id	sid	tid	token	lemma	pos
ejpam-3660	1	1	european	european	PROPN
ejpam-3660	1	2	journal	journal	PROPN
ejpam-3660	1	3	of	of	ADP
ejpam-3660	1	4	pure	pure	ADJ
ejpam-3660	1	5	and	and	CCONJ
ejpam-3660	1	6	applied	apply	VERB
ejpam-3660	1	7	mathematics	mathematic	NOUN
ejpam-3660	1	8	vol	vol	NOUN
ejpam-3660	1	9	.	.	PROPN
ejpam-3660	2	1	13	13	NUM
ejpam-3660	2	2	,	,	PUNCT
ejpam-3660	2	3	no	no	INTJ
ejpam-3660	2	4	.	.	NOUN
ejpam-3660	2	5	2	2	NUM
ejpam-3660	2	6	,	,	PUNCT
ejpam-3660	2	7	2020	2020	NUM
ejpam-3660	2	8	,	,	PUNCT
ejpam-3660	2	9	246	246	NUM
ejpam-3660	2	10	-	-	SYM
ejpam-3660	2	11	257	257	NUM
ejpam-3660	2	12	issn	issn	PROPN
ejpam-3660	2	13	1307	1307	NUM
ejpam-3660	2	14	-	-	SYM
ejpam-3660	2	15	5543	5543	NUM
ejpam-3660	2	16	–	–	PUNCT
ejpam-3660	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3660	2	18	published	publish	VERB
ejpam-3660	2	19	by	by	ADP
ejpam-3660	2	20	new	new	PROPN
ejpam-3660	2	21	york	york	PROPN
ejpam-3660	2	22	business	business	PROPN
ejpam-3660	2	23	global	global	PROPN
ejpam-3660	2	24	on	on	ADP
ejpam-3660	2	25	intuitionistic	intuitionistic	ADJ
ejpam-3660	2	26	fuzzy	fuzzy	ADJ
ejpam-3660	2	27	hyper	hyper	ADJ
ejpam-3660	2	28	gr	gr	NOUN
ejpam-3660	2	29	-	-	PUNCT
ejpam-3660	2	30	ideals	ideal	NOUN
ejpam-3660	2	31	in	in	ADP
ejpam-3660	2	32	hyper	hyper	ADJ
ejpam-3660	2	33	gr	gr	NOUN
ejpam-3660	2	34	-	-	PUNCT
ejpam-3660	2	35	algebras	algebras	PROPN
ejpam-3660	2	36	amila	amila	PROPN
ejpam-3660	2	37	p.	p.	PROPN
ejpam-3660	2	38	macodi	macodi	PROPN
ejpam-3660	2	39	-	-	PUNCT
ejpam-3660	2	40	ringia1	ringia1	NOUN
ejpam-3660	2	41	,	,	PUNCT
ejpam-3660	2	42	*	*	PUNCT
ejpam-3660	2	43	,	,	PUNCT
ejpam-3660	2	44	gaudencio	gaudencio	PROPN
ejpam-3660	2	45	c.	c.	PROPN
ejpam-3660	2	46	petalcorin	petalcorin	PROPN
ejpam-3660	2	47	,	,	PUNCT
ejpam-3660	2	48	jr.2	jr.2	PROPN
ejpam-3660	2	49	1	1	NUM
ejpam-3660	2	50	mathematics	mathematics	PROPN
ejpam-3660	2	51	department	department	NOUN
ejpam-3660	2	52	,	,	PUNCT
ejpam-3660	2	53	college	college	NOUN
ejpam-3660	2	54	of	of	ADP
ejpam-3660	2	55	natural	natural	ADJ
ejpam-3660	2	56	sciences	science	NOUN
ejpam-3660	2	57	and	and	CCONJ
ejpam-3660	2	58	mathematics	mathematic	NOUN
ejpam-3660	2	59	,	,	PUNCT
ejpam-3660	2	60	msu	msu	PROPN
ejpam-3660	2	61	-	-	ADJ
ejpam-3660	2	62	general	general	ADJ
ejpam-3660	2	63	santos	santos	PROPN
ejpam-3660	2	64	,	,	PUNCT
ejpam-3660	2	65	general	general	ADJ
ejpam-3660	2	66	santos	santos	PROPN
ejpam-3660	2	67	city	city	PROPN
ejpam-3660	2	68	,	,	PUNCT
ejpam-3660	2	69	philippines	philippines	PROPN
ejpam-3660	2	70	2	2	NUM
ejpam-3660	2	71	department	department	NOUN
ejpam-3660	2	72	of	of	ADP
ejpam-3660	2	73	mathematics	mathematic	NOUN
ejpam-3660	2	74	and	and	CCONJ
ejpam-3660	2	75	statistics	statistic	NOUN
ejpam-3660	2	76	,	,	PUNCT
ejpam-3660	2	77	college	college	NOUN
ejpam-3660	2	78	of	of	ADP
ejpam-3660	2	79	science	science	NOUN
ejpam-3660	2	80	and	and	CCONJ
ejpam-3660	2	81	mathematics	mathematic	NOUN
ejpam-3660	2	82	,	,	PUNCT
ejpam-3660	2	83	msu	msu	PROPN
ejpam-3660	2	84	-	-	PUNCT
ejpam-3660	2	85	iligan	iligan	PROPN
ejpam-3660	2	86	institute	institute	PROPN
ejpam-3660	2	87	of	of	ADP
ejpam-3660	2	88	technology	technology	PROPN
ejpam-3660	2	89	,	,	PUNCT
ejpam-3660	2	90	iligan	iligan	PROPN
ejpam-3660	2	91	city	city	PROPN
ejpam-3660	2	92	,	,	PUNCT
ejpam-3660	2	93	philippines	philippine	NOUN
ejpam-3660	2	94	abstract	abstract	ADJ
ejpam-3660	2	95	.	.	PUNCT
ejpam-3660	3	1	in	in	ADP
ejpam-3660	3	2	this	this	DET
ejpam-3660	3	3	paper	paper	NOUN
ejpam-3660	3	4	,	,	PUNCT
ejpam-3660	3	5	fuzzy	fuzzy	ADJ
ejpam-3660	3	6	set	set	ADJ
ejpam-3660	3	7	and	and	CCONJ
ejpam-3660	3	8	intuitionistic	intuitionistic	ADJ
ejpam-3660	3	9	fuzzy	fuzzy	ADJ
ejpam-3660	3	10	set	set	NOUN
ejpam-3660	3	11	are	be	AUX
ejpam-3660	3	12	applied	apply	VERB
ejpam-3660	3	13	to	to	ADP
ejpam-3660	3	14	hyper	hyper	ADJ
ejpam-3660	3	15	gr	gr	NOUN
ejpam-3660	3	16	-	-	NOUN
ejpam-3660	3	17	algebra	algebra	NOUN
ejpam-3660	3	18	.	.	PUNCT
ejpam-3660	4	1	particularly	particularly	ADV
ejpam-3660	4	2	,	,	PUNCT
ejpam-3660	4	3	the	the	DET
ejpam-3660	4	4	fuzzy	fuzzy	ADJ
ejpam-3660	4	5	hyper	hyper	ADJ
ejpam-3660	4	6	gr	gr	NOUN
ejpam-3660	4	7	-	-	PUNCT
ejpam-3660	4	8	ideal	ideal	NOUN
ejpam-3660	4	9	of	of	ADP
ejpam-3660	4	10	type	type	NOUN
ejpam-3660	4	11	1	1	NUM
ejpam-3660	4	12	and	and	CCONJ
ejpam-3660	4	13	the	the	DET
ejpam-3660	4	14	intuitionistic	intuitionistic	ADJ
ejpam-3660	4	15	fuzzy	fuzzy	ADJ
ejpam-3660	4	16	hyper	hyper	ADJ
ejpam-3660	4	17	gr	gr	ADJ
ejpam-3660	4	18	-	-	PUNCT
ejpam-3660	4	19	ideal	ideal	NOUN
ejpam-3660	4	20	are	be	AUX
ejpam-3660	4	21	introduced	introduce	VERB
ejpam-3660	4	22	,	,	PUNCT
ejpam-3660	4	23	and	and	CCONJ
ejpam-3660	4	24	a	a	DET
ejpam-3660	4	25	relationship	relationship	NOUN
ejpam-3660	4	26	between	between	ADP
ejpam-3660	4	27	them	they	PRON
ejpam-3660	4	28	are	be	AUX
ejpam-3660	4	29	obtained	obtain	VERB
ejpam-3660	4	30	.	.	PUNCT
ejpam-3660	5	1	moreover	moreover	ADV
ejpam-3660	5	2	,	,	PUNCT
ejpam-3660	5	3	some	some	PRON
ejpam-3660	5	4	of	of	ADP
ejpam-3660	5	5	their	their	PRON
ejpam-3660	5	6	characterizations	characterization	NOUN
ejpam-3660	5	7	are	be	AUX
ejpam-3660	5	8	established	establish	VERB
ejpam-3660	5	9	by	by	ADP
ejpam-3660	5	10	the	the	DET
ejpam-3660	5	11	use	use	NOUN
ejpam-3660	5	12	of	of	ADP
ejpam-3660	5	13	their	their	PRON
ejpam-3660	5	14	level	level	NOUN
ejpam-3660	5	15	subsets	subset	NOUN
ejpam-3660	5	16	.	.	PUNCT
ejpam-3660	6	1	2020	2020	NUM
ejpam-3660	6	2	mathematics	mathematic	NOUN
ejpam-3660	6	3	subject	subject	NOUN
ejpam-3660	6	4	classifications	classification	NOUN
ejpam-3660	6	5	:	:	PUNCT
ejpam-3660	6	6	20n20	20n20	NUM
ejpam-3660	6	7	,	,	PUNCT
ejpam-3660	6	8	06f35	06f35	NUM
ejpam-3660	6	9	,	,	PUNCT
ejpam-3660	6	10	03g25	03g25	NUM
ejpam-3660	6	11	,	,	PUNCT
ejpam-3660	6	12	03e72	03e72	NUM
ejpam-3660	6	13	,	,	PUNCT
ejpam-3660	6	14	03b52	03b52	NUM
ejpam-3660	6	15	,	,	PUNCT
ejpam-3660	6	16	08a72	08a72	NOUN
ejpam-3660	6	17	key	key	ADJ
ejpam-3660	6	18	words	word	NOUN
ejpam-3660	6	19	and	and	CCONJ
ejpam-3660	6	20	phrases	phrase	NOUN
ejpam-3660	6	21	:	:	PUNCT
ejpam-3660	6	22	hyper	hyper	ADJ
ejpam-3660	6	23	gr	gr	NOUN
ejpam-3660	6	24	-	-	PUNCT
ejpam-3660	6	25	algebras	algebra	NOUN
ejpam-3660	6	26	,	,	PUNCT
ejpam-3660	6	27	hyper	hyper	ADJ
ejpam-3660	6	28	gr	gr	NOUN
ejpam-3660	6	29	-	-	PUNCT
ejpam-3660	6	30	ideals	ideal	NOUN
ejpam-3660	6	31	,	,	PUNCT
ejpam-3660	6	32	hyper	hyper	ADJ
ejpam-3660	6	33	gr	gr	NOUN
ejpam-3660	6	34	-	-	PUNCT
ejpam-3660	6	35	ideals	ideal	NOUN
ejpam-3660	6	36	,	,	PUNCT
ejpam-3660	6	37	fuzzy	fuzzy	ADJ
ejpam-3660	6	38	hyper	hyper	ADJ
ejpam-3660	6	39	gr	gr	NOUN
ejpam-3660	6	40	-	-	PUNCT
ejpam-3660	6	41	ideals	ideal	NOUN
ejpam-3660	6	42	of	of	ADP
ejpam-3660	6	43	type	type	NOUN
ejpam-3660	6	44	1	1	NUM
ejpam-3660	6	45	,	,	PUNCT
ejpam-3660	6	46	intuitionistic	intuitionistic	ADJ
ejpam-3660	6	47	fuzzy	fuzzy	ADJ
ejpam-3660	6	48	hyper	hyper	ADJ
ejpam-3660	6	49	gr	gr	NOUN
ejpam-3660	6	50	-	-	PUNCT
ejpam-3660	6	51	ideals	ideal	NOUN
ejpam-3660	6	52	1	1	NUM
ejpam-3660	6	53	.	.	PUNCT
ejpam-3660	6	54	introduction	introduction	NOUN
ejpam-3660	6	55	in	in	ADP
ejpam-3660	6	56	1934	1934	NUM
ejpam-3660	6	57	,	,	PUNCT
ejpam-3660	6	58	hyperstructure	hyperstructure	NOUN
ejpam-3660	6	59	theory	theory	NOUN
ejpam-3660	6	60	was	be	AUX
ejpam-3660	6	61	introduced	introduce	VERB
ejpam-3660	6	62	in	in	ADP
ejpam-3660	6	63	1934	1934	NUM
ejpam-3660	6	64	by	by	ADP
ejpam-3660	6	65	f.	f.	PROPN
ejpam-3660	6	66	marty	marty	PROPN
ejpam-3660	7	1	[	[	X
ejpam-3660	7	2	13	13	NUM
ejpam-3660	7	3	]	]	PUNCT
ejpam-3660	7	4	during	during	ADP
ejpam-3660	7	5	the	the	DET
ejpam-3660	7	6	8th	8th	ADJ
ejpam-3660	7	7	congress	congress	NOUN
ejpam-3660	7	8	of	of	ADP
ejpam-3660	7	9	scandinavian	scandinavian	ADJ
ejpam-3660	7	10	mathematicians	mathematician	NOUN
ejpam-3660	7	11	.	.	PUNCT
ejpam-3660	8	1	around	around	ADP
ejpam-3660	8	2	the	the	DET
ejpam-3660	8	3	40	40	NUM
ejpam-3660	8	4	’s	’s	NOUN
ejpam-3660	8	5	,	,	PUNCT
ejpam-3660	8	6	several	several	ADJ
ejpam-3660	8	7	authors	author	NOUN
ejpam-3660	8	8	worked	work	VERB
ejpam-3660	8	9	on	on	ADP
ejpam-3660	8	10	hypergroups	hypergroup	NOUN
ejpam-3660	8	11	,	,	PUNCT
ejpam-3660	8	12	especially	especially	ADV
ejpam-3660	8	13	,	,	PUNCT
ejpam-3660	8	14	in	in	ADP
ejpam-3660	8	15	france	france	PROPN
ejpam-3660	8	16	and	and	CCONJ
ejpam-3660	8	17	in	in	ADP
ejpam-3660	8	18	the	the	DET
ejpam-3660	8	19	united	united	PROPN
ejpam-3660	8	20	states	states	PROPN
ejpam-3660	8	21	,	,	PUNCT
ejpam-3660	8	22	but	but	CCONJ
ejpam-3660	8	23	also	also	ADV
ejpam-3660	8	24	in	in	ADP
ejpam-3660	8	25	italy	italy	PROPN
ejpam-3660	8	26	,	,	PUNCT
ejpam-3660	8	27	russia	russia	PROPN
ejpam-3660	8	28	and	and	CCONJ
ejpam-3660	8	29	japan	japan	PROPN
ejpam-3660	8	30	.	.	PUNCT
ejpam-3660	9	1	over	over	ADP
ejpam-3660	9	2	the	the	DET
ejpam-3660	9	3	following	follow	VERB
ejpam-3660	9	4	decades	decade	NOUN
ejpam-3660	9	5	,	,	PUNCT
ejpam-3660	9	6	many	many	ADJ
ejpam-3660	9	7	important	important	ADJ
ejpam-3660	9	8	results	result	NOUN
ejpam-3660	9	9	appeared	appear	VERB
ejpam-3660	9	10	,	,	PUNCT
ejpam-3660	9	11	but	but	CCONJ
ejpam-3660	9	12	above	above	ADP
ejpam-3660	9	13	all	all	PRON
ejpam-3660	9	14	since	since	SCONJ
ejpam-3660	9	15	the	the	DET
ejpam-3660	9	16	70	70	NUM
ejpam-3660	9	17	’s	’s	NOUN
ejpam-3660	9	18	onwards	onwards	ADP
ejpam-3660	9	19	the	the	DET
ejpam-3660	9	20	most	most	ADV
ejpam-3660	9	21	luxuriant	luxuriant	ADJ
ejpam-3660	9	22	flourishing	flourish	VERB
ejpam-3660	9	23	hyperstructures	hyperstructure	NOUN
ejpam-3660	9	24	has	have	AUX
ejpam-3660	9	25	been	be	AUX
ejpam-3660	9	26	seen	see	VERB
ejpam-3660	9	27	.	.	PUNCT
ejpam-3660	10	1	hyperstructures	hyperstructure	NOUN
ejpam-3660	10	2	have	have	VERB
ejpam-3660	10	3	many	many	ADJ
ejpam-3660	10	4	application	application	NOUN
ejpam-3660	10	5	to	to	ADP
ejpam-3660	10	6	several	several	ADJ
ejpam-3660	10	7	sectors	sector	NOUN
ejpam-3660	10	8	of	of	ADP
ejpam-3660	10	9	both	both	CCONJ
ejpam-3660	10	10	pure	pure	ADJ
ejpam-3660	10	11	and	and	CCONJ
ejpam-3660	10	12	applied	applied	ADJ
ejpam-3660	10	13	sciences	science	NOUN
ejpam-3660	10	14	.	.	PUNCT
ejpam-3660	11	1	davvaz	davvaz	PROPN
ejpam-3660	11	2	et	et	PROPN
ejpam-3660	11	3	al	al	PROPN
ejpam-3660	11	4	.	.	PUNCT
ejpam-3660	12	1	[	[	X
ejpam-3660	12	2	5	5	NUM
ejpam-3660	12	3	]	]	PUNCT
ejpam-3660	12	4	applied	apply	VERB
ejpam-3660	12	5	this	this	DET
ejpam-3660	12	6	concept	concept	NOUN
ejpam-3660	12	7	to	to	ADP
ejpam-3660	12	8	elementary	elementary	ADJ
ejpam-3660	12	9	particles	particle	NOUN
ejpam-3660	12	10	in	in	ADP
ejpam-3660	12	11	physical	physical	ADJ
ejpam-3660	12	12	theory	theory	NOUN
ejpam-3660	12	13	.	.	PUNCT
ejpam-3660	13	1	while	while	SCONJ
ejpam-3660	13	2	,	,	PUNCT
ejpam-3660	13	3	xin	xin	PROPN
ejpam-3660	14	1	[	[	X
ejpam-3660	14	2	11	11	NUM
ejpam-3660	14	3	]	]	PUNCT
ejpam-3660	14	4	applied	apply	VERB
ejpam-3660	14	5	this	this	DET
ejpam-3660	14	6	concept	concept	NOUN
ejpam-3660	14	7	to	to	ADP
ejpam-3660	14	8	bci	bci	NOUN
ejpam-3660	14	9	-	-	PUNCT
ejpam-3660	14	10	algebras	algebras	PROPN
ejpam-3660	14	11	and	and	CCONJ
ejpam-3660	14	12	proved	prove	VERB
ejpam-3660	14	13	that	that	PRON
ejpam-3660	14	14	hyper	hyper	ADJ
ejpam-3660	14	15	bci	bci	NOUN
ejpam-3660	14	16	-	-	PUNCT
ejpam-3660	14	17	algebras	algebra	NOUN
ejpam-3660	14	18	are	be	AUX
ejpam-3660	14	19	one	one	NUM
ejpam-3660	14	20	of	of	ADP
ejpam-3660	14	21	the	the	DET
ejpam-3660	14	22	generalizations	generalization	NOUN
ejpam-3660	14	23	of	of	ADP
ejpam-3660	14	24	bci	bci	NOUN
ejpam-3660	14	25	-	-	PUNCT
ejpam-3660	14	26	algebras	algebra	NOUN
ejpam-3660	14	27	.	.	PUNCT
ejpam-3660	15	1	after	after	ADP
ejpam-3660	15	2	the	the	DET
ejpam-3660	15	3	introduction	introduction	NOUN
ejpam-3660	15	4	on	on	ADP
ejpam-3660	15	5	the	the	DET
ejpam-3660	15	6	concept	concept	NOUN
ejpam-3660	15	7	of	of	ADP
ejpam-3660	15	8	hyper	hyper	ADJ
ejpam-3660	15	9	bci	bci	NOUN
ejpam-3660	15	10	-	-	PUNCT
ejpam-3660	15	11	algebras	algebra	NOUN
ejpam-3660	15	12	,	,	PUNCT
ejpam-3660	15	13	several	several	ADJ
ejpam-3660	15	14	researches	research	NOUN
ejpam-3660	15	15	were	be	AUX
ejpam-3660	15	16	conducted	conduct	VERB
ejpam-3660	15	17	.	.	PUNCT
ejpam-3660	16	1	one	one	NUM
ejpam-3660	16	2	of	of	ADP
ejpam-3660	16	3	these	these	DET
ejpam-3660	16	4	studies	study	NOUN
ejpam-3660	16	5	is	be	AUX
ejpam-3660	16	6	the	the	DET
ejpam-3660	16	7	hyper	hyper	ADJ
ejpam-3660	16	8	gr	gr	NOUN
ejpam-3660	16	9	-	-	PUNCT
ejpam-3660	16	10	algebras	algebra	NOUN
ejpam-3660	16	11	.	.	PUNCT
ejpam-3660	17	1	in	in	ADP
ejpam-3660	17	2	2016	2016	NUM
ejpam-3660	17	3	,	,	PUNCT
ejpam-3660	17	4	indangan	indangan	NOUN
ejpam-3660	17	5	et	et	PROPN
ejpam-3660	17	6	al	al	PROPN
ejpam-3660	17	7	.	.	PUNCT
ejpam-3660	18	1	[	[	X
ejpam-3660	18	2	6	6	NUM
ejpam-3660	18	3	]	]	PUNCT
ejpam-3660	18	4	introduced	introduce	VERB
ejpam-3660	18	5	hyper	hyper	ADJ
ejpam-3660	18	6	gr	gr	NOUN
ejpam-3660	18	7	-	-	PUNCT
ejpam-3660	18	8	algebras	algebra	NOUN
ejpam-3660	18	9	and	and	CCONJ
ejpam-3660	18	10	the	the	DET
ejpam-3660	18	11	faithful	faithful	ADJ
ejpam-3660	18	12	hyper	hyper	ADJ
ejpam-3660	18	13	gr	gr	NOUN
ejpam-3660	18	14	-	-	PUNCT
ejpam-3660	18	15	algebra	algebra	NOUN
ejpam-3660	18	16	’s	’s	PART
ejpam-3660	18	17	hyper	hyper	ADJ
ejpam-3660	18	18	operation	operation	NOUN
ejpam-3660	18	19	properties	property	NOUN
ejpam-3660	18	20	were	be	AUX
ejpam-3660	18	21	established	establish	VERB
ejpam-3660	18	22	including	include	VERB
ejpam-3660	18	23	some	some	DET
ejpam-3660	18	24	properties	property	NOUN
ejpam-3660	18	25	of	of	ADP
ejpam-3660	18	26	hyper	hyper	ADJ
ejpam-3660	18	27	gr	gr	NOUN
ejpam-3660	18	28	-	-	PUNCT
ejpam-3660	18	29	ideals	ideal	NOUN
ejpam-3660	18	30	.	.	PUNCT
ejpam-3660	19	1	in	in	ADP
ejpam-3660	19	2	2017	2017	NUM
ejpam-3660	19	3	,	,	PUNCT
ejpam-3660	19	4	some	some	DET
ejpam-3660	19	5	hyper	hyper	ADJ
ejpam-3660	19	6	homomorphic	homomorphic	ADJ
ejpam-3660	19	7	properties	property	NOUN
ejpam-3660	19	8	on	on	ADP
ejpam-3660	19	9	hyper	hyper	ADJ
ejpam-3660	19	10	∗corresponding	∗corresponding	NOUN
ejpam-3660	19	11	author	author	NOUN
ejpam-3660	19	12	.	.	PUNCT
ejpam-3660	20	1	doi	doi	NOUN
ejpam-3660	20	2	:	:	PUNCT
ejpam-3660	20	3	https://doi.org/10.29020/nybg.ejpam.v13i2.3660	https://doi.org/10.29020/nybg.ejpam.v13i2.3660	NOUN
ejpam-3660	20	4	email	email	NOUN
ejpam-3660	20	5	addresses	address	NOUN
ejpam-3660	20	6	:	:	PUNCT
ejpam-3660	20	7	amila.macodi-ringia@g.msuiit.edu.ph	amila.macodi-ringia@g.msuiit.edu.ph	PROPN
ejpam-3660	20	8	(	(	PUNCT
ejpam-3660	20	9	a.	a.	NOUN
ejpam-3660	20	10	macodi	macodi	NOUN
ejpam-3660	20	11	-	-	PUNCT
ejpam-3660	20	12	ringia	ringia	NOUN
ejpam-3660	20	13	)	)	PUNCT
ejpam-3660	20	14	,	,	PUNCT
ejpam-3660	20	15	gaudencio.petalcorin@g.msuiit.edu.ph	gaudencio.petalcorin@g.msuiit.edu.ph	PROPN
ejpam-3660	20	16	(	(	PUNCT
ejpam-3660	20	17	g.	g.	PROPN
ejpam-3660	20	18	petalcorin	petalcorin	PROPN
ejpam-3660	20	19	,	,	PUNCT
ejpam-3660	20	20	jr	jr	PROPN
ejpam-3660	20	21	.	.	PUNCT
ejpam-3660	20	22	)	)	PUNCT
ejpam-3660	20	23	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3660	21	1	246	246	NUM
ejpam-3660	21	2	©	©	PROPN
ejpam-3660	21	3	2020	2020	NUM
ejpam-3660	21	4	ejpam	ejpam	VERB
ejpam-3660	21	5	all	all	DET
ejpam-3660	21	6	rights	right	NOUN
ejpam-3660	21	7	reserved	reserve	VERB
ejpam-3660	21	8	.	.	PUNCT
ejpam-3660	22	1	a.	a.	NOUN
ejpam-3660	22	2	macodi	macodi	PROPN
ejpam-3660	22	3	-	-	PUNCT
ejpam-3660	22	4	ringia	ringia	ADJ
ejpam-3660	22	5	,	,	PUNCT
ejpam-3660	22	6	g.	g.	PROPN
ejpam-3660	22	7	petalcorin	petalcorin	PROPN
ejpam-3660	22	8	,	,	PUNCT
ejpam-3660	22	9	jr	jr	PROPN
ejpam-3660	22	10	.	.	PROPN
ejpam-3660	22	11	/	/	SYM
ejpam-3660	22	12	eur	eur	PROPN
ejpam-3660	22	13	.	.	PUNCT
ejpam-3660	23	1	j.	j.	PROPN
ejpam-3660	23	2	pure	pure	PROPN
ejpam-3660	23	3	appl	appl	PROPN
ejpam-3660	23	4	.	.	PROPN
ejpam-3660	23	5	math	math	PROPN
ejpam-3660	23	6	,	,	PUNCT
ejpam-3660	23	7	13	13	NUM
ejpam-3660	23	8	(	(	PUNCT
ejpam-3660	23	9	2	2	NUM
ejpam-3660	23	10	)	)	PUNCT
ejpam-3660	23	11	(	(	PUNCT
ejpam-3660	23	12	2020	2020	NUM
ejpam-3660	23	13	)	)	PUNCT
ejpam-3660	23	14	,	,	PUNCT
ejpam-3660	23	15	246	246	NUM
ejpam-3660	23	16	-	-	SYM
ejpam-3660	23	17	257	257	NUM
ejpam-3660	23	18	247	247	NUM
ejpam-3660	23	19	gr	gr	NOUN
ejpam-3660	23	20	-	-	PUNCT
ejpam-3660	23	21	algebra	algebra	NOUN
ejpam-3660	23	22	together	together	ADV
ejpam-3660	23	23	with	with	ADP
ejpam-3660	23	24	the	the	DET
ejpam-3660	23	25	construction	construction	NOUN
ejpam-3660	23	26	of	of	ADP
ejpam-3660	23	27	the	the	DET
ejpam-3660	23	28	quotient	quotient	NOUN
ejpam-3660	23	29	hyper	hyper	ADJ
ejpam-3660	23	30	gr	gr	NOUN
ejpam-3660	23	31	-	-	NOUN
ejpam-3660	23	32	algebra	algebra	NOUN
ejpam-3660	23	33	via	via	ADP
ejpam-3660	23	34	regular	regular	ADJ
ejpam-3660	23	35	congruence	congruence	NOUN
ejpam-3660	23	36	relation	relation	NOUN
ejpam-3660	23	37	were	be	AUX
ejpam-3660	23	38	presented	present	VERB
ejpam-3660	23	39	by	by	ADP
ejpam-3660	23	40	indangan	indangan	NOUN
ejpam-3660	23	41	et	et	PROPN
ejpam-3660	23	42	al	al	PROPN
ejpam-3660	23	43	.	.	PUNCT
ejpam-3660	24	1	[	[	X
ejpam-3660	24	2	7	7	NUM
ejpam-3660	24	3	]	]	PUNCT
ejpam-3660	24	4	.	.	PUNCT
ejpam-3660	25	1	uncertainty	uncertainty	NOUN
ejpam-3660	25	2	is	be	AUX
ejpam-3660	25	3	an	an	DET
ejpam-3660	25	4	attribute	attribute	NOUN
ejpam-3660	25	5	of	of	ADP
ejpam-3660	25	6	information	information	NOUN
ejpam-3660	25	7	and	and	CCONJ
ejpam-3660	25	8	uncertain	uncertain	ADJ
ejpam-3660	25	9	data	datum	NOUN
ejpam-3660	25	10	are	be	AUX
ejpam-3660	25	11	presented	present	VERB
ejpam-3660	25	12	in	in	ADP
ejpam-3660	25	13	various	various	ADJ
ejpam-3660	25	14	domains	domain	NOUN
ejpam-3660	25	15	.	.	PUNCT
ejpam-3660	26	1	the	the	DET
ejpam-3660	26	2	most	most	ADV
ejpam-3660	26	3	appropriate	appropriate	ADJ
ejpam-3660	26	4	theory	theory	NOUN
ejpam-3660	26	5	for	for	ADP
ejpam-3660	26	6	dealing	deal	VERB
ejpam-3660	26	7	with	with	ADP
ejpam-3660	26	8	uncertainties	uncertainty	NOUN
ejpam-3660	26	9	is	be	AUX
ejpam-3660	26	10	the	the	DET
ejpam-3660	26	11	theory	theory	NOUN
ejpam-3660	26	12	of	of	ADP
ejpam-3660	26	13	fuzzy	fuzzy	ADJ
ejpam-3660	26	14	sets	set	NOUN
ejpam-3660	26	15	developed	develop	VERB
ejpam-3660	26	16	by	by	ADP
ejpam-3660	26	17	zadeh	zadeh	PROPN
ejpam-3660	27	1	[	[	X
ejpam-3660	27	2	16	16	NUM
ejpam-3660	27	3	]	]	PUNCT
ejpam-3660	27	4	in	in	ADP
ejpam-3660	27	5	1965	1965	NUM
ejpam-3660	27	6	.	.	PUNCT
ejpam-3660	28	1	it	it	PRON
ejpam-3660	28	2	has	have	AUX
ejpam-3660	28	3	been	be	AUX
ejpam-3660	28	4	well	well	ADV
ejpam-3660	28	5	developed	develop	VERB
ejpam-3660	28	6	in	in	ADP
ejpam-3660	28	7	the	the	DET
ejpam-3660	28	8	context	context	NOUN
ejpam-3660	28	9	of	of	ADP
ejpam-3660	28	10	hyperstructure	hyperstructure	NOUN
ejpam-3660	28	11	theory	theory	PROPN
ejpam-3660	28	12	.	.	PUNCT
ejpam-3660	29	1	several	several	ADJ
ejpam-3660	29	2	studies	study	NOUN
ejpam-3660	29	3	were	be	AUX
ejpam-3660	29	4	fuzzy	fuzzy	ADJ
ejpam-3660	29	5	theory	theory	NOUN
ejpam-3660	29	6	is	be	AUX
ejpam-3660	29	7	applied	apply	VERB
ejpam-3660	29	8	to	to	ADP
ejpam-3660	29	9	hyperstructure	hyperstructure	NOUN
ejpam-3660	29	10	are	be	AUX
ejpam-3660	29	11	fuzzy	fuzzy	ADJ
ejpam-3660	29	12	hyper	hyper	ADJ
ejpam-3660	29	13	bck	bck	NOUN
ejpam-3660	29	14	-	-	PUNCT
ejpam-3660	29	15	ideals	ideal	NOUN
ejpam-3660	29	16	of	of	ADP
ejpam-3660	29	17	hyper	hyper	ADJ
ejpam-3660	29	18	bck	bck	NOUN
ejpam-3660	29	19	-	-	PUNCT
ejpam-3660	29	20	algebras	algebras	X
ejpam-3660	30	1	[	[	X
ejpam-3660	30	2	8	8	NUM
ejpam-3660	30	3	]	]	PUNCT
ejpam-3660	30	4	,	,	PUNCT
ejpam-3660	30	5	fuzzy	fuzzy	ADJ
ejpam-3660	30	6	ideals	ideal	NOUN
ejpam-3660	30	7	in	in	ADP
ejpam-3660	30	8	hyper	hyper	ADJ
ejpam-3660	30	9	bci	bci	NOUN
ejpam-3660	30	10	-	-	PUNCT
ejpam-3660	30	11	algebras	algebras	X
ejpam-3660	31	1	[	[	X
ejpam-3660	31	2	14	14	NUM
ejpam-3660	31	3	]	]	PUNCT
ejpam-3660	31	4	,	,	PUNCT
ejpam-3660	31	5	fuzzy	fuzzy	ADJ
ejpam-3660	31	6	implicative	implicative	ADJ
ejpam-3660	31	7	hyper	hyper	ADJ
ejpam-3660	31	8	bck	bck	NOUN
ejpam-3660	31	9	-	-	PUNCT
ejpam-3660	31	10	ideals	ideal	NOUN
ejpam-3660	31	11	of	of	ADP
ejpam-3660	31	12	hyper	hyper	ADJ
ejpam-3660	31	13	bck	bck	NOUN
ejpam-3660	31	14	-	-	PUNCT
ejpam-3660	31	15	algebras	algebras	X
ejpam-3660	32	1	[	[	X
ejpam-3660	32	2	9	9	NUM
ejpam-3660	32	3	]	]	PUNCT
ejpam-3660	32	4	,	,	PUNCT
ejpam-3660	32	5	and	and	CCONJ
ejpam-3660	32	6	some	some	DET
ejpam-3660	32	7	results	result	NOUN
ejpam-3660	32	8	on	on	ADP
ejpam-3660	32	9	fuzzy	fuzzy	ADJ
ejpam-3660	32	10	implicative	implicative	ADJ
ejpam-3660	32	11	hyper	hyper	ADJ
ejpam-3660	32	12	gr	gr	NOUN
ejpam-3660	32	13	-	-	PUNCT
ejpam-3660	32	14	ideals	ideal	NOUN
ejpam-3660	32	15	[	[	X
ejpam-3660	32	16	12	12	NUM
ejpam-3660	32	17	]	]	PUNCT
ejpam-3660	32	18	.	.	PUNCT
ejpam-3660	33	1	these	these	DET
ejpam-3660	33	2	studies	study	NOUN
ejpam-3660	33	3	obtained	obtain	VERB
ejpam-3660	33	4	some	some	DET
ejpam-3660	33	5	characterizations	characterization	NOUN
ejpam-3660	33	6	where	where	SCONJ
ejpam-3660	33	7	level	level	NOUN
ejpam-3660	33	8	subsets	subset	NOUN
ejpam-3660	33	9	of	of	ADP
ejpam-3660	33	10	fuzzy	fuzzy	ADJ
ejpam-3660	33	11	set	set	NOUN
ejpam-3660	33	12	are	be	AUX
ejpam-3660	33	13	being	be	AUX
ejpam-3660	33	14	used	use	VERB
ejpam-3660	33	15	.	.	PUNCT
ejpam-3660	34	1	on	on	ADP
ejpam-3660	34	2	the	the	DET
ejpam-3660	34	3	contrary	contrary	ADJ
ejpam-3660	34	4	,	,	PUNCT
ejpam-3660	34	5	fuzzy	fuzzy	ADJ
ejpam-3660	34	6	set	set	NOUN
ejpam-3660	34	7	theory	theory	NOUN
ejpam-3660	34	8	has	have	VERB
ejpam-3660	34	9	no	no	DET
ejpam-3660	34	10	means	mean	NOUN
ejpam-3660	34	11	to	to	PART
ejpam-3660	34	12	incorporate	incorporate	VERB
ejpam-3660	34	13	the	the	DET
ejpam-3660	34	14	hesitation	hesitation	NOUN
ejpam-3660	34	15	or	or	CCONJ
ejpam-3660	34	16	uncertainty	uncertainty	NOUN
ejpam-3660	34	17	in	in	ADP
ejpam-3660	34	18	the	the	DET
ejpam-3660	34	19	membership	membership	NOUN
ejpam-3660	34	20	degrees	degree	NOUN
ejpam-3660	34	21	.	.	PUNCT
ejpam-3660	35	1	atanassov	atanassov	PROPN
ejpam-3660	36	1	[	[	X
ejpam-3660	36	2	1	1	NUM
ejpam-3660	36	3	,	,	PUNCT
ejpam-3660	36	4	2	2	NUM
ejpam-3660	36	5	]	]	PUNCT
ejpam-3660	36	6	introduced	introduce	VERB
ejpam-3660	36	7	the	the	DET
ejpam-3660	36	8	concept	concept	NOUN
ejpam-3660	36	9	of	of	ADP
ejpam-3660	36	10	intuitionistic	intuitionistic	ADJ
ejpam-3660	36	11	fuzzy	fuzzy	ADJ
ejpam-3660	36	12	sets	set	NOUN
ejpam-3660	36	13	in	in	ADP
ejpam-3660	36	14	a	a	DET
ejpam-3660	36	15	non	non	ADJ
ejpam-3660	36	16	-	-	ADJ
ejpam-3660	36	17	empty	empty	ADJ
ejpam-3660	36	18	set	set	NOUN
ejpam-3660	36	19	x	x	PUNCT
ejpam-3660	36	20	which	which	PRON
ejpam-3660	36	21	give	give	VERB
ejpam-3660	36	22	both	both	PRON
ejpam-3660	36	23	a	a	DET
ejpam-3660	36	24	membership	membership	NOUN
ejpam-3660	36	25	degree	degree	NOUN
ejpam-3660	36	26	and	and	CCONJ
ejpam-3660	36	27	a	a	DET
ejpam-3660	36	28	non	non	ADJ
ejpam-3660	36	29	-	-	ADJ
ejpam-3660	36	30	membership	membership	ADJ
ejpam-3660	36	31	degree	degree	NOUN
ejpam-3660	36	32	.	.	PUNCT
ejpam-3660	37	1	since	since	SCONJ
ejpam-3660	37	2	then	then	ADV
ejpam-3660	37	3	,	,	PUNCT
ejpam-3660	37	4	the	the	DET
ejpam-3660	37	5	notion	notion	NOUN
ejpam-3660	37	6	of	of	ADP
ejpam-3660	37	7	intuitionistic	intuitionistic	ADJ
ejpam-3660	37	8	fuzzy	fuzzy	ADJ
ejpam-3660	37	9	set	set	NOUN
ejpam-3660	37	10	has	have	AUX
ejpam-3660	37	11	been	be	AUX
ejpam-3660	37	12	explored	explore	VERB
ejpam-3660	37	13	by	by	ADP
ejpam-3660	37	14	researchers	researcher	NOUN
ejpam-3660	37	15	and	and	CCONJ
ejpam-3660	37	16	a	a	DET
ejpam-3660	37	17	number	number	NOUN
ejpam-3660	37	18	of	of	ADP
ejpam-3660	37	19	theoritical	theoritical	ADJ
ejpam-3660	37	20	and	and	CCONJ
ejpam-3660	37	21	practical	practical	ADJ
ejpam-3660	37	22	results	result	NOUN
ejpam-3660	37	23	have	have	AUX
ejpam-3660	37	24	appeared	appear	VERB
ejpam-3660	37	25	.	.	PUNCT
ejpam-3660	38	1	the	the	DET
ejpam-3660	38	2	relations	relation	NOUN
ejpam-3660	38	3	between	between	ADP
ejpam-3660	38	4	intuitionistic	intuitionistic	ADJ
ejpam-3660	38	5	fuzzy	fuzzy	ADJ
ejpam-3660	38	6	sets	set	NOUN
ejpam-3660	38	7	and	and	CCONJ
ejpam-3660	38	8	algebraic	algebraic	ADJ
ejpam-3660	38	9	hyperstructures	hyperstructure	NOUN
ejpam-3660	38	10	have	have	AUX
ejpam-3660	38	11	been	be	AUX
ejpam-3660	38	12	already	already	ADV
ejpam-3660	38	13	considered	consider	VERB
ejpam-3660	38	14	by	by	ADP
ejpam-3660	38	15	many	many	ADJ
ejpam-3660	38	16	mathematicians	mathematician	NOUN
ejpam-3660	38	17	.	.	PUNCT
ejpam-3660	39	1	some	some	PRON
ejpam-3660	39	2	of	of	ADP
ejpam-3660	39	3	these	these	DET
ejpam-3660	39	4	studies	study	NOUN
ejpam-3660	39	5	are	be	AUX
ejpam-3660	39	6	intuitionistic	intuitionistic	ADJ
ejpam-3660	39	7	fuzzy	fuzzy	ADJ
ejpam-3660	39	8	hyper	hyper	ADJ
ejpam-3660	39	9	bck	bck	NOUN
ejpam-3660	39	10	-	-	PUNCT
ejpam-3660	39	11	ideals	ideal	NOUN
ejpam-3660	39	12	of	of	ADP
ejpam-3660	39	13	hyper	hyper	ADJ
ejpam-3660	39	14	bck	bck	NOUN
ejpam-3660	39	15	-	-	PUNCT
ejpam-3660	39	16	algebras	algebras	X
ejpam-3660	40	1	[	[	X
ejpam-3660	40	2	3	3	NUM
ejpam-3660	40	3	]	]	PUNCT
ejpam-3660	40	4	and	and	CCONJ
ejpam-3660	40	5	intuitionistic	intuitionistic	ADJ
ejpam-3660	40	6	fuzzy	fuzzy	ADJ
ejpam-3660	40	7	ideals	ideal	NOUN
ejpam-3660	40	8	in	in	ADP
ejpam-3660	40	9	hyper	hyper	ADJ
ejpam-3660	40	10	bci	bci	NOUN
ejpam-3660	40	11	-	-	PUNCT
ejpam-3660	40	12	algebras	algebras	X
ejpam-3660	41	1	[	[	X
ejpam-3660	41	2	15	15	NUM
ejpam-3660	41	3	]	]	PUNCT
ejpam-3660	41	4	.	.	PUNCT
ejpam-3660	42	1	both	both	PRON
ejpam-3660	42	2	of	of	ADP
ejpam-3660	42	3	these	these	PRON
ejpam-3660	42	4	researches	research	NOUN
ejpam-3660	42	5	used	use	VERB
ejpam-3660	42	6	level	level	NOUN
ejpam-3660	42	7	subsets	subset	NOUN
ejpam-3660	42	8	of	of	ADP
ejpam-3660	42	9	intuitionistic	intuitionistic	ADJ
ejpam-3660	42	10	fuzzy	fuzzy	ADJ
ejpam-3660	42	11	set	set	NOUN
ejpam-3660	42	12	to	to	PART
ejpam-3660	42	13	establish	establish	VERB
ejpam-3660	42	14	some	some	DET
ejpam-3660	42	15	characterizations	characterization	NOUN
ejpam-3660	42	16	of	of	ADP
ejpam-3660	42	17	intuitionistic	intuitionistic	ADJ
ejpam-3660	42	18	fuzzy	fuzzy	ADJ
ejpam-3660	42	19	hyper	hyper	ADJ
ejpam-3660	42	20	bck	bck	NOUN
ejpam-3660	42	21	-	-	PUNCT
ejpam-3660	42	22	ideals	ideal	NOUN
ejpam-3660	42	23	and	and	CCONJ
ejpam-3660	42	24	intuitionistic	intuitionistic	ADJ
ejpam-3660	42	25	fuzzy	fuzzy	ADJ
ejpam-3660	42	26	hyper	hyper	ADJ
ejpam-3660	42	27	bci	bci	NOUN
ejpam-3660	42	28	-	-	NOUN
ejpam-3660	42	29	ideals	ideal	NOUN
ejpam-3660	42	30	.	.	PUNCT
ejpam-3660	43	1	in	in	ADP
ejpam-3660	43	2	this	this	DET
ejpam-3660	43	3	paper	paper	NOUN
ejpam-3660	43	4	,	,	PUNCT
ejpam-3660	43	5	we	we	PRON
ejpam-3660	43	6	intoduce	intoduce	VERB
ejpam-3660	43	7	fuzzy	fuzzy	ADJ
ejpam-3660	43	8	hyper	hyper	ADJ
ejpam-3660	43	9	gr	gr	NOUN
ejpam-3660	43	10	-	-	PUNCT
ejpam-3660	43	11	ideals	ideal	NOUN
ejpam-3660	43	12	of	of	ADP
ejpam-3660	43	13	type	type	NOUN
ejpam-3660	43	14	1	1	NUM
ejpam-3660	43	15	and	and	CCONJ
ejpam-3660	43	16	intuitionistic	intuitionistic	ADJ
ejpam-3660	43	17	fuzzy	fuzzy	ADJ
ejpam-3660	43	18	hyper	hyper	ADJ
ejpam-3660	43	19	gr	gr	NOUN
ejpam-3660	43	20	-	-	PUNCT
ejpam-3660	43	21	ideals	ideal	NOUN
ejpam-3660	43	22	including	include	VERB
ejpam-3660	43	23	some	some	PRON
ejpam-3660	43	24	of	of	ADP
ejpam-3660	43	25	thier	thier	PRON
ejpam-3660	43	26	properties	property	NOUN
ejpam-3660	43	27	and	and	CCONJ
ejpam-3660	43	28	characterizations	characterization	NOUN
ejpam-3660	43	29	by	by	ADP
ejpam-3660	43	30	following	follow	VERB
ejpam-3660	43	31	the	the	DET
ejpam-3660	43	32	works	work	NOUN
ejpam-3660	43	33	of	of	ADP
ejpam-3660	43	34	borzooei	borzooei	PROPN
ejpam-3660	43	35	et	et	PROPN
ejpam-3660	43	36	al	al	PROPN
ejpam-3660	43	37	.	.	PUNCT
ejpam-3660	44	1	[	[	X
ejpam-3660	44	2	3	3	NUM
ejpam-3660	44	3	]	]	PUNCT
ejpam-3660	44	4	,	,	PUNCT
ejpam-3660	44	5	jun	jun	PROPN
ejpam-3660	44	6	et	et	PROPN
ejpam-3660	44	7	al	al	PROPN
ejpam-3660	44	8	.	.	PUNCT
ejpam-3660	45	1	[	[	X
ejpam-3660	45	2	8	8	NUM
ejpam-3660	45	3	,	,	PUNCT
ejpam-3660	45	4	9	9	NUM
ejpam-3660	45	5	]	]	PUNCT
ejpam-3660	45	6	,	,	PUNCT
ejpam-3660	45	7	nisar	nisar	PROPN
ejpam-3660	45	8	et	et	PROPN
ejpam-3660	45	9	al	al	PROPN
ejpam-3660	45	10	.	.	PUNCT
ejpam-3660	46	1	[	[	X
ejpam-3660	46	2	14	14	NUM
ejpam-3660	46	3	]	]	PUNCT
ejpam-3660	46	4	,	,	PUNCT
ejpam-3660	46	5	and	and	CCONJ
ejpam-3660	46	6	palaniappan	palaniappan	NOUN
ejpam-3660	46	7	et	et	PROPN
ejpam-3660	46	8	al	al	PROPN
ejpam-3660	46	9	.	.	PUNCT
ejpam-3660	47	1	[	[	X
ejpam-3660	47	2	15	15	NUM
ejpam-3660	47	3	]	]	SYM
ejpam-3660	47	4	.	.	PUNCT
ejpam-3660	48	1	2	2	X
ejpam-3660	48	2	.	.	X
ejpam-3660	48	3	preliminaries	preliminary	NOUN
ejpam-3660	48	4	let	let	VERB
ejpam-3660	48	5	h	h	NOUN
ejpam-3660	48	6	be	be	AUX
ejpam-3660	48	7	a	a	DET
ejpam-3660	48	8	nonempty	nonempty	NOUN
ejpam-3660	48	9	set	set	VERB
ejpam-3660	48	10	with	with	ADP
ejpam-3660	48	11	a	a	DET
ejpam-3660	48	12	hyperoperation	hyperoperation	NOUN
ejpam-3660	48	13	“	"	PUNCT
ejpam-3660	48	14	~	~	NOUN
ejpam-3660	48	15	”	"	PUNCT
ejpam-3660	48	16	.	.	PUNCT
ejpam-3660	49	1	for	for	ADP
ejpam-3660	49	2	any	any	DET
ejpam-3660	49	3	two	two	NUM
ejpam-3660	49	4	subsets	subset	NOUN
ejpam-3660	49	5	a	a	PRON
ejpam-3660	49	6	and	and	CCONJ
ejpam-3660	49	7	b	b	NOUN
ejpam-3660	49	8	of	of	ADP
ejpam-3660	49	9	h	h	NOUN
ejpam-3660	49	10	and	and	CCONJ
ejpam-3660	49	11	x	x	PUNCT
ejpam-3660	49	12	∈	∈	PROPN
ejpam-3660	49	13	h	h	NOUN
ejpam-3660	49	14	,	,	PUNCT
ejpam-3660	49	15	we	we	PRON
ejpam-3660	49	16	define	define	VERB
ejpam-3660	49	17	a	a	DET
ejpam-3660	49	18	~	~	PUNCT
ejpam-3660	49	19	b	b	X
ejpam-3660	49	20	=	=	PUNCT
ejpam-3660	49	21	⋃	⋃	PROPN
ejpam-3660	49	22	a∈a	a∈a	ADJ
ejpam-3660	49	23	,	,	PUNCT
ejpam-3660	49	24	b∈b	b∈b	VERB
ejpam-3660	49	25	a	a	DET
ejpam-3660	49	26	~	~	PUNCT
ejpam-3660	49	27	b	b	X
ejpam-3660	49	28	,	,	PUNCT
ejpam-3660	49	29	a	a	PRON
ejpam-3660	49	30	~	~	PUNCT
ejpam-3660	49	31	x	x	SYM
ejpam-3660	49	32	=	=	PUNCT
ejpam-3660	49	33	a	a	X
ejpam-3660	49	34	~	~	PUNCT
ejpam-3660	49	35	{	{	PUNCT
ejpam-3660	49	36	x	x	NOUN
ejpam-3660	49	37	}	}	PUNCT
ejpam-3660	49	38	,	,	PUNCT
ejpam-3660	49	39	and	and	CCONJ
ejpam-3660	49	40	x	x	X
ejpam-3660	49	41	~	~	PUNCT
ejpam-3660	49	42	b	b	X
ejpam-3660	49	43	=	=	SYM
ejpam-3660	49	44	{	{	PUNCT
ejpam-3660	49	45	x	x	NOUN
ejpam-3660	49	46	}	}	PUNCT
ejpam-3660	49	47	~	~	PUNCT
ejpam-3660	49	48	b.	b.	PROPN
ejpam-3660	50	1	moreover	moreover	ADV
ejpam-3660	50	2	,	,	PUNCT
ejpam-3660	50	3	x	x	PROPN
ejpam-3660	50	4	�	�	PROPN
ejpam-3660	50	5	y	y	PROPN
ejpam-3660	50	6	is	be	AUX
ejpam-3660	50	7	defined	define	VERB
ejpam-3660	50	8	by	by	ADP
ejpam-3660	50	9	0	0	NUM
ejpam-3660	50	10	∈	∈	PROPN
ejpam-3660	50	11	x	x	X
ejpam-3660	50	12	~	~	PUNCT
ejpam-3660	50	13	y	y	PROPN
ejpam-3660	50	14	and	and	CCONJ
ejpam-3660	50	15	a	a	DET
ejpam-3660	50	16	�	�	PROPN
ejpam-3660	50	17	b	b	PROPN
ejpam-3660	50	18	is	be	AUX
ejpam-3660	50	19	defined	define	VERB
ejpam-3660	50	20	by	by	ADP
ejpam-3660	50	21	for	for	ADP
ejpam-3660	50	22	all	all	DET
ejpam-3660	50	23	a	a	DET
ejpam-3660	50	24	∈	∈	PROPN
ejpam-3660	50	25	a	a	PRON
ejpam-3660	50	26	,	,	PUNCT
ejpam-3660	50	27	there	there	PRON
ejpam-3660	50	28	exist	exist	VERB
ejpam-3660	50	29	b	b	PROPN
ejpam-3660	50	30	∈	∈	PROPN
ejpam-3660	50	31	b	b	NOUN
ejpam-3660	50	32	such	such	ADJ
ejpam-3660	50	33	that	that	SCONJ
ejpam-3660	50	34	a	a	DET
ejpam-3660	50	35	�	�	PROPN
ejpam-3660	50	36	b.	b.	PROPN
ejpam-3660	50	37	the	the	DET
ejpam-3660	50	38	symbol	symbol	NOUN
ejpam-3660	50	39	“	"	PUNCT
ejpam-3660	50	40	�	�	PROPN
ejpam-3660	50	41	”	"	PUNCT
ejpam-3660	50	42	is	be	AUX
ejpam-3660	50	43	called	call	VERB
ejpam-3660	50	44	a	a	DET
ejpam-3660	50	45	hyperorder	hyperorder	NOUN
ejpam-3660	50	46	on	on	ADP
ejpam-3660	50	47	h.	h.	PROPN
ejpam-3660	50	48	definition	definition	NOUN
ejpam-3660	50	49	2.1	2.1	NUM
ejpam-3660	50	50	.	.	PUNCT
ejpam-3660	51	1	[	[	X
ejpam-3660	51	2	10	10	NUM
ejpam-3660	51	3	]	]	PUNCT
ejpam-3660	51	4	let	let	VERB
ejpam-3660	51	5	h	h	PRON
ejpam-3660	51	6	be	be	AUX
ejpam-3660	51	7	a	a	DET
ejpam-3660	51	8	nonempty	nonempty	ADJ
ejpam-3660	51	9	set	set	VERB
ejpam-3660	51	10	endowed	endow	VERB
ejpam-3660	51	11	with	with	ADP
ejpam-3660	51	12	a	a	DET
ejpam-3660	51	13	hyperoperation	hyperoperation	NOUN
ejpam-3660	51	14	~	~	PUNCT
ejpam-3660	51	15	and	and	CCONJ
ejpam-3660	51	16	a	a	DET
ejpam-3660	51	17	constant	constant	ADJ
ejpam-3660	51	18	0	0	NUM
ejpam-3660	51	19	.	.	PUNCT
ejpam-3660	52	1	then	then	ADV
ejpam-3660	52	2	(	(	PUNCT
ejpam-3660	52	3	h,~	h,~	NOUN
ejpam-3660	52	4	,	,	PUNCT
ejpam-3660	52	5	0	0	NUM
ejpam-3660	52	6	)	)	PUNCT
ejpam-3660	52	7	is	be	AUX
ejpam-3660	52	8	called	call	VERB
ejpam-3660	52	9	a	a	DET
ejpam-3660	52	10	hyper	hyper	ADJ
ejpam-3660	52	11	bck	bck	NOUN
ejpam-3660	52	12	-	-	PUNCT
ejpam-3660	52	13	algebra	algebra	NOUN
ejpam-3660	52	14	if	if	SCONJ
ejpam-3660	52	15	it	it	PRON
ejpam-3660	52	16	satisfies	satisfy	VERB
ejpam-3660	52	17	the	the	DET
ejpam-3660	52	18	following	following	ADJ
ejpam-3660	52	19	axioms	axiom	NOUN
ejpam-3660	52	20	,	,	PUNCT
ejpam-3660	52	21	for	for	ADP
ejpam-3660	52	22	all	all	DET
ejpam-3660	52	23	x	x	NOUN
ejpam-3660	52	24	,	,	PUNCT
ejpam-3660	52	25	y	y	PROPN
ejpam-3660	52	26	,	,	PUNCT
ejpam-3660	52	27	z	z	PROPN
ejpam-3660	52	28	∈	∈	PROPN
ejpam-3660	52	29	h	h	NOUN
ejpam-3660	52	30	:	:	PUNCT
ejpam-3660	52	31	(	(	PUNCT
ejpam-3660	52	32	i	i	NOUN
ejpam-3660	52	33	)	)	PUNCT
ejpam-3660	52	34	(	(	PUNCT
ejpam-3660	52	35	x	x	X
ejpam-3660	52	36	~	~	PUNCT
ejpam-3660	52	37	z	z	X
ejpam-3660	52	38	)	)	PUNCT
ejpam-3660	52	39	~	~	PUNCT
ejpam-3660	52	40	(	(	PUNCT
ejpam-3660	52	41	y	y	X
ejpam-3660	52	42	~	~	PUNCT
ejpam-3660	52	43	z	z	X
ejpam-3660	52	44	)	)	PUNCT
ejpam-3660	52	45	�	�	PROPN
ejpam-3660	52	46	x	x	PUNCT
ejpam-3660	52	47	~	~	PUNCT
ejpam-3660	52	48	y	y	X
ejpam-3660	52	49	;	;	PUNCT
ejpam-3660	52	50	(	(	PUNCT
ejpam-3660	52	51	ii	ii	NOUN
ejpam-3660	52	52	)	)	PUNCT
ejpam-3660	52	53	(	(	PUNCT
ejpam-3660	52	54	x	x	X
ejpam-3660	52	55	~	~	PUNCT
ejpam-3660	52	56	y	y	X
ejpam-3660	52	57	)	)	PUNCT
ejpam-3660	52	58	~	~	PUNCT
ejpam-3660	53	1	z	z	X
ejpam-3660	53	2	=	=	SYM
ejpam-3660	53	3	(	(	PUNCT
ejpam-3660	53	4	x	x	SYM
ejpam-3660	53	5	~	~	PUNCT
ejpam-3660	53	6	z	z	X
ejpam-3660	53	7	)	)	PUNCT
ejpam-3660	53	8	~	~	PUNCT
ejpam-3660	53	9	y	y	X
ejpam-3660	53	10	;	;	PUNCT
ejpam-3660	53	11	(	(	PUNCT
ejpam-3660	53	12	iii	iii	X
ejpam-3660	53	13	)	)	PUNCT
ejpam-3660	53	14	x	x	SYM
ejpam-3660	53	15	~h	~h	PROPN
ejpam-3660	53	16	�	�	PROPN
ejpam-3660	53	17	{	{	PUNCT
ejpam-3660	53	18	x	x	NOUN
ejpam-3660	53	19	}	}	PUNCT
ejpam-3660	53	20	;	;	PUNCT
ejpam-3660	53	21	and	and	CCONJ
ejpam-3660	53	22	a.	a.	NOUN
ejpam-3660	53	23	macodi	macodi	NOUN
ejpam-3660	53	24	-	-	PUNCT
ejpam-3660	53	25	ringia	ringia	ADJ
ejpam-3660	53	26	,	,	PUNCT
ejpam-3660	53	27	g.	g.	PROPN
ejpam-3660	53	28	petalcorin	petalcorin	PROPN
ejpam-3660	53	29	,	,	PUNCT
ejpam-3660	53	30	jr	jr	PROPN
ejpam-3660	53	31	.	.	PROPN
ejpam-3660	53	32	/	/	SYM
ejpam-3660	53	33	eur	eur	PROPN
ejpam-3660	53	34	.	.	PUNCT
ejpam-3660	54	1	j.	j.	PROPN
ejpam-3660	54	2	pure	pure	PROPN
ejpam-3660	54	3	appl	appl	PROPN
ejpam-3660	54	4	.	.	PROPN
ejpam-3660	54	5	math	math	PROPN
ejpam-3660	54	6	,	,	PUNCT
ejpam-3660	54	7	13	13	NUM
ejpam-3660	54	8	(	(	PUNCT
ejpam-3660	54	9	2	2	NUM
ejpam-3660	54	10	)	)	PUNCT
ejpam-3660	54	11	(	(	PUNCT
ejpam-3660	54	12	2020	2020	NUM
ejpam-3660	54	13	)	)	PUNCT
ejpam-3660	54	14	,	,	PUNCT
ejpam-3660	54	15	246	246	NUM
ejpam-3660	54	16	-	-	SYM
ejpam-3660	54	17	257	257	NUM
ejpam-3660	54	18	248	248	NUM
ejpam-3660	54	19	(	(	PUNCT
ejpam-3660	54	20	iv	iv	X
ejpam-3660	54	21	)	)	PUNCT
ejpam-3660	54	22	x	x	NOUN
ejpam-3660	54	23	�	�	PROPN
ejpam-3660	54	24	y	y	PROPN
ejpam-3660	54	25	and	and	CCONJ
ejpam-3660	54	26	y	y	PROPN
ejpam-3660	54	27	�	�	PROPN
ejpam-3660	54	28	x	x	PUNCT
ejpam-3660	54	29	imply	imply	VERB
ejpam-3660	54	30	x	x	X
ejpam-3660	54	31	=	=	PUNCT
ejpam-3660	54	32	y.	y.	NOUN
ejpam-3660	54	33	definition	definition	NOUN
ejpam-3660	54	34	2.2	2.2	NUM
ejpam-3660	54	35	.	.	PUNCT
ejpam-3660	55	1	[	[	X
ejpam-3660	55	2	11	11	NUM
ejpam-3660	55	3	]	]	PUNCT
ejpam-3660	55	4	let	let	VERB
ejpam-3660	55	5	h	h	PRON
ejpam-3660	55	6	be	be	AUX
ejpam-3660	55	7	a	a	DET
ejpam-3660	55	8	nonempty	nonempty	ADV
ejpam-3660	55	9	set	set	VERB
ejpam-3660	55	10	and	and	CCONJ
ejpam-3660	55	11	~	~	PUNCT
ejpam-3660	55	12	be	be	AUX
ejpam-3660	55	13	a	a	DET
ejpam-3660	55	14	hyperoperation	hyperoperation	NOUN
ejpam-3660	55	15	on	on	ADP
ejpam-3660	55	16	h.	h.	PROPN
ejpam-3660	55	17	then	then	ADV
ejpam-3660	55	18	(	(	PUNCT
ejpam-3660	55	19	h,~	h,~	NOUN
ejpam-3660	55	20	,	,	PUNCT
ejpam-3660	55	21	0	0	NUM
ejpam-3660	55	22	)	)	PUNCT
ejpam-3660	55	23	is	be	AUX
ejpam-3660	55	24	called	call	VERB
ejpam-3660	55	25	a	a	DET
ejpam-3660	55	26	hyper	hyper	ADJ
ejpam-3660	55	27	bci	bci	NOUN
ejpam-3660	55	28	-	-	NOUN
ejpam-3660	55	29	algebra	algebra	NOUN
ejpam-3660	55	30	if	if	SCONJ
ejpam-3660	55	31	it	it	PRON
ejpam-3660	55	32	contains	contain	VERB
ejpam-3660	55	33	a	a	DET
ejpam-3660	55	34	constant	constant	ADJ
ejpam-3660	55	35	0	0	NUM
ejpam-3660	55	36	∈	∈	PROPN
ejpam-3660	55	37	h	h	NOUN
ejpam-3660	55	38	and	and	CCONJ
ejpam-3660	55	39	satisfies	satisfy	VERB
ejpam-3660	55	40	the	the	DET
ejpam-3660	55	41	following	follow	VERB
ejpam-3660	55	42	axioms	axiom	NOUN
ejpam-3660	55	43	,	,	PUNCT
ejpam-3660	55	44	for	for	ADP
ejpam-3660	55	45	all	all	DET
ejpam-3660	55	46	x	x	NOUN
ejpam-3660	55	47	,	,	PUNCT
ejpam-3660	55	48	y	y	PROPN
ejpam-3660	55	49	,	,	PUNCT
ejpam-3660	55	50	z	z	PROPN
ejpam-3660	55	51	∈	∈	PROPN
ejpam-3660	55	52	h	h	NOUN
ejpam-3660	55	53	:	:	PUNCT
ejpam-3660	55	54	(	(	PUNCT
ejpam-3660	55	55	i	i	NOUN
ejpam-3660	55	56	)	)	PUNCT
ejpam-3660	55	57	(	(	PUNCT
ejpam-3660	55	58	x	x	X
ejpam-3660	55	59	~	~	PUNCT
ejpam-3660	55	60	z	z	X
ejpam-3660	55	61	)	)	PUNCT
ejpam-3660	55	62	~	~	PUNCT
ejpam-3660	55	63	(	(	PUNCT
ejpam-3660	55	64	y	y	X
ejpam-3660	55	65	~	~	PUNCT
ejpam-3660	55	66	z	z	X
ejpam-3660	55	67	)	)	PUNCT
ejpam-3660	55	68	�	�	PROPN
ejpam-3660	55	69	x	x	PUNCT
ejpam-3660	55	70	~	~	PUNCT
ejpam-3660	55	71	y	y	X
ejpam-3660	55	72	;	;	PUNCT
ejpam-3660	55	73	(	(	PUNCT
ejpam-3660	55	74	ii	ii	NOUN
ejpam-3660	55	75	)	)	PUNCT
ejpam-3660	55	76	(	(	PUNCT
ejpam-3660	55	77	x	x	X
ejpam-3660	55	78	~	~	PUNCT
ejpam-3660	55	79	y	y	X
ejpam-3660	55	80	)	)	PUNCT
ejpam-3660	55	81	~	~	PUNCT
ejpam-3660	56	1	z	z	X
ejpam-3660	56	2	=	=	SYM
ejpam-3660	56	3	(	(	PUNCT
ejpam-3660	56	4	x	x	SYM
ejpam-3660	56	5	~	~	PUNCT
ejpam-3660	56	6	z	z	X
ejpam-3660	56	7	)	)	PUNCT
ejpam-3660	56	8	~	~	PUNCT
ejpam-3660	56	9	y	y	X
ejpam-3660	56	10	;	;	PUNCT
ejpam-3660	56	11	(	(	PUNCT
ejpam-3660	56	12	iii	iii	X
ejpam-3660	56	13	)	)	PUNCT
ejpam-3660	56	14	x	x	NOUN
ejpam-3660	56	15	�	�	PROPN
ejpam-3660	56	16	x	x	SYM
ejpam-3660	56	17	;	;	PUNCT
ejpam-3660	56	18	(	(	PUNCT
ejpam-3660	56	19	iv	iv	X
ejpam-3660	56	20	)	)	PUNCT
ejpam-3660	56	21	x	x	NOUN
ejpam-3660	56	22	�	�	PROPN
ejpam-3660	56	23	y	y	PROPN
ejpam-3660	56	24	and	and	CCONJ
ejpam-3660	56	25	y	y	PROPN
ejpam-3660	56	26	�	�	PROPN
ejpam-3660	56	27	x	x	PUNCT
ejpam-3660	56	28	imply	imply	VERB
ejpam-3660	56	29	x	x	X
ejpam-3660	56	30	=	=	SYM
ejpam-3660	56	31	y	y	PROPN
ejpam-3660	56	32	;	;	PUNCT
ejpam-3660	56	33	and	and	CCONJ
ejpam-3660	56	34	(	(	PUNCT
ejpam-3660	56	35	v	v	NOUN
ejpam-3660	56	36	)	)	PUNCT
ejpam-3660	56	37	0	0	NUM
ejpam-3660	57	1	~	~	PUNCT
ejpam-3660	57	2	(	(	PUNCT
ejpam-3660	57	3	0	0	NUM
ejpam-3660	57	4	~	~	SYM
ejpam-3660	57	5	x	x	X
ejpam-3660	57	6	)	)	PUNCT
ejpam-3660	57	7	�	�	PROPN
ejpam-3660	57	8	x	x	SYM
ejpam-3660	57	9	,	,	PUNCT
ejpam-3660	57	10	x	x	INTJ
ejpam-3660	57	11	,	,	PUNCT
ejpam-3660	57	12	0	0	NUM
ejpam-3660	57	13	;	;	PUNCT
ejpam-3660	57	14	definition	definition	NOUN
ejpam-3660	57	15	2.3	2.3	NUM
ejpam-3660	57	16	.	.	PUNCT
ejpam-3660	58	1	[	[	X
ejpam-3660	58	2	6	6	NUM
ejpam-3660	58	3	]	]	PUNCT
ejpam-3660	58	4	let	let	VERB
ejpam-3660	58	5	h	h	PRON
ejpam-3660	58	6	be	be	AUX
ejpam-3660	58	7	a	a	DET
ejpam-3660	58	8	nonempty	nonempty	ADV
ejpam-3660	58	9	set	set	VERB
ejpam-3660	58	10	and	and	CCONJ
ejpam-3660	58	11	~	~	PUNCT
ejpam-3660	58	12	be	be	AUX
ejpam-3660	58	13	a	a	DET
ejpam-3660	58	14	hyperoperation	hyperoperation	NOUN
ejpam-3660	58	15	on	on	ADP
ejpam-3660	58	16	h.	h.	PROPN
ejpam-3660	58	17	if	if	SCONJ
ejpam-3660	58	18	h	h	NOUN
ejpam-3660	58	19	contains	contain	VERB
ejpam-3660	58	20	a	a	DET
ejpam-3660	58	21	constant	constant	ADJ
ejpam-3660	58	22	0	0	NOUN
ejpam-3660	58	23	and	and	CCONJ
ejpam-3660	58	24	the	the	DET
ejpam-3660	58	25	following	following	ADJ
ejpam-3660	58	26	axioms	axiom	NOUN
ejpam-3660	58	27	(	(	PUNCT
ejpam-3660	58	28	hgr1	hgr1	PROPN
ejpam-3660	58	29	)	)	PUNCT
ejpam-3660	59	1	(	(	PUNCT
ejpam-3660	59	2	x	x	X
ejpam-3660	59	3	~	~	PUNCT
ejpam-3660	59	4	z	z	X
ejpam-3660	59	5	)	)	PUNCT
ejpam-3660	59	6	~	~	PUNCT
ejpam-3660	59	7	(	(	PUNCT
ejpam-3660	59	8	y	y	X
ejpam-3660	59	9	~	~	PUNCT
ejpam-3660	59	10	z	z	X
ejpam-3660	59	11	)	)	PUNCT
ejpam-3660	59	12	�	�	PROPN
ejpam-3660	59	13	x	x	PUNCT
ejpam-3660	59	14	~	~	PUNCT
ejpam-3660	59	15	y	y	X
ejpam-3660	59	16	,	,	PUNCT
ejpam-3660	59	17	(	(	PUNCT
ejpam-3660	59	18	hgr2	hgr2	NOUN
ejpam-3660	59	19	)	)	PUNCT
ejpam-3660	60	1	(	(	PUNCT
ejpam-3660	60	2	x	x	X
ejpam-3660	60	3	~	~	PUNCT
ejpam-3660	60	4	y	y	X
ejpam-3660	60	5	)	)	PUNCT
ejpam-3660	60	6	~	~	PUNCT
ejpam-3660	60	7	z	z	X
ejpam-3660	60	8	=	=	SYM
ejpam-3660	60	9	(	(	PUNCT
ejpam-3660	60	10	x	x	SYM
ejpam-3660	60	11	~	~	PUNCT
ejpam-3660	60	12	z	z	X
ejpam-3660	60	13	)	)	PUNCT
ejpam-3660	60	14	~	~	PUNCT
ejpam-3660	60	15	y	y	X
ejpam-3660	60	16	,	,	PUNCT
ejpam-3660	60	17	(	(	PUNCT
ejpam-3660	60	18	hgr3	hgr3	PROPN
ejpam-3660	60	19	)	)	PUNCT
ejpam-3660	60	20	x	x	NOUN
ejpam-3660	60	21	�	�	PROPN
ejpam-3660	60	22	x	x	SYM
ejpam-3660	60	23	,	,	PUNCT
ejpam-3660	60	24	(	(	PUNCT
ejpam-3660	60	25	hgr4	hgr4	NOUN
ejpam-3660	60	26	)	)	PUNCT
ejpam-3660	60	27	0	0	NUM
ejpam-3660	61	1	~	~	PUNCT
ejpam-3660	61	2	(	(	PUNCT
ejpam-3660	61	3	0	0	NUM
ejpam-3660	61	4	~	~	SYM
ejpam-3660	61	5	x	x	X
ejpam-3660	61	6	)	)	PUNCT
ejpam-3660	61	7	�	�	PROPN
ejpam-3660	61	8	x	x	SYM
ejpam-3660	61	9	,	,	PUNCT
ejpam-3660	61	10	x	x	INTJ
ejpam-3660	61	11	,	,	PUNCT
ejpam-3660	61	12	0	0	NUM
ejpam-3660	61	13	,	,	PUNCT
ejpam-3660	61	14	and	and	CCONJ
ejpam-3660	61	15	(	(	PUNCT
ejpam-3660	61	16	hgr5	hgr5	PROPN
ejpam-3660	61	17	)	)	PUNCT
ejpam-3660	61	18	(	(	PUNCT
ejpam-3660	61	19	x	x	X
ejpam-3660	61	20	~	~	PUNCT
ejpam-3660	61	21	y	y	X
ejpam-3660	61	22	)	)	PUNCT
ejpam-3660	61	23	~	~	PUNCT
ejpam-3660	61	24	z	z	X
ejpam-3660	61	25	�	�	PROPN
ejpam-3660	61	26	y	y	PROPN
ejpam-3660	61	27	~	~	PUNCT
ejpam-3660	61	28	z	z	NOUN
ejpam-3660	61	29	are	be	AUX
ejpam-3660	61	30	satisfied	satisfied	ADJ
ejpam-3660	61	31	for	for	ADP
ejpam-3660	61	32	all	all	DET
ejpam-3660	61	33	x	x	NOUN
ejpam-3660	61	34	,	,	PUNCT
ejpam-3660	61	35	y	y	PROPN
ejpam-3660	61	36	,	,	PUNCT
ejpam-3660	61	37	z	z	PROPN
ejpam-3660	61	38	∈	∈	PROPN
ejpam-3660	61	39	h	h	NOUN
ejpam-3660	61	40	,	,	PUNCT
ejpam-3660	61	41	then	then	ADV
ejpam-3660	61	42	(	(	PUNCT
ejpam-3660	61	43	h,~	h,~	NOUN
ejpam-3660	61	44	,	,	PUNCT
ejpam-3660	61	45	0	0	NUM
ejpam-3660	61	46	)	)	PUNCT
ejpam-3660	61	47	is	be	AUX
ejpam-3660	61	48	said	say	VERB
ejpam-3660	61	49	to	to	PART
ejpam-3660	61	50	be	be	AUX
ejpam-3660	61	51	a	a	DET
ejpam-3660	61	52	hyper	hyper	ADJ
ejpam-3660	61	53	gr	gr	NOUN
ejpam-3660	61	54	-	-	NOUN
ejpam-3660	61	55	algebra	algebra	NOUN
ejpam-3660	61	56	.	.	PUNCT
ejpam-3660	62	1	for	for	ADP
ejpam-3660	62	2	the	the	DET
ejpam-3660	62	3	sake	sake	NOUN
ejpam-3660	62	4	of	of	ADP
ejpam-3660	62	5	simplicity	simplicity	NOUN
ejpam-3660	62	6	,	,	PUNCT
ejpam-3660	62	7	we	we	PRON
ejpam-3660	62	8	say	say	VERB
ejpam-3660	62	9	h	h	NOUN
ejpam-3660	62	10	is	be	AUX
ejpam-3660	62	11	a	a	DET
ejpam-3660	62	12	hyper	hyper	ADJ
ejpam-3660	62	13	gr	gr	NOUN
ejpam-3660	62	14	-	-	NOUN
ejpam-3660	62	15	algebra	algebra	NOUN
ejpam-3660	62	16	.	.	PUNCT
ejpam-3660	63	1	definition	definition	NOUN
ejpam-3660	63	2	2.4	2.4	NUM
ejpam-3660	63	3	.	.	PUNCT
ejpam-3660	64	1	[	[	X
ejpam-3660	64	2	6	6	NUM
ejpam-3660	64	3	]	]	PUNCT
ejpam-3660	64	4	a	a	DET
ejpam-3660	64	5	subset	subset	NOUN
ejpam-3660	64	6	i	i	PRON
ejpam-3660	64	7	of	of	ADP
ejpam-3660	64	8	a	a	DET
ejpam-3660	64	9	hyper	hyper	ADJ
ejpam-3660	64	10	gr	gr	NOUN
ejpam-3660	64	11	-	-	PUNCT
ejpam-3660	64	12	algebra	algebra	NOUN
ejpam-3660	64	13	h	h	NOUN
ejpam-3660	64	14	is	be	AUX
ejpam-3660	64	15	called	call	VERB
ejpam-3660	64	16	a	a	DET
ejpam-3660	64	17	hyper	hyper	ADJ
ejpam-3660	64	18	gr	gr	NOUN
ejpam-3660	64	19	-	-	PUNCT
ejpam-3660	64	20	ideal	ideal	NOUN
ejpam-3660	64	21	of	of	ADP
ejpam-3660	64	22	h	h	NOUN
ejpam-3660	64	23	if	if	SCONJ
ejpam-3660	64	24	it	it	PRON
ejpam-3660	64	25	contains	contain	VERB
ejpam-3660	64	26	0	0	PUNCT
ejpam-3660	64	27	and	and	CCONJ
ejpam-3660	64	28	for	for	ADP
ejpam-3660	64	29	all	all	DET
ejpam-3660	64	30	x	x	NOUN
ejpam-3660	64	31	,	,	PUNCT
ejpam-3660	64	32	y	y	PROPN
ejpam-3660	64	33	∈	∈	PROPN
ejpam-3660	64	34	h	h	NOUN
ejpam-3660	64	35	,	,	PUNCT
ejpam-3660	64	36	x	x	X
ejpam-3660	64	37	~	~	PUNCT
ejpam-3660	64	38	y	y	PROPN
ejpam-3660	64	39	⊆	⊆	NUM
ejpam-3660	64	40	i	i	PROPN
ejpam-3660	64	41	and	and	CCONJ
ejpam-3660	64	42	y	y	PROPN
ejpam-3660	64	43	∈	∈	PROPN
ejpam-3660	65	1	i	i	PRON
ejpam-3660	65	2	imply	imply	VERB
ejpam-3660	65	3	that	that	SCONJ
ejpam-3660	65	4	x	x	X
ejpam-3660	65	5	∈	∈	PROPN
ejpam-3660	65	6	i.	i.	NOUN
ejpam-3660	65	7	definition	definition	NOUN
ejpam-3660	65	8	2.5	2.5	NUM
ejpam-3660	65	9	.	.	PUNCT
ejpam-3660	66	1	[	[	X
ejpam-3660	66	2	16	16	NUM
ejpam-3660	66	3	]	]	X
ejpam-3660	66	4	a	a	DET
ejpam-3660	66	5	fuzzy	fuzzy	ADJ
ejpam-3660	66	6	set	set	VERB
ejpam-3660	66	7	µ	µ	NOUN
ejpam-3660	66	8	of	of	ADP
ejpam-3660	66	9	a	a	DET
ejpam-3660	66	10	nonempty	nonempty	ADV
ejpam-3660	66	11	set	set	VERB
ejpam-3660	66	12	m	m	VERB
ejpam-3660	66	13	is	be	AUX
ejpam-3660	66	14	a	a	DET
ejpam-3660	66	15	function	function	NOUN
ejpam-3660	66	16	µ	µ	NOUN
ejpam-3660	66	17	:	:	PUNCT
ejpam-3660	66	18	m→	m→	PUNCT
ejpam-3660	67	1	[	[	X
ejpam-3660	67	2	0	0	NUM
ejpam-3660	67	3	,	,	PUNCT
ejpam-3660	67	4	1	1	NUM
ejpam-3660	67	5	]	]	PUNCT
ejpam-3660	67	6	.	.	PUNCT
ejpam-3660	68	1	definition	definition	NOUN
ejpam-3660	68	2	2.6	2.6	NUM
ejpam-3660	68	3	.	.	PUNCT
ejpam-3660	69	1	[	[	X
ejpam-3660	69	2	4	4	X
ejpam-3660	69	3	]	]	PUNCT
ejpam-3660	69	4	let	let	VERB
ejpam-3660	69	5	µ	µ	X
ejpam-3660	69	6	be	be	AUX
ejpam-3660	69	7	a	a	DET
ejpam-3660	69	8	fuzzy	fuzzy	ADJ
ejpam-3660	69	9	set	set	NOUN
ejpam-3660	69	10	of	of	ADP
ejpam-3660	69	11	m.	m.	NOUN
ejpam-3660	69	12	for	for	ADP
ejpam-3660	69	13	a	a	DET
ejpam-3660	69	14	fixed	fix	VERB
ejpam-3660	69	15	t	t	NOUN
ejpam-3660	69	16	∈	∈	PROPN
ejpam-3660	70	1	[	[	X
ejpam-3660	70	2	0	0	NUM
ejpam-3660	70	3	,	,	PUNCT
ejpam-3660	70	4	1	1	NUM
ejpam-3660	70	5	]	]	PUNCT
ejpam-3660	70	6	,	,	PUNCT
ejpam-3660	70	7	the	the	DET
ejpam-3660	70	8	set	set	NOUN
ejpam-3660	70	9	µt	µt	X
ejpam-3660	70	10	=	=	PUNCT
ejpam-3660	70	11	{	{	PUNCT
ejpam-3660	70	12	x	x	NOUN
ejpam-3660	70	13	∈m|µ(x	∈m|µ(x	NUM
ejpam-3660	70	14	)	)	PUNCT
ejpam-3660	70	15	≥	≥	PROPN
ejpam-3660	70	16	t	t	PROPN
ejpam-3660	70	17	}	}	PUNCT
ejpam-3660	70	18	is	be	AUX
ejpam-3660	70	19	called	call	VERB
ejpam-3660	70	20	a	a	DET
ejpam-3660	70	21	level	level	NOUN
ejpam-3660	70	22	subset	subset	NOUN
ejpam-3660	70	23	of	of	ADP
ejpam-3660	70	24	µ.	µ.	PROPN
ejpam-3660	70	25	definition	definition	NOUN
ejpam-3660	70	26	2.7	2.7	NUM
ejpam-3660	70	27	.	.	PUNCT
ejpam-3660	71	1	[	[	X
ejpam-3660	71	2	1	1	X
ejpam-3660	71	3	]	]	PUNCT
ejpam-3660	71	4	an	an	DET
ejpam-3660	71	5	intuitionistic	intuitionistic	ADJ
ejpam-3660	71	6	fuzzy	fuzzy	ADJ
ejpam-3660	71	7	set	set	VERB
ejpam-3660	71	8	a	a	PRON
ejpam-3660	71	9	in	in	ADP
ejpam-3660	71	10	a	a	DET
ejpam-3660	71	11	nonempty	nonempty	ADV
ejpam-3660	71	12	set	set	VERB
ejpam-3660	71	13	h	h	NOUN
ejpam-3660	71	14	is	be	AUX
ejpam-3660	71	15	an	an	DET
ejpam-3660	71	16	object	object	NOUN
ejpam-3660	71	17	having	have	VERB
ejpam-3660	71	18	the	the	DET
ejpam-3660	71	19	form	form	NOUN
ejpam-3660	71	20	a	a	PRON
ejpam-3660	71	21	=	=	X
ejpam-3660	71	22	{	{	PUNCT
ejpam-3660	71	23	(	(	PUNCT
ejpam-3660	71	24	x	x	NOUN
ejpam-3660	71	25	,	,	PUNCT
ejpam-3660	71	26	µa(x	µa(x	NOUN
ejpam-3660	71	27	)	)	PUNCT
ejpam-3660	71	28	,	,	PUNCT
ejpam-3660	71	29	γa(x))|x	γa(x))|x	PROPN
ejpam-3660	71	30	∈	∈	PROPN
ejpam-3660	71	31	h	h	NOUN
ejpam-3660	71	32	}	}	PUNCT
ejpam-3660	71	33	where	where	SCONJ
ejpam-3660	71	34	the	the	DET
ejpam-3660	71	35	function	function	NOUN
ejpam-3660	71	36	µa	µa	NOUN
ejpam-3660	71	37	:	:	PUNCT
ejpam-3660	71	38	h	h	NOUN
ejpam-3660	71	39	→	→	PUNCT
ejpam-3660	72	1	[	[	X
ejpam-3660	72	2	0	0	NUM
ejpam-3660	72	3	,	,	PUNCT
ejpam-3660	72	4	1	1	NUM
ejpam-3660	72	5	]	]	PUNCT
ejpam-3660	72	6	and	and	CCONJ
ejpam-3660	72	7	γa	γa	PRON
ejpam-3660	72	8	:	:	PUNCT
ejpam-3660	72	9	h	h	X
ejpam-3660	72	10	→	→	PUNCT
ejpam-3660	73	1	[	[	X
ejpam-3660	73	2	0	0	NUM
ejpam-3660	73	3	,	,	PUNCT
ejpam-3660	73	4	1	1	NUM
ejpam-3660	73	5	]	]	PUNCT
ejpam-3660	73	6	denote	denote	VERB
ejpam-3660	73	7	the	the	DET
ejpam-3660	73	8	degree	degree	NOUN
ejpam-3660	73	9	of	of	ADP
ejpam-3660	73	10	membership	membership	NOUN
ejpam-3660	73	11	and	and	CCONJ
ejpam-3660	73	12	the	the	DET
ejpam-3660	73	13	degree	degree	NOUN
ejpam-3660	73	14	of	of	ADP
ejpam-3660	73	15	nonmembership	nonmembership	NOUN
ejpam-3660	73	16	,	,	PUNCT
ejpam-3660	73	17	respectively	respectively	ADV
ejpam-3660	73	18	,	,	PUNCT
ejpam-3660	73	19	and	and	CCONJ
ejpam-3660	73	20	for	for	ADP
ejpam-3660	73	21	all	all	DET
ejpam-3660	73	22	x	x	SYM
ejpam-3660	73	23	∈	∈	PROPN
ejpam-3660	73	24	h	h	NOUN
ejpam-3660	73	25	,	,	PUNCT
ejpam-3660	73	26	0	0	NUM
ejpam-3660	73	27	≤	≤	NOUN
ejpam-3660	73	28	µa(x	µa(x	NOUN
ejpam-3660	73	29	)	)	PUNCT
ejpam-3660	74	1	+	+	CCONJ
ejpam-3660	75	1	γa(x	γa(x	X
ejpam-3660	75	2	)	)	PUNCT
ejpam-3660	75	3	≤	≤	NUM
ejpam-3660	75	4	1	1	NUM
ejpam-3660	75	5	.	.	PUNCT
ejpam-3660	76	1	furthermore	furthermore	ADV
ejpam-3660	76	2	,	,	PUNCT
ejpam-3660	76	3	we	we	PRON
ejpam-3660	76	4	have	have	VERB
ejpam-3660	76	5	πa(x	πa(x	NOUN
ejpam-3660	76	6	)	)	PUNCT
ejpam-3660	76	7	=	=	SYM
ejpam-3660	77	1	1−µa(x)−γa(x	1−µa(x)−γa(x	X
ejpam-3660	77	2	)	)	PUNCT
ejpam-3660	77	3	called	call	VERB
ejpam-3660	77	4	the	the	DET
ejpam-3660	77	5	intuitionistic	intuitionistic	ADJ
ejpam-3660	77	6	fuzzy	fuzzy	ADJ
ejpam-3660	77	7	set	set	VERB
ejpam-3660	77	8	index	index	NOUN
ejpam-3660	77	9	or	or	CCONJ
ejpam-3660	77	10	hesitation	hesitation	NOUN
ejpam-3660	77	11	margin	margin	NOUN
ejpam-3660	77	12	of	of	ADP
ejpam-3660	77	13	x	x	PUNCT
ejpam-3660	77	14	in	in	ADP
ejpam-3660	77	15	a.	a.	NOUN
ejpam-3660	77	16	πa(x	πa(x	NOUN
ejpam-3660	77	17	)	)	PUNCT
ejpam-3660	77	18	is	be	AUX
ejpam-3660	77	19	the	the	DET
ejpam-3660	77	20	degree	degree	NOUN
ejpam-3660	77	21	of	of	ADP
ejpam-3660	77	22	indeterminancy	indeterminancy	NOUN
ejpam-3660	77	23	of	of	ADP
ejpam-3660	77	24	x	x	PUNCT
ejpam-3660	77	25	∈	∈	PROPN
ejpam-3660	77	26	h	h	NOUN
ejpam-3660	77	27	to	to	PART
ejpam-3660	77	28	intuitionistic	intuitionistic	ADJ
ejpam-3660	77	29	fuzzy	fuzzy	ADJ
ejpam-3660	77	30	set	set	VERB
ejpam-3660	77	31	a	a	DET
ejpam-3660	77	32	and	and	CCONJ
ejpam-3660	77	33	πa(x	πa(x	NOUN
ejpam-3660	77	34	)	)	PUNCT
ejpam-3660	77	35	∈	∈	NOUN
ejpam-3660	78	1	[	[	X
ejpam-3660	78	2	0	0	NUM
ejpam-3660	78	3	,	,	PUNCT
ejpam-3660	78	4	1	1	NUM
ejpam-3660	78	5	]	]	PUNCT
ejpam-3660	78	6	.	.	PUNCT
ejpam-3660	79	1	πa(x	πa(x	NOUN
ejpam-3660	79	2	)	)	PUNCT
ejpam-3660	79	3	expresses	express	VERB
ejpam-3660	79	4	the	the	DET
ejpam-3660	79	5	lack	lack	NOUN
ejpam-3660	79	6	of	of	ADP
ejpam-3660	79	7	knowledge	knowledge	NOUN
ejpam-3660	79	8	of	of	ADP
ejpam-3660	79	9	whether	whether	SCONJ
ejpam-3660	79	10	x	x	PRON
ejpam-3660	79	11	belongs	belong	VERB
ejpam-3660	79	12	to	to	ADP
ejpam-3660	79	13	intuitionistic	intuitionistic	ADJ
ejpam-3660	79	14	fuzzy	fuzzy	ADJ
ejpam-3660	79	15	set	set	VERB
ejpam-3660	79	16	a	a	PRON
ejpam-3660	79	17	or	or	CCONJ
ejpam-3660	79	18	not	not	PART
ejpam-3660	79	19	.	.	PUNCT
ejpam-3660	80	1	a.	a.	NOUN
ejpam-3660	80	2	macodi	macodi	PROPN
ejpam-3660	80	3	-	-	PUNCT
ejpam-3660	80	4	ringia	ringia	ADJ
ejpam-3660	80	5	,	,	PUNCT
ejpam-3660	80	6	g.	g.	PROPN
ejpam-3660	80	7	petalcorin	petalcorin	PROPN
ejpam-3660	80	8	,	,	PUNCT
ejpam-3660	80	9	jr	jr	PROPN
ejpam-3660	80	10	.	.	PROPN
ejpam-3660	80	11	/	/	SYM
ejpam-3660	80	12	eur	eur	PROPN
ejpam-3660	80	13	.	.	PUNCT
ejpam-3660	81	1	j.	j.	PROPN
ejpam-3660	81	2	pure	pure	PROPN
ejpam-3660	81	3	appl	appl	PROPN
ejpam-3660	81	4	.	.	PROPN
ejpam-3660	81	5	math	math	PROPN
ejpam-3660	81	6	,	,	PUNCT
ejpam-3660	81	7	13	13	NUM
ejpam-3660	81	8	(	(	PUNCT
ejpam-3660	81	9	2	2	NUM
ejpam-3660	81	10	)	)	PUNCT
ejpam-3660	81	11	(	(	PUNCT
ejpam-3660	81	12	2020	2020	NUM
ejpam-3660	81	13	)	)	PUNCT
ejpam-3660	81	14	,	,	PUNCT
ejpam-3660	81	15	246	246	NUM
ejpam-3660	81	16	-	-	SYM
ejpam-3660	81	17	257	257	NUM
ejpam-3660	81	18	249	249	NUM
ejpam-3660	81	19	we	we	PRON
ejpam-3660	81	20	shall	shall	AUX
ejpam-3660	81	21	use	use	VERB
ejpam-3660	81	22	the	the	DET
ejpam-3660	81	23	symbol	symbol	NOUN
ejpam-3660	81	24	a	a	PRON
ejpam-3660	81	25	=	=	X
ejpam-3660	81	26	(	(	PUNCT
ejpam-3660	81	27	µa	µa	PROPN
ejpam-3660	81	28	,	,	PUNCT
ejpam-3660	81	29	γa	γa	PROPN
ejpam-3660	81	30	)	)	PUNCT
ejpam-3660	81	31	for	for	ADP
ejpam-3660	81	32	the	the	DET
ejpam-3660	81	33	intuitionistic	intuitionistic	ADJ
ejpam-3660	81	34	fuzzy	fuzzy	ADJ
ejpam-3660	81	35	set	set	VERB
ejpam-3660	81	36	a	a	DET
ejpam-3660	81	37	=	=	X
ejpam-3660	81	38	{	{	PUNCT
ejpam-3660	81	39	(	(	PUNCT
ejpam-3660	81	40	x	x	NOUN
ejpam-3660	81	41	,	,	PUNCT
ejpam-3660	81	42	µa(x	µa(x	NOUN
ejpam-3660	81	43	)	)	PUNCT
ejpam-3660	81	44	,	,	PUNCT
ejpam-3660	81	45	γa(x))|x	γa(x))|x	PROPN
ejpam-3660	81	46	∈	∈	PROPN
ejpam-3660	81	47	h	h	NOUN
ejpam-3660	81	48	}	}	PUNCT
ejpam-3660	81	49	.	.	PUNCT
ejpam-3660	82	1	definition	definition	NOUN
ejpam-3660	82	2	2.8	2.8	NUM
ejpam-3660	82	3	.	.	PUNCT
ejpam-3660	83	1	[	[	X
ejpam-3660	83	2	15	15	NUM
ejpam-3660	83	3	]	]	X
ejpam-3660	83	4	for	for	ADP
ejpam-3660	83	5	an	an	DET
ejpam-3660	83	6	intuitionistic	intuitionistic	ADJ
ejpam-3660	83	7	fuzzy	fuzzy	ADJ
ejpam-3660	83	8	set	set	VERB
ejpam-3660	83	9	a	a	PRON
ejpam-3660	83	10	=	=	X
ejpam-3660	83	11	(	(	PUNCT
ejpam-3660	83	12	µa	µa	PROPN
ejpam-3660	83	13	,	,	PUNCT
ejpam-3660	83	14	γa	γa	NOUN
ejpam-3660	83	15	)	)	PUNCT
ejpam-3660	83	16	in	in	ADP
ejpam-3660	83	17	h	h	PROPN
ejpam-3660	83	18	and	and	CCONJ
ejpam-3660	83	19	s	s	PROPN
ejpam-3660	83	20	,	,	PUNCT
ejpam-3660	83	21	t	t	PROPN
ejpam-3660	83	22	∈	∈	PROPN
ejpam-3660	84	1	[	[	X
ejpam-3660	84	2	0	0	NUM
ejpam-3660	84	3	,	,	PUNCT
ejpam-3660	84	4	1	1	NUM
ejpam-3660	84	5	]	]	PUNCT
ejpam-3660	84	6	,	,	PUNCT
ejpam-3660	84	7	the	the	DET
ejpam-3660	84	8	set	set	NOUN
ejpam-3660	84	9	a〈t	a〈t	NUM
ejpam-3660	84	10	,	,	PUNCT
ejpam-3660	84	11	s	s	PROPN
ejpam-3660	84	12	〉	〉	NOUN
ejpam-3660	84	13	=	=	SYM
ejpam-3660	84	14	{	{	PUNCT
ejpam-3660	84	15	x	x	NOUN
ejpam-3660	84	16	∈	∈	PROPN
ejpam-3660	84	17	h|µa(x	h|µa(x	NOUN
ejpam-3660	84	18	)	)	PUNCT
ejpam-3660	84	19	≥	≥	PROPN
ejpam-3660	84	20	t	t	PROPN
ejpam-3660	84	21	,	,	PUNCT
ejpam-3660	84	22	γa(x	γa(x	NUM
ejpam-3660	84	23	)	)	PUNCT
ejpam-3660	84	24	≤	≤	NOUN
ejpam-3660	85	1	s	s	VERB
ejpam-3660	85	2	}	}	PUNCT
ejpam-3660	85	3	is	be	AUX
ejpam-3660	85	4	called	call	VERB
ejpam-3660	85	5	a	a	DET
ejpam-3660	85	6	level	level	NOUN
ejpam-3660	85	7	subset	subset	NOUN
ejpam-3660	85	8	of	of	ADP
ejpam-3660	85	9	a.	a.	NOUN
ejpam-3660	85	10	3	3	NUM
ejpam-3660	85	11	.	.	PUNCT
ejpam-3660	85	12	fuzzy	fuzzy	ADJ
ejpam-3660	85	13	hyper	hyper	ADJ
ejpam-3660	85	14	gr	gr	NOUN
ejpam-3660	85	15	-	-	PUNCT
ejpam-3660	85	16	ideals	ideal	NOUN
ejpam-3660	85	17	of	of	ADP
ejpam-3660	85	18	type	type	NOUN
ejpam-3660	85	19	1	1	NUM
ejpam-3660	85	20	definition	definition	NOUN
ejpam-3660	85	21	3.1	3.1	NUM
ejpam-3660	85	22	.	.	PUNCT
ejpam-3660	86	1	a	a	DET
ejpam-3660	86	2	fuzzy	fuzzy	ADJ
ejpam-3660	86	3	set	set	VERB
ejpam-3660	86	4	µ	µ	NOUN
ejpam-3660	86	5	in	in	ADP
ejpam-3660	86	6	a	a	DET
ejpam-3660	86	7	hyper	hyper	ADJ
ejpam-3660	86	8	gr	gr	NOUN
ejpam-3660	86	9	-	-	PUNCT
ejpam-3660	86	10	algebra	algebra	NOUN
ejpam-3660	86	11	h	h	NOUN
ejpam-3660	86	12	is	be	AUX
ejpam-3660	86	13	a	a	DET
ejpam-3660	86	14	fuzzy	fuzzy	ADJ
ejpam-3660	86	15	hyper	hyper	ADJ
ejpam-3660	86	16	gr	gr	NOUN
ejpam-3660	86	17	-	-	PUNCT
ejpam-3660	86	18	ideal	ideal	NOUN
ejpam-3660	86	19	of	of	ADP
ejpam-3660	86	20	type	type	NOUN
ejpam-3660	86	21	1	1	NUM
ejpam-3660	86	22	if	if	SCONJ
ejpam-3660	86	23	for	for	ADP
ejpam-3660	86	24	all	all	DET
ejpam-3660	86	25	x	x	NOUN
ejpam-3660	86	26	,	,	PUNCT
ejpam-3660	86	27	y	y	PROPN
ejpam-3660	86	28	∈	∈	PROPN
ejpam-3660	86	29	h	h	NOUN
ejpam-3660	86	30	,	,	PUNCT
ejpam-3660	86	31	(	(	PUNCT
ejpam-3660	86	32	f1	f1	NOUN
ejpam-3660	86	33	)	)	PUNCT
ejpam-3660	86	34	µ(0	µ(0	PROPN
ejpam-3660	86	35	)	)	PUNCT
ejpam-3660	86	36	≥	≥	NOUN
ejpam-3660	86	37	µ(x	µ(x	NOUN
ejpam-3660	86	38	)	)	PUNCT
ejpam-3660	86	39	≥	≥	NOUN
ejpam-3660	86	40	min	min	PROPN
ejpam-3660	86	41	{	{	PUNCT
ejpam-3660	86	42	inf	inf	NOUN
ejpam-3660	86	43	u∈x	u∈x	PROPN
ejpam-3660	86	44	~	~	PROPN
ejpam-3660	86	45	y	y	PROPN
ejpam-3660	86	46	µ(u	µ(u	PROPN
ejpam-3660	86	47	)	)	PUNCT
ejpam-3660	86	48	,	,	PUNCT
ejpam-3660	86	49	µ(y	µ(y	PROPN
ejpam-3660	86	50	)	)	PUNCT
ejpam-3660	86	51	}	}	PUNCT
ejpam-3660	86	52	.	.	PUNCT
ejpam-3660	87	1	example	example	NOUN
ejpam-3660	87	2	3.2	3.2	NUM
ejpam-3660	87	3	.	.	PUNCT
ejpam-3660	88	1	let	let	VERB
ejpam-3660	88	2	h	h	NOUN
ejpam-3660	88	3	=	=	PUNCT
ejpam-3660	89	1	[	[	X
ejpam-3660	89	2	0	0	NUM
ejpam-3660	89	3	,	,	PUNCT
ejpam-3660	89	4	1	1	NUM
ejpam-3660	89	5	]	]	PUNCT
ejpam-3660	89	6	such	such	ADJ
ejpam-3660	89	7	that	that	PRON
ejpam-3660	89	8	for	for	ADP
ejpam-3660	89	9	any	any	DET
ejpam-3660	89	10	a	a	NOUN
ejpam-3660	89	11	,	,	PUNCT
ejpam-3660	89	12	b	b	X
ejpam-3660	89	13	∈	∈	PROPN
ejpam-3660	90	1	[	[	X
ejpam-3660	90	2	0	0	NUM
ejpam-3660	90	3	,	,	PUNCT
ejpam-3660	90	4	1	1	NUM
ejpam-3660	90	5	]	]	PUNCT
ejpam-3660	90	6	,	,	PUNCT
ejpam-3660	90	7	a	a	DET
ejpam-3660	90	8	~	~	PUNCT
ejpam-3660	90	9	b	b	X
ejpam-3660	90	10	=	=	SYM
ejpam-3660	90	11	{	{	PUNCT
ejpam-3660	90	12	[	[	X
ejpam-3660	90	13	0	0	NUM
ejpam-3660	90	14	,	,	PUNCT
ejpam-3660	90	15	0.3	0.3	NUM
ejpam-3660	90	16	]	]	PUNCT
ejpam-3660	90	17	,	,	PUNCT
ejpam-3660	90	18	if	if	SCONJ
ejpam-3660	90	19	b	b	X
ejpam-3660	90	20	,	,	PUNCT
ejpam-3660	90	21	0	0	NUM
ejpam-3660	90	22	or	or	CCONJ
ejpam-3660	90	23	a	a	DET
ejpam-3660	90	24	=	=	SYM
ejpam-3660	90	25	0	0	NUM
ejpam-3660	90	26	=	=	SYM
ejpam-3660	90	27	b	b	NOUN
ejpam-3660	90	28	;	;	PUNCT
ejpam-3660	90	29	{	{	PUNCT
ejpam-3660	90	30	a	a	X
ejpam-3660	90	31	}	}	PUNCT
ejpam-3660	90	32	,	,	PUNCT
ejpam-3660	90	33	if	if	SCONJ
ejpam-3660	90	34	a	a	PRON
ejpam-3660	90	35	,	,	PUNCT
ejpam-3660	90	36	0	0	NUM
ejpam-3660	90	37	and	and	CCONJ
ejpam-3660	90	38	b	b	X
ejpam-3660	90	39	=	=	SYM
ejpam-3660	90	40	0	0	PROPN
ejpam-3660	90	41	.	.	PUNCT
ejpam-3660	91	1	it	it	PRON
ejpam-3660	91	2	can	can	AUX
ejpam-3660	91	3	be	be	AUX
ejpam-3660	91	4	seen	see	VERB
ejpam-3660	91	5	that	that	SCONJ
ejpam-3660	91	6	h	h	NOUN
ejpam-3660	91	7	is	be	AUX
ejpam-3660	91	8	a	a	DET
ejpam-3660	91	9	hyper	hyper	ADJ
ejpam-3660	91	10	gr	gr	NOUN
ejpam-3660	91	11	-	-	NOUN
ejpam-3660	91	12	algebra	algebra	NOUN
ejpam-3660	91	13	.	.	PUNCT
ejpam-3660	92	1	define	define	VERB
ejpam-3660	92	2	a	a	DET
ejpam-3660	92	3	fuzzy	fuzzy	ADJ
ejpam-3660	92	4	set	set	VERB
ejpam-3660	92	5	µ	µ	NOUN
ejpam-3660	92	6	in	in	ADP
ejpam-3660	92	7	h	h	NOUN
ejpam-3660	92	8	by	by	ADP
ejpam-3660	92	9	µ(a	µ(a	PROPN
ejpam-3660	92	10	)	)	PUNCT
ejpam-3660	92	11	=	=	PRON
ejpam-3660	92	12	{	{	PUNCT
ejpam-3660	92	13	l	l	NOUN
ejpam-3660	92	14	,	,	PUNCT
ejpam-3660	92	15	if	if	SCONJ
ejpam-3660	92	16	a	a	PRON
ejpam-3660	92	17	=	=	NOUN
ejpam-3660	92	18	0	0	NUM
ejpam-3660	93	1	k	k	NOUN
ejpam-3660	93	2	,	,	PUNCT
ejpam-3660	93	3	if	if	SCONJ
ejpam-3660	93	4	a	a	PRON
ejpam-3660	93	5	,	,	PUNCT
ejpam-3660	93	6	0	0	X
ejpam-3660	93	7	.	.	PUNCT
ejpam-3660	94	1	where	where	SCONJ
ejpam-3660	94	2	k	k	NOUN
ejpam-3660	94	3	,	,	PUNCT
ejpam-3660	94	4	l	l	PROPN
ejpam-3660	94	5	∈	∈	PROPN
ejpam-3660	95	1	[	[	X
ejpam-3660	95	2	0	0	NUM
ejpam-3660	95	3	,	,	PUNCT
ejpam-3660	95	4	1	1	NUM
ejpam-3660	95	5	]	]	PUNCT
ejpam-3660	95	6	and	and	CCONJ
ejpam-3660	95	7	k	k	X
ejpam-3660	95	8	<	<	X
ejpam-3660	95	9	l.	l.	PROPN
ejpam-3660	95	10	by	by	ADP
ejpam-3660	95	11	routine	routine	ADJ
ejpam-3660	95	12	calculations	calculation	NOUN
ejpam-3660	95	13	,	,	PUNCT
ejpam-3660	95	14	we	we	PRON
ejpam-3660	95	15	see	see	VERB
ejpam-3660	95	16	thatµ	thatµ	PROPN
ejpam-3660	95	17	is	be	AUX
ejpam-3660	95	18	a	a	DET
ejpam-3660	95	19	fuzzy	fuzzy	ADJ
ejpam-3660	95	20	hyper	hyper	ADJ
ejpam-3660	95	21	gr	gr	NOUN
ejpam-3660	95	22	-	-	PUNCT
ejpam-3660	95	23	ideal	ideal	NOUN
ejpam-3660	95	24	of	of	ADP
ejpam-3660	95	25	type	type	NOUN
ejpam-3660	95	26	1	1	NUM
ejpam-3660	95	27	in	in	ADP
ejpam-3660	95	28	h.	h.	PROPN
ejpam-3660	95	29	example	example	NOUN
ejpam-3660	95	30	3.3	3.3	NUM
ejpam-3660	95	31	.	.	PUNCT
ejpam-3660	96	1	consider	consider	VERB
ejpam-3660	96	2	the	the	DET
ejpam-3660	96	3	hyper	hyper	ADJ
ejpam-3660	96	4	gr	gr	NOUN
ejpam-3660	96	5	-	-	PUNCT
ejpam-3660	96	6	algebra	algebra	NOUN
ejpam-3660	96	7	h	h	NOUN
ejpam-3660	96	8	in	in	ADP
ejpam-3660	96	9	example	example	NOUN
ejpam-3660	96	10	3.2	3.2	NUM
ejpam-3660	96	11	.	.	PUNCT
ejpam-3660	97	1	define	define	VERB
ejpam-3660	97	2	a	a	DET
ejpam-3660	97	3	fuzzy	fuzzy	ADJ
ejpam-3660	97	4	set	set	VERB
ejpam-3660	97	5	µ	µ	NOUN
ejpam-3660	97	6	in	in	ADP
ejpam-3660	97	7	h	h	NOUN
ejpam-3660	97	8	by	by	ADP
ejpam-3660	97	9	µ(x	µ(x	NOUN
ejpam-3660	97	10	)	)	PUNCT
ejpam-3660	97	11	=	=	SYM
ejpam-3660	98	1			PROPN
ejpam-3660	98	2	1	1	NUM
ejpam-3660	98	3	,	,	PUNCT
ejpam-3660	98	4	if	if	SCONJ
ejpam-3660	98	5	x	x	ADP
ejpam-3660	98	6	=	=	SYM
ejpam-3660	98	7	0	0	NUM
ejpam-3660	98	8	,	,	PUNCT
ejpam-3660	98	9	0.3	0.3	NUM
ejpam-3660	98	10	+	+	CCONJ
ejpam-3660	98	11	x	x	X
ejpam-3660	98	12	,	,	PUNCT
ejpam-3660	98	13	if	if	SCONJ
ejpam-3660	98	14	x	x	SYM
ejpam-3660	98	15	∈	∈	PROPN
ejpam-3660	98	16	(	(	PUNCT
ejpam-3660	98	17	0	0	NUM
ejpam-3660	98	18	,	,	PUNCT
ejpam-3660	98	19	0.3	0.3	NUM
ejpam-3660	98	20	]	]	PUNCT
ejpam-3660	98	21	,	,	PUNCT
ejpam-3660	98	22	0.7	0.7	NUM
ejpam-3660	98	23	,	,	PUNCT
ejpam-3660	98	24	if	if	SCONJ
ejpam-3660	98	25	x	x	SYM
ejpam-3660	98	26	∈	∈	PROPN
ejpam-3660	98	27	(	(	PUNCT
ejpam-3660	98	28	0.3	0.3	NUM
ejpam-3660	98	29	,	,	PUNCT
ejpam-3660	98	30	1	1	NUM
ejpam-3660	98	31	]	]	PUNCT
ejpam-3660	98	32	.	.	PUNCT
ejpam-3660	99	1	it	it	PRON
ejpam-3660	99	2	can	can	AUX
ejpam-3660	99	3	be	be	AUX
ejpam-3660	99	4	shown	show	VERB
ejpam-3660	99	5	that	that	SCONJ
ejpam-3660	99	6	µ	µ	NOUN
ejpam-3660	99	7	is	be	AUX
ejpam-3660	99	8	a	a	DET
ejpam-3660	99	9	fuzzy	fuzzy	ADJ
ejpam-3660	99	10	hyper	hyper	ADJ
ejpam-3660	99	11	gr	gr	NOUN
ejpam-3660	99	12	-	-	PUNCT
ejpam-3660	99	13	ideal	ideal	NOUN
ejpam-3660	99	14	of	of	ADP
ejpam-3660	99	15	type	type	NOUN
ejpam-3660	99	16	1	1	NUM
ejpam-3660	99	17	in	in	ADP
ejpam-3660	99	18	h.	h.	PROPN
ejpam-3660	99	19	proposition	proposition	PROPN
ejpam-3660	99	20	3.4	3.4	NUM
ejpam-3660	99	21	.	.	PUNCT
ejpam-3660	100	1	let	let	VERB
ejpam-3660	100	2	h	h	PRON
ejpam-3660	100	3	be	be	AUX
ejpam-3660	100	4	a	a	DET
ejpam-3660	100	5	hyper	hyper	ADJ
ejpam-3660	100	6	gr	gr	NOUN
ejpam-3660	100	7	-	-	NOUN
ejpam-3660	100	8	algebra	algebra	NOUN
ejpam-3660	100	9	.	.	PUNCT
ejpam-3660	101	1	if	if	SCONJ
ejpam-3660	101	2	µ	µ	NOUN
ejpam-3660	101	3	is	be	AUX
ejpam-3660	101	4	a	a	DET
ejpam-3660	101	5	fuzzy	fuzzy	ADJ
ejpam-3660	101	6	hyper	hyper	ADJ
ejpam-3660	101	7	gr	gr	NOUN
ejpam-3660	101	8	-	-	PUNCT
ejpam-3660	101	9	ideal	ideal	NOUN
ejpam-3660	101	10	of	of	ADP
ejpam-3660	101	11	type	type	NOUN
ejpam-3660	101	12	1	1	NUM
ejpam-3660	101	13	in	in	ADP
ejpam-3660	101	14	h	h	NOUN
ejpam-3660	101	15	such	such	ADJ
ejpam-3660	101	16	that	that	DET
ejpam-3660	101	17	inf	inf	PROPN
ejpam-3660	101	18	u∈x	u∈x	NOUN
ejpam-3660	101	19	~	~	SYM
ejpam-3660	101	20	y	y	PROPN
ejpam-3660	101	21	µ(u	µ(u	PROPN
ejpam-3660	101	22	)	)	PUNCT
ejpam-3660	101	23	=	=	SYM
ejpam-3660	101	24	µ(0	µ(0	NOUN
ejpam-3660	101	25	)	)	PUNCT
ejpam-3660	101	26	=	=	SYM
ejpam-3660	101	27	inf	inf	NOUN
ejpam-3660	101	28	u∈y	u∈y	NOUN
ejpam-3660	101	29	~	~	PROPN
ejpam-3660	101	30	x	x	SYM
ejpam-3660	101	31	µ(u	µ(u	NOUN
ejpam-3660	101	32	)	)	PUNCT
ejpam-3660	101	33	for	for	ADP
ejpam-3660	101	34	x	x	SYM
ejpam-3660	101	35	,	,	PUNCT
ejpam-3660	101	36	y	y	PROPN
ejpam-3660	101	37	,	,	PUNCT
ejpam-3660	101	38	then	then	ADV
ejpam-3660	101	39	µ(x	µ(x	X
ejpam-3660	101	40	)	)	PUNCT
ejpam-3660	101	41	=	=	SYM
ejpam-3660	101	42	µ(y	µ(y	PROPN
ejpam-3660	101	43	)	)	PUNCT
ejpam-3660	101	44	.	.	PUNCT
ejpam-3660	102	1	proof	proof	NOUN
ejpam-3660	102	2	.	.	PUNCT
ejpam-3660	103	1	let	let	VERB
ejpam-3660	103	2	x	x	PRON
ejpam-3660	103	3	,	,	PUNCT
ejpam-3660	103	4	y	y	PROPN
ejpam-3660	103	5	∈	∈	PROPN
ejpam-3660	103	6	h	h	NOUN
ejpam-3660	104	1	such	such	ADJ
ejpam-3660	104	2	that	that	SCONJ
ejpam-3660	104	3	x	x	SYM
ejpam-3660	104	4	,	,	PUNCT
ejpam-3660	104	5	y	y	PROPN
ejpam-3660	104	6	and	and	CCONJ
ejpam-3660	104	7	inf	inf	PROPN
ejpam-3660	104	8	u∈x	u∈x	PROPN
ejpam-3660	104	9	~	~	SYM
ejpam-3660	104	10	y	y	PROPN
ejpam-3660	104	11	µ(u	µ(u	PROPN
ejpam-3660	104	12	)	)	PUNCT
ejpam-3660	104	13	=	=	SYM
ejpam-3660	104	14	µ(0	µ(0	NOUN
ejpam-3660	104	15	)	)	PUNCT
ejpam-3660	104	16	=	=	SYM
ejpam-3660	104	17	inf	inf	NOUN
ejpam-3660	104	18	u∈y	u∈y	NOUN
ejpam-3660	104	19	~	~	PROPN
ejpam-3660	104	20	x	x	SYM
ejpam-3660	104	21	µ(u	µ(u	NOUN
ejpam-3660	104	22	)	)	PUNCT
ejpam-3660	104	23	.	.	PUNCT
ejpam-3660	105	1	by	by	ADP
ejpam-3660	105	2	f1	f1	NOUN
ejpam-3660	105	3	,	,	PUNCT
ejpam-3660	105	4	µ(x	µ(x	NOUN
ejpam-3660	105	5	)	)	PUNCT
ejpam-3660	105	6	≥	≥	NOUN
ejpam-3660	105	7	min	min	PROPN
ejpam-3660	105	8	{	{	PUNCT
ejpam-3660	105	9	inf	inf	NOUN
ejpam-3660	105	10	u∈x	u∈x	PROPN
ejpam-3660	105	11	~	~	PROPN
ejpam-3660	105	12	y	y	PROPN
ejpam-3660	105	13	µ(u	µ(u	PROPN
ejpam-3660	105	14	)	)	PUNCT
ejpam-3660	105	15	,	,	PUNCT
ejpam-3660	105	16	µ(y	µ(y	PROPN
ejpam-3660	105	17	)	)	PUNCT
ejpam-3660	105	18	}	}	PUNCT
ejpam-3660	105	19	=	=	SYM
ejpam-3660	105	20	min{µ(0	min{µ(0	NOUN
ejpam-3660	105	21	)	)	PUNCT
ejpam-3660	105	22	,	,	PUNCT
ejpam-3660	105	23	µ(y	µ(y	PROPN
ejpam-3660	105	24	)	)	PUNCT
ejpam-3660	105	25	}	}	PUNCT
ejpam-3660	105	26	=	=	SYM
ejpam-3660	105	27	µ(y	µ(y	NOUN
ejpam-3660	105	28	)	)	PUNCT
ejpam-3660	105	29	and	and	CCONJ
ejpam-3660	105	30	µ(y	µ(y	PROPN
ejpam-3660	105	31	)	)	PUNCT
ejpam-3660	105	32	≥	≥	NOUN
ejpam-3660	105	33	min	min	PROPN
ejpam-3660	105	34	{	{	PUNCT
ejpam-3660	105	35	inf	inf	NOUN
ejpam-3660	105	36	u∈y	u∈y	PROPN
ejpam-3660	105	37	~	~	PROPN
ejpam-3660	105	38	x	x	SYM
ejpam-3660	105	39	µ(u	µ(u	NOUN
ejpam-3660	105	40	)	)	PUNCT
ejpam-3660	105	41	,	,	PUNCT
ejpam-3660	105	42	µ(x	µ(x	X
ejpam-3660	105	43	)	)	PUNCT
ejpam-3660	105	44	}	}	PUNCT
ejpam-3660	105	45	=	=	SYM
ejpam-3660	105	46	min{µ(0	min{µ(0	NOUN
ejpam-3660	105	47	)	)	PUNCT
ejpam-3660	105	48	,	,	PUNCT
ejpam-3660	105	49	µ(x	µ(x	NOUN
ejpam-3660	105	50	)	)	PUNCT
ejpam-3660	105	51	}	}	PUNCT
ejpam-3660	105	52	=	=	SYM
ejpam-3660	105	53	µ(x	µ(x	NUM
ejpam-3660	105	54	)	)	PUNCT
ejpam-3660	105	55	.	.	PUNCT
ejpam-3660	106	1	a.	a.	NOUN
ejpam-3660	106	2	macodi	macodi	PROPN
ejpam-3660	106	3	-	-	PUNCT
ejpam-3660	106	4	ringia	ringia	ADJ
ejpam-3660	106	5	,	,	PUNCT
ejpam-3660	106	6	g.	g.	PROPN
ejpam-3660	106	7	petalcorin	petalcorin	PROPN
ejpam-3660	106	8	,	,	PUNCT
ejpam-3660	106	9	jr	jr	PROPN
ejpam-3660	106	10	.	.	PROPN
ejpam-3660	106	11	/	/	SYM
ejpam-3660	106	12	eur	eur	PROPN
ejpam-3660	106	13	.	.	PUNCT
ejpam-3660	107	1	j.	j.	PROPN
ejpam-3660	107	2	pure	pure	PROPN
ejpam-3660	107	3	appl	appl	PROPN
ejpam-3660	107	4	.	.	PROPN
ejpam-3660	107	5	math	math	PROPN
ejpam-3660	107	6	,	,	PUNCT
ejpam-3660	107	7	13	13	NUM
ejpam-3660	107	8	(	(	PUNCT
ejpam-3660	107	9	2	2	NUM
ejpam-3660	107	10	)	)	PUNCT
ejpam-3660	107	11	(	(	PUNCT
ejpam-3660	107	12	2020	2020	NUM
ejpam-3660	107	13	)	)	PUNCT
ejpam-3660	107	14	,	,	PUNCT
ejpam-3660	107	15	246	246	NUM
ejpam-3660	107	16	-	-	SYM
ejpam-3660	107	17	257	257	NUM
ejpam-3660	107	18	250	250	NUM
ejpam-3660	107	19	thus	thus	ADV
ejpam-3660	107	20	,	,	PUNCT
ejpam-3660	107	21	µ(x	µ(x	X
ejpam-3660	107	22	)	)	PUNCT
ejpam-3660	107	23	=	=	SYM
ejpam-3660	107	24	µ(y	µ(y	PROPN
ejpam-3660	107	25	)	)	PUNCT
ejpam-3660	107	26	.	.	PUNCT
ejpam-3660	108	1	�	�	PROPN
ejpam-3660	108	2	theorem	theorem	VERB
ejpam-3660	108	3	3.5	3.5	NUM
ejpam-3660	108	4	.	.	PUNCT
ejpam-3660	109	1	a	a	DET
ejpam-3660	109	2	fuzzy	fuzzy	ADJ
ejpam-3660	109	3	set	set	VERB
ejpam-3660	109	4	µ	µ	NOUN
ejpam-3660	109	5	in	in	ADP
ejpam-3660	109	6	a	a	DET
ejpam-3660	109	7	hyper	hyper	ADJ
ejpam-3660	109	8	gr	gr	NOUN
ejpam-3660	109	9	-	-	PUNCT
ejpam-3660	109	10	algebra	algebra	NOUN
ejpam-3660	109	11	h	h	NOUN
ejpam-3660	109	12	is	be	AUX
ejpam-3660	109	13	a	a	DET
ejpam-3660	109	14	fuzzy	fuzzy	ADJ
ejpam-3660	109	15	hyper	hyper	ADJ
ejpam-3660	109	16	gr	gr	NOUN
ejpam-3660	109	17	-	-	PUNCT
ejpam-3660	109	18	ideal	ideal	NOUN
ejpam-3660	109	19	of	of	ADP
ejpam-3660	109	20	type	type	NOUN
ejpam-3660	109	21	1	1	NUM
ejpam-3660	109	22	if	if	SCONJ
ejpam-3660	109	23	and	and	CCONJ
ejpam-3660	109	24	only	only	ADV
ejpam-3660	109	25	if	if	SCONJ
ejpam-3660	109	26	µt	µt	PRON
ejpam-3660	109	27	is	be	AUX
ejpam-3660	109	28	a	a	DET
ejpam-3660	109	29	hyper	hyper	ADJ
ejpam-3660	109	30	gr	gr	NOUN
ejpam-3660	109	31	-	-	PUNCT
ejpam-3660	109	32	ideal	ideal	NOUN
ejpam-3660	109	33	of	of	ADP
ejpam-3660	109	34	h	h	NOUN
ejpam-3660	109	35	whenever	whenever	SCONJ
ejpam-3660	109	36	µt	µt	X
ejpam-3660	109	37	,	,	PUNCT
ejpam-3660	109	38	∅	∅	NOUN
ejpam-3660	109	39	and	and	CCONJ
ejpam-3660	109	40	t	t	NOUN
ejpam-3660	109	41	∈	∈	PROPN
ejpam-3660	110	1	[	[	X
ejpam-3660	110	2	0	0	NUM
ejpam-3660	110	3	,	,	PUNCT
ejpam-3660	110	4	1	1	NUM
ejpam-3660	110	5	]	]	PUNCT
ejpam-3660	110	6	.	.	PUNCT
ejpam-3660	111	1	proof	proof	NOUN
ejpam-3660	111	2	.	.	PUNCT
ejpam-3660	112	1	suppose	suppose	VERB
ejpam-3660	112	2	µ	µ	PRON
ejpam-3660	112	3	is	be	AUX
ejpam-3660	112	4	a	a	DET
ejpam-3660	112	5	fuzzy	fuzzy	ADJ
ejpam-3660	112	6	hyper	hyper	ADJ
ejpam-3660	112	7	gr	gr	NOUN
ejpam-3660	112	8	-	-	PUNCT
ejpam-3660	112	9	ideal	ideal	NOUN
ejpam-3660	112	10	of	of	ADP
ejpam-3660	112	11	type	type	NOUN
ejpam-3660	112	12	1	1	NUM
ejpam-3660	112	13	.	.	PUNCT
ejpam-3660	113	1	let	let	VERB
ejpam-3660	113	2	t	t	PROPN
ejpam-3660	113	3	∈	∈	PROPN
ejpam-3660	114	1	[	[	X
ejpam-3660	114	2	0	0	NUM
ejpam-3660	114	3	,	,	PUNCT
ejpam-3660	114	4	1	1	NUM
ejpam-3660	114	5	]	]	PUNCT
ejpam-3660	114	6	such	such	ADJ
ejpam-3660	114	7	that	that	SCONJ
ejpam-3660	114	8	µt	µt	PROPN
ejpam-3660	114	9	,	,	PUNCT
ejpam-3660	114	10	∅.	∅.	PROPN
ejpam-3660	114	11	then	then	ADV
ejpam-3660	114	12	there	there	PRON
ejpam-3660	114	13	exists	exist	VERB
ejpam-3660	114	14	a	a	DET
ejpam-3660	114	15	∈	∈	ADJ
ejpam-3660	114	16	µt	µt	PROPN
ejpam-3660	114	17	.	.	PUNCT
ejpam-3660	114	18	by	by	ADP
ejpam-3660	114	19	f1,µ(0	f1,µ(0	NOUN
ejpam-3660	114	20	)	)	PUNCT
ejpam-3660	114	21	≥	≥	NOUN
ejpam-3660	114	22	µ(a	µ(a	NOUN
ejpam-3660	114	23	)	)	PUNCT
ejpam-3660	114	24	≥	≥	NOUN
ejpam-3660	115	1	t.	t.	NOUN
ejpam-3660	115	2	then	then	ADV
ejpam-3660	115	3	,	,	PUNCT
ejpam-3660	115	4	0	0	NUM
ejpam-3660	115	5	∈	∈	PROPN
ejpam-3660	115	6	µt	µt	PROPN
ejpam-3660	115	7	.	.	PUNCT
ejpam-3660	115	8	let	let	VERB
ejpam-3660	115	9	x	x	PRON
ejpam-3660	115	10	,	,	PUNCT
ejpam-3660	115	11	y	y	PROPN
ejpam-3660	115	12	∈	∈	PROPN
ejpam-3660	115	13	h	h	NOUN
ejpam-3660	115	14	such	such	ADJ
ejpam-3660	115	15	that	that	SCONJ
ejpam-3660	115	16	x	x	X
ejpam-3660	115	17	~	~	PUNCT
ejpam-3660	115	18	y	y	PRON
ejpam-3660	115	19	⊆	⊆	NUM
ejpam-3660	115	20	µt	µt	ADJ
ejpam-3660	115	21	and	and	CCONJ
ejpam-3660	115	22	y	y	PROPN
ejpam-3660	115	23	∈	∈	PROPN
ejpam-3660	115	24	µt	µt	PROPN
ejpam-3660	115	25	.	.	PUNCT
ejpam-3660	115	26	then	then	ADV
ejpam-3660	115	27	µ(y	µ(y	PROPN
ejpam-3660	115	28	)	)	PUNCT
ejpam-3660	115	29	≥	≥	NOUN
ejpam-3660	115	30	t	t	NOUN
ejpam-3660	115	31	and	and	CCONJ
ejpam-3660	115	32	µ(u	µ(u	NOUN
ejpam-3660	115	33	)	)	PUNCT
ejpam-3660	115	34	≥	≥	NOUN
ejpam-3660	115	35	t	t	NOUN
ejpam-3660	115	36	for	for	ADP
ejpam-3660	115	37	any	any	DET
ejpam-3660	115	38	u	u	NOUN
ejpam-3660	115	39	∈	∈	PROPN
ejpam-3660	115	40	x	x	PRON
ejpam-3660	115	41	~	~	PUNCT
ejpam-3660	115	42	y.	y.	NOUN
ejpam-3660	115	43	this	this	PRON
ejpam-3660	115	44	implies	imply	VERB
ejpam-3660	115	45	that	that	SCONJ
ejpam-3660	115	46	t	t	PROPN
ejpam-3660	115	47	is	be	AUX
ejpam-3660	115	48	a	a	DET
ejpam-3660	115	49	lowerbound	lowerbound	NOUN
ejpam-3660	115	50	of	of	ADP
ejpam-3660	115	51	{	{	PUNCT
ejpam-3660	115	52	µ(u	µ(u	NOUN
ejpam-3660	115	53	)	)	PUNCT
ejpam-3660	115	54	:	:	PUNCT
ejpam-3660	115	55	u	u	NOUN
ejpam-3660	115	56	∈	∈	PROPN
ejpam-3660	115	57	x	x	X
ejpam-3660	115	58	~	~	PUNCT
ejpam-3660	115	59	y	y	X
ejpam-3660	115	60	}	}	PUNCT
ejpam-3660	115	61	.	.	PUNCT
ejpam-3660	116	1	thus	thus	ADV
ejpam-3660	116	2	,	,	PUNCT
ejpam-3660	116	3	inf	inf	PROPN
ejpam-3660	116	4	u∈x	u∈x	NOUN
ejpam-3660	116	5	~	~	SYM
ejpam-3660	116	6	y	y	PROPN
ejpam-3660	116	7	µ(u	µ(u	PROPN
ejpam-3660	116	8	)	)	PUNCT
ejpam-3660	116	9	≥	≥	NOUN
ejpam-3660	116	10	t.	t.	NOUN
ejpam-3660	116	11	by	by	ADP
ejpam-3660	116	12	f1,µ(x	f1,µ(x	NOUN
ejpam-3660	116	13	)	)	PUNCT
ejpam-3660	116	14	≥	≥	PROPN
ejpam-3660	116	15	min	min	PROPN
ejpam-3660	116	16	{	{	PUNCT
ejpam-3660	116	17	inf	inf	NOUN
ejpam-3660	116	18	u∈x	u∈x	PROPN
ejpam-3660	116	19	~	~	PROPN
ejpam-3660	116	20	y	y	PROPN
ejpam-3660	116	21	µ(u	µ(u	PROPN
ejpam-3660	116	22	)	)	PUNCT
ejpam-3660	116	23	,	,	PUNCT
ejpam-3660	116	24	µ(y	µ(y	PROPN
ejpam-3660	116	25	)	)	PUNCT
ejpam-3660	116	26	}	}	PUNCT
ejpam-3660	116	27	≥	≥	NOUN
ejpam-3660	116	28	min{t	min{t	PROPN
ejpam-3660	116	29	,	,	PUNCT
ejpam-3660	116	30	t	t	PROPN
ejpam-3660	116	31	}	}	PUNCT
ejpam-3660	116	32	=	=	SYM
ejpam-3660	116	33	t.	t.	NOUN
ejpam-3660	116	34	hence	hence	ADV
ejpam-3660	116	35	,	,	PUNCT
ejpam-3660	116	36	x	x	PUNCT
ejpam-3660	116	37	∈	∈	ADJ
ejpam-3660	116	38	µt	µt	X
ejpam-3660	116	39	and	and	CCONJ
ejpam-3660	116	40	so	so	ADV
ejpam-3660	116	41	µt	µt	PRON
ejpam-3660	116	42	is	be	AUX
ejpam-3660	116	43	a	a	DET
ejpam-3660	116	44	hyper	hyper	ADJ
ejpam-3660	116	45	gr	gr	NOUN
ejpam-3660	116	46	-	-	PUNCT
ejpam-3660	116	47	ideal	ideal	NOUN
ejpam-3660	116	48	of	of	ADP
ejpam-3660	116	49	h.	h.	NOUN
ejpam-3660	116	50	conversely	conversely	ADV
ejpam-3660	116	51	,	,	PUNCT
ejpam-3660	116	52	let	let	VERB
ejpam-3660	116	53	µt	µt	PART
ejpam-3660	116	54	be	be	AUX
ejpam-3660	116	55	a	a	DET
ejpam-3660	116	56	hyper	hyper	ADJ
ejpam-3660	116	57	gr	gr	NOUN
ejpam-3660	116	58	-	-	PUNCT
ejpam-3660	116	59	ideal	ideal	NOUN
ejpam-3660	116	60	of	of	ADP
ejpam-3660	116	61	h	h	NOUN
ejpam-3660	116	62	for	for	ADP
ejpam-3660	116	63	any	any	DET
ejpam-3660	116	64	t	t	NOUN
ejpam-3660	116	65	∈	∈	PROPN
ejpam-3660	117	1	[	[	X
ejpam-3660	117	2	0	0	NUM
ejpam-3660	117	3	,	,	PUNCT
ejpam-3660	117	4	1	1	NUM
ejpam-3660	117	5	]	]	PUNCT
ejpam-3660	117	6	.	.	PUNCT
ejpam-3660	118	1	let	let	VERB
ejpam-3660	118	2	x	x	SYM
ejpam-3660	118	3	∈	∈	PROPN
ejpam-3660	118	4	h	h	NOUN
ejpam-3660	118	5	and	and	CCONJ
ejpam-3660	118	6	let	let	VERB
ejpam-3660	118	7	k	k	PROPN
ejpam-3660	118	8	∈	∈	PROPN
ejpam-3660	119	1	[	[	X
ejpam-3660	119	2	0	0	NUM
ejpam-3660	119	3	,	,	PUNCT
ejpam-3660	119	4	1	1	NUM
ejpam-3660	119	5	]	]	PUNCT
ejpam-3660	119	6	such	such	ADJ
ejpam-3660	119	7	that	that	SCONJ
ejpam-3660	119	8	k	k	PROPN
ejpam-3660	119	9	=	=	PUNCT
ejpam-3660	119	10	µ(x	µ(x	X
ejpam-3660	119	11	)	)	PUNCT
ejpam-3660	119	12	.	.	PUNCT
ejpam-3660	120	1	since	since	SCONJ
ejpam-3660	120	2	0	0	NUM
ejpam-3660	120	3	∈	∈	PROPN
ejpam-3660	120	4	µk	µk	NOUN
ejpam-3660	120	5	,	,	PUNCT
ejpam-3660	120	6	µ(0	µ(0	PROPN
ejpam-3660	120	7	)	)	PUNCT
ejpam-3660	120	8	≥	≥	NOUN
ejpam-3660	120	9	k	k	NOUN
ejpam-3660	120	10	=	=	PUNCT
ejpam-3660	120	11	µ(x	µ(x	X
ejpam-3660	120	12	)	)	PUNCT
ejpam-3660	120	13	.	.	PUNCT
ejpam-3660	121	1	moreover	moreover	ADV
ejpam-3660	121	2	,	,	PUNCT
ejpam-3660	121	3	let	let	VERB
ejpam-3660	121	4	x	x	PRON
ejpam-3660	121	5	,	,	PUNCT
ejpam-3660	121	6	y	y	PROPN
ejpam-3660	121	7	,	,	PUNCT
ejpam-3660	121	8	z	z	PROPN
ejpam-3660	121	9	∈	∈	PROPN
ejpam-3660	121	10	h	h	NOUN
ejpam-3660	121	11	and	and	CCONJ
ejpam-3660	121	12	let	let	VERB
ejpam-3660	121	13	l	l	NOUN
ejpam-3660	121	14	∈	∈	PROPN
ejpam-3660	122	1	[	[	X
ejpam-3660	122	2	0	0	NUM
ejpam-3660	122	3	,	,	PUNCT
ejpam-3660	122	4	1	1	NUM
ejpam-3660	122	5	]	]	PUNCT
ejpam-3660	122	6	such	such	ADJ
ejpam-3660	122	7	that	that	SCONJ
ejpam-3660	122	8	l	l	NOUN
ejpam-3660	122	9	=	=	SYM
ejpam-3660	122	10	min	min	PROPN
ejpam-3660	122	11	{	{	PUNCT
ejpam-3660	122	12	inf	inf	NOUN
ejpam-3660	122	13	u∈x	u∈x	PROPN
ejpam-3660	122	14	~	~	PROPN
ejpam-3660	122	15	y	y	PROPN
ejpam-3660	122	16	µ(u	µ(u	PROPN
ejpam-3660	122	17	)	)	PUNCT
ejpam-3660	122	18	,	,	PUNCT
ejpam-3660	122	19	µ(y	µ(y	PROPN
ejpam-3660	122	20	)	)	PUNCT
ejpam-3660	122	21	}	}	PUNCT
ejpam-3660	122	22	.	.	PUNCT
ejpam-3660	123	1	since	since	SCONJ
ejpam-3660	123	2	µ(y	µ(y	PROPN
ejpam-3660	123	3	)	)	PUNCT
ejpam-3660	123	4	≥	≥	NOUN
ejpam-3660	123	5	min	min	PROPN
ejpam-3660	123	6	{	{	PUNCT
ejpam-3660	123	7	inf	inf	NOUN
ejpam-3660	123	8	u∈x	u∈x	PROPN
ejpam-3660	123	9	~	~	PROPN
ejpam-3660	123	10	y	y	PROPN
ejpam-3660	123	11	µ(u	µ(u	PROPN
ejpam-3660	123	12	)	)	PUNCT
ejpam-3660	123	13	,	,	PUNCT
ejpam-3660	123	14	µ(y	µ(y	PROPN
ejpam-3660	123	15	)	)	PUNCT
ejpam-3660	123	16	}	}	PUNCT
ejpam-3660	123	17	=	=	SYM
ejpam-3660	123	18	l	l	NOUN
ejpam-3660	123	19	,	,	PUNCT
ejpam-3660	123	20	y	y	PROPN
ejpam-3660	123	21	∈	∈	PROPN
ejpam-3660	123	22	µl	µl	NOUN
ejpam-3660	123	23	.	.	PUNCT
ejpam-3660	124	1	let	let	VERB
ejpam-3660	124	2	w	w	NOUN
ejpam-3660	124	3	∈	∈	NOUN
ejpam-3660	124	4	x	x	X
ejpam-3660	124	5	~	~	PUNCT
ejpam-3660	124	6	y.	y.	NOUN
ejpam-3660	124	7	then	then	ADV
ejpam-3660	124	8	µ(w	µ(w	NUM
ejpam-3660	124	9	)	)	PUNCT
ejpam-3660	124	10	≥	≥	PROPN
ejpam-3660	124	11	inf	inf	PROPN
ejpam-3660	124	12	u∈x	u∈x	PROPN
ejpam-3660	124	13	~	~	PROPN
ejpam-3660	124	14	y	y	PROPN
ejpam-3660	124	15	µ(u	µ(u	PROPN
ejpam-3660	124	16	)	)	PUNCT
ejpam-3660	124	17	≥	≥	PROPN
ejpam-3660	124	18	min	min	PROPN
ejpam-3660	124	19	{	{	PUNCT
ejpam-3660	124	20	inf	inf	NOUN
ejpam-3660	124	21	u∈x	u∈x	PROPN
ejpam-3660	124	22	~	~	PROPN
ejpam-3660	124	23	y	y	PROPN
ejpam-3660	124	24	µ(u	µ(u	PROPN
ejpam-3660	124	25	)	)	PUNCT
ejpam-3660	124	26	,	,	PUNCT
ejpam-3660	124	27	µ(y	µ(y	PROPN
ejpam-3660	124	28	)	)	PUNCT
ejpam-3660	124	29	}	}	PUNCT
ejpam-3660	124	30	=	=	PUNCT
ejpam-3660	125	1	l.	l.	PROPN
ejpam-3660	125	2	it	it	PRON
ejpam-3660	125	3	follows	follow	VERB
ejpam-3660	125	4	that	that	SCONJ
ejpam-3660	125	5	w	w	PROPN
ejpam-3660	125	6	∈	∈	PROPN
ejpam-3660	125	7	µl	µl	ADP
ejpam-3660	125	8	and	and	CCONJ
ejpam-3660	125	9	so	so	ADV
ejpam-3660	125	10	x	x	X
ejpam-3660	125	11	~	~	PUNCT
ejpam-3660	125	12	y	y	PROPN
ejpam-3660	125	13	⊆	⊆	NUM
ejpam-3660	125	14	µl	µl	NOUN
ejpam-3660	125	15	.	.	PUNCT
ejpam-3660	126	1	since	since	SCONJ
ejpam-3660	126	2	µl	µl	ADV
ejpam-3660	126	3	is	be	AUX
ejpam-3660	126	4	a	a	DET
ejpam-3660	126	5	hyper	hyper	ADJ
ejpam-3660	126	6	gr	gr	NOUN
ejpam-3660	126	7	-	-	PUNCT
ejpam-3660	126	8	ideal	ideal	NOUN
ejpam-3660	126	9	of	of	ADP
ejpam-3660	126	10	h	h	NOUN
ejpam-3660	126	11	,	,	PUNCT
ejpam-3660	126	12	x	x	SYM
ejpam-3660	126	13	∈	∈	NOUN
ejpam-3660	126	14	µl	µl	NOUN
ejpam-3660	126	15	.	.	PUNCT
ejpam-3660	127	1	it	it	PRON
ejpam-3660	127	2	implies	imply	VERB
ejpam-3660	127	3	that	that	SCONJ
ejpam-3660	127	4	µ(x	µ(x	VERB
ejpam-3660	127	5	)	)	PUNCT
ejpam-3660	127	6	≥	≥	NOUN
ejpam-3660	127	7	l	l	NOUN
ejpam-3660	127	8	=	=	SYM
ejpam-3660	127	9	min	min	PROPN
ejpam-3660	127	10	{	{	PUNCT
ejpam-3660	127	11	inf	inf	NOUN
ejpam-3660	127	12	u∈x	u∈x	PROPN
ejpam-3660	127	13	~	~	PROPN
ejpam-3660	127	14	y	y	PROPN
ejpam-3660	127	15	µ(u	µ(u	PROPN
ejpam-3660	127	16	)	)	PUNCT
ejpam-3660	127	17	,	,	PUNCT
ejpam-3660	127	18	µ(y	µ(y	PROPN
ejpam-3660	127	19	)	)	PUNCT
ejpam-3660	127	20	}	}	PUNCT
ejpam-3660	127	21	.	.	PUNCT
ejpam-3660	128	1	thus	thus	ADV
ejpam-3660	128	2	,	,	PUNCT
ejpam-3660	128	3	µ	µ	X
ejpam-3660	128	4	is	be	AUX
ejpam-3660	128	5	a	a	DET
ejpam-3660	128	6	fuzzy	fuzzy	ADJ
ejpam-3660	128	7	hyper	hyper	ADJ
ejpam-3660	128	8	gr	gr	NOUN
ejpam-3660	128	9	-	-	PUNCT
ejpam-3660	128	10	ideal	ideal	NOUN
ejpam-3660	128	11	of	of	ADP
ejpam-3660	128	12	type	type	NOUN
ejpam-3660	128	13	1	1	NUM
ejpam-3660	128	14	.	.	PUNCT
ejpam-3660	128	15	�	�	PROPN
ejpam-3660	128	16	corollary	corollary	ADJ
ejpam-3660	128	17	3.6	3.6	NUM
ejpam-3660	128	18	.	.	PUNCT
ejpam-3660	129	1	for	for	ADP
ejpam-3660	129	2	any	any	DET
ejpam-3660	129	3	nonempty	nonempty	NOUN
ejpam-3660	129	4	subset	subset	VERB
ejpam-3660	129	5	a	a	PRON
ejpam-3660	129	6	of	of	ADP
ejpam-3660	129	7	h	h	NOUN
ejpam-3660	129	8	,	,	PUNCT
ejpam-3660	129	9	let	let	VERB
ejpam-3660	129	10	µa	µa	PART
ejpam-3660	129	11	be	be	AUX
ejpam-3660	129	12	a	a	DET
ejpam-3660	129	13	fuzzy	fuzzy	ADJ
ejpam-3660	129	14	set	set	NOUN
ejpam-3660	129	15	in	in	ADP
ejpam-3660	129	16	hyper	hyper	ADJ
ejpam-3660	129	17	gr	gr	PROPN
ejpam-3660	129	18	-	-	PUNCT
ejpam-3660	129	19	algebra	algebra	NOUN
ejpam-3660	129	20	h	h	NOUN
ejpam-3660	129	21	defined	define	VERB
ejpam-3660	129	22	by	by	ADP
ejpam-3660	129	23	µa(x	µa(x	NOUN
ejpam-3660	129	24	)	)	PUNCT
ejpam-3660	129	25	=	=	PRON
ejpam-3660	129	26	{	{	PUNCT
ejpam-3660	129	27	n	n	CCONJ
ejpam-3660	129	28	,	,	PUNCT
ejpam-3660	129	29	if	if	SCONJ
ejpam-3660	129	30	x	x	PROPN
ejpam-3660	129	31	∈	∈	PROPN
ejpam-3660	129	32	a	a	PRON
ejpam-3660	129	33	,	,	PUNCT
ejpam-3660	129	34	m	m	PRON
ejpam-3660	129	35	,	,	PUNCT
ejpam-3660	129	36	otherwise	otherwise	ADV
ejpam-3660	129	37	,	,	PUNCT
ejpam-3660	129	38	for	for	ADP
ejpam-3660	129	39	all	all	DET
ejpam-3660	129	40	x	x	SYM
ejpam-3660	129	41	∈	∈	PROPN
ejpam-3660	129	42	h	h	NOUN
ejpam-3660	129	43	where	where	SCONJ
ejpam-3660	129	44	n	n	CCONJ
ejpam-3660	129	45	,	,	PUNCT
ejpam-3660	129	46	m	m	VERB
ejpam-3660	129	47	∈	∈	NOUN
ejpam-3660	130	1	[	[	X
ejpam-3660	130	2	0	0	NUM
ejpam-3660	130	3	,	,	PUNCT
ejpam-3660	130	4	1	1	NUM
ejpam-3660	130	5	]	]	PUNCT
ejpam-3660	130	6	with	with	ADP
ejpam-3660	130	7	n	n	PROPN
ejpam-3660	130	8	>	>	X
ejpam-3660	130	9	m.	m.	NOUN
ejpam-3660	130	10	then	then	ADV
ejpam-3660	130	11	a	a	PRON
ejpam-3660	130	12	is	be	AUX
ejpam-3660	130	13	a	a	DET
ejpam-3660	130	14	hyper	hyper	ADJ
ejpam-3660	130	15	gr	gr	NOUN
ejpam-3660	130	16	-	-	PUNCT
ejpam-3660	130	17	ideal	ideal	NOUN
ejpam-3660	130	18	of	of	ADP
ejpam-3660	130	19	h	h	NOUN
ejpam-3660	130	20	if	if	SCONJ
ejpam-3660	131	1	and	and	CCONJ
ejpam-3660	131	2	only	only	ADV
ejpam-3660	131	3	if	if	SCONJ
ejpam-3660	131	4	µa	µa	NOUN
ejpam-3660	131	5	is	be	AUX
ejpam-3660	131	6	a	a	DET
ejpam-3660	131	7	fuzzy	fuzzy	ADJ
ejpam-3660	131	8	hyper	hyper	ADJ
ejpam-3660	131	9	gr	gr	NOUN
ejpam-3660	131	10	-	-	PUNCT
ejpam-3660	131	11	ideal	ideal	NOUN
ejpam-3660	131	12	of	of	ADP
ejpam-3660	131	13	type	type	NOUN
ejpam-3660	131	14	1	1	NUM
ejpam-3660	131	15	in	in	ADP
ejpam-3660	131	16	h.	h.	NOUN
ejpam-3660	131	17	proof	proof	NOUN
ejpam-3660	131	18	.	.	PUNCT
ejpam-3660	132	1	note	note	VERB
ejpam-3660	132	2	that	that	SCONJ
ejpam-3660	132	3	(	(	PUNCT
ejpam-3660	132	4	µa)t	µa)t	ADV
ejpam-3660	132	5	=	=	SYM
ejpam-3660	132	6			PROPN
ejpam-3660	132	7	∅	∅	NOUN
ejpam-3660	132	8	,	,	PUNCT
ejpam-3660	132	9	if	if	SCONJ
ejpam-3660	132	10	n	n	ADV
ejpam-3660	132	11	<	<	X
ejpam-3660	132	12	t	t	X
ejpam-3660	132	13	≤	≤	NUM
ejpam-3660	132	14	1	1	NUM
ejpam-3660	132	15	,	,	PUNCT
ejpam-3660	132	16	a	a	PRON
ejpam-3660	132	17	,	,	PUNCT
ejpam-3660	132	18	if	if	SCONJ
ejpam-3660	132	19	m	m	VERB
ejpam-3660	132	20	<	<	X
ejpam-3660	132	21	t	t	X
ejpam-3660	132	22	≤	≤	NUM
ejpam-3660	132	23	n	n	CCONJ
ejpam-3660	132	24	,	,	PUNCT
ejpam-3660	132	25	h	h	NOUN
ejpam-3660	132	26	,	,	PUNCT
ejpam-3660	132	27	if	if	SCONJ
ejpam-3660	132	28	0	0	NUM
ejpam-3660	132	29	≤	≤	NUM
ejpam-3660	132	30	t	t	NOUN
ejpam-3660	132	31	≤	≤	NUM
ejpam-3660	132	32	m	m	VERB
ejpam-3660	132	33	(	(	PUNCT
ejpam-3660	132	34	1	1	NUM
ejpam-3660	132	35	)	)	PUNCT
ejpam-3660	132	36	are	be	AUX
ejpam-3660	132	37	all	all	PRON
ejpam-3660	132	38	possible	possible	ADJ
ejpam-3660	132	39	level	level	NOUN
ejpam-3660	132	40	subsets	subset	NOUN
ejpam-3660	132	41	of	of	ADP
ejpam-3660	132	42	µa	µa	PRON
ejpam-3660	132	43	where	where	SCONJ
ejpam-3660	132	44	t	t	PROPN
ejpam-3660	132	45	∈	∈	PROPN
ejpam-3660	133	1	[	[	X
ejpam-3660	133	2	0	0	NUM
ejpam-3660	133	3	,	,	PUNCT
ejpam-3660	133	4	1	1	NUM
ejpam-3660	133	5	]	]	PUNCT
ejpam-3660	133	6	.	.	PUNCT
ejpam-3660	134	1	then	then	ADV
ejpam-3660	134	2	,	,	PUNCT
ejpam-3660	134	3	(	(	PUNCT
ejpam-3660	134	4	µa)t	µa)t	ADV
ejpam-3660	134	5	=	=	PRON
ejpam-3660	134	6	a	a	PRON
ejpam-3660	134	7	is	be	AUX
ejpam-3660	134	8	a	a	DET
ejpam-3660	134	9	nonempty	nonempty	ADJ
ejpam-3660	134	10	level	level	NOUN
ejpam-3660	134	11	subsets	subset	NOUN
ejpam-3660	134	12	of	of	ADP
ejpam-3660	134	13	µa	µa	PROPN
ejpam-3660	134	14	.	.	PUNCT
ejpam-3660	135	1	thus	thus	ADV
ejpam-3660	135	2	,	,	PUNCT
ejpam-3660	135	3	by	by	ADP
ejpam-3660	135	4	theorem	theorem	NOUN
ejpam-3660	135	5	3.5	3.5	NUM
ejpam-3660	135	6	,	,	PUNCT
ejpam-3660	135	7	a	a	PRON
ejpam-3660	135	8	is	be	AUX
ejpam-3660	135	9	a	a	DET
ejpam-3660	135	10	hyper	hyper	ADJ
ejpam-3660	135	11	gr	gr	NOUN
ejpam-3660	135	12	-	-	PUNCT
ejpam-3660	135	13	ideal	ideal	NOUN
ejpam-3660	135	14	of	of	ADP
ejpam-3660	135	15	h	h	NOUN
ejpam-3660	135	16	if	if	SCONJ
ejpam-3660	136	1	and	and	CCONJ
ejpam-3660	136	2	only	only	ADV
ejpam-3660	136	3	if	if	SCONJ
ejpam-3660	136	4	µa	µa	NOUN
ejpam-3660	136	5	is	be	AUX
ejpam-3660	136	6	a	a	DET
ejpam-3660	136	7	fuzzy	fuzzy	ADJ
ejpam-3660	136	8	hyper	hyper	ADJ
ejpam-3660	136	9	gr	gr	NOUN
ejpam-3660	136	10	-	-	PUNCT
ejpam-3660	136	11	ideal	ideal	NOUN
ejpam-3660	136	12	of	of	ADP
ejpam-3660	136	13	type	type	NOUN
ejpam-3660	136	14	1	1	NUM
ejpam-3660	136	15	in	in	ADP
ejpam-3660	136	16	h.	h.	PROPN
ejpam-3660	136	17	�	�	PROPN
ejpam-3660	136	18	theorem	theorem	VERB
ejpam-3660	136	19	3.7	3.7	NUM
ejpam-3660	136	20	.	.	PUNCT
ejpam-3660	137	1	if	if	SCONJ
ejpam-3660	137	2	µ	µ	NOUN
ejpam-3660	137	3	is	be	AUX
ejpam-3660	137	4	a	a	DET
ejpam-3660	137	5	fuzzy	fuzzy	ADJ
ejpam-3660	137	6	hyper	hyper	ADJ
ejpam-3660	137	7	gr	gr	NOUN
ejpam-3660	137	8	-	-	PUNCT
ejpam-3660	137	9	ideal	ideal	NOUN
ejpam-3660	137	10	of	of	ADP
ejpam-3660	137	11	type	type	NOUN
ejpam-3660	137	12	1	1	NUM
ejpam-3660	137	13	of	of	ADP
ejpam-3660	137	14	a	a	DET
ejpam-3660	137	15	hyper	hyper	ADJ
ejpam-3660	137	16	gr	gr	NOUN
ejpam-3660	137	17	-	-	PUNCT
ejpam-3660	137	18	algebra	algebra	NOUN
ejpam-3660	137	19	h	h	NOUN
ejpam-3660	137	20	,	,	PUNCT
ejpam-3660	137	21	then	then	ADV
ejpam-3660	137	22	the	the	DET
ejpam-3660	137	23	set	set	NOUN
ejpam-3660	137	24	a	a	X
ejpam-3660	137	25	=	=	SYM
ejpam-3660	137	26	{	{	PUNCT
ejpam-3660	137	27	x	x	PUNCT
ejpam-3660	137	28	∈	∈	NOUN
ejpam-3660	137	29	h|µ(x	h|µ(x	NOUN
ejpam-3660	137	30	)	)	PUNCT
ejpam-3660	137	31	=	=	SYM
ejpam-3660	137	32	µ(0	µ(0	NOUN
ejpam-3660	137	33	)	)	PUNCT
ejpam-3660	137	34	}	}	PUNCT
ejpam-3660	137	35	is	be	AUX
ejpam-3660	137	36	a	a	DET
ejpam-3660	137	37	hyper	hyper	ADJ
ejpam-3660	137	38	gr	gr	NOUN
ejpam-3660	137	39	-	-	PUNCT
ejpam-3660	137	40	ideal	ideal	NOUN
ejpam-3660	137	41	of	of	ADP
ejpam-3660	137	42	h.	h.	NOUN
ejpam-3660	137	43	proof	proof	NOUN
ejpam-3660	137	44	.	.	PUNCT
ejpam-3660	138	1	suppose	suppose	VERB
ejpam-3660	138	2	µ	µ	PRON
ejpam-3660	138	3	is	be	AUX
ejpam-3660	138	4	a	a	DET
ejpam-3660	138	5	fuzzy	fuzzy	ADJ
ejpam-3660	138	6	hyper	hyper	ADJ
ejpam-3660	138	7	gr	gr	NOUN
ejpam-3660	138	8	-	-	PUNCT
ejpam-3660	138	9	ideal	ideal	NOUN
ejpam-3660	138	10	of	of	ADP
ejpam-3660	138	11	type	type	NOUN
ejpam-3660	138	12	1	1	NUM
ejpam-3660	138	13	of	of	ADP
ejpam-3660	138	14	a	a	DET
ejpam-3660	138	15	hyper	hyper	ADJ
ejpam-3660	138	16	gr	gr	NOUN
ejpam-3660	138	17	-	-	PUNCT
ejpam-3660	138	18	algebra	algebra	NOUN
ejpam-3660	138	19	h.	h.	NOUN
ejpam-3660	138	20	let	let	VERB
ejpam-3660	138	21	x	x	PRON
ejpam-3660	138	22	,	,	PUNCT
ejpam-3660	138	23	y	y	PROPN
ejpam-3660	138	24	∈	∈	PROPN
ejpam-3660	138	25	h	h	NOUN
ejpam-3660	138	26	such	such	ADJ
ejpam-3660	138	27	that	that	SCONJ
ejpam-3660	138	28	x	x	X
ejpam-3660	138	29	~	~	PUNCT
ejpam-3660	138	30	y	y	PROPN
ejpam-3660	138	31	⊆	⊆	NUM
ejpam-3660	138	32	a	a	PRON
ejpam-3660	138	33	and	and	CCONJ
ejpam-3660	138	34	y	y	PROPN
ejpam-3660	138	35	∈	∈	PROPN
ejpam-3660	138	36	a.	a.	NOUN
ejpam-3660	138	37	then	then	ADV
ejpam-3660	138	38	µ(y	µ(y	PROPN
ejpam-3660	138	39	)	)	PUNCT
ejpam-3660	138	40	=	=	PUNCT
ejpam-3660	138	41	µ(0	µ(0	NOUN
ejpam-3660	138	42	)	)	PUNCT
ejpam-3660	138	43	and	and	CCONJ
ejpam-3660	138	44	µ(u	µ(u	NOUN
ejpam-3660	138	45	)	)	PUNCT
ejpam-3660	139	1	=	=	SYM
ejpam-3660	139	2	µ(0	µ(0	NOUN
ejpam-3660	139	3	)	)	PUNCT
ejpam-3660	139	4	for	for	ADP
ejpam-3660	139	5	all	all	DET
ejpam-3660	139	6	u	u	NOUN
ejpam-3660	139	7	∈	∈	NOUN
ejpam-3660	139	8	x	x	X
ejpam-3660	139	9	~	~	PUNCT
ejpam-3660	139	10	y.	y.	NOUN
ejpam-3660	139	11	by	by	ADP
ejpam-3660	139	12	the	the	DET
ejpam-3660	139	13	hypothesis	hypothesis	NOUN
ejpam-3660	139	14	,	,	PUNCT
ejpam-3660	139	15	µ(0	µ(0	NOUN
ejpam-3660	139	16	)	)	PUNCT
ejpam-3660	139	17	≥	≥	NOUN
ejpam-3660	139	18	µ(x	µ(x	NOUN
ejpam-3660	139	19	)	)	PUNCT
ejpam-3660	139	20	≥	≥	NOUN
ejpam-3660	139	21	min	min	PROPN
ejpam-3660	139	22	{	{	PUNCT
ejpam-3660	139	23	inf	inf	NOUN
ejpam-3660	139	24	u∈x	u∈x	PROPN
ejpam-3660	139	25	~	~	PROPN
ejpam-3660	139	26	y	y	PROPN
ejpam-3660	139	27	µ(u	µ(u	PROPN
ejpam-3660	139	28	)	)	PUNCT
ejpam-3660	139	29	,	,	PUNCT
ejpam-3660	139	30	µ(y	µ(y	PROPN
ejpam-3660	139	31	)	)	PUNCT
ejpam-3660	139	32	}	}	PUNCT
ejpam-3660	139	33	=	=	PUNCT
ejpam-3660	139	34	µ(0	µ(0	NOUN
ejpam-3660	139	35	)	)	PUNCT
ejpam-3660	139	36	.	.	PUNCT
ejpam-3660	140	1	hence	hence	ADV
ejpam-3660	140	2	,	,	PUNCT
ejpam-3660	140	3	µ(x	µ(x	X
ejpam-3660	140	4	)	)	PUNCT
ejpam-3660	140	5	=	=	SYM
ejpam-3660	140	6	µ(0	µ(0	NOUN
ejpam-3660	140	7	)	)	PUNCT
ejpam-3660	140	8	and	and	CCONJ
ejpam-3660	140	9	so	so	ADV
ejpam-3660	140	10	x	x	SYM
ejpam-3660	140	11	∈	∈	NOUN
ejpam-3660	140	12	a.	a.	NOUN
ejpam-3660	140	13	thus	thus	ADV
ejpam-3660	140	14	,	,	PUNCT
ejpam-3660	140	15	a	a	PRON
ejpam-3660	140	16	is	be	AUX
ejpam-3660	140	17	a	a	DET
ejpam-3660	140	18	hyper	hyper	ADJ
ejpam-3660	140	19	gr	gr	NOUN
ejpam-3660	140	20	-	-	PUNCT
ejpam-3660	140	21	ideal	ideal	NOUN
ejpam-3660	140	22	of	of	ADP
ejpam-3660	140	23	h.	h.	PROPN
ejpam-3660	140	24	�	�	PROPN
ejpam-3660	140	25	a.	a.	PROPN
ejpam-3660	140	26	macodi	macodi	PROPN
ejpam-3660	140	27	-	-	PUNCT
ejpam-3660	140	28	ringia	ringia	ADJ
ejpam-3660	140	29	,	,	PUNCT
ejpam-3660	140	30	g.	g.	PROPN
ejpam-3660	140	31	petalcorin	petalcorin	PROPN
ejpam-3660	140	32	,	,	PUNCT
ejpam-3660	140	33	jr	jr	PROPN
ejpam-3660	140	34	.	.	PROPN
ejpam-3660	140	35	/	/	SYM
ejpam-3660	140	36	eur	eur	PROPN
ejpam-3660	140	37	.	.	PUNCT
ejpam-3660	141	1	j.	j.	PROPN
ejpam-3660	141	2	pure	pure	PROPN
ejpam-3660	141	3	appl	appl	PROPN
ejpam-3660	141	4	.	.	PROPN
ejpam-3660	141	5	math	math	PROPN
ejpam-3660	141	6	,	,	PUNCT
ejpam-3660	141	7	13	13	NUM
ejpam-3660	141	8	(	(	PUNCT
ejpam-3660	141	9	2	2	NUM
ejpam-3660	141	10	)	)	PUNCT
ejpam-3660	141	11	(	(	PUNCT
ejpam-3660	141	12	2020	2020	NUM
ejpam-3660	141	13	)	)	PUNCT
ejpam-3660	141	14	,	,	PUNCT
ejpam-3660	141	15	246	246	NUM
ejpam-3660	141	16	-	-	SYM
ejpam-3660	141	17	257	257	NUM
ejpam-3660	141	18	251	251	NUM
ejpam-3660	141	19	4	4	NUM
ejpam-3660	141	20	.	.	PUNCT
ejpam-3660	142	1	intuitionistic	intuitionistic	ADJ
ejpam-3660	142	2	fuzzy	fuzzy	ADJ
ejpam-3660	142	3	hyper	hyper	ADJ
ejpam-3660	142	4	gr	gr	ADJ
ejpam-3660	142	5	-	-	PUNCT
ejpam-3660	142	6	ideals	ideal	NOUN
ejpam-3660	142	7	definition	definition	NOUN
ejpam-3660	142	8	4.1	4.1	NUM
ejpam-3660	142	9	.	.	PUNCT
ejpam-3660	143	1	an	an	DET
ejpam-3660	143	2	intuitionistic	intuitionistic	ADJ
ejpam-3660	143	3	fuzzy	fuzzy	NOUN
ejpam-3660	143	4	set	set	VERB
ejpam-3660	143	5	a	a	PRON
ejpam-3660	143	6	=	=	X
ejpam-3660	143	7	(	(	PUNCT
ejpam-3660	143	8	µa	µa	PROPN
ejpam-3660	143	9	,	,	PUNCT
ejpam-3660	143	10	γa	γa	NOUN
ejpam-3660	143	11	)	)	PUNCT
ejpam-3660	143	12	in	in	ADP
ejpam-3660	143	13	a	a	DET
ejpam-3660	143	14	hyper	hyper	ADJ
ejpam-3660	143	15	gr	gr	NOUN
ejpam-3660	143	16	-	-	PUNCT
ejpam-3660	143	17	algebra	algebra	NOUN
ejpam-3660	143	18	h	h	NOUN
ejpam-3660	143	19	is	be	AUX
ejpam-3660	143	20	an	an	DET
ejpam-3660	143	21	intuitionistic	intuitionistic	ADJ
ejpam-3660	143	22	fuzzy	fuzzy	ADJ
ejpam-3660	143	23	hyper	hyper	ADJ
ejpam-3660	143	24	gr	gr	NOUN
ejpam-3660	143	25	-	-	PUNCT
ejpam-3660	143	26	ideal	ideal	NOUN
ejpam-3660	143	27	if	if	SCONJ
ejpam-3660	143	28	for	for	ADP
ejpam-3660	143	29	all	all	DET
ejpam-3660	143	30	x	x	NOUN
ejpam-3660	143	31	,	,	PUNCT
ejpam-3660	143	32	y	y	PROPN
ejpam-3660	143	33	∈	∈	PROPN
ejpam-3660	143	34	h	h	NOUN
ejpam-3660	143	35	the	the	DET
ejpam-3660	143	36	following	follow	VERB
ejpam-3660	143	37	hold	hold	NOUN
ejpam-3660	143	38	:	:	PUNCT
ejpam-3660	143	39	(	(	PUNCT
ejpam-3660	143	40	ifgr1	ifgr1	X
ejpam-3660	143	41	)	)	PUNCT
ejpam-3660	143	42	µa(0	µa(0	NOUN
ejpam-3660	143	43	)	)	PUNCT
ejpam-3660	143	44	≥	≥	NOUN
ejpam-3660	143	45	µa(x	µa(x	NOUN
ejpam-3660	143	46	)	)	PUNCT
ejpam-3660	143	47	and	and	CCONJ
ejpam-3660	143	48	γa(0	γa(0	NOUN
ejpam-3660	143	49	)	)	PUNCT
ejpam-3660	143	50	≤	≤	NOUN
ejpam-3660	143	51	γa(x	γa(x	NUM
ejpam-3660	143	52	)	)	PUNCT
ejpam-3660	143	53	;	;	PUNCT
ejpam-3660	143	54	(	(	PUNCT
ejpam-3660	143	55	ifgr2	ifgr2	NOUN
ejpam-3660	143	56	)	)	PUNCT
ejpam-3660	143	57	µa(x	µa(x	NOUN
ejpam-3660	143	58	)	)	PUNCT
ejpam-3660	143	59	≥	≥	PROPN
ejpam-3660	143	60	min	min	PROPN
ejpam-3660	143	61	{	{	PUNCT
ejpam-3660	143	62	inf	inf	NOUN
ejpam-3660	143	63	u∈x	u∈x	NOUN
ejpam-3660	143	64	~	~	PROPN
ejpam-3660	143	65	y	y	PROPN
ejpam-3660	143	66	µa(u	µa(u	NOUN
ejpam-3660	143	67	)	)	PUNCT
ejpam-3660	143	68	,	,	PUNCT
ejpam-3660	143	69	µa(y	µa(y	NOUN
ejpam-3660	143	70	)	)	PUNCT
ejpam-3660	143	71	}	}	PUNCT
ejpam-3660	143	72	;	;	PUNCT
ejpam-3660	143	73	and	and	CCONJ
ejpam-3660	143	74	(	(	PUNCT
ejpam-3660	143	75	ifgr3	ifgr3	NOUN
ejpam-3660	143	76	)	)	PUNCT
ejpam-3660	143	77	γa(x	γa(x	NUM
ejpam-3660	143	78	)	)	PUNCT
ejpam-3660	143	79	≤	≤	NUM
ejpam-3660	144	1	max	max	PROPN
ejpam-3660	144	2			PUNCT
ejpam-3660	144	3	sup	sup	NOUN
ejpam-3660	144	4	v∈x	v∈x	NOUN
ejpam-3660	144	5	~	~	SYM
ejpam-3660	144	6	y	y	PROPN
ejpam-3660	144	7	γa(v	γa(v	PUNCT
ejpam-3660	144	8	)	)	PUNCT
ejpam-3660	144	9	,	,	PUNCT
ejpam-3660	144	10	γa(y	γa(y	X
ejpam-3660	144	11	)	)	PUNCT
ejpam-3660	144	12	.	.	PROPN
ejpam-3660	144	13	for	for	ADP
ejpam-3660	144	14	the	the	DET
ejpam-3660	144	15	sake	sake	NOUN
ejpam-3660	144	16	of	of	ADP
ejpam-3660	144	17	simplicity	simplicity	NOUN
ejpam-3660	144	18	,	,	PUNCT
ejpam-3660	144	19	we	we	PRON
ejpam-3660	144	20	shall	shall	AUX
ejpam-3660	144	21	use	use	VERB
ejpam-3660	144	22	the	the	DET
ejpam-3660	144	23	symbol	symbol	NOUN
ejpam-3660	144	24	a	a	PRON
ejpam-3660	144	25	=	=	X
ejpam-3660	144	26	(	(	PUNCT
ejpam-3660	144	27	µa	µa	PROPN
ejpam-3660	144	28	,	,	PUNCT
ejpam-3660	144	29	γa	γa	PROPN
ejpam-3660	144	30	)	)	PUNCT
ejpam-3660	144	31	for	for	ADP
ejpam-3660	144	32	the	the	DET
ejpam-3660	144	33	intuitionistic	intuitionistic	ADJ
ejpam-3660	144	34	fuzzy	fuzzy	ADJ
ejpam-3660	144	35	set	set	VERB
ejpam-3660	144	36	a	a	PRON
ejpam-3660	144	37	=	=	X
ejpam-3660	144	38	{	{	PUNCT
ejpam-3660	144	39	(	(	PUNCT
ejpam-3660	144	40	x	x	NOUN
ejpam-3660	144	41	,	,	PUNCT
ejpam-3660	144	42	µa(x	µa(x	NOUN
ejpam-3660	144	43	)	)	PUNCT
ejpam-3660	144	44	,	,	PUNCT
ejpam-3660	144	45	γa(x))|x	γa(x))|x	PROPN
ejpam-3660	144	46	∈	∈	PROPN
ejpam-3660	144	47	h	h	NOUN
ejpam-3660	144	48	}	}	PUNCT
ejpam-3660	144	49	.	.	PUNCT
ejpam-3660	145	1	example	example	NOUN
ejpam-3660	145	2	4.2	4.2	NUM
ejpam-3660	145	3	.	.	PUNCT
ejpam-3660	146	1	consider	consider	VERB
ejpam-3660	146	2	the	the	DET
ejpam-3660	146	3	hyper	hyper	ADJ
ejpam-3660	146	4	gr	gr	NOUN
ejpam-3660	146	5	-	-	PUNCT
ejpam-3660	146	6	algebra	algebra	NOUN
ejpam-3660	146	7	h	h	NOUN
ejpam-3660	146	8	in	in	ADP
ejpam-3660	146	9	example	example	NOUN
ejpam-3660	146	10	3.3	3.3	NUM
ejpam-3660	146	11	and	and	CCONJ
ejpam-3660	146	12	its	its	PRON
ejpam-3660	146	13	fuzzy	fuzzy	ADJ
ejpam-3660	146	14	set	set	VERB
ejpam-3660	146	15	µ.	µ.	NOUN
ejpam-3660	146	16	let	let	VERB
ejpam-3660	146	17	a	a	DET
ejpam-3660	146	18	=	=	SYM
ejpam-3660	146	19	(	(	PUNCT
ejpam-3660	146	20	µa	µa	PROPN
ejpam-3660	146	21	,	,	PUNCT
ejpam-3660	146	22	γa	γa	NOUN
ejpam-3660	146	23	)	)	PUNCT
ejpam-3660	146	24	in	in	ADP
ejpam-3660	146	25	h	h	NOUN
ejpam-3660	146	26	be	be	AUX
ejpam-3660	146	27	an	an	DET
ejpam-3660	146	28	intuitionistic	intuitionistic	ADJ
ejpam-3660	146	29	fuzzy	fuzzy	ADJ
ejpam-3660	146	30	set	set	NOUN
ejpam-3660	146	31	where	where	SCONJ
ejpam-3660	146	32	µa	µa	NOUN
ejpam-3660	146	33	=	=	SYM
ejpam-3660	146	34	µ	µ	X
ejpam-3660	146	35	and	and	CCONJ
ejpam-3660	146	36	γa(x	γa(x	NUM
ejpam-3660	146	37	)	)	PUNCT
ejpam-3660	146	38	=	=	PUNCT
ejpam-3660	147	1			PROPN
ejpam-3660	147	2	0	0	NUM
ejpam-3660	147	3	,	,	PUNCT
ejpam-3660	147	4	if	if	SCONJ
ejpam-3660	147	5	x	x	ADP
ejpam-3660	147	6	=	=	SYM
ejpam-3660	147	7	0	0	NUM
ejpam-3660	147	8	,	,	PUNCT
ejpam-3660	147	9	0.7	0.7	NUM
ejpam-3660	147	10	−	−	NOUN
ejpam-3660	147	11	x	x	SYM
ejpam-3660	147	12	,	,	PUNCT
ejpam-3660	147	13	if	if	SCONJ
ejpam-3660	147	14	x	x	SYM
ejpam-3660	147	15	∈	∈	PROPN
ejpam-3660	147	16	(	(	PUNCT
ejpam-3660	147	17	0	0	NUM
ejpam-3660	147	18	,	,	PUNCT
ejpam-3660	147	19	0.3	0.3	NUM
ejpam-3660	147	20	]	]	PUNCT
ejpam-3660	147	21	,	,	PUNCT
ejpam-3660	147	22	0.1	0.1	NUM
ejpam-3660	147	23	,	,	PUNCT
ejpam-3660	147	24	if	if	SCONJ
ejpam-3660	147	25	x	x	SYM
ejpam-3660	147	26	∈	∈	PROPN
ejpam-3660	147	27	(	(	PUNCT
ejpam-3660	147	28	0.3	0.3	NUM
ejpam-3660	147	29	,	,	PUNCT
ejpam-3660	147	30	1	1	NUM
ejpam-3660	147	31	]	]	PUNCT
ejpam-3660	147	32	.	.	PUNCT
ejpam-3660	148	1	by	by	ADP
ejpam-3660	148	2	routine	routine	ADJ
ejpam-3660	148	3	calculations	calculation	NOUN
ejpam-3660	148	4	,	,	PUNCT
ejpam-3660	148	5	a	a	PRON
ejpam-3660	148	6	is	be	AUX
ejpam-3660	148	7	an	an	DET
ejpam-3660	148	8	intuitionistic	intuitionistic	ADJ
ejpam-3660	148	9	fuzzy	fuzzy	ADJ
ejpam-3660	148	10	hyper	hyper	ADJ
ejpam-3660	148	11	gr	gr	NOUN
ejpam-3660	148	12	-	-	PUNCT
ejpam-3660	148	13	ideal	ideal	NOUN
ejpam-3660	148	14	in	in	ADP
ejpam-3660	148	15	h.	h.	PROPN
ejpam-3660	148	16	theorem	theorem	PROPN
ejpam-3660	148	17	4.3	4.3	NUM
ejpam-3660	148	18	.	.	PUNCT
ejpam-3660	149	1	let	let	VERB
ejpam-3660	149	2	a	a	DET
ejpam-3660	149	3	=	=	SYM
ejpam-3660	149	4	(	(	PUNCT
ejpam-3660	149	5	µa	µa	PROPN
ejpam-3660	149	6	,	,	PUNCT
ejpam-3660	149	7	γa	γa	PROPN
ejpam-3660	149	8	)	)	PUNCT
ejpam-3660	149	9	be	be	VERB
ejpam-3660	149	10	an	an	DET
ejpam-3660	149	11	intuitionistic	intuitionistic	ADJ
ejpam-3660	149	12	fuzzy	fuzzy	ADJ
ejpam-3660	149	13	set	set	NOUN
ejpam-3660	149	14	in	in	ADP
ejpam-3660	149	15	a	a	DET
ejpam-3660	149	16	hyper	hyper	ADJ
ejpam-3660	149	17	gr	gr	NOUN
ejpam-3660	149	18	-	-	PUNCT
ejpam-3660	149	19	algebra	algebra	NOUN
ejpam-3660	149	20	h.	h.	PROPN
ejpam-3660	149	21	a〈t	a〈t	PROPN
ejpam-3660	149	22	,	,	PUNCT
ejpam-3660	149	23	s	s	PROPN
ejpam-3660	149	24	〉	〉	PROPN
ejpam-3660	149	25	is	be	AUX
ejpam-3660	149	26	a	a	DET
ejpam-3660	149	27	hyper	hyper	ADJ
ejpam-3660	149	28	gr	gr	NOUN
ejpam-3660	149	29	-	-	PUNCT
ejpam-3660	149	30	ideal	ideal	NOUN
ejpam-3660	149	31	of	of	ADP
ejpam-3660	149	32	h	h	NOUN
ejpam-3660	149	33	if	if	SCONJ
ejpam-3660	150	1	and	and	CCONJ
ejpam-3660	150	2	only	only	ADV
ejpam-3660	150	3	if	if	SCONJ
ejpam-3660	150	4	a	a	PRON
ejpam-3660	150	5	is	be	AUX
ejpam-3660	150	6	an	an	DET
ejpam-3660	150	7	intuitionistic	intuitionistic	ADJ
ejpam-3660	150	8	fuzzy	fuzzy	ADJ
ejpam-3660	150	9	hyper	hyper	ADJ
ejpam-3660	150	10	gr	gr	NOUN
ejpam-3660	150	11	-	-	PUNCT
ejpam-3660	150	12	ideal	ideal	NOUN
ejpam-3660	150	13	of	of	ADP
ejpam-3660	150	14	h	h	NOUN
ejpam-3660	150	15	whenever	whenever	SCONJ
ejpam-3660	150	16	a〈t	a〈t	NUM
ejpam-3660	150	17	,	,	PUNCT
ejpam-3660	150	18	s	s	PROPN
ejpam-3660	150	19	〉	〉	NOUN
ejpam-3660	150	20	,	,	PUNCT
ejpam-3660	150	21	∅	∅	NOUN
ejpam-3660	150	22	and	and	CCONJ
ejpam-3660	150	23	t	t	PROPN
ejpam-3660	150	24	,	,	PUNCT
ejpam-3660	150	25	s	s	PART
ejpam-3660	150	26	∈	∈	PROPN
ejpam-3660	151	1	[	[	X
ejpam-3660	151	2	0	0	NUM
ejpam-3660	151	3	,	,	PUNCT
ejpam-3660	151	4	1	1	NUM
ejpam-3660	151	5	]	]	PUNCT
ejpam-3660	151	6	.	.	PUNCT
ejpam-3660	152	1	proof	proof	NOUN
ejpam-3660	152	2	.	.	PUNCT
ejpam-3660	153	1	suppose	suppose	VERB
ejpam-3660	153	2	a〈t	a〈t	PROPN
ejpam-3660	153	3	,	,	PUNCT
ejpam-3660	153	4	s	s	PROPN
ejpam-3660	153	5	〉	〉	PROPN
ejpam-3660	153	6	is	be	AUX
ejpam-3660	153	7	a	a	DET
ejpam-3660	153	8	hyper	hyper	ADJ
ejpam-3660	153	9	gr	gr	NOUN
ejpam-3660	153	10	-	-	PUNCT
ejpam-3660	153	11	ideal	ideal	NOUN
ejpam-3660	153	12	of	of	ADP
ejpam-3660	153	13	h	h	NOUN
ejpam-3660	153	14	for	for	ADP
ejpam-3660	153	15	any	any	DET
ejpam-3660	153	16	t	t	NOUN
ejpam-3660	153	17	,	,	PUNCT
ejpam-3660	153	18	s	s	PART
ejpam-3660	153	19	∈	∈	PROPN
ejpam-3660	154	1	[	[	X
ejpam-3660	154	2	0	0	NUM
ejpam-3660	154	3	,	,	PUNCT
ejpam-3660	154	4	1	1	NUM
ejpam-3660	154	5	]	]	PUNCT
ejpam-3660	154	6	.	.	PUNCT
ejpam-3660	155	1	let	let	VERB
ejpam-3660	155	2	x	x	SYM
ejpam-3660	155	3	∈	∈	PROPN
ejpam-3660	155	4	h	h	NOUN
ejpam-3660	155	5	and	and	CCONJ
ejpam-3660	155	6	let	let	VERB
ejpam-3660	155	7	k	k	NOUN
ejpam-3660	155	8	,	,	PUNCT
ejpam-3660	155	9	l	l	PROPN
ejpam-3660	155	10	∈	∈	PROPN
ejpam-3660	156	1	[	[	X
ejpam-3660	156	2	0	0	NUM
ejpam-3660	156	3	,	,	PUNCT
ejpam-3660	156	4	1	1	NUM
ejpam-3660	156	5	]	]	PUNCT
ejpam-3660	156	6	such	such	ADJ
ejpam-3660	156	7	that	that	SCONJ
ejpam-3660	156	8	k	k	PROPN
ejpam-3660	156	9	=	=	PUNCT
ejpam-3660	156	10	µa(x	µa(x	PROPN
ejpam-3660	156	11	)	)	PUNCT
ejpam-3660	156	12	and	and	CCONJ
ejpam-3660	156	13	l	l	NOUN
ejpam-3660	156	14	=	=	SYM
ejpam-3660	156	15	γa(x	γa(x	NUM
ejpam-3660	156	16	)	)	PUNCT
ejpam-3660	156	17	.	.	PUNCT
ejpam-3660	157	1	since	since	SCONJ
ejpam-3660	157	2	a〈k	a〈k	NUM
ejpam-3660	157	3	,	,	PUNCT
ejpam-3660	157	4	l	l	PROPN
ejpam-3660	157	5	〉	〉	NOUN
ejpam-3660	157	6	is	be	AUX
ejpam-3660	157	7	a	a	DET
ejpam-3660	157	8	hyper	hyper	ADJ
ejpam-3660	157	9	gr	gr	NOUN
ejpam-3660	157	10	-	-	PUNCT
ejpam-3660	157	11	ideal	ideal	NOUN
ejpam-3660	157	12	of	of	ADP
ejpam-3660	157	13	h	h	NOUN
ejpam-3660	157	14	,	,	PUNCT
ejpam-3660	157	15	0	0	NUM
ejpam-3660	157	16	∈	∈	PROPN
ejpam-3660	157	17	a〈k	a〈k	PUNCT
ejpam-3660	157	18	,	,	PUNCT
ejpam-3660	157	19	l	l	PROPN
ejpam-3660	157	20	〉	〉	NOUN
ejpam-3660	157	21	.	.	PUNCT
ejpam-3660	158	1	then	then	ADV
ejpam-3660	158	2	µa(0	µa(0	NOUN
ejpam-3660	158	3	)	)	PUNCT
ejpam-3660	158	4	≥	≥	NOUN
ejpam-3660	158	5	k	k	NOUN
ejpam-3660	158	6	=	=	PUNCT
ejpam-3660	158	7	µa(x	µa(x	PROPN
ejpam-3660	158	8	)	)	PUNCT
ejpam-3660	158	9	and	and	CCONJ
ejpam-3660	158	10	γa(0	γa(0	NOUN
ejpam-3660	158	11	)	)	PUNCT
ejpam-3660	158	12	≤	≤	NOUN
ejpam-3660	158	13	l	l	NOUN
ejpam-3660	158	14	=	=	SYM
ejpam-3660	158	15	γa(x	γa(x	NUM
ejpam-3660	158	16	)	)	PUNCT
ejpam-3660	158	17	.	.	PUNCT
ejpam-3660	159	1	moreover	moreover	ADV
ejpam-3660	159	2	,	,	PUNCT
ejpam-3660	159	3	let	let	VERB
ejpam-3660	159	4	x	x	PRON
ejpam-3660	159	5	,	,	PUNCT
ejpam-3660	159	6	y	y	PROPN
ejpam-3660	159	7	∈	∈	PROPN
ejpam-3660	159	8	h	h	NOUN
ejpam-3660	159	9	and	and	CCONJ
ejpam-3660	159	10	let	let	VERB
ejpam-3660	159	11	t̃	t̃	PROPN
ejpam-3660	159	12	,	,	PUNCT
ejpam-3660	159	13	s̃	s̃	PROPN
ejpam-3660	159	14	∈	∈	PROPN
ejpam-3660	160	1	[	[	X
ejpam-3660	160	2	0	0	NUM
ejpam-3660	160	3	,	,	PUNCT
ejpam-3660	160	4	1	1	NUM
ejpam-3660	160	5	]	]	PUNCT
ejpam-3660	161	1	such	such	ADJ
ejpam-3660	161	2	that	that	SCONJ
ejpam-3660	161	3	t̃	t̃	PROPN
ejpam-3660	161	4	=	=	PUNCT
ejpam-3660	161	5	min	min	PROPN
ejpam-3660	161	6	{	{	PUNCT
ejpam-3660	161	7	inf	inf	NOUN
ejpam-3660	161	8	u∈x	u∈x	NOUN
ejpam-3660	161	9	~	~	PROPN
ejpam-3660	161	10	y	y	PROPN
ejpam-3660	161	11	µa(u	µa(u	NOUN
ejpam-3660	161	12	)	)	PUNCT
ejpam-3660	161	13	,	,	PUNCT
ejpam-3660	161	14	µa(y	µa(y	NOUN
ejpam-3660	161	15	)	)	PUNCT
ejpam-3660	161	16	}	}	PUNCT
ejpam-3660	161	17	and	and	CCONJ
ejpam-3660	161	18	s̃	s̃	PROPN
ejpam-3660	161	19	=	=	SYM
ejpam-3660	161	20	max	max	PROPN
ejpam-3660	161	21			PUNCT
ejpam-3660	161	22	sup	sup	NOUN
ejpam-3660	161	23	v∈x	v∈x	NOUN
ejpam-3660	161	24	~	~	SYM
ejpam-3660	161	25	y	y	PROPN
ejpam-3660	161	26	γa(v	γa(v	PUNCT
ejpam-3660	161	27	)	)	PUNCT
ejpam-3660	161	28	,	,	PUNCT
ejpam-3660	161	29	γa(y	γa(y	X
ejpam-3660	161	30	)	)	PUNCT
ejpam-3660	161	31	.	.	PROPN
ejpam-3660	161	32	suppose	suppose	VERB
ejpam-3660	161	33	w	w	PROPN
ejpam-3660	161	34	∈	∈	PROPN
ejpam-3660	161	35	x	x	PUNCT
ejpam-3660	161	36	~	~	PUNCT
ejpam-3660	161	37	y.	y.	PROPN
ejpam-3660	161	38	then	then	ADV
ejpam-3660	161	39	,	,	PUNCT
ejpam-3660	161	40	µa(w	µa(w	PUNCT
ejpam-3660	161	41	)	)	PUNCT
ejpam-3660	161	42	≥	≥	PROPN
ejpam-3660	161	43	inf	inf	PROPN
ejpam-3660	161	44	u∈x	u∈x	PROPN
ejpam-3660	161	45	~	~	PROPN
ejpam-3660	161	46	y	y	PROPN
ejpam-3660	161	47	µa(u	µa(u	X
ejpam-3660	161	48	)	)	PUNCT
ejpam-3660	161	49	≥	≥	PROPN
ejpam-3660	161	50	min	min	PROPN
ejpam-3660	161	51	{	{	PUNCT
ejpam-3660	161	52	inf	inf	NOUN
ejpam-3660	161	53	u∈x	u∈x	NOUN
ejpam-3660	161	54	~	~	PROPN
ejpam-3660	161	55	y	y	PROPN
ejpam-3660	161	56	µa(u	µa(u	NOUN
ejpam-3660	161	57	)	)	PUNCT
ejpam-3660	161	58	,	,	PUNCT
ejpam-3660	161	59	µa(y	µa(y	NOUN
ejpam-3660	161	60	)	)	PUNCT
ejpam-3660	161	61	}	}	PUNCT
ejpam-3660	161	62	=	=	SYM
ejpam-3660	161	63	t̃	t̃	PROPN
ejpam-3660	161	64	and	and	CCONJ
ejpam-3660	161	65	γa(w	γa(w	NUM
ejpam-3660	161	66	)	)	PUNCT
ejpam-3660	161	67	≤	≤	NUM
ejpam-3660	161	68	sup	sup	NOUN
ejpam-3660	161	69	v∈x	v∈x	NOUN
ejpam-3660	161	70	~	~	SYM
ejpam-3660	161	71	y	y	PROPN
ejpam-3660	161	72	γa(v	γa(v	PUNCT
ejpam-3660	161	73	)	)	PUNCT
ejpam-3660	161	74	≤	≤	NUM
ejpam-3660	162	1	max	max	PROPN
ejpam-3660	162	2			PUNCT
ejpam-3660	162	3	sup	sup	NOUN
ejpam-3660	162	4	v∈x	v∈x	NOUN
ejpam-3660	162	5	~	~	SYM
ejpam-3660	162	6	y	y	PROPN
ejpam-3660	162	7	γa(v	γa(v	PUNCT
ejpam-3660	162	8	)	)	PUNCT
ejpam-3660	162	9	,	,	PUNCT
ejpam-3660	162	10	γa(y	γa(y	X
ejpam-3660	162	11	)	)	PUNCT
ejpam-3660	162	12			PROPN
ejpam-3660	162	13	=	=	PUNCT
ejpam-3660	162	14	s̃.	s̃.	VERB
ejpam-3660	162	15	these	these	PRON
ejpam-3660	162	16	imply	imply	VERB
ejpam-3660	162	17	that	that	SCONJ
ejpam-3660	162	18	w	w	PROPN
ejpam-3660	162	19	∈	∈	PROPN
ejpam-3660	162	20	a	a	DET
ejpam-3660	162	21	〈	〈	PROPN
ejpam-3660	162	22	t̃,s̃	t̃,s̃	ADP
ejpam-3660	162	23	〉	〉	NOUN
ejpam-3660	162	24	and	and	CCONJ
ejpam-3660	162	25	so	so	ADV
ejpam-3660	162	26	x	x	X
ejpam-3660	162	27	~	~	PUNCT
ejpam-3660	162	28	y	y	PROPN
ejpam-3660	162	29	⊆	⊆	NUM
ejpam-3660	162	30	a	a	DET
ejpam-3660	162	31	〈	〈	PROPN
ejpam-3660	162	32	t̃,s̃	t̃,s̃	NOUN
ejpam-3660	162	33	〉	〉	PROPN
ejpam-3660	162	34	.	.	PUNCT
ejpam-3660	163	1	note	note	VERB
ejpam-3660	163	2	that	that	PRON
ejpam-3660	163	3	µa(y	µa(y	NOUN
ejpam-3660	163	4	)	)	PUNCT
ejpam-3660	163	5	≥	≥	PROPN
ejpam-3660	163	6	min	min	PROPN
ejpam-3660	163	7	{	{	PUNCT
ejpam-3660	163	8	inf	inf	NOUN
ejpam-3660	163	9	u∈x	u∈x	NOUN
ejpam-3660	163	10	~	~	PROPN
ejpam-3660	163	11	y	y	PROPN
ejpam-3660	163	12	µa(u	µa(u	NOUN
ejpam-3660	163	13	)	)	PUNCT
ejpam-3660	163	14	,	,	PUNCT
ejpam-3660	163	15	µa(y	µa(y	NOUN
ejpam-3660	163	16	)	)	PUNCT
ejpam-3660	163	17	}	}	PUNCT
ejpam-3660	164	1	=	=	SYM
ejpam-3660	164	2	t̃	t̃	PROPN
ejpam-3660	164	3	and	and	CCONJ
ejpam-3660	164	4	γa(y	γa(y	NUM
ejpam-3660	164	5	)	)	PUNCT
ejpam-3660	164	6	≤	≤	NUM
ejpam-3660	165	1	max	max	PROPN
ejpam-3660	165	2			PUNCT
ejpam-3660	165	3	sup	sup	NOUN
ejpam-3660	165	4	v∈x	v∈x	NOUN
ejpam-3660	165	5	~	~	SYM
ejpam-3660	165	6	y	y	PROPN
ejpam-3660	165	7	γa(v	γa(v	PUNCT
ejpam-3660	165	8	)	)	PUNCT
ejpam-3660	165	9	,	,	PUNCT
ejpam-3660	165	10	γa(y	γa(y	X
ejpam-3660	165	11	)	)	PUNCT
ejpam-3660	165	12			PROPN
ejpam-3660	165	13	=	=	PUNCT
ejpam-3660	165	14	s̃.	s̃.	PROPN
ejpam-3660	165	15	then	then	ADV
ejpam-3660	165	16	,	,	PUNCT
ejpam-3660	165	17	y	y	PROPN
ejpam-3660	165	18	∈	∈	PROPN
ejpam-3660	165	19	a	a	DET
ejpam-3660	165	20	〈	〈	PROPN
ejpam-3660	165	21	t̃,s̃	t̃,s̃	NOUN
ejpam-3660	165	22	〉	〉	PROPN
ejpam-3660	165	23	.	.	PUNCT
ejpam-3660	166	1	since	since	SCONJ
ejpam-3660	166	2	a	a	DET
ejpam-3660	166	3	〈	〈	PROPN
ejpam-3660	166	4	t̃,s̃	t̃,s̃	ADP
ejpam-3660	166	5	〉	〉	PROPN
ejpam-3660	166	6	is	be	AUX
ejpam-3660	166	7	a	a	DET
ejpam-3660	166	8	hyper	hyper	ADJ
ejpam-3660	166	9	gr	gr	NOUN
ejpam-3660	166	10	-	-	PUNCT
ejpam-3660	166	11	ideal	ideal	NOUN
ejpam-3660	166	12	of	of	ADP
ejpam-3660	166	13	h	h	NOUN
ejpam-3660	166	14	,	,	PUNCT
ejpam-3660	166	15	x	x	SYM
ejpam-3660	166	16	∈	∈	VERB
ejpam-3660	166	17	a	a	DET
ejpam-3660	166	18	〈	〈	PROPN
ejpam-3660	166	19	t̃,s̃	t̃,s̃	NOUN
ejpam-3660	166	20	〉	〉	NOUN
ejpam-3660	166	21	.	.	PUNCT
ejpam-3660	167	1	it	it	PRON
ejpam-3660	167	2	follows	follow	VERB
ejpam-3660	167	3	that	that	SCONJ
ejpam-3660	167	4	a.	a.	NOUN
ejpam-3660	167	5	macodi	macodi	NOUN
ejpam-3660	167	6	-	-	PUNCT
ejpam-3660	167	7	ringia	ringia	ADJ
ejpam-3660	167	8	,	,	PUNCT
ejpam-3660	167	9	g.	g.	PROPN
ejpam-3660	167	10	petalcorin	petalcorin	PROPN
ejpam-3660	167	11	,	,	PUNCT
ejpam-3660	167	12	jr	jr	PROPN
ejpam-3660	167	13	.	.	PROPN
ejpam-3660	167	14	/	/	SYM
ejpam-3660	167	15	eur	eur	PROPN
ejpam-3660	167	16	.	.	PUNCT
ejpam-3660	168	1	j.	j.	PROPN
ejpam-3660	168	2	pure	pure	PROPN
ejpam-3660	168	3	appl	appl	PROPN
ejpam-3660	168	4	.	.	PROPN
ejpam-3660	168	5	math	math	PROPN
ejpam-3660	168	6	,	,	PUNCT
ejpam-3660	168	7	13	13	NUM
ejpam-3660	168	8	(	(	PUNCT
ejpam-3660	168	9	2	2	NUM
ejpam-3660	168	10	)	)	PUNCT
ejpam-3660	168	11	(	(	PUNCT
ejpam-3660	168	12	2020	2020	NUM
ejpam-3660	168	13	)	)	PUNCT
ejpam-3660	168	14	,	,	PUNCT
ejpam-3660	168	15	246	246	NUM
ejpam-3660	168	16	-	-	SYM
ejpam-3660	168	17	257	257	NUM
ejpam-3660	168	18	252	252	NUM
ejpam-3660	168	19	µa(x	µa(x	NOUN
ejpam-3660	168	20	)	)	PUNCT
ejpam-3660	168	21	≥	≥	NOUN
ejpam-3660	168	22	t̃	t̃	PROPN
ejpam-3660	168	23	=	=	PUNCT
ejpam-3660	168	24	min	min	PROPN
ejpam-3660	168	25	{	{	PUNCT
ejpam-3660	168	26	inf	inf	NOUN
ejpam-3660	168	27	u∈x	u∈x	NOUN
ejpam-3660	168	28	~	~	PROPN
ejpam-3660	168	29	y	y	PROPN
ejpam-3660	168	30	µa(u	µa(u	NOUN
ejpam-3660	168	31	)	)	PUNCT
ejpam-3660	168	32	,	,	PUNCT
ejpam-3660	168	33	µa(y	µa(y	NOUN
ejpam-3660	168	34	)	)	PUNCT
ejpam-3660	168	35	}	}	PUNCT
ejpam-3660	168	36	and	and	CCONJ
ejpam-3660	168	37	γa(x	γa(x	NUM
ejpam-3660	168	38	)	)	PUNCT
ejpam-3660	168	39	≤	≤	PUNCT
ejpam-3660	169	1	s̃	s̃	PROPN
ejpam-3660	169	2	=	=	SYM
ejpam-3660	169	3	max	max	PROPN
ejpam-3660	169	4			PUNCT
ejpam-3660	169	5	sup	sup	NOUN
ejpam-3660	169	6	v∈x	v∈x	NOUN
ejpam-3660	169	7	~	~	SYM
ejpam-3660	169	8	y	y	PROPN
ejpam-3660	169	9	γa(v	γa(v	PUNCT
ejpam-3660	169	10	)	)	PUNCT
ejpam-3660	169	11	,	,	PUNCT
ejpam-3660	169	12	γa(y	γa(y	NUM
ejpam-3660	169	13	)	)	PUNCT
ejpam-3660	169	14	.	.	PROPN
ejpam-3660	169	15	by	by	ADP
ejpam-3660	169	16	definition	definition	NOUN
ejpam-3660	169	17	4.1	4.1	NUM
ejpam-3660	169	18	,	,	PUNCT
ejpam-3660	169	19	a	a	DET
ejpam-3660	169	20	=	=	X
ejpam-3660	169	21	(	(	PUNCT
ejpam-3660	169	22	µa	µa	PROPN
ejpam-3660	169	23	,	,	PUNCT
ejpam-3660	169	24	γa	γa	PROPN
ejpam-3660	169	25	)	)	PUNCT
ejpam-3660	169	26	is	be	AUX
ejpam-3660	169	27	an	an	DET
ejpam-3660	169	28	intuitionistic	intuitionistic	ADJ
ejpam-3660	169	29	fuzzy	fuzzy	ADJ
ejpam-3660	169	30	hyper	hyper	ADJ
ejpam-3660	169	31	gr	gr	NOUN
ejpam-3660	169	32	-	-	PUNCT
ejpam-3660	169	33	ideal	ideal	NOUN
ejpam-3660	169	34	in	in	ADP
ejpam-3660	169	35	h.	h.	NOUN
ejpam-3660	169	36	conversely	conversely	ADV
ejpam-3660	169	37	,	,	PUNCT
ejpam-3660	169	38	suppose	suppose	VERB
ejpam-3660	169	39	a	a	DET
ejpam-3660	169	40	=	=	X
ejpam-3660	169	41	(	(	PUNCT
ejpam-3660	169	42	µa	µa	PROPN
ejpam-3660	169	43	,	,	PUNCT
ejpam-3660	169	44	γa	γa	PROPN
ejpam-3660	169	45	)	)	PUNCT
ejpam-3660	169	46	is	be	AUX
ejpam-3660	169	47	an	an	DET
ejpam-3660	169	48	intuitionistic	intuitionistic	ADJ
ejpam-3660	169	49	fuzzy	fuzzy	ADJ
ejpam-3660	169	50	hyper	hyper	ADJ
ejpam-3660	169	51	gr	gr	NOUN
ejpam-3660	169	52	-	-	PUNCT
ejpam-3660	169	53	ideal	ideal	NOUN
ejpam-3660	169	54	in	in	ADP
ejpam-3660	169	55	h.	h.	PROPN
ejpam-3660	169	56	then	then	ADV
ejpam-3660	169	57	,	,	PUNCT
ejpam-3660	169	58	µa(0	µa(0	NOUN
ejpam-3660	169	59	)	)	PUNCT
ejpam-3660	169	60	≥	≥	NOUN
ejpam-3660	169	61	µa(x	µa(x	NOUN
ejpam-3660	169	62	)	)	PUNCT
ejpam-3660	169	63	for	for	ADP
ejpam-3660	169	64	all	all	PRON
ejpam-3660	169	65	x	x	SYM
ejpam-3660	169	66	∈	∈	PROPN
ejpam-3660	169	67	h.	h.	NOUN
ejpam-3660	169	68	let	let	VERB
ejpam-3660	169	69	t	t	PROPN
ejpam-3660	169	70	,	,	PUNCT
ejpam-3660	169	71	s	s	PART
ejpam-3660	169	72	∈	∈	PROPN
ejpam-3660	170	1	[	[	X
ejpam-3660	170	2	0	0	NUM
ejpam-3660	170	3	,	,	PUNCT
ejpam-3660	170	4	1	1	NUM
ejpam-3660	170	5	]	]	PUNCT
ejpam-3660	170	6	.	.	PUNCT
ejpam-3660	171	1	since	since	SCONJ
ejpam-3660	171	2	a〈t	a〈t	NUM
ejpam-3660	171	3	,	,	PUNCT
ejpam-3660	171	4	s	s	PROPN
ejpam-3660	171	5	〉	〉	NUM
ejpam-3660	171	6	,	,	PUNCT
ejpam-3660	171	7	∅	∅	NOUN
ejpam-3660	171	8	,	,	PUNCT
ejpam-3660	171	9	there	there	PRON
ejpam-3660	171	10	exists	exist	VERB
ejpam-3660	171	11	z	z	PROPN
ejpam-3660	171	12	∈	∈	PROPN
ejpam-3660	171	13	a〈t	a〈t	PROPN
ejpam-3660	171	14	,	,	PUNCT
ejpam-3660	171	15	s	s	PROPN
ejpam-3660	171	16	〉	〉	NUM
ejpam-3660	171	17	such	such	ADJ
ejpam-3660	171	18	that	that	DET
ejpam-3660	171	19	µa(0	µa(0	NOUN
ejpam-3660	171	20	)	)	PUNCT
ejpam-3660	171	21	≥	≥	NOUN
ejpam-3660	171	22	µa(z	µa(z	PUNCT
ejpam-3660	171	23	)	)	PUNCT
ejpam-3660	171	24	≥	≥	PROPN
ejpam-3660	171	25	t	t	PROPN
ejpam-3660	171	26	and	and	CCONJ
ejpam-3660	171	27	γa(0	γa(0	NOUN
ejpam-3660	171	28	)	)	PUNCT
ejpam-3660	171	29	≤	≤	NOUN
ejpam-3660	171	30	γa(z	γa(z	NOUN
ejpam-3660	171	31	)	)	PUNCT
ejpam-3660	171	32	≤	≤	PROPN
ejpam-3660	172	1	s.	s.	PROPN
ejpam-3660	172	2	thus	thus	ADV
ejpam-3660	172	3	,	,	PUNCT
ejpam-3660	172	4	0	0	NUM
ejpam-3660	172	5	∈	∈	PROPN
ejpam-3660	172	6	a〈t	a〈t	PUNCT
ejpam-3660	172	7	,	,	PUNCT
ejpam-3660	172	8	s	s	PROPN
ejpam-3660	172	9	〉	〉	NOUN
ejpam-3660	172	10	.	.	PUNCT
ejpam-3660	173	1	let	let	VERB
ejpam-3660	173	2	x	x	PRON
ejpam-3660	173	3	,	,	PUNCT
ejpam-3660	173	4	y	y	PROPN
ejpam-3660	173	5	∈	∈	PROPN
ejpam-3660	173	6	h	h	NOUN
ejpam-3660	173	7	such	such	ADJ
ejpam-3660	173	8	that	that	SCONJ
ejpam-3660	173	9	x	x	X
ejpam-3660	173	10	~	~	PUNCT
ejpam-3660	173	11	y	y	PROPN
ejpam-3660	173	12	⊆	⊆	NUM
ejpam-3660	173	13	a〈t	a〈t	NUM
ejpam-3660	173	14	,	,	PUNCT
ejpam-3660	173	15	s	s	PROPN
ejpam-3660	173	16	〉	〉	NUM
ejpam-3660	173	17	and	and	CCONJ
ejpam-3660	173	18	y	y	PROPN
ejpam-3660	173	19	∈	∈	PROPN
ejpam-3660	173	20	a〈t	a〈t	PROPN
ejpam-3660	173	21	,	,	PUNCT
ejpam-3660	173	22	s	s	PROPN
ejpam-3660	173	23	〉	〉	NUM
ejpam-3660	173	24	.	.	PUNCT
ejpam-3660	174	1	then	then	ADV
ejpam-3660	174	2	,	,	PUNCT
ejpam-3660	174	3	µa(y	µa(y	NOUN
ejpam-3660	174	4	)	)	PUNCT
ejpam-3660	174	5	≥	≥	PROPN
ejpam-3660	174	6	t	t	PROPN
ejpam-3660	174	7	,	,	PUNCT
ejpam-3660	174	8	γa(y	γa(y	NUM
ejpam-3660	174	9	)	)	PUNCT
ejpam-3660	174	10	≤	≤	NUM
ejpam-3660	174	11	s	s	NOUN
ejpam-3660	174	12	,	,	PUNCT
ejpam-3660	174	13	µa(u	µa(u	PUNCT
ejpam-3660	174	14	)	)	PUNCT
ejpam-3660	174	15	≥	≥	PROPN
ejpam-3660	174	16	t	t	NOUN
ejpam-3660	174	17	and	and	CCONJ
ejpam-3660	174	18	γa(v	γa(v	PUNCT
ejpam-3660	174	19	)	)	PUNCT
ejpam-3660	174	20	≤	≤	NUM
ejpam-3660	174	21	s	s	VERB
ejpam-3660	174	22	for	for	ADP
ejpam-3660	174	23	any	any	DET
ejpam-3660	174	24	u	u	NOUN
ejpam-3660	174	25	,	,	PUNCT
ejpam-3660	174	26	v	v	NOUN
ejpam-3660	174	27	∈	∈	PROPN
ejpam-3660	175	1	x~	x~	PROPN
ejpam-3660	176	1	y.	y.	PROPN
ejpam-3660	177	1	it	it	PRON
ejpam-3660	177	2	follows	follow	VERB
ejpam-3660	177	3	that	that	SCONJ
ejpam-3660	177	4	t	t	PROPN
ejpam-3660	177	5	is	be	AUX
ejpam-3660	177	6	a	a	DET
ejpam-3660	177	7	lowerbound	lowerbound	NOUN
ejpam-3660	177	8	for	for	ADP
ejpam-3660	177	9	{	{	PUNCT
ejpam-3660	177	10	µa(u	µa(u	NOUN
ejpam-3660	177	11	)	)	PUNCT
ejpam-3660	177	12	:	:	PUNCT
ejpam-3660	177	13	u	u	NOUN
ejpam-3660	177	14	∈	∈	PROPN
ejpam-3660	177	15	x~	x~	PROPN
ejpam-3660	177	16	y	y	X
ejpam-3660	177	17	}	}	PUNCT
ejpam-3660	177	18	and	and	CCONJ
ejpam-3660	177	19	s	s	VERB
ejpam-3660	177	20	is	be	AUX
ejpam-3660	177	21	an	an	DET
ejpam-3660	177	22	upperbound	upperbound	NOUN
ejpam-3660	177	23	for	for	ADP
ejpam-3660	177	24	{	{	PUNCT
ejpam-3660	177	25	γa(v	γa(v	PUNCT
ejpam-3660	177	26	)	)	PUNCT
ejpam-3660	177	27	:	:	PUNCT
ejpam-3660	177	28	v	v	X
ejpam-3660	177	29	∈	∈	NOUN
ejpam-3660	177	30	x	x	X
ejpam-3660	177	31	~	~	PUNCT
ejpam-3660	177	32	y	y	X
ejpam-3660	177	33	}	}	PUNCT
ejpam-3660	177	34	.	.	PUNCT
ejpam-3660	178	1	then	then	ADV
ejpam-3660	178	2	,	,	PUNCT
ejpam-3660	178	3	inf	inf	PROPN
ejpam-3660	178	4	u∈x	u∈x	NOUN
ejpam-3660	178	5	~	~	PROPN
ejpam-3660	178	6	y	y	PROPN
ejpam-3660	178	7	µa(u	µa(u	PUNCT
ejpam-3660	178	8	)	)	PUNCT
ejpam-3660	178	9	≥	≥	PROPN
ejpam-3660	178	10	t	t	NOUN
ejpam-3660	178	11	and	and	CCONJ
ejpam-3660	178	12	sup	sup	PROPN
ejpam-3660	178	13	v∈x	v∈x	PROPN
ejpam-3660	178	14	~	~	SYM
ejpam-3660	178	15	y	y	PROPN
ejpam-3660	178	16	γa(v	γa(v	PUNCT
ejpam-3660	178	17	)	)	PUNCT
ejpam-3660	178	18	≤	≤	NOUN
ejpam-3660	178	19	s.	s.	PROPN
ejpam-3660	178	20	by	by	ADP
ejpam-3660	178	21	ifgr2	ifgr2	NOUN
ejpam-3660	178	22	and	and	CCONJ
ejpam-3660	178	23	ifgr3	ifgr3	NOUN
ejpam-3660	178	24	,	,	PUNCT
ejpam-3660	178	25	µa(x	µa(x	NOUN
ejpam-3660	178	26	)	)	PUNCT
ejpam-3660	178	27	≥	≥	PROPN
ejpam-3660	178	28	min	min	PROPN
ejpam-3660	178	29	{	{	PUNCT
ejpam-3660	178	30	inf	inf	NOUN
ejpam-3660	178	31	u∈x	u∈x	NOUN
ejpam-3660	178	32	~	~	PROPN
ejpam-3660	178	33	y	y	PROPN
ejpam-3660	178	34	µa(u	µa(u	NOUN
ejpam-3660	178	35	)	)	PUNCT
ejpam-3660	178	36	,	,	PUNCT
ejpam-3660	178	37	µa(y	µa(y	NOUN
ejpam-3660	178	38	)	)	PUNCT
ejpam-3660	178	39	}	}	PUNCT
ejpam-3660	178	40	≥	≥	NOUN
ejpam-3660	178	41	min{t	min{t	PROPN
ejpam-3660	178	42	,	,	PUNCT
ejpam-3660	178	43	t	t	PROPN
ejpam-3660	178	44	}	}	PUNCT
ejpam-3660	178	45	=	=	SYM
ejpam-3660	178	46	t	t	NOUN
ejpam-3660	178	47	and	and	CCONJ
ejpam-3660	178	48	γa(x	γa(x	NUM
ejpam-3660	178	49	)	)	PUNCT
ejpam-3660	178	50	≤	≤	NUM
ejpam-3660	178	51	max	max	PROPN
ejpam-3660	178	52			PUNCT
ejpam-3660	178	53	sup	sup	NOUN
ejpam-3660	178	54	v∈x	v∈x	NOUN
ejpam-3660	178	55	~	~	SYM
ejpam-3660	178	56	y	y	PROPN
ejpam-3660	178	57	γa(v	γa(v	PUNCT
ejpam-3660	178	58	)	)	PUNCT
ejpam-3660	178	59	,	,	PUNCT
ejpam-3660	178	60	γa(y	γa(y	X
ejpam-3660	178	61	)	)	PUNCT
ejpam-3660	179	1			PROPN
ejpam-3660	179	2	≤	≤	NOUN
ejpam-3660	179	3	max{s	max{	NOUN
ejpam-3660	179	4	,	,	PUNCT
ejpam-3660	179	5	s	s	X
ejpam-3660	179	6	}	}	PUNCT
ejpam-3660	179	7	=	=	SYM
ejpam-3660	179	8	s.	s.	PROPN
ejpam-3660	179	9	hence	hence	ADV
ejpam-3660	179	10	,	,	PUNCT
ejpam-3660	179	11	x	x	PROPN
ejpam-3660	179	12	∈	∈	PROPN
ejpam-3660	179	13	a〈t	a〈t	PUNCT
ejpam-3660	179	14	,	,	PUNCT
ejpam-3660	179	15	s	s	PROPN
ejpam-3660	179	16	〉	〉	NUM
ejpam-3660	179	17	and	and	CCONJ
ejpam-3660	179	18	so	so	ADV
ejpam-3660	179	19	a〈t	a〈t	PROPN
ejpam-3660	179	20	,	,	PUNCT
ejpam-3660	179	21	s	s	PROPN
ejpam-3660	179	22	〉	〉	PROPN
ejpam-3660	179	23	is	be	AUX
ejpam-3660	179	24	a	a	DET
ejpam-3660	179	25	hyper	hyper	ADJ
ejpam-3660	179	26	gr	gr	NOUN
ejpam-3660	179	27	-	-	PUNCT
ejpam-3660	179	28	ideal	ideal	NOUN
ejpam-3660	179	29	of	of	ADP
ejpam-3660	179	30	h.	h.	PROPN
ejpam-3660	179	31	�	�	PROPN
ejpam-3660	179	32	lemma	lemma	PROPN
ejpam-3660	179	33	4.4	4.4	NUM
ejpam-3660	179	34	.	.	PUNCT
ejpam-3660	180	1	let	let	VERB
ejpam-3660	180	2	µ	µ	X
ejpam-3660	180	3	:	:	PUNCT
ejpam-3660	180	4	h→	h→	SYM
ejpam-3660	181	1	[	[	X
ejpam-3660	181	2	0	0	NUM
ejpam-3660	181	3	,	,	PUNCT
ejpam-3660	181	4	1	1	NUM
ejpam-3660	181	5	]	]	PUNCT
ejpam-3660	181	6	be	be	AUX
ejpam-3660	181	7	a	a	DET
ejpam-3660	181	8	fuzzy	fuzzy	ADJ
ejpam-3660	181	9	set	set	NOUN
ejpam-3660	181	10	and	and	CCONJ
ejpam-3660	181	11	s	s	NOUN
ejpam-3660	182	1	⊆	⊆	NUM
ejpam-3660	182	2	h.	h.	NOUN
ejpam-3660	182	3	then	then	ADV
ejpam-3660	182	4	(	(	PUNCT
ejpam-3660	182	5	a	a	X
ejpam-3660	182	6	)	)	PUNCT
ejpam-3660	182	7	1	1	NUM
ejpam-3660	182	8	−	−	NOUN
ejpam-3660	182	9	sup	sup	NOUN
ejpam-3660	182	10	x∈s	x∈s	NOUN
ejpam-3660	182	11	µ(x	µ(x	ADJ
ejpam-3660	182	12	)	)	PUNCT
ejpam-3660	182	13	=	=	SYM
ejpam-3660	182	14	inf	inf	NOUN
ejpam-3660	182	15	x∈s	x∈s	NOUN
ejpam-3660	182	16	(	(	PUNCT
ejpam-3660	182	17	1	1	NUM
ejpam-3660	182	18	−	−	NOUN
ejpam-3660	182	19	µ(x	µ(x	NOUN
ejpam-3660	182	20	)	)	PUNCT
ejpam-3660	182	21	)	)	PUNCT
ejpam-3660	182	22	,	,	PUNCT
ejpam-3660	182	23	and	and	CCONJ
ejpam-3660	182	24	(	(	PUNCT
ejpam-3660	182	25	b	b	X
ejpam-3660	182	26	)	)	PUNCT
ejpam-3660	182	27	1	1	NUM
ejpam-3660	182	28	−	−	PROPN
ejpam-3660	182	29	inf	inf	PROPN
ejpam-3660	182	30	x∈s	x∈s	X
ejpam-3660	182	31	µ(x	µ(x	PROPN
ejpam-3660	182	32	)	)	PUNCT
ejpam-3660	182	33	=	=	SYM
ejpam-3660	182	34	sup	sup	NOUN
ejpam-3660	182	35	x∈s	x∈s	X
ejpam-3660	182	36	(	(	PUNCT
ejpam-3660	182	37	1	1	NUM
ejpam-3660	182	38	−	−	NOUN
ejpam-3660	182	39	µ(x	µ(x	NOUN
ejpam-3660	182	40	)	)	PUNCT
ejpam-3660	182	41	)	)	PUNCT
ejpam-3660	182	42	.	.	PUNCT
ejpam-3660	183	1	proof	proof	NOUN
ejpam-3660	183	2	.	.	PUNCT
ejpam-3660	184	1	let	let	VERB
ejpam-3660	184	2	x	x	SYM
ejpam-3660	184	3	∈	∈	PROPN
ejpam-3660	184	4	s.	s.	PROPN
ejpam-3660	184	5	(	(	PUNCT
ejpam-3660	184	6	a	a	X
ejpam-3660	184	7	)	)	PUNCT
ejpam-3660	184	8	since	since	SCONJ
ejpam-3660	184	9	µ(x	µ(x	NOUN
ejpam-3660	184	10	)	)	PUNCT
ejpam-3660	184	11	≤	≤	NUM
ejpam-3660	184	12	sup	sup	NOUN
ejpam-3660	184	13	x∈s	x∈s	NOUN
ejpam-3660	184	14	µ(x	µ(x	PROPN
ejpam-3660	184	15	)	)	PUNCT
ejpam-3660	184	16	,	,	PUNCT
ejpam-3660	184	17	1−µ(x	1−µ(x	NUM
ejpam-3660	184	18	)	)	PUNCT
ejpam-3660	184	19	≥	≥	NOUN
ejpam-3660	184	20	1−	1−	NUM
ejpam-3660	184	21	sup	sup	NOUN
ejpam-3660	184	22	x∈s	x∈s	NOUN
ejpam-3660	184	23	µ(x	µ(x	NOUN
ejpam-3660	184	24	)	)	PUNCT
ejpam-3660	184	25	.	.	PUNCT
ejpam-3660	185	1	then	then	ADV
ejpam-3660	185	2	,	,	PUNCT
ejpam-3660	185	3	1−	1−	NUM
ejpam-3660	185	4	sup	sup	NOUN
ejpam-3660	185	5	x∈s	x∈s	NOUN
ejpam-3660	185	6	µ(x	µ(x	PROPN
ejpam-3660	185	7	)	)	PUNCT
ejpam-3660	185	8	is	be	AUX
ejpam-3660	185	9	a	a	DET
ejpam-3660	185	10	lowerbound	lowerbound	NOUN
ejpam-3660	185	11	for	for	ADP
ejpam-3660	185	12	{	{	PUNCT
ejpam-3660	185	13	1−µ(x)|x	1−µ(x)|x	NUM
ejpam-3660	185	14	∈	∈	NOUN
ejpam-3660	185	15	s	s	PART
ejpam-3660	185	16	}	}	PUNCT
ejpam-3660	185	17	.	.	PUNCT
ejpam-3660	186	1	it	it	PRON
ejpam-3660	186	2	implies	imply	VERB
ejpam-3660	186	3	that	that	SCONJ
ejpam-3660	186	4	1−sup	1−sup	NUM
ejpam-3660	186	5	x∈s	x∈s	PUNCT
ejpam-3660	186	6	µ(x	µ(x	PROPN
ejpam-3660	186	7	)	)	PUNCT
ejpam-3660	186	8	≤	≤	NUM
ejpam-3660	186	9	inf	inf	NOUN
ejpam-3660	186	10	x∈s	x∈s	PROPN
ejpam-3660	187	1	(	(	PUNCT
ejpam-3660	187	2	1	1	NUM
ejpam-3660	187	3	−	−	NOUN
ejpam-3660	187	4	µ(x	µ(x	NOUN
ejpam-3660	187	5	)	)	PUNCT
ejpam-3660	187	6	)	)	PUNCT
ejpam-3660	187	7	.	.	PUNCT
ejpam-3660	188	1	since	since	SCONJ
ejpam-3660	188	2	inf	inf	PROPN
ejpam-3660	188	3	x∈s	x∈s	PROPN
ejpam-3660	188	4	(	(	PUNCT
ejpam-3660	188	5	1−µ(x	1−µ(x	NUM
ejpam-3660	188	6	)	)	PUNCT
ejpam-3660	188	7	)	)	PUNCT
ejpam-3660	188	8	≤	≤	NUM
ejpam-3660	188	9	1−µ(x	1−µ(x	NUM
ejpam-3660	188	10	)	)	PUNCT
ejpam-3660	188	11	,	,	PUNCT
ejpam-3660	188	12	µ(x	µ(x	NOUN
ejpam-3660	188	13	)	)	PUNCT
ejpam-3660	188	14	≤	≤	NUM
ejpam-3660	189	1	1	1	NUM
ejpam-3660	189	2	−	−	PROPN
ejpam-3660	189	3	inf	inf	PROPN
ejpam-3660	189	4	x∈s	x∈s	PROPN
ejpam-3660	189	5	(	(	PUNCT
ejpam-3660	189	6	1	1	NUM
ejpam-3660	189	7	−	−	NOUN
ejpam-3660	189	8	µ(x	µ(x	NOUN
ejpam-3660	189	9	)	)	PUNCT
ejpam-3660	189	10	)	)	PUNCT
ejpam-3660	189	11	.	.	PUNCT
ejpam-3660	190	1	thus	thus	ADV
ejpam-3660	190	2	,	,	PUNCT
ejpam-3660	190	3	1	1	NUM
ejpam-3660	190	4	−	−	PROPN
ejpam-3660	190	5	inf	inf	PROPN
ejpam-3660	190	6	x∈s	x∈s	PROPN
ejpam-3660	190	7	(	(	PUNCT
ejpam-3660	190	8	1	1	NUM
ejpam-3660	190	9	−	−	PRON
ejpam-3660	190	10	µ(x	µ(x	NOUN
ejpam-3660	190	11	)	)	PUNCT
ejpam-3660	190	12	)	)	PUNCT
ejpam-3660	190	13	is	be	AUX
ejpam-3660	190	14	an	an	DET
ejpam-3660	190	15	upperbound	upperbound	NOUN
ejpam-3660	190	16	for	for	ADP
ejpam-3660	190	17	{	{	PUNCT
ejpam-3660	190	18	µ(x	µ(x	NOUN
ejpam-3660	190	19	)	)	PUNCT
ejpam-3660	190	20	:	:	PUNCT
ejpam-3660	191	1	x	x	X
ejpam-3660	191	2	∈	∈	NOUN
ejpam-3660	191	3	s	s	PART
ejpam-3660	191	4	}	}	PUNCT
ejpam-3660	191	5	.	.	PUNCT
ejpam-3660	192	1	then	then	ADV
ejpam-3660	192	2	sup	sup	INTJ
ejpam-3660	192	3	x∈s	x∈s	INTJ
ejpam-3660	192	4	µ(x	µ(x	X
ejpam-3660	192	5	)	)	PUNCT
ejpam-3660	192	6	≤	≤	NUM
ejpam-3660	192	7	1	1	NUM
ejpam-3660	192	8	−	−	PROPN
ejpam-3660	192	9	inf	inf	PROPN
ejpam-3660	192	10	x∈s	x∈s	PROPN
ejpam-3660	192	11	(	(	PUNCT
ejpam-3660	192	12	1	1	NUM
ejpam-3660	192	13	−	−	NOUN
ejpam-3660	192	14	µ(x	µ(x	NOUN
ejpam-3660	192	15	)	)	PUNCT
ejpam-3660	192	16	)	)	PUNCT
ejpam-3660	192	17	and	and	CCONJ
ejpam-3660	192	18	so	so	ADV
ejpam-3660	192	19	inf	inf	PROPN
ejpam-3660	192	20	x∈s	x∈s	PROPN
ejpam-3660	192	21	(	(	PUNCT
ejpam-3660	192	22	1	1	NUM
ejpam-3660	192	23	−	−	PRON
ejpam-3660	192	24	µ(x	µ(x	NOUN
ejpam-3660	192	25	)	)	PUNCT
ejpam-3660	192	26	)	)	PUNCT
ejpam-3660	192	27	≤	≤	NUM
ejpam-3660	192	28	1	1	NUM
ejpam-3660	192	29	−	−	NOUN
ejpam-3660	192	30	sup	sup	NOUN
ejpam-3660	192	31	x∈s	x∈s	NOUN
ejpam-3660	192	32	µ(x	µ(x	PROPN
ejpam-3660	192	33	)	)	PUNCT
ejpam-3660	192	34	.	.	PUNCT
ejpam-3660	193	1	therefore	therefore	ADV
ejpam-3660	193	2	,	,	PUNCT
ejpam-3660	193	3	1	1	NUM
ejpam-3660	193	4	−	−	NOUN
ejpam-3660	193	5	sup	sup	NOUN
ejpam-3660	193	6	x∈s	x∈s	NOUN
ejpam-3660	193	7	µ(x	µ(x	ADJ
ejpam-3660	193	8	)	)	PUNCT
ejpam-3660	193	9	=	=	SYM
ejpam-3660	193	10	inf	inf	NOUN
ejpam-3660	193	11	x∈s	x∈s	NOUN
ejpam-3660	193	12	(	(	PUNCT
ejpam-3660	193	13	1	1	NUM
ejpam-3660	193	14	−	−	NOUN
ejpam-3660	193	15	µ(x	µ(x	NOUN
ejpam-3660	193	16	)	)	PUNCT
ejpam-3660	193	17	)	)	PUNCT
ejpam-3660	193	18	.	.	PUNCT
ejpam-3660	194	1	(	(	PUNCT
ejpam-3660	194	2	b	b	X
ejpam-3660	194	3	)	)	PUNCT
ejpam-3660	194	4	note	note	NOUN
ejpam-3660	194	5	that	that	SCONJ
ejpam-3660	194	6	µ(x	µ(x	VERB
ejpam-3660	194	7	)	)	PUNCT
ejpam-3660	194	8	≥	≥	NOUN
ejpam-3660	194	9	inf	inf	NOUN
ejpam-3660	194	10	x∈s	x∈s	PROPN
ejpam-3660	194	11	µ(x	µ(x	PROPN
ejpam-3660	194	12	)	)	PUNCT
ejpam-3660	194	13	.	.	PUNCT
ejpam-3660	195	1	then	then	ADV
ejpam-3660	195	2	,	,	PUNCT
ejpam-3660	195	3	1	1	NUM
ejpam-3660	195	4	−	−	NOUN
ejpam-3660	195	5	µ(x	µ(x	NOUN
ejpam-3660	195	6	)	)	PUNCT
ejpam-3660	195	7	≤	≤	NUM
ejpam-3660	195	8	1	1	NUM
ejpam-3660	195	9	−	−	PROPN
ejpam-3660	195	10	inf	inf	NOUN
ejpam-3660	195	11	x∈s	x∈s	PUNCT
ejpam-3660	195	12	µ(x	µ(x	PROPN
ejpam-3660	195	13	)	)	PUNCT
ejpam-3660	195	14	.	.	PUNCT
ejpam-3660	196	1	this	this	PRON
ejpam-3660	196	2	implies	imply	VERB
ejpam-3660	196	3	that	that	SCONJ
ejpam-3660	196	4	1	1	NUM
ejpam-3660	196	5	−	−	PROPN
ejpam-3660	196	6	inf	inf	NOUN
ejpam-3660	196	7	x∈s	x∈s	X
ejpam-3660	196	8	µ(x	µ(x	PROPN
ejpam-3660	196	9	)	)	PUNCT
ejpam-3660	196	10	is	be	AUX
ejpam-3660	196	11	an	an	DET
ejpam-3660	196	12	upperbound	upperbound	NOUN
ejpam-3660	196	13	for	for	ADP
ejpam-3660	196	14	{	{	PUNCT
ejpam-3660	196	15	1	1	NUM
ejpam-3660	196	16	−	−	PROPN
ejpam-3660	196	17	µ(x)|x	µ(x)|x	PROPN
ejpam-3660	196	18	∈	∈	PROPN
ejpam-3660	196	19	s	s	PART
ejpam-3660	196	20	}	}	PUNCT
ejpam-3660	196	21	.	.	PUNCT
ejpam-3660	197	1	it	it	PRON
ejpam-3660	197	2	follows	follow	VERB
ejpam-3660	197	3	that	that	SCONJ
ejpam-3660	197	4	sup	sup	NOUN
ejpam-3660	197	5	x∈s	x∈s	X
ejpam-3660	197	6	(	(	PUNCT
ejpam-3660	197	7	1	1	NUM
ejpam-3660	197	8	−	−	NOUN
ejpam-3660	197	9	µ(x	µ(x	NOUN
ejpam-3660	197	10	)	)	PUNCT
ejpam-3660	197	11	)	)	PUNCT
ejpam-3660	197	12	≤	≤	NUM
ejpam-3660	197	13	1	1	NUM
ejpam-3660	197	14	−	−	PROPN
ejpam-3660	197	15	inf	inf	NOUN
ejpam-3660	197	16	x∈s	x∈s	PUNCT
ejpam-3660	197	17	µ(x	µ(x	PROPN
ejpam-3660	197	18	)	)	PUNCT
ejpam-3660	197	19	.	.	PUNCT
ejpam-3660	198	1	since	since	SCONJ
ejpam-3660	198	2	1	1	NUM
ejpam-3660	198	3	−	−	PRON
ejpam-3660	198	4	µ(x	µ(x	NOUN
ejpam-3660	198	5	)	)	PUNCT
ejpam-3660	198	6	≤	≤	NUM
ejpam-3660	198	7	sup	sup	NOUN
ejpam-3660	198	8	x∈s	x∈s	PROPN
ejpam-3660	198	9	(	(	PUNCT
ejpam-3660	198	10	1	1	NUM
ejpam-3660	198	11	−	−	NOUN
ejpam-3660	198	12	µ(x	µ(x	NOUN
ejpam-3660	198	13	)	)	PUNCT
ejpam-3660	198	14	)	)	PUNCT
ejpam-3660	198	15	,	,	PUNCT
ejpam-3660	198	16	1	1	NUM
ejpam-3660	198	17	−	−	NOUN
ejpam-3660	198	18	sup	sup	NOUN
ejpam-3660	198	19	x∈s	x∈s	PROPN
ejpam-3660	198	20	(	(	PUNCT
ejpam-3660	198	21	1	1	NUM
ejpam-3660	198	22	−	−	NOUN
ejpam-3660	198	23	µ(x	µ(x	NOUN
ejpam-3660	198	24	)	)	PUNCT
ejpam-3660	198	25	)	)	PUNCT
ejpam-3660	198	26	≤	≤	NOUN
ejpam-3660	198	27	µ(x	µ(x	NOUN
ejpam-3660	198	28	)	)	PUNCT
ejpam-3660	198	29	.	.	PUNCT
ejpam-3660	199	1	then	then	ADV
ejpam-3660	199	2	,	,	PUNCT
ejpam-3660	199	3	1	1	NUM
ejpam-3660	199	4	−	−	NOUN
ejpam-3660	199	5	sup	sup	NOUN
ejpam-3660	199	6	x∈s	x∈s	PROPN
ejpam-3660	199	7	(	(	PUNCT
ejpam-3660	199	8	1	1	NUM
ejpam-3660	199	9	−	−	NOUN
ejpam-3660	199	10	µ(x	µ(x	NOUN
ejpam-3660	199	11	)	)	PUNCT
ejpam-3660	199	12	)	)	PUNCT
ejpam-3660	199	13	is	be	AUX
ejpam-3660	199	14	a	a	DET
ejpam-3660	199	15	lowerbound	lowerbound	NOUN
ejpam-3660	199	16	for	for	ADP
ejpam-3660	199	17	{	{	PUNCT
ejpam-3660	199	18	µ(x)|x	µ(x)|x	PROPN
ejpam-3660	199	19	∈	∈	NOUN
ejpam-3660	199	20	s	s	PART
ejpam-3660	199	21	}	}	PUNCT
ejpam-3660	199	22	.	.	PUNCT
ejpam-3660	200	1	this	this	PRON
ejpam-3660	200	2	implies	imply	VERB
ejpam-3660	200	3	that	that	SCONJ
ejpam-3660	200	4	1	1	NUM
ejpam-3660	200	5	−	−	NOUN
ejpam-3660	200	6	sup	sup	NOUN
ejpam-3660	200	7	x∈s	x∈s	PROPN
ejpam-3660	200	8	(	(	PUNCT
ejpam-3660	200	9	1	1	NUM
ejpam-3660	200	10	−	−	NOUN
ejpam-3660	200	11	µ(x	µ(x	NOUN
ejpam-3660	200	12	)	)	PUNCT
ejpam-3660	200	13	)	)	PUNCT
ejpam-3660	200	14	≤	≤	NUM
ejpam-3660	200	15	inf	inf	PROPN
ejpam-3660	200	16	x∈s	x∈s	X
ejpam-3660	200	17	µ(x	µ(x	PROPN
ejpam-3660	200	18	)	)	PUNCT
ejpam-3660	200	19	and	and	CCONJ
ejpam-3660	200	20	so	so	ADV
ejpam-3660	200	21	1	1	NUM
ejpam-3660	200	22	−	−	PROPN
ejpam-3660	200	23	inf	inf	NOUN
ejpam-3660	200	24	x∈s	x∈s	X
ejpam-3660	200	25	µ(x	µ(x	PROPN
ejpam-3660	200	26	)	)	PUNCT
ejpam-3660	200	27	≤	≤	NUM
ejpam-3660	200	28	sup	sup	NOUN
ejpam-3660	200	29	x∈s	x∈s	PROPN
ejpam-3660	200	30	(	(	PUNCT
ejpam-3660	200	31	1	1	NUM
ejpam-3660	200	32	−	−	NOUN
ejpam-3660	200	33	µ(x	µ(x	NOUN
ejpam-3660	200	34	)	)	PUNCT
ejpam-3660	200	35	)	)	PUNCT
ejpam-3660	200	36	.	.	PUNCT
ejpam-3660	201	1	hence	hence	ADV
ejpam-3660	201	2	,	,	PUNCT
ejpam-3660	201	3	1	1	NUM
ejpam-3660	201	4	−	−	PROPN
ejpam-3660	201	5	inf	inf	PROPN
ejpam-3660	201	6	x∈s	x∈s	X
ejpam-3660	201	7	µ(x	µ(x	PROPN
ejpam-3660	201	8	)	)	PUNCT
ejpam-3660	201	9	=	=	SYM
ejpam-3660	201	10	sup	sup	NOUN
ejpam-3660	201	11	x∈s	x∈s	X
ejpam-3660	201	12	(	(	PUNCT
ejpam-3660	201	13	1	1	NUM
ejpam-3660	201	14	−	−	NOUN
ejpam-3660	201	15	µ(x	µ(x	NOUN
ejpam-3660	201	16	)	)	PUNCT
ejpam-3660	201	17	)	)	PUNCT
ejpam-3660	201	18	.	.	PUNCT
ejpam-3660	202	1	�	�	PROPN
ejpam-3660	203	1	the	the	DET
ejpam-3660	203	2	following	follow	VERB
ejpam-3660	203	3	corollary	corollary	NOUN
ejpam-3660	203	4	follows	follow	VERB
ejpam-3660	203	5	from	from	ADP
ejpam-3660	203	6	lemma	lemma	PROPN
ejpam-3660	203	7	4.4	4.4	NUM
ejpam-3660	203	8	.	.	PUNCT
ejpam-3660	204	1	a.	a.	NOUN
ejpam-3660	204	2	macodi	macodi	PROPN
ejpam-3660	204	3	-	-	PUNCT
ejpam-3660	204	4	ringia	ringia	ADJ
ejpam-3660	204	5	,	,	PUNCT
ejpam-3660	204	6	g.	g.	PROPN
ejpam-3660	204	7	petalcorin	petalcorin	PROPN
ejpam-3660	204	8	,	,	PUNCT
ejpam-3660	204	9	jr	jr	PROPN
ejpam-3660	204	10	.	.	PROPN
ejpam-3660	204	11	/	/	SYM
ejpam-3660	204	12	eur	eur	PROPN
ejpam-3660	204	13	.	.	PUNCT
ejpam-3660	205	1	j.	j.	PROPN
ejpam-3660	205	2	pure	pure	PROPN
ejpam-3660	205	3	appl	appl	PROPN
ejpam-3660	205	4	.	.	PROPN
ejpam-3660	205	5	math	math	PROPN
ejpam-3660	205	6	,	,	PUNCT
ejpam-3660	205	7	13	13	NUM
ejpam-3660	205	8	(	(	PUNCT
ejpam-3660	205	9	2	2	NUM
ejpam-3660	205	10	)	)	PUNCT
ejpam-3660	205	11	(	(	PUNCT
ejpam-3660	205	12	2020	2020	NUM
ejpam-3660	205	13	)	)	PUNCT
ejpam-3660	205	14	,	,	PUNCT
ejpam-3660	205	15	246	246	NUM
ejpam-3660	205	16	-	-	SYM
ejpam-3660	205	17	257	257	NUM
ejpam-3660	205	18	253	253	NUM
ejpam-3660	205	19	corollary	corollary	ADJ
ejpam-3660	205	20	4.5	4.5	NUM
ejpam-3660	205	21	.	.	PUNCT
ejpam-3660	206	1	let	let	VERB
ejpam-3660	206	2	µ	µ	X
ejpam-3660	206	3	:	:	PUNCT
ejpam-3660	206	4	h→	h→	SYM
ejpam-3660	207	1	[	[	X
ejpam-3660	207	2	0	0	NUM
ejpam-3660	207	3	,	,	PUNCT
ejpam-3660	207	4	1	1	NUM
ejpam-3660	207	5	]	]	PUNCT
ejpam-3660	207	6	be	be	AUX
ejpam-3660	207	7	a	a	DET
ejpam-3660	207	8	fuzzy	fuzzy	ADJ
ejpam-3660	207	9	set	set	NOUN
ejpam-3660	207	10	and	and	CCONJ
ejpam-3660	207	11	s	s	NOUN
ejpam-3660	208	1	⊆	⊆	NUM
ejpam-3660	208	2	h.	h.	NOUN
ejpam-3660	208	3	then	then	ADV
ejpam-3660	208	4	(	(	PUNCT
ejpam-3660	208	5	a	a	X
ejpam-3660	208	6	)	)	PUNCT
ejpam-3660	208	7	1	1	NUM
ejpam-3660	208	8	−max	−max	NUM
ejpam-3660	208	9	x∈s	x∈s	PROPN
ejpam-3660	208	10	µ(x	µ(x	PROPN
ejpam-3660	208	11	)	)	PUNCT
ejpam-3660	208	12	=	=	SYM
ejpam-3660	208	13	min	min	NOUN
ejpam-3660	208	14	x∈s	x∈s	NOUN
ejpam-3660	208	15	(	(	PUNCT
ejpam-3660	208	16	1	1	NUM
ejpam-3660	208	17	−	−	PRON
ejpam-3660	208	18	µ(x	µ(x	NOUN
ejpam-3660	208	19	)	)	PUNCT
ejpam-3660	208	20	)	)	PUNCT
ejpam-3660	208	21	,	,	PUNCT
ejpam-3660	208	22	(	(	PUNCT
ejpam-3660	208	23	b	b	X
ejpam-3660	208	24	)	)	PUNCT
ejpam-3660	208	25	1	1	NUM
ejpam-3660	208	26	−min	−min	NOUN
ejpam-3660	208	27	x∈s	x∈s	PROPN
ejpam-3660	208	28	µ(x	µ(x	PROPN
ejpam-3660	208	29	)	)	PUNCT
ejpam-3660	208	30	=	=	SYM
ejpam-3660	208	31	max	max	PROPN
ejpam-3660	208	32	x∈s	x∈s	PROPN
ejpam-3660	208	33	(	(	PUNCT
ejpam-3660	208	34	1	1	NUM
ejpam-3660	208	35	−	−	NOUN
ejpam-3660	208	36	µ(x	µ(x	NOUN
ejpam-3660	208	37	)	)	PUNCT
ejpam-3660	208	38	)	)	PUNCT
ejpam-3660	208	39	.	.	PUNCT
ejpam-3660	209	1	lemma	lemma	PROPN
ejpam-3660	209	2	4.6	4.6	NUM
ejpam-3660	209	3	.	.	PUNCT
ejpam-3660	210	1	an	an	DET
ejpam-3660	210	2	intuitionistic	intuitionistic	ADJ
ejpam-3660	210	3	fuzzy	fuzzy	NOUN
ejpam-3660	210	4	set	set	VERB
ejpam-3660	210	5	a	a	PRON
ejpam-3660	210	6	=	=	X
ejpam-3660	210	7	(	(	PUNCT
ejpam-3660	210	8	µa	µa	PROPN
ejpam-3660	210	9	,	,	PUNCT
ejpam-3660	210	10	γa	γa	PROPN
ejpam-3660	210	11	)	)	PUNCT
ejpam-3660	210	12	is	be	AUX
ejpam-3660	210	13	an	an	DET
ejpam-3660	210	14	intuitionistic	intuitionistic	ADJ
ejpam-3660	210	15	fuzzy	fuzzy	ADJ
ejpam-3660	210	16	hyper	hyper	ADJ
ejpam-3660	210	17	gr	gr	NOUN
ejpam-3660	210	18	-	-	PUNCT
ejpam-3660	210	19	ideal	ideal	NOUN
ejpam-3660	210	20	in	in	ADP
ejpam-3660	210	21	a	a	DET
ejpam-3660	210	22	hyper	hyper	ADJ
ejpam-3660	210	23	gr	gr	NOUN
ejpam-3660	210	24	-	-	PUNCT
ejpam-3660	210	25	algebra	algebra	NOUN
ejpam-3660	210	26	h	h	NOUN
ejpam-3660	210	27	if	if	SCONJ
ejpam-3660	211	1	and	and	CCONJ
ejpam-3660	211	2	only	only	ADV
ejpam-3660	211	3	if	if	SCONJ
ejpam-3660	211	4	the	the	DET
ejpam-3660	211	5	fuzzy	fuzzy	ADJ
ejpam-3660	211	6	sets	set	VERB
ejpam-3660	211	7	µa	µa	NOUN
ejpam-3660	211	8	and	and	CCONJ
ejpam-3660	211	9	γ̄a	γ̄a	PROPN
ejpam-3660	211	10	are	be	AUX
ejpam-3660	211	11	fuzzy	fuzzy	ADJ
ejpam-3660	211	12	hyper	hyper	ADJ
ejpam-3660	211	13	gr	gr	NOUN
ejpam-3660	211	14	-	-	PUNCT
ejpam-3660	211	15	ideals	ideal	NOUN
ejpam-3660	211	16	of	of	ADP
ejpam-3660	211	17	type	type	NOUN
ejpam-3660	211	18	1	1	NUM
ejpam-3660	211	19	in	in	ADP
ejpam-3660	211	20	h.	h.	NOUN
ejpam-3660	211	21	proof	proof	NOUN
ejpam-3660	211	22	.	.	PUNCT
ejpam-3660	212	1	suppose	suppose	VERB
ejpam-3660	212	2	a	a	DET
ejpam-3660	212	3	=	=	X
ejpam-3660	212	4	(	(	PUNCT
ejpam-3660	212	5	µa	µa	PROPN
ejpam-3660	212	6	,	,	PUNCT
ejpam-3660	212	7	γa	γa	PROPN
ejpam-3660	212	8	)	)	PUNCT
ejpam-3660	212	9	is	be	AUX
ejpam-3660	212	10	an	an	DET
ejpam-3660	212	11	intuitionistic	intuitionistic	ADJ
ejpam-3660	212	12	fuzzy	fuzzy	ADJ
ejpam-3660	212	13	hyper	hyper	ADJ
ejpam-3660	212	14	gr	gr	NOUN
ejpam-3660	212	15	-	-	PUNCT
ejpam-3660	212	16	ideal	ideal	NOUN
ejpam-3660	212	17	in	in	ADP
ejpam-3660	212	18	h.	h.	PROPN
ejpam-3660	212	19	clearly	clearly	ADV
ejpam-3660	212	20	,	,	PUNCT
ejpam-3660	212	21	µa	µa	ADV
ejpam-3660	212	22	is	be	AUX
ejpam-3660	212	23	a	a	DET
ejpam-3660	212	24	fuzzy	fuzzy	ADJ
ejpam-3660	212	25	hyper	hyper	ADJ
ejpam-3660	212	26	gr	gr	NOUN
ejpam-3660	212	27	-	-	PUNCT
ejpam-3660	212	28	ideal	ideal	NOUN
ejpam-3660	212	29	of	of	ADP
ejpam-3660	212	30	type	type	NOUN
ejpam-3660	212	31	1	1	NUM
ejpam-3660	212	32	in	in	ADP
ejpam-3660	212	33	h	h	NOUN
ejpam-3660	212	34	and	and	CCONJ
ejpam-3660	212	35	γa(x	γa(x	NUM
ejpam-3660	212	36	)	)	PUNCT
ejpam-3660	212	37	≥	≥	NUM
ejpam-3660	212	38	γa(0	γa(0	NOUN
ejpam-3660	212	39	)	)	PUNCT
ejpam-3660	212	40	for	for	ADP
ejpam-3660	212	41	all	all	DET
ejpam-3660	212	42	x	x	SYM
ejpam-3660	212	43	∈	∈	PROPN
ejpam-3660	212	44	h.	h.	NOUN
ejpam-3660	212	45	then	then	ADV
ejpam-3660	212	46	,	,	PUNCT
ejpam-3660	212	47	γ̄a(x	γ̄a(x	NOUN
ejpam-3660	212	48	)	)	PUNCT
ejpam-3660	212	49	=	=	SYM
ejpam-3660	213	1	1	1	NUM
ejpam-3660	213	2	−	−	NUM
ejpam-3660	213	3	γa(x	γa(x	NUM
ejpam-3660	213	4	)	)	PUNCT
ejpam-3660	213	5	≤	≤	NUM
ejpam-3660	213	6	1	1	NUM
ejpam-3660	213	7	−	−	NOUN
ejpam-3660	213	8	γa(0	γa(0	NOUN
ejpam-3660	213	9	)	)	PUNCT
ejpam-3660	213	10	=	=	PUNCT
ejpam-3660	213	11	γ̄a(0	γ̄a(0	NUM
ejpam-3660	213	12	)	)	PUNCT
ejpam-3660	213	13	.	.	PUNCT
ejpam-3660	214	1	let	let	VERB
ejpam-3660	214	2	x	x	PRON
ejpam-3660	214	3	,	,	PUNCT
ejpam-3660	214	4	y	y	PROPN
ejpam-3660	214	5	∈	∈	PROPN
ejpam-3660	214	6	h.	h.	PROPN
ejpam-3660	214	7	then	then	ADV
ejpam-3660	214	8	,	,	PUNCT
ejpam-3660	214	9	γ̄a(x	γ̄a(x	NOUN
ejpam-3660	214	10	)	)	PUNCT
ejpam-3660	214	11	=	=	SYM
ejpam-3660	215	1	1	1	NUM
ejpam-3660	215	2	−	−	NUM
ejpam-3660	215	3	γa(x	γa(x	NUM
ejpam-3660	215	4	)	)	PUNCT
ejpam-3660	215	5	≥	≥	NOUN
ejpam-3660	215	6	1	1	NUM
ejpam-3660	215	7	−max	−max	NOUN
ejpam-3660	215	8			NUM
ejpam-3660	215	9	sup	sup	NOUN
ejpam-3660	215	10	v∈x	v∈x	NOUN
ejpam-3660	215	11	~	~	SYM
ejpam-3660	215	12	y	y	PROPN
ejpam-3660	215	13	γa(v	γa(v	PUNCT
ejpam-3660	215	14	)	)	PUNCT
ejpam-3660	215	15	,	,	PUNCT
ejpam-3660	215	16	γa(y	γa(y	X
ejpam-3660	215	17	)	)	PUNCT
ejpam-3660	215	18			NOUN
ejpam-3660	215	19	.	.	PUNCT
ejpam-3660	216	1	(	(	PUNCT
ejpam-3660	216	2	2	2	X
ejpam-3660	216	3	)	)	PUNCT
ejpam-3660	216	4	case	case	NOUN
ejpam-3660	216	5	1	1	NUM
ejpam-3660	216	6	.	.	PUNCT
ejpam-3660	216	7	suppose	suppose	VERB
ejpam-3660	216	8	max	max	PROPN
ejpam-3660	216	9			PROPN
ejpam-3660	216	10	sup	sup	PROPN
ejpam-3660	216	11	v∈x	v∈x	NOUN
ejpam-3660	216	12	~	~	SYM
ejpam-3660	216	13	y	y	PROPN
ejpam-3660	216	14	γa(v	γa(v	PUNCT
ejpam-3660	216	15	)	)	PUNCT
ejpam-3660	216	16	,	,	PUNCT
ejpam-3660	216	17	γa(y	γa(y	X
ejpam-3660	216	18	)	)	PUNCT
ejpam-3660	217	1			NOUN
ejpam-3660	217	2	=	=	NOUN
ejpam-3660	217	3	sup	sup	NOUN
ejpam-3660	217	4	v∈x	v∈x	NOUN
ejpam-3660	217	5	~	~	SYM
ejpam-3660	217	6	y	y	PROPN
ejpam-3660	217	7	γa(v	γa(v	PUNCT
ejpam-3660	217	8	)	)	PUNCT
ejpam-3660	217	9	.	.	PUNCT
ejpam-3660	218	1	then	then	ADV
ejpam-3660	218	2	,	,	PUNCT
ejpam-3660	218	3	1	1	NUM
ejpam-3660	218	4	−max	−max	NOUN
ejpam-3660	218	5			NUM
ejpam-3660	218	6	sup	sup	NOUN
ejpam-3660	218	7	v∈x	v∈x	NOUN
ejpam-3660	218	8	~	~	SYM
ejpam-3660	218	9	y	y	PROPN
ejpam-3660	218	10	γa(v	γa(v	PUNCT
ejpam-3660	218	11	)	)	PUNCT
ejpam-3660	218	12	,	,	PUNCT
ejpam-3660	218	13	γa(y	γa(y	X
ejpam-3660	218	14	)	)	PUNCT
ejpam-3660	218	15			NOUN
ejpam-3660	218	16	=	=	NOUN
ejpam-3660	218	17	1	1	NUM
ejpam-3660	218	18	−	−	NUM
ejpam-3660	218	19	sup	sup	NOUN
ejpam-3660	218	20	v∈x	v∈x	NOUN
ejpam-3660	218	21	~	~	SYM
ejpam-3660	218	22	y	y	PROPN
ejpam-3660	218	23	γa(v	γa(v	PUNCT
ejpam-3660	218	24	)	)	PUNCT
ejpam-3660	218	25	.	.	PUNCT
ejpam-3660	219	1	by	by	ADP
ejpam-3660	219	2	corollary	corollary	ADJ
ejpam-3660	219	3	4.5	4.5	NUM
ejpam-3660	219	4	,	,	PUNCT
ejpam-3660	219	5	1	1	NUM
ejpam-3660	219	6	−	−	NOUN
ejpam-3660	219	7	sup	sup	NOUN
ejpam-3660	219	8	v∈x	v∈x	NOUN
ejpam-3660	219	9	~	~	SYM
ejpam-3660	219	10	y	y	PROPN
ejpam-3660	219	11	γa(v	γa(v	PUNCT
ejpam-3660	219	12	)	)	PUNCT
ejpam-3660	219	13	=	=	SYM
ejpam-3660	219	14	inf	inf	PROPN
ejpam-3660	219	15	v∈x	v∈x	NOUN
ejpam-3660	219	16	~	~	SYM
ejpam-3660	219	17	y	y	PROPN
ejpam-3660	219	18	(	(	PUNCT
ejpam-3660	219	19	1	1	NUM
ejpam-3660	219	20	−	−	NUM
ejpam-3660	219	21	γa(v	γa(v	PUNCT
ejpam-3660	219	22	)	)	PUNCT
ejpam-3660	219	23	)	)	PUNCT
ejpam-3660	220	1	=	=	SYM
ejpam-3660	220	2	inf	inf	PROPN
ejpam-3660	220	3	v∈x	v∈x	NOUN
ejpam-3660	220	4	~	~	PROPN
ejpam-3660	220	5	y	y	PROPN
ejpam-3660	220	6	γ̄a(v	γ̄a(v	PROPN
ejpam-3660	220	7	)	)	PUNCT
ejpam-3660	220	8	≥	≥	NOUN
ejpam-3660	220	9	min	min	PROPN
ejpam-3660	220	10	{	{	PUNCT
ejpam-3660	220	11	inf	inf	PROPN
ejpam-3660	220	12	v∈x	v∈x	PROPN
ejpam-3660	220	13	~	~	PROPN
ejpam-3660	220	14	y	y	PROPN
ejpam-3660	220	15	γ̄a(v	γ̄a(v	PROPN
ejpam-3660	220	16	)	)	PUNCT
ejpam-3660	220	17	,	,	PUNCT
ejpam-3660	220	18	γ̄a(y	γ̄a(y	PROPN
ejpam-3660	220	19	)	)	PUNCT
ejpam-3660	220	20	}	}	PUNCT
ejpam-3660	220	21	.	.	PUNCT
ejpam-3660	221	1	by	by	ADP
ejpam-3660	221	2	(	(	PUNCT
ejpam-3660	221	3	2	2	NUM
ejpam-3660	221	4	)	)	PUNCT
ejpam-3660	221	5	,	,	PUNCT
ejpam-3660	221	6	we	we	PRON
ejpam-3660	221	7	have	have	VERB
ejpam-3660	221	8	γ̄a(x	γ̄a(x	NOUN
ejpam-3660	221	9	)	)	PUNCT
ejpam-3660	221	10	≥	≥	NOUN
ejpam-3660	221	11	min	min	PROPN
ejpam-3660	221	12	{	{	PUNCT
ejpam-3660	221	13	inf	inf	PROPN
ejpam-3660	221	14	v∈x	v∈x	PROPN
ejpam-3660	221	15	~	~	PROPN
ejpam-3660	221	16	y	y	PROPN
ejpam-3660	221	17	γ̄a(v	γ̄a(v	PROPN
ejpam-3660	221	18	)	)	PUNCT
ejpam-3660	221	19	,	,	PUNCT
ejpam-3660	221	20	γ̄a(y	γ̄a(y	PROPN
ejpam-3660	221	21	)	)	PUNCT
ejpam-3660	221	22	}	}	PUNCT
ejpam-3660	221	23	.	.	PUNCT
ejpam-3660	222	1	case	case	NOUN
ejpam-3660	222	2	2	2	X
ejpam-3660	222	3	.	.	PUNCT
ejpam-3660	222	4	suppose	suppose	VERB
ejpam-3660	222	5	max	max	PROPN
ejpam-3660	222	6			PROPN
ejpam-3660	222	7	sup	sup	PROPN
ejpam-3660	222	8	v∈x	v∈x	NOUN
ejpam-3660	222	9	~	~	SYM
ejpam-3660	222	10	y	y	PROPN
ejpam-3660	222	11	γa(v	γa(v	PUNCT
ejpam-3660	222	12	)	)	PUNCT
ejpam-3660	222	13	,	,	PUNCT
ejpam-3660	222	14	γa(y	γa(y	X
ejpam-3660	222	15	)	)	PUNCT
ejpam-3660	222	16			NOUN
ejpam-3660	222	17	=	=	SYM
ejpam-3660	222	18	γa(y	γa(y	NUM
ejpam-3660	222	19	)	)	PUNCT
ejpam-3660	222	20	.	.	PUNCT
ejpam-3660	223	1	then	then	ADV
ejpam-3660	223	2	,	,	PUNCT
ejpam-3660	223	3	1	1	NUM
ejpam-3660	223	4	−max	−max	NOUN
ejpam-3660	223	5			NUM
ejpam-3660	223	6	sup	sup	NOUN
ejpam-3660	223	7	v∈x	v∈x	NOUN
ejpam-3660	223	8	~	~	SYM
ejpam-3660	223	9	y	y	PROPN
ejpam-3660	223	10	γa(v	γa(v	PUNCT
ejpam-3660	223	11	)	)	PUNCT
ejpam-3660	223	12	,	,	PUNCT
ejpam-3660	223	13	γa(y	γa(y	X
ejpam-3660	223	14	)	)	PUNCT
ejpam-3660	223	15			NOUN
ejpam-3660	223	16	=	=	NOUN
ejpam-3660	223	17	1	1	NUM
ejpam-3660	223	18	−	−	NOUN
ejpam-3660	223	19	γa(y	γa(y	NUM
ejpam-3660	223	20	)	)	PUNCT
ejpam-3660	223	21	=	=	SYM
ejpam-3660	224	1	γ̄a(y	γ̄a(y	PROPN
ejpam-3660	224	2	)	)	PUNCT
ejpam-3660	224	3	≥	≥	NOUN
ejpam-3660	224	4	min	min	PROPN
ejpam-3660	224	5	{	{	PUNCT
ejpam-3660	224	6	inf	inf	PROPN
ejpam-3660	224	7	v∈x	v∈x	PROPN
ejpam-3660	224	8	~	~	PROPN
ejpam-3660	224	9	y	y	PROPN
ejpam-3660	224	10	γ̄a(v	γ̄a(v	PROPN
ejpam-3660	224	11	)	)	PUNCT
ejpam-3660	224	12	,	,	PUNCT
ejpam-3660	224	13	γ̄a(y	γ̄a(y	PROPN
ejpam-3660	224	14	)	)	PUNCT
ejpam-3660	224	15	}	}	PUNCT
ejpam-3660	224	16	.	.	PUNCT
ejpam-3660	225	1	it	it	PRON
ejpam-3660	225	2	follows	follow	VERB
ejpam-3660	225	3	from	from	ADP
ejpam-3660	225	4	(	(	PUNCT
ejpam-3660	225	5	2	2	NUM
ejpam-3660	225	6	)	)	PUNCT
ejpam-3660	225	7	that	that	SCONJ
ejpam-3660	225	8	γ̄a(x	γ̄a(x	ADJ
ejpam-3660	225	9	)	)	PUNCT
ejpam-3660	225	10	≥	≥	NOUN
ejpam-3660	225	11	min	min	PROPN
ejpam-3660	225	12	{	{	PUNCT
ejpam-3660	225	13	inf	inf	PROPN
ejpam-3660	225	14	v∈x	v∈x	PROPN
ejpam-3660	225	15	~	~	PROPN
ejpam-3660	225	16	y	y	PROPN
ejpam-3660	225	17	γ̄a(v	γ̄a(v	PROPN
ejpam-3660	225	18	)	)	PUNCT
ejpam-3660	225	19	,	,	PUNCT
ejpam-3660	225	20	γ̄a(y	γ̄a(y	PROPN
ejpam-3660	225	21	)	)	PUNCT
ejpam-3660	225	22	}	}	PUNCT
ejpam-3660	225	23	.	.	PUNCT
ejpam-3660	226	1	therefore	therefore	ADV
ejpam-3660	226	2	,	,	PUNCT
ejpam-3660	226	3	γ̄a	γ̄a	PROPN
ejpam-3660	226	4	is	be	AUX
ejpam-3660	226	5	a	a	DET
ejpam-3660	226	6	fuzzy	fuzzy	ADJ
ejpam-3660	226	7	hyper	hyper	ADJ
ejpam-3660	226	8	gr	gr	NOUN
ejpam-3660	226	9	-	-	PUNCT
ejpam-3660	226	10	ideal	ideal	NOUN
ejpam-3660	226	11	of	of	ADP
ejpam-3660	226	12	type	type	NOUN
ejpam-3660	226	13	1	1	NUM
ejpam-3660	226	14	in	in	ADP
ejpam-3660	226	15	h.	h.	NOUN
ejpam-3660	226	16	conversely	conversely	ADV
ejpam-3660	226	17	,	,	PUNCT
ejpam-3660	226	18	suppose	suppose	VERB
ejpam-3660	226	19	µa	µa	NOUN
ejpam-3660	226	20	and	and	CCONJ
ejpam-3660	226	21	γ̄a	γ̄a	PROPN
ejpam-3660	226	22	are	be	AUX
ejpam-3660	226	23	fuzzy	fuzzy	ADJ
ejpam-3660	226	24	hyper	hyper	ADJ
ejpam-3660	226	25	gr	gr	NOUN
ejpam-3660	226	26	-	-	PUNCT
ejpam-3660	226	27	ideals	ideal	NOUN
ejpam-3660	226	28	of	of	ADP
ejpam-3660	226	29	type	type	NOUN
ejpam-3660	226	30	1	1	NUM
ejpam-3660	226	31	.	.	PUNCT
ejpam-3660	227	1	let	let	VERB
ejpam-3660	227	2	x	x	SYM
ejpam-3660	227	3	∈	∈	PROPN
ejpam-3660	227	4	h.	h.	PROPN
ejpam-3660	227	5	clearly	clearly	ADV
ejpam-3660	227	6	,	,	PUNCT
ejpam-3660	227	7	γ̄a(x	γ̄a(x	NOUN
ejpam-3660	227	8	)	)	PUNCT
ejpam-3660	227	9	≤	≤	NOUN
ejpam-3660	227	10	γ̄a(0	γ̄a(0	NUM
ejpam-3660	227	11	)	)	PUNCT
ejpam-3660	227	12	.	.	PUNCT
ejpam-3660	228	1	then	then	ADV
ejpam-3660	228	2	,	,	PUNCT
ejpam-3660	228	3	1	1	NUM
ejpam-3660	228	4	−	−	NOUN
ejpam-3660	228	5	γa(x	γa(x	NOUN
ejpam-3660	228	6	)	)	PUNCT
ejpam-3660	228	7	≤	≤	NUM
ejpam-3660	228	8	1	1	NUM
ejpam-3660	228	9	−	−	NOUN
ejpam-3660	228	10	γa(0	γa(0	NOUN
ejpam-3660	228	11	)	)	PUNCT
ejpam-3660	228	12	and	and	CCONJ
ejpam-3660	228	13	so	so	ADV
ejpam-3660	228	14	γa(x	γa(x	NUM
ejpam-3660	228	15	)	)	PUNCT
ejpam-3660	228	16	≥	≥	NUM
ejpam-3660	228	17	γa(0	γa(0	NOUN
ejpam-3660	228	18	)	)	PUNCT
ejpam-3660	228	19	.	.	PUNCT
ejpam-3660	229	1	let	let	VERB
ejpam-3660	229	2	x	x	PRON
ejpam-3660	229	3	,	,	PUNCT
ejpam-3660	229	4	y	y	PROPN
ejpam-3660	229	5	∈	∈	PROPN
ejpam-3660	229	6	h.	h.	PROPN
ejpam-3660	229	7	by	by	ADP
ejpam-3660	229	8	ifgr3	ifgr3	NOUN
ejpam-3660	229	9	and	and	CCONJ
ejpam-3660	229	10	lemma	lemma	PROPN
ejpam-3660	229	11	4.4	4.4	NUM
ejpam-3660	229	12	,	,	PUNCT
ejpam-3660	229	13	1	1	NUM
ejpam-3660	229	14	−	−	NOUN
ejpam-3660	229	15	γa(x	γa(x	NUM
ejpam-3660	229	16	)	)	PUNCT
ejpam-3660	230	1	=	=	SYM
ejpam-3660	230	2	γ̄a(x	γ̄a(x	NOUN
ejpam-3660	230	3	)	)	PUNCT
ejpam-3660	230	4	≥	≥	NOUN
ejpam-3660	230	5	min	min	PROPN
ejpam-3660	230	6	{	{	PUNCT
ejpam-3660	230	7	inf	inf	PROPN
ejpam-3660	230	8	v∈x	v∈x	PROPN
ejpam-3660	230	9	~	~	PROPN
ejpam-3660	230	10	y	y	PROPN
ejpam-3660	230	11	γ̄a(v	γ̄a(v	PROPN
ejpam-3660	230	12	)	)	PUNCT
ejpam-3660	230	13	,	,	PUNCT
ejpam-3660	230	14	γ̄a(y	γ̄a(y	PROPN
ejpam-3660	230	15	)	)	PUNCT
ejpam-3660	230	16	}	}	PUNCT
ejpam-3660	230	17	a.	a.	NOUN
ejpam-3660	230	18	macodi	macodi	NOUN
ejpam-3660	230	19	-	-	PUNCT
ejpam-3660	230	20	ringia	ringia	ADJ
ejpam-3660	230	21	,	,	PUNCT
ejpam-3660	230	22	g.	g.	PROPN
ejpam-3660	230	23	petalcorin	petalcorin	PROPN
ejpam-3660	230	24	,	,	PUNCT
ejpam-3660	230	25	jr	jr	PROPN
ejpam-3660	230	26	.	.	PROPN
ejpam-3660	230	27	/	/	SYM
ejpam-3660	230	28	eur	eur	PROPN
ejpam-3660	230	29	.	.	PUNCT
ejpam-3660	231	1	j.	j.	PROPN
ejpam-3660	231	2	pure	pure	PROPN
ejpam-3660	231	3	appl	appl	PROPN
ejpam-3660	231	4	.	.	PROPN
ejpam-3660	231	5	math	math	PROPN
ejpam-3660	231	6	,	,	PUNCT
ejpam-3660	231	7	13	13	NUM
ejpam-3660	231	8	(	(	PUNCT
ejpam-3660	231	9	2	2	NUM
ejpam-3660	231	10	)	)	PUNCT
ejpam-3660	231	11	(	(	PUNCT
ejpam-3660	231	12	2020	2020	NUM
ejpam-3660	231	13	)	)	PUNCT
ejpam-3660	231	14	,	,	PUNCT
ejpam-3660	231	15	246	246	NUM
ejpam-3660	231	16	-	-	SYM
ejpam-3660	231	17	257	257	NUM
ejpam-3660	231	18	254	254	NUM
ejpam-3660	231	19	=	=	SYM
ejpam-3660	231	20	min	min	NOUN
ejpam-3660	231	21	{	{	PUNCT
ejpam-3660	231	22	inf	inf	NOUN
ejpam-3660	231	23	v∈x	v∈x	PROPN
ejpam-3660	231	24	~	~	SYM
ejpam-3660	231	25	y	y	PROPN
ejpam-3660	231	26	(	(	PUNCT
ejpam-3660	231	27	1	1	NUM
ejpam-3660	231	28	−	−	NUM
ejpam-3660	231	29	γa(v	γa(v	PUNCT
ejpam-3660	231	30	)	)	PUNCT
ejpam-3660	231	31	)	)	PUNCT
ejpam-3660	231	32	,	,	PUNCT
ejpam-3660	231	33	1	1	NUM
ejpam-3660	231	34	−	−	NOUN
ejpam-3660	231	35	γa(y	γa(y	NUM
ejpam-3660	231	36	)	)	PUNCT
ejpam-3660	231	37	}	}	PUNCT
ejpam-3660	232	1	=	=	NUM
ejpam-3660	232	2	min	min	NOUN
ejpam-3660	232	3	1	1	PROPN
ejpam-3660	232	4	−	−	PROPN
ejpam-3660	232	5	sup	sup	NOUN
ejpam-3660	232	6	v∈x	v∈x	NOUN
ejpam-3660	232	7	~	~	SYM
ejpam-3660	232	8	y	y	PROPN
ejpam-3660	232	9	γa(v	γa(v	PUNCT
ejpam-3660	232	10	)	)	PUNCT
ejpam-3660	232	11	,	,	PUNCT
ejpam-3660	232	12	1	1	NUM
ejpam-3660	232	13	−	−	NOUN
ejpam-3660	232	14	γa(y	γa(y	NOUN
ejpam-3660	232	15	)	)	PUNCT
ejpam-3660	233	1			NOUN
ejpam-3660	233	2	=	=	SYM
ejpam-3660	233	3	1	1	NUM
ejpam-3660	233	4	−max	−max	NOUN
ejpam-3660	233	5			NUM
ejpam-3660	233	6	sup	sup	NOUN
ejpam-3660	233	7	v∈x	v∈x	NOUN
ejpam-3660	233	8	~	~	SYM
ejpam-3660	233	9	y	y	PROPN
ejpam-3660	233	10	γa(v	γa(v	PUNCT
ejpam-3660	233	11	)	)	PUNCT
ejpam-3660	233	12	,	,	PUNCT
ejpam-3660	233	13	γa(y	γa(y	X
ejpam-3660	233	14	)	)	PUNCT
ejpam-3660	233	15			NOUN
ejpam-3660	233	16	.	.	PUNCT
ejpam-3660	234	1	it	it	PRON
ejpam-3660	234	2	follows	follow	VERB
ejpam-3660	234	3	that	that	SCONJ
ejpam-3660	234	4	−γa(x	−γa(x	NOUN
ejpam-3660	234	5	)	)	PUNCT
ejpam-3660	234	6	≥	≥	NOUN
ejpam-3660	234	7	−max	−max	NOUN
ejpam-3660	234	8			NUM
ejpam-3660	234	9	sup	sup	NOUN
ejpam-3660	234	10	v∈x	v∈x	NOUN
ejpam-3660	234	11	~	~	SYM
ejpam-3660	234	12	y	y	PROPN
ejpam-3660	234	13	γa(v	γa(v	PUNCT
ejpam-3660	234	14	)	)	PUNCT
ejpam-3660	234	15	,	,	PUNCT
ejpam-3660	234	16	γa(y	γa(y	X
ejpam-3660	234	17	)	)	PUNCT
ejpam-3660	234	18			NOUN
ejpam-3660	234	19	and	and	CCONJ
ejpam-3660	234	20	so	so	ADV
ejpam-3660	234	21	γa(x	γa(x	NUM
ejpam-3660	234	22	)	)	PUNCT
ejpam-3660	234	23	≤	≤	NUM
ejpam-3660	234	24	max	max	PROPN
ejpam-3660	234	25			PUNCT
ejpam-3660	234	26	sup	sup	NOUN
ejpam-3660	234	27	v∈x	v∈x	NOUN
ejpam-3660	234	28	~	~	SYM
ejpam-3660	234	29	y	y	PROPN
ejpam-3660	234	30	γa(v	γa(v	PUNCT
ejpam-3660	234	31	)	)	PUNCT
ejpam-3660	234	32	,	,	PUNCT
ejpam-3660	234	33	γa(y	γa(y	NUM
ejpam-3660	234	34	)	)	PUNCT
ejpam-3660	234	35	.	.	PROPN
ejpam-3660	234	36	therefore	therefore	ADV
ejpam-3660	234	37	,	,	PUNCT
ejpam-3660	234	38	a	a	PRON
ejpam-3660	234	39	is	be	AUX
ejpam-3660	234	40	an	an	DET
ejpam-3660	234	41	intuitionistic	intuitionistic	ADJ
ejpam-3660	234	42	fuzzy	fuzzy	ADJ
ejpam-3660	234	43	hyper	hyper	ADJ
ejpam-3660	234	44	gr	gr	NOUN
ejpam-3660	234	45	-	-	PUNCT
ejpam-3660	234	46	ideal	ideal	NOUN
ejpam-3660	234	47	in	in	ADP
ejpam-3660	234	48	h.	h.	PROPN
ejpam-3660	234	49	�	�	PROPN
ejpam-3660	234	50	theorem	theorem	VERB
ejpam-3660	234	51	4.7	4.7	NUM
ejpam-3660	234	52	.	.	PUNCT
ejpam-3660	235	1	let	let	VERB
ejpam-3660	235	2	a	a	DET
ejpam-3660	235	3	=	=	SYM
ejpam-3660	235	4	(	(	PUNCT
ejpam-3660	235	5	µa	µa	PROPN
ejpam-3660	235	6	,	,	PUNCT
ejpam-3660	235	7	γa	γa	PROPN
ejpam-3660	235	8	)	)	PUNCT
ejpam-3660	235	9	be	be	VERB
ejpam-3660	235	10	an	an	DET
ejpam-3660	235	11	intuitionistic	intuitionistic	ADJ
ejpam-3660	235	12	fuzzy	fuzzy	ADJ
ejpam-3660	235	13	set	set	NOUN
ejpam-3660	235	14	in	in	ADP
ejpam-3660	235	15	a	a	DET
ejpam-3660	235	16	hyper	hyper	ADJ
ejpam-3660	235	17	gr	gr	NOUN
ejpam-3660	235	18	-	-	PUNCT
ejpam-3660	235	19	algebra	algebra	NOUN
ejpam-3660	235	20	h.	h.	NOUN
ejpam-3660	235	21	then	then	ADV
ejpam-3660	235	22	,	,	PUNCT
ejpam-3660	235	23	a	a	PRON
ejpam-3660	235	24	is	be	AUX
ejpam-3660	235	25	an	an	DET
ejpam-3660	235	26	intuitionistic	intuitionistic	ADJ
ejpam-3660	235	27	fuzzy	fuzzy	ADJ
ejpam-3660	235	28	hyper	hyper	ADJ
ejpam-3660	235	29	gr	gr	NOUN
ejpam-3660	235	30	-	-	PUNCT
ejpam-3660	235	31	ideal	ideal	NOUN
ejpam-3660	235	32	in	in	ADP
ejpam-3660	235	33	h	h	NOUN
ejpam-3660	235	34	if	if	SCONJ
ejpam-3660	236	1	and	and	CCONJ
ejpam-3660	236	2	only	only	ADV
ejpam-3660	236	3	if	if	SCONJ
ejpam-3660	236	4	â	â	X
ejpam-3660	236	5	=	=	SYM
ejpam-3660	236	6	(	(	PUNCT
ejpam-3660	236	7	µa	µa	NOUN
ejpam-3660	236	8	,	,	PUNCT
ejpam-3660	236	9	µ̄a	µ̄a	ADJ
ejpam-3660	236	10	)	)	PUNCT
ejpam-3660	236	11	and	and	CCONJ
ejpam-3660	236	12	ã	ã	PROPN
ejpam-3660	236	13	=	=	SYM
ejpam-3660	236	14	(	(	PUNCT
ejpam-3660	236	15	γ̄a	γ̄a	PROPN
ejpam-3660	236	16	,	,	PUNCT
ejpam-3660	236	17	γa	γa	PROPN
ejpam-3660	236	18	)	)	PUNCT
ejpam-3660	236	19	are	be	AUX
ejpam-3660	236	20	intuitionistic	intuitionistic	ADJ
ejpam-3660	236	21	fuzzy	fuzzy	ADJ
ejpam-3660	236	22	hyper	hyper	ADJ
ejpam-3660	236	23	gr	gr	NOUN
ejpam-3660	236	24	-	-	PUNCT
ejpam-3660	236	25	ideals	ideal	NOUN
ejpam-3660	236	26	of	of	ADP
ejpam-3660	236	27	h.	h.	NOUN
ejpam-3660	236	28	proof	proof	NOUN
ejpam-3660	236	29	.	.	PUNCT
ejpam-3660	237	1	suppose	suppose	VERB
ejpam-3660	237	2	a	a	DET
ejpam-3660	237	3	=	=	X
ejpam-3660	237	4	(	(	PUNCT
ejpam-3660	237	5	µa	µa	PROPN
ejpam-3660	237	6	,	,	PUNCT
ejpam-3660	237	7	γa	γa	PROPN
ejpam-3660	237	8	)	)	PUNCT
ejpam-3660	237	9	is	be	AUX
ejpam-3660	237	10	an	an	DET
ejpam-3660	237	11	intuitionistic	intuitionistic	ADJ
ejpam-3660	237	12	fuzzy	fuzzy	ADJ
ejpam-3660	237	13	hyper	hyper	ADJ
ejpam-3660	237	14	gr	gr	NOUN
ejpam-3660	237	15	-	-	PUNCT
ejpam-3660	237	16	ideal	ideal	NOUN
ejpam-3660	237	17	in	in	ADP
ejpam-3660	237	18	h.	h.	PROPN
ejpam-3660	237	19	by	by	ADP
ejpam-3660	237	20	lemma	lemma	PROPN
ejpam-3660	237	21	4.6	4.6	NUM
ejpam-3660	237	22	,	,	PUNCT
ejpam-3660	237	23	µa	µa	NOUN
ejpam-3660	237	24	and	and	CCONJ
ejpam-3660	237	25	γ̄a	γ̄a	PROPN
ejpam-3660	237	26	are	be	AUX
ejpam-3660	237	27	fuzzy	fuzzy	ADJ
ejpam-3660	237	28	hyper	hyper	ADJ
ejpam-3660	237	29	gr	gr	NOUN
ejpam-3660	237	30	-	-	PUNCT
ejpam-3660	237	31	ideals	ideal	NOUN
ejpam-3660	237	32	of	of	ADP
ejpam-3660	237	33	type	type	NOUN
ejpam-3660	237	34	1	1	NUM
ejpam-3660	237	35	in	in	ADP
ejpam-3660	237	36	h.	h.	PROPN
ejpam-3660	237	37	let	let	VERB
ejpam-3660	237	38	x	x	PRON
ejpam-3660	237	39	,	,	PUNCT
ejpam-3660	237	40	y	y	PROPN
ejpam-3660	237	41	∈	∈	PROPN
ejpam-3660	237	42	h.	h.	PROPN
ejpam-3660	237	43	then	then	ADV
ejpam-3660	237	44	,	,	PUNCT
ejpam-3660	237	45	µ̄a(x	µ̄a(x	PROPN
ejpam-3660	237	46	)	)	PUNCT
ejpam-3660	237	47	=	=	SYM
ejpam-3660	237	48	1	1	NUM
ejpam-3660	237	49	−	−	NOUN
ejpam-3660	237	50	µa(x	µa(x	NOUN
ejpam-3660	237	51	)	)	PUNCT
ejpam-3660	237	52	≥	≥	NOUN
ejpam-3660	237	53	1	1	NUM
ejpam-3660	237	54	−	−	NOUN
ejpam-3660	237	55	µa(0	µa(0	NOUN
ejpam-3660	237	56	)	)	PUNCT
ejpam-3660	237	57	=	=	PUNCT
ejpam-3660	237	58	µ̄a(0	µ̄a(0	X
ejpam-3660	237	59	)	)	PUNCT
ejpam-3660	237	60	.	.	PUNCT
ejpam-3660	238	1	by	by	ADP
ejpam-3660	238	2	lemma	lemma	PROPN
ejpam-3660	238	3	4.4	4.4	NUM
ejpam-3660	238	4	,	,	PUNCT
ejpam-3660	238	5	µ̄a(x	µ̄a(x	PROPN
ejpam-3660	238	6	)	)	PUNCT
ejpam-3660	238	7	=	=	SYM
ejpam-3660	238	8	1	1	NUM
ejpam-3660	238	9	−	−	NUM
ejpam-3660	238	10	µa(x	µa(x	NOUN
ejpam-3660	238	11	)	)	PUNCT
ejpam-3660	238	12	≤	≤	NUM
ejpam-3660	238	13	1	1	NUM
ejpam-3660	238	14	−min	−min	NOUN
ejpam-3660	238	15	{	{	PUNCT
ejpam-3660	238	16	inf	inf	NOUN
ejpam-3660	238	17	u∈x	u∈x	NOUN
ejpam-3660	238	18	~	~	PROPN
ejpam-3660	238	19	y	y	PROPN
ejpam-3660	238	20	µa(u	µa(u	NOUN
ejpam-3660	238	21	)	)	PUNCT
ejpam-3660	238	22	,	,	PUNCT
ejpam-3660	238	23	µa(y	µa(y	NOUN
ejpam-3660	238	24	)	)	PUNCT
ejpam-3660	238	25	}	}	PUNCT
ejpam-3660	238	26	=	=	SYM
ejpam-3660	238	27	max	max	X
ejpam-3660	238	28	{	{	PUNCT
ejpam-3660	238	29	1	1	NUM
ejpam-3660	238	30	−	−	PROPN
ejpam-3660	238	31	inf	inf	PROPN
ejpam-3660	238	32	u∈x	u∈x	NOUN
ejpam-3660	238	33	~	~	PROPN
ejpam-3660	238	34	y	y	PROPN
ejpam-3660	238	35	µa(u	µa(u	NOUN
ejpam-3660	238	36	)	)	PUNCT
ejpam-3660	238	37	,	,	PUNCT
ejpam-3660	238	38	1	1	NUM
ejpam-3660	238	39	−	−	NOUN
ejpam-3660	238	40	µa(y	µa(y	NOUN
ejpam-3660	238	41	)	)	PUNCT
ejpam-3660	238	42	}	}	PUNCT
ejpam-3660	239	1	=	=	SYM
ejpam-3660	239	2	max	max	PROPN
ejpam-3660	239	3			PUNCT
ejpam-3660	239	4	sup	sup	NOUN
ejpam-3660	239	5	u∈x	u∈x	NOUN
ejpam-3660	239	6	~	~	SYM
ejpam-3660	239	7	y	y	PROPN
ejpam-3660	239	8	(	(	PUNCT
ejpam-3660	239	9	1	1	NUM
ejpam-3660	239	10	−	−	NOUN
ejpam-3660	239	11	µa(u	µa(u	NOUN
ejpam-3660	239	12	)	)	PUNCT
ejpam-3660	239	13	)	)	PUNCT
ejpam-3660	239	14	,	,	PUNCT
ejpam-3660	239	15	µ̄a(y	µ̄a(y	NOUN
ejpam-3660	239	16	)	)	PUNCT
ejpam-3660	239	17			PROPN
ejpam-3660	239	18	=	=	PUNCT
ejpam-3660	239	19	max	max	PROPN
ejpam-3660	239	20			PUNCT
ejpam-3660	239	21	sup	sup	NOUN
ejpam-3660	239	22	u∈x	u∈x	NOUN
ejpam-3660	239	23	~	~	SYM
ejpam-3660	239	24	y	y	PROPN
ejpam-3660	239	25	µ̄a(u	µ̄a(u	NOUN
ejpam-3660	239	26	)	)	PUNCT
ejpam-3660	239	27	,	,	PUNCT
ejpam-3660	239	28	µ̄a(y	µ̄a(y	NOUN
ejpam-3660	239	29	)	)	PUNCT
ejpam-3660	239	30			PROPN
ejpam-3660	239	31	.	.	PUNCT
ejpam-3660	240	1	hence	hence	ADV
ejpam-3660	240	2	by	by	ADP
ejpam-3660	240	3	definition	definition	NOUN
ejpam-3660	240	4	4.1	4.1	NUM
ejpam-3660	240	5	,	,	PUNCT
ejpam-3660	240	6	â	â	X
ejpam-3660	240	7	=	=	SYM
ejpam-3660	240	8	(	(	PUNCT
ejpam-3660	240	9	µa	µa	NOUN
ejpam-3660	240	10	,	,	PUNCT
ejpam-3660	240	11	µ̄a	µ̄a	ADJ
ejpam-3660	240	12	)	)	PUNCT
ejpam-3660	240	13	and	and	CCONJ
ejpam-3660	240	14	ã	ã	PROPN
ejpam-3660	240	15	=	=	SYM
ejpam-3660	240	16	(	(	PUNCT
ejpam-3660	240	17	γ̄a	γ̄a	PROPN
ejpam-3660	240	18	,	,	PUNCT
ejpam-3660	240	19	γa	γa	PROPN
ejpam-3660	240	20	)	)	PUNCT
ejpam-3660	240	21	are	be	AUX
ejpam-3660	240	22	intuitionistic	intuitionistic	ADJ
ejpam-3660	240	23	fuzzy	fuzzy	ADJ
ejpam-3660	240	24	hyper	hyper	ADJ
ejpam-3660	240	25	gr	gr	NOUN
ejpam-3660	240	26	-	-	PUNCT
ejpam-3660	240	27	ideals	ideal	NOUN
ejpam-3660	240	28	in	in	ADP
ejpam-3660	240	29	h.	h.	NOUN
ejpam-3660	240	30	conversely	conversely	ADV
ejpam-3660	240	31	,	,	PUNCT
ejpam-3660	240	32	let	let	VERB
ejpam-3660	240	33	â	â	X
ejpam-3660	240	34	=	=	SYM
ejpam-3660	240	35	(	(	PUNCT
ejpam-3660	240	36	µa	µa	NOUN
ejpam-3660	240	37	,	,	PUNCT
ejpam-3660	240	38	µ̄a	µ̄a	ADJ
ejpam-3660	240	39	)	)	PUNCT
ejpam-3660	240	40	and	and	CCONJ
ejpam-3660	240	41	ã	ã	PROPN
ejpam-3660	240	42	=	=	SYM
ejpam-3660	240	43	(	(	PUNCT
ejpam-3660	240	44	γ̄a	γ̄a	PROPN
ejpam-3660	240	45	,	,	PUNCT
ejpam-3660	240	46	γa	γa	PROPN
ejpam-3660	240	47	)	)	PUNCT
ejpam-3660	240	48	be	be	AUX
ejpam-3660	240	49	intuitionistic	intuitionistic	ADJ
ejpam-3660	240	50	fuzzy	fuzzy	ADJ
ejpam-3660	240	51	hyper	hyper	ADJ
ejpam-3660	240	52	gr	gr	NOUN
ejpam-3660	240	53	-	-	PUNCT
ejpam-3660	240	54	ideals	ideal	NOUN
ejpam-3660	240	55	in	in	ADP
ejpam-3660	240	56	h.	h.	PROPN
ejpam-3660	240	57	then	then	ADV
ejpam-3660	240	58	by	by	ADP
ejpam-3660	240	59	lemma	lemma	PROPN
ejpam-3660	240	60	4.6	4.6	NUM
ejpam-3660	240	61	,	,	PUNCT
ejpam-3660	240	62	µa	µa	NOUN
ejpam-3660	240	63	and	and	CCONJ
ejpam-3660	240	64	γ̄a	γ̄a	PROPN
ejpam-3660	240	65	are	be	AUX
ejpam-3660	240	66	fuzzy	fuzzy	ADJ
ejpam-3660	240	67	hyper	hyper	ADJ
ejpam-3660	240	68	gr	gr	NOUN
ejpam-3660	240	69	-	-	PUNCT
ejpam-3660	240	70	ideals	ideal	NOUN
ejpam-3660	240	71	of	of	ADP
ejpam-3660	240	72	type	type	NOUN
ejpam-3660	240	73	1	1	NUM
ejpam-3660	240	74	in	in	ADP
ejpam-3660	240	75	h.	h.	NOUN
ejpam-3660	240	76	thus	thus	ADV
ejpam-3660	240	77	by	by	ADP
ejpam-3660	240	78	lemma	lemma	PROPN
ejpam-3660	240	79	4.6	4.6	NUM
ejpam-3660	240	80	,	,	PUNCT
ejpam-3660	240	81	a	a	DET
ejpam-3660	240	82	=	=	X
ejpam-3660	240	83	(	(	PUNCT
ejpam-3660	240	84	µa	µa	PROPN
ejpam-3660	240	85	,	,	PUNCT
ejpam-3660	240	86	γa	γa	PROPN
ejpam-3660	240	87	)	)	PUNCT
ejpam-3660	240	88	is	be	AUX
ejpam-3660	240	89	an	an	DET
ejpam-3660	240	90	intuitionistic	intuitionistic	ADJ
ejpam-3660	240	91	fuzzy	fuzzy	ADJ
ejpam-3660	240	92	hyper	hyper	ADJ
ejpam-3660	240	93	gr	gr	NOUN
ejpam-3660	240	94	-	-	PUNCT
ejpam-3660	240	95	ideal	ideal	NOUN
ejpam-3660	240	96	in	in	ADP
ejpam-3660	240	97	h.	h.	PROPN
ejpam-3660	240	98	�	�	PROPN
ejpam-3660	240	99	a.	a.	PROPN
ejpam-3660	240	100	macodi	macodi	PROPN
ejpam-3660	240	101	-	-	PUNCT
ejpam-3660	240	102	ringia	ringia	ADJ
ejpam-3660	240	103	,	,	PUNCT
ejpam-3660	240	104	g.	g.	PROPN
ejpam-3660	240	105	petalcorin	petalcorin	PROPN
ejpam-3660	240	106	,	,	PUNCT
ejpam-3660	240	107	jr	jr	PROPN
ejpam-3660	240	108	.	.	PROPN
ejpam-3660	240	109	/	/	SYM
ejpam-3660	240	110	eur	eur	PROPN
ejpam-3660	240	111	.	.	PUNCT
ejpam-3660	241	1	j.	j.	PROPN
ejpam-3660	241	2	pure	pure	PROPN
ejpam-3660	241	3	appl	appl	PROPN
ejpam-3660	241	4	.	.	PROPN
ejpam-3660	241	5	math	math	PROPN
ejpam-3660	241	6	,	,	PUNCT
ejpam-3660	241	7	13	13	NUM
ejpam-3660	241	8	(	(	PUNCT
ejpam-3660	241	9	2	2	NUM
ejpam-3660	241	10	)	)	PUNCT
ejpam-3660	241	11	(	(	PUNCT
ejpam-3660	241	12	2020	2020	NUM
ejpam-3660	241	13	)	)	PUNCT
ejpam-3660	241	14	,	,	PUNCT
ejpam-3660	241	15	246	246	NUM
ejpam-3660	241	16	-	-	SYM
ejpam-3660	241	17	257	257	NUM
ejpam-3660	241	18	255	255	NUM
ejpam-3660	241	19	theorem	theorem	VERB
ejpam-3660	241	20	4.8	4.8	NUM
ejpam-3660	241	21	.	.	PUNCT
ejpam-3660	242	1	for	for	ADP
ejpam-3660	242	2	any	any	DET
ejpam-3660	242	3	subset	subset	NOUN
ejpam-3660	242	4	i	i	PRON
ejpam-3660	242	5	of	of	ADP
ejpam-3660	242	6	a	a	DET
ejpam-3660	242	7	hyper	hyper	ADJ
ejpam-3660	242	8	gr	gr	NOUN
ejpam-3660	242	9	-	-	PUNCT
ejpam-3660	242	10	algebra	algebra	NOUN
ejpam-3660	242	11	h	h	NOUN
ejpam-3660	242	12	,	,	PUNCT
ejpam-3660	242	13	let	let	VERB
ejpam-3660	242	14	a(i	a(i	VERB
ejpam-3660	242	15	)	)	PUNCT
ejpam-3660	243	1	=	=	SYM
ejpam-3660	243	2	(	(	PUNCT
ejpam-3660	243	3	µa(i	µa(i	X
ejpam-3660	243	4	)	)	PUNCT
ejpam-3660	243	5	,	,	PUNCT
ejpam-3660	243	6	γa(i	γa(i	NOUN
ejpam-3660	243	7	)	)	PUNCT
ejpam-3660	243	8	)	)	PUNCT
ejpam-3660	243	9	be	be	AUX
ejpam-3660	243	10	an	an	DET
ejpam-3660	243	11	intuitionistic	intuitionistic	ADJ
ejpam-3660	243	12	fuzzy	fuzzy	ADJ
ejpam-3660	243	13	set	set	NOUN
ejpam-3660	243	14	in	in	ADP
ejpam-3660	243	15	h	h	NOUN
ejpam-3660	243	16	defined	define	VERB
ejpam-3660	243	17	by	by	ADP
ejpam-3660	243	18	the	the	DET
ejpam-3660	243	19	following	following	NOUN
ejpam-3660	243	20	,	,	PUNCT
ejpam-3660	243	21	respectively	respectively	ADV
ejpam-3660	243	22	:	:	PUNCT
ejpam-3660	243	23	(	(	PUNCT
ejpam-3660	243	24	µa(i))(x	µa(i))(x	NOUN
ejpam-3660	243	25	)	)	PUNCT
ejpam-3660	243	26	=	=	SYM
ejpam-3660	243	27	{	{	PUNCT
ejpam-3660	243	28	k1	k1	NOUN
ejpam-3660	243	29	,	,	PUNCT
ejpam-3660	243	30	if	if	SCONJ
ejpam-3660	243	31	x	x	PROPN
ejpam-3660	243	32	∈	∈	PROPN
ejpam-3660	243	33	i	i	NOUN
ejpam-3660	243	34	k2	k2	NOUN
ejpam-3660	243	35	,	,	PUNCT
ejpam-3660	243	36	otherwise	otherwise	ADV
ejpam-3660	243	37	(	(	PUNCT
ejpam-3660	243	38	γa(i))(x	γa(i))(x	PROPN
ejpam-3660	243	39	)	)	PUNCT
ejpam-3660	243	40	=	=	PRON
ejpam-3660	243	41	{	{	PUNCT
ejpam-3660	243	42	m1	m1	NOUN
ejpam-3660	243	43	,	,	PUNCT
ejpam-3660	243	44	if	if	SCONJ
ejpam-3660	243	45	x	x	SYM
ejpam-3660	243	46	∈	∈	PROPN
ejpam-3660	243	47	i	i	NOUN
ejpam-3660	243	48	m2	m2	PROPN
ejpam-3660	243	49	,	,	PUNCT
ejpam-3660	243	50	otherwise	otherwise	ADV
ejpam-3660	243	51	for	for	ADP
ejpam-3660	243	52	all	all	DET
ejpam-3660	243	53	x	x	SYM
ejpam-3660	243	54	∈	∈	PROPN
ejpam-3660	243	55	h	h	NOUN
ejpam-3660	243	56	,	,	PUNCT
ejpam-3660	243	57	where	where	SCONJ
ejpam-3660	243	58	k1	k1	NOUN
ejpam-3660	243	59	,	,	PUNCT
ejpam-3660	243	60	k2,m1,m2	k2,m1,m2	PRON
ejpam-3660	243	61	∈	∈	PROPN
ejpam-3660	244	1	[	[	X
ejpam-3660	244	2	0	0	NUM
ejpam-3660	244	3	,	,	PUNCT
ejpam-3660	244	4	1	1	NUM
ejpam-3660	244	5	]	]	PUNCT
ejpam-3660	244	6	with	with	ADP
ejpam-3660	244	7	k1	k1	PROPN
ejpam-3660	244	8	>	>	X
ejpam-3660	244	9	k2	k2	PROPN
ejpam-3660	244	10	,	,	PUNCT
ejpam-3660	244	11	m1	m1	PROPN
ejpam-3660	244	12	<	<	X
ejpam-3660	244	13	m2	m2	PROPN
ejpam-3660	244	14	,	,	PUNCT
ejpam-3660	244	15	ki	ki	PROPN
ejpam-3660	244	16	+	+	CCONJ
ejpam-3660	244	17	mi	mi	PROPN
ejpam-3660	244	18	≤	≤	ADV
ejpam-3660	244	19	1	1	NUM
ejpam-3660	244	20	for	for	ADP
ejpam-3660	244	21	i	i	PRON
ejpam-3660	244	22	=	=	NOUN
ejpam-3660	244	23	1	1	NUM
ejpam-3660	244	24	,	,	PUNCT
ejpam-3660	244	25	2	2	NUM
ejpam-3660	244	26	.	.	PUNCT
ejpam-3660	245	1	then	then	ADV
ejpam-3660	245	2	,	,	PUNCT
ejpam-3660	245	3	i	i	PRON
ejpam-3660	245	4	is	be	AUX
ejpam-3660	245	5	a	a	DET
ejpam-3660	245	6	hyper	hyper	ADJ
ejpam-3660	245	7	gr	gr	NOUN
ejpam-3660	245	8	-	-	PUNCT
ejpam-3660	245	9	ideal	ideal	NOUN
ejpam-3660	245	10	of	of	ADP
ejpam-3660	245	11	h	h	NOUN
ejpam-3660	245	12	if	if	SCONJ
ejpam-3660	246	1	and	and	CCONJ
ejpam-3660	246	2	only	only	ADV
ejpam-3660	246	3	if	if	SCONJ
ejpam-3660	246	4	a(i	a(i	NOUN
ejpam-3660	246	5	)	)	PUNCT
ejpam-3660	247	1	=	=	SYM
ejpam-3660	247	2	(	(	PUNCT
ejpam-3660	247	3	µa(i	µa(i	X
ejpam-3660	247	4	)	)	PUNCT
ejpam-3660	247	5	,	,	PUNCT
ejpam-3660	247	6	γa(i	γa(i	NOUN
ejpam-3660	247	7	)	)	PUNCT
ejpam-3660	247	8	)	)	PUNCT
ejpam-3660	247	9	is	be	AUX
ejpam-3660	247	10	an	an	DET
ejpam-3660	247	11	intuitionistic	intuitionistic	ADJ
ejpam-3660	247	12	fuzzy	fuzzy	ADJ
ejpam-3660	247	13	hyper	hyper	ADJ
ejpam-3660	247	14	gr	gr	NOUN
ejpam-3660	247	15	-	-	PUNCT
ejpam-3660	247	16	ideal	ideal	NOUN
ejpam-3660	247	17	in	in	ADP
ejpam-3660	247	18	h.	h.	PROPN
ejpam-3660	247	19	proof	proof	PROPN
ejpam-3660	247	20	.	.	PUNCT
ejpam-3660	248	1	note	note	VERB
ejpam-3660	248	2	that	that	SCONJ
ejpam-3660	248	3	the	the	DET
ejpam-3660	248	4	level	level	NOUN
ejpam-3660	248	5	subsets	subset	NOUN
ejpam-3660	248	6	of	of	ADP
ejpam-3660	248	7	µa(i	µa(i	NOUN
ejpam-3660	248	8	)	)	PUNCT
ejpam-3660	248	9	are	be	AUX
ejpam-3660	248	10	(	(	PUNCT
ejpam-3660	248	11	µa(i	µa(i	X
ejpam-3660	248	12	)	)	PUNCT
ejpam-3660	248	13	)	)	PUNCT
ejpam-3660	249	1	t1	t1	NOUN
ejpam-3660	249	2	=	=	PUNCT
ejpam-3660	250	1			NUM
ejpam-3660	250	2	∅	∅	NOUN
ejpam-3660	250	3	,	,	PUNCT
ejpam-3660	250	4	if	if	SCONJ
ejpam-3660	250	5	k1	k1	PROPN
ejpam-3660	250	6	<	<	X
ejpam-3660	250	7	t1	t1	PROPN
ejpam-3660	250	8	≤	≤	NUM
ejpam-3660	250	9	1	1	NUM
ejpam-3660	250	10	i	i	PRON
ejpam-3660	250	11	,	,	PUNCT
ejpam-3660	250	12	if	if	SCONJ
ejpam-3660	250	13	k2	k2	PROPN
ejpam-3660	250	14	<	<	X
ejpam-3660	250	15	t1	t1	PROPN
ejpam-3660	250	16	≤	≤	NUM
ejpam-3660	250	17	k1	k1	NOUN
ejpam-3660	250	18	h	h	NOUN
ejpam-3660	250	19	,	,	PUNCT
ejpam-3660	250	20	if	if	SCONJ
ejpam-3660	250	21	0	0	NUM
ejpam-3660	250	22	≤	≤	NUM
ejpam-3660	250	23	t1	t1	NOUN
ejpam-3660	250	24	≤	≤	ADJ
ejpam-3660	250	25	k2	k2	NOUN
ejpam-3660	250	26	.	.	PUNCT
ejpam-3660	251	1	(	(	PUNCT
ejpam-3660	251	2	3	3	NUM
ejpam-3660	251	3	)	)	PUNCT
ejpam-3660	251	4	since	since	SCONJ
ejpam-3660	251	5	(	(	PUNCT
ejpam-3660	251	6	γ̄a(i))(x	γ̄a(i))(x	PROPN
ejpam-3660	251	7	)	)	PUNCT
ejpam-3660	251	8	=	=	PRON
ejpam-3660	251	9	{	{	PUNCT
ejpam-3660	251	10	1	1	NUM
ejpam-3660	251	11	−m1	−m1	NOUN
ejpam-3660	251	12	,	,	PUNCT
ejpam-3660	251	13	if	if	SCONJ
ejpam-3660	251	14	x	x	SYM
ejpam-3660	251	15	∈	∈	PROPN
ejpam-3660	251	16	i	i	NOUN
ejpam-3660	251	17	1	1	NUM
ejpam-3660	251	18	−m2	−m2	NOUN
ejpam-3660	251	19	,	,	PUNCT
ejpam-3660	251	20	otherwise	otherwise	ADV
ejpam-3660	251	21	and	and	CCONJ
ejpam-3660	251	22	1	1	NUM
ejpam-3660	251	23	−m1	−m1	NOUN
ejpam-3660	251	24	>	>	SYM
ejpam-3660	251	25	1	1	NUM
ejpam-3660	251	26	−m2	−m2	NOUN
ejpam-3660	251	27	,	,	PUNCT
ejpam-3660	251	28	(	(	PUNCT
ejpam-3660	251	29	γ̄a(i	γ̄a(i	PROPN
ejpam-3660	251	30	)	)	PUNCT
ejpam-3660	251	31	)	)	PUNCT
ejpam-3660	252	1	t2	t2	NOUN
ejpam-3660	252	2	=	=	SYM
ejpam-3660	252	3			PROPN
ejpam-3660	252	4	∅	∅	NOUN
ejpam-3660	252	5	,	,	PUNCT
ejpam-3660	252	6	if	if	SCONJ
ejpam-3660	252	7	1	1	NUM
ejpam-3660	252	8	−m1	−m1	VERB
ejpam-3660	252	9	<	<	X
ejpam-3660	252	10	t2	t2	PROPN
ejpam-3660	252	11	≤	≤	NUM
ejpam-3660	252	12	1	1	NUM
ejpam-3660	252	13	i	i	NOUN
ejpam-3660	252	14	,	,	PUNCT
ejpam-3660	252	15	if	if	SCONJ
ejpam-3660	252	16	1	1	NUM
ejpam-3660	252	17	−m2	−m2	NOUN
ejpam-3660	252	18	<	<	X
ejpam-3660	252	19	t2	t2	PROPN
ejpam-3660	252	20	≤	≤	NUM
ejpam-3660	252	21	1	1	NUM
ejpam-3660	252	22	−m1	−m1	NOUN
ejpam-3660	252	23	h	h	NOUN
ejpam-3660	252	24	,	,	PUNCT
ejpam-3660	252	25	if	if	SCONJ
ejpam-3660	252	26	0	0	NUM
ejpam-3660	252	27	≤	≤	NUM
ejpam-3660	252	28	t2	t2	NOUN
ejpam-3660	252	29	≤	≤	NOUN
ejpam-3660	252	30	1	1	NUM
ejpam-3660	252	31	−m2	−m2	NOUN
ejpam-3660	252	32	.	.	PUNCT
ejpam-3660	252	33	suppose	suppose	VERB
ejpam-3660	252	34	i	i	PRON
ejpam-3660	252	35	is	be	AUX
ejpam-3660	252	36	a	a	DET
ejpam-3660	252	37	hyper	hyper	ADJ
ejpam-3660	252	38	gr	gr	NOUN
ejpam-3660	252	39	-	-	PUNCT
ejpam-3660	252	40	ideal	ideal	NOUN
ejpam-3660	252	41	of	of	ADP
ejpam-3660	252	42	h.	h.	PROPN
ejpam-3660	252	43	then	then	ADV
ejpam-3660	252	44	the	the	DET
ejpam-3660	252	45	nonempty	nonempty	ADJ
ejpam-3660	252	46	level	level	NOUN
ejpam-3660	252	47	subsets	subset	NOUN
ejpam-3660	252	48	(	(	PUNCT
ejpam-3660	252	49	µa(i	µa(i	X
ejpam-3660	252	50	)	)	PUNCT
ejpam-3660	252	51	)	)	PUNCT
ejpam-3660	253	1	t1	t1	NOUN
ejpam-3660	253	2	and	and	CCONJ
ejpam-3660	253	3	(	(	PUNCT
ejpam-3660	253	4	γ̄a(i	γ̄a(i	PROPN
ejpam-3660	253	5	)	)	PUNCT
ejpam-3660	253	6	)	)	PUNCT
ejpam-3660	254	1	t2	t2	NOUN
ejpam-3660	254	2	are	be	AUX
ejpam-3660	254	3	hyper	hyper	ADJ
ejpam-3660	254	4	gr	gr	NOUN
ejpam-3660	254	5	-	-	PUNCT
ejpam-3660	254	6	ideals	ideal	NOUN
ejpam-3660	254	7	of	of	ADP
ejpam-3660	254	8	h.	h.	NOUN
ejpam-3660	254	9	by	by	ADP
ejpam-3660	254	10	theorem	theorem	NOUN
ejpam-3660	254	11	3.5	3.5	NUM
ejpam-3660	254	12	,	,	PUNCT
ejpam-3660	254	13	µa(i	µa(i	NOUN
ejpam-3660	254	14	)	)	PUNCT
ejpam-3660	254	15	and	and	CCONJ
ejpam-3660	254	16	γ̄a(i	γ̄a(i	NOUN
ejpam-3660	254	17	)	)	PUNCT
ejpam-3660	254	18	are	be	AUX
ejpam-3660	254	19	fuzzy	fuzzy	ADJ
ejpam-3660	254	20	hyper	hyper	ADJ
ejpam-3660	254	21	gr	gr	NOUN
ejpam-3660	254	22	-	-	PUNCT
ejpam-3660	254	23	ideals	ideal	NOUN
ejpam-3660	254	24	of	of	ADP
ejpam-3660	254	25	type	type	NOUN
ejpam-3660	254	26	1	1	NUM
ejpam-3660	254	27	.	.	PUNCT
ejpam-3660	254	28	by	by	ADP
ejpam-3660	254	29	lemma	lemma	PROPN
ejpam-3660	254	30	4.6	4.6	NUM
ejpam-3660	254	31	,	,	PUNCT
ejpam-3660	254	32	a(i	a(i	NOUN
ejpam-3660	254	33	)	)	PUNCT
ejpam-3660	255	1	=	=	SYM
ejpam-3660	255	2	(	(	PUNCT
ejpam-3660	255	3	µa(i	µa(i	X
ejpam-3660	255	4	)	)	PUNCT
ejpam-3660	255	5	,	,	PUNCT
ejpam-3660	255	6	γa(i	γa(i	NOUN
ejpam-3660	255	7	)	)	PUNCT
ejpam-3660	255	8	)	)	PUNCT
ejpam-3660	255	9	is	be	AUX
ejpam-3660	255	10	an	an	DET
ejpam-3660	255	11	intuitionistic	intuitionistic	ADJ
ejpam-3660	255	12	fuzzy	fuzzy	ADJ
ejpam-3660	255	13	hyper	hyper	ADJ
ejpam-3660	255	14	gr	gr	NOUN
ejpam-3660	255	15	-	-	PUNCT
ejpam-3660	255	16	ideal	ideal	NOUN
ejpam-3660	255	17	in	in	ADP
ejpam-3660	255	18	h.	h.	NOUN
ejpam-3660	255	19	conversely	conversely	ADV
ejpam-3660	255	20	,	,	PUNCT
ejpam-3660	255	21	suppose	suppose	VERB
ejpam-3660	255	22	a(i	a(i	VERB
ejpam-3660	255	23	)	)	PUNCT
ejpam-3660	255	24	=	=	SYM
ejpam-3660	255	25	(	(	PUNCT
ejpam-3660	255	26	µa(i	µa(i	X
ejpam-3660	255	27	)	)	PUNCT
ejpam-3660	255	28	,	,	PUNCT
ejpam-3660	255	29	γa(i	γa(i	NOUN
ejpam-3660	255	30	)	)	PUNCT
ejpam-3660	255	31	)	)	PUNCT
ejpam-3660	255	32	is	be	AUX
ejpam-3660	255	33	an	an	DET
ejpam-3660	255	34	intuitionistic	intuitionistic	ADJ
ejpam-3660	255	35	fuzzy	fuzzy	ADJ
ejpam-3660	255	36	hyper	hyper	ADJ
ejpam-3660	255	37	gr	gr	NOUN
ejpam-3660	255	38	-	-	PUNCT
ejpam-3660	255	39	ideal	ideal	NOUN
ejpam-3660	255	40	in	in	ADP
ejpam-3660	255	41	h.	h.	PROPN
ejpam-3660	255	42	by	by	ADP
ejpam-3660	255	43	lemma	lemma	PROPN
ejpam-3660	255	44	4.6	4.6	NUM
ejpam-3660	255	45	,	,	PUNCT
ejpam-3660	255	46	µa(i	µa(i	PUNCT
ejpam-3660	255	47	)	)	PUNCT
ejpam-3660	255	48	and	and	CCONJ
ejpam-3660	255	49	γ̄a(i	γ̄a(i	NOUN
ejpam-3660	255	50	)	)	PUNCT
ejpam-3660	255	51	are	be	AUX
ejpam-3660	255	52	fuzzy	fuzzy	ADJ
ejpam-3660	255	53	hyper	hyper	ADJ
ejpam-3660	255	54	gr	gr	NOUN
ejpam-3660	255	55	-	-	PUNCT
ejpam-3660	255	56	ideals	ideal	NOUN
ejpam-3660	255	57	in	in	ADP
ejpam-3660	255	58	h.	h.	PROPN
ejpam-3660	255	59	it	it	PRON
ejpam-3660	255	60	follows	follow	VERB
ejpam-3660	255	61	from	from	ADP
ejpam-3660	255	62	theorem	theorem	ADJ
ejpam-3660	255	63	3.5	3.5	NUM
ejpam-3660	255	64	that	that	PRON
ejpam-3660	255	65	i	i	PRON
ejpam-3660	255	66	=	=	PUNCT
ejpam-3660	255	67	(	(	PUNCT
ejpam-3660	255	68	µa(i	µa(i	X
ejpam-3660	255	69	)	)	PUNCT
ejpam-3660	255	70	)	)	PUNCT
ejpam-3660	256	1	t1	t1	NOUN
ejpam-3660	256	2	is	be	AUX
ejpam-3660	256	3	a	a	DET
ejpam-3660	256	4	hyper	hyper	ADJ
ejpam-3660	256	5	gr	gr	NOUN
ejpam-3660	256	6	-	-	PUNCT
ejpam-3660	256	7	ideal	ideal	NOUN
ejpam-3660	256	8	of	of	ADP
ejpam-3660	256	9	h.	h.	PROPN
ejpam-3660	256	10	�	�	PROPN
ejpam-3660	256	11	theorem	theorem	VERB
ejpam-3660	256	12	4.9	4.9	NUM
ejpam-3660	256	13	.	.	PUNCT
ejpam-3660	257	1	if	if	SCONJ
ejpam-3660	257	2	a	a	PRON
ejpam-3660	257	3	=	=	X
ejpam-3660	257	4	(	(	PUNCT
ejpam-3660	257	5	µa	µa	PROPN
ejpam-3660	257	6	,	,	PUNCT
ejpam-3660	257	7	γa	γa	PROPN
ejpam-3660	257	8	)	)	PUNCT
ejpam-3660	257	9	is	be	AUX
ejpam-3660	257	10	an	an	DET
ejpam-3660	257	11	intuitionistic	intuitionistic	ADJ
ejpam-3660	257	12	fuzzy	fuzzy	ADJ
ejpam-3660	257	13	hyper	hyper	ADJ
ejpam-3660	257	14	gr	gr	NOUN
ejpam-3660	257	15	-	-	PUNCT
ejpam-3660	257	16	ideal	ideal	NOUN
ejpam-3660	257	17	of	of	ADP
ejpam-3660	257	18	a	a	DET
ejpam-3660	257	19	hyper	hyper	ADJ
ejpam-3660	257	20	gr	gr	NOUN
ejpam-3660	257	21	-	-	PUNCT
ejpam-3660	257	22	algebra	algebra	NOUN
ejpam-3660	257	23	h	h	NOUN
ejpam-3660	257	24	,	,	PUNCT
ejpam-3660	257	25	then	then	ADV
ejpam-3660	257	26	the	the	DET
ejpam-3660	257	27	set	set	NOUN
ejpam-3660	257	28	i	i	PRON
ejpam-3660	257	29	=	=	PUNCT
ejpam-3660	257	30	{	{	PUNCT
ejpam-3660	257	31	x	x	PROPN
ejpam-3660	257	32	∈	∈	NOUN
ejpam-3660	257	33	h|µa(x	h|µa(x	NOUN
ejpam-3660	257	34	)	)	PUNCT
ejpam-3660	257	35	=	=	SYM
ejpam-3660	257	36	µa(0	µa(0	NOUN
ejpam-3660	257	37	)	)	PUNCT
ejpam-3660	257	38	and	and	CCONJ
ejpam-3660	257	39	γa(x	γa(x	NUM
ejpam-3660	257	40	)	)	PUNCT
ejpam-3660	257	41	=	=	SYM
ejpam-3660	257	42	γa(0	γa(0	NOUN
ejpam-3660	257	43	)	)	PUNCT
ejpam-3660	257	44	}	}	PUNCT
ejpam-3660	257	45	is	be	AUX
ejpam-3660	257	46	a	a	DET
ejpam-3660	257	47	hyper	hyper	ADJ
ejpam-3660	257	48	gr	gr	NOUN
ejpam-3660	257	49	-	-	PUNCT
ejpam-3660	257	50	ideal	ideal	NOUN
ejpam-3660	257	51	of	of	ADP
ejpam-3660	257	52	h.	h.	NOUN
ejpam-3660	257	53	proof	proof	NOUN
ejpam-3660	257	54	.	.	PUNCT
ejpam-3660	258	1	let	let	VERB
ejpam-3660	258	2	a	a	DET
ejpam-3660	258	3	=	=	SYM
ejpam-3660	258	4	(	(	PUNCT
ejpam-3660	258	5	µa	µa	PROPN
ejpam-3660	258	6	,	,	PUNCT
ejpam-3660	258	7	γa	γa	PROPN
ejpam-3660	258	8	)	)	PUNCT
ejpam-3660	258	9	be	be	VERB
ejpam-3660	258	10	an	an	DET
ejpam-3660	258	11	intuitionistic	intuitionistic	ADJ
ejpam-3660	258	12	fuzzy	fuzzy	ADJ
ejpam-3660	258	13	hyper	hyper	ADJ
ejpam-3660	258	14	gr	gr	NOUN
ejpam-3660	258	15	-	-	PUNCT
ejpam-3660	258	16	ideal	ideal	NOUN
ejpam-3660	258	17	in	in	ADP
ejpam-3660	258	18	h.	h.	PROPN
ejpam-3660	258	19	clearly	clearly	ADV
ejpam-3660	258	20	,	,	PUNCT
ejpam-3660	258	21	0	0	NUM
ejpam-3660	258	22	∈	∈	PROPN
ejpam-3660	258	23	i.	i.	NOUN
ejpam-3660	258	24	let	let	VERB
ejpam-3660	258	25	x	x	PRON
ejpam-3660	258	26	,	,	PUNCT
ejpam-3660	258	27	y	y	PROPN
ejpam-3660	258	28	∈	∈	PROPN
ejpam-3660	258	29	h	h	NOUN
ejpam-3660	258	30	such	such	ADJ
ejpam-3660	258	31	that	that	SCONJ
ejpam-3660	258	32	x	x	X
ejpam-3660	258	33	~	~	PUNCT
ejpam-3660	258	34	y	y	PROPN
ejpam-3660	258	35	⊆	⊆	NUM
ejpam-3660	258	36	i	i	PROPN
ejpam-3660	258	37	and	and	CCONJ
ejpam-3660	258	38	y	y	PROPN
ejpam-3660	258	39	∈	∈	PROPN
ejpam-3660	258	40	i.	i.	NOUN
ejpam-3660	258	41	then	then	ADV
ejpam-3660	258	42	,	,	PUNCT
ejpam-3660	258	43	µa(y	µa(y	NOUN
ejpam-3660	258	44	)	)	PUNCT
ejpam-3660	259	1	=	=	SYM
ejpam-3660	259	2	µa(0	µa(0	NOUN
ejpam-3660	259	3	)	)	PUNCT
ejpam-3660	259	4	,	,	PUNCT
ejpam-3660	259	5	γa(y	γa(y	NOUN
ejpam-3660	259	6	)	)	PUNCT
ejpam-3660	260	1	=	=	PUNCT
ejpam-3660	260	2	γa(0	γa(0	NOUN
ejpam-3660	260	3	)	)	PUNCT
ejpam-3660	260	4	,	,	PUNCT
ejpam-3660	260	5	µa(u	µa(u	PUNCT
ejpam-3660	260	6	)	)	PUNCT
ejpam-3660	260	7	=	=	SYM
ejpam-3660	260	8	µa(0	µa(0	NOUN
ejpam-3660	260	9	)	)	PUNCT
ejpam-3660	260	10	and	and	CCONJ
ejpam-3660	260	11	γa(v	γa(v	PUNCT
ejpam-3660	260	12	)	)	PUNCT
ejpam-3660	261	1	=	=	PUNCT
ejpam-3660	261	2	γa(0	γa(0	NOUN
ejpam-3660	261	3	)	)	PUNCT
ejpam-3660	261	4	for	for	ADP
ejpam-3660	261	5	any	any	DET
ejpam-3660	261	6	u	u	NOUN
ejpam-3660	261	7	,	,	PUNCT
ejpam-3660	261	8	v	v	NOUN
ejpam-3660	261	9	∈	∈	NOUN
ejpam-3660	261	10	x	x	X
ejpam-3660	261	11	~	~	PUNCT
ejpam-3660	261	12	y.	y.	NOUN
ejpam-3660	261	13	by	by	ADP
ejpam-3660	261	14	ifgr1	ifgr1	PROPN
ejpam-3660	261	15	and	and	CCONJ
ejpam-3660	261	16	ifgr2	ifgr2	NOUN
ejpam-3660	261	17	,	,	PUNCT
ejpam-3660	261	18	µa(0	µa(0	NOUN
ejpam-3660	261	19	)	)	PUNCT
ejpam-3660	261	20	≥	≥	NOUN
ejpam-3660	261	21	µa(x	µa(x	NOUN
ejpam-3660	261	22	)	)	PUNCT
ejpam-3660	261	23	≥	≥	PROPN
ejpam-3660	261	24	min	min	PROPN
ejpam-3660	261	25	{	{	PUNCT
ejpam-3660	261	26	inf	inf	NOUN
ejpam-3660	261	27	u∈x	u∈x	NOUN
ejpam-3660	261	28	~	~	PROPN
ejpam-3660	261	29	y	y	PROPN
ejpam-3660	261	30	µa(u	µa(u	NOUN
ejpam-3660	261	31	)	)	PUNCT
ejpam-3660	261	32	,	,	PUNCT
ejpam-3660	261	33	µa(y	µa(y	NOUN
ejpam-3660	261	34	)	)	PUNCT
ejpam-3660	261	35	}	}	PUNCT
ejpam-3660	262	1	=	=	SYM
ejpam-3660	262	2	µa(0	µa(0	NOUN
ejpam-3660	262	3	)	)	PUNCT
ejpam-3660	262	4	and	and	CCONJ
ejpam-3660	262	5	references	reference	NOUN
ejpam-3660	262	6	256	256	NUM
ejpam-3660	262	7	γa(0	γa(0	NOUN
ejpam-3660	262	8	)	)	PUNCT
ejpam-3660	262	9	≤	≤	NOUN
ejpam-3660	262	10	γa(x	γa(x	NUM
ejpam-3660	262	11	)	)	PUNCT
ejpam-3660	262	12	≤	≤	NUM
ejpam-3660	262	13	max	max	PROPN
ejpam-3660	262	14			PUNCT
ejpam-3660	262	15	sup	sup	NOUN
ejpam-3660	262	16	v∈x	v∈x	NOUN
ejpam-3660	262	17	~	~	SYM
ejpam-3660	262	18	y	y	PROPN
ejpam-3660	262	19	γa(v	γa(v	PUNCT
ejpam-3660	262	20	)	)	PUNCT
ejpam-3660	262	21	,	,	PUNCT
ejpam-3660	262	22	γa(y	γa(y	X
ejpam-3660	262	23	)	)	PUNCT
ejpam-3660	263	1			PROPN
ejpam-3660	263	2	=	=	SYM
ejpam-3660	263	3	γa(0	γa(0	NOUN
ejpam-3660	263	4	)	)	PUNCT
ejpam-3660	263	5	.	.	PUNCT
ejpam-3660	264	1	this	this	PRON
ejpam-3660	264	2	implies	imply	VERB
ejpam-3660	264	3	that	that	SCONJ
ejpam-3660	264	4	µa(x	µa(x	NOUN
ejpam-3660	264	5	)	)	PUNCT
ejpam-3660	264	6	=	=	SYM
ejpam-3660	264	7	µa(0	µa(0	NOUN
ejpam-3660	264	8	)	)	PUNCT
ejpam-3660	264	9	and	and	CCONJ
ejpam-3660	264	10	γa(x	γa(x	NUM
ejpam-3660	264	11	)	)	PUNCT
ejpam-3660	264	12	=	=	SYM
ejpam-3660	264	13	γa(0	γa(0	NOUN
ejpam-3660	264	14	)	)	PUNCT
ejpam-3660	264	15	and	and	CCONJ
ejpam-3660	264	16	so	so	ADV
ejpam-3660	264	17	x	x	SYM
ejpam-3660	264	18	∈	∈	PROPN
ejpam-3660	264	19	i.	i.	NOUN
ejpam-3660	264	20	hence	hence	ADV
ejpam-3660	264	21	,	,	PUNCT
ejpam-3660	264	22	i	i	PRON
ejpam-3660	264	23	is	be	AUX
ejpam-3660	264	24	a	a	DET
ejpam-3660	264	25	hyper	hyper	ADJ
ejpam-3660	264	26	gr	gr	NOUN
ejpam-3660	264	27	-	-	PUNCT
ejpam-3660	264	28	ideal	ideal	NOUN
ejpam-3660	264	29	of	of	ADP
ejpam-3660	264	30	h.	h.	PROPN
ejpam-3660	264	31	�	�	PROPN
ejpam-3660	264	32	references	reference	NOUN
ejpam-3660	264	33	[	[	X
ejpam-3660	264	34	1	1	NUM
ejpam-3660	264	35	]	]	PUNCT
ejpam-3660	264	36	k	k	PROPN
ejpam-3660	264	37	atanassov	atanassov	PROPN
ejpam-3660	264	38	.	.	PUNCT
ejpam-3660	265	1	intuitionistic	intuitionistic	ADJ
ejpam-3660	265	2	fuzzy	fuzzy	ADJ
ejpam-3660	265	3	sets	set	NOUN
ejpam-3660	265	4	.	.	PUNCT
ejpam-3660	266	1	fuzzy	fuzzy	ADJ
ejpam-3660	266	2	sets	set	NOUN
ejpam-3660	266	3	and	and	CCONJ
ejpam-3660	266	4	systems	system	NOUN
ejpam-3660	266	5	,	,	PUNCT
ejpam-3660	266	6	20:87–96	20:87–96	NUM
ejpam-3660	266	7	,	,	PUNCT
ejpam-3660	266	8	1986	1986	NUM
ejpam-3660	266	9	.	.	PUNCT
ejpam-3660	267	1	[	[	X
ejpam-3660	267	2	2	2	NUM
ejpam-3660	267	3	]	]	PUNCT
ejpam-3660	267	4	k	k	PROPN
ejpam-3660	267	5	atanassov	atanassov	PROPN
ejpam-3660	267	6	.	.	PUNCT
ejpam-3660	268	1	new	new	ADJ
ejpam-3660	268	2	operations	operation	NOUN
ejpam-3660	268	3	defined	define	VERB
ejpam-3660	268	4	over	over	ADP
ejpam-3660	268	5	the	the	DET
ejpam-3660	268	6	intuitionistic	intuitionistic	ADJ
ejpam-3660	268	7	fuzzy	fuzzy	ADJ
ejpam-3660	268	8	sets	set	NOUN
ejpam-3660	268	9	.	.	PUNCT
ejpam-3660	269	1	fuzzy	fuzzy	ADJ
ejpam-3660	269	2	sets	set	NOUN
ejpam-3660	269	3	and	and	CCONJ
ejpam-3660	269	4	systems	system	NOUN
ejpam-3660	269	5	,	,	PUNCT
ejpam-3660	269	6	61:137–142	61:137–142	NUM
ejpam-3660	269	7	,	,	PUNCT
ejpam-3660	269	8	1994	1994	NUM
ejpam-3660	269	9	.	.	PUNCT
ejpam-3660	270	1	[	[	X
ejpam-3660	270	2	3	3	NUM
ejpam-3660	270	3	]	]	X
ejpam-3660	270	4	r	r	NOUN
ejpam-3660	270	5	borzooei	borzooei	PROPN
ejpam-3660	270	6	and	and	CCONJ
ejpam-3660	270	7	y	y	PROPN
ejpam-3660	270	8	jun	jun	PROPN
ejpam-3660	270	9	.	.	PROPN
ejpam-3660	271	1	intuitionistic	intuitionistic	ADJ
ejpam-3660	271	2	fuzzy	fuzzy	ADJ
ejpam-3660	271	3	hyper	hyper	ADJ
ejpam-3660	271	4	bck	bck	NOUN
ejpam-3660	271	5	-	-	PUNCT
ejpam-3660	271	6	ideals	ideal	NOUN
ejpam-3660	271	7	of	of	ADP
ejpam-3660	271	8	hyper	hyper	ADJ
ejpam-3660	271	9	bck	bck	NOUN
ejpam-3660	271	10	-	-	PUNCT
ejpam-3660	271	11	algebras	algebras	PROPN
ejpam-3660	271	12	.	.	PUNCT
ejpam-3660	272	1	iranian	iranian	PROPN
ejpam-3660	272	2	journal	journal	PROPN
ejpam-3660	272	3	of	of	ADP
ejpam-3660	272	4	fuzzy	fuzzy	ADJ
ejpam-3660	272	5	systems	system	NOUN
ejpam-3660	272	6	,	,	PUNCT
ejpam-3660	272	7	1(1):61–73	1(1):61–73	NUM
ejpam-3660	272	8	,	,	PUNCT
ejpam-3660	272	9	2004	2004	NUM
ejpam-3660	272	10	.	.	PUNCT
ejpam-3660	273	1	[	[	X
ejpam-3660	273	2	4	4	X
ejpam-3660	273	3	]	]	X
ejpam-3660	273	4	p	p	X
ejpam-3660	273	5	das	das	PROPN
ejpam-3660	273	6	.	.	PUNCT
ejpam-3660	273	7	fuzzy	fuzzy	ADJ
ejpam-3660	273	8	groups	group	NOUN
ejpam-3660	273	9	and	and	CCONJ
ejpam-3660	273	10	level	level	NOUN
ejpam-3660	273	11	subgroups	subgroup	NOUN
ejpam-3660	273	12	.	.	PUNCT
ejpam-3660	274	1	j.	j.	PROPN
ejpam-3660	274	2	math	math	PROPN
ejpam-3660	274	3	.	.	PUNCT
ejpam-3660	275	1	anal	anal	PROPN
ejpam-3660	275	2	.	.	PUNCT
ejpam-3660	276	1	appl	appl	PROPN
ejpam-3660	276	2	.	.	PROPN
ejpam-3660	277	1	,	,	PUNCT
ejpam-3660	277	2	67:549–564	67:549–564	PROPN
ejpam-3660	277	3	,	,	PUNCT
ejpam-3660	277	4	1979	1979	NUM
ejpam-3660	277	5	.	.	PUNCT
ejpam-3660	278	1	[	[	X
ejpam-3660	278	2	5	5	NUM
ejpam-3660	278	3	]	]	SYM
ejpam-3660	278	4	b	b	X
ejpam-3660	278	5	davvaz	davvaz	NOUN
ejpam-3660	278	6	,	,	PUNCT
ejpam-3660	278	7	a	a	DET
ejpam-3660	278	8	nezhad	nezhad	ADJ
ejpam-3660	278	9	,	,	PUNCT
ejpam-3660	278	10	m	m	VERB
ejpam-3660	278	11	nadjafikhahb	nadjafikhahb	NOUN
ejpam-3660	278	12	,	,	PUNCT
ejpam-3660	278	13	and	and	CCONJ
ejpam-3660	278	14	s	s	X
ejpam-3660	278	15	moosavi	moosavi	ADJ
ejpam-3660	278	16	nejadc	nejadc	NOUN
ejpam-3660	278	17	.	.	PUNCT
ejpam-3660	279	1	a	a	DET
ejpam-3660	279	2	physical	physical	ADJ
ejpam-3660	279	3	example	example	NOUN
ejpam-3660	279	4	of	of	ADP
ejpam-3660	279	5	algebraic	algebraic	ADJ
ejpam-3660	279	6	hyperstructures	hyperstructure	NOUN
ejpam-3660	279	7	:	:	PUNCT
ejpam-3660	279	8	leptons	lepton	NOUN
ejpam-3660	279	9	.	.	PUNCT
ejpam-3660	280	1	indian	indian	PROPN
ejpam-3660	280	2	j	j	PROPN
ejpam-3660	280	3	phys	phys	PROPN
ejpam-3660	280	4	,	,	PUNCT
ejpam-3660	280	5	86(11):1027–1032	86(11):1027–1032	NUM
ejpam-3660	280	6	,	,	PUNCT
ejpam-3660	280	7	2012	2012	NUM
ejpam-3660	280	8	.	.	PUNCT
ejpam-3660	281	1	[	[	X
ejpam-3660	281	2	6	6	NUM
ejpam-3660	281	3	]	]	SYM
ejpam-3660	281	4	r	r	NOUN
ejpam-3660	281	5	indangan	indangan	NOUN
ejpam-3660	281	6	and	and	CCONJ
ejpam-3660	281	7	g	g	PROPN
ejpam-3660	281	8	petalcorin	petalcorin	NOUN
ejpam-3660	281	9	.	.	PUNCT
ejpam-3660	282	1	some	some	DET
ejpam-3660	282	2	results	result	NOUN
ejpam-3660	282	3	on	on	ADP
ejpam-3660	282	4	hyper	hyper	ADJ
ejpam-3660	282	5	gr	gr	NOUN
ejpam-3660	282	6	-	-	PUNCT
ejpam-3660	282	7	ideals	ideal	NOUN
ejpam-3660	282	8	of	of	ADP
ejpam-3660	282	9	a	a	DET
ejpam-3660	282	10	hyper	hyper	ADJ
ejpam-3660	282	11	gralgebra	gralgebra	NOUN
ejpam-3660	282	12	.	.	PUNCT
ejpam-3660	283	1	journal	journal	NOUN
ejpam-3660	283	2	of	of	ADP
ejpam-3660	283	3	algebra	algebra	PROPN
ejpam-3660	283	4	and	and	CCONJ
ejpam-3660	283	5	applied	apply	VERB
ejpam-3660	283	6	mathematics	mathematic	NOUN
ejpam-3660	283	7	,	,	PUNCT
ejpam-3660	283	8	14:101–119	14:101–119	NUM
ejpam-3660	283	9	,	,	PUNCT
ejpam-3660	283	10	2016	2016	NUM
ejpam-3660	283	11	.	.	PUNCT
ejpam-3660	284	1	[	[	X
ejpam-3660	284	2	7	7	NUM
ejpam-3660	284	3	]	]	X
ejpam-3660	284	4	r	r	NOUN
ejpam-3660	284	5	indangan	indangan	NOUN
ejpam-3660	284	6	,	,	PUNCT
ejpam-3660	284	7	g	g	NOUN
ejpam-3660	284	8	petalcorin	petalcorin	NOUN
ejpam-3660	284	9	,	,	PUNCT
ejpam-3660	284	10	and	and	CCONJ
ejpam-3660	284	11	a	a	DET
ejpam-3660	284	12	villa	villa	NOUN
ejpam-3660	284	13	.	.	PUNCT
ejpam-3660	285	1	some	some	DET
ejpam-3660	285	2	hyper	hyper	ADJ
ejpam-3660	285	3	homomorphic	homomorphic	ADJ
ejpam-3660	285	4	properties	property	NOUN
ejpam-3660	285	5	on	on	ADP
ejpam-3660	285	6	hyper	hyper	ADJ
ejpam-3660	285	7	gr	gr	NOUN
ejpam-3660	285	8	-	-	PUNCT
ejpam-3660	285	9	algebras	algebra	NOUN
ejpam-3660	285	10	.	.	PUNCT
ejpam-3660	285	11	journal	journal	PROPN
ejpam-3660	285	12	of	of	ADP
ejpam-3660	285	13	algebra	algebra	PROPN
ejpam-3660	285	14	and	and	CCONJ
ejpam-3660	285	15	applied	apply	VERB
ejpam-3660	285	16	mathematics	mathematic	NOUN
ejpam-3660	285	17	,	,	PUNCT
ejpam-3660	285	18	15:100–121	15:100–121	PROPN
ejpam-3660	285	19	,	,	PUNCT
ejpam-3660	285	20	2017	2017	NUM
ejpam-3660	285	21	.	.	PUNCT
ejpam-3660	286	1	[	[	X
ejpam-3660	286	2	8	8	NUM
ejpam-3660	286	3	]	]	X
ejpam-3660	286	4	y	y	PROPN
ejpam-3660	286	5	jun	jun	PROPN
ejpam-3660	286	6	and	and	CCONJ
ejpam-3660	286	7	x	x	SYM
ejpam-3660	286	8	long	long	ADV
ejpam-3660	286	9	.	.	PUNCT
ejpam-3660	287	1	fuzzy	fuzzy	ADJ
ejpam-3660	287	2	hyper	hyper	ADJ
ejpam-3660	287	3	bck	bck	NOUN
ejpam-3660	287	4	-	-	PUNCT
ejpam-3660	287	5	ideals	ideal	NOUN
ejpam-3660	287	6	of	of	ADP
ejpam-3660	287	7	hyper	hyper	ADJ
ejpam-3660	287	8	bck	bck	NOUN
ejpam-3660	287	9	-	-	PUNCT
ejpam-3660	287	10	algebras	algebras	PROPN
ejpam-3660	287	11	.	.	PUNCT
ejpam-3660	288	1	scientiae	scientiae	PROPN
ejpam-3660	288	2	mathematics	mathematics	PROPN
ejpam-3660	288	3	japonicae	japonicae	PROPN
ejpam-3660	288	4	online	online	ADV
ejpam-3660	288	5	,	,	PUNCT
ejpam-3660	288	6	4:415–422	4:415–422	NOUN
ejpam-3660	288	7	,	,	PUNCT
ejpam-3660	288	8	2001	2001	NUM
ejpam-3660	288	9	.	.	PUNCT
ejpam-3660	289	1	[	[	X
ejpam-3660	289	2	9	9	NUM
ejpam-3660	289	3	]	]	X
ejpam-3660	289	4	y	y	PROPN
ejpam-3660	289	5	jun	jun	PROPN
ejpam-3660	289	6	and	and	CCONJ
ejpam-3660	289	7	w	w	NOUN
ejpam-3660	289	8	shim	shim	NOUN
ejpam-3660	289	9	.	.	PUNCT
ejpam-3660	290	1	fuzzy	fuzzy	ADJ
ejpam-3660	290	2	implicative	implicative	ADJ
ejpam-3660	290	3	hyper	hyper	ADJ
ejpam-3660	290	4	bck	bck	NOUN
ejpam-3660	290	5	-	-	PUNCT
ejpam-3660	290	6	ideals	ideal	NOUN
ejpam-3660	290	7	of	of	ADP
ejpam-3660	290	8	hyper	hyper	ADJ
ejpam-3660	290	9	bck	bck	NOUN
ejpam-3660	290	10	-	-	PUNCT
ejpam-3660	290	11	algebras	algebras	PROPN
ejpam-3660	290	12	.	.	PUNCT
ejpam-3660	291	1	international	international	ADJ
ejpam-3660	291	2	journal	journal	PROPN
ejpam-3660	291	3	of	of	ADP
ejpam-3660	291	4	mathematics	mathematics	PROPN
ejpam-3660	291	5	and	and	CCONJ
ejpam-3660	291	6	mathematical	mathematical	ADJ
ejpam-3660	291	7	sciences	science	NOUN
ejpam-3660	291	8	,	,	PUNCT
ejpam-3660	291	9	29(2):63–70	29(2):63–70	NUM
ejpam-3660	291	10	,	,	PUNCT
ejpam-3660	291	11	2002	2002	NUM
ejpam-3660	291	12	.	.	PUNCT
ejpam-3660	292	1	[	[	X
ejpam-3660	292	2	10	10	NUM
ejpam-3660	292	3	]	]	X
ejpam-3660	292	4	y	y	PROPN
ejpam-3660	292	5	jun	jun	PROPN
ejpam-3660	292	6	,	,	PUNCT
ejpam-3660	292	7	m	m	PROPN
ejpam-3660	292	8	zahedi	zahedi	PROPN
ejpam-3660	292	9	,	,	PUNCT
ejpam-3660	292	10	x	x	X
ejpam-3660	292	11	xin	xin	PROPN
ejpam-3660	292	12	,	,	PUNCT
ejpam-3660	292	13	and	and	CCONJ
ejpam-3660	292	14	r	r	NOUN
ejpam-3660	292	15	borzoei	borzoei	NOUN
ejpam-3660	292	16	.	.	PUNCT
ejpam-3660	293	1	on	on	ADP
ejpam-3660	293	2	hyper	hyper	ADJ
ejpam-3660	293	3	bck	bck	NOUN
ejpam-3660	293	4	-	-	PUNCT
ejpam-3660	293	5	algebras	algebras	PROPN
ejpam-3660	293	6	.	.	PUNCT
ejpam-3660	294	1	italian	italian	ADJ
ejpam-3660	294	2	journal	journal	NOUN
ejpam-3660	294	3	of	of	ADP
ejpam-3660	294	4	pure	pure	ADJ
ejpam-3660	294	5	and	and	CCONJ
ejpam-3660	294	6	applied	applied	ADJ
ejpam-3660	294	7	mathematics	mathematic	NOUN
ejpam-3660	294	8	,	,	PUNCT
ejpam-3660	294	9	8:127–136	8:127–136	NUM
ejpam-3660	294	10	,	,	PUNCT
ejpam-3660	294	11	2000	2000	NUM
ejpam-3660	294	12	.	.	PUNCT
ejpam-3660	295	1	[	[	X
ejpam-3660	295	2	11	11	NUM
ejpam-3660	295	3	]	]	PUNCT
ejpam-3660	295	4	x	x	X
ejpam-3660	295	5	long	long	ADV
ejpam-3660	295	6	.	.	PUNCT
ejpam-3660	296	1	hyper	hyper	ADJ
ejpam-3660	296	2	bci	bci	NOUN
ejpam-3660	296	3	-	-	PUNCT
ejpam-3660	296	4	algebras	algebras	X
ejpam-3660	296	5	.	.	PUNCT
ejpam-3660	297	1	discuss	discuss	PROPN
ejpam-3660	297	2	math	math	NOUN
ejpam-3660	297	3	.	.	PUNCT
ejpam-3660	298	1	soc	soc	PROPN
ejpam-3660	298	2	.	.	PUNCT
ejpam-3660	298	3	,	,	PUNCT
ejpam-3660	298	4	26:5–19	26:5–19	NUM
ejpam-3660	298	5	,	,	PUNCT
ejpam-3660	298	6	2006	2006	NUM
ejpam-3660	298	7	.	.	PUNCT
ejpam-3660	299	1	[	[	X
ejpam-3660	299	2	12	12	NUM
ejpam-3660	299	3	]	]	PUNCT
ejpam-3660	299	4	a.	a.	NOUN
ejpam-3660	299	5	macodi	macodi	PROPN
ejpam-3660	299	6	-	-	PUNCT
ejpam-3660	299	7	ringia	ringia	PROPN
ejpam-3660	299	8	and	and	CCONJ
ejpam-3660	299	9	g.	g.	PROPN
ejpam-3660	299	10	petalcorin	petalcorin	PROPN
ejpam-3660	299	11	.	.	PUNCT
ejpam-3660	300	1	some	some	DET
ejpam-3660	300	2	results	result	NOUN
ejpam-3660	300	3	on	on	ADP
ejpam-3660	300	4	fuzzy	fuzzy	ADJ
ejpam-3660	300	5	implicative	implicative	ADJ
ejpam-3660	300	6	hyper	hyper	ADJ
ejpam-3660	300	7	gr	gr	NOUN
ejpam-3660	300	8	-	-	PUNCT
ejpam-3660	300	9	ideals	ideal	NOUN
ejpam-3660	300	10	.	.	PUNCT
ejpam-3660	301	1	european	european	ADJ
ejpam-3660	301	2	journal	journal	PROPN
ejpam-3660	301	3	of	of	ADP
ejpam-3660	301	4	pure	pure	ADJ
ejpam-3660	301	5	and	and	CCONJ
ejpam-3660	301	6	applied	applied	ADJ
ejpam-3660	301	7	mathematics	mathematic	NOUN
ejpam-3660	301	8	,	,	PUNCT
ejpam-3660	301	9	12(2):409–417	12(2):409–417	NUM
ejpam-3660	301	10	,	,	PUNCT
ejpam-3660	301	11	2019	2019	NUM
ejpam-3660	301	12	.	.	PUNCT
ejpam-3660	302	1	[	[	X
ejpam-3660	302	2	13	13	NUM
ejpam-3660	302	3	]	]	X
ejpam-3660	302	4	f	f	PROPN
ejpam-3660	302	5	marty	marty	PROPN
ejpam-3660	302	6	.	.	PUNCT
ejpam-3660	303	1	sur	sur	PROPN
ejpam-3660	303	2	une	une	PROPN
ejpam-3660	303	3	generalization	generalization	PROPN
ejpam-3660	303	4	de	de	X
ejpam-3660	303	5	la	la	PROPN
ejpam-3660	303	6	notion	notion	NOUN
ejpam-3660	303	7	de	de	PROPN
ejpam-3660	303	8	group	group	NOUN
ejpam-3660	303	9	.	.	PUNCT
ejpam-3660	304	1	8th	8th	ADJ
ejpam-3660	304	2	congress	congress	PROPN
ejpam-3660	304	3	math	math	NOUN
ejpam-3660	304	4	.	.	PUNCT
ejpam-3660	305	1	scandenaves	scandenave	NOUN
ejpam-3660	305	2	(	(	PUNCT
ejpam-3660	305	3	stockholm	stockholm	PROPN
ejpam-3660	305	4	)	)	PUNCT
ejpam-3660	305	5	,	,	PUNCT
ejpam-3660	305	6	pages	page	NOUN
ejpam-3660	305	7	45–49	45–49	NUM
ejpam-3660	305	8	,	,	PUNCT
ejpam-3660	305	9	1934	1934	NUM
ejpam-3660	305	10	.	.	PUNCT
ejpam-3660	306	1	[	[	X
ejpam-3660	306	2	14	14	NUM
ejpam-3660	306	3	]	]	X
ejpam-3660	306	4	f	f	X
ejpam-3660	306	5	nisar	nisar	PROPN
ejpam-3660	306	6	,	,	PUNCT
ejpam-3660	306	7	r	r	NOUN
ejpam-3660	306	8	tariq	tariq	NOUN
ejpam-3660	306	9	,	,	PUNCT
ejpam-3660	306	10	and	and	CCONJ
ejpam-3660	306	11	s	s	AUX
ejpam-3660	306	12	bhatti	bhatti	NOUN
ejpam-3660	306	13	.	.	PUNCT
ejpam-3660	307	1	fuzzy	fuzzy	ADJ
ejpam-3660	307	2	ideals	ideal	NOUN
ejpam-3660	307	3	in	in	ADP
ejpam-3660	307	4	hyper	hyper	ADJ
ejpam-3660	307	5	bci	bci	NOUN
ejpam-3660	307	6	-	-	PUNCT
ejpam-3660	307	7	algebras	algebra	NOUN
ejpam-3660	307	8	.	.	PUNCT
ejpam-3660	308	1	world	world	PROPN
ejpam-3660	308	2	applied	apply	VERB
ejpam-3660	308	3	sciences	science	NOUN
ejpam-3660	308	4	journal	journal	NOUN
ejpam-3660	308	5	,	,	PUNCT
ejpam-3660	308	6	16(12):1771–1777	16(12):1771–1777	PROPN
ejpam-3660	308	7	,	,	PUNCT
ejpam-3660	308	8	2012	2012	NUM
ejpam-3660	308	9	.	.	PUNCT
ejpam-3660	309	1	references	reference	NOUN
ejpam-3660	309	2	257	257	NUM
ejpam-3660	310	1	[	[	X
ejpam-3660	310	2	15	15	NUM
ejpam-3660	310	3	]	]	X
ejpam-3660	310	4	n	n	PRON
ejpam-3660	310	5	palaniappan	palaniappan	NOUN
ejpam-3660	310	6	,	,	PUNCT
ejpam-3660	310	7	p	p	NOUN
ejpam-3660	310	8	veerappan	veerappan	NOUN
ejpam-3660	310	9	,	,	PUNCT
ejpam-3660	310	10	and	and	CCONJ
ejpam-3660	310	11	r	r	NOUN
ejpam-3660	310	12	devi	devi	PROPN
ejpam-3660	310	13	.	.	PUNCT
ejpam-3660	311	1	intuitionistic	intuitionistic	ADJ
ejpam-3660	311	2	fuzzy	fuzzy	ADJ
ejpam-3660	311	3	ideals	ideal	NOUN
ejpam-3660	311	4	in	in	ADP
ejpam-3660	311	5	hyper	hyper	ADJ
ejpam-3660	311	6	bcialgebras	bcialgebra	NOUN
ejpam-3660	311	7	.	.	PUNCT
ejpam-3660	312	1	international	international	ADJ
ejpam-3660	312	2	journal	journal	PROPN
ejpam-3660	312	3	of	of	ADP
ejpam-3660	312	4	computational	computational	ADJ
ejpam-3660	312	5	science	science	NOUN
ejpam-3660	312	6	and	and	CCONJ
ejpam-3660	312	7	mathematics	mathematic	NOUN
ejpam-3660	312	8	,	,	PUNCT
ejpam-3660	312	9	4(3):271–285	4(3):271–285	PROPN
ejpam-3660	312	10	,	,	PUNCT
ejpam-3660	312	11	2012	2012	NUM
ejpam-3660	312	12	.	.	PUNCT
ejpam-3660	313	1	[	[	X
ejpam-3660	313	2	16	16	NUM
ejpam-3660	313	3	]	]	PUNCT
ejpam-3660	313	4	l	l	PROPN
ejpam-3660	313	5	zadeh	zadeh	PROPN
ejpam-3660	313	6	.	.	PUNCT
ejpam-3660	313	7	fuzzy	fuzzy	ADJ
ejpam-3660	313	8	sets	set	NOUN
ejpam-3660	313	9	.	.	PUNCT
ejpam-3660	314	1	information	information	NOUN
ejpam-3660	314	2	and	and	CCONJ
ejpam-3660	314	3	control	control	NOUN
ejpam-3660	314	4	,	,	PUNCT
ejpam-3660	314	5	8:338–353	8:338–353	NUM
ejpam-3660	314	6	,	,	PUNCT
ejpam-3660	314	7	1965	1965	NUM
ejpam-3660	314	8	.	.	PUNCT