id	sid	tid	token	lemma	pos
ejpam-4143	1	1	european	european	PROPN
ejpam-4143	1	2	journal	journal	PROPN
ejpam-4143	1	3	of	of	ADP
ejpam-4143	1	4	pure	pure	ADJ
ejpam-4143	1	5	and	and	CCONJ
ejpam-4143	1	6	applied	apply	VERB
ejpam-4143	1	7	mathematics	mathematic	NOUN
ejpam-4143	1	8	vol	vol	NOUN
ejpam-4143	1	9	.	.	PUNCT
ejpam-4143	2	1	14	14	NUM
ejpam-4143	2	2	,	,	PUNCT
ejpam-4143	2	3	no	no	INTJ
ejpam-4143	2	4	.	.	NOUN
ejpam-4143	2	5	4	4	NUM
ejpam-4143	2	6	,	,	PUNCT
ejpam-4143	2	7	2021	2021	NUM
ejpam-4143	2	8	,	,	PUNCT
ejpam-4143	2	9	1388	1388	NUM
ejpam-4143	2	10	-	-	SYM
ejpam-4143	2	11	1401	1401	NUM
ejpam-4143	2	12	issn	issn	PROPN
ejpam-4143	2	13	1307	1307	NUM
ejpam-4143	2	14	-	-	SYM
ejpam-4143	2	15	5543	5543	NUM
ejpam-4143	2	16	–	–	PUNCT
ejpam-4143	2	17	ejpam.com	ejpam.com	X
ejpam-4143	2	18	published	publish	VERB
ejpam-4143	2	19	by	by	ADP
ejpam-4143	2	20	new	new	PROPN
ejpam-4143	2	21	york	york	PROPN
ejpam-4143	2	22	business	business	PROPN
ejpam-4143	2	23	global	global	ADJ
ejpam-4143	2	24	fuzzy	fuzzy	ADJ
ejpam-4143	2	25	sets	set	NOUN
ejpam-4143	2	26	in	in	ADP
ejpam-4143	2	27	hyper	hyper	ADJ
ejpam-4143	2	28	up	up	ADP
ejpam-4143	2	29	-	-	PUNCT
ejpam-4143	2	30	algebras	algebras	PROPN
ejpam-4143	2	31	rohaima	rohaima	PROPN
ejpam-4143	2	32	m.	m.	PROPN
ejpam-4143	2	33	amairanto1,∗	amairanto1,∗	PROPN
ejpam-4143	2	34	,	,	PUNCT
ejpam-4143	3	1	rowena	rowena	PROPN
ejpam-4143	3	2	t.	t.	PROPN
ejpam-4143	3	3	isla2	isla2	PROPN
ejpam-4143	3	4	1	1	NUM
ejpam-4143	3	5	department	department	NOUN
ejpam-4143	3	6	of	of	ADP
ejpam-4143	3	7	mathematics	mathematic	NOUN
ejpam-4143	3	8	,	,	PUNCT
ejpam-4143	3	9	mindanao	mindanao	PROPN
ejpam-4143	3	10	state	state	PROPN
ejpam-4143	3	11	university	university	PROPN
ejpam-4143	3	12	-	-	PUNCT
ejpam-4143	3	13	university	university	NOUN
ejpam-4143	3	14	training	training	NOUN
ejpam-4143	3	15	center	center	NOUN
ejpam-4143	3	16	,	,	PUNCT
ejpam-4143	3	17	9700	9700	NUM
ejpam-4143	3	18	marawi	marawi	PROPN
ejpam-4143	3	19	city	city	PROPN
ejpam-4143	3	20	,	,	PUNCT
ejpam-4143	3	21	philippines	philippines	PROPN
ejpam-4143	3	22	2	2	NUM
ejpam-4143	3	23	department	department	NOUN
ejpam-4143	3	24	of	of	ADP
ejpam-4143	3	25	mathematics	mathematic	NOUN
ejpam-4143	3	26	and	and	CCONJ
ejpam-4143	3	27	statistics	statistic	NOUN
ejpam-4143	3	28	,	,	PUNCT
ejpam-4143	3	29	college	college	NOUN
ejpam-4143	3	30	of	of	ADP
ejpam-4143	3	31	science	science	NOUN
ejpam-4143	3	32	and	and	CCONJ
ejpam-4143	3	33	mathematics	mathematic	NOUN
ejpam-4143	3	34	,	,	PUNCT
ejpam-4143	3	35	mindanao	mindanao	PROPN
ejpam-4143	3	36	state	state	PROPN
ejpam-4143	3	37	university	university	PROPN
ejpam-4143	3	38	-	-	PUNCT
ejpam-4143	3	39	iligan	iligan	PROPN
ejpam-4143	3	40	institute	institute	PROPN
ejpam-4143	3	41	of	of	ADP
ejpam-4143	3	42	technology	technology	PROPN
ejpam-4143	3	43	,	,	PUNCT
ejpam-4143	3	44	9200	9200	NUM
ejpam-4143	3	45	iligan	iligan	ADJ
ejpam-4143	3	46	city	city	NOUN
ejpam-4143	3	47	,	,	PUNCT
ejpam-4143	3	48	philippines	philippine	NOUN
ejpam-4143	3	49	abstract	abstract	ADJ
ejpam-4143	3	50	.	.	PUNCT
ejpam-4143	4	1	in	in	ADP
ejpam-4143	4	2	this	this	DET
ejpam-4143	4	3	paper	paper	NOUN
ejpam-4143	4	4	,	,	PUNCT
ejpam-4143	4	5	we	we	PRON
ejpam-4143	4	6	apply	apply	VERB
ejpam-4143	4	7	the	the	DET
ejpam-4143	4	8	concept	concept	NOUN
ejpam-4143	4	9	of	of	ADP
ejpam-4143	4	10	fuzzy	fuzzy	ADJ
ejpam-4143	4	11	set	set	NOUN
ejpam-4143	4	12	to	to	PART
ejpam-4143	4	13	hyper	hyper	VERB
ejpam-4143	4	14	up	up	ADP
ejpam-4143	4	15	-	-	PUNCT
ejpam-4143	4	16	subalgebras	subalgebras	X
ejpam-4143	4	17	.	.	PUNCT
ejpam-4143	5	1	we	we	PRON
ejpam-4143	5	2	introduce	introduce	VERB
ejpam-4143	5	3	the	the	DET
ejpam-4143	5	4	notions	notion	NOUN
ejpam-4143	5	5	of	of	ADP
ejpam-4143	5	6	fuzzy	fuzzy	ADJ
ejpam-4143	5	7	hyper	hyper	ADJ
ejpam-4143	5	8	up	up	ADP
ejpam-4143	5	9	-	-	PUNCT
ejpam-4143	5	10	subalgebra	subalgebra	NOUN
ejpam-4143	5	11	and	and	CCONJ
ejpam-4143	5	12	fuzzy	fuzzy	ADJ
ejpam-4143	5	13	hyper	hyper	ADJ
ejpam-4143	5	14	up	up	ADJ
ejpam-4143	5	15	-	-	PUNCT
ejpam-4143	5	16	filter	filter	NOUN
ejpam-4143	5	17	and	and	CCONJ
ejpam-4143	5	18	establish	establish	VERB
ejpam-4143	5	19	some	some	PRON
ejpam-4143	5	20	of	of	ADP
ejpam-4143	5	21	their	their	PRON
ejpam-4143	5	22	properties	property	NOUN
ejpam-4143	5	23	.	.	PUNCT
ejpam-4143	6	1	furthermore	furthermore	ADV
ejpam-4143	6	2	,	,	PUNCT
ejpam-4143	6	3	some	some	DET
ejpam-4143	6	4	properties	property	NOUN
ejpam-4143	6	5	of	of	ADP
ejpam-4143	6	6	hyper	hyper	ADJ
ejpam-4143	6	7	homomorphism	homomorphism	NOUN
ejpam-4143	6	8	in	in	ADP
ejpam-4143	6	9	relation	relation	NOUN
ejpam-4143	6	10	to	to	ADP
ejpam-4143	6	11	fuzzy	fuzzy	ADJ
ejpam-4143	6	12	hyper	hyper	ADJ
ejpam-4143	6	13	upsubalgebras	upsubalgebra	NOUN
ejpam-4143	6	14	and	and	CCONJ
ejpam-4143	6	15	fuzzy	fuzzy	ADJ
ejpam-4143	6	16	hyper	hyper	ADJ
ejpam-4143	6	17	up	up	ADP
ejpam-4143	6	18	-	-	PUNCT
ejpam-4143	6	19	filters	filter	NOUN
ejpam-4143	6	20	are	be	AUX
ejpam-4143	6	21	also	also	ADV
ejpam-4143	6	22	presented	present	VERB
ejpam-4143	6	23	2020	2020	NUM
ejpam-4143	6	24	mathematics	mathematic	NOUN
ejpam-4143	6	25	subject	subject	NOUN
ejpam-4143	6	26	classifications	classification	NOUN
ejpam-4143	6	27	:	:	PUNCT
ejpam-4143	6	28	08a30	08a30	NOUN
ejpam-4143	6	29	,	,	PUNCT
ejpam-4143	6	30	08a72	08a72	NOUN
ejpam-4143	6	31	key	key	ADJ
ejpam-4143	6	32	words	word	NOUN
ejpam-4143	6	33	and	and	CCONJ
ejpam-4143	6	34	phrases	phrase	NOUN
ejpam-4143	6	35	:	:	PUNCT
ejpam-4143	6	36	hyper	hyper	ADJ
ejpam-4143	6	37	up	up	ADP
ejpam-4143	6	38	-	-	PUNCT
ejpam-4143	6	39	algebra	algebra	NOUN
ejpam-4143	6	40	,	,	PUNCT
ejpam-4143	6	41	hyper	hyper	ADJ
ejpam-4143	6	42	up	up	ADJ
ejpam-4143	6	43	-	-	PUNCT
ejpam-4143	6	44	filter	filter	NOUN
ejpam-4143	6	45	,	,	PUNCT
ejpam-4143	6	46	fuzzy	fuzzy	ADJ
ejpam-4143	6	47	set	set	NOUN
ejpam-4143	6	48	,	,	PUNCT
ejpam-4143	6	49	fuzzy	fuzzy	ADJ
ejpam-4143	6	50	hyper	hyper	ADJ
ejpam-4143	6	51	upsubalgebra	upsubalgebra	NOUN
ejpam-4143	6	52	,	,	PUNCT
ejpam-4143	6	53	fuzzy	fuzzy	ADJ
ejpam-4143	6	54	hyper	hyper	ADJ
ejpam-4143	6	55	up	up	ADJ
ejpam-4143	6	56	-	-	PUNCT
ejpam-4143	6	57	filter	filter	NOUN
ejpam-4143	6	58	1	1	NUM
ejpam-4143	6	59	.	.	PUNCT
ejpam-4143	7	1	introduction	introduction	NOUN
ejpam-4143	7	2	the	the	DET
ejpam-4143	7	3	concept	concept	NOUN
ejpam-4143	7	4	of	of	ADP
ejpam-4143	7	5	hypergraphs	hypergraph	NOUN
ejpam-4143	7	6	,	,	PUNCT
ejpam-4143	7	7	which	which	PRON
ejpam-4143	7	8	is	be	AUX
ejpam-4143	7	9	a	a	DET
ejpam-4143	7	10	generalization	generalization	NOUN
ejpam-4143	7	11	of	of	ADP
ejpam-4143	7	12	the	the	DET
ejpam-4143	7	13	notion	notion	NOUN
ejpam-4143	7	14	of	of	ADP
ejpam-4143	7	15	classical	classical	ADJ
ejpam-4143	7	16	algebraic	algebraic	ADJ
ejpam-4143	7	17	groups	group	NOUN
ejpam-4143	7	18	,	,	PUNCT
ejpam-4143	7	19	was	be	AUX
ejpam-4143	7	20	introduced	introduce	VERB
ejpam-4143	7	21	by	by	ADP
ejpam-4143	7	22	f.	f.	PROPN
ejpam-4143	7	23	marty	marty	PROPN
ejpam-4143	8	1	[	[	X
ejpam-4143	8	2	14	14	NUM
ejpam-4143	8	3	]	]	PUNCT
ejpam-4143	8	4	in	in	ADP
ejpam-4143	8	5	1934	1934	NUM
ejpam-4143	8	6	.	.	PUNCT
ejpam-4143	9	1	since	since	SCONJ
ejpam-4143	9	2	then	then	ADV
ejpam-4143	9	3	,	,	PUNCT
ejpam-4143	9	4	hyperstructure	hyperstructure	PROPN
ejpam-4143	9	5	theory	theory	NOUN
ejpam-4143	9	6	has	have	AUX
ejpam-4143	9	7	seen	see	VERB
ejpam-4143	9	8	tremendous	tremendous	ADJ
ejpam-4143	9	9	development	development	NOUN
ejpam-4143	9	10	.	.	PUNCT
ejpam-4143	10	1	for	for	ADP
ejpam-4143	10	2	basic	basic	ADJ
ejpam-4143	10	3	notions	notion	NOUN
ejpam-4143	10	4	and	and	CCONJ
ejpam-4143	10	5	results	result	NOUN
ejpam-4143	10	6	on	on	ADP
ejpam-4143	10	7	hyperstructure	hyperstructure	NOUN
ejpam-4143	10	8	theory	theory	NOUN
ejpam-4143	10	9	and	and	CCONJ
ejpam-4143	10	10	some	some	PRON
ejpam-4143	10	11	of	of	ADP
ejpam-4143	10	12	its	its	PRON
ejpam-4143	10	13	applications	application	NOUN
ejpam-4143	10	14	,	,	PUNCT
ejpam-4143	10	15	see	see	VERB
ejpam-4143	10	16	p.	p.	NOUN
ejpam-4143	10	17	corcini	corcini	NOUN
ejpam-4143	10	18	and	and	CCONJ
ejpam-4143	11	1	v.	v.	ADP
ejpam-4143	11	2	leoreanu	leoreanu	NOUN
ejpam-4143	11	3	[	[	X
ejpam-4143	11	4	4	4	NUM
ejpam-4143	11	5	]	]	PUNCT
ejpam-4143	11	6	.	.	PUNCT
ejpam-4143	12	1	l.	l.	PROPN
ejpam-4143	12	2	zadeh	zadeh	PROPN
ejpam-4143	13	1	[	[	X
ejpam-4143	13	2	21	21	NUM
ejpam-4143	13	3	]	]	PUNCT
ejpam-4143	13	4	defined	define	VERB
ejpam-4143	13	5	a	a	DET
ejpam-4143	13	6	fuzzy	fuzzy	ADJ
ejpam-4143	13	7	set	set	NOUN
ejpam-4143	13	8	as	as	ADP
ejpam-4143	13	9	a	a	DET
ejpam-4143	13	10	class	class	NOUN
ejpam-4143	13	11	of	of	ADP
ejpam-4143	13	12	objects	object	NOUN
ejpam-4143	13	13	with	with	ADP
ejpam-4143	13	14	a	a	DET
ejpam-4143	13	15	continuum	continuum	NOUN
ejpam-4143	13	16	of	of	ADP
ejpam-4143	13	17	grades	grade	NOUN
ejpam-4143	13	18	of	of	ADP
ejpam-4143	13	19	membership	membership	NOUN
ejpam-4143	13	20	,	,	PUNCT
ejpam-4143	13	21	as	as	SCONJ
ejpam-4143	13	22	inspired	inspire	VERB
ejpam-4143	13	23	by	by	ADP
ejpam-4143	13	24	the	the	DET
ejpam-4143	13	25	process	process	NOUN
ejpam-4143	13	26	of	of	ADP
ejpam-4143	13	27	human	human	ADJ
ejpam-4143	13	28	perception	perception	NOUN
ejpam-4143	13	29	and	and	CCONJ
ejpam-4143	13	30	recognition	recognition	NOUN
ejpam-4143	13	31	.	.	PUNCT
ejpam-4143	14	1	from	from	ADP
ejpam-4143	14	2	its	its	PRON
ejpam-4143	14	3	inception	inception	NOUN
ejpam-4143	14	4	in	in	ADP
ejpam-4143	14	5	1965	1965	NUM
ejpam-4143	14	6	,	,	PUNCT
ejpam-4143	14	7	fuzzy	fuzzy	ADJ
ejpam-4143	14	8	set	set	NOUN
ejpam-4143	14	9	theory	theory	NOUN
ejpam-4143	14	10	became	become	VERB
ejpam-4143	14	11	a	a	DET
ejpam-4143	14	12	phenomenon	phenomenon	NOUN
ejpam-4143	14	13	since	since	SCONJ
ejpam-4143	14	14	its	its	PRON
ejpam-4143	14	15	logic	logic	NOUN
ejpam-4143	14	16	can	can	AUX
ejpam-4143	14	17	deal	deal	VERB
ejpam-4143	14	18	with	with	ADP
ejpam-4143	14	19	information	information	NOUN
ejpam-4143	14	20	that	that	PRON
ejpam-4143	14	21	is	be	AUX
ejpam-4143	14	22	imprecise	imprecise	ADV
ejpam-4143	14	23	,	,	PUNCT
ejpam-4143	14	24	vague	vague	ADJ
ejpam-4143	14	25	,	,	PUNCT
ejpam-4143	14	26	partially	partially	ADV
ejpam-4143	14	27	true	true	ADJ
ejpam-4143	14	28	,	,	PUNCT
ejpam-4143	14	29	or	or	CCONJ
ejpam-4143	14	30	without	without	ADP
ejpam-4143	14	31	sharp	sharp	ADJ
ejpam-4143	14	32	boundaries	boundary	NOUN
ejpam-4143	14	33	.	.	PUNCT
ejpam-4143	15	1	the	the	DET
ejpam-4143	15	2	reader	reader	NOUN
ejpam-4143	15	3	may	may	AUX
ejpam-4143	15	4	refer	refer	VERB
ejpam-4143	15	5	to	to	ADP
ejpam-4143	15	6	[	[	X
ejpam-4143	15	7	19	19	NUM
ejpam-4143	15	8	]	]	PUNCT
ejpam-4143	15	9	for	for	ADP
ejpam-4143	15	10	a	a	DET
ejpam-4143	15	11	compilation	compilation	NOUN
ejpam-4143	15	12	of	of	ADP
ejpam-4143	15	13	articles	article	NOUN
ejpam-4143	15	14	on	on	ADP
ejpam-4143	15	15	fuzzy	fuzzy	ADJ
ejpam-4143	15	16	sets	set	NOUN
ejpam-4143	15	17	,	,	PUNCT
ejpam-4143	15	18	fuzzy	fuzzy	ADJ
ejpam-4143	15	19	logic	logic	NOUN
ejpam-4143	15	20	and	and	CCONJ
ejpam-4143	15	21	their	their	PRON
ejpam-4143	15	22	applications	application	NOUN
ejpam-4143	15	23	.	.	PUNCT
ejpam-4143	16	1	fuzzy	fuzzy	ADJ
ejpam-4143	16	2	hyperstructures	hyperstructure	NOUN
ejpam-4143	16	3	is	be	AUX
ejpam-4143	16	4	an	an	DET
ejpam-4143	16	5	application	application	NOUN
ejpam-4143	16	6	of	of	ADP
ejpam-4143	16	7	the	the	DET
ejpam-4143	16	8	notion	notion	NOUN
ejpam-4143	16	9	of	of	ADP
ejpam-4143	16	10	fuzzy	fuzzy	ADJ
ejpam-4143	16	11	sets	set	NOUN
ejpam-4143	16	12	and	and	CCONJ
ejpam-4143	16	13	their	their	PRON
ejpam-4143	16	14	variants	variant	NOUN
ejpam-4143	16	15	to	to	ADP
ejpam-4143	16	16	algebra	algebra	NOUN
ejpam-4143	16	17	.	.	PUNCT
ejpam-4143	17	1	many	many	ADJ
ejpam-4143	17	2	articles	article	NOUN
ejpam-4143	17	3	and	and	CCONJ
ejpam-4143	17	4	several	several	ADJ
ejpam-4143	17	5	books	book	NOUN
ejpam-4143	17	6	are	be	AUX
ejpam-4143	17	7	available	available	ADJ
ejpam-4143	17	8	on	on	ADP
ejpam-4143	17	9	fuzzy	fuzzy	ADJ
ejpam-4143	17	10	hyperstructures	hyperstructure	NOUN
ejpam-4143	17	11	,	,	PUNCT
ejpam-4143	17	12	such	such	ADJ
ejpam-4143	17	13	as	as	ADP
ejpam-4143	17	14	:	:	PUNCT
ejpam-4143	17	15	in	in	ADP
ejpam-4143	17	16	1997	1997	NUM
ejpam-4143	17	17	,	,	PUNCT
ejpam-4143	17	18	p.	p.	NOUN
ejpam-4143	17	19	corcini	corcini	PROPN
ejpam-4143	17	20	and	and	CCONJ
ejpam-4143	17	21	i.	i.	PROPN
ejpam-4143	17	22	tofan	tofan	PROPN
ejpam-4143	18	1	[	[	X
ejpam-4143	18	2	5	5	NUM
ejpam-4143	18	3	]	]	PUNCT
ejpam-4143	18	4	introduced	introduce	VERB
ejpam-4143	18	5	and	and	CCONJ
ejpam-4143	18	6	investigated	investigate	VERB
ejpam-4143	18	7	fuzzy	fuzzy	ADJ
ejpam-4143	18	8	hypergroups	hypergroup	NOUN
ejpam-4143	18	9	.	.	PUNCT
ejpam-4143	19	1	in	in	ADP
ejpam-4143	19	2	2001	2001	NUM
ejpam-4143	19	3	,	,	PUNCT
ejpam-4143	19	4	y.b	y.b	PROPN
ejpam-4143	19	5	.	.	PROPN
ejpam-4143	19	6	jun	jun	PROPN
ejpam-4143	19	7	and	and	CCONJ
ejpam-4143	19	8	x.l	x.l	PROPN
ejpam-4143	19	9	.	.	PUNCT
ejpam-4143	19	10	xin	xin	PROPN
ejpam-4143	20	1	[	[	X
ejpam-4143	20	2	9	9	X
ejpam-4143	20	3	]	]	PUNCT
ejpam-4143	20	4	considered	consider	VERB
ejpam-4143	20	5	the	the	DET
ejpam-4143	20	6	fuzzification	fuzzification	NOUN
ejpam-4143	20	7	of	of	ADP
ejpam-4143	20	8	the	the	DET
ejpam-4143	20	9	notion	notion	NOUN
ejpam-4143	20	10	of	of	ADP
ejpam-4143	20	11	a	a	DET
ejpam-4143	20	12	(	(	PUNCT
ejpam-4143	20	13	weak	weak	ADJ
ejpam-4143	20	14	,	,	PUNCT
ejpam-4143	20	15	strong	strong	ADJ
ejpam-4143	20	16	,	,	PUNCT
ejpam-4143	20	17	reflexive	reflexive	ADJ
ejpam-4143	20	18	)	)	PUNCT
ejpam-4143	20	19	hyper	hyper	ADJ
ejpam-4143	20	20	bck	bck	NOUN
ejpam-4143	20	21	-	-	PUNCT
ejpam-4143	20	22	ideal	ideal	NOUN
ejpam-4143	20	23	,	,	PUNCT
ejpam-4143	20	24	gave	give	VERB
ejpam-4143	20	25	relations	relation	NOUN
ejpam-4143	20	26	among	among	ADP
ejpam-4143	20	27	them	they	PRON
ejpam-4143	20	28	,	,	PUNCT
ejpam-4143	20	29	and	and	CCONJ
ejpam-4143	20	30	investigated	investigate	VERB
ejpam-4143	20	31	some	some	DET
ejpam-4143	20	32	related	relate	VERB
ejpam-4143	20	33	properties	property	NOUN
ejpam-4143	20	34	.	.	PUNCT
ejpam-4143	21	1	v.	v.	ADP
ejpam-4143	21	2	leoreanu	leoreanu	PROPN
ejpam-4143	21	3	-	-	PUNCT
ejpam-4143	21	4	fotea	fotea	NOUN
ejpam-4143	21	5	and	and	CCONJ
ejpam-4143	21	6	b.	b.	PROPN
ejpam-4143	21	7	davvaz	davvaz	NOUN
ejpam-4143	22	1	[	[	X
ejpam-4143	22	2	11	11	NUM
ejpam-4143	22	3	]	]	PUNCT
ejpam-4143	22	4	introduced	introduce	VERB
ejpam-4143	22	5	and	and	CCONJ
ejpam-4143	22	6	investigated	investigate	VERB
ejpam-4143	22	7	∗corresponding	∗corresponde	VERB
ejpam-4143	22	8	author	author	NOUN
ejpam-4143	22	9	.	.	PUNCT
ejpam-4143	23	1	doi	doi	NOUN
ejpam-4143	23	2	:	:	PUNCT
ejpam-4143	23	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4143	https://doi.org/10.29020/nybg.ejpam.v14i4.4143	PROPN
ejpam-4143	23	4	email	email	NOUN
ejpam-4143	23	5	addresses	address	VERB
ejpam-4143	23	6	:	:	PUNCT
ejpam-4143	24	1	rohaima87@yahoo.com	rohaima87@yahoo.com	PROPN
ejpam-4143	24	2	(	(	PUNCT
ejpam-4143	24	3	r.	r.	PROPN
ejpam-4143	24	4	amairanto	amairanto	PROPN
ejpam-4143	24	5	)	)	PUNCT
ejpam-4143	24	6	,	,	PUNCT
ejpam-4143	24	7	rowena.isla@g.msuiit.edu.ph	rowena.isla@g.msuiit.edu.ph	PROPN
ejpam-4143	24	8	(	(	PUNCT
ejpam-4143	24	9	r.	r.	PROPN
ejpam-4143	24	10	isla	isla	PROPN
ejpam-4143	24	11	)	)	PUNCT
ejpam-4143	24	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4143	24	13	1388	1388	NUM
ejpam-4143	25	1	©	©	PROPN
ejpam-4143	25	2	2021	2021	NUM
ejpam-4143	25	3	ejpam	ejpam	VERB
ejpam-4143	25	4	all	all	DET
ejpam-4143	25	5	rights	right	NOUN
ejpam-4143	25	6	reserved	reserve	VERB
ejpam-4143	25	7	.	.	PUNCT
ejpam-4143	26	1	r.	r.	PROPN
ejpam-4143	26	2	amairanto	amairanto	PROPN
ejpam-4143	26	3	,	,	PUNCT
ejpam-4143	26	4	r.	r.	PROPN
ejpam-4143	26	5	isla	isla	PROPN
ejpam-4143	26	6	/	/	SYM
ejpam-4143	26	7	eur	eur	PROPN
ejpam-4143	26	8	.	.	PUNCT
ejpam-4143	27	1	j.	j.	PROPN
ejpam-4143	27	2	pure	pure	PROPN
ejpam-4143	27	3	appl	appl	PROPN
ejpam-4143	27	4	.	.	PROPN
ejpam-4143	27	5	math	math	PROPN
ejpam-4143	27	6	,	,	PUNCT
ejpam-4143	27	7	14	14	NUM
ejpam-4143	27	8	(	(	PUNCT
ejpam-4143	27	9	4	4	NUM
ejpam-4143	27	10	)	)	PUNCT
ejpam-4143	27	11	(	(	PUNCT
ejpam-4143	27	12	2021	2021	NUM
ejpam-4143	27	13	)	)	PUNCT
ejpam-4143	27	14	,	,	PUNCT
ejpam-4143	27	15	1388	1388	NUM
ejpam-4143	27	16	-	-	SYM
ejpam-4143	27	17	1401	1401	NUM
ejpam-4143	27	18	1389	1389	NUM
ejpam-4143	27	19	fuzzy	fuzzy	ADJ
ejpam-4143	27	20	hyperrings	hyperring	NOUN
ejpam-4143	27	21	in	in	ADP
ejpam-4143	27	22	2009	2009	NUM
ejpam-4143	27	23	.	.	PUNCT
ejpam-4143	28	1	they	they	PRON
ejpam-4143	28	2	analyzed	analyze	VERB
ejpam-4143	28	3	fuzzy	fuzzy	ADJ
ejpam-4143	28	4	substructures	substructure	NOUN
ejpam-4143	28	5	and	and	CCONJ
ejpam-4143	28	6	homomorphisms	homomorphism	NOUN
ejpam-4143	28	7	between	between	ADP
ejpam-4143	28	8	fuzzy	fuzzy	ADJ
ejpam-4143	28	9	hyperrings	hyperring	NOUN
ejpam-4143	28	10	.	.	PUNCT
ejpam-4143	29	1	in	in	ADP
ejpam-4143	29	2	2011	2011	NUM
ejpam-4143	29	3	,	,	PUNCT
ejpam-4143	29	4	r.	r.	PROPN
ejpam-4143	29	5	ameri	ameri	PROPN
ejpam-4143	29	6	and	and	CCONJ
ejpam-4143	29	7	t.	t.	NOUN
ejpam-4143	29	8	nozari	nozari	PROPN
ejpam-4143	30	1	[	[	X
ejpam-4143	30	2	2	2	X
ejpam-4143	30	3	]	]	PUNCT
ejpam-4143	30	4	introduced	introduce	VERB
ejpam-4143	30	5	the	the	DET
ejpam-4143	30	6	concept	concept	NOUN
ejpam-4143	30	7	of	of	ADP
ejpam-4143	30	8	fuzzy	fuzzy	ADJ
ejpam-4143	30	9	regular	regular	ADJ
ejpam-4143	30	10	(	(	PUNCT
ejpam-4143	30	11	resp	resp	NOUN
ejpam-4143	30	12	.	.	PUNCT
ejpam-4143	30	13	,	,	PUNCT
ejpam-4143	30	14	fuzzy	fuzzy	ADJ
ejpam-4143	30	15	strongly	strongly	ADV
ejpam-4143	30	16	regular	regular	ADJ
ejpam-4143	30	17	)	)	PUNCT
ejpam-4143	30	18	relations	relation	NOUN
ejpam-4143	30	19	of	of	ADP
ejpam-4143	30	20	hyperalgebras	hyperalgebra	NOUN
ejpam-4143	30	21	and	and	CCONJ
ejpam-4143	30	22	obtained	obtain	VERB
ejpam-4143	30	23	their	their	PRON
ejpam-4143	30	24	basic	basic	ADJ
ejpam-4143	30	25	properties	property	NOUN
ejpam-4143	30	26	.	.	PUNCT
ejpam-4143	31	1	they	they	PRON
ejpam-4143	31	2	also	also	ADV
ejpam-4143	31	3	proved	prove	VERB
ejpam-4143	31	4	that	that	SCONJ
ejpam-4143	31	5	with	with	ADP
ejpam-4143	31	6	every	every	DET
ejpam-4143	31	7	fuzzy	fuzzy	ADJ
ejpam-4143	31	8	hyper	hyper	ADJ
ejpam-4143	31	9	algebra	algebra	NOUN
ejpam-4143	31	10	,	,	PUNCT
ejpam-4143	31	11	a	a	DET
ejpam-4143	31	12	unique	unique	ADJ
ejpam-4143	31	13	hyperalgebra	hyperalgebra	NOUN
ejpam-4143	31	14	can	can	AUX
ejpam-4143	31	15	be	be	AUX
ejpam-4143	31	16	associated	associate	VERB
ejpam-4143	31	17	via	via	ADP
ejpam-4143	31	18	a	a	DET
ejpam-4143	31	19	regular	regular	ADJ
ejpam-4143	31	20	(	(	PUNCT
ejpam-4143	31	21	resp	resp	NOUN
ejpam-4143	31	22	.	.	PUNCT
ejpam-4143	31	23	,	,	PUNCT
ejpam-4143	31	24	strongly	strongly	ADV
ejpam-4143	31	25	regular	regular	ADJ
ejpam-4143	31	26	)	)	PUNCT
ejpam-4143	31	27	relation	relation	NOUN
ejpam-4143	31	28	.	.	PUNCT
ejpam-4143	32	1	in	in	ADP
ejpam-4143	32	2	2012	2012	NUM
ejpam-4143	32	3	,	,	PUNCT
ejpam-4143	32	4	f.	f.	PROPN
ejpam-4143	32	5	nisar	nisar	PROPN
ejpam-4143	32	6	et	et	PROPN
ejpam-4143	32	7	al	al	PROPN
ejpam-4143	32	8	.	.	PUNCT
ejpam-4143	33	1	[	[	X
ejpam-4143	33	2	7	7	X
ejpam-4143	33	3	]	]	PUNCT
ejpam-4143	33	4	introduced	introduce	VERB
ejpam-4143	33	5	distributive	distributive	ADJ
ejpam-4143	33	6	hyper	hyper	ADJ
ejpam-4143	33	7	bci	bci	NOUN
ejpam-4143	33	8	-	-	NOUN
ejpam-4143	33	9	ideals	ideal	NOUN
ejpam-4143	33	10	and	and	CCONJ
ejpam-4143	33	11	applied	apply	VERB
ejpam-4143	33	12	the	the	DET
ejpam-4143	33	13	concept	concept	NOUN
ejpam-4143	33	14	of	of	ADP
ejpam-4143	33	15	fuzzy	fuzzy	ADJ
ejpam-4143	33	16	set	set	NOUN
ejpam-4143	33	17	to	to	PART
ejpam-4143	33	18	investigate	investigate	VERB
ejpam-4143	33	19	the	the	DET
ejpam-4143	33	20	relations	relation	NOUN
ejpam-4143	33	21	between	between	ADP
ejpam-4143	33	22	fuzzy	fuzzy	ADJ
ejpam-4143	33	23	distributive	distributive	ADJ
ejpam-4143	33	24	hyper	hyper	ADJ
ejpam-4143	33	25	bci	bci	NOUN
ejpam-4143	33	26	-	-	NOUN
ejpam-4143	33	27	ideals	ideal	NOUN
ejpam-4143	33	28	and	and	CCONJ
ejpam-4143	33	29	distributive	distributive	ADJ
ejpam-4143	33	30	hyper	hyper	ADJ
ejpam-4143	33	31	bci	bci	NOUN
ejpam-4143	33	32	-	-	NOUN
ejpam-4143	33	33	ideals	ideal	NOUN
ejpam-4143	33	34	of	of	ADP
ejpam-4143	33	35	a	a	DET
ejpam-4143	33	36	hyper	hyper	ADJ
ejpam-4143	33	37	bci	bci	NOUN
ejpam-4143	33	38	-	-	NOUN
ejpam-4143	33	39	algebra	algebra	NOUN
ejpam-4143	33	40	.	.	PUNCT
ejpam-4143	34	1	in	in	ADP
ejpam-4143	34	2	2015	2015	NUM
ejpam-4143	34	3	,	,	PUNCT
ejpam-4143	34	4	b.	b.	PROPN
ejpam-4143	34	5	davvaz	davvaz	PROPN
ejpam-4143	34	6	and	and	CCONJ
ejpam-4143	34	7	i.	i.	PROPN
ejpam-4143	34	8	cristea	cristea	PROPN
ejpam-4143	35	1	[	[	X
ejpam-4143	35	2	6	6	NUM
ejpam-4143	35	3	]	]	PUNCT
ejpam-4143	35	4	summarized	summarize	VERB
ejpam-4143	35	5	the	the	DET
ejpam-4143	35	6	research	research	NOUN
ejpam-4143	35	7	progress	progress	NOUN
ejpam-4143	35	8	of	of	ADP
ejpam-4143	35	9	fuzzy	fuzzy	ADJ
ejpam-4143	35	10	hyperstructures	hyperstructure	NOUN
ejpam-4143	35	11	.	.	PUNCT
ejpam-4143	36	1	in	in	ADP
ejpam-4143	36	2	2017	2017	NUM
ejpam-4143	36	3	,	,	PUNCT
ejpam-4143	36	4	p.	p.	NOUN
ejpam-4143	36	5	corcini	corcini	NOUN
ejpam-4143	37	1	[	[	X
ejpam-4143	37	2	3	3	X
ejpam-4143	37	3	]	]	PUNCT
ejpam-4143	37	4	gave	give	VERB
ejpam-4143	37	5	a	a	DET
ejpam-4143	37	6	brief	brief	ADJ
ejpam-4143	37	7	excursus	excursus	NOUN
ejpam-4143	37	8	on	on	ADP
ejpam-4143	37	9	some	some	DET
ejpam-4143	37	10	results	result	NOUN
ejpam-4143	37	11	on	on	ADP
ejpam-4143	37	12	hyperstructures	hyperstructure	NOUN
ejpam-4143	37	13	,	,	PUNCT
ejpam-4143	37	14	their	their	PRON
ejpam-4143	37	15	connections	connection	NOUN
ejpam-4143	37	16	with	with	ADP
ejpam-4143	37	17	fuzzy	fuzzy	ADJ
ejpam-4143	37	18	sets	set	NOUN
ejpam-4143	37	19	,	,	PUNCT
ejpam-4143	37	20	and	and	CCONJ
ejpam-4143	37	21	extensions	extension	NOUN
ejpam-4143	37	22	to	to	ADP
ejpam-4143	37	23	weak	weak	ADJ
ejpam-4143	37	24	structures	structure	NOUN
ejpam-4143	37	25	.	.	PUNCT
ejpam-4143	38	1	in	in	ADP
ejpam-4143	38	2	2019	2019	NUM
ejpam-4143	38	3	,	,	PUNCT
ejpam-4143	38	4	x.	x.	NOUN
ejpam-4143	38	5	xin	xin	PROPN
ejpam-4143	38	6	et	et	PROPN
ejpam-4143	38	7	al	al	PROPN
ejpam-4143	38	8	.	.	PUNCT
ejpam-4143	39	1	[	[	X
ejpam-4143	39	2	20	20	NUM
ejpam-4143	39	3	]	]	PUNCT
ejpam-4143	39	4	introduced	introduce	VERB
ejpam-4143	39	5	the	the	DET
ejpam-4143	39	6	notions	notion	NOUN
ejpam-4143	39	7	of	of	ADP
ejpam-4143	39	8	intuitionistic	intuitionistic	ADJ
ejpam-4143	39	9	fuzzy	fuzzy	ADJ
ejpam-4143	39	10	soft	soft	ADJ
ejpam-4143	39	11	(	(	PUNCT
ejpam-4143	39	12	resp	resp	NOUN
ejpam-4143	39	13	.	.	PUNCT
ejpam-4143	39	14	,	,	PUNCT
ejpam-4143	39	15	weak	weak	ADJ
ejpam-4143	39	16	,	,	PUNCT
ejpam-4143	39	17	s	s	NOUN
ejpam-4143	39	18	-	-	PUNCT
ejpam-4143	39	19	weak	weak	ADJ
ejpam-4143	39	20	,	,	PUNCT
ejpam-4143	39	21	strong	strong	ADJ
ejpam-4143	39	22	)	)	PUNCT
ejpam-4143	39	23	hyper	hyper	ADJ
ejpam-4143	39	24	bck	bck	NOUN
ejpam-4143	39	25	-	-	PUNCT
ejpam-4143	39	26	ideal	ideal	NOUN
ejpam-4143	39	27	and	and	CCONJ
ejpam-4143	39	28	investigated	investigate	VERB
ejpam-4143	39	29	related	related	ADJ
ejpam-4143	39	30	properties	property	NOUN
ejpam-4143	39	31	and	and	CCONJ
ejpam-4143	39	32	relations	relation	NOUN
ejpam-4143	39	33	.	.	PUNCT
ejpam-4143	40	1	moreover	moreover	ADV
ejpam-4143	40	2	,	,	PUNCT
ejpam-4143	40	3	g.	g.	PROPN
ejpam-4143	40	4	tabaranza	tabaranza	PROPN
ejpam-4143	40	5	and	and	CCONJ
ejpam-4143	40	6	j.	j.	PROPN
ejpam-4143	40	7	vilela	vilela	PROPN
ejpam-4143	41	1	[	[	X
ejpam-4143	41	2	18	18	NUM
ejpam-4143	41	3	]	]	PUNCT
ejpam-4143	41	4	applied	apply	VERB
ejpam-4143	41	5	the	the	DET
ejpam-4143	41	6	fuzzy	fuzzy	ADJ
ejpam-4143	41	7	set	set	NOUN
ejpam-4143	41	8	to	to	ADP
ejpam-4143	41	9	hyper	hyper	NOUN
ejpam-4143	41	10	b	b	NOUN
ejpam-4143	41	11	-	-	PUNCT
ejpam-4143	41	12	algebras	algebras	X
ejpam-4143	41	13	,	,	PUNCT
ejpam-4143	41	14	while	while	SCONJ
ejpam-4143	41	15	a.	a.	NOUN
ejpam-4143	41	16	macodi	macodi	PROPN
ejpam-4143	41	17	-	-	PUNCT
ejpam-4143	41	18	ringia	ringia	PROPN
ejpam-4143	41	19	and	and	CCONJ
ejpam-4143	41	20	g.	g.	PROPN
ejpam-4143	41	21	petalcorin	petalcorin	PROPN
ejpam-4143	41	22	jr	jr	PROPN
ejpam-4143	41	23	.	.	PUNCT
ejpam-4143	42	1	[	[	X
ejpam-4143	42	2	12	12	NUM
ejpam-4143	42	3	]	]	PUNCT
ejpam-4143	42	4	introduced	introduce	VERB
ejpam-4143	42	5	the	the	DET
ejpam-4143	42	6	implicative	implicative	ADJ
ejpam-4143	42	7	hyper	hyper	ADJ
ejpam-4143	42	8	gr	gr	NOUN
ejpam-4143	42	9	-	-	PUNCT
ejpam-4143	42	10	ideal	ideal	NOUN
ejpam-4143	42	11	and	and	CCONJ
ejpam-4143	42	12	the	the	DET
ejpam-4143	42	13	fuzzy	fuzzy	ADJ
ejpam-4143	42	14	implicative	implicative	ADJ
ejpam-4143	42	15	hyper	hyper	ADJ
ejpam-4143	42	16	gr	gr	NOUN
ejpam-4143	42	17	-	-	PUNCT
ejpam-4143	42	18	ideal	ideal	NOUN
ejpam-4143	42	19	of	of	ADP
ejpam-4143	42	20	type	type	NOUN
ejpam-4143	42	21	1	1	NUM
ejpam-4143	42	22	(	(	PUNCT
ejpam-4143	42	23	resp	resp	NOUN
ejpam-4143	42	24	.	.	PUNCT
ejpam-4143	42	25	,	,	PUNCT
ejpam-4143	42	26	of	of	ADP
ejpam-4143	42	27	type	type	NOUN
ejpam-4143	42	28	2	2	NUM
ejpam-4143	42	29	)	)	PUNCT
ejpam-4143	42	30	,	,	PUNCT
ejpam-4143	42	31	and	and	CCONJ
ejpam-4143	42	32	investigated	investigate	VERB
ejpam-4143	42	33	several	several	ADJ
ejpam-4143	42	34	properties	property	NOUN
ejpam-4143	42	35	.	.	PUNCT
ejpam-4143	43	1	characterizations	characterization	NOUN
ejpam-4143	43	2	of	of	ADP
ejpam-4143	43	3	fuzzy	fuzzy	ADJ
ejpam-4143	43	4	implicative	implicative	ADJ
ejpam-4143	43	5	hyper	hyper	ADJ
ejpam-4143	43	6	gr	gr	NOUN
ejpam-4143	43	7	-	-	PUNCT
ejpam-4143	43	8	ideals	ideal	NOUN
ejpam-4143	43	9	of	of	ADP
ejpam-4143	43	10	type	type	NOUN
ejpam-4143	43	11	1	1	NUM
ejpam-4143	43	12	are	be	AUX
ejpam-4143	43	13	also	also	ADV
ejpam-4143	43	14	given	give	VERB
ejpam-4143	43	15	.	.	PUNCT
ejpam-4143	44	1	ringia	ringia	PROPN
ejpam-4143	44	2	and	and	CCONJ
ejpam-4143	44	3	petalcorin	petalcorin	NOUN
ejpam-4143	45	1	[	[	X
ejpam-4143	45	2	13	13	NUM
ejpam-4143	45	3	]	]	PUNCT
ejpam-4143	45	4	also	also	ADV
ejpam-4143	45	5	investigated	investigate	VERB
ejpam-4143	45	6	intuitionistic	intuitionistic	ADJ
ejpam-4143	45	7	fuzzy	fuzzy	ADJ
ejpam-4143	45	8	hyper	hyper	ADJ
ejpam-4143	45	9	gr	gr	NOUN
ejpam-4143	45	10	-	-	PUNCT
ejpam-4143	45	11	ideals	ideal	NOUN
ejpam-4143	45	12	in	in	ADP
ejpam-4143	45	13	hyper	hyper	ADJ
ejpam-4143	45	14	gr	gr	NOUN
ejpam-4143	45	15	-	-	PUNCT
ejpam-4143	45	16	algebras	algebras	NOUN
ejpam-4143	45	17	in	in	ADP
ejpam-4143	45	18	2020	2020	NUM
ejpam-4143	45	19	.	.	PUNCT
ejpam-4143	46	1	in	in	ADP
ejpam-4143	46	2	2017	2017	NUM
ejpam-4143	46	3	,	,	PUNCT
ejpam-4143	46	4	a.	a.	NOUN
ejpam-4143	46	5	iampan	iampan	NOUN
ejpam-4143	46	6	[	[	X
ejpam-4143	46	7	8	8	X
ejpam-4143	46	8	]	]	PUNCT
ejpam-4143	46	9	defined	define	VERB
ejpam-4143	46	10	a	a	DET
ejpam-4143	46	11	new	new	ADJ
ejpam-4143	46	12	algebraic	algebraic	ADJ
ejpam-4143	46	13	structure	structure	NOUN
ejpam-4143	46	14	called	call	VERB
ejpam-4143	46	15	up	up	ADP
ejpam-4143	46	16	-	-	PUNCT
ejpam-4143	46	17	algebra	algebra	NOUN
ejpam-4143	46	18	and	and	CCONJ
ejpam-4143	46	19	showed	show	VERB
ejpam-4143	46	20	that	that	SCONJ
ejpam-4143	46	21	the	the	DET
ejpam-4143	46	22	notion	notion	NOUN
ejpam-4143	46	23	of	of	ADP
ejpam-4143	46	24	up	up	ADP
ejpam-4143	46	25	-	-	PUNCT
ejpam-4143	46	26	algebra	algebra	NOUN
ejpam-4143	46	27	is	be	AUX
ejpam-4143	46	28	a	a	DET
ejpam-4143	46	29	generalization	generalization	NOUN
ejpam-4143	46	30	of	of	ADP
ejpam-4143	46	31	ku	ku	PROPN
ejpam-4143	46	32	-	-	PUNCT
ejpam-4143	46	33	algebra	algebra	PROPN
ejpam-4143	46	34	that	that	PRON
ejpam-4143	46	35	was	be	AUX
ejpam-4143	46	36	introduced	introduce	VERB
ejpam-4143	46	37	by	by	ADP
ejpam-4143	46	38	c.	c.	PROPN
ejpam-4143	46	39	prabpayak	prabpayak	NOUN
ejpam-4143	46	40	and	and	CCONJ
ejpam-4143	46	41	u.	u.	NOUN
ejpam-4143	46	42	leerawat	leerawat	NOUN
ejpam-4143	47	1	[	[	X
ejpam-4143	47	2	15	15	NUM
ejpam-4143	47	3	]	]	PUNCT
ejpam-4143	47	4	.	.	PUNCT
ejpam-4143	48	1	in	in	ADP
ejpam-4143	48	2	the	the	DET
ejpam-4143	48	3	same	same	ADJ
ejpam-4143	48	4	year	year	NOUN
ejpam-4143	48	5	,	,	PUNCT
ejpam-4143	48	6	s.	s.	PROPN
ejpam-4143	48	7	mostafa	mostafa	PROPN
ejpam-4143	48	8	et	et	PROPN
ejpam-4143	48	9	al	al	PROPN
ejpam-4143	48	10	.	.	PUNCT
ejpam-4143	49	1	[	[	X
ejpam-4143	49	2	17	17	NUM
ejpam-4143	49	3	]	]	PUNCT
ejpam-4143	49	4	applied	apply	VERB
ejpam-4143	49	5	the	the	DET
ejpam-4143	49	6	hyper	hyper	ADJ
ejpam-4143	49	7	structure	structure	NOUN
ejpam-4143	49	8	theory	theory	NOUN
ejpam-4143	49	9	to	to	ADP
ejpam-4143	49	10	ku	ku	PROPN
ejpam-4143	49	11	-	-	PUNCT
ejpam-4143	49	12	algebras	algebras	PROPN
ejpam-4143	49	13	.	.	PUNCT
ejpam-4143	50	1	in	in	ADP
ejpam-4143	50	2	2019	2019	NUM
ejpam-4143	50	3	,	,	PUNCT
ejpam-4143	50	4	d.	d.	PROPN
ejpam-4143	50	5	romano	romano	VERB
ejpam-4143	51	1	[	[	X
ejpam-4143	51	2	16	16	NUM
ejpam-4143	51	3	]	]	PUNCT
ejpam-4143	51	4	introduced	introduce	VERB
ejpam-4143	51	5	the	the	DET
ejpam-4143	51	6	concept	concept	NOUN
ejpam-4143	51	7	of	of	ADP
ejpam-4143	51	8	hyper	hyper	ADJ
ejpam-4143	51	9	up	up	ADP
ejpam-4143	51	10	-	-	PUNCT
ejpam-4143	51	11	algebra	algebra	NOUN
ejpam-4143	51	12	,	,	PUNCT
ejpam-4143	51	13	presented	present	VERB
ejpam-4143	51	14	some	some	DET
ejpam-4143	51	15	related	relate	VERB
ejpam-4143	51	16	properties	property	NOUN
ejpam-4143	51	17	,	,	PUNCT
ejpam-4143	51	18	and	and	CCONJ
ejpam-4143	51	19	considered	consider	VERB
ejpam-4143	51	20	homomorphisms	homomorphism	NOUN
ejpam-4143	51	21	between	between	ADP
ejpam-4143	51	22	hyper	hyper	NOUN
ejpam-4143	51	23	up	up	ADP
ejpam-4143	51	24	-	-	PUNCT
ejpam-4143	51	25	algebras	algebras	X
ejpam-4143	51	26	.	.	PUNCT
ejpam-4143	52	1	in	in	ADP
ejpam-4143	52	2	2020	2020	NUM
ejpam-4143	52	3	,	,	PUNCT
ejpam-4143	52	4	r.	r.	PROPN
ejpam-4143	52	5	amairanto	amairanto	PROPN
ejpam-4143	52	6	and	and	CCONJ
ejpam-4143	52	7	r.	r.	PROPN
ejpam-4143	52	8	isla	isla	PROPN
ejpam-4143	53	1	[	[	X
ejpam-4143	53	2	1	1	NUM
ejpam-4143	53	3	]	]	PUNCT
ejpam-4143	53	4	investigated	investigate	VERB
ejpam-4143	53	5	the	the	DET
ejpam-4143	53	6	concept	concept	NOUN
ejpam-4143	53	7	of	of	ADP
ejpam-4143	53	8	regular	regular	ADJ
ejpam-4143	53	9	congruence	congruence	NOUN
ejpam-4143	53	10	relation	relation	NOUN
ejpam-4143	53	11	on	on	ADP
ejpam-4143	53	12	hyper	hyper	ADJ
ejpam-4143	53	13	up	up	ADP
ejpam-4143	53	14	-	-	PUNCT
ejpam-4143	53	15	algebras	algebras	PROPN
ejpam-4143	53	16	and	and	CCONJ
ejpam-4143	53	17	established	establish	VERB
ejpam-4143	53	18	some	some	DET
ejpam-4143	53	19	homomorphism	homomorphism	NOUN
ejpam-4143	53	20	theorems	theorem	NOUN
ejpam-4143	53	21	on	on	ADP
ejpam-4143	53	22	such	such	ADJ
ejpam-4143	53	23	algebras	algebra	NOUN
ejpam-4143	53	24	.	.	PUNCT
ejpam-4143	54	1	they	they	PRON
ejpam-4143	54	2	also	also	ADV
ejpam-4143	54	3	examined	examine	VERB
ejpam-4143	54	4	the	the	DET
ejpam-4143	54	5	notion	notion	NOUN
ejpam-4143	54	6	of	of	ADP
ejpam-4143	54	7	hyper	hyper	ADJ
ejpam-4143	54	8	product	product	NOUN
ejpam-4143	54	9	of	of	ADP
ejpam-4143	54	10	hyper	hyper	ADJ
ejpam-4143	54	11	up	up	ADP
ejpam-4143	54	12	-	-	PUNCT
ejpam-4143	54	13	algebras	algebras	X
ejpam-4143	54	14	.	.	PUNCT
ejpam-4143	55	1	in	in	ADP
ejpam-4143	55	2	this	this	DET
ejpam-4143	55	3	paper	paper	NOUN
ejpam-4143	55	4	,	,	PUNCT
ejpam-4143	55	5	we	we	PRON
ejpam-4143	55	6	apply	apply	VERB
ejpam-4143	55	7	the	the	DET
ejpam-4143	55	8	concept	concept	NOUN
ejpam-4143	55	9	of	of	ADP
ejpam-4143	55	10	fuzzy	fuzzy	ADJ
ejpam-4143	55	11	set	set	NOUN
ejpam-4143	55	12	to	to	PART
ejpam-4143	55	13	hyper	hyper	VERB
ejpam-4143	55	14	up	up	ADP
ejpam-4143	55	15	-	-	PUNCT
ejpam-4143	55	16	algebras	algebras	X
ejpam-4143	55	17	.	.	PUNCT
ejpam-4143	56	1	we	we	PRON
ejpam-4143	56	2	introduce	introduce	VERB
ejpam-4143	56	3	the	the	DET
ejpam-4143	56	4	notions	notion	NOUN
ejpam-4143	56	5	of	of	ADP
ejpam-4143	56	6	fuzzy	fuzzy	ADJ
ejpam-4143	56	7	hyper	hyper	ADJ
ejpam-4143	56	8	up	up	ADP
ejpam-4143	56	9	-	-	PUNCT
ejpam-4143	56	10	subalgebra	subalgebra	NOUN
ejpam-4143	56	11	and	and	CCONJ
ejpam-4143	56	12	fuzzy	fuzzy	ADJ
ejpam-4143	56	13	hyper	hyper	ADJ
ejpam-4143	56	14	up	up	ADJ
ejpam-4143	56	15	-	-	PUNCT
ejpam-4143	56	16	filter	filter	NOUN
ejpam-4143	56	17	and	and	CCONJ
ejpam-4143	56	18	investigate	investigate	VERB
ejpam-4143	56	19	their	their	PRON
ejpam-4143	56	20	basic	basic	ADJ
ejpam-4143	56	21	properties	property	NOUN
ejpam-4143	56	22	.	.	PUNCT
ejpam-4143	57	1	some	some	DET
ejpam-4143	57	2	properties	property	NOUN
ejpam-4143	57	3	of	of	ADP
ejpam-4143	57	4	hyper	hyper	ADJ
ejpam-4143	57	5	homomorphism	homomorphism	NOUN
ejpam-4143	57	6	in	in	ADP
ejpam-4143	57	7	relation	relation	NOUN
ejpam-4143	57	8	to	to	ADP
ejpam-4143	57	9	fuzzy	fuzzy	ADJ
ejpam-4143	57	10	hyper	hyper	ADJ
ejpam-4143	57	11	up	up	ADP
ejpam-4143	57	12	-	-	PUNCT
ejpam-4143	57	13	subalgebra	subalgebra	NOUN
ejpam-4143	57	14	and	and	CCONJ
ejpam-4143	57	15	fuzzy	fuzzy	ADJ
ejpam-4143	57	16	hyper	hyper	ADJ
ejpam-4143	57	17	up	up	ADP
ejpam-4143	57	18	-	-	PUNCT
ejpam-4143	57	19	filter	filter	NOUN
ejpam-4143	57	20	are	be	AUX
ejpam-4143	57	21	also	also	ADV
ejpam-4143	57	22	provided	provide	VERB
ejpam-4143	57	23	.	.	PUNCT
ejpam-4143	58	1	2	2	X
ejpam-4143	58	2	.	.	X
ejpam-4143	58	3	preliminaries	preliminary	NOUN
ejpam-4143	58	4	let	let	VERB
ejpam-4143	58	5	h	h	NOUN
ejpam-4143	58	6	be	be	AUX
ejpam-4143	58	7	a	a	DET
ejpam-4143	58	8	nonempty	nonempty	ADV
ejpam-4143	58	9	set	set	VERB
ejpam-4143	58	10	and	and	CCONJ
ejpam-4143	58	11	p∗(h	p∗(h	PROPN
ejpam-4143	58	12	)	)	PUNCT
ejpam-4143	58	13	be	be	VERB
ejpam-4143	58	14	the	the	DET
ejpam-4143	58	15	set	set	NOUN
ejpam-4143	58	16	of	of	ADP
ejpam-4143	58	17	all	all	DET
ejpam-4143	58	18	nonempty	nonempty	ADJ
ejpam-4143	58	19	subsets	subset	NOUN
ejpam-4143	58	20	of	of	ADP
ejpam-4143	58	21	h.	h.	PROPN
ejpam-4143	58	22	a	a	DET
ejpam-4143	58	23	hyperoperation	hyperoperation	NOUN
ejpam-4143	58	24	on	on	ADP
ejpam-4143	58	25	h	h	NOUN
ejpam-4143	58	26	is	be	AUX
ejpam-4143	58	27	a	a	DET
ejpam-4143	58	28	mapping	mapping	NOUN
ejpam-4143	58	29	from	from	ADP
ejpam-4143	58	30	h	h	NOUN
ejpam-4143	58	31	×h	×h	PROPN
ejpam-4143	58	32	into	into	ADP
ejpam-4143	58	33	p∗(h	p∗(h	PROPN
ejpam-4143	58	34	)	)	PUNCT
ejpam-4143	58	35	.	.	PUNCT
ejpam-4143	59	1	definition	definition	NOUN
ejpam-4143	59	2	1	1	NUM
ejpam-4143	59	3	.	.	PUNCT
ejpam-4143	60	1	[	[	X
ejpam-4143	60	2	16	16	NUM
ejpam-4143	60	3	]	]	X
ejpam-4143	60	4	a	a	DET
ejpam-4143	60	5	hyper	hyper	ADJ
ejpam-4143	60	6	up	up	ADP
ejpam-4143	60	7	-	-	PUNCT
ejpam-4143	60	8	algebra	algebra	NOUN
ejpam-4143	60	9	is	be	AUX
ejpam-4143	60	10	a	a	DET
ejpam-4143	60	11	set	set	ADJ
ejpam-4143	60	12	h	h	NOUN
ejpam-4143	60	13	with	with	ADP
ejpam-4143	60	14	constant	constant	ADJ
ejpam-4143	60	15	0	0	NUM
ejpam-4143	60	16	and	and	CCONJ
ejpam-4143	60	17	hyperoperation	hyperoperation	NOUN
ejpam-4143	60	18	⊛	⊛	NOUN
ejpam-4143	60	19	satisfying	satisfy	VERB
ejpam-4143	60	20	the	the	DET
ejpam-4143	60	21	following	follow	VERB
ejpam-4143	60	22	axioms	axiom	NOUN
ejpam-4143	60	23	:	:	PUNCT
ejpam-4143	60	24	for	for	ADP
ejpam-4143	60	25	all	all	DET
ejpam-4143	60	26	x	x	NOUN
ejpam-4143	60	27	,	,	PUNCT
ejpam-4143	60	28	y	y	PROPN
ejpam-4143	60	29	,	,	PUNCT
ejpam-4143	60	30	z	z	PROPN
ejpam-4143	60	31	∈	∈	PROPN
ejpam-4143	60	32	h	h	NOUN
ejpam-4143	60	33	,	,	PUNCT
ejpam-4143	60	34	(	(	PUNCT
ejpam-4143	60	35	hup1	hup1	PROPN
ejpam-4143	60	36	)	)	PUNCT
ejpam-4143	61	1	y	y	PROPN
ejpam-4143	61	2	⊛	⊛	ADV
ejpam-4143	61	3	z	z	NOUN
ejpam-4143	61	4	≪	≪	PUNCT
ejpam-4143	61	5	[	[	X
ejpam-4143	61	6	(	(	PUNCT
ejpam-4143	61	7	x⊛	x⊛	INTJ
ejpam-4143	61	8	y)⊛	y)⊛	PROPN
ejpam-4143	61	9	(	(	PUNCT
ejpam-4143	61	10	x⊛	x⊛	PROPN
ejpam-4143	61	11	z	z	NOUN
ejpam-4143	61	12	)	)	PUNCT
ejpam-4143	61	13	]	]	PUNCT
ejpam-4143	61	14	,	,	PUNCT
ejpam-4143	61	15	(	(	PUNCT
ejpam-4143	61	16	hup2	hup2	PROPN
ejpam-4143	61	17	)	)	PUNCT
ejpam-4143	62	1	x⊛	x⊛	PROPN
ejpam-4143	62	2	0	0	PUNCT
ejpam-4143	63	1	=	=	SYM
ejpam-4143	63	2	{	{	PUNCT
ejpam-4143	63	3	0	0	NUM
ejpam-4143	63	4	}	}	PUNCT
ejpam-4143	63	5	,	,	PUNCT
ejpam-4143	63	6	(	(	PUNCT
ejpam-4143	63	7	hup3	hup3	NOUN
ejpam-4143	63	8	)	)	PUNCT
ejpam-4143	63	9	0⊛	0⊛	NUM
ejpam-4143	63	10	x	x	X
ejpam-4143	63	11	=	=	PRON
ejpam-4143	63	12	{	{	PUNCT
ejpam-4143	63	13	x	x	NOUN
ejpam-4143	63	14	}	}	PUNCT
ejpam-4143	63	15	,	,	PUNCT
ejpam-4143	63	16	r.	r.	PROPN
ejpam-4143	63	17	amairanto	amairanto	PROPN
ejpam-4143	63	18	,	,	PUNCT
ejpam-4143	63	19	r.	r.	PROPN
ejpam-4143	63	20	isla	isla	PROPN
ejpam-4143	63	21	/	/	SYM
ejpam-4143	63	22	eur	eur	PROPN
ejpam-4143	63	23	.	.	PUNCT
ejpam-4143	64	1	j.	j.	PROPN
ejpam-4143	64	2	pure	pure	PROPN
ejpam-4143	64	3	appl	appl	PROPN
ejpam-4143	64	4	.	.	PROPN
ejpam-4143	64	5	math	math	PROPN
ejpam-4143	64	6	,	,	PUNCT
ejpam-4143	64	7	14	14	NUM
ejpam-4143	64	8	(	(	PUNCT
ejpam-4143	64	9	4	4	NUM
ejpam-4143	64	10	)	)	PUNCT
ejpam-4143	64	11	(	(	PUNCT
ejpam-4143	64	12	2021	2021	NUM
ejpam-4143	64	13	)	)	PUNCT
ejpam-4143	64	14	,	,	PUNCT
ejpam-4143	64	15	1388	1388	NUM
ejpam-4143	64	16	-	-	SYM
ejpam-4143	64	17	1401	1401	NUM
ejpam-4143	64	18	1390	1390	NUM
ejpam-4143	64	19	(	(	PUNCT
ejpam-4143	64	20	hup4	hup4	PROPN
ejpam-4143	64	21	)	)	PUNCT
ejpam-4143	64	22	x	x	SYM
ejpam-4143	64	23	≪	≪	PUNCT
ejpam-4143	64	24	y	y	PROPN
ejpam-4143	64	25	and	and	CCONJ
ejpam-4143	64	26	y	y	PROPN
ejpam-4143	64	27	≪	≪	NOUN
ejpam-4143	64	28	x	x	X
ejpam-4143	64	29	imply	imply	ADV
ejpam-4143	64	30	x	x	X
ejpam-4143	64	31	=	=	SYM
ejpam-4143	64	32	y	y	PROPN
ejpam-4143	64	33	,	,	PUNCT
ejpam-4143	64	34	where	where	SCONJ
ejpam-4143	64	35	x	x	X
ejpam-4143	64	36	≪	≪	PUNCT
ejpam-4143	64	37	y	y	PROPN
ejpam-4143	64	38	is	be	AUX
ejpam-4143	64	39	defined	define	VERB
ejpam-4143	64	40	by	by	ADP
ejpam-4143	64	41	0	0	NUM
ejpam-4143	64	42	∈	∈	PROPN
ejpam-4143	64	43	x	x	SYM
ejpam-4143	64	44	⊛	⊛	NUM
ejpam-4143	64	45	y	y	PROPN
ejpam-4143	64	46	and	and	CCONJ
ejpam-4143	64	47	for	for	ADP
ejpam-4143	64	48	every	every	DET
ejpam-4143	64	49	a	a	PROPN
ejpam-4143	64	50	,	,	PUNCT
ejpam-4143	64	51	b	b	PROPN
ejpam-4143	64	52	⊆	⊆	NUM
ejpam-4143	64	53	p∗(h	p∗(h	NOUN
ejpam-4143	64	54	)	)	PUNCT
ejpam-4143	64	55	,	,	PUNCT
ejpam-4143	64	56	a	a	DET
ejpam-4143	64	57	≪	≪	ADJ
ejpam-4143	64	58	b	b	NOUN
ejpam-4143	64	59	is	be	AUX
ejpam-4143	64	60	defined	define	VERB
ejpam-4143	64	61	by	by	ADP
ejpam-4143	64	62	:	:	PUNCT
ejpam-4143	64	63	for	for	ADP
ejpam-4143	64	64	all	all	DET
ejpam-4143	64	65	a	a	DET
ejpam-4143	64	66	∈	∈	PROPN
ejpam-4143	64	67	a	a	PRON
ejpam-4143	64	68	,	,	PUNCT
ejpam-4143	64	69	there	there	PRON
ejpam-4143	64	70	exists	exist	VERB
ejpam-4143	64	71	b	b	PROPN
ejpam-4143	64	72	∈	∈	PROPN
ejpam-4143	64	73	b	b	NOUN
ejpam-4143	64	74	such	such	ADJ
ejpam-4143	64	75	that	that	SCONJ
ejpam-4143	64	76	a	a	DET
ejpam-4143	64	77	≪	≪	ADJ
ejpam-4143	64	78	b.	b.	NOUN
ejpam-4143	64	79	in	in	ADP
ejpam-4143	64	80	such	such	ADJ
ejpam-4143	64	81	case	case	NOUN
ejpam-4143	64	82	,	,	PUNCT
ejpam-4143	64	83	we	we	PRON
ejpam-4143	64	84	call	call	VERB
ejpam-4143	64	85	“	"	PUNCT
ejpam-4143	64	86	≪	≪	PROPN
ejpam-4143	64	87	”	"	PUNCT
ejpam-4143	64	88	the	the	DET
ejpam-4143	64	89	hyperorder	hyperorder	NOUN
ejpam-4143	64	90	in	in	ADP
ejpam-4143	64	91	h.	h.	PROPN
ejpam-4143	64	92	a	a	DET
ejpam-4143	64	93	hyper	hyper	ADJ
ejpam-4143	64	94	up	up	ADP
ejpam-4143	64	95	-	-	PUNCT
ejpam-4143	64	96	algebra	algebra	NOUN
ejpam-4143	64	97	h	h	NOUN
ejpam-4143	64	98	with	with	ADP
ejpam-4143	64	99	constant	constant	ADJ
ejpam-4143	64	100	0	0	NUM
ejpam-4143	64	101	and	and	CCONJ
ejpam-4143	64	102	hyperoperation	hyperoperation	NOUN
ejpam-4143	64	103	⊛	⊛	NUM
ejpam-4143	64	104	is	be	AUX
ejpam-4143	64	105	denoted	denote	VERB
ejpam-4143	64	106	by	by	ADP
ejpam-4143	64	107	(	(	PUNCT
ejpam-4143	64	108	h;⊛	h;⊛	NUM
ejpam-4143	64	109	,	,	PUNCT
ejpam-4143	64	110	0	0	NUM
ejpam-4143	64	111	)	)	PUNCT
ejpam-4143	64	112	.	.	PUNCT
ejpam-4143	65	1	by	by	ADP
ejpam-4143	65	2	(	(	PUNCT
ejpam-4143	65	3	hup2	hup2	PROPN
ejpam-4143	65	4	)	)	PUNCT
ejpam-4143	65	5	or	or	CCONJ
ejpam-4143	65	6	(	(	PUNCT
ejpam-4143	65	7	hup3	hup3	PROPN
ejpam-4143	65	8	)	)	PUNCT
ejpam-4143	65	9	,	,	PUNCT
ejpam-4143	65	10	x⊛	x⊛	PROPN
ejpam-4143	65	11	y	y	PROPN
ejpam-4143	65	12	̸=	̸=	PROPN
ejpam-4143	65	13	∅	∅	NOUN
ejpam-4143	65	14	for	for	ADP
ejpam-4143	65	15	all	all	DET
ejpam-4143	65	16	x	x	NOUN
ejpam-4143	65	17	,	,	PUNCT
ejpam-4143	65	18	y	y	PROPN
ejpam-4143	65	19	∈	∈	PROPN
ejpam-4143	65	20	h.	h.	PROPN
ejpam-4143	65	21	example	example	NOUN
ejpam-4143	65	22	1	1	X
ejpam-4143	65	23	.	.	PUNCT
ejpam-4143	66	1	let	let	VERB
ejpam-4143	66	2	h	h	NOUN
ejpam-4143	66	3	=	=	PRON
ejpam-4143	66	4	{	{	PUNCT
ejpam-4143	66	5	0	0	NUM
ejpam-4143	66	6	,	,	PUNCT
ejpam-4143	66	7	a	a	DET
ejpam-4143	66	8	,	,	PUNCT
ejpam-4143	66	9	b	b	NOUN
ejpam-4143	66	10	,	,	PUNCT
ejpam-4143	66	11	c	c	NOUN
ejpam-4143	66	12	,	,	PUNCT
ejpam-4143	66	13	d	d	AUX
ejpam-4143	66	14	}	}	PUNCT
ejpam-4143	66	15	be	be	AUX
ejpam-4143	66	16	a	a	DET
ejpam-4143	66	17	set	set	NOUN
ejpam-4143	66	18	with	with	ADP
ejpam-4143	66	19	a	a	DET
ejpam-4143	66	20	binary	binary	ADJ
ejpam-4143	66	21	operation	operation	NOUN
ejpam-4143	66	22	⊛	⊛	NUM
ejpam-4143	66	23	defined	define	VERB
ejpam-4143	66	24	by	by	ADP
ejpam-4143	66	25	the	the	DET
ejpam-4143	66	26	following	following	ADJ
ejpam-4143	66	27	cayley	cayley	ADJ
ejpam-4143	66	28	table	table	NOUN
ejpam-4143	66	29	:	:	PUNCT
ejpam-4143	66	30	⊛	⊛	NUM
ejpam-4143	66	31	0	0	NUM
ejpam-4143	67	1	a	a	DET
ejpam-4143	67	2	b	b	NOUN
ejpam-4143	67	3	c	c	NOUN
ejpam-4143	67	4	d	d	SYM
ejpam-4143	67	5	0	0	NUM
ejpam-4143	67	6	{	{	PUNCT
ejpam-4143	67	7	0	0	NUM
ejpam-4143	67	8	}	}	PUNCT
ejpam-4143	67	9	{	{	PUNCT
ejpam-4143	67	10	a	a	NOUN
ejpam-4143	67	11	}	}	PUNCT
ejpam-4143	67	12	{	{	PUNCT
ejpam-4143	67	13	b	b	NOUN
ejpam-4143	67	14	}	}	PUNCT
ejpam-4143	67	15	{	{	PUNCT
ejpam-4143	67	16	c	c	NOUN
ejpam-4143	67	17	}	}	PUNCT
ejpam-4143	67	18	{	{	PUNCT
ejpam-4143	67	19	d	d	NOUN
ejpam-4143	67	20	}	}	PUNCT
ejpam-4143	67	21	a	a	DET
ejpam-4143	67	22	{	{	PUNCT
ejpam-4143	67	23	0	0	NUM
ejpam-4143	67	24	}	}	PUNCT
ejpam-4143	67	25	{	{	PUNCT
ejpam-4143	67	26	0,a	0,a	NOUN
ejpam-4143	67	27	}	}	PUNCT
ejpam-4143	67	28	{	{	PUNCT
ejpam-4143	67	29	0,b	0,b	NOUN
ejpam-4143	67	30	}	}	PUNCT
ejpam-4143	67	31	{	{	PUNCT
ejpam-4143	67	32	c	c	NOUN
ejpam-4143	67	33	}	}	PUNCT
ejpam-4143	67	34	{	{	PUNCT
ejpam-4143	67	35	d	d	NOUN
ejpam-4143	67	36	}	}	PUNCT
ejpam-4143	67	37	b	b	PROPN
ejpam-4143	67	38	{	{	PUNCT
ejpam-4143	67	39	0	0	NUM
ejpam-4143	67	40	}	}	PUNCT
ejpam-4143	67	41	{	{	PUNCT
ejpam-4143	67	42	a	a	NOUN
ejpam-4143	67	43	}	}	PUNCT
ejpam-4143	67	44	{	{	PUNCT
ejpam-4143	67	45	0,b	0,b	NOUN
ejpam-4143	67	46	}	}	PUNCT
ejpam-4143	67	47	{	{	PUNCT
ejpam-4143	67	48	c	c	NOUN
ejpam-4143	67	49	}	}	PUNCT
ejpam-4143	67	50	{	{	PUNCT
ejpam-4143	67	51	d	d	NOUN
ejpam-4143	67	52	}	}	PUNCT
ejpam-4143	67	53	c	c	NOUN
ejpam-4143	67	54	{	{	PUNCT
ejpam-4143	67	55	0	0	NUM
ejpam-4143	67	56	}	}	PUNCT
ejpam-4143	67	57	{	{	PUNCT
ejpam-4143	67	58	0,a	0,a	NOUN
ejpam-4143	67	59	}	}	PUNCT
ejpam-4143	67	60	{	{	PUNCT
ejpam-4143	67	61	0,b	0,b	NOUN
ejpam-4143	67	62	}	}	PUNCT
ejpam-4143	67	63	{	{	PUNCT
ejpam-4143	67	64	0,a	0,a	PROPN
ejpam-4143	67	65	,	,	PUNCT
ejpam-4143	67	66	c	c	NOUN
ejpam-4143	67	67	}	}	PUNCT
ejpam-4143	67	68	{	{	PUNCT
ejpam-4143	67	69	d	d	NOUN
ejpam-4143	67	70	}	}	PUNCT
ejpam-4143	67	71	d	d	NOUN
ejpam-4143	67	72	{	{	PUNCT
ejpam-4143	67	73	0	0	NUM
ejpam-4143	67	74	}	}	PUNCT
ejpam-4143	67	75	{	{	PUNCT
ejpam-4143	67	76	0,a	0,a	NOUN
ejpam-4143	67	77	}	}	PUNCT
ejpam-4143	67	78	{	{	PUNCT
ejpam-4143	67	79	0,b	0,b	NOUN
ejpam-4143	67	80	}	}	PUNCT
ejpam-4143	67	81	{	{	PUNCT
ejpam-4143	67	82	0,a	0,a	PROPN
ejpam-4143	67	83	,	,	PUNCT
ejpam-4143	67	84	c	c	NOUN
ejpam-4143	67	85	}	}	PUNCT
ejpam-4143	67	86	{	{	PUNCT
ejpam-4143	67	87	0,d	0,d	NOUN
ejpam-4143	67	88	}	}	PUNCT
ejpam-4143	67	89	by	by	ADP
ejpam-4143	67	90	routine	routine	ADJ
ejpam-4143	67	91	calculations	calculation	NOUN
ejpam-4143	67	92	,	,	PUNCT
ejpam-4143	67	93	(	(	PUNCT
ejpam-4143	67	94	h;⊛	h;⊛	X
ejpam-4143	67	95	,	,	PUNCT
ejpam-4143	67	96	0	0	NUM
ejpam-4143	67	97	)	)	PUNCT
ejpam-4143	67	98	is	be	AUX
ejpam-4143	67	99	a	a	DET
ejpam-4143	67	100	hyper	hyper	ADJ
ejpam-4143	67	101	up	up	NOUN
ejpam-4143	67	102	-	-	PUNCT
ejpam-4143	67	103	algebra	algebra	NOUN
ejpam-4143	67	104	.	.	PUNCT
ejpam-4143	68	1	definition	definition	NOUN
ejpam-4143	68	2	2	2	NUM
ejpam-4143	68	3	.	.	PUNCT
ejpam-4143	69	1	[	[	X
ejpam-4143	69	2	16	16	NUM
ejpam-4143	69	3	]	]	X
ejpam-4143	69	4	let	let	VERB
ejpam-4143	69	5	(	(	PUNCT
ejpam-4143	69	6	h,⊛	h,⊛	ADV
ejpam-4143	69	7	,	,	PUNCT
ejpam-4143	69	8	0	0	NUM
ejpam-4143	69	9	)	)	PUNCT
ejpam-4143	69	10	be	be	AUX
ejpam-4143	69	11	a	a	DET
ejpam-4143	69	12	hyper	hyper	ADJ
ejpam-4143	69	13	up	up	NOUN
ejpam-4143	69	14	-	-	PUNCT
ejpam-4143	69	15	algebra	algebra	NOUN
ejpam-4143	69	16	and	and	CCONJ
ejpam-4143	69	17	let	let	VERB
ejpam-4143	69	18	i	i	PRON
ejpam-4143	69	19	be	be	AUX
ejpam-4143	69	20	a	a	DET
ejpam-4143	69	21	subset	subset	NOUN
ejpam-4143	69	22	of	of	ADP
ejpam-4143	69	23	h	h	NOUN
ejpam-4143	69	24	containing	contain	VERB
ejpam-4143	69	25	0	0	NUM
ejpam-4143	69	26	.	.	PUNCT
ejpam-4143	70	1	if	if	SCONJ
ejpam-4143	70	2	i	i	PRON
ejpam-4143	70	3	is	be	AUX
ejpam-4143	70	4	a	a	DET
ejpam-4143	70	5	hyper	hyper	ADJ
ejpam-4143	70	6	up	up	NOUN
ejpam-4143	70	7	-	-	PUNCT
ejpam-4143	70	8	algebra	algebra	NOUN
ejpam-4143	70	9	with	with	ADP
ejpam-4143	70	10	respect	respect	NOUN
ejpam-4143	70	11	to	to	ADP
ejpam-4143	70	12	the	the	DET
ejpam-4143	70	13	hyper	hyper	ADJ
ejpam-4143	70	14	operation	operation	NOUN
ejpam-4143	70	15	“	"	PUNCT
ejpam-4143	70	16	⊛	⊛	NUM
ejpam-4143	70	17	”	"	PUNCT
ejpam-4143	70	18	on	on	ADP
ejpam-4143	70	19	h	h	NOUN
ejpam-4143	70	20	,	,	PUNCT
ejpam-4143	70	21	we	we	PRON
ejpam-4143	70	22	say	say	VERB
ejpam-4143	70	23	that	that	SCONJ
ejpam-4143	70	24	i	i	PRON
ejpam-4143	70	25	is	be	AUX
ejpam-4143	70	26	a	a	DET
ejpam-4143	70	27	hyper	hyper	ADJ
ejpam-4143	70	28	up	up	ADP
ejpam-4143	70	29	-	-	PUNCT
ejpam-4143	70	30	subalgebra	subalgebra	NOUN
ejpam-4143	70	31	of	of	ADP
ejpam-4143	70	32	h.	h.	PROPN
ejpam-4143	70	33	example	example	PROPN
ejpam-4143	71	1	2	2	X
ejpam-4143	71	2	.	.	X
ejpam-4143	71	3	in	in	ADP
ejpam-4143	71	4	exampe	exampe	NOUN
ejpam-4143	71	5	1	1	NUM
ejpam-4143	71	6	,	,	PUNCT
ejpam-4143	71	7	it	it	PRON
ejpam-4143	71	8	can	can	AUX
ejpam-4143	71	9	be	be	AUX
ejpam-4143	71	10	verified	verify	VERB
ejpam-4143	71	11	that	that	SCONJ
ejpam-4143	71	12	the	the	DET
ejpam-4143	71	13	set	set	NOUN
ejpam-4143	71	14	{	{	PUNCT
ejpam-4143	71	15	0	0	NUM
ejpam-4143	71	16	,	,	PUNCT
ejpam-4143	71	17	a	a	DET
ejpam-4143	71	18	,	,	PUNCT
ejpam-4143	71	19	b	b	NOUN
ejpam-4143	71	20	,	,	PUNCT
ejpam-4143	71	21	c	c	NOUN
ejpam-4143	71	22	}	}	PUNCT
ejpam-4143	71	23	is	be	AUX
ejpam-4143	71	24	a	a	DET
ejpam-4143	71	25	hyper	hyper	ADJ
ejpam-4143	71	26	up	up	NOUN
ejpam-4143	71	27	-	-	PUNCT
ejpam-4143	71	28	algebra	algebra	NOUN
ejpam-4143	71	29	.	.	PUNCT
ejpam-4143	72	1	thus	thus	ADV
ejpam-4143	72	2	,	,	PUNCT
ejpam-4143	72	3	{	{	PUNCT
ejpam-4143	72	4	0	0	NUM
ejpam-4143	72	5	,	,	PUNCT
ejpam-4143	72	6	a	a	DET
ejpam-4143	72	7	,	,	PUNCT
ejpam-4143	72	8	b	b	NOUN
ejpam-4143	72	9	,	,	PUNCT
ejpam-4143	72	10	c	c	NOUN
ejpam-4143	72	11	}	}	PUNCT
ejpam-4143	72	12	is	be	AUX
ejpam-4143	72	13	a	a	DET
ejpam-4143	72	14	hyper	hyper	ADJ
ejpam-4143	72	15	up	up	ADP
ejpam-4143	72	16	-	-	PUNCT
ejpam-4143	72	17	subalgebra	subalgebra	NOUN
ejpam-4143	72	18	of	of	ADP
ejpam-4143	72	19	h.	h.	PROPN
ejpam-4143	72	20	example	example	PROPN
ejpam-4143	72	21	3	3	X
ejpam-4143	72	22	.	.	PUNCT
ejpam-4143	72	23	let	let	VERB
ejpam-4143	72	24	k	k	NOUN
ejpam-4143	72	25	=	=	PUNCT
ejpam-4143	72	26	{	{	PUNCT
ejpam-4143	72	27	0	0	NUM
ejpam-4143	72	28	,	,	PUNCT
ejpam-4143	72	29	1	1	NUM
ejpam-4143	72	30	,	,	PUNCT
ejpam-4143	72	31	2	2	NUM
ejpam-4143	72	32	}	}	PUNCT
ejpam-4143	72	33	be	be	AUX
ejpam-4143	72	34	a	a	DET
ejpam-4143	72	35	set	set	NOUN
ejpam-4143	72	36	with	with	ADP
ejpam-4143	72	37	a	a	DET
ejpam-4143	72	38	binary	binary	ADJ
ejpam-4143	72	39	operation	operation	NOUN
ejpam-4143	72	40	⊛	⊛	NUM
ejpam-4143	72	41	defined	define	VERB
ejpam-4143	72	42	by	by	ADP
ejpam-4143	72	43	the	the	DET
ejpam-4143	72	44	following	following	ADJ
ejpam-4143	72	45	cayley	cayley	ADJ
ejpam-4143	72	46	table	table	NOUN
ejpam-4143	72	47	:	:	PUNCT
ejpam-4143	72	48	⊛	⊛	NUM
ejpam-4143	72	49	0	0	NUM
ejpam-4143	72	50	1	1	NUM
ejpam-4143	72	51	2	2	NUM
ejpam-4143	72	52	0	0	NUM
ejpam-4143	72	53	{	{	PUNCT
ejpam-4143	72	54	0	0	NUM
ejpam-4143	72	55	}	}	PUNCT
ejpam-4143	72	56	{	{	PUNCT
ejpam-4143	72	57	1	1	NUM
ejpam-4143	72	58	}	}	PUNCT
ejpam-4143	72	59	{	{	PUNCT
ejpam-4143	72	60	2	2	NUM
ejpam-4143	72	61	}	}	SYM
ejpam-4143	72	62	1	1	NUM
ejpam-4143	72	63	{	{	PUNCT
ejpam-4143	72	64	0	0	NUM
ejpam-4143	72	65	}	}	PUNCT
ejpam-4143	72	66	{	{	PUNCT
ejpam-4143	72	67	0,2	0,2	NUM
ejpam-4143	72	68	}	}	PUNCT
ejpam-4143	72	69	{	{	PUNCT
ejpam-4143	72	70	0,2	0,2	NUM
ejpam-4143	72	71	}	}	SYM
ejpam-4143	72	72	2	2	NUM
ejpam-4143	72	73	{	{	PUNCT
ejpam-4143	72	74	0	0	NUM
ejpam-4143	72	75	}	}	PUNCT
ejpam-4143	72	76	{	{	PUNCT
ejpam-4143	72	77	1	1	NUM
ejpam-4143	72	78	}	}	PUNCT
ejpam-4143	72	79	{	{	PUNCT
ejpam-4143	72	80	0,2	0,2	NUM
ejpam-4143	72	81	}	}	PUNCT
ejpam-4143	72	82	by	by	ADP
ejpam-4143	72	83	routine	routine	ADJ
ejpam-4143	72	84	calculations	calculation	NOUN
ejpam-4143	72	85	,	,	PUNCT
ejpam-4143	72	86	(	(	PUNCT
ejpam-4143	72	87	k;⊛	k;⊛	NOUN
ejpam-4143	72	88	,	,	PUNCT
ejpam-4143	72	89	0	0	NUM
ejpam-4143	72	90	)	)	PUNCT
ejpam-4143	72	91	is	be	AUX
ejpam-4143	72	92	a	a	DET
ejpam-4143	72	93	hyper	hyper	ADJ
ejpam-4143	72	94	up	up	NOUN
ejpam-4143	72	95	-	-	PUNCT
ejpam-4143	72	96	algebra	algebra	NOUN
ejpam-4143	72	97	.	.	PUNCT
ejpam-4143	73	1	note	note	VERB
ejpam-4143	73	2	that	that	SCONJ
ejpam-4143	73	3	if	if	SCONJ
ejpam-4143	73	4	i	i	PRON
ejpam-4143	73	5	=	=	SYM
ejpam-4143	73	6	{	{	PUNCT
ejpam-4143	73	7	0	0	NUM
ejpam-4143	73	8	,	,	PUNCT
ejpam-4143	73	9	1	1	NUM
ejpam-4143	73	10	}	}	PUNCT
ejpam-4143	73	11	,	,	PUNCT
ejpam-4143	73	12	i	i	PRON
ejpam-4143	73	13	is	be	AUX
ejpam-4143	73	14	not	not	PART
ejpam-4143	73	15	a	a	DET
ejpam-4143	73	16	hyper	hyper	ADJ
ejpam-4143	73	17	up	up	ADP
ejpam-4143	73	18	-	-	PUNCT
ejpam-4143	73	19	subalgebra	subalgebra	NOUN
ejpam-4143	73	20	since	since	SCONJ
ejpam-4143	73	21	1⊛	1⊛	NUM
ejpam-4143	73	22	1	1	NUM
ejpam-4143	73	23	=	=	SYM
ejpam-4143	73	24	{	{	PUNCT
ejpam-4143	73	25	0	0	NUM
ejpam-4143	73	26	,	,	PUNCT
ejpam-4143	73	27	2	2	NUM
ejpam-4143	73	28	}	}	PUNCT
ejpam-4143	73	29	⊈	⊈	PROPN
ejpam-4143	73	30	i.	i.	NOUN
ejpam-4143	73	31	proposition	proposition	NOUN
ejpam-4143	73	32	1	1	NUM
ejpam-4143	73	33	.	.	PUNCT
ejpam-4143	74	1	[	[	X
ejpam-4143	74	2	16	16	NUM
ejpam-4143	74	3	]	]	X
ejpam-4143	74	4	let	let	VERB
ejpam-4143	74	5	(	(	PUNCT
ejpam-4143	74	6	h;⊛	h;⊛	NUM
ejpam-4143	74	7	,	,	PUNCT
ejpam-4143	74	8	0	0	NUM
ejpam-4143	74	9	)	)	PUNCT
ejpam-4143	74	10	be	be	AUX
ejpam-4143	74	11	a	a	DET
ejpam-4143	74	12	hyper	hyper	ADJ
ejpam-4143	74	13	up	up	NOUN
ejpam-4143	74	14	-	-	PUNCT
ejpam-4143	74	15	algebra	algebra	NOUN
ejpam-4143	74	16	.	.	PUNCT
ejpam-4143	75	1	then	then	ADV
ejpam-4143	75	2	the	the	DET
ejpam-4143	75	3	following	follow	VERB
ejpam-4143	75	4	hold	hold	NOUN
ejpam-4143	75	5	for	for	ADP
ejpam-4143	75	6	all	all	DET
ejpam-4143	75	7	x	x	NOUN
ejpam-4143	75	8	,	,	PUNCT
ejpam-4143	75	9	y	y	PROPN
ejpam-4143	75	10	∈	∈	PROPN
ejpam-4143	75	11	h	h	NOUN
ejpam-4143	75	12	and	and	CCONJ
ejpam-4143	75	13	for	for	ADP
ejpam-4143	75	14	every	every	DET
ejpam-4143	75	15	nonempty	nonempty	NOUN
ejpam-4143	75	16	subsets	subset	NOUN
ejpam-4143	75	17	a	a	PRON
ejpam-4143	75	18	,	,	PUNCT
ejpam-4143	75	19	b	b	PROPN
ejpam-4143	75	20	⊆	⊆	NUM
ejpam-4143	75	21	h	h	NOUN
ejpam-4143	75	22	:	:	PUNCT
ejpam-4143	75	23	(	(	PUNCT
ejpam-4143	75	24	i	i	NOUN
ejpam-4143	75	25	)	)	PUNCT
ejpam-4143	75	26	0⊛	0⊛	NUM
ejpam-4143	75	27	0	0	NUM
ejpam-4143	76	1	=	=	SYM
ejpam-4143	76	2	{	{	PUNCT
ejpam-4143	76	3	0	0	NUM
ejpam-4143	76	4	}	}	PUNCT
ejpam-4143	76	5	(	(	PUNCT
ejpam-4143	76	6	ii	ii	NOUN
ejpam-4143	76	7	)	)	PUNCT
ejpam-4143	76	8	x	x	PUNCT
ejpam-4143	76	9	≪	≪	ADJ
ejpam-4143	76	10	0	0	NUM
ejpam-4143	76	11	(	(	PUNCT
ejpam-4143	76	12	iii	iii	NOUN
ejpam-4143	76	13	)	)	PUNCT
ejpam-4143	76	14	x	x	PUNCT
ejpam-4143	76	15	≪	≪	ADJ
ejpam-4143	76	16	x	x	SYM
ejpam-4143	76	17	(	(	PUNCT
ejpam-4143	76	18	iv	iv	X
ejpam-4143	76	19	)	)	PUNCT
ejpam-4143	76	20	y	y	PROPN
ejpam-4143	76	21	≪	≪	VERB
ejpam-4143	76	22	x⊛	x⊛	PROPN
ejpam-4143	76	23	y	y	PROPN
ejpam-4143	76	24	(	(	PUNCT
ejpam-4143	76	25	v	v	NOUN
ejpam-4143	76	26	)	)	PUNCT
ejpam-4143	76	27	a	a	DET
ejpam-4143	76	28	⊆	⊆	NUM
ejpam-4143	76	29	b	b	NOUN
ejpam-4143	76	30	implies	imply	VERB
ejpam-4143	76	31	a	a	DET
ejpam-4143	76	32	≪	≪	ADJ
ejpam-4143	76	33	b	b	X
ejpam-4143	76	34	(	(	PUNCT
ejpam-4143	76	35	vi	vi	NOUN
ejpam-4143	76	36	)	)	PUNCT
ejpam-4143	76	37	0⊛a	0⊛a	NOUN
ejpam-4143	76	38	=	=	PUNCT
ejpam-4143	76	39	a	a	DET
ejpam-4143	76	40	(	(	PUNCT
ejpam-4143	76	41	vii	vii	PROPN
ejpam-4143	76	42	)	)	PUNCT
ejpam-4143	76	43	a⊛	a⊛	NOUN
ejpam-4143	76	44	0	0	NUM
ejpam-4143	76	45	=	=	SYM
ejpam-4143	76	46	{	{	PUNCT
ejpam-4143	76	47	0	0	NUM
ejpam-4143	76	48	}	}	PUNCT
ejpam-4143	76	49	r.	r.	NOUN
ejpam-4143	76	50	amairanto	amairanto	PROPN
ejpam-4143	76	51	,	,	PUNCT
ejpam-4143	76	52	r.	r.	PROPN
ejpam-4143	76	53	isla	isla	PROPN
ejpam-4143	76	54	/	/	SYM
ejpam-4143	76	55	eur	eur	PROPN
ejpam-4143	76	56	.	.	PUNCT
ejpam-4143	77	1	j.	j.	PROPN
ejpam-4143	77	2	pure	pure	PROPN
ejpam-4143	77	3	appl	appl	PROPN
ejpam-4143	77	4	.	.	PROPN
ejpam-4143	77	5	math	math	PROPN
ejpam-4143	77	6	,	,	PUNCT
ejpam-4143	77	7	14	14	NUM
ejpam-4143	77	8	(	(	PUNCT
ejpam-4143	77	9	4	4	NUM
ejpam-4143	77	10	)	)	PUNCT
ejpam-4143	77	11	(	(	PUNCT
ejpam-4143	77	12	2021	2021	NUM
ejpam-4143	77	13	)	)	PUNCT
ejpam-4143	77	14	,	,	PUNCT
ejpam-4143	77	15	1388	1388	NUM
ejpam-4143	77	16	-	-	SYM
ejpam-4143	77	17	1401	1401	NUM
ejpam-4143	77	18	1391	1391	NUM
ejpam-4143	77	19	proposition	proposition	NOUN
ejpam-4143	77	20	2	2	NUM
ejpam-4143	77	21	.	.	PUNCT
ejpam-4143	78	1	[	[	X
ejpam-4143	78	2	16	16	NUM
ejpam-4143	78	3	]	]	PUNCT
ejpam-4143	78	4	let	let	VERB
ejpam-4143	78	5	i	i	PRON
ejpam-4143	78	6	be	be	AUX
ejpam-4143	78	7	a	a	DET
ejpam-4143	78	8	non	non	ADJ
ejpam-4143	78	9	-	-	ADJ
ejpam-4143	78	10	empty	empty	ADJ
ejpam-4143	78	11	subset	subset	NOUN
ejpam-4143	78	12	of	of	ADP
ejpam-4143	78	13	a	a	DET
ejpam-4143	78	14	hyper	hyper	ADJ
ejpam-4143	78	15	up	up	ADP
ejpam-4143	78	16	-	-	PUNCT
ejpam-4143	78	17	algebra	algebra	NOUN
ejpam-4143	78	18	(	(	PUNCT
ejpam-4143	78	19	h,⊛	h,⊛	PROPN
ejpam-4143	78	20	,	,	PUNCT
ejpam-4143	78	21	0	0	NUM
ejpam-4143	78	22	)	)	PUNCT
ejpam-4143	78	23	.	.	PUNCT
ejpam-4143	79	1	then	then	ADV
ejpam-4143	79	2	i	i	PRON
ejpam-4143	79	3	is	be	AUX
ejpam-4143	79	4	a	a	DET
ejpam-4143	79	5	hyper	hyper	ADJ
ejpam-4143	79	6	up	up	ADP
ejpam-4143	79	7	-	-	PUNCT
ejpam-4143	79	8	subalgebra	subalgebra	NOUN
ejpam-4143	79	9	of	of	ADP
ejpam-4143	79	10	h	h	NOUN
ejpam-4143	79	11	if	if	SCONJ
ejpam-4143	80	1	and	and	CCONJ
ejpam-4143	80	2	only	only	ADV
ejpam-4143	80	3	if	if	SCONJ
ejpam-4143	80	4	for	for	ADP
ejpam-4143	80	5	all	all	DET
ejpam-4143	80	6	x	x	NOUN
ejpam-4143	80	7	,	,	PUNCT
ejpam-4143	80	8	y	y	PROPN
ejpam-4143	80	9	∈	∈	PROPN
ejpam-4143	81	1	i	i	PRON
ejpam-4143	81	2	,	,	PUNCT
ejpam-4143	81	3	x⊛	x⊛	PROPN
ejpam-4143	81	4	y	y	PROPN
ejpam-4143	81	5	⊆	⊆	NUM
ejpam-4143	81	6	i	i	PRON
ejpam-4143	81	7	holds	hold	VERB
ejpam-4143	81	8	.	.	PUNCT
ejpam-4143	82	1	definition	definition	NOUN
ejpam-4143	82	2	3	3	NUM
ejpam-4143	82	3	.	.	PUNCT
ejpam-4143	83	1	[	[	X
ejpam-4143	83	2	16	16	NUM
ejpam-4143	83	3	]	]	X
ejpam-4143	83	4	let	let	VERB
ejpam-4143	83	5	(	(	PUNCT
ejpam-4143	83	6	h;⊛	h;⊛	NUM
ejpam-4143	83	7	,	,	PUNCT
ejpam-4143	83	8	0	0	NUM
ejpam-4143	83	9	)	)	PUNCT
ejpam-4143	83	10	and	and	CCONJ
ejpam-4143	83	11	(	(	PUNCT
ejpam-4143	83	12	h	h	NOUN
ejpam-4143	83	13	′;⊛′	′;⊛′	PROPN
ejpam-4143	83	14	,	,	PUNCT
ejpam-4143	83	15	0′	0′	NUM
ejpam-4143	83	16	)	)	PUNCT
ejpam-4143	83	17	be	be	AUX
ejpam-4143	83	18	hyper	hyper	ADJ
ejpam-4143	83	19	up	up	ADP
ejpam-4143	83	20	-	-	PUNCT
ejpam-4143	83	21	algebras	algebras	X
ejpam-4143	83	22	.	.	PUNCT
ejpam-4143	84	1	a	a	DET
ejpam-4143	84	2	mapping	mapping	NOUN
ejpam-4143	84	3	f	f	NOUN
ejpam-4143	84	4	:	:	PUNCT
ejpam-4143	84	5	h	h	NOUN
ejpam-4143	84	6	→	→	SYM
ejpam-4143	84	7	h	h	NOUN
ejpam-4143	84	8	′	′	NOUN
ejpam-4143	84	9	is	be	AUX
ejpam-4143	84	10	called	call	VERB
ejpam-4143	84	11	a	a	DET
ejpam-4143	84	12	hyper	hyper	ADJ
ejpam-4143	84	13	homomorphism	homomorphism	NOUN
ejpam-4143	84	14	if	if	SCONJ
ejpam-4143	84	15	(	(	PUNCT
ejpam-4143	84	16	hh1	hh1	NOUN
ejpam-4143	84	17	)	)	PUNCT
ejpam-4143	84	18	f(0	f(0	NOUN
ejpam-4143	84	19	)	)	PUNCT
ejpam-4143	84	20	=	=	SYM
ejpam-4143	84	21	0′	0′	NUM
ejpam-4143	84	22	,	,	PUNCT
ejpam-4143	84	23	and	and	CCONJ
ejpam-4143	84	24	(	(	PUNCT
ejpam-4143	84	25	hh2	hh2	NOUN
ejpam-4143	84	26	)	)	PUNCT
ejpam-4143	84	27	f(x⊛	f(x⊛	NOUN
ejpam-4143	84	28	y	y	NOUN
ejpam-4143	84	29	)	)	PUNCT
ejpam-4143	84	30	=	=	PROPN
ejpam-4143	84	31	f(x)⊛′	f(x)⊛′	ADP
ejpam-4143	84	32	f(y	f(y	NOUN
ejpam-4143	84	33	)	)	PUNCT
ejpam-4143	84	34	for	for	ADP
ejpam-4143	84	35	all	all	DET
ejpam-4143	84	36	x	x	NOUN
ejpam-4143	84	37	,	,	PUNCT
ejpam-4143	84	38	y	y	PROPN
ejpam-4143	84	39	∈	∈	PROPN
ejpam-4143	84	40	h.	h.	PROPN
ejpam-4143	84	41	definition	definition	NOUN
ejpam-4143	84	42	4	4	NUM
ejpam-4143	84	43	.	.	PUNCT
ejpam-4143	85	1	[	[	X
ejpam-4143	85	2	21	21	NUM
ejpam-4143	85	3	]	]	X
ejpam-4143	85	4	a	a	DET
ejpam-4143	85	5	fuzzy	fuzzy	ADJ
ejpam-4143	85	6	set	set	NOUN
ejpam-4143	85	7	in	in	ADP
ejpam-4143	85	8	a	a	DET
ejpam-4143	85	9	nonempty	nonempty	ADV
ejpam-4143	85	10	set	set	VERB
ejpam-4143	85	11	h	h	NOUN
ejpam-4143	85	12	(	(	PUNCT
ejpam-4143	85	13	or	or	CCONJ
ejpam-4143	85	14	a	a	DET
ejpam-4143	85	15	fuzzy	fuzzy	ADJ
ejpam-4143	85	16	subset	subset	NOUN
ejpam-4143	85	17	of	of	ADP
ejpam-4143	85	18	h	h	NOUN
ejpam-4143	85	19	)	)	PUNCT
ejpam-4143	85	20	is	be	AUX
ejpam-4143	85	21	an	an	DET
ejpam-4143	85	22	arbitrary	arbitrary	ADJ
ejpam-4143	85	23	function	function	NOUN
ejpam-4143	85	24	µ	µ	NOUN
ejpam-4143	85	25	:	:	PUNCT
ejpam-4143	86	1	h	h	NOUN
ejpam-4143	86	2	−→	−→	NOUN
ejpam-4143	87	1	[	[	X
ejpam-4143	87	2	0	0	NUM
ejpam-4143	87	3	,	,	PUNCT
ejpam-4143	87	4	1	1	NUM
ejpam-4143	87	5	]	]	PUNCT
ejpam-4143	87	6	,	,	PUNCT
ejpam-4143	87	7	where	where	SCONJ
ejpam-4143	87	8	[	[	X
ejpam-4143	87	9	0	0	NUM
ejpam-4143	87	10	,	,	PUNCT
ejpam-4143	87	11	1	1	NUM
ejpam-4143	87	12	]	]	PUNCT
ejpam-4143	87	13	is	be	AUX
ejpam-4143	87	14	the	the	DET
ejpam-4143	87	15	unit	unit	NOUN
ejpam-4143	87	16	segment	segment	NOUN
ejpam-4143	87	17	of	of	ADP
ejpam-4143	87	18	the	the	DET
ejpam-4143	87	19	real	real	ADJ
ejpam-4143	87	20	line	line	NOUN
ejpam-4143	87	21	.	.	PUNCT
ejpam-4143	88	1	if	if	SCONJ
ejpam-4143	88	2	i	i	PRON
ejpam-4143	88	3	⊆	⊆	NUM
ejpam-4143	88	4	h	h	NOUN
ejpam-4143	88	5	,	,	PUNCT
ejpam-4143	88	6	the	the	DET
ejpam-4143	88	7	characteristic	characteristic	ADJ
ejpam-4143	88	8	function	function	NOUN
ejpam-4143	88	9	µi	µi	INTJ
ejpam-4143	88	10	of	of	ADP
ejpam-4143	88	11	h	h	NOUN
ejpam-4143	88	12	is	be	AUX
ejpam-4143	88	13	a	a	DET
ejpam-4143	88	14	function	function	NOUN
ejpam-4143	88	15	of	of	ADP
ejpam-4143	88	16	h	h	NOUN
ejpam-4143	88	17	into	into	ADP
ejpam-4143	88	18	{	{	PUNCT
ejpam-4143	88	19	0	0	NUM
ejpam-4143	88	20	,	,	PUNCT
ejpam-4143	88	21	1	1	NUM
ejpam-4143	88	22	}	}	PUNCT
ejpam-4143	88	23	defined	define	VERB
ejpam-4143	88	24	as	as	ADP
ejpam-4143	88	25	follows	follow	VERB
ejpam-4143	88	26	:	:	PUNCT
ejpam-4143	88	27	µi(x	µi(x	NUM
ejpam-4143	88	28	)	)	PUNCT
ejpam-4143	89	1	=	=	PRON
ejpam-4143	89	2	{	{	PUNCT
ejpam-4143	89	3	1	1	NUM
ejpam-4143	89	4	,	,	PUNCT
ejpam-4143	89	5	if	if	SCONJ
ejpam-4143	89	6	x	x	SYM
ejpam-4143	89	7	∈	∈	NOUN
ejpam-4143	89	8	i	i	PRON
ejpam-4143	89	9	0	0	NUM
ejpam-4143	89	10	,	,	PUNCT
ejpam-4143	89	11	if	if	SCONJ
ejpam-4143	89	12	x	x	X
ejpam-4143	89	13	/∈	/∈	PUNCT
ejpam-4143	89	14	i.	i.	NOUN
ejpam-4143	89	15	by	by	ADP
ejpam-4143	89	16	the	the	DET
ejpam-4143	89	17	definition	definition	NOUN
ejpam-4143	89	18	of	of	ADP
ejpam-4143	89	19	characteristic	characteristic	ADJ
ejpam-4143	89	20	function	function	NOUN
ejpam-4143	89	21	,	,	PUNCT
ejpam-4143	89	22	µi	µi	PROPN
ejpam-4143	89	23	is	be	AUX
ejpam-4143	89	24	a	a	DET
ejpam-4143	89	25	function	function	NOUN
ejpam-4143	89	26	of	of	ADP
ejpam-4143	89	27	h	h	NOUN
ejpam-4143	89	28	into	into	ADP
ejpam-4143	89	29	{	{	PUNCT
ejpam-4143	89	30	0	0	NUM
ejpam-4143	89	31	,	,	PUNCT
ejpam-4143	89	32	1	1	NUM
ejpam-4143	89	33	}	}	PUNCT
ejpam-4143	89	34	⊂	⊂	PROPN
ejpam-4143	90	1	[	[	X
ejpam-4143	90	2	0	0	NUM
ejpam-4143	90	3	,	,	PUNCT
ejpam-4143	90	4	1	1	NUM
ejpam-4143	90	5	]	]	PUNCT
ejpam-4143	90	6	.	.	PUNCT
ejpam-4143	91	1	then	then	ADV
ejpam-4143	91	2	,	,	PUNCT
ejpam-4143	91	3	µi	µi	PROPN
ejpam-4143	91	4	is	be	AUX
ejpam-4143	91	5	a	a	DET
ejpam-4143	91	6	fuzzy	fuzzy	ADJ
ejpam-4143	91	7	set	set	NOUN
ejpam-4143	91	8	in	in	ADP
ejpam-4143	91	9	h.	h.	PROPN
ejpam-4143	91	10	definition	definition	NOUN
ejpam-4143	91	11	5	5	NUM
ejpam-4143	91	12	.	.	PUNCT
ejpam-4143	92	1	[	[	X
ejpam-4143	92	2	10	10	NUM
ejpam-4143	92	3	]	]	PUNCT
ejpam-4143	92	4	let	let	VERB
ejpam-4143	92	5	x	x	PRON
ejpam-4143	92	6	and	and	CCONJ
ejpam-4143	92	7	y	y	PROPN
ejpam-4143	92	8	be	be	AUX
ejpam-4143	92	9	two	two	NUM
ejpam-4143	92	10	nonempty	nonempty	ADJ
ejpam-4143	92	11	sets	set	NOUN
ejpam-4143	92	12	,	,	PUNCT
ejpam-4143	92	13	µ	µ	DET
ejpam-4143	92	14	a	a	DET
ejpam-4143	92	15	fuzzy	fuzzy	ADJ
ejpam-4143	92	16	set	set	NOUN
ejpam-4143	92	17	of	of	ADP
ejpam-4143	92	18	y	y	PROPN
ejpam-4143	92	19	and	and	CCONJ
ejpam-4143	92	20	f	f	PROPN
ejpam-4143	92	21	:	:	PUNCT
ejpam-4143	92	22	x	x	PUNCT
ejpam-4143	92	23	−→	−→	NOUN
ejpam-4143	92	24	y	y	PROPN
ejpam-4143	92	25	a	a	DET
ejpam-4143	92	26	mapping	mapping	NOUN
ejpam-4143	92	27	.	.	PUNCT
ejpam-4143	93	1	the	the	DET
ejpam-4143	93	2	preimage	preimage	NOUN
ejpam-4143	93	3	of	of	ADP
ejpam-4143	93	4	µ	µ	NUM
ejpam-4143	93	5	under	under	ADP
ejpam-4143	93	6	f	f	PROPN
ejpam-4143	93	7	,	,	PUNCT
ejpam-4143	93	8	denoted	denote	VERB
ejpam-4143	93	9	by	by	ADP
ejpam-4143	93	10	µf	µf	X
ejpam-4143	93	11	,	,	PUNCT
ejpam-4143	93	12	is	be	AUX
ejpam-4143	93	13	the	the	DET
ejpam-4143	93	14	fuzzy	fuzzy	ADJ
ejpam-4143	93	15	set	set	NOUN
ejpam-4143	93	16	of	of	ADP
ejpam-4143	93	17	x	x	PUNCT
ejpam-4143	93	18	defined	define	VERB
ejpam-4143	93	19	by	by	ADP
ejpam-4143	93	20	µf	µf	X
ejpam-4143	93	21	(	(	PUNCT
ejpam-4143	93	22	x	x	NOUN
ejpam-4143	93	23	)	)	PUNCT
ejpam-4143	93	24	=	=	SYM
ejpam-4143	93	25	µ(f(x	µ(f(x	PROPN
ejpam-4143	93	26	)	)	PUNCT
ejpam-4143	93	27	)	)	PUNCT
ejpam-4143	93	28	for	for	ADP
ejpam-4143	93	29	all	all	DET
ejpam-4143	93	30	x	x	SYM
ejpam-4143	93	31	∈	∈	PROPN
ejpam-4143	93	32	x	x	NOUN
ejpam-4143	93	33	,	,	PUNCT
ejpam-4143	93	34	that	that	ADV
ejpam-4143	93	35	is	is	ADV
ejpam-4143	93	36	,	,	PUNCT
ejpam-4143	93	37	µf	µf	ADP
ejpam-4143	93	38	=	=	SYM
ejpam-4143	93	39	µ	µ	DET
ejpam-4143	93	40	◦	◦	NOUN
ejpam-4143	93	41	f.	f.	PROPN
ejpam-4143	93	42	definition	definition	NOUN
ejpam-4143	93	43	6	6	NUM
ejpam-4143	93	44	.	.	PUNCT
ejpam-4143	94	1	[	[	X
ejpam-4143	94	2	10	10	NUM
ejpam-4143	94	3	]	]	PUNCT
ejpam-4143	94	4	let	let	VERB
ejpam-4143	94	5	µ	µ	X
ejpam-4143	94	6	be	be	AUX
ejpam-4143	94	7	a	a	DET
ejpam-4143	94	8	fuzzy	fuzzy	ADJ
ejpam-4143	94	9	set	set	NOUN
ejpam-4143	94	10	of	of	ADP
ejpam-4143	94	11	x	x	PROPN
ejpam-4143	94	12	and	and	CCONJ
ejpam-4143	94	13	f	f	X
ejpam-4143	94	14	:	:	PUNCT
ejpam-4143	94	15	x	x	PUNCT
ejpam-4143	94	16	−→	−→	NOUN
ejpam-4143	94	17	y	y	PROPN
ejpam-4143	94	18	a	a	DET
ejpam-4143	94	19	mapping	mapping	NOUN
ejpam-4143	94	20	.	.	PUNCT
ejpam-4143	95	1	the	the	DET
ejpam-4143	95	2	mapping	mapping	NOUN
ejpam-4143	95	3	f(µ	f(µ	PROPN
ejpam-4143	95	4	)	)	PUNCT
ejpam-4143	95	5	:	:	PUNCT
ejpam-4143	96	1	y	y	PROPN
ejpam-4143	96	2	−→	−→	NOUN
ejpam-4143	96	3	[	[	X
ejpam-4143	96	4	0	0	NUM
ejpam-4143	96	5	,	,	PUNCT
ejpam-4143	96	6	1	1	NUM
ejpam-4143	96	7	]	]	PUNCT
ejpam-4143	96	8	defined	define	VERB
ejpam-4143	96	9	by	by	ADP
ejpam-4143	96	10	f(µ)(y	f(µ)(y	NUM
ejpam-4143	96	11	)	)	PUNCT
ejpam-4143	96	12	=	=	PRON
ejpam-4143	96	13	{	{	PUNCT
ejpam-4143	96	14	supx∈f−1(y){µ(x	supx∈f−1(y){µ(x	NOUN
ejpam-4143	96	15	)	)	PUNCT
ejpam-4143	96	16	}	}	PUNCT
ejpam-4143	96	17	,	,	PUNCT
ejpam-4143	96	18	if	if	SCONJ
ejpam-4143	96	19	f−1(y	f−1(y	PROPN
ejpam-4143	96	20	)	)	PUNCT
ejpam-4143	96	21	̸=	̸=	PROPN
ejpam-4143	96	22	∅	∅	NOUN
ejpam-4143	96	23	,	,	PUNCT
ejpam-4143	96	24	0	0	NUM
ejpam-4143	96	25	,	,	PUNCT
ejpam-4143	96	26	if	if	SCONJ
ejpam-4143	96	27	f−1(y	f−1(y	PROPN
ejpam-4143	96	28	)	)	PUNCT
ejpam-4143	96	29	=	=	NOUN
ejpam-4143	96	30	∅	∅	NOUN
ejpam-4143	96	31	,	,	PUNCT
ejpam-4143	96	32	is	be	AUX
ejpam-4143	96	33	called	call	VERB
ejpam-4143	96	34	the	the	DET
ejpam-4143	96	35	image	image	NOUN
ejpam-4143	96	36	of	of	ADP
ejpam-4143	96	37	µ	µ	NOUN
ejpam-4143	96	38	under	under	ADP
ejpam-4143	96	39	f	f	PROPN
ejpam-4143	96	40	,	,	PUNCT
ejpam-4143	96	41	where	where	SCONJ
ejpam-4143	96	42	f−1(y	f−1(y	PROPN
ejpam-4143	96	43	)	)	PUNCT
ejpam-4143	97	1	=	=	PRON
ejpam-4143	97	2	{	{	PUNCT
ejpam-4143	97	3	x	x	PUNCT
ejpam-4143	97	4	∈	∈	NOUN
ejpam-4143	97	5	x	x	X
ejpam-4143	97	6	:	:	PUNCT
ejpam-4143	97	7	f(x	f(x	PROPN
ejpam-4143	97	8	)	)	PUNCT
ejpam-4143	97	9	=	=	SYM
ejpam-4143	98	1	y	y	PROPN
ejpam-4143	98	2	}	}	PUNCT
ejpam-4143	98	3	.	.	PUNCT
ejpam-4143	99	1	definition	definition	NOUN
ejpam-4143	99	2	7	7	NUM
ejpam-4143	99	3	.	.	PUNCT
ejpam-4143	100	1	[	[	X
ejpam-4143	100	2	10	10	NUM
ejpam-4143	100	3	]	]	X
ejpam-4143	100	4	let	let	VERB
ejpam-4143	100	5	{	{	PUNCT
ejpam-4143	100	6	µα	µα	ADP
ejpam-4143	100	7	:	:	PUNCT
ejpam-4143	100	8	α	α	PROPN
ejpam-4143	100	9	∈	∈	PROPN
ejpam-4143	100	10	a	a	DET
ejpam-4143	100	11	}	}	PUNCT
ejpam-4143	100	12	be	be	AUX
ejpam-4143	100	13	a	a	DET
ejpam-4143	100	14	nonempty	nonempty	ADJ
ejpam-4143	100	15	family	family	NOUN
ejpam-4143	100	16	of	of	ADP
ejpam-4143	100	17	fuzzy	fuzzy	ADJ
ejpam-4143	100	18	sets	set	NOUN
ejpam-4143	100	19	of	of	ADP
ejpam-4143	100	20	x	x	NOUN
ejpam-4143	100	21	,	,	PUNCT
ejpam-4143	100	22	where	where	SCONJ
ejpam-4143	100	23	a	a	PRON
ejpam-4143	100	24	is	be	AUX
ejpam-4143	100	25	an	an	DET
ejpam-4143	100	26	arbitrary	arbitrary	ADJ
ejpam-4143	100	27	index	index	NOUN
ejpam-4143	100	28	set	set	NOUN
ejpam-4143	100	29	.	.	PUNCT
ejpam-4143	101	1	the	the	DET
ejpam-4143	101	2	intersection	intersection	NOUN
ejpam-4143	101	3	of	of	ADP
ejpam-4143	101	4	µα	µα	ADP
ejpam-4143	101	5	,	,	PUNCT
ejpam-4143	101	6	denoted	denote	VERB
ejpam-4143	101	7	by	by	ADP
ejpam-4143	101	8	∧α∈aµα	∧α∈aµα	PROPN
ejpam-4143	101	9	,	,	PUNCT
ejpam-4143	101	10	is	be	AUX
ejpam-4143	101	11	defined	define	VERB
ejpam-4143	101	12	by	by	ADP
ejpam-4143	101	13	∧α∈aµα(x	∧α∈aµα(x	PROPN
ejpam-4143	101	14	)	)	PUNCT
ejpam-4143	101	15	=	=	SYM
ejpam-4143	101	16	infα∈a{µα(x	infα∈a{µα(x	NOUN
ejpam-4143	101	17	)	)	PUNCT
ejpam-4143	101	18	}	}	PUNCT
ejpam-4143	101	19	for	for	ADP
ejpam-4143	101	20	all	all	DET
ejpam-4143	101	21	x	x	SYM
ejpam-4143	101	22	∈	∈	NOUN
ejpam-4143	101	23	x.	x.	NOUN
ejpam-4143	102	1	3	3	X
ejpam-4143	102	2	.	.	X
ejpam-4143	102	3	fuzzy	fuzzy	ADJ
ejpam-4143	102	4	hyper	hyper	ADJ
ejpam-4143	102	5	up	up	ADP
ejpam-4143	102	6	-	-	PUNCT
ejpam-4143	102	7	subalgebras	subalgebras	PROPN
ejpam-4143	102	8	in	in	ADP
ejpam-4143	102	9	this	this	DET
ejpam-4143	102	10	section	section	NOUN
ejpam-4143	102	11	,	,	PUNCT
ejpam-4143	102	12	we	we	PRON
ejpam-4143	102	13	introduce	introduce	VERB
ejpam-4143	102	14	the	the	DET
ejpam-4143	102	15	notion	notion	NOUN
ejpam-4143	102	16	of	of	ADP
ejpam-4143	102	17	fuzzy	fuzzy	ADJ
ejpam-4143	102	18	hyper	hyper	ADJ
ejpam-4143	102	19	up	up	ADP
ejpam-4143	102	20	-	-	PUNCT
ejpam-4143	102	21	subalgebra	subalgebra	NOUN
ejpam-4143	102	22	and	and	CCONJ
ejpam-4143	102	23	study	study	VERB
ejpam-4143	102	24	some	some	PRON
ejpam-4143	102	25	of	of	ADP
ejpam-4143	102	26	its	its	PRON
ejpam-4143	102	27	basic	basic	ADJ
ejpam-4143	102	28	properties	property	NOUN
ejpam-4143	102	29	.	.	PUNCT
ejpam-4143	103	1	for	for	ADP
ejpam-4143	103	2	brevity	brevity	NOUN
ejpam-4143	103	3	,	,	PUNCT
ejpam-4143	103	4	we	we	PRON
ejpam-4143	103	5	denote	denote	VERB
ejpam-4143	103	6	a	a	DET
ejpam-4143	103	7	hyper	hyper	ADJ
ejpam-4143	103	8	up	up	ADP
ejpam-4143	103	9	-	-	PUNCT
ejpam-4143	103	10	algebra	algebra	NOUN
ejpam-4143	103	11	(	(	PUNCT
ejpam-4143	103	12	h;⊛	h;⊛	NUM
ejpam-4143	103	13	,	,	PUNCT
ejpam-4143	103	14	0	0	NUM
ejpam-4143	103	15	)	)	PUNCT
ejpam-4143	103	16	by	by	ADP
ejpam-4143	103	17	h	h	NOUN
ejpam-4143	103	18	,	,	PUNCT
ejpam-4143	103	19	from	from	ADP
ejpam-4143	103	20	here	here	ADV
ejpam-4143	103	21	onwards	onward	NOUN
ejpam-4143	103	22	.	.	PUNCT
ejpam-4143	104	1	definition	definition	NOUN
ejpam-4143	104	2	8	8	NUM
ejpam-4143	104	3	.	.	PUNCT
ejpam-4143	105	1	a	a	DET
ejpam-4143	105	2	fuzzy	fuzzy	ADJ
ejpam-4143	105	3	set	set	VERB
ejpam-4143	105	4	µ	µ	NOUN
ejpam-4143	105	5	in	in	ADP
ejpam-4143	105	6	a	a	DET
ejpam-4143	105	7	hyper	hyper	ADJ
ejpam-4143	105	8	up	up	ADP
ejpam-4143	105	9	-	-	PUNCT
ejpam-4143	105	10	algebrah	algebrah	NOUN
ejpam-4143	105	11	is	be	AUX
ejpam-4143	105	12	called	call	VERB
ejpam-4143	105	13	a	a	DET
ejpam-4143	105	14	fuzzy	fuzzy	ADJ
ejpam-4143	105	15	hyper	hyper	ADJ
ejpam-4143	105	16	up	up	ADP
ejpam-4143	105	17	-	-	PUNCT
ejpam-4143	105	18	subalgebra	subalgebra	NOUN
ejpam-4143	105	19	of	of	ADP
ejpam-4143	105	20	h	h	NOUN
ejpam-4143	105	21	if	if	SCONJ
ejpam-4143	105	22	for	for	ADP
ejpam-4143	105	23	any	any	DET
ejpam-4143	105	24	x	x	NOUN
ejpam-4143	105	25	,	,	PUNCT
ejpam-4143	105	26	y	y	PROPN
ejpam-4143	105	27	∈	∈	PROPN
ejpam-4143	105	28	h	h	NOUN
ejpam-4143	105	29	,	,	PUNCT
ejpam-4143	105	30	infa∈x⊛y	infa∈x⊛y	X
ejpam-4143	105	31	{	{	PUNCT
ejpam-4143	105	32	µ(a	µ(a	PROPN
ejpam-4143	105	33	)	)	PUNCT
ejpam-4143	105	34	}	}	PUNCT
ejpam-4143	105	35	≥	≥	NOUN
ejpam-4143	105	36	min{µ(x	min{µ(x	NOUN
ejpam-4143	105	37	)	)	PUNCT
ejpam-4143	105	38	,	,	PUNCT
ejpam-4143	105	39	µ(y	µ(y	PROPN
ejpam-4143	105	40	)	)	PUNCT
ejpam-4143	105	41	}	}	PUNCT
ejpam-4143	105	42	.	.	PUNCT
ejpam-4143	106	1	r.	r.	PROPN
ejpam-4143	106	2	amairanto	amairanto	PROPN
ejpam-4143	106	3	,	,	PUNCT
ejpam-4143	106	4	r.	r.	PROPN
ejpam-4143	106	5	isla	isla	PROPN
ejpam-4143	106	6	/	/	SYM
ejpam-4143	106	7	eur	eur	PROPN
ejpam-4143	106	8	.	.	PUNCT
ejpam-4143	107	1	j.	j.	PROPN
ejpam-4143	107	2	pure	pure	PROPN
ejpam-4143	107	3	appl	appl	PROPN
ejpam-4143	107	4	.	.	PROPN
ejpam-4143	107	5	math	math	PROPN
ejpam-4143	107	6	,	,	PUNCT
ejpam-4143	107	7	14	14	NUM
ejpam-4143	107	8	(	(	PUNCT
ejpam-4143	107	9	4	4	NUM
ejpam-4143	107	10	)	)	PUNCT
ejpam-4143	107	11	(	(	PUNCT
ejpam-4143	107	12	2021	2021	NUM
ejpam-4143	107	13	)	)	PUNCT
ejpam-4143	107	14	,	,	PUNCT
ejpam-4143	107	15	1388	1388	NUM
ejpam-4143	107	16	-	-	SYM
ejpam-4143	107	17	1401	1401	NUM
ejpam-4143	107	18	1392	1392	NUM
ejpam-4143	107	19	example	example	NOUN
ejpam-4143	107	20	4	4	NUM
ejpam-4143	107	21	.	.	NOUN
ejpam-4143	107	22	1	1	NUM
ejpam-4143	107	23	.	.	PUNCT
ejpam-4143	108	1	by	by	ADP
ejpam-4143	108	2	examples	example	NOUN
ejpam-4143	108	3	1	1	NUM
ejpam-4143	108	4	and	and	CCONJ
ejpam-4143	108	5	2	2	NUM
ejpam-4143	108	6	,	,	PUNCT
ejpam-4143	108	7	h	h	NOUN
ejpam-4143	108	8	=	=	SYM
ejpam-4143	108	9	{	{	PUNCT
ejpam-4143	108	10	0	0	NUM
ejpam-4143	108	11	,	,	PUNCT
ejpam-4143	108	12	a	a	DET
ejpam-4143	108	13	,	,	PUNCT
ejpam-4143	108	14	b	b	NOUN
ejpam-4143	108	15	,	,	PUNCT
ejpam-4143	108	16	c	c	NOUN
ejpam-4143	108	17	,	,	PUNCT
ejpam-4143	108	18	d	d	X
ejpam-4143	108	19	}	}	PUNCT
ejpam-4143	108	20	is	be	AUX
ejpam-4143	108	21	a	a	DET
ejpam-4143	108	22	hyper	hyper	ADJ
ejpam-4143	108	23	up	up	NOUN
ejpam-4143	108	24	-	-	PUNCT
ejpam-4143	108	25	algebra	algebra	NOUN
ejpam-4143	108	26	and	and	CCONJ
ejpam-4143	108	27	the	the	DET
ejpam-4143	108	28	set	set	NOUN
ejpam-4143	108	29	{	{	PUNCT
ejpam-4143	108	30	0	0	NUM
ejpam-4143	108	31	,	,	PUNCT
ejpam-4143	108	32	a	a	DET
ejpam-4143	108	33	,	,	PUNCT
ejpam-4143	108	34	b	b	NOUN
ejpam-4143	108	35	,	,	PUNCT
ejpam-4143	108	36	c	c	NOUN
ejpam-4143	108	37	}	}	PUNCT
ejpam-4143	108	38	is	be	AUX
ejpam-4143	108	39	a	a	DET
ejpam-4143	108	40	hyper	hyper	ADJ
ejpam-4143	108	41	up	up	ADJ
ejpam-4143	108	42	-	-	PUNCT
ejpam-4143	108	43	subalgebra	subalgebra	NOUN
ejpam-4143	108	44	.	.	PUNCT
ejpam-4143	109	1	it	it	PRON
ejpam-4143	109	2	can	can	AUX
ejpam-4143	109	3	be	be	AUX
ejpam-4143	109	4	easily	easily	ADV
ejpam-4143	109	5	verified	verify	VERB
ejpam-4143	109	6	that	that	SCONJ
ejpam-4143	109	7	µ(x	µ(x	VERB
ejpam-4143	109	8	)	)	PUNCT
ejpam-4143	109	9	=	=	NOUN
ejpam-4143	109	10	{	{	PUNCT
ejpam-4143	109	11	1	1	NUM
ejpam-4143	109	12	,	,	PUNCT
ejpam-4143	109	13	if	if	SCONJ
ejpam-4143	109	14	x	x	SYM
ejpam-4143	109	15	∈	∈	NOUN
ejpam-4143	109	16	{	{	PUNCT
ejpam-4143	109	17	0	0	NUM
ejpam-4143	109	18	,	,	PUNCT
ejpam-4143	109	19	a	a	DET
ejpam-4143	109	20	,	,	PUNCT
ejpam-4143	109	21	b	b	NOUN
ejpam-4143	109	22	,	,	PUNCT
ejpam-4143	109	23	c	c	NOUN
ejpam-4143	109	24	}	}	PUNCT
ejpam-4143	109	25	0	0	NUM
ejpam-4143	109	26	,	,	PUNCT
ejpam-4143	109	27	if	if	SCONJ
ejpam-4143	109	28	x	x	SYM
ejpam-4143	109	29	∈	∈	NOUN
ejpam-4143	109	30	{	{	PUNCT
ejpam-4143	109	31	d	d	NOUN
ejpam-4143	109	32	}	}	PUNCT
ejpam-4143	109	33	is	be	AUX
ejpam-4143	109	34	a	a	DET
ejpam-4143	109	35	fuzzy	fuzzy	ADJ
ejpam-4143	109	36	hyper	hyper	ADJ
ejpam-4143	109	37	up	up	ADP
ejpam-4143	109	38	-	-	PUNCT
ejpam-4143	109	39	subalgebra	subalgebra	NOUN
ejpam-4143	109	40	of	of	ADP
ejpam-4143	109	41	h.	h.	PROPN
ejpam-4143	109	42	2	2	NUM
ejpam-4143	109	43	.	.	PUNCT
ejpam-4143	110	1	let	let	VERB
ejpam-4143	110	2	h	h	NOUN
ejpam-4143	110	3	=	=	PRON
ejpam-4143	110	4	{	{	PUNCT
ejpam-4143	110	5	0	0	NUM
ejpam-4143	110	6	,	,	PUNCT
ejpam-4143	110	7	1	1	NUM
ejpam-4143	110	8	,	,	PUNCT
ejpam-4143	110	9	2	2	NUM
ejpam-4143	110	10	}	}	PUNCT
ejpam-4143	110	11	be	be	AUX
ejpam-4143	110	12	a	a	DET
ejpam-4143	110	13	set	set	NOUN
ejpam-4143	110	14	with	with	ADP
ejpam-4143	110	15	a	a	DET
ejpam-4143	110	16	binary	binary	ADJ
ejpam-4143	110	17	operation	operation	NOUN
ejpam-4143	110	18	⊛	⊛	NUM
ejpam-4143	110	19	defined	define	VERB
ejpam-4143	110	20	by	by	ADP
ejpam-4143	110	21	the	the	DET
ejpam-4143	110	22	following	following	ADJ
ejpam-4143	110	23	cayley	cayley	ADJ
ejpam-4143	110	24	table	table	NOUN
ejpam-4143	110	25	:	:	PUNCT
ejpam-4143	110	26	⊛	⊛	NUM
ejpam-4143	110	27	0	0	NUM
ejpam-4143	110	28	1	1	NUM
ejpam-4143	110	29	2	2	NUM
ejpam-4143	110	30	0	0	NUM
ejpam-4143	110	31	{	{	PUNCT
ejpam-4143	110	32	0	0	NUM
ejpam-4143	110	33	}	}	PUNCT
ejpam-4143	110	34	{	{	PUNCT
ejpam-4143	110	35	1	1	NUM
ejpam-4143	110	36	}	}	PUNCT
ejpam-4143	110	37	{	{	PUNCT
ejpam-4143	110	38	2	2	NUM
ejpam-4143	110	39	}	}	SYM
ejpam-4143	110	40	1	1	NUM
ejpam-4143	110	41	{	{	PUNCT
ejpam-4143	110	42	0	0	NUM
ejpam-4143	110	43	}	}	PUNCT
ejpam-4143	110	44	{	{	PUNCT
ejpam-4143	110	45	0,2	0,2	NUM
ejpam-4143	110	46	}	}	PUNCT
ejpam-4143	110	47	{	{	PUNCT
ejpam-4143	110	48	0,2	0,2	NUM
ejpam-4143	110	49	}	}	SYM
ejpam-4143	110	50	2	2	NUM
ejpam-4143	110	51	{	{	PUNCT
ejpam-4143	110	52	0	0	NUM
ejpam-4143	110	53	}	}	PUNCT
ejpam-4143	110	54	{	{	PUNCT
ejpam-4143	110	55	1	1	NUM
ejpam-4143	110	56	}	}	PUNCT
ejpam-4143	110	57	{	{	PUNCT
ejpam-4143	110	58	0,2	0,2	NUM
ejpam-4143	110	59	}	}	PUNCT
ejpam-4143	110	60	define	define	VERB
ejpam-4143	110	61	a	a	DET
ejpam-4143	110	62	fuzzy	fuzzy	ADJ
ejpam-4143	110	63	subset	subset	ADJ
ejpam-4143	110	64	µ	µ	X
ejpam-4143	110	65	:	:	PUNCT
ejpam-4143	110	66	h	h	NOUN
ejpam-4143	110	67	→	→	PUNCT
ejpam-4143	111	1	[	[	X
ejpam-4143	111	2	0	0	NUM
ejpam-4143	111	3	,	,	PUNCT
ejpam-4143	111	4	1	1	NUM
ejpam-4143	111	5	]	]	PUNCT
ejpam-4143	111	6	by	by	ADP
ejpam-4143	111	7	µ(0	µ(0	NOUN
ejpam-4143	111	8	)	)	PUNCT
ejpam-4143	111	9	=	=	SYM
ejpam-4143	111	10	0.9	0.9	NUM
ejpam-4143	111	11	,	,	PUNCT
ejpam-4143	111	12	µ(1	µ(1	PROPN
ejpam-4143	111	13	)	)	PUNCT
ejpam-4143	111	14	=	=	NOUN
ejpam-4143	111	15	0.5	0.5	NUM
ejpam-4143	111	16	,	,	PUNCT
ejpam-4143	111	17	µ(2	µ(2	PROPN
ejpam-4143	111	18	)	)	PUNCT
ejpam-4143	111	19	=	=	PUNCT
ejpam-4143	112	1	0.3	0.3	NUM
ejpam-4143	112	2	.	.	PUNCT
ejpam-4143	113	1	then	then	ADV
ejpam-4143	113	2	µ	µ	X
ejpam-4143	113	3	is	be	AUX
ejpam-4143	113	4	not	not	PART
ejpam-4143	113	5	a	a	DET
ejpam-4143	113	6	fuzzy	fuzzy	ADJ
ejpam-4143	113	7	hyper	hyper	ADJ
ejpam-4143	113	8	up	up	ADP
ejpam-4143	113	9	-	-	PUNCT
ejpam-4143	113	10	subalgebra	subalgebra	NOUN
ejpam-4143	113	11	of	of	ADP
ejpam-4143	113	12	h	h	NOUN
ejpam-4143	113	13	since	since	SCONJ
ejpam-4143	113	14	0.3	0.3	NUM
ejpam-4143	113	15	=	=	SYM
ejpam-4143	113	16	µ(2	µ(2	PROPN
ejpam-4143	113	17	)	)	PUNCT
ejpam-4143	113	18	=	=	NOUN
ejpam-4143	113	19	infa∈1⊛1	infa∈1⊛1	PROPN
ejpam-4143	113	20	{	{	PUNCT
ejpam-4143	113	21	µ(a	µ(a	PROPN
ejpam-4143	113	22	)	)	PUNCT
ejpam-4143	113	23	}	}	PUNCT
ejpam-4143	113	24	<	<	X
ejpam-4143	113	25	min{µ(1	min{µ(1	NOUN
ejpam-4143	113	26	)	)	PUNCT
ejpam-4143	113	27	,	,	PUNCT
ejpam-4143	113	28	µ(1	µ(1	PROPN
ejpam-4143	113	29	)	)	PUNCT
ejpam-4143	113	30	}	}	PUNCT
ejpam-4143	113	31	=	=	SYM
ejpam-4143	113	32	0.5	0.5	NUM
ejpam-4143	113	33	.	.	PUNCT
ejpam-4143	114	1	lemma	lemma	PROPN
ejpam-4143	114	2	1	1	X
ejpam-4143	114	3	.	.	PUNCT
ejpam-4143	115	1	let	let	VERB
ejpam-4143	115	2	µ	µ	X
ejpam-4143	115	3	be	be	AUX
ejpam-4143	115	4	a	a	DET
ejpam-4143	115	5	fuzzy	fuzzy	ADJ
ejpam-4143	115	6	hyper	hyper	ADJ
ejpam-4143	115	7	up	up	ADP
ejpam-4143	115	8	-	-	PUNCT
ejpam-4143	115	9	subalgebra	subalgebra	NOUN
ejpam-4143	115	10	of	of	ADP
ejpam-4143	115	11	a	a	DET
ejpam-4143	115	12	hyper	hyper	ADJ
ejpam-4143	115	13	up	up	ADP
ejpam-4143	115	14	-	-	PUNCT
ejpam-4143	115	15	algebra	algebra	NOUN
ejpam-4143	115	16	h.	h.	NOUN
ejpam-4143	115	17	then	then	ADV
ejpam-4143	115	18	µ(0	µ(0	PROPN
ejpam-4143	115	19	)	)	PUNCT
ejpam-4143	115	20	≥	≥	NOUN
ejpam-4143	115	21	µ(x	µ(x	VERB
ejpam-4143	115	22	)	)	PUNCT
ejpam-4143	115	23	for	for	ADP
ejpam-4143	115	24	all	all	DET
ejpam-4143	115	25	x	x	SYM
ejpam-4143	115	26	∈	∈	PROPN
ejpam-4143	115	27	h.	h.	PROPN
ejpam-4143	115	28	moreover	moreover	ADV
ejpam-4143	115	29	,	,	PUNCT
ejpam-4143	115	30	if	if	SCONJ
ejpam-4143	115	31	µ	µ	NOUN
ejpam-4143	115	32	is	be	AUX
ejpam-4143	115	33	onto	onto	ADP
ejpam-4143	115	34	,	,	PUNCT
ejpam-4143	115	35	then	then	ADV
ejpam-4143	115	36	µ(0	µ(0	PROPN
ejpam-4143	115	37	)	)	PUNCT
ejpam-4143	115	38	=	=	SYM
ejpam-4143	116	1	1	1	X
ejpam-4143	116	2	.	.	PUNCT
ejpam-4143	116	3	proof	proof	NOUN
ejpam-4143	116	4	.	.	PUNCT
ejpam-4143	117	1	let	let	VERB
ejpam-4143	117	2	x	x	SYM
ejpam-4143	117	3	∈	∈	PROPN
ejpam-4143	117	4	h.	h.	PROPN
ejpam-4143	117	5	by	by	ADP
ejpam-4143	117	6	proposition	proposition	NOUN
ejpam-4143	117	7	1(iii	1(iii	NUM
ejpam-4143	117	8	)	)	PUNCT
ejpam-4143	117	9	,	,	PUNCT
ejpam-4143	117	10	x	x	SYM
ejpam-4143	117	11	≪	≪	PUNCT
ejpam-4143	117	12	x	x	X
ejpam-4143	117	13	,	,	PUNCT
ejpam-4143	117	14	that	that	ADV
ejpam-4143	117	15	is	is	ADV
ejpam-4143	117	16	,	,	PUNCT
ejpam-4143	117	17	0	0	NUM
ejpam-4143	117	18	∈	∈	PROPN
ejpam-4143	117	19	x	x	SYM
ejpam-4143	117	20	⊛	⊛	NUM
ejpam-4143	117	21	x.	x.	NOUN
ejpam-4143	117	22	then	then	ADV
ejpam-4143	117	23	µ(0	µ(0	PROPN
ejpam-4143	117	24	)	)	PUNCT
ejpam-4143	117	25	≥	≥	NOUN
ejpam-4143	117	26	infa∈x⊛x	infa∈x⊛x	PROPN
ejpam-4143	117	27	{	{	PUNCT
ejpam-4143	117	28	µ(a	µ(a	PROPN
ejpam-4143	117	29	)	)	PUNCT
ejpam-4143	117	30	}	}	PUNCT
ejpam-4143	117	31	≥	≥	NOUN
ejpam-4143	117	32	min{µ(x	min{µ(x	NOUN
ejpam-4143	117	33	)	)	PUNCT
ejpam-4143	117	34	,	,	PUNCT
ejpam-4143	117	35	µ(x	µ(x	NOUN
ejpam-4143	117	36	)	)	PUNCT
ejpam-4143	117	37	}	}	PUNCT
ejpam-4143	117	38	=	=	SYM
ejpam-4143	117	39	µ(x	µ(x	NUM
ejpam-4143	117	40	)	)	PUNCT
ejpam-4143	117	41	.	.	PUNCT
ejpam-4143	118	1	if	if	SCONJ
ejpam-4143	118	2	µ	µ	NOUN
ejpam-4143	118	3	is	be	AUX
ejpam-4143	118	4	onto	onto	ADP
ejpam-4143	118	5	,	,	PUNCT
ejpam-4143	118	6	then	then	ADV
ejpam-4143	118	7	µ(y	µ(y	PROPN
ejpam-4143	118	8	)	)	PUNCT
ejpam-4143	118	9	=	=	SYM
ejpam-4143	118	10	1	1	NUM
ejpam-4143	118	11	,	,	PUNCT
ejpam-4143	118	12	for	for	ADP
ejpam-4143	118	13	some	some	DET
ejpam-4143	118	14	y	y	PROPN
ejpam-4143	118	15	∈	∈	PROPN
ejpam-4143	118	16	h.	h.	PROPN
ejpam-4143	118	17	thus	thus	ADV
ejpam-4143	118	18	,	,	PUNCT
ejpam-4143	118	19	1	1	NUM
ejpam-4143	118	20	=	=	SYM
ejpam-4143	118	21	µ(y	µ(y	NOUN
ejpam-4143	118	22	)	)	PUNCT
ejpam-4143	118	23	≤	≤	PUNCT
ejpam-4143	118	24	µ(0	µ(0	NOUN
ejpam-4143	118	25	)	)	PUNCT
ejpam-4143	118	26	≤	≤	NUM
ejpam-4143	118	27	1	1	NUM
ejpam-4143	118	28	.	.	PUNCT
ejpam-4143	119	1	hence	hence	ADV
ejpam-4143	119	2	,	,	PUNCT
ejpam-4143	119	3	µ(0	µ(0	NOUN
ejpam-4143	119	4	)	)	PUNCT
ejpam-4143	119	5	=	=	SYM
ejpam-4143	119	6	1	1	X
ejpam-4143	119	7	.	.	X
ejpam-4143	119	8	theorem	theorem	NOUN
ejpam-4143	119	9	1	1	NUM
ejpam-4143	119	10	.	.	PUNCT
ejpam-4143	120	1	let	let	VERB
ejpam-4143	120	2	µ	µ	X
ejpam-4143	120	3	be	be	AUX
ejpam-4143	120	4	a	a	DET
ejpam-4143	120	5	fuzzy	fuzzy	ADJ
ejpam-4143	120	6	hyper	hyper	ADJ
ejpam-4143	120	7	up	up	ADP
ejpam-4143	120	8	-	-	PUNCT
ejpam-4143	120	9	subalgebra	subalgebra	NOUN
ejpam-4143	120	10	of	of	ADP
ejpam-4143	120	11	a	a	DET
ejpam-4143	120	12	hyper	hyper	ADJ
ejpam-4143	120	13	up	up	ADP
ejpam-4143	120	14	-	-	PUNCT
ejpam-4143	120	15	algebra	algebra	NOUN
ejpam-4143	120	16	h.	h.	NOUN
ejpam-4143	120	17	then	then	ADV
ejpam-4143	120	18	there	there	PRON
ejpam-4143	120	19	exists	exist	VERB
ejpam-4143	120	20	a	a	DET
ejpam-4143	120	21	sequence	sequence	NOUN
ejpam-4143	120	22	⟨xn⟩	⟨xn⟩	NOUN
ejpam-4143	121	1	⊆	⊆	NUM
ejpam-4143	121	2	h	h	NOUN
ejpam-4143	121	3	such	such	ADJ
ejpam-4143	121	4	that	that	SCONJ
ejpam-4143	121	5	limn→∞	limn→∞	PROPN
ejpam-4143	121	6	µ(xn	µ(xn	NOUN
ejpam-4143	121	7	)	)	PUNCT
ejpam-4143	121	8	=	=	SYM
ejpam-4143	121	9	1	1	NUM
ejpam-4143	121	10	if	if	SCONJ
ejpam-4143	121	11	and	and	CCONJ
ejpam-4143	121	12	only	only	ADV
ejpam-4143	121	13	if	if	SCONJ
ejpam-4143	121	14	µ(0	µ(0	NOUN
ejpam-4143	121	15	)	)	PUNCT
ejpam-4143	121	16	=	=	SYM
ejpam-4143	121	17	1	1	X
ejpam-4143	121	18	.	.	PUNCT
ejpam-4143	122	1	proof	proof	NOUN
ejpam-4143	122	2	.	.	PUNCT
ejpam-4143	123	1	suppose	suppose	VERB
ejpam-4143	123	2	that	that	SCONJ
ejpam-4143	123	3	there	there	PRON
ejpam-4143	123	4	exists	exist	VERB
ejpam-4143	123	5	⟨xn⟩	⟨xn⟩	NOUN
ejpam-4143	123	6	⊆	⊆	NUM
ejpam-4143	123	7	h	h	NOUN
ejpam-4143	123	8	such	such	ADJ
ejpam-4143	123	9	that	that	SCONJ
ejpam-4143	123	10	limn→∞	limn→∞	PROPN
ejpam-4143	123	11	µ(xn	µ(xn	NOUN
ejpam-4143	123	12	)	)	PUNCT
ejpam-4143	123	13	=	=	SYM
ejpam-4143	123	14	1	1	X
ejpam-4143	123	15	.	.	PUNCT
ejpam-4143	123	16	by	by	ADP
ejpam-4143	123	17	lemma	lemma	PROPN
ejpam-4143	123	18	1	1	NUM
ejpam-4143	123	19	,	,	PUNCT
ejpam-4143	123	20	it	it	PRON
ejpam-4143	123	21	will	will	AUX
ejpam-4143	123	22	follow	follow	VERB
ejpam-4143	123	23	that	that	DET
ejpam-4143	123	24	µ(0	µ(0	NOUN
ejpam-4143	123	25	)	)	PUNCT
ejpam-4143	123	26	≥	≥	NOUN
ejpam-4143	123	27	µ(xn	µ(xn	NOUN
ejpam-4143	123	28	)	)	PUNCT
ejpam-4143	123	29	for	for	ADP
ejpam-4143	123	30	all	all	DET
ejpam-4143	123	31	n.	n.	NOUN
ejpam-4143	123	32	this	this	PRON
ejpam-4143	123	33	implies	imply	VERB
ejpam-4143	123	34	that	that	SCONJ
ejpam-4143	123	35	1	1	NUM
ejpam-4143	123	36	≥	≥	NOUN
ejpam-4143	123	37	µ(0	µ(0	NUM
ejpam-4143	123	38	)	)	PUNCT
ejpam-4143	124	1	=	=	SYM
ejpam-4143	124	2	limn→∞	limn→∞	X
ejpam-4143	124	3	µ(0	µ(0	NOUN
ejpam-4143	124	4	)	)	PUNCT
ejpam-4143	124	5	≥	≥	NOUN
ejpam-4143	124	6	limn→∞	limn→∞	X
ejpam-4143	124	7	µ(xn	µ(xn	NOUN
ejpam-4143	124	8	)	)	PUNCT
ejpam-4143	124	9	=	=	SYM
ejpam-4143	124	10	1	1	NUM
ejpam-4143	124	11	,	,	PUNCT
ejpam-4143	124	12	that	that	ADV
ejpam-4143	124	13	is	is	ADV
ejpam-4143	124	14	,	,	PUNCT
ejpam-4143	124	15	µ(0	µ(0	NOUN
ejpam-4143	124	16	)	)	PUNCT
ejpam-4143	124	17	=	=	SYM
ejpam-4143	125	1	1	1	X
ejpam-4143	125	2	.	.	PUNCT
ejpam-4143	125	3	conversely	conversely	ADV
ejpam-4143	125	4	,	,	PUNCT
ejpam-4143	125	5	assume	assume	VERB
ejpam-4143	125	6	that	that	SCONJ
ejpam-4143	125	7	µ(0	µ(0	NOUN
ejpam-4143	125	8	)	)	PUNCT
ejpam-4143	125	9	=	=	SYM
ejpam-4143	125	10	1	1	X
ejpam-4143	125	11	.	.	X
ejpam-4143	125	12	consider	consider	VERB
ejpam-4143	125	13	the	the	DET
ejpam-4143	125	14	sequence	sequence	NOUN
ejpam-4143	125	15	⟨xn⟩	⟨xn⟩	NOUN
ejpam-4143	125	16	=	=	PUNCT
ejpam-4143	126	1	⟨0	⟨0	PROPN
ejpam-4143	126	2	,	,	PUNCT
ejpam-4143	126	3	0	0	NUM
ejpam-4143	126	4	,	,	PUNCT
ejpam-4143	126	5	0	0	NUM
ejpam-4143	126	6	,	,	PUNCT
ejpam-4143	126	7	·	·	PUNCT
ejpam-4143	126	8	·	·	PUNCT
ejpam-4143	126	9	·	·	PUNCT
ejpam-4143	126	10	,	,	PUNCT
ejpam-4143	126	11	0	0	NUM
ejpam-4143	126	12	,	,	PUNCT
ejpam-4143	126	13	·	·	PUNCT
ejpam-4143	126	14	·	·	PUNCT
ejpam-4143	126	15	·	·	PUNCT
ejpam-4143	126	16	⟩	⟩	NOUN
ejpam-4143	126	17	in	in	ADP
ejpam-4143	126	18	h.	h.	PROPN
ejpam-4143	126	19	thus	thus	ADV
ejpam-4143	126	20	,	,	PUNCT
ejpam-4143	126	21	⟨µ(xn)⟩	⟨µ(xn)⟩	VERB
ejpam-4143	126	22	=	=	PUNCT
ejpam-4143	126	23	⟨µ(0	⟨µ(0	NOUN
ejpam-4143	126	24	)	)	PUNCT
ejpam-4143	126	25	,	,	PUNCT
ejpam-4143	126	26	µ(0	µ(0	NOUN
ejpam-4143	126	27	)	)	PUNCT
ejpam-4143	126	28	,	,	PUNCT
ejpam-4143	126	29	µ(0	µ(0	NOUN
ejpam-4143	126	30	)	)	PUNCT
ejpam-4143	126	31	,	,	PUNCT
ejpam-4143	126	32	·	·	PUNCT
ejpam-4143	126	33	·	·	PUNCT
ejpam-4143	126	34	·	·	PUNCT
ejpam-4143	126	35	,	,	PUNCT
ejpam-4143	126	36	µ(0	µ(0	NOUN
ejpam-4143	126	37	)	)	PUNCT
ejpam-4143	126	38	,	,	PUNCT
ejpam-4143	126	39	·	·	PUNCT
ejpam-4143	126	40	·	·	PUNCT
ejpam-4143	126	41	·	·	PUNCT
ejpam-4143	127	1	⟩	⟩	NOUN
ejpam-4143	127	2	=	=	SYM
ejpam-4143	127	3	⟨1	⟨1	PROPN
ejpam-4143	127	4	,	,	PUNCT
ejpam-4143	127	5	1	1	NUM
ejpam-4143	127	6	,	,	PUNCT
ejpam-4143	127	7	1	1	NUM
ejpam-4143	127	8	,	,	PUNCT
ejpam-4143	127	9	·	·	PUNCT
ejpam-4143	127	10	·	·	PUNCT
ejpam-4143	127	11	·	·	PUNCT
ejpam-4143	127	12	,	,	PUNCT
ejpam-4143	127	13	1	1	X
ejpam-4143	127	14	,	,	PUNCT
ejpam-4143	127	15	·	·	PUNCT
ejpam-4143	127	16	·	·	PUNCT
ejpam-4143	127	17	·	·	PUNCT
ejpam-4143	127	18	⟩	⟩	NOUN
ejpam-4143	127	19	.	.	PUNCT
ejpam-4143	128	1	hence	hence	ADV
ejpam-4143	128	2	,	,	PUNCT
ejpam-4143	128	3	limn→∞	limn→∞	PROPN
ejpam-4143	128	4	µ(xn	µ(xn	X
ejpam-4143	128	5	)	)	PUNCT
ejpam-4143	128	6	=	=	SYM
ejpam-4143	128	7	1	1	X
ejpam-4143	128	8	.	.	PUNCT
ejpam-4143	128	9	definition	definition	NOUN
ejpam-4143	128	10	9	9	NUM
ejpam-4143	128	11	.	.	PUNCT
ejpam-4143	129	1	let	let	VERB
ejpam-4143	129	2	µ	µ	X
ejpam-4143	129	3	be	be	AUX
ejpam-4143	129	4	a	a	DET
ejpam-4143	129	5	fuzzy	fuzzy	ADJ
ejpam-4143	129	6	subset	subset	NOUN
ejpam-4143	129	7	of	of	ADP
ejpam-4143	129	8	a	a	DET
ejpam-4143	129	9	hyper	hyper	ADJ
ejpam-4143	129	10	up	up	ADP
ejpam-4143	129	11	-	-	PUNCT
ejpam-4143	129	12	algebra	algebra	NOUN
ejpam-4143	129	13	h	h	NOUN
ejpam-4143	129	14	and	and	CCONJ
ejpam-4143	129	15	t	t	NOUN
ejpam-4143	129	16	∈	∈	PROPN
ejpam-4143	130	1	[	[	X
ejpam-4143	130	2	0	0	NUM
ejpam-4143	130	3	,	,	PUNCT
ejpam-4143	130	4	1	1	NUM
ejpam-4143	130	5	]	]	PUNCT
ejpam-4143	130	6	.	.	PUNCT
ejpam-4143	131	1	then	then	ADV
ejpam-4143	131	2	the	the	DET
ejpam-4143	131	3	upper	upper	ADJ
ejpam-4143	131	4	level	level	NOUN
ejpam-4143	131	5	set	set	NOUN
ejpam-4143	131	6	µt	µt	PUNCT
ejpam-4143	131	7	is	be	AUX
ejpam-4143	131	8	the	the	DET
ejpam-4143	131	9	set	set	NOUN
ejpam-4143	131	10	µt	µt	X
ejpam-4143	131	11	=	=	PUNCT
ejpam-4143	131	12	{	{	PUNCT
ejpam-4143	131	13	x	x	PUNCT
ejpam-4143	131	14	∈	∈	PROPN
ejpam-4143	131	15	h	h	NOUN
ejpam-4143	131	16	:	:	PUNCT
ejpam-4143	131	17	µ(x	µ(x	X
ejpam-4143	131	18	)	)	PUNCT
ejpam-4143	131	19	≥	≥	NOUN
ejpam-4143	131	20	t	t	PROPN
ejpam-4143	131	21	}	}	PUNCT
ejpam-4143	131	22	.	.	PUNCT
ejpam-4143	132	1	theorem	theorem	NOUN
ejpam-4143	132	2	2	2	NUM
ejpam-4143	132	3	.	.	PUNCT
ejpam-4143	132	4	let	let	VERB
ejpam-4143	132	5	µ	µ	X
ejpam-4143	132	6	be	be	AUX
ejpam-4143	132	7	a	a	DET
ejpam-4143	132	8	fuzzy	fuzzy	ADJ
ejpam-4143	132	9	subset	subset	NOUN
ejpam-4143	132	10	of	of	ADP
ejpam-4143	132	11	a	a	DET
ejpam-4143	132	12	hyper	hyper	ADJ
ejpam-4143	132	13	up	up	ADP
ejpam-4143	132	14	-	-	PUNCT
ejpam-4143	132	15	algebra	algebra	NOUN
ejpam-4143	132	16	h.	h.	NOUN
ejpam-4143	132	17	then	then	ADV
ejpam-4143	132	18	µ	µ	PROPN
ejpam-4143	132	19	is	be	AUX
ejpam-4143	132	20	a	a	DET
ejpam-4143	132	21	fuzzy	fuzzy	ADJ
ejpam-4143	132	22	hyper	hyper	ADJ
ejpam-4143	132	23	up	up	ADP
ejpam-4143	132	24	-	-	PUNCT
ejpam-4143	132	25	subalgebra	subalgebra	NOUN
ejpam-4143	132	26	of	of	ADP
ejpam-4143	132	27	h	h	NOUN
ejpam-4143	132	28	if	if	SCONJ
ejpam-4143	133	1	and	and	CCONJ
ejpam-4143	133	2	only	only	ADV
ejpam-4143	133	3	if	if	SCONJ
ejpam-4143	133	4	for	for	ADP
ejpam-4143	133	5	all	all	DET
ejpam-4143	133	6	t	t	NOUN
ejpam-4143	133	7	∈	∈	PROPN
ejpam-4143	134	1	[	[	X
ejpam-4143	134	2	0	0	NUM
ejpam-4143	134	3	,	,	PUNCT
ejpam-4143	134	4	1	1	NUM
ejpam-4143	134	5	]	]	PUNCT
ejpam-4143	134	6	,	,	PUNCT
ejpam-4143	134	7	∅	∅	NOUN
ejpam-4143	134	8	̸=	̸=	PROPN
ejpam-4143	134	9	µt	µt	PRON
ejpam-4143	134	10	is	be	AUX
ejpam-4143	134	11	a	a	DET
ejpam-4143	134	12	hyper	hyper	ADJ
ejpam-4143	134	13	up	up	ADP
ejpam-4143	134	14	-	-	PUNCT
ejpam-4143	134	15	subalgebra	subalgebra	NOUN
ejpam-4143	134	16	of	of	ADP
ejpam-4143	134	17	h.	h.	NOUN
ejpam-4143	134	18	proof	proof	NOUN
ejpam-4143	134	19	.	.	PUNCT
ejpam-4143	135	1	suppose	suppose	VERB
ejpam-4143	135	2	that	that	SCONJ
ejpam-4143	135	3	µ	µ	NOUN
ejpam-4143	135	4	is	be	AUX
ejpam-4143	135	5	a	a	DET
ejpam-4143	135	6	fuzzy	fuzzy	ADJ
ejpam-4143	135	7	hyper	hyper	ADJ
ejpam-4143	135	8	up	up	ADP
ejpam-4143	135	9	-	-	PUNCT
ejpam-4143	135	10	subalgebra	subalgebra	NOUN
ejpam-4143	135	11	of	of	ADP
ejpam-4143	135	12	h	h	NOUN
ejpam-4143	135	13	and	and	CCONJ
ejpam-4143	135	14	µt	µt	DET
ejpam-4143	135	15	̸=	̸=	PROPN
ejpam-4143	135	16	∅.	∅.	ADV
ejpam-4143	135	17	let	let	VERB
ejpam-4143	135	18	x	x	PRON
ejpam-4143	135	19	,	,	PUNCT
ejpam-4143	135	20	y	y	PROPN
ejpam-4143	135	21	∈	∈	PROPN
ejpam-4143	135	22	µt	µt	X
ejpam-4143	135	23	and	and	CCONJ
ejpam-4143	135	24	let	let	VERB
ejpam-4143	135	25	a	a	DET
ejpam-4143	135	26	∈	∈	NOUN
ejpam-4143	135	27	x	x	PUNCT
ejpam-4143	135	28	⊛	⊛	ADP
ejpam-4143	135	29	y.	y.	NOUN
ejpam-4143	135	30	then	then	ADV
ejpam-4143	135	31	µ(x	µ(x	NOUN
ejpam-4143	135	32	)	)	PUNCT
ejpam-4143	135	33	,	,	PUNCT
ejpam-4143	135	34	µ(y	µ(y	PROPN
ejpam-4143	135	35	)	)	PUNCT
ejpam-4143	135	36	≥	≥	NOUN
ejpam-4143	135	37	t	t	NOUN
ejpam-4143	135	38	and	and	CCONJ
ejpam-4143	135	39	so	so	ADV
ejpam-4143	135	40	min{µ(x	min{µ(x	PROPN
ejpam-4143	135	41	)	)	PUNCT
ejpam-4143	135	42	,	,	PUNCT
ejpam-4143	135	43	µ(y	µ(y	PROPN
ejpam-4143	135	44	)	)	PUNCT
ejpam-4143	135	45	}	}	PUNCT
ejpam-4143	135	46	≥	≥	NOUN
ejpam-4143	135	47	t.	t.	NOUN
ejpam-4143	135	48	since	since	SCONJ
ejpam-4143	135	49	µ	µ	PROPN
ejpam-4143	135	50	is	be	AUX
ejpam-4143	135	51	a	a	DET
ejpam-4143	135	52	fuzzy	fuzzy	ADJ
ejpam-4143	135	53	hyper	hyper	ADJ
ejpam-4143	135	54	up	up	ADP
ejpam-4143	135	55	-	-	PUNCT
ejpam-4143	135	56	subalgebra	subalgebra	NOUN
ejpam-4143	135	57	of	of	ADP
ejpam-4143	135	58	h	h	NOUN
ejpam-4143	135	59	,	,	PUNCT
ejpam-4143	135	60	by	by	ADP
ejpam-4143	135	61	definition	definition	NOUN
ejpam-4143	135	62	8	8	NUM
ejpam-4143	135	63	,	,	PUNCT
ejpam-4143	135	64	µ(a	µ(a	PROPN
ejpam-4143	135	65	)	)	PUNCT
ejpam-4143	135	66	≥	≥	NOUN
ejpam-4143	135	67	infa′∈x⊛y	infa′∈x⊛y	X
ejpam-4143	135	68	{	{	PUNCT
ejpam-4143	135	69	µ(a′	µ(a′	PROPN
ejpam-4143	135	70	)	)	PUNCT
ejpam-4143	135	71	}	}	PUNCT
ejpam-4143	135	72	≥	≥	X
ejpam-4143	135	73	t.	t.	NOUN
ejpam-4143	135	74	it	it	PRON
ejpam-4143	135	75	follows	follow	VERB
ejpam-4143	135	76	that	that	SCONJ
ejpam-4143	135	77	a	a	DET
ejpam-4143	135	78	∈	∈	PROPN
ejpam-4143	135	79	µt	µt	PROPN
ejpam-4143	135	80	.	.	PUNCT
ejpam-4143	136	1	since	since	SCONJ
ejpam-4143	136	2	a	a	PRON
ejpam-4143	136	3	is	be	AUX
ejpam-4143	136	4	arbitrary	arbitrary	ADJ
ejpam-4143	136	5	,	,	PUNCT
ejpam-4143	136	6	x⊛	x⊛	PROPN
ejpam-4143	136	7	y	y	PROPN
ejpam-4143	136	8	⊆	⊆	NUM
ejpam-4143	136	9	µt	µt	NOUN
ejpam-4143	136	10	.	.	PUNCT
ejpam-4143	137	1	by	by	ADP
ejpam-4143	137	2	proposition	proposition	NOUN
ejpam-4143	137	3	2	2	NUM
ejpam-4143	137	4	,	,	PUNCT
ejpam-4143	137	5	µt	µt	PRON
ejpam-4143	137	6	is	be	AUX
ejpam-4143	137	7	a	a	DET
ejpam-4143	137	8	hyper	hyper	ADJ
ejpam-4143	137	9	up	up	ADP
ejpam-4143	137	10	-	-	PUNCT
ejpam-4143	137	11	subalgebra	subalgebra	NOUN
ejpam-4143	137	12	of	of	ADP
ejpam-4143	137	13	h.	h.	NOUN
ejpam-4143	137	14	conversely	conversely	ADV
ejpam-4143	137	15	,	,	PUNCT
ejpam-4143	137	16	suppose	suppose	VERB
ejpam-4143	137	17	µt	µt	PRON
ejpam-4143	137	18	is	be	AUX
ejpam-4143	137	19	a	a	DET
ejpam-4143	137	20	hyper	hyper	ADJ
ejpam-4143	137	21	up	up	ADP
ejpam-4143	137	22	-	-	PUNCT
ejpam-4143	137	23	subalgebra	subalgebra	NOUN
ejpam-4143	137	24	of	of	ADP
ejpam-4143	137	25	h	h	NOUN
ejpam-4143	137	26	for	for	ADP
ejpam-4143	137	27	each	each	DET
ejpam-4143	137	28	t	t	NOUN
ejpam-4143	137	29	∈	∈	PROPN
ejpam-4143	138	1	[	[	X
ejpam-4143	138	2	0	0	NUM
ejpam-4143	138	3	,	,	PUNCT
ejpam-4143	138	4	1	1	NUM
ejpam-4143	138	5	]	]	PUNCT
ejpam-4143	138	6	.	.	PUNCT
ejpam-4143	139	1	let	let	VERB
ejpam-4143	139	2	x	x	PRON
ejpam-4143	139	3	,	,	PUNCT
ejpam-4143	139	4	y	y	PROPN
ejpam-4143	139	5	∈	∈	PROPN
ejpam-4143	139	6	h.	h.	PROPN
ejpam-4143	139	7	r.	r.	PROPN
ejpam-4143	139	8	amairanto	amairanto	PROPN
ejpam-4143	139	9	,	,	PUNCT
ejpam-4143	139	10	r.	r.	PROPN
ejpam-4143	139	11	isla	isla	PROPN
ejpam-4143	139	12	/	/	SYM
ejpam-4143	139	13	eur	eur	PROPN
ejpam-4143	139	14	.	.	PUNCT
ejpam-4143	140	1	j.	j.	PROPN
ejpam-4143	140	2	pure	pure	PROPN
ejpam-4143	140	3	appl	appl	PROPN
ejpam-4143	140	4	.	.	PROPN
ejpam-4143	140	5	math	math	PROPN
ejpam-4143	140	6	,	,	PUNCT
ejpam-4143	140	7	14	14	NUM
ejpam-4143	140	8	(	(	PUNCT
ejpam-4143	140	9	4	4	NUM
ejpam-4143	140	10	)	)	PUNCT
ejpam-4143	140	11	(	(	PUNCT
ejpam-4143	140	12	2021	2021	NUM
ejpam-4143	140	13	)	)	PUNCT
ejpam-4143	140	14	,	,	PUNCT
ejpam-4143	140	15	1388	1388	NUM
ejpam-4143	140	16	-	-	SYM
ejpam-4143	140	17	1401	1401	NUM
ejpam-4143	140	18	1393	1393	NUM
ejpam-4143	140	19	then	then	ADV
ejpam-4143	140	20	µ(x	µ(x	NOUN
ejpam-4143	140	21	)	)	PUNCT
ejpam-4143	140	22	≥	≥	NOUN
ejpam-4143	140	23	min{µ(x	min{µ(x	NOUN
ejpam-4143	140	24	)	)	PUNCT
ejpam-4143	140	25	,	,	PUNCT
ejpam-4143	140	26	µ(y	µ(y	PROPN
ejpam-4143	140	27	)	)	PUNCT
ejpam-4143	140	28	}	}	PUNCT
ejpam-4143	140	29	and	and	CCONJ
ejpam-4143	140	30	µ(y	µ(y	PROPN
ejpam-4143	140	31	)	)	PUNCT
ejpam-4143	140	32	≥	≥	NOUN
ejpam-4143	140	33	min{µ(x	min{µ(x	NOUN
ejpam-4143	140	34	)	)	PUNCT
ejpam-4143	140	35	,	,	PUNCT
ejpam-4143	140	36	µ(y	µ(y	PROPN
ejpam-4143	140	37	)	)	PUNCT
ejpam-4143	140	38	}	}	PUNCT
ejpam-4143	140	39	.	.	PUNCT
ejpam-4143	141	1	take	take	VERB
ejpam-4143	141	2	t0	t0	NOUN
ejpam-4143	141	3	=	=	PUNCT
ejpam-4143	141	4	min{µ(x	min{µ(x	PROPN
ejpam-4143	141	5	)	)	PUNCT
ejpam-4143	141	6	,	,	PUNCT
ejpam-4143	141	7	µ(y	µ(y	PROPN
ejpam-4143	141	8	)	)	PUNCT
ejpam-4143	141	9	}	}	PUNCT
ejpam-4143	141	10	.	.	PUNCT
ejpam-4143	142	1	then	then	ADV
ejpam-4143	142	2	x	x	X
ejpam-4143	142	3	,	,	PUNCT
ejpam-4143	142	4	y	y	PROPN
ejpam-4143	142	5	∈	∈	PROPN
ejpam-4143	142	6	µt0	µt0	PROPN
ejpam-4143	142	7	and	and	CCONJ
ejpam-4143	142	8	so	so	ADV
ejpam-4143	142	9	x	x	PUNCT
ejpam-4143	142	10	⊛	⊛	NUM
ejpam-4143	142	11	y	y	PROPN
ejpam-4143	142	12	⊆	⊆	NUM
ejpam-4143	142	13	µt0	µt0	PROPN
ejpam-4143	142	14	.	.	PUNCT
ejpam-4143	143	1	let	let	VERB
ejpam-4143	143	2	a	a	DET
ejpam-4143	143	3	∈	∈	NOUN
ejpam-4143	143	4	x	x	PUNCT
ejpam-4143	143	5	⊛	⊛	NUM
ejpam-4143	143	6	y.	y.	PROPN
ejpam-4143	143	7	then	then	ADV
ejpam-4143	143	8	µ(a	µ(a	PROPN
ejpam-4143	143	9	)	)	PUNCT
ejpam-4143	143	10	≥	≥	NUM
ejpam-4143	143	11	t0	t0	NOUN
ejpam-4143	143	12	which	which	PRON
ejpam-4143	143	13	implies	imply	VERB
ejpam-4143	143	14	that	that	SCONJ
ejpam-4143	143	15	infa∈x⊛y	infa∈x⊛y	ADJ
ejpam-4143	143	16	{	{	PUNCT
ejpam-4143	143	17	µ(a	µ(a	PROPN
ejpam-4143	143	18	)	)	PUNCT
ejpam-4143	143	19	}	}	PUNCT
ejpam-4143	143	20	≥	≥	NOUN
ejpam-4143	143	21	t0	t0	NOUN
ejpam-4143	143	22	=	=	PUNCT
ejpam-4143	143	23	min{µ(x	min{µ(x	PROPN
ejpam-4143	143	24	)	)	PUNCT
ejpam-4143	143	25	,	,	PUNCT
ejpam-4143	143	26	µ(y	µ(y	PROPN
ejpam-4143	143	27	)	)	PUNCT
ejpam-4143	143	28	}	}	PUNCT
ejpam-4143	143	29	.	.	PUNCT
ejpam-4143	144	1	thus	thus	ADV
ejpam-4143	144	2	,	,	PUNCT
ejpam-4143	144	3	µ	µ	X
ejpam-4143	144	4	is	be	AUX
ejpam-4143	144	5	a	a	DET
ejpam-4143	144	6	fuzzy	fuzzy	ADJ
ejpam-4143	144	7	hyper	hyper	ADJ
ejpam-4143	144	8	up	up	ADP
ejpam-4143	144	9	-	-	PUNCT
ejpam-4143	144	10	subalgebra	subalgebra	NOUN
ejpam-4143	144	11	of	of	ADP
ejpam-4143	144	12	h.	h.	PROPN
ejpam-4143	144	13	theorem	theorem	PROPN
ejpam-4143	144	14	3	3	X
ejpam-4143	144	15	.	.	PUNCT
ejpam-4143	145	1	let	let	VERB
ejpam-4143	145	2	µ	µ	X
ejpam-4143	145	3	be	be	AUX
ejpam-4143	145	4	a	a	DET
ejpam-4143	145	5	fuzzy	fuzzy	ADJ
ejpam-4143	145	6	hyper	hyper	ADJ
ejpam-4143	145	7	up	up	ADP
ejpam-4143	145	8	-	-	PUNCT
ejpam-4143	145	9	subalgebra	subalgebra	NOUN
ejpam-4143	145	10	of	of	ADP
ejpam-4143	145	11	a	a	DET
ejpam-4143	145	12	hyper	hyper	ADJ
ejpam-4143	145	13	up	up	ADP
ejpam-4143	145	14	-	-	PUNCT
ejpam-4143	145	15	algebra	algebra	NOUN
ejpam-4143	145	16	h.	h.	NOUN
ejpam-4143	145	17	then	then	ADV
ejpam-4143	145	18	the	the	DET
ejpam-4143	145	19	set	set	NOUN
ejpam-4143	145	20	hµ	hµ	NOUN
ejpam-4143	145	21	=	=	SYM
ejpam-4143	145	22	{	{	PUNCT
ejpam-4143	145	23	x	x	PUNCT
ejpam-4143	145	24	∈	∈	PROPN
ejpam-4143	145	25	h	h	NOUN
ejpam-4143	145	26	:	:	PUNCT
ejpam-4143	145	27	µ(x	µ(x	X
ejpam-4143	145	28	)	)	PUNCT
ejpam-4143	145	29	=	=	SYM
ejpam-4143	145	30	µ(0	µ(0	NOUN
ejpam-4143	145	31	)	)	PUNCT
ejpam-4143	145	32	}	}	PUNCT
ejpam-4143	145	33	is	be	AUX
ejpam-4143	145	34	a	a	DET
ejpam-4143	145	35	hyper	hyper	ADJ
ejpam-4143	145	36	up	up	ADP
ejpam-4143	145	37	-	-	PUNCT
ejpam-4143	145	38	subalgebra	subalgebra	NOUN
ejpam-4143	145	39	of	of	ADP
ejpam-4143	145	40	h.	h.	NOUN
ejpam-4143	145	41	proof	proof	NOUN
ejpam-4143	145	42	.	.	PUNCT
ejpam-4143	146	1	note	note	VERB
ejpam-4143	146	2	that	that	SCONJ
ejpam-4143	146	3	0	0	NUM
ejpam-4143	146	4	∈	∈	NOUN
ejpam-4143	146	5	hµ	hµ	NOUN
ejpam-4143	146	6	so	so	SCONJ
ejpam-4143	146	7	that	that	SCONJ
ejpam-4143	146	8	hµ	hµ	NOUN
ejpam-4143	146	9	̸=	̸=	PROPN
ejpam-4143	146	10	∅.	∅.	ADV
ejpam-4143	146	11	let	let	VERB
ejpam-4143	146	12	x	x	PRON
ejpam-4143	146	13	,	,	PUNCT
ejpam-4143	146	14	y	y	PROPN
ejpam-4143	146	15	∈	∈	PROPN
ejpam-4143	146	16	hµ	hµ	INTJ
ejpam-4143	146	17	and	and	CCONJ
ejpam-4143	146	18	let	let	VERB
ejpam-4143	146	19	a	a	DET
ejpam-4143	146	20	∈	∈	NOUN
ejpam-4143	146	21	x	x	PUNCT
ejpam-4143	146	22	⊛	⊛	ADP
ejpam-4143	146	23	y.	y.	PROPN
ejpam-4143	146	24	then	then	ADV
ejpam-4143	146	25	µ(x	µ(x	X
ejpam-4143	146	26	)	)	PUNCT
ejpam-4143	146	27	=	=	SYM
ejpam-4143	146	28	µ(y	µ(y	NOUN
ejpam-4143	146	29	)	)	PUNCT
ejpam-4143	146	30	=	=	PUNCT
ejpam-4143	146	31	µ(0	µ(0	NOUN
ejpam-4143	146	32	)	)	PUNCT
ejpam-4143	146	33	.	.	PUNCT
ejpam-4143	147	1	since	since	SCONJ
ejpam-4143	147	2	µ	µ	NOUN
ejpam-4143	147	3	is	be	AUX
ejpam-4143	147	4	a	a	DET
ejpam-4143	147	5	fuzzy	fuzzy	ADJ
ejpam-4143	147	6	hyper	hyper	ADJ
ejpam-4143	147	7	up	up	ADP
ejpam-4143	147	8	-	-	PUNCT
ejpam-4143	147	9	subalgebra	subalgebra	NOUN
ejpam-4143	147	10	,	,	PUNCT
ejpam-4143	147	11	µ(a	µ(a	PROPN
ejpam-4143	147	12	)	)	PUNCT
ejpam-4143	147	13	≥	≥	NOUN
ejpam-4143	147	14	µ(0	µ(0	NOUN
ejpam-4143	147	15	)	)	PUNCT
ejpam-4143	147	16	by	by	ADP
ejpam-4143	147	17	definition	definition	NOUN
ejpam-4143	147	18	8	8	NUM
ejpam-4143	147	19	.	.	PUNCT
ejpam-4143	148	1	thus	thus	ADV
ejpam-4143	148	2	,	,	PUNCT
ejpam-4143	148	3	by	by	ADP
ejpam-4143	148	4	lemma	lemma	PROPN
ejpam-4143	148	5	1	1	NUM
ejpam-4143	148	6	,	,	PUNCT
ejpam-4143	148	7	µ(a	µ(a	PROPN
ejpam-4143	148	8	)	)	PUNCT
ejpam-4143	148	9	=	=	PUNCT
ejpam-4143	148	10	µ(0	µ(0	NOUN
ejpam-4143	148	11	)	)	PUNCT
ejpam-4143	148	12	for	for	ADP
ejpam-4143	148	13	all	all	DET
ejpam-4143	148	14	a	a	DET
ejpam-4143	148	15	∈	∈	NOUN
ejpam-4143	148	16	x⊛	x⊛	PROPN
ejpam-4143	148	17	y	y	PROPN
ejpam-4143	148	18	,	,	PUNCT
ejpam-4143	148	19	that	that	ADV
ejpam-4143	148	20	is	is	ADV
ejpam-4143	148	21	,	,	PUNCT
ejpam-4143	148	22	a	a	DET
ejpam-4143	148	23	∈	∈	PROPN
ejpam-4143	148	24	hµ.	hµ.	NOUN
ejpam-4143	148	25	since	since	SCONJ
ejpam-4143	148	26	a	a	PRON
ejpam-4143	148	27	is	be	AUX
ejpam-4143	148	28	an	an	DET
ejpam-4143	148	29	arbitrary	arbitrary	ADJ
ejpam-4143	148	30	element	element	NOUN
ejpam-4143	148	31	of	of	ADP
ejpam-4143	148	32	x⊛y	x⊛y	PROPN
ejpam-4143	148	33	,	,	PUNCT
ejpam-4143	148	34	it	it	PRON
ejpam-4143	148	35	follows	follow	VERB
ejpam-4143	148	36	that	that	SCONJ
ejpam-4143	148	37	x⊛y	x⊛y	PROPN
ejpam-4143	148	38	⊆	⊆	NUM
ejpam-4143	148	39	hµ.	hµ.	PROPN
ejpam-4143	148	40	thus	thus	ADV
ejpam-4143	148	41	,	,	PUNCT
ejpam-4143	148	42	hµ	hµ	INTJ
ejpam-4143	148	43	is	be	VERB
ejpam-4143	148	44	a	a	DET
ejpam-4143	148	45	hyper	hyper	ADJ
ejpam-4143	148	46	up	up	ADP
ejpam-4143	148	47	-	-	PUNCT
ejpam-4143	148	48	subalgebra	subalgebra	NOUN
ejpam-4143	148	49	of	of	ADP
ejpam-4143	148	50	h.	h.	PROPN
ejpam-4143	148	51	lemma	lemma	PROPN
ejpam-4143	149	1	2	2	X
ejpam-4143	149	2	.	.	PUNCT
ejpam-4143	150	1	let	let	VERB
ejpam-4143	150	2	{	{	PUNCT
ejpam-4143	150	3	µα	µα	ADP
ejpam-4143	150	4	:	:	PUNCT
ejpam-4143	150	5	α	α	PROPN
ejpam-4143	150	6	∈	∈	PROPN
ejpam-4143	150	7	a	a	DET
ejpam-4143	150	8	}	}	PUNCT
ejpam-4143	150	9	be	be	AUX
ejpam-4143	150	10	a	a	DET
ejpam-4143	150	11	nonempty	nonempty	ADJ
ejpam-4143	150	12	family	family	NOUN
ejpam-4143	150	13	of	of	ADP
ejpam-4143	150	14	fuzzy	fuzzy	ADJ
ejpam-4143	150	15	hyper	hyper	ADJ
ejpam-4143	150	16	up	up	ADP
ejpam-4143	150	17	-	-	PUNCT
ejpam-4143	150	18	algebras	algebra	NOUN
ejpam-4143	150	19	of	of	ADP
ejpam-4143	150	20	a	a	DET
ejpam-4143	150	21	hyper	hyper	ADJ
ejpam-4143	150	22	up	up	ADP
ejpam-4143	150	23	-	-	PUNCT
ejpam-4143	150	24	algebra	algebra	NOUN
ejpam-4143	150	25	h.	h.	NOUN
ejpam-4143	150	26	then	then	ADV
ejpam-4143	150	27	(	(	PUNCT
ejpam-4143	150	28	i	i	NOUN
ejpam-4143	150	29	)	)	PUNCT
ejpam-4143	150	30	inf	inf	PROPN
ejpam-4143	150	31	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	150	32	{	{	PUNCT
ejpam-4143	150	33	inf	inf	PROPN
ejpam-4143	150	34	α∈a	α∈a	PROPN
ejpam-4143	150	35	{	{	PUNCT
ejpam-4143	150	36	µα(a	µα(a	NOUN
ejpam-4143	150	37	)	)	PUNCT
ejpam-4143	150	38	}	}	PUNCT
ejpam-4143	150	39	}	}	PUNCT
ejpam-4143	150	40	≥	≥	PROPN
ejpam-4143	150	41	inf	inf	PROPN
ejpam-4143	150	42	α∈a	α∈a	PROPN
ejpam-4143	150	43	{	{	PUNCT
ejpam-4143	150	44	inf	inf	PROPN
ejpam-4143	150	45	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	150	46	{	{	PUNCT
ejpam-4143	150	47	µα(a	µα(a	NOUN
ejpam-4143	150	48	)	)	PUNCT
ejpam-4143	150	49	}	}	PUNCT
ejpam-4143	150	50	}	}	PUNCT
ejpam-4143	150	51	.	.	PUNCT
ejpam-4143	151	1	(	(	PUNCT
ejpam-4143	151	2	ii	ii	NOUN
ejpam-4143	151	3	)	)	PUNCT
ejpam-4143	151	4	infα∈a{min{µα(x	infα∈a{min{µα(x	PROPN
ejpam-4143	151	5	)	)	PUNCT
ejpam-4143	151	6	,	,	PUNCT
ejpam-4143	151	7	µα(y	µα(y	NOUN
ejpam-4143	151	8	)	)	PUNCT
ejpam-4143	151	9	}	}	PUNCT
ejpam-4143	151	10	}	}	PUNCT
ejpam-4143	151	11	≥	≥	NOUN
ejpam-4143	151	12	min	min	PROPN
ejpam-4143	151	13	{	{	PUNCT
ejpam-4143	151	14	inf	inf	NOUN
ejpam-4143	151	15	α∈a	α∈a	PROPN
ejpam-4143	151	16	{	{	PUNCT
ejpam-4143	151	17	µα(x	µα(x	NUM
ejpam-4143	151	18	)	)	PUNCT
ejpam-4143	151	19	}	}	PUNCT
ejpam-4143	151	20	,	,	PUNCT
ejpam-4143	151	21	inf	inf	PROPN
ejpam-4143	151	22	α∈a	α∈a	NOUN
ejpam-4143	151	23	{	{	PUNCT
ejpam-4143	151	24	µα(y	µα(y	NOUN
ejpam-4143	151	25	)	)	PUNCT
ejpam-4143	151	26	}	}	PUNCT
ejpam-4143	151	27	}	}	PUNCT
ejpam-4143	151	28	.	.	PUNCT
ejpam-4143	152	1	proof	proof	NOUN
ejpam-4143	152	2	.	.	PUNCT
ejpam-4143	153	1	let	let	VERB
ejpam-4143	153	2	{	{	PUNCT
ejpam-4143	153	3	µα	µα	ADP
ejpam-4143	153	4	:	:	PUNCT
ejpam-4143	153	5	α	α	PROPN
ejpam-4143	153	6	∈	∈	PROPN
ejpam-4143	153	7	a	a	DET
ejpam-4143	153	8	}	}	PUNCT
ejpam-4143	153	9	be	be	AUX
ejpam-4143	153	10	a	a	DET
ejpam-4143	153	11	nonempty	nonempty	ADJ
ejpam-4143	153	12	family	family	NOUN
ejpam-4143	153	13	of	of	ADP
ejpam-4143	153	14	fuzzy	fuzzy	ADJ
ejpam-4143	153	15	hyper	hyper	ADJ
ejpam-4143	153	16	up	up	ADP
ejpam-4143	153	17	-	-	PUNCT
ejpam-4143	153	18	subalgebras	subalgebra	NOUN
ejpam-4143	153	19	of	of	ADP
ejpam-4143	153	20	h	h	NOUN
ejpam-4143	153	21	and	and	CCONJ
ejpam-4143	153	22	let	let	VERB
ejpam-4143	153	23	x	x	PRON
ejpam-4143	153	24	,	,	PUNCT
ejpam-4143	153	25	y	y	PROPN
ejpam-4143	153	26	∈	∈	PROPN
ejpam-4143	153	27	h.	h.	PROPN
ejpam-4143	153	28	(	(	PUNCT
ejpam-4143	153	29	i	i	NOUN
ejpam-4143	153	30	)	)	PUNCT
ejpam-4143	153	31	for	for	ADP
ejpam-4143	153	32	all	all	DET
ejpam-4143	153	33	a	a	DET
ejpam-4143	153	34	∈	∈	NOUN
ejpam-4143	153	35	x	x	PUNCT
ejpam-4143	153	36	⊛	⊛	NUM
ejpam-4143	153	37	y	y	PROPN
ejpam-4143	153	38	,	,	PUNCT
ejpam-4143	153	39	we	we	PRON
ejpam-4143	153	40	have	have	VERB
ejpam-4143	153	41	µα(a	µα(a	NUM
ejpam-4143	153	42	)	)	PUNCT
ejpam-4143	153	43	≥	≥	PROPN
ejpam-4143	153	44	infa∈x⊛y{µα(a	infa∈x⊛y{µα(a	NOUN
ejpam-4143	153	45	)	)	PUNCT
ejpam-4143	153	46	}	}	PUNCT
ejpam-4143	153	47	for	for	ADP
ejpam-4143	153	48	all	all	DET
ejpam-4143	153	49	α	α	DET
ejpam-4143	153	50	∈	∈	NOUN
ejpam-4143	153	51	a.	a.	NOUN
ejpam-4143	153	52	thus	thus	ADV
ejpam-4143	153	53	,	,	PUNCT
ejpam-4143	153	54	for	for	ADP
ejpam-4143	153	55	all	all	DET
ejpam-4143	153	56	a	a	DET
ejpam-4143	153	57	∈	∈	NOUN
ejpam-4143	153	58	x⊛	x⊛	PROPN
ejpam-4143	153	59	y	y	PROPN
ejpam-4143	153	60	,	,	PUNCT
ejpam-4143	153	61	infα∈a{µα(a	infα∈a{µα(a	NOUN
ejpam-4143	153	62	)	)	PUNCT
ejpam-4143	153	63	}	}	PUNCT
ejpam-4143	153	64	≥	≥	PROPN
ejpam-4143	153	65	infa∈x⊛y{µα(a	infa∈x⊛y{µα(a	NOUN
ejpam-4143	153	66	)	)	PUNCT
ejpam-4143	153	67	}	}	PUNCT
ejpam-4143	153	68	≥	≥	NOUN
ejpam-4143	153	69	infα∈a{infa∈x⊛y{µα(a	infα∈a{infa∈x⊛y{µα(a	NOUN
ejpam-4143	153	70	)	)	PUNCT
ejpam-4143	153	71	}	}	PUNCT
ejpam-4143	153	72	}	}	PUNCT
ejpam-4143	153	73	.	.	PUNCT
ejpam-4143	154	1	hence	hence	ADV
ejpam-4143	154	2	,	,	PUNCT
ejpam-4143	154	3	infa∈x⊛y{infα∈a{µα(a	infa∈x⊛y{infα∈a{µα(a	PROPN
ejpam-4143	154	4	)	)	PUNCT
ejpam-4143	154	5	}	}	PUNCT
ejpam-4143	154	6	}	}	PUNCT
ejpam-4143	154	7	≥	≥	NOUN
ejpam-4143	154	8	infα∈a{infa∈x⊛y{µα(a	infα∈a{infa∈x⊛y{µα(a	NOUN
ejpam-4143	154	9	)	)	PUNCT
ejpam-4143	154	10	}	}	PUNCT
ejpam-4143	154	11	}	}	PUNCT
ejpam-4143	154	12	.	.	PUNCT
ejpam-4143	155	1	(	(	PUNCT
ejpam-4143	155	2	ii	ii	NOUN
ejpam-4143	155	3	)	)	PUNCT
ejpam-4143	155	4	note	note	VERB
ejpam-4143	155	5	that	that	SCONJ
ejpam-4143	155	6	µα(x	µα(x	NUM
ejpam-4143	155	7	)	)	PUNCT
ejpam-4143	155	8	≥	≥	NOUN
ejpam-4143	155	9	infα∈a{µα(x	infα∈a{µα(x	NUM
ejpam-4143	155	10	)	)	PUNCT
ejpam-4143	155	11	}	}	PUNCT
ejpam-4143	155	12	and	and	CCONJ
ejpam-4143	155	13	µα(y	µα(y	NOUN
ejpam-4143	155	14	)	)	PUNCT
ejpam-4143	155	15	≥	≥	NOUN
ejpam-4143	155	16	infα∈a{µα(y	infα∈a{µα(y	NUM
ejpam-4143	155	17	)	)	PUNCT
ejpam-4143	155	18	}	}	PUNCT
ejpam-4143	155	19	.	.	PUNCT
ejpam-4143	156	1	then	then	ADV
ejpam-4143	156	2	,	,	PUNCT
ejpam-4143	156	3	{	{	PUNCT
ejpam-4143	156	4	min{µα(x	min{µα(x	PROPN
ejpam-4143	156	5	)	)	PUNCT
ejpam-4143	156	6	,	,	PUNCT
ejpam-4143	156	7	µα(y	µα(y	NOUN
ejpam-4143	156	8	)	)	PUNCT
ejpam-4143	156	9	}	}	PUNCT
ejpam-4143	156	10	}	}	PUNCT
ejpam-4143	156	11	≥	≥	NOUN
ejpam-4143	156	12	min	min	PROPN
ejpam-4143	156	13	{	{	PUNCT
ejpam-4143	156	14	inf	inf	NOUN
ejpam-4143	156	15	α∈a	α∈a	PROPN
ejpam-4143	156	16	{	{	PUNCT
ejpam-4143	156	17	µα(x	µα(x	NUM
ejpam-4143	156	18	)	)	PUNCT
ejpam-4143	156	19	}	}	PUNCT
ejpam-4143	156	20	,	,	PUNCT
ejpam-4143	156	21	inf	inf	PROPN
ejpam-4143	156	22	α∈a	α∈a	NOUN
ejpam-4143	156	23	{	{	PUNCT
ejpam-4143	156	24	µα(y	µα(y	NOUN
ejpam-4143	156	25	)	)	PUNCT
ejpam-4143	156	26	}	}	PUNCT
ejpam-4143	156	27	.	.	PUNCT
ejpam-4143	157	1	thus	thus	ADV
ejpam-4143	157	2	,	,	PUNCT
ejpam-4143	157	3	infα∈a{min{µα(x	infα∈a{min{µα(x	PROPN
ejpam-4143	157	4	)	)	PUNCT
ejpam-4143	157	5	,	,	PUNCT
ejpam-4143	157	6	µα(y	µα(y	NOUN
ejpam-4143	157	7	)	)	PUNCT
ejpam-4143	157	8	}	}	PUNCT
ejpam-4143	157	9	}	}	PUNCT
ejpam-4143	157	10	≥	≥	NOUN
ejpam-4143	157	11	min	min	PROPN
ejpam-4143	157	12	{	{	PUNCT
ejpam-4143	157	13	inf	inf	NOUN
ejpam-4143	157	14	α∈a	α∈a	PROPN
ejpam-4143	157	15	{	{	PUNCT
ejpam-4143	157	16	µα(x	µα(x	NUM
ejpam-4143	157	17	)	)	PUNCT
ejpam-4143	157	18	}	}	PUNCT
ejpam-4143	157	19	,	,	PUNCT
ejpam-4143	157	20	inf	inf	PROPN
ejpam-4143	157	21	α∈a	α∈a	NOUN
ejpam-4143	157	22	{	{	PUNCT
ejpam-4143	157	23	µα(y	µα(y	NOUN
ejpam-4143	157	24	)	)	PUNCT
ejpam-4143	157	25	}	}	PUNCT
ejpam-4143	157	26	.	.	PUNCT
ejpam-4143	158	1	hence	hence	ADV
ejpam-4143	158	2	,	,	PUNCT
ejpam-4143	158	3	the	the	DET
ejpam-4143	158	4	conclusion	conclusion	NOUN
ejpam-4143	158	5	follows	follow	VERB
ejpam-4143	158	6	.	.	PUNCT
ejpam-4143	159	1	example	example	NOUN
ejpam-4143	159	2	5	5	NUM
ejpam-4143	159	3	.	.	PUNCT
ejpam-4143	160	1	let	let	VERB
ejpam-4143	160	2	h	h	NOUN
ejpam-4143	160	3	=	=	PRON
ejpam-4143	160	4	{	{	PUNCT
ejpam-4143	160	5	0	0	NUM
ejpam-4143	160	6	,	,	PUNCT
ejpam-4143	160	7	1	1	NUM
ejpam-4143	160	8	,	,	PUNCT
ejpam-4143	160	9	2	2	NUM
ejpam-4143	160	10	,	,	PUNCT
ejpam-4143	160	11	3	3	NUM
ejpam-4143	160	12	}	}	PUNCT
ejpam-4143	160	13	be	be	AUX
ejpam-4143	160	14	a	a	DET
ejpam-4143	160	15	set	set	NOUN
ejpam-4143	160	16	.	.	PUNCT
ejpam-4143	161	1	define	define	VERB
ejpam-4143	161	2	the	the	DET
ejpam-4143	161	3	hyperoperation	hyperoperation	NOUN
ejpam-4143	161	4	⊛	⊛	NUM
ejpam-4143	161	5	by	by	ADP
ejpam-4143	161	6	the	the	DET
ejpam-4143	161	7	following	following	ADJ
ejpam-4143	161	8	cayley	cayley	ADJ
ejpam-4143	161	9	table	table	NOUN
ejpam-4143	161	10	:	:	PUNCT
ejpam-4143	161	11	⊛	⊛	NUM
ejpam-4143	162	1	0	0	NUM
ejpam-4143	162	2	1	1	NUM
ejpam-4143	162	3	2	2	NUM
ejpam-4143	162	4	3	3	NUM
ejpam-4143	162	5	0	0	NUM
ejpam-4143	162	6	{	{	PUNCT
ejpam-4143	162	7	0	0	NUM
ejpam-4143	162	8	}	}	PUNCT
ejpam-4143	162	9	{	{	PUNCT
ejpam-4143	162	10	1	1	NUM
ejpam-4143	162	11	}	}	PUNCT
ejpam-4143	162	12	{	{	PUNCT
ejpam-4143	162	13	2	2	NUM
ejpam-4143	162	14	}	}	PUNCT
ejpam-4143	162	15	{	{	PUNCT
ejpam-4143	162	16	3	3	NUM
ejpam-4143	162	17	}	}	SYM
ejpam-4143	162	18	1	1	NUM
ejpam-4143	162	19	{	{	PUNCT
ejpam-4143	162	20	0	0	NUM
ejpam-4143	162	21	}	}	PUNCT
ejpam-4143	162	22	{	{	PUNCT
ejpam-4143	162	23	0	0	NUM
ejpam-4143	162	24	,	,	PUNCT
ejpam-4143	162	25	1	1	NUM
ejpam-4143	162	26	}	}	PUNCT
ejpam-4143	162	27	{	{	PUNCT
ejpam-4143	162	28	1	1	NUM
ejpam-4143	162	29	,	,	PUNCT
ejpam-4143	162	30	2	2	NUM
ejpam-4143	162	31	,	,	PUNCT
ejpam-4143	162	32	3	3	NUM
ejpam-4143	162	33	}	}	PUNCT
ejpam-4143	162	34	{	{	PUNCT
ejpam-4143	162	35	0	0	NUM
ejpam-4143	162	36	,	,	PUNCT
ejpam-4143	162	37	3	3	NUM
ejpam-4143	162	38	}	}	SYM
ejpam-4143	162	39	2	2	NUM
ejpam-4143	162	40	{	{	PUNCT
ejpam-4143	162	41	0	0	NUM
ejpam-4143	162	42	}	}	PUNCT
ejpam-4143	162	43	{	{	PUNCT
ejpam-4143	162	44	0	0	NUM
ejpam-4143	162	45	,	,	PUNCT
ejpam-4143	162	46	1	1	NUM
ejpam-4143	162	47	}	}	PUNCT
ejpam-4143	162	48	{	{	PUNCT
ejpam-4143	162	49	0	0	NUM
ejpam-4143	162	50	,	,	PUNCT
ejpam-4143	162	51	2	2	NUM
ejpam-4143	162	52	}	}	PUNCT
ejpam-4143	162	53	{	{	PUNCT
ejpam-4143	162	54	0	0	NUM
ejpam-4143	162	55	,	,	PUNCT
ejpam-4143	162	56	3	3	NUM
ejpam-4143	162	57	}	}	SYM
ejpam-4143	162	58	3	3	NUM
ejpam-4143	162	59	{	{	PUNCT
ejpam-4143	162	60	0	0	NUM
ejpam-4143	162	61	}	}	PUNCT
ejpam-4143	162	62	{	{	PUNCT
ejpam-4143	162	63	1	1	NUM
ejpam-4143	162	64	}	}	PUNCT
ejpam-4143	162	65	{	{	PUNCT
ejpam-4143	162	66	1	1	NUM
ejpam-4143	162	67	,	,	PUNCT
ejpam-4143	162	68	2	2	NUM
ejpam-4143	162	69	,	,	PUNCT
ejpam-4143	162	70	3	3	NUM
ejpam-4143	162	71	}	}	PUNCT
ejpam-4143	162	72	{	{	PUNCT
ejpam-4143	162	73	0	0	NUM
ejpam-4143	162	74	,	,	PUNCT
ejpam-4143	162	75	3	3	NUM
ejpam-4143	162	76	}	}	PUNCT
ejpam-4143	162	77	by	by	ADP
ejpam-4143	162	78	routine	routine	ADJ
ejpam-4143	162	79	calculations	calculation	NOUN
ejpam-4143	162	80	,	,	PUNCT
ejpam-4143	162	81	(	(	PUNCT
ejpam-4143	162	82	h;⊛	h;⊛	X
ejpam-4143	162	83	,	,	PUNCT
ejpam-4143	162	84	0	0	NUM
ejpam-4143	162	85	)	)	PUNCT
ejpam-4143	162	86	is	be	AUX
ejpam-4143	162	87	a	a	DET
ejpam-4143	162	88	hyper	hyper	ADJ
ejpam-4143	162	89	up	up	NOUN
ejpam-4143	162	90	-	-	PUNCT
ejpam-4143	162	91	algebra	algebra	NOUN
ejpam-4143	162	92	.	.	PUNCT
ejpam-4143	163	1	define	define	VERB
ejpam-4143	163	2	a	a	DET
ejpam-4143	163	3	fuzzy	fuzzy	ADJ
ejpam-4143	163	4	subset	subset	ADJ
ejpam-4143	163	5	µ	µ	X
ejpam-4143	163	6	:	:	PUNCT
ejpam-4143	163	7	h	h	NOUN
ejpam-4143	163	8	→	→	PUNCT
ejpam-4143	164	1	[	[	X
ejpam-4143	164	2	0	0	NUM
ejpam-4143	164	3	,	,	PUNCT
ejpam-4143	164	4	1	1	NUM
ejpam-4143	164	5	]	]	PUNCT
ejpam-4143	164	6	by	by	ADP
ejpam-4143	164	7	µ(0	µ(0	NOUN
ejpam-4143	164	8	)	)	PUNCT
ejpam-4143	164	9	=	=	SYM
ejpam-4143	164	10	0.9	0.9	NUM
ejpam-4143	164	11	,	,	PUNCT
ejpam-4143	164	12	µ(1	µ(1	PROPN
ejpam-4143	164	13	)	)	PUNCT
ejpam-4143	164	14	=	=	PUNCT
ejpam-4143	164	15	0.7	0.7	NUM
ejpam-4143	164	16	,	,	PUNCT
ejpam-4143	164	17	µ(2	µ(2	PROPN
ejpam-4143	164	18	)	)	PUNCT
ejpam-4143	164	19	=	=	NUM
ejpam-4143	164	20	0.4	0.4	NUM
ejpam-4143	164	21	,	,	PUNCT
ejpam-4143	164	22	µ(3	µ(3	PROPN
ejpam-4143	164	23	)	)	PUNCT
ejpam-4143	164	24	=	=	PUNCT
ejpam-4143	164	25	0.2	0.2	NUM
ejpam-4143	164	26	.	.	PUNCT
ejpam-4143	165	1	let	let	VERB
ejpam-4143	165	2	a	a	PRON
ejpam-4143	165	3	=	=	PUNCT
ejpam-4143	165	4	{	{	PUNCT
ejpam-4143	165	5	0	0	NUM
ejpam-4143	165	6	,	,	PUNCT
ejpam-4143	165	7	1	1	NUM
ejpam-4143	165	8	}	}	PUNCT
ejpam-4143	165	9	and	and	CCONJ
ejpam-4143	165	10	b	b	X
ejpam-4143	165	11	=	=	SYM
ejpam-4143	165	12	{	{	PUNCT
ejpam-4143	165	13	0	0	NUM
ejpam-4143	165	14	,	,	PUNCT
ejpam-4143	165	15	2	2	NUM
ejpam-4143	165	16	}	}	PUNCT
ejpam-4143	165	17	.	.	PUNCT
ejpam-4143	166	1	by	by	ADP
ejpam-4143	166	2	routine	routine	ADJ
ejpam-4143	166	3	calculations	calculation	NOUN
ejpam-4143	166	4	,	,	PUNCT
ejpam-4143	166	5	µa	µa	ADV
ejpam-4143	166	6	and	and	CCONJ
ejpam-4143	166	7	µb	µb	VERB
ejpam-4143	166	8	are	be	AUX
ejpam-4143	166	9	fuzzy	fuzzy	ADJ
ejpam-4143	166	10	hyper	hyper	ADJ
ejpam-4143	166	11	up	up	ADP
ejpam-4143	166	12	-	-	PUNCT
ejpam-4143	166	13	subalgebras	subalgebras	PROPN
ejpam-4143	166	14	of	of	ADP
ejpam-4143	166	15	h.	h.	PROPN
ejpam-4143	166	16	but	but	CCONJ
ejpam-4143	166	17	µa∪b	µa∪b	ADJ
ejpam-4143	166	18	is	be	AUX
ejpam-4143	166	19	not	not	PART
ejpam-4143	166	20	a	a	DET
ejpam-4143	166	21	fuzzy	fuzzy	ADJ
ejpam-4143	166	22	hyper	hyper	ADJ
ejpam-4143	166	23	up	up	ADP
ejpam-4143	166	24	-	-	PUNCT
ejpam-4143	166	25	subalgebra	subalgebra	NOUN
ejpam-4143	166	26	of	of	ADP
ejpam-4143	166	27	h	h	NOUN
ejpam-4143	166	28	since	since	SCONJ
ejpam-4143	166	29	0.2	0.2	NUM
ejpam-4143	166	30	=	=	SYM
ejpam-4143	166	31	infa∈1⊛2{µ(a	infa∈1⊛2{µ(a	PROPN
ejpam-4143	166	32	)	)	PUNCT
ejpam-4143	166	33	}	}	PUNCT
ejpam-4143	166	34	<	<	X
ejpam-4143	166	35	min{µ(1	min{µ(1	PROPN
ejpam-4143	166	36	)	)	PUNCT
ejpam-4143	166	37	,	,	PUNCT
ejpam-4143	166	38	µ(2	µ(2	PROPN
ejpam-4143	166	39	)	)	PUNCT
ejpam-4143	166	40	}	}	PUNCT
ejpam-4143	166	41	=	=	PUNCT
ejpam-4143	166	42	0.4	0.4	NUM
ejpam-4143	166	43	.	.	PUNCT
ejpam-4143	167	1	r.	r.	PROPN
ejpam-4143	167	2	amairanto	amairanto	PROPN
ejpam-4143	167	3	,	,	PUNCT
ejpam-4143	167	4	r.	r.	PROPN
ejpam-4143	167	5	isla	isla	PROPN
ejpam-4143	167	6	/	/	SYM
ejpam-4143	167	7	eur	eur	PROPN
ejpam-4143	167	8	.	.	PUNCT
ejpam-4143	168	1	j.	j.	PROPN
ejpam-4143	168	2	pure	pure	PROPN
ejpam-4143	168	3	appl	appl	PROPN
ejpam-4143	168	4	.	.	PROPN
ejpam-4143	168	5	math	math	PROPN
ejpam-4143	168	6	,	,	PUNCT
ejpam-4143	168	7	14	14	NUM
ejpam-4143	168	8	(	(	PUNCT
ejpam-4143	168	9	4	4	NUM
ejpam-4143	168	10	)	)	PUNCT
ejpam-4143	168	11	(	(	PUNCT
ejpam-4143	168	12	2021	2021	NUM
ejpam-4143	168	13	)	)	PUNCT
ejpam-4143	168	14	,	,	PUNCT
ejpam-4143	168	15	1388	1388	NUM
ejpam-4143	168	16	-	-	SYM
ejpam-4143	168	17	1401	1401	NUM
ejpam-4143	168	18	1394	1394	NUM
ejpam-4143	168	19	remark	remark	NOUN
ejpam-4143	168	20	1	1	NUM
ejpam-4143	168	21	.	.	PUNCT
ejpam-4143	169	1	the	the	DET
ejpam-4143	169	2	union	union	NOUN
ejpam-4143	169	3	of	of	ADP
ejpam-4143	169	4	two	two	NUM
ejpam-4143	169	5	fuzzy	fuzzy	ADJ
ejpam-4143	169	6	hyper	hyper	ADJ
ejpam-4143	169	7	up	up	ADP
ejpam-4143	169	8	-	-	PUNCT
ejpam-4143	169	9	subalgebras	subalgebra	NOUN
ejpam-4143	169	10	of	of	ADP
ejpam-4143	169	11	a	a	DET
ejpam-4143	169	12	hyper	hyper	ADJ
ejpam-4143	169	13	up	up	ADP
ejpam-4143	169	14	-	-	PUNCT
ejpam-4143	169	15	algebra	algebra	NOUN
ejpam-4143	169	16	h	h	NOUN
ejpam-4143	169	17	is	be	AUX
ejpam-4143	169	18	not	not	PART
ejpam-4143	169	19	necessarily	necessarily	ADV
ejpam-4143	169	20	a	a	DET
ejpam-4143	169	21	fuzzy	fuzzy	ADJ
ejpam-4143	169	22	hyper	hyper	ADJ
ejpam-4143	169	23	up	up	ADP
ejpam-4143	169	24	-	-	PUNCT
ejpam-4143	169	25	subalgebra	subalgebra	NOUN
ejpam-4143	169	26	of	of	ADP
ejpam-4143	169	27	h.	h.	PROPN
ejpam-4143	169	28	theorem	theorem	PROPN
ejpam-4143	169	29	4	4	NUM
ejpam-4143	169	30	.	.	PUNCT
ejpam-4143	170	1	the	the	DET
ejpam-4143	170	2	intersection	intersection	NOUN
ejpam-4143	170	3	of	of	ADP
ejpam-4143	170	4	any	any	DET
ejpam-4143	170	5	nonempty	nonempty	ADJ
ejpam-4143	170	6	family	family	NOUN
ejpam-4143	170	7	of	of	ADP
ejpam-4143	170	8	fuzzy	fuzzy	ADJ
ejpam-4143	170	9	hyper	hyper	ADJ
ejpam-4143	170	10	up	up	ADP
ejpam-4143	170	11	-	-	PUNCT
ejpam-4143	170	12	subalgebras	subalgebra	NOUN
ejpam-4143	170	13	of	of	ADP
ejpam-4143	170	14	a	a	DET
ejpam-4143	170	15	hyper	hyper	ADJ
ejpam-4143	170	16	up	up	ADP
ejpam-4143	170	17	-	-	PUNCT
ejpam-4143	170	18	algebra	algebra	NOUN
ejpam-4143	170	19	h	h	NOUN
ejpam-4143	170	20	is	be	AUX
ejpam-4143	170	21	also	also	ADV
ejpam-4143	170	22	a	a	DET
ejpam-4143	170	23	fuzzy	fuzzy	ADJ
ejpam-4143	170	24	hyper	hyper	ADJ
ejpam-4143	170	25	up	up	ADP
ejpam-4143	170	26	-	-	PUNCT
ejpam-4143	170	27	subalgebra	subalgebra	NOUN
ejpam-4143	170	28	of	of	ADP
ejpam-4143	170	29	h.	h.	NOUN
ejpam-4143	170	30	proof	proof	NOUN
ejpam-4143	170	31	.	.	PUNCT
ejpam-4143	171	1	let	let	VERB
ejpam-4143	171	2	{	{	PUNCT
ejpam-4143	171	3	µα	µα	ADP
ejpam-4143	171	4	:	:	PUNCT
ejpam-4143	171	5	α	α	PROPN
ejpam-4143	171	6	∈	∈	PROPN
ejpam-4143	171	7	a	a	DET
ejpam-4143	171	8	}	}	PUNCT
ejpam-4143	171	9	be	be	AUX
ejpam-4143	171	10	a	a	DET
ejpam-4143	171	11	nonempty	nonempty	ADJ
ejpam-4143	171	12	family	family	NOUN
ejpam-4143	171	13	of	of	ADP
ejpam-4143	171	14	fuzzy	fuzzy	ADJ
ejpam-4143	171	15	hyper	hyper	ADJ
ejpam-4143	171	16	up	up	ADP
ejpam-4143	171	17	-	-	PUNCT
ejpam-4143	171	18	subalgebras	subalgebras	PROPN
ejpam-4143	171	19	of	of	ADP
ejpam-4143	171	20	h.	h.	PROPN
ejpam-4143	171	21	let	let	VERB
ejpam-4143	171	22	x	x	PRON
ejpam-4143	171	23	,	,	PUNCT
ejpam-4143	171	24	y	y	PROPN
ejpam-4143	171	25	∈	∈	PROPN
ejpam-4143	171	26	h.	h.	PROPN
ejpam-4143	171	27	then	then	ADV
ejpam-4143	171	28	by	by	ADP
ejpam-4143	171	29	definitions	definition	NOUN
ejpam-4143	171	30	7	7	NUM
ejpam-4143	171	31	and	and	CCONJ
ejpam-4143	171	32	8	8	NUM
ejpam-4143	171	33	and	and	CCONJ
ejpam-4143	171	34	lemma	lemma	PROPN
ejpam-4143	171	35	2(i	2(i	NUM
ejpam-4143	171	36	)	)	PUNCT
ejpam-4143	171	37	and	and	CCONJ
ejpam-4143	171	38	(	(	PUNCT
ejpam-4143	171	39	ii	ii	NOUN
ejpam-4143	171	40	)	)	PUNCT
ejpam-4143	171	41	,	,	PUNCT
ejpam-4143	171	42	inf	inf	PROPN
ejpam-4143	171	43	a∈x⊛y	a∈x⊛y	NOUN
ejpam-4143	171	44	{	{	PUNCT
ejpam-4143	171	45	∧α∈aµα(a	∧α∈aµα(a	NOUN
ejpam-4143	171	46	)	)	PUNCT
ejpam-4143	171	47	}	}	PUNCT
ejpam-4143	171	48	=	=	SYM
ejpam-4143	172	1	inf	inf	ADJ
ejpam-4143	172	2	a∈x⊛y	a∈x⊛y	NOUN
ejpam-4143	172	3	{	{	PUNCT
ejpam-4143	172	4	inf	inf	PROPN
ejpam-4143	172	5	α∈a	α∈a	PROPN
ejpam-4143	172	6	{	{	PUNCT
ejpam-4143	172	7	µα(a	µα(a	NOUN
ejpam-4143	172	8	)	)	PUNCT
ejpam-4143	172	9	}	}	PUNCT
ejpam-4143	172	10	}	}	PUNCT
ejpam-4143	172	11	≥	≥	NOUN
ejpam-4143	172	12	infα∈a{infa∈x⊛y{µα(a	infα∈a{infa∈x⊛y{µα(a	NOUN
ejpam-4143	172	13	)	)	PUNCT
ejpam-4143	172	14	}	}	PUNCT
ejpam-4143	172	15	}	}	PUNCT
ejpam-4143	172	16	≥	≥	X
ejpam-4143	172	17	infα∈a{min{µα(x	infα∈a{min{µα(x	PROPN
ejpam-4143	172	18	)	)	PUNCT
ejpam-4143	172	19	,	,	PUNCT
ejpam-4143	172	20	µα(y	µα(y	NOUN
ejpam-4143	172	21	)	)	PUNCT
ejpam-4143	172	22	}	}	PUNCT
ejpam-4143	172	23	}	}	PUNCT
ejpam-4143	172	24	≥	≥	PROPN
ejpam-4143	172	25	min{infα∈a{µα(x	min{infα∈a{µα(x	PROPN
ejpam-4143	172	26	)	)	PUNCT
ejpam-4143	172	27	}	}	PUNCT
ejpam-4143	172	28	,	,	PUNCT
ejpam-4143	172	29	infα∈a{µα(y	infα∈a{µα(y	X
ejpam-4143	172	30	)	)	PUNCT
ejpam-4143	172	31	}	}	PUNCT
ejpam-4143	172	32	}	}	PUNCT
ejpam-4143	172	33	=	=	SYM
ejpam-4143	172	34	min{∧α∈aµα(x),∧α∈aµα(y	min{∧α∈aµα(x),∧α∈aµα(y	NOUN
ejpam-4143	172	35	)	)	PUNCT
ejpam-4143	172	36	}	}	PUNCT
ejpam-4143	172	37	.	.	PUNCT
ejpam-4143	173	1	hence	hence	ADV
ejpam-4143	173	2	,	,	PUNCT
ejpam-4143	173	3	the	the	DET
ejpam-4143	173	4	conclusion	conclusion	NOUN
ejpam-4143	173	5	follows	follow	VERB
ejpam-4143	173	6	.	.	PUNCT
ejpam-4143	174	1	theorem	theorem	ADJ
ejpam-4143	174	2	5	5	NUM
ejpam-4143	174	3	.	.	PUNCT
ejpam-4143	175	1	let	let	VERB
ejpam-4143	175	2	k	k	PRON
ejpam-4143	175	3	be	be	AUX
ejpam-4143	175	4	a	a	DET
ejpam-4143	175	5	nonempty	nonempty	ADJ
ejpam-4143	175	6	subset	subset	NOUN
ejpam-4143	175	7	of	of	ADP
ejpam-4143	175	8	a	a	DET
ejpam-4143	175	9	hyper	hyper	ADJ
ejpam-4143	175	10	up	up	ADP
ejpam-4143	175	11	-	-	PUNCT
ejpam-4143	175	12	algebra	algebra	NOUN
ejpam-4143	175	13	h	h	NOUN
ejpam-4143	175	14	and	and	CCONJ
ejpam-4143	175	15	let	let	VERB
ejpam-4143	175	16	α	α	PRON
ejpam-4143	175	17	,	,	PUNCT
ejpam-4143	175	18	β	β	X
ejpam-4143	175	19	∈	∈	PROPN
ejpam-4143	176	1	[	[	X
ejpam-4143	176	2	0	0	NUM
ejpam-4143	176	3	,	,	PUNCT
ejpam-4143	176	4	1	1	NUM
ejpam-4143	176	5	]	]	PUNCT
ejpam-4143	176	6	with	with	ADP
ejpam-4143	176	7	α	α	PROPN
ejpam-4143	176	8	>	>	X
ejpam-4143	176	9	β	β	X
ejpam-4143	176	10	.	.	PUNCT
ejpam-4143	177	1	let	let	VERB
ejpam-4143	177	2	µk	µk	PRON
ejpam-4143	177	3	be	be	AUX
ejpam-4143	177	4	a	a	DET
ejpam-4143	177	5	fuzzy	fuzzy	ADJ
ejpam-4143	177	6	subset	subset	NOUN
ejpam-4143	177	7	of	of	ADP
ejpam-4143	177	8	h	h	NOUN
ejpam-4143	177	9	defined	define	VERB
ejpam-4143	177	10	by	by	ADP
ejpam-4143	177	11	µk(x	µk(x	NOUN
ejpam-4143	177	12	)	)	PUNCT
ejpam-4143	178	1	=	=	SYM
ejpam-4143	178	2	{	{	PUNCT
ejpam-4143	178	3	α	α	NOUN
ejpam-4143	178	4	,	,	PUNCT
ejpam-4143	178	5	if	if	SCONJ
ejpam-4143	178	6	x	x	PROPN
ejpam-4143	178	7	∈	∈	PROPN
ejpam-4143	178	8	k	k	X
ejpam-4143	179	1	β	β	X
ejpam-4143	179	2	,	,	PUNCT
ejpam-4143	179	3	if	if	SCONJ
ejpam-4143	179	4	x	x	X
ejpam-4143	179	5	/∈	/∈	PROPN
ejpam-4143	179	6	k	k	PROPN
ejpam-4143	179	7	for	for	ADP
ejpam-4143	179	8	all	all	DET
ejpam-4143	179	9	x	x	SYM
ejpam-4143	179	10	∈	∈	PROPN
ejpam-4143	179	11	h.	h.	NOUN
ejpam-4143	179	12	then	then	ADV
ejpam-4143	179	13	µk	µk	PRON
ejpam-4143	179	14	is	be	AUX
ejpam-4143	179	15	a	a	DET
ejpam-4143	179	16	fuzzy	fuzzy	ADJ
ejpam-4143	179	17	hyper	hyper	ADJ
ejpam-4143	179	18	up	up	ADP
ejpam-4143	179	19	-	-	PUNCT
ejpam-4143	179	20	subalgebra	subalgebra	NOUN
ejpam-4143	179	21	of	of	ADP
ejpam-4143	179	22	h	h	NOUN
ejpam-4143	179	23	if	if	SCONJ
ejpam-4143	180	1	and	and	CCONJ
ejpam-4143	180	2	only	only	ADV
ejpam-4143	180	3	if	if	SCONJ
ejpam-4143	180	4	k	k	PROPN
ejpam-4143	180	5	is	be	AUX
ejpam-4143	180	6	a	a	DET
ejpam-4143	180	7	hyper	hyper	ADJ
ejpam-4143	180	8	up	up	ADP
ejpam-4143	180	9	-	-	PUNCT
ejpam-4143	180	10	subalgebra	subalgebra	NOUN
ejpam-4143	180	11	of	of	ADP
ejpam-4143	180	12	h.	h.	NOUN
ejpam-4143	180	13	proof	proof	NOUN
ejpam-4143	180	14	.	.	PUNCT
ejpam-4143	181	1	suppose	suppose	VERB
ejpam-4143	181	2	that	that	SCONJ
ejpam-4143	181	3	µk	µk	PROPN
ejpam-4143	181	4	is	be	AUX
ejpam-4143	181	5	a	a	DET
ejpam-4143	181	6	fuzzy	fuzzy	ADJ
ejpam-4143	181	7	hyper	hyper	ADJ
ejpam-4143	181	8	up	up	ADP
ejpam-4143	181	9	-	-	PUNCT
ejpam-4143	181	10	subalgebra	subalgebra	NOUN
ejpam-4143	181	11	of	of	ADP
ejpam-4143	181	12	h	h	NOUN
ejpam-4143	181	13	and	and	CCONJ
ejpam-4143	181	14	let	let	VERB
ejpam-4143	181	15	x	x	PRON
ejpam-4143	181	16	,	,	PUNCT
ejpam-4143	181	17	y	y	PROPN
ejpam-4143	181	18	∈	∈	PROPN
ejpam-4143	181	19	k.	k.	PROPN
ejpam-4143	181	20	then	then	ADV
ejpam-4143	181	21	µk(x	µk(x	PUNCT
ejpam-4143	181	22	)	)	PUNCT
ejpam-4143	181	23	=	=	SYM
ejpam-4143	181	24	α	α	NOUN
ejpam-4143	181	25	=	=	SYM
ejpam-4143	181	26	µk(y	µk(y	NOUN
ejpam-4143	181	27	)	)	PUNCT
ejpam-4143	181	28	.	.	PUNCT
ejpam-4143	182	1	by	by	ADP
ejpam-4143	182	2	definition	definition	NOUN
ejpam-4143	182	3	8	8	NUM
ejpam-4143	182	4	,	,	PUNCT
ejpam-4143	182	5	infa∈x⊛y{µk(a	infa∈x⊛y{µk(a	X
ejpam-4143	182	6	)	)	PUNCT
ejpam-4143	182	7	}	}	PUNCT
ejpam-4143	182	8	≥	≥	NUM
ejpam-4143	182	9	α	α	NOUN
ejpam-4143	182	10	.	.	PUNCT
ejpam-4143	183	1	since	since	SCONJ
ejpam-4143	183	2	β	β	X
ejpam-4143	183	3	<	<	X
ejpam-4143	183	4	α	α	PROPN
ejpam-4143	183	5	,	,	PUNCT
ejpam-4143	183	6	µk(a	µk(a	X
ejpam-4143	183	7	)	)	PUNCT
ejpam-4143	183	8	=	=	SYM
ejpam-4143	183	9	α	α	PROPN
ejpam-4143	183	10	for	for	ADP
ejpam-4143	183	11	all	all	DET
ejpam-4143	183	12	a	a	DET
ejpam-4143	183	13	∈	∈	NOUN
ejpam-4143	183	14	x⊛	x⊛	PUNCT
ejpam-4143	184	1	y.	y.	NOUN
ejpam-4143	184	2	this	this	PRON
ejpam-4143	184	3	implies	imply	VERB
ejpam-4143	184	4	that	that	PRON
ejpam-4143	184	5	x⊛	x⊛	PROPN
ejpam-4143	184	6	y	y	PROPN
ejpam-4143	184	7	⊆	⊆	NUM
ejpam-4143	184	8	k.	k.	PROPN
ejpam-4143	185	1	thus	thus	ADV
ejpam-4143	185	2	,	,	PUNCT
ejpam-4143	185	3	k	k	PROPN
ejpam-4143	185	4	is	be	AUX
ejpam-4143	185	5	a	a	DET
ejpam-4143	185	6	hyper	hyper	ADJ
ejpam-4143	185	7	up	up	ADP
ejpam-4143	185	8	-	-	PUNCT
ejpam-4143	185	9	subalgebra	subalgebra	NOUN
ejpam-4143	185	10	of	of	ADP
ejpam-4143	185	11	h.	h.	NOUN
ejpam-4143	185	12	conversely	conversely	ADV
ejpam-4143	185	13	,	,	PUNCT
ejpam-4143	185	14	suppose	suppose	VERB
ejpam-4143	185	15	k	k	PROPN
ejpam-4143	185	16	is	be	AUX
ejpam-4143	185	17	a	a	DET
ejpam-4143	185	18	hyper	hyper	ADJ
ejpam-4143	185	19	up	up	ADP
ejpam-4143	185	20	-	-	PUNCT
ejpam-4143	185	21	subalgebra	subalgebra	NOUN
ejpam-4143	185	22	of	of	ADP
ejpam-4143	185	23	h.	h.	PROPN
ejpam-4143	185	24	let	let	VERB
ejpam-4143	185	25	x	x	PRON
ejpam-4143	185	26	,	,	PUNCT
ejpam-4143	185	27	y	y	PROPN
ejpam-4143	185	28	∈	∈	PROPN
ejpam-4143	185	29	h.	h.	NOUN
ejpam-4143	186	1	if	if	SCONJ
ejpam-4143	186	2	x	x	X
ejpam-4143	186	3	,	,	PUNCT
ejpam-4143	186	4	y	y	PROPN
ejpam-4143	186	5	∈	∈	PROPN
ejpam-4143	186	6	k	k	NOUN
ejpam-4143	186	7	,	,	PUNCT
ejpam-4143	186	8	then	then	ADV
ejpam-4143	186	9	x	x	X
ejpam-4143	186	10	⊛	⊛	ADJ
ejpam-4143	186	11	y	y	PROPN
ejpam-4143	186	12	∈	∈	PROPN
ejpam-4143	186	13	k	k	PROPN
ejpam-4143	186	14	since	since	SCONJ
ejpam-4143	186	15	k	k	PROPN
ejpam-4143	186	16	is	be	AUX
ejpam-4143	186	17	a	a	DET
ejpam-4143	186	18	hyper	hyper	ADJ
ejpam-4143	186	19	up	up	ADP
ejpam-4143	186	20	-	-	PUNCT
ejpam-4143	186	21	subalgebra	subalgebra	NOUN
ejpam-4143	186	22	of	of	ADP
ejpam-4143	186	23	h.	h.	PROPN
ejpam-4143	186	24	hence	hence	ADV
ejpam-4143	186	25	,	,	PUNCT
ejpam-4143	186	26	infa∈x⊛y(µk(a	infa∈x⊛y(µk(a	NOUN
ejpam-4143	186	27	)	)	PUNCT
ejpam-4143	186	28	)	)	PUNCT
ejpam-4143	187	1	=	=	SYM
ejpam-4143	187	2	α	α	X
ejpam-4143	187	3	=	=	SYM
ejpam-4143	187	4	min{µk(x	min{µk(x	PROPN
ejpam-4143	187	5	)	)	PUNCT
ejpam-4143	187	6	,	,	PUNCT
ejpam-4143	187	7	µk(y	µk(y	NOUN
ejpam-4143	187	8	)	)	PUNCT
ejpam-4143	187	9	}	}	PUNCT
ejpam-4143	187	10	.	.	PUNCT
ejpam-4143	188	1	suppose	suppose	VERB
ejpam-4143	188	2	x	x	X
ejpam-4143	188	3	/∈	/∈	PUNCT
ejpam-4143	189	1	k	k	PROPN
ejpam-4143	189	2	or	or	CCONJ
ejpam-4143	189	3	y	y	PROPN
ejpam-4143	189	4	/∈	/∈	PUNCT
ejpam-4143	190	1	k.	k.	PROPN
ejpam-4143	191	1	then	then	ADV
ejpam-4143	191	2	min{µk(x	min{µk(x	NOUN
ejpam-4143	191	3	)	)	PUNCT
ejpam-4143	191	4	,	,	PUNCT
ejpam-4143	191	5	µk(y	µk(y	NOUN
ejpam-4143	191	6	)	)	PUNCT
ejpam-4143	191	7	}	}	PUNCT
ejpam-4143	192	1	=	=	SYM
ejpam-4143	192	2	β	β	X
ejpam-4143	192	3	.	.	PUNCT
ejpam-4143	193	1	thus	thus	ADV
ejpam-4143	193	2	,	,	PUNCT
ejpam-4143	193	3	infa∈x⊛y	infa∈x⊛y	NUM
ejpam-4143	193	4	µk(a	µk(a	NOUN
ejpam-4143	193	5	)	)	PUNCT
ejpam-4143	193	6	≥	≥	PROPN
ejpam-4143	193	7	min{µk(x	min{µk(x	NOUN
ejpam-4143	193	8	)	)	PUNCT
ejpam-4143	193	9	,	,	PUNCT
ejpam-4143	193	10	µk(y	µk(y	NOUN
ejpam-4143	193	11	)	)	PUNCT
ejpam-4143	193	12	}	}	PUNCT
ejpam-4143	193	13	.	.	PUNCT
ejpam-4143	194	1	this	this	PRON
ejpam-4143	194	2	shows	show	VERB
ejpam-4143	194	3	that	that	SCONJ
ejpam-4143	194	4	µk	µk	PRON
ejpam-4143	194	5	is	be	AUX
ejpam-4143	194	6	a	a	DET
ejpam-4143	194	7	fuzzy	fuzzy	ADJ
ejpam-4143	194	8	hyper	hyper	ADJ
ejpam-4143	194	9	up	up	ADP
ejpam-4143	194	10	-	-	PUNCT
ejpam-4143	194	11	subalgebra	subalgebra	NOUN
ejpam-4143	194	12	of	of	ADP
ejpam-4143	194	13	h.	h.	PROPN
ejpam-4143	194	14	theorem	theorem	PROPN
ejpam-4143	194	15	6	6	NUM
ejpam-4143	194	16	.	.	PUNCT
ejpam-4143	195	1	let	let	VERB
ejpam-4143	195	2	h	h	PRON
ejpam-4143	195	3	be	be	AUX
ejpam-4143	195	4	a	a	DET
ejpam-4143	195	5	hyper	hyper	ADJ
ejpam-4143	195	6	up	up	NOUN
ejpam-4143	195	7	-	-	PUNCT
ejpam-4143	195	8	algebra	algebra	NOUN
ejpam-4143	195	9	.	.	PUNCT
ejpam-4143	196	1	then	then	ADV
ejpam-4143	196	2	every	every	DET
ejpam-4143	196	3	hyper	hyper	ADJ
ejpam-4143	196	4	up	up	ADP
ejpam-4143	196	5	-	-	PUNCT
ejpam-4143	196	6	subalgebra	subalgebra	NOUN
ejpam-4143	196	7	of	of	ADP
ejpam-4143	196	8	h	h	NOUN
ejpam-4143	196	9	is	be	AUX
ejpam-4143	196	10	an	an	DET
ejpam-4143	196	11	upper	upper	ADJ
ejpam-4143	196	12	level	level	NOUN
ejpam-4143	196	13	hyper	hyper	ADJ
ejpam-4143	196	14	up	up	ADP
ejpam-4143	196	15	-	-	PUNCT
ejpam-4143	196	16	subalgebra	subalgebra	NOUN
ejpam-4143	196	17	of	of	ADP
ejpam-4143	196	18	a	a	DET
ejpam-4143	196	19	fuzzy	fuzzy	ADJ
ejpam-4143	196	20	hyper	hyper	ADJ
ejpam-4143	196	21	up	up	ADP
ejpam-4143	196	22	-	-	PUNCT
ejpam-4143	196	23	subalgebra	subalgebra	NOUN
ejpam-4143	196	24	of	of	ADP
ejpam-4143	196	25	h.	h.	NOUN
ejpam-4143	196	26	proof	proof	NOUN
ejpam-4143	196	27	.	.	PUNCT
ejpam-4143	197	1	let	let	VERB
ejpam-4143	197	2	k	k	PRON
ejpam-4143	197	3	be	be	AUX
ejpam-4143	197	4	a	a	DET
ejpam-4143	197	5	hyper	hyper	ADJ
ejpam-4143	197	6	up	up	ADP
ejpam-4143	197	7	-	-	PUNCT
ejpam-4143	197	8	subalgebra	subalgebra	NOUN
ejpam-4143	197	9	of	of	ADP
ejpam-4143	197	10	h.	h.	NOUN
ejpam-4143	197	11	for	for	ADP
ejpam-4143	197	12	a	a	DET
ejpam-4143	197	13	fixed	fix	VERB
ejpam-4143	197	14	t	t	NOUN
ejpam-4143	197	15	∈	∈	PROPN
ejpam-4143	197	16	(	(	PUNCT
ejpam-4143	197	17	0	0	NUM
ejpam-4143	197	18	,	,	PUNCT
ejpam-4143	197	19	1	1	NUM
ejpam-4143	197	20	]	]	PUNCT
ejpam-4143	197	21	,	,	PUNCT
ejpam-4143	197	22	we	we	PRON
ejpam-4143	197	23	consider	consider	VERB
ejpam-4143	197	24	the	the	DET
ejpam-4143	197	25	fuzzy	fuzzy	ADJ
ejpam-4143	197	26	subset	subset	NOUN
ejpam-4143	197	27	µ	µ	VERB
ejpam-4143	197	28	defined	define	VERB
ejpam-4143	197	29	by	by	ADP
ejpam-4143	197	30	µ(x	µ(x	NOUN
ejpam-4143	197	31	)	)	PUNCT
ejpam-4143	197	32	=	=	SYM
ejpam-4143	197	33	{	{	PUNCT
ejpam-4143	197	34	t	t	PROPN
ejpam-4143	197	35	,	,	PUNCT
ejpam-4143	197	36	if	if	SCONJ
ejpam-4143	197	37	x	x	PROPN
ejpam-4143	197	38	∈	∈	PROPN
ejpam-4143	197	39	k	k	NOUN
ejpam-4143	197	40	0	0	PUNCT
ejpam-4143	197	41	,	,	PUNCT
ejpam-4143	197	42	if	if	SCONJ
ejpam-4143	197	43	x	x	X
ejpam-4143	197	44	/∈	/∈	PUNCT
ejpam-4143	197	45	k.	k.	NOUN
ejpam-4143	197	46	by	by	ADP
ejpam-4143	197	47	theorem	theorem	NOUN
ejpam-4143	197	48	5	5	NUM
ejpam-4143	197	49	,	,	PUNCT
ejpam-4143	197	50	µ	µ	PRON
ejpam-4143	197	51	is	be	AUX
ejpam-4143	197	52	a	a	DET
ejpam-4143	197	53	fuzzy	fuzzy	ADJ
ejpam-4143	197	54	hyper	hyper	ADJ
ejpam-4143	197	55	up	up	ADP
ejpam-4143	197	56	-	-	PUNCT
ejpam-4143	197	57	subalgebra	subalgebra	NOUN
ejpam-4143	197	58	of	of	ADP
ejpam-4143	197	59	h.	h.	NOUN
ejpam-4143	197	60	since	since	SCONJ
ejpam-4143	197	61	0	0	NUM
ejpam-4143	197	62	∈	∈	PROPN
ejpam-4143	197	63	k,µ(0	k,µ(0	NOUN
ejpam-4143	197	64	)	)	PUNCT
ejpam-4143	198	1	=	=	SYM
ejpam-4143	199	1	t.	t.	NOUN
ejpam-4143	199	2	hence	hence	ADV
ejpam-4143	199	3	,	,	PUNCT
ejpam-4143	199	4	0	0	NUM
ejpam-4143	199	5	∈	∈	NOUN
ejpam-4143	199	6	µt	µt	ADP
ejpam-4143	199	7	=	=	PUNCT
ejpam-4143	199	8	{	{	PUNCT
ejpam-4143	199	9	x	x	PUNCT
ejpam-4143	199	10	∈	∈	PROPN
ejpam-4143	199	11	h	h	NOUN
ejpam-4143	199	12	:	:	PUNCT
ejpam-4143	199	13	µ(x	µ(x	X
ejpam-4143	199	14	)	)	PUNCT
ejpam-4143	199	15	=	=	SYM
ejpam-4143	199	16	t	t	PROPN
ejpam-4143	199	17	}	}	PUNCT
ejpam-4143	199	18	.	.	PUNCT
ejpam-4143	200	1	by	by	ADP
ejpam-4143	200	2	theorem	theorem	NOUN
ejpam-4143	200	3	2	2	NUM
ejpam-4143	200	4	,	,	PUNCT
ejpam-4143	200	5	µt	µt	PRON
ejpam-4143	200	6	is	be	AUX
ejpam-4143	200	7	a	a	DET
ejpam-4143	200	8	hyper	hyper	ADJ
ejpam-4143	200	9	up	up	ADP
ejpam-4143	200	10	-	-	PUNCT
ejpam-4143	200	11	subalgebra	subalgebra	NOUN
ejpam-4143	200	12	of	of	ADP
ejpam-4143	200	13	h.	h.	PROPN
ejpam-4143	200	14	let	let	VERB
ejpam-4143	200	15	r.	r.	PROPN
ejpam-4143	200	16	amairanto	amairanto	PROPN
ejpam-4143	200	17	,	,	PUNCT
ejpam-4143	200	18	r.	r.	PROPN
ejpam-4143	200	19	isla	isla	PROPN
ejpam-4143	200	20	/	/	SYM
ejpam-4143	200	21	eur	eur	PROPN
ejpam-4143	200	22	.	.	PUNCT
ejpam-4143	201	1	j.	j.	PROPN
ejpam-4143	201	2	pure	pure	PROPN
ejpam-4143	201	3	appl	appl	PROPN
ejpam-4143	201	4	.	.	PROPN
ejpam-4143	201	5	math	math	PROPN
ejpam-4143	201	6	,	,	PUNCT
ejpam-4143	201	7	14	14	NUM
ejpam-4143	201	8	(	(	PUNCT
ejpam-4143	201	9	4	4	NUM
ejpam-4143	201	10	)	)	PUNCT
ejpam-4143	201	11	(	(	PUNCT
ejpam-4143	201	12	2021	2021	NUM
ejpam-4143	201	13	)	)	PUNCT
ejpam-4143	201	14	,	,	PUNCT
ejpam-4143	201	15	1388	1388	NUM
ejpam-4143	201	16	-	-	SYM
ejpam-4143	201	17	1401	1401	NUM
ejpam-4143	201	18	1395	1395	NUM
ejpam-4143	201	19	x	x	SYM
ejpam-4143	201	20	∈	∈	PROPN
ejpam-4143	201	21	k.	k.	NOUN
ejpam-4143	201	22	then	then	ADV
ejpam-4143	201	23	µ(x	µ(x	X
ejpam-4143	201	24	)	)	PUNCT
ejpam-4143	201	25	=	=	SYM
ejpam-4143	201	26	t	t	NOUN
ejpam-4143	201	27	which	which	PRON
ejpam-4143	201	28	implies	imply	VERB
ejpam-4143	201	29	that	that	SCONJ
ejpam-4143	201	30	x	x	PUNCT
ejpam-4143	201	31	∈	∈	PROPN
ejpam-4143	201	32	µt	µt	PROPN
ejpam-4143	201	33	.	.	PUNCT
ejpam-4143	202	1	thus	thus	ADV
ejpam-4143	202	2	,	,	PUNCT
ejpam-4143	202	3	k	k	PROPN
ejpam-4143	202	4	⊆	⊆	NUM
ejpam-4143	202	5	µt	µt	NOUN
ejpam-4143	202	6	.	.	PROPN
ejpam-4143	202	7	on	on	ADP
ejpam-4143	202	8	the	the	DET
ejpam-4143	202	9	other	other	ADJ
ejpam-4143	202	10	hand	hand	NOUN
ejpam-4143	202	11	,	,	PUNCT
ejpam-4143	202	12	suppose	suppose	VERB
ejpam-4143	202	13	that	that	SCONJ
ejpam-4143	202	14	x	x	PROPN
ejpam-4143	202	15	∈	∈	PROPN
ejpam-4143	202	16	µt	µt	PROPN
ejpam-4143	202	17	.	.	PUNCT
ejpam-4143	202	18	then	then	ADV
ejpam-4143	202	19	µ(x	µ(x	NOUN
ejpam-4143	202	20	)	)	PUNCT
ejpam-4143	202	21	=	=	SYM
ejpam-4143	202	22	t	t	NOUN
ejpam-4143	202	23	which	which	PRON
ejpam-4143	202	24	means	mean	VERB
ejpam-4143	202	25	that	that	SCONJ
ejpam-4143	202	26	x	x	PROPN
ejpam-4143	202	27	∈	∈	PROPN
ejpam-4143	202	28	k.	k.	PROPN
ejpam-4143	203	1	thus	thus	ADV
ejpam-4143	203	2	,	,	PUNCT
ejpam-4143	203	3	µt	µt	PRON
ejpam-4143	203	4	⊆	⊆	NUM
ejpam-4143	203	5	k.	k.	NOUN
ejpam-4143	203	6	hence	hence	ADV
ejpam-4143	203	7	,	,	PUNCT
ejpam-4143	203	8	k	k	PROPN
ejpam-4143	203	9	=	=	SYM
ejpam-4143	203	10	µt	µt	PROPN
ejpam-4143	203	11	.	.	PROPN
ejpam-4143	203	12	recall	recall	VERB
ejpam-4143	203	13	that	that	SCONJ
ejpam-4143	203	14	each	each	DET
ejpam-4143	203	15	hyper	hyper	ADJ
ejpam-4143	203	16	up	up	ADP
ejpam-4143	203	17	-	-	PUNCT
ejpam-4143	203	18	subalgebra	subalgebra	NOUN
ejpam-4143	203	19	of	of	ADP
ejpam-4143	203	20	a	a	DET
ejpam-4143	203	21	hyper	hyper	ADJ
ejpam-4143	203	22	up	up	ADP
ejpam-4143	203	23	-	-	PUNCT
ejpam-4143	203	24	algebra	algebra	NOUN
ejpam-4143	203	25	h	h	NOUN
ejpam-4143	203	26	contains	contain	VERB
ejpam-4143	203	27	the	the	DET
ejpam-4143	203	28	element	element	NOUN
ejpam-4143	203	29	0	0	NUM
ejpam-4143	203	30	.	.	PUNCT
ejpam-4143	204	1	thus	thus	ADV
ejpam-4143	204	2	,	,	PUNCT
ejpam-4143	204	3	for	for	SCONJ
ejpam-4143	204	4	any	any	DET
ejpam-4143	204	5	family	family	NOUN
ejpam-4143	204	6	{	{	PUNCT
ejpam-4143	204	7	kn	kn	PROPN
ejpam-4143	204	8	}	}	PUNCT
ejpam-4143	204	9	of	of	ADP
ejpam-4143	204	10	hyper	hyper	ADJ
ejpam-4143	204	11	up	up	ADP
ejpam-4143	204	12	-	-	PUNCT
ejpam-4143	204	13	subalgebras	subalgebras	NOUN
ejpam-4143	204	14	of	of	ADP
ejpam-4143	204	15	h	h	NOUN
ejpam-4143	204	16	,	,	PUNCT
ejpam-4143	204	17	0	0	NUM
ejpam-4143	204	18	∈	∈	NOUN
ejpam-4143	204	19	⋂∞	⋂∞	NOUN
ejpam-4143	204	20	n=1kn	n=1kn	NOUN
ejpam-4143	204	21	and	and	CCONJ
ejpam-4143	204	22	so	so	ADV
ejpam-4143	204	23	⋂∞	⋂∞	NOUN
ejpam-4143	204	24	n=1kn	n=1kn	NOUN
ejpam-4143	204	25	̸=	̸=	PROPN
ejpam-4143	204	26	∅.	∅.	ADV
ejpam-4143	204	27	theorem	theorem	VERB
ejpam-4143	204	28	7	7	NUM
ejpam-4143	204	29	.	.	PUNCT
ejpam-4143	205	1	let	let	VERB
ejpam-4143	205	2	h	h	PRON
ejpam-4143	205	3	be	be	AUX
ejpam-4143	205	4	a	a	DET
ejpam-4143	205	5	hyper	hyper	ADJ
ejpam-4143	205	6	up	up	NOUN
ejpam-4143	205	7	-	-	PUNCT
ejpam-4143	205	8	algebra	algebra	NOUN
ejpam-4143	205	9	and	and	CCONJ
ejpam-4143	205	10	let	let	VERB
ejpam-4143	205	11	{	{	PUNCT
ejpam-4143	205	12	kn	kn	NOUN
ejpam-4143	205	13	:	:	PUNCT
ejpam-4143	205	14	n	n	PROPN
ejpam-4143	205	15	=	=	SYM
ejpam-4143	205	16	1	1	NUM
ejpam-4143	205	17	,	,	PUNCT
ejpam-4143	205	18	2	2	NUM
ejpam-4143	205	19	,	,	PUNCT
ejpam-4143	205	20	·	·	PUNCT
ejpam-4143	205	21	·	·	PUNCT
ejpam-4143	205	22	·	·	PUNCT
ejpam-4143	205	23	}	}	PUNCT
ejpam-4143	205	24	be	be	AUX
ejpam-4143	205	25	a	a	DET
ejpam-4143	205	26	family	family	NOUN
ejpam-4143	205	27	of	of	ADP
ejpam-4143	205	28	hyper	hyper	ADJ
ejpam-4143	205	29	up	up	ADP
ejpam-4143	205	30	-	-	PUNCT
ejpam-4143	205	31	subalgebras	subalgebra	NOUN
ejpam-4143	205	32	of	of	ADP
ejpam-4143	205	33	h	h	PRON
ejpam-4143	205	34	such	such	ADJ
ejpam-4143	205	35	that	that	DET
ejpam-4143	205	36	h	h	NOUN
ejpam-4143	205	37	=	=	SYM
ejpam-4143	205	38	k1	k1	PROPN
ejpam-4143	205	39	⊇	⊇	PROPN
ejpam-4143	205	40	k2	k2	PROPN
ejpam-4143	205	41	⊇	⊇	PROPN
ejpam-4143	205	42	·	·	PUNCT
ejpam-4143	205	43	·	·	PUNCT
ejpam-4143	205	44	·	·	PUNCT
ejpam-4143	205	45	.	.	PUNCT
ejpam-4143	206	1	let	let	VERB
ejpam-4143	206	2	µ	µ	X
ejpam-4143	206	3	be	be	AUX
ejpam-4143	206	4	a	a	DET
ejpam-4143	206	5	fuzzy	fuzzy	ADJ
ejpam-4143	206	6	set	set	NOUN
ejpam-4143	206	7	in	in	ADP
ejpam-4143	206	8	h	h	NOUN
ejpam-4143	206	9	defined	define	VERB
ejpam-4143	206	10	by	by	ADP
ejpam-4143	206	11	µ(x	µ(x	NOUN
ejpam-4143	206	12	)	)	PUNCT
ejpam-4143	206	13	=	=	NOUN
ejpam-4143	206	14	{	{	PUNCT
ejpam-4143	206	15	n	n	NOUN
ejpam-4143	206	16	n+1	n+1	PROPN
ejpam-4143	206	17	,	,	PUNCT
ejpam-4143	206	18	if	if	SCONJ
ejpam-4143	206	19	x	x	X
ejpam-4143	206	20	∈	∈	PROPN
ejpam-4143	206	21	kn\kn+1	kn\kn+1	PROPN
ejpam-4143	206	22	,	,	PUNCT
ejpam-4143	206	23	1	1	NUM
ejpam-4143	206	24	,	,	PUNCT
ejpam-4143	206	25	if	if	SCONJ
ejpam-4143	206	26	x	x	X
ejpam-4143	206	27	∈	∈	NOUN
ejpam-4143	206	28	⋂∞	⋂∞	NOUN
ejpam-4143	206	29	n=1kn	n=1kn	NOUN
ejpam-4143	206	30	.	.	PUNCT
ejpam-4143	207	1	then	then	ADV
ejpam-4143	207	2	µ	µ	X
ejpam-4143	207	3	is	be	AUX
ejpam-4143	207	4	a	a	DET
ejpam-4143	207	5	fuzzy	fuzzy	ADJ
ejpam-4143	207	6	hyper	hyper	ADJ
ejpam-4143	207	7	up	up	ADP
ejpam-4143	207	8	-	-	PUNCT
ejpam-4143	207	9	subalgebra	subalgebra	NOUN
ejpam-4143	207	10	of	of	ADP
ejpam-4143	207	11	h.	h.	NOUN
ejpam-4143	207	12	proof	proof	NOUN
ejpam-4143	207	13	.	.	PUNCT
ejpam-4143	208	1	let	let	VERB
ejpam-4143	208	2	x	x	PRON
ejpam-4143	208	3	,	,	PUNCT
ejpam-4143	208	4	y	y	PROPN
ejpam-4143	208	5	∈	∈	PROPN
ejpam-4143	208	6	h.	h.	PROPN
ejpam-4143	208	7	consider	consider	VERB
ejpam-4143	208	8	the	the	DET
ejpam-4143	208	9	following	follow	VERB
ejpam-4143	208	10	cases	case	NOUN
ejpam-4143	208	11	.	.	PUNCT
ejpam-4143	209	1	case	case	NOUN
ejpam-4143	209	2	1	1	NUM
ejpam-4143	209	3	:	:	SYM
ejpam-4143	209	4	x	x	X
ejpam-4143	209	5	,	,	PUNCT
ejpam-4143	209	6	y	y	PROPN
ejpam-4143	209	7	∈	∈	PROPN
ejpam-4143	209	8	kn\kn+1	kn\kn+1	PROPN
ejpam-4143	209	9	.	.	PUNCT
ejpam-4143	210	1	then	then	ADV
ejpam-4143	210	2	µ(x	µ(x	NOUN
ejpam-4143	210	3	)	)	PUNCT
ejpam-4143	210	4	=	=	SYM
ejpam-4143	210	5	n	n	CCONJ
ejpam-4143	210	6	n+1	n+1	PROPN
ejpam-4143	210	7	=	=	SYM
ejpam-4143	210	8	µ(y	µ(y	PROPN
ejpam-4143	210	9	)	)	PUNCT
ejpam-4143	210	10	.	.	PUNCT
ejpam-4143	211	1	since	since	SCONJ
ejpam-4143	211	2	kn	kn	PROPN
ejpam-4143	211	3	is	be	AUX
ejpam-4143	211	4	a	a	DET
ejpam-4143	211	5	hyper	hyper	ADJ
ejpam-4143	211	6	upsubalgebra	upsubalgebra	NOUN
ejpam-4143	211	7	,	,	PUNCT
ejpam-4143	211	8	x	x	X
ejpam-4143	211	9	⊛	⊛	NUM
ejpam-4143	211	10	y	y	PROPN
ejpam-4143	211	11	⊆	⊆	NUM
ejpam-4143	211	12	kn	kn	PROPN
ejpam-4143	211	13	.	.	PUNCT
ejpam-4143	212	1	then	then	ADV
ejpam-4143	212	2	x	x	X
ejpam-4143	212	3	⊛	⊛	NUM
ejpam-4143	212	4	y	y	PROPN
ejpam-4143	212	5	⊆	⊆	NUM
ejpam-4143	212	6	kn+1	kn+1	PROPN
ejpam-4143	212	7	or	or	CCONJ
ejpam-4143	212	8	x	x	PROPN
ejpam-4143	212	9	⊛	⊛	ADJ
ejpam-4143	212	10	y	y	PROPN
ejpam-4143	212	11	⊈	⊈	PROPN
ejpam-4143	212	12	kn+1	kn+1	PROPN
ejpam-4143	212	13	.	.	PUNCT
ejpam-4143	213	1	if	if	SCONJ
ejpam-4143	213	2	x	x	PROPN
ejpam-4143	213	3	⊛	⊛	NUM
ejpam-4143	213	4	y	y	PROPN
ejpam-4143	213	5	⊈	⊈	PROPN
ejpam-4143	213	6	kn+1	kn+1	PROPN
ejpam-4143	213	7	,	,	PUNCT
ejpam-4143	213	8	then	then	ADV
ejpam-4143	213	9	x	x	X
ejpam-4143	213	10	⊛	⊛	NUM
ejpam-4143	213	11	y	y	PROPN
ejpam-4143	213	12	⊆	⊆	NUM
ejpam-4143	213	13	kn\kn+1	kn\kn+1	PROPN
ejpam-4143	213	14	and	and	CCONJ
ejpam-4143	213	15	for	for	ADP
ejpam-4143	213	16	all	all	DET
ejpam-4143	213	17	a	a	DET
ejpam-4143	213	18	∈	∈	NOUN
ejpam-4143	213	19	x	x	SYM
ejpam-4143	213	20	⊛	⊛	NUM
ejpam-4143	213	21	y	y	PROPN
ejpam-4143	213	22	,	,	PUNCT
ejpam-4143	213	23	µ(a	µ(a	PROPN
ejpam-4143	213	24	)	)	PUNCT
ejpam-4143	213	25	=	=	SYM
ejpam-4143	214	1	n	n	NOUN
ejpam-4143	214	2	n+1	n+1	PROPN
ejpam-4143	214	3	.	.	PUNCT
ejpam-4143	215	1	thus	thus	ADV
ejpam-4143	215	2	,	,	PUNCT
ejpam-4143	215	3	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	PROPN
ejpam-4143	215	4	)	)	PUNCT
ejpam-4143	215	5	}	}	PUNCT
ejpam-4143	215	6	=	=	SYM
ejpam-4143	215	7	n	n	CCONJ
ejpam-4143	215	8	n+1	n+1	PROPN
ejpam-4143	215	9	=	=	SYM
ejpam-4143	215	10	min{µ(x	min{µ(x	PROPN
ejpam-4143	215	11	)	)	PUNCT
ejpam-4143	215	12	,	,	PUNCT
ejpam-4143	215	13	µ(y	µ(y	PROPN
ejpam-4143	215	14	)	)	PUNCT
ejpam-4143	215	15	}	}	PUNCT
ejpam-4143	215	16	.	.	PUNCT
ejpam-4143	216	1	suppose	suppose	VERB
ejpam-4143	216	2	x	x	SYM
ejpam-4143	216	3	⊛	⊛	NUM
ejpam-4143	216	4	y	y	PROPN
ejpam-4143	216	5	⊈	⊈	PROPN
ejpam-4143	216	6	kn\kn+1	kn\kn+1	PROPN
ejpam-4143	216	7	.	.	PUNCT
ejpam-4143	217	1	if	if	SCONJ
ejpam-4143	217	2	x	x	PROPN
ejpam-4143	217	3	⊛	⊛	ADV
ejpam-4143	217	4	y	y	PROPN
ejpam-4143	217	5	⊆	⊆	NUM
ejpam-4143	217	6	∩∞	∩∞	PUNCT
ejpam-4143	217	7	m=1	m=1	NOUN
ejpam-4143	217	8	km	km	NOUN
ejpam-4143	217	9	,	,	PUNCT
ejpam-4143	217	10	then	then	ADV
ejpam-4143	217	11	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	PROPN
ejpam-4143	217	12	)	)	PUNCT
ejpam-4143	217	13	}	}	PUNCT
ejpam-4143	217	14	=	=	SYM
ejpam-4143	217	15	1	1	X
ejpam-4143	217	16	>	>	SYM
ejpam-4143	217	17	n	n	CCONJ
ejpam-4143	217	18	n+1	n+1	PROPN
ejpam-4143	217	19	=	=	SYM
ejpam-4143	217	20	min{µ(x	min{µ(x	PROPN
ejpam-4143	217	21	)	)	PUNCT
ejpam-4143	217	22	,	,	PUNCT
ejpam-4143	217	23	µ(y	µ(y	PROPN
ejpam-4143	217	24	)	)	PUNCT
ejpam-4143	217	25	}	}	PUNCT
ejpam-4143	217	26	.	.	PUNCT
ejpam-4143	218	1	suppose	suppose	VERB
ejpam-4143	218	2	x	x	SYM
ejpam-4143	218	3	⊛	⊛	ADJ
ejpam-4143	218	4	y	y	PROPN
ejpam-4143	218	5	⊈	⊈	PROPN
ejpam-4143	218	6	km	km	PROPN
ejpam-4143	218	7	.	.	PUNCT
ejpam-4143	219	1	then	then	ADV
ejpam-4143	219	2	there	there	PRON
ejpam-4143	219	3	exists	exist	VERB
ejpam-4143	219	4	a	a	DET
ejpam-4143	219	5	∈	∈	NOUN
ejpam-4143	219	6	x	x	PUNCT
ejpam-4143	219	7	⊛	⊛	NUM
ejpam-4143	219	8	y	y	PRON
ejpam-4143	219	9	such	such	ADJ
ejpam-4143	219	10	that	that	SCONJ
ejpam-4143	219	11	a	a	DET
ejpam-4143	219	12	∈	∈	NOUN
ejpam-4143	219	13	km\km+1	km\km+1	X
ejpam-4143	219	14	for	for	ADP
ejpam-4143	219	15	some	some	DET
ejpam-4143	219	16	m	m	NOUN
ejpam-4143	219	17	≥	≥	NOUN
ejpam-4143	219	18	n.	n.	VERB
ejpam-4143	219	19	by	by	ADP
ejpam-4143	219	20	the	the	DET
ejpam-4143	219	21	well	well	ADV
ejpam-4143	219	22	-	-	PUNCT
ejpam-4143	219	23	ordering	order	VERB
ejpam-4143	219	24	principle	principle	NOUN
ejpam-4143	219	25	,	,	PUNCT
ejpam-4143	219	26	there	there	PRON
ejpam-4143	219	27	exists	exist	VERB
ejpam-4143	219	28	a	a	DET
ejpam-4143	219	29	smallest	small	ADJ
ejpam-4143	219	30	positive	positive	ADJ
ejpam-4143	219	31	integer	integer	NOUN
ejpam-4143	219	32	p	p	NOUN
ejpam-4143	219	33	≥	≥	NOUN
ejpam-4143	219	34	n	n	CCONJ
ejpam-4143	219	35	such	such	ADJ
ejpam-4143	219	36	that	that	SCONJ
ejpam-4143	219	37	z	z	PROPN
ejpam-4143	219	38	∈	∈	PROPN
ejpam-4143	219	39	kp\kp+1	kp\kp+1	PROPN
ejpam-4143	219	40	for	for	ADP
ejpam-4143	219	41	some	some	DET
ejpam-4143	219	42	z	z	NOUN
ejpam-4143	219	43	∈	∈	PROPN
ejpam-4143	220	1	x⊛	x⊛	PROPN
ejpam-4143	221	1	y.	y.	PROPN
ejpam-4143	221	2	hence	hence	ADV
ejpam-4143	221	3	,	,	PUNCT
ejpam-4143	221	4	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	PROPN
ejpam-4143	221	5	)	)	PUNCT
ejpam-4143	221	6	}	}	PUNCT
ejpam-4143	222	1	=	=	PUNCT
ejpam-4143	223	1	p	p	X
ejpam-4143	223	2	p+1	p+1	NOUN
ejpam-4143	223	3	≥	≥	NOUN
ejpam-4143	223	4	n	n	NOUN
ejpam-4143	223	5	n+1	n+1	PROPN
ejpam-4143	223	6	.	.	PUNCT
ejpam-4143	224	1	case	case	NOUN
ejpam-4143	224	2	2	2	NUM
ejpam-4143	224	3	:	:	PUNCT
ejpam-4143	224	4	x	x	SYM
ejpam-4143	224	5	∈	∈	PROPN
ejpam-4143	224	6	ks\ks+1	ks\ks+1	NOUN
ejpam-4143	224	7	,	,	PUNCT
ejpam-4143	224	8	y	y	PROPN
ejpam-4143	224	9	∈	∈	PROPN
ejpam-4143	224	10	kr\kr+1	kr\kr+1	PROPN
ejpam-4143	224	11	.	.	PUNCT
ejpam-4143	225	1	without	without	ADP
ejpam-4143	225	2	loss	loss	NOUN
ejpam-4143	225	3	of	of	ADP
ejpam-4143	225	4	generality	generality	NOUN
ejpam-4143	225	5	,	,	PUNCT
ejpam-4143	225	6	assume	assume	VERB
ejpam-4143	225	7	that	that	SCONJ
ejpam-4143	225	8	s	s	VERB
ejpam-4143	225	9	<	<	X
ejpam-4143	225	10	r.	r.	X
ejpam-4143	225	11	the	the	DET
ejpam-4143	225	12	s	s	X
ejpam-4143	225	13	s+1	s+1	NOUN
ejpam-4143	225	14	<	<	X
ejpam-4143	225	15	r	r	X
ejpam-4143	225	16	r+1	r+1	PROPN
ejpam-4143	225	17	and	and	CCONJ
ejpam-4143	225	18	ks	ks	PROPN
ejpam-4143	225	19	⊇	⊇	PROPN
ejpam-4143	225	20	kr	kr	PROPN
ejpam-4143	225	21	.	.	PROPN
ejpam-4143	226	1	since	since	SCONJ
ejpam-4143	226	2	ks	ks	PROPN
ejpam-4143	226	3	is	be	AUX
ejpam-4143	226	4	a	a	DET
ejpam-4143	226	5	hyper	hyper	ADJ
ejpam-4143	226	6	up	up	ADP
ejpam-4143	226	7	-	-	PUNCT
ejpam-4143	226	8	subalgebra	subalgebra	NOUN
ejpam-4143	226	9	,	,	PUNCT
ejpam-4143	226	10	x⊛	x⊛	PROPN
ejpam-4143	226	11	y	y	PROPN
ejpam-4143	226	12	⊆	⊆	NUM
ejpam-4143	226	13	ks	k	NOUN
ejpam-4143	226	14	.	.	PUNCT
ejpam-4143	227	1	as	as	ADP
ejpam-4143	227	2	in	in	ADP
ejpam-4143	227	3	the	the	DET
ejpam-4143	227	4	case	case	NOUN
ejpam-4143	227	5	of	of	ADP
ejpam-4143	227	6	a	a	DET
ejpam-4143	227	7	portion	portion	NOUN
ejpam-4143	227	8	of	of	ADP
ejpam-4143	227	9	case	case	NOUN
ejpam-4143	227	10	1	1	NUM
ejpam-4143	227	11	,	,	PUNCT
ejpam-4143	227	12	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	NOUN
ejpam-4143	227	13	)	)	PUNCT
ejpam-4143	227	14	}	}	PUNCT
ejpam-4143	227	15	=	=	NOUN
ejpam-4143	227	16	s+j	s+j	X
ejpam-4143	227	17	s+j+1	s+j+1	NOUN
ejpam-4143	227	18	>	>	X
ejpam-4143	227	19	s	s	PART
ejpam-4143	227	20	s+1	s+1	NOUN
ejpam-4143	227	21	=	=	SYM
ejpam-4143	227	22	min{µ(x	min{µ(x	PROPN
ejpam-4143	227	23	)	)	PUNCT
ejpam-4143	227	24	,	,	PUNCT
ejpam-4143	227	25	µ(y	µ(y	PROPN
ejpam-4143	227	26	)	)	PUNCT
ejpam-4143	227	27	}	}	PUNCT
ejpam-4143	227	28	.	.	PUNCT
ejpam-4143	228	1	case	case	NOUN
ejpam-4143	228	2	3	3	NUM
ejpam-4143	228	3	:	:	SYM
ejpam-4143	228	4	x	x	X
ejpam-4143	228	5	,	,	PUNCT
ejpam-4143	228	6	y	y	PROPN
ejpam-4143	228	7	∈	∈	PROPN
ejpam-4143	228	8	⋂∞	⋂∞	NOUN
ejpam-4143	228	9	n=1kn	n=1kn	NOUN
ejpam-4143	228	10	.	.	PUNCT
ejpam-4143	229	1	then	then	ADV
ejpam-4143	229	2	x⊛	x⊛	PROPN
ejpam-4143	229	3	y	y	PROPN
ejpam-4143	229	4	⊆	⊆	NUM
ejpam-4143	229	5	⋂∞	⋂∞	NOUN
ejpam-4143	229	6	n=1kn	n=1kn	NOUN
ejpam-4143	230	1	so	so	SCONJ
ejpam-4143	230	2	that	that	SCONJ
ejpam-4143	230	3	for	for	ADP
ejpam-4143	230	4	all	all	DET
ejpam-4143	230	5	a	a	DET
ejpam-4143	230	6	∈	∈	NOUN
ejpam-4143	230	7	x⊛	x⊛	PROPN
ejpam-4143	230	8	y	y	NOUN
ejpam-4143	230	9	,	,	PUNCT
ejpam-4143	230	10	µ(a	µ(a	PROPN
ejpam-4143	230	11	)	)	PUNCT
ejpam-4143	230	12	=	=	SYM
ejpam-4143	230	13	1	1	X
ejpam-4143	230	14	.	.	PUNCT
ejpam-4143	230	15	thus	thus	ADV
ejpam-4143	230	16	,	,	PUNCT
ejpam-4143	230	17	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	PROPN
ejpam-4143	230	18	)	)	PUNCT
ejpam-4143	230	19	}	}	PUNCT
ejpam-4143	230	20	=	=	SYM
ejpam-4143	230	21	1	1	NUM
ejpam-4143	230	22	=	=	SYM
ejpam-4143	230	23	min{µ(x	min{µ(x	NOUN
ejpam-4143	230	24	)	)	PUNCT
ejpam-4143	230	25	,	,	PUNCT
ejpam-4143	230	26	µ(y	µ(y	PROPN
ejpam-4143	230	27	)	)	PUNCT
ejpam-4143	230	28	}	}	PUNCT
ejpam-4143	230	29	.	.	PUNCT
ejpam-4143	231	1	case	case	NOUN
ejpam-4143	231	2	4	4	NUM
ejpam-4143	231	3	:	:	PUNCT
ejpam-4143	231	4	x	x	SYM
ejpam-4143	231	5	∈	∈	NOUN
ejpam-4143	231	6	⋂∞	⋂∞	NOUN
ejpam-4143	231	7	n=1kn	n=1kn	NOUN
ejpam-4143	231	8	,	,	PUNCT
ejpam-4143	231	9	and	and	CCONJ
ejpam-4143	231	10	y	y	PROPN
ejpam-4143	231	11	/∈	/∈	PUNCT
ejpam-4143	231	12	⋂∞	⋂∞	NOUN
ejpam-4143	231	13	n=1kn	n=1kn	NOUN
ejpam-4143	232	1	or	or	CCONJ
ejpam-4143	233	1	(	(	PUNCT
ejpam-4143	233	2	x	x	X
ejpam-4143	233	3	/∈	/∈	INTJ
ejpam-4143	233	4	⋂∞	⋂∞	NOUN
ejpam-4143	233	5	n=1kn	n=1kn	NOUN
ejpam-4143	234	1	and	and	CCONJ
ejpam-4143	234	2	y	y	PROPN
ejpam-4143	234	3	∈	∈	PROPN
ejpam-4143	234	4	⋂∞	⋂∞	NOUN
ejpam-4143	234	5	n=1kn	n=1kn	NOUN
ejpam-4143	234	6	.	.	PUNCT
ejpam-4143	234	7	)	)	PUNCT
ejpam-4143	235	1	without	without	ADP
ejpam-4143	235	2	loss	loss	NOUN
ejpam-4143	235	3	of	of	ADP
ejpam-4143	235	4	generality	generality	NOUN
ejpam-4143	235	5	,	,	PUNCT
ejpam-4143	235	6	assume	assume	VERB
ejpam-4143	235	7	that	that	SCONJ
ejpam-4143	235	8	x	x	SYM
ejpam-4143	235	9	∈	∈	NOUN
ejpam-4143	235	10	⋂∞	⋂∞	NOUN
ejpam-4143	235	11	n=1kn	n=1kn	NOUN
ejpam-4143	235	12	and	and	CCONJ
ejpam-4143	235	13	y	y	PROPN
ejpam-4143	235	14	/∈	/∈	PUNCT
ejpam-4143	236	1	⋂∞	⋂∞	NOUN
ejpam-4143	236	2	n=1kn	n=1kn	NOUN
ejpam-4143	236	3	.	.	PUNCT
ejpam-4143	237	1	this	this	PRON
ejpam-4143	237	2	means	mean	VERB
ejpam-4143	237	3	that	that	SCONJ
ejpam-4143	237	4	there	there	PRON
ejpam-4143	237	5	exists	exist	VERB
ejpam-4143	237	6	r	r	NOUN
ejpam-4143	237	7	such	such	ADJ
ejpam-4143	237	8	that	that	PRON
ejpam-4143	237	9	y	y	PROPN
ejpam-4143	237	10	/∈	/∈	PUNCT
ejpam-4143	238	1	kr	kr	PROPN
ejpam-4143	238	2	.	.	PUNCT
ejpam-4143	239	1	thus	thus	ADV
ejpam-4143	239	2	,	,	PUNCT
ejpam-4143	239	3	the	the	DET
ejpam-4143	239	4	set	set	NOUN
ejpam-4143	239	5	s	s	PART
ejpam-4143	239	6	=	=	PUNCT
ejpam-4143	239	7	{	{	PUNCT
ejpam-4143	239	8	q	q	NOUN
ejpam-4143	239	9	:	:	PUNCT
ejpam-4143	239	10	y	y	PROPN
ejpam-4143	239	11	/∈	/∈	PUNCT
ejpam-4143	239	12	kq	kq	PROPN
ejpam-4143	239	13	}	}	PUNCT
ejpam-4143	239	14	̸=	̸=	PROPN
ejpam-4143	239	15	∅.	∅.	ADV
ejpam-4143	239	16	by	by	ADP
ejpam-4143	239	17	well	well	ADV
ejpam-4143	239	18	-	-	PUNCT
ejpam-4143	239	19	ordering	order	VERB
ejpam-4143	239	20	principle	principle	NOUN
ejpam-4143	239	21	,	,	PUNCT
ejpam-4143	239	22	there	there	PRON
ejpam-4143	239	23	exists	exist	VERB
ejpam-4143	239	24	a	a	DET
ejpam-4143	239	25	smallest	small	ADJ
ejpam-4143	239	26	element	element	NOUN
ejpam-4143	239	27	t	t	PROPN
ejpam-4143	239	28	∈	∈	PROPN
ejpam-4143	239	29	s.	s.	PROPN
ejpam-4143	239	30	this	this	PRON
ejpam-4143	239	31	means	mean	VERB
ejpam-4143	239	32	that	that	SCONJ
ejpam-4143	239	33	y	y	PROPN
ejpam-4143	239	34	∈	∈	PROPN
ejpam-4143	239	35	kt−1\kt	kt−1\kt	PROPN
ejpam-4143	240	1	so	so	SCONJ
ejpam-4143	240	2	that	that	SCONJ
ejpam-4143	240	3	µ(y	µ(y	NOUN
ejpam-4143	240	4	)	)	PUNCT
ejpam-4143	240	5	=	=	SYM
ejpam-4143	241	1	t−1	t−1	PROPN
ejpam-4143	241	2	t	t	NOUN
ejpam-4143	241	3	.	.	PUNCT
ejpam-4143	242	1	so	so	ADV
ejpam-4143	242	2	,	,	PUNCT
ejpam-4143	242	3	min{µ(x	min{µ(x	PROPN
ejpam-4143	242	4	)	)	PUNCT
ejpam-4143	242	5	,	,	PUNCT
ejpam-4143	242	6	µ(y	µ(y	PROPN
ejpam-4143	242	7	)	)	PUNCT
ejpam-4143	242	8	}	}	PUNCT
ejpam-4143	242	9	=	=	SYM
ejpam-4143	242	10	min{1	min{1	PROPN
ejpam-4143	242	11	,	,	PUNCT
ejpam-4143	242	12	t−1	t−1	PROPN
ejpam-4143	242	13	t	t	NOUN
ejpam-4143	242	14	}	}	PUNCT
ejpam-4143	242	15	=	=	PUNCT
ejpam-4143	243	1	t−1	t−1	PROPN
ejpam-4143	243	2	t	t	NOUN
ejpam-4143	243	3	.	.	PUNCT
ejpam-4143	244	1	as	as	ADP
ejpam-4143	244	2	in	in	ADP
ejpam-4143	244	3	the	the	DET
ejpam-4143	244	4	case	case	NOUN
ejpam-4143	244	5	of	of	ADP
ejpam-4143	244	6	a	a	DET
ejpam-4143	244	7	part	part	NOUN
ejpam-4143	244	8	of	of	ADP
ejpam-4143	244	9	case	case	NOUN
ejpam-4143	244	10	1	1	NUM
ejpam-4143	244	11	,	,	PUNCT
ejpam-4143	244	12	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	NOUN
ejpam-4143	244	13	)	)	PUNCT
ejpam-4143	244	14	}	}	PUNCT
ejpam-4143	244	15	=	=	SYM
ejpam-4143	244	16	t+j	t+j	NUM
ejpam-4143	245	1	t+j+1	t+j+1	INTJ
ejpam-4143	245	2	>	>	X
ejpam-4143	245	3	t−1	t−1	PROPN
ejpam-4143	245	4	t	t	NOUN
ejpam-4143	245	5	=	=	SYM
ejpam-4143	245	6	min{µ(x	min{µ(x	PROPN
ejpam-4143	245	7	)	)	PUNCT
ejpam-4143	245	8	,	,	PUNCT
ejpam-4143	245	9	µ(y	µ(y	PROPN
ejpam-4143	245	10	)	)	PUNCT
ejpam-4143	245	11	}	}	PUNCT
ejpam-4143	245	12	.	.	PUNCT
ejpam-4143	246	1	corollary	corollary	ADJ
ejpam-4143	246	2	1	1	NUM
ejpam-4143	246	3	.	.	PUNCT
ejpam-4143	247	1	let	let	VERB
ejpam-4143	247	2	h	h	PRON
ejpam-4143	247	3	be	be	AUX
ejpam-4143	247	4	a	a	DET
ejpam-4143	247	5	hyper	hyper	ADJ
ejpam-4143	247	6	up	up	NOUN
ejpam-4143	247	7	-	-	PUNCT
ejpam-4143	247	8	algebra	algebra	NOUN
ejpam-4143	247	9	.	.	PUNCT
ejpam-4143	248	1	then	then	ADV
ejpam-4143	248	2	for	for	ADP
ejpam-4143	248	3	any	any	DET
ejpam-4143	248	4	family	family	NOUN
ejpam-4143	248	5	of	of	ADP
ejpam-4143	248	6	hyper	hyper	ADJ
ejpam-4143	248	7	up	up	ADP
ejpam-4143	248	8	-	-	PUNCT
ejpam-4143	248	9	subalgebras	subalgebras	X
ejpam-4143	248	10	{	{	PUNCT
ejpam-4143	248	11	kn	kn	NOUN
ejpam-4143	248	12	:	:	PUNCT
ejpam-4143	248	13	n	n	PROPN
ejpam-4143	248	14	=	=	SYM
ejpam-4143	248	15	1	1	NUM
ejpam-4143	248	16	,	,	PUNCT
ejpam-4143	248	17	2	2	NUM
ejpam-4143	248	18	,	,	PUNCT
ejpam-4143	248	19	·	·	PUNCT
ejpam-4143	248	20	·	·	PUNCT
ejpam-4143	248	21	·	·	PUNCT
ejpam-4143	248	22	}	}	PUNCT
ejpam-4143	248	23	of	of	ADP
ejpam-4143	248	24	h	h	NOUN
ejpam-4143	248	25	such	such	ADJ
ejpam-4143	248	26	that	that	PRON
ejpam-4143	248	27	h	h	NOUN
ejpam-4143	248	28	=	=	SYM
ejpam-4143	248	29	k1	k1	PROPN
ejpam-4143	248	30	⊇	⊇	PROPN
ejpam-4143	248	31	k2	k2	PROPN
ejpam-4143	248	32	⊇	⊇	PROPN
ejpam-4143	248	33	·	·	PUNCT
ejpam-4143	248	34	·	·	PUNCT
ejpam-4143	248	35	·	·	PUNCT
ejpam-4143	248	36	,	,	PUNCT
ejpam-4143	248	37	there	there	PRON
ejpam-4143	248	38	exists	exist	VERB
ejpam-4143	248	39	fuzzy	fuzzy	ADJ
ejpam-4143	248	40	hyper	hyper	ADJ
ejpam-4143	248	41	upsubalgebras	upsubalgebra	NOUN
ejpam-4143	248	42	of	of	ADP
ejpam-4143	248	43	h	h	PROPN
ejpam-4143	248	44	whose	whose	DET
ejpam-4143	248	45	upper	upper	ADJ
ejpam-4143	248	46	level	level	NOUN
ejpam-4143	248	47	sets	set	NOUN
ejpam-4143	248	48	are	be	AUX
ejpam-4143	248	49	exactly	exactly	ADV
ejpam-4143	248	50	the	the	DET
ejpam-4143	248	51	hyper	hyper	ADJ
ejpam-4143	248	52	up	up	NOUN
ejpam-4143	248	53	-	-	PUNCT
ejpam-4143	248	54	subalgebras	subalgebras	PROPN
ejpam-4143	248	55	in	in	ADP
ejpam-4143	248	56	the	the	DET
ejpam-4143	248	57	family	family	NOUN
ejpam-4143	248	58	.	.	PUNCT
ejpam-4143	249	1	r.	r.	PROPN
ejpam-4143	249	2	amairanto	amairanto	PROPN
ejpam-4143	249	3	,	,	PUNCT
ejpam-4143	249	4	r.	r.	PROPN
ejpam-4143	249	5	isla	isla	PROPN
ejpam-4143	249	6	/	/	SYM
ejpam-4143	249	7	eur	eur	PROPN
ejpam-4143	249	8	.	.	PUNCT
ejpam-4143	250	1	j.	j.	PROPN
ejpam-4143	250	2	pure	pure	PROPN
ejpam-4143	250	3	appl	appl	PROPN
ejpam-4143	250	4	.	.	PROPN
ejpam-4143	250	5	math	math	PROPN
ejpam-4143	250	6	,	,	PUNCT
ejpam-4143	250	7	14	14	NUM
ejpam-4143	250	8	(	(	PUNCT
ejpam-4143	250	9	4	4	NUM
ejpam-4143	250	10	)	)	PUNCT
ejpam-4143	250	11	(	(	PUNCT
ejpam-4143	250	12	2021	2021	NUM
ejpam-4143	250	13	)	)	PUNCT
ejpam-4143	250	14	,	,	PUNCT
ejpam-4143	250	15	1388	1388	NUM
ejpam-4143	250	16	-	-	SYM
ejpam-4143	250	17	1401	1401	NUM
ejpam-4143	250	18	1396	1396	NUM
ejpam-4143	250	19	proof	proof	NOUN
ejpam-4143	250	20	.	.	PUNCT
ejpam-4143	251	1	define	define	VERB
ejpam-4143	251	2	a	a	DET
ejpam-4143	251	3	fuzzy	fuzzy	ADJ
ejpam-4143	251	4	set	set	VERB
ejpam-4143	251	5	µ	µ	NOUN
ejpam-4143	251	6	of	of	ADP
ejpam-4143	251	7	h	h	NOUN
ejpam-4143	251	8	by	by	ADP
ejpam-4143	251	9	µ(x	µ(x	NOUN
ejpam-4143	251	10	)	)	PUNCT
ejpam-4143	251	11	=	=	NOUN
ejpam-4143	251	12	{	{	PUNCT
ejpam-4143	251	13	n	n	NOUN
ejpam-4143	251	14	n+1	n+1	PROPN
ejpam-4143	251	15	,	,	PUNCT
ejpam-4143	251	16	if	if	SCONJ
ejpam-4143	251	17	x	x	X
ejpam-4143	251	18	∈	∈	PROPN
ejpam-4143	251	19	kn\kn+1	kn\kn+1	PROPN
ejpam-4143	251	20	,	,	PUNCT
ejpam-4143	251	21	1	1	NUM
ejpam-4143	251	22	,	,	PUNCT
ejpam-4143	251	23	if	if	SCONJ
ejpam-4143	251	24	x	x	X
ejpam-4143	251	25	∈	∈	NOUN
ejpam-4143	251	26	⋂∞	⋂∞	NOUN
ejpam-4143	251	27	n=1kn	n=1kn	NOUN
ejpam-4143	251	28	.	.	PUNCT
ejpam-4143	252	1	then	then	ADV
ejpam-4143	252	2	by	by	ADP
ejpam-4143	252	3	theorem	theorem	NOUN
ejpam-4143	252	4	7	7	NUM
ejpam-4143	252	5	,	,	PUNCT
ejpam-4143	252	6	µ	µ	PRON
ejpam-4143	252	7	is	be	AUX
ejpam-4143	252	8	a	a	DET
ejpam-4143	252	9	fuzzy	fuzzy	ADJ
ejpam-4143	252	10	hyper	hyper	ADJ
ejpam-4143	252	11	up	up	ADP
ejpam-4143	252	12	-	-	PUNCT
ejpam-4143	252	13	subalgebra	subalgebra	NOUN
ejpam-4143	252	14	of	of	ADP
ejpam-4143	252	15	h.	h.	NOUN
ejpam-4143	252	16	let	let	VERB
ejpam-4143	252	17	x	x	SYM
ejpam-4143	252	18	∈	∈	PROPN
ejpam-4143	252	19	h.	h.	PROPN
ejpam-4143	252	20	for	for	ADP
ejpam-4143	252	21	each	each	DET
ejpam-4143	252	22	n	n	CCONJ
ejpam-4143	252	23	,	,	PUNCT
ejpam-4143	252	24	consider	consider	VERB
ejpam-4143	252	25	µ	µ	PRON
ejpam-4143	252	26	n	n	NOUN
ejpam-4143	252	27	n+1	n+1	PROPN
ejpam-4143	252	28	=	=	PUNCT
ejpam-4143	252	29	{	{	PUNCT
ejpam-4143	252	30	x	x	PUNCT
ejpam-4143	252	31	∈	∈	PROPN
ejpam-4143	252	32	h	h	NOUN
ejpam-4143	252	33	:	:	PUNCT
ejpam-4143	252	34	µ(x	µ(x	X
ejpam-4143	252	35	)	)	PUNCT
ejpam-4143	252	36	≥	≥	NOUN
ejpam-4143	252	37	n	n	NOUN
ejpam-4143	252	38	n+1	n+1	PROPN
ejpam-4143	252	39	}	}	PUNCT
ejpam-4143	252	40	.	.	PUNCT
ejpam-4143	253	1	let	let	VERB
ejpam-4143	253	2	x	x	SYM
ejpam-4143	253	3	∈	∈	PROPN
ejpam-4143	253	4	kn	kn	PROPN
ejpam-4143	253	5	.	.	PUNCT
ejpam-4143	254	1	if	if	SCONJ
ejpam-4143	254	2	x	x	SYM
ejpam-4143	254	3	∈	∈	PROPN
ejpam-4143	254	4	kn\kn+1	kn\kn+1	PROPN
ejpam-4143	254	5	,	,	PUNCT
ejpam-4143	254	6	then	then	ADV
ejpam-4143	254	7	µ(x	µ(x	NOUN
ejpam-4143	254	8	)	)	PUNCT
ejpam-4143	254	9	=	=	SYM
ejpam-4143	254	10	n	n	NOUN
ejpam-4143	254	11	n+1	n+1	PROPN
ejpam-4143	254	12	.	.	PUNCT
ejpam-4143	255	1	if	if	SCONJ
ejpam-4143	255	2	x	x	SYM
ejpam-4143	255	3	∈	∈	PROPN
ejpam-4143	255	4	∩∞	∩∞	PUNCT
ejpam-4143	255	5	m=1	m=1	X
ejpam-4143	255	6	km	km	NOUN
ejpam-4143	255	7	,	,	PUNCT
ejpam-4143	255	8	then	then	ADV
ejpam-4143	255	9	µ(x	µ(x	X
ejpam-4143	255	10	)	)	PUNCT
ejpam-4143	255	11	=	=	SYM
ejpam-4143	255	12	1	1	X
ejpam-4143	255	13	>	>	SYM
ejpam-4143	255	14	n	n	PRON
ejpam-4143	255	15	n+1	n+1	PROPN
ejpam-4143	255	16	.	.	PUNCT
ejpam-4143	256	1	hence	hence	ADV
ejpam-4143	256	2	,	,	PUNCT
ejpam-4143	256	3	x	x	PUNCT
ejpam-4143	256	4	∈	∈	PROPN
ejpam-4143	256	5	µ	µ	X
ejpam-4143	256	6	n	n	NOUN
ejpam-4143	256	7	n+1	n+1	NUM
ejpam-4143	256	8	,	,	PUNCT
ejpam-4143	256	9	showing	show	VERB
ejpam-4143	256	10	that	that	SCONJ
ejpam-4143	256	11	kn	kn	PROPN
ejpam-4143	256	12	⊆	⊆	NUM
ejpam-4143	256	13	µ	µ	PROPN
ejpam-4143	256	14	n	n	NOUN
ejpam-4143	256	15	n+1	n+1	PROPN
ejpam-4143	256	16	.	.	PUNCT
ejpam-4143	257	1	if	if	SCONJ
ejpam-4143	257	2	y	y	PROPN
ejpam-4143	257	3	∈	∈	PROPN
ejpam-4143	257	4	µ	µ	PROPN
ejpam-4143	257	5	n	n	NOUN
ejpam-4143	257	6	n+1	n+1	PROPN
ejpam-4143	257	7	,	,	PUNCT
ejpam-4143	257	8	then	then	ADV
ejpam-4143	257	9	µ(y	µ(y	PROPN
ejpam-4143	257	10	)	)	PUNCT
ejpam-4143	257	11	≥	≥	NOUN
ejpam-4143	257	12	n	n	NOUN
ejpam-4143	257	13	n+1	n+1	PROPN
ejpam-4143	257	14	.	.	PUNCT
ejpam-4143	258	1	if	if	SCONJ
ejpam-4143	258	2	µ(y	µ(y	NUM
ejpam-4143	258	3	)	)	PUNCT
ejpam-4143	258	4	=	=	SYM
ejpam-4143	258	5	1	1	NUM
ejpam-4143	258	6	,	,	PUNCT
ejpam-4143	258	7	then	then	ADV
ejpam-4143	258	8	y	y	PROPN
ejpam-4143	258	9	∈	∈	PROPN
ejpam-4143	258	10	∩∞	∩∞	PUNCT
ejpam-4143	259	1	m=1	m=1	X
ejpam-4143	259	2	km	km	NOUN
ejpam-4143	259	3	.	.	PUNCT
ejpam-4143	260	1	hence	hence	ADV
ejpam-4143	260	2	,	,	PUNCT
ejpam-4143	260	3	y	y	PROPN
ejpam-4143	260	4	∈	∈	PROPN
ejpam-4143	260	5	kn	kn	PROPN
ejpam-4143	260	6	.	.	PROPN
ejpam-4143	260	7	suppose	suppose	VERB
ejpam-4143	260	8	that	that	SCONJ
ejpam-4143	260	9	y	y	PROPN
ejpam-4143	260	10	/∈	/∈	PUNCT
ejpam-4143	260	11	∩∞	∩∞	PUNCT
ejpam-4143	261	1	m=1	m=1	X
ejpam-4143	261	2	km	km	NOUN
ejpam-4143	261	3	.	.	PUNCT
ejpam-4143	262	1	choose	choose	VERB
ejpam-4143	262	2	the	the	DET
ejpam-4143	262	3	smallest	small	ADJ
ejpam-4143	262	4	integer	integer	NOUN
ejpam-4143	262	5	p	p	PRON
ejpam-4143	262	6	such	such	ADJ
ejpam-4143	262	7	that	that	SCONJ
ejpam-4143	262	8	y	y	PROPN
ejpam-4143	262	9	/∈	/∈	PUNCT
ejpam-4143	263	1	kp	kp	PROPN
ejpam-4143	263	2	.	.	PUNCT
ejpam-4143	264	1	then	then	ADV
ejpam-4143	264	2	y	y	PROPN
ejpam-4143	264	3	∈	∈	PROPN
ejpam-4143	264	4	kp−1\kp	kp−1\kp	PROPN
ejpam-4143	264	5	and	and	CCONJ
ejpam-4143	264	6	µ(y	µ(y	NUM
ejpam-4143	264	7	)	)	PUNCT
ejpam-4143	264	8	=	=	SYM
ejpam-4143	265	1	p−1	p−1	PROPN
ejpam-4143	265	2	p	p	PROPN
ejpam-4143	265	3	≥	≥	NOUN
ejpam-4143	265	4	n	n	NOUN
ejpam-4143	265	5	n+1	n+1	PROPN
ejpam-4143	265	6	.	.	PUNCT
ejpam-4143	266	1	hence	hence	ADV
ejpam-4143	266	2	,	,	PUNCT
ejpam-4143	266	3	p	p	PROPN
ejpam-4143	266	4	−	−	PROPN
ejpam-4143	266	5	1	1	NUM
ejpam-4143	266	6	≥	≥	NOUN
ejpam-4143	266	7	n.	n.	NOUN
ejpam-4143	266	8	this	this	PRON
ejpam-4143	266	9	implies	imply	VERB
ejpam-4143	266	10	that	that	SCONJ
ejpam-4143	266	11	y	y	PROPN
ejpam-4143	266	12	∈	∈	PROPN
ejpam-4143	266	13	kn	kn	PROPN
ejpam-4143	266	14	and	and	CCONJ
ejpam-4143	266	15	µ	µ	PROPN
ejpam-4143	266	16	n	n	CCONJ
ejpam-4143	266	17	n+1	n+1	PROPN
ejpam-4143	266	18	⊆	⊆	NUM
ejpam-4143	266	19	kn	kn	PROPN
ejpam-4143	266	20	.	.	PUNCT
ejpam-4143	267	1	thus	thus	ADV
ejpam-4143	267	2	,	,	PUNCT
ejpam-4143	267	3	n	n	PROPN
ejpam-4143	267	4	n+1	n+1	PROPN
ejpam-4143	267	5	=	=	SYM
ejpam-4143	267	6	kn	kn	PROPN
ejpam-4143	267	7	.	.	PROPN
ejpam-4143	267	8	4	4	NUM
ejpam-4143	267	9	.	.	X
ejpam-4143	267	10	fuzzy	fuzzy	ADJ
ejpam-4143	267	11	hyper	hyper	ADJ
ejpam-4143	267	12	up	up	ADJ
ejpam-4143	267	13	-	-	PUNCT
ejpam-4143	267	14	filter	filter	NOUN
ejpam-4143	267	15	in	in	ADP
ejpam-4143	267	16	this	this	DET
ejpam-4143	267	17	section	section	NOUN
ejpam-4143	267	18	,	,	PUNCT
ejpam-4143	267	19	we	we	PRON
ejpam-4143	267	20	introduce	introduce	VERB
ejpam-4143	267	21	the	the	DET
ejpam-4143	267	22	notion	notion	NOUN
ejpam-4143	267	23	of	of	ADP
ejpam-4143	267	24	fuzzy	fuzzy	ADJ
ejpam-4143	267	25	hyper	hyper	ADJ
ejpam-4143	267	26	up	up	ADJ
ejpam-4143	267	27	-	-	PUNCT
ejpam-4143	267	28	filter	filter	NOUN
ejpam-4143	267	29	of	of	ADP
ejpam-4143	267	30	a	a	DET
ejpam-4143	267	31	hyper	hyper	ADJ
ejpam-4143	267	32	up	up	NOUN
ejpam-4143	267	33	-	-	PUNCT
ejpam-4143	267	34	algebra	algebra	NOUN
ejpam-4143	267	35	and	and	CCONJ
ejpam-4143	267	36	study	study	VERB
ejpam-4143	267	37	some	some	PRON
ejpam-4143	267	38	of	of	ADP
ejpam-4143	267	39	its	its	PRON
ejpam-4143	267	40	basic	basic	ADJ
ejpam-4143	267	41	properties	property	NOUN
ejpam-4143	267	42	.	.	PUNCT
ejpam-4143	268	1	definition	definition	NOUN
ejpam-4143	268	2	10	10	NUM
ejpam-4143	268	3	.	.	PUNCT
ejpam-4143	269	1	a	a	DET
ejpam-4143	269	2	subset	subset	NOUN
ejpam-4143	269	3	g	g	NOUN
ejpam-4143	269	4	of	of	ADP
ejpam-4143	269	5	a	a	DET
ejpam-4143	269	6	hyper	hyper	ADJ
ejpam-4143	269	7	up	up	ADP
ejpam-4143	269	8	-	-	PUNCT
ejpam-4143	269	9	algebra	algebra	NOUN
ejpam-4143	269	10	h	h	NOUN
ejpam-4143	269	11	is	be	AUX
ejpam-4143	269	12	called	call	VERB
ejpam-4143	269	13	a	a	DET
ejpam-4143	269	14	hyper	hyper	ADJ
ejpam-4143	269	15	up	up	ADJ
ejpam-4143	269	16	-	-	PUNCT
ejpam-4143	269	17	filter	filter	NOUN
ejpam-4143	269	18	of	of	ADP
ejpam-4143	269	19	h	h	NOUN
ejpam-4143	269	20	if	if	SCONJ
ejpam-4143	269	21	it	it	PRON
ejpam-4143	269	22	satisfies	satisfy	VERB
ejpam-4143	269	23	the	the	DET
ejpam-4143	269	24	following	follow	VERB
ejpam-4143	269	25	properties	property	NOUN
ejpam-4143	269	26	:	:	PUNCT
ejpam-4143	269	27	(	(	PUNCT
ejpam-4143	269	28	i	i	NOUN
ejpam-4143	269	29	)	)	PUNCT
ejpam-4143	269	30	0	0	PUNCT
ejpam-4143	270	1	∈	∈	PROPN
ejpam-4143	270	2	g	g	PROPN
ejpam-4143	270	3	(	(	PUNCT
ejpam-4143	270	4	ii	ii	PROPN
ejpam-4143	270	5	)	)	PUNCT
ejpam-4143	270	6	for	for	ADP
ejpam-4143	270	7	any	any	DET
ejpam-4143	270	8	x	x	NOUN
ejpam-4143	270	9	,	,	PUNCT
ejpam-4143	270	10	y	y	PROPN
ejpam-4143	270	11	∈	∈	PROPN
ejpam-4143	270	12	h	h	NOUN
ejpam-4143	270	13	,	,	PUNCT
ejpam-4143	270	14	x	x	PROPN
ejpam-4143	270	15	∈	∈	PROPN
ejpam-4143	270	16	g	g	PROPN
ejpam-4143	270	17	and	and	CCONJ
ejpam-4143	270	18	x⊛	x⊛	PROPN
ejpam-4143	270	19	y	y	PROPN
ejpam-4143	270	20	⊆	⊆	NUM
ejpam-4143	270	21	g	g	PROPN
ejpam-4143	270	22	imply	imply	VERB
ejpam-4143	270	23	y	y	PROPN
ejpam-4143	270	24	∈	∈	PROPN
ejpam-4143	270	25	g.	g.	NOUN
ejpam-4143	270	26	in	in	ADP
ejpam-4143	270	27	example	example	NOUN
ejpam-4143	270	28	1	1	NUM
ejpam-4143	270	29	,	,	PUNCT
ejpam-4143	270	30	it	it	PRON
ejpam-4143	270	31	can	can	AUX
ejpam-4143	270	32	be	be	AUX
ejpam-4143	270	33	verified	verify	VERB
ejpam-4143	270	34	by	by	ADP
ejpam-4143	270	35	routine	routine	ADJ
ejpam-4143	270	36	calculations	calculation	NOUN
ejpam-4143	270	37	that	that	SCONJ
ejpam-4143	270	38	the	the	DET
ejpam-4143	270	39	set	set	NOUN
ejpam-4143	270	40	{	{	PUNCT
ejpam-4143	270	41	0	0	NUM
ejpam-4143	270	42	,	,	PUNCT
ejpam-4143	270	43	a	a	PRON
ejpam-4143	270	44	,	,	PUNCT
ejpam-4143	270	45	c	c	NOUN
ejpam-4143	270	46	}	}	PUNCT
ejpam-4143	270	47	is	be	AUX
ejpam-4143	270	48	a	a	DET
ejpam-4143	270	49	hyper	hyper	ADJ
ejpam-4143	270	50	up	up	ADJ
ejpam-4143	270	51	-	-	PUNCT
ejpam-4143	270	52	filter	filter	NOUN
ejpam-4143	270	53	of	of	ADP
ejpam-4143	270	54	h.	h.	PROPN
ejpam-4143	270	55	definition	definition	NOUN
ejpam-4143	270	56	11	11	NUM
ejpam-4143	270	57	.	.	PUNCT
ejpam-4143	271	1	a	a	DET
ejpam-4143	271	2	fuzzy	fuzzy	ADJ
ejpam-4143	271	3	set	set	VERB
ejpam-4143	271	4	µ	µ	NOUN
ejpam-4143	271	5	in	in	ADP
ejpam-4143	271	6	a	a	DET
ejpam-4143	271	7	hyper	hyper	ADJ
ejpam-4143	271	8	up	up	ADP
ejpam-4143	271	9	-	-	PUNCT
ejpam-4143	271	10	algebra	algebra	NOUN
ejpam-4143	271	11	h	h	NOUN
ejpam-4143	271	12	is	be	AUX
ejpam-4143	271	13	called	call	VERB
ejpam-4143	271	14	a	a	DET
ejpam-4143	271	15	fuzzy	fuzzy	ADJ
ejpam-4143	271	16	hyper	hyper	ADJ
ejpam-4143	271	17	up	up	ADJ
ejpam-4143	271	18	-	-	PUNCT
ejpam-4143	271	19	filter	filter	NOUN
ejpam-4143	271	20	of	of	ADP
ejpam-4143	271	21	h	h	NOUN
ejpam-4143	271	22	if	if	SCONJ
ejpam-4143	271	23	it	it	PRON
ejpam-4143	271	24	satifies	satifie	VERB
ejpam-4143	271	25	the	the	DET
ejpam-4143	271	26	following	follow	VERB
ejpam-4143	271	27	properties	property	NOUN
ejpam-4143	271	28	:	:	PUNCT
ejpam-4143	271	29	for	for	ADP
ejpam-4143	271	30	any	any	DET
ejpam-4143	271	31	x	x	NOUN
ejpam-4143	271	32	,	,	PUNCT
ejpam-4143	271	33	y	y	PROPN
ejpam-4143	271	34	∈	∈	PROPN
ejpam-4143	271	35	h	h	NOUN
ejpam-4143	271	36	,	,	PUNCT
ejpam-4143	271	37	(	(	PUNCT
ejpam-4143	271	38	i	i	NOUN
ejpam-4143	271	39	)	)	PUNCT
ejpam-4143	271	40	µ(0	µ(0	NOUN
ejpam-4143	271	41	)	)	PUNCT
ejpam-4143	271	42	≥	≥	NOUN
ejpam-4143	271	43	µ(x	µ(x	VERB
ejpam-4143	271	44	)	)	PUNCT
ejpam-4143	271	45	,	,	PUNCT
ejpam-4143	271	46	(	(	PUNCT
ejpam-4143	271	47	ii	ii	NOUN
ejpam-4143	271	48	)	)	PUNCT
ejpam-4143	271	49	µ(y	µ(y	PROPN
ejpam-4143	271	50	)	)	PUNCT
ejpam-4143	271	51	≥	≥	NOUN
ejpam-4143	271	52	min{µ(x	min{µ(x	NOUN
ejpam-4143	271	53	)	)	PUNCT
ejpam-4143	271	54	,	,	PUNCT
ejpam-4143	271	55	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	PROPN
ejpam-4143	271	56	)	)	PUNCT
ejpam-4143	271	57	}	}	PUNCT
ejpam-4143	271	58	}	}	PUNCT
ejpam-4143	271	59	.	.	PUNCT
ejpam-4143	272	1	remark	remark	NOUN
ejpam-4143	272	2	2	2	NUM
ejpam-4143	272	3	.	.	PUNCT
ejpam-4143	273	1	a	a	DET
ejpam-4143	273	2	fuzzy	fuzzy	ADJ
ejpam-4143	273	3	hyper	hyper	ADJ
ejpam-4143	273	4	up	up	ADJ
ejpam-4143	273	5	-	-	PUNCT
ejpam-4143	273	6	filter	filter	NOUN
ejpam-4143	273	7	need	need	AUX
ejpam-4143	273	8	not	not	PART
ejpam-4143	273	9	be	be	AUX
ejpam-4143	273	10	a	a	DET
ejpam-4143	273	11	fuzzy	fuzzy	ADJ
ejpam-4143	273	12	hyper	hyper	ADJ
ejpam-4143	273	13	up	up	ADP
ejpam-4143	273	14	-	-	PUNCT
ejpam-4143	273	15	subalgebra	subalgebra	NOUN
ejpam-4143	273	16	.	.	PUNCT
ejpam-4143	274	1	example	example	NOUN
ejpam-4143	274	2	6	6	NUM
ejpam-4143	274	3	.	.	PUNCT
ejpam-4143	274	4	consider	consider	VERB
ejpam-4143	274	5	the	the	DET
ejpam-4143	274	6	hyper	hyper	ADJ
ejpam-4143	274	7	up	up	ADJ
ejpam-4143	274	8	-	-	PUNCT
ejpam-4143	274	9	filter	filter	NOUN
ejpam-4143	274	10	{	{	PUNCT
ejpam-4143	274	11	0	0	NUM
ejpam-4143	274	12	,	,	PUNCT
ejpam-4143	274	13	a	a	DET
ejpam-4143	274	14	,	,	PUNCT
ejpam-4143	274	15	c	c	NOUN
ejpam-4143	274	16	}	}	PUNCT
ejpam-4143	274	17	of	of	ADP
ejpam-4143	274	18	h	h	NOUN
ejpam-4143	274	19	in	in	ADP
ejpam-4143	274	20	example	example	NOUN
ejpam-4143	274	21	1	1	X
ejpam-4143	274	22	.	.	PUNCT
ejpam-4143	275	1	it	it	PRON
ejpam-4143	275	2	can	can	AUX
ejpam-4143	275	3	be	be	AUX
ejpam-4143	275	4	easily	easily	ADV
ejpam-4143	275	5	verified	verify	VERB
ejpam-4143	275	6	that	that	SCONJ
ejpam-4143	275	7	µ(x	µ(x	VERB
ejpam-4143	275	8	)	)	PUNCT
ejpam-4143	275	9	=	=	NOUN
ejpam-4143	275	10	{	{	PUNCT
ejpam-4143	275	11	1	1	NUM
ejpam-4143	275	12	,	,	PUNCT
ejpam-4143	275	13	if	if	SCONJ
ejpam-4143	275	14	x	x	SYM
ejpam-4143	275	15	∈	∈	NOUN
ejpam-4143	275	16	{	{	PUNCT
ejpam-4143	275	17	0	0	NUM
ejpam-4143	275	18	,	,	PUNCT
ejpam-4143	275	19	a	a	PRON
ejpam-4143	275	20	,	,	PUNCT
ejpam-4143	275	21	c	c	NOUN
ejpam-4143	275	22	}	}	PUNCT
ejpam-4143	275	23	0	0	NUM
ejpam-4143	275	24	,	,	PUNCT
ejpam-4143	275	25	if	if	SCONJ
ejpam-4143	275	26	x	x	SYM
ejpam-4143	275	27	∈	∈	PROPN
ejpam-4143	275	28	{	{	PUNCT
ejpam-4143	275	29	b	b	NOUN
ejpam-4143	275	30	,	,	PUNCT
ejpam-4143	275	31	d	d	NOUN
ejpam-4143	275	32	}	}	PUNCT
ejpam-4143	275	33	is	be	AUX
ejpam-4143	275	34	a	a	DET
ejpam-4143	275	35	fuzzy	fuzzy	ADJ
ejpam-4143	275	36	hyper	hyper	ADJ
ejpam-4143	275	37	up	up	ADJ
ejpam-4143	275	38	-	-	PUNCT
ejpam-4143	275	39	filter	filter	NOUN
ejpam-4143	275	40	of	of	ADP
ejpam-4143	275	41	h.	h.	PROPN
ejpam-4143	275	42	example	example	PROPN
ejpam-4143	275	43	7	7	X
ejpam-4143	275	44	.	.	X
ejpam-4143	275	45	consider	consider	VERB
ejpam-4143	275	46	the	the	DET
ejpam-4143	275	47	fuzzy	fuzzy	ADJ
ejpam-4143	275	48	set	set	VERB
ejpam-4143	275	49	µ	µ	NOUN
ejpam-4143	275	50	in	in	ADP
ejpam-4143	275	51	example	example	NOUN
ejpam-4143	275	52	4(2	4(2	NUM
ejpam-4143	275	53	)	)	PUNCT
ejpam-4143	275	54	.	.	PUNCT
ejpam-4143	276	1	note	note	VERB
ejpam-4143	276	2	that	that	SCONJ
ejpam-4143	276	3	µ	µ	NOUN
ejpam-4143	276	4	is	be	AUX
ejpam-4143	276	5	not	not	PART
ejpam-4143	276	6	a	a	DET
ejpam-4143	276	7	fuzzy	fuzzy	ADJ
ejpam-4143	276	8	hyper	hyper	ADJ
ejpam-4143	276	9	up	up	ADP
ejpam-4143	276	10	-	-	PUNCT
ejpam-4143	276	11	subalgebra	subalgebra	NOUN
ejpam-4143	276	12	of	of	ADP
ejpam-4143	276	13	h	h	NOUN
ejpam-4143	276	14	but	but	CCONJ
ejpam-4143	276	15	by	by	ADP
ejpam-4143	276	16	routine	routine	ADJ
ejpam-4143	276	17	calculations	calculation	NOUN
ejpam-4143	276	18	,	,	PUNCT
ejpam-4143	276	19	µ	µ	X
ejpam-4143	276	20	is	be	AUX
ejpam-4143	276	21	a	a	DET
ejpam-4143	276	22	fuzzy	fuzzy	ADJ
ejpam-4143	276	23	hyper	hyper	ADJ
ejpam-4143	276	24	up	up	ADJ
ejpam-4143	276	25	-	-	PUNCT
ejpam-4143	276	26	filter	filter	NOUN
ejpam-4143	276	27	of	of	ADP
ejpam-4143	276	28	h.	h.	PROPN
ejpam-4143	276	29	r.	r.	PROPN
ejpam-4143	276	30	amairanto	amairanto	PROPN
ejpam-4143	276	31	,	,	PUNCT
ejpam-4143	276	32	r.	r.	PROPN
ejpam-4143	276	33	isla	isla	PROPN
ejpam-4143	276	34	/	/	SYM
ejpam-4143	276	35	eur	eur	PROPN
ejpam-4143	276	36	.	.	PUNCT
ejpam-4143	277	1	j.	j.	PROPN
ejpam-4143	277	2	pure	pure	PROPN
ejpam-4143	277	3	appl	appl	PROPN
ejpam-4143	277	4	.	.	PROPN
ejpam-4143	277	5	math	math	PROPN
ejpam-4143	277	6	,	,	PUNCT
ejpam-4143	277	7	14	14	NUM
ejpam-4143	277	8	(	(	PUNCT
ejpam-4143	277	9	4	4	NUM
ejpam-4143	277	10	)	)	PUNCT
ejpam-4143	277	11	(	(	PUNCT
ejpam-4143	277	12	2021	2021	NUM
ejpam-4143	277	13	)	)	PUNCT
ejpam-4143	277	14	,	,	PUNCT
ejpam-4143	277	15	1388	1388	NUM
ejpam-4143	277	16	-	-	SYM
ejpam-4143	277	17	1401	1401	NUM
ejpam-4143	277	18	1397	1397	NUM
ejpam-4143	277	19	proposition	proposition	NOUN
ejpam-4143	277	20	3	3	X
ejpam-4143	277	21	.	.	PUNCT
ejpam-4143	278	1	let	let	VERB
ejpam-4143	278	2	µ	µ	X
ejpam-4143	278	3	be	be	AUX
ejpam-4143	278	4	a	a	DET
ejpam-4143	278	5	fuzzy	fuzzy	ADJ
ejpam-4143	278	6	subset	subset	NOUN
ejpam-4143	278	7	of	of	ADP
ejpam-4143	278	8	a	a	DET
ejpam-4143	278	9	hyper	hyper	ADJ
ejpam-4143	278	10	up	up	ADP
ejpam-4143	278	11	-	-	PUNCT
ejpam-4143	278	12	algebra	algebra	NOUN
ejpam-4143	278	13	h.	h.	NOUN
ejpam-4143	278	14	if	if	SCONJ
ejpam-4143	278	15	µ	µ	NOUN
ejpam-4143	278	16	is	be	AUX
ejpam-4143	278	17	a	a	DET
ejpam-4143	278	18	fuzzy	fuzzy	ADJ
ejpam-4143	278	19	hyper	hyper	ADJ
ejpam-4143	278	20	up	up	ADJ
ejpam-4143	278	21	-	-	PUNCT
ejpam-4143	278	22	filter	filter	NOUN
ejpam-4143	278	23	of	of	ADP
ejpam-4143	278	24	h	h	NOUN
ejpam-4143	278	25	,	,	PUNCT
ejpam-4143	278	26	then	then	ADV
ejpam-4143	278	27	µt	µt	PRON
ejpam-4143	278	28	is	be	AUX
ejpam-4143	278	29	a	a	DET
ejpam-4143	278	30	hyper	hyper	ADJ
ejpam-4143	278	31	up	up	ADJ
ejpam-4143	278	32	-	-	PUNCT
ejpam-4143	278	33	filter	filter	NOUN
ejpam-4143	278	34	of	of	ADP
ejpam-4143	278	35	h	h	NOUN
ejpam-4143	278	36	for	for	ADP
ejpam-4143	278	37	each	each	DET
ejpam-4143	278	38	t	t	NOUN
ejpam-4143	278	39	∈	∈	PROPN
ejpam-4143	279	1	[	[	X
ejpam-4143	279	2	0	0	NUM
ejpam-4143	279	3	,	,	PUNCT
ejpam-4143	279	4	1	1	NUM
ejpam-4143	279	5	]	]	PUNCT
ejpam-4143	279	6	with	with	ADP
ejpam-4143	279	7	µt	µt	DET
ejpam-4143	279	8	̸=	̸=	PROPN
ejpam-4143	279	9	∅.	∅.	ADP
ejpam-4143	279	10	proof	proof	NOUN
ejpam-4143	279	11	.	.	PUNCT
ejpam-4143	280	1	suppose	suppose	VERB
ejpam-4143	280	2	that	that	SCONJ
ejpam-4143	280	3	µ	µ	NOUN
ejpam-4143	280	4	is	be	AUX
ejpam-4143	280	5	a	a	DET
ejpam-4143	280	6	fuzzy	fuzzy	ADJ
ejpam-4143	280	7	hyper	hyper	ADJ
ejpam-4143	280	8	up	up	ADJ
ejpam-4143	280	9	-	-	PUNCT
ejpam-4143	280	10	filter	filter	NOUN
ejpam-4143	280	11	of	of	ADP
ejpam-4143	280	12	h	h	NOUN
ejpam-4143	280	13	and	and	CCONJ
ejpam-4143	280	14	µt	µt	DET
ejpam-4143	280	15	̸=	̸=	PROPN
ejpam-4143	280	16	∅	∅	NOUN
ejpam-4143	280	17	,	,	PUNCT
ejpam-4143	280	18	where	where	SCONJ
ejpam-4143	280	19	t	t	PROPN
ejpam-4143	280	20	∈	∈	PROPN
ejpam-4143	281	1	[	[	X
ejpam-4143	281	2	0	0	NUM
ejpam-4143	281	3	,	,	PUNCT
ejpam-4143	281	4	1	1	NUM
ejpam-4143	281	5	]	]	PUNCT
ejpam-4143	281	6	.	.	PUNCT
ejpam-4143	282	1	then	then	ADV
ejpam-4143	282	2	there	there	PRON
ejpam-4143	282	3	exists	exist	VERB
ejpam-4143	282	4	a	a	DET
ejpam-4143	282	5	∈	∈	ADJ
ejpam-4143	282	6	µt	µt	X
ejpam-4143	282	7	and	and	CCONJ
ejpam-4143	282	8	so	so	ADV
ejpam-4143	282	9	µ(a	µ(a	PROPN
ejpam-4143	282	10	)	)	PUNCT
ejpam-4143	282	11	≥	≥	NOUN
ejpam-4143	282	12	t.	t.	NOUN
ejpam-4143	282	13	by	by	ADP
ejpam-4143	282	14	definition	definition	NOUN
ejpam-4143	282	15	11	11	NUM
ejpam-4143	282	16	,	,	PUNCT
ejpam-4143	282	17	µ(0	µ(0	NOUN
ejpam-4143	282	18	)	)	PUNCT
ejpam-4143	282	19	≥	≥	NOUN
ejpam-4143	282	20	µ(a	µ(a	NOUN
ejpam-4143	282	21	)	)	PUNCT
ejpam-4143	282	22	≥	≥	NOUN
ejpam-4143	282	23	t	t	PROPN
ejpam-4143	282	24	,	,	PUNCT
ejpam-4143	282	25	that	that	ADV
ejpam-4143	282	26	is	is	ADV
ejpam-4143	282	27	,	,	PUNCT
ejpam-4143	282	28	0	0	NUM
ejpam-4143	282	29	∈	∈	PROPN
ejpam-4143	283	1	µt	µt	PROPN
ejpam-4143	283	2	.	.	PUNCT
ejpam-4143	283	3	let	let	VERB
ejpam-4143	283	4	x	x	PRON
ejpam-4143	283	5	,	,	PUNCT
ejpam-4143	283	6	y	y	PROPN
ejpam-4143	283	7	∈	∈	PROPN
ejpam-4143	283	8	h	h	NOUN
ejpam-4143	283	9	with	with	ADP
ejpam-4143	283	10	x	x	SYM
ejpam-4143	283	11	∈	∈	PROPN
ejpam-4143	283	12	µt	µt	X
ejpam-4143	283	13	and	and	CCONJ
ejpam-4143	283	14	x	x	PROPN
ejpam-4143	283	15	⊛	⊛	NUM
ejpam-4143	283	16	y	y	PROPN
ejpam-4143	283	17	⊆	⊆	NUM
ejpam-4143	283	18	µt	µt	PROPN
ejpam-4143	283	19	.	.	PROPN
ejpam-4143	283	20	then	then	ADV
ejpam-4143	283	21	µ(x	µ(x	NOUN
ejpam-4143	283	22	)	)	PUNCT
ejpam-4143	283	23	≥	≥	NOUN
ejpam-4143	283	24	t	t	NOUN
ejpam-4143	283	25	and	and	CCONJ
ejpam-4143	283	26	for	for	ADP
ejpam-4143	283	27	all	all	DET
ejpam-4143	283	28	a	a	DET
ejpam-4143	283	29	∈	∈	NOUN
ejpam-4143	283	30	x	x	SYM
ejpam-4143	283	31	⊛	⊛	NUM
ejpam-4143	283	32	y	y	PROPN
ejpam-4143	283	33	,	,	PUNCT
ejpam-4143	283	34	µ(a	µ(a	PROPN
ejpam-4143	283	35	)	)	PUNCT
ejpam-4143	283	36	≥	≥	NOUN
ejpam-4143	283	37	t.	t.	NOUN
ejpam-4143	283	38	hence	hence	ADV
ejpam-4143	283	39	,	,	PUNCT
ejpam-4143	283	40	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	PROPN
ejpam-4143	283	41	)	)	PUNCT
ejpam-4143	283	42	}	}	PUNCT
ejpam-4143	283	43	≥	≥	NOUN
ejpam-4143	283	44	t.	t.	NOUN
ejpam-4143	283	45	since	since	SCONJ
ejpam-4143	283	46	µ	µ	PROPN
ejpam-4143	283	47	is	be	AUX
ejpam-4143	283	48	a	a	DET
ejpam-4143	283	49	fuzzy	fuzzy	ADJ
ejpam-4143	283	50	hyper	hyper	ADJ
ejpam-4143	283	51	up	up	ADJ
ejpam-4143	283	52	-	-	PUNCT
ejpam-4143	283	53	filter	filter	NOUN
ejpam-4143	283	54	,	,	PUNCT
ejpam-4143	283	55	µ(y	µ(y	PROPN
ejpam-4143	283	56	)	)	PUNCT
ejpam-4143	283	57	≥	≥	NOUN
ejpam-4143	283	58	min{µ(x	min{µ(x	NOUN
ejpam-4143	283	59	)	)	PUNCT
ejpam-4143	283	60	,	,	PUNCT
ejpam-4143	283	61	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	PROPN
ejpam-4143	283	62	)	)	PUNCT
ejpam-4143	283	63	}	}	PUNCT
ejpam-4143	283	64	}	}	PUNCT
ejpam-4143	283	65	≥	≥	NOUN
ejpam-4143	283	66	t.	t.	NOUN
ejpam-4143	283	67	hence	hence	ADV
ejpam-4143	283	68	,	,	PUNCT
ejpam-4143	283	69	y	y	PROPN
ejpam-4143	283	70	∈	∈	PROPN
ejpam-4143	283	71	µt	µt	X
ejpam-4143	284	1	and	and	CCONJ
ejpam-4143	284	2	so	so	ADV
ejpam-4143	284	3	µt	µt	PRON
ejpam-4143	284	4	is	be	AUX
ejpam-4143	284	5	a	a	DET
ejpam-4143	284	6	hyper	hyper	ADJ
ejpam-4143	284	7	up	up	ADJ
ejpam-4143	284	8	-	-	PUNCT
ejpam-4143	284	9	filter	filter	NOUN
ejpam-4143	284	10	of	of	ADP
ejpam-4143	284	11	h.	h.	NOUN
ejpam-4143	284	12	for	for	ADP
ejpam-4143	284	13	any	any	DET
ejpam-4143	284	14	nonempty	nonempty	NOUN
ejpam-4143	284	15	subset	subset	VERB
ejpam-4143	285	1	k	k	PROPN
ejpam-4143	285	2	of	of	ADP
ejpam-4143	285	3	a	a	DET
ejpam-4143	285	4	hyper	hyper	ADJ
ejpam-4143	285	5	up	up	ADP
ejpam-4143	285	6	-	-	PUNCT
ejpam-4143	285	7	algebra	algebra	NOUN
ejpam-4143	285	8	h	h	NOUN
ejpam-4143	285	9	,	,	PUNCT
ejpam-4143	285	10	we	we	PRON
ejpam-4143	285	11	define	define	VERB
ejpam-4143	285	12	a	a	DET
ejpam-4143	285	13	fuzzy	fuzzy	ADJ
ejpam-4143	285	14	set	set	VERB
ejpam-4143	285	15	µk	µk	NOUN
ejpam-4143	285	16	in	in	ADP
ejpam-4143	285	17	h	h	NOUN
ejpam-4143	285	18	by	by	ADP
ejpam-4143	285	19	µk(x	µk(x	NOUN
ejpam-4143	285	20	)	)	PUNCT
ejpam-4143	285	21	=	=	SYM
ejpam-4143	285	22	{	{	PUNCT
ejpam-4143	285	23	α	α	NOUN
ejpam-4143	285	24	,	,	PUNCT
ejpam-4143	285	25	if	if	SCONJ
ejpam-4143	285	26	x	x	PROPN
ejpam-4143	285	27	∈	∈	PROPN
ejpam-4143	285	28	k	k	X
ejpam-4143	285	29	β	β	X
ejpam-4143	285	30	,	,	PUNCT
ejpam-4143	285	31	if	if	SCONJ
ejpam-4143	285	32	x	x	X
ejpam-4143	285	33	/∈	/∈	PROPN
ejpam-4143	285	34	k	k	PROPN
ejpam-4143	285	35	for	for	ADP
ejpam-4143	285	36	all	all	DET
ejpam-4143	285	37	x	x	SYM
ejpam-4143	285	38	∈	∈	PROPN
ejpam-4143	285	39	h	h	NOUN
ejpam-4143	285	40	and	and	CCONJ
ejpam-4143	285	41	α	α	NOUN
ejpam-4143	285	42	,	,	PUNCT
ejpam-4143	285	43	β	β	X
ejpam-4143	285	44	∈	∈	PROPN
ejpam-4143	286	1	[	[	X
ejpam-4143	286	2	0	0	NUM
ejpam-4143	286	3	,	,	PUNCT
ejpam-4143	286	4	1	1	NUM
ejpam-4143	286	5	]	]	PUNCT
ejpam-4143	286	6	with	with	ADP
ejpam-4143	286	7	α	α	PROPN
ejpam-4143	286	8	>	>	X
ejpam-4143	286	9	β	β	PROPN
ejpam-4143	286	10	.	.	PUNCT
ejpam-4143	287	1	lemma	lemma	PROPN
ejpam-4143	287	2	3	3	X
ejpam-4143	287	3	.	.	PUNCT
ejpam-4143	288	1	let	let	VERB
ejpam-4143	288	2	k	k	PRON
ejpam-4143	288	3	be	be	AUX
ejpam-4143	288	4	a	a	DET
ejpam-4143	288	5	nonempty	nonempty	ADJ
ejpam-4143	288	6	subset	subset	NOUN
ejpam-4143	288	7	of	of	ADP
ejpam-4143	288	8	a	a	DET
ejpam-4143	288	9	hyper	hyper	ADJ
ejpam-4143	288	10	up	up	ADP
ejpam-4143	288	11	-	-	PUNCT
ejpam-4143	288	12	algebra	algebra	NOUN
ejpam-4143	288	13	h.	h.	NOUN
ejpam-4143	288	14	if	if	SCONJ
ejpam-4143	288	15	µk	µk	PRON
ejpam-4143	288	16	is	be	AUX
ejpam-4143	288	17	a	a	DET
ejpam-4143	288	18	fuzzy	fuzzy	ADJ
ejpam-4143	288	19	hyper	hyper	ADJ
ejpam-4143	288	20	up	up	ADJ
ejpam-4143	288	21	-	-	PUNCT
ejpam-4143	288	22	filter	filter	NOUN
ejpam-4143	288	23	of	of	ADP
ejpam-4143	288	24	h	h	NOUN
ejpam-4143	288	25	,	,	PUNCT
ejpam-4143	288	26	then	then	ADV
ejpam-4143	288	27	0	0	NUM
ejpam-4143	288	28	∈	∈	PROPN
ejpam-4143	288	29	k.	k.	NOUN
ejpam-4143	288	30	proof	proof	NOUN
ejpam-4143	288	31	.	.	PUNCT
ejpam-4143	289	1	let	let	VERB
ejpam-4143	289	2	µk	µk	PRON
ejpam-4143	289	3	be	be	AUX
ejpam-4143	289	4	a	a	DET
ejpam-4143	289	5	fuzzy	fuzzy	ADJ
ejpam-4143	289	6	hyper	hyper	ADJ
ejpam-4143	289	7	up	up	ADJ
ejpam-4143	289	8	-	-	PUNCT
ejpam-4143	289	9	filter	filter	NOUN
ejpam-4143	289	10	of	of	ADP
ejpam-4143	289	11	h.	h.	NOUN
ejpam-4143	289	12	since	since	SCONJ
ejpam-4143	289	13	k	k	PROPN
ejpam-4143	289	14	̸=	̸=	PROPN
ejpam-4143	289	15	∅	∅	NOUN
ejpam-4143	289	16	,	,	PUNCT
ejpam-4143	289	17	it	it	PRON
ejpam-4143	289	18	follows	follow	VERB
ejpam-4143	289	19	that	that	SCONJ
ejpam-4143	289	20	there	there	PRON
ejpam-4143	289	21	exists	exist	VERB
ejpam-4143	289	22	a	a	DET
ejpam-4143	289	23	∈	∈	PROPN
ejpam-4143	289	24	k	k	NOUN
ejpam-4143	289	25	with	with	ADP
ejpam-4143	289	26	µk(a	µk(a	NOUN
ejpam-4143	289	27	)	)	PUNCT
ejpam-4143	289	28	=	=	SYM
ejpam-4143	290	1	α	α	X
ejpam-4143	290	2	.	.	PUNCT
ejpam-4143	291	1	by	by	ADP
ejpam-4143	291	2	definition	definition	NOUN
ejpam-4143	291	3	11(i	11(i	NUM
ejpam-4143	291	4	)	)	PUNCT
ejpam-4143	291	5	,	,	PUNCT
ejpam-4143	291	6	µk(0	µk(0	NOUN
ejpam-4143	291	7	)	)	PUNCT
ejpam-4143	291	8	≥	≥	NOUN
ejpam-4143	291	9	µk(a	µk(a	PUNCT
ejpam-4143	291	10	)	)	PUNCT
ejpam-4143	291	11	=	=	SYM
ejpam-4143	291	12	α	α	X
ejpam-4143	291	13	.	.	PUNCT
ejpam-4143	292	1	since	since	SCONJ
ejpam-4143	292	2	α	α	X
ejpam-4143	292	3	>	>	X
ejpam-4143	292	4	β	β	X
ejpam-4143	292	5	,	,	PUNCT
ejpam-4143	292	6	we	we	PRON
ejpam-4143	292	7	have	have	VERB
ejpam-4143	292	8	µk(0	µk(0	NOUN
ejpam-4143	292	9	)	)	PUNCT
ejpam-4143	293	1	=	=	SYM
ejpam-4143	293	2	α	α	X
ejpam-4143	293	3	.	.	PUNCT
ejpam-4143	294	1	hence	hence	ADV
ejpam-4143	294	2	,	,	PUNCT
ejpam-4143	294	3	0	0	NUM
ejpam-4143	294	4	∈	∈	PROPN
ejpam-4143	294	5	k.	k.	PROPN
ejpam-4143	294	6	theorem	theorem	VERB
ejpam-4143	294	7	8	8	NUM
ejpam-4143	294	8	.	.	PUNCT
ejpam-4143	295	1	let	let	VERB
ejpam-4143	295	2	k	k	PRON
ejpam-4143	295	3	be	be	AUX
ejpam-4143	295	4	a	a	DET
ejpam-4143	295	5	nonempty	nonempty	ADJ
ejpam-4143	295	6	subset	subset	NOUN
ejpam-4143	295	7	of	of	ADP
ejpam-4143	295	8	a	a	DET
ejpam-4143	295	9	hyper	hyper	ADJ
ejpam-4143	295	10	up	up	ADP
ejpam-4143	295	11	-	-	PUNCT
ejpam-4143	295	12	algebra	algebra	NOUN
ejpam-4143	295	13	h.	h.	NOUN
ejpam-4143	295	14	if	if	SCONJ
ejpam-4143	295	15	µk	µk	PRON
ejpam-4143	295	16	is	be	AUX
ejpam-4143	295	17	a	a	DET
ejpam-4143	295	18	fuzzy	fuzzy	ADJ
ejpam-4143	295	19	hyper	hyper	ADJ
ejpam-4143	295	20	up	up	ADJ
ejpam-4143	295	21	-	-	PUNCT
ejpam-4143	295	22	filter	filter	NOUN
ejpam-4143	295	23	of	of	ADP
ejpam-4143	295	24	h	h	NOUN
ejpam-4143	295	25	,	,	PUNCT
ejpam-4143	295	26	then	then	ADV
ejpam-4143	295	27	k	k	PROPN
ejpam-4143	295	28	is	be	AUX
ejpam-4143	295	29	a	a	DET
ejpam-4143	295	30	hyper	hyper	ADJ
ejpam-4143	295	31	up	up	ADJ
ejpam-4143	295	32	-	-	PUNCT
ejpam-4143	295	33	filter	filter	NOUN
ejpam-4143	295	34	of	of	ADP
ejpam-4143	295	35	h.	h.	NOUN
ejpam-4143	295	36	proof	proof	NOUN
ejpam-4143	295	37	.	.	PUNCT
ejpam-4143	296	1	suppose	suppose	VERB
ejpam-4143	296	2	that	that	SCONJ
ejpam-4143	296	3	µk	µk	PROPN
ejpam-4143	296	4	is	be	AUX
ejpam-4143	296	5	a	a	DET
ejpam-4143	296	6	fuzzy	fuzzy	ADJ
ejpam-4143	296	7	hyper	hyper	ADJ
ejpam-4143	296	8	up	up	ADJ
ejpam-4143	296	9	-	-	PUNCT
ejpam-4143	296	10	filter	filter	NOUN
ejpam-4143	296	11	of	of	ADP
ejpam-4143	296	12	h.	h.	PROPN
ejpam-4143	296	13	let	let	VERB
ejpam-4143	296	14	x	x	PRON
ejpam-4143	296	15	,	,	PUNCT
ejpam-4143	296	16	y	y	PROPN
ejpam-4143	296	17	∈	∈	PROPN
ejpam-4143	296	18	h	h	NOUN
ejpam-4143	296	19	with	with	ADP
ejpam-4143	296	20	x	x	PROPN
ejpam-4143	296	21	∈	∈	PROPN
ejpam-4143	296	22	k	k	PROPN
ejpam-4143	296	23	and	and	CCONJ
ejpam-4143	296	24	x	x	PROPN
ejpam-4143	296	25	⊛	⊛	NUM
ejpam-4143	296	26	y	y	PROPN
ejpam-4143	296	27	⊆	⊆	NUM
ejpam-4143	296	28	k.	k.	NOUN
ejpam-4143	296	29	then	then	ADV
ejpam-4143	296	30	for	for	ADP
ejpam-4143	296	31	all	all	DET
ejpam-4143	296	32	a	a	DET
ejpam-4143	296	33	∈	∈	NOUN
ejpam-4143	296	34	x	x	PUNCT
ejpam-4143	296	35	⊛	⊛	NUM
ejpam-4143	296	36	y	y	PROPN
ejpam-4143	296	37	,	,	PUNCT
ejpam-4143	296	38	we	we	PRON
ejpam-4143	296	39	have	have	VERB
ejpam-4143	296	40	a	a	DET
ejpam-4143	296	41	∈	∈	ADJ
ejpam-4143	296	42	k	k	NOUN
ejpam-4143	296	43	,	,	PUNCT
ejpam-4143	296	44	that	that	ADV
ejpam-4143	296	45	is	is	ADV
ejpam-4143	296	46	,	,	PUNCT
ejpam-4143	296	47	µk(a	µk(a	X
ejpam-4143	296	48	)	)	PUNCT
ejpam-4143	296	49	=	=	SYM
ejpam-4143	297	1	α	α	X
ejpam-4143	297	2	.	.	PUNCT
ejpam-4143	298	1	it	it	PRON
ejpam-4143	298	2	follows	follow	VERB
ejpam-4143	298	3	that	that	SCONJ
ejpam-4143	298	4	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	PROPN
ejpam-4143	298	5	)	)	PUNCT
ejpam-4143	298	6	}	}	PUNCT
ejpam-4143	298	7	=	=	SYM
ejpam-4143	299	1	α	α	X
ejpam-4143	299	2	.	.	PUNCT
ejpam-4143	300	1	by	by	ADP
ejpam-4143	300	2	definition	definition	NOUN
ejpam-4143	300	3	11(ii	11(ii	NUM
ejpam-4143	300	4	)	)	PUNCT
ejpam-4143	300	5	,	,	PUNCT
ejpam-4143	300	6	µ(y	µ(y	PROPN
ejpam-4143	300	7	)	)	PUNCT
ejpam-4143	300	8	≥	≥	NOUN
ejpam-4143	300	9	min{µ(x	min{µ(x	NOUN
ejpam-4143	300	10	)	)	PUNCT
ejpam-4143	300	11	,	,	PUNCT
ejpam-4143	300	12	infa∈x⊛y{µ(a	infa∈x⊛y{µ(a	PROPN
ejpam-4143	300	13	)	)	PUNCT
ejpam-4143	300	14	}	}	PUNCT
ejpam-4143	300	15	}	}	PUNCT
ejpam-4143	300	16	=	=	SYM
ejpam-4143	301	1	α	α	X
ejpam-4143	301	2	.	.	PUNCT
ejpam-4143	302	1	since	since	SCONJ
ejpam-4143	302	2	α	α	X
ejpam-4143	302	3	>	>	X
ejpam-4143	302	4	β	β	X
ejpam-4143	302	5	,	,	PUNCT
ejpam-4143	302	6	it	it	PRON
ejpam-4143	302	7	follows	follow	VERB
ejpam-4143	302	8	that	that	SCONJ
ejpam-4143	302	9	µk(y	µk(y	PUNCT
ejpam-4143	302	10	)	)	PUNCT
ejpam-4143	303	1	=	=	SYM
ejpam-4143	303	2	α	α	X
ejpam-4143	303	3	.	.	PUNCT
ejpam-4143	304	1	hence	hence	ADV
ejpam-4143	304	2	,	,	PUNCT
ejpam-4143	304	3	y	y	PROPN
ejpam-4143	304	4	∈	∈	PROPN
ejpam-4143	304	5	µk	µk	NOUN
ejpam-4143	304	6	and	and	CCONJ
ejpam-4143	304	7	since	since	SCONJ
ejpam-4143	304	8	0	0	NUM
ejpam-4143	304	9	∈	∈	PROPN
ejpam-4143	304	10	k	k	NOUN
ejpam-4143	304	11	by	by	ADP
ejpam-4143	304	12	lemma	lemma	PROPN
ejpam-4143	304	13	3	3	NUM
ejpam-4143	304	14	,	,	PUNCT
ejpam-4143	304	15	µk	µk	PRON
ejpam-4143	304	16	is	be	AUX
ejpam-4143	304	17	a	a	DET
ejpam-4143	304	18	hyper	hyper	ADJ
ejpam-4143	304	19	up	up	ADJ
ejpam-4143	304	20	-	-	PUNCT
ejpam-4143	304	21	filter	filter	NOUN
ejpam-4143	304	22	of	of	ADP
ejpam-4143	304	23	h.	h.	PROPN
ejpam-4143	304	24	lemma	lemma	PROPN
ejpam-4143	304	25	4	4	X
ejpam-4143	304	26	.	.	PUNCT
ejpam-4143	305	1	let	let	VERB
ejpam-4143	305	2	{	{	PUNCT
ejpam-4143	305	3	µα	µα	ADP
ejpam-4143	305	4	:	:	PUNCT
ejpam-4143	305	5	α	α	PROPN
ejpam-4143	305	6	∈	∈	PROPN
ejpam-4143	305	7	a	a	PRON
ejpam-4143	305	8	}	}	PUNCT
ejpam-4143	305	9	be	be	AUX
ejpam-4143	305	10	a	a	DET
ejpam-4143	305	11	nonempty	nonempty	ADJ
ejpam-4143	305	12	family	family	NOUN
ejpam-4143	305	13	of	of	ADP
ejpam-4143	305	14	fuzzy	fuzzy	ADJ
ejpam-4143	305	15	subsets	subset	NOUN
ejpam-4143	305	16	of	of	ADP
ejpam-4143	305	17	a	a	DET
ejpam-4143	305	18	hyper	hyper	ADJ
ejpam-4143	305	19	up	up	ADP
ejpam-4143	305	20	-	-	PUNCT
ejpam-4143	305	21	algebra	algebra	NOUN
ejpam-4143	305	22	h.	h.	NOUN
ejpam-4143	305	23	then	then	ADV
ejpam-4143	305	24	inf	inf	PROPN
ejpam-4143	305	25	α∈a	α∈a	PROPN
ejpam-4143	305	26	{	{	PUNCT
ejpam-4143	305	27	min	min	NOUN
ejpam-4143	305	28	{	{	PUNCT
ejpam-4143	305	29	µα(x	µα(x	NUM
ejpam-4143	305	30	)	)	PUNCT
ejpam-4143	305	31	,	,	PUNCT
ejpam-4143	305	32	inf	inf	PROPN
ejpam-4143	305	33	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	305	34	{	{	PUNCT
ejpam-4143	305	35	µα(a	µα(a	NOUN
ejpam-4143	305	36	)	)	PUNCT
ejpam-4143	305	37	}	}	PUNCT
ejpam-4143	305	38	}	}	PUNCT
ejpam-4143	305	39	}	}	PUNCT
ejpam-4143	305	40	≥	≥	PROPN
ejpam-4143	305	41	min	min	PROPN
ejpam-4143	305	42	{	{	PUNCT
ejpam-4143	305	43	inf	inf	NOUN
ejpam-4143	305	44	α∈a	α∈a	PROPN
ejpam-4143	305	45	{	{	PUNCT
ejpam-4143	305	46	µα(x	µα(x	NUM
ejpam-4143	305	47	)	)	PUNCT
ejpam-4143	305	48	}	}	PUNCT
ejpam-4143	305	49	,	,	PUNCT
ejpam-4143	305	50	inf	inf	PROPN
ejpam-4143	305	51	α∈a	α∈a	PROPN
ejpam-4143	305	52	{	{	PUNCT
ejpam-4143	305	53	inf	inf	PROPN
ejpam-4143	305	54	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	305	55	{	{	PUNCT
ejpam-4143	305	56	µα(a	µα(a	NOUN
ejpam-4143	305	57	)	)	PUNCT
ejpam-4143	305	58	}	}	PUNCT
ejpam-4143	305	59	}	}	PUNCT
ejpam-4143	305	60	}	}	PUNCT
ejpam-4143	305	61	.	.	PUNCT
ejpam-4143	306	1	proof	proof	NOUN
ejpam-4143	306	2	.	.	PUNCT
ejpam-4143	307	1	let	let	VERB
ejpam-4143	307	2	x	x	PRON
ejpam-4143	307	3	,	,	PUNCT
ejpam-4143	307	4	y	y	PROPN
ejpam-4143	307	5	∈	∈	PROPN
ejpam-4143	307	6	h.	h.	PROPN
ejpam-4143	307	7	note	note	VERB
ejpam-4143	307	8	that	that	SCONJ
ejpam-4143	307	9	∀α	∀α	VERB
ejpam-4143	307	10	∈	∈	PROPN
ejpam-4143	307	11	a	a	PRON
ejpam-4143	307	12	,	,	PUNCT
ejpam-4143	307	13	µα(x	µα(x	NUM
ejpam-4143	307	14	)	)	PUNCT
ejpam-4143	307	15	≥	≥	NOUN
ejpam-4143	307	16	infα∈a{µα(x	infα∈a{µα(x	NUM
ejpam-4143	307	17	)	)	PUNCT
ejpam-4143	307	18	}	}	PUNCT
ejpam-4143	307	19	and	and	CCONJ
ejpam-4143	307	20	infa∈x⊛y{µα(a	infa∈x⊛y{µα(a	NOUN
ejpam-4143	307	21	)	)	PUNCT
ejpam-4143	307	22	}	}	PUNCT
ejpam-4143	307	23	≥	≥	NOUN
ejpam-4143	307	24	infα∈a{infa∈x⊛y{µα(a	infα∈a{infa∈x⊛y{µα(a	NOUN
ejpam-4143	307	25	)	)	PUNCT
ejpam-4143	307	26	}	}	PUNCT
ejpam-4143	307	27	}	}	PUNCT
ejpam-4143	307	28	.	.	PUNCT
ejpam-4143	308	1	thus	thus	ADV
ejpam-4143	308	2	,	,	PUNCT
ejpam-4143	308	3	∀	∀	X
ejpam-4143	308	4	α	α	NOUN
ejpam-4143	308	5	∈	∈	PROPN
ejpam-4143	308	6	a	a	PRON
ejpam-4143	308	7	,	,	PUNCT
ejpam-4143	308	8	we	we	PRON
ejpam-4143	308	9	have	have	VERB
ejpam-4143	308	10	min{µα(x	min{µα(x	PROPN
ejpam-4143	308	11	)	)	PUNCT
ejpam-4143	308	12	,	,	PUNCT
ejpam-4143	308	13	inf	inf	PROPN
ejpam-4143	308	14	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	308	15	{	{	PUNCT
ejpam-4143	308	16	µα(a	µα(a	NOUN
ejpam-4143	308	17	)	)	PUNCT
ejpam-4143	308	18	}	}	PUNCT
ejpam-4143	308	19	}	}	PUNCT
ejpam-4143	308	20	≥	≥	PROPN
ejpam-4143	308	21	min	min	PROPN
ejpam-4143	308	22	{	{	PUNCT
ejpam-4143	308	23	inf	inf	NOUN
ejpam-4143	308	24	α∈a	α∈a	PROPN
ejpam-4143	308	25	{	{	PUNCT
ejpam-4143	308	26	µα(x	µα(x	NUM
ejpam-4143	308	27	)	)	PUNCT
ejpam-4143	308	28	}	}	PUNCT
ejpam-4143	308	29	,	,	PUNCT
ejpam-4143	308	30	inf	inf	PROPN
ejpam-4143	308	31	α∈a	α∈a	PROPN
ejpam-4143	308	32	{	{	PUNCT
ejpam-4143	308	33	inf	inf	PROPN
ejpam-4143	308	34	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	308	35	{	{	PUNCT
ejpam-4143	308	36	µα(a	µα(a	NOUN
ejpam-4143	308	37	)	)	PUNCT
ejpam-4143	308	38	}	}	PUNCT
ejpam-4143	308	39	}	}	PUNCT
ejpam-4143	308	40	}	}	PUNCT
ejpam-4143	308	41	.	.	PUNCT
ejpam-4143	309	1	hence	hence	ADV
ejpam-4143	309	2	,	,	PUNCT
ejpam-4143	309	3	inf	inf	PROPN
ejpam-4143	309	4	α∈a	α∈a	PROPN
ejpam-4143	309	5	{	{	PUNCT
ejpam-4143	309	6	min	min	NOUN
ejpam-4143	309	7	{	{	PUNCT
ejpam-4143	309	8	µα(x	µα(x	NUM
ejpam-4143	309	9	)	)	PUNCT
ejpam-4143	309	10	,	,	PUNCT
ejpam-4143	309	11	inf	inf	PROPN
ejpam-4143	309	12	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	309	13	{	{	PUNCT
ejpam-4143	309	14	µα(a	µα(a	NOUN
ejpam-4143	309	15	)	)	PUNCT
ejpam-4143	309	16	}	}	PUNCT
ejpam-4143	309	17	}	}	PUNCT
ejpam-4143	309	18	}	}	PUNCT
ejpam-4143	309	19	≥	≥	PROPN
ejpam-4143	309	20	min	min	PROPN
ejpam-4143	309	21	{	{	PUNCT
ejpam-4143	309	22	inf	inf	NOUN
ejpam-4143	309	23	α∈a	α∈a	PROPN
ejpam-4143	309	24	{	{	PUNCT
ejpam-4143	309	25	µα(x	µα(x	NUM
ejpam-4143	309	26	)	)	PUNCT
ejpam-4143	309	27	}	}	PUNCT
ejpam-4143	309	28	,	,	PUNCT
ejpam-4143	309	29	inf	inf	PROPN
ejpam-4143	309	30	α∈a	α∈a	PROPN
ejpam-4143	309	31	{	{	PUNCT
ejpam-4143	309	32	inf	inf	PROPN
ejpam-4143	309	33	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	309	34	{	{	PUNCT
ejpam-4143	309	35	µα(a	µα(a	NOUN
ejpam-4143	309	36	)	)	PUNCT
ejpam-4143	309	37	}	}	PUNCT
ejpam-4143	309	38	}	}	PUNCT
ejpam-4143	309	39	}	}	PUNCT
ejpam-4143	309	40	.	.	PUNCT
ejpam-4143	310	1	r.	r.	PROPN
ejpam-4143	310	2	amairanto	amairanto	PROPN
ejpam-4143	310	3	,	,	PUNCT
ejpam-4143	310	4	r.	r.	PROPN
ejpam-4143	310	5	isla	isla	PROPN
ejpam-4143	310	6	/	/	SYM
ejpam-4143	310	7	eur	eur	PROPN
ejpam-4143	310	8	.	.	PUNCT
ejpam-4143	311	1	j.	j.	PROPN
ejpam-4143	311	2	pure	pure	PROPN
ejpam-4143	311	3	appl	appl	PROPN
ejpam-4143	311	4	.	.	PROPN
ejpam-4143	311	5	math	math	PROPN
ejpam-4143	311	6	,	,	PUNCT
ejpam-4143	311	7	14	14	NUM
ejpam-4143	311	8	(	(	PUNCT
ejpam-4143	311	9	4	4	NUM
ejpam-4143	311	10	)	)	PUNCT
ejpam-4143	311	11	(	(	PUNCT
ejpam-4143	311	12	2021	2021	NUM
ejpam-4143	311	13	)	)	PUNCT
ejpam-4143	311	14	,	,	PUNCT
ejpam-4143	311	15	1388	1388	NUM
ejpam-4143	311	16	-	-	SYM
ejpam-4143	311	17	1401	1401	NUM
ejpam-4143	311	18	1398	1398	NUM
ejpam-4143	311	19	theorem	theorem	NOUN
ejpam-4143	311	20	9	9	NUM
ejpam-4143	311	21	.	.	PUNCT
ejpam-4143	312	1	let	let	VERB
ejpam-4143	312	2	{	{	PUNCT
ejpam-4143	312	3	µα	µα	ADP
ejpam-4143	312	4	:	:	PUNCT
ejpam-4143	312	5	α	α	PROPN
ejpam-4143	312	6	∈	∈	PROPN
ejpam-4143	312	7	a	a	DET
ejpam-4143	312	8	}	}	PUNCT
ejpam-4143	312	9	be	be	AUX
ejpam-4143	312	10	a	a	DET
ejpam-4143	312	11	nonempty	nonempty	ADJ
ejpam-4143	312	12	family	family	NOUN
ejpam-4143	312	13	of	of	ADP
ejpam-4143	312	14	fuzzy	fuzzy	ADJ
ejpam-4143	312	15	subsets	subset	NOUN
ejpam-4143	312	16	of	of	ADP
ejpam-4143	312	17	a	a	DET
ejpam-4143	312	18	hyper	hyper	ADJ
ejpam-4143	312	19	upalgebra	upalgebra	NOUN
ejpam-4143	312	20	h.	h.	PROPN
ejpam-4143	313	1	if	if	SCONJ
ejpam-4143	313	2	µα	µα	ADV
ejpam-4143	313	3	is	be	AUX
ejpam-4143	313	4	a	a	DET
ejpam-4143	313	5	fuzzy	fuzzy	ADJ
ejpam-4143	313	6	hyper	hyper	ADJ
ejpam-4143	313	7	up	up	ADJ
ejpam-4143	313	8	-	-	PUNCT
ejpam-4143	313	9	filter	filter	NOUN
ejpam-4143	313	10	of	of	ADP
ejpam-4143	313	11	h	h	NOUN
ejpam-4143	313	12	for	for	ADP
ejpam-4143	313	13	all	all	DET
ejpam-4143	313	14	α	α	NOUN
ejpam-4143	313	15	∈	∈	PROPN
ejpam-4143	313	16	a	a	PRON
ejpam-4143	313	17	,	,	PUNCT
ejpam-4143	313	18	then	then	ADV
ejpam-4143	313	19	so	so	ADV
ejpam-4143	313	20	is	be	AUX
ejpam-4143	313	21	∧α∈aµα	∧α∈aµα	X
ejpam-4143	313	22	.	.	PUNCT
ejpam-4143	313	23	proof	proof	NOUN
ejpam-4143	313	24	.	.	PUNCT
ejpam-4143	314	1	let	let	VERB
ejpam-4143	314	2	x	x	PRON
ejpam-4143	314	3	,	,	PUNCT
ejpam-4143	314	4	y	y	PROPN
ejpam-4143	314	5	∈	∈	PROPN
ejpam-4143	314	6	h.	h.	PROPN
ejpam-4143	314	7	since	since	SCONJ
ejpam-4143	314	8	each	each	PRON
ejpam-4143	314	9	µα	µα	NOUN
ejpam-4143	314	10	is	be	AUX
ejpam-4143	314	11	a	a	DET
ejpam-4143	314	12	fuzzy	fuzzy	ADJ
ejpam-4143	314	13	hyper	hyper	ADJ
ejpam-4143	314	14	up	up	ADJ
ejpam-4143	314	15	-	-	PUNCT
ejpam-4143	314	16	filter	filter	NOUN
ejpam-4143	314	17	of	of	ADP
ejpam-4143	314	18	h,µα(0	h,µα(0	NOUN
ejpam-4143	314	19	)	)	PUNCT
ejpam-4143	314	20	≥	≥	NOUN
ejpam-4143	314	21	µα(x	µα(x	NUM
ejpam-4143	314	22	)	)	PUNCT
ejpam-4143	314	23	for	for	ADP
ejpam-4143	314	24	all	all	DET
ejpam-4143	314	25	α	α	DET
ejpam-4143	314	26	∈	∈	NOUN
ejpam-4143	314	27	a.	a.	NOUN
ejpam-4143	314	28	thus	thus	ADV
ejpam-4143	314	29	for	for	ADP
ejpam-4143	314	30	all	all	DET
ejpam-4143	314	31	α	α	NOUN
ejpam-4143	314	32	∈	∈	PROPN
ejpam-4143	314	33	a	a	DET
ejpam-4143	314	34	,	,	PUNCT
ejpam-4143	314	35	infα∈a{µα(0	infα∈a{µα(0	NOUN
ejpam-4143	314	36	)	)	PUNCT
ejpam-4143	314	37	}	}	PUNCT
ejpam-4143	314	38	≥	≥	NOUN
ejpam-4143	314	39	µα(x	µα(x	NUM
ejpam-4143	314	40	)	)	PUNCT
ejpam-4143	314	41	.	.	PUNCT
ejpam-4143	315	1	hence	hence	ADV
ejpam-4143	315	2	,	,	PUNCT
ejpam-4143	315	3	infα∈a{µα(0	infα∈a{µα(0	ADV
ejpam-4143	315	4	)	)	PUNCT
ejpam-4143	315	5	}	}	PUNCT
ejpam-4143	315	6	≥	≥	PROPN
ejpam-4143	315	7	infα∈a{µα(x	infα∈a{µα(x	NUM
ejpam-4143	315	8	)	)	PUNCT
ejpam-4143	315	9	}	}	PUNCT
ejpam-4143	315	10	,	,	PUNCT
ejpam-4143	315	11	or	or	CCONJ
ejpam-4143	315	12	equivalently	equivalently	ADV
ejpam-4143	315	13	,	,	PUNCT
ejpam-4143	315	14	∧α∈aµα(0	∧α∈aµα(0	NOUN
ejpam-4143	315	15	)	)	PUNCT
ejpam-4143	315	16	≥	≥	NOUN
ejpam-4143	315	17	∧α∈aµα(x	∧α∈aµα(x	PROPN
ejpam-4143	315	18	)	)	PUNCT
ejpam-4143	315	19	.	.	PUNCT
ejpam-4143	316	1	now	now	ADV
ejpam-4143	316	2	,	,	PUNCT
ejpam-4143	316	3	by	by	ADP
ejpam-4143	316	4	definitions	definition	NOUN
ejpam-4143	316	5	11	11	NUM
ejpam-4143	316	6	and	and	CCONJ
ejpam-4143	316	7	7	7	NUM
ejpam-4143	316	8	and	and	CCONJ
ejpam-4143	316	9	lemma	lemma	PROPN
ejpam-4143	316	10	4	4	NUM
ejpam-4143	316	11	,	,	PUNCT
ejpam-4143	316	12	∧α∈aµα(y	∧α∈aµα(y	NOUN
ejpam-4143	316	13	)	)	PUNCT
ejpam-4143	316	14	=	=	SYM
ejpam-4143	316	15	inf	inf	NOUN
ejpam-4143	316	16	α∈a	α∈a	NOUN
ejpam-4143	316	17	{	{	PUNCT
ejpam-4143	316	18	µα(y	µα(y	NOUN
ejpam-4143	316	19	)	)	PUNCT
ejpam-4143	316	20	}	}	PUNCT
ejpam-4143	316	21	≥	≥	PROPN
ejpam-4143	316	22	inf	inf	PROPN
ejpam-4143	316	23	α∈a	α∈a	PROPN
ejpam-4143	316	24	{	{	PUNCT
ejpam-4143	316	25	min{µα(x	min{µα(x	PROPN
ejpam-4143	316	26	)	)	PUNCT
ejpam-4143	316	27	,	,	PUNCT
ejpam-4143	316	28	inf	inf	PROPN
ejpam-4143	316	29	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	316	30	{	{	PUNCT
ejpam-4143	316	31	µα(a	µα(a	NOUN
ejpam-4143	316	32	)	)	PUNCT
ejpam-4143	316	33	}	}	PUNCT
ejpam-4143	316	34	}	}	PUNCT
ejpam-4143	316	35	}	}	PUNCT
ejpam-4143	316	36	≥	≥	NOUN
ejpam-4143	316	37	min	min	PROPN
ejpam-4143	316	38	{	{	PUNCT
ejpam-4143	316	39	inf	inf	NOUN
ejpam-4143	316	40	α∈a	α∈a	PROPN
ejpam-4143	316	41	{	{	PUNCT
ejpam-4143	316	42	µα(x	µα(x	NUM
ejpam-4143	316	43	)	)	PUNCT
ejpam-4143	316	44	,	,	PUNCT
ejpam-4143	316	45	inf	inf	PROPN
ejpam-4143	316	46	α∈a	α∈a	PROPN
ejpam-4143	316	47	{	{	PUNCT
ejpam-4143	316	48	inf	inf	PROPN
ejpam-4143	316	49	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	316	50	{	{	PUNCT
ejpam-4143	316	51	µα(a	µα(a	NOUN
ejpam-4143	316	52	)	)	PUNCT
ejpam-4143	316	53	}	}	PUNCT
ejpam-4143	316	54	}	}	PUNCT
ejpam-4143	316	55	}	}	PUNCT
ejpam-4143	316	56	≥	≥	NOUN
ejpam-4143	316	57	min	min	PROPN
ejpam-4143	316	58	{	{	PUNCT
ejpam-4143	316	59	inf	inf	NOUN
ejpam-4143	316	60	α∈a	α∈a	PROPN
ejpam-4143	316	61	{	{	PUNCT
ejpam-4143	316	62	µα(x	µα(x	NUM
ejpam-4143	316	63	)	)	PUNCT
ejpam-4143	316	64	,	,	PUNCT
ejpam-4143	316	65	inf	inf	PROPN
ejpam-4143	316	66	a∈x⊛y	a∈x⊛y	PROPN
ejpam-4143	316	67	{	{	PUNCT
ejpam-4143	316	68	inf	inf	PROPN
ejpam-4143	316	69	α∈a	α∈a	PROPN
ejpam-4143	316	70	{	{	PUNCT
ejpam-4143	316	71	µα(a	µα(a	NOUN
ejpam-4143	316	72	)	)	PUNCT
ejpam-4143	316	73	}	}	PUNCT
ejpam-4143	316	74	}	}	PUNCT
ejpam-4143	316	75	}	}	PUNCT
ejpam-4143	316	76	=	=	SYM
ejpam-4143	316	77	min	min	NOUN
ejpam-4143	316	78	{	{	PUNCT
ejpam-4143	316	79	∧α∈aµα(x	∧α∈aµα(x	PROPN
ejpam-4143	316	80	)	)	PUNCT
ejpam-4143	316	81	,	,	PUNCT
ejpam-4143	316	82	inf	inf	PROPN
ejpam-4143	316	83	a∈x⊛y	a∈x⊛y	NOUN
ejpam-4143	316	84	{	{	PUNCT
ejpam-4143	316	85	∧α∈a{µα(a	∧α∈a{µα(a	PROPN
ejpam-4143	316	86	)	)	PUNCT
ejpam-4143	316	87	}	}	PUNCT
ejpam-4143	316	88	}	}	PUNCT
ejpam-4143	316	89	}	}	PUNCT
ejpam-4143	316	90	.	.	PUNCT
ejpam-4143	317	1	hence	hence	ADV
ejpam-4143	317	2	,	,	PUNCT
ejpam-4143	317	3	the	the	DET
ejpam-4143	317	4	conclusion	conclusion	NOUN
ejpam-4143	317	5	follows	follow	VERB
ejpam-4143	317	6	.	.	PUNCT
ejpam-4143	318	1	5	5	X
ejpam-4143	318	2	.	.	X
ejpam-4143	318	3	hyper	hyper	ADJ
ejpam-4143	318	4	homomorphism	homomorphism	NOUN
ejpam-4143	318	5	of	of	ADP
ejpam-4143	318	6	fuzzy	fuzzy	ADJ
ejpam-4143	318	7	hyper	hyper	ADJ
ejpam-4143	318	8	up	up	ADP
ejpam-4143	318	9	-	-	PUNCT
ejpam-4143	318	10	algebras	algebra	NOUN
ejpam-4143	318	11	this	this	DET
ejpam-4143	318	12	section	section	NOUN
ejpam-4143	318	13	provides	provide	VERB
ejpam-4143	318	14	some	some	DET
ejpam-4143	318	15	properties	property	NOUN
ejpam-4143	318	16	of	of	ADP
ejpam-4143	318	17	hyper	hyper	ADJ
ejpam-4143	318	18	homomorphism	homomorphism	NOUN
ejpam-4143	318	19	in	in	ADP
ejpam-4143	318	20	relation	relation	NOUN
ejpam-4143	318	21	to	to	ADP
ejpam-4143	318	22	the	the	DET
ejpam-4143	318	23	concepts	concept	NOUN
ejpam-4143	318	24	of	of	ADP
ejpam-4143	318	25	fuzzy	fuzzy	ADJ
ejpam-4143	318	26	hyper	hyper	ADJ
ejpam-4143	318	27	up	up	ADP
ejpam-4143	318	28	-	-	PUNCT
ejpam-4143	318	29	subalgebra	subalgebra	NOUN
ejpam-4143	318	30	and	and	CCONJ
ejpam-4143	318	31	fuzzy	fuzzy	ADJ
ejpam-4143	318	32	hyper	hyper	ADJ
ejpam-4143	318	33	up	up	ADJ
ejpam-4143	318	34	-	-	PUNCT
ejpam-4143	318	35	filter	filter	NOUN
ejpam-4143	318	36	.	.	PUNCT
ejpam-4143	319	1	by	by	ADP
ejpam-4143	319	2	definitions	definition	NOUN
ejpam-4143	319	3	3	3	NUM
ejpam-4143	319	4	,	,	PUNCT
ejpam-4143	319	5	5	5	NUM
ejpam-4143	319	6	,	,	PUNCT
ejpam-4143	319	7	7	7	NUM
ejpam-4143	319	8	and	and	CCONJ
ejpam-4143	319	9	lemma	lemma	PROPN
ejpam-4143	319	10	1	1	NUM
ejpam-4143	319	11	,	,	PUNCT
ejpam-4143	319	12	we	we	PRON
ejpam-4143	319	13	deduce	deduce	VERB
ejpam-4143	319	14	the	the	DET
ejpam-4143	319	15	following	follow	VERB
ejpam-4143	319	16	proposition	proposition	NOUN
ejpam-4143	319	17	:	:	PUNCT
ejpam-4143	319	18	proposition	proposition	NOUN
ejpam-4143	319	19	4	4	NUM
ejpam-4143	319	20	.	.	PUNCT
ejpam-4143	320	1	let	let	VERB
ejpam-4143	320	2	f	f	NOUN
ejpam-4143	320	3	:	:	PUNCT
ejpam-4143	320	4	g	g	PROPN
ejpam-4143	320	5	→	→	SYM
ejpam-4143	320	6	h	h	NOUN
ejpam-4143	320	7	be	be	AUX
ejpam-4143	320	8	a	a	DET
ejpam-4143	320	9	hyper	hyper	ADJ
ejpam-4143	320	10	homomorphism	homomorphism	NOUN
ejpam-4143	320	11	of	of	ADP
ejpam-4143	320	12	hyper	hyper	ADJ
ejpam-4143	320	13	up	up	ADP
ejpam-4143	320	14	-	-	PUNCT
ejpam-4143	320	15	algebras	algebras	NOUN
ejpam-4143	320	16	g	g	PROPN
ejpam-4143	320	17	and	and	CCONJ
ejpam-4143	320	18	h.	h.	PROPN
ejpam-4143	321	1	(	(	PUNCT
ejpam-4143	321	2	i	i	NOUN
ejpam-4143	321	3	)	)	PUNCT
ejpam-4143	321	4	if	if	SCONJ
ejpam-4143	321	5	µ	µ	NOUN
ejpam-4143	321	6	is	be	AUX
ejpam-4143	321	7	a	a	DET
ejpam-4143	321	8	fuzzy	fuzzy	ADJ
ejpam-4143	321	9	hyper	hyper	ADJ
ejpam-4143	321	10	up	up	ADP
ejpam-4143	321	11	-	-	PUNCT
ejpam-4143	321	12	subalgebra	subalgebra	NOUN
ejpam-4143	321	13	of	of	ADP
ejpam-4143	321	14	g	g	NOUN
ejpam-4143	321	15	,	,	PUNCT
ejpam-4143	321	16	then	then	ADV
ejpam-4143	321	17	f(µ)(0h	f(µ)(0h	PROPN
ejpam-4143	321	18	)	)	PUNCT
ejpam-4143	321	19	=	=	PUNCT
ejpam-4143	322	1	µ(0	µ(0	NOUN
ejpam-4143	322	2	g	g	NOUN
ejpam-4143	322	3	)	)	PUNCT
ejpam-4143	322	4	.	.	PUNCT
ejpam-4143	323	1	(	(	PUNCT
ejpam-4143	323	2	ii	ii	NOUN
ejpam-4143	323	3	)	)	PUNCT
ejpam-4143	323	4	if	if	SCONJ
ejpam-4143	323	5	µ	µ	NOUN
ejpam-4143	323	6	is	be	AUX
ejpam-4143	323	7	a	a	DET
ejpam-4143	323	8	fuzzy	fuzzy	ADJ
ejpam-4143	323	9	hyper	hyper	ADJ
ejpam-4143	323	10	up	up	ADP
ejpam-4143	323	11	-	-	PUNCT
ejpam-4143	323	12	subalgebra	subalgebra	NOUN
ejpam-4143	323	13	of	of	ADP
ejpam-4143	323	14	h	h	NOUN
ejpam-4143	323	15	,	,	PUNCT
ejpam-4143	323	16	then	then	ADV
ejpam-4143	323	17	µf	µf	X
ejpam-4143	323	18	(	(	PUNCT
ejpam-4143	323	19	0	0	NUM
ejpam-4143	323	20	g	g	NOUN
ejpam-4143	323	21	)	)	PUNCT
ejpam-4143	323	22	=	=	SYM
ejpam-4143	324	1	0h	0h	NOUN
ejpam-4143	324	2	.	.	PUNCT
ejpam-4143	325	1	proof	proof	NOUN
ejpam-4143	325	2	.	.	PUNCT
ejpam-4143	326	1	let	let	VERB
ejpam-4143	326	2	f	f	NOUN
ejpam-4143	326	3	:	:	PUNCT
ejpam-4143	326	4	g	g	PROPN
ejpam-4143	326	5	→	→	SYM
ejpam-4143	326	6	h	h	NOUN
ejpam-4143	326	7	be	be	AUX
ejpam-4143	326	8	a	a	DET
ejpam-4143	326	9	hyper	hyper	ADJ
ejpam-4143	326	10	homomorphism	homomorphism	NOUN
ejpam-4143	326	11	.	.	PUNCT
ejpam-4143	327	1	(	(	PUNCT
ejpam-4143	327	2	i	i	NOUN
ejpam-4143	327	3	)	)	PUNCT
ejpam-4143	327	4	by	by	ADP
ejpam-4143	327	5	definition	definition	NOUN
ejpam-4143	327	6	3	3	NUM
ejpam-4143	327	7	,	,	PUNCT
ejpam-4143	327	8	0	0	NUM
ejpam-4143	327	9	g	g	PROPN
ejpam-4143	327	10	∈	∈	PROPN
ejpam-4143	327	11	f−1(0h	f−1(0h	NOUN
ejpam-4143	327	12	)	)	PUNCT
ejpam-4143	327	13	and	and	CCONJ
ejpam-4143	327	14	so	so	ADV
ejpam-4143	327	15	f−1(0h	f−1(0h	NOUN
ejpam-4143	327	16	)	)	PUNCT
ejpam-4143	328	1	̸=	̸=	PROPN
ejpam-4143	328	2	∅.	∅.	VERB
ejpam-4143	328	3	by	by	ADP
ejpam-4143	328	4	definition	definition	NOUN
ejpam-4143	328	5	6	6	NUM
ejpam-4143	328	6	and	and	CCONJ
ejpam-4143	328	7	lemma	lemma	PROPN
ejpam-4143	328	8	1	1	NUM
ejpam-4143	328	9	,	,	PUNCT
ejpam-4143	328	10	f(µ)(0h	f(µ)(0h	PROPN
ejpam-4143	328	11	)	)	PUNCT
ejpam-4143	328	12	=	=	SYM
ejpam-4143	328	13	supx∈f−1(0h){µ(x	supx∈f−1(0h){µ(x	NOUN
ejpam-4143	328	14	)	)	PUNCT
ejpam-4143	328	15	}	}	PUNCT
ejpam-4143	328	16	=	=	PUNCT
ejpam-4143	328	17	µ(0	µ(0	NOUN
ejpam-4143	328	18	g	g	NOUN
ejpam-4143	328	19	)	)	PUNCT
ejpam-4143	328	20	.	.	PUNCT
ejpam-4143	329	1	(	(	PUNCT
ejpam-4143	329	2	ii	ii	NOUN
ejpam-4143	329	3	)	)	PUNCT
ejpam-4143	329	4	by	by	ADP
ejpam-4143	329	5	definitions	definition	NOUN
ejpam-4143	329	6	3	3	NUM
ejpam-4143	329	7	and	and	CCONJ
ejpam-4143	329	8	5	5	NUM
ejpam-4143	329	9	,	,	PUNCT
ejpam-4143	329	10	µf	µf	X
ejpam-4143	329	11	(	(	PUNCT
ejpam-4143	329	12	0	0	NUM
ejpam-4143	329	13	g	g	NOUN
ejpam-4143	329	14	)	)	PUNCT
ejpam-4143	329	15	=	=	PUNCT
ejpam-4143	330	1	µ(f(0	µ(f(0	PROPN
ejpam-4143	330	2	g	g	NOUN
ejpam-4143	330	3	)	)	PUNCT
ejpam-4143	330	4	)	)	PUNCT
ejpam-4143	330	5	=	=	SYM
ejpam-4143	330	6	µ(0h	µ(0h	PROPN
ejpam-4143	330	7	)	)	PUNCT
ejpam-4143	330	8	.	.	PUNCT
ejpam-4143	331	1	lemma	lemma	PROPN
ejpam-4143	331	2	5	5	X
ejpam-4143	331	3	.	.	PUNCT
ejpam-4143	332	1	let	let	VERB
ejpam-4143	332	2	f	f	NOUN
ejpam-4143	332	3	:	:	PUNCT
ejpam-4143	332	4	g	g	PROPN
ejpam-4143	332	5	→	→	SYM
ejpam-4143	332	6	h	h	NOUN
ejpam-4143	332	7	be	be	AUX
ejpam-4143	332	8	a	a	DET
ejpam-4143	332	9	hyper	hyper	ADJ
ejpam-4143	332	10	homomorphism	homomorphism	NOUN
ejpam-4143	332	11	of	of	ADP
ejpam-4143	332	12	hyper	hyper	ADJ
ejpam-4143	332	13	up	up	ADP
ejpam-4143	332	14	-	-	PUNCT
ejpam-4143	332	15	algebras	algebras	NOUN
ejpam-4143	332	16	g	g	PROPN
ejpam-4143	332	17	and	and	CCONJ
ejpam-4143	332	18	h	h	NOUN
ejpam-4143	332	19	,	,	PUNCT
ejpam-4143	333	1	µ	µ	X
ejpam-4143	333	2	be	be	VERB
ejpam-4143	333	3	a	a	DET
ejpam-4143	333	4	fuzzy	fuzzy	ADJ
ejpam-4143	333	5	subset	subset	NOUN
ejpam-4143	333	6	of	of	ADP
ejpam-4143	333	7	h	h	NOUN
ejpam-4143	333	8	and	and	CCONJ
ejpam-4143	333	9	µf	µf	PART
ejpam-4143	333	10	be	be	AUX
ejpam-4143	333	11	a	a	DET
ejpam-4143	333	12	fuzzy	fuzzy	ADJ
ejpam-4143	333	13	hyper	hyper	ADJ
ejpam-4143	333	14	up	up	ADP
ejpam-4143	333	15	-	-	PUNCT
ejpam-4143	333	16	subalgebra	subalgebra	NOUN
ejpam-4143	333	17	of	of	ADP
ejpam-4143	333	18	g.	g.	PROPN
ejpam-4143	333	19	if	if	SCONJ
ejpam-4143	333	20	a	a	DET
ejpam-4143	333	21	=	=	PUNCT
ejpam-4143	333	22	{	{	PUNCT
ejpam-4143	333	23	µ(f(a	µ(f(a	PROPN
ejpam-4143	333	24	)	)	PUNCT
ejpam-4143	333	25	)	)	PUNCT
ejpam-4143	334	1	=	=	SYM
ejpam-4143	334	2	µf	µf	X
ejpam-4143	334	3	(	(	PUNCT
ejpam-4143	334	4	a	a	X
ejpam-4143	334	5	)	)	PUNCT
ejpam-4143	334	6	:	:	PUNCT
ejpam-4143	334	7	a	a	DET
ejpam-4143	334	8	∈	∈	PROPN
ejpam-4143	334	9	x⊛g	x⊛g	PUNCT
ejpam-4143	334	10	y	y	X
ejpam-4143	334	11	}	}	PUNCT
ejpam-4143	334	12	and	and	CCONJ
ejpam-4143	334	13	b	b	X
ejpam-4143	334	14	=	=	SYM
ejpam-4143	334	15	{	{	PUNCT
ejpam-4143	334	16	µ(f(a	µ(f(a	PROPN
ejpam-4143	334	17	)	)	PUNCT
ejpam-4143	334	18	)	)	PUNCT
ejpam-4143	335	1	=	=	SYM
ejpam-4143	335	2	µf	µf	X
ejpam-4143	335	3	(	(	PUNCT
ejpam-4143	335	4	a	a	NOUN
ejpam-4143	335	5	)	)	PUNCT
ejpam-4143	335	6	:	:	PUNCT
ejpam-4143	335	7	f(a	f(a	X
ejpam-4143	335	8	)	)	PUNCT
ejpam-4143	335	9	∈	∈	PROPN
ejpam-4143	335	10	f(x)⊛h	f(x)⊛h	NOUN
ejpam-4143	335	11	f(y	f(y	NOUN
ejpam-4143	335	12	)	)	PUNCT
ejpam-4143	335	13	}	}	PUNCT
ejpam-4143	335	14	,	,	PUNCT
ejpam-4143	335	15	then	then	ADV
ejpam-4143	335	16	a	a	DET
ejpam-4143	335	17	=	=	PROPN
ejpam-4143	335	18	b.	b.	PROPN
ejpam-4143	335	19	r.	r.	PROPN
ejpam-4143	335	20	amairanto	amairanto	PROPN
ejpam-4143	335	21	,	,	PUNCT
ejpam-4143	335	22	r.	r.	PROPN
ejpam-4143	335	23	isla	isla	PROPN
ejpam-4143	335	24	/	/	SYM
ejpam-4143	335	25	eur	eur	PROPN
ejpam-4143	335	26	.	.	PUNCT
ejpam-4143	336	1	j.	j.	PROPN
ejpam-4143	336	2	pure	pure	PROPN
ejpam-4143	336	3	appl	appl	PROPN
ejpam-4143	336	4	.	.	PROPN
ejpam-4143	336	5	math	math	PROPN
ejpam-4143	336	6	,	,	PUNCT
ejpam-4143	336	7	14	14	NUM
ejpam-4143	336	8	(	(	PUNCT
ejpam-4143	336	9	4	4	NUM
ejpam-4143	336	10	)	)	PUNCT
ejpam-4143	336	11	(	(	PUNCT
ejpam-4143	336	12	2021	2021	NUM
ejpam-4143	336	13	)	)	PUNCT
ejpam-4143	336	14	,	,	PUNCT
ejpam-4143	336	15	1388	1388	NUM
ejpam-4143	336	16	-	-	SYM
ejpam-4143	336	17	1401	1401	NUM
ejpam-4143	336	18	1399	1399	NUM
ejpam-4143	336	19	proof	proof	NOUN
ejpam-4143	336	20	.	.	PUNCT
ejpam-4143	337	1	let	let	VERB
ejpam-4143	337	2	z	z	NOUN
ejpam-4143	337	3	∈	∈	PROPN
ejpam-4143	337	4	a.	a.	NOUN
ejpam-4143	337	5	then	then	ADV
ejpam-4143	337	6	z	z	PROPN
ejpam-4143	337	7	=	=	SYM
ejpam-4143	337	8	µ(f(a	µ(f(a	PROPN
ejpam-4143	337	9	)	)	PUNCT
ejpam-4143	337	10	)	)	PUNCT
ejpam-4143	337	11	for	for	ADP
ejpam-4143	337	12	some	some	PRON
ejpam-4143	337	13	a	a	DET
ejpam-4143	337	14	∈	∈	NOUN
ejpam-4143	337	15	x	x	PUNCT
ejpam-4143	337	16	⊛g	⊛g	X
ejpam-4143	337	17	y.	y.	NOUN
ejpam-4143	337	18	since	since	SCONJ
ejpam-4143	337	19	f	f	PROPN
ejpam-4143	337	20	is	be	AUX
ejpam-4143	337	21	a	a	DET
ejpam-4143	337	22	hyper	hyper	ADJ
ejpam-4143	337	23	homomorphism	homomorphism	NOUN
ejpam-4143	337	24	,	,	PUNCT
ejpam-4143	337	25	we	we	PRON
ejpam-4143	337	26	have	have	VERB
ejpam-4143	337	27	f(a	f(a	NOUN
ejpam-4143	337	28	)	)	PUNCT
ejpam-4143	337	29	∈	∈	PROPN
ejpam-4143	337	30	f(x	f(x	PROPN
ejpam-4143	337	31	⊛g	⊛g	VERB
ejpam-4143	337	32	y	y	PROPN
ejpam-4143	337	33	)	)	PUNCT
ejpam-4143	338	1	=	=	SYM
ejpam-4143	338	2	f(x	f(x	PROPN
ejpam-4143	338	3	)	)	PUNCT
ejpam-4143	338	4	⊛h	⊛h	NUM
ejpam-4143	338	5	f(y	f(y	NOUN
ejpam-4143	338	6	)	)	PUNCT
ejpam-4143	338	7	.	.	PUNCT
ejpam-4143	339	1	thus	thus	ADV
ejpam-4143	339	2	z	z	PROPN
ejpam-4143	339	3	∈	∈	PROPN
ejpam-4143	339	4	b	b	PROPN
ejpam-4143	339	5	and	and	CCONJ
ejpam-4143	339	6	so	so	ADV
ejpam-4143	339	7	a	a	DET
ejpam-4143	339	8	⊆	⊆	NUM
ejpam-4143	339	9	b.	b.	NOUN
ejpam-4143	339	10	conversely	conversely	ADV
ejpam-4143	339	11	,	,	PUNCT
ejpam-4143	339	12	suppose	suppose	VERB
ejpam-4143	339	13	that	that	SCONJ
ejpam-4143	339	14	z	z	PROPN
ejpam-4143	339	15	∈	∈	PROPN
ejpam-4143	339	16	b.	b.	PROPN
ejpam-4143	339	17	then	then	ADV
ejpam-4143	339	18	z	z	PROPN
ejpam-4143	339	19	=	=	SYM
ejpam-4143	339	20	µ(f(a	µ(f(a	PROPN
ejpam-4143	339	21	)	)	PUNCT
ejpam-4143	339	22	)	)	PUNCT
ejpam-4143	339	23	for	for	ADP
ejpam-4143	339	24	some	some	DET
ejpam-4143	339	25	f(a	f(a	NOUN
ejpam-4143	339	26	)	)	PUNCT
ejpam-4143	339	27	∈	∈	PROPN
ejpam-4143	339	28	f(x)⊛h	f(x)⊛h	NOUN
ejpam-4143	339	29	f(y	f(y	NOUN
ejpam-4143	339	30	)	)	PUNCT
ejpam-4143	339	31	.	.	PUNCT
ejpam-4143	340	1	since	since	SCONJ
ejpam-4143	340	2	f	f	PROPN
ejpam-4143	340	3	is	be	AUX
ejpam-4143	340	4	a	a	DET
ejpam-4143	340	5	hyper	hyper	ADJ
ejpam-4143	340	6	homomorphism	homomorphism	NOUN
ejpam-4143	340	7	,	,	PUNCT
ejpam-4143	340	8	f(a	f(a	NOUN
ejpam-4143	340	9	)	)	PUNCT
ejpam-4143	340	10	∈	∈	PROPN
ejpam-4143	340	11	f(x	f(x	PROPN
ejpam-4143	340	12	)	)	PUNCT
ejpam-4143	340	13	⊛h	⊛h	NOUN
ejpam-4143	340	14	f(y	f(y	NOUN
ejpam-4143	340	15	)	)	PUNCT
ejpam-4143	341	1	=	=	SYM
ejpam-4143	341	2	f(x	f(x	PROPN
ejpam-4143	341	3	⊛g	⊛g	VERB
ejpam-4143	341	4	y	y	PROPN
ejpam-4143	341	5	)	)	PUNCT
ejpam-4143	341	6	.	.	PUNCT
ejpam-4143	342	1	thus	thus	ADV
ejpam-4143	342	2	,	,	PUNCT
ejpam-4143	342	3	f(a	f(a	NOUN
ejpam-4143	342	4	)	)	PUNCT
ejpam-4143	342	5	=	=	SYM
ejpam-4143	342	6	f(a′	f(a′	PROPN
ejpam-4143	342	7	)	)	PUNCT
ejpam-4143	342	8	,	,	PUNCT
ejpam-4143	342	9	where	where	SCONJ
ejpam-4143	342	10	a′	a′	PROPN
ejpam-4143	342	11	∈	∈	PROPN
ejpam-4143	342	12	x⊛g	x⊛g	PROPN
ejpam-4143	343	1	y.	y.	PROPN
ejpam-4143	344	1	so	so	ADV
ejpam-4143	344	2	,	,	PUNCT
ejpam-4143	344	3	z	z	PROPN
ejpam-4143	344	4	=	=	PUNCT
ejpam-4143	344	5	µ(f(a′	µ(f(a′	PROPN
ejpam-4143	344	6	)	)	PUNCT
ejpam-4143	344	7	)	)	PUNCT
ejpam-4143	344	8	,	,	PUNCT
ejpam-4143	344	9	where	where	SCONJ
ejpam-4143	344	10	a′	a′	PROPN
ejpam-4143	344	11	∈	∈	PROPN
ejpam-4143	344	12	x⊛g	x⊛g	PROPN
ejpam-4143	344	13	y.	y.	PROPN
ejpam-4143	344	14	hence	hence	ADV
ejpam-4143	344	15	,	,	PUNCT
ejpam-4143	344	16	z	z	PROPN
ejpam-4143	344	17	∈	∈	PROPN
ejpam-4143	344	18	a	a	PRON
ejpam-4143	344	19	which	which	PRON
ejpam-4143	344	20	means	mean	VERB
ejpam-4143	344	21	that	that	SCONJ
ejpam-4143	344	22	b	b	NOUN
ejpam-4143	344	23	⊆	⊆	NUM
ejpam-4143	344	24	a.	a.	NOUN
ejpam-4143	344	25	therefore	therefore	ADV
ejpam-4143	344	26	,	,	PUNCT
ejpam-4143	344	27	a	a	DET
ejpam-4143	344	28	=	=	X
ejpam-4143	344	29	b.	b.	PROPN
ejpam-4143	344	30	theorem	theorem	NOUN
ejpam-4143	344	31	10	10	NUM
ejpam-4143	344	32	.	.	PUNCT
ejpam-4143	345	1	let	let	VERB
ejpam-4143	345	2	f	f	NOUN
ejpam-4143	345	3	:	:	PUNCT
ejpam-4143	345	4	g	g	PROPN
ejpam-4143	345	5	→	→	SYM
ejpam-4143	345	6	h	h	NOUN
ejpam-4143	345	7	be	be	AUX
ejpam-4143	345	8	a	a	DET
ejpam-4143	345	9	hyper	hyper	ADJ
ejpam-4143	345	10	epimorphism	epimorphism	NOUN
ejpam-4143	345	11	of	of	ADP
ejpam-4143	345	12	hyper	hyper	ADJ
ejpam-4143	345	13	up	up	ADP
ejpam-4143	345	14	-	-	PUNCT
ejpam-4143	345	15	algebras	algebras	NOUN
ejpam-4143	345	16	g	g	PROPN
ejpam-4143	345	17	and	and	CCONJ
ejpam-4143	345	18	h	h	PROPN
ejpam-4143	345	19	and	and	CCONJ
ejpam-4143	345	20	µ	µ	PRON
ejpam-4143	345	21	be	be	AUX
ejpam-4143	345	22	a	a	DET
ejpam-4143	345	23	fuzzy	fuzzy	ADJ
ejpam-4143	345	24	subset	subset	NOUN
ejpam-4143	345	25	of	of	ADP
ejpam-4143	345	26	h.	h.	PROPN
ejpam-4143	345	27	if	if	SCONJ
ejpam-4143	345	28	µf	µf	PROPN
ejpam-4143	345	29	is	be	AUX
ejpam-4143	345	30	a	a	DET
ejpam-4143	345	31	fuzzy	fuzzy	ADJ
ejpam-4143	345	32	hyper	hyper	ADJ
ejpam-4143	345	33	up	up	ADP
ejpam-4143	345	34	-	-	PUNCT
ejpam-4143	345	35	subalgebra	subalgebra	NOUN
ejpam-4143	345	36	of	of	ADP
ejpam-4143	345	37	g	g	NOUN
ejpam-4143	345	38	,	,	PUNCT
ejpam-4143	345	39	then	then	ADV
ejpam-4143	345	40	µ	µ	NOUN
ejpam-4143	345	41	is	be	AUX
ejpam-4143	345	42	a	a	DET
ejpam-4143	345	43	fuzzy	fuzzy	ADJ
ejpam-4143	345	44	hyper	hyper	ADJ
ejpam-4143	345	45	up	up	ADP
ejpam-4143	345	46	-	-	PUNCT
ejpam-4143	345	47	subalgebra	subalgebra	NOUN
ejpam-4143	345	48	of	of	ADP
ejpam-4143	345	49	h.	h.	NOUN
ejpam-4143	345	50	proof	proof	NOUN
ejpam-4143	345	51	.	.	PUNCT
ejpam-4143	346	1	let	let	VERB
ejpam-4143	346	2	f	f	PRON
ejpam-4143	346	3	be	be	AUX
ejpam-4143	346	4	a	a	DET
ejpam-4143	346	5	hyper	hyper	ADJ
ejpam-4143	346	6	epimorphism	epimorphism	NOUN
ejpam-4143	346	7	of	of	ADP
ejpam-4143	346	8	hyper	hyper	ADJ
ejpam-4143	346	9	up	up	ADP
ejpam-4143	346	10	-	-	PUNCT
ejpam-4143	346	11	algebras	algebras	NOUN
ejpam-4143	346	12	g	g	PROPN
ejpam-4143	346	13	and	and	CCONJ
ejpam-4143	346	14	h	h	PROPN
ejpam-4143	346	15	and	and	CCONJ
ejpam-4143	346	16	suppose	suppose	VERB
ejpam-4143	346	17	µf	µf	PART
ejpam-4143	346	18	is	be	AUX
ejpam-4143	346	19	a	a	DET
ejpam-4143	346	20	fuzzy	fuzzy	ADJ
ejpam-4143	346	21	hyper	hyper	ADJ
ejpam-4143	346	22	up	up	ADP
ejpam-4143	346	23	-	-	PUNCT
ejpam-4143	346	24	subalgebra	subalgebra	NOUN
ejpam-4143	346	25	of	of	ADP
ejpam-4143	346	26	g.	g.	PROPN
ejpam-4143	346	27	let	let	VERB
ejpam-4143	346	28	x	x	PRON
ejpam-4143	346	29	,	,	PUNCT
ejpam-4143	346	30	y	y	PROPN
ejpam-4143	346	31	∈	∈	PROPN
ejpam-4143	346	32	h.	h.	PROPN
ejpam-4143	346	33	since	since	SCONJ
ejpam-4143	346	34	f	f	PROPN
ejpam-4143	346	35	is	be	AUX
ejpam-4143	346	36	onto	onto	ADP
ejpam-4143	346	37	,	,	PUNCT
ejpam-4143	346	38	there	there	PRON
ejpam-4143	346	39	exist	exist	VERB
ejpam-4143	346	40	x′	x′	NUM
ejpam-4143	346	41	,	,	PUNCT
ejpam-4143	346	42	y′	y′	NOUN
ejpam-4143	346	43	∈	∈	PROPN
ejpam-4143	346	44	g	g	PROPN
ejpam-4143	346	45	such	such	ADJ
ejpam-4143	346	46	that	that	DET
ejpam-4143	346	47	f(x′	f(x′	NOUN
ejpam-4143	346	48	)	)	PUNCT
ejpam-4143	346	49	=	=	SYM
ejpam-4143	346	50	x	x	NOUN
ejpam-4143	346	51	and	and	CCONJ
ejpam-4143	346	52	f(y′	f(y′	NOUN
ejpam-4143	346	53	)	)	PUNCT
ejpam-4143	346	54	=	=	SYM
ejpam-4143	347	1	y.	y.	NOUN
ejpam-4143	347	2	hence	hence	ADV
ejpam-4143	347	3	,	,	PUNCT
ejpam-4143	347	4	µ(x	µ(x	X
ejpam-4143	347	5	)	)	PUNCT
ejpam-4143	347	6	=	=	SYM
ejpam-4143	347	7	µf	µf	X
ejpam-4143	347	8	(	(	PUNCT
ejpam-4143	347	9	x′	x′	NUM
ejpam-4143	347	10	)	)	PUNCT
ejpam-4143	347	11	and	and	CCONJ
ejpam-4143	347	12	µ(y	µ(y	NUM
ejpam-4143	347	13	)	)	PUNCT
ejpam-4143	347	14	=	=	SYM
ejpam-4143	347	15	µf	µf	X
ejpam-4143	347	16	(	(	PUNCT
ejpam-4143	347	17	y′	y′	NUM
ejpam-4143	347	18	)	)	PUNCT
ejpam-4143	347	19	.	.	PUNCT
ejpam-4143	348	1	let	let	VERB
ejpam-4143	348	2	z	z	NOUN
ejpam-4143	348	3	∈	∈	PROPN
ejpam-4143	348	4	x	x	X
ejpam-4143	348	5	⊛h	⊛h	PROPN
ejpam-4143	348	6	y.	y.	PROPN
ejpam-4143	348	7	then	then	ADV
ejpam-4143	348	8	f	f	PROPN
ejpam-4143	348	9	is	be	AUX
ejpam-4143	348	10	onto	onto	ADP
ejpam-4143	348	11	implies	implie	NOUN
ejpam-4143	348	12	that	that	SCONJ
ejpam-4143	348	13	there	there	PRON
ejpam-4143	348	14	exists	exist	VERB
ejpam-4143	348	15	z′	z′	NUM
ejpam-4143	348	16	∈	∈	PROPN
ejpam-4143	348	17	g	g	NOUN
ejpam-4143	348	18	such	such	ADJ
ejpam-4143	348	19	that	that	SCONJ
ejpam-4143	348	20	f(z′	f(z′	PROPN
ejpam-4143	348	21	)	)	PUNCT
ejpam-4143	349	1	=	=	SYM
ejpam-4143	350	1	z	z	X
ejpam-4143	350	2	,	,	PUNCT
ejpam-4143	350	3	that	that	ADV
ejpam-4143	350	4	is	is	ADV
ejpam-4143	350	5	,	,	PUNCT
ejpam-4143	350	6	µf	µf	X
ejpam-4143	350	7	(	(	PUNCT
ejpam-4143	350	8	z′	z′	NUM
ejpam-4143	350	9	)	)	PUNCT
ejpam-4143	350	10	=	=	SYM
ejpam-4143	350	11	µ(z	µ(z	PROPN
ejpam-4143	350	12	)	)	PUNCT
ejpam-4143	350	13	.	.	PUNCT
ejpam-4143	351	1	note	note	VERB
ejpam-4143	351	2	that	that	SCONJ
ejpam-4143	351	3	f(z′	f(z′	ADV
ejpam-4143	351	4	)	)	PUNCT
ejpam-4143	351	5	=	=	PUNCT
ejpam-4143	351	6	z	z	NOUN
ejpam-4143	351	7	∈	∈	PROPN
ejpam-4143	351	8	x	x	X
ejpam-4143	351	9	⊛h	⊛h	NUM
ejpam-4143	351	10	y	y	PROPN
ejpam-4143	351	11	=	=	SYM
ejpam-4143	351	12	f(x′	f(x′	PROPN
ejpam-4143	351	13	)	)	PUNCT
ejpam-4143	351	14	⊛h	⊛h	NUM
ejpam-4143	351	15	f(y′	f(y′	NOUN
ejpam-4143	351	16	)	)	PUNCT
ejpam-4143	351	17	.	.	PUNCT
ejpam-4143	352	1	hence	hence	ADV
ejpam-4143	352	2	,	,	PUNCT
ejpam-4143	352	3	by	by	ADP
ejpam-4143	352	4	lemma	lemma	PROPN
ejpam-4143	352	5	5	5	NUM
ejpam-4143	352	6	,	,	PUNCT
ejpam-4143	352	7	z′	z′	PROPN
ejpam-4143	352	8	∈	∈	PROPN
ejpam-4143	352	9	x′	x′	PROPN
ejpam-4143	352	10	⊛g	⊛g	NOUN
ejpam-4143	352	11	y′.	y′.	NOUN
ejpam-4143	352	12	by	by	ADP
ejpam-4143	352	13	definition	definition	NOUN
ejpam-4143	352	14	8	8	NUM
ejpam-4143	352	15	and	and	CCONJ
ejpam-4143	352	16	the	the	DET
ejpam-4143	352	17	assumption	assumption	NOUN
ejpam-4143	352	18	that	that	SCONJ
ejpam-4143	352	19	µf	µf	NOUN
ejpam-4143	352	20	is	be	AUX
ejpam-4143	352	21	a	a	DET
ejpam-4143	352	22	fuzzy	fuzzy	ADJ
ejpam-4143	352	23	hyper	hyper	ADJ
ejpam-4143	352	24	up	up	ADP
ejpam-4143	352	25	-	-	PUNCT
ejpam-4143	352	26	subalgebra	subalgebra	NOUN
ejpam-4143	352	27	of	of	ADP
ejpam-4143	352	28	g	g	NOUN
ejpam-4143	352	29	,	,	PUNCT
ejpam-4143	352	30	we	we	PRON
ejpam-4143	352	31	have	have	VERB
ejpam-4143	352	32	µ(z	µ(z	NOUN
ejpam-4143	352	33	)	)	PUNCT
ejpam-4143	353	1	=	=	SYM
ejpam-4143	353	2	µf	µf	X
ejpam-4143	353	3	(	(	PUNCT
ejpam-4143	353	4	z′	z′	NUM
ejpam-4143	353	5	)	)	PUNCT
ejpam-4143	353	6	≥	≥	NOUN
ejpam-4143	353	7	infa∈x′⊛gy′{µf	infa∈x′⊛gy′{µf	NOUN
ejpam-4143	353	8	(	(	PUNCT
ejpam-4143	353	9	a	a	X
ejpam-4143	353	10	)	)	PUNCT
ejpam-4143	353	11	}	}	PUNCT
ejpam-4143	353	12	≥	≥	NOUN
ejpam-4143	353	13	min{µf	min{µf	PROPN
ejpam-4143	353	14	(	(	PUNCT
ejpam-4143	353	15	x′	x′	NUM
ejpam-4143	353	16	)	)	PUNCT
ejpam-4143	353	17	,	,	PUNCT
ejpam-4143	353	18	µf	µf	X
ejpam-4143	353	19	(	(	PUNCT
ejpam-4143	353	20	y′	y′	NUM
ejpam-4143	353	21	)	)	PUNCT
ejpam-4143	353	22	}	}	PUNCT
ejpam-4143	353	23	=	=	SYM
ejpam-4143	353	24	min{µ(f(x′	min{µ(f(x′	X
ejpam-4143	353	25	)	)	PUNCT
ejpam-4143	353	26	)	)	PUNCT
ejpam-4143	353	27	,	,	PUNCT
ejpam-4143	353	28	µ(f(y′	µ(f(y′	NOUN
ejpam-4143	353	29	)	)	PUNCT
ejpam-4143	353	30	)	)	PUNCT
ejpam-4143	353	31	}	}	PUNCT
ejpam-4143	353	32	=	=	SYM
ejpam-4143	354	1	min{µ(x	min{µ(x	NOUN
ejpam-4143	354	2	)	)	PUNCT
ejpam-4143	354	3	,	,	PUNCT
ejpam-4143	354	4	µ(y	µ(y	PROPN
ejpam-4143	354	5	)	)	PUNCT
ejpam-4143	354	6	}	}	PUNCT
ejpam-4143	354	7	.	.	PUNCT
ejpam-4143	355	1	thus	thus	ADV
ejpam-4143	355	2	,	,	PUNCT
ejpam-4143	355	3	infz∈x⊛hy{µ(z	infz∈x⊛hy{µ(z	PROPN
ejpam-4143	355	4	)	)	PUNCT
ejpam-4143	355	5	}	}	PUNCT
ejpam-4143	355	6	≥	≥	NOUN
ejpam-4143	356	1	min{µ(x	min{µ(x	NOUN
ejpam-4143	356	2	)	)	PUNCT
ejpam-4143	356	3	,	,	PUNCT
ejpam-4143	356	4	µ(y	µ(y	PROPN
ejpam-4143	356	5	)	)	PUNCT
ejpam-4143	356	6	}	}	PUNCT
ejpam-4143	356	7	.	.	PUNCT
ejpam-4143	357	1	hence	hence	ADV
ejpam-4143	357	2	,	,	PUNCT
ejpam-4143	357	3	µ	µ	X
ejpam-4143	357	4	is	be	AUX
ejpam-4143	357	5	a	a	DET
ejpam-4143	357	6	fuzzy	fuzzy	ADJ
ejpam-4143	357	7	hyper	hyper	ADJ
ejpam-4143	357	8	up	up	ADP
ejpam-4143	357	9	-	-	PUNCT
ejpam-4143	357	10	subalgebra	subalgebra	NOUN
ejpam-4143	357	11	of	of	ADP
ejpam-4143	357	12	h.	h.	PROPN
ejpam-4143	357	13	theorem	theorem	PROPN
ejpam-4143	357	14	11	11	NUM
ejpam-4143	357	15	.	.	PUNCT
ejpam-4143	358	1	let	let	VERB
ejpam-4143	358	2	f	f	NOUN
ejpam-4143	358	3	:	:	PUNCT
ejpam-4143	358	4	g	g	PROPN
ejpam-4143	358	5	→	→	SYM
ejpam-4143	358	6	h	h	NOUN
ejpam-4143	358	7	be	be	AUX
ejpam-4143	358	8	a	a	DET
ejpam-4143	358	9	hyper	hyper	ADJ
ejpam-4143	358	10	homomorphism	homomorphism	NOUN
ejpam-4143	358	11	of	of	ADP
ejpam-4143	358	12	hyper	hyper	ADJ
ejpam-4143	358	13	up	up	ADP
ejpam-4143	358	14	-	-	PUNCT
ejpam-4143	358	15	algebras	algebras	NOUN
ejpam-4143	358	16	g	g	PROPN
ejpam-4143	358	17	and	and	CCONJ
ejpam-4143	358	18	h.	h.	PROPN
ejpam-4143	358	19	if	if	SCONJ
ejpam-4143	358	20	µ	µ	PRON
ejpam-4143	358	21	is	be	AUX
ejpam-4143	358	22	a	a	DET
ejpam-4143	358	23	fuzzy	fuzzy	ADJ
ejpam-4143	358	24	hyper	hyper	ADJ
ejpam-4143	358	25	up	up	ADJ
ejpam-4143	358	26	-	-	PUNCT
ejpam-4143	358	27	filter	filter	NOUN
ejpam-4143	358	28	of	of	ADP
ejpam-4143	358	29	h	h	NOUN
ejpam-4143	358	30	,	,	PUNCT
ejpam-4143	358	31	then	then	ADV
ejpam-4143	358	32	µf	µf	PROPN
ejpam-4143	358	33	is	be	AUX
ejpam-4143	358	34	a	a	DET
ejpam-4143	358	35	fuzzy	fuzzy	ADJ
ejpam-4143	358	36	hyper	hyper	ADJ
ejpam-4143	358	37	up	up	ADJ
ejpam-4143	358	38	-	-	PUNCT
ejpam-4143	358	39	filter	filter	NOUN
ejpam-4143	358	40	of	of	ADP
ejpam-4143	358	41	g.	g.	PROPN
ejpam-4143	358	42	proof	proof	NOUN
ejpam-4143	358	43	.	.	PUNCT
ejpam-4143	359	1	let	let	VERB
ejpam-4143	359	2	x	x	SYM
ejpam-4143	359	3	∈	∈	PROPN
ejpam-4143	359	4	g.	g.	NOUN
ejpam-4143	359	5	then	then	ADV
ejpam-4143	360	1	f(x	f(x	PROPN
ejpam-4143	360	2	)	)	PUNCT
ejpam-4143	360	3	∈	∈	PROPN
ejpam-4143	360	4	h.	h.	PROPN
ejpam-4143	360	5	since	since	SCONJ
ejpam-4143	360	6	µ	µ	X
ejpam-4143	360	7	:	:	PUNCT
ejpam-4143	361	1	h	h	NOUN
ejpam-4143	361	2	−→	−→	NOUN
ejpam-4143	362	1	[	[	X
ejpam-4143	362	2	0	0	NUM
ejpam-4143	362	3	,	,	PUNCT
ejpam-4143	362	4	1	1	NUM
ejpam-4143	362	5	]	]	PUNCT
ejpam-4143	362	6	is	be	AUX
ejpam-4143	362	7	a	a	DET
ejpam-4143	362	8	fuzzy	fuzzy	ADJ
ejpam-4143	362	9	hyper	hyper	ADJ
ejpam-4143	362	10	up	up	ADJ
ejpam-4143	362	11	-	-	PUNCT
ejpam-4143	362	12	filter	filter	NOUN
ejpam-4143	362	13	of	of	ADP
ejpam-4143	362	14	h,µ(0h	h,µ(0h	PROPN
ejpam-4143	362	15	)	)	PUNCT
ejpam-4143	362	16	=	=	PUNCT
ejpam-4143	363	1	µ(f(0	µ(f(0	PROPN
ejpam-4143	363	2	g	g	NOUN
ejpam-4143	363	3	)	)	PUNCT
ejpam-4143	363	4	)	)	PUNCT
ejpam-4143	363	5	≥	≥	PROPN
ejpam-4143	363	6	µ(f(x	µ(f(x	PROPN
ejpam-4143	363	7	)	)	PUNCT
ejpam-4143	363	8	)	)	PUNCT
ejpam-4143	363	9	,	,	PUNCT
ejpam-4143	363	10	that	that	ADV
ejpam-4143	363	11	is	is	ADV
ejpam-4143	363	12	,	,	PUNCT
ejpam-4143	363	13	µf	µf	X
ejpam-4143	363	14	(	(	PUNCT
ejpam-4143	363	15	0	0	NUM
ejpam-4143	363	16	g	g	NOUN
ejpam-4143	363	17	)	)	PUNCT
ejpam-4143	363	18	≥	≥	NOUN
ejpam-4143	363	19	µf	µf	X
ejpam-4143	363	20	(	(	PUNCT
ejpam-4143	363	21	x	x	X
ejpam-4143	363	22	)	)	PUNCT
ejpam-4143	363	23	for	for	ADP
ejpam-4143	363	24	all	all	DET
ejpam-4143	363	25	x	x	SYM
ejpam-4143	363	26	∈	∈	PROPN
ejpam-4143	363	27	g.	g.	NOUN
ejpam-4143	363	28	next	next	ADV
ejpam-4143	363	29	,	,	PUNCT
ejpam-4143	363	30	let	let	VERB
ejpam-4143	363	31	x	x	PRON
ejpam-4143	363	32	,	,	PUNCT
ejpam-4143	363	33	y	y	PROPN
ejpam-4143	363	34	∈	∈	PROPN
ejpam-4143	363	35	g.	g.	NOUN
ejpam-4143	363	36	then	then	ADV
ejpam-4143	363	37	f(x	f(x	PROPN
ejpam-4143	363	38	)	)	PUNCT
ejpam-4143	363	39	,	,	PUNCT
ejpam-4143	363	40	f(y	f(y	NOUN
ejpam-4143	363	41	)	)	PUNCT
ejpam-4143	363	42	∈	∈	PROPN
ejpam-4143	363	43	h.	h.	NOUN
ejpam-4143	363	44	again	again	ADV
ejpam-4143	363	45	,	,	PUNCT
ejpam-4143	363	46	by	by	ADP
ejpam-4143	363	47	our	our	PRON
ejpam-4143	363	48	assumption	assumption	NOUN
ejpam-4143	363	49	on	on	ADP
ejpam-4143	363	50	µ	µ	NUM
ejpam-4143	363	51	,	,	PUNCT
ejpam-4143	363	52	and	and	CCONJ
ejpam-4143	363	53	by	by	ADP
ejpam-4143	363	54	lemma	lemma	PROPN
ejpam-4143	363	55	5	5	NUM
ejpam-4143	363	56	,	,	PUNCT
ejpam-4143	363	57	µ(f(y	µ(f(y	NUM
ejpam-4143	363	58	)	)	PUNCT
ejpam-4143	363	59	)	)	PUNCT
ejpam-4143	364	1	=	=	SYM
ejpam-4143	364	2	µf	µf	X
ejpam-4143	364	3	(	(	PUNCT
ejpam-4143	364	4	y	y	PROPN
ejpam-4143	364	5	)	)	PUNCT
ejpam-4143	364	6	≥	≥	PROPN
ejpam-4143	364	7	min{µ(f(x	min{µ(f(x	PROPN
ejpam-4143	364	8	)	)	PUNCT
ejpam-4143	364	9	)	)	PUNCT
ejpam-4143	364	10	,	,	PUNCT
ejpam-4143	364	11	inf	inf	PROPN
ejpam-4143	364	12	f(z)∈f(x)⊛hf(y	f(z)∈f(x)⊛hf(y	NOUN
ejpam-4143	364	13	)	)	PUNCT
ejpam-4143	364	14	{	{	PUNCT
ejpam-4143	364	15	µ(f(z	µ(f(z	NUM
ejpam-4143	364	16	)	)	PUNCT
ejpam-4143	364	17	)	)	PUNCT
ejpam-4143	364	18	}	}	PUNCT
ejpam-4143	364	19	}	}	PUNCT
ejpam-4143	364	20	=	=	SYM
ejpam-4143	364	21	min{µf	min{µf	ADP
ejpam-4143	364	22	(	(	PUNCT
ejpam-4143	364	23	x	x	X
ejpam-4143	364	24	)	)	PUNCT
ejpam-4143	364	25	,	,	PUNCT
ejpam-4143	364	26	inf	inf	PROPN
ejpam-4143	364	27	z∈x⊛gy	z∈x⊛gy	PROPN
ejpam-4143	364	28	{	{	PUNCT
ejpam-4143	364	29	µf	µf	X
ejpam-4143	364	30	(	(	PUNCT
ejpam-4143	364	31	z	z	NOUN
ejpam-4143	364	32	)	)	PUNCT
ejpam-4143	364	33	}	}	PUNCT
ejpam-4143	364	34	}	}	PUNCT
ejpam-4143	364	35	.	.	PUNCT
ejpam-4143	365	1	hence	hence	ADV
ejpam-4143	365	2	,	,	PUNCT
ejpam-4143	365	3	µf	µf	PROPN
ejpam-4143	365	4	is	be	AUX
ejpam-4143	365	5	a	a	DET
ejpam-4143	365	6	fuzzy	fuzzy	ADJ
ejpam-4143	365	7	hyper	hyper	ADJ
ejpam-4143	365	8	up	up	ADJ
ejpam-4143	365	9	-	-	PUNCT
ejpam-4143	365	10	filter	filter	NOUN
ejpam-4143	365	11	of	of	ADP
ejpam-4143	365	12	g.	g.	PROPN
ejpam-4143	365	13	acknowledgements	acknowledgement	NOUN
ejpam-4143	365	14	this	this	DET
ejpam-4143	365	15	research	research	NOUN
ejpam-4143	365	16	is	be	AUX
ejpam-4143	365	17	funded	fund	VERB
ejpam-4143	365	18	by	by	ADP
ejpam-4143	365	19	the	the	DET
ejpam-4143	365	20	philippine	philippine	PROPN
ejpam-4143	365	21	department	department	PROPN
ejpam-4143	365	22	of	of	ADP
ejpam-4143	365	23	science	science	NOUN
ejpam-4143	365	24	and	and	CCONJ
ejpam-4143	365	25	technologyaccelerated	technologyaccelerated	ADJ
ejpam-4143	365	26	science	science	NOUN
ejpam-4143	365	27	and	and	CCONJ
ejpam-4143	365	28	technology	technology	NOUN
ejpam-4143	365	29	human	human	ADJ
ejpam-4143	365	30	resource	resource	NOUN
ejpam-4143	365	31	development	development	NOUN
ejpam-4143	365	32	program	program	NOUN
ejpam-4143	365	33	(	(	PUNCT
ejpam-4143	365	34	dostasthrdp	dostasthrdp	PROPN
ejpam-4143	365	35	)	)	PUNCT
ejpam-4143	365	36	and	and	CCONJ
ejpam-4143	365	37	the	the	DET
ejpam-4143	365	38	mindanao	mindanao	PROPN
ejpam-4143	365	39	state	state	PROPN
ejpam-4143	365	40	university	university	PROPN
ejpam-4143	365	41	-	-	PUNCT
ejpam-4143	365	42	iligan	iligan	PROPN
ejpam-4143	365	43	institute	institute	PROPN
ejpam-4143	365	44	of	of	ADP
ejpam-4143	365	45	technology	technology	PROPN
ejpam-4143	365	46	.	.	PUNCT
ejpam-4143	366	1	the	the	DET
ejpam-4143	366	2	authors	author	NOUN
ejpam-4143	366	3	would	would	AUX
ejpam-4143	366	4	like	like	VERB
ejpam-4143	366	5	to	to	PART
ejpam-4143	366	6	thank	thank	VERB
ejpam-4143	366	7	the	the	DET
ejpam-4143	366	8	reviewers	reviewer	NOUN
ejpam-4143	366	9	for	for	ADP
ejpam-4143	366	10	their	their	PRON
ejpam-4143	366	11	invaluable	invaluable	ADJ
ejpam-4143	366	12	comments	comment	NOUN
ejpam-4143	366	13	and	and	CCONJ
ejpam-4143	366	14	suggestions	suggestion	NOUN
ejpam-4143	366	15	that	that	PRON
ejpam-4143	366	16	led	lead	VERB
ejpam-4143	366	17	to	to	ADP
ejpam-4143	366	18	this	this	DET
ejpam-4143	366	19	improved	improve	VERB
ejpam-4143	366	20	version	version	NOUN
ejpam-4143	366	21	of	of	ADP
ejpam-4143	366	22	the	the	DET
ejpam-4143	366	23	paper	paper	NOUN
ejpam-4143	366	24	.	.	PUNCT
ejpam-4143	367	1	references	reference	NOUN
ejpam-4143	367	2	1400	1400	NUM
ejpam-4143	367	3	references	reference	NOUN
ejpam-4143	367	4	[	[	X
ejpam-4143	367	5	1	1	NUM
ejpam-4143	367	6	]	]	X
ejpam-4143	367	7	r.	r.	PROPN
ejpam-4143	367	8	amairanto	amairanto	PROPN
ejpam-4143	367	9	and	and	CCONJ
ejpam-4143	367	10	r.	r.	PROPN
ejpam-4143	367	11	isla	isla	PROPN
ejpam-4143	367	12	.	.	PUNCT
ejpam-4143	368	1	hyper	hyper	PROPN
ejpam-4143	368	2	homomorphism	homomorphism	PROPN
ejpam-4143	368	3	and	and	CCONJ
ejpam-4143	368	4	hyper	hyper	ADJ
ejpam-4143	368	5	product	product	NOUN
ejpam-4143	368	6	of	of	ADP
ejpam-4143	368	7	hyper	hyper	ADJ
ejpam-4143	368	8	upalgebras	upalgebra	NOUN
ejpam-4143	368	9	.	.	PUNCT
ejpam-4143	369	1	european	european	PROPN
ejpam-4143	369	2	journal	journal	PROPN
ejpam-4143	369	3	of	of	ADP
ejpam-4143	369	4	pure	pure	ADJ
ejpam-4143	369	5	and	and	CCONJ
ejpam-4143	369	6	applied	applied	ADJ
ejpam-4143	369	7	mathematics	mathematic	NOUN
ejpam-4143	369	8	,	,	PUNCT
ejpam-4143	369	9	13(3):483–497	13(3):483–497	NUM
ejpam-4143	369	10	,	,	PUNCT
ejpam-4143	369	11	2020	2020	NUM
ejpam-4143	369	12	.	.	PUNCT
ejpam-4143	370	1	[	[	X
ejpam-4143	370	2	2	2	NUM
ejpam-4143	370	3	]	]	X
ejpam-4143	370	4	r.	r.	PROPN
ejpam-4143	370	5	ameri	ameri	PROPN
ejpam-4143	370	6	and	and	CCONJ
ejpam-4143	370	7	t.	t.	PROPN
ejpam-4143	370	8	nozari	nozari	PROPN
ejpam-4143	370	9	.	.	PUNCT
ejpam-4143	371	1	fuzzy	fuzzy	PROPN
ejpam-4143	371	2	hyperalgebras	hyperalgebra	NOUN
ejpam-4143	371	3	.	.	PUNCT
ejpam-4143	372	1	computers	computer	NOUN
ejpam-4143	372	2	and	and	CCONJ
ejpam-4143	372	3	mathematics	mathematic	NOUN
ejpam-4143	372	4	with	with	ADP
ejpam-4143	372	5	applications	application	NOUN
ejpam-4143	372	6	,	,	PUNCT
ejpam-4143	372	7	61:149–154	61:149–154	PROPN
ejpam-4143	372	8	,	,	PUNCT
ejpam-4143	372	9	2011	2011	NUM
ejpam-4143	372	10	.	.	PUNCT
ejpam-4143	373	1	[	[	X
ejpam-4143	373	2	3	3	NUM
ejpam-4143	373	3	]	]	X
ejpam-4143	373	4	p.	p.	NOUN
ejpam-4143	373	5	corcini	corcini	NOUN
ejpam-4143	373	6	.	.	PUNCT
ejpam-4143	374	1	some	some	DET
ejpam-4143	374	2	remarks	remark	NOUN
ejpam-4143	374	3	on	on	ADP
ejpam-4143	374	4	hyperstructures	hyperstructure	NOUN
ejpam-4143	374	5	their	their	PRON
ejpam-4143	374	6	connections	connection	NOUN
ejpam-4143	374	7	with	with	ADP
ejpam-4143	374	8	fuzzy	fuzzy	ADJ
ejpam-4143	374	9	sets	set	NOUN
ejpam-4143	374	10	and	and	CCONJ
ejpam-4143	374	11	extensions	extension	NOUN
ejpam-4143	374	12	to	to	ADP
ejpam-4143	374	13	weak	weak	ADJ
ejpam-4143	374	14	structures	structure	NOUN
ejpam-4143	374	15	.	.	PUNCT
ejpam-4143	375	1	ratio	ratio	NOUN
ejpam-4143	375	2	mathematika	mathematika	NOUN
ejpam-4143	375	3	,	,	PUNCT
ejpam-4143	375	4	33:61–76	33:61–76	NUM
ejpam-4143	375	5	,	,	PUNCT
ejpam-4143	375	6	2017	2017	NUM
ejpam-4143	375	7	.	.	PUNCT
ejpam-4143	376	1	[	[	X
ejpam-4143	376	2	4	4	X
ejpam-4143	376	3	]	]	X
ejpam-4143	376	4	p.	p.	NOUN
ejpam-4143	376	5	corcini	corcini	NOUN
ejpam-4143	376	6	and	and	CCONJ
ejpam-4143	376	7	v.	v.	ADP
ejpam-4143	376	8	leoreanu	leoreanu	PROPN
ejpam-4143	376	9	.	.	PUNCT
ejpam-4143	377	1	applications	application	NOUN
ejpam-4143	377	2	of	of	ADP
ejpam-4143	377	3	hyperstructure	hyperstructure	PROPN
ejpam-4143	377	4	theory	theory	PROPN
ejpam-4143	377	5	.	.	PUNCT
ejpam-4143	378	1	springer	springer	NOUN
ejpam-4143	378	2	-	-	PUNCT
ejpam-4143	378	3	us	us	PROPN
ejpam-4143	378	4	,	,	PUNCT
ejpam-4143	378	5	2003	2003	NUM
ejpam-4143	378	6	.	.	PUNCT
ejpam-4143	379	1	[	[	X
ejpam-4143	379	2	5	5	X
ejpam-4143	379	3	]	]	PUNCT
ejpam-4143	379	4	p.	p.	NOUN
ejpam-4143	379	5	corsini	corsini	PROPN
ejpam-4143	379	6	and	and	CCONJ
ejpam-4143	379	7	i.	i.	PROPN
ejpam-4143	379	8	tofan	tofan	PROPN
ejpam-4143	379	9	.	.	PUNCT
ejpam-4143	380	1	on	on	ADP
ejpam-4143	380	2	fuzzy	fuzzy	ADJ
ejpam-4143	380	3	hypergroups	hypergroup	NOUN
ejpam-4143	380	4	.	.	PUNCT
ejpam-4143	381	1	pure	pure	ADJ
ejpam-4143	381	2	mathematics	mathematic	NOUN
ejpam-4143	381	3	and	and	CCONJ
ejpam-4143	381	4	applications	application	NOUN
ejpam-4143	381	5	,	,	PUNCT
ejpam-4143	381	6	8(1):29–37	8(1):29–37	NUM
ejpam-4143	381	7	,	,	PUNCT
ejpam-4143	381	8	1997	1997	NUM
ejpam-4143	381	9	.	.	PUNCT
ejpam-4143	382	1	[	[	X
ejpam-4143	382	2	6	6	NUM
ejpam-4143	382	3	]	]	PUNCT
ejpam-4143	382	4	b.	b.	PROPN
ejpam-4143	382	5	davvaz	davvaz	PROPN
ejpam-4143	382	6	and	and	CCONJ
ejpam-4143	382	7	i.	i.	PROPN
ejpam-4143	382	8	cristea	cristea	PROPN
ejpam-4143	382	9	.	.	PUNCT
ejpam-4143	383	1	fuzzy	fuzzy	ADJ
ejpam-4143	383	2	algebraic	algebraic	ADJ
ejpam-4143	383	3	hyperstructures	hyperstructure	NOUN
ejpam-4143	383	4	.	.	PUNCT
ejpam-4143	384	1	springer	springer	NOUN
ejpam-4143	384	2	:	:	PUNCT
ejpam-4143	384	3	cham	cham	PROPN
ejpam-4143	384	4	,	,	PUNCT
ejpam-4143	384	5	switzerland	switzerland	PROPN
ejpam-4143	384	6	,	,	PUNCT
ejpam-4143	384	7	2015	2015	NUM
ejpam-4143	384	8	.	.	PUNCT
ejpam-4143	385	1	[	[	X
ejpam-4143	385	2	7	7	X
ejpam-4143	385	3	]	]	X
ejpam-4143	385	4	s.a	s.a	PROPN
ejpam-4143	385	5	.	.	PROPN
ejpam-4143	385	6	bhatti	bhatti	PROPN
ejpam-4143	385	7	f.	f.	PROPN
ejpam-4143	385	8	nisar	nisar	PROPN
ejpam-4143	385	9	,	,	PUNCT
ejpam-4143	385	10	r.s	r.s	PROPN
ejpam-4143	385	11	.	.	PROPN
ejpam-4143	385	12	tariq	tariq	PROPN
ejpam-4143	385	13	.	.	PUNCT
ejpam-4143	386	1	fuzzy	fuzzy	ADJ
ejpam-4143	386	2	ideals	ideal	NOUN
ejpam-4143	386	3	in	in	ADP
ejpam-4143	386	4	hyper	hyper	ADJ
ejpam-4143	386	5	bci	bci	NOUN
ejpam-4143	386	6	-	-	PUNCT
ejpam-4143	386	7	algebras	algebra	NOUN
ejpam-4143	386	8	.	.	PUNCT
ejpam-4143	387	1	world	world	PROPN
ejpam-4143	387	2	applied	apply	VERB
ejpam-4143	387	3	sciences	science	NOUN
ejpam-4143	387	4	journal	journal	NOUN
ejpam-4143	387	5	,	,	PUNCT
ejpam-4143	387	6	16(12):1771–1777	16(12):1771–1777	PROPN
ejpam-4143	387	7	,	,	PUNCT
ejpam-4143	387	8	2012	2012	NUM
ejpam-4143	387	9	.	.	PUNCT
ejpam-4143	388	1	[	[	X
ejpam-4143	388	2	8	8	NUM
ejpam-4143	388	3	]	]	PUNCT
ejpam-4143	388	4	a.	a.	NOUN
ejpam-4143	388	5	iampan	iampan	PROPN
ejpam-4143	388	6	.	.	PUNCT
ejpam-4143	389	1	a	a	DET
ejpam-4143	389	2	new	new	ADJ
ejpam-4143	389	3	branch	branch	NOUN
ejpam-4143	389	4	of	of	ADP
ejpam-4143	389	5	the	the	DET
ejpam-4143	389	6	logical	logical	ADJ
ejpam-4143	389	7	algebra	algebra	NOUN
ejpam-4143	389	8	:	:	PUNCT
ejpam-4143	389	9	up	up	ADP
ejpam-4143	389	10	-	-	PUNCT
ejpam-4143	389	11	algebras	algebras	X
ejpam-4143	389	12	.	.	PUNCT
ejpam-4143	389	13	journal	journal	PROPN
ejpam-4143	389	14	of	of	ADP
ejpam-4143	389	15	algebra	algebra	PROPN
ejpam-4143	389	16	and	and	CCONJ
ejpam-4143	389	17	related	related	ADJ
ejpam-4143	389	18	topics	topic	NOUN
ejpam-4143	389	19	,	,	PUNCT
ejpam-4143	389	20	5(1):35–54	5(1):35–54	NUM
ejpam-4143	389	21	,	,	PUNCT
ejpam-4143	389	22	2017	2017	NUM
ejpam-4143	389	23	.	.	PUNCT
ejpam-4143	390	1	[	[	X
ejpam-4143	390	2	9	9	NUM
ejpam-4143	390	3	]	]	X
ejpam-4143	390	4	y.b	y.b	PROPN
ejpam-4143	390	5	.	.	PROPN
ejpam-4143	390	6	jun	jun	PROPN
ejpam-4143	390	7	and	and	CCONJ
ejpam-4143	390	8	x.l	x.l	PROPN
ejpam-4143	390	9	.	.	PUNCT
ejpam-4143	391	1	xin	xin	PROPN
ejpam-4143	391	2	.	.	PUNCT
ejpam-4143	392	1	fuzzy	fuzzy	ADJ
ejpam-4143	392	2	hyper	hyper	ADJ
ejpam-4143	392	3	bck	bck	NOUN
ejpam-4143	392	4	-	-	PUNCT
ejpam-4143	392	5	ideals	ideal	NOUN
ejpam-4143	392	6	of	of	ADP
ejpam-4143	392	7	hyper	hyper	ADJ
ejpam-4143	392	8	bck	bck	NOUN
ejpam-4143	392	9	-	-	PUNCT
ejpam-4143	392	10	algebras	algebras	PROPN
ejpam-4143	392	11	.	.	PUNCT
ejpam-4143	393	1	scientia	scientia	PROPN
ejpam-4143	393	2	mathematicae	mathematicae	PROPN
ejpam-4143	393	3	japonicae	japonicae	PROPN
ejpam-4143	393	4	,	,	PUNCT
ejpam-4143	393	5	53(2):353–360	53(2):353–360	PROPN
ejpam-4143	393	6	,	,	PUNCT
ejpam-4143	393	7	2001	2001	NUM
ejpam-4143	393	8	.	.	PUNCT
ejpam-4143	394	1	[	[	X
ejpam-4143	394	2	10	10	NUM
ejpam-4143	394	3	]	]	X
ejpam-4143	394	4	k.h	k.h	PROPN
ejpam-4143	394	5	.	.	PROPN
ejpam-4143	394	6	lee	lee	PROPN
ejpam-4143	394	7	.	.	PUNCT
ejpam-4143	395	1	first	first	ADJ
ejpam-4143	395	2	course	course	NOUN
ejpam-4143	395	3	on	on	ADP
ejpam-4143	395	4	fuzzy	fuzzy	ADJ
ejpam-4143	395	5	theory	theory	NOUN
ejpam-4143	395	6	and	and	CCONJ
ejpam-4143	395	7	applications	application	NOUN
ejpam-4143	395	8	.	.	PUNCT
ejpam-4143	396	1	springer	springer	NOUN
ejpam-4143	396	2	-	-	PUNCT
ejpam-4143	396	3	verlag	verlag	PROPN
ejpam-4143	396	4	berlin	berlin	PROPN
ejpam-4143	396	5	heidelberg	heidelberg	PROPN
ejpam-4143	396	6	,	,	PUNCT
ejpam-4143	396	7	2005	2005	NUM
ejpam-4143	396	8	.	.	PUNCT
ejpam-4143	397	1	[	[	X
ejpam-4143	397	2	11	11	NUM
ejpam-4143	397	3	]	]	PUNCT
ejpam-4143	397	4	v.	v.	CCONJ
ejpam-4143	397	5	leoreanu	leoreanu	PROPN
ejpam-4143	397	6	-	-	PUNCT
ejpam-4143	397	7	fotea	fotea	NOUN
ejpam-4143	397	8	and	and	CCONJ
ejpam-4143	397	9	b.	b.	PROPN
ejpam-4143	397	10	davvaz	davvaz	PROPN
ejpam-4143	397	11	.	.	PUNCT
ejpam-4143	398	1	fuzzy	fuzzy	ADJ
ejpam-4143	398	2	hyperrings	hyperring	NOUN
ejpam-4143	398	3	.	.	PUNCT
ejpam-4143	399	1	fuzzy	fuzzy	ADJ
ejpam-4143	399	2	sets	set	VERB
ejpam-4143	399	3	syst	syst	PROPN
ejpam-4143	399	4	.	.	PUNCT
ejpam-4143	399	5	,	,	PUNCT
ejpam-4143	399	6	160:2366–2378	160:2366–2378	NUM
ejpam-4143	399	7	,	,	PUNCT
ejpam-4143	399	8	2009	2009	NUM
ejpam-4143	399	9	.	.	PUNCT
ejpam-4143	400	1	[	[	X
ejpam-4143	400	2	12	12	NUM
ejpam-4143	400	3	]	]	PUNCT
ejpam-4143	400	4	a.	a.	NOUN
ejpam-4143	400	5	macodi	macodi	PROPN
ejpam-4143	400	6	-	-	PUNCT
ejpam-4143	400	7	ringia	ringia	PROPN
ejpam-4143	400	8	and	and	CCONJ
ejpam-4143	400	9	jr	jr	PROPN
ejpam-4143	400	10	g.	g.	PROPN
ejpam-4143	400	11	petalcorin	petalcorin	PROPN
ejpam-4143	400	12	.	.	PUNCT
ejpam-4143	401	1	some	some	DET
ejpam-4143	401	2	results	result	NOUN
ejpam-4143	401	3	on	on	ADP
ejpam-4143	401	4	fuzzy	fuzzy	ADJ
ejpam-4143	401	5	implicative	implicative	ADJ
ejpam-4143	401	6	hyper	hyper	ADJ
ejpam-4143	401	7	gr	gr	NOUN
ejpam-4143	401	8	-	-	PUNCT
ejpam-4143	401	9	ideals	ideal	NOUN
ejpam-4143	401	10	.	.	PUNCT
ejpam-4143	402	1	european	european	ADJ
ejpam-4143	402	2	journal	journal	PROPN
ejpam-4143	402	3	of	of	ADP
ejpam-4143	402	4	pure	pure	ADJ
ejpam-4143	402	5	and	and	CCONJ
ejpam-4143	402	6	applied	applied	ADJ
ejpam-4143	402	7	mathematics	mathematic	NOUN
ejpam-4143	402	8	,	,	PUNCT
ejpam-4143	402	9	12(2):409–417	12(2):409–417	NUM
ejpam-4143	402	10	,	,	PUNCT
ejpam-4143	402	11	2019	2019	NUM
ejpam-4143	402	12	.	.	PUNCT
ejpam-4143	403	1	[	[	X
ejpam-4143	403	2	13	13	NUM
ejpam-4143	403	3	]	]	PUNCT
ejpam-4143	403	4	a.	a.	NOUN
ejpam-4143	403	5	macodi	macodi	PROPN
ejpam-4143	403	6	-	-	PUNCT
ejpam-4143	403	7	ringia	ringia	PROPN
ejpam-4143	403	8	and	and	CCONJ
ejpam-4143	403	9	jr	jr	PROPN
ejpam-4143	403	10	g.	g.	PROPN
ejpam-4143	403	11	petalcorin	petalcorin	PROPN
ejpam-4143	403	12	.	.	PUNCT
ejpam-4143	404	1	on	on	ADP
ejpam-4143	404	2	intuitionistic	intuitionistic	ADJ
ejpam-4143	404	3	fuzzy	fuzzy	ADJ
ejpam-4143	404	4	hyper	hyper	ADJ
ejpam-4143	404	5	gr	gr	NOUN
ejpam-4143	404	6	-	-	PUNCT
ejpam-4143	404	7	ideals	ideal	NOUN
ejpam-4143	404	8	in	in	ADP
ejpam-4143	404	9	hyper	hyper	ADJ
ejpam-4143	404	10	gr	gr	NOUN
ejpam-4143	404	11	-	-	PUNCT
ejpam-4143	404	12	algebras	algebra	NOUN
ejpam-4143	404	13	.	.	PUNCT
ejpam-4143	404	14	european	european	PROPN
ejpam-4143	404	15	journal	journal	PROPN
ejpam-4143	404	16	of	of	ADP
ejpam-4143	404	17	pure	pure	ADJ
ejpam-4143	404	18	and	and	CCONJ
ejpam-4143	404	19	applied	applied	ADJ
ejpam-4143	404	20	mathematics	mathematic	NOUN
ejpam-4143	404	21	,	,	PUNCT
ejpam-4143	404	22	13(2):246	13(2):246	NUM
ejpam-4143	404	23	–	–	PUNCT
ejpam-4143	404	24	257	257	NUM
ejpam-4143	404	25	,	,	PUNCT
ejpam-4143	404	26	2020	2020	NUM
ejpam-4143	404	27	.	.	PUNCT
ejpam-4143	405	1	[	[	X
ejpam-4143	405	2	14	14	NUM
ejpam-4143	405	3	]	]	X
ejpam-4143	405	4	f.	f.	PROPN
ejpam-4143	405	5	marty	marty	PROPN
ejpam-4143	405	6	.	.	PUNCT
ejpam-4143	406	1	sur	sur	PROPN
ejpam-4143	406	2	une	une	PROPN
ejpam-4143	406	3	generalisation	generalisation	PROPN
ejpam-4143	406	4	de	de	X
ejpam-4143	406	5	la	la	PROPN
ejpam-4143	406	6	notion	notion	PROPN
ejpam-4143	406	7	de	de	X
ejpam-4143	406	8	groupe	groupe	PROPN
ejpam-4143	406	9	.	.	PUNCT
ejpam-4143	407	1	in	in	ADP
ejpam-4143	407	2	8th	8th	ADJ
ejpam-4143	407	3	congress	congress	PROPN
ejpam-4143	407	4	des	des	PROPN
ejpam-4143	407	5	mathematician	mathematician	PROPN
ejpam-4143	407	6	scandinaves	scandinaves	PROPN
ejpam-4143	407	7	,	,	PUNCT
ejpam-4143	407	8	pages	page	NOUN
ejpam-4143	407	9	45–49	45–49	PROPN
ejpam-4143	407	10	,	,	PUNCT
ejpam-4143	407	11	stockholm	stockholm	PROPN
ejpam-4143	407	12	,	,	PUNCT
ejpam-4143	407	13	1934	1934	NUM
ejpam-4143	407	14	.	.	PUNCT
ejpam-4143	408	1	[	[	X
ejpam-4143	408	2	15	15	NUM
ejpam-4143	408	3	]	]	X
ejpam-4143	408	4	c.	c.	NOUN
ejpam-4143	408	5	prabpayak	prabpayak	NOUN
ejpam-4143	408	6	and	and	CCONJ
ejpam-4143	408	7	u.	u.	NOUN
ejpam-4143	408	8	leerawat	leerawat	PROPN
ejpam-4143	408	9	.	.	PUNCT
ejpam-4143	409	1	on	on	ADP
ejpam-4143	409	2	ideals	ideal	NOUN
ejpam-4143	409	3	and	and	CCONJ
ejpam-4143	409	4	congruence	congruence	NOUN
ejpam-4143	409	5	in	in	ADP
ejpam-4143	409	6	ku	ku	PROPN
ejpam-4143	409	7	-	-	PUNCT
ejpam-4143	409	8	algebras	algebras	PROPN
ejpam-4143	409	9	.	.	PUNCT
ejpam-4143	410	1	scientia	scientia	PROPN
ejpam-4143	410	2	magna	magna	PROPN
ejpam-4143	410	3	journal	journal	PROPN
ejpam-4143	410	4	,	,	PUNCT
ejpam-4143	410	5	5(1):54–57	5(1):54–57	NUM
ejpam-4143	410	6	,	,	PUNCT
ejpam-4143	410	7	2009	2009	NUM
ejpam-4143	410	8	.	.	PUNCT
ejpam-4143	411	1	[	[	X
ejpam-4143	411	2	16	16	NUM
ejpam-4143	411	3	]	]	X
ejpam-4143	411	4	d.	d.	PROPN
ejpam-4143	411	5	romano	romano	PROPN
ejpam-4143	411	6	.	.	PUNCT
ejpam-4143	412	1	hyper	hyper	PROPN
ejpam-4143	412	2	up	up	ADP
ejpam-4143	412	3	-	-	PUNCT
ejpam-4143	412	4	algebras	algebras	PROPN
ejpam-4143	412	5	.	.	PUNCT
ejpam-4143	413	1	journal	journal	PROPN
ejpam-4143	413	2	of	of	ADP
ejpam-4143	413	3	hyperstructures	hyperstructure	NOUN
ejpam-4143	413	4	,	,	PUNCT
ejpam-4143	413	5	8(2):112–122	8(2):112–122	NUM
ejpam-4143	413	6	,	,	PUNCT
ejpam-4143	413	7	2019	2019	NUM
ejpam-4143	413	8	.	.	PUNCT
ejpam-4143	414	1	references	reference	NOUN
ejpam-4143	414	2	1401	1401	NUM
ejpam-4143	415	1	[	[	X
ejpam-4143	415	2	17	17	NUM
ejpam-4143	415	3	]	]	X
ejpam-4143	415	4	f.	f.	PROPN
ejpam-4143	415	5	kareem	kareem	PROPN
ejpam-4143	415	6	s.	s.	PROPN
ejpam-4143	415	7	mostafa	mostafa	PROPN
ejpam-4143	415	8	and	and	CCONJ
ejpam-4143	415	9	b.	b.	PROPN
ejpam-4143	415	10	davvaz	davvaz	PROPN
ejpam-4143	415	11	.	.	PUNCT
ejpam-4143	416	1	hyper	hyper	ADJ
ejpam-4143	416	2	structure	structure	NOUN
ejpam-4143	416	3	theory	theory	NOUN
ejpam-4143	416	4	applied	apply	VERB
ejpam-4143	416	5	to	to	ADP
ejpam-4143	416	6	ku	ku	PROPN
ejpam-4143	416	7	-	-	PUNCT
ejpam-4143	416	8	algebras	algebras	PROPN
ejpam-4143	416	9	.	.	PUNCT
ejpam-4143	417	1	journal	journal	PROPN
ejpam-4143	417	2	of	of	ADP
ejpam-4143	417	3	hyperstructures	hyperstructure	NOUN
ejpam-4143	417	4	,	,	PUNCT
ejpam-4143	417	5	6(2):82–95	6(2):82–95	NUM
ejpam-4143	417	6	,	,	PUNCT
ejpam-4143	417	7	2017	2017	NUM
ejpam-4143	417	8	.	.	PUNCT
ejpam-4143	418	1	[	[	X
ejpam-4143	418	2	18	18	NUM
ejpam-4143	418	3	]	]	X
ejpam-4143	418	4	g.	g.	NOUN
ejpam-4143	418	5	tabaranza	tabaranza	PROPN
ejpam-4143	418	6	and	and	CCONJ
ejpam-4143	418	7	j.	j.	PROPN
ejpam-4143	418	8	vilela	vilela	PROPN
ejpam-4143	418	9	.	.	PUNCT
ejpam-4143	419	1	fuzzy	fuzzy	ADJ
ejpam-4143	419	2	hyper	hyper	ADJ
ejpam-4143	419	3	b	b	NOUN
ejpam-4143	419	4	-	-	PUNCT
ejpam-4143	419	5	algebras	algebras	PROPN
ejpam-4143	419	6	.	.	PUNCT
ejpam-4143	420	1	jp	jp	PROPN
ejpam-4143	420	2	journal	journal	PROPN
ejpam-4143	420	3	of	of	ADP
ejpam-4143	420	4	algebra	algebra	PROPN
ejpam-4143	420	5	,	,	PUNCT
ejpam-4143	420	6	number	number	NOUN
ejpam-4143	420	7	theory	theory	NOUN
ejpam-4143	420	8	and	and	CCONJ
ejpam-4143	420	9	applications	application	NOUN
ejpam-4143	420	10	.	.	PUNCT
ejpam-4143	421	1	,	,	PUNCT
ejpam-4143	421	2	41(2):205–218	41(2):205–218	NOUN
ejpam-4143	421	3	,	,	PUNCT
ejpam-4143	421	4	2019	2019	NUM
ejpam-4143	421	5	.	.	PUNCT
ejpam-4143	422	1	[	[	X
ejpam-4143	422	2	19	19	NUM
ejpam-4143	422	3	]	]	PUNCT
ejpam-4143	422	4	m.	m.	NOUN
ejpam-4143	422	5	voskoglou	voskoglou	PROPN
ejpam-4143	422	6	.	.	PUNCT
ejpam-4143	423	1	fuzzy	fuzzy	ADJ
ejpam-4143	423	2	sets	set	NOUN
ejpam-4143	423	3	,	,	PUNCT
ejpam-4143	423	4	fuzzy	fuzzy	ADJ
ejpam-4143	423	5	logic	logic	NOUN
ejpam-4143	423	6	and	and	CCONJ
ejpam-4143	423	7	their	their	PRON
ejpam-4143	423	8	applications	application	NOUN
ejpam-4143	423	9	.	.	PUNCT
ejpam-4143	424	1	mdpi	mdpi	PROPN
ejpam-4143	424	2	ag	ag	PROPN
ejpam-4143	424	3	,	,	PUNCT
ejpam-4143	424	4	2020	2020	NUM
ejpam-4143	424	5	.	.	PUNCT
ejpam-4143	425	1	[	[	X
ejpam-4143	425	2	20	20	NUM
ejpam-4143	425	3	]	]	PUNCT
ejpam-4143	425	4	m.	m.	NOUN
ejpam-4143	425	5	bakhshi	bakhshi	PROPN
ejpam-4143	425	6	x.	x.	PROPN
ejpam-4143	425	7	xin	xin	PROPN
ejpam-4143	425	8	,	,	PUNCT
ejpam-4143	425	9	r.a	r.a	PROPN
ejpam-4143	425	10	.	.	PROPN
ejpam-4143	425	11	borzooie	borzooie	PROPN
ejpam-4143	425	12	and	and	CCONJ
ejpam-4143	425	13	y.b	y.b	PROPN
ejpam-4143	425	14	.	.	PROPN
ejpam-4143	425	15	jun	jun	PROPN
ejpam-4143	425	16	.	.	PROPN
ejpam-4143	426	1	intuitionistic	intuitionistic	ADJ
ejpam-4143	426	2	fuzzy	fuzzy	ADJ
ejpam-4143	426	3	soft	soft	ADJ
ejpam-4143	426	4	hyper	hyper	ADJ
ejpam-4143	426	5	bck	bck	NOUN
ejpam-4143	426	6	-	-	PUNCT
ejpam-4143	426	7	algebras	algebras	PROPN
ejpam-4143	426	8	.	.	PUNCT
ejpam-4143	426	9	symmetry	symmetry	PROPN
ejpam-4143	426	10	,	,	PUNCT
ejpam-4143	426	11	11(3):399	11(3):399	PROPN
ejpam-4143	426	12	(	(	PUNCT
ejpam-4143	426	13	article	article	NOUN
ejpam-4143	426	14	code	code	PROPN
ejpam-4143	426	15	)	)	PUNCT
ejpam-4143	426	16	,	,	PUNCT
ejpam-4143	426	17	2019	2019	NUM
ejpam-4143	426	18	.	.	PUNCT
ejpam-4143	427	1	[	[	X
ejpam-4143	427	2	21	21	NUM
ejpam-4143	427	3	]	]	X
ejpam-4143	427	4	l.	l.	PROPN
ejpam-4143	427	5	zadeh	zadeh	PROPN
ejpam-4143	427	6	.	.	PUNCT
ejpam-4143	427	7	fuzzy	fuzzy	ADJ
ejpam-4143	427	8	sets	set	NOUN
ejpam-4143	427	9	.	.	PUNCT
ejpam-4143	428	1	information	information	NOUN
ejpam-4143	428	2	and	and	CCONJ
ejpam-4143	428	3	control	control	NOUN
ejpam-4143	428	4	,	,	PUNCT
ejpam-4143	428	5	41:338–353	41:338–353	PROPN
ejpam-4143	428	6	,	,	PUNCT
ejpam-4143	428	7	1965	1965	NUM
ejpam-4143	428	8	.	.	PUNCT