	NOUN
ejpam-7074	283	2	,	,	PUNCT
ejpam-7074	283	3	then	then	ADV
ejpam-7074	283	4	µa(d	µa(d	PUNCT
ejpam-7074	283	5	g	g	NOUN
ejpam-7074	283	6	|	|	NOUN
ejpam-7074	283	7	dg	dg	PROPN
ejpam-7074	283	8	)	)	PUNCT
ejpam-7074	283	9	≥	≥	NOUN
ejpam-7074	284	1	[	[	X
ejpam-7074	284	2	η1	η1	NOUN
ejpam-7074	284	3	,	,	PUNCT
ejpam-7074	284	4	η2	η2	X
ejpam-7074	284	5	]	]	PUNCT
ejpam-7074	284	6	=	=	SYM
ejpam-7074	284	7	rmin{µa(d	rmin{µa(d	X
ejpam-7074	284	8	)	)	PUNCT
ejpam-7074	284	9	,	,	PUNCT
ejpam-7074	284	10	µa(g	µa(g	NOUN
ejpam-7074	284	11	)	)	PUNCT
ejpam-7074	284	12	}	}	PUNCT
ejpam-7074	284	13	and	and	CCONJ
ejpam-7074	284	14	γa(d	γa(d	NUM
ejpam-7074	284	15	g	g	PROPN
ejpam-7074	284	16	|	|	NOUN
ejpam-7074	284	17	dg	dg	PROPN
ejpam-7074	284	18	)	)	PUNCT
ejpam-7074	284	19	≤	≤	NOUN
ejpam-7074	285	1	[	[	X
ejpam-7074	285	2	θ1	θ1	NOUN
ejpam-7074	285	3	,	,	PUNCT
ejpam-7074	285	4	θ2	θ2	PROPN
ejpam-7074	285	5	]	]	PUNCT
ejpam-7074	285	6	=	=	SYM
ejpam-7074	285	7	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	285	8	)	)	PUNCT
ejpam-7074	285	9	,	,	PUNCT
ejpam-7074	285	10	γa(g	γa(g	ADP
ejpam-7074	285	11	)	)	PUNCT
ejpam-7074	285	12	}	}	PUNCT
ejpam-7074	285	13	.	.	PUNCT
ejpam-7074	286	1	hence	hence	ADV
ejpam-7074	286	2	,	,	PUNCT
ejpam-7074	286	3	a	a	DET
ejpam-7074	286	4	=	=	X
ejpam-7074	286	5	(	(	PUNCT
ejpam-7074	286	6	µa	µa	PROPN
ejpam-7074	286	7	,	,	PUNCT
ejpam-7074	286	8	γa	γa	PROPN
ejpam-7074	286	9	)	)	PUNCT
ejpam-7074	286	10	is	be	AUX
ejpam-7074	286	11	an	an	DET
ejpam-7074	286	12	ivifss	ivifss	ADJ
ejpam-7074	286	13	-	-	PUNCT
ejpam-7074	286	14	subalgebra	subalgebra	NOUN
ejpam-7074	286	15	of	of	ADP
ejpam-7074	286	16	sh	sh	PROPN
ejpam-7074	286	17	.	.	PUNCT
ejpam-7074	287	1	now	now	ADV
ejpam-7074	287	2	,	,	PUNCT
ejpam-7074	287	3	µ∗	µ∗	VERB
ejpam-7074	287	4	a	a	DET
ejpam-7074	287	5	=	=	SYM
ejpam-7074	287	6	{	{	PUNCT
ejpam-7074	287	7	d	d	X
ejpam-7074	287	8	∈	∈	PROPN
ejpam-7074	287	9	sh	sh	INTJ
ejpam-7074	287	10	|	|	ADV
ejpam-7074	287	11	µa(d	µa(d	PUNCT
ejpam-7074	287	12	)	)	PUNCT
ejpam-7074	287	13	=	=	SYM
ejpam-7074	287	14	µa(0	µa(0	NOUN
ejpam-7074	287	15	)	)	PUNCT
ejpam-7074	287	16	}	}	PUNCT
ejpam-7074	287	17	=	=	PUNCT
ejpam-7074	288	1	{	{	PUNCT
ejpam-7074	288	2	d	d	X
ejpam-7074	288	3	∈	∈	PROPN
ejpam-7074	288	4	sh	sh	INTJ
ejpam-7074	288	5	|	|	ADV
ejpam-7074	288	6	µa(d	µa(d	PUNCT
ejpam-7074	288	7	)	)	PUNCT
ejpam-7074	288	8	=	=	PUNCT
ejpam-7074	289	1	[	[	X
ejpam-7074	289	2	ϑ1	ϑ1	NOUN
ejpam-7074	289	3	,	,	PUNCT
ejpam-7074	289	4	ϑ2	ϑ2	NOUN
ejpam-7074	289	5	]	]	PUNCT
ejpam-7074	289	6	}	}	PUNCT
ejpam-7074	289	7	=	=	SYM
ejpam-7074	289	8	b	b	PROPN
ejpam-7074	289	9	and	and	CCONJ
ejpam-7074	289	10	γ∗a	γ∗a	PUNCT
ejpam-7074	289	11	=	=	SYM
ejpam-7074	289	12	{	{	PUNCT
ejpam-7074	289	13	d	d	X
ejpam-7074	289	14	∈	∈	PROPN
ejpam-7074	289	15	sh	sh	INTJ
ejpam-7074	289	16	|	|	ADV
ejpam-7074	289	17	γa(d	γa(d	PUNCT
ejpam-7074	289	18	)	)	PUNCT
ejpam-7074	289	19	=	=	PUNCT
ejpam-7074	289	20	γa(0	γa(0	NOUN
ejpam-7074	289	21	)	)	PUNCT
ejpam-7074	289	22	}	}	PUNCT
ejpam-7074	289	23	=	=	PUNCT
ejpam-7074	289	24	{	{	PUNCT
ejpam-7074	289	25	d	d	X
ejpam-7074	289	26	∈	∈	PROPN
ejpam-7074	289	27	sh	sh	INTJ
ejpam-7074	289	28	|	|	ADV
ejpam-7074	289	29	γa(d	γa(d	PUNCT
ejpam-7074	289	30	)	)	PUNCT
ejpam-7074	289	31	=	=	PUNCT
ejpam-7074	290	1	[	[	X
ejpam-7074	290	2	ϖ1	ϖ1	ADJ
ejpam-7074	290	3	,	,	PUNCT
ejpam-7074	290	4	ϖ2	ϖ2	NOUN
ejpam-7074	290	5	]	]	X
ejpam-7074	290	6	}	}	PUNCT
ejpam-7074	290	7	=	=	SYM
ejpam-7074	290	8	b.	b.	NOUN
ejpam-7074	290	9	to	to	PART
ejpam-7074	290	10	confirm	confirm	VERB
ejpam-7074	290	11	that	that	SCONJ
ejpam-7074	290	12	an	an	DET
ejpam-7074	290	13	ivifss	ivifss	ADJ
ejpam-7074	290	14	-	-	PUNCT
ejpam-7074	290	15	subalgebra	subalgebra	NOUN
ejpam-7074	290	16	aligns	align	VERB
ejpam-7074	290	17	with	with	ADP
ejpam-7074	290	18	the	the	DET
ejpam-7074	290	19	underlying	underlie	VERB
ejpam-7074	290	20	crisp	crisp	ADJ
ejpam-7074	290	21	structure	structure	NOUN
ejpam-7074	290	22	,	,	PUNCT
ejpam-7074	290	23	we	we	PRON
ejpam-7074	290	24	examine	examine	VERB
ejpam-7074	290	25	its	its	PRON
ejpam-7074	290	26	level	level	NOUN
ejpam-7074	290	27	subsets	subset	NOUN
ejpam-7074	290	28	.	.	PUNCT
ejpam-7074	291	1	specifically	specifically	ADV
ejpam-7074	291	2	,	,	PUNCT
ejpam-7074	291	3	we	we	PRON
ejpam-7074	291	4	define	define	VERB
ejpam-7074	291	5	αand	αand	ADV
ejpam-7074	291	6	β	β	NOUN
ejpam-7074	291	7	-	-	PUNCT
ejpam-7074	291	8	level	level	NOUN
ejpam-7074	291	9	sets	set	NOUN
ejpam-7074	291	10	and	and	CCONJ
ejpam-7074	291	11	verify	verify	VERB
ejpam-7074	291	12	that	that	SCONJ
ejpam-7074	291	13	these	these	DET
ejpam-7074	291	14	subsets	subset	NOUN
ejpam-7074	291	15	form	form	VERB
ejpam-7074	291	16	classical	classical	ADJ
ejpam-7074	291	17	subalgebras	subalgebra	NOUN
ejpam-7074	291	18	of	of	ADP
ejpam-7074	291	19	the	the	DET
ejpam-7074	291	20	ssha	ssha	PROPN
ejpam-7074	291	21	.	.	PUNCT
ejpam-7074	292	1	this	this	PRON
ejpam-7074	292	2	ensures	ensure	VERB
ejpam-7074	292	3	that	that	SCONJ
ejpam-7074	292	4	the	the	DET
ejpam-7074	292	5	fuzzy	fuzzy	ADJ
ejpam-7074	292	6	extension	extension	NOUN
ejpam-7074	292	7	preserves	preserve	VERB
ejpam-7074	292	8	the	the	DET
ejpam-7074	292	9	essential	essential	ADJ
ejpam-7074	292	10	algebraic	algebraic	ADJ
ejpam-7074	292	11	properties	property	NOUN
ejpam-7074	292	12	.	.	PUNCT
ejpam-7074	293	1	definition	definition	NOUN
ejpam-7074	293	2	8	8	NUM
ejpam-7074	293	3	.	.	PUNCT
ejpam-7074	294	1	let	let	VERB
ejpam-7074	294	2	sh	sh	NOUN
ejpam-7074	294	3	:	:	PUNCT
ejpam-7074	294	4	=	=	SYM
ejpam-7074	294	5	(	(	PUNCT
ejpam-7074	294	6	sh	sh	INTJ
ejpam-7074	294	7	,	,	PUNCT
ejpam-7074	294	8	|	|	ADV
ejpam-7074	294	9	,	,	PUNCT
ejpam-7074	294	10	0	0	NUM
ejpam-7074	294	11	)	)	PUNCT
ejpam-7074	294	12	be	be	AUX
ejpam-7074	294	13	an	an	DET
ejpam-7074	294	14	ssha	ssha	NOUN
ejpam-7074	294	15	.	.	PUNCT
ejpam-7074	295	1	let	let	VERB
ejpam-7074	295	2	a	a	DET
ejpam-7074	295	3	=	=	SYM
ejpam-7074	295	4	(	(	PUNCT
ejpam-7074	295	5	µa	µa	PROPN
ejpam-7074	295	6	,	,	PUNCT
ejpam-7074	295	7	γa	γa	PROPN
ejpam-7074	295	8	)	)	PUNCT
ejpam-7074	295	9	is	be	AUX
ejpam-7074	295	10	an	an	DET
ejpam-7074	295	11	ivifss	ivifss	ADJ
ejpam-7074	295	12	-	-	PUNCT
ejpam-7074	295	13	subalgebra	subalgebra	NOUN
ejpam-7074	295	14	of	of	ADP
ejpam-7074	295	15	sh	sh	PROPN
ejpam-7074	295	16	.	.	PUNCT
ejpam-7074	296	1	for	for	ADP
ejpam-7074	296	2	[	[	X
ejpam-7074	296	3	p1	p1	NOUN
ejpam-7074	296	4	,	,	PUNCT
ejpam-7074	296	5	p2	p2	NOUN
ejpam-7074	296	6	]	]	PUNCT
ejpam-7074	296	7	,	,	PUNCT
ejpam-7074	296	8	[	[	X
ejpam-7074	296	9	q1	q1	X
ejpam-7074	296	10	,	,	PUNCT
ejpam-7074	296	11	q2	q2	NOUN
ejpam-7074	296	12	]	]	PUNCT
ejpam-7074	296	13	∈	∈	PROPN
ejpam-7074	297	1	d	d	X
ejpam-7074	298	1	[	[	X
ejpam-7074	298	2	0	0	NUM
ejpam-7074	298	3	,	,	PUNCT
ejpam-7074	298	4	1	1	NUM
ejpam-7074	298	5	]	]	PUNCT
ejpam-7074	298	6	,	,	PUNCT
ejpam-7074	298	7	the	the	DET
ejpam-7074	298	8	set	set	ADJ
ejpam-7074	298	9	u	u	NOUN
ejpam-7074	298	10	(	(	PUNCT
ejpam-7074	298	11	µa	µa	INTJ
ejpam-7074	298	12	:	:	PUNCT
ejpam-7074	299	1	[	[	X
ejpam-7074	299	2	p1	p1	NOUN
ejpam-7074	299	3	,	,	PUNCT
ejpam-7074	299	4	p2	p2	X
ejpam-7074	299	5	]	]	PUNCT
ejpam-7074	299	6	)	)	PUNCT
ejpam-7074	299	7	=	=	SYM
ejpam-7074	299	8	{	{	PUNCT
ejpam-7074	299	9	d	d	X
ejpam-7074	299	10	∈	∈	PROPN
ejpam-7074	299	11	sh	sh	INTJ
ejpam-7074	299	12	|	|	NOUN
ejpam-7074	299	13	µa(d	µa(d	PUNCT
ejpam-7074	299	14	)	)	PUNCT
ejpam-7074	299	15	≥	≥	PUNCT
ejpam-7074	300	1	[	[	X
ejpam-7074	300	2	p1	p1	NOUN
ejpam-7074	300	3	,	,	PUNCT
ejpam-7074	300	4	p2	p2	PROPN
ejpam-7074	300	5	]	]	PUNCT
ejpam-7074	300	6	}	}	PUNCT
ejpam-7074	300	7	is	be	AUX
ejpam-7074	300	8	called	call	VERB
ejpam-7074	300	9	an	an	DET
ejpam-7074	300	10	upper	upper	ADJ
ejpam-7074	300	11	[	[	X
ejpam-7074	300	12	p1	p1	NOUN
ejpam-7074	300	13	,	,	PUNCT
ejpam-7074	300	14	p2]-level	p2]-level	NOUN
ejpam-7074	300	15	of	of	ADP
ejpam-7074	300	16	a	a	PRON
ejpam-7074	300	17	and	and	CCONJ
ejpam-7074	300	18	l	l	NOUN
ejpam-7074	300	19	(	(	PUNCT
ejpam-7074	300	20	γa	γa	NOUN
ejpam-7074	300	21	:	:	PUNCT
ejpam-7074	301	1	[	[	X
ejpam-7074	301	2	q1	q1	X
ejpam-7074	301	3	,	,	PUNCT
ejpam-7074	301	4	q2	q2	NOUN
ejpam-7074	301	5	]	]	PUNCT
ejpam-7074	301	6	)	)	PUNCT
ejpam-7074	301	7	=	=	SYM
ejpam-7074	302	1	{	{	PUNCT
ejpam-7074	302	2	d	d	X
ejpam-7074	302	3	∈	∈	PROPN
ejpam-7074	302	4	sh	sh	INTJ
ejpam-7074	302	5	|	|	ADV
ejpam-7074	302	6	γa(d	γa(d	NOUN
ejpam-7074	302	7	)	)	PUNCT
ejpam-7074	302	8	≤	≤	NOUN
ejpam-7074	303	1	[	[	X
ejpam-7074	303	2	q1	q1	NOUN
ejpam-7074	303	3	,	,	PUNCT
ejpam-7074	303	4	q2	q2	NOUN
ejpam-7074	303	5	]	]	PUNCT
ejpam-7074	303	6	}	}	PUNCT
ejpam-7074	303	7	is	be	AUX
ejpam-7074	303	8	called	call	VERB
ejpam-7074	303	9	a	a	DET
ejpam-7074	303	10	lower	low	ADJ
ejpam-7074	303	11	[	[	X
ejpam-7074	303	12	q1	q1	NOUN
ejpam-7074	303	13	,	,	PUNCT
ejpam-7074	303	14	q2]-level	q2]-level	NOUN
ejpam-7074	303	15	of	of	ADP
ejpam-7074	303	16	a.	a.	NOUN
ejpam-7074	303	17	theorem	theorem	NOUN
ejpam-7074	303	18	6	6	NUM
ejpam-7074	303	19	.	.	PUNCT
ejpam-7074	304	1	let	let	VERB
ejpam-7074	304	2	sh	sh	NOUN
ejpam-7074	304	3	:	:	PUNCT
ejpam-7074	304	4	=	=	SYM
ejpam-7074	304	5	(	(	PUNCT
ejpam-7074	304	6	sh	sh	INTJ
ejpam-7074	304	7	,	,	PUNCT
ejpam-7074	304	8	|	|	ADV
ejpam-7074	304	9	,	,	PUNCT
ejpam-7074	304	10	0	0	NUM
ejpam-7074	304	11	)	)	PUNCT
ejpam-7074	304	12	be	be	AUX
ejpam-7074	304	13	an	an	DET
ejpam-7074	304	14	ssha	ssha	NOUN
ejpam-7074	304	15	.	.	PUNCT
ejpam-7074	305	1	if	if	SCONJ
ejpam-7074	305	2	a	a	DET
ejpam-7074	305	3	=	=	X
ejpam-7074	305	4	(	(	PUNCT
ejpam-7074	305	5	µa	µa	PROPN
ejpam-7074	305	6	,	,	PUNCT
ejpam-7074	305	7	γa	γa	PROPN
ejpam-7074	305	8	)	)	PUNCT
ejpam-7074	305	9	is	be	AUX
ejpam-7074	305	10	an	an	DET
ejpam-7074	305	11	ivifss	ivifss	ADJ
ejpam-7074	305	12	-	-	PUNCT
ejpam-7074	305	13	subalgebra	subalgebra	NOUN
ejpam-7074	305	14	of	of	ADP
ejpam-7074	305	15	sh	sh	PROPN
ejpam-7074	305	16	,	,	PUNCT
ejpam-7074	305	17	then	then	ADV
ejpam-7074	305	18	the	the	DET
ejpam-7074	305	19	upper	upper	ADJ
ejpam-7074	305	20	[	[	X
ejpam-7074	305	21	p1	p1	NOUN
ejpam-7074	305	22	,	,	PUNCT
ejpam-7074	305	23	p2]-level	p2]-level	NOUN
ejpam-7074	305	24	and	and	CCONJ
ejpam-7074	305	25	lower	low	ADJ
ejpam-7074	305	26	[	[	X
ejpam-7074	305	27	q1	q1	NOUN
ejpam-7074	305	28	,	,	PUNCT
ejpam-7074	305	29	q2]-level	q2]-level	NOUN
ejpam-7074	305	30	of	of	ADP
ejpam-7074	305	31	a	a	PRON
ejpam-7074	305	32	are	be	AUX
ejpam-7074	305	33	subalgebras	subalgebra	NOUN
ejpam-7074	305	34	of	of	ADP
ejpam-7074	305	35	sh	sh	PROPN
ejpam-7074	305	36	.	.	PUNCT
ejpam-7074	306	1	proof	proof	NOUN
ejpam-7074	306	2	.	.	PUNCT
ejpam-7074	307	1	let	let	VERB
ejpam-7074	307	2	d	d	X
ejpam-7074	307	3	,	,	PUNCT
ejpam-7074	307	4	g	g	PROPN
ejpam-7074	307	5	∈	∈	PROPN
ejpam-7074	307	6	u	u	NOUN
ejpam-7074	307	7	(	(	PUNCT
ejpam-7074	307	8	µa	µa	INTJ
ejpam-7074	307	9	:	:	PUNCT
ejpam-7074	307	10	[	[	X
ejpam-7074	307	11	s1	s1	NOUN
ejpam-7074	307	12	,	,	PUNCT
ejpam-7074	307	13	s2	s2	NOUN
ejpam-7074	307	14	]	]	PUNCT
ejpam-7074	307	15	)	)	PUNCT
ejpam-7074	307	16	.	.	PUNCT
ejpam-7074	308	1	then	then	ADV
ejpam-7074	308	2	µa(d	µa(d	PUNCT
ejpam-7074	308	3	)	)	PUNCT
ejpam-7074	308	4	≤	≤	NOUN
ejpam-7074	309	1	[	[	X
ejpam-7074	309	2	p1	p1	NOUN
ejpam-7074	309	3	,	,	PUNCT
ejpam-7074	309	4	p2	p2	X
ejpam-7074	309	5	]	]	PUNCT
ejpam-7074	309	6	and	and	CCONJ
ejpam-7074	309	7	µa(g	µa(g	NOUN
ejpam-7074	309	8	)	)	PUNCT
ejpam-7074	309	9	≤	≤	NOUN
ejpam-7074	310	1	[	[	X
ejpam-7074	310	2	p1	p1	NOUN
ejpam-7074	310	3	,	,	PUNCT
ejpam-7074	310	4	p2	p2	NOUN
ejpam-7074	310	5	]	]	PUNCT
ejpam-7074	310	6	.	.	PUNCT
ejpam-7074	311	1	it	it	PRON
ejpam-7074	311	2	follows	follow	VERB
ejpam-7074	311	3	that	that	SCONJ
ejpam-7074	311	4	µa(d	µa(d	PUNCT
ejpam-7074	311	5	g	g	NOUN
ejpam-7074	311	6	|	|	NOUN
ejpam-7074	311	7	dg	dg	PROPN
ejpam-7074	311	8	)	)	PUNCT
ejpam-7074	311	9	≤	≤	NOUN
ejpam-7074	311	10	rmin{µa(d	rmin{µa(d	ADV
ejpam-7074	311	11	)	)	PUNCT
ejpam-7074	311	12	,	,	PUNCT
ejpam-7074	311	13	µa(g	µa(g	PUNCT
ejpam-7074	311	14	)	)	PUNCT
ejpam-7074	311	15	}	}	PUNCT
ejpam-7074	311	16	≤	≤	NOUN
ejpam-7074	312	1	[	[	X
ejpam-7074	312	2	p1	p1	NOUN
ejpam-7074	312	3	,	,	PUNCT
ejpam-7074	312	4	p2	p2	NOUN
ejpam-7074	312	5	]	]	PUNCT
ejpam-7074	312	6	so	so	SCONJ
ejpam-7074	312	7	that	that	SCONJ
ejpam-7074	312	8	dg	dg	VERB
ejpam-7074	312	9	|	|	ADV
ejpam-7074	312	10	dg	dg	VERB
ejpam-7074	312	11	∈	∈	PROPN
ejpam-7074	312	12	u	u	NOUN
ejpam-7074	312	13	(	(	PUNCT
ejpam-7074	312	14	µa	µa	INTJ
ejpam-7074	312	15	:	:	PUNCT
ejpam-7074	313	1	[	[	X
ejpam-7074	313	2	p1	p1	NOUN
ejpam-7074	313	3	,	,	PUNCT
ejpam-7074	313	4	p2	p2	X
ejpam-7074	313	5	]	]	PUNCT
ejpam-7074	313	6	)	)	PUNCT
ejpam-7074	313	7	.	.	PUNCT
ejpam-7074	314	1	hence	hence	ADV
ejpam-7074	314	2	,	,	PUNCT
ejpam-7074	314	3	u	u	PROPN
ejpam-7074	314	4	(	(	PUNCT
ejpam-7074	314	5	µa	µa	INTJ
ejpam-7074	314	6	:	:	PUNCT
ejpam-7074	315	1	[	[	X
ejpam-7074	315	2	p1	p1	NOUN
ejpam-7074	315	3	,	,	PUNCT
ejpam-7074	315	4	p2	p2	X
ejpam-7074	315	5	]	]	PUNCT
ejpam-7074	315	6	)	)	PUNCT
ejpam-7074	315	7	is	be	AUX
ejpam-7074	315	8	a	a	DET
ejpam-7074	315	9	subalgebra	subalgebra	NOUN
ejpam-7074	315	10	of	of	ADP
ejpam-7074	315	11	sh	sh	PROPN
ejpam-7074	315	12	.	.	PUNCT
ejpam-7074	316	1	let	let	VERB
ejpam-7074	316	2	d	d	X
ejpam-7074	316	3	,	,	PUNCT
ejpam-7074	316	4	g	g	PROPN
ejpam-7074	316	5	∈	∈	PROPN
ejpam-7074	316	6	l	l	NOUN
ejpam-7074	316	7	(	(	PUNCT
ejpam-7074	316	8	γa	γa	NOUN
ejpam-7074	316	9	:	:	PUNCT
ejpam-7074	317	1	[	[	X
ejpam-7074	317	2	q1	q1	X
ejpam-7074	317	3	,	,	PUNCT
ejpam-7074	317	4	q2	q2	NOUN
ejpam-7074	317	5	]	]	PUNCT
ejpam-7074	317	6	)	)	PUNCT
ejpam-7074	317	7	.	.	PUNCT
ejpam-7074	318	1	then	then	ADV
ejpam-7074	318	2	γa(d	γa(d	X
ejpam-7074	318	3	)	)	PUNCT
ejpam-7074	318	4	≤	≤	NOUN
ejpam-7074	319	1	[	[	X
ejpam-7074	319	2	q1	q1	NOUN
ejpam-7074	319	3	,	,	PUNCT
ejpam-7074	319	4	q2	q2	NOUN
ejpam-7074	319	5	]	]	PUNCT
ejpam-7074	319	6	and	and	CCONJ
ejpam-7074	319	7	γa(g	γa(g	NOUN
ejpam-7074	319	8	)	)	PUNCT
ejpam-7074	319	9	≤	≤	NOUN
ejpam-7074	320	1	[	[	X
ejpam-7074	320	2	q1	q1	NOUN
ejpam-7074	320	3	,	,	PUNCT
ejpam-7074	320	4	q2	q2	NOUN
ejpam-7074	320	5	]	]	PUNCT
ejpam-7074	320	6	.	.	PUNCT
ejpam-7074	321	1	it	it	PRON
ejpam-7074	321	2	follows	follow	VERB
ejpam-7074	321	3	that	that	SCONJ
ejpam-7074	321	4	γa(d	γa(d	PRON
ejpam-7074	322	1	g	g	PROPN
ejpam-7074	322	2	|	|	ADV
ejpam-7074	322	3	dg	dg	PROPN
ejpam-7074	322	4	)	)	PUNCT
ejpam-7074	322	5	≤	≤	NUM
ejpam-7074	322	6	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	322	7	)	)	PUNCT
ejpam-7074	322	8	,	,	PUNCT
ejpam-7074	322	9	γa(g	γa(g	ADP
ejpam-7074	322	10	)	)	PUNCT
ejpam-7074	322	11	}	}	PUNCT
ejpam-7074	322	12	≤	≤	NOUN
ejpam-7074	323	1	[	[	X
ejpam-7074	323	2	q1	q1	NOUN
ejpam-7074	323	3	,	,	PUNCT
ejpam-7074	323	4	q2	q2	NOUN
ejpam-7074	323	5	]	]	PUNCT
ejpam-7074	323	6	so	so	SCONJ
ejpam-7074	323	7	that	that	SCONJ
ejpam-7074	323	8	dg	dg	VERB
ejpam-7074	323	9	|	|	ADV
ejpam-7074	323	10	dg	dg	VERB
ejpam-7074	323	11	∈	∈	PROPN
ejpam-7074	323	12	l	l	NOUN
ejpam-7074	323	13	(	(	PUNCT
ejpam-7074	323	14	γa	γa	NOUN
ejpam-7074	323	15	:	:	PUNCT
ejpam-7074	323	16	[	[	X
ejpam-7074	323	17	q1	q1	X
ejpam-7074	323	18	,	,	PUNCT
ejpam-7074	323	19	q2	q2	NOUN
ejpam-7074	323	20	]	]	PUNCT
ejpam-7074	323	21	)	)	PUNCT
ejpam-7074	323	22	.	.	PUNCT
ejpam-7074	324	1	hence	hence	ADV
ejpam-7074	324	2	,	,	PUNCT
ejpam-7074	324	3	l	l	PROPN
ejpam-7074	324	4	(	(	PUNCT
ejpam-7074	324	5	γa	γa	NOUN
ejpam-7074	324	6	:	:	PUNCT
ejpam-7074	324	7	[	[	X
ejpam-7074	324	8	q1	q1	X
ejpam-7074	324	9	,	,	PUNCT
ejpam-7074	324	10	q2	q2	NOUN
ejpam-7074	324	11	]	]	PUNCT
ejpam-7074	324	12	)	)	PUNCT
ejpam-7074	324	13	is	be	AUX
ejpam-7074	324	14	a	a	DET
ejpam-7074	324	15	subalgebra	subalgebra	NOUN
ejpam-7074	324	16	of	of	ADP
ejpam-7074	324	17	sh	sh	PROPN
ejpam-7074	324	18	.	.	PUNCT
ejpam-7074	325	1	theorem	theorem	ADJ
ejpam-7074	325	2	7	7	NUM
ejpam-7074	325	3	.	.	PUNCT
ejpam-7074	326	1	let	let	VERB
ejpam-7074	326	2	sh	sh	NOUN
ejpam-7074	326	3	:	:	PUNCT
ejpam-7074	326	4	=	=	SYM
ejpam-7074	326	5	(	(	PUNCT
ejpam-7074	326	6	sh	sh	INTJ
ejpam-7074	326	7	,	,	PUNCT
ejpam-7074	326	8	|	|	ADV
ejpam-7074	326	9	,	,	PUNCT
ejpam-7074	326	10	0	0	NUM
ejpam-7074	326	11	)	)	PUNCT
ejpam-7074	326	12	be	be	AUX
ejpam-7074	326	13	an	an	DET
ejpam-7074	326	14	ssha	ssha	NOUN
ejpam-7074	326	15	.	.	PUNCT
ejpam-7074	327	1	let	let	VERB
ejpam-7074	327	2	a	a	PRON
ejpam-7074	327	3	=	=	SYM
ejpam-7074	327	4	(	(	PUNCT
ejpam-7074	327	5	µa	µa	PROPN
ejpam-7074	327	6	,	,	PUNCT
ejpam-7074	327	7	γa	γa	PROPN
ejpam-7074	327	8	)	)	PUNCT
ejpam-7074	327	9	be	be	VERB
ejpam-7074	327	10	an	an	DET
ejpam-7074	327	11	ivifs	ivif	NOUN
ejpam-7074	327	12	in	in	ADP
ejpam-7074	327	13	sh	sh	PROPN
ejpam-7074	327	14	such	such	ADJ
ejpam-7074	327	15	that	that	SCONJ
ejpam-7074	327	16	the	the	DET
ejpam-7074	327	17	sets	set	NOUN
ejpam-7074	327	18	u	u	NOUN
ejpam-7074	327	19	(	(	PUNCT
ejpam-7074	327	20	µa	µa	INTJ
ejpam-7074	327	21	:	:	PUNCT
ejpam-7074	328	1	[	[	X
ejpam-7074	328	2	p1	p1	NOUN
ejpam-7074	328	3	,	,	PUNCT
ejpam-7074	328	4	p2	p2	X
ejpam-7074	328	5	]	]	PUNCT
ejpam-7074	328	6	)	)	PUNCT
ejpam-7074	328	7	and	and	CCONJ
ejpam-7074	328	8	l	l	NOUN
ejpam-7074	328	9	(	(	PUNCT
ejpam-7074	328	10	γa	γa	NOUN
ejpam-7074	328	11	:	:	PUNCT
ejpam-7074	329	1	[	[	X
ejpam-7074	329	2	q1	q1	X
ejpam-7074	329	3	,	,	PUNCT
ejpam-7074	329	4	q2	q2	NOUN
ejpam-7074	329	5	]	]	PUNCT
ejpam-7074	329	6	)	)	PUNCT
ejpam-7074	329	7	are	be	AUX
ejpam-7074	329	8	subalgebras	subalgebra	NOUN
ejpam-7074	329	9	of	of	ADP
ejpam-7074	329	10	sh	sh	PROPN
ejpam-7074	329	11	for	for	ADP
ejpam-7074	329	12	every	every	DET
ejpam-7074	329	13	[	[	X
ejpam-7074	329	14	p1	p1	NOUN
ejpam-7074	329	15	,	,	PUNCT
ejpam-7074	329	16	p2	p2	NOUN
ejpam-7074	329	17	]	]	PUNCT
ejpam-7074	329	18	,	,	PUNCT
ejpam-7074	329	19	[	[	X
ejpam-7074	329	20	q1	q1	X
ejpam-7074	329	21	,	,	PUNCT
ejpam-7074	329	22	q2	q2	NOUN
ejpam-7074	329	23	]	]	PUNCT
ejpam-7074	329	24	∈	∈	PROPN
ejpam-7074	330	1	d	d	X
ejpam-7074	331	1	[	[	X
ejpam-7074	331	2	0	0	NUM
ejpam-7074	331	3	,	,	PUNCT
ejpam-7074	331	4	1	1	NUM
ejpam-7074	331	5	]	]	PUNCT
ejpam-7074	331	6	.	.	PUNCT
ejpam-7074	332	1	then	then	ADV
ejpam-7074	332	2	a	a	DET
ejpam-7074	332	3	=	=	SYM
ejpam-7074	332	4	(	(	PUNCT
ejpam-7074	332	5	µa	µa	PROPN
ejpam-7074	332	6	,	,	PUNCT
ejpam-7074	332	7	γa	γa	PROPN
ejpam-7074	332	8	)	)	PUNCT
ejpam-7074	332	9	is	be	AUX
ejpam-7074	332	10	an	an	DET
ejpam-7074	332	11	ivifss	ivifss	ADJ
ejpam-7074	332	12	-	-	PUNCT
ejpam-7074	332	13	subalgebra	subalgebra	NOUN
ejpam-7074	332	14	of	of	ADP
ejpam-7074	332	15	sh	sh	PROPN
ejpam-7074	332	16	.	.	PUNCT
ejpam-7074	333	1	a.	a.	PROPN
ejpam-7074	333	2	iampan	iampan	PROPN
ejpam-7074	333	3	et	et	PROPN
ejpam-7074	333	4	al	al	PROPN
ejpam-7074	333	5	.	.	PUNCT
ejpam-7074	333	6	/	/	SYM
ejpam-7074	333	7	eur	eur	PROPN
ejpam-7074	333	8	.	.	PUNCT
ejpam-7074	334	1	j.	j.	PROPN
ejpam-7074	334	2	pure	pure	PROPN
ejpam-7074	334	3	appl	appl	PROPN
ejpam-7074	334	4	.	.	PROPN
ejpam-7074	334	5	math	math	PROPN
ejpam-7074	334	6	,	,	PUNCT
ejpam-7074	334	7	18	18	NUM
ejpam-7074	334	8	(	(	PUNCT
ejpam-7074	334	9	4	4	NUM
ejpam-7074	334	10	)	)	PUNCT
ejpam-7074	334	11	(	(	PUNCT
ejpam-7074	334	12	2025	2025	NUM
ejpam-7074	334	13	)	)	PUNCT
ejpam-7074	334	14	,	,	PUNCT
ejpam-7074	334	15	7074	7074	NUM
ejpam-7074	334	16	10	10	NUM
ejpam-7074	334	17	of	of	ADP
ejpam-7074	334	18	14	14	NUM
ejpam-7074	334	19	proof	proof	NOUN
ejpam-7074	334	20	.	.	PUNCT
ejpam-7074	335	1	let	let	VERB
ejpam-7074	335	2	for	for	ADP
ejpam-7074	335	3	every	every	DET
ejpam-7074	335	4	[	[	X
ejpam-7074	335	5	p1	p1	NOUN
ejpam-7074	335	6	,	,	PUNCT
ejpam-7074	335	7	p2	p2	NOUN
ejpam-7074	335	8	]	]	PUNCT
ejpam-7074	335	9	,	,	PUNCT
ejpam-7074	335	10	[	[	X
ejpam-7074	335	11	q1	q1	X
ejpam-7074	335	12	,	,	PUNCT
ejpam-7074	335	13	q2	q2	NOUN
ejpam-7074	335	14	]	]	PUNCT
ejpam-7074	335	15	∈	∈	PROPN
ejpam-7074	336	1	d	d	X
ejpam-7074	337	1	[	[	X
ejpam-7074	337	2	0	0	NUM
ejpam-7074	337	3	,	,	PUNCT
ejpam-7074	337	4	1	1	NUM
ejpam-7074	337	5	]	]	PUNCT
ejpam-7074	337	6	,	,	PUNCT
ejpam-7074	337	7	u	u	NOUN
ejpam-7074	337	8	(	(	PUNCT
ejpam-7074	337	9	µa	µa	INTJ
ejpam-7074	337	10	:	:	PUNCT
ejpam-7074	337	11	[	[	X
ejpam-7074	337	12	p1	p1	NOUN
ejpam-7074	337	13	,	,	PUNCT
ejpam-7074	337	14	p2	p2	X
ejpam-7074	337	15	]	]	PUNCT
ejpam-7074	337	16	)	)	PUNCT
ejpam-7074	337	17	and	and	CCONJ
ejpam-7074	337	18	l	l	NOUN
ejpam-7074	337	19	(	(	PUNCT
ejpam-7074	337	20	γa	γa	NOUN
ejpam-7074	337	21	:	:	PUNCT
ejpam-7074	338	1	[	[	X
ejpam-7074	338	2	q1	q1	X
ejpam-7074	338	3	,	,	PUNCT
ejpam-7074	338	4	q2	q2	NOUN
ejpam-7074	338	5	]	]	PUNCT
ejpam-7074	338	6	)	)	PUNCT
ejpam-7074	338	7	are	be	AUX
ejpam-7074	338	8	subalgebras	subalgebra	NOUN
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ejpam-7074	338	10	sh	sh	PROPN
ejpam-7074	338	11	.	.	PUNCT
ejpam-7074	339	1	in	in	ADP
ejpam-7074	339	2	contrary	contrary	NOUN
ejpam-7074	339	3	,	,	PUNCT
ejpam-7074	339	4	let	let	VERB
ejpam-7074	339	5	d0	d0	NOUN
ejpam-7074	339	6	,	,	PUNCT
ejpam-7074	339	7	g0	g0	PROPN
ejpam-7074	339	8	∈	∈	PROPN
ejpam-7074	339	9	sh	sh	INTJ
ejpam-7074	339	10	be	be	AUX
ejpam-7074	339	11	such	such	ADJ
ejpam-7074	339	12	that	that	SCONJ
ejpam-7074	339	13	µa(d	µa(d	PUNCT
ejpam-7074	339	14	g0	g0	NOUN
ejpam-7074	339	15	0	0	PUNCT
ejpam-7074	340	1	|	|	ADV
ejpam-7074	340	2	dg00	dg00	PROPN
ejpam-7074	340	3	)	)	PUNCT
ejpam-7074	340	4	<	<	X
ejpam-7074	340	5	rmin{µa(d0	rmin{µa(d0	NOUN
ejpam-7074	340	6	)	)	PUNCT
ejpam-7074	340	7	,	,	PUNCT
ejpam-7074	340	8	µa(g0	µa(g0	NUM
ejpam-7074	340	9	)	)	PUNCT
ejpam-7074	340	10	}	}	PUNCT
ejpam-7074	340	11	.	.	PUNCT
ejpam-7074	341	1	let	let	VERB
ejpam-7074	341	2	µa(d0	µa(d0	NOUN
ejpam-7074	341	3	)	)	PUNCT
ejpam-7074	341	4	=	=	NOUN
ejpam-7074	342	1	[	[	X
ejpam-7074	342	2	θ1	θ1	NOUN
ejpam-7074	342	3	,	,	PUNCT
ejpam-7074	342	4	θ2	θ2	PROPN
ejpam-7074	342	5	]	]	PUNCT
ejpam-7074	342	6	,	,	PUNCT
ejpam-7074	342	7	µa(g0	µa(g0	NUM
ejpam-7074	342	8	)	)	PUNCT
ejpam-7074	342	9	=	=	PUNCT
ejpam-7074	343	1	[	[	X
ejpam-7074	343	2	θ3	θ3	NOUN
ejpam-7074	343	3	,	,	PUNCT
ejpam-7074	343	4	θ4	θ4	NOUN
ejpam-7074	343	5	]	]	PUNCT
ejpam-7074	343	6	and	and	CCONJ
ejpam-7074	343	7	µa(d	µa(d	X
ejpam-7074	343	8	g0	g0	NOUN
ejpam-7074	343	9	0	0	NUM
ejpam-7074	344	1	|	|	ADV
ejpam-7074	344	2	dg00	dg00	PROPN
ejpam-7074	344	3	)	)	PUNCT
ejpam-7074	345	1	=	=	PUNCT
ejpam-7074	346	1	[	[	X
ejpam-7074	346	2	p1	p1	NOUN
ejpam-7074	346	3	,	,	PUNCT
ejpam-7074	346	4	p2	p2	NOUN
ejpam-7074	346	5	]	]	PUNCT
ejpam-7074	346	6	.	.	PUNCT
ejpam-7074	347	1	then	then	ADV
ejpam-7074	347	2	[	[	X
ejpam-7074	347	3	p1	p1	NOUN
ejpam-7074	347	4	,	,	PUNCT
ejpam-7074	347	5	p2	p2	X
ejpam-7074	347	6	]	]	PUNCT
ejpam-7074	347	7	<	<	X
ejpam-7074	347	8	rmin{[θ1	rmin{[θ1	X
ejpam-7074	347	9	,	,	PUNCT
ejpam-7074	347	10	θ2	θ2	PROPN
ejpam-7074	347	11	]	]	PUNCT
ejpam-7074	347	12	,	,	PUNCT
ejpam-7074	347	13	[	[	X
ejpam-7074	347	14	θ3	θ3	NOUN
ejpam-7074	347	15	,	,	PUNCT
ejpam-7074	347	16	θ4	θ4	NOUN
ejpam-7074	347	17	]	]	PUNCT
ejpam-7074	347	18	}	}	PUNCT
ejpam-7074	347	19	=	=	SYM
ejpam-7074	348	1	[	[	X
ejpam-7074	348	2	min{θ1	min{θ1	ADJ
ejpam-7074	348	3	,	,	PUNCT
ejpam-7074	348	4	θ3},min{θ2	θ3},min{θ2	X
ejpam-7074	348	5	,	,	PUNCT
ejpam-7074	348	6	θ4	θ4	NOUN
ejpam-7074	348	7	}	}	PUNCT
ejpam-7074	348	8	]	]	PUNCT
ejpam-7074	348	9	.	.	PUNCT
ejpam-7074	349	1	so	so	ADV
ejpam-7074	349	2	,	,	PUNCT
ejpam-7074	349	3	p1	p1	PROPN
ejpam-7074	349	4	<	<	X
ejpam-7074	349	5	min{θ1	min{θ1	PROPN
ejpam-7074	349	6	,	,	PUNCT
ejpam-7074	349	7	θ3	θ3	NOUN
ejpam-7074	349	8	}	}	PUNCT
ejpam-7074	349	9	and	and	CCONJ
ejpam-7074	349	10	p2	p2	X
ejpam-7074	349	11	<	<	X
ejpam-7074	349	12	min{θ2	min{θ2	NOUN
ejpam-7074	349	13	,	,	PUNCT
ejpam-7074	349	14	θ4	θ4	NOUN
ejpam-7074	349	15	}	}	PUNCT
ejpam-7074	349	16	.	.	PUNCT
ejpam-7074	350	1	consider	consider	VERB
ejpam-7074	350	2	,	,	PUNCT
ejpam-7074	350	3	[	[	X
ejpam-7074	350	4	ρ1	ρ1	NOUN
ejpam-7074	350	5	,	,	PUNCT
ejpam-7074	350	6	ρ2	ρ2	NOUN
ejpam-7074	350	7	]	]	PUNCT
ejpam-7074	350	8	=	=	SYM
ejpam-7074	350	9	1	1	NUM
ejpam-7074	350	10	2	2	NUM
ejpam-7074	350	11	[	[	X
ejpam-7074	350	12	µa(d	µa(d	X
ejpam-7074	350	13	g0	g0	NOUN
ejpam-7074	350	14	0	0	PUNCT
ejpam-7074	351	1	|	|	ADV
ejpam-7074	351	2	dg00	dg00	PROPN
ejpam-7074	351	3	)	)	PUNCT
ejpam-7074	352	1	+	+	NUM
ejpam-7074	352	2	rmin{µa(d0	rmin{µa(d0	NOUN
ejpam-7074	352	3	)	)	PUNCT
ejpam-7074	352	4	,	,	PUNCT
ejpam-7074	352	5	µa(g0	µa(g0	NUM
ejpam-7074	352	6	)	)	PUNCT
ejpam-7074	352	7	}	}	PUNCT
ejpam-7074	352	8	]	]	PUNCT
ejpam-7074	353	1	=	=	SYM
ejpam-7074	353	2	1	1	NUM
ejpam-7074	353	3	2	2	NUM
ejpam-7074	354	1	[	[	X
ejpam-7074	354	2	[	[	X
ejpam-7074	354	3	p1	p1	NOUN
ejpam-7074	354	4	,	,	PUNCT
ejpam-7074	354	5	p2	p2	X
ejpam-7074	354	6	]	]	PUNCT
ejpam-7074	355	1	+	+	CCONJ
ejpam-7074	355	2	[	[	X
ejpam-7074	355	3	min{θ1	min{θ1	ADJ
ejpam-7074	355	4	,	,	PUNCT
ejpam-7074	355	5	θ3},min{θ2	θ3},min{θ2	X
ejpam-7074	355	6	,	,	PUNCT
ejpam-7074	355	7	θ4	θ4	NOUN
ejpam-7074	355	8	}	}	PUNCT
ejpam-7074	355	9	]	]	PUNCT
ejpam-7074	355	10	]	]	PUNCT
ejpam-7074	356	1	=	=	PUNCT
ejpam-7074	357	1	[	[	X
ejpam-7074	357	2	12(p1	12(p1	NUM
ejpam-7074	357	3	+	+	ADJ
ejpam-7074	357	4	min{θ1	min{θ1	ADJ
ejpam-7074	357	5	,	,	PUNCT
ejpam-7074	357	6	θ3	θ3	NOUN
ejpam-7074	357	7	}	}	PUNCT
ejpam-7074	357	8	)	)	PUNCT
ejpam-7074	357	9	,	,	PUNCT
ejpam-7074	357	10	12(p2	12(p2	NUM
ejpam-7074	358	1	+	+	NOUN
ejpam-7074	358	2	min{θ2	min{θ2	NOUN
ejpam-7074	358	3	,	,	PUNCT
ejpam-7074	358	4	θ4	θ4	NOUN
ejpam-7074	358	5	}	}	PUNCT
ejpam-7074	358	6	)	)	PUNCT
ejpam-7074	358	7	]	]	PUNCT
ejpam-7074	358	8	.	.	PUNCT
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ejpam-7074	359	2	,	,	PUNCT
ejpam-7074	359	3	min{θ1	min{θ1	ADJ
ejpam-7074	359	4	,	,	PUNCT
ejpam-7074	359	5	θ3	θ3	NOUN
ejpam-7074	359	6	}	}	PUNCT
ejpam-7074	359	7	>	>	PUNCT
ejpam-7074	359	8	ρ1	ρ1	NOUN
ejpam-7074	359	9	=	=	SYM
ejpam-7074	359	10	1	1	NUM
ejpam-7074	359	11	2(p1	2(p1	NUM
ejpam-7074	359	12	+	+	CCONJ
ejpam-7074	359	13	min{θ1	min{θ1	ADJ
ejpam-7074	359	14	,	,	PUNCT
ejpam-7074	359	15	θ3	θ3	NOUN
ejpam-7074	359	16	}	}	PUNCT
ejpam-7074	359	17	)	)	PUNCT
ejpam-7074	360	1	>	>	X
ejpam-7074	360	2	p1	p1	PROPN
ejpam-7074	360	3	and	and	CCONJ
ejpam-7074	360	4	min{θ2	min{θ2	NOUN
ejpam-7074	360	5	,	,	PUNCT
ejpam-7074	360	6	θ4	θ4	NOUN
ejpam-7074	360	7	}	}	PUNCT
ejpam-7074	360	8	>	>	X
ejpam-7074	360	9	ρ2	ρ2	NOUN
ejpam-7074	360	10	=	=	SYM
ejpam-7074	360	11	1	1	NUM
ejpam-7074	360	12	2(p2	2(p2	NUM
ejpam-7074	360	13	+	+	CCONJ
ejpam-7074	360	14	min{θ2	min{θ2	NOUN
ejpam-7074	360	15	,	,	PUNCT
ejpam-7074	360	16	θ4	θ4	NOUN
ejpam-7074	360	17	}	}	PUNCT
ejpam-7074	360	18	)	)	PUNCT
ejpam-7074	360	19	>	>	X
ejpam-7074	360	20	p2	p2	PROPN
ejpam-7074	360	21	.	.	PUNCT
ejpam-7074	361	1	hence	hence	ADV
ejpam-7074	361	2	,	,	PUNCT
ejpam-7074	361	3	[	[	X
ejpam-7074	361	4	min{θ1	min{θ1	ADJ
ejpam-7074	361	5	,	,	PUNCT
ejpam-7074	361	6	θ3},min{θ2	θ3},min{θ2	X
ejpam-7074	361	7	,	,	PUNCT
ejpam-7074	361	8	θ4	θ4	NOUN
ejpam-7074	361	9	}	}	PUNCT
ejpam-7074	361	10	]	]	PUNCT
ejpam-7074	361	11	>	>	X
ejpam-7074	362	1	[	[	X
ejpam-7074	362	2	ρ1	ρ1	NOUN
ejpam-7074	362	3	,	,	PUNCT
ejpam-7074	362	4	ρ2	ρ2	NOUN
ejpam-7074	362	5	]	]	PUNCT
ejpam-7074	362	6	>	>	X
ejpam-7074	363	1	[	[	X
ejpam-7074	363	2	p1	p1	NOUN
ejpam-7074	363	3	,	,	PUNCT
ejpam-7074	363	4	p2	p2	NOUN
ejpam-7074	363	5	]	]	PUNCT
ejpam-7074	363	6	,	,	PUNCT
ejpam-7074	363	7	so	so	SCONJ
ejpam-7074	363	8	that	that	SCONJ
ejpam-7074	363	9	dg00	dg00	PROPN
ejpam-7074	363	10	|	|	ADV
ejpam-7074	363	11	dg00	dg00	PROPN
ejpam-7074	363	12	/∈	/∈	PUNCT
ejpam-7074	363	13	u	u	NOUN
ejpam-7074	363	14	(	(	PUNCT
ejpam-7074	363	15	µa	µa	INTJ
ejpam-7074	363	16	:	:	PUNCT
ejpam-7074	363	17	[	[	X
ejpam-7074	363	18	p1	p1	NOUN
ejpam-7074	363	19	,	,	PUNCT
ejpam-7074	363	20	p2	p2	X
ejpam-7074	363	21	]	]	PUNCT
ejpam-7074	363	22	)	)	PUNCT
ejpam-7074	363	23	,	,	PUNCT
ejpam-7074	363	24	a	a	DET
ejpam-7074	363	25	contradiction	contradiction	NOUN
ejpam-7074	363	26	,	,	PUNCT
ejpam-7074	363	27	since	since	SCONJ
ejpam-7074	363	28	µa(d0	µa(d0	NOUN
ejpam-7074	363	29	)	)	PUNCT
ejpam-7074	363	30	=	=	NOUN
ejpam-7074	364	1	[	[	X
ejpam-7074	364	2	θ1	θ1	NOUN
ejpam-7074	364	3	,	,	PUNCT
ejpam-7074	364	4	θ2	θ2	PROPN
ejpam-7074	364	5	]	]	PUNCT
ejpam-7074	364	6	≥	≥	X
ejpam-7074	364	7	[	[	X
ejpam-7074	364	8	min{θ1	min{θ1	ADJ
ejpam-7074	364	9	,	,	PUNCT
ejpam-7074	364	10	θ3},min{θ2	θ3},min{θ2	X
ejpam-7074	364	11	,	,	PUNCT
ejpam-7074	364	12	θ4	θ4	NOUN
ejpam-7074	364	13	}	}	PUNCT
ejpam-7074	364	14	]	]	PUNCT
ejpam-7074	364	15	>	>	X
ejpam-7074	365	1	[	[	X
ejpam-7074	365	2	ρ1	ρ1	NOUN
ejpam-7074	365	3	,	,	PUNCT
ejpam-7074	365	4	ρ2	ρ2	NOUN
ejpam-7074	365	5	]	]	PUNCT
ejpam-7074	365	6	and	and	CCONJ
ejpam-7074	365	7	µa(g0	µa(g0	NUM
ejpam-7074	365	8	)	)	PUNCT
ejpam-7074	365	9	=	=	PUNCT
ejpam-7074	366	1	[	[	X
ejpam-7074	366	2	θ3	θ3	NOUN
ejpam-7074	366	3	,	,	PUNCT
ejpam-7074	366	4	θ4	θ4	NOUN
ejpam-7074	366	5	]	]	PUNCT
ejpam-7074	366	6	≥	≥	X
ejpam-7074	367	1	[	[	X
ejpam-7074	367	2	min{θ1	min{θ1	ADJ
ejpam-7074	367	3	,	,	PUNCT
ejpam-7074	367	4	θ3},min{θ2	θ3},min{θ2	X
ejpam-7074	367	5	,	,	PUNCT
ejpam-7074	367	6	θ4	θ4	NOUN
ejpam-7074	367	7	}	}	PUNCT
ejpam-7074	367	8	]	]	PUNCT
ejpam-7074	367	9	>	>	X
ejpam-7074	368	1	[	[	X
ejpam-7074	368	2	ρ1	ρ1	NOUN
ejpam-7074	368	3	,	,	PUNCT
ejpam-7074	368	4	ρ2	ρ2	NOUN
ejpam-7074	368	5	]	]	PUNCT
ejpam-7074	368	6	.	.	PUNCT
ejpam-7074	369	1	this	this	PRON
ejpam-7074	369	2	implies	imply	VERB
ejpam-7074	369	3	dg00	dg00	PROPN
ejpam-7074	369	4	|	|	ADV
ejpam-7074	369	5	dg00	dg00	PROPN
ejpam-7074	369	6	∈	∈	PROPN
ejpam-7074	369	7	u	u	NOUN
ejpam-7074	369	8	(	(	PUNCT
ejpam-7074	369	9	µa	µa	INTJ
ejpam-7074	369	10	:	:	PUNCT
ejpam-7074	369	11	[	[	X
ejpam-7074	369	12	p1	p1	NOUN
ejpam-7074	369	13	,	,	PUNCT
ejpam-7074	369	14	p2	p2	X
ejpam-7074	369	15	]	]	PUNCT
ejpam-7074	369	16	)	)	PUNCT
ejpam-7074	369	17	.	.	PUNCT
ejpam-7074	370	1	thus	thus	ADV
ejpam-7074	370	2	µa(d	µa(d	PUNCT
ejpam-7074	370	3	g	g	NOUN
ejpam-7074	370	4	|	|	NOUN
ejpam-7074	370	5	dg	dg	PROPN
ejpam-7074	370	6	)	)	PUNCT
ejpam-7074	370	7	≤	≤	NOUN
ejpam-7074	370	8	rmin{µa(d	rmin{µa(d	ADV
ejpam-7074	370	9	)	)	PUNCT
ejpam-7074	370	10	,	,	PUNCT
ejpam-7074	370	11	µa(g	µa(g	NOUN
ejpam-7074	370	12	)	)	PUNCT
ejpam-7074	370	13	}	}	PUNCT
ejpam-7074	370	14	for	for	ADP
ejpam-7074	370	15	all	all	DET
ejpam-7074	370	16	d	d	PROPN
ejpam-7074	370	17	,	,	PUNCT
ejpam-7074	370	18	g	g	PROPN
ejpam-7074	370	19	∈	∈	PROPN
ejpam-7074	370	20	sh	sh	INTJ
ejpam-7074	370	21	.	.	PUNCT
ejpam-7074	371	1	again	again	ADV
ejpam-7074	371	2	,	,	PUNCT
ejpam-7074	371	3	in	in	ADP
ejpam-7074	371	4	contrary	contrary	NOUN
ejpam-7074	371	5	,	,	PUNCT
ejpam-7074	371	6	let	let	VERB
ejpam-7074	371	7	d0	d0	NOUN
ejpam-7074	371	8	,	,	PUNCT
ejpam-7074	371	9	g0	g0	PROPN
ejpam-7074	371	10	∈	∈	PROPN
ejpam-7074	371	11	sh	sh	INTJ
ejpam-7074	371	12	be	be	AUX
ejpam-7074	371	13	such	such	ADJ
ejpam-7074	371	14	that	that	SCONJ
ejpam-7074	371	15	γa(d	γa(d	NUM
ejpam-7074	371	16	g0	g0	PROPN
ejpam-7074	371	17	0	0	PUNCT
ejpam-7074	372	1	|	|	ADV
ejpam-7074	372	2	dg00	dg00	PROPN
ejpam-7074	372	3	)	)	PUNCT
ejpam-7074	372	4	>	>	SYM
ejpam-7074	372	5	rmax{γa(d0	rmax{γa(d0	PROPN
ejpam-7074	372	6	)	)	PUNCT
ejpam-7074	372	7	,	,	PUNCT
ejpam-7074	372	8	γa(g0	γa(g0	NUM
ejpam-7074	372	9	)	)	PUNCT
ejpam-7074	372	10	}	}	PUNCT
ejpam-7074	372	11	.	.	PUNCT
ejpam-7074	373	1	let	let	VERB
ejpam-7074	373	2	γa(d0	γa(d0	X
ejpam-7074	373	3	)	)	PUNCT
ejpam-7074	374	1	=	=	PUNCT
ejpam-7074	375	1	[	[	X
ejpam-7074	375	2	η1	η1	NOUN
ejpam-7074	375	3	,	,	PUNCT
ejpam-7074	375	4	η2	η2	PROPN
ejpam-7074	375	5	]	]	PUNCT
ejpam-7074	375	6	,	,	PUNCT
ejpam-7074	375	7	γa(g0	γa(g0	NUM
ejpam-7074	375	8	)	)	PUNCT
ejpam-7074	375	9	=	=	NOUN
ejpam-7074	376	1	[	[	X
ejpam-7074	376	2	η3	η3	NOUN
ejpam-7074	376	3	,	,	PUNCT
ejpam-7074	376	4	η4	η4	VERB
ejpam-7074	376	5	]	]	PUNCT
ejpam-7074	376	6	and	and	CCONJ
ejpam-7074	376	7	γa(d	γa(d	NUM
ejpam-7074	376	8	g0	g0	PROPN
ejpam-7074	376	9	0	0	NUM
ejpam-7074	377	1	|	|	ADV
ejpam-7074	377	2	dg00	dg00	PROPN
ejpam-7074	377	3	)	)	PUNCT
ejpam-7074	378	1	=	=	PUNCT
ejpam-7074	379	1	[	[	X
ejpam-7074	379	2	q1	q1	PROPN
ejpam-7074	379	3	,	,	PUNCT
ejpam-7074	379	4	q2	q2	NOUN
ejpam-7074	379	5	]	]	PUNCT
ejpam-7074	379	6	.	.	PUNCT
ejpam-7074	380	1	then	then	ADV
ejpam-7074	380	2	[	[	X
ejpam-7074	380	3	q1	q1	NOUN
ejpam-7074	380	4	,	,	PUNCT
ejpam-7074	380	5	q2	q2	NOUN
ejpam-7074	380	6	]	]	PUNCT
ejpam-7074	380	7	>	>	X
ejpam-7074	380	8	rmax{[η1	rmax{[η1	X
ejpam-7074	380	9	,	,	PUNCT
ejpam-7074	380	10	η2	η2	PROPN
ejpam-7074	380	11	]	]	PUNCT
ejpam-7074	380	12	,	,	PUNCT
ejpam-7074	380	13	[	[	X
ejpam-7074	380	14	η3	η3	NOUN
ejpam-7074	380	15	,	,	PUNCT
ejpam-7074	380	16	η4	η4	VERB
ejpam-7074	380	17	]	]	PUNCT
ejpam-7074	380	18	}	}	PUNCT
ejpam-7074	380	19	=	=	SYM
ejpam-7074	381	1	[	[	X
ejpam-7074	381	2	max{η1	max{η1	NOUN
ejpam-7074	381	3	,	,	PUNCT
ejpam-7074	381	4	η3},max{η2	η3},max{η2	NOUN
ejpam-7074	381	5	,	,	PUNCT
ejpam-7074	381	6	η4	η4	VERB
ejpam-7074	381	7	}	}	PUNCT
ejpam-7074	381	8	]	]	PUNCT
ejpam-7074	381	9	.	.	PUNCT
ejpam-7074	382	1	so	so	ADV
ejpam-7074	382	2	,	,	PUNCT
ejpam-7074	382	3	q1	q1	PROPN
ejpam-7074	382	4	>	>	X
ejpam-7074	382	5	max{η1	max{η1	PROPN
ejpam-7074	382	6	,	,	PUNCT
ejpam-7074	382	7	η3	η3	NOUN
ejpam-7074	382	8	}	}	PUNCT
ejpam-7074	382	9	and	and	CCONJ
ejpam-7074	382	10	q2	q2	X
ejpam-7074	382	11	>	>	X
ejpam-7074	382	12	max{η2	max{η2	PROPN
ejpam-7074	382	13	,	,	PUNCT
ejpam-7074	382	14	η4	η4	VERB
ejpam-7074	382	15	}	}	PUNCT
ejpam-7074	382	16	.	.	PUNCT
ejpam-7074	383	1	let	let	VERB
ejpam-7074	383	2	us	we	PRON
ejpam-7074	383	3	consider	consider	VERB
ejpam-7074	383	4	,	,	PUNCT
ejpam-7074	383	5	[	[	X
ejpam-7074	383	6	λ1	λ1	ADJ
ejpam-7074	383	7	,	,	PUNCT
ejpam-7074	383	8	λ2	λ2	NOUN
ejpam-7074	383	9	]	]	X
ejpam-7074	384	1	=	=	SYM
ejpam-7074	384	2	1	1	NUM
ejpam-7074	384	3	2	2	NUM
ejpam-7074	384	4	[	[	X
ejpam-7074	384	5	γa(d	γa(d	X
ejpam-7074	384	6	g0	g0	NOUN
ejpam-7074	384	7	0	0	PUNCT
ejpam-7074	385	1	|	|	ADV
ejpam-7074	385	2	dg00	dg00	PROPN
ejpam-7074	385	3	)	)	PUNCT
ejpam-7074	386	1	+	+	NUM
ejpam-7074	386	2	rmax{γa(d0	rmax{γa(d0	NOUN
ejpam-7074	386	3	)	)	PUNCT
ejpam-7074	386	4	,	,	PUNCT
ejpam-7074	386	5	γa(g0	γa(g0	NUM
ejpam-7074	386	6	)	)	PUNCT
ejpam-7074	386	7	}	}	PUNCT
ejpam-7074	386	8	]	]	PUNCT
ejpam-7074	387	1	=	=	SYM
ejpam-7074	387	2	1	1	NUM
ejpam-7074	387	3	2	2	NUM
ejpam-7074	387	4	[	[	X
ejpam-7074	387	5	[	[	X
ejpam-7074	387	6	q1	q1	PROPN
ejpam-7074	387	7	,	,	PUNCT
ejpam-7074	387	8	q2	q2	NOUN
ejpam-7074	387	9	]	]	PUNCT
ejpam-7074	387	10	+	+	CCONJ
ejpam-7074	388	1	[	[	X
ejpam-7074	388	2	max{η1	max{η1	NOUN
ejpam-7074	388	3	,	,	PUNCT
ejpam-7074	388	4	η3},max{η2	η3},max{η2	NOUN
ejpam-7074	388	5	,	,	PUNCT
ejpam-7074	388	6	η4	η4	VERB
ejpam-7074	388	7	}	}	PUNCT
ejpam-7074	388	8	]	]	PUNCT
ejpam-7074	388	9	=	=	SYM
ejpam-7074	388	10	1	1	NUM
ejpam-7074	388	11	2(q1	2(q1	NUM
ejpam-7074	389	1	+	+	NOUN
ejpam-7074	389	2	max{η1	max{η1	NOUN
ejpam-7074	389	3	,	,	PUNCT
ejpam-7074	389	4	η3	η3	NOUN
ejpam-7074	389	5	}	}	PUNCT
ejpam-7074	389	6	)	)	PUNCT
ejpam-7074	389	7	,	,	PUNCT
ejpam-7074	389	8	12(q2	12(q2	NUM
ejpam-7074	390	1	+	+	ADJ
ejpam-7074	390	2	max{η2	max{η2	X
ejpam-7074	390	3	,	,	PUNCT
ejpam-7074	390	4	η4	η4	VERB
ejpam-7074	390	5	}	}	PUNCT
ejpam-7074	390	6	)	)	PUNCT
ejpam-7074	390	7	.	.	PUNCT
ejpam-7074	391	1	therefore	therefore	ADV
ejpam-7074	391	2	,	,	PUNCT
ejpam-7074	391	3	max{η1	max{η1	NOUN
ejpam-7074	391	4	,	,	PUNCT
ejpam-7074	391	5	η3	η3	NOUN
ejpam-7074	391	6	}	}	PUNCT
ejpam-7074	391	7	<	<	X
ejpam-7074	391	8	λ1	λ1	PROPN
ejpam-7074	391	9	=	=	SYM
ejpam-7074	391	10	1	1	NUM
ejpam-7074	391	11	2	2	NUM
ejpam-7074	391	12	[	[	X
ejpam-7074	391	13	(	(	PUNCT
ejpam-7074	391	14	q1+max{η1	q1+max{η1	NOUN
ejpam-7074	391	15	,	,	PUNCT
ejpam-7074	391	16	η3	η3	NOUN
ejpam-7074	391	17	}	}	PUNCT
ejpam-7074	391	18	)	)	PUNCT
ejpam-7074	391	19	]	]	PUNCT
ejpam-7074	391	20	<	<	X
ejpam-7074	391	21	q1	q1	PROPN
ejpam-7074	391	22	and	and	CCONJ
ejpam-7074	391	23	max{η2	max{η2	PROPN
ejpam-7074	391	24	,	,	PUNCT
ejpam-7074	391	25	η4	η4	VERB
ejpam-7074	391	26	}	}	PUNCT
ejpam-7074	391	27	<	<	X
ejpam-7074	391	28	λ2	λ2	NOUN
ejpam-7074	391	29	=	=	SYM
ejpam-7074	391	30	1	1	NUM
ejpam-7074	391	31	2	2	NUM
ejpam-7074	391	32	[	[	X
ejpam-7074	391	33	(	(	PUNCT
ejpam-7074	391	34	q2	q2	NOUN
ejpam-7074	391	35	+	+	X
ejpam-7074	391	36	max{η2	max{η2	NOUN
ejpam-7074	391	37	,	,	PUNCT
ejpam-7074	391	38	η4	η4	VERB
ejpam-7074	391	39	}	}	PUNCT
ejpam-7074	391	40	)	)	PUNCT
ejpam-7074	391	41	]	]	PUNCT
ejpam-7074	391	42	<	<	X
ejpam-7074	391	43	q2	q2	NOUN
ejpam-7074	391	44	.	.	PUNCT
ejpam-7074	392	1	hence	hence	ADV
ejpam-7074	392	2	,	,	PUNCT
ejpam-7074	392	3	[	[	X
ejpam-7074	392	4	max{η1	max{η1	X
ejpam-7074	392	5	,	,	PUNCT
ejpam-7074	392	6	η3},max{η2	η3},max{η2	NOUN
ejpam-7074	392	7	,	,	PUNCT
ejpam-7074	392	8	η4	η4	VERB
ejpam-7074	392	9	}	}	PUNCT
ejpam-7074	392	10	]	]	PUNCT
ejpam-7074	392	11	<	<	X
ejpam-7074	393	1	[	[	X
ejpam-7074	393	2	λ1	λ1	ADJ
ejpam-7074	393	3	,	,	PUNCT
ejpam-7074	393	4	λ2	λ2	NOUN
ejpam-7074	393	5	]	]	PUNCT
ejpam-7074	393	6	<	<	X
ejpam-7074	394	1	[	[	X
ejpam-7074	394	2	q1	q1	PROPN
ejpam-7074	394	3	,	,	PUNCT
ejpam-7074	394	4	q2	q2	NOUN
ejpam-7074	394	5	]	]	PUNCT
ejpam-7074	395	1	so	so	SCONJ
ejpam-7074	395	2	that	that	SCONJ
ejpam-7074	395	3	dg00	dg00	PROPN
ejpam-7074	395	4	|	|	ADV
ejpam-7074	395	5	dg00	dg00	PROPN
ejpam-7074	395	6	/∈	/∈	PUNCT
ejpam-7074	395	7	l	l	PROPN
ejpam-7074	395	8	(	(	PUNCT
ejpam-7074	395	9	γa	γa	NOUN
ejpam-7074	395	10	:	:	PUNCT
ejpam-7074	396	1	[	[	X
ejpam-7074	396	2	q1	q1	X
ejpam-7074	396	3	,	,	PUNCT
ejpam-7074	396	4	q2	q2	NOUN
ejpam-7074	396	5	]	]	PUNCT
ejpam-7074	396	6	)	)	PUNCT
ejpam-7074	396	7	,	,	PUNCT
ejpam-7074	396	8	a	a	DET
ejpam-7074	396	9	contradiction	contradiction	NOUN
ejpam-7074	396	10	,	,	PUNCT
ejpam-7074	396	11	since	since	SCONJ
ejpam-7074	396	12	γa(x0	γa(x0	NOUN
ejpam-7074	396	13	)	)	PUNCT
ejpam-7074	396	14	=	=	PUNCT
ejpam-7074	397	1	[	[	X
ejpam-7074	397	2	η1	η1	NOUN
ejpam-7074	397	3	,	,	PUNCT
ejpam-7074	397	4	η2	η2	X
ejpam-7074	397	5	]	]	PUNCT
ejpam-7074	397	6	≤	≤	NOUN
ejpam-7074	398	1	[	[	X
ejpam-7074	398	2	max{η1	max{η1	NOUN
ejpam-7074	398	3	,	,	PUNCT
ejpam-7074	398	4	η3},max{η2	η3},max{η2	NOUN
ejpam-7074	398	5	,	,	PUNCT
ejpam-7074	398	6	η4	η4	VERB
ejpam-7074	398	7	}	}	PUNCT
ejpam-7074	398	8	]	]	PUNCT
ejpam-7074	398	9	>	>	X
ejpam-7074	399	1	[	[	X
ejpam-7074	399	2	β1	β1	PROPN
ejpam-7074	399	3	,	,	PUNCT
ejpam-7074	399	4	β2	β2	NOUN
ejpam-7074	399	5	]	]	PUNCT
ejpam-7074	399	6	and	and	CCONJ
ejpam-7074	399	7	γa(g0	γa(g0	NUM
ejpam-7074	399	8	)	)	PUNCT
ejpam-7074	399	9	=	=	NOUN
ejpam-7074	400	1	[	[	X
ejpam-7074	400	2	η3	η3	NOUN
ejpam-7074	400	3	,	,	PUNCT
ejpam-7074	400	4	η4	η4	VERB
ejpam-7074	400	5	]	]	PUNCT
ejpam-7074	400	6	≥	≥	X
ejpam-7074	400	7	[	[	X
ejpam-7074	400	8	max{η1	max{η1	X
ejpam-7074	400	9	,	,	PUNCT
ejpam-7074	400	10	η3},max{η2	η3},max{η2	NOUN
ejpam-7074	400	11	,	,	PUNCT
ejpam-7074	400	12	η4	η4	VERB
ejpam-7074	400	13	}	}	PUNCT
ejpam-7074	400	14	]	]	PUNCT
ejpam-7074	400	15	>	>	X
ejpam-7074	401	1	[	[	X
ejpam-7074	401	2	β1	β1	PROPN
ejpam-7074	401	3	,	,	PUNCT
ejpam-7074	401	4	β2	β2	NOUN
ejpam-7074	401	5	]	]	PUNCT
ejpam-7074	401	6	.	.	PUNCT
ejpam-7074	402	1	hence	hence	ADV
ejpam-7074	402	2	,	,	PUNCT
ejpam-7074	402	3	dg00	dg00	PROPN
ejpam-7074	402	4	|	|	ADV
ejpam-7074	402	5	dg00	dg00	PROPN
ejpam-7074	402	6	∈	∈	PROPN
ejpam-7074	402	7	l	l	NOUN
ejpam-7074	402	8	(	(	PUNCT
ejpam-7074	402	9	γa	γa	NOUN
ejpam-7074	402	10	:	:	PUNCT
ejpam-7074	403	1	[	[	X
ejpam-7074	403	2	q1	q1	X
ejpam-7074	403	3	,	,	PUNCT
ejpam-7074	403	4	q2	q2	NOUN
ejpam-7074	403	5	]	]	PUNCT
ejpam-7074	403	6	)	)	PUNCT
ejpam-7074	403	7	.	.	PUNCT
ejpam-7074	404	1	thus	thus	ADV
ejpam-7074	404	2	,	,	PUNCT
ejpam-7074	404	3	γa(d	γa(d	PROPN
ejpam-7074	404	4	g	g	PROPN
ejpam-7074	404	5	|	|	ADV
ejpam-7074	404	6	dg	dg	PROPN
ejpam-7074	404	7	)	)	PUNCT
ejpam-7074	404	8	≥	≥	NUM
ejpam-7074	404	9	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	404	10	)	)	PUNCT
ejpam-7074	404	11	,	,	PUNCT
ejpam-7074	404	12	γa(g	γa(g	ADP
ejpam-7074	404	13	)	)	PUNCT
ejpam-7074	404	14	}	}	PUNCT
ejpam-7074	404	15	for	for	ADP
ejpam-7074	404	16	all	all	DET
ejpam-7074	404	17	d	d	PROPN
ejpam-7074	404	18	,	,	PUNCT
ejpam-7074	404	19	g	g	PROPN
ejpam-7074	404	20	∈	∈	PROPN
ejpam-7074	404	21	sh	sh	INTJ
ejpam-7074	404	22	.	.	PUNCT
ejpam-7074	405	1	theorem	theorem	ADJ
ejpam-7074	405	2	8	8	NUM
ejpam-7074	405	3	.	.	PUNCT
ejpam-7074	406	1	let	let	VERB
ejpam-7074	406	2	sh	sh	NOUN
ejpam-7074	406	3	:	:	PUNCT
ejpam-7074	406	4	=	=	SYM
ejpam-7074	406	5	(	(	PUNCT
ejpam-7074	406	6	sh	sh	INTJ
ejpam-7074	406	7	,	,	PUNCT
ejpam-7074	406	8	|	|	ADV
ejpam-7074	406	9	,	,	PUNCT
ejpam-7074	406	10	0	0	NUM
ejpam-7074	406	11	)	)	PUNCT
ejpam-7074	406	12	be	be	AUX
ejpam-7074	406	13	an	an	DET
ejpam-7074	406	14	ssha	ssha	NOUN
ejpam-7074	406	15	.	.	PUNCT
ejpam-7074	407	1	any	any	DET
ejpam-7074	407	2	subalgebra	subalgebra	NOUN
ejpam-7074	407	3	of	of	ADP
ejpam-7074	407	4	sh	sh	PROPN
ejpam-7074	407	5	can	can	AUX
ejpam-7074	407	6	be	be	AUX
ejpam-7074	407	7	realized	realize	VERB
ejpam-7074	407	8	as	as	ADP
ejpam-7074	407	9	both	both	CCONJ
ejpam-7074	407	10	the	the	DET
ejpam-7074	407	11	upper	upper	ADJ
ejpam-7074	407	12	[	[	X
ejpam-7074	407	13	p1	p1	NOUN
ejpam-7074	407	14	,	,	PUNCT
ejpam-7074	407	15	p2]-level	p2]-level	NOUN
ejpam-7074	407	16	and	and	CCONJ
ejpam-7074	407	17	lower	low	ADJ
ejpam-7074	407	18	[	[	X
ejpam-7074	407	19	q1	q1	NOUN
ejpam-7074	407	20	,	,	PUNCT
ejpam-7074	407	21	q2]-level	q2]-level	NOUN
ejpam-7074	407	22	of	of	ADP
ejpam-7074	407	23	some	some	DET
ejpam-7074	407	24	ivifss	ivifss	ADJ
ejpam-7074	407	25	-	-	PUNCT
ejpam-7074	407	26	subalgebra	subalgebra	NOUN
ejpam-7074	407	27	of	of	ADP
ejpam-7074	407	28	sh	sh	PROPN
ejpam-7074	407	29	.	.	PUNCT
ejpam-7074	408	1	proof	proof	NOUN
ejpam-7074	408	2	.	.	PUNCT
ejpam-7074	409	1	let	let	VERB
ejpam-7074	409	2	b	b	X
ejpam-7074	409	3	be	be	AUX
ejpam-7074	409	4	a	a	DET
ejpam-7074	409	5	subalgebra	subalgebra	NOUN
ejpam-7074	409	6	of	of	ADP
ejpam-7074	409	7	sh	sh	PROPN
ejpam-7074	409	8	,	,	PUNCT
ejpam-7074	409	9	and	and	CCONJ
ejpam-7074	409	10	a	a	DET
ejpam-7074	409	11	=	=	X
ejpam-7074	409	12	(	(	PUNCT
ejpam-7074	409	13	µa	µa	PROPN
ejpam-7074	409	14	,	,	PUNCT
ejpam-7074	409	15	γa	γa	PROPN
ejpam-7074	409	16	)	)	PUNCT
ejpam-7074	409	17	be	be	VERB
ejpam-7074	409	18	an	an	DET
ejpam-7074	409	19	ivifs	ivif	NOUN
ejpam-7074	409	20	on	on	ADP
ejpam-7074	409	21	sh	sh	PRON
ejpam-7074	409	22	defined	define	VERB
ejpam-7074	409	23	by	by	ADP
ejpam-7074	409	24	µa(d	µa(d	PUNCT
ejpam-7074	409	25	)	)	PUNCT
ejpam-7074	409	26	=	=	PRON
ejpam-7074	409	27	{	{	PUNCT
ejpam-7074	410	1	[	[	X
ejpam-7074	410	2	ϱ1	ϱ1	NOUN
ejpam-7074	410	3	,	,	PUNCT
ejpam-7074	410	4	ϱ2	ϱ2	NOUN
ejpam-7074	410	5	]	]	PUNCT
ejpam-7074	411	1	if	if	SCONJ
ejpam-7074	411	2	d	d	PROPN
ejpam-7074	411	3	∈	∈	PROPN
ejpam-7074	411	4	b	b	PROPN
ejpam-7074	412	1	[	[	X
ejpam-7074	412	2	0	0	NUM
ejpam-7074	412	3	,	,	PUNCT
ejpam-7074	412	4	0	0	NUM
ejpam-7074	412	5	]	]	PUNCT
ejpam-7074	412	6	otherwise	otherwise	ADV
ejpam-7074	412	7	and	and	CCONJ
ejpam-7074	412	8	γa(d	γa(d	PUNCT
ejpam-7074	412	9	)	)	PUNCT
ejpam-7074	413	1	=	=	PRON
ejpam-7074	413	2	{	{	PUNCT
ejpam-7074	414	1	[	[	X
ejpam-7074	414	2	ϑ1	ϑ1	NOUN
ejpam-7074	414	3	,	,	PUNCT
ejpam-7074	414	4	ϑ2	ϑ2	PROPN
ejpam-7074	414	5	]	]	PUNCT
ejpam-7074	415	1	if	if	SCONJ
ejpam-7074	415	2	d	d	PROPN
ejpam-7074	415	3	∈	∈	PROPN
ejpam-7074	415	4	b	b	PROPN
ejpam-7074	416	1	[	[	X
ejpam-7074	416	2	1	1	NUM
ejpam-7074	416	3	,	,	PUNCT
ejpam-7074	416	4	1	1	NUM
ejpam-7074	416	5	]	]	PUNCT
ejpam-7074	416	6	otherwise	otherwise	ADV
ejpam-7074	416	7	for	for	ADP
ejpam-7074	416	8	all	all	DET
ejpam-7074	416	9	[	[	X
ejpam-7074	416	10	ϱ1	ϱ1	NOUN
ejpam-7074	416	11	,	,	PUNCT
ejpam-7074	416	12	ϱ2	ϱ2	NOUN
ejpam-7074	416	13	]	]	PUNCT
ejpam-7074	416	14	,	,	PUNCT
ejpam-7074	416	15	[	[	X
ejpam-7074	416	16	ϑ1	ϑ1	NOUN
ejpam-7074	416	17	,	,	PUNCT
ejpam-7074	416	18	ϑ2	ϑ2	PROPN
ejpam-7074	416	19	]	]	X
ejpam-7074	417	1	∈	∈	PROPN
ejpam-7074	418	1	d	d	X
ejpam-7074	419	1	[	[	X
ejpam-7074	419	2	0	0	NUM
ejpam-7074	419	3	,	,	PUNCT
ejpam-7074	419	4	1	1	NUM
ejpam-7074	419	5	]	]	PUNCT
ejpam-7074	419	6	and	and	CCONJ
ejpam-7074	419	7	ϱ2	ϱ2	PROPN
ejpam-7074	419	8	+	+	CCONJ
ejpam-7074	419	9	ϑ2	ϑ2	PROPN
ejpam-7074	419	10	≤	≤	NOUN
ejpam-7074	419	11	1	1	NUM
ejpam-7074	419	12	.	.	PUNCT
ejpam-7074	420	1	we	we	PRON
ejpam-7074	420	2	consider	consider	VERB
ejpam-7074	420	3	the	the	DET
ejpam-7074	420	4	following	follow	VERB
ejpam-7074	420	5	cases	case	NOUN
ejpam-7074	420	6	:	:	PUNCT
ejpam-7074	420	7	a.	a.	NOUN
ejpam-7074	420	8	iampan	iampan	NOUN
ejpam-7074	420	9	et	et	PROPN
ejpam-7074	420	10	al	al	PROPN
ejpam-7074	420	11	.	.	PUNCT
ejpam-7074	420	12	/	/	SYM
ejpam-7074	420	13	eur	eur	PROPN
ejpam-7074	420	14	.	.	PUNCT
ejpam-7074	421	1	j.	j.	PROPN
ejpam-7074	421	2	pure	pure	PROPN
ejpam-7074	421	3	appl	appl	PROPN
ejpam-7074	421	4	.	.	PROPN
ejpam-7074	421	5	math	math	PROPN
ejpam-7074	421	6	,	,	PUNCT
ejpam-7074	421	7	18	18	NUM
ejpam-7074	421	8	(	(	PUNCT
ejpam-7074	421	9	4	4	NUM
ejpam-7074	421	10	)	)	PUNCT
ejpam-7074	421	11	(	(	PUNCT
ejpam-7074	421	12	2025	2025	NUM
ejpam-7074	421	13	)	)	PUNCT
ejpam-7074	421	14	,	,	PUNCT
ejpam-7074	421	15	7074	7074	NUM
ejpam-7074	421	16	11	11	NUM
ejpam-7074	421	17	of	of	ADP
ejpam-7074	421	18	14	14	NUM
ejpam-7074	421	19	case	case	NOUN
ejpam-7074	421	20	(	(	PUNCT
ejpam-7074	421	21	i	i	NOUN
ejpam-7074	421	22	):	):	PUNCT
ejpam-7074	421	23	if	if	SCONJ
ejpam-7074	421	24	d	d	X
ejpam-7074	421	25	,	,	PUNCT
ejpam-7074	421	26	g	g	PROPN
ejpam-7074	421	27	∈	∈	PROPN
ejpam-7074	421	28	b	b	PROPN
ejpam-7074	421	29	,	,	PUNCT
ejpam-7074	421	30	then	then	ADV
ejpam-7074	421	31	µa(d	µa(d	PUNCT
ejpam-7074	421	32	)	)	PUNCT
ejpam-7074	421	33	=	=	PUNCT
ejpam-7074	422	1	[	[	X
ejpam-7074	422	2	ϱ1	ϱ1	NOUN
ejpam-7074	422	3	,	,	PUNCT
ejpam-7074	422	4	ϱ2	ϱ2	NOUN
ejpam-7074	422	5	]	]	PUNCT
ejpam-7074	422	6	,	,	PUNCT
ejpam-7074	422	7	γa(d	γa(d	NUM
ejpam-7074	422	8	)	)	PUNCT
ejpam-7074	422	9	=	=	PUNCT
ejpam-7074	423	1	[	[	X
ejpam-7074	423	2	ϑ1	ϑ1	NOUN
ejpam-7074	423	3	,	,	PUNCT
ejpam-7074	423	4	ϑ2	ϑ2	PROPN
ejpam-7074	423	5	]	]	PUNCT
ejpam-7074	423	6	and	and	CCONJ
ejpam-7074	423	7	µa(g	µa(g	PUNCT
ejpam-7074	423	8	)	)	PUNCT
ejpam-7074	423	9	=	=	PUNCT
ejpam-7074	424	1	[	[	X
ejpam-7074	424	2	ϱ1	ϱ1	NOUN
ejpam-7074	424	3	,	,	PUNCT
ejpam-7074	424	4	ϱ2	ϱ2	NOUN
ejpam-7074	424	5	]	]	PUNCT
ejpam-7074	424	6	,	,	PUNCT
ejpam-7074	424	7	γa(g	γa(g	ADP
ejpam-7074	424	8	)	)	PUNCT
ejpam-7074	424	9	=	=	PUNCT
ejpam-7074	425	1	[	[	X
ejpam-7074	425	2	β1	β1	PROPN
ejpam-7074	425	3	,	,	PUNCT
ejpam-7074	425	4	β2	β2	NOUN
ejpam-7074	425	5	]	]	PUNCT
ejpam-7074	425	6	.	.	PUNCT
ejpam-7074	426	1	thus	thus	ADV
ejpam-7074	426	2	,	,	PUNCT
ejpam-7074	426	3	µa(d	µa(d	PUNCT
ejpam-7074	426	4	g	g	NOUN
ejpam-7074	426	5	|	|	NOUN
ejpam-7074	426	6	dg	dg	PRON
ejpam-7074	426	7	)	)	PUNCT
ejpam-7074	426	8	=	=	PUNCT
ejpam-7074	427	1	[	[	X
ejpam-7074	427	2	ϱ1	ϱ1	NOUN
ejpam-7074	427	3	,	,	PUNCT
ejpam-7074	427	4	ϱ2	ϱ2	NOUN
ejpam-7074	427	5	]	]	X
ejpam-7074	427	6	=	=	SYM
ejpam-7074	427	7	rmin{[ϱ1	rmin{[ϱ1	NOUN
ejpam-7074	427	8	,	,	PUNCT
ejpam-7074	427	9	ϱ2	ϱ2	NOUN
ejpam-7074	427	10	]	]	PUNCT
ejpam-7074	427	11	,	,	PUNCT
ejpam-7074	427	12	[	[	X
ejpam-7074	427	13	α1	α1	PROPN
ejpam-7074	427	14	,	,	PUNCT
ejpam-7074	427	15	α2	α2	PROPN
ejpam-7074	427	16	]	]	PUNCT
ejpam-7074	427	17	}	}	PUNCT
ejpam-7074	427	18	=	=	PUNCT
ejpam-7074	427	19	rmin{µa(d	rmin{µa(d	ADJ
ejpam-7074	427	20	)	)	PUNCT
ejpam-7074	427	21	,	,	PUNCT
ejpam-7074	427	22	µa(g	µa(g	NOUN
ejpam-7074	427	23	)	)	PUNCT
ejpam-7074	427	24	}	}	PUNCT
ejpam-7074	427	25	and	and	CCONJ
ejpam-7074	427	26	γa(d	γa(d	NUM
ejpam-7074	427	27	g	g	PROPN
ejpam-7074	427	28	|	|	ADV
ejpam-7074	427	29	dg	dg	PROPN
ejpam-7074	427	30	)	)	PUNCT
ejpam-7074	427	31	=	=	PUNCT
ejpam-7074	428	1	[	[	X
ejpam-7074	428	2	ϑ1	ϑ1	NOUN
ejpam-7074	428	3	,	,	PUNCT
ejpam-7074	428	4	ϑ2	ϑ2	PROPN
ejpam-7074	428	5	]	]	X
ejpam-7074	428	6	=	=	SYM
ejpam-7074	428	7	rmax{[ϑ1	rmax{[ϑ1	NOUN
ejpam-7074	428	8	,	,	PUNCT
ejpam-7074	428	9	ϑ2	ϑ2	PROPN
ejpam-7074	428	10	]	]	PUNCT
ejpam-7074	428	11	,	,	PUNCT
ejpam-7074	428	12	[	[	X
ejpam-7074	428	13	ϑ1	ϑ1	NOUN
ejpam-7074	428	14	,	,	PUNCT
ejpam-7074	428	15	ϑ2	ϑ2	NOUN
ejpam-7074	428	16	]	]	PUNCT
ejpam-7074	428	17	}	}	PUNCT
ejpam-7074	428	18	=	=	SYM
ejpam-7074	428	19	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	428	20	)	)	PUNCT
ejpam-7074	428	21	,	,	PUNCT
ejpam-7074	428	22	γa(g	γa(g	ADP
ejpam-7074	428	23	)	)	PUNCT
ejpam-7074	428	24	}	}	PUNCT
ejpam-7074	428	25	.	.	PUNCT
ejpam-7074	429	1	case	case	NOUN
ejpam-7074	429	2	(	(	PUNCT
ejpam-7074	429	3	ii	ii	NOUN
ejpam-7074	429	4	):	):	PUNCT
ejpam-7074	429	5	if	if	SCONJ
ejpam-7074	429	6	d	d	PROPN
ejpam-7074	429	7	∈	∈	PROPN
ejpam-7074	429	8	b	b	PROPN
ejpam-7074	429	9	and	and	CCONJ
ejpam-7074	429	10	g	g	PROPN
ejpam-7074	429	11	/∈	/∈	PROPN
ejpam-7074	430	1	b	b	NOUN
ejpam-7074	430	2	,	,	PUNCT
ejpam-7074	430	3	then	then	ADV
ejpam-7074	430	4	µa(d	µa(d	PUNCT
ejpam-7074	430	5	)	)	PUNCT
ejpam-7074	430	6	=	=	PUNCT
ejpam-7074	431	1	[	[	X
ejpam-7074	431	2	ϱ1	ϱ1	NOUN
ejpam-7074	431	3	,	,	PUNCT
ejpam-7074	431	4	ϱ2	ϱ2	NOUN
ejpam-7074	431	5	]	]	PUNCT
ejpam-7074	431	6	,	,	PUNCT
ejpam-7074	431	7	γa(d	γa(d	NUM
ejpam-7074	431	8	)	)	PUNCT
ejpam-7074	431	9	=	=	PUNCT
ejpam-7074	432	1	[	[	X
ejpam-7074	432	2	ϑ1	ϑ1	NOUN
ejpam-7074	432	3	,	,	PUNCT
ejpam-7074	432	4	ϑ2	ϑ2	PROPN
ejpam-7074	432	5	]	]	PUNCT
ejpam-7074	432	6	and	and	CCONJ
ejpam-7074	432	7	µa(g	µa(g	PUNCT
ejpam-7074	432	8	)	)	PUNCT
ejpam-7074	432	9	=	=	PUNCT
ejpam-7074	433	1	[	[	X
ejpam-7074	433	2	0	0	NUM
ejpam-7074	433	3	,	,	PUNCT
ejpam-7074	433	4	0	0	NUM
ejpam-7074	433	5	]	]	PUNCT
ejpam-7074	433	6	,	,	PUNCT
ejpam-7074	433	7	γa(g	γa(g	ADP
ejpam-7074	433	8	)	)	PUNCT
ejpam-7074	433	9	=	=	PUNCT
ejpam-7074	434	1	[	[	X
ejpam-7074	434	2	1	1	NUM
ejpam-7074	434	3	,	,	PUNCT
ejpam-7074	434	4	1	1	NUM
ejpam-7074	434	5	]	]	PUNCT
ejpam-7074	434	6	.	.	PUNCT
ejpam-7074	435	1	thus	thus	ADV
ejpam-7074	435	2	,	,	PUNCT
ejpam-7074	435	3	µa(d	µa(d	PUNCT
ejpam-7074	435	4	g	g	PROPN
ejpam-7074	435	5	|	|	NOUN
ejpam-7074	435	6	dg	dg	PROPN
ejpam-7074	435	7	)	)	PUNCT
ejpam-7074	435	8	≥	≥	NOUN
ejpam-7074	436	1	[	[	X
ejpam-7074	436	2	0	0	NUM
ejpam-7074	436	3	,	,	PUNCT
ejpam-7074	436	4	0	0	NUM
ejpam-7074	436	5	]	]	X
ejpam-7074	436	6	=	=	SYM
ejpam-7074	436	7	rmin{[ϱ1	rmin{[ϱ1	NOUN
ejpam-7074	436	8	,	,	PUNCT
ejpam-7074	436	9	ϱ2	ϱ2	NOUN
ejpam-7074	436	10	]	]	PUNCT
ejpam-7074	436	11	,	,	PUNCT
ejpam-7074	436	12	[	[	X
ejpam-7074	436	13	0	0	NUM
ejpam-7074	436	14	,	,	PUNCT
ejpam-7074	436	15	0	0	NUM
ejpam-7074	436	16	]	]	PUNCT
ejpam-7074	436	17	}	}	PUNCT
ejpam-7074	436	18	=	=	PUNCT
ejpam-7074	436	19	rmin{µa(d	rmin{µa(d	ADJ
ejpam-7074	436	20	)	)	PUNCT
ejpam-7074	436	21	,	,	PUNCT
ejpam-7074	436	22	µa(g	µa(g	NOUN
ejpam-7074	436	23	)	)	PUNCT
ejpam-7074	436	24	}	}	PUNCT
ejpam-7074	436	25	and	and	CCONJ
ejpam-7074	436	26	γa(d	γa(d	NUM
ejpam-7074	436	27	g	g	PROPN
ejpam-7074	436	28	|	|	ADV
ejpam-7074	436	29	dg	dg	PROPN
ejpam-7074	436	30	)	)	PUNCT
ejpam-7074	436	31	≥	≥	NOUN
ejpam-7074	437	1	[	[	X
ejpam-7074	437	2	1	1	NUM
ejpam-7074	437	3	,	,	PUNCT
ejpam-7074	437	4	1	1	NUM
ejpam-7074	437	5	]	]	PUNCT
ejpam-7074	437	6	=	=	SYM
ejpam-7074	437	7	rmax{[ϑ1	rmax{[ϑ1	NOUN
ejpam-7074	437	8	,	,	PUNCT
ejpam-7074	437	9	ϑ2	ϑ2	PROPN
ejpam-7074	437	10	]	]	PUNCT
ejpam-7074	437	11	,	,	PUNCT
ejpam-7074	437	12	[	[	X
ejpam-7074	437	13	1	1	NUM
ejpam-7074	437	14	,	,	PUNCT
ejpam-7074	437	15	1	1	NUM
ejpam-7074	437	16	]	]	PUNCT
ejpam-7074	437	17	}	}	PUNCT
ejpam-7074	437	18	=	=	SYM
ejpam-7074	437	19	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	437	20	)	)	PUNCT
ejpam-7074	437	21	,	,	PUNCT
ejpam-7074	437	22	γa(g	γa(g	ADP
ejpam-7074	437	23	)	)	PUNCT
ejpam-7074	437	24	}	}	PUNCT
ejpam-7074	437	25	.	.	PUNCT
ejpam-7074	438	1	case	case	NOUN
ejpam-7074	438	2	(	(	PUNCT
ejpam-7074	438	3	iii	iii	NOUN
ejpam-7074	438	4	):	):	PUNCT
ejpam-7074	438	5	if	if	SCONJ
ejpam-7074	438	6	d	d	PROPN
ejpam-7074	438	7	/∈	/∈	PROPN
ejpam-7074	438	8	b	b	NOUN
ejpam-7074	438	9	and	and	CCONJ
ejpam-7074	438	10	g	g	PROPN
ejpam-7074	438	11	∈	∈	PROPN
ejpam-7074	438	12	b	b	PROPN
ejpam-7074	438	13	,	,	PUNCT
ejpam-7074	438	14	then	then	ADV
ejpam-7074	438	15	µa(d	µa(d	PUNCT
ejpam-7074	438	16	)	)	PUNCT
ejpam-7074	439	1	=	=	PUNCT
ejpam-7074	440	1	[	[	X
ejpam-7074	440	2	0	0	NUM
ejpam-7074	440	3	,	,	PUNCT
ejpam-7074	440	4	0	0	NUM
ejpam-7074	440	5	]	]	PUNCT
ejpam-7074	440	6	,	,	PUNCT
ejpam-7074	440	7	γa(d	γa(d	NUM
ejpam-7074	440	8	)	)	PUNCT
ejpam-7074	440	9	=	=	PUNCT
ejpam-7074	441	1	[	[	X
ejpam-7074	441	2	1	1	NUM
ejpam-7074	441	3	,	,	PUNCT
ejpam-7074	441	4	1	1	NUM
ejpam-7074	441	5	]	]	PUNCT
ejpam-7074	441	6	,	,	PUNCT
ejpam-7074	441	7	µa(g	µa(g	PUNCT
ejpam-7074	441	8	)	)	PUNCT
ejpam-7074	441	9	=	=	PUNCT
ejpam-7074	442	1	[	[	X
ejpam-7074	442	2	α1	α1	PROPN
ejpam-7074	442	3	,	,	PUNCT
ejpam-7074	442	4	α2	α2	PROPN
ejpam-7074	442	5	]	]	PUNCT
ejpam-7074	442	6	,	,	PUNCT
ejpam-7074	442	7	γa(g	γa(g	ADP
ejpam-7074	442	8	)	)	PUNCT
ejpam-7074	442	9	=	=	PUNCT
ejpam-7074	443	1	[	[	X
ejpam-7074	443	2	ϑ1	ϑ1	NOUN
ejpam-7074	443	3	,	,	PUNCT
ejpam-7074	443	4	ϑ2	ϑ2	PROPN
ejpam-7074	443	5	]	]	PUNCT
ejpam-7074	443	6	.	.	PUNCT
ejpam-7074	444	1	thus	thus	ADV
ejpam-7074	444	2	,	,	PUNCT
ejpam-7074	444	3	µa(d	µa(d	PUNCT
ejpam-7074	444	4	g	g	PROPN
ejpam-7074	444	5	|	|	NOUN
ejpam-7074	444	6	dg	dg	PROPN
ejpam-7074	444	7	)	)	PUNCT
ejpam-7074	444	8	≥	≥	NOUN
ejpam-7074	445	1	[	[	X
ejpam-7074	445	2	0	0	NUM
ejpam-7074	445	3	,	,	PUNCT
ejpam-7074	445	4	0	0	NUM
ejpam-7074	445	5	]	]	X
ejpam-7074	445	6	=	=	SYM
ejpam-7074	445	7	rmin{[0	rmin{[0	NOUN
ejpam-7074	445	8	,	,	PUNCT
ejpam-7074	445	9	0	0	NUM
ejpam-7074	445	10	]	]	PUNCT
ejpam-7074	445	11	,	,	PUNCT
ejpam-7074	445	12	[	[	X
ejpam-7074	445	13	ϱ1	ϱ1	NOUN
ejpam-7074	445	14	,	,	PUNCT
ejpam-7074	445	15	ϱ2	ϱ2	NOUN
ejpam-7074	445	16	]	]	X
ejpam-7074	445	17	}	}	PUNCT
ejpam-7074	445	18	=	=	PUNCT
ejpam-7074	445	19	rmin{µa(d	rmin{µa(d	ADJ
ejpam-7074	445	20	)	)	PUNCT
ejpam-7074	445	21	,	,	PUNCT
ejpam-7074	445	22	µa(g	µa(g	NOUN
ejpam-7074	445	23	)	)	PUNCT
ejpam-7074	445	24	}	}	PUNCT
ejpam-7074	445	25	and	and	CCONJ
ejpam-7074	445	26	γa(d	γa(d	NUM
ejpam-7074	445	27	g	g	PROPN
ejpam-7074	445	28	|	|	NOUN
ejpam-7074	445	29	dg	dg	PROPN
ejpam-7074	445	30	)	)	PUNCT
ejpam-7074	445	31	≤	≤	NOUN
ejpam-7074	446	1	[	[	X
ejpam-7074	446	2	1	1	NUM
ejpam-7074	446	3	,	,	PUNCT
ejpam-7074	446	4	1	1	NUM
ejpam-7074	446	5	]	]	PUNCT
ejpam-7074	446	6	=	=	SYM
ejpam-7074	446	7	rmax{[1	rmax{[1	NOUN
ejpam-7074	446	8	,	,	PUNCT
ejpam-7074	446	9	1	1	NUM
ejpam-7074	446	10	]	]	PUNCT
ejpam-7074	446	11	,	,	PUNCT
ejpam-7074	446	12	[	[	X
ejpam-7074	446	13	β1	β1	NOUN
ejpam-7074	446	14	,	,	PUNCT
ejpam-7074	446	15	β2	β2	NOUN
ejpam-7074	446	16	]	]	PUNCT
ejpam-7074	446	17	}	}	PUNCT
ejpam-7074	446	18	=	=	SYM
ejpam-7074	446	19	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	446	20	)	)	PUNCT
ejpam-7074	446	21	,	,	PUNCT
ejpam-7074	446	22	γa(g	γa(g	ADP
ejpam-7074	446	23	)	)	PUNCT
ejpam-7074	446	24	}	}	PUNCT
ejpam-7074	446	25	.	.	PUNCT
ejpam-7074	447	1	case	case	NOUN
ejpam-7074	447	2	(	(	PUNCT
ejpam-7074	447	3	iv	iv	NUM
ejpam-7074	447	4	):	):	PUNCT
ejpam-7074	447	5	if	if	SCONJ
ejpam-7074	447	6	d	d	PROPN
ejpam-7074	447	7	/∈	/∈	PROPN
ejpam-7074	447	8	b	b	NOUN
ejpam-7074	447	9	and	and	CCONJ
ejpam-7074	447	10	g	g	PROPN
ejpam-7074	447	11	/∈	/∈	PROPN
ejpam-7074	448	1	b	b	NOUN
ejpam-7074	448	2	,	,	PUNCT
ejpam-7074	448	3	then	then	ADV
ejpam-7074	448	4	µa(d	µa(d	PUNCT
ejpam-7074	448	5	)	)	PUNCT
ejpam-7074	448	6	=	=	PUNCT
ejpam-7074	449	1	[	[	X
ejpam-7074	449	2	0	0	NUM
ejpam-7074	449	3	,	,	PUNCT
ejpam-7074	449	4	0	0	NUM
ejpam-7074	449	5	]	]	PUNCT
ejpam-7074	449	6	,	,	PUNCT
ejpam-7074	449	7	γa(d	γa(d	NUM
ejpam-7074	449	8	)	)	PUNCT
ejpam-7074	449	9	=	=	PUNCT
ejpam-7074	450	1	[	[	X
ejpam-7074	450	2	1	1	NUM
ejpam-7074	450	3	,	,	PUNCT
ejpam-7074	450	4	1	1	NUM
ejpam-7074	450	5	]	]	PUNCT
ejpam-7074	450	6	and	and	CCONJ
ejpam-7074	450	7	µa(g	µa(g	PUNCT
ejpam-7074	450	8	)	)	PUNCT
ejpam-7074	450	9	=	=	PUNCT
ejpam-7074	451	1	[	[	X
ejpam-7074	451	2	0	0	NUM
ejpam-7074	451	3	,	,	PUNCT
ejpam-7074	451	4	0	0	NUM
ejpam-7074	451	5	]	]	PUNCT
ejpam-7074	451	6	,	,	PUNCT
ejpam-7074	451	7	γa(g	γa(g	ADP
ejpam-7074	451	8	)	)	PUNCT
ejpam-7074	451	9	=	=	PUNCT
ejpam-7074	452	1	[	[	X
ejpam-7074	452	2	1	1	NUM
ejpam-7074	452	3	,	,	PUNCT
ejpam-7074	452	4	1	1	NUM
ejpam-7074	452	5	]	]	PUNCT
ejpam-7074	452	6	.	.	PUNCT
ejpam-7074	453	1	now	now	ADV
ejpam-7074	453	2	,	,	PUNCT
ejpam-7074	453	3	µa(d	µa(d	PUNCT
ejpam-7074	453	4	g	g	NOUN
ejpam-7074	453	5	|	|	NOUN
ejpam-7074	453	6	dg	dg	PROPN
ejpam-7074	453	7	)	)	PUNCT
ejpam-7074	453	8	≤	≤	PUNCT
ejpam-7074	454	1	[	[	X
ejpam-7074	454	2	0	0	NUM
ejpam-7074	454	3	,	,	PUNCT
ejpam-7074	454	4	0	0	NUM
ejpam-7074	454	5	]	]	X
ejpam-7074	454	6	=	=	SYM
ejpam-7074	454	7	rmin{[0	rmin{[0	NOUN
ejpam-7074	454	8	,	,	PUNCT
ejpam-7074	454	9	0	0	NUM
ejpam-7074	454	10	]	]	PUNCT
ejpam-7074	454	11	,	,	PUNCT
ejpam-7074	454	12	[	[	X
ejpam-7074	454	13	0	0	NUM
ejpam-7074	454	14	,	,	PUNCT
ejpam-7074	454	15	0	0	NUM
ejpam-7074	454	16	]	]	PUNCT
ejpam-7074	454	17	}	}	PUNCT
ejpam-7074	454	18	=	=	PUNCT
ejpam-7074	454	19	rmin{µa(d	rmin{µa(d	ADJ
ejpam-7074	454	20	)	)	PUNCT
ejpam-7074	454	21	,	,	PUNCT
ejpam-7074	454	22	µa(g	µa(g	NOUN
ejpam-7074	454	23	)	)	PUNCT
ejpam-7074	454	24	}	}	PUNCT
ejpam-7074	454	25	and	and	CCONJ
ejpam-7074	454	26	γa(d	γa(d	NUM
ejpam-7074	454	27	g	g	PROPN
ejpam-7074	454	28	|	|	ADV
ejpam-7074	454	29	dg	dg	PROPN
ejpam-7074	454	30	)	)	PUNCT
ejpam-7074	454	31	≥	≥	NOUN
ejpam-7074	455	1	[	[	X
ejpam-7074	455	2	1	1	NUM
ejpam-7074	455	3	,	,	PUNCT
ejpam-7074	455	4	1	1	NUM
ejpam-7074	455	5	]	]	PUNCT
ejpam-7074	455	6	=	=	SYM
ejpam-7074	455	7	rmax{[1	rmax{[1	NOUN
ejpam-7074	455	8	,	,	PUNCT
ejpam-7074	455	9	1	1	NUM
ejpam-7074	455	10	]	]	PUNCT
ejpam-7074	455	11	,	,	PUNCT
ejpam-7074	455	12	[	[	X
ejpam-7074	455	13	1	1	NUM
ejpam-7074	455	14	,	,	PUNCT
ejpam-7074	455	15	1	1	NUM
ejpam-7074	455	16	]	]	PUNCT
ejpam-7074	455	17	}	}	PUNCT
ejpam-7074	455	18	=	=	SYM
ejpam-7074	455	19	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	455	20	)	)	PUNCT
ejpam-7074	455	21	,	,	PUNCT
ejpam-7074	455	22	γa(g	γa(g	ADP
ejpam-7074	455	23	)	)	PUNCT
ejpam-7074	455	24	}	}	PUNCT
ejpam-7074	455	25	.	.	PUNCT
ejpam-7074	456	1	therefore	therefore	ADV
ejpam-7074	456	2	,	,	PUNCT
ejpam-7074	456	3	a	a	DET
ejpam-7074	456	4	=	=	X
ejpam-7074	456	5	(	(	PUNCT
ejpam-7074	456	6	µa	µa	PROPN
ejpam-7074	456	7	,	,	PUNCT
ejpam-7074	456	8	γa	γa	PROPN
ejpam-7074	456	9	)	)	PUNCT
ejpam-7074	456	10	is	be	AUX
ejpam-7074	456	11	an	an	DET
ejpam-7074	456	12	ivifss	ivifss	ADJ
ejpam-7074	456	13	-	-	PUNCT
ejpam-7074	456	14	subalgebra	subalgebra	NOUN
ejpam-7074	456	15	of	of	ADP
ejpam-7074	456	16	sh	sh	PROPN
ejpam-7074	456	17	.	.	PUNCT
ejpam-7074	457	1	theorem	theorem	ADJ
ejpam-7074	457	2	9	9	NUM
ejpam-7074	457	3	.	.	PUNCT
ejpam-7074	458	1	let	let	VERB
ejpam-7074	458	2	sh	sh	NOUN
ejpam-7074	458	3	:	:	PUNCT
ejpam-7074	458	4	=	=	SYM
ejpam-7074	458	5	(	(	PUNCT
ejpam-7074	458	6	sh	sh	INTJ
ejpam-7074	458	7	,	,	PUNCT
ejpam-7074	458	8	|	|	ADV
ejpam-7074	458	9	,	,	PUNCT
ejpam-7074	458	10	0	0	NUM
ejpam-7074	458	11	)	)	PUNCT
ejpam-7074	458	12	be	be	AUX
ejpam-7074	458	13	an	an	DET
ejpam-7074	458	14	ssha	ssha	NOUN
ejpam-7074	458	15	.	.	PUNCT
ejpam-7074	459	1	let	let	VERB
ejpam-7074	459	2	b	b	X
ejpam-7074	459	3	be	be	AUX
ejpam-7074	459	4	a	a	DET
ejpam-7074	459	5	subset	subset	NOUN
ejpam-7074	459	6	of	of	ADP
ejpam-7074	459	7	sh	sh	PROPN
ejpam-7074	459	8	and	and	CCONJ
ejpam-7074	459	9	a	a	DET
ejpam-7074	459	10	=	=	X
ejpam-7074	459	11	(	(	PUNCT
ejpam-7074	459	12	µa	µa	PROPN
ejpam-7074	459	13	,	,	PUNCT
ejpam-7074	459	14	γa	γa	PROPN
ejpam-7074	459	15	)	)	PUNCT
ejpam-7074	459	16	be	be	VERB
ejpam-7074	459	17	an	an	DET
ejpam-7074	459	18	ivifs	ivif	NOUN
ejpam-7074	459	19	on	on	ADP
ejpam-7074	459	20	sh	sh	PRON
ejpam-7074	459	21	defined	define	VERB
ejpam-7074	459	22	by	by	ADP
ejpam-7074	459	23	µa(d	µa(d	PUNCT
ejpam-7074	459	24	)	)	PUNCT
ejpam-7074	459	25	=	=	PRON
ejpam-7074	459	26	{	{	PUNCT
ejpam-7074	460	1	[	[	X
ejpam-7074	460	2	ϱ1	ϱ1	NOUN
ejpam-7074	460	3	,	,	PUNCT
ejpam-7074	460	4	ϱ2	ϱ2	NOUN
ejpam-7074	460	5	]	]	PUNCT
ejpam-7074	461	1	if	if	SCONJ
ejpam-7074	461	2	d	d	PROPN
ejpam-7074	461	3	∈	∈	PROPN
ejpam-7074	461	4	b	b	PROPN
ejpam-7074	462	1	[	[	X
ejpam-7074	462	2	0	0	NUM
ejpam-7074	462	3	,	,	PUNCT
ejpam-7074	462	4	0	0	NUM
ejpam-7074	462	5	]	]	PUNCT
ejpam-7074	462	6	otherwise	otherwise	ADV
ejpam-7074	462	7	and	and	CCONJ
ejpam-7074	462	8	γa(d	γa(d	PUNCT
ejpam-7074	462	9	)	)	PUNCT
ejpam-7074	463	1	=	=	PRON
ejpam-7074	463	2	{	{	PUNCT
ejpam-7074	464	1	[	[	X
ejpam-7074	464	2	ϑ1	ϑ1	NOUN
ejpam-7074	464	3	,	,	PUNCT
ejpam-7074	464	4	ϑ2	ϑ2	PROPN
ejpam-7074	464	5	]	]	PUNCT
ejpam-7074	465	1	if	if	SCONJ
ejpam-7074	465	2	d	d	PROPN
ejpam-7074	465	3	∈	∈	PROPN
ejpam-7074	465	4	b	b	PROPN
ejpam-7074	466	1	[	[	X
ejpam-7074	466	2	1	1	NUM
ejpam-7074	466	3	,	,	PUNCT
ejpam-7074	466	4	1	1	NUM
ejpam-7074	466	5	]	]	PUNCT
ejpam-7074	466	6	otherwise	otherwise	ADV
ejpam-7074	466	7	for	for	ADP
ejpam-7074	466	8	all	all	DET
ejpam-7074	466	9	[	[	X
ejpam-7074	466	10	ϱ1	ϱ1	NOUN
ejpam-7074	466	11	,	,	PUNCT
ejpam-7074	466	12	ϱ2	ϱ2	NOUN
ejpam-7074	466	13	]	]	PUNCT
ejpam-7074	466	14	,	,	PUNCT
ejpam-7074	466	15	[	[	X
ejpam-7074	466	16	ϑ1	ϑ1	NOUN
ejpam-7074	466	17	,	,	PUNCT
ejpam-7074	466	18	ϑ2	ϑ2	PROPN
ejpam-7074	466	19	]	]	X
ejpam-7074	467	1	∈	∈	PROPN
ejpam-7074	468	1	d	d	X
ejpam-7074	469	1	[	[	X
ejpam-7074	469	2	0	0	NUM
ejpam-7074	469	3	,	,	PUNCT
ejpam-7074	469	4	1	1	NUM
ejpam-7074	469	5	]	]	PUNCT
ejpam-7074	469	6	and	and	CCONJ
ejpam-7074	469	7	ϱ2+ϑ2	ϱ2+ϑ2	PROPN
ejpam-7074	469	8	≤	≤	NOUN
ejpam-7074	469	9	1	1	NUM
ejpam-7074	469	10	.	.	PUNCT
ejpam-7074	470	1	if	if	SCONJ
ejpam-7074	470	2	a	a	PRON
ejpam-7074	470	3	=	=	X
ejpam-7074	470	4	(	(	PUNCT
ejpam-7074	470	5	µa	µa	PROPN
ejpam-7074	470	6	,	,	PUNCT
ejpam-7074	470	7	γa	γa	PROPN
ejpam-7074	470	8	)	)	PUNCT
ejpam-7074	470	9	is	be	AUX
ejpam-7074	470	10	realized	realize	VERB
ejpam-7074	470	11	as	as	ADP
ejpam-7074	470	12	a	a	DET
ejpam-7074	470	13	lower	low	ADJ
ejpam-7074	470	14	-	-	PUNCT
ejpam-7074	470	15	level	level	NOUN
ejpam-7074	470	16	subalgebra	subalgebra	NOUN
ejpam-7074	470	17	and	and	CCONJ
ejpam-7074	470	18	an	an	DET
ejpam-7074	470	19	upper	upper	ADJ
ejpam-7074	470	20	-	-	PUNCT
ejpam-7074	470	21	level	level	NOUN
ejpam-7074	470	22	subalgebra	subalgebra	NOUN
ejpam-7074	470	23	of	of	ADP
ejpam-7074	470	24	some	some	DET
ejpam-7074	470	25	ivifss	ivifss	ADJ
ejpam-7074	470	26	-	-	PUNCT
ejpam-7074	470	27	subalgebra	subalgebra	NOUN
ejpam-7074	470	28	of	of	ADP
ejpam-7074	470	29	sh	sh	PROPN
ejpam-7074	470	30	,	,	PUNCT
ejpam-7074	470	31	then	then	ADV
ejpam-7074	470	32	b	b	X
ejpam-7074	470	33	is	be	AUX
ejpam-7074	470	34	a	a	DET
ejpam-7074	470	35	subalgebra	subalgebra	NOUN
ejpam-7074	470	36	of	of	ADP
ejpam-7074	470	37	sh	sh	PROPN
ejpam-7074	470	38	.	.	PUNCT
ejpam-7074	471	1	a.	a.	PROPN
ejpam-7074	471	2	iampan	iampan	PROPN
ejpam-7074	471	3	et	et	PROPN
ejpam-7074	471	4	al	al	PROPN
ejpam-7074	471	5	.	.	PUNCT
ejpam-7074	471	6	/	/	SYM
ejpam-7074	471	7	eur	eur	PROPN
ejpam-7074	471	8	.	.	PUNCT
ejpam-7074	472	1	j.	j.	PROPN
ejpam-7074	472	2	pure	pure	PROPN
ejpam-7074	472	3	appl	appl	PROPN
ejpam-7074	472	4	.	.	PROPN
ejpam-7074	472	5	math	math	PROPN
ejpam-7074	472	6	,	,	PUNCT
ejpam-7074	472	7	18	18	NUM
ejpam-7074	472	8	(	(	PUNCT
ejpam-7074	472	9	4	4	NUM
ejpam-7074	472	10	)	)	PUNCT
ejpam-7074	472	11	(	(	PUNCT
ejpam-7074	472	12	2025	2025	NUM
ejpam-7074	472	13	)	)	PUNCT
ejpam-7074	472	14	,	,	PUNCT
ejpam-7074	472	15	7074	7074	NUM
ejpam-7074	472	16	12	12	NUM
ejpam-7074	472	17	of	of	ADP
ejpam-7074	472	18	14	14	NUM
ejpam-7074	472	19	proof	proof	NOUN
ejpam-7074	472	20	.	.	PUNCT
ejpam-7074	473	1	let	let	VERB
ejpam-7074	473	2	a	a	DET
ejpam-7074	473	3	=	=	SYM
ejpam-7074	473	4	(	(	PUNCT
ejpam-7074	473	5	µa	µa	PROPN
ejpam-7074	473	6	,	,	PUNCT
ejpam-7074	473	7	γa	γa	PROPN
ejpam-7074	473	8	)	)	PUNCT
ejpam-7074	473	9	be	be	AUX
ejpam-7074	473	10	an	an	DET
ejpam-7074	473	11	ivifss	ivifss	ADJ
ejpam-7074	473	12	-	-	PUNCT
ejpam-7074	473	13	subalgebra	subalgebra	NOUN
ejpam-7074	473	14	of	of	ADP
ejpam-7074	473	15	sh	sh	PROPN
ejpam-7074	473	16	,	,	PUNCT
ejpam-7074	473	17	and	and	CCONJ
ejpam-7074	473	18	d	d	NOUN
ejpam-7074	473	19	,	,	PUNCT
ejpam-7074	473	20	g	g	PROPN
ejpam-7074	473	21	∈	∈	PROPN
ejpam-7074	473	22	b.	b.	PROPN
ejpam-7074	473	23	then	then	ADV
ejpam-7074	473	24	µa(d	µa(d	PUNCT
ejpam-7074	473	25	)	)	PUNCT
ejpam-7074	473	26	=	=	PUNCT
ejpam-7074	474	1	[	[	X
ejpam-7074	474	2	ϱ1	ϱ1	NOUN
ejpam-7074	474	3	,	,	PUNCT
ejpam-7074	474	4	ϱ2	ϱ2	NOUN
ejpam-7074	474	5	]	]	X
ejpam-7074	474	6	=	=	SYM
ejpam-7074	474	7	µa(g	µa(g	X
ejpam-7074	474	8	)	)	PUNCT
ejpam-7074	474	9	and	and	CCONJ
ejpam-7074	474	10	γa(d	γa(d	NUM
ejpam-7074	474	11	)	)	PUNCT
ejpam-7074	474	12	=	=	NOUN
ejpam-7074	475	1	[	[	X
ejpam-7074	475	2	β1	β1	PROPN
ejpam-7074	475	3	,	,	PUNCT
ejpam-7074	475	4	β2	β2	NOUN
ejpam-7074	475	5	]	]	X
ejpam-7074	475	6	=	=	PUNCT
ejpam-7074	475	7	γa(g	γa(g	NOUN
ejpam-7074	475	8	)	)	PUNCT
ejpam-7074	475	9	.	.	PUNCT
ejpam-7074	476	1	thus	thus	ADV
ejpam-7074	476	2	,	,	PUNCT
ejpam-7074	476	3	µa(d	µa(d	PUNCT
ejpam-7074	476	4	g	g	PROPN
ejpam-7074	476	5	|	|	NOUN
ejpam-7074	476	6	dg	dg	PROPN
ejpam-7074	476	7	)	)	PUNCT
ejpam-7074	476	8	≤	≤	NOUN
ejpam-7074	476	9	rmin{µa(d	rmin{µa(d	ADV
ejpam-7074	476	10	)	)	PUNCT
ejpam-7074	476	11	,	,	PUNCT
ejpam-7074	476	12	µa(g	µa(g	NOUN
ejpam-7074	476	13	)	)	PUNCT
ejpam-7074	476	14	}	}	PUNCT
ejpam-7074	476	15	=	=	SYM
ejpam-7074	476	16	rmin{[ϱ1	rmin{[ϱ1	NOUN
ejpam-7074	476	17	,	,	PUNCT
ejpam-7074	476	18	ϱ2	ϱ2	NOUN
ejpam-7074	476	19	]	]	PUNCT
ejpam-7074	476	20	,	,	PUNCT
ejpam-7074	476	21	[	[	X
ejpam-7074	476	22	ϱ1	ϱ1	NOUN
ejpam-7074	476	23	,	,	PUNCT
ejpam-7074	476	24	ϱ2	ϱ2	NOUN
ejpam-7074	476	25	]	]	X
ejpam-7074	476	26	}	}	PUNCT
ejpam-7074	476	27	=	=	PUNCT
ejpam-7074	477	1	[	[	X
ejpam-7074	477	2	ϱ1	ϱ1	NOUN
ejpam-7074	477	3	,	,	PUNCT
ejpam-7074	477	4	ϱ2	ϱ2	NOUN
ejpam-7074	477	5	]	]	PUNCT
ejpam-7074	477	6	and	and	CCONJ
ejpam-7074	477	7	γa(d	γa(d	NUM
ejpam-7074	477	8	g	g	PROPN
ejpam-7074	477	9	|	|	ADV
ejpam-7074	477	10	dg	dg	PROPN
ejpam-7074	477	11	)	)	PUNCT
ejpam-7074	477	12	≥	≥	NUM
ejpam-7074	477	13	rmax{γa(d	rmax{γa(d	NOUN
ejpam-7074	477	14	)	)	PUNCT
ejpam-7074	477	15	,	,	PUNCT
ejpam-7074	477	16	γa(g	γa(g	ADP
ejpam-7074	477	17	)	)	PUNCT
ejpam-7074	477	18	}	}	PUNCT
ejpam-7074	477	19	=	=	SYM
ejpam-7074	477	20	rmax{[ϑ1	rmax{[ϑ1	NOUN
ejpam-7074	477	21	,	,	PUNCT
ejpam-7074	477	22	ϑ2	ϑ2	PROPN
ejpam-7074	477	23	]	]	PUNCT
ejpam-7074	477	24	,	,	PUNCT
ejpam-7074	477	25	[	[	X
ejpam-7074	477	26	ϑ1	ϑ1	NOUN
ejpam-7074	477	27	,	,	PUNCT
ejpam-7074	477	28	ϑ2	ϑ2	NOUN
ejpam-7074	477	29	]	]	PUNCT
ejpam-7074	477	30	}	}	PUNCT
ejpam-7074	477	31	=	=	PUNCT
ejpam-7074	478	1	[	[	X
ejpam-7074	478	2	ϑ1	ϑ1	NOUN
ejpam-7074	478	3	,	,	PUNCT
ejpam-7074	478	4	β2	β2	NOUN
ejpam-7074	478	5	]	]	PUNCT
ejpam-7074	478	6	,	,	PUNCT
ejpam-7074	478	7	which	which	PRON
ejpam-7074	478	8	imply	imply	VERB
ejpam-7074	478	9	that	that	SCONJ
ejpam-7074	478	10	dg	dg	VERB
ejpam-7074	478	11	|	|	ADV
ejpam-7074	478	12	dg	dg	ADP
ejpam-7074	478	13	∈	∈	PROPN
ejpam-7074	478	14	b.	b.	PROPN
ejpam-7074	478	15	4	4	X
ejpam-7074	478	16	.	.	X
ejpam-7074	478	17	conclusion	conclusion	NOUN
ejpam-7074	478	18	this	this	DET
ejpam-7074	478	19	study	study	NOUN
ejpam-7074	478	20	explored	explore	VERB
ejpam-7074	478	21	the	the	DET
ejpam-7074	478	22	fundamental	fundamental	ADJ
ejpam-7074	478	23	properties	property	NOUN
ejpam-7074	478	24	of	of	ADP
ejpam-7074	478	25	interval	interval	NOUN
ejpam-7074	478	26	-	-	PUNCT
ejpam-7074	478	27	valued	value	VERB
ejpam-7074	478	28	intuitionistic	intuitionistic	ADJ
ejpam-7074	478	29	fuzzy	fuzzy	ADJ
ejpam-7074	478	30	(	(	PUNCT
ejpam-7074	478	31	ivif	ivif	NOUN
ejpam-7074	478	32	)	)	PUNCT
ejpam-7074	478	33	subsets	subset	NOUN
ejpam-7074	478	34	and	and	CCONJ
ejpam-7074	478	35	subalgebras	subalgebras	PROPN
ejpam-7074	478	36	within	within	ADP
ejpam-7074	478	37	sheffer	sheffer	PROPN
ejpam-7074	478	38	stroke	stroke	PROPN
ejpam-7074	478	39	hilbert	hilbert	PROPN
ejpam-7074	478	40	algebras	algebras	PROPN
ejpam-7074	478	41	,	,	PUNCT
ejpam-7074	478	42	highlighting	highlight	VERB
ejpam-7074	478	43	their	their	PRON
ejpam-7074	478	44	algebraic	algebraic	ADJ
ejpam-7074	478	45	behavior	behavior	NOUN
ejpam-7074	478	46	and	and	CCONJ
ejpam-7074	478	47	relationships	relationship	NOUN
ejpam-7074	478	48	under	under	ADP
ejpam-7074	478	49	various	various	ADJ
ejpam-7074	478	50	set	set	ADJ
ejpam-7074	478	51	operations	operation	NOUN
ejpam-7074	478	52	.	.	PUNCT
ejpam-7074	479	1	the	the	DET
ejpam-7074	479	2	results	result	NOUN
ejpam-7074	479	3	demonstrated	demonstrate	VERB
ejpam-7074	479	4	that	that	SCONJ
ejpam-7074	479	5	these	these	DET
ejpam-7074	479	6	fuzzy	fuzzy	ADJ
ejpam-7074	479	7	structures	structure	NOUN
ejpam-7074	479	8	could	could	AUX
ejpam-7074	479	9	serve	serve	VERB
ejpam-7074	479	10	as	as	ADP
ejpam-7074	479	11	effective	effective	ADJ
ejpam-7074	479	12	extensions	extension	NOUN
ejpam-7074	479	13	of	of	ADP
ejpam-7074	479	14	classical	classical	ADJ
ejpam-7074	479	15	algebraic	algebraic	ADJ
ejpam-7074	479	16	systems	system	NOUN
ejpam-7074	479	17	,	,	PUNCT
ejpam-7074	479	18	allowing	allow	VERB
ejpam-7074	479	19	for	for	ADP
ejpam-7074	479	20	the	the	DET
ejpam-7074	479	21	flexible	flexible	ADJ
ejpam-7074	479	22	capture	capture	NOUN
ejpam-7074	479	23	of	of	ADP
ejpam-7074	479	24	uncertainty	uncertainty	NOUN
ejpam-7074	479	25	and	and	CCONJ
ejpam-7074	479	26	partial	partial	ADJ
ejpam-7074	479	27	membership	membership	NOUN
ejpam-7074	479	28	.	.	PUNCT
ejpam-7074	480	1	the	the	DET
ejpam-7074	480	2	theoretical	theoretical	ADJ
ejpam-7074	480	3	insights	insight	NOUN
ejpam-7074	480	4	provided	provide	VERB
ejpam-7074	480	5	by	by	ADP
ejpam-7074	480	6	this	this	DET
ejpam-7074	480	7	work	work	NOUN
ejpam-7074	480	8	lay	lie	VERB
ejpam-7074	480	9	a	a	DET
ejpam-7074	480	10	foundation	foundation	NOUN
ejpam-7074	480	11	for	for	ADP
ejpam-7074	480	12	integrating	integrate	VERB
ejpam-7074	480	13	fuzzy	fuzzy	ADJ
ejpam-7074	480	14	logic	logic	NOUN
ejpam-7074	480	15	principles	principle	NOUN
ejpam-7074	480	16	into	into	ADP
ejpam-7074	480	17	algebraic	algebraic	ADJ
ejpam-7074	480	18	frameworks	framework	NOUN
ejpam-7074	480	19	,	,	PUNCT
ejpam-7074	480	20	with	with	ADP
ejpam-7074	480	21	potential	potential	ADJ
ejpam-7074	480	22	applications	application	NOUN
ejpam-7074	480	23	in	in	ADP
ejpam-7074	480	24	logical	logical	ADJ
ejpam-7074	480	25	reasoning	reasoning	NOUN
ejpam-7074	480	26	,	,	PUNCT
ejpam-7074	480	27	decision	decision	NOUN
ejpam-7074	480	28	-	-	PUNCT
ejpam-7074	480	29	making	making	NOUN
ejpam-7074	480	30	,	,	PUNCT
ejpam-7074	480	31	and	and	CCONJ
ejpam-7074	480	32	information	information	NOUN
ejpam-7074	480	33	processing	processing	NOUN
ejpam-7074	480	34	.	.	PUNCT
ejpam-7074	481	1	future	future	ADJ
ejpam-7074	481	2	research	research	NOUN
ejpam-7074	481	3	could	could	AUX
ejpam-7074	481	4	focus	focus	VERB
ejpam-7074	481	5	on	on	ADP
ejpam-7074	481	6	extending	extend	VERB
ejpam-7074	481	7	the	the	DET
ejpam-7074	481	8	concept	concept	NOUN
ejpam-7074	481	9	of	of	ADP
ejpam-7074	481	10	ivif	ivif	NOUN
ejpam-7074	481	11	subsets	subset	NOUN
ejpam-7074	481	12	and	and	CCONJ
ejpam-7074	481	13	ideals	ideal	NOUN
ejpam-7074	481	14	to	to	ADP
ejpam-7074	481	15	other	other	ADJ
ejpam-7074	481	16	algebraic	algebraic	ADJ
ejpam-7074	481	17	systems	system	NOUN
ejpam-7074	481	18	such	such	ADJ
ejpam-7074	481	19	as	as	ADP
ejpam-7074	481	20	boolean	boolean	ADJ
ejpam-7074	481	21	algebras	algebra	NOUN
ejpam-7074	481	22	,	,	PUNCT
ejpam-7074	481	23	orthomodular	orthomodular	ADJ
ejpam-7074	481	24	lattices	lattice	NOUN
ejpam-7074	481	25	,	,	PUNCT
ejpam-7074	481	26	and	and	CCONJ
ejpam-7074	481	27	residuated	residuate	VERB
ejpam-7074	481	28	structures	structure	NOUN
ejpam-7074	481	29	.	.	PUNCT
ejpam-7074	482	1	developing	develop	VERB
ejpam-7074	482	2	computational	computational	ADJ
ejpam-7074	482	3	algorithms	algorithm	NOUN
ejpam-7074	482	4	for	for	ADP
ejpam-7074	482	5	the	the	DET
ejpam-7074	482	6	automatic	automatic	ADJ
ejpam-7074	482	7	identification	identification	NOUN
ejpam-7074	482	8	and	and	CCONJ
ejpam-7074	482	9	manipulation	manipulation	NOUN
ejpam-7074	482	10	of	of	ADP
ejpam-7074	482	11	ivif	ivif	NOUN
ejpam-7074	482	12	subalgebras	subalgebras	PROPN
ejpam-7074	482	13	will	will	AUX
ejpam-7074	482	14	facilitate	facilitate	VERB
ejpam-7074	482	15	practical	practical	ADJ
ejpam-7074	482	16	applications	application	NOUN
ejpam-7074	482	17	in	in	ADP
ejpam-7074	482	18	areas	area	NOUN
ejpam-7074	482	19	such	such	ADJ
ejpam-7074	482	20	as	as	ADP
ejpam-7074	482	21	artificial	artificial	ADJ
ejpam-7074	482	22	intelligence	intelligence	NOUN
ejpam-7074	482	23	,	,	PUNCT
ejpam-7074	482	24	fuzzy	fuzzy	ADJ
ejpam-7074	482	25	decision	decision	NOUN
ejpam-7074	482	26	-	-	PUNCT
ejpam-7074	482	27	making	making	NOUN
ejpam-7074	482	28	,	,	PUNCT
ejpam-7074	482	29	and	and	CCONJ
ejpam-7074	482	30	data	datum	NOUN
ejpam-7074	482	31	analysis	analysis	NOUN
ejpam-7074	482	32	.	.	PUNCT
ejpam-7074	483	1	additionally	additionally	ADV
ejpam-7074	483	2	,	,	PUNCT
ejpam-7074	483	3	investigating	investigate	VERB
ejpam-7074	483	4	the	the	DET
ejpam-7074	483	5	application	application	NOUN
ejpam-7074	483	6	of	of	ADP
ejpam-7074	483	7	these	these	DET
ejpam-7074	483	8	fuzzy	fuzzy	ADJ
ejpam-7074	483	9	algebraic	algebraic	ADJ
ejpam-7074	483	10	structures	structure	NOUN
ejpam-7074	483	11	in	in	ADP
ejpam-7074	483	12	real	real	ADJ
ejpam-7074	483	13	-	-	PUNCT
ejpam-7074	483	14	world	world	NOUN
ejpam-7074	483	15	scenarios	scenario	NOUN
ejpam-7074	483	16	—	—	PUNCT
ejpam-7074	483	17	such	such	ADJ
ejpam-7074	483	18	as	as	ADP
ejpam-7074	483	19	medical	medical	ADJ
ejpam-7074	483	20	diagnosis	diagnosis	NOUN
ejpam-7074	483	21	,	,	PUNCT
ejpam-7074	483	22	control	control	NOUN
ejpam-7074	483	23	systems	system	NOUN
ejpam-7074	483	24	,	,	PUNCT
ejpam-7074	483	25	and	and	CCONJ
ejpam-7074	483	26	information	information	NOUN
ejpam-7074	483	27	security	security	NOUN
ejpam-7074	483	28	—	—	PUNCT
ejpam-7074	483	29	may	may	AUX
ejpam-7074	483	30	provide	provide	VERB
ejpam-7074	483	31	valuable	valuable	ADJ
ejpam-7074	483	32	insights	insight	NOUN
ejpam-7074	483	33	and	and	CCONJ
ejpam-7074	483	34	enhance	enhance	VERB
ejpam-7074	483	35	their	their	PRON
ejpam-7074	483	36	practical	practical	ADJ
ejpam-7074	483	37	utility	utility	NOUN
ejpam-7074	483	38	.	.	PUNCT
ejpam-7074	484	1	further	further	ADJ
ejpam-7074	484	2	exploration	exploration	NOUN
ejpam-7074	484	3	of	of	ADP
ejpam-7074	484	4	their	their	PRON
ejpam-7074	484	5	interactions	interaction	NOUN
ejpam-7074	484	6	with	with	ADP
ejpam-7074	484	7	probabilistic	probabilistic	ADJ
ejpam-7074	484	8	and	and	CCONJ
ejpam-7074	484	9	other	other	ADJ
ejpam-7074	484	10	uncertainty	uncertainty	NOUN
ejpam-7074	484	11	-	-	PUNCT
ejpam-7074	484	12	based	base	VERB
ejpam-7074	484	13	frameworks	framework	NOUN
ejpam-7074	484	14	can	can	AUX
ejpam-7074	484	15	also	also	ADV
ejpam-7074	484	16	open	open	VERB
ejpam-7074	484	17	new	new	ADJ
ejpam-7074	484	18	avenues	avenue	NOUN
ejpam-7074	484	19	for	for	ADP
ejpam-7074	484	20	theoretical	theoretical	ADJ
ejpam-7074	484	21	advancement	advancement	NOUN
ejpam-7074	484	22	.	.	PUNCT
ejpam-7074	485	1	acknowledgements	acknowledgement	NOUN
ejpam-7074	485	2	this	this	DET
ejpam-7074	485	3	research	research	NOUN
ejpam-7074	485	4	was	be	AUX
ejpam-7074	485	5	supported	support	VERB
ejpam-7074	485	6	by	by	ADP
ejpam-7074	485	7	university	university	NOUN
ejpam-7074	485	8	of	of	ADP
ejpam-7074	485	9	phayao	phayao	NOUN
ejpam-7074	485	10	and	and	CCONJ
ejpam-7074	485	11	thailand	thailand	PROPN
ejpam-7074	485	12	science	science	PROPN
ejpam-7074	485	13	research	research	PROPN
ejpam-7074	485	14	and	and	CCONJ
ejpam-7074	485	15	innovation	innovation	NOUN
ejpam-7074	485	16	fund	fund	NOUN
ejpam-7074	485	17	(	(	PUNCT
ejpam-7074	485	18	fundamental	fundamental	ADJ
ejpam-7074	485	19	fund	fund	NOUN
ejpam-7074	485	20	2026	2026	NUM
ejpam-7074	485	21	,	,	PUNCT
ejpam-7074	485	22	grant	grant	VERB
ejpam-7074	485	23	no	no	NOUN
ejpam-7074	485	24	.	.	PUNCT
ejpam-7074	485	25	2252/2568	2252/2568	NUM
ejpam-7074	485	26	)	)	PUNCT
ejpam-7074	485	27	.	.	PUNCT
ejpam-7074	486	1	references	reference	NOUN
ejpam-7074	486	2	[	[	X
ejpam-7074	486	3	1	1	NUM
ejpam-7074	486	4	]	]	PUNCT
ejpam-7074	486	5	t.	t.	NOUN
ejpam-7074	486	6	oner	oner	NOUN
ejpam-7074	486	7	and	and	CCONJ
ejpam-7074	486	8	i.	i.	PROPN
ejpam-7074	486	9	senturk	senturk	PROPN
ejpam-7074	486	10	.	.	PUNCT
ejpam-7074	487	1	the	the	DET
ejpam-7074	487	2	sheffer	sheffer	PROPN
ejpam-7074	487	3	stroke	stroke	NOUN
ejpam-7074	487	4	operation	operation	NOUN
ejpam-7074	487	5	reducts	reduct	NOUN
ejpam-7074	487	6	of	of	ADP
ejpam-7074	487	7	basic	basic	ADJ
ejpam-7074	487	8	algebra	algebra	NOUN
ejpam-7074	487	9	.	.	PUNCT
ejpam-7074	488	1	open	open	ADJ
ejpam-7074	488	2	mathematics	mathematic	NOUN
ejpam-7074	488	3	,	,	PUNCT
ejpam-7074	488	4	15(1):926–935	15(1):926–935	PROPN
ejpam-7074	488	5	,	,	PUNCT
ejpam-7074	488	6	2017	2017	NUM
ejpam-7074	488	7	.	.	PUNCT
ejpam-7074	489	1	[	[	X
ejpam-7074	489	2	2	2	NUM
ejpam-7074	489	3	]	]	PUNCT
ejpam-7074	489	4	i.	i.	NOUN
ejpam-7074	489	5	senturk	senturk	PROPN
ejpam-7074	489	6	,	,	PUNCT
ejpam-7074	489	7	t.	t.	PROPN
ejpam-7074	489	8	oner	oner	NOUN
ejpam-7074	489	9	,	,	PUNCT
ejpam-7074	489	10	and	and	CCONJ
ejpam-7074	489	11	a.	a.	PROPN
ejpam-7074	489	12	borumand	borumand	PROPN
ejpam-7074	489	13	saeid	saeid	PROPN
ejpam-7074	489	14	.	.	PUNCT
ejpam-7074	490	1	congruences	congruence	NOUN
ejpam-7074	490	2	of	of	ADP
ejpam-7074	490	3	sheffer	sheffer	NOUN
ejpam-7074	490	4	stroke	stroke	NOUN
ejpam-7074	490	5	basic	basic	ADJ
ejpam-7074	490	6	algebras	algebra	NOUN
ejpam-7074	490	7	.	.	PUNCT
ejpam-7074	491	1	analele	analele	PROPN
ejpam-7074	491	2	stiintifice	stiintifice	PROPN
ejpam-7074	491	3	ale	ale	PROPN
ejpam-7074	491	4	universitatii	universitatii	PROPN
ejpam-7074	491	5	ovidius	ovidius	PROPN
ejpam-7074	491	6	constanta	constanta	PROPN
ejpam-7074	491	7	,	,	PUNCT
ejpam-7074	491	8	seria	seria	PROPN
ejpam-7074	491	9	matematica	matematica	PROPN
ejpam-7074	491	10	,	,	PUNCT
ejpam-7074	491	11	28(2):209–228	28(2):209–228	PROPN
ejpam-7074	491	12	,	,	PUNCT
ejpam-7074	491	13	2020	2020	NUM
ejpam-7074	491	14	.	.	PUNCT
ejpam-7074	492	1	a.	a.	NOUN
ejpam-7074	492	2	iampan	iampan	PROPN
ejpam-7074	492	3	et	et	PROPN
ejpam-7074	492	4	al	al	PROPN
ejpam-7074	492	5	.	.	PUNCT
ejpam-7074	492	6	/	/	SYM
ejpam-7074	492	7	eur	eur	PROPN
ejpam-7074	492	8	.	.	PUNCT
ejpam-7074	493	1	j.	j.	PROPN
ejpam-7074	493	2	pure	pure	PROPN
ejpam-7074	493	3	appl	appl	PROPN
ejpam-7074	493	4	.	.	PROPN
ejpam-7074	493	5	math	math	PROPN
ejpam-7074	493	6	,	,	PUNCT
ejpam-7074	493	7	18	18	NUM
ejpam-7074	493	8	(	(	PUNCT
ejpam-7074	493	9	4	4	NUM
ejpam-7074	493	10	)	)	PUNCT
ejpam-7074	493	11	(	(	PUNCT
ejpam-7074	493	12	2025	2025	NUM
ejpam-7074	493	13	)	)	PUNCT
ejpam-7074	493	14	,	,	PUNCT
ejpam-7074	493	15	7074	7074	NUM
ejpam-7074	493	16	13	13	NUM
ejpam-7074	493	17	of	of	ADP
ejpam-7074	493	18	14	14	NUM
ejpam-7074	493	19	[	[	SYM
ejpam-7074	493	20	3	3	NUM
ejpam-7074	493	21	]	]	X
ejpam-7074	493	22	i.	i.	NOUN
ejpam-7074	493	23	senturk	senturk	PROPN
ejpam-7074	493	24	and	and	CCONJ
ejpam-7074	493	25	t.	t.	PROPN
ejpam-7074	493	26	oner	oner	NOUN
ejpam-7074	493	27	.	.	PUNCT
ejpam-7074	494	1	a	a	DET
ejpam-7074	494	2	construction	construction	NOUN
ejpam-7074	494	3	of	of	ADP
ejpam-7074	494	4	very	very	ADV
ejpam-7074	494	5	true	true	ADJ
ejpam-7074	494	6	operator	operator	NOUN
ejpam-7074	494	7	on	on	ADP
ejpam-7074	494	8	sheffer	sheffer	PROPN
ejpam-7074	494	9	stroke	stroke	PROPN
ejpam-7074	494	10	mtlalgebras	mtlalgebras	PROPN
ejpam-7074	494	11	.	.	PUNCT
ejpam-7074	495	1	international	international	ADJ
ejpam-7074	495	2	journal	journal	PROPN
ejpam-7074	495	3	of	of	ADP
ejpam-7074	495	4	maps	map	NOUN
ejpam-7074	495	5	in	in	ADP
ejpam-7074	495	6	mathematics	mathematic	NOUN
ejpam-7074	495	7	,	,	PUNCT
ejpam-7074	495	8	4(2):93–106	4(2):93–106	NUM
ejpam-7074	495	9	,	,	PUNCT
ejpam-7074	495	10	2021	2021	NUM
ejpam-7074	495	11	.	.	PUNCT
ejpam-7074	496	1	[	[	X
ejpam-7074	496	2	4	4	NUM
ejpam-7074	496	3	]	]	PUNCT
ejpam-7074	496	4	i.	i.	NOUN
ejpam-7074	496	5	chajda	chajda	PROPN
ejpam-7074	496	6	.	.	PUNCT
ejpam-7074	497	1	sheffer	sheffer	PROPN
ejpam-7074	497	2	operation	operation	NOUN
ejpam-7074	497	3	in	in	ADP
ejpam-7074	497	4	ortholattices	ortholattice	NOUN
ejpam-7074	497	5	.	.	PUNCT
ejpam-7074	498	1	acta	acta	PROPN
ejpam-7074	498	2	universitatis	universitatis	PROPN
ejpam-7074	498	3	palackianae	palackianae	VERB
ejpam-7074	498	4	olomucensis	olomucensis	NOUN
ejpam-7074	498	5	.	.	PUNCT
ejpam-7074	499	1	facultas	facultas	PROPN
ejpam-7074	499	2	rerum	rerum	PROPN
ejpam-7074	499	3	naturalium	naturalium	PROPN
ejpam-7074	499	4	.	.	PUNCT
ejpam-7074	500	1	mathematica	mathematica	PROPN
ejpam-7074	500	2	,	,	PUNCT
ejpam-7074	500	3	44(1):19–23	44(1):19–23	NUM
ejpam-7074	500	4	,	,	PUNCT
ejpam-7074	500	5	2005	2005	NUM
ejpam-7074	500	6	.	.	PUNCT
ejpam-7074	501	1	[	[	X
ejpam-7074	501	2	5	5	NUM
ejpam-7074	501	3	]	]	X
ejpam-7074	501	4	n.	n.	NOUN
ejpam-7074	501	5	chunsee	chunsee	PROPN
ejpam-7074	501	6	,	,	PUNCT
ejpam-7074	501	7	p.	p.	PROPN
ejpam-7074	501	8	julatha	julatha	PROPN
ejpam-7074	501	9	,	,	PUNCT
ejpam-7074	501	10	and	and	CCONJ
ejpam-7074	501	11	a.	a.	NOUN
ejpam-7074	501	12	iampan	iampan	PROPN
ejpam-7074	501	13	.	.	PUNCT
ejpam-7074	502	1	fuzzy	fuzzy	ADJ
ejpam-7074	502	2	set	set	VERB
ejpam-7074	502	3	approach	approach	NOUN
ejpam-7074	502	4	to	to	ADP
ejpam-7074	502	5	ideal	ideal	ADJ
ejpam-7074	502	6	theory	theory	NOUN
ejpam-7074	502	7	on	on	ADP
ejpam-7074	502	8	sheffer	sheffer	PROPN
ejpam-7074	502	9	stroke	stroke	NOUN
ejpam-7074	502	10	be	be	AUX
ejpam-7074	502	11	-	-	PUNCT
ejpam-7074	502	12	algebras	algebra	NOUN
ejpam-7074	502	13	.	.	PUNCT
ejpam-7074	503	1	journal	journal	PROPN
ejpam-7074	503	2	of	of	ADP
ejpam-7074	503	3	mathematics	mathematic	NOUN
ejpam-7074	503	4	and	and	CCONJ
ejpam-7074	503	5	computer	computer	NOUN
ejpam-7074	503	6	science	science	NOUN
ejpam-7074	503	7	,	,	PUNCT
ejpam-7074	503	8	34(3):283–294	34(3):283–294	NUM
ejpam-7074	503	9	,	,	PUNCT
ejpam-7074	503	10	2024	2024	NUM
ejpam-7074	503	11	.	.	PUNCT
ejpam-7074	504	1	[	[	X
ejpam-7074	504	2	6	6	NUM
ejpam-7074	504	3	]	]	PUNCT
ejpam-7074	504	4	l.	l.	PROPN
ejpam-7074	504	5	a.	a.	PROPN
ejpam-7074	504	6	zadeh	zadeh	PROPN
ejpam-7074	504	7	.	.	PUNCT
ejpam-7074	504	8	fuzzy	fuzzy	ADJ
ejpam-7074	504	9	sets	set	NOUN
ejpam-7074	504	10	.	.	PUNCT
ejpam-7074	505	1	information	information	NOUN
ejpam-7074	505	2	and	and	CCONJ
ejpam-7074	505	3	control	control	NOUN
ejpam-7074	505	4	,	,	PUNCT
ejpam-7074	505	5	8(3):338–353	8(3):338–353	NUM
ejpam-7074	505	6	,	,	PUNCT
ejpam-7074	505	7	1965	1965	NUM
ejpam-7074	505	8	.	.	PUNCT
ejpam-7074	506	1	[	[	X
ejpam-7074	506	2	7	7	X
ejpam-7074	506	3	]	]	X
ejpam-7074	506	4	b.	b.	PROPN
ejpam-7074	506	5	ahmad	ahmad	PROPN
ejpam-7074	506	6	and	and	CCONJ
ejpam-7074	506	7	a.	a.	PROPN
ejpam-7074	506	8	kharal	kharal	PROPN
ejpam-7074	506	9	.	.	PUNCT
ejpam-7074	507	1	on	on	ADP
ejpam-7074	507	2	fuzzy	fuzzy	ADJ
ejpam-7074	507	3	soft	soft	ADJ
ejpam-7074	507	4	sets	set	NOUN
ejpam-7074	507	5	.	.	PUNCT
ejpam-7074	508	1	advances	advance	NOUN
ejpam-7074	508	2	in	in	ADP
ejpam-7074	508	3	fuzzy	fuzzy	ADJ
ejpam-7074	508	4	systems	system	NOUN
ejpam-7074	508	5	,	,	PUNCT
ejpam-7074	508	6	2009	2009	NUM
ejpam-7074	508	7	:	:	PUNCT
ejpam-7074	508	8	article	article	NOUN
ejpam-7074	508	9	i	i	PROPN
ejpam-7074	508	10	d	d	PROPN
ejpam-7074	508	11	586507	586507	NUM
ejpam-7074	508	12	,	,	PUNCT
ejpam-7074	508	13	6	6	NUM
ejpam-7074	508	14	pages	page	NOUN
ejpam-7074	508	15	,	,	PUNCT
ejpam-7074	508	16	2009	2009	NUM
ejpam-7074	508	17	.	.	PUNCT
ejpam-7074	509	1	[	[	X
ejpam-7074	509	2	8	8	NUM
ejpam-7074	509	3	]	]	X
ejpam-7074	509	4	m.	m.	NOUN
ejpam-7074	509	5	atef	atef	PROPN
ejpam-7074	509	6	,	,	PUNCT
ejpam-7074	509	7	m.	m.	PROPN
ejpam-7074	509	8	i.	i.	PROPN
ejpam-7074	509	9	ali	ali	PROPN
ejpam-7074	509	10	,	,	PUNCT
ejpam-7074	509	11	and	and	CCONJ
ejpam-7074	509	12	t.	t.	PROPN
ejpam-7074	509	13	m.	m.	PROPN
ejpam-7074	509	14	al	al	PROPN
ejpam-7074	509	15	-	-	PUNCT
ejpam-7074	509	16	shami	shami	PROPN
ejpam-7074	509	17	.	.	PUNCT
ejpam-7074	510	1	fuzzy	fuzzy	ADJ
ejpam-7074	510	2	soft	soft	ADJ
ejpam-7074	510	3	covering	covering	NOUN
ejpam-7074	510	4	-	-	PUNCT
ejpam-7074	510	5	based	base	VERB
ejpam-7074	510	6	multi	multi	ADJ
ejpam-7074	510	7	-	-	ADJ
ejpam-7074	510	8	granulation	granulation	ADJ
ejpam-7074	510	9	fuzzy	fuzzy	ADJ
ejpam-7074	510	10	rough	rough	ADJ
ejpam-7074	510	11	sets	set	NOUN
ejpam-7074	510	12	and	and	CCONJ
ejpam-7074	510	13	their	their	PRON
ejpam-7074	510	14	applications	application	NOUN
ejpam-7074	510	15	.	.	PUNCT
ejpam-7074	511	1	computational	computational	ADJ
ejpam-7074	511	2	and	and	CCONJ
ejpam-7074	511	3	applied	applied	ADJ
ejpam-7074	511	4	mathematics	mathematic	NOUN
ejpam-7074	511	5	,	,	PUNCT
ejpam-7074	511	6	40	40	NUM
ejpam-7074	511	7	:	:	PUNCT
ejpam-7074	511	8	article	article	NOUN
ejpam-7074	511	9	number	number	NOUN
ejpam-7074	511	10	115	115	NUM
ejpam-7074	511	11	,	,	PUNCT
ejpam-7074	511	12	2021	2021	NUM
ejpam-7074	511	13	.	.	PUNCT
ejpam-7074	512	1	[	[	X
ejpam-7074	512	2	9	9	NUM
ejpam-7074	512	3	]	]	X
ejpam-7074	512	4	n.	n.	NOUN
ejpam-7074	512	5	cǎgman	cǎgman	NOUN
ejpam-7074	512	6	,	,	PUNCT
ejpam-7074	512	7	s.	s.	PROPN
ejpam-7074	512	8	enginǒglu	enginǒglu	PROPN
ejpam-7074	512	9	,	,	PUNCT
ejpam-7074	512	10	and	and	CCONJ
ejpam-7074	512	11	f.	f.	PROPN
ejpam-7074	512	12	citak	citak	PROPN
ejpam-7074	512	13	.	.	PUNCT
ejpam-7074	513	1	fuzzy	fuzzy	ADJ
ejpam-7074	513	2	soft	soft	ADJ
ejpam-7074	513	3	set	set	NOUN
ejpam-7074	513	4	theory	theory	NOUN
ejpam-7074	513	5	and	and	CCONJ
ejpam-7074	513	6	its	its	PRON
ejpam-7074	513	7	application	application	NOUN
ejpam-7074	513	8	.	.	PUNCT
ejpam-7074	514	1	iranian	iranian	ADJ
ejpam-7074	514	2	journal	journal	PROPN
ejpam-7074	514	3	of	of	ADP
ejpam-7074	514	4	fuzzy	fuzzy	ADJ
ejpam-7074	514	5	systems	system	NOUN
ejpam-7074	514	6	,	,	PUNCT
ejpam-7074	514	7	8(3):137–147	8(3):137–147	NUM
ejpam-7074	514	8	,	,	PUNCT
ejpam-7074	514	9	2011	2011	NUM
ejpam-7074	514	10	.	.	PUNCT
ejpam-7074	515	1	[	[	X
ejpam-7074	515	2	10	10	NUM
ejpam-7074	515	3	]	]	PUNCT
ejpam-7074	515	4	k.	k.	PROPN
ejpam-7074	515	5	t.	t.	PROPN
ejpam-7074	515	6	atanassov	atanassov	PROPN
ejpam-7074	515	7	.	.	PUNCT
ejpam-7074	516	1	intuitionistic	intuitionistic	ADJ
ejpam-7074	516	2	fuzzy	fuzzy	ADJ
ejpam-7074	516	3	sets	set	NOUN
ejpam-7074	516	4	.	.	PUNCT
ejpam-7074	517	1	fuzzy	fuzzy	ADJ
ejpam-7074	517	2	sets	set	NOUN
ejpam-7074	517	3	and	and	CCONJ
ejpam-7074	517	4	systems	system	NOUN
ejpam-7074	517	5	,	,	PUNCT
ejpam-7074	517	6	20(1):87–96	20(1):87–96	NUM
ejpam-7074	517	7	,	,	PUNCT
ejpam-7074	517	8	1986	1986	NUM
ejpam-7074	517	9	.	.	PUNCT
ejpam-7074	518	1	[	[	X
ejpam-7074	518	2	11	11	NUM
ejpam-7074	518	3	]	]	X
ejpam-7074	518	4	h.	h.	PROPN
ejpam-7074	518	5	garg	garg	PROPN
ejpam-7074	518	6	and	and	CCONJ
ejpam-7074	518	7	s.	s.	PROPN
ejpam-7074	518	8	singh	singh	PROPN
ejpam-7074	518	9	.	.	PUNCT
ejpam-7074	519	1	a	a	DET
ejpam-7074	519	2	novel	novel	ADJ
ejpam-7074	519	3	triangular	triangular	NOUN
ejpam-7074	519	4	interval	interval	NOUN
ejpam-7074	519	5	type-2	type-2	NUM
ejpam-7074	519	6	intuitionistic	intuitionistic	ADJ
ejpam-7074	519	7	fuzzy	fuzzy	ADJ
ejpam-7074	519	8	sets	set	NOUN
ejpam-7074	519	9	and	and	CCONJ
ejpam-7074	519	10	their	their	PRON
ejpam-7074	519	11	aggregation	aggregation	NOUN
ejpam-7074	519	12	operators	operator	NOUN
ejpam-7074	519	13	.	.	PUNCT
ejpam-7074	520	1	iranian	iranian	ADJ
ejpam-7074	520	2	journal	journal	PROPN
ejpam-7074	520	3	of	of	ADP
ejpam-7074	520	4	fuzzy	fuzzy	ADJ
ejpam-7074	520	5	systems	system	NOUN
ejpam-7074	520	6	,	,	PUNCT
ejpam-7074	520	7	15(5):69–93	15(5):69–93	NUM
ejpam-7074	520	8	,	,	PUNCT
ejpam-7074	520	9	2018	2018	NUM
ejpam-7074	520	10	.	.	PUNCT
ejpam-7074	521	1	[	[	X
ejpam-7074	521	2	12	12	NUM
ejpam-7074	521	3	]	]	X
ejpam-7074	521	4	h.	h.	PROPN
ejpam-7074	521	5	garg	garg	PROPN
ejpam-7074	521	6	and	and	CCONJ
ejpam-7074	521	7	k.	k.	PROPN
ejpam-7074	521	8	kumar	kumar	PROPN
ejpam-7074	521	9	.	.	PUNCT
ejpam-7074	522	1	an	an	DET
ejpam-7074	522	2	advanced	advanced	ADJ
ejpam-7074	522	3	study	study	NOUN
ejpam-7074	522	4	on	on	ADP
ejpam-7074	522	5	the	the	DET
ejpam-7074	522	6	similarity	similarity	NOUN
ejpam-7074	522	7	measures	measure	NOUN
ejpam-7074	522	8	of	of	ADP
ejpam-7074	522	9	intuitionistic	intuitionistic	ADJ
ejpam-7074	522	10	fuzzy	fuzzy	ADJ
ejpam-7074	522	11	sets	set	NOUN
ejpam-7074	522	12	based	base	VERB
ejpam-7074	522	13	on	on	ADP
ejpam-7074	522	14	the	the	DET
ejpam-7074	522	15	set	set	VERB
ejpam-7074	522	16	pair	pair	NOUN
ejpam-7074	522	17	analysis	analysis	NOUN
ejpam-7074	522	18	theory	theory	NOUN
ejpam-7074	522	19	and	and	CCONJ
ejpam-7074	522	20	their	their	PRON
ejpam-7074	522	21	application	application	NOUN
ejpam-7074	522	22	in	in	ADP
ejpam-7074	522	23	decision	decision	NOUN
ejpam-7074	522	24	making	making	NOUN
ejpam-7074	522	25	.	.	PUNCT
ejpam-7074	523	1	soft	soft	ADJ
ejpam-7074	523	2	computing	computing	NOUN
ejpam-7074	523	3	,	,	PUNCT
ejpam-7074	523	4	22:4959–4970	22:4959–4970	NUM
ejpam-7074	523	5	,	,	PUNCT
ejpam-7074	523	6	2018	2018	NUM
ejpam-7074	523	7	.	.	PUNCT
ejpam-7074	524	1	[	[	X
ejpam-7074	524	2	13	13	NUM
ejpam-7074	524	3	]	]	X
ejpam-7074	524	4	h.	h.	PROPN
ejpam-7074	524	5	garg	garg	PROPN
ejpam-7074	524	6	and	and	CCONJ
ejpam-7074	524	7	k.	k.	PROPN
ejpam-7074	524	8	kumar	kumar	PROPN
ejpam-7074	524	9	.	.	PROPN
ejpam-7074	525	1	distance	distance	NOUN
ejpam-7074	525	2	measures	measure	NOUN
ejpam-7074	525	3	for	for	ADP
ejpam-7074	525	4	connection	connection	NOUN
ejpam-7074	525	5	number	number	NOUN
ejpam-7074	525	6	sets	set	NOUN
ejpam-7074	525	7	based	base	VERB
ejpam-7074	525	8	on	on	ADP
ejpam-7074	525	9	set	set	VERB
ejpam-7074	525	10	pair	pair	NOUN
ejpam-7074	525	11	analysis	analysis	NOUN
ejpam-7074	525	12	and	and	CCONJ
ejpam-7074	525	13	its	its	PRON
ejpam-7074	525	14	applications	application	NOUN
ejpam-7074	525	15	to	to	ADP
ejpam-7074	525	16	decision	decision	NOUN
ejpam-7074	525	17	-	-	PUNCT
ejpam-7074	525	18	making	make	VERB
ejpam-7074	525	19	process	process	NOUN
ejpam-7074	525	20	.	.	PUNCT
ejpam-7074	526	1	applied	apply	VERB
ejpam-7074	526	2	intelligence	intelligence	NOUN
ejpam-7074	526	3	,	,	PUNCT
ejpam-7074	526	4	48:3346–3359	48:3346–3359	NUM
ejpam-7074	526	5	,	,	PUNCT
ejpam-7074	526	6	2018	2018	NUM
ejpam-7074	526	7	.	.	PUNCT
ejpam-7074	527	1	[	[	X
ejpam-7074	527	2	14	14	NUM
ejpam-7074	527	3	]	]	X
ejpam-7074	527	4	l.	l.	PROPN
ejpam-7074	527	5	henkin	henkin	PROPN
ejpam-7074	527	6	.	.	PUNCT
ejpam-7074	528	1	an	an	DET
ejpam-7074	528	2	algebraic	algebraic	ADJ
ejpam-7074	528	3	characterization	characterization	NOUN
ejpam-7074	528	4	of	of	ADP
ejpam-7074	528	5	quantifiers	quantifier	NOUN
ejpam-7074	528	6	.	.	PUNCT
ejpam-7074	529	1	fundamenta	fundamenta	PROPN
ejpam-7074	529	2	mathematicae	mathematicae	PROPN
ejpam-7074	529	3	,	,	PUNCT
ejpam-7074	529	4	37(1):63–74	37(1):63–74	NUM
ejpam-7074	529	5	,	,	PUNCT
ejpam-7074	529	6	1950	1950	NUM
ejpam-7074	529	7	.	.	PUNCT
ejpam-7074	530	1	[	[	X
ejpam-7074	530	2	15	15	NUM
ejpam-7074	530	3	]	]	X
ejpam-7074	530	4	a.	a.	NOUN
ejpam-7074	530	5	diego	diego	PROPN
ejpam-7074	530	6	.	.	PUNCT
ejpam-7074	531	1	sur	sur	PROPN
ejpam-7074	531	2	les	les	PROPN
ejpam-7074	531	3	algèbres	algèbre	NOUN
ejpam-7074	531	4	de	de	X
ejpam-7074	531	5	hilbert	hilbert	NOUN
ejpam-7074	531	6	,	,	PUNCT
ejpam-7074	531	7	volume	volume	NOUN
ejpam-7074	531	8	21	21	NUM
ejpam-7074	531	9	of	of	ADP
ejpam-7074	531	10	collection	collection	NOUN
ejpam-7074	531	11	de	de	X
ejpam-7074	531	12	logique	logique	X
ejpam-7074	531	13	mathematique	mathematique	NOUN
ejpam-7074	531	14	,	,	PUNCT
ejpam-7074	531	15	serie	serie	PROPN
ejpam-7074	531	16	a.	a.	PROPN
ejpam-7074	531	17	gauthier	gauthier	PROPN
ejpam-7074	531	18	-	-	PUNCT
ejpam-7074	531	19	villars	villars	PROPN
ejpam-7074	531	20	,	,	PUNCT
ejpam-7074	531	21	paris	paris	PROPN
ejpam-7074	531	22	,	,	PUNCT
ejpam-7074	531	23	1966	1966	NUM
ejpam-7074	531	24	.	.	PUNCT
ejpam-7074	532	1	[	[	X
ejpam-7074	532	2	16	16	NUM
ejpam-7074	532	3	]	]	X
ejpam-7074	532	4	d.	d.	PROPN
ejpam-7074	532	5	busneag	busneag	PROPN
ejpam-7074	532	6	.	.	PUNCT
ejpam-7074	533	1	a	a	DET
ejpam-7074	533	2	note	note	NOUN
ejpam-7074	533	3	on	on	ADP
ejpam-7074	533	4	deductive	deductive	ADJ
ejpam-7074	533	5	systems	system	NOUN
ejpam-7074	533	6	of	of	ADP
ejpam-7074	533	7	a	a	DET
ejpam-7074	533	8	hilbert	hilbert	NOUN
ejpam-7074	533	9	algebra	algebra	NOUN
ejpam-7074	533	10	.	.	PUNCT
ejpam-7074	534	1	kobe	kobe	PROPN
ejpam-7074	534	2	journal	journal	PROPN
ejpam-7074	534	3	of	of	ADP
ejpam-7074	534	4	mathematics	mathematics	PROPN
ejpam-7074	534	5	,	,	PUNCT
ejpam-7074	534	6	2:29–35	2:29–35	NUM
ejpam-7074	534	7	,	,	PUNCT
ejpam-7074	534	8	1985	1985	NUM
ejpam-7074	534	9	.	.	PUNCT
ejpam-7074	535	1	[	[	X
ejpam-7074	535	2	17	17	NUM
ejpam-7074	535	3	]	]	X
ejpam-7074	535	4	d.	d.	PROPN
ejpam-7074	535	5	busneag	busneag	PROPN
ejpam-7074	535	6	.	.	PUNCT
ejpam-7074	536	1	hilbert	hilbert	PROPN
ejpam-7074	536	2	algebras	algebras	PROPN
ejpam-7074	536	3	of	of	ADP
ejpam-7074	536	4	fractions	fraction	NOUN
ejpam-7074	536	5	and	and	CCONJ
ejpam-7074	536	6	maximal	maximal	ADJ
ejpam-7074	536	7	hilbert	hilbert	NOUN
ejpam-7074	536	8	algebras	algebra	NOUN
ejpam-7074	536	9	of	of	ADP
ejpam-7074	536	10	quotients	quotient	NOUN
ejpam-7074	536	11	.	.	PUNCT
ejpam-7074	537	1	kobe	kobe	PROPN
ejpam-7074	537	2	journal	journal	PROPN
ejpam-7074	537	3	of	of	ADP
ejpam-7074	537	4	mathematics	mathematic	NOUN
ejpam-7074	537	5	,	,	PUNCT
ejpam-7074	537	6	5:161–172	5:161–172	NOUN
ejpam-7074	537	7	,	,	PUNCT
ejpam-7074	537	8	1988	1988	NUM
ejpam-7074	537	9	.	.	PUNCT
ejpam-7074	538	1	[	[	X
ejpam-7074	538	2	18	18	NUM
ejpam-7074	538	3	]	]	X
ejpam-7074	538	4	y.	y.	PROPN
ejpam-7074	538	5	b.	b.	PROPN
ejpam-7074	538	6	jun	jun	PROPN
ejpam-7074	538	7	.	.	PROPN
ejpam-7074	538	8	deductive	deductive	ADJ
ejpam-7074	538	9	systems	system	NOUN
ejpam-7074	538	10	of	of	ADP
ejpam-7074	538	11	hilbert	hilbert	PROPN
ejpam-7074	538	12	algebras	algebras	PROPN
ejpam-7074	538	13	.	.	PUNCT
ejpam-7074	539	1	mathematica	mathematica	PROPN
ejpam-7074	539	2	japonica	japonica	PROPN
ejpam-7074	539	3	,	,	PUNCT
ejpam-7074	539	4	43:51–54	43:51–54	NUM
ejpam-7074	539	5	,	,	PUNCT
ejpam-7074	539	6	1996	1996	NUM
ejpam-7074	539	7	.	.	PUNCT
ejpam-7074	540	1	[	[	X
ejpam-7074	540	2	19	19	NUM
ejpam-7074	540	3	]	]	PUNCT
ejpam-7074	540	4	w.	w.	PROPN
ejpam-7074	540	5	a.	a.	PROPN
ejpam-7074	540	6	dudek	dudek	PROPN
ejpam-7074	540	7	.	.	PUNCT
ejpam-7074	541	1	on	on	ADP
ejpam-7074	541	2	fuzzification	fuzzification	NOUN
ejpam-7074	541	3	in	in	ADP
ejpam-7074	541	4	hilbert	hilbert	PROPN
ejpam-7074	541	5	algebras	algebras	PROPN
ejpam-7074	541	6	.	.	PUNCT
ejpam-7074	542	1	in	in	ADP
ejpam-7074	542	2	proceedings	proceeding	NOUN
ejpam-7074	542	3	of	of	ADP
ejpam-7074	542	4	the	the	DET
ejpam-7074	542	5	olomouc	olomouc	PROPN
ejpam-7074	542	6	workshop	workshop	NOUN
ejpam-7074	542	7	’	'	PUNCT
ejpam-7074	542	8	98	98	NUM
ejpam-7074	542	9	and	and	CCONJ
ejpam-7074	542	10	summer	summer	NOUN
ejpam-7074	542	11	school	school	NOUN
ejpam-7074	542	12	’	'	PUNCT
ejpam-7074	542	13	98	98	NUM
ejpam-7074	542	14	,	,	PUNCT
ejpam-7074	542	15	volume	volume	NOUN
ejpam-7074	542	16	11	11	NUM
ejpam-7074	542	17	,	,	PUNCT
ejpam-7074	542	18	pages	page	NOUN
ejpam-7074	542	19	77–83	77–83	NUM
ejpam-7074	542	20	.	.	PUNCT
ejpam-7074	543	1	contributions	contribution	NOUN
ejpam-7074	543	2	to	to	ADP
ejpam-7074	543	3	general	general	ADJ
ejpam-7074	543	4	algebra	algebra	NOUN
ejpam-7074	543	5	,	,	PUNCT
ejpam-7074	543	6	1999	1999	NUM
ejpam-7074	543	7	.	.	PUNCT
ejpam-7074	544	1	[	[	X
ejpam-7074	544	2	20	20	NUM
ejpam-7074	544	3	]	]	PUNCT
ejpam-7074	544	4	t.	t.	NOUN
ejpam-7074	544	5	oner	oner	NOUN
ejpam-7074	544	6	,	,	PUNCT
ejpam-7074	544	7	t.	t.	PROPN
ejpam-7074	544	8	katican	katican	PROPN
ejpam-7074	544	9	,	,	PUNCT
ejpam-7074	544	10	and	and	CCONJ
ejpam-7074	544	11	a.	a.	PROPN
ejpam-7074	544	12	borumand	borumand	PROPN
ejpam-7074	544	13	saeid	saeid	PROPN
ejpam-7074	544	14	.	.	PUNCT
ejpam-7074	545	1	relation	relation	NOUN
ejpam-7074	545	2	between	between	ADP
ejpam-7074	545	3	sheffer	sheffer	PROPN
ejpam-7074	545	4	stroke	stroke	PROPN
ejpam-7074	545	5	and	and	CCONJ
ejpam-7074	545	6	hilbert	hilbert	PROPN
ejpam-7074	545	7	algebras	algebras	PROPN
ejpam-7074	545	8	.	.	PUNCT
ejpam-7074	545	9	categories	category	NOUN
ejpam-7074	545	10	and	and	CCONJ
ejpam-7074	545	11	general	general	ADJ
ejpam-7074	545	12	algebraic	algebraic	ADJ
ejpam-7074	545	13	structures	structure	NOUN
ejpam-7074	545	14	with	with	ADP
ejpam-7074	545	15	applications	application	NOUN
ejpam-7074	545	16	,	,	PUNCT
ejpam-7074	545	17	14(1):245–268	14(1):245–268	NUM
ejpam-7074	545	18	,	,	PUNCT
ejpam-7074	545	19	2021	2021	NUM
ejpam-7074	545	20	.	.	PUNCT
ejpam-7074	546	1	[	[	X
ejpam-7074	546	2	21	21	NUM
ejpam-7074	546	3	]	]	PUNCT
ejpam-7074	546	4	t.	t.	PROPN
ejpam-7074	546	5	katican	katican	PROPN
ejpam-7074	546	6	and	and	CCONJ
ejpam-7074	546	7	h.	h.	PROPN
ejpam-7074	546	8	bordbar	bordbar	PROPN
ejpam-7074	546	9	.	.	PUNCT
ejpam-7074	547	1	sheffer	sheffer	PROPN
ejpam-7074	547	2	stroke	stroke	PROPN
ejpam-7074	547	3	hilbert	hilbert	PROPN
ejpam-7074	547	4	algebras	algebras	PROPN
ejpam-7074	547	5	stabilizing	stabilize	VERB
ejpam-7074	547	6	by	by	ADP
ejpam-7074	547	7	ideals	ideal	NOUN
ejpam-7074	547	8	.	.	PUNCT
ejpam-7074	548	1	axioms	axiom	NOUN
ejpam-7074	548	2	,	,	PUNCT
ejpam-7074	548	3	13(2):97	13(2):97	NUM
ejpam-7074	548	4	,	,	PUNCT
ejpam-7074	548	5	2024	2024	NUM
ejpam-7074	548	6	.	.	PUNCT
ejpam-7074	549	1	[	[	X
ejpam-7074	549	2	22	22	NUM
ejpam-7074	549	3	]	]	PUNCT
ejpam-7074	549	4	t.	t.	NOUN
ejpam-7074	549	5	oner	oner	NOUN
ejpam-7074	549	6	,	,	PUNCT
ejpam-7074	549	7	t.	t.	PROPN
ejpam-7074	549	8	katican	katican	PROPN
ejpam-7074	549	9	,	,	PUNCT
ejpam-7074	549	10	and	and	CCONJ
ejpam-7074	549	11	a.	a.	PROPN
ejpam-7074	549	12	borumand	borumand	PROPN
ejpam-7074	549	13	saeid	saeid	PROPN
ejpam-7074	549	14	.	.	PUNCT
ejpam-7074	550	1	fuzzy	fuzzy	ADJ
ejpam-7074	550	2	filters	filter	NOUN
ejpam-7074	550	3	of	of	ADP
ejpam-7074	550	4	sheffer	sheffer	PROPN
ejpam-7074	550	5	stroke	stroke	PROPN
ejpam-7074	550	6	hilbert	hilbert	PROPN
ejpam-7074	550	7	a.	a.	PROPN
ejpam-7074	550	8	iampan	iampan	PROPN
ejpam-7074	550	9	et	et	PROPN
ejpam-7074	550	10	al	al	PROPN
ejpam-7074	550	11	.	.	PUNCT
ejpam-7074	550	12	/	/	SYM
ejpam-7074	550	13	eur	eur	PROPN
ejpam-7074	550	14	.	.	PUNCT
ejpam-7074	551	1	j.	j.	PROPN
ejpam-7074	551	2	pure	pure	PROPN
ejpam-7074	551	3	appl	appl	PROPN
ejpam-7074	551	4	.	.	PROPN
ejpam-7074	551	5	math	math	PROPN
ejpam-7074	551	6	,	,	PUNCT
ejpam-7074	551	7	18	18	NUM
ejpam-7074	551	8	(	(	PUNCT
ejpam-7074	551	9	4	4	NUM
ejpam-7074	551	10	)	)	PUNCT
ejpam-7074	551	11	(	(	PUNCT
ejpam-7074	551	12	2025	2025	NUM
ejpam-7074	551	13	)	)	PUNCT
ejpam-7074	551	14	,	,	PUNCT
ejpam-7074	551	15	7074	7074	NUM
ejpam-7074	551	16	14	14	NUM
ejpam-7074	551	17	of	of	ADP
ejpam-7074	551	18	14	14	NUM
ejpam-7074	551	19	algebras	algebra	NOUN
ejpam-7074	551	20	.	.	PUNCT
ejpam-7074	552	1	journal	journal	PROPN
ejpam-7074	552	2	of	of	ADP
ejpam-7074	552	3	intelligent	intelligent	ADJ
ejpam-7074	552	4	and	and	CCONJ
ejpam-7074	552	5	fuzzy	fuzzy	ADJ
ejpam-7074	552	6	systems	system	NOUN
ejpam-7074	552	7	,	,	PUNCT
ejpam-7074	552	8	40(1):759–772	40(1):759–772	NOUN
ejpam-7074	552	9	,	,	PUNCT
ejpam-7074	552	10	2021	2021	NUM
ejpam-7074	552	11	.	.	PUNCT
ejpam-7074	553	1	[	[	X
ejpam-7074	553	2	23	23	NUM
ejpam-7074	553	3	]	]	PUNCT
ejpam-7074	553	4	t.	t.	NOUN
ejpam-7074	553	5	oner	oner	NOUN
ejpam-7074	553	6	,	,	PUNCT
ejpam-7074	553	7	t.	t.	PROPN
ejpam-7074	553	8	katican	katican	PROPN
ejpam-7074	553	9	,	,	PUNCT
ejpam-7074	553	10	and	and	CCONJ
ejpam-7074	553	11	a.	a.	PROPN
ejpam-7074	553	12	borumand	borumand	PROPN
ejpam-7074	553	13	saeid	saeid	PROPN
ejpam-7074	553	14	.	.	PUNCT
ejpam-7074	554	1	fuzzy	fuzzy	ADJ
ejpam-7074	554	2	ideals	ideal	NOUN
ejpam-7074	554	3	of	of	ADP
ejpam-7074	554	4	sheffer	sheffer	PROPN
ejpam-7074	554	5	stroke	stroke	PROPN
ejpam-7074	554	6	hilbert	hilbert	PROPN
ejpam-7074	554	7	algebras	algebras	PROPN
ejpam-7074	554	8	.	.	PUNCT
ejpam-7074	555	1	proceedings	proceeding	NOUN
ejpam-7074	555	2	of	of	ADP
ejpam-7074	555	3	the	the	DET
ejpam-7074	555	4	national	national	PROPN
ejpam-7074	555	5	academy	academy	PROPN
ejpam-7074	555	6	of	of	ADP
ejpam-7074	555	7	sciences	sciences	PROPN
ejpam-7074	555	8	,	,	PUNCT
ejpam-7074	555	9	india	india	PROPN
ejpam-7074	555	10	section	section	PROPN
ejpam-7074	555	11	a	a	PRON
ejpam-7074	555	12	:	:	PUNCT
ejpam-7074	555	13	physical	physical	ADJ
ejpam-7074	555	14	sciences	science	NOUN
ejpam-7074	555	15	,	,	PUNCT
ejpam-7074	555	16	93:85–94	93:85–94	NUM
ejpam-7074	555	17	,	,	PUNCT
ejpam-7074	555	18	2023	2023	NUM
ejpam-7074	555	19	.	.	PUNCT
ejpam-7074	556	1	[	[	X
ejpam-7074	556	2	24	24	NUM
ejpam-7074	556	3	]	]	X
ejpam-7074	556	4	n.	n.	PROPN
ejpam-7074	556	5	rajesh	rajesh	PROPN
ejpam-7074	556	6	,	,	PUNCT
ejpam-7074	556	7	a.	a.	NOUN
ejpam-7074	556	8	iampan	iampan	PROPN
ejpam-7074	556	9	,	,	PUNCT
ejpam-7074	556	10	t.	t.	PROPN
ejpam-7074	556	11	oner	oner	NOUN
ejpam-7074	556	12	,	,	PUNCT
ejpam-7074	556	13	and	and	CCONJ
ejpam-7074	556	14	a.	a.	PROPN
ejpam-7074	556	15	borumand	borumand	PROPN
ejpam-7074	556	16	saeid	saeid	PROPN
ejpam-7074	556	17	.	.	PUNCT
ejpam-7074	557	1	generalized	generalize	VERB
ejpam-7074	557	2	fuzzy	fuzzy	ADJ
ejpam-7074	557	3	subalgebras	subalgebra	NOUN
ejpam-7074	557	4	of	of	ADP
ejpam-7074	557	5	sheffer	sheffer	PROPN
ejpam-7074	557	6	stroke	stroke	PROPN
ejpam-7074	557	7	hilbert	hilbert	PROPN
ejpam-7074	557	8	algebras	algebras	PROPN
ejpam-7074	557	9	.	.	PUNCT
ejpam-7074	558	1	european	european	PROPN
ejpam-7074	558	2	journal	journal	PROPN
ejpam-7074	558	3	of	of	ADP
ejpam-7074	558	4	pure	pure	ADJ
ejpam-7074	558	5	and	and	CCONJ
ejpam-7074	558	6	applied	applied	ADJ
ejpam-7074	558	7	mathematics	mathematic	NOUN
ejpam-7074	558	8	,	,	PUNCT
ejpam-7074	558	9	18(3):6500	18(3):6500	NUM
ejpam-7074	558	10	,	,	PUNCT
ejpam-7074	558	11	2025	2025	NUM
ejpam-7074	558	12	.	.	PUNCT
ejpam-7074	559	1	[	[	X
ejpam-7074	559	2	25	25	NUM
ejpam-7074	559	3	]	]	X
ejpam-7074	559	4	n.	n.	PROPN
ejpam-7074	559	5	rajesh	rajesh	PROPN
ejpam-7074	559	6	,	,	PUNCT
ejpam-7074	559	7	t.	t.	PROPN
ejpam-7074	559	8	oner	oner	NOUN
ejpam-7074	559	9	,	,	PUNCT
ejpam-7074	559	10	a.	a.	NOUN
ejpam-7074	559	11	iampan	iampan	PROPN
ejpam-7074	559	12	,	,	PUNCT
ejpam-7074	559	13	and	and	CCONJ
ejpam-7074	559	14	a.	a.	NOUN
ejpam-7074	559	15	rezaei	rezaei	PROPN
ejpam-7074	559	16	.	.	PUNCT
ejpam-7074	560	1	investigating	investigate	VERB
ejpam-7074	560	2	length	length	NOUN
ejpam-7074	560	3	and	and	CCONJ
ejpam-7074	560	4	mean	mean	ADJ
ejpam-7074	560	5	-	-	PUNCT
ejpam-7074	560	6	fuzzy	fuzzy	ADJ
ejpam-7074	560	7	subalgebras	subalgebra	NOUN
ejpam-7074	560	8	in	in	ADP
ejpam-7074	560	9	sheffer	sheffer	PROPN
ejpam-7074	560	10	stroke	stroke	PROPN
ejpam-7074	560	11	hilbert	hilbert	PROPN
ejpam-7074	560	12	algebras	algebras	PROPN
ejpam-7074	560	13	.	.	PUNCT
ejpam-7074	561	1	european	european	PROPN
ejpam-7074	561	2	journal	journal	PROPN
ejpam-7074	561	3	of	of	ADP
ejpam-7074	561	4	pure	pure	ADJ
ejpam-7074	561	5	and	and	CCONJ
ejpam-7074	561	6	applied	applied	ADJ
ejpam-7074	561	7	mathematics	mathematic	NOUN
ejpam-7074	561	8	,	,	PUNCT
ejpam-7074	561	9	18(2):5914	18(2):5914	NUM
ejpam-7074	561	10	,	,	PUNCT
ejpam-7074	561	11	2025	2025	NUM
ejpam-7074	561	12	.	.	PUNCT
ejpam-7074	562	1	[	[	X
ejpam-7074	562	2	26	26	NUM
ejpam-7074	562	3	]	]	X
ejpam-7074	562	4	n.	n.	PROPN
ejpam-7074	562	5	rajesh	rajesh	PROPN
ejpam-7074	562	6	,	,	PUNCT
ejpam-7074	562	7	t.	t.	PROPN
ejpam-7074	562	8	oner	oner	NOUN
ejpam-7074	562	9	,	,	PUNCT
ejpam-7074	562	10	a.	a.	NOUN
ejpam-7074	562	11	iampan	iampan	PROPN
ejpam-7074	562	12	,	,	PUNCT
ejpam-7074	562	13	and	and	CCONJ
ejpam-7074	562	14	i.	i.	PROPN
ejpam-7074	562	15	senturk	senturk	PROPN
ejpam-7074	562	16	.	.	PUNCT
ejpam-7074	563	1	on	on	ADP
ejpam-7074	563	2	length	length	NOUN
ejpam-7074	563	3	and	and	CCONJ
ejpam-7074	563	4	mean	mean	VERB
ejpam-7074	563	5	fuzzy	fuzzy	ADJ
ejpam-7074	563	6	ideals	ideal	NOUN
ejpam-7074	563	7	of	of	ADP
ejpam-7074	563	8	sheffer	sheffer	PROPN
ejpam-7074	563	9	stroke	stroke	PROPN
ejpam-7074	563	10	hilbert	hilbert	PROPN
ejpam-7074	563	11	algebras	algebras	PROPN
ejpam-7074	563	12	.	.	PUNCT
ejpam-7074	564	1	european	european	PROPN
ejpam-7074	564	2	journal	journal	PROPN
ejpam-7074	564	3	of	of	ADP
ejpam-7074	564	4	pure	pure	ADJ
ejpam-7074	564	5	and	and	CCONJ
ejpam-7074	564	6	applied	applied	ADJ
ejpam-7074	564	7	mathematics	mathematic	NOUN
ejpam-7074	564	8	,	,	PUNCT
ejpam-7074	564	9	18(1):5779	18(1):5779	NUM
ejpam-7074	564	10	,	,	PUNCT
ejpam-7074	564	11	2025	2025	NUM
ejpam-7074	564	12	.	.	PUNCT
ejpam-7074	565	1	[	[	X
ejpam-7074	565	2	27	27	NUM
ejpam-7074	565	3	]	]	PUNCT
ejpam-7074	565	4	t.	t.	NOUN
ejpam-7074	565	5	oner	oner	NOUN
ejpam-7074	565	6	,	,	PUNCT
ejpam-7074	565	7	n.	n.	PROPN
ejpam-7074	565	8	rajesh	rajesh	PROPN
ejpam-7074	565	9	,	,	PUNCT
ejpam-7074	565	10	a.	a.	NOUN
ejpam-7074	565	11	iampan	iampan	PROPN
ejpam-7074	565	12	,	,	PUNCT
ejpam-7074	565	13	and	and	CCONJ
ejpam-7074	565	14	a.	a.	PROPN
ejpam-7074	565	15	borumand	borumand	PROPN
ejpam-7074	565	16	saeid	saeid	PROPN
ejpam-7074	565	17	.	.	PUNCT
ejpam-7074	565	18	soft	soft	ADJ
ejpam-7074	565	19	subalgebras	subalgebra	NOUN
ejpam-7074	565	20	and	and	CCONJ
ejpam-7074	565	21	ideals	ideal	NOUN
ejpam-7074	565	22	of	of	ADP
ejpam-7074	565	23	sheffer	sheffer	PROPN
ejpam-7074	565	24	stroke	stroke	PROPN
ejpam-7074	565	25	hilbert	hilbert	PROPN
ejpam-7074	565	26	algebras	algebras	PROPN
ejpam-7074	565	27	based	base	VERB
ejpam-7074	565	28	on	on	ADP
ejpam-7074	565	29	n	n	DET
ejpam-7074	565	30	-structures	-structure	NOUN
ejpam-7074	565	31	.	.	PUNCT
ejpam-7074	566	1	european	european	ADJ
ejpam-7074	566	2	journal	journal	PROPN
ejpam-7074	566	3	of	of	ADP
ejpam-7074	566	4	pure	pure	ADJ
ejpam-7074	566	5	and	and	CCONJ
ejpam-7074	566	6	applied	applied	ADJ
ejpam-7074	566	7	mathematics	mathematic	NOUN
ejpam-7074	566	8	,	,	PUNCT
ejpam-7074	566	9	18(2):6018	18(2):6018	NUM
ejpam-7074	566	10	,	,	PUNCT
ejpam-7074	566	11	2025	2025	NUM
ejpam-7074	566	12	.	.	PUNCT
ejpam-7074	567	1	[	[	X
ejpam-7074	567	2	28	28	NUM
ejpam-7074	567	3	]	]	X
ejpam-7074	567	4	h.	h.	PROPN
ejpam-7074	567	5	m.	m.	PROPN
ejpam-7074	567	6	sheffer	sheffer	PROPN
ejpam-7074	567	7	.	.	PUNCT
ejpam-7074	568	1	a	a	DET
ejpam-7074	568	2	set	set	NOUN
ejpam-7074	568	3	of	of	ADP
ejpam-7074	568	4	five	five	NUM
ejpam-7074	568	5	independent	independent	ADJ
ejpam-7074	568	6	postulates	postulate	NOUN
ejpam-7074	568	7	for	for	ADP
ejpam-7074	568	8	boolean	boolean	ADJ
ejpam-7074	568	9	algebras	algebra	NOUN
ejpam-7074	568	10	,	,	PUNCT
ejpam-7074	568	11	with	with	ADP
ejpam-7074	568	12	application	application	NOUN
ejpam-7074	568	13	to	to	ADP
ejpam-7074	568	14	logical	logical	ADJ
ejpam-7074	568	15	constants	constant	NOUN
ejpam-7074	568	16	.	.	PUNCT
ejpam-7074	569	1	transactions	transaction	NOUN
ejpam-7074	569	2	of	of	ADP
ejpam-7074	569	3	the	the	DET
ejpam-7074	569	4	american	american	PROPN
ejpam-7074	569	5	mathematical	mathematical	PROPN
ejpam-7074	569	6	society	society	NOUN
ejpam-7074	569	7	,	,	PUNCT
ejpam-7074	569	8	14(4):481–488	14(4):481–488	NUM
ejpam-7074	569	9	,	,	PUNCT
ejpam-7074	569	10	1913	1913	NUM
ejpam-7074	569	11	.	.	PUNCT