id	sid	tid	token	lemma	pos
ejpam-3335	1	1	anti	anti	ADJ
ejpam-3335	1	2	-	-	ADJ
ejpam-3335	1	3	type	type	NOUN
ejpam-3335	1	4	of	of	ADP
ejpam-3335	1	5	hesitant	hesitant	ADJ
ejpam-3335	1	6	fuzzy	fuzzy	ADJ
ejpam-3335	1	7	sets	set	NOUN
ejpam-3335	1	8	on	on	ADP
ejpam-3335	1	9	up	up	ADV
ejpam-3335	1	10	-	-	PUNCT
ejpam-3335	1	11	algebras	algebras	ADJ
ejpam-3335	1	12	european	european	PROPN
ejpam-3335	1	13	journal	journal	PROPN
ejpam-3335	1	14	of	of	ADP
ejpam-3335	1	15	pure	pure	ADJ
ejpam-3335	1	16	and	and	CCONJ
ejpam-3335	1	17	applied	apply	VERB
ejpam-3335	1	18	mathematics	mathematic	NOUN
ejpam-3335	1	19	vol	vol	NOUN
ejpam-3335	1	20	.	.	PUNCT
ejpam-3335	2	1	11	11	NUM
ejpam-3335	2	2	,	,	PUNCT
ejpam-3335	2	3	no	no	INTJ
ejpam-3335	2	4	.	.	NOUN
ejpam-3335	2	5	4	4	NUM
ejpam-3335	2	6	,	,	PUNCT
ejpam-3335	2	7	2018	2018	NUM
ejpam-3335	2	8	,	,	PUNCT
ejpam-3335	2	9	976	976	NUM
ejpam-3335	2	10	-	-	SYM
ejpam-3335	2	11	1002	1002	NUM
ejpam-3335	2	12	issn	issn	PROPN
ejpam-3335	2	13	1307	1307	NUM
ejpam-3335	2	14	-	-	SYM
ejpam-3335	2	15	5543	5543	NUM
ejpam-3335	2	16	–	–	PUNCT
ejpam-3335	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3335	2	18	published	publish	VERB
ejpam-3335	2	19	by	by	ADP
ejpam-3335	2	20	new	new	PROPN
ejpam-3335	2	21	york	york	PROPN
ejpam-3335	2	22	business	business	PROPN
ejpam-3335	2	23	global	global	ADJ
ejpam-3335	2	24	anti	anti	ADJ
ejpam-3335	2	25	-	-	NOUN
ejpam-3335	2	26	type	type	NOUN
ejpam-3335	2	27	of	of	ADP
ejpam-3335	2	28	hesitant	hesitant	ADJ
ejpam-3335	2	29	fuzzy	fuzzy	ADJ
ejpam-3335	2	30	sets	set	NOUN
ejpam-3335	2	31	on	on	ADP
ejpam-3335	2	32	up	up	ADP
ejpam-3335	2	33	-	-	PUNCT
ejpam-3335	2	34	algebras∗	algebras∗	NOUN
ejpam-3335	2	35	phakawat	phakawat	NOUN
ejpam-3335	2	36	mosrijai1	mosrijai1	ADJ
ejpam-3335	2	37	,	,	PUNCT
ejpam-3335	2	38	aiyared	aiyare	VERB
ejpam-3335	2	39	iampan1,†	iampan1,†	PROPN
ejpam-3335	2	40	1	1	NUM
ejpam-3335	2	41	department	department	NOUN
ejpam-3335	2	42	of	of	ADP
ejpam-3335	2	43	mathematics	mathematic	NOUN
ejpam-3335	2	44	,	,	PUNCT
ejpam-3335	2	45	school	school	NOUN
ejpam-3335	2	46	of	of	ADP
ejpam-3335	2	47	science	science	NOUN
ejpam-3335	2	48	,	,	PUNCT
ejpam-3335	2	49	university	university	NOUN
ejpam-3335	2	50	of	of	ADP
ejpam-3335	2	51	phayao	phayao	NOUN
ejpam-3335	2	52	,	,	PUNCT
ejpam-3335	2	53	phayao	phayao	NOUN
ejpam-3335	2	54	56000	56000	NUM
ejpam-3335	2	55	,	,	PUNCT
ejpam-3335	2	56	thailand	thailand	PROPN
ejpam-3335	2	57	abstract	abstract	NOUN
ejpam-3335	2	58	.	.	PUNCT
ejpam-3335	3	1	this	this	DET
ejpam-3335	3	2	paper	paper	NOUN
ejpam-3335	3	3	aims	aim	VERB
ejpam-3335	3	4	to	to	PART
ejpam-3335	3	5	introduce	introduce	VERB
ejpam-3335	3	6	the	the	DET
ejpam-3335	3	7	notions	notion	NOUN
ejpam-3335	3	8	of	of	ADP
ejpam-3335	3	9	anti	anti	ADJ
ejpam-3335	3	10	-	-	ADJ
ejpam-3335	3	11	hesitant	hesitant	ADJ
ejpam-3335	3	12	fuzzy	fuzzy	ADJ
ejpam-3335	3	13	up	up	ADP
ejpam-3335	3	14	-	-	PUNCT
ejpam-3335	3	15	subalgebras	subalgebra	NOUN
ejpam-3335	3	16	of	of	ADP
ejpam-3335	3	17	up	up	ADP
ejpam-3335	3	18	-	-	PUNCT
ejpam-3335	3	19	algebras	algebra	NOUN
ejpam-3335	3	20	,	,	PUNCT
ejpam-3335	3	21	anti	anti	ADJ
ejpam-3335	3	22	-	-	ADJ
ejpam-3335	3	23	hesitant	hesitant	ADJ
ejpam-3335	3	24	fuzzy	fuzzy	ADJ
ejpam-3335	3	25	up	up	NOUN
ejpam-3335	3	26	-	-	PUNCT
ejpam-3335	3	27	filters	filter	NOUN
ejpam-3335	3	28	,	,	PUNCT
ejpam-3335	3	29	anti	anti	ADJ
ejpam-3335	3	30	-	-	ADJ
ejpam-3335	3	31	hesitant	hesitant	ADJ
ejpam-3335	3	32	fuzzy	fuzzy	ADJ
ejpam-3335	3	33	up	up	NOUN
ejpam-3335	3	34	-	-	PUNCT
ejpam-3335	3	35	ideals	ideal	NOUN
ejpam-3335	3	36	,	,	PUNCT
ejpam-3335	3	37	and	and	CCONJ
ejpam-3335	3	38	anti	anti	ADJ
ejpam-3335	3	39	-	-	ADJ
ejpam-3335	3	40	hesitant	hesitant	ADJ
ejpam-3335	3	41	fuzzy	fuzzy	ADJ
ejpam-3335	3	42	strongly	strongly	ADV
ejpam-3335	3	43	up	up	ADP
ejpam-3335	3	44	-	-	PUNCT
ejpam-3335	3	45	ideals	ideal	NOUN
ejpam-3335	3	46	,	,	PUNCT
ejpam-3335	3	47	and	and	CCONJ
ejpam-3335	3	48	prove	prove	VERB
ejpam-3335	3	49	some	some	DET
ejpam-3335	3	50	results	result	NOUN
ejpam-3335	3	51	.	.	PUNCT
ejpam-3335	4	1	furthermore	furthermore	ADV
ejpam-3335	4	2	,	,	PUNCT
ejpam-3335	4	3	we	we	PRON
ejpam-3335	4	4	discuss	discuss	VERB
ejpam-3335	4	5	the	the	DET
ejpam-3335	4	6	relationships	relationship	NOUN
ejpam-3335	4	7	between	between	ADP
ejpam-3335	4	8	anti	anti	ADJ
ejpam-3335	4	9	-	-	ADJ
ejpam-3335	4	10	hesitant	hesitant	ADJ
ejpam-3335	4	11	fuzzy	fuzzy	ADJ
ejpam-3335	4	12	up	up	ADP
ejpam-3335	4	13	-	-	PUNCT
ejpam-3335	4	14	subalgebras	subalgebras	PROPN
ejpam-3335	4	15	(	(	PUNCT
ejpam-3335	4	16	resp	resp	NOUN
ejpam-3335	4	17	.	.	PUNCT
ejpam-3335	4	18	,	,	PUNCT
ejpam-3335	4	19	anti	anti	ADJ
ejpam-3335	4	20	-	-	ADJ
ejpam-3335	4	21	hesitant	hesitant	ADJ
ejpam-3335	4	22	fuzzy	fuzzy	ADJ
ejpam-3335	4	23	up	up	NOUN
ejpam-3335	4	24	-	-	PUNCT
ejpam-3335	4	25	filters	filter	NOUN
ejpam-3335	4	26	,	,	PUNCT
ejpam-3335	4	27	anti	anti	ADJ
ejpam-3335	4	28	-	-	ADJ
ejpam-3335	4	29	hesitant	hesitant	ADJ
ejpam-3335	4	30	fuzzy	fuzzy	ADJ
ejpam-3335	4	31	upideals	upideal	NOUN
ejpam-3335	4	32	,	,	PUNCT
ejpam-3335	4	33	anti	anti	ADJ
ejpam-3335	4	34	-	-	ADJ
ejpam-3335	4	35	hesitant	hesitant	ADJ
ejpam-3335	4	36	fuzzy	fuzzy	ADJ
ejpam-3335	4	37	strongly	strongly	ADV
ejpam-3335	4	38	up	up	ADP
ejpam-3335	4	39	-	-	PUNCT
ejpam-3335	4	40	ideals	ideal	NOUN
ejpam-3335	4	41	)	)	PUNCT
ejpam-3335	4	42	and	and	CCONJ
ejpam-3335	4	43	some	some	DET
ejpam-3335	4	44	level	level	NOUN
ejpam-3335	4	45	subsets	subset	NOUN
ejpam-3335	4	46	of	of	ADP
ejpam-3335	4	47	hesitant	hesitant	ADJ
ejpam-3335	4	48	fuzzy	fuzzy	ADJ
ejpam-3335	4	49	sets	set	NOUN
ejpam-3335	4	50	on	on	ADP
ejpam-3335	4	51	up	up	ADP
ejpam-3335	4	52	-	-	PUNCT
ejpam-3335	4	53	algebras	algebras	X
ejpam-3335	4	54	.	.	PUNCT
ejpam-3335	5	1	2010	2010	NUM
ejpam-3335	5	2	mathematics	mathematic	NOUN
ejpam-3335	5	3	subject	subject	NOUN
ejpam-3335	5	4	classifications	classification	NOUN
ejpam-3335	5	5	:	:	PUNCT
ejpam-3335	5	6	03g25	03g25	NUM
ejpam-3335	5	7	key	key	ADJ
ejpam-3335	5	8	words	word	NOUN
ejpam-3335	5	9	and	and	CCONJ
ejpam-3335	5	10	phrases	phrase	NOUN
ejpam-3335	5	11	:	:	PUNCT
ejpam-3335	5	12	up	up	ADP
ejpam-3335	5	13	-	-	PUNCT
ejpam-3335	5	14	algebra	algebra	NOUN
ejpam-3335	5	15	,	,	PUNCT
ejpam-3335	5	16	anti	anti	ADJ
ejpam-3335	5	17	-	-	ADJ
ejpam-3335	5	18	hesitant	hesitant	ADJ
ejpam-3335	5	19	fuzzy	fuzzy	ADJ
ejpam-3335	5	20	strongly	strongly	ADV
ejpam-3335	5	21	up	up	ADP
ejpam-3335	5	22	-	-	PUNCT
ejpam-3335	5	23	ideal	ideal	ADJ
ejpam-3335	5	24	,	,	PUNCT
ejpam-3335	5	25	anti	anti	ADJ
ejpam-3335	5	26	-	-	ADJ
ejpam-3335	5	27	hesitant	hesitant	ADJ
ejpam-3335	5	28	fuzzy	fuzzy	ADJ
ejpam-3335	5	29	up	up	ADP
ejpam-3335	5	30	-	-	PUNCT
ejpam-3335	5	31	ideal	ideal	ADJ
ejpam-3335	5	32	,	,	PUNCT
ejpam-3335	5	33	anti	anti	ADJ
ejpam-3335	5	34	-	-	ADJ
ejpam-3335	5	35	hesitant	hesitant	ADJ
ejpam-3335	5	36	fuzzy	fuzzy	ADJ
ejpam-3335	5	37	up	up	ADJ
ejpam-3335	5	38	-	-	PUNCT
ejpam-3335	5	39	filter	filter	NOUN
ejpam-3335	5	40	and	and	CCONJ
ejpam-3335	5	41	anti	anti	ADJ
ejpam-3335	5	42	-	-	ADJ
ejpam-3335	5	43	hesitant	hesitant	ADJ
ejpam-3335	5	44	fuzzy	fuzzy	ADJ
ejpam-3335	5	45	up	up	ADP
ejpam-3335	5	46	-	-	PUNCT
ejpam-3335	5	47	subalgebra	subalgebra	NOUN
ejpam-3335	5	48	1	1	NUM
ejpam-3335	5	49	.	.	X
ejpam-3335	5	50	introduction	introduction	NOUN
ejpam-3335	5	51	the	the	DET
ejpam-3335	5	52	branch	branch	NOUN
ejpam-3335	5	53	of	of	ADP
ejpam-3335	5	54	the	the	DET
ejpam-3335	5	55	logical	logical	ADJ
ejpam-3335	5	56	algebra	algebra	NOUN
ejpam-3335	5	57	,	,	PUNCT
ejpam-3335	5	58	up	up	ADP
ejpam-3335	5	59	-	-	PUNCT
ejpam-3335	5	60	algebras	algebras	PROPN
ejpam-3335	5	61	was	be	AUX
ejpam-3335	5	62	introduced	introduce	VERB
ejpam-3335	5	63	by	by	ADP
ejpam-3335	5	64	iampan	iampan	NOUN
ejpam-3335	5	65	[	[	X
ejpam-3335	5	66	2	2	X
ejpam-3335	5	67	]	]	PUNCT
ejpam-3335	5	68	in	in	ADP
ejpam-3335	5	69	2017	2017	NUM
ejpam-3335	5	70	,	,	PUNCT
ejpam-3335	5	71	and	and	CCONJ
ejpam-3335	5	72	it	it	PRON
ejpam-3335	5	73	is	be	AUX
ejpam-3335	5	74	known	know	VERB
ejpam-3335	5	75	that	that	SCONJ
ejpam-3335	5	76	the	the	DET
ejpam-3335	5	77	class	class	NOUN
ejpam-3335	5	78	of	of	ADP
ejpam-3335	5	79	ku	ku	PROPN
ejpam-3335	5	80	-	-	PUNCT
ejpam-3335	5	81	algebras	algebras	PROPN
ejpam-3335	6	1	[	[	X
ejpam-3335	6	2	8	8	NUM
ejpam-3335	6	3	]	]	PUNCT
ejpam-3335	6	4	is	be	AUX
ejpam-3335	6	5	a	a	DET
ejpam-3335	6	6	proper	proper	ADJ
ejpam-3335	6	7	subclass	subclass	NOUN
ejpam-3335	6	8	of	of	ADP
ejpam-3335	6	9	the	the	DET
ejpam-3335	6	10	class	class	NOUN
ejpam-3335	6	11	of	of	ADP
ejpam-3335	6	12	up	up	NOUN
ejpam-3335	6	13	-	-	PUNCT
ejpam-3335	6	14	algebras	algebras	X
ejpam-3335	6	15	.	.	PUNCT
ejpam-3335	7	1	it	it	PRON
ejpam-3335	7	2	have	have	AUX
ejpam-3335	7	3	been	be	AUX
ejpam-3335	7	4	examined	examine	VERB
ejpam-3335	7	5	by	by	ADP
ejpam-3335	7	6	several	several	ADJ
ejpam-3335	7	7	researchers	researcher	NOUN
ejpam-3335	7	8	,	,	PUNCT
ejpam-3335	7	9	for	for	ADP
ejpam-3335	7	10	example	example	NOUN
ejpam-3335	7	11	,	,	PUNCT
ejpam-3335	7	12	somjanta	somjanta	NOUN
ejpam-3335	7	13	et	et	PROPN
ejpam-3335	7	14	al	al	PROPN
ejpam-3335	7	15	.	.	PUNCT
ejpam-3335	8	1	[	[	X
ejpam-3335	8	2	14	14	NUM
ejpam-3335	8	3	]	]	PUNCT
ejpam-3335	8	4	introduced	introduce	VERB
ejpam-3335	8	5	the	the	DET
ejpam-3335	8	6	notion	notion	NOUN
ejpam-3335	8	7	of	of	ADP
ejpam-3335	8	8	fuzzy	fuzzy	ADJ
ejpam-3335	8	9	sets	set	NOUN
ejpam-3335	8	10	in	in	ADP
ejpam-3335	8	11	up	up	ADP
ejpam-3335	8	12	-	-	PUNCT
ejpam-3335	8	13	algebras	algebras	X
ejpam-3335	8	14	,	,	PUNCT
ejpam-3335	8	15	the	the	DET
ejpam-3335	8	16	notion	notion	NOUN
ejpam-3335	8	17	of	of	ADP
ejpam-3335	8	18	intuitionistic	intuitionistic	ADJ
ejpam-3335	8	19	fuzzy	fuzzy	ADJ
ejpam-3335	8	20	sets	set	NOUN
ejpam-3335	8	21	in	in	ADP
ejpam-3335	8	22	up	up	ADV
ejpam-3335	8	23	-	-	PUNCT
ejpam-3335	8	24	algebras	algebras	PROPN
ejpam-3335	8	25	was	be	AUX
ejpam-3335	8	26	introduced	introduce	VERB
ejpam-3335	8	27	by	by	ADP
ejpam-3335	8	28	kesorn	kesorn	PROPN
ejpam-3335	8	29	et	et	PROPN
ejpam-3335	8	30	al	al	PROPN
ejpam-3335	8	31	.	.	PUNCT
ejpam-3335	9	1	[	[	X
ejpam-3335	9	2	5	5	NUM
ejpam-3335	9	3	]	]	PUNCT
ejpam-3335	9	4	,	,	PUNCT
ejpam-3335	9	5	kaijae	kaijae	PROPN
ejpam-3335	9	6	et	et	PROPN
ejpam-3335	9	7	al	al	PROPN
ejpam-3335	9	8	.	.	PUNCT
ejpam-3335	10	1	[	[	X
ejpam-3335	10	2	4	4	X
ejpam-3335	10	3	]	]	PUNCT
ejpam-3335	10	4	introduced	introduce	VERB
ejpam-3335	10	5	the	the	DET
ejpam-3335	10	6	notions	notion	NOUN
ejpam-3335	10	7	of	of	ADP
ejpam-3335	10	8	anti	anti	ADJ
ejpam-3335	10	9	-	-	ADJ
ejpam-3335	10	10	fuzzy	fuzzy	ADJ
ejpam-3335	10	11	up	up	ADJ
ejpam-3335	10	12	-	-	PUNCT
ejpam-3335	10	13	ideals	ideal	NOUN
ejpam-3335	10	14	and	and	CCONJ
ejpam-3335	10	15	anti	anti	ADJ
ejpam-3335	10	16	-	-	ADJ
ejpam-3335	10	17	fuzzy	fuzzy	ADJ
ejpam-3335	10	18	up	up	ADP
ejpam-3335	10	19	-	-	PUNCT
ejpam-3335	10	20	subalgebras	subalgebra	NOUN
ejpam-3335	10	21	of	of	ADP
ejpam-3335	10	22	up	up	ADP
ejpam-3335	10	23	-	-	PUNCT
ejpam-3335	10	24	algebras	algebras	X
ejpam-3335	10	25	,	,	PUNCT
ejpam-3335	10	26	the	the	DET
ejpam-3335	10	27	notion	notion	NOUN
ejpam-3335	10	28	of	of	ADP
ejpam-3335	10	29	q	q	ADJ
ejpam-3335	10	30	-	-	PUNCT
ejpam-3335	10	31	fuzzy	fuzzy	ADJ
ejpam-3335	10	32	sets	set	NOUN
ejpam-3335	10	33	in	in	ADP
ejpam-3335	10	34	up	up	ADV
ejpam-3335	10	35	-	-	PUNCT
ejpam-3335	10	36	algebras	algebras	PROPN
ejpam-3335	10	37	was	be	AUX
ejpam-3335	10	38	introduced	introduce	VERB
ejpam-3335	10	39	by	by	ADP
ejpam-3335	10	40	tanamoon	tanamoon	NOUN
ejpam-3335	10	41	et	et	NOUN
ejpam-3335	10	42	al	al	PROPN
ejpam-3335	10	43	.	.	PUNCT
ejpam-3335	11	1	[	[	X
ejpam-3335	11	2	17	17	NUM
ejpam-3335	11	3	]	]	PUNCT
ejpam-3335	11	4	,	,	PUNCT
ejpam-3335	11	5	sripaeng	sripaeng	NOUN
ejpam-3335	11	6	et	et	PROPN
ejpam-3335	11	7	al	al	PROPN
ejpam-3335	11	8	.	.	PUNCT
ejpam-3335	12	1	[	[	X
ejpam-3335	12	2	16	16	NUM
ejpam-3335	12	3	]	]	PUNCT
ejpam-3335	12	4	introduced	introduce	VERB
ejpam-3335	12	5	the	the	DET
ejpam-3335	12	6	notion	notion	NOUN
ejpam-3335	12	7	anti	anti	ADJ
ejpam-3335	12	8	q	q	ADJ
ejpam-3335	12	9	-	-	ADJ
ejpam-3335	12	10	fuzzy	fuzzy	ADJ
ejpam-3335	12	11	up	up	NOUN
ejpam-3335	12	12	-	-	PUNCT
ejpam-3335	12	13	ideals	ideal	NOUN
ejpam-3335	12	14	and	and	CCONJ
ejpam-3335	12	15	anti	anti	ADJ
ejpam-3335	12	16	q	q	ADJ
ejpam-3335	12	17	-	-	ADJ
ejpam-3335	12	18	fuzzy	fuzzy	ADJ
ejpam-3335	12	19	up	up	ADP
ejpam-3335	12	20	-	-	PUNCT
ejpam-3335	12	21	subalgebras	subalgebra	NOUN
ejpam-3335	12	22	of	of	ADP
ejpam-3335	12	23	up	up	ADP
ejpam-3335	12	24	-	-	PUNCT
ejpam-3335	12	25	algebras	algebras	X
ejpam-3335	12	26	,	,	PUNCT
ejpam-3335	12	27	the	the	DET
ejpam-3335	12	28	notion	notion	NOUN
ejpam-3335	12	29	of	of	ADP
ejpam-3335	12	30	n	n	PRON
ejpam-3335	12	31	-fuzzy	-fuzzy	PROPN
ejpam-3335	12	32	sets	set	NOUN
ejpam-3335	12	33	in	in	ADP
ejpam-3335	12	34	up	up	ADV
ejpam-3335	12	35	-	-	PUNCT
ejpam-3335	12	36	algebras	algebras	PROPN
ejpam-3335	12	37	was	be	AUX
ejpam-3335	12	38	introduced	introduce	VERB
ejpam-3335	12	39	by	by	ADP
ejpam-3335	12	40	songsaeng	songsaeng	PROPN
ejpam-3335	12	41	and	and	CCONJ
ejpam-3335	12	42	iampan	iampan	NOUN
ejpam-3335	12	43	[	[	X
ejpam-3335	12	44	15	15	NUM
ejpam-3335	12	45	]	]	X
ejpam-3335	12	46	,	,	PUNCT
ejpam-3335	12	47	senapati	senapati	PROPN
ejpam-3335	12	48	et	et	PROPN
ejpam-3335	12	49	al	al	PROPN
ejpam-3335	12	50	.	.	PUNCT
ejpam-3335	13	1	[	[	X
ejpam-3335	13	2	12	12	NUM
ejpam-3335	13	3	,	,	PUNCT
ejpam-3335	13	4	13	13	NUM
ejpam-3335	13	5	]	]	PUNCT
ejpam-3335	13	6	applied	apply	VERB
ejpam-3335	13	7	cubic	cubic	ADJ
ejpam-3335	13	8	set	set	NOUN
ejpam-3335	13	9	and	and	CCONJ
ejpam-3335	13	10	interval	interval	NOUN
ejpam-3335	13	11	-	-	PUNCT
ejpam-3335	13	12	valued	value	VERB
ejpam-3335	13	13	intuitionistic	intuitionistic	ADJ
ejpam-3335	13	14	fuzzy	fuzzy	ADJ
ejpam-3335	13	15	structure	structure	NOUN
ejpam-3335	13	16	in	in	ADP
ejpam-3335	13	17	up	up	ADP
ejpam-3335	13	18	-	-	PUNCT
ejpam-3335	13	19	algebras	algebras	ADV
ejpam-3335	13	20	,	,	PUNCT
ejpam-3335	13	21	romano	romano	NOUN
ejpam-3335	14	1	[	[	PUNCT
ejpam-3335	14	2	9	9	NUM
ejpam-3335	14	3	]	]	PUNCT
ejpam-3335	14	4	introduced	introduce	VERB
ejpam-3335	14	5	the	the	DET
ejpam-3335	14	6	notion	notion	NOUN
ejpam-3335	14	7	of	of	ADP
ejpam-3335	14	8	proper	proper	ADJ
ejpam-3335	14	9	up	up	NOUN
ejpam-3335	14	10	-	-	PUNCT
ejpam-3335	14	11	filters	filter	NOUN
ejpam-3335	14	12	in	in	ADP
ejpam-3335	14	13	up	up	ADP
ejpam-3335	14	14	-	-	PUNCT
ejpam-3335	14	15	algebras	algebras	X
ejpam-3335	14	16	,	,	PUNCT
ejpam-3335	14	17	etc	etc	X
ejpam-3335	14	18	.	.	X
ejpam-3335	15	1	a	a	DET
ejpam-3335	15	2	hesitant	hesitant	ADJ
ejpam-3335	15	3	fuzzy	fuzzy	ADJ
ejpam-3335	15	4	set	set	NOUN
ejpam-3335	15	5	on	on	ADP
ejpam-3335	15	6	a	a	DET
ejpam-3335	15	7	set	set	NOUN
ejpam-3335	15	8	is	be	AUX
ejpam-3335	15	9	a	a	DET
ejpam-3335	15	10	function	function	NOUN
ejpam-3335	15	11	from	from	ADP
ejpam-3335	15	12	a	a	DET
ejpam-3335	15	13	reference	reference	NOUN
ejpam-3335	15	14	set	set	VERB
ejpam-3335	15	15	to	to	ADP
ejpam-3335	15	16	a	a	DET
ejpam-3335	15	17	power	power	NOUN
ejpam-3335	15	18	set	set	NOUN
ejpam-3335	15	19	of	of	ADP
ejpam-3335	15	20	the	the	DET
ejpam-3335	15	21	unit	unit	NOUN
ejpam-3335	15	22	interval	interval	NOUN
ejpam-3335	15	23	.	.	PUNCT
ejpam-3335	16	1	the	the	DET
ejpam-3335	16	2	notion	notion	NOUN
ejpam-3335	16	3	of	of	ADP
ejpam-3335	16	4	a	a	DET
ejpam-3335	16	5	hesitant	hesitant	ADJ
ejpam-3335	16	6	fuzzy	fuzzy	ADJ
ejpam-3335	16	7	set	set	NOUN
ejpam-3335	16	8	on	on	ADP
ejpam-3335	16	9	a	a	DET
ejpam-3335	16	10	set	set	NOUN
ejpam-3335	16	11	was	be	AUX
ejpam-3335	16	12	first	first	ADV
ejpam-3335	16	13	considered	consider	VERB
ejpam-3335	16	14	by	by	ADP
ejpam-3335	16	15	torra	torra	NOUN
ejpam-3335	16	16	[	[	X
ejpam-3335	16	17	18	18	NUM
ejpam-3335	16	18	]	]	PUNCT
ejpam-3335	16	19	in	in	ADP
ejpam-3335	16	20	2010	2010	NUM
ejpam-3335	16	21	.	.	PUNCT
ejpam-3335	17	1	the	the	DET
ejpam-3335	17	2	hesitant	hesitant	ADJ
ejpam-3335	17	3	fuzzy	fuzzy	ADJ
ejpam-3335	17	4	set	set	NOUN
ejpam-3335	17	5	,	,	PUNCT
ejpam-3335	17	6	which	which	PRON
ejpam-3335	17	7	can	can	AUX
ejpam-3335	17	8	be	be	AUX
ejpam-3335	17	9	perfectly	perfectly	ADV
ejpam-3335	17	10	described	describe	VERB
ejpam-3335	17	11	in	in	ADP
ejpam-3335	17	12	terms	term	NOUN
ejpam-3335	17	13	of	of	ADP
ejpam-3335	17	14	the	the	DET
ejpam-3335	17	15	opinions	opinion	NOUN
ejpam-3335	17	16	∗this	∗this	PRON
ejpam-3335	17	17	work	work	NOUN
ejpam-3335	17	18	was	be	AUX
ejpam-3335	17	19	financially	financially	ADV
ejpam-3335	17	20	supported	support	VERB
ejpam-3335	17	21	by	by	ADP
ejpam-3335	17	22	the	the	DET
ejpam-3335	17	23	university	university	NOUN
ejpam-3335	17	24	of	of	ADP
ejpam-3335	17	25	phayao	phayao	NOUN
ejpam-3335	17	26	.	.	PUNCT
ejpam-3335	18	1	†corresponding	†corresponde	VERB
ejpam-3335	18	2	author	author	NOUN
ejpam-3335	18	3	.	.	PUNCT
ejpam-3335	19	1	doi	doi	NOUN
ejpam-3335	19	2	:	:	PUNCT
ejpam-3335	19	3	https://doi.org/10.29020/nybg.ejpam.v11i4.3335	https://doi.org/10.29020/nybg.ejpam.v11i4.3335	NOUN
ejpam-3335	19	4	email	email	NOUN
ejpam-3335	19	5	addresses	address	NOUN
ejpam-3335	19	6	:	:	PUNCT
ejpam-3335	19	7	phakawat.mo@gmail.com	phakawat.mo@gmail.com	PROPN
ejpam-3335	19	8	(	(	PUNCT
ejpam-3335	19	9	p.	p.	NOUN
ejpam-3335	19	10	mosrijai	mosrijai	PROPN
ejpam-3335	19	11	)	)	PUNCT
ejpam-3335	19	12	,	,	PUNCT
ejpam-3335	19	13	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-3335	19	14	(	(	PUNCT
ejpam-3335	19	15	a.	a.	NOUN
ejpam-3335	19	16	iampan	iampan	PROPN
ejpam-3335	19	17	)	)	PUNCT
ejpam-3335	19	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3335	20	1	976	976	NUM
ejpam-3335	20	2	c	c	NOUN
ejpam-3335	20	3	©	©	PROPN
ejpam-3335	20	4	2018	2018	NUM
ejpam-3335	20	5	ejpam	ejpam	VERB
ejpam-3335	20	6	all	all	DET
ejpam-3335	20	7	rights	right	NOUN
ejpam-3335	20	8	reserved	reserve	VERB
ejpam-3335	20	9	.	.	PUNCT
ejpam-3335	21	1	p.	p.	NOUN
ejpam-3335	21	2	mosrijai	mosrijai	PROPN
ejpam-3335	21	3	,	,	PUNCT
ejpam-3335	21	4	a.	a.	NOUN
ejpam-3335	21	5	iampan	iampan	PROPN
ejpam-3335	21	6	/	/	SYM
ejpam-3335	21	7	eur	eur	PROPN
ejpam-3335	21	8	.	.	PUNCT
ejpam-3335	22	1	j.	j.	PROPN
ejpam-3335	22	2	pure	pure	PROPN
ejpam-3335	22	3	appl	appl	PROPN
ejpam-3335	22	4	.	.	PROPN
ejpam-3335	22	5	math	math	PROPN
ejpam-3335	22	6	,	,	PUNCT
ejpam-3335	22	7	11	11	NUM
ejpam-3335	22	8	(	(	PUNCT
ejpam-3335	22	9	4	4	NUM
ejpam-3335	22	10	)	)	PUNCT
ejpam-3335	22	11	(	(	PUNCT
ejpam-3335	22	12	2018	2018	NUM
ejpam-3335	22	13	)	)	PUNCT
ejpam-3335	22	14	,	,	PUNCT
ejpam-3335	22	15	976	976	NUM
ejpam-3335	22	16	-	-	SYM
ejpam-3335	22	17	1002	1002	NUM
ejpam-3335	22	18	977	977	NUM
ejpam-3335	22	19	of	of	ADP
ejpam-3335	22	20	decision	decision	NOUN
ejpam-3335	22	21	makers	maker	NOUN
ejpam-3335	22	22	is	be	AUX
ejpam-3335	22	23	a	a	DET
ejpam-3335	22	24	very	very	ADV
ejpam-3335	22	25	useful	useful	ADJ
ejpam-3335	22	26	tool	tool	NOUN
ejpam-3335	22	27	to	to	PART
ejpam-3335	22	28	deal	deal	VERB
ejpam-3335	22	29	with	with	ADP
ejpam-3335	22	30	uncertainty	uncertainty	NOUN
ejpam-3335	22	31	.	.	PUNCT
ejpam-3335	23	1	the	the	DET
ejpam-3335	23	2	hesitant	hesitant	ADJ
ejpam-3335	23	3	fuzzy	fuzzy	ADJ
ejpam-3335	23	4	set	set	NOUN
ejpam-3335	23	5	theories	theory	NOUN
ejpam-3335	23	6	developed	develop	VERB
ejpam-3335	23	7	by	by	ADP
ejpam-3335	23	8	torra	torra	NOUN
ejpam-3335	23	9	and	and	CCONJ
ejpam-3335	23	10	others	other	NOUN
ejpam-3335	23	11	have	have	AUX
ejpam-3335	23	12	found	find	VERB
ejpam-3335	23	13	many	many	ADJ
ejpam-3335	23	14	applications	application	NOUN
ejpam-3335	23	15	in	in	ADP
ejpam-3335	23	16	the	the	DET
ejpam-3335	23	17	domain	domain	NOUN
ejpam-3335	23	18	of	of	ADP
ejpam-3335	23	19	mathematics	mathematic	NOUN
ejpam-3335	23	20	and	and	CCONJ
ejpam-3335	23	21	elsewhere	elsewhere	ADV
ejpam-3335	23	22	.	.	PUNCT
ejpam-3335	24	1	in	in	ADP
ejpam-3335	24	2	up	up	ADP
ejpam-3335	24	3	-	-	PUNCT
ejpam-3335	24	4	algebras	algebras	X
ejpam-3335	24	5	,	,	PUNCT
ejpam-3335	24	6	mosrijai	mosrijai	PROPN
ejpam-3335	24	7	et	et	PROPN
ejpam-3335	24	8	al	al	PROPN
ejpam-3335	24	9	.	.	PUNCT
ejpam-3335	25	1	[	[	X
ejpam-3335	25	2	6	6	NUM
ejpam-3335	25	3	]	]	PUNCT
ejpam-3335	25	4	extended	extend	VERB
ejpam-3335	25	5	the	the	DET
ejpam-3335	25	6	notion	notion	NOUN
ejpam-3335	25	7	of	of	ADP
ejpam-3335	25	8	fuzzy	fuzzy	ADJ
ejpam-3335	25	9	sets	set	NOUN
ejpam-3335	25	10	in	in	ADP
ejpam-3335	25	11	up	up	ADV
ejpam-3335	25	12	-	-	PUNCT
ejpam-3335	25	13	algebras	algebras	ADJ
ejpam-3335	25	14	to	to	ADP
ejpam-3335	25	15	hesitant	hesitant	ADJ
ejpam-3335	25	16	fuzzy	fuzzy	ADJ
ejpam-3335	25	17	sets	set	NOUN
ejpam-3335	25	18	on	on	ADP
ejpam-3335	25	19	up	up	ADP
ejpam-3335	25	20	-	-	PUNCT
ejpam-3335	25	21	algebras	algebras	X
ejpam-3335	25	22	,	,	PUNCT
ejpam-3335	25	23	and	and	CCONJ
ejpam-3335	25	24	satirad	satirad	PROPN
ejpam-3335	25	25	et	et	PROPN
ejpam-3335	25	26	al	al	PROPN
ejpam-3335	25	27	.	.	PUNCT
ejpam-3335	26	1	[	[	X
ejpam-3335	26	2	11	11	NUM
ejpam-3335	26	3	]	]	PUNCT
ejpam-3335	26	4	considered	consider	VERB
ejpam-3335	26	5	level	level	NOUN
ejpam-3335	26	6	subsets	subset	NOUN
ejpam-3335	26	7	of	of	ADP
ejpam-3335	26	8	a	a	DET
ejpam-3335	26	9	hesitant	hesitant	ADJ
ejpam-3335	26	10	fuzzy	fuzzy	ADJ
ejpam-3335	26	11	set	set	NOUN
ejpam-3335	26	12	on	on	ADP
ejpam-3335	26	13	up	up	ADV
ejpam-3335	26	14	-	-	PUNCT
ejpam-3335	26	15	algebras	algebras	NOUN
ejpam-3335	26	16	in	in	ADP
ejpam-3335	26	17	2017	2017	NUM
ejpam-3335	26	18	.	.	PUNCT
ejpam-3335	27	1	the	the	DET
ejpam-3335	27	2	notion	notion	NOUN
ejpam-3335	27	3	of	of	ADP
ejpam-3335	27	4	partial	partial	ADJ
ejpam-3335	27	5	constant	constant	ADJ
ejpam-3335	27	6	hesitant	hesitant	ADJ
ejpam-3335	27	7	fuzzy	fuzzy	ADJ
ejpam-3335	27	8	sets	set	NOUN
ejpam-3335	27	9	on	on	ADP
ejpam-3335	27	10	up	up	ADV
ejpam-3335	27	11	-	-	PUNCT
ejpam-3335	27	12	algebras	algebras	PROPN
ejpam-3335	27	13	was	be	AUX
ejpam-3335	27	14	introduced	introduce	VERB
ejpam-3335	27	15	by	by	ADP
ejpam-3335	27	16	mosrijai	mosrijai	PROPN
ejpam-3335	27	17	et	et	PROPN
ejpam-3335	27	18	al	al	PROPN
ejpam-3335	27	19	.	.	PUNCT
ejpam-3335	28	1	[	[	X
ejpam-3335	28	2	7	7	X
ejpam-3335	28	3	]	]	PUNCT
ejpam-3335	28	4	afterwards	afterwards	ADV
ejpam-3335	28	5	.	.	PUNCT
ejpam-3335	29	1	in	in	ADP
ejpam-3335	29	2	this	this	DET
ejpam-3335	29	3	paper	paper	NOUN
ejpam-3335	29	4	,	,	PUNCT
ejpam-3335	29	5	the	the	DET
ejpam-3335	29	6	notion	notion	NOUN
ejpam-3335	29	7	of	of	ADP
ejpam-3335	29	8	anti	anti	ADJ
ejpam-3335	29	9	-	-	ADJ
ejpam-3335	29	10	hesitant	hesitant	ADJ
ejpam-3335	29	11	fuzzy	fuzzy	ADJ
ejpam-3335	29	12	up	up	ADP
ejpam-3335	29	13	-	-	PUNCT
ejpam-3335	29	14	subalgebras	subalgebras	PROPN
ejpam-3335	29	15	(	(	PUNCT
ejpam-3335	29	16	resp	resp	NOUN
ejpam-3335	29	17	.	.	PUNCT
ejpam-3335	29	18	,	,	PUNCT
ejpam-3335	29	19	anti	anti	ADJ
ejpam-3335	29	20	-	-	ADJ
ejpam-3335	29	21	hesitant	hesitant	ADJ
ejpam-3335	29	22	fuzzy	fuzzy	ADJ
ejpam-3335	29	23	up	up	NOUN
ejpam-3335	29	24	-	-	PUNCT
ejpam-3335	29	25	filters	filter	NOUN
ejpam-3335	29	26	,	,	PUNCT
ejpam-3335	29	27	anti	anti	ADJ
ejpam-3335	29	28	-	-	ADJ
ejpam-3335	29	29	hesitant	hesitant	ADJ
ejpam-3335	29	30	fuzzy	fuzzy	ADJ
ejpam-3335	29	31	up	up	NOUN
ejpam-3335	29	32	-	-	PUNCT
ejpam-3335	29	33	ideals	ideal	NOUN
ejpam-3335	29	34	and	and	CCONJ
ejpam-3335	29	35	anti	anti	ADJ
ejpam-3335	29	36	-	-	ADJ
ejpam-3335	29	37	hesitant	hesitant	ADJ
ejpam-3335	29	38	fuzzy	fuzzy	ADJ
ejpam-3335	29	39	strongly	strongly	ADV
ejpam-3335	29	40	up	up	ADP
ejpam-3335	29	41	-	-	PUNCT
ejpam-3335	29	42	ideals	ideal	NOUN
ejpam-3335	29	43	)	)	PUNCT
ejpam-3335	29	44	of	of	ADP
ejpam-3335	29	45	up	up	ADV
ejpam-3335	29	46	-	-	PUNCT
ejpam-3335	29	47	algebras	algebra	NOUN
ejpam-3335	29	48	are	be	AUX
ejpam-3335	29	49	introduced	introduce	VERB
ejpam-3335	29	50	and	and	CCONJ
ejpam-3335	29	51	proved	prove	VERB
ejpam-3335	29	52	some	some	DET
ejpam-3335	29	53	results	result	NOUN
ejpam-3335	29	54	.	.	PUNCT
ejpam-3335	30	1	further	far	ADV
ejpam-3335	30	2	,	,	PUNCT
ejpam-3335	30	3	we	we	PRON
ejpam-3335	30	4	discuss	discuss	VERB
ejpam-3335	30	5	the	the	DET
ejpam-3335	30	6	relation	relation	NOUN
ejpam-3335	30	7	between	between	ADP
ejpam-3335	30	8	anti	anti	ADJ
ejpam-3335	30	9	-	-	ADJ
ejpam-3335	30	10	hesitant	hesitant	ADJ
ejpam-3335	30	11	fuzzy	fuzzy	ADJ
ejpam-3335	30	12	up	up	ADP
ejpam-3335	30	13	-	-	PUNCT
ejpam-3335	30	14	subalgebras	subalgebras	PROPN
ejpam-3335	30	15	(	(	PUNCT
ejpam-3335	30	16	resp	resp	NOUN
ejpam-3335	30	17	.	.	PUNCT
ejpam-3335	30	18	,	,	PUNCT
ejpam-3335	30	19	anti	anti	ADJ
ejpam-3335	30	20	-	-	ADJ
ejpam-3335	30	21	hesitant	hesitant	ADJ
ejpam-3335	30	22	fuzzy	fuzzy	ADJ
ejpam-3335	30	23	up	up	NOUN
ejpam-3335	30	24	-	-	PUNCT
ejpam-3335	30	25	filters	filter	NOUN
ejpam-3335	30	26	,	,	PUNCT
ejpam-3335	30	27	antihesitant	antihesitant	NOUN
ejpam-3335	30	28	fuzzy	fuzzy	ADJ
ejpam-3335	30	29	up	up	NOUN
ejpam-3335	30	30	-	-	PUNCT
ejpam-3335	30	31	ideals	ideal	NOUN
ejpam-3335	30	32	and	and	CCONJ
ejpam-3335	30	33	anti	anti	ADJ
ejpam-3335	30	34	-	-	ADJ
ejpam-3335	30	35	hesitant	hesitant	ADJ
ejpam-3335	30	36	fuzzy	fuzzy	ADJ
ejpam-3335	30	37	strongly	strongly	ADV
ejpam-3335	30	38	up	up	ADP
ejpam-3335	30	39	-	-	PUNCT
ejpam-3335	30	40	ideals	ideal	NOUN
ejpam-3335	30	41	)	)	PUNCT
ejpam-3335	30	42	and	and	CCONJ
ejpam-3335	30	43	level	level	NOUN
ejpam-3335	30	44	subsets	subset	NOUN
ejpam-3335	30	45	of	of	ADP
ejpam-3335	30	46	a	a	DET
ejpam-3335	30	47	hesitant	hesitant	ADJ
ejpam-3335	30	48	fuzzy	fuzzy	ADJ
ejpam-3335	30	49	set	set	NOUN
ejpam-3335	30	50	.	.	PUNCT
ejpam-3335	31	1	2	2	X
ejpam-3335	31	2	.	.	X
ejpam-3335	31	3	basic	basic	ADJ
ejpam-3335	31	4	results	result	NOUN
ejpam-3335	31	5	on	on	ADP
ejpam-3335	31	6	up	up	ADV
ejpam-3335	31	7	-	-	PUNCT
ejpam-3335	31	8	algebras	algebra	NOUN
ejpam-3335	31	9	before	before	SCONJ
ejpam-3335	31	10	we	we	PRON
ejpam-3335	31	11	begin	begin	VERB
ejpam-3335	31	12	our	our	PRON
ejpam-3335	31	13	study	study	NOUN
ejpam-3335	31	14	,	,	PUNCT
ejpam-3335	31	15	we	we	PRON
ejpam-3335	31	16	will	will	AUX
ejpam-3335	31	17	introduce	introduce	VERB
ejpam-3335	31	18	the	the	DET
ejpam-3335	31	19	definition	definition	NOUN
ejpam-3335	31	20	of	of	ADP
ejpam-3335	31	21	a	a	DET
ejpam-3335	31	22	up	up	NOUN
ejpam-3335	31	23	-	-	PUNCT
ejpam-3335	31	24	algebra	algebra	NOUN
ejpam-3335	31	25	.	.	PUNCT
ejpam-3335	32	1	definition	definition	NOUN
ejpam-3335	32	2	1	1	NUM
ejpam-3335	32	3	.	.	PUNCT
ejpam-3335	33	1	[	[	X
ejpam-3335	33	2	2	2	X
ejpam-3335	33	3	]	]	PUNCT
ejpam-3335	33	4	an	an	DET
ejpam-3335	33	5	algebra	algebra	NOUN
ejpam-3335	33	6	a	a	X
ejpam-3335	33	7	=	=	X
ejpam-3335	33	8	(	(	PUNCT
ejpam-3335	33	9	a	a	PRON
ejpam-3335	33	10	,	,	PUNCT
ejpam-3335	33	11	·	·	PUNCT
ejpam-3335	33	12	,	,	PUNCT
ejpam-3335	33	13	0	0	NUM
ejpam-3335	33	14	)	)	PUNCT
ejpam-3335	33	15	of	of	ADP
ejpam-3335	33	16	type	type	NOUN
ejpam-3335	33	17	(	(	PUNCT
ejpam-3335	33	18	2	2	NUM
ejpam-3335	33	19	,	,	PUNCT
ejpam-3335	33	20	0	0	NUM
ejpam-3335	33	21	)	)	PUNCT
ejpam-3335	33	22	is	be	AUX
ejpam-3335	33	23	called	call	VERB
ejpam-3335	33	24	a	a	DET
ejpam-3335	33	25	up	up	NOUN
ejpam-3335	33	26	-	-	PUNCT
ejpam-3335	33	27	algebra	algebra	NOUN
ejpam-3335	33	28	where	where	SCONJ
ejpam-3335	33	29	a	a	PRON
ejpam-3335	33	30	is	be	AUX
ejpam-3335	33	31	a	a	DET
ejpam-3335	33	32	nonempty	nonempty	ADJ
ejpam-3335	33	33	set	set	VERB
ejpam-3335	33	34	,	,	PUNCT
ejpam-3335	33	35	·	·	PUNCT
ejpam-3335	33	36	is	be	AUX
ejpam-3335	33	37	a	a	DET
ejpam-3335	33	38	binary	binary	ADJ
ejpam-3335	33	39	operation	operation	NOUN
ejpam-3335	33	40	on	on	ADP
ejpam-3335	33	41	a	a	PRON
ejpam-3335	33	42	,	,	PUNCT
ejpam-3335	33	43	and	and	CCONJ
ejpam-3335	33	44	0	0	NUM
ejpam-3335	33	45	is	be	AUX
ejpam-3335	33	46	a	a	DET
ejpam-3335	33	47	fixed	fix	VERB
ejpam-3335	33	48	element	element	NOUN
ejpam-3335	33	49	of	of	ADP
ejpam-3335	33	50	a	a	DET
ejpam-3335	33	51	(	(	PUNCT
ejpam-3335	33	52	i.e.	i.e.	X
ejpam-3335	33	53	,	,	PUNCT
ejpam-3335	33	54	a	a	DET
ejpam-3335	33	55	nullary	nullary	ADJ
ejpam-3335	33	56	operation	operation	NOUN
ejpam-3335	33	57	)	)	PUNCT
ejpam-3335	33	58	if	if	SCONJ
ejpam-3335	33	59	it	it	PRON
ejpam-3335	33	60	satisfies	satisfy	VERB
ejpam-3335	33	61	the	the	DET
ejpam-3335	33	62	following	follow	VERB
ejpam-3335	33	63	axioms	axiom	NOUN
ejpam-3335	33	64	:	:	PUNCT
ejpam-3335	33	65	for	for	ADP
ejpam-3335	33	66	any	any	DET
ejpam-3335	33	67	x	x	NOUN
ejpam-3335	33	68	,	,	PUNCT
ejpam-3335	33	69	y	y	PROPN
ejpam-3335	33	70	,	,	PUNCT
ejpam-3335	33	71	z	z	PROPN
ejpam-3335	33	72	∈	∈	PROPN
ejpam-3335	33	73	a	a	DET
ejpam-3335	33	74	,	,	PUNCT
ejpam-3335	33	75	(	(	PUNCT
ejpam-3335	33	76	up-1	up-1	NOUN
ejpam-3335	33	77	)	)	PUNCT
ejpam-3335	33	78	(	(	PUNCT
ejpam-3335	33	79	y	y	PROPN
ejpam-3335	33	80	·	·	PUNCT
ejpam-3335	33	81	z	z	X
ejpam-3335	33	82	)	)	PUNCT
ejpam-3335	33	83	·	·	PUNCT
ejpam-3335	33	84	(	(	PUNCT
ejpam-3335	33	85	(	(	PUNCT
ejpam-3335	33	86	x	x	SYM
ejpam-3335	33	87	·	·	PUNCT
ejpam-3335	33	88	y	y	X
ejpam-3335	33	89	)	)	PUNCT
ejpam-3335	33	90	·	·	PUNCT
ejpam-3335	34	1	(	(	PUNCT
ejpam-3335	34	2	x	x	X
ejpam-3335	34	3	·	·	PUNCT
ejpam-3335	34	4	z	z	NOUN
ejpam-3335	34	5	)	)	PUNCT
ejpam-3335	34	6	)	)	PUNCT
ejpam-3335	35	1	=	=	SYM
ejpam-3335	35	2	0	0	NUM
ejpam-3335	35	3	,	,	PUNCT
ejpam-3335	35	4	(	(	PUNCT
ejpam-3335	35	5	up-2	up-2	NUM
ejpam-3335	35	6	)	)	PUNCT
ejpam-3335	35	7	0	0	NUM
ejpam-3335	35	8	·	·	PUNCT
ejpam-3335	35	9	x	x	PUNCT
ejpam-3335	35	10	=	=	SYM
ejpam-3335	35	11	x	x	X
ejpam-3335	35	12	,	,	PUNCT
ejpam-3335	35	13	(	(	PUNCT
ejpam-3335	35	14	up-3	up-3	NOUN
ejpam-3335	35	15	)	)	PUNCT
ejpam-3335	35	16	x	x	X
ejpam-3335	35	17	·	·	PUNCT
ejpam-3335	35	18	0	0	PUNCT
ejpam-3335	36	1	=	=	SYM
ejpam-3335	36	2	0	0	NUM
ejpam-3335	36	3	,	,	PUNCT
ejpam-3335	36	4	and	and	CCONJ
ejpam-3335	36	5	(	(	PUNCT
ejpam-3335	36	6	up-4	up-4	ADV
ejpam-3335	36	7	)	)	PUNCT
ejpam-3335	36	8	x	x	X
ejpam-3335	36	9	·	·	PUNCT
ejpam-3335	36	10	y	y	X
ejpam-3335	36	11	=	=	SYM
ejpam-3335	36	12	0	0	PROPN
ejpam-3335	36	13	and	and	CCONJ
ejpam-3335	36	14	y	y	PROPN
ejpam-3335	36	15	·	·	PUNCT
ejpam-3335	36	16	x	x	PUNCT
ejpam-3335	37	1	=	=	SYM
ejpam-3335	37	2	0	0	NUM
ejpam-3335	37	3	imply	imply	VERB
ejpam-3335	37	4	x	x	X
ejpam-3335	37	5	=	=	PUNCT
ejpam-3335	37	6	y.	y.	NOUN
ejpam-3335	37	7	from	from	ADP
ejpam-3335	37	8	[	[	X
ejpam-3335	37	9	2	2	NUM
ejpam-3335	37	10	]	]	PUNCT
ejpam-3335	37	11	,	,	PUNCT
ejpam-3335	37	12	we	we	PRON
ejpam-3335	37	13	know	know	VERB
ejpam-3335	37	14	that	that	SCONJ
ejpam-3335	37	15	the	the	DET
ejpam-3335	37	16	notion	notion	NOUN
ejpam-3335	37	17	of	of	ADP
ejpam-3335	37	18	up	up	ADV
ejpam-3335	37	19	-	-	PUNCT
ejpam-3335	37	20	algebras	algebras	PROPN
ejpam-3335	37	21	is	be	AUX
ejpam-3335	37	22	a	a	DET
ejpam-3335	37	23	generalization	generalization	NOUN
ejpam-3335	37	24	of	of	ADP
ejpam-3335	37	25	ku	ku	PROPN
ejpam-3335	37	26	-	-	PUNCT
ejpam-3335	37	27	algebras	algebras	PROPN
ejpam-3335	37	28	.	.	PUNCT
ejpam-3335	37	29	example	example	NOUN
ejpam-3335	38	1	1	1	NUM
ejpam-3335	38	2	.	.	PUNCT
ejpam-3335	39	1	[	[	X
ejpam-3335	39	2	10	10	NUM
ejpam-3335	39	3	]	]	PUNCT
ejpam-3335	39	4	let	let	VERB
ejpam-3335	39	5	x	x	PRON
ejpam-3335	39	6	be	be	AUX
ejpam-3335	39	7	a	a	DET
ejpam-3335	39	8	universal	universal	ADJ
ejpam-3335	39	9	set	set	NOUN
ejpam-3335	39	10	and	and	CCONJ
ejpam-3335	39	11	let	let	VERB
ejpam-3335	39	12	ω	ω	NUM
ejpam-3335	39	13	∈	∈	PROPN
ejpam-3335	39	14	p(x	p(x	PROPN
ejpam-3335	39	15	)	)	PUNCT
ejpam-3335	39	16	.	.	PUNCT
ejpam-3335	40	1	let	let	VERB
ejpam-3335	40	2	pω(x	pω(x	X
ejpam-3335	40	3	)	)	PUNCT
ejpam-3335	40	4	=	=	SYM
ejpam-3335	40	5	{	{	PUNCT
ejpam-3335	40	6	a	a	DET
ejpam-3335	40	7	∈	∈	PROPN
ejpam-3335	40	8	p(x	p(x	NOUN
ejpam-3335	40	9	)	)	PUNCT
ejpam-3335	40	10	|	|	ADV
ejpam-3335	40	11	ω	ω	NUM
ejpam-3335	40	12	⊆	⊆	NUM
ejpam-3335	40	13	a	a	PRON
ejpam-3335	40	14	}	}	PUNCT
ejpam-3335	40	15	.	.	PUNCT
ejpam-3335	41	1	define	define	VERB
ejpam-3335	41	2	a	a	DET
ejpam-3335	41	3	binary	binary	ADJ
ejpam-3335	41	4	operation	operation	NOUN
ejpam-3335	41	5	·	·	PUNCT
ejpam-3335	41	6	on	on	ADP
ejpam-3335	41	7	pω(x	pω(x	NOUN
ejpam-3335	41	8	)	)	PUNCT
ejpam-3335	41	9	by	by	ADP
ejpam-3335	41	10	putting	put	VERB
ejpam-3335	41	11	a	a	DET
ejpam-3335	41	12	·	·	PUNCT
ejpam-3335	41	13	b	b	X
ejpam-3335	41	14	=	=	SYM
ejpam-3335	41	15	b	b	PROPN
ejpam-3335	41	16	∩	∩	NOUN
ejpam-3335	41	17	(	(	PUNCT
ejpam-3335	41	18	a′	a′	PROPN
ejpam-3335	41	19	∪	∪	X
ejpam-3335	41	20	ω	ω	NOUN
ejpam-3335	41	21	)	)	PUNCT
ejpam-3335	41	22	for	for	ADP
ejpam-3335	41	23	all	all	DET
ejpam-3335	41	24	a	a	DET
ejpam-3335	41	25	,	,	PUNCT
ejpam-3335	41	26	b	b	NOUN
ejpam-3335	41	27	∈	∈	NOUN
ejpam-3335	41	28	pω(x	pω(x	NOUN
ejpam-3335	41	29	)	)	PUNCT
ejpam-3335	41	30	.	.	PUNCT
ejpam-3335	42	1	then	then	ADV
ejpam-3335	42	2	(	(	PUNCT
ejpam-3335	42	3	pω(x	pω(x	NOUN
ejpam-3335	42	4	)	)	PUNCT
ejpam-3335	42	5	,	,	PUNCT
ejpam-3335	42	6	·	·	PUNCT
ejpam-3335	42	7	,	,	PUNCT
ejpam-3335	42	8	ω	ω	NUM
ejpam-3335	42	9	)	)	PUNCT
ejpam-3335	42	10	is	be	AUX
ejpam-3335	42	11	a	a	DET
ejpam-3335	42	12	up	up	NOUN
ejpam-3335	42	13	-	-	PUNCT
ejpam-3335	42	14	algebra	algebra	NOUN
ejpam-3335	42	15	and	and	CCONJ
ejpam-3335	42	16	we	we	PRON
ejpam-3335	42	17	shall	shall	AUX
ejpam-3335	42	18	call	call	VERB
ejpam-3335	42	19	it	it	PRON
ejpam-3335	42	20	the	the	DET
ejpam-3335	42	21	generalized	generalized	ADJ
ejpam-3335	42	22	power	power	NOUN
ejpam-3335	42	23	up	up	ADP
ejpam-3335	42	24	-	-	PUNCT
ejpam-3335	42	25	algebra	algebra	NOUN
ejpam-3335	42	26	of	of	ADP
ejpam-3335	42	27	type	type	NOUN
ejpam-3335	42	28	1	1	NUM
ejpam-3335	42	29	with	with	ADP
ejpam-3335	42	30	respect	respect	NOUN
ejpam-3335	42	31	to	to	ADP
ejpam-3335	42	32	ω	ω	NUM
ejpam-3335	42	33	.	.	PUNCT
ejpam-3335	42	34	example	example	NOUN
ejpam-3335	43	1	2	2	NUM
ejpam-3335	43	2	.	.	PUNCT
ejpam-3335	44	1	[	[	X
ejpam-3335	44	2	10	10	NUM
ejpam-3335	44	3	]	]	PUNCT
ejpam-3335	44	4	let	let	VERB
ejpam-3335	44	5	x	x	PRON
ejpam-3335	44	6	be	be	AUX
ejpam-3335	44	7	a	a	DET
ejpam-3335	44	8	universal	universal	ADJ
ejpam-3335	44	9	set	set	NOUN
ejpam-3335	44	10	and	and	CCONJ
ejpam-3335	44	11	let	let	VERB
ejpam-3335	44	12	ω	ω	NUM
ejpam-3335	44	13	∈	∈	PROPN
ejpam-3335	44	14	p(x	p(x	PROPN
ejpam-3335	44	15	)	)	PUNCT
ejpam-3335	44	16	.	.	PUNCT
ejpam-3335	45	1	let	let	VERB
ejpam-3335	45	2	pω(x	pω(x	X
ejpam-3335	45	3	)	)	PUNCT
ejpam-3335	45	4	=	=	SYM
ejpam-3335	45	5	{	{	PUNCT
ejpam-3335	45	6	a	a	DET
ejpam-3335	45	7	∈	∈	PROPN
ejpam-3335	45	8	p(x	p(x	NOUN
ejpam-3335	45	9	)	)	PUNCT
ejpam-3335	45	10	|	|	ADV
ejpam-3335	45	11	a	a	DET
ejpam-3335	45	12	⊆	⊆	NUM
ejpam-3335	45	13	ω	ω	NUM
ejpam-3335	45	14	}	}	PUNCT
ejpam-3335	45	15	.	.	PUNCT
ejpam-3335	46	1	define	define	VERB
ejpam-3335	46	2	a	a	DET
ejpam-3335	46	3	binary	binary	ADJ
ejpam-3335	46	4	operation	operation	NOUN
ejpam-3335	46	5	∗	∗	NOUN
ejpam-3335	46	6	on	on	ADP
ejpam-3335	46	7	pω(x	pω(x	NOUN
ejpam-3335	46	8	)	)	PUNCT
ejpam-3335	46	9	by	by	ADP
ejpam-3335	46	10	putting	put	VERB
ejpam-3335	46	11	a	a	DET
ejpam-3335	46	12	∗	∗	NOUN
ejpam-3335	46	13	b	b	NOUN
ejpam-3335	46	14	=	=	SYM
ejpam-3335	46	15	b	b	X
ejpam-3335	46	16	∪	∪	X
ejpam-3335	46	17	(	(	PUNCT
ejpam-3335	46	18	a′	a′	PROPN
ejpam-3335	46	19	∩	∩	ADJ
ejpam-3335	46	20	ω	ω	NOUN
ejpam-3335	46	21	)	)	PUNCT
ejpam-3335	46	22	for	for	ADP
ejpam-3335	46	23	all	all	DET
ejpam-3335	46	24	a	a	DET
ejpam-3335	46	25	,	,	PUNCT
ejpam-3335	46	26	b	b	NOUN
ejpam-3335	46	27	∈	∈	NOUN
ejpam-3335	46	28	pω(x	pω(x	NOUN
ejpam-3335	46	29	)	)	PUNCT
ejpam-3335	46	30	.	.	PUNCT
ejpam-3335	47	1	then	then	ADV
ejpam-3335	47	2	(	(	PUNCT
ejpam-3335	47	3	pω(x	pω(x	NOUN
ejpam-3335	47	4	)	)	PUNCT
ejpam-3335	47	5	,	,	PUNCT
ejpam-3335	47	6	∗,ω	∗,ω	PROPN
ejpam-3335	47	7	)	)	PUNCT
ejpam-3335	47	8	is	be	AUX
ejpam-3335	47	9	a	a	DET
ejpam-3335	47	10	up	up	NOUN
ejpam-3335	47	11	-	-	PUNCT
ejpam-3335	47	12	algebra	algebra	NOUN
ejpam-3335	47	13	and	and	CCONJ
ejpam-3335	47	14	we	we	PRON
ejpam-3335	47	15	shall	shall	AUX
ejpam-3335	47	16	call	call	VERB
ejpam-3335	47	17	it	it	PRON
ejpam-3335	47	18	the	the	DET
ejpam-3335	47	19	generalized	generalized	ADJ
ejpam-3335	47	20	power	power	NOUN
ejpam-3335	47	21	up	up	ADP
ejpam-3335	47	22	-	-	PUNCT
ejpam-3335	47	23	algebra	algebra	NOUN
ejpam-3335	47	24	of	of	ADP
ejpam-3335	47	25	type	type	NOUN
ejpam-3335	47	26	2	2	NUM
ejpam-3335	47	27	with	with	ADP
ejpam-3335	47	28	respect	respect	NOUN
ejpam-3335	47	29	to	to	ADP
ejpam-3335	47	30	ω	ω	NUM
ejpam-3335	47	31	.	.	PUNCT
ejpam-3335	48	1	p.	p.	NOUN
ejpam-3335	48	2	mosrijai	mosrijai	PROPN
ejpam-3335	48	3	,	,	PUNCT
ejpam-3335	48	4	a.	a.	NOUN
ejpam-3335	48	5	iampan	iampan	PROPN
ejpam-3335	48	6	/	/	SYM
ejpam-3335	48	7	eur	eur	PROPN
ejpam-3335	48	8	.	.	PUNCT
ejpam-3335	49	1	j.	j.	PROPN
ejpam-3335	49	2	pure	pure	PROPN
ejpam-3335	49	3	appl	appl	PROPN
ejpam-3335	49	4	.	.	PROPN
ejpam-3335	49	5	math	math	PROPN
ejpam-3335	49	6	,	,	PUNCT
ejpam-3335	49	7	11	11	NUM
ejpam-3335	49	8	(	(	PUNCT
ejpam-3335	49	9	4	4	NUM
ejpam-3335	49	10	)	)	PUNCT
ejpam-3335	49	11	(	(	PUNCT
ejpam-3335	49	12	2018	2018	NUM
ejpam-3335	49	13	)	)	PUNCT
ejpam-3335	49	14	,	,	PUNCT
ejpam-3335	49	15	976	976	NUM
ejpam-3335	49	16	-	-	SYM
ejpam-3335	49	17	1002	1002	NUM
ejpam-3335	49	18	978	978	NUM
ejpam-3335	49	19	example	example	NOUN
ejpam-3335	49	20	3	3	NUM
ejpam-3335	49	21	.	.	PUNCT
ejpam-3335	50	1	let	let	VERB
ejpam-3335	50	2	a	a	PRON
ejpam-3335	50	3	=	=	PUNCT
ejpam-3335	50	4	{	{	PUNCT
ejpam-3335	50	5	0	0	NUM
ejpam-3335	50	6	,	,	PUNCT
ejpam-3335	50	7	1	1	NUM
ejpam-3335	50	8	,	,	PUNCT
ejpam-3335	50	9	2	2	NUM
ejpam-3335	50	10	,	,	PUNCT
ejpam-3335	50	11	3	3	NUM
ejpam-3335	50	12	,	,	PUNCT
ejpam-3335	50	13	4	4	NUM
ejpam-3335	50	14	}	}	PUNCT
ejpam-3335	50	15	be	be	AUX
ejpam-3335	50	16	a	a	DET
ejpam-3335	50	17	set	set	NOUN
ejpam-3335	50	18	with	with	ADP
ejpam-3335	50	19	a	a	DET
ejpam-3335	50	20	binary	binary	ADJ
ejpam-3335	50	21	operation	operation	NOUN
ejpam-3335	50	22	·	·	PUNCT
ejpam-3335	50	23	defined	define	VERB
ejpam-3335	50	24	by	by	ADP
ejpam-3335	50	25	the	the	DET
ejpam-3335	50	26	following	following	ADJ
ejpam-3335	50	27	cayley	cayley	ADJ
ejpam-3335	50	28	table	table	NOUN
ejpam-3335	50	29	:	:	PUNCT
ejpam-3335	50	30	·	·	PUNCT
ejpam-3335	50	31	0	0	NUM
ejpam-3335	51	1	1	1	NUM
ejpam-3335	51	2	2	2	NUM
ejpam-3335	51	3	3	3	NUM
ejpam-3335	51	4	4	4	NUM
ejpam-3335	51	5	0	0	NUM
ejpam-3335	51	6	0	0	NUM
ejpam-3335	51	7	1	1	NUM
ejpam-3335	51	8	2	2	NUM
ejpam-3335	51	9	3	3	NUM
ejpam-3335	51	10	4	4	NUM
ejpam-3335	51	11	1	1	NUM
ejpam-3335	51	12	0	0	NUM
ejpam-3335	51	13	0	0	NUM
ejpam-3335	51	14	1	1	NUM
ejpam-3335	51	15	3	3	NUM
ejpam-3335	51	16	3	3	NUM
ejpam-3335	51	17	2	2	NUM
ejpam-3335	51	18	0	0	NUM
ejpam-3335	51	19	0	0	NUM
ejpam-3335	51	20	0	0	NUM
ejpam-3335	51	21	3	3	NUM
ejpam-3335	51	22	3	3	NUM
ejpam-3335	51	23	3	3	NUM
ejpam-3335	51	24	0	0	NUM
ejpam-3335	51	25	0	0	NUM
ejpam-3335	51	26	0	0	NUM
ejpam-3335	51	27	0	0	NUM
ejpam-3335	51	28	3	3	NUM
ejpam-3335	51	29	4	4	NUM
ejpam-3335	51	30	0	0	NUM
ejpam-3335	51	31	0	0	NUM
ejpam-3335	51	32	0	0	NUM
ejpam-3335	51	33	0	0	NUM
ejpam-3335	51	34	0	0	NUM
ejpam-3335	52	1	then	then	ADV
ejpam-3335	52	2	(	(	PUNCT
ejpam-3335	52	3	a	a	PRON
ejpam-3335	52	4	,	,	PUNCT
ejpam-3335	52	5	·	·	PUNCT
ejpam-3335	52	6	,	,	PUNCT
ejpam-3335	52	7	0	0	NUM
ejpam-3335	52	8	)	)	PUNCT
ejpam-3335	52	9	is	be	AUX
ejpam-3335	52	10	a	a	DET
ejpam-3335	52	11	up	up	NOUN
ejpam-3335	52	12	-	-	PUNCT
ejpam-3335	52	13	algebra	algebra	NOUN
ejpam-3335	52	14	which	which	PRON
ejpam-3335	52	15	is	be	AUX
ejpam-3335	52	16	not	not	PART
ejpam-3335	52	17	a	a	DET
ejpam-3335	52	18	ku	ku	NOUN
ejpam-3335	52	19	-	-	PUNCT
ejpam-3335	52	20	algebra	algebra	PROPN
ejpam-3335	52	21	because	because	SCONJ
ejpam-3335	52	22	(	(	PUNCT
ejpam-3335	52	23	0	0	NUM
ejpam-3335	52	24	·	·	SYM
ejpam-3335	52	25	2)((2	2)((2	NUM
ejpam-3335	52	26	·	·	PUNCT
ejpam-3335	52	27	4	4	X
ejpam-3335	52	28	)	)	PUNCT
ejpam-3335	52	29	·	·	PUNCT
ejpam-3335	53	1	(	(	PUNCT
ejpam-3335	53	2	0	0	NUM
ejpam-3335	53	3	·	·	SYM
ejpam-3335	53	4	4	4	NUM
ejpam-3335	53	5	)	)	PUNCT
ejpam-3335	53	6	)	)	PUNCT
ejpam-3335	54	1	=	=	SYM
ejpam-3335	54	2	2	2	X
ejpam-3335	54	3	·	·	PUNCT
ejpam-3335	54	4	(	(	PUNCT
ejpam-3335	54	5	3	3	NUM
ejpam-3335	54	6	·	·	SYM
ejpam-3335	54	7	4	4	NUM
ejpam-3335	54	8	)	)	PUNCT
ejpam-3335	54	9	=	=	SYM
ejpam-3335	54	10	2	2	NUM
ejpam-3335	54	11	·	·	SYM
ejpam-3335	54	12	3	3	NUM
ejpam-3335	54	13	=	=	SYM
ejpam-3335	54	14	3	3	NUM
ejpam-3335	54	15	6=	6=	NUM
ejpam-3335	54	16	0	0	NUM
ejpam-3335	54	17	(	(	PUNCT
ejpam-3335	54	18	see	see	VERB
ejpam-3335	54	19	the	the	DET
ejpam-3335	54	20	definition	definition	NOUN
ejpam-3335	54	21	in	in	ADP
ejpam-3335	54	22	[	[	X
ejpam-3335	54	23	8	8	NUM
ejpam-3335	54	24	]	]	NUM
ejpam-3335	54	25	)	)	PUNCT
ejpam-3335	54	26	.	.	PUNCT
ejpam-3335	55	1	in	in	ADP
ejpam-3335	55	2	what	what	PRON
ejpam-3335	55	3	follows	follow	VERB
ejpam-3335	55	4	,	,	PUNCT
ejpam-3335	55	5	let	let	VERB
ejpam-3335	55	6	a	a	DET
ejpam-3335	55	7	denote	denote	NOUN
ejpam-3335	55	8	up	up	ADP
ejpam-3335	55	9	-	-	PUNCT
ejpam-3335	55	10	algebras	algebras	X
ejpam-3335	55	11	unless	unless	SCONJ
ejpam-3335	55	12	otherwise	otherwise	ADV
ejpam-3335	55	13	specified	specify	VERB
ejpam-3335	55	14	.	.	PUNCT
ejpam-3335	56	1	the	the	DET
ejpam-3335	56	2	following	follow	VERB
ejpam-3335	56	3	proposition	proposition	NOUN
ejpam-3335	56	4	is	be	AUX
ejpam-3335	56	5	very	very	ADV
ejpam-3335	56	6	important	important	ADJ
ejpam-3335	56	7	for	for	ADP
ejpam-3335	56	8	the	the	DET
ejpam-3335	56	9	study	study	NOUN
ejpam-3335	56	10	of	of	ADP
ejpam-3335	56	11	up	up	ADP
ejpam-3335	56	12	-	-	PUNCT
ejpam-3335	56	13	algebras	algebras	X
ejpam-3335	56	14	.	.	PUNCT
ejpam-3335	57	1	proposition	proposition	NOUN
ejpam-3335	57	2	1	1	NUM
ejpam-3335	57	3	.	.	PUNCT
ejpam-3335	58	1	[	[	X
ejpam-3335	58	2	2	2	NUM
ejpam-3335	58	3	,	,	PUNCT
ejpam-3335	58	4	3	3	NUM
ejpam-3335	58	5	]	]	PUNCT
ejpam-3335	58	6	in	in	ADP
ejpam-3335	58	7	a	a	DET
ejpam-3335	58	8	up	up	NOUN
ejpam-3335	58	9	-	-	PUNCT
ejpam-3335	58	10	algebra	algebra	NOUN
ejpam-3335	58	11	a	a	PRON
ejpam-3335	58	12	=	=	X
ejpam-3335	58	13	(	(	PUNCT
ejpam-3335	58	14	a	a	PRON
ejpam-3335	58	15	,	,	PUNCT
ejpam-3335	58	16	·	·	PUNCT
ejpam-3335	58	17	,	,	PUNCT
ejpam-3335	58	18	0	0	NUM
ejpam-3335	58	19	)	)	PUNCT
ejpam-3335	58	20	,	,	PUNCT
ejpam-3335	58	21	the	the	DET
ejpam-3335	58	22	following	follow	VERB
ejpam-3335	58	23	properties	property	NOUN
ejpam-3335	58	24	hold	hold	VERB
ejpam-3335	58	25	:	:	PUNCT
ejpam-3335	58	26	(	(	PUNCT
ejpam-3335	58	27	1	1	X
ejpam-3335	58	28	)	)	PUNCT
ejpam-3335	58	29	(	(	PUNCT
ejpam-3335	58	30	∀x	∀x	X
ejpam-3335	58	31	∈	∈	NOUN
ejpam-3335	58	32	a)(x	a)(x	NOUN
ejpam-3335	58	33	·	·	PUNCT
ejpam-3335	58	34	x	x	SYM
ejpam-3335	59	1	=	=	PUNCT
ejpam-3335	59	2	0	0	NUM
ejpam-3335	59	3	)	)	PUNCT
ejpam-3335	59	4	,	,	PUNCT
ejpam-3335	59	5	(	(	PUNCT
ejpam-3335	59	6	2	2	X
ejpam-3335	59	7	)	)	PUNCT
ejpam-3335	59	8	(	(	PUNCT
ejpam-3335	59	9	∀x	∀x	X
ejpam-3335	59	10	,	,	PUNCT
ejpam-3335	59	11	y	y	PROPN
ejpam-3335	59	12	,	,	PUNCT
ejpam-3335	59	13	z	z	NOUN
ejpam-3335	59	14	∈	∈	NOUN
ejpam-3335	59	15	a)(x	a)(x	NOUN
ejpam-3335	59	16	·	·	PUNCT
ejpam-3335	59	17	y	y	X
ejpam-3335	59	18	=	=	SYM
ejpam-3335	59	19	0	0	PROPN
ejpam-3335	59	20	,	,	PUNCT
ejpam-3335	59	21	y	y	PROPN
ejpam-3335	59	22	·	·	PUNCT
ejpam-3335	59	23	z	z	X
ejpam-3335	59	24	=	=	SYM
ejpam-3335	59	25	0⇒	0⇒	NUM
ejpam-3335	59	26	x	x	SYM
ejpam-3335	60	1	·	·	PUNCT
ejpam-3335	60	2	z	z	X
ejpam-3335	60	3	=	=	SYM
ejpam-3335	60	4	0	0	NUM
ejpam-3335	60	5	)	)	PUNCT
ejpam-3335	60	6	,	,	PUNCT
ejpam-3335	60	7	(	(	PUNCT
ejpam-3335	60	8	3	3	X
ejpam-3335	60	9	)	)	PUNCT
ejpam-3335	60	10	(	(	PUNCT
ejpam-3335	60	11	∀x	∀x	X
ejpam-3335	60	12	,	,	PUNCT
ejpam-3335	60	13	y	y	PROPN
ejpam-3335	60	14	,	,	PUNCT
ejpam-3335	60	15	z	z	NOUN
ejpam-3335	60	16	∈	∈	NOUN
ejpam-3335	60	17	a)(x	a)(x	NOUN
ejpam-3335	60	18	·	·	PUNCT
ejpam-3335	60	19	y	y	X
ejpam-3335	60	20	=	=	SYM
ejpam-3335	60	21	0⇒	0⇒	PROPN
ejpam-3335	60	22	(	(	PUNCT
ejpam-3335	60	23	z	z	NOUN
ejpam-3335	60	24	·	·	PUNCT
ejpam-3335	60	25	x	x	X
ejpam-3335	60	26	)	)	PUNCT
ejpam-3335	60	27	·	·	PUNCT
ejpam-3335	60	28	(	(	PUNCT
ejpam-3335	60	29	z	z	X
ejpam-3335	60	30	·	·	PUNCT
ejpam-3335	60	31	y	y	X
ejpam-3335	60	32	)	)	PUNCT
ejpam-3335	61	1	=	=	NOUN
ejpam-3335	61	2	0	0	NUM
ejpam-3335	61	3	)	)	PUNCT
ejpam-3335	61	4	,	,	PUNCT
ejpam-3335	61	5	(	(	PUNCT
ejpam-3335	61	6	4	4	X
ejpam-3335	61	7	)	)	PUNCT
ejpam-3335	61	8	(	(	PUNCT
ejpam-3335	61	9	∀x	∀x	X
ejpam-3335	61	10	,	,	PUNCT
ejpam-3335	61	11	y	y	PROPN
ejpam-3335	61	12	,	,	PUNCT
ejpam-3335	61	13	z	z	NOUN
ejpam-3335	61	14	∈	∈	NOUN
ejpam-3335	61	15	a)(x	a)(x	NOUN
ejpam-3335	61	16	·	·	PUNCT
ejpam-3335	62	1	y	y	X
ejpam-3335	62	2	=	=	SYM
ejpam-3335	62	3	0⇒	0⇒	PROPN
ejpam-3335	62	4	(	(	PUNCT
ejpam-3335	62	5	y	y	PROPN
ejpam-3335	62	6	·	·	PUNCT
ejpam-3335	62	7	z	z	X
ejpam-3335	62	8	)	)	PUNCT
ejpam-3335	62	9	·	·	PUNCT
ejpam-3335	62	10	(	(	PUNCT
ejpam-3335	62	11	x	x	X
ejpam-3335	62	12	·	·	PUNCT
ejpam-3335	63	1	z	z	X
ejpam-3335	63	2	)	)	PUNCT
ejpam-3335	63	3	=	=	SYM
ejpam-3335	63	4	0	0	NUM
ejpam-3335	63	5	)	)	PUNCT
ejpam-3335	63	6	,	,	PUNCT
ejpam-3335	63	7	(	(	PUNCT
ejpam-3335	63	8	5	5	X
ejpam-3335	63	9	)	)	PUNCT
ejpam-3335	63	10	(	(	PUNCT
ejpam-3335	63	11	∀x	∀x	X
ejpam-3335	63	12	,	,	PUNCT
ejpam-3335	63	13	y	y	PROPN
ejpam-3335	63	14	∈	∈	PROPN
ejpam-3335	63	15	a)(x	a)(x	PROPN
ejpam-3335	63	16	·	·	PUNCT
ejpam-3335	63	17	(	(	PUNCT
ejpam-3335	63	18	y	y	NOUN
ejpam-3335	63	19	·	·	PUNCT
ejpam-3335	63	20	x	x	X
ejpam-3335	63	21	)	)	PUNCT
ejpam-3335	63	22	=	=	SYM
ejpam-3335	63	23	0	0	NUM
ejpam-3335	63	24	)	)	PUNCT
ejpam-3335	63	25	,	,	PUNCT
ejpam-3335	63	26	(	(	PUNCT
ejpam-3335	63	27	6	6	NUM
ejpam-3335	63	28	)	)	PUNCT
ejpam-3335	63	29	(	(	PUNCT
ejpam-3335	63	30	∀x	∀x	X
ejpam-3335	63	31	,	,	PUNCT
ejpam-3335	63	32	y	y	PROPN
ejpam-3335	63	33	∈	∈	PROPN
ejpam-3335	63	34	a)((y	a)((y	NOUN
ejpam-3335	63	35	·	·	PUNCT
ejpam-3335	63	36	x	x	X
ejpam-3335	63	37	)	)	PUNCT
ejpam-3335	63	38	·	·	PUNCT
ejpam-3335	63	39	x	x	PUNCT
ejpam-3335	64	1	=	=	PUNCT
ejpam-3335	64	2	0⇔	0⇔	NOUN
ejpam-3335	64	3	x	x	X
ejpam-3335	65	1	=	=	PUNCT
ejpam-3335	65	2	y	y	PROPN
ejpam-3335	65	3	·	·	PUNCT
ejpam-3335	65	4	x	x	X
ejpam-3335	65	5	)	)	PUNCT
ejpam-3335	65	6	,	,	PUNCT
ejpam-3335	65	7	(	(	PUNCT
ejpam-3335	65	8	7	7	X
ejpam-3335	65	9	)	)	PUNCT
ejpam-3335	65	10	(	(	PUNCT
ejpam-3335	65	11	∀x	∀x	X
ejpam-3335	65	12	,	,	PUNCT
ejpam-3335	65	13	y	y	PROPN
ejpam-3335	65	14	∈	∈	PROPN
ejpam-3335	65	15	a)(x	a)(x	PROPN
ejpam-3335	65	16	·	·	PUNCT
ejpam-3335	65	17	(	(	PUNCT
ejpam-3335	65	18	y	y	PROPN
ejpam-3335	65	19	·	·	PUNCT
ejpam-3335	65	20	y	y	X
ejpam-3335	65	21	)	)	PUNCT
ejpam-3335	65	22	=	=	SYM
ejpam-3335	65	23	0	0	NUM
ejpam-3335	65	24	)	)	PUNCT
ejpam-3335	65	25	,	,	PUNCT
ejpam-3335	65	26	(	(	PUNCT
ejpam-3335	65	27	8)	8)	NUM
ejpam-3335	65	28	(	(	PUNCT
ejpam-3335	65	29	∀a	∀a	NOUN
ejpam-3335	65	30	,	,	PUNCT
ejpam-3335	65	31	x	x	X
ejpam-3335	65	32	,	,	PUNCT
ejpam-3335	65	33	y	y	PROPN
ejpam-3335	65	34	,	,	PUNCT
ejpam-3335	65	35	z	z	PROPN
ejpam-3335	65	36	∈	∈	PROPN
ejpam-3335	65	37	a)((x	a)((x	NOUN
ejpam-3335	65	38	·	·	PUNCT
ejpam-3335	65	39	(	(	PUNCT
ejpam-3335	65	40	y	y	PROPN
ejpam-3335	65	41	·	·	PUNCT
ejpam-3335	65	42	z	z	NOUN
ejpam-3335	65	43	)	)	PUNCT
ejpam-3335	65	44	)	)	PUNCT
ejpam-3335	65	45	·	·	PUNCT
ejpam-3335	66	1	(	(	PUNCT
ejpam-3335	66	2	x	x	X
ejpam-3335	66	3	·	·	PUNCT
ejpam-3335	66	4	(	(	PUNCT
ejpam-3335	66	5	(	(	PUNCT
ejpam-3335	66	6	a	a	DET
ejpam-3335	66	7	·	·	PUNCT
ejpam-3335	66	8	y	y	NOUN
ejpam-3335	66	9	)	)	PUNCT
ejpam-3335	66	10	·	·	PUNCT
ejpam-3335	66	11	(	(	PUNCT
ejpam-3335	66	12	a	a	DET
ejpam-3335	66	13	·	·	PUNCT
ejpam-3335	66	14	z	z	NOUN
ejpam-3335	66	15	)	)	PUNCT
ejpam-3335	66	16	)	)	PUNCT
ejpam-3335	66	17	)	)	PUNCT
ejpam-3335	67	1	=	=	PUNCT
ejpam-3335	67	2	0	0	NUM
ejpam-3335	67	3	)	)	PUNCT
ejpam-3335	67	4	,	,	PUNCT
ejpam-3335	67	5	(	(	PUNCT
ejpam-3335	67	6	9	9	NUM
ejpam-3335	67	7	)	)	PUNCT
ejpam-3335	67	8	(	(	PUNCT
ejpam-3335	67	9	∀a	∀a	X
ejpam-3335	67	10	,	,	PUNCT
ejpam-3335	67	11	x	x	X
ejpam-3335	67	12	,	,	PUNCT
ejpam-3335	67	13	y	y	PROPN
ejpam-3335	67	14	,	,	PUNCT
ejpam-3335	67	15	z	z	PROPN
ejpam-3335	67	16	∈	∈	PROPN
ejpam-3335	67	17	a)((((a	a)((((a	NOUN
ejpam-3335	67	18	·	·	PUNCT
ejpam-3335	67	19	x	x	X
ejpam-3335	67	20	)	)	PUNCT
ejpam-3335	67	21	·	·	PUNCT
ejpam-3335	67	22	(	(	PUNCT
ejpam-3335	67	23	a	a	DET
ejpam-3335	67	24	·	·	PUNCT
ejpam-3335	67	25	y	y	NOUN
ejpam-3335	67	26	)	)	PUNCT
ejpam-3335	67	27	)	)	PUNCT
ejpam-3335	67	28	·	·	PUNCT
ejpam-3335	68	1	z	z	X
ejpam-3335	68	2	)	)	PUNCT
ejpam-3335	68	3	·	·	PUNCT
ejpam-3335	68	4	(	(	PUNCT
ejpam-3335	68	5	(	(	PUNCT
ejpam-3335	68	6	x	x	SYM
ejpam-3335	68	7	·	·	PUNCT
ejpam-3335	68	8	y	y	X
ejpam-3335	68	9	)	)	PUNCT
ejpam-3335	68	10	·	·	PUNCT
ejpam-3335	69	1	z	z	X
ejpam-3335	69	2	)	)	PUNCT
ejpam-3335	69	3	=	=	SYM
ejpam-3335	69	4	0	0	NUM
ejpam-3335	69	5	)	)	PUNCT
ejpam-3335	69	6	,	,	PUNCT
ejpam-3335	69	7	(	(	PUNCT
ejpam-3335	69	8	10	10	NUM
ejpam-3335	69	9	)	)	PUNCT
ejpam-3335	69	10	(	(	PUNCT
ejpam-3335	69	11	∀x	∀x	X
ejpam-3335	69	12	,	,	PUNCT
ejpam-3335	69	13	y	y	PROPN
ejpam-3335	69	14	,	,	PUNCT
ejpam-3335	69	15	z	z	NOUN
ejpam-3335	69	16	∈	∈	PROPN
ejpam-3335	69	17	a)(((x	a)(((x	NOUN
ejpam-3335	69	18	·	·	SYM
ejpam-3335	69	19	y	y	X
ejpam-3335	69	20	)	)	PUNCT
ejpam-3335	69	21	·	·	PUNCT
ejpam-3335	70	1	z	z	X
ejpam-3335	70	2	)	)	PUNCT
ejpam-3335	70	3	·	·	PUNCT
ejpam-3335	70	4	(	(	PUNCT
ejpam-3335	70	5	y	y	PROPN
ejpam-3335	70	6	·	·	PUNCT
ejpam-3335	70	7	z	z	X
ejpam-3335	70	8	)	)	PUNCT
ejpam-3335	70	9	=	=	SYM
ejpam-3335	70	10	0	0	NUM
ejpam-3335	70	11	)	)	PUNCT
ejpam-3335	70	12	,	,	PUNCT
ejpam-3335	70	13	(	(	PUNCT
ejpam-3335	70	14	11	11	NUM
ejpam-3335	70	15	)	)	PUNCT
ejpam-3335	70	16	(	(	PUNCT
ejpam-3335	70	17	∀x	∀x	X
ejpam-3335	70	18	,	,	PUNCT
ejpam-3335	70	19	y	y	PROPN
ejpam-3335	70	20	,	,	PUNCT
ejpam-3335	70	21	z	z	NOUN
ejpam-3335	70	22	∈	∈	NOUN
ejpam-3335	70	23	a)(x	a)(x	NOUN
ejpam-3335	70	24	·	·	PUNCT
ejpam-3335	70	25	y	y	X
ejpam-3335	70	26	=	=	SYM
ejpam-3335	70	27	0⇒	0⇒	PROPN
ejpam-3335	70	28	x	x	SYM
ejpam-3335	70	29	·	·	PUNCT
ejpam-3335	70	30	(	(	PUNCT
ejpam-3335	70	31	z	z	NOUN
ejpam-3335	70	32	·	·	PUNCT
ejpam-3335	70	33	y	y	X
ejpam-3335	70	34	)	)	PUNCT
ejpam-3335	70	35	=	=	NOUN
ejpam-3335	70	36	0	0	NUM
ejpam-3335	70	37	)	)	PUNCT
ejpam-3335	70	38	,	,	PUNCT
ejpam-3335	70	39	(	(	PUNCT
ejpam-3335	70	40	12	12	NUM
ejpam-3335	70	41	)	)	PUNCT
ejpam-3335	70	42	(	(	PUNCT
ejpam-3335	70	43	∀x	∀x	X
ejpam-3335	70	44	,	,	PUNCT
ejpam-3335	70	45	y	y	PROPN
ejpam-3335	70	46	,	,	PUNCT
ejpam-3335	70	47	z	z	NOUN
ejpam-3335	70	48	∈	∈	PROPN
ejpam-3335	70	49	a)(((x	a)(((x	NOUN
ejpam-3335	70	50	·	·	SYM
ejpam-3335	70	51	y	y	X
ejpam-3335	70	52	)	)	PUNCT
ejpam-3335	70	53	·	·	PUNCT
ejpam-3335	71	1	z	z	X
ejpam-3335	71	2	)	)	PUNCT
ejpam-3335	71	3	·	·	PUNCT
ejpam-3335	71	4	(	(	PUNCT
ejpam-3335	71	5	x	x	X
ejpam-3335	71	6	·	·	PUNCT
ejpam-3335	71	7	(	(	PUNCT
ejpam-3335	71	8	y	y	PROPN
ejpam-3335	71	9	·	·	PUNCT
ejpam-3335	71	10	z	z	NOUN
ejpam-3335	71	11	)	)	PUNCT
ejpam-3335	71	12	)	)	PUNCT
ejpam-3335	72	1	=	=	PUNCT
ejpam-3335	72	2	0	0	NUM
ejpam-3335	72	3	)	)	PUNCT
ejpam-3335	72	4	,	,	PUNCT
ejpam-3335	72	5	and	and	CCONJ
ejpam-3335	72	6	(	(	PUNCT
ejpam-3335	72	7	13	13	NUM
ejpam-3335	72	8	)	)	PUNCT
ejpam-3335	72	9	(	(	PUNCT
ejpam-3335	72	10	∀a	∀a	X
ejpam-3335	72	11	,	,	PUNCT
ejpam-3335	72	12	x	x	X
ejpam-3335	72	13	,	,	PUNCT
ejpam-3335	72	14	y	y	PROPN
ejpam-3335	72	15	,	,	PUNCT
ejpam-3335	72	16	z	z	NOUN
ejpam-3335	72	17	∈	∈	PROPN
ejpam-3335	72	18	a)(((x	a)(((x	NOUN
ejpam-3335	72	19	·	·	SYM
ejpam-3335	72	20	y	y	X
ejpam-3335	72	21	)	)	PUNCT
ejpam-3335	72	22	·	·	PUNCT
ejpam-3335	73	1	z	z	X
ejpam-3335	73	2	)	)	PUNCT
ejpam-3335	73	3	·	·	PUNCT
ejpam-3335	73	4	(	(	PUNCT
ejpam-3335	73	5	y	y	PROPN
ejpam-3335	73	6	·	·	PUNCT
ejpam-3335	73	7	(	(	PUNCT
ejpam-3335	73	8	a	a	DET
ejpam-3335	73	9	·	·	PUNCT
ejpam-3335	73	10	z	z	NOUN
ejpam-3335	73	11	)	)	PUNCT
ejpam-3335	73	12	)	)	PUNCT
ejpam-3335	74	1	=	=	PUNCT
ejpam-3335	74	2	0	0	NUM
ejpam-3335	74	3	)	)	PUNCT
ejpam-3335	74	4	.	.	PUNCT
ejpam-3335	75	1	on	on	ADP
ejpam-3335	75	2	a	a	DET
ejpam-3335	75	3	up	up	NOUN
ejpam-3335	75	4	-	-	PUNCT
ejpam-3335	75	5	algebra	algebra	NOUN
ejpam-3335	75	6	a	a	PRON
ejpam-3335	75	7	=	=	X
ejpam-3335	75	8	(	(	PUNCT
ejpam-3335	75	9	a	a	PRON
ejpam-3335	75	10	,	,	PUNCT
ejpam-3335	75	11	·	·	PUNCT
ejpam-3335	75	12	,	,	PUNCT
ejpam-3335	75	13	0	0	NUM
ejpam-3335	75	14	)	)	PUNCT
ejpam-3335	75	15	,	,	PUNCT
ejpam-3335	75	16	we	we	PRON
ejpam-3335	75	17	define	define	VERB
ejpam-3335	75	18	a	a	DET
ejpam-3335	75	19	binary	binary	ADJ
ejpam-3335	75	20	relation	relation	NOUN
ejpam-3335	75	21	≤	≤	NUM
ejpam-3335	75	22	on	on	ADP
ejpam-3335	75	23	a	a	DET
ejpam-3335	75	24	[	[	X
ejpam-3335	75	25	2	2	NUM
ejpam-3335	75	26	]	]	PUNCT
ejpam-3335	75	27	as	as	SCONJ
ejpam-3335	75	28	follows	follow	VERB
ejpam-3335	75	29	:	:	PUNCT
ejpam-3335	75	30	for	for	ADP
ejpam-3335	75	31	any	any	DET
ejpam-3335	75	32	x	x	NOUN
ejpam-3335	75	33	,	,	PUNCT
ejpam-3335	75	34	y	y	PROPN
ejpam-3335	75	35	∈	∈	PROPN
ejpam-3335	75	36	a	a	DET
ejpam-3335	75	37	,	,	PUNCT
ejpam-3335	75	38	x	x	PUNCT
ejpam-3335	75	39	≤	≤	ADJ
ejpam-3335	75	40	y	y	NOUN
ejpam-3335	76	1	if	if	SCONJ
ejpam-3335	77	1	and	and	CCONJ
ejpam-3335	77	2	only	only	ADV
ejpam-3335	77	3	if	if	SCONJ
ejpam-3335	77	4	x	x	X
ejpam-3335	77	5	·	·	PUNCT
ejpam-3335	77	6	y	y	SYM
ejpam-3335	77	7	=	=	SYM
ejpam-3335	77	8	0	0	PROPN
ejpam-3335	77	9	.	.	PUNCT
ejpam-3335	78	1	definition	definition	NOUN
ejpam-3335	78	2	2	2	NUM
ejpam-3335	78	3	.	.	PUNCT
ejpam-3335	79	1	[	[	X
ejpam-3335	79	2	1	1	NUM
ejpam-3335	79	3	,	,	PUNCT
ejpam-3335	79	4	2	2	NUM
ejpam-3335	79	5	,	,	PUNCT
ejpam-3335	79	6	14	14	NUM
ejpam-3335	79	7	]	]	PUNCT
ejpam-3335	79	8	a	a	DET
ejpam-3335	79	9	nonempty	nonempty	ADV
ejpam-3335	79	10	subset	subset	VERB
ejpam-3335	79	11	s	s	NOUN
ejpam-3335	79	12	of	of	ADP
ejpam-3335	79	13	a	a	DET
ejpam-3335	79	14	up	up	NOUN
ejpam-3335	79	15	-	-	PUNCT
ejpam-3335	79	16	algebra	algebra	NOUN
ejpam-3335	79	17	(	(	PUNCT
ejpam-3335	79	18	a	a	PRON
ejpam-3335	79	19	,	,	PUNCT
ejpam-3335	79	20	·	·	PUNCT
ejpam-3335	79	21	,	,	PUNCT
ejpam-3335	79	22	0	0	NUM
ejpam-3335	79	23	)	)	PUNCT
ejpam-3335	79	24	is	be	AUX
ejpam-3335	79	25	called	call	VERB
ejpam-3335	79	26	(	(	PUNCT
ejpam-3335	79	27	1	1	NUM
ejpam-3335	79	28	)	)	PUNCT
ejpam-3335	79	29	a	a	DET
ejpam-3335	79	30	up	up	ADJ
ejpam-3335	79	31	-	-	PUNCT
ejpam-3335	79	32	subalgebra	subalgebra	NOUN
ejpam-3335	79	33	of	of	ADP
ejpam-3335	79	34	a	a	DET
ejpam-3335	79	35	if	if	NOUN
ejpam-3335	79	36	for	for	ADP
ejpam-3335	79	37	any	any	DET
ejpam-3335	79	38	x	x	NOUN
ejpam-3335	79	39	,	,	PUNCT
ejpam-3335	79	40	y	y	PROPN
ejpam-3335	79	41	∈	∈	PROPN
ejpam-3335	79	42	s	s	PROPN
ejpam-3335	79	43	,	,	PUNCT
ejpam-3335	79	44	x	x	PUNCT
ejpam-3335	79	45	·	·	PUNCT
ejpam-3335	79	46	y	y	PROPN
ejpam-3335	79	47	∈	∈	PROPN
ejpam-3335	79	48	s.	s.	PROPN
ejpam-3335	79	49	p.	p.	PROPN
ejpam-3335	79	50	mosrijai	mosrijai	PROPN
ejpam-3335	79	51	,	,	PUNCT
ejpam-3335	79	52	a.	a.	NOUN
ejpam-3335	79	53	iampan	iampan	PROPN
ejpam-3335	79	54	/	/	SYM
ejpam-3335	79	55	eur	eur	PROPN
ejpam-3335	79	56	.	.	PUNCT
ejpam-3335	80	1	j.	j.	PROPN
ejpam-3335	80	2	pure	pure	PROPN
ejpam-3335	80	3	appl	appl	PROPN
ejpam-3335	80	4	.	.	PROPN
ejpam-3335	80	5	math	math	PROPN
ejpam-3335	80	6	,	,	PUNCT
ejpam-3335	80	7	11	11	NUM
ejpam-3335	80	8	(	(	PUNCT
ejpam-3335	80	9	4	4	NUM
ejpam-3335	80	10	)	)	PUNCT
ejpam-3335	80	11	(	(	PUNCT
ejpam-3335	80	12	2018	2018	NUM
ejpam-3335	80	13	)	)	PUNCT
ejpam-3335	80	14	,	,	PUNCT
ejpam-3335	80	15	976	976	NUM
ejpam-3335	80	16	-	-	SYM
ejpam-3335	80	17	1002	1002	NUM
ejpam-3335	80	18	979	979	NUM
ejpam-3335	80	19	(	(	PUNCT
ejpam-3335	80	20	2	2	NUM
ejpam-3335	80	21	)	)	PUNCT
ejpam-3335	80	22	a	a	DET
ejpam-3335	80	23	up	up	ADJ
ejpam-3335	80	24	-	-	PUNCT
ejpam-3335	80	25	filter	filter	NOUN
ejpam-3335	80	26	of	of	ADP
ejpam-3335	80	27	a	a	DET
ejpam-3335	80	28	if	if	NOUN
ejpam-3335	80	29	(	(	PUNCT
ejpam-3335	80	30	i	i	NOUN
ejpam-3335	80	31	)	)	PUNCT
ejpam-3335	80	32	the	the	DET
ejpam-3335	80	33	constant	constant	ADJ
ejpam-3335	80	34	0	0	NUM
ejpam-3335	80	35	of	of	ADP
ejpam-3335	80	36	a	a	PRON
ejpam-3335	80	37	is	be	AUX
ejpam-3335	80	38	in	in	ADP
ejpam-3335	80	39	s	s	PROPN
ejpam-3335	80	40	,	,	PUNCT
ejpam-3335	80	41	and	and	CCONJ
ejpam-3335	80	42	(	(	PUNCT
ejpam-3335	80	43	ii	ii	NOUN
ejpam-3335	80	44	)	)	PUNCT
ejpam-3335	80	45	for	for	ADP
ejpam-3335	80	46	any	any	DET
ejpam-3335	80	47	x	x	NOUN
ejpam-3335	80	48	,	,	PUNCT
ejpam-3335	80	49	y	y	PROPN
ejpam-3335	80	50	∈	∈	PROPN
ejpam-3335	80	51	a	a	PRON
ejpam-3335	80	52	,	,	PUNCT
ejpam-3335	80	53	x	x	X
ejpam-3335	80	54	·	·	PUNCT
ejpam-3335	80	55	y	y	X
ejpam-3335	80	56	∈	∈	PROPN
ejpam-3335	80	57	s	s	PART
ejpam-3335	80	58	and	and	CCONJ
ejpam-3335	80	59	x	x	SYM
ejpam-3335	80	60	∈	∈	NOUN
ejpam-3335	80	61	s	s	AUX
ejpam-3335	80	62	imply	imply	VERB
ejpam-3335	80	63	y	y	PROPN
ejpam-3335	80	64	∈	∈	PROPN
ejpam-3335	80	65	s.	s.	PROPN
ejpam-3335	80	66	(	(	PUNCT
ejpam-3335	80	67	3	3	X
ejpam-3335	80	68	)	)	PUNCT
ejpam-3335	80	69	a	a	DET
ejpam-3335	80	70	up	up	ADJ
ejpam-3335	80	71	-	-	PUNCT
ejpam-3335	80	72	ideal	ideal	NOUN
ejpam-3335	80	73	of	of	ADP
ejpam-3335	80	74	a	a	DET
ejpam-3335	80	75	if	if	NOUN
ejpam-3335	80	76	(	(	PUNCT
ejpam-3335	80	77	i	i	NOUN
ejpam-3335	80	78	)	)	PUNCT
ejpam-3335	80	79	the	the	DET
ejpam-3335	80	80	constant	constant	ADJ
ejpam-3335	80	81	0	0	NUM
ejpam-3335	80	82	of	of	ADP
ejpam-3335	80	83	a	a	PRON
ejpam-3335	80	84	is	be	AUX
ejpam-3335	80	85	in	in	ADP
ejpam-3335	80	86	s	s	PROPN
ejpam-3335	80	87	,	,	PUNCT
ejpam-3335	80	88	and	and	CCONJ
ejpam-3335	80	89	(	(	PUNCT
ejpam-3335	80	90	ii	ii	NOUN
ejpam-3335	80	91	)	)	PUNCT
ejpam-3335	80	92	for	for	ADP
ejpam-3335	80	93	any	any	DET
ejpam-3335	80	94	x	x	NOUN
ejpam-3335	80	95	,	,	PUNCT
ejpam-3335	80	96	y	y	PROPN
ejpam-3335	80	97	,	,	PUNCT
ejpam-3335	80	98	z	z	PROPN
ejpam-3335	80	99	∈	∈	PROPN
ejpam-3335	80	100	a	a	PRON
ejpam-3335	80	101	,	,	PUNCT
ejpam-3335	80	102	x	x	X
ejpam-3335	80	103	·	·	PUNCT
ejpam-3335	80	104	(	(	PUNCT
ejpam-3335	80	105	y	y	PROPN
ejpam-3335	80	106	·	·	PUNCT
ejpam-3335	80	107	z	z	X
ejpam-3335	80	108	)	)	PUNCT
ejpam-3335	80	109	∈	∈	PROPN
ejpam-3335	80	110	s	s	PART
ejpam-3335	80	111	and	and	CCONJ
ejpam-3335	80	112	y	y	PROPN
ejpam-3335	80	113	∈	∈	PROPN
ejpam-3335	80	114	s	s	VERB
ejpam-3335	80	115	imply	imply	NOUN
ejpam-3335	80	116	x	x	X
ejpam-3335	80	117	·	·	PUNCT
ejpam-3335	80	118	z	z	SYM
ejpam-3335	80	119	∈	∈	PROPN
ejpam-3335	80	120	s.	s.	PROPN
ejpam-3335	80	121	(	(	PUNCT
ejpam-3335	80	122	4	4	X
ejpam-3335	80	123	)	)	PUNCT
ejpam-3335	80	124	a	a	DET
ejpam-3335	80	125	strongly	strongly	ADV
ejpam-3335	80	126	up	up	ADJ
ejpam-3335	80	127	-	-	PUNCT
ejpam-3335	80	128	ideal	ideal	NOUN
ejpam-3335	80	129	of	of	ADP
ejpam-3335	80	130	a	a	DET
ejpam-3335	80	131	if	if	NOUN
ejpam-3335	80	132	(	(	PUNCT
ejpam-3335	80	133	i	i	NOUN
ejpam-3335	80	134	)	)	PUNCT
ejpam-3335	80	135	the	the	DET
ejpam-3335	80	136	constant	constant	ADJ
ejpam-3335	80	137	0	0	NUM
ejpam-3335	80	138	of	of	ADP
ejpam-3335	80	139	a	a	PRON
ejpam-3335	80	140	is	be	AUX
ejpam-3335	80	141	in	in	ADP
ejpam-3335	80	142	s	s	PROPN
ejpam-3335	80	143	,	,	PUNCT
ejpam-3335	80	144	and	and	CCONJ
ejpam-3335	80	145	(	(	PUNCT
ejpam-3335	80	146	ii	ii	NOUN
ejpam-3335	80	147	)	)	PUNCT
ejpam-3335	80	148	for	for	ADP
ejpam-3335	80	149	any	any	DET
ejpam-3335	80	150	x	x	NOUN
ejpam-3335	80	151	,	,	PUNCT
ejpam-3335	80	152	y	y	PROPN
ejpam-3335	80	153	,	,	PUNCT
ejpam-3335	80	154	z	z	PROPN
ejpam-3335	80	155	∈	∈	PROPN
ejpam-3335	80	156	a	a	DET
ejpam-3335	80	157	,	,	PUNCT
ejpam-3335	80	158	(	(	PUNCT
ejpam-3335	80	159	z	z	NOUN
ejpam-3335	80	160	·	·	PUNCT
ejpam-3335	80	161	y	y	X
ejpam-3335	80	162	)	)	PUNCT
ejpam-3335	80	163	·	·	PUNCT
ejpam-3335	81	1	(	(	PUNCT
ejpam-3335	81	2	z	z	NOUN
ejpam-3335	81	3	·	·	PUNCT
ejpam-3335	81	4	x	x	X
ejpam-3335	81	5	)	)	PUNCT
ejpam-3335	81	6	∈	∈	PROPN
ejpam-3335	81	7	s	s	PART
ejpam-3335	81	8	and	and	CCONJ
ejpam-3335	81	9	y	y	PROPN
ejpam-3335	81	10	∈	∈	PROPN
ejpam-3335	81	11	s	s	VERB
ejpam-3335	81	12	imply	imply	ADV
ejpam-3335	81	13	x	x	X
ejpam-3335	81	14	∈	∈	PROPN
ejpam-3335	81	15	s.	s.	PROPN
ejpam-3335	81	16	guntasow	guntasow	PROPN
ejpam-3335	81	17	et	et	PROPN
ejpam-3335	81	18	al	al	PROPN
ejpam-3335	81	19	.	.	PUNCT
ejpam-3335	82	1	[	[	X
ejpam-3335	82	2	1	1	X
ejpam-3335	82	3	]	]	PUNCT
ejpam-3335	82	4	proved	prove	VERB
ejpam-3335	82	5	the	the	DET
ejpam-3335	82	6	generalization	generalization	NOUN
ejpam-3335	82	7	that	that	SCONJ
ejpam-3335	82	8	the	the	DET
ejpam-3335	82	9	notion	notion	NOUN
ejpam-3335	82	10	of	of	ADP
ejpam-3335	82	11	up	up	ADV
ejpam-3335	82	12	-	-	PUNCT
ejpam-3335	82	13	subalgebras	subalgebras	PROPN
ejpam-3335	82	14	is	be	AUX
ejpam-3335	82	15	a	a	DET
ejpam-3335	82	16	generalization	generalization	NOUN
ejpam-3335	82	17	of	of	ADP
ejpam-3335	82	18	up	up	ADJ
ejpam-3335	82	19	-	-	PUNCT
ejpam-3335	82	20	filters	filter	NOUN
ejpam-3335	82	21	,	,	PUNCT
ejpam-3335	82	22	the	the	DET
ejpam-3335	82	23	notion	notion	NOUN
ejpam-3335	82	24	of	of	ADP
ejpam-3335	82	25	up	up	ADP
ejpam-3335	82	26	-	-	PUNCT
ejpam-3335	82	27	filters	filter	NOUN
ejpam-3335	82	28	is	be	AUX
ejpam-3335	82	29	a	a	DET
ejpam-3335	82	30	generalization	generalization	NOUN
ejpam-3335	82	31	of	of	ADP
ejpam-3335	82	32	up	up	ADJ
ejpam-3335	82	33	-	-	PUNCT
ejpam-3335	82	34	ideals	ideal	NOUN
ejpam-3335	82	35	,	,	PUNCT
ejpam-3335	82	36	and	and	CCONJ
ejpam-3335	82	37	the	the	DET
ejpam-3335	82	38	notion	notion	NOUN
ejpam-3335	82	39	of	of	ADP
ejpam-3335	82	40	up	up	ADJ
ejpam-3335	82	41	-	-	PUNCT
ejpam-3335	82	42	ideals	ideal	NOUN
ejpam-3335	82	43	is	be	AUX
ejpam-3335	82	44	a	a	DET
ejpam-3335	82	45	generalization	generalization	NOUN
ejpam-3335	82	46	of	of	ADP
ejpam-3335	82	47	strongly	strongly	ADV
ejpam-3335	82	48	up	up	ADJ
ejpam-3335	82	49	-	-	PUNCT
ejpam-3335	82	50	ideals	ideal	NOUN
ejpam-3335	82	51	.	.	PUNCT
ejpam-3335	83	1	moreover	moreover	ADV
ejpam-3335	83	2	,	,	PUNCT
ejpam-3335	83	3	they	they	PRON
ejpam-3335	83	4	also	also	ADV
ejpam-3335	83	5	proved	prove	VERB
ejpam-3335	83	6	that	that	SCONJ
ejpam-3335	83	7	a	a	DET
ejpam-3335	83	8	up	up	NOUN
ejpam-3335	83	9	-	-	PUNCT
ejpam-3335	83	10	algebra	algebra	NOUN
ejpam-3335	83	11	a	a	PRON
ejpam-3335	83	12	is	be	AUX
ejpam-3335	83	13	the	the	DET
ejpam-3335	83	14	only	only	ADJ
ejpam-3335	83	15	one	one	NUM
ejpam-3335	83	16	strongly	strongly	ADV
ejpam-3335	83	17	up	up	ADP
ejpam-3335	83	18	-	-	PUNCT
ejpam-3335	83	19	ideal	ideal	NOUN
ejpam-3335	83	20	of	of	ADP
ejpam-3335	83	21	itself	itself	PRON
ejpam-3335	83	22	.	.	PUNCT
ejpam-3335	84	1	3	3	X
ejpam-3335	84	2	.	.	X
ejpam-3335	84	3	basic	basic	ADJ
ejpam-3335	84	4	results	result	NOUN
ejpam-3335	84	5	on	on	ADP
ejpam-3335	84	6	hesitant	hesitant	ADJ
ejpam-3335	84	7	fuzzy	fuzzy	ADJ
ejpam-3335	84	8	sets	set	NOUN
ejpam-3335	84	9	definition	definition	NOUN
ejpam-3335	84	10	3	3	NUM
ejpam-3335	84	11	.	.	PUNCT
ejpam-3335	85	1	[	[	X
ejpam-3335	85	2	18	18	NUM
ejpam-3335	85	3	]	]	PUNCT
ejpam-3335	85	4	let	let	VERB
ejpam-3335	85	5	x	x	PRON
ejpam-3335	85	6	be	be	AUX
ejpam-3335	85	7	a	a	DET
ejpam-3335	85	8	reference	reference	NOUN
ejpam-3335	85	9	set	set	VERB
ejpam-3335	85	10	.	.	PUNCT
ejpam-3335	86	1	a	a	DET
ejpam-3335	86	2	hesitant	hesitant	ADJ
ejpam-3335	86	3	fuzzy	fuzzy	ADJ
ejpam-3335	86	4	set	set	NOUN
ejpam-3335	86	5	on	on	ADP
ejpam-3335	86	6	x	x	PUNCT
ejpam-3335	86	7	is	be	AUX
ejpam-3335	86	8	defined	define	VERB
ejpam-3335	86	9	in	in	ADP
ejpam-3335	86	10	term	term	NOUN
ejpam-3335	86	11	of	of	ADP
ejpam-3335	86	12	a	a	DET
ejpam-3335	86	13	function	function	NOUN
ejpam-3335	86	14	hh	hh	VERB
ejpam-3335	86	15	that	that	SCONJ
ejpam-3335	86	16	when	when	SCONJ
ejpam-3335	86	17	applied	apply	VERB
ejpam-3335	86	18	to	to	ADP
ejpam-3335	86	19	x	x	PART
ejpam-3335	86	20	return	return	VERB
ejpam-3335	86	21	a	a	DET
ejpam-3335	86	22	subset	subset	NOUN
ejpam-3335	86	23	of	of	ADP
ejpam-3335	86	24	[	[	X
ejpam-3335	86	25	0	0	NUM
ejpam-3335	86	26	,	,	PUNCT
ejpam-3335	86	27	1	1	NUM
ejpam-3335	86	28	]	]	PUNCT
ejpam-3335	86	29	,	,	PUNCT
ejpam-3335	86	30	that	that	ADV
ejpam-3335	86	31	is	is	ADV
ejpam-3335	86	32	,	,	PUNCT
ejpam-3335	86	33	hh	hh	INTJ
ejpam-3335	86	34	:	:	PUNCT
ejpam-3335	86	35	x	x	X
ejpam-3335	86	36	→	→	SYM
ejpam-3335	86	37	p([0	p([0	ADJ
ejpam-3335	86	38	,	,	PUNCT
ejpam-3335	86	39	1	1	NUM
ejpam-3335	86	40	]	]	NUM
ejpam-3335	86	41	)	)	PUNCT
ejpam-3335	86	42	.	.	PUNCT
ejpam-3335	87	1	a	a	DET
ejpam-3335	87	2	hesitant	hesitant	ADJ
ejpam-3335	87	3	fuzzy	fuzzy	ADJ
ejpam-3335	87	4	set	set	VERB
ejpam-3335	87	5	hh	hh	NOUN
ejpam-3335	87	6	can	can	AUX
ejpam-3335	87	7	also	also	ADV
ejpam-3335	87	8	be	be	AUX
ejpam-3335	87	9	viewed	view	VERB
ejpam-3335	87	10	as	as	ADP
ejpam-3335	87	11	the	the	DET
ejpam-3335	87	12	following	following	ADJ
ejpam-3335	87	13	mathematical	mathematical	ADJ
ejpam-3335	87	14	representation	representation	NOUN
ejpam-3335	87	15	:	:	PUNCT
ejpam-3335	87	16	h	h	NOUN
ejpam-3335	87	17	:	:	PUNCT
ejpam-3335	87	18	=	=	SYM
ejpam-3335	87	19	{	{	PUNCT
ejpam-3335	87	20	(	(	PUNCT
ejpam-3335	87	21	x	x	NOUN
ejpam-3335	87	22	,	,	PUNCT
ejpam-3335	87	23	hh(x	hh(x	NOUN
ejpam-3335	87	24	)	)	PUNCT
ejpam-3335	87	25	)	)	PUNCT
ejpam-3335	88	1	|	|	ADV
ejpam-3335	88	2	x	x	SYM
ejpam-3335	88	3	∈	∈	NOUN
ejpam-3335	88	4	x	x	X
ejpam-3335	88	5	}	}	PUNCT
ejpam-3335	88	6	where	where	SCONJ
ejpam-3335	88	7	hh(x	hh(x	X
ejpam-3335	88	8	)	)	PUNCT
ejpam-3335	88	9	is	be	AUX
ejpam-3335	88	10	a	a	DET
ejpam-3335	88	11	set	set	NOUN
ejpam-3335	88	12	of	of	ADP
ejpam-3335	88	13	some	some	DET
ejpam-3335	88	14	values	value	NOUN
ejpam-3335	88	15	in	in	ADP
ejpam-3335	88	16	[	[	X
ejpam-3335	88	17	0	0	NUM
ejpam-3335	88	18	,	,	PUNCT
ejpam-3335	88	19	1	1	NUM
ejpam-3335	88	20	]	]	PUNCT
ejpam-3335	88	21	,	,	PUNCT
ejpam-3335	88	22	denoting	denote	VERB
ejpam-3335	88	23	the	the	DET
ejpam-3335	88	24	possible	possible	ADJ
ejpam-3335	88	25	membership	membership	NOUN
ejpam-3335	88	26	degrees	degree	NOUN
ejpam-3335	88	27	of	of	ADP
ejpam-3335	88	28	the	the	DET
ejpam-3335	88	29	elements	element	NOUN
ejpam-3335	88	30	x	x	PUNCT
ejpam-3335	88	31	∈	∈	NOUN
ejpam-3335	88	32	x	x	X
ejpam-3335	88	33	to	to	ADP
ejpam-3335	88	34	the	the	DET
ejpam-3335	88	35	set	set	NOUN
ejpam-3335	88	36	h.	h.	NOUN
ejpam-3335	88	37	we	we	PRON
ejpam-3335	88	38	say	say	VERB
ejpam-3335	88	39	that	that	SCONJ
ejpam-3335	88	40	a	a	DET
ejpam-3335	88	41	hesitant	hesitant	ADJ
ejpam-3335	88	42	fuzzy	fuzzy	ADJ
ejpam-3335	88	43	set	set	VERB
ejpam-3335	88	44	h	h	NOUN
ejpam-3335	88	45	on	on	ADP
ejpam-3335	88	46	x	x	PUNCT
ejpam-3335	88	47	is	be	AUX
ejpam-3335	88	48	a	a	DET
ejpam-3335	88	49	constant	constant	ADJ
ejpam-3335	88	50	hesitant	hesitant	ADJ
ejpam-3335	88	51	fuzzy	fuzzy	ADJ
ejpam-3335	88	52	set	set	NOUN
ejpam-3335	88	53	if	if	SCONJ
ejpam-3335	88	54	its	its	PRON
ejpam-3335	88	55	function	function	NOUN
ejpam-3335	88	56	hh	hh	VERB
ejpam-3335	88	57	is	be	AUX
ejpam-3335	88	58	constant	constant	ADJ
ejpam-3335	88	59	.	.	PUNCT
ejpam-3335	89	1	definition	definition	NOUN
ejpam-3335	89	2	4	4	NUM
ejpam-3335	89	3	.	.	PUNCT
ejpam-3335	90	1	[	[	X
ejpam-3335	90	2	6	6	NUM
ejpam-3335	90	3	]	]	PUNCT
ejpam-3335	90	4	let	let	VERB
ejpam-3335	90	5	h	h	PRON
ejpam-3335	90	6	be	be	AUX
ejpam-3335	90	7	a	a	DET
ejpam-3335	90	8	hesitant	hesitant	ADJ
ejpam-3335	90	9	fuzzy	fuzzy	ADJ
ejpam-3335	90	10	set	set	NOUN
ejpam-3335	90	11	on	on	ADP
ejpam-3335	90	12	a.	a.	NOUN
ejpam-3335	90	13	the	the	DET
ejpam-3335	90	14	hesitant	hesitant	ADJ
ejpam-3335	90	15	fuzzy	fuzzy	ADJ
ejpam-3335	90	16	set	set	NOUN
ejpam-3335	90	17	h	h	NOUN
ejpam-3335	90	18	defined	define	VERB
ejpam-3335	90	19	by	by	ADP
ejpam-3335	90	20	hh(x	hh(x	NOUN
ejpam-3335	90	21	)	)	PUNCT
ejpam-3335	90	22	=	=	PUNCT
ejpam-3335	91	1	[	[	X
ejpam-3335	91	2	0	0	NUM
ejpam-3335	91	3	,	,	PUNCT
ejpam-3335	91	4	1]−	1]−	NUM
ejpam-3335	91	5	hh(x	hh(x	NOUN
ejpam-3335	91	6	)	)	PUNCT
ejpam-3335	91	7	for	for	ADP
ejpam-3335	91	8	all	all	DET
ejpam-3335	91	9	x	x	SYM
ejpam-3335	91	10	∈	∈	PROPN
ejpam-3335	91	11	a	a	PRON
ejpam-3335	91	12	is	be	AUX
ejpam-3335	91	13	said	say	VERB
ejpam-3335	91	14	to	to	PART
ejpam-3335	91	15	be	be	AUX
ejpam-3335	91	16	the	the	DET
ejpam-3335	91	17	complement	complement	NOUN
ejpam-3335	91	18	of	of	ADP
ejpam-3335	91	19	h	h	NOUN
ejpam-3335	91	20	on	on	ADP
ejpam-3335	91	21	a.	a.	NOUN
ejpam-3335	91	22	remark	remark	NOUN
ejpam-3335	91	23	1	1	NUM
ejpam-3335	91	24	.	.	PUNCT
ejpam-3335	92	1	[	[	X
ejpam-3335	92	2	6	6	NUM
ejpam-3335	92	3	]	]	PUNCT
ejpam-3335	92	4	for	for	ADP
ejpam-3335	92	5	all	all	DET
ejpam-3335	92	6	hesitant	hesitant	ADJ
ejpam-3335	92	7	fuzzy	fuzzy	ADJ
ejpam-3335	92	8	set	set	VERB
ejpam-3335	92	9	h	h	NOUN
ejpam-3335	92	10	on	on	ADP
ejpam-3335	92	11	a	a	PRON
ejpam-3335	92	12	,	,	PUNCT
ejpam-3335	92	13	we	we	PRON
ejpam-3335	92	14	have	have	VERB
ejpam-3335	92	15	h	h	NOUN
ejpam-3335	92	16	=	=	SYM
ejpam-3335	92	17	h.	h.	PROPN
ejpam-3335	92	18	theorem	theorem	VERB
ejpam-3335	92	19	1	1	NUM
ejpam-3335	92	20	.	.	PUNCT
ejpam-3335	93	1	a	a	DET
ejpam-3335	93	2	hesitant	hesitant	ADJ
ejpam-3335	93	3	fuzzy	fuzzy	ADJ
ejpam-3335	93	4	set	set	NOUN
ejpam-3335	93	5	h	h	NOUN
ejpam-3335	93	6	is	be	AUX
ejpam-3335	93	7	a	a	DET
ejpam-3335	93	8	constant	constant	ADJ
ejpam-3335	93	9	hesitant	hesitant	ADJ
ejpam-3335	93	10	fuzzy	fuzzy	ADJ
ejpam-3335	93	11	set	set	VERB
ejpam-3335	93	12	on	on	ADP
ejpam-3335	93	13	a	a	DET
ejpam-3335	93	14	if	if	NOUN
ejpam-3335	93	15	and	and	CCONJ
ejpam-3335	93	16	only	only	ADV
ejpam-3335	93	17	if	if	SCONJ
ejpam-3335	93	18	the	the	DET
ejpam-3335	93	19	complement	complement	NOUN
ejpam-3335	93	20	of	of	ADP
ejpam-3335	93	21	h	h	NOUN
ejpam-3335	93	22	is	be	AUX
ejpam-3335	93	23	a	a	DET
ejpam-3335	93	24	constant	constant	ADJ
ejpam-3335	93	25	hesitant	hesitant	ADJ
ejpam-3335	93	26	fuzzy	fuzzy	ADJ
ejpam-3335	93	27	set	set	VERB
ejpam-3335	93	28	on	on	ADP
ejpam-3335	93	29	a.	a.	NOUN
ejpam-3335	93	30	proof	proof	NOUN
ejpam-3335	93	31	.	.	PUNCT
ejpam-3335	94	1	let	let	VERB
ejpam-3335	94	2	h	h	PRON
ejpam-3335	94	3	be	be	AUX
ejpam-3335	94	4	a	a	DET
ejpam-3335	94	5	constant	constant	ADJ
ejpam-3335	94	6	hesitant	hesitant	ADJ
ejpam-3335	94	7	fuzzy	fuzzy	ADJ
ejpam-3335	94	8	set	set	VERB
ejpam-3335	94	9	on	on	ADP
ejpam-3335	94	10	a.	a.	NOUN
ejpam-3335	94	11	then	then	ADV
ejpam-3335	94	12	hh(x	hh(x	PRON
ejpam-3335	94	13	)	)	PUNCT
ejpam-3335	95	1	=	=	SYM
ejpam-3335	95	2	hh(0	hh(0	NOUN
ejpam-3335	95	3	)	)	PUNCT
ejpam-3335	95	4	for	for	ADP
ejpam-3335	95	5	all	all	PRON
ejpam-3335	95	6	x	x	SYM
ejpam-3335	95	7	∈	∈	NOUN
ejpam-3335	95	8	a.	a.	NOUN
ejpam-3335	95	9	thus	thus	ADV
ejpam-3335	95	10	[	[	X
ejpam-3335	95	11	0	0	NUM
ejpam-3335	95	12	,	,	PUNCT
ejpam-3335	95	13	1]−	1]−	NUM
ejpam-3335	95	14	hh(x	hh(x	NOUN
ejpam-3335	95	15	)	)	PUNCT
ejpam-3335	95	16	=	=	PUNCT
ejpam-3335	96	1	[	[	X
ejpam-3335	96	2	0	0	NUM
ejpam-3335	96	3	,	,	PUNCT
ejpam-3335	96	4	1]−	1]−	NUM
ejpam-3335	96	5	hh(0	hh(0	NOUN
ejpam-3335	96	6	)	)	PUNCT
ejpam-3335	96	7	for	for	ADP
ejpam-3335	96	8	all	all	DET
ejpam-3335	96	9	x	x	SYM
ejpam-3335	96	10	∈	∈	PROPN
ejpam-3335	96	11	a.	a.	NOUN
ejpam-3335	96	12	therefore	therefore	ADV
ejpam-3335	96	13	,	,	PUNCT
ejpam-3335	96	14	hh(x	hh(x	X
ejpam-3335	96	15	)	)	PUNCT
ejpam-3335	96	16	=	=	SYM
ejpam-3335	97	1	hh(0	hh(0	NOUN
ejpam-3335	97	2	)	)	PUNCT
ejpam-3335	97	3	for	for	ADP
ejpam-3335	97	4	all	all	PRON
ejpam-3335	97	5	x	x	SYM
ejpam-3335	97	6	∈	∈	NOUN
ejpam-3335	97	7	a.	a.	NOUN
ejpam-3335	97	8	hence	hence	ADV
ejpam-3335	97	9	,	,	PUNCT
ejpam-3335	97	10	h	h	NOUN
ejpam-3335	97	11	is	be	AUX
ejpam-3335	97	12	a	a	DET
ejpam-3335	97	13	constant	constant	ADJ
ejpam-3335	97	14	hesitant	hesitant	ADJ
ejpam-3335	97	15	fuzzy	fuzzy	ADJ
ejpam-3335	97	16	set	set	VERB
ejpam-3335	97	17	on	on	ADP
ejpam-3335	97	18	a.	a.	NOUN
ejpam-3335	97	19	conversely	conversely	ADV
ejpam-3335	97	20	,	,	PUNCT
ejpam-3335	97	21	let	let	VERB
ejpam-3335	97	22	h	h	PRON
ejpam-3335	97	23	be	be	AUX
ejpam-3335	97	24	a	a	DET
ejpam-3335	97	25	constant	constant	ADJ
ejpam-3335	97	26	hesitant	hesitant	ADJ
ejpam-3335	97	27	fuzzy	fuzzy	ADJ
ejpam-3335	97	28	set	set	VERB
ejpam-3335	97	29	on	on	ADP
ejpam-3335	97	30	a.	a.	NOUN
ejpam-3335	97	31	then	then	ADV
ejpam-3335	97	32	hh(x	hh(x	PRON
ejpam-3335	97	33	)	)	PUNCT
ejpam-3335	98	1	=	=	SYM
ejpam-3335	98	2	hh(0	hh(0	NOUN
ejpam-3335	98	3	)	)	PUNCT
ejpam-3335	98	4	for	for	ADP
ejpam-3335	98	5	all	all	PRON
ejpam-3335	98	6	x	x	SYM
ejpam-3335	98	7	∈	∈	NOUN
ejpam-3335	98	8	a.	a.	NOUN
ejpam-3335	98	9	thus	thus	ADV
ejpam-3335	98	10	[	[	X
ejpam-3335	98	11	0	0	NUM
ejpam-3335	98	12	,	,	PUNCT
ejpam-3335	98	13	1]−	1]−	NUM
ejpam-3335	98	14	hh(x	hh(x	NOUN
ejpam-3335	98	15	)	)	PUNCT
ejpam-3335	98	16	=	=	PUNCT
ejpam-3335	99	1	[	[	X
ejpam-3335	99	2	0	0	NUM
ejpam-3335	99	3	,	,	PUNCT
ejpam-3335	99	4	1]−	1]−	NUM
ejpam-3335	99	5	hh(0	hh(0	NOUN
ejpam-3335	99	6	)	)	PUNCT
ejpam-3335	99	7	for	for	ADP
ejpam-3335	99	8	all	all	DET
ejpam-3335	99	9	x	x	SYM
ejpam-3335	99	10	∈	∈	PROPN
ejpam-3335	99	11	a.	a.	NOUN
ejpam-3335	99	12	therefore	therefore	ADV
ejpam-3335	99	13	,	,	PUNCT
ejpam-3335	99	14	hh(x	hh(x	X
ejpam-3335	99	15	)	)	PUNCT
ejpam-3335	99	16	=	=	SYM
ejpam-3335	100	1	hh(0	hh(0	NOUN
ejpam-3335	100	2	)	)	PUNCT
ejpam-3335	100	3	for	for	ADP
ejpam-3335	100	4	all	all	PRON
ejpam-3335	100	5	x	x	SYM
ejpam-3335	100	6	∈	∈	NOUN
ejpam-3335	100	7	a.	a.	NOUN
ejpam-3335	100	8	hence	hence	ADV
ejpam-3335	100	9	,	,	PUNCT
ejpam-3335	100	10	h	h	NOUN
ejpam-3335	100	11	is	be	AUX
ejpam-3335	100	12	a	a	DET
ejpam-3335	100	13	constant	constant	ADJ
ejpam-3335	100	14	hesitant	hesitant	ADJ
ejpam-3335	100	15	fuzzy	fuzzy	ADJ
ejpam-3335	100	16	set	set	VERB
ejpam-3335	100	17	on	on	ADP
ejpam-3335	100	18	a.	a.	PROPN
ejpam-3335	100	19	p.	p.	PROPN
ejpam-3335	100	20	mosrijai	mosrijai	PROPN
ejpam-3335	100	21	,	,	PUNCT
ejpam-3335	100	22	a.	a.	NOUN
ejpam-3335	100	23	iampan	iampan	PROPN
ejpam-3335	100	24	/	/	SYM
ejpam-3335	100	25	eur	eur	PROPN
ejpam-3335	100	26	.	.	PUNCT
ejpam-3335	101	1	j.	j.	PROPN
ejpam-3335	101	2	pure	pure	PROPN
ejpam-3335	101	3	appl	appl	PROPN
ejpam-3335	101	4	.	.	PROPN
ejpam-3335	101	5	math	math	PROPN
ejpam-3335	101	6	,	,	PUNCT
ejpam-3335	101	7	11	11	NUM
ejpam-3335	101	8	(	(	PUNCT
ejpam-3335	101	9	4	4	NUM
ejpam-3335	101	10	)	)	PUNCT
ejpam-3335	101	11	(	(	PUNCT
ejpam-3335	101	12	2018	2018	NUM
ejpam-3335	101	13	)	)	PUNCT
ejpam-3335	101	14	,	,	PUNCT
ejpam-3335	101	15	976	976	NUM
ejpam-3335	101	16	-	-	SYM
ejpam-3335	101	17	1002	1002	NUM
ejpam-3335	101	18	980	980	NUM
ejpam-3335	101	19	definition	definition	NOUN
ejpam-3335	101	20	5	5	NUM
ejpam-3335	101	21	.	.	PUNCT
ejpam-3335	102	1	[	[	X
ejpam-3335	102	2	6	6	NUM
ejpam-3335	102	3	]	]	PUNCT
ejpam-3335	102	4	a	a	DET
ejpam-3335	102	5	hesitant	hesitant	ADJ
ejpam-3335	102	6	fuzzy	fuzzy	ADJ
ejpam-3335	102	7	set	set	VERB
ejpam-3335	102	8	h	h	NOUN
ejpam-3335	102	9	on	on	ADP
ejpam-3335	102	10	a	a	DET
ejpam-3335	102	11	a	a	PRON
ejpam-3335	102	12	is	be	AUX
ejpam-3335	102	13	called	call	VERB
ejpam-3335	102	14	(	(	PUNCT
ejpam-3335	102	15	1	1	NUM
ejpam-3335	102	16	)	)	PUNCT
ejpam-3335	102	17	a	a	DET
ejpam-3335	102	18	hesitant	hesitant	ADJ
ejpam-3335	102	19	fuzzy	fuzzy	ADJ
ejpam-3335	102	20	up	up	NOUN
ejpam-3335	102	21	-	-	PUNCT
ejpam-3335	102	22	subalgebra	subalgebra	NOUN
ejpam-3335	102	23	of	of	ADP
ejpam-3335	102	24	a	a	PRON
ejpam-3335	102	25	if	if	SCONJ
ejpam-3335	102	26	it	it	PRON
ejpam-3335	102	27	satisfies	satisfy	VERB
ejpam-3335	102	28	the	the	DET
ejpam-3335	102	29	following	follow	VERB
ejpam-3335	102	30	property	property	NOUN
ejpam-3335	102	31	:	:	PUNCT
ejpam-3335	102	32	for	for	ADP
ejpam-3335	102	33	any	any	DET
ejpam-3335	102	34	x	x	NOUN
ejpam-3335	102	35	,	,	PUNCT
ejpam-3335	102	36	y	y	PROPN
ejpam-3335	102	37	∈	∈	PROPN
ejpam-3335	102	38	a	a	PRON
ejpam-3335	102	39	,	,	PUNCT
ejpam-3335	102	40	hh(x	hh(x	PUNCT
ejpam-3335	102	41	·	·	PUNCT
ejpam-3335	102	42	y	y	X
ejpam-3335	102	43	)	)	PUNCT
ejpam-3335	102	44	⊇	⊇	NOUN
ejpam-3335	102	45	hh(x	hh(x	X
ejpam-3335	102	46	)	)	PUNCT
ejpam-3335	102	47	∩	∩	NOUN
ejpam-3335	102	48	hh(y	hh(y	NUM
ejpam-3335	102	49	)	)	PUNCT
ejpam-3335	102	50	.	.	PUNCT
ejpam-3335	103	1	(	(	PUNCT
ejpam-3335	103	2	2	2	X
ejpam-3335	103	3	)	)	PUNCT
ejpam-3335	103	4	a	a	DET
ejpam-3335	103	5	hesitant	hesitant	ADJ
ejpam-3335	103	6	fuzzy	fuzzy	ADJ
ejpam-3335	103	7	up	up	NOUN
ejpam-3335	103	8	-	-	PUNCT
ejpam-3335	103	9	filter	filter	NOUN
ejpam-3335	103	10	of	of	ADP
ejpam-3335	103	11	a	a	PRON
ejpam-3335	103	12	if	if	SCONJ
ejpam-3335	103	13	it	it	PRON
ejpam-3335	103	14	satisfies	satisfy	VERB
ejpam-3335	103	15	the	the	DET
ejpam-3335	103	16	following	follow	VERB
ejpam-3335	103	17	properties	property	NOUN
ejpam-3335	103	18	:	:	PUNCT
ejpam-3335	103	19	for	for	ADP
ejpam-3335	103	20	any	any	DET
ejpam-3335	103	21	x	x	NOUN
ejpam-3335	103	22	,	,	PUNCT
ejpam-3335	103	23	y	y	PROPN
ejpam-3335	103	24	∈	∈	PROPN
ejpam-3335	103	25	a	a	DET
ejpam-3335	103	26	,	,	PUNCT
ejpam-3335	103	27	(	(	PUNCT
ejpam-3335	103	28	1	1	X
ejpam-3335	103	29	)	)	PUNCT
ejpam-3335	103	30	hh(0	hh(0	NOUN
ejpam-3335	103	31	)	)	PUNCT
ejpam-3335	103	32	⊇	⊇	NOUN
ejpam-3335	103	33	hh(x	hh(x	NOUN
ejpam-3335	103	34	)	)	PUNCT
ejpam-3335	103	35	,	,	PUNCT
ejpam-3335	103	36	and	and	CCONJ
ejpam-3335	103	37	(	(	PUNCT
ejpam-3335	103	38	2	2	NUM
ejpam-3335	103	39	)	)	PUNCT
ejpam-3335	103	40	hh(y	hh(y	ADJ
ejpam-3335	103	41	)	)	PUNCT
ejpam-3335	103	42	⊇	⊇	NOUN
ejpam-3335	103	43	hh(x	hh(x	X
ejpam-3335	103	44	·	·	PUNCT
ejpam-3335	103	45	y	y	X
ejpam-3335	103	46	)	)	PUNCT
ejpam-3335	103	47	∩	∩	NOUN
ejpam-3335	103	48	hh(x	hh(x	X
ejpam-3335	103	49	)	)	PUNCT
ejpam-3335	103	50	.	.	PUNCT
ejpam-3335	104	1	(	(	PUNCT
ejpam-3335	104	2	3	3	X
ejpam-3335	104	3	)	)	PUNCT
ejpam-3335	104	4	a	a	DET
ejpam-3335	104	5	hesitant	hesitant	ADJ
ejpam-3335	104	6	fuzzy	fuzzy	ADJ
ejpam-3335	104	7	up	up	NOUN
ejpam-3335	104	8	-	-	PUNCT
ejpam-3335	104	9	ideal	ideal	NOUN
ejpam-3335	104	10	of	of	ADP
ejpam-3335	104	11	a	a	PRON
ejpam-3335	104	12	if	if	SCONJ
ejpam-3335	104	13	it	it	PRON
ejpam-3335	104	14	satisfies	satisfy	VERB
ejpam-3335	104	15	the	the	DET
ejpam-3335	104	16	following	follow	VERB
ejpam-3335	104	17	properties	property	NOUN
ejpam-3335	104	18	:	:	PUNCT
ejpam-3335	104	19	for	for	ADP
ejpam-3335	104	20	any	any	DET
ejpam-3335	104	21	x	x	NOUN
ejpam-3335	104	22	,	,	PUNCT
ejpam-3335	104	23	y	y	PROPN
ejpam-3335	104	24	,	,	PUNCT
ejpam-3335	104	25	z	z	PROPN
ejpam-3335	104	26	∈	∈	PROPN
ejpam-3335	105	1	a	a	DET
ejpam-3335	105	2	,	,	PUNCT
ejpam-3335	105	3	(	(	PUNCT
ejpam-3335	105	4	1	1	X
ejpam-3335	105	5	)	)	PUNCT
ejpam-3335	105	6	hh(0	hh(0	NOUN
ejpam-3335	105	7	)	)	PUNCT
ejpam-3335	105	8	⊇	⊇	NOUN
ejpam-3335	105	9	hh(x	hh(x	NOUN
ejpam-3335	105	10	)	)	PUNCT
ejpam-3335	105	11	,	,	PUNCT
ejpam-3335	105	12	and	and	CCONJ
ejpam-3335	105	13	(	(	PUNCT
ejpam-3335	105	14	2	2	NUM
ejpam-3335	105	15	)	)	PUNCT
ejpam-3335	105	16	hh(x	hh(x	X
ejpam-3335	105	17	·	·	PUNCT
ejpam-3335	105	18	z	z	X
ejpam-3335	105	19	)	)	PUNCT
ejpam-3335	105	20	⊇	⊇	NOUN
ejpam-3335	105	21	hh(x	hh(x	X
ejpam-3335	105	22	·	·	PUNCT
ejpam-3335	105	23	(	(	PUNCT
ejpam-3335	105	24	y	y	PROPN
ejpam-3335	105	25	·	·	PUNCT
ejpam-3335	105	26	z	z	NOUN
ejpam-3335	105	27	)	)	PUNCT
ejpam-3335	105	28	)	)	PUNCT
ejpam-3335	105	29	∩	∩	NOUN
ejpam-3335	105	30	hh(y	hh(y	NUM
ejpam-3335	105	31	)	)	PUNCT
ejpam-3335	105	32	.	.	PUNCT
ejpam-3335	106	1	(	(	PUNCT
ejpam-3335	106	2	4	4	X
ejpam-3335	106	3	)	)	PUNCT
ejpam-3335	106	4	a	a	PRON
ejpam-3335	106	5	hesitant	hesitant	ADJ
ejpam-3335	106	6	fuzzy	fuzzy	ADJ
ejpam-3335	106	7	strongly	strongly	ADV
ejpam-3335	106	8	up	up	ADP
ejpam-3335	106	9	-	-	PUNCT
ejpam-3335	106	10	ideal	ideal	NOUN
ejpam-3335	106	11	of	of	ADP
ejpam-3335	106	12	a	a	PRON
ejpam-3335	106	13	if	if	SCONJ
ejpam-3335	106	14	it	it	PRON
ejpam-3335	106	15	satisfies	satisfy	VERB
ejpam-3335	106	16	the	the	DET
ejpam-3335	106	17	following	follow	VERB
ejpam-3335	106	18	properties	property	NOUN
ejpam-3335	106	19	:	:	PUNCT
ejpam-3335	106	20	for	for	ADP
ejpam-3335	106	21	any	any	DET
ejpam-3335	106	22	x	x	NOUN
ejpam-3335	106	23	,	,	PUNCT
ejpam-3335	106	24	y	y	PROPN
ejpam-3335	106	25	,	,	PUNCT
ejpam-3335	106	26	z	z	PROPN
ejpam-3335	106	27	∈	∈	PROPN
ejpam-3335	106	28	a	a	DET
ejpam-3335	106	29	,	,	PUNCT
ejpam-3335	106	30	(	(	PUNCT
ejpam-3335	106	31	1	1	X
ejpam-3335	106	32	)	)	PUNCT
ejpam-3335	106	33	hh(0	hh(0	NOUN
ejpam-3335	106	34	)	)	PUNCT
ejpam-3335	106	35	⊇	⊇	NOUN
ejpam-3335	106	36	hh(x	hh(x	NOUN
ejpam-3335	106	37	)	)	PUNCT
ejpam-3335	106	38	,	,	PUNCT
ejpam-3335	106	39	and	and	CCONJ
ejpam-3335	106	40	(	(	PUNCT
ejpam-3335	106	41	2	2	NUM
ejpam-3335	106	42	)	)	PUNCT
ejpam-3335	106	43	hh(x	hh(x	NOUN
ejpam-3335	106	44	)	)	PUNCT
ejpam-3335	107	1	⊇	⊇	PROPN
ejpam-3335	107	2	hh((z	hh((z	PROPN
ejpam-3335	107	3	·	·	PUNCT
ejpam-3335	107	4	y	y	X
ejpam-3335	107	5	)	)	PUNCT
ejpam-3335	107	6	·	·	PUNCT
ejpam-3335	107	7	(	(	PUNCT
ejpam-3335	107	8	z	z	NOUN
ejpam-3335	107	9	·	·	PUNCT
ejpam-3335	107	10	x	x	X
ejpam-3335	107	11	)	)	PUNCT
ejpam-3335	107	12	)	)	PUNCT
ejpam-3335	107	13	∩	∩	NOUN
ejpam-3335	107	14	hh(y	hh(y	NUM
ejpam-3335	107	15	)	)	PUNCT
ejpam-3335	107	16	.	.	PUNCT
ejpam-3335	108	1	mosrijai	mosrijai	PROPN
ejpam-3335	108	2	et	et	PROPN
ejpam-3335	108	3	al	al	PROPN
ejpam-3335	108	4	.	.	PUNCT
ejpam-3335	109	1	[	[	X
ejpam-3335	109	2	6	6	NUM
ejpam-3335	109	3	]	]	PUNCT
ejpam-3335	109	4	proved	prove	VERB
ejpam-3335	109	5	that	that	SCONJ
ejpam-3335	109	6	the	the	DET
ejpam-3335	109	7	notion	notion	NOUN
ejpam-3335	109	8	of	of	ADP
ejpam-3335	109	9	hesitant	hesitant	ADJ
ejpam-3335	109	10	fuzzy	fuzzy	ADJ
ejpam-3335	109	11	up	up	NOUN
ejpam-3335	109	12	-	-	PUNCT
ejpam-3335	109	13	subalgebras	subalgebra	NOUN
ejpam-3335	109	14	of	of	ADP
ejpam-3335	109	15	upalgebras	upalgebra	NOUN
ejpam-3335	109	16	is	be	AUX
ejpam-3335	109	17	a	a	DET
ejpam-3335	109	18	generalization	generalization	NOUN
ejpam-3335	109	19	of	of	ADP
ejpam-3335	109	20	hesitant	hesitant	ADJ
ejpam-3335	109	21	fuzzy	fuzzy	ADJ
ejpam-3335	109	22	up	up	NOUN
ejpam-3335	109	23	-	-	PUNCT
ejpam-3335	109	24	filters	filter	NOUN
ejpam-3335	109	25	,	,	PUNCT
ejpam-3335	109	26	the	the	DET
ejpam-3335	109	27	notion	notion	NOUN
ejpam-3335	109	28	of	of	ADP
ejpam-3335	109	29	hesitant	hesitant	ADJ
ejpam-3335	109	30	fuzzy	fuzzy	ADJ
ejpam-3335	109	31	upfilters	upfilter	NOUN
ejpam-3335	109	32	of	of	ADP
ejpam-3335	109	33	up	up	ADV
ejpam-3335	109	34	-	-	PUNCT
ejpam-3335	109	35	algebras	algebras	PROPN
ejpam-3335	109	36	is	be	AUX
ejpam-3335	109	37	a	a	DET
ejpam-3335	109	38	generalization	generalization	NOUN
ejpam-3335	109	39	of	of	ADP
ejpam-3335	109	40	hesitant	hesitant	ADJ
ejpam-3335	109	41	fuzzy	fuzzy	ADJ
ejpam-3335	109	42	up	up	NOUN
ejpam-3335	109	43	-	-	PUNCT
ejpam-3335	109	44	ideals	ideal	NOUN
ejpam-3335	109	45	,	,	PUNCT
ejpam-3335	109	46	and	and	CCONJ
ejpam-3335	109	47	the	the	DET
ejpam-3335	109	48	notion	notion	NOUN
ejpam-3335	109	49	of	of	ADP
ejpam-3335	109	50	hesitant	hesitant	ADJ
ejpam-3335	109	51	fuzzy	fuzzy	ADJ
ejpam-3335	109	52	up	up	NOUN
ejpam-3335	109	53	-	-	PUNCT
ejpam-3335	109	54	ideals	ideal	NOUN
ejpam-3335	109	55	of	of	ADP
ejpam-3335	109	56	up	up	ADV
ejpam-3335	109	57	-	-	PUNCT
ejpam-3335	109	58	algebras	algebras	PROPN
ejpam-3335	109	59	is	be	AUX
ejpam-3335	109	60	a	a	DET
ejpam-3335	109	61	generalization	generalization	NOUN
ejpam-3335	109	62	of	of	ADP
ejpam-3335	109	63	hesitant	hesitant	ADJ
ejpam-3335	109	64	fuzzy	fuzzy	ADJ
ejpam-3335	109	65	strongly	strongly	ADV
ejpam-3335	109	66	upideals	upideal	NOUN
ejpam-3335	109	67	.	.	PUNCT
ejpam-3335	110	1	theorem	theorem	NOUN
ejpam-3335	110	2	2	2	NUM
ejpam-3335	110	3	.	.	PUNCT
ejpam-3335	111	1	[	[	X
ejpam-3335	111	2	6	6	NUM
ejpam-3335	111	3	]	]	PUNCT
ejpam-3335	111	4	a	a	DET
ejpam-3335	111	5	hesitant	hesitant	ADJ
ejpam-3335	111	6	fuzzy	fuzzy	ADJ
ejpam-3335	111	7	set	set	VERB
ejpam-3335	111	8	h	h	NOUN
ejpam-3335	111	9	on	on	ADP
ejpam-3335	111	10	a	a	PRON
ejpam-3335	111	11	is	be	AUX
ejpam-3335	111	12	a	a	DET
ejpam-3335	111	13	hesitant	hesitant	ADJ
ejpam-3335	111	14	fuzzy	fuzzy	ADJ
ejpam-3335	111	15	strongly	strongly	ADV
ejpam-3335	111	16	up	up	ADP
ejpam-3335	111	17	-	-	PUNCT
ejpam-3335	111	18	ideal	ideal	NOUN
ejpam-3335	111	19	of	of	ADP
ejpam-3335	111	20	a	a	DET
ejpam-3335	111	21	if	if	NOUN
ejpam-3335	111	22	and	and	CCONJ
ejpam-3335	111	23	only	only	ADV
ejpam-3335	111	24	if	if	SCONJ
ejpam-3335	111	25	it	it	PRON
ejpam-3335	111	26	is	be	AUX
ejpam-3335	111	27	a	a	DET
ejpam-3335	111	28	constant	constant	ADJ
ejpam-3335	111	29	hesitant	hesitant	ADJ
ejpam-3335	111	30	fuzzy	fuzzy	ADJ
ejpam-3335	111	31	set	set	VERB
ejpam-3335	111	32	on	on	ADP
ejpam-3335	111	33	a.	a.	NOUN
ejpam-3335	111	34	4	4	NUM
ejpam-3335	111	35	.	.	PUNCT
ejpam-3335	111	36	anti	anti	ADJ
ejpam-3335	111	37	-	-	ADJ
ejpam-3335	111	38	type	type	NOUN
ejpam-3335	111	39	of	of	ADP
ejpam-3335	111	40	hesitant	hesitant	ADJ
ejpam-3335	111	41	fuzzy	fuzzy	ADJ
ejpam-3335	111	42	sets	set	NOUN
ejpam-3335	111	43	in	in	ADP
ejpam-3335	111	44	this	this	DET
ejpam-3335	111	45	section	section	NOUN
ejpam-3335	111	46	,	,	PUNCT
ejpam-3335	111	47	we	we	PRON
ejpam-3335	111	48	introduce	introduce	VERB
ejpam-3335	111	49	the	the	DET
ejpam-3335	111	50	notions	notion	NOUN
ejpam-3335	111	51	of	of	ADP
ejpam-3335	111	52	anti	anti	ADJ
ejpam-3335	111	53	-	-	ADJ
ejpam-3335	111	54	hesitant	hesitant	ADJ
ejpam-3335	111	55	fuzzy	fuzzy	ADJ
ejpam-3335	111	56	up	up	ADP
ejpam-3335	111	57	-	-	PUNCT
ejpam-3335	111	58	subalgebras	subalgebras	PROPN
ejpam-3335	111	59	,	,	PUNCT
ejpam-3335	111	60	antihesitant	antihesitant	NOUN
ejpam-3335	111	61	fuzzy	fuzzy	ADJ
ejpam-3335	111	62	up	up	ADP
ejpam-3335	111	63	-	-	PUNCT
ejpam-3335	111	64	filters	filter	NOUN
ejpam-3335	111	65	,	,	PUNCT
ejpam-3335	111	66	anti	anti	ADJ
ejpam-3335	111	67	-	-	ADJ
ejpam-3335	111	68	hesitant	hesitant	ADJ
ejpam-3335	111	69	fuzzy	fuzzy	ADJ
ejpam-3335	111	70	up	up	NOUN
ejpam-3335	111	71	-	-	PUNCT
ejpam-3335	111	72	ideals	ideal	NOUN
ejpam-3335	111	73	and	and	CCONJ
ejpam-3335	111	74	anti	anti	ADJ
ejpam-3335	111	75	-	-	ADJ
ejpam-3335	111	76	hesitant	hesitant	ADJ
ejpam-3335	111	77	fuzzy	fuzzy	ADJ
ejpam-3335	111	78	strongly	strongly	ADV
ejpam-3335	111	79	up	up	ADP
ejpam-3335	111	80	-	-	PUNCT
ejpam-3335	111	81	ideals	ideal	NOUN
ejpam-3335	111	82	of	of	ADP
ejpam-3335	111	83	up	up	ADP
ejpam-3335	111	84	-	-	PUNCT
ejpam-3335	111	85	algebras	algebras	X
ejpam-3335	111	86	,	,	PUNCT
ejpam-3335	111	87	provide	provide	VERB
ejpam-3335	111	88	the	the	DET
ejpam-3335	111	89	necessary	necessary	ADJ
ejpam-3335	111	90	examples	example	NOUN
ejpam-3335	111	91	and	and	CCONJ
ejpam-3335	111	92	prove	prove	VERB
ejpam-3335	111	93	its	its	PRON
ejpam-3335	111	94	generalizations	generalization	NOUN
ejpam-3335	111	95	.	.	PUNCT
ejpam-3335	112	1	definition	definition	NOUN
ejpam-3335	112	2	6	6	NUM
ejpam-3335	112	3	.	.	PUNCT
ejpam-3335	113	1	a	a	DET
ejpam-3335	113	2	hesitant	hesitant	ADJ
ejpam-3335	113	3	fuzzy	fuzzy	ADJ
ejpam-3335	113	4	set	set	VERB
ejpam-3335	113	5	h	h	NOUN
ejpam-3335	113	6	on	on	ADP
ejpam-3335	113	7	a	a	DET
ejpam-3335	113	8	a	a	PRON
ejpam-3335	113	9	is	be	AUX
ejpam-3335	113	10	called	call	VERB
ejpam-3335	113	11	an	an	DET
ejpam-3335	113	12	anti	anti	ADJ
ejpam-3335	113	13	-	-	ADJ
ejpam-3335	113	14	hesitant	hesitant	ADJ
ejpam-3335	113	15	fuzzy	fuzzy	ADJ
ejpam-3335	113	16	up	up	NOUN
ejpam-3335	113	17	-	-	PUNCT
ejpam-3335	113	18	subalgebra	subalgebra	NOUN
ejpam-3335	113	19	of	of	ADP
ejpam-3335	113	20	a	a	PRON
ejpam-3335	113	21	if	if	SCONJ
ejpam-3335	113	22	it	it	PRON
ejpam-3335	113	23	satisfies	satisfy	VERB
ejpam-3335	113	24	the	the	DET
ejpam-3335	113	25	following	follow	VERB
ejpam-3335	113	26	property	property	NOUN
ejpam-3335	113	27	:	:	PUNCT
ejpam-3335	113	28	for	for	ADP
ejpam-3335	113	29	any	any	DET
ejpam-3335	113	30	x	x	NOUN
ejpam-3335	113	31	,	,	PUNCT
ejpam-3335	113	32	y	y	PROPN
ejpam-3335	113	33	∈	∈	PROPN
ejpam-3335	113	34	a	a	PRON
ejpam-3335	113	35	,	,	PUNCT
ejpam-3335	113	36	hh(x	hh(x	PUNCT
ejpam-3335	113	37	·	·	PUNCT
ejpam-3335	113	38	y	y	X
ejpam-3335	113	39	)	)	PUNCT
ejpam-3335	113	40	⊆	⊆	NUM
ejpam-3335	113	41	hh(x	hh(x	NOUN
ejpam-3335	113	42	)	)	PUNCT
ejpam-3335	113	43	∪	∪	ADP
ejpam-3335	113	44	hh(y	hh(y	NOUN
ejpam-3335	113	45	)	)	PUNCT
ejpam-3335	113	46	.	.	PUNCT
ejpam-3335	114	1	by	by	ADP
ejpam-3335	114	2	proposition	proposition	NOUN
ejpam-3335	114	3	1	1	NUM
ejpam-3335	114	4	(	(	PUNCT
ejpam-3335	114	5	1	1	NUM
ejpam-3335	114	6	)	)	PUNCT
ejpam-3335	114	7	,	,	PUNCT
ejpam-3335	114	8	we	we	PRON
ejpam-3335	114	9	have	have	VERB
ejpam-3335	114	10	hh(0	hh(0	NOUN
ejpam-3335	114	11	)	)	PUNCT
ejpam-3335	114	12	=	=	SYM
ejpam-3335	114	13	hh(x	hh(x	X
ejpam-3335	114	14	·	·	PUNCT
ejpam-3335	114	15	x	x	X
ejpam-3335	114	16	)	)	PUNCT
ejpam-3335	114	17	⊆	⊆	NUM
ejpam-3335	114	18	hh(x)∪hh(x	hh(x)∪hh(x	PROPN
ejpam-3335	114	19	)	)	PUNCT
ejpam-3335	114	20	=	=	SYM
ejpam-3335	114	21	hh(x	hh(x	X
ejpam-3335	114	22	)	)	PUNCT
ejpam-3335	114	23	for	for	ADP
ejpam-3335	114	24	all	all	DET
ejpam-3335	114	25	x	x	SYM
ejpam-3335	114	26	∈	∈	PROPN
ejpam-3335	114	27	a.	a.	NOUN
ejpam-3335	114	28	p.	p.	NOUN
ejpam-3335	114	29	mosrijai	mosrijai	PROPN
ejpam-3335	114	30	,	,	PUNCT
ejpam-3335	114	31	a.	a.	NOUN
ejpam-3335	114	32	iampan	iampan	PROPN
ejpam-3335	114	33	/	/	SYM
ejpam-3335	114	34	eur	eur	PROPN
ejpam-3335	114	35	.	.	PUNCT
ejpam-3335	115	1	j.	j.	PROPN
ejpam-3335	115	2	pure	pure	PROPN
ejpam-3335	115	3	appl	appl	PROPN
ejpam-3335	115	4	.	.	PROPN
ejpam-3335	115	5	math	math	PROPN
ejpam-3335	115	6	,	,	PUNCT
ejpam-3335	115	7	11	11	NUM
ejpam-3335	115	8	(	(	PUNCT
ejpam-3335	115	9	4	4	NUM
ejpam-3335	115	10	)	)	PUNCT
ejpam-3335	115	11	(	(	PUNCT
ejpam-3335	115	12	2018	2018	NUM
ejpam-3335	115	13	)	)	PUNCT
ejpam-3335	115	14	,	,	PUNCT
ejpam-3335	115	15	976	976	NUM
ejpam-3335	115	16	-	-	SYM
ejpam-3335	115	17	1002	1002	NUM
ejpam-3335	115	18	981	981	NUM
ejpam-3335	115	19	example	example	NOUN
ejpam-3335	115	20	4	4	NUM
ejpam-3335	115	21	.	.	PUNCT
ejpam-3335	116	1	let	let	VERB
ejpam-3335	116	2	a	a	PRON
ejpam-3335	116	3	=	=	PUNCT
ejpam-3335	116	4	{	{	PUNCT
ejpam-3335	116	5	0	0	NUM
ejpam-3335	116	6	,	,	PUNCT
ejpam-3335	116	7	1	1	NUM
ejpam-3335	116	8	,	,	PUNCT
ejpam-3335	116	9	2	2	NUM
ejpam-3335	116	10	,	,	PUNCT
ejpam-3335	116	11	3	3	NUM
ejpam-3335	116	12	}	}	PUNCT
ejpam-3335	116	13	be	be	AUX
ejpam-3335	116	14	a	a	DET
ejpam-3335	116	15	set	set	NOUN
ejpam-3335	116	16	with	with	ADP
ejpam-3335	116	17	a	a	DET
ejpam-3335	116	18	binary	binary	ADJ
ejpam-3335	116	19	operation	operation	NOUN
ejpam-3335	116	20	·	·	PUNCT
ejpam-3335	116	21	defined	define	VERB
ejpam-3335	116	22	by	by	ADP
ejpam-3335	116	23	the	the	DET
ejpam-3335	116	24	following	following	ADJ
ejpam-3335	116	25	cayley	cayley	ADJ
ejpam-3335	116	26	table	table	NOUN
ejpam-3335	116	27	:	:	PUNCT
ejpam-3335	116	28	·	·	PUNCT
ejpam-3335	116	29	0	0	NUM
ejpam-3335	117	1	1	1	NUM
ejpam-3335	117	2	2	2	NUM
ejpam-3335	117	3	3	3	NUM
ejpam-3335	117	4	0	0	NUM
ejpam-3335	117	5	0	0	NUM
ejpam-3335	117	6	1	1	NUM
ejpam-3335	117	7	2	2	NUM
ejpam-3335	117	8	3	3	NUM
ejpam-3335	117	9	1	1	NUM
ejpam-3335	117	10	0	0	NUM
ejpam-3335	117	11	0	0	NUM
ejpam-3335	117	12	2	2	NUM
ejpam-3335	117	13	3	3	NUM
ejpam-3335	117	14	2	2	NUM
ejpam-3335	117	15	0	0	NUM
ejpam-3335	117	16	0	0	NUM
ejpam-3335	117	17	0	0	NUM
ejpam-3335	117	18	3	3	NUM
ejpam-3335	117	19	3	3	NUM
ejpam-3335	117	20	0	0	NUM
ejpam-3335	117	21	0	0	NUM
ejpam-3335	117	22	0	0	NUM
ejpam-3335	117	23	0	0	NUM
ejpam-3335	118	1	then	then	ADV
ejpam-3335	118	2	(	(	PUNCT
ejpam-3335	118	3	a	a	PRON
ejpam-3335	118	4	,	,	PUNCT
ejpam-3335	118	5	·	·	PUNCT
ejpam-3335	118	6	,	,	PUNCT
ejpam-3335	118	7	0	0	NUM
ejpam-3335	118	8	)	)	PUNCT
ejpam-3335	118	9	is	be	AUX
ejpam-3335	118	10	a	a	DET
ejpam-3335	118	11	up	up	NOUN
ejpam-3335	118	12	-	-	PUNCT
ejpam-3335	118	13	algebra	algebra	NOUN
ejpam-3335	118	14	.	.	PUNCT
ejpam-3335	119	1	we	we	PRON
ejpam-3335	119	2	define	define	VERB
ejpam-3335	119	3	a	a	DET
ejpam-3335	119	4	hesitant	hesitant	ADJ
ejpam-3335	119	5	fuzzy	fuzzy	ADJ
ejpam-3335	119	6	set	set	VERB
ejpam-3335	119	7	h	h	NOUN
ejpam-3335	119	8	on	on	ADP
ejpam-3335	119	9	a	a	PRON
ejpam-3335	119	10	as	as	SCONJ
ejpam-3335	119	11	follows	follow	VERB
ejpam-3335	119	12	:	:	PUNCT
ejpam-3335	119	13	hh(0	hh(0	NOUN
ejpam-3335	119	14	)	)	PUNCT
ejpam-3335	119	15	=	=	SYM
ejpam-3335	119	16	∅	∅	NOUN
ejpam-3335	119	17	,	,	PUNCT
ejpam-3335	119	18	hh(1	hh(1	NOUN
ejpam-3335	119	19	)	)	PUNCT
ejpam-3335	119	20	=	=	PRON
ejpam-3335	119	21	{	{	PUNCT
ejpam-3335	119	22	0.5},hh(2	0.5},hh(2	NUM
ejpam-3335	119	23	)	)	PUNCT
ejpam-3335	119	24	=	=	PUNCT
ejpam-3335	119	25	{	{	PUNCT
ejpam-3335	119	26	0.6	0.6	NUM
ejpam-3335	119	27	}	}	PUNCT
ejpam-3335	119	28	,	,	PUNCT
ejpam-3335	119	29	and	and	CCONJ
ejpam-3335	119	30	hh(3	hh(3	X
ejpam-3335	119	31	)	)	PUNCT
ejpam-3335	119	32	=	=	PUNCT
ejpam-3335	120	1	[	[	X
ejpam-3335	120	2	0.5	0.5	NUM
ejpam-3335	120	3	,	,	PUNCT
ejpam-3335	120	4	0.6	0.6	NUM
ejpam-3335	120	5	]	]	PUNCT
ejpam-3335	120	6	.	.	PUNCT
ejpam-3335	121	1	using	use	VERB
ejpam-3335	121	2	this	this	DET
ejpam-3335	121	3	data	datum	NOUN
ejpam-3335	121	4	,	,	PUNCT
ejpam-3335	121	5	we	we	PRON
ejpam-3335	121	6	can	can	AUX
ejpam-3335	121	7	show	show	VERB
ejpam-3335	121	8	that	that	SCONJ
ejpam-3335	121	9	h	h	NOUN
ejpam-3335	121	10	is	be	AUX
ejpam-3335	121	11	an	an	DET
ejpam-3335	121	12	anti	anti	ADJ
ejpam-3335	121	13	-	-	ADJ
ejpam-3335	121	14	hesitant	hesitant	ADJ
ejpam-3335	121	15	fuzzy	fuzzy	ADJ
ejpam-3335	121	16	up	up	NOUN
ejpam-3335	121	17	-	-	PUNCT
ejpam-3335	121	18	subalgebra	subalgebra	NOUN
ejpam-3335	121	19	of	of	ADP
ejpam-3335	121	20	a.	a.	NOUN
ejpam-3335	121	21	definition	definition	NOUN
ejpam-3335	121	22	7	7	NUM
ejpam-3335	121	23	.	.	PUNCT
ejpam-3335	122	1	a	a	DET
ejpam-3335	122	2	hesitant	hesitant	ADJ
ejpam-3335	122	3	fuzzy	fuzzy	ADJ
ejpam-3335	122	4	set	set	VERB
ejpam-3335	122	5	h	h	NOUN
ejpam-3335	122	6	on	on	ADP
ejpam-3335	122	7	a	a	DET
ejpam-3335	122	8	a	a	PRON
ejpam-3335	122	9	is	be	AUX
ejpam-3335	122	10	called	call	VERB
ejpam-3335	122	11	an	an	DET
ejpam-3335	122	12	anti	anti	ADJ
ejpam-3335	122	13	-	-	ADJ
ejpam-3335	122	14	hesitant	hesitant	ADJ
ejpam-3335	122	15	fuzzy	fuzzy	ADJ
ejpam-3335	122	16	up	up	NOUN
ejpam-3335	122	17	-	-	PUNCT
ejpam-3335	122	18	filter	filter	NOUN
ejpam-3335	122	19	of	of	ADP
ejpam-3335	122	20	a	a	PRON
ejpam-3335	122	21	if	if	SCONJ
ejpam-3335	122	22	it	it	PRON
ejpam-3335	122	23	satisfies	satisfy	VERB
ejpam-3335	122	24	the	the	DET
ejpam-3335	122	25	following	follow	VERB
ejpam-3335	122	26	properties	property	NOUN
ejpam-3335	122	27	:	:	PUNCT
ejpam-3335	122	28	for	for	ADP
ejpam-3335	122	29	any	any	DET
ejpam-3335	122	30	x	x	NOUN
ejpam-3335	122	31	,	,	PUNCT
ejpam-3335	122	32	y	y	PROPN
ejpam-3335	122	33	∈	∈	PROPN
ejpam-3335	122	34	a	a	PRON
ejpam-3335	122	35	,	,	PUNCT
ejpam-3335	122	36	(	(	PUNCT
ejpam-3335	122	37	1	1	X
ejpam-3335	122	38	)	)	PUNCT
ejpam-3335	122	39	hh(0	hh(0	NOUN
ejpam-3335	122	40	)	)	PUNCT
ejpam-3335	122	41	⊆	⊆	NUM
ejpam-3335	122	42	hh(x	hh(x	NOUN
ejpam-3335	122	43	)	)	PUNCT
ejpam-3335	122	44	,	,	PUNCT
ejpam-3335	122	45	and	and	CCONJ
ejpam-3335	122	46	(	(	PUNCT
ejpam-3335	122	47	2	2	NUM
ejpam-3335	122	48	)	)	PUNCT
ejpam-3335	122	49	hh(y	hh(y	ADP
ejpam-3335	122	50	)	)	PUNCT
ejpam-3335	122	51	⊆	⊆	NUM
ejpam-3335	122	52	hh(x	hh(x	X
ejpam-3335	122	53	·	·	PUNCT
ejpam-3335	122	54	y	y	X
ejpam-3335	122	55	)	)	PUNCT
ejpam-3335	122	56	∪	∪	ADP
ejpam-3335	122	57	hh(x	hh(x	NOUN
ejpam-3335	122	58	)	)	PUNCT
ejpam-3335	122	59	.	.	PUNCT
ejpam-3335	123	1	example	example	NOUN
ejpam-3335	124	1	5	5	NUM
ejpam-3335	124	2	.	.	PUNCT
ejpam-3335	124	3	let	let	VERB
ejpam-3335	124	4	a	a	PRON
ejpam-3335	124	5	=	=	PUNCT
ejpam-3335	124	6	{	{	PUNCT
ejpam-3335	124	7	0	0	NUM
ejpam-3335	124	8	,	,	PUNCT
ejpam-3335	124	9	1	1	NUM
ejpam-3335	124	10	,	,	PUNCT
ejpam-3335	124	11	2	2	NUM
ejpam-3335	124	12	,	,	PUNCT
ejpam-3335	124	13	3	3	NUM
ejpam-3335	124	14	,	,	PUNCT
ejpam-3335	124	15	4	4	NUM
ejpam-3335	124	16	}	}	PUNCT
ejpam-3335	124	17	be	be	AUX
ejpam-3335	124	18	a	a	DET
ejpam-3335	124	19	set	set	NOUN
ejpam-3335	124	20	with	with	ADP
ejpam-3335	124	21	a	a	DET
ejpam-3335	124	22	binary	binary	ADJ
ejpam-3335	124	23	operation	operation	NOUN
ejpam-3335	124	24	·	·	PUNCT
ejpam-3335	124	25	defined	define	VERB
ejpam-3335	124	26	by	by	ADP
ejpam-3335	124	27	the	the	DET
ejpam-3335	124	28	following	following	ADJ
ejpam-3335	124	29	cayley	cayley	ADJ
ejpam-3335	124	30	table	table	NOUN
ejpam-3335	124	31	:	:	PUNCT
ejpam-3335	124	32	·	·	PUNCT
ejpam-3335	124	33	0	0	NUM
ejpam-3335	125	1	1	1	NUM
ejpam-3335	125	2	2	2	NUM
ejpam-3335	125	3	3	3	NUM
ejpam-3335	125	4	4	4	NUM
ejpam-3335	125	5	0	0	NUM
ejpam-3335	125	6	0	0	NUM
ejpam-3335	125	7	1	1	NUM
ejpam-3335	125	8	2	2	NUM
ejpam-3335	125	9	3	3	NUM
ejpam-3335	125	10	4	4	NUM
ejpam-3335	125	11	1	1	NUM
ejpam-3335	125	12	0	0	NUM
ejpam-3335	125	13	0	0	NUM
ejpam-3335	125	14	2	2	NUM
ejpam-3335	125	15	3	3	NUM
ejpam-3335	125	16	4	4	NUM
ejpam-3335	125	17	2	2	NUM
ejpam-3335	125	18	0	0	NUM
ejpam-3335	125	19	0	0	NUM
ejpam-3335	125	20	0	0	NUM
ejpam-3335	125	21	3	3	NUM
ejpam-3335	125	22	3	3	NUM
ejpam-3335	125	23	3	3	NUM
ejpam-3335	125	24	0	0	NUM
ejpam-3335	125	25	1	1	NUM
ejpam-3335	125	26	2	2	NUM
ejpam-3335	125	27	0	0	NUM
ejpam-3335	125	28	3	3	NUM
ejpam-3335	125	29	4	4	NUM
ejpam-3335	125	30	0	0	NUM
ejpam-3335	125	31	1	1	NUM
ejpam-3335	125	32	2	2	NUM
ejpam-3335	125	33	0	0	NUM
ejpam-3335	125	34	0	0	NUM
ejpam-3335	125	35	then	then	ADV
ejpam-3335	125	36	(	(	PUNCT
ejpam-3335	125	37	a	a	PRON
ejpam-3335	125	38	,	,	PUNCT
ejpam-3335	125	39	·	·	PUNCT
ejpam-3335	125	40	,	,	PUNCT
ejpam-3335	125	41	0	0	NUM
ejpam-3335	125	42	)	)	PUNCT
ejpam-3335	125	43	is	be	AUX
ejpam-3335	125	44	a	a	DET
ejpam-3335	125	45	up	up	NOUN
ejpam-3335	125	46	-	-	PUNCT
ejpam-3335	125	47	algebra	algebra	NOUN
ejpam-3335	125	48	.	.	PUNCT
ejpam-3335	126	1	we	we	PRON
ejpam-3335	126	2	define	define	VERB
ejpam-3335	126	3	a	a	DET
ejpam-3335	126	4	hesitant	hesitant	ADJ
ejpam-3335	126	5	fuzzy	fuzzy	ADJ
ejpam-3335	126	6	set	set	VERB
ejpam-3335	126	7	h	h	NOUN
ejpam-3335	126	8	on	on	ADP
ejpam-3335	126	9	a	a	DET
ejpam-3335	126	10	as	as	SCONJ
ejpam-3335	126	11	follows	follow	VERB
ejpam-3335	126	12	:	:	PUNCT
ejpam-3335	126	13	hh(0	hh(0	NOUN
ejpam-3335	126	14	)	)	PUNCT
ejpam-3335	126	15	=	=	PRON
ejpam-3335	126	16	{	{	PUNCT
ejpam-3335	126	17	0.8},hh(1	0.8},hh(1	NUM
ejpam-3335	126	18	)	)	PUNCT
ejpam-3335	126	19	=	=	PUNCT
ejpam-3335	127	1	[	[	X
ejpam-3335	127	2	0.8	0.8	NUM
ejpam-3335	127	3	,	,	PUNCT
ejpam-3335	127	4	0.9),hh(2	0.9),hh(2	NOUN
ejpam-3335	127	5	)	)	PUNCT
ejpam-3335	127	6	=	=	PUNCT
ejpam-3335	128	1	[	[	X
ejpam-3335	128	2	0.8	0.8	NUM
ejpam-3335	128	3	,	,	PUNCT
ejpam-3335	128	4	0.9],hh(3	0.9],hh(3	NOUN
ejpam-3335	128	5	)	)	PUNCT
ejpam-3335	129	1	=	=	PUNCT
ejpam-3335	130	1	[	[	X
ejpam-3335	130	2	0.6	0.6	NUM
ejpam-3335	130	3	,	,	PUNCT
ejpam-3335	130	4	0.9	0.9	NUM
ejpam-3335	130	5	]	]	PUNCT
ejpam-3335	130	6	,	,	PUNCT
ejpam-3335	130	7	and	and	CCONJ
ejpam-3335	130	8	hh(4	hh(4	NOUN
ejpam-3335	130	9	)	)	PUNCT
ejpam-3335	130	10	=	=	PUNCT
ejpam-3335	131	1	[	[	X
ejpam-3335	131	2	0.6	0.6	NUM
ejpam-3335	131	3	,	,	PUNCT
ejpam-3335	131	4	0.9	0.9	NUM
ejpam-3335	131	5	]	]	PUNCT
ejpam-3335	131	6	.	.	PUNCT
ejpam-3335	132	1	using	use	VERB
ejpam-3335	132	2	this	this	DET
ejpam-3335	132	3	data	datum	NOUN
ejpam-3335	132	4	,	,	PUNCT
ejpam-3335	132	5	we	we	PRON
ejpam-3335	132	6	can	can	AUX
ejpam-3335	132	7	show	show	VERB
ejpam-3335	132	8	that	that	SCONJ
ejpam-3335	132	9	h	h	NOUN
ejpam-3335	132	10	is	be	AUX
ejpam-3335	132	11	an	an	DET
ejpam-3335	132	12	anti	anti	ADJ
ejpam-3335	132	13	-	-	ADJ
ejpam-3335	132	14	hesitant	hesitant	ADJ
ejpam-3335	132	15	fuzzy	fuzzy	ADJ
ejpam-3335	132	16	up	up	NOUN
ejpam-3335	132	17	-	-	PUNCT
ejpam-3335	132	18	filter	filter	NOUN
ejpam-3335	132	19	of	of	ADP
ejpam-3335	132	20	a.	a.	NOUN
ejpam-3335	132	21	definition	definition	NOUN
ejpam-3335	132	22	8	8	NUM
ejpam-3335	132	23	.	.	PUNCT
ejpam-3335	133	1	a	a	DET
ejpam-3335	133	2	hesitant	hesitant	ADJ
ejpam-3335	133	3	fuzzy	fuzzy	ADJ
ejpam-3335	133	4	set	set	VERB
ejpam-3335	133	5	h	h	NOUN
ejpam-3335	133	6	on	on	ADP
ejpam-3335	133	7	a	a	DET
ejpam-3335	133	8	a	a	PRON
ejpam-3335	133	9	is	be	AUX
ejpam-3335	133	10	called	call	VERB
ejpam-3335	133	11	an	an	DET
ejpam-3335	133	12	anti	anti	ADJ
ejpam-3335	133	13	-	-	ADJ
ejpam-3335	133	14	hesitant	hesitant	ADJ
ejpam-3335	133	15	fuzzy	fuzzy	ADJ
ejpam-3335	133	16	up	up	NOUN
ejpam-3335	133	17	-	-	PUNCT
ejpam-3335	133	18	ideal	ideal	NOUN
ejpam-3335	133	19	of	of	ADP
ejpam-3335	133	20	a	a	PRON
ejpam-3335	133	21	if	if	SCONJ
ejpam-3335	133	22	it	it	PRON
ejpam-3335	133	23	satisfies	satisfy	VERB
ejpam-3335	133	24	the	the	DET
ejpam-3335	133	25	following	follow	VERB
ejpam-3335	133	26	properties	property	NOUN
ejpam-3335	133	27	:	:	PUNCT
ejpam-3335	133	28	for	for	ADP
ejpam-3335	133	29	any	any	DET
ejpam-3335	133	30	x	x	NOUN
ejpam-3335	133	31	,	,	PUNCT
ejpam-3335	133	32	y	y	PROPN
ejpam-3335	133	33	,	,	PUNCT
ejpam-3335	133	34	z	z	PROPN
ejpam-3335	133	35	∈	∈	PROPN
ejpam-3335	133	36	a	a	DET
ejpam-3335	133	37	,	,	PUNCT
ejpam-3335	133	38	(	(	PUNCT
ejpam-3335	133	39	1	1	X
ejpam-3335	133	40	)	)	PUNCT
ejpam-3335	133	41	hh(0	hh(0	NOUN
ejpam-3335	133	42	)	)	PUNCT
ejpam-3335	133	43	⊆	⊆	NUM
ejpam-3335	133	44	hh(x	hh(x	NOUN
ejpam-3335	133	45	)	)	PUNCT
ejpam-3335	133	46	,	,	PUNCT
ejpam-3335	133	47	and	and	CCONJ
ejpam-3335	133	48	(	(	PUNCT
ejpam-3335	133	49	2	2	NUM
ejpam-3335	133	50	)	)	PUNCT
ejpam-3335	133	51	hh(x	hh(x	X
ejpam-3335	133	52	·	·	PUNCT
ejpam-3335	134	1	z	z	X
ejpam-3335	134	2	)	)	PUNCT
ejpam-3335	134	3	⊆	⊆	NUM
ejpam-3335	134	4	hh(x	hh(x	X
ejpam-3335	134	5	·	·	PUNCT
ejpam-3335	134	6	(	(	PUNCT
ejpam-3335	134	7	y	y	PROPN
ejpam-3335	134	8	·	·	PUNCT
ejpam-3335	134	9	z	z	NOUN
ejpam-3335	134	10	)	)	PUNCT
ejpam-3335	134	11	)	)	PUNCT
ejpam-3335	134	12	∪	∪	ADP
ejpam-3335	134	13	hh(y	hh(y	NOUN
ejpam-3335	134	14	)	)	PUNCT
ejpam-3335	134	15	.	.	PUNCT
ejpam-3335	135	1	example	example	NOUN
ejpam-3335	136	1	6	6	NUM
ejpam-3335	136	2	.	.	PUNCT
ejpam-3335	136	3	let	let	VERB
ejpam-3335	136	4	a	a	PRON
ejpam-3335	136	5	=	=	PUNCT
ejpam-3335	136	6	{	{	PUNCT
ejpam-3335	136	7	0	0	NUM
ejpam-3335	136	8	,	,	PUNCT
ejpam-3335	136	9	1	1	NUM
ejpam-3335	136	10	,	,	PUNCT
ejpam-3335	136	11	2	2	NUM
ejpam-3335	136	12	,	,	PUNCT
ejpam-3335	136	13	3	3	NUM
ejpam-3335	136	14	}	}	PUNCT
ejpam-3335	136	15	be	be	AUX
ejpam-3335	136	16	a	a	DET
ejpam-3335	136	17	set	set	NOUN
ejpam-3335	136	18	with	with	ADP
ejpam-3335	136	19	a	a	DET
ejpam-3335	136	20	binary	binary	ADJ
ejpam-3335	136	21	operation	operation	NOUN
ejpam-3335	136	22	·	·	PUNCT
ejpam-3335	136	23	defined	define	VERB
ejpam-3335	136	24	by	by	ADP
ejpam-3335	136	25	the	the	DET
ejpam-3335	136	26	following	following	ADJ
ejpam-3335	136	27	cayley	cayley	ADJ
ejpam-3335	136	28	table	table	NOUN
ejpam-3335	136	29	:	:	PUNCT
ejpam-3335	136	30	·	·	PUNCT
ejpam-3335	136	31	0	0	NUM
ejpam-3335	137	1	1	1	NUM
ejpam-3335	137	2	2	2	NUM
ejpam-3335	137	3	3	3	NUM
ejpam-3335	137	4	0	0	NUM
ejpam-3335	137	5	0	0	NUM
ejpam-3335	137	6	1	1	NUM
ejpam-3335	137	7	2	2	NUM
ejpam-3335	137	8	3	3	NUM
ejpam-3335	137	9	1	1	NUM
ejpam-3335	137	10	0	0	NUM
ejpam-3335	137	11	0	0	NUM
ejpam-3335	137	12	2	2	NUM
ejpam-3335	137	13	3	3	NUM
ejpam-3335	137	14	2	2	NUM
ejpam-3335	137	15	0	0	NUM
ejpam-3335	137	16	1	1	NUM
ejpam-3335	137	17	0	0	NUM
ejpam-3335	137	18	3	3	NUM
ejpam-3335	137	19	3	3	NUM
ejpam-3335	137	20	0	0	NUM
ejpam-3335	137	21	1	1	NUM
ejpam-3335	137	22	2	2	NUM
ejpam-3335	137	23	0	0	NUM
ejpam-3335	137	24	then	then	ADV
ejpam-3335	137	25	(	(	PUNCT
ejpam-3335	137	26	a	a	PRON
ejpam-3335	137	27	,	,	PUNCT
ejpam-3335	137	28	·	·	PUNCT
ejpam-3335	137	29	,	,	PUNCT
ejpam-3335	137	30	0	0	NUM
ejpam-3335	137	31	)	)	PUNCT
ejpam-3335	137	32	is	be	AUX
ejpam-3335	137	33	a	a	DET
ejpam-3335	137	34	up	up	NOUN
ejpam-3335	137	35	-	-	PUNCT
ejpam-3335	137	36	algebra	algebra	NOUN
ejpam-3335	137	37	.	.	PUNCT
ejpam-3335	138	1	we	we	PRON
ejpam-3335	138	2	define	define	VERB
ejpam-3335	138	3	a	a	DET
ejpam-3335	138	4	hesitant	hesitant	ADJ
ejpam-3335	138	5	fuzzy	fuzzy	ADJ
ejpam-3335	138	6	set	set	VERB
ejpam-3335	138	7	h	h	NOUN
ejpam-3335	138	8	on	on	ADP
ejpam-3335	138	9	a	a	PRON
ejpam-3335	138	10	as	as	SCONJ
ejpam-3335	138	11	follows	follow	VERB
ejpam-3335	138	12	:	:	PUNCT
ejpam-3335	138	13	p.	p.	NOUN
ejpam-3335	138	14	mosrijai	mosrijai	PROPN
ejpam-3335	138	15	,	,	PUNCT
ejpam-3335	138	16	a.	a.	NOUN
ejpam-3335	138	17	iampan	iampan	PROPN
ejpam-3335	138	18	/	/	SYM
ejpam-3335	138	19	eur	eur	PROPN
ejpam-3335	138	20	.	.	PUNCT
ejpam-3335	139	1	j.	j.	PROPN
ejpam-3335	139	2	pure	pure	PROPN
ejpam-3335	139	3	appl	appl	PROPN
ejpam-3335	139	4	.	.	PROPN
ejpam-3335	139	5	math	math	PROPN
ejpam-3335	139	6	,	,	PUNCT
ejpam-3335	139	7	11	11	NUM
ejpam-3335	139	8	(	(	PUNCT
ejpam-3335	139	9	4	4	NUM
ejpam-3335	139	10	)	)	PUNCT
ejpam-3335	139	11	(	(	PUNCT
ejpam-3335	139	12	2018	2018	NUM
ejpam-3335	139	13	)	)	PUNCT
ejpam-3335	139	14	,	,	PUNCT
ejpam-3335	139	15	976	976	NUM
ejpam-3335	139	16	-	-	SYM
ejpam-3335	139	17	1002	1002	NUM
ejpam-3335	139	18	982	982	NUM
ejpam-3335	139	19	hh(0	hh(0	NOUN
ejpam-3335	139	20	)	)	PUNCT
ejpam-3335	139	21	=	=	PUNCT
ejpam-3335	139	22	{	{	PUNCT
ejpam-3335	139	23	1	1	NUM
ejpam-3335	139	24	}	}	PUNCT
ejpam-3335	139	25	,	,	PUNCT
ejpam-3335	139	26	hh(1	hh(1	PROPN
ejpam-3335	139	27	)	)	PUNCT
ejpam-3335	139	28	=	=	PRON
ejpam-3335	139	29	{	{	PUNCT
ejpam-3335	139	30	1},hh(2	1},hh(2	NUM
ejpam-3335	139	31	)	)	PUNCT
ejpam-3335	139	32	=	=	SYM
ejpam-3335	139	33	{	{	PUNCT
ejpam-3335	139	34	0	0	NUM
ejpam-3335	139	35	,	,	PUNCT
ejpam-3335	139	36	1	1	NUM
ejpam-3335	139	37	}	}	PUNCT
ejpam-3335	139	38	,	,	PUNCT
ejpam-3335	139	39	and	and	CCONJ
ejpam-3335	139	40	hh(3	hh(3	X
ejpam-3335	139	41	)	)	PUNCT
ejpam-3335	139	42	=	=	PUNCT
ejpam-3335	140	1	[	[	X
ejpam-3335	140	2	0	0	NUM
ejpam-3335	140	3	,	,	PUNCT
ejpam-3335	140	4	1	1	NUM
ejpam-3335	140	5	]	]	PUNCT
ejpam-3335	140	6	.	.	PUNCT
ejpam-3335	141	1	using	use	VERB
ejpam-3335	141	2	this	this	DET
ejpam-3335	141	3	data	datum	NOUN
ejpam-3335	141	4	,	,	PUNCT
ejpam-3335	141	5	we	we	PRON
ejpam-3335	141	6	can	can	AUX
ejpam-3335	141	7	show	show	VERB
ejpam-3335	141	8	that	that	SCONJ
ejpam-3335	141	9	h	h	NOUN
ejpam-3335	141	10	is	be	AUX
ejpam-3335	141	11	an	an	DET
ejpam-3335	141	12	anti	anti	ADJ
ejpam-3335	141	13	-	-	ADJ
ejpam-3335	141	14	hesitant	hesitant	ADJ
ejpam-3335	141	15	fuzzy	fuzzy	ADJ
ejpam-3335	141	16	up	up	NOUN
ejpam-3335	141	17	-	-	PUNCT
ejpam-3335	141	18	ideal	ideal	NOUN
ejpam-3335	141	19	of	of	ADP
ejpam-3335	141	20	a.	a.	NOUN
ejpam-3335	141	21	definition	definition	NOUN
ejpam-3335	141	22	9	9	NUM
ejpam-3335	141	23	.	.	PUNCT
ejpam-3335	142	1	a	a	DET
ejpam-3335	142	2	hesitant	hesitant	ADJ
ejpam-3335	142	3	fuzzy	fuzzy	ADJ
ejpam-3335	142	4	set	set	VERB
ejpam-3335	142	5	h	h	NOUN
ejpam-3335	142	6	on	on	ADP
ejpam-3335	142	7	a	a	DET
ejpam-3335	142	8	a	a	PRON
ejpam-3335	142	9	is	be	AUX
ejpam-3335	142	10	called	call	VERB
ejpam-3335	142	11	an	an	DET
ejpam-3335	142	12	anti	anti	ADJ
ejpam-3335	142	13	-	-	ADJ
ejpam-3335	142	14	hesitant	hesitant	ADJ
ejpam-3335	142	15	fuzzy	fuzzy	ADJ
ejpam-3335	142	16	strongly	strongly	ADV
ejpam-3335	142	17	up	up	ADP
ejpam-3335	142	18	-	-	PUNCT
ejpam-3335	142	19	ideal	ideal	NOUN
ejpam-3335	142	20	of	of	ADP
ejpam-3335	142	21	a	a	PRON
ejpam-3335	142	22	if	if	SCONJ
ejpam-3335	142	23	it	it	PRON
ejpam-3335	142	24	satisfies	satisfy	VERB
ejpam-3335	142	25	the	the	DET
ejpam-3335	142	26	following	follow	VERB
ejpam-3335	142	27	properties	property	NOUN
ejpam-3335	142	28	:	:	PUNCT
ejpam-3335	142	29	for	for	ADP
ejpam-3335	142	30	any	any	DET
ejpam-3335	142	31	x	x	NOUN
ejpam-3335	142	32	,	,	PUNCT
ejpam-3335	142	33	y	y	PROPN
ejpam-3335	142	34	,	,	PUNCT
ejpam-3335	142	35	z	z	PROPN
ejpam-3335	142	36	∈	∈	PROPN
ejpam-3335	142	37	a	a	DET
ejpam-3335	142	38	,	,	PUNCT
ejpam-3335	142	39	(	(	PUNCT
ejpam-3335	142	40	1	1	X
ejpam-3335	142	41	)	)	PUNCT
ejpam-3335	142	42	hh(0	hh(0	NOUN
ejpam-3335	142	43	)	)	PUNCT
ejpam-3335	142	44	⊆	⊆	NUM
ejpam-3335	142	45	hh(x	hh(x	NOUN
ejpam-3335	142	46	)	)	PUNCT
ejpam-3335	142	47	,	,	PUNCT
ejpam-3335	142	48	and	and	CCONJ
ejpam-3335	142	49	(	(	PUNCT
ejpam-3335	142	50	2	2	X
ejpam-3335	142	51	)	)	PUNCT
ejpam-3335	142	52	hh(x	hh(x	NOUN
ejpam-3335	142	53	)	)	PUNCT
ejpam-3335	143	1	⊆	⊆	X
ejpam-3335	143	2	hh((z	hh((z	X
ejpam-3335	143	3	·	·	PUNCT
ejpam-3335	143	4	y	y	X
ejpam-3335	143	5	)	)	PUNCT
ejpam-3335	143	6	·	·	PUNCT
ejpam-3335	143	7	(	(	PUNCT
ejpam-3335	143	8	z	z	NOUN
ejpam-3335	143	9	·	·	PUNCT
ejpam-3335	143	10	x	x	X
ejpam-3335	143	11	)	)	PUNCT
ejpam-3335	143	12	)	)	PUNCT
ejpam-3335	143	13	∪	∪	ADP
ejpam-3335	143	14	hh(y	hh(y	NOUN
ejpam-3335	143	15	)	)	PUNCT
ejpam-3335	143	16	.	.	PUNCT
ejpam-3335	143	17	example	example	NOUN
ejpam-3335	144	1	7	7	NUM
ejpam-3335	144	2	.	.	PUNCT
ejpam-3335	145	1	let	let	VERB
ejpam-3335	145	2	a	a	PRON
ejpam-3335	145	3	=	=	PUNCT
ejpam-3335	145	4	{	{	PUNCT
ejpam-3335	145	5	0	0	NUM
ejpam-3335	145	6	,	,	PUNCT
ejpam-3335	145	7	1	1	NUM
ejpam-3335	145	8	,	,	PUNCT
ejpam-3335	145	9	2	2	NUM
ejpam-3335	145	10	,	,	PUNCT
ejpam-3335	145	11	3	3	NUM
ejpam-3335	145	12	}	}	PUNCT
ejpam-3335	145	13	be	be	AUX
ejpam-3335	145	14	a	a	DET
ejpam-3335	145	15	set	set	NOUN
ejpam-3335	145	16	with	with	ADP
ejpam-3335	145	17	a	a	DET
ejpam-3335	145	18	binary	binary	ADJ
ejpam-3335	145	19	operation	operation	NOUN
ejpam-3335	145	20	·	·	PUNCT
ejpam-3335	145	21	defined	define	VERB
ejpam-3335	145	22	by	by	ADP
ejpam-3335	145	23	the	the	DET
ejpam-3335	145	24	following	following	ADJ
ejpam-3335	145	25	cayley	cayley	ADJ
ejpam-3335	145	26	table	table	NOUN
ejpam-3335	145	27	:	:	PUNCT
ejpam-3335	145	28	·	·	PUNCT
ejpam-3335	145	29	0	0	NUM
ejpam-3335	146	1	1	1	NUM
ejpam-3335	146	2	2	2	NUM
ejpam-3335	146	3	3	3	NUM
ejpam-3335	146	4	0	0	NUM
ejpam-3335	146	5	0	0	NUM
ejpam-3335	146	6	1	1	NUM
ejpam-3335	146	7	2	2	NUM
ejpam-3335	146	8	3	3	NUM
ejpam-3335	146	9	1	1	NUM
ejpam-3335	146	10	0	0	NUM
ejpam-3335	146	11	0	0	NUM
ejpam-3335	146	12	2	2	NUM
ejpam-3335	146	13	2	2	NUM
ejpam-3335	146	14	2	2	NUM
ejpam-3335	146	15	0	0	NUM
ejpam-3335	146	16	1	1	NUM
ejpam-3335	146	17	0	0	NUM
ejpam-3335	146	18	1	1	NUM
ejpam-3335	146	19	3	3	NUM
ejpam-3335	146	20	0	0	NUM
ejpam-3335	146	21	0	0	NUM
ejpam-3335	146	22	0	0	NUM
ejpam-3335	146	23	0	0	NUM
ejpam-3335	147	1	then	then	ADV
ejpam-3335	147	2	(	(	PUNCT
ejpam-3335	147	3	a	a	PRON
ejpam-3335	147	4	,	,	PUNCT
ejpam-3335	147	5	·	·	PUNCT
ejpam-3335	147	6	,	,	PUNCT
ejpam-3335	147	7	0	0	NUM
ejpam-3335	147	8	)	)	PUNCT
ejpam-3335	147	9	is	be	AUX
ejpam-3335	147	10	a	a	DET
ejpam-3335	147	11	up	up	NOUN
ejpam-3335	147	12	-	-	PUNCT
ejpam-3335	147	13	algebra	algebra	NOUN
ejpam-3335	147	14	.	.	PUNCT
ejpam-3335	148	1	we	we	PRON
ejpam-3335	148	2	define	define	VERB
ejpam-3335	148	3	a	a	DET
ejpam-3335	148	4	hesitant	hesitant	ADJ
ejpam-3335	148	5	fuzzy	fuzzy	ADJ
ejpam-3335	148	6	set	set	VERB
ejpam-3335	148	7	h	h	NOUN
ejpam-3335	148	8	on	on	ADP
ejpam-3335	148	9	a	a	DET
ejpam-3335	148	10	as	as	SCONJ
ejpam-3335	148	11	follows	follow	VERB
ejpam-3335	148	12	:	:	PUNCT
ejpam-3335	148	13	hh(0	hh(0	NOUN
ejpam-3335	148	14	)	)	PUNCT
ejpam-3335	148	15	=	=	SYM
ejpam-3335	148	16	{	{	PUNCT
ejpam-3335	148	17	0	0	NUM
ejpam-3335	148	18	,	,	PUNCT
ejpam-3335	148	19	0.2	0.2	NUM
ejpam-3335	148	20	}	}	PUNCT
ejpam-3335	148	21	,	,	PUNCT
ejpam-3335	148	22	hh(1	hh(1	PROPN
ejpam-3335	148	23	)	)	PUNCT
ejpam-3335	148	24	=	=	PUNCT
ejpam-3335	148	25	{	{	PUNCT
ejpam-3335	148	26	0	0	NUM
ejpam-3335	148	27	,	,	PUNCT
ejpam-3335	148	28	0.2},hh(2	0.2},hh(2	NOUN
ejpam-3335	148	29	)	)	PUNCT
ejpam-3335	148	30	=	=	PRON
ejpam-3335	148	31	{	{	PUNCT
ejpam-3335	148	32	0	0	NUM
ejpam-3335	148	33	,	,	PUNCT
ejpam-3335	148	34	0.2	0.2	NUM
ejpam-3335	148	35	}	}	PUNCT
ejpam-3335	148	36	,	,	PUNCT
ejpam-3335	148	37	and	and	CCONJ
ejpam-3335	148	38	hh(3	hh(3	X
ejpam-3335	148	39	)	)	PUNCT
ejpam-3335	148	40	=	=	SYM
ejpam-3335	148	41	{	{	PUNCT
ejpam-3335	148	42	0	0	NUM
ejpam-3335	148	43	,	,	PUNCT
ejpam-3335	148	44	0.2	0.2	NUM
ejpam-3335	148	45	}	}	PUNCT
ejpam-3335	148	46	.	.	PUNCT
ejpam-3335	149	1	using	use	VERB
ejpam-3335	149	2	this	this	DET
ejpam-3335	149	3	data	datum	NOUN
ejpam-3335	149	4	,	,	PUNCT
ejpam-3335	149	5	we	we	PRON
ejpam-3335	149	6	can	can	AUX
ejpam-3335	149	7	show	show	VERB
ejpam-3335	149	8	that	that	SCONJ
ejpam-3335	149	9	h	h	NOUN
ejpam-3335	149	10	is	be	AUX
ejpam-3335	149	11	an	an	DET
ejpam-3335	149	12	anti	anti	ADJ
ejpam-3335	149	13	-	-	ADJ
ejpam-3335	149	14	hesitant	hesitant	ADJ
ejpam-3335	149	15	fuzzy	fuzzy	ADJ
ejpam-3335	149	16	strongly	strongly	ADV
ejpam-3335	149	17	up	up	ADP
ejpam-3335	149	18	-	-	PUNCT
ejpam-3335	149	19	ideal	ideal	NOUN
ejpam-3335	149	20	of	of	ADP
ejpam-3335	149	21	a.	a.	NOUN
ejpam-3335	149	22	theorem	theorem	NOUN
ejpam-3335	149	23	3	3	NUM
ejpam-3335	149	24	.	.	PUNCT
ejpam-3335	149	25	a	a	DET
ejpam-3335	149	26	hesitant	hesitant	ADJ
ejpam-3335	149	27	fuzzy	fuzzy	ADJ
ejpam-3335	149	28	set	set	VERB
ejpam-3335	149	29	h	h	NOUN
ejpam-3335	149	30	on	on	ADP
ejpam-3335	149	31	a	a	PRON
ejpam-3335	149	32	is	be	AUX
ejpam-3335	149	33	an	an	DET
ejpam-3335	149	34	anti	anti	ADJ
ejpam-3335	149	35	-	-	ADJ
ejpam-3335	149	36	hesitant	hesitant	ADJ
ejpam-3335	149	37	fuzzy	fuzzy	ADJ
ejpam-3335	149	38	strongly	strongly	ADV
ejpam-3335	149	39	up	up	ADP
ejpam-3335	149	40	-	-	PUNCT
ejpam-3335	149	41	ideal	ideal	NOUN
ejpam-3335	149	42	of	of	ADP
ejpam-3335	149	43	a	a	DET
ejpam-3335	149	44	if	if	NOUN
ejpam-3335	149	45	and	and	CCONJ
ejpam-3335	149	46	only	only	ADV
ejpam-3335	149	47	if	if	SCONJ
ejpam-3335	149	48	it	it	PRON
ejpam-3335	149	49	is	be	AUX
ejpam-3335	149	50	a	a	DET
ejpam-3335	149	51	constant	constant	ADJ
ejpam-3335	149	52	hesitant	hesitant	ADJ
ejpam-3335	149	53	fuzzy	fuzzy	ADJ
ejpam-3335	149	54	set	set	VERB
ejpam-3335	149	55	on	on	ADP
ejpam-3335	149	56	a.	a.	NOUN
ejpam-3335	149	57	proof	proof	NOUN
ejpam-3335	149	58	.	.	PUNCT
ejpam-3335	150	1	assume	assume	VERB
ejpam-3335	150	2	that	that	SCONJ
ejpam-3335	150	3	h	h	NOUN
ejpam-3335	150	4	is	be	AUX
ejpam-3335	150	5	an	an	DET
ejpam-3335	150	6	anti	anti	ADJ
ejpam-3335	150	7	-	-	ADJ
ejpam-3335	150	8	hesitant	hesitant	ADJ
ejpam-3335	150	9	fuzzy	fuzzy	ADJ
ejpam-3335	150	10	strongly	strongly	ADV
ejpam-3335	150	11	up	up	ADP
ejpam-3335	150	12	-	-	PUNCT
ejpam-3335	150	13	ideal	ideal	NOUN
ejpam-3335	150	14	of	of	ADP
ejpam-3335	150	15	a.	a.	NOUN
ejpam-3335	150	16	then	then	ADV
ejpam-3335	150	17	hh(0	hh(0	NOUN
ejpam-3335	150	18	)	)	PUNCT
ejpam-3335	150	19	⊆	⊆	NUM
ejpam-3335	150	20	hh(x	hh(x	NUM
ejpam-3335	150	21	)	)	PUNCT
ejpam-3335	150	22	and	and	CCONJ
ejpam-3335	150	23	hh(x	hh(x	NOUN
ejpam-3335	150	24	)	)	PUNCT
ejpam-3335	151	1	⊆	⊆	NUM
ejpam-3335	151	2	hh((z	hh((z	X
ejpam-3335	151	3	·	·	PUNCT
ejpam-3335	151	4	y	y	X
ejpam-3335	151	5	)	)	PUNCT
ejpam-3335	151	6	·	·	PUNCT
ejpam-3335	151	7	(	(	PUNCT
ejpam-3335	151	8	z	z	NOUN
ejpam-3335	151	9	·	·	SYM
ejpam-3335	151	10	x))∪	x))∪	NOUN
ejpam-3335	151	11	hh(y	hh(y	NOUN
ejpam-3335	151	12	)	)	PUNCT
ejpam-3335	151	13	for	for	ADP
ejpam-3335	151	14	all	all	DET
ejpam-3335	151	15	x	x	PROPN
ejpam-3335	151	16	,	,	PUNCT
ejpam-3335	151	17	y	y	PROPN
ejpam-3335	151	18	,	,	PUNCT
ejpam-3335	151	19	z	z	PROPN
ejpam-3335	151	20	∈	∈	PROPN
ejpam-3335	151	21	a.	a.	NOUN
ejpam-3335	151	22	for	for	ADP
ejpam-3335	151	23	any	any	DET
ejpam-3335	151	24	x	x	SYM
ejpam-3335	151	25	∈	∈	PROPN
ejpam-3335	151	26	a	a	X
ejpam-3335	151	27	,	,	PUNCT
ejpam-3335	151	28	we	we	PRON
ejpam-3335	151	29	choose	choose	VERB
ejpam-3335	151	30	z	z	NOUN
ejpam-3335	151	31	=	=	PUNCT
ejpam-3335	151	32	x	x	PROPN
ejpam-3335	151	33	and	and	CCONJ
ejpam-3335	151	34	y	y	PROPN
ejpam-3335	151	35	=	=	SYM
ejpam-3335	151	36	0	0	PROPN
ejpam-3335	151	37	.	.	PUNCT
ejpam-3335	152	1	then	then	ADV
ejpam-3335	152	2	hh(x	hh(x	PUNCT
ejpam-3335	152	3	)	)	PUNCT
ejpam-3335	152	4	⊆	⊆	NUM
ejpam-3335	152	5	hh((x	hh((x	X
ejpam-3335	152	6	·	·	PUNCT
ejpam-3335	152	7	0	0	NUM
ejpam-3335	152	8	)	)	PUNCT
ejpam-3335	152	9	·	·	PUNCT
ejpam-3335	152	10	(	(	PUNCT
ejpam-3335	152	11	x	x	X
ejpam-3335	152	12	·	·	PUNCT
ejpam-3335	152	13	x	x	X
ejpam-3335	152	14	)	)	PUNCT
ejpam-3335	152	15	)	)	PUNCT
ejpam-3335	152	16	∪	∪	ADP
ejpam-3335	152	17	hh(0	hh(0	NOUN
ejpam-3335	152	18	)	)	PUNCT
ejpam-3335	152	19	=	=	SYM
ejpam-3335	152	20	hh(0	hh(0	NOUN
ejpam-3335	152	21	·	·	PUNCT
ejpam-3335	152	22	0	0	X
ejpam-3335	152	23	)	)	PUNCT
ejpam-3335	152	24	∪	∪	ADP
ejpam-3335	152	25	hh(0	hh(0	NOUN
ejpam-3335	152	26	)	)	PUNCT
ejpam-3335	152	27	(	(	PUNCT
ejpam-3335	152	28	(	(	PUNCT
ejpam-3335	152	29	up-3	up-3	NOUN
ejpam-3335	152	30	)	)	PUNCT
ejpam-3335	152	31	and	and	CCONJ
ejpam-3335	152	32	proposition	proposition	NOUN
ejpam-3335	152	33	1	1	NUM
ejpam-3335	152	34	(	(	PUNCT
ejpam-3335	152	35	1	1	NUM
ejpam-3335	152	36	)	)	PUNCT
ejpam-3335	152	37	)	)	PUNCT
ejpam-3335	153	1	=	=	PUNCT
ejpam-3335	153	2	hh(0	hh(0	NOUN
ejpam-3335	153	3	)	)	PUNCT
ejpam-3335	153	4	∪	∪	ADP
ejpam-3335	153	5	hh(0	hh(0	NOUN
ejpam-3335	153	6	)	)	PUNCT
ejpam-3335	153	7	(	(	PUNCT
ejpam-3335	153	8	(	(	PUNCT
ejpam-3335	153	9	up-2	up-2	NUM
ejpam-3335	153	10	)	)	PUNCT
ejpam-3335	153	11	)	)	PUNCT
ejpam-3335	154	1	=	=	PUNCT
ejpam-3335	154	2	hh(0	hh(0	NOUN
ejpam-3335	154	3	)	)	PUNCT
ejpam-3335	154	4	⊆	⊆	NUM
ejpam-3335	154	5	hh(x	hh(x	NOUN
ejpam-3335	154	6	)	)	PUNCT
ejpam-3335	154	7	,	,	PUNCT
ejpam-3335	154	8	so	so	SCONJ
ejpam-3335	154	9	hh(0	hh(0	NOUN
ejpam-3335	154	10	)	)	PUNCT
ejpam-3335	154	11	=	=	SYM
ejpam-3335	154	12	hh(x	hh(x	X
ejpam-3335	154	13	)	)	PUNCT
ejpam-3335	154	14	.	.	PUNCT
ejpam-3335	155	1	hence	hence	ADV
ejpam-3335	155	2	,	,	PUNCT
ejpam-3335	155	3	h	h	NOUN
ejpam-3335	155	4	is	be	AUX
ejpam-3335	155	5	a	a	DET
ejpam-3335	155	6	constant	constant	ADJ
ejpam-3335	155	7	hesitant	hesitant	ADJ
ejpam-3335	155	8	fuzzy	fuzzy	ADJ
ejpam-3335	155	9	set	set	VERB
ejpam-3335	155	10	on	on	ADP
ejpam-3335	155	11	a.	a.	NOUN
ejpam-3335	155	12	conversely	conversely	ADV
ejpam-3335	155	13	,	,	PUNCT
ejpam-3335	155	14	assume	assume	VERB
ejpam-3335	155	15	that	that	SCONJ
ejpam-3335	155	16	h	h	NOUN
ejpam-3335	155	17	is	be	AUX
ejpam-3335	155	18	a	a	DET
ejpam-3335	155	19	constant	constant	ADJ
ejpam-3335	155	20	hesitant	hesitant	ADJ
ejpam-3335	155	21	fuzzy	fuzzy	ADJ
ejpam-3335	155	22	set	set	VERB
ejpam-3335	155	23	on	on	ADP
ejpam-3335	155	24	a.	a.	NOUN
ejpam-3335	155	25	then	then	ADV
ejpam-3335	155	26	,	,	PUNCT
ejpam-3335	155	27	for	for	ADP
ejpam-3335	155	28	any	any	DET
ejpam-3335	155	29	x	x	SYM
ejpam-3335	155	30	∈	∈	PROPN
ejpam-3335	155	31	a	a	DET
ejpam-3335	155	32	,	,	PUNCT
ejpam-3335	155	33	hh(0	hh(0	NOUN
ejpam-3335	155	34	)	)	PUNCT
ejpam-3335	155	35	=	=	SYM
ejpam-3335	155	36	hh(x	hh(x	X
ejpam-3335	155	37	)	)	PUNCT
ejpam-3335	155	38	,	,	PUNCT
ejpam-3335	155	39	so	so	SCONJ
ejpam-3335	155	40	hh(0	hh(0	NOUN
ejpam-3335	155	41	)	)	PUNCT
ejpam-3335	155	42	⊆	⊆	NUM
ejpam-3335	155	43	hh(x	hh(x	X
ejpam-3335	155	44	)	)	PUNCT
ejpam-3335	155	45	.	.	PUNCT
ejpam-3335	156	1	for	for	ADP
ejpam-3335	156	2	any	any	DET
ejpam-3335	156	3	x	x	NOUN
ejpam-3335	156	4	,	,	PUNCT
ejpam-3335	156	5	y	y	PROPN
ejpam-3335	156	6	,	,	PUNCT
ejpam-3335	156	7	z	z	PROPN
ejpam-3335	156	8	∈	∈	PROPN
ejpam-3335	156	9	a	a	PRON
ejpam-3335	156	10	,	,	PUNCT
ejpam-3335	156	11	hh(x	hh(x	NOUN
ejpam-3335	156	12	)	)	PUNCT
ejpam-3335	156	13	=	=	SYM
ejpam-3335	156	14	hh((z·y)·(z·x	hh((z·y)·(z·x	PROPN
ejpam-3335	156	15	)	)	PUNCT
ejpam-3335	156	16	)	)	PUNCT
ejpam-3335	157	1	=	=	NOUN
ejpam-3335	157	2	hh(y	hh(y	NOUN
ejpam-3335	157	3	)	)	PUNCT
ejpam-3335	157	4	,	,	PUNCT
ejpam-3335	157	5	so	so	CCONJ
ejpam-3335	157	6	hh(x	hh(x	PUNCT
ejpam-3335	157	7	)	)	PUNCT
ejpam-3335	158	1	=	=	VERB
ejpam-3335	158	2	hh((z	hh((z	X
ejpam-3335	158	3	·	·	PUNCT
ejpam-3335	158	4	y	y	X
ejpam-3335	158	5	)	)	PUNCT
ejpam-3335	158	6	·	·	PUNCT
ejpam-3335	158	7	(	(	PUNCT
ejpam-3335	158	8	z	z	NOUN
ejpam-3335	158	9	·	·	PUNCT
ejpam-3335	158	10	x	x	X
ejpam-3335	158	11	)	)	PUNCT
ejpam-3335	158	12	)	)	PUNCT
ejpam-3335	158	13	∪	∪	ADP
ejpam-3335	158	14	hh(y	hh(y	NOUN
ejpam-3335	158	15	)	)	PUNCT
ejpam-3335	158	16	.	.	PUNCT
ejpam-3335	159	1	thus	thus	ADV
ejpam-3335	159	2	hh(x	hh(x	PUNCT
ejpam-3335	159	3	)	)	PUNCT
ejpam-3335	160	1	⊆	⊆	NUM
ejpam-3335	160	2	hh((z	hh((z	X
ejpam-3335	160	3	·	·	PUNCT
ejpam-3335	160	4	y	y	X
ejpam-3335	160	5	)	)	PUNCT
ejpam-3335	160	6	·	·	PUNCT
ejpam-3335	160	7	(	(	PUNCT
ejpam-3335	160	8	z	z	NOUN
ejpam-3335	160	9	·	·	PUNCT
ejpam-3335	160	10	x	x	X
ejpam-3335	160	11	)	)	PUNCT
ejpam-3335	160	12	)	)	PUNCT
ejpam-3335	160	13	∪	∪	ADP
ejpam-3335	160	14	hh(y	hh(y	NOUN
ejpam-3335	160	15	)	)	PUNCT
ejpam-3335	160	16	.	.	PUNCT
ejpam-3335	161	1	hence	hence	ADV
ejpam-3335	161	2	,	,	PUNCT
ejpam-3335	161	3	h	h	PROPN
ejpam-3335	161	4	is	be	AUX
ejpam-3335	161	5	an	an	DET
ejpam-3335	161	6	anti	anti	ADJ
ejpam-3335	161	7	-	-	ADJ
ejpam-3335	161	8	hesitant	hesitant	ADJ
ejpam-3335	161	9	fuzzy	fuzzy	ADJ
ejpam-3335	161	10	strongly	strongly	ADV
ejpam-3335	161	11	up	up	ADP
ejpam-3335	161	12	-	-	PUNCT
ejpam-3335	161	13	ideal	ideal	NOUN
ejpam-3335	161	14	of	of	ADP
ejpam-3335	161	15	a.	a.	NOUN
ejpam-3335	161	16	corollary	corollary	NOUN
ejpam-3335	161	17	1	1	PROPN
ejpam-3335	161	18	.	.	PUNCT
ejpam-3335	162	1	for	for	ADP
ejpam-3335	162	2	up	up	ADV
ejpam-3335	162	3	-	-	PUNCT
ejpam-3335	162	4	algebras	algebras	X
ejpam-3335	162	5	,	,	PUNCT
ejpam-3335	162	6	we	we	PRON
ejpam-3335	162	7	can	can	AUX
ejpam-3335	162	8	conclude	conclude	VERB
ejpam-3335	162	9	that	that	SCONJ
ejpam-3335	162	10	the	the	DET
ejpam-3335	162	11	notions	notion	NOUN
ejpam-3335	162	12	of	of	ADP
ejpam-3335	162	13	anti	anti	ADJ
ejpam-3335	162	14	-	-	ADJ
ejpam-3335	162	15	hesitant	hesitant	ADJ
ejpam-3335	162	16	fuzzy	fuzzy	ADJ
ejpam-3335	162	17	strongly	strongly	ADV
ejpam-3335	162	18	up	up	ADP
ejpam-3335	162	19	-	-	PUNCT
ejpam-3335	162	20	ideals	ideal	NOUN
ejpam-3335	162	21	and	and	CCONJ
ejpam-3335	162	22	hesitant	hesitant	ADJ
ejpam-3335	162	23	fuzzy	fuzzy	ADJ
ejpam-3335	162	24	strongly	strongly	ADV
ejpam-3335	162	25	up	up	ADP
ejpam-3335	162	26	-	-	PUNCT
ejpam-3335	162	27	ideals	ideal	NOUN
ejpam-3335	162	28	coincide	coincide	NOUN
ejpam-3335	162	29	.	.	PUNCT
ejpam-3335	163	1	p.	p.	NOUN
ejpam-3335	163	2	mosrijai	mosrijai	PROPN
ejpam-3335	163	3	,	,	PUNCT
ejpam-3335	163	4	a.	a.	NOUN
ejpam-3335	163	5	iampan	iampan	PROPN
ejpam-3335	163	6	/	/	SYM
ejpam-3335	163	7	eur	eur	PROPN
ejpam-3335	163	8	.	.	PUNCT
ejpam-3335	164	1	j.	j.	PROPN
ejpam-3335	164	2	pure	pure	PROPN
ejpam-3335	164	3	appl	appl	PROPN
ejpam-3335	164	4	.	.	PROPN
ejpam-3335	164	5	math	math	PROPN
ejpam-3335	164	6	,	,	PUNCT
ejpam-3335	164	7	11	11	NUM
ejpam-3335	164	8	(	(	PUNCT
ejpam-3335	164	9	4	4	NUM
ejpam-3335	164	10	)	)	PUNCT
ejpam-3335	164	11	(	(	PUNCT
ejpam-3335	164	12	2018	2018	NUM
ejpam-3335	164	13	)	)	PUNCT
ejpam-3335	164	14	,	,	PUNCT
ejpam-3335	164	15	976	976	NUM
ejpam-3335	164	16	-	-	SYM
ejpam-3335	164	17	1002	1002	NUM
ejpam-3335	164	18	983	983	NUM
ejpam-3335	164	19	proof	proof	NOUN
ejpam-3335	164	20	.	.	PUNCT
ejpam-3335	165	1	it	it	PRON
ejpam-3335	165	2	is	be	AUX
ejpam-3335	165	3	straightforward	straightforward	ADJ
ejpam-3335	165	4	by	by	ADP
ejpam-3335	165	5	theorem	theorem	NOUN
ejpam-3335	165	6	2	2	NUM
ejpam-3335	165	7	and	and	CCONJ
ejpam-3335	165	8	3	3	NUM
ejpam-3335	165	9	.	.	PUNCT
ejpam-3335	165	10	corollary	corollary	ADJ
ejpam-3335	165	11	2	2	NUM
ejpam-3335	165	12	.	.	PUNCT
ejpam-3335	166	1	a	a	DET
ejpam-3335	166	2	hesitant	hesitant	ADJ
ejpam-3335	166	3	fuzzy	fuzzy	ADJ
ejpam-3335	166	4	set	set	VERB
ejpam-3335	166	5	h	h	NOUN
ejpam-3335	166	6	on	on	ADP
ejpam-3335	166	7	a	a	PRON
ejpam-3335	166	8	is	be	AUX
ejpam-3335	166	9	an	an	DET
ejpam-3335	166	10	anti	anti	ADJ
ejpam-3335	166	11	-	-	ADJ
ejpam-3335	166	12	hesitant	hesitant	ADJ
ejpam-3335	166	13	fuzzy	fuzzy	ADJ
ejpam-3335	166	14	strongly	strongly	ADV
ejpam-3335	166	15	up	up	ADP
ejpam-3335	166	16	-	-	PUNCT
ejpam-3335	166	17	ideal	ideal	NOUN
ejpam-3335	166	18	of	of	ADP
ejpam-3335	166	19	a	a	DET
ejpam-3335	166	20	if	if	NOUN
ejpam-3335	166	21	and	and	CCONJ
ejpam-3335	166	22	only	only	ADV
ejpam-3335	166	23	if	if	SCONJ
ejpam-3335	166	24	h	h	NOUN
ejpam-3335	166	25	on	on	ADP
ejpam-3335	166	26	a	a	PRON
ejpam-3335	166	27	is	be	AUX
ejpam-3335	166	28	an	an	DET
ejpam-3335	166	29	anti	anti	ADJ
ejpam-3335	166	30	-	-	ADJ
ejpam-3335	166	31	hesitant	hesitant	ADJ
ejpam-3335	166	32	fuzzy	fuzzy	ADJ
ejpam-3335	166	33	strongly	strongly	ADV
ejpam-3335	166	34	up	up	ADP
ejpam-3335	166	35	-	-	PUNCT
ejpam-3335	166	36	ideal	ideal	NOUN
ejpam-3335	166	37	of	of	ADP
ejpam-3335	166	38	a.	a.	NOUN
ejpam-3335	166	39	proof	proof	NOUN
ejpam-3335	166	40	.	.	PUNCT
ejpam-3335	167	1	it	it	PRON
ejpam-3335	167	2	is	be	AUX
ejpam-3335	167	3	straightforward	straightforward	ADJ
ejpam-3335	167	4	by	by	ADP
ejpam-3335	167	5	theorem	theorem	NOUN
ejpam-3335	167	6	1	1	NUM
ejpam-3335	167	7	and	and	CCONJ
ejpam-3335	167	8	3	3	NUM
ejpam-3335	167	9	.	.	PUNCT
ejpam-3335	167	10	by	by	ADP
ejpam-3335	167	11	using	use	VERB
ejpam-3335	167	12	corollary	corollary	ADJ
ejpam-3335	167	13	1	1	NUM
ejpam-3335	167	14	,	,	PUNCT
ejpam-3335	167	15	we	we	PRON
ejpam-3335	167	16	can	can	AUX
ejpam-3335	167	17	show	show	VERB
ejpam-3335	167	18	that	that	SCONJ
ejpam-3335	167	19	a	a	DET
ejpam-3335	167	20	hesitant	hesitant	ADJ
ejpam-3335	167	21	fuzzy	fuzzy	ADJ
ejpam-3335	167	22	set	set	VERB
ejpam-3335	167	23	h	h	NOUN
ejpam-3335	167	24	on	on	ADP
ejpam-3335	167	25	a	a	PRON
ejpam-3335	167	26	is	be	AUX
ejpam-3335	167	27	an	an	DET
ejpam-3335	167	28	anti	anti	ADJ
ejpam-3335	167	29	-	-	ADJ
ejpam-3335	167	30	hesitant	hesitant	ADJ
ejpam-3335	167	31	fuzzy	fuzzy	ADJ
ejpam-3335	167	32	strongly	strongly	ADV
ejpam-3335	167	33	up	up	ADP
ejpam-3335	167	34	-	-	PUNCT
ejpam-3335	167	35	ideal	ideal	NOUN
ejpam-3335	167	36	of	of	ADP
ejpam-3335	167	37	a	a	DET
ejpam-3335	167	38	if	if	NOUN
ejpam-3335	167	39	and	and	CCONJ
ejpam-3335	167	40	only	only	ADV
ejpam-3335	167	41	if	if	SCONJ
ejpam-3335	167	42	h	h	NOUN
ejpam-3335	167	43	on	on	ADP
ejpam-3335	167	44	a	a	PRON
ejpam-3335	167	45	is	be	AUX
ejpam-3335	167	46	an	an	DET
ejpam-3335	167	47	anti	anti	ADJ
ejpam-3335	167	48	-	-	ADJ
ejpam-3335	167	49	hesitant	hesitant	ADJ
ejpam-3335	167	50	fuzzy	fuzzy	ADJ
ejpam-3335	167	51	strongly	strongly	ADV
ejpam-3335	167	52	up	up	ADP
ejpam-3335	167	53	-	-	PUNCT
ejpam-3335	167	54	ideal	ideal	NOUN
ejpam-3335	167	55	of	of	ADP
ejpam-3335	167	56	a.	a.	NOUN
ejpam-3335	167	57	theorem	theorem	NOUN
ejpam-3335	167	58	4	4	NUM
ejpam-3335	167	59	.	.	PUNCT
ejpam-3335	168	1	every	every	DET
ejpam-3335	168	2	anti	anti	ADJ
ejpam-3335	168	3	-	-	ADJ
ejpam-3335	168	4	hesitant	hesitant	ADJ
ejpam-3335	168	5	fuzzy	fuzzy	ADJ
ejpam-3335	168	6	up	up	NOUN
ejpam-3335	168	7	-	-	PUNCT
ejpam-3335	168	8	filter	filter	NOUN
ejpam-3335	168	9	of	of	ADP
ejpam-3335	168	10	a	a	PRON
ejpam-3335	168	11	is	be	AUX
ejpam-3335	168	12	an	an	DET
ejpam-3335	168	13	anti	anti	ADJ
ejpam-3335	168	14	-	-	ADJ
ejpam-3335	168	15	hesitant	hesitant	ADJ
ejpam-3335	168	16	fuzzy	fuzzy	ADJ
ejpam-3335	168	17	up	up	NOUN
ejpam-3335	168	18	-	-	PUNCT
ejpam-3335	168	19	subalgebra	subalgebra	NOUN
ejpam-3335	168	20	of	of	ADP
ejpam-3335	168	21	a.	a.	NOUN
ejpam-3335	168	22	proof	proof	NOUN
ejpam-3335	168	23	.	.	PUNCT
ejpam-3335	169	1	assume	assume	VERB
ejpam-3335	169	2	that	that	SCONJ
ejpam-3335	169	3	h	h	NOUN
ejpam-3335	169	4	is	be	AUX
ejpam-3335	169	5	an	an	DET
ejpam-3335	169	6	anti	anti	ADJ
ejpam-3335	169	7	-	-	ADJ
ejpam-3335	169	8	hesitant	hesitant	ADJ
ejpam-3335	169	9	fuzzy	fuzzy	ADJ
ejpam-3335	169	10	up	up	NOUN
ejpam-3335	169	11	-	-	PUNCT
ejpam-3335	169	12	filter	filter	NOUN
ejpam-3335	169	13	of	of	ADP
ejpam-3335	169	14	a.	a.	NOUN
ejpam-3335	169	15	then	then	ADV
ejpam-3335	169	16	for	for	ADP
ejpam-3335	169	17	any	any	DET
ejpam-3335	169	18	x	x	NOUN
ejpam-3335	169	19	,	,	PUNCT
ejpam-3335	169	20	y	y	PROPN
ejpam-3335	169	21	∈	∈	PROPN
ejpam-3335	169	22	a	a	PRON
ejpam-3335	169	23	,	,	PUNCT
ejpam-3335	169	24	hh(x	hh(x	PUNCT
ejpam-3335	169	25	·	·	PUNCT
ejpam-3335	169	26	y	y	X
ejpam-3335	169	27	)	)	PUNCT
ejpam-3335	169	28	⊆	⊆	NUM
ejpam-3335	169	29	hh(y	hh(y	NOUN
ejpam-3335	169	30	·	·	PUNCT
ejpam-3335	169	31	(	(	PUNCT
ejpam-3335	169	32	x	x	X
ejpam-3335	169	33	·	·	PUNCT
ejpam-3335	169	34	y	y	NOUN
ejpam-3335	169	35	)	)	PUNCT
ejpam-3335	169	36	)	)	PUNCT
ejpam-3335	169	37	∪	∪	ADP
ejpam-3335	169	38	hh(y	hh(y	NOUN
ejpam-3335	169	39	)	)	PUNCT
ejpam-3335	169	40	(	(	PUNCT
ejpam-3335	169	41	definition	definition	NOUN
ejpam-3335	169	42	7	7	NUM
ejpam-3335	169	43	(	(	PUNCT
ejpam-3335	169	44	2	2	NUM
ejpam-3335	169	45	)	)	PUNCT
ejpam-3335	169	46	)	)	PUNCT
ejpam-3335	170	1	=	=	PUNCT
ejpam-3335	170	2	hh(0	hh(0	NOUN
ejpam-3335	170	3	)	)	PUNCT
ejpam-3335	170	4	∪	∪	ADP
ejpam-3335	170	5	hh(y	hh(y	NOUN
ejpam-3335	170	6	)	)	PUNCT
ejpam-3335	170	7	(	(	PUNCT
ejpam-3335	170	8	proposition	proposition	NOUN
ejpam-3335	170	9	1	1	NUM
ejpam-3335	170	10	(	(	PUNCT
ejpam-3335	170	11	5	5	NUM
ejpam-3335	170	12	)	)	PUNCT
ejpam-3335	170	13	)	)	PUNCT
ejpam-3335	170	14	=	=	SYM
ejpam-3335	171	1	hh(y	hh(y	X
ejpam-3335	171	2	)	)	PUNCT
ejpam-3335	171	3	(	(	PUNCT
ejpam-3335	171	4	definition	definition	NOUN
ejpam-3335	171	5	7	7	NUM
ejpam-3335	171	6	(	(	PUNCT
ejpam-3335	171	7	1	1	NUM
ejpam-3335	171	8	)	)	PUNCT
ejpam-3335	171	9	)	)	PUNCT
ejpam-3335	171	10	⊆	⊆	NUM
ejpam-3335	171	11	hh(x	hh(x	NOUN
ejpam-3335	171	12	)	)	PUNCT
ejpam-3335	171	13	∪	∪	ADP
ejpam-3335	171	14	hh(y	hh(y	NOUN
ejpam-3335	171	15	)	)	PUNCT
ejpam-3335	171	16	.	.	PUNCT
ejpam-3335	172	1	hence	hence	ADV
ejpam-3335	172	2	,	,	PUNCT
ejpam-3335	172	3	h	h	PROPN
ejpam-3335	172	4	is	be	AUX
ejpam-3335	172	5	an	an	DET
ejpam-3335	172	6	anti	anti	ADJ
ejpam-3335	172	7	-	-	ADJ
ejpam-3335	172	8	hesitant	hesitant	ADJ
ejpam-3335	172	9	fuzzy	fuzzy	ADJ
ejpam-3335	172	10	up	up	NOUN
ejpam-3335	172	11	-	-	PUNCT
ejpam-3335	172	12	subalgebra	subalgebra	NOUN
ejpam-3335	172	13	of	of	ADP
ejpam-3335	172	14	a.	a.	NOUN
ejpam-3335	172	15	the	the	DET
ejpam-3335	172	16	converse	converse	NOUN
ejpam-3335	172	17	of	of	ADP
ejpam-3335	172	18	theorem	theorem	NOUN
ejpam-3335	172	19	4	4	NUM
ejpam-3335	172	20	is	be	AUX
ejpam-3335	172	21	not	not	PART
ejpam-3335	172	22	true	true	ADJ
ejpam-3335	172	23	in	in	ADP
ejpam-3335	172	24	general	general	ADJ
ejpam-3335	172	25	.	.	PUNCT
ejpam-3335	173	1	by	by	ADP
ejpam-3335	173	2	example	example	NOUN
ejpam-3335	173	3	4	4	NUM
ejpam-3335	173	4	,	,	PUNCT
ejpam-3335	173	5	we	we	PRON
ejpam-3335	173	6	obtain	obtain	VERB
ejpam-3335	173	7	h	h	NOUN
ejpam-3335	173	8	is	be	AUX
ejpam-3335	173	9	an	an	DET
ejpam-3335	173	10	anti	anti	ADJ
ejpam-3335	173	11	-	-	ADJ
ejpam-3335	173	12	hesitant	hesitant	ADJ
ejpam-3335	173	13	fuzzy	fuzzy	ADJ
ejpam-3335	173	14	up	up	NOUN
ejpam-3335	173	15	-	-	PUNCT
ejpam-3335	173	16	subalgebra	subalgebra	NOUN
ejpam-3335	173	17	of	of	ADP
ejpam-3335	173	18	a.	a.	NOUN
ejpam-3335	173	19	since	since	SCONJ
ejpam-3335	173	20	hh(1	hh(1	NOUN
ejpam-3335	173	21	)	)	PUNCT
ejpam-3335	173	22	=	=	PUNCT
ejpam-3335	173	23	{	{	PUNCT
ejpam-3335	173	24	0.5	0.5	NUM
ejpam-3335	173	25	}	}	PUNCT
ejpam-3335	173	26	*	*	PUNCT
ejpam-3335	173	27	{	{	PUNCT
ejpam-3335	173	28	0.6	0.6	NUM
ejpam-3335	173	29	}	}	PUNCT
ejpam-3335	173	30	=	=	SYM
ejpam-3335	173	31	∅∪{0.6	∅∪{0.6	NOUN
ejpam-3335	173	32	}	}	PUNCT
ejpam-3335	173	33	=	=	PUNCT
ejpam-3335	173	34	hh(0)∪	hh(0)∪	VERB
ejpam-3335	173	35	hh(2	hh(2	NOUN
ejpam-3335	173	36	)	)	PUNCT
ejpam-3335	173	37	=	=	SYM
ejpam-3335	173	38	hh(2·1)∪hh(2	hh(2·1)∪hh(2	NOUN
ejpam-3335	173	39	)	)	PUNCT
ejpam-3335	173	40	,	,	PUNCT
ejpam-3335	173	41	we	we	PRON
ejpam-3335	173	42	have	have	VERB
ejpam-3335	173	43	h	h	NOUN
ejpam-3335	173	44	is	be	AUX
ejpam-3335	173	45	not	not	PART
ejpam-3335	173	46	an	an	DET
ejpam-3335	173	47	anti	anti	ADJ
ejpam-3335	173	48	-	-	ADJ
ejpam-3335	173	49	hesitant	hesitant	ADJ
ejpam-3335	173	50	fuzzy	fuzzy	ADJ
ejpam-3335	173	51	up	up	NOUN
ejpam-3335	173	52	-	-	PUNCT
ejpam-3335	173	53	filter	filter	NOUN
ejpam-3335	173	54	of	of	ADP
ejpam-3335	173	55	a.	a.	NOUN
ejpam-3335	173	56	therefore	therefore	ADV
ejpam-3335	173	57	,	,	PUNCT
ejpam-3335	173	58	the	the	DET
ejpam-3335	173	59	notion	notion	NOUN
ejpam-3335	173	60	of	of	ADP
ejpam-3335	173	61	anti	anti	ADJ
ejpam-3335	173	62	-	-	ADJ
ejpam-3335	173	63	hesitant	hesitant	ADJ
ejpam-3335	173	64	fuzzy	fuzzy	ADJ
ejpam-3335	173	65	up	up	ADP
ejpam-3335	173	66	-	-	PUNCT
ejpam-3335	173	67	subalgebras	subalgebra	NOUN
ejpam-3335	173	68	of	of	ADP
ejpam-3335	173	69	up	up	ADV
ejpam-3335	173	70	-	-	PUNCT
ejpam-3335	173	71	algebras	algebras	PROPN
ejpam-3335	173	72	is	be	AUX
ejpam-3335	173	73	generalization	generalization	NOUN
ejpam-3335	173	74	of	of	ADP
ejpam-3335	173	75	antihesitant	antihesitant	PROPN
ejpam-3335	173	76	fuzzy	fuzzy	PROPN
ejpam-3335	173	77	up	up	NOUN
ejpam-3335	173	78	-	-	PUNCT
ejpam-3335	173	79	filters	filter	NOUN
ejpam-3335	173	80	.	.	PUNCT
ejpam-3335	174	1	theorem	theorem	NOUN
ejpam-3335	174	2	5	5	NUM
ejpam-3335	174	3	.	.	PUNCT
ejpam-3335	175	1	every	every	DET
ejpam-3335	175	2	anti	anti	ADJ
ejpam-3335	175	3	-	-	ADJ
ejpam-3335	175	4	hesitant	hesitant	ADJ
ejpam-3335	175	5	fuzzy	fuzzy	ADJ
ejpam-3335	175	6	up	up	NOUN
ejpam-3335	175	7	-	-	PUNCT
ejpam-3335	175	8	ideal	ideal	NOUN
ejpam-3335	175	9	of	of	ADP
ejpam-3335	175	10	a	a	PRON
ejpam-3335	175	11	is	be	AUX
ejpam-3335	175	12	an	an	DET
ejpam-3335	175	13	anti	anti	ADJ
ejpam-3335	175	14	-	-	ADJ
ejpam-3335	175	15	hesitant	hesitant	ADJ
ejpam-3335	175	16	fuzzy	fuzzy	ADJ
ejpam-3335	175	17	up	up	NOUN
ejpam-3335	175	18	-	-	PUNCT
ejpam-3335	175	19	filter	filter	NOUN
ejpam-3335	175	20	of	of	ADP
ejpam-3335	175	21	a.	a.	NOUN
ejpam-3335	175	22	proof	proof	NOUN
ejpam-3335	175	23	.	.	PUNCT
ejpam-3335	176	1	assume	assume	VERB
ejpam-3335	176	2	that	that	SCONJ
ejpam-3335	176	3	h	h	NOUN
ejpam-3335	176	4	is	be	AUX
ejpam-3335	176	5	an	an	DET
ejpam-3335	176	6	anti	anti	ADJ
ejpam-3335	176	7	-	-	ADJ
ejpam-3335	176	8	hesitant	hesitant	ADJ
ejpam-3335	176	9	fuzzy	fuzzy	ADJ
ejpam-3335	176	10	up	up	NOUN
ejpam-3335	176	11	-	-	PUNCT
ejpam-3335	176	12	ideal	ideal	NOUN
ejpam-3335	176	13	of	of	ADP
ejpam-3335	176	14	a.	a.	NOUN
ejpam-3335	176	15	then	then	ADV
ejpam-3335	176	16	for	for	ADP
ejpam-3335	176	17	any	any	DET
ejpam-3335	176	18	x	x	NOUN
ejpam-3335	176	19	,	,	PUNCT
ejpam-3335	176	20	y	y	PROPN
ejpam-3335	176	21	∈	∈	PROPN
ejpam-3335	176	22	a	a	PRON
ejpam-3335	176	23	,	,	PUNCT
ejpam-3335	176	24	hh(0	hh(0	NOUN
ejpam-3335	176	25	)	)	PUNCT
ejpam-3335	176	26	⊆	⊆	NUM
ejpam-3335	176	27	hh(x	hh(x	NUM
ejpam-3335	176	28	)	)	PUNCT
ejpam-3335	176	29	and	and	CCONJ
ejpam-3335	176	30	hh(y	hh(y	NOUN
ejpam-3335	176	31	)	)	PUNCT
ejpam-3335	177	1	=	=	SYM
ejpam-3335	177	2	hh(0	hh(0	NOUN
ejpam-3335	177	3	·	·	PUNCT
ejpam-3335	177	4	y	y	X
ejpam-3335	177	5	)	)	PUNCT
ejpam-3335	177	6	(	(	PUNCT
ejpam-3335	177	7	(	(	PUNCT
ejpam-3335	177	8	up-2	up-2	NUM
ejpam-3335	177	9	)	)	PUNCT
ejpam-3335	177	10	)	)	PUNCT
ejpam-3335	178	1	⊆	⊆	NUM
ejpam-3335	178	2	hh(0	hh(0	NOUN
ejpam-3335	178	3	·	·	PUNCT
ejpam-3335	178	4	(	(	PUNCT
ejpam-3335	178	5	x	x	X
ejpam-3335	178	6	·	·	PUNCT
ejpam-3335	178	7	y	y	NOUN
ejpam-3335	178	8	)	)	PUNCT
ejpam-3335	178	9	)	)	PUNCT
ejpam-3335	178	10	∪	∪	ADP
ejpam-3335	178	11	hh(x	hh(x	PRON
ejpam-3335	178	12	)	)	PUNCT
ejpam-3335	178	13	(	(	PUNCT
ejpam-3335	178	14	definition	definition	NOUN
ejpam-3335	178	15	8	8	NUM
ejpam-3335	178	16	(	(	PUNCT
ejpam-3335	178	17	2	2	NUM
ejpam-3335	178	18	)	)	PUNCT
ejpam-3335	178	19	)	)	PUNCT
ejpam-3335	178	20	=	=	SYM
ejpam-3335	178	21	hh(x	hh(x	X
ejpam-3335	178	22	·	·	PUNCT
ejpam-3335	178	23	y	y	X
ejpam-3335	178	24	)	)	PUNCT
ejpam-3335	178	25	∪	∪	ADP
ejpam-3335	178	26	hh(x	hh(x	NOUN
ejpam-3335	178	27	)	)	PUNCT
ejpam-3335	178	28	.	.	PUNCT
ejpam-3335	179	1	(	(	PUNCT
ejpam-3335	179	2	(	(	PUNCT
ejpam-3335	179	3	up-2	up-2	NUM
ejpam-3335	179	4	)	)	PUNCT
ejpam-3335	179	5	)	)	PUNCT
ejpam-3335	179	6	hence	hence	ADV
ejpam-3335	179	7	,	,	PUNCT
ejpam-3335	179	8	h	h	NOUN
ejpam-3335	179	9	is	be	AUX
ejpam-3335	179	10	an	an	DET
ejpam-3335	179	11	anti	anti	ADJ
ejpam-3335	179	12	-	-	ADJ
ejpam-3335	179	13	hesitant	hesitant	ADJ
ejpam-3335	179	14	fuzzy	fuzzy	ADJ
ejpam-3335	179	15	up	up	NOUN
ejpam-3335	179	16	-	-	PUNCT
ejpam-3335	179	17	filter	filter	NOUN
ejpam-3335	179	18	of	of	ADP
ejpam-3335	179	19	a.	a.	NOUN
ejpam-3335	179	20	the	the	DET
ejpam-3335	179	21	converse	converse	NOUN
ejpam-3335	179	22	of	of	ADP
ejpam-3335	179	23	theorem	theorem	NOUN
ejpam-3335	179	24	5	5	NUM
ejpam-3335	179	25	is	be	AUX
ejpam-3335	179	26	not	not	PART
ejpam-3335	179	27	true	true	ADJ
ejpam-3335	179	28	in	in	ADP
ejpam-3335	179	29	general	general	ADJ
ejpam-3335	179	30	.	.	PUNCT
ejpam-3335	180	1	by	by	ADP
ejpam-3335	180	2	example	example	NOUN
ejpam-3335	180	3	5	5	NUM
ejpam-3335	180	4	,	,	PUNCT
ejpam-3335	180	5	we	we	PRON
ejpam-3335	180	6	obtain	obtain	VERB
ejpam-3335	180	7	h	h	NOUN
ejpam-3335	180	8	is	be	AUX
ejpam-3335	180	9	an	an	DET
ejpam-3335	180	10	anti	anti	ADJ
ejpam-3335	180	11	-	-	ADJ
ejpam-3335	180	12	hesitant	hesitant	ADJ
ejpam-3335	180	13	fuzzy	fuzzy	ADJ
ejpam-3335	180	14	up	up	NOUN
ejpam-3335	180	15	-	-	PUNCT
ejpam-3335	180	16	filter	filter	NOUN
ejpam-3335	180	17	of	of	ADP
ejpam-3335	180	18	a.	a.	NOUN
ejpam-3335	180	19	since	since	SCONJ
ejpam-3335	180	20	hh(3	hh(3	PROPN
ejpam-3335	180	21	·	·	PUNCT
ejpam-3335	180	22	4	4	X
ejpam-3335	180	23	)	)	PUNCT
ejpam-3335	180	24	=	=	SYM
ejpam-3335	180	25	hh(3	hh(3	NOUN
ejpam-3335	180	26	)	)	PUNCT
ejpam-3335	180	27	=	=	NOUN
ejpam-3335	181	1	[	[	X
ejpam-3335	181	2	0.6	0.6	NUM
ejpam-3335	181	3	,	,	PUNCT
ejpam-3335	181	4	0.9	0.9	NUM
ejpam-3335	181	5	]	]	PUNCT
ejpam-3335	181	6	*	*	PUNCT
ejpam-3335	182	1	[	[	X
ejpam-3335	182	2	0.8	0.8	NUM
ejpam-3335	182	3	,	,	PUNCT
ejpam-3335	182	4	0.9	0.9	NUM
ejpam-3335	182	5	)	)	PUNCT
ejpam-3335	182	6	=	=	PRON
ejpam-3335	182	7	{	{	PUNCT
ejpam-3335	182	8	0.8}∪	0.8}∪	X
ejpam-3335	183	1	[	[	X
ejpam-3335	183	2	0.8	0.8	NUM
ejpam-3335	183	3	,	,	PUNCT
ejpam-3335	183	4	0.9	0.9	NUM
ejpam-3335	183	5	)	)	PUNCT
ejpam-3335	183	6	=	=	SYM
ejpam-3335	183	7	hh(0)∪hh(2	hh(0)∪hh(2	NOUN
ejpam-3335	183	8	)	)	PUNCT
ejpam-3335	183	9	=	=	PUNCT
ejpam-3335	184	1	hh(3	hh(3	X
ejpam-3335	184	2	·	·	PUNCT
ejpam-3335	184	3	(	(	PUNCT
ejpam-3335	184	4	2	2	NUM
ejpam-3335	184	5	·	·	SYM
ejpam-3335	184	6	4))∪hh(2	4))∪hh(2	NOUN
ejpam-3335	184	7	)	)	PUNCT
ejpam-3335	184	8	,	,	PUNCT
ejpam-3335	184	9	we	we	PRON
ejpam-3335	184	10	have	have	VERB
ejpam-3335	184	11	h	h	NOUN
ejpam-3335	184	12	is	be	AUX
ejpam-3335	184	13	not	not	PART
ejpam-3335	184	14	an	an	DET
ejpam-3335	184	15	anti	anti	ADJ
ejpam-3335	184	16	-	-	ADJ
ejpam-3335	184	17	hesitant	hesitant	ADJ
ejpam-3335	184	18	fuzzy	fuzzy	ADJ
ejpam-3335	184	19	up	up	NOUN
ejpam-3335	184	20	-	-	PUNCT
ejpam-3335	184	21	ideal	ideal	NOUN
ejpam-3335	184	22	of	of	ADP
ejpam-3335	184	23	a.	a.	NOUN
ejpam-3335	184	24	therefore	therefore	ADV
ejpam-3335	184	25	,	,	PUNCT
ejpam-3335	184	26	the	the	DET
ejpam-3335	184	27	notion	notion	NOUN
ejpam-3335	184	28	of	of	ADP
ejpam-3335	184	29	anti	anti	ADJ
ejpam-3335	184	30	-	-	ADJ
ejpam-3335	184	31	hesitant	hesitant	ADJ
ejpam-3335	184	32	fuzzy	fuzzy	ADJ
ejpam-3335	184	33	up	up	NOUN
ejpam-3335	184	34	-	-	PUNCT
ejpam-3335	184	35	filters	filter	NOUN
ejpam-3335	184	36	of	of	ADP
ejpam-3335	184	37	up	up	ADV
ejpam-3335	184	38	-	-	PUNCT
ejpam-3335	184	39	algebras	algebras	PROPN
ejpam-3335	184	40	is	be	AUX
ejpam-3335	184	41	generalization	generalization	NOUN
ejpam-3335	184	42	of	of	ADP
ejpam-3335	184	43	anti	anti	ADJ
ejpam-3335	184	44	-	-	ADJ
ejpam-3335	184	45	hesitant	hesitant	ADJ
ejpam-3335	184	46	fuzzy	fuzzy	ADJ
ejpam-3335	184	47	up	up	NOUN
ejpam-3335	184	48	-	-	PUNCT
ejpam-3335	184	49	ideals	ideal	NOUN
ejpam-3335	184	50	.	.	PUNCT
ejpam-3335	185	1	p.	p.	NOUN
ejpam-3335	185	2	mosrijai	mosrijai	PROPN
ejpam-3335	185	3	,	,	PUNCT
ejpam-3335	185	4	a.	a.	NOUN
ejpam-3335	185	5	iampan	iampan	PROPN
ejpam-3335	185	6	/	/	SYM
ejpam-3335	185	7	eur	eur	PROPN
ejpam-3335	185	8	.	.	PUNCT
ejpam-3335	186	1	j.	j.	PROPN
ejpam-3335	186	2	pure	pure	PROPN
ejpam-3335	186	3	appl	appl	PROPN
ejpam-3335	186	4	.	.	PROPN
ejpam-3335	186	5	math	math	PROPN
ejpam-3335	186	6	,	,	PUNCT
ejpam-3335	186	7	11	11	NUM
ejpam-3335	186	8	(	(	PUNCT
ejpam-3335	186	9	4	4	NUM
ejpam-3335	186	10	)	)	PUNCT
ejpam-3335	186	11	(	(	PUNCT
ejpam-3335	186	12	2018	2018	NUM
ejpam-3335	186	13	)	)	PUNCT
ejpam-3335	186	14	,	,	PUNCT
ejpam-3335	186	15	976	976	NUM
ejpam-3335	186	16	-	-	SYM
ejpam-3335	186	17	1002	1002	NUM
ejpam-3335	186	18	984	984	NUM
ejpam-3335	186	19	theorem	theorem	VERB
ejpam-3335	186	20	6	6	NUM
ejpam-3335	186	21	.	.	PUNCT
ejpam-3335	187	1	every	every	DET
ejpam-3335	187	2	anti	anti	ADJ
ejpam-3335	187	3	-	-	ADJ
ejpam-3335	187	4	hesitant	hesitant	ADJ
ejpam-3335	187	5	fuzzy	fuzzy	ADJ
ejpam-3335	187	6	strongly	strongly	ADV
ejpam-3335	187	7	up	up	ADP
ejpam-3335	187	8	-	-	PUNCT
ejpam-3335	187	9	ideal	ideal	NOUN
ejpam-3335	187	10	of	of	ADP
ejpam-3335	187	11	a	a	PRON
ejpam-3335	187	12	is	be	AUX
ejpam-3335	187	13	an	an	DET
ejpam-3335	187	14	anti	anti	ADJ
ejpam-3335	187	15	-	-	ADJ
ejpam-3335	187	16	hesitant	hesitant	ADJ
ejpam-3335	187	17	fuzzy	fuzzy	ADJ
ejpam-3335	187	18	up	up	NOUN
ejpam-3335	187	19	-	-	PUNCT
ejpam-3335	187	20	ideal	ideal	NOUN
ejpam-3335	187	21	of	of	ADP
ejpam-3335	187	22	a.	a.	NOUN
ejpam-3335	187	23	proof	proof	NOUN
ejpam-3335	187	24	.	.	PUNCT
ejpam-3335	188	1	assume	assume	VERB
ejpam-3335	188	2	that	that	SCONJ
ejpam-3335	188	3	h	h	NOUN
ejpam-3335	188	4	is	be	AUX
ejpam-3335	188	5	an	an	DET
ejpam-3335	188	6	anti	anti	ADJ
ejpam-3335	188	7	-	-	ADJ
ejpam-3335	188	8	hesitant	hesitant	ADJ
ejpam-3335	188	9	fuzzy	fuzzy	ADJ
ejpam-3335	188	10	strongly	strongly	ADV
ejpam-3335	188	11	up	up	ADP
ejpam-3335	188	12	-	-	PUNCT
ejpam-3335	188	13	ideal	ideal	NOUN
ejpam-3335	188	14	of	of	ADP
ejpam-3335	188	15	a.	a.	NOUN
ejpam-3335	188	16	then	then	ADV
ejpam-3335	188	17	for	for	ADP
ejpam-3335	188	18	any	any	DET
ejpam-3335	188	19	x	x	NOUN
ejpam-3335	188	20	,	,	PUNCT
ejpam-3335	188	21	y	y	PROPN
ejpam-3335	188	22	∈	∈	PROPN
ejpam-3335	188	23	a	a	PRON
ejpam-3335	188	24	,	,	PUNCT
ejpam-3335	188	25	hh(0	hh(0	NOUN
ejpam-3335	188	26	)	)	PUNCT
ejpam-3335	188	27	⊆	⊆	NUM
ejpam-3335	188	28	hh(x	hh(x	NUM
ejpam-3335	188	29	)	)	PUNCT
ejpam-3335	188	30	and	and	CCONJ
ejpam-3335	188	31	hh(x	hh(x	X
ejpam-3335	188	32	·	·	PUNCT
ejpam-3335	189	1	z	z	X
ejpam-3335	189	2	)	)	PUNCT
ejpam-3335	189	3	⊆	⊆	NUM
ejpam-3335	189	4	hh((z	hh((z	X
ejpam-3335	189	5	·	·	PUNCT
ejpam-3335	189	6	y	y	X
ejpam-3335	189	7	)	)	PUNCT
ejpam-3335	189	8	·	·	PUNCT
ejpam-3335	189	9	(	(	PUNCT
ejpam-3335	189	10	z	z	NOUN
ejpam-3335	189	11	·	·	PUNCT
ejpam-3335	189	12	(	(	PUNCT
ejpam-3335	189	13	x	x	X
ejpam-3335	189	14	·	·	PUNCT
ejpam-3335	189	15	z	z	NOUN
ejpam-3335	189	16	)	)	PUNCT
ejpam-3335	189	17	)	)	PUNCT
ejpam-3335	189	18	)	)	PUNCT
ejpam-3335	189	19	∩	∩	NOUN
ejpam-3335	189	20	hh(y	hh(y	NOUN
ejpam-3335	189	21	)	)	PUNCT
ejpam-3335	189	22	(	(	PUNCT
ejpam-3335	189	23	definition	definition	NOUN
ejpam-3335	189	24	9	9	NUM
ejpam-3335	189	25	(	(	PUNCT
ejpam-3335	189	26	2	2	NUM
ejpam-3335	189	27	)	)	PUNCT
ejpam-3335	189	28	)	)	PUNCT
ejpam-3335	189	29	=	=	PUNCT
ejpam-3335	190	1	hh((z	hh((z	X
ejpam-3335	190	2	·	·	PUNCT
ejpam-3335	190	3	y	y	X
ejpam-3335	190	4	)	)	PUNCT
ejpam-3335	190	5	·	·	PUNCT
ejpam-3335	190	6	0	0	X
ejpam-3335	190	7	)	)	PUNCT
ejpam-3335	190	8	∩	∩	NOUN
ejpam-3335	190	9	hh(y	hh(y	NUM
ejpam-3335	190	10	)	)	PUNCT
ejpam-3335	190	11	(	(	PUNCT
ejpam-3335	190	12	proposition	proposition	NOUN
ejpam-3335	190	13	1	1	NUM
ejpam-3335	190	14	(	(	PUNCT
ejpam-3335	190	15	5	5	NUM
ejpam-3335	190	16	)	)	PUNCT
ejpam-3335	190	17	)	)	PUNCT
ejpam-3335	190	18	=	=	PUNCT
ejpam-3335	191	1	hh(0	hh(0	NOUN
ejpam-3335	191	2	)	)	PUNCT
ejpam-3335	191	3	∩	∩	NOUN
ejpam-3335	191	4	hh(y	hh(y	NUM
ejpam-3335	191	5	)	)	PUNCT
ejpam-3335	191	6	(	(	PUNCT
ejpam-3335	191	7	(	(	PUNCT
ejpam-3335	191	8	up-3	up-3	NOUN
ejpam-3335	191	9	)	)	PUNCT
ejpam-3335	191	10	)	)	PUNCT
ejpam-3335	192	1	=	=	SYM
ejpam-3335	192	2	hh(y	hh(y	X
ejpam-3335	192	3	)	)	PUNCT
ejpam-3335	192	4	(	(	PUNCT
ejpam-3335	192	5	definition	definition	NOUN
ejpam-3335	192	6	9	9	NUM
ejpam-3335	192	7	(	(	PUNCT
ejpam-3335	192	8	1	1	NUM
ejpam-3335	192	9	)	)	PUNCT
ejpam-3335	192	10	)	)	PUNCT
ejpam-3335	192	11	=	=	SYM
ejpam-3335	192	12	hh(x	hh(x	X
ejpam-3335	192	13	·	·	PUNCT
ejpam-3335	192	14	(	(	PUNCT
ejpam-3335	192	15	y	y	PROPN
ejpam-3335	192	16	·	·	PUNCT
ejpam-3335	192	17	z	z	NOUN
ejpam-3335	192	18	)	)	PUNCT
ejpam-3335	192	19	)	)	PUNCT
ejpam-3335	192	20	∩	∩	NOUN
ejpam-3335	192	21	hh(y	hh(y	NUM
ejpam-3335	192	22	)	)	PUNCT
ejpam-3335	192	23	.	.	PUNCT
ejpam-3335	193	1	hence	hence	ADV
ejpam-3335	193	2	,	,	PUNCT
ejpam-3335	193	3	h	h	PROPN
ejpam-3335	193	4	is	be	AUX
ejpam-3335	193	5	an	an	DET
ejpam-3335	193	6	anti	anti	ADJ
ejpam-3335	193	7	-	-	ADJ
ejpam-3335	193	8	hesitant	hesitant	ADJ
ejpam-3335	193	9	fuzzy	fuzzy	ADJ
ejpam-3335	193	10	up	up	NOUN
ejpam-3335	193	11	-	-	PUNCT
ejpam-3335	193	12	ideal	ideal	NOUN
ejpam-3335	193	13	of	of	ADP
ejpam-3335	193	14	a.	a.	NOUN
ejpam-3335	193	15	the	the	DET
ejpam-3335	193	16	converse	converse	NOUN
ejpam-3335	193	17	of	of	ADP
ejpam-3335	193	18	theorem	theorem	NOUN
ejpam-3335	193	19	6	6	NUM
ejpam-3335	193	20	is	be	AUX
ejpam-3335	193	21	not	not	PART
ejpam-3335	193	22	true	true	ADJ
ejpam-3335	193	23	in	in	ADP
ejpam-3335	193	24	general	general	ADJ
ejpam-3335	193	25	.	.	PUNCT
ejpam-3335	194	1	by	by	ADP
ejpam-3335	194	2	theorem	theorem	NOUN
ejpam-3335	194	3	3	3	NUM
ejpam-3335	194	4	,	,	PUNCT
ejpam-3335	194	5	we	we	PRON
ejpam-3335	194	6	obtain	obtain	VERB
ejpam-3335	194	7	an	an	DET
ejpam-3335	194	8	antihesitant	antihesitant	ADJ
ejpam-3335	194	9	fuzzy	fuzzy	NOUN
ejpam-3335	194	10	strongly	strongly	ADV
ejpam-3335	194	11	up	up	ADP
ejpam-3335	194	12	-	-	PUNCT
ejpam-3335	194	13	ideal	ideal	NOUN
ejpam-3335	194	14	is	be	AUX
ejpam-3335	194	15	a	a	DET
ejpam-3335	194	16	constant	constant	ADJ
ejpam-3335	194	17	hesitant	hesitant	ADJ
ejpam-3335	194	18	fuzzy	fuzzy	ADJ
ejpam-3335	194	19	set	set	NOUN
ejpam-3335	194	20	.	.	PUNCT
ejpam-3335	195	1	but	but	CCONJ
ejpam-3335	195	2	anti	anti	ADJ
ejpam-3335	195	3	-	-	ADJ
ejpam-3335	195	4	hesitant	hesitant	ADJ
ejpam-3335	195	5	fuzzy	fuzzy	ADJ
ejpam-3335	195	6	up	up	ADP
ejpam-3335	195	7	-	-	PUNCT
ejpam-3335	195	8	ideal	ideal	NOUN
ejpam-3335	195	9	is	be	AUX
ejpam-3335	195	10	not	not	PART
ejpam-3335	195	11	a	a	DET
ejpam-3335	195	12	constant	constant	ADJ
ejpam-3335	195	13	hesitant	hesitant	ADJ
ejpam-3335	195	14	fuzzy	fuzzy	ADJ
ejpam-3335	195	15	set	set	NOUN
ejpam-3335	195	16	in	in	ADP
ejpam-3335	195	17	general	general	ADJ
ejpam-3335	195	18	.	.	PUNCT
ejpam-3335	196	1	therefore	therefore	ADV
ejpam-3335	196	2	,	,	PUNCT
ejpam-3335	196	3	the	the	DET
ejpam-3335	196	4	notion	notion	NOUN
ejpam-3335	196	5	of	of	ADP
ejpam-3335	196	6	antihesitant	antihesitant	PROPN
ejpam-3335	196	7	fuzzy	fuzzy	ADJ
ejpam-3335	196	8	up	up	NOUN
ejpam-3335	196	9	-	-	PUNCT
ejpam-3335	196	10	ideals	ideal	NOUN
ejpam-3335	196	11	of	of	ADP
ejpam-3335	196	12	up	up	ADV
ejpam-3335	196	13	-	-	PUNCT
ejpam-3335	196	14	algebras	algebras	PROPN
ejpam-3335	196	15	is	be	AUX
ejpam-3335	196	16	generalization	generalization	NOUN
ejpam-3335	196	17	of	of	ADP
ejpam-3335	196	18	anti	anti	ADJ
ejpam-3335	196	19	-	-	ADJ
ejpam-3335	196	20	hesitant	hesitant	ADJ
ejpam-3335	196	21	fuzzy	fuzzy	ADJ
ejpam-3335	196	22	strongly	strongly	ADV
ejpam-3335	196	23	up	up	ADP
ejpam-3335	196	24	-	-	PUNCT
ejpam-3335	196	25	ideals	ideal	NOUN
ejpam-3335	196	26	.	.	PUNCT
ejpam-3335	197	1	proposition	proposition	NOUN
ejpam-3335	197	2	2	2	NUM
ejpam-3335	197	3	.	.	PUNCT
ejpam-3335	198	1	let	let	VERB
ejpam-3335	198	2	h	h	PRON
ejpam-3335	198	3	be	be	AUX
ejpam-3335	198	4	an	an	DET
ejpam-3335	198	5	anti	anti	ADJ
ejpam-3335	198	6	-	-	ADJ
ejpam-3335	198	7	hesitant	hesitant	ADJ
ejpam-3335	198	8	fuzzy	fuzzy	ADJ
ejpam-3335	198	9	up	up	NOUN
ejpam-3335	198	10	-	-	PUNCT
ejpam-3335	198	11	filter	filter	NOUN
ejpam-3335	198	12	(	(	PUNCT
ejpam-3335	198	13	and	and	CCONJ
ejpam-3335	198	14	also	also	ADV
ejpam-3335	198	15	anti	anti	ADJ
ejpam-3335	198	16	-	-	ADJ
ejpam-3335	198	17	hesitant	hesitant	ADJ
ejpam-3335	198	18	fuzzy	fuzzy	ADJ
ejpam-3335	198	19	up	up	ADP
ejpam-3335	198	20	-	-	PUNCT
ejpam-3335	198	21	ideal	ideal	ADJ
ejpam-3335	198	22	,	,	PUNCT
ejpam-3335	198	23	anti	anti	ADJ
ejpam-3335	198	24	-	-	ADJ
ejpam-3335	198	25	hesitant	hesitant	ADJ
ejpam-3335	198	26	fuzzy	fuzzy	ADJ
ejpam-3335	198	27	strongly	strongly	ADV
ejpam-3335	198	28	up	up	ADP
ejpam-3335	198	29	-	-	PUNCT
ejpam-3335	198	30	ideal	ideal	NOUN
ejpam-3335	198	31	)	)	PUNCT
ejpam-3335	198	32	of	of	ADP
ejpam-3335	198	33	a.	a.	NOUN
ejpam-3335	198	34	then	then	ADV
ejpam-3335	198	35	for	for	ADP
ejpam-3335	198	36	any	any	DET
ejpam-3335	198	37	x	x	NOUN
ejpam-3335	198	38	,	,	PUNCT
ejpam-3335	198	39	y	y	PROPN
ejpam-3335	198	40	∈	∈	PROPN
ejpam-3335	198	41	a	a	PRON
ejpam-3335	198	42	,	,	PUNCT
ejpam-3335	198	43	x	x	SYM
ejpam-3335	198	44	≤	≤	ADJ
ejpam-3335	198	45	y	y	PROPN
ejpam-3335	198	46	implies	imply	VERB
ejpam-3335	198	47	hh(x	hh(x	NOUN
ejpam-3335	198	48	)	)	PUNCT
ejpam-3335	198	49	⊇	⊇	NOUN
ejpam-3335	198	50	hh(y	hh(y	ADJ
ejpam-3335	198	51	)	)	PUNCT
ejpam-3335	198	52	⊇	⊇	NOUN
ejpam-3335	198	53	hh(x	hh(x	X
ejpam-3335	198	54	·	·	PUNCT
ejpam-3335	198	55	y	y	X
ejpam-3335	198	56	)	)	PUNCT
ejpam-3335	198	57	.	.	PUNCT
ejpam-3335	199	1	proof	proof	NOUN
ejpam-3335	199	2	.	.	PUNCT
ejpam-3335	200	1	let	let	VERB
ejpam-3335	200	2	x	x	PRON
ejpam-3335	200	3	,	,	PUNCT
ejpam-3335	200	4	y	y	PROPN
ejpam-3335	200	5	∈	∈	PROPN
ejpam-3335	200	6	a	a	PRON
ejpam-3335	200	7	be	be	AUX
ejpam-3335	200	8	such	such	ADJ
ejpam-3335	200	9	that	that	SCONJ
ejpam-3335	200	10	x	x	X
ejpam-3335	200	11	≤	≤	X
ejpam-3335	200	12	y.	y.	NOUN
ejpam-3335	200	13	then	then	ADV
ejpam-3335	200	14	x	x	X
ejpam-3335	200	15	·	·	PUNCT
ejpam-3335	200	16	y	y	X
ejpam-3335	200	17	=	=	NOUN
ejpam-3335	200	18	0	0	X
ejpam-3335	200	19	.	.	PUNCT
ejpam-3335	201	1	since	since	SCONJ
ejpam-3335	201	2	h	h	NOUN
ejpam-3335	201	3	is	be	AUX
ejpam-3335	201	4	an	an	DET
ejpam-3335	201	5	anti	anti	ADJ
ejpam-3335	201	6	-	-	ADJ
ejpam-3335	201	7	hesitant	hesitant	ADJ
ejpam-3335	201	8	fuzzy	fuzzy	ADJ
ejpam-3335	201	9	up	up	NOUN
ejpam-3335	201	10	-	-	PUNCT
ejpam-3335	201	11	filter	filter	NOUN
ejpam-3335	201	12	(	(	PUNCT
ejpam-3335	201	13	resp	resp	NOUN
ejpam-3335	201	14	.	.	PUNCT
ejpam-3335	201	15	,	,	PUNCT
ejpam-3335	201	16	anti	anti	ADJ
ejpam-3335	201	17	-	-	ADJ
ejpam-3335	201	18	hesitant	hesitant	ADJ
ejpam-3335	201	19	fuzzy	fuzzy	ADJ
ejpam-3335	201	20	up	up	ADP
ejpam-3335	201	21	-	-	PUNCT
ejpam-3335	201	22	ideal	ideal	ADJ
ejpam-3335	201	23	,	,	PUNCT
ejpam-3335	201	24	anti	anti	ADJ
ejpam-3335	201	25	-	-	ADJ
ejpam-3335	201	26	hesitant	hesitant	ADJ
ejpam-3335	201	27	fuzzy	fuzzy	ADJ
ejpam-3335	201	28	strongly	strongly	ADV
ejpam-3335	201	29	up	up	ADP
ejpam-3335	201	30	-	-	PUNCT
ejpam-3335	201	31	ideal	ideal	NOUN
ejpam-3335	201	32	)	)	PUNCT
ejpam-3335	201	33	of	of	ADP
ejpam-3335	201	34	a	a	PRON
ejpam-3335	201	35	,	,	PUNCT
ejpam-3335	201	36	we	we	PRON
ejpam-3335	201	37	have	have	VERB
ejpam-3335	201	38	hh(y	hh(y	NOUN
ejpam-3335	201	39	)	)	PUNCT
ejpam-3335	202	1	⊆	⊆	NUM
ejpam-3335	202	2	hh(x	hh(x	X
ejpam-3335	202	3	·	·	PUNCT
ejpam-3335	202	4	y	y	X
ejpam-3335	202	5	)	)	PUNCT
ejpam-3335	202	6	∪	∪	ADP
ejpam-3335	202	7	hh(x	hh(x	X
ejpam-3335	202	8	)	)	PUNCT
ejpam-3335	202	9	=	=	SYM
ejpam-3335	203	1	hh(0	hh(0	NOUN
ejpam-3335	203	2	)	)	PUNCT
ejpam-3335	203	3	∪	∪	ADP
ejpam-3335	203	4	hh(x	hh(x	X
ejpam-3335	203	5	)	)	PUNCT
ejpam-3335	203	6	=	=	SYM
ejpam-3335	203	7	hh(x	hh(x	X
ejpam-3335	203	8	)	)	PUNCT
ejpam-3335	203	9	.	.	PUNCT
ejpam-3335	204	1	by	by	ADP
ejpam-3335	204	2	proposition	proposition	NOUN
ejpam-3335	204	3	1	1	NUM
ejpam-3335	204	4	(	(	PUNCT
ejpam-3335	204	5	5	5	NUM
ejpam-3335	204	6	)	)	PUNCT
ejpam-3335	204	7	,	,	PUNCT
ejpam-3335	204	8	we	we	PRON
ejpam-3335	204	9	obtain	obtain	VERB
ejpam-3335	204	10	y	y	NOUN
ejpam-3335	204	11	≤	≤	NUM
ejpam-3335	204	12	x	x	X
ejpam-3335	204	13	·	·	PUNCT
ejpam-3335	204	14	y	y	NOUN
ejpam-3335	204	15	and	and	CCONJ
ejpam-3335	204	16	thus	thus	ADV
ejpam-3335	204	17	hh(y	hh(y	X
ejpam-3335	204	18	)	)	PUNCT
ejpam-3335	204	19	⊇	⊇	NOUN
ejpam-3335	204	20	hh(x	hh(x	X
ejpam-3335	204	21	·	·	PUNCT
ejpam-3335	204	22	y	y	X
ejpam-3335	204	23	)	)	PUNCT
ejpam-3335	204	24	.	.	PUNCT
ejpam-3335	205	1	5	5	X
ejpam-3335	205	2	.	.	NOUN
ejpam-3335	205	3	level	level	NOUN
ejpam-3335	205	4	subsets	subset	NOUN
ejpam-3335	205	5	of	of	ADP
ejpam-3335	205	6	a	a	DET
ejpam-3335	205	7	hesitant	hesitant	ADJ
ejpam-3335	205	8	fuzzy	fuzzy	ADJ
ejpam-3335	205	9	set	set	VERB
ejpam-3335	205	10	definition	definition	NOUN
ejpam-3335	205	11	10	10	NUM
ejpam-3335	205	12	.	.	PUNCT
ejpam-3335	206	1	[	[	X
ejpam-3335	206	2	11	11	NUM
ejpam-3335	206	3	]	]	PUNCT
ejpam-3335	206	4	let	let	VERB
ejpam-3335	206	5	h	h	PRON
ejpam-3335	206	6	be	be	AUX
ejpam-3335	206	7	a	a	DET
ejpam-3335	206	8	hesitant	hesitant	ADJ
ejpam-3335	206	9	fuzzy	fuzzy	ADJ
ejpam-3335	206	10	set	set	VERB
ejpam-3335	206	11	on	on	ADP
ejpam-3335	206	12	a.	a.	NOUN
ejpam-3335	206	13	for	for	ADP
ejpam-3335	206	14	any	any	DET
ejpam-3335	206	15	ε	ε	PROPN
ejpam-3335	206	16	∈	∈	PROPN
ejpam-3335	206	17	p([0	p([0	NOUN
ejpam-3335	206	18	,	,	PUNCT
ejpam-3335	206	19	1	1	NUM
ejpam-3335	206	20	]	]	NUM
ejpam-3335	206	21	)	)	PUNCT
ejpam-3335	206	22	,	,	PUNCT
ejpam-3335	206	23	the	the	DET
ejpam-3335	206	24	sets	set	NOUN
ejpam-3335	206	25	u(h	u(h	PROPN
ejpam-3335	206	26	;	;	PUNCT
ejpam-3335	206	27	ε	ε	PROPN
ejpam-3335	206	28	)	)	PUNCT
ejpam-3335	206	29	=	=	PRON
ejpam-3335	207	1	{	{	PUNCT
ejpam-3335	207	2	x	x	PUNCT
ejpam-3335	207	3	∈	∈	PROPN
ejpam-3335	207	4	a	a	DET
ejpam-3335	207	5	|	|	NOUN
ejpam-3335	207	6	hh(x	hh(x	NOUN
ejpam-3335	207	7	)	)	PUNCT
ejpam-3335	207	8	⊇	⊇	PROPN
ejpam-3335	207	9	ε	ε	PROPN
ejpam-3335	207	10	}	}	PUNCT
ejpam-3335	207	11	and	and	CCONJ
ejpam-3335	207	12	u+(h	u+(h	ADV
ejpam-3335	207	13	;	;	PUNCT
ejpam-3335	207	14	ε	ε	PROPN
ejpam-3335	207	15	)	)	PUNCT
ejpam-3335	207	16	=	=	PRON
ejpam-3335	207	17	{	{	PUNCT
ejpam-3335	207	18	x	x	PUNCT
ejpam-3335	207	19	∈	∈	PROPN
ejpam-3335	207	20	a	a	DET
ejpam-3335	207	21	|	|	NOUN
ejpam-3335	207	22	hh(x	hh(x	PUNCT
ejpam-3335	207	23	)	)	PUNCT
ejpam-3335	207	24	⊃	⊃	NOUN
ejpam-3335	207	25	ε	ε	PROPN
ejpam-3335	207	26	}	}	PUNCT
ejpam-3335	207	27	are	be	AUX
ejpam-3335	207	28	called	call	VERB
ejpam-3335	207	29	an	an	DET
ejpam-3335	207	30	upper	upper	ADJ
ejpam-3335	207	31	ε	ε	NOUN
ejpam-3335	207	32	-	-	PUNCT
ejpam-3335	207	33	level	level	NOUN
ejpam-3335	207	34	subset	subset	NOUN
ejpam-3335	207	35	and	and	CCONJ
ejpam-3335	207	36	an	an	DET
ejpam-3335	207	37	upper	upper	ADJ
ejpam-3335	207	38	ε	ε	NOUN
ejpam-3335	207	39	-	-	PUNCT
ejpam-3335	207	40	strong	strong	ADJ
ejpam-3335	207	41	level	level	NOUN
ejpam-3335	207	42	subset	subset	NOUN
ejpam-3335	207	43	of	of	ADP
ejpam-3335	207	44	h	h	NOUN
ejpam-3335	207	45	,	,	PUNCT
ejpam-3335	207	46	respectively	respectively	ADV
ejpam-3335	207	47	.	.	PUNCT
ejpam-3335	208	1	the	the	DET
ejpam-3335	208	2	sets	set	NOUN
ejpam-3335	208	3	l(h	l(h	PROPN
ejpam-3335	208	4	;	;	PUNCT
ejpam-3335	208	5	ε	ε	PROPN
ejpam-3335	208	6	)	)	PUNCT
ejpam-3335	208	7	=	=	PRON
ejpam-3335	209	1	{	{	PUNCT
ejpam-3335	209	2	x	x	PUNCT
ejpam-3335	209	3	∈	∈	PROPN
ejpam-3335	209	4	a	a	DET
ejpam-3335	209	5	|	|	NOUN
ejpam-3335	209	6	hh(x	hh(x	NOUN
ejpam-3335	209	7	)	)	PUNCT
ejpam-3335	209	8	⊆	⊆	NUM
ejpam-3335	209	9	ε	ε	PROPN
ejpam-3335	209	10	}	}	PUNCT
ejpam-3335	209	11	and	and	CCONJ
ejpam-3335	209	12	l−(h	l−(h	PROPN
ejpam-3335	209	13	;	;	PUNCT
ejpam-3335	209	14	ε	ε	PROPN
ejpam-3335	209	15	)	)	PUNCT
ejpam-3335	209	16	=	=	PRON
ejpam-3335	209	17	{	{	PUNCT
ejpam-3335	209	18	x	x	PUNCT
ejpam-3335	209	19	∈	∈	PROPN
ejpam-3335	209	20	a	a	DET
ejpam-3335	209	21	|	|	NOUN
ejpam-3335	209	22	hh(x	hh(x	PUNCT
ejpam-3335	209	23	)	)	PUNCT
ejpam-3335	210	1	⊂	⊂	PUNCT
ejpam-3335	210	2	ε	ε	PROPN
ejpam-3335	210	3	}	}	PUNCT
ejpam-3335	210	4	are	be	AUX
ejpam-3335	210	5	called	call	VERB
ejpam-3335	210	6	a	a	DET
ejpam-3335	210	7	lower	low	ADJ
ejpam-3335	210	8	ε	ε	NOUN
ejpam-3335	210	9	-	-	PUNCT
ejpam-3335	210	10	level	level	NOUN
ejpam-3335	210	11	subset	subset	NOUN
ejpam-3335	210	12	and	and	CCONJ
ejpam-3335	210	13	a	a	DET
ejpam-3335	210	14	lower	low	ADJ
ejpam-3335	210	15	ε	ε	NOUN
ejpam-3335	210	16	-	-	PUNCT
ejpam-3335	210	17	strong	strong	ADJ
ejpam-3335	210	18	level	level	NOUN
ejpam-3335	210	19	subset	subset	NOUN
ejpam-3335	210	20	of	of	ADP
ejpam-3335	210	21	h	h	NOUN
ejpam-3335	210	22	,	,	PUNCT
ejpam-3335	210	23	respectively	respectively	ADV
ejpam-3335	210	24	.	.	PUNCT
ejpam-3335	211	1	the	the	DET
ejpam-3335	211	2	set	set	PROPN
ejpam-3335	211	3	p.	p.	PROPN
ejpam-3335	211	4	mosrijai	mosrijai	PROPN
ejpam-3335	211	5	,	,	PUNCT
ejpam-3335	211	6	a.	a.	NOUN
ejpam-3335	211	7	iampan	iampan	PROPN
ejpam-3335	211	8	/	/	SYM
ejpam-3335	211	9	eur	eur	PROPN
ejpam-3335	211	10	.	.	PUNCT
ejpam-3335	212	1	j.	j.	PROPN
ejpam-3335	212	2	pure	pure	PROPN
ejpam-3335	212	3	appl	appl	PROPN
ejpam-3335	212	4	.	.	PROPN
ejpam-3335	212	5	math	math	PROPN
ejpam-3335	212	6	,	,	PUNCT
ejpam-3335	212	7	11	11	NUM
ejpam-3335	212	8	(	(	PUNCT
ejpam-3335	212	9	4	4	NUM
ejpam-3335	212	10	)	)	PUNCT
ejpam-3335	212	11	(	(	PUNCT
ejpam-3335	212	12	2018	2018	NUM
ejpam-3335	212	13	)	)	PUNCT
ejpam-3335	212	14	,	,	PUNCT
ejpam-3335	212	15	976	976	NUM
ejpam-3335	212	16	-	-	SYM
ejpam-3335	212	17	1002	1002	NUM
ejpam-3335	212	18	985	985	NUM
ejpam-3335	212	19	e(h	e(h	X
ejpam-3335	212	20	;	;	PUNCT
ejpam-3335	212	21	ε	ε	PROPN
ejpam-3335	212	22	)	)	PUNCT
ejpam-3335	212	23	=	=	PRON
ejpam-3335	212	24	{	{	PUNCT
ejpam-3335	212	25	x	x	PUNCT
ejpam-3335	212	26	∈	∈	PROPN
ejpam-3335	212	27	a	a	DET
ejpam-3335	212	28	|	|	NOUN
ejpam-3335	212	29	hh(x	hh(x	PUNCT
ejpam-3335	212	30	)	)	PUNCT
ejpam-3335	212	31	=	=	SYM
ejpam-3335	212	32	ε	ε	PROPN
ejpam-3335	212	33	}	}	PUNCT
ejpam-3335	212	34	is	be	AUX
ejpam-3335	212	35	called	call	VERB
ejpam-3335	212	36	an	an	DET
ejpam-3335	212	37	equal	equal	ADJ
ejpam-3335	212	38	ε	ε	NOUN
ejpam-3335	212	39	-	-	PUNCT
ejpam-3335	212	40	level	level	NOUN
ejpam-3335	212	41	subset	subset	NOUN
ejpam-3335	212	42	of	of	ADP
ejpam-3335	212	43	h.	h.	PROPN
ejpam-3335	212	44	then	then	ADV
ejpam-3335	212	45	u(h	u(h	PROPN
ejpam-3335	212	46	;	;	PUNCT
ejpam-3335	212	47	ε	ε	PROPN
ejpam-3335	212	48	)	)	PUNCT
ejpam-3335	212	49	=	=	PUNCT
ejpam-3335	212	50	u+(h	u+(h	PROPN
ejpam-3335	212	51	;	;	PUNCT
ejpam-3335	212	52	ε	ε	PROPN
ejpam-3335	212	53	)	)	PUNCT
ejpam-3335	212	54	∪	∪	ADP
ejpam-3335	212	55	e(h	e(h	PROPN
ejpam-3335	212	56	;	;	PUNCT
ejpam-3335	212	57	ε	ε	PROPN
ejpam-3335	212	58	)	)	PUNCT
ejpam-3335	212	59	and	and	CCONJ
ejpam-3335	212	60	l(h	l(h	PROPN
ejpam-3335	212	61	;	;	PUNCT
ejpam-3335	212	62	ε	ε	PROPN
ejpam-3335	212	63	)	)	PUNCT
ejpam-3335	212	64	=	=	SYM
ejpam-3335	212	65	l−(h	l−(h	PROPN
ejpam-3335	212	66	;	;	PUNCT
ejpam-3335	212	67	ε	ε	PROPN
ejpam-3335	212	68	)	)	PUNCT
ejpam-3335	212	69	∪	∪	ADP
ejpam-3335	212	70	e(h	e(h	PROPN
ejpam-3335	212	71	;	;	PUNCT
ejpam-3335	212	72	ε	ε	PROPN
ejpam-3335	212	73	)	)	PUNCT
ejpam-3335	212	74	.	.	PUNCT
ejpam-3335	213	1	proposition	proposition	NOUN
ejpam-3335	213	2	3	3	X
ejpam-3335	213	3	.	.	PUNCT
ejpam-3335	214	1	let	let	VERB
ejpam-3335	214	2	h	h	PRON
ejpam-3335	214	3	be	be	AUX
ejpam-3335	214	4	a	a	DET
ejpam-3335	214	5	hesitant	hesitant	ADJ
ejpam-3335	214	6	fuzzy	fuzzy	ADJ
ejpam-3335	214	7	set	set	NOUN
ejpam-3335	214	8	on	on	ADP
ejpam-3335	214	9	a	a	PRON
ejpam-3335	214	10	and	and	CCONJ
ejpam-3335	214	11	let	let	VERB
ejpam-3335	214	12	ε	ε	PROPN
ejpam-3335	214	13	∈	∈	PROPN
ejpam-3335	214	14	p([0	p([0	PROPN
ejpam-3335	214	15	,	,	PUNCT
ejpam-3335	214	16	1	1	NUM
ejpam-3335	214	17	]	]	NUM
ejpam-3335	214	18	)	)	PUNCT
ejpam-3335	214	19	.	.	PUNCT
ejpam-3335	215	1	then	then	ADV
ejpam-3335	215	2	the	the	DET
ejpam-3335	215	3	following	follow	VERB
ejpam-3335	215	4	statements	statement	NOUN
ejpam-3335	215	5	hold	hold	VERB
ejpam-3335	215	6	:	:	PUNCT
ejpam-3335	215	7	(	(	PUNCT
ejpam-3335	215	8	1	1	X
ejpam-3335	215	9	)	)	PUNCT
ejpam-3335	215	10	u(h	u(h	PROPN
ejpam-3335	215	11	;	;	PUNCT
ejpam-3335	215	12	ε	ε	PROPN
ejpam-3335	215	13	)	)	PUNCT
ejpam-3335	215	14	=	=	SYM
ejpam-3335	216	1	l(h	l(h	PROPN
ejpam-3335	216	2	;	;	PUNCT
ejpam-3335	216	3	[	[	X
ejpam-3335	216	4	0	0	NUM
ejpam-3335	216	5	,	,	PUNCT
ejpam-3335	216	6	1]−	1]−	NUM
ejpam-3335	216	7	ε	ε	PROPN
ejpam-3335	216	8	)	)	PUNCT
ejpam-3335	216	9	,	,	PUNCT
ejpam-3335	216	10	(	(	PUNCT
ejpam-3335	216	11	2	2	X
ejpam-3335	216	12	)	)	PUNCT
ejpam-3335	216	13	u+(h	u+(h	NUM
ejpam-3335	216	14	;	;	PUNCT
ejpam-3335	216	15	ε	ε	PROPN
ejpam-3335	216	16	)	)	PUNCT
ejpam-3335	216	17	=	=	SYM
ejpam-3335	216	18	l−(h	l−(h	PROPN
ejpam-3335	216	19	;	;	PUNCT
ejpam-3335	216	20	[	[	X
ejpam-3335	216	21	0	0	NUM
ejpam-3335	216	22	,	,	PUNCT
ejpam-3335	216	23	1]−	1]−	NUM
ejpam-3335	216	24	ε	ε	PROPN
ejpam-3335	216	25	)	)	PUNCT
ejpam-3335	216	26	,	,	PUNCT
ejpam-3335	216	27	(	(	PUNCT
ejpam-3335	216	28	3	3	X
ejpam-3335	216	29	)	)	PUNCT
ejpam-3335	216	30	l(h	l(h	PROPN
ejpam-3335	216	31	;	;	PUNCT
ejpam-3335	216	32	ε	ε	PROPN
ejpam-3335	216	33	)	)	PUNCT
ejpam-3335	216	34	=	=	SYM
ejpam-3335	217	1	u(h	u(h	PROPN
ejpam-3335	217	2	;	;	PUNCT
ejpam-3335	217	3	[	[	X
ejpam-3335	217	4	0	0	NUM
ejpam-3335	217	5	,	,	PUNCT
ejpam-3335	217	6	1]−	1]−	NUM
ejpam-3335	217	7	ε	ε	PROPN
ejpam-3335	217	8	)	)	PUNCT
ejpam-3335	217	9	,	,	PUNCT
ejpam-3335	217	10	and	and	CCONJ
ejpam-3335	217	11	(	(	PUNCT
ejpam-3335	217	12	4	4	X
ejpam-3335	217	13	)	)	PUNCT
ejpam-3335	217	14	l−(h	l−(h	PROPN
ejpam-3335	217	15	;	;	PUNCT
ejpam-3335	217	16	ε	ε	PROPN
ejpam-3335	217	17	)	)	PUNCT
ejpam-3335	217	18	=	=	PUNCT
ejpam-3335	217	19	u+(h	u+(h	PROPN
ejpam-3335	217	20	;	;	PUNCT
ejpam-3335	217	21	[	[	X
ejpam-3335	217	22	0	0	NUM
ejpam-3335	217	23	,	,	PUNCT
ejpam-3335	217	24	1]−	1]−	NUM
ejpam-3335	217	25	ε	ε	PROPN
ejpam-3335	217	26	)	)	PUNCT
ejpam-3335	217	27	.	.	PUNCT
ejpam-3335	218	1	proof	proof	NOUN
ejpam-3335	218	2	.	.	PUNCT
ejpam-3335	219	1	(	(	PUNCT
ejpam-3335	219	2	1	1	X
ejpam-3335	219	3	)	)	PUNCT
ejpam-3335	219	4	let	let	VERB
ejpam-3335	219	5	x	x	SYM
ejpam-3335	219	6	∈	∈	PROPN
ejpam-3335	219	7	a	a	PRON
ejpam-3335	219	8	and	and	CCONJ
ejpam-3335	219	9	let	let	VERB
ejpam-3335	219	10	ε	ε	PROPN
ejpam-3335	219	11	∈	∈	PROPN
ejpam-3335	219	12	p([0	p([0	PROPN
ejpam-3335	219	13	,	,	PUNCT
ejpam-3335	219	14	1	1	NUM
ejpam-3335	219	15	]	]	NUM
ejpam-3335	219	16	)	)	PUNCT
ejpam-3335	219	17	.	.	PUNCT
ejpam-3335	220	1	then	then	ADV
ejpam-3335	220	2	x	x	SYM
ejpam-3335	220	3	∈	∈	PROPN
ejpam-3335	220	4	u(h	u(h	PROPN
ejpam-3335	220	5	;	;	PUNCT
ejpam-3335	220	6	ε	ε	PROPN
ejpam-3335	220	7	)	)	PUNCT
ejpam-3335	220	8	if	if	SCONJ
ejpam-3335	220	9	and	and	CCONJ
ejpam-3335	220	10	only	only	ADV
ejpam-3335	220	11	if	if	SCONJ
ejpam-3335	220	12	hh(x	hh(x	NOUN
ejpam-3335	220	13	)	)	PUNCT
ejpam-3335	220	14	⊇	⊇	PROPN
ejpam-3335	220	15	ε	ε	PROPN
ejpam-3335	220	16	if	if	SCONJ
ejpam-3335	220	17	and	and	CCONJ
ejpam-3335	220	18	only	only	ADV
ejpam-3335	220	19	if	if	SCONJ
ejpam-3335	220	20	[	[	X
ejpam-3335	220	21	0	0	NUM
ejpam-3335	220	22	,	,	PUNCT
ejpam-3335	220	23	1	1	NUM
ejpam-3335	220	24	]	]	PUNCT
ejpam-3335	220	25	−	−	NOUN
ejpam-3335	220	26	hh(x	hh(x	SYM
ejpam-3335	220	27	)	)	PUNCT
ejpam-3335	220	28	⊆	⊆	NUM
ejpam-3335	221	1	[	[	X
ejpam-3335	221	2	0	0	NUM
ejpam-3335	221	3	,	,	PUNCT
ejpam-3335	221	4	1	1	NUM
ejpam-3335	221	5	]	]	PUNCT
ejpam-3335	221	6	−	−	PROPN
ejpam-3335	221	7	ε	ε	PROPN
ejpam-3335	221	8	if	if	SCONJ
ejpam-3335	221	9	and	and	CCONJ
ejpam-3335	221	10	only	only	ADV
ejpam-3335	221	11	if	if	SCONJ
ejpam-3335	221	12	hh(x	hh(x	NOUN
ejpam-3335	221	13	)	)	PUNCT
ejpam-3335	221	14	⊆	⊆	NUM
ejpam-3335	222	1	[	[	X
ejpam-3335	222	2	0	0	NUM
ejpam-3335	222	3	,	,	PUNCT
ejpam-3335	222	4	1	1	NUM
ejpam-3335	222	5	]	]	PUNCT
ejpam-3335	222	6	−	−	PROPN
ejpam-3335	222	7	ε	ε	PROPN
ejpam-3335	222	8	if	if	SCONJ
ejpam-3335	222	9	and	and	CCONJ
ejpam-3335	222	10	only	only	ADV
ejpam-3335	222	11	if	if	SCONJ
ejpam-3335	222	12	x	x	SYM
ejpam-3335	222	13	∈	∈	PROPN
ejpam-3335	222	14	l(h	l(h	PROPN
ejpam-3335	222	15	;	;	PUNCT
ejpam-3335	222	16	[	[	X
ejpam-3335	222	17	0	0	NUM
ejpam-3335	222	18	,	,	PUNCT
ejpam-3335	222	19	1]−	1]−	NUM
ejpam-3335	222	20	ε	ε	PROPN
ejpam-3335	222	21	)	)	PUNCT
ejpam-3335	222	22	.	.	PUNCT
ejpam-3335	223	1	therefore	therefore	ADV
ejpam-3335	223	2	,	,	PUNCT
ejpam-3335	223	3	u(h	u(h	PROPN
ejpam-3335	223	4	;	;	PUNCT
ejpam-3335	223	5	ε	ε	PROPN
ejpam-3335	223	6	)	)	PUNCT
ejpam-3335	223	7	=	=	SYM
ejpam-3335	223	8	l(h	l(h	PROPN
ejpam-3335	223	9	;	;	PUNCT
ejpam-3335	223	10	[	[	X
ejpam-3335	223	11	0	0	NUM
ejpam-3335	223	12	,	,	PUNCT
ejpam-3335	223	13	1]−	1]−	NUM
ejpam-3335	223	14	ε	ε	PROPN
ejpam-3335	223	15	)	)	PUNCT
ejpam-3335	223	16	.	.	PUNCT
ejpam-3335	224	1	(	(	PUNCT
ejpam-3335	224	2	2	2	X
ejpam-3335	224	3	)	)	PUNCT
ejpam-3335	224	4	let	let	VERB
ejpam-3335	224	5	x	x	SYM
ejpam-3335	224	6	∈	∈	PROPN
ejpam-3335	224	7	a	a	PRON
ejpam-3335	224	8	and	and	CCONJ
ejpam-3335	224	9	let	let	VERB
ejpam-3335	224	10	ε	ε	PROPN
ejpam-3335	224	11	∈	∈	PROPN
ejpam-3335	224	12	p([0	p([0	PROPN
ejpam-3335	224	13	,	,	PUNCT
ejpam-3335	224	14	1	1	NUM
ejpam-3335	224	15	]	]	NUM
ejpam-3335	224	16	)	)	PUNCT
ejpam-3335	224	17	.	.	PUNCT
ejpam-3335	225	1	then	then	ADV
ejpam-3335	225	2	x	x	PUNCT
ejpam-3335	225	3	∈	∈	PROPN
ejpam-3335	225	4	u+(h	u+(h	NOUN
ejpam-3335	225	5	;	;	PUNCT
ejpam-3335	225	6	ε	ε	PROPN
ejpam-3335	225	7	)	)	PUNCT
ejpam-3335	225	8	if	if	SCONJ
ejpam-3335	225	9	and	and	CCONJ
ejpam-3335	225	10	only	only	ADV
ejpam-3335	225	11	if	if	SCONJ
ejpam-3335	225	12	hh(x	hh(x	NOUN
ejpam-3335	225	13	)	)	PUNCT
ejpam-3335	225	14	⊃	⊃	NOUN
ejpam-3335	225	15	ε	ε	PROPN
ejpam-3335	225	16	if	if	SCONJ
ejpam-3335	225	17	and	and	CCONJ
ejpam-3335	225	18	only	only	ADV
ejpam-3335	225	19	if	if	SCONJ
ejpam-3335	225	20	[	[	X
ejpam-3335	225	21	0	0	NUM
ejpam-3335	225	22	,	,	PUNCT
ejpam-3335	225	23	1	1	NUM
ejpam-3335	225	24	]	]	SYM
ejpam-3335	225	25	−	−	NOUN
ejpam-3335	225	26	hh(x	hh(x	NUM
ejpam-3335	225	27	)	)	PUNCT
ejpam-3335	225	28	⊂	⊂	PROPN
ejpam-3335	226	1	[	[	X
ejpam-3335	226	2	0	0	NUM
ejpam-3335	226	3	,	,	PUNCT
ejpam-3335	226	4	1	1	NUM
ejpam-3335	226	5	]	]	PUNCT
ejpam-3335	226	6	−	−	PROPN
ejpam-3335	226	7	ε	ε	PROPN
ejpam-3335	226	8	if	if	SCONJ
ejpam-3335	226	9	and	and	CCONJ
ejpam-3335	226	10	only	only	ADV
ejpam-3335	226	11	if	if	SCONJ
ejpam-3335	226	12	hh(x	hh(x	NUM
ejpam-3335	226	13	)	)	PUNCT
ejpam-3335	227	1	⊂	⊂	PROPN
ejpam-3335	228	1	[	[	X
ejpam-3335	228	2	0	0	NUM
ejpam-3335	228	3	,	,	PUNCT
ejpam-3335	228	4	1	1	NUM
ejpam-3335	228	5	]	]	PUNCT
ejpam-3335	228	6	−	−	PROPN
ejpam-3335	228	7	ε	ε	PROPN
ejpam-3335	228	8	if	if	SCONJ
ejpam-3335	228	9	and	and	CCONJ
ejpam-3335	228	10	only	only	ADV
ejpam-3335	228	11	if	if	SCONJ
ejpam-3335	228	12	x	x	PROPN
ejpam-3335	228	13	∈	∈	PROPN
ejpam-3335	228	14	l−(h	l−(h	PROPN
ejpam-3335	228	15	;	;	PUNCT
ejpam-3335	228	16	[	[	X
ejpam-3335	228	17	0	0	NUM
ejpam-3335	228	18	,	,	PUNCT
ejpam-3335	228	19	1]−	1]−	NUM
ejpam-3335	228	20	ε	ε	PROPN
ejpam-3335	228	21	)	)	PUNCT
ejpam-3335	228	22	.	.	PUNCT
ejpam-3335	229	1	therefore	therefore	ADV
ejpam-3335	229	2	,	,	PUNCT
ejpam-3335	229	3	u+(h	u+(h	NOUN
ejpam-3335	229	4	;	;	PUNCT
ejpam-3335	229	5	ε	ε	PROPN
ejpam-3335	229	6	)	)	PUNCT
ejpam-3335	229	7	=	=	SYM
ejpam-3335	229	8	l−(h	l−(h	PROPN
ejpam-3335	229	9	;	;	PUNCT
ejpam-3335	229	10	[	[	X
ejpam-3335	229	11	0	0	NUM
ejpam-3335	229	12	,	,	PUNCT
ejpam-3335	229	13	1]−	1]−	NUM
ejpam-3335	229	14	ε	ε	PROPN
ejpam-3335	229	15	)	)	PUNCT
ejpam-3335	229	16	.	.	PUNCT
ejpam-3335	230	1	(	(	PUNCT
ejpam-3335	230	2	3	3	X
ejpam-3335	230	3	)	)	PUNCT
ejpam-3335	230	4	let	let	VERB
ejpam-3335	230	5	x	x	SYM
ejpam-3335	230	6	∈	∈	PROPN
ejpam-3335	230	7	a	a	PRON
ejpam-3335	230	8	and	and	CCONJ
ejpam-3335	230	9	let	let	VERB
ejpam-3335	230	10	ε	ε	PROPN
ejpam-3335	230	11	∈	∈	PROPN
ejpam-3335	230	12	p([0	p([0	PROPN
ejpam-3335	230	13	,	,	PUNCT
ejpam-3335	230	14	1	1	NUM
ejpam-3335	230	15	]	]	NUM
ejpam-3335	230	16	)	)	PUNCT
ejpam-3335	230	17	.	.	PUNCT
ejpam-3335	231	1	then	then	ADV
ejpam-3335	231	2	x	x	X
ejpam-3335	231	3	∈	∈	PROPN
ejpam-3335	231	4	l(h	l(h	PROPN
ejpam-3335	231	5	;	;	PUNCT
ejpam-3335	231	6	ε	ε	PROPN
ejpam-3335	231	7	)	)	PUNCT
ejpam-3335	231	8	if	if	SCONJ
ejpam-3335	231	9	and	and	CCONJ
ejpam-3335	231	10	only	only	ADV
ejpam-3335	231	11	if	if	SCONJ
ejpam-3335	231	12	hh(x	hh(x	NOUN
ejpam-3335	231	13	)	)	PUNCT
ejpam-3335	231	14	⊆	⊆	NUM
ejpam-3335	231	15	ε	ε	PROPN
ejpam-3335	231	16	if	if	SCONJ
ejpam-3335	231	17	and	and	CCONJ
ejpam-3335	231	18	only	only	ADV
ejpam-3335	231	19	if	if	SCONJ
ejpam-3335	231	20	[	[	X
ejpam-3335	231	21	0	0	NUM
ejpam-3335	231	22	,	,	PUNCT
ejpam-3335	231	23	1	1	NUM
ejpam-3335	231	24	]	]	SYM
ejpam-3335	231	25	−	−	NOUN
ejpam-3335	231	26	hh(x	hh(x	SYM
ejpam-3335	231	27	)	)	PUNCT
ejpam-3335	231	28	⊇	⊇	NOUN
ejpam-3335	232	1	[	[	X
ejpam-3335	232	2	0	0	NUM
ejpam-3335	232	3	,	,	PUNCT
ejpam-3335	232	4	1	1	NUM
ejpam-3335	232	5	]	]	PUNCT
ejpam-3335	232	6	−	−	PROPN
ejpam-3335	232	7	ε	ε	PROPN
ejpam-3335	232	8	if	if	SCONJ
ejpam-3335	232	9	and	and	CCONJ
ejpam-3335	232	10	only	only	ADV
ejpam-3335	232	11	if	if	SCONJ
ejpam-3335	232	12	hh(x	hh(x	NOUN
ejpam-3335	232	13	)	)	PUNCT
ejpam-3335	232	14	⊇	⊇	NOUN
ejpam-3335	233	1	[	[	X
ejpam-3335	233	2	0	0	NUM
ejpam-3335	233	3	,	,	PUNCT
ejpam-3335	233	4	1	1	NUM
ejpam-3335	233	5	]	]	PUNCT
ejpam-3335	233	6	−	−	PROPN
ejpam-3335	233	7	ε	ε	PROPN
ejpam-3335	234	1	if	if	SCONJ
ejpam-3335	234	2	and	and	CCONJ
ejpam-3335	234	3	only	only	ADV
ejpam-3335	234	4	if	if	SCONJ
ejpam-3335	234	5	x	x	SYM
ejpam-3335	234	6	∈	∈	PROPN
ejpam-3335	234	7	u(h	u(h	PROPN
ejpam-3335	234	8	;	;	PUNCT
ejpam-3335	234	9	[	[	X
ejpam-3335	234	10	0	0	NUM
ejpam-3335	234	11	,	,	PUNCT
ejpam-3335	234	12	1]−	1]−	NUM
ejpam-3335	234	13	ε	ε	PROPN
ejpam-3335	234	14	)	)	PUNCT
ejpam-3335	234	15	.	.	PUNCT
ejpam-3335	235	1	therefore	therefore	ADV
ejpam-3335	235	2	,	,	PUNCT
ejpam-3335	235	3	l(h	l(h	PROPN
ejpam-3335	235	4	;	;	PUNCT
ejpam-3335	235	5	ε	ε	PROPN
ejpam-3335	235	6	)	)	PUNCT
ejpam-3335	235	7	=	=	SYM
ejpam-3335	236	1	u(h	u(h	PROPN
ejpam-3335	236	2	;	;	PUNCT
ejpam-3335	236	3	[	[	X
ejpam-3335	236	4	0	0	NUM
ejpam-3335	236	5	,	,	PUNCT
ejpam-3335	236	6	1]−	1]−	NUM
ejpam-3335	236	7	ε	ε	PROPN
ejpam-3335	236	8	)	)	PUNCT
ejpam-3335	236	9	.	.	PUNCT
ejpam-3335	237	1	(	(	PUNCT
ejpam-3335	237	2	4	4	X
ejpam-3335	237	3	)	)	PUNCT
ejpam-3335	237	4	let	let	VERB
ejpam-3335	237	5	x	x	SYM
ejpam-3335	237	6	∈	∈	PROPN
ejpam-3335	237	7	a	a	PRON
ejpam-3335	237	8	and	and	CCONJ
ejpam-3335	237	9	let	let	VERB
ejpam-3335	237	10	ε	ε	PROPN
ejpam-3335	237	11	∈	∈	PROPN
ejpam-3335	237	12	p([0	p([0	PROPN
ejpam-3335	237	13	,	,	PUNCT
ejpam-3335	237	14	1	1	NUM
ejpam-3335	237	15	]	]	NUM
ejpam-3335	237	16	)	)	PUNCT
ejpam-3335	237	17	.	.	PUNCT
ejpam-3335	238	1	then	then	ADV
ejpam-3335	238	2	x	x	X
ejpam-3335	238	3	∈	∈	PROPN
ejpam-3335	238	4	l−(h	l−(h	PROPN
ejpam-3335	238	5	;	;	PUNCT
ejpam-3335	238	6	ε	ε	PROPN
ejpam-3335	238	7	)	)	PUNCT
ejpam-3335	238	8	if	if	SCONJ
ejpam-3335	238	9	and	and	CCONJ
ejpam-3335	238	10	only	only	ADV
ejpam-3335	238	11	if	if	SCONJ
ejpam-3335	238	12	hh(x	hh(x	NUM
ejpam-3335	238	13	)	)	PUNCT
ejpam-3335	239	1	⊂	⊂	PROPN
ejpam-3335	239	2	ε	ε	PROPN
ejpam-3335	239	3	if	if	SCONJ
ejpam-3335	239	4	and	and	CCONJ
ejpam-3335	239	5	only	only	ADV
ejpam-3335	239	6	if	if	SCONJ
ejpam-3335	239	7	[	[	X
ejpam-3335	239	8	0	0	NUM
ejpam-3335	239	9	,	,	PUNCT
ejpam-3335	239	10	1	1	NUM
ejpam-3335	239	11	]	]	SYM
ejpam-3335	239	12	−	−	NOUN
ejpam-3335	239	13	hh(x	hh(x	SYM
ejpam-3335	239	14	)	)	PUNCT
ejpam-3335	239	15	⊃	⊃	PROPN
ejpam-3335	240	1	[	[	X
ejpam-3335	240	2	0	0	NUM
ejpam-3335	240	3	,	,	PUNCT
ejpam-3335	240	4	1	1	NUM
ejpam-3335	240	5	]	]	PUNCT
ejpam-3335	240	6	−	−	PROPN
ejpam-3335	240	7	ε	ε	PROPN
ejpam-3335	240	8	if	if	SCONJ
ejpam-3335	240	9	and	and	CCONJ
ejpam-3335	240	10	only	only	ADV
ejpam-3335	240	11	if	if	SCONJ
ejpam-3335	240	12	hh(x	hh(x	NOUN
ejpam-3335	240	13	)	)	PUNCT
ejpam-3335	240	14	⊃	⊃	NOUN
ejpam-3335	240	15	[	[	X
ejpam-3335	240	16	0	0	NUM
ejpam-3335	240	17	,	,	PUNCT
ejpam-3335	240	18	1	1	NUM
ejpam-3335	240	19	]	]	PUNCT
ejpam-3335	240	20	−	−	PROPN
ejpam-3335	240	21	ε	ε	PROPN
ejpam-3335	240	22	if	if	SCONJ
ejpam-3335	240	23	and	and	CCONJ
ejpam-3335	240	24	only	only	ADV
ejpam-3335	240	25	if	if	SCONJ
ejpam-3335	240	26	x	x	SYM
ejpam-3335	240	27	∈	∈	PROPN
ejpam-3335	240	28	u+(h	u+(h	NOUN
ejpam-3335	240	29	;	;	PUNCT
ejpam-3335	240	30	[	[	X
ejpam-3335	240	31	0	0	NUM
ejpam-3335	240	32	,	,	PUNCT
ejpam-3335	240	33	1]−	1]−	NUM
ejpam-3335	240	34	ε	ε	PROPN
ejpam-3335	240	35	)	)	PUNCT
ejpam-3335	240	36	.	.	PUNCT
ejpam-3335	241	1	therefore	therefore	ADV
ejpam-3335	241	2	,	,	PUNCT
ejpam-3335	241	3	l−(h	l−(h	PROPN
ejpam-3335	241	4	;	;	PUNCT
ejpam-3335	241	5	ε	ε	PROPN
ejpam-3335	241	6	)	)	PUNCT
ejpam-3335	241	7	=	=	PUNCT
ejpam-3335	241	8	u+(h	u+(h	PROPN
ejpam-3335	241	9	;	;	PUNCT
ejpam-3335	241	10	[	[	X
ejpam-3335	241	11	0	0	NUM
ejpam-3335	241	12	,	,	PUNCT
ejpam-3335	241	13	1]−	1]−	NUM
ejpam-3335	241	14	ε	ε	PROPN
ejpam-3335	241	15	)	)	PUNCT
ejpam-3335	241	16	.	.	PUNCT
ejpam-3335	242	1	lemma	lemma	PROPN
ejpam-3335	242	2	1	1	NUM
ejpam-3335	242	3	.	.	PUNCT
ejpam-3335	243	1	[	[	X
ejpam-3335	243	2	11	11	NUM
ejpam-3335	243	3	]	]	PUNCT
ejpam-3335	243	4	let	let	VERB
ejpam-3335	243	5	h	h	PRON
ejpam-3335	243	6	be	be	AUX
ejpam-3335	243	7	a	a	DET
ejpam-3335	243	8	hesitant	hesitant	ADJ
ejpam-3335	243	9	fuzzy	fuzzy	ADJ
ejpam-3335	243	10	set	set	NOUN
ejpam-3335	243	11	on	on	ADP
ejpam-3335	243	12	a.	a.	NOUN
ejpam-3335	243	13	then	then	ADV
ejpam-3335	243	14	the	the	DET
ejpam-3335	243	15	following	following	ADJ
ejpam-3335	243	16	statements	statement	NOUN
ejpam-3335	243	17	hold	hold	VERB
ejpam-3335	243	18	:	:	PUNCT
ejpam-3335	243	19	for	for	ADP
ejpam-3335	243	20	any	any	DET
ejpam-3335	243	21	x	x	NOUN
ejpam-3335	243	22	,	,	PUNCT
ejpam-3335	243	23	y	y	PROPN
ejpam-3335	243	24	∈	∈	PROPN
ejpam-3335	243	25	a	a	PRON
ejpam-3335	243	26	,	,	PUNCT
ejpam-3335	243	27	(	(	PUNCT
ejpam-3335	243	28	1	1	X
ejpam-3335	243	29	)	)	PUNCT
ejpam-3335	244	1	[	[	X
ejpam-3335	244	2	0	0	NUM
ejpam-3335	244	3	,	,	PUNCT
ejpam-3335	244	4	1]−	1]−	NUM
ejpam-3335	244	5	(	(	PUNCT
ejpam-3335	244	6	hh(x	hh(x	NOUN
ejpam-3335	244	7	)	)	PUNCT
ejpam-3335	244	8	∪	∪	ADP
ejpam-3335	244	9	hh(y	hh(y	NOUN
ejpam-3335	244	10	)	)	PUNCT
ejpam-3335	244	11	)	)	PUNCT
ejpam-3335	245	1	=	=	PUNCT
ejpam-3335	245	2	(	(	PUNCT
ejpam-3335	245	3	[	[	X
ejpam-3335	245	4	0	0	NUM
ejpam-3335	245	5	,	,	PUNCT
ejpam-3335	245	6	1]−	1]−	NUM
ejpam-3335	245	7	hh(x	hh(x	NOUN
ejpam-3335	245	8	)	)	PUNCT
ejpam-3335	245	9	)	)	PUNCT
ejpam-3335	246	1	∩	∩	NOUN
ejpam-3335	246	2	(	(	PUNCT
ejpam-3335	246	3	[	[	X
ejpam-3335	246	4	0	0	NUM
ejpam-3335	246	5	,	,	PUNCT
ejpam-3335	246	6	1]−	1]−	NUM
ejpam-3335	246	7	hh(y	hh(y	NOUN
ejpam-3335	246	8	)	)	PUNCT
ejpam-3335	246	9	)	)	PUNCT
ejpam-3335	246	10	,	,	PUNCT
ejpam-3335	246	11	and	and	CCONJ
ejpam-3335	246	12	(	(	PUNCT
ejpam-3335	246	13	2	2	X
ejpam-3335	246	14	)	)	PUNCT
ejpam-3335	247	1	[	[	X
ejpam-3335	247	2	0	0	NUM
ejpam-3335	247	3	,	,	PUNCT
ejpam-3335	247	4	1]−	1]−	NUM
ejpam-3335	247	5	(	(	PUNCT
ejpam-3335	247	6	hh(x	hh(x	NOUN
ejpam-3335	247	7	)	)	PUNCT
ejpam-3335	247	8	∩	∩	NOUN
ejpam-3335	247	9	hh(y	hh(y	NOUN
ejpam-3335	247	10	)	)	PUNCT
ejpam-3335	247	11	)	)	PUNCT
ejpam-3335	248	1	=	=	PUNCT
ejpam-3335	248	2	(	(	PUNCT
ejpam-3335	248	3	[	[	X
ejpam-3335	248	4	0	0	NUM
ejpam-3335	248	5	,	,	PUNCT
ejpam-3335	248	6	1]−	1]−	NUM
ejpam-3335	248	7	hh(x	hh(x	NOUN
ejpam-3335	248	8	)	)	PUNCT
ejpam-3335	248	9	)	)	PUNCT
ejpam-3335	248	10	∪	∪	ADP
ejpam-3335	248	11	(	(	PUNCT
ejpam-3335	248	12	[	[	X
ejpam-3335	248	13	0	0	NUM
ejpam-3335	248	14	,	,	PUNCT
ejpam-3335	248	15	1]−	1]−	NUM
ejpam-3335	248	16	hh(y	hh(y	NOUN
ejpam-3335	248	17	)	)	PUNCT
ejpam-3335	248	18	)	)	PUNCT
ejpam-3335	248	19	.	.	PUNCT
ejpam-3335	249	1	5.1	5.1	NUM
ejpam-3335	249	2	.	.	PUNCT
ejpam-3335	250	1	lower	low	ADJ
ejpam-3335	250	2	ε	ε	NOUN
ejpam-3335	250	3	-	-	PUNCT
ejpam-3335	250	4	level	level	NOUN
ejpam-3335	250	5	subsets	subset	NOUN
ejpam-3335	250	6	theorem	theorem	VERB
ejpam-3335	250	7	7	7	NUM
ejpam-3335	250	8	.	.	PUNCT
ejpam-3335	251	1	a	a	DET
ejpam-3335	251	2	hesitant	hesitant	ADJ
ejpam-3335	251	3	fuzzy	fuzzy	ADJ
ejpam-3335	251	4	set	set	VERB
ejpam-3335	251	5	h	h	NOUN
ejpam-3335	251	6	on	on	ADP
ejpam-3335	251	7	a	a	PRON
ejpam-3335	251	8	is	be	AUX
ejpam-3335	251	9	an	an	DET
ejpam-3335	251	10	anti	anti	ADJ
ejpam-3335	251	11	-	-	ADJ
ejpam-3335	251	12	hesitant	hesitant	ADJ
ejpam-3335	251	13	fuzzy	fuzzy	ADJ
ejpam-3335	251	14	up	up	NOUN
ejpam-3335	251	15	-	-	PUNCT
ejpam-3335	251	16	subalgebra	subalgebra	NOUN
ejpam-3335	251	17	of	of	ADP
ejpam-3335	251	18	a	a	DET
ejpam-3335	251	19	if	if	NOUN
ejpam-3335	251	20	and	and	CCONJ
ejpam-3335	251	21	only	only	ADV
ejpam-3335	251	22	if	if	SCONJ
ejpam-3335	251	23	for	for	ADP
ejpam-3335	251	24	all	all	DET
ejpam-3335	251	25	ε	ε	PROPN
ejpam-3335	251	26	∈	∈	PROPN
ejpam-3335	251	27	p([0	p([0	NOUN
ejpam-3335	251	28	,	,	PUNCT
ejpam-3335	251	29	1	1	NUM
ejpam-3335	251	30	]	]	NUM
ejpam-3335	251	31	)	)	PUNCT
ejpam-3335	251	32	,	,	PUNCT
ejpam-3335	251	33	a	a	DET
ejpam-3335	251	34	nonempty	nonempty	NOUN
ejpam-3335	251	35	subset	subset	VERB
ejpam-3335	251	36	l(h	l(h	PROPN
ejpam-3335	251	37	;	;	PUNCT
ejpam-3335	251	38	ε	ε	PROPN
ejpam-3335	251	39	)	)	PUNCT
ejpam-3335	251	40	of	of	ADP
ejpam-3335	251	41	a	a	PRON
ejpam-3335	251	42	is	be	AUX
ejpam-3335	251	43	a	a	DET
ejpam-3335	251	44	up	up	ADJ
ejpam-3335	251	45	-	-	PUNCT
ejpam-3335	251	46	subalgebra	subalgebra	NOUN
ejpam-3335	251	47	of	of	ADP
ejpam-3335	251	48	a.	a.	NOUN
ejpam-3335	251	49	proof	proof	NOUN
ejpam-3335	251	50	.	.	PUNCT
ejpam-3335	252	1	assume	assume	VERB
ejpam-3335	252	2	that	that	SCONJ
ejpam-3335	252	3	h	h	NOUN
ejpam-3335	252	4	is	be	AUX
ejpam-3335	252	5	an	an	DET
ejpam-3335	252	6	anti	anti	ADJ
ejpam-3335	252	7	-	-	ADJ
ejpam-3335	252	8	hesitant	hesitant	ADJ
ejpam-3335	252	9	fuzzy	fuzzy	ADJ
ejpam-3335	252	10	up	up	NOUN
ejpam-3335	252	11	-	-	PUNCT
ejpam-3335	252	12	subalgebra	subalgebra	NOUN
ejpam-3335	252	13	of	of	ADP
ejpam-3335	252	14	a.	a.	NOUN
ejpam-3335	252	15	let	let	VERB
ejpam-3335	252	16	ε	ε	PROPN
ejpam-3335	252	17	∈	∈	PROPN
ejpam-3335	252	18	p([0	p([0	PROPN
ejpam-3335	252	19	,	,	PUNCT
ejpam-3335	252	20	1	1	NUM
ejpam-3335	252	21	]	]	PUNCT
ejpam-3335	252	22	)	)	PUNCT
ejpam-3335	252	23	be	be	AUX
ejpam-3335	252	24	such	such	ADJ
ejpam-3335	252	25	that	that	SCONJ
ejpam-3335	252	26	l(h	l(h	PROPN
ejpam-3335	252	27	;	;	PUNCT
ejpam-3335	252	28	ε	ε	PROPN
ejpam-3335	252	29	)	)	PUNCT
ejpam-3335	252	30	6=	6=	NOUN
ejpam-3335	252	31	∅	∅	NOUN
ejpam-3335	252	32	,	,	PUNCT
ejpam-3335	252	33	and	and	CCONJ
ejpam-3335	252	34	let	let	VERB
ejpam-3335	252	35	x	x	PRON
ejpam-3335	252	36	,	,	PUNCT
ejpam-3335	252	37	y	y	PROPN
ejpam-3335	252	38	∈	∈	PROPN
ejpam-3335	252	39	a	a	DET
ejpam-3335	252	40	be	be	AUX
ejpam-3335	252	41	such	such	ADJ
ejpam-3335	252	42	that	that	SCONJ
ejpam-3335	252	43	x	x	SYM
ejpam-3335	252	44	∈	∈	PROPN
ejpam-3335	252	45	l(h	l(h	PROPN
ejpam-3335	252	46	;	;	PUNCT
ejpam-3335	252	47	ε	ε	PROPN
ejpam-3335	252	48	)	)	PUNCT
ejpam-3335	252	49	and	and	CCONJ
ejpam-3335	252	50	y	y	PROPN
ejpam-3335	252	51	∈	∈	PROPN
ejpam-3335	252	52	l(h	l(h	PROPN
ejpam-3335	252	53	;	;	PUNCT
ejpam-3335	252	54	ε	ε	PROPN
ejpam-3335	252	55	)	)	PUNCT
ejpam-3335	252	56	.	.	PUNCT
ejpam-3335	253	1	then	then	ADV
ejpam-3335	253	2	hh(x	hh(x	PUNCT
ejpam-3335	253	3	)	)	PUNCT
ejpam-3335	253	4	⊆	⊆	NUM
ejpam-3335	253	5	ε	ε	PROPN
ejpam-3335	253	6	and	and	CCONJ
ejpam-3335	253	7	hh(y	hh(y	NOUN
ejpam-3335	253	8	)	)	PUNCT
ejpam-3335	253	9	⊆	⊆	NUM
ejpam-3335	253	10	ε	ε	PROPN
ejpam-3335	253	11	.	.	PROPN
ejpam-3335	254	1	since	since	SCONJ
ejpam-3335	254	2	h	h	NOUN
ejpam-3335	254	3	is	be	AUX
ejpam-3335	254	4	an	an	DET
ejpam-3335	254	5	anti	anti	ADJ
ejpam-3335	254	6	-	-	ADJ
ejpam-3335	254	7	hesitant	hesitant	ADJ
ejpam-3335	254	8	fuzzy	fuzzy	ADJ
ejpam-3335	254	9	up	up	NOUN
ejpam-3335	254	10	-	-	PUNCT
ejpam-3335	254	11	subalgebra	subalgebra	NOUN
ejpam-3335	254	12	of	of	ADP
ejpam-3335	254	13	a	a	PRON
ejpam-3335	254	14	,	,	PUNCT
ejpam-3335	254	15	we	we	PRON
ejpam-3335	254	16	have	have	VERB
ejpam-3335	254	17	hh(x	hh(x	X
ejpam-3335	254	18	·	·	PUNCT
ejpam-3335	254	19	y	y	X
ejpam-3335	254	20	)	)	PUNCT
ejpam-3335	254	21	⊆	⊆	NUM
ejpam-3335	254	22	hh(x)∪	hh(x)∪	NOUN
ejpam-3335	254	23	hh(y	hh(y	NOUN
ejpam-3335	254	24	)	)	PUNCT
ejpam-3335	254	25	⊆	⊆	NUM
ejpam-3335	254	26	ε	ε	PROPN
ejpam-3335	254	27	and	and	CCONJ
ejpam-3335	254	28	thus	thus	ADV
ejpam-3335	254	29	x	x	X
ejpam-3335	254	30	·	·	PUNCT
ejpam-3335	254	31	y	y	X
ejpam-3335	254	32	∈	∈	PROPN
ejpam-3335	254	33	l(h	l(h	PROPN
ejpam-3335	254	34	;	;	PUNCT
ejpam-3335	254	35	ε	ε	PROPN
ejpam-3335	254	36	)	)	PUNCT
ejpam-3335	254	37	.	.	PUNCT
ejpam-3335	255	1	hence	hence	ADV
ejpam-3335	255	2	,	,	PUNCT
ejpam-3335	255	3	l(h	l(h	PROPN
ejpam-3335	255	4	;	;	PUNCT
ejpam-3335	255	5	ε	ε	PROPN
ejpam-3335	255	6	)	)	PUNCT
ejpam-3335	255	7	is	be	AUX
ejpam-3335	255	8	a	a	DET
ejpam-3335	255	9	up	up	ADJ
ejpam-3335	255	10	-	-	PUNCT
ejpam-3335	255	11	subalgebra	subalgebra	NOUN
ejpam-3335	255	12	of	of	ADP
ejpam-3335	255	13	a.	a.	PROPN
ejpam-3335	255	14	p.	p.	PROPN
ejpam-3335	255	15	mosrijai	mosrijai	PROPN
ejpam-3335	255	16	,	,	PUNCT
ejpam-3335	255	17	a.	a.	NOUN
ejpam-3335	255	18	iampan	iampan	PROPN
ejpam-3335	255	19	/	/	SYM
ejpam-3335	255	20	eur	eur	PROPN
ejpam-3335	255	21	.	.	PUNCT
ejpam-3335	256	1	j.	j.	PROPN
ejpam-3335	256	2	pure	pure	PROPN
ejpam-3335	256	3	appl	appl	PROPN
ejpam-3335	256	4	.	.	PROPN
ejpam-3335	256	5	math	math	PROPN
ejpam-3335	256	6	,	,	PUNCT
ejpam-3335	256	7	11	11	NUM
ejpam-3335	256	8	(	(	PUNCT
ejpam-3335	256	9	4	4	NUM
ejpam-3335	256	10	)	)	PUNCT
ejpam-3335	256	11	(	(	PUNCT
ejpam-3335	256	12	2018	2018	NUM
ejpam-3335	256	13	)	)	PUNCT
ejpam-3335	256	14	,	,	PUNCT
ejpam-3335	256	15	976	976	NUM
ejpam-3335	256	16	-	-	SYM
ejpam-3335	256	17	1002	1002	NUM
ejpam-3335	256	18	986	986	NUM
ejpam-3335	256	19	conversely	conversely	ADV
ejpam-3335	256	20	,	,	PUNCT
ejpam-3335	256	21	assume	assume	VERB
ejpam-3335	256	22	that	that	SCONJ
ejpam-3335	256	23	for	for	ADP
ejpam-3335	256	24	all	all	DET
ejpam-3335	256	25	ε	ε	PROPN
ejpam-3335	256	26	∈	∈	PROPN
ejpam-3335	256	27	p([0	p([0	NOUN
ejpam-3335	256	28	,	,	PUNCT
ejpam-3335	256	29	1	1	NUM
ejpam-3335	256	30	]	]	NUM
ejpam-3335	256	31	)	)	PUNCT
ejpam-3335	256	32	,	,	PUNCT
ejpam-3335	256	33	a	a	DET
ejpam-3335	256	34	nonempty	nonempty	NOUN
ejpam-3335	256	35	subset	subset	VERB
ejpam-3335	256	36	l(h	l(h	PROPN
ejpam-3335	256	37	;	;	PUNCT
ejpam-3335	256	38	ε	ε	PROPN
ejpam-3335	256	39	)	)	PUNCT
ejpam-3335	256	40	of	of	ADP
ejpam-3335	256	41	a	a	PRON
ejpam-3335	256	42	is	be	AUX
ejpam-3335	256	43	a	a	DET
ejpam-3335	256	44	upsubalgebra	upsubalgebra	NOUN
ejpam-3335	256	45	of	of	ADP
ejpam-3335	256	46	a.	a.	NOUN
ejpam-3335	256	47	let	let	VERB
ejpam-3335	256	48	x	x	PRON
ejpam-3335	256	49	,	,	PUNCT
ejpam-3335	256	50	y	y	PROPN
ejpam-3335	256	51	∈	∈	PROPN
ejpam-3335	256	52	a.	a.	NOUN
ejpam-3335	256	53	then	then	ADV
ejpam-3335	256	54	hh(x),hh(y	hh(x),hh(y	AUX
ejpam-3335	256	55	)	)	PUNCT
ejpam-3335	256	56	∈	∈	NOUN
ejpam-3335	256	57	p([0	p([0	NOUN
ejpam-3335	256	58	,	,	PUNCT
ejpam-3335	256	59	1	1	NUM
ejpam-3335	256	60	]	]	NUM
ejpam-3335	256	61	)	)	PUNCT
ejpam-3335	256	62	.	.	PUNCT
ejpam-3335	257	1	choose	choose	VERB
ejpam-3335	257	2	ε	ε	PROPN
ejpam-3335	257	3	=	=	SYM
ejpam-3335	257	4	hh(x)∪hh(y	hh(x)∪hh(y	PROPN
ejpam-3335	257	5	)	)	PUNCT
ejpam-3335	257	6	∈	∈	PROPN
ejpam-3335	257	7	p([0	p([0	NOUN
ejpam-3335	257	8	,	,	PUNCT
ejpam-3335	257	9	1	1	NUM
ejpam-3335	257	10	]	]	NUM
ejpam-3335	257	11	)	)	PUNCT
ejpam-3335	257	12	.	.	PUNCT
ejpam-3335	258	1	then	then	ADV
ejpam-3335	258	2	hh(x	hh(x	PUNCT
ejpam-3335	258	3	)	)	PUNCT
ejpam-3335	258	4	⊆	⊆	NUM
ejpam-3335	258	5	ε	ε	PROPN
ejpam-3335	258	6	and	and	CCONJ
ejpam-3335	258	7	hh(y	hh(y	NOUN
ejpam-3335	258	8	)	)	PUNCT
ejpam-3335	258	9	⊆	⊆	NUM
ejpam-3335	258	10	ε	ε	PROPN
ejpam-3335	258	11	.	.	PUNCT
ejpam-3335	259	1	thus	thus	ADV
ejpam-3335	259	2	x	x	X
ejpam-3335	259	3	,	,	PUNCT
ejpam-3335	259	4	y	y	PROPN
ejpam-3335	259	5	∈	∈	PROPN
ejpam-3335	259	6	l(h	l(h	PROPN
ejpam-3335	259	7	;	;	PUNCT
ejpam-3335	259	8	ε	ε	PROPN
ejpam-3335	259	9	)	)	PUNCT
ejpam-3335	259	10	6=	6=	ADP
ejpam-3335	259	11	∅.	∅.	ADP
ejpam-3335	259	12	by	by	ADP
ejpam-3335	259	13	assumption	assumption	NOUN
ejpam-3335	259	14	,	,	PUNCT
ejpam-3335	259	15	l(h	l(h	PROPN
ejpam-3335	259	16	;	;	PUNCT
ejpam-3335	259	17	ε	ε	PROPN
ejpam-3335	259	18	)	)	PUNCT
ejpam-3335	259	19	is	be	AUX
ejpam-3335	259	20	a	a	DET
ejpam-3335	259	21	up	up	ADJ
ejpam-3335	259	22	-	-	PUNCT
ejpam-3335	259	23	subalgebra	subalgebra	NOUN
ejpam-3335	259	24	of	of	ADP
ejpam-3335	259	25	a	a	PRON
ejpam-3335	259	26	and	and	CCONJ
ejpam-3335	259	27	thus	thus	ADV
ejpam-3335	259	28	x	x	X
ejpam-3335	259	29	·	·	PUNCT
ejpam-3335	259	30	y	y	X
ejpam-3335	259	31	∈	∈	PROPN
ejpam-3335	259	32	l(h	l(h	PROPN
ejpam-3335	259	33	;	;	PUNCT
ejpam-3335	259	34	ε	ε	PROPN
ejpam-3335	259	35	)	)	PUNCT
ejpam-3335	259	36	.	.	PUNCT
ejpam-3335	260	1	therefore	therefore	ADV
ejpam-3335	260	2	,	,	PUNCT
ejpam-3335	260	3	hh(x	hh(x	PUNCT
ejpam-3335	260	4	·	·	PUNCT
ejpam-3335	260	5	y	y	X
ejpam-3335	260	6	)	)	PUNCT
ejpam-3335	260	7	⊆	⊆	NUM
ejpam-3335	260	8	ε	ε	PROPN
ejpam-3335	260	9	=	=	SYM
ejpam-3335	260	10	hh(x	hh(x	X
ejpam-3335	260	11	)	)	PUNCT
ejpam-3335	260	12	∪	∪	ADP
ejpam-3335	260	13	hh(y	hh(y	NOUN
ejpam-3335	260	14	)	)	PUNCT
ejpam-3335	260	15	.	.	PUNCT
ejpam-3335	261	1	hence	hence	ADV
ejpam-3335	261	2	,	,	PUNCT
ejpam-3335	261	3	h	h	PROPN
ejpam-3335	261	4	is	be	AUX
ejpam-3335	261	5	an	an	DET
ejpam-3335	261	6	anti	anti	ADJ
ejpam-3335	261	7	-	-	ADJ
ejpam-3335	261	8	hesitant	hesitant	ADJ
ejpam-3335	261	9	fuzzy	fuzzy	ADJ
ejpam-3335	261	10	up	up	NOUN
ejpam-3335	261	11	-	-	PUNCT
ejpam-3335	261	12	subalgebra	subalgebra	NOUN
ejpam-3335	261	13	of	of	ADP
ejpam-3335	261	14	a.	a.	NOUN
ejpam-3335	261	15	theorem	theorem	NOUN
ejpam-3335	261	16	8	8	NUM
ejpam-3335	261	17	.	.	PUNCT
ejpam-3335	262	1	a	a	DET
ejpam-3335	262	2	hesitant	hesitant	ADJ
ejpam-3335	262	3	fuzzy	fuzzy	ADJ
ejpam-3335	262	4	set	set	VERB
ejpam-3335	262	5	h	h	NOUN
ejpam-3335	262	6	on	on	ADP
ejpam-3335	262	7	a	a	PRON
ejpam-3335	262	8	is	be	AUX
ejpam-3335	262	9	an	an	DET
ejpam-3335	262	10	anti	anti	ADJ
ejpam-3335	262	11	-	-	ADJ
ejpam-3335	262	12	hesitant	hesitant	ADJ
ejpam-3335	262	13	fuzzy	fuzzy	ADJ
ejpam-3335	262	14	up	up	NOUN
ejpam-3335	262	15	-	-	PUNCT
ejpam-3335	262	16	filter	filter	NOUN
ejpam-3335	262	17	of	of	ADP
ejpam-3335	262	18	a	a	DET
ejpam-3335	262	19	if	if	NOUN
ejpam-3335	262	20	and	and	CCONJ
ejpam-3335	262	21	only	only	ADV
ejpam-3335	262	22	if	if	SCONJ
ejpam-3335	262	23	for	for	ADP
ejpam-3335	262	24	all	all	DET
ejpam-3335	262	25	ε	ε	PROPN
ejpam-3335	262	26	∈	∈	PROPN
ejpam-3335	262	27	p([0	p([0	NOUN
ejpam-3335	262	28	,	,	PUNCT
ejpam-3335	262	29	1	1	NUM
ejpam-3335	262	30	]	]	NUM
ejpam-3335	262	31	)	)	PUNCT
ejpam-3335	262	32	,	,	PUNCT
ejpam-3335	262	33	a	a	DET
ejpam-3335	262	34	nonempty	nonempty	NOUN
ejpam-3335	262	35	subset	subset	VERB
ejpam-3335	262	36	l(h	l(h	PROPN
ejpam-3335	262	37	;	;	PUNCT
ejpam-3335	262	38	ε	ε	PROPN
ejpam-3335	262	39	)	)	PUNCT
ejpam-3335	262	40	of	of	ADP
ejpam-3335	262	41	a	a	PRON
ejpam-3335	262	42	is	be	AUX
ejpam-3335	262	43	a	a	DET
ejpam-3335	262	44	up	up	ADJ
ejpam-3335	262	45	-	-	PUNCT
ejpam-3335	262	46	filter	filter	NOUN
ejpam-3335	262	47	of	of	ADP
ejpam-3335	262	48	a.	a.	NOUN
ejpam-3335	262	49	proof	proof	NOUN
ejpam-3335	262	50	.	.	PUNCT
ejpam-3335	263	1	assume	assume	VERB
ejpam-3335	263	2	that	that	SCONJ
ejpam-3335	263	3	h	h	NOUN
ejpam-3335	263	4	is	be	AUX
ejpam-3335	263	5	an	an	DET
ejpam-3335	263	6	anti	anti	ADJ
ejpam-3335	263	7	-	-	ADJ
ejpam-3335	263	8	hesitant	hesitant	ADJ
ejpam-3335	263	9	fuzzy	fuzzy	ADJ
ejpam-3335	263	10	up	up	NOUN
ejpam-3335	263	11	-	-	PUNCT
ejpam-3335	263	12	filter	filter	NOUN
ejpam-3335	263	13	of	of	ADP
ejpam-3335	263	14	a.	a.	NOUN
ejpam-3335	263	15	let	let	VERB
ejpam-3335	263	16	ε	ε	PROPN
ejpam-3335	263	17	∈	∈	PROPN
ejpam-3335	263	18	p([0	p([0	PROPN
ejpam-3335	263	19	,	,	PUNCT
ejpam-3335	263	20	1	1	NUM
ejpam-3335	263	21	]	]	PUNCT
ejpam-3335	263	22	)	)	PUNCT
ejpam-3335	263	23	be	be	AUX
ejpam-3335	263	24	such	such	ADJ
ejpam-3335	263	25	that	that	SCONJ
ejpam-3335	263	26	l(h	l(h	PROPN
ejpam-3335	263	27	;	;	PUNCT
ejpam-3335	263	28	ε	ε	PROPN
ejpam-3335	263	29	)	)	PUNCT
ejpam-3335	263	30	6=	6=	NOUN
ejpam-3335	263	31	∅	∅	NOUN
ejpam-3335	263	32	and	and	CCONJ
ejpam-3335	263	33	let	let	VERB
ejpam-3335	263	34	x	x	SYM
ejpam-3335	263	35	∈	∈	PROPN
ejpam-3335	263	36	a	a	DET
ejpam-3335	263	37	be	be	AUX
ejpam-3335	263	38	such	such	ADJ
ejpam-3335	263	39	that	that	SCONJ
ejpam-3335	263	40	x	x	SYM
ejpam-3335	263	41	∈	∈	PROPN
ejpam-3335	263	42	l(h	l(h	PROPN
ejpam-3335	263	43	;	;	PUNCT
ejpam-3335	263	44	ε	ε	PROPN
ejpam-3335	263	45	)	)	PUNCT
ejpam-3335	263	46	.	.	PUNCT
ejpam-3335	264	1	then	then	ADV
ejpam-3335	264	2	hh(x	hh(x	PUNCT
ejpam-3335	264	3	)	)	PUNCT
ejpam-3335	264	4	⊆	⊆	NUM
ejpam-3335	264	5	ε	ε	PROPN
ejpam-3335	264	6	.	.	PROPN
ejpam-3335	265	1	since	since	SCONJ
ejpam-3335	265	2	h	h	NOUN
ejpam-3335	265	3	is	be	AUX
ejpam-3335	265	4	an	an	DET
ejpam-3335	265	5	anti	anti	ADJ
ejpam-3335	265	6	-	-	ADJ
ejpam-3335	265	7	hesitant	hesitant	ADJ
ejpam-3335	265	8	fuzzy	fuzzy	ADJ
ejpam-3335	265	9	up	up	NOUN
ejpam-3335	265	10	-	-	PUNCT
ejpam-3335	265	11	filter	filter	NOUN
ejpam-3335	265	12	of	of	ADP
ejpam-3335	265	13	a	a	PRON
ejpam-3335	265	14	,	,	PUNCT
ejpam-3335	265	15	we	we	PRON
ejpam-3335	265	16	have	have	VERB
ejpam-3335	265	17	hh(0	hh(0	NOUN
ejpam-3335	265	18	)	)	PUNCT
ejpam-3335	265	19	⊆	⊆	NUM
ejpam-3335	265	20	hh(x	hh(x	NOUN
ejpam-3335	265	21	)	)	PUNCT
ejpam-3335	265	22	⊆	⊆	NUM
ejpam-3335	265	23	ε	ε	PROPN
ejpam-3335	265	24	and	and	CCONJ
ejpam-3335	265	25	thus	thus	ADV
ejpam-3335	265	26	0	0	X
ejpam-3335	265	27	∈	∈	PROPN
ejpam-3335	265	28	l(h	l(h	PROPN
ejpam-3335	265	29	;	;	PUNCT
ejpam-3335	265	30	ε	ε	PROPN
ejpam-3335	265	31	)	)	PUNCT
ejpam-3335	265	32	.	.	PUNCT
ejpam-3335	266	1	next	next	ADV
ejpam-3335	266	2	,	,	PUNCT
ejpam-3335	266	3	let	let	VERB
ejpam-3335	266	4	x	x	PRON
ejpam-3335	266	5	,	,	PUNCT
ejpam-3335	266	6	y	y	PROPN
ejpam-3335	266	7	∈	∈	PROPN
ejpam-3335	266	8	a	a	PRON
ejpam-3335	266	9	be	be	AUX
ejpam-3335	266	10	such	such	ADJ
ejpam-3335	266	11	that	that	SCONJ
ejpam-3335	266	12	x	x	X
ejpam-3335	266	13	·	·	PUNCT
ejpam-3335	266	14	y	y	X
ejpam-3335	266	15	∈	∈	PROPN
ejpam-3335	266	16	l(h	l(h	PROPN
ejpam-3335	266	17	;	;	PUNCT
ejpam-3335	266	18	ε	ε	PROPN
ejpam-3335	266	19	)	)	PUNCT
ejpam-3335	266	20	and	and	CCONJ
ejpam-3335	266	21	x	x	PUNCT
ejpam-3335	266	22	∈	∈	PROPN
ejpam-3335	266	23	l(h	l(h	PROPN
ejpam-3335	266	24	;	;	PUNCT
ejpam-3335	266	25	ε	ε	PROPN
ejpam-3335	266	26	)	)	PUNCT
ejpam-3335	266	27	.	.	PUNCT
ejpam-3335	267	1	then	then	ADV
ejpam-3335	267	2	hh(x	hh(x	PUNCT
ejpam-3335	267	3	·	·	PUNCT
ejpam-3335	267	4	y	y	X
ejpam-3335	267	5	)	)	PUNCT
ejpam-3335	267	6	⊆	⊆	NUM
ejpam-3335	267	7	ε	ε	PROPN
ejpam-3335	267	8	and	and	CCONJ
ejpam-3335	267	9	hh(x	hh(x	NOUN
ejpam-3335	267	10	)	)	PUNCT
ejpam-3335	268	1	⊆	⊆	NUM
ejpam-3335	268	2	ε	ε	PROPN
ejpam-3335	268	3	.	.	PROPN
ejpam-3335	269	1	since	since	SCONJ
ejpam-3335	269	2	h	h	NOUN
ejpam-3335	269	3	is	be	AUX
ejpam-3335	269	4	an	an	DET
ejpam-3335	269	5	anti	anti	ADJ
ejpam-3335	269	6	-	-	ADJ
ejpam-3335	269	7	hesitant	hesitant	ADJ
ejpam-3335	269	8	fuzzy	fuzzy	ADJ
ejpam-3335	269	9	up	up	NOUN
ejpam-3335	269	10	-	-	PUNCT
ejpam-3335	269	11	filter	filter	NOUN
ejpam-3335	269	12	of	of	ADP
ejpam-3335	269	13	a	a	PRON
ejpam-3335	269	14	,	,	PUNCT
ejpam-3335	269	15	we	we	PRON
ejpam-3335	269	16	have	have	VERB
ejpam-3335	269	17	hh(y	hh(y	NOUN
ejpam-3335	269	18	)	)	PUNCT
ejpam-3335	270	1	⊆	⊆	NUM
ejpam-3335	270	2	hh(x	hh(x	X
ejpam-3335	270	3	·	·	PUNCT
ejpam-3335	270	4	y	y	X
ejpam-3335	270	5	)	)	PUNCT
ejpam-3335	270	6	∪	∪	ADP
ejpam-3335	270	7	hh(x	hh(x	NOUN
ejpam-3335	270	8	)	)	PUNCT
ejpam-3335	270	9	⊆	⊆	NUM
ejpam-3335	270	10	ε	ε	PROPN
ejpam-3335	270	11	and	and	CCONJ
ejpam-3335	270	12	thus	thus	ADV
ejpam-3335	270	13	y	y	PROPN
ejpam-3335	270	14	∈	∈	PROPN
ejpam-3335	270	15	l(h	l(h	PROPN
ejpam-3335	270	16	;	;	PUNCT
ejpam-3335	270	17	ε	ε	PROPN
ejpam-3335	270	18	)	)	PUNCT
ejpam-3335	270	19	.	.	PUNCT
ejpam-3335	271	1	hence	hence	ADV
ejpam-3335	271	2	,	,	PUNCT
ejpam-3335	271	3	l(h	l(h	PROPN
ejpam-3335	271	4	;	;	PUNCT
ejpam-3335	271	5	ε	ε	PROPN
ejpam-3335	271	6	)	)	PUNCT
ejpam-3335	271	7	is	be	AUX
ejpam-3335	271	8	a	a	DET
ejpam-3335	271	9	up	up	ADJ
ejpam-3335	271	10	-	-	PUNCT
ejpam-3335	271	11	filter	filter	NOUN
ejpam-3335	271	12	of	of	ADP
ejpam-3335	271	13	a.	a.	NOUN
ejpam-3335	271	14	conversely	conversely	ADV
ejpam-3335	271	15	,	,	PUNCT
ejpam-3335	271	16	assume	assume	VERB
ejpam-3335	271	17	that	that	SCONJ
ejpam-3335	271	18	for	for	ADP
ejpam-3335	271	19	all	all	DET
ejpam-3335	271	20	ε	ε	PROPN
ejpam-3335	271	21	∈	∈	PROPN
ejpam-3335	271	22	p([0	p([0	NOUN
ejpam-3335	271	23	,	,	PUNCT
ejpam-3335	271	24	1	1	NUM
ejpam-3335	271	25	]	]	NUM
ejpam-3335	271	26	)	)	PUNCT
ejpam-3335	271	27	,	,	PUNCT
ejpam-3335	271	28	a	a	DET
ejpam-3335	271	29	nonempty	nonempty	NOUN
ejpam-3335	271	30	subset	subset	VERB
ejpam-3335	271	31	l(h	l(h	PROPN
ejpam-3335	271	32	;	;	PUNCT
ejpam-3335	271	33	ε	ε	PROPN
ejpam-3335	271	34	)	)	PUNCT
ejpam-3335	271	35	of	of	ADP
ejpam-3335	271	36	a	a	PRON
ejpam-3335	271	37	is	be	AUX
ejpam-3335	271	38	a	a	DET
ejpam-3335	271	39	up	up	ADJ
ejpam-3335	271	40	-	-	PUNCT
ejpam-3335	271	41	filter	filter	NOUN
ejpam-3335	271	42	of	of	ADP
ejpam-3335	271	43	a.	a.	NOUN
ejpam-3335	271	44	let	let	VERB
ejpam-3335	271	45	x	x	X
ejpam-3335	271	46	∈	∈	VERB
ejpam-3335	271	47	a.	a.	NOUN
ejpam-3335	271	48	then	then	ADV
ejpam-3335	271	49	hh(x	hh(x	PUNCT
ejpam-3335	271	50	)	)	PUNCT
ejpam-3335	271	51	∈	∈	PROPN
ejpam-3335	271	52	p([0	p([0	NOUN
ejpam-3335	271	53	,	,	PUNCT
ejpam-3335	271	54	1	1	NUM
ejpam-3335	271	55	]	]	NUM
ejpam-3335	271	56	)	)	PUNCT
ejpam-3335	271	57	.	.	PUNCT
ejpam-3335	272	1	choose	choose	VERB
ejpam-3335	272	2	ε	ε	PROPN
ejpam-3335	272	3	=	=	SYM
ejpam-3335	272	4	hh(x	hh(x	X
ejpam-3335	272	5	)	)	PUNCT
ejpam-3335	272	6	∈	∈	PROPN
ejpam-3335	272	7	p([0	p([0	NOUN
ejpam-3335	272	8	,	,	PUNCT
ejpam-3335	272	9	1	1	NUM
ejpam-3335	272	10	]	]	NUM
ejpam-3335	272	11	)	)	PUNCT
ejpam-3335	272	12	.	.	PUNCT
ejpam-3335	273	1	then	then	ADV
ejpam-3335	273	2	hh(x	hh(x	PUNCT
ejpam-3335	273	3	)	)	PUNCT
ejpam-3335	273	4	⊆	⊆	NUM
ejpam-3335	273	5	ε	ε	PROPN
ejpam-3335	273	6	.	.	PUNCT
ejpam-3335	274	1	thus	thus	ADV
ejpam-3335	274	2	x	x	X
ejpam-3335	274	3	∈	∈	PROPN
ejpam-3335	274	4	l(h	l(h	PROPN
ejpam-3335	274	5	;	;	PUNCT
ejpam-3335	274	6	ε	ε	PROPN
ejpam-3335	274	7	)	)	PUNCT
ejpam-3335	274	8	.	.	PUNCT
ejpam-3335	275	1	by	by	ADP
ejpam-3335	275	2	assumption	assumption	NOUN
ejpam-3335	275	3	,	,	PUNCT
ejpam-3335	275	4	we	we	PRON
ejpam-3335	275	5	have	have	AUX
ejpam-3335	275	6	l(h	l(h	PROPN
ejpam-3335	275	7	;	;	PUNCT
ejpam-3335	275	8	ε	ε	PROPN
ejpam-3335	275	9	)	)	PUNCT
ejpam-3335	275	10	is	be	AUX
ejpam-3335	275	11	a	a	DET
ejpam-3335	275	12	up	up	ADJ
ejpam-3335	275	13	-	-	PUNCT
ejpam-3335	275	14	filter	filter	NOUN
ejpam-3335	275	15	of	of	ADP
ejpam-3335	275	16	a	a	PRON
ejpam-3335	275	17	and	and	CCONJ
ejpam-3335	275	18	so	so	ADV
ejpam-3335	275	19	0	0	NUM
ejpam-3335	275	20	∈	∈	PROPN
ejpam-3335	275	21	l(h	l(h	PROPN
ejpam-3335	275	22	;	;	PUNCT
ejpam-3335	275	23	ε	ε	PROPN
ejpam-3335	275	24	)	)	PUNCT
ejpam-3335	275	25	.	.	PUNCT
ejpam-3335	276	1	therefore	therefore	ADV
ejpam-3335	276	2	,	,	PUNCT
ejpam-3335	276	3	hh(0	hh(0	NOUN
ejpam-3335	276	4	)	)	PUNCT
ejpam-3335	276	5	⊆	⊆	NUM
ejpam-3335	276	6	ε	ε	NOUN
ejpam-3335	276	7	=	=	SYM
ejpam-3335	276	8	hh(x	hh(x	X
ejpam-3335	276	9	)	)	PUNCT
ejpam-3335	276	10	.	.	PUNCT
ejpam-3335	277	1	next	next	ADV
ejpam-3335	277	2	,	,	PUNCT
ejpam-3335	277	3	let	let	VERB
ejpam-3335	277	4	x	x	PRON
ejpam-3335	277	5	,	,	PUNCT
ejpam-3335	277	6	y	y	PROPN
ejpam-3335	277	7	∈	∈	PROPN
ejpam-3335	277	8	a.	a.	NOUN
ejpam-3335	277	9	then	then	ADV
ejpam-3335	277	10	hh(x	hh(x	X
ejpam-3335	277	11	·	·	PUNCT
ejpam-3335	277	12	y	y	X
ejpam-3335	277	13	)	)	PUNCT
ejpam-3335	277	14	,	,	PUNCT
ejpam-3335	277	15	hh(x	hh(x	NOUN
ejpam-3335	277	16	)	)	PUNCT
ejpam-3335	277	17	∈	∈	PROPN
ejpam-3335	277	18	p([0	p([0	NOUN
ejpam-3335	277	19	,	,	PUNCT
ejpam-3335	277	20	1	1	NUM
ejpam-3335	277	21	]	]	NUM
ejpam-3335	277	22	)	)	PUNCT
ejpam-3335	277	23	.	.	PUNCT
ejpam-3335	278	1	choose	choose	VERB
ejpam-3335	278	2	ε	ε	PROPN
ejpam-3335	278	3	=	=	SYM
ejpam-3335	278	4	hh(x	hh(x	X
ejpam-3335	278	5	·	·	PUNCT
ejpam-3335	278	6	y	y	X
ejpam-3335	278	7	)	)	PUNCT
ejpam-3335	278	8	∪	∪	ADP
ejpam-3335	278	9	hh(x	hh(x	NOUN
ejpam-3335	278	10	)	)	PUNCT
ejpam-3335	278	11	∈	∈	PROPN
ejpam-3335	278	12	p([0	p([0	NOUN
ejpam-3335	278	13	,	,	PUNCT
ejpam-3335	278	14	1	1	NUM
ejpam-3335	278	15	]	]	NUM
ejpam-3335	278	16	)	)	PUNCT
ejpam-3335	278	17	.	.	PUNCT
ejpam-3335	279	1	then	then	ADV
ejpam-3335	279	2	hh(x·y	hh(x·y	NUM
ejpam-3335	279	3	)	)	PUNCT
ejpam-3335	279	4	⊆	⊆	NUM
ejpam-3335	279	5	ε	ε	PROPN
ejpam-3335	279	6	and	and	CCONJ
ejpam-3335	279	7	hh(x	hh(x	NOUN
ejpam-3335	279	8	)	)	PUNCT
ejpam-3335	279	9	⊆	⊆	NUM
ejpam-3335	279	10	ε	ε	PROPN
ejpam-3335	279	11	.	.	PUNCT
ejpam-3335	280	1	thus	thus	ADV
ejpam-3335	280	2	x·y	x·y	PROPN
ejpam-3335	280	3	,	,	PUNCT
ejpam-3335	280	4	x	x	SYM
ejpam-3335	280	5	∈	∈	PROPN
ejpam-3335	280	6	l(h	l(h	PROPN
ejpam-3335	280	7	;	;	PUNCT
ejpam-3335	280	8	ε	ε	PROPN
ejpam-3335	280	9	)	)	PUNCT
ejpam-3335	281	1	6=	6=	ADP
ejpam-3335	281	2	∅.	∅.	ADP
ejpam-3335	281	3	by	by	ADP
ejpam-3335	281	4	assumption	assumption	NOUN
ejpam-3335	281	5	,	,	PUNCT
ejpam-3335	281	6	we	we	PRON
ejpam-3335	281	7	have	have	AUX
ejpam-3335	281	8	l(h	l(h	PROPN
ejpam-3335	281	9	;	;	PUNCT
ejpam-3335	281	10	ε	ε	PROPN
ejpam-3335	281	11	)	)	PUNCT
ejpam-3335	281	12	is	be	AUX
ejpam-3335	281	13	a	a	DET
ejpam-3335	281	14	up	up	ADJ
ejpam-3335	281	15	-	-	PUNCT
ejpam-3335	281	16	filter	filter	NOUN
ejpam-3335	281	17	of	of	ADP
ejpam-3335	281	18	a	a	PRON
ejpam-3335	281	19	and	and	CCONJ
ejpam-3335	281	20	so	so	ADV
ejpam-3335	281	21	y	y	PROPN
ejpam-3335	281	22	∈	∈	PROPN
ejpam-3335	282	1	l(h	l(h	PROPN
ejpam-3335	282	2	;	;	PUNCT
ejpam-3335	282	3	ε	ε	PROPN
ejpam-3335	282	4	)	)	PUNCT
ejpam-3335	282	5	.	.	PUNCT
ejpam-3335	283	1	therefore	therefore	ADV
ejpam-3335	283	2	,	,	PUNCT
ejpam-3335	283	3	hh(y	hh(y	ADJ
ejpam-3335	283	4	)	)	PUNCT
ejpam-3335	283	5	⊆	⊆	NUM
ejpam-3335	283	6	ε	ε	PROPN
ejpam-3335	283	7	=	=	PUNCT
ejpam-3335	283	8	hh(x·y)∪hh(x	hh(x·y)∪hh(x	PROPN
ejpam-3335	283	9	)	)	PUNCT
ejpam-3335	283	10	.	.	PUNCT
ejpam-3335	284	1	hence	hence	ADV
ejpam-3335	284	2	,	,	PUNCT
ejpam-3335	284	3	h	h	PROPN
ejpam-3335	284	4	is	be	AUX
ejpam-3335	284	5	an	an	DET
ejpam-3335	284	6	anti	anti	ADJ
ejpam-3335	284	7	-	-	ADJ
ejpam-3335	284	8	hesitant	hesitant	ADJ
ejpam-3335	284	9	fuzzy	fuzzy	ADJ
ejpam-3335	284	10	up	up	NOUN
ejpam-3335	284	11	-	-	PUNCT
ejpam-3335	284	12	filter	filter	NOUN
ejpam-3335	284	13	of	of	ADP
ejpam-3335	284	14	a.	a.	NOUN
ejpam-3335	284	15	theorem	theorem	NOUN
ejpam-3335	284	16	9	9	NUM
ejpam-3335	284	17	.	.	PUNCT
ejpam-3335	285	1	a	a	DET
ejpam-3335	285	2	hesitant	hesitant	ADJ
ejpam-3335	285	3	fuzzy	fuzzy	ADJ
ejpam-3335	285	4	set	set	VERB
ejpam-3335	285	5	h	h	NOUN
ejpam-3335	285	6	on	on	ADP
ejpam-3335	285	7	a	a	PRON
ejpam-3335	285	8	is	be	AUX
ejpam-3335	285	9	an	an	DET
ejpam-3335	285	10	anti	anti	ADJ
ejpam-3335	285	11	-	-	ADJ
ejpam-3335	285	12	hesitant	hesitant	ADJ
ejpam-3335	285	13	fuzzy	fuzzy	ADJ
ejpam-3335	285	14	up	up	NOUN
ejpam-3335	285	15	-	-	PUNCT
ejpam-3335	285	16	ideal	ideal	NOUN
ejpam-3335	285	17	of	of	ADP
ejpam-3335	285	18	a	a	DET
ejpam-3335	285	19	if	if	NOUN
ejpam-3335	285	20	and	and	CCONJ
ejpam-3335	285	21	only	only	ADV
ejpam-3335	285	22	if	if	SCONJ
ejpam-3335	285	23	for	for	ADP
ejpam-3335	285	24	all	all	DET
ejpam-3335	285	25	ε	ε	PROPN
ejpam-3335	285	26	∈	∈	PROPN
ejpam-3335	285	27	p([0	p([0	NOUN
ejpam-3335	285	28	,	,	PUNCT
ejpam-3335	285	29	1	1	NUM
ejpam-3335	285	30	]	]	NUM
ejpam-3335	285	31	)	)	PUNCT
ejpam-3335	285	32	,	,	PUNCT
ejpam-3335	285	33	a	a	DET
ejpam-3335	285	34	nonempty	nonempty	NOUN
ejpam-3335	285	35	subset	subset	VERB
ejpam-3335	285	36	l(h	l(h	PROPN
ejpam-3335	285	37	;	;	PUNCT
ejpam-3335	285	38	ε	ε	PROPN
ejpam-3335	285	39	)	)	PUNCT
ejpam-3335	285	40	of	of	ADP
ejpam-3335	285	41	a	a	PRON
ejpam-3335	285	42	is	be	AUX
ejpam-3335	285	43	a	a	DET
ejpam-3335	285	44	up	up	ADJ
ejpam-3335	285	45	-	-	PUNCT
ejpam-3335	285	46	ideal	ideal	NOUN
ejpam-3335	285	47	of	of	ADP
ejpam-3335	285	48	a.	a.	NOUN
ejpam-3335	285	49	proof	proof	NOUN
ejpam-3335	285	50	.	.	PUNCT
ejpam-3335	286	1	assume	assume	VERB
ejpam-3335	286	2	that	that	SCONJ
ejpam-3335	286	3	h	h	NOUN
ejpam-3335	286	4	is	be	AUX
ejpam-3335	286	5	an	an	DET
ejpam-3335	286	6	anti	anti	ADJ
ejpam-3335	286	7	-	-	ADJ
ejpam-3335	286	8	hesitant	hesitant	ADJ
ejpam-3335	286	9	fuzzy	fuzzy	ADJ
ejpam-3335	286	10	up	up	NOUN
ejpam-3335	286	11	-	-	PUNCT
ejpam-3335	286	12	ideal	ideal	NOUN
ejpam-3335	286	13	of	of	ADP
ejpam-3335	286	14	a.	a.	NOUN
ejpam-3335	286	15	let	let	VERB
ejpam-3335	286	16	ε	ε	PROPN
ejpam-3335	286	17	∈	∈	PROPN
ejpam-3335	286	18	p([0	p([0	PROPN
ejpam-3335	286	19	,	,	PUNCT
ejpam-3335	286	20	1	1	NUM
ejpam-3335	286	21	]	]	PUNCT
ejpam-3335	286	22	)	)	PUNCT
ejpam-3335	286	23	be	be	AUX
ejpam-3335	286	24	such	such	ADJ
ejpam-3335	286	25	that	that	SCONJ
ejpam-3335	286	26	l(h	l(h	PROPN
ejpam-3335	286	27	;	;	PUNCT
ejpam-3335	286	28	ε	ε	PROPN
ejpam-3335	286	29	)	)	PUNCT
ejpam-3335	286	30	6=	6=	NOUN
ejpam-3335	286	31	∅	∅	NOUN
ejpam-3335	286	32	and	and	CCONJ
ejpam-3335	286	33	let	let	VERB
ejpam-3335	286	34	x	x	SYM
ejpam-3335	286	35	∈	∈	PROPN
ejpam-3335	286	36	a	a	DET
ejpam-3335	286	37	be	be	AUX
ejpam-3335	286	38	such	such	ADJ
ejpam-3335	286	39	that	that	SCONJ
ejpam-3335	286	40	x	x	SYM
ejpam-3335	286	41	∈	∈	PROPN
ejpam-3335	286	42	l(h	l(h	PROPN
ejpam-3335	286	43	;	;	PUNCT
ejpam-3335	286	44	ε	ε	PROPN
ejpam-3335	286	45	)	)	PUNCT
ejpam-3335	286	46	.	.	PUNCT
ejpam-3335	287	1	then	then	ADV
ejpam-3335	287	2	hh(x	hh(x	PUNCT
ejpam-3335	287	3	)	)	PUNCT
ejpam-3335	287	4	⊆	⊆	NUM
ejpam-3335	287	5	ε	ε	PROPN
ejpam-3335	287	6	.	.	PROPN
ejpam-3335	288	1	since	since	SCONJ
ejpam-3335	288	2	h	h	NOUN
ejpam-3335	288	3	is	be	AUX
ejpam-3335	288	4	an	an	DET
ejpam-3335	288	5	anti	anti	ADJ
ejpam-3335	288	6	-	-	ADJ
ejpam-3335	288	7	hesitant	hesitant	ADJ
ejpam-3335	288	8	fuzzy	fuzzy	ADJ
ejpam-3335	288	9	up	up	NOUN
ejpam-3335	288	10	-	-	PUNCT
ejpam-3335	288	11	ideal	ideal	NOUN
ejpam-3335	288	12	of	of	ADP
ejpam-3335	288	13	a	a	PRON
ejpam-3335	288	14	,	,	PUNCT
ejpam-3335	288	15	we	we	PRON
ejpam-3335	288	16	have	have	VERB
ejpam-3335	288	17	hh(0	hh(0	NOUN
ejpam-3335	288	18	)	)	PUNCT
ejpam-3335	288	19	⊆	⊆	NUM
ejpam-3335	288	20	hh(x	hh(x	NOUN
ejpam-3335	288	21	)	)	PUNCT
ejpam-3335	288	22	⊆	⊆	NUM
ejpam-3335	288	23	ε	ε	PROPN
ejpam-3335	288	24	and	and	CCONJ
ejpam-3335	288	25	thus	thus	ADV
ejpam-3335	288	26	0	0	X
ejpam-3335	288	27	∈	∈	PROPN
ejpam-3335	288	28	l(h	l(h	PROPN
ejpam-3335	288	29	;	;	PUNCT
ejpam-3335	288	30	ε	ε	PROPN
ejpam-3335	288	31	)	)	PUNCT
ejpam-3335	288	32	.	.	PUNCT
ejpam-3335	289	1	next	next	ADV
ejpam-3335	289	2	,	,	PUNCT
ejpam-3335	289	3	let	let	VERB
ejpam-3335	289	4	x	x	PRON
ejpam-3335	289	5	,	,	PUNCT
ejpam-3335	289	6	y	y	PROPN
ejpam-3335	289	7	,	,	PUNCT
ejpam-3335	289	8	z	z	PROPN
ejpam-3335	289	9	∈	∈	PROPN
ejpam-3335	289	10	a	a	DET
ejpam-3335	289	11	be	be	AUX
ejpam-3335	289	12	such	such	ADJ
ejpam-3335	289	13	that	that	SCONJ
ejpam-3335	289	14	x	x	PART
ejpam-3335	289	15	·	·	PUNCT
ejpam-3335	289	16	(	(	PUNCT
ejpam-3335	289	17	y	y	PROPN
ejpam-3335	289	18	·	·	PUNCT
ejpam-3335	289	19	z	z	X
ejpam-3335	289	20	)	)	PUNCT
ejpam-3335	289	21	∈	∈	PROPN
ejpam-3335	289	22	l(h	l(h	PROPN
ejpam-3335	289	23	;	;	PUNCT
ejpam-3335	289	24	ε	ε	PROPN
ejpam-3335	289	25	)	)	PUNCT
ejpam-3335	289	26	and	and	CCONJ
ejpam-3335	289	27	y	y	PROPN
ejpam-3335	289	28	∈	∈	PROPN
ejpam-3335	290	1	l(h	l(h	PROPN
ejpam-3335	290	2	;	;	PUNCT
ejpam-3335	290	3	ε	ε	PROPN
ejpam-3335	290	4	)	)	PUNCT
ejpam-3335	290	5	.	.	PUNCT
ejpam-3335	291	1	then	then	ADV
ejpam-3335	291	2	hh(x	hh(x	PUNCT
ejpam-3335	291	3	·	·	PUNCT
ejpam-3335	291	4	(	(	PUNCT
ejpam-3335	291	5	y	y	PROPN
ejpam-3335	291	6	·	·	PUNCT
ejpam-3335	291	7	z	z	NOUN
ejpam-3335	291	8	)	)	PUNCT
ejpam-3335	291	9	)	)	PUNCT
ejpam-3335	292	1	⊆	⊆	NUM
ejpam-3335	292	2	ε	ε	PROPN
ejpam-3335	292	3	and	and	CCONJ
ejpam-3335	292	4	hh(y	hh(y	NOUN
ejpam-3335	292	5	)	)	PUNCT
ejpam-3335	292	6	⊆	⊆	NUM
ejpam-3335	292	7	ε	ε	PROPN
ejpam-3335	292	8	.	.	PROPN
ejpam-3335	293	1	since	since	SCONJ
ejpam-3335	293	2	h	h	NOUN
ejpam-3335	293	3	is	be	AUX
ejpam-3335	293	4	an	an	DET
ejpam-3335	293	5	anti	anti	ADJ
ejpam-3335	293	6	-	-	ADJ
ejpam-3335	293	7	hesitant	hesitant	ADJ
ejpam-3335	293	8	fuzzy	fuzzy	ADJ
ejpam-3335	293	9	up	up	NOUN
ejpam-3335	293	10	-	-	PUNCT
ejpam-3335	293	11	ideal	ideal	NOUN
ejpam-3335	293	12	of	of	ADP
ejpam-3335	293	13	a	a	PRON
ejpam-3335	293	14	,	,	PUNCT
ejpam-3335	293	15	we	we	PRON
ejpam-3335	293	16	have	have	VERB
ejpam-3335	293	17	hh(x	hh(x	X
ejpam-3335	293	18	·	·	PUNCT
ejpam-3335	293	19	z	z	X
ejpam-3335	293	20	)	)	PUNCT
ejpam-3335	293	21	⊆	⊆	NUM
ejpam-3335	293	22	hh(x	hh(x	X
ejpam-3335	293	23	·	·	PUNCT
ejpam-3335	293	24	(	(	PUNCT
ejpam-3335	293	25	y	y	X
ejpam-3335	293	26	·	·	PUNCT
ejpam-3335	293	27	z))∪hh(y	z))∪hh(y	NUM
ejpam-3335	293	28	)	)	PUNCT
ejpam-3335	293	29	⊆	⊆	NUM
ejpam-3335	293	30	ε	ε	PROPN
ejpam-3335	293	31	and	and	CCONJ
ejpam-3335	293	32	thus	thus	ADV
ejpam-3335	293	33	x	x	X
ejpam-3335	293	34	·	·	PUNCT
ejpam-3335	293	35	z	z	X
ejpam-3335	293	36	∈	∈	PROPN
ejpam-3335	293	37	l(h	l(h	PROPN
ejpam-3335	293	38	;	;	PUNCT
ejpam-3335	293	39	ε	ε	PROPN
ejpam-3335	293	40	)	)	PUNCT
ejpam-3335	293	41	.	.	PUNCT
ejpam-3335	294	1	hence	hence	ADV
ejpam-3335	294	2	,	,	PUNCT
ejpam-3335	294	3	l(h	l(h	PROPN
ejpam-3335	294	4	;	;	PUNCT
ejpam-3335	294	5	ε	ε	PROPN
ejpam-3335	294	6	)	)	PUNCT
ejpam-3335	294	7	is	be	AUX
ejpam-3335	294	8	a	a	DET
ejpam-3335	294	9	up	up	ADJ
ejpam-3335	294	10	-	-	PUNCT
ejpam-3335	294	11	ideal	ideal	NOUN
ejpam-3335	294	12	of	of	ADP
ejpam-3335	294	13	a.	a.	NOUN
ejpam-3335	294	14	conversely	conversely	ADV
ejpam-3335	294	15	,	,	PUNCT
ejpam-3335	294	16	assume	assume	VERB
ejpam-3335	294	17	that	that	SCONJ
ejpam-3335	294	18	for	for	ADP
ejpam-3335	294	19	all	all	DET
ejpam-3335	294	20	ε	ε	PROPN
ejpam-3335	294	21	∈	∈	PROPN
ejpam-3335	294	22	p([0	p([0	NOUN
ejpam-3335	294	23	,	,	PUNCT
ejpam-3335	294	24	1	1	NUM
ejpam-3335	294	25	]	]	NUM
ejpam-3335	294	26	)	)	PUNCT
ejpam-3335	294	27	,	,	PUNCT
ejpam-3335	294	28	a	a	DET
ejpam-3335	294	29	nonempty	nonempty	NOUN
ejpam-3335	294	30	subset	subset	VERB
ejpam-3335	294	31	l(h	l(h	PROPN
ejpam-3335	294	32	;	;	PUNCT
ejpam-3335	294	33	ε	ε	PROPN
ejpam-3335	294	34	)	)	PUNCT
ejpam-3335	294	35	of	of	ADP
ejpam-3335	294	36	a	a	PRON
ejpam-3335	294	37	is	be	AUX
ejpam-3335	294	38	a	a	DET
ejpam-3335	294	39	up	up	ADJ
ejpam-3335	294	40	-	-	PUNCT
ejpam-3335	294	41	ideal	ideal	NOUN
ejpam-3335	294	42	of	of	ADP
ejpam-3335	294	43	a.	a.	NOUN
ejpam-3335	294	44	let	let	VERB
ejpam-3335	294	45	x	x	X
ejpam-3335	294	46	∈	∈	VERB
ejpam-3335	294	47	a.	a.	NOUN
ejpam-3335	294	48	then	then	ADV
ejpam-3335	294	49	hh(x	hh(x	PUNCT
ejpam-3335	294	50	)	)	PUNCT
ejpam-3335	294	51	∈	∈	PROPN
ejpam-3335	294	52	p([0	p([0	NOUN
ejpam-3335	294	53	,	,	PUNCT
ejpam-3335	294	54	1	1	NUM
ejpam-3335	294	55	]	]	NUM
ejpam-3335	294	56	)	)	PUNCT
ejpam-3335	294	57	.	.	PUNCT
ejpam-3335	295	1	choose	choose	VERB
ejpam-3335	295	2	ε	ε	PROPN
ejpam-3335	295	3	=	=	SYM
ejpam-3335	295	4	hh(x	hh(x	X
ejpam-3335	295	5	)	)	PUNCT
ejpam-3335	295	6	∈	∈	PROPN
ejpam-3335	295	7	p([0	p([0	NOUN
ejpam-3335	295	8	,	,	PUNCT
ejpam-3335	295	9	1	1	NUM
ejpam-3335	295	10	]	]	NUM
ejpam-3335	295	11	)	)	PUNCT
ejpam-3335	295	12	.	.	PUNCT
ejpam-3335	296	1	then	then	ADV
ejpam-3335	296	2	hh(x	hh(x	PUNCT
ejpam-3335	296	3	)	)	PUNCT
ejpam-3335	296	4	⊆	⊆	NUM
ejpam-3335	296	5	ε	ε	PROPN
ejpam-3335	296	6	.	.	PUNCT
ejpam-3335	297	1	thus	thus	ADV
ejpam-3335	297	2	x	x	X
ejpam-3335	297	3	∈	∈	PROPN
ejpam-3335	297	4	l(h	l(h	PROPN
ejpam-3335	297	5	;	;	PUNCT
ejpam-3335	297	6	ε	ε	PROPN
ejpam-3335	297	7	)	)	PUNCT
ejpam-3335	297	8	6=	6=	ADP
ejpam-3335	297	9	∅.	∅.	ADP
ejpam-3335	297	10	by	by	ADP
ejpam-3335	297	11	assumption	assumption	NOUN
ejpam-3335	297	12	,	,	PUNCT
ejpam-3335	297	13	we	we	PRON
ejpam-3335	297	14	have	have	AUX
ejpam-3335	297	15	l(h	l(h	PROPN
ejpam-3335	297	16	;	;	PUNCT
ejpam-3335	297	17	ε	ε	PROPN
ejpam-3335	297	18	)	)	PUNCT
ejpam-3335	297	19	is	be	AUX
ejpam-3335	297	20	a	a	DET
ejpam-3335	297	21	up	up	ADJ
ejpam-3335	297	22	-	-	PUNCT
ejpam-3335	297	23	ideal	ideal	NOUN
ejpam-3335	297	24	of	of	ADP
ejpam-3335	297	25	a	a	PRON
ejpam-3335	297	26	and	and	CCONJ
ejpam-3335	297	27	so	so	ADV
ejpam-3335	297	28	0	0	NUM
ejpam-3335	298	1	∈	∈	PROPN
ejpam-3335	299	1	l(h	l(h	PROPN
ejpam-3335	299	2	;	;	PUNCT
ejpam-3335	299	3	ε	ε	PROPN
ejpam-3335	299	4	)	)	PUNCT
ejpam-3335	299	5	.	.	PUNCT
ejpam-3335	300	1	therefore	therefore	ADV
ejpam-3335	300	2	,	,	PUNCT
ejpam-3335	300	3	hh(0	hh(0	NOUN
ejpam-3335	300	4	)	)	PUNCT
ejpam-3335	300	5	⊆	⊆	NUM
ejpam-3335	300	6	ε	ε	NOUN
ejpam-3335	300	7	=	=	SYM
ejpam-3335	300	8	hh(x	hh(x	X
ejpam-3335	300	9	)	)	PUNCT
ejpam-3335	300	10	.	.	PUNCT
ejpam-3335	301	1	next	next	ADV
ejpam-3335	301	2	,	,	PUNCT
ejpam-3335	301	3	let	let	VERB
ejpam-3335	301	4	x	x	PRON
ejpam-3335	301	5	,	,	PUNCT
ejpam-3335	301	6	y	y	PROPN
ejpam-3335	301	7	,	,	PUNCT
ejpam-3335	301	8	z	z	PROPN
ejpam-3335	301	9	∈	∈	PROPN
ejpam-3335	301	10	a.	a.	NOUN
ejpam-3335	301	11	then	then	ADV
ejpam-3335	301	12	hh(x	hh(x	X
ejpam-3335	301	13	·	·	PUNCT
ejpam-3335	301	14	(	(	PUNCT
ejpam-3335	301	15	y	y	X
ejpam-3335	301	16	·	·	PUNCT
ejpam-3335	301	17	z)),hh(y	z)),hh(y	NUM
ejpam-3335	301	18	)	)	PUNCT
ejpam-3335	301	19	∈	∈	PROPN
ejpam-3335	301	20	p([0	p([0	NOUN
ejpam-3335	301	21	,	,	PUNCT
ejpam-3335	301	22	1	1	NUM
ejpam-3335	301	23	]	]	NUM
ejpam-3335	301	24	)	)	PUNCT
ejpam-3335	301	25	.	.	PUNCT
ejpam-3335	302	1	choose	choose	VERB
ejpam-3335	302	2	ε	ε	PROPN
ejpam-3335	302	3	=	=	SYM
ejpam-3335	302	4	hh(x	hh(x	X
ejpam-3335	302	5	·	·	PUNCT
ejpam-3335	302	6	(	(	PUNCT
ejpam-3335	302	7	y	y	X
ejpam-3335	302	8	·	·	PUNCT
ejpam-3335	302	9	z))∪	z))∪	NOUN
ejpam-3335	302	10	hh(y	hh(y	ADV
ejpam-3335	302	11	)	)	PUNCT
ejpam-3335	302	12	∈	∈	PROPN
ejpam-3335	302	13	p([0	p([0	NOUN
ejpam-3335	302	14	,	,	PUNCT
ejpam-3335	302	15	1	1	NUM
ejpam-3335	302	16	]	]	NUM
ejpam-3335	302	17	)	)	PUNCT
ejpam-3335	302	18	.	.	PUNCT
ejpam-3335	303	1	then	then	ADV
ejpam-3335	303	2	hh(x	hh(x	PUNCT
ejpam-3335	303	3	·	·	PUNCT
ejpam-3335	303	4	(	(	PUNCT
ejpam-3335	303	5	y	y	PROPN
ejpam-3335	303	6	·	·	PUNCT
ejpam-3335	303	7	z	z	NOUN
ejpam-3335	303	8	)	)	PUNCT
ejpam-3335	303	9	)	)	PUNCT
ejpam-3335	304	1	⊆	⊆	NUM
ejpam-3335	304	2	ε	ε	PROPN
ejpam-3335	304	3	and	and	CCONJ
ejpam-3335	304	4	hh(y	hh(y	NOUN
ejpam-3335	304	5	)	)	PUNCT
ejpam-3335	304	6	⊆	⊆	NUM
ejpam-3335	304	7	ε	ε	PROPN
ejpam-3335	304	8	.	.	PUNCT
ejpam-3335	305	1	thus	thus	ADV
ejpam-3335	305	2	x	x	X
ejpam-3335	305	3	·	·	PUNCT
ejpam-3335	305	4	(	(	PUNCT
ejpam-3335	305	5	y	y	PROPN
ejpam-3335	305	6	·	·	PUNCT
ejpam-3335	305	7	z	z	X
ejpam-3335	305	8	)	)	PUNCT
ejpam-3335	305	9	,	,	PUNCT
ejpam-3335	305	10	y	y	PROPN
ejpam-3335	305	11	∈	∈	PROPN
ejpam-3335	305	12	l(h	l(h	PROPN
ejpam-3335	305	13	;	;	PUNCT
ejpam-3335	305	14	ε	ε	PROPN
ejpam-3335	305	15	)	)	PUNCT
ejpam-3335	305	16	6=	6=	ADP
ejpam-3335	305	17	∅.	∅.	ADP
ejpam-3335	305	18	by	by	ADP
ejpam-3335	305	19	assumption	assumption	NOUN
ejpam-3335	305	20	,	,	PUNCT
ejpam-3335	305	21	we	we	PRON
ejpam-3335	305	22	have	have	AUX
ejpam-3335	305	23	l(h	l(h	PROPN
ejpam-3335	305	24	;	;	PUNCT
ejpam-3335	305	25	ε	ε	PROPN
ejpam-3335	305	26	)	)	PUNCT
ejpam-3335	305	27	is	be	AUX
ejpam-3335	305	28	a	a	DET
ejpam-3335	305	29	up	up	ADJ
ejpam-3335	305	30	-	-	PUNCT
ejpam-3335	305	31	ideal	ideal	NOUN
ejpam-3335	305	32	of	of	ADP
ejpam-3335	305	33	a	a	PRON
ejpam-3335	305	34	and	and	CCONJ
ejpam-3335	305	35	so	so	ADV
ejpam-3335	305	36	x	x	X
ejpam-3335	306	1	·	·	PUNCT
ejpam-3335	306	2	z	z	X
ejpam-3335	306	3	∈	∈	PROPN
ejpam-3335	306	4	l(h	l(h	PROPN
ejpam-3335	306	5	;	;	PUNCT
ejpam-3335	306	6	ε	ε	PROPN
ejpam-3335	306	7	)	)	PUNCT
ejpam-3335	306	8	.	.	PUNCT
ejpam-3335	307	1	therefore	therefore	ADV
ejpam-3335	307	2	,	,	PUNCT
ejpam-3335	307	3	hh(x	hh(x	PUNCT
ejpam-3335	307	4	·	·	PUNCT
ejpam-3335	307	5	z	z	X
ejpam-3335	307	6	)	)	PUNCT
ejpam-3335	307	7	⊆	⊆	NUM
ejpam-3335	307	8	ε	ε	X
ejpam-3335	307	9	=	=	SYM
ejpam-3335	307	10	hh(x	hh(x	X
ejpam-3335	307	11	·	·	PUNCT
ejpam-3335	307	12	(	(	PUNCT
ejpam-3335	307	13	y	y	PROPN
ejpam-3335	307	14	·	·	PUNCT
ejpam-3335	307	15	z	z	NOUN
ejpam-3335	307	16	)	)	PUNCT
ejpam-3335	307	17	)	)	PUNCT
ejpam-3335	307	18	∪	∪	ADP
ejpam-3335	307	19	hh(y	hh(y	NOUN
ejpam-3335	307	20	)	)	PUNCT
ejpam-3335	307	21	.	.	PUNCT
ejpam-3335	308	1	hence	hence	ADV
ejpam-3335	308	2	,	,	PUNCT
ejpam-3335	308	3	h	h	PROPN
ejpam-3335	308	4	is	be	AUX
ejpam-3335	308	5	an	an	DET
ejpam-3335	308	6	anti	anti	ADJ
ejpam-3335	308	7	-	-	ADJ
ejpam-3335	308	8	hesitant	hesitant	ADJ
ejpam-3335	308	9	fuzzy	fuzzy	ADJ
ejpam-3335	308	10	up	up	NOUN
ejpam-3335	308	11	-	-	PUNCT
ejpam-3335	308	12	ideal	ideal	NOUN
ejpam-3335	308	13	of	of	ADP
ejpam-3335	308	14	a.	a.	PROPN
ejpam-3335	308	15	p.	p.	PROPN
ejpam-3335	308	16	mosrijai	mosrijai	PROPN
ejpam-3335	308	17	,	,	PUNCT
ejpam-3335	308	18	a.	a.	NOUN
ejpam-3335	308	19	iampan	iampan	PROPN
ejpam-3335	308	20	/	/	SYM
ejpam-3335	308	21	eur	eur	PROPN
ejpam-3335	308	22	.	.	PUNCT
ejpam-3335	309	1	j.	j.	PROPN
ejpam-3335	309	2	pure	pure	PROPN
ejpam-3335	309	3	appl	appl	PROPN
ejpam-3335	309	4	.	.	PROPN
ejpam-3335	309	5	math	math	PROPN
ejpam-3335	309	6	,	,	PUNCT
ejpam-3335	309	7	11	11	NUM
ejpam-3335	309	8	(	(	PUNCT
ejpam-3335	309	9	4	4	NUM
ejpam-3335	309	10	)	)	PUNCT
ejpam-3335	309	11	(	(	PUNCT
ejpam-3335	309	12	2018	2018	NUM
ejpam-3335	309	13	)	)	PUNCT
ejpam-3335	309	14	,	,	PUNCT
ejpam-3335	309	15	976	976	NUM
ejpam-3335	309	16	-	-	SYM
ejpam-3335	309	17	1002	1002	NUM
ejpam-3335	309	18	987	987	NUM
ejpam-3335	309	19	theorem	theorem	NOUN
ejpam-3335	309	20	10	10	NUM
ejpam-3335	309	21	.	.	PUNCT
ejpam-3335	310	1	let	let	VERB
ejpam-3335	310	2	h	h	PRON
ejpam-3335	310	3	be	be	AUX
ejpam-3335	310	4	a	a	DET
ejpam-3335	310	5	hesitant	hesitant	ADJ
ejpam-3335	310	6	fuzzy	fuzzy	ADJ
ejpam-3335	310	7	set	set	NOUN
ejpam-3335	310	8	on	on	ADP
ejpam-3335	310	9	a.	a.	NOUN
ejpam-3335	310	10	then	then	ADV
ejpam-3335	310	11	the	the	DET
ejpam-3335	310	12	following	follow	VERB
ejpam-3335	310	13	statements	statement	NOUN
ejpam-3335	310	14	are	be	AUX
ejpam-3335	310	15	equivalent	equivalent	ADJ
ejpam-3335	310	16	:	:	PUNCT
ejpam-3335	310	17	(	(	PUNCT
ejpam-3335	310	18	1	1	X
ejpam-3335	310	19	)	)	PUNCT
ejpam-3335	310	20	h	h	NOUN
ejpam-3335	310	21	is	be	AUX
ejpam-3335	310	22	an	an	DET
ejpam-3335	310	23	anti	anti	ADJ
ejpam-3335	310	24	-	-	ADJ
ejpam-3335	310	25	hesitant	hesitant	ADJ
ejpam-3335	310	26	fuzzy	fuzzy	ADJ
ejpam-3335	310	27	strongly	strongly	ADV
ejpam-3335	310	28	up	up	ADP
ejpam-3335	310	29	-	-	PUNCT
ejpam-3335	310	30	ideal	ideal	NOUN
ejpam-3335	310	31	of	of	ADP
ejpam-3335	310	32	a	a	DET
ejpam-3335	310	33	,	,	PUNCT
ejpam-3335	310	34	(	(	PUNCT
ejpam-3335	310	35	2	2	X
ejpam-3335	310	36	)	)	PUNCT
ejpam-3335	310	37	a	a	DET
ejpam-3335	310	38	nonempty	nonempty	NOUN
ejpam-3335	310	39	subset	subset	VERB
ejpam-3335	310	40	l(h	l(h	PROPN
ejpam-3335	310	41	;	;	PUNCT
ejpam-3335	310	42	ε	ε	PROPN
ejpam-3335	310	43	)	)	PUNCT
ejpam-3335	310	44	of	of	ADP
ejpam-3335	310	45	a	a	PRON
ejpam-3335	310	46	is	be	AUX
ejpam-3335	310	47	a	a	DET
ejpam-3335	310	48	strongly	strongly	ADV
ejpam-3335	310	49	up	up	ADJ
ejpam-3335	310	50	-	-	PUNCT
ejpam-3335	310	51	ideal	ideal	NOUN
ejpam-3335	310	52	of	of	ADP
ejpam-3335	310	53	a	a	PRON
ejpam-3335	310	54	for	for	ADP
ejpam-3335	310	55	all	all	DET
ejpam-3335	310	56	ε	ε	PROPN
ejpam-3335	310	57	∈	∈	PROPN
ejpam-3335	310	58	p([0	p([0	NOUN
ejpam-3335	310	59	,	,	PUNCT
ejpam-3335	310	60	1	1	NUM
ejpam-3335	310	61	]	]	NUM
ejpam-3335	310	62	)	)	PUNCT
ejpam-3335	310	63	,	,	PUNCT
ejpam-3335	310	64	and	and	CCONJ
ejpam-3335	310	65	(	(	PUNCT
ejpam-3335	310	66	3	3	X
ejpam-3335	310	67	)	)	PUNCT
ejpam-3335	310	68	a	a	DET
ejpam-3335	310	69	nonempty	nonempty	NOUN
ejpam-3335	310	70	subset	subset	VERB
ejpam-3335	310	71	u(h	u(h	PROPN
ejpam-3335	310	72	;	;	PUNCT
ejpam-3335	310	73	ε	ε	PROPN
ejpam-3335	310	74	)	)	PUNCT
ejpam-3335	310	75	of	of	ADP
ejpam-3335	310	76	a	a	PRON
ejpam-3335	310	77	is	be	AUX
ejpam-3335	310	78	a	a	DET
ejpam-3335	310	79	strongly	strongly	ADV
ejpam-3335	310	80	up	up	ADJ
ejpam-3335	310	81	-	-	PUNCT
ejpam-3335	310	82	ideal	ideal	NOUN
ejpam-3335	310	83	of	of	ADP
ejpam-3335	310	84	a	a	PRON
ejpam-3335	310	85	for	for	ADP
ejpam-3335	310	86	all	all	DET
ejpam-3335	310	87	ε	ε	PROPN
ejpam-3335	310	88	∈	∈	PROPN
ejpam-3335	310	89	p([0	p([0	NOUN
ejpam-3335	310	90	,	,	PUNCT
ejpam-3335	310	91	1	1	NUM
ejpam-3335	310	92	]	]	NUM
ejpam-3335	310	93	)	)	PUNCT
ejpam-3335	310	94	.	.	PUNCT
ejpam-3335	311	1	proof	proof	NOUN
ejpam-3335	311	2	.	.	PUNCT
ejpam-3335	312	1	(	(	PUNCT
ejpam-3335	312	2	1)⇒(2	1)⇒(2	X
ejpam-3335	312	3	)	)	PUNCT
ejpam-3335	312	4	assume	assume	VERB
ejpam-3335	312	5	that	that	SCONJ
ejpam-3335	312	6	h	h	NOUN
ejpam-3335	312	7	is	be	AUX
ejpam-3335	312	8	an	an	DET
ejpam-3335	312	9	anti	anti	ADJ
ejpam-3335	312	10	-	-	ADJ
ejpam-3335	312	11	hesitant	hesitant	ADJ
ejpam-3335	312	12	fuzzy	fuzzy	ADJ
ejpam-3335	312	13	strongly	strongly	ADV
ejpam-3335	312	14	up	up	ADP
ejpam-3335	312	15	-	-	PUNCT
ejpam-3335	312	16	ideal	ideal	NOUN
ejpam-3335	312	17	of	of	ADP
ejpam-3335	312	18	a.	a.	NOUN
ejpam-3335	312	19	by	by	ADP
ejpam-3335	312	20	theorem	theorem	NOUN
ejpam-3335	312	21	3	3	NUM
ejpam-3335	312	22	,	,	PUNCT
ejpam-3335	312	23	we	we	PRON
ejpam-3335	312	24	obtain	obtain	VERB
ejpam-3335	312	25	h	h	NOUN
ejpam-3335	312	26	is	be	AUX
ejpam-3335	312	27	a	a	DET
ejpam-3335	312	28	constant	constant	ADJ
ejpam-3335	312	29	hesitant	hesitant	ADJ
ejpam-3335	312	30	fuzzy	fuzzy	ADJ
ejpam-3335	312	31	set	set	VERB
ejpam-3335	312	32	on	on	ADP
ejpam-3335	312	33	a	a	DET
ejpam-3335	312	34	and	and	CCONJ
ejpam-3335	312	35	so	so	ADV
ejpam-3335	312	36	hh(x	hh(x	PUNCT
ejpam-3335	312	37	)	)	PUNCT
ejpam-3335	312	38	=	=	SYM
ejpam-3335	313	1	hh(y	hh(y	X
ejpam-3335	313	2	)	)	PUNCT
ejpam-3335	313	3	for	for	ADP
ejpam-3335	313	4	all	all	DET
ejpam-3335	313	5	x	x	NOUN
ejpam-3335	313	6	,	,	PUNCT
ejpam-3335	313	7	y	y	PROPN
ejpam-3335	313	8	∈	∈	PROPN
ejpam-3335	313	9	a.	a.	NOUN
ejpam-3335	313	10	let	let	VERB
ejpam-3335	313	11	ε	ε	PROPN
ejpam-3335	313	12	∈	∈	PROPN
ejpam-3335	313	13	p([0	p([0	PROPN
ejpam-3335	313	14	,	,	PUNCT
ejpam-3335	313	15	1	1	NUM
ejpam-3335	313	16	]	]	PUNCT
ejpam-3335	313	17	)	)	PUNCT
ejpam-3335	313	18	be	be	AUX
ejpam-3335	313	19	such	such	ADJ
ejpam-3335	313	20	that	that	SCONJ
ejpam-3335	313	21	l(h	l(h	PROPN
ejpam-3335	313	22	;	;	PUNCT
ejpam-3335	313	23	ε	ε	PROPN
ejpam-3335	313	24	)	)	PUNCT
ejpam-3335	313	25	6=	6=	ADP
ejpam-3335	313	26	∅.	∅.	VERB
ejpam-3335	313	27	there	there	ADV
ejpam-3335	313	28	exists	exist	VERB
ejpam-3335	313	29	a	a	DET
ejpam-3335	313	30	∈	∈	NOUN
ejpam-3335	313	31	l(h	l(h	PROPN
ejpam-3335	313	32	;	;	PUNCT
ejpam-3335	313	33	ε	ε	AUX
ejpam-3335	313	34	)	)	PUNCT
ejpam-3335	313	35	be	be	VERB
ejpam-3335	313	36	such	such	ADJ
ejpam-3335	313	37	that	that	DET
ejpam-3335	313	38	hh(a	hh(a	NOUN
ejpam-3335	313	39	)	)	PUNCT
ejpam-3335	314	1	⊆	⊆	NUM
ejpam-3335	314	2	ε	ε	PROPN
ejpam-3335	314	3	.	.	PUNCT
ejpam-3335	314	4	thus	thus	ADV
ejpam-3335	314	5	hh(x	hh(x	X
ejpam-3335	314	6	)	)	PUNCT
ejpam-3335	314	7	=	=	SYM
ejpam-3335	314	8	hh(a	hh(a	NUM
ejpam-3335	314	9	)	)	PUNCT
ejpam-3335	314	10	⊆	⊆	NUM
ejpam-3335	314	11	ε	ε	PROPN
ejpam-3335	314	12	for	for	ADP
ejpam-3335	314	13	all	all	DET
ejpam-3335	314	14	x	x	SYM
ejpam-3335	314	15	∈	∈	PROPN
ejpam-3335	314	16	a	a	PRON
ejpam-3335	315	1	and	and	CCONJ
ejpam-3335	315	2	so	so	ADV
ejpam-3335	315	3	x	x	SYM
ejpam-3335	315	4	∈	∈	PROPN
ejpam-3335	315	5	l(h	l(h	PROPN
ejpam-3335	315	6	;	;	PUNCT
ejpam-3335	315	7	ε	ε	PROPN
ejpam-3335	315	8	)	)	PUNCT
ejpam-3335	315	9	for	for	ADP
ejpam-3335	315	10	all	all	DET
ejpam-3335	315	11	x	x	SYM
ejpam-3335	315	12	∈	∈	PROPN
ejpam-3335	315	13	a.	a.	NOUN
ejpam-3335	315	14	therefore	therefore	ADV
ejpam-3335	315	15	,	,	PUNCT
ejpam-3335	315	16	l(h	l(h	PROPN
ejpam-3335	315	17	;	;	PUNCT
ejpam-3335	315	18	ε	ε	PROPN
ejpam-3335	315	19	)	)	PUNCT
ejpam-3335	315	20	=	=	NOUN
ejpam-3335	315	21	a.	a.	NOUN
ejpam-3335	315	22	hence	hence	ADV
ejpam-3335	315	23	,	,	PUNCT
ejpam-3335	315	24	l(h	l(h	PROPN
ejpam-3335	315	25	;	;	PUNCT
ejpam-3335	315	26	ε	ε	PROPN
ejpam-3335	315	27	)	)	PUNCT
ejpam-3335	315	28	is	be	AUX
ejpam-3335	315	29	a	a	DET
ejpam-3335	315	30	strongly	strongly	ADV
ejpam-3335	315	31	up	up	ADJ
ejpam-3335	315	32	-	-	PUNCT
ejpam-3335	315	33	ideal	ideal	NOUN
ejpam-3335	315	34	of	of	ADP
ejpam-3335	315	35	a.	a.	NOUN
ejpam-3335	315	36	(	(	PUNCT
ejpam-3335	315	37	2)⇒(3	2)⇒(3	NUM
ejpam-3335	315	38	)	)	PUNCT
ejpam-3335	315	39	assume	assume	VERB
ejpam-3335	315	40	that	that	SCONJ
ejpam-3335	315	41	for	for	ADP
ejpam-3335	315	42	all	all	DET
ejpam-3335	315	43	ε	ε	PROPN
ejpam-3335	315	44	∈	∈	PROPN
ejpam-3335	315	45	p([0	p([0	NOUN
ejpam-3335	315	46	,	,	PUNCT
ejpam-3335	315	47	1	1	NUM
ejpam-3335	315	48	]	]	NUM
ejpam-3335	315	49	)	)	PUNCT
ejpam-3335	315	50	,	,	PUNCT
ejpam-3335	315	51	a	a	DET
ejpam-3335	315	52	nonempty	nonempty	NOUN
ejpam-3335	315	53	subset	subset	VERB
ejpam-3335	315	54	l(h	l(h	PROPN
ejpam-3335	315	55	;	;	PUNCT
ejpam-3335	315	56	ε	ε	PROPN
ejpam-3335	315	57	)	)	PUNCT
ejpam-3335	315	58	of	of	ADP
ejpam-3335	315	59	a	a	PRON
ejpam-3335	315	60	is	be	AUX
ejpam-3335	315	61	a	a	DET
ejpam-3335	315	62	strongly	strongly	ADV
ejpam-3335	315	63	up	up	ADJ
ejpam-3335	315	64	-	-	PUNCT
ejpam-3335	315	65	ideal	ideal	NOUN
ejpam-3335	315	66	of	of	ADP
ejpam-3335	315	67	a.	a.	NOUN
ejpam-3335	315	68	let	let	VERB
ejpam-3335	315	69	ε	ε	PROPN
ejpam-3335	315	70	∈	∈	PROPN
ejpam-3335	315	71	p([0	p([0	PROPN
ejpam-3335	315	72	,	,	PUNCT
ejpam-3335	315	73	1	1	NUM
ejpam-3335	315	74	]	]	PUNCT
ejpam-3335	315	75	)	)	PUNCT
ejpam-3335	315	76	be	be	AUX
ejpam-3335	315	77	such	such	ADJ
ejpam-3335	315	78	that	that	SCONJ
ejpam-3335	315	79	u(h	u(h	PROPN
ejpam-3335	315	80	;	;	PUNCT
ejpam-3335	315	81	ε	ε	PROPN
ejpam-3335	315	82	)	)	PUNCT
ejpam-3335	315	83	6=	6=	ADP
ejpam-3335	315	84	∅.	∅.	ADP
ejpam-3335	315	85	if	if	SCONJ
ejpam-3335	315	86	u(h	u(h	PROPN
ejpam-3335	315	87	;	;	PUNCT
ejpam-3335	315	88	ε	ε	PROPN
ejpam-3335	315	89	)	)	PUNCT
ejpam-3335	315	90	6=	6=	ADP
ejpam-3335	315	91	a	a	X
ejpam-3335	315	92	,	,	PUNCT
ejpam-3335	315	93	then	then	ADV
ejpam-3335	315	94	there	there	PRON
ejpam-3335	315	95	exist	exist	VERB
ejpam-3335	315	96	x	x	SYM
ejpam-3335	315	97	∈	∈	PROPN
ejpam-3335	315	98	u(h	u(h	PROPN
ejpam-3335	315	99	;	;	PUNCT
ejpam-3335	315	100	ε	ε	PROPN
ejpam-3335	315	101	)	)	PUNCT
ejpam-3335	315	102	and	and	CCONJ
ejpam-3335	315	103	y	y	PROPN
ejpam-3335	315	104	/∈	/∈	PUNCT
ejpam-3335	316	1	u(h	u(h	PROPN
ejpam-3335	316	2	;	;	PUNCT
ejpam-3335	316	3	ε	ε	PROPN
ejpam-3335	316	4	)	)	PUNCT
ejpam-3335	316	5	.	.	PUNCT
ejpam-3335	317	1	so	so	ADV
ejpam-3335	317	2	hh(x	hh(x	PUNCT
ejpam-3335	317	3	)	)	PUNCT
ejpam-3335	317	4	⊇	⊇	PROPN
ejpam-3335	317	5	ε	ε	PROPN
ejpam-3335	317	6	and	and	CCONJ
ejpam-3335	317	7	hh(y	hh(y	NOUN
ejpam-3335	317	8	)	)	PUNCT
ejpam-3335	318	1	+	+	CCONJ
ejpam-3335	318	2	ε	ε	AUX
ejpam-3335	318	3	.	.	PUNCT
ejpam-3335	318	4	consider	consider	VERB
ejpam-3335	318	5	,	,	PUNCT
ejpam-3335	318	6	εy	εy	VERB
ejpam-3335	318	7	=	=	SYM
ejpam-3335	318	8	hh(y	hh(y	CCONJ
ejpam-3335	318	9	)	)	PUNCT
ejpam-3335	318	10	∈	∈	NOUN
ejpam-3335	318	11	p([0	p([0	NOUN
ejpam-3335	318	12	,	,	PUNCT
ejpam-3335	318	13	1	1	NUM
ejpam-3335	318	14	]	]	NUM
ejpam-3335	318	15	)	)	PUNCT
ejpam-3335	318	16	.	.	PUNCT
ejpam-3335	319	1	then	then	ADV
ejpam-3335	319	2	y	y	PROPN
ejpam-3335	319	3	∈	∈	PROPN
ejpam-3335	319	4	l(h	l(h	PROPN
ejpam-3335	319	5	;	;	PUNCT
ejpam-3335	319	6	εy	εy	NOUN
ejpam-3335	319	7	)	)	PUNCT
ejpam-3335	319	8	and	and	CCONJ
ejpam-3335	319	9	εy	εy	VERB
ejpam-3335	319	10	+	+	CCONJ
ejpam-3335	319	11	ε	ε	PROPN
ejpam-3335	319	12	.	.	PUNCT
ejpam-3335	319	13	by	by	ADP
ejpam-3335	319	14	assumption	assumption	NOUN
ejpam-3335	319	15	,	,	PUNCT
ejpam-3335	319	16	we	we	PRON
ejpam-3335	319	17	have	have	VERB
ejpam-3335	319	18	l(h	l(h	PROPN
ejpam-3335	319	19	;	;	PUNCT
ejpam-3335	319	20	εy	εy	NOUN
ejpam-3335	319	21	)	)	PUNCT
ejpam-3335	319	22	is	be	AUX
ejpam-3335	319	23	a	a	DET
ejpam-3335	319	24	strongly	strongly	ADV
ejpam-3335	319	25	up	up	ADJ
ejpam-3335	319	26	-	-	PUNCT
ejpam-3335	319	27	ideal	ideal	NOUN
ejpam-3335	319	28	of	of	ADP
ejpam-3335	319	29	a	a	PRON
ejpam-3335	319	30	and	and	CCONJ
ejpam-3335	319	31	so	so	ADV
ejpam-3335	319	32	l(h	l(h	PROPN
ejpam-3335	319	33	;	;	PUNCT
ejpam-3335	319	34	εy	εy	NOUN
ejpam-3335	319	35	)	)	PUNCT
ejpam-3335	319	36	=	=	PUNCT
ejpam-3335	319	37	a.	a.	NOUN
ejpam-3335	319	38	thus	thus	ADV
ejpam-3335	319	39	hh(x	hh(x	PUNCT
ejpam-3335	319	40	)	)	PUNCT
ejpam-3335	319	41	⊆	⊆	NUM
ejpam-3335	319	42	εy	εy	NOUN
ejpam-3335	319	43	.	.	PUNCT
ejpam-3335	320	1	since	since	SCONJ
ejpam-3335	320	2	hh(x	hh(x	NOUN
ejpam-3335	320	3	)	)	PUNCT
ejpam-3335	320	4	⊇	⊇	PROPN
ejpam-3335	320	5	ε	ε	PROPN
ejpam-3335	320	6	,	,	PUNCT
ejpam-3335	320	7	we	we	PRON
ejpam-3335	320	8	have	have	VERB
ejpam-3335	320	9	εy	εy	NOUN
ejpam-3335	320	10	⊇	⊇	PROPN
ejpam-3335	320	11	ε	ε	PROPN
ejpam-3335	320	12	,	,	PUNCT
ejpam-3335	320	13	a	a	DET
ejpam-3335	320	14	contradiction	contradiction	NOUN
ejpam-3335	320	15	.	.	PUNCT
ejpam-3335	321	1	therefore	therefore	ADV
ejpam-3335	321	2	,	,	PUNCT
ejpam-3335	321	3	u(h	u(h	PROPN
ejpam-3335	321	4	;	;	PUNCT
ejpam-3335	321	5	ε	ε	PROPN
ejpam-3335	321	6	)	)	PUNCT
ejpam-3335	321	7	=	=	NOUN
ejpam-3335	321	8	a.	a.	NOUN
ejpam-3335	321	9	hence	hence	ADV
ejpam-3335	321	10	,	,	PUNCT
ejpam-3335	321	11	u(h	u(h	PROPN
ejpam-3335	321	12	;	;	PUNCT
ejpam-3335	321	13	ε	ε	PROPN
ejpam-3335	321	14	)	)	PUNCT
ejpam-3335	321	15	is	be	AUX
ejpam-3335	321	16	a	a	DET
ejpam-3335	321	17	strongly	strongly	ADV
ejpam-3335	321	18	up	up	ADJ
ejpam-3335	321	19	-	-	PUNCT
ejpam-3335	321	20	ideal	ideal	NOUN
ejpam-3335	321	21	of	of	ADP
ejpam-3335	321	22	a.	a.	NOUN
ejpam-3335	321	23	(	(	PUNCT
ejpam-3335	321	24	3)⇒(1	3)⇒(1	PROPN
ejpam-3335	321	25	)	)	PUNCT
ejpam-3335	321	26	assume	assume	VERB
ejpam-3335	321	27	that	that	SCONJ
ejpam-3335	321	28	for	for	ADP
ejpam-3335	321	29	all	all	DET
ejpam-3335	321	30	ε	ε	PROPN
ejpam-3335	321	31	∈	∈	PROPN
ejpam-3335	321	32	p([0	p([0	NOUN
ejpam-3335	321	33	,	,	PUNCT
ejpam-3335	321	34	1	1	NUM
ejpam-3335	321	35	]	]	NUM
ejpam-3335	321	36	)	)	PUNCT
ejpam-3335	321	37	,	,	PUNCT
ejpam-3335	321	38	a	a	DET
ejpam-3335	321	39	nonempty	nonempty	NOUN
ejpam-3335	321	40	subset	subset	VERB
ejpam-3335	321	41	u(h	u(h	PROPN
ejpam-3335	321	42	;	;	PUNCT
ejpam-3335	321	43	ε	ε	PROPN
ejpam-3335	321	44	)	)	PUNCT
ejpam-3335	321	45	of	of	ADP
ejpam-3335	321	46	a	a	PRON
ejpam-3335	321	47	is	be	AUX
ejpam-3335	321	48	a	a	DET
ejpam-3335	321	49	strongly	strongly	ADV
ejpam-3335	321	50	up	up	ADJ
ejpam-3335	321	51	-	-	PUNCT
ejpam-3335	321	52	ideal	ideal	NOUN
ejpam-3335	321	53	of	of	ADP
ejpam-3335	321	54	a.	a.	NOUN
ejpam-3335	321	55	assume	assume	VERB
ejpam-3335	321	56	that	that	SCONJ
ejpam-3335	321	57	h	h	NOUN
ejpam-3335	321	58	is	be	AUX
ejpam-3335	321	59	not	not	PART
ejpam-3335	321	60	a	a	DET
ejpam-3335	321	61	constant	constant	ADJ
ejpam-3335	321	62	hesitant	hesitant	ADJ
ejpam-3335	321	63	fuzzy	fuzzy	ADJ
ejpam-3335	321	64	set	set	VERB
ejpam-3335	321	65	on	on	ADP
ejpam-3335	321	66	a.	a.	NOUN
ejpam-3335	321	67	there	there	ADV
ejpam-3335	321	68	exist	exist	VERB
ejpam-3335	321	69	x	x	NOUN
ejpam-3335	321	70	,	,	PUNCT
ejpam-3335	321	71	y	y	PROPN
ejpam-3335	321	72	∈	∈	PROPN
ejpam-3335	321	73	a	a	PRON
ejpam-3335	321	74	be	be	AUX
ejpam-3335	321	75	such	such	ADJ
ejpam-3335	321	76	that	that	PRON
ejpam-3335	321	77	hh(x	hh(x	PRON
ejpam-3335	321	78	)	)	PUNCT
ejpam-3335	321	79	6=	6=	ADP
ejpam-3335	321	80	hh(y	hh(y	NOUN
ejpam-3335	321	81	)	)	PUNCT
ejpam-3335	321	82	.	.	PUNCT
ejpam-3335	322	1	now	now	ADV
ejpam-3335	322	2	,	,	PUNCT
ejpam-3335	322	3	x	x	PUNCT
ejpam-3335	322	4	∈	∈	PROPN
ejpam-3335	322	5	u(h	u(h	PROPN
ejpam-3335	322	6	;	;	PUNCT
ejpam-3335	322	7	hh(x	hh(x	X
ejpam-3335	322	8	)	)	PUNCT
ejpam-3335	322	9	)	)	PUNCT
ejpam-3335	323	1	6=	6=	ADP
ejpam-3335	323	2	∅	∅	NOUN
ejpam-3335	323	3	and	and	CCONJ
ejpam-3335	323	4	y	y	PROPN
ejpam-3335	323	5	∈	∈	PROPN
ejpam-3335	323	6	u(h	u(h	PROPN
ejpam-3335	323	7	;	;	PUNCT
ejpam-3335	323	8	hh(y	hh(y	NUM
ejpam-3335	323	9	)	)	PUNCT
ejpam-3335	323	10	)	)	PUNCT
ejpam-3335	323	11	6=	6=	ADP
ejpam-3335	323	12	∅.	∅.	ADP
ejpam-3335	323	13	by	by	ADP
ejpam-3335	323	14	assumption	assumption	NOUN
ejpam-3335	323	15	,	,	PUNCT
ejpam-3335	323	16	we	we	PRON
ejpam-3335	323	17	have	have	AUX
ejpam-3335	323	18	u(h	u(h	VERB
ejpam-3335	323	19	;	;	PUNCT
ejpam-3335	323	20	hh(x	hh(x	X
ejpam-3335	323	21	)	)	PUNCT
ejpam-3335	323	22	)	)	PUNCT
ejpam-3335	323	23	and	and	CCONJ
ejpam-3335	323	24	u(h	u(h	PROPN
ejpam-3335	323	25	;	;	PUNCT
ejpam-3335	323	26	hh(y	hh(y	NUM
ejpam-3335	323	27	)	)	PUNCT
ejpam-3335	323	28	)	)	PUNCT
ejpam-3335	323	29	are	be	AUX
ejpam-3335	323	30	strongly	strongly	ADV
ejpam-3335	323	31	up	up	ADP
ejpam-3335	323	32	-	-	PUNCT
ejpam-3335	323	33	ideals	ideal	NOUN
ejpam-3335	323	34	of	of	ADP
ejpam-3335	323	35	a	a	PRON
ejpam-3335	323	36	and	and	CCONJ
ejpam-3335	323	37	thus	thus	ADV
ejpam-3335	323	38	u(h	u(h	PROPN
ejpam-3335	323	39	;	;	PUNCT
ejpam-3335	323	40	hh(x	hh(x	X
ejpam-3335	323	41	)	)	PUNCT
ejpam-3335	323	42	)	)	PUNCT
ejpam-3335	324	1	=	=	PUNCT
ejpam-3335	325	1	a	a	DET
ejpam-3335	325	2	=	=	SYM
ejpam-3335	325	3	u(h	u(h	PROPN
ejpam-3335	325	4	;	;	PUNCT
ejpam-3335	325	5	hh(y	hh(y	NUM
ejpam-3335	325	6	)	)	PUNCT
ejpam-3335	325	7	)	)	PUNCT
ejpam-3335	325	8	.	.	PUNCT
ejpam-3335	326	1	then	then	ADV
ejpam-3335	326	2	x	x	SYM
ejpam-3335	326	3	∈	∈	PROPN
ejpam-3335	326	4	u(h	u(h	PROPN
ejpam-3335	326	5	;	;	PUNCT
ejpam-3335	326	6	hh(y	hh(y	NUM
ejpam-3335	326	7	)	)	PUNCT
ejpam-3335	326	8	)	)	PUNCT
ejpam-3335	326	9	and	and	CCONJ
ejpam-3335	326	10	y	y	PROPN
ejpam-3335	326	11	∈	∈	PROPN
ejpam-3335	326	12	u(h	u(h	PROPN
ejpam-3335	326	13	;	;	PUNCT
ejpam-3335	326	14	hh(x	hh(x	X
ejpam-3335	326	15	)	)	PUNCT
ejpam-3335	326	16	)	)	PUNCT
ejpam-3335	326	17	.	.	PUNCT
ejpam-3335	327	1	thus	thus	ADV
ejpam-3335	327	2	hh(x	hh(x	X
ejpam-3335	327	3	)	)	PUNCT
ejpam-3335	327	4	⊇	⊇	NOUN
ejpam-3335	327	5	hh(y	hh(y	NOUN
ejpam-3335	327	6	)	)	PUNCT
ejpam-3335	327	7	and	and	CCONJ
ejpam-3335	327	8	hh(y	hh(y	NOUN
ejpam-3335	327	9	)	)	PUNCT
ejpam-3335	327	10	⊇	⊇	NOUN
ejpam-3335	327	11	hh(x	hh(x	NOUN
ejpam-3335	327	12	)	)	PUNCT
ejpam-3335	327	13	.	.	PUNCT
ejpam-3335	328	1	so	so	ADV
ejpam-3335	328	2	hh(x	hh(x	PUNCT
ejpam-3335	328	3	)	)	PUNCT
ejpam-3335	328	4	=	=	SYM
ejpam-3335	328	5	hh(y	hh(y	NOUN
ejpam-3335	328	6	)	)	PUNCT
ejpam-3335	328	7	,	,	PUNCT
ejpam-3335	328	8	a	a	DET
ejpam-3335	328	9	contradiction	contradiction	NOUN
ejpam-3335	328	10	.	.	PUNCT
ejpam-3335	329	1	therefore	therefore	ADV
ejpam-3335	329	2	,	,	PUNCT
ejpam-3335	329	3	h	h	NOUN
ejpam-3335	329	4	is	be	AUX
ejpam-3335	329	5	a	a	DET
ejpam-3335	329	6	constant	constant	ADJ
ejpam-3335	329	7	hesitant	hesitant	ADJ
ejpam-3335	329	8	fuzzy	fuzzy	ADJ
ejpam-3335	329	9	set	set	VERB
ejpam-3335	329	10	on	on	ADP
ejpam-3335	329	11	a.	a.	NOUN
ejpam-3335	329	12	by	by	ADP
ejpam-3335	329	13	theorem	theorem	NOUN
ejpam-3335	329	14	3	3	NUM
ejpam-3335	329	15	,	,	PUNCT
ejpam-3335	329	16	we	we	PRON
ejpam-3335	329	17	obtain	obtain	VERB
ejpam-3335	329	18	h	h	NOUN
ejpam-3335	329	19	is	be	AUX
ejpam-3335	329	20	an	an	DET
ejpam-3335	329	21	anti	anti	ADJ
ejpam-3335	329	22	-	-	ADJ
ejpam-3335	329	23	hesitant	hesitant	ADJ
ejpam-3335	329	24	fuzzy	fuzzy	ADJ
ejpam-3335	329	25	strongly	strongly	ADV
ejpam-3335	329	26	up	up	ADP
ejpam-3335	329	27	-	-	PUNCT
ejpam-3335	329	28	ideal	ideal	NOUN
ejpam-3335	329	29	of	of	ADP
ejpam-3335	329	30	a.	a.	NOUN
ejpam-3335	329	31	5.2	5.2	NUM
ejpam-3335	329	32	.	.	PUNCT
ejpam-3335	330	1	lower	low	ADJ
ejpam-3335	330	2	ε	ε	VERB
ejpam-3335	330	3	-	-	PUNCT
ejpam-3335	330	4	strong	strong	ADJ
ejpam-3335	330	5	level	level	NOUN
ejpam-3335	330	6	subsets	subset	NOUN
ejpam-3335	330	7	theorem	theorem	VERB
ejpam-3335	330	8	11	11	NUM
ejpam-3335	330	9	.	.	PUNCT
ejpam-3335	331	1	let	let	VERB
ejpam-3335	331	2	h	h	PRON
ejpam-3335	331	3	be	be	AUX
ejpam-3335	331	4	a	a	DET
ejpam-3335	331	5	hesitant	hesitant	ADJ
ejpam-3335	331	6	fuzzy	fuzzy	ADJ
ejpam-3335	331	7	set	set	NOUN
ejpam-3335	331	8	on	on	ADP
ejpam-3335	331	9	a.	a.	NOUN
ejpam-3335	331	10	then	then	ADV
ejpam-3335	331	11	the	the	DET
ejpam-3335	331	12	following	follow	VERB
ejpam-3335	331	13	statements	statement	NOUN
ejpam-3335	331	14	hold	hold	VERB
ejpam-3335	331	15	:	:	PUNCT
ejpam-3335	331	16	(	(	PUNCT
ejpam-3335	331	17	1	1	X
ejpam-3335	331	18	)	)	PUNCT
ejpam-3335	331	19	if	if	SCONJ
ejpam-3335	331	20	h	h	NOUN
ejpam-3335	331	21	is	be	AUX
ejpam-3335	331	22	an	an	DET
ejpam-3335	331	23	anti	anti	ADJ
ejpam-3335	331	24	-	-	ADJ
ejpam-3335	331	25	hesitant	hesitant	ADJ
ejpam-3335	331	26	fuzzy	fuzzy	ADJ
ejpam-3335	331	27	up	up	NOUN
ejpam-3335	331	28	-	-	PUNCT
ejpam-3335	331	29	subalgebra	subalgebra	NOUN
ejpam-3335	331	30	of	of	ADP
ejpam-3335	331	31	a	a	PRON
ejpam-3335	331	32	,	,	PUNCT
ejpam-3335	331	33	then	then	ADV
ejpam-3335	331	34	for	for	ADP
ejpam-3335	331	35	all	all	DET
ejpam-3335	331	36	ε	ε	PROPN
ejpam-3335	331	37	∈	∈	PROPN
ejpam-3335	331	38	p([0	p([0	NOUN
ejpam-3335	331	39	,	,	PUNCT
ejpam-3335	331	40	1	1	NUM
ejpam-3335	331	41	]	]	NUM
ejpam-3335	331	42	)	)	PUNCT
ejpam-3335	331	43	,	,	PUNCT
ejpam-3335	331	44	l−(h	l−(h	PROPN
ejpam-3335	331	45	;	;	PUNCT
ejpam-3335	331	46	ε	ε	PROPN
ejpam-3335	331	47	)	)	PUNCT
ejpam-3335	331	48	is	be	AUX
ejpam-3335	331	49	a	a	DET
ejpam-3335	331	50	up	up	ADJ
ejpam-3335	331	51	-	-	PUNCT
ejpam-3335	331	52	subalgebra	subalgebra	NOUN
ejpam-3335	331	53	of	of	ADP
ejpam-3335	331	54	a	a	DET
ejpam-3335	331	55	if	if	SCONJ
ejpam-3335	331	56	l−(h	l−(h	PROPN
ejpam-3335	331	57	;	;	PUNCT
ejpam-3335	331	58	ε	ε	PROPN
ejpam-3335	331	59	)	)	PUNCT
ejpam-3335	331	60	is	be	AUX
ejpam-3335	331	61	nonempty	nonempty	ADJ
ejpam-3335	331	62	,	,	PUNCT
ejpam-3335	331	63	and	and	CCONJ
ejpam-3335	331	64	(	(	PUNCT
ejpam-3335	331	65	2	2	X
ejpam-3335	331	66	)	)	PUNCT
ejpam-3335	331	67	if	if	SCONJ
ejpam-3335	331	68	im(h	im(h	NOUN
ejpam-3335	331	69	)	)	PUNCT
ejpam-3335	331	70	is	be	AUX
ejpam-3335	331	71	a	a	DET
ejpam-3335	331	72	chain	chain	NOUN
ejpam-3335	331	73	and	and	CCONJ
ejpam-3335	331	74	for	for	ADP
ejpam-3335	331	75	all	all	DET
ejpam-3335	331	76	ε	ε	PROPN
ejpam-3335	331	77	∈	∈	PROPN
ejpam-3335	331	78	p([0	p([0	NOUN
ejpam-3335	331	79	,	,	PUNCT
ejpam-3335	331	80	1	1	NUM
ejpam-3335	331	81	]	]	NUM
ejpam-3335	331	82	)	)	PUNCT
ejpam-3335	331	83	,	,	PUNCT
ejpam-3335	331	84	a	a	DET
ejpam-3335	331	85	nonempty	nonempty	NOUN
ejpam-3335	331	86	subset	subset	VERB
ejpam-3335	331	87	l−(h	l−(h	PROPN
ejpam-3335	331	88	;	;	PUNCT
ejpam-3335	331	89	ε	ε	PROPN
ejpam-3335	331	90	)	)	PUNCT
ejpam-3335	331	91	of	of	ADP
ejpam-3335	331	92	a	a	PRON
ejpam-3335	331	93	is	be	AUX
ejpam-3335	331	94	a	a	DET
ejpam-3335	331	95	up	up	ADJ
ejpam-3335	331	96	-	-	PUNCT
ejpam-3335	331	97	subalgebra	subalgebra	NOUN
ejpam-3335	331	98	of	of	ADP
ejpam-3335	331	99	a	a	PRON
ejpam-3335	331	100	,	,	PUNCT
ejpam-3335	331	101	then	then	ADV
ejpam-3335	331	102	h	h	PROPN
ejpam-3335	331	103	is	be	AUX
ejpam-3335	331	104	an	an	DET
ejpam-3335	331	105	anti	anti	ADJ
ejpam-3335	331	106	-	-	ADJ
ejpam-3335	331	107	hesitant	hesitant	ADJ
ejpam-3335	331	108	fuzzy	fuzzy	ADJ
ejpam-3335	331	109	up	up	NOUN
ejpam-3335	331	110	-	-	PUNCT
ejpam-3335	331	111	subalgebra	subalgebra	NOUN
ejpam-3335	331	112	of	of	ADP
ejpam-3335	331	113	a.	a.	NOUN
ejpam-3335	331	114	proof	proof	NOUN
ejpam-3335	331	115	.	.	PUNCT
ejpam-3335	332	1	(	(	PUNCT
ejpam-3335	332	2	1	1	X
ejpam-3335	332	3	)	)	PUNCT
ejpam-3335	332	4	assume	assume	VERB
ejpam-3335	332	5	that	that	SCONJ
ejpam-3335	332	6	h	h	NOUN
ejpam-3335	332	7	is	be	AUX
ejpam-3335	332	8	an	an	DET
ejpam-3335	332	9	anti	anti	ADJ
ejpam-3335	332	10	-	-	ADJ
ejpam-3335	332	11	hesitant	hesitant	ADJ
ejpam-3335	332	12	fuzzy	fuzzy	ADJ
ejpam-3335	332	13	up	up	NOUN
ejpam-3335	332	14	-	-	PUNCT
ejpam-3335	332	15	subalgebra	subalgebra	NOUN
ejpam-3335	332	16	of	of	ADP
ejpam-3335	332	17	a.	a.	NOUN
ejpam-3335	332	18	let	let	VERB
ejpam-3335	332	19	ε	ε	PROPN
ejpam-3335	332	20	∈	∈	PROPN
ejpam-3335	332	21	p([0	p([0	PROPN
ejpam-3335	332	22	,	,	PUNCT
ejpam-3335	332	23	1	1	NUM
ejpam-3335	332	24	]	]	PUNCT
ejpam-3335	332	25	)	)	PUNCT
ejpam-3335	332	26	be	be	AUX
ejpam-3335	332	27	such	such	ADJ
ejpam-3335	332	28	that	that	SCONJ
ejpam-3335	332	29	l−(h	l−(h	PROPN
ejpam-3335	332	30	;	;	PUNCT
ejpam-3335	332	31	ε	ε	PROPN
ejpam-3335	332	32	)	)	PUNCT
ejpam-3335	332	33	6=	6=	NOUN
ejpam-3335	332	34	∅	∅	NOUN
ejpam-3335	332	35	,	,	PUNCT
ejpam-3335	332	36	and	and	CCONJ
ejpam-3335	332	37	let	let	VERB
ejpam-3335	332	38	x	x	PRON
ejpam-3335	332	39	,	,	PUNCT
ejpam-3335	332	40	y	y	PROPN
ejpam-3335	332	41	∈	∈	PROPN
ejpam-3335	332	42	a	a	DET
ejpam-3335	332	43	be	be	AUX
ejpam-3335	332	44	such	such	ADJ
ejpam-3335	332	45	that	that	SCONJ
ejpam-3335	332	46	x	x	SYM
ejpam-3335	332	47	∈	∈	PROPN
ejpam-3335	332	48	l−(h	l−(h	PROPN
ejpam-3335	332	49	;	;	PUNCT
ejpam-3335	332	50	ε	ε	PROPN
ejpam-3335	332	51	)	)	PUNCT
ejpam-3335	332	52	and	and	CCONJ
ejpam-3335	332	53	y	y	PROPN
ejpam-3335	332	54	∈	∈	PROPN
ejpam-3335	332	55	l−(h	l−(h	PROPN
ejpam-3335	332	56	;	;	PUNCT
ejpam-3335	332	57	ε	ε	PROPN
ejpam-3335	332	58	)	)	PUNCT
ejpam-3335	332	59	.	.	PUNCT
ejpam-3335	333	1	then	then	ADV
ejpam-3335	333	2	hh(x	hh(x	PUNCT
ejpam-3335	333	3	)	)	PUNCT
ejpam-3335	334	1	⊂	⊂	PROPN
ejpam-3335	334	2	ε	ε	PROPN
ejpam-3335	334	3	and	and	CCONJ
ejpam-3335	334	4	hh(y	hh(y	NOUN
ejpam-3335	334	5	)	)	PUNCT
ejpam-3335	335	1	⊂	⊂	PROPN
ejpam-3335	335	2	ε	ε	PROPN
ejpam-3335	335	3	.	.	PUNCT
ejpam-3335	336	1	since	since	SCONJ
ejpam-3335	336	2	h	h	NOUN
ejpam-3335	336	3	is	be	AUX
ejpam-3335	336	4	an	an	DET
ejpam-3335	336	5	anti	anti	ADJ
ejpam-3335	336	6	-	-	ADJ
ejpam-3335	336	7	hesitant	hesitant	ADJ
ejpam-3335	336	8	fuzzy	fuzzy	ADJ
ejpam-3335	336	9	upsubalgebra	upsubalgebra	NOUN
ejpam-3335	336	10	of	of	ADP
ejpam-3335	336	11	a	a	PRON
ejpam-3335	336	12	,	,	PUNCT
ejpam-3335	336	13	we	we	PRON
ejpam-3335	336	14	have	have	VERB
ejpam-3335	336	15	hh(x	hh(x	X
ejpam-3335	336	16	·	·	PUNCT
ejpam-3335	336	17	y	y	X
ejpam-3335	336	18	)	)	PUNCT
ejpam-3335	336	19	⊆	⊆	NUM
ejpam-3335	336	20	hh(x)∪	hh(x)∪	NOUN
ejpam-3335	336	21	hh(y	hh(y	NOUN
ejpam-3335	336	22	)	)	PUNCT
ejpam-3335	336	23	⊂	⊂	PROPN
ejpam-3335	336	24	ε	ε	PROPN
ejpam-3335	336	25	and	and	CCONJ
ejpam-3335	336	26	thus	thus	ADV
ejpam-3335	336	27	x	x	X
ejpam-3335	336	28	·	·	PUNCT
ejpam-3335	336	29	y	y	PROPN
ejpam-3335	336	30	∈	∈	PROPN
ejpam-3335	336	31	l−(h	l−(h	PROPN
ejpam-3335	336	32	;	;	PUNCT
ejpam-3335	336	33	ε	ε	PROPN
ejpam-3335	336	34	)	)	PUNCT
ejpam-3335	336	35	.	.	PUNCT
ejpam-3335	337	1	hence	hence	ADV
ejpam-3335	337	2	,	,	PUNCT
ejpam-3335	337	3	l−(h	l−(h	PROPN
ejpam-3335	337	4	;	;	PUNCT
ejpam-3335	337	5	ε	ε	PROPN
ejpam-3335	337	6	)	)	PUNCT
ejpam-3335	337	7	is	be	AUX
ejpam-3335	337	8	a	a	DET
ejpam-3335	337	9	up	up	ADJ
ejpam-3335	337	10	-	-	PUNCT
ejpam-3335	337	11	subalgebra	subalgebra	NOUN
ejpam-3335	337	12	of	of	ADP
ejpam-3335	337	13	a.	a.	NOUN
ejpam-3335	337	14	(	(	PUNCT
ejpam-3335	337	15	2	2	X
ejpam-3335	337	16	)	)	PUNCT
ejpam-3335	337	17	assume	assume	VERB
ejpam-3335	337	18	that	that	SCONJ
ejpam-3335	337	19	im(h	im(h	NOUN
ejpam-3335	337	20	)	)	PUNCT
ejpam-3335	337	21	is	be	AUX
ejpam-3335	337	22	a	a	DET
ejpam-3335	337	23	chain	chain	NOUN
ejpam-3335	337	24	and	and	CCONJ
ejpam-3335	337	25	for	for	ADP
ejpam-3335	337	26	all	all	DET
ejpam-3335	337	27	ε	ε	PROPN
ejpam-3335	337	28	∈	∈	PROPN
ejpam-3335	337	29	p([0	p([0	NOUN
ejpam-3335	337	30	,	,	PUNCT
ejpam-3335	337	31	1	1	NUM
ejpam-3335	337	32	]	]	NUM
ejpam-3335	337	33	)	)	PUNCT
ejpam-3335	337	34	,	,	PUNCT
ejpam-3335	337	35	a	a	DET
ejpam-3335	337	36	nonempty	nonempty	NOUN
ejpam-3335	337	37	subset	subset	VERB
ejpam-3335	337	38	l−(h	l−(h	PROPN
ejpam-3335	337	39	;	;	PUNCT
ejpam-3335	337	40	ε	ε	PROPN
ejpam-3335	337	41	)	)	PUNCT
ejpam-3335	337	42	of	of	ADP
ejpam-3335	337	43	a	a	PRON
ejpam-3335	337	44	is	be	AUX
ejpam-3335	337	45	a	a	DET
ejpam-3335	337	46	up	up	ADJ
ejpam-3335	337	47	-	-	PUNCT
ejpam-3335	337	48	subalgebra	subalgebra	NOUN
ejpam-3335	337	49	of	of	ADP
ejpam-3335	337	50	a.	a.	NOUN
ejpam-3335	337	51	assume	assume	VERB
ejpam-3335	337	52	that	that	SCONJ
ejpam-3335	337	53	there	there	PRON
ejpam-3335	337	54	exist	exist	VERB
ejpam-3335	337	55	x	x	NOUN
ejpam-3335	337	56	,	,	PUNCT
ejpam-3335	337	57	y	y	PROPN
ejpam-3335	337	58	∈	∈	PROPN
ejpam-3335	337	59	a	a	DET
ejpam-3335	337	60	such	such	ADJ
ejpam-3335	337	61	that	that	PRON
ejpam-3335	337	62	hh(x	hh(x	X
ejpam-3335	337	63	·	·	PUNCT
ejpam-3335	337	64	y	y	X
ejpam-3335	337	65	)	)	PUNCT
ejpam-3335	337	66	*	*	PUNCT
ejpam-3335	338	1	p.	p.	NOUN
ejpam-3335	338	2	mosrijai	mosrijai	PROPN
ejpam-3335	338	3	,	,	PUNCT
ejpam-3335	338	4	a.	a.	NOUN
ejpam-3335	338	5	iampan	iampan	PROPN
ejpam-3335	338	6	/	/	SYM
ejpam-3335	338	7	eur	eur	PROPN
ejpam-3335	338	8	.	.	PUNCT
ejpam-3335	339	1	j.	j.	PROPN
ejpam-3335	339	2	pure	pure	PROPN
ejpam-3335	339	3	appl	appl	PROPN
ejpam-3335	339	4	.	.	PROPN
ejpam-3335	339	5	math	math	PROPN
ejpam-3335	339	6	,	,	PUNCT
ejpam-3335	339	7	11	11	NUM
ejpam-3335	339	8	(	(	PUNCT
ejpam-3335	339	9	4	4	NUM
ejpam-3335	339	10	)	)	PUNCT
ejpam-3335	339	11	(	(	PUNCT
ejpam-3335	339	12	2018	2018	NUM
ejpam-3335	339	13	)	)	PUNCT
ejpam-3335	339	14	,	,	PUNCT
ejpam-3335	339	15	976	976	NUM
ejpam-3335	339	16	-	-	SYM
ejpam-3335	339	17	1002	1002	NUM
ejpam-3335	339	18	988	988	NUM
ejpam-3335	339	19	hh(x	hh(x	NOUN
ejpam-3335	339	20	)	)	PUNCT
ejpam-3335	339	21	∪	∪	ADP
ejpam-3335	339	22	hh(y	hh(y	NOUN
ejpam-3335	339	23	)	)	PUNCT
ejpam-3335	339	24	.	.	PUNCT
ejpam-3335	340	1	since	since	SCONJ
ejpam-3335	340	2	im(h	im(h	NOUN
ejpam-3335	340	3	)	)	PUNCT
ejpam-3335	340	4	is	be	AUX
ejpam-3335	340	5	a	a	DET
ejpam-3335	340	6	chain	chain	NOUN
ejpam-3335	340	7	,	,	PUNCT
ejpam-3335	340	8	we	we	PRON
ejpam-3335	340	9	have	have	VERB
ejpam-3335	340	10	hh(x	hh(x	X
ejpam-3335	340	11	·	·	PUNCT
ejpam-3335	340	12	y	y	X
ejpam-3335	340	13	)	)	PUNCT
ejpam-3335	340	14	⊃	⊃	NOUN
ejpam-3335	340	15	hh(x	hh(x	X
ejpam-3335	340	16	)	)	PUNCT
ejpam-3335	340	17	∪	∪	ADP
ejpam-3335	340	18	hh(y	hh(y	NOUN
ejpam-3335	340	19	)	)	PUNCT
ejpam-3335	340	20	.	.	PUNCT
ejpam-3335	341	1	choose	choose	VERB
ejpam-3335	341	2	ε	ε	PROPN
ejpam-3335	341	3	=	=	SYM
ejpam-3335	341	4	hh(x	hh(x	X
ejpam-3335	341	5	·	·	PUNCT
ejpam-3335	341	6	y	y	X
ejpam-3335	341	7	)	)	PUNCT
ejpam-3335	341	8	∈	∈	PROPN
ejpam-3335	341	9	p([0	p([0	NOUN
ejpam-3335	341	10	,	,	PUNCT
ejpam-3335	341	11	1	1	NUM
ejpam-3335	341	12	]	]	NUM
ejpam-3335	341	13	)	)	PUNCT
ejpam-3335	341	14	.	.	PUNCT
ejpam-3335	342	1	then	then	ADV
ejpam-3335	342	2	hh(x	hh(x	PUNCT
ejpam-3335	342	3	)	)	PUNCT
ejpam-3335	343	1	⊂	⊂	PROPN
ejpam-3335	343	2	ε	ε	PROPN
ejpam-3335	343	3	and	and	CCONJ
ejpam-3335	343	4	hh(y	hh(y	NOUN
ejpam-3335	343	5	)	)	PUNCT
ejpam-3335	344	1	⊂	⊂	PROPN
ejpam-3335	344	2	ε	ε	PROPN
ejpam-3335	344	3	.	.	PUNCT
ejpam-3335	344	4	thus	thus	ADV
ejpam-3335	344	5	x	x	X
ejpam-3335	344	6	,	,	PUNCT
ejpam-3335	344	7	y	y	PROPN
ejpam-3335	344	8	∈	∈	PROPN
ejpam-3335	344	9	l−(h	l−(h	PROPN
ejpam-3335	344	10	;	;	PUNCT
ejpam-3335	344	11	ε	ε	PROPN
ejpam-3335	344	12	)	)	PUNCT
ejpam-3335	344	13	6=	6=	ADP
ejpam-3335	344	14	∅.	∅.	ADP
ejpam-3335	344	15	by	by	ADP
ejpam-3335	344	16	assumption	assumption	NOUN
ejpam-3335	344	17	,	,	PUNCT
ejpam-3335	344	18	we	we	PRON
ejpam-3335	344	19	have	have	VERB
ejpam-3335	344	20	l−(h	l−(h	PROPN
ejpam-3335	344	21	;	;	PUNCT
ejpam-3335	344	22	ε	ε	PROPN
ejpam-3335	344	23	)	)	PUNCT
ejpam-3335	344	24	is	be	AUX
ejpam-3335	344	25	a	a	DET
ejpam-3335	344	26	up	up	ADJ
ejpam-3335	344	27	-	-	PUNCT
ejpam-3335	344	28	subalgebra	subalgebra	NOUN
ejpam-3335	344	29	of	of	ADP
ejpam-3335	344	30	a	a	PRON
ejpam-3335	344	31	and	and	CCONJ
ejpam-3335	344	32	so	so	ADV
ejpam-3335	344	33	x	x	SYM
ejpam-3335	344	34	·	·	PUNCT
ejpam-3335	344	35	y	y	PROPN
ejpam-3335	344	36	∈	∈	PROPN
ejpam-3335	344	37	l−(h	l−(h	PROPN
ejpam-3335	344	38	;	;	PUNCT
ejpam-3335	344	39	ε	ε	PROPN
ejpam-3335	344	40	)	)	PUNCT
ejpam-3335	344	41	.	.	PUNCT
ejpam-3335	345	1	thus	thus	ADV
ejpam-3335	345	2	hh(x	hh(x	X
ejpam-3335	345	3	·	·	PUNCT
ejpam-3335	345	4	y	y	X
ejpam-3335	345	5	)	)	PUNCT
ejpam-3335	345	6	⊂	⊂	PROPN
ejpam-3335	345	7	ε	ε	PROPN
ejpam-3335	345	8	=	=	SYM
ejpam-3335	345	9	hh(x	hh(x	X
ejpam-3335	345	10	·	·	PUNCT
ejpam-3335	345	11	y	y	X
ejpam-3335	345	12	)	)	PUNCT
ejpam-3335	345	13	,	,	PUNCT
ejpam-3335	345	14	a	a	DET
ejpam-3335	345	15	contradiction	contradiction	NOUN
ejpam-3335	345	16	.	.	PUNCT
ejpam-3335	346	1	therefore	therefore	ADV
ejpam-3335	346	2	,	,	PUNCT
ejpam-3335	346	3	hh(x	hh(x	PUNCT
ejpam-3335	346	4	·	·	PUNCT
ejpam-3335	346	5	y	y	X
ejpam-3335	346	6	)	)	PUNCT
ejpam-3335	346	7	⊆	⊆	NUM
ejpam-3335	346	8	hh(x	hh(x	NOUN
ejpam-3335	346	9	)	)	PUNCT
ejpam-3335	346	10	∪	∪	ADP
ejpam-3335	346	11	hh(y	hh(y	NOUN
ejpam-3335	346	12	)	)	PUNCT
ejpam-3335	346	13	for	for	ADP
ejpam-3335	346	14	all	all	DET
ejpam-3335	346	15	x	x	NOUN
ejpam-3335	346	16	,	,	PUNCT
ejpam-3335	346	17	y	y	PROPN
ejpam-3335	346	18	∈	∈	PROPN
ejpam-3335	346	19	a.	a.	NOUN
ejpam-3335	346	20	hence	hence	ADV
ejpam-3335	346	21	,	,	PUNCT
ejpam-3335	346	22	h	h	PROPN
ejpam-3335	346	23	is	be	AUX
ejpam-3335	346	24	an	an	DET
ejpam-3335	346	25	anti	anti	ADJ
ejpam-3335	346	26	-	-	ADJ
ejpam-3335	346	27	hesitant	hesitant	ADJ
ejpam-3335	346	28	fuzzy	fuzzy	ADJ
ejpam-3335	346	29	up	up	NOUN
ejpam-3335	346	30	-	-	PUNCT
ejpam-3335	346	31	subalgebra	subalgebra	NOUN
ejpam-3335	346	32	of	of	ADP
ejpam-3335	346	33	a.	a.	NOUN
ejpam-3335	346	34	example	example	NOUN
ejpam-3335	346	35	8	8	NUM
ejpam-3335	346	36	.	.	PUNCT
ejpam-3335	347	1	let	let	VERB
ejpam-3335	347	2	a	a	PRON
ejpam-3335	347	3	=	=	PUNCT
ejpam-3335	347	4	{	{	PUNCT
ejpam-3335	347	5	0	0	NUM
ejpam-3335	347	6	,	,	PUNCT
ejpam-3335	347	7	1	1	NUM
ejpam-3335	347	8	,	,	PUNCT
ejpam-3335	347	9	2	2	NUM
ejpam-3335	347	10	,	,	PUNCT
ejpam-3335	347	11	3	3	NUM
ejpam-3335	347	12	,	,	PUNCT
ejpam-3335	347	13	4	4	NUM
ejpam-3335	347	14	}	}	PUNCT
ejpam-3335	347	15	be	be	AUX
ejpam-3335	347	16	a	a	DET
ejpam-3335	347	17	set	set	NOUN
ejpam-3335	347	18	with	with	ADP
ejpam-3335	347	19	a	a	DET
ejpam-3335	347	20	binary	binary	ADJ
ejpam-3335	347	21	operation	operation	NOUN
ejpam-3335	347	22	·	·	PUNCT
ejpam-3335	347	23	defined	define	VERB
ejpam-3335	347	24	by	by	ADP
ejpam-3335	347	25	the	the	DET
ejpam-3335	347	26	following	following	ADJ
ejpam-3335	347	27	cayley	cayley	ADJ
ejpam-3335	347	28	table	table	NOUN
ejpam-3335	347	29	:	:	PUNCT
ejpam-3335	347	30	·	·	PUNCT
ejpam-3335	347	31	0	0	NUM
ejpam-3335	348	1	1	1	NUM
ejpam-3335	348	2	2	2	NUM
ejpam-3335	348	3	3	3	NUM
ejpam-3335	348	4	4	4	NUM
ejpam-3335	348	5	0	0	NUM
ejpam-3335	348	6	0	0	NUM
ejpam-3335	348	7	1	1	NUM
ejpam-3335	348	8	2	2	NUM
ejpam-3335	348	9	3	3	NUM
ejpam-3335	348	10	4	4	NUM
ejpam-3335	348	11	1	1	NUM
ejpam-3335	348	12	0	0	NUM
ejpam-3335	348	13	0	0	NUM
ejpam-3335	348	14	0	0	NUM
ejpam-3335	348	15	0	0	NUM
ejpam-3335	348	16	0	0	NUM
ejpam-3335	348	17	2	2	NUM
ejpam-3335	348	18	0	0	NUM
ejpam-3335	348	19	2	2	NUM
ejpam-3335	348	20	0	0	NUM
ejpam-3335	348	21	0	0	NUM
ejpam-3335	348	22	0	0	NUM
ejpam-3335	348	23	3	3	NUM
ejpam-3335	348	24	0	0	NUM
ejpam-3335	348	25	2	2	NUM
ejpam-3335	348	26	2	2	NUM
ejpam-3335	348	27	0	0	NUM
ejpam-3335	348	28	0	0	NUM
ejpam-3335	348	29	4	4	NUM
ejpam-3335	348	30	0	0	NUM
ejpam-3335	348	31	2	2	NUM
ejpam-3335	348	32	2	2	NUM
ejpam-3335	348	33	4	4	NUM
ejpam-3335	348	34	0	0	NUM
ejpam-3335	348	35	then	then	ADV
ejpam-3335	348	36	(	(	PUNCT
ejpam-3335	348	37	a	a	PRON
ejpam-3335	348	38	,	,	PUNCT
ejpam-3335	348	39	·	·	PUNCT
ejpam-3335	348	40	,	,	PUNCT
ejpam-3335	348	41	0	0	NUM
ejpam-3335	348	42	)	)	PUNCT
ejpam-3335	348	43	is	be	AUX
ejpam-3335	348	44	a	a	DET
ejpam-3335	348	45	up	up	NOUN
ejpam-3335	348	46	-	-	PUNCT
ejpam-3335	348	47	algebra	algebra	NOUN
ejpam-3335	348	48	.	.	PUNCT
ejpam-3335	349	1	we	we	PRON
ejpam-3335	349	2	define	define	VERB
ejpam-3335	349	3	a	a	DET
ejpam-3335	349	4	hesitant	hesitant	ADJ
ejpam-3335	349	5	fuzzy	fuzzy	ADJ
ejpam-3335	349	6	set	set	VERB
ejpam-3335	349	7	h	h	NOUN
ejpam-3335	349	8	on	on	ADP
ejpam-3335	349	9	a	a	DET
ejpam-3335	349	10	as	as	SCONJ
ejpam-3335	349	11	follows	follow	VERB
ejpam-3335	349	12	:	:	PUNCT
ejpam-3335	349	13	hh(0	hh(0	NOUN
ejpam-3335	349	14	)	)	PUNCT
ejpam-3335	349	15	=	=	SYM
ejpam-3335	349	16	(	(	PUNCT
ejpam-3335	349	17	0	0	NUM
ejpam-3335	349	18	,	,	PUNCT
ejpam-3335	349	19	1),hh(1	1),hh(1	NUM
ejpam-3335	349	20	)	)	PUNCT
ejpam-3335	349	21	=	=	PUNCT
ejpam-3335	350	1	[	[	X
ejpam-3335	350	2	0	0	NUM
ejpam-3335	350	3	,	,	PUNCT
ejpam-3335	350	4	1	1	NUM
ejpam-3335	350	5	)	)	PUNCT
ejpam-3335	350	6	,	,	PUNCT
ejpam-3335	350	7	hh(2	hh(2	NOUN
ejpam-3335	350	8	)	)	PUNCT
ejpam-3335	350	9	=	=	SYM
ejpam-3335	350	10	(	(	PUNCT
ejpam-3335	350	11	0	0	NUM
ejpam-3335	350	12	,	,	PUNCT
ejpam-3335	350	13	1	1	NUM
ejpam-3335	350	14	]	]	PUNCT
ejpam-3335	350	15	,	,	PUNCT
ejpam-3335	350	16	hh(3	hh(3	NOUN
ejpam-3335	350	17	)	)	PUNCT
ejpam-3335	351	1	=	=	PUNCT
ejpam-3335	352	1	[	[	X
ejpam-3335	352	2	0	0	NUM
ejpam-3335	352	3	,	,	PUNCT
ejpam-3335	352	4	1	1	NUM
ejpam-3335	352	5	)	)	PUNCT
ejpam-3335	352	6	,	,	PUNCT
ejpam-3335	352	7	and	and	CCONJ
ejpam-3335	352	8	hh(4	hh(4	NOUN
ejpam-3335	352	9	)	)	PUNCT
ejpam-3335	352	10	=	=	PUNCT
ejpam-3335	353	1	[	[	X
ejpam-3335	353	2	0	0	NUM
ejpam-3335	353	3	,	,	PUNCT
ejpam-3335	353	4	1	1	NUM
ejpam-3335	353	5	]	]	PUNCT
ejpam-3335	353	6	.	.	PUNCT
ejpam-3335	354	1	then	then	ADV
ejpam-3335	354	2	im(h	im(h	NOUN
ejpam-3335	354	3	)	)	PUNCT
ejpam-3335	354	4	is	be	AUX
ejpam-3335	354	5	not	not	PART
ejpam-3335	354	6	a	a	DET
ejpam-3335	354	7	chain	chain	NOUN
ejpam-3335	354	8	.	.	PUNCT
ejpam-3335	355	1	if	if	SCONJ
ejpam-3335	355	2	ε	ε	PROPN
ejpam-3335	355	3	⊆	⊆	NUM
ejpam-3335	355	4	(	(	PUNCT
ejpam-3335	355	5	0	0	NUM
ejpam-3335	355	6	,	,	PUNCT
ejpam-3335	355	7	1	1	NUM
ejpam-3335	355	8	)	)	PUNCT
ejpam-3335	355	9	,	,	PUNCT
ejpam-3335	355	10	then	then	ADV
ejpam-3335	355	11	l−(h	l−(h	PROPN
ejpam-3335	355	12	;	;	PUNCT
ejpam-3335	355	13	ε	ε	PROPN
ejpam-3335	355	14	)	)	PUNCT
ejpam-3335	355	15	=	=	PUNCT
ejpam-3335	355	16	∅.	∅.	NOUN
ejpam-3335	355	17	if	if	SCONJ
ejpam-3335	355	18	ε	ε	PROPN
ejpam-3335	355	19	=	=	PUNCT
ejpam-3335	356	1	[	[	X
ejpam-3335	356	2	0	0	NUM
ejpam-3335	356	3	,	,	PUNCT
ejpam-3335	356	4	1	1	NUM
ejpam-3335	356	5	)	)	PUNCT
ejpam-3335	356	6	or	or	CCONJ
ejpam-3335	356	7	ε	ε	PROPN
ejpam-3335	356	8	=	=	SYM
ejpam-3335	356	9	(	(	PUNCT
ejpam-3335	356	10	0	0	NUM
ejpam-3335	356	11	,	,	PUNCT
ejpam-3335	356	12	1	1	NUM
ejpam-3335	356	13	]	]	PUNCT
ejpam-3335	356	14	,	,	PUNCT
ejpam-3335	356	15	then	then	ADV
ejpam-3335	356	16	l−(h	l−(h	PROPN
ejpam-3335	356	17	;	;	PUNCT
ejpam-3335	356	18	ε	ε	PROPN
ejpam-3335	356	19	)	)	PUNCT
ejpam-3335	356	20	=	=	PUNCT
ejpam-3335	356	21	{	{	PUNCT
ejpam-3335	356	22	0	0	NUM
ejpam-3335	356	23	}	}	PUNCT
ejpam-3335	356	24	.	.	PUNCT
ejpam-3335	357	1	if	if	SCONJ
ejpam-3335	357	2	ε	ε	PROPN
ejpam-3335	357	3	=	=	PUNCT
ejpam-3335	358	1	[	[	X
ejpam-3335	358	2	0	0	NUM
ejpam-3335	358	3	,	,	PUNCT
ejpam-3335	358	4	1	1	NUM
ejpam-3335	358	5	]	]	PUNCT
ejpam-3335	358	6	,	,	PUNCT
ejpam-3335	358	7	then	then	ADV
ejpam-3335	358	8	.	.	PUNCT
ejpam-3335	359	1	l−(h	l−(h	PROPN
ejpam-3335	359	2	;	;	PUNCT
ejpam-3335	359	3	ε	ε	PROPN
ejpam-3335	359	4	)	)	PUNCT
ejpam-3335	359	5	=	=	SYM
ejpam-3335	359	6	{	{	PUNCT
ejpam-3335	359	7	0	0	NUM
ejpam-3335	359	8	,	,	PUNCT
ejpam-3335	359	9	1	1	NUM
ejpam-3335	359	10	,	,	PUNCT
ejpam-3335	359	11	2	2	NUM
ejpam-3335	359	12	,	,	PUNCT
ejpam-3335	359	13	3	3	NUM
ejpam-3335	359	14	}	}	PUNCT
ejpam-3335	359	15	.	.	PUNCT
ejpam-3335	360	1	using	use	VERB
ejpam-3335	360	2	this	this	DET
ejpam-3335	360	3	data	datum	NOUN
ejpam-3335	360	4	,	,	PUNCT
ejpam-3335	360	5	we	we	PRON
ejpam-3335	360	6	can	can	AUX
ejpam-3335	360	7	show	show	VERB
ejpam-3335	360	8	that	that	SCONJ
ejpam-3335	360	9	all	all	DET
ejpam-3335	360	10	nonempty	nonempty	ADV
ejpam-3335	360	11	subset	subset	VERB
ejpam-3335	360	12	l−(h	l−(h	PROPN
ejpam-3335	360	13	;	;	PUNCT
ejpam-3335	360	14	ε	ε	PROPN
ejpam-3335	360	15	)	)	PUNCT
ejpam-3335	360	16	of	of	ADP
ejpam-3335	360	17	a	a	PRON
ejpam-3335	360	18	is	be	AUX
ejpam-3335	360	19	a	a	DET
ejpam-3335	360	20	up	up	ADJ
ejpam-3335	360	21	-	-	PUNCT
ejpam-3335	360	22	subalgebra	subalgebra	NOUN
ejpam-3335	360	23	of	of	ADP
ejpam-3335	360	24	a.	a.	NOUN
ejpam-3335	360	25	since	since	SCONJ
ejpam-3335	360	26	hh(3	hh(3	PROPN
ejpam-3335	360	27	·	·	SYM
ejpam-3335	360	28	1	1	NUM
ejpam-3335	360	29	)	)	PUNCT
ejpam-3335	360	30	=	=	SYM
ejpam-3335	360	31	hh(2	hh(2	NOUN
ejpam-3335	360	32	)	)	PUNCT
ejpam-3335	360	33	=	=	SYM
ejpam-3335	360	34	(	(	PUNCT
ejpam-3335	360	35	0	0	NUM
ejpam-3335	360	36	,	,	PUNCT
ejpam-3335	360	37	1	1	NUM
ejpam-3335	360	38	]	]	PUNCT
ejpam-3335	360	39	*	*	PUNCT
ejpam-3335	361	1	[	[	X
ejpam-3335	361	2	0	0	NUM
ejpam-3335	361	3	,	,	PUNCT
ejpam-3335	361	4	1	1	NUM
ejpam-3335	361	5	)	)	PUNCT
ejpam-3335	361	6	=	=	SYM
ejpam-3335	361	7	hh(3	hh(3	NOUN
ejpam-3335	361	8	)	)	PUNCT
ejpam-3335	361	9	∪	∪	ADP
ejpam-3335	361	10	hh(1	hh(1	PROPN
ejpam-3335	361	11	)	)	PUNCT
ejpam-3335	361	12	,	,	PUNCT
ejpam-3335	361	13	we	we	PRON
ejpam-3335	361	14	have	have	VERB
ejpam-3335	361	15	h	h	NOUN
ejpam-3335	361	16	is	be	AUX
ejpam-3335	361	17	not	not	PART
ejpam-3335	361	18	an	an	DET
ejpam-3335	361	19	anti	anti	ADJ
ejpam-3335	361	20	-	-	ADJ
ejpam-3335	361	21	hesitant	hesitant	ADJ
ejpam-3335	361	22	fuzzy	fuzzy	ADJ
ejpam-3335	361	23	up	up	NOUN
ejpam-3335	361	24	-	-	PUNCT
ejpam-3335	361	25	subalgebra	subalgebra	NOUN
ejpam-3335	361	26	of	of	ADP
ejpam-3335	361	27	a.	a.	NOUN
ejpam-3335	361	28	theorem	theorem	NOUN
ejpam-3335	361	29	12	12	NUM
ejpam-3335	361	30	.	.	PUNCT
ejpam-3335	362	1	let	let	VERB
ejpam-3335	362	2	h	h	PRON
ejpam-3335	362	3	be	be	AUX
ejpam-3335	362	4	a	a	DET
ejpam-3335	362	5	hesitant	hesitant	ADJ
ejpam-3335	362	6	fuzzy	fuzzy	ADJ
ejpam-3335	362	7	set	set	NOUN
ejpam-3335	362	8	on	on	ADP
ejpam-3335	362	9	a.	a.	NOUN
ejpam-3335	362	10	then	then	ADV
ejpam-3335	362	11	the	the	DET
ejpam-3335	362	12	following	follow	VERB
ejpam-3335	362	13	statements	statement	NOUN
ejpam-3335	362	14	hold	hold	VERB
ejpam-3335	362	15	:	:	PUNCT
ejpam-3335	362	16	(	(	PUNCT
ejpam-3335	362	17	1	1	X
ejpam-3335	362	18	)	)	PUNCT
ejpam-3335	362	19	if	if	SCONJ
ejpam-3335	362	20	h	h	NOUN
ejpam-3335	362	21	is	be	AUX
ejpam-3335	362	22	an	an	DET
ejpam-3335	362	23	anti	anti	ADJ
ejpam-3335	362	24	-	-	ADJ
ejpam-3335	362	25	hesitant	hesitant	ADJ
ejpam-3335	362	26	fuzzy	fuzzy	ADJ
ejpam-3335	362	27	up	up	NOUN
ejpam-3335	362	28	-	-	PUNCT
ejpam-3335	362	29	filter	filter	NOUN
ejpam-3335	362	30	of	of	ADP
ejpam-3335	362	31	a	a	PRON
ejpam-3335	362	32	,	,	PUNCT
ejpam-3335	362	33	then	then	ADV
ejpam-3335	362	34	for	for	ADP
ejpam-3335	362	35	all	all	DET
ejpam-3335	362	36	ε	ε	PROPN
ejpam-3335	362	37	∈	∈	PROPN
ejpam-3335	362	38	p([0	p([0	NOUN
ejpam-3335	362	39	,	,	PUNCT
ejpam-3335	362	40	1	1	NUM
ejpam-3335	362	41	]	]	NUM
ejpam-3335	362	42	)	)	PUNCT
ejpam-3335	362	43	,	,	PUNCT
ejpam-3335	362	44	l−(h	l−(h	PROPN
ejpam-3335	362	45	;	;	PUNCT
ejpam-3335	362	46	ε	ε	PROPN
ejpam-3335	362	47	)	)	PUNCT
ejpam-3335	362	48	is	be	AUX
ejpam-3335	362	49	a	a	DET
ejpam-3335	362	50	up	up	ADJ
ejpam-3335	362	51	-	-	PUNCT
ejpam-3335	362	52	filter	filter	NOUN
ejpam-3335	362	53	of	of	ADP
ejpam-3335	362	54	a	a	DET
ejpam-3335	362	55	if	if	SCONJ
ejpam-3335	362	56	l−(h	l−(h	PROPN
ejpam-3335	362	57	;	;	PUNCT
ejpam-3335	362	58	ε	ε	PROPN
ejpam-3335	362	59	)	)	PUNCT
ejpam-3335	362	60	is	be	AUX
ejpam-3335	362	61	nonempty	nonempty	ADJ
ejpam-3335	362	62	,	,	PUNCT
ejpam-3335	362	63	and	and	CCONJ
ejpam-3335	362	64	(	(	PUNCT
ejpam-3335	362	65	2	2	X
ejpam-3335	362	66	)	)	PUNCT
ejpam-3335	362	67	if	if	SCONJ
ejpam-3335	362	68	im(h	im(h	NOUN
ejpam-3335	362	69	)	)	PUNCT
ejpam-3335	362	70	is	be	AUX
ejpam-3335	362	71	a	a	DET
ejpam-3335	362	72	chain	chain	NOUN
ejpam-3335	362	73	and	and	CCONJ
ejpam-3335	362	74	for	for	ADP
ejpam-3335	362	75	all	all	DET
ejpam-3335	362	76	ε	ε	PROPN
ejpam-3335	362	77	∈	∈	PROPN
ejpam-3335	362	78	p([0	p([0	NOUN
ejpam-3335	362	79	,	,	PUNCT
ejpam-3335	362	80	1	1	NUM
ejpam-3335	362	81	]	]	NUM
ejpam-3335	362	82	)	)	PUNCT
ejpam-3335	362	83	,	,	PUNCT
ejpam-3335	362	84	a	a	DET
ejpam-3335	362	85	nonempty	nonempty	NOUN
ejpam-3335	362	86	subset	subset	VERB
ejpam-3335	362	87	l−(h	l−(h	PROPN
ejpam-3335	362	88	;	;	PUNCT
ejpam-3335	362	89	ε	ε	PROPN
ejpam-3335	362	90	)	)	PUNCT
ejpam-3335	362	91	of	of	ADP
ejpam-3335	362	92	a	a	PRON
ejpam-3335	362	93	is	be	AUX
ejpam-3335	362	94	a	a	DET
ejpam-3335	362	95	up	up	ADJ
ejpam-3335	362	96	-	-	PUNCT
ejpam-3335	362	97	filter	filter	NOUN
ejpam-3335	362	98	of	of	ADP
ejpam-3335	362	99	a	a	PRON
ejpam-3335	362	100	,	,	PUNCT
ejpam-3335	362	101	then	then	ADV
ejpam-3335	362	102	h	h	PROPN
ejpam-3335	362	103	is	be	AUX
ejpam-3335	362	104	an	an	DET
ejpam-3335	362	105	anti	anti	ADJ
ejpam-3335	362	106	-	-	ADJ
ejpam-3335	362	107	hesitant	hesitant	ADJ
ejpam-3335	362	108	fuzzy	fuzzy	ADJ
ejpam-3335	362	109	up	up	NOUN
ejpam-3335	362	110	-	-	PUNCT
ejpam-3335	362	111	filter	filter	NOUN
ejpam-3335	362	112	of	of	ADP
ejpam-3335	362	113	a.	a.	NOUN
ejpam-3335	362	114	proof	proof	NOUN
ejpam-3335	362	115	.	.	PUNCT
ejpam-3335	363	1	(	(	PUNCT
ejpam-3335	363	2	1	1	X
ejpam-3335	363	3	)	)	PUNCT
ejpam-3335	363	4	assume	assume	VERB
ejpam-3335	363	5	that	that	SCONJ
ejpam-3335	363	6	h	h	NOUN
ejpam-3335	363	7	is	be	AUX
ejpam-3335	363	8	an	an	DET
ejpam-3335	363	9	anti	anti	ADJ
ejpam-3335	363	10	-	-	ADJ
ejpam-3335	363	11	hesitant	hesitant	ADJ
ejpam-3335	363	12	fuzzy	fuzzy	ADJ
ejpam-3335	363	13	up	up	NOUN
ejpam-3335	363	14	-	-	PUNCT
ejpam-3335	363	15	filter	filter	NOUN
ejpam-3335	363	16	of	of	ADP
ejpam-3335	363	17	a.	a.	NOUN
ejpam-3335	363	18	let	let	VERB
ejpam-3335	363	19	ε	ε	PROPN
ejpam-3335	363	20	∈	∈	PROPN
ejpam-3335	363	21	p([0	p([0	PROPN
ejpam-3335	363	22	,	,	PUNCT
ejpam-3335	363	23	1	1	NUM
ejpam-3335	363	24	]	]	PUNCT
ejpam-3335	363	25	)	)	PUNCT
ejpam-3335	363	26	be	be	AUX
ejpam-3335	363	27	such	such	ADJ
ejpam-3335	363	28	that	that	SCONJ
ejpam-3335	363	29	l−(h	l−(h	PROPN
ejpam-3335	363	30	;	;	PUNCT
ejpam-3335	363	31	ε	ε	PROPN
ejpam-3335	363	32	)	)	PUNCT
ejpam-3335	363	33	6=	6=	NOUN
ejpam-3335	363	34	∅	∅	NOUN
ejpam-3335	363	35	and	and	CCONJ
ejpam-3335	363	36	let	let	VERB
ejpam-3335	363	37	x	x	SYM
ejpam-3335	363	38	∈	∈	PROPN
ejpam-3335	363	39	a	a	DET
ejpam-3335	363	40	be	be	AUX
ejpam-3335	363	41	such	such	ADJ
ejpam-3335	363	42	that	that	SCONJ
ejpam-3335	363	43	x	x	SYM
ejpam-3335	363	44	∈	∈	PROPN
ejpam-3335	363	45	l−(h	l−(h	PROPN
ejpam-3335	363	46	;	;	PUNCT
ejpam-3335	363	47	ε	ε	PROPN
ejpam-3335	363	48	)	)	PUNCT
ejpam-3335	363	49	.	.	PUNCT
ejpam-3335	364	1	then	then	ADV
ejpam-3335	364	2	hh(x	hh(x	PUNCT
ejpam-3335	364	3	)	)	PUNCT
ejpam-3335	364	4	⊂	⊂	PROPN
ejpam-3335	364	5	ε	ε	AUX
ejpam-3335	364	6	.	.	PUNCT
ejpam-3335	364	7	since	since	SCONJ
ejpam-3335	364	8	h	h	NOUN
ejpam-3335	364	9	is	be	AUX
ejpam-3335	364	10	an	an	DET
ejpam-3335	364	11	anti	anti	ADJ
ejpam-3335	364	12	-	-	ADJ
ejpam-3335	364	13	hesitant	hesitant	ADJ
ejpam-3335	364	14	fuzzy	fuzzy	ADJ
ejpam-3335	364	15	up	up	NOUN
ejpam-3335	364	16	-	-	PUNCT
ejpam-3335	364	17	filter	filter	NOUN
ejpam-3335	364	18	of	of	ADP
ejpam-3335	364	19	a	a	PRON
ejpam-3335	364	20	,	,	PUNCT
ejpam-3335	364	21	we	we	PRON
ejpam-3335	364	22	have	have	VERB
ejpam-3335	364	23	hh(0	hh(0	NOUN
ejpam-3335	364	24	)	)	PUNCT
ejpam-3335	364	25	⊆	⊆	NUM
ejpam-3335	364	26	hh(x	hh(x	X
ejpam-3335	364	27	)	)	PUNCT
ejpam-3335	364	28	⊂	⊂	PROPN
ejpam-3335	364	29	ε	ε	PROPN
ejpam-3335	364	30	and	and	CCONJ
ejpam-3335	364	31	thus	thus	ADV
ejpam-3335	364	32	0	0	NUM
ejpam-3335	364	33	∈	∈	PROPN
ejpam-3335	364	34	l−(h	l−(h	PROPN
ejpam-3335	364	35	;	;	PUNCT
ejpam-3335	364	36	ε	ε	PROPN
ejpam-3335	364	37	)	)	PUNCT
ejpam-3335	364	38	.	.	PUNCT
ejpam-3335	365	1	next	next	ADV
ejpam-3335	365	2	,	,	PUNCT
ejpam-3335	365	3	let	let	VERB
ejpam-3335	365	4	x	x	PRON
ejpam-3335	365	5	,	,	PUNCT
ejpam-3335	365	6	y	y	PROPN
ejpam-3335	365	7	∈	∈	PROPN
ejpam-3335	365	8	a	a	PRON
ejpam-3335	365	9	be	be	AUX
ejpam-3335	365	10	such	such	ADJ
ejpam-3335	365	11	that	that	SCONJ
ejpam-3335	365	12	x	x	X
ejpam-3335	365	13	·	·	PUNCT
ejpam-3335	365	14	y	y	PROPN
ejpam-3335	365	15	∈	∈	PROPN
ejpam-3335	365	16	l−(h	l−(h	PROPN
ejpam-3335	365	17	;	;	PUNCT
ejpam-3335	365	18	ε	ε	PROPN
ejpam-3335	365	19	)	)	PUNCT
ejpam-3335	365	20	and	and	CCONJ
ejpam-3335	365	21	x	x	PROPN
ejpam-3335	365	22	∈	∈	PROPN
ejpam-3335	365	23	l−(h	l−(h	PROPN
ejpam-3335	365	24	;	;	PUNCT
ejpam-3335	365	25	ε	ε	PROPN
ejpam-3335	365	26	)	)	PUNCT
ejpam-3335	365	27	.	.	PUNCT
ejpam-3335	366	1	then	then	ADV
ejpam-3335	366	2	hh(x	hh(x	PUNCT
ejpam-3335	366	3	·	·	PUNCT
ejpam-3335	366	4	y	y	X
ejpam-3335	366	5	)	)	PUNCT
ejpam-3335	366	6	⊂	⊂	PROPN
ejpam-3335	366	7	ε	ε	PROPN
ejpam-3335	366	8	and	and	CCONJ
ejpam-3335	366	9	hh(x	hh(x	PUNCT
ejpam-3335	366	10	)	)	PUNCT
ejpam-3335	367	1	⊂	⊂	PROPN
ejpam-3335	367	2	ε	ε	PROPN
ejpam-3335	367	3	.	.	PUNCT
ejpam-3335	368	1	since	since	SCONJ
ejpam-3335	368	2	h	h	NOUN
ejpam-3335	368	3	is	be	AUX
ejpam-3335	368	4	an	an	DET
ejpam-3335	368	5	anti	anti	ADJ
ejpam-3335	368	6	-	-	ADJ
ejpam-3335	368	7	hesitant	hesitant	ADJ
ejpam-3335	368	8	fuzzy	fuzzy	ADJ
ejpam-3335	368	9	up	up	NOUN
ejpam-3335	368	10	-	-	PUNCT
ejpam-3335	368	11	filter	filter	NOUN
ejpam-3335	368	12	of	of	ADP
ejpam-3335	368	13	a	a	PRON
ejpam-3335	368	14	,	,	PUNCT
ejpam-3335	368	15	we	we	PRON
ejpam-3335	368	16	have	have	VERB
ejpam-3335	368	17	hh(y	hh(y	NOUN
ejpam-3335	368	18	)	)	PUNCT
ejpam-3335	369	1	⊆	⊆	NUM
ejpam-3335	369	2	hh(x	hh(x	X
ejpam-3335	369	3	·	·	PUNCT
ejpam-3335	369	4	y	y	X
ejpam-3335	369	5	)	)	PUNCT
ejpam-3335	369	6	∪	∪	ADP
ejpam-3335	369	7	hh(x	hh(x	X
ejpam-3335	369	8	)	)	PUNCT
ejpam-3335	369	9	⊂	⊂	PROPN
ejpam-3335	369	10	ε	ε	PROPN
ejpam-3335	369	11	and	and	CCONJ
ejpam-3335	369	12	thus	thus	ADV
ejpam-3335	369	13	y	y	PROPN
ejpam-3335	369	14	∈	∈	PROPN
ejpam-3335	369	15	l−(h	l−(h	PROPN
ejpam-3335	369	16	;	;	PUNCT
ejpam-3335	369	17	ε	ε	PROPN
ejpam-3335	369	18	)	)	PUNCT
ejpam-3335	369	19	.	.	PUNCT
ejpam-3335	370	1	hence	hence	ADV
ejpam-3335	370	2	,	,	PUNCT
ejpam-3335	370	3	l−(h	l−(h	PROPN
ejpam-3335	370	4	;	;	PUNCT
ejpam-3335	370	5	ε	ε	PROPN
ejpam-3335	370	6	)	)	PUNCT
ejpam-3335	370	7	is	be	AUX
ejpam-3335	370	8	a	a	DET
ejpam-3335	370	9	up	up	ADJ
ejpam-3335	370	10	-	-	PUNCT
ejpam-3335	370	11	filter	filter	NOUN
ejpam-3335	370	12	of	of	ADP
ejpam-3335	370	13	a.	a.	NOUN
ejpam-3335	370	14	(	(	PUNCT
ejpam-3335	370	15	2	2	X
ejpam-3335	370	16	)	)	PUNCT
ejpam-3335	370	17	assume	assume	VERB
ejpam-3335	370	18	that	that	SCONJ
ejpam-3335	370	19	im(h	im(h	NOUN
ejpam-3335	370	20	)	)	PUNCT
ejpam-3335	370	21	is	be	AUX
ejpam-3335	370	22	a	a	DET
ejpam-3335	370	23	chain	chain	NOUN
ejpam-3335	370	24	and	and	CCONJ
ejpam-3335	370	25	for	for	ADP
ejpam-3335	370	26	all	all	DET
ejpam-3335	370	27	ε	ε	PROPN
ejpam-3335	370	28	∈	∈	PROPN
ejpam-3335	370	29	p([0	p([0	NOUN
ejpam-3335	370	30	,	,	PUNCT
ejpam-3335	370	31	1	1	NUM
ejpam-3335	370	32	]	]	NUM
ejpam-3335	370	33	)	)	PUNCT
ejpam-3335	370	34	,	,	PUNCT
ejpam-3335	370	35	a	a	DET
ejpam-3335	370	36	nonempty	nonempty	NOUN
ejpam-3335	370	37	subset	subset	VERB
ejpam-3335	370	38	l−(h	l−(h	PROPN
ejpam-3335	370	39	;	;	PUNCT
ejpam-3335	370	40	ε	ε	PROPN
ejpam-3335	370	41	)	)	PUNCT
ejpam-3335	370	42	of	of	ADP
ejpam-3335	370	43	a	a	PRON
ejpam-3335	370	44	is	be	AUX
ejpam-3335	370	45	a	a	DET
ejpam-3335	370	46	up	up	ADJ
ejpam-3335	370	47	-	-	PUNCT
ejpam-3335	370	48	filter	filter	NOUN
ejpam-3335	370	49	of	of	ADP
ejpam-3335	370	50	a.	a.	NOUN
ejpam-3335	370	51	assume	assume	VERB
ejpam-3335	370	52	that	that	SCONJ
ejpam-3335	370	53	there	there	PRON
ejpam-3335	370	54	exists	exist	VERB
ejpam-3335	370	55	x	x	X
ejpam-3335	370	56	∈	∈	PROPN
ejpam-3335	370	57	a	a	DET
ejpam-3335	370	58	such	such	ADJ
ejpam-3335	370	59	that	that	SCONJ
ejpam-3335	370	60	hh(0	hh(0	NOUN
ejpam-3335	370	61	)	)	PUNCT
ejpam-3335	370	62	*	*	PUNCT
ejpam-3335	370	63	hh(x	hh(x	X
ejpam-3335	370	64	)	)	PUNCT
ejpam-3335	370	65	.	.	PUNCT
ejpam-3335	371	1	since	since	SCONJ
ejpam-3335	371	2	im(h	im(h	NOUN
ejpam-3335	371	3	)	)	PUNCT
ejpam-3335	371	4	is	be	AUX
ejpam-3335	371	5	a	a	DET
ejpam-3335	371	6	chain	chain	NOUN
ejpam-3335	371	7	,	,	PUNCT
ejpam-3335	371	8	we	we	PRON
ejpam-3335	371	9	have	have	VERB
ejpam-3335	371	10	hh(0	hh(0	NOUN
ejpam-3335	371	11	)	)	PUNCT
ejpam-3335	371	12	⊃	⊃	NOUN
ejpam-3335	371	13	hh(x	hh(x	X
ejpam-3335	371	14	)	)	PUNCT
ejpam-3335	371	15	.	.	PUNCT
ejpam-3335	372	1	choose	choose	VERB
ejpam-3335	372	2	ε	ε	PROPN
ejpam-3335	372	3	=	=	SYM
ejpam-3335	372	4	hh(0	hh(0	PROPN
ejpam-3335	372	5	)	)	PUNCT
ejpam-3335	372	6	∈	∈	PROPN
ejpam-3335	372	7	p([0	p([0	NOUN
ejpam-3335	372	8	,	,	PUNCT
ejpam-3335	372	9	1	1	NUM
ejpam-3335	372	10	]	]	NUM
ejpam-3335	372	11	)	)	PUNCT
ejpam-3335	372	12	.	.	PUNCT
ejpam-3335	373	1	then	then	ADV
ejpam-3335	373	2	hh(x	hh(x	PUNCT
ejpam-3335	373	3	)	)	PUNCT
ejpam-3335	374	1	⊂	⊂	PROPN
ejpam-3335	374	2	hh(0	hh(0	NOUN
ejpam-3335	374	3	)	)	PUNCT
ejpam-3335	374	4	=	=	SYM
ejpam-3335	374	5	ε	ε	PROPN
ejpam-3335	374	6	.	.	PUNCT
ejpam-3335	375	1	thus	thus	ADV
ejpam-3335	375	2	x	x	X
ejpam-3335	375	3	∈	∈	PROPN
ejpam-3335	375	4	l−(h	l−(h	PROPN
ejpam-3335	375	5	;	;	PUNCT
ejpam-3335	375	6	ε	ε	PROPN
ejpam-3335	375	7	)	)	PUNCT
ejpam-3335	375	8	6=	6=	ADP
ejpam-3335	375	9	∅.	∅.	ADP
ejpam-3335	375	10	by	by	ADP
ejpam-3335	375	11	assumption	assumption	NOUN
ejpam-3335	375	12	,	,	PUNCT
ejpam-3335	375	13	we	we	PRON
ejpam-3335	375	14	have	have	VERB
ejpam-3335	375	15	l−(h	l−(h	PROPN
ejpam-3335	375	16	;	;	PUNCT
ejpam-3335	375	17	ε	ε	PROPN
ejpam-3335	375	18	)	)	PUNCT
ejpam-3335	375	19	is	be	AUX
ejpam-3335	375	20	a	a	DET
ejpam-3335	375	21	upfilter	upfilter	NOUN
ejpam-3335	375	22	of	of	ADP
ejpam-3335	375	23	a	a	DET
ejpam-3335	375	24	and	and	CCONJ
ejpam-3335	375	25	so	so	ADV
ejpam-3335	375	26	0	0	NUM
ejpam-3335	375	27	∈	∈	PROPN
ejpam-3335	375	28	l−(h	l−(h	PROPN
ejpam-3335	375	29	;	;	PUNCT
ejpam-3335	375	30	ε	ε	PROPN
ejpam-3335	375	31	)	)	PUNCT
ejpam-3335	375	32	.	.	PUNCT
ejpam-3335	376	1	therefore	therefore	ADV
ejpam-3335	376	2	,	,	PUNCT
ejpam-3335	376	3	hh(0	hh(0	NOUN
ejpam-3335	376	4	)	)	PUNCT
ejpam-3335	376	5	⊂	⊂	PROPN
ejpam-3335	376	6	ε	ε	PROPN
ejpam-3335	376	7	=	=	PUNCT
ejpam-3335	376	8	hh(0	hh(0	NOUN
ejpam-3335	376	9	)	)	PUNCT
ejpam-3335	376	10	,	,	PUNCT
ejpam-3335	376	11	a	a	DET
ejpam-3335	376	12	contradiction	contradiction	NOUN
ejpam-3335	376	13	.	.	PUNCT
ejpam-3335	377	1	hence	hence	ADV
ejpam-3335	377	2	,	,	PUNCT
ejpam-3335	377	3	hh(0	hh(0	NOUN
ejpam-3335	377	4	)	)	PUNCT
ejpam-3335	377	5	⊆	⊆	NUM
ejpam-3335	377	6	hh(x	hh(x	NOUN
ejpam-3335	377	7	)	)	PUNCT
ejpam-3335	377	8	for	for	ADP
ejpam-3335	377	9	all	all	DET
ejpam-3335	377	10	x	x	SYM
ejpam-3335	377	11	∈	∈	PROPN
ejpam-3335	377	12	a.	a.	NOUN
ejpam-3335	377	13	p.	p.	NOUN
ejpam-3335	377	14	mosrijai	mosrijai	PROPN
ejpam-3335	377	15	,	,	PUNCT
ejpam-3335	377	16	a.	a.	NOUN
ejpam-3335	377	17	iampan	iampan	PROPN
ejpam-3335	377	18	/	/	SYM
ejpam-3335	377	19	eur	eur	PROPN
ejpam-3335	377	20	.	.	PUNCT
ejpam-3335	378	1	j.	j.	PROPN
ejpam-3335	378	2	pure	pure	PROPN
ejpam-3335	378	3	appl	appl	PROPN
ejpam-3335	378	4	.	.	PROPN
ejpam-3335	378	5	math	math	PROPN
ejpam-3335	378	6	,	,	PUNCT
ejpam-3335	378	7	11	11	NUM
ejpam-3335	378	8	(	(	PUNCT
ejpam-3335	378	9	4	4	NUM
ejpam-3335	378	10	)	)	PUNCT
ejpam-3335	378	11	(	(	PUNCT
ejpam-3335	378	12	2018	2018	NUM
ejpam-3335	378	13	)	)	PUNCT
ejpam-3335	378	14	,	,	PUNCT
ejpam-3335	378	15	976	976	NUM
ejpam-3335	378	16	-	-	SYM
ejpam-3335	378	17	1002	1002	NUM
ejpam-3335	378	18	989	989	NUM
ejpam-3335	378	19	next	next	ADV
ejpam-3335	378	20	,	,	PUNCT
ejpam-3335	378	21	assume	assume	VERB
ejpam-3335	378	22	that	that	SCONJ
ejpam-3335	378	23	there	there	PRON
ejpam-3335	378	24	exist	exist	VERB
ejpam-3335	378	25	x	x	NOUN
ejpam-3335	378	26	,	,	PUNCT
ejpam-3335	378	27	y	y	PROPN
ejpam-3335	378	28	∈	∈	PROPN
ejpam-3335	378	29	a	a	DET
ejpam-3335	378	30	such	such	ADJ
ejpam-3335	378	31	that	that	PRON
ejpam-3335	378	32	hh(y	hh(y	NOUN
ejpam-3335	378	33	)	)	PUNCT
ejpam-3335	378	34	*	*	PUNCT
ejpam-3335	378	35	hh(x	hh(x	X
ejpam-3335	378	36	·	·	PUNCT
ejpam-3335	378	37	y	y	X
ejpam-3335	378	38	)	)	PUNCT
ejpam-3335	378	39	∪	∪	ADP
ejpam-3335	378	40	hh(x	hh(x	NOUN
ejpam-3335	378	41	)	)	PUNCT
ejpam-3335	378	42	.	.	PUNCT
ejpam-3335	379	1	since	since	SCONJ
ejpam-3335	379	2	im(h	im(h	NOUN
ejpam-3335	379	3	)	)	PUNCT
ejpam-3335	379	4	is	be	AUX
ejpam-3335	379	5	a	a	DET
ejpam-3335	379	6	chain	chain	NOUN
ejpam-3335	379	7	,	,	PUNCT
ejpam-3335	379	8	we	we	PRON
ejpam-3335	379	9	have	have	VERB
ejpam-3335	379	10	hh(y	hh(y	NOUN
ejpam-3335	379	11	)	)	PUNCT
ejpam-3335	379	12	⊃	⊃	NOUN
ejpam-3335	379	13	hh(x	hh(x	X
ejpam-3335	379	14	·	·	PUNCT
ejpam-3335	379	15	y	y	X
ejpam-3335	379	16	)	)	PUNCT
ejpam-3335	379	17	∪	∪	ADP
ejpam-3335	379	18	hh(x	hh(x	NOUN
ejpam-3335	379	19	)	)	PUNCT
ejpam-3335	379	20	.	.	PUNCT
ejpam-3335	380	1	choose	choose	VERB
ejpam-3335	380	2	ε	ε	PROPN
ejpam-3335	380	3	=	=	SYM
ejpam-3335	380	4	hh(y	hh(y	X
ejpam-3335	380	5	)	)	PUNCT
ejpam-3335	380	6	∈	∈	NOUN
ejpam-3335	380	7	p([0	p([0	NOUN
ejpam-3335	380	8	,	,	PUNCT
ejpam-3335	380	9	1	1	NUM
ejpam-3335	380	10	]	]	NUM
ejpam-3335	380	11	)	)	PUNCT
ejpam-3335	380	12	.	.	PUNCT
ejpam-3335	381	1	then	then	ADV
ejpam-3335	381	2	hh(x	hh(x	PUNCT
ejpam-3335	381	3	·	·	PUNCT
ejpam-3335	381	4	y	y	X
ejpam-3335	381	5	)	)	PUNCT
ejpam-3335	381	6	⊂	⊂	PROPN
ejpam-3335	381	7	ε	ε	PROPN
ejpam-3335	381	8	and	and	CCONJ
ejpam-3335	381	9	hh(x	hh(x	PUNCT
ejpam-3335	381	10	)	)	PUNCT
ejpam-3335	382	1	⊂	⊂	PROPN
ejpam-3335	382	2	ε	ε	PROPN
ejpam-3335	382	3	.	.	PUNCT
ejpam-3335	382	4	thus	thus	ADV
ejpam-3335	382	5	x	x	X
ejpam-3335	382	6	·	·	PUNCT
ejpam-3335	382	7	y	y	X
ejpam-3335	382	8	,	,	PUNCT
ejpam-3335	382	9	x	x	SYM
ejpam-3335	382	10	∈	∈	PROPN
ejpam-3335	382	11	l−(h	l−(h	PROPN
ejpam-3335	382	12	;	;	PUNCT
ejpam-3335	382	13	ε	ε	PROPN
ejpam-3335	382	14	)	)	PUNCT
ejpam-3335	382	15	6=	6=	ADP
ejpam-3335	382	16	∅.	∅.	ADP
ejpam-3335	382	17	by	by	ADP
ejpam-3335	382	18	assumption	assumption	NOUN
ejpam-3335	382	19	,	,	PUNCT
ejpam-3335	382	20	we	we	PRON
ejpam-3335	382	21	have	have	VERB
ejpam-3335	382	22	l−(h	l−(h	PROPN
ejpam-3335	382	23	;	;	PUNCT
ejpam-3335	382	24	ε	ε	PROPN
ejpam-3335	382	25	)	)	PUNCT
ejpam-3335	382	26	is	be	AUX
ejpam-3335	382	27	a	a	DET
ejpam-3335	382	28	up	up	ADJ
ejpam-3335	382	29	-	-	PUNCT
ejpam-3335	382	30	filter	filter	NOUN
ejpam-3335	382	31	of	of	ADP
ejpam-3335	382	32	a	a	PRON
ejpam-3335	382	33	and	and	CCONJ
ejpam-3335	382	34	so	so	ADV
ejpam-3335	382	35	y	y	PROPN
ejpam-3335	382	36	∈	∈	PROPN
ejpam-3335	382	37	l−(h	l−(h	PROPN
ejpam-3335	382	38	;	;	PUNCT
ejpam-3335	382	39	ε	ε	PROPN
ejpam-3335	382	40	)	)	PUNCT
ejpam-3335	382	41	.	.	PUNCT
ejpam-3335	383	1	thus	thus	ADV
ejpam-3335	383	2	hh(y	hh(y	NOUN
ejpam-3335	383	3	)	)	PUNCT
ejpam-3335	383	4	⊂	⊂	PROPN
ejpam-3335	383	5	ε	ε	PROPN
ejpam-3335	383	6	=	=	PUNCT
ejpam-3335	383	7	hh(y	hh(y	X
ejpam-3335	383	8	)	)	PUNCT
ejpam-3335	383	9	,	,	PUNCT
ejpam-3335	383	10	a	a	DET
ejpam-3335	383	11	contradiction	contradiction	NOUN
ejpam-3335	383	12	.	.	PUNCT
ejpam-3335	384	1	therefore	therefore	ADV
ejpam-3335	384	2	,	,	PUNCT
ejpam-3335	384	3	hh(y	hh(y	ADJ
ejpam-3335	384	4	)	)	PUNCT
ejpam-3335	384	5	⊆	⊆	NUM
ejpam-3335	384	6	hh(x	hh(x	X
ejpam-3335	384	7	·	·	PUNCT
ejpam-3335	384	8	y	y	X
ejpam-3335	384	9	)	)	PUNCT
ejpam-3335	384	10	∪	∪	ADP
ejpam-3335	384	11	hh(x	hh(x	NOUN
ejpam-3335	384	12	)	)	PUNCT
ejpam-3335	384	13	for	for	ADP
ejpam-3335	384	14	all	all	DET
ejpam-3335	384	15	x	x	NOUN
ejpam-3335	384	16	,	,	PUNCT
ejpam-3335	384	17	y	y	PROPN
ejpam-3335	384	18	∈	∈	PROPN
ejpam-3335	384	19	a.	a.	NOUN
ejpam-3335	384	20	hence	hence	ADV
ejpam-3335	384	21	,	,	PUNCT
ejpam-3335	384	22	h	h	PROPN
ejpam-3335	384	23	is	be	AUX
ejpam-3335	384	24	an	an	DET
ejpam-3335	384	25	anti	anti	ADJ
ejpam-3335	384	26	-	-	ADJ
ejpam-3335	384	27	hesitant	hesitant	ADJ
ejpam-3335	384	28	fuzzy	fuzzy	ADJ
ejpam-3335	384	29	up	up	NOUN
ejpam-3335	384	30	-	-	PUNCT
ejpam-3335	384	31	filter	filter	NOUN
ejpam-3335	384	32	of	of	ADP
ejpam-3335	384	33	a.	a.	NOUN
ejpam-3335	384	34	example	example	NOUN
ejpam-3335	385	1	9	9	NUM
ejpam-3335	385	2	.	.	PUNCT
ejpam-3335	386	1	let	let	VERB
ejpam-3335	386	2	a	a	PRON
ejpam-3335	386	3	=	=	PUNCT
ejpam-3335	386	4	{	{	PUNCT
ejpam-3335	386	5	0	0	NUM
ejpam-3335	386	6	,	,	PUNCT
ejpam-3335	386	7	1	1	NUM
ejpam-3335	386	8	,	,	PUNCT
ejpam-3335	386	9	2	2	NUM
ejpam-3335	386	10	,	,	PUNCT
ejpam-3335	386	11	3	3	NUM
ejpam-3335	386	12	,	,	PUNCT
ejpam-3335	386	13	4	4	NUM
ejpam-3335	386	14	}	}	PUNCT
ejpam-3335	386	15	be	be	AUX
ejpam-3335	386	16	a	a	DET
ejpam-3335	386	17	set	set	NOUN
ejpam-3335	386	18	with	with	ADP
ejpam-3335	386	19	a	a	DET
ejpam-3335	386	20	binary	binary	ADJ
ejpam-3335	386	21	operation	operation	NOUN
ejpam-3335	386	22	·	·	PUNCT
ejpam-3335	386	23	defined	define	VERB
ejpam-3335	386	24	by	by	ADP
ejpam-3335	386	25	the	the	DET
ejpam-3335	386	26	following	following	ADJ
ejpam-3335	386	27	cayley	cayley	ADJ
ejpam-3335	386	28	table	table	NOUN
ejpam-3335	386	29	:	:	PUNCT
ejpam-3335	386	30	·	·	PUNCT
ejpam-3335	386	31	0	0	NUM
ejpam-3335	387	1	1	1	NUM
ejpam-3335	387	2	2	2	NUM
ejpam-3335	387	3	3	3	NUM
ejpam-3335	387	4	4	4	NUM
ejpam-3335	387	5	0	0	NUM
ejpam-3335	387	6	0	0	NUM
ejpam-3335	387	7	1	1	NUM
ejpam-3335	387	8	2	2	NUM
ejpam-3335	387	9	3	3	NUM
ejpam-3335	387	10	4	4	NUM
ejpam-3335	387	11	1	1	NUM
ejpam-3335	387	12	0	0	NUM
ejpam-3335	387	13	0	0	NUM
ejpam-3335	387	14	1	1	NUM
ejpam-3335	387	15	3	3	NUM
ejpam-3335	387	16	4	4	NUM
ejpam-3335	387	17	2	2	NUM
ejpam-3335	387	18	0	0	NUM
ejpam-3335	387	19	0	0	NUM
ejpam-3335	387	20	0	0	NUM
ejpam-3335	387	21	3	3	NUM
ejpam-3335	387	22	4	4	NUM
ejpam-3335	387	23	3	3	NUM
ejpam-3335	387	24	0	0	NUM
ejpam-3335	387	25	0	0	NUM
ejpam-3335	387	26	0	0	NUM
ejpam-3335	387	27	0	0	NUM
ejpam-3335	387	28	4	4	NUM
ejpam-3335	387	29	4	4	NUM
ejpam-3335	387	30	0	0	NUM
ejpam-3335	387	31	0	0	NUM
ejpam-3335	387	32	0	0	NUM
ejpam-3335	387	33	0	0	NUM
ejpam-3335	387	34	0	0	NUM
ejpam-3335	388	1	then	then	ADV
ejpam-3335	388	2	(	(	PUNCT
ejpam-3335	388	3	a	a	PRON
ejpam-3335	388	4	,	,	PUNCT
ejpam-3335	388	5	·	·	PUNCT
ejpam-3335	388	6	,	,	PUNCT
ejpam-3335	388	7	0	0	NUM
ejpam-3335	388	8	)	)	PUNCT
ejpam-3335	388	9	is	be	AUX
ejpam-3335	388	10	a	a	DET
ejpam-3335	388	11	up	up	NOUN
ejpam-3335	388	12	-	-	PUNCT
ejpam-3335	388	13	algebra	algebra	NOUN
ejpam-3335	388	14	.	.	PUNCT
ejpam-3335	389	1	we	we	PRON
ejpam-3335	389	2	define	define	VERB
ejpam-3335	389	3	a	a	DET
ejpam-3335	389	4	hesitant	hesitant	ADJ
ejpam-3335	389	5	fuzzy	fuzzy	ADJ
ejpam-3335	389	6	set	set	VERB
ejpam-3335	389	7	h	h	NOUN
ejpam-3335	389	8	on	on	ADP
ejpam-3335	389	9	a	a	DET
ejpam-3335	389	10	as	as	SCONJ
ejpam-3335	389	11	follows	follow	VERB
ejpam-3335	389	12	:	:	PUNCT
ejpam-3335	389	13	hh(0	hh(0	NOUN
ejpam-3335	389	14	)	)	PUNCT
ejpam-3335	389	15	=	=	SYM
ejpam-3335	389	16	(	(	PUNCT
ejpam-3335	389	17	0	0	NUM
ejpam-3335	389	18	,	,	PUNCT
ejpam-3335	389	19	1),hh(1	1),hh(1	NUM
ejpam-3335	389	20	)	)	PUNCT
ejpam-3335	389	21	=	=	PUNCT
ejpam-3335	390	1	[	[	X
ejpam-3335	390	2	0	0	NUM
ejpam-3335	390	3	,	,	PUNCT
ejpam-3335	390	4	1	1	NUM
ejpam-3335	390	5	)	)	PUNCT
ejpam-3335	390	6	,	,	PUNCT
ejpam-3335	390	7	hh(2	hh(2	NOUN
ejpam-3335	390	8	)	)	PUNCT
ejpam-3335	390	9	=	=	SYM
ejpam-3335	390	10	(	(	PUNCT
ejpam-3335	390	11	0	0	NUM
ejpam-3335	390	12	,	,	PUNCT
ejpam-3335	390	13	1	1	NUM
ejpam-3335	390	14	]	]	PUNCT
ejpam-3335	390	15	,	,	PUNCT
ejpam-3335	390	16	hh(3	hh(3	NOUN
ejpam-3335	390	17	)	)	PUNCT
ejpam-3335	391	1	=	=	PUNCT
ejpam-3335	392	1	[	[	X
ejpam-3335	392	2	0	0	NUM
ejpam-3335	392	3	,	,	PUNCT
ejpam-3335	392	4	1	1	NUM
ejpam-3335	392	5	]	]	PUNCT
ejpam-3335	392	6	,	,	PUNCT
ejpam-3335	392	7	and	and	CCONJ
ejpam-3335	392	8	hh(4	hh(4	NOUN
ejpam-3335	392	9	)	)	PUNCT
ejpam-3335	392	10	=	=	PUNCT
ejpam-3335	393	1	[	[	X
ejpam-3335	393	2	0	0	NUM
ejpam-3335	393	3	,	,	PUNCT
ejpam-3335	393	4	1	1	NUM
ejpam-3335	393	5	]	]	PUNCT
ejpam-3335	393	6	.	.	PUNCT
ejpam-3335	394	1	then	then	ADV
ejpam-3335	394	2	im(h	im(h	NOUN
ejpam-3335	394	3	)	)	PUNCT
ejpam-3335	394	4	is	be	AUX
ejpam-3335	394	5	not	not	PART
ejpam-3335	394	6	a	a	DET
ejpam-3335	394	7	chain	chain	NOUN
ejpam-3335	394	8	.	.	PUNCT
ejpam-3335	395	1	if	if	SCONJ
ejpam-3335	395	2	ε	ε	PROPN
ejpam-3335	395	3	⊆	⊆	NUM
ejpam-3335	395	4	(	(	PUNCT
ejpam-3335	395	5	0	0	NUM
ejpam-3335	395	6	,	,	PUNCT
ejpam-3335	395	7	1	1	NUM
ejpam-3335	395	8	)	)	PUNCT
ejpam-3335	395	9	,	,	PUNCT
ejpam-3335	395	10	then	then	ADV
ejpam-3335	395	11	l−(h	l−(h	PROPN
ejpam-3335	395	12	;	;	PUNCT
ejpam-3335	395	13	ε	ε	PROPN
ejpam-3335	395	14	)	)	PUNCT
ejpam-3335	395	15	=	=	PUNCT
ejpam-3335	395	16	∅.	∅.	NOUN
ejpam-3335	395	17	if	if	SCONJ
ejpam-3335	395	18	ε	ε	PROPN
ejpam-3335	395	19	=	=	PUNCT
ejpam-3335	396	1	[	[	X
ejpam-3335	396	2	0	0	NUM
ejpam-3335	396	3	,	,	PUNCT
ejpam-3335	396	4	1	1	NUM
ejpam-3335	396	5	)	)	PUNCT
ejpam-3335	396	6	or	or	CCONJ
ejpam-3335	396	7	ε	ε	PROPN
ejpam-3335	396	8	=	=	SYM
ejpam-3335	396	9	(	(	PUNCT
ejpam-3335	396	10	0	0	NUM
ejpam-3335	396	11	,	,	PUNCT
ejpam-3335	396	12	1	1	NUM
ejpam-3335	396	13	]	]	PUNCT
ejpam-3335	396	14	,	,	PUNCT
ejpam-3335	396	15	then	then	ADV
ejpam-3335	396	16	l−(h	l−(h	PROPN
ejpam-3335	396	17	;	;	PUNCT
ejpam-3335	396	18	ε	ε	PROPN
ejpam-3335	396	19	)	)	PUNCT
ejpam-3335	396	20	=	=	PUNCT
ejpam-3335	396	21	{	{	PUNCT
ejpam-3335	396	22	0	0	NUM
ejpam-3335	396	23	}	}	PUNCT
ejpam-3335	396	24	.	.	PUNCT
ejpam-3335	397	1	if	if	SCONJ
ejpam-3335	397	2	ε	ε	PROPN
ejpam-3335	397	3	=	=	PUNCT
ejpam-3335	398	1	[	[	X
ejpam-3335	398	2	0	0	NUM
ejpam-3335	398	3	,	,	PUNCT
ejpam-3335	398	4	1	1	NUM
ejpam-3335	398	5	]	]	PUNCT
ejpam-3335	398	6	,	,	PUNCT
ejpam-3335	398	7	then	then	ADV
ejpam-3335	398	8	l−(h	l−(h	PROPN
ejpam-3335	398	9	;	;	PUNCT
ejpam-3335	398	10	ε	ε	PROPN
ejpam-3335	398	11	)	)	PUNCT
ejpam-3335	398	12	=	=	SYM
ejpam-3335	398	13	{	{	PUNCT
ejpam-3335	398	14	0	0	NUM
ejpam-3335	398	15	,	,	PUNCT
ejpam-3335	398	16	1	1	NUM
ejpam-3335	398	17	,	,	PUNCT
ejpam-3335	398	18	2	2	NUM
ejpam-3335	398	19	}	}	PUNCT
ejpam-3335	398	20	.	.	PUNCT
ejpam-3335	399	1	using	use	VERB
ejpam-3335	399	2	this	this	DET
ejpam-3335	399	3	data	datum	NOUN
ejpam-3335	399	4	,	,	PUNCT
ejpam-3335	399	5	we	we	PRON
ejpam-3335	399	6	can	can	AUX
ejpam-3335	399	7	show	show	VERB
ejpam-3335	399	8	that	that	SCONJ
ejpam-3335	399	9	all	all	DET
ejpam-3335	399	10	nonempty	nonempty	ADV
ejpam-3335	399	11	subset	subset	VERB
ejpam-3335	399	12	l−(h	l−(h	PROPN
ejpam-3335	399	13	;	;	PUNCT
ejpam-3335	399	14	ε	ε	PROPN
ejpam-3335	399	15	)	)	PUNCT
ejpam-3335	399	16	of	of	ADP
ejpam-3335	399	17	a	a	PRON
ejpam-3335	399	18	is	be	AUX
ejpam-3335	399	19	a	a	DET
ejpam-3335	399	20	up	up	ADJ
ejpam-3335	399	21	-	-	PUNCT
ejpam-3335	399	22	filter	filter	NOUN
ejpam-3335	399	23	of	of	ADP
ejpam-3335	399	24	a.	a.	NOUN
ejpam-3335	399	25	since	since	SCONJ
ejpam-3335	399	26	hh(2	hh(2	NOUN
ejpam-3335	399	27	)	)	PUNCT
ejpam-3335	399	28	=	=	PUNCT
ejpam-3335	399	29	(	(	PUNCT
ejpam-3335	399	30	0	0	NUM
ejpam-3335	399	31	,	,	PUNCT
ejpam-3335	399	32	1	1	NUM
ejpam-3335	399	33	]	]	PUNCT
ejpam-3335	399	34	*	*	PUNCT
ejpam-3335	400	1	[	[	X
ejpam-3335	400	2	0	0	NUM
ejpam-3335	400	3	,	,	PUNCT
ejpam-3335	400	4	1	1	NUM
ejpam-3335	400	5	)	)	PUNCT
ejpam-3335	400	6	=	=	PUNCT
ejpam-3335	400	7	hh(1	hh(1	NOUN
ejpam-3335	400	8	)	)	PUNCT
ejpam-3335	400	9	∪	∪	ADP
ejpam-3335	400	10	hh(1	hh(1	NOUN
ejpam-3335	400	11	)	)	PUNCT
ejpam-3335	400	12	=	=	PUNCT
ejpam-3335	401	1	hh(1	hh(1	NOUN
ejpam-3335	401	2	·	·	PUNCT
ejpam-3335	401	3	2	2	X
ejpam-3335	401	4	)	)	PUNCT
ejpam-3335	401	5	∪	∪	ADP
ejpam-3335	401	6	hh(1	hh(1	PROPN
ejpam-3335	401	7	)	)	PUNCT
ejpam-3335	401	8	,	,	PUNCT
ejpam-3335	401	9	we	we	PRON
ejpam-3335	401	10	have	have	VERB
ejpam-3335	401	11	h	h	NOUN
ejpam-3335	401	12	is	be	AUX
ejpam-3335	401	13	not	not	PART
ejpam-3335	401	14	an	an	DET
ejpam-3335	401	15	anti	anti	ADJ
ejpam-3335	401	16	-	-	ADJ
ejpam-3335	401	17	hesitant	hesitant	ADJ
ejpam-3335	401	18	fuzzy	fuzzy	ADJ
ejpam-3335	401	19	up	up	NOUN
ejpam-3335	401	20	-	-	PUNCT
ejpam-3335	401	21	filter	filter	NOUN
ejpam-3335	401	22	of	of	ADP
ejpam-3335	401	23	a.	a.	NOUN
ejpam-3335	401	24	theorem	theorem	NOUN
ejpam-3335	401	25	13	13	NUM
ejpam-3335	401	26	.	.	PUNCT
ejpam-3335	402	1	let	let	VERB
ejpam-3335	402	2	h	h	PRON
ejpam-3335	402	3	be	be	AUX
ejpam-3335	402	4	a	a	DET
ejpam-3335	402	5	hesitant	hesitant	ADJ
ejpam-3335	402	6	fuzzy	fuzzy	ADJ
ejpam-3335	402	7	set	set	NOUN
ejpam-3335	402	8	on	on	ADP
ejpam-3335	402	9	a.	a.	NOUN
ejpam-3335	402	10	then	then	ADV
ejpam-3335	402	11	the	the	DET
ejpam-3335	402	12	following	follow	VERB
ejpam-3335	402	13	statements	statement	NOUN
ejpam-3335	402	14	hold	hold	VERB
ejpam-3335	402	15	:	:	PUNCT
ejpam-3335	402	16	(	(	PUNCT
ejpam-3335	402	17	1	1	X
ejpam-3335	402	18	)	)	PUNCT
ejpam-3335	402	19	if	if	SCONJ
ejpam-3335	402	20	h	h	NOUN
ejpam-3335	402	21	is	be	AUX
ejpam-3335	402	22	an	an	DET
ejpam-3335	402	23	anti	anti	ADJ
ejpam-3335	402	24	-	-	ADJ
ejpam-3335	402	25	hesitant	hesitant	ADJ
ejpam-3335	402	26	fuzzy	fuzzy	ADJ
ejpam-3335	402	27	up	up	NOUN
ejpam-3335	402	28	-	-	PUNCT
ejpam-3335	402	29	ideal	ideal	NOUN
ejpam-3335	402	30	of	of	ADP
ejpam-3335	402	31	a	a	PRON
ejpam-3335	402	32	,	,	PUNCT
ejpam-3335	402	33	then	then	ADV
ejpam-3335	402	34	for	for	ADP
ejpam-3335	402	35	all	all	DET
ejpam-3335	402	36	ε	ε	PROPN
ejpam-3335	402	37	∈	∈	PROPN
ejpam-3335	402	38	p([0	p([0	NOUN
ejpam-3335	402	39	,	,	PUNCT
ejpam-3335	402	40	1	1	NUM
ejpam-3335	402	41	]	]	NUM
ejpam-3335	402	42	)	)	PUNCT
ejpam-3335	402	43	,	,	PUNCT
ejpam-3335	402	44	l−(h	l−(h	PROPN
ejpam-3335	402	45	;	;	PUNCT
ejpam-3335	402	46	ε	ε	PROPN
ejpam-3335	402	47	)	)	PUNCT
ejpam-3335	402	48	is	be	AUX
ejpam-3335	402	49	a	a	DET
ejpam-3335	402	50	up	up	ADJ
ejpam-3335	402	51	-	-	PUNCT
ejpam-3335	402	52	ideal	ideal	NOUN
ejpam-3335	402	53	of	of	ADP
ejpam-3335	402	54	a	a	DET
ejpam-3335	402	55	if	if	SCONJ
ejpam-3335	402	56	l−(h	l−(h	PROPN
ejpam-3335	402	57	;	;	PUNCT
ejpam-3335	402	58	ε	ε	PROPN
ejpam-3335	402	59	)	)	PUNCT
ejpam-3335	402	60	is	be	AUX
ejpam-3335	402	61	nonempty	nonempty	ADJ
ejpam-3335	402	62	,	,	PUNCT
ejpam-3335	402	63	and	and	CCONJ
ejpam-3335	402	64	(	(	PUNCT
ejpam-3335	402	65	2	2	X
ejpam-3335	402	66	)	)	PUNCT
ejpam-3335	402	67	if	if	SCONJ
ejpam-3335	402	68	im(h	im(h	NOUN
ejpam-3335	402	69	)	)	PUNCT
ejpam-3335	402	70	is	be	AUX
ejpam-3335	402	71	a	a	DET
ejpam-3335	402	72	chain	chain	NOUN
ejpam-3335	402	73	and	and	CCONJ
ejpam-3335	402	74	for	for	ADP
ejpam-3335	402	75	all	all	DET
ejpam-3335	402	76	ε	ε	PROPN
ejpam-3335	402	77	∈	∈	PROPN
ejpam-3335	402	78	p([0	p([0	NOUN
ejpam-3335	402	79	,	,	PUNCT
ejpam-3335	402	80	1	1	NUM
ejpam-3335	402	81	]	]	NUM
ejpam-3335	402	82	)	)	PUNCT
ejpam-3335	402	83	,	,	PUNCT
ejpam-3335	402	84	a	a	DET
ejpam-3335	402	85	nonempty	nonempty	NOUN
ejpam-3335	402	86	subset	subset	VERB
ejpam-3335	402	87	l−(h	l−(h	PROPN
ejpam-3335	402	88	;	;	PUNCT
ejpam-3335	402	89	ε	ε	PROPN
ejpam-3335	402	90	)	)	PUNCT
ejpam-3335	402	91	of	of	ADP
ejpam-3335	402	92	a	a	PRON
ejpam-3335	402	93	is	be	AUX
ejpam-3335	402	94	a	a	DET
ejpam-3335	402	95	up	up	ADJ
ejpam-3335	402	96	-	-	PUNCT
ejpam-3335	402	97	ideal	ideal	NOUN
ejpam-3335	402	98	of	of	ADP
ejpam-3335	402	99	a	a	PRON
ejpam-3335	402	100	,	,	PUNCT
ejpam-3335	402	101	then	then	ADV
ejpam-3335	402	102	h	h	PROPN
ejpam-3335	402	103	is	be	AUX
ejpam-3335	402	104	an	an	DET
ejpam-3335	402	105	anti	anti	ADJ
ejpam-3335	402	106	-	-	ADJ
ejpam-3335	402	107	hesitant	hesitant	ADJ
ejpam-3335	402	108	fuzzy	fuzzy	ADJ
ejpam-3335	402	109	up	up	NOUN
ejpam-3335	402	110	-	-	PUNCT
ejpam-3335	402	111	ideal	ideal	NOUN
ejpam-3335	402	112	of	of	ADP
ejpam-3335	402	113	a.	a.	NOUN
ejpam-3335	402	114	proof	proof	NOUN
ejpam-3335	402	115	.	.	PUNCT
ejpam-3335	403	1	(	(	PUNCT
ejpam-3335	403	2	1	1	X
ejpam-3335	403	3	)	)	PUNCT
ejpam-3335	403	4	assume	assume	VERB
ejpam-3335	403	5	that	that	SCONJ
ejpam-3335	403	6	h	h	NOUN
ejpam-3335	403	7	is	be	AUX
ejpam-3335	403	8	an	an	DET
ejpam-3335	403	9	anti	anti	ADJ
ejpam-3335	403	10	-	-	ADJ
ejpam-3335	403	11	hesitant	hesitant	ADJ
ejpam-3335	403	12	fuzzy	fuzzy	ADJ
ejpam-3335	403	13	up	up	NOUN
ejpam-3335	403	14	-	-	PUNCT
ejpam-3335	403	15	ideal	ideal	NOUN
ejpam-3335	403	16	of	of	ADP
ejpam-3335	403	17	a.	a.	NOUN
ejpam-3335	403	18	let	let	VERB
ejpam-3335	403	19	ε	ε	PROPN
ejpam-3335	403	20	∈	∈	PROPN
ejpam-3335	403	21	p([0	p([0	PROPN
ejpam-3335	403	22	,	,	PUNCT
ejpam-3335	403	23	1	1	NUM
ejpam-3335	403	24	]	]	PUNCT
ejpam-3335	403	25	)	)	PUNCT
ejpam-3335	403	26	be	be	AUX
ejpam-3335	403	27	such	such	ADJ
ejpam-3335	403	28	that	that	SCONJ
ejpam-3335	403	29	l−(h	l−(h	PROPN
ejpam-3335	403	30	;	;	PUNCT
ejpam-3335	403	31	ε	ε	PROPN
ejpam-3335	403	32	)	)	PUNCT
ejpam-3335	403	33	6=	6=	NOUN
ejpam-3335	403	34	∅	∅	NOUN
ejpam-3335	403	35	and	and	CCONJ
ejpam-3335	403	36	let	let	VERB
ejpam-3335	403	37	x	x	SYM
ejpam-3335	403	38	∈	∈	PROPN
ejpam-3335	403	39	a	a	DET
ejpam-3335	403	40	be	be	AUX
ejpam-3335	403	41	such	such	ADJ
ejpam-3335	403	42	that	that	SCONJ
ejpam-3335	403	43	x	x	SYM
ejpam-3335	403	44	∈	∈	PROPN
ejpam-3335	403	45	l−(h	l−(h	PROPN
ejpam-3335	403	46	;	;	PUNCT
ejpam-3335	403	47	ε	ε	PROPN
ejpam-3335	403	48	)	)	PUNCT
ejpam-3335	403	49	.	.	PUNCT
ejpam-3335	404	1	then	then	ADV
ejpam-3335	404	2	hh(x	hh(x	PUNCT
ejpam-3335	404	3	)	)	PUNCT
ejpam-3335	404	4	⊂	⊂	PROPN
ejpam-3335	404	5	ε	ε	AUX
ejpam-3335	404	6	.	.	PUNCT
ejpam-3335	404	7	since	since	SCONJ
ejpam-3335	404	8	h	h	NOUN
ejpam-3335	404	9	is	be	AUX
ejpam-3335	404	10	an	an	DET
ejpam-3335	404	11	anti	anti	ADJ
ejpam-3335	404	12	-	-	ADJ
ejpam-3335	404	13	hesitant	hesitant	ADJ
ejpam-3335	404	14	fuzzy	fuzzy	ADJ
ejpam-3335	404	15	up	up	NOUN
ejpam-3335	404	16	-	-	PUNCT
ejpam-3335	404	17	ideal	ideal	NOUN
ejpam-3335	404	18	of	of	ADP
ejpam-3335	404	19	a	a	PRON
ejpam-3335	404	20	,	,	PUNCT
ejpam-3335	404	21	we	we	PRON
ejpam-3335	404	22	have	have	VERB
ejpam-3335	404	23	hh(0	hh(0	NOUN
ejpam-3335	404	24	)	)	PUNCT
ejpam-3335	404	25	⊆	⊆	NUM
ejpam-3335	404	26	hh(x	hh(x	X
ejpam-3335	404	27	)	)	PUNCT
ejpam-3335	404	28	⊂	⊂	PROPN
ejpam-3335	404	29	ε	ε	PROPN
ejpam-3335	404	30	and	and	CCONJ
ejpam-3335	404	31	thus	thus	ADV
ejpam-3335	404	32	0	0	NUM
ejpam-3335	404	33	∈	∈	PROPN
ejpam-3335	404	34	l−(h	l−(h	PROPN
ejpam-3335	404	35	;	;	PUNCT
ejpam-3335	404	36	ε	ε	PROPN
ejpam-3335	404	37	)	)	PUNCT
ejpam-3335	404	38	.	.	PUNCT
ejpam-3335	405	1	next	next	ADV
ejpam-3335	405	2	,	,	PUNCT
ejpam-3335	405	3	let	let	VERB
ejpam-3335	405	4	x	x	PRON
ejpam-3335	405	5	,	,	PUNCT
ejpam-3335	405	6	y	y	PROPN
ejpam-3335	405	7	,	,	PUNCT
ejpam-3335	405	8	z	z	PROPN
ejpam-3335	405	9	∈	∈	PROPN
ejpam-3335	405	10	a	a	DET
ejpam-3335	405	11	be	be	AUX
ejpam-3335	405	12	such	such	ADJ
ejpam-3335	405	13	that	that	SCONJ
ejpam-3335	405	14	x	x	PART
ejpam-3335	405	15	·	·	PUNCT
ejpam-3335	405	16	(	(	PUNCT
ejpam-3335	405	17	y	y	PROPN
ejpam-3335	405	18	·	·	PUNCT
ejpam-3335	405	19	z	z	X
ejpam-3335	405	20	)	)	PUNCT
ejpam-3335	405	21	∈	∈	PROPN
ejpam-3335	405	22	l−(h	l−(h	PROPN
ejpam-3335	405	23	;	;	PUNCT
ejpam-3335	405	24	ε	ε	PROPN
ejpam-3335	405	25	)	)	PUNCT
ejpam-3335	405	26	and	and	CCONJ
ejpam-3335	405	27	y	y	PROPN
ejpam-3335	405	28	∈	∈	PROPN
ejpam-3335	405	29	l−(h	l−(h	PROPN
ejpam-3335	405	30	;	;	PUNCT
ejpam-3335	405	31	ε	ε	PROPN
ejpam-3335	405	32	)	)	PUNCT
ejpam-3335	405	33	.	.	PUNCT
ejpam-3335	406	1	then	then	ADV
ejpam-3335	406	2	hh(x	hh(x	PUNCT
ejpam-3335	406	3	·	·	PUNCT
ejpam-3335	406	4	(	(	PUNCT
ejpam-3335	406	5	y	y	PROPN
ejpam-3335	406	6	·	·	PUNCT
ejpam-3335	406	7	z	z	NOUN
ejpam-3335	406	8	)	)	PUNCT
ejpam-3335	406	9	)	)	PUNCT
ejpam-3335	407	1	⊂	⊂	PROPN
ejpam-3335	407	2	ε	ε	PROPN
ejpam-3335	407	3	and	and	CCONJ
ejpam-3335	407	4	hh(y	hh(y	NOUN
ejpam-3335	407	5	)	)	PUNCT
ejpam-3335	408	1	⊂	⊂	PROPN
ejpam-3335	408	2	ε	ε	PROPN
ejpam-3335	408	3	.	.	PUNCT
ejpam-3335	409	1	since	since	SCONJ
ejpam-3335	409	2	h	h	NOUN
ejpam-3335	409	3	is	be	AUX
ejpam-3335	409	4	an	an	DET
ejpam-3335	409	5	anti	anti	ADJ
ejpam-3335	409	6	-	-	ADJ
ejpam-3335	409	7	hesitant	hesitant	ADJ
ejpam-3335	409	8	fuzzy	fuzzy	ADJ
ejpam-3335	409	9	up	up	NOUN
ejpam-3335	409	10	-	-	PUNCT
ejpam-3335	409	11	ideal	ideal	NOUN
ejpam-3335	409	12	of	of	ADP
ejpam-3335	409	13	a	a	PRON
ejpam-3335	409	14	,	,	PUNCT
ejpam-3335	409	15	we	we	PRON
ejpam-3335	409	16	have	have	VERB
ejpam-3335	409	17	hh(x	hh(x	X
ejpam-3335	409	18	·	·	PUNCT
ejpam-3335	409	19	z	z	X
ejpam-3335	409	20	)	)	PUNCT
ejpam-3335	409	21	⊆	⊆	NUM
ejpam-3335	409	22	hh(x	hh(x	X
ejpam-3335	409	23	·	·	PUNCT
ejpam-3335	409	24	(	(	PUNCT
ejpam-3335	409	25	y	y	PROPN
ejpam-3335	409	26	·	·	PUNCT
ejpam-3335	409	27	z	z	NOUN
ejpam-3335	409	28	)	)	PUNCT
ejpam-3335	409	29	)	)	PUNCT
ejpam-3335	409	30	∪	∪	ADP
ejpam-3335	409	31	hh(y	hh(y	NOUN
ejpam-3335	409	32	)	)	PUNCT
ejpam-3335	409	33	⊂	⊂	PROPN
ejpam-3335	409	34	ε	ε	PROPN
ejpam-3335	409	35	and	and	CCONJ
ejpam-3335	409	36	thus	thus	ADV
ejpam-3335	409	37	x	x	X
ejpam-3335	409	38	·	·	PUNCT
ejpam-3335	409	39	z	z	X
ejpam-3335	409	40	∈	∈	PROPN
ejpam-3335	409	41	l−(h	l−(h	PROPN
ejpam-3335	409	42	;	;	PUNCT
ejpam-3335	409	43	ε	ε	PROPN
ejpam-3335	409	44	)	)	PUNCT
ejpam-3335	409	45	.	.	PUNCT
ejpam-3335	410	1	hence	hence	ADV
ejpam-3335	410	2	,	,	PUNCT
ejpam-3335	410	3	l−(h	l−(h	PROPN
ejpam-3335	410	4	;	;	PUNCT
ejpam-3335	410	5	ε	ε	PROPN
ejpam-3335	410	6	)	)	PUNCT
ejpam-3335	410	7	is	be	AUX
ejpam-3335	410	8	a	a	DET
ejpam-3335	410	9	up	up	ADJ
ejpam-3335	410	10	-	-	PUNCT
ejpam-3335	410	11	ideal	ideal	NOUN
ejpam-3335	410	12	of	of	ADP
ejpam-3335	410	13	a.	a.	NOUN
ejpam-3335	410	14	(	(	PUNCT
ejpam-3335	410	15	2	2	X
ejpam-3335	410	16	)	)	PUNCT
ejpam-3335	410	17	assume	assume	VERB
ejpam-3335	410	18	that	that	SCONJ
ejpam-3335	410	19	im(h	im(h	NOUN
ejpam-3335	410	20	)	)	PUNCT
ejpam-3335	410	21	is	be	AUX
ejpam-3335	410	22	a	a	DET
ejpam-3335	410	23	chain	chain	NOUN
ejpam-3335	410	24	and	and	CCONJ
ejpam-3335	410	25	for	for	ADP
ejpam-3335	410	26	all	all	DET
ejpam-3335	410	27	ε	ε	PROPN
ejpam-3335	410	28	∈	∈	PROPN
ejpam-3335	410	29	p([0	p([0	NOUN
ejpam-3335	410	30	,	,	PUNCT
ejpam-3335	410	31	1	1	NUM
ejpam-3335	410	32	]	]	NUM
ejpam-3335	410	33	)	)	PUNCT
ejpam-3335	410	34	,	,	PUNCT
ejpam-3335	410	35	a	a	DET
ejpam-3335	410	36	nonempty	nonempty	NOUN
ejpam-3335	410	37	subset	subset	VERB
ejpam-3335	410	38	l−(h	l−(h	PROPN
ejpam-3335	410	39	;	;	PUNCT
ejpam-3335	410	40	ε	ε	PROPN
ejpam-3335	410	41	)	)	PUNCT
ejpam-3335	410	42	of	of	ADP
ejpam-3335	410	43	a	a	PRON
ejpam-3335	410	44	is	be	AUX
ejpam-3335	410	45	a	a	DET
ejpam-3335	410	46	up	up	ADJ
ejpam-3335	410	47	-	-	PUNCT
ejpam-3335	410	48	ideal	ideal	NOUN
ejpam-3335	410	49	of	of	ADP
ejpam-3335	410	50	a.	a.	NOUN
ejpam-3335	410	51	assume	assume	VERB
ejpam-3335	410	52	that	that	SCONJ
ejpam-3335	410	53	there	there	PRON
ejpam-3335	410	54	exists	exist	VERB
ejpam-3335	410	55	x	x	X
ejpam-3335	410	56	∈	∈	PROPN
ejpam-3335	410	57	a	a	DET
ejpam-3335	410	58	such	such	ADJ
ejpam-3335	410	59	that	that	SCONJ
ejpam-3335	410	60	hh(0	hh(0	NOUN
ejpam-3335	410	61	)	)	PUNCT
ejpam-3335	410	62	*	*	PUNCT
ejpam-3335	410	63	hh(x	hh(x	X
ejpam-3335	410	64	)	)	PUNCT
ejpam-3335	410	65	.	.	PUNCT
ejpam-3335	411	1	since	since	SCONJ
ejpam-3335	411	2	im(h	im(h	NOUN
ejpam-3335	411	3	)	)	PUNCT
ejpam-3335	411	4	is	be	AUX
ejpam-3335	411	5	a	a	DET
ejpam-3335	411	6	chain	chain	NOUN
ejpam-3335	411	7	,	,	PUNCT
ejpam-3335	411	8	we	we	PRON
ejpam-3335	411	9	have	have	VERB
ejpam-3335	411	10	hh(0	hh(0	NOUN
ejpam-3335	411	11	)	)	PUNCT
ejpam-3335	411	12	⊃	⊃	NOUN
ejpam-3335	411	13	hh(x	hh(x	X
ejpam-3335	411	14	)	)	PUNCT
ejpam-3335	411	15	.	.	PUNCT
ejpam-3335	412	1	choose	choose	VERB
ejpam-3335	412	2	ε	ε	PROPN
ejpam-3335	412	3	=	=	SYM
ejpam-3335	412	4	hh(0	hh(0	PROPN
ejpam-3335	412	5	)	)	PUNCT
ejpam-3335	412	6	∈	∈	PROPN
ejpam-3335	412	7	p([0	p([0	NOUN
ejpam-3335	412	8	,	,	PUNCT
ejpam-3335	412	9	1	1	NUM
ejpam-3335	412	10	]	]	NUM
ejpam-3335	412	11	)	)	PUNCT
ejpam-3335	412	12	.	.	PUNCT
ejpam-3335	413	1	then	then	ADV
ejpam-3335	413	2	hh(x	hh(x	PUNCT
ejpam-3335	413	3	)	)	PUNCT
ejpam-3335	414	1	⊂	⊂	PROPN
ejpam-3335	414	2	hh(0	hh(0	NOUN
ejpam-3335	414	3	)	)	PUNCT
ejpam-3335	414	4	=	=	SYM
ejpam-3335	414	5	ε	ε	PROPN
ejpam-3335	414	6	.	.	PUNCT
ejpam-3335	415	1	thus	thus	ADV
ejpam-3335	415	2	x	x	X
ejpam-3335	415	3	∈	∈	PROPN
ejpam-3335	415	4	l−(h	l−(h	PROPN
ejpam-3335	415	5	;	;	PUNCT
ejpam-3335	415	6	ε	ε	PROPN
ejpam-3335	415	7	)	)	PUNCT
ejpam-3335	415	8	6=	6=	ADP
ejpam-3335	415	9	∅.	∅.	ADP
ejpam-3335	415	10	by	by	ADP
ejpam-3335	415	11	assumption	assumption	NOUN
ejpam-3335	415	12	,	,	PUNCT
ejpam-3335	415	13	we	we	PRON
ejpam-3335	415	14	have	have	VERB
ejpam-3335	415	15	l−(h	l−(h	PROPN
ejpam-3335	415	16	;	;	PUNCT
ejpam-3335	415	17	ε	ε	PROPN
ejpam-3335	415	18	)	)	PUNCT
ejpam-3335	415	19	is	be	AUX
ejpam-3335	415	20	a	a	DET
ejpam-3335	415	21	upideal	upideal	NOUN
ejpam-3335	415	22	of	of	ADP
ejpam-3335	415	23	a	a	DET
ejpam-3335	415	24	and	and	CCONJ
ejpam-3335	415	25	so	so	ADV
ejpam-3335	415	26	0	0	NUM
ejpam-3335	415	27	∈	∈	PROPN
ejpam-3335	415	28	l−(h	l−(h	PROPN
ejpam-3335	415	29	;	;	PUNCT
ejpam-3335	415	30	ε	ε	PROPN
ejpam-3335	415	31	)	)	PUNCT
ejpam-3335	415	32	.	.	PUNCT
ejpam-3335	416	1	therefore	therefore	ADV
ejpam-3335	416	2	,	,	PUNCT
ejpam-3335	416	3	hh(0	hh(0	NOUN
ejpam-3335	416	4	)	)	PUNCT
ejpam-3335	416	5	⊂	⊂	PROPN
ejpam-3335	416	6	ε	ε	PROPN
ejpam-3335	416	7	=	=	PUNCT
ejpam-3335	416	8	hh(0	hh(0	NOUN
ejpam-3335	416	9	)	)	PUNCT
ejpam-3335	416	10	,	,	PUNCT
ejpam-3335	416	11	a	a	DET
ejpam-3335	416	12	contradiction	contradiction	NOUN
ejpam-3335	416	13	.	.	PUNCT
ejpam-3335	417	1	hence	hence	ADV
ejpam-3335	417	2	,	,	PUNCT
ejpam-3335	417	3	hh(0	hh(0	NOUN
ejpam-3335	417	4	)	)	PUNCT
ejpam-3335	417	5	⊆	⊆	NUM
ejpam-3335	417	6	hh(x	hh(x	NOUN
ejpam-3335	417	7	)	)	PUNCT
ejpam-3335	417	8	for	for	ADP
ejpam-3335	417	9	all	all	DET
ejpam-3335	417	10	x	x	SYM
ejpam-3335	417	11	∈	∈	PROPN
ejpam-3335	417	12	a.	a.	NOUN
ejpam-3335	417	13	p.	p.	NOUN
ejpam-3335	417	14	mosrijai	mosrijai	PROPN
ejpam-3335	417	15	,	,	PUNCT
ejpam-3335	417	16	a.	a.	NOUN
ejpam-3335	417	17	iampan	iampan	PROPN
ejpam-3335	417	18	/	/	SYM
ejpam-3335	417	19	eur	eur	PROPN
ejpam-3335	417	20	.	.	PUNCT
ejpam-3335	418	1	j.	j.	PROPN
ejpam-3335	418	2	pure	pure	PROPN
ejpam-3335	418	3	appl	appl	PROPN
ejpam-3335	418	4	.	.	PROPN
ejpam-3335	418	5	math	math	PROPN
ejpam-3335	418	6	,	,	PUNCT
ejpam-3335	418	7	11	11	NUM
ejpam-3335	418	8	(	(	PUNCT
ejpam-3335	418	9	4	4	NUM
ejpam-3335	418	10	)	)	PUNCT
ejpam-3335	418	11	(	(	PUNCT
ejpam-3335	418	12	2018	2018	NUM
ejpam-3335	418	13	)	)	PUNCT
ejpam-3335	418	14	,	,	PUNCT
ejpam-3335	418	15	976	976	NUM
ejpam-3335	418	16	-	-	SYM
ejpam-3335	418	17	1002	1002	NUM
ejpam-3335	418	18	990	990	NUM
ejpam-3335	418	19	next	next	ADV
ejpam-3335	418	20	,	,	PUNCT
ejpam-3335	418	21	assume	assume	VERB
ejpam-3335	418	22	that	that	SCONJ
ejpam-3335	418	23	there	there	PRON
ejpam-3335	418	24	exist	exist	VERB
ejpam-3335	418	25	x	x	NOUN
ejpam-3335	418	26	,	,	PUNCT
ejpam-3335	418	27	y	y	PROPN
ejpam-3335	418	28	,	,	PUNCT
ejpam-3335	418	29	z	z	PROPN
ejpam-3335	418	30	∈	∈	PROPN
ejpam-3335	418	31	a	a	DET
ejpam-3335	418	32	such	such	ADJ
ejpam-3335	418	33	that	that	DET
ejpam-3335	418	34	hh(x·z	hh(x·z	PROPN
ejpam-3335	418	35	)	)	PUNCT
ejpam-3335	418	36	*	*	PUNCT
ejpam-3335	418	37	hh(x·(y·z))∪hh(y	hh(x·(y·z))∪hh(y	ADJ
ejpam-3335	418	38	)	)	PUNCT
ejpam-3335	418	39	.	.	PUNCT
ejpam-3335	419	1	since	since	SCONJ
ejpam-3335	419	2	im(h	im(h	NOUN
ejpam-3335	419	3	)	)	PUNCT
ejpam-3335	419	4	is	be	AUX
ejpam-3335	419	5	a	a	DET
ejpam-3335	419	6	chain	chain	NOUN
ejpam-3335	419	7	,	,	PUNCT
ejpam-3335	419	8	we	we	PRON
ejpam-3335	419	9	have	have	AUX
ejpam-3335	419	10	hh(x·z	hh(x·z	PROPN
ejpam-3335	419	11	)	)	PUNCT
ejpam-3335	419	12	⊃	⊃	PROPN
ejpam-3335	419	13	hh(x·(y	hh(x·(y	VERB
ejpam-3335	419	14	·	·	PUNCT
ejpam-3335	419	15	z))∪hh(y	z))∪hh(y	NUM
ejpam-3335	419	16	)	)	PUNCT
ejpam-3335	419	17	.	.	PUNCT
ejpam-3335	420	1	choose	choose	VERB
ejpam-3335	420	2	ε	ε	PROPN
ejpam-3335	420	3	=	=	SYM
ejpam-3335	420	4	hh(x·z	hh(x·z	PROPN
ejpam-3335	420	5	)	)	PUNCT
ejpam-3335	420	6	∈	∈	PROPN
ejpam-3335	420	7	p([0	p([0	NOUN
ejpam-3335	420	8	,	,	PUNCT
ejpam-3335	420	9	1	1	NUM
ejpam-3335	420	10	]	]	NUM
ejpam-3335	420	11	)	)	PUNCT
ejpam-3335	420	12	.	.	PUNCT
ejpam-3335	421	1	then	then	ADV
ejpam-3335	421	2	hh(x	hh(x	PUNCT
ejpam-3335	421	3	·	·	PUNCT
ejpam-3335	421	4	(	(	PUNCT
ejpam-3335	421	5	y	y	PROPN
ejpam-3335	421	6	·	·	PUNCT
ejpam-3335	421	7	z	z	NOUN
ejpam-3335	421	8	)	)	PUNCT
ejpam-3335	421	9	)	)	PUNCT
ejpam-3335	422	1	⊂	⊂	PROPN
ejpam-3335	422	2	ε	ε	PROPN
ejpam-3335	422	3	and	and	CCONJ
ejpam-3335	422	4	hh(y	hh(y	NOUN
ejpam-3335	422	5	)	)	PUNCT
ejpam-3335	423	1	⊂	⊂	PROPN
ejpam-3335	423	2	ε	ε	AUX
ejpam-3335	423	3	.	.	PUNCT
ejpam-3335	423	4	thus	thus	ADV
ejpam-3335	423	5	x	x	X
ejpam-3335	423	6	·	·	PUNCT
ejpam-3335	423	7	(	(	PUNCT
ejpam-3335	423	8	y	y	PROPN
ejpam-3335	423	9	·	·	PUNCT
ejpam-3335	423	10	z	z	X
ejpam-3335	423	11	)	)	PUNCT
ejpam-3335	423	12	,	,	PUNCT
ejpam-3335	423	13	y	y	PROPN
ejpam-3335	423	14	∈	∈	PROPN
ejpam-3335	423	15	l−(h	l−(h	PROPN
ejpam-3335	423	16	;	;	PUNCT
ejpam-3335	423	17	ε	ε	PROPN
ejpam-3335	423	18	)	)	PUNCT
ejpam-3335	423	19	6=	6=	ADP
ejpam-3335	423	20	∅.	∅.	ADP
ejpam-3335	423	21	by	by	ADP
ejpam-3335	423	22	assumption	assumption	NOUN
ejpam-3335	423	23	,	,	PUNCT
ejpam-3335	423	24	we	we	PRON
ejpam-3335	423	25	have	have	VERB
ejpam-3335	423	26	l−(h	l−(h	PROPN
ejpam-3335	423	27	;	;	PUNCT
ejpam-3335	423	28	ε	ε	PROPN
ejpam-3335	423	29	)	)	PUNCT
ejpam-3335	423	30	is	be	AUX
ejpam-3335	423	31	a	a	DET
ejpam-3335	423	32	up	up	ADJ
ejpam-3335	423	33	-	-	PUNCT
ejpam-3335	423	34	ideal	ideal	NOUN
ejpam-3335	423	35	of	of	ADP
ejpam-3335	423	36	a	a	PRON
ejpam-3335	423	37	and	and	CCONJ
ejpam-3335	423	38	so	so	ADV
ejpam-3335	423	39	x	x	X
ejpam-3335	423	40	·	·	PUNCT
ejpam-3335	423	41	z	z	PROPN
ejpam-3335	423	42	∈	∈	PROPN
ejpam-3335	423	43	l−(h	l−(h	PROPN
ejpam-3335	423	44	;	;	PUNCT
ejpam-3335	423	45	ε	ε	PROPN
ejpam-3335	423	46	)	)	PUNCT
ejpam-3335	423	47	.	.	PUNCT
ejpam-3335	424	1	thus	thus	ADV
ejpam-3335	424	2	hh(x	hh(x	X
ejpam-3335	424	3	·	·	PUNCT
ejpam-3335	424	4	z	z	X
ejpam-3335	424	5	)	)	PUNCT
ejpam-3335	424	6	⊂	⊂	PROPN
ejpam-3335	424	7	ε	ε	PROPN
ejpam-3335	424	8	=	=	SYM
ejpam-3335	424	9	hh(x	hh(x	X
ejpam-3335	424	10	·	·	PUNCT
ejpam-3335	424	11	z	z	X
ejpam-3335	424	12	)	)	PUNCT
ejpam-3335	424	13	,	,	PUNCT
ejpam-3335	424	14	a	a	DET
ejpam-3335	424	15	contradiction	contradiction	NOUN
ejpam-3335	424	16	.	.	PUNCT
ejpam-3335	425	1	therefore	therefore	ADV
ejpam-3335	425	2	,	,	PUNCT
ejpam-3335	425	3	hh(x	hh(x	PUNCT
ejpam-3335	425	4	·	·	PUNCT
ejpam-3335	426	1	z	z	X
ejpam-3335	426	2	)	)	PUNCT
ejpam-3335	426	3	⊆	⊆	NUM
ejpam-3335	426	4	hh(x	hh(x	X
ejpam-3335	426	5	·	·	PUNCT
ejpam-3335	426	6	(	(	PUNCT
ejpam-3335	426	7	y	y	PROPN
ejpam-3335	426	8	·	·	PUNCT
ejpam-3335	426	9	z	z	NOUN
ejpam-3335	426	10	)	)	PUNCT
ejpam-3335	426	11	)	)	PUNCT
ejpam-3335	426	12	∪	∪	ADP
ejpam-3335	426	13	hh(y	hh(y	NOUN
ejpam-3335	426	14	)	)	PUNCT
ejpam-3335	426	15	for	for	ADP
ejpam-3335	426	16	all	all	DET
ejpam-3335	426	17	x	x	PROPN
ejpam-3335	426	18	,	,	PUNCT
ejpam-3335	426	19	y	y	PROPN
ejpam-3335	426	20	,	,	PUNCT
ejpam-3335	426	21	z	z	PROPN
ejpam-3335	426	22	∈	∈	PROPN
ejpam-3335	426	23	a.	a.	NOUN
ejpam-3335	426	24	hence	hence	ADV
ejpam-3335	426	25	,	,	PUNCT
ejpam-3335	426	26	h	h	PROPN
ejpam-3335	426	27	is	be	AUX
ejpam-3335	426	28	an	an	DET
ejpam-3335	426	29	anti	anti	ADJ
ejpam-3335	426	30	-	-	ADJ
ejpam-3335	426	31	hesitant	hesitant	ADJ
ejpam-3335	426	32	fuzzy	fuzzy	ADJ
ejpam-3335	426	33	up	up	NOUN
ejpam-3335	426	34	-	-	PUNCT
ejpam-3335	426	35	ideal	ideal	NOUN
ejpam-3335	426	36	of	of	ADP
ejpam-3335	426	37	a.	a.	NOUN
ejpam-3335	426	38	example	example	NOUN
ejpam-3335	426	39	10	10	NUM
ejpam-3335	426	40	.	.	PUNCT
ejpam-3335	427	1	let	let	VERB
ejpam-3335	427	2	a	a	PRON
ejpam-3335	427	3	=	=	PUNCT
ejpam-3335	427	4	{	{	PUNCT
ejpam-3335	427	5	0	0	NUM
ejpam-3335	427	6	,	,	PUNCT
ejpam-3335	427	7	1	1	NUM
ejpam-3335	427	8	,	,	PUNCT
ejpam-3335	427	9	2	2	NUM
ejpam-3335	427	10	,	,	PUNCT
ejpam-3335	427	11	3	3	NUM
ejpam-3335	427	12	,	,	PUNCT
ejpam-3335	427	13	4	4	NUM
ejpam-3335	427	14	}	}	PUNCT
ejpam-3335	427	15	be	be	AUX
ejpam-3335	427	16	a	a	DET
ejpam-3335	427	17	set	set	NOUN
ejpam-3335	427	18	with	with	ADP
ejpam-3335	427	19	a	a	DET
ejpam-3335	427	20	binary	binary	ADJ
ejpam-3335	427	21	operation	operation	NOUN
ejpam-3335	427	22	·	·	PUNCT
ejpam-3335	427	23	defined	define	VERB
ejpam-3335	427	24	by	by	ADP
ejpam-3335	427	25	the	the	DET
ejpam-3335	427	26	following	following	ADJ
ejpam-3335	427	27	cayley	cayley	ADJ
ejpam-3335	427	28	table	table	NOUN
ejpam-3335	427	29	:	:	PUNCT
ejpam-3335	427	30	·	·	PUNCT
ejpam-3335	427	31	0	0	NUM
ejpam-3335	428	1	1	1	NUM
ejpam-3335	428	2	2	2	NUM
ejpam-3335	428	3	3	3	NUM
ejpam-3335	428	4	4	4	NUM
ejpam-3335	428	5	0	0	NUM
ejpam-3335	428	6	0	0	NUM
ejpam-3335	428	7	1	1	NUM
ejpam-3335	428	8	2	2	NUM
ejpam-3335	428	9	3	3	NUM
ejpam-3335	428	10	4	4	NUM
ejpam-3335	428	11	1	1	NUM
ejpam-3335	428	12	0	0	NUM
ejpam-3335	428	13	0	0	NUM
ejpam-3335	428	14	2	2	NUM
ejpam-3335	428	15	3	3	NUM
ejpam-3335	428	16	4	4	NUM
ejpam-3335	428	17	2	2	NUM
ejpam-3335	428	18	0	0	NUM
ejpam-3335	428	19	0	0	NUM
ejpam-3335	428	20	0	0	NUM
ejpam-3335	428	21	3	3	NUM
ejpam-3335	428	22	4	4	NUM
ejpam-3335	428	23	3	3	NUM
ejpam-3335	428	24	0	0	NUM
ejpam-3335	428	25	0	0	NUM
ejpam-3335	428	26	2	2	NUM
ejpam-3335	428	27	0	0	NUM
ejpam-3335	428	28	4	4	NUM
ejpam-3335	428	29	4	4	NUM
ejpam-3335	428	30	0	0	NUM
ejpam-3335	428	31	0	0	NUM
ejpam-3335	428	32	0	0	NUM
ejpam-3335	428	33	0	0	NUM
ejpam-3335	428	34	0	0	NUM
ejpam-3335	429	1	then	then	ADV
ejpam-3335	429	2	(	(	PUNCT
ejpam-3335	429	3	a	a	PRON
ejpam-3335	429	4	,	,	PUNCT
ejpam-3335	429	5	·	·	PUNCT
ejpam-3335	429	6	,	,	PUNCT
ejpam-3335	429	7	0	0	NUM
ejpam-3335	429	8	)	)	PUNCT
ejpam-3335	429	9	is	be	AUX
ejpam-3335	429	10	a	a	DET
ejpam-3335	429	11	up	up	NOUN
ejpam-3335	429	12	-	-	PUNCT
ejpam-3335	429	13	algebra	algebra	NOUN
ejpam-3335	429	14	.	.	PUNCT
ejpam-3335	430	1	we	we	PRON
ejpam-3335	430	2	define	define	VERB
ejpam-3335	430	3	a	a	DET
ejpam-3335	430	4	hesitant	hesitant	ADJ
ejpam-3335	430	5	fuzzy	fuzzy	ADJ
ejpam-3335	430	6	set	set	VERB
ejpam-3335	430	7	h	h	NOUN
ejpam-3335	430	8	on	on	ADP
ejpam-3335	430	9	a	a	DET
ejpam-3335	430	10	as	as	SCONJ
ejpam-3335	430	11	follows	follow	VERB
ejpam-3335	430	12	:	:	PUNCT
ejpam-3335	430	13	hh(0	hh(0	NOUN
ejpam-3335	430	14	)	)	PUNCT
ejpam-3335	430	15	=	=	SYM
ejpam-3335	430	16	(	(	PUNCT
ejpam-3335	430	17	0	0	NUM
ejpam-3335	430	18	,	,	PUNCT
ejpam-3335	430	19	1),hh(1	1),hh(1	NUM
ejpam-3335	430	20	)	)	PUNCT
ejpam-3335	430	21	=	=	PUNCT
ejpam-3335	431	1	[	[	X
ejpam-3335	431	2	0	0	NUM
ejpam-3335	431	3	,	,	PUNCT
ejpam-3335	431	4	1	1	NUM
ejpam-3335	431	5	)	)	PUNCT
ejpam-3335	431	6	,	,	PUNCT
ejpam-3335	431	7	hh(2	hh(2	NOUN
ejpam-3335	431	8	)	)	PUNCT
ejpam-3335	431	9	=	=	PUNCT
ejpam-3335	432	1	[	[	X
ejpam-3335	432	2	0	0	NUM
ejpam-3335	432	3	,	,	PUNCT
ejpam-3335	432	4	1	1	NUM
ejpam-3335	432	5	]	]	PUNCT
ejpam-3335	432	6	,	,	PUNCT
ejpam-3335	432	7	hh(3	hh(3	NOUN
ejpam-3335	432	8	)	)	PUNCT
ejpam-3335	432	9	=	=	SYM
ejpam-3335	432	10	(	(	PUNCT
ejpam-3335	432	11	0	0	NUM
ejpam-3335	432	12	,	,	PUNCT
ejpam-3335	432	13	1	1	NUM
ejpam-3335	432	14	]	]	PUNCT
ejpam-3335	432	15	,	,	PUNCT
ejpam-3335	432	16	and	and	CCONJ
ejpam-3335	432	17	hh(4	hh(4	NOUN
ejpam-3335	432	18	)	)	PUNCT
ejpam-3335	432	19	=	=	PUNCT
ejpam-3335	433	1	[	[	X
ejpam-3335	433	2	0	0	NUM
ejpam-3335	433	3	,	,	PUNCT
ejpam-3335	433	4	1	1	NUM
ejpam-3335	433	5	]	]	PUNCT
ejpam-3335	433	6	.	.	PUNCT
ejpam-3335	434	1	then	then	ADV
ejpam-3335	434	2	im(h	im(h	NOUN
ejpam-3335	434	3	)	)	PUNCT
ejpam-3335	434	4	is	be	AUX
ejpam-3335	434	5	not	not	PART
ejpam-3335	434	6	a	a	DET
ejpam-3335	434	7	chain	chain	NOUN
ejpam-3335	434	8	.	.	PUNCT
ejpam-3335	435	1	if	if	SCONJ
ejpam-3335	435	2	ε	ε	PROPN
ejpam-3335	435	3	⊆	⊆	NUM
ejpam-3335	435	4	(	(	PUNCT
ejpam-3335	435	5	0	0	NUM
ejpam-3335	435	6	,	,	PUNCT
ejpam-3335	435	7	1	1	NUM
ejpam-3335	435	8	)	)	PUNCT
ejpam-3335	435	9	,	,	PUNCT
ejpam-3335	435	10	then	then	ADV
ejpam-3335	435	11	l−(h	l−(h	PROPN
ejpam-3335	435	12	;	;	PUNCT
ejpam-3335	435	13	ε	ε	PROPN
ejpam-3335	435	14	)	)	PUNCT
ejpam-3335	435	15	=	=	PUNCT
ejpam-3335	435	16	∅.	∅.	NOUN
ejpam-3335	435	17	if	if	SCONJ
ejpam-3335	435	18	ε	ε	PROPN
ejpam-3335	435	19	=	=	PUNCT
ejpam-3335	436	1	[	[	X
ejpam-3335	436	2	0	0	NUM
ejpam-3335	436	3	,	,	PUNCT
ejpam-3335	436	4	1	1	NUM
ejpam-3335	436	5	)	)	PUNCT
ejpam-3335	436	6	or	or	CCONJ
ejpam-3335	436	7	ε	ε	PROPN
ejpam-3335	436	8	=	=	SYM
ejpam-3335	436	9	(	(	PUNCT
ejpam-3335	436	10	0	0	NUM
ejpam-3335	436	11	,	,	PUNCT
ejpam-3335	436	12	1	1	NUM
ejpam-3335	436	13	]	]	PUNCT
ejpam-3335	436	14	,	,	PUNCT
ejpam-3335	436	15	then	then	ADV
ejpam-3335	436	16	l−(h	l−(h	PROPN
ejpam-3335	436	17	;	;	PUNCT
ejpam-3335	436	18	ε	ε	PROPN
ejpam-3335	436	19	)	)	PUNCT
ejpam-3335	436	20	=	=	PUNCT
ejpam-3335	436	21	{	{	PUNCT
ejpam-3335	436	22	0	0	NUM
ejpam-3335	436	23	}	}	PUNCT
ejpam-3335	436	24	.	.	PUNCT
ejpam-3335	437	1	if	if	SCONJ
ejpam-3335	437	2	ε	ε	PROPN
ejpam-3335	437	3	=	=	PUNCT
ejpam-3335	438	1	[	[	X
ejpam-3335	438	2	0	0	NUM
ejpam-3335	438	3	,	,	PUNCT
ejpam-3335	438	4	1	1	NUM
ejpam-3335	438	5	]	]	PUNCT
ejpam-3335	438	6	,	,	PUNCT
ejpam-3335	438	7	then	then	ADV
ejpam-3335	438	8	l−(h	l−(h	PROPN
ejpam-3335	438	9	;	;	PUNCT
ejpam-3335	438	10	ε	ε	PROPN
ejpam-3335	438	11	)	)	PUNCT
ejpam-3335	438	12	=	=	SYM
ejpam-3335	438	13	{	{	PUNCT
ejpam-3335	438	14	0	0	NUM
ejpam-3335	438	15	,	,	PUNCT
ejpam-3335	438	16	1	1	NUM
ejpam-3335	438	17	,	,	PUNCT
ejpam-3335	438	18	3	3	NUM
ejpam-3335	438	19	}	}	PUNCT
ejpam-3335	438	20	.	.	PUNCT
ejpam-3335	439	1	using	use	VERB
ejpam-3335	439	2	this	this	DET
ejpam-3335	439	3	data	datum	NOUN
ejpam-3335	439	4	,	,	PUNCT
ejpam-3335	439	5	we	we	PRON
ejpam-3335	439	6	can	can	AUX
ejpam-3335	439	7	show	show	VERB
ejpam-3335	439	8	that	that	SCONJ
ejpam-3335	439	9	all	all	DET
ejpam-3335	439	10	nonempty	nonempty	ADV
ejpam-3335	439	11	subset	subset	VERB
ejpam-3335	439	12	l−(h	l−(h	PROPN
ejpam-3335	439	13	;	;	PUNCT
ejpam-3335	439	14	ε	ε	PROPN
ejpam-3335	439	15	)	)	PUNCT
ejpam-3335	439	16	of	of	ADP
ejpam-3335	439	17	a	a	PRON
ejpam-3335	439	18	is	be	AUX
ejpam-3335	439	19	a	a	DET
ejpam-3335	439	20	up	up	ADJ
ejpam-3335	439	21	-	-	PUNCT
ejpam-3335	439	22	ideal	ideal	NOUN
ejpam-3335	439	23	of	of	ADP
ejpam-3335	439	24	a.	a.	NOUN
ejpam-3335	439	25	since	since	SCONJ
ejpam-3335	439	26	hh(0	hh(0	NOUN
ejpam-3335	439	27	·	·	PUNCT
ejpam-3335	439	28	1	1	X
ejpam-3335	439	29	)	)	PUNCT
ejpam-3335	439	30	=	=	PUNCT
ejpam-3335	439	31	hh(1	hh(1	NOUN
ejpam-3335	439	32	)	)	PUNCT
ejpam-3335	439	33	=	=	PUNCT
ejpam-3335	440	1	[	[	X
ejpam-3335	440	2	0	0	NUM
ejpam-3335	440	3	,	,	PUNCT
ejpam-3335	440	4	1	1	NUM
ejpam-3335	440	5	)	)	PUNCT
ejpam-3335	440	6	*	*	PUNCT
ejpam-3335	440	7	(	(	PUNCT
ejpam-3335	440	8	0	0	NUM
ejpam-3335	440	9	,	,	PUNCT
ejpam-3335	440	10	1	1	NUM
ejpam-3335	440	11	]	]	PUNCT
ejpam-3335	440	12	=	=	PUNCT
ejpam-3335	440	13	hh(0	hh(0	NOUN
ejpam-3335	440	14	)	)	PUNCT
ejpam-3335	440	15	∪	∪	X
ejpam-3335	440	16	hh(3	hh(3	NOUN
ejpam-3335	440	17	)	)	PUNCT
ejpam-3335	440	18	=	=	SYM
ejpam-3335	440	19	hh(0	hh(0	NOUN
ejpam-3335	440	20	·	·	PUNCT
ejpam-3335	440	21	(	(	PUNCT
ejpam-3335	440	22	3	3	NUM
ejpam-3335	440	23	·	·	SYM
ejpam-3335	440	24	1	1	NUM
ejpam-3335	440	25	)	)	PUNCT
ejpam-3335	440	26	)	)	PUNCT
ejpam-3335	440	27	∪	∪	ADP
ejpam-3335	440	28	hh(3	hh(3	NOUN
ejpam-3335	440	29	)	)	PUNCT
ejpam-3335	440	30	,	,	PUNCT
ejpam-3335	440	31	we	we	PRON
ejpam-3335	440	32	have	have	VERB
ejpam-3335	440	33	h	h	NOUN
ejpam-3335	440	34	is	be	AUX
ejpam-3335	440	35	not	not	PART
ejpam-3335	440	36	an	an	DET
ejpam-3335	440	37	anti	anti	ADJ
ejpam-3335	440	38	-	-	ADJ
ejpam-3335	440	39	hesitant	hesitant	ADJ
ejpam-3335	440	40	fuzzy	fuzzy	ADJ
ejpam-3335	440	41	up	up	NOUN
ejpam-3335	440	42	-	-	PUNCT
ejpam-3335	440	43	ideal	ideal	NOUN
ejpam-3335	440	44	of	of	ADP
ejpam-3335	440	45	a.	a.	NOUN
ejpam-3335	440	46	theorem	theorem	NOUN
ejpam-3335	440	47	14	14	NUM
ejpam-3335	440	48	.	.	PUNCT
ejpam-3335	441	1	let	let	VERB
ejpam-3335	441	2	h	h	PRON
ejpam-3335	441	3	be	be	AUX
ejpam-3335	441	4	a	a	DET
ejpam-3335	441	5	hesitant	hesitant	ADJ
ejpam-3335	441	6	fuzzy	fuzzy	ADJ
ejpam-3335	441	7	set	set	NOUN
ejpam-3335	441	8	on	on	ADP
ejpam-3335	441	9	a.	a.	NOUN
ejpam-3335	441	10	then	then	ADV
ejpam-3335	441	11	the	the	DET
ejpam-3335	441	12	following	follow	VERB
ejpam-3335	441	13	statements	statement	NOUN
ejpam-3335	441	14	hold	hold	VERB
ejpam-3335	441	15	:	:	PUNCT
ejpam-3335	441	16	(	(	PUNCT
ejpam-3335	441	17	1	1	X
ejpam-3335	441	18	)	)	PUNCT
ejpam-3335	441	19	if	if	SCONJ
ejpam-3335	441	20	h	h	NOUN
ejpam-3335	441	21	is	be	AUX
ejpam-3335	441	22	an	an	DET
ejpam-3335	441	23	anti	anti	ADJ
ejpam-3335	441	24	-	-	ADJ
ejpam-3335	441	25	hesitant	hesitant	ADJ
ejpam-3335	441	26	fuzzy	fuzzy	ADJ
ejpam-3335	441	27	strongly	strongly	ADV
ejpam-3335	441	28	up	up	ADP
ejpam-3335	441	29	-	-	PUNCT
ejpam-3335	441	30	ideal	ideal	NOUN
ejpam-3335	441	31	of	of	ADP
ejpam-3335	441	32	a	a	PRON
ejpam-3335	441	33	,	,	PUNCT
ejpam-3335	441	34	then	then	ADV
ejpam-3335	441	35	for	for	ADP
ejpam-3335	441	36	all	all	DET
ejpam-3335	441	37	ε	ε	PROPN
ejpam-3335	441	38	∈	∈	PROPN
ejpam-3335	441	39	p([0	p([0	NOUN
ejpam-3335	441	40	,	,	PUNCT
ejpam-3335	441	41	1	1	NUM
ejpam-3335	441	42	]	]	NUM
ejpam-3335	441	43	)	)	PUNCT
ejpam-3335	441	44	,	,	PUNCT
ejpam-3335	441	45	l−(h	l−(h	PROPN
ejpam-3335	441	46	;	;	PUNCT
ejpam-3335	441	47	ε	ε	PROPN
ejpam-3335	441	48	)	)	PUNCT
ejpam-3335	441	49	is	be	AUX
ejpam-3335	441	50	a	a	DET
ejpam-3335	441	51	strongly	strongly	ADV
ejpam-3335	441	52	up	up	ADJ
ejpam-3335	441	53	-	-	PUNCT
ejpam-3335	441	54	ideal	ideal	NOUN
ejpam-3335	441	55	of	of	ADP
ejpam-3335	441	56	a	a	DET
ejpam-3335	441	57	if	if	SCONJ
ejpam-3335	441	58	l−(h	l−(h	PROPN
ejpam-3335	441	59	;	;	PUNCT
ejpam-3335	441	60	ε	ε	PROPN
ejpam-3335	441	61	)	)	PUNCT
ejpam-3335	441	62	is	be	AUX
ejpam-3335	441	63	nonempty	nonempty	ADJ
ejpam-3335	441	64	,	,	PUNCT
ejpam-3335	441	65	and	and	CCONJ
ejpam-3335	441	66	(	(	PUNCT
ejpam-3335	441	67	2	2	X
ejpam-3335	441	68	)	)	PUNCT
ejpam-3335	441	69	if	if	SCONJ
ejpam-3335	441	70	im(h	im(h	NOUN
ejpam-3335	441	71	)	)	PUNCT
ejpam-3335	441	72	is	be	AUX
ejpam-3335	441	73	a	a	DET
ejpam-3335	441	74	chain	chain	NOUN
ejpam-3335	441	75	and	and	CCONJ
ejpam-3335	441	76	for	for	ADP
ejpam-3335	441	77	all	all	DET
ejpam-3335	441	78	ε	ε	PROPN
ejpam-3335	441	79	∈	∈	PROPN
ejpam-3335	441	80	p([0	p([0	NOUN
ejpam-3335	441	81	,	,	PUNCT
ejpam-3335	441	82	1	1	NUM
ejpam-3335	441	83	]	]	NUM
ejpam-3335	441	84	)	)	PUNCT
ejpam-3335	441	85	,	,	PUNCT
ejpam-3335	441	86	a	a	DET
ejpam-3335	441	87	nonempty	nonempty	NOUN
ejpam-3335	441	88	subset	subset	VERB
ejpam-3335	441	89	l−(h	l−(h	PROPN
ejpam-3335	441	90	;	;	PUNCT
ejpam-3335	441	91	ε	ε	PROPN
ejpam-3335	441	92	)	)	PUNCT
ejpam-3335	441	93	of	of	ADP
ejpam-3335	441	94	a	a	PRON
ejpam-3335	441	95	is	be	AUX
ejpam-3335	441	96	a	a	DET
ejpam-3335	441	97	strongly	strongly	ADV
ejpam-3335	441	98	up	up	ADJ
ejpam-3335	441	99	-	-	PUNCT
ejpam-3335	441	100	ideal	ideal	NOUN
ejpam-3335	441	101	of	of	ADP
ejpam-3335	441	102	a	a	PRON
ejpam-3335	441	103	,	,	PUNCT
ejpam-3335	441	104	then	then	ADV
ejpam-3335	441	105	h	h	PROPN
ejpam-3335	441	106	is	be	AUX
ejpam-3335	441	107	an	an	DET
ejpam-3335	441	108	anti	anti	ADJ
ejpam-3335	441	109	-	-	ADJ
ejpam-3335	441	110	hesitant	hesitant	ADJ
ejpam-3335	441	111	fuzzy	fuzzy	ADJ
ejpam-3335	441	112	strongly	strongly	ADV
ejpam-3335	441	113	up	up	ADP
ejpam-3335	441	114	-	-	PUNCT
ejpam-3335	441	115	ideal	ideal	NOUN
ejpam-3335	441	116	of	of	ADP
ejpam-3335	441	117	a.	a.	NOUN
ejpam-3335	441	118	proof	proof	NOUN
ejpam-3335	441	119	.	.	PUNCT
ejpam-3335	442	1	(	(	PUNCT
ejpam-3335	442	2	1	1	X
ejpam-3335	442	3	)	)	PUNCT
ejpam-3335	442	4	assume	assume	VERB
ejpam-3335	442	5	that	that	SCONJ
ejpam-3335	442	6	h	h	NOUN
ejpam-3335	442	7	is	be	AUX
ejpam-3335	442	8	an	an	DET
ejpam-3335	442	9	anti	anti	ADJ
ejpam-3335	442	10	-	-	ADJ
ejpam-3335	442	11	hesitant	hesitant	ADJ
ejpam-3335	442	12	fuzzy	fuzzy	ADJ
ejpam-3335	442	13	strongly	strongly	ADV
ejpam-3335	442	14	up	up	ADP
ejpam-3335	442	15	-	-	PUNCT
ejpam-3335	442	16	ideal	ideal	NOUN
ejpam-3335	442	17	of	of	ADP
ejpam-3335	442	18	a.	a.	NOUN
ejpam-3335	442	19	by	by	ADP
ejpam-3335	442	20	theorem	theorem	NOUN
ejpam-3335	442	21	3	3	NUM
ejpam-3335	442	22	,	,	PUNCT
ejpam-3335	442	23	we	we	PRON
ejpam-3335	442	24	obtain	obtain	VERB
ejpam-3335	442	25	h	h	NOUN
ejpam-3335	442	26	is	be	AUX
ejpam-3335	442	27	a	a	DET
ejpam-3335	442	28	constant	constant	ADJ
ejpam-3335	442	29	hesitant	hesitant	ADJ
ejpam-3335	442	30	fuzzy	fuzzy	ADJ
ejpam-3335	442	31	set	set	VERB
ejpam-3335	442	32	on	on	ADP
ejpam-3335	442	33	a	a	DET
ejpam-3335	442	34	and	and	CCONJ
ejpam-3335	442	35	so	so	ADV
ejpam-3335	442	36	hh(x	hh(x	PUNCT
ejpam-3335	442	37	)	)	PUNCT
ejpam-3335	442	38	=	=	SYM
ejpam-3335	443	1	hh(y	hh(y	X
ejpam-3335	443	2	)	)	PUNCT
ejpam-3335	443	3	for	for	ADP
ejpam-3335	443	4	all	all	DET
ejpam-3335	443	5	x	x	NOUN
ejpam-3335	443	6	,	,	PUNCT
ejpam-3335	443	7	y	y	PROPN
ejpam-3335	443	8	∈	∈	PROPN
ejpam-3335	443	9	a.	a.	NOUN
ejpam-3335	443	10	let	let	VERB
ejpam-3335	443	11	ε	ε	PROPN
ejpam-3335	443	12	∈	∈	PROPN
ejpam-3335	443	13	p([0	p([0	PROPN
ejpam-3335	443	14	,	,	PUNCT
ejpam-3335	443	15	1	1	NUM
ejpam-3335	443	16	]	]	PUNCT
ejpam-3335	443	17	)	)	PUNCT
ejpam-3335	443	18	be	be	AUX
ejpam-3335	443	19	such	such	ADJ
ejpam-3335	443	20	that	that	SCONJ
ejpam-3335	443	21	l−(h	l−(h	PROPN
ejpam-3335	443	22	;	;	PUNCT
ejpam-3335	443	23	ε	ε	PROPN
ejpam-3335	443	24	)	)	PUNCT
ejpam-3335	444	1	6=	6=	ADP
ejpam-3335	444	2	∅.	∅.	VERB
ejpam-3335	444	3	there	there	ADV
ejpam-3335	444	4	exists	exist	VERB
ejpam-3335	444	5	a	a	DET
ejpam-3335	444	6	∈	∈	PROPN
ejpam-3335	444	7	l−(h	l−(h	PROPN
ejpam-3335	444	8	;	;	PUNCT
ejpam-3335	444	9	ε	ε	PROPN
ejpam-3335	444	10	)	)	PUNCT
ejpam-3335	444	11	be	be	VERB
ejpam-3335	444	12	such	such	ADJ
ejpam-3335	444	13	that	that	DET
ejpam-3335	444	14	hh(a	hh(a	NOUN
ejpam-3335	444	15	)	)	PUNCT
ejpam-3335	445	1	⊂	⊂	PROPN
ejpam-3335	445	2	ε	ε	PROPN
ejpam-3335	445	3	.	.	PUNCT
ejpam-3335	445	4	thus	thus	ADV
ejpam-3335	445	5	hh(x	hh(x	X
ejpam-3335	445	6	)	)	PUNCT
ejpam-3335	445	7	=	=	SYM
ejpam-3335	445	8	hh(a	hh(a	NUM
ejpam-3335	445	9	)	)	PUNCT
ejpam-3335	445	10	⊂	⊂	PROPN
ejpam-3335	445	11	ε	ε	PROPN
ejpam-3335	445	12	for	for	ADP
ejpam-3335	445	13	all	all	DET
ejpam-3335	445	14	x	x	SYM
ejpam-3335	445	15	∈	∈	PROPN
ejpam-3335	445	16	a	a	PRON
ejpam-3335	446	1	and	and	CCONJ
ejpam-3335	446	2	so	so	ADV
ejpam-3335	446	3	x	x	PUNCT
ejpam-3335	446	4	∈	∈	PROPN
ejpam-3335	446	5	l−(h	l−(h	PROPN
ejpam-3335	446	6	;	;	PUNCT
ejpam-3335	446	7	ε	ε	PROPN
ejpam-3335	446	8	)	)	PUNCT
ejpam-3335	446	9	for	for	ADP
ejpam-3335	446	10	all	all	DET
ejpam-3335	446	11	x	x	SYM
ejpam-3335	446	12	∈	∈	PROPN
ejpam-3335	446	13	a.	a.	NOUN
ejpam-3335	446	14	therefore	therefore	ADV
ejpam-3335	446	15	,	,	PUNCT
ejpam-3335	446	16	l−(h	l−(h	PROPN
ejpam-3335	446	17	;	;	PUNCT
ejpam-3335	446	18	ε	ε	PROPN
ejpam-3335	446	19	)	)	PUNCT
ejpam-3335	446	20	=	=	NOUN
ejpam-3335	446	21	a.	a.	NOUN
ejpam-3335	446	22	hence	hence	ADV
ejpam-3335	446	23	,	,	PUNCT
ejpam-3335	446	24	l−(h	l−(h	PROPN
ejpam-3335	446	25	;	;	PUNCT
ejpam-3335	446	26	ε	ε	PROPN
ejpam-3335	446	27	)	)	PUNCT
ejpam-3335	446	28	is	be	AUX
ejpam-3335	446	29	a	a	DET
ejpam-3335	446	30	strongly	strongly	ADV
ejpam-3335	446	31	up	up	ADJ
ejpam-3335	446	32	-	-	PUNCT
ejpam-3335	446	33	ideal	ideal	NOUN
ejpam-3335	446	34	of	of	ADP
ejpam-3335	446	35	a.	a.	NOUN
ejpam-3335	446	36	(	(	PUNCT
ejpam-3335	446	37	2	2	X
ejpam-3335	446	38	)	)	PUNCT
ejpam-3335	446	39	assume	assume	VERB
ejpam-3335	446	40	that	that	SCONJ
ejpam-3335	446	41	im(h	im(h	NOUN
ejpam-3335	446	42	)	)	PUNCT
ejpam-3335	446	43	is	be	AUX
ejpam-3335	446	44	a	a	DET
ejpam-3335	446	45	chain	chain	NOUN
ejpam-3335	446	46	and	and	CCONJ
ejpam-3335	446	47	for	for	ADP
ejpam-3335	446	48	all	all	DET
ejpam-3335	446	49	ε	ε	PROPN
ejpam-3335	446	50	∈	∈	PROPN
ejpam-3335	446	51	p([0	p([0	NOUN
ejpam-3335	446	52	,	,	PUNCT
ejpam-3335	446	53	1	1	NUM
ejpam-3335	446	54	]	]	NUM
ejpam-3335	446	55	)	)	PUNCT
ejpam-3335	446	56	,	,	PUNCT
ejpam-3335	446	57	a	a	DET
ejpam-3335	446	58	nonempty	nonempty	NOUN
ejpam-3335	446	59	subset	subset	VERB
ejpam-3335	446	60	l−(h	l−(h	PROPN
ejpam-3335	446	61	;	;	PUNCT
ejpam-3335	446	62	ε	ε	PROPN
ejpam-3335	446	63	)	)	PUNCT
ejpam-3335	446	64	of	of	ADP
ejpam-3335	446	65	a	a	PRON
ejpam-3335	446	66	is	be	AUX
ejpam-3335	446	67	a	a	DET
ejpam-3335	446	68	strongly	strongly	ADV
ejpam-3335	446	69	up	up	ADJ
ejpam-3335	446	70	-	-	PUNCT
ejpam-3335	446	71	ideal	ideal	NOUN
ejpam-3335	446	72	of	of	ADP
ejpam-3335	446	73	a.	a.	NOUN
ejpam-3335	446	74	assume	assume	VERB
ejpam-3335	446	75	that	that	SCONJ
ejpam-3335	446	76	h	h	NOUN
ejpam-3335	446	77	is	be	AUX
ejpam-3335	446	78	not	not	PART
ejpam-3335	446	79	a	a	DET
ejpam-3335	446	80	constant	constant	ADJ
ejpam-3335	446	81	hesitant	hesitant	ADJ
ejpam-3335	446	82	fuzzy	fuzzy	ADJ
ejpam-3335	446	83	set	set	VERB
ejpam-3335	446	84	on	on	ADP
ejpam-3335	446	85	a.	a.	NOUN
ejpam-3335	446	86	there	there	ADV
ejpam-3335	446	87	exist	exist	VERB
ejpam-3335	446	88	x	x	NOUN
ejpam-3335	446	89	,	,	PUNCT
ejpam-3335	446	90	y	y	PROPN
ejpam-3335	446	91	∈	∈	PROPN
ejpam-3335	446	92	a	a	PRON
ejpam-3335	446	93	be	be	AUX
ejpam-3335	446	94	such	such	ADJ
ejpam-3335	446	95	that	that	PRON
ejpam-3335	446	96	hh(x	hh(x	PRON
ejpam-3335	446	97	)	)	PUNCT
ejpam-3335	446	98	6=	6=	ADP
ejpam-3335	446	99	hh(y	hh(y	NOUN
ejpam-3335	446	100	)	)	PUNCT
ejpam-3335	446	101	.	.	PUNCT
ejpam-3335	447	1	since	since	SCONJ
ejpam-3335	447	2	im(h	im(h	NOUN
ejpam-3335	447	3	)	)	PUNCT
ejpam-3335	447	4	is	be	AUX
ejpam-3335	447	5	a	a	DET
ejpam-3335	447	6	chain	chain	NOUN
ejpam-3335	447	7	,	,	PUNCT
ejpam-3335	447	8	we	we	PRON
ejpam-3335	447	9	have	have	VERB
ejpam-3335	447	10	hh(x	hh(x	NOUN
ejpam-3335	447	11	)	)	PUNCT
ejpam-3335	447	12	⊂	⊂	PROPN
ejpam-3335	447	13	hh(y	hh(y	NOUN
ejpam-3335	447	14	)	)	PUNCT
ejpam-3335	447	15	or	or	CCONJ
ejpam-3335	447	16	hh(x	hh(x	NOUN
ejpam-3335	447	17	)	)	PUNCT
ejpam-3335	447	18	⊃	⊃	PROPN
ejpam-3335	447	19	hh(y	hh(y	X
ejpam-3335	447	20	)	)	PUNCT
ejpam-3335	447	21	.	.	PUNCT
ejpam-3335	448	1	without	without	ADP
ejpam-3335	448	2	loss	loss	NOUN
ejpam-3335	448	3	of	of	ADP
ejpam-3335	448	4	generality	generality	NOUN
ejpam-3335	448	5	,	,	PUNCT
ejpam-3335	448	6	assume	assume	VERB
ejpam-3335	448	7	that	that	SCONJ
ejpam-3335	448	8	hh(x	hh(x	PUNCT
ejpam-3335	448	9	)	)	PUNCT
ejpam-3335	448	10	⊂	⊂	PROPN
ejpam-3335	448	11	hh(y	hh(y	NOUN
ejpam-3335	448	12	)	)	PUNCT
ejpam-3335	448	13	,	,	PUNCT
ejpam-3335	448	14	then	then	ADV
ejpam-3335	448	15	x	x	PART
ejpam-3335	448	16	∈	∈	PROPN
ejpam-3335	448	17	l−(h	l−(h	PROPN
ejpam-3335	448	18	;	;	PUNCT
ejpam-3335	448	19	hh(y	hh(y	NUM
ejpam-3335	448	20	)	)	PUNCT
ejpam-3335	448	21	)	)	PUNCT
ejpam-3335	448	22	6=	6=	ADP
ejpam-3335	448	23	∅.	∅.	ADP
ejpam-3335	448	24	by	by	ADP
ejpam-3335	448	25	assumption	assumption	NOUN
ejpam-3335	448	26	,	,	PUNCT
ejpam-3335	448	27	we	we	PRON
ejpam-3335	448	28	have	have	VERB
ejpam-3335	448	29	l−(h	l−(h	NOUN
ejpam-3335	448	30	;	;	PUNCT
ejpam-3335	448	31	hh(y	hh(y	NUM
ejpam-3335	448	32	)	)	PUNCT
ejpam-3335	448	33	)	)	PUNCT
ejpam-3335	448	34	is	be	AUX
ejpam-3335	448	35	a	a	DET
ejpam-3335	448	36	strongly	strongly	ADV
ejpam-3335	448	37	up	up	ADJ
ejpam-3335	448	38	-	-	PUNCT
ejpam-3335	448	39	ideal	ideal	NOUN
ejpam-3335	448	40	of	of	ADP
ejpam-3335	448	41	a	a	DET
ejpam-3335	448	42	and	and	CCONJ
ejpam-3335	448	43	so	so	ADV
ejpam-3335	448	44	l−(h	l−(h	PROPN
ejpam-3335	448	45	;	;	PUNCT
ejpam-3335	448	46	hh(y	hh(y	NUM
ejpam-3335	448	47	)	)	PUNCT
ejpam-3335	448	48	)	)	PUNCT
ejpam-3335	449	1	=	=	PUNCT
ejpam-3335	449	2	a.	a.	NOUN
ejpam-3335	449	3	thus	thus	ADV
ejpam-3335	449	4	y	y	PROPN
ejpam-3335	449	5	∈	∈	PROPN
ejpam-3335	449	6	a	a	DET
ejpam-3335	449	7	=	=	X
ejpam-3335	449	8	l−(h	l−(h	PROPN
ejpam-3335	449	9	;	;	PUNCT
ejpam-3335	449	10	hh(y	hh(y	NOUN
ejpam-3335	449	11	)	)	PUNCT
ejpam-3335	449	12	)	)	PUNCT
ejpam-3335	449	13	and	and	CCONJ
ejpam-3335	449	14	so	so	ADV
ejpam-3335	449	15	hh(y	hh(y	PUNCT
ejpam-3335	449	16	)	)	PUNCT
ejpam-3335	449	17	⊂	⊂	PROPN
ejpam-3335	449	18	hh(y	hh(y	NOUN
ejpam-3335	449	19	)	)	PUNCT
ejpam-3335	449	20	,	,	PUNCT
ejpam-3335	449	21	a	a	DET
ejpam-3335	449	22	contradiction	contradiction	NOUN
ejpam-3335	449	23	.	.	PUNCT
ejpam-3335	450	1	therefore	therefore	ADV
ejpam-3335	450	2	,	,	PUNCT
ejpam-3335	450	3	h	h	NOUN
ejpam-3335	450	4	is	be	AUX
ejpam-3335	450	5	a	a	DET
ejpam-3335	450	6	constant	constant	ADJ
ejpam-3335	450	7	hesitant	hesitant	ADJ
ejpam-3335	450	8	fuzzy	fuzzy	ADJ
ejpam-3335	450	9	set	set	VERB
ejpam-3335	450	10	on	on	ADP
ejpam-3335	450	11	a.	a.	NOUN
ejpam-3335	450	12	by	by	ADP
ejpam-3335	450	13	theorem	theorem	NOUN
ejpam-3335	450	14	3	3	NUM
ejpam-3335	450	15	,	,	PUNCT
ejpam-3335	450	16	we	we	PRON
ejpam-3335	450	17	obtain	obtain	VERB
ejpam-3335	450	18	h	h	NOUN
ejpam-3335	450	19	is	be	AUX
ejpam-3335	450	20	an	an	DET
ejpam-3335	450	21	anti	anti	ADJ
ejpam-3335	450	22	-	-	ADJ
ejpam-3335	450	23	hesitant	hesitant	ADJ
ejpam-3335	450	24	fuzzy	fuzzy	ADJ
ejpam-3335	450	25	strongly	strongly	ADV
ejpam-3335	450	26	up	up	ADP
ejpam-3335	450	27	-	-	PUNCT
ejpam-3335	450	28	ideal	ideal	NOUN
ejpam-3335	450	29	of	of	ADP
ejpam-3335	450	30	a.	a.	PROPN
ejpam-3335	450	31	p.	p.	PROPN
ejpam-3335	450	32	mosrijai	mosrijai	PROPN
ejpam-3335	450	33	,	,	PUNCT
ejpam-3335	450	34	a.	a.	NOUN
ejpam-3335	450	35	iampan	iampan	PROPN
ejpam-3335	450	36	/	/	SYM
ejpam-3335	450	37	eur	eur	PROPN
ejpam-3335	450	38	.	.	PUNCT
ejpam-3335	451	1	j.	j.	PROPN
ejpam-3335	451	2	pure	pure	PROPN
ejpam-3335	451	3	appl	appl	PROPN
ejpam-3335	451	4	.	.	PROPN
ejpam-3335	451	5	math	math	PROPN
ejpam-3335	451	6	,	,	PUNCT
ejpam-3335	451	7	11	11	NUM
ejpam-3335	451	8	(	(	PUNCT
ejpam-3335	451	9	4	4	NUM
ejpam-3335	451	10	)	)	PUNCT
ejpam-3335	451	11	(	(	PUNCT
ejpam-3335	451	12	2018	2018	NUM
ejpam-3335	451	13	)	)	PUNCT
ejpam-3335	451	14	,	,	PUNCT
ejpam-3335	451	15	976	976	NUM
ejpam-3335	451	16	-	-	SYM
ejpam-3335	451	17	1002	1002	NUM
ejpam-3335	451	18	991	991	NUM
ejpam-3335	451	19	example	example	NOUN
ejpam-3335	451	20	11	11	NUM
ejpam-3335	451	21	.	.	PUNCT
ejpam-3335	452	1	let	let	VERB
ejpam-3335	452	2	a	a	PRON
ejpam-3335	452	3	=	=	PUNCT
ejpam-3335	452	4	{	{	PUNCT
ejpam-3335	452	5	0	0	NUM
ejpam-3335	452	6	,	,	PUNCT
ejpam-3335	452	7	1	1	NUM
ejpam-3335	452	8	}	}	PUNCT
ejpam-3335	452	9	be	be	AUX
ejpam-3335	452	10	a	a	DET
ejpam-3335	452	11	set	set	NOUN
ejpam-3335	452	12	with	with	ADP
ejpam-3335	452	13	a	a	DET
ejpam-3335	452	14	binary	binary	ADJ
ejpam-3335	452	15	operation	operation	NOUN
ejpam-3335	452	16	·	·	PUNCT
ejpam-3335	452	17	defined	define	VERB
ejpam-3335	452	18	by	by	ADP
ejpam-3335	452	19	the	the	DET
ejpam-3335	452	20	following	following	ADJ
ejpam-3335	452	21	cayley	cayley	ADJ
ejpam-3335	452	22	table	table	NOUN
ejpam-3335	452	23	:	:	PUNCT
ejpam-3335	452	24	·	·	PUNCT
ejpam-3335	452	25	0	0	NUM
ejpam-3335	453	1	1	1	NUM
ejpam-3335	453	2	0	0	NUM
ejpam-3335	453	3	0	0	NUM
ejpam-3335	453	4	1	1	NUM
ejpam-3335	453	5	1	1	NUM
ejpam-3335	453	6	0	0	NUM
ejpam-3335	453	7	0	0	NUM
ejpam-3335	453	8	then	then	ADV
ejpam-3335	453	9	(	(	PUNCT
ejpam-3335	453	10	a	a	PRON
ejpam-3335	453	11	,	,	PUNCT
ejpam-3335	453	12	·	·	PUNCT
ejpam-3335	453	13	,	,	PUNCT
ejpam-3335	453	14	0	0	NUM
ejpam-3335	453	15	)	)	PUNCT
ejpam-3335	453	16	is	be	AUX
ejpam-3335	453	17	a	a	DET
ejpam-3335	453	18	up	up	NOUN
ejpam-3335	453	19	-	-	PUNCT
ejpam-3335	453	20	algebra	algebra	NOUN
ejpam-3335	453	21	.	.	PUNCT
ejpam-3335	454	1	we	we	PRON
ejpam-3335	454	2	define	define	VERB
ejpam-3335	454	3	a	a	DET
ejpam-3335	454	4	hesitant	hesitant	ADJ
ejpam-3335	454	5	fuzzy	fuzzy	ADJ
ejpam-3335	454	6	set	set	VERB
ejpam-3335	454	7	h	h	NOUN
ejpam-3335	454	8	on	on	ADP
ejpam-3335	454	9	a	a	DET
ejpam-3335	454	10	as	as	SCONJ
ejpam-3335	454	11	follows	follow	VERB
ejpam-3335	454	12	:	:	PUNCT
ejpam-3335	454	13	hh(0	hh(0	NOUN
ejpam-3335	454	14	)	)	PUNCT
ejpam-3335	454	15	=	=	SYM
ejpam-3335	454	16	(	(	PUNCT
ejpam-3335	454	17	0	0	NUM
ejpam-3335	454	18	,	,	PUNCT
ejpam-3335	454	19	1	1	NUM
ejpam-3335	454	20	]	]	PUNCT
ejpam-3335	454	21	,	,	PUNCT
ejpam-3335	454	22	and	and	CCONJ
ejpam-3335	454	23	hh(1	hh(1	NOUN
ejpam-3335	454	24	)	)	PUNCT
ejpam-3335	454	25	=	=	PUNCT
ejpam-3335	455	1	[	[	X
ejpam-3335	455	2	0	0	NUM
ejpam-3335	455	3	,	,	PUNCT
ejpam-3335	455	4	1	1	NUM
ejpam-3335	455	5	)	)	PUNCT
ejpam-3335	455	6	.	.	PUNCT
ejpam-3335	456	1	then	then	ADV
ejpam-3335	456	2	im(h	im(h	NOUN
ejpam-3335	456	3	)	)	PUNCT
ejpam-3335	456	4	is	be	AUX
ejpam-3335	456	5	not	not	PART
ejpam-3335	456	6	a	a	DET
ejpam-3335	456	7	chain	chain	NOUN
ejpam-3335	456	8	.	.	PUNCT
ejpam-3335	457	1	if	if	SCONJ
ejpam-3335	457	2	ε	ε	PROPN
ejpam-3335	457	3	⊆	⊆	NUM
ejpam-3335	457	4	[	[	X
ejpam-3335	457	5	0	0	NUM
ejpam-3335	457	6	,	,	PUNCT
ejpam-3335	457	7	1	1	NUM
ejpam-3335	457	8	)	)	PUNCT
ejpam-3335	457	9	or	or	CCONJ
ejpam-3335	457	10	ε	ε	PROPN
ejpam-3335	457	11	⊆	⊆	NUM
ejpam-3335	457	12	(	(	PUNCT
ejpam-3335	457	13	0	0	NUM
ejpam-3335	457	14	,	,	PUNCT
ejpam-3335	457	15	1	1	NUM
ejpam-3335	457	16	]	]	PUNCT
ejpam-3335	457	17	,	,	PUNCT
ejpam-3335	457	18	then	then	ADV
ejpam-3335	457	19	l−(h	l−(h	PROPN
ejpam-3335	457	20	;	;	PUNCT
ejpam-3335	457	21	ε	ε	PROPN
ejpam-3335	457	22	)	)	PUNCT
ejpam-3335	457	23	=	=	PUNCT
ejpam-3335	457	24	∅.	∅.	NOUN
ejpam-3335	457	25	if	if	SCONJ
ejpam-3335	457	26	ε	ε	PROPN
ejpam-3335	457	27	=	=	PUNCT
ejpam-3335	458	1	[	[	X
ejpam-3335	458	2	0	0	NUM
ejpam-3335	458	3	,	,	PUNCT
ejpam-3335	458	4	1	1	NUM
ejpam-3335	458	5	]	]	PUNCT
ejpam-3335	458	6	,	,	PUNCT
ejpam-3335	458	7	then	then	ADV
ejpam-3335	458	8	l−(h	l−(h	PROPN
ejpam-3335	458	9	;	;	PUNCT
ejpam-3335	458	10	ε	ε	PROPN
ejpam-3335	458	11	)	)	PUNCT
ejpam-3335	458	12	=	=	PUNCT
ejpam-3335	458	13	a.	a.	NOUN
ejpam-3335	458	14	thus	thus	ADV
ejpam-3335	458	15	a	a	DET
ejpam-3335	458	16	nonempty	nonempty	ADV
ejpam-3335	458	17	subset	subset	VERB
ejpam-3335	458	18	l−(h	l−(h	PROPN
ejpam-3335	458	19	;	;	PUNCT
ejpam-3335	458	20	ε	ε	PROPN
ejpam-3335	458	21	)	)	PUNCT
ejpam-3335	458	22	of	of	ADP
ejpam-3335	458	23	a	a	PRON
ejpam-3335	458	24	is	be	AUX
ejpam-3335	458	25	a	a	DET
ejpam-3335	458	26	strongly	strongly	ADV
ejpam-3335	458	27	up	up	ADJ
ejpam-3335	458	28	-	-	PUNCT
ejpam-3335	458	29	ideal	ideal	NOUN
ejpam-3335	458	30	of	of	ADP
ejpam-3335	458	31	a.	a.	NOUN
ejpam-3335	458	32	by	by	ADP
ejpam-3335	458	33	theorem	theorem	NOUN
ejpam-3335	458	34	3	3	NUM
ejpam-3335	458	35	and	and	CCONJ
ejpam-3335	458	36	h	h	NOUN
ejpam-3335	458	37	is	be	AUX
ejpam-3335	458	38	not	not	PART
ejpam-3335	458	39	a	a	DET
ejpam-3335	458	40	constant	constant	ADJ
ejpam-3335	458	41	hesitant	hesitant	ADJ
ejpam-3335	458	42	fuzzy	fuzzy	ADJ
ejpam-3335	458	43	set	set	NOUN
ejpam-3335	458	44	on	on	ADP
ejpam-3335	458	45	a	a	PRON
ejpam-3335	458	46	,	,	PUNCT
ejpam-3335	458	47	we	we	PRON
ejpam-3335	458	48	have	have	VERB
ejpam-3335	458	49	h	h	NOUN
ejpam-3335	458	50	is	be	AUX
ejpam-3335	458	51	not	not	PART
ejpam-3335	458	52	an	an	DET
ejpam-3335	458	53	anti	anti	ADJ
ejpam-3335	458	54	-	-	ADJ
ejpam-3335	458	55	hesitant	hesitant	ADJ
ejpam-3335	458	56	fuzzy	fuzzy	ADJ
ejpam-3335	458	57	strongly	strongly	ADV
ejpam-3335	458	58	up	up	ADP
ejpam-3335	458	59	-	-	PUNCT
ejpam-3335	458	60	ideal	ideal	NOUN
ejpam-3335	458	61	of	of	ADP
ejpam-3335	458	62	a.	a.	NOUN
ejpam-3335	458	63	5.3	5.3	NUM
ejpam-3335	458	64	.	.	PUNCT
ejpam-3335	459	1	upper	upper	ADJ
ejpam-3335	459	2	ε	ε	PROPN
ejpam-3335	459	3	-	-	PUNCT
ejpam-3335	459	4	level	level	NOUN
ejpam-3335	459	5	subsets	subset	NOUN
ejpam-3335	459	6	theorem	theorem	VERB
ejpam-3335	459	7	15	15	NUM
ejpam-3335	459	8	.	.	PUNCT
ejpam-3335	460	1	a	a	DET
ejpam-3335	460	2	hesitant	hesitant	ADJ
ejpam-3335	460	3	fuzzy	fuzzy	ADJ
ejpam-3335	460	4	set	set	VERB
ejpam-3335	460	5	h	h	NOUN
ejpam-3335	460	6	on	on	ADP
ejpam-3335	460	7	a	a	PRON
ejpam-3335	460	8	is	be	AUX
ejpam-3335	460	9	an	an	DET
ejpam-3335	460	10	anti	anti	ADJ
ejpam-3335	460	11	-	-	ADJ
ejpam-3335	460	12	hesitant	hesitant	ADJ
ejpam-3335	460	13	fuzzy	fuzzy	ADJ
ejpam-3335	460	14	up	up	NOUN
ejpam-3335	460	15	-	-	PUNCT
ejpam-3335	460	16	subalgebra	subalgebra	NOUN
ejpam-3335	460	17	of	of	ADP
ejpam-3335	460	18	a	a	DET
ejpam-3335	460	19	if	if	NOUN
ejpam-3335	460	20	and	and	CCONJ
ejpam-3335	460	21	only	only	ADV
ejpam-3335	460	22	if	if	SCONJ
ejpam-3335	460	23	for	for	ADP
ejpam-3335	460	24	all	all	DET
ejpam-3335	460	25	ε	ε	PROPN
ejpam-3335	460	26	∈	∈	PROPN
ejpam-3335	460	27	p([0	p([0	NOUN
ejpam-3335	460	28	,	,	PUNCT
ejpam-3335	460	29	1	1	NUM
ejpam-3335	460	30	]	]	NUM
ejpam-3335	460	31	)	)	PUNCT
ejpam-3335	460	32	,	,	PUNCT
ejpam-3335	460	33	a	a	DET
ejpam-3335	460	34	nonempty	nonempty	NOUN
ejpam-3335	460	35	subset	subset	VERB
ejpam-3335	460	36	u(h	u(h	PROPN
ejpam-3335	460	37	;	;	PUNCT
ejpam-3335	460	38	ε	ε	PROPN
ejpam-3335	460	39	)	)	PUNCT
ejpam-3335	460	40	of	of	ADP
ejpam-3335	460	41	a	a	PRON
ejpam-3335	460	42	is	be	AUX
ejpam-3335	460	43	a	a	DET
ejpam-3335	460	44	up	up	ADJ
ejpam-3335	460	45	-	-	PUNCT
ejpam-3335	460	46	subalgebra	subalgebra	NOUN
ejpam-3335	460	47	of	of	ADP
ejpam-3335	460	48	a.	a.	NOUN
ejpam-3335	460	49	proof	proof	NOUN
ejpam-3335	460	50	.	.	PUNCT
ejpam-3335	461	1	assume	assume	VERB
ejpam-3335	461	2	that	that	SCONJ
ejpam-3335	461	3	h	h	NOUN
ejpam-3335	461	4	is	be	AUX
ejpam-3335	461	5	an	an	DET
ejpam-3335	461	6	anti	anti	ADJ
ejpam-3335	461	7	-	-	ADJ
ejpam-3335	461	8	hesitant	hesitant	ADJ
ejpam-3335	461	9	fuzzy	fuzzy	ADJ
ejpam-3335	461	10	up	up	NOUN
ejpam-3335	461	11	-	-	PUNCT
ejpam-3335	461	12	subalgebra	subalgebra	NOUN
ejpam-3335	461	13	of	of	ADP
ejpam-3335	461	14	a.	a.	NOUN
ejpam-3335	461	15	let	let	VERB
ejpam-3335	461	16	ε	ε	PROPN
ejpam-3335	461	17	∈	∈	PROPN
ejpam-3335	461	18	p([0	p([0	PROPN
ejpam-3335	461	19	,	,	PUNCT
ejpam-3335	461	20	1	1	NUM
ejpam-3335	461	21	]	]	PUNCT
ejpam-3335	461	22	)	)	PUNCT
ejpam-3335	461	23	be	be	AUX
ejpam-3335	461	24	such	such	ADJ
ejpam-3335	461	25	that	that	SCONJ
ejpam-3335	461	26	u(h	u(h	PROPN
ejpam-3335	461	27	;	;	PUNCT
ejpam-3335	461	28	ε	ε	PROPN
ejpam-3335	461	29	)	)	PUNCT
ejpam-3335	461	30	6=	6=	NOUN
ejpam-3335	461	31	∅	∅	NOUN
ejpam-3335	461	32	,	,	PUNCT
ejpam-3335	461	33	and	and	CCONJ
ejpam-3335	461	34	let	let	VERB
ejpam-3335	461	35	x	x	PRON
ejpam-3335	461	36	,	,	PUNCT
ejpam-3335	461	37	y	y	PROPN
ejpam-3335	461	38	∈	∈	PROPN
ejpam-3335	461	39	a	a	DET
ejpam-3335	461	40	be	be	AUX
ejpam-3335	461	41	such	such	ADJ
ejpam-3335	461	42	that	that	SCONJ
ejpam-3335	461	43	x	x	SYM
ejpam-3335	461	44	∈	∈	PROPN
ejpam-3335	461	45	u(h	u(h	PROPN
ejpam-3335	461	46	;	;	PUNCT
ejpam-3335	461	47	ε	ε	PROPN
ejpam-3335	461	48	)	)	PUNCT
ejpam-3335	461	49	and	and	CCONJ
ejpam-3335	461	50	y	y	PROPN
ejpam-3335	461	51	∈	∈	PROPN
ejpam-3335	461	52	u(h	u(h	PROPN
ejpam-3335	461	53	;	;	PUNCT
ejpam-3335	461	54	ε	ε	PROPN
ejpam-3335	461	55	)	)	PUNCT
ejpam-3335	461	56	.	.	PUNCT
ejpam-3335	462	1	then	then	ADV
ejpam-3335	462	2	hh(x	hh(x	X
ejpam-3335	462	3	)	)	PUNCT
ejpam-3335	462	4	⊇	⊇	PROPN
ejpam-3335	462	5	ε	ε	PROPN
ejpam-3335	462	6	and	and	CCONJ
ejpam-3335	462	7	hh(y	hh(y	NOUN
ejpam-3335	462	8	)	)	PUNCT
ejpam-3335	462	9	⊇	⊇	PROPN
ejpam-3335	462	10	ε	ε	PROPN
ejpam-3335	462	11	.	.	PROPN
ejpam-3335	463	1	since	since	SCONJ
ejpam-3335	463	2	h	h	NOUN
ejpam-3335	463	3	is	be	AUX
ejpam-3335	463	4	an	an	DET
ejpam-3335	463	5	anti	anti	ADJ
ejpam-3335	463	6	-	-	ADJ
ejpam-3335	463	7	hesitant	hesitant	ADJ
ejpam-3335	463	8	fuzzy	fuzzy	ADJ
ejpam-3335	463	9	up	up	NOUN
ejpam-3335	463	10	-	-	PUNCT
ejpam-3335	463	11	subalgebra	subalgebra	NOUN
ejpam-3335	463	12	of	of	ADP
ejpam-3335	463	13	a	a	PRON
ejpam-3335	463	14	,	,	PUNCT
ejpam-3335	463	15	we	we	PRON
ejpam-3335	463	16	obtain	obtain	VERB
ejpam-3335	463	17	hh(x	hh(x	X
ejpam-3335	463	18	·	·	PUNCT
ejpam-3335	463	19	y	y	X
ejpam-3335	463	20	)	)	PUNCT
ejpam-3335	463	21	⊆	⊆	NUM
ejpam-3335	463	22	hh(x	hh(x	NOUN
ejpam-3335	463	23	)	)	PUNCT
ejpam-3335	463	24	∪	∪	ADP
ejpam-3335	463	25	hh(y	hh(y	NOUN
ejpam-3335	463	26	)	)	PUNCT
ejpam-3335	463	27	.	.	PUNCT
ejpam-3335	464	1	by	by	ADP
ejpam-3335	464	2	lemma	lemma	PROPN
ejpam-3335	464	3	1	1	NUM
ejpam-3335	464	4	(	(	PUNCT
ejpam-3335	464	5	2	2	NUM
ejpam-3335	464	6	)	)	PUNCT
ejpam-3335	464	7	,	,	PUNCT
ejpam-3335	464	8	we	we	PRON
ejpam-3335	464	9	have	have	VERB
ejpam-3335	464	10	[	[	X
ejpam-3335	464	11	0	0	NUM
ejpam-3335	464	12	,	,	PUNCT
ejpam-3335	464	13	1	1	NUM
ejpam-3335	464	14	]	]	SYM
ejpam-3335	464	15	−	−	NUM
ejpam-3335	464	16	hh(x	hh(x	X
ejpam-3335	464	17	·	·	PUNCT
ejpam-3335	464	18	y	y	X
ejpam-3335	464	19	)	)	PUNCT
ejpam-3335	464	20	⊆	⊆	NUM
ejpam-3335	464	21	(	(	PUNCT
ejpam-3335	464	22	[	[	X
ejpam-3335	464	23	0	0	NUM
ejpam-3335	464	24	,	,	PUNCT
ejpam-3335	464	25	1]−hh(x))∪([0	1]−hh(x))∪([0	NUM
ejpam-3335	464	26	,	,	PUNCT
ejpam-3335	464	27	1]−hh(y	1]−hh(y	NUM
ejpam-3335	464	28	)	)	PUNCT
ejpam-3335	464	29	)	)	PUNCT
ejpam-3335	465	1	=	=	PUNCT
ejpam-3335	466	1	[	[	X
ejpam-3335	466	2	0	0	NUM
ejpam-3335	466	3	,	,	PUNCT
ejpam-3335	466	4	1]−(hh(x)∩hh(y	1]−(hh(x)∩hh(y	NUM
ejpam-3335	466	5	)	)	PUNCT
ejpam-3335	466	6	)	)	PUNCT
ejpam-3335	466	7	.	.	PUNCT
ejpam-3335	467	1	thus	thus	ADV
ejpam-3335	467	2	hh(x·y	hh(x·y	NUM
ejpam-3335	467	3	)	)	PUNCT
ejpam-3335	467	4	⊇	⊇	ADJ
ejpam-3335	467	5	hh(x)∩hh(y	hh(x)∩hh(y	ADJ
ejpam-3335	467	6	)	)	PUNCT
ejpam-3335	467	7	⊇	⊇	PROPN
ejpam-3335	467	8	ε	ε	PROPN
ejpam-3335	467	9	.	.	PUNCT
ejpam-3335	467	10	therefore	therefore	ADV
ejpam-3335	467	11	,	,	PUNCT
ejpam-3335	467	12	x	x	X
ejpam-3335	467	13	·	·	PUNCT
ejpam-3335	467	14	y	y	SYM
ejpam-3335	467	15	∈	∈	PROPN
ejpam-3335	467	16	u(h	u(h	PROPN
ejpam-3335	467	17	;	;	PUNCT
ejpam-3335	467	18	ε	ε	PROPN
ejpam-3335	467	19	)	)	PUNCT
ejpam-3335	467	20	.	.	PUNCT
ejpam-3335	468	1	hence	hence	ADV
ejpam-3335	468	2	,	,	PUNCT
ejpam-3335	468	3	u(h	u(h	PROPN
ejpam-3335	468	4	;	;	PUNCT
ejpam-3335	468	5	ε	ε	PROPN
ejpam-3335	468	6	)	)	PUNCT
ejpam-3335	468	7	is	be	AUX
ejpam-3335	468	8	a	a	DET
ejpam-3335	468	9	up	up	ADJ
ejpam-3335	468	10	-	-	PUNCT
ejpam-3335	468	11	subalgebra	subalgebra	NOUN
ejpam-3335	468	12	of	of	ADP
ejpam-3335	468	13	a.	a.	NOUN
ejpam-3335	468	14	conversely	conversely	ADV
ejpam-3335	468	15	,	,	PUNCT
ejpam-3335	468	16	assume	assume	VERB
ejpam-3335	468	17	that	that	SCONJ
ejpam-3335	468	18	for	for	ADP
ejpam-3335	468	19	all	all	DET
ejpam-3335	468	20	ε	ε	PROPN
ejpam-3335	468	21	∈	∈	PROPN
ejpam-3335	468	22	p([0	p([0	NOUN
ejpam-3335	468	23	,	,	PUNCT
ejpam-3335	468	24	1	1	NUM
ejpam-3335	468	25	]	]	NUM
ejpam-3335	468	26	)	)	PUNCT
ejpam-3335	468	27	,	,	PUNCT
ejpam-3335	468	28	a	a	DET
ejpam-3335	468	29	nonempty	nonempty	NOUN
ejpam-3335	468	30	subset	subset	VERB
ejpam-3335	468	31	u(h	u(h	PROPN
ejpam-3335	468	32	;	;	PUNCT
ejpam-3335	468	33	ε	ε	PROPN
ejpam-3335	468	34	)	)	PUNCT
ejpam-3335	468	35	of	of	ADP
ejpam-3335	468	36	a	a	PRON
ejpam-3335	468	37	is	be	AUX
ejpam-3335	468	38	a	a	DET
ejpam-3335	468	39	upsubalgebra	upsubalgebra	NOUN
ejpam-3335	468	40	of	of	ADP
ejpam-3335	468	41	a.	a.	NOUN
ejpam-3335	468	42	let	let	VERB
ejpam-3335	468	43	x	x	PRON
ejpam-3335	468	44	,	,	PUNCT
ejpam-3335	468	45	y	y	PROPN
ejpam-3335	468	46	∈	∈	PROPN
ejpam-3335	468	47	a.	a.	NOUN
ejpam-3335	468	48	choose	choose	VERB
ejpam-3335	468	49	ε	ε	PROPN
ejpam-3335	468	50	=	=	SYM
ejpam-3335	468	51	hh(x)∩hh(y	hh(x)∩hh(y	ADJ
ejpam-3335	468	52	)	)	PUNCT
ejpam-3335	468	53	∈	∈	PROPN
ejpam-3335	468	54	p([0	p([0	NOUN
ejpam-3335	468	55	,	,	PUNCT
ejpam-3335	468	56	1	1	NUM
ejpam-3335	468	57	]	]	NUM
ejpam-3335	468	58	)	)	PUNCT
ejpam-3335	468	59	.	.	PUNCT
ejpam-3335	469	1	then	then	ADV
ejpam-3335	469	2	hh(x	hh(x	X
ejpam-3335	469	3	)	)	PUNCT
ejpam-3335	469	4	⊇	⊇	PROPN
ejpam-3335	469	5	ε	ε	PROPN
ejpam-3335	469	6	and	and	CCONJ
ejpam-3335	469	7	hh(y	hh(y	NOUN
ejpam-3335	469	8	)	)	PUNCT
ejpam-3335	469	9	⊇	⊇	PROPN
ejpam-3335	469	10	ε	ε	PROPN
ejpam-3335	469	11	.	.	PUNCT
ejpam-3335	470	1	thus	thus	ADV
ejpam-3335	470	2	x	x	X
ejpam-3335	470	3	,	,	PUNCT
ejpam-3335	470	4	y	y	PROPN
ejpam-3335	470	5	∈	∈	PROPN
ejpam-3335	470	6	u(h	u(h	PROPN
ejpam-3335	470	7	;	;	PUNCT
ejpam-3335	470	8	ε	ε	PROPN
ejpam-3335	470	9	)	)	PUNCT
ejpam-3335	470	10	6=	6=	ADP
ejpam-3335	470	11	∅.	∅.	ADP
ejpam-3335	470	12	by	by	ADP
ejpam-3335	470	13	assumption	assumption	NOUN
ejpam-3335	470	14	,	,	PUNCT
ejpam-3335	470	15	we	we	PRON
ejpam-3335	470	16	have	have	AUX
ejpam-3335	470	17	u(h	u(h	PROPN
ejpam-3335	470	18	;	;	PUNCT
ejpam-3335	470	19	ε	ε	PROPN
ejpam-3335	470	20	)	)	PUNCT
ejpam-3335	470	21	is	be	AUX
ejpam-3335	470	22	a	a	DET
ejpam-3335	470	23	up	up	ADJ
ejpam-3335	470	24	-	-	PUNCT
ejpam-3335	470	25	subalgebra	subalgebra	NOUN
ejpam-3335	470	26	of	of	ADP
ejpam-3335	470	27	a	a	PRON
ejpam-3335	470	28	and	and	CCONJ
ejpam-3335	470	29	so	so	ADV
ejpam-3335	470	30	x	x	SYM
ejpam-3335	470	31	·	·	PUNCT
ejpam-3335	470	32	y	y	SYM
ejpam-3335	470	33	∈	∈	PROPN
ejpam-3335	470	34	u(h	u(h	PROPN
ejpam-3335	470	35	;	;	PUNCT
ejpam-3335	470	36	ε	ε	PROPN
ejpam-3335	470	37	)	)	PUNCT
ejpam-3335	470	38	.	.	PUNCT
ejpam-3335	471	1	therefore	therefore	ADV
ejpam-3335	471	2	,	,	PUNCT
ejpam-3335	471	3	hh(x	hh(x	PUNCT
ejpam-3335	471	4	·	·	PUNCT
ejpam-3335	471	5	y	y	X
ejpam-3335	471	6	)	)	PUNCT
ejpam-3335	471	7	⊇	⊇	PROPN
ejpam-3335	471	8	ε	ε	PROPN
ejpam-3335	471	9	=	=	SYM
ejpam-3335	471	10	hh(x	hh(x	X
ejpam-3335	471	11	)	)	PUNCT
ejpam-3335	471	12	∩	∩	NOUN
ejpam-3335	471	13	hh(y	hh(y	NUM
ejpam-3335	471	14	)	)	PUNCT
ejpam-3335	471	15	.	.	PUNCT
ejpam-3335	472	1	by	by	ADP
ejpam-3335	472	2	lemma	lemma	PROPN
ejpam-3335	472	3	1	1	NUM
ejpam-3335	472	4	(	(	PUNCT
ejpam-3335	472	5	2	2	NUM
ejpam-3335	472	6	)	)	PUNCT
ejpam-3335	472	7	,	,	PUNCT
ejpam-3335	472	8	we	we	PRON
ejpam-3335	472	9	have	have	VERB
ejpam-3335	472	10	hh(x	hh(x	X
ejpam-3335	472	11	·	·	PUNCT
ejpam-3335	472	12	y	y	X
ejpam-3335	472	13	)	)	PUNCT
ejpam-3335	472	14	=	=	PUNCT
ejpam-3335	473	1	[	[	X
ejpam-3335	473	2	0	0	NUM
ejpam-3335	473	3	,	,	PUNCT
ejpam-3335	473	4	1]−	1]−	NUM
ejpam-3335	473	5	hh(x	hh(x	X
ejpam-3335	473	6	·	·	PUNCT
ejpam-3335	473	7	y	y	X
ejpam-3335	473	8	)	)	PUNCT
ejpam-3335	473	9	⊆	⊆	NUM
ejpam-3335	473	10	[	[	X
ejpam-3335	473	11	0	0	NUM
ejpam-3335	473	12	,	,	PUNCT
ejpam-3335	473	13	1]−	1]−	NUM
ejpam-3335	473	14	(	(	PUNCT
ejpam-3335	473	15	hh(x	hh(x	NOUN
ejpam-3335	473	16	)	)	PUNCT
ejpam-3335	473	17	∩	∩	NOUN
ejpam-3335	473	18	hh(y	hh(y	NOUN
ejpam-3335	473	19	)	)	PUNCT
ejpam-3335	473	20	)	)	PUNCT
ejpam-3335	474	1	=	=	PUNCT
ejpam-3335	474	2	(	(	PUNCT
ejpam-3335	474	3	[	[	X
ejpam-3335	474	4	0	0	NUM
ejpam-3335	474	5	,	,	PUNCT
ejpam-3335	474	6	1]−	1]−	NUM
ejpam-3335	474	7	hh(x	hh(x	NOUN
ejpam-3335	474	8	)	)	PUNCT
ejpam-3335	474	9	)	)	PUNCT
ejpam-3335	474	10	∪	∪	ADP
ejpam-3335	474	11	(	(	PUNCT
ejpam-3335	474	12	[	[	X
ejpam-3335	474	13	0	0	NUM
ejpam-3335	474	14	,	,	PUNCT
ejpam-3335	474	15	1]−	1]−	NUM
ejpam-3335	474	16	hh(y	hh(y	NOUN
ejpam-3335	474	17	)	)	PUNCT
ejpam-3335	474	18	)	)	PUNCT
ejpam-3335	474	19	=	=	SYM
ejpam-3335	474	20	hh(x	hh(x	X
ejpam-3335	474	21	)	)	PUNCT
ejpam-3335	474	22	∪	∪	ADP
ejpam-3335	474	23	hh(y	hh(y	NOUN
ejpam-3335	474	24	)	)	PUNCT
ejpam-3335	474	25	.	.	PUNCT
ejpam-3335	475	1	hence	hence	ADV
ejpam-3335	475	2	,	,	PUNCT
ejpam-3335	475	3	h	h	PROPN
ejpam-3335	475	4	is	be	AUX
ejpam-3335	475	5	an	an	DET
ejpam-3335	475	6	anti	anti	ADJ
ejpam-3335	475	7	-	-	ADJ
ejpam-3335	475	8	hesitant	hesitant	ADJ
ejpam-3335	475	9	fuzzy	fuzzy	ADJ
ejpam-3335	475	10	up	up	NOUN
ejpam-3335	475	11	-	-	PUNCT
ejpam-3335	475	12	subalgebra	subalgebra	NOUN
ejpam-3335	475	13	of	of	ADP
ejpam-3335	475	14	a.	a.	NOUN
ejpam-3335	475	15	theorem	theorem	NOUN
ejpam-3335	475	16	16	16	NUM
ejpam-3335	475	17	.	.	PUNCT
ejpam-3335	476	1	a	a	DET
ejpam-3335	476	2	hesitant	hesitant	ADJ
ejpam-3335	476	3	fuzzy	fuzzy	ADJ
ejpam-3335	476	4	set	set	VERB
ejpam-3335	476	5	h	h	NOUN
ejpam-3335	476	6	on	on	ADP
ejpam-3335	476	7	a	a	PRON
ejpam-3335	476	8	is	be	AUX
ejpam-3335	476	9	an	an	DET
ejpam-3335	476	10	anti	anti	ADJ
ejpam-3335	476	11	-	-	ADJ
ejpam-3335	476	12	hesitant	hesitant	ADJ
ejpam-3335	476	13	fuzzy	fuzzy	ADJ
ejpam-3335	476	14	up	up	NOUN
ejpam-3335	476	15	-	-	PUNCT
ejpam-3335	476	16	filter	filter	NOUN
ejpam-3335	476	17	of	of	ADP
ejpam-3335	476	18	a	a	DET
ejpam-3335	476	19	if	if	NOUN
ejpam-3335	476	20	and	and	CCONJ
ejpam-3335	476	21	only	only	ADV
ejpam-3335	476	22	if	if	SCONJ
ejpam-3335	476	23	for	for	ADP
ejpam-3335	476	24	all	all	DET
ejpam-3335	476	25	ε	ε	PROPN
ejpam-3335	476	26	∈	∈	PROPN
ejpam-3335	476	27	p([0	p([0	NOUN
ejpam-3335	476	28	,	,	PUNCT
ejpam-3335	476	29	1	1	NUM
ejpam-3335	476	30	]	]	NUM
ejpam-3335	476	31	)	)	PUNCT
ejpam-3335	476	32	,	,	PUNCT
ejpam-3335	476	33	a	a	DET
ejpam-3335	476	34	nonempty	nonempty	NOUN
ejpam-3335	476	35	subset	subset	VERB
ejpam-3335	476	36	u(h	u(h	PROPN
ejpam-3335	476	37	;	;	PUNCT
ejpam-3335	476	38	ε	ε	PROPN
ejpam-3335	476	39	)	)	PUNCT
ejpam-3335	476	40	of	of	ADP
ejpam-3335	476	41	a	a	PRON
ejpam-3335	476	42	is	be	AUX
ejpam-3335	476	43	a	a	DET
ejpam-3335	476	44	up	up	ADJ
ejpam-3335	476	45	-	-	PUNCT
ejpam-3335	476	46	filter	filter	NOUN
ejpam-3335	476	47	of	of	ADP
ejpam-3335	476	48	a.	a.	NOUN
ejpam-3335	476	49	proof	proof	NOUN
ejpam-3335	476	50	.	.	PUNCT
ejpam-3335	477	1	assume	assume	VERB
ejpam-3335	477	2	that	that	SCONJ
ejpam-3335	477	3	h	h	NOUN
ejpam-3335	477	4	is	be	AUX
ejpam-3335	477	5	an	an	DET
ejpam-3335	477	6	anti	anti	ADJ
ejpam-3335	477	7	-	-	ADJ
ejpam-3335	477	8	hesitant	hesitant	ADJ
ejpam-3335	477	9	fuzzy	fuzzy	ADJ
ejpam-3335	477	10	up	up	NOUN
ejpam-3335	477	11	-	-	PUNCT
ejpam-3335	477	12	filter	filter	NOUN
ejpam-3335	477	13	of	of	ADP
ejpam-3335	477	14	a.	a.	NOUN
ejpam-3335	477	15	let	let	VERB
ejpam-3335	477	16	ε	ε	PROPN
ejpam-3335	477	17	∈	∈	PROPN
ejpam-3335	477	18	p([0	p([0	PROPN
ejpam-3335	477	19	,	,	PUNCT
ejpam-3335	477	20	1	1	NUM
ejpam-3335	477	21	]	]	PUNCT
ejpam-3335	477	22	)	)	PUNCT
ejpam-3335	477	23	be	be	AUX
ejpam-3335	477	24	such	such	ADJ
ejpam-3335	477	25	that	that	SCONJ
ejpam-3335	477	26	u(h	u(h	PROPN
ejpam-3335	477	27	;	;	PUNCT
ejpam-3335	477	28	ε	ε	PROPN
ejpam-3335	477	29	)	)	PUNCT
ejpam-3335	477	30	6=	6=	NOUN
ejpam-3335	477	31	∅	∅	NOUN
ejpam-3335	477	32	,	,	PUNCT
ejpam-3335	477	33	and	and	CCONJ
ejpam-3335	477	34	let	let	VERB
ejpam-3335	477	35	x	x	SYM
ejpam-3335	477	36	∈	∈	PROPN
ejpam-3335	477	37	a	a	DET
ejpam-3335	477	38	be	be	AUX
ejpam-3335	477	39	such	such	ADJ
ejpam-3335	477	40	that	that	SCONJ
ejpam-3335	477	41	x	x	SYM
ejpam-3335	477	42	∈	∈	PROPN
ejpam-3335	477	43	u(h	u(h	PROPN
ejpam-3335	477	44	;	;	PUNCT
ejpam-3335	477	45	ε	ε	PROPN
ejpam-3335	477	46	)	)	PUNCT
ejpam-3335	477	47	.	.	PUNCT
ejpam-3335	478	1	then	then	ADV
ejpam-3335	478	2	hh(x	hh(x	X
ejpam-3335	478	3	)	)	PUNCT
ejpam-3335	478	4	⊇	⊇	PROPN
ejpam-3335	478	5	ε	ε	PROPN
ejpam-3335	478	6	.	.	PUNCT
ejpam-3335	479	1	since	since	SCONJ
ejpam-3335	479	2	p.	p.	PROPN
ejpam-3335	479	3	mosrijai	mosrijai	PROPN
ejpam-3335	479	4	,	,	PUNCT
ejpam-3335	479	5	a.	a.	NOUN
ejpam-3335	479	6	iampan	iampan	PROPN
ejpam-3335	479	7	/	/	SYM
ejpam-3335	479	8	eur	eur	PROPN
ejpam-3335	479	9	.	.	PUNCT
ejpam-3335	480	1	j.	j.	PROPN
ejpam-3335	480	2	pure	pure	PROPN
ejpam-3335	480	3	appl	appl	PROPN
ejpam-3335	480	4	.	.	PROPN
ejpam-3335	480	5	math	math	PROPN
ejpam-3335	480	6	,	,	PUNCT
ejpam-3335	480	7	11	11	NUM
ejpam-3335	480	8	(	(	PUNCT
ejpam-3335	480	9	4	4	NUM
ejpam-3335	480	10	)	)	PUNCT
ejpam-3335	480	11	(	(	PUNCT
ejpam-3335	480	12	2018	2018	NUM
ejpam-3335	480	13	)	)	PUNCT
ejpam-3335	480	14	,	,	PUNCT
ejpam-3335	480	15	976	976	NUM
ejpam-3335	480	16	-	-	SYM
ejpam-3335	480	17	1002	1002	NUM
ejpam-3335	480	18	992	992	NUM
ejpam-3335	480	19	h	h	NOUN
ejpam-3335	480	20	is	be	AUX
ejpam-3335	480	21	an	an	DET
ejpam-3335	480	22	anti	anti	ADJ
ejpam-3335	480	23	-	-	ADJ
ejpam-3335	480	24	hesitant	hesitant	ADJ
ejpam-3335	480	25	fuzzy	fuzzy	ADJ
ejpam-3335	480	26	up	up	NOUN
ejpam-3335	480	27	-	-	PUNCT
ejpam-3335	480	28	filter	filter	NOUN
ejpam-3335	480	29	of	of	ADP
ejpam-3335	480	30	a	a	PRON
ejpam-3335	480	31	,	,	PUNCT
ejpam-3335	480	32	we	we	PRON
ejpam-3335	480	33	have	have	VERB
ejpam-3335	480	34	hh(0	hh(0	NOUN
ejpam-3335	480	35	)	)	PUNCT
ejpam-3335	480	36	⊆	⊆	NUM
ejpam-3335	480	37	hh(x	hh(x	NOUN
ejpam-3335	480	38	)	)	PUNCT
ejpam-3335	480	39	.	.	PUNCT
ejpam-3335	481	1	thus	thus	ADV
ejpam-3335	481	2	[	[	X
ejpam-3335	481	3	0	0	NUM
ejpam-3335	481	4	,	,	PUNCT
ejpam-3335	481	5	1]−	1]−	NUM
ejpam-3335	481	6	hh(0	hh(0	NOUN
ejpam-3335	481	7	)	)	PUNCT
ejpam-3335	481	8	⊆	⊆	NUM
ejpam-3335	482	1	[	[	X
ejpam-3335	482	2	0	0	NUM
ejpam-3335	482	3	,	,	PUNCT
ejpam-3335	482	4	1]−	1]−	NUM
ejpam-3335	482	5	hh(x	hh(x	NOUN
ejpam-3335	482	6	)	)	PUNCT
ejpam-3335	482	7	.	.	PUNCT
ejpam-3335	483	1	therefore	therefore	ADV
ejpam-3335	483	2	,	,	PUNCT
ejpam-3335	483	3	hh(0	hh(0	NOUN
ejpam-3335	483	4	)	)	PUNCT
ejpam-3335	483	5	⊇	⊇	NOUN
ejpam-3335	483	6	hh(x	hh(x	X
ejpam-3335	483	7	)	)	PUNCT
ejpam-3335	483	8	⊇	⊇	PROPN
ejpam-3335	483	9	ε	ε	PROPN
ejpam-3335	483	10	.	.	PUNCT
ejpam-3335	484	1	hence	hence	ADV
ejpam-3335	484	2	,	,	PUNCT
ejpam-3335	484	3	0	0	NUM
ejpam-3335	484	4	∈	∈	PROPN
ejpam-3335	484	5	u(hh	u(hh	PROPN
ejpam-3335	484	6	;	;	PUNCT
ejpam-3335	484	7	ε	ε	PROPN
ejpam-3335	484	8	)	)	PUNCT
ejpam-3335	484	9	.	.	PUNCT
ejpam-3335	485	1	next	next	ADV
ejpam-3335	485	2	,	,	PUNCT
ejpam-3335	485	3	let	let	VERB
ejpam-3335	485	4	x	x	PRON
ejpam-3335	485	5	,	,	PUNCT
ejpam-3335	485	6	y	y	PROPN
ejpam-3335	485	7	∈	∈	PROPN
ejpam-3335	485	8	a	a	PRON
ejpam-3335	485	9	be	be	AUX
ejpam-3335	485	10	such	such	ADJ
ejpam-3335	485	11	that	that	SCONJ
ejpam-3335	485	12	x	x	X
ejpam-3335	485	13	·	·	PUNCT
ejpam-3335	485	14	y	y	PROPN
ejpam-3335	485	15	∈	∈	PROPN
ejpam-3335	485	16	u(h	u(h	PROPN
ejpam-3335	485	17	;	;	PUNCT
ejpam-3335	485	18	ε	ε	PROPN
ejpam-3335	485	19	)	)	PUNCT
ejpam-3335	485	20	and	and	CCONJ
ejpam-3335	485	21	x	x	PUNCT
ejpam-3335	485	22	∈	∈	PROPN
ejpam-3335	485	23	u(h	u(h	PROPN
ejpam-3335	485	24	;	;	PUNCT
ejpam-3335	485	25	ε	ε	PROPN
ejpam-3335	485	26	)	)	PUNCT
ejpam-3335	485	27	.	.	PUNCT
ejpam-3335	486	1	then	then	ADV
ejpam-3335	486	2	hh(x	hh(x	PUNCT
ejpam-3335	486	3	·	·	SYM
ejpam-3335	486	4	y	y	X
ejpam-3335	486	5	)	)	PUNCT
ejpam-3335	486	6	⊇	⊇	PROPN
ejpam-3335	486	7	ε	ε	PROPN
ejpam-3335	486	8	and	and	CCONJ
ejpam-3335	486	9	hh(x	hh(x	NOUN
ejpam-3335	486	10	)	)	PUNCT
ejpam-3335	486	11	⊇	⊇	PROPN
ejpam-3335	486	12	ε	ε	PROPN
ejpam-3335	486	13	.	.	PROPN
ejpam-3335	487	1	since	since	SCONJ
ejpam-3335	487	2	h	h	NOUN
ejpam-3335	487	3	is	be	AUX
ejpam-3335	487	4	an	an	DET
ejpam-3335	487	5	anti	anti	ADJ
ejpam-3335	487	6	-	-	ADJ
ejpam-3335	487	7	hesitant	hesitant	ADJ
ejpam-3335	487	8	fuzzy	fuzzy	ADJ
ejpam-3335	487	9	up	up	NOUN
ejpam-3335	487	10	-	-	PUNCT
ejpam-3335	487	11	filter	filter	NOUN
ejpam-3335	487	12	of	of	ADP
ejpam-3335	487	13	a	a	PRON
ejpam-3335	487	14	,	,	PUNCT
ejpam-3335	487	15	we	we	PRON
ejpam-3335	487	16	have	have	VERB
ejpam-3335	487	17	hh(y	hh(y	NOUN
ejpam-3335	487	18	)	)	PUNCT
ejpam-3335	488	1	⊆	⊆	NUM
ejpam-3335	488	2	hh(x	hh(x	X
ejpam-3335	488	3	·	·	PUNCT
ejpam-3335	488	4	y	y	X
ejpam-3335	488	5	)	)	PUNCT
ejpam-3335	488	6	∪	∪	ADP
ejpam-3335	488	7	hh(x	hh(x	NOUN
ejpam-3335	488	8	)	)	PUNCT
ejpam-3335	488	9	.	.	PUNCT
ejpam-3335	489	1	by	by	ADP
ejpam-3335	489	2	lemma	lemma	PROPN
ejpam-3335	489	3	1	1	NUM
ejpam-3335	489	4	(	(	PUNCT
ejpam-3335	489	5	2	2	NUM
ejpam-3335	489	6	)	)	PUNCT
ejpam-3335	489	7	,	,	PUNCT
ejpam-3335	489	8	we	we	PRON
ejpam-3335	489	9	have	have	VERB
ejpam-3335	489	10	[	[	X
ejpam-3335	489	11	0	0	NUM
ejpam-3335	489	12	,	,	PUNCT
ejpam-3335	489	13	1	1	NUM
ejpam-3335	489	14	]	]	PUNCT
ejpam-3335	489	15	−	−	NOUN
ejpam-3335	489	16	hh(y	hh(y	NOUN
ejpam-3335	489	17	)	)	PUNCT
ejpam-3335	489	18	⊆	⊆	X
ejpam-3335	489	19	(	(	PUNCT
ejpam-3335	489	20	[	[	X
ejpam-3335	489	21	0	0	NUM
ejpam-3335	489	22	,	,	PUNCT
ejpam-3335	489	23	1	1	NUM
ejpam-3335	489	24	]	]	SYM
ejpam-3335	489	25	−	−	NUM
ejpam-3335	489	26	hh(x	hh(x	X
ejpam-3335	489	27	·	·	PUNCT
ejpam-3335	489	28	y	y	X
ejpam-3335	489	29	)	)	PUNCT
ejpam-3335	489	30	)	)	PUNCT
ejpam-3335	490	1	∪	∪	ADP
ejpam-3335	490	2	(	(	PUNCT
ejpam-3335	490	3	[	[	X
ejpam-3335	490	4	0	0	NUM
ejpam-3335	490	5	,	,	PUNCT
ejpam-3335	490	6	1	1	NUM
ejpam-3335	490	7	]	]	SYM
ejpam-3335	490	8	−	−	NOUN
ejpam-3335	490	9	hh(x	hh(x	NOUN
ejpam-3335	490	10	)	)	PUNCT
ejpam-3335	490	11	)	)	PUNCT
ejpam-3335	491	1	=	=	PUNCT
ejpam-3335	492	1	[	[	X
ejpam-3335	492	2	0	0	NUM
ejpam-3335	492	3	,	,	PUNCT
ejpam-3335	492	4	1	1	NUM
ejpam-3335	492	5	]	]	SYM
ejpam-3335	492	6	−	−	PROPN
ejpam-3335	492	7	(	(	PUNCT
ejpam-3335	492	8	hh(x	hh(x	X
ejpam-3335	492	9	·	·	PUNCT
ejpam-3335	492	10	y	y	X
ejpam-3335	492	11	)	)	PUNCT
ejpam-3335	492	12	∩	∩	NOUN
ejpam-3335	492	13	hh(x	hh(x	X
ejpam-3335	492	14	)	)	PUNCT
ejpam-3335	492	15	)	)	PUNCT
ejpam-3335	492	16	.	.	PUNCT
ejpam-3335	493	1	thus	thus	ADV
ejpam-3335	493	2	hh(y	hh(y	X
ejpam-3335	493	3	)	)	PUNCT
ejpam-3335	493	4	⊇	⊇	NOUN
ejpam-3335	493	5	hh(x	hh(x	X
ejpam-3335	493	6	·	·	PUNCT
ejpam-3335	493	7	y	y	X
ejpam-3335	493	8	)	)	PUNCT
ejpam-3335	493	9	∩	∩	NOUN
ejpam-3335	493	10	hh(x	hh(x	PRON
ejpam-3335	493	11	)	)	PUNCT
ejpam-3335	493	12	⊇	⊇	PROPN
ejpam-3335	493	13	ε	ε	PROPN
ejpam-3335	493	14	.	.	PUNCT
ejpam-3335	494	1	therefore	therefore	ADV
ejpam-3335	494	2	,	,	PUNCT
ejpam-3335	494	3	y	y	PROPN
ejpam-3335	494	4	∈	∈	PROPN
ejpam-3335	494	5	u(h	u(h	PROPN
ejpam-3335	494	6	;	;	PUNCT
ejpam-3335	494	7	ε	ε	PROPN
ejpam-3335	494	8	)	)	PUNCT
ejpam-3335	494	9	.	.	PUNCT
ejpam-3335	495	1	hence	hence	ADV
ejpam-3335	495	2	,	,	PUNCT
ejpam-3335	495	3	u(h	u(h	PROPN
ejpam-3335	495	4	;	;	PUNCT
ejpam-3335	495	5	ε	ε	PROPN
ejpam-3335	495	6	)	)	PUNCT
ejpam-3335	495	7	is	be	AUX
ejpam-3335	495	8	a	a	DET
ejpam-3335	495	9	up	up	ADJ
ejpam-3335	495	10	-	-	PUNCT
ejpam-3335	495	11	filter	filter	NOUN
ejpam-3335	495	12	of	of	ADP
ejpam-3335	495	13	a.	a.	NOUN
ejpam-3335	495	14	conversely	conversely	ADV
ejpam-3335	495	15	,	,	PUNCT
ejpam-3335	495	16	assume	assume	VERB
ejpam-3335	495	17	that	that	SCONJ
ejpam-3335	495	18	for	for	ADP
ejpam-3335	495	19	all	all	DET
ejpam-3335	495	20	ε	ε	PROPN
ejpam-3335	495	21	∈	∈	PROPN
ejpam-3335	495	22	p([0	p([0	NOUN
ejpam-3335	495	23	,	,	PUNCT
ejpam-3335	495	24	1	1	NUM
ejpam-3335	495	25	]	]	NUM
ejpam-3335	495	26	)	)	PUNCT
ejpam-3335	495	27	,	,	PUNCT
ejpam-3335	495	28	a	a	DET
ejpam-3335	495	29	nonempty	nonempty	NOUN
ejpam-3335	495	30	subset	subset	VERB
ejpam-3335	495	31	u(h	u(h	PROPN
ejpam-3335	495	32	;	;	PUNCT
ejpam-3335	495	33	ε	ε	PROPN
ejpam-3335	495	34	)	)	PUNCT
ejpam-3335	495	35	of	of	ADP
ejpam-3335	495	36	a	a	PRON
ejpam-3335	495	37	is	be	AUX
ejpam-3335	495	38	a	a	DET
ejpam-3335	495	39	up	up	ADJ
ejpam-3335	495	40	-	-	PUNCT
ejpam-3335	495	41	filter	filter	NOUN
ejpam-3335	495	42	of	of	ADP
ejpam-3335	495	43	a.	a.	NOUN
ejpam-3335	495	44	let	let	VERB
ejpam-3335	495	45	x	x	X
ejpam-3335	495	46	∈	∈	PROPN
ejpam-3335	495	47	a.	a.	NOUN
ejpam-3335	495	48	choose	choose	VERB
ejpam-3335	495	49	ε	ε	PROPN
ejpam-3335	495	50	=	=	SYM
ejpam-3335	495	51	hh(x	hh(x	X
ejpam-3335	495	52	)	)	PUNCT
ejpam-3335	495	53	∈	∈	PROPN
ejpam-3335	495	54	p([0	p([0	NOUN
ejpam-3335	495	55	,	,	PUNCT
ejpam-3335	495	56	1	1	NUM
ejpam-3335	495	57	]	]	NUM
ejpam-3335	495	58	)	)	PUNCT
ejpam-3335	495	59	.	.	PUNCT
ejpam-3335	496	1	then	then	ADV
ejpam-3335	496	2	hh(x	hh(x	X
ejpam-3335	496	3	)	)	PUNCT
ejpam-3335	496	4	⊇	⊇	PROPN
ejpam-3335	496	5	ε	ε	PROPN
ejpam-3335	496	6	.	.	PUNCT
ejpam-3335	497	1	thus	thus	ADV
ejpam-3335	497	2	x	x	SYM
ejpam-3335	497	3	∈	∈	PROPN
ejpam-3335	497	4	u(h	u(h	PROPN
ejpam-3335	497	5	;	;	PUNCT
ejpam-3335	497	6	ε	ε	PROPN
ejpam-3335	497	7	)	)	PUNCT
ejpam-3335	497	8	6=	6=	ADP
ejpam-3335	497	9	∅.	∅.	ADP
ejpam-3335	497	10	by	by	ADP
ejpam-3335	497	11	assumption	assumption	NOUN
ejpam-3335	497	12	,	,	PUNCT
ejpam-3335	497	13	we	we	PRON
ejpam-3335	497	14	have	have	AUX
ejpam-3335	497	15	u(h	u(h	PROPN
ejpam-3335	497	16	;	;	PUNCT
ejpam-3335	497	17	ε	ε	PROPN
ejpam-3335	497	18	)	)	PUNCT
ejpam-3335	497	19	is	be	AUX
ejpam-3335	497	20	a	a	DET
ejpam-3335	497	21	up	up	ADJ
ejpam-3335	497	22	-	-	PUNCT
ejpam-3335	497	23	filter	filter	NOUN
ejpam-3335	497	24	of	of	ADP
ejpam-3335	497	25	a	a	PRON
ejpam-3335	497	26	and	and	CCONJ
ejpam-3335	497	27	so	so	ADV
ejpam-3335	497	28	0	0	NUM
ejpam-3335	497	29	∈	∈	PROPN
ejpam-3335	497	30	u(h	u(h	PROPN
ejpam-3335	497	31	;	;	PUNCT
ejpam-3335	497	32	ε	ε	PROPN
ejpam-3335	497	33	)	)	PUNCT
ejpam-3335	497	34	.	.	PUNCT
ejpam-3335	498	1	therefore	therefore	ADV
ejpam-3335	498	2	,	,	PUNCT
ejpam-3335	498	3	hh(0	hh(0	NOUN
ejpam-3335	498	4	)	)	PUNCT
ejpam-3335	498	5	⊇	⊇	PROPN
ejpam-3335	498	6	ε	ε	PROPN
ejpam-3335	498	7	=	=	SYM
ejpam-3335	498	8	hh(x	hh(x	X
ejpam-3335	498	9	)	)	PUNCT
ejpam-3335	498	10	.	.	PUNCT
ejpam-3335	499	1	hence	hence	ADV
ejpam-3335	499	2	,	,	PUNCT
ejpam-3335	499	3	hh(0	hh(0	NOUN
ejpam-3335	499	4	)	)	PUNCT
ejpam-3335	499	5	=	=	PUNCT
ejpam-3335	500	1	[	[	X
ejpam-3335	500	2	0	0	NUM
ejpam-3335	500	3	,	,	PUNCT
ejpam-3335	500	4	1]−	1]−	NUM
ejpam-3335	500	5	hh(0	hh(0	NOUN
ejpam-3335	500	6	)	)	PUNCT
ejpam-3335	500	7	⊆	⊆	NUM
ejpam-3335	500	8	[	[	X
ejpam-3335	500	9	0	0	NUM
ejpam-3335	500	10	,	,	PUNCT
ejpam-3335	500	11	1]−	1]−	NUM
ejpam-3335	500	12	hh(x	hh(x	NOUN
ejpam-3335	500	13	)	)	PUNCT
ejpam-3335	500	14	=	=	SYM
ejpam-3335	500	15	hh(x	hh(x	X
ejpam-3335	500	16	)	)	PUNCT
ejpam-3335	500	17	.	.	PUNCT
ejpam-3335	501	1	next	next	ADV
ejpam-3335	501	2	,	,	PUNCT
ejpam-3335	501	3	let	let	VERB
ejpam-3335	501	4	x	x	PRON
ejpam-3335	501	5	,	,	PUNCT
ejpam-3335	501	6	y	y	PROPN
ejpam-3335	501	7	∈	∈	PROPN
ejpam-3335	501	8	a.	a.	NOUN
ejpam-3335	501	9	choose	choose	VERB
ejpam-3335	501	10	ε	ε	PROPN
ejpam-3335	501	11	=	=	SYM
ejpam-3335	501	12	hh(x	hh(x	X
ejpam-3335	501	13	·	·	PUNCT
ejpam-3335	501	14	y	y	X
ejpam-3335	501	15	)	)	PUNCT
ejpam-3335	501	16	∩	∩	NOUN
ejpam-3335	501	17	hh(x	hh(x	X
ejpam-3335	501	18	)	)	PUNCT
ejpam-3335	501	19	∈	∈	PROPN
ejpam-3335	501	20	p([0	p([0	NOUN
ejpam-3335	501	21	,	,	PUNCT
ejpam-3335	501	22	1	1	NUM
ejpam-3335	501	23	]	]	NUM
ejpam-3335	501	24	)	)	PUNCT
ejpam-3335	501	25	.	.	PUNCT
ejpam-3335	502	1	then	then	ADV
ejpam-3335	502	2	hh(x	hh(x	PUNCT
ejpam-3335	502	3	·	·	PUNCT
ejpam-3335	502	4	y	y	X
ejpam-3335	502	5	)	)	PUNCT
ejpam-3335	502	6	⊇	⊇	PROPN
ejpam-3335	502	7	ε	ε	PROPN
ejpam-3335	502	8	and	and	CCONJ
ejpam-3335	502	9	hh(x	hh(x	NOUN
ejpam-3335	502	10	)	)	PUNCT
ejpam-3335	502	11	⊇	⊇	PROPN
ejpam-3335	502	12	ε	ε	PROPN
ejpam-3335	502	13	.	.	PUNCT
ejpam-3335	503	1	thus	thus	ADV
ejpam-3335	503	2	x	x	X
ejpam-3335	503	3	·	·	PUNCT
ejpam-3335	503	4	y	y	X
ejpam-3335	503	5	,	,	PUNCT
ejpam-3335	503	6	x	x	SYM
ejpam-3335	503	7	∈	∈	PROPN
ejpam-3335	503	8	u(h	u(h	PROPN
ejpam-3335	503	9	;	;	PUNCT
ejpam-3335	503	10	ε	ε	PROPN
ejpam-3335	503	11	)	)	PUNCT
ejpam-3335	503	12	6=	6=	ADP
ejpam-3335	503	13	∅.	∅.	ADP
ejpam-3335	503	14	by	by	ADP
ejpam-3335	503	15	assumption	assumption	NOUN
ejpam-3335	503	16	,	,	PUNCT
ejpam-3335	503	17	we	we	PRON
ejpam-3335	503	18	have	have	AUX
ejpam-3335	503	19	u(h	u(h	PROPN
ejpam-3335	503	20	;	;	PUNCT
ejpam-3335	503	21	ε	ε	PROPN
ejpam-3335	503	22	)	)	PUNCT
ejpam-3335	503	23	is	be	AUX
ejpam-3335	503	24	a	a	DET
ejpam-3335	503	25	up	up	ADJ
ejpam-3335	503	26	-	-	PUNCT
ejpam-3335	503	27	filter	filter	NOUN
ejpam-3335	503	28	of	of	ADP
ejpam-3335	503	29	a	a	PRON
ejpam-3335	503	30	and	and	CCONJ
ejpam-3335	503	31	so	so	ADV
ejpam-3335	503	32	y	y	PROPN
ejpam-3335	503	33	∈	∈	PROPN
ejpam-3335	503	34	u(h	u(h	PROPN
ejpam-3335	503	35	;	;	PUNCT
ejpam-3335	503	36	ε	ε	PROPN
ejpam-3335	503	37	)	)	PUNCT
ejpam-3335	503	38	.	.	PUNCT
ejpam-3335	504	1	therefore	therefore	ADV
ejpam-3335	504	2	,	,	PUNCT
ejpam-3335	504	3	hh(y	hh(y	ADJ
ejpam-3335	504	4	)	)	PUNCT
ejpam-3335	504	5	⊇	⊇	X
ejpam-3335	504	6	ε	ε	PROPN
ejpam-3335	504	7	=	=	SYM
ejpam-3335	504	8	hh(x	hh(x	X
ejpam-3335	504	9	·	·	PUNCT
ejpam-3335	504	10	y	y	X
ejpam-3335	504	11	)	)	PUNCT
ejpam-3335	504	12	∩	∩	NOUN
ejpam-3335	504	13	hh(x	hh(x	X
ejpam-3335	504	14	)	)	PUNCT
ejpam-3335	504	15	.	.	PUNCT
ejpam-3335	505	1	by	by	ADP
ejpam-3335	505	2	lemma	lemma	PROPN
ejpam-3335	505	3	1	1	NUM
ejpam-3335	505	4	(	(	PUNCT
ejpam-3335	505	5	2	2	NUM
ejpam-3335	505	6	)	)	PUNCT
ejpam-3335	505	7	,	,	PUNCT
ejpam-3335	505	8	we	we	PRON
ejpam-3335	505	9	have	have	VERB
ejpam-3335	505	10	hh(y	hh(y	NOUN
ejpam-3335	505	11	)	)	PUNCT
ejpam-3335	505	12	=	=	PUNCT
ejpam-3335	506	1	[	[	X
ejpam-3335	506	2	0	0	NUM
ejpam-3335	506	3	,	,	PUNCT
ejpam-3335	506	4	1]−	1]−	NUM
ejpam-3335	506	5	hh(y	hh(y	NOUN
ejpam-3335	506	6	)	)	PUNCT
ejpam-3335	506	7	⊆	⊆	NUM
ejpam-3335	506	8	[	[	X
ejpam-3335	506	9	0	0	NUM
ejpam-3335	506	10	,	,	PUNCT
ejpam-3335	506	11	1]−	1]−	NUM
ejpam-3335	506	12	(	(	PUNCT
ejpam-3335	506	13	hh(x	hh(x	X
ejpam-3335	506	14	·	·	PUNCT
ejpam-3335	506	15	y	y	X
ejpam-3335	506	16	)	)	PUNCT
ejpam-3335	506	17	∩	∩	NOUN
ejpam-3335	506	18	hh(x	hh(x	X
ejpam-3335	506	19	)	)	PUNCT
ejpam-3335	506	20	)	)	PUNCT
ejpam-3335	507	1	=	=	PUNCT
ejpam-3335	507	2	(	(	PUNCT
ejpam-3335	507	3	[	[	X
ejpam-3335	507	4	0	0	NUM
ejpam-3335	507	5	,	,	PUNCT
ejpam-3335	507	6	1]−	1]−	NUM
ejpam-3335	507	7	hh(x	hh(x	X
ejpam-3335	507	8	·	·	PUNCT
ejpam-3335	507	9	y	y	X
ejpam-3335	507	10	)	)	PUNCT
ejpam-3335	507	11	)	)	PUNCT
ejpam-3335	507	12	∪	∪	ADP
ejpam-3335	507	13	(	(	PUNCT
ejpam-3335	507	14	[	[	X
ejpam-3335	507	15	0	0	NUM
ejpam-3335	507	16	,	,	PUNCT
ejpam-3335	507	17	1]−	1]−	NUM
ejpam-3335	507	18	hh(x	hh(x	NOUN
ejpam-3335	507	19	)	)	PUNCT
ejpam-3335	507	20	)	)	PUNCT
ejpam-3335	508	1	=	=	SYM
ejpam-3335	508	2	hh(x	hh(x	X
ejpam-3335	508	3	·	·	PUNCT
ejpam-3335	508	4	y	y	X
ejpam-3335	508	5	)	)	PUNCT
ejpam-3335	508	6	∪	∪	ADP
ejpam-3335	508	7	hh(x	hh(x	NOUN
ejpam-3335	508	8	)	)	PUNCT
ejpam-3335	508	9	.	.	PUNCT
ejpam-3335	509	1	hence	hence	ADV
ejpam-3335	509	2	,	,	PUNCT
ejpam-3335	509	3	h	h	PROPN
ejpam-3335	509	4	is	be	AUX
ejpam-3335	509	5	an	an	DET
ejpam-3335	509	6	anti	anti	ADJ
ejpam-3335	509	7	-	-	ADJ
ejpam-3335	509	8	hesitant	hesitant	ADJ
ejpam-3335	509	9	fuzzy	fuzzy	ADJ
ejpam-3335	509	10	up	up	NOUN
ejpam-3335	509	11	-	-	PUNCT
ejpam-3335	509	12	filter	filter	NOUN
ejpam-3335	509	13	of	of	ADP
ejpam-3335	509	14	a.	a.	NOUN
ejpam-3335	509	15	theorem	theorem	NOUN
ejpam-3335	509	16	17	17	NUM
ejpam-3335	509	17	.	.	PUNCT
ejpam-3335	510	1	a	a	DET
ejpam-3335	510	2	hesitant	hesitant	ADJ
ejpam-3335	510	3	fuzzy	fuzzy	ADJ
ejpam-3335	510	4	set	set	VERB
ejpam-3335	510	5	h	h	NOUN
ejpam-3335	510	6	on	on	ADP
ejpam-3335	510	7	a	a	PRON
ejpam-3335	510	8	is	be	AUX
ejpam-3335	510	9	an	an	DET
ejpam-3335	510	10	anti	anti	ADJ
ejpam-3335	510	11	-	-	ADJ
ejpam-3335	510	12	hesitant	hesitant	ADJ
ejpam-3335	510	13	fuzzy	fuzzy	ADJ
ejpam-3335	510	14	up	up	NOUN
ejpam-3335	510	15	-	-	PUNCT
ejpam-3335	510	16	ideal	ideal	NOUN
ejpam-3335	510	17	of	of	ADP
ejpam-3335	510	18	a	a	DET
ejpam-3335	510	19	if	if	NOUN
ejpam-3335	510	20	and	and	CCONJ
ejpam-3335	510	21	only	only	ADV
ejpam-3335	510	22	if	if	SCONJ
ejpam-3335	510	23	for	for	ADP
ejpam-3335	510	24	all	all	DET
ejpam-3335	510	25	ε	ε	PROPN
ejpam-3335	510	26	∈	∈	PROPN
ejpam-3335	510	27	p([0	p([0	NOUN
ejpam-3335	510	28	,	,	PUNCT
ejpam-3335	510	29	1	1	NUM
ejpam-3335	510	30	]	]	NUM
ejpam-3335	510	31	)	)	PUNCT
ejpam-3335	510	32	,	,	PUNCT
ejpam-3335	510	33	a	a	DET
ejpam-3335	510	34	nonempty	nonempty	NOUN
ejpam-3335	510	35	subset	subset	VERB
ejpam-3335	510	36	u(h	u(h	PROPN
ejpam-3335	510	37	;	;	PUNCT
ejpam-3335	510	38	ε	ε	PROPN
ejpam-3335	510	39	)	)	PUNCT
ejpam-3335	510	40	of	of	ADP
ejpam-3335	510	41	a	a	PRON
ejpam-3335	510	42	is	be	AUX
ejpam-3335	510	43	a	a	DET
ejpam-3335	510	44	up	up	ADJ
ejpam-3335	510	45	-	-	PUNCT
ejpam-3335	510	46	ideal	ideal	NOUN
ejpam-3335	510	47	of	of	ADP
ejpam-3335	510	48	a.	a.	NOUN
ejpam-3335	510	49	proof	proof	NOUN
ejpam-3335	510	50	.	.	PUNCT
ejpam-3335	511	1	assume	assume	VERB
ejpam-3335	511	2	that	that	SCONJ
ejpam-3335	511	3	h	h	NOUN
ejpam-3335	511	4	is	be	AUX
ejpam-3335	511	5	an	an	DET
ejpam-3335	511	6	anti	anti	ADJ
ejpam-3335	511	7	-	-	ADJ
ejpam-3335	511	8	hesitant	hesitant	ADJ
ejpam-3335	511	9	fuzzy	fuzzy	ADJ
ejpam-3335	511	10	up	up	NOUN
ejpam-3335	511	11	-	-	PUNCT
ejpam-3335	511	12	ideal	ideal	NOUN
ejpam-3335	511	13	of	of	ADP
ejpam-3335	511	14	a.	a.	NOUN
ejpam-3335	511	15	let	let	VERB
ejpam-3335	511	16	ε	ε	PROPN
ejpam-3335	511	17	∈	∈	PROPN
ejpam-3335	511	18	p([0	p([0	PROPN
ejpam-3335	511	19	,	,	PUNCT
ejpam-3335	511	20	1	1	NUM
ejpam-3335	511	21	]	]	PUNCT
ejpam-3335	511	22	)	)	PUNCT
ejpam-3335	511	23	be	be	AUX
ejpam-3335	511	24	such	such	ADJ
ejpam-3335	511	25	that	that	SCONJ
ejpam-3335	511	26	u(h	u(h	PROPN
ejpam-3335	511	27	;	;	PUNCT
ejpam-3335	511	28	ε	ε	PROPN
ejpam-3335	511	29	)	)	PUNCT
ejpam-3335	511	30	6=	6=	NOUN
ejpam-3335	511	31	∅	∅	NOUN
ejpam-3335	511	32	,	,	PUNCT
ejpam-3335	511	33	and	and	CCONJ
ejpam-3335	511	34	let	let	VERB
ejpam-3335	511	35	x	x	SYM
ejpam-3335	511	36	∈	∈	PROPN
ejpam-3335	511	37	a	a	DET
ejpam-3335	511	38	be	be	AUX
ejpam-3335	511	39	such	such	ADJ
ejpam-3335	511	40	that	that	SCONJ
ejpam-3335	511	41	x	x	SYM
ejpam-3335	511	42	∈	∈	PROPN
ejpam-3335	511	43	u(h	u(h	PROPN
ejpam-3335	511	44	;	;	PUNCT
ejpam-3335	511	45	ε	ε	PROPN
ejpam-3335	511	46	)	)	PUNCT
ejpam-3335	511	47	.	.	PUNCT
ejpam-3335	512	1	then	then	ADV
ejpam-3335	512	2	hh(x	hh(x	X
ejpam-3335	512	3	)	)	PUNCT
ejpam-3335	512	4	⊇	⊇	PROPN
ejpam-3335	512	5	ε	ε	PROPN
ejpam-3335	512	6	.	.	PROPN
ejpam-3335	513	1	since	since	SCONJ
ejpam-3335	513	2	h	h	NOUN
ejpam-3335	513	3	is	be	AUX
ejpam-3335	513	4	an	an	DET
ejpam-3335	513	5	anti	anti	ADJ
ejpam-3335	513	6	-	-	ADJ
ejpam-3335	513	7	hesitant	hesitant	ADJ
ejpam-3335	513	8	fuzzy	fuzzy	ADJ
ejpam-3335	513	9	up	up	NOUN
ejpam-3335	513	10	-	-	PUNCT
ejpam-3335	513	11	ideal	ideal	NOUN
ejpam-3335	513	12	of	of	ADP
ejpam-3335	513	13	a	a	PRON
ejpam-3335	513	14	,	,	PUNCT
ejpam-3335	513	15	we	we	PRON
ejpam-3335	513	16	have	have	VERB
ejpam-3335	513	17	hh(0	hh(0	NOUN
ejpam-3335	513	18	)	)	PUNCT
ejpam-3335	513	19	⊆	⊆	NUM
ejpam-3335	513	20	hh(x	hh(x	NOUN
ejpam-3335	513	21	)	)	PUNCT
ejpam-3335	513	22	.	.	PUNCT
ejpam-3335	514	1	thus	thus	ADV
ejpam-3335	514	2	[	[	X
ejpam-3335	514	3	0	0	NUM
ejpam-3335	514	4	,	,	PUNCT
ejpam-3335	514	5	1]−	1]−	NUM
ejpam-3335	514	6	hh(0	hh(0	NOUN
ejpam-3335	514	7	)	)	PUNCT
ejpam-3335	514	8	⊆	⊆	NUM
ejpam-3335	515	1	[	[	X
ejpam-3335	515	2	0	0	NUM
ejpam-3335	515	3	,	,	PUNCT
ejpam-3335	515	4	1]−	1]−	NUM
ejpam-3335	515	5	hh(x	hh(x	NOUN
ejpam-3335	515	6	)	)	PUNCT
ejpam-3335	515	7	.	.	PUNCT
ejpam-3335	516	1	therefore	therefore	ADV
ejpam-3335	516	2	,	,	PUNCT
ejpam-3335	516	3	hh(0	hh(0	NOUN
ejpam-3335	516	4	)	)	PUNCT
ejpam-3335	516	5	⊇	⊇	NOUN
ejpam-3335	516	6	hh(x	hh(x	X
ejpam-3335	516	7	)	)	PUNCT
ejpam-3335	516	8	⊇	⊇	PROPN
ejpam-3335	516	9	ε	ε	PROPN
ejpam-3335	516	10	.	.	PUNCT
ejpam-3335	517	1	hence	hence	ADV
ejpam-3335	517	2	,	,	PUNCT
ejpam-3335	517	3	0	0	NUM
ejpam-3335	517	4	∈	∈	PROPN
ejpam-3335	517	5	u(h	u(h	PROPN
ejpam-3335	517	6	;	;	PUNCT
ejpam-3335	517	7	ε	ε	PROPN
ejpam-3335	517	8	)	)	PUNCT
ejpam-3335	517	9	.	.	PUNCT
ejpam-3335	518	1	next	next	ADV
ejpam-3335	518	2	,	,	PUNCT
ejpam-3335	518	3	let	let	VERB
ejpam-3335	518	4	x	x	PRON
ejpam-3335	518	5	,	,	PUNCT
ejpam-3335	518	6	y	y	PROPN
ejpam-3335	518	7	,	,	PUNCT
ejpam-3335	518	8	z	z	PROPN
ejpam-3335	518	9	∈	∈	PROPN
ejpam-3335	518	10	a	a	DET
ejpam-3335	518	11	be	be	AUX
ejpam-3335	518	12	such	such	ADJ
ejpam-3335	518	13	that	that	SCONJ
ejpam-3335	518	14	x	x	PART
ejpam-3335	518	15	·	·	PUNCT
ejpam-3335	518	16	(	(	PUNCT
ejpam-3335	518	17	y	y	PROPN
ejpam-3335	518	18	·	·	PUNCT
ejpam-3335	518	19	z	z	X
ejpam-3335	518	20	)	)	PUNCT
ejpam-3335	518	21	∈	∈	PROPN
ejpam-3335	518	22	u(h	u(h	PROPN
ejpam-3335	518	23	;	;	PUNCT
ejpam-3335	518	24	ε	ε	PROPN
ejpam-3335	518	25	)	)	PUNCT
ejpam-3335	518	26	and	and	CCONJ
ejpam-3335	518	27	y	y	PROPN
ejpam-3335	518	28	∈	∈	PROPN
ejpam-3335	518	29	u(h	u(h	PROPN
ejpam-3335	518	30	;	;	PUNCT
ejpam-3335	518	31	ε	ε	PROPN
ejpam-3335	518	32	)	)	PUNCT
ejpam-3335	518	33	.	.	PUNCT
ejpam-3335	519	1	then	then	ADV
ejpam-3335	519	2	hh(x	hh(x	PUNCT
ejpam-3335	519	3	·	·	PUNCT
ejpam-3335	519	4	(	(	PUNCT
ejpam-3335	519	5	y	y	PROPN
ejpam-3335	519	6	·	·	PUNCT
ejpam-3335	519	7	z	z	NOUN
ejpam-3335	519	8	)	)	PUNCT
ejpam-3335	519	9	)	)	PUNCT
ejpam-3335	519	10	⊇	⊇	PROPN
ejpam-3335	519	11	ε	ε	PROPN
ejpam-3335	519	12	and	and	CCONJ
ejpam-3335	519	13	hh(y	hh(y	NOUN
ejpam-3335	519	14	)	)	PUNCT
ejpam-3335	519	15	⊇	⊇	PROPN
ejpam-3335	519	16	ε	ε	PROPN
ejpam-3335	519	17	.	.	PROPN
ejpam-3335	519	18	since	since	SCONJ
ejpam-3335	519	19	h	h	NOUN
ejpam-3335	519	20	is	be	AUX
ejpam-3335	519	21	an	an	DET
ejpam-3335	519	22	anti	anti	ADJ
ejpam-3335	519	23	-	-	ADJ
ejpam-3335	519	24	hesitant	hesitant	ADJ
ejpam-3335	519	25	fuzzy	fuzzy	ADJ
ejpam-3335	519	26	up	up	NOUN
ejpam-3335	519	27	-	-	PUNCT
ejpam-3335	519	28	ideal	ideal	NOUN
ejpam-3335	519	29	of	of	ADP
ejpam-3335	519	30	a	a	PRON
ejpam-3335	519	31	,	,	PUNCT
ejpam-3335	519	32	we	we	PRON
ejpam-3335	519	33	obtain	obtain	VERB
ejpam-3335	519	34	hh(x	hh(x	X
ejpam-3335	519	35	·	·	PUNCT
ejpam-3335	520	1	z	z	X
ejpam-3335	520	2	)	)	PUNCT
ejpam-3335	520	3	⊆	⊆	NUM
ejpam-3335	520	4	hh(x	hh(x	X
ejpam-3335	520	5	·	·	PUNCT
ejpam-3335	520	6	(	(	PUNCT
ejpam-3335	520	7	y	y	PROPN
ejpam-3335	520	8	·	·	PUNCT
ejpam-3335	520	9	z	z	NOUN
ejpam-3335	520	10	)	)	PUNCT
ejpam-3335	520	11	)	)	PUNCT
ejpam-3335	520	12	∪	∪	ADP
ejpam-3335	520	13	hh(y	hh(y	NOUN
ejpam-3335	520	14	)	)	PUNCT
ejpam-3335	520	15	.	.	PUNCT
ejpam-3335	521	1	by	by	ADP
ejpam-3335	521	2	lemma	lemma	PROPN
ejpam-3335	521	3	1	1	NUM
ejpam-3335	521	4	(	(	PUNCT
ejpam-3335	521	5	2	2	NUM
ejpam-3335	521	6	)	)	PUNCT
ejpam-3335	521	7	,	,	PUNCT
ejpam-3335	521	8	we	we	PRON
ejpam-3335	521	9	have	have	VERB
ejpam-3335	521	10	[	[	X
ejpam-3335	521	11	0	0	NUM
ejpam-3335	521	12	,	,	PUNCT
ejpam-3335	521	13	1	1	NUM
ejpam-3335	521	14	]	]	SYM
ejpam-3335	521	15	−	−	NOUN
ejpam-3335	521	16	hh(x	hh(x	X
ejpam-3335	521	17	·	·	PUNCT
ejpam-3335	522	1	z	z	X
ejpam-3335	522	2	)	)	PUNCT
ejpam-3335	522	3	⊆	⊆	NUM
ejpam-3335	522	4	(	(	PUNCT
ejpam-3335	522	5	[	[	X
ejpam-3335	522	6	0	0	NUM
ejpam-3335	522	7	,	,	PUNCT
ejpam-3335	522	8	1	1	NUM
ejpam-3335	522	9	]	]	SYM
ejpam-3335	522	10	−	−	NOUN
ejpam-3335	522	11	hh(x	hh(x	X
ejpam-3335	522	12	·	·	PUNCT
ejpam-3335	522	13	(	(	PUNCT
ejpam-3335	522	14	y	y	PROPN
ejpam-3335	522	15	·	·	PUNCT
ejpam-3335	522	16	z	z	NOUN
ejpam-3335	522	17	)	)	PUNCT
ejpam-3335	522	18	)	)	PUNCT
ejpam-3335	522	19	)	)	PUNCT
ejpam-3335	523	1	∪	∪	ADV
ejpam-3335	523	2	(	(	PUNCT
ejpam-3335	523	3	[	[	X
ejpam-3335	523	4	0	0	NUM
ejpam-3335	523	5	,	,	PUNCT
ejpam-3335	523	6	1	1	NUM
ejpam-3335	523	7	]	]	PUNCT
ejpam-3335	523	8	−	−	NOUN
ejpam-3335	523	9	hh(y	hh(y	NOUN
ejpam-3335	523	10	)	)	PUNCT
ejpam-3335	523	11	)	)	PUNCT
ejpam-3335	524	1	=	=	PUNCT
ejpam-3335	525	1	[	[	X
ejpam-3335	525	2	0	0	NUM
ejpam-3335	525	3	,	,	PUNCT
ejpam-3335	525	4	1	1	NUM
ejpam-3335	525	5	]	]	SYM
ejpam-3335	525	6	−	−	PROPN
ejpam-3335	525	7	(	(	PUNCT
ejpam-3335	525	8	hh(x	hh(x	X
ejpam-3335	525	9	·	·	PUNCT
ejpam-3335	525	10	(	(	PUNCT
ejpam-3335	525	11	y	y	PROPN
ejpam-3335	525	12	·	·	PUNCT
ejpam-3335	525	13	z	z	NOUN
ejpam-3335	525	14	)	)	PUNCT
ejpam-3335	525	15	)	)	PUNCT
ejpam-3335	525	16	∩	∩	NOUN
ejpam-3335	525	17	hh(y	hh(y	NOUN
ejpam-3335	525	18	)	)	PUNCT
ejpam-3335	525	19	)	)	PUNCT
ejpam-3335	525	20	.	.	PUNCT
ejpam-3335	526	1	thus	thus	ADV
ejpam-3335	526	2	hh(x	hh(x	X
ejpam-3335	526	3	·	·	PUNCT
ejpam-3335	526	4	z	z	X
ejpam-3335	526	5	)	)	PUNCT
ejpam-3335	526	6	⊇	⊇	NOUN
ejpam-3335	526	7	hh(x	hh(x	X
ejpam-3335	526	8	·	·	PUNCT
ejpam-3335	526	9	(	(	PUNCT
ejpam-3335	526	10	y	y	PROPN
ejpam-3335	526	11	·	·	PUNCT
ejpam-3335	526	12	z	z	NOUN
ejpam-3335	526	13	)	)	PUNCT
ejpam-3335	526	14	)	)	PUNCT
ejpam-3335	526	15	∪	∪	ADP
ejpam-3335	526	16	hh(y	hh(y	NOUN
ejpam-3335	526	17	)	)	PUNCT
ejpam-3335	526	18	⊇	⊇	PROPN
ejpam-3335	526	19	ε	ε	PROPN
ejpam-3335	526	20	.	.	PUNCT
ejpam-3335	526	21	therefore	therefore	ADV
ejpam-3335	526	22	,	,	PUNCT
ejpam-3335	526	23	x	x	X
ejpam-3335	526	24	·	·	PUNCT
ejpam-3335	526	25	z	z	X
ejpam-3335	526	26	∈	∈	PROPN
ejpam-3335	527	1	u(h	u(h	PROPN
ejpam-3335	527	2	;	;	PUNCT
ejpam-3335	527	3	ε	ε	PROPN
ejpam-3335	527	4	)	)	PUNCT
ejpam-3335	527	5	.	.	PUNCT
ejpam-3335	528	1	hence	hence	ADV
ejpam-3335	528	2	,	,	PUNCT
ejpam-3335	528	3	u(h	u(h	PROPN
ejpam-3335	528	4	;	;	PUNCT
ejpam-3335	528	5	ε	ε	PROPN
ejpam-3335	528	6	)	)	PUNCT
ejpam-3335	528	7	is	be	AUX
ejpam-3335	528	8	a	a	DET
ejpam-3335	528	9	up	up	ADJ
ejpam-3335	528	10	-	-	PUNCT
ejpam-3335	528	11	ideal	ideal	NOUN
ejpam-3335	528	12	of	of	ADP
ejpam-3335	528	13	a.	a.	NOUN
ejpam-3335	528	14	conversely	conversely	ADV
ejpam-3335	528	15	,	,	PUNCT
ejpam-3335	528	16	assume	assume	VERB
ejpam-3335	528	17	that	that	SCONJ
ejpam-3335	528	18	for	for	ADP
ejpam-3335	528	19	all	all	DET
ejpam-3335	528	20	ε	ε	PROPN
ejpam-3335	528	21	∈	∈	PROPN
ejpam-3335	528	22	p([0	p([0	NOUN
ejpam-3335	528	23	,	,	PUNCT
ejpam-3335	528	24	1	1	NUM
ejpam-3335	528	25	]	]	NUM
ejpam-3335	528	26	)	)	PUNCT
ejpam-3335	528	27	,	,	PUNCT
ejpam-3335	528	28	a	a	DET
ejpam-3335	528	29	nonempty	nonempty	NOUN
ejpam-3335	528	30	subset	subset	VERB
ejpam-3335	528	31	u(h	u(h	PROPN
ejpam-3335	528	32	;	;	PUNCT
ejpam-3335	528	33	ε	ε	PROPN
ejpam-3335	528	34	)	)	PUNCT
ejpam-3335	528	35	of	of	ADP
ejpam-3335	528	36	a	a	PRON
ejpam-3335	528	37	is	be	AUX
ejpam-3335	528	38	a	a	DET
ejpam-3335	528	39	up	up	ADJ
ejpam-3335	528	40	-	-	PUNCT
ejpam-3335	528	41	ideal	ideal	NOUN
ejpam-3335	528	42	of	of	ADP
ejpam-3335	528	43	a.	a.	NOUN
ejpam-3335	528	44	let	let	VERB
ejpam-3335	528	45	x	x	X
ejpam-3335	528	46	∈	∈	PROPN
ejpam-3335	528	47	a.	a.	NOUN
ejpam-3335	528	48	choose	choose	VERB
ejpam-3335	528	49	ε	ε	PROPN
ejpam-3335	528	50	=	=	SYM
ejpam-3335	528	51	hh(x	hh(x	X
ejpam-3335	528	52	)	)	PUNCT
ejpam-3335	528	53	∈	∈	PROPN
ejpam-3335	528	54	p([0	p([0	NOUN
ejpam-3335	528	55	,	,	PUNCT
ejpam-3335	528	56	1	1	NUM
ejpam-3335	528	57	]	]	NUM
ejpam-3335	528	58	)	)	PUNCT
ejpam-3335	528	59	.	.	PUNCT
ejpam-3335	529	1	then	then	ADV
ejpam-3335	529	2	hh(x	hh(x	X
ejpam-3335	529	3	)	)	PUNCT
ejpam-3335	529	4	⊇	⊇	PROPN
ejpam-3335	529	5	ε	ε	PROPN
ejpam-3335	529	6	.	.	PUNCT
ejpam-3335	530	1	thus	thus	ADV
ejpam-3335	530	2	x	x	SYM
ejpam-3335	530	3	∈	∈	PROPN
ejpam-3335	530	4	u(h	u(h	PROPN
ejpam-3335	530	5	;	;	PUNCT
ejpam-3335	530	6	ε	ε	PROPN
ejpam-3335	530	7	)	)	PUNCT
ejpam-3335	530	8	6=	6=	ADP
ejpam-3335	530	9	∅.	∅.	ADP
ejpam-3335	530	10	by	by	ADP
ejpam-3335	530	11	assumption	assumption	NOUN
ejpam-3335	530	12	,	,	PUNCT
ejpam-3335	530	13	we	we	PRON
ejpam-3335	530	14	have	have	AUX
ejpam-3335	530	15	u(h	u(h	PROPN
ejpam-3335	530	16	;	;	PUNCT
ejpam-3335	530	17	ε	ε	PROPN
ejpam-3335	530	18	)	)	PUNCT
ejpam-3335	530	19	is	be	AUX
ejpam-3335	530	20	a	a	DET
ejpam-3335	530	21	up	up	ADJ
ejpam-3335	530	22	-	-	PUNCT
ejpam-3335	530	23	ideal	ideal	NOUN
ejpam-3335	530	24	of	of	ADP
ejpam-3335	530	25	a	a	PRON
ejpam-3335	530	26	and	and	CCONJ
ejpam-3335	530	27	so	so	ADV
ejpam-3335	530	28	0	0	NUM
ejpam-3335	530	29	∈	∈	PROPN
ejpam-3335	530	30	u(h	u(h	PROPN
ejpam-3335	530	31	;	;	PUNCT
ejpam-3335	530	32	ε	ε	PROPN
ejpam-3335	530	33	)	)	PUNCT
ejpam-3335	530	34	.	.	PUNCT
ejpam-3335	531	1	therefore	therefore	ADV
ejpam-3335	531	2	,	,	PUNCT
ejpam-3335	531	3	hh(0	hh(0	NOUN
ejpam-3335	531	4	)	)	PUNCT
ejpam-3335	531	5	⊇	⊇	PROPN
ejpam-3335	531	6	ε	ε	PROPN
ejpam-3335	531	7	=	=	SYM
ejpam-3335	531	8	hh(x	hh(x	X
ejpam-3335	531	9	)	)	PUNCT
ejpam-3335	531	10	.	.	PUNCT
ejpam-3335	532	1	hence	hence	ADV
ejpam-3335	532	2	,	,	PUNCT
ejpam-3335	532	3	hh(0	hh(0	NOUN
ejpam-3335	532	4	)	)	PUNCT
ejpam-3335	532	5	=	=	PUNCT
ejpam-3335	533	1	[	[	X
ejpam-3335	533	2	0	0	NUM
ejpam-3335	533	3	,	,	PUNCT
ejpam-3335	533	4	1]−	1]−	NUM
ejpam-3335	533	5	hh(0	hh(0	NOUN
ejpam-3335	533	6	)	)	PUNCT
ejpam-3335	533	7	⊆	⊆	NUM
ejpam-3335	533	8	[	[	X
ejpam-3335	533	9	0	0	NUM
ejpam-3335	533	10	,	,	PUNCT
ejpam-3335	533	11	1]−	1]−	NUM
ejpam-3335	533	12	hh(x	hh(x	NOUN
ejpam-3335	533	13	)	)	PUNCT
ejpam-3335	533	14	=	=	SYM
ejpam-3335	533	15	hh(x	hh(x	X
ejpam-3335	533	16	)	)	PUNCT
ejpam-3335	533	17	.	.	PUNCT
ejpam-3335	534	1	next	next	ADV
ejpam-3335	534	2	,	,	PUNCT
ejpam-3335	534	3	let	let	VERB
ejpam-3335	534	4	x	x	PRON
ejpam-3335	534	5	,	,	PUNCT
ejpam-3335	534	6	y	y	PROPN
ejpam-3335	534	7	,	,	PUNCT
ejpam-3335	534	8	z	z	PROPN
ejpam-3335	534	9	∈	∈	PROPN
ejpam-3335	534	10	a.	a.	NOUN
ejpam-3335	534	11	choose	choose	NOUN
ejpam-3335	534	12	ε	ε	PROPN
ejpam-3335	534	13	=	=	SYM
ejpam-3335	534	14	hh(x·(y·z))∩hh(y	hh(x·(y·z))∩hh(y	ADJ
ejpam-3335	534	15	)	)	PUNCT
ejpam-3335	534	16	∈	∈	PROPN
ejpam-3335	534	17	p([0	p([0	NOUN
ejpam-3335	534	18	,	,	PUNCT
ejpam-3335	534	19	1	1	NUM
ejpam-3335	534	20	]	]	NUM
ejpam-3335	534	21	)	)	PUNCT
ejpam-3335	534	22	.	.	PUNCT
ejpam-3335	535	1	then	then	ADV
ejpam-3335	535	2	hh(x·(y·z	hh(x·(y·z	PROPN
ejpam-3335	535	3	)	)	PUNCT
ejpam-3335	535	4	)	)	PUNCT
ejpam-3335	535	5	⊇	⊇	PROPN
ejpam-3335	535	6	ε	ε	PROPN
ejpam-3335	535	7	and	and	CCONJ
ejpam-3335	535	8	hh(y	hh(y	NOUN
ejpam-3335	535	9	)	)	PUNCT
ejpam-3335	535	10	⊇	⊇	PROPN
ejpam-3335	535	11	ε	ε	PROPN
ejpam-3335	535	12	.	.	PUNCT
ejpam-3335	536	1	thus	thus	ADV
ejpam-3335	536	2	x	x	X
ejpam-3335	536	3	·	·	PUNCT
ejpam-3335	536	4	(	(	PUNCT
ejpam-3335	536	5	y	y	PROPN
ejpam-3335	536	6	·	·	PUNCT
ejpam-3335	536	7	z	z	X
ejpam-3335	536	8	)	)	PUNCT
ejpam-3335	536	9	,	,	PUNCT
ejpam-3335	536	10	y	y	PROPN
ejpam-3335	536	11	∈	∈	PROPN
ejpam-3335	536	12	u(h	u(h	PROPN
ejpam-3335	536	13	;	;	PUNCT
ejpam-3335	536	14	ε	ε	PROPN
ejpam-3335	536	15	)	)	PUNCT
ejpam-3335	536	16	6=	6=	ADP
ejpam-3335	536	17	∅.	∅.	ADP
ejpam-3335	536	18	by	by	ADP
ejpam-3335	536	19	assumption	assumption	NOUN
ejpam-3335	536	20	,	,	PUNCT
ejpam-3335	536	21	we	we	PRON
ejpam-3335	536	22	have	have	AUX
ejpam-3335	536	23	u(h	u(h	PROPN
ejpam-3335	536	24	;	;	PUNCT
ejpam-3335	536	25	ε	ε	PROPN
ejpam-3335	536	26	)	)	PUNCT
ejpam-3335	536	27	is	be	AUX
ejpam-3335	536	28	a	a	DET
ejpam-3335	536	29	up	up	ADJ
ejpam-3335	536	30	-	-	PUNCT
ejpam-3335	536	31	ideal	ideal	NOUN
ejpam-3335	536	32	of	of	ADP
ejpam-3335	536	33	a	a	PRON
ejpam-3335	536	34	and	and	CCONJ
ejpam-3335	537	1	so	so	ADV
ejpam-3335	537	2	x	x	X
ejpam-3335	537	3	·	·	PUNCT
ejpam-3335	537	4	z	z	SYM
ejpam-3335	537	5	∈	∈	PROPN
ejpam-3335	537	6	u(h	u(h	PROPN
ejpam-3335	537	7	;	;	PUNCT
ejpam-3335	537	8	ε	ε	PROPN
ejpam-3335	537	9	)	)	PUNCT
ejpam-3335	537	10	.	.	PUNCT
ejpam-3335	538	1	therefore	therefore	ADV
ejpam-3335	538	2	,	,	PUNCT
ejpam-3335	538	3	hh(x	hh(x	PUNCT
ejpam-3335	538	4	·	·	PUNCT
ejpam-3335	538	5	z	z	X
ejpam-3335	538	6	)	)	PUNCT
ejpam-3335	538	7	⊇	⊇	PROPN
ejpam-3335	538	8	ε	ε	PROPN
ejpam-3335	538	9	=	=	SYM
ejpam-3335	538	10	hh(x	hh(x	X
ejpam-3335	538	11	·	·	PUNCT
ejpam-3335	538	12	(	(	PUNCT
ejpam-3335	538	13	y	y	X
ejpam-3335	538	14	·	·	PUNCT
ejpam-3335	538	15	z))∩	z))∩	NUM
ejpam-3335	538	16	hh(y	hh(y	NOUN
ejpam-3335	538	17	)	)	PUNCT
ejpam-3335	538	18	.	.	PUNCT
ejpam-3335	539	1	by	by	ADP
ejpam-3335	539	2	lemma	lemma	PROPN
ejpam-3335	539	3	1	1	NUM
ejpam-3335	539	4	(	(	PUNCT
ejpam-3335	539	5	2	2	NUM
ejpam-3335	539	6	)	)	PUNCT
ejpam-3335	539	7	,	,	PUNCT
ejpam-3335	539	8	we	we	PRON
ejpam-3335	539	9	have	have	VERB
ejpam-3335	539	10	hh(x	hh(x	X
ejpam-3335	539	11	·	·	PUNCT
ejpam-3335	540	1	z	z	X
ejpam-3335	540	2	)	)	PUNCT
ejpam-3335	540	3	=	=	PUNCT
ejpam-3335	541	1	[	[	X
ejpam-3335	541	2	0	0	NUM
ejpam-3335	541	3	,	,	PUNCT
ejpam-3335	541	4	1]−	1]−	NUM
ejpam-3335	541	5	hh(x	hh(x	X
ejpam-3335	541	6	·	·	PUNCT
ejpam-3335	541	7	z	z	X
ejpam-3335	541	8	)	)	PUNCT
ejpam-3335	541	9	p.	p.	NOUN
ejpam-3335	541	10	mosrijai	mosrijai	PROPN
ejpam-3335	541	11	,	,	PUNCT
ejpam-3335	541	12	a.	a.	NOUN
ejpam-3335	541	13	iampan	iampan	PROPN
ejpam-3335	541	14	/	/	SYM
ejpam-3335	541	15	eur	eur	PROPN
ejpam-3335	541	16	.	.	PUNCT
ejpam-3335	542	1	j.	j.	PROPN
ejpam-3335	542	2	pure	pure	PROPN
ejpam-3335	542	3	appl	appl	PROPN
ejpam-3335	542	4	.	.	PROPN
ejpam-3335	542	5	math	math	PROPN
ejpam-3335	542	6	,	,	PUNCT
ejpam-3335	542	7	11	11	NUM
ejpam-3335	542	8	(	(	PUNCT
ejpam-3335	542	9	4	4	NUM
ejpam-3335	542	10	)	)	PUNCT
ejpam-3335	542	11	(	(	PUNCT
ejpam-3335	542	12	2018	2018	NUM
ejpam-3335	542	13	)	)	PUNCT
ejpam-3335	542	14	,	,	PUNCT
ejpam-3335	542	15	976	976	NUM
ejpam-3335	542	16	-	-	SYM
ejpam-3335	542	17	1002	1002	NUM
ejpam-3335	542	18	993	993	NUM
ejpam-3335	542	19	⊆	⊆	NUM
ejpam-3335	543	1	[	[	X
ejpam-3335	543	2	0	0	NUM
ejpam-3335	543	3	,	,	PUNCT
ejpam-3335	543	4	1]−	1]−	NUM
ejpam-3335	543	5	(	(	PUNCT
ejpam-3335	543	6	hh(x	hh(x	X
ejpam-3335	543	7	·	·	PUNCT
ejpam-3335	543	8	(	(	PUNCT
ejpam-3335	543	9	y	y	PROPN
ejpam-3335	543	10	·	·	PUNCT
ejpam-3335	543	11	z	z	NOUN
ejpam-3335	543	12	)	)	PUNCT
ejpam-3335	543	13	)	)	PUNCT
ejpam-3335	543	14	∩	∩	NOUN
ejpam-3335	543	15	hh(y	hh(y	NOUN
ejpam-3335	543	16	)	)	PUNCT
ejpam-3335	543	17	)	)	PUNCT
ejpam-3335	544	1	=	=	PUNCT
ejpam-3335	544	2	(	(	PUNCT
ejpam-3335	544	3	[	[	X
ejpam-3335	544	4	0	0	NUM
ejpam-3335	544	5	,	,	PUNCT
ejpam-3335	544	6	1]−	1]−	NUM
ejpam-3335	544	7	hh(x	hh(x	X
ejpam-3335	544	8	·	·	PUNCT
ejpam-3335	544	9	(	(	PUNCT
ejpam-3335	544	10	y	y	PROPN
ejpam-3335	544	11	·	·	PUNCT
ejpam-3335	544	12	z	z	NOUN
ejpam-3335	544	13	)	)	PUNCT
ejpam-3335	544	14	)	)	PUNCT
ejpam-3335	544	15	)	)	PUNCT
ejpam-3335	545	1	∪	∪	ADV
ejpam-3335	545	2	(	(	PUNCT
ejpam-3335	545	3	[	[	X
ejpam-3335	545	4	0	0	NUM
ejpam-3335	545	5	,	,	PUNCT
ejpam-3335	545	6	1]−	1]−	NUM
ejpam-3335	545	7	hh(y	hh(y	NOUN
ejpam-3335	545	8	)	)	PUNCT
ejpam-3335	545	9	)	)	PUNCT
ejpam-3335	545	10	=	=	SYM
ejpam-3335	545	11	hh(x	hh(x	X
ejpam-3335	545	12	·	·	PUNCT
ejpam-3335	545	13	(	(	PUNCT
ejpam-3335	545	14	y	y	PROPN
ejpam-3335	545	15	·	·	PUNCT
ejpam-3335	545	16	z	z	NOUN
ejpam-3335	545	17	)	)	PUNCT
ejpam-3335	545	18	)	)	PUNCT
ejpam-3335	545	19	∪	∪	ADP
ejpam-3335	545	20	hh(y	hh(y	NOUN
ejpam-3335	545	21	)	)	PUNCT
ejpam-3335	545	22	.	.	PUNCT
ejpam-3335	546	1	hence	hence	ADV
ejpam-3335	546	2	,	,	PUNCT
ejpam-3335	546	3	h	h	PROPN
ejpam-3335	546	4	is	be	AUX
ejpam-3335	546	5	an	an	DET
ejpam-3335	546	6	anti	anti	ADJ
ejpam-3335	546	7	-	-	ADJ
ejpam-3335	546	8	hesitant	hesitant	ADJ
ejpam-3335	546	9	fuzzy	fuzzy	ADJ
ejpam-3335	546	10	up	up	NOUN
ejpam-3335	546	11	-	-	PUNCT
ejpam-3335	546	12	ideal	ideal	NOUN
ejpam-3335	546	13	of	of	ADP
ejpam-3335	546	14	a.	a.	NOUN
ejpam-3335	546	15	theorem	theorem	NOUN
ejpam-3335	546	16	18	18	NUM
ejpam-3335	546	17	.	.	PUNCT
ejpam-3335	547	1	let	let	VERB
ejpam-3335	547	2	h	h	PRON
ejpam-3335	547	3	be	be	AUX
ejpam-3335	547	4	a	a	DET
ejpam-3335	547	5	hesitant	hesitant	ADJ
ejpam-3335	547	6	fuzzy	fuzzy	ADJ
ejpam-3335	547	7	set	set	NOUN
ejpam-3335	547	8	on	on	ADP
ejpam-3335	547	9	a.	a.	NOUN
ejpam-3335	547	10	then	then	ADV
ejpam-3335	547	11	the	the	DET
ejpam-3335	547	12	following	follow	VERB
ejpam-3335	547	13	statements	statement	NOUN
ejpam-3335	547	14	are	be	AUX
ejpam-3335	547	15	equivalent	equivalent	ADJ
ejpam-3335	547	16	:	:	PUNCT
ejpam-3335	547	17	(	(	PUNCT
ejpam-3335	547	18	1	1	X
ejpam-3335	547	19	)	)	PUNCT
ejpam-3335	547	20	h	h	NOUN
ejpam-3335	547	21	is	be	AUX
ejpam-3335	547	22	an	an	DET
ejpam-3335	547	23	anti	anti	ADJ
ejpam-3335	547	24	-	-	ADJ
ejpam-3335	547	25	hesitant	hesitant	ADJ
ejpam-3335	547	26	fuzzy	fuzzy	ADJ
ejpam-3335	547	27	strongly	strongly	ADV
ejpam-3335	547	28	up	up	ADP
ejpam-3335	547	29	-	-	PUNCT
ejpam-3335	547	30	ideal	ideal	NOUN
ejpam-3335	547	31	of	of	ADP
ejpam-3335	547	32	a	a	DET
ejpam-3335	547	33	,	,	PUNCT
ejpam-3335	547	34	(	(	PUNCT
ejpam-3335	547	35	2	2	X
ejpam-3335	547	36	)	)	PUNCT
ejpam-3335	547	37	a	a	DET
ejpam-3335	547	38	nonempty	nonempty	NOUN
ejpam-3335	547	39	subset	subset	VERB
ejpam-3335	547	40	u(h	u(h	PROPN
ejpam-3335	547	41	;	;	PUNCT
ejpam-3335	547	42	ε	ε	PROPN
ejpam-3335	547	43	)	)	PUNCT
ejpam-3335	547	44	of	of	ADP
ejpam-3335	547	45	a	a	PRON
ejpam-3335	547	46	is	be	AUX
ejpam-3335	547	47	a	a	DET
ejpam-3335	547	48	strongly	strongly	ADV
ejpam-3335	547	49	up	up	ADJ
ejpam-3335	547	50	-	-	PUNCT
ejpam-3335	547	51	ideal	ideal	NOUN
ejpam-3335	547	52	of	of	ADP
ejpam-3335	547	53	a	a	PRON
ejpam-3335	547	54	for	for	ADP
ejpam-3335	547	55	all	all	DET
ejpam-3335	547	56	ε	ε	PROPN
ejpam-3335	547	57	∈	∈	PROPN
ejpam-3335	547	58	p([0	p([0	NOUN
ejpam-3335	547	59	,	,	PUNCT
ejpam-3335	547	60	1	1	NUM
ejpam-3335	547	61	]	]	NUM
ejpam-3335	547	62	)	)	PUNCT
ejpam-3335	547	63	,	,	PUNCT
ejpam-3335	547	64	and	and	CCONJ
ejpam-3335	547	65	(	(	PUNCT
ejpam-3335	547	66	3	3	X
ejpam-3335	547	67	)	)	PUNCT
ejpam-3335	547	68	a	a	DET
ejpam-3335	547	69	nonempty	nonempty	NOUN
ejpam-3335	547	70	subset	subset	VERB
ejpam-3335	547	71	l(h	l(h	PROPN
ejpam-3335	547	72	;	;	PUNCT
ejpam-3335	547	73	ε	ε	PROPN
ejpam-3335	547	74	)	)	PUNCT
ejpam-3335	547	75	of	of	ADP
ejpam-3335	547	76	a	a	PRON
ejpam-3335	547	77	is	be	AUX
ejpam-3335	547	78	a	a	DET
ejpam-3335	547	79	strongly	strongly	ADV
ejpam-3335	547	80	up	up	ADJ
ejpam-3335	547	81	-	-	PUNCT
ejpam-3335	547	82	ideal	ideal	NOUN
ejpam-3335	547	83	of	of	ADP
ejpam-3335	547	84	a	a	PRON
ejpam-3335	547	85	for	for	ADP
ejpam-3335	547	86	all	all	DET
ejpam-3335	547	87	ε	ε	PROPN
ejpam-3335	547	88	∈	∈	PROPN
ejpam-3335	547	89	p([0	p([0	NOUN
ejpam-3335	547	90	,	,	PUNCT
ejpam-3335	547	91	1	1	NUM
ejpam-3335	547	92	]	]	NUM
ejpam-3335	547	93	)	)	PUNCT
ejpam-3335	547	94	.	.	PUNCT
ejpam-3335	548	1	proof	proof	NOUN
ejpam-3335	548	2	.	.	PUNCT
ejpam-3335	549	1	it	it	PRON
ejpam-3335	549	2	is	be	AUX
ejpam-3335	549	3	straightforward	straightforward	ADJ
ejpam-3335	549	4	by	by	ADP
ejpam-3335	549	5	theorem	theorem	ADJ
ejpam-3335	549	6	10	10	NUM
ejpam-3335	549	7	and	and	CCONJ
ejpam-3335	549	8	corollary	corollary	ADJ
ejpam-3335	549	9	2	2	NUM
ejpam-3335	549	10	.	.	NOUN
ejpam-3335	549	11	5.4	5.4	NUM
ejpam-3335	549	12	.	.	PUNCT
ejpam-3335	550	1	upper	upper	ADJ
ejpam-3335	550	2	ε	ε	PROPN
ejpam-3335	550	3	-	-	PUNCT
ejpam-3335	550	4	strong	strong	ADJ
ejpam-3335	550	5	level	level	NOUN
ejpam-3335	550	6	subsets	subset	NOUN
ejpam-3335	550	7	theorem	theorem	VERB
ejpam-3335	550	8	19	19	NUM
ejpam-3335	550	9	.	.	PUNCT
ejpam-3335	551	1	let	let	VERB
ejpam-3335	551	2	h	h	PRON
ejpam-3335	551	3	be	be	AUX
ejpam-3335	551	4	a	a	DET
ejpam-3335	551	5	hesitant	hesitant	ADJ
ejpam-3335	551	6	fuzzy	fuzzy	ADJ
ejpam-3335	551	7	set	set	NOUN
ejpam-3335	551	8	on	on	ADP
ejpam-3335	551	9	a.	a.	NOUN
ejpam-3335	551	10	then	then	ADV
ejpam-3335	551	11	the	the	DET
ejpam-3335	551	12	following	follow	VERB
ejpam-3335	551	13	statements	statement	NOUN
ejpam-3335	551	14	hold	hold	VERB
ejpam-3335	551	15	:	:	PUNCT
ejpam-3335	551	16	(	(	PUNCT
ejpam-3335	551	17	1	1	X
ejpam-3335	551	18	)	)	PUNCT
ejpam-3335	551	19	if	if	SCONJ
ejpam-3335	551	20	h	h	NOUN
ejpam-3335	551	21	is	be	AUX
ejpam-3335	551	22	an	an	DET
ejpam-3335	551	23	anti	anti	ADJ
ejpam-3335	551	24	-	-	ADJ
ejpam-3335	551	25	hesitant	hesitant	ADJ
ejpam-3335	551	26	fuzzy	fuzzy	ADJ
ejpam-3335	551	27	up	up	NOUN
ejpam-3335	551	28	-	-	PUNCT
ejpam-3335	551	29	subalgebra	subalgebra	NOUN
ejpam-3335	551	30	of	of	ADP
ejpam-3335	551	31	a	a	PRON
ejpam-3335	551	32	,	,	PUNCT
ejpam-3335	551	33	then	then	ADV
ejpam-3335	551	34	for	for	ADP
ejpam-3335	551	35	all	all	DET
ejpam-3335	551	36	ε	ε	PROPN
ejpam-3335	551	37	∈	∈	PROPN
ejpam-3335	551	38	p([0	p([0	NOUN
ejpam-3335	551	39	,	,	PUNCT
ejpam-3335	551	40	1	1	NUM
ejpam-3335	551	41	]	]	NUM
ejpam-3335	551	42	)	)	PUNCT
ejpam-3335	551	43	,	,	PUNCT
ejpam-3335	551	44	u+(h	u+(h	PROPN
ejpam-3335	551	45	;	;	PUNCT
ejpam-3335	551	46	ε	ε	PROPN
ejpam-3335	551	47	)	)	PUNCT
ejpam-3335	551	48	is	be	AUX
ejpam-3335	551	49	a	a	DET
ejpam-3335	551	50	up	up	ADJ
ejpam-3335	551	51	-	-	PUNCT
ejpam-3335	551	52	subalgebra	subalgebra	NOUN
ejpam-3335	551	53	of	of	ADP
ejpam-3335	551	54	a	a	DET
ejpam-3335	551	55	if	if	NOUN
ejpam-3335	551	56	u+(h	u+(h	PROPN
ejpam-3335	551	57	;	;	PUNCT
ejpam-3335	551	58	ε	ε	PROPN
ejpam-3335	551	59	)	)	PUNCT
ejpam-3335	551	60	is	be	AUX
ejpam-3335	551	61	nonempty	nonempty	ADJ
ejpam-3335	551	62	,	,	PUNCT
ejpam-3335	551	63	and	and	CCONJ
ejpam-3335	551	64	(	(	PUNCT
ejpam-3335	551	65	2	2	X
ejpam-3335	551	66	)	)	PUNCT
ejpam-3335	551	67	if	if	SCONJ
ejpam-3335	551	68	im(h	im(h	NOUN
ejpam-3335	551	69	)	)	PUNCT
ejpam-3335	551	70	is	be	AUX
ejpam-3335	551	71	a	a	DET
ejpam-3335	551	72	chain	chain	NOUN
ejpam-3335	551	73	and	and	CCONJ
ejpam-3335	551	74	for	for	ADP
ejpam-3335	551	75	all	all	DET
ejpam-3335	551	76	ε	ε	PROPN
ejpam-3335	551	77	∈	∈	PROPN
ejpam-3335	551	78	p([0	p([0	NOUN
ejpam-3335	551	79	,	,	PUNCT
ejpam-3335	551	80	1	1	NUM
ejpam-3335	551	81	]	]	NUM
ejpam-3335	551	82	)	)	PUNCT
ejpam-3335	551	83	,	,	PUNCT
ejpam-3335	551	84	a	a	DET
ejpam-3335	551	85	nonempty	nonempty	NOUN
ejpam-3335	551	86	subset	subset	VERB
ejpam-3335	551	87	u+(h	u+(h	NOUN
ejpam-3335	551	88	;	;	PUNCT
ejpam-3335	551	89	ε	ε	PROPN
ejpam-3335	551	90	)	)	PUNCT
ejpam-3335	551	91	of	of	ADP
ejpam-3335	551	92	a	a	PRON
ejpam-3335	551	93	is	be	AUX
ejpam-3335	551	94	a	a	DET
ejpam-3335	551	95	up	up	ADJ
ejpam-3335	551	96	-	-	PUNCT
ejpam-3335	551	97	subalgebra	subalgebra	NOUN
ejpam-3335	551	98	of	of	ADP
ejpam-3335	551	99	a	a	PRON
ejpam-3335	551	100	,	,	PUNCT
ejpam-3335	551	101	then	then	ADV
ejpam-3335	551	102	h	h	PROPN
ejpam-3335	551	103	is	be	AUX
ejpam-3335	551	104	an	an	DET
ejpam-3335	551	105	anti	anti	ADJ
ejpam-3335	551	106	-	-	ADJ
ejpam-3335	551	107	hesitant	hesitant	ADJ
ejpam-3335	551	108	fuzzy	fuzzy	ADJ
ejpam-3335	551	109	up	up	NOUN
ejpam-3335	551	110	-	-	PUNCT
ejpam-3335	551	111	subalgebra	subalgebra	NOUN
ejpam-3335	551	112	of	of	ADP
ejpam-3335	551	113	a.	a.	NOUN
ejpam-3335	551	114	proof	proof	NOUN
ejpam-3335	551	115	.	.	PUNCT
ejpam-3335	552	1	(	(	PUNCT
ejpam-3335	552	2	1	1	X
ejpam-3335	552	3	)	)	PUNCT
ejpam-3335	552	4	assume	assume	VERB
ejpam-3335	552	5	that	that	SCONJ
ejpam-3335	552	6	h	h	NOUN
ejpam-3335	552	7	is	be	AUX
ejpam-3335	552	8	an	an	DET
ejpam-3335	552	9	anti	anti	ADJ
ejpam-3335	552	10	-	-	ADJ
ejpam-3335	552	11	hesitant	hesitant	ADJ
ejpam-3335	552	12	fuzzy	fuzzy	ADJ
ejpam-3335	552	13	up	up	NOUN
ejpam-3335	552	14	-	-	PUNCT
ejpam-3335	552	15	subalgebra	subalgebra	NOUN
ejpam-3335	552	16	of	of	ADP
ejpam-3335	552	17	a.	a.	NOUN
ejpam-3335	552	18	let	let	VERB
ejpam-3335	552	19	ε	ε	PROPN
ejpam-3335	552	20	∈	∈	PROPN
ejpam-3335	552	21	p([0	p([0	PROPN
ejpam-3335	552	22	,	,	PUNCT
ejpam-3335	552	23	1	1	NUM
ejpam-3335	552	24	]	]	PUNCT
ejpam-3335	552	25	)	)	PUNCT
ejpam-3335	552	26	be	be	AUX
ejpam-3335	552	27	such	such	ADJ
ejpam-3335	552	28	that	that	SCONJ
ejpam-3335	552	29	u+(h	u+(h	PROPN
ejpam-3335	552	30	;	;	PUNCT
ejpam-3335	552	31	ε	ε	PROPN
ejpam-3335	552	32	)	)	PUNCT
ejpam-3335	552	33	6=	6=	NOUN
ejpam-3335	552	34	∅	∅	NOUN
ejpam-3335	552	35	,	,	PUNCT
ejpam-3335	552	36	and	and	CCONJ
ejpam-3335	552	37	let	let	VERB
ejpam-3335	552	38	x	x	PRON
ejpam-3335	552	39	,	,	PUNCT
ejpam-3335	552	40	y	y	PROPN
ejpam-3335	552	41	∈	∈	PROPN
ejpam-3335	552	42	a	a	DET
ejpam-3335	552	43	be	be	AUX
ejpam-3335	552	44	such	such	ADJ
ejpam-3335	552	45	that	that	SCONJ
ejpam-3335	552	46	x	x	SYM
ejpam-3335	552	47	∈	∈	PROPN
ejpam-3335	552	48	u+(h	u+(h	NOUN
ejpam-3335	552	49	;	;	PUNCT
ejpam-3335	552	50	ε	ε	PROPN
ejpam-3335	552	51	)	)	PUNCT
ejpam-3335	552	52	and	and	CCONJ
ejpam-3335	552	53	y	y	PROPN
ejpam-3335	552	54	∈	∈	PROPN
ejpam-3335	553	1	u+(h	u+(h	NOUN
ejpam-3335	553	2	;	;	PUNCT
ejpam-3335	553	3	ε	ε	PROPN
ejpam-3335	553	4	)	)	PUNCT
ejpam-3335	553	5	.	.	PUNCT
ejpam-3335	554	1	then	then	ADV
ejpam-3335	554	2	hh(x	hh(x	PUNCT
ejpam-3335	554	3	)	)	PUNCT
ejpam-3335	554	4	⊃	⊃	PROPN
ejpam-3335	554	5	ε	ε	PROPN
ejpam-3335	554	6	and	and	CCONJ
ejpam-3335	554	7	hh(y	hh(y	NOUN
ejpam-3335	554	8	)	)	PUNCT
ejpam-3335	554	9	⊃	⊃	PROPN
ejpam-3335	554	10	ε	ε	PROPN
ejpam-3335	554	11	.	.	PROPN
ejpam-3335	555	1	since	since	SCONJ
ejpam-3335	555	2	h	h	NOUN
ejpam-3335	555	3	is	be	AUX
ejpam-3335	555	4	an	an	DET
ejpam-3335	555	5	anti	anti	ADJ
ejpam-3335	555	6	-	-	ADJ
ejpam-3335	555	7	hesitant	hesitant	ADJ
ejpam-3335	555	8	fuzzy	fuzzy	ADJ
ejpam-3335	555	9	up	up	NOUN
ejpam-3335	555	10	-	-	PUNCT
ejpam-3335	555	11	subalgebra	subalgebra	NOUN
ejpam-3335	555	12	of	of	ADP
ejpam-3335	555	13	a	a	PRON
ejpam-3335	555	14	,	,	PUNCT
ejpam-3335	555	15	we	we	PRON
ejpam-3335	555	16	obtain	obtain	VERB
ejpam-3335	555	17	hh(x	hh(x	X
ejpam-3335	555	18	·	·	PUNCT
ejpam-3335	555	19	y	y	X
ejpam-3335	555	20	)	)	PUNCT
ejpam-3335	555	21	⊆	⊆	NUM
ejpam-3335	555	22	hh(x	hh(x	NOUN
ejpam-3335	555	23	)	)	PUNCT
ejpam-3335	555	24	∪	∪	ADP
ejpam-3335	555	25	hh(y	hh(y	NOUN
ejpam-3335	555	26	)	)	PUNCT
ejpam-3335	555	27	.	.	PUNCT
ejpam-3335	556	1	by	by	ADP
ejpam-3335	556	2	lemma	lemma	PROPN
ejpam-3335	556	3	1	1	NUM
ejpam-3335	556	4	(	(	PUNCT
ejpam-3335	556	5	2	2	NUM
ejpam-3335	556	6	)	)	PUNCT
ejpam-3335	556	7	,	,	PUNCT
ejpam-3335	556	8	we	we	PRON
ejpam-3335	556	9	have	have	VERB
ejpam-3335	556	10	[	[	X
ejpam-3335	556	11	0	0	NUM
ejpam-3335	556	12	,	,	PUNCT
ejpam-3335	556	13	1]−	1]−	NUM
ejpam-3335	556	14	hh(x	hh(x	X
ejpam-3335	556	15	·	·	PUNCT
ejpam-3335	556	16	y	y	X
ejpam-3335	556	17	)	)	PUNCT
ejpam-3335	556	18	⊆	⊆	NUM
ejpam-3335	556	19	(	(	PUNCT
ejpam-3335	556	20	[	[	X
ejpam-3335	556	21	0	0	NUM
ejpam-3335	556	22	,	,	PUNCT
ejpam-3335	556	23	1]−hh(x))∪([0	1]−hh(x))∪([0	NUM
ejpam-3335	556	24	,	,	PUNCT
ejpam-3335	556	25	1]−hh(y	1]−hh(y	NUM
ejpam-3335	556	26	)	)	PUNCT
ejpam-3335	556	27	)	)	PUNCT
ejpam-3335	557	1	=	=	PUNCT
ejpam-3335	558	1	[	[	X
ejpam-3335	558	2	0	0	NUM
ejpam-3335	558	3	,	,	PUNCT
ejpam-3335	558	4	1]−(hh(x)∩hh(y	1]−(hh(x)∩hh(y	NUM
ejpam-3335	558	5	)	)	PUNCT
ejpam-3335	558	6	)	)	PUNCT
ejpam-3335	558	7	.	.	PUNCT
ejpam-3335	559	1	thus	thus	ADV
ejpam-3335	559	2	hh(x·y	hh(x·y	NUM
ejpam-3335	559	3	)	)	PUNCT
ejpam-3335	559	4	⊇	⊇	PROPN
ejpam-3335	559	5	hh(x)∩hh(y	hh(x)∩hh(y	PROPN
ejpam-3335	559	6	)	)	PUNCT
ejpam-3335	559	7	⊃	⊃	PROPN
ejpam-3335	559	8	ε	ε	PROPN
ejpam-3335	559	9	.	.	PUNCT
ejpam-3335	559	10	therefore	therefore	ADV
ejpam-3335	559	11	,	,	PUNCT
ejpam-3335	559	12	x	x	X
ejpam-3335	559	13	·	·	PUNCT
ejpam-3335	559	14	y	y	X
ejpam-3335	559	15	∈	∈	PROPN
ejpam-3335	560	1	u+(h	u+(h	NOUN
ejpam-3335	560	2	;	;	PUNCT
ejpam-3335	560	3	ε	ε	PROPN
ejpam-3335	560	4	)	)	PUNCT
ejpam-3335	560	5	.	.	PUNCT
ejpam-3335	561	1	hence	hence	ADV
ejpam-3335	561	2	,	,	PUNCT
ejpam-3335	561	3	u+(h	u+(h	PROPN
ejpam-3335	561	4	;	;	PUNCT
ejpam-3335	561	5	ε	ε	PROPN
ejpam-3335	561	6	)	)	PUNCT
ejpam-3335	561	7	is	be	AUX
ejpam-3335	561	8	a	a	DET
ejpam-3335	561	9	up	up	ADJ
ejpam-3335	561	10	-	-	PUNCT
ejpam-3335	561	11	subalgebra	subalgebra	NOUN
ejpam-3335	561	12	of	of	ADP
ejpam-3335	561	13	a.	a.	NOUN
ejpam-3335	561	14	(	(	PUNCT
ejpam-3335	561	15	2	2	X
ejpam-3335	561	16	)	)	PUNCT
ejpam-3335	561	17	assume	assume	VERB
ejpam-3335	561	18	that	that	SCONJ
ejpam-3335	561	19	im(h	im(h	NOUN
ejpam-3335	561	20	)	)	PUNCT
ejpam-3335	561	21	is	be	AUX
ejpam-3335	561	22	a	a	DET
ejpam-3335	561	23	chain	chain	NOUN
ejpam-3335	561	24	and	and	CCONJ
ejpam-3335	561	25	for	for	ADP
ejpam-3335	561	26	all	all	DET
ejpam-3335	561	27	ε	ε	PROPN
ejpam-3335	561	28	∈	∈	PROPN
ejpam-3335	561	29	p([0	p([0	NOUN
ejpam-3335	561	30	,	,	PUNCT
ejpam-3335	561	31	1	1	NUM
ejpam-3335	561	32	]	]	NUM
ejpam-3335	561	33	)	)	PUNCT
ejpam-3335	561	34	,	,	PUNCT
ejpam-3335	561	35	a	a	DET
ejpam-3335	561	36	nonempty	nonempty	NOUN
ejpam-3335	561	37	subset	subset	VERB
ejpam-3335	561	38	u+(h	u+(h	NOUN
ejpam-3335	561	39	;	;	PUNCT
ejpam-3335	561	40	ε	ε	PROPN
ejpam-3335	561	41	)	)	PUNCT
ejpam-3335	561	42	of	of	ADP
ejpam-3335	561	43	a	a	PRON
ejpam-3335	561	44	is	be	AUX
ejpam-3335	561	45	a	a	DET
ejpam-3335	561	46	up	up	ADJ
ejpam-3335	561	47	-	-	PUNCT
ejpam-3335	561	48	subalgebra	subalgebra	NOUN
ejpam-3335	561	49	of	of	ADP
ejpam-3335	561	50	a.	a.	NOUN
ejpam-3335	561	51	assume	assume	VERB
ejpam-3335	561	52	that	that	SCONJ
ejpam-3335	561	53	there	there	PRON
ejpam-3335	561	54	exist	exist	VERB
ejpam-3335	561	55	x	x	NOUN
ejpam-3335	561	56	,	,	PUNCT
ejpam-3335	561	57	y	y	PROPN
ejpam-3335	561	58	∈	∈	PROPN
ejpam-3335	561	59	a	a	DET
ejpam-3335	561	60	such	such	ADJ
ejpam-3335	561	61	that	that	PRON
ejpam-3335	561	62	hh(x	hh(x	X
ejpam-3335	561	63	·	·	PUNCT
ejpam-3335	561	64	y	y	X
ejpam-3335	561	65	)	)	PUNCT
ejpam-3335	561	66	*	*	PUNCT
ejpam-3335	561	67	hh(x	hh(x	X
ejpam-3335	561	68	)	)	PUNCT
ejpam-3335	561	69	∪	∪	ADP
ejpam-3335	561	70	hh(y	hh(y	NOUN
ejpam-3335	561	71	)	)	PUNCT
ejpam-3335	561	72	.	.	PUNCT
ejpam-3335	562	1	since	since	SCONJ
ejpam-3335	562	2	im(h	im(h	NOUN
ejpam-3335	562	3	)	)	PUNCT
ejpam-3335	562	4	is	be	AUX
ejpam-3335	562	5	a	a	DET
ejpam-3335	562	6	chain	chain	NOUN
ejpam-3335	562	7	,	,	PUNCT
ejpam-3335	562	8	we	we	PRON
ejpam-3335	562	9	have	have	VERB
ejpam-3335	562	10	hh(x	hh(x	X
ejpam-3335	562	11	·	·	PUNCT
ejpam-3335	562	12	y	y	X
ejpam-3335	562	13	)	)	PUNCT
ejpam-3335	562	14	⊃	⊃	NOUN
ejpam-3335	562	15	hh(x	hh(x	X
ejpam-3335	562	16	)	)	PUNCT
ejpam-3335	562	17	∪	∪	ADP
ejpam-3335	562	18	hh(y	hh(y	NOUN
ejpam-3335	562	19	)	)	PUNCT
ejpam-3335	562	20	.	.	PUNCT
ejpam-3335	563	1	by	by	ADP
ejpam-3335	563	2	lemma	lemma	PROPN
ejpam-3335	563	3	1	1	NUM
ejpam-3335	563	4	(	(	PUNCT
ejpam-3335	563	5	2	2	NUM
ejpam-3335	563	6	)	)	PUNCT
ejpam-3335	563	7	,	,	PUNCT
ejpam-3335	563	8	we	we	PRON
ejpam-3335	563	9	have	have	VERB
ejpam-3335	563	10	[	[	X
ejpam-3335	563	11	0	0	NUM
ejpam-3335	563	12	,	,	PUNCT
ejpam-3335	563	13	1]−hh(x	1]−hh(x	NUM
ejpam-3335	563	14	·	·	PUNCT
ejpam-3335	563	15	y	y	X
ejpam-3335	563	16	)	)	PUNCT
ejpam-3335	563	17	⊃	⊃	NOUN
ejpam-3335	563	18	(	(	PUNCT
ejpam-3335	563	19	[	[	X
ejpam-3335	563	20	0	0	NUM
ejpam-3335	563	21	,	,	PUNCT
ejpam-3335	563	22	1]−hh(x))∪	1]−hh(x))∪	NUM
ejpam-3335	563	23	(	(	PUNCT
ejpam-3335	563	24	[	[	X
ejpam-3335	563	25	0	0	NUM
ejpam-3335	563	26	,	,	PUNCT
ejpam-3335	563	27	1]−hh(y	1]−hh(y	NUM
ejpam-3335	563	28	)	)	PUNCT
ejpam-3335	563	29	)	)	PUNCT
ejpam-3335	564	1	=	=	PUNCT
ejpam-3335	565	1	[	[	X
ejpam-3335	565	2	0	0	NUM
ejpam-3335	565	3	,	,	PUNCT
ejpam-3335	565	4	1]−	1]−	NUM
ejpam-3335	565	5	(	(	PUNCT
ejpam-3335	565	6	hh(x)∩hh(y	hh(x)∩hh(y	ADJ
ejpam-3335	565	7	)	)	PUNCT
ejpam-3335	565	8	)	)	PUNCT
ejpam-3335	565	9	.	.	PUNCT
ejpam-3335	566	1	thus	thus	ADV
ejpam-3335	566	2	hh(x	hh(x	X
ejpam-3335	566	3	·	·	PUNCT
ejpam-3335	566	4	y	y	X
ejpam-3335	566	5	)	)	PUNCT
ejpam-3335	566	6	⊂	⊂	PROPN
ejpam-3335	566	7	hh(x	hh(x	X
ejpam-3335	566	8	)	)	PUNCT
ejpam-3335	566	9	∩	∩	NOUN
ejpam-3335	566	10	hh(y	hh(y	NUM
ejpam-3335	566	11	)	)	PUNCT
ejpam-3335	566	12	.	.	PUNCT
ejpam-3335	567	1	choose	choose	VERB
ejpam-3335	567	2	ε	ε	PROPN
ejpam-3335	567	3	=	=	SYM
ejpam-3335	567	4	hh(x	hh(x	X
ejpam-3335	567	5	·	·	PUNCT
ejpam-3335	567	6	y	y	X
ejpam-3335	567	7	)	)	PUNCT
ejpam-3335	567	8	∈	∈	PROPN
ejpam-3335	567	9	p([0	p([0	NOUN
ejpam-3335	567	10	,	,	PUNCT
ejpam-3335	567	11	1	1	NUM
ejpam-3335	567	12	]	]	NUM
ejpam-3335	567	13	)	)	PUNCT
ejpam-3335	567	14	.	.	PUNCT
ejpam-3335	568	1	then	then	ADV
ejpam-3335	568	2	hh(x	hh(x	PUNCT
ejpam-3335	568	3	)	)	PUNCT
ejpam-3335	568	4	⊃	⊃	PROPN
ejpam-3335	568	5	ε	ε	PROPN
ejpam-3335	568	6	and	and	CCONJ
ejpam-3335	568	7	hh(y	hh(y	NOUN
ejpam-3335	568	8	)	)	PUNCT
ejpam-3335	568	9	⊃	⊃	PROPN
ejpam-3335	568	10	ε	ε	PROPN
ejpam-3335	568	11	.	.	PUNCT
ejpam-3335	569	1	thus	thus	ADV
ejpam-3335	569	2	x	x	X
ejpam-3335	569	3	,	,	PUNCT
ejpam-3335	569	4	y	y	PROPN
ejpam-3335	569	5	∈	∈	PROPN
ejpam-3335	569	6	u+(h	u+(h	NOUN
ejpam-3335	569	7	;	;	PUNCT
ejpam-3335	569	8	ε	ε	PROPN
ejpam-3335	569	9	)	)	PUNCT
ejpam-3335	569	10	6=	6=	ADP
ejpam-3335	569	11	∅.	∅.	ADP
ejpam-3335	569	12	by	by	ADP
ejpam-3335	569	13	assumption	assumption	NOUN
ejpam-3335	569	14	,	,	PUNCT
ejpam-3335	569	15	we	we	PRON
ejpam-3335	569	16	have	have	AUX
ejpam-3335	569	17	u+(h	u+(h	ADV
ejpam-3335	569	18	;	;	PUNCT
ejpam-3335	569	19	ε	ε	PROPN
ejpam-3335	569	20	)	)	PUNCT
ejpam-3335	569	21	is	be	AUX
ejpam-3335	569	22	a	a	DET
ejpam-3335	569	23	upsubalgebra	upsubalgebra	NOUN
ejpam-3335	569	24	of	of	ADP
ejpam-3335	569	25	a	a	PRON
ejpam-3335	569	26	and	and	CCONJ
ejpam-3335	569	27	so	so	ADV
ejpam-3335	569	28	x	x	SYM
ejpam-3335	569	29	·	·	PUNCT
ejpam-3335	569	30	y	y	X
ejpam-3335	569	31	∈	∈	PROPN
ejpam-3335	569	32	u+(h	u+(h	NOUN
ejpam-3335	569	33	;	;	PUNCT
ejpam-3335	569	34	ε	ε	PROPN
ejpam-3335	569	35	)	)	PUNCT
ejpam-3335	569	36	.	.	PUNCT
ejpam-3335	570	1	thus	thus	ADV
ejpam-3335	570	2	hh(x	hh(x	X
ejpam-3335	570	3	·	·	PUNCT
ejpam-3335	570	4	y	y	X
ejpam-3335	570	5	)	)	PUNCT
ejpam-3335	570	6	⊃	⊃	PROPN
ejpam-3335	570	7	ε	ε	PROPN
ejpam-3335	570	8	=	=	SYM
ejpam-3335	570	9	hh(x	hh(x	X
ejpam-3335	570	10	·	·	PUNCT
ejpam-3335	570	11	y	y	X
ejpam-3335	570	12	)	)	PUNCT
ejpam-3335	570	13	,	,	PUNCT
ejpam-3335	570	14	a	a	DET
ejpam-3335	570	15	contradiction	contradiction	NOUN
ejpam-3335	570	16	.	.	PUNCT
ejpam-3335	571	1	therefore	therefore	ADV
ejpam-3335	571	2	,	,	PUNCT
ejpam-3335	571	3	hh(x	hh(x	PUNCT
ejpam-3335	571	4	·	·	PUNCT
ejpam-3335	571	5	y	y	X
ejpam-3335	571	6	)	)	PUNCT
ejpam-3335	571	7	⊆	⊆	NUM
ejpam-3335	571	8	hh(x	hh(x	NOUN
ejpam-3335	571	9	)	)	PUNCT
ejpam-3335	571	10	∪	∪	ADP
ejpam-3335	571	11	hh(y	hh(y	NOUN
ejpam-3335	571	12	)	)	PUNCT
ejpam-3335	571	13	for	for	ADP
ejpam-3335	571	14	all	all	DET
ejpam-3335	571	15	x	x	NOUN
ejpam-3335	571	16	,	,	PUNCT
ejpam-3335	571	17	y	y	PROPN
ejpam-3335	571	18	∈	∈	PROPN
ejpam-3335	571	19	a.	a.	NOUN
ejpam-3335	571	20	hence	hence	ADV
ejpam-3335	571	21	,	,	PUNCT
ejpam-3335	571	22	h	h	PROPN
ejpam-3335	571	23	is	be	AUX
ejpam-3335	571	24	an	an	DET
ejpam-3335	571	25	anti	anti	ADJ
ejpam-3335	571	26	-	-	ADJ
ejpam-3335	571	27	hesitant	hesitant	ADJ
ejpam-3335	571	28	fuzzy	fuzzy	ADJ
ejpam-3335	571	29	up	up	NOUN
ejpam-3335	571	30	-	-	PUNCT
ejpam-3335	571	31	subalgebra	subalgebra	NOUN
ejpam-3335	571	32	of	of	ADP
ejpam-3335	571	33	a.	a.	NOUN
ejpam-3335	571	34	example	example	NOUN
ejpam-3335	571	35	12	12	NUM
ejpam-3335	571	36	.	.	PUNCT
ejpam-3335	572	1	let	let	VERB
ejpam-3335	572	2	a	a	PRON
ejpam-3335	572	3	=	=	PUNCT
ejpam-3335	572	4	{	{	PUNCT
ejpam-3335	572	5	0	0	NUM
ejpam-3335	572	6	,	,	PUNCT
ejpam-3335	572	7	1	1	NUM
ejpam-3335	572	8	,	,	PUNCT
ejpam-3335	572	9	2	2	NUM
ejpam-3335	572	10	,	,	PUNCT
ejpam-3335	572	11	3	3	NUM
ejpam-3335	572	12	,	,	PUNCT
ejpam-3335	572	13	4	4	NUM
ejpam-3335	572	14	}	}	PUNCT
ejpam-3335	572	15	be	be	AUX
ejpam-3335	572	16	a	a	DET
ejpam-3335	572	17	set	set	NOUN
ejpam-3335	572	18	with	with	ADP
ejpam-3335	572	19	a	a	DET
ejpam-3335	572	20	binary	binary	ADJ
ejpam-3335	572	21	operation	operation	NOUN
ejpam-3335	572	22	·	·	PUNCT
ejpam-3335	572	23	defined	define	VERB
ejpam-3335	572	24	by	by	ADP
ejpam-3335	572	25	the	the	DET
ejpam-3335	572	26	cayley	cayley	ADJ
ejpam-3335	572	27	table	table	NOUN
ejpam-3335	572	28	from	from	ADP
ejpam-3335	572	29	example	example	NOUN
ejpam-3335	572	30	8	8	NUM
ejpam-3335	572	31	.	.	PUNCT
ejpam-3335	573	1	then	then	ADV
ejpam-3335	573	2	(	(	PUNCT
ejpam-3335	573	3	a	a	PRON
ejpam-3335	573	4	,	,	PUNCT
ejpam-3335	573	5	·	·	PUNCT
ejpam-3335	573	6	,	,	PUNCT
ejpam-3335	573	7	0	0	NUM
ejpam-3335	573	8	)	)	PUNCT
ejpam-3335	573	9	is	be	AUX
ejpam-3335	573	10	a	a	DET
ejpam-3335	573	11	up	up	NOUN
ejpam-3335	573	12	-	-	PUNCT
ejpam-3335	573	13	algebra	algebra	NOUN
ejpam-3335	573	14	.	.	PUNCT
ejpam-3335	574	1	we	we	PRON
ejpam-3335	574	2	define	define	VERB
ejpam-3335	574	3	a	a	DET
ejpam-3335	574	4	hesitant	hesitant	ADJ
ejpam-3335	574	5	fuzzy	fuzzy	ADJ
ejpam-3335	574	6	set	set	VERB
ejpam-3335	574	7	h	h	NOUN
ejpam-3335	574	8	on	on	ADP
ejpam-3335	574	9	a	a	PRON
ejpam-3335	574	10	as	as	SCONJ
ejpam-3335	574	11	follows	follow	VERB
ejpam-3335	574	12	:	:	PUNCT
ejpam-3335	574	13	p.	p.	NOUN
ejpam-3335	574	14	mosrijai	mosrijai	PROPN
ejpam-3335	574	15	,	,	PUNCT
ejpam-3335	574	16	a.	a.	NOUN
ejpam-3335	574	17	iampan	iampan	PROPN
ejpam-3335	574	18	/	/	SYM
ejpam-3335	574	19	eur	eur	PROPN
ejpam-3335	574	20	.	.	PUNCT
ejpam-3335	575	1	j.	j.	PROPN
ejpam-3335	575	2	pure	pure	PROPN
ejpam-3335	575	3	appl	appl	PROPN
ejpam-3335	575	4	.	.	PROPN
ejpam-3335	575	5	math	math	PROPN
ejpam-3335	575	6	,	,	PUNCT
ejpam-3335	575	7	11	11	NUM
ejpam-3335	575	8	(	(	PUNCT
ejpam-3335	575	9	4	4	NUM
ejpam-3335	575	10	)	)	PUNCT
ejpam-3335	575	11	(	(	PUNCT
ejpam-3335	575	12	2018	2018	NUM
ejpam-3335	575	13	)	)	PUNCT
ejpam-3335	575	14	,	,	PUNCT
ejpam-3335	575	15	976	976	NUM
ejpam-3335	575	16	-	-	SYM
ejpam-3335	575	17	1002	1002	NUM
ejpam-3335	575	18	994	994	NUM
ejpam-3335	575	19	hh(0	hh(0	NOUN
ejpam-3335	575	20	)	)	PUNCT
ejpam-3335	575	21	=	=	SYM
ejpam-3335	575	22	{	{	PUNCT
ejpam-3335	575	23	0	0	NUM
ejpam-3335	575	24	,	,	PUNCT
ejpam-3335	575	25	1},hh(1	1},hh(1	NUM
ejpam-3335	575	26	)	)	PUNCT
ejpam-3335	575	27	=	=	PUNCT
ejpam-3335	575	28	{	{	PUNCT
ejpam-3335	575	29	1	1	NUM
ejpam-3335	575	30	}	}	PUNCT
ejpam-3335	575	31	,	,	PUNCT
ejpam-3335	575	32	hh(2	hh(2	NOUN
ejpam-3335	575	33	)	)	PUNCT
ejpam-3335	575	34	=	=	SYM
ejpam-3335	575	35	{	{	PUNCT
ejpam-3335	575	36	0},hh(3	0},hh(3	NOUN
ejpam-3335	575	37	)	)	PUNCT
ejpam-3335	575	38	=	=	PRON
ejpam-3335	575	39	{	{	PUNCT
ejpam-3335	575	40	1	1	NUM
ejpam-3335	575	41	}	}	PUNCT
ejpam-3335	575	42	,	,	PUNCT
ejpam-3335	575	43	and	and	CCONJ
ejpam-3335	575	44	hh(4	hh(4	NOUN
ejpam-3335	575	45	)	)	PUNCT
ejpam-3335	575	46	=	=	PUNCT
ejpam-3335	575	47	∅.	∅.	NOUN
ejpam-3335	575	48	then	then	ADV
ejpam-3335	575	49	im(h	im(h	NOUN
ejpam-3335	575	50	)	)	PUNCT
ejpam-3335	575	51	is	be	AUX
ejpam-3335	575	52	not	not	PART
ejpam-3335	575	53	a	a	DET
ejpam-3335	575	54	chain	chain	NOUN
ejpam-3335	575	55	.	.	PUNCT
ejpam-3335	576	1	if	if	SCONJ
ejpam-3335	576	2	ε	ε	PROPN
ejpam-3335	576	3	=	=	PUNCT
ejpam-3335	576	4	{	{	PUNCT
ejpam-3335	576	5	1	1	NUM
ejpam-3335	576	6	}	}	PUNCT
ejpam-3335	576	7	or	or	CCONJ
ejpam-3335	576	8	ε	ε	PROPN
ejpam-3335	576	9	=	=	PUNCT
ejpam-3335	576	10	{	{	PUNCT
ejpam-3335	576	11	0	0	NUM
ejpam-3335	576	12	}	}	PUNCT
ejpam-3335	576	13	,	,	PUNCT
ejpam-3335	576	14	then	then	ADV
ejpam-3335	576	15	u+(h	u+(h	NUM
ejpam-3335	576	16	;	;	PUNCT
ejpam-3335	576	17	ε	ε	PROPN
ejpam-3335	576	18	)	)	PUNCT
ejpam-3335	576	19	=	=	PUNCT
ejpam-3335	576	20	{	{	PUNCT
ejpam-3335	576	21	0	0	NUM
ejpam-3335	576	22	}	}	PUNCT
ejpam-3335	576	23	.	.	PUNCT
ejpam-3335	577	1	if	if	SCONJ
ejpam-3335	577	2	ε	ε	PROPN
ejpam-3335	577	3	=	=	SYM
ejpam-3335	577	4	∅	∅	NOUN
ejpam-3335	577	5	,	,	PUNCT
ejpam-3335	577	6	then	then	ADV
ejpam-3335	577	7	u+(h	u+(h	NUM
ejpam-3335	577	8	;	;	PUNCT
ejpam-3335	577	9	ε	ε	PROPN
ejpam-3335	577	10	)	)	PUNCT
ejpam-3335	577	11	=	=	SYM
ejpam-3335	577	12	{	{	PUNCT
ejpam-3335	577	13	0	0	NUM
ejpam-3335	577	14	,	,	PUNCT
ejpam-3335	577	15	1	1	NUM
ejpam-3335	577	16	,	,	PUNCT
ejpam-3335	577	17	3	3	NUM
ejpam-3335	577	18	}	}	PUNCT
ejpam-3335	577	19	.	.	PUNCT
ejpam-3335	578	1	otherwise	otherwise	ADV
ejpam-3335	578	2	,	,	PUNCT
ejpam-3335	578	3	u+(h	u+(h	NOUN
ejpam-3335	578	4	;	;	PUNCT
ejpam-3335	578	5	ε	ε	PROPN
ejpam-3335	578	6	)	)	PUNCT
ejpam-3335	578	7	=	=	PUNCT
ejpam-3335	578	8	∅.	∅.	VERB
ejpam-3335	578	9	using	use	VERB
ejpam-3335	578	10	this	this	DET
ejpam-3335	578	11	data	datum	NOUN
ejpam-3335	578	12	,	,	PUNCT
ejpam-3335	578	13	we	we	PRON
ejpam-3335	578	14	can	can	AUX
ejpam-3335	578	15	show	show	VERB
ejpam-3335	578	16	that	that	SCONJ
ejpam-3335	578	17	all	all	DET
ejpam-3335	578	18	nonempty	nonempty	ADV
ejpam-3335	578	19	subset	subset	VERB
ejpam-3335	578	20	u+(h	u+(h	NOUN
ejpam-3335	578	21	;	;	PUNCT
ejpam-3335	578	22	ε	ε	PROPN
ejpam-3335	578	23	)	)	PUNCT
ejpam-3335	578	24	of	of	ADP
ejpam-3335	578	25	a	a	PRON
ejpam-3335	578	26	is	be	AUX
ejpam-3335	578	27	a	a	DET
ejpam-3335	578	28	up	up	ADJ
ejpam-3335	578	29	-	-	PUNCT
ejpam-3335	578	30	subalgebra	subalgebra	NOUN
ejpam-3335	578	31	of	of	ADP
ejpam-3335	578	32	a.	a.	NOUN
ejpam-3335	578	33	by	by	ADP
ejpam-3335	578	34	definition	definition	NOUN
ejpam-3335	578	35	4	4	NUM
ejpam-3335	578	36	,	,	PUNCT
ejpam-3335	578	37	we	we	PRON
ejpam-3335	578	38	have	have	VERB
ejpam-3335	578	39	hh(0	hh(0	NOUN
ejpam-3335	578	40	)	)	PUNCT
ejpam-3335	578	41	=	=	SYM
ejpam-3335	578	42	(	(	PUNCT
ejpam-3335	578	43	0	0	NUM
ejpam-3335	578	44	,	,	PUNCT
ejpam-3335	578	45	1),hh(1	1),hh(1	NUM
ejpam-3335	578	46	)	)	PUNCT
ejpam-3335	578	47	=	=	PUNCT
ejpam-3335	579	1	[	[	X
ejpam-3335	579	2	0	0	NUM
ejpam-3335	579	3	,	,	PUNCT
ejpam-3335	579	4	1	1	NUM
ejpam-3335	579	5	)	)	PUNCT
ejpam-3335	579	6	,	,	PUNCT
ejpam-3335	579	7	hh(2	hh(2	NOUN
ejpam-3335	579	8	)	)	PUNCT
ejpam-3335	579	9	=	=	SYM
ejpam-3335	579	10	(	(	PUNCT
ejpam-3335	579	11	0	0	NUM
ejpam-3335	579	12	,	,	PUNCT
ejpam-3335	579	13	1	1	NUM
ejpam-3335	579	14	]	]	PUNCT
ejpam-3335	579	15	,	,	PUNCT
ejpam-3335	579	16	hh(3	hh(3	NOUN
ejpam-3335	579	17	)	)	PUNCT
ejpam-3335	580	1	=	=	PUNCT
ejpam-3335	581	1	[	[	X
ejpam-3335	581	2	0	0	NUM
ejpam-3335	581	3	,	,	PUNCT
ejpam-3335	581	4	1	1	NUM
ejpam-3335	581	5	)	)	PUNCT
ejpam-3335	581	6	,	,	PUNCT
ejpam-3335	581	7	and	and	CCONJ
ejpam-3335	581	8	hh(3	hh(3	X
ejpam-3335	581	9	)	)	PUNCT
ejpam-3335	581	10	=	=	PUNCT
ejpam-3335	582	1	[	[	X
ejpam-3335	582	2	0	0	NUM
ejpam-3335	582	3	,	,	PUNCT
ejpam-3335	582	4	1	1	NUM
ejpam-3335	582	5	]	]	PUNCT
ejpam-3335	582	6	.	.	PUNCT
ejpam-3335	583	1	since	since	SCONJ
ejpam-3335	583	2	hh(3	hh(3	PROPN
ejpam-3335	583	3	·	·	SYM
ejpam-3335	583	4	1	1	NUM
ejpam-3335	583	5	)	)	PUNCT
ejpam-3335	583	6	=	=	SYM
ejpam-3335	583	7	hh(2	hh(2	NOUN
ejpam-3335	583	8	)	)	PUNCT
ejpam-3335	583	9	=	=	SYM
ejpam-3335	583	10	(	(	PUNCT
ejpam-3335	583	11	0	0	NUM
ejpam-3335	583	12	,	,	PUNCT
ejpam-3335	583	13	1	1	NUM
ejpam-3335	583	14	]	]	PUNCT
ejpam-3335	583	15	*	*	PUNCT
ejpam-3335	584	1	[	[	X
ejpam-3335	584	2	0	0	NUM
ejpam-3335	584	3	,	,	PUNCT
ejpam-3335	584	4	1	1	NUM
ejpam-3335	584	5	)	)	PUNCT
ejpam-3335	584	6	=	=	PUNCT
ejpam-3335	584	7	hh(3)∪hh(1	hh(3)∪hh(1	NOUN
ejpam-3335	584	8	)	)	PUNCT
ejpam-3335	584	9	,	,	PUNCT
ejpam-3335	584	10	we	we	PRON
ejpam-3335	584	11	have	have	VERB
ejpam-3335	584	12	h	h	NOUN
ejpam-3335	584	13	is	be	AUX
ejpam-3335	584	14	not	not	PART
ejpam-3335	584	15	an	an	DET
ejpam-3335	584	16	anti	anti	ADJ
ejpam-3335	584	17	-	-	ADJ
ejpam-3335	584	18	hesitant	hesitant	ADJ
ejpam-3335	584	19	fuzzy	fuzzy	ADJ
ejpam-3335	584	20	up	up	NOUN
ejpam-3335	584	21	-	-	PUNCT
ejpam-3335	584	22	subalgebra	subalgebra	NOUN
ejpam-3335	584	23	of	of	ADP
ejpam-3335	584	24	a.	a.	NOUN
ejpam-3335	584	25	theorem	theorem	NOUN
ejpam-3335	584	26	20	20	NUM
ejpam-3335	584	27	.	.	PUNCT
ejpam-3335	585	1	let	let	VERB
ejpam-3335	585	2	h	h	PRON
ejpam-3335	585	3	be	be	AUX
ejpam-3335	585	4	a	a	DET
ejpam-3335	585	5	hesitant	hesitant	ADJ
ejpam-3335	585	6	fuzzy	fuzzy	ADJ
ejpam-3335	585	7	set	set	NOUN
ejpam-3335	585	8	on	on	ADP
ejpam-3335	585	9	a.	a.	NOUN
ejpam-3335	585	10	then	then	ADV
ejpam-3335	585	11	the	the	DET
ejpam-3335	585	12	following	follow	VERB
ejpam-3335	585	13	statements	statement	NOUN
ejpam-3335	585	14	hold	hold	VERB
ejpam-3335	585	15	:	:	PUNCT
ejpam-3335	585	16	(	(	PUNCT
ejpam-3335	585	17	1	1	X
ejpam-3335	585	18	)	)	PUNCT
ejpam-3335	585	19	if	if	SCONJ
ejpam-3335	585	20	h	h	NOUN
ejpam-3335	585	21	is	be	AUX
ejpam-3335	585	22	an	an	DET
ejpam-3335	585	23	anti	anti	ADJ
ejpam-3335	585	24	-	-	ADJ
ejpam-3335	585	25	hesitant	hesitant	ADJ
ejpam-3335	585	26	fuzzy	fuzzy	ADJ
ejpam-3335	585	27	up	up	NOUN
ejpam-3335	585	28	-	-	PUNCT
ejpam-3335	585	29	filter	filter	NOUN
ejpam-3335	585	30	of	of	ADP
ejpam-3335	585	31	a	a	PRON
ejpam-3335	585	32	,	,	PUNCT
ejpam-3335	585	33	then	then	ADV
ejpam-3335	585	34	for	for	SCONJ
ejpam-3335	585	35	all	all	DET
ejpam-3335	585	36	ε	ε	PROPN
ejpam-3335	585	37	∈	∈	PROPN
ejpam-3335	585	38	p([0	p([0	NOUN
ejpam-3335	585	39	,	,	PUNCT
ejpam-3335	585	40	1	1	NUM
ejpam-3335	585	41	]	]	NUM
ejpam-3335	585	42	)	)	PUNCT
ejpam-3335	585	43	,	,	PUNCT
ejpam-3335	585	44	u+(h	u+(h	PROPN
ejpam-3335	585	45	;	;	PUNCT
ejpam-3335	585	46	ε	ε	PROPN
ejpam-3335	585	47	)	)	PUNCT
ejpam-3335	585	48	is	be	AUX
ejpam-3335	585	49	a	a	DET
ejpam-3335	585	50	up	up	ADJ
ejpam-3335	585	51	-	-	PUNCT
ejpam-3335	585	52	filter	filter	NOUN
ejpam-3335	585	53	of	of	ADP
ejpam-3335	585	54	a	a	DET
ejpam-3335	585	55	if	if	NOUN
ejpam-3335	585	56	u+(h	u+(h	PROPN
ejpam-3335	585	57	;	;	PUNCT
ejpam-3335	585	58	ε	ε	PROPN
ejpam-3335	585	59	)	)	PUNCT
ejpam-3335	585	60	is	be	AUX
ejpam-3335	585	61	nonempty	nonempty	ADJ
ejpam-3335	585	62	,	,	PUNCT
ejpam-3335	585	63	and	and	CCONJ
ejpam-3335	585	64	(	(	PUNCT
ejpam-3335	585	65	2	2	X
ejpam-3335	585	66	)	)	PUNCT
ejpam-3335	585	67	if	if	SCONJ
ejpam-3335	585	68	im(h	im(h	NOUN
ejpam-3335	585	69	)	)	PUNCT
ejpam-3335	585	70	is	be	AUX
ejpam-3335	585	71	a	a	DET
ejpam-3335	585	72	chain	chain	NOUN
ejpam-3335	585	73	and	and	CCONJ
ejpam-3335	585	74	for	for	ADP
ejpam-3335	585	75	all	all	DET
ejpam-3335	585	76	ε	ε	PROPN
ejpam-3335	585	77	∈	∈	PROPN
ejpam-3335	585	78	p([0	p([0	NOUN
ejpam-3335	585	79	,	,	PUNCT
ejpam-3335	585	80	1	1	NUM
ejpam-3335	585	81	]	]	NUM
ejpam-3335	585	82	)	)	PUNCT
ejpam-3335	585	83	,	,	PUNCT
ejpam-3335	585	84	a	a	DET
ejpam-3335	585	85	nonempty	nonempty	NOUN
ejpam-3335	585	86	subset	subset	VERB
ejpam-3335	585	87	u+(h	u+(h	NOUN
ejpam-3335	585	88	;	;	PUNCT
ejpam-3335	585	89	ε	ε	PROPN
ejpam-3335	585	90	)	)	PUNCT
ejpam-3335	585	91	of	of	ADP
ejpam-3335	585	92	a	a	PRON
ejpam-3335	585	93	is	be	AUX
ejpam-3335	585	94	a	a	DET
ejpam-3335	585	95	up	up	ADJ
ejpam-3335	585	96	-	-	PUNCT
ejpam-3335	585	97	filter	filter	NOUN
ejpam-3335	585	98	of	of	ADP
ejpam-3335	585	99	a	a	PRON
ejpam-3335	585	100	,	,	PUNCT
ejpam-3335	585	101	then	then	ADV
ejpam-3335	585	102	h	h	PROPN
ejpam-3335	585	103	is	be	AUX
ejpam-3335	585	104	an	an	DET
ejpam-3335	585	105	anti	anti	ADJ
ejpam-3335	585	106	-	-	ADJ
ejpam-3335	585	107	hesitant	hesitant	ADJ
ejpam-3335	585	108	fuzzy	fuzzy	ADJ
ejpam-3335	585	109	up	up	NOUN
ejpam-3335	585	110	-	-	PUNCT
ejpam-3335	585	111	filter	filter	NOUN
ejpam-3335	585	112	of	of	ADP
ejpam-3335	585	113	a.	a.	NOUN
ejpam-3335	585	114	proof	proof	NOUN
ejpam-3335	585	115	.	.	PUNCT
ejpam-3335	586	1	(	(	PUNCT
ejpam-3335	586	2	1	1	X
ejpam-3335	586	3	)	)	PUNCT
ejpam-3335	586	4	assume	assume	VERB
ejpam-3335	586	5	that	that	SCONJ
ejpam-3335	586	6	h	h	NOUN
ejpam-3335	586	7	is	be	AUX
ejpam-3335	586	8	an	an	DET
ejpam-3335	586	9	anti	anti	ADJ
ejpam-3335	586	10	-	-	ADJ
ejpam-3335	586	11	hesitant	hesitant	ADJ
ejpam-3335	586	12	fuzzy	fuzzy	ADJ
ejpam-3335	586	13	up	up	NOUN
ejpam-3335	586	14	-	-	PUNCT
ejpam-3335	586	15	filter	filter	NOUN
ejpam-3335	586	16	of	of	ADP
ejpam-3335	586	17	a.	a.	NOUN
ejpam-3335	586	18	let	let	VERB
ejpam-3335	586	19	ε	ε	PROPN
ejpam-3335	586	20	∈	∈	PROPN
ejpam-3335	586	21	p([0	p([0	PROPN
ejpam-3335	586	22	,	,	PUNCT
ejpam-3335	586	23	1	1	NUM
ejpam-3335	586	24	]	]	PUNCT
ejpam-3335	586	25	)	)	PUNCT
ejpam-3335	586	26	be	be	AUX
ejpam-3335	586	27	such	such	ADJ
ejpam-3335	586	28	that	that	SCONJ
ejpam-3335	586	29	u+(h	u+(h	PROPN
ejpam-3335	586	30	;	;	PUNCT
ejpam-3335	586	31	ε	ε	PROPN
ejpam-3335	586	32	)	)	PUNCT
ejpam-3335	586	33	6=	6=	NOUN
ejpam-3335	586	34	∅	∅	NOUN
ejpam-3335	586	35	,	,	PUNCT
ejpam-3335	586	36	and	and	CCONJ
ejpam-3335	586	37	let	let	VERB
ejpam-3335	586	38	x	x	SYM
ejpam-3335	586	39	∈	∈	PROPN
ejpam-3335	586	40	a	a	DET
ejpam-3335	586	41	be	be	AUX
ejpam-3335	586	42	such	such	ADJ
ejpam-3335	586	43	that	that	SCONJ
ejpam-3335	586	44	x	x	SYM
ejpam-3335	586	45	∈	∈	PROPN
ejpam-3335	586	46	u+(h	u+(h	NOUN
ejpam-3335	586	47	;	;	PUNCT
ejpam-3335	586	48	ε	ε	PROPN
ejpam-3335	586	49	)	)	PUNCT
ejpam-3335	586	50	.	.	PUNCT
ejpam-3335	587	1	then	then	ADV
ejpam-3335	587	2	hh(x	hh(x	NOUN
ejpam-3335	587	3	)	)	PUNCT
ejpam-3335	587	4	⊃	⊃	PROPN
ejpam-3335	587	5	ε	ε	PROPN
ejpam-3335	587	6	.	.	PROPN
ejpam-3335	587	7	since	since	SCONJ
ejpam-3335	587	8	h	h	NOUN
ejpam-3335	587	9	is	be	AUX
ejpam-3335	587	10	an	an	DET
ejpam-3335	587	11	anti	anti	ADJ
ejpam-3335	587	12	-	-	ADJ
ejpam-3335	587	13	hesitant	hesitant	ADJ
ejpam-3335	587	14	fuzzy	fuzzy	ADJ
ejpam-3335	587	15	up	up	NOUN
ejpam-3335	587	16	-	-	PUNCT
ejpam-3335	587	17	filter	filter	NOUN
ejpam-3335	587	18	of	of	ADP
ejpam-3335	587	19	a	a	PRON
ejpam-3335	587	20	,	,	PUNCT
ejpam-3335	587	21	we	we	PRON
ejpam-3335	587	22	have	have	VERB
ejpam-3335	587	23	hh(0	hh(0	NOUN
ejpam-3335	587	24	)	)	PUNCT
ejpam-3335	587	25	⊆	⊆	NUM
ejpam-3335	587	26	hh(x	hh(x	NOUN
ejpam-3335	587	27	)	)	PUNCT
ejpam-3335	587	28	.	.	PUNCT
ejpam-3335	588	1	thus	thus	ADV
ejpam-3335	588	2	[	[	X
ejpam-3335	588	3	0	0	NUM
ejpam-3335	588	4	,	,	PUNCT
ejpam-3335	588	5	1]−	1]−	NUM
ejpam-3335	588	6	hh(0	hh(0	NOUN
ejpam-3335	588	7	)	)	PUNCT
ejpam-3335	588	8	⊆	⊆	NUM
ejpam-3335	589	1	[	[	X
ejpam-3335	589	2	0	0	NUM
ejpam-3335	589	3	,	,	PUNCT
ejpam-3335	589	4	1]−	1]−	NUM
ejpam-3335	589	5	hh(x	hh(x	NOUN
ejpam-3335	589	6	)	)	PUNCT
ejpam-3335	589	7	.	.	PUNCT
ejpam-3335	590	1	therefore	therefore	ADV
ejpam-3335	590	2	,	,	PUNCT
ejpam-3335	590	3	hh(0	hh(0	NOUN
ejpam-3335	590	4	)	)	PUNCT
ejpam-3335	590	5	⊇	⊇	NOUN
ejpam-3335	590	6	hh(x	hh(x	X
ejpam-3335	590	7	)	)	PUNCT
ejpam-3335	590	8	⊃	⊃	PROPN
ejpam-3335	590	9	ε	ε	PROPN
ejpam-3335	590	10	.	.	PUNCT
ejpam-3335	591	1	hence	hence	ADV
ejpam-3335	591	2	,	,	PUNCT
ejpam-3335	591	3	0	0	NUM
ejpam-3335	591	4	∈	∈	PROPN
ejpam-3335	591	5	u+(hh	u+(hh	NOUN
ejpam-3335	591	6	;	;	PUNCT
ejpam-3335	591	7	ε	ε	PROPN
ejpam-3335	591	8	)	)	PUNCT
ejpam-3335	591	9	.	.	PUNCT
ejpam-3335	592	1	next	next	ADV
ejpam-3335	592	2	,	,	PUNCT
ejpam-3335	592	3	let	let	VERB
ejpam-3335	592	4	x	x	PRON
ejpam-3335	592	5	,	,	PUNCT
ejpam-3335	592	6	y	y	PROPN
ejpam-3335	592	7	∈	∈	PROPN
ejpam-3335	592	8	a	a	PRON
ejpam-3335	592	9	be	be	AUX
ejpam-3335	592	10	such	such	ADJ
ejpam-3335	592	11	that	that	SCONJ
ejpam-3335	592	12	x	x	X
ejpam-3335	592	13	·	·	PUNCT
ejpam-3335	592	14	y	y	X
ejpam-3335	592	15	∈	∈	PROPN
ejpam-3335	592	16	u+(h	u+(h	NOUN
ejpam-3335	592	17	;	;	PUNCT
ejpam-3335	592	18	ε	ε	PROPN
ejpam-3335	592	19	)	)	PUNCT
ejpam-3335	592	20	and	and	CCONJ
ejpam-3335	592	21	x	x	PUNCT
ejpam-3335	592	22	∈	∈	PROPN
ejpam-3335	592	23	u+(h	u+(h	NOUN
ejpam-3335	592	24	;	;	PUNCT
ejpam-3335	592	25	ε	ε	PROPN
ejpam-3335	592	26	)	)	PUNCT
ejpam-3335	592	27	.	.	PUNCT
ejpam-3335	593	1	then	then	ADV
ejpam-3335	593	2	hh(x	hh(x	PUNCT
ejpam-3335	593	3	·	·	PUNCT
ejpam-3335	593	4	y	y	X
ejpam-3335	593	5	)	)	PUNCT
ejpam-3335	593	6	⊃	⊃	PROPN
ejpam-3335	593	7	ε	ε	PROPN
ejpam-3335	593	8	and	and	CCONJ
ejpam-3335	593	9	hh(x	hh(x	NOUN
ejpam-3335	593	10	)	)	PUNCT
ejpam-3335	593	11	⊃	⊃	PROPN
ejpam-3335	593	12	ε	ε	PROPN
ejpam-3335	593	13	.	.	PROPN
ejpam-3335	594	1	since	since	SCONJ
ejpam-3335	594	2	h	h	NOUN
ejpam-3335	594	3	is	be	AUX
ejpam-3335	594	4	an	an	DET
ejpam-3335	594	5	anti	anti	ADJ
ejpam-3335	594	6	-	-	ADJ
ejpam-3335	594	7	hesitant	hesitant	ADJ
ejpam-3335	594	8	fuzzy	fuzzy	ADJ
ejpam-3335	594	9	up	up	NOUN
ejpam-3335	594	10	-	-	PUNCT
ejpam-3335	594	11	filter	filter	NOUN
ejpam-3335	594	12	of	of	ADP
ejpam-3335	594	13	a	a	PRON
ejpam-3335	594	14	,	,	PUNCT
ejpam-3335	594	15	we	we	PRON
ejpam-3335	594	16	have	have	VERB
ejpam-3335	594	17	hh(y	hh(y	NOUN
ejpam-3335	594	18	)	)	PUNCT
ejpam-3335	595	1	⊆	⊆	NUM
ejpam-3335	595	2	hh(x	hh(x	X
ejpam-3335	595	3	·	·	PUNCT
ejpam-3335	595	4	y)∪hh(x	y)∪hh(x	NUM
ejpam-3335	595	5	)	)	PUNCT
ejpam-3335	595	6	.	.	PUNCT
ejpam-3335	596	1	by	by	ADP
ejpam-3335	596	2	lemma	lemma	PROPN
ejpam-3335	596	3	1	1	NUM
ejpam-3335	596	4	(	(	PUNCT
ejpam-3335	596	5	2	2	NUM
ejpam-3335	596	6	)	)	PUNCT
ejpam-3335	596	7	,	,	PUNCT
ejpam-3335	596	8	we	we	PRON
ejpam-3335	596	9	have	have	VERB
ejpam-3335	596	10	[	[	X
ejpam-3335	596	11	0	0	NUM
ejpam-3335	596	12	,	,	PUNCT
ejpam-3335	596	13	1]−hh(y	1]−hh(y	NUM
ejpam-3335	596	14	)	)	PUNCT
ejpam-3335	596	15	⊆	⊆	NUM
ejpam-3335	596	16	(	(	PUNCT
ejpam-3335	596	17	[	[	X
ejpam-3335	596	18	0	0	NUM
ejpam-3335	596	19	,	,	PUNCT
ejpam-3335	596	20	1]−hh(x	1]−hh(x	NUM
ejpam-3335	596	21	·	·	SYM
ejpam-3335	596	22	y))∪	y))∪	NOUN
ejpam-3335	596	23	(	(	PUNCT
ejpam-3335	596	24	[	[	X
ejpam-3335	596	25	0	0	NUM
ejpam-3335	596	26	,	,	PUNCT
ejpam-3335	596	27	1]−hh(x	1]−hh(x	NUM
ejpam-3335	596	28	)	)	PUNCT
ejpam-3335	596	29	)	)	PUNCT
ejpam-3335	597	1	=	=	PUNCT
ejpam-3335	598	1	[	[	X
ejpam-3335	598	2	0	0	NUM
ejpam-3335	598	3	,	,	PUNCT
ejpam-3335	598	4	1]−	1]−	NUM
ejpam-3335	598	5	(	(	PUNCT
ejpam-3335	598	6	hh(x	hh(x	X
ejpam-3335	598	7	·	·	PUNCT
ejpam-3335	598	8	y	y	X
ejpam-3335	598	9	)	)	PUNCT
ejpam-3335	598	10	∩	∩	NOUN
ejpam-3335	598	11	hh(x	hh(x	X
ejpam-3335	598	12	)	)	PUNCT
ejpam-3335	598	13	)	)	PUNCT
ejpam-3335	598	14	.	.	PUNCT
ejpam-3335	599	1	thus	thus	ADV
ejpam-3335	599	2	hh(y	hh(y	X
ejpam-3335	599	3	)	)	PUNCT
ejpam-3335	599	4	⊇	⊇	NOUN
ejpam-3335	599	5	hh(x	hh(x	X
ejpam-3335	599	6	·	·	PUNCT
ejpam-3335	599	7	y	y	X
ejpam-3335	599	8	)	)	PUNCT
ejpam-3335	599	9	∩	∩	NOUN
ejpam-3335	599	10	hh(x	hh(x	X
ejpam-3335	599	11	)	)	PUNCT
ejpam-3335	599	12	⊃	⊃	PROPN
ejpam-3335	599	13	ε	ε	PROPN
ejpam-3335	599	14	.	.	PUNCT
ejpam-3335	599	15	therefore	therefore	ADV
ejpam-3335	599	16	,	,	PUNCT
ejpam-3335	599	17	y	y	PROPN
ejpam-3335	599	18	∈	∈	PROPN
ejpam-3335	599	19	u+(h	u+(h	NOUN
ejpam-3335	599	20	;	;	PUNCT
ejpam-3335	599	21	ε	ε	PROPN
ejpam-3335	599	22	)	)	PUNCT
ejpam-3335	599	23	.	.	PUNCT
ejpam-3335	600	1	hence	hence	ADV
ejpam-3335	600	2	,	,	PUNCT
ejpam-3335	600	3	u+(h	u+(h	PROPN
ejpam-3335	600	4	;	;	PUNCT
ejpam-3335	600	5	ε	ε	PROPN
ejpam-3335	600	6	)	)	PUNCT
ejpam-3335	600	7	is	be	AUX
ejpam-3335	600	8	a	a	DET
ejpam-3335	600	9	up	up	ADJ
ejpam-3335	600	10	-	-	PUNCT
ejpam-3335	600	11	filter	filter	NOUN
ejpam-3335	600	12	of	of	ADP
ejpam-3335	600	13	a.	a.	NOUN
ejpam-3335	600	14	(	(	PUNCT
ejpam-3335	600	15	2	2	X
ejpam-3335	600	16	)	)	PUNCT
ejpam-3335	600	17	assume	assume	VERB
ejpam-3335	600	18	that	that	SCONJ
ejpam-3335	600	19	im(h	im(h	NOUN
ejpam-3335	600	20	)	)	PUNCT
ejpam-3335	600	21	is	be	AUX
ejpam-3335	600	22	a	a	DET
ejpam-3335	600	23	chain	chain	NOUN
ejpam-3335	600	24	and	and	CCONJ
ejpam-3335	600	25	for	for	ADP
ejpam-3335	600	26	all	all	DET
ejpam-3335	600	27	ε	ε	PROPN
ejpam-3335	600	28	∈	∈	PROPN
ejpam-3335	600	29	p([0	p([0	NOUN
ejpam-3335	600	30	,	,	PUNCT
ejpam-3335	600	31	1	1	NUM
ejpam-3335	600	32	]	]	NUM
ejpam-3335	600	33	)	)	PUNCT
ejpam-3335	600	34	,	,	PUNCT
ejpam-3335	600	35	a	a	DET
ejpam-3335	600	36	nonempty	nonempty	NOUN
ejpam-3335	600	37	subset	subset	VERB
ejpam-3335	600	38	u+(h	u+(h	NOUN
ejpam-3335	600	39	;	;	PUNCT
ejpam-3335	600	40	ε	ε	PROPN
ejpam-3335	600	41	)	)	PUNCT
ejpam-3335	600	42	of	of	ADP
ejpam-3335	600	43	a	a	PRON
ejpam-3335	600	44	is	be	AUX
ejpam-3335	600	45	a	a	DET
ejpam-3335	600	46	up	up	ADJ
ejpam-3335	600	47	-	-	PUNCT
ejpam-3335	600	48	filter	filter	NOUN
ejpam-3335	600	49	of	of	ADP
ejpam-3335	600	50	a.	a.	NOUN
ejpam-3335	600	51	assume	assume	VERB
ejpam-3335	600	52	that	that	SCONJ
ejpam-3335	600	53	there	there	PRON
ejpam-3335	600	54	exists	exist	VERB
ejpam-3335	600	55	x	x	X
ejpam-3335	600	56	∈	∈	PROPN
ejpam-3335	600	57	a	a	DET
ejpam-3335	600	58	such	such	ADJ
ejpam-3335	600	59	that	that	SCONJ
ejpam-3335	600	60	hh(0	hh(0	NOUN
ejpam-3335	600	61	)	)	PUNCT
ejpam-3335	600	62	*	*	PUNCT
ejpam-3335	600	63	hh(x	hh(x	X
ejpam-3335	600	64	)	)	PUNCT
ejpam-3335	600	65	.	.	PUNCT
ejpam-3335	601	1	since	since	SCONJ
ejpam-3335	601	2	im(h	im(h	NOUN
ejpam-3335	601	3	)	)	PUNCT
ejpam-3335	601	4	is	be	AUX
ejpam-3335	601	5	a	a	DET
ejpam-3335	601	6	chain	chain	NOUN
ejpam-3335	601	7	,	,	PUNCT
ejpam-3335	601	8	we	we	PRON
ejpam-3335	601	9	have	have	VERB
ejpam-3335	601	10	hh(0	hh(0	NOUN
ejpam-3335	601	11	)	)	PUNCT
ejpam-3335	601	12	⊃	⊃	NOUN
ejpam-3335	601	13	hh(x	hh(x	X
ejpam-3335	601	14	)	)	PUNCT
ejpam-3335	601	15	.	.	PUNCT
ejpam-3335	602	1	and	and	CCONJ
ejpam-3335	602	2	thus	thus	ADV
ejpam-3335	602	3	[	[	X
ejpam-3335	602	4	0	0	NUM
ejpam-3335	602	5	,	,	PUNCT
ejpam-3335	602	6	1	1	NUM
ejpam-3335	602	7	]	]	PUNCT
ejpam-3335	602	8	−	−	PROPN
ejpam-3335	602	9	hh(0	hh(0	NOUN
ejpam-3335	602	10	)	)	PUNCT
ejpam-3335	602	11	⊃	⊃	PROPN
ejpam-3335	603	1	[	[	X
ejpam-3335	603	2	0	0	NUM
ejpam-3335	603	3	,	,	PUNCT
ejpam-3335	603	4	1	1	NUM
ejpam-3335	603	5	]	]	PUNCT
ejpam-3335	603	6	−	−	NOUN
ejpam-3335	603	7	hh(x	hh(x	NOUN
ejpam-3335	603	8	)	)	PUNCT
ejpam-3335	603	9	.	.	PUNCT
ejpam-3335	604	1	so	so	ADV
ejpam-3335	604	2	hh(0	hh(0	NOUN
ejpam-3335	604	3	)	)	PUNCT
ejpam-3335	604	4	⊂	⊂	PRON
ejpam-3335	604	5	hh(x	hh(x	PROPN
ejpam-3335	604	6	)	)	PUNCT
ejpam-3335	604	7	.	.	PUNCT
ejpam-3335	605	1	choose	choose	VERB
ejpam-3335	605	2	ε	ε	PROPN
ejpam-3335	605	3	=	=	SYM
ejpam-3335	605	4	hh(0	hh(0	PROPN
ejpam-3335	605	5	)	)	PUNCT
ejpam-3335	605	6	∈	∈	PROPN
ejpam-3335	605	7	p([0	p([0	NOUN
ejpam-3335	605	8	,	,	PUNCT
ejpam-3335	605	9	1	1	NUM
ejpam-3335	605	10	]	]	NUM
ejpam-3335	605	11	)	)	PUNCT
ejpam-3335	605	12	.	.	PUNCT
ejpam-3335	606	1	then	then	ADV
ejpam-3335	606	2	hh(x	hh(x	NOUN
ejpam-3335	606	3	)	)	PUNCT
ejpam-3335	606	4	⊃	⊃	PROPN
ejpam-3335	606	5	ε	ε	PROPN
ejpam-3335	606	6	.	.	PUNCT
ejpam-3335	607	1	thus	thus	ADV
ejpam-3335	607	2	x	x	SYM
ejpam-3335	607	3	∈	∈	PROPN
ejpam-3335	607	4	u+(h	u+(h	NOUN
ejpam-3335	607	5	;	;	PUNCT
ejpam-3335	607	6	ε	ε	PROPN
ejpam-3335	607	7	)	)	PUNCT
ejpam-3335	607	8	6=	6=	ADP
ejpam-3335	607	9	∅.	∅.	ADP
ejpam-3335	607	10	by	by	ADP
ejpam-3335	607	11	assumption	assumption	NOUN
ejpam-3335	607	12	,	,	PUNCT
ejpam-3335	607	13	we	we	PRON
ejpam-3335	607	14	have	have	AUX
ejpam-3335	607	15	u+(h	u+(h	ADV
ejpam-3335	607	16	;	;	PUNCT
ejpam-3335	607	17	ε	ε	PROPN
ejpam-3335	607	18	)	)	PUNCT
ejpam-3335	607	19	is	be	AUX
ejpam-3335	607	20	a	a	DET
ejpam-3335	607	21	up	up	ADJ
ejpam-3335	607	22	-	-	PUNCT
ejpam-3335	607	23	filter	filter	NOUN
ejpam-3335	607	24	of	of	ADP
ejpam-3335	607	25	a	a	PRON
ejpam-3335	607	26	and	and	CCONJ
ejpam-3335	608	1	so	so	ADV
ejpam-3335	608	2	0	0	NUM
ejpam-3335	608	3	∈	∈	PROPN
ejpam-3335	608	4	l−(h	l−(h	PROPN
ejpam-3335	608	5	;	;	PUNCT
ejpam-3335	608	6	ε	ε	PROPN
ejpam-3335	608	7	)	)	PUNCT
ejpam-3335	608	8	.	.	PUNCT
ejpam-3335	609	1	therefore	therefore	ADV
ejpam-3335	609	2	,	,	PUNCT
ejpam-3335	609	3	hh(0	hh(0	NOUN
ejpam-3335	609	4	)	)	PUNCT
ejpam-3335	609	5	⊃	⊃	PROPN
ejpam-3335	609	6	ε	ε	PROPN
ejpam-3335	609	7	=	=	PUNCT
ejpam-3335	609	8	hh(0	hh(0	NOUN
ejpam-3335	609	9	)	)	PUNCT
ejpam-3335	609	10	,	,	PUNCT
ejpam-3335	609	11	a	a	DET
ejpam-3335	609	12	contradiction	contradiction	NOUN
ejpam-3335	609	13	.	.	PUNCT
ejpam-3335	610	1	hence	hence	ADV
ejpam-3335	610	2	,	,	PUNCT
ejpam-3335	610	3	hh(0	hh(0	NOUN
ejpam-3335	610	4	)	)	PUNCT
ejpam-3335	610	5	⊆	⊆	NUM
ejpam-3335	610	6	hh(x	hh(x	NOUN
ejpam-3335	610	7	)	)	PUNCT
ejpam-3335	610	8	for	for	ADP
ejpam-3335	610	9	all	all	PRON
ejpam-3335	610	10	x	x	SYM
ejpam-3335	610	11	∈	∈	NOUN
ejpam-3335	610	12	a.	a.	NOUN
ejpam-3335	610	13	next	next	ADV
ejpam-3335	610	14	,	,	PUNCT
ejpam-3335	610	15	assume	assume	VERB
ejpam-3335	610	16	that	that	SCONJ
ejpam-3335	610	17	there	there	PRON
ejpam-3335	610	18	exist	exist	VERB
ejpam-3335	610	19	x	x	NOUN
ejpam-3335	610	20	,	,	PUNCT
ejpam-3335	610	21	y	y	PROPN
ejpam-3335	610	22	∈	∈	PROPN
ejpam-3335	610	23	a	a	DET
ejpam-3335	610	24	such	such	ADJ
ejpam-3335	610	25	that	that	PRON
ejpam-3335	610	26	hh(y	hh(y	NUM
ejpam-3335	610	27	)	)	PUNCT
ejpam-3335	611	1	*	*	PUNCT
ejpam-3335	611	2	hh(x·y)∪hh(x	hh(x·y)∪hh(x	NOUN
ejpam-3335	611	3	)	)	PUNCT
ejpam-3335	611	4	.	.	PUNCT
ejpam-3335	612	1	since	since	SCONJ
ejpam-3335	612	2	im(h	im(h	NOUN
ejpam-3335	612	3	)	)	PUNCT
ejpam-3335	612	4	is	be	AUX
ejpam-3335	612	5	a	a	DET
ejpam-3335	612	6	chain	chain	NOUN
ejpam-3335	612	7	,	,	PUNCT
ejpam-3335	612	8	we	we	PRON
ejpam-3335	612	9	have	have	VERB
ejpam-3335	612	10	hh(y	hh(y	NOUN
ejpam-3335	612	11	)	)	PUNCT
ejpam-3335	612	12	⊃	⊃	NOUN
ejpam-3335	612	13	hh(x	hh(x	X
ejpam-3335	612	14	·	·	PUNCT
ejpam-3335	612	15	y	y	X
ejpam-3335	612	16	)	)	PUNCT
ejpam-3335	612	17	∪	∪	ADP
ejpam-3335	612	18	hh(x	hh(x	NOUN
ejpam-3335	612	19	)	)	PUNCT
ejpam-3335	612	20	.	.	PUNCT
ejpam-3335	613	1	by	by	ADP
ejpam-3335	613	2	lemma	lemma	PROPN
ejpam-3335	613	3	1	1	NUM
ejpam-3335	613	4	(	(	PUNCT
ejpam-3335	613	5	2	2	NUM
ejpam-3335	613	6	)	)	PUNCT
ejpam-3335	613	7	,	,	PUNCT
ejpam-3335	613	8	we	we	PRON
ejpam-3335	613	9	have	have	VERB
ejpam-3335	613	10	[	[	X
ejpam-3335	613	11	0	0	NUM
ejpam-3335	613	12	,	,	PUNCT
ejpam-3335	613	13	1]−	1]−	NUM
ejpam-3335	613	14	hh(y	hh(y	NOUN
ejpam-3335	613	15	)	)	PUNCT
ejpam-3335	613	16	⊃	⊃	NOUN
ejpam-3335	613	17	(	(	PUNCT
ejpam-3335	613	18	[	[	X
ejpam-3335	613	19	0	0	NUM
ejpam-3335	613	20	,	,	PUNCT
ejpam-3335	613	21	1]−hh(x·y))∪([0	1]−hh(x·y))∪([0	NUM
ejpam-3335	613	22	,	,	PUNCT
ejpam-3335	613	23	1]−hh(x	1]−hh(x	NUM
ejpam-3335	613	24	)	)	PUNCT
ejpam-3335	613	25	)	)	PUNCT
ejpam-3335	614	1	=	=	PUNCT
ejpam-3335	615	1	[	[	X
ejpam-3335	615	2	0	0	NUM
ejpam-3335	615	3	,	,	PUNCT
ejpam-3335	615	4	1]−(hh(x·y)∩hh(x	1]−(hh(x·y)∩hh(x	NUM
ejpam-3335	615	5	)	)	PUNCT
ejpam-3335	615	6	)	)	PUNCT
ejpam-3335	615	7	.	.	PUNCT
ejpam-3335	616	1	thus	thus	ADV
ejpam-3335	616	2	hh(y	hh(y	NOUN
ejpam-3335	616	3	)	)	PUNCT
ejpam-3335	616	4	⊂	⊂	PROPN
ejpam-3335	616	5	hh(x·y)∩hh(x	hh(x·y)∩hh(x	PROPN
ejpam-3335	616	6	)	)	PUNCT
ejpam-3335	616	7	.	.	PUNCT
ejpam-3335	617	1	choose	choose	VERB
ejpam-3335	617	2	ε	ε	PROPN
ejpam-3335	617	3	=	=	SYM
ejpam-3335	617	4	hh(y	hh(y	X
ejpam-3335	617	5	)	)	PUNCT
ejpam-3335	617	6	∈	∈	NOUN
ejpam-3335	617	7	p([0	p([0	NOUN
ejpam-3335	617	8	,	,	PUNCT
ejpam-3335	617	9	1	1	NUM
ejpam-3335	617	10	]	]	NUM
ejpam-3335	617	11	)	)	PUNCT
ejpam-3335	617	12	.	.	PUNCT
ejpam-3335	618	1	then	then	ADV
ejpam-3335	618	2	hh(x	hh(x	PUNCT
ejpam-3335	618	3	·	·	PUNCT
ejpam-3335	618	4	y	y	X
ejpam-3335	618	5	)	)	PUNCT
ejpam-3335	618	6	⊃	⊃	PROPN
ejpam-3335	618	7	ε	ε	PROPN
ejpam-3335	618	8	and	and	CCONJ
ejpam-3335	618	9	hh(x	hh(x	NOUN
ejpam-3335	618	10	)	)	PUNCT
ejpam-3335	618	11	⊃	⊃	PROPN
ejpam-3335	618	12	ε	ε	PROPN
ejpam-3335	618	13	.	.	PUNCT
ejpam-3335	619	1	thus	thus	ADV
ejpam-3335	619	2	x	x	X
ejpam-3335	619	3	·	·	PUNCT
ejpam-3335	619	4	y	y	X
ejpam-3335	619	5	,	,	PUNCT
ejpam-3335	619	6	x	x	SYM
ejpam-3335	619	7	∈	∈	PROPN
ejpam-3335	619	8	u+(h	u+(h	NOUN
ejpam-3335	619	9	;	;	PUNCT
ejpam-3335	619	10	ε	ε	PROPN
ejpam-3335	619	11	)	)	PUNCT
ejpam-3335	619	12	6=	6=	ADP
ejpam-3335	619	13	∅.	∅.	ADP
ejpam-3335	619	14	by	by	ADP
ejpam-3335	619	15	assumption	assumption	NOUN
ejpam-3335	619	16	,	,	PUNCT
ejpam-3335	619	17	we	we	PRON
ejpam-3335	619	18	have	have	AUX
ejpam-3335	619	19	u+(h	u+(h	ADV
ejpam-3335	619	20	;	;	PUNCT
ejpam-3335	619	21	ε	ε	PROPN
ejpam-3335	619	22	)	)	PUNCT
ejpam-3335	619	23	is	be	AUX
ejpam-3335	619	24	a	a	DET
ejpam-3335	619	25	up	up	ADJ
ejpam-3335	619	26	-	-	PUNCT
ejpam-3335	619	27	filter	filter	NOUN
ejpam-3335	619	28	of	of	ADP
ejpam-3335	619	29	a	a	PRON
ejpam-3335	620	1	and	and	CCONJ
ejpam-3335	620	2	so	so	ADV
ejpam-3335	620	3	y	y	PROPN
ejpam-3335	620	4	∈	∈	PROPN
ejpam-3335	620	5	u+(h	u+(h	NOUN
ejpam-3335	620	6	;	;	PUNCT
ejpam-3335	620	7	ε	ε	PROPN
ejpam-3335	620	8	)	)	PUNCT
ejpam-3335	620	9	.	.	PUNCT
ejpam-3335	621	1	thus	thus	ADV
ejpam-3335	621	2	hh(y	hh(y	NOUN
ejpam-3335	621	3	)	)	PUNCT
ejpam-3335	621	4	⊃	⊃	PROPN
ejpam-3335	621	5	ε	ε	X
ejpam-3335	621	6	=	=	PUNCT
ejpam-3335	621	7	hh(y	hh(y	X
ejpam-3335	621	8	)	)	PUNCT
ejpam-3335	621	9	,	,	PUNCT
ejpam-3335	621	10	a	a	DET
ejpam-3335	621	11	contradiction	contradiction	NOUN
ejpam-3335	621	12	.	.	PUNCT
ejpam-3335	622	1	therefore	therefore	ADV
ejpam-3335	622	2	,	,	PUNCT
ejpam-3335	622	3	hh(y	hh(y	ADJ
ejpam-3335	622	4	)	)	PUNCT
ejpam-3335	622	5	⊆	⊆	NUM
ejpam-3335	622	6	hh(x	hh(x	X
ejpam-3335	622	7	·	·	PUNCT
ejpam-3335	622	8	y	y	X
ejpam-3335	622	9	)	)	PUNCT
ejpam-3335	622	10	∪	∪	ADP
ejpam-3335	622	11	hh(x	hh(x	NOUN
ejpam-3335	622	12	)	)	PUNCT
ejpam-3335	622	13	for	for	ADP
ejpam-3335	622	14	all	all	DET
ejpam-3335	622	15	x	x	NOUN
ejpam-3335	622	16	,	,	PUNCT
ejpam-3335	622	17	y	y	PROPN
ejpam-3335	622	18	∈	∈	PROPN
ejpam-3335	622	19	a.	a.	NOUN
ejpam-3335	622	20	hence	hence	ADV
ejpam-3335	622	21	,	,	PUNCT
ejpam-3335	622	22	h	h	PROPN
ejpam-3335	622	23	is	be	AUX
ejpam-3335	622	24	an	an	DET
ejpam-3335	622	25	anti	anti	ADJ
ejpam-3335	622	26	-	-	ADJ
ejpam-3335	622	27	hesitant	hesitant	ADJ
ejpam-3335	622	28	fuzzy	fuzzy	ADJ
ejpam-3335	622	29	up	up	NOUN
ejpam-3335	622	30	-	-	PUNCT
ejpam-3335	622	31	filter	filter	NOUN
ejpam-3335	622	32	of	of	ADP
ejpam-3335	622	33	a.	a.	NOUN
ejpam-3335	622	34	example	example	NOUN
ejpam-3335	622	35	13	13	NUM
ejpam-3335	622	36	.	.	PUNCT
ejpam-3335	623	1	let	let	VERB
ejpam-3335	623	2	a	a	PRON
ejpam-3335	623	3	=	=	PUNCT
ejpam-3335	623	4	{	{	PUNCT
ejpam-3335	623	5	0	0	NUM
ejpam-3335	623	6	,	,	PUNCT
ejpam-3335	623	7	1	1	NUM
ejpam-3335	623	8	,	,	PUNCT
ejpam-3335	623	9	2	2	NUM
ejpam-3335	623	10	,	,	PUNCT
ejpam-3335	623	11	3	3	NUM
ejpam-3335	623	12	,	,	PUNCT
ejpam-3335	623	13	4	4	NUM
ejpam-3335	623	14	}	}	PUNCT
ejpam-3335	623	15	be	be	AUX
ejpam-3335	623	16	a	a	DET
ejpam-3335	623	17	set	set	NOUN
ejpam-3335	623	18	with	with	ADP
ejpam-3335	623	19	a	a	DET
ejpam-3335	623	20	binary	binary	ADJ
ejpam-3335	623	21	operation	operation	NOUN
ejpam-3335	623	22	·	·	PUNCT
ejpam-3335	623	23	defined	define	VERB
ejpam-3335	623	24	by	by	ADP
ejpam-3335	623	25	the	the	DET
ejpam-3335	623	26	cayley	cayley	ADJ
ejpam-3335	623	27	table	table	NOUN
ejpam-3335	623	28	from	from	ADP
ejpam-3335	623	29	example	example	NOUN
ejpam-3335	623	30	9	9	NUM
ejpam-3335	623	31	.	.	PUNCT
ejpam-3335	624	1	then	then	ADV
ejpam-3335	624	2	(	(	PUNCT
ejpam-3335	624	3	a	a	PRON
ejpam-3335	624	4	,	,	PUNCT
ejpam-3335	624	5	·	·	PUNCT
ejpam-3335	624	6	,	,	PUNCT
ejpam-3335	624	7	0	0	NUM
ejpam-3335	624	8	)	)	PUNCT
ejpam-3335	624	9	is	be	AUX
ejpam-3335	624	10	a	a	DET
ejpam-3335	624	11	up	up	NOUN
ejpam-3335	624	12	-	-	PUNCT
ejpam-3335	624	13	algebra	algebra	NOUN
ejpam-3335	624	14	.	.	PUNCT
ejpam-3335	625	1	we	we	PRON
ejpam-3335	625	2	define	define	VERB
ejpam-3335	625	3	a	a	DET
ejpam-3335	625	4	hesitant	hesitant	ADJ
ejpam-3335	625	5	fuzzy	fuzzy	ADJ
ejpam-3335	625	6	set	set	VERB
ejpam-3335	625	7	h	h	NOUN
ejpam-3335	625	8	on	on	ADP
ejpam-3335	625	9	a	a	PRON
ejpam-3335	625	10	as	as	SCONJ
ejpam-3335	625	11	follows	follow	VERB
ejpam-3335	625	12	:	:	PUNCT
ejpam-3335	625	13	p.	p.	NOUN
ejpam-3335	625	14	mosrijai	mosrijai	PROPN
ejpam-3335	625	15	,	,	PUNCT
ejpam-3335	625	16	a.	a.	NOUN
ejpam-3335	625	17	iampan	iampan	PROPN
ejpam-3335	625	18	/	/	SYM
ejpam-3335	625	19	eur	eur	PROPN
ejpam-3335	625	20	.	.	PUNCT
ejpam-3335	626	1	j.	j.	PROPN
ejpam-3335	626	2	pure	pure	PROPN
ejpam-3335	626	3	appl	appl	PROPN
ejpam-3335	626	4	.	.	PROPN
ejpam-3335	626	5	math	math	PROPN
ejpam-3335	626	6	,	,	PUNCT
ejpam-3335	626	7	11	11	NUM
ejpam-3335	626	8	(	(	PUNCT
ejpam-3335	626	9	4	4	NUM
ejpam-3335	626	10	)	)	PUNCT
ejpam-3335	626	11	(	(	PUNCT
ejpam-3335	626	12	2018	2018	NUM
ejpam-3335	626	13	)	)	PUNCT
ejpam-3335	626	14	,	,	PUNCT
ejpam-3335	626	15	976	976	NUM
ejpam-3335	626	16	-	-	SYM
ejpam-3335	626	17	1002	1002	NUM
ejpam-3335	626	18	995	995	NUM
ejpam-3335	626	19	hh(0	hh(0	NOUN
ejpam-3335	626	20	)	)	PUNCT
ejpam-3335	626	21	=	=	SYM
ejpam-3335	626	22	{	{	PUNCT
ejpam-3335	626	23	0	0	NUM
ejpam-3335	626	24	,	,	PUNCT
ejpam-3335	626	25	1	1	NUM
ejpam-3335	626	26	}	}	PUNCT
ejpam-3335	626	27	,	,	PUNCT
ejpam-3335	626	28	hh(1	hh(1	PROPN
ejpam-3335	626	29	)	)	PUNCT
ejpam-3335	626	30	=	=	PRON
ejpam-3335	626	31	{	{	PUNCT
ejpam-3335	626	32	1},hh(2	1},hh(2	NUM
ejpam-3335	626	33	)	)	PUNCT
ejpam-3335	626	34	=	=	SYM
ejpam-3335	626	35	{	{	PUNCT
ejpam-3335	626	36	0},hh(3	0},hh(3	NOUN
ejpam-3335	626	37	)	)	PUNCT
ejpam-3335	626	38	=	=	NOUN
ejpam-3335	626	39	∅	∅	NOUN
ejpam-3335	626	40	,	,	PUNCT
ejpam-3335	626	41	and	and	CCONJ
ejpam-3335	626	42	hh(4	hh(4	NOUN
ejpam-3335	626	43	)	)	PUNCT
ejpam-3335	626	44	=	=	PUNCT
ejpam-3335	626	45	∅.	∅.	NOUN
ejpam-3335	626	46	then	then	ADV
ejpam-3335	626	47	im(h	im(h	NOUN
ejpam-3335	626	48	)	)	PUNCT
ejpam-3335	626	49	is	be	AUX
ejpam-3335	626	50	not	not	PART
ejpam-3335	626	51	a	a	DET
ejpam-3335	626	52	chain	chain	NOUN
ejpam-3335	626	53	.	.	PUNCT
ejpam-3335	627	1	if	if	SCONJ
ejpam-3335	627	2	ε	ε	PROPN
ejpam-3335	627	3	=	=	PUNCT
ejpam-3335	627	4	{	{	PUNCT
ejpam-3335	627	5	1	1	NUM
ejpam-3335	627	6	}	}	PUNCT
ejpam-3335	627	7	or	or	CCONJ
ejpam-3335	627	8	ε	ε	PROPN
ejpam-3335	627	9	=	=	PUNCT
ejpam-3335	627	10	{	{	PUNCT
ejpam-3335	627	11	0	0	NUM
ejpam-3335	627	12	}	}	PUNCT
ejpam-3335	627	13	,	,	PUNCT
ejpam-3335	627	14	then	then	ADV
ejpam-3335	627	15	u+(h	u+(h	NUM
ejpam-3335	627	16	;	;	PUNCT
ejpam-3335	627	17	ε	ε	PROPN
ejpam-3335	627	18	)	)	PUNCT
ejpam-3335	627	19	=	=	PUNCT
ejpam-3335	627	20	{	{	PUNCT
ejpam-3335	627	21	0	0	NUM
ejpam-3335	627	22	}	}	PUNCT
ejpam-3335	627	23	.	.	PUNCT
ejpam-3335	628	1	if	if	SCONJ
ejpam-3335	628	2	ε	ε	PROPN
ejpam-3335	628	3	=	=	SYM
ejpam-3335	628	4	∅	∅	NOUN
ejpam-3335	628	5	,	,	PUNCT
ejpam-3335	628	6	then	then	ADV
ejpam-3335	628	7	u+(h	u+(h	NUM
ejpam-3335	628	8	;	;	PUNCT
ejpam-3335	628	9	ε	ε	PROPN
ejpam-3335	628	10	)	)	PUNCT
ejpam-3335	628	11	=	=	SYM
ejpam-3335	628	12	{	{	PUNCT
ejpam-3335	628	13	0	0	NUM
ejpam-3335	628	14	,	,	PUNCT
ejpam-3335	628	15	1	1	NUM
ejpam-3335	628	16	,	,	PUNCT
ejpam-3335	628	17	2	2	NUM
ejpam-3335	628	18	}	}	PUNCT
ejpam-3335	628	19	.	.	PUNCT
ejpam-3335	629	1	otherwise	otherwise	ADV
ejpam-3335	629	2	,	,	PUNCT
ejpam-3335	629	3	u+(h	u+(h	NOUN
ejpam-3335	629	4	;	;	PUNCT
ejpam-3335	629	5	ε	ε	PROPN
ejpam-3335	629	6	)	)	PUNCT
ejpam-3335	629	7	=	=	PUNCT
ejpam-3335	629	8	∅.	∅.	VERB
ejpam-3335	629	9	using	use	VERB
ejpam-3335	629	10	this	this	DET
ejpam-3335	629	11	data	datum	NOUN
ejpam-3335	629	12	,	,	PUNCT
ejpam-3335	629	13	we	we	PRON
ejpam-3335	629	14	can	can	AUX
ejpam-3335	629	15	show	show	VERB
ejpam-3335	629	16	that	that	SCONJ
ejpam-3335	629	17	all	all	DET
ejpam-3335	629	18	nonempty	nonempty	ADV
ejpam-3335	629	19	subset	subset	VERB
ejpam-3335	629	20	u+(h	u+(h	NOUN
ejpam-3335	629	21	;	;	PUNCT
ejpam-3335	629	22	ε	ε	PROPN
ejpam-3335	629	23	)	)	PUNCT
ejpam-3335	629	24	of	of	ADP
ejpam-3335	629	25	a	a	PRON
ejpam-3335	629	26	is	be	AUX
ejpam-3335	629	27	a	a	DET
ejpam-3335	629	28	up	up	ADJ
ejpam-3335	629	29	-	-	PUNCT
ejpam-3335	629	30	filter	filter	NOUN
ejpam-3335	629	31	of	of	ADP
ejpam-3335	629	32	a.	a.	NOUN
ejpam-3335	629	33	by	by	ADP
ejpam-3335	629	34	definition	definition	NOUN
ejpam-3335	629	35	4	4	NUM
ejpam-3335	629	36	,	,	PUNCT
ejpam-3335	629	37	we	we	PRON
ejpam-3335	629	38	have	have	VERB
ejpam-3335	629	39	hh(0	hh(0	NOUN
ejpam-3335	629	40	)	)	PUNCT
ejpam-3335	629	41	=	=	SYM
ejpam-3335	629	42	(	(	PUNCT
ejpam-3335	629	43	0	0	NUM
ejpam-3335	629	44	,	,	PUNCT
ejpam-3335	629	45	1),hh(1	1),hh(1	NUM
ejpam-3335	629	46	)	)	PUNCT
ejpam-3335	629	47	=	=	PUNCT
ejpam-3335	630	1	[	[	X
ejpam-3335	630	2	0	0	NUM
ejpam-3335	630	3	,	,	PUNCT
ejpam-3335	630	4	1	1	NUM
ejpam-3335	630	5	)	)	PUNCT
ejpam-3335	630	6	,	,	PUNCT
ejpam-3335	630	7	hh(2	hh(2	NOUN
ejpam-3335	630	8	)	)	PUNCT
ejpam-3335	630	9	=	=	SYM
ejpam-3335	630	10	(	(	PUNCT
ejpam-3335	630	11	0	0	NUM
ejpam-3335	630	12	,	,	PUNCT
ejpam-3335	630	13	1	1	NUM
ejpam-3335	630	14	]	]	PUNCT
ejpam-3335	630	15	,	,	PUNCT
ejpam-3335	630	16	hh(3	hh(3	NOUN
ejpam-3335	630	17	)	)	PUNCT
ejpam-3335	631	1	=	=	PUNCT
ejpam-3335	632	1	[	[	X
ejpam-3335	632	2	0	0	NUM
ejpam-3335	632	3	,	,	PUNCT
ejpam-3335	632	4	1	1	NUM
ejpam-3335	632	5	]	]	PUNCT
ejpam-3335	632	6	,	,	PUNCT
ejpam-3335	632	7	and	and	CCONJ
ejpam-3335	632	8	hh(4	hh(4	NOUN
ejpam-3335	632	9	)	)	PUNCT
ejpam-3335	632	10	=	=	PUNCT
ejpam-3335	633	1	[	[	X
ejpam-3335	633	2	0	0	NUM
ejpam-3335	633	3	,	,	PUNCT
ejpam-3335	633	4	1	1	NUM
ejpam-3335	633	5	]	]	PUNCT
ejpam-3335	633	6	.	.	PUNCT
ejpam-3335	634	1	since	since	SCONJ
ejpam-3335	634	2	hh(2	hh(2	NOUN
ejpam-3335	634	3	)	)	PUNCT
ejpam-3335	634	4	=	=	PUNCT
ejpam-3335	634	5	(	(	PUNCT
ejpam-3335	634	6	0	0	NUM
ejpam-3335	634	7	,	,	PUNCT
ejpam-3335	634	8	1	1	NUM
ejpam-3335	634	9	]	]	PUNCT
ejpam-3335	634	10	*	*	PUNCT
ejpam-3335	635	1	[	[	X
ejpam-3335	635	2	0	0	NUM
ejpam-3335	635	3	,	,	PUNCT
ejpam-3335	635	4	1	1	NUM
ejpam-3335	635	5	)	)	PUNCT
ejpam-3335	635	6	=	=	PUNCT
ejpam-3335	635	7	hh(1	hh(1	NOUN
ejpam-3335	635	8	)	)	PUNCT
ejpam-3335	635	9	∪	∪	ADP
ejpam-3335	635	10	hh(1	hh(1	NOUN
ejpam-3335	635	11	)	)	PUNCT
ejpam-3335	635	12	=	=	PUNCT
ejpam-3335	636	1	hh(1	hh(1	NOUN
ejpam-3335	636	2	·	·	PUNCT
ejpam-3335	636	3	2	2	X
ejpam-3335	636	4	)	)	PUNCT
ejpam-3335	636	5	∪	∪	ADP
ejpam-3335	636	6	hh(1	hh(1	PROPN
ejpam-3335	636	7	)	)	PUNCT
ejpam-3335	636	8	,	,	PUNCT
ejpam-3335	636	9	we	we	PRON
ejpam-3335	636	10	have	have	VERB
ejpam-3335	636	11	h	h	NOUN
ejpam-3335	636	12	is	be	AUX
ejpam-3335	636	13	not	not	PART
ejpam-3335	636	14	an	an	DET
ejpam-3335	636	15	anti	anti	ADJ
ejpam-3335	636	16	-	-	ADJ
ejpam-3335	636	17	hesitant	hesitant	ADJ
ejpam-3335	636	18	fuzzy	fuzzy	ADJ
ejpam-3335	636	19	up	up	NOUN
ejpam-3335	636	20	-	-	PUNCT
ejpam-3335	636	21	filter	filter	NOUN
ejpam-3335	636	22	of	of	ADP
ejpam-3335	636	23	a.	a.	NOUN
ejpam-3335	636	24	theorem	theorem	NOUN
ejpam-3335	636	25	21	21	NUM
ejpam-3335	636	26	.	.	PUNCT
ejpam-3335	637	1	let	let	AUX
ejpam-3335	637	2	h	h	PRON
ejpam-3335	637	3	be	be	AUX
ejpam-3335	637	4	a	a	DET
ejpam-3335	637	5	hesitant	hesitant	ADJ
ejpam-3335	637	6	fuzzy	fuzzy	ADJ
ejpam-3335	637	7	set	set	NOUN
ejpam-3335	637	8	on	on	ADP
ejpam-3335	637	9	a.	a.	NOUN
ejpam-3335	637	10	then	then	ADV
ejpam-3335	637	11	the	the	DET
ejpam-3335	637	12	following	follow	VERB
ejpam-3335	637	13	statements	statement	NOUN
ejpam-3335	637	14	hold	hold	VERB
ejpam-3335	637	15	:	:	PUNCT
ejpam-3335	637	16	(	(	PUNCT
ejpam-3335	637	17	1	1	X
ejpam-3335	637	18	)	)	PUNCT
ejpam-3335	637	19	if	if	SCONJ
ejpam-3335	637	20	h	h	NOUN
ejpam-3335	637	21	is	be	AUX
ejpam-3335	637	22	an	an	DET
ejpam-3335	637	23	anti	anti	ADJ
ejpam-3335	637	24	-	-	ADJ
ejpam-3335	637	25	hesitant	hesitant	ADJ
ejpam-3335	637	26	fuzzy	fuzzy	ADJ
ejpam-3335	637	27	up	up	NOUN
ejpam-3335	637	28	-	-	PUNCT
ejpam-3335	637	29	ideal	ideal	NOUN
ejpam-3335	637	30	of	of	ADP
ejpam-3335	637	31	a	a	PRON
ejpam-3335	637	32	,	,	PUNCT
ejpam-3335	637	33	then	then	ADV
ejpam-3335	637	34	for	for	SCONJ
ejpam-3335	637	35	all	all	DET
ejpam-3335	637	36	ε	ε	PROPN
ejpam-3335	637	37	∈	∈	PROPN
ejpam-3335	637	38	p([0	p([0	NOUN
ejpam-3335	637	39	,	,	PUNCT
ejpam-3335	637	40	1	1	NUM
ejpam-3335	637	41	]	]	NUM
ejpam-3335	637	42	)	)	PUNCT
ejpam-3335	637	43	,	,	PUNCT
ejpam-3335	637	44	u+(h	u+(h	PROPN
ejpam-3335	637	45	;	;	PUNCT
ejpam-3335	637	46	ε	ε	PROPN
ejpam-3335	637	47	)	)	PUNCT
ejpam-3335	637	48	is	be	AUX
ejpam-3335	637	49	a	a	DET
ejpam-3335	637	50	up	up	ADJ
ejpam-3335	637	51	-	-	PUNCT
ejpam-3335	637	52	ideal	ideal	NOUN
ejpam-3335	637	53	of	of	ADP
ejpam-3335	637	54	a	a	DET
ejpam-3335	637	55	if	if	NOUN
ejpam-3335	637	56	u+(h	u+(h	PROPN
ejpam-3335	637	57	;	;	PUNCT
ejpam-3335	637	58	ε	ε	PROPN
ejpam-3335	637	59	)	)	PUNCT
ejpam-3335	637	60	is	be	AUX
ejpam-3335	637	61	nonempty	nonempty	ADJ
ejpam-3335	637	62	,	,	PUNCT
ejpam-3335	637	63	and	and	CCONJ
ejpam-3335	637	64	(	(	PUNCT
ejpam-3335	637	65	2	2	X
ejpam-3335	637	66	)	)	PUNCT
ejpam-3335	637	67	if	if	SCONJ
ejpam-3335	637	68	im(h	im(h	NOUN
ejpam-3335	637	69	)	)	PUNCT
ejpam-3335	637	70	is	be	AUX
ejpam-3335	637	71	a	a	DET
ejpam-3335	637	72	chain	chain	NOUN
ejpam-3335	637	73	and	and	CCONJ
ejpam-3335	637	74	for	for	ADP
ejpam-3335	637	75	all	all	DET
ejpam-3335	637	76	ε	ε	PROPN
ejpam-3335	637	77	∈	∈	PROPN
ejpam-3335	637	78	p([0	p([0	NOUN
ejpam-3335	637	79	,	,	PUNCT
ejpam-3335	637	80	1	1	NUM
ejpam-3335	637	81	]	]	NUM
ejpam-3335	637	82	)	)	PUNCT
ejpam-3335	637	83	,	,	PUNCT
ejpam-3335	637	84	a	a	DET
ejpam-3335	637	85	nonempty	nonempty	NOUN
ejpam-3335	637	86	subset	subset	VERB
ejpam-3335	637	87	u+(h	u+(h	NOUN
ejpam-3335	637	88	;	;	PUNCT
ejpam-3335	637	89	ε	ε	PROPN
ejpam-3335	637	90	)	)	PUNCT
ejpam-3335	637	91	of	of	ADP
ejpam-3335	637	92	a	a	PRON
ejpam-3335	637	93	is	be	AUX
ejpam-3335	637	94	a	a	DET
ejpam-3335	637	95	up	up	ADJ
ejpam-3335	637	96	-	-	PUNCT
ejpam-3335	637	97	ideal	ideal	NOUN
ejpam-3335	637	98	of	of	ADP
ejpam-3335	637	99	a	a	PRON
ejpam-3335	637	100	,	,	PUNCT
ejpam-3335	637	101	then	then	ADV
ejpam-3335	637	102	h	h	PROPN
ejpam-3335	637	103	is	be	AUX
ejpam-3335	637	104	an	an	DET
ejpam-3335	637	105	anti	anti	ADJ
ejpam-3335	637	106	-	-	ADJ
ejpam-3335	637	107	hesitant	hesitant	ADJ
ejpam-3335	637	108	fuzzy	fuzzy	ADJ
ejpam-3335	637	109	up	up	NOUN
ejpam-3335	637	110	-	-	PUNCT
ejpam-3335	637	111	ideal	ideal	NOUN
ejpam-3335	637	112	of	of	ADP
ejpam-3335	637	113	a.	a.	NOUN
ejpam-3335	637	114	proof	proof	NOUN
ejpam-3335	637	115	.	.	PUNCT
ejpam-3335	638	1	(	(	PUNCT
ejpam-3335	638	2	1	1	X
ejpam-3335	638	3	)	)	PUNCT
ejpam-3335	638	4	assume	assume	VERB
ejpam-3335	638	5	that	that	SCONJ
ejpam-3335	638	6	h	h	NOUN
ejpam-3335	638	7	is	be	AUX
ejpam-3335	638	8	an	an	DET
ejpam-3335	638	9	anti	anti	ADJ
ejpam-3335	638	10	-	-	ADJ
ejpam-3335	638	11	hesitant	hesitant	ADJ
ejpam-3335	638	12	fuzzy	fuzzy	ADJ
ejpam-3335	638	13	up	up	NOUN
ejpam-3335	638	14	-	-	PUNCT
ejpam-3335	638	15	ideal	ideal	NOUN
ejpam-3335	638	16	of	of	ADP
ejpam-3335	638	17	a.	a.	NOUN
ejpam-3335	638	18	let	let	VERB
ejpam-3335	638	19	ε	ε	PROPN
ejpam-3335	638	20	∈	∈	PROPN
ejpam-3335	638	21	p([0	p([0	PROPN
ejpam-3335	638	22	,	,	PUNCT
ejpam-3335	638	23	1	1	NUM
ejpam-3335	638	24	]	]	PUNCT
ejpam-3335	638	25	)	)	PUNCT
ejpam-3335	638	26	be	be	AUX
ejpam-3335	638	27	such	such	ADJ
ejpam-3335	638	28	that	that	SCONJ
ejpam-3335	638	29	u+(h	u+(h	PROPN
ejpam-3335	638	30	;	;	PUNCT
ejpam-3335	638	31	ε	ε	PROPN
ejpam-3335	638	32	)	)	PUNCT
ejpam-3335	638	33	6=	6=	NOUN
ejpam-3335	638	34	∅	∅	NOUN
ejpam-3335	638	35	,	,	PUNCT
ejpam-3335	638	36	and	and	CCONJ
ejpam-3335	638	37	let	let	VERB
ejpam-3335	638	38	x	x	SYM
ejpam-3335	638	39	∈	∈	PROPN
ejpam-3335	638	40	a	a	DET
ejpam-3335	638	41	be	be	AUX
ejpam-3335	638	42	such	such	ADJ
ejpam-3335	638	43	that	that	SCONJ
ejpam-3335	638	44	x	x	SYM
ejpam-3335	638	45	∈	∈	PROPN
ejpam-3335	638	46	u(h	u(h	PROPN
ejpam-3335	638	47	;	;	PUNCT
ejpam-3335	638	48	ε	ε	PROPN
ejpam-3335	638	49	)	)	PUNCT
ejpam-3335	638	50	.	.	PUNCT
ejpam-3335	639	1	then	then	ADV
ejpam-3335	639	2	hh(x	hh(x	NOUN
ejpam-3335	639	3	)	)	PUNCT
ejpam-3335	639	4	⊃	⊃	PROPN
ejpam-3335	639	5	ε	ε	PROPN
ejpam-3335	639	6	.	.	PROPN
ejpam-3335	639	7	since	since	SCONJ
ejpam-3335	639	8	h	h	NOUN
ejpam-3335	639	9	is	be	AUX
ejpam-3335	639	10	an	an	DET
ejpam-3335	639	11	anti	anti	ADJ
ejpam-3335	639	12	-	-	ADJ
ejpam-3335	639	13	hesitant	hesitant	ADJ
ejpam-3335	639	14	fuzzy	fuzzy	ADJ
ejpam-3335	639	15	up	up	NOUN
ejpam-3335	639	16	-	-	PUNCT
ejpam-3335	639	17	ideal	ideal	NOUN
ejpam-3335	639	18	of	of	ADP
ejpam-3335	639	19	a	a	PRON
ejpam-3335	639	20	,	,	PUNCT
ejpam-3335	639	21	we	we	PRON
ejpam-3335	639	22	have	have	VERB
ejpam-3335	639	23	hh(0	hh(0	NOUN
ejpam-3335	639	24	)	)	PUNCT
ejpam-3335	639	25	⊆	⊆	NUM
ejpam-3335	639	26	hh(x	hh(x	NOUN
ejpam-3335	639	27	)	)	PUNCT
ejpam-3335	639	28	.	.	PUNCT
ejpam-3335	640	1	thus	thus	ADV
ejpam-3335	640	2	[	[	X
ejpam-3335	640	3	0	0	NUM
ejpam-3335	640	4	,	,	PUNCT
ejpam-3335	640	5	1]−	1]−	NUM
ejpam-3335	640	6	hh(0	hh(0	NOUN
ejpam-3335	640	7	)	)	PUNCT
ejpam-3335	640	8	⊆	⊆	NUM
ejpam-3335	641	1	[	[	X
ejpam-3335	641	2	0	0	NUM
ejpam-3335	641	3	,	,	PUNCT
ejpam-3335	641	4	1]−	1]−	NUM
ejpam-3335	641	5	hh(x	hh(x	NOUN
ejpam-3335	641	6	)	)	PUNCT
ejpam-3335	641	7	.	.	PUNCT
ejpam-3335	642	1	therefore	therefore	ADV
ejpam-3335	642	2	,	,	PUNCT
ejpam-3335	642	3	hh(0	hh(0	NOUN
ejpam-3335	642	4	)	)	PUNCT
ejpam-3335	642	5	⊇	⊇	NOUN
ejpam-3335	642	6	hh(x	hh(x	X
ejpam-3335	642	7	)	)	PUNCT
ejpam-3335	642	8	⊃	⊃	PROPN
ejpam-3335	642	9	ε	ε	PROPN
ejpam-3335	642	10	.	.	PUNCT
ejpam-3335	643	1	hence	hence	ADV
ejpam-3335	643	2	,	,	PUNCT
ejpam-3335	643	3	0	0	X
ejpam-3335	643	4	∈	∈	PROPN
ejpam-3335	643	5	u+(h	u+(h	NOUN
ejpam-3335	643	6	;	;	PUNCT
ejpam-3335	643	7	ε	ε	PROPN
ejpam-3335	643	8	)	)	PUNCT
ejpam-3335	643	9	.	.	PUNCT
ejpam-3335	644	1	next	next	ADV
ejpam-3335	644	2	,	,	PUNCT
ejpam-3335	644	3	let	let	VERB
ejpam-3335	644	4	x	x	PRON
ejpam-3335	644	5	,	,	PUNCT
ejpam-3335	644	6	y	y	PROPN
ejpam-3335	644	7	,	,	PUNCT
ejpam-3335	644	8	z	z	PROPN
ejpam-3335	644	9	∈	∈	PROPN
ejpam-3335	644	10	a	a	DET
ejpam-3335	644	11	be	be	AUX
ejpam-3335	644	12	such	such	ADJ
ejpam-3335	644	13	that	that	SCONJ
ejpam-3335	644	14	x	x	PART
ejpam-3335	644	15	·	·	PUNCT
ejpam-3335	644	16	(	(	PUNCT
ejpam-3335	644	17	y	y	PROPN
ejpam-3335	644	18	·	·	PUNCT
ejpam-3335	644	19	z	z	X
ejpam-3335	644	20	)	)	PUNCT
ejpam-3335	644	21	∈	∈	PROPN
ejpam-3335	644	22	u+(h	u+(h	NOUN
ejpam-3335	644	23	;	;	PUNCT
ejpam-3335	644	24	ε	ε	PROPN
ejpam-3335	644	25	)	)	PUNCT
ejpam-3335	644	26	and	and	CCONJ
ejpam-3335	644	27	y	y	PROPN
ejpam-3335	644	28	∈	∈	PROPN
ejpam-3335	645	1	u+(h	u+(h	NOUN
ejpam-3335	645	2	;	;	PUNCT
ejpam-3335	645	3	ε	ε	PROPN
ejpam-3335	645	4	)	)	PUNCT
ejpam-3335	645	5	.	.	PUNCT
ejpam-3335	646	1	then	then	ADV
ejpam-3335	646	2	hh(x	hh(x	PUNCT
ejpam-3335	646	3	·	·	PUNCT
ejpam-3335	646	4	(	(	PUNCT
ejpam-3335	646	5	y	y	PROPN
ejpam-3335	646	6	·	·	PUNCT
ejpam-3335	646	7	z	z	NOUN
ejpam-3335	646	8	)	)	PUNCT
ejpam-3335	646	9	)	)	PUNCT
ejpam-3335	647	1	⊃	⊃	PROPN
ejpam-3335	647	2	ε	ε	PROPN
ejpam-3335	647	3	and	and	CCONJ
ejpam-3335	647	4	hh(y	hh(y	NOUN
ejpam-3335	647	5	)	)	PUNCT
ejpam-3335	647	6	⊃	⊃	PROPN
ejpam-3335	647	7	ε	ε	PROPN
ejpam-3335	647	8	.	.	PROPN
ejpam-3335	648	1	since	since	SCONJ
ejpam-3335	648	2	h	h	NOUN
ejpam-3335	648	3	is	be	AUX
ejpam-3335	648	4	an	an	DET
ejpam-3335	648	5	anti	anti	ADJ
ejpam-3335	648	6	-	-	ADJ
ejpam-3335	648	7	hesitant	hesitant	ADJ
ejpam-3335	648	8	fuzzy	fuzzy	ADJ
ejpam-3335	648	9	up	up	NOUN
ejpam-3335	648	10	-	-	PUNCT
ejpam-3335	648	11	ideal	ideal	NOUN
ejpam-3335	648	12	of	of	ADP
ejpam-3335	648	13	a	a	PRON
ejpam-3335	648	14	,	,	PUNCT
ejpam-3335	648	15	we	we	PRON
ejpam-3335	648	16	obtain	obtain	VERB
ejpam-3335	648	17	hh(x	hh(x	X
ejpam-3335	648	18	·	·	PUNCT
ejpam-3335	649	1	z	z	X
ejpam-3335	649	2	)	)	PUNCT
ejpam-3335	649	3	⊆	⊆	NUM
ejpam-3335	649	4	hh(x	hh(x	X
ejpam-3335	649	5	·	·	PUNCT
ejpam-3335	649	6	(	(	PUNCT
ejpam-3335	649	7	y	y	PROPN
ejpam-3335	649	8	·	·	PUNCT
ejpam-3335	649	9	z	z	NOUN
ejpam-3335	649	10	)	)	PUNCT
ejpam-3335	649	11	)	)	PUNCT
ejpam-3335	649	12	∪	∪	ADP
ejpam-3335	649	13	hh(y	hh(y	NOUN
ejpam-3335	649	14	)	)	PUNCT
ejpam-3335	649	15	.	.	PUNCT
ejpam-3335	650	1	by	by	ADP
ejpam-3335	650	2	lemma	lemma	PROPN
ejpam-3335	650	3	1	1	NUM
ejpam-3335	650	4	(	(	PUNCT
ejpam-3335	650	5	2	2	NUM
ejpam-3335	650	6	)	)	PUNCT
ejpam-3335	650	7	,	,	PUNCT
ejpam-3335	650	8	we	we	PRON
ejpam-3335	650	9	have	have	VERB
ejpam-3335	650	10	[	[	X
ejpam-3335	650	11	0	0	NUM
ejpam-3335	650	12	,	,	PUNCT
ejpam-3335	650	13	1	1	NUM
ejpam-3335	650	14	]	]	SYM
ejpam-3335	650	15	−	−	NOUN
ejpam-3335	650	16	hh(x	hh(x	X
ejpam-3335	650	17	·	·	PUNCT
ejpam-3335	651	1	z	z	X
ejpam-3335	651	2	)	)	PUNCT
ejpam-3335	651	3	⊆	⊆	NUM
ejpam-3335	651	4	(	(	PUNCT
ejpam-3335	651	5	[	[	X
ejpam-3335	651	6	0	0	NUM
ejpam-3335	651	7	,	,	PUNCT
ejpam-3335	651	8	1	1	NUM
ejpam-3335	651	9	]	]	SYM
ejpam-3335	651	10	−	−	NOUN
ejpam-3335	651	11	hh(x	hh(x	X
ejpam-3335	651	12	·	·	PUNCT
ejpam-3335	651	13	(	(	PUNCT
ejpam-3335	651	14	y	y	PROPN
ejpam-3335	651	15	·	·	PUNCT
ejpam-3335	651	16	z	z	NOUN
ejpam-3335	651	17	)	)	PUNCT
ejpam-3335	651	18	)	)	PUNCT
ejpam-3335	651	19	)	)	PUNCT
ejpam-3335	652	1	∪	∪	ADV
ejpam-3335	652	2	(	(	PUNCT
ejpam-3335	652	3	[	[	X
ejpam-3335	652	4	0	0	NUM
ejpam-3335	652	5	,	,	PUNCT
ejpam-3335	652	6	1	1	NUM
ejpam-3335	652	7	]	]	PUNCT
ejpam-3335	652	8	−	−	NOUN
ejpam-3335	652	9	hh(y	hh(y	NOUN
ejpam-3335	652	10	)	)	PUNCT
ejpam-3335	652	11	)	)	PUNCT
ejpam-3335	653	1	=	=	PUNCT
ejpam-3335	654	1	[	[	X
ejpam-3335	654	2	0	0	NUM
ejpam-3335	654	3	,	,	PUNCT
ejpam-3335	654	4	1	1	NUM
ejpam-3335	654	5	]	]	SYM
ejpam-3335	654	6	−	−	PROPN
ejpam-3335	654	7	(	(	PUNCT
ejpam-3335	654	8	hh(x	hh(x	X
ejpam-3335	654	9	·	·	PUNCT
ejpam-3335	654	10	(	(	PUNCT
ejpam-3335	654	11	y	y	PROPN
ejpam-3335	654	12	·	·	PUNCT
ejpam-3335	654	13	z	z	NOUN
ejpam-3335	654	14	)	)	PUNCT
ejpam-3335	654	15	)	)	PUNCT
ejpam-3335	654	16	∩	∩	NOUN
ejpam-3335	654	17	hh(y	hh(y	NOUN
ejpam-3335	654	18	)	)	PUNCT
ejpam-3335	654	19	)	)	PUNCT
ejpam-3335	654	20	.	.	PUNCT
ejpam-3335	655	1	thus	thus	ADV
ejpam-3335	655	2	hh(x	hh(x	X
ejpam-3335	655	3	·	·	PUNCT
ejpam-3335	655	4	z	z	X
ejpam-3335	655	5	)	)	PUNCT
ejpam-3335	655	6	⊇	⊇	NOUN
ejpam-3335	655	7	hh(x	hh(x	X
ejpam-3335	655	8	·	·	PUNCT
ejpam-3335	655	9	(	(	PUNCT
ejpam-3335	655	10	y	y	PROPN
ejpam-3335	655	11	·	·	PUNCT
ejpam-3335	655	12	z	z	NOUN
ejpam-3335	655	13	)	)	PUNCT
ejpam-3335	655	14	)	)	PUNCT
ejpam-3335	655	15	∩	∩	NOUN
ejpam-3335	655	16	hh(y	hh(y	NUM
ejpam-3335	655	17	)	)	PUNCT
ejpam-3335	655	18	⊃	⊃	PROPN
ejpam-3335	655	19	ε	ε	PROPN
ejpam-3335	655	20	.	.	PUNCT
ejpam-3335	655	21	therefore	therefore	ADV
ejpam-3335	655	22	,	,	PUNCT
ejpam-3335	655	23	x	x	X
ejpam-3335	655	24	·	·	PUNCT
ejpam-3335	655	25	z	z	X
ejpam-3335	655	26	∈	∈	PROPN
ejpam-3335	655	27	u+(h	u+(h	NOUN
ejpam-3335	655	28	;	;	PUNCT
ejpam-3335	655	29	ε	ε	PROPN
ejpam-3335	655	30	)	)	PUNCT
ejpam-3335	655	31	.	.	PUNCT
ejpam-3335	656	1	hence	hence	ADV
ejpam-3335	656	2	,	,	PUNCT
ejpam-3335	656	3	u+(h	u+(h	PROPN
ejpam-3335	656	4	;	;	PUNCT
ejpam-3335	656	5	ε	ε	PROPN
ejpam-3335	656	6	)	)	PUNCT
ejpam-3335	656	7	is	be	AUX
ejpam-3335	656	8	a	a	DET
ejpam-3335	656	9	up	up	ADJ
ejpam-3335	656	10	-	-	PUNCT
ejpam-3335	656	11	ideal	ideal	NOUN
ejpam-3335	656	12	of	of	ADP
ejpam-3335	656	13	a.	a.	NOUN
ejpam-3335	656	14	(	(	PUNCT
ejpam-3335	656	15	2	2	X
ejpam-3335	656	16	)	)	PUNCT
ejpam-3335	656	17	assume	assume	VERB
ejpam-3335	656	18	that	that	SCONJ
ejpam-3335	656	19	im(h	im(h	NOUN
ejpam-3335	656	20	)	)	PUNCT
ejpam-3335	656	21	is	be	AUX
ejpam-3335	656	22	a	a	DET
ejpam-3335	656	23	chain	chain	NOUN
ejpam-3335	656	24	and	and	CCONJ
ejpam-3335	656	25	for	for	ADP
ejpam-3335	656	26	all	all	DET
ejpam-3335	656	27	ε	ε	PROPN
ejpam-3335	656	28	∈	∈	PROPN
ejpam-3335	656	29	p([0	p([0	NOUN
ejpam-3335	656	30	,	,	PUNCT
ejpam-3335	656	31	1	1	NUM
ejpam-3335	656	32	]	]	NUM
ejpam-3335	656	33	)	)	PUNCT
ejpam-3335	656	34	,	,	PUNCT
ejpam-3335	656	35	a	a	DET
ejpam-3335	656	36	nonempty	nonempty	NOUN
ejpam-3335	656	37	subset	subset	VERB
ejpam-3335	656	38	u+(h	u+(h	NOUN
ejpam-3335	656	39	;	;	PUNCT
ejpam-3335	656	40	ε	ε	PROPN
ejpam-3335	656	41	)	)	PUNCT
ejpam-3335	656	42	of	of	ADP
ejpam-3335	656	43	a	a	PRON
ejpam-3335	656	44	is	be	AUX
ejpam-3335	656	45	a	a	DET
ejpam-3335	656	46	up	up	ADJ
ejpam-3335	656	47	-	-	PUNCT
ejpam-3335	656	48	ideal	ideal	NOUN
ejpam-3335	656	49	of	of	ADP
ejpam-3335	656	50	a.	a.	NOUN
ejpam-3335	656	51	assume	assume	VERB
ejpam-3335	656	52	that	that	SCONJ
ejpam-3335	656	53	there	there	PRON
ejpam-3335	656	54	exists	exist	VERB
ejpam-3335	656	55	x	x	X
ejpam-3335	656	56	∈	∈	PROPN
ejpam-3335	656	57	a	a	DET
ejpam-3335	656	58	such	such	ADJ
ejpam-3335	656	59	that	that	SCONJ
ejpam-3335	656	60	hh(0	hh(0	NOUN
ejpam-3335	656	61	)	)	PUNCT
ejpam-3335	656	62	*	*	PUNCT
ejpam-3335	656	63	hh(x	hh(x	X
ejpam-3335	656	64	)	)	PUNCT
ejpam-3335	656	65	.	.	PUNCT
ejpam-3335	657	1	since	since	SCONJ
ejpam-3335	657	2	im(h	im(h	NOUN
ejpam-3335	657	3	)	)	PUNCT
ejpam-3335	657	4	is	be	AUX
ejpam-3335	657	5	a	a	DET
ejpam-3335	657	6	chain	chain	NOUN
ejpam-3335	657	7	,	,	PUNCT
ejpam-3335	657	8	we	we	PRON
ejpam-3335	657	9	have	have	VERB
ejpam-3335	657	10	hh(0	hh(0	NOUN
ejpam-3335	657	11	)	)	PUNCT
ejpam-3335	657	12	⊃	⊃	NOUN
ejpam-3335	657	13	hh(x	hh(x	X
ejpam-3335	657	14	)	)	PUNCT
ejpam-3335	657	15	.	.	PUNCT
ejpam-3335	658	1	then	then	ADV
ejpam-3335	658	2	[	[	X
ejpam-3335	658	3	0	0	NUM
ejpam-3335	658	4	,	,	PUNCT
ejpam-3335	658	5	1	1	NUM
ejpam-3335	658	6	]	]	PUNCT
ejpam-3335	658	7	−	−	PROPN
ejpam-3335	658	8	hh(0	hh(0	NOUN
ejpam-3335	658	9	)	)	PUNCT
ejpam-3335	658	10	⊃	⊃	PROPN
ejpam-3335	659	1	[	[	X
ejpam-3335	659	2	0	0	NUM
ejpam-3335	659	3	,	,	PUNCT
ejpam-3335	659	4	1	1	NUM
ejpam-3335	659	5	]	]	PUNCT
ejpam-3335	659	6	−	−	NOUN
ejpam-3335	659	7	hh(x	hh(x	NOUN
ejpam-3335	659	8	)	)	PUNCT
ejpam-3335	659	9	.	.	PUNCT
ejpam-3335	660	1	thus	thus	ADV
ejpam-3335	660	2	hh(0	hh(0	NOUN
ejpam-3335	660	3	)	)	PUNCT
ejpam-3335	660	4	⊂	⊂	PRON
ejpam-3335	660	5	hh(x	hh(x	PROPN
ejpam-3335	660	6	)	)	PUNCT
ejpam-3335	660	7	.	.	PUNCT
ejpam-3335	661	1	choose	choose	VERB
ejpam-3335	661	2	ε	ε	PROPN
ejpam-3335	661	3	=	=	SYM
ejpam-3335	661	4	hh(0	hh(0	PROPN
ejpam-3335	661	5	)	)	PUNCT
ejpam-3335	661	6	∈	∈	PROPN
ejpam-3335	661	7	p([0	p([0	NOUN
ejpam-3335	661	8	,	,	PUNCT
ejpam-3335	661	9	1	1	NUM
ejpam-3335	661	10	]	]	NUM
ejpam-3335	661	11	)	)	PUNCT
ejpam-3335	661	12	.	.	PUNCT
ejpam-3335	662	1	then	then	ADV
ejpam-3335	662	2	hh(x	hh(x	NOUN
ejpam-3335	662	3	)	)	PUNCT
ejpam-3335	662	4	⊃	⊃	PROPN
ejpam-3335	662	5	ε	ε	PROPN
ejpam-3335	662	6	.	.	PUNCT
ejpam-3335	663	1	thus	thus	ADV
ejpam-3335	663	2	x	x	SYM
ejpam-3335	663	3	∈	∈	PROPN
ejpam-3335	663	4	u+(h	u+(h	NOUN
ejpam-3335	663	5	;	;	PUNCT
ejpam-3335	663	6	ε	ε	PROPN
ejpam-3335	663	7	)	)	PUNCT
ejpam-3335	663	8	6=	6=	ADP
ejpam-3335	663	9	∅.	∅.	ADP
ejpam-3335	663	10	by	by	ADP
ejpam-3335	663	11	assumption	assumption	NOUN
ejpam-3335	663	12	,	,	PUNCT
ejpam-3335	663	13	we	we	PRON
ejpam-3335	663	14	have	have	AUX
ejpam-3335	663	15	u+(h	u+(h	ADV
ejpam-3335	663	16	;	;	PUNCT
ejpam-3335	663	17	ε	ε	PROPN
ejpam-3335	663	18	)	)	PUNCT
ejpam-3335	663	19	is	be	AUX
ejpam-3335	663	20	a	a	DET
ejpam-3335	663	21	up	up	ADJ
ejpam-3335	663	22	-	-	PUNCT
ejpam-3335	663	23	ideal	ideal	NOUN
ejpam-3335	663	24	of	of	ADP
ejpam-3335	663	25	a	a	PRON
ejpam-3335	663	26	and	and	CCONJ
ejpam-3335	664	1	so	so	ADV
ejpam-3335	664	2	0	0	NUM
ejpam-3335	665	1	∈	∈	PROPN
ejpam-3335	666	1	u+(h	u+(h	NOUN
ejpam-3335	666	2	;	;	PUNCT
ejpam-3335	666	3	ε	ε	PROPN
ejpam-3335	666	4	)	)	PUNCT
ejpam-3335	666	5	.	.	PUNCT
ejpam-3335	667	1	therefore	therefore	ADV
ejpam-3335	667	2	,	,	PUNCT
ejpam-3335	667	3	hh(0	hh(0	NOUN
ejpam-3335	667	4	)	)	PUNCT
ejpam-3335	667	5	⊃	⊃	PROPN
ejpam-3335	667	6	ε	ε	PROPN
ejpam-3335	667	7	=	=	PUNCT
ejpam-3335	667	8	hh(0	hh(0	NOUN
ejpam-3335	667	9	)	)	PUNCT
ejpam-3335	667	10	,	,	PUNCT
ejpam-3335	667	11	a	a	DET
ejpam-3335	667	12	contradiction	contradiction	NOUN
ejpam-3335	667	13	.	.	PUNCT
ejpam-3335	668	1	hence	hence	ADV
ejpam-3335	668	2	,	,	PUNCT
ejpam-3335	668	3	hh(0	hh(0	NOUN
ejpam-3335	668	4	)	)	PUNCT
ejpam-3335	668	5	⊆	⊆	NUM
ejpam-3335	668	6	hh(x	hh(x	NOUN
ejpam-3335	668	7	)	)	PUNCT
ejpam-3335	668	8	for	for	ADP
ejpam-3335	668	9	any	any	DET
ejpam-3335	668	10	x	x	SYM
ejpam-3335	668	11	∈	∈	PROPN
ejpam-3335	668	12	a.	a.	NOUN
ejpam-3335	668	13	next	next	ADV
ejpam-3335	668	14	,	,	PUNCT
ejpam-3335	668	15	assume	assume	VERB
ejpam-3335	668	16	that	that	SCONJ
ejpam-3335	668	17	there	there	PRON
ejpam-3335	668	18	exist	exist	VERB
ejpam-3335	668	19	x	x	NOUN
ejpam-3335	668	20	,	,	PUNCT
ejpam-3335	668	21	y	y	PROPN
ejpam-3335	668	22	,	,	PUNCT
ejpam-3335	668	23	z	z	PROPN
ejpam-3335	668	24	∈	∈	PROPN
ejpam-3335	668	25	a	a	DET
ejpam-3335	668	26	such	such	ADJ
ejpam-3335	668	27	that	that	PRON
ejpam-3335	668	28	hh(x	hh(x	X
ejpam-3335	668	29	·	·	PUNCT
ejpam-3335	669	1	z	z	X
ejpam-3335	669	2	)	)	PUNCT
ejpam-3335	669	3	*	*	PUNCT
ejpam-3335	669	4	hh(x	hh(x	X
ejpam-3335	669	5	·	·	PUNCT
ejpam-3335	669	6	(	(	PUNCT
ejpam-3335	669	7	y	y	PROPN
ejpam-3335	669	8	·	·	PUNCT
ejpam-3335	669	9	z	z	NOUN
ejpam-3335	669	10	)	)	PUNCT
ejpam-3335	669	11	)	)	PUNCT
ejpam-3335	669	12	∪	∪	ADP
ejpam-3335	669	13	hh(y	hh(y	NOUN
ejpam-3335	669	14	)	)	PUNCT
ejpam-3335	669	15	.	.	PUNCT
ejpam-3335	670	1	since	since	SCONJ
ejpam-3335	670	2	im(h	im(h	NOUN
ejpam-3335	670	3	)	)	PUNCT
ejpam-3335	670	4	is	be	AUX
ejpam-3335	670	5	a	a	DET
ejpam-3335	670	6	chain	chain	NOUN
ejpam-3335	670	7	,	,	PUNCT
ejpam-3335	670	8	we	we	PRON
ejpam-3335	670	9	have	have	VERB
ejpam-3335	670	10	hh(x	hh(x	X
ejpam-3335	670	11	·	·	SYM
ejpam-3335	670	12	z	z	X
ejpam-3335	670	13	)	)	PUNCT
ejpam-3335	670	14	⊃	⊃	NOUN
ejpam-3335	670	15	hh(x	hh(x	X
ejpam-3335	670	16	·	·	PUNCT
ejpam-3335	670	17	(	(	PUNCT
ejpam-3335	670	18	y	y	PROPN
ejpam-3335	670	19	·	·	PUNCT
ejpam-3335	670	20	z))∪hh(y	z))∪hh(y	NUM
ejpam-3335	670	21	)	)	PUNCT
ejpam-3335	670	22	.	.	PUNCT
ejpam-3335	671	1	by	by	ADP
ejpam-3335	671	2	lemma	lemma	PROPN
ejpam-3335	671	3	1	1	NUM
ejpam-3335	671	4	(	(	PUNCT
ejpam-3335	671	5	2	2	NUM
ejpam-3335	671	6	)	)	PUNCT
ejpam-3335	671	7	,	,	PUNCT
ejpam-3335	671	8	we	we	PRON
ejpam-3335	671	9	have	have	VERB
ejpam-3335	671	10	[	[	X
ejpam-3335	671	11	0	0	NUM
ejpam-3335	671	12	,	,	PUNCT
ejpam-3335	671	13	1]−hh(x·z	1]−hh(x·z	NUM
ejpam-3335	671	14	)	)	PUNCT
ejpam-3335	672	1	⊃	⊃	NOUN
ejpam-3335	672	2	(	(	PUNCT
ejpam-3335	672	3	[	[	X
ejpam-3335	672	4	0	0	NUM
ejpam-3335	672	5	,	,	PUNCT
ejpam-3335	672	6	1]−hh(x·(y·z)))∪([0	1]−hh(x·(y·z)))∪([0	NUM
ejpam-3335	672	7	,	,	PUNCT
ejpam-3335	672	8	1]−hh(y	1]−hh(y	NUM
ejpam-3335	672	9	)	)	PUNCT
ejpam-3335	672	10	)	)	PUNCT
ejpam-3335	673	1	=	=	PUNCT
ejpam-3335	674	1	[	[	X
ejpam-3335	674	2	0	0	NUM
ejpam-3335	674	3	,	,	PUNCT
ejpam-3335	674	4	1]−(hh(x·(y·z))∩hh(y	1]−(hh(x·(y·z))∩hh(y	NUM
ejpam-3335	674	5	)	)	PUNCT
ejpam-3335	674	6	)	)	PUNCT
ejpam-3335	674	7	.	.	PUNCT
ejpam-3335	675	1	thus	thus	ADV
ejpam-3335	675	2	hh(x	hh(x	X
ejpam-3335	675	3	·	·	PUNCT
ejpam-3335	675	4	z	z	X
ejpam-3335	675	5	)	)	PUNCT
ejpam-3335	675	6	⊂	⊂	PROPN
ejpam-3335	675	7	hh(x	hh(x	X
ejpam-3335	675	8	·	·	PUNCT
ejpam-3335	675	9	(	(	PUNCT
ejpam-3335	675	10	y	y	PROPN
ejpam-3335	675	11	·	·	PUNCT
ejpam-3335	675	12	z))∩hh(y	z))∩hh(y	PROPN
ejpam-3335	675	13	)	)	PUNCT
ejpam-3335	675	14	.	.	PUNCT
ejpam-3335	676	1	choose	choose	VERB
ejpam-3335	676	2	ε	ε	PROPN
ejpam-3335	676	3	=	=	SYM
ejpam-3335	676	4	hh(x	hh(x	X
ejpam-3335	676	5	·	·	PUNCT
ejpam-3335	676	6	z	z	X
ejpam-3335	676	7	)	)	PUNCT
ejpam-3335	676	8	∈	∈	PROPN
ejpam-3335	676	9	p([0	p([0	NOUN
ejpam-3335	676	10	,	,	PUNCT
ejpam-3335	676	11	1	1	NUM
ejpam-3335	676	12	]	]	NUM
ejpam-3335	676	13	)	)	PUNCT
ejpam-3335	676	14	.	.	PUNCT
ejpam-3335	677	1	then	then	ADV
ejpam-3335	677	2	hh(x	hh(x	PUNCT
ejpam-3335	677	3	·	·	PUNCT
ejpam-3335	677	4	(	(	PUNCT
ejpam-3335	677	5	y	y	PROPN
ejpam-3335	677	6	·	·	PUNCT
ejpam-3335	677	7	z	z	NOUN
ejpam-3335	677	8	)	)	PUNCT
ejpam-3335	677	9	)	)	PUNCT
ejpam-3335	678	1	⊃	⊃	PROPN
ejpam-3335	678	2	ε	ε	PROPN
ejpam-3335	678	3	and	and	CCONJ
ejpam-3335	678	4	hh(y	hh(y	NOUN
ejpam-3335	678	5	)	)	PUNCT
ejpam-3335	678	6	⊃	⊃	PROPN
ejpam-3335	678	7	ε	ε	PROPN
ejpam-3335	678	8	.	.	PUNCT
ejpam-3335	679	1	thus	thus	ADV
ejpam-3335	679	2	x	x	X
ejpam-3335	679	3	·	·	PUNCT
ejpam-3335	679	4	(	(	PUNCT
ejpam-3335	679	5	y	y	PROPN
ejpam-3335	679	6	·	·	PUNCT
ejpam-3335	679	7	z	z	X
ejpam-3335	679	8	)	)	PUNCT
ejpam-3335	679	9	,	,	PUNCT
ejpam-3335	679	10	y	y	PROPN
ejpam-3335	679	11	∈	∈	PROPN
ejpam-3335	679	12	u+(h	u+(h	NOUN
ejpam-3335	679	13	;	;	PUNCT
ejpam-3335	679	14	ε	ε	PROPN
ejpam-3335	679	15	)	)	PUNCT
ejpam-3335	679	16	6=	6=	ADP
ejpam-3335	679	17	∅.	∅.	ADP
ejpam-3335	679	18	by	by	ADP
ejpam-3335	679	19	assumption	assumption	NOUN
ejpam-3335	679	20	,	,	PUNCT
ejpam-3335	679	21	we	we	PRON
ejpam-3335	679	22	have	have	AUX
ejpam-3335	679	23	u+(h	u+(h	ADV
ejpam-3335	679	24	;	;	PUNCT
ejpam-3335	679	25	ε	ε	PROPN
ejpam-3335	679	26	)	)	PUNCT
ejpam-3335	679	27	is	be	AUX
ejpam-3335	679	28	a	a	DET
ejpam-3335	679	29	up	up	ADJ
ejpam-3335	679	30	-	-	PUNCT
ejpam-3335	679	31	ideal	ideal	NOUN
ejpam-3335	679	32	of	of	ADP
ejpam-3335	679	33	a	a	PRON
ejpam-3335	679	34	and	and	CCONJ
ejpam-3335	679	35	so	so	ADV
ejpam-3335	679	36	x	x	SYM
ejpam-3335	679	37	·	·	PUNCT
ejpam-3335	679	38	z	z	SYM
ejpam-3335	679	39	∈	∈	PROPN
ejpam-3335	679	40	l−(h	l−(h	PROPN
ejpam-3335	679	41	;	;	PUNCT
ejpam-3335	679	42	ε	ε	PROPN
ejpam-3335	679	43	)	)	PUNCT
ejpam-3335	679	44	.	.	PUNCT
ejpam-3335	680	1	thus	thus	ADV
ejpam-3335	680	2	,	,	PUNCT
ejpam-3335	680	3	hh(x	hh(x	PUNCT
ejpam-3335	680	4	·	·	PUNCT
ejpam-3335	680	5	z	z	X
ejpam-3335	680	6	)	)	PUNCT
ejpam-3335	680	7	⊃	⊃	PROPN
ejpam-3335	680	8	ε	ε	X
ejpam-3335	680	9	=	=	SYM
ejpam-3335	680	10	hh(x	hh(x	X
ejpam-3335	680	11	·	·	PUNCT
ejpam-3335	680	12	z	z	X
ejpam-3335	680	13	)	)	PUNCT
ejpam-3335	680	14	,	,	PUNCT
ejpam-3335	680	15	a	a	DET
ejpam-3335	680	16	contradiction	contradiction	NOUN
ejpam-3335	680	17	.	.	PUNCT
ejpam-3335	681	1	therefore	therefore	ADV
ejpam-3335	681	2	,	,	PUNCT
ejpam-3335	681	3	hh(x	hh(x	PUNCT
ejpam-3335	681	4	·	·	PUNCT
ejpam-3335	681	5	z	z	X
ejpam-3335	681	6	)	)	PUNCT
ejpam-3335	681	7	⊆	⊆	NUM
ejpam-3335	681	8	hh(x	hh(x	X
ejpam-3335	681	9	·	·	PUNCT
ejpam-3335	681	10	(	(	PUNCT
ejpam-3335	681	11	y	y	NOUN
ejpam-3335	681	12	·	·	PUNCT
ejpam-3335	681	13	z))∪hh(y	z))∪hh(y	NUM
ejpam-3335	681	14	)	)	PUNCT
ejpam-3335	681	15	for	for	ADP
ejpam-3335	681	16	all	all	DET
ejpam-3335	681	17	x	x	NOUN
ejpam-3335	681	18	,	,	PUNCT
ejpam-3335	681	19	y	y	PROPN
ejpam-3335	681	20	,	,	PUNCT
ejpam-3335	681	21	z	z	PROPN
ejpam-3335	681	22	∈	∈	PROPN
ejpam-3335	681	23	a.	a.	NOUN
ejpam-3335	681	24	hence	hence	ADV
ejpam-3335	681	25	,	,	PUNCT
ejpam-3335	681	26	h	h	PROPN
ejpam-3335	681	27	is	be	AUX
ejpam-3335	681	28	an	an	DET
ejpam-3335	681	29	anti	anti	ADJ
ejpam-3335	681	30	-	-	ADJ
ejpam-3335	681	31	hesitant	hesitant	ADJ
ejpam-3335	681	32	fuzzy	fuzzy	ADJ
ejpam-3335	681	33	up	up	NOUN
ejpam-3335	681	34	-	-	PUNCT
ejpam-3335	681	35	ideal	ideal	NOUN
ejpam-3335	681	36	of	of	ADP
ejpam-3335	681	37	a.	a.	NOUN
ejpam-3335	681	38	example	example	NOUN
ejpam-3335	681	39	14	14	NUM
ejpam-3335	681	40	.	.	PUNCT
ejpam-3335	682	1	let	let	VERB
ejpam-3335	682	2	a	a	PRON
ejpam-3335	682	3	=	=	PUNCT
ejpam-3335	682	4	{	{	PUNCT
ejpam-3335	682	5	0	0	NUM
ejpam-3335	682	6	,	,	PUNCT
ejpam-3335	682	7	1	1	NUM
ejpam-3335	682	8	,	,	PUNCT
ejpam-3335	682	9	2	2	NUM
ejpam-3335	682	10	,	,	PUNCT
ejpam-3335	682	11	3	3	NUM
ejpam-3335	682	12	,	,	PUNCT
ejpam-3335	682	13	4	4	NUM
ejpam-3335	682	14	}	}	PUNCT
ejpam-3335	682	15	be	be	AUX
ejpam-3335	682	16	a	a	DET
ejpam-3335	682	17	set	set	NOUN
ejpam-3335	682	18	with	with	ADP
ejpam-3335	682	19	a	a	DET
ejpam-3335	682	20	binary	binary	ADJ
ejpam-3335	682	21	operation	operation	NOUN
ejpam-3335	682	22	·	·	PUNCT
ejpam-3335	682	23	defined	define	VERB
ejpam-3335	682	24	by	by	ADP
ejpam-3335	682	25	the	the	DET
ejpam-3335	682	26	cayley	cayley	ADJ
ejpam-3335	682	27	table	table	NOUN
ejpam-3335	682	28	from	from	ADP
ejpam-3335	682	29	example	example	NOUN
ejpam-3335	682	30	10	10	NUM
ejpam-3335	682	31	.	.	PUNCT
ejpam-3335	683	1	then	then	ADV
ejpam-3335	683	2	(	(	PUNCT
ejpam-3335	683	3	a	a	PRON
ejpam-3335	683	4	,	,	PUNCT
ejpam-3335	683	5	·	·	PUNCT
ejpam-3335	683	6	,	,	PUNCT
ejpam-3335	683	7	0	0	NUM
ejpam-3335	683	8	)	)	PUNCT
ejpam-3335	683	9	is	be	AUX
ejpam-3335	683	10	a	a	DET
ejpam-3335	683	11	up	up	NOUN
ejpam-3335	683	12	-	-	PUNCT
ejpam-3335	683	13	algebra	algebra	NOUN
ejpam-3335	683	14	.	.	PUNCT
ejpam-3335	684	1	we	we	PRON
ejpam-3335	684	2	define	define	VERB
ejpam-3335	684	3	a	a	DET
ejpam-3335	684	4	hesitant	hesitant	ADJ
ejpam-3335	684	5	fuzzy	fuzzy	ADJ
ejpam-3335	684	6	set	set	VERB
ejpam-3335	684	7	h	h	NOUN
ejpam-3335	684	8	on	on	ADP
ejpam-3335	684	9	a	a	PRON
ejpam-3335	684	10	as	as	SCONJ
ejpam-3335	684	11	follows	follow	VERB
ejpam-3335	684	12	:	:	PUNCT
ejpam-3335	684	13	p.	p.	NOUN
ejpam-3335	684	14	mosrijai	mosrijai	PROPN
ejpam-3335	684	15	,	,	PUNCT
ejpam-3335	684	16	a.	a.	NOUN
ejpam-3335	684	17	iampan	iampan	PROPN
ejpam-3335	684	18	/	/	SYM
ejpam-3335	684	19	eur	eur	PROPN
ejpam-3335	684	20	.	.	PUNCT
ejpam-3335	685	1	j.	j.	PROPN
ejpam-3335	685	2	pure	pure	PROPN
ejpam-3335	685	3	appl	appl	PROPN
ejpam-3335	685	4	.	.	PROPN
ejpam-3335	685	5	math	math	PROPN
ejpam-3335	685	6	,	,	PUNCT
ejpam-3335	685	7	11	11	NUM
ejpam-3335	685	8	(	(	PUNCT
ejpam-3335	685	9	4	4	NUM
ejpam-3335	685	10	)	)	PUNCT
ejpam-3335	685	11	(	(	PUNCT
ejpam-3335	685	12	2018	2018	NUM
ejpam-3335	685	13	)	)	PUNCT
ejpam-3335	685	14	,	,	PUNCT
ejpam-3335	685	15	976	976	NUM
ejpam-3335	685	16	-	-	SYM
ejpam-3335	685	17	1002	1002	NUM
ejpam-3335	685	18	996	996	NUM
ejpam-3335	685	19	hh(0	hh(0	NOUN
ejpam-3335	685	20	)	)	PUNCT
ejpam-3335	685	21	=	=	SYM
ejpam-3335	685	22	{	{	PUNCT
ejpam-3335	685	23	0	0	NUM
ejpam-3335	685	24	,	,	PUNCT
ejpam-3335	685	25	1	1	NUM
ejpam-3335	685	26	}	}	PUNCT
ejpam-3335	685	27	,	,	PUNCT
ejpam-3335	685	28	hh(1	hh(1	PROPN
ejpam-3335	685	29	)	)	PUNCT
ejpam-3335	685	30	=	=	PRON
ejpam-3335	685	31	{	{	PUNCT
ejpam-3335	685	32	1},hh(2	1},hh(2	NUM
ejpam-3335	685	33	)	)	PUNCT
ejpam-3335	685	34	=	=	NOUN
ejpam-3335	685	35	∅	∅	NOUN
ejpam-3335	685	36	,	,	PUNCT
ejpam-3335	685	37	hh(3	hh(3	NOUN
ejpam-3335	685	38	)	)	PUNCT
ejpam-3335	685	39	=	=	SYM
ejpam-3335	685	40	{	{	PUNCT
ejpam-3335	685	41	0	0	NUM
ejpam-3335	685	42	}	}	PUNCT
ejpam-3335	685	43	,	,	PUNCT
ejpam-3335	685	44	and	and	CCONJ
ejpam-3335	685	45	hh(4	hh(4	NOUN
ejpam-3335	685	46	)	)	PUNCT
ejpam-3335	685	47	=	=	PUNCT
ejpam-3335	685	48	∅.	∅.	NOUN
ejpam-3335	685	49	then	then	ADV
ejpam-3335	685	50	im(h	im(h	NOUN
ejpam-3335	685	51	)	)	PUNCT
ejpam-3335	685	52	is	be	AUX
ejpam-3335	685	53	not	not	PART
ejpam-3335	685	54	a	a	DET
ejpam-3335	685	55	chain	chain	NOUN
ejpam-3335	685	56	.	.	PUNCT
ejpam-3335	686	1	if	if	SCONJ
ejpam-3335	686	2	ε	ε	PROPN
ejpam-3335	686	3	=	=	PUNCT
ejpam-3335	686	4	{	{	PUNCT
ejpam-3335	686	5	1	1	NUM
ejpam-3335	686	6	}	}	PUNCT
ejpam-3335	686	7	or	or	CCONJ
ejpam-3335	686	8	ε	ε	PROPN
ejpam-3335	686	9	=	=	PUNCT
ejpam-3335	686	10	{	{	PUNCT
ejpam-3335	686	11	0	0	NUM
ejpam-3335	686	12	}	}	PUNCT
ejpam-3335	686	13	,	,	PUNCT
ejpam-3335	686	14	then	then	ADV
ejpam-3335	686	15	u+(h	u+(h	NUM
ejpam-3335	686	16	;	;	PUNCT
ejpam-3335	686	17	ε	ε	PROPN
ejpam-3335	686	18	)	)	PUNCT
ejpam-3335	686	19	=	=	PUNCT
ejpam-3335	686	20	{	{	PUNCT
ejpam-3335	686	21	0	0	NUM
ejpam-3335	686	22	}	}	PUNCT
ejpam-3335	686	23	.	.	PUNCT
ejpam-3335	687	1	if	if	SCONJ
ejpam-3335	687	2	ε	ε	PROPN
ejpam-3335	687	3	=	=	SYM
ejpam-3335	687	4	∅	∅	NOUN
ejpam-3335	687	5	,	,	PUNCT
ejpam-3335	687	6	then	then	ADV
ejpam-3335	687	7	u+(h	u+(h	NUM
ejpam-3335	687	8	;	;	PUNCT
ejpam-3335	687	9	ε	ε	PROPN
ejpam-3335	687	10	)	)	PUNCT
ejpam-3335	687	11	=	=	SYM
ejpam-3335	687	12	{	{	PUNCT
ejpam-3335	687	13	0	0	NUM
ejpam-3335	687	14	,	,	PUNCT
ejpam-3335	687	15	1	1	NUM
ejpam-3335	687	16	,	,	PUNCT
ejpam-3335	687	17	3	3	NUM
ejpam-3335	687	18	}	}	PUNCT
ejpam-3335	687	19	.	.	PUNCT
ejpam-3335	688	1	otherwise	otherwise	ADV
ejpam-3335	688	2	,	,	PUNCT
ejpam-3335	688	3	u+(h	u+(h	NOUN
ejpam-3335	688	4	;	;	PUNCT
ejpam-3335	688	5	ε	ε	PROPN
ejpam-3335	688	6	)	)	PUNCT
ejpam-3335	688	7	=	=	PUNCT
ejpam-3335	688	8	∅.	∅.	VERB
ejpam-3335	688	9	using	use	VERB
ejpam-3335	688	10	this	this	DET
ejpam-3335	688	11	data	datum	NOUN
ejpam-3335	688	12	,	,	PUNCT
ejpam-3335	688	13	we	we	PRON
ejpam-3335	688	14	can	can	AUX
ejpam-3335	688	15	show	show	VERB
ejpam-3335	688	16	that	that	SCONJ
ejpam-3335	688	17	all	all	DET
ejpam-3335	688	18	nonempty	nonempty	ADV
ejpam-3335	688	19	subset	subset	VERB
ejpam-3335	688	20	u+(h	u+(h	NOUN
ejpam-3335	688	21	;	;	PUNCT
ejpam-3335	688	22	ε	ε	PROPN
ejpam-3335	688	23	)	)	PUNCT
ejpam-3335	688	24	of	of	ADP
ejpam-3335	688	25	a	a	PRON
ejpam-3335	688	26	is	be	AUX
ejpam-3335	688	27	a	a	DET
ejpam-3335	688	28	up	up	ADJ
ejpam-3335	688	29	-	-	PUNCT
ejpam-3335	688	30	ideal	ideal	NOUN
ejpam-3335	688	31	of	of	ADP
ejpam-3335	688	32	a.	a.	NOUN
ejpam-3335	688	33	by	by	ADP
ejpam-3335	688	34	definition	definition	NOUN
ejpam-3335	688	35	4	4	NUM
ejpam-3335	688	36	,	,	PUNCT
ejpam-3335	688	37	we	we	PRON
ejpam-3335	688	38	have	have	VERB
ejpam-3335	688	39	hh(0	hh(0	NOUN
ejpam-3335	688	40	)	)	PUNCT
ejpam-3335	688	41	=	=	SYM
ejpam-3335	688	42	(	(	PUNCT
ejpam-3335	688	43	0	0	NUM
ejpam-3335	688	44	,	,	PUNCT
ejpam-3335	688	45	1),hh(1	1),hh(1	NUM
ejpam-3335	688	46	)	)	PUNCT
ejpam-3335	688	47	=	=	PUNCT
ejpam-3335	689	1	[	[	X
ejpam-3335	689	2	0	0	NUM
ejpam-3335	689	3	,	,	PUNCT
ejpam-3335	689	4	1	1	NUM
ejpam-3335	689	5	)	)	PUNCT
ejpam-3335	689	6	,	,	PUNCT
ejpam-3335	689	7	hh(2	hh(2	NOUN
ejpam-3335	689	8	)	)	PUNCT
ejpam-3335	689	9	=	=	PUNCT
ejpam-3335	690	1	[	[	X
ejpam-3335	690	2	0	0	NUM
ejpam-3335	690	3	,	,	PUNCT
ejpam-3335	690	4	1	1	NUM
ejpam-3335	690	5	]	]	PUNCT
ejpam-3335	690	6	,	,	PUNCT
ejpam-3335	690	7	hh(3	hh(3	NOUN
ejpam-3335	690	8	)	)	PUNCT
ejpam-3335	690	9	=	=	SYM
ejpam-3335	690	10	(	(	PUNCT
ejpam-3335	690	11	0	0	NUM
ejpam-3335	690	12	,	,	PUNCT
ejpam-3335	690	13	1	1	NUM
ejpam-3335	690	14	]	]	PUNCT
ejpam-3335	690	15	,	,	PUNCT
ejpam-3335	690	16	and	and	CCONJ
ejpam-3335	690	17	hh(4	hh(4	NOUN
ejpam-3335	690	18	)	)	PUNCT
ejpam-3335	690	19	=	=	PUNCT
ejpam-3335	691	1	[	[	X
ejpam-3335	691	2	0	0	NUM
ejpam-3335	691	3	,	,	PUNCT
ejpam-3335	691	4	1	1	NUM
ejpam-3335	691	5	]	]	PUNCT
ejpam-3335	691	6	.	.	PUNCT
ejpam-3335	692	1	since	since	SCONJ
ejpam-3335	692	2	hh(0	hh(0	NOUN
ejpam-3335	692	3	·	·	PUNCT
ejpam-3335	692	4	1	1	X
ejpam-3335	692	5	)	)	PUNCT
ejpam-3335	692	6	=	=	PUNCT
ejpam-3335	692	7	hh(1	hh(1	NOUN
ejpam-3335	692	8	)	)	PUNCT
ejpam-3335	692	9	=	=	PUNCT
ejpam-3335	693	1	[	[	X
ejpam-3335	693	2	0	0	NUM
ejpam-3335	693	3	,	,	PUNCT
ejpam-3335	693	4	1	1	NUM
ejpam-3335	693	5	)	)	PUNCT
ejpam-3335	693	6	*	*	PUNCT
ejpam-3335	693	7	(	(	PUNCT
ejpam-3335	693	8	0	0	NUM
ejpam-3335	693	9	,	,	PUNCT
ejpam-3335	693	10	1	1	NUM
ejpam-3335	693	11	]	]	PUNCT
ejpam-3335	693	12	=	=	PUNCT
ejpam-3335	693	13	hh(0	hh(0	NOUN
ejpam-3335	693	14	)	)	PUNCT
ejpam-3335	693	15	∪	∪	X
ejpam-3335	693	16	hh(3	hh(3	NOUN
ejpam-3335	693	17	)	)	PUNCT
ejpam-3335	693	18	=	=	SYM
ejpam-3335	693	19	hh(0	hh(0	NOUN
ejpam-3335	693	20	·	·	PUNCT
ejpam-3335	693	21	(	(	PUNCT
ejpam-3335	693	22	3	3	NUM
ejpam-3335	693	23	·	·	SYM
ejpam-3335	693	24	1	1	NUM
ejpam-3335	693	25	)	)	PUNCT
ejpam-3335	693	26	)	)	PUNCT
ejpam-3335	693	27	∪	∪	ADP
ejpam-3335	693	28	hh(3	hh(3	NOUN
ejpam-3335	693	29	)	)	PUNCT
ejpam-3335	693	30	,	,	PUNCT
ejpam-3335	693	31	we	we	PRON
ejpam-3335	693	32	have	have	VERB
ejpam-3335	693	33	h	h	NOUN
ejpam-3335	693	34	is	be	AUX
ejpam-3335	693	35	not	not	PART
ejpam-3335	693	36	an	an	DET
ejpam-3335	693	37	anti	anti	ADJ
ejpam-3335	693	38	-	-	ADJ
ejpam-3335	693	39	hesitant	hesitant	ADJ
ejpam-3335	693	40	fuzzy	fuzzy	ADJ
ejpam-3335	693	41	up	up	NOUN
ejpam-3335	693	42	-	-	PUNCT
ejpam-3335	693	43	ideal	ideal	NOUN
ejpam-3335	693	44	of	of	ADP
ejpam-3335	693	45	a.	a.	NOUN
ejpam-3335	693	46	theorem	theorem	NOUN
ejpam-3335	693	47	22	22	NUM
ejpam-3335	693	48	.	.	PUNCT
ejpam-3335	694	1	let	let	VERB
ejpam-3335	694	2	h	h	PRON
ejpam-3335	694	3	be	be	AUX
ejpam-3335	694	4	a	a	DET
ejpam-3335	694	5	hesitant	hesitant	ADJ
ejpam-3335	694	6	fuzzy	fuzzy	ADJ
ejpam-3335	694	7	set	set	NOUN
ejpam-3335	694	8	on	on	ADP
ejpam-3335	694	9	a.	a.	NOUN
ejpam-3335	694	10	then	then	ADV
ejpam-3335	694	11	the	the	DET
ejpam-3335	694	12	following	follow	VERB
ejpam-3335	694	13	statements	statement	NOUN
ejpam-3335	694	14	hold	hold	VERB
ejpam-3335	694	15	:	:	PUNCT
ejpam-3335	694	16	(	(	PUNCT
ejpam-3335	694	17	1	1	X
ejpam-3335	694	18	)	)	PUNCT
ejpam-3335	694	19	if	if	SCONJ
ejpam-3335	694	20	h	h	NOUN
ejpam-3335	694	21	is	be	AUX
ejpam-3335	694	22	an	an	DET
ejpam-3335	694	23	anti	anti	ADJ
ejpam-3335	694	24	-	-	ADJ
ejpam-3335	694	25	hesitant	hesitant	ADJ
ejpam-3335	694	26	fuzzy	fuzzy	ADJ
ejpam-3335	694	27	strongly	strongly	ADV
ejpam-3335	694	28	up	up	ADP
ejpam-3335	694	29	-	-	PUNCT
ejpam-3335	694	30	ideal	ideal	NOUN
ejpam-3335	694	31	of	of	ADP
ejpam-3335	694	32	a	a	PRON
ejpam-3335	694	33	,	,	PUNCT
ejpam-3335	694	34	then	then	ADV
ejpam-3335	694	35	for	for	SCONJ
ejpam-3335	694	36	all	all	DET
ejpam-3335	694	37	ε	ε	PROPN
ejpam-3335	694	38	∈	∈	PROPN
ejpam-3335	694	39	p([0	p([0	NOUN
ejpam-3335	694	40	,	,	PUNCT
ejpam-3335	694	41	1	1	NUM
ejpam-3335	694	42	]	]	NUM
ejpam-3335	694	43	)	)	PUNCT
ejpam-3335	694	44	,	,	PUNCT
ejpam-3335	694	45	u+(h	u+(h	PROPN
ejpam-3335	694	46	;	;	PUNCT
ejpam-3335	694	47	ε	ε	PROPN
ejpam-3335	694	48	)	)	PUNCT
ejpam-3335	694	49	is	be	AUX
ejpam-3335	694	50	a	a	DET
ejpam-3335	694	51	strongly	strongly	ADV
ejpam-3335	694	52	up	up	ADJ
ejpam-3335	694	53	-	-	PUNCT
ejpam-3335	694	54	ideal	ideal	NOUN
ejpam-3335	694	55	of	of	ADP
ejpam-3335	694	56	a	a	DET
ejpam-3335	694	57	if	if	NOUN
ejpam-3335	694	58	u+(h	u+(h	PROPN
ejpam-3335	694	59	;	;	PUNCT
ejpam-3335	694	60	ε	ε	PROPN
ejpam-3335	694	61	)	)	PUNCT
ejpam-3335	694	62	is	be	AUX
ejpam-3335	694	63	nonempty	nonempty	ADJ
ejpam-3335	694	64	,	,	PUNCT
ejpam-3335	694	65	and	and	CCONJ
ejpam-3335	694	66	(	(	PUNCT
ejpam-3335	694	67	2	2	X
ejpam-3335	694	68	)	)	PUNCT
ejpam-3335	694	69	if	if	SCONJ
ejpam-3335	694	70	im(h	im(h	NOUN
ejpam-3335	694	71	)	)	PUNCT
ejpam-3335	694	72	is	be	AUX
ejpam-3335	694	73	a	a	DET
ejpam-3335	694	74	chain	chain	NOUN
ejpam-3335	694	75	and	and	CCONJ
ejpam-3335	694	76	for	for	ADP
ejpam-3335	694	77	all	all	DET
ejpam-3335	694	78	ε	ε	PROPN
ejpam-3335	694	79	∈	∈	PROPN
ejpam-3335	694	80	p([0	p([0	NOUN
ejpam-3335	694	81	,	,	PUNCT
ejpam-3335	694	82	1	1	NUM
ejpam-3335	694	83	]	]	NUM
ejpam-3335	694	84	)	)	PUNCT
ejpam-3335	694	85	,	,	PUNCT
ejpam-3335	694	86	a	a	DET
ejpam-3335	694	87	nonempty	nonempty	NOUN
ejpam-3335	694	88	subset	subset	VERB
ejpam-3335	694	89	u+(h	u+(h	NOUN
ejpam-3335	694	90	;	;	PUNCT
ejpam-3335	694	91	ε	ε	PROPN
ejpam-3335	694	92	)	)	PUNCT
ejpam-3335	694	93	of	of	ADP
ejpam-3335	694	94	a	a	PRON
ejpam-3335	694	95	is	be	AUX
ejpam-3335	694	96	a	a	DET
ejpam-3335	694	97	strongly	strongly	ADV
ejpam-3335	694	98	up	up	ADJ
ejpam-3335	694	99	-	-	PUNCT
ejpam-3335	694	100	ideal	ideal	NOUN
ejpam-3335	694	101	of	of	ADP
ejpam-3335	694	102	a	a	PRON
ejpam-3335	694	103	,	,	PUNCT
ejpam-3335	694	104	then	then	ADV
ejpam-3335	694	105	h	h	PROPN
ejpam-3335	694	106	is	be	AUX
ejpam-3335	694	107	an	an	DET
ejpam-3335	694	108	anti	anti	ADJ
ejpam-3335	694	109	-	-	ADJ
ejpam-3335	694	110	hesitant	hesitant	ADJ
ejpam-3335	694	111	fuzzy	fuzzy	ADJ
ejpam-3335	694	112	strongly	strongly	ADV
ejpam-3335	694	113	up	up	ADP
ejpam-3335	694	114	-	-	PUNCT
ejpam-3335	694	115	ideal	ideal	NOUN
ejpam-3335	694	116	of	of	ADP
ejpam-3335	694	117	a.	a.	NOUN
ejpam-3335	694	118	proof	proof	NOUN
ejpam-3335	694	119	.	.	PUNCT
ejpam-3335	695	1	(	(	PUNCT
ejpam-3335	695	2	1	1	X
ejpam-3335	695	3	)	)	PUNCT
ejpam-3335	695	4	assume	assume	VERB
ejpam-3335	695	5	that	that	SCONJ
ejpam-3335	695	6	h	h	NOUN
ejpam-3335	695	7	is	be	AUX
ejpam-3335	695	8	an	an	DET
ejpam-3335	695	9	anti	anti	ADJ
ejpam-3335	695	10	-	-	ADJ
ejpam-3335	695	11	hesitant	hesitant	ADJ
ejpam-3335	695	12	fuzzy	fuzzy	ADJ
ejpam-3335	695	13	strongly	strongly	ADV
ejpam-3335	695	14	up	up	ADP
ejpam-3335	695	15	-	-	PUNCT
ejpam-3335	695	16	ideal	ideal	NOUN
ejpam-3335	695	17	of	of	ADP
ejpam-3335	695	18	a.	a.	NOUN
ejpam-3335	695	19	by	by	ADP
ejpam-3335	695	20	theorem	theorem	NOUN
ejpam-3335	695	21	3	3	NUM
ejpam-3335	695	22	,	,	PUNCT
ejpam-3335	695	23	we	we	PRON
ejpam-3335	695	24	obtain	obtain	VERB
ejpam-3335	695	25	h	h	NOUN
ejpam-3335	695	26	is	be	AUX
ejpam-3335	695	27	a	a	DET
ejpam-3335	695	28	constant	constant	ADJ
ejpam-3335	695	29	hesitant	hesitant	ADJ
ejpam-3335	695	30	fuzzy	fuzzy	ADJ
ejpam-3335	695	31	set	set	VERB
ejpam-3335	695	32	on	on	ADP
ejpam-3335	695	33	a.	a.	NOUN
ejpam-3335	695	34	by	by	ADP
ejpam-3335	695	35	corollary	corollary	ADJ
ejpam-3335	695	36	2	2	NUM
ejpam-3335	695	37	,	,	PUNCT
ejpam-3335	695	38	we	we	PRON
ejpam-3335	695	39	have	have	VERB
ejpam-3335	695	40	h	h	NOUN
ejpam-3335	695	41	is	be	AUX
ejpam-3335	695	42	a	a	DET
ejpam-3335	695	43	constant	constant	ADJ
ejpam-3335	695	44	hesitant	hesitant	ADJ
ejpam-3335	695	45	fuzzy	fuzzy	ADJ
ejpam-3335	695	46	set	set	VERB
ejpam-3335	695	47	on	on	ADP
ejpam-3335	695	48	a	a	DET
ejpam-3335	695	49	and	and	CCONJ
ejpam-3335	695	50	so	so	ADV
ejpam-3335	695	51	hh(x	hh(x	PUNCT
ejpam-3335	695	52	)	)	PUNCT
ejpam-3335	695	53	=	=	SYM
ejpam-3335	696	1	hh(y	hh(y	X
ejpam-3335	696	2	)	)	PUNCT
ejpam-3335	696	3	for	for	ADP
ejpam-3335	696	4	all	all	DET
ejpam-3335	696	5	x	x	NOUN
ejpam-3335	696	6	,	,	PUNCT
ejpam-3335	696	7	y	y	PROPN
ejpam-3335	696	8	∈	∈	PROPN
ejpam-3335	696	9	a.	a.	NOUN
ejpam-3335	696	10	let	let	VERB
ejpam-3335	696	11	ε	ε	PROPN
ejpam-3335	696	12	∈	∈	PROPN
ejpam-3335	696	13	p([0	p([0	PROPN
ejpam-3335	696	14	,	,	PUNCT
ejpam-3335	696	15	1	1	NUM
ejpam-3335	696	16	]	]	PUNCT
ejpam-3335	696	17	)	)	PUNCT
ejpam-3335	696	18	be	be	AUX
ejpam-3335	696	19	such	such	ADJ
ejpam-3335	696	20	that	that	SCONJ
ejpam-3335	696	21	u+(h	u+(h	PROPN
ejpam-3335	696	22	;	;	PUNCT
ejpam-3335	696	23	ε	ε	PROPN
ejpam-3335	696	24	)	)	PUNCT
ejpam-3335	696	25	6=	6=	ADP
ejpam-3335	696	26	∅.	∅.	VERB
ejpam-3335	696	27	there	there	ADV
ejpam-3335	696	28	exists	exist	VERB
ejpam-3335	696	29	a	a	DET
ejpam-3335	696	30	∈	∈	NOUN
ejpam-3335	696	31	u+(h	u+(h	NOUN
ejpam-3335	696	32	;	;	PUNCT
ejpam-3335	696	33	ε	ε	AUX
ejpam-3335	696	34	)	)	PUNCT
ejpam-3335	696	35	be	be	VERB
ejpam-3335	696	36	such	such	ADJ
ejpam-3335	696	37	that	that	DET
ejpam-3335	696	38	hh(a	hh(a	NOUN
ejpam-3335	696	39	)	)	PUNCT
ejpam-3335	696	40	⊃	⊃	PROPN
ejpam-3335	696	41	ε	ε	AUX
ejpam-3335	696	42	.	.	PUNCT
ejpam-3335	696	43	thus	thus	ADV
ejpam-3335	696	44	hh(x	hh(x	X
ejpam-3335	696	45	)	)	PUNCT
ejpam-3335	696	46	=	=	SYM
ejpam-3335	696	47	hh(a	hh(a	NUM
ejpam-3335	696	48	)	)	PUNCT
ejpam-3335	696	49	⊃	⊃	PROPN
ejpam-3335	696	50	ε	ε	VERB
ejpam-3335	696	51	for	for	ADP
ejpam-3335	696	52	all	all	DET
ejpam-3335	696	53	x	x	SYM
ejpam-3335	696	54	∈	∈	PROPN
ejpam-3335	696	55	a	a	PRON
ejpam-3335	697	1	and	and	CCONJ
ejpam-3335	697	2	so	so	ADV
ejpam-3335	697	3	x	x	SYM
ejpam-3335	697	4	∈	∈	PROPN
ejpam-3335	697	5	u+(h	u+(h	NOUN
ejpam-3335	697	6	;	;	PUNCT
ejpam-3335	697	7	ε	ε	PROPN
ejpam-3335	697	8	)	)	PUNCT
ejpam-3335	697	9	for	for	ADP
ejpam-3335	697	10	all	all	DET
ejpam-3335	697	11	x	x	SYM
ejpam-3335	697	12	∈	∈	PROPN
ejpam-3335	697	13	a.	a.	NOUN
ejpam-3335	697	14	therefore	therefore	ADV
ejpam-3335	697	15	,	,	PUNCT
ejpam-3335	697	16	u+(h	u+(h	NOUN
ejpam-3335	697	17	;	;	PUNCT
ejpam-3335	697	18	ε	ε	PROPN
ejpam-3335	697	19	)	)	PUNCT
ejpam-3335	697	20	=	=	NOUN
ejpam-3335	697	21	a.	a.	NOUN
ejpam-3335	697	22	hence	hence	ADV
ejpam-3335	697	23	,	,	PUNCT
ejpam-3335	697	24	u+(h	u+(h	NOUN
ejpam-3335	697	25	;	;	PUNCT
ejpam-3335	697	26	ε	ε	PROPN
ejpam-3335	697	27	)	)	PUNCT
ejpam-3335	697	28	is	be	AUX
ejpam-3335	697	29	a	a	DET
ejpam-3335	697	30	strongly	strongly	ADV
ejpam-3335	697	31	up	up	ADJ
ejpam-3335	697	32	-	-	PUNCT
ejpam-3335	697	33	ideal	ideal	NOUN
ejpam-3335	697	34	of	of	ADP
ejpam-3335	697	35	a.	a.	NOUN
ejpam-3335	697	36	(	(	PUNCT
ejpam-3335	697	37	2	2	X
ejpam-3335	697	38	)	)	PUNCT
ejpam-3335	697	39	assume	assume	VERB
ejpam-3335	697	40	that	that	SCONJ
ejpam-3335	697	41	im(h	im(h	NOUN
ejpam-3335	697	42	)	)	PUNCT
ejpam-3335	697	43	is	be	AUX
ejpam-3335	697	44	a	a	DET
ejpam-3335	697	45	chain	chain	NOUN
ejpam-3335	697	46	and	and	CCONJ
ejpam-3335	697	47	for	for	ADP
ejpam-3335	697	48	all	all	DET
ejpam-3335	697	49	ε	ε	PROPN
ejpam-3335	697	50	∈	∈	PROPN
ejpam-3335	697	51	p([0	p([0	NOUN
ejpam-3335	697	52	,	,	PUNCT
ejpam-3335	697	53	1	1	NUM
ejpam-3335	697	54	]	]	NUM
ejpam-3335	697	55	)	)	PUNCT
ejpam-3335	697	56	,	,	PUNCT
ejpam-3335	697	57	a	a	DET
ejpam-3335	697	58	nonempty	nonempty	NOUN
ejpam-3335	697	59	subset	subset	VERB
ejpam-3335	697	60	u+(h	u+(h	NOUN
ejpam-3335	697	61	;	;	PUNCT
ejpam-3335	697	62	ε	ε	PROPN
ejpam-3335	697	63	)	)	PUNCT
ejpam-3335	697	64	of	of	ADP
ejpam-3335	697	65	a	a	PRON
ejpam-3335	697	66	is	be	AUX
ejpam-3335	697	67	a	a	DET
ejpam-3335	697	68	strongly	strongly	ADV
ejpam-3335	697	69	up	up	ADJ
ejpam-3335	697	70	-	-	PUNCT
ejpam-3335	697	71	ideal	ideal	NOUN
ejpam-3335	697	72	of	of	ADP
ejpam-3335	697	73	a.	a.	NOUN
ejpam-3335	697	74	assume	assume	VERB
ejpam-3335	697	75	that	that	SCONJ
ejpam-3335	697	76	h	h	NOUN
ejpam-3335	697	77	is	be	AUX
ejpam-3335	697	78	not	not	PART
ejpam-3335	697	79	a	a	DET
ejpam-3335	697	80	constant	constant	ADJ
ejpam-3335	697	81	hesitant	hesitant	ADJ
ejpam-3335	697	82	fuzzy	fuzzy	ADJ
ejpam-3335	697	83	set	set	VERB
ejpam-3335	697	84	on	on	ADP
ejpam-3335	697	85	a.	a.	NOUN
ejpam-3335	697	86	by	by	ADP
ejpam-3335	697	87	corollary	corollary	ADJ
ejpam-3335	697	88	2	2	NUM
ejpam-3335	697	89	,	,	PUNCT
ejpam-3335	697	90	we	we	PRON
ejpam-3335	697	91	have	have	VERB
ejpam-3335	697	92	h	h	NOUN
ejpam-3335	697	93	is	be	AUX
ejpam-3335	697	94	not	not	PART
ejpam-3335	697	95	a	a	DET
ejpam-3335	697	96	constant	constant	ADJ
ejpam-3335	697	97	hesitant	hesitant	ADJ
ejpam-3335	697	98	fuzzy	fuzzy	ADJ
ejpam-3335	697	99	set	set	VERB
ejpam-3335	697	100	on	on	ADP
ejpam-3335	697	101	a.	a.	NOUN
ejpam-3335	697	102	there	there	ADV
ejpam-3335	697	103	exist	exist	VERB
ejpam-3335	697	104	x	x	NOUN
ejpam-3335	697	105	,	,	PUNCT
ejpam-3335	697	106	y	y	PROPN
ejpam-3335	697	107	∈	∈	PROPN
ejpam-3335	697	108	a	a	PRON
ejpam-3335	697	109	be	be	AUX
ejpam-3335	697	110	such	such	ADJ
ejpam-3335	697	111	that	that	PRON
ejpam-3335	697	112	hh(x	hh(x	PRON
ejpam-3335	697	113	)	)	PUNCT
ejpam-3335	697	114	6=	6=	ADP
ejpam-3335	697	115	hh(y	hh(y	NOUN
ejpam-3335	697	116	)	)	PUNCT
ejpam-3335	697	117	.	.	PUNCT
ejpam-3335	698	1	since	since	SCONJ
ejpam-3335	698	2	im(h	im(h	NOUN
ejpam-3335	698	3	)	)	PUNCT
ejpam-3335	698	4	is	be	AUX
ejpam-3335	698	5	a	a	DET
ejpam-3335	698	6	chain	chain	NOUN
ejpam-3335	698	7	,	,	PUNCT
ejpam-3335	698	8	we	we	PRON
ejpam-3335	698	9	have	have	VERB
ejpam-3335	698	10	hh(x	hh(x	NOUN
ejpam-3335	698	11	)	)	PUNCT
ejpam-3335	698	12	⊂	⊂	PROPN
ejpam-3335	698	13	hh(y	hh(y	NOUN
ejpam-3335	698	14	)	)	PUNCT
ejpam-3335	698	15	or	or	CCONJ
ejpam-3335	698	16	hh(x	hh(x	NOUN
ejpam-3335	698	17	)	)	PUNCT
ejpam-3335	698	18	⊃	⊃	PROPN
ejpam-3335	698	19	hh(y	hh(y	X
ejpam-3335	698	20	)	)	PUNCT
ejpam-3335	698	21	.	.	PUNCT
ejpam-3335	699	1	without	without	ADP
ejpam-3335	699	2	loss	loss	NOUN
ejpam-3335	699	3	of	of	ADP
ejpam-3335	699	4	generality	generality	NOUN
ejpam-3335	699	5	,	,	PUNCT
ejpam-3335	699	6	assume	assume	VERB
ejpam-3335	699	7	that	that	SCONJ
ejpam-3335	699	8	hh(x	hh(x	PUNCT
ejpam-3335	699	9	)	)	PUNCT
ejpam-3335	699	10	⊂	⊂	PROPN
ejpam-3335	699	11	hh(y	hh(y	NOUN
ejpam-3335	699	12	)	)	PUNCT
ejpam-3335	699	13	,	,	PUNCT
ejpam-3335	699	14	then	then	ADV
ejpam-3335	699	15	y	y	PROPN
ejpam-3335	699	16	∈	∈	PROPN
ejpam-3335	699	17	u+(h	u+(h	NOUN
ejpam-3335	699	18	;	;	PUNCT
ejpam-3335	699	19	hh(x	hh(x	X
ejpam-3335	699	20	)	)	PUNCT
ejpam-3335	699	21	)	)	PUNCT
ejpam-3335	699	22	6=	6=	ADP
ejpam-3335	699	23	∅.	∅.	ADP
ejpam-3335	699	24	by	by	ADP
ejpam-3335	699	25	assumption	assumption	NOUN
ejpam-3335	699	26	,	,	PUNCT
ejpam-3335	699	27	we	we	PRON
ejpam-3335	699	28	have	have	VERB
ejpam-3335	699	29	u+(h	u+(h	NUM
ejpam-3335	699	30	;	;	PUNCT
ejpam-3335	699	31	hh(x	hh(x	X
ejpam-3335	699	32	)	)	PUNCT
ejpam-3335	699	33	)	)	PUNCT
ejpam-3335	700	1	is	be	AUX
ejpam-3335	700	2	a	a	DET
ejpam-3335	700	3	strongly	strongly	ADV
ejpam-3335	700	4	up	up	ADJ
ejpam-3335	700	5	-	-	PUNCT
ejpam-3335	700	6	ideal	ideal	NOUN
ejpam-3335	700	7	of	of	ADP
ejpam-3335	700	8	a	a	PRON
ejpam-3335	700	9	and	and	CCONJ
ejpam-3335	700	10	so	so	ADV
ejpam-3335	700	11	u+(h	u+(h	ADV
ejpam-3335	700	12	;	;	PUNCT
ejpam-3335	700	13	hh(x	hh(x	X
ejpam-3335	700	14	)	)	PUNCT
ejpam-3335	700	15	)	)	PUNCT
ejpam-3335	701	1	=	=	PUNCT
ejpam-3335	702	1	a.	a.	NOUN
ejpam-3335	702	2	thus	thus	ADV
ejpam-3335	702	3	x	x	X
ejpam-3335	702	4	∈	∈	PROPN
ejpam-3335	702	5	a	a	X
ejpam-3335	702	6	=	=	SYM
ejpam-3335	702	7	u+(h	u+(h	NOUN
ejpam-3335	702	8	;	;	PUNCT
ejpam-3335	702	9	hh(x	hh(x	X
ejpam-3335	702	10	)	)	PUNCT
ejpam-3335	702	11	)	)	PUNCT
ejpam-3335	702	12	and	and	CCONJ
ejpam-3335	702	13	so	so	ADV
ejpam-3335	702	14	hh(x	hh(x	PUNCT
ejpam-3335	702	15	)	)	PUNCT
ejpam-3335	702	16	⊂	⊂	PROPN
ejpam-3335	702	17	hh(x	hh(x	PROPN
ejpam-3335	702	18	)	)	PUNCT
ejpam-3335	702	19	,	,	PUNCT
ejpam-3335	702	20	a	a	DET
ejpam-3335	702	21	contradiction	contradiction	NOUN
ejpam-3335	702	22	.	.	PUNCT
ejpam-3335	703	1	therefore	therefore	ADV
ejpam-3335	703	2	,	,	PUNCT
ejpam-3335	703	3	h	h	NOUN
ejpam-3335	703	4	is	be	AUX
ejpam-3335	703	5	a	a	DET
ejpam-3335	703	6	constant	constant	ADJ
ejpam-3335	703	7	hesitant	hesitant	ADJ
ejpam-3335	703	8	fuzzy	fuzzy	ADJ
ejpam-3335	703	9	set	set	VERB
ejpam-3335	703	10	on	on	ADP
ejpam-3335	703	11	a.	a.	NOUN
ejpam-3335	703	12	by	by	ADP
ejpam-3335	703	13	theorem	theorem	NOUN
ejpam-3335	703	14	3	3	NUM
ejpam-3335	703	15	,	,	PUNCT
ejpam-3335	703	16	we	we	PRON
ejpam-3335	703	17	obtain	obtain	VERB
ejpam-3335	703	18	h	h	NOUN
ejpam-3335	703	19	is	be	AUX
ejpam-3335	703	20	an	an	DET
ejpam-3335	703	21	anti	anti	ADJ
ejpam-3335	703	22	-	-	ADJ
ejpam-3335	703	23	hesitant	hesitant	ADJ
ejpam-3335	703	24	fuzzy	fuzzy	ADJ
ejpam-3335	703	25	strongly	strongly	ADV
ejpam-3335	703	26	up	up	ADP
ejpam-3335	703	27	-	-	PUNCT
ejpam-3335	703	28	ideal	ideal	NOUN
ejpam-3335	703	29	of	of	ADP
ejpam-3335	703	30	a.	a.	NOUN
ejpam-3335	703	31	example	example	NOUN
ejpam-3335	703	32	15	15	NUM
ejpam-3335	703	33	.	.	PUNCT
ejpam-3335	704	1	let	let	VERB
ejpam-3335	704	2	a	a	PRON
ejpam-3335	704	3	=	=	PUNCT
ejpam-3335	704	4	{	{	PUNCT
ejpam-3335	704	5	0	0	NUM
ejpam-3335	704	6	,	,	PUNCT
ejpam-3335	704	7	1	1	NUM
ejpam-3335	704	8	}	}	PUNCT
ejpam-3335	704	9	be	be	AUX
ejpam-3335	704	10	a	a	DET
ejpam-3335	704	11	set	set	NOUN
ejpam-3335	704	12	with	with	ADP
ejpam-3335	704	13	a	a	DET
ejpam-3335	704	14	binary	binary	ADJ
ejpam-3335	704	15	operation	operation	NOUN
ejpam-3335	704	16	·	·	PUNCT
ejpam-3335	704	17	defined	define	VERB
ejpam-3335	704	18	by	by	ADP
ejpam-3335	704	19	the	the	DET
ejpam-3335	704	20	cayley	cayley	ADJ
ejpam-3335	704	21	table	table	NOUN
ejpam-3335	704	22	from	from	ADP
ejpam-3335	704	23	example	example	NOUN
ejpam-3335	704	24	11	11	NUM
ejpam-3335	704	25	.	.	PUNCT
ejpam-3335	705	1	then	then	ADV
ejpam-3335	705	2	(	(	PUNCT
ejpam-3335	705	3	a	a	PRON
ejpam-3335	705	4	,	,	PUNCT
ejpam-3335	705	5	·	·	PUNCT
ejpam-3335	705	6	,	,	PUNCT
ejpam-3335	705	7	0	0	NUM
ejpam-3335	705	8	)	)	PUNCT
ejpam-3335	705	9	is	be	AUX
ejpam-3335	705	10	a	a	DET
ejpam-3335	705	11	up	up	NOUN
ejpam-3335	705	12	-	-	PUNCT
ejpam-3335	705	13	algebra	algebra	NOUN
ejpam-3335	705	14	.	.	PUNCT
ejpam-3335	706	1	we	we	PRON
ejpam-3335	706	2	define	define	VERB
ejpam-3335	706	3	a	a	DET
ejpam-3335	706	4	hesitant	hesitant	ADJ
ejpam-3335	706	5	fuzzy	fuzzy	ADJ
ejpam-3335	706	6	set	set	VERB
ejpam-3335	706	7	h	h	NOUN
ejpam-3335	706	8	on	on	ADP
ejpam-3335	706	9	a	a	DET
ejpam-3335	706	10	as	as	SCONJ
ejpam-3335	706	11	follows	follow	VERB
ejpam-3335	706	12	:	:	PUNCT
ejpam-3335	706	13	hh(0	hh(0	NOUN
ejpam-3335	706	14	)	)	PUNCT
ejpam-3335	706	15	=	=	SYM
ejpam-3335	706	16	{	{	PUNCT
ejpam-3335	706	17	0	0	NUM
ejpam-3335	706	18	}	}	PUNCT
ejpam-3335	706	19	,	,	PUNCT
ejpam-3335	706	20	and	and	CCONJ
ejpam-3335	706	21	hh(1	hh(1	NOUN
ejpam-3335	706	22	)	)	PUNCT
ejpam-3335	706	23	=	=	PUNCT
ejpam-3335	706	24	{	{	PUNCT
ejpam-3335	706	25	1	1	NUM
ejpam-3335	706	26	}	}	PUNCT
ejpam-3335	706	27	.	.	PUNCT
ejpam-3335	707	1	then	then	ADV
ejpam-3335	707	2	im(h	im(h	NOUN
ejpam-3335	707	3	)	)	PUNCT
ejpam-3335	707	4	is	be	AUX
ejpam-3335	707	5	not	not	PART
ejpam-3335	707	6	a	a	DET
ejpam-3335	707	7	chain	chain	NOUN
ejpam-3335	707	8	.	.	PUNCT
ejpam-3335	708	1	if	if	SCONJ
ejpam-3335	708	2	ε	ε	PROPN
ejpam-3335	708	3	=	=	SYM
ejpam-3335	708	4	∅	∅	NOUN
ejpam-3335	708	5	,	,	PUNCT
ejpam-3335	708	6	then	then	ADV
ejpam-3335	708	7	u+(h	u+(h	NUM
ejpam-3335	708	8	;	;	PUNCT
ejpam-3335	708	9	ε	ε	PROPN
ejpam-3335	708	10	)	)	PUNCT
ejpam-3335	708	11	=	=	SYM
ejpam-3335	708	12	a.	a.	NOUN
ejpam-3335	708	13	otherwise	otherwise	ADV
ejpam-3335	708	14	,	,	PUNCT
ejpam-3335	708	15	u+(h	u+(h	NOUN
ejpam-3335	708	16	;	;	PUNCT
ejpam-3335	708	17	ε	ε	PROPN
ejpam-3335	708	18	)	)	PUNCT
ejpam-3335	708	19	=	=	VERB
ejpam-3335	708	20	∅.	∅.	VERB
ejpam-3335	708	21	thus	thus	ADV
ejpam-3335	708	22	a	a	DET
ejpam-3335	708	23	nonempty	nonempty	NOUN
ejpam-3335	708	24	subset	subset	VERB
ejpam-3335	708	25	u+(h	u+(h	NOUN
ejpam-3335	708	26	;	;	PUNCT
ejpam-3335	708	27	ε	ε	PROPN
ejpam-3335	708	28	)	)	PUNCT
ejpam-3335	708	29	of	of	ADP
ejpam-3335	708	30	a	a	PRON
ejpam-3335	708	31	is	be	AUX
ejpam-3335	708	32	a	a	DET
ejpam-3335	708	33	strongly	strongly	ADV
ejpam-3335	708	34	up	up	ADJ
ejpam-3335	708	35	-	-	PUNCT
ejpam-3335	708	36	ideal	ideal	NOUN
ejpam-3335	708	37	of	of	ADP
ejpam-3335	708	38	a.	a.	NOUN
ejpam-3335	708	39	by	by	ADP
ejpam-3335	708	40	definition	definition	NOUN
ejpam-3335	708	41	4	4	NUM
ejpam-3335	708	42	,	,	PUNCT
ejpam-3335	708	43	we	we	PRON
ejpam-3335	708	44	have	have	VERB
ejpam-3335	708	45	hh(0	hh(0	NOUN
ejpam-3335	708	46	)	)	PUNCT
ejpam-3335	708	47	=	=	SYM
ejpam-3335	708	48	(	(	PUNCT
ejpam-3335	708	49	0	0	NUM
ejpam-3335	708	50	,	,	PUNCT
ejpam-3335	708	51	1	1	NUM
ejpam-3335	708	52	]	]	PUNCT
ejpam-3335	708	53	,	,	PUNCT
ejpam-3335	708	54	and	and	CCONJ
ejpam-3335	708	55	hh(1	hh(1	NOUN
ejpam-3335	708	56	)	)	PUNCT
ejpam-3335	708	57	=	=	PUNCT
ejpam-3335	709	1	[	[	X
ejpam-3335	709	2	0	0	NUM
ejpam-3335	709	3	,	,	PUNCT
ejpam-3335	709	4	1	1	NUM
ejpam-3335	709	5	)	)	PUNCT
ejpam-3335	709	6	.	.	PUNCT
ejpam-3335	710	1	by	by	ADP
ejpam-3335	710	2	theorem	theorem	NOUN
ejpam-3335	710	3	3	3	NUM
ejpam-3335	710	4	and	and	CCONJ
ejpam-3335	710	5	because	because	SCONJ
ejpam-3335	710	6	h	h	NOUN
ejpam-3335	710	7	is	be	AUX
ejpam-3335	710	8	not	not	PART
ejpam-3335	710	9	a	a	DET
ejpam-3335	710	10	constant	constant	ADJ
ejpam-3335	710	11	hesitant	hesitant	ADJ
ejpam-3335	710	12	fuzzy	fuzzy	ADJ
ejpam-3335	710	13	set	set	NOUN
ejpam-3335	710	14	on	on	ADP
ejpam-3335	710	15	a	a	PRON
ejpam-3335	710	16	,	,	PUNCT
ejpam-3335	710	17	we	we	PRON
ejpam-3335	710	18	have	have	VERB
ejpam-3335	710	19	h	h	NOUN
ejpam-3335	710	20	is	be	AUX
ejpam-3335	710	21	not	not	PART
ejpam-3335	710	22	an	an	DET
ejpam-3335	710	23	anti	anti	ADJ
ejpam-3335	710	24	-	-	ADJ
ejpam-3335	710	25	hesitant	hesitant	ADJ
ejpam-3335	710	26	fuzzy	fuzzy	ADJ
ejpam-3335	710	27	strongly	strongly	ADV
ejpam-3335	710	28	up	up	ADP
ejpam-3335	710	29	-	-	PUNCT
ejpam-3335	710	30	ideal	ideal	NOUN
ejpam-3335	710	31	of	of	ADP
ejpam-3335	710	32	a.	a.	PROPN
ejpam-3335	710	33	p.	p.	PROPN
ejpam-3335	710	34	mosrijai	mosrijai	PROPN
ejpam-3335	710	35	,	,	PUNCT
ejpam-3335	710	36	a.	a.	NOUN
ejpam-3335	710	37	iampan	iampan	PROPN
ejpam-3335	710	38	/	/	SYM
ejpam-3335	710	39	eur	eur	PROPN
ejpam-3335	710	40	.	.	PUNCT
ejpam-3335	711	1	j.	j.	PROPN
ejpam-3335	711	2	pure	pure	PROPN
ejpam-3335	711	3	appl	appl	PROPN
ejpam-3335	711	4	.	.	PROPN
ejpam-3335	711	5	math	math	PROPN
ejpam-3335	711	6	,	,	PUNCT
ejpam-3335	711	7	11	11	NUM
ejpam-3335	711	8	(	(	PUNCT
ejpam-3335	711	9	4	4	NUM
ejpam-3335	711	10	)	)	PUNCT
ejpam-3335	711	11	(	(	PUNCT
ejpam-3335	711	12	2018	2018	NUM
ejpam-3335	711	13	)	)	PUNCT
ejpam-3335	711	14	,	,	PUNCT
ejpam-3335	711	15	976	976	NUM
ejpam-3335	711	16	-	-	SYM
ejpam-3335	711	17	1002	1002	NUM
ejpam-3335	711	18	997	997	NUM
ejpam-3335	711	19	5.5	5.5	NUM
ejpam-3335	711	20	.	.	PUNCT
ejpam-3335	712	1	equal	equal	ADJ
ejpam-3335	712	2	ε	ε	NOUN
ejpam-3335	712	3	-	-	PUNCT
ejpam-3335	712	4	level	level	NOUN
ejpam-3335	712	5	subsets	subset	NOUN
ejpam-3335	712	6	theorem	theorem	VERB
ejpam-3335	712	7	23	23	NUM
ejpam-3335	712	8	.	.	PUNCT
ejpam-3335	713	1	if	if	SCONJ
ejpam-3335	713	2	a	a	DET
ejpam-3335	713	3	hesitant	hesitant	ADJ
ejpam-3335	713	4	fuzzy	fuzzy	ADJ
ejpam-3335	713	5	set	set	VERB
ejpam-3335	713	6	h	h	NOUN
ejpam-3335	713	7	on	on	ADP
ejpam-3335	713	8	a	a	PRON
ejpam-3335	713	9	is	be	AUX
ejpam-3335	713	10	an	an	DET
ejpam-3335	713	11	anti	anti	ADJ
ejpam-3335	713	12	-	-	ADJ
ejpam-3335	713	13	hesitant	hesitant	ADJ
ejpam-3335	713	14	fuzzy	fuzzy	ADJ
ejpam-3335	713	15	up	up	NOUN
ejpam-3335	713	16	-	-	PUNCT
ejpam-3335	713	17	subalgebra	subalgebra	NOUN
ejpam-3335	713	18	of	of	ADP
ejpam-3335	713	19	a	a	PRON
ejpam-3335	713	20	,	,	PUNCT
ejpam-3335	713	21	then	then	ADV
ejpam-3335	713	22	for	for	ADP
ejpam-3335	713	23	all	all	DET
ejpam-3335	713	24	ε	ε	PROPN
ejpam-3335	713	25	∈	∈	PROPN
ejpam-3335	713	26	p([0	p([0	NOUN
ejpam-3335	713	27	,	,	PUNCT
ejpam-3335	713	28	1	1	NUM
ejpam-3335	713	29	]	]	NUM
ejpam-3335	713	30	)	)	PUNCT
ejpam-3335	713	31	,	,	PUNCT
ejpam-3335	713	32	a	a	DET
ejpam-3335	713	33	nonempty	nonempty	NOUN
ejpam-3335	713	34	subset	subset	VERB
ejpam-3335	713	35	e(h	e(h	PROPN
ejpam-3335	713	36	;	;	PUNCT
ejpam-3335	713	37	ε	ε	PROPN
ejpam-3335	713	38	)	)	PUNCT
ejpam-3335	713	39	of	of	ADP
ejpam-3335	713	40	a	a	PRON
ejpam-3335	713	41	is	be	AUX
ejpam-3335	713	42	a	a	DET
ejpam-3335	713	43	up	up	ADJ
ejpam-3335	713	44	-	-	PUNCT
ejpam-3335	713	45	subalgebra	subalgebra	NOUN
ejpam-3335	713	46	of	of	ADP
ejpam-3335	713	47	a	a	DET
ejpam-3335	713	48	where	where	SCONJ
ejpam-3335	713	49	l−(h	l−(h	NOUN
ejpam-3335	713	50	;	;	PUNCT
ejpam-3335	713	51	ε	ε	PROPN
ejpam-3335	713	52	)	)	PUNCT
ejpam-3335	713	53	is	be	AUX
ejpam-3335	713	54	empty	empty	ADJ
ejpam-3335	713	55	.	.	PUNCT
ejpam-3335	714	1	proof	proof	NOUN
ejpam-3335	714	2	.	.	PUNCT
ejpam-3335	715	1	assume	assume	VERB
ejpam-3335	715	2	that	that	SCONJ
ejpam-3335	715	3	h	h	NOUN
ejpam-3335	715	4	is	be	AUX
ejpam-3335	715	5	an	an	DET
ejpam-3335	715	6	anti	anti	ADJ
ejpam-3335	715	7	-	-	ADJ
ejpam-3335	715	8	hesitant	hesitant	ADJ
ejpam-3335	715	9	fuzzy	fuzzy	ADJ
ejpam-3335	715	10	up	up	NOUN
ejpam-3335	715	11	-	-	PUNCT
ejpam-3335	715	12	subalgebra	subalgebra	NOUN
ejpam-3335	715	13	of	of	ADP
ejpam-3335	715	14	a.	a.	NOUN
ejpam-3335	715	15	let	let	VERB
ejpam-3335	715	16	ε	ε	PROPN
ejpam-3335	715	17	∈	∈	PROPN
ejpam-3335	715	18	p([0	p([0	PROPN
ejpam-3335	715	19	,	,	PUNCT
ejpam-3335	715	20	1	1	NUM
ejpam-3335	715	21	]	]	PUNCT
ejpam-3335	715	22	)	)	PUNCT
ejpam-3335	715	23	be	be	AUX
ejpam-3335	715	24	such	such	ADJ
ejpam-3335	715	25	that	that	SCONJ
ejpam-3335	715	26	e(h	e(h	PROPN
ejpam-3335	715	27	;	;	PUNCT
ejpam-3335	715	28	ε	ε	PROPN
ejpam-3335	715	29	)	)	PUNCT
ejpam-3335	715	30	6=	6=	NOUN
ejpam-3335	715	31	∅	∅	NOUN
ejpam-3335	715	32	but	but	CCONJ
ejpam-3335	715	33	l−(h	l−(h	PROPN
ejpam-3335	715	34	;	;	PUNCT
ejpam-3335	715	35	ε	ε	PROPN
ejpam-3335	715	36	)	)	PUNCT
ejpam-3335	715	37	=	=	NOUN
ejpam-3335	715	38	∅	∅	NOUN
ejpam-3335	715	39	,	,	PUNCT
ejpam-3335	715	40	and	and	CCONJ
ejpam-3335	715	41	let	let	VERB
ejpam-3335	715	42	x	x	PRON
ejpam-3335	715	43	,	,	PUNCT
ejpam-3335	715	44	y	y	PROPN
ejpam-3335	715	45	∈	∈	PROPN
ejpam-3335	715	46	a	a	DET
ejpam-3335	715	47	be	be	AUX
ejpam-3335	715	48	such	such	ADJ
ejpam-3335	715	49	that	that	SCONJ
ejpam-3335	715	50	x	x	SYM
ejpam-3335	715	51	∈	∈	PROPN
ejpam-3335	715	52	e(h	e(h	X
ejpam-3335	715	53	;	;	PUNCT
ejpam-3335	715	54	ε	ε	PROPN
ejpam-3335	715	55	)	)	PUNCT
ejpam-3335	715	56	and	and	CCONJ
ejpam-3335	715	57	y	y	PROPN
ejpam-3335	715	58	∈	∈	PROPN
ejpam-3335	715	59	e(h	e(h	X
ejpam-3335	715	60	;	;	PUNCT
ejpam-3335	715	61	ε	ε	PROPN
ejpam-3335	715	62	)	)	PUNCT
ejpam-3335	715	63	.	.	PUNCT
ejpam-3335	716	1	then	then	ADV
ejpam-3335	716	2	hh(x	hh(x	PUNCT
ejpam-3335	716	3	)	)	PUNCT
ejpam-3335	716	4	=	=	SYM
ejpam-3335	716	5	ε	ε	PROPN
ejpam-3335	716	6	and	and	CCONJ
ejpam-3335	716	7	hh(y	hh(y	NOUN
ejpam-3335	716	8	)	)	PUNCT
ejpam-3335	716	9	=	=	SYM
ejpam-3335	716	10	ε	ε	PROPN
ejpam-3335	716	11	.	.	PUNCT
ejpam-3335	717	1	because	because	SCONJ
ejpam-3335	717	2	h	h	NOUN
ejpam-3335	717	3	is	be	AUX
ejpam-3335	717	4	an	an	DET
ejpam-3335	717	5	anti	anti	ADJ
ejpam-3335	717	6	-	-	ADJ
ejpam-3335	717	7	hesitant	hesitant	ADJ
ejpam-3335	717	8	fuzzy	fuzzy	ADJ
ejpam-3335	717	9	up	up	NOUN
ejpam-3335	717	10	-	-	PUNCT
ejpam-3335	717	11	subalgebra	subalgebra	NOUN
ejpam-3335	717	12	of	of	ADP
ejpam-3335	717	13	a	a	PRON
ejpam-3335	717	14	,	,	PUNCT
ejpam-3335	717	15	we	we	PRON
ejpam-3335	717	16	have	have	VERB
ejpam-3335	717	17	hh(x	hh(x	X
ejpam-3335	717	18	·	·	PUNCT
ejpam-3335	717	19	y	y	X
ejpam-3335	717	20	)	)	PUNCT
ejpam-3335	717	21	⊆	⊆	NUM
ejpam-3335	717	22	hh(x	hh(x	NOUN
ejpam-3335	717	23	)	)	PUNCT
ejpam-3335	717	24	∪	∪	ADP
ejpam-3335	717	25	hh(y	hh(y	NOUN
ejpam-3335	717	26	)	)	PUNCT
ejpam-3335	717	27	=	=	SYM
ejpam-3335	717	28	ε	ε	PROPN
ejpam-3335	717	29	.	.	PUNCT
ejpam-3335	717	30	thus	thus	ADV
ejpam-3335	717	31	x	x	X
ejpam-3335	717	32	·	·	PUNCT
ejpam-3335	717	33	y	y	X
ejpam-3335	717	34	∈	∈	PROPN
ejpam-3335	717	35	l(h	l(h	PROPN
ejpam-3335	717	36	;	;	PUNCT
ejpam-3335	717	37	ε	ε	PROPN
ejpam-3335	717	38	)	)	PUNCT
ejpam-3335	717	39	.	.	PUNCT
ejpam-3335	718	1	since	since	SCONJ
ejpam-3335	718	2	l−(h	l−(h	PROPN
ejpam-3335	718	3	;	;	PUNCT
ejpam-3335	718	4	ε	ε	PROPN
ejpam-3335	718	5	)	)	PUNCT
ejpam-3335	718	6	is	be	AUX
ejpam-3335	718	7	empty	empty	ADJ
ejpam-3335	718	8	,	,	PUNCT
ejpam-3335	718	9	we	we	PRON
ejpam-3335	718	10	obtain	obtain	VERB
ejpam-3335	718	11	l(h	l(h	PROPN
ejpam-3335	718	12	;	;	PUNCT
ejpam-3335	718	13	ε	ε	PROPN
ejpam-3335	718	14	)	)	PUNCT
ejpam-3335	718	15	=	=	SYM
ejpam-3335	718	16	l−(h	l−(h	PROPN
ejpam-3335	718	17	;	;	PUNCT
ejpam-3335	718	18	ε)∪e(h	ε)∪e(h	NOUN
ejpam-3335	718	19	;	;	PUNCT
ejpam-3335	718	20	ε	ε	PROPN
ejpam-3335	718	21	)	)	PUNCT
ejpam-3335	718	22	=	=	SYM
ejpam-3335	718	23	∅	∅	NOUN
ejpam-3335	718	24	∪e(h	∪e(h	NOUN
ejpam-3335	718	25	;	;	PUNCT
ejpam-3335	718	26	ε	ε	PROPN
ejpam-3335	718	27	)	)	PUNCT
ejpam-3335	718	28	=	=	SYM
ejpam-3335	718	29	e(h	e(h	X
ejpam-3335	718	30	;	;	PUNCT
ejpam-3335	718	31	ε	ε	PROPN
ejpam-3335	718	32	)	)	PUNCT
ejpam-3335	718	33	.	.	PUNCT
ejpam-3335	719	1	therefore	therefore	ADV
ejpam-3335	719	2	,	,	PUNCT
ejpam-3335	719	3	x	x	X
ejpam-3335	719	4	·	·	PUNCT
ejpam-3335	719	5	y	y	PROPN
ejpam-3335	719	6	∈	∈	PROPN
ejpam-3335	719	7	e(h	e(h	X
ejpam-3335	719	8	;	;	PUNCT
ejpam-3335	719	9	ε	ε	PROPN
ejpam-3335	719	10	)	)	PUNCT
ejpam-3335	719	11	.	.	PUNCT
ejpam-3335	720	1	hence	hence	ADV
ejpam-3335	720	2	,	,	PUNCT
ejpam-3335	720	3	e(h	e(h	PROPN
ejpam-3335	720	4	;	;	PUNCT
ejpam-3335	720	5	ε	ε	PROPN
ejpam-3335	720	6	)	)	PUNCT
ejpam-3335	720	7	is	be	AUX
ejpam-3335	720	8	a	a	DET
ejpam-3335	720	9	up	up	ADJ
ejpam-3335	720	10	-	-	PUNCT
ejpam-3335	720	11	subalgebra	subalgebra	NOUN
ejpam-3335	720	12	of	of	ADP
ejpam-3335	720	13	a.	a.	NOUN
ejpam-3335	720	14	the	the	DET
ejpam-3335	720	15	following	follow	VERB
ejpam-3335	720	16	example	example	NOUN
ejpam-3335	720	17	show	show	VERB
ejpam-3335	720	18	that	that	SCONJ
ejpam-3335	720	19	the	the	DET
ejpam-3335	720	20	converse	converse	NOUN
ejpam-3335	720	21	of	of	ADP
ejpam-3335	720	22	theorem	theorem	NOUN
ejpam-3335	720	23	23	23	NUM
ejpam-3335	720	24	is	be	AUX
ejpam-3335	720	25	not	not	PART
ejpam-3335	720	26	true	true	ADJ
ejpam-3335	720	27	in	in	ADP
ejpam-3335	720	28	general	general	ADJ
ejpam-3335	720	29	.	.	PUNCT
ejpam-3335	720	30	example	example	NOUN
ejpam-3335	721	1	16	16	NUM
ejpam-3335	721	2	.	.	PUNCT
ejpam-3335	722	1	let	let	VERB
ejpam-3335	722	2	a	a	PRON
ejpam-3335	722	3	=	=	PUNCT
ejpam-3335	722	4	{	{	PUNCT
ejpam-3335	722	5	0	0	NUM
ejpam-3335	722	6	,	,	PUNCT
ejpam-3335	722	7	1	1	NUM
ejpam-3335	722	8	,	,	PUNCT
ejpam-3335	722	9	2	2	NUM
ejpam-3335	722	10	,	,	PUNCT
ejpam-3335	722	11	3	3	NUM
ejpam-3335	722	12	}	}	PUNCT
ejpam-3335	722	13	be	be	AUX
ejpam-3335	722	14	a	a	DET
ejpam-3335	722	15	set	set	NOUN
ejpam-3335	722	16	with	with	ADP
ejpam-3335	722	17	a	a	DET
ejpam-3335	722	18	binary	binary	ADJ
ejpam-3335	722	19	operation	operation	NOUN
ejpam-3335	722	20	·	·	PUNCT
ejpam-3335	722	21	defined	define	VERB
ejpam-3335	722	22	by	by	ADP
ejpam-3335	722	23	the	the	DET
ejpam-3335	722	24	following	following	ADJ
ejpam-3335	722	25	cayley	cayley	ADJ
ejpam-3335	722	26	table	table	NOUN
ejpam-3335	722	27	:	:	PUNCT
ejpam-3335	722	28	·	·	PUNCT
ejpam-3335	722	29	0	0	NUM
ejpam-3335	723	1	1	1	NUM
ejpam-3335	723	2	2	2	NUM
ejpam-3335	723	3	3	3	NUM
ejpam-3335	723	4	0	0	NUM
ejpam-3335	723	5	0	0	NUM
ejpam-3335	723	6	1	1	NUM
ejpam-3335	723	7	2	2	NUM
ejpam-3335	723	8	3	3	NUM
ejpam-3335	723	9	1	1	NUM
ejpam-3335	723	10	0	0	NUM
ejpam-3335	723	11	0	0	NUM
ejpam-3335	723	12	1	1	NUM
ejpam-3335	723	13	3	3	NUM
ejpam-3335	723	14	2	2	NUM
ejpam-3335	723	15	0	0	NUM
ejpam-3335	723	16	0	0	NUM
ejpam-3335	723	17	0	0	NUM
ejpam-3335	723	18	3	3	NUM
ejpam-3335	723	19	3	3	NUM
ejpam-3335	723	20	0	0	NUM
ejpam-3335	723	21	1	1	NUM
ejpam-3335	723	22	1	1	NUM
ejpam-3335	723	23	0	0	NUM
ejpam-3335	723	24	then	then	ADV
ejpam-3335	723	25	(	(	PUNCT
ejpam-3335	723	26	a	a	PRON
ejpam-3335	723	27	,	,	PUNCT
ejpam-3335	723	28	·	·	PUNCT
ejpam-3335	723	29	,	,	PUNCT
ejpam-3335	723	30	0	0	NUM
ejpam-3335	723	31	)	)	PUNCT
ejpam-3335	723	32	is	be	AUX
ejpam-3335	723	33	a	a	DET
ejpam-3335	723	34	up	up	NOUN
ejpam-3335	723	35	-	-	PUNCT
ejpam-3335	723	36	algebra	algebra	NOUN
ejpam-3335	723	37	.	.	PUNCT
ejpam-3335	724	1	we	we	PRON
ejpam-3335	724	2	define	define	VERB
ejpam-3335	724	3	a	a	DET
ejpam-3335	724	4	hesitant	hesitant	ADJ
ejpam-3335	724	5	fuzzy	fuzzy	ADJ
ejpam-3335	724	6	set	set	VERB
ejpam-3335	724	7	h	h	NOUN
ejpam-3335	724	8	on	on	ADP
ejpam-3335	724	9	a	a	PRON
ejpam-3335	724	10	as	as	SCONJ
ejpam-3335	724	11	follows	follow	VERB
ejpam-3335	724	12	:	:	PUNCT
ejpam-3335	724	13	hh(0	hh(0	NOUN
ejpam-3335	724	14	)	)	PUNCT
ejpam-3335	724	15	=	=	SYM
ejpam-3335	724	16	∅	∅	NOUN
ejpam-3335	724	17	,	,	PUNCT
ejpam-3335	724	18	hh(1	hh(1	NOUN
ejpam-3335	724	19	)	)	PUNCT
ejpam-3335	724	20	=	=	PUNCT
ejpam-3335	725	1	[	[	X
ejpam-3335	725	2	0	0	NUM
ejpam-3335	725	3	,	,	PUNCT
ejpam-3335	725	4	0.6	0.6	NUM
ejpam-3335	725	5	]	]	PUNCT
ejpam-3335	725	6	,	,	PUNCT
ejpam-3335	725	7	hh(2	hh(2	NOUN
ejpam-3335	725	8	)	)	PUNCT
ejpam-3335	725	9	=	=	PUNCT
ejpam-3335	726	1	[	[	X
ejpam-3335	726	2	0	0	NUM
ejpam-3335	726	3	,	,	PUNCT
ejpam-3335	726	4	0.3	0.3	NUM
ejpam-3335	726	5	]	]	PUNCT
ejpam-3335	726	6	,	,	PUNCT
ejpam-3335	726	7	and	and	CCONJ
ejpam-3335	726	8	hh(3	hh(3	X
ejpam-3335	726	9	)	)	PUNCT
ejpam-3335	726	10	=	=	PUNCT
ejpam-3335	727	1	[	[	X
ejpam-3335	727	2	0	0	NUM
ejpam-3335	727	3	,	,	PUNCT
ejpam-3335	727	4	0.3	0.3	NUM
ejpam-3335	727	5	]	]	PUNCT
ejpam-3335	727	6	.	.	PUNCT
ejpam-3335	728	1	if	if	SCONJ
ejpam-3335	728	2	ε	ε	PROPN
ejpam-3335	728	3	6=	6=	NUM
ejpam-3335	728	4	∅	∅	NOUN
ejpam-3335	728	5	,	,	PUNCT
ejpam-3335	728	6	then	then	ADV
ejpam-3335	728	7	l−(h	l−(h	PROPN
ejpam-3335	728	8	;	;	PUNCT
ejpam-3335	728	9	ε	ε	PROPN
ejpam-3335	728	10	)	)	PUNCT
ejpam-3335	728	11	6=	6=	ADP
ejpam-3335	728	12	∅.	∅.	ADP
ejpam-3335	728	13	if	if	SCONJ
ejpam-3335	728	14	ε	ε	PROPN
ejpam-3335	728	15	=	=	SYM
ejpam-3335	728	16	∅	∅	NOUN
ejpam-3335	728	17	,	,	PUNCT
ejpam-3335	728	18	then	then	ADV
ejpam-3335	728	19	l−(h	l−(h	PROPN
ejpam-3335	728	20	;	;	PUNCT
ejpam-3335	728	21	ε	ε	PROPN
ejpam-3335	728	22	)	)	PUNCT
ejpam-3335	728	23	=	=	NOUN
ejpam-3335	728	24	∅	∅	NOUN
ejpam-3335	728	25	and	and	CCONJ
ejpam-3335	728	26	e(h	e(h	PROPN
ejpam-3335	728	27	;	;	PUNCT
ejpam-3335	728	28	ε	ε	PROPN
ejpam-3335	728	29	)	)	PUNCT
ejpam-3335	728	30	=	=	PUNCT
ejpam-3335	728	31	{	{	PUNCT
ejpam-3335	728	32	0	0	NUM
ejpam-3335	728	33	}	}	PUNCT
ejpam-3335	728	34	.	.	PUNCT
ejpam-3335	729	1	thus	thus	ADV
ejpam-3335	729	2	e(h	e(h	X
ejpam-3335	729	3	;	;	PUNCT
ejpam-3335	729	4	ε	ε	PROPN
ejpam-3335	729	5	)	)	PUNCT
ejpam-3335	729	6	is	be	AUX
ejpam-3335	729	7	clearly	clearly	ADV
ejpam-3335	729	8	a	a	DET
ejpam-3335	729	9	up	up	ADJ
ejpam-3335	729	10	-	-	PUNCT
ejpam-3335	729	11	subalgebra	subalgebra	NOUN
ejpam-3335	729	12	of	of	ADP
ejpam-3335	729	13	a.	a.	NOUN
ejpam-3335	729	14	since	since	SCONJ
ejpam-3335	729	15	hh(3·2	hh(3·2	PROPN
ejpam-3335	729	16	)	)	PUNCT
ejpam-3335	729	17	=	=	PUNCT
ejpam-3335	729	18	hh(1	hh(1	NOUN
ejpam-3335	729	19	)	)	PUNCT
ejpam-3335	729	20	=	=	PUNCT
ejpam-3335	730	1	[	[	X
ejpam-3335	730	2	0	0	NUM
ejpam-3335	730	3	,	,	PUNCT
ejpam-3335	730	4	0.6	0.6	NUM
ejpam-3335	730	5	]	]	PUNCT
ejpam-3335	730	6	*	*	PUNCT
ejpam-3335	731	1	[	[	X
ejpam-3335	731	2	0	0	NUM
ejpam-3335	731	3	,	,	PUNCT
ejpam-3335	731	4	0.3	0.3	NUM
ejpam-3335	731	5	]	]	PUNCT
ejpam-3335	731	6	=	=	SYM
ejpam-3335	731	7	hh(3)∪hh(2	hh(3)∪hh(2	NOUN
ejpam-3335	731	8	)	)	PUNCT
ejpam-3335	731	9	,	,	PUNCT
ejpam-3335	731	10	we	we	PRON
ejpam-3335	731	11	have	have	VERB
ejpam-3335	731	12	h	h	NOUN
ejpam-3335	731	13	is	be	AUX
ejpam-3335	731	14	not	not	PART
ejpam-3335	731	15	an	an	DET
ejpam-3335	731	16	anti	anti	ADJ
ejpam-3335	731	17	-	-	ADJ
ejpam-3335	731	18	hesitant	hesitant	ADJ
ejpam-3335	731	19	fuzzy	fuzzy	ADJ
ejpam-3335	731	20	up	up	NOUN
ejpam-3335	731	21	-	-	PUNCT
ejpam-3335	731	22	subalgebra	subalgebra	NOUN
ejpam-3335	731	23	of	of	ADP
ejpam-3335	731	24	a.	a.	NOUN
ejpam-3335	731	25	theorem	theorem	NOUN
ejpam-3335	731	26	24	24	NUM
ejpam-3335	731	27	.	.	PUNCT
ejpam-3335	732	1	if	if	SCONJ
ejpam-3335	732	2	a	a	DET
ejpam-3335	732	3	hesitant	hesitant	ADJ
ejpam-3335	732	4	fuzzy	fuzzy	ADJ
ejpam-3335	732	5	set	set	VERB
ejpam-3335	732	6	h	h	NOUN
ejpam-3335	732	7	on	on	ADP
ejpam-3335	732	8	a	a	PRON
ejpam-3335	732	9	is	be	AUX
ejpam-3335	732	10	an	an	DET
ejpam-3335	732	11	anti	anti	ADJ
ejpam-3335	732	12	-	-	ADJ
ejpam-3335	732	13	hesitant	hesitant	ADJ
ejpam-3335	732	14	fuzzy	fuzzy	ADJ
ejpam-3335	732	15	up	up	NOUN
ejpam-3335	732	16	-	-	PUNCT
ejpam-3335	732	17	filter	filter	NOUN
ejpam-3335	732	18	of	of	ADP
ejpam-3335	732	19	a	a	PRON
ejpam-3335	732	20	,	,	PUNCT
ejpam-3335	732	21	then	then	ADV
ejpam-3335	732	22	for	for	ADP
ejpam-3335	732	23	all	all	DET
ejpam-3335	732	24	ε	ε	PROPN
ejpam-3335	732	25	∈	∈	PROPN
ejpam-3335	732	26	p([0	p([0	NOUN
ejpam-3335	732	27	,	,	PUNCT
ejpam-3335	732	28	1	1	NUM
ejpam-3335	732	29	]	]	NUM
ejpam-3335	732	30	)	)	PUNCT
ejpam-3335	732	31	,	,	PUNCT
ejpam-3335	732	32	a	a	DET
ejpam-3335	732	33	nonempty	nonempty	NOUN
ejpam-3335	732	34	subset	subset	VERB
ejpam-3335	732	35	e(h	e(h	PROPN
ejpam-3335	732	36	;	;	PUNCT
ejpam-3335	732	37	ε	ε	PROPN
ejpam-3335	732	38	)	)	PUNCT
ejpam-3335	732	39	of	of	ADP
ejpam-3335	732	40	a	a	PRON
ejpam-3335	732	41	is	be	AUX
ejpam-3335	732	42	a	a	DET
ejpam-3335	732	43	up	up	ADJ
ejpam-3335	732	44	-	-	PUNCT
ejpam-3335	732	45	filter	filter	NOUN
ejpam-3335	732	46	of	of	ADP
ejpam-3335	732	47	a	a	DET
ejpam-3335	732	48	where	where	SCONJ
ejpam-3335	732	49	l−(h	l−(h	NOUN
ejpam-3335	732	50	;	;	PUNCT
ejpam-3335	732	51	ε	ε	PROPN
ejpam-3335	732	52	)	)	PUNCT
ejpam-3335	732	53	is	be	AUX
ejpam-3335	732	54	empty	empty	ADJ
ejpam-3335	732	55	.	.	PUNCT
ejpam-3335	733	1	proof	proof	NOUN
ejpam-3335	733	2	.	.	PUNCT
ejpam-3335	734	1	assume	assume	VERB
ejpam-3335	734	2	that	that	SCONJ
ejpam-3335	734	3	h	h	NOUN
ejpam-3335	734	4	is	be	AUX
ejpam-3335	734	5	an	an	DET
ejpam-3335	734	6	anti	anti	ADJ
ejpam-3335	734	7	-	-	ADJ
ejpam-3335	734	8	hesitant	hesitant	ADJ
ejpam-3335	734	9	fuzzy	fuzzy	ADJ
ejpam-3335	734	10	up	up	NOUN
ejpam-3335	734	11	-	-	PUNCT
ejpam-3335	734	12	filter	filter	NOUN
ejpam-3335	734	13	of	of	ADP
ejpam-3335	734	14	a.	a.	NOUN
ejpam-3335	734	15	let	let	VERB
ejpam-3335	734	16	ε	ε	PROPN
ejpam-3335	734	17	∈	∈	PROPN
ejpam-3335	734	18	p([0	p([0	PROPN
ejpam-3335	734	19	,	,	PUNCT
ejpam-3335	734	20	1	1	NUM
ejpam-3335	734	21	]	]	PUNCT
ejpam-3335	734	22	)	)	PUNCT
ejpam-3335	734	23	be	be	AUX
ejpam-3335	734	24	such	such	ADJ
ejpam-3335	734	25	that	that	SCONJ
ejpam-3335	734	26	e(h	e(h	PROPN
ejpam-3335	734	27	;	;	PUNCT
ejpam-3335	734	28	ε	ε	PROPN
ejpam-3335	734	29	)	)	PUNCT
ejpam-3335	734	30	6=	6=	NOUN
ejpam-3335	734	31	∅	∅	NOUN
ejpam-3335	734	32	but	but	CCONJ
ejpam-3335	734	33	l−(h	l−(h	PROPN
ejpam-3335	734	34	;	;	PUNCT
ejpam-3335	734	35	ε	ε	PROPN
ejpam-3335	734	36	)	)	PUNCT
ejpam-3335	734	37	=	=	NOUN
ejpam-3335	734	38	∅	∅	NOUN
ejpam-3335	734	39	,	,	PUNCT
ejpam-3335	734	40	and	and	CCONJ
ejpam-3335	734	41	let	let	VERB
ejpam-3335	734	42	x	x	SYM
ejpam-3335	734	43	∈	∈	PROPN
ejpam-3335	734	44	a	a	DET
ejpam-3335	734	45	be	be	AUX
ejpam-3335	734	46	such	such	ADJ
ejpam-3335	734	47	that	that	SCONJ
ejpam-3335	734	48	x	x	SYM
ejpam-3335	734	49	∈	∈	PROPN
ejpam-3335	734	50	e(h	e(h	X
ejpam-3335	734	51	;	;	PUNCT
ejpam-3335	734	52	ε	ε	PROPN
ejpam-3335	734	53	)	)	PUNCT
ejpam-3335	734	54	.	.	PUNCT
ejpam-3335	735	1	then	then	ADV
ejpam-3335	735	2	hh(x	hh(x	PUNCT
ejpam-3335	735	3	)	)	PUNCT
ejpam-3335	735	4	=	=	SYM
ejpam-3335	735	5	ε	ε	PROPN
ejpam-3335	735	6	.	.	PUNCT
ejpam-3335	736	1	because	because	SCONJ
ejpam-3335	736	2	h	h	NOUN
ejpam-3335	736	3	is	be	AUX
ejpam-3335	736	4	an	an	DET
ejpam-3335	736	5	anti	anti	ADJ
ejpam-3335	736	6	-	-	ADJ
ejpam-3335	736	7	hesitant	hesitant	ADJ
ejpam-3335	736	8	fuzzy	fuzzy	ADJ
ejpam-3335	736	9	up	up	NOUN
ejpam-3335	736	10	-	-	PUNCT
ejpam-3335	736	11	filter	filter	NOUN
ejpam-3335	736	12	of	of	ADP
ejpam-3335	736	13	a	a	PRON
ejpam-3335	736	14	,	,	PUNCT
ejpam-3335	736	15	we	we	PRON
ejpam-3335	736	16	obtain	obtain	VERB
ejpam-3335	736	17	hh(0	hh(0	NOUN
ejpam-3335	736	18	)	)	PUNCT
ejpam-3335	736	19	⊆	⊆	NUM
ejpam-3335	736	20	hh(x	hh(x	NOUN
ejpam-3335	736	21	)	)	PUNCT
ejpam-3335	736	22	=	=	SYM
ejpam-3335	736	23	ε	ε	PROPN
ejpam-3335	736	24	and	and	CCONJ
ejpam-3335	736	25	thus	thus	ADV
ejpam-3335	736	26	0	0	X
ejpam-3335	736	27	∈	∈	PROPN
ejpam-3335	736	28	l(h	l(h	PROPN
ejpam-3335	736	29	;	;	PUNCT
ejpam-3335	736	30	ε	ε	PROPN
ejpam-3335	736	31	)	)	PUNCT
ejpam-3335	736	32	.	.	PUNCT
ejpam-3335	737	1	since	since	SCONJ
ejpam-3335	737	2	l−(h	l−(h	PROPN
ejpam-3335	737	3	;	;	PUNCT
ejpam-3335	737	4	ε	ε	PROPN
ejpam-3335	737	5	)	)	PUNCT
ejpam-3335	737	6	is	be	AUX
ejpam-3335	737	7	empty	empty	ADJ
ejpam-3335	737	8	,	,	PUNCT
ejpam-3335	737	9	we	we	PRON
ejpam-3335	737	10	have	have	VERB
ejpam-3335	737	11	0	0	NUM
ejpam-3335	737	12	∈	∈	PROPN
ejpam-3335	737	13	l(h	l(h	PROPN
ejpam-3335	737	14	;	;	PUNCT
ejpam-3335	737	15	ε	ε	PROPN
ejpam-3335	737	16	)	)	PUNCT
ejpam-3335	737	17	=	=	SYM
ejpam-3335	737	18	e(h	e(h	X
ejpam-3335	737	19	;	;	PUNCT
ejpam-3335	737	20	ε	ε	PROPN
ejpam-3335	737	21	)	)	PUNCT
ejpam-3335	737	22	.	.	PUNCT
ejpam-3335	738	1	next	next	ADV
ejpam-3335	738	2	,	,	PUNCT
ejpam-3335	738	3	let	let	VERB
ejpam-3335	738	4	x	x	PRON
ejpam-3335	738	5	,	,	PUNCT
ejpam-3335	738	6	y	y	PROPN
ejpam-3335	738	7	∈	∈	PROPN
ejpam-3335	738	8	a	a	PRON
ejpam-3335	738	9	be	be	AUX
ejpam-3335	738	10	such	such	ADJ
ejpam-3335	738	11	that	that	SCONJ
ejpam-3335	738	12	x	x	X
ejpam-3335	738	13	·	·	PUNCT
ejpam-3335	738	14	y	y	PROPN
ejpam-3335	738	15	∈	∈	PROPN
ejpam-3335	738	16	e(h	e(h	X
ejpam-3335	738	17	;	;	PUNCT
ejpam-3335	738	18	ε	ε	PROPN
ejpam-3335	738	19	)	)	PUNCT
ejpam-3335	738	20	and	and	CCONJ
ejpam-3335	738	21	x	x	PUNCT
ejpam-3335	738	22	∈	∈	PROPN
ejpam-3335	738	23	e(h	e(h	X
ejpam-3335	738	24	;	;	PUNCT
ejpam-3335	738	25	ε	ε	PROPN
ejpam-3335	738	26	)	)	PUNCT
ejpam-3335	738	27	.	.	PUNCT
ejpam-3335	739	1	then	then	ADV
ejpam-3335	739	2	hh(x	hh(x	PUNCT
ejpam-3335	739	3	·	·	PUNCT
ejpam-3335	739	4	y	y	X
ejpam-3335	739	5	)	)	PUNCT
ejpam-3335	739	6	=	=	SYM
ejpam-3335	739	7	ε	ε	PROPN
ejpam-3335	739	8	and	and	CCONJ
ejpam-3335	739	9	hh(x	hh(x	PUNCT
ejpam-3335	739	10	)	)	PUNCT
ejpam-3335	739	11	=	=	SYM
ejpam-3335	739	12	ε	ε	PROPN
ejpam-3335	739	13	.	.	PUNCT
ejpam-3335	740	1	because	because	SCONJ
ejpam-3335	740	2	h	h	NOUN
ejpam-3335	740	3	is	be	AUX
ejpam-3335	740	4	an	an	DET
ejpam-3335	740	5	anti	anti	ADJ
ejpam-3335	740	6	-	-	ADJ
ejpam-3335	740	7	hesitant	hesitant	ADJ
ejpam-3335	740	8	fuzzy	fuzzy	ADJ
ejpam-3335	740	9	up	up	NOUN
ejpam-3335	740	10	-	-	PUNCT
ejpam-3335	740	11	filter	filter	NOUN
ejpam-3335	740	12	of	of	ADP
ejpam-3335	740	13	a	a	PRON
ejpam-3335	740	14	,	,	PUNCT
ejpam-3335	740	15	we	we	PRON
ejpam-3335	740	16	have	have	VERB
ejpam-3335	740	17	hh(y	hh(y	NOUN
ejpam-3335	740	18	)	)	PUNCT
ejpam-3335	741	1	⊆	⊆	NUM
ejpam-3335	741	2	hh(x	hh(x	X
ejpam-3335	741	3	·	·	PUNCT
ejpam-3335	741	4	y	y	X
ejpam-3335	741	5	)	)	PUNCT
ejpam-3335	741	6	∪	∪	ADP
ejpam-3335	741	7	hh(x	hh(x	X
ejpam-3335	741	8	)	)	PUNCT
ejpam-3335	741	9	=	=	SYM
ejpam-3335	741	10	ε	ε	PROPN
ejpam-3335	741	11	.	.	PUNCT
ejpam-3335	742	1	thus	thus	ADV
ejpam-3335	742	2	y	y	PROPN
ejpam-3335	742	3	∈	∈	PROPN
ejpam-3335	742	4	l(h	l(h	PROPN
ejpam-3335	742	5	;	;	PUNCT
ejpam-3335	742	6	ε	ε	PROPN
ejpam-3335	742	7	)	)	PUNCT
ejpam-3335	742	8	.	.	PUNCT
ejpam-3335	743	1	since	since	SCONJ
ejpam-3335	743	2	l−(h	l−(h	PROPN
ejpam-3335	743	3	;	;	PUNCT
ejpam-3335	743	4	ε	ε	PROPN
ejpam-3335	743	5	)	)	PUNCT
ejpam-3335	743	6	is	be	AUX
ejpam-3335	743	7	empty	empty	ADJ
ejpam-3335	743	8	,	,	PUNCT
ejpam-3335	743	9	we	we	PRON
ejpam-3335	743	10	obtain	obtain	VERB
ejpam-3335	743	11	l(h	l(h	PROPN
ejpam-3335	743	12	;	;	PUNCT
ejpam-3335	743	13	ε	ε	PROPN
ejpam-3335	743	14	)	)	PUNCT
ejpam-3335	743	15	=	=	SYM
ejpam-3335	744	1	e(h	e(h	X
ejpam-3335	744	2	;	;	PUNCT
ejpam-3335	744	3	ε	ε	PROPN
ejpam-3335	744	4	)	)	PUNCT
ejpam-3335	744	5	.	.	PUNCT
ejpam-3335	745	1	therefore	therefore	ADV
ejpam-3335	745	2	,	,	PUNCT
ejpam-3335	745	3	y	y	PROPN
ejpam-3335	745	4	∈	∈	PROPN
ejpam-3335	745	5	e(h	e(h	X
ejpam-3335	745	6	;	;	PUNCT
ejpam-3335	745	7	ε	ε	PROPN
ejpam-3335	745	8	)	)	PUNCT
ejpam-3335	745	9	.	.	PUNCT
ejpam-3335	746	1	hence	hence	ADV
ejpam-3335	746	2	,	,	PUNCT
ejpam-3335	746	3	e(h	e(h	PROPN
ejpam-3335	746	4	;	;	PUNCT
ejpam-3335	746	5	ε	ε	PROPN
ejpam-3335	746	6	)	)	PUNCT
ejpam-3335	746	7	is	be	AUX
ejpam-3335	746	8	a	a	DET
ejpam-3335	746	9	up	up	ADJ
ejpam-3335	746	10	-	-	PUNCT
ejpam-3335	746	11	filter	filter	NOUN
ejpam-3335	746	12	of	of	ADP
ejpam-3335	746	13	a.	a.	NOUN
ejpam-3335	746	14	the	the	DET
ejpam-3335	746	15	converse	converse	NOUN
ejpam-3335	746	16	of	of	ADP
ejpam-3335	746	17	theorem	theorem	ADJ
ejpam-3335	746	18	24	24	NUM
ejpam-3335	746	19	is	be	AUX
ejpam-3335	746	20	not	not	PART
ejpam-3335	746	21	true	true	ADJ
ejpam-3335	746	22	in	in	ADP
ejpam-3335	746	23	general	general	ADJ
ejpam-3335	746	24	.	.	PUNCT
ejpam-3335	747	1	by	by	ADP
ejpam-3335	747	2	example	example	NOUN
ejpam-3335	747	3	16	16	NUM
ejpam-3335	747	4	,	,	PUNCT
ejpam-3335	747	5	we	we	PRON
ejpam-3335	747	6	still	still	ADV
ejpam-3335	747	7	have	have	VERB
ejpam-3335	747	8	e(h	e(h	NUM
ejpam-3335	747	9	;	;	PUNCT
ejpam-3335	747	10	ε	ε	PROPN
ejpam-3335	747	11	)	)	PUNCT
ejpam-3335	747	12	=	=	SYM
ejpam-3335	747	13	{	{	PUNCT
ejpam-3335	747	14	0	0	NUM
ejpam-3335	747	15	}	}	PUNCT
ejpam-3335	747	16	is	be	AUX
ejpam-3335	747	17	a	a	DET
ejpam-3335	747	18	up	up	ADJ
ejpam-3335	747	19	-	-	PUNCT
ejpam-3335	747	20	filter	filter	NOUN
ejpam-3335	747	21	of	of	ADP
ejpam-3335	747	22	a.	a.	NOUN
ejpam-3335	747	23	since	since	SCONJ
ejpam-3335	747	24	hh(1	hh(1	NOUN
ejpam-3335	747	25	)	)	PUNCT
ejpam-3335	747	26	=	=	PUNCT
ejpam-3335	748	1	[	[	X
ejpam-3335	748	2	0	0	NUM
ejpam-3335	748	3	,	,	PUNCT
ejpam-3335	748	4	0.6	0.6	NUM
ejpam-3335	748	5	]	]	PUNCT
ejpam-3335	748	6	*	*	PUNCT
ejpam-3335	749	1	[	[	X
ejpam-3335	749	2	0	0	NUM
ejpam-3335	749	3	,	,	PUNCT
ejpam-3335	749	4	0.3	0.3	NUM
ejpam-3335	749	5	]	]	PUNCT
ejpam-3335	749	6	=	=	SYM
ejpam-3335	749	7	hh(0	hh(0	NOUN
ejpam-3335	749	8	)	)	PUNCT
ejpam-3335	749	9	∪	∪	PROPN
ejpam-3335	749	10	hh(2	hh(2	NOUN
ejpam-3335	749	11	)	)	PUNCT
ejpam-3335	749	12	=	=	SYM
ejpam-3335	749	13	hh(2	hh(2	PROPN
ejpam-3335	749	14	·	·	SYM
ejpam-3335	749	15	1	1	NUM
ejpam-3335	749	16	)	)	PUNCT
ejpam-3335	749	17	∪	∪	ADP
ejpam-3335	749	18	hh(2	hh(2	PROPN
ejpam-3335	749	19	)	)	PUNCT
ejpam-3335	749	20	,	,	PUNCT
ejpam-3335	749	21	we	we	PRON
ejpam-3335	749	22	have	have	VERB
ejpam-3335	749	23	h	h	NOUN
ejpam-3335	749	24	is	be	AUX
ejpam-3335	749	25	not	not	PART
ejpam-3335	749	26	an	an	DET
ejpam-3335	749	27	anti	anti	ADJ
ejpam-3335	749	28	-	-	ADJ
ejpam-3335	749	29	hesitant	hesitant	ADJ
ejpam-3335	749	30	fuzzy	fuzzy	ADJ
ejpam-3335	749	31	up	up	NOUN
ejpam-3335	749	32	-	-	PUNCT
ejpam-3335	749	33	filter	filter	NOUN
ejpam-3335	749	34	of	of	ADP
ejpam-3335	749	35	a.	a.	PROPN
ejpam-3335	749	36	p.	p.	PROPN
ejpam-3335	749	37	mosrijai	mosrijai	PROPN
ejpam-3335	749	38	,	,	PUNCT
ejpam-3335	749	39	a.	a.	NOUN
ejpam-3335	749	40	iampan	iampan	PROPN
ejpam-3335	749	41	/	/	SYM
ejpam-3335	749	42	eur	eur	PROPN
ejpam-3335	749	43	.	.	PUNCT
ejpam-3335	750	1	j.	j.	PROPN
ejpam-3335	750	2	pure	pure	PROPN
ejpam-3335	750	3	appl	appl	PROPN
ejpam-3335	750	4	.	.	PROPN
ejpam-3335	750	5	math	math	PROPN
ejpam-3335	750	6	,	,	PUNCT
ejpam-3335	750	7	11	11	NUM
ejpam-3335	750	8	(	(	PUNCT
ejpam-3335	750	9	4	4	NUM
ejpam-3335	750	10	)	)	PUNCT
ejpam-3335	750	11	(	(	PUNCT
ejpam-3335	750	12	2018	2018	NUM
ejpam-3335	750	13	)	)	PUNCT
ejpam-3335	750	14	,	,	PUNCT
ejpam-3335	750	15	976	976	NUM
ejpam-3335	750	16	-	-	SYM
ejpam-3335	750	17	1002	1002	NUM
ejpam-3335	750	18	998	998	NUM
ejpam-3335	750	19	theorem	theorem	NOUN
ejpam-3335	750	20	25	25	NUM
ejpam-3335	750	21	.	.	PUNCT
ejpam-3335	751	1	if	if	SCONJ
ejpam-3335	751	2	a	a	DET
ejpam-3335	751	3	hesitant	hesitant	ADJ
ejpam-3335	751	4	fuzzy	fuzzy	ADJ
ejpam-3335	751	5	set	set	VERB
ejpam-3335	751	6	h	h	NOUN
ejpam-3335	751	7	on	on	ADP
ejpam-3335	751	8	a	a	PRON
ejpam-3335	751	9	is	be	AUX
ejpam-3335	751	10	an	an	DET
ejpam-3335	751	11	anti	anti	ADJ
ejpam-3335	751	12	-	-	ADJ
ejpam-3335	751	13	hesitant	hesitant	ADJ
ejpam-3335	751	14	fuzzy	fuzzy	ADJ
ejpam-3335	751	15	up	up	NOUN
ejpam-3335	751	16	-	-	PUNCT
ejpam-3335	751	17	ideal	ideal	NOUN
ejpam-3335	751	18	of	of	ADP
ejpam-3335	751	19	a	a	DET
ejpam-3335	751	20	,	,	PUNCT
ejpam-3335	751	21	then	then	ADV
ejpam-3335	751	22	ε	ε	PROPN
ejpam-3335	751	23	∈	∈	PROPN
ejpam-3335	751	24	p([0	p([0	PROPN
ejpam-3335	751	25	,	,	PUNCT
ejpam-3335	751	26	1	1	NUM
ejpam-3335	751	27	]	]	NUM
ejpam-3335	751	28	)	)	PUNCT
ejpam-3335	751	29	,	,	PUNCT
ejpam-3335	751	30	a	a	DET
ejpam-3335	751	31	nonempty	nonempty	NOUN
ejpam-3335	751	32	subset	subset	VERB
ejpam-3335	751	33	e(h	e(h	PROPN
ejpam-3335	751	34	;	;	PUNCT
ejpam-3335	751	35	ε	ε	PROPN
ejpam-3335	751	36	)	)	PUNCT
ejpam-3335	751	37	of	of	ADP
ejpam-3335	751	38	a	a	PRON
ejpam-3335	751	39	is	be	AUX
ejpam-3335	751	40	a	a	DET
ejpam-3335	751	41	up	up	ADJ
ejpam-3335	751	42	-	-	PUNCT
ejpam-3335	751	43	ideal	ideal	NOUN
ejpam-3335	751	44	of	of	ADP
ejpam-3335	751	45	a	a	DET
ejpam-3335	751	46	where	where	SCONJ
ejpam-3335	751	47	l−(h	l−(h	NOUN
ejpam-3335	751	48	;	;	PUNCT
ejpam-3335	751	49	ε	ε	PROPN
ejpam-3335	751	50	)	)	PUNCT
ejpam-3335	751	51	is	be	AUX
ejpam-3335	751	52	empty	empty	ADJ
ejpam-3335	751	53	.	.	PUNCT
ejpam-3335	752	1	proof	proof	NOUN
ejpam-3335	752	2	.	.	PUNCT
ejpam-3335	753	1	assume	assume	VERB
ejpam-3335	753	2	that	that	SCONJ
ejpam-3335	753	3	h	h	NOUN
ejpam-3335	753	4	is	be	AUX
ejpam-3335	753	5	an	an	DET
ejpam-3335	753	6	anti	anti	ADJ
ejpam-3335	753	7	-	-	ADJ
ejpam-3335	753	8	hesitant	hesitant	ADJ
ejpam-3335	753	9	fuzzy	fuzzy	ADJ
ejpam-3335	753	10	up	up	NOUN
ejpam-3335	753	11	-	-	PUNCT
ejpam-3335	753	12	ideal	ideal	NOUN
ejpam-3335	753	13	of	of	ADP
ejpam-3335	753	14	a.	a.	NOUN
ejpam-3335	753	15	let	let	VERB
ejpam-3335	753	16	ε	ε	PROPN
ejpam-3335	753	17	∈	∈	PROPN
ejpam-3335	753	18	p([0	p([0	PROPN
ejpam-3335	753	19	,	,	PUNCT
ejpam-3335	753	20	1	1	NUM
ejpam-3335	753	21	]	]	PUNCT
ejpam-3335	753	22	)	)	PUNCT
ejpam-3335	753	23	be	be	AUX
ejpam-3335	753	24	such	such	ADJ
ejpam-3335	753	25	that	that	SCONJ
ejpam-3335	753	26	e(h	e(h	PROPN
ejpam-3335	753	27	;	;	PUNCT
ejpam-3335	753	28	ε	ε	PROPN
ejpam-3335	753	29	)	)	PUNCT
ejpam-3335	753	30	6=	6=	NOUN
ejpam-3335	753	31	∅	∅	NOUN
ejpam-3335	753	32	but	but	CCONJ
ejpam-3335	753	33	l−(h	l−(h	PROPN
ejpam-3335	753	34	;	;	PUNCT
ejpam-3335	753	35	ε	ε	PROPN
ejpam-3335	753	36	)	)	PUNCT
ejpam-3335	753	37	=	=	NOUN
ejpam-3335	753	38	∅	∅	NOUN
ejpam-3335	753	39	,	,	PUNCT
ejpam-3335	753	40	and	and	CCONJ
ejpam-3335	753	41	let	let	VERB
ejpam-3335	753	42	x	x	SYM
ejpam-3335	753	43	∈	∈	PROPN
ejpam-3335	753	44	a	a	DET
ejpam-3335	753	45	be	be	AUX
ejpam-3335	753	46	such	such	ADJ
ejpam-3335	753	47	that	that	SCONJ
ejpam-3335	753	48	x	x	SYM
ejpam-3335	753	49	∈	∈	PROPN
ejpam-3335	753	50	e(h	e(h	X
ejpam-3335	753	51	;	;	PUNCT
ejpam-3335	753	52	ε	ε	PROPN
ejpam-3335	753	53	)	)	PUNCT
ejpam-3335	753	54	.	.	PUNCT
ejpam-3335	754	1	then	then	ADV
ejpam-3335	754	2	hh(x	hh(x	PUNCT
ejpam-3335	754	3	)	)	PUNCT
ejpam-3335	754	4	=	=	SYM
ejpam-3335	754	5	ε	ε	PROPN
ejpam-3335	754	6	.	.	PUNCT
ejpam-3335	755	1	because	because	SCONJ
ejpam-3335	755	2	h	h	NOUN
ejpam-3335	755	3	is	be	AUX
ejpam-3335	755	4	an	an	DET
ejpam-3335	755	5	anti	anti	ADJ
ejpam-3335	755	6	-	-	ADJ
ejpam-3335	755	7	hesitant	hesitant	ADJ
ejpam-3335	755	8	fuzzy	fuzzy	ADJ
ejpam-3335	755	9	up	up	NOUN
ejpam-3335	755	10	-	-	PUNCT
ejpam-3335	755	11	ideal	ideal	NOUN
ejpam-3335	755	12	of	of	ADP
ejpam-3335	755	13	a	a	PRON
ejpam-3335	755	14	,	,	PUNCT
ejpam-3335	755	15	we	we	PRON
ejpam-3335	755	16	obtain	obtain	VERB
ejpam-3335	755	17	hh(0	hh(0	NOUN
ejpam-3335	755	18	)	)	PUNCT
ejpam-3335	755	19	⊆	⊆	NUM
ejpam-3335	755	20	hh(x	hh(x	NOUN
ejpam-3335	755	21	)	)	PUNCT
ejpam-3335	755	22	=	=	SYM
ejpam-3335	755	23	ε	ε	PROPN
ejpam-3335	755	24	and	and	CCONJ
ejpam-3335	755	25	thus	thus	ADV
ejpam-3335	755	26	0	0	X
ejpam-3335	755	27	∈	∈	PROPN
ejpam-3335	755	28	l(h	l(h	PROPN
ejpam-3335	755	29	;	;	PUNCT
ejpam-3335	755	30	ε	ε	PROPN
ejpam-3335	755	31	)	)	PUNCT
ejpam-3335	755	32	.	.	PUNCT
ejpam-3335	756	1	since	since	SCONJ
ejpam-3335	756	2	l−(h	l−(h	PROPN
ejpam-3335	756	3	;	;	PUNCT
ejpam-3335	756	4	ε	ε	PROPN
ejpam-3335	756	5	)	)	PUNCT
ejpam-3335	756	6	is	be	AUX
ejpam-3335	756	7	empty	empty	ADJ
ejpam-3335	756	8	,	,	PUNCT
ejpam-3335	756	9	we	we	PRON
ejpam-3335	756	10	have	have	VERB
ejpam-3335	756	11	0	0	NUM
ejpam-3335	756	12	∈	∈	PROPN
ejpam-3335	756	13	l(h	l(h	PROPN
ejpam-3335	756	14	;	;	PUNCT
ejpam-3335	756	15	ε	ε	PROPN
ejpam-3335	756	16	)	)	PUNCT
ejpam-3335	756	17	=	=	SYM
ejpam-3335	756	18	e(h	e(h	X
ejpam-3335	756	19	;	;	PUNCT
ejpam-3335	756	20	ε	ε	PROPN
ejpam-3335	756	21	)	)	PUNCT
ejpam-3335	756	22	.	.	PUNCT
ejpam-3335	757	1	next	next	ADV
ejpam-3335	757	2	,	,	PUNCT
ejpam-3335	757	3	let	let	VERB
ejpam-3335	757	4	x	x	PRON
ejpam-3335	757	5	,	,	PUNCT
ejpam-3335	757	6	y	y	PROPN
ejpam-3335	757	7	,	,	PUNCT
ejpam-3335	757	8	z	z	PROPN
ejpam-3335	757	9	∈	∈	PROPN
ejpam-3335	757	10	a	a	DET
ejpam-3335	757	11	be	be	AUX
ejpam-3335	757	12	such	such	ADJ
ejpam-3335	757	13	that	that	SCONJ
ejpam-3335	757	14	x	x	PART
ejpam-3335	757	15	·	·	PUNCT
ejpam-3335	757	16	(	(	PUNCT
ejpam-3335	757	17	y	y	PROPN
ejpam-3335	757	18	·	·	PUNCT
ejpam-3335	757	19	z	z	X
ejpam-3335	757	20	)	)	PUNCT
ejpam-3335	757	21	∈	∈	PROPN
ejpam-3335	757	22	e(h	e(h	X
ejpam-3335	757	23	;	;	PUNCT
ejpam-3335	757	24	ε	ε	PROPN
ejpam-3335	757	25	)	)	PUNCT
ejpam-3335	757	26	and	and	CCONJ
ejpam-3335	757	27	y	y	PROPN
ejpam-3335	757	28	∈	∈	PROPN
ejpam-3335	757	29	e(h	e(h	X
ejpam-3335	757	30	;	;	PUNCT
ejpam-3335	757	31	ε	ε	PROPN
ejpam-3335	757	32	)	)	PUNCT
ejpam-3335	757	33	.	.	PUNCT
ejpam-3335	758	1	then	then	ADV
ejpam-3335	758	2	hh(x	hh(x	PUNCT
ejpam-3335	758	3	·	·	PUNCT
ejpam-3335	758	4	(	(	PUNCT
ejpam-3335	758	5	y	y	PROPN
ejpam-3335	758	6	·	·	PUNCT
ejpam-3335	758	7	z	z	NOUN
ejpam-3335	758	8	)	)	PUNCT
ejpam-3335	758	9	)	)	PUNCT
ejpam-3335	758	10	=	=	SYM
ejpam-3335	758	11	ε	ε	PROPN
ejpam-3335	758	12	and	and	CCONJ
ejpam-3335	758	13	hh(y	hh(y	NOUN
ejpam-3335	758	14	)	)	PUNCT
ejpam-3335	758	15	=	=	SYM
ejpam-3335	758	16	ε	ε	PROPN
ejpam-3335	758	17	.	.	PUNCT
ejpam-3335	759	1	because	because	SCONJ
ejpam-3335	759	2	h	h	NOUN
ejpam-3335	759	3	is	be	AUX
ejpam-3335	759	4	an	an	DET
ejpam-3335	759	5	anti	anti	ADJ
ejpam-3335	759	6	-	-	ADJ
ejpam-3335	759	7	hesitant	hesitant	ADJ
ejpam-3335	759	8	fuzzy	fuzzy	ADJ
ejpam-3335	759	9	up	up	NOUN
ejpam-3335	759	10	-	-	PUNCT
ejpam-3335	759	11	ideal	ideal	NOUN
ejpam-3335	759	12	of	of	ADP
ejpam-3335	759	13	a	a	PRON
ejpam-3335	759	14	,	,	PUNCT
ejpam-3335	759	15	we	we	PRON
ejpam-3335	759	16	have	have	VERB
ejpam-3335	759	17	hh(x	hh(x	X
ejpam-3335	759	18	·	·	PUNCT
ejpam-3335	759	19	z	z	X
ejpam-3335	759	20	)	)	PUNCT
ejpam-3335	759	21	⊆	⊆	NUM
ejpam-3335	759	22	hh(x	hh(x	X
ejpam-3335	759	23	·	·	PUNCT
ejpam-3335	759	24	(	(	PUNCT
ejpam-3335	759	25	y	y	PROPN
ejpam-3335	759	26	·	·	PUNCT
ejpam-3335	759	27	z	z	NOUN
ejpam-3335	759	28	)	)	PUNCT
ejpam-3335	759	29	)	)	PUNCT
ejpam-3335	759	30	∪	∪	ADP
ejpam-3335	759	31	hh(y	hh(y	NOUN
ejpam-3335	759	32	)	)	PUNCT
ejpam-3335	759	33	=	=	SYM
ejpam-3335	759	34	ε	ε	PROPN
ejpam-3335	759	35	.	.	PUNCT
ejpam-3335	759	36	thus	thus	ADV
ejpam-3335	759	37	x	x	X
ejpam-3335	759	38	·	·	PUNCT
ejpam-3335	759	39	z	z	X
ejpam-3335	759	40	∈	∈	PROPN
ejpam-3335	759	41	l(h	l(h	PROPN
ejpam-3335	759	42	;	;	PUNCT
ejpam-3335	759	43	ε	ε	PROPN
ejpam-3335	759	44	)	)	PUNCT
ejpam-3335	759	45	.	.	PUNCT
ejpam-3335	760	1	since	since	SCONJ
ejpam-3335	760	2	l−(h	l−(h	PROPN
ejpam-3335	760	3	;	;	PUNCT
ejpam-3335	760	4	ε	ε	PROPN
ejpam-3335	760	5	)	)	PUNCT
ejpam-3335	760	6	is	be	AUX
ejpam-3335	760	7	empty	empty	ADJ
ejpam-3335	760	8	,	,	PUNCT
ejpam-3335	760	9	we	we	PRON
ejpam-3335	760	10	obtain	obtain	VERB
ejpam-3335	760	11	l(h	l(h	PROPN
ejpam-3335	760	12	;	;	PUNCT
ejpam-3335	760	13	ε	ε	PROPN
ejpam-3335	760	14	)	)	PUNCT
ejpam-3335	760	15	=	=	SYM
ejpam-3335	761	1	e(h	e(h	X
ejpam-3335	761	2	;	;	PUNCT
ejpam-3335	761	3	ε	ε	PROPN
ejpam-3335	761	4	)	)	PUNCT
ejpam-3335	761	5	.	.	PUNCT
ejpam-3335	762	1	therefore	therefore	ADV
ejpam-3335	762	2	,	,	PUNCT
ejpam-3335	762	3	x	x	X
ejpam-3335	762	4	·	·	PUNCT
ejpam-3335	762	5	z	z	X
ejpam-3335	762	6	∈	∈	PROPN
ejpam-3335	762	7	e(h	e(h	X
ejpam-3335	762	8	;	;	PUNCT
ejpam-3335	762	9	ε	ε	PROPN
ejpam-3335	762	10	)	)	PUNCT
ejpam-3335	762	11	.	.	PUNCT
ejpam-3335	763	1	hence	hence	ADV
ejpam-3335	763	2	,	,	PUNCT
ejpam-3335	763	3	e(h	e(h	PROPN
ejpam-3335	763	4	;	;	PUNCT
ejpam-3335	763	5	ε	ε	PROPN
ejpam-3335	763	6	)	)	PUNCT
ejpam-3335	763	7	is	be	AUX
ejpam-3335	763	8	a	a	DET
ejpam-3335	763	9	up	up	ADJ
ejpam-3335	763	10	-	-	PUNCT
ejpam-3335	763	11	ideal	ideal	NOUN
ejpam-3335	763	12	of	of	ADP
ejpam-3335	763	13	a.	a.	NOUN
ejpam-3335	763	14	the	the	DET
ejpam-3335	763	15	converse	converse	NOUN
ejpam-3335	763	16	of	of	ADP
ejpam-3335	763	17	theorem	theorem	NOUN
ejpam-3335	763	18	25	25	NUM
ejpam-3335	763	19	is	be	AUX
ejpam-3335	763	20	not	not	PART
ejpam-3335	763	21	true	true	ADJ
ejpam-3335	763	22	in	in	ADP
ejpam-3335	763	23	general	general	ADJ
ejpam-3335	763	24	.	.	PUNCT
ejpam-3335	764	1	by	by	ADP
ejpam-3335	764	2	example	example	NOUN
ejpam-3335	764	3	16	16	NUM
ejpam-3335	764	4	,	,	PUNCT
ejpam-3335	764	5	we	we	PRON
ejpam-3335	764	6	still	still	ADV
ejpam-3335	764	7	have	have	VERB
ejpam-3335	764	8	e(h	e(h	NUM
ejpam-3335	764	9	;	;	PUNCT
ejpam-3335	764	10	ε	ε	PROPN
ejpam-3335	764	11	)	)	PUNCT
ejpam-3335	764	12	=	=	SYM
ejpam-3335	764	13	{	{	PUNCT
ejpam-3335	764	14	0	0	NUM
ejpam-3335	764	15	}	}	PUNCT
ejpam-3335	764	16	is	be	AUX
ejpam-3335	764	17	a	a	DET
ejpam-3335	764	18	up	up	ADJ
ejpam-3335	764	19	-	-	PUNCT
ejpam-3335	764	20	ideal	ideal	NOUN
ejpam-3335	764	21	of	of	ADP
ejpam-3335	764	22	a.	a.	NOUN
ejpam-3335	764	23	since	since	SCONJ
ejpam-3335	764	24	hh(0	hh(0	NOUN
ejpam-3335	764	25	·	·	PUNCT
ejpam-3335	764	26	1	1	X
ejpam-3335	764	27	)	)	PUNCT
ejpam-3335	764	28	=	=	PUNCT
ejpam-3335	764	29	hh(1	hh(1	NOUN
ejpam-3335	764	30	)	)	PUNCT
ejpam-3335	764	31	=	=	PUNCT
ejpam-3335	765	1	[	[	X
ejpam-3335	765	2	0	0	NUM
ejpam-3335	765	3	,	,	PUNCT
ejpam-3335	765	4	0.6	0.6	NUM
ejpam-3335	765	5	]	]	PUNCT
ejpam-3335	765	6	*	*	PUNCT
ejpam-3335	766	1	[	[	X
ejpam-3335	766	2	0	0	NUM
ejpam-3335	766	3	,	,	PUNCT
ejpam-3335	766	4	0.3	0.3	NUM
ejpam-3335	766	5	]	]	PUNCT
ejpam-3335	766	6	=	=	SYM
ejpam-3335	766	7	hh(0	hh(0	NOUN
ejpam-3335	766	8	)	)	PUNCT
ejpam-3335	766	9	∪	∪	PROPN
ejpam-3335	766	10	hh(2	hh(2	NOUN
ejpam-3335	766	11	)	)	PUNCT
ejpam-3335	766	12	=	=	SYM
ejpam-3335	766	13	hh(0	hh(0	NOUN
ejpam-3335	766	14	·	·	PUNCT
ejpam-3335	766	15	(	(	PUNCT
ejpam-3335	766	16	2	2	NUM
ejpam-3335	766	17	·	·	SYM
ejpam-3335	766	18	1	1	NUM
ejpam-3335	766	19	)	)	PUNCT
ejpam-3335	766	20	)	)	PUNCT
ejpam-3335	766	21	∪	∪	ADP
ejpam-3335	766	22	hh(2	hh(2	PROPN
ejpam-3335	766	23	)	)	PUNCT
ejpam-3335	766	24	,	,	PUNCT
ejpam-3335	766	25	we	we	PRON
ejpam-3335	766	26	have	have	VERB
ejpam-3335	766	27	h	h	NOUN
ejpam-3335	766	28	is	be	AUX
ejpam-3335	766	29	not	not	PART
ejpam-3335	766	30	an	an	DET
ejpam-3335	766	31	anti	anti	ADJ
ejpam-3335	766	32	-	-	ADJ
ejpam-3335	766	33	hesitant	hesitant	ADJ
ejpam-3335	766	34	fuzzy	fuzzy	ADJ
ejpam-3335	766	35	up	up	NOUN
ejpam-3335	766	36	-	-	PUNCT
ejpam-3335	766	37	ideal	ideal	NOUN
ejpam-3335	766	38	of	of	ADP
ejpam-3335	766	39	a.	a.	NOUN
ejpam-3335	766	40	theorem	theorem	NOUN
ejpam-3335	766	41	26	26	NUM
ejpam-3335	766	42	.	.	PUNCT
ejpam-3335	767	1	a	a	DET
ejpam-3335	767	2	hesitant	hesitant	ADJ
ejpam-3335	767	3	fuzzy	fuzzy	ADJ
ejpam-3335	767	4	set	set	VERB
ejpam-3335	767	5	h	h	NOUN
ejpam-3335	767	6	on	on	ADP
ejpam-3335	767	7	a	a	PRON
ejpam-3335	767	8	is	be	AUX
ejpam-3335	767	9	an	an	DET
ejpam-3335	767	10	anti	anti	ADJ
ejpam-3335	767	11	-	-	ADJ
ejpam-3335	767	12	hesitant	hesitant	ADJ
ejpam-3335	767	13	fuzzy	fuzzy	ADJ
ejpam-3335	767	14	strongly	strongly	ADV
ejpam-3335	767	15	up	up	ADP
ejpam-3335	767	16	-	-	PUNCT
ejpam-3335	767	17	ideal	ideal	NOUN
ejpam-3335	767	18	of	of	ADP
ejpam-3335	767	19	a	a	DET
ejpam-3335	767	20	if	if	NOUN
ejpam-3335	767	21	and	and	CCONJ
ejpam-3335	767	22	only	only	ADV
ejpam-3335	767	23	if	if	SCONJ
ejpam-3335	767	24	e(h	e(h	PROPN
ejpam-3335	767	25	;	;	PUNCT
ejpam-3335	767	26	hh(0	hh(0	NOUN
ejpam-3335	767	27	)	)	PUNCT
ejpam-3335	767	28	)	)	PUNCT
ejpam-3335	767	29	is	be	AUX
ejpam-3335	767	30	a	a	DET
ejpam-3335	767	31	strongly	strongly	ADV
ejpam-3335	767	32	up	up	ADJ
ejpam-3335	767	33	-	-	PUNCT
ejpam-3335	767	34	ideal	ideal	NOUN
ejpam-3335	767	35	of	of	ADP
ejpam-3335	767	36	a.	a.	NOUN
ejpam-3335	767	37	proof	proof	NOUN
ejpam-3335	767	38	.	.	PUNCT
ejpam-3335	768	1	assume	assume	VERB
ejpam-3335	768	2	that	that	SCONJ
ejpam-3335	768	3	h	h	NOUN
ejpam-3335	768	4	is	be	AUX
ejpam-3335	768	5	an	an	DET
ejpam-3335	768	6	anti	anti	ADJ
ejpam-3335	768	7	-	-	ADJ
ejpam-3335	768	8	hesitant	hesitant	ADJ
ejpam-3335	768	9	fuzzy	fuzzy	ADJ
ejpam-3335	768	10	strongly	strongly	ADV
ejpam-3335	768	11	up	up	ADP
ejpam-3335	768	12	-	-	PUNCT
ejpam-3335	768	13	ideal	ideal	NOUN
ejpam-3335	768	14	of	of	ADP
ejpam-3335	768	15	a.	a.	NOUN
ejpam-3335	768	16	by	by	ADP
ejpam-3335	768	17	theorem	theorem	NOUN
ejpam-3335	768	18	3	3	NUM
ejpam-3335	768	19	,	,	PUNCT
ejpam-3335	768	20	we	we	PRON
ejpam-3335	768	21	obtain	obtain	VERB
ejpam-3335	768	22	h	h	NOUN
ejpam-3335	768	23	is	be	AUX
ejpam-3335	768	24	a	a	DET
ejpam-3335	768	25	constant	constant	ADJ
ejpam-3335	768	26	hesitant	hesitant	ADJ
ejpam-3335	768	27	fuzzy	fuzzy	ADJ
ejpam-3335	768	28	set	set	VERB
ejpam-3335	768	29	on	on	ADP
ejpam-3335	768	30	a	a	DET
ejpam-3335	768	31	and	and	CCONJ
ejpam-3335	768	32	so	so	ADV
ejpam-3335	768	33	hh(x	hh(x	PUNCT
ejpam-3335	768	34	)	)	PUNCT
ejpam-3335	769	1	=	=	SYM
ejpam-3335	769	2	hh(0	hh(0	NOUN
ejpam-3335	769	3	)	)	PUNCT
ejpam-3335	769	4	for	for	ADP
ejpam-3335	769	5	all	all	DET
ejpam-3335	769	6	x	x	SYM
ejpam-3335	769	7	∈	∈	NOUN
ejpam-3335	769	8	a.	a.	NOUN
ejpam-3335	769	9	then	then	ADV
ejpam-3335	769	10	e(h	e(h	PROPN
ejpam-3335	769	11	;	;	PUNCT
ejpam-3335	769	12	hh(0	hh(0	NOUN
ejpam-3335	769	13	)	)	PUNCT
ejpam-3335	769	14	)	)	PUNCT
ejpam-3335	770	1	=	=	SYM
ejpam-3335	770	2	a.	a.	NOUN
ejpam-3335	770	3	hence	hence	ADV
ejpam-3335	770	4	,	,	PUNCT
ejpam-3335	770	5	e(h	e(h	PROPN
ejpam-3335	770	6	;	;	PUNCT
ejpam-3335	770	7	hh(0	hh(0	NOUN
ejpam-3335	770	8	)	)	PUNCT
ejpam-3335	770	9	)	)	PUNCT
ejpam-3335	770	10	is	be	AUX
ejpam-3335	770	11	a	a	DET
ejpam-3335	770	12	strongly	strongly	ADV
ejpam-3335	770	13	up	up	ADJ
ejpam-3335	770	14	-	-	PUNCT
ejpam-3335	770	15	ideal	ideal	NOUN
ejpam-3335	770	16	of	of	ADP
ejpam-3335	770	17	a.	a.	NOUN
ejpam-3335	770	18	conversely	conversely	ADV
ejpam-3335	770	19	,	,	PUNCT
ejpam-3335	770	20	assume	assume	VERB
ejpam-3335	770	21	that	that	SCONJ
ejpam-3335	770	22	e(h	e(h	PROPN
ejpam-3335	770	23	;	;	PUNCT
ejpam-3335	770	24	hh(0	hh(0	NOUN
ejpam-3335	770	25	)	)	PUNCT
ejpam-3335	770	26	)	)	PUNCT
ejpam-3335	770	27	is	be	AUX
ejpam-3335	770	28	a	a	DET
ejpam-3335	770	29	strongly	strongly	ADV
ejpam-3335	770	30	up	up	ADJ
ejpam-3335	770	31	-	-	PUNCT
ejpam-3335	770	32	ideal	ideal	NOUN
ejpam-3335	770	33	of	of	ADP
ejpam-3335	770	34	a.	a.	NOUN
ejpam-3335	770	35	then	then	ADV
ejpam-3335	770	36	e(h	e(h	PROPN
ejpam-3335	770	37	;	;	PUNCT
ejpam-3335	770	38	hh(0	hh(0	NOUN
ejpam-3335	770	39	)	)	PUNCT
ejpam-3335	770	40	)	)	PUNCT
ejpam-3335	771	1	=	=	PUNCT
ejpam-3335	772	1	a	a	PRON
ejpam-3335	772	2	and	and	CCONJ
ejpam-3335	772	3	so	so	ADV
ejpam-3335	772	4	hh(x	hh(x	PUNCT
ejpam-3335	772	5	)	)	PUNCT
ejpam-3335	773	1	=	=	SYM
ejpam-3335	773	2	hh(0	hh(0	NOUN
ejpam-3335	773	3	)	)	PUNCT
ejpam-3335	773	4	for	for	ADP
ejpam-3335	773	5	all	all	DET
ejpam-3335	773	6	x	x	SYM
ejpam-3335	773	7	∈	∈	PROPN
ejpam-3335	773	8	a.	a.	NOUN
ejpam-3335	773	9	therefore	therefore	ADV
ejpam-3335	773	10	,	,	PUNCT
ejpam-3335	773	11	h	h	NOUN
ejpam-3335	773	12	is	be	AUX
ejpam-3335	773	13	a	a	DET
ejpam-3335	773	14	constant	constant	ADJ
ejpam-3335	773	15	hesitant	hesitant	ADJ
ejpam-3335	773	16	fuzzy	fuzzy	ADJ
ejpam-3335	773	17	set	set	VERB
ejpam-3335	773	18	on	on	ADP
ejpam-3335	773	19	a.	a.	NOUN
ejpam-3335	773	20	by	by	ADP
ejpam-3335	773	21	theorem	theorem	NOUN
ejpam-3335	773	22	3	3	NUM
ejpam-3335	773	23	,	,	PUNCT
ejpam-3335	773	24	h	h	NOUN
ejpam-3335	773	25	is	be	AUX
ejpam-3335	773	26	an	an	DET
ejpam-3335	773	27	anti	anti	ADJ
ejpam-3335	773	28	-	-	ADJ
ejpam-3335	773	29	hesitant	hesitant	ADJ
ejpam-3335	773	30	fuzzy	fuzzy	ADJ
ejpam-3335	773	31	strongly	strongly	ADV
ejpam-3335	773	32	up	up	ADP
ejpam-3335	773	33	-	-	PUNCT
ejpam-3335	773	34	ideal	ideal	NOUN
ejpam-3335	773	35	of	of	ADP
ejpam-3335	773	36	a.	a.	NOUN
ejpam-3335	773	37	moreover	moreover	ADV
ejpam-3335	773	38	,	,	PUNCT
ejpam-3335	773	39	we	we	PRON
ejpam-3335	773	40	still	still	ADV
ejpam-3335	773	41	obtain	obtain	VERB
ejpam-3335	773	42	theorems	theorem	NOUN
ejpam-3335	773	43	of	of	ADP
ejpam-3335	773	44	equal	equal	ADJ
ejpam-3335	773	45	ε	ε	NOUN
ejpam-3335	773	46	-	-	PUNCT
ejpam-3335	773	47	level	level	NOUN
ejpam-3335	773	48	subsets	subset	NOUN
ejpam-3335	773	49	with	with	ADP
ejpam-3335	773	50	a	a	DET
ejpam-3335	773	51	hesitant	hesitant	ADJ
ejpam-3335	773	52	fuzzy	fuzzy	ADJ
ejpam-3335	773	53	up	up	NOUN
ejpam-3335	773	54	-	-	PUNCT
ejpam-3335	773	55	subalgebra	subalgebra	NOUN
ejpam-3335	773	56	.	.	PUNCT
ejpam-3335	774	1	(	(	PUNCT
ejpam-3335	774	2	resp	resp	NOUN
ejpam-3335	774	3	.	.	PUNCT
ejpam-3335	775	1	,	,	PUNCT
ejpam-3335	775	2	hesitant	hesitant	ADJ
ejpam-3335	775	3	fuzzy	fuzzy	ADJ
ejpam-3335	775	4	up	up	NOUN
ejpam-3335	775	5	-	-	PUNCT
ejpam-3335	775	6	filter	filter	NOUN
ejpam-3335	775	7	,	,	PUNCT
ejpam-3335	775	8	hesitant	hesitant	ADJ
ejpam-3335	775	9	fuzzy	fuzzy	ADJ
ejpam-3335	775	10	up	up	ADP
ejpam-3335	775	11	-	-	PUNCT
ejpam-3335	775	12	ideal	ideal	ADJ
ejpam-3335	775	13	,	,	PUNCT
ejpam-3335	775	14	hesitant	hesitant	ADJ
ejpam-3335	775	15	fuzzy	fuzzy	ADJ
ejpam-3335	775	16	strongly	strongly	ADV
ejpam-3335	775	17	up	up	ADP
ejpam-3335	775	18	-	-	PUNCT
ejpam-3335	775	19	ideal	ideal	NOUN
ejpam-3335	775	20	)	)	PUNCT
ejpam-3335	775	21	theorem	theorem	VERB
ejpam-3335	775	22	27	27	NUM
ejpam-3335	775	23	.	.	PUNCT
ejpam-3335	776	1	if	if	SCONJ
ejpam-3335	776	2	a	a	DET
ejpam-3335	776	3	hesitant	hesitant	ADJ
ejpam-3335	776	4	fuzzy	fuzzy	ADJ
ejpam-3335	776	5	set	set	VERB
ejpam-3335	776	6	h	h	NOUN
ejpam-3335	776	7	on	on	ADP
ejpam-3335	776	8	a	a	PRON
ejpam-3335	776	9	is	be	AUX
ejpam-3335	776	10	an	an	DET
ejpam-3335	776	11	anti	anti	ADJ
ejpam-3335	776	12	-	-	ADJ
ejpam-3335	776	13	hesitant	hesitant	ADJ
ejpam-3335	776	14	fuzzy	fuzzy	ADJ
ejpam-3335	776	15	up	up	NOUN
ejpam-3335	776	16	-	-	PUNCT
ejpam-3335	776	17	subalgebra	subalgebra	NOUN
ejpam-3335	776	18	of	of	ADP
ejpam-3335	776	19	a	a	PRON
ejpam-3335	776	20	,	,	PUNCT
ejpam-3335	776	21	then	then	ADV
ejpam-3335	776	22	for	for	ADP
ejpam-3335	776	23	all	all	DET
ejpam-3335	776	24	ε	ε	PROPN
ejpam-3335	776	25	∈	∈	PROPN
ejpam-3335	776	26	p([0	p([0	NOUN
ejpam-3335	776	27	,	,	PUNCT
ejpam-3335	776	28	1	1	NUM
ejpam-3335	776	29	]	]	NUM
ejpam-3335	776	30	)	)	PUNCT
ejpam-3335	776	31	,	,	PUNCT
ejpam-3335	776	32	a	a	DET
ejpam-3335	776	33	nonempty	nonempty	NOUN
ejpam-3335	776	34	subset	subset	VERB
ejpam-3335	776	35	e(h	e(h	PROPN
ejpam-3335	776	36	;	;	PUNCT
ejpam-3335	776	37	ε	ε	PROPN
ejpam-3335	776	38	)	)	PUNCT
ejpam-3335	776	39	of	of	ADP
ejpam-3335	776	40	a	a	PRON
ejpam-3335	776	41	is	be	AUX
ejpam-3335	776	42	a	a	DET
ejpam-3335	776	43	up	up	ADJ
ejpam-3335	776	44	-	-	PUNCT
ejpam-3335	776	45	subalgebra	subalgebra	NOUN
ejpam-3335	776	46	of	of	ADP
ejpam-3335	776	47	a	a	DET
ejpam-3335	776	48	where	where	SCONJ
ejpam-3335	776	49	u+(h	u+(h	NOUN
ejpam-3335	776	50	;	;	PUNCT
ejpam-3335	776	51	ε	ε	PROPN
ejpam-3335	776	52	)	)	PUNCT
ejpam-3335	776	53	is	be	AUX
ejpam-3335	776	54	empty	empty	ADJ
ejpam-3335	776	55	.	.	PUNCT
ejpam-3335	777	1	proof	proof	NOUN
ejpam-3335	777	2	.	.	PUNCT
ejpam-3335	778	1	assume	assume	VERB
ejpam-3335	778	2	that	that	SCONJ
ejpam-3335	778	3	h	h	NOUN
ejpam-3335	778	4	is	be	AUX
ejpam-3335	778	5	an	an	DET
ejpam-3335	778	6	anti	anti	ADJ
ejpam-3335	778	7	-	-	ADJ
ejpam-3335	778	8	hesitant	hesitant	ADJ
ejpam-3335	778	9	fuzzy	fuzzy	ADJ
ejpam-3335	778	10	up	up	NOUN
ejpam-3335	778	11	-	-	PUNCT
ejpam-3335	778	12	subalgebra	subalgebra	NOUN
ejpam-3335	778	13	of	of	ADP
ejpam-3335	778	14	a.	a.	NOUN
ejpam-3335	778	15	let	let	VERB
ejpam-3335	778	16	ε	ε	PROPN
ejpam-3335	778	17	∈	∈	PROPN
ejpam-3335	778	18	p([0	p([0	PROPN
ejpam-3335	778	19	,	,	PUNCT
ejpam-3335	778	20	1	1	NUM
ejpam-3335	778	21	]	]	PUNCT
ejpam-3335	778	22	)	)	PUNCT
ejpam-3335	778	23	be	be	AUX
ejpam-3335	778	24	such	such	ADJ
ejpam-3335	778	25	that	that	SCONJ
ejpam-3335	778	26	e(h	e(h	PROPN
ejpam-3335	778	27	;	;	PUNCT
ejpam-3335	778	28	ε	ε	PROPN
ejpam-3335	778	29	)	)	PUNCT
ejpam-3335	778	30	6=	6=	NOUN
ejpam-3335	778	31	∅	∅	NOUN
ejpam-3335	778	32	but	but	CCONJ
ejpam-3335	778	33	u+(h	u+(h	NUM
ejpam-3335	778	34	;	;	PUNCT
ejpam-3335	778	35	ε	ε	PROPN
ejpam-3335	778	36	)	)	PUNCT
ejpam-3335	778	37	=	=	NOUN
ejpam-3335	778	38	∅	∅	NOUN
ejpam-3335	778	39	,	,	PUNCT
ejpam-3335	778	40	and	and	CCONJ
ejpam-3335	778	41	let	let	VERB
ejpam-3335	778	42	x	x	PRON
ejpam-3335	778	43	,	,	PUNCT
ejpam-3335	778	44	y	y	PROPN
ejpam-3335	778	45	∈	∈	PROPN
ejpam-3335	778	46	a	a	DET
ejpam-3335	778	47	be	be	AUX
ejpam-3335	778	48	such	such	ADJ
ejpam-3335	778	49	that	that	SCONJ
ejpam-3335	778	50	x	x	SYM
ejpam-3335	778	51	∈	∈	PROPN
ejpam-3335	778	52	e(h	e(h	X
ejpam-3335	778	53	;	;	PUNCT
ejpam-3335	778	54	ε	ε	PROPN
ejpam-3335	778	55	)	)	PUNCT
ejpam-3335	778	56	and	and	CCONJ
ejpam-3335	778	57	y	y	PROPN
ejpam-3335	778	58	∈	∈	PROPN
ejpam-3335	778	59	e(h	e(h	X
ejpam-3335	778	60	;	;	PUNCT
ejpam-3335	778	61	ε	ε	PROPN
ejpam-3335	778	62	)	)	PUNCT
ejpam-3335	778	63	.	.	PUNCT
ejpam-3335	779	1	then	then	ADV
ejpam-3335	779	2	hh(x	hh(x	PUNCT
ejpam-3335	779	3	)	)	PUNCT
ejpam-3335	779	4	=	=	SYM
ejpam-3335	779	5	ε	ε	PROPN
ejpam-3335	779	6	and	and	CCONJ
ejpam-3335	779	7	hh(y	hh(y	NOUN
ejpam-3335	779	8	)	)	PUNCT
ejpam-3335	780	1	=	=	SYM
ejpam-3335	780	2	ε	ε	PROPN
ejpam-3335	780	3	.	.	PUNCT
ejpam-3335	781	1	since	since	SCONJ
ejpam-3335	781	2	h	h	NOUN
ejpam-3335	781	3	is	be	AUX
ejpam-3335	781	4	an	an	DET
ejpam-3335	781	5	anti	anti	ADJ
ejpam-3335	781	6	-	-	ADJ
ejpam-3335	781	7	hesitant	hesitant	ADJ
ejpam-3335	781	8	fuzzy	fuzzy	ADJ
ejpam-3335	781	9	up	up	NOUN
ejpam-3335	781	10	-	-	PUNCT
ejpam-3335	781	11	subalgebra	subalgebra	NOUN
ejpam-3335	781	12	of	of	ADP
ejpam-3335	781	13	a	a	PRON
ejpam-3335	781	14	,	,	PUNCT
ejpam-3335	781	15	we	we	PRON
ejpam-3335	781	16	have	have	VERB
ejpam-3335	781	17	hh(x	hh(x	X
ejpam-3335	781	18	·	·	PUNCT
ejpam-3335	781	19	y	y	X
ejpam-3335	781	20	)	)	PUNCT
ejpam-3335	781	21	⊇	⊇	NOUN
ejpam-3335	781	22	hh(x	hh(x	X
ejpam-3335	781	23	)	)	PUNCT
ejpam-3335	781	24	∩	∩	NOUN
ejpam-3335	781	25	hh(y	hh(y	NUM
ejpam-3335	781	26	)	)	PUNCT
ejpam-3335	781	27	=	=	SYM
ejpam-3335	781	28	ε	ε	PROPN
ejpam-3335	781	29	.	.	PUNCT
ejpam-3335	781	30	thus	thus	ADV
ejpam-3335	781	31	x	x	X
ejpam-3335	781	32	·	·	PUNCT
ejpam-3335	781	33	y	y	SYM
ejpam-3335	781	34	∈	∈	PROPN
ejpam-3335	781	35	u(h	u(h	PROPN
ejpam-3335	781	36	;	;	PUNCT
ejpam-3335	781	37	ε	ε	PROPN
ejpam-3335	781	38	)	)	PUNCT
ejpam-3335	781	39	.	.	PUNCT
ejpam-3335	782	1	since	since	SCONJ
ejpam-3335	782	2	u+(h	u+(h	PROPN
ejpam-3335	782	3	;	;	PUNCT
ejpam-3335	782	4	ε	ε	PROPN
ejpam-3335	782	5	)	)	PUNCT
ejpam-3335	782	6	is	be	AUX
ejpam-3335	782	7	empty	empty	ADJ
ejpam-3335	782	8	,	,	PUNCT
ejpam-3335	782	9	we	we	PRON
ejpam-3335	782	10	obtain	obtain	VERB
ejpam-3335	782	11	u(h	u(h	PROPN
ejpam-3335	782	12	;	;	PUNCT
ejpam-3335	782	13	ε	ε	PROPN
ejpam-3335	782	14	)	)	PUNCT
ejpam-3335	782	15	=	=	PUNCT
ejpam-3335	783	1	u+(h	u+(h	PROPN
ejpam-3335	783	2	;	;	PUNCT
ejpam-3335	783	3	ε	ε	PROPN
ejpam-3335	783	4	)	)	PUNCT
ejpam-3335	783	5	∪	∪	ADP
ejpam-3335	783	6	e(h	e(h	PROPN
ejpam-3335	783	7	;	;	PUNCT
ejpam-3335	783	8	ε	ε	PROPN
ejpam-3335	783	9	)	)	PUNCT
ejpam-3335	783	10	=	=	NOUN
ejpam-3335	783	11	∅	∅	NOUN
ejpam-3335	783	12	∪	∪	ADP
ejpam-3335	783	13	e(h	e(h	PROPN
ejpam-3335	783	14	;	;	PUNCT
ejpam-3335	783	15	ε	ε	PROPN
ejpam-3335	783	16	)	)	PUNCT
ejpam-3335	783	17	=	=	SYM
ejpam-3335	783	18	e(h	e(h	X
ejpam-3335	783	19	;	;	PUNCT
ejpam-3335	783	20	ε	ε	PROPN
ejpam-3335	783	21	)	)	PUNCT
ejpam-3335	783	22	.	.	PUNCT
ejpam-3335	784	1	therefore	therefore	ADV
ejpam-3335	784	2	,	,	PUNCT
ejpam-3335	784	3	x	x	X
ejpam-3335	784	4	·	·	PUNCT
ejpam-3335	784	5	y	y	PROPN
ejpam-3335	784	6	∈	∈	PROPN
ejpam-3335	784	7	e(h	e(h	X
ejpam-3335	784	8	;	;	PUNCT
ejpam-3335	784	9	ε	ε	PROPN
ejpam-3335	784	10	)	)	PUNCT
ejpam-3335	784	11	.	.	PUNCT
ejpam-3335	785	1	hence	hence	ADV
ejpam-3335	785	2	,	,	PUNCT
ejpam-3335	785	3	e(h	e(h	PROPN
ejpam-3335	785	4	;	;	PUNCT
ejpam-3335	785	5	ε	ε	PROPN
ejpam-3335	785	6	)	)	PUNCT
ejpam-3335	785	7	is	be	AUX
ejpam-3335	785	8	a	a	DET
ejpam-3335	785	9	up	up	ADJ
ejpam-3335	785	10	-	-	PUNCT
ejpam-3335	785	11	subalgebra	subalgebra	NOUN
ejpam-3335	785	12	of	of	ADP
ejpam-3335	785	13	a.	a.	NOUN
ejpam-3335	785	14	the	the	DET
ejpam-3335	785	15	following	follow	VERB
ejpam-3335	785	16	example	example	NOUN
ejpam-3335	785	17	show	show	VERB
ejpam-3335	785	18	that	that	SCONJ
ejpam-3335	785	19	the	the	DET
ejpam-3335	785	20	converse	converse	NOUN
ejpam-3335	785	21	of	of	ADP
ejpam-3335	785	22	theorem	theorem	ADJ
ejpam-3335	785	23	27	27	NUM
ejpam-3335	785	24	is	be	AUX
ejpam-3335	785	25	not	not	PART
ejpam-3335	785	26	true	true	ADJ
ejpam-3335	785	27	in	in	ADP
ejpam-3335	785	28	general	general	ADJ
ejpam-3335	785	29	.	.	PUNCT
ejpam-3335	785	30	example	example	NOUN
ejpam-3335	786	1	17	17	NUM
ejpam-3335	786	2	.	.	PUNCT
ejpam-3335	787	1	let	let	VERB
ejpam-3335	787	2	a	a	PRON
ejpam-3335	787	3	=	=	PUNCT
ejpam-3335	787	4	{	{	PUNCT
ejpam-3335	787	5	0	0	NUM
ejpam-3335	787	6	,	,	PUNCT
ejpam-3335	787	7	1	1	NUM
ejpam-3335	787	8	,	,	PUNCT
ejpam-3335	787	9	2	2	NUM
ejpam-3335	787	10	,	,	PUNCT
ejpam-3335	787	11	3	3	NUM
ejpam-3335	787	12	}	}	PUNCT
ejpam-3335	787	13	be	be	AUX
ejpam-3335	787	14	a	a	DET
ejpam-3335	787	15	set	set	NOUN
ejpam-3335	787	16	with	with	ADP
ejpam-3335	787	17	a	a	DET
ejpam-3335	787	18	binary	binary	ADJ
ejpam-3335	787	19	operation	operation	NOUN
ejpam-3335	787	20	·	·	PUNCT
ejpam-3335	787	21	defined	define	VERB
ejpam-3335	787	22	by	by	ADP
ejpam-3335	787	23	the	the	DET
ejpam-3335	787	24	following	follow	VERB
ejpam-3335	787	25	p.	p.	PROPN
ejpam-3335	787	26	mosrijai	mosrijai	PROPN
ejpam-3335	787	27	,	,	PUNCT
ejpam-3335	787	28	a.	a.	NOUN
ejpam-3335	787	29	iampan	iampan	PROPN
ejpam-3335	787	30	/	/	SYM
ejpam-3335	787	31	eur	eur	PROPN
ejpam-3335	787	32	.	.	PUNCT
ejpam-3335	788	1	j.	j.	PROPN
ejpam-3335	788	2	pure	pure	PROPN
ejpam-3335	788	3	appl	appl	PROPN
ejpam-3335	788	4	.	.	PROPN
ejpam-3335	788	5	math	math	PROPN
ejpam-3335	788	6	,	,	PUNCT
ejpam-3335	788	7	11	11	NUM
ejpam-3335	788	8	(	(	PUNCT
ejpam-3335	788	9	4	4	NUM
ejpam-3335	788	10	)	)	PUNCT
ejpam-3335	788	11	(	(	PUNCT
ejpam-3335	788	12	2018	2018	NUM
ejpam-3335	788	13	)	)	PUNCT
ejpam-3335	788	14	,	,	PUNCT
ejpam-3335	788	15	976	976	NUM
ejpam-3335	788	16	-	-	SYM
ejpam-3335	788	17	1002	1002	NUM
ejpam-3335	788	18	999	999	NUM
ejpam-3335	788	19	cayley	cayley	ADJ
ejpam-3335	788	20	table	table	NOUN
ejpam-3335	788	21	:	:	PUNCT
ejpam-3335	788	22	·	·	PUNCT
ejpam-3335	788	23	0	0	NUM
ejpam-3335	789	1	1	1	NUM
ejpam-3335	789	2	2	2	NUM
ejpam-3335	789	3	3	3	NUM
ejpam-3335	789	4	0	0	NUM
ejpam-3335	789	5	0	0	NUM
ejpam-3335	789	6	1	1	NUM
ejpam-3335	789	7	2	2	NUM
ejpam-3335	789	8	3	3	NUM
ejpam-3335	789	9	1	1	NUM
ejpam-3335	789	10	0	0	NUM
ejpam-3335	789	11	0	0	NUM
ejpam-3335	789	12	2	2	NUM
ejpam-3335	789	13	3	3	NUM
ejpam-3335	789	14	2	2	NUM
ejpam-3335	789	15	0	0	NUM
ejpam-3335	789	16	0	0	NUM
ejpam-3335	789	17	0	0	NUM
ejpam-3335	789	18	0	0	NUM
ejpam-3335	789	19	3	3	NUM
ejpam-3335	789	20	0	0	NUM
ejpam-3335	789	21	0	0	NUM
ejpam-3335	789	22	1	1	NUM
ejpam-3335	789	23	0	0	NUM
ejpam-3335	789	24	then	then	ADV
ejpam-3335	789	25	(	(	PUNCT
ejpam-3335	789	26	a	a	PRON
ejpam-3335	789	27	,	,	PUNCT
ejpam-3335	789	28	·	·	PUNCT
ejpam-3335	789	29	,	,	PUNCT
ejpam-3335	789	30	0	0	NUM
ejpam-3335	789	31	)	)	PUNCT
ejpam-3335	789	32	is	be	AUX
ejpam-3335	789	33	a	a	DET
ejpam-3335	789	34	up	up	NOUN
ejpam-3335	789	35	-	-	PUNCT
ejpam-3335	789	36	algebra	algebra	NOUN
ejpam-3335	789	37	.	.	PUNCT
ejpam-3335	790	1	we	we	PRON
ejpam-3335	790	2	define	define	VERB
ejpam-3335	790	3	a	a	DET
ejpam-3335	790	4	hesitant	hesitant	ADJ
ejpam-3335	790	5	fuzzy	fuzzy	ADJ
ejpam-3335	790	6	set	set	VERB
ejpam-3335	790	7	h	h	NOUN
ejpam-3335	790	8	on	on	ADP
ejpam-3335	790	9	a	a	DET
ejpam-3335	790	10	as	as	SCONJ
ejpam-3335	790	11	follows	follow	VERB
ejpam-3335	790	12	:	:	PUNCT
ejpam-3335	790	13	hh(0	hh(0	NOUN
ejpam-3335	790	14	)	)	PUNCT
ejpam-3335	790	15	=	=	PUNCT
ejpam-3335	791	1	[	[	X
ejpam-3335	791	2	0	0	NUM
ejpam-3335	791	3	,	,	PUNCT
ejpam-3335	791	4	1],hh(1	1],hh(1	NUM
ejpam-3335	791	5	)	)	PUNCT
ejpam-3335	791	6	=	=	PRON
ejpam-3335	791	7	{	{	PUNCT
ejpam-3335	791	8	0},hh(2	0},hh(2	NOUN
ejpam-3335	791	9	)	)	PUNCT
ejpam-3335	791	10	=	=	PUNCT
ejpam-3335	792	1	[	[	X
ejpam-3335	792	2	0	0	NUM
ejpam-3335	792	3	,	,	PUNCT
ejpam-3335	792	4	0.1	0.1	NUM
ejpam-3335	792	5	]	]	PUNCT
ejpam-3335	792	6	,	,	PUNCT
ejpam-3335	792	7	and	and	CCONJ
ejpam-3335	792	8	hh(3	hh(3	X
ejpam-3335	792	9	)	)	PUNCT
ejpam-3335	792	10	=	=	PUNCT
ejpam-3335	793	1	[	[	X
ejpam-3335	793	2	0	0	NUM
ejpam-3335	793	3	,	,	PUNCT
ejpam-3335	793	4	0.1	0.1	NUM
ejpam-3335	793	5	]	]	PUNCT
ejpam-3335	793	6	.	.	PUNCT
ejpam-3335	794	1	if	if	SCONJ
ejpam-3335	794	2	ε	ε	PROPN
ejpam-3335	794	3	6=	6=	PROPN
ejpam-3335	795	1	[	[	X
ejpam-3335	795	2	0	0	NUM
ejpam-3335	795	3	,	,	PUNCT
ejpam-3335	795	4	1	1	NUM
ejpam-3335	795	5	]	]	PUNCT
ejpam-3335	795	6	,	,	PUNCT
ejpam-3335	795	7	then	then	ADV
ejpam-3335	795	8	u+(h	u+(h	NUM
ejpam-3335	795	9	;	;	PUNCT
ejpam-3335	795	10	ε	ε	PROPN
ejpam-3335	795	11	)	)	PUNCT
ejpam-3335	795	12	6=	6=	ADP
ejpam-3335	795	13	∅.	∅.	ADP
ejpam-3335	795	14	if	if	SCONJ
ejpam-3335	795	15	ε	ε	PROPN
ejpam-3335	795	16	=	=	PUNCT
ejpam-3335	796	1	[	[	X
ejpam-3335	796	2	0	0	NUM
ejpam-3335	796	3	,	,	PUNCT
ejpam-3335	796	4	1	1	NUM
ejpam-3335	796	5	]	]	PUNCT
ejpam-3335	796	6	,	,	PUNCT
ejpam-3335	796	7	then	then	ADV
ejpam-3335	796	8	u+(h	u+(h	NUM
ejpam-3335	796	9	;	;	PUNCT
ejpam-3335	796	10	ε	ε	PROPN
ejpam-3335	796	11	)	)	PUNCT
ejpam-3335	796	12	=	=	NOUN
ejpam-3335	796	13	∅	∅	NOUN
ejpam-3335	796	14	and	and	CCONJ
ejpam-3335	796	15	e(h	e(h	PROPN
ejpam-3335	796	16	;	;	PUNCT
ejpam-3335	796	17	ε	ε	PROPN
ejpam-3335	796	18	)	)	PUNCT
ejpam-3335	796	19	=	=	PUNCT
ejpam-3335	796	20	{	{	PUNCT
ejpam-3335	796	21	0	0	NUM
ejpam-3335	796	22	}	}	PUNCT
ejpam-3335	796	23	.	.	PUNCT
ejpam-3335	797	1	thus	thus	ADV
ejpam-3335	797	2	e(h	e(h	X
ejpam-3335	797	3	;	;	PUNCT
ejpam-3335	797	4	ε	ε	PROPN
ejpam-3335	797	5	)	)	PUNCT
ejpam-3335	797	6	is	be	AUX
ejpam-3335	797	7	clearly	clearly	ADV
ejpam-3335	797	8	a	a	DET
ejpam-3335	797	9	up	up	ADJ
ejpam-3335	797	10	-	-	PUNCT
ejpam-3335	797	11	subalgebra	subalgebra	NOUN
ejpam-3335	797	12	of	of	ADP
ejpam-3335	797	13	a.	a.	NOUN
ejpam-3335	797	14	since	since	SCONJ
ejpam-3335	797	15	hh(3	hh(3	PROPN
ejpam-3335	797	16	·	·	PUNCT
ejpam-3335	797	17	2	2	X
ejpam-3335	797	18	)	)	PUNCT
ejpam-3335	797	19	=	=	PUNCT
ejpam-3335	797	20	hh(1	hh(1	NOUN
ejpam-3335	797	21	)	)	PUNCT
ejpam-3335	797	22	=	=	PRON
ejpam-3335	797	23	{	{	PUNCT
ejpam-3335	797	24	0	0	NUM
ejpam-3335	797	25	}	}	PUNCT
ejpam-3335	797	26	+	+	PROPN
ejpam-3335	798	1	[	[	X
ejpam-3335	798	2	0	0	NUM
ejpam-3335	798	3	,	,	PUNCT
ejpam-3335	798	4	0.1	0.1	NUM
ejpam-3335	798	5	]	]	PUNCT
ejpam-3335	798	6	=	=	SYM
ejpam-3335	798	7	hh(3	hh(3	NOUN
ejpam-3335	798	8	)	)	PUNCT
ejpam-3335	798	9	∩	∩	PROPN
ejpam-3335	798	10	hh(2	hh(2	PROPN
ejpam-3335	798	11	)	)	PUNCT
ejpam-3335	798	12	,	,	PUNCT
ejpam-3335	798	13	we	we	PRON
ejpam-3335	798	14	have	have	VERB
ejpam-3335	798	15	h	h	NOUN
ejpam-3335	798	16	is	be	AUX
ejpam-3335	798	17	not	not	PART
ejpam-3335	798	18	an	an	DET
ejpam-3335	798	19	anti	anti	ADJ
ejpam-3335	798	20	-	-	ADJ
ejpam-3335	798	21	hesitant	hesitant	ADJ
ejpam-3335	798	22	fuzzy	fuzzy	ADJ
ejpam-3335	798	23	up	up	NOUN
ejpam-3335	798	24	-	-	PUNCT
ejpam-3335	798	25	subalgebra	subalgebra	NOUN
ejpam-3335	798	26	of	of	ADP
ejpam-3335	798	27	a.	a.	NOUN
ejpam-3335	798	28	theorem	theorem	NOUN
ejpam-3335	798	29	28	28	NUM
ejpam-3335	798	30	.	.	PUNCT
ejpam-3335	799	1	if	if	SCONJ
ejpam-3335	799	2	a	a	DET
ejpam-3335	799	3	hesitant	hesitant	ADJ
ejpam-3335	799	4	fuzzy	fuzzy	ADJ
ejpam-3335	799	5	set	set	VERB
ejpam-3335	799	6	h	h	NOUN
ejpam-3335	799	7	on	on	ADP
ejpam-3335	799	8	a	a	PRON
ejpam-3335	799	9	is	be	AUX
ejpam-3335	799	10	an	an	DET
ejpam-3335	799	11	anti	anti	ADJ
ejpam-3335	799	12	-	-	ADJ
ejpam-3335	799	13	hesitant	hesitant	ADJ
ejpam-3335	799	14	fuzzy	fuzzy	ADJ
ejpam-3335	799	15	up	up	NOUN
ejpam-3335	799	16	-	-	PUNCT
ejpam-3335	799	17	filter	filter	NOUN
ejpam-3335	799	18	of	of	ADP
ejpam-3335	799	19	a	a	PRON
ejpam-3335	799	20	,	,	PUNCT
ejpam-3335	799	21	then	then	ADV
ejpam-3335	799	22	for	for	ADP
ejpam-3335	799	23	all	all	DET
ejpam-3335	799	24	ε	ε	PROPN
ejpam-3335	799	25	∈	∈	PROPN
ejpam-3335	799	26	p([0	p([0	NOUN
ejpam-3335	799	27	,	,	PUNCT
ejpam-3335	799	28	1	1	NUM
ejpam-3335	799	29	]	]	NUM
ejpam-3335	799	30	)	)	PUNCT
ejpam-3335	799	31	,	,	PUNCT
ejpam-3335	799	32	a	a	DET
ejpam-3335	799	33	nonempty	nonempty	NOUN
ejpam-3335	799	34	subset	subset	VERB
ejpam-3335	799	35	e(h	e(h	PROPN
ejpam-3335	799	36	;	;	PUNCT
ejpam-3335	799	37	ε	ε	PROPN
ejpam-3335	799	38	)	)	PUNCT
ejpam-3335	799	39	of	of	ADP
ejpam-3335	799	40	a	a	PRON
ejpam-3335	799	41	is	be	AUX
ejpam-3335	799	42	a	a	DET
ejpam-3335	799	43	up	up	ADJ
ejpam-3335	799	44	-	-	PUNCT
ejpam-3335	799	45	filter	filter	NOUN
ejpam-3335	799	46	of	of	ADP
ejpam-3335	799	47	a	a	DET
ejpam-3335	799	48	where	where	SCONJ
ejpam-3335	799	49	u+(h	u+(h	NOUN
ejpam-3335	799	50	;	;	PUNCT
ejpam-3335	799	51	ε	ε	PROPN
ejpam-3335	799	52	)	)	PUNCT
ejpam-3335	799	53	is	be	AUX
ejpam-3335	799	54	empty	empty	ADJ
ejpam-3335	799	55	.	.	PUNCT
ejpam-3335	800	1	proof	proof	NOUN
ejpam-3335	800	2	.	.	PUNCT
ejpam-3335	801	1	assume	assume	VERB
ejpam-3335	801	2	that	that	SCONJ
ejpam-3335	801	3	h	h	NOUN
ejpam-3335	801	4	is	be	AUX
ejpam-3335	801	5	an	an	DET
ejpam-3335	801	6	anti	anti	ADJ
ejpam-3335	801	7	-	-	ADJ
ejpam-3335	801	8	hesitant	hesitant	ADJ
ejpam-3335	801	9	fuzzy	fuzzy	ADJ
ejpam-3335	801	10	up	up	NOUN
ejpam-3335	801	11	-	-	PUNCT
ejpam-3335	801	12	filter	filter	NOUN
ejpam-3335	801	13	of	of	ADP
ejpam-3335	801	14	a.	a.	NOUN
ejpam-3335	801	15	let	let	VERB
ejpam-3335	801	16	ε	ε	PROPN
ejpam-3335	801	17	∈	∈	PROPN
ejpam-3335	801	18	p([0	p([0	PROPN
ejpam-3335	801	19	,	,	PUNCT
ejpam-3335	801	20	1	1	NUM
ejpam-3335	801	21	]	]	PUNCT
ejpam-3335	801	22	)	)	PUNCT
ejpam-3335	801	23	be	be	AUX
ejpam-3335	801	24	such	such	ADJ
ejpam-3335	801	25	that	that	SCONJ
ejpam-3335	801	26	e(h	e(h	PROPN
ejpam-3335	801	27	;	;	PUNCT
ejpam-3335	801	28	ε	ε	PROPN
ejpam-3335	801	29	)	)	PUNCT
ejpam-3335	801	30	6=	6=	NOUN
ejpam-3335	801	31	∅	∅	NOUN
ejpam-3335	801	32	but	but	CCONJ
ejpam-3335	801	33	u+(h	u+(h	NUM
ejpam-3335	801	34	;	;	PUNCT
ejpam-3335	801	35	ε	ε	PROPN
ejpam-3335	801	36	)	)	PUNCT
ejpam-3335	801	37	=	=	NOUN
ejpam-3335	801	38	∅	∅	NOUN
ejpam-3335	801	39	,	,	PUNCT
ejpam-3335	801	40	and	and	CCONJ
ejpam-3335	801	41	let	let	VERB
ejpam-3335	801	42	x	x	SYM
ejpam-3335	801	43	∈	∈	PROPN
ejpam-3335	801	44	a	a	DET
ejpam-3335	801	45	be	be	AUX
ejpam-3335	801	46	such	such	ADJ
ejpam-3335	801	47	that	that	SCONJ
ejpam-3335	801	48	x	x	SYM
ejpam-3335	801	49	∈	∈	PROPN
ejpam-3335	801	50	e(h	e(h	X
ejpam-3335	801	51	;	;	PUNCT
ejpam-3335	801	52	ε	ε	PROPN
ejpam-3335	801	53	)	)	PUNCT
ejpam-3335	801	54	.	.	PUNCT
ejpam-3335	802	1	then	then	ADV
ejpam-3335	802	2	hh(x	hh(x	PUNCT
ejpam-3335	802	3	)	)	PUNCT
ejpam-3335	802	4	=	=	SYM
ejpam-3335	802	5	ε	ε	PROPN
ejpam-3335	802	6	.	.	PUNCT
ejpam-3335	803	1	because	because	SCONJ
ejpam-3335	803	2	h	h	NOUN
ejpam-3335	803	3	is	be	AUX
ejpam-3335	803	4	an	an	DET
ejpam-3335	803	5	anti	anti	ADJ
ejpam-3335	803	6	-	-	ADJ
ejpam-3335	803	7	hesitant	hesitant	ADJ
ejpam-3335	803	8	fuzzy	fuzzy	ADJ
ejpam-3335	803	9	up	up	NOUN
ejpam-3335	803	10	-	-	PUNCT
ejpam-3335	803	11	filter	filter	NOUN
ejpam-3335	803	12	of	of	ADP
ejpam-3335	803	13	a	a	PRON
ejpam-3335	803	14	,	,	PUNCT
ejpam-3335	803	15	we	we	PRON
ejpam-3335	803	16	obtain	obtain	VERB
ejpam-3335	803	17	hh(0	hh(0	NOUN
ejpam-3335	803	18	)	)	PUNCT
ejpam-3335	803	19	⊇	⊇	NOUN
ejpam-3335	803	20	hh(x	hh(x	X
ejpam-3335	803	21	)	)	PUNCT
ejpam-3335	803	22	=	=	SYM
ejpam-3335	803	23	ε	ε	PROPN
ejpam-3335	803	24	and	and	CCONJ
ejpam-3335	803	25	thus	thus	ADV
ejpam-3335	803	26	0	0	NUM
ejpam-3335	803	27	∈	∈	PROPN
ejpam-3335	803	28	u(h	u(h	PROPN
ejpam-3335	803	29	;	;	PUNCT
ejpam-3335	803	30	ε	ε	PROPN
ejpam-3335	803	31	)	)	PUNCT
ejpam-3335	803	32	.	.	PUNCT
ejpam-3335	804	1	since	since	SCONJ
ejpam-3335	804	2	u+(h	u+(h	PROPN
ejpam-3335	804	3	;	;	PUNCT
ejpam-3335	804	4	ε	ε	PROPN
ejpam-3335	804	5	)	)	PUNCT
ejpam-3335	804	6	is	be	AUX
ejpam-3335	804	7	empty	empty	ADJ
ejpam-3335	804	8	,	,	PUNCT
ejpam-3335	804	9	we	we	PRON
ejpam-3335	804	10	have	have	VERB
ejpam-3335	804	11	0	0	NUM
ejpam-3335	804	12	∈	∈	PROPN
ejpam-3335	804	13	u(h	u(h	PROPN
ejpam-3335	804	14	;	;	PUNCT
ejpam-3335	804	15	ε	ε	PROPN
ejpam-3335	804	16	)	)	PUNCT
ejpam-3335	804	17	=	=	SYM
ejpam-3335	804	18	e(h	e(h	X
ejpam-3335	804	19	;	;	PUNCT
ejpam-3335	804	20	ε	ε	PROPN
ejpam-3335	804	21	)	)	PUNCT
ejpam-3335	804	22	.	.	PUNCT
ejpam-3335	805	1	next	next	ADV
ejpam-3335	805	2	,	,	PUNCT
ejpam-3335	805	3	let	let	VERB
ejpam-3335	805	4	x	x	PRON
ejpam-3335	805	5	,	,	PUNCT
ejpam-3335	805	6	y	y	PROPN
ejpam-3335	805	7	∈	∈	PROPN
ejpam-3335	805	8	a	a	PRON
ejpam-3335	805	9	be	be	AUX
ejpam-3335	805	10	such	such	ADJ
ejpam-3335	805	11	that	that	SCONJ
ejpam-3335	805	12	x	x	X
ejpam-3335	805	13	·	·	PUNCT
ejpam-3335	805	14	y	y	PROPN
ejpam-3335	805	15	∈	∈	PROPN
ejpam-3335	805	16	e(h	e(h	X
ejpam-3335	805	17	;	;	PUNCT
ejpam-3335	805	18	ε	ε	PROPN
ejpam-3335	805	19	)	)	PUNCT
ejpam-3335	805	20	and	and	CCONJ
ejpam-3335	805	21	x	x	PUNCT
ejpam-3335	805	22	∈	∈	PROPN
ejpam-3335	805	23	e(h	e(h	X
ejpam-3335	805	24	;	;	PUNCT
ejpam-3335	805	25	ε	ε	PROPN
ejpam-3335	805	26	)	)	PUNCT
ejpam-3335	805	27	.	.	PUNCT
ejpam-3335	806	1	then	then	ADV
ejpam-3335	806	2	hh(x	hh(x	PUNCT
ejpam-3335	806	3	·	·	PUNCT
ejpam-3335	806	4	y	y	X
ejpam-3335	806	5	)	)	PUNCT
ejpam-3335	806	6	=	=	SYM
ejpam-3335	806	7	ε	ε	PROPN
ejpam-3335	806	8	and	and	CCONJ
ejpam-3335	806	9	hh(x	hh(x	PUNCT
ejpam-3335	806	10	)	)	PUNCT
ejpam-3335	806	11	=	=	SYM
ejpam-3335	806	12	ε	ε	PROPN
ejpam-3335	806	13	.	.	PUNCT
ejpam-3335	807	1	because	because	SCONJ
ejpam-3335	807	2	h	h	NOUN
ejpam-3335	807	3	is	be	AUX
ejpam-3335	807	4	an	an	DET
ejpam-3335	807	5	anti	anti	ADJ
ejpam-3335	807	6	-	-	ADJ
ejpam-3335	807	7	hesitant	hesitant	ADJ
ejpam-3335	807	8	fuzzy	fuzzy	ADJ
ejpam-3335	807	9	up	up	NOUN
ejpam-3335	807	10	-	-	PUNCT
ejpam-3335	807	11	filter	filter	NOUN
ejpam-3335	807	12	of	of	ADP
ejpam-3335	807	13	a	a	PRON
ejpam-3335	807	14	,	,	PUNCT
ejpam-3335	807	15	we	we	PRON
ejpam-3335	807	16	have	have	VERB
ejpam-3335	807	17	hh(y	hh(y	NOUN
ejpam-3335	807	18	)	)	PUNCT
ejpam-3335	807	19	⊇	⊇	NOUN
ejpam-3335	807	20	hh(x	hh(x	X
ejpam-3335	807	21	·	·	PUNCT
ejpam-3335	807	22	y	y	X
ejpam-3335	807	23	)	)	PUNCT
ejpam-3335	807	24	∩	∩	NOUN
ejpam-3335	807	25	hh(x	hh(x	X
ejpam-3335	807	26	)	)	PUNCT
ejpam-3335	807	27	=	=	SYM
ejpam-3335	807	28	ε	ε	PROPN
ejpam-3335	807	29	.	.	PUNCT
ejpam-3335	808	1	thus	thus	ADV
ejpam-3335	808	2	y	y	PROPN
ejpam-3335	808	3	∈	∈	PROPN
ejpam-3335	808	4	l(h	l(h	PROPN
ejpam-3335	808	5	;	;	PUNCT
ejpam-3335	808	6	ε	ε	PROPN
ejpam-3335	808	7	)	)	PUNCT
ejpam-3335	808	8	.	.	PUNCT
ejpam-3335	809	1	since	since	SCONJ
ejpam-3335	809	2	u+(h	u+(h	PROPN
ejpam-3335	809	3	;	;	PUNCT
ejpam-3335	809	4	ε	ε	PROPN
ejpam-3335	809	5	)	)	PUNCT
ejpam-3335	809	6	is	be	AUX
ejpam-3335	809	7	empty	empty	ADJ
ejpam-3335	809	8	,	,	PUNCT
ejpam-3335	809	9	we	we	PRON
ejpam-3335	809	10	obtain	obtain	VERB
ejpam-3335	809	11	u(h	u(h	PROPN
ejpam-3335	809	12	;	;	PUNCT
ejpam-3335	809	13	ε	ε	PROPN
ejpam-3335	809	14	)	)	PUNCT
ejpam-3335	809	15	=	=	SYM
ejpam-3335	809	16	e(h	e(h	X
ejpam-3335	809	17	;	;	PUNCT
ejpam-3335	809	18	ε	ε	PROPN
ejpam-3335	809	19	)	)	PUNCT
ejpam-3335	809	20	.	.	PUNCT
ejpam-3335	810	1	therefore	therefore	ADV
ejpam-3335	810	2	,	,	PUNCT
ejpam-3335	810	3	y	y	PROPN
ejpam-3335	810	4	∈	∈	PROPN
ejpam-3335	810	5	e(h	e(h	X
ejpam-3335	810	6	;	;	PUNCT
ejpam-3335	810	7	ε	ε	PROPN
ejpam-3335	810	8	)	)	PUNCT
ejpam-3335	810	9	.	.	PUNCT
ejpam-3335	811	1	hence	hence	ADV
ejpam-3335	811	2	,	,	PUNCT
ejpam-3335	811	3	e(h	e(h	PROPN
ejpam-3335	811	4	;	;	PUNCT
ejpam-3335	811	5	ε	ε	PROPN
ejpam-3335	811	6	)	)	PUNCT
ejpam-3335	811	7	is	be	AUX
ejpam-3335	811	8	a	a	DET
ejpam-3335	811	9	up	up	ADJ
ejpam-3335	811	10	-	-	PUNCT
ejpam-3335	811	11	filter	filter	NOUN
ejpam-3335	811	12	of	of	ADP
ejpam-3335	811	13	a.	a.	NOUN
ejpam-3335	811	14	the	the	DET
ejpam-3335	811	15	converse	converse	NOUN
ejpam-3335	811	16	of	of	ADP
ejpam-3335	811	17	theorem	theorem	PROPN
ejpam-3335	811	18	28	28	NUM
ejpam-3335	811	19	is	be	AUX
ejpam-3335	811	20	not	not	PART
ejpam-3335	811	21	true	true	ADJ
ejpam-3335	811	22	in	in	ADP
ejpam-3335	811	23	general	general	ADJ
ejpam-3335	811	24	.	.	PUNCT
ejpam-3335	812	1	by	by	ADP
ejpam-3335	812	2	example	example	NOUN
ejpam-3335	812	3	17	17	NUM
ejpam-3335	812	4	,	,	PUNCT
ejpam-3335	812	5	we	we	PRON
ejpam-3335	812	6	still	still	ADV
ejpam-3335	812	7	have	have	VERB
ejpam-3335	812	8	e(h	e(h	NUM
ejpam-3335	812	9	;	;	PUNCT
ejpam-3335	812	10	ε	ε	PROPN
ejpam-3335	812	11	)	)	PUNCT
ejpam-3335	812	12	=	=	SYM
ejpam-3335	812	13	{	{	PUNCT
ejpam-3335	812	14	0	0	NUM
ejpam-3335	812	15	}	}	PUNCT
ejpam-3335	812	16	is	be	AUX
ejpam-3335	812	17	a	a	DET
ejpam-3335	812	18	up	up	ADJ
ejpam-3335	812	19	-	-	PUNCT
ejpam-3335	812	20	filter	filter	NOUN
ejpam-3335	812	21	of	of	ADP
ejpam-3335	812	22	a.	a.	NOUN
ejpam-3335	812	23	since	since	SCONJ
ejpam-3335	812	24	hh(1	hh(1	NOUN
ejpam-3335	812	25	)	)	PUNCT
ejpam-3335	812	26	=	=	PUNCT
ejpam-3335	812	27	{	{	PUNCT
ejpam-3335	812	28	0	0	NUM
ejpam-3335	812	29	}	}	PUNCT
ejpam-3335	812	30	+	+	PROPN
ejpam-3335	813	1	[	[	X
ejpam-3335	813	2	0	0	NUM
ejpam-3335	813	3	,	,	PUNCT
ejpam-3335	813	4	0.1	0.1	NUM
ejpam-3335	813	5	]	]	PUNCT
ejpam-3335	813	6	=	=	SYM
ejpam-3335	813	7	hh(0	hh(0	NOUN
ejpam-3335	813	8	)	)	PUNCT
ejpam-3335	813	9	∩	∩	ADJ
ejpam-3335	813	10	hh(3	hh(3	NOUN
ejpam-3335	813	11	)	)	PUNCT
ejpam-3335	813	12	=	=	SYM
ejpam-3335	813	13	hh(3	hh(3	X
ejpam-3335	813	14	·	·	PUNCT
ejpam-3335	813	15	1	1	X
ejpam-3335	813	16	)	)	PUNCT
ejpam-3335	813	17	∩	∩	PROPN
ejpam-3335	813	18	hh(3	hh(3	NOUN
ejpam-3335	813	19	)	)	PUNCT
ejpam-3335	813	20	,	,	PUNCT
ejpam-3335	813	21	we	we	PRON
ejpam-3335	813	22	have	have	VERB
ejpam-3335	813	23	h	h	NOUN
ejpam-3335	813	24	is	be	AUX
ejpam-3335	813	25	not	not	PART
ejpam-3335	813	26	an	an	DET
ejpam-3335	813	27	anti	anti	ADJ
ejpam-3335	813	28	-	-	ADJ
ejpam-3335	813	29	hesitant	hesitant	ADJ
ejpam-3335	813	30	fuzzy	fuzzy	ADJ
ejpam-3335	813	31	up	up	NOUN
ejpam-3335	813	32	-	-	PUNCT
ejpam-3335	813	33	filter	filter	NOUN
ejpam-3335	813	34	of	of	ADP
ejpam-3335	813	35	a.	a.	NOUN
ejpam-3335	813	36	theorem	theorem	NOUN
ejpam-3335	813	37	29	29	NUM
ejpam-3335	813	38	.	.	PUNCT
ejpam-3335	814	1	if	if	SCONJ
ejpam-3335	814	2	a	a	DET
ejpam-3335	814	3	hesitant	hesitant	ADJ
ejpam-3335	814	4	fuzzy	fuzzy	ADJ
ejpam-3335	814	5	set	set	VERB
ejpam-3335	814	6	h	h	NOUN
ejpam-3335	814	7	on	on	ADP
ejpam-3335	814	8	a	a	PRON
ejpam-3335	814	9	is	be	AUX
ejpam-3335	814	10	an	an	DET
ejpam-3335	814	11	anti	anti	ADJ
ejpam-3335	814	12	-	-	ADJ
ejpam-3335	814	13	hesitant	hesitant	ADJ
ejpam-3335	814	14	fuzzy	fuzzy	ADJ
ejpam-3335	814	15	up	up	NOUN
ejpam-3335	814	16	-	-	PUNCT
ejpam-3335	814	17	ideal	ideal	NOUN
ejpam-3335	814	18	of	of	ADP
ejpam-3335	814	19	a	a	PRON
ejpam-3335	814	20	,	,	PUNCT
ejpam-3335	814	21	then	then	ADV
ejpam-3335	814	22	for	for	ADP
ejpam-3335	814	23	all	all	DET
ejpam-3335	814	24	ε	ε	PROPN
ejpam-3335	814	25	∈	∈	PROPN
ejpam-3335	814	26	p([0	p([0	NOUN
ejpam-3335	814	27	,	,	PUNCT
ejpam-3335	814	28	1	1	NUM
ejpam-3335	814	29	]	]	NUM
ejpam-3335	814	30	)	)	PUNCT
ejpam-3335	814	31	,	,	PUNCT
ejpam-3335	814	32	a	a	DET
ejpam-3335	814	33	nonempty	nonempty	NOUN
ejpam-3335	814	34	subset	subset	VERB
ejpam-3335	814	35	e(h	e(h	PROPN
ejpam-3335	814	36	;	;	PUNCT
ejpam-3335	814	37	ε	ε	PROPN
ejpam-3335	814	38	)	)	PUNCT
ejpam-3335	814	39	of	of	ADP
ejpam-3335	814	40	a	a	PRON
ejpam-3335	814	41	is	be	AUX
ejpam-3335	814	42	a	a	DET
ejpam-3335	814	43	up	up	ADJ
ejpam-3335	814	44	-	-	PUNCT
ejpam-3335	814	45	ideal	ideal	NOUN
ejpam-3335	814	46	of	of	ADP
ejpam-3335	814	47	a	a	DET
ejpam-3335	814	48	where	where	SCONJ
ejpam-3335	814	49	u+(h	u+(h	NOUN
ejpam-3335	814	50	;	;	PUNCT
ejpam-3335	814	51	ε	ε	PROPN
ejpam-3335	814	52	)	)	PUNCT
ejpam-3335	814	53	is	be	AUX
ejpam-3335	814	54	empty	empty	ADJ
ejpam-3335	814	55	.	.	PUNCT
ejpam-3335	815	1	proof	proof	NOUN
ejpam-3335	815	2	.	.	PUNCT
ejpam-3335	816	1	assume	assume	VERB
ejpam-3335	816	2	that	that	SCONJ
ejpam-3335	816	3	h	h	NOUN
ejpam-3335	816	4	is	be	AUX
ejpam-3335	816	5	an	an	DET
ejpam-3335	816	6	anti	anti	ADJ
ejpam-3335	816	7	-	-	ADJ
ejpam-3335	816	8	hesitant	hesitant	ADJ
ejpam-3335	816	9	fuzzy	fuzzy	ADJ
ejpam-3335	816	10	up	up	NOUN
ejpam-3335	816	11	-	-	PUNCT
ejpam-3335	816	12	ideal	ideal	NOUN
ejpam-3335	816	13	of	of	ADP
ejpam-3335	816	14	a.	a.	NOUN
ejpam-3335	816	15	let	let	VERB
ejpam-3335	816	16	ε	ε	PROPN
ejpam-3335	816	17	∈	∈	PROPN
ejpam-3335	816	18	p([0	p([0	PROPN
ejpam-3335	816	19	,	,	PUNCT
ejpam-3335	816	20	1	1	NUM
ejpam-3335	816	21	]	]	PUNCT
ejpam-3335	816	22	)	)	PUNCT
ejpam-3335	816	23	be	be	AUX
ejpam-3335	816	24	such	such	ADJ
ejpam-3335	816	25	that	that	SCONJ
ejpam-3335	816	26	e(h	e(h	PROPN
ejpam-3335	816	27	;	;	PUNCT
ejpam-3335	816	28	ε	ε	PROPN
ejpam-3335	816	29	)	)	PUNCT
ejpam-3335	816	30	6=	6=	NOUN
ejpam-3335	816	31	∅	∅	NOUN
ejpam-3335	816	32	but	but	CCONJ
ejpam-3335	816	33	u+(h	u+(h	NUM
ejpam-3335	816	34	;	;	PUNCT
ejpam-3335	816	35	ε	ε	PROPN
ejpam-3335	816	36	)	)	PUNCT
ejpam-3335	816	37	=	=	NOUN
ejpam-3335	816	38	∅	∅	NOUN
ejpam-3335	816	39	,	,	PUNCT
ejpam-3335	816	40	and	and	CCONJ
ejpam-3335	816	41	let	let	VERB
ejpam-3335	816	42	x	x	SYM
ejpam-3335	816	43	∈	∈	PROPN
ejpam-3335	816	44	a	a	DET
ejpam-3335	816	45	be	be	AUX
ejpam-3335	816	46	such	such	ADJ
ejpam-3335	816	47	that	that	SCONJ
ejpam-3335	816	48	x	x	SYM
ejpam-3335	816	49	∈	∈	PROPN
ejpam-3335	816	50	e(h	e(h	X
ejpam-3335	816	51	;	;	PUNCT
ejpam-3335	816	52	ε	ε	PROPN
ejpam-3335	816	53	)	)	PUNCT
ejpam-3335	816	54	.	.	PUNCT
ejpam-3335	817	1	then	then	ADV
ejpam-3335	817	2	hh(x	hh(x	PUNCT
ejpam-3335	817	3	)	)	PUNCT
ejpam-3335	817	4	=	=	SYM
ejpam-3335	817	5	ε	ε	PROPN
ejpam-3335	817	6	.	.	PUNCT
ejpam-3335	818	1	because	because	SCONJ
ejpam-3335	818	2	h	h	NOUN
ejpam-3335	818	3	is	be	AUX
ejpam-3335	818	4	an	an	DET
ejpam-3335	818	5	anti	anti	ADJ
ejpam-3335	818	6	-	-	ADJ
ejpam-3335	818	7	hesitant	hesitant	ADJ
ejpam-3335	818	8	fuzzy	fuzzy	ADJ
ejpam-3335	818	9	up	up	NOUN
ejpam-3335	818	10	-	-	PUNCT
ejpam-3335	818	11	filter	filter	NOUN
ejpam-3335	818	12	of	of	ADP
ejpam-3335	818	13	a	a	PRON
ejpam-3335	818	14	,	,	PUNCT
ejpam-3335	818	15	we	we	PRON
ejpam-3335	818	16	obtain	obtain	VERB
ejpam-3335	818	17	hh(0	hh(0	NOUN
ejpam-3335	818	18	)	)	PUNCT
ejpam-3335	818	19	⊇	⊇	NOUN
ejpam-3335	818	20	hh(x	hh(x	X
ejpam-3335	818	21	)	)	PUNCT
ejpam-3335	818	22	=	=	SYM
ejpam-3335	818	23	ε	ε	PROPN
ejpam-3335	818	24	and	and	CCONJ
ejpam-3335	818	25	thus	thus	ADV
ejpam-3335	818	26	0	0	NUM
ejpam-3335	818	27	∈	∈	PROPN
ejpam-3335	818	28	u(h	u(h	PROPN
ejpam-3335	818	29	;	;	PUNCT
ejpam-3335	818	30	ε	ε	PROPN
ejpam-3335	818	31	)	)	PUNCT
ejpam-3335	818	32	.	.	PUNCT
ejpam-3335	819	1	since	since	SCONJ
ejpam-3335	819	2	u+(h	u+(h	PROPN
ejpam-3335	819	3	;	;	PUNCT
ejpam-3335	819	4	ε	ε	PROPN
ejpam-3335	819	5	)	)	PUNCT
ejpam-3335	819	6	is	be	AUX
ejpam-3335	819	7	empty	empty	ADJ
ejpam-3335	819	8	,	,	PUNCT
ejpam-3335	819	9	we	we	PRON
ejpam-3335	819	10	have	have	VERB
ejpam-3335	819	11	0	0	NUM
ejpam-3335	819	12	∈	∈	PROPN
ejpam-3335	819	13	u(h	u(h	PROPN
ejpam-3335	819	14	;	;	PUNCT
ejpam-3335	819	15	ε	ε	PROPN
ejpam-3335	819	16	)	)	PUNCT
ejpam-3335	819	17	=	=	SYM
ejpam-3335	819	18	e(h	e(h	X
ejpam-3335	819	19	;	;	PUNCT
ejpam-3335	819	20	ε	ε	PROPN
ejpam-3335	819	21	)	)	PUNCT
ejpam-3335	819	22	.	.	PUNCT
ejpam-3335	820	1	next	next	ADV
ejpam-3335	820	2	,	,	PUNCT
ejpam-3335	820	3	let	let	VERB
ejpam-3335	820	4	x	x	PRON
ejpam-3335	820	5	,	,	PUNCT
ejpam-3335	820	6	y	y	PROPN
ejpam-3335	820	7	,	,	PUNCT
ejpam-3335	820	8	z	z	PROPN
ejpam-3335	820	9	∈	∈	PROPN
ejpam-3335	820	10	a	a	DET
ejpam-3335	820	11	be	be	AUX
ejpam-3335	820	12	such	such	ADJ
ejpam-3335	820	13	that	that	SCONJ
ejpam-3335	820	14	x	x	PART
ejpam-3335	820	15	·	·	PUNCT
ejpam-3335	820	16	(	(	PUNCT
ejpam-3335	820	17	y	y	PROPN
ejpam-3335	820	18	·	·	PUNCT
ejpam-3335	820	19	z	z	X
ejpam-3335	820	20	)	)	PUNCT
ejpam-3335	820	21	∈	∈	PROPN
ejpam-3335	820	22	e(h	e(h	X
ejpam-3335	820	23	;	;	PUNCT
ejpam-3335	820	24	ε	ε	PROPN
ejpam-3335	820	25	)	)	PUNCT
ejpam-3335	820	26	and	and	CCONJ
ejpam-3335	820	27	y	y	PROPN
ejpam-3335	820	28	∈	∈	PROPN
ejpam-3335	820	29	e(h	e(h	X
ejpam-3335	820	30	;	;	PUNCT
ejpam-3335	820	31	ε	ε	PROPN
ejpam-3335	820	32	)	)	PUNCT
ejpam-3335	820	33	.	.	PUNCT
ejpam-3335	821	1	then	then	ADV
ejpam-3335	821	2	hh(x	hh(x	PUNCT
ejpam-3335	821	3	·	·	PUNCT
ejpam-3335	821	4	(	(	PUNCT
ejpam-3335	821	5	y	y	PROPN
ejpam-3335	821	6	·	·	PUNCT
ejpam-3335	821	7	z	z	NOUN
ejpam-3335	821	8	)	)	PUNCT
ejpam-3335	821	9	)	)	PUNCT
ejpam-3335	821	10	=	=	SYM
ejpam-3335	821	11	ε	ε	PROPN
ejpam-3335	821	12	and	and	CCONJ
ejpam-3335	821	13	hh(y	hh(y	NOUN
ejpam-3335	821	14	)	)	PUNCT
ejpam-3335	822	1	=	=	SYM
ejpam-3335	822	2	ε	ε	PROPN
ejpam-3335	822	3	.	.	PUNCT
ejpam-3335	823	1	since	since	SCONJ
ejpam-3335	823	2	h	h	NOUN
ejpam-3335	823	3	is	be	AUX
ejpam-3335	823	4	an	an	DET
ejpam-3335	823	5	anti	anti	ADJ
ejpam-3335	823	6	-	-	ADJ
ejpam-3335	823	7	hesitant	hesitant	ADJ
ejpam-3335	823	8	fuzzy	fuzzy	ADJ
ejpam-3335	823	9	up	up	NOUN
ejpam-3335	823	10	-	-	PUNCT
ejpam-3335	823	11	ideal	ideal	NOUN
ejpam-3335	823	12	of	of	ADP
ejpam-3335	823	13	a	a	PRON
ejpam-3335	823	14	,	,	PUNCT
ejpam-3335	823	15	we	we	PRON
ejpam-3335	823	16	have	have	VERB
ejpam-3335	823	17	hh(x	hh(x	X
ejpam-3335	823	18	·	·	PUNCT
ejpam-3335	823	19	z	z	X
ejpam-3335	823	20	)	)	PUNCT
ejpam-3335	823	21	⊇	⊇	NOUN
ejpam-3335	823	22	hh(x	hh(x	X
ejpam-3335	823	23	·	·	PUNCT
ejpam-3335	823	24	(	(	PUNCT
ejpam-3335	823	25	y	y	PROPN
ejpam-3335	823	26	·	·	PUNCT
ejpam-3335	823	27	z	z	NOUN
ejpam-3335	823	28	)	)	PUNCT
ejpam-3335	823	29	)	)	PUNCT
ejpam-3335	823	30	∩	∩	NOUN
ejpam-3335	823	31	hh(y	hh(y	NUM
ejpam-3335	823	32	)	)	PUNCT
ejpam-3335	823	33	=	=	SYM
ejpam-3335	823	34	ε	ε	PROPN
ejpam-3335	823	35	.	.	PUNCT
ejpam-3335	823	36	thus	thus	ADV
ejpam-3335	823	37	x	x	X
ejpam-3335	823	38	·	·	PUNCT
ejpam-3335	823	39	z	z	X
ejpam-3335	823	40	∈	∈	PROPN
ejpam-3335	823	41	u(h	u(h	PROPN
ejpam-3335	823	42	;	;	PUNCT
ejpam-3335	823	43	ε	ε	PROPN
ejpam-3335	823	44	)	)	PUNCT
ejpam-3335	823	45	.	.	PUNCT
ejpam-3335	824	1	since	since	SCONJ
ejpam-3335	824	2	l−(h	l−(h	PROPN
ejpam-3335	824	3	;	;	PUNCT
ejpam-3335	824	4	ε	ε	PROPN
ejpam-3335	824	5	)	)	PUNCT
ejpam-3335	824	6	is	be	AUX
ejpam-3335	824	7	empty	empty	ADJ
ejpam-3335	824	8	,	,	PUNCT
ejpam-3335	824	9	we	we	PRON
ejpam-3335	824	10	obtain	obtain	VERB
ejpam-3335	824	11	u(h	u(h	PROPN
ejpam-3335	824	12	;	;	PUNCT
ejpam-3335	824	13	ε	ε	PROPN
ejpam-3335	824	14	)	)	PUNCT
ejpam-3335	824	15	=	=	SYM
ejpam-3335	824	16	e(h	e(h	X
ejpam-3335	824	17	;	;	PUNCT
ejpam-3335	824	18	ε	ε	PROPN
ejpam-3335	824	19	)	)	PUNCT
ejpam-3335	824	20	.	.	PUNCT
ejpam-3335	825	1	therefore	therefore	ADV
ejpam-3335	825	2	,	,	PUNCT
ejpam-3335	825	3	x	x	X
ejpam-3335	825	4	·	·	PUNCT
ejpam-3335	825	5	z	z	X
ejpam-3335	825	6	∈	∈	PROPN
ejpam-3335	825	7	e(h	e(h	X
ejpam-3335	825	8	;	;	PUNCT
ejpam-3335	825	9	ε	ε	PROPN
ejpam-3335	825	10	)	)	PUNCT
ejpam-3335	825	11	.	.	PUNCT
ejpam-3335	826	1	hence	hence	ADV
ejpam-3335	826	2	,	,	PUNCT
ejpam-3335	826	3	e(h	e(h	PROPN
ejpam-3335	826	4	;	;	PUNCT
ejpam-3335	826	5	ε	ε	PROPN
ejpam-3335	826	6	)	)	PUNCT
ejpam-3335	826	7	is	be	AUX
ejpam-3335	826	8	a	a	DET
ejpam-3335	826	9	up	up	ADJ
ejpam-3335	826	10	-	-	PUNCT
ejpam-3335	826	11	ideal	ideal	NOUN
ejpam-3335	826	12	of	of	ADP
ejpam-3335	826	13	a.	a.	NOUN
ejpam-3335	826	14	the	the	DET
ejpam-3335	826	15	converse	converse	NOUN
ejpam-3335	826	16	of	of	ADP
ejpam-3335	826	17	theorem	theorem	NOUN
ejpam-3335	826	18	29	29	NUM
ejpam-3335	826	19	is	be	AUX
ejpam-3335	826	20	not	not	PART
ejpam-3335	826	21	true	true	ADJ
ejpam-3335	826	22	in	in	ADP
ejpam-3335	826	23	general	general	ADJ
ejpam-3335	826	24	.	.	PUNCT
ejpam-3335	827	1	by	by	ADP
ejpam-3335	827	2	example	example	NOUN
ejpam-3335	827	3	17	17	NUM
ejpam-3335	827	4	,	,	PUNCT
ejpam-3335	827	5	we	we	PRON
ejpam-3335	827	6	still	still	ADV
ejpam-3335	827	7	have	have	VERB
ejpam-3335	827	8	e(h	e(h	NUM
ejpam-3335	827	9	;	;	PUNCT
ejpam-3335	827	10	ε	ε	PROPN
ejpam-3335	827	11	)	)	PUNCT
ejpam-3335	827	12	=	=	SYM
ejpam-3335	827	13	{	{	PUNCT
ejpam-3335	827	14	0	0	NUM
ejpam-3335	827	15	}	}	PUNCT
ejpam-3335	827	16	is	be	AUX
ejpam-3335	827	17	a	a	DET
ejpam-3335	827	18	up	up	ADJ
ejpam-3335	827	19	-	-	PUNCT
ejpam-3335	827	20	ideal	ideal	NOUN
ejpam-3335	827	21	of	of	ADP
ejpam-3335	827	22	a.	a.	NOUN
ejpam-3335	827	23	since	since	SCONJ
ejpam-3335	827	24	hh(3·2	hh(3·2	PROPN
ejpam-3335	827	25	)	)	PUNCT
ejpam-3335	828	1	=	=	PUNCT
ejpam-3335	828	2	hh(1	hh(1	NOUN
ejpam-3335	828	3	)	)	PUNCT
ejpam-3335	828	4	=	=	PRON
ejpam-3335	828	5	{	{	PUNCT
ejpam-3335	828	6	0	0	NUM
ejpam-3335	828	7	}	}	PUNCT
ejpam-3335	828	8	+	+	PROPN
ejpam-3335	829	1	[	[	X
ejpam-3335	829	2	0	0	NUM
ejpam-3335	829	3	,	,	PUNCT
ejpam-3335	829	4	0.1	0.1	NUM
ejpam-3335	829	5	]	]	PUNCT
ejpam-3335	829	6	=	=	SYM
ejpam-3335	829	7	hh(0)∩hh(2	hh(0)∩hh(2	NOUN
ejpam-3335	829	8	)	)	PUNCT
ejpam-3335	829	9	=	=	PUNCT
ejpam-3335	830	1	hh(3	hh(3	X
ejpam-3335	830	2	·	·	PUNCT
ejpam-3335	830	3	(	(	PUNCT
ejpam-3335	830	4	2	2	NUM
ejpam-3335	830	5	·	·	SYM
ejpam-3335	830	6	2	2	NUM
ejpam-3335	830	7	)	)	PUNCT
ejpam-3335	830	8	)	)	PUNCT
ejpam-3335	830	9	∩	∩	PROPN
ejpam-3335	830	10	hh(2	hh(2	PROPN
ejpam-3335	830	11	)	)	PUNCT
ejpam-3335	830	12	,	,	PUNCT
ejpam-3335	830	13	we	we	PRON
ejpam-3335	830	14	have	have	VERB
ejpam-3335	830	15	h	h	NOUN
ejpam-3335	830	16	is	be	AUX
ejpam-3335	830	17	not	not	PART
ejpam-3335	830	18	an	an	DET
ejpam-3335	830	19	anti	anti	ADJ
ejpam-3335	830	20	-	-	ADJ
ejpam-3335	830	21	hesitant	hesitant	ADJ
ejpam-3335	830	22	fuzzy	fuzzy	ADJ
ejpam-3335	830	23	up	up	NOUN
ejpam-3335	830	24	-	-	PUNCT
ejpam-3335	830	25	ideal	ideal	NOUN
ejpam-3335	830	26	of	of	ADP
ejpam-3335	830	27	a.	a.	PROPN
ejpam-3335	830	28	p.	p.	PROPN
ejpam-3335	830	29	mosrijai	mosrijai	PROPN
ejpam-3335	830	30	,	,	PUNCT
ejpam-3335	830	31	a.	a.	NOUN
ejpam-3335	830	32	iampan	iampan	PROPN
ejpam-3335	830	33	/	/	SYM
ejpam-3335	830	34	eur	eur	PROPN
ejpam-3335	830	35	.	.	PUNCT
ejpam-3335	831	1	j.	j.	PROPN
ejpam-3335	831	2	pure	pure	PROPN
ejpam-3335	831	3	appl	appl	PROPN
ejpam-3335	831	4	.	.	PROPN
ejpam-3335	831	5	math	math	PROPN
ejpam-3335	831	6	,	,	PUNCT
ejpam-3335	831	7	11	11	NUM
ejpam-3335	831	8	(	(	PUNCT
ejpam-3335	831	9	4	4	NUM
ejpam-3335	831	10	)	)	PUNCT
ejpam-3335	831	11	(	(	PUNCT
ejpam-3335	831	12	2018	2018	NUM
ejpam-3335	831	13	)	)	PUNCT
ejpam-3335	831	14	,	,	PUNCT
ejpam-3335	831	15	976	976	NUM
ejpam-3335	831	16	-	-	SYM
ejpam-3335	831	17	1002	1002	NUM
ejpam-3335	831	18	1000	1000	NUM
ejpam-3335	831	19	theorem	theorem	NOUN
ejpam-3335	831	20	30	30	NUM
ejpam-3335	831	21	.	.	PUNCT
ejpam-3335	832	1	a	a	DET
ejpam-3335	832	2	hesitant	hesitant	ADJ
ejpam-3335	832	3	fuzzy	fuzzy	ADJ
ejpam-3335	832	4	set	set	VERB
ejpam-3335	832	5	h	h	NOUN
ejpam-3335	832	6	on	on	ADP
ejpam-3335	832	7	a	a	PRON
ejpam-3335	832	8	is	be	AUX
ejpam-3335	832	9	an	an	DET
ejpam-3335	832	10	anti	anti	ADJ
ejpam-3335	832	11	-	-	ADJ
ejpam-3335	832	12	hesitant	hesitant	ADJ
ejpam-3335	832	13	fuzzy	fuzzy	ADJ
ejpam-3335	832	14	strongly	strongly	ADV
ejpam-3335	832	15	up	up	ADP
ejpam-3335	832	16	-	-	PUNCT
ejpam-3335	832	17	ideal	ideal	NOUN
ejpam-3335	832	18	of	of	ADP
ejpam-3335	832	19	a	a	DET
ejpam-3335	832	20	if	if	NOUN
ejpam-3335	832	21	and	and	CCONJ
ejpam-3335	832	22	only	only	ADV
ejpam-3335	832	23	if	if	SCONJ
ejpam-3335	832	24	e(h	e(h	PROPN
ejpam-3335	832	25	;	;	PUNCT
ejpam-3335	832	26	hh(0	hh(0	NOUN
ejpam-3335	832	27	)	)	PUNCT
ejpam-3335	832	28	)	)	PUNCT
ejpam-3335	832	29	is	be	AUX
ejpam-3335	832	30	a	a	DET
ejpam-3335	832	31	strongly	strongly	ADV
ejpam-3335	832	32	up	up	ADJ
ejpam-3335	832	33	-	-	PUNCT
ejpam-3335	832	34	ideal	ideal	NOUN
ejpam-3335	832	35	of	of	ADP
ejpam-3335	832	36	a.	a.	NOUN
ejpam-3335	832	37	proof	proof	NOUN
ejpam-3335	832	38	.	.	PUNCT
ejpam-3335	833	1	it	it	PRON
ejpam-3335	833	2	is	be	AUX
ejpam-3335	833	3	straightforward	straightforward	ADJ
ejpam-3335	833	4	by	by	ADP
ejpam-3335	833	5	theorem	theorem	NOUN
ejpam-3335	833	6	26	26	NUM
ejpam-3335	833	7	and	and	CCONJ
ejpam-3335	833	8	3	3	NUM
ejpam-3335	833	9	.	.	NOUN
ejpam-3335	833	10	6	6	NUM
ejpam-3335	833	11	.	.	X
ejpam-3335	834	1	conclusions	conclusion	NOUN
ejpam-3335	834	2	and	and	CCONJ
ejpam-3335	834	3	future	future	ADJ
ejpam-3335	834	4	work	work	NOUN
ejpam-3335	834	5	in	in	ADP
ejpam-3335	834	6	this	this	DET
ejpam-3335	834	7	paper	paper	NOUN
ejpam-3335	834	8	,	,	PUNCT
ejpam-3335	834	9	we	we	PRON
ejpam-3335	834	10	have	have	AUX
ejpam-3335	834	11	introduced	introduce	VERB
ejpam-3335	834	12	the	the	DET
ejpam-3335	834	13	notion	notion	NOUN
ejpam-3335	834	14	of	of	ADP
ejpam-3335	834	15	anti	anti	ADJ
ejpam-3335	834	16	-	-	ADJ
ejpam-3335	834	17	hesitant	hesitant	ADJ
ejpam-3335	834	18	fuzzy	fuzzy	ADJ
ejpam-3335	834	19	up	up	ADP
ejpam-3335	834	20	-	-	PUNCT
ejpam-3335	834	21	subalgebras	subalgebras	PROPN
ejpam-3335	834	22	(	(	PUNCT
ejpam-3335	834	23	resp	resp	NOUN
ejpam-3335	834	24	.	.	PUNCT
ejpam-3335	834	25	,	,	PUNCT
ejpam-3335	834	26	anti	anti	ADJ
ejpam-3335	834	27	-	-	ADJ
ejpam-3335	834	28	hesitant	hesitant	ADJ
ejpam-3335	834	29	fuzzy	fuzzy	ADJ
ejpam-3335	834	30	up	up	NOUN
ejpam-3335	834	31	-	-	PUNCT
ejpam-3335	834	32	filters	filter	NOUN
ejpam-3335	834	33	,	,	PUNCT
ejpam-3335	834	34	anti	anti	ADJ
ejpam-3335	834	35	-	-	ADJ
ejpam-3335	834	36	hesitant	hesitant	ADJ
ejpam-3335	834	37	fuzzy	fuzzy	ADJ
ejpam-3335	834	38	up	up	NOUN
ejpam-3335	834	39	-	-	PUNCT
ejpam-3335	834	40	ideals	ideal	NOUN
ejpam-3335	834	41	and	and	CCONJ
ejpam-3335	834	42	anti	anti	ADJ
ejpam-3335	834	43	-	-	ADJ
ejpam-3335	834	44	hesitant	hesitant	ADJ
ejpam-3335	834	45	fuzzy	fuzzy	ADJ
ejpam-3335	834	46	strongly	strongly	ADV
ejpam-3335	834	47	up	up	ADP
ejpam-3335	834	48	-	-	PUNCT
ejpam-3335	834	49	ideals	ideal	NOUN
ejpam-3335	834	50	)	)	PUNCT
ejpam-3335	834	51	of	of	ADP
ejpam-3335	834	52	up	up	ADV
ejpam-3335	834	53	-	-	PUNCT
ejpam-3335	834	54	algebras	algebras	PROPN
ejpam-3335	834	55	and	and	CCONJ
ejpam-3335	834	56	investigated	investigate	VERB
ejpam-3335	834	57	some	some	PRON
ejpam-3335	834	58	of	of	ADP
ejpam-3335	834	59	its	its	PRON
ejpam-3335	834	60	important	important	ADJ
ejpam-3335	834	61	properties	property	NOUN
ejpam-3335	834	62	.	.	PUNCT
ejpam-3335	835	1	then	then	ADV
ejpam-3335	835	2	we	we	PRON
ejpam-3335	835	3	have	have	VERB
ejpam-3335	835	4	the	the	DET
ejpam-3335	835	5	diagram	diagram	NOUN
ejpam-3335	835	6	of	of	ADP
ejpam-3335	835	7	anti	anti	ADJ
ejpam-3335	835	8	-	-	ADJ
ejpam-3335	835	9	type	type	NOUN
ejpam-3335	835	10	of	of	ADP
ejpam-3335	835	11	hesitant	hesitant	ADJ
ejpam-3335	835	12	fuzzy	fuzzy	ADJ
ejpam-3335	835	13	sets	set	NOUN
ejpam-3335	835	14	on	on	ADP
ejpam-3335	835	15	up	up	ADV
ejpam-3335	835	16	-	-	PUNCT
ejpam-3335	835	17	algebras	algebras	NOUN
ejpam-3335	835	18	below	below	ADV
ejpam-3335	835	19	.	.	PUNCT
ejpam-3335	836	1	in	in	ADP
ejpam-3335	836	2	our	our	PRON
ejpam-3335	836	3	future	future	ADJ
ejpam-3335	836	4	study	study	NOUN
ejpam-3335	836	5	of	of	ADP
ejpam-3335	836	6	up	up	ADP
ejpam-3335	836	7	-	-	PUNCT
ejpam-3335	836	8	algebras	algebras	X
ejpam-3335	836	9	,	,	PUNCT
ejpam-3335	836	10	may	may	AUX
ejpam-3335	836	11	be	be	AUX
ejpam-3335	836	12	the	the	DET
ejpam-3335	836	13	following	follow	VERB
ejpam-3335	836	14	topics	topic	NOUN
ejpam-3335	836	15	should	should	AUX
ejpam-3335	836	16	be	be	AUX
ejpam-3335	836	17	considered	consider	VERB
ejpam-3335	836	18	:	:	PUNCT
ejpam-3335	836	19	•	•	ADP
ejpam-3335	836	20	to	to	PART
ejpam-3335	836	21	get	get	VERB
ejpam-3335	836	22	more	more	ADJ
ejpam-3335	836	23	results	result	NOUN
ejpam-3335	836	24	in	in	ADP
ejpam-3335	836	25	anti	anti	ADJ
ejpam-3335	836	26	-	-	ADJ
ejpam-3335	836	27	hesitant	hesitant	ADJ
ejpam-3335	836	28	fuzzy	fuzzy	ADJ
ejpam-3335	836	29	up	up	ADP
ejpam-3335	836	30	-	-	PUNCT
ejpam-3335	836	31	subalgebras	subalgebras	PROPN
ejpam-3335	836	32	,	,	PUNCT
ejpam-3335	836	33	anti	anti	ADJ
ejpam-3335	836	34	-	-	ADJ
ejpam-3335	836	35	hesitant	hesitant	ADJ
ejpam-3335	836	36	fuzzy	fuzzy	ADJ
ejpam-3335	836	37	upfilters	upfilter	NOUN
ejpam-3335	836	38	,	,	PUNCT
ejpam-3335	836	39	anti	anti	ADJ
ejpam-3335	836	40	-	-	ADJ
ejpam-3335	836	41	hesitant	hesitant	ADJ
ejpam-3335	836	42	fuzzy	fuzzy	ADJ
ejpam-3335	836	43	up	up	NOUN
ejpam-3335	836	44	-	-	PUNCT
ejpam-3335	836	45	ideals	ideal	NOUN
ejpam-3335	836	46	,	,	PUNCT
ejpam-3335	836	47	and	and	CCONJ
ejpam-3335	836	48	anti	anti	ADJ
ejpam-3335	836	49	-	-	ADJ
ejpam-3335	836	50	hesitant	hesitant	ADJ
ejpam-3335	836	51	fuzzy	fuzzy	ADJ
ejpam-3335	836	52	strongly	strongly	ADV
ejpam-3335	836	53	up	up	ADP
ejpam-3335	836	54	-	-	PUNCT
ejpam-3335	836	55	ideals	ideal	NOUN
ejpam-3335	836	56	of	of	ADP
ejpam-3335	836	57	up	up	ADP
ejpam-3335	836	58	-	-	PUNCT
ejpam-3335	836	59	algebras	algebras	X
ejpam-3335	836	60	.	.	NOUN
ejpam-3335	837	1	•	•	NUM
ejpam-3335	837	2	to	to	PART
ejpam-3335	837	3	define	define	VERB
ejpam-3335	837	4	anti	anti	ADJ
ejpam-3335	837	5	-	-	ADJ
ejpam-3335	837	6	hesitant	hesitant	ADJ
ejpam-3335	837	7	fuzzy	fuzzy	ADJ
ejpam-3335	837	8	soft	soft	ADJ
ejpam-3335	837	9	up	up	ADP
ejpam-3335	837	10	-	-	PUNCT
ejpam-3335	837	11	subalgebras	subalgebras	X
ejpam-3335	837	12	,	,	PUNCT
ejpam-3335	837	13	anti	anti	ADJ
ejpam-3335	837	14	-	-	ADJ
ejpam-3335	837	15	hesitant	hesitant	ADJ
ejpam-3335	837	16	fuzzy	fuzzy	ADJ
ejpam-3335	837	17	soft	soft	ADJ
ejpam-3335	837	18	up	up	ADP
ejpam-3335	837	19	-	-	PUNCT
ejpam-3335	837	20	filters	filter	NOUN
ejpam-3335	837	21	,	,	PUNCT
ejpam-3335	837	22	anti	anti	ADJ
ejpam-3335	837	23	-	-	ADJ
ejpam-3335	837	24	hesitant	hesitant	ADJ
ejpam-3335	837	25	fuzzy	fuzzy	ADJ
ejpam-3335	837	26	soft	soft	ADJ
ejpam-3335	837	27	up	up	NOUN
ejpam-3335	837	28	-	-	PUNCT
ejpam-3335	837	29	ideals	ideal	NOUN
ejpam-3335	837	30	,	,	PUNCT
ejpam-3335	837	31	and	and	CCONJ
ejpam-3335	837	32	anti	anti	ADJ
ejpam-3335	837	33	-	-	ADJ
ejpam-3335	837	34	hesitant	hesitant	ADJ
ejpam-3335	837	35	fuzzy	fuzzy	ADJ
ejpam-3335	837	36	soft	soft	ADJ
ejpam-3335	837	37	strongly	strongly	ADV
ejpam-3335	837	38	up	up	ADP
ejpam-3335	837	39	-	-	PUNCT
ejpam-3335	837	40	ideals	ideal	NOUN
ejpam-3335	837	41	over	over	ADP
ejpam-3335	837	42	up	up	ADV
ejpam-3335	837	43	-	-	PUNCT
ejpam-3335	837	44	algebras	algebras	X
ejpam-3335	837	45	.	.	NOUN
ejpam-3335	838	1	•	•	NUM
ejpam-3335	838	2	to	to	PART
ejpam-3335	838	3	define	define	VERB
ejpam-3335	838	4	operations	operation	NOUN
ejpam-3335	838	5	of	of	ADP
ejpam-3335	838	6	hesitant	hesitant	ADJ
ejpam-3335	838	7	fuzzy	fuzzy	ADJ
ejpam-3335	838	8	soft	soft	ADJ
ejpam-3335	838	9	sets	set	NOUN
ejpam-3335	838	10	over	over	ADP
ejpam-3335	838	11	up	up	ADV
ejpam-3335	838	12	-	-	PUNCT
ejpam-3335	838	13	algebras	algebras	X
ejpam-3335	838	14	.	.	PUNCT
ejpam-3335	839	1	acknowledgements	acknowledgement	NOUN
ejpam-3335	839	2	the	the	DET
ejpam-3335	839	3	authors	author	NOUN
ejpam-3335	839	4	wish	wish	VERB
ejpam-3335	839	5	to	to	PART
ejpam-3335	839	6	express	express	VERB
ejpam-3335	839	7	their	their	PRON
ejpam-3335	839	8	sincere	sincere	ADJ
ejpam-3335	839	9	thanks	thank	NOUN
ejpam-3335	839	10	to	to	ADP
ejpam-3335	839	11	the	the	DET
ejpam-3335	839	12	referees	referee	NOUN
ejpam-3335	839	13	for	for	ADP
ejpam-3335	839	14	the	the	DET
ejpam-3335	839	15	valuable	valuable	ADJ
ejpam-3335	839	16	suggestions	suggestion	NOUN
ejpam-3335	839	17	which	which	PRON
ejpam-3335	839	18	lead	lead	VERB
ejpam-3335	839	19	to	to	ADP
ejpam-3335	839	20	an	an	DET
ejpam-3335	839	21	improvement	improvement	NOUN
ejpam-3335	839	22	of	of	ADP
ejpam-3335	839	23	this	this	DET
ejpam-3335	839	24	paper	paper	NOUN
ejpam-3335	839	25	.	.	PUNCT
ejpam-3335	840	1	references	reference	NOUN
ejpam-3335	840	2	1001	1001	NUM
ejpam-3335	840	3	references	reference	NOUN
ejpam-3335	840	4	[	[	X
ejpam-3335	840	5	1	1	NUM
ejpam-3335	840	6	]	]	PUNCT
ejpam-3335	840	7	t.	t.	NOUN
ejpam-3335	840	8	guntasow	guntasow	NOUN
ejpam-3335	840	9	,	,	PUNCT
ejpam-3335	840	10	s.	s.	PROPN
ejpam-3335	840	11	sajak	sajak	PROPN
ejpam-3335	840	12	,	,	PUNCT
ejpam-3335	840	13	a.	a.	PROPN
ejpam-3335	840	14	jomkham	jomkham	PROPN
ejpam-3335	840	15	,	,	PUNCT
ejpam-3335	840	16	and	and	CCONJ
ejpam-3335	840	17	a.	a.	NOUN
ejpam-3335	840	18	iampan	iampan	PROPN
ejpam-3335	840	19	.	.	PUNCT
ejpam-3335	841	1	fuzzy	fuzzy	ADJ
ejpam-3335	841	2	translations	translation	NOUN
ejpam-3335	841	3	of	of	ADP
ejpam-3335	841	4	a	a	DET
ejpam-3335	841	5	fuzzy	fuzzy	ADJ
ejpam-3335	841	6	set	set	NOUN
ejpam-3335	841	7	in	in	ADP
ejpam-3335	841	8	up	up	ADP
ejpam-3335	841	9	-	-	PUNCT
ejpam-3335	841	10	algebras	algebras	X
ejpam-3335	841	11	.	.	PUNCT
ejpam-3335	842	1	j.	j.	PROPN
ejpam-3335	842	2	indones	indones	PROPN
ejpam-3335	842	3	.	.	PUNCT
ejpam-3335	843	1	math	math	NOUN
ejpam-3335	843	2	.	.	PUNCT
ejpam-3335	844	1	soc	soc	PROPN
ejpam-3335	844	2	.	.	PROPN
ejpam-3335	844	3	,	,	PUNCT
ejpam-3335	844	4	23(2):1–19	23(2):1–19	NUM
ejpam-3335	844	5	,	,	PUNCT
ejpam-3335	844	6	2017	2017	NUM
ejpam-3335	844	7	.	.	PUNCT
ejpam-3335	845	1	[	[	X
ejpam-3335	845	2	2	2	NUM
ejpam-3335	845	3	]	]	PUNCT
ejpam-3335	845	4	a.	a.	NOUN
ejpam-3335	845	5	iampan	iampan	PROPN
ejpam-3335	845	6	.	.	PUNCT
ejpam-3335	846	1	a	a	DET
ejpam-3335	846	2	new	new	ADJ
ejpam-3335	846	3	branch	branch	NOUN
ejpam-3335	846	4	of	of	ADP
ejpam-3335	846	5	the	the	DET
ejpam-3335	846	6	logical	logical	ADJ
ejpam-3335	846	7	algebra	algebra	NOUN
ejpam-3335	846	8	:	:	PUNCT
ejpam-3335	846	9	up	up	ADP
ejpam-3335	846	10	-	-	PUNCT
ejpam-3335	846	11	algebras	algebras	X
ejpam-3335	846	12	.	.	PUNCT
ejpam-3335	847	1	j.	j.	PROPN
ejpam-3335	847	2	algebra	algebra	PROPN
ejpam-3335	847	3	relat	relat	PROPN
ejpam-3335	847	4	.	.	PUNCT
ejpam-3335	848	1	top	top	PROPN
ejpam-3335	848	2	.	.	PROPN
ejpam-3335	848	3	,	,	PUNCT
ejpam-3335	848	4	5(1):35–54	5(1):35–54	NUM
ejpam-3335	848	5	,	,	PUNCT
ejpam-3335	848	6	2017	2017	NUM
ejpam-3335	848	7	.	.	PUNCT
ejpam-3335	849	1	[	[	X
ejpam-3335	849	2	3	3	NUM
ejpam-3335	849	3	]	]	PUNCT
ejpam-3335	849	4	a.	a.	NOUN
ejpam-3335	849	5	iampan	iampan	PROPN
ejpam-3335	849	6	.	.	PUNCT
ejpam-3335	850	1	introducing	introduce	VERB
ejpam-3335	850	2	fully	fully	ADV
ejpam-3335	850	3	up	up	ADP
ejpam-3335	850	4	-	-	PUNCT
ejpam-3335	850	5	semigroups	semigroup	NOUN
ejpam-3335	850	6	.	.	PUNCT
ejpam-3335	851	1	manuscript	manuscript	NOUN
ejpam-3335	851	2	accepted	accept	VERB
ejpam-3335	851	3	for	for	ADP
ejpam-3335	851	4	publication	publication	NOUN
ejpam-3335	851	5	in	in	ADP
ejpam-3335	851	6	discuss	discuss	PROPN
ejpam-3335	851	7	.	.	PUNCT
ejpam-3335	852	1	math	math	NOUN
ejpam-3335	852	2	.	.	PUNCT
ejpam-3335	852	3	,	,	PUNCT
ejpam-3335	852	4	gen	gen	PROPN
ejpam-3335	852	5	.	.	PROPN
ejpam-3335	852	6	algebra	algebra	PROPN
ejpam-3335	852	7	appl	appl	PROPN
ejpam-3335	852	8	.	.	PROPN
ejpam-3335	852	9	,	,	PUNCT
ejpam-3335	852	10	september	september	PROPN
ejpam-3335	852	11	2018	2018	NUM
ejpam-3335	852	12	.	.	PUNCT
ejpam-3335	853	1	[	[	X
ejpam-3335	853	2	4	4	X
ejpam-3335	853	3	]	]	X
ejpam-3335	853	4	w.	w.	PROPN
ejpam-3335	853	5	kaijae	kaijae	PROPN
ejpam-3335	853	6	,	,	PUNCT
ejpam-3335	853	7	p.	p.	PROPN
ejpam-3335	853	8	poungsumpao	poungsumpao	PROPN
ejpam-3335	853	9	,	,	PUNCT
ejpam-3335	853	10	s.	s.	PROPN
ejpam-3335	853	11	arayarangsi	arayarangsi	PROPN
ejpam-3335	853	12	,	,	PUNCT
ejpam-3335	853	13	and	and	CCONJ
ejpam-3335	853	14	a.	a.	NOUN
ejpam-3335	853	15	iampan	iampan	PROPN
ejpam-3335	853	16	.	.	PUNCT
ejpam-3335	854	1	up	up	ADV
ejpam-3335	854	2	-	-	PUNCT
ejpam-3335	854	3	algebras	algebras	PROPN
ejpam-3335	854	4	characterized	characterize	VERB
ejpam-3335	854	5	by	by	ADP
ejpam-3335	854	6	their	their	PRON
ejpam-3335	854	7	anti	anti	ADJ
ejpam-3335	854	8	-	-	ADJ
ejpam-3335	854	9	fuzzy	fuzzy	ADJ
ejpam-3335	854	10	up	up	ADJ
ejpam-3335	854	11	-	-	PUNCT
ejpam-3335	854	12	ideals	ideal	NOUN
ejpam-3335	854	13	and	and	CCONJ
ejpam-3335	854	14	anti	anti	ADJ
ejpam-3335	854	15	-	-	ADJ
ejpam-3335	854	16	fuzzy	fuzzy	ADJ
ejpam-3335	854	17	up	up	ADP
ejpam-3335	854	18	-	-	PUNCT
ejpam-3335	854	19	subalgebras	subalgebras	PROPN
ejpam-3335	854	20	.	.	PUNCT
ejpam-3335	855	1	ital	ital	PROPN
ejpam-3335	855	2	.	.	PUNCT
ejpam-3335	856	1	j.	j.	PROPN
ejpam-3335	856	2	pure	pure	PROPN
ejpam-3335	856	3	appl	appl	PROPN
ejpam-3335	856	4	.	.	PUNCT
ejpam-3335	856	5	math	math	PROPN
ejpam-3335	856	6	.	.	PUNCT
ejpam-3335	856	7	,	,	PUNCT
ejpam-3335	857	1	36:667–692	36:667–692	NUM
ejpam-3335	857	2	,	,	PUNCT
ejpam-3335	857	3	2016	2016	NUM
ejpam-3335	857	4	.	.	PUNCT
ejpam-3335	858	1	[	[	X
ejpam-3335	858	2	5	5	X
ejpam-3335	858	3	]	]	PUNCT
ejpam-3335	858	4	b.	b.	PROPN
ejpam-3335	858	5	kesorn	kesorn	PROPN
ejpam-3335	858	6	,	,	PUNCT
ejpam-3335	858	7	k.	k.	PROPN
ejpam-3335	858	8	maimun	maimun	PROPN
ejpam-3335	858	9	,	,	PUNCT
ejpam-3335	858	10	w.	w.	PROPN
ejpam-3335	858	11	ratbandan	ratbandan	PROPN
ejpam-3335	858	12	,	,	PUNCT
ejpam-3335	858	13	and	and	CCONJ
ejpam-3335	858	14	a.	a.	NOUN
ejpam-3335	858	15	iampan	iampan	PROPN
ejpam-3335	858	16	.	.	PUNCT
ejpam-3335	859	1	intuitionistic	intuitionistic	ADJ
ejpam-3335	859	2	fuzzy	fuzzy	ADJ
ejpam-3335	859	3	sets	set	NOUN
ejpam-3335	859	4	in	in	ADP
ejpam-3335	859	5	up	up	ADP
ejpam-3335	859	6	-	-	PUNCT
ejpam-3335	859	7	algebras	algebras	X
ejpam-3335	859	8	.	.	PUNCT
ejpam-3335	860	1	ital	ital	PROPN
ejpam-3335	860	2	.	.	PUNCT
ejpam-3335	861	1	j.	j.	PROPN
ejpam-3335	861	2	pure	pure	PROPN
ejpam-3335	861	3	appl	appl	PROPN
ejpam-3335	861	4	.	.	PUNCT
ejpam-3335	861	5	math	math	PROPN
ejpam-3335	861	6	.	.	PUNCT
ejpam-3335	861	7	,	,	PUNCT
ejpam-3335	862	1	34:339–364	34:339–364	NUM
ejpam-3335	862	2	,	,	PUNCT
ejpam-3335	862	3	2015	2015	NUM
ejpam-3335	862	4	.	.	PUNCT
ejpam-3335	863	1	[	[	X
ejpam-3335	863	2	6	6	NUM
ejpam-3335	863	3	]	]	PUNCT
ejpam-3335	863	4	p.	p.	NOUN
ejpam-3335	863	5	mosrijai	mosrijai	PROPN
ejpam-3335	863	6	,	,	PUNCT
ejpam-3335	863	7	w.	w.	PROPN
ejpam-3335	863	8	kamti	kamti	PROPN
ejpam-3335	863	9	,	,	PUNCT
ejpam-3335	863	10	a.	a.	PROPN
ejpam-3335	863	11	satirad	satirad	PROPN
ejpam-3335	863	12	,	,	PUNCT
ejpam-3335	863	13	and	and	CCONJ
ejpam-3335	863	14	a.	a.	NOUN
ejpam-3335	863	15	iampan	iampan	PROPN
ejpam-3335	863	16	.	.	PUNCT
ejpam-3335	864	1	hesitant	hesitant	ADJ
ejpam-3335	864	2	fuzzy	fuzzy	ADJ
ejpam-3335	864	3	sets	set	NOUN
ejpam-3335	864	4	on	on	ADP
ejpam-3335	864	5	upalgebras	upalgebra	NOUN
ejpam-3335	864	6	.	.	PUNCT
ejpam-3335	865	1	konuralp	konuralp	PROPN
ejpam-3335	865	2	j.	j.	PROPN
ejpam-3335	865	3	math	math	PROPN
ejpam-3335	865	4	.	.	PUNCT
ejpam-3335	865	5	,	,	PUNCT
ejpam-3335	865	6	5(2):268–280	5(2):268–280	NUM
ejpam-3335	865	7	,	,	PUNCT
ejpam-3335	865	8	2017	2017	NUM
ejpam-3335	865	9	.	.	PUNCT
ejpam-3335	866	1	[	[	X
ejpam-3335	866	2	7	7	X
ejpam-3335	866	3	]	]	PUNCT
ejpam-3335	866	4	p.	p.	NOUN
ejpam-3335	866	5	mosrijai	mosrijai	PROPN
ejpam-3335	866	6	,	,	PUNCT
ejpam-3335	866	7	a.	a.	PROPN
ejpam-3335	866	8	satirad	satirad	PROPN
ejpam-3335	866	9	,	,	PUNCT
ejpam-3335	866	10	and	and	CCONJ
ejpam-3335	866	11	a.	a.	NOUN
ejpam-3335	866	12	iampan	iampan	PROPN
ejpam-3335	866	13	.	.	PUNCT
ejpam-3335	867	1	partial	partial	ADJ
ejpam-3335	867	2	constant	constant	ADJ
ejpam-3335	867	3	hesitant	hesitant	ADJ
ejpam-3335	867	4	fuzzy	fuzzy	ADJ
ejpam-3335	867	5	sets	set	NOUN
ejpam-3335	867	6	on	on	ADP
ejpam-3335	867	7	upalgebras	upalgebra	NOUN
ejpam-3335	867	8	.	.	PUNCT
ejpam-3335	868	1	j.	j.	PROPN
ejpam-3335	868	2	new	new	PROPN
ejpam-3335	868	3	theory	theory	NOUN
ejpam-3335	868	4	,	,	PUNCT
ejpam-3335	868	5	22:39–50	22:39–50	NUM
ejpam-3335	868	6	,	,	PUNCT
ejpam-3335	868	7	2018	2018	NUM
ejpam-3335	868	8	.	.	PUNCT
ejpam-3335	869	1	[	[	X
ejpam-3335	869	2	8	8	NUM
ejpam-3335	869	3	]	]	X
ejpam-3335	869	4	c.	c.	NOUN
ejpam-3335	869	5	prabpayak	prabpayak	NOUN
ejpam-3335	869	6	and	and	CCONJ
ejpam-3335	869	7	u.	u.	NOUN
ejpam-3335	869	8	leerawat	leerawat	PROPN
ejpam-3335	869	9	.	.	PUNCT
ejpam-3335	870	1	on	on	ADP
ejpam-3335	870	2	ideals	ideal	NOUN
ejpam-3335	870	3	and	and	CCONJ
ejpam-3335	870	4	congruences	congruence	NOUN
ejpam-3335	870	5	in	in	ADP
ejpam-3335	870	6	ku	ku	PROPN
ejpam-3335	870	7	-	-	PUNCT
ejpam-3335	870	8	algebras	algebras	PROPN
ejpam-3335	870	9	.	.	PUNCT
ejpam-3335	871	1	sci	sci	PROPN
ejpam-3335	871	2	.	.	PROPN
ejpam-3335	871	3	magna	magna	PROPN
ejpam-3335	871	4	,	,	PUNCT
ejpam-3335	871	5	5(1):54–57	5(1):54–57	NUM
ejpam-3335	871	6	,	,	PUNCT
ejpam-3335	871	7	2009	2009	NUM
ejpam-3335	871	8	.	.	PUNCT
ejpam-3335	872	1	[	[	X
ejpam-3335	872	2	9	9	NUM
ejpam-3335	872	3	]	]	X
ejpam-3335	872	4	d.	d.	PROPN
ejpam-3335	872	5	a.	a.	PROPN
ejpam-3335	872	6	romano	romano	PROPN
ejpam-3335	872	7	.	.	PUNCT
ejpam-3335	873	1	proper	proper	ADJ
ejpam-3335	873	2	up	up	ADP
ejpam-3335	873	3	-	-	PUNCT
ejpam-3335	873	4	filters	filter	NOUN
ejpam-3335	873	5	of	of	ADP
ejpam-3335	873	6	up	up	NOUN
ejpam-3335	873	7	-	-	PUNCT
ejpam-3335	873	8	algebra	algebra	NOUN
ejpam-3335	873	9	.	.	PUNCT
ejpam-3335	874	1	univ	univ	PROPN
ejpam-3335	874	2	.	.	PUNCT
ejpam-3335	875	1	j.	j.	PROPN
ejpam-3335	875	2	math	math	PROPN
ejpam-3335	875	3	.	.	PUNCT
ejpam-3335	876	1	appl	appl	PROPN
ejpam-3335	876	2	.	.	PROPN
ejpam-3335	876	3	,	,	PUNCT
ejpam-3335	876	4	1(2):98–100	1(2):98–100	NUM
ejpam-3335	876	5	,	,	PUNCT
ejpam-3335	876	6	2018	2018	NUM
ejpam-3335	876	7	.	.	PUNCT
ejpam-3335	877	1	[	[	X
ejpam-3335	877	2	10	10	NUM
ejpam-3335	877	3	]	]	PUNCT
ejpam-3335	877	4	a.	a.	NOUN
ejpam-3335	877	5	satirad	satirad	PROPN
ejpam-3335	877	6	,	,	PUNCT
ejpam-3335	877	7	p.	p.	PROPN
ejpam-3335	877	8	mosrijai	mosrijai	PROPN
ejpam-3335	877	9	,	,	PUNCT
ejpam-3335	877	10	and	and	CCONJ
ejpam-3335	877	11	a.	a.	NOUN
ejpam-3335	877	12	iampan	iampan	PROPN
ejpam-3335	877	13	.	.	PUNCT
ejpam-3335	878	1	generalized	generalized	ADJ
ejpam-3335	878	2	power	power	NOUN
ejpam-3335	878	3	up	up	ADP
ejpam-3335	878	4	-	-	PUNCT
ejpam-3335	878	5	algebras	algebras	X
ejpam-3335	878	6	.	.	PUNCT
ejpam-3335	879	1	manuscript	manuscript	NOUN
ejpam-3335	879	2	accepted	accept	VERB
ejpam-3335	879	3	for	for	ADP
ejpam-3335	879	4	publication	publication	NOUN
ejpam-3335	879	5	in	in	ADP
ejpam-3335	879	6	int	int	NOUN
ejpam-3335	879	7	.	.	PUNCT
ejpam-3335	880	1	j.	j.	PROPN
ejpam-3335	880	2	math	math	PROPN
ejpam-3335	880	3	.	.	PUNCT
ejpam-3335	881	1	comput	comput	NOUN
ejpam-3335	881	2	.	.	PUNCT
ejpam-3335	882	1	sci	sci	PROPN
ejpam-3335	882	2	.	.	PROPN
ejpam-3335	882	3	,	,	PUNCT
ejpam-3335	882	4	may	may	PROPN
ejpam-3335	882	5	2018	2018	NUM
ejpam-3335	882	6	.	.	PUNCT
ejpam-3335	883	1	[	[	X
ejpam-3335	883	2	11	11	NUM
ejpam-3335	883	3	]	]	PUNCT
ejpam-3335	883	4	a.	a.	NOUN
ejpam-3335	883	5	satirad	satirad	PROPN
ejpam-3335	883	6	,	,	PUNCT
ejpam-3335	883	7	p.	p.	PROPN
ejpam-3335	883	8	mosrijai	mosrijai	PROPN
ejpam-3335	883	9	,	,	PUNCT
ejpam-3335	883	10	w.	w.	PROPN
ejpam-3335	883	11	kamti	kamti	PROPN
ejpam-3335	883	12	,	,	PUNCT
ejpam-3335	883	13	and	and	CCONJ
ejpam-3335	883	14	a.	a.	NOUN
ejpam-3335	883	15	iampan	iampan	PROPN
ejpam-3335	883	16	.	.	PUNCT
ejpam-3335	884	1	level	level	NOUN
ejpam-3335	884	2	subsets	subset	NOUN
ejpam-3335	884	3	of	of	ADP
ejpam-3335	884	4	a	a	DET
ejpam-3335	884	5	hesitant	hesitant	ADJ
ejpam-3335	884	6	fuzzy	fuzzy	ADJ
ejpam-3335	884	7	set	set	NOUN
ejpam-3335	884	8	on	on	ADP
ejpam-3335	884	9	up	up	ADP
ejpam-3335	884	10	-	-	PUNCT
ejpam-3335	884	11	algebras	algebras	PROPN
ejpam-3335	884	12	.	.	PUNCT
ejpam-3335	885	1	ann	ann	PROPN
ejpam-3335	885	2	.	.	PUNCT
ejpam-3335	885	3	fuzzy	fuzzy	ADJ
ejpam-3335	885	4	math	math	NOUN
ejpam-3335	885	5	.	.	PUNCT
ejpam-3335	886	1	inform	inform	NOUN
ejpam-3335	886	2	.	.	PUNCT
ejpam-3335	886	3	,	,	PUNCT
ejpam-3335	886	4	14(3):279–302	14(3):279–302	NUM
ejpam-3335	886	5	,	,	PUNCT
ejpam-3335	886	6	2017	2017	NUM
ejpam-3335	886	7	.	.	PUNCT
ejpam-3335	887	1	[	[	X
ejpam-3335	887	2	12	12	NUM
ejpam-3335	887	3	]	]	PUNCT
ejpam-3335	887	4	t.	t.	NOUN
ejpam-3335	887	5	senapati	senapati	PROPN
ejpam-3335	887	6	,	,	PUNCT
ejpam-3335	887	7	y.	y.	PROPN
ejpam-3335	887	8	b.	b.	PROPN
ejpam-3335	887	9	jun	jun	PROPN
ejpam-3335	887	10	,	,	PUNCT
ejpam-3335	887	11	and	and	CCONJ
ejpam-3335	887	12	k.	k.	PROPN
ejpam-3335	887	13	p.	p.	PROPN
ejpam-3335	887	14	shum	shum	PROPN
ejpam-3335	887	15	.	.	PUNCT
ejpam-3335	888	1	cubic	cubic	ADJ
ejpam-3335	888	2	set	set	VERB
ejpam-3335	888	3	structure	structure	NOUN
ejpam-3335	888	4	applied	apply	VERB
ejpam-3335	888	5	in	in	ADP
ejpam-3335	888	6	up	up	ADP
ejpam-3335	888	7	-	-	PUNCT
ejpam-3335	888	8	algebras	algebras	X
ejpam-3335	888	9	.	.	PUNCT
ejpam-3335	889	1	discrete	discrete	ADJ
ejpam-3335	889	2	math	math	NOUN
ejpam-3335	889	3	.	.	PUNCT
ejpam-3335	890	1	algorithms	algorithms	PROPN
ejpam-3335	890	2	appl	appl	PROPN
ejpam-3335	890	3	.	.	PROPN
ejpam-3335	890	4	,	,	PUNCT
ejpam-3335	890	5	10(4):1850049	10(4):1850049	NUM
ejpam-3335	890	6	,	,	PUNCT
ejpam-3335	890	7	2018	2018	NUM
ejpam-3335	890	8	.	.	PUNCT
ejpam-3335	891	1	[	[	X
ejpam-3335	891	2	13	13	NUM
ejpam-3335	891	3	]	]	PUNCT
ejpam-3335	891	4	t.	t.	NOUN
ejpam-3335	891	5	senapati	senapati	PROPN
ejpam-3335	891	6	,	,	PUNCT
ejpam-3335	891	7	g.	g.	PROPN
ejpam-3335	891	8	muhiuddin	muhiuddin	PROPN
ejpam-3335	891	9	,	,	PUNCT
ejpam-3335	891	10	and	and	CCONJ
ejpam-3335	891	11	k.	k.	PROPN
ejpam-3335	891	12	p.	p.	PROPN
ejpam-3335	891	13	shum	shum	PROPN
ejpam-3335	891	14	.	.	PUNCT
ejpam-3335	892	1	representation	representation	NOUN
ejpam-3335	892	2	of	of	ADP
ejpam-3335	892	3	up	up	ADV
ejpam-3335	892	4	-	-	PUNCT
ejpam-3335	892	5	algebras	algebras	NOUN
ejpam-3335	892	6	in	in	ADP
ejpam-3335	892	7	interval	interval	NOUN
ejpam-3335	892	8	-	-	PUNCT
ejpam-3335	892	9	valued	value	VERB
ejpam-3335	892	10	intuitionistic	intuitionistic	ADJ
ejpam-3335	892	11	fuzzy	fuzzy	ADJ
ejpam-3335	892	12	environment	environment	NOUN
ejpam-3335	892	13	.	.	PUNCT
ejpam-3335	893	1	ital	ital	PROPN
ejpam-3335	893	2	.	.	PUNCT
ejpam-3335	894	1	j.	j.	PROPN
ejpam-3335	894	2	pure	pure	PROPN
ejpam-3335	894	3	appl	appl	PROPN
ejpam-3335	894	4	.	.	PUNCT
ejpam-3335	894	5	math	math	PROPN
ejpam-3335	894	6	.	.	PUNCT
ejpam-3335	894	7	,	,	PUNCT
ejpam-3335	894	8	38:497	38:497	NUM
ejpam-3335	894	9	–	–	PUNCT
ejpam-3335	894	10	517	517	NUM
ejpam-3335	894	11	,	,	PUNCT
ejpam-3335	894	12	2017	2017	NUM
ejpam-3335	894	13	.	.	PUNCT
ejpam-3335	895	1	[	[	X
ejpam-3335	895	2	14	14	NUM
ejpam-3335	895	3	]	]	X
ejpam-3335	895	4	j.	j.	PROPN
ejpam-3335	895	5	somjanta	somjanta	PROPN
ejpam-3335	895	6	,	,	PUNCT
ejpam-3335	895	7	n.	n.	PROPN
ejpam-3335	895	8	thuekaew	thuekaew	PROPN
ejpam-3335	895	9	,	,	PUNCT
ejpam-3335	895	10	p.	p.	NOUN
ejpam-3335	895	11	kumpeangkeaw	kumpeangkeaw	PROPN
ejpam-3335	895	12	,	,	PUNCT
ejpam-3335	895	13	and	and	CCONJ
ejpam-3335	895	14	a.	a.	NOUN
ejpam-3335	895	15	iampan	iampan	PROPN
ejpam-3335	895	16	.	.	PUNCT
ejpam-3335	896	1	fuzzy	fuzzy	ADJ
ejpam-3335	896	2	sets	set	NOUN
ejpam-3335	896	3	in	in	ADP
ejpam-3335	896	4	upalgebras	upalgebra	NOUN
ejpam-3335	896	5	.	.	PUNCT
ejpam-3335	897	1	ann	ann	PROPN
ejpam-3335	897	2	.	.	PUNCT
ejpam-3335	897	3	fuzzy	fuzzy	ADJ
ejpam-3335	897	4	math	math	NOUN
ejpam-3335	897	5	.	.	PUNCT
ejpam-3335	898	1	inform	inform	NOUN
ejpam-3335	898	2	.	.	PUNCT
ejpam-3335	898	3	,	,	PUNCT
ejpam-3335	898	4	12(6):739–756	12(6):739–756	PROPN
ejpam-3335	898	5	,	,	PUNCT
ejpam-3335	898	6	2016	2016	NUM
ejpam-3335	898	7	.	.	PUNCT
ejpam-3335	899	1	[	[	X
ejpam-3335	899	2	15	15	NUM
ejpam-3335	899	3	]	]	X
ejpam-3335	899	4	m.	m.	NOUN
ejpam-3335	899	5	songsaeng	songsaeng	PROPN
ejpam-3335	899	6	and	and	CCONJ
ejpam-3335	899	7	a.	a.	NOUN
ejpam-3335	899	8	iampan	iampan	PROPN
ejpam-3335	899	9	.	.	PUNCT
ejpam-3335	900	1	n	n	PRON
ejpam-3335	900	2	-fuzzy	-fuzzy	NOUN
ejpam-3335	900	3	up	up	ADV
ejpam-3335	900	4	-	-	PUNCT
ejpam-3335	900	5	algebras	algebra	NOUN
ejpam-3335	900	6	and	and	CCONJ
ejpam-3335	900	7	its	its	PRON
ejpam-3335	900	8	level	level	NOUN
ejpam-3335	900	9	subsets	subset	NOUN
ejpam-3335	900	10	.	.	PUNCT
ejpam-3335	901	1	j.	j.	PROPN
ejpam-3335	901	2	algebra	algebra	PROPN
ejpam-3335	901	3	relat	relat	PROPN
ejpam-3335	901	4	.	.	PUNCT
ejpam-3335	902	1	top	top	NOUN
ejpam-3335	902	2	.	.	PUNCT
ejpam-3335	902	3	,	,	PUNCT
ejpam-3335	902	4	6(1):1–24	6(1):1–24	NUM
ejpam-3335	902	5	,	,	PUNCT
ejpam-3335	902	6	2018	2018	NUM
ejpam-3335	902	7	.	.	PUNCT
ejpam-3335	903	1	references	reference	NOUN
ejpam-3335	903	2	1002	1002	NUM
ejpam-3335	903	3	[	[	X
ejpam-3335	903	4	16	16	NUM
ejpam-3335	903	5	]	]	PUNCT
ejpam-3335	903	6	s.	s.	PROPN
ejpam-3335	903	7	sripaeng	sripaeng	PROPN
ejpam-3335	903	8	,	,	PUNCT
ejpam-3335	903	9	k.	k.	PROPN
ejpam-3335	903	10	tanamoon	tanamoon	PROPN
ejpam-3335	903	11	,	,	PUNCT
ejpam-3335	903	12	and	and	CCONJ
ejpam-3335	903	13	a.	a.	NOUN
ejpam-3335	903	14	iampan	iampan	PROPN
ejpam-3335	903	15	.	.	PUNCT
ejpam-3335	904	1	on	on	ADP
ejpam-3335	904	2	anti	anti	ADJ
ejpam-3335	904	3	q	q	ADJ
ejpam-3335	904	4	-	-	ADJ
ejpam-3335	904	5	fuzzy	fuzzy	ADJ
ejpam-3335	904	6	up	up	NOUN
ejpam-3335	904	7	-	-	PUNCT
ejpam-3335	904	8	ideals	ideal	NOUN
ejpam-3335	904	9	and	and	CCONJ
ejpam-3335	904	10	anti	anti	ADJ
ejpam-3335	904	11	q	q	ADJ
ejpam-3335	904	12	-	-	ADJ
ejpam-3335	904	13	fuzzy	fuzzy	ADJ
ejpam-3335	904	14	up	up	ADP
ejpam-3335	904	15	-	-	PUNCT
ejpam-3335	904	16	subalgebras	subalgebra	NOUN
ejpam-3335	904	17	of	of	ADP
ejpam-3335	904	18	up	up	ADP
ejpam-3335	904	19	-	-	PUNCT
ejpam-3335	904	20	algebras	algebras	X
ejpam-3335	904	21	.	.	PUNCT
ejpam-3335	905	1	j.	j.	PROPN
ejpam-3335	905	2	inf	inf	PROPN
ejpam-3335	905	3	.	.	PROPN
ejpam-3335	905	4	optim	optim	PROPN
ejpam-3335	905	5	.	.	PUNCT
ejpam-3335	906	1	sci	sci	PROPN
ejpam-3335	906	2	.	.	PROPN
ejpam-3335	906	3	,	,	PUNCT
ejpam-3335	906	4	39(5):1095–1127	39(5):1095–1127	NUM
ejpam-3335	906	5	,	,	PUNCT
ejpam-3335	906	6	2018	2018	NUM
ejpam-3335	906	7	.	.	PUNCT
ejpam-3335	907	1	[	[	X
ejpam-3335	907	2	17	17	NUM
ejpam-3335	907	3	]	]	PUNCT
ejpam-3335	907	4	k.	k.	PROPN
ejpam-3335	907	5	tanamoon	tanamoon	PROPN
ejpam-3335	907	6	,	,	PUNCT
ejpam-3335	907	7	s.	s.	PROPN
ejpam-3335	907	8	sripaeng	sripaeng	PROPN
ejpam-3335	907	9	,	,	PUNCT
ejpam-3335	907	10	and	and	CCONJ
ejpam-3335	907	11	a.	a.	NOUN
ejpam-3335	907	12	iampan	iampan	PROPN
ejpam-3335	907	13	.	.	PUNCT
ejpam-3335	908	1	q	q	ADJ
ejpam-3335	908	2	-	-	ADJ
ejpam-3335	908	3	fuzzy	fuzzy	ADJ
ejpam-3335	908	4	sets	set	NOUN
ejpam-3335	908	5	in	in	ADP
ejpam-3335	908	6	up	up	ADP
ejpam-3335	908	7	-	-	PUNCT
ejpam-3335	908	8	algebras	algebras	X
ejpam-3335	908	9	.	.	PUNCT
ejpam-3335	909	1	songklanakarin	songklanakarin	PROPN
ejpam-3335	909	2	j.	j.	PROPN
ejpam-3335	909	3	sci	sci	PROPN
ejpam-3335	909	4	.	.	PROPN
ejpam-3335	909	5	technol	technol	PROPN
ejpam-3335	909	6	.	.	PROPN
ejpam-3335	909	7	,	,	PUNCT
ejpam-3335	909	8	40(1):9–29	40(1):9–29	NUM
ejpam-3335	909	9	,	,	PUNCT
ejpam-3335	909	10	2018	2018	NUM
ejpam-3335	909	11	.	.	PUNCT
ejpam-3335	910	1	[	[	X
ejpam-3335	910	2	18	18	NUM
ejpam-3335	910	3	]	]	X
ejpam-3335	910	4	v.	v.	CCONJ
ejpam-3335	910	5	torra	torra	PROPN
ejpam-3335	910	6	.	.	PUNCT
ejpam-3335	911	1	hesitant	hesitant	ADJ
ejpam-3335	911	2	fuzzy	fuzzy	ADJ
ejpam-3335	911	3	sets	set	NOUN
ejpam-3335	911	4	.	.	PUNCT
ejpam-3335	912	1	int	int	NOUN
ejpam-3335	912	2	.	.	PUNCT
ejpam-3335	913	1	j.	j.	PROPN
ejpam-3335	913	2	intell	intell	PROPN
ejpam-3335	913	3	.	.	PUNCT
ejpam-3335	914	1	syst	syst	PROPN
ejpam-3335	914	2	.	.	PUNCT
ejpam-3335	914	3	,	,	PUNCT
ejpam-3335	915	1	25(6):529–539	25(6):529–539	NUM
ejpam-3335	915	2	,	,	PUNCT
ejpam-3335	915	3	2010	2010	NUM
ejpam-3335	915	4	.	.	PUNCT