id	sid	tid	token	lemma	pos
ejpam-4254	1	1	european	european	PROPN
ejpam-4254	1	2	journal	journal	PROPN
ejpam-4254	1	3	of	of	ADP
ejpam-4254	1	4	pure	pure	ADJ
ejpam-4254	1	5	and	and	CCONJ
ejpam-4254	1	6	applied	apply	VERB
ejpam-4254	1	7	mathematics	mathematic	NOUN
ejpam-4254	1	8	vol	vol	NOUN
ejpam-4254	1	9	.	.	PROPN
ejpam-4254	2	1	15	15	NUM
ejpam-4254	2	2	,	,	PUNCT
ejpam-4254	2	3	no	no	INTJ
ejpam-4254	2	4	.	.	NOUN
ejpam-4254	2	5	1	1	NUM
ejpam-4254	2	6	,	,	PUNCT
ejpam-4254	2	7	2022	2022	NUM
ejpam-4254	2	8	,	,	PUNCT
ejpam-4254	2	9	169	169	NUM
ejpam-4254	2	10	-	-	SYM
ejpam-4254	2	11	198	198	NUM
ejpam-4254	2	12	issn	issn	PROPN
ejpam-4254	2	13	1307	1307	NUM
ejpam-4254	2	14	-	-	SYM
ejpam-4254	2	15	5543	5543	NUM
ejpam-4254	2	16	–	–	PUNCT
ejpam-4254	3	1	ejpam.com	ejpam.com	X
ejpam-4254	3	2	published	publish	VERB
ejpam-4254	3	3	by	by	ADP
ejpam-4254	3	4	new	new	PROPN
ejpam-4254	3	5	york	york	PROPN
ejpam-4254	3	6	business	business	PROPN
ejpam-4254	3	7	global	global	ADJ
ejpam-4254	3	8	rough	rough	ADJ
ejpam-4254	3	9	pythagorean	pythagorean	PROPN
ejpam-4254	3	10	fuzzy	fuzzy	ADJ
ejpam-4254	3	11	sets	set	NOUN
ejpam-4254	3	12	in	in	ADP
ejpam-4254	3	13	up	up	ADV
ejpam-4254	3	14	-	-	PUNCT
ejpam-4254	3	15	algebras	algebras	NOUN
ejpam-4254	3	16	akarachai	akarachai	PROPN
ejpam-4254	3	17	satirad1	satirad1	PROPN
ejpam-4254	3	18	,	,	PUNCT
ejpam-4254	3	19	ronnason	ronnason	NOUN
ejpam-4254	3	20	chinram2	chinram2	PROPN
ejpam-4254	3	21	,	,	PUNCT
ejpam-4254	3	22	pongpun	pongpun	ADJ
ejpam-4254	3	23	julatha3	julatha3	PROPN
ejpam-4254	3	24	,	,	PUNCT
ejpam-4254	3	25	aiyared	aiyare	VERB
ejpam-4254	3	26	iampan1,∗	iampan1,∗	NOUN
ejpam-4254	3	27	1	1	NUM
ejpam-4254	3	28	fuzzy	fuzzy	ADJ
ejpam-4254	3	29	algebras	algebra	NOUN
ejpam-4254	3	30	and	and	CCONJ
ejpam-4254	3	31	decision	decision	NOUN
ejpam-4254	3	32	-	-	PUNCT
ejpam-4254	3	33	making	make	VERB
ejpam-4254	3	34	problems	problem	NOUN
ejpam-4254	3	35	research	research	NOUN
ejpam-4254	3	36	unit	unit	NOUN
ejpam-4254	3	37	,	,	PUNCT
ejpam-4254	3	38	department	department	NOUN
ejpam-4254	3	39	of	of	ADP
ejpam-4254	3	40	mathematics	mathematic	NOUN
ejpam-4254	3	41	,	,	PUNCT
ejpam-4254	3	42	school	school	NOUN
ejpam-4254	3	43	of	of	ADP
ejpam-4254	3	44	science	science	NOUN
ejpam-4254	3	45	,	,	PUNCT
ejpam-4254	3	46	university	university	NOUN
ejpam-4254	3	47	of	of	ADP
ejpam-4254	3	48	phayao	phayao	NOUN
ejpam-4254	3	49	,	,	PUNCT
ejpam-4254	3	50	mae	mae	PROPN
ejpam-4254	3	51	ka	ka	PROPN
ejpam-4254	3	52	,	,	PUNCT
ejpam-4254	3	53	mueang	mueang	PROPN
ejpam-4254	3	54	,	,	PUNCT
ejpam-4254	3	55	phayao	phayao	NOUN
ejpam-4254	3	56	56000	56000	NUM
ejpam-4254	3	57	,	,	PUNCT
ejpam-4254	3	58	thailand	thailand	PROPN
ejpam-4254	3	59	2	2	NUM
ejpam-4254	3	60	division	division	NOUN
ejpam-4254	3	61	of	of	ADP
ejpam-4254	3	62	computational	computational	ADJ
ejpam-4254	3	63	science	science	NOUN
ejpam-4254	3	64	,	,	PUNCT
ejpam-4254	3	65	faculty	faculty	NOUN
ejpam-4254	3	66	of	of	ADP
ejpam-4254	3	67	science	science	NOUN
ejpam-4254	3	68	,	,	PUNCT
ejpam-4254	3	69	prince	prince	NOUN
ejpam-4254	3	70	of	of	ADP
ejpam-4254	3	71	songkla	songkla	PROPN
ejpam-4254	3	72	university	university	PROPN
ejpam-4254	3	73	,	,	PUNCT
ejpam-4254	3	74	hat	hat	PROPN
ejpam-4254	3	75	yai	yai	PROPN
ejpam-4254	3	76	,	,	PUNCT
ejpam-4254	3	77	songkhla	songkhla	VERB
ejpam-4254	3	78	90110	90110	NUM
ejpam-4254	3	79	,	,	PUNCT
ejpam-4254	3	80	thailand	thailand	PROPN
ejpam-4254	3	81	3	3	NUM
ejpam-4254	3	82	department	department	NOUN
ejpam-4254	3	83	of	of	ADP
ejpam-4254	3	84	mathematics	mathematic	NOUN
ejpam-4254	3	85	,	,	PUNCT
ejpam-4254	3	86	faculty	faculty	NOUN
ejpam-4254	3	87	of	of	ADP
ejpam-4254	3	88	science	science	NOUN
ejpam-4254	3	89	and	and	CCONJ
ejpam-4254	3	90	technology	technology	NOUN
ejpam-4254	3	91	,	,	PUNCT
ejpam-4254	3	92	pibulsongkram	pibulsongkram	PROPN
ejpam-4254	3	93	rajabhat	rajabhat	PROPN
ejpam-4254	3	94	university	university	NOUN
ejpam-4254	3	95	,	,	PUNCT
ejpam-4254	3	96	phitsanulok	phitsanulok	NOUN
ejpam-4254	3	97	65000	65000	NUM
ejpam-4254	3	98	,	,	PUNCT
ejpam-4254	3	99	thailand	thailand	PROPN
ejpam-4254	3	100	abstract	abstract	NOUN
ejpam-4254	3	101	.	.	PUNCT
ejpam-4254	4	1	this	this	DET
ejpam-4254	4	2	paper	paper	NOUN
ejpam-4254	4	3	aims	aim	VERB
ejpam-4254	4	4	to	to	PART
ejpam-4254	4	5	apply	apply	VERB
ejpam-4254	4	6	the	the	DET
ejpam-4254	4	7	concept	concept	NOUN
ejpam-4254	4	8	of	of	ADP
ejpam-4254	4	9	rough	rough	ADJ
ejpam-4254	4	10	sets	set	NOUN
ejpam-4254	4	11	to	to	PART
ejpam-4254	4	12	pythagorean	pythagorean	VERB
ejpam-4254	4	13	fuzzy	fuzzy	ADJ
ejpam-4254	4	14	sets	set	NOUN
ejpam-4254	4	15	in	in	ADP
ejpam-4254	4	16	upalgebras	upalgebra	NOUN
ejpam-4254	4	17	.	.	PUNCT
ejpam-4254	5	1	then	then	ADV
ejpam-4254	5	2	we	we	PRON
ejpam-4254	5	3	introduce	introduce	VERB
ejpam-4254	5	4	fifteen	fifteen	NUM
ejpam-4254	5	5	types	type	NOUN
ejpam-4254	5	6	of	of	ADP
ejpam-4254	5	7	rough	rough	ADJ
ejpam-4254	5	8	pythagorean	pythagorean	ADJ
ejpam-4254	5	9	fuzzy	fuzzy	ADJ
ejpam-4254	5	10	sets	set	NOUN
ejpam-4254	5	11	in	in	ADP
ejpam-4254	5	12	up	up	ADV
ejpam-4254	5	13	-	-	PUNCT
ejpam-4254	5	14	algebras	algebra	NOUN
ejpam-4254	5	15	and	and	CCONJ
ejpam-4254	5	16	study	study	VERB
ejpam-4254	5	17	their	their	PRON
ejpam-4254	5	18	generalization	generalization	NOUN
ejpam-4254	5	19	.	.	PUNCT
ejpam-4254	6	1	in	in	ADP
ejpam-4254	6	2	addition	addition	NOUN
ejpam-4254	6	3	,	,	PUNCT
ejpam-4254	6	4	we	we	PRON
ejpam-4254	6	5	will	will	AUX
ejpam-4254	6	6	also	also	ADV
ejpam-4254	6	7	discuss	discuss	VERB
ejpam-4254	6	8	t	t	NOUN
ejpam-4254	6	9	-	-	PUNCT
ejpam-4254	6	10	level	level	NOUN
ejpam-4254	6	11	subsets	subset	NOUN
ejpam-4254	6	12	of	of	ADP
ejpam-4254	6	13	rough	rough	ADJ
ejpam-4254	6	14	pythagorean	pythagorean	NOUN
ejpam-4254	6	15	fuzzy	fuzzy	ADJ
ejpam-4254	6	16	sets	set	NOUN
ejpam-4254	6	17	in	in	ADP
ejpam-4254	6	18	up	up	ADV
ejpam-4254	6	19	-	-	PUNCT
ejpam-4254	6	20	algebras	algebras	PROPN
ejpam-4254	6	21	to	to	PART
ejpam-4254	6	22	study	study	VERB
ejpam-4254	6	23	the	the	DET
ejpam-4254	6	24	relationships	relationship	NOUN
ejpam-4254	6	25	between	between	ADP
ejpam-4254	6	26	rough	rough	ADJ
ejpam-4254	6	27	pythagorean	pythagorean	ADJ
ejpam-4254	6	28	fuzzy	fuzzy	ADJ
ejpam-4254	6	29	sets	set	NOUN
ejpam-4254	6	30	and	and	CCONJ
ejpam-4254	6	31	rough	rough	ADJ
ejpam-4254	6	32	sets	set	NOUN
ejpam-4254	6	33	in	in	ADP
ejpam-4254	6	34	up	up	ADP
ejpam-4254	6	35	-	-	PUNCT
ejpam-4254	6	36	algebras	algebras	X
ejpam-4254	6	37	.	.	PUNCT
ejpam-4254	7	1	2020	2020	NUM
ejpam-4254	7	2	mathematics	mathematics	PROPN
ejpam-4254	7	3	subject	subject	NOUN
ejpam-4254	7	4	classifications	classification	NOUN
ejpam-4254	7	5	:	:	PUNCT
ejpam-4254	7	6	03g25	03g25	NUM
ejpam-4254	7	7	,	,	PUNCT
ejpam-4254	7	8	03e72	03e72	NUM
ejpam-4254	7	9	,	,	PUNCT
ejpam-4254	7	10	08a72	08a72	NOUN
ejpam-4254	7	11	key	key	ADJ
ejpam-4254	7	12	words	word	NOUN
ejpam-4254	7	13	and	and	CCONJ
ejpam-4254	7	14	phrases	phrase	NOUN
ejpam-4254	7	15	:	:	PUNCT
ejpam-4254	7	16	up	up	ADP
ejpam-4254	7	17	-	-	PUNCT
ejpam-4254	7	18	algebra	algebra	NOUN
ejpam-4254	7	19	,	,	PUNCT
ejpam-4254	7	20	pythagorean	pythagorean	PROPN
ejpam-4254	7	21	fuzzy	fuzzy	ADJ
ejpam-4254	7	22	set	set	NOUN
ejpam-4254	7	23	,	,	PUNCT
ejpam-4254	7	24	upper	upper	ADJ
ejpam-4254	7	25	approximation	approximation	NOUN
ejpam-4254	7	26	,	,	PUNCT
ejpam-4254	7	27	lower	low	ADJ
ejpam-4254	7	28	approximation	approximation	NOUN
ejpam-4254	7	29	,	,	PUNCT
ejpam-4254	7	30	rough	rough	ADJ
ejpam-4254	7	31	set	set	NOUN
ejpam-4254	7	32	,	,	PUNCT
ejpam-4254	7	33	rough	rough	ADJ
ejpam-4254	7	34	pyhagorean	pyhagorean	NOUN
ejpam-4254	7	35	fuzzy	fuzzy	ADJ
ejpam-4254	7	36	set	set	NOUN
ejpam-4254	7	37	,	,	PUNCT
ejpam-4254	7	38	t	t	NOUN
ejpam-4254	7	39	-	-	PUNCT
ejpam-4254	7	40	level	level	NOUN
ejpam-4254	7	41	subset	subset	NOUN
ejpam-4254	7	42	1	1	NUM
ejpam-4254	7	43	.	.	X
ejpam-4254	7	44	introduction	introduction	NOUN
ejpam-4254	7	45	and	and	CCONJ
ejpam-4254	7	46	preliminaries	preliminary	NOUN
ejpam-4254	7	47	the	the	DET
ejpam-4254	7	48	concept	concept	NOUN
ejpam-4254	7	49	of	of	ADP
ejpam-4254	7	50	fuzzy	fuzzy	ADJ
ejpam-4254	7	51	sets	set	NOUN
ejpam-4254	7	52	(	(	PUNCT
ejpam-4254	7	53	fss	fss	NOUN
ejpam-4254	7	54	)	)	PUNCT
ejpam-4254	7	55	was	be	AUX
ejpam-4254	7	56	first	first	ADV
ejpam-4254	7	57	considered	consider	VERB
ejpam-4254	7	58	by	by	ADP
ejpam-4254	7	59	zadeh	zadeh	PROPN
ejpam-4254	8	1	[	[	X
ejpam-4254	8	2	29	29	NUM
ejpam-4254	8	3	]	]	PUNCT
ejpam-4254	8	4	in	in	ADP
ejpam-4254	8	5	1965	1965	NUM
ejpam-4254	8	6	.	.	PUNCT
ejpam-4254	9	1	zadeh	zadeh	PROPN
ejpam-4254	9	2	’s	’s	PART
ejpam-4254	9	3	and	and	CCONJ
ejpam-4254	9	4	others	other	NOUN
ejpam-4254	9	5	’	'	PUNCT
ejpam-4254	9	6	fs	fs	X
ejpam-4254	9	7	concepts	concept	NOUN
ejpam-4254	9	8	have	have	AUX
ejpam-4254	9	9	found	find	VERB
ejpam-4254	9	10	numerous	numerous	ADJ
ejpam-4254	9	11	applications	application	NOUN
ejpam-4254	9	12	in	in	ADP
ejpam-4254	9	13	mathematics	mathematic	NOUN
ejpam-4254	9	14	and	and	CCONJ
ejpam-4254	9	15	other	other	ADJ
ejpam-4254	9	16	fields	field	NOUN
ejpam-4254	9	17	.	.	PUNCT
ejpam-4254	10	1	following	follow	VERB
ejpam-4254	10	2	the	the	DET
ejpam-4254	10	3	introduction	introduction	NOUN
ejpam-4254	10	4	of	of	ADP
ejpam-4254	10	5	the	the	DET
ejpam-4254	10	6	concept	concept	NOUN
ejpam-4254	10	7	of	of	ADP
ejpam-4254	10	8	fss	fss	ADJ
ejpam-4254	10	9	,	,	PUNCT
ejpam-4254	10	10	various	various	ADJ
ejpam-4254	10	11	researchers	researcher	NOUN
ejpam-4254	10	12	were	be	AUX
ejpam-4254	10	13	interviewed	interview	VERB
ejpam-4254	10	14	about	about	ADP
ejpam-4254	10	15	generalizations	generalization	NOUN
ejpam-4254	10	16	of	of	ADP
ejpam-4254	10	17	the	the	DET
ejpam-4254	10	18	concept	concept	NOUN
ejpam-4254	10	19	of	of	ADP
ejpam-4254	10	20	fss	fss	NOUN
ejpam-4254	10	21	,	,	PUNCT
ejpam-4254	10	22	including	include	VERB
ejpam-4254	10	23	:	:	PUNCT
ejpam-4254	10	24	atanassov	atanassov	PROPN
ejpam-4254	11	1	[	[	X
ejpam-4254	11	2	5	5	NUM
ejpam-4254	11	3	]	]	PUNCT
ejpam-4254	11	4	defined	define	VERB
ejpam-4254	11	5	a	a	DET
ejpam-4254	11	6	new	new	ADJ
ejpam-4254	11	7	concept	concept	NOUN
ejpam-4254	11	8	called	call	VERB
ejpam-4254	11	9	an	an	DET
ejpam-4254	11	10	intuitionistic	intuitionistic	ADJ
ejpam-4254	11	11	fuzzy	fuzzy	ADJ
ejpam-4254	11	12	set	set	NOUN
ejpam-4254	11	13	(	(	PUNCT
ejpam-4254	11	14	ifs	ifs	PROPN
ejpam-4254	11	15	)	)	PUNCT
ejpam-4254	11	16	which	which	PRON
ejpam-4254	11	17	is	be	AUX
ejpam-4254	11	18	a	a	DET
ejpam-4254	11	19	generalization	generalization	NOUN
ejpam-4254	11	20	of	of	ADP
ejpam-4254	11	21	a	a	DET
ejpam-4254	11	22	fs	fs	PROPN
ejpam-4254	11	23	,	,	PUNCT
ejpam-4254	11	24	yager	yager	NOUN
ejpam-4254	12	1	[	[	X
ejpam-4254	12	2	27	27	NUM
ejpam-4254	12	3	]	]	PUNCT
ejpam-4254	12	4	introduced	introduce	VERB
ejpam-4254	12	5	a	a	DET
ejpam-4254	12	6	new	new	ADJ
ejpam-4254	12	7	class	class	NOUN
ejpam-4254	12	8	of	of	ADP
ejpam-4254	12	9	non	non	ADJ
ejpam-4254	12	10	-	-	ADJ
ejpam-4254	12	11	standard	standard	ADJ
ejpam-4254	12	12	fuzzy	fuzzy	ADJ
ejpam-4254	12	13	subsets	subset	NOUN
ejpam-4254	12	14	called	call	VERB
ejpam-4254	12	15	a	a	DET
ejpam-4254	12	16	pythagorean	pythagorean	ADJ
ejpam-4254	12	17	fuzzy	fuzzy	ADJ
ejpam-4254	12	18	set	set	NOUN
ejpam-4254	12	19	(	(	PUNCT
ejpam-4254	12	20	pfs	pfs	PROPN
ejpam-4254	12	21	)	)	PUNCT
ejpam-4254	12	22	and	and	CCONJ
ejpam-4254	12	23	the	the	DET
ejpam-4254	12	24	related	related	ADJ
ejpam-4254	12	25	idea	idea	NOUN
ejpam-4254	12	26	of	of	ADP
ejpam-4254	12	27	pythagorean	pythagorean	PROPN
ejpam-4254	12	28	membership	membership	NOUN
ejpam-4254	12	29	grades	grade	NOUN
ejpam-4254	12	30	.	.	PUNCT
ejpam-4254	13	1	the	the	DET
ejpam-4254	13	2	concept	concept	NOUN
ejpam-4254	13	3	of	of	ADP
ejpam-4254	13	4	rough	rough	ADJ
ejpam-4254	13	5	sets	set	NOUN
ejpam-4254	13	6	(	(	PUNCT
ejpam-4254	13	7	rss	rss	NOUN
ejpam-4254	13	8	)	)	PUNCT
ejpam-4254	13	9	was	be	AUX
ejpam-4254	13	10	first	first	ADV
ejpam-4254	13	11	considered	consider	VERB
ejpam-4254	13	12	by	by	ADP
ejpam-4254	13	13	pawlak	pawlak	ADJ
ejpam-4254	13	14	[	[	X
ejpam-4254	13	15	18	18	NUM
ejpam-4254	13	16	]	]	PUNCT
ejpam-4254	13	17	in	in	ADP
ejpam-4254	13	18	1982	1982	NUM
ejpam-4254	13	19	.	.	PUNCT
ejpam-4254	14	1	after	after	ADP
ejpam-4254	14	2	the	the	DET
ejpam-4254	14	3	introduction	introduction	NOUN
ejpam-4254	14	4	of	of	ADP
ejpam-4254	14	5	the	the	DET
ejpam-4254	14	6	concept	concept	NOUN
ejpam-4254	14	7	of	of	ADP
ejpam-4254	14	8	rss	rss	NOUN
ejpam-4254	14	9	,	,	PUNCT
ejpam-4254	14	10	several	several	ADJ
ejpam-4254	14	11	authors	author	NOUN
ejpam-4254	14	12	have	have	AUX
ejpam-4254	14	13	applied	apply	VERB
ejpam-4254	14	14	the	the	DET
ejpam-4254	14	15	concept	concept	NOUN
ejpam-4254	14	16	of	of	ADP
ejpam-4254	14	17	rss	rss	NOUN
ejpam-4254	14	18	to	to	ADP
ejpam-4254	14	19	the	the	DET
ejpam-4254	14	20	generalizations	generalization	NOUN
ejpam-4254	14	21	of	of	ADP
ejpam-4254	14	22	the	the	DET
ejpam-4254	14	23	concept	concept	NOUN
ejpam-4254	14	24	of	of	ADP
ejpam-4254	14	25	fss	fss	NOUN
ejpam-4254	14	26	in	in	ADP
ejpam-4254	14	27	many	many	ADJ
ejpam-4254	14	28	algebraic	algebraic	ADJ
ejpam-4254	14	29	structures	structure	NOUN
ejpam-4254	14	30	such	such	ADJ
ejpam-4254	14	31	as	as	ADP
ejpam-4254	14	32	:	:	PUNCT
ejpam-4254	14	33	chen	chen	PROPN
ejpam-4254	14	34	and	and	CCONJ
ejpam-4254	14	35	wang	wang	PROPN
ejpam-4254	15	1	[	[	X
ejpam-4254	15	2	6	6	NUM
ejpam-4254	15	3	]	]	PUNCT
ejpam-4254	15	4	combined	combine	VERB
ejpam-4254	15	5	rss	rss	NOUN
ejpam-4254	15	6	and	and	CCONJ
ejpam-4254	15	7	fuzzy	fuzzy	ADJ
ejpam-4254	15	8	subalgebras	subalgebra	NOUN
ejpam-4254	15	9	(	(	PUNCT
ejpam-4254	15	10	fuzzy	fuzzy	ADJ
ejpam-4254	15	11	ideals	ideal	NOUN
ejpam-4254	15	12	)	)	PUNCT
ejpam-4254	15	13	fruitfully	fruitfully	ADV
ejpam-4254	15	14	by	by	ADP
ejpam-4254	15	15	defining	define	VERB
ejpam-4254	15	16	rough	rough	ADJ
ejpam-4254	15	17	fuzzy	fuzzy	ADJ
ejpam-4254	15	18	subalgebras	subalgebra	NOUN
ejpam-4254	15	19	(	(	PUNCT
ejpam-4254	15	20	rough	rough	ADJ
ejpam-4254	15	21	fuzzy	fuzzy	ADJ
ejpam-4254	15	22	ideals	ideal	NOUN
ejpam-4254	15	23	)	)	PUNCT
ejpam-4254	15	24	of	of	ADP
ejpam-4254	15	25	bci	bci	PROPN
ejpam-4254	15	26	-	-	PUNCT
ejpam-4254	15	27	algebras	algebra	NOUN
ejpam-4254	15	28	,	,	PUNCT
ejpam-4254	15	29	moradiana	moradiana	PROPN
ejpam-4254	15	30	et	et	PROPN
ejpam-4254	15	31	al	al	PROPN
ejpam-4254	15	32	.	.	PUNCT
ejpam-4254	16	1	[	[	X
ejpam-4254	16	2	17	17	NUM
ejpam-4254	16	3	]	]	PUNCT
ejpam-4254	16	4	presented	present	VERB
ejpam-4254	16	5	a	a	DET
ejpam-4254	16	6	∗corresponding	∗corresponding	NOUN
ejpam-4254	16	7	author	author	NOUN
ejpam-4254	16	8	.	.	PUNCT
ejpam-4254	17	1	doi	doi	NOUN
ejpam-4254	17	2	:	:	PUNCT
ejpam-4254	17	3	https://doi.org/10.29020/nybg.ejpam.v15i1.4254	https://doi.org/10.29020/nybg.ejpam.v15i1.4254	ADJ
ejpam-4254	17	4	email	email	NOUN
ejpam-4254	17	5	addresses	address	NOUN
ejpam-4254	17	6	:	:	PUNCT
ejpam-4254	17	7	akarachai.sa@gmail.com	akarachai.sa@gmail.com	PROPN
ejpam-4254	17	8	(	(	PUNCT
ejpam-4254	17	9	a.	a.	PROPN
ejpam-4254	17	10	satirad	satirad	PROPN
ejpam-4254	17	11	)	)	PUNCT
ejpam-4254	17	12	,	,	PUNCT
ejpam-4254	17	13	ronnason.c@psu.ac.th	ronnason.c@psu.ac.th	PROPN
ejpam-4254	17	14	(	(	PUNCT
ejpam-4254	17	15	r.	r.	PROPN
ejpam-4254	17	16	chinram	chinram	PROPN
ejpam-4254	17	17	)	)	PUNCT
ejpam-4254	17	18	,	,	PUNCT
ejpam-4254	17	19	pongpun.j@psru.ac.th	pongpun.j@psru.ac.th	PROPN
ejpam-4254	17	20	(	(	PUNCT
ejpam-4254	17	21	p.	p.	NOUN
ejpam-4254	17	22	julatha	julatha	NOUN
ejpam-4254	17	23	)	)	PUNCT
ejpam-4254	17	24	,	,	PUNCT
ejpam-4254	17	25	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-4254	17	26	(	(	PUNCT
ejpam-4254	17	27	a.	a.	NOUN
ejpam-4254	17	28	iampan	iampan	PROPN
ejpam-4254	17	29	)	)	PUNCT
ejpam-4254	17	30	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4254	18	1	169	169	NUM
ejpam-4254	18	2	©	©	PROPN
ejpam-4254	18	3	2022	2022	NUM
ejpam-4254	18	4	ejpam	ejpam	VERB
ejpam-4254	18	5	all	all	DET
ejpam-4254	18	6	rights	right	NOUN
ejpam-4254	18	7	reserved	reserve	VERB
ejpam-4254	18	8	.	.	PUNCT
ejpam-4254	19	1	a.	a.	PROPN
ejpam-4254	19	2	iampan	iampan	PROPN
ejpam-4254	19	3	et	et	PROPN
ejpam-4254	19	4	al	al	PROPN
ejpam-4254	19	5	.	.	PUNCT
ejpam-4254	19	6	/	/	SYM
ejpam-4254	19	7	eur	eur	PROPN
ejpam-4254	19	8	.	.	PUNCT
ejpam-4254	20	1	j.	j.	PROPN
ejpam-4254	20	2	pure	pure	PROPN
ejpam-4254	20	3	appl	appl	PROPN
ejpam-4254	20	4	.	.	PROPN
ejpam-4254	20	5	math	math	PROPN
ejpam-4254	20	6	,	,	PUNCT
ejpam-4254	20	7	15	15	NUM
ejpam-4254	20	8	(	(	PUNCT
ejpam-4254	20	9	1	1	NUM
ejpam-4254	20	10	)	)	PUNCT
ejpam-4254	20	11	(	(	PUNCT
ejpam-4254	20	12	2022	2022	NUM
ejpam-4254	20	13	)	)	PUNCT
ejpam-4254	20	14	,	,	PUNCT
ejpam-4254	20	15	169	169	NUM
ejpam-4254	20	16	-	-	SYM
ejpam-4254	20	17	198	198	NUM
ejpam-4254	20	18	170	170	NUM
ejpam-4254	20	19	definition	definition	NOUN
ejpam-4254	20	20	of	of	ADP
ejpam-4254	20	21	the	the	DET
ejpam-4254	20	22	lower	low	ADJ
ejpam-4254	20	23	and	and	CCONJ
ejpam-4254	20	24	upper	upper	ADJ
ejpam-4254	20	25	approximation	approximation	NOUN
ejpam-4254	20	26	of	of	ADP
ejpam-4254	20	27	subsets	subset	NOUN
ejpam-4254	20	28	of	of	ADP
ejpam-4254	20	29	bck	bck	NOUN
ejpam-4254	20	30	-	-	PUNCT
ejpam-4254	20	31	algebras	algebra	NOUN
ejpam-4254	20	32	concerning	concern	VERB
ejpam-4254	20	33	a	a	DET
ejpam-4254	20	34	fuzzy	fuzzy	ADJ
ejpam-4254	20	35	ideal	ideal	NOUN
ejpam-4254	20	36	.	.	PUNCT
ejpam-4254	21	1	ahn	ahn	PROPN
ejpam-4254	21	2	and	and	CCONJ
ejpam-4254	21	3	kim	kim	PROPN
ejpam-4254	22	1	[	[	X
ejpam-4254	22	2	1	1	X
ejpam-4254	22	3	]	]	PUNCT
ejpam-4254	22	4	introduced	introduce	VERB
ejpam-4254	22	5	the	the	DET
ejpam-4254	22	6	concept	concept	NOUN
ejpam-4254	22	7	of	of	ADP
ejpam-4254	22	8	rough	rough	ADJ
ejpam-4254	22	9	fuzzy	fuzzy	ADJ
ejpam-4254	22	10	filters	filter	NOUN
ejpam-4254	22	11	in	in	ADP
ejpam-4254	22	12	be	be	AUX
ejpam-4254	22	13	-	-	PUNCT
ejpam-4254	22	14	algebras	algebra	NOUN
ejpam-4254	22	15	,	,	PUNCT
ejpam-4254	22	16	ahn	ahn	PROPN
ejpam-4254	22	17	and	and	CCONJ
ejpam-4254	22	18	ko	ko	PROPN
ejpam-4254	22	19	[	[	X
ejpam-4254	22	20	2	2	X
ejpam-4254	22	21	]	]	PUNCT
ejpam-4254	22	22	introduced	introduce	VERB
ejpam-4254	22	23	the	the	DET
ejpam-4254	22	24	concept	concept	NOUN
ejpam-4254	22	25	of	of	ADP
ejpam-4254	22	26	rough	rough	ADJ
ejpam-4254	22	27	ideals	ideal	NOUN
ejpam-4254	22	28	and	and	CCONJ
ejpam-4254	22	29	rough	rough	ADJ
ejpam-4254	22	30	fuzzy	fuzzy	ADJ
ejpam-4254	22	31	ideals	ideal	NOUN
ejpam-4254	22	32	in	in	ADP
ejpam-4254	22	33	bck	bck	PROPN
ejpam-4254	22	34	/	/	SYM
ejpam-4254	22	35	bcialgebras	bcialgebras	PROPN
ejpam-4254	22	36	,	,	PUNCT
ejpam-4254	22	37	hussain	hussain	PROPN
ejpam-4254	22	38	et	et	PROPN
ejpam-4254	22	39	al	al	PROPN
ejpam-4254	22	40	.	.	PUNCT
ejpam-4254	23	1	[	[	X
ejpam-4254	23	2	10	10	NUM
ejpam-4254	23	3	]	]	PUNCT
ejpam-4254	23	4	introduced	introduce	VERB
ejpam-4254	23	5	the	the	DET
ejpam-4254	23	6	concept	concept	NOUN
ejpam-4254	23	7	of	of	ADP
ejpam-4254	23	8	rough	rough	ADJ
ejpam-4254	23	9	pythagorean	pythagorean	ADJ
ejpam-4254	23	10	fuzzy	fuzzy	ADJ
ejpam-4254	23	11	ideals	ideal	NOUN
ejpam-4254	23	12	in	in	ADP
ejpam-4254	23	13	semigroups	semigroup	NOUN
ejpam-4254	23	14	,	,	PUNCT
ejpam-4254	23	15	chinram	chinram	NOUN
ejpam-4254	23	16	and	and	CCONJ
ejpam-4254	23	17	panityakul	panityakul	NOUN
ejpam-4254	23	18	[	[	X
ejpam-4254	23	19	7	7	X
ejpam-4254	23	20	]	]	PUNCT
ejpam-4254	23	21	introduced	introduce	VERB
ejpam-4254	23	22	rough	rough	ADJ
ejpam-4254	23	23	pythagorean	pythagorean	ADJ
ejpam-4254	23	24	fuzzy	fuzzy	ADJ
ejpam-4254	23	25	ideals	ideal	NOUN
ejpam-4254	23	26	in	in	ADP
ejpam-4254	23	27	ternary	ternary	ADJ
ejpam-4254	23	28	semigroups	semigroup	NOUN
ejpam-4254	23	29	and	and	CCONJ
ejpam-4254	23	30	gave	give	VERB
ejpam-4254	23	31	some	some	DET
ejpam-4254	23	32	remarkable	remarkable	ADJ
ejpam-4254	23	33	properties	property	NOUN
ejpam-4254	23	34	.	.	PUNCT
ejpam-4254	24	1	jun	jun	PROPN
ejpam-4254	24	2	et	et	PROPN
ejpam-4254	24	3	al	al	PROPN
ejpam-4254	24	4	.	.	PUNCT
ejpam-4254	25	1	[	[	X
ejpam-4254	25	2	15	15	NUM
ejpam-4254	25	3	]	]	PUNCT
ejpam-4254	25	4	studied	study	VERB
ejpam-4254	25	5	the	the	DET
ejpam-4254	25	6	concept	concept	NOUN
ejpam-4254	25	7	of	of	ADP
ejpam-4254	25	8	a	a	DET
ejpam-4254	25	9	(	(	PUNCT
ejpam-4254	25	10	strong	strong	ADJ
ejpam-4254	25	11	)	)	PUNCT
ejpam-4254	25	12	set	set	NOUN
ejpam-4254	25	13	-	-	PUNCT
ejpam-4254	25	14	valued	value	VERB
ejpam-4254	25	15	bck	bck	PROPN
ejpam-4254	25	16	/	/	SYM
ejpam-4254	25	17	bci	bci	NOUN
ejpam-4254	25	18	-	-	NOUN
ejpam-4254	25	19	morphism	morphism	NOUN
ejpam-4254	25	20	and	and	CCONJ
ejpam-4254	25	21	introduced	introduce	VERB
ejpam-4254	25	22	the	the	DET
ejpam-4254	25	23	concept	concept	NOUN
ejpam-4254	25	24	of	of	ADP
ejpam-4254	25	25	a	a	DET
ejpam-4254	25	26	generalized	generalized	ADJ
ejpam-4254	25	27	rough	rough	ADJ
ejpam-4254	25	28	subalgebra	subalgebra	NOUN
ejpam-4254	25	29	(	(	PUNCT
ejpam-4254	25	30	ideal	ideal	ADJ
ejpam-4254	25	31	)	)	PUNCT
ejpam-4254	25	32	in	in	ADP
ejpam-4254	25	33	bck	bck	PROPN
ejpam-4254	25	34	/	/	SYM
ejpam-4254	25	35	bci	bci	NOUN
ejpam-4254	25	36	-	-	PUNCT
ejpam-4254	25	37	algebras	algebras	X
ejpam-4254	25	38	.	.	PUNCT
ejpam-4254	26	1	in	in	ADP
ejpam-4254	26	2	this	this	DET
ejpam-4254	26	3	study	study	NOUN
ejpam-4254	26	4	,	,	PUNCT
ejpam-4254	26	5	we	we	PRON
ejpam-4254	26	6	extend	extend	VERB
ejpam-4254	26	7	the	the	DET
ejpam-4254	26	8	rs	rs	ADJ
ejpam-4254	26	9	concept	concept	NOUN
ejpam-4254	26	10	to	to	ADP
ejpam-4254	26	11	pfss	pfss	VERB
ejpam-4254	26	12	in	in	ADP
ejpam-4254	26	13	up	up	ADV
ejpam-4254	26	14	-	-	PUNCT
ejpam-4254	26	15	algebras	algebras	ADV
ejpam-4254	26	16	and	and	CCONJ
ejpam-4254	26	17	establish	establish	VERB
ejpam-4254	26	18	fifteen	fifteen	NUM
ejpam-4254	26	19	different	different	ADJ
ejpam-4254	26	20	types	type	NOUN
ejpam-4254	26	21	of	of	ADP
ejpam-4254	26	22	rough	rough	ADJ
ejpam-4254	26	23	pythagorean	pythagorean	ADJ
ejpam-4254	26	24	fuzzy	fuzzy	ADJ
ejpam-4254	26	25	sets	set	NOUN
ejpam-4254	26	26	(	(	PUNCT
ejpam-4254	26	27	rpfss	rpfss	NOUN
ejpam-4254	26	28	)	)	PUNCT
ejpam-4254	26	29	in	in	ADP
ejpam-4254	26	30	up	up	ADP
ejpam-4254	26	31	-	-	PUNCT
ejpam-4254	26	32	algebras	algebra	NOUN
ejpam-4254	26	33	:	:	PUNCT
ejpam-4254	26	34	upper	upper	ADJ
ejpam-4254	26	35	rough	rough	ADJ
ejpam-4254	26	36	pythagorean	pythagorean	NOUN
ejpam-4254	26	37	fuzzy	fuzzy	ADJ
ejpam-4254	26	38	up	up	ADP
ejpam-4254	26	39	-	-	PUNCT
ejpam-4254	26	40	subalgebras	subalgebras	PROPN
ejpam-4254	26	41	(	(	PUNCT
ejpam-4254	26	42	uprpfupss	uprpfupss	PROPN
ejpam-4254	26	43	)	)	PUNCT
ejpam-4254	26	44	,	,	PUNCT
ejpam-4254	26	45	upper	upper	ADJ
ejpam-4254	26	46	rough	rough	ADJ
ejpam-4254	26	47	pythagorean	pythagorean	NOUN
ejpam-4254	26	48	fuzzy	fuzzy	NOUN
ejpam-4254	26	49	near	near	ADP
ejpam-4254	26	50	up	up	ADP
ejpam-4254	26	51	-	-	PUNCT
ejpam-4254	26	52	filters	filter	NOUN
ejpam-4254	26	53	(	(	PUNCT
ejpam-4254	26	54	uprpfnupfs	uprpfnupfs	PROPN
ejpam-4254	26	55	)	)	PUNCT
ejpam-4254	26	56	,	,	PUNCT
ejpam-4254	26	57	upper	upper	ADJ
ejpam-4254	26	58	rough	rough	ADJ
ejpam-4254	26	59	pythagorean	pythagorean	NOUN
ejpam-4254	26	60	fuzzy	fuzzy	ADJ
ejpam-4254	26	61	up	up	NOUN
ejpam-4254	26	62	-	-	PUNCT
ejpam-4254	26	63	filters	filter	NOUN
ejpam-4254	26	64	(	(	PUNCT
ejpam-4254	26	65	uprpfupfs	uprpfupf	NOUN
ejpam-4254	26	66	)	)	PUNCT
ejpam-4254	26	67	,	,	PUNCT
ejpam-4254	26	68	upper	upper	ADJ
ejpam-4254	26	69	rough	rough	ADJ
ejpam-4254	26	70	pythagorean	pythagorean	NOUN
ejpam-4254	26	71	fuzzy	fuzzy	ADJ
ejpam-4254	26	72	up	up	NOUN
ejpam-4254	26	73	-	-	PUNCT
ejpam-4254	26	74	ideals	ideal	NOUN
ejpam-4254	26	75	(	(	PUNCT
ejpam-4254	26	76	uprpfupis	uprpfupis	ADJ
ejpam-4254	26	77	)	)	PUNCT
ejpam-4254	26	78	,	,	PUNCT
ejpam-4254	26	79	upper	upper	ADJ
ejpam-4254	26	80	rough	rough	ADJ
ejpam-4254	26	81	pythagorean	pythagorean	NOUN
ejpam-4254	26	82	fuzzy	fuzzy	NOUN
ejpam-4254	26	83	strong	strong	ADJ
ejpam-4254	26	84	up	up	ADP
ejpam-4254	26	85	-	-	PUNCT
ejpam-4254	26	86	ideals	ideal	NOUN
ejpam-4254	26	87	(	(	PUNCT
ejpam-4254	26	88	uprpfsupis	uprpfsupis	ADJ
ejpam-4254	26	89	)	)	PUNCT
ejpam-4254	26	90	,	,	PUNCT
ejpam-4254	26	91	lower	low	ADJ
ejpam-4254	26	92	rough	rough	ADJ
ejpam-4254	26	93	pythagorean	pythagorean	NOUN
ejpam-4254	26	94	fuzzy	fuzzy	ADJ
ejpam-4254	26	95	up	up	ADP
ejpam-4254	26	96	-	-	PUNCT
ejpam-4254	26	97	subalgebras	subalgebras	PROPN
ejpam-4254	26	98	(	(	PUNCT
ejpam-4254	26	99	lorpfupss	lorpfupss	PROPN
ejpam-4254	26	100	)	)	PUNCT
ejpam-4254	26	101	,	,	PUNCT
ejpam-4254	26	102	lower	low	ADJ
ejpam-4254	26	103	rough	rough	ADJ
ejpam-4254	26	104	pythagorean	pythagorean	NOUN
ejpam-4254	26	105	fuzzy	fuzzy	NOUN
ejpam-4254	26	106	near	near	ADP
ejpam-4254	26	107	up	up	ADP
ejpam-4254	26	108	-	-	PUNCT
ejpam-4254	26	109	filters	filter	NOUN
ejpam-4254	26	110	(	(	PUNCT
ejpam-4254	26	111	lorpfnupfs	lorpfnupfs	PROPN
ejpam-4254	26	112	)	)	PUNCT
ejpam-4254	26	113	,	,	PUNCT
ejpam-4254	26	114	lower	low	ADJ
ejpam-4254	26	115	rough	rough	ADJ
ejpam-4254	26	116	pythagorean	pythagorean	NOUN
ejpam-4254	26	117	fuzzy	fuzzy	ADJ
ejpam-4254	26	118	up	up	NOUN
ejpam-4254	26	119	-	-	PUNCT
ejpam-4254	26	120	filters	filter	NOUN
ejpam-4254	26	121	(	(	PUNCT
ejpam-4254	26	122	lorpfupfs	lorpfupfs	PROPN
ejpam-4254	26	123	)	)	PUNCT
ejpam-4254	26	124	,	,	PUNCT
ejpam-4254	26	125	lower	low	ADJ
ejpam-4254	26	126	rough	rough	ADJ
ejpam-4254	26	127	pythagorean	pythagorean	NOUN
ejpam-4254	26	128	fuzzy	fuzzy	ADJ
ejpam-4254	26	129	up	up	NOUN
ejpam-4254	26	130	-	-	PUNCT
ejpam-4254	26	131	ideals	ideal	NOUN
ejpam-4254	26	132	(	(	PUNCT
ejpam-4254	26	133	lorpfupis	lorpfupis	NOUN
ejpam-4254	26	134	)	)	PUNCT
ejpam-4254	26	135	,	,	PUNCT
ejpam-4254	26	136	lower	low	ADJ
ejpam-4254	26	137	rough	rough	ADJ
ejpam-4254	26	138	pythagorean	pythagorean	NOUN
ejpam-4254	26	139	fuzzy	fuzzy	NOUN
ejpam-4254	26	140	strong	strong	ADJ
ejpam-4254	26	141	up	up	ADP
ejpam-4254	26	142	-	-	PUNCT
ejpam-4254	26	143	ideals	ideal	NOUN
ejpam-4254	26	144	(	(	PUNCT
ejpam-4254	26	145	lorpfsupis	lorpfsupis	ADJ
ejpam-4254	26	146	)	)	PUNCT
ejpam-4254	26	147	,	,	PUNCT
ejpam-4254	26	148	rough	rough	ADJ
ejpam-4254	26	149	pythagorean	pythagorean	PROPN
ejpam-4254	26	150	fuzzy	fuzzy	ADJ
ejpam-4254	26	151	up	up	ADP
ejpam-4254	26	152	-	-	PUNCT
ejpam-4254	26	153	subalgebras	subalgebras	PROPN
ejpam-4254	26	154	(	(	PUNCT
ejpam-4254	26	155	rpfupss	rpfupss	PROPN
ejpam-4254	26	156	)	)	PUNCT
ejpam-4254	26	157	,	,	PUNCT
ejpam-4254	26	158	rough	rough	ADJ
ejpam-4254	26	159	pythagorean	pythagorean	PROPN
ejpam-4254	26	160	fuzzy	fuzzy	NOUN
ejpam-4254	26	161	near	near	ADP
ejpam-4254	26	162	up	up	ADP
ejpam-4254	26	163	-	-	PUNCT
ejpam-4254	26	164	filters	filter	NOUN
ejpam-4254	26	165	(	(	PUNCT
ejpam-4254	26	166	rpfnupfs	rpfnupfs	PROPN
ejpam-4254	26	167	)	)	PUNCT
ejpam-4254	26	168	,	,	PUNCT
ejpam-4254	26	169	rough	rough	ADJ
ejpam-4254	26	170	pythagorean	pythagorean	PROPN
ejpam-4254	26	171	fuzzy	fuzzy	ADJ
ejpam-4254	26	172	up	up	NOUN
ejpam-4254	26	173	-	-	PUNCT
ejpam-4254	26	174	filters	filter	NOUN
ejpam-4254	26	175	(	(	PUNCT
ejpam-4254	26	176	rpfupfs	rpfupf	NOUN
ejpam-4254	26	177	)	)	PUNCT
ejpam-4254	26	178	,	,	PUNCT
ejpam-4254	26	179	rough	rough	ADJ
ejpam-4254	26	180	pythagorean	pythagorean	PROPN
ejpam-4254	26	181	fuzzy	fuzzy	ADJ
ejpam-4254	26	182	up	up	NOUN
ejpam-4254	26	183	-	-	PUNCT
ejpam-4254	26	184	ideals	ideal	NOUN
ejpam-4254	26	185	(	(	PUNCT
ejpam-4254	26	186	rpfupis	rpfupis	NOUN
ejpam-4254	26	187	)	)	PUNCT
ejpam-4254	26	188	,	,	PUNCT
ejpam-4254	26	189	and	and	CCONJ
ejpam-4254	26	190	rough	rough	ADJ
ejpam-4254	26	191	pythagorean	pythagorean	PROPN
ejpam-4254	26	192	fuzzy	fuzzy	NOUN
ejpam-4254	26	193	strong	strong	ADJ
ejpam-4254	26	194	up	up	ADP
ejpam-4254	26	195	-	-	PUNCT
ejpam-4254	26	196	ideals	ideal	NOUN
ejpam-4254	26	197	(	(	PUNCT
ejpam-4254	26	198	rpfsupis	rpfsupis	PROPN
ejpam-4254	26	199	)	)	PUNCT
ejpam-4254	26	200	.	.	PUNCT
ejpam-4254	27	1	moreover	moreover	ADV
ejpam-4254	27	2	,	,	PUNCT
ejpam-4254	27	3	we	we	PRON
ejpam-4254	27	4	verify	verify	VERB
ejpam-4254	27	5	their	their	PRON
ejpam-4254	27	6	generalization	generalization	NOUN
ejpam-4254	27	7	of	of	ADP
ejpam-4254	27	8	theirs	theirs	PROPN
ejpam-4254	27	9	.	.	PUNCT
ejpam-4254	28	1	then	then	ADV
ejpam-4254	28	2	,	,	PUNCT
ejpam-4254	28	3	to	to	PART
ejpam-4254	28	4	investigate	investigate	VERB
ejpam-4254	28	5	the	the	DET
ejpam-4254	28	6	relationships	relationship	NOUN
ejpam-4254	28	7	between	between	ADP
ejpam-4254	28	8	pfss	pfss	ADJ
ejpam-4254	28	9	and	and	CCONJ
ejpam-4254	28	10	special	special	ADJ
ejpam-4254	28	11	subsets	subset	NOUN
ejpam-4254	28	12	of	of	ADP
ejpam-4254	28	13	up	up	ADP
ejpam-4254	28	14	-	-	PUNCT
ejpam-4254	28	15	algebras	algebras	X
ejpam-4254	28	16	,	,	PUNCT
ejpam-4254	28	17	we	we	PRON
ejpam-4254	28	18	explore	explore	VERB
ejpam-4254	28	19	t	t	NOUN
ejpam-4254	28	20	-	-	PUNCT
ejpam-4254	28	21	level	level	NOUN
ejpam-4254	28	22	subsets	subset	NOUN
ejpam-4254	28	23	of	of	ADP
ejpam-4254	28	24	pfss	pfss	NOUN
ejpam-4254	28	25	.	.	PUNCT
ejpam-4254	29	1	finally	finally	ADV
ejpam-4254	29	2	,	,	PUNCT
ejpam-4254	29	3	we	we	PRON
ejpam-4254	29	4	study	study	VERB
ejpam-4254	29	5	the	the	DET
ejpam-4254	29	6	relationships	relationship	NOUN
ejpam-4254	29	7	between	between	ADP
ejpam-4254	29	8	rpfss	rpfss	NOUN
ejpam-4254	29	9	and	and	CCONJ
ejpam-4254	29	10	rss	rss	VERB
ejpam-4254	29	11	in	in	ADP
ejpam-4254	29	12	up	up	ADV
ejpam-4254	29	13	-	-	PUNCT
ejpam-4254	29	14	algebras	algebra	VERB
ejpam-4254	29	15	by	by	ADP
ejpam-4254	29	16	analyzing	analyze	VERB
ejpam-4254	29	17	t	t	PROPN
ejpam-4254	29	18	-	-	PUNCT
ejpam-4254	29	19	level	level	NOUN
ejpam-4254	29	20	subsets	subset	NOUN
ejpam-4254	29	21	of	of	ADP
ejpam-4254	29	22	rpfss	rpfss	NOUN
ejpam-4254	29	23	.	.	PUNCT
ejpam-4254	30	1	let	let	VERB
ejpam-4254	30	2	’s	’s	NOUN
ejpam-4254	30	3	go	go	VERB
ejpam-4254	30	4	through	through	ADP
ejpam-4254	30	5	the	the	DET
ejpam-4254	30	6	definition	definition	NOUN
ejpam-4254	30	7	of	of	ADP
ejpam-4254	30	8	up	up	ADV
ejpam-4254	30	9	-	-	PUNCT
ejpam-4254	30	10	algebras	algebras	NOUN
ejpam-4254	30	11	first	first	ADV
ejpam-4254	30	12	.	.	PUNCT
ejpam-4254	31	1	definition	definition	NOUN
ejpam-4254	31	2	1	1	NUM
ejpam-4254	31	3	.	.	PUNCT
ejpam-4254	32	1	[	[	X
ejpam-4254	32	2	11	11	NUM
ejpam-4254	32	3	]	]	X
ejpam-4254	32	4	a	a	DET
ejpam-4254	32	5	up	up	ADP
ejpam-4254	32	6	-	-	PUNCT
ejpam-4254	32	7	algebra	algebra	NOUN
ejpam-4254	32	8	is	be	AUX
ejpam-4254	32	9	one	one	NUM
ejpam-4254	32	10	that	that	PRON
ejpam-4254	32	11	has	have	VERB
ejpam-4254	32	12	the	the	DET
ejpam-4254	32	13	algebra	algebra	NOUN
ejpam-4254	32	14	u	u	NOUN
ejpam-4254	32	15	=	=	X
ejpam-4254	32	16	(	(	PUNCT
ejpam-4254	32	17	u	u	NOUN
ejpam-4254	32	18	,	,	PUNCT
ejpam-4254	32	19	⋆	⋆	INTJ
ejpam-4254	32	20	,	,	PUNCT
ejpam-4254	32	21	0	0	NUM
ejpam-4254	32	22	)	)	PUNCT
ejpam-4254	32	23	of	of	ADP
ejpam-4254	32	24	type	type	NOUN
ejpam-4254	32	25	(	(	PUNCT
ejpam-4254	32	26	2	2	NUM
ejpam-4254	32	27	,	,	PUNCT
ejpam-4254	32	28	0	0	NUM
ejpam-4254	32	29	)	)	PUNCT
ejpam-4254	32	30	,	,	PUNCT
ejpam-4254	32	31	where	where	SCONJ
ejpam-4254	32	32	u	u	NOUN
ejpam-4254	32	33	is	be	AUX
ejpam-4254	32	34	a	a	DET
ejpam-4254	32	35	nonempty	nonempty	ADJ
ejpam-4254	32	36	set	set	NOUN
ejpam-4254	32	37	,	,	PUNCT
ejpam-4254	32	38	⋆	⋆	VERB
ejpam-4254	32	39	is	be	AUX
ejpam-4254	32	40	a	a	DET
ejpam-4254	32	41	binary	binary	ADJ
ejpam-4254	32	42	operation	operation	NOUN
ejpam-4254	32	43	on	on	ADP
ejpam-4254	32	44	u	u	PROPN
ejpam-4254	32	45	,	,	PUNCT
ejpam-4254	32	46	and	and	CCONJ
ejpam-4254	32	47	0	0	NUM
ejpam-4254	32	48	is	be	AUX
ejpam-4254	32	49	a	a	DET
ejpam-4254	32	50	fixed	fix	VERB
ejpam-4254	32	51	element	element	NOUN
ejpam-4254	32	52	of	of	ADP
ejpam-4254	32	53	u	u	PRON
ejpam-4254	32	54	if	if	SCONJ
ejpam-4254	32	55	it	it	PRON
ejpam-4254	32	56	meets	meet	VERB
ejpam-4254	32	57	the	the	DET
ejpam-4254	32	58	following	following	ADJ
ejpam-4254	32	59	axioms	axiom	NOUN
ejpam-4254	32	60	:	:	PUNCT
ejpam-4254	32	61	(	(	PUNCT
ejpam-4254	32	62	up-1	up-1	NOUN
ejpam-4254	32	63	)	)	PUNCT
ejpam-4254	32	64	(	(	PUNCT
ejpam-4254	32	65	∀a	∀a	X
ejpam-4254	32	66	,	,	PUNCT
ejpam-4254	32	67	b	b	NOUN
ejpam-4254	32	68	,	,	PUNCT
ejpam-4254	32	69	c	c	PROPN
ejpam-4254	32	70	∈	∈	PROPN
ejpam-4254	32	71	u)((b	u)((b	AUX
ejpam-4254	32	72	⋆	⋆	NOUN
ejpam-4254	32	73	c	c	NOUN
ejpam-4254	32	74	)	)	PUNCT
ejpam-4254	32	75	⋆	⋆	NOUN
ejpam-4254	32	76	(	(	PUNCT
ejpam-4254	32	77	(	(	PUNCT
ejpam-4254	32	78	a	a	DET
ejpam-4254	32	79	⋆	⋆	NOUN
ejpam-4254	32	80	b	b	NOUN
ejpam-4254	32	81	)	)	PUNCT
ejpam-4254	32	82	⋆	⋆	NOUN
ejpam-4254	32	83	(	(	PUNCT
ejpam-4254	32	84	a	a	DET
ejpam-4254	32	85	⋆	⋆	NOUN
ejpam-4254	32	86	c	c	NOUN
ejpam-4254	32	87	)	)	PUNCT
ejpam-4254	32	88	)	)	PUNCT
ejpam-4254	33	1	=	=	PUNCT
ejpam-4254	33	2	0	0	NUM
ejpam-4254	33	3	)	)	PUNCT
ejpam-4254	33	4	,	,	PUNCT
ejpam-4254	33	5	(	(	PUNCT
ejpam-4254	33	6	up-2	up-2	NUM
ejpam-4254	33	7	)	)	PUNCT
ejpam-4254	33	8	(	(	PUNCT
ejpam-4254	33	9	∀a	∀a	NOUN
ejpam-4254	33	10	∈	∈	NOUN
ejpam-4254	33	11	u)(0	u)(0	NOUN
ejpam-4254	33	12	⋆	⋆	VERB
ejpam-4254	33	13	a	a	DET
ejpam-4254	33	14	=	=	PUNCT
ejpam-4254	33	15	a	a	NOUN
ejpam-4254	33	16	)	)	PUNCT
ejpam-4254	33	17	,	,	PUNCT
ejpam-4254	33	18	(	(	PUNCT
ejpam-4254	33	19	up-3	up-3	NOUN
ejpam-4254	33	20	)	)	PUNCT
ejpam-4254	33	21	(	(	PUNCT
ejpam-4254	33	22	∀a	∀a	NOUN
ejpam-4254	33	23	∈	∈	NOUN
ejpam-4254	33	24	u)(a	u)(a	NUM
ejpam-4254	33	25	⋆	⋆	X
ejpam-4254	33	26	0	0	NUM
ejpam-4254	33	27	=	=	SYM
ejpam-4254	33	28	0	0	NUM
ejpam-4254	33	29	)	)	PUNCT
ejpam-4254	33	30	,	,	PUNCT
ejpam-4254	33	31	(	(	PUNCT
ejpam-4254	33	32	up-4	up-4	ADV
ejpam-4254	33	33	)	)	PUNCT
ejpam-4254	33	34	(	(	PUNCT
ejpam-4254	33	35	∀a	∀a	X
ejpam-4254	33	36	,	,	PUNCT
ejpam-4254	33	37	b	b	PROPN
ejpam-4254	33	38	∈	∈	PROPN
ejpam-4254	33	39	u)(a	u)(a	NUM
ejpam-4254	33	40	⋆	⋆	X
ejpam-4254	33	41	b	b	NOUN
ejpam-4254	33	42	=	=	SYM
ejpam-4254	33	43	0	0	PROPN
ejpam-4254	33	44	,	,	PUNCT
ejpam-4254	33	45	b	b	X
ejpam-4254	33	46	⋆	⋆	VERB
ejpam-4254	33	47	a	a	PRON
ejpam-4254	33	48	=	=	SYM
ejpam-4254	33	49	0	0	NUM
ejpam-4254	33	50	⇒	⇒	NOUN
ejpam-4254	33	51	a	a	DET
ejpam-4254	33	52	=	=	ADJ
ejpam-4254	33	53	b	b	NOUN
ejpam-4254	33	54	)	)	PUNCT
ejpam-4254	33	55	.	.	PUNCT
ejpam-4254	34	1	for	for	ADP
ejpam-4254	34	2	more	more	ADJ
ejpam-4254	34	3	examples	example	NOUN
ejpam-4254	34	4	of	of	ADP
ejpam-4254	34	5	up	up	ADP
ejpam-4254	34	6	-	-	PUNCT
ejpam-4254	34	7	algebras	algebras	X
ejpam-4254	34	8	,	,	PUNCT
ejpam-4254	34	9	see	see	VERB
ejpam-4254	34	10	[	[	X
ejpam-4254	34	11	3	3	NUM
ejpam-4254	34	12	,	,	PUNCT
ejpam-4254	34	13	4	4	NUM
ejpam-4254	34	14	,	,	PUNCT
ejpam-4254	34	15	8	8	NUM
ejpam-4254	34	16	,	,	PUNCT
ejpam-4254	34	17	12	12	NUM
ejpam-4254	34	18	,	,	PUNCT
ejpam-4254	34	19	14	14	NUM
ejpam-4254	34	20	,	,	PUNCT
ejpam-4254	34	21	22–25	22–25	NUM
ejpam-4254	34	22	]	]	PUNCT
ejpam-4254	34	23	.	.	PUNCT
ejpam-4254	35	1	according	accord	VERB
ejpam-4254	35	2	to	to	ADP
ejpam-4254	35	3	[	[	X
ejpam-4254	35	4	11	11	NUM
ejpam-4254	35	5	]	]	PUNCT
ejpam-4254	35	6	,	,	PUNCT
ejpam-4254	35	7	we	we	PRON
ejpam-4254	35	8	know	know	VERB
ejpam-4254	35	9	that	that	SCONJ
ejpam-4254	35	10	the	the	DET
ejpam-4254	35	11	concept	concept	NOUN
ejpam-4254	35	12	of	of	ADP
ejpam-4254	35	13	up	up	ADV
ejpam-4254	35	14	-	-	PUNCT
ejpam-4254	35	15	algebras	algebras	PROPN
ejpam-4254	35	16	is	be	AUX
ejpam-4254	35	17	a	a	DET
ejpam-4254	35	18	generalization	generalization	NOUN
ejpam-4254	35	19	of	of	ADP
ejpam-4254	35	20	ku	ku	PROPN
ejpam-4254	35	21	-	-	PUNCT
ejpam-4254	35	22	algebras	algebras	PROPN
ejpam-4254	35	23	(	(	PUNCT
ejpam-4254	35	24	see	see	VERB
ejpam-4254	35	25	[	[	X
ejpam-4254	35	26	19	19	NUM
ejpam-4254	35	27	]	]	NUM
ejpam-4254	35	28	)	)	PUNCT
ejpam-4254	35	29	.	.	PUNCT
ejpam-4254	36	1	unless	unless	SCONJ
ejpam-4254	36	2	otherwise	otherwise	ADV
ejpam-4254	36	3	indicated	indicate	VERB
ejpam-4254	36	4	,	,	PUNCT
ejpam-4254	36	5	we	we	PRON
ejpam-4254	36	6	will	will	AUX
ejpam-4254	36	7	assume	assume	VERB
ejpam-4254	36	8	that	that	SCONJ
ejpam-4254	36	9	u	u	PRON
ejpam-4254	36	10	is	be	AUX
ejpam-4254	36	11	a	a	DET
ejpam-4254	36	12	up	up	NOUN
ejpam-4254	36	13	-	-	PUNCT
ejpam-4254	36	14	algebra	algebra	NOUN
ejpam-4254	36	15	(	(	PUNCT
ejpam-4254	36	16	u	u	NOUN
ejpam-4254	36	17	,	,	PUNCT
ejpam-4254	36	18	⋆	⋆	INTJ
ejpam-4254	36	19	,	,	PUNCT
ejpam-4254	36	20	0	0	NUM
ejpam-4254	36	21	)	)	PUNCT
ejpam-4254	36	22	.	.	PUNCT
ejpam-4254	37	1	in	in	ADP
ejpam-4254	37	2	u	u	PROPN
ejpam-4254	37	3	,	,	PUNCT
ejpam-4254	37	4	the	the	DET
ejpam-4254	37	5	following	follow	VERB
ejpam-4254	37	6	assertions	assertion	NOUN
ejpam-4254	37	7	are	be	AUX
ejpam-4254	37	8	valid	valid	ADJ
ejpam-4254	37	9	(	(	PUNCT
ejpam-4254	37	10	see	see	VERB
ejpam-4254	37	11	[	[	X
ejpam-4254	37	12	11	11	NUM
ejpam-4254	37	13	,	,	PUNCT
ejpam-4254	37	14	12	12	NUM
ejpam-4254	37	15	]	]	PUNCT
ejpam-4254	37	16	)	)	PUNCT
ejpam-4254	37	17	.	.	PUNCT
ejpam-4254	38	1	(	(	PUNCT
ejpam-4254	38	2	∀a	∀a	NOUN
ejpam-4254	38	3	∈	∈	NOUN
ejpam-4254	38	4	u)(a	u)(a	NUM
ejpam-4254	38	5	⋆	⋆	VERB
ejpam-4254	38	6	a	a	DET
ejpam-4254	38	7	=	=	NOUN
ejpam-4254	38	8	0	0	NUM
ejpam-4254	38	9	)	)	PUNCT
ejpam-4254	38	10	,	,	PUNCT
ejpam-4254	38	11	(	(	PUNCT
ejpam-4254	38	12	1.1	1.1	NUM
ejpam-4254	38	13	)	)	PUNCT
ejpam-4254	38	14	(	(	PUNCT
ejpam-4254	38	15	∀a	∀a	X
ejpam-4254	38	16	,	,	PUNCT
ejpam-4254	38	17	b	b	NOUN
ejpam-4254	38	18	,	,	PUNCT
ejpam-4254	38	19	c	c	PROPN
ejpam-4254	38	20	∈	∈	PROPN
ejpam-4254	38	21	u)(a	u)(a	NUM
ejpam-4254	38	22	⋆	⋆	X
ejpam-4254	38	23	b	b	NOUN
ejpam-4254	38	24	=	=	SYM
ejpam-4254	38	25	0	0	PROPN
ejpam-4254	38	26	,	,	PUNCT
ejpam-4254	38	27	b	b	NOUN
ejpam-4254	38	28	⋆	⋆	X
ejpam-4254	38	29	c	c	NOUN
ejpam-4254	38	30	=	=	SYM
ejpam-4254	38	31	0	0	PROPN
ejpam-4254	38	32	⇒	⇒	NOUN
ejpam-4254	38	33	a	a	DET
ejpam-4254	38	34	⋆	⋆	NOUN
ejpam-4254	38	35	c	c	NOUN
ejpam-4254	38	36	=	=	SYM
ejpam-4254	38	37	0	0	NUM
ejpam-4254	38	38	)	)	PUNCT
ejpam-4254	38	39	,	,	PUNCT
ejpam-4254	38	40	(	(	PUNCT
ejpam-4254	38	41	1.2	1.2	NUM
ejpam-4254	38	42	)	)	PUNCT
ejpam-4254	38	43	a.	a.	NOUN
ejpam-4254	38	44	iampan	iampan	NOUN
ejpam-4254	38	45	et	et	PROPN
ejpam-4254	38	46	al	al	PROPN
ejpam-4254	38	47	.	.	PUNCT
ejpam-4254	38	48	/	/	SYM
ejpam-4254	38	49	eur	eur	PROPN
ejpam-4254	38	50	.	.	PUNCT
ejpam-4254	39	1	j.	j.	PROPN
ejpam-4254	39	2	pure	pure	PROPN
ejpam-4254	39	3	appl	appl	PROPN
ejpam-4254	39	4	.	.	PROPN
ejpam-4254	39	5	math	math	PROPN
ejpam-4254	39	6	,	,	PUNCT
ejpam-4254	39	7	15	15	NUM
ejpam-4254	39	8	(	(	PUNCT
ejpam-4254	39	9	1	1	NUM
ejpam-4254	39	10	)	)	PUNCT
ejpam-4254	39	11	(	(	PUNCT
ejpam-4254	39	12	2022	2022	NUM
ejpam-4254	39	13	)	)	PUNCT
ejpam-4254	39	14	,	,	PUNCT
ejpam-4254	39	15	169	169	NUM
ejpam-4254	39	16	-	-	SYM
ejpam-4254	39	17	198	198	NUM
ejpam-4254	39	18	171	171	NUM
ejpam-4254	39	19	(	(	PUNCT
ejpam-4254	39	20	∀a	∀a	X
ejpam-4254	39	21	,	,	PUNCT
ejpam-4254	39	22	b	b	NOUN
ejpam-4254	39	23	,	,	PUNCT
ejpam-4254	39	24	c	c	PROPN
ejpam-4254	39	25	∈	∈	PROPN
ejpam-4254	39	26	u)(a	u)(a	NUM
ejpam-4254	39	27	⋆	⋆	X
ejpam-4254	39	28	b	b	NOUN
ejpam-4254	39	29	=	=	SYM
ejpam-4254	39	30	0	0	NUM
ejpam-4254	39	31	⇒	⇒	NOUN
ejpam-4254	39	32	(	(	PUNCT
ejpam-4254	39	33	c	c	NOUN
ejpam-4254	39	34	⋆	⋆	NOUN
ejpam-4254	39	35	a	a	NOUN
ejpam-4254	39	36	)	)	PUNCT
ejpam-4254	39	37	⋆	⋆	X
ejpam-4254	39	38	(	(	PUNCT
ejpam-4254	39	39	c	c	NOUN
ejpam-4254	39	40	⋆	⋆	NOUN
ejpam-4254	39	41	b	b	NOUN
ejpam-4254	39	42	)	)	PUNCT
ejpam-4254	39	43	=	=	SYM
ejpam-4254	39	44	0	0	NUM
ejpam-4254	39	45	)	)	PUNCT
ejpam-4254	39	46	,	,	PUNCT
ejpam-4254	39	47	(	(	PUNCT
ejpam-4254	39	48	1.3	1.3	NUM
ejpam-4254	39	49	)	)	PUNCT
ejpam-4254	39	50	(	(	PUNCT
ejpam-4254	39	51	∀a	∀a	X
ejpam-4254	39	52	,	,	PUNCT
ejpam-4254	39	53	b	b	NOUN
ejpam-4254	39	54	,	,	PUNCT
ejpam-4254	39	55	c	c	PROPN
ejpam-4254	39	56	∈	∈	PROPN
ejpam-4254	39	57	u)(a	u)(a	NUM
ejpam-4254	39	58	⋆	⋆	X
ejpam-4254	39	59	b	b	NOUN
ejpam-4254	39	60	=	=	SYM
ejpam-4254	39	61	0	0	NUM
ejpam-4254	40	1	⇒	⇒	NOUN
ejpam-4254	40	2	(	(	PUNCT
ejpam-4254	40	3	b	b	X
ejpam-4254	40	4	⋆	⋆	NOUN
ejpam-4254	40	5	c	c	NOUN
ejpam-4254	40	6	)	)	PUNCT
ejpam-4254	40	7	⋆	⋆	NOUN
ejpam-4254	40	8	(	(	PUNCT
ejpam-4254	40	9	a	a	DET
ejpam-4254	40	10	⋆	⋆	NOUN
ejpam-4254	40	11	c	c	NOUN
ejpam-4254	40	12	)	)	PUNCT
ejpam-4254	40	13	=	=	SYM
ejpam-4254	40	14	0	0	NUM
ejpam-4254	40	15	)	)	PUNCT
ejpam-4254	40	16	,	,	PUNCT
ejpam-4254	40	17	(	(	PUNCT
ejpam-4254	40	18	1.4	1.4	NUM
ejpam-4254	40	19	)	)	PUNCT
ejpam-4254	40	20	(	(	PUNCT
ejpam-4254	40	21	∀a	∀a	X
ejpam-4254	40	22	,	,	PUNCT
ejpam-4254	40	23	b	b	PROPN
ejpam-4254	40	24	∈	∈	PROPN
ejpam-4254	40	25	u)(a	u)(a	NUM
ejpam-4254	40	26	⋆	⋆	X
ejpam-4254	40	27	(	(	PUNCT
ejpam-4254	40	28	b	b	NOUN
ejpam-4254	40	29	⋆	⋆	NOUN
ejpam-4254	40	30	a	a	NOUN
ejpam-4254	40	31	)	)	PUNCT
ejpam-4254	40	32	=	=	SYM
ejpam-4254	40	33	0	0	NUM
ejpam-4254	40	34	)	)	PUNCT
ejpam-4254	40	35	,	,	PUNCT
ejpam-4254	40	36	(	(	PUNCT
ejpam-4254	40	37	1.5	1.5	NUM
ejpam-4254	40	38	)	)	PUNCT
ejpam-4254	40	39	(	(	PUNCT
ejpam-4254	40	40	∀a	∀a	X
ejpam-4254	40	41	,	,	PUNCT
ejpam-4254	40	42	b	b	PROPN
ejpam-4254	40	43	∈	∈	PROPN
ejpam-4254	40	44	u)((b	u)((b	VERB
ejpam-4254	40	45	⋆	⋆	NOUN
ejpam-4254	40	46	a	a	NOUN
ejpam-4254	40	47	)	)	PUNCT
ejpam-4254	40	48	⋆	⋆	X
ejpam-4254	40	49	a	a	PRON
ejpam-4254	40	50	=	=	SYM
ejpam-4254	40	51	0	0	NUM
ejpam-4254	40	52	⇔	⇔	NOUN
ejpam-4254	40	53	a	a	PROPN
ejpam-4254	40	54	=	=	X
ejpam-4254	40	55	b	b	PROPN
ejpam-4254	40	56	⋆	⋆	NOUN
ejpam-4254	40	57	a	a	NOUN
ejpam-4254	40	58	)	)	PUNCT
ejpam-4254	40	59	,	,	PUNCT
ejpam-4254	40	60	(	(	PUNCT
ejpam-4254	40	61	1.6	1.6	NUM
ejpam-4254	40	62	)	)	PUNCT
ejpam-4254	40	63	(	(	PUNCT
ejpam-4254	40	64	∀a	∀a	X
ejpam-4254	40	65	,	,	PUNCT
ejpam-4254	40	66	b	b	PROPN
ejpam-4254	40	67	∈	∈	PROPN
ejpam-4254	40	68	u)(a	u)(a	NUM
ejpam-4254	40	69	⋆	⋆	X
ejpam-4254	40	70	(	(	PUNCT
ejpam-4254	40	71	b	b	NOUN
ejpam-4254	40	72	⋆	⋆	NOUN
ejpam-4254	40	73	b	b	NOUN
ejpam-4254	40	74	)	)	PUNCT
ejpam-4254	40	75	=	=	SYM
ejpam-4254	40	76	0	0	NUM
ejpam-4254	40	77	)	)	PUNCT
ejpam-4254	40	78	,	,	PUNCT
ejpam-4254	40	79	(	(	PUNCT
ejpam-4254	40	80	1.7	1.7	NUM
ejpam-4254	40	81	)	)	PUNCT
ejpam-4254	40	82	(	(	PUNCT
ejpam-4254	40	83	∀u	∀u	NOUN
ejpam-4254	40	84	,	,	PUNCT
ejpam-4254	40	85	a	a	DET
ejpam-4254	40	86	,	,	PUNCT
ejpam-4254	40	87	b	b	NOUN
ejpam-4254	40	88	,	,	PUNCT
ejpam-4254	40	89	c	c	PROPN
ejpam-4254	40	90	∈	∈	PROPN
ejpam-4254	40	91	u)((a	u)((a	X
ejpam-4254	40	92	⋆	⋆	X
ejpam-4254	40	93	(	(	PUNCT
ejpam-4254	40	94	b	b	X
ejpam-4254	40	95	⋆	⋆	ADJ
ejpam-4254	40	96	c	c	NOUN
ejpam-4254	40	97	)	)	PUNCT
ejpam-4254	40	98	)	)	PUNCT
ejpam-4254	41	1	⋆	⋆	X
ejpam-4254	41	2	(	(	PUNCT
ejpam-4254	41	3	a	a	DET
ejpam-4254	41	4	⋆	⋆	X
ejpam-4254	41	5	(	(	PUNCT
ejpam-4254	41	6	(	(	PUNCT
ejpam-4254	41	7	u	u	NOUN
ejpam-4254	41	8	⋆	⋆	X
ejpam-4254	41	9	b	b	NOUN
ejpam-4254	41	10	)	)	PUNCT
ejpam-4254	41	11	⋆	⋆	NOUN
ejpam-4254	41	12	(	(	PUNCT
ejpam-4254	41	13	u	u	NOUN
ejpam-4254	41	14	⋆	⋆	NOUN
ejpam-4254	41	15	c	c	NOUN
ejpam-4254	41	16	)	)	PUNCT
ejpam-4254	41	17	)	)	PUNCT
ejpam-4254	41	18	)	)	PUNCT
ejpam-4254	41	19	=	=	PUNCT
ejpam-4254	42	1	0	0	NUM
ejpam-4254	42	2	)	)	PUNCT
ejpam-4254	42	3	,	,	PUNCT
ejpam-4254	42	4	(	(	PUNCT
ejpam-4254	42	5	1.8	1.8	NUM
ejpam-4254	42	6	)	)	PUNCT
ejpam-4254	42	7	(	(	PUNCT
ejpam-4254	42	8	∀u	∀u	NOUN
ejpam-4254	42	9	,	,	PUNCT
ejpam-4254	42	10	a	a	DET
ejpam-4254	42	11	,	,	PUNCT
ejpam-4254	42	12	b	b	NOUN
ejpam-4254	42	13	,	,	PUNCT
ejpam-4254	42	14	c	c	PROPN
ejpam-4254	42	15	∈	∈	PROPN
ejpam-4254	42	16	u)((((u	u)((((u	NOUN
ejpam-4254	42	17	⋆	⋆	VERB
ejpam-4254	42	18	a	a	NOUN
ejpam-4254	42	19	)	)	PUNCT
ejpam-4254	42	20	⋆	⋆	NOUN
ejpam-4254	42	21	(	(	PUNCT
ejpam-4254	42	22	u	u	NOUN
ejpam-4254	42	23	⋆	⋆	NOUN
ejpam-4254	42	24	b	b	NOUN
ejpam-4254	42	25	)	)	PUNCT
ejpam-4254	42	26	)	)	PUNCT
ejpam-4254	43	1	⋆	⋆	VERB
ejpam-4254	43	2	c	c	NOUN
ejpam-4254	43	3	)	)	PUNCT
ejpam-4254	43	4	⋆	⋆	NOUN
ejpam-4254	43	5	(	(	PUNCT
ejpam-4254	43	6	(	(	PUNCT
ejpam-4254	43	7	a	a	DET
ejpam-4254	43	8	⋆	⋆	NOUN
ejpam-4254	43	9	b	b	NOUN
ejpam-4254	43	10	)	)	PUNCT
ejpam-4254	43	11	⋆	⋆	VERB
ejpam-4254	43	12	c	c	NOUN
ejpam-4254	43	13	)	)	PUNCT
ejpam-4254	43	14	=	=	SYM
ejpam-4254	43	15	0	0	NUM
ejpam-4254	43	16	)	)	PUNCT
ejpam-4254	43	17	,	,	PUNCT
ejpam-4254	43	18	(	(	PUNCT
ejpam-4254	43	19	1.9	1.9	NUM
ejpam-4254	43	20	)	)	PUNCT
ejpam-4254	43	21	(	(	PUNCT
ejpam-4254	43	22	∀a	∀a	X
ejpam-4254	43	23	,	,	PUNCT
ejpam-4254	43	24	b	b	NOUN
ejpam-4254	43	25	,	,	PUNCT
ejpam-4254	43	26	c	c	PROPN
ejpam-4254	43	27	∈	∈	PROPN
ejpam-4254	43	28	u)(((a	u)(((a	NOUN
ejpam-4254	43	29	⋆	⋆	PUNCT
ejpam-4254	43	30	b	b	NOUN
ejpam-4254	43	31	)	)	PUNCT
ejpam-4254	43	32	⋆	⋆	VERB
ejpam-4254	43	33	c	c	NOUN
ejpam-4254	43	34	)	)	PUNCT
ejpam-4254	44	1	⋆	⋆	X
ejpam-4254	44	2	(	(	PUNCT
ejpam-4254	44	3	b	b	X
ejpam-4254	44	4	⋆	⋆	NOUN
ejpam-4254	44	5	c	c	NOUN
ejpam-4254	44	6	)	)	PUNCT
ejpam-4254	44	7	=	=	SYM
ejpam-4254	45	1	0	0	NUM
ejpam-4254	45	2	)	)	PUNCT
ejpam-4254	45	3	,	,	PUNCT
ejpam-4254	45	4	(	(	PUNCT
ejpam-4254	45	5	1.10	1.10	NUM
ejpam-4254	45	6	)	)	PUNCT
ejpam-4254	45	7	(	(	PUNCT
ejpam-4254	45	8	∀a	∀a	X
ejpam-4254	45	9	,	,	PUNCT
ejpam-4254	45	10	b	b	NOUN
ejpam-4254	45	11	,	,	PUNCT
ejpam-4254	45	12	c	c	PROPN
ejpam-4254	45	13	∈	∈	PROPN
ejpam-4254	45	14	u)(a	u)(a	NUM
ejpam-4254	45	15	⋆	⋆	X
ejpam-4254	45	16	b	b	NOUN
ejpam-4254	45	17	=	=	SYM
ejpam-4254	45	18	0	0	PROPN
ejpam-4254	45	19	⇒	⇒	NOUN
ejpam-4254	45	20	a	a	DET
ejpam-4254	45	21	⋆	⋆	X
ejpam-4254	45	22	(	(	PUNCT
ejpam-4254	45	23	c	c	NOUN
ejpam-4254	45	24	⋆	⋆	NOUN
ejpam-4254	45	25	b	b	NOUN
ejpam-4254	45	26	)	)	PUNCT
ejpam-4254	45	27	=	=	SYM
ejpam-4254	45	28	0	0	NUM
ejpam-4254	45	29	)	)	PUNCT
ejpam-4254	45	30	,	,	PUNCT
ejpam-4254	45	31	(	(	PUNCT
ejpam-4254	45	32	1.11	1.11	NUM
ejpam-4254	45	33	)	)	PUNCT
ejpam-4254	45	34	(	(	PUNCT
ejpam-4254	45	35	∀a	∀a	X
ejpam-4254	45	36	,	,	PUNCT
ejpam-4254	45	37	b	b	NOUN
ejpam-4254	45	38	,	,	PUNCT
ejpam-4254	45	39	c	c	PROPN
ejpam-4254	45	40	∈	∈	PROPN
ejpam-4254	45	41	u)(((a	u)(((a	NOUN
ejpam-4254	45	42	⋆	⋆	PUNCT
ejpam-4254	45	43	b	b	NOUN
ejpam-4254	45	44	)	)	PUNCT
ejpam-4254	45	45	⋆	⋆	VERB
ejpam-4254	45	46	c	c	NOUN
ejpam-4254	45	47	)	)	PUNCT
ejpam-4254	45	48	⋆	⋆	NOUN
ejpam-4254	45	49	(	(	PUNCT
ejpam-4254	45	50	a	a	DET
ejpam-4254	45	51	⋆	⋆	X
ejpam-4254	45	52	(	(	PUNCT
ejpam-4254	45	53	b	b	NOUN
ejpam-4254	45	54	⋆	⋆	ADJ
ejpam-4254	45	55	c	c	NOUN
ejpam-4254	45	56	)	)	PUNCT
ejpam-4254	45	57	)	)	PUNCT
ejpam-4254	46	1	=	=	PUNCT
ejpam-4254	46	2	0	0	NUM
ejpam-4254	46	3	)	)	PUNCT
ejpam-4254	46	4	,	,	PUNCT
ejpam-4254	46	5	(	(	PUNCT
ejpam-4254	46	6	1.12	1.12	NUM
ejpam-4254	46	7	)	)	PUNCT
ejpam-4254	46	8	(	(	PUNCT
ejpam-4254	46	9	∀u	∀u	NOUN
ejpam-4254	46	10	,	,	PUNCT
ejpam-4254	46	11	a	a	DET
ejpam-4254	46	12	,	,	PUNCT
ejpam-4254	46	13	b	b	NOUN
ejpam-4254	46	14	,	,	PUNCT
ejpam-4254	46	15	c	c	PROPN
ejpam-4254	46	16	∈	∈	PROPN
ejpam-4254	46	17	u)(((a	u)(((a	NOUN
ejpam-4254	46	18	⋆	⋆	PUNCT
ejpam-4254	46	19	b	b	NOUN
ejpam-4254	46	20	)	)	PUNCT
ejpam-4254	46	21	⋆	⋆	VERB
ejpam-4254	46	22	c	c	NOUN
ejpam-4254	46	23	)	)	PUNCT
ejpam-4254	46	24	⋆	⋆	X
ejpam-4254	46	25	(	(	PUNCT
ejpam-4254	46	26	b	b	X
ejpam-4254	46	27	⋆	⋆	X
ejpam-4254	46	28	(	(	PUNCT
ejpam-4254	46	29	u	u	NOUN
ejpam-4254	46	30	⋆	⋆	NOUN
ejpam-4254	46	31	c	c	NOUN
ejpam-4254	46	32	)	)	PUNCT
ejpam-4254	46	33	)	)	PUNCT
ejpam-4254	47	1	=	=	PUNCT
ejpam-4254	47	2	0	0	NUM
ejpam-4254	47	3	)	)	PUNCT
ejpam-4254	47	4	.	.	PUNCT
ejpam-4254	48	1	(	(	PUNCT
ejpam-4254	48	2	1.13	1.13	NUM
ejpam-4254	48	3	)	)	PUNCT
ejpam-4254	48	4	according	accord	VERB
ejpam-4254	48	5	to	to	ADP
ejpam-4254	48	6	[	[	X
ejpam-4254	48	7	11	11	NUM
ejpam-4254	48	8	]	]	PUNCT
ejpam-4254	48	9	,	,	PUNCT
ejpam-4254	48	10	the	the	DET
ejpam-4254	48	11	binary	binary	PROPN
ejpam-4254	48	12	relation	relation	NOUN
ejpam-4254	48	13	≤	≤	PROPN
ejpam-4254	48	14	on	on	ADP
ejpam-4254	48	15	u	u	NOUN
ejpam-4254	48	16	is	be	AUX
ejpam-4254	48	17	defined	define	VERB
ejpam-4254	48	18	as	as	SCONJ
ejpam-4254	48	19	follows	follow	VERB
ejpam-4254	48	20	:	:	PUNCT
ejpam-4254	48	21	(	(	PUNCT
ejpam-4254	48	22	∀a	∀a	X
ejpam-4254	48	23	,	,	PUNCT
ejpam-4254	48	24	b	b	X
ejpam-4254	48	25	∈	∈	PROPN
ejpam-4254	48	26	u)(a	u)(a	NUM
ejpam-4254	49	1	≤	≤	PROPN
ejpam-4254	49	2	b	b	X
ejpam-4254	49	3	⇔	⇔	X
ejpam-4254	49	4	a	a	DET
ejpam-4254	49	5	⋆	⋆	NOUN
ejpam-4254	49	6	b	b	NOUN
ejpam-4254	49	7	=	=	NOUN
ejpam-4254	49	8	0	0	NUM
ejpam-4254	49	9	)	)	PUNCT
ejpam-4254	49	10	.	.	PUNCT
ejpam-4254	50	1	definition	definition	NOUN
ejpam-4254	50	2	2	2	NUM
ejpam-4254	50	3	.	.	PUNCT
ejpam-4254	51	1	[	[	X
ejpam-4254	51	2	9	9	NUM
ejpam-4254	51	3	,	,	PUNCT
ejpam-4254	51	4	11	11	NUM
ejpam-4254	51	5	,	,	PUNCT
ejpam-4254	51	6	26	26	NUM
ejpam-4254	51	7	]	]	PUNCT
ejpam-4254	51	8	a	a	DET
ejpam-4254	51	9	nonempty	nonempty	NOUN
ejpam-4254	51	10	subset	subset	VERB
ejpam-4254	51	11	s	s	NOUN
ejpam-4254	51	12	of	of	ADP
ejpam-4254	51	13	u	u	NOUN
ejpam-4254	51	14	is	be	AUX
ejpam-4254	51	15	called	call	VERB
ejpam-4254	51	16	(	(	PUNCT
ejpam-4254	51	17	1	1	NUM
ejpam-4254	51	18	)	)	PUNCT
ejpam-4254	51	19	a	a	DET
ejpam-4254	51	20	up	up	ADJ
ejpam-4254	51	21	-	-	PUNCT
ejpam-4254	51	22	subalgebra	subalgebra	NOUN
ejpam-4254	51	23	(	(	PUNCT
ejpam-4254	51	24	ups	up	NOUN
ejpam-4254	51	25	)	)	PUNCT
ejpam-4254	51	26	of	of	ADP
ejpam-4254	51	27	u	u	PRON
ejpam-4254	51	28	if	if	SCONJ
ejpam-4254	51	29	it	it	PRON
ejpam-4254	51	30	satisfies	satisfy	VERB
ejpam-4254	51	31	the	the	DET
ejpam-4254	51	32	following	follow	VERB
ejpam-4254	51	33	condition	condition	NOUN
ejpam-4254	51	34	:	:	PUNCT
ejpam-4254	51	35	(	(	PUNCT
ejpam-4254	51	36	∀a	∀a	X
ejpam-4254	51	37	,	,	PUNCT
ejpam-4254	51	38	b	b	PROPN
ejpam-4254	51	39	∈	∈	PROPN
ejpam-4254	51	40	s)(a	s)(a	NUM
ejpam-4254	52	1	⋆	⋆	PUNCT
ejpam-4254	52	2	b	b	X
ejpam-4254	52	3	∈	∈	PROPN
ejpam-4254	52	4	s	s	NOUN
ejpam-4254	52	5	)	)	PUNCT
ejpam-4254	52	6	,	,	PUNCT
ejpam-4254	52	7	(	(	PUNCT
ejpam-4254	52	8	1.14	1.14	NUM
ejpam-4254	52	9	)	)	PUNCT
ejpam-4254	52	10	(	(	PUNCT
ejpam-4254	52	11	2	2	X
ejpam-4254	52	12	)	)	PUNCT
ejpam-4254	52	13	a	a	DET
ejpam-4254	52	14	near	near	ADJ
ejpam-4254	52	15	up	up	ADP
ejpam-4254	52	16	-	-	PUNCT
ejpam-4254	52	17	filter	filter	NOUN
ejpam-4254	52	18	(	(	PUNCT
ejpam-4254	52	19	nupf	nupf	VERB
ejpam-4254	52	20	)	)	PUNCT
ejpam-4254	52	21	of	of	ADP
ejpam-4254	52	22	u	u	PRON
ejpam-4254	52	23	if	if	SCONJ
ejpam-4254	52	24	it	it	PRON
ejpam-4254	52	25	satisfies	satisfy	VERB
ejpam-4254	52	26	the	the	DET
ejpam-4254	52	27	following	follow	VERB
ejpam-4254	52	28	condition	condition	NOUN
ejpam-4254	52	29	:	:	PUNCT
ejpam-4254	52	30	(	(	PUNCT
ejpam-4254	52	31	∀a	∀a	X
ejpam-4254	52	32	,	,	PUNCT
ejpam-4254	52	33	b	b	PROPN
ejpam-4254	52	34	∈	∈	PROPN
ejpam-4254	52	35	u)(b	u)(b	PROPN
ejpam-4254	52	36	∈	∈	PROPN
ejpam-4254	52	37	s	s	PART
ejpam-4254	52	38	⇒	⇒	NOUN
ejpam-4254	52	39	a	a	DET
ejpam-4254	52	40	⋆	⋆	NOUN
ejpam-4254	52	41	b	b	X
ejpam-4254	52	42	∈	∈	PROPN
ejpam-4254	52	43	s	s	NOUN
ejpam-4254	52	44	)	)	PUNCT
ejpam-4254	52	45	,	,	PUNCT
ejpam-4254	52	46	(	(	PUNCT
ejpam-4254	52	47	1.15	1.15	NUM
ejpam-4254	52	48	)	)	PUNCT
ejpam-4254	52	49	(	(	PUNCT
ejpam-4254	52	50	3	3	X
ejpam-4254	52	51	)	)	PUNCT
ejpam-4254	52	52	a	a	DET
ejpam-4254	52	53	up	up	ADJ
ejpam-4254	52	54	-	-	PUNCT
ejpam-4254	52	55	filter	filter	NOUN
ejpam-4254	52	56	(	(	PUNCT
ejpam-4254	52	57	upf	upf	PROPN
ejpam-4254	52	58	)	)	PUNCT
ejpam-4254	52	59	of	of	ADP
ejpam-4254	52	60	u	u	PRON
ejpam-4254	52	61	if	if	SCONJ
ejpam-4254	52	62	it	it	PRON
ejpam-4254	52	63	satisfies	satisfy	VERB
ejpam-4254	52	64	the	the	DET
ejpam-4254	52	65	following	follow	VERB
ejpam-4254	52	66	conditions	condition	NOUN
ejpam-4254	52	67	:	:	PUNCT
ejpam-4254	52	68	the	the	DET
ejpam-4254	52	69	constant	constant	ADJ
ejpam-4254	52	70	0	0	NUM
ejpam-4254	52	71	of	of	ADP
ejpam-4254	52	72	u	u	NOUN
ejpam-4254	52	73	is	be	AUX
ejpam-4254	52	74	in	in	ADP
ejpam-4254	52	75	s	s	PROPN
ejpam-4254	52	76	,	,	PUNCT
ejpam-4254	52	77	(	(	PUNCT
ejpam-4254	52	78	1.16	1.16	NUM
ejpam-4254	52	79	)	)	PUNCT
ejpam-4254	52	80	(	(	PUNCT
ejpam-4254	52	81	∀a	∀a	X
ejpam-4254	52	82	,	,	PUNCT
ejpam-4254	52	83	b	b	PROPN
ejpam-4254	52	84	∈	∈	PROPN
ejpam-4254	52	85	u)(a	u)(a	NUM
ejpam-4254	52	86	⋆	⋆	ADP
ejpam-4254	52	87	b	b	PROPN
ejpam-4254	52	88	∈	∈	PROPN
ejpam-4254	52	89	s	s	PROPN
ejpam-4254	52	90	,	,	PUNCT
ejpam-4254	52	91	a	a	DET
ejpam-4254	52	92	∈	∈	PROPN
ejpam-4254	52	93	s	s	PART
ejpam-4254	52	94	⇒	⇒	NOUN
ejpam-4254	52	95	b	b	PROPN
ejpam-4254	52	96	∈	∈	PROPN
ejpam-4254	52	97	s	s	NOUN
ejpam-4254	52	98	)	)	PUNCT
ejpam-4254	52	99	,	,	PUNCT
ejpam-4254	52	100	(	(	PUNCT
ejpam-4254	52	101	1.17	1.17	NUM
ejpam-4254	52	102	)	)	PUNCT
ejpam-4254	52	103	(	(	PUNCT
ejpam-4254	52	104	4	4	X
ejpam-4254	52	105	)	)	PUNCT
ejpam-4254	52	106	a	a	DET
ejpam-4254	52	107	up	up	ADJ
ejpam-4254	52	108	-	-	PUNCT
ejpam-4254	52	109	ideal	ideal	NOUN
ejpam-4254	52	110	(	(	PUNCT
ejpam-4254	52	111	upi	upi	PROPN
ejpam-4254	52	112	)	)	PUNCT
ejpam-4254	52	113	of	of	ADP
ejpam-4254	52	114	u	u	PRON
ejpam-4254	52	115	if	if	SCONJ
ejpam-4254	52	116	it	it	PRON
ejpam-4254	52	117	satisfies	satisfy	VERB
ejpam-4254	52	118	the	the	DET
ejpam-4254	52	119	condition	condition	NOUN
ejpam-4254	52	120	(	(	PUNCT
ejpam-4254	52	121	1.16	1.16	NUM
ejpam-4254	52	122	)	)	PUNCT
ejpam-4254	52	123	and	and	CCONJ
ejpam-4254	52	124	the	the	DET
ejpam-4254	52	125	following	follow	VERB
ejpam-4254	52	126	condition	condition	NOUN
ejpam-4254	52	127	:	:	PUNCT
ejpam-4254	52	128	(	(	PUNCT
ejpam-4254	52	129	∀a	∀a	X
ejpam-4254	52	130	,	,	PUNCT
ejpam-4254	52	131	b	b	NOUN
ejpam-4254	52	132	,	,	PUNCT
ejpam-4254	52	133	c	c	PROPN
ejpam-4254	52	134	∈	∈	PROPN
ejpam-4254	53	1	u)(a	u)(a	NUM
ejpam-4254	53	2	⋆	⋆	X
ejpam-4254	53	3	(	(	PUNCT
ejpam-4254	53	4	b	b	X
ejpam-4254	53	5	⋆	⋆	NOUN
ejpam-4254	53	6	c	c	NOUN
ejpam-4254	53	7	)	)	PUNCT
ejpam-4254	53	8	∈	∈	PROPN
ejpam-4254	53	9	s	s	PROPN
ejpam-4254	53	10	,	,	PUNCT
ejpam-4254	53	11	b	b	PROPN
ejpam-4254	53	12	∈	∈	PROPN
ejpam-4254	53	13	s	s	PART
ejpam-4254	53	14	⇒	⇒	NOUN
ejpam-4254	53	15	a	a	DET
ejpam-4254	53	16	⋆	⋆	NOUN
ejpam-4254	53	17	c	c	NOUN
ejpam-4254	53	18	∈	∈	PROPN
ejpam-4254	53	19	s	s	NOUN
ejpam-4254	53	20	)	)	PUNCT
ejpam-4254	53	21	,	,	PUNCT
ejpam-4254	53	22	(	(	PUNCT
ejpam-4254	53	23	1.18	1.18	NUM
ejpam-4254	53	24	)	)	PUNCT
ejpam-4254	53	25	(	(	PUNCT
ejpam-4254	53	26	5	5	X
ejpam-4254	53	27	)	)	PUNCT
ejpam-4254	53	28	a	a	DET
ejpam-4254	53	29	strong	strong	ADJ
ejpam-4254	53	30	up	up	ADJ
ejpam-4254	53	31	-	-	PUNCT
ejpam-4254	53	32	ideal	ideal	NOUN
ejpam-4254	53	33	(	(	PUNCT
ejpam-4254	53	34	supi	supi	NOUN
ejpam-4254	53	35	)	)	PUNCT
ejpam-4254	53	36	of	of	ADP
ejpam-4254	53	37	u	u	PRON
ejpam-4254	53	38	if	if	SCONJ
ejpam-4254	53	39	it	it	PRON
ejpam-4254	53	40	satisfies	satisfy	VERB
ejpam-4254	53	41	the	the	DET
ejpam-4254	53	42	condition	condition	NOUN
ejpam-4254	53	43	(	(	PUNCT
ejpam-4254	53	44	1.16	1.16	NUM
ejpam-4254	53	45	)	)	PUNCT
ejpam-4254	53	46	and	and	CCONJ
ejpam-4254	53	47	the	the	DET
ejpam-4254	53	48	following	follow	VERB
ejpam-4254	53	49	condition	condition	NOUN
ejpam-4254	53	50	:	:	PUNCT
ejpam-4254	53	51	(	(	PUNCT
ejpam-4254	53	52	∀a	∀a	X
ejpam-4254	53	53	,	,	PUNCT
ejpam-4254	53	54	b	b	NOUN
ejpam-4254	53	55	,	,	PUNCT
ejpam-4254	53	56	c	c	PROPN
ejpam-4254	53	57	∈	∈	PROPN
ejpam-4254	53	58	u)((c	u)((c	ADV
ejpam-4254	53	59	⋆	⋆	NOUN
ejpam-4254	53	60	b	b	NOUN
ejpam-4254	53	61	)	)	PUNCT
ejpam-4254	53	62	⋆	⋆	X
ejpam-4254	53	63	(	(	PUNCT
ejpam-4254	53	64	c	c	NOUN
ejpam-4254	53	65	⋆	⋆	NOUN
ejpam-4254	53	66	a	a	PRON
ejpam-4254	53	67	)	)	PUNCT
ejpam-4254	53	68	∈	∈	PROPN
ejpam-4254	53	69	s	s	PROPN
ejpam-4254	53	70	,	,	PUNCT
ejpam-4254	53	71	b	b	PROPN
ejpam-4254	53	72	∈	∈	PROPN
ejpam-4254	53	73	s	s	PART
ejpam-4254	53	74	⇒	⇒	NOUN
ejpam-4254	53	75	a	a	DET
ejpam-4254	53	76	∈	∈	PROPN
ejpam-4254	53	77	s	s	NOUN
ejpam-4254	53	78	)	)	PUNCT
ejpam-4254	53	79	.	.	PUNCT
ejpam-4254	54	1	(	(	PUNCT
ejpam-4254	54	2	1.19	1.19	NUM
ejpam-4254	54	3	)	)	PUNCT
ejpam-4254	54	4	guntasow	guntasow	NOUN
ejpam-4254	54	5	et	et	NOUN
ejpam-4254	54	6	al	al	PROPN
ejpam-4254	54	7	.	.	PUNCT
ejpam-4254	55	1	[	[	X
ejpam-4254	55	2	9	9	NUM
ejpam-4254	55	3	]	]	PUNCT
ejpam-4254	55	4	and	and	CCONJ
ejpam-4254	55	5	iampan	iampan	NOUN
ejpam-4254	55	6	[	[	X
ejpam-4254	55	7	13	13	NUM
ejpam-4254	55	8	]	]	PUNCT
ejpam-4254	55	9	proved	prove	VERB
ejpam-4254	55	10	that	that	SCONJ
ejpam-4254	55	11	the	the	DET
ejpam-4254	55	12	concept	concept	NOUN
ejpam-4254	55	13	of	of	ADP
ejpam-4254	55	14	upss	upss	PROPN
ejpam-4254	55	15	is	be	AUX
ejpam-4254	55	16	a	a	DET
ejpam-4254	55	17	generalization	generalization	NOUN
ejpam-4254	55	18	of	of	ADP
ejpam-4254	55	19	nupfs	nupfs	PROPN
ejpam-4254	55	20	,	,	PUNCT
ejpam-4254	55	21	nupfs	nupfs	PROPN
ejpam-4254	55	22	is	be	AUX
ejpam-4254	55	23	a	a	DET
ejpam-4254	55	24	generalization	generalization	NOUN
ejpam-4254	55	25	of	of	ADP
ejpam-4254	55	26	upfs	upfs	PROPN
ejpam-4254	55	27	,	,	PUNCT
ejpam-4254	55	28	upfs	upfs	PROPN
ejpam-4254	55	29	is	be	AUX
ejpam-4254	55	30	a	a	DET
ejpam-4254	55	31	generalization	generalization	NOUN
ejpam-4254	55	32	of	of	ADP
ejpam-4254	55	33	upis	upis	NOUN
ejpam-4254	55	34	,	,	PUNCT
ejpam-4254	55	35	and	and	CCONJ
ejpam-4254	55	36	upis	upis	ADJ
ejpam-4254	55	37	is	be	AUX
ejpam-4254	55	38	a	a	DET
ejpam-4254	55	39	generalization	generalization	NOUN
ejpam-4254	55	40	of	of	ADP
ejpam-4254	55	41	supis	supis	PROPN
ejpam-4254	55	42	.	.	PUNCT
ejpam-4254	56	1	they	they	PRON
ejpam-4254	56	2	also	also	ADV
ejpam-4254	56	3	proved	prove	VERB
ejpam-4254	56	4	that	that	SCONJ
ejpam-4254	56	5	u	u	NOUN
ejpam-4254	56	6	is	be	AUX
ejpam-4254	56	7	the	the	DET
ejpam-4254	56	8	only	only	ADJ
ejpam-4254	56	9	supi	supi	NOUN
ejpam-4254	56	10	.	.	PUNCT
ejpam-4254	57	1	a.	a.	PROPN
ejpam-4254	57	2	iampan	iampan	PROPN
ejpam-4254	57	3	et	et	PROPN
ejpam-4254	57	4	al	al	PROPN
ejpam-4254	57	5	.	.	PUNCT
ejpam-4254	57	6	/	/	SYM
ejpam-4254	57	7	eur	eur	PROPN
ejpam-4254	57	8	.	.	PUNCT
ejpam-4254	58	1	j.	j.	PROPN
ejpam-4254	58	2	pure	pure	PROPN
ejpam-4254	58	3	appl	appl	PROPN
ejpam-4254	58	4	.	.	PROPN
ejpam-4254	58	5	math	math	PROPN
ejpam-4254	58	6	,	,	PUNCT
ejpam-4254	58	7	15	15	NUM
ejpam-4254	58	8	(	(	PUNCT
ejpam-4254	58	9	1	1	NUM
ejpam-4254	58	10	)	)	PUNCT
ejpam-4254	58	11	(	(	PUNCT
ejpam-4254	58	12	2022	2022	NUM
ejpam-4254	58	13	)	)	PUNCT
ejpam-4254	58	14	,	,	PUNCT
ejpam-4254	58	15	169	169	NUM
ejpam-4254	58	16	-	-	SYM
ejpam-4254	58	17	198	198	NUM
ejpam-4254	58	18	172	172	NUM
ejpam-4254	58	19	definition	definition	NOUN
ejpam-4254	58	20	3	3	NUM
ejpam-4254	58	21	.	.	PUNCT
ejpam-4254	59	1	[	[	X
ejpam-4254	59	2	29	29	NUM
ejpam-4254	59	3	]	]	X
ejpam-4254	59	4	a	a	DET
ejpam-4254	59	5	fuzzy	fuzzy	ADJ
ejpam-4254	59	6	set	set	NOUN
ejpam-4254	59	7	(	(	PUNCT
ejpam-4254	59	8	fs	fs	PROPN
ejpam-4254	59	9	)	)	PUNCT
ejpam-4254	59	10	f	f	PROPN
ejpam-4254	59	11	in	in	ADP
ejpam-4254	59	12	a	a	DET
ejpam-4254	59	13	nonempty	nonempty	ADV
ejpam-4254	59	14	set	set	VERB
ejpam-4254	59	15	u	u	NOUN
ejpam-4254	59	16	is	be	AUX
ejpam-4254	59	17	described	describe	VERB
ejpam-4254	59	18	by	by	ADP
ejpam-4254	59	19	its	its	PRON
ejpam-4254	59	20	membership	membership	NOUN
ejpam-4254	59	21	function	function	NOUN
ejpam-4254	59	22	µf	µf	NOUN
ejpam-4254	59	23	.	.	PUNCT
ejpam-4254	60	1	to	to	ADP
ejpam-4254	60	2	every	every	DET
ejpam-4254	60	3	point	point	NOUN
ejpam-4254	60	4	a	a	DET
ejpam-4254	60	5	∈	∈	PROPN
ejpam-4254	60	6	u	u	NOUN
ejpam-4254	60	7	,	,	PUNCT
ejpam-4254	60	8	this	this	DET
ejpam-4254	60	9	function	function	NOUN
ejpam-4254	60	10	associates	associate	VERB
ejpam-4254	60	11	a	a	DET
ejpam-4254	60	12	real	real	ADJ
ejpam-4254	60	13	number	number	NOUN
ejpam-4254	60	14	µf(a	µf(a	NUM
ejpam-4254	60	15	)	)	PUNCT
ejpam-4254	60	16	in	in	ADP
ejpam-4254	60	17	the	the	DET
ejpam-4254	60	18	closed	closed	ADJ
ejpam-4254	60	19	interval	interval	NOUN
ejpam-4254	60	20	[	[	X
ejpam-4254	60	21	0	0	NUM
ejpam-4254	60	22	,	,	PUNCT
ejpam-4254	60	23	1	1	NUM
ejpam-4254	60	24	]	]	PUNCT
ejpam-4254	60	25	.	.	PUNCT
ejpam-4254	61	1	the	the	DET
ejpam-4254	61	2	real	real	ADJ
ejpam-4254	61	3	number	number	NOUN
ejpam-4254	61	4	µf(a	µf(a	PRON
ejpam-4254	61	5	)	)	PUNCT
ejpam-4254	61	6	is	be	AUX
ejpam-4254	61	7	interpreted	interpret	VERB
ejpam-4254	61	8	for	for	ADP
ejpam-4254	61	9	the	the	DET
ejpam-4254	61	10	point	point	NOUN
ejpam-4254	61	11	as	as	ADP
ejpam-4254	61	12	a	a	DET
ejpam-4254	61	13	degree	degree	NOUN
ejpam-4254	61	14	of	of	ADP
ejpam-4254	61	15	membership	membership	NOUN
ejpam-4254	61	16	of	of	ADP
ejpam-4254	61	17	an	an	DET
ejpam-4254	61	18	object	object	NOUN
ejpam-4254	61	19	a	a	DET
ejpam-4254	61	20	∈	∈	NOUN
ejpam-4254	61	21	u	u	NOUN
ejpam-4254	61	22	to	to	ADP
ejpam-4254	61	23	the	the	DET
ejpam-4254	61	24	fs	fs	X
ejpam-4254	61	25	f	f	X
ejpam-4254	61	26	,	,	PUNCT
ejpam-4254	61	27	that	that	ADV
ejpam-4254	61	28	is	is	ADV
ejpam-4254	61	29	,	,	PUNCT
ejpam-4254	61	30	f	f	X
ejpam-4254	61	31	:	:	PUNCT
ejpam-4254	61	32	=	=	SYM
ejpam-4254	61	33	{	{	PUNCT
ejpam-4254	61	34	(	(	PUNCT
ejpam-4254	61	35	a	a	PRON
ejpam-4254	61	36	,	,	PUNCT
ejpam-4254	61	37	µf(a	µf(a	NUM
ejpam-4254	61	38	)	)	PUNCT
ejpam-4254	61	39	)	)	PUNCT
ejpam-4254	62	1	|	|	ADV
ejpam-4254	62	2	a	a	DET
ejpam-4254	62	3	∈	∈	PROPN
ejpam-4254	62	4	u	u	NOUN
ejpam-4254	62	5	}	}	PUNCT
ejpam-4254	62	6	.	.	PUNCT
ejpam-4254	63	1	we	we	PRON
ejpam-4254	63	2	say	say	VERB
ejpam-4254	63	3	that	that	SCONJ
ejpam-4254	63	4	a	a	DET
ejpam-4254	63	5	fs	fs	ADP
ejpam-4254	63	6	f	f	PROPN
ejpam-4254	63	7	in	in	ADP
ejpam-4254	63	8	u	u	NOUN
ejpam-4254	63	9	is	be	AUX
ejpam-4254	63	10	constant	constant	ADJ
ejpam-4254	63	11	fuzzy	fuzzy	ADJ
ejpam-4254	63	12	set	set	NOUN
ejpam-4254	63	13	if	if	SCONJ
ejpam-4254	63	14	its	its	PRON
ejpam-4254	63	15	membership	membership	NOUN
ejpam-4254	63	16	function	function	VERB
ejpam-4254	63	17	µf	µf	NOUN
ejpam-4254	63	18	is	be	AUX
ejpam-4254	63	19	constant	constant	ADJ
ejpam-4254	63	20	.	.	PUNCT
ejpam-4254	64	1	in	in	ADP
ejpam-4254	64	2	2013	2013	NUM
ejpam-4254	64	3	,	,	PUNCT
ejpam-4254	64	4	yager	yager	NOUN
ejpam-4254	65	1	[	[	X
ejpam-4254	65	2	27	27	NUM
ejpam-4254	65	3	]	]	PUNCT
ejpam-4254	65	4	and	and	CCONJ
ejpam-4254	65	5	yager	yager	NOUN
ejpam-4254	65	6	and	and	CCONJ
ejpam-4254	65	7	abbasov	abbasov	NOUN
ejpam-4254	65	8	[	[	X
ejpam-4254	65	9	28	28	NUM
ejpam-4254	65	10	]	]	PUNCT
ejpam-4254	65	11	introduced	introduce	VERB
ejpam-4254	65	12	the	the	DET
ejpam-4254	65	13	concept	concept	NOUN
ejpam-4254	65	14	of	of	ADP
ejpam-4254	65	15	pfss	pfss	NOUN
ejpam-4254	65	16	for	for	ADP
ejpam-4254	65	17	the	the	DET
ejpam-4254	65	18	first	first	ADJ
ejpam-4254	65	19	time	time	NOUN
ejpam-4254	65	20	.	.	PUNCT
ejpam-4254	66	1	definition	definition	NOUN
ejpam-4254	66	2	4	4	NUM
ejpam-4254	66	3	.	.	PUNCT
ejpam-4254	67	1	[	[	X
ejpam-4254	67	2	27	27	NUM
ejpam-4254	67	3	,	,	PUNCT
ejpam-4254	67	4	28	28	NUM
ejpam-4254	67	5	]	]	PUNCT
ejpam-4254	67	6	a	a	DET
ejpam-4254	67	7	pythagorean	pythagorean	PROPN
ejpam-4254	67	8	fuzzy	fuzzy	ADJ
ejpam-4254	67	9	set	set	NOUN
ejpam-4254	67	10	(	(	PUNCT
ejpam-4254	67	11	pfs	pfs	PROPN
ejpam-4254	67	12	)	)	PUNCT
ejpam-4254	67	13	p	p	NOUN
ejpam-4254	67	14	in	in	ADP
ejpam-4254	67	15	a	a	DET
ejpam-4254	67	16	nonempty	nonempty	ADV
ejpam-4254	67	17	set	set	VERB
ejpam-4254	67	18	u	u	NOUN
ejpam-4254	67	19	is	be	AUX
ejpam-4254	67	20	described	describe	VERB
ejpam-4254	67	21	by	by	ADP
ejpam-4254	67	22	their	their	PRON
ejpam-4254	67	23	membership	membership	NOUN
ejpam-4254	67	24	function	function	VERB
ejpam-4254	67	25	µp	µp	NOUN
ejpam-4254	67	26	and	and	CCONJ
ejpam-4254	67	27	non	non	ADJ
ejpam-4254	67	28	-	-	ADJ
ejpam-4254	67	29	membership	membership	ADJ
ejpam-4254	67	30	function	function	NOUN
ejpam-4254	67	31	νp	νp	VERB
ejpam-4254	67	32	.	.	PUNCT
ejpam-4254	67	33	to	to	ADP
ejpam-4254	67	34	every	every	DET
ejpam-4254	67	35	point	point	NOUN
ejpam-4254	67	36	a	a	DET
ejpam-4254	67	37	∈	∈	PROPN
ejpam-4254	67	38	u	u	NOUN
ejpam-4254	67	39	,	,	PUNCT
ejpam-4254	67	40	these	these	DET
ejpam-4254	67	41	functions	function	NOUN
ejpam-4254	67	42	associate	associate	VERB
ejpam-4254	67	43	real	real	ADJ
ejpam-4254	67	44	numbers	number	NOUN
ejpam-4254	67	45	µp(a	µp(a	NUM
ejpam-4254	67	46	)	)	PUNCT
ejpam-4254	67	47	and	and	CCONJ
ejpam-4254	67	48	νp(a	νp(a	NUM
ejpam-4254	67	49	)	)	PUNCT
ejpam-4254	67	50	in	in	ADP
ejpam-4254	67	51	the	the	DET
ejpam-4254	67	52	closed	closed	ADJ
ejpam-4254	67	53	interval	interval	NOUN
ejpam-4254	67	54	[	[	X
ejpam-4254	67	55	0	0	NUM
ejpam-4254	67	56	,	,	PUNCT
ejpam-4254	67	57	1	1	NUM
ejpam-4254	67	58	]	]	PUNCT
ejpam-4254	67	59	,	,	PUNCT
ejpam-4254	67	60	with	with	ADP
ejpam-4254	67	61	the	the	DET
ejpam-4254	67	62	following	follow	VERB
ejpam-4254	67	63	condition	condition	NOUN
ejpam-4254	67	64	:	:	PUNCT
ejpam-4254	67	65	(	(	PUNCT
ejpam-4254	68	1	∀a	∀a	X
ejpam-4254	68	2	∈	∈	NOUN
ejpam-4254	68	3	u)(0	u)(0	NOUN
ejpam-4254	68	4	≤	≤	NOUN
ejpam-4254	68	5	µp(a	µp(a	NUM
ejpam-4254	68	6	)	)	PUNCT
ejpam-4254	68	7	2	2	NUM
ejpam-4254	69	1	+	+	CCONJ
ejpam-4254	69	2	νp(a	νp(a	NUM
ejpam-4254	69	3	)	)	PUNCT
ejpam-4254	69	4	2	2	NUM
ejpam-4254	69	5	≤	≤	NUM
ejpam-4254	69	6	1	1	NUM
ejpam-4254	69	7	)	)	PUNCT
ejpam-4254	69	8	.	.	PUNCT
ejpam-4254	70	1	(	(	PUNCT
ejpam-4254	70	2	1.20	1.20	NUM
ejpam-4254	70	3	)	)	PUNCT
ejpam-4254	70	4	the	the	DET
ejpam-4254	70	5	real	real	ADJ
ejpam-4254	70	6	numbers	number	NOUN
ejpam-4254	70	7	µp(a	µp(a	NUM
ejpam-4254	70	8	)	)	PUNCT
ejpam-4254	70	9	and	and	CCONJ
ejpam-4254	70	10	νp(a	νp(a	NUM
ejpam-4254	70	11	)	)	PUNCT
ejpam-4254	70	12	are	be	AUX
ejpam-4254	70	13	interpreted	interpret	VERB
ejpam-4254	70	14	for	for	ADP
ejpam-4254	70	15	the	the	DET
ejpam-4254	70	16	point	point	NOUN
ejpam-4254	70	17	as	as	ADP
ejpam-4254	70	18	a	a	DET
ejpam-4254	70	19	degree	degree	NOUN
ejpam-4254	70	20	of	of	ADP
ejpam-4254	70	21	membership	membership	NOUN
ejpam-4254	70	22	and	and	CCONJ
ejpam-4254	70	23	non	non	ADJ
ejpam-4254	70	24	-	-	NOUN
ejpam-4254	70	25	membership	membership	NOUN
ejpam-4254	70	26	of	of	ADP
ejpam-4254	70	27	an	an	DET
ejpam-4254	70	28	object	object	NOUN
ejpam-4254	70	29	a	a	DET
ejpam-4254	70	30	∈	∈	PROPN
ejpam-4254	70	31	u	u	NOUN
ejpam-4254	70	32	,	,	PUNCT
ejpam-4254	70	33	respectively	respectively	ADV
ejpam-4254	70	34	,	,	PUNCT
ejpam-4254	70	35	to	to	ADP
ejpam-4254	70	36	the	the	DET
ejpam-4254	70	37	pfs	pfs	PROPN
ejpam-4254	70	38	p	p	X
ejpam-4254	70	39	,	,	PUNCT
ejpam-4254	70	40	that	that	ADV
ejpam-4254	70	41	is	is	ADV
ejpam-4254	70	42	,	,	PUNCT
ejpam-4254	70	43	p	p	X
ejpam-4254	70	44	:	:	PUNCT
ejpam-4254	70	45	=	=	SYM
ejpam-4254	70	46	{	{	PUNCT
ejpam-4254	70	47	(	(	PUNCT
ejpam-4254	70	48	a	a	PRON
ejpam-4254	70	49	,	,	PUNCT
ejpam-4254	70	50	µp(a	µp(a	NUM
ejpam-4254	70	51	)	)	PUNCT
ejpam-4254	70	52	,	,	PUNCT
ejpam-4254	70	53	νp(a	νp(a	NUM
ejpam-4254	70	54	)	)	PUNCT
ejpam-4254	70	55	)	)	PUNCT
ejpam-4254	71	1	|	|	ADV
ejpam-4254	71	2	a	a	DET
ejpam-4254	71	3	∈	∈	PROPN
ejpam-4254	71	4	u	u	NOUN
ejpam-4254	71	5	}	}	PUNCT
ejpam-4254	71	6	.	.	PUNCT
ejpam-4254	72	1	for	for	ADP
ejpam-4254	72	2	the	the	DET
ejpam-4254	72	3	sake	sake	NOUN
ejpam-4254	72	4	of	of	ADP
ejpam-4254	72	5	simplicity	simplicity	NOUN
ejpam-4254	72	6	,	,	PUNCT
ejpam-4254	72	7	a	a	DET
ejpam-4254	72	8	pfs	pfs	PROPN
ejpam-4254	72	9	p	p	NOUN
ejpam-4254	72	10	is	be	AUX
ejpam-4254	72	11	denoted	denote	VERB
ejpam-4254	72	12	by	by	ADP
ejpam-4254	72	13	p	p	PROPN
ejpam-4254	72	14	=	=	SYM
ejpam-4254	72	15	(	(	PUNCT
ejpam-4254	72	16	µp	µp	PROPN
ejpam-4254	72	17	,	,	PUNCT
ejpam-4254	72	18	νp	νp	NOUN
ejpam-4254	72	19	)	)	PUNCT
ejpam-4254	72	20	.	.	PUNCT
ejpam-4254	73	1	we	we	PRON
ejpam-4254	73	2	say	say	VERB
ejpam-4254	73	3	that	that	SCONJ
ejpam-4254	73	4	a	a	DET
ejpam-4254	73	5	pfs	pfs	PROPN
ejpam-4254	73	6	p	p	NOUN
ejpam-4254	73	7	in	in	ADP
ejpam-4254	73	8	u	u	NOUN
ejpam-4254	73	9	is	be	AUX
ejpam-4254	73	10	constant	constant	ADJ
ejpam-4254	73	11	pythagorean	pythagorean	NOUN
ejpam-4254	73	12	fuzzy	fuzzy	NOUN
ejpam-4254	73	13	set	set	VERB
ejpam-4254	73	14	if	if	SCONJ
ejpam-4254	73	15	their	their	PRON
ejpam-4254	73	16	membership	membership	NOUN
ejpam-4254	73	17	function	function	VERB
ejpam-4254	73	18	µp	µp	NOUN
ejpam-4254	73	19	and	and	CCONJ
ejpam-4254	73	20	non	non	ADJ
ejpam-4254	73	21	-	-	ADJ
ejpam-4254	73	22	membership	membership	ADJ
ejpam-4254	73	23	function	function	NOUN
ejpam-4254	73	24	νp	νp	NOUN
ejpam-4254	73	25	are	be	AUX
ejpam-4254	73	26	constant	constant	ADJ
ejpam-4254	73	27	.	.	PUNCT
ejpam-4254	74	1	definition	definition	NOUN
ejpam-4254	74	2	5	5	NUM
ejpam-4254	74	3	.	.	PUNCT
ejpam-4254	75	1	[	[	X
ejpam-4254	75	2	20	20	NUM
ejpam-4254	75	3	,	,	PUNCT
ejpam-4254	75	4	21	21	NUM
ejpam-4254	75	5	]	]	PUNCT
ejpam-4254	75	6	a	a	DET
ejpam-4254	75	7	pfs	pfs	PROPN
ejpam-4254	76	1	p	p	X
ejpam-4254	77	1	=	=	X
ejpam-4254	77	2	(	(	PUNCT
ejpam-4254	77	3	µp	µp	PROPN
ejpam-4254	77	4	,	,	PUNCT
ejpam-4254	77	5	νp	νp	NOUN
ejpam-4254	77	6	)	)	PUNCT
ejpam-4254	77	7	in	in	ADP
ejpam-4254	77	8	u	u	NOUN
ejpam-4254	77	9	is	be	AUX
ejpam-4254	77	10	called	call	VERB
ejpam-4254	77	11	(	(	PUNCT
ejpam-4254	77	12	1	1	NUM
ejpam-4254	77	13	)	)	PUNCT
ejpam-4254	77	14	a	a	DET
ejpam-4254	77	15	pythagorean	pythagorean	PROPN
ejpam-4254	77	16	fuzzy	fuzzy	ADJ
ejpam-4254	77	17	up	up	NOUN
ejpam-4254	77	18	-	-	PUNCT
ejpam-4254	77	19	subalgebra	subalgebra	NOUN
ejpam-4254	77	20	(	(	PUNCT
ejpam-4254	77	21	pfups	pfup	NOUN
ejpam-4254	77	22	)	)	PUNCT
ejpam-4254	77	23	of	of	ADP
ejpam-4254	77	24	u	u	PRON
ejpam-4254	77	25	if	if	SCONJ
ejpam-4254	77	26	it	it	PRON
ejpam-4254	77	27	satisfies	satisfy	VERB
ejpam-4254	77	28	the	the	DET
ejpam-4254	77	29	following	follow	VERB
ejpam-4254	77	30	conditions	condition	NOUN
ejpam-4254	77	31	:	:	PUNCT
ejpam-4254	77	32	(	(	PUNCT
ejpam-4254	77	33	∀a	∀a	X
ejpam-4254	77	34	,	,	PUNCT
ejpam-4254	77	35	b	b	X
ejpam-4254	77	36	∈	∈	PROPN
ejpam-4254	77	37	u)(µp(a	u)(µp(a	NOUN
ejpam-4254	77	38	⋆	⋆	NOUN
ejpam-4254	77	39	b	b	NOUN
ejpam-4254	77	40	)	)	PUNCT
ejpam-4254	77	41	≥	≥	NOUN
ejpam-4254	77	42	min{µp(a	min{µp(a	NOUN
ejpam-4254	77	43	)	)	PUNCT
ejpam-4254	77	44	,	,	PUNCT
ejpam-4254	77	45	µp(b	µp(b	ADJ
ejpam-4254	77	46	)	)	PUNCT
ejpam-4254	77	47	}	}	PUNCT
ejpam-4254	77	48	)	)	PUNCT
ejpam-4254	77	49	,	,	PUNCT
ejpam-4254	77	50	(	(	PUNCT
ejpam-4254	77	51	1.21	1.21	NUM
ejpam-4254	77	52	)	)	PUNCT
ejpam-4254	77	53	(	(	PUNCT
ejpam-4254	77	54	∀a	∀a	X
ejpam-4254	77	55	,	,	PUNCT
ejpam-4254	77	56	b	b	X
ejpam-4254	77	57	∈	∈	PROPN
ejpam-4254	77	58	u)(νp(a	u)(νp(a	NOUN
ejpam-4254	77	59	⋆	⋆	NOUN
ejpam-4254	77	60	b	b	NOUN
ejpam-4254	77	61	)	)	PUNCT
ejpam-4254	77	62	≤	≤	NOUN
ejpam-4254	77	63	max{νp(a	max{νp(a	NOUN
ejpam-4254	77	64	)	)	PUNCT
ejpam-4254	77	65	,	,	PUNCT
ejpam-4254	77	66	νp(b	νp(b	NOUN
ejpam-4254	77	67	)	)	PUNCT
ejpam-4254	77	68	}	}	PUNCT
ejpam-4254	77	69	)	)	PUNCT
ejpam-4254	77	70	,	,	PUNCT
ejpam-4254	77	71	(	(	PUNCT
ejpam-4254	77	72	1.22	1.22	NUM
ejpam-4254	77	73	)	)	PUNCT
ejpam-4254	77	74	(	(	PUNCT
ejpam-4254	77	75	2	2	X
ejpam-4254	77	76	)	)	PUNCT
ejpam-4254	77	77	a	a	DET
ejpam-4254	77	78	pythagorean	pythagorean	PROPN
ejpam-4254	77	79	fuzzy	fuzzy	NOUN
ejpam-4254	77	80	near	near	ADP
ejpam-4254	77	81	up	up	ADP
ejpam-4254	77	82	-	-	PUNCT
ejpam-4254	77	83	filter	filter	NOUN
ejpam-4254	77	84	(	(	PUNCT
ejpam-4254	77	85	pfnupf	pfnupf	NOUN
ejpam-4254	77	86	)	)	PUNCT
ejpam-4254	77	87	of	of	ADP
ejpam-4254	77	88	u	u	PRON
ejpam-4254	77	89	if	if	SCONJ
ejpam-4254	77	90	it	it	PRON
ejpam-4254	77	91	satisfies	satisfy	VERB
ejpam-4254	77	92	the	the	DET
ejpam-4254	77	93	following	follow	VERB
ejpam-4254	77	94	conditions	condition	NOUN
ejpam-4254	77	95	:	:	PUNCT
ejpam-4254	77	96	(	(	PUNCT
ejpam-4254	77	97	∀a	∀a	X
ejpam-4254	77	98	,	,	PUNCT
ejpam-4254	77	99	b	b	X
ejpam-4254	77	100	∈	∈	PROPN
ejpam-4254	77	101	u)(µp(a	u)(µp(a	NOUN
ejpam-4254	77	102	⋆	⋆	NOUN
ejpam-4254	77	103	b	b	NOUN
ejpam-4254	77	104	)	)	PUNCT
ejpam-4254	77	105	≥	≥	NOUN
ejpam-4254	77	106	µp(b	µp(b	NOUN
ejpam-4254	77	107	)	)	PUNCT
ejpam-4254	77	108	)	)	PUNCT
ejpam-4254	77	109	,	,	PUNCT
ejpam-4254	77	110	(	(	PUNCT
ejpam-4254	77	111	1.23	1.23	NUM
ejpam-4254	77	112	)	)	PUNCT
ejpam-4254	77	113	(	(	PUNCT
ejpam-4254	77	114	∀a	∀a	X
ejpam-4254	77	115	,	,	PUNCT
ejpam-4254	77	116	b	b	X
ejpam-4254	77	117	∈	∈	PROPN
ejpam-4254	77	118	u)(νp(a	u)(νp(a	NOUN
ejpam-4254	77	119	⋆	⋆	NOUN
ejpam-4254	77	120	b	b	NOUN
ejpam-4254	77	121	)	)	PUNCT
ejpam-4254	77	122	≤	≤	NOUN
ejpam-4254	77	123	νp(b	νp(b	NOUN
ejpam-4254	77	124	)	)	PUNCT
ejpam-4254	77	125	)	)	PUNCT
ejpam-4254	77	126	,	,	PUNCT
ejpam-4254	77	127	(	(	PUNCT
ejpam-4254	77	128	1.24	1.24	NUM
ejpam-4254	77	129	)	)	PUNCT
ejpam-4254	77	130	(	(	PUNCT
ejpam-4254	77	131	3	3	X
ejpam-4254	77	132	)	)	PUNCT
ejpam-4254	77	133	a	a	DET
ejpam-4254	77	134	pythagorean	pythagorean	PROPN
ejpam-4254	77	135	fuzzy	fuzzy	ADJ
ejpam-4254	77	136	up	up	NOUN
ejpam-4254	77	137	-	-	PUNCT
ejpam-4254	77	138	filter	filter	NOUN
ejpam-4254	77	139	(	(	PUNCT
ejpam-4254	77	140	pfupf	pfupf	NOUN
ejpam-4254	77	141	)	)	PUNCT
ejpam-4254	77	142	of	of	ADP
ejpam-4254	77	143	u	u	PRON
ejpam-4254	77	144	if	if	SCONJ
ejpam-4254	77	145	it	it	PRON
ejpam-4254	77	146	satisfies	satisfy	VERB
ejpam-4254	77	147	the	the	DET
ejpam-4254	77	148	following	follow	VERB
ejpam-4254	77	149	conditions	condition	NOUN
ejpam-4254	77	150	:	:	PUNCT
ejpam-4254	77	151	(	(	PUNCT
ejpam-4254	77	152	∀a	∀a	NOUN
ejpam-4254	77	153	∈	∈	NOUN
ejpam-4254	77	154	u)(µp(0	u)(µp(0	NOUN
ejpam-4254	77	155	)	)	PUNCT
ejpam-4254	77	156	≥	≥	NOUN
ejpam-4254	77	157	µp(a	µp(a	NUM
ejpam-4254	77	158	)	)	PUNCT
ejpam-4254	77	159	)	)	PUNCT
ejpam-4254	77	160	,	,	PUNCT
ejpam-4254	77	161	(	(	PUNCT
ejpam-4254	77	162	1.25	1.25	NUM
ejpam-4254	77	163	)	)	PUNCT
ejpam-4254	77	164	(	(	PUNCT
ejpam-4254	77	165	∀a	∀a	NOUN
ejpam-4254	77	166	∈	∈	NOUN
ejpam-4254	77	167	u)(νp(0	u)(νp(0	NOUN
ejpam-4254	77	168	)	)	PUNCT
ejpam-4254	77	169	≤	≤	NOUN
ejpam-4254	77	170	νp(a	νp(a	NUM
ejpam-4254	77	171	)	)	PUNCT
ejpam-4254	77	172	)	)	PUNCT
ejpam-4254	77	173	,	,	PUNCT
ejpam-4254	77	174	(	(	PUNCT
ejpam-4254	77	175	1.26	1.26	NUM
ejpam-4254	77	176	)	)	PUNCT
ejpam-4254	77	177	(	(	PUNCT
ejpam-4254	77	178	∀a	∀a	X
ejpam-4254	77	179	,	,	PUNCT
ejpam-4254	77	180	b	b	X
ejpam-4254	77	181	∈	∈	PROPN
ejpam-4254	77	182	u)(µp(b	u)(µp(b	PROPN
ejpam-4254	77	183	)	)	PUNCT
ejpam-4254	77	184	≥	≥	NOUN
ejpam-4254	77	185	min{µp(a	min{µp(a	NOUN
ejpam-4254	77	186	⋆	⋆	X
ejpam-4254	77	187	b	b	NOUN
ejpam-4254	77	188	)	)	PUNCT
ejpam-4254	77	189	,	,	PUNCT
ejpam-4254	77	190	µp(a	µp(a	NUM
ejpam-4254	77	191	)	)	PUNCT
ejpam-4254	77	192	}	}	PUNCT
ejpam-4254	77	193	)	)	PUNCT
ejpam-4254	77	194	,	,	PUNCT
ejpam-4254	77	195	(	(	PUNCT
ejpam-4254	77	196	1.27	1.27	NUM
ejpam-4254	77	197	)	)	PUNCT
ejpam-4254	77	198	(	(	PUNCT
ejpam-4254	77	199	∀a	∀a	X
ejpam-4254	77	200	,	,	PUNCT
ejpam-4254	77	201	b	b	PROPN
ejpam-4254	77	202	∈	∈	PROPN
ejpam-4254	77	203	u)(νp(b	u)(νp(b	NOUN
ejpam-4254	77	204	)	)	PUNCT
ejpam-4254	77	205	≤	≤	NOUN
ejpam-4254	77	206	max{νp(a	max{νp(a	NOUN
ejpam-4254	77	207	⋆	⋆	NOUN
ejpam-4254	77	208	b	b	NOUN
ejpam-4254	77	209	)	)	PUNCT
ejpam-4254	77	210	,	,	PUNCT
ejpam-4254	77	211	νp(a	νp(a	NUM
ejpam-4254	77	212	)	)	PUNCT
ejpam-4254	77	213	}	}	PUNCT
ejpam-4254	77	214	)	)	PUNCT
ejpam-4254	77	215	,	,	PUNCT
ejpam-4254	77	216	(	(	PUNCT
ejpam-4254	77	217	1.28	1.28	NUM
ejpam-4254	77	218	)	)	PUNCT
ejpam-4254	77	219	a.	a.	NOUN
ejpam-4254	77	220	iampan	iampan	NOUN
ejpam-4254	77	221	et	et	PROPN
ejpam-4254	77	222	al	al	PROPN
ejpam-4254	77	223	.	.	PUNCT
ejpam-4254	77	224	/	/	SYM
ejpam-4254	77	225	eur	eur	PROPN
ejpam-4254	77	226	.	.	PUNCT
ejpam-4254	78	1	j.	j.	PROPN
ejpam-4254	78	2	pure	pure	PROPN
ejpam-4254	78	3	appl	appl	PROPN
ejpam-4254	78	4	.	.	PROPN
ejpam-4254	78	5	math	math	PROPN
ejpam-4254	78	6	,	,	PUNCT
ejpam-4254	78	7	15	15	NUM
ejpam-4254	78	8	(	(	PUNCT
ejpam-4254	78	9	1	1	NUM
ejpam-4254	78	10	)	)	PUNCT
ejpam-4254	78	11	(	(	PUNCT
ejpam-4254	78	12	2022	2022	NUM
ejpam-4254	78	13	)	)	PUNCT
ejpam-4254	78	14	,	,	PUNCT
ejpam-4254	78	15	169	169	NUM
ejpam-4254	78	16	-	-	SYM
ejpam-4254	78	17	198	198	NUM
ejpam-4254	78	18	173	173	NUM
ejpam-4254	78	19	(	(	PUNCT
ejpam-4254	78	20	4	4	NUM
ejpam-4254	78	21	)	)	PUNCT
ejpam-4254	78	22	a	a	DET
ejpam-4254	78	23	pythagorean	pythagorean	PROPN
ejpam-4254	78	24	fuzzy	fuzzy	ADJ
ejpam-4254	78	25	up	up	NOUN
ejpam-4254	78	26	-	-	PUNCT
ejpam-4254	78	27	ideal	ideal	NOUN
ejpam-4254	78	28	(	(	PUNCT
ejpam-4254	78	29	pfupi	pfupi	NOUN
ejpam-4254	78	30	)	)	PUNCT
ejpam-4254	78	31	of	of	ADP
ejpam-4254	78	32	u	u	PRON
ejpam-4254	78	33	if	if	SCONJ
ejpam-4254	78	34	it	it	PRON
ejpam-4254	78	35	satisfies	satisfy	VERB
ejpam-4254	78	36	the	the	DET
ejpam-4254	78	37	conditions	condition	NOUN
ejpam-4254	78	38	(	(	PUNCT
ejpam-4254	78	39	1.25	1.25	NUM
ejpam-4254	78	40	)	)	PUNCT
ejpam-4254	78	41	and	and	CCONJ
ejpam-4254	78	42	(	(	PUNCT
ejpam-4254	78	43	1.26	1.26	NUM
ejpam-4254	78	44	)	)	PUNCT
ejpam-4254	78	45	and	and	CCONJ
ejpam-4254	78	46	the	the	DET
ejpam-4254	78	47	following	follow	VERB
ejpam-4254	78	48	conditions	condition	NOUN
ejpam-4254	78	49	:	:	PUNCT
ejpam-4254	78	50	(	(	PUNCT
ejpam-4254	78	51	∀a	∀a	X
ejpam-4254	78	52	,	,	PUNCT
ejpam-4254	78	53	b	b	NOUN
ejpam-4254	78	54	,	,	PUNCT
ejpam-4254	78	55	c	c	PROPN
ejpam-4254	78	56	∈	∈	PROPN
ejpam-4254	78	57	u)(µp(a	u)(µp(a	NOUN
ejpam-4254	78	58	⋆	⋆	PUNCT
ejpam-4254	78	59	c	c	NOUN
ejpam-4254	78	60	)	)	PUNCT
ejpam-4254	78	61	≥	≥	NOUN
ejpam-4254	78	62	min{µp(a	min{µp(a	NOUN
ejpam-4254	78	63	⋆	⋆	X
ejpam-4254	78	64	(	(	PUNCT
ejpam-4254	78	65	b	b	X
ejpam-4254	78	66	⋆	⋆	ADJ
ejpam-4254	78	67	c	c	NOUN
ejpam-4254	78	68	)	)	PUNCT
ejpam-4254	78	69	)	)	PUNCT
ejpam-4254	78	70	,	,	PUNCT
ejpam-4254	78	71	µp(b	µp(b	NOUN
ejpam-4254	78	72	)	)	PUNCT
ejpam-4254	78	73	}	}	PUNCT
ejpam-4254	78	74	)	)	PUNCT
ejpam-4254	78	75	,	,	PUNCT
ejpam-4254	78	76	(	(	PUNCT
ejpam-4254	78	77	1.29	1.29	NUM
ejpam-4254	78	78	)	)	PUNCT
ejpam-4254	78	79	(	(	PUNCT
ejpam-4254	78	80	∀a	∀a	X
ejpam-4254	78	81	,	,	PUNCT
ejpam-4254	78	82	b	b	NOUN
ejpam-4254	78	83	,	,	PUNCT
ejpam-4254	78	84	c	c	PROPN
ejpam-4254	78	85	∈	∈	PROPN
ejpam-4254	79	1	u)(νp(a	u)(νp(a	NOUN
ejpam-4254	79	2	⋆	⋆	PUNCT
ejpam-4254	79	3	c	c	NOUN
ejpam-4254	79	4	)	)	PUNCT
ejpam-4254	79	5	≤	≤	NOUN
ejpam-4254	79	6	max{νp(a	max{νp(a	NOUN
ejpam-4254	79	7	⋆	⋆	X
ejpam-4254	79	8	(	(	PUNCT
ejpam-4254	79	9	b	b	NOUN
ejpam-4254	79	10	⋆	⋆	ADJ
ejpam-4254	79	11	c	c	NOUN
ejpam-4254	79	12	)	)	PUNCT
ejpam-4254	79	13	)	)	PUNCT
ejpam-4254	79	14	,	,	PUNCT
ejpam-4254	79	15	νp(b	νp(b	NOUN
ejpam-4254	79	16	)	)	PUNCT
ejpam-4254	79	17	}	}	PUNCT
ejpam-4254	79	18	)	)	PUNCT
ejpam-4254	79	19	,	,	PUNCT
ejpam-4254	79	20	(	(	PUNCT
ejpam-4254	79	21	1.30	1.30	NUM
ejpam-4254	79	22	)	)	PUNCT
ejpam-4254	79	23	(	(	PUNCT
ejpam-4254	79	24	5	5	X
ejpam-4254	79	25	)	)	PUNCT
ejpam-4254	79	26	a	a	DET
ejpam-4254	79	27	pythagorean	pythagorean	ADJ
ejpam-4254	79	28	fuzzy	fuzzy	NOUN
ejpam-4254	79	29	strong	strong	ADJ
ejpam-4254	79	30	up	up	ADP
ejpam-4254	79	31	-	-	PUNCT
ejpam-4254	79	32	ideal	ideal	NOUN
ejpam-4254	79	33	(	(	PUNCT
ejpam-4254	79	34	pfsupi	pfsupi	NOUN
ejpam-4254	79	35	)	)	PUNCT
ejpam-4254	79	36	of	of	ADP
ejpam-4254	79	37	u	u	PRON
ejpam-4254	79	38	if	if	SCONJ
ejpam-4254	79	39	it	it	PRON
ejpam-4254	79	40	satisfies	satisfy	VERB
ejpam-4254	79	41	the	the	DET
ejpam-4254	79	42	conditions	condition	NOUN
ejpam-4254	79	43	(	(	PUNCT
ejpam-4254	79	44	1.25	1.25	NUM
ejpam-4254	79	45	)	)	PUNCT
ejpam-4254	79	46	and	and	CCONJ
ejpam-4254	79	47	(	(	PUNCT
ejpam-4254	79	48	1.26	1.26	NUM
ejpam-4254	79	49	)	)	PUNCT
ejpam-4254	79	50	and	and	CCONJ
ejpam-4254	79	51	the	the	DET
ejpam-4254	79	52	following	follow	VERB
ejpam-4254	79	53	conditions	condition	NOUN
ejpam-4254	79	54	:	:	PUNCT
ejpam-4254	79	55	(	(	PUNCT
ejpam-4254	79	56	∀a	∀a	X
ejpam-4254	79	57	,	,	PUNCT
ejpam-4254	79	58	b	b	NOUN
ejpam-4254	79	59	,	,	PUNCT
ejpam-4254	79	60	c	c	PROPN
ejpam-4254	79	61	∈	∈	PROPN
ejpam-4254	79	62	u)(µp(a	u)(µp(a	NOUN
ejpam-4254	79	63	)	)	PUNCT
ejpam-4254	79	64	≥	≥	NOUN
ejpam-4254	79	65	min{µp((c	min{µp((c	INTJ
ejpam-4254	79	66	⋆	⋆	NOUN
ejpam-4254	79	67	b	b	NOUN
ejpam-4254	79	68	)	)	PUNCT
ejpam-4254	80	1	⋆	⋆	NOUN
ejpam-4254	80	2	(	(	PUNCT
ejpam-4254	80	3	c	c	NOUN
ejpam-4254	80	4	⋆	⋆	VERB
ejpam-4254	80	5	a	a	NOUN
ejpam-4254	80	6	)	)	PUNCT
ejpam-4254	80	7	)	)	PUNCT
ejpam-4254	80	8	,	,	PUNCT
ejpam-4254	80	9	µp(b	µp(b	NOUN
ejpam-4254	80	10	)	)	PUNCT
ejpam-4254	80	11	}	}	PUNCT
ejpam-4254	80	12	)	)	PUNCT
ejpam-4254	80	13	,	,	PUNCT
ejpam-4254	80	14	(	(	PUNCT
ejpam-4254	80	15	1.31	1.31	NUM
ejpam-4254	80	16	)	)	PUNCT
ejpam-4254	80	17	(	(	PUNCT
ejpam-4254	80	18	∀a	∀a	X
ejpam-4254	80	19	,	,	PUNCT
ejpam-4254	80	20	b	b	NOUN
ejpam-4254	80	21	,	,	PUNCT
ejpam-4254	80	22	c	c	PROPN
ejpam-4254	80	23	∈	∈	PROPN
ejpam-4254	80	24	u)(νp(a	u)(νp(a	NOUN
ejpam-4254	80	25	)	)	PUNCT
ejpam-4254	80	26	≤	≤	NOUN
ejpam-4254	80	27	max{νp((c	max{νp((c	PROPN
ejpam-4254	80	28	⋆	⋆	PUNCT
ejpam-4254	80	29	b	b	NOUN
ejpam-4254	80	30	)	)	PUNCT
ejpam-4254	80	31	⋆	⋆	X
ejpam-4254	80	32	(	(	PUNCT
ejpam-4254	80	33	c	c	NOUN
ejpam-4254	80	34	⋆	⋆	VERB
ejpam-4254	80	35	a	a	NOUN
ejpam-4254	80	36	)	)	PUNCT
ejpam-4254	80	37	)	)	PUNCT
ejpam-4254	80	38	,	,	PUNCT
ejpam-4254	80	39	νp(b	νp(b	NOUN
ejpam-4254	80	40	)	)	PUNCT
ejpam-4254	80	41	}	}	PUNCT
ejpam-4254	80	42	)	)	PUNCT
ejpam-4254	80	43	.	.	PUNCT
ejpam-4254	81	1	(	(	PUNCT
ejpam-4254	81	2	1.32	1.32	NUM
ejpam-4254	81	3	)	)	PUNCT
ejpam-4254	81	4	satirad	satirad	PROPN
ejpam-4254	81	5	et	et	PROPN
ejpam-4254	81	6	al	al	PROPN
ejpam-4254	81	7	.	.	PUNCT
ejpam-4254	82	1	[	[	X
ejpam-4254	82	2	20	20	NUM
ejpam-4254	82	3	]	]	PUNCT
ejpam-4254	82	4	proved	prove	VERB
ejpam-4254	82	5	that	that	SCONJ
ejpam-4254	82	6	the	the	DET
ejpam-4254	82	7	concept	concept	NOUN
ejpam-4254	82	8	of	of	ADP
ejpam-4254	82	9	pfupss	pfupss	PROPN
ejpam-4254	82	10	is	be	AUX
ejpam-4254	82	11	a	a	DET
ejpam-4254	82	12	generalization	generalization	NOUN
ejpam-4254	82	13	of	of	ADP
ejpam-4254	82	14	pfnupfs	pfnupfs	PROPN
ejpam-4254	82	15	,	,	PUNCT
ejpam-4254	82	16	pfnupfs	pfnupfs	PROPN
ejpam-4254	82	17	is	be	AUX
ejpam-4254	82	18	a	a	DET
ejpam-4254	82	19	generalization	generalization	NOUN
ejpam-4254	82	20	of	of	ADP
ejpam-4254	82	21	pfupfs	pfupfs	PROPN
ejpam-4254	82	22	,	,	PUNCT
ejpam-4254	82	23	pfupfs	pfupfs	PROPN
ejpam-4254	82	24	is	be	AUX
ejpam-4254	82	25	a	a	DET
ejpam-4254	82	26	generalization	generalization	NOUN
ejpam-4254	82	27	of	of	ADP
ejpam-4254	82	28	pfupis	pfupis	NOUN
ejpam-4254	82	29	,	,	PUNCT
ejpam-4254	82	30	and	and	CCONJ
ejpam-4254	82	31	pfupis	pfupis	NOUN
ejpam-4254	82	32	is	be	AUX
ejpam-4254	82	33	a	a	DET
ejpam-4254	82	34	generalization	generalization	NOUN
ejpam-4254	82	35	of	of	ADP
ejpam-4254	82	36	pfsupis	pfsupis	NOUN
ejpam-4254	82	37	.	.	PUNCT
ejpam-4254	83	1	furthermore	furthermore	ADV
ejpam-4254	83	2	,	,	PUNCT
ejpam-4254	83	3	they	they	PRON
ejpam-4254	83	4	proved	prove	VERB
ejpam-4254	83	5	that	that	SCONJ
ejpam-4254	83	6	pfsupis	pfsupis	ADJ
ejpam-4254	83	7	and	and	CCONJ
ejpam-4254	83	8	constant	constant	ADJ
ejpam-4254	83	9	pfss	pfss	ADJ
ejpam-4254	83	10	coincide	coincide	NOUN
ejpam-4254	83	11	in	in	ADP
ejpam-4254	83	12	u	u	PROPN
ejpam-4254	83	13	.	.	PUNCT
ejpam-4254	84	1	let	let	VERB
ejpam-4254	84	2	ρ	ρ	NOUN
ejpam-4254	84	3	be	be	AUX
ejpam-4254	84	4	an	an	DET
ejpam-4254	84	5	equivalence	equivalence	NOUN
ejpam-4254	84	6	relation	relation	NOUN
ejpam-4254	84	7	(	(	PUNCT
ejpam-4254	84	8	er	er	INTJ
ejpam-4254	84	9	)	)	PUNCT
ejpam-4254	84	10	on	on	ADP
ejpam-4254	84	11	a	a	DET
ejpam-4254	84	12	set	set	NOUN
ejpam-4254	84	13	u	u	NOUN
ejpam-4254	84	14	.	.	PUNCT
ejpam-4254	85	1	if	if	SCONJ
ejpam-4254	85	2	a	a	DET
ejpam-4254	85	3	∈	∈	PROPN
ejpam-4254	85	4	u	u	NOUN
ejpam-4254	85	5	,	,	PUNCT
ejpam-4254	85	6	then	then	ADV
ejpam-4254	85	7	the	the	DET
ejpam-4254	85	8	ρ	ρ	NOUN
ejpam-4254	85	9	-	-	PUNCT
ejpam-4254	85	10	class	class	NOUN
ejpam-4254	85	11	of	of	ADP
ejpam-4254	85	12	a	a	PRON
ejpam-4254	85	13	is	be	AUX
ejpam-4254	85	14	the	the	DET
ejpam-4254	85	15	set	set	NOUN
ejpam-4254	85	16	(	(	PUNCT
ejpam-4254	85	17	a)ρ	a)ρ	NOUN
ejpam-4254	85	18	defined	define	VERB
ejpam-4254	85	19	as	as	SCONJ
ejpam-4254	85	20	follows	follow	VERB
ejpam-4254	85	21	:	:	PUNCT
ejpam-4254	85	22	(	(	PUNCT
ejpam-4254	85	23	a)ρ	a)ρ	NOUN
ejpam-4254	85	24	=	=	SYM
ejpam-4254	85	25	{	{	PUNCT
ejpam-4254	85	26	b	b	X
ejpam-4254	85	27	∈	∈	PROPN
ejpam-4254	85	28	u	u	NOUN
ejpam-4254	85	29	|	|	NOUN
ejpam-4254	85	30	(	(	PUNCT
ejpam-4254	85	31	a	a	PRON
ejpam-4254	85	32	,	,	PUNCT
ejpam-4254	85	33	b	b	NOUN
ejpam-4254	85	34	)	)	PUNCT
ejpam-4254	85	35	∈	∈	PROPN
ejpam-4254	85	36	ρ	ρ	PROPN
ejpam-4254	85	37	}	}	PUNCT
ejpam-4254	85	38	.	.	PUNCT
ejpam-4254	86	1	an	an	DET
ejpam-4254	86	2	er	er	INTJ
ejpam-4254	86	3	ρ	ρ	NOUN
ejpam-4254	86	4	on	on	ADP
ejpam-4254	86	5	u	u	NOUN
ejpam-4254	86	6	is	be	AUX
ejpam-4254	86	7	called	call	VERB
ejpam-4254	86	8	a	a	DET
ejpam-4254	86	9	congruence	congruence	NOUN
ejpam-4254	86	10	relation	relation	NOUN
ejpam-4254	86	11	(	(	PUNCT
ejpam-4254	86	12	cr	cr	NOUN
ejpam-4254	86	13	)	)	PUNCT
ejpam-4254	86	14	if	if	SCONJ
ejpam-4254	86	15	(	(	PUNCT
ejpam-4254	86	16	∀a	∀a	X
ejpam-4254	86	17	,	,	PUNCT
ejpam-4254	86	18	b	b	NOUN
ejpam-4254	86	19	,	,	PUNCT
ejpam-4254	86	20	c	c	PROPN
ejpam-4254	86	21	∈	∈	PROPN
ejpam-4254	86	22	u)((a	u)((a	PROPN
ejpam-4254	86	23	,	,	PUNCT
ejpam-4254	86	24	b	b	NOUN
ejpam-4254	86	25	)	)	PUNCT
ejpam-4254	86	26	∈	∈	PROPN
ejpam-4254	86	27	ρ	ρ	PROPN
ejpam-4254	86	28	⇒	⇒	PROPN
ejpam-4254	86	29	(	(	PUNCT
ejpam-4254	86	30	a	a	DET
ejpam-4254	86	31	⋆	⋆	INTJ
ejpam-4254	86	32	c	c	NOUN
ejpam-4254	86	33	,	,	PUNCT
ejpam-4254	86	34	b	b	PROPN
ejpam-4254	86	35	⋆	⋆	NOUN
ejpam-4254	86	36	c	c	NOUN
ejpam-4254	86	37	)	)	PUNCT
ejpam-4254	86	38	∈	∈	PROPN
ejpam-4254	86	39	ρ	ρ	PROPN
ejpam-4254	86	40	,	,	PUNCT
ejpam-4254	86	41	(	(	PUNCT
ejpam-4254	86	42	c	c	NOUN
ejpam-4254	86	43	⋆	⋆	NOUN
ejpam-4254	86	44	a	a	NOUN
ejpam-4254	86	45	,	,	PUNCT
ejpam-4254	86	46	c	c	PROPN
ejpam-4254	86	47	⋆	⋆	NOUN
ejpam-4254	86	48	b	b	X
ejpam-4254	86	49	)	)	PUNCT
ejpam-4254	86	50	∈	∈	PROPN
ejpam-4254	86	51	ρ	ρ	PROPN
ejpam-4254	86	52	)	)	PUNCT
ejpam-4254	86	53	.	.	PUNCT
ejpam-4254	87	1	definition	definition	NOUN
ejpam-4254	87	2	6	6	NUM
ejpam-4254	87	3	.	.	PUNCT
ejpam-4254	88	1	for	for	ADP
ejpam-4254	88	2	nonempty	nonempty	ADJ
ejpam-4254	88	3	subsets	subset	NOUN
ejpam-4254	88	4	a	a	PRON
ejpam-4254	88	5	and	and	CCONJ
ejpam-4254	88	6	b	b	NOUN
ejpam-4254	88	7	of	of	ADP
ejpam-4254	88	8	u	u	PROPN
ejpam-4254	88	9	,	,	PUNCT
ejpam-4254	88	10	we	we	PRON
ejpam-4254	88	11	denote	denote	VERB
ejpam-4254	88	12	ab	ab	PROPN
ejpam-4254	88	13	=	=	PUNCT
ejpam-4254	88	14	a	a	DET
ejpam-4254	88	15	⋆	⋆	X
ejpam-4254	88	16	b	b	NOUN
ejpam-4254	88	17	=	=	PRON
ejpam-4254	88	18	{	{	PUNCT
ejpam-4254	88	19	u	u	NOUN
ejpam-4254	88	20	⋆	⋆	NOUN
ejpam-4254	88	21	v	v	ADP
ejpam-4254	88	22	|	|	ADV
ejpam-4254	88	23	u	u	NOUN
ejpam-4254	88	24	∈	∈	PROPN
ejpam-4254	88	25	a	a	PRON
ejpam-4254	88	26	and	and	CCONJ
ejpam-4254	88	27	v	v	ADP
ejpam-4254	88	28	∈	∈	PROPN
ejpam-4254	88	29	b	b	NOUN
ejpam-4254	88	30	}	}	PUNCT
ejpam-4254	88	31	.	.	PUNCT
ejpam-4254	89	1	if	if	SCONJ
ejpam-4254	89	2	ρ	ρ	PROPN
ejpam-4254	89	3	is	be	AUX
ejpam-4254	89	4	a	a	DET
ejpam-4254	89	5	cr	cr	NOUN
ejpam-4254	89	6	on	on	ADP
ejpam-4254	89	7	u	u	PROPN
ejpam-4254	89	8	,	,	PUNCT
ejpam-4254	89	9	then	then	ADV
ejpam-4254	89	10	(	(	PUNCT
ejpam-4254	89	11	∀a	∀a	NOUN
ejpam-4254	89	12	,	,	PUNCT
ejpam-4254	89	13	b	b	PROPN
ejpam-4254	89	14	∈	∈	PROPN
ejpam-4254	89	15	u)((a)ρ(b)ρ	u)((a)ρ(b)ρ	CCONJ
ejpam-4254	89	16	⊆	⊆	NUM
ejpam-4254	89	17	(	(	PUNCT
ejpam-4254	89	18	a	a	DET
ejpam-4254	89	19	⋆	⋆	NOUN
ejpam-4254	89	20	b)ρ	b)ρ	NOUN
ejpam-4254	89	21	)	)	PUNCT
ejpam-4254	89	22	.	.	PUNCT
ejpam-4254	90	1	(	(	PUNCT
ejpam-4254	90	2	see	see	VERB
ejpam-4254	90	3	[	[	X
ejpam-4254	90	4	16	16	NUM
ejpam-4254	90	5	]	]	SYM
ejpam-4254	90	6	)	)	PUNCT
ejpam-4254	90	7	definition	definition	NOUN
ejpam-4254	90	8	7	7	NUM
ejpam-4254	90	9	.	.	PUNCT
ejpam-4254	91	1	let	let	VERB
ejpam-4254	91	2	ρ	ρ	NOUN
ejpam-4254	91	3	be	be	AUX
ejpam-4254	91	4	an	an	DET
ejpam-4254	91	5	er	er	INTJ
ejpam-4254	91	6	on	on	ADP
ejpam-4254	91	7	a	a	DET
ejpam-4254	91	8	nonempty	nonempty	ADV
ejpam-4254	91	9	set	set	VERB
ejpam-4254	91	10	u	u	NOUN
ejpam-4254	91	11	and	and	CCONJ
ejpam-4254	91	12	s	s	NOUN
ejpam-4254	91	13	∈	∈	NOUN
ejpam-4254	91	14	p(u	p(u	NOUN
ejpam-4254	91	15	)	)	PUNCT
ejpam-4254	91	16	.	.	PUNCT
ejpam-4254	92	1	the	the	DET
ejpam-4254	92	2	upper	upper	ADJ
ejpam-4254	92	3	approximation	approximation	NOUN
ejpam-4254	92	4	of	of	ADP
ejpam-4254	92	5	s	s	PRON
ejpam-4254	92	6	is	be	AUX
ejpam-4254	92	7	defined	define	VERB
ejpam-4254	92	8	by	by	ADP
ejpam-4254	92	9	ρ+(s	ρ+(s	PRON
ejpam-4254	92	10	)	)	PUNCT
ejpam-4254	93	1	=	=	PRON
ejpam-4254	93	2	{	{	PUNCT
ejpam-4254	93	3	a	a	DET
ejpam-4254	93	4	∈	∈	PROPN
ejpam-4254	93	5	u	u	NOUN
ejpam-4254	93	6	|	|	NOUN
ejpam-4254	93	7	(	(	PUNCT
ejpam-4254	93	8	a)ρ	a)ρ	NOUN
ejpam-4254	93	9	⊆	⊆	NUM
ejpam-4254	93	10	s	s	NOUN
ejpam-4254	93	11	}	}	PUNCT
ejpam-4254	93	12	,	,	PUNCT
ejpam-4254	93	13	the	the	DET
ejpam-4254	93	14	lower	low	ADJ
ejpam-4254	93	15	approximation	approximation	NOUN
ejpam-4254	93	16	of	of	ADP
ejpam-4254	93	17	s	s	PRON
ejpam-4254	93	18	is	be	AUX
ejpam-4254	93	19	defined	define	VERB
ejpam-4254	93	20	by	by	ADP
ejpam-4254	93	21	ρ−(s	ρ−(s	PROPN
ejpam-4254	93	22	)	)	PUNCT
ejpam-4254	93	23	=	=	PRON
ejpam-4254	93	24	{	{	PUNCT
ejpam-4254	93	25	a	a	DET
ejpam-4254	93	26	∈	∈	PROPN
ejpam-4254	93	27	u	u	NOUN
ejpam-4254	93	28	|	|	NOUN
ejpam-4254	93	29	(	(	PUNCT
ejpam-4254	93	30	a)ρ	a)ρ	NOUN
ejpam-4254	93	31	∩	∩	NOUN
ejpam-4254	93	32	s	s	PART
ejpam-4254	93	33	̸=	̸=	PROPN
ejpam-4254	93	34	∅	∅	NOUN
ejpam-4254	93	35	}	}	PUNCT
ejpam-4254	93	36	.	.	PUNCT
ejpam-4254	94	1	we	we	PRON
ejpam-4254	94	2	know	know	VERB
ejpam-4254	94	3	that	that	SCONJ
ejpam-4254	94	4	ρ+(s	ρ+(s	NUM
ejpam-4254	94	5	)	)	PUNCT
ejpam-4254	94	6	and	and	CCONJ
ejpam-4254	94	7	ρ−(s	ρ−(	VERB
ejpam-4254	94	8	)	)	PUNCT
ejpam-4254	94	9	are	be	AUX
ejpam-4254	94	10	subset	subset	VERB
ejpam-4254	94	11	of	of	ADP
ejpam-4254	94	12	u	u	PROPN
ejpam-4254	94	13	.	.	PUNCT
ejpam-4254	95	1	then	then	ADV
ejpam-4254	95	2	we	we	PRON
ejpam-4254	95	3	call	call	VERB
ejpam-4254	95	4	s	s	PRON
ejpam-4254	95	5	that	that	SCONJ
ejpam-4254	95	6	a	a	DET
ejpam-4254	95	7	rough	rough	ADJ
ejpam-4254	95	8	set	set	NOUN
ejpam-4254	95	9	(	(	PUNCT
ejpam-4254	95	10	rs	rs	NOUN
ejpam-4254	95	11	)	)	PUNCT
ejpam-4254	95	12	of	of	ADP
ejpam-4254	95	13	u	u	PROPN
ejpam-4254	95	14	.	.	PUNCT
ejpam-4254	96	1	definition	definition	NOUN
ejpam-4254	96	2	8	8	NUM
ejpam-4254	96	3	.	.	PUNCT
ejpam-4254	97	1	[	[	X
ejpam-4254	97	2	16	16	NUM
ejpam-4254	97	3	]	]	PUNCT
ejpam-4254	97	4	let	let	VERB
ejpam-4254	97	5	ρ	ρ	NOUN
ejpam-4254	97	6	be	be	AUX
ejpam-4254	97	7	an	an	DET
ejpam-4254	97	8	er	er	INTJ
ejpam-4254	97	9	on	on	ADP
ejpam-4254	97	10	u	u	PROPN
ejpam-4254	97	11	.	.	PUNCT
ejpam-4254	98	1	then	then	ADV
ejpam-4254	98	2	a	a	DET
ejpam-4254	98	3	nonempty	nonempty	NOUN
ejpam-4254	98	4	subset	subset	VERB
ejpam-4254	98	5	s	s	NOUN
ejpam-4254	98	6	of	of	ADP
ejpam-4254	98	7	u	u	NOUN
ejpam-4254	98	8	is	be	AUX
ejpam-4254	98	9	called	call	VERB
ejpam-4254	98	10	(	(	PUNCT
ejpam-4254	98	11	1	1	NUM
ejpam-4254	98	12	)	)	PUNCT
ejpam-4254	98	13	an	an	DET
ejpam-4254	98	14	upper	upper	ADJ
ejpam-4254	98	15	rough	rough	ADJ
ejpam-4254	98	16	up	up	ADJ
ejpam-4254	98	17	-	-	PUNCT
ejpam-4254	98	18	subalgebra	subalgebra	NOUN
ejpam-4254	98	19	(	(	PUNCT
ejpam-4254	98	20	uprups	uprup	NOUN
ejpam-4254	98	21	)	)	PUNCT
ejpam-4254	98	22	of	of	ADP
ejpam-4254	98	23	u	u	PRON
ejpam-4254	98	24	if	if	SCONJ
ejpam-4254	98	25	ρ+(s	ρ+(s	PRON
ejpam-4254	98	26	)	)	PUNCT
ejpam-4254	98	27	is	be	AUX
ejpam-4254	98	28	a	a	DET
ejpam-4254	98	29	ups	up	NOUN
ejpam-4254	98	30	of	of	ADP
ejpam-4254	98	31	u	u	NOUN
ejpam-4254	98	32	,	,	PUNCT
ejpam-4254	98	33	a.	a.	NOUN
ejpam-4254	98	34	iampan	iampan	NOUN
ejpam-4254	98	35	et	et	PROPN
ejpam-4254	98	36	al	al	PROPN
ejpam-4254	98	37	.	.	PUNCT
ejpam-4254	98	38	/	/	SYM
ejpam-4254	98	39	eur	eur	PROPN
ejpam-4254	98	40	.	.	PUNCT
ejpam-4254	99	1	j.	j.	PROPN
ejpam-4254	99	2	pure	pure	PROPN
ejpam-4254	99	3	appl	appl	PROPN
ejpam-4254	99	4	.	.	PROPN
ejpam-4254	99	5	math	math	PROPN
ejpam-4254	99	6	,	,	PUNCT
ejpam-4254	99	7	15	15	NUM
ejpam-4254	99	8	(	(	PUNCT
ejpam-4254	99	9	1	1	NUM
ejpam-4254	99	10	)	)	PUNCT
ejpam-4254	99	11	(	(	PUNCT
ejpam-4254	99	12	2022	2022	NUM
ejpam-4254	99	13	)	)	PUNCT
ejpam-4254	99	14	,	,	PUNCT
ejpam-4254	99	15	169	169	NUM
ejpam-4254	99	16	-	-	SYM
ejpam-4254	99	17	198	198	NUM
ejpam-4254	99	18	174	174	NUM
ejpam-4254	99	19	(	(	PUNCT
ejpam-4254	99	20	2	2	NUM
ejpam-4254	99	21	)	)	PUNCT
ejpam-4254	99	22	an	an	DET
ejpam-4254	99	23	upper	upper	ADJ
ejpam-4254	99	24	rough	rough	NOUN
ejpam-4254	99	25	near	near	ADP
ejpam-4254	99	26	up	up	ADJ
ejpam-4254	99	27	-	-	PUNCT
ejpam-4254	99	28	filter	filter	NOUN
ejpam-4254	99	29	(	(	PUNCT
ejpam-4254	99	30	uprnupf	uprnupf	NOUN
ejpam-4254	99	31	)	)	PUNCT
ejpam-4254	99	32	of	of	ADP
ejpam-4254	99	33	u	u	PRON
ejpam-4254	99	34	if	if	SCONJ
ejpam-4254	99	35	ρ+(s	ρ+(s	PRON
ejpam-4254	99	36	)	)	PUNCT
ejpam-4254	99	37	is	be	AUX
ejpam-4254	99	38	a	a	DET
ejpam-4254	99	39	nupf	nupf	NOUN
ejpam-4254	99	40	of	of	ADP
ejpam-4254	99	41	u	u	NOUN
ejpam-4254	99	42	,	,	PUNCT
ejpam-4254	99	43	(	(	PUNCT
ejpam-4254	99	44	3	3	X
ejpam-4254	99	45	)	)	PUNCT
ejpam-4254	99	46	an	an	DET
ejpam-4254	99	47	upper	upper	ADJ
ejpam-4254	99	48	rough	rough	ADJ
ejpam-4254	99	49	up	up	ADJ
ejpam-4254	99	50	-	-	PUNCT
ejpam-4254	99	51	filter	filter	NOUN
ejpam-4254	99	52	(	(	PUNCT
ejpam-4254	99	53	uprupf	uprupf	NOUN
ejpam-4254	99	54	)	)	PUNCT
ejpam-4254	99	55	of	of	ADP
ejpam-4254	99	56	u	u	PRON
ejpam-4254	99	57	if	if	SCONJ
ejpam-4254	99	58	ρ+(p	ρ+(p	NOUN
ejpam-4254	99	59	)	)	PUNCT
ejpam-4254	99	60	is	be	AUX
ejpam-4254	99	61	a	a	DET
ejpam-4254	99	62	upf	upf	NOUN
ejpam-4254	99	63	of	of	ADP
ejpam-4254	99	64	u	u	PROPN
ejpam-4254	99	65	,	,	PUNCT
ejpam-4254	99	66	(	(	PUNCT
ejpam-4254	99	67	4	4	X
ejpam-4254	99	68	)	)	PUNCT
ejpam-4254	99	69	an	an	DET
ejpam-4254	99	70	upper	upper	ADJ
ejpam-4254	99	71	rough	rough	ADJ
ejpam-4254	99	72	up	up	ADJ
ejpam-4254	99	73	-	-	PUNCT
ejpam-4254	99	74	ideal	ideal	NOUN
ejpam-4254	99	75	(	(	PUNCT
ejpam-4254	99	76	uprupi	uprupi	PROPN
ejpam-4254	99	77	)	)	PUNCT
ejpam-4254	99	78	of	of	ADP
ejpam-4254	99	79	u	u	PRON
ejpam-4254	99	80	if	if	SCONJ
ejpam-4254	99	81	ρ+(s	ρ+(s	PRON
ejpam-4254	99	82	)	)	PUNCT
ejpam-4254	99	83	is	be	AUX
ejpam-4254	99	84	a	a	DET
ejpam-4254	99	85	upi	upi	NOUN
ejpam-4254	99	86	of	of	ADP
ejpam-4254	99	87	u	u	PROPN
ejpam-4254	99	88	,	,	PUNCT
ejpam-4254	99	89	(	(	PUNCT
ejpam-4254	99	90	5	5	X
ejpam-4254	99	91	)	)	PUNCT
ejpam-4254	99	92	an	an	DET
ejpam-4254	99	93	upper	upper	ADJ
ejpam-4254	99	94	rough	rough	NOUN
ejpam-4254	99	95	strong	strong	ADJ
ejpam-4254	99	96	up	up	ADJ
ejpam-4254	99	97	-	-	PUNCT
ejpam-4254	99	98	ideal	ideal	NOUN
ejpam-4254	99	99	(	(	PUNCT
ejpam-4254	99	100	uprsupi	uprsupi	PROPN
ejpam-4254	99	101	)	)	PUNCT
ejpam-4254	99	102	of	of	ADP
ejpam-4254	99	103	u	u	PRON
ejpam-4254	99	104	if	if	SCONJ
ejpam-4254	99	105	ρ+(s	ρ+(s	PRON
ejpam-4254	99	106	)	)	PUNCT
ejpam-4254	99	107	is	be	AUX
ejpam-4254	99	108	a	a	DET
ejpam-4254	99	109	supi	supi	NOUN
ejpam-4254	99	110	of	of	ADP
ejpam-4254	99	111	u	u	NOUN
ejpam-4254	99	112	,	,	PUNCT
ejpam-4254	99	113	(	(	PUNCT
ejpam-4254	99	114	6	6	NUM
ejpam-4254	99	115	)	)	PUNCT
ejpam-4254	99	116	a	a	DET
ejpam-4254	99	117	lower	low	ADJ
ejpam-4254	99	118	rough	rough	ADJ
ejpam-4254	99	119	up	up	ADJ
ejpam-4254	99	120	-	-	PUNCT
ejpam-4254	99	121	subalgebra	subalgebra	NOUN
ejpam-4254	99	122	(	(	PUNCT
ejpam-4254	99	123	lorups	lorup	NOUN
ejpam-4254	99	124	)	)	PUNCT
ejpam-4254	99	125	of	of	ADP
ejpam-4254	99	126	u	u	PRON
ejpam-4254	99	127	if	if	SCONJ
ejpam-4254	99	128	∅	∅	NOUN
ejpam-4254	99	129	=	=	NOUN
ejpam-4254	99	130	̸	̸	ADV
ejpam-4254	99	131	ρ−(s	ρ−(s	ADJ
ejpam-4254	99	132	)	)	PUNCT
ejpam-4254	99	133	is	be	AUX
ejpam-4254	99	134	a	a	DET
ejpam-4254	99	135	ups	up	NOUN
ejpam-4254	99	136	of	of	ADP
ejpam-4254	99	137	u	u	NOUN
ejpam-4254	99	138	,	,	PUNCT
ejpam-4254	99	139	(	(	PUNCT
ejpam-4254	99	140	7	7	X
ejpam-4254	99	141	)	)	PUNCT
ejpam-4254	99	142	a	a	DET
ejpam-4254	99	143	lower	low	ADJ
ejpam-4254	99	144	rough	rough	ADJ
ejpam-4254	99	145	near	near	ADP
ejpam-4254	99	146	up	up	ADJ
ejpam-4254	99	147	-	-	PUNCT
ejpam-4254	99	148	filter	filter	NOUN
ejpam-4254	99	149	(	(	PUNCT
ejpam-4254	99	150	lornupf	lornupf	NOUN
ejpam-4254	99	151	)	)	PUNCT
ejpam-4254	99	152	of	of	ADP
ejpam-4254	99	153	u	u	PRON
ejpam-4254	99	154	if	if	SCONJ
ejpam-4254	99	155	∅	∅	NOUN
ejpam-4254	99	156	=	=	NOUN
ejpam-4254	99	157	̸	̸	ADV
ejpam-4254	99	158	ρ−(s	ρ−(s	ADJ
ejpam-4254	99	159	)	)	PUNCT
ejpam-4254	99	160	is	be	AUX
ejpam-4254	99	161	a	a	DET
ejpam-4254	99	162	nupf	nupf	NOUN
ejpam-4254	99	163	of	of	ADP
ejpam-4254	99	164	u	u	NOUN
ejpam-4254	99	165	,	,	PUNCT
ejpam-4254	99	166	(	(	PUNCT
ejpam-4254	99	167	8)	8)	NUM
ejpam-4254	99	168	a	a	DET
ejpam-4254	99	169	lower	low	ADJ
ejpam-4254	99	170	rough	rough	ADJ
ejpam-4254	99	171	up	up	ADJ
ejpam-4254	99	172	-	-	PUNCT
ejpam-4254	99	173	filter	filter	NOUN
ejpam-4254	99	174	(	(	PUNCT
ejpam-4254	99	175	lorupf	lorupf	ADV
ejpam-4254	99	176	)	)	PUNCT
ejpam-4254	99	177	of	of	ADP
ejpam-4254	99	178	u	u	PRON
ejpam-4254	99	179	if	if	SCONJ
ejpam-4254	99	180	∅	∅	NOUN
ejpam-4254	99	181	=	=	NOUN
ejpam-4254	99	182	̸	̸	ADV
ejpam-4254	99	183	ρ−(s	ρ−(s	ADJ
ejpam-4254	99	184	)	)	PUNCT
ejpam-4254	99	185	is	be	AUX
ejpam-4254	99	186	a	a	DET
ejpam-4254	99	187	upf	upf	NOUN
ejpam-4254	99	188	of	of	ADP
ejpam-4254	99	189	u	u	PROPN
ejpam-4254	99	190	,	,	PUNCT
ejpam-4254	99	191	(	(	PUNCT
ejpam-4254	99	192	9	9	X
ejpam-4254	99	193	)	)	PUNCT
ejpam-4254	99	194	a	a	DET
ejpam-4254	99	195	lower	low	ADJ
ejpam-4254	99	196	rough	rough	ADJ
ejpam-4254	99	197	up	up	ADJ
ejpam-4254	99	198	-	-	PUNCT
ejpam-4254	99	199	ideal	ideal	NOUN
ejpam-4254	99	200	(	(	PUNCT
ejpam-4254	99	201	lorupi	lorupi	NOUN
ejpam-4254	99	202	)	)	PUNCT
ejpam-4254	99	203	of	of	ADP
ejpam-4254	99	204	u	u	PRON
ejpam-4254	99	205	if	if	SCONJ
ejpam-4254	99	206	∅	∅	NOUN
ejpam-4254	99	207	=	=	NOUN
ejpam-4254	99	208	̸	̸	ADV
ejpam-4254	99	209	ρ−(s	ρ−(s	ADJ
ejpam-4254	99	210	)	)	PUNCT
ejpam-4254	99	211	is	be	AUX
ejpam-4254	99	212	a	a	DET
ejpam-4254	99	213	upi	upi	NOUN
ejpam-4254	99	214	of	of	ADP
ejpam-4254	99	215	u	u	PROPN
ejpam-4254	99	216	,	,	PUNCT
ejpam-4254	99	217	(	(	PUNCT
ejpam-4254	99	218	10	10	NUM
ejpam-4254	99	219	)	)	PUNCT
ejpam-4254	99	220	a	a	PRON
ejpam-4254	99	221	lower	low	ADJ
ejpam-4254	99	222	rough	rough	ADJ
ejpam-4254	99	223	strong	strong	ADJ
ejpam-4254	99	224	up	up	ADP
ejpam-4254	99	225	-	-	PUNCT
ejpam-4254	99	226	ideal	ideal	NOUN
ejpam-4254	99	227	(	(	PUNCT
ejpam-4254	99	228	lorsupi	lorsupi	PROPN
ejpam-4254	99	229	)	)	PUNCT
ejpam-4254	99	230	of	of	ADP
ejpam-4254	99	231	u	u	PRON
ejpam-4254	99	232	if	if	SCONJ
ejpam-4254	99	233	∅	∅	NOUN
ejpam-4254	99	234	=	=	NOUN
ejpam-4254	99	235	̸	̸	ADV
ejpam-4254	99	236	ρ−(s	ρ−(s	ADJ
ejpam-4254	99	237	)	)	PUNCT
ejpam-4254	99	238	is	be	AUX
ejpam-4254	99	239	a	a	DET
ejpam-4254	99	240	supi	supi	NOUN
ejpam-4254	99	241	of	of	ADP
ejpam-4254	99	242	u	u	NOUN
ejpam-4254	99	243	,	,	PUNCT
ejpam-4254	99	244	(	(	PUNCT
ejpam-4254	99	245	11	11	NUM
ejpam-4254	99	246	)	)	PUNCT
ejpam-4254	99	247	a	a	DET
ejpam-4254	99	248	rough	rough	ADJ
ejpam-4254	99	249	up	up	ADJ
ejpam-4254	99	250	-	-	PUNCT
ejpam-4254	99	251	subalgebra	subalgebra	NOUN
ejpam-4254	99	252	(	(	PUNCT
ejpam-4254	99	253	rups	rup	NOUN
ejpam-4254	99	254	)	)	PUNCT
ejpam-4254	99	255	of	of	ADP
ejpam-4254	99	256	u	u	PRON
ejpam-4254	99	257	if	if	SCONJ
ejpam-4254	99	258	it	it	PRON
ejpam-4254	99	259	is	be	AUX
ejpam-4254	99	260	both	both	CCONJ
ejpam-4254	99	261	an	an	DET
ejpam-4254	99	262	uprups	uprup	NOUN
ejpam-4254	99	263	and	and	CCONJ
ejpam-4254	99	264	a	a	DET
ejpam-4254	99	265	lorups	lorup	NOUN
ejpam-4254	99	266	of	of	ADP
ejpam-4254	99	267	u	u	NOUN
ejpam-4254	99	268	,	,	PUNCT
ejpam-4254	99	269	(	(	PUNCT
ejpam-4254	99	270	12	12	NUM
ejpam-4254	99	271	)	)	PUNCT
ejpam-4254	99	272	a	a	DET
ejpam-4254	99	273	rough	rough	ADJ
ejpam-4254	99	274	near	near	ADP
ejpam-4254	99	275	up	up	ADJ
ejpam-4254	99	276	-	-	PUNCT
ejpam-4254	99	277	filter	filter	NOUN
ejpam-4254	99	278	(	(	PUNCT
ejpam-4254	99	279	rnupf	rnupf	NOUN
ejpam-4254	99	280	)	)	PUNCT
ejpam-4254	99	281	of	of	ADP
ejpam-4254	99	282	u	u	PRON
ejpam-4254	99	283	if	if	SCONJ
ejpam-4254	99	284	it	it	PRON
ejpam-4254	99	285	is	be	AUX
ejpam-4254	99	286	both	both	CCONJ
ejpam-4254	99	287	an	an	DET
ejpam-4254	99	288	uprnupf	uprnupf	NOUN
ejpam-4254	99	289	and	and	CCONJ
ejpam-4254	99	290	a	a	DET
ejpam-4254	99	291	lornupf	lornupf	NOUN
ejpam-4254	99	292	of	of	ADP
ejpam-4254	99	293	u	u	NOUN
ejpam-4254	99	294	,	,	PUNCT
ejpam-4254	99	295	(	(	PUNCT
ejpam-4254	99	296	13	13	NUM
ejpam-4254	99	297	)	)	PUNCT
ejpam-4254	99	298	a	a	DET
ejpam-4254	99	299	rough	rough	ADJ
ejpam-4254	99	300	up	up	ADJ
ejpam-4254	99	301	-	-	PUNCT
ejpam-4254	99	302	filter	filter	NOUN
ejpam-4254	99	303	(	(	PUNCT
ejpam-4254	99	304	rupf	rupf	NOUN
ejpam-4254	99	305	)	)	PUNCT
ejpam-4254	99	306	of	of	ADP
ejpam-4254	99	307	u	u	PRON
ejpam-4254	99	308	if	if	SCONJ
ejpam-4254	99	309	it	it	PRON
ejpam-4254	99	310	is	be	AUX
ejpam-4254	99	311	both	both	CCONJ
ejpam-4254	99	312	an	an	DET
ejpam-4254	99	313	uprupf	uprupf	NOUN
ejpam-4254	99	314	and	and	CCONJ
ejpam-4254	99	315	a	a	DET
ejpam-4254	99	316	lorupf	lorupf	NOUN
ejpam-4254	99	317	of	of	ADP
ejpam-4254	99	318	u	u	NOUN
ejpam-4254	99	319	,	,	PUNCT
ejpam-4254	99	320	(	(	PUNCT
ejpam-4254	99	321	14	14	NUM
ejpam-4254	99	322	)	)	PUNCT
ejpam-4254	99	323	a	a	DET
ejpam-4254	99	324	rough	rough	ADJ
ejpam-4254	99	325	up	up	ADJ
ejpam-4254	99	326	-	-	PUNCT
ejpam-4254	99	327	ideal	ideal	NOUN
ejpam-4254	99	328	(	(	PUNCT
ejpam-4254	99	329	rupi	rupi	NOUN
ejpam-4254	99	330	)	)	PUNCT
ejpam-4254	99	331	of	of	ADP
ejpam-4254	99	332	u	u	PRON
ejpam-4254	99	333	if	if	SCONJ
ejpam-4254	99	334	it	it	PRON
ejpam-4254	99	335	is	be	AUX
ejpam-4254	99	336	both	both	CCONJ
ejpam-4254	99	337	an	an	DET
ejpam-4254	99	338	uprupi	uprupi	NOUN
ejpam-4254	99	339	and	and	CCONJ
ejpam-4254	99	340	a	a	DET
ejpam-4254	99	341	lorupi	lorupi	NOUN
ejpam-4254	99	342	of	of	ADP
ejpam-4254	99	343	u	u	NOUN
ejpam-4254	99	344	,	,	PUNCT
ejpam-4254	99	345	and	and	CCONJ
ejpam-4254	99	346	(	(	PUNCT
ejpam-4254	99	347	15	15	NUM
ejpam-4254	99	348	)	)	PUNCT
ejpam-4254	99	349	a	a	DET
ejpam-4254	99	350	rough	rough	ADJ
ejpam-4254	99	351	strong	strong	ADJ
ejpam-4254	99	352	up	up	ADJ
ejpam-4254	99	353	-	-	PUNCT
ejpam-4254	99	354	ideal	ideal	NOUN
ejpam-4254	99	355	(	(	PUNCT
ejpam-4254	99	356	rsupi	rsupi	PROPN
ejpam-4254	99	357	)	)	PUNCT
ejpam-4254	99	358	of	of	ADP
ejpam-4254	99	359	u	u	PRON
ejpam-4254	99	360	if	if	SCONJ
ejpam-4254	99	361	it	it	PRON
ejpam-4254	99	362	is	be	AUX
ejpam-4254	99	363	both	both	PRON
ejpam-4254	99	364	an	an	DET
ejpam-4254	99	365	uprsupi	uprsupi	NOUN
ejpam-4254	99	366	and	and	CCONJ
ejpam-4254	99	367	a	a	DET
ejpam-4254	99	368	lorsupi	lorsupi	NOUN
ejpam-4254	99	369	of	of	ADP
ejpam-4254	99	370	u	u	NOUN
ejpam-4254	99	371	.	.	PUNCT
ejpam-4254	100	1	2	2	X
ejpam-4254	100	2	.	.	X
ejpam-4254	100	3	rpfss	rpfss	NOUN
ejpam-4254	100	4	in	in	ADP
ejpam-4254	100	5	up	up	ADV
ejpam-4254	100	6	-	-	PUNCT
ejpam-4254	100	7	algebras	algebras	NOUN
ejpam-4254	100	8	definition	definition	NOUN
ejpam-4254	100	9	9	9	NUM
ejpam-4254	100	10	.	.	PUNCT
ejpam-4254	101	1	let	let	VERB
ejpam-4254	101	2	ρ	ρ	NOUN
ejpam-4254	101	3	be	be	AUX
ejpam-4254	101	4	an	an	DET
ejpam-4254	101	5	er	er	INTJ
ejpam-4254	101	6	on	on	ADP
ejpam-4254	101	7	a	a	DET
ejpam-4254	101	8	nonempty	nonempty	ADV
ejpam-4254	101	9	set	set	VERB
ejpam-4254	101	10	u	u	NOUN
ejpam-4254	101	11	and	and	CCONJ
ejpam-4254	101	12	p	p	NOUN
ejpam-4254	101	13	=	=	PUNCT
ejpam-4254	101	14	(	(	PUNCT
ejpam-4254	101	15	µp	µp	PROPN
ejpam-4254	101	16	,	,	PUNCT
ejpam-4254	101	17	νp	νp	NOUN
ejpam-4254	101	18	)	)	PUNCT
ejpam-4254	101	19	a	a	DET
ejpam-4254	101	20	pfs	pfs	NOUN
ejpam-4254	101	21	in	in	ADP
ejpam-4254	101	22	u	u	PROPN
ejpam-4254	101	23	.	.	PUNCT
ejpam-4254	102	1	the	the	DET
ejpam-4254	102	2	upper	upper	ADJ
ejpam-4254	102	3	approximation	approximation	NOUN
ejpam-4254	102	4	of	of	ADP
ejpam-4254	102	5	p	p	NOUN
ejpam-4254	102	6	is	be	AUX
ejpam-4254	102	7	defined	define	VERB
ejpam-4254	102	8	by	by	ADP
ejpam-4254	102	9	ρ+(p	ρ+(p	NOUN
ejpam-4254	102	10	)	)	PUNCT
ejpam-4254	102	11	=	=	PRON
ejpam-4254	102	12	{	{	PUNCT
ejpam-4254	102	13	(	(	PUNCT
ejpam-4254	102	14	a	a	PRON
ejpam-4254	102	15	,	,	PUNCT
ejpam-4254	102	16	µp(a	µp(a	NUM
ejpam-4254	102	17	)	)	PUNCT
ejpam-4254	102	18	,	,	PUNCT
ejpam-4254	102	19	νp(a	νp(a	NUM
ejpam-4254	102	20	)	)	PUNCT
ejpam-4254	102	21	)	)	PUNCT
ejpam-4254	103	1	|	|	ADV
ejpam-4254	103	2	a	a	DET
ejpam-4254	103	3	∈	∈	PROPN
ejpam-4254	103	4	u	u	NOUN
ejpam-4254	103	5	}	}	PUNCT
ejpam-4254	103	6	,	,	PUNCT
ejpam-4254	103	7	where	where	SCONJ
ejpam-4254	103	8	µp(a	µp(a	NUM
ejpam-4254	103	9	)	)	PUNCT
ejpam-4254	103	10	=	=	PUNCT
ejpam-4254	104	1	sup	sup	NOUN
ejpam-4254	104	2	u∈(a)ρ	u∈(a)ρ	PROPN
ejpam-4254	104	3	{	{	PUNCT
ejpam-4254	104	4	µp(u	µp(u	NOUN
ejpam-4254	104	5	)	)	PUNCT
ejpam-4254	104	6	}	}	PUNCT
ejpam-4254	104	7	and	and	CCONJ
ejpam-4254	104	8	νp(a	νp(a	NUM
ejpam-4254	104	9	)	)	PUNCT
ejpam-4254	104	10	=	=	VERB
ejpam-4254	104	11	inf	inf	NOUN
ejpam-4254	104	12	u∈(a)ρ	u∈(a)ρ	X
ejpam-4254	104	13	{	{	PUNCT
ejpam-4254	104	14	νp(u	νp(u	NOUN
ejpam-4254	104	15	)	)	PUNCT
ejpam-4254	104	16	}	}	PUNCT
ejpam-4254	104	17	.	.	PUNCT
ejpam-4254	105	1	the	the	DET
ejpam-4254	105	2	lower	low	ADJ
ejpam-4254	105	3	approximation	approximation	NOUN
ejpam-4254	105	4	of	of	ADP
ejpam-4254	105	5	p	p	NOUN
ejpam-4254	105	6	is	be	AUX
ejpam-4254	105	7	defined	define	VERB
ejpam-4254	105	8	by	by	ADP
ejpam-4254	105	9	ρ−(p	ρ−(p	NOUN
ejpam-4254	105	10	)	)	PUNCT
ejpam-4254	106	1	=	=	PRON
ejpam-4254	106	2	{	{	PUNCT
ejpam-4254	106	3	(	(	PUNCT
ejpam-4254	106	4	a	a	PROPN
ejpam-4254	106	5	,	,	PUNCT
ejpam-4254	106	6	µ	µ	X
ejpam-4254	106	7	p	p	X
ejpam-4254	106	8	(	(	PUNCT
ejpam-4254	106	9	a	a	NOUN
ejpam-4254	106	10	)	)	PUNCT
ejpam-4254	106	11	,	,	PUNCT
ejpam-4254	106	12	νp(a	νp(a	NUM
ejpam-4254	106	13	)	)	PUNCT
ejpam-4254	106	14	)	)	PUNCT
ejpam-4254	107	1	|	|	ADV
ejpam-4254	107	2	a	a	DET
ejpam-4254	107	3	∈	∈	PROPN
ejpam-4254	107	4	u	u	NOUN
ejpam-4254	107	5	}	}	PUNCT
ejpam-4254	107	6	,	,	PUNCT
ejpam-4254	107	7	where	where	SCONJ
ejpam-4254	107	8	µ	µ	X
ejpam-4254	107	9	p	p	X
ejpam-4254	107	10	(	(	PUNCT
ejpam-4254	107	11	a	a	NOUN
ejpam-4254	107	12	)	)	PUNCT
ejpam-4254	107	13	=	=	SYM
ejpam-4254	107	14	inf	inf	NOUN
ejpam-4254	107	15	u∈(a)ρ	u∈(a)ρ	X
ejpam-4254	107	16	{	{	PUNCT
ejpam-4254	107	17	µp(u	µp(u	NOUN
ejpam-4254	107	18	)	)	PUNCT
ejpam-4254	107	19	}	}	PUNCT
ejpam-4254	107	20	and	and	CCONJ
ejpam-4254	107	21	νp(a	νp(a	NUM
ejpam-4254	107	22	)	)	PUNCT
ejpam-4254	108	1	=	=	PUNCT
ejpam-4254	108	2	sup	sup	NOUN
ejpam-4254	108	3	u∈(a)ρ	u∈(a)ρ	PROPN
ejpam-4254	108	4	{	{	PUNCT
ejpam-4254	108	5	νp(u	νp(u	NOUN
ejpam-4254	108	6	)	)	PUNCT
ejpam-4254	108	7	}	}	PUNCT
ejpam-4254	108	8	.	.	PUNCT
ejpam-4254	109	1	it	it	PRON
ejpam-4254	109	2	is	be	AUX
ejpam-4254	109	3	easy	easy	ADJ
ejpam-4254	109	4	to	to	PART
ejpam-4254	109	5	proof	proof	NOUN
ejpam-4254	109	6	that	that	SCONJ
ejpam-4254	109	7	ρ+(p	ρ+(p	VERB
ejpam-4254	109	8	)	)	PUNCT
ejpam-4254	109	9	and	and	CCONJ
ejpam-4254	109	10	ρ−(p	ρ−(p	PROPN
ejpam-4254	109	11	)	)	PUNCT
ejpam-4254	109	12	are	be	AUX
ejpam-4254	109	13	pfss	pfss	ADJ
ejpam-4254	109	14	in	in	ADP
ejpam-4254	109	15	u	u	PROPN
ejpam-4254	109	16	.	.	PUNCT
ejpam-4254	110	1	then	then	ADV
ejpam-4254	110	2	we	we	PRON
ejpam-4254	110	3	call	call	VERB
ejpam-4254	110	4	p	p	PRON
ejpam-4254	110	5	that	that	SCONJ
ejpam-4254	110	6	a	a	DET
ejpam-4254	110	7	rough	rough	ADJ
ejpam-4254	110	8	pythagorean	pythagorean	NOUN
ejpam-4254	110	9	fuzzy	fuzzy	ADJ
ejpam-4254	110	10	set	set	NOUN
ejpam-4254	110	11	(	(	PUNCT
ejpam-4254	110	12	rpfs	rpf	NOUN
ejpam-4254	110	13	)	)	PUNCT
ejpam-4254	110	14	in	in	ADP
ejpam-4254	110	15	u	u	PROPN
ejpam-4254	110	16	.	.	PUNCT
ejpam-4254	111	1	thus	thus	ADV
ejpam-4254	111	2	we	we	PRON
ejpam-4254	111	3	can	can	AUX
ejpam-4254	111	4	denote	denote	VERB
ejpam-4254	111	5	the	the	DET
ejpam-4254	111	6	upper	upper	ADJ
ejpam-4254	111	7	approximation	approximation	NOUN
ejpam-4254	111	8	and	and	CCONJ
ejpam-4254	111	9	the	the	DET
ejpam-4254	111	10	lower	low	ADJ
ejpam-4254	111	11	approximation	approximation	NOUN
ejpam-4254	111	12	by	by	ADP
ejpam-4254	111	13	ρ+(p	ρ+(p	NOUN
ejpam-4254	111	14	)	)	PUNCT
ejpam-4254	111	15	=	=	SYM
ejpam-4254	111	16	(	(	PUNCT
ejpam-4254	111	17	µp	µp	NOUN
ejpam-4254	111	18	,	,	PUNCT
ejpam-4254	111	19	νp	νp	NOUN
ejpam-4254	111	20	)	)	PUNCT
ejpam-4254	111	21	and	and	CCONJ
ejpam-4254	111	22	ρ−(p	ρ−(p	PROPN
ejpam-4254	111	23	)	)	PUNCT
ejpam-4254	111	24	=	=	PUNCT
ejpam-4254	111	25	(	(	PUNCT
ejpam-4254	111	26	µ	µ	X
ejpam-4254	111	27	p	p	NOUN
ejpam-4254	111	28	,	,	PUNCT
ejpam-4254	111	29	νp	νp	NOUN
ejpam-4254	111	30	)	)	PUNCT
ejpam-4254	111	31	,	,	PUNCT
ejpam-4254	111	32	respectively	respectively	ADV
ejpam-4254	111	33	.	.	PUNCT
ejpam-4254	112	1	a.	a.	PROPN
ejpam-4254	112	2	iampan	iampan	PROPN
ejpam-4254	112	3	et	et	PROPN
ejpam-4254	112	4	al	al	PROPN
ejpam-4254	112	5	.	.	PUNCT
ejpam-4254	112	6	/	/	SYM
ejpam-4254	112	7	eur	eur	PROPN
ejpam-4254	112	8	.	.	PUNCT
ejpam-4254	113	1	j.	j.	PROPN
ejpam-4254	113	2	pure	pure	PROPN
ejpam-4254	113	3	appl	appl	PROPN
ejpam-4254	113	4	.	.	PROPN
ejpam-4254	113	5	math	math	PROPN
ejpam-4254	113	6	,	,	PUNCT
ejpam-4254	113	7	15	15	NUM
ejpam-4254	113	8	(	(	PUNCT
ejpam-4254	113	9	1	1	NUM
ejpam-4254	113	10	)	)	PUNCT
ejpam-4254	113	11	(	(	PUNCT
ejpam-4254	113	12	2022	2022	NUM
ejpam-4254	113	13	)	)	PUNCT
ejpam-4254	113	14	,	,	PUNCT
ejpam-4254	113	15	169	169	NUM
ejpam-4254	113	16	-	-	SYM
ejpam-4254	113	17	198	198	NUM
ejpam-4254	113	18	175	175	NUM
ejpam-4254	113	19	definition	definition	NOUN
ejpam-4254	113	20	10	10	NUM
ejpam-4254	113	21	.	.	PUNCT
ejpam-4254	114	1	let	let	VERB
ejpam-4254	114	2	ρ	ρ	NOUN
ejpam-4254	114	3	be	be	AUX
ejpam-4254	114	4	an	an	DET
ejpam-4254	114	5	er	er	INTJ
ejpam-4254	114	6	on	on	ADP
ejpam-4254	114	7	u	u	NOUN
ejpam-4254	114	8	and	and	CCONJ
ejpam-4254	114	9	p	p	NOUN
ejpam-4254	114	10	=	=	PUNCT
ejpam-4254	114	11	(	(	PUNCT
ejpam-4254	114	12	µp	µp	PROPN
ejpam-4254	114	13	,	,	PUNCT
ejpam-4254	114	14	νp	νp	NOUN
ejpam-4254	114	15	)	)	PUNCT
ejpam-4254	114	16	a	a	DET
ejpam-4254	114	17	pfs	pfs	PROPN
ejpam-4254	114	18	in	in	ADP
ejpam-4254	114	19	u	u	PROPN
ejpam-4254	114	20	.	.	PUNCT
ejpam-4254	115	1	then	then	ADV
ejpam-4254	115	2	a	a	DET
ejpam-4254	115	3	rpfs	rpfs	NOUN
ejpam-4254	115	4	p	p	NOUN
ejpam-4254	115	5	in	in	ADP
ejpam-4254	115	6	u	u	NOUN
ejpam-4254	115	7	is	be	AUX
ejpam-4254	115	8	called	call	VERB
ejpam-4254	115	9	constant	constant	ADJ
ejpam-4254	115	10	rough	rough	ADJ
ejpam-4254	115	11	pythagorean	pythagorean	NOUN
ejpam-4254	115	12	fuzzy	fuzzy	NOUN
ejpam-4254	115	13	set	set	VERB
ejpam-4254	115	14	in	in	ADP
ejpam-4254	115	15	u	u	NOUN
ejpam-4254	115	16	if	if	SCONJ
ejpam-4254	115	17	their	their	PRON
ejpam-4254	115	18	membership	membership	NOUN
ejpam-4254	115	19	functions	function	VERB
ejpam-4254	115	20	µp	µp	NOUN
ejpam-4254	115	21	,	,	PUNCT
ejpam-4254	115	22	µp	µp	ADJ
ejpam-4254	115	23	and	and	CCONJ
ejpam-4254	115	24	non	non	ADJ
ejpam-4254	115	25	-	-	ADJ
ejpam-4254	115	26	membership	membership	ADJ
ejpam-4254	115	27	functions	function	NOUN
ejpam-4254	115	28	νp	νp	VERB
ejpam-4254	115	29	,	,	PUNCT
ejpam-4254	115	30	νp	νp	NOUN
ejpam-4254	115	31	are	be	AUX
ejpam-4254	115	32	constant	constant	ADJ
ejpam-4254	115	33	.	.	PUNCT
ejpam-4254	116	1	next	next	ADV
ejpam-4254	116	2	,	,	PUNCT
ejpam-4254	116	3	we	we	PRON
ejpam-4254	116	4	apply	apply	VERB
ejpam-4254	116	5	the	the	DET
ejpam-4254	116	6	concept	concept	NOUN
ejpam-4254	116	7	of	of	ADP
ejpam-4254	116	8	rpfss	rpfss	NOUN
ejpam-4254	116	9	to	to	PART
ejpam-4254	116	10	up	up	ADV
ejpam-4254	116	11	-	-	PUNCT
ejpam-4254	116	12	algebras	algebra	NOUN
ejpam-4254	116	13	and	and	CCONJ
ejpam-4254	116	14	introduce	introduce	VERB
ejpam-4254	116	15	the	the	DET
ejpam-4254	116	16	fifteen	fifteen	ADJ
ejpam-4254	116	17	types	type	NOUN
ejpam-4254	116	18	of	of	ADP
ejpam-4254	116	19	rpfss	rpfss	NOUN
ejpam-4254	116	20	in	in	ADP
ejpam-4254	116	21	up	up	ADV
ejpam-4254	116	22	-	-	PUNCT
ejpam-4254	116	23	algebras	algebras	X
ejpam-4254	116	24	.	.	PUNCT
ejpam-4254	117	1	definition	definition	NOUN
ejpam-4254	117	2	11	11	NUM
ejpam-4254	117	3	.	.	PUNCT
ejpam-4254	118	1	let	let	VERB
ejpam-4254	118	2	ρ	ρ	NOUN
ejpam-4254	118	3	be	be	AUX
ejpam-4254	118	4	an	an	DET
ejpam-4254	118	5	er	er	INTJ
ejpam-4254	118	6	on	on	ADP
ejpam-4254	118	7	u	u	PROPN
ejpam-4254	118	8	.	.	PUNCT
ejpam-4254	119	1	then	then	ADV
ejpam-4254	119	2	a	a	DET
ejpam-4254	119	3	pfs	pfs	PROPN
ejpam-4254	119	4	p	p	NOUN
ejpam-4254	119	5	=	=	X
ejpam-4254	119	6	(	(	PUNCT
ejpam-4254	119	7	µp	µp	PROPN
ejpam-4254	119	8	,	,	PUNCT
ejpam-4254	119	9	νp	νp	NOUN
ejpam-4254	119	10	)	)	PUNCT
ejpam-4254	119	11	in	in	ADP
ejpam-4254	119	12	u	u	NOUN
ejpam-4254	119	13	is	be	AUX
ejpam-4254	119	14	called	call	VERB
ejpam-4254	119	15	(	(	PUNCT
ejpam-4254	119	16	1	1	NUM
ejpam-4254	119	17	)	)	PUNCT
ejpam-4254	119	18	an	an	DET
ejpam-4254	119	19	upper	upper	ADJ
ejpam-4254	119	20	rough	rough	ADJ
ejpam-4254	119	21	pythagorean	pythagorean	NOUN
ejpam-4254	119	22	fuzzy	fuzzy	ADJ
ejpam-4254	119	23	up	up	NOUN
ejpam-4254	119	24	-	-	PUNCT
ejpam-4254	119	25	subalgebra	subalgebra	NOUN
ejpam-4254	119	26	(	(	PUNCT
ejpam-4254	119	27	uprpfups	uprpfup	NOUN
ejpam-4254	119	28	)	)	PUNCT
ejpam-4254	119	29	of	of	ADP
ejpam-4254	119	30	u	u	PRON
ejpam-4254	119	31	if	if	SCONJ
ejpam-4254	119	32	ρ+(p	ρ+(p	NOUN
ejpam-4254	119	33	)	)	PUNCT
ejpam-4254	119	34	is	be	AUX
ejpam-4254	119	35	a	a	DET
ejpam-4254	119	36	pfups	pfup	NOUN
ejpam-4254	119	37	of	of	ADP
ejpam-4254	119	38	u	u	PRON
ejpam-4254	119	39	,	,	PUNCT
ejpam-4254	119	40	(	(	PUNCT
ejpam-4254	119	41	2	2	X
ejpam-4254	119	42	)	)	PUNCT
ejpam-4254	119	43	an	an	DET
ejpam-4254	119	44	upper	upper	ADJ
ejpam-4254	119	45	rough	rough	ADJ
ejpam-4254	119	46	pythagorean	pythagorean	NOUN
ejpam-4254	119	47	fuzzy	fuzzy	NOUN
ejpam-4254	119	48	near	near	ADP
ejpam-4254	119	49	up	up	ADP
ejpam-4254	119	50	-	-	PUNCT
ejpam-4254	119	51	filter	filter	NOUN
ejpam-4254	119	52	(	(	PUNCT
ejpam-4254	119	53	uprpfnupf	uprpfnupf	NOUN
ejpam-4254	119	54	)	)	PUNCT
ejpam-4254	119	55	of	of	ADP
ejpam-4254	119	56	u	u	PRON
ejpam-4254	119	57	if	if	SCONJ
ejpam-4254	119	58	ρ+(p	ρ+(p	NOUN
ejpam-4254	119	59	)	)	PUNCT
ejpam-4254	119	60	is	be	AUX
ejpam-4254	119	61	a	a	DET
ejpam-4254	119	62	pfnupf	pfnupf	NOUN
ejpam-4254	119	63	of	of	ADP
ejpam-4254	119	64	u	u	NOUN
ejpam-4254	119	65	,	,	PUNCT
ejpam-4254	119	66	(	(	PUNCT
ejpam-4254	119	67	3	3	X
ejpam-4254	119	68	)	)	PUNCT
ejpam-4254	119	69	an	an	DET
ejpam-4254	119	70	upper	upper	ADJ
ejpam-4254	119	71	rough	rough	ADJ
ejpam-4254	119	72	pythagorean	pythagorean	NOUN
ejpam-4254	119	73	fuzzy	fuzzy	ADJ
ejpam-4254	119	74	up	up	NOUN
ejpam-4254	119	75	-	-	PUNCT
ejpam-4254	119	76	filter	filter	NOUN
ejpam-4254	119	77	(	(	PUNCT
ejpam-4254	119	78	uprpfupf	uprpfupf	ADJ
ejpam-4254	119	79	)	)	PUNCT
ejpam-4254	119	80	of	of	ADP
ejpam-4254	119	81	u	u	PRON
ejpam-4254	119	82	if	if	SCONJ
ejpam-4254	119	83	ρ+(p	ρ+(p	NOUN
ejpam-4254	119	84	)	)	PUNCT
ejpam-4254	119	85	is	be	AUX
ejpam-4254	119	86	a	a	DET
ejpam-4254	119	87	pfupf	pfupf	NOUN
ejpam-4254	119	88	of	of	ADP
ejpam-4254	119	89	u	u	NOUN
ejpam-4254	119	90	,	,	PUNCT
ejpam-4254	119	91	(	(	PUNCT
ejpam-4254	119	92	4	4	X
ejpam-4254	119	93	)	)	PUNCT
ejpam-4254	119	94	an	an	DET
ejpam-4254	119	95	upper	upper	ADJ
ejpam-4254	119	96	rough	rough	ADJ
ejpam-4254	119	97	pythagorean	pythagorean	NOUN
ejpam-4254	119	98	fuzzy	fuzzy	ADJ
ejpam-4254	119	99	up	up	ADP
ejpam-4254	119	100	-	-	PUNCT
ejpam-4254	119	101	ideal	ideal	NOUN
ejpam-4254	119	102	(	(	PUNCT
ejpam-4254	119	103	uprpfupi	uprpfupi	NOUN
ejpam-4254	119	104	)	)	PUNCT
ejpam-4254	119	105	of	of	ADP
ejpam-4254	119	106	u	u	PRON
ejpam-4254	119	107	if	if	SCONJ
ejpam-4254	119	108	ρ+(p	ρ+(p	NOUN
ejpam-4254	119	109	)	)	PUNCT
ejpam-4254	119	110	is	be	AUX
ejpam-4254	119	111	a	a	DET
ejpam-4254	119	112	pfupi	pfupi	NOUN
ejpam-4254	119	113	of	of	ADP
ejpam-4254	119	114	u	u	NOUN
ejpam-4254	119	115	,	,	PUNCT
ejpam-4254	119	116	(	(	PUNCT
ejpam-4254	119	117	5	5	X
ejpam-4254	119	118	)	)	PUNCT
ejpam-4254	119	119	an	an	DET
ejpam-4254	119	120	upper	upper	ADJ
ejpam-4254	119	121	rough	rough	ADJ
ejpam-4254	119	122	pythagorean	pythagorean	NOUN
ejpam-4254	119	123	fuzzy	fuzzy	NOUN
ejpam-4254	119	124	strong	strong	ADJ
ejpam-4254	119	125	up	up	ADP
ejpam-4254	119	126	-	-	PUNCT
ejpam-4254	119	127	ideal	ideal	NOUN
ejpam-4254	119	128	(	(	PUNCT
ejpam-4254	119	129	uprpfsupi	uprpfsupi	NOUN
ejpam-4254	119	130	)	)	PUNCT
ejpam-4254	119	131	of	of	ADP
ejpam-4254	119	132	u	u	PRON
ejpam-4254	119	133	if	if	SCONJ
ejpam-4254	119	134	ρ+(p	ρ+(p	NOUN
ejpam-4254	119	135	)	)	PUNCT
ejpam-4254	119	136	is	be	AUX
ejpam-4254	119	137	a	a	DET
ejpam-4254	119	138	pfsupi	pfsupi	NOUN
ejpam-4254	119	139	of	of	ADP
ejpam-4254	119	140	u	u	NOUN
ejpam-4254	119	141	,	,	PUNCT
ejpam-4254	119	142	(	(	PUNCT
ejpam-4254	119	143	6	6	NUM
ejpam-4254	119	144	)	)	PUNCT
ejpam-4254	119	145	a	a	DET
ejpam-4254	119	146	lower	low	ADJ
ejpam-4254	119	147	rough	rough	ADJ
ejpam-4254	119	148	pythagorean	pythagorean	NOUN
ejpam-4254	119	149	fuzzy	fuzzy	ADJ
ejpam-4254	119	150	up	up	NOUN
ejpam-4254	119	151	-	-	PUNCT
ejpam-4254	119	152	subalgebra	subalgebra	NOUN
ejpam-4254	119	153	(	(	PUNCT
ejpam-4254	119	154	lorpfups	lorpfup	NOUN
ejpam-4254	119	155	)	)	PUNCT
ejpam-4254	119	156	of	of	ADP
ejpam-4254	119	157	u	u	PRON
ejpam-4254	119	158	if	if	SCONJ
ejpam-4254	119	159	ρ−(p	ρ−(p	NOUN
ejpam-4254	119	160	)	)	PUNCT
ejpam-4254	119	161	is	be	AUX
ejpam-4254	119	162	a	a	DET
ejpam-4254	119	163	pfups	pfup	NOUN
ejpam-4254	119	164	of	of	ADP
ejpam-4254	119	165	u	u	PRON
ejpam-4254	119	166	,	,	PUNCT
ejpam-4254	119	167	(	(	PUNCT
ejpam-4254	119	168	7	7	X
ejpam-4254	119	169	)	)	PUNCT
ejpam-4254	119	170	a	a	DET
ejpam-4254	119	171	lower	low	ADJ
ejpam-4254	119	172	rough	rough	ADJ
ejpam-4254	119	173	pythagorean	pythagorean	NOUN
ejpam-4254	119	174	fuzzy	fuzzy	NOUN
ejpam-4254	119	175	near	near	ADP
ejpam-4254	119	176	up	up	ADP
ejpam-4254	119	177	-	-	PUNCT
ejpam-4254	119	178	filter	filter	NOUN
ejpam-4254	119	179	(	(	PUNCT
ejpam-4254	119	180	lorpfnupf	lorpfnupf	NOUN
ejpam-4254	119	181	)	)	PUNCT
ejpam-4254	119	182	of	of	ADP
ejpam-4254	119	183	u	u	PRON
ejpam-4254	119	184	if	if	SCONJ
ejpam-4254	119	185	ρ−(p	ρ−(p	NOUN
ejpam-4254	119	186	)	)	PUNCT
ejpam-4254	119	187	is	be	AUX
ejpam-4254	119	188	a	a	DET
ejpam-4254	119	189	pfnupf	pfnupf	NOUN
ejpam-4254	119	190	of	of	ADP
ejpam-4254	119	191	u	u	NOUN
ejpam-4254	119	192	,	,	PUNCT
ejpam-4254	119	193	(	(	PUNCT
ejpam-4254	119	194	8)	8)	NUM
ejpam-4254	119	195	a	a	DET
ejpam-4254	119	196	lower	low	ADJ
ejpam-4254	119	197	rough	rough	ADJ
ejpam-4254	119	198	pythagorean	pythagorean	NOUN
ejpam-4254	119	199	fuzzy	fuzzy	ADJ
ejpam-4254	119	200	up	up	NOUN
ejpam-4254	119	201	-	-	PUNCT
ejpam-4254	119	202	filter	filter	NOUN
ejpam-4254	119	203	(	(	PUNCT
ejpam-4254	119	204	lorpfupf	lorpfupf	NOUN
ejpam-4254	119	205	)	)	PUNCT
ejpam-4254	119	206	of	of	ADP
ejpam-4254	119	207	u	u	PRON
ejpam-4254	119	208	if	if	SCONJ
ejpam-4254	119	209	ρ−(p	ρ−(p	NOUN
ejpam-4254	119	210	)	)	PUNCT
ejpam-4254	119	211	is	be	AUX
ejpam-4254	119	212	a	a	DET
ejpam-4254	119	213	pfupf	pfupf	NOUN
ejpam-4254	119	214	of	of	ADP
ejpam-4254	119	215	u	u	NOUN
ejpam-4254	119	216	,	,	PUNCT
ejpam-4254	119	217	(	(	PUNCT
ejpam-4254	119	218	9	9	X
ejpam-4254	119	219	)	)	PUNCT
ejpam-4254	119	220	a	a	DET
ejpam-4254	119	221	lower	low	ADJ
ejpam-4254	119	222	rough	rough	ADJ
ejpam-4254	119	223	pythagorean	pythagorean	NOUN
ejpam-4254	119	224	fuzzy	fuzzy	ADJ
ejpam-4254	119	225	up	up	ADP
ejpam-4254	119	226	-	-	PUNCT
ejpam-4254	119	227	ideal	ideal	NOUN
ejpam-4254	119	228	(	(	PUNCT
ejpam-4254	119	229	lorpfupi	lorpfupi	NOUN
ejpam-4254	119	230	)	)	PUNCT
ejpam-4254	119	231	of	of	ADP
ejpam-4254	119	232	u	u	PRON
ejpam-4254	119	233	if	if	SCONJ
ejpam-4254	119	234	ρ−(p	ρ−(p	NOUN
ejpam-4254	119	235	)	)	PUNCT
ejpam-4254	119	236	is	be	AUX
ejpam-4254	119	237	a	a	DET
ejpam-4254	119	238	pfupi	pfupi	NOUN
ejpam-4254	119	239	of	of	ADP
ejpam-4254	119	240	u	u	NOUN
ejpam-4254	119	241	,	,	PUNCT
ejpam-4254	119	242	(	(	PUNCT
ejpam-4254	119	243	10	10	NUM
ejpam-4254	119	244	)	)	PUNCT
ejpam-4254	119	245	a	a	DET
ejpam-4254	119	246	lower	low	ADJ
ejpam-4254	119	247	rough	rough	ADJ
ejpam-4254	119	248	pythagorean	pythagorean	NOUN
ejpam-4254	119	249	fuzzy	fuzzy	NOUN
ejpam-4254	119	250	strong	strong	ADJ
ejpam-4254	119	251	up	up	ADP
ejpam-4254	119	252	-	-	PUNCT
ejpam-4254	119	253	ideal	ideal	NOUN
ejpam-4254	119	254	(	(	PUNCT
ejpam-4254	119	255	lorpfsupi	lorpfsupi	PROPN
ejpam-4254	119	256	)	)	PUNCT
ejpam-4254	119	257	of	of	ADP
ejpam-4254	119	258	u	u	PRON
ejpam-4254	119	259	if	if	SCONJ
ejpam-4254	119	260	ρ−(p	ρ−(p	NOUN
ejpam-4254	119	261	)	)	PUNCT
ejpam-4254	119	262	is	be	AUX
ejpam-4254	119	263	a	a	DET
ejpam-4254	119	264	pfsupi	pfsupi	NOUN
ejpam-4254	119	265	of	of	ADP
ejpam-4254	119	266	u	u	NOUN
ejpam-4254	119	267	,	,	PUNCT
ejpam-4254	119	268	(	(	PUNCT
ejpam-4254	119	269	11	11	NUM
ejpam-4254	119	270	)	)	PUNCT
ejpam-4254	119	271	a	a	DET
ejpam-4254	119	272	rough	rough	ADJ
ejpam-4254	119	273	pythagorean	pythagorean	NOUN
ejpam-4254	119	274	fuzzy	fuzzy	ADJ
ejpam-4254	119	275	up	up	NOUN
ejpam-4254	119	276	-	-	PUNCT
ejpam-4254	119	277	subalgebra	subalgebra	NOUN
ejpam-4254	119	278	(	(	PUNCT
ejpam-4254	119	279	rpfups	rpfup	NOUN
ejpam-4254	119	280	)	)	PUNCT
ejpam-4254	119	281	of	of	ADP
ejpam-4254	119	282	u	u	PRON
ejpam-4254	119	283	if	if	SCONJ
ejpam-4254	119	284	it	it	PRON
ejpam-4254	119	285	is	be	AUX
ejpam-4254	119	286	both	both	PRON
ejpam-4254	119	287	an	an	DET
ejpam-4254	119	288	uprpfups	uprpfup	NOUN
ejpam-4254	119	289	and	and	CCONJ
ejpam-4254	119	290	a	a	DET
ejpam-4254	119	291	lorpfups	lorpfup	NOUN
ejpam-4254	119	292	of	of	ADP
ejpam-4254	119	293	u	u	NOUN
ejpam-4254	119	294	,	,	PUNCT
ejpam-4254	119	295	(	(	PUNCT
ejpam-4254	119	296	12	12	NUM
ejpam-4254	119	297	)	)	PUNCT
ejpam-4254	119	298	a	a	DET
ejpam-4254	119	299	rough	rough	ADJ
ejpam-4254	119	300	pythagorean	pythagorean	NOUN
ejpam-4254	119	301	fuzzy	fuzzy	NOUN
ejpam-4254	119	302	near	near	ADP
ejpam-4254	119	303	up	up	ADP
ejpam-4254	119	304	-	-	PUNCT
ejpam-4254	119	305	filter	filter	NOUN
ejpam-4254	119	306	(	(	PUNCT
ejpam-4254	119	307	rpfnupf	rpfnupf	NOUN
ejpam-4254	119	308	)	)	PUNCT
ejpam-4254	119	309	of	of	ADP
ejpam-4254	119	310	u	u	PRON
ejpam-4254	119	311	if	if	SCONJ
ejpam-4254	119	312	it	it	PRON
ejpam-4254	119	313	is	be	AUX
ejpam-4254	119	314	both	both	CCONJ
ejpam-4254	119	315	an	an	DET
ejpam-4254	119	316	uprpfnupf	uprpfnupf	NOUN
ejpam-4254	119	317	and	and	CCONJ
ejpam-4254	119	318	a	a	DET
ejpam-4254	119	319	lorpfnupf	lorpfnupf	NOUN
ejpam-4254	119	320	of	of	ADP
ejpam-4254	119	321	u	u	PROPN
ejpam-4254	119	322	,	,	PUNCT
ejpam-4254	119	323	(	(	PUNCT
ejpam-4254	119	324	13	13	NUM
ejpam-4254	119	325	)	)	PUNCT
ejpam-4254	119	326	a	a	DET
ejpam-4254	119	327	rough	rough	ADJ
ejpam-4254	119	328	pythagorean	pythagorean	NOUN
ejpam-4254	119	329	fuzzy	fuzzy	ADJ
ejpam-4254	119	330	up	up	NOUN
ejpam-4254	119	331	-	-	PUNCT
ejpam-4254	119	332	filter	filter	NOUN
ejpam-4254	119	333	(	(	PUNCT
ejpam-4254	119	334	rpfupf	rpfupf	NOUN
ejpam-4254	119	335	)	)	PUNCT
ejpam-4254	119	336	of	of	ADP
ejpam-4254	119	337	u	u	PRON
ejpam-4254	119	338	if	if	SCONJ
ejpam-4254	119	339	it	it	PRON
ejpam-4254	119	340	is	be	AUX
ejpam-4254	119	341	both	both	CCONJ
ejpam-4254	119	342	an	an	DET
ejpam-4254	119	343	uprpfupf	uprpfupf	ADJ
ejpam-4254	119	344	and	and	CCONJ
ejpam-4254	119	345	a	a	DET
ejpam-4254	119	346	lorpfupf	lorpfupf	NOUN
ejpam-4254	119	347	of	of	ADP
ejpam-4254	119	348	u	u	PROPN
ejpam-4254	119	349	,	,	PUNCT
ejpam-4254	120	1	a.	a.	NOUN
ejpam-4254	120	2	iampan	iampan	NOUN
ejpam-4254	120	3	et	et	PROPN
ejpam-4254	120	4	al	al	PROPN
ejpam-4254	120	5	.	.	PUNCT
ejpam-4254	120	6	/	/	SYM
ejpam-4254	120	7	eur	eur	PROPN
ejpam-4254	120	8	.	.	PUNCT
ejpam-4254	121	1	j.	j.	PROPN
ejpam-4254	121	2	pure	pure	PROPN
ejpam-4254	121	3	appl	appl	PROPN
ejpam-4254	121	4	.	.	PROPN
ejpam-4254	121	5	math	math	PROPN
ejpam-4254	121	6	,	,	PUNCT
ejpam-4254	121	7	15	15	NUM
ejpam-4254	121	8	(	(	PUNCT
ejpam-4254	121	9	1	1	NUM
ejpam-4254	121	10	)	)	PUNCT
ejpam-4254	121	11	(	(	PUNCT
ejpam-4254	121	12	2022	2022	NUM
ejpam-4254	121	13	)	)	PUNCT
ejpam-4254	121	14	,	,	PUNCT
ejpam-4254	121	15	169	169	NUM
ejpam-4254	121	16	-	-	SYM
ejpam-4254	121	17	198	198	NUM
ejpam-4254	121	18	176	176	NUM
ejpam-4254	121	19	(	(	PUNCT
ejpam-4254	121	20	14	14	NUM
ejpam-4254	121	21	)	)	PUNCT
ejpam-4254	121	22	a	a	DET
ejpam-4254	121	23	rough	rough	ADJ
ejpam-4254	121	24	pythagorean	pythagorean	NOUN
ejpam-4254	121	25	fuzzy	fuzzy	ADJ
ejpam-4254	121	26	up	up	ADP
ejpam-4254	121	27	-	-	PUNCT
ejpam-4254	121	28	ideal	ideal	NOUN
ejpam-4254	121	29	(	(	PUNCT
ejpam-4254	121	30	rpfupi	rpfupi	NOUN
ejpam-4254	121	31	)	)	PUNCT
ejpam-4254	121	32	of	of	ADP
ejpam-4254	121	33	u	u	PRON
ejpam-4254	121	34	if	if	SCONJ
ejpam-4254	121	35	it	it	PRON
ejpam-4254	121	36	is	be	AUX
ejpam-4254	121	37	both	both	CCONJ
ejpam-4254	121	38	an	an	DET
ejpam-4254	121	39	uprpfupi	uprpfupi	NOUN
ejpam-4254	121	40	and	and	CCONJ
ejpam-4254	121	41	a	a	DET
ejpam-4254	121	42	lorpfupi	lorpfupi	NOUN
ejpam-4254	121	43	of	of	ADP
ejpam-4254	121	44	u	u	PROPN
ejpam-4254	121	45	,	,	PUNCT
ejpam-4254	121	46	and	and	CCONJ
ejpam-4254	121	47	(	(	PUNCT
ejpam-4254	121	48	15	15	NUM
ejpam-4254	121	49	)	)	PUNCT
ejpam-4254	121	50	a	a	DET
ejpam-4254	121	51	rough	rough	ADJ
ejpam-4254	121	52	pythagorean	pythagorean	NOUN
ejpam-4254	121	53	fuzzy	fuzzy	NOUN
ejpam-4254	121	54	strong	strong	ADJ
ejpam-4254	121	55	up	up	ADP
ejpam-4254	121	56	-	-	PUNCT
ejpam-4254	121	57	ideal	ideal	NOUN
ejpam-4254	121	58	(	(	PUNCT
ejpam-4254	121	59	rpfsupi	rpfsupi	NOUN
ejpam-4254	121	60	)	)	PUNCT
ejpam-4254	121	61	of	of	ADP
ejpam-4254	121	62	u	u	PRON
ejpam-4254	121	63	if	if	SCONJ
ejpam-4254	121	64	it	it	PRON
ejpam-4254	121	65	is	be	AUX
ejpam-4254	121	66	both	both	CCONJ
ejpam-4254	121	67	an	an	DET
ejpam-4254	121	68	uprpfsupi	uprpfsupi	NOUN
ejpam-4254	121	69	and	and	CCONJ
ejpam-4254	121	70	a	a	DET
ejpam-4254	121	71	lorpfsupi	lorpfsupi	NOUN
ejpam-4254	121	72	of	of	ADP
ejpam-4254	121	73	u	u	NOUN
ejpam-4254	121	74	.	.	PUNCT
ejpam-4254	122	1	it	it	PRON
ejpam-4254	122	2	is	be	AUX
ejpam-4254	122	3	simple	simple	ADJ
ejpam-4254	122	4	to	to	PART
ejpam-4254	122	5	verify	verify	VERB
ejpam-4254	122	6	the	the	DET
ejpam-4254	122	7	generalizations	generalization	NOUN
ejpam-4254	122	8	of	of	ADP
ejpam-4254	122	9	rpfss	rpfss	NOUN
ejpam-4254	122	10	in	in	ADP
ejpam-4254	122	11	up	up	ADV
ejpam-4254	122	12	-	-	PUNCT
ejpam-4254	122	13	algebras	algebras	X
ejpam-4254	122	14	.	.	PUNCT
ejpam-4254	123	1	as	as	ADP
ejpam-4254	123	2	a	a	DET
ejpam-4254	123	3	result	result	NOUN
ejpam-4254	123	4	,	,	PUNCT
ejpam-4254	123	5	we	we	PRON
ejpam-4254	123	6	obtain	obtain	VERB
ejpam-4254	123	7	the	the	DET
ejpam-4254	123	8	diagram	diagram	NOUN
ejpam-4254	123	9	of	of	ADP
ejpam-4254	123	10	the	the	DET
ejpam-4254	123	11	generalization	generalization	NOUN
ejpam-4254	123	12	of	of	ADP
ejpam-4254	123	13	rpfss	rpfss	NOUN
ejpam-4254	123	14	in	in	ADP
ejpam-4254	123	15	up	up	ADP
ejpam-4254	123	16	-	-	PUNCT
ejpam-4254	123	17	algebras	algebra	NOUN
ejpam-4254	123	18	,	,	PUNCT
ejpam-4254	123	19	which	which	PRON
ejpam-4254	123	20	is	be	AUX
ejpam-4254	123	21	shown	show	VERB
ejpam-4254	123	22	in	in	ADP
ejpam-4254	123	23	figure	figure	NOUN
ejpam-4254	123	24	1	1	NUM
ejpam-4254	123	25	.	.	PUNCT
ejpam-4254	123	26	figure	figure	NOUN
ejpam-4254	123	27	1	1	NUM
ejpam-4254	123	28	:	:	PUNCT
ejpam-4254	123	29	rough	rough	ADJ
ejpam-4254	123	30	pythagorean	pythagorean	ADJ
ejpam-4254	123	31	fuzzy	fuzzy	ADJ
ejpam-4254	123	32	sets	set	NOUN
ejpam-4254	123	33	in	in	ADP
ejpam-4254	123	34	up	up	ADV
ejpam-4254	123	35	-	-	PUNCT
ejpam-4254	123	36	algebras	algebras	NOUN
ejpam-4254	123	37	theorem	theorem	VERB
ejpam-4254	123	38	1	1	NUM
ejpam-4254	123	39	.	.	PUNCT
ejpam-4254	124	1	let	let	VERB
ejpam-4254	124	2	ρ	ρ	NOUN
ejpam-4254	124	3	be	be	AUX
ejpam-4254	124	4	an	an	DET
ejpam-4254	124	5	er	er	INTJ
ejpam-4254	124	6	(	(	PUNCT
ejpam-4254	124	7	cr	cr	NOUN
ejpam-4254	124	8	)	)	PUNCT
ejpam-4254	124	9	on	on	ADP
ejpam-4254	124	10	u	u	NOUN
ejpam-4254	124	11	and	and	CCONJ
ejpam-4254	124	12	p	p	NOUN
ejpam-4254	124	13	=	=	PUNCT
ejpam-4254	124	14	(	(	PUNCT
ejpam-4254	124	15	µp	µp	PROPN
ejpam-4254	124	16	,	,	PUNCT
ejpam-4254	124	17	νp	νp	NOUN
ejpam-4254	124	18	)	)	PUNCT
ejpam-4254	124	19	a	a	DET
ejpam-4254	124	20	pfs	pfs	PROPN
ejpam-4254	124	21	in	in	ADP
ejpam-4254	124	22	u	u	NOUN
ejpam-4254	124	23	.	.	PUNCT
ejpam-4254	125	1	if	if	SCONJ
ejpam-4254	125	2	p	p	NOUN
ejpam-4254	125	3	is	be	AUX
ejpam-4254	125	4	a	a	DET
ejpam-4254	125	5	pfsupi	pfsupi	NOUN
ejpam-4254	125	6	of	of	ADP
ejpam-4254	125	7	u	u	NOUN
ejpam-4254	125	8	,	,	PUNCT
ejpam-4254	125	9	then	then	ADV
ejpam-4254	125	10	p	p	NOUN
ejpam-4254	125	11	is	be	AUX
ejpam-4254	125	12	a	a	DET
ejpam-4254	125	13	rpfsupi	rpfsupi	NOUN
ejpam-4254	125	14	of	of	ADP
ejpam-4254	125	15	u	u	PROPN
ejpam-4254	125	16	.	.	PUNCT
ejpam-4254	126	1	proof	proof	NOUN
ejpam-4254	126	2	.	.	PUNCT
ejpam-4254	127	1	let	let	VERB
ejpam-4254	127	2	p	p	PRON
ejpam-4254	127	3	be	be	AUX
ejpam-4254	127	4	a	a	DET
ejpam-4254	127	5	pfsupi	pfsupi	NOUN
ejpam-4254	127	6	of	of	ADP
ejpam-4254	127	7	u	u	NOUN
ejpam-4254	127	8	.	.	PUNCT
ejpam-4254	128	1	then	then	ADV
ejpam-4254	128	2	it	it	PRON
ejpam-4254	128	3	is	be	AUX
ejpam-4254	128	4	constant	constant	ADJ
ejpam-4254	128	5	.	.	PUNCT
ejpam-4254	129	1	for	for	ADP
ejpam-4254	129	2	all	all	DET
ejpam-4254	129	3	a	a	PRON
ejpam-4254	129	4	,	,	PUNCT
ejpam-4254	129	5	b	b	X
ejpam-4254	129	6	∈	∈	PROPN
ejpam-4254	129	7	u	u	NOUN
ejpam-4254	129	8	,	,	PUNCT
ejpam-4254	129	9	µp(a	µp(a	NUM
ejpam-4254	129	10	)	)	PUNCT
ejpam-4254	129	11	=	=	SYM
ejpam-4254	129	12	µp(b	µp(b	X
ejpam-4254	129	13	)	)	PUNCT
ejpam-4254	129	14	and	and	CCONJ
ejpam-4254	129	15	νp(a	νp(a	NUM
ejpam-4254	129	16	)	)	PUNCT
ejpam-4254	129	17	=	=	SYM
ejpam-4254	129	18	νp(b	νp(b	NOUN
ejpam-4254	129	19	)	)	PUNCT
ejpam-4254	129	20	.	.	PUNCT
ejpam-4254	130	1	let	let	VERB
ejpam-4254	130	2	u	u	NOUN
ejpam-4254	130	3	,	,	PUNCT
ejpam-4254	130	4	v	v	PROPN
ejpam-4254	130	5	∈	∈	PROPN
ejpam-4254	130	6	u	u	NOUN
ejpam-4254	130	7	.	.	PUNCT
ejpam-4254	131	1	then	then	ADV
ejpam-4254	131	2	µp(u	µp(u	PUNCT
ejpam-4254	131	3	)	)	PUNCT
ejpam-4254	131	4	=	=	SYM
ejpam-4254	131	5	sup	sup	NOUN
ejpam-4254	131	6	a∈(u)ρ	a∈(u)ρ	NUM
ejpam-4254	131	7	{	{	PUNCT
ejpam-4254	131	8	µp(a	µp(a	NUM
ejpam-4254	131	9	)	)	PUNCT
ejpam-4254	131	10	}	}	PUNCT
ejpam-4254	131	11	=	=	SYM
ejpam-4254	131	12	sup	sup	NOUN
ejpam-4254	131	13	b∈(v)ρ	b∈(v)ρ	PROPN
ejpam-4254	131	14	{	{	PUNCT
ejpam-4254	131	15	µp(b	µp(b	NOUN
ejpam-4254	131	16	)	)	PUNCT
ejpam-4254	131	17	}	}	PUNCT
ejpam-4254	131	18	=	=	SYM
ejpam-4254	131	19	µp(v	µp(v	NOUN
ejpam-4254	131	20	)	)	PUNCT
ejpam-4254	131	21	,	,	PUNCT
ejpam-4254	131	22	νp(u	νp(u	X
ejpam-4254	131	23	)	)	PUNCT
ejpam-4254	131	24	=	=	SYM
ejpam-4254	131	25	inf	inf	NOUN
ejpam-4254	131	26	a∈(u)ρ	a∈(u)ρ	NOUN
ejpam-4254	131	27	{	{	PUNCT
ejpam-4254	131	28	νp(a	νp(a	NUM
ejpam-4254	131	29	)	)	PUNCT
ejpam-4254	131	30	}	}	PUNCT
ejpam-4254	131	31	=	=	SYM
ejpam-4254	131	32	inf	inf	PROPN
ejpam-4254	131	33	b∈(v)ρ	b∈(v)ρ	PROPN
ejpam-4254	131	34	{	{	PUNCT
ejpam-4254	131	35	νp(b	νp(b	NOUN
ejpam-4254	131	36	)	)	PUNCT
ejpam-4254	131	37	}	}	PUNCT
ejpam-4254	131	38	=	=	SYM
ejpam-4254	131	39	νp(v	νp(v	NOUN
ejpam-4254	131	40	)	)	PUNCT
ejpam-4254	131	41	,	,	PUNCT
ejpam-4254	131	42	µ	µ	X
ejpam-4254	131	43	p	p	X
ejpam-4254	131	44	(	(	PUNCT
ejpam-4254	131	45	u	u	NOUN
ejpam-4254	131	46	)	)	PUNCT
ejpam-4254	131	47	=	=	SYM
ejpam-4254	131	48	inf	inf	NOUN
ejpam-4254	131	49	a∈(u)ρ	a∈(u)ρ	NOUN
ejpam-4254	131	50	{	{	PUNCT
ejpam-4254	131	51	µp(a	µp(a	NUM
ejpam-4254	131	52	)	)	PUNCT
ejpam-4254	131	53	}	}	PUNCT
ejpam-4254	131	54	=	=	SYM
ejpam-4254	131	55	inf	inf	PROPN
ejpam-4254	131	56	b∈(v)ρ	b∈(v)ρ	PROPN
ejpam-4254	131	57	{	{	PUNCT
ejpam-4254	131	58	µp(b	µp(b	NOUN
ejpam-4254	131	59	)	)	PUNCT
ejpam-4254	131	60	}	}	PUNCT
ejpam-4254	131	61	=	=	SYM
ejpam-4254	131	62	µ	µ	X
ejpam-4254	131	63	p	p	X
ejpam-4254	131	64	(	(	PUNCT
ejpam-4254	131	65	v	v	NOUN
ejpam-4254	131	66	)	)	PUNCT
ejpam-4254	131	67	,	,	PUNCT
ejpam-4254	131	68	and	and	CCONJ
ejpam-4254	131	69	νp(u	νp(u	NUM
ejpam-4254	131	70	)	)	PUNCT
ejpam-4254	131	71	=	=	SYM
ejpam-4254	131	72	sup	sup	NOUN
ejpam-4254	131	73	a∈(u)ρ	a∈(u)ρ	NUM
ejpam-4254	131	74	{	{	PUNCT
ejpam-4254	131	75	νp(a	νp(a	NUM
ejpam-4254	131	76	)	)	PUNCT
ejpam-4254	131	77	}	}	PUNCT
ejpam-4254	132	1	=	=	PUNCT
ejpam-4254	132	2	sup	sup	NOUN
ejpam-4254	132	3	b∈(v)ρ	b∈(v)ρ	PROPN
ejpam-4254	132	4	{	{	PUNCT
ejpam-4254	132	5	νp(b	νp(b	NOUN
ejpam-4254	132	6	)	)	PUNCT
ejpam-4254	132	7	}	}	PUNCT
ejpam-4254	132	8	=	=	SYM
ejpam-4254	132	9	νp(v	νp(v	NOUN
ejpam-4254	132	10	)	)	PUNCT
ejpam-4254	132	11	.	.	PUNCT
ejpam-4254	133	1	so	so	ADV
ejpam-4254	133	2	ρ+(p	ρ+(p	ADV
ejpam-4254	133	3	)	)	PUNCT
ejpam-4254	133	4	and	and	CCONJ
ejpam-4254	133	5	ρ−(p	ρ−(p	PROPN
ejpam-4254	133	6	)	)	PUNCT
ejpam-4254	133	7	are	be	AUX
ejpam-4254	133	8	constant	constant	ADJ
ejpam-4254	133	9	.	.	PUNCT
ejpam-4254	134	1	this	this	PRON
ejpam-4254	134	2	means	mean	VERB
ejpam-4254	134	3	that	that	SCONJ
ejpam-4254	134	4	ρ+(p	ρ+(p	NOUN
ejpam-4254	134	5	)	)	PUNCT
ejpam-4254	134	6	and	and	CCONJ
ejpam-4254	134	7	ρ−(p	ρ−(p	PROPN
ejpam-4254	134	8	)	)	PUNCT
ejpam-4254	134	9	are	be	AUX
ejpam-4254	134	10	pfsupis	pfsupi	VERB
ejpam-4254	134	11	of	of	ADP
ejpam-4254	134	12	u	u	NOUN
ejpam-4254	134	13	.	.	PUNCT
ejpam-4254	135	1	therefore	therefore	ADV
ejpam-4254	135	2	,	,	PUNCT
ejpam-4254	135	3	p	p	PRON
ejpam-4254	135	4	is	be	AUX
ejpam-4254	135	5	a	a	DET
ejpam-4254	135	6	rpfsupi	rpfsupi	NOUN
ejpam-4254	135	7	of	of	ADP
ejpam-4254	135	8	u	u	NOUN
ejpam-4254	135	9	.	.	PUNCT
ejpam-4254	136	1	the	the	DET
ejpam-4254	136	2	following	follow	VERB
ejpam-4254	136	3	examples	example	NOUN
ejpam-4254	136	4	show	show	VERB
ejpam-4254	136	5	the	the	DET
ejpam-4254	136	6	relationships	relationship	NOUN
ejpam-4254	136	7	between	between	ADP
ejpam-4254	136	8	pfss	pfss	NOUN
ejpam-4254	136	9	in	in	ADP
ejpam-4254	136	10	u	u	NOUN
ejpam-4254	136	11	and	and	CCONJ
ejpam-4254	136	12	rpfss	rpfss	VERB
ejpam-4254	136	13	in	in	ADP
ejpam-4254	136	14	u	u	NOUN
ejpam-4254	136	15	with	with	ADP
ejpam-4254	136	16	ρ	ρ	PROPN
ejpam-4254	136	17	is	be	AUX
ejpam-4254	136	18	an	an	DET
ejpam-4254	136	19	er	er	INTJ
ejpam-4254	136	20	on	on	ADP
ejpam-4254	136	21	u	u	PROPN
ejpam-4254	136	22	.	.	PUNCT
ejpam-4254	137	1	a.	a.	PROPN
ejpam-4254	137	2	iampan	iampan	PROPN
ejpam-4254	137	3	et	et	PROPN
ejpam-4254	137	4	al	al	PROPN
ejpam-4254	137	5	.	.	PUNCT
ejpam-4254	137	6	/	/	SYM
ejpam-4254	137	7	eur	eur	PROPN
ejpam-4254	137	8	.	.	PUNCT
ejpam-4254	138	1	j.	j.	PROPN
ejpam-4254	138	2	pure	pure	PROPN
ejpam-4254	138	3	appl	appl	PROPN
ejpam-4254	138	4	.	.	PROPN
ejpam-4254	138	5	math	math	PROPN
ejpam-4254	138	6	,	,	PUNCT
ejpam-4254	138	7	15	15	NUM
ejpam-4254	138	8	(	(	PUNCT
ejpam-4254	138	9	1	1	NUM
ejpam-4254	138	10	)	)	PUNCT
ejpam-4254	138	11	(	(	PUNCT
ejpam-4254	138	12	2022	2022	NUM
ejpam-4254	138	13	)	)	PUNCT
ejpam-4254	138	14	,	,	PUNCT
ejpam-4254	138	15	169	169	NUM
ejpam-4254	138	16	-	-	SYM
ejpam-4254	138	17	198	198	NUM
ejpam-4254	138	18	177	177	NUM
ejpam-4254	138	19	example	example	NOUN
ejpam-4254	138	20	1	1	NUM
ejpam-4254	138	21	.	.	X
ejpam-4254	138	22	consider	consider	VERB
ejpam-4254	138	23	a	a	DET
ejpam-4254	138	24	up	up	NOUN
ejpam-4254	138	25	-	-	PUNCT
ejpam-4254	138	26	algebra	algebra	NOUN
ejpam-4254	138	27	u	u	NOUN
ejpam-4254	138	28	=	=	PUNCT
ejpam-4254	138	29	(	(	PUNCT
ejpam-4254	138	30	u	u	NOUN
ejpam-4254	138	31	,	,	PUNCT
ejpam-4254	138	32	⋆	⋆	INTJ
ejpam-4254	138	33	,	,	PUNCT
ejpam-4254	138	34	0	0	NUM
ejpam-4254	138	35	)	)	PUNCT
ejpam-4254	138	36	,	,	PUNCT
ejpam-4254	138	37	where	where	SCONJ
ejpam-4254	138	38	u	u	NOUN
ejpam-4254	138	39	=	=	PUNCT
ejpam-4254	138	40	{	{	PUNCT
ejpam-4254	138	41	0	0	NUM
ejpam-4254	138	42	,	,	PUNCT
ejpam-4254	138	43	1	1	NUM
ejpam-4254	138	44	,	,	PUNCT
ejpam-4254	138	45	2	2	NUM
ejpam-4254	138	46	,	,	PUNCT
ejpam-4254	138	47	3	3	NUM
ejpam-4254	138	48	}	}	PUNCT
ejpam-4254	138	49	is	be	AUX
ejpam-4254	138	50	defined	define	VERB
ejpam-4254	138	51	in	in	ADP
ejpam-4254	138	52	the	the	DET
ejpam-4254	138	53	cayley	cayley	ADJ
ejpam-4254	138	54	table	table	NOUN
ejpam-4254	138	55	below	below	ADV
ejpam-4254	138	56	.	.	PUNCT
ejpam-4254	139	1	⋆	⋆	VERB
ejpam-4254	140	1	0	0	NUM
ejpam-4254	140	2	1	1	NUM
ejpam-4254	140	3	2	2	NUM
ejpam-4254	140	4	3	3	NUM
ejpam-4254	140	5	0	0	NUM
ejpam-4254	140	6	0	0	NUM
ejpam-4254	140	7	1	1	NUM
ejpam-4254	140	8	2	2	NUM
ejpam-4254	140	9	3	3	NUM
ejpam-4254	140	10	1	1	NUM
ejpam-4254	140	11	0	0	NUM
ejpam-4254	140	12	0	0	NUM
ejpam-4254	140	13	2	2	NUM
ejpam-4254	140	14	2	2	NUM
ejpam-4254	140	15	2	2	NUM
ejpam-4254	140	16	0	0	NUM
ejpam-4254	140	17	1	1	NUM
ejpam-4254	140	18	0	0	NUM
ejpam-4254	140	19	2	2	NUM
ejpam-4254	140	20	3	3	NUM
ejpam-4254	140	21	0	0	NUM
ejpam-4254	140	22	1	1	NUM
ejpam-4254	140	23	0	0	NUM
ejpam-4254	140	24	0	0	NUM
ejpam-4254	140	25	we	we	PRON
ejpam-4254	140	26	define	define	VERB
ejpam-4254	140	27	a	a	DET
ejpam-4254	140	28	pfs	pfs	PROPN
ejpam-4254	140	29	p	p	NOUN
ejpam-4254	140	30	=	=	X
ejpam-4254	140	31	(	(	PUNCT
ejpam-4254	140	32	µp	µp	PROPN
ejpam-4254	140	33	,	,	PUNCT
ejpam-4254	140	34	νp	νp	NOUN
ejpam-4254	140	35	)	)	PUNCT
ejpam-4254	140	36	in	in	ADP
ejpam-4254	140	37	u	u	NOUN
ejpam-4254	140	38	as	as	SCONJ
ejpam-4254	140	39	follows	follow	VERB
ejpam-4254	140	40	:	:	PUNCT
ejpam-4254	140	41	u	u	NOUN
ejpam-4254	140	42	0	0	NUM
ejpam-4254	140	43	1	1	NUM
ejpam-4254	140	44	2	2	NUM
ejpam-4254	140	45	3	3	NUM
ejpam-4254	140	46	µp	µp	NOUN
ejpam-4254	140	47	0.7	0.7	NUM
ejpam-4254	140	48	0.3	0.3	NUM
ejpam-4254	140	49	0.6	0.6	NUM
ejpam-4254	140	50	0.6	0.6	NUM
ejpam-4254	140	51	νp	νp	ADP
ejpam-4254	140	52	0.1	0.1	NUM
ejpam-4254	140	53	0.8	0.8	NUM
ejpam-4254	140	54	0.4	0.4	NUM
ejpam-4254	140	55	0.4	0.4	NUM
ejpam-4254	140	56	then	then	ADV
ejpam-4254	140	57	p	p	NOUN
ejpam-4254	140	58	is	be	AUX
ejpam-4254	140	59	a	a	DET
ejpam-4254	140	60	pfupi	pfupi	NOUN
ejpam-4254	140	61	(	(	PUNCT
ejpam-4254	140	62	resp	resp	NOUN
ejpam-4254	140	63	.	.	PUNCT
ejpam-4254	140	64	,	,	PUNCT
ejpam-4254	140	65	pfupf	pfupf	NOUN
ejpam-4254	140	66	,	,	PUNCT
ejpam-4254	140	67	pfnupf	pfnupf	NOUN
ejpam-4254	140	68	,	,	PUNCT
ejpam-4254	140	69	and	and	CCONJ
ejpam-4254	140	70	pfups	pfup	NOUN
ejpam-4254	140	71	)	)	PUNCT
ejpam-4254	140	72	of	of	ADP
ejpam-4254	140	73	u	u	PROPN
ejpam-4254	140	74	.	.	PUNCT
ejpam-4254	141	1	let	let	VERB
ejpam-4254	141	2	ρ	ρ	PROPN
ejpam-4254	141	3	=	=	SYM
ejpam-4254	141	4	{	{	PUNCT
ejpam-4254	141	5	(	(	PUNCT
ejpam-4254	141	6	0	0	NUM
ejpam-4254	141	7	,	,	PUNCT
ejpam-4254	141	8	0	0	NUM
ejpam-4254	141	9	)	)	PUNCT
ejpam-4254	141	10	,	,	PUNCT
ejpam-4254	141	11	(	(	PUNCT
ejpam-4254	141	12	1	1	NUM
ejpam-4254	141	13	,	,	PUNCT
ejpam-4254	141	14	1	1	NUM
ejpam-4254	141	15	)	)	PUNCT
ejpam-4254	141	16	,	,	PUNCT
ejpam-4254	141	17	(	(	PUNCT
ejpam-4254	141	18	2	2	NUM
ejpam-4254	141	19	,	,	PUNCT
ejpam-4254	141	20	2	2	NUM
ejpam-4254	141	21	)	)	PUNCT
ejpam-4254	141	22	,	,	PUNCT
ejpam-4254	141	23	(	(	PUNCT
ejpam-4254	141	24	3	3	NUM
ejpam-4254	141	25	,	,	PUNCT
ejpam-4254	141	26	3	3	NUM
ejpam-4254	141	27	)	)	PUNCT
ejpam-4254	141	28	,	,	PUNCT
ejpam-4254	141	29	(	(	PUNCT
ejpam-4254	141	30	0	0	NUM
ejpam-4254	141	31	,	,	PUNCT
ejpam-4254	141	32	1	1	NUM
ejpam-4254	141	33	)	)	PUNCT
ejpam-4254	141	34	,	,	PUNCT
ejpam-4254	141	35	(	(	PUNCT
ejpam-4254	141	36	1	1	NUM
ejpam-4254	141	37	,	,	PUNCT
ejpam-4254	141	38	0	0	NUM
ejpam-4254	141	39	)	)	PUNCT
ejpam-4254	141	40	,	,	PUNCT
ejpam-4254	141	41	(	(	PUNCT
ejpam-4254	141	42	0	0	NUM
ejpam-4254	141	43	,	,	PUNCT
ejpam-4254	141	44	3	3	NUM
ejpam-4254	141	45	)	)	PUNCT
ejpam-4254	141	46	,	,	PUNCT
ejpam-4254	141	47	(	(	PUNCT
ejpam-4254	141	48	3	3	NUM
ejpam-4254	141	49	,	,	PUNCT
ejpam-4254	141	50	0	0	NUM
ejpam-4254	141	51	)	)	PUNCT
ejpam-4254	141	52	,	,	PUNCT
ejpam-4254	141	53	(	(	PUNCT
ejpam-4254	141	54	1	1	NUM
ejpam-4254	141	55	,	,	PUNCT
ejpam-4254	141	56	3	3	NUM
ejpam-4254	141	57	)	)	PUNCT
ejpam-4254	141	58	,	,	PUNCT
ejpam-4254	141	59	(	(	PUNCT
ejpam-4254	141	60	3	3	NUM
ejpam-4254	141	61	,	,	PUNCT
ejpam-4254	141	62	1	1	NUM
ejpam-4254	141	63	)	)	PUNCT
ejpam-4254	141	64	}	}	PUNCT
ejpam-4254	141	65	.	.	PUNCT
ejpam-4254	142	1	then	then	ADV
ejpam-4254	142	2	ρ	ρ	PROPN
ejpam-4254	142	3	is	be	AUX
ejpam-4254	142	4	an	an	DET
ejpam-4254	142	5	er	er	INTJ
ejpam-4254	142	6	on	on	ADP
ejpam-4254	142	7	u	u	PROPN
ejpam-4254	142	8	.	.	PUNCT
ejpam-4254	143	1	but	but	CCONJ
ejpam-4254	143	2	ρ+(p	ρ+(p	NUM
ejpam-4254	143	3	)	)	PUNCT
ejpam-4254	143	4	and	and	CCONJ
ejpam-4254	143	5	ρ−(p	ρ−(p	PROPN
ejpam-4254	143	6	)	)	PUNCT
ejpam-4254	143	7	are	be	AUX
ejpam-4254	143	8	not	not	PART
ejpam-4254	143	9	pfupis	pfupis	ADJ
ejpam-4254	143	10	(	(	PUNCT
ejpam-4254	143	11	resp	resp	PROPN
ejpam-4254	143	12	.	.	PUNCT
ejpam-4254	143	13	,	,	PUNCT
ejpam-4254	143	14	pfupfs	pfupfs	PROPN
ejpam-4254	143	15	,	,	PUNCT
ejpam-4254	143	16	pfnupfs	pfnupfs	PROPN
ejpam-4254	143	17	,	,	PUNCT
ejpam-4254	143	18	and	and	CCONJ
ejpam-4254	143	19	pfupss	pfupss	NOUN
ejpam-4254	143	20	)	)	PUNCT
ejpam-4254	143	21	of	of	ADP
ejpam-4254	143	22	u	u	PROPN
ejpam-4254	143	23	.	.	PUNCT
ejpam-4254	144	1	from	from	ADP
ejpam-4254	144	2	example	example	NOUN
ejpam-4254	144	3	1	1	NUM
ejpam-4254	144	4	,	,	PUNCT
ejpam-4254	144	5	we	we	PRON
ejpam-4254	144	6	get	get	VERB
ejpam-4254	144	7	the	the	DET
ejpam-4254	144	8	results	result	NOUN
ejpam-4254	144	9	that	that	SCONJ
ejpam-4254	144	10	if	if	SCONJ
ejpam-4254	144	11	p	p	NOUN
ejpam-4254	144	12	is	be	AUX
ejpam-4254	144	13	a	a	DET
ejpam-4254	144	14	pfups	pfup	NOUN
ejpam-4254	144	15	(	(	PUNCT
ejpam-4254	144	16	resp	resp	NOUN
ejpam-4254	144	17	.	.	PUNCT
ejpam-4254	144	18	,	,	PUNCT
ejpam-4254	144	19	pfnupf	pfnupf	PROPN
ejpam-4254	144	20	,	,	PUNCT
ejpam-4254	144	21	pfupf	pfupf	NOUN
ejpam-4254	144	22	,	,	PUNCT
ejpam-4254	144	23	and	and	CCONJ
ejpam-4254	144	24	pfupi	pfupi	NOUN
ejpam-4254	144	25	)	)	PUNCT
ejpam-4254	144	26	,	,	PUNCT
ejpam-4254	144	27	then	then	ADV
ejpam-4254	144	28	it	it	PRON
ejpam-4254	144	29	may	may	AUX
ejpam-4254	144	30	not	not	PART
ejpam-4254	144	31	be	be	AUX
ejpam-4254	144	32	a	a	DET
ejpam-4254	144	33	rpfups	rpfup	NOUN
ejpam-4254	144	34	(	(	PUNCT
ejpam-4254	144	35	resp	resp	NOUN
ejpam-4254	144	36	.	.	PUNCT
ejpam-4254	144	37	,	,	PUNCT
ejpam-4254	144	38	rpfnupf	rpfnupf	PROPN
ejpam-4254	144	39	,	,	PUNCT
ejpam-4254	144	40	rpfupf	rpfupf	ADJ
ejpam-4254	144	41	,	,	PUNCT
ejpam-4254	144	42	and	and	CCONJ
ejpam-4254	144	43	rpfupi	rpfupi	NOUN
ejpam-4254	144	44	)	)	PUNCT
ejpam-4254	144	45	.	.	PUNCT
ejpam-4254	145	1	example	example	NOUN
ejpam-4254	146	1	2	2	NUM
ejpam-4254	146	2	.	.	X
ejpam-4254	146	3	consider	consider	VERB
ejpam-4254	146	4	a	a	DET
ejpam-4254	146	5	up	up	NOUN
ejpam-4254	146	6	-	-	PUNCT
ejpam-4254	146	7	algebra	algebra	NOUN
ejpam-4254	146	8	u	u	NOUN
ejpam-4254	146	9	=	=	PUNCT
ejpam-4254	146	10	(	(	PUNCT
ejpam-4254	146	11	u	u	NOUN
ejpam-4254	146	12	,	,	PUNCT
ejpam-4254	146	13	⋆	⋆	INTJ
ejpam-4254	146	14	,	,	PUNCT
ejpam-4254	146	15	0	0	NUM
ejpam-4254	146	16	)	)	PUNCT
ejpam-4254	146	17	,	,	PUNCT
ejpam-4254	146	18	where	where	SCONJ
ejpam-4254	146	19	u	u	NOUN
ejpam-4254	146	20	=	=	PUNCT
ejpam-4254	146	21	{	{	PUNCT
ejpam-4254	146	22	0	0	NUM
ejpam-4254	146	23	,	,	PUNCT
ejpam-4254	146	24	1	1	NUM
ejpam-4254	146	25	,	,	PUNCT
ejpam-4254	146	26	2	2	NUM
ejpam-4254	146	27	,	,	PUNCT
ejpam-4254	146	28	3	3	NUM
ejpam-4254	146	29	}	}	PUNCT
ejpam-4254	146	30	is	be	AUX
ejpam-4254	146	31	defined	define	VERB
ejpam-4254	146	32	in	in	ADP
ejpam-4254	146	33	the	the	DET
ejpam-4254	146	34	cayley	cayley	ADJ
ejpam-4254	146	35	table	table	NOUN
ejpam-4254	146	36	below	below	ADV
ejpam-4254	146	37	.	.	PUNCT
ejpam-4254	147	1	⋆	⋆	VERB
ejpam-4254	148	1	0	0	NUM
ejpam-4254	148	2	1	1	NUM
ejpam-4254	148	3	2	2	NUM
ejpam-4254	148	4	3	3	NUM
ejpam-4254	148	5	0	0	NUM
ejpam-4254	148	6	0	0	NUM
ejpam-4254	148	7	1	1	NUM
ejpam-4254	148	8	2	2	NUM
ejpam-4254	148	9	3	3	NUM
ejpam-4254	148	10	1	1	NUM
ejpam-4254	148	11	0	0	NUM
ejpam-4254	148	12	0	0	NUM
ejpam-4254	148	13	1	1	NUM
ejpam-4254	148	14	2	2	NUM
ejpam-4254	148	15	2	2	NUM
ejpam-4254	148	16	0	0	NUM
ejpam-4254	148	17	0	0	NUM
ejpam-4254	148	18	0	0	NUM
ejpam-4254	148	19	1	1	NUM
ejpam-4254	148	20	3	3	NUM
ejpam-4254	148	21	0	0	NUM
ejpam-4254	148	22	0	0	NUM
ejpam-4254	148	23	0	0	NUM
ejpam-4254	148	24	0	0	NUM
ejpam-4254	148	25	we	we	PRON
ejpam-4254	148	26	define	define	VERB
ejpam-4254	148	27	a	a	DET
ejpam-4254	148	28	pfs	pfs	PROPN
ejpam-4254	148	29	p	p	NOUN
ejpam-4254	148	30	=	=	X
ejpam-4254	148	31	(	(	PUNCT
ejpam-4254	148	32	µp	µp	PROPN
ejpam-4254	148	33	,	,	PUNCT
ejpam-4254	148	34	νp	νp	NOUN
ejpam-4254	148	35	)	)	PUNCT
ejpam-4254	148	36	in	in	ADP
ejpam-4254	148	37	u	u	NOUN
ejpam-4254	148	38	as	as	SCONJ
ejpam-4254	148	39	follows	follow	VERB
ejpam-4254	148	40	:	:	PUNCT
ejpam-4254	148	41	u	u	NOUN
ejpam-4254	148	42	0	0	NUM
ejpam-4254	148	43	1	1	NUM
ejpam-4254	148	44	2	2	NUM
ejpam-4254	148	45	3	3	NUM
ejpam-4254	148	46	µp	µp	NOUN
ejpam-4254	148	47	0.8	0.8	NUM
ejpam-4254	148	48	0.5	0.5	NUM
ejpam-4254	148	49	0.4	0.4	NUM
ejpam-4254	148	50	0.5	0.5	NUM
ejpam-4254	148	51	νp	νp	ADP
ejpam-4254	148	52	0.2	0.2	NUM
ejpam-4254	148	53	0.4	0.4	NUM
ejpam-4254	148	54	0.7	0.7	NUM
ejpam-4254	148	55	0.4	0.4	NUM
ejpam-4254	148	56	then	then	ADV
ejpam-4254	148	57	p	p	NOUN
ejpam-4254	148	58	is	be	AUX
ejpam-4254	148	59	not	not	PART
ejpam-4254	148	60	a	a	DET
ejpam-4254	148	61	pfups	pfup	NOUN
ejpam-4254	148	62	(	(	PUNCT
ejpam-4254	148	63	resp	resp	NOUN
ejpam-4254	148	64	.	.	PUNCT
ejpam-4254	148	65	,	,	PUNCT
ejpam-4254	148	66	pfnupf	pfnupf	PROPN
ejpam-4254	148	67	,	,	PUNCT
ejpam-4254	148	68	pfupf	pfupf	NOUN
ejpam-4254	148	69	,	,	PUNCT
ejpam-4254	148	70	and	and	CCONJ
ejpam-4254	148	71	pfupi	pfupi	NOUN
ejpam-4254	148	72	)	)	PUNCT
ejpam-4254	148	73	of	of	ADP
ejpam-4254	148	74	u	u	PROPN
ejpam-4254	148	75	.	.	PUNCT
ejpam-4254	149	1	let	let	VERB
ejpam-4254	149	2	ρ	ρ	PROPN
ejpam-4254	149	3	=	=	SYM
ejpam-4254	149	4	{	{	PUNCT
ejpam-4254	149	5	(	(	PUNCT
ejpam-4254	149	6	0	0	NUM
ejpam-4254	149	7	,	,	PUNCT
ejpam-4254	149	8	0	0	NUM
ejpam-4254	149	9	)	)	PUNCT
ejpam-4254	149	10	,	,	PUNCT
ejpam-4254	149	11	(	(	PUNCT
ejpam-4254	149	12	1	1	NUM
ejpam-4254	149	13	,	,	PUNCT
ejpam-4254	149	14	1	1	NUM
ejpam-4254	149	15	)	)	PUNCT
ejpam-4254	149	16	,	,	PUNCT
ejpam-4254	149	17	(	(	PUNCT
ejpam-4254	149	18	2	2	NUM
ejpam-4254	149	19	,	,	PUNCT
ejpam-4254	149	20	2	2	NUM
ejpam-4254	149	21	)	)	PUNCT
ejpam-4254	149	22	,	,	PUNCT
ejpam-4254	149	23	(	(	PUNCT
ejpam-4254	149	24	3	3	NUM
ejpam-4254	149	25	,	,	PUNCT
ejpam-4254	149	26	3	3	NUM
ejpam-4254	149	27	)	)	PUNCT
ejpam-4254	149	28	,	,	PUNCT
ejpam-4254	149	29	(	(	PUNCT
ejpam-4254	149	30	1	1	NUM
ejpam-4254	149	31	,	,	PUNCT
ejpam-4254	149	32	2	2	NUM
ejpam-4254	149	33	)	)	PUNCT
ejpam-4254	149	34	,	,	PUNCT
ejpam-4254	149	35	(	(	PUNCT
ejpam-4254	149	36	2	2	NUM
ejpam-4254	149	37	,	,	PUNCT
ejpam-4254	149	38	1	1	NUM
ejpam-4254	149	39	)	)	PUNCT
ejpam-4254	149	40	,	,	PUNCT
ejpam-4254	149	41	(	(	PUNCT
ejpam-4254	149	42	2	2	NUM
ejpam-4254	149	43	,	,	PUNCT
ejpam-4254	149	44	3	3	NUM
ejpam-4254	149	45	)	)	PUNCT
ejpam-4254	149	46	,	,	PUNCT
ejpam-4254	149	47	(	(	PUNCT
ejpam-4254	149	48	3	3	NUM
ejpam-4254	149	49	,	,	PUNCT
ejpam-4254	149	50	2	2	NUM
ejpam-4254	149	51	)	)	PUNCT
ejpam-4254	149	52	,	,	PUNCT
ejpam-4254	149	53	(	(	PUNCT
ejpam-4254	149	54	1	1	NUM
ejpam-4254	149	55	,	,	PUNCT
ejpam-4254	149	56	3	3	NUM
ejpam-4254	149	57	)	)	PUNCT
ejpam-4254	149	58	,	,	PUNCT
ejpam-4254	149	59	(	(	PUNCT
ejpam-4254	149	60	3	3	NUM
ejpam-4254	149	61	,	,	PUNCT
ejpam-4254	149	62	1	1	NUM
ejpam-4254	149	63	)	)	PUNCT
ejpam-4254	149	64	}	}	PUNCT
ejpam-4254	149	65	.	.	PUNCT
ejpam-4254	150	1	then	then	ADV
ejpam-4254	150	2	ρ	ρ	PROPN
ejpam-4254	150	3	is	be	AUX
ejpam-4254	150	4	an	an	DET
ejpam-4254	150	5	er	er	INTJ
ejpam-4254	150	6	on	on	ADP
ejpam-4254	150	7	u	u	PROPN
ejpam-4254	150	8	.	.	PUNCT
ejpam-4254	151	1	but	but	CCONJ
ejpam-4254	151	2	ρ+(p	ρ+(p	NUM
ejpam-4254	151	3	)	)	PUNCT
ejpam-4254	151	4	and	and	CCONJ
ejpam-4254	151	5	ρ−(p	ρ−(p	PROPN
ejpam-4254	151	6	)	)	PUNCT
ejpam-4254	151	7	are	be	AUX
ejpam-4254	151	8	pfupss	pfupss	NOUN
ejpam-4254	151	9	(	(	PUNCT
ejpam-4254	151	10	resp	resp	PROPN
ejpam-4254	151	11	.	.	PUNCT
ejpam-4254	151	12	,	,	PUNCT
ejpam-4254	151	13	pfnupfs	pfnupfs	PROPN
ejpam-4254	151	14	,	,	PUNCT
ejpam-4254	151	15	pfupfs	pfupf	NOUN
ejpam-4254	151	16	,	,	PUNCT
ejpam-4254	151	17	and	and	CCONJ
ejpam-4254	151	18	pfupis	pfupis	ADJ
ejpam-4254	151	19	)	)	PUNCT
ejpam-4254	151	20	of	of	ADP
ejpam-4254	151	21	u	u	PROPN
ejpam-4254	151	22	.	.	PUNCT
ejpam-4254	152	1	a.	a.	PROPN
ejpam-4254	152	2	iampan	iampan	PROPN
ejpam-4254	152	3	et	et	PROPN
ejpam-4254	152	4	al	al	PROPN
ejpam-4254	152	5	.	.	PUNCT
ejpam-4254	152	6	/	/	SYM
ejpam-4254	152	7	eur	eur	PROPN
ejpam-4254	152	8	.	.	PUNCT
ejpam-4254	153	1	j.	j.	PROPN
ejpam-4254	153	2	pure	pure	PROPN
ejpam-4254	153	3	appl	appl	PROPN
ejpam-4254	153	4	.	.	PROPN
ejpam-4254	153	5	math	math	PROPN
ejpam-4254	153	6	,	,	PUNCT
ejpam-4254	153	7	15	15	NUM
ejpam-4254	153	8	(	(	PUNCT
ejpam-4254	153	9	1	1	NUM
ejpam-4254	153	10	)	)	PUNCT
ejpam-4254	153	11	(	(	PUNCT
ejpam-4254	153	12	2022	2022	NUM
ejpam-4254	153	13	)	)	PUNCT
ejpam-4254	153	14	,	,	PUNCT
ejpam-4254	153	15	169	169	NUM
ejpam-4254	153	16	-	-	SYM
ejpam-4254	153	17	198	198	NUM
ejpam-4254	153	18	178	178	NUM
ejpam-4254	153	19	example	example	NOUN
ejpam-4254	153	20	3	3	NUM
ejpam-4254	153	21	.	.	X
ejpam-4254	153	22	consider	consider	VERB
ejpam-4254	153	23	a	a	DET
ejpam-4254	153	24	up	up	NOUN
ejpam-4254	153	25	-	-	PUNCT
ejpam-4254	153	26	algebra	algebra	NOUN
ejpam-4254	153	27	u	u	NOUN
ejpam-4254	153	28	=	=	PUNCT
ejpam-4254	153	29	(	(	PUNCT
ejpam-4254	153	30	u	u	NOUN
ejpam-4254	153	31	,	,	PUNCT
ejpam-4254	153	32	⋆	⋆	INTJ
ejpam-4254	153	33	,	,	PUNCT
ejpam-4254	153	34	0	0	NUM
ejpam-4254	153	35	)	)	PUNCT
ejpam-4254	153	36	,	,	PUNCT
ejpam-4254	153	37	where	where	SCONJ
ejpam-4254	153	38	u	u	NOUN
ejpam-4254	153	39	=	=	PUNCT
ejpam-4254	153	40	{	{	PUNCT
ejpam-4254	153	41	0	0	NUM
ejpam-4254	153	42	,	,	PUNCT
ejpam-4254	153	43	1	1	NUM
ejpam-4254	153	44	,	,	PUNCT
ejpam-4254	153	45	2	2	NUM
ejpam-4254	153	46	,	,	PUNCT
ejpam-4254	153	47	3	3	NUM
ejpam-4254	153	48	}	}	PUNCT
ejpam-4254	153	49	is	be	AUX
ejpam-4254	153	50	defined	define	VERB
ejpam-4254	153	51	in	in	ADP
ejpam-4254	153	52	the	the	DET
ejpam-4254	153	53	cayley	cayley	ADJ
ejpam-4254	153	54	table	table	NOUN
ejpam-4254	153	55	below	below	ADV
ejpam-4254	153	56	.	.	PUNCT
ejpam-4254	154	1	⋆	⋆	VERB
ejpam-4254	155	1	0	0	NUM
ejpam-4254	155	2	1	1	NUM
ejpam-4254	155	3	2	2	NUM
ejpam-4254	155	4	3	3	NUM
ejpam-4254	155	5	0	0	NUM
ejpam-4254	155	6	0	0	NUM
ejpam-4254	155	7	1	1	NUM
ejpam-4254	155	8	2	2	NUM
ejpam-4254	155	9	3	3	NUM
ejpam-4254	155	10	1	1	NUM
ejpam-4254	155	11	0	0	NUM
ejpam-4254	155	12	0	0	NUM
ejpam-4254	155	13	0	0	NUM
ejpam-4254	155	14	0	0	NUM
ejpam-4254	155	15	2	2	NUM
ejpam-4254	155	16	0	0	NUM
ejpam-4254	155	17	1	1	NUM
ejpam-4254	155	18	0	0	NUM
ejpam-4254	155	19	0	0	NUM
ejpam-4254	155	20	3	3	NUM
ejpam-4254	155	21	0	0	NUM
ejpam-4254	155	22	1	1	NUM
ejpam-4254	155	23	2	2	NUM
ejpam-4254	155	24	0	0	NUM
ejpam-4254	155	25	we	we	PRON
ejpam-4254	155	26	define	define	VERB
ejpam-4254	155	27	a	a	DET
ejpam-4254	155	28	pfs	pfs	PROPN
ejpam-4254	155	29	p	p	NOUN
ejpam-4254	155	30	=	=	X
ejpam-4254	155	31	(	(	PUNCT
ejpam-4254	155	32	µp	µp	PROPN
ejpam-4254	155	33	,	,	PUNCT
ejpam-4254	155	34	νp	νp	NOUN
ejpam-4254	155	35	)	)	PUNCT
ejpam-4254	155	36	in	in	ADP
ejpam-4254	155	37	u	u	NOUN
ejpam-4254	155	38	as	as	SCONJ
ejpam-4254	155	39	follows	follow	VERB
ejpam-4254	155	40	:	:	PUNCT
ejpam-4254	155	41	u	u	NOUN
ejpam-4254	155	42	0	0	NUM
ejpam-4254	155	43	1	1	NUM
ejpam-4254	155	44	2	2	NUM
ejpam-4254	155	45	3	3	NUM
ejpam-4254	155	46	µp	µp	NOUN
ejpam-4254	155	47	0.5	0.5	NUM
ejpam-4254	155	48	0.4	0.4	NUM
ejpam-4254	155	49	0.3	0.3	NUM
ejpam-4254	155	50	0.2	0.2	NUM
ejpam-4254	155	51	νp	νp	ADP
ejpam-4254	155	52	0.1	0.1	NUM
ejpam-4254	155	53	0.2	0.2	NUM
ejpam-4254	155	54	0.3	0.3	NUM
ejpam-4254	155	55	0.4	0.4	NUM
ejpam-4254	155	56	then	then	ADV
ejpam-4254	155	57	p	p	NOUN
ejpam-4254	155	58	is	be	AUX
ejpam-4254	155	59	not	not	PART
ejpam-4254	155	60	a	a	DET
ejpam-4254	155	61	pfsupi	pfsupi	NOUN
ejpam-4254	155	62	of	of	ADP
ejpam-4254	155	63	u	u	PROPN
ejpam-4254	155	64	.	.	PUNCT
ejpam-4254	156	1	let	let	VERB
ejpam-4254	156	2	ρ	ρ	PROPN
ejpam-4254	156	3	=	=	SYM
ejpam-4254	156	4	{	{	PUNCT
ejpam-4254	156	5	(	(	PUNCT
ejpam-4254	156	6	0	0	NUM
ejpam-4254	156	7	,	,	PUNCT
ejpam-4254	156	8	0	0	NUM
ejpam-4254	156	9	)	)	PUNCT
ejpam-4254	156	10	,	,	PUNCT
ejpam-4254	156	11	(	(	PUNCT
ejpam-4254	156	12	1	1	NUM
ejpam-4254	156	13	,	,	PUNCT
ejpam-4254	156	14	1	1	NUM
ejpam-4254	156	15	)	)	PUNCT
ejpam-4254	156	16	,	,	PUNCT
ejpam-4254	156	17	(	(	PUNCT
ejpam-4254	156	18	2	2	NUM
ejpam-4254	156	19	,	,	PUNCT
ejpam-4254	156	20	2	2	NUM
ejpam-4254	156	21	)	)	PUNCT
ejpam-4254	156	22	,	,	PUNCT
ejpam-4254	156	23	(	(	PUNCT
ejpam-4254	156	24	3	3	NUM
ejpam-4254	156	25	,	,	PUNCT
ejpam-4254	156	26	3	3	NUM
ejpam-4254	156	27	)	)	PUNCT
ejpam-4254	156	28	,	,	PUNCT
ejpam-4254	156	29	(	(	PUNCT
ejpam-4254	156	30	0	0	NUM
ejpam-4254	156	31	,	,	PUNCT
ejpam-4254	156	32	1	1	NUM
ejpam-4254	156	33	)	)	PUNCT
ejpam-4254	156	34	,	,	PUNCT
ejpam-4254	156	35	(	(	PUNCT
ejpam-4254	156	36	1	1	NUM
ejpam-4254	156	37	,	,	PUNCT
ejpam-4254	156	38	0	0	NUM
ejpam-4254	156	39	)	)	PUNCT
ejpam-4254	156	40	,	,	PUNCT
ejpam-4254	156	41	(	(	PUNCT
ejpam-4254	156	42	0	0	NUM
ejpam-4254	156	43	,	,	PUNCT
ejpam-4254	156	44	2	2	NUM
ejpam-4254	156	45	)	)	PUNCT
ejpam-4254	156	46	,	,	PUNCT
ejpam-4254	156	47	(	(	PUNCT
ejpam-4254	156	48	2	2	NUM
ejpam-4254	156	49	,	,	PUNCT
ejpam-4254	156	50	0	0	NUM
ejpam-4254	156	51	)	)	PUNCT
ejpam-4254	156	52	,	,	PUNCT
ejpam-4254	156	53	(	(	PUNCT
ejpam-4254	156	54	0	0	NUM
ejpam-4254	156	55	,	,	PUNCT
ejpam-4254	156	56	3	3	NUM
ejpam-4254	156	57	)	)	PUNCT
ejpam-4254	156	58	,	,	PUNCT
ejpam-4254	156	59	(	(	PUNCT
ejpam-4254	156	60	3	3	NUM
ejpam-4254	156	61	,	,	PUNCT
ejpam-4254	156	62	0	0	NUM
ejpam-4254	156	63	)	)	PUNCT
ejpam-4254	156	64	,	,	PUNCT
ejpam-4254	156	65	(	(	PUNCT
ejpam-4254	156	66	1	1	NUM
ejpam-4254	156	67	,	,	PUNCT
ejpam-4254	156	68	2	2	NUM
ejpam-4254	156	69	)	)	PUNCT
ejpam-4254	156	70	,	,	PUNCT
ejpam-4254	156	71	(	(	PUNCT
ejpam-4254	156	72	2	2	NUM
ejpam-4254	156	73	,	,	PUNCT
ejpam-4254	156	74	1	1	NUM
ejpam-4254	156	75	)	)	PUNCT
ejpam-4254	156	76	,	,	PUNCT
ejpam-4254	156	77	(	(	PUNCT
ejpam-4254	156	78	2	2	NUM
ejpam-4254	156	79	,	,	PUNCT
ejpam-4254	156	80	3	3	NUM
ejpam-4254	156	81	)	)	PUNCT
ejpam-4254	156	82	,	,	PUNCT
ejpam-4254	156	83	(	(	PUNCT
ejpam-4254	156	84	3	3	NUM
ejpam-4254	156	85	,	,	PUNCT
ejpam-4254	156	86	2	2	NUM
ejpam-4254	156	87	)	)	PUNCT
ejpam-4254	156	88	,	,	PUNCT
ejpam-4254	156	89	(	(	PUNCT
ejpam-4254	156	90	1	1	NUM
ejpam-4254	156	91	,	,	PUNCT
ejpam-4254	156	92	3	3	NUM
ejpam-4254	156	93	)	)	PUNCT
ejpam-4254	156	94	,	,	PUNCT
ejpam-4254	156	95	(	(	PUNCT
ejpam-4254	156	96	3	3	NUM
ejpam-4254	156	97	,	,	PUNCT
ejpam-4254	156	98	1	1	NUM
ejpam-4254	156	99	)	)	PUNCT
ejpam-4254	156	100	}	}	PUNCT
ejpam-4254	156	101	.	.	PUNCT
ejpam-4254	157	1	then	then	ADV
ejpam-4254	157	2	ρ	ρ	PROPN
ejpam-4254	157	3	is	be	AUX
ejpam-4254	157	4	an	an	DET
ejpam-4254	157	5	er	er	INTJ
ejpam-4254	157	6	on	on	ADP
ejpam-4254	157	7	u	u	PROPN
ejpam-4254	157	8	.	.	PUNCT
ejpam-4254	158	1	but	but	CCONJ
ejpam-4254	158	2	ρ+(p	ρ+(p	NUM
ejpam-4254	158	3	)	)	PUNCT
ejpam-4254	158	4	and	and	CCONJ
ejpam-4254	158	5	ρ−(p	ρ−(p	PROPN
ejpam-4254	158	6	)	)	PUNCT
ejpam-4254	158	7	are	be	AUX
ejpam-4254	158	8	pfsupis	pfsupi	VERB
ejpam-4254	158	9	of	of	ADP
ejpam-4254	158	10	u	u	NOUN
ejpam-4254	158	11	.	.	PUNCT
ejpam-4254	159	1	from	from	ADP
ejpam-4254	159	2	examples	example	NOUN
ejpam-4254	159	3	2	2	NUM
ejpam-4254	159	4	and	and	CCONJ
ejpam-4254	159	5	3	3	NUM
ejpam-4254	159	6	,	,	PUNCT
ejpam-4254	159	7	we	we	PRON
ejpam-4254	159	8	get	get	VERB
ejpam-4254	159	9	the	the	DET
ejpam-4254	159	10	results	result	NOUN
ejpam-4254	159	11	that	that	SCONJ
ejpam-4254	159	12	if	if	SCONJ
ejpam-4254	159	13	p	p	NOUN
ejpam-4254	159	14	is	be	AUX
ejpam-4254	159	15	a	a	DET
ejpam-4254	159	16	rpfups	rpfup	NOUN
ejpam-4254	159	17	(	(	PUNCT
ejpam-4254	159	18	resp	resp	NOUN
ejpam-4254	159	19	.	.	PUNCT
ejpam-4254	159	20	,	,	PUNCT
ejpam-4254	159	21	rpfnupf	rpfnupf	PROPN
ejpam-4254	159	22	,	,	PUNCT
ejpam-4254	159	23	rpfupf	rpfupf	PROPN
ejpam-4254	159	24	,	,	PUNCT
ejpam-4254	159	25	rpfupi	rpfupi	NOUN
ejpam-4254	159	26	,	,	PUNCT
ejpam-4254	159	27	and	and	CCONJ
ejpam-4254	159	28	rpfsupi	rpfsupi	NOUN
ejpam-4254	159	29	)	)	PUNCT
ejpam-4254	159	30	,	,	PUNCT
ejpam-4254	159	31	then	then	ADV
ejpam-4254	159	32	it	it	PRON
ejpam-4254	159	33	may	may	AUX
ejpam-4254	159	34	not	not	PART
ejpam-4254	159	35	be	be	AUX
ejpam-4254	159	36	a	a	DET
ejpam-4254	159	37	pfups	pfup	NOUN
ejpam-4254	159	38	(	(	PUNCT
ejpam-4254	159	39	resp	resp	NOUN
ejpam-4254	159	40	.	.	PUNCT
ejpam-4254	159	41	,	,	PUNCT
ejpam-4254	159	42	pfnupf	pfnupf	PROPN
ejpam-4254	159	43	,	,	PUNCT
ejpam-4254	159	44	pfupf	pfupf	NOUN
ejpam-4254	159	45	,	,	PUNCT
ejpam-4254	159	46	pfupi	pfupi	NOUN
ejpam-4254	159	47	,	,	PUNCT
ejpam-4254	159	48	and	and	CCONJ
ejpam-4254	159	49	pfsupi	pfsupi	NOUN
ejpam-4254	159	50	)	)	PUNCT
ejpam-4254	159	51	.	.	PUNCT
ejpam-4254	160	1	example	example	NOUN
ejpam-4254	161	1	4	4	X
ejpam-4254	161	2	.	.	X
ejpam-4254	161	3	consider	consider	VERB
ejpam-4254	161	4	a	a	DET
ejpam-4254	161	5	up	up	NOUN
ejpam-4254	161	6	-	-	PUNCT
ejpam-4254	161	7	algebra	algebra	NOUN
ejpam-4254	161	8	u	u	NOUN
ejpam-4254	161	9	=	=	PUNCT
ejpam-4254	161	10	(	(	PUNCT
ejpam-4254	161	11	u	u	NOUN
ejpam-4254	161	12	,	,	PUNCT
ejpam-4254	161	13	⋆	⋆	INTJ
ejpam-4254	161	14	,	,	PUNCT
ejpam-4254	161	15	0	0	NUM
ejpam-4254	161	16	)	)	PUNCT
ejpam-4254	161	17	,	,	PUNCT
ejpam-4254	161	18	where	where	SCONJ
ejpam-4254	161	19	u	u	NOUN
ejpam-4254	161	20	=	=	PUNCT
ejpam-4254	161	21	{	{	PUNCT
ejpam-4254	161	22	0	0	NUM
ejpam-4254	161	23	,	,	PUNCT
ejpam-4254	161	24	1	1	NUM
ejpam-4254	161	25	,	,	PUNCT
ejpam-4254	161	26	2	2	NUM
ejpam-4254	161	27	,	,	PUNCT
ejpam-4254	161	28	3	3	NUM
ejpam-4254	161	29	}	}	PUNCT
ejpam-4254	161	30	is	be	AUX
ejpam-4254	161	31	defined	define	VERB
ejpam-4254	161	32	in	in	ADP
ejpam-4254	161	33	the	the	DET
ejpam-4254	161	34	cayley	cayley	ADJ
ejpam-4254	161	35	table	table	NOUN
ejpam-4254	161	36	below	below	ADV
ejpam-4254	161	37	.	.	PUNCT
ejpam-4254	162	1	⋆	⋆	VERB
ejpam-4254	163	1	0	0	NUM
ejpam-4254	163	2	1	1	NUM
ejpam-4254	163	3	2	2	NUM
ejpam-4254	163	4	3	3	NUM
ejpam-4254	163	5	0	0	NUM
ejpam-4254	163	6	0	0	NUM
ejpam-4254	163	7	1	1	NUM
ejpam-4254	163	8	2	2	NUM
ejpam-4254	163	9	3	3	NUM
ejpam-4254	163	10	1	1	NUM
ejpam-4254	163	11	0	0	NUM
ejpam-4254	163	12	0	0	NUM
ejpam-4254	163	13	2	2	NUM
ejpam-4254	163	14	3	3	NUM
ejpam-4254	163	15	2	2	NUM
ejpam-4254	163	16	0	0	NUM
ejpam-4254	163	17	1	1	NUM
ejpam-4254	163	18	0	0	NUM
ejpam-4254	163	19	0	0	NUM
ejpam-4254	163	20	3	3	NUM
ejpam-4254	163	21	0	0	NUM
ejpam-4254	163	22	1	1	NUM
ejpam-4254	163	23	2	2	NUM
ejpam-4254	163	24	0	0	NUM
ejpam-4254	163	25	we	we	PRON
ejpam-4254	163	26	define	define	VERB
ejpam-4254	163	27	a	a	DET
ejpam-4254	163	28	pfs	pfs	PROPN
ejpam-4254	163	29	p	p	NOUN
ejpam-4254	163	30	=	=	X
ejpam-4254	163	31	(	(	PUNCT
ejpam-4254	163	32	µp	µp	PROPN
ejpam-4254	163	33	,	,	PUNCT
ejpam-4254	163	34	νp	νp	NOUN
ejpam-4254	163	35	)	)	PUNCT
ejpam-4254	163	36	in	in	ADP
ejpam-4254	163	37	u	u	NOUN
ejpam-4254	163	38	as	as	SCONJ
ejpam-4254	163	39	follows	follow	VERB
ejpam-4254	163	40	:	:	PUNCT
ejpam-4254	163	41	u	u	NOUN
ejpam-4254	163	42	0	0	NUM
ejpam-4254	163	43	1	1	NUM
ejpam-4254	163	44	2	2	NUM
ejpam-4254	163	45	3	3	NUM
ejpam-4254	163	46	µp	µp	NOUN
ejpam-4254	163	47	1	1	NUM
ejpam-4254	163	48	0.2	0.2	NUM
ejpam-4254	163	49	0.1	0.1	NUM
ejpam-4254	163	50	0.2	0.2	NUM
ejpam-4254	163	51	νp	νp	ADP
ejpam-4254	163	52	0	0	NUM
ejpam-4254	163	53	0.6	0.6	NUM
ejpam-4254	163	54	0.9	0.9	NUM
ejpam-4254	163	55	0.6	0.6	NUM
ejpam-4254	163	56	then	then	ADV
ejpam-4254	163	57	p	p	NOUN
ejpam-4254	163	58	is	be	AUX
ejpam-4254	163	59	a	a	DET
ejpam-4254	163	60	pfupi	pfupi	NOUN
ejpam-4254	163	61	(	(	PUNCT
ejpam-4254	163	62	resp	resp	NOUN
ejpam-4254	163	63	.	.	PUNCT
ejpam-4254	163	64	,	,	PUNCT
ejpam-4254	163	65	pfupf	pfupf	NOUN
ejpam-4254	163	66	,	,	PUNCT
ejpam-4254	163	67	pfnupf	pfnupf	NOUN
ejpam-4254	163	68	,	,	PUNCT
ejpam-4254	163	69	and	and	CCONJ
ejpam-4254	163	70	pfups	pfup	NOUN
ejpam-4254	163	71	)	)	PUNCT
ejpam-4254	163	72	of	of	ADP
ejpam-4254	163	73	u	u	PROPN
ejpam-4254	163	74	.	.	PUNCT
ejpam-4254	164	1	let	let	VERB
ejpam-4254	164	2	ρ	ρ	PROPN
ejpam-4254	164	3	=	=	SYM
ejpam-4254	164	4	{	{	PUNCT
ejpam-4254	164	5	(	(	PUNCT
ejpam-4254	164	6	0	0	NUM
ejpam-4254	164	7	,	,	PUNCT
ejpam-4254	164	8	0	0	NUM
ejpam-4254	164	9	)	)	PUNCT
ejpam-4254	164	10	,	,	PUNCT
ejpam-4254	164	11	(	(	PUNCT
ejpam-4254	164	12	1	1	NUM
ejpam-4254	164	13	,	,	PUNCT
ejpam-4254	164	14	1	1	NUM
ejpam-4254	164	15	)	)	PUNCT
ejpam-4254	164	16	,	,	PUNCT
ejpam-4254	164	17	(	(	PUNCT
ejpam-4254	164	18	2	2	NUM
ejpam-4254	164	19	,	,	PUNCT
ejpam-4254	164	20	2	2	NUM
ejpam-4254	164	21	)	)	PUNCT
ejpam-4254	164	22	,	,	PUNCT
ejpam-4254	164	23	(	(	PUNCT
ejpam-4254	164	24	3	3	NUM
ejpam-4254	164	25	,	,	PUNCT
ejpam-4254	164	26	3	3	NUM
ejpam-4254	164	27	)	)	PUNCT
ejpam-4254	164	28	,	,	PUNCT
ejpam-4254	164	29	(	(	PUNCT
ejpam-4254	164	30	1	1	NUM
ejpam-4254	164	31	,	,	PUNCT
ejpam-4254	164	32	2	2	NUM
ejpam-4254	164	33	)	)	PUNCT
ejpam-4254	164	34	,	,	PUNCT
ejpam-4254	164	35	(	(	PUNCT
ejpam-4254	164	36	2	2	NUM
ejpam-4254	164	37	,	,	PUNCT
ejpam-4254	164	38	1	1	NUM
ejpam-4254	164	39	)	)	PUNCT
ejpam-4254	164	40	}	}	PUNCT
ejpam-4254	164	41	.	.	PUNCT
ejpam-4254	165	1	then	then	ADV
ejpam-4254	165	2	ρ	ρ	PROPN
ejpam-4254	165	3	is	be	AUX
ejpam-4254	165	4	an	an	DET
ejpam-4254	165	5	er	er	INTJ
ejpam-4254	165	6	on	on	ADP
ejpam-4254	165	7	u	u	PROPN
ejpam-4254	165	8	.	.	PUNCT
ejpam-4254	166	1	thus	thus	ADV
ejpam-4254	166	2	ρ+(p	ρ+(p	VERB
ejpam-4254	166	3	)	)	PUNCT
ejpam-4254	166	4	and	and	CCONJ
ejpam-4254	166	5	ρ−(p	ρ−(p	PROPN
ejpam-4254	166	6	)	)	PUNCT
ejpam-4254	166	7	are	be	AUX
ejpam-4254	166	8	pfupis	pfupis	ADJ
ejpam-4254	166	9	(	(	PUNCT
ejpam-4254	166	10	resp	resp	PROPN
ejpam-4254	166	11	.	.	PUNCT
ejpam-4254	166	12	,	,	PUNCT
ejpam-4254	166	13	pfupfs	pfupfs	PROPN
ejpam-4254	166	14	,	,	PUNCT
ejpam-4254	166	15	pfnupfs	pfnupfs	PROPN
ejpam-4254	166	16	,	,	PUNCT
ejpam-4254	166	17	and	and	CCONJ
ejpam-4254	166	18	pfupss	pfupss	NOUN
ejpam-4254	166	19	)	)	PUNCT
ejpam-4254	166	20	of	of	ADP
ejpam-4254	166	21	u	u	PROPN
ejpam-4254	166	22	.	.	PUNCT
ejpam-4254	167	1	a.	a.	PROPN
ejpam-4254	167	2	iampan	iampan	PROPN
ejpam-4254	167	3	et	et	PROPN
ejpam-4254	167	4	al	al	PROPN
ejpam-4254	167	5	.	.	PUNCT
ejpam-4254	167	6	/	/	SYM
ejpam-4254	167	7	eur	eur	PROPN
ejpam-4254	167	8	.	.	PUNCT
ejpam-4254	168	1	j.	j.	PROPN
ejpam-4254	168	2	pure	pure	PROPN
ejpam-4254	168	3	appl	appl	PROPN
ejpam-4254	168	4	.	.	PROPN
ejpam-4254	168	5	math	math	PROPN
ejpam-4254	168	6	,	,	PUNCT
ejpam-4254	168	7	15	15	NUM
ejpam-4254	168	8	(	(	PUNCT
ejpam-4254	168	9	1	1	NUM
ejpam-4254	168	10	)	)	PUNCT
ejpam-4254	168	11	(	(	PUNCT
ejpam-4254	168	12	2022	2022	NUM
ejpam-4254	168	13	)	)	PUNCT
ejpam-4254	168	14	,	,	PUNCT
ejpam-4254	168	15	169	169	NUM
ejpam-4254	168	16	-	-	SYM
ejpam-4254	168	17	198	198	NUM
ejpam-4254	168	18	179	179	NUM
ejpam-4254	168	19	from	from	ADP
ejpam-4254	168	20	example	example	NOUN
ejpam-4254	168	21	4	4	NUM
ejpam-4254	168	22	and	and	CCONJ
ejpam-4254	168	23	theorem	theorem	VERB
ejpam-4254	168	24	1	1	NUM
ejpam-4254	168	25	,	,	PUNCT
ejpam-4254	168	26	we	we	PRON
ejpam-4254	168	27	get	get	VERB
ejpam-4254	168	28	the	the	DET
ejpam-4254	168	29	results	result	NOUN
ejpam-4254	168	30	that	that	PRON
ejpam-4254	168	31	p	p	PROPN
ejpam-4254	168	32	can	can	AUX
ejpam-4254	168	33	be	be	AUX
ejpam-4254	168	34	a	a	DET
ejpam-4254	168	35	rpfups	rpfup	NOUN
ejpam-4254	168	36	(	(	PUNCT
ejpam-4254	168	37	resp	resp	NOUN
ejpam-4254	168	38	.	.	PUNCT
ejpam-4254	168	39	,	,	PUNCT
ejpam-4254	168	40	rpfnupf	rpfnupf	PROPN
ejpam-4254	168	41	,	,	PUNCT
ejpam-4254	168	42	rpfupf	rpfupf	PROPN
ejpam-4254	168	43	,	,	PUNCT
ejpam-4254	168	44	rpfupi	rpfupi	NOUN
ejpam-4254	168	45	,	,	PUNCT
ejpam-4254	168	46	and	and	CCONJ
ejpam-4254	168	47	rpfsupi	rpfsupi	NOUN
ejpam-4254	168	48	)	)	PUNCT
ejpam-4254	168	49	and	and	CCONJ
ejpam-4254	168	50	a	a	DET
ejpam-4254	168	51	pfups	pfup	NOUN
ejpam-4254	168	52	(	(	PUNCT
ejpam-4254	168	53	resp	resp	NOUN
ejpam-4254	168	54	.	.	PUNCT
ejpam-4254	168	55	,	,	PUNCT
ejpam-4254	168	56	pfnupf	pfnupf	PROPN
ejpam-4254	168	57	,	,	PUNCT
ejpam-4254	168	58	pfupf	pfupf	NOUN
ejpam-4254	168	59	,	,	PUNCT
ejpam-4254	168	60	pfupi	pfupi	NOUN
ejpam-4254	168	61	,	,	PUNCT
ejpam-4254	168	62	and	and	CCONJ
ejpam-4254	168	63	pfsupi	pfsupi	NOUN
ejpam-4254	168	64	)	)	PUNCT
ejpam-4254	168	65	in	in	ADP
ejpam-4254	168	66	the	the	DET
ejpam-4254	168	67	same	same	ADJ
ejpam-4254	168	68	time	time	NOUN
ejpam-4254	168	69	.	.	PUNCT
ejpam-4254	169	1	the	the	DET
ejpam-4254	169	2	following	follow	VERB
ejpam-4254	169	3	examples	example	NOUN
ejpam-4254	169	4	show	show	VERB
ejpam-4254	169	5	the	the	DET
ejpam-4254	169	6	relationships	relationship	NOUN
ejpam-4254	169	7	between	between	ADP
ejpam-4254	169	8	pfss	pfss	NOUN
ejpam-4254	169	9	in	in	ADP
ejpam-4254	169	10	u	u	NOUN
ejpam-4254	169	11	and	and	CCONJ
ejpam-4254	169	12	rpfss	rpfss	VERB
ejpam-4254	169	13	in	in	ADP
ejpam-4254	169	14	u	u	NOUN
ejpam-4254	169	15	with	with	ADP
ejpam-4254	169	16	ρ	ρ	PROPN
ejpam-4254	169	17	is	be	AUX
ejpam-4254	169	18	a	a	DET
ejpam-4254	169	19	cr	cr	NOUN
ejpam-4254	169	20	on	on	ADP
ejpam-4254	169	21	u	u	PROPN
ejpam-4254	169	22	.	.	PUNCT
ejpam-4254	169	23	example	example	NOUN
ejpam-4254	170	1	5	5	NUM
ejpam-4254	170	2	.	.	X
ejpam-4254	170	3	consider	consider	VERB
ejpam-4254	170	4	a	a	DET
ejpam-4254	170	5	up	up	NOUN
ejpam-4254	170	6	-	-	PUNCT
ejpam-4254	170	7	algebra	algebra	NOUN
ejpam-4254	170	8	u	u	NOUN
ejpam-4254	170	9	=	=	PUNCT
ejpam-4254	170	10	(	(	PUNCT
ejpam-4254	170	11	u	u	NOUN
ejpam-4254	170	12	,	,	PUNCT
ejpam-4254	170	13	⋆	⋆	INTJ
ejpam-4254	170	14	,	,	PUNCT
ejpam-4254	170	15	0	0	NUM
ejpam-4254	170	16	)	)	PUNCT
ejpam-4254	170	17	,	,	PUNCT
ejpam-4254	170	18	where	where	SCONJ
ejpam-4254	170	19	u	u	NOUN
ejpam-4254	170	20	=	=	PUNCT
ejpam-4254	170	21	{	{	PUNCT
ejpam-4254	170	22	0	0	NUM
ejpam-4254	170	23	,	,	PUNCT
ejpam-4254	170	24	1	1	NUM
ejpam-4254	170	25	,	,	PUNCT
ejpam-4254	170	26	2	2	NUM
ejpam-4254	170	27	,	,	PUNCT
ejpam-4254	170	28	3	3	NUM
ejpam-4254	170	29	}	}	PUNCT
ejpam-4254	170	30	is	be	AUX
ejpam-4254	170	31	defined	define	VERB
ejpam-4254	170	32	in	in	ADP
ejpam-4254	170	33	the	the	DET
ejpam-4254	170	34	cayley	cayley	ADJ
ejpam-4254	170	35	table	table	NOUN
ejpam-4254	170	36	below	below	ADV
ejpam-4254	170	37	.	.	PUNCT
ejpam-4254	171	1	⋆	⋆	VERB
ejpam-4254	172	1	0	0	NUM
ejpam-4254	172	2	1	1	NUM
ejpam-4254	172	3	2	2	NUM
ejpam-4254	172	4	3	3	NUM
ejpam-4254	172	5	0	0	NUM
ejpam-4254	172	6	0	0	NUM
ejpam-4254	172	7	1	1	NUM
ejpam-4254	172	8	2	2	NUM
ejpam-4254	172	9	3	3	NUM
ejpam-4254	172	10	1	1	NUM
ejpam-4254	172	11	0	0	NUM
ejpam-4254	172	12	0	0	NUM
ejpam-4254	172	13	2	2	NUM
ejpam-4254	172	14	3	3	NUM
ejpam-4254	172	15	2	2	NUM
ejpam-4254	172	16	0	0	NUM
ejpam-4254	172	17	1	1	NUM
ejpam-4254	172	18	0	0	NUM
ejpam-4254	172	19	3	3	NUM
ejpam-4254	172	20	3	3	NUM
ejpam-4254	172	21	0	0	NUM
ejpam-4254	172	22	1	1	NUM
ejpam-4254	172	23	2	2	NUM
ejpam-4254	172	24	0	0	NUM
ejpam-4254	172	25	we	we	PRON
ejpam-4254	172	26	define	define	VERB
ejpam-4254	172	27	a	a	DET
ejpam-4254	172	28	pfs	pfs	PROPN
ejpam-4254	172	29	p	p	NOUN
ejpam-4254	172	30	=	=	X
ejpam-4254	172	31	(	(	PUNCT
ejpam-4254	172	32	µp	µp	PROPN
ejpam-4254	172	33	,	,	PUNCT
ejpam-4254	172	34	νp	νp	NOUN
ejpam-4254	172	35	)	)	PUNCT
ejpam-4254	172	36	in	in	ADP
ejpam-4254	172	37	u	u	NOUN
ejpam-4254	172	38	as	as	SCONJ
ejpam-4254	172	39	follows	follow	VERB
ejpam-4254	172	40	:	:	PUNCT
ejpam-4254	172	41	u	u	NOUN
ejpam-4254	172	42	0	0	NUM
ejpam-4254	172	43	1	1	NUM
ejpam-4254	172	44	2	2	NUM
ejpam-4254	172	45	3	3	NUM
ejpam-4254	172	46	µp	µp	NOUN
ejpam-4254	172	47	0.8	0.8	NUM
ejpam-4254	172	48	0.3	0.3	NUM
ejpam-4254	172	49	0.5	0.5	NUM
ejpam-4254	172	50	0.5	0.5	NUM
ejpam-4254	172	51	νp	νp	ADP
ejpam-4254	172	52	0.2	0.2	NUM
ejpam-4254	172	53	0.8	0.8	NUM
ejpam-4254	172	54	0.3	0.3	NUM
ejpam-4254	172	55	0.3	0.3	NUM
ejpam-4254	172	56	then	then	ADV
ejpam-4254	172	57	p	p	NOUN
ejpam-4254	172	58	is	be	AUX
ejpam-4254	172	59	a	a	DET
ejpam-4254	172	60	pfupi	pfupi	NOUN
ejpam-4254	172	61	(	(	PUNCT
ejpam-4254	172	62	resp	resp	NOUN
ejpam-4254	172	63	.	.	PUNCT
ejpam-4254	172	64	,	,	PUNCT
ejpam-4254	172	65	pfupf	pfupf	NOUN
ejpam-4254	172	66	,	,	PUNCT
ejpam-4254	172	67	pfnupf	pfnupf	NOUN
ejpam-4254	172	68	,	,	PUNCT
ejpam-4254	172	69	and	and	CCONJ
ejpam-4254	172	70	pfups	pfup	NOUN
ejpam-4254	172	71	)	)	PUNCT
ejpam-4254	172	72	of	of	ADP
ejpam-4254	172	73	u	u	PROPN
ejpam-4254	172	74	.	.	PUNCT
ejpam-4254	173	1	let	let	VERB
ejpam-4254	173	2	ρ	ρ	PROPN
ejpam-4254	173	3	=	=	SYM
ejpam-4254	173	4	{	{	PUNCT
ejpam-4254	173	5	(	(	PUNCT
ejpam-4254	173	6	0	0	NUM
ejpam-4254	173	7	,	,	PUNCT
ejpam-4254	173	8	0	0	NUM
ejpam-4254	173	9	)	)	PUNCT
ejpam-4254	173	10	,	,	PUNCT
ejpam-4254	173	11	(	(	PUNCT
ejpam-4254	173	12	1	1	NUM
ejpam-4254	173	13	,	,	PUNCT
ejpam-4254	173	14	1	1	NUM
ejpam-4254	173	15	)	)	PUNCT
ejpam-4254	173	16	,	,	PUNCT
ejpam-4254	173	17	(	(	PUNCT
ejpam-4254	173	18	2	2	NUM
ejpam-4254	173	19	,	,	PUNCT
ejpam-4254	173	20	2	2	NUM
ejpam-4254	173	21	)	)	PUNCT
ejpam-4254	173	22	,	,	PUNCT
ejpam-4254	173	23	(	(	PUNCT
ejpam-4254	173	24	3	3	NUM
ejpam-4254	173	25	,	,	PUNCT
ejpam-4254	173	26	3	3	NUM
ejpam-4254	173	27	)	)	PUNCT
ejpam-4254	173	28	,	,	PUNCT
ejpam-4254	173	29	(	(	PUNCT
ejpam-4254	173	30	0	0	NUM
ejpam-4254	173	31	,	,	PUNCT
ejpam-4254	173	32	1	1	NUM
ejpam-4254	173	33	)	)	PUNCT
ejpam-4254	173	34	,	,	PUNCT
ejpam-4254	173	35	(	(	PUNCT
ejpam-4254	173	36	1	1	NUM
ejpam-4254	173	37	,	,	PUNCT
ejpam-4254	173	38	0	0	NUM
ejpam-4254	173	39	)	)	PUNCT
ejpam-4254	173	40	}	}	PUNCT
ejpam-4254	173	41	.	.	PUNCT
ejpam-4254	174	1	then	then	ADV
ejpam-4254	174	2	ρ	ρ	PROPN
ejpam-4254	174	3	is	be	AUX
ejpam-4254	174	4	a	a	DET
ejpam-4254	174	5	cr	cr	NOUN
ejpam-4254	174	6	on	on	ADP
ejpam-4254	174	7	u	u	PROPN
ejpam-4254	174	8	.	.	PUNCT
ejpam-4254	175	1	but	but	CCONJ
ejpam-4254	175	2	ρ−(p	ρ−(p	PROPN
ejpam-4254	175	3	)	)	PUNCT
ejpam-4254	175	4	is	be	AUX
ejpam-4254	175	5	not	not	PART
ejpam-4254	175	6	a	a	DET
ejpam-4254	175	7	pfupi	pfupi	NOUN
ejpam-4254	175	8	(	(	PUNCT
ejpam-4254	175	9	resp	resp	NOUN
ejpam-4254	175	10	.	.	PUNCT
ejpam-4254	175	11	,	,	PUNCT
ejpam-4254	175	12	pfupf	pfupf	NOUN
ejpam-4254	175	13	,	,	PUNCT
ejpam-4254	175	14	pfnupf	pfnupf	NOUN
ejpam-4254	175	15	,	,	PUNCT
ejpam-4254	175	16	and	and	CCONJ
ejpam-4254	175	17	pfups	pfup	NOUN
ejpam-4254	175	18	)	)	PUNCT
ejpam-4254	175	19	of	of	ADP
ejpam-4254	175	20	u	u	PROPN
ejpam-4254	175	21	.	.	PUNCT
ejpam-4254	176	1	from	from	ADP
ejpam-4254	176	2	example	example	NOUN
ejpam-4254	176	3	5	5	NUM
ejpam-4254	176	4	,	,	PUNCT
ejpam-4254	176	5	we	we	PRON
ejpam-4254	176	6	get	get	VERB
ejpam-4254	176	7	the	the	DET
ejpam-4254	176	8	results	result	NOUN
ejpam-4254	176	9	that	that	SCONJ
ejpam-4254	176	10	if	if	SCONJ
ejpam-4254	176	11	p	p	NOUN
ejpam-4254	176	12	is	be	AUX
ejpam-4254	176	13	a	a	DET
ejpam-4254	176	14	pfups	pfup	NOUN
ejpam-4254	176	15	(	(	PUNCT
ejpam-4254	176	16	resp	resp	NOUN
ejpam-4254	176	17	.	.	PUNCT
ejpam-4254	176	18	,	,	PUNCT
ejpam-4254	176	19	pfnupf	pfnupf	PROPN
ejpam-4254	176	20	,	,	PUNCT
ejpam-4254	176	21	pfupf	pfupf	NOUN
ejpam-4254	176	22	,	,	PUNCT
ejpam-4254	176	23	and	and	CCONJ
ejpam-4254	176	24	pfupi	pfupi	NOUN
ejpam-4254	176	25	)	)	PUNCT
ejpam-4254	176	26	,	,	PUNCT
ejpam-4254	176	27	then	then	ADV
ejpam-4254	176	28	it	it	PRON
ejpam-4254	176	29	may	may	AUX
ejpam-4254	176	30	not	not	PART
ejpam-4254	176	31	be	be	AUX
ejpam-4254	176	32	a	a	DET
ejpam-4254	176	33	rpfups	rpfup	NOUN
ejpam-4254	176	34	(	(	PUNCT
ejpam-4254	176	35	resp	resp	NOUN
ejpam-4254	176	36	.	.	PUNCT
ejpam-4254	176	37	,	,	PUNCT
ejpam-4254	176	38	rpfnupf	rpfnupf	PROPN
ejpam-4254	176	39	,	,	PUNCT
ejpam-4254	176	40	rpfupf	rpfupf	ADJ
ejpam-4254	176	41	,	,	PUNCT
ejpam-4254	176	42	and	and	CCONJ
ejpam-4254	176	43	rpfupi	rpfupi	NOUN
ejpam-4254	176	44	)	)	PUNCT
ejpam-4254	176	45	.	.	PUNCT
ejpam-4254	177	1	example	example	NOUN
ejpam-4254	178	1	6	6	NUM
ejpam-4254	178	2	.	.	PUNCT
ejpam-4254	178	3	consider	consider	VERB
ejpam-4254	178	4	a	a	DET
ejpam-4254	178	5	up	up	NOUN
ejpam-4254	178	6	-	-	PUNCT
ejpam-4254	178	7	algebra	algebra	NOUN
ejpam-4254	178	8	u	u	NOUN
ejpam-4254	178	9	=	=	PUNCT
ejpam-4254	178	10	(	(	PUNCT
ejpam-4254	178	11	u	u	NOUN
ejpam-4254	178	12	,	,	PUNCT
ejpam-4254	178	13	⋆	⋆	INTJ
ejpam-4254	178	14	,	,	PUNCT
ejpam-4254	178	15	0	0	NUM
ejpam-4254	178	16	)	)	PUNCT
ejpam-4254	178	17	,	,	PUNCT
ejpam-4254	178	18	where	where	SCONJ
ejpam-4254	178	19	u	u	NOUN
ejpam-4254	178	20	=	=	PUNCT
ejpam-4254	178	21	{	{	PUNCT
ejpam-4254	178	22	0	0	NUM
ejpam-4254	178	23	,	,	PUNCT
ejpam-4254	178	24	1	1	NUM
ejpam-4254	178	25	,	,	PUNCT
ejpam-4254	178	26	2	2	NUM
ejpam-4254	178	27	,	,	PUNCT
ejpam-4254	178	28	3	3	NUM
ejpam-4254	178	29	}	}	PUNCT
ejpam-4254	178	30	is	be	AUX
ejpam-4254	178	31	defined	define	VERB
ejpam-4254	178	32	in	in	ADP
ejpam-4254	178	33	the	the	DET
ejpam-4254	178	34	cayley	cayley	ADJ
ejpam-4254	178	35	table	table	NOUN
ejpam-4254	178	36	below	below	ADV
ejpam-4254	178	37	.	.	PUNCT
ejpam-4254	179	1	⋆	⋆	VERB
ejpam-4254	180	1	0	0	NUM
ejpam-4254	180	2	1	1	NUM
ejpam-4254	180	3	2	2	NUM
ejpam-4254	180	4	3	3	NUM
ejpam-4254	180	5	0	0	NUM
ejpam-4254	180	6	0	0	NUM
ejpam-4254	180	7	1	1	NUM
ejpam-4254	180	8	2	2	NUM
ejpam-4254	180	9	3	3	NUM
ejpam-4254	180	10	1	1	NUM
ejpam-4254	180	11	0	0	NUM
ejpam-4254	180	12	0	0	NUM
ejpam-4254	180	13	2	2	NUM
ejpam-4254	180	14	3	3	NUM
ejpam-4254	180	15	2	2	NUM
ejpam-4254	180	16	0	0	NUM
ejpam-4254	180	17	0	0	NUM
ejpam-4254	180	18	0	0	NUM
ejpam-4254	180	19	3	3	NUM
ejpam-4254	180	20	3	3	NUM
ejpam-4254	180	21	0	0	NUM
ejpam-4254	180	22	1	1	NUM
ejpam-4254	180	23	2	2	NUM
ejpam-4254	180	24	0	0	NUM
ejpam-4254	180	25	we	we	PRON
ejpam-4254	180	26	define	define	VERB
ejpam-4254	180	27	a	a	DET
ejpam-4254	180	28	pfs	pfs	PROPN
ejpam-4254	180	29	p	p	NOUN
ejpam-4254	180	30	=	=	X
ejpam-4254	180	31	(	(	PUNCT
ejpam-4254	180	32	µp	µp	PROPN
ejpam-4254	180	33	,	,	PUNCT
ejpam-4254	180	34	νp	νp	NOUN
ejpam-4254	180	35	)	)	PUNCT
ejpam-4254	180	36	in	in	ADP
ejpam-4254	180	37	u	u	NOUN
ejpam-4254	180	38	as	as	SCONJ
ejpam-4254	180	39	follows	follow	VERB
ejpam-4254	180	40	:	:	PUNCT
ejpam-4254	180	41	u	u	NOUN
ejpam-4254	180	42	0	0	NUM
ejpam-4254	180	43	1	1	NUM
ejpam-4254	180	44	2	2	NUM
ejpam-4254	180	45	3	3	NUM
ejpam-4254	180	46	µp	µp	NOUN
ejpam-4254	180	47	0.5	0.5	NUM
ejpam-4254	180	48	0.4	0.4	NUM
ejpam-4254	180	49	0.3	0.3	NUM
ejpam-4254	180	50	0.2	0.2	NUM
ejpam-4254	180	51	νp	νp	ADP
ejpam-4254	180	52	0.1	0.1	NUM
ejpam-4254	180	53	0.2	0.2	NUM
ejpam-4254	180	54	0.3	0.3	NUM
ejpam-4254	180	55	0.4	0.4	NUM
ejpam-4254	180	56	then	then	ADV
ejpam-4254	180	57	p	p	NOUN
ejpam-4254	180	58	is	be	AUX
ejpam-4254	180	59	not	not	PART
ejpam-4254	180	60	a	a	DET
ejpam-4254	180	61	pfups	pfup	NOUN
ejpam-4254	180	62	(	(	PUNCT
ejpam-4254	180	63	resp	resp	NOUN
ejpam-4254	180	64	.	.	PUNCT
ejpam-4254	180	65	,	,	PUNCT
ejpam-4254	180	66	pfnupf	pfnupf	PROPN
ejpam-4254	180	67	,	,	PUNCT
ejpam-4254	180	68	pfupi	pfupi	NOUN
ejpam-4254	180	69	,	,	PUNCT
ejpam-4254	180	70	and	and	CCONJ
ejpam-4254	180	71	pfsupi	pfsupi	NOUN
ejpam-4254	180	72	)	)	PUNCT
ejpam-4254	180	73	of	of	ADP
ejpam-4254	180	74	u	u	PROPN
ejpam-4254	180	75	.	.	PUNCT
ejpam-4254	181	1	let	let	VERB
ejpam-4254	181	2	ρ	ρ	PROPN
ejpam-4254	181	3	=	=	SYM
ejpam-4254	181	4	{	{	PUNCT
ejpam-4254	181	5	(	(	PUNCT
ejpam-4254	181	6	0	0	NUM
ejpam-4254	181	7	,	,	PUNCT
ejpam-4254	181	8	0	0	NUM
ejpam-4254	181	9	)	)	PUNCT
ejpam-4254	181	10	,	,	PUNCT
ejpam-4254	181	11	(	(	PUNCT
ejpam-4254	181	12	1	1	NUM
ejpam-4254	181	13	,	,	PUNCT
ejpam-4254	181	14	1	1	NUM
ejpam-4254	181	15	)	)	PUNCT
ejpam-4254	181	16	,	,	PUNCT
ejpam-4254	181	17	(	(	PUNCT
ejpam-4254	181	18	2	2	NUM
ejpam-4254	181	19	,	,	PUNCT
ejpam-4254	181	20	2	2	NUM
ejpam-4254	181	21	)	)	PUNCT
ejpam-4254	181	22	,	,	PUNCT
ejpam-4254	181	23	(	(	PUNCT
ejpam-4254	181	24	3	3	NUM
ejpam-4254	181	25	,	,	PUNCT
ejpam-4254	181	26	3	3	NUM
ejpam-4254	181	27	)	)	PUNCT
ejpam-4254	181	28	,	,	PUNCT
ejpam-4254	181	29	(	(	PUNCT
ejpam-4254	181	30	0	0	NUM
ejpam-4254	181	31	,	,	PUNCT
ejpam-4254	181	32	1	1	NUM
ejpam-4254	181	33	)	)	PUNCT
ejpam-4254	181	34	,	,	PUNCT
ejpam-4254	181	35	(	(	PUNCT
ejpam-4254	181	36	1	1	NUM
ejpam-4254	181	37	,	,	PUNCT
ejpam-4254	181	38	0	0	NUM
ejpam-4254	181	39	)	)	PUNCT
ejpam-4254	181	40	,	,	PUNCT
ejpam-4254	181	41	(	(	PUNCT
ejpam-4254	181	42	0	0	NUM
ejpam-4254	181	43	,	,	PUNCT
ejpam-4254	181	44	2	2	NUM
ejpam-4254	181	45	)	)	PUNCT
ejpam-4254	181	46	,	,	PUNCT
ejpam-4254	181	47	(	(	PUNCT
ejpam-4254	181	48	2	2	NUM
ejpam-4254	181	49	,	,	PUNCT
ejpam-4254	181	50	0	0	NUM
ejpam-4254	181	51	)	)	PUNCT
ejpam-4254	181	52	,	,	PUNCT
ejpam-4254	181	53	(	(	PUNCT
ejpam-4254	181	54	0	0	NUM
ejpam-4254	181	55	,	,	PUNCT
ejpam-4254	181	56	3	3	NUM
ejpam-4254	181	57	)	)	PUNCT
ejpam-4254	181	58	,	,	PUNCT
ejpam-4254	181	59	(	(	PUNCT
ejpam-4254	181	60	3	3	NUM
ejpam-4254	181	61	,	,	PUNCT
ejpam-4254	181	62	0	0	NUM
ejpam-4254	181	63	)	)	PUNCT
ejpam-4254	181	64	,	,	PUNCT
ejpam-4254	181	65	a.	a.	NOUN
ejpam-4254	181	66	iampan	iampan	NOUN
ejpam-4254	181	67	et	et	PROPN
ejpam-4254	181	68	al	al	PROPN
ejpam-4254	181	69	.	.	PUNCT
ejpam-4254	181	70	/	/	SYM
ejpam-4254	181	71	eur	eur	PROPN
ejpam-4254	181	72	.	.	PUNCT
ejpam-4254	182	1	j.	j.	PROPN
ejpam-4254	182	2	pure	pure	PROPN
ejpam-4254	182	3	appl	appl	PROPN
ejpam-4254	182	4	.	.	PROPN
ejpam-4254	182	5	math	math	PROPN
ejpam-4254	182	6	,	,	PUNCT
ejpam-4254	182	7	15	15	NUM
ejpam-4254	182	8	(	(	PUNCT
ejpam-4254	182	9	1	1	NUM
ejpam-4254	182	10	)	)	PUNCT
ejpam-4254	182	11	(	(	PUNCT
ejpam-4254	182	12	2022	2022	NUM
ejpam-4254	182	13	)	)	PUNCT
ejpam-4254	182	14	,	,	PUNCT
ejpam-4254	182	15	169	169	NUM
ejpam-4254	182	16	-	-	SYM
ejpam-4254	182	17	198	198	NUM
ejpam-4254	182	18	180	180	NUM
ejpam-4254	182	19	(	(	PUNCT
ejpam-4254	182	20	1	1	NUM
ejpam-4254	182	21	,	,	PUNCT
ejpam-4254	182	22	2	2	NUM
ejpam-4254	182	23	)	)	PUNCT
ejpam-4254	182	24	,	,	PUNCT
ejpam-4254	182	25	(	(	PUNCT
ejpam-4254	182	26	2	2	NUM
ejpam-4254	182	27	,	,	PUNCT
ejpam-4254	182	28	1	1	NUM
ejpam-4254	182	29	)	)	PUNCT
ejpam-4254	182	30	,	,	PUNCT
ejpam-4254	182	31	(	(	PUNCT
ejpam-4254	182	32	2	2	NUM
ejpam-4254	182	33	,	,	PUNCT
ejpam-4254	182	34	3	3	NUM
ejpam-4254	182	35	)	)	PUNCT
ejpam-4254	182	36	,	,	PUNCT
ejpam-4254	182	37	(	(	PUNCT
ejpam-4254	182	38	3	3	NUM
ejpam-4254	182	39	,	,	PUNCT
ejpam-4254	182	40	2	2	NUM
ejpam-4254	182	41	)	)	PUNCT
ejpam-4254	182	42	,	,	PUNCT
ejpam-4254	182	43	(	(	PUNCT
ejpam-4254	182	44	1	1	NUM
ejpam-4254	182	45	,	,	PUNCT
ejpam-4254	182	46	3	3	NUM
ejpam-4254	182	47	)	)	PUNCT
ejpam-4254	182	48	,	,	PUNCT
ejpam-4254	182	49	(	(	PUNCT
ejpam-4254	182	50	3	3	NUM
ejpam-4254	182	51	,	,	PUNCT
ejpam-4254	182	52	1	1	NUM
ejpam-4254	182	53	)	)	PUNCT
ejpam-4254	182	54	}	}	PUNCT
ejpam-4254	182	55	.	.	PUNCT
ejpam-4254	183	1	then	then	ADV
ejpam-4254	183	2	ρ	ρ	PROPN
ejpam-4254	183	3	is	be	AUX
ejpam-4254	183	4	a	a	DET
ejpam-4254	183	5	cr	cr	NOUN
ejpam-4254	183	6	on	on	ADP
ejpam-4254	183	7	u	u	PROPN
ejpam-4254	183	8	.	.	PUNCT
ejpam-4254	184	1	but	but	CCONJ
ejpam-4254	184	2	ρ+(p	ρ+(p	NUM
ejpam-4254	184	3	)	)	PUNCT
ejpam-4254	184	4	and	and	CCONJ
ejpam-4254	184	5	ρ−(p	ρ−(p	PROPN
ejpam-4254	184	6	)	)	PUNCT
ejpam-4254	184	7	are	be	AUX
ejpam-4254	184	8	pfupss	pfupss	NOUN
ejpam-4254	184	9	(	(	PUNCT
ejpam-4254	184	10	resp	resp	PROPN
ejpam-4254	184	11	.	.	PUNCT
ejpam-4254	184	12	,	,	PUNCT
ejpam-4254	184	13	pfnupfs	pfnupfs	PROPN
ejpam-4254	184	14	,	,	PUNCT
ejpam-4254	184	15	pfupfs	pfupf	NOUN
ejpam-4254	184	16	,	,	PUNCT
ejpam-4254	184	17	pfupis	pfupis	ADJ
ejpam-4254	184	18	,	,	PUNCT
ejpam-4254	184	19	and	and	CCONJ
ejpam-4254	184	20	pfsupis	pfsupi	VERB
ejpam-4254	184	21	)	)	PUNCT
ejpam-4254	184	22	of	of	ADP
ejpam-4254	184	23	u	u	PROPN
ejpam-4254	184	24	.	.	PUNCT
ejpam-4254	185	1	from	from	ADP
ejpam-4254	185	2	example	example	NOUN
ejpam-4254	185	3	6	6	NUM
ejpam-4254	185	4	,	,	PUNCT
ejpam-4254	185	5	we	we	PRON
ejpam-4254	185	6	get	get	VERB
ejpam-4254	185	7	the	the	DET
ejpam-4254	185	8	results	result	NOUN
ejpam-4254	185	9	that	that	SCONJ
ejpam-4254	185	10	if	if	SCONJ
ejpam-4254	185	11	p	p	NOUN
ejpam-4254	185	12	is	be	AUX
ejpam-4254	185	13	a	a	DET
ejpam-4254	185	14	rpfups	rpfup	NOUN
ejpam-4254	185	15	(	(	PUNCT
ejpam-4254	185	16	resp	resp	NOUN
ejpam-4254	185	17	.	.	PUNCT
ejpam-4254	185	18	,	,	PUNCT
ejpam-4254	185	19	rpfnupf	rpfnupf	PROPN
ejpam-4254	185	20	,	,	PUNCT
ejpam-4254	185	21	rpfupf	rpfupf	PROPN
ejpam-4254	185	22	,	,	PUNCT
ejpam-4254	185	23	rpfupi	rpfupi	NOUN
ejpam-4254	185	24	,	,	PUNCT
ejpam-4254	185	25	and	and	CCONJ
ejpam-4254	185	26	rpfsupi	rpfsupi	NOUN
ejpam-4254	185	27	)	)	PUNCT
ejpam-4254	185	28	,	,	PUNCT
ejpam-4254	185	29	then	then	ADV
ejpam-4254	185	30	it	it	PRON
ejpam-4254	185	31	may	may	AUX
ejpam-4254	185	32	not	not	PART
ejpam-4254	185	33	be	be	AUX
ejpam-4254	185	34	a	a	DET
ejpam-4254	185	35	pfups	pfup	NOUN
ejpam-4254	185	36	(	(	PUNCT
ejpam-4254	185	37	resp	resp	NOUN
ejpam-4254	185	38	.	.	PUNCT
ejpam-4254	185	39	,	,	PUNCT
ejpam-4254	185	40	pfnupf	pfnupf	PROPN
ejpam-4254	185	41	,	,	PUNCT
ejpam-4254	185	42	pfupf	pfupf	NOUN
ejpam-4254	185	43	,	,	PUNCT
ejpam-4254	185	44	pfupi	pfupi	NOUN
ejpam-4254	185	45	,	,	PUNCT
ejpam-4254	185	46	and	and	CCONJ
ejpam-4254	185	47	pfsupi	pfsupi	NOUN
ejpam-4254	185	48	)	)	PUNCT
ejpam-4254	185	49	.	.	PUNCT
ejpam-4254	186	1	example	example	NOUN
ejpam-4254	187	1	7	7	X
ejpam-4254	187	2	.	.	X
ejpam-4254	187	3	consider	consider	VERB
ejpam-4254	187	4	a	a	DET
ejpam-4254	187	5	up	up	NOUN
ejpam-4254	187	6	-	-	PUNCT
ejpam-4254	187	7	algebra	algebra	NOUN
ejpam-4254	187	8	u	u	NOUN
ejpam-4254	187	9	=	=	PUNCT
ejpam-4254	187	10	(	(	PUNCT
ejpam-4254	187	11	u	u	NOUN
ejpam-4254	187	12	,	,	PUNCT
ejpam-4254	187	13	⋆	⋆	INTJ
ejpam-4254	187	14	,	,	PUNCT
ejpam-4254	187	15	0	0	NUM
ejpam-4254	187	16	)	)	PUNCT
ejpam-4254	187	17	,	,	PUNCT
ejpam-4254	187	18	where	where	SCONJ
ejpam-4254	187	19	u	u	NOUN
ejpam-4254	187	20	=	=	PUNCT
ejpam-4254	187	21	{	{	PUNCT
ejpam-4254	187	22	0	0	NUM
ejpam-4254	187	23	,	,	PUNCT
ejpam-4254	187	24	1	1	NUM
ejpam-4254	187	25	,	,	PUNCT
ejpam-4254	187	26	2	2	NUM
ejpam-4254	187	27	,	,	PUNCT
ejpam-4254	187	28	3	3	NUM
ejpam-4254	187	29	}	}	PUNCT
ejpam-4254	187	30	is	be	AUX
ejpam-4254	187	31	defined	define	VERB
ejpam-4254	187	32	in	in	ADP
ejpam-4254	187	33	the	the	DET
ejpam-4254	187	34	cayley	cayley	ADJ
ejpam-4254	187	35	table	table	NOUN
ejpam-4254	187	36	below	below	ADV
ejpam-4254	187	37	.	.	PUNCT
ejpam-4254	188	1	⋆	⋆	VERB
ejpam-4254	189	1	0	0	NUM
ejpam-4254	189	2	1	1	NUM
ejpam-4254	189	3	2	2	NUM
ejpam-4254	189	4	3	3	NUM
ejpam-4254	189	5	0	0	NUM
ejpam-4254	189	6	0	0	NUM
ejpam-4254	189	7	1	1	NUM
ejpam-4254	189	8	2	2	NUM
ejpam-4254	189	9	3	3	NUM
ejpam-4254	189	10	1	1	NUM
ejpam-4254	189	11	0	0	NUM
ejpam-4254	189	12	0	0	NUM
ejpam-4254	189	13	3	3	NUM
ejpam-4254	189	14	3	3	NUM
ejpam-4254	189	15	2	2	NUM
ejpam-4254	189	16	0	0	NUM
ejpam-4254	189	17	1	1	NUM
ejpam-4254	189	18	0	0	NUM
ejpam-4254	189	19	0	0	NUM
ejpam-4254	189	20	3	3	NUM
ejpam-4254	189	21	0	0	NUM
ejpam-4254	189	22	1	1	NUM
ejpam-4254	189	23	2	2	NUM
ejpam-4254	189	24	0	0	NUM
ejpam-4254	189	25	we	we	PRON
ejpam-4254	189	26	define	define	VERB
ejpam-4254	189	27	a	a	DET
ejpam-4254	189	28	pfs	pfs	PROPN
ejpam-4254	189	29	p	p	NOUN
ejpam-4254	189	30	=	=	X
ejpam-4254	189	31	(	(	PUNCT
ejpam-4254	189	32	µp	µp	PROPN
ejpam-4254	189	33	,	,	PUNCT
ejpam-4254	189	34	νp	νp	NOUN
ejpam-4254	189	35	)	)	PUNCT
ejpam-4254	189	36	in	in	ADP
ejpam-4254	189	37	u	u	NOUN
ejpam-4254	189	38	as	as	SCONJ
ejpam-4254	189	39	follows	follow	VERB
ejpam-4254	189	40	:	:	PUNCT
ejpam-4254	189	41	u	u	NOUN
ejpam-4254	189	42	0	0	NUM
ejpam-4254	189	43	1	1	NUM
ejpam-4254	189	44	2	2	NUM
ejpam-4254	189	45	3	3	NUM
ejpam-4254	189	46	µp	µp	NOUN
ejpam-4254	189	47	0.9	0.9	NUM
ejpam-4254	189	48	0.2	0.2	NUM
ejpam-4254	189	49	0.3	0.3	NUM
ejpam-4254	189	50	0.3	0.3	NUM
ejpam-4254	189	51	νp	νp	ADP
ejpam-4254	189	52	0.2	0.2	NUM
ejpam-4254	189	53	0.6	0.6	NUM
ejpam-4254	189	54	0.5	0.5	NUM
ejpam-4254	189	55	0.5	0.5	NUM
ejpam-4254	189	56	then	then	ADV
ejpam-4254	189	57	p	p	NOUN
ejpam-4254	189	58	is	be	AUX
ejpam-4254	189	59	a	a	DET
ejpam-4254	189	60	pfupi	pfupi	NOUN
ejpam-4254	189	61	(	(	PUNCT
ejpam-4254	189	62	resp	resp	NOUN
ejpam-4254	189	63	.	.	PUNCT
ejpam-4254	189	64	,	,	PUNCT
ejpam-4254	189	65	pfupf	pfupf	NOUN
ejpam-4254	189	66	,	,	PUNCT
ejpam-4254	189	67	pfnupf	pfnupf	NOUN
ejpam-4254	189	68	,	,	PUNCT
ejpam-4254	189	69	and	and	CCONJ
ejpam-4254	189	70	pfups	pfup	NOUN
ejpam-4254	189	71	)	)	PUNCT
ejpam-4254	189	72	of	of	ADP
ejpam-4254	189	73	u	u	PROPN
ejpam-4254	189	74	.	.	PUNCT
ejpam-4254	190	1	let	let	VERB
ejpam-4254	190	2	ρ	ρ	PROPN
ejpam-4254	190	3	=	=	SYM
ejpam-4254	190	4	{	{	PUNCT
ejpam-4254	190	5	(	(	PUNCT
ejpam-4254	190	6	0	0	NUM
ejpam-4254	190	7	,	,	PUNCT
ejpam-4254	190	8	0	0	NUM
ejpam-4254	190	9	)	)	PUNCT
ejpam-4254	190	10	,	,	PUNCT
ejpam-4254	190	11	(	(	PUNCT
ejpam-4254	190	12	1	1	NUM
ejpam-4254	190	13	,	,	PUNCT
ejpam-4254	190	14	1	1	NUM
ejpam-4254	190	15	)	)	PUNCT
ejpam-4254	190	16	,	,	PUNCT
ejpam-4254	190	17	(	(	PUNCT
ejpam-4254	190	18	2	2	NUM
ejpam-4254	190	19	,	,	PUNCT
ejpam-4254	190	20	2	2	NUM
ejpam-4254	190	21	)	)	PUNCT
ejpam-4254	190	22	,	,	PUNCT
ejpam-4254	190	23	(	(	PUNCT
ejpam-4254	190	24	3	3	NUM
ejpam-4254	190	25	,	,	PUNCT
ejpam-4254	190	26	3	3	NUM
ejpam-4254	190	27	)	)	PUNCT
ejpam-4254	190	28	,	,	PUNCT
ejpam-4254	190	29	(	(	PUNCT
ejpam-4254	190	30	0	0	NUM
ejpam-4254	190	31	,	,	PUNCT
ejpam-4254	190	32	3	3	NUM
ejpam-4254	190	33	)	)	PUNCT
ejpam-4254	190	34	,	,	PUNCT
ejpam-4254	190	35	(	(	PUNCT
ejpam-4254	190	36	3	3	NUM
ejpam-4254	190	37	,	,	PUNCT
ejpam-4254	190	38	0	0	NUM
ejpam-4254	190	39	)	)	PUNCT
ejpam-4254	190	40	}	}	PUNCT
ejpam-4254	190	41	.	.	PUNCT
ejpam-4254	191	1	then	then	ADV
ejpam-4254	191	2	ρ	ρ	PROPN
ejpam-4254	191	3	is	be	AUX
ejpam-4254	191	4	a	a	DET
ejpam-4254	191	5	cr	cr	NOUN
ejpam-4254	191	6	on	on	ADP
ejpam-4254	191	7	u	u	PROPN
ejpam-4254	191	8	.	.	PUNCT
ejpam-4254	192	1	thus	thus	ADV
ejpam-4254	192	2	ρ+(p	ρ+(p	VERB
ejpam-4254	192	3	)	)	PUNCT
ejpam-4254	192	4	and	and	CCONJ
ejpam-4254	192	5	ρ−(p	ρ−(p	PROPN
ejpam-4254	192	6	)	)	PUNCT
ejpam-4254	192	7	are	be	AUX
ejpam-4254	192	8	pfupis	pfupis	ADJ
ejpam-4254	192	9	(	(	PUNCT
ejpam-4254	192	10	resp	resp	PROPN
ejpam-4254	192	11	.	.	PUNCT
ejpam-4254	192	12	,	,	PUNCT
ejpam-4254	192	13	pfupfs	pfupfs	PROPN
ejpam-4254	192	14	,	,	PUNCT
ejpam-4254	192	15	pfnupfs	pfnupfs	PROPN
ejpam-4254	192	16	,	,	PUNCT
ejpam-4254	192	17	and	and	CCONJ
ejpam-4254	192	18	pfupss	pfupss	NOUN
ejpam-4254	192	19	)	)	PUNCT
ejpam-4254	192	20	of	of	ADP
ejpam-4254	192	21	u	u	PROPN
ejpam-4254	192	22	.	.	PUNCT
ejpam-4254	193	1	from	from	ADP
ejpam-4254	193	2	example	example	NOUN
ejpam-4254	193	3	7	7	NUM
ejpam-4254	193	4	,	,	PUNCT
ejpam-4254	193	5	we	we	PRON
ejpam-4254	193	6	get	get	VERB
ejpam-4254	193	7	the	the	DET
ejpam-4254	193	8	results	result	NOUN
ejpam-4254	193	9	that	that	PRON
ejpam-4254	193	10	p	p	PROPN
ejpam-4254	193	11	can	can	AUX
ejpam-4254	193	12	be	be	AUX
ejpam-4254	193	13	a	a	DET
ejpam-4254	193	14	rpfups	rpfup	NOUN
ejpam-4254	193	15	(	(	PUNCT
ejpam-4254	193	16	resp	resp	NOUN
ejpam-4254	193	17	.	.	PUNCT
ejpam-4254	193	18	,	,	PUNCT
ejpam-4254	193	19	rpfnupf	rpfnupf	PROPN
ejpam-4254	193	20	,	,	PUNCT
ejpam-4254	193	21	rpfupf	rpfupf	PROPN
ejpam-4254	193	22	,	,	PUNCT
ejpam-4254	193	23	rpfupi	rpfupi	NOUN
ejpam-4254	193	24	,	,	PUNCT
ejpam-4254	193	25	and	and	CCONJ
ejpam-4254	193	26	rpfsupi	rpfsupi	NOUN
ejpam-4254	193	27	)	)	PUNCT
ejpam-4254	193	28	and	and	CCONJ
ejpam-4254	193	29	a	a	DET
ejpam-4254	193	30	pfups	pfup	NOUN
ejpam-4254	193	31	(	(	PUNCT
ejpam-4254	193	32	resp	resp	NOUN
ejpam-4254	193	33	.	.	PUNCT
ejpam-4254	193	34	,	,	PUNCT
ejpam-4254	193	35	pfnupf	pfnupf	PROPN
ejpam-4254	193	36	,	,	PUNCT
ejpam-4254	193	37	pfupf	pfupf	NOUN
ejpam-4254	193	38	,	,	PUNCT
ejpam-4254	193	39	pfupi	pfupi	NOUN
ejpam-4254	193	40	,	,	PUNCT
ejpam-4254	193	41	and	and	CCONJ
ejpam-4254	193	42	pfsupi	pfsupi	NOUN
ejpam-4254	193	43	)	)	PUNCT
ejpam-4254	193	44	in	in	ADP
ejpam-4254	193	45	the	the	DET
ejpam-4254	193	46	same	same	ADJ
ejpam-4254	193	47	time	time	NOUN
ejpam-4254	193	48	.	.	PUNCT
ejpam-4254	194	1	hence	hence	ADV
ejpam-4254	194	2	,	,	PUNCT
ejpam-4254	194	3	we	we	PRON
ejpam-4254	194	4	get	get	VERB
ejpam-4254	194	5	the	the	DET
ejpam-4254	194	6	diagram	diagram	NOUN
ejpam-4254	194	7	of	of	ADP
ejpam-4254	194	8	the	the	DET
ejpam-4254	194	9	relationships	relationship	NOUN
ejpam-4254	194	10	between	between	ADP
ejpam-4254	194	11	rpfss	rpfss	NOUN
ejpam-4254	194	12	and	and	CCONJ
ejpam-4254	194	13	pfss	pfss	NOUN
ejpam-4254	194	14	in	in	ADP
ejpam-4254	194	15	upalgebras	upalgebra	NOUN
ejpam-4254	194	16	,	,	PUNCT
ejpam-4254	194	17	which	which	PRON
ejpam-4254	194	18	is	be	AUX
ejpam-4254	194	19	shown	show	VERB
ejpam-4254	194	20	with	with	ADP
ejpam-4254	194	21	figure	figure	NOUN
ejpam-4254	194	22	2	2	NUM
ejpam-4254	194	23	.	.	NOUN
ejpam-4254	195	1	3	3	NUM
ejpam-4254	195	2	.	.	X
ejpam-4254	195	3	t	t	NOUN
ejpam-4254	195	4	-	-	PUNCT
ejpam-4254	195	5	level	level	NOUN
ejpam-4254	195	6	subsets	subset	NOUN
ejpam-4254	195	7	of	of	ADP
ejpam-4254	195	8	a	a	DET
ejpam-4254	195	9	pfs	pfs	NOUN
ejpam-4254	195	10	in	in	ADP
ejpam-4254	195	11	this	this	DET
ejpam-4254	195	12	section	section	NOUN
ejpam-4254	195	13	,	,	PUNCT
ejpam-4254	195	14	we	we	PRON
ejpam-4254	195	15	shall	shall	AUX
ejpam-4254	195	16	let	let	VERB
ejpam-4254	195	17	p	p	PRON
ejpam-4254	195	18	be	be	AUX
ejpam-4254	195	19	a	a	DET
ejpam-4254	195	20	pfs	pfs	PROPN
ejpam-4254	195	21	p	p	NOUN
ejpam-4254	195	22	=	=	X
ejpam-4254	195	23	(	(	PUNCT
ejpam-4254	195	24	µp	µp	PROPN
ejpam-4254	195	25	,	,	PUNCT
ejpam-4254	195	26	νp	νp	NOUN
ejpam-4254	195	27	)	)	PUNCT
ejpam-4254	195	28	in	in	ADP
ejpam-4254	195	29	u	u	NOUN
ejpam-4254	195	30	.	.	PUNCT
ejpam-4254	196	1	we	we	PRON
ejpam-4254	196	2	shall	shall	AUX
ejpam-4254	196	3	discuss	discuss	VERB
ejpam-4254	196	4	the	the	DET
ejpam-4254	196	5	relationships	relationship	NOUN
ejpam-4254	196	6	between	between	ADP
ejpam-4254	196	7	pfupss	pfupss	PROPN
ejpam-4254	196	8	(	(	PUNCT
ejpam-4254	196	9	resp	resp	PROPN
ejpam-4254	196	10	.	.	PUNCT
ejpam-4254	196	11	,	,	PUNCT
ejpam-4254	196	12	pfnupfs	pfnupfs	PROPN
ejpam-4254	196	13	,	,	PUNCT
ejpam-4254	196	14	pfupfs	pfupf	NOUN
ejpam-4254	196	15	,	,	PUNCT
ejpam-4254	196	16	pfupis	pfupis	ADJ
ejpam-4254	196	17	,	,	PUNCT
ejpam-4254	196	18	pfsupis	pfsupis	PROPN
ejpam-4254	196	19	,	,	PUNCT
ejpam-4254	196	20	rpfupss	rpfupss	PROPN
ejpam-4254	196	21	,	,	PUNCT
ejpam-4254	196	22	rpfnupfs	rpfnupfs	PROPN
ejpam-4254	196	23	,	,	PUNCT
ejpam-4254	196	24	rpfupfs	rpfupf	NOUN
ejpam-4254	196	25	,	,	PUNCT
ejpam-4254	196	26	rpfupis	rpfupis	NOUN
ejpam-4254	196	27	,	,	PUNCT
ejpam-4254	196	28	and	and	CCONJ
ejpam-4254	196	29	rpfsupis	rpfsupis	PROPN
ejpam-4254	196	30	)	)	PUNCT
ejpam-4254	196	31	of	of	ADP
ejpam-4254	196	32	up	up	ADV
ejpam-4254	196	33	-	-	PUNCT
ejpam-4254	196	34	algebras	algebra	NOUN
ejpam-4254	196	35	and	and	CCONJ
ejpam-4254	196	36	their	their	PRON
ejpam-4254	196	37	t	t	NOUN
ejpam-4254	196	38	-	-	PUNCT
ejpam-4254	196	39	level	level	NOUN
ejpam-4254	196	40	subsets	subset	NOUN
ejpam-4254	196	41	.	.	PUNCT
ejpam-4254	197	1	definition	definition	NOUN
ejpam-4254	197	2	12	12	NUM
ejpam-4254	197	3	.	.	PUNCT
ejpam-4254	198	1	[	[	X
ejpam-4254	198	2	26	26	NUM
ejpam-4254	198	3	]	]	PUNCT
ejpam-4254	198	4	let	let	VERB
ejpam-4254	198	5	f	f	PRON
ejpam-4254	198	6	be	be	AUX
ejpam-4254	198	7	a	a	DET
ejpam-4254	198	8	fs	fs	NOUN
ejpam-4254	198	9	with	with	ADP
ejpam-4254	198	10	the	the	DET
ejpam-4254	198	11	membership	membership	NOUN
ejpam-4254	198	12	function	function	VERB
ejpam-4254	198	13	µf	µf	NOUN
ejpam-4254	198	14	in	in	ADP
ejpam-4254	198	15	u	u	PROPN
ejpam-4254	198	16	.	.	PUNCT
ejpam-4254	199	1	the	the	DET
ejpam-4254	199	2	sets	set	NOUN
ejpam-4254	199	3	u(µf	u(µf	NOUN
ejpam-4254	199	4	,	,	PUNCT
ejpam-4254	199	5	t	t	PROPN
ejpam-4254	199	6	)	)	PUNCT
ejpam-4254	199	7	=	=	PRON
ejpam-4254	199	8	{	{	PUNCT
ejpam-4254	199	9	a	a	DET
ejpam-4254	199	10	∈	∈	PROPN
ejpam-4254	199	11	u	u	NOUN
ejpam-4254	199	12	|	|	NOUN
ejpam-4254	199	13	µf(a	µf(a	PRON
ejpam-4254	199	14	)	)	PUNCT
ejpam-4254	199	15	≥	≥	PROPN
ejpam-4254	199	16	t	t	PROPN
ejpam-4254	199	17	}	}	PUNCT
ejpam-4254	199	18	,	,	PUNCT
ejpam-4254	199	19	u+(µf	u+(µf	PROPN
ejpam-4254	199	20	,	,	PUNCT
ejpam-4254	199	21	t	t	PROPN
ejpam-4254	199	22	)	)	PUNCT
ejpam-4254	199	23	=	=	PRON
ejpam-4254	199	24	{	{	PUNCT
ejpam-4254	199	25	a	a	DET
ejpam-4254	199	26	∈	∈	PROPN
ejpam-4254	199	27	u	u	NOUN
ejpam-4254	199	28	|	|	NOUN
ejpam-4254	199	29	µf(a	µf(a	PRON
ejpam-4254	199	30	)	)	PUNCT
ejpam-4254	199	31	>	>	X
ejpam-4254	199	32	t	t	PROPN
ejpam-4254	199	33	}	}	PUNCT
ejpam-4254	199	34	,	,	PUNCT
ejpam-4254	199	35	a.	a.	NOUN
ejpam-4254	199	36	iampan	iampan	NOUN
ejpam-4254	199	37	et	et	PROPN
ejpam-4254	199	38	al	al	PROPN
ejpam-4254	199	39	.	.	PUNCT
ejpam-4254	199	40	/	/	SYM
ejpam-4254	199	41	eur	eur	PROPN
ejpam-4254	199	42	.	.	PUNCT
ejpam-4254	200	1	j.	j.	PROPN
ejpam-4254	200	2	pure	pure	PROPN
ejpam-4254	200	3	appl	appl	PROPN
ejpam-4254	200	4	.	.	PROPN
ejpam-4254	200	5	math	math	PROPN
ejpam-4254	200	6	,	,	PUNCT
ejpam-4254	200	7	15	15	NUM
ejpam-4254	200	8	(	(	PUNCT
ejpam-4254	200	9	1	1	NUM
ejpam-4254	200	10	)	)	PUNCT
ejpam-4254	200	11	(	(	PUNCT
ejpam-4254	200	12	2022	2022	NUM
ejpam-4254	200	13	)	)	PUNCT
ejpam-4254	200	14	,	,	PUNCT
ejpam-4254	200	15	169	169	NUM
ejpam-4254	200	16	-	-	SYM
ejpam-4254	200	17	198	198	NUM
ejpam-4254	200	18	181	181	NUM
ejpam-4254	200	19	figure	figure	NOUN
ejpam-4254	200	20	2	2	NUM
ejpam-4254	200	21	:	:	PUNCT
ejpam-4254	200	22	relationships	relationship	NOUN
ejpam-4254	200	23	between	between	ADP
ejpam-4254	200	24	rough	rough	ADJ
ejpam-4254	200	25	pythagorean	pythagorean	ADJ
ejpam-4254	200	26	fuzzy	fuzzy	ADJ
ejpam-4254	200	27	sets	set	NOUN
ejpam-4254	200	28	and	and	CCONJ
ejpam-4254	200	29	pythagorean	pythagorean	VERB
ejpam-4254	200	30	fuzzy	fuzzy	ADJ
ejpam-4254	200	31	sets	set	NOUN
ejpam-4254	200	32	in	in	ADP
ejpam-4254	200	33	up	up	ADV
ejpam-4254	200	34	-	-	PUNCT
ejpam-4254	200	35	algebras	algebras	NOUN
ejpam-4254	200	36	l(µf	l(µf	PROPN
ejpam-4254	200	37	,	,	PUNCT
ejpam-4254	200	38	t	t	PROPN
ejpam-4254	200	39	)	)	PUNCT
ejpam-4254	200	40	=	=	PRON
ejpam-4254	200	41	{	{	PUNCT
ejpam-4254	200	42	a	a	DET
ejpam-4254	200	43	∈	∈	PROPN
ejpam-4254	200	44	u	u	NOUN
ejpam-4254	200	45	|	|	NOUN
ejpam-4254	200	46	µf(a	µf(a	NOUN
ejpam-4254	200	47	)	)	PUNCT
ejpam-4254	200	48	≤	≤	NUM
ejpam-4254	200	49	t	t	PROPN
ejpam-4254	200	50	}	}	PUNCT
ejpam-4254	200	51	,	,	PUNCT
ejpam-4254	200	52	l−(µf	l−(µf	PROPN
ejpam-4254	200	53	,	,	PUNCT
ejpam-4254	200	54	t	t	PROPN
ejpam-4254	200	55	)	)	PUNCT
ejpam-4254	200	56	=	=	PRON
ejpam-4254	200	57	{	{	PUNCT
ejpam-4254	200	58	a	a	DET
ejpam-4254	200	59	∈	∈	PROPN
ejpam-4254	200	60	u	u	NOUN
ejpam-4254	200	61	|	|	NOUN
ejpam-4254	200	62	µf(a	µf(a	PRON
ejpam-4254	200	63	)	)	PUNCT
ejpam-4254	200	64	<	<	X
ejpam-4254	200	65	t	t	PROPN
ejpam-4254	200	66	}	}	PUNCT
ejpam-4254	200	67	,	,	PUNCT
ejpam-4254	200	68	e(µf	e(µf	PROPN
ejpam-4254	200	69	,	,	PUNCT
ejpam-4254	200	70	t	t	PROPN
ejpam-4254	200	71	)	)	PUNCT
ejpam-4254	200	72	=	=	PRON
ejpam-4254	200	73	{	{	PUNCT
ejpam-4254	200	74	a	a	DET
ejpam-4254	200	75	∈	∈	PROPN
ejpam-4254	200	76	u	u	NOUN
ejpam-4254	200	77	|	|	NOUN
ejpam-4254	200	78	µf(a	µf(a	PRON
ejpam-4254	200	79	)	)	PUNCT
ejpam-4254	200	80	=	=	SYM
ejpam-4254	200	81	t	t	PROPN
ejpam-4254	200	82	}	}	PUNCT
ejpam-4254	200	83	are	be	AUX
ejpam-4254	200	84	referred	refer	VERB
ejpam-4254	200	85	to	to	ADP
ejpam-4254	200	86	as	as	ADP
ejpam-4254	200	87	an	an	DET
ejpam-4254	200	88	upper	upper	ADJ
ejpam-4254	200	89	t	t	NOUN
ejpam-4254	200	90	-	-	PUNCT
ejpam-4254	200	91	level	level	NOUN
ejpam-4254	200	92	subset	subset	NOUN
ejpam-4254	200	93	,	,	PUNCT
ejpam-4254	200	94	an	an	DET
ejpam-4254	200	95	upper	upper	ADJ
ejpam-4254	200	96	t	t	NOUN
ejpam-4254	200	97	-	-	PUNCT
ejpam-4254	200	98	strong	strong	ADJ
ejpam-4254	200	99	level	level	NOUN
ejpam-4254	200	100	subset	subset	NOUN
ejpam-4254	200	101	,	,	PUNCT
ejpam-4254	200	102	a	a	DET
ejpam-4254	200	103	lower	low	ADJ
ejpam-4254	200	104	t	t	NOUN
ejpam-4254	200	105	-	-	PUNCT
ejpam-4254	200	106	level	level	NOUN
ejpam-4254	200	107	subset	subset	NOUN
ejpam-4254	200	108	,	,	PUNCT
ejpam-4254	200	109	a	a	DET
ejpam-4254	200	110	lower	low	ADJ
ejpam-4254	200	111	t	t	NOUN
ejpam-4254	200	112	-	-	PUNCT
ejpam-4254	200	113	strong	strong	ADJ
ejpam-4254	200	114	level	level	NOUN
ejpam-4254	200	115	subset	subset	NOUN
ejpam-4254	200	116	,	,	PUNCT
ejpam-4254	200	117	and	and	CCONJ
ejpam-4254	200	118	an	an	DET
ejpam-4254	200	119	equal	equal	ADJ
ejpam-4254	200	120	t	t	NOUN
ejpam-4254	200	121	-	-	PUNCT
ejpam-4254	200	122	level	level	NOUN
ejpam-4254	200	123	subset	subset	NOUN
ejpam-4254	200	124	of	of	ADP
ejpam-4254	200	125	f	f	PROPN
ejpam-4254	200	126	,	,	PUNCT
ejpam-4254	200	127	respectively	respectively	ADV
ejpam-4254	200	128	,	,	PUNCT
ejpam-4254	200	129	for	for	ADP
ejpam-4254	200	130	any	any	DET
ejpam-4254	200	131	t	t	NOUN
ejpam-4254	200	132	∈	∈	PROPN
ejpam-4254	201	1	[	[	X
ejpam-4254	201	2	0	0	NUM
ejpam-4254	201	3	,	,	PUNCT
ejpam-4254	201	4	1	1	NUM
ejpam-4254	201	5	]	]	PUNCT
ejpam-4254	201	6	.	.	PUNCT
ejpam-4254	202	1	theorem	theorem	NOUN
ejpam-4254	202	2	2	2	NUM
ejpam-4254	202	3	.	.	X
ejpam-4254	203	1	p	p	NOUN
ejpam-4254	203	2	is	be	AUX
ejpam-4254	203	3	a	a	DET
ejpam-4254	203	4	pfups	pfup	NOUN
ejpam-4254	203	5	of	of	ADP
ejpam-4254	203	6	u	u	PRON
ejpam-4254	203	7	if	if	SCONJ
ejpam-4254	203	8	and	and	CCONJ
ejpam-4254	203	9	only	only	ADV
ejpam-4254	203	10	if	if	SCONJ
ejpam-4254	203	11	u(µp	u(µp	NOUN
ejpam-4254	203	12	,	,	PUNCT
ejpam-4254	203	13	t	t	PROPN
ejpam-4254	203	14	)	)	PUNCT
ejpam-4254	203	15	and	and	CCONJ
ejpam-4254	203	16	l(νp	l(νp	PROPN
ejpam-4254	203	17	,	,	PUNCT
ejpam-4254	203	18	t	t	PROPN
ejpam-4254	203	19	)	)	PUNCT
ejpam-4254	203	20	are	be	AUX
ejpam-4254	203	21	,	,	PUNCT
ejpam-4254	203	22	if	if	SCONJ
ejpam-4254	203	23	the	the	DET
ejpam-4254	203	24	sets	set	NOUN
ejpam-4254	203	25	are	be	AUX
ejpam-4254	203	26	nonempty	nonempty	ADJ
ejpam-4254	203	27	,	,	PUNCT
ejpam-4254	203	28	upss	upss	ADV
ejpam-4254	203	29	of	of	ADP
ejpam-4254	203	30	u	u	NOUN
ejpam-4254	203	31	for	for	ADP
ejpam-4254	203	32	every	every	DET
ejpam-4254	203	33	t	t	NOUN
ejpam-4254	203	34	∈	∈	PROPN
ejpam-4254	204	1	[	[	X
ejpam-4254	204	2	0	0	NUM
ejpam-4254	204	3	,	,	PUNCT
ejpam-4254	204	4	1	1	NUM
ejpam-4254	204	5	]	]	PUNCT
ejpam-4254	204	6	.	.	PUNCT
ejpam-4254	205	1	proof	proof	NOUN
ejpam-4254	205	2	.	.	PUNCT
ejpam-4254	206	1	assume	assume	VERB
ejpam-4254	206	2	p	p	X
ejpam-4254	206	3	=	=	X
ejpam-4254	206	4	(	(	PUNCT
ejpam-4254	206	5	µp	µp	PROPN
ejpam-4254	206	6	,	,	PUNCT
ejpam-4254	206	7	νp	νp	NOUN
ejpam-4254	206	8	)	)	PUNCT
ejpam-4254	206	9	is	be	AUX
ejpam-4254	206	10	a	a	DET
ejpam-4254	206	11	pfups	pfup	NOUN
ejpam-4254	206	12	of	of	ADP
ejpam-4254	206	13	u	u	PROPN
ejpam-4254	206	14	.	.	PUNCT
ejpam-4254	207	1	let	let	VERB
ejpam-4254	207	2	t	t	X
ejpam-4254	207	3	∈	∈	PROPN
ejpam-4254	208	1	[	[	X
ejpam-4254	208	2	0	0	NUM
ejpam-4254	208	3	,	,	PUNCT
ejpam-4254	208	4	1	1	NUM
ejpam-4254	208	5	]	]	PUNCT
ejpam-4254	208	6	be	be	AUX
ejpam-4254	208	7	such	such	ADJ
ejpam-4254	208	8	that	that	SCONJ
ejpam-4254	208	9	u(µp	u(µp	NOUN
ejpam-4254	208	10	,	,	PUNCT
ejpam-4254	208	11	t	t	PROPN
ejpam-4254	208	12	)	)	PUNCT
ejpam-4254	208	13	,	,	PUNCT
ejpam-4254	208	14	l(νp	l(νp	PROPN
ejpam-4254	208	15	,	,	PUNCT
ejpam-4254	208	16	t	t	PROPN
ejpam-4254	208	17	)	)	PUNCT
ejpam-4254	208	18	̸=	̸=	PROPN
ejpam-4254	208	19	∅.	∅.	ADV
ejpam-4254	208	20	let	let	VERB
ejpam-4254	208	21	a	a	DET
ejpam-4254	208	22	,	,	PUNCT
ejpam-4254	208	23	b	b	X
ejpam-4254	208	24	∈	∈	PROPN
ejpam-4254	208	25	u	u	NOUN
ejpam-4254	208	26	.	.	PUNCT
ejpam-4254	209	1	then	then	ADV
ejpam-4254	209	2	a	a	DET
ejpam-4254	209	3	,	,	PUNCT
ejpam-4254	209	4	b	b	PROPN
ejpam-4254	209	5	∈	∈	PROPN
ejpam-4254	209	6	u(µp	u(µp	PROPN
ejpam-4254	209	7	,	,	PUNCT
ejpam-4254	209	8	t	t	PROPN
ejpam-4254	209	9	)	)	PUNCT
ejpam-4254	209	10	⇒	⇒	NOUN
ejpam-4254	209	11	µp(a	µp(a	NUM
ejpam-4254	209	12	)	)	PUNCT
ejpam-4254	209	13	≥	≥	NOUN
ejpam-4254	209	14	t	t	PROPN
ejpam-4254	209	15	,	,	PUNCT
ejpam-4254	209	16	µp(b	µp(b	ADJ
ejpam-4254	209	17	)	)	PUNCT
ejpam-4254	209	18	≥	≥	NOUN
ejpam-4254	209	19	t	t	PROPN
ejpam-4254	209	20	⇒	⇒	PROPN
ejpam-4254	209	21	min{µp(a	min{µp(a	NOUN
ejpam-4254	209	22	)	)	PUNCT
ejpam-4254	209	23	,	,	PUNCT
ejpam-4254	209	24	µp(b	µp(b	ADJ
ejpam-4254	209	25	)	)	PUNCT
ejpam-4254	209	26	}	}	PUNCT
ejpam-4254	209	27	≥	≥	PROPN
ejpam-4254	209	28	t	t	PROPN
ejpam-4254	209	29	⇒	⇒	NOUN
ejpam-4254	209	30	µp(a	µp(a	PUNCT
ejpam-4254	209	31	⋆	⋆	NOUN
ejpam-4254	209	32	b	b	NOUN
ejpam-4254	209	33	)	)	PUNCT
ejpam-4254	209	34	≥	≥	NOUN
ejpam-4254	209	35	min{µp(a	min{µp(a	NOUN
ejpam-4254	209	36	)	)	PUNCT
ejpam-4254	209	37	,	,	PUNCT
ejpam-4254	209	38	µp(b	µp(b	ADJ
ejpam-4254	209	39	)	)	PUNCT
ejpam-4254	209	40	}	}	PUNCT
ejpam-4254	209	41	≥	≥	PROPN
ejpam-4254	209	42	t	t	PROPN
ejpam-4254	209	43	(	(	PUNCT
ejpam-4254	209	44	(	(	PUNCT
ejpam-4254	209	45	1.21	1.21	NUM
ejpam-4254	209	46	)	)	PUNCT
ejpam-4254	209	47	)	)	PUNCT
ejpam-4254	209	48	⇒	⇒	VERB
ejpam-4254	209	49	a	a	DET
ejpam-4254	209	50	⋆	⋆	NOUN
ejpam-4254	209	51	b	b	NOUN
ejpam-4254	209	52	∈	∈	PROPN
ejpam-4254	209	53	u(µp	u(µp	PROPN
ejpam-4254	209	54	,	,	PUNCT
ejpam-4254	209	55	t	t	PROPN
ejpam-4254	209	56	)	)	PUNCT
ejpam-4254	209	57	and	and	CCONJ
ejpam-4254	209	58	a	a	PRON
ejpam-4254	209	59	,	,	PUNCT
ejpam-4254	209	60	b	b	PROPN
ejpam-4254	209	61	∈	∈	PROPN
ejpam-4254	209	62	l(νp	l(νp	PROPN
ejpam-4254	209	63	,	,	PUNCT
ejpam-4254	209	64	t	t	PROPN
ejpam-4254	209	65	)	)	PUNCT
ejpam-4254	209	66	⇒	⇒	NOUN
ejpam-4254	209	67	νp(a	νp(a	NUM
ejpam-4254	209	68	)	)	PUNCT
ejpam-4254	209	69	≤	≤	NOUN
ejpam-4254	209	70	t	t	PROPN
ejpam-4254	209	71	,	,	PUNCT
ejpam-4254	209	72	νp(b	νp(b	NOUN
ejpam-4254	209	73	)	)	PUNCT
ejpam-4254	209	74	≤	≤	PUNCT
ejpam-4254	210	1	t	t	PROPN
ejpam-4254	210	2	⇒	⇒	PROPN
ejpam-4254	210	3	max{µp(a	max{µp(a	PROPN
ejpam-4254	210	4	)	)	PUNCT
ejpam-4254	210	5	,	,	PUNCT
ejpam-4254	210	6	νp(b	νp(b	NOUN
ejpam-4254	210	7	)	)	PUNCT
ejpam-4254	210	8	}	}	PUNCT
ejpam-4254	210	9	≤	≤	NUM
ejpam-4254	210	10	t	t	PROPN
ejpam-4254	210	11	a.	a.	NOUN
ejpam-4254	210	12	iampan	iampan	PROPN
ejpam-4254	210	13	et	et	PROPN
ejpam-4254	210	14	al	al	PROPN
ejpam-4254	210	15	.	.	PUNCT
ejpam-4254	210	16	/	/	SYM
ejpam-4254	210	17	eur	eur	PROPN
ejpam-4254	210	18	.	.	PUNCT
ejpam-4254	211	1	j.	j.	PROPN
ejpam-4254	211	2	pure	pure	PROPN
ejpam-4254	211	3	appl	appl	PROPN
ejpam-4254	211	4	.	.	PROPN
ejpam-4254	211	5	math	math	PROPN
ejpam-4254	211	6	,	,	PUNCT
ejpam-4254	211	7	15	15	NUM
ejpam-4254	211	8	(	(	PUNCT
ejpam-4254	211	9	1	1	NUM
ejpam-4254	211	10	)	)	PUNCT
ejpam-4254	211	11	(	(	PUNCT
ejpam-4254	211	12	2022	2022	NUM
ejpam-4254	211	13	)	)	PUNCT
ejpam-4254	211	14	,	,	PUNCT
ejpam-4254	211	15	169	169	NUM
ejpam-4254	211	16	-	-	SYM
ejpam-4254	211	17	198	198	NUM
ejpam-4254	211	18	182	182	NUM
ejpam-4254	211	19	⇒	⇒	NOUN
ejpam-4254	211	20	νp(a	νp(a	ADV
ejpam-4254	211	21	⋆	⋆	PUNCT
ejpam-4254	211	22	b	b	NOUN
ejpam-4254	211	23	)	)	PUNCT
ejpam-4254	211	24	≤	≤	NOUN
ejpam-4254	211	25	max{νp(a	max{νp(a	NOUN
ejpam-4254	211	26	)	)	PUNCT
ejpam-4254	211	27	,	,	PUNCT
ejpam-4254	211	28	νp(b	νp(b	NOUN
ejpam-4254	211	29	)	)	PUNCT
ejpam-4254	211	30	}	}	PUNCT
ejpam-4254	211	31	≤	≤	PROPN
ejpam-4254	211	32	t	t	NOUN
ejpam-4254	211	33	(	(	PUNCT
ejpam-4254	211	34	(	(	PUNCT
ejpam-4254	211	35	1.22	1.22	NUM
ejpam-4254	211	36	)	)	PUNCT
ejpam-4254	211	37	)	)	PUNCT
ejpam-4254	211	38	⇒	⇒	VERB
ejpam-4254	211	39	a	a	DET
ejpam-4254	211	40	⋆	⋆	NOUN
ejpam-4254	211	41	b	b	PROPN
ejpam-4254	211	42	∈	∈	PROPN
ejpam-4254	211	43	l(νp	l(νp	PROPN
ejpam-4254	211	44	,	,	PUNCT
ejpam-4254	211	45	t	t	PROPN
ejpam-4254	211	46	)	)	PUNCT
ejpam-4254	211	47	.	.	PUNCT
ejpam-4254	212	1	hence	hence	ADV
ejpam-4254	212	2	,	,	PUNCT
ejpam-4254	212	3	u(µp	u(µp	PROPN
ejpam-4254	212	4	,	,	PUNCT
ejpam-4254	212	5	t	t	PROPN
ejpam-4254	212	6	)	)	PUNCT
ejpam-4254	212	7	and	and	CCONJ
ejpam-4254	212	8	l(νp	l(νp	PROPN
ejpam-4254	212	9	,	,	PUNCT
ejpam-4254	212	10	t	t	PROPN
ejpam-4254	212	11	)	)	PUNCT
ejpam-4254	212	12	are	be	AUX
ejpam-4254	212	13	upss	upss	NOUN
ejpam-4254	212	14	of	of	ADP
ejpam-4254	212	15	u	u	NOUN
ejpam-4254	212	16	.	.	PUNCT
ejpam-4254	213	1	conversely	conversely	ADV
ejpam-4254	213	2	,	,	PUNCT
ejpam-4254	213	3	assume	assume	VERB
ejpam-4254	213	4	for	for	ADP
ejpam-4254	213	5	all	all	DET
ejpam-4254	213	6	t	t	NOUN
ejpam-4254	213	7	∈	∈	PROPN
ejpam-4254	214	1	[	[	X
ejpam-4254	214	2	0	0	NUM
ejpam-4254	214	3	,	,	PUNCT
ejpam-4254	214	4	1	1	NUM
ejpam-4254	214	5	]	]	PUNCT
ejpam-4254	214	6	,	,	PUNCT
ejpam-4254	214	7	u(µp	u(µp	PROPN
ejpam-4254	214	8	,	,	PUNCT
ejpam-4254	214	9	t	t	PROPN
ejpam-4254	214	10	)	)	PUNCT
ejpam-4254	214	11	and	and	CCONJ
ejpam-4254	214	12	l(νp	l(νp	PROPN
ejpam-4254	214	13	,	,	PUNCT
ejpam-4254	214	14	t	t	PROPN
ejpam-4254	214	15	)	)	PUNCT
ejpam-4254	214	16	are	be	AUX
ejpam-4254	214	17	upss	upss	NOUN
ejpam-4254	214	18	of	of	ADP
ejpam-4254	214	19	u	u	PRON
ejpam-4254	214	20	if	if	SCONJ
ejpam-4254	214	21	the	the	DET
ejpam-4254	214	22	sets	set	NOUN
ejpam-4254	214	23	are	be	AUX
ejpam-4254	214	24	nonempty	nonempty	ADJ
ejpam-4254	214	25	.	.	PUNCT
ejpam-4254	215	1	let	let	VERB
ejpam-4254	215	2	a	a	DET
ejpam-4254	215	3	,	,	PUNCT
ejpam-4254	215	4	b	b	X
ejpam-4254	215	5	∈	∈	PROPN
ejpam-4254	215	6	u	u	NOUN
ejpam-4254	215	7	.	.	PUNCT
ejpam-4254	216	1	choose	choose	VERB
ejpam-4254	216	2	t	t	NOUN
ejpam-4254	216	3	=	=	SYM
ejpam-4254	216	4	min{µp(a	min{µp(a	NOUN
ejpam-4254	216	5	)	)	PUNCT
ejpam-4254	216	6	,	,	PUNCT
ejpam-4254	216	7	µp(b	µp(b	ADJ
ejpam-4254	216	8	)	)	PUNCT
ejpam-4254	216	9	}	}	PUNCT
ejpam-4254	216	10	∈	∈	PROPN
ejpam-4254	217	1	[	[	X
ejpam-4254	217	2	0	0	NUM
ejpam-4254	217	3	,	,	PUNCT
ejpam-4254	217	4	1	1	NUM
ejpam-4254	217	5	]	]	PUNCT
ejpam-4254	217	6	.	.	PUNCT
ejpam-4254	218	1	then	then	ADV
ejpam-4254	218	2	µp(a	µp(a	NUM
ejpam-4254	218	3	)	)	PUNCT
ejpam-4254	218	4	≥	≥	NOUN
ejpam-4254	218	5	t	t	NOUN
ejpam-4254	218	6	and	and	CCONJ
ejpam-4254	218	7	µp(b	µp(b	ADJ
ejpam-4254	218	8	)	)	PUNCT
ejpam-4254	218	9	≥	≥	NOUN
ejpam-4254	218	10	t.	t.	NOUN
ejpam-4254	218	11	thus	thus	ADV
ejpam-4254	218	12	a	a	PRON
ejpam-4254	218	13	,	,	PUNCT
ejpam-4254	218	14	b	b	PROPN
ejpam-4254	218	15	∈	∈	PROPN
ejpam-4254	218	16	u(µp	u(µp	PROPN
ejpam-4254	218	17	,	,	PUNCT
ejpam-4254	218	18	t	t	PROPN
ejpam-4254	218	19	)	)	PUNCT
ejpam-4254	218	20	̸=	̸=	PROPN
ejpam-4254	218	21	∅.	∅.	ADV
ejpam-4254	218	22	as	as	ADP
ejpam-4254	218	23	a	a	DET
ejpam-4254	218	24	hypothesis	hypothesis	NOUN
ejpam-4254	218	25	,	,	PUNCT
ejpam-4254	218	26	we	we	PRON
ejpam-4254	218	27	get	get	VERB
ejpam-4254	218	28	u(µp	u(µp	NOUN
ejpam-4254	218	29	,	,	PUNCT
ejpam-4254	218	30	t	t	PROPN
ejpam-4254	218	31	)	)	PUNCT
ejpam-4254	218	32	is	be	AUX
ejpam-4254	218	33	a	a	DET
ejpam-4254	218	34	ups	up	NOUN
ejpam-4254	218	35	of	of	ADP
ejpam-4254	218	36	u	u	NOUN
ejpam-4254	219	1	and	and	CCONJ
ejpam-4254	219	2	so	so	ADV
ejpam-4254	219	3	a⋆b	a⋆b	ADP
ejpam-4254	219	4	∈	∈	PROPN
ejpam-4254	219	5	u(µp	u(µp	NOUN
ejpam-4254	219	6	,	,	PUNCT
ejpam-4254	219	7	t	t	PROPN
ejpam-4254	219	8	)	)	PUNCT
ejpam-4254	219	9	.	.	PUNCT
ejpam-4254	220	1	thus	thus	ADV
ejpam-4254	220	2	µp(a	µp(a	PUNCT
ejpam-4254	220	3	⋆	⋆	ADP
ejpam-4254	220	4	b	b	NOUN
ejpam-4254	220	5	)	)	PUNCT
ejpam-4254	220	6	≥	≥	NOUN
ejpam-4254	220	7	t	t	NOUN
ejpam-4254	220	8	=	=	SYM
ejpam-4254	220	9	min{µp(a	min{µp(a	NOUN
ejpam-4254	220	10	)	)	PUNCT
ejpam-4254	220	11	,	,	PUNCT
ejpam-4254	220	12	µp(b	µp(b	ADJ
ejpam-4254	220	13	)	)	PUNCT
ejpam-4254	220	14	}	}	PUNCT
ejpam-4254	220	15	.	.	PUNCT
ejpam-4254	221	1	choose	choose	VERB
ejpam-4254	221	2	t	t	NOUN
ejpam-4254	221	3	=	=	SYM
ejpam-4254	221	4	max{νp(a	max{νp(a	NOUN
ejpam-4254	221	5	)	)	PUNCT
ejpam-4254	221	6	,	,	PUNCT
ejpam-4254	221	7	νp(b	νp(b	NOUN
ejpam-4254	221	8	)	)	PUNCT
ejpam-4254	221	9	}	}	PUNCT
ejpam-4254	221	10	∈	∈	PROPN
ejpam-4254	222	1	[	[	X
ejpam-4254	222	2	0	0	NUM
ejpam-4254	222	3	,	,	PUNCT
ejpam-4254	222	4	1	1	NUM
ejpam-4254	222	5	]	]	PUNCT
ejpam-4254	222	6	.	.	PUNCT
ejpam-4254	223	1	then	then	ADV
ejpam-4254	223	2	νp(a	νp(a	NUM
ejpam-4254	223	3	)	)	PUNCT
ejpam-4254	223	4	≤	≤	NOUN
ejpam-4254	223	5	t	t	NOUN
ejpam-4254	223	6	and	and	CCONJ
ejpam-4254	223	7	νp(b	νp(b	NOUN
ejpam-4254	223	8	)	)	PUNCT
ejpam-4254	223	9	≤	≤	NOUN
ejpam-4254	224	1	t.	t.	NOUN
ejpam-4254	224	2	thus	thus	ADV
ejpam-4254	224	3	a	a	PRON
ejpam-4254	224	4	,	,	PUNCT
ejpam-4254	224	5	b	b	PROPN
ejpam-4254	224	6	∈	∈	PROPN
ejpam-4254	224	7	l(νp	l(νp	PROPN
ejpam-4254	224	8	,	,	PUNCT
ejpam-4254	224	9	t	t	PROPN
ejpam-4254	224	10	)	)	PUNCT
ejpam-4254	224	11	̸=	̸=	PROPN
ejpam-4254	224	12	∅.	∅.	ADV
ejpam-4254	224	13	as	as	ADP
ejpam-4254	224	14	a	a	DET
ejpam-4254	224	15	hypothesis	hypothesis	NOUN
ejpam-4254	224	16	,	,	PUNCT
ejpam-4254	224	17	we	we	PRON
ejpam-4254	224	18	get	get	VERB
ejpam-4254	224	19	l(νp	l(νp	PROPN
ejpam-4254	224	20	,	,	PUNCT
ejpam-4254	224	21	t	t	PROPN
ejpam-4254	224	22	)	)	PUNCT
ejpam-4254	224	23	is	be	AUX
ejpam-4254	224	24	a	a	DET
ejpam-4254	224	25	ups	up	NOUN
ejpam-4254	224	26	of	of	ADP
ejpam-4254	224	27	u	u	NOUN
ejpam-4254	224	28	and	and	CCONJ
ejpam-4254	224	29	so	so	ADV
ejpam-4254	224	30	a	a	DET
ejpam-4254	224	31	⋆	⋆	X
ejpam-4254	224	32	b	b	PROPN
ejpam-4254	224	33	∈	∈	PROPN
ejpam-4254	224	34	u(νp	u(νp	PROPN
ejpam-4254	224	35	,	,	PUNCT
ejpam-4254	224	36	t	t	PROPN
ejpam-4254	224	37	)	)	PUNCT
ejpam-4254	224	38	.	.	PUNCT
ejpam-4254	225	1	thus	thus	ADV
ejpam-4254	225	2	νp(a	νp(a	NUM
ejpam-4254	225	3	⋆	⋆	ADJ
ejpam-4254	225	4	b	b	NOUN
ejpam-4254	225	5	)	)	PUNCT
ejpam-4254	225	6	≤	≤	NOUN
ejpam-4254	225	7	t	t	NOUN
ejpam-4254	225	8	=	=	SYM
ejpam-4254	225	9	max{νp(a	max{νp(a	NOUN
ejpam-4254	225	10	)	)	PUNCT
ejpam-4254	225	11	,	,	PUNCT
ejpam-4254	225	12	νp(b	νp(b	NOUN
ejpam-4254	225	13	)	)	PUNCT
ejpam-4254	225	14	}	}	PUNCT
ejpam-4254	225	15	.	.	PUNCT
ejpam-4254	226	1	hence	hence	ADV
ejpam-4254	226	2	,	,	PUNCT
ejpam-4254	226	3	p	p	PROPN
ejpam-4254	226	4	is	be	AUX
ejpam-4254	226	5	a	a	DET
ejpam-4254	226	6	pfups	pfup	NOUN
ejpam-4254	226	7	of	of	ADP
ejpam-4254	226	8	u	u	PROPN
ejpam-4254	226	9	.	.	PUNCT
ejpam-4254	227	1	theorem	theorem	NOUN
ejpam-4254	227	2	3	3	NUM
ejpam-4254	227	3	.	.	PUNCT
ejpam-4254	228	1	p	p	NOUN
ejpam-4254	228	2	is	be	AUX
ejpam-4254	228	3	a	a	DET
ejpam-4254	228	4	pfups	pfup	NOUN
ejpam-4254	228	5	of	of	ADP
ejpam-4254	228	6	u	u	PRON
ejpam-4254	228	7	if	if	SCONJ
ejpam-4254	228	8	and	and	CCONJ
ejpam-4254	228	9	only	only	ADV
ejpam-4254	228	10	if	if	SCONJ
ejpam-4254	228	11	u+(µp	u+(µp	NOUN
ejpam-4254	228	12	,	,	PUNCT
ejpam-4254	228	13	t	t	PROPN
ejpam-4254	228	14	)	)	PUNCT
ejpam-4254	228	15	and	and	CCONJ
ejpam-4254	228	16	l−(νp	l−(νp	PROPN
ejpam-4254	228	17	,	,	PUNCT
ejpam-4254	228	18	t	t	PROPN
ejpam-4254	228	19	)	)	PUNCT
ejpam-4254	228	20	are	be	AUX
ejpam-4254	228	21	,	,	PUNCT
ejpam-4254	228	22	if	if	SCONJ
ejpam-4254	228	23	the	the	DET
ejpam-4254	228	24	sets	set	NOUN
ejpam-4254	228	25	are	be	AUX
ejpam-4254	228	26	nonempty	nonempty	ADJ
ejpam-4254	228	27	,	,	PUNCT
ejpam-4254	228	28	upss	upss	ADV
ejpam-4254	228	29	of	of	ADP
ejpam-4254	228	30	u	u	NOUN
ejpam-4254	228	31	for	for	ADP
ejpam-4254	228	32	every	every	DET
ejpam-4254	228	33	t	t	NOUN
ejpam-4254	228	34	∈	∈	PROPN
ejpam-4254	229	1	[	[	X
ejpam-4254	229	2	0	0	NUM
ejpam-4254	229	3	,	,	PUNCT
ejpam-4254	229	4	1	1	NUM
ejpam-4254	229	5	]	]	PUNCT
ejpam-4254	229	6	.	.	PUNCT
ejpam-4254	230	1	proof	proof	NOUN
ejpam-4254	230	2	.	.	PUNCT
ejpam-4254	231	1	assume	assume	VERB
ejpam-4254	231	2	p	p	X
ejpam-4254	231	3	=	=	X
ejpam-4254	231	4	(	(	PUNCT
ejpam-4254	231	5	µp	µp	PROPN
ejpam-4254	231	6	,	,	PUNCT
ejpam-4254	231	7	νp	νp	NOUN
ejpam-4254	231	8	)	)	PUNCT
ejpam-4254	231	9	is	be	AUX
ejpam-4254	231	10	a	a	DET
ejpam-4254	231	11	pfups	pfup	NOUN
ejpam-4254	231	12	of	of	ADP
ejpam-4254	231	13	u	u	PROPN
ejpam-4254	231	14	.	.	PUNCT
ejpam-4254	232	1	let	let	VERB
ejpam-4254	232	2	t	t	X
ejpam-4254	232	3	∈	∈	PROPN
ejpam-4254	233	1	[	[	X
ejpam-4254	233	2	0	0	NUM
ejpam-4254	233	3	,	,	PUNCT
ejpam-4254	233	4	1	1	NUM
ejpam-4254	233	5	]	]	PUNCT
ejpam-4254	233	6	be	be	AUX
ejpam-4254	233	7	such	such	ADJ
ejpam-4254	233	8	that	that	SCONJ
ejpam-4254	233	9	u+(µp	u+(µp	NOUN
ejpam-4254	233	10	,	,	PUNCT
ejpam-4254	233	11	t	t	PROPN
ejpam-4254	233	12	)	)	PUNCT
ejpam-4254	233	13	,	,	PUNCT
ejpam-4254	233	14	l−(νp	l−(νp	PROPN
ejpam-4254	233	15	,	,	PUNCT
ejpam-4254	233	16	t	t	PROPN
ejpam-4254	233	17	)	)	PUNCT
ejpam-4254	233	18	̸=	̸=	PROPN
ejpam-4254	233	19	∅.	∅.	ADV
ejpam-4254	233	20	let	let	VERB
ejpam-4254	233	21	a	a	DET
ejpam-4254	233	22	,	,	PUNCT
ejpam-4254	233	23	b	b	X
ejpam-4254	233	24	∈	∈	PROPN
ejpam-4254	233	25	u	u	NOUN
ejpam-4254	233	26	.	.	PUNCT
ejpam-4254	234	1	then	then	ADV
ejpam-4254	234	2	a	a	DET
ejpam-4254	234	3	,	,	PUNCT
ejpam-4254	234	4	b	b	PROPN
ejpam-4254	234	5	∈	∈	PROPN
ejpam-4254	234	6	u+(µp	u+(µp	PROPN
ejpam-4254	234	7	,	,	PUNCT
ejpam-4254	234	8	t	t	PROPN
ejpam-4254	234	9	)	)	PUNCT
ejpam-4254	234	10	⇒	⇒	NOUN
ejpam-4254	234	11	µp(a	µp(a	NUM
ejpam-4254	234	12	)	)	PUNCT
ejpam-4254	234	13	>	>	X
ejpam-4254	234	14	t	t	PROPN
ejpam-4254	234	15	,	,	PUNCT
ejpam-4254	234	16	µp(b	µp(b	ADJ
ejpam-4254	234	17	)	)	PUNCT
ejpam-4254	234	18	>	>	X
ejpam-4254	234	19	t	t	PROPN
ejpam-4254	234	20	⇒	⇒	VERB
ejpam-4254	234	21	min{µp(a	min{µp(a	NOUN
ejpam-4254	234	22	)	)	PUNCT
ejpam-4254	234	23	,	,	PUNCT
ejpam-4254	234	24	µp(b	µp(b	ADJ
ejpam-4254	234	25	)	)	PUNCT
ejpam-4254	234	26	}	}	PUNCT
ejpam-4254	234	27	>	>	PUNCT
ejpam-4254	234	28	t	t	PROPN
ejpam-4254	234	29	⇒	⇒	NOUN
ejpam-4254	234	30	µp(a	µp(a	PUNCT
ejpam-4254	234	31	⋆	⋆	PROPN
ejpam-4254	234	32	b	b	NOUN
ejpam-4254	234	33	)	)	PUNCT
ejpam-4254	234	34	≥	≥	NOUN
ejpam-4254	234	35	min{µp(a	min{µp(a	NOUN
ejpam-4254	234	36	)	)	PUNCT
ejpam-4254	234	37	,	,	PUNCT
ejpam-4254	234	38	µp(b	µp(b	ADJ
ejpam-4254	234	39	)	)	PUNCT
ejpam-4254	234	40	}	}	PUNCT
ejpam-4254	234	41	>	>	X
ejpam-4254	234	42	t	t	PROPN
ejpam-4254	234	43	(	(	PUNCT
ejpam-4254	234	44	(	(	PUNCT
ejpam-4254	234	45	1.21	1.21	NUM
ejpam-4254	234	46	)	)	PUNCT
ejpam-4254	234	47	)	)	PUNCT
ejpam-4254	234	48	⇒	⇒	VERB
ejpam-4254	234	49	a	a	DET
ejpam-4254	234	50	⋆	⋆	NOUN
ejpam-4254	234	51	b	b	PROPN
ejpam-4254	234	52	∈	∈	PROPN
ejpam-4254	234	53	u+(µp	u+(µp	PROPN
ejpam-4254	234	54	,	,	PUNCT
ejpam-4254	234	55	t	t	PROPN
ejpam-4254	234	56	)	)	PUNCT
ejpam-4254	234	57	and	and	CCONJ
ejpam-4254	234	58	a	a	PRON
ejpam-4254	234	59	,	,	PUNCT
ejpam-4254	234	60	b	b	X
ejpam-4254	234	61	∈	∈	PROPN
ejpam-4254	234	62	l−(νp	l−(νp	PROPN
ejpam-4254	234	63	,	,	PUNCT
ejpam-4254	234	64	t	t	PROPN
ejpam-4254	234	65	)	)	PUNCT
ejpam-4254	234	66	⇒	⇒	NOUN
ejpam-4254	234	67	νp(a	νp(a	NUM
ejpam-4254	234	68	)	)	PUNCT
ejpam-4254	234	69	<	<	X
ejpam-4254	234	70	t	t	PROPN
ejpam-4254	234	71	,	,	PUNCT
ejpam-4254	234	72	νp(b	νp(b	NOUN
ejpam-4254	234	73	)	)	PUNCT
ejpam-4254	235	1	<	<	X
ejpam-4254	235	2	t	t	X
ejpam-4254	235	3	⇒	⇒	PROPN
ejpam-4254	235	4	max{µp(a	max{µp(a	PROPN
ejpam-4254	235	5	)	)	PUNCT
ejpam-4254	235	6	,	,	PUNCT
ejpam-4254	235	7	νp(b	νp(b	NOUN
ejpam-4254	235	8	)	)	PUNCT
ejpam-4254	235	9	}	}	PUNCT
ejpam-4254	235	10	<	<	X
ejpam-4254	235	11	t	t	PROPN
ejpam-4254	235	12	⇒	⇒	NOUN
ejpam-4254	235	13	νp(a	νp(a	ADV
ejpam-4254	235	14	⋆	⋆	NOUN
ejpam-4254	235	15	b	b	NOUN
ejpam-4254	235	16	)	)	PUNCT
ejpam-4254	235	17	≤	≤	NOUN
ejpam-4254	235	18	max{νp(a	max{νp(a	NOUN
ejpam-4254	235	19	)	)	PUNCT
ejpam-4254	235	20	,	,	PUNCT
ejpam-4254	235	21	νp(b	νp(b	NOUN
ejpam-4254	235	22	)	)	PUNCT
ejpam-4254	235	23	}	}	PUNCT
ejpam-4254	235	24	<	<	X
ejpam-4254	235	25	t	t	X
ejpam-4254	235	26	(	(	PUNCT
ejpam-4254	235	27	(	(	PUNCT
ejpam-4254	235	28	1.22	1.22	NUM
ejpam-4254	235	29	)	)	PUNCT
ejpam-4254	235	30	)	)	PUNCT
ejpam-4254	235	31	⇒	⇒	VERB
ejpam-4254	235	32	a	a	DET
ejpam-4254	235	33	⋆	⋆	NOUN
ejpam-4254	235	34	b	b	X
ejpam-4254	235	35	∈	∈	PROPN
ejpam-4254	235	36	l−(νp	l−(νp	PROPN
ejpam-4254	235	37	,	,	PUNCT
ejpam-4254	235	38	t	t	PROPN
ejpam-4254	235	39	)	)	PUNCT
ejpam-4254	235	40	.	.	PUNCT
ejpam-4254	236	1	hence	hence	ADV
ejpam-4254	236	2	,	,	PUNCT
ejpam-4254	236	3	u+(µp	u+(µp	PROPN
ejpam-4254	236	4	,	,	PUNCT
ejpam-4254	236	5	t	t	PROPN
ejpam-4254	236	6	)	)	PUNCT
ejpam-4254	236	7	and	and	CCONJ
ejpam-4254	236	8	l−(νp	l−(νp	PROPN
ejpam-4254	236	9	,	,	PUNCT
ejpam-4254	236	10	t	t	PROPN
ejpam-4254	236	11	)	)	PUNCT
ejpam-4254	236	12	are	be	AUX
ejpam-4254	236	13	upss	upss	NOUN
ejpam-4254	236	14	of	of	ADP
ejpam-4254	236	15	u	u	NOUN
ejpam-4254	236	16	.	.	PUNCT
ejpam-4254	237	1	conversely	conversely	ADV
ejpam-4254	237	2	,	,	PUNCT
ejpam-4254	237	3	assume	assume	VERB
ejpam-4254	237	4	for	for	ADP
ejpam-4254	237	5	all	all	DET
ejpam-4254	237	6	t	t	NOUN
ejpam-4254	237	7	∈	∈	PROPN
ejpam-4254	238	1	[	[	X
ejpam-4254	238	2	0	0	NUM
ejpam-4254	238	3	,	,	PUNCT
ejpam-4254	238	4	1	1	NUM
ejpam-4254	238	5	]	]	PUNCT
ejpam-4254	238	6	,	,	PUNCT
ejpam-4254	238	7	u+(µp	u+(µp	PROPN
ejpam-4254	238	8	,	,	PUNCT
ejpam-4254	238	9	t	t	PROPN
ejpam-4254	238	10	)	)	PUNCT
ejpam-4254	238	11	and	and	CCONJ
ejpam-4254	238	12	l−(νp	l−(νp	PROPN
ejpam-4254	238	13	,	,	PUNCT
ejpam-4254	238	14	t	t	PROPN
ejpam-4254	238	15	)	)	PUNCT
ejpam-4254	238	16	are	be	AUX
ejpam-4254	238	17	upss	upss	NOUN
ejpam-4254	238	18	of	of	ADP
ejpam-4254	238	19	u	u	PRON
ejpam-4254	238	20	if	if	SCONJ
ejpam-4254	238	21	the	the	DET
ejpam-4254	238	22	sets	set	NOUN
ejpam-4254	238	23	are	be	AUX
ejpam-4254	238	24	nonempty	nonempty	ADJ
ejpam-4254	238	25	.	.	PUNCT
ejpam-4254	239	1	suppose	suppose	VERB
ejpam-4254	239	2	there	there	PRON
ejpam-4254	239	3	exist	exist	VERB
ejpam-4254	239	4	a	a	DET
ejpam-4254	239	5	,	,	PUNCT
ejpam-4254	239	6	b	b	X
ejpam-4254	239	7	∈	∈	PROPN
ejpam-4254	239	8	u	u	NOUN
ejpam-4254	239	9	such	such	ADJ
ejpam-4254	239	10	that	that	PRON
ejpam-4254	239	11	µp(a⋆b	µp(a⋆b	NUM
ejpam-4254	239	12	)	)	PUNCT
ejpam-4254	239	13	<	<	X
ejpam-4254	239	14	min{µp(a	min{µp(a	NOUN
ejpam-4254	239	15	)	)	PUNCT
ejpam-4254	239	16	,	,	PUNCT
ejpam-4254	239	17	µp(b	µp(b	ADJ
ejpam-4254	239	18	)	)	PUNCT
ejpam-4254	239	19	}	}	PUNCT
ejpam-4254	239	20	.	.	PUNCT
ejpam-4254	240	1	choose	choose	VERB
ejpam-4254	240	2	t	t	PROPN
ejpam-4254	240	3	=	=	PUNCT
ejpam-4254	240	4	µp(a⋆	µp(a⋆	PROPN
ejpam-4254	240	5	b	b	NOUN
ejpam-4254	240	6	)	)	PUNCT
ejpam-4254	240	7	∈	∈	PROPN
ejpam-4254	241	1	[	[	X
ejpam-4254	241	2	0	0	NUM
ejpam-4254	241	3	,	,	PUNCT
ejpam-4254	241	4	1	1	NUM
ejpam-4254	241	5	]	]	PUNCT
ejpam-4254	241	6	.	.	PUNCT
ejpam-4254	242	1	then	then	ADV
ejpam-4254	242	2	µp(a	µp(a	NUM
ejpam-4254	242	3	)	)	PUNCT
ejpam-4254	242	4	>	>	X
ejpam-4254	243	1	t	t	PROPN
ejpam-4254	243	2	and	and	CCONJ
ejpam-4254	243	3	µp(b	µp(b	ADP
ejpam-4254	243	4	)	)	PUNCT
ejpam-4254	243	5	>	>	PUNCT
ejpam-4254	244	1	t.	t.	X
ejpam-4254	244	2	thus	thus	ADV
ejpam-4254	244	3	a	a	PRON
ejpam-4254	244	4	,	,	PUNCT
ejpam-4254	244	5	b	b	PROPN
ejpam-4254	244	6	∈	∈	PROPN
ejpam-4254	244	7	u+(µp	u+(µp	PROPN
ejpam-4254	244	8	,	,	PUNCT
ejpam-4254	244	9	t	t	PROPN
ejpam-4254	244	10	)	)	PUNCT
ejpam-4254	244	11	̸=	̸=	PROPN
ejpam-4254	244	12	∅.	∅.	ADV
ejpam-4254	244	13	as	as	ADP
ejpam-4254	244	14	a	a	DET
ejpam-4254	244	15	hypothesis	hypothesis	NOUN
ejpam-4254	244	16	,	,	PUNCT
ejpam-4254	244	17	we	we	PRON
ejpam-4254	244	18	get	get	VERB
ejpam-4254	244	19	u+(µp	u+(µp	NOUN
ejpam-4254	244	20	,	,	PUNCT
ejpam-4254	244	21	t	t	PROPN
ejpam-4254	244	22	)	)	PUNCT
ejpam-4254	244	23	is	be	AUX
ejpam-4254	244	24	a	a	DET
ejpam-4254	244	25	ups	up	NOUN
ejpam-4254	244	26	of	of	ADP
ejpam-4254	244	27	u	u	NOUN
ejpam-4254	244	28	and	and	CCONJ
ejpam-4254	244	29	so	so	ADV
ejpam-4254	244	30	a	a	DET
ejpam-4254	244	31	⋆	⋆	NOUN
ejpam-4254	244	32	b	b	PROPN
ejpam-4254	244	33	∈	∈	PROPN
ejpam-4254	244	34	u+(µp	u+(µp	PROPN
ejpam-4254	244	35	,	,	PUNCT
ejpam-4254	244	36	t	t	PROPN
ejpam-4254	244	37	)	)	PUNCT
ejpam-4254	244	38	.	.	PUNCT
ejpam-4254	245	1	thus	thus	ADV
ejpam-4254	245	2	µp(a	µp(a	PUNCT
ejpam-4254	245	3	⋆	⋆	ADP
ejpam-4254	245	4	b	b	NOUN
ejpam-4254	245	5	)	)	PUNCT
ejpam-4254	245	6	>	>	PUNCT
ejpam-4254	246	1	t	t	PROPN
ejpam-4254	246	2	=	=	PUNCT
ejpam-4254	246	3	µp(a	µp(a	NUM
ejpam-4254	246	4	⋆	⋆	X
ejpam-4254	246	5	b	b	NOUN
ejpam-4254	246	6	)	)	PUNCT
ejpam-4254	246	7	,	,	PUNCT
ejpam-4254	246	8	a	a	DET
ejpam-4254	246	9	contradiction	contradiction	NOUN
ejpam-4254	246	10	.	.	PUNCT
ejpam-4254	247	1	hence	hence	ADV
ejpam-4254	247	2	,	,	PUNCT
ejpam-4254	247	3	µp(a	µp(a	PUNCT
ejpam-4254	247	4	⋆	⋆	X
ejpam-4254	247	5	b	b	NOUN
ejpam-4254	247	6	)	)	PUNCT
ejpam-4254	247	7	≥	≥	NOUN
ejpam-4254	247	8	min{µp(a	min{µp(a	NOUN
ejpam-4254	247	9	)	)	PUNCT
ejpam-4254	247	10	,	,	PUNCT
ejpam-4254	247	11	µp(b	µp(b	ADJ
ejpam-4254	247	12	)	)	PUNCT
ejpam-4254	247	13	}	}	PUNCT
ejpam-4254	247	14	for	for	ADP
ejpam-4254	247	15	all	all	DET
ejpam-4254	247	16	a	a	DET
ejpam-4254	247	17	,	,	PUNCT
ejpam-4254	247	18	b	b	X
ejpam-4254	247	19	∈	∈	PROPN
ejpam-4254	247	20	u	u	NOUN
ejpam-4254	247	21	.	.	PUNCT
ejpam-4254	247	22	suppose	suppose	VERB
ejpam-4254	247	23	there	there	PRON
ejpam-4254	247	24	exist	exist	VERB
ejpam-4254	247	25	a	a	DET
ejpam-4254	247	26	,	,	PUNCT
ejpam-4254	247	27	b	b	X
ejpam-4254	247	28	∈	∈	PROPN
ejpam-4254	247	29	u	u	NOUN
ejpam-4254	247	30	such	such	ADJ
ejpam-4254	248	1	that	that	SCONJ
ejpam-4254	248	2	νp(a⋆b	νp(a⋆b	NOUN
ejpam-4254	248	3	)	)	PUNCT
ejpam-4254	248	4	>	>	X
ejpam-4254	248	5	max{νp(a	max{νp(a	NOUN
ejpam-4254	248	6	)	)	PUNCT
ejpam-4254	248	7	,	,	PUNCT
ejpam-4254	248	8	νp(b	νp(b	NOUN
ejpam-4254	248	9	)	)	PUNCT
ejpam-4254	248	10	}	}	PUNCT
ejpam-4254	248	11	.	.	PUNCT
ejpam-4254	249	1	choose	choose	VERB
ejpam-4254	249	2	t	t	PROPN
ejpam-4254	249	3	=	=	SYM
ejpam-4254	249	4	νp(a⋆	νp(a⋆	PROPN
ejpam-4254	249	5	b	b	X
ejpam-4254	249	6	)	)	PUNCT
ejpam-4254	249	7	∈	∈	PROPN
ejpam-4254	250	1	[	[	X
ejpam-4254	250	2	0	0	NUM
ejpam-4254	250	3	,	,	PUNCT
ejpam-4254	250	4	1	1	NUM
ejpam-4254	250	5	]	]	PUNCT
ejpam-4254	250	6	.	.	PUNCT
ejpam-4254	251	1	then	then	ADV
ejpam-4254	251	2	νp(a	νp(a	NUM
ejpam-4254	251	3	)	)	PUNCT
ejpam-4254	251	4	<	<	X
ejpam-4254	251	5	t	t	NOUN
ejpam-4254	251	6	and	and	CCONJ
ejpam-4254	251	7	νp(b	νp(b	NOUN
ejpam-4254	251	8	)	)	PUNCT
ejpam-4254	252	1	<	<	X
ejpam-4254	252	2	t.	t.	X
ejpam-4254	252	3	thus	thus	ADV
ejpam-4254	252	4	a	a	PRON
ejpam-4254	252	5	,	,	PUNCT
ejpam-4254	252	6	b	b	X
ejpam-4254	252	7	∈	∈	PROPN
ejpam-4254	252	8	l−(νp	l−(νp	PROPN
ejpam-4254	252	9	,	,	PUNCT
ejpam-4254	252	10	t	t	PROPN
ejpam-4254	252	11	)	)	PUNCT
ejpam-4254	252	12	̸=	̸=	PROPN
ejpam-4254	252	13	∅.	∅.	ADV
ejpam-4254	252	14	as	as	ADP
ejpam-4254	252	15	a	a	DET
ejpam-4254	252	16	hypothesis	hypothesis	NOUN
ejpam-4254	252	17	,	,	PUNCT
ejpam-4254	252	18	we	we	PRON
ejpam-4254	252	19	get	get	VERB
ejpam-4254	252	20	l−(νp	l−(νp	PROPN
ejpam-4254	252	21	,	,	PUNCT
ejpam-4254	252	22	t	t	PROPN
ejpam-4254	252	23	)	)	PUNCT
ejpam-4254	252	24	is	be	AUX
ejpam-4254	252	25	a	a	DET
ejpam-4254	252	26	ups	up	NOUN
ejpam-4254	252	27	of	of	ADP
ejpam-4254	252	28	u	u	NOUN
ejpam-4254	252	29	and	and	CCONJ
ejpam-4254	252	30	so	so	ADV
ejpam-4254	252	31	a	a	DET
ejpam-4254	252	32	⋆	⋆	X
ejpam-4254	252	33	b	b	X
ejpam-4254	252	34	∈	∈	PROPN
ejpam-4254	252	35	l−(νp	l−(νp	PROPN
ejpam-4254	252	36	,	,	PUNCT
ejpam-4254	252	37	t	t	PROPN
ejpam-4254	252	38	)	)	PUNCT
ejpam-4254	252	39	.	.	PUNCT
ejpam-4254	253	1	thus	thus	ADV
ejpam-4254	253	2	νp(a	νp(a	NUM
ejpam-4254	253	3	⋆	⋆	ADJ
ejpam-4254	253	4	b	b	NOUN
ejpam-4254	253	5	)	)	PUNCT
ejpam-4254	253	6	<	<	X
ejpam-4254	253	7	t	t	PROPN
ejpam-4254	253	8	=	=	SYM
ejpam-4254	253	9	νp(a	νp(a	NUM
ejpam-4254	253	10	⋆	⋆	X
ejpam-4254	253	11	b	b	NOUN
ejpam-4254	253	12	)	)	PUNCT
ejpam-4254	253	13	,	,	PUNCT
ejpam-4254	253	14	a	a	DET
ejpam-4254	253	15	contradiction	contradiction	NOUN
ejpam-4254	253	16	.	.	PUNCT
ejpam-4254	254	1	hence	hence	ADV
ejpam-4254	254	2	,	,	PUNCT
ejpam-4254	254	3	νp(a	νp(a	NUM
ejpam-4254	254	4	⋆	⋆	ADP
ejpam-4254	254	5	b	b	NOUN
ejpam-4254	254	6	)	)	PUNCT
ejpam-4254	254	7	≤	≤	NOUN
ejpam-4254	254	8	max{νp(a	max{νp(a	NOUN
ejpam-4254	254	9	)	)	PUNCT
ejpam-4254	254	10	,	,	PUNCT
ejpam-4254	254	11	νp(b	νp(b	NOUN
ejpam-4254	254	12	)	)	PUNCT
ejpam-4254	254	13	}	}	PUNCT
ejpam-4254	254	14	for	for	ADP
ejpam-4254	254	15	all	all	DET
ejpam-4254	254	16	a	a	DET
ejpam-4254	254	17	,	,	PUNCT
ejpam-4254	254	18	b	b	X
ejpam-4254	254	19	∈	∈	PROPN
ejpam-4254	254	20	u	u	NOUN
ejpam-4254	254	21	.	.	PUNCT
ejpam-4254	255	1	therefore	therefore	ADV
ejpam-4254	255	2	,	,	PUNCT
ejpam-4254	255	3	p	p	PRON
ejpam-4254	255	4	is	be	AUX
ejpam-4254	255	5	a	a	DET
ejpam-4254	255	6	pfups	pfup	NOUN
ejpam-4254	255	7	of	of	ADP
ejpam-4254	255	8	u	u	PROPN
ejpam-4254	255	9	.	.	PUNCT
ejpam-4254	256	1	a.	a.	PROPN
ejpam-4254	256	2	iampan	iampan	PROPN
ejpam-4254	256	3	et	et	PROPN
ejpam-4254	256	4	al	al	PROPN
ejpam-4254	256	5	.	.	PUNCT
ejpam-4254	256	6	/	/	SYM
ejpam-4254	256	7	eur	eur	PROPN
ejpam-4254	256	8	.	.	PUNCT
ejpam-4254	257	1	j.	j.	PROPN
ejpam-4254	257	2	pure	pure	PROPN
ejpam-4254	257	3	appl	appl	PROPN
ejpam-4254	257	4	.	.	PROPN
ejpam-4254	257	5	math	math	PROPN
ejpam-4254	257	6	,	,	PUNCT
ejpam-4254	257	7	15	15	NUM
ejpam-4254	257	8	(	(	PUNCT
ejpam-4254	257	9	1	1	NUM
ejpam-4254	257	10	)	)	PUNCT
ejpam-4254	257	11	(	(	PUNCT
ejpam-4254	257	12	2022	2022	NUM
ejpam-4254	257	13	)	)	PUNCT
ejpam-4254	257	14	,	,	PUNCT
ejpam-4254	257	15	169	169	NUM
ejpam-4254	257	16	-	-	SYM
ejpam-4254	257	17	198	198	NUM
ejpam-4254	257	18	183	183	NUM
ejpam-4254	257	19	theorem	theorem	NOUN
ejpam-4254	257	20	4	4	NUM
ejpam-4254	257	21	.	.	PUNCT
ejpam-4254	258	1	p	p	NOUN
ejpam-4254	258	2	is	be	AUX
ejpam-4254	258	3	a	a	DET
ejpam-4254	258	4	pfnupf	pfnupf	NOUN
ejpam-4254	258	5	of	of	ADP
ejpam-4254	258	6	u	u	PRON
ejpam-4254	258	7	if	if	SCONJ
ejpam-4254	258	8	and	and	CCONJ
ejpam-4254	258	9	only	only	ADV
ejpam-4254	258	10	if	if	SCONJ
ejpam-4254	258	11	u(µp	u(µp	NOUN
ejpam-4254	258	12	,	,	PUNCT
ejpam-4254	258	13	t	t	PROPN
ejpam-4254	258	14	)	)	PUNCT
ejpam-4254	258	15	and	and	CCONJ
ejpam-4254	258	16	l(νp	l(νp	PROPN
ejpam-4254	258	17	,	,	PUNCT
ejpam-4254	258	18	t	t	PROPN
ejpam-4254	258	19	)	)	PUNCT
ejpam-4254	258	20	are	be	AUX
ejpam-4254	258	21	,	,	PUNCT
ejpam-4254	258	22	if	if	SCONJ
ejpam-4254	258	23	the	the	DET
ejpam-4254	258	24	sets	set	NOUN
ejpam-4254	258	25	are	be	AUX
ejpam-4254	258	26	nonempty	nonempty	ADJ
ejpam-4254	258	27	,	,	PUNCT
ejpam-4254	258	28	nupfs	nupf	NOUN
ejpam-4254	258	29	for	for	ADP
ejpam-4254	258	30	every	every	DET
ejpam-4254	258	31	t	t	NOUN
ejpam-4254	258	32	∈	∈	PROPN
ejpam-4254	259	1	[	[	X
ejpam-4254	259	2	0	0	NUM
ejpam-4254	259	3	,	,	PUNCT
ejpam-4254	259	4	1	1	NUM
ejpam-4254	259	5	]	]	PUNCT
ejpam-4254	259	6	.	.	PUNCT
ejpam-4254	260	1	proof	proof	NOUN
ejpam-4254	260	2	.	.	PUNCT
ejpam-4254	261	1	assume	assume	VERB
ejpam-4254	261	2	p	p	X
ejpam-4254	261	3	=	=	X
ejpam-4254	261	4	(	(	PUNCT
ejpam-4254	261	5	µp	µp	PROPN
ejpam-4254	261	6	,	,	PUNCT
ejpam-4254	261	7	νp	νp	NOUN
ejpam-4254	261	8	)	)	PUNCT
ejpam-4254	261	9	is	be	AUX
ejpam-4254	261	10	a	a	DET
ejpam-4254	261	11	pfnupf	pfnupf	NOUN
ejpam-4254	261	12	of	of	ADP
ejpam-4254	261	13	u	u	PROPN
ejpam-4254	261	14	.	.	PUNCT
ejpam-4254	262	1	let	let	VERB
ejpam-4254	262	2	t	t	X
ejpam-4254	262	3	∈	∈	PROPN
ejpam-4254	263	1	[	[	X
ejpam-4254	263	2	0	0	NUM
ejpam-4254	263	3	,	,	PUNCT
ejpam-4254	263	4	1	1	NUM
ejpam-4254	263	5	]	]	PUNCT
ejpam-4254	263	6	be	be	AUX
ejpam-4254	263	7	such	such	ADJ
ejpam-4254	263	8	that	that	SCONJ
ejpam-4254	263	9	u(µp	u(µp	NOUN
ejpam-4254	263	10	,	,	PUNCT
ejpam-4254	263	11	t	t	PROPN
ejpam-4254	263	12	)	)	PUNCT
ejpam-4254	263	13	,	,	PUNCT
ejpam-4254	263	14	l(νp	l(νp	PROPN
ejpam-4254	263	15	,	,	PUNCT
ejpam-4254	263	16	t	t	PROPN
ejpam-4254	263	17	)	)	PUNCT
ejpam-4254	263	18	̸=	̸=	PROPN
ejpam-4254	263	19	∅.	∅.	ADV
ejpam-4254	263	20	let	let	VERB
ejpam-4254	263	21	a	a	DET
ejpam-4254	263	22	,	,	PUNCT
ejpam-4254	263	23	b	b	X
ejpam-4254	263	24	∈	∈	PROPN
ejpam-4254	263	25	u	u	NOUN
ejpam-4254	263	26	.	.	PUNCT
ejpam-4254	264	1	then	then	ADV
ejpam-4254	264	2	b	b	X
ejpam-4254	264	3	∈	∈	PROPN
ejpam-4254	264	4	u(µp	u(µp	PROPN
ejpam-4254	264	5	,	,	PUNCT
ejpam-4254	264	6	t	t	PROPN
ejpam-4254	264	7	)	)	PUNCT
ejpam-4254	264	8	⇒	⇒	NOUN
ejpam-4254	264	9	µp(b	µp(b	ADJ
ejpam-4254	264	10	)	)	PUNCT
ejpam-4254	264	11	≥	≥	NOUN
ejpam-4254	264	12	t	t	PROPN
ejpam-4254	264	13	⇒	⇒	NOUN
ejpam-4254	264	14	µp(a	µp(a	PUNCT
ejpam-4254	264	15	⋆	⋆	PROPN
ejpam-4254	264	16	b	b	NOUN
ejpam-4254	264	17	)	)	PUNCT
ejpam-4254	264	18	≥	≥	NOUN
ejpam-4254	264	19	µp(b	µp(b	NOUN
ejpam-4254	264	20	)	)	PUNCT
ejpam-4254	264	21	≥	≥	PROPN
ejpam-4254	264	22	t	t	PROPN
ejpam-4254	264	23	(	(	PUNCT
ejpam-4254	264	24	(	(	PUNCT
ejpam-4254	264	25	1.23	1.23	NUM
ejpam-4254	264	26	)	)	PUNCT
ejpam-4254	264	27	)	)	PUNCT
ejpam-4254	264	28	⇒	⇒	VERB
ejpam-4254	264	29	a	a	DET
ejpam-4254	264	30	⋆	⋆	NOUN
ejpam-4254	264	31	b	b	NOUN
ejpam-4254	264	32	∈	∈	PROPN
ejpam-4254	264	33	u(µp	u(µp	PROPN
ejpam-4254	264	34	,	,	PUNCT
ejpam-4254	264	35	t	t	PROPN
ejpam-4254	264	36	)	)	PUNCT
ejpam-4254	264	37	and	and	CCONJ
ejpam-4254	264	38	a	a	PRON
ejpam-4254	264	39	,	,	PUNCT
ejpam-4254	264	40	b	b	PROPN
ejpam-4254	264	41	∈	∈	PROPN
ejpam-4254	264	42	l(νp	l(νp	PROPN
ejpam-4254	264	43	,	,	PUNCT
ejpam-4254	264	44	t	t	PROPN
ejpam-4254	264	45	)	)	PUNCT
ejpam-4254	264	46	⇒	⇒	NOUN
ejpam-4254	264	47	νp(b	νp(b	NOUN
ejpam-4254	264	48	)	)	PUNCT
ejpam-4254	264	49	≤	≤	PUNCT
ejpam-4254	264	50	t	t	PROPN
ejpam-4254	264	51	⇒	⇒	NOUN
ejpam-4254	264	52	νp(a	νp(a	PROPN
ejpam-4254	264	53	⋆	⋆	NOUN
ejpam-4254	264	54	b	b	NOUN
ejpam-4254	264	55	)	)	PUNCT
ejpam-4254	264	56	≤	≤	NOUN
ejpam-4254	264	57	νp(b	νp(b	NOUN
ejpam-4254	264	58	)	)	PUNCT
ejpam-4254	264	59	≤	≤	NOUN
ejpam-4254	264	60	t	t	NOUN
ejpam-4254	264	61	(	(	PUNCT
ejpam-4254	264	62	(	(	PUNCT
ejpam-4254	264	63	1.24	1.24	NUM
ejpam-4254	264	64	)	)	PUNCT
ejpam-4254	264	65	)	)	PUNCT
ejpam-4254	264	66	⇒	⇒	VERB
ejpam-4254	264	67	a	a	DET
ejpam-4254	264	68	⋆	⋆	NOUN
ejpam-4254	264	69	b	b	PROPN
ejpam-4254	264	70	∈	∈	PROPN
ejpam-4254	264	71	l(νp	l(νp	PROPN
ejpam-4254	264	72	,	,	PUNCT
ejpam-4254	264	73	t	t	PROPN
ejpam-4254	264	74	)	)	PUNCT
ejpam-4254	264	75	.	.	PUNCT
ejpam-4254	265	1	hence	hence	ADV
ejpam-4254	265	2	,	,	PUNCT
ejpam-4254	265	3	u(µp	u(µp	PROPN
ejpam-4254	265	4	,	,	PUNCT
ejpam-4254	265	5	t	t	PROPN
ejpam-4254	265	6	)	)	PUNCT
ejpam-4254	265	7	and	and	CCONJ
ejpam-4254	265	8	l(νp	l(νp	PROPN
ejpam-4254	265	9	,	,	PUNCT
ejpam-4254	265	10	t	t	PROPN
ejpam-4254	265	11	)	)	PUNCT
ejpam-4254	265	12	are	be	AUX
ejpam-4254	265	13	nupfs	nupf	NOUN
ejpam-4254	265	14	of	of	ADP
ejpam-4254	265	15	u	u	PROPN
ejpam-4254	265	16	.	.	PUNCT
ejpam-4254	266	1	conversely	conversely	ADV
ejpam-4254	266	2	,	,	PUNCT
ejpam-4254	266	3	assume	assume	VERB
ejpam-4254	266	4	for	for	ADP
ejpam-4254	266	5	all	all	DET
ejpam-4254	266	6	t	t	NOUN
ejpam-4254	266	7	∈	∈	PROPN
ejpam-4254	267	1	[	[	X
ejpam-4254	267	2	0	0	NUM
ejpam-4254	267	3	,	,	PUNCT
ejpam-4254	267	4	1	1	NUM
ejpam-4254	267	5	]	]	PUNCT
ejpam-4254	267	6	,	,	PUNCT
ejpam-4254	267	7	u(µp	u(µp	PROPN
ejpam-4254	267	8	,	,	PUNCT
ejpam-4254	267	9	t	t	PROPN
ejpam-4254	267	10	)	)	PUNCT
ejpam-4254	267	11	and	and	CCONJ
ejpam-4254	267	12	l(νp	l(νp	PROPN
ejpam-4254	267	13	,	,	PUNCT
ejpam-4254	267	14	t	t	PROPN
ejpam-4254	267	15	)	)	PUNCT
ejpam-4254	267	16	are	be	AUX
ejpam-4254	267	17	nupfs	nupf	NOUN
ejpam-4254	267	18	of	of	ADP
ejpam-4254	267	19	u	u	PRON
ejpam-4254	267	20	if	if	SCONJ
ejpam-4254	267	21	the	the	DET
ejpam-4254	267	22	sets	set	NOUN
ejpam-4254	267	23	are	be	AUX
ejpam-4254	267	24	nonempty	nonempty	ADJ
ejpam-4254	267	25	.	.	PUNCT
ejpam-4254	268	1	let	let	VERB
ejpam-4254	268	2	a	a	DET
ejpam-4254	268	3	,	,	PUNCT
ejpam-4254	268	4	b	b	X
ejpam-4254	268	5	∈	∈	PROPN
ejpam-4254	268	6	u	u	NOUN
ejpam-4254	268	7	.	.	PUNCT
ejpam-4254	269	1	choose	choose	VERB
ejpam-4254	269	2	t	t	PROPN
ejpam-4254	269	3	=	=	SYM
ejpam-4254	269	4	µp(b	µp(b	X
ejpam-4254	269	5	)	)	PUNCT
ejpam-4254	269	6	∈	∈	PROPN
ejpam-4254	270	1	[	[	X
ejpam-4254	270	2	0	0	NUM
ejpam-4254	270	3	,	,	PUNCT
ejpam-4254	270	4	1	1	NUM
ejpam-4254	270	5	]	]	PUNCT
ejpam-4254	270	6	.	.	PUNCT
ejpam-4254	271	1	then	then	ADV
ejpam-4254	271	2	µp(b	µp(b	PUNCT
ejpam-4254	271	3	)	)	PUNCT
ejpam-4254	271	4	≥	≥	NOUN
ejpam-4254	271	5	t.	t.	NOUN
ejpam-4254	271	6	thus	thus	ADV
ejpam-4254	271	7	b	b	PROPN
ejpam-4254	271	8	∈	∈	PROPN
ejpam-4254	271	9	u(µp	u(µp	PROPN
ejpam-4254	271	10	,	,	PUNCT
ejpam-4254	271	11	t	t	PROPN
ejpam-4254	271	12	)	)	PUNCT
ejpam-4254	271	13	̸=	̸=	PROPN
ejpam-4254	271	14	∅.	∅.	ADV
ejpam-4254	271	15	as	as	ADP
ejpam-4254	271	16	a	a	DET
ejpam-4254	271	17	hypothesis	hypothesis	NOUN
ejpam-4254	271	18	,	,	PUNCT
ejpam-4254	271	19	we	we	PRON
ejpam-4254	271	20	get	get	VERB
ejpam-4254	271	21	u(µp	u(µp	NOUN
ejpam-4254	271	22	,	,	PUNCT
ejpam-4254	271	23	t	t	PROPN
ejpam-4254	271	24	)	)	PUNCT
ejpam-4254	271	25	is	be	AUX
ejpam-4254	271	26	a	a	DET
ejpam-4254	271	27	nupf	nupf	NOUN
ejpam-4254	271	28	of	of	ADP
ejpam-4254	271	29	u	u	NOUN
ejpam-4254	271	30	and	and	CCONJ
ejpam-4254	271	31	so	so	ADV
ejpam-4254	271	32	a	a	DET
ejpam-4254	271	33	⋆	⋆	NOUN
ejpam-4254	271	34	b	b	NOUN
ejpam-4254	271	35	∈	∈	PROPN
ejpam-4254	271	36	u(µp	u(µp	PROPN
ejpam-4254	271	37	,	,	PUNCT
ejpam-4254	271	38	t	t	PROPN
ejpam-4254	271	39	)	)	PUNCT
ejpam-4254	271	40	.	.	PUNCT
ejpam-4254	272	1	thus	thus	ADV
ejpam-4254	272	2	µp(a	µp(a	PUNCT
ejpam-4254	272	3	⋆	⋆	ADP
ejpam-4254	272	4	b	b	NOUN
ejpam-4254	272	5	)	)	PUNCT
ejpam-4254	272	6	≥	≥	NOUN
ejpam-4254	272	7	t	t	NOUN
ejpam-4254	272	8	=	=	SYM
ejpam-4254	272	9	µp(b	µp(b	NOUN
ejpam-4254	272	10	)	)	PUNCT
ejpam-4254	272	11	.	.	PUNCT
ejpam-4254	273	1	choose	choose	VERB
ejpam-4254	273	2	t	t	NOUN
ejpam-4254	273	3	=	=	SYM
ejpam-4254	273	4	νp(b	νp(b	NOUN
ejpam-4254	273	5	)	)	PUNCT
ejpam-4254	273	6	∈	∈	PROPN
ejpam-4254	274	1	[	[	X
ejpam-4254	274	2	0	0	NUM
ejpam-4254	274	3	,	,	PUNCT
ejpam-4254	274	4	1	1	NUM
ejpam-4254	274	5	]	]	PUNCT
ejpam-4254	274	6	.	.	PUNCT
ejpam-4254	275	1	the	the	DET
ejpam-4254	275	2	νp(b	νp(b	NOUN
ejpam-4254	275	3	)	)	PUNCT
ejpam-4254	275	4	≤	≤	NOUN
ejpam-4254	275	5	t.	t.	NOUN
ejpam-4254	275	6	thus	thus	ADV
ejpam-4254	275	7	b	b	PROPN
ejpam-4254	275	8	∈	∈	PROPN
ejpam-4254	275	9	l(νp	l(νp	PROPN
ejpam-4254	275	10	,	,	PUNCT
ejpam-4254	275	11	t	t	PROPN
ejpam-4254	275	12	)	)	PUNCT
ejpam-4254	275	13	̸=	̸=	PROPN
ejpam-4254	275	14	∅.	∅.	ADV
ejpam-4254	275	15	as	as	ADP
ejpam-4254	275	16	a	a	DET
ejpam-4254	275	17	hypothesis	hypothesis	NOUN
ejpam-4254	275	18	,	,	PUNCT
ejpam-4254	275	19	we	we	PRON
ejpam-4254	275	20	get	get	VERB
ejpam-4254	275	21	l(νp	l(νp	PROPN
ejpam-4254	275	22	,	,	PUNCT
ejpam-4254	275	23	t	t	PROPN
ejpam-4254	275	24	)	)	PUNCT
ejpam-4254	275	25	is	be	AUX
ejpam-4254	275	26	a	a	DET
ejpam-4254	275	27	nupf	nupf	NOUN
ejpam-4254	275	28	of	of	ADP
ejpam-4254	275	29	u	u	NOUN
ejpam-4254	275	30	and	and	CCONJ
ejpam-4254	275	31	so	so	ADV
ejpam-4254	275	32	a	a	DET
ejpam-4254	275	33	⋆	⋆	X
ejpam-4254	275	34	b	b	PROPN
ejpam-4254	275	35	∈	∈	PROPN
ejpam-4254	275	36	u(νp	u(νp	PROPN
ejpam-4254	275	37	,	,	PUNCT
ejpam-4254	275	38	t	t	PROPN
ejpam-4254	275	39	)	)	PUNCT
ejpam-4254	275	40	.	.	PUNCT
ejpam-4254	276	1	thus	thus	ADV
ejpam-4254	276	2	νp(a	νp(a	NUM
ejpam-4254	276	3	⋆	⋆	ADJ
ejpam-4254	276	4	b	b	NOUN
ejpam-4254	276	5	)	)	PUNCT
ejpam-4254	276	6	≤	≤	NOUN
ejpam-4254	276	7	t	t	NOUN
ejpam-4254	276	8	=	=	PUNCT
ejpam-4254	276	9	νp(b	νp(b	PROPN
ejpam-4254	276	10	)	)	PUNCT
ejpam-4254	276	11	.	.	PUNCT
ejpam-4254	277	1	hence	hence	ADV
ejpam-4254	277	2	,	,	PUNCT
ejpam-4254	277	3	p	p	PROPN
ejpam-4254	277	4	is	be	AUX
ejpam-4254	277	5	a	a	DET
ejpam-4254	277	6	pfnupf	pfnupf	NOUN
ejpam-4254	277	7	of	of	ADP
ejpam-4254	277	8	u	u	PROPN
ejpam-4254	277	9	.	.	PUNCT
ejpam-4254	278	1	theorem	theorem	ADJ
ejpam-4254	278	2	5	5	NUM
ejpam-4254	278	3	.	.	PUNCT
ejpam-4254	279	1	p	p	NOUN
ejpam-4254	279	2	is	be	AUX
ejpam-4254	279	3	a	a	DET
ejpam-4254	279	4	pfnupf	pfnupf	NOUN
ejpam-4254	279	5	of	of	ADP
ejpam-4254	279	6	u	u	PRON
ejpam-4254	279	7	if	if	SCONJ
ejpam-4254	279	8	and	and	CCONJ
ejpam-4254	279	9	only	only	ADV
ejpam-4254	279	10	if	if	SCONJ
ejpam-4254	279	11	u+(µp	u+(µp	NOUN
ejpam-4254	279	12	,	,	PUNCT
ejpam-4254	279	13	t	t	PROPN
ejpam-4254	279	14	)	)	PUNCT
ejpam-4254	279	15	and	and	CCONJ
ejpam-4254	279	16	l−(νp	l−(νp	PROPN
ejpam-4254	279	17	,	,	PUNCT
ejpam-4254	279	18	t	t	PROPN
ejpam-4254	279	19	)	)	PUNCT
ejpam-4254	279	20	are	be	AUX
ejpam-4254	279	21	,	,	PUNCT
ejpam-4254	279	22	if	if	SCONJ
ejpam-4254	279	23	the	the	DET
ejpam-4254	279	24	sets	set	NOUN
ejpam-4254	279	25	are	be	AUX
ejpam-4254	279	26	nonempty	nonempty	ADJ
ejpam-4254	279	27	,	,	PUNCT
ejpam-4254	279	28	nupfs	nupf	NOUN
ejpam-4254	279	29	of	of	ADP
ejpam-4254	279	30	u	u	NOUN
ejpam-4254	279	31	for	for	ADP
ejpam-4254	279	32	every	every	DET
ejpam-4254	279	33	t	t	NOUN
ejpam-4254	279	34	∈	∈	PROPN
ejpam-4254	280	1	[	[	X
ejpam-4254	280	2	0	0	NUM
ejpam-4254	280	3	,	,	PUNCT
ejpam-4254	280	4	1	1	NUM
ejpam-4254	280	5	]	]	PUNCT
ejpam-4254	280	6	.	.	PUNCT
ejpam-4254	281	1	proof	proof	NOUN
ejpam-4254	281	2	.	.	PUNCT
ejpam-4254	282	1	assume	assume	VERB
ejpam-4254	282	2	p	p	X
ejpam-4254	282	3	=	=	X
ejpam-4254	282	4	(	(	PUNCT
ejpam-4254	282	5	µp	µp	PROPN
ejpam-4254	282	6	,	,	PUNCT
ejpam-4254	282	7	νp	νp	NOUN
ejpam-4254	282	8	)	)	PUNCT
ejpam-4254	282	9	is	be	AUX
ejpam-4254	282	10	a	a	DET
ejpam-4254	282	11	pfnupf	pfnupf	NOUN
ejpam-4254	282	12	of	of	ADP
ejpam-4254	282	13	u	u	PROPN
ejpam-4254	282	14	.	.	PUNCT
ejpam-4254	283	1	let	let	VERB
ejpam-4254	283	2	t	t	X
ejpam-4254	283	3	∈	∈	PROPN
ejpam-4254	284	1	[	[	X
ejpam-4254	284	2	0	0	NUM
ejpam-4254	284	3	,	,	PUNCT
ejpam-4254	284	4	1	1	NUM
ejpam-4254	284	5	]	]	PUNCT
ejpam-4254	284	6	be	be	AUX
ejpam-4254	284	7	such	such	ADJ
ejpam-4254	284	8	that	that	SCONJ
ejpam-4254	284	9	u+(µp	u+(µp	NOUN
ejpam-4254	284	10	,	,	PUNCT
ejpam-4254	284	11	t	t	PROPN
ejpam-4254	284	12	)	)	PUNCT
ejpam-4254	284	13	,	,	PUNCT
ejpam-4254	284	14	l	l	PROPN
ejpam-4254	284	15	−(νp	−(νp	PROPN
ejpam-4254	284	16	,	,	PUNCT
ejpam-4254	284	17	t	t	PROPN
ejpam-4254	284	18	)	)	PUNCT
ejpam-4254	284	19	̸=	̸=	PROPN
ejpam-4254	284	20	∅.	∅.	ADV
ejpam-4254	284	21	let	let	VERB
ejpam-4254	284	22	a	a	DET
ejpam-4254	284	23	,	,	PUNCT
ejpam-4254	284	24	b	b	X
ejpam-4254	284	25	∈	∈	PROPN
ejpam-4254	284	26	u	u	NOUN
ejpam-4254	284	27	.	.	PUNCT
ejpam-4254	285	1	then	then	ADV
ejpam-4254	285	2	b	b	PROPN
ejpam-4254	285	3	∈	∈	PROPN
ejpam-4254	285	4	u+(µp	u+(µp	PROPN
ejpam-4254	285	5	,	,	PUNCT
ejpam-4254	285	6	t	t	PROPN
ejpam-4254	285	7	)	)	PUNCT
ejpam-4254	285	8	⇒	⇒	NOUN
ejpam-4254	285	9	µp(b	µp(b	ADJ
ejpam-4254	285	10	)	)	PUNCT
ejpam-4254	285	11	>	>	X
ejpam-4254	285	12	t	t	PROPN
ejpam-4254	285	13	⇒	⇒	NOUN
ejpam-4254	285	14	µp(a	µp(a	PUNCT
ejpam-4254	285	15	⋆	⋆	PROPN
ejpam-4254	285	16	b	b	NOUN
ejpam-4254	285	17	)	)	PUNCT
ejpam-4254	285	18	≥	≥	NOUN
ejpam-4254	285	19	µp(b	µp(b	NOUN
ejpam-4254	285	20	)	)	PUNCT
ejpam-4254	285	21	>	>	X
ejpam-4254	285	22	t	t	PROPN
ejpam-4254	285	23	(	(	PUNCT
ejpam-4254	285	24	(	(	PUNCT
ejpam-4254	285	25	1.23	1.23	NUM
ejpam-4254	285	26	)	)	PUNCT
ejpam-4254	285	27	)	)	PUNCT
ejpam-4254	285	28	⇒	⇒	VERB
ejpam-4254	285	29	a	a	DET
ejpam-4254	285	30	⋆	⋆	NOUN
ejpam-4254	285	31	b	b	PROPN
ejpam-4254	285	32	∈	∈	PROPN
ejpam-4254	285	33	u+(µp	u+(µp	PROPN
ejpam-4254	285	34	,	,	PUNCT
ejpam-4254	285	35	t	t	PROPN
ejpam-4254	285	36	)	)	PUNCT
ejpam-4254	285	37	and	and	CCONJ
ejpam-4254	285	38	b	b	X
ejpam-4254	285	39	∈	∈	PROPN
ejpam-4254	285	40	l−(νp	l−(νp	PROPN
ejpam-4254	285	41	,	,	PUNCT
ejpam-4254	285	42	t	t	PROPN
ejpam-4254	285	43	)	)	PUNCT
ejpam-4254	285	44	⇒	⇒	NOUN
ejpam-4254	285	45	νp(b	νp(b	NOUN
ejpam-4254	285	46	)	)	PUNCT
ejpam-4254	285	47	<	<	X
ejpam-4254	285	48	t	t	PROPN
ejpam-4254	285	49	⇒	⇒	NOUN
ejpam-4254	285	50	νp(a	νp(a	ADV
ejpam-4254	285	51	⋆	⋆	NOUN
ejpam-4254	285	52	b	b	NOUN
ejpam-4254	285	53	)	)	PUNCT
ejpam-4254	285	54	≤	≤	NOUN
ejpam-4254	285	55	νp(b	νp(b	NOUN
ejpam-4254	285	56	)	)	PUNCT
ejpam-4254	285	57	<	<	X
ejpam-4254	285	58	t	t	PROPN
ejpam-4254	285	59	(	(	PUNCT
ejpam-4254	285	60	(	(	PUNCT
ejpam-4254	285	61	1.24	1.24	NUM
ejpam-4254	285	62	)	)	PUNCT
ejpam-4254	285	63	)	)	PUNCT
ejpam-4254	285	64	⇒	⇒	VERB
ejpam-4254	285	65	a	a	DET
ejpam-4254	285	66	⋆	⋆	NOUN
ejpam-4254	285	67	b	b	X
ejpam-4254	285	68	∈	∈	PROPN
ejpam-4254	285	69	l−(νp	l−(νp	PROPN
ejpam-4254	285	70	,	,	PUNCT
ejpam-4254	285	71	t	t	PROPN
ejpam-4254	285	72	)	)	PUNCT
ejpam-4254	285	73	.	.	PUNCT
ejpam-4254	286	1	hence	hence	ADV
ejpam-4254	286	2	,	,	PUNCT
ejpam-4254	286	3	u+(µp	u+(µp	PROPN
ejpam-4254	286	4	,	,	PUNCT
ejpam-4254	286	5	t	t	PROPN
ejpam-4254	286	6	)	)	PUNCT
ejpam-4254	286	7	and	and	CCONJ
ejpam-4254	286	8	l−(νp	l−(νp	PROPN
ejpam-4254	286	9	,	,	PUNCT
ejpam-4254	286	10	t	t	PROPN
ejpam-4254	286	11	)	)	PUNCT
ejpam-4254	286	12	are	be	AUX
ejpam-4254	286	13	nupfs	nupf	NOUN
ejpam-4254	286	14	of	of	ADP
ejpam-4254	286	15	u	u	PROPN
ejpam-4254	286	16	.	.	PUNCT
ejpam-4254	287	1	conversely	conversely	ADV
ejpam-4254	287	2	,	,	PUNCT
ejpam-4254	287	3	assume	assume	VERB
ejpam-4254	287	4	for	for	ADP
ejpam-4254	287	5	all	all	DET
ejpam-4254	287	6	t	t	NOUN
ejpam-4254	287	7	∈	∈	PROPN
ejpam-4254	288	1	[	[	X
ejpam-4254	288	2	0	0	NUM
ejpam-4254	288	3	,	,	PUNCT
ejpam-4254	288	4	1	1	NUM
ejpam-4254	288	5	]	]	PUNCT
ejpam-4254	288	6	,	,	PUNCT
ejpam-4254	288	7	u+(µp	u+(µp	PROPN
ejpam-4254	288	8	,	,	PUNCT
ejpam-4254	288	9	t	t	PROPN
ejpam-4254	288	10	)	)	PUNCT
ejpam-4254	288	11	and	and	CCONJ
ejpam-4254	288	12	l−(νp	l−(νp	PROPN
ejpam-4254	288	13	,	,	PUNCT
ejpam-4254	288	14	t	t	PROPN
ejpam-4254	288	15	)	)	PUNCT
ejpam-4254	288	16	are	be	AUX
ejpam-4254	288	17	nupfs	nupf	NOUN
ejpam-4254	288	18	of	of	ADP
ejpam-4254	288	19	u	u	PRON
ejpam-4254	288	20	if	if	SCONJ
ejpam-4254	288	21	the	the	DET
ejpam-4254	288	22	sets	set	NOUN
ejpam-4254	288	23	are	be	AUX
ejpam-4254	288	24	nonempty	nonempty	ADJ
ejpam-4254	288	25	.	.	PUNCT
ejpam-4254	289	1	a.	a.	NOUN
ejpam-4254	289	2	iampan	iampan	PROPN
ejpam-4254	289	3	et	et	PROPN
ejpam-4254	289	4	al	al	PROPN
ejpam-4254	289	5	.	.	PUNCT
ejpam-4254	289	6	/	/	SYM
ejpam-4254	289	7	eur	eur	PROPN
ejpam-4254	289	8	.	.	PUNCT
ejpam-4254	290	1	j.	j.	PROPN
ejpam-4254	290	2	pure	pure	PROPN
ejpam-4254	290	3	appl	appl	PROPN
ejpam-4254	290	4	.	.	PROPN
ejpam-4254	290	5	math	math	PROPN
ejpam-4254	290	6	,	,	PUNCT
ejpam-4254	290	7	15	15	NUM
ejpam-4254	290	8	(	(	PUNCT
ejpam-4254	290	9	1	1	NUM
ejpam-4254	290	10	)	)	PUNCT
ejpam-4254	290	11	(	(	PUNCT
ejpam-4254	290	12	2022	2022	NUM
ejpam-4254	290	13	)	)	PUNCT
ejpam-4254	290	14	,	,	PUNCT
ejpam-4254	290	15	169	169	NUM
ejpam-4254	290	16	-	-	SYM
ejpam-4254	290	17	198	198	NUM
ejpam-4254	290	18	184	184	NUM
ejpam-4254	290	19	suppose	suppose	VERB
ejpam-4254	290	20	there	there	PRON
ejpam-4254	290	21	exist	exist	VERB
ejpam-4254	290	22	a	a	DET
ejpam-4254	290	23	,	,	PUNCT
ejpam-4254	290	24	b	b	X
ejpam-4254	290	25	∈	∈	PROPN
ejpam-4254	290	26	u	u	NOUN
ejpam-4254	290	27	such	such	ADJ
ejpam-4254	290	28	that	that	PRON
ejpam-4254	290	29	µp(a	µp(a	PUNCT
ejpam-4254	290	30	⋆	⋆	X
ejpam-4254	290	31	b	b	NOUN
ejpam-4254	290	32	)	)	PUNCT
ejpam-4254	290	33	<	<	X
ejpam-4254	290	34	µp(b	µp(b	NOUN
ejpam-4254	290	35	)	)	PUNCT
ejpam-4254	290	36	.	.	PUNCT
ejpam-4254	291	1	choose	choose	VERB
ejpam-4254	291	2	t	t	NOUN
ejpam-4254	291	3	=	=	SYM
ejpam-4254	291	4	µp(a	µp(a	NUM
ejpam-4254	291	5	⋆	⋆	X
ejpam-4254	291	6	b	b	NOUN
ejpam-4254	291	7	)	)	PUNCT
ejpam-4254	291	8	∈	∈	PROPN
ejpam-4254	292	1	[	[	X
ejpam-4254	292	2	0	0	NUM
ejpam-4254	292	3	,	,	PUNCT
ejpam-4254	292	4	1	1	NUM
ejpam-4254	292	5	]	]	PUNCT
ejpam-4254	292	6	.	.	PUNCT
ejpam-4254	293	1	then	then	ADV
ejpam-4254	293	2	µp(b	µp(b	PUNCT
ejpam-4254	293	3	)	)	PUNCT
ejpam-4254	293	4	>	>	PUNCT
ejpam-4254	293	5	t.	t.	X
ejpam-4254	293	6	thus	thus	ADV
ejpam-4254	293	7	b	b	PROPN
ejpam-4254	293	8	∈	∈	PROPN
ejpam-4254	293	9	u+(µp	u+(µp	PROPN
ejpam-4254	293	10	,	,	PUNCT
ejpam-4254	293	11	t	t	PROPN
ejpam-4254	293	12	)	)	PUNCT
ejpam-4254	293	13	̸=	̸=	PROPN
ejpam-4254	293	14	∅.	∅.	ADV
ejpam-4254	293	15	as	as	ADP
ejpam-4254	293	16	a	a	DET
ejpam-4254	293	17	hypothesis	hypothesis	NOUN
ejpam-4254	293	18	,	,	PUNCT
ejpam-4254	293	19	we	we	PRON
ejpam-4254	293	20	get	get	VERB
ejpam-4254	293	21	u+(µp	u+(µp	NOUN
ejpam-4254	293	22	,	,	PUNCT
ejpam-4254	293	23	t	t	PROPN
ejpam-4254	293	24	)	)	PUNCT
ejpam-4254	293	25	is	be	AUX
ejpam-4254	293	26	a	a	DET
ejpam-4254	293	27	nupf	nupf	NOUN
ejpam-4254	293	28	of	of	ADP
ejpam-4254	293	29	u	u	NOUN
ejpam-4254	293	30	and	and	CCONJ
ejpam-4254	293	31	so	so	ADV
ejpam-4254	293	32	a	a	DET
ejpam-4254	293	33	⋆	⋆	NOUN
ejpam-4254	293	34	b	b	PROPN
ejpam-4254	293	35	∈	∈	PROPN
ejpam-4254	293	36	u+(µp	u+(µp	PROPN
ejpam-4254	293	37	,	,	PUNCT
ejpam-4254	293	38	t	t	PROPN
ejpam-4254	293	39	)	)	PUNCT
ejpam-4254	293	40	.	.	PUNCT
ejpam-4254	294	1	thus	thus	ADV
ejpam-4254	294	2	µp(a	µp(a	PUNCT
ejpam-4254	294	3	⋆	⋆	ADP
ejpam-4254	294	4	b	b	NOUN
ejpam-4254	294	5	)	)	PUNCT
ejpam-4254	294	6	>	>	PUNCT
ejpam-4254	295	1	t	t	PROPN
ejpam-4254	295	2	=	=	PUNCT
ejpam-4254	295	3	µp(a	µp(a	NUM
ejpam-4254	295	4	⋆	⋆	X
ejpam-4254	295	5	b	b	NOUN
ejpam-4254	295	6	)	)	PUNCT
ejpam-4254	295	7	,	,	PUNCT
ejpam-4254	295	8	a	a	DET
ejpam-4254	295	9	contradiction	contradiction	NOUN
ejpam-4254	295	10	.	.	PUNCT
ejpam-4254	296	1	hence	hence	ADV
ejpam-4254	296	2	,	,	PUNCT
ejpam-4254	296	3	µp(a	µp(a	PUNCT
ejpam-4254	296	4	⋆	⋆	X
ejpam-4254	296	5	b	b	NOUN
ejpam-4254	296	6	)	)	PUNCT
ejpam-4254	296	7	≥	≥	NOUN
ejpam-4254	296	8	µp(b	µp(b	NOUN
ejpam-4254	296	9	)	)	PUNCT
ejpam-4254	296	10	for	for	ADP
ejpam-4254	296	11	all	all	DET
ejpam-4254	296	12	a	a	PRON
ejpam-4254	296	13	,	,	PUNCT
ejpam-4254	296	14	b	b	X
ejpam-4254	296	15	∈	∈	PROPN
ejpam-4254	296	16	u	u	NOUN
ejpam-4254	296	17	.	.	PUNCT
ejpam-4254	296	18	suppose	suppose	VERB
ejpam-4254	296	19	there	there	PRON
ejpam-4254	296	20	exist	exist	VERB
ejpam-4254	296	21	a	a	DET
ejpam-4254	296	22	,	,	PUNCT
ejpam-4254	296	23	b	b	X
ejpam-4254	296	24	∈	∈	PROPN
ejpam-4254	296	25	u	u	NOUN
ejpam-4254	296	26	such	such	ADJ
ejpam-4254	296	27	that	that	SCONJ
ejpam-4254	296	28	νp(a	νp(a	NUM
ejpam-4254	296	29	⋆	⋆	X
ejpam-4254	296	30	b	b	NOUN
ejpam-4254	296	31	)	)	PUNCT
ejpam-4254	296	32	>	>	X
ejpam-4254	296	33	νp(b	νp(b	NOUN
ejpam-4254	296	34	)	)	PUNCT
ejpam-4254	296	35	.	.	PUNCT
ejpam-4254	297	1	choose	choose	VERB
ejpam-4254	297	2	t	t	PROPN
ejpam-4254	297	3	=	=	SYM
ejpam-4254	297	4	νp(a	νp(a	NUM
ejpam-4254	297	5	⋆	⋆	NOUN
ejpam-4254	297	6	b	b	X
ejpam-4254	297	7	)	)	PUNCT
ejpam-4254	297	8	∈	∈	PROPN
ejpam-4254	298	1	[	[	X
ejpam-4254	298	2	0	0	NUM
ejpam-4254	298	3	,	,	PUNCT
ejpam-4254	298	4	1	1	NUM
ejpam-4254	298	5	]	]	PUNCT
ejpam-4254	298	6	.	.	PUNCT
ejpam-4254	299	1	then	then	ADV
ejpam-4254	299	2	νp(b	νp(b	PUNCT
ejpam-4254	299	3	)	)	PUNCT
ejpam-4254	299	4	<	<	X
ejpam-4254	300	1	t.	t.	X
ejpam-4254	300	2	thus	thus	ADV
ejpam-4254	300	3	b	b	PROPN
ejpam-4254	300	4	∈	∈	PROPN
ejpam-4254	300	5	l−(νp	l−(νp	PROPN
ejpam-4254	300	6	,	,	PUNCT
ejpam-4254	300	7	t	t	PROPN
ejpam-4254	300	8	)	)	PUNCT
ejpam-4254	300	9	̸=	̸=	PROPN
ejpam-4254	300	10	∅.	∅.	ADV
ejpam-4254	300	11	as	as	ADP
ejpam-4254	300	12	a	a	DET
ejpam-4254	300	13	hypothesis	hypothesis	NOUN
ejpam-4254	300	14	,	,	PUNCT
ejpam-4254	300	15	we	we	PRON
ejpam-4254	300	16	get	get	VERB
ejpam-4254	300	17	l−(νp	l−(νp	PROPN
ejpam-4254	300	18	,	,	PUNCT
ejpam-4254	300	19	t	t	PROPN
ejpam-4254	300	20	)	)	PUNCT
ejpam-4254	300	21	is	be	AUX
ejpam-4254	300	22	a	a	DET
ejpam-4254	300	23	nupf	nupf	NOUN
ejpam-4254	300	24	of	of	ADP
ejpam-4254	300	25	u	u	NOUN
ejpam-4254	300	26	and	and	CCONJ
ejpam-4254	300	27	so	so	ADV
ejpam-4254	300	28	a	a	DET
ejpam-4254	300	29	⋆	⋆	X
ejpam-4254	300	30	b	b	X
ejpam-4254	300	31	∈	∈	PROPN
ejpam-4254	300	32	l−(νp	l−(νp	PROPN
ejpam-4254	300	33	,	,	PUNCT
ejpam-4254	300	34	t	t	PROPN
ejpam-4254	300	35	)	)	PUNCT
ejpam-4254	300	36	.	.	PUNCT
ejpam-4254	301	1	thus	thus	ADV
ejpam-4254	301	2	νp(a	νp(a	NUM
ejpam-4254	301	3	⋆	⋆	ADJ
ejpam-4254	301	4	b	b	NOUN
ejpam-4254	301	5	)	)	PUNCT
ejpam-4254	301	6	<	<	X
ejpam-4254	301	7	t	t	PROPN
ejpam-4254	301	8	=	=	SYM
ejpam-4254	301	9	νp(a	νp(a	NUM
ejpam-4254	301	10	⋆	⋆	X
ejpam-4254	301	11	b	b	NOUN
ejpam-4254	301	12	)	)	PUNCT
ejpam-4254	301	13	,	,	PUNCT
ejpam-4254	301	14	a	a	DET
ejpam-4254	301	15	contradiction	contradiction	NOUN
ejpam-4254	301	16	.	.	PUNCT
ejpam-4254	302	1	hence	hence	ADV
ejpam-4254	302	2	,	,	PUNCT
ejpam-4254	302	3	νp(a	νp(a	NUM
ejpam-4254	302	4	⋆	⋆	ADP
ejpam-4254	302	5	b	b	NOUN
ejpam-4254	302	6	)	)	PUNCT
ejpam-4254	302	7	≤	≤	NUM
ejpam-4254	302	8	νp(b	νp(b	NOUN
ejpam-4254	302	9	)	)	PUNCT
ejpam-4254	302	10	for	for	ADP
ejpam-4254	302	11	all	all	DET
ejpam-4254	302	12	a	a	PRON
ejpam-4254	302	13	,	,	PUNCT
ejpam-4254	302	14	b	b	X
ejpam-4254	302	15	∈	∈	PROPN
ejpam-4254	302	16	u	u	NOUN
ejpam-4254	302	17	.	.	PUNCT
ejpam-4254	303	1	therefore	therefore	ADV
ejpam-4254	303	2	,	,	PUNCT
ejpam-4254	303	3	p	p	PRON
ejpam-4254	303	4	is	be	AUX
ejpam-4254	303	5	a	a	DET
ejpam-4254	303	6	pfnupf	pfnupf	NOUN
ejpam-4254	303	7	of	of	ADP
ejpam-4254	303	8	u	u	PROPN
ejpam-4254	303	9	.	.	PUNCT
ejpam-4254	304	1	theorem	theorem	VERB
ejpam-4254	304	2	6	6	NUM
ejpam-4254	304	3	.	.	PUNCT
ejpam-4254	305	1	p	p	NOUN
ejpam-4254	305	2	is	be	AUX
ejpam-4254	305	3	a	a	DET
ejpam-4254	305	4	pfupf	pfupf	NOUN
ejpam-4254	305	5	of	of	ADP
ejpam-4254	305	6	u	u	PRON
ejpam-4254	305	7	if	if	SCONJ
ejpam-4254	305	8	and	and	CCONJ
ejpam-4254	305	9	only	only	ADV
ejpam-4254	305	10	if	if	SCONJ
ejpam-4254	305	11	u(µp	u(µp	NOUN
ejpam-4254	305	12	,	,	PUNCT
ejpam-4254	305	13	t	t	PROPN
ejpam-4254	305	14	)	)	PUNCT
ejpam-4254	305	15	and	and	CCONJ
ejpam-4254	305	16	l(νp	l(νp	PROPN
ejpam-4254	305	17	,	,	PUNCT
ejpam-4254	305	18	t	t	PROPN
ejpam-4254	305	19	)	)	PUNCT
ejpam-4254	305	20	are	be	AUX
ejpam-4254	305	21	,	,	PUNCT
ejpam-4254	305	22	if	if	SCONJ
ejpam-4254	305	23	the	the	DET
ejpam-4254	305	24	sets	set	NOUN
ejpam-4254	305	25	are	be	AUX
ejpam-4254	305	26	nonempty	nonempty	ADJ
ejpam-4254	305	27	,	,	PUNCT
ejpam-4254	305	28	upfs	upf	NOUN
ejpam-4254	305	29	for	for	ADP
ejpam-4254	305	30	every	every	DET
ejpam-4254	305	31	t	t	NOUN
ejpam-4254	305	32	∈	∈	PROPN
ejpam-4254	306	1	[	[	X
ejpam-4254	306	2	0	0	NUM
ejpam-4254	306	3	,	,	PUNCT
ejpam-4254	306	4	1	1	NUM
ejpam-4254	306	5	]	]	PUNCT
ejpam-4254	306	6	.	.	PUNCT
ejpam-4254	307	1	proof	proof	NOUN
ejpam-4254	307	2	.	.	PUNCT
ejpam-4254	308	1	assume	assume	VERB
ejpam-4254	308	2	p	p	X
ejpam-4254	308	3	=	=	X
ejpam-4254	308	4	(	(	PUNCT
ejpam-4254	308	5	µp	µp	PROPN
ejpam-4254	308	6	,	,	PUNCT
ejpam-4254	308	7	νp	νp	NOUN
ejpam-4254	308	8	)	)	PUNCT
ejpam-4254	308	9	is	be	AUX
ejpam-4254	308	10	a	a	DET
ejpam-4254	308	11	pfupf	pfupf	NOUN
ejpam-4254	308	12	of	of	ADP
ejpam-4254	308	13	u	u	PROPN
ejpam-4254	308	14	.	.	PUNCT
ejpam-4254	309	1	let	let	VERB
ejpam-4254	309	2	t	t	X
ejpam-4254	309	3	∈	∈	PROPN
ejpam-4254	310	1	[	[	X
ejpam-4254	310	2	0	0	NUM
ejpam-4254	310	3	,	,	PUNCT
ejpam-4254	310	4	1	1	NUM
ejpam-4254	310	5	]	]	PUNCT
ejpam-4254	310	6	be	be	AUX
ejpam-4254	310	7	such	such	ADJ
ejpam-4254	310	8	that	that	SCONJ
ejpam-4254	310	9	u(µp	u(µp	NOUN
ejpam-4254	310	10	,	,	PUNCT
ejpam-4254	310	11	t	t	PROPN
ejpam-4254	310	12	)	)	PUNCT
ejpam-4254	310	13	,	,	PUNCT
ejpam-4254	310	14	l(νp	l(νp	PROPN
ejpam-4254	310	15	,	,	PUNCT
ejpam-4254	310	16	t	t	PROPN
ejpam-4254	310	17	)	)	PUNCT
ejpam-4254	310	18	̸=	̸=	PROPN
ejpam-4254	310	19	∅.	∅.	ADV
ejpam-4254	310	20	let	let	VERB
ejpam-4254	310	21	a	a	DET
ejpam-4254	310	22	,	,	PUNCT
ejpam-4254	310	23	b	b	X
ejpam-4254	310	24	∈	∈	PROPN
ejpam-4254	310	25	u	u	NOUN
ejpam-4254	310	26	.	.	PUNCT
ejpam-4254	311	1	then	then	ADV
ejpam-4254	311	2	a	a	DET
ejpam-4254	311	3	∈	∈	PROPN
ejpam-4254	311	4	u(µp	u(µp	NOUN
ejpam-4254	311	5	,	,	PUNCT
ejpam-4254	311	6	t	t	PROPN
ejpam-4254	311	7	)	)	PUNCT
ejpam-4254	311	8	⇒	⇒	NOUN
ejpam-4254	311	9	µp(a	µp(a	NUM
ejpam-4254	311	10	)	)	PUNCT
ejpam-4254	311	11	≥	≥	NOUN
ejpam-4254	311	12	t	t	PROPN
ejpam-4254	311	13	⇒	⇒	PROPN
ejpam-4254	311	14	µp(0	µp(0	NOUN
ejpam-4254	311	15	)	)	PUNCT
ejpam-4254	311	16	≥	≥	NOUN
ejpam-4254	311	17	µp(a	µp(a	NUM
ejpam-4254	311	18	)	)	PUNCT
ejpam-4254	311	19	≥	≥	NOUN
ejpam-4254	311	20	t	t	PROPN
ejpam-4254	311	21	(	(	PUNCT
ejpam-4254	311	22	(	(	PUNCT
ejpam-4254	311	23	1.25	1.25	NUM
ejpam-4254	311	24	)	)	PUNCT
ejpam-4254	311	25	)	)	PUNCT
ejpam-4254	311	26	⇒	⇒	VERB
ejpam-4254	311	27	0	0	NUM
ejpam-4254	312	1	∈	∈	PROPN
ejpam-4254	312	2	u(µp	u(µp	NOUN
ejpam-4254	312	3	,	,	PUNCT
ejpam-4254	312	4	t	t	PROPN
ejpam-4254	312	5	)	)	PUNCT
ejpam-4254	312	6	,	,	PUNCT
ejpam-4254	312	7	a	a	DET
ejpam-4254	312	8	⋆	⋆	PROPN
ejpam-4254	312	9	b	b	NOUN
ejpam-4254	312	10	,	,	PUNCT
ejpam-4254	312	11	a	a	DET
ejpam-4254	312	12	∈	∈	PROPN
ejpam-4254	312	13	u(µp	u(µp	NOUN
ejpam-4254	312	14	,	,	PUNCT
ejpam-4254	312	15	t	t	PROPN
ejpam-4254	312	16	)	)	PUNCT
ejpam-4254	312	17	⇒	⇒	NOUN
ejpam-4254	312	18	µp(a	µp(a	PUNCT
ejpam-4254	312	19	⋆	⋆	NOUN
ejpam-4254	312	20	b	b	NOUN
ejpam-4254	312	21	)	)	PUNCT
ejpam-4254	312	22	≥	≥	NOUN
ejpam-4254	312	23	t	t	PROPN
ejpam-4254	312	24	,	,	PUNCT
ejpam-4254	312	25	µp(a	µp(a	NUM
ejpam-4254	312	26	)	)	PUNCT
ejpam-4254	312	27	≥	≥	NOUN
ejpam-4254	312	28	t	t	PROPN
ejpam-4254	312	29	⇒	⇒	NOUN
ejpam-4254	312	30	min{µp(a	min{µp(a	NOUN
ejpam-4254	312	31	⋆	⋆	X
ejpam-4254	312	32	b	b	NOUN
ejpam-4254	312	33	)	)	PUNCT
ejpam-4254	312	34	,	,	PUNCT
ejpam-4254	312	35	µp(a	µp(a	NUM
ejpam-4254	312	36	)	)	PUNCT
ejpam-4254	312	37	}	}	PUNCT
ejpam-4254	312	38	≥	≥	X
ejpam-4254	312	39	t	t	PROPN
ejpam-4254	312	40	⇒	⇒	NOUN
ejpam-4254	312	41	µp(b	µp(b	PUNCT
ejpam-4254	312	42	)	)	PUNCT
ejpam-4254	312	43	≥	≥	NOUN
ejpam-4254	312	44	min{µp(a	min{µp(a	NOUN
ejpam-4254	312	45	⋆	⋆	X
ejpam-4254	312	46	b	b	NOUN
ejpam-4254	312	47	)	)	PUNCT
ejpam-4254	312	48	,	,	PUNCT
ejpam-4254	312	49	µp(a	µp(a	NUM
ejpam-4254	312	50	)	)	PUNCT
ejpam-4254	312	51	}	}	PUNCT
ejpam-4254	312	52	≥	≥	PROPN
ejpam-4254	312	53	t	t	PROPN
ejpam-4254	312	54	(	(	PUNCT
ejpam-4254	312	55	(	(	PUNCT
ejpam-4254	312	56	1.27	1.27	NUM
ejpam-4254	312	57	)	)	PUNCT
ejpam-4254	312	58	)	)	PUNCT
ejpam-4254	312	59	⇒	⇒	VERB
ejpam-4254	312	60	b	b	PROPN
ejpam-4254	312	61	∈	∈	PROPN
ejpam-4254	312	62	u(µp	u(µp	PROPN
ejpam-4254	312	63	,	,	PUNCT
ejpam-4254	312	64	t	t	PROPN
ejpam-4254	312	65	)	)	PUNCT
ejpam-4254	312	66	,	,	PUNCT
ejpam-4254	312	67	a	a	DET
ejpam-4254	312	68	∈	∈	PROPN
ejpam-4254	312	69	l(νp	l(νp	PROPN
ejpam-4254	312	70	,	,	PUNCT
ejpam-4254	312	71	t	t	PROPN
ejpam-4254	312	72	)	)	PUNCT
ejpam-4254	312	73	⇒	⇒	NOUN
ejpam-4254	312	74	νp(a	νp(a	NUM
ejpam-4254	312	75	)	)	PUNCT
ejpam-4254	312	76	≤	≤	PUNCT
ejpam-4254	312	77	t	t	PROPN
ejpam-4254	312	78	⇒	⇒	PROPN
ejpam-4254	312	79	νp(0	νp(0	PROPN
ejpam-4254	312	80	)	)	PUNCT
ejpam-4254	312	81	≤	≤	NOUN
ejpam-4254	312	82	νp(a	νp(a	NUM
ejpam-4254	312	83	)	)	PUNCT
ejpam-4254	312	84	≤	≤	NUM
ejpam-4254	312	85	t	t	NOUN
ejpam-4254	312	86	(	(	PUNCT
ejpam-4254	312	87	(	(	PUNCT
ejpam-4254	312	88	1.26	1.26	NUM
ejpam-4254	312	89	)	)	PUNCT
ejpam-4254	312	90	)	)	PUNCT
ejpam-4254	312	91	⇒	⇒	VERB
ejpam-4254	312	92	0	0	NUM
ejpam-4254	312	93	∈	∈	PROPN
ejpam-4254	312	94	l(νp	l(νp	PROPN
ejpam-4254	312	95	,	,	PUNCT
ejpam-4254	312	96	t	t	PROPN
ejpam-4254	312	97	)	)	PUNCT
ejpam-4254	312	98	,	,	PUNCT
ejpam-4254	312	99	and	and	CCONJ
ejpam-4254	312	100	a	a	DET
ejpam-4254	312	101	⋆	⋆	NOUN
ejpam-4254	312	102	b	b	NOUN
ejpam-4254	312	103	,	,	PUNCT
ejpam-4254	312	104	a	a	DET
ejpam-4254	312	105	∈	∈	PROPN
ejpam-4254	312	106	l(νp	l(νp	PROPN
ejpam-4254	312	107	,	,	PUNCT
ejpam-4254	312	108	t	t	PROPN
ejpam-4254	312	109	)	)	PUNCT
ejpam-4254	312	110	⇒	⇒	NOUN
ejpam-4254	312	111	νp(a	νp(a	NUM
ejpam-4254	312	112	⋆	⋆	NOUN
ejpam-4254	312	113	b	b	NOUN
ejpam-4254	312	114	)	)	PUNCT
ejpam-4254	312	115	≤	≤	NOUN
ejpam-4254	312	116	t	t	PROPN
ejpam-4254	312	117	,	,	PUNCT
ejpam-4254	312	118	νp(a	νp(a	NUM
ejpam-4254	312	119	)	)	PUNCT
ejpam-4254	313	1	≤	≤	PUNCT
ejpam-4254	314	1	t	t	PROPN
ejpam-4254	314	2	⇒	⇒	NOUN
ejpam-4254	314	3	max{µp(a	max{µp(a	PROPN
ejpam-4254	314	4	⋆	⋆	PUNCT
ejpam-4254	314	5	b	b	NOUN
ejpam-4254	314	6	)	)	PUNCT
ejpam-4254	314	7	,	,	PUNCT
ejpam-4254	314	8	νp(a	νp(a	NUM
ejpam-4254	314	9	)	)	PUNCT
ejpam-4254	314	10	}	}	PUNCT
ejpam-4254	314	11	≤	≤	NUM
ejpam-4254	314	12	t	t	PROPN
ejpam-4254	314	13	⇒	⇒	NOUN
ejpam-4254	314	14	νp(b	νp(b	PROPN
ejpam-4254	314	15	)	)	PUNCT
ejpam-4254	314	16	≤	≤	NOUN
ejpam-4254	314	17	max{νp(a	max{νp(a	NOUN
ejpam-4254	314	18	⋆	⋆	NOUN
ejpam-4254	314	19	b	b	NOUN
ejpam-4254	314	20	)	)	PUNCT
ejpam-4254	314	21	,	,	PUNCT
ejpam-4254	314	22	νp(a	νp(a	NUM
ejpam-4254	314	23	)	)	PUNCT
ejpam-4254	314	24	}	}	PUNCT
ejpam-4254	314	25	≤	≤	NUM
ejpam-4254	314	26	t	t	NOUN
ejpam-4254	314	27	(	(	PUNCT
ejpam-4254	314	28	(	(	PUNCT
ejpam-4254	314	29	1.28	1.28	NUM
ejpam-4254	314	30	)	)	PUNCT
ejpam-4254	314	31	)	)	PUNCT
ejpam-4254	314	32	⇒	⇒	VERB
ejpam-4254	314	33	b	b	PROPN
ejpam-4254	314	34	∈	∈	PROPN
ejpam-4254	314	35	l(νp	l(νp	PROPN
ejpam-4254	314	36	,	,	PUNCT
ejpam-4254	314	37	t	t	PROPN
ejpam-4254	314	38	)	)	PUNCT
ejpam-4254	314	39	.	.	PUNCT
ejpam-4254	315	1	hence	hence	ADV
ejpam-4254	315	2	,	,	PUNCT
ejpam-4254	315	3	u(µp	u(µp	PROPN
ejpam-4254	315	4	,	,	PUNCT
ejpam-4254	315	5	t	t	PROPN
ejpam-4254	315	6	)	)	PUNCT
ejpam-4254	315	7	and	and	CCONJ
ejpam-4254	315	8	l(νp	l(νp	PROPN
ejpam-4254	315	9	,	,	PUNCT
ejpam-4254	315	10	t	t	PROPN
ejpam-4254	315	11	)	)	PUNCT
ejpam-4254	315	12	are	be	AUX
ejpam-4254	315	13	upfs	upf	NOUN
ejpam-4254	315	14	of	of	ADP
ejpam-4254	315	15	u	u	PROPN
ejpam-4254	315	16	.	.	PUNCT
ejpam-4254	316	1	conversely	conversely	ADV
ejpam-4254	316	2	,	,	PUNCT
ejpam-4254	316	3	assume	assume	VERB
ejpam-4254	316	4	for	for	ADP
ejpam-4254	316	5	all	all	DET
ejpam-4254	316	6	t	t	NOUN
ejpam-4254	316	7	∈	∈	PROPN
ejpam-4254	317	1	[	[	X
ejpam-4254	317	2	0	0	NUM
ejpam-4254	317	3	,	,	PUNCT
ejpam-4254	317	4	1	1	NUM
ejpam-4254	317	5	]	]	PUNCT
ejpam-4254	317	6	,	,	PUNCT
ejpam-4254	317	7	u(µp	u(µp	PROPN
ejpam-4254	317	8	,	,	PUNCT
ejpam-4254	317	9	t	t	PROPN
ejpam-4254	317	10	)	)	PUNCT
ejpam-4254	317	11	and	and	CCONJ
ejpam-4254	317	12	l(νp	l(νp	PROPN
ejpam-4254	317	13	,	,	PUNCT
ejpam-4254	317	14	t	t	PROPN
ejpam-4254	317	15	)	)	PUNCT
ejpam-4254	317	16	are	be	AUX
ejpam-4254	317	17	upfs	upf	NOUN
ejpam-4254	317	18	of	of	ADP
ejpam-4254	317	19	u	u	PRON
ejpam-4254	317	20	if	if	SCONJ
ejpam-4254	317	21	the	the	DET
ejpam-4254	317	22	sets	set	NOUN
ejpam-4254	317	23	are	be	AUX
ejpam-4254	317	24	nonempty	nonempty	ADJ
ejpam-4254	317	25	.	.	PUNCT
ejpam-4254	318	1	let	let	VERB
ejpam-4254	318	2	a	a	DET
ejpam-4254	318	3	,	,	PUNCT
ejpam-4254	318	4	b	b	X
ejpam-4254	318	5	∈	∈	PROPN
ejpam-4254	318	6	u	u	NOUN
ejpam-4254	318	7	.	.	PUNCT
ejpam-4254	319	1	choose	choose	VERB
ejpam-4254	319	2	t	t	NOUN
ejpam-4254	319	3	=	=	SYM
ejpam-4254	319	4	µp(a	µp(a	PRON
ejpam-4254	319	5	)	)	PUNCT
ejpam-4254	319	6	∈	∈	NOUN
ejpam-4254	320	1	[	[	X
ejpam-4254	320	2	0	0	NUM
ejpam-4254	320	3	,	,	PUNCT
ejpam-4254	320	4	1	1	NUM
ejpam-4254	320	5	]	]	PUNCT
ejpam-4254	320	6	.	.	PUNCT
ejpam-4254	321	1	then	then	ADV
ejpam-4254	321	2	µp(a	µp(a	NUM
ejpam-4254	321	3	)	)	PUNCT
ejpam-4254	321	4	≥	≥	NOUN
ejpam-4254	321	5	t.	t.	NOUN
ejpam-4254	321	6	thus	thus	ADV
ejpam-4254	321	7	a	a	DET
ejpam-4254	321	8	∈	∈	NOUN
ejpam-4254	321	9	u(µp	u(µp	NOUN
ejpam-4254	321	10	,	,	PUNCT
ejpam-4254	321	11	t	t	PROPN
ejpam-4254	321	12	)	)	PUNCT
ejpam-4254	321	13	̸=	̸=	PROPN
ejpam-4254	321	14	∅.	∅.	ADV
ejpam-4254	321	15	as	as	ADP
ejpam-4254	321	16	a	a	DET
ejpam-4254	321	17	hypothesis	hypothesis	NOUN
ejpam-4254	321	18	,	,	PUNCT
ejpam-4254	321	19	we	we	PRON
ejpam-4254	321	20	get	get	VERB
ejpam-4254	321	21	u(µp	u(µp	NOUN
ejpam-4254	321	22	,	,	PUNCT
ejpam-4254	321	23	t	t	PROPN
ejpam-4254	321	24	)	)	PUNCT
ejpam-4254	321	25	is	be	AUX
ejpam-4254	321	26	a	a	DET
ejpam-4254	321	27	upf	upf	NOUN
ejpam-4254	321	28	of	of	ADP
ejpam-4254	321	29	u	u	NOUN
ejpam-4254	321	30	and	and	CCONJ
ejpam-4254	321	31	so	so	ADV
ejpam-4254	321	32	0	0	NUM
ejpam-4254	321	33	∈	∈	PROPN
ejpam-4254	321	34	u(µp	u(µp	NOUN
ejpam-4254	321	35	,	,	PUNCT
ejpam-4254	321	36	t	t	PROPN
ejpam-4254	321	37	)	)	PUNCT
ejpam-4254	321	38	.	.	PUNCT
ejpam-4254	322	1	thus	thus	ADV
ejpam-4254	322	2	µp(0	µp(0	NOUN
ejpam-4254	322	3	)	)	PUNCT
ejpam-4254	322	4	≥	≥	NOUN
ejpam-4254	322	5	t	t	NOUN
ejpam-4254	322	6	=	=	PUNCT
ejpam-4254	322	7	µp(a	µp(a	NUM
ejpam-4254	322	8	)	)	PUNCT
ejpam-4254	322	9	.	.	PUNCT
ejpam-4254	323	1	a.	a.	PROPN
ejpam-4254	323	2	iampan	iampan	PROPN
ejpam-4254	323	3	et	et	PROPN
ejpam-4254	323	4	al	al	PROPN
ejpam-4254	323	5	.	.	PUNCT
ejpam-4254	323	6	/	/	SYM
ejpam-4254	323	7	eur	eur	PROPN
ejpam-4254	323	8	.	.	PUNCT
ejpam-4254	324	1	j.	j.	PROPN
ejpam-4254	324	2	pure	pure	PROPN
ejpam-4254	324	3	appl	appl	PROPN
ejpam-4254	324	4	.	.	PROPN
ejpam-4254	324	5	math	math	PROPN
ejpam-4254	324	6	,	,	PUNCT
ejpam-4254	324	7	15	15	NUM
ejpam-4254	324	8	(	(	PUNCT
ejpam-4254	324	9	1	1	NUM
ejpam-4254	324	10	)	)	PUNCT
ejpam-4254	324	11	(	(	PUNCT
ejpam-4254	324	12	2022	2022	NUM
ejpam-4254	324	13	)	)	PUNCT
ejpam-4254	324	14	,	,	PUNCT
ejpam-4254	324	15	169	169	NUM
ejpam-4254	324	16	-	-	SYM
ejpam-4254	324	17	198	198	NUM
ejpam-4254	324	18	185	185	NUM
ejpam-4254	324	19	choose	choose	NOUN
ejpam-4254	324	20	t	t	NOUN
ejpam-4254	324	21	=	=	PUNCT
ejpam-4254	324	22	min{µp(a	min{µp(a	NOUN
ejpam-4254	324	23	⋆	⋆	X
ejpam-4254	324	24	b	b	NOUN
ejpam-4254	324	25	)	)	PUNCT
ejpam-4254	324	26	,	,	PUNCT
ejpam-4254	324	27	µp(a	µp(a	NUM
ejpam-4254	324	28	)	)	PUNCT
ejpam-4254	324	29	}	}	PUNCT
ejpam-4254	324	30	∈	∈	PROPN
ejpam-4254	325	1	[	[	X
ejpam-4254	325	2	0	0	NUM
ejpam-4254	325	3	,	,	PUNCT
ejpam-4254	325	4	1	1	NUM
ejpam-4254	325	5	]	]	PUNCT
ejpam-4254	325	6	.	.	PUNCT
ejpam-4254	326	1	then	then	ADV
ejpam-4254	326	2	µp(a	µp(a	PUNCT
ejpam-4254	326	3	⋆	⋆	PROPN
ejpam-4254	326	4	b	b	NOUN
ejpam-4254	326	5	)	)	PUNCT
ejpam-4254	326	6	≥	≥	NOUN
ejpam-4254	326	7	t	t	NOUN
ejpam-4254	326	8	and	and	CCONJ
ejpam-4254	326	9	µp(a	µp(a	NUM
ejpam-4254	326	10	)	)	PUNCT
ejpam-4254	326	11	≥	≥	NOUN
ejpam-4254	326	12	t.	t.	NOUN
ejpam-4254	326	13	thus	thus	ADV
ejpam-4254	326	14	a⋆b	a⋆b	NOUN
ejpam-4254	326	15	,	,	PUNCT
ejpam-4254	326	16	a	a	DET
ejpam-4254	326	17	∈	∈	PROPN
ejpam-4254	326	18	u(µp	u(µp	PROPN
ejpam-4254	326	19	,	,	PUNCT
ejpam-4254	326	20	t	t	PROPN
ejpam-4254	326	21	)	)	PUNCT
ejpam-4254	326	22	̸=	̸=	PROPN
ejpam-4254	326	23	∅.	∅.	ADV
ejpam-4254	326	24	as	as	ADP
ejpam-4254	326	25	a	a	DET
ejpam-4254	326	26	hypothesis	hypothesis	NOUN
ejpam-4254	326	27	,	,	PUNCT
ejpam-4254	326	28	we	we	PRON
ejpam-4254	326	29	get	get	VERB
ejpam-4254	326	30	u(µp	u(µp	NOUN
ejpam-4254	326	31	,	,	PUNCT
ejpam-4254	326	32	t	t	PROPN
ejpam-4254	326	33	)	)	PUNCT
ejpam-4254	326	34	is	be	AUX
ejpam-4254	326	35	a	a	DET
ejpam-4254	326	36	upf	upf	NOUN
ejpam-4254	326	37	of	of	ADP
ejpam-4254	326	38	u	u	NOUN
ejpam-4254	326	39	and	and	CCONJ
ejpam-4254	326	40	so	so	ADV
ejpam-4254	326	41	b	b	PROPN
ejpam-4254	326	42	∈	∈	PROPN
ejpam-4254	326	43	u(µp	u(µp	PROPN
ejpam-4254	326	44	,	,	PUNCT
ejpam-4254	326	45	t	t	PROPN
ejpam-4254	326	46	)	)	PUNCT
ejpam-4254	326	47	.	.	PUNCT
ejpam-4254	327	1	thus	thus	ADV
ejpam-4254	327	2	µp(b	µp(b	PUNCT
ejpam-4254	327	3	)	)	PUNCT
ejpam-4254	327	4	≥	≥	NOUN
ejpam-4254	327	5	t	t	NOUN
ejpam-4254	327	6	=	=	SYM
ejpam-4254	327	7	min{µp(a	min{µp(a	NOUN
ejpam-4254	327	8	⋆	⋆	X
ejpam-4254	327	9	b	b	NOUN
ejpam-4254	327	10	)	)	PUNCT
ejpam-4254	327	11	,	,	PUNCT
ejpam-4254	327	12	µp(a	µp(a	NUM
ejpam-4254	327	13	)	)	PUNCT
ejpam-4254	327	14	}	}	PUNCT
ejpam-4254	327	15	.	.	PUNCT
ejpam-4254	328	1	choose	choose	VERB
ejpam-4254	328	2	t	t	NOUN
ejpam-4254	328	3	=	=	SYM
ejpam-4254	328	4	νp(a	νp(a	X
ejpam-4254	328	5	)	)	PUNCT
ejpam-4254	328	6	∈	∈	NOUN
ejpam-4254	329	1	[	[	X
ejpam-4254	329	2	0	0	NUM
ejpam-4254	329	3	,	,	PUNCT
ejpam-4254	329	4	1	1	NUM
ejpam-4254	329	5	]	]	PUNCT
ejpam-4254	329	6	.	.	PUNCT
ejpam-4254	330	1	the	the	DET
ejpam-4254	330	2	νp(a	νp(a	NUM
ejpam-4254	330	3	)	)	PUNCT
ejpam-4254	330	4	≤	≤	NOUN
ejpam-4254	330	5	t.	t.	NOUN
ejpam-4254	330	6	thus	thus	ADV
ejpam-4254	330	7	a	a	DET
ejpam-4254	330	8	∈	∈	PROPN
ejpam-4254	330	9	l(νp	l(νp	PROPN
ejpam-4254	330	10	,	,	PUNCT
ejpam-4254	330	11	t	t	PROPN
ejpam-4254	330	12	)	)	PUNCT
ejpam-4254	330	13	̸=	̸=	PROPN
ejpam-4254	330	14	∅.	∅.	ADV
ejpam-4254	330	15	as	as	ADP
ejpam-4254	330	16	a	a	DET
ejpam-4254	330	17	hypothesis	hypothesis	NOUN
ejpam-4254	330	18	,	,	PUNCT
ejpam-4254	330	19	we	we	PRON
ejpam-4254	330	20	get	get	VERB
ejpam-4254	330	21	l(νp	l(νp	PROPN
ejpam-4254	330	22	,	,	PUNCT
ejpam-4254	330	23	t	t	PROPN
ejpam-4254	330	24	)	)	PUNCT
ejpam-4254	330	25	is	be	AUX
ejpam-4254	330	26	a	a	DET
ejpam-4254	330	27	upf	upf	NOUN
ejpam-4254	330	28	of	of	ADP
ejpam-4254	330	29	u	u	NOUN
ejpam-4254	330	30	and	and	CCONJ
ejpam-4254	330	31	so	so	ADV
ejpam-4254	330	32	0	0	NUM
ejpam-4254	330	33	∈	∈	PROPN
ejpam-4254	330	34	u(νp	u(νp	PROPN
ejpam-4254	330	35	,	,	PUNCT
ejpam-4254	330	36	t	t	PROPN
ejpam-4254	330	37	)	)	PUNCT
ejpam-4254	330	38	.	.	PUNCT
ejpam-4254	331	1	thus	thus	ADV
ejpam-4254	331	2	νp(0	νp(0	NOUN
ejpam-4254	331	3	)	)	PUNCT
ejpam-4254	331	4	≤	≤	NOUN
ejpam-4254	331	5	t	t	NOUN
ejpam-4254	331	6	=	=	PUNCT
ejpam-4254	331	7	νp(a	νp(a	NUM
ejpam-4254	331	8	)	)	PUNCT
ejpam-4254	331	9	.	.	PUNCT
ejpam-4254	332	1	choose	choose	VERB
ejpam-4254	332	2	t	t	PROPN
ejpam-4254	332	3	=	=	SYM
ejpam-4254	332	4	max{νp(a	max{νp(a	PROPN
ejpam-4254	332	5	⋆	⋆	NOUN
ejpam-4254	332	6	b	b	NOUN
ejpam-4254	332	7	)	)	PUNCT
ejpam-4254	332	8	,	,	PUNCT
ejpam-4254	332	9	νp(a	νp(a	NUM
ejpam-4254	332	10	)	)	PUNCT
ejpam-4254	332	11	}	}	PUNCT
ejpam-4254	332	12	∈	∈	PROPN
ejpam-4254	333	1	[	[	X
ejpam-4254	333	2	0	0	NUM
ejpam-4254	333	3	,	,	PUNCT
ejpam-4254	333	4	1	1	NUM
ejpam-4254	333	5	]	]	PUNCT
ejpam-4254	333	6	.	.	PUNCT
ejpam-4254	334	1	then	then	ADV
ejpam-4254	334	2	νp(a	νp(a	NUM
ejpam-4254	334	3	⋆	⋆	ADJ
ejpam-4254	334	4	b	b	NOUN
ejpam-4254	334	5	)	)	PUNCT
ejpam-4254	334	6	≤	≤	NOUN
ejpam-4254	334	7	t	t	NOUN
ejpam-4254	334	8	and	and	CCONJ
ejpam-4254	334	9	νp(a	νp(a	NUM
ejpam-4254	334	10	)	)	PUNCT
ejpam-4254	334	11	≤	≤	NOUN
ejpam-4254	335	1	t.	t.	NOUN
ejpam-4254	335	2	thus	thus	ADV
ejpam-4254	335	3	a	a	DET
ejpam-4254	335	4	⋆	⋆	NOUN
ejpam-4254	335	5	b	b	NOUN
ejpam-4254	335	6	,	,	PUNCT
ejpam-4254	335	7	a	a	DET
ejpam-4254	335	8	∈	∈	NOUN
ejpam-4254	335	9	l(µp	l(µp	NOUN
ejpam-4254	335	10	,	,	PUNCT
ejpam-4254	335	11	t	t	PROPN
ejpam-4254	335	12	)	)	PUNCT
ejpam-4254	335	13	̸=	̸=	PROPN
ejpam-4254	335	14	∅.	∅.	ADV
ejpam-4254	335	15	as	as	ADP
ejpam-4254	335	16	a	a	DET
ejpam-4254	335	17	hypothesis	hypothesis	NOUN
ejpam-4254	335	18	,	,	PUNCT
ejpam-4254	335	19	we	we	PRON
ejpam-4254	335	20	get	get	VERB
ejpam-4254	335	21	l(µp	l(µp	NOUN
ejpam-4254	335	22	,	,	PUNCT
ejpam-4254	335	23	t	t	PROPN
ejpam-4254	335	24	)	)	PUNCT
ejpam-4254	335	25	is	be	AUX
ejpam-4254	335	26	a	a	DET
ejpam-4254	335	27	upf	upf	NOUN
ejpam-4254	335	28	of	of	ADP
ejpam-4254	335	29	u	u	NOUN
ejpam-4254	335	30	and	and	CCONJ
ejpam-4254	335	31	so	so	ADV
ejpam-4254	335	32	b	b	PROPN
ejpam-4254	335	33	∈	∈	PROPN
ejpam-4254	335	34	l(µp	l(µp	NOUN
ejpam-4254	335	35	,	,	PUNCT
ejpam-4254	335	36	t	t	PROPN
ejpam-4254	335	37	)	)	PUNCT
ejpam-4254	335	38	.	.	PUNCT
ejpam-4254	336	1	thus	thus	ADV
ejpam-4254	336	2	νp(b	νp(b	NOUN
ejpam-4254	336	3	)	)	PUNCT
ejpam-4254	336	4	≤	≤	NOUN
ejpam-4254	336	5	t	t	NOUN
ejpam-4254	336	6	=	=	SYM
ejpam-4254	336	7	max{νp(a	max{νp(a	PROPN
ejpam-4254	336	8	⋆	⋆	NOUN
ejpam-4254	336	9	b	b	NOUN
ejpam-4254	336	10	)	)	PUNCT
ejpam-4254	336	11	,	,	PUNCT
ejpam-4254	336	12	νp(a	νp(a	NUM
ejpam-4254	336	13	)	)	PUNCT
ejpam-4254	336	14	}	}	PUNCT
ejpam-4254	336	15	.	.	PUNCT
ejpam-4254	337	1	hence	hence	ADV
ejpam-4254	337	2	,	,	PUNCT
ejpam-4254	337	3	p	p	PROPN
ejpam-4254	337	4	is	be	AUX
ejpam-4254	337	5	a	a	DET
ejpam-4254	337	6	pfupf	pfupf	NOUN
ejpam-4254	337	7	of	of	ADP
ejpam-4254	337	8	u	u	PROPN
ejpam-4254	337	9	.	.	PUNCT
ejpam-4254	338	1	theorem	theorem	VERB
ejpam-4254	338	2	7	7	NUM
ejpam-4254	338	3	.	.	PUNCT
ejpam-4254	339	1	p	p	NOUN
ejpam-4254	339	2	is	be	AUX
ejpam-4254	339	3	a	a	DET
ejpam-4254	339	4	pfupf	pfupf	NOUN
ejpam-4254	339	5	of	of	ADP
ejpam-4254	339	6	u	u	PRON
ejpam-4254	339	7	if	if	SCONJ
ejpam-4254	339	8	and	and	CCONJ
ejpam-4254	339	9	only	only	ADV
ejpam-4254	339	10	if	if	SCONJ
ejpam-4254	339	11	u+(µp	u+(µp	NOUN
ejpam-4254	339	12	,	,	PUNCT
ejpam-4254	339	13	t	t	PROPN
ejpam-4254	339	14	)	)	PUNCT
ejpam-4254	339	15	and	and	CCONJ
ejpam-4254	339	16	l−(νp	l−(νp	PROPN
ejpam-4254	339	17	,	,	PUNCT
ejpam-4254	339	18	t	t	PROPN
ejpam-4254	339	19	)	)	PUNCT
ejpam-4254	339	20	are	be	AUX
ejpam-4254	339	21	,	,	PUNCT
ejpam-4254	339	22	if	if	SCONJ
ejpam-4254	339	23	the	the	DET
ejpam-4254	339	24	sets	set	NOUN
ejpam-4254	339	25	are	be	AUX
ejpam-4254	339	26	nonempty	nonempty	ADJ
ejpam-4254	339	27	,	,	PUNCT
ejpam-4254	339	28	upfs	upf	NOUN
ejpam-4254	339	29	of	of	ADP
ejpam-4254	339	30	u	u	PROPN
ejpam-4254	339	31	for	for	ADP
ejpam-4254	339	32	every	every	DET
ejpam-4254	339	33	t	t	NOUN
ejpam-4254	339	34	∈	∈	PROPN
ejpam-4254	340	1	[	[	X
ejpam-4254	340	2	0	0	NUM
ejpam-4254	340	3	,	,	PUNCT
ejpam-4254	340	4	1	1	NUM
ejpam-4254	340	5	]	]	PUNCT
ejpam-4254	340	6	.	.	PUNCT
ejpam-4254	341	1	proof	proof	NOUN
ejpam-4254	341	2	.	.	PUNCT
ejpam-4254	342	1	assume	assume	VERB
ejpam-4254	342	2	p	p	X
ejpam-4254	342	3	=	=	X
ejpam-4254	342	4	(	(	PUNCT
ejpam-4254	342	5	µp	µp	PROPN
ejpam-4254	342	6	,	,	PUNCT
ejpam-4254	342	7	νp	νp	NOUN
ejpam-4254	342	8	)	)	PUNCT
ejpam-4254	342	9	is	be	AUX
ejpam-4254	342	10	a	a	DET
ejpam-4254	342	11	pfupf	pfupf	NOUN
ejpam-4254	342	12	of	of	ADP
ejpam-4254	342	13	u	u	PROPN
ejpam-4254	342	14	.	.	PUNCT
ejpam-4254	343	1	let	let	VERB
ejpam-4254	343	2	t	t	X
ejpam-4254	343	3	∈	∈	PROPN
ejpam-4254	344	1	[	[	X
ejpam-4254	344	2	0	0	NUM
ejpam-4254	344	3	,	,	PUNCT
ejpam-4254	344	4	1	1	NUM
ejpam-4254	344	5	]	]	PUNCT
ejpam-4254	344	6	be	be	AUX
ejpam-4254	344	7	such	such	ADJ
ejpam-4254	344	8	that	that	SCONJ
ejpam-4254	344	9	u+(µp	u+(µp	NOUN
ejpam-4254	344	10	,	,	PUNCT
ejpam-4254	344	11	t	t	PROPN
ejpam-4254	344	12	)	)	PUNCT
ejpam-4254	344	13	,	,	PUNCT
ejpam-4254	344	14	l−(νp	l−(νp	PROPN
ejpam-4254	344	15	,	,	PUNCT
ejpam-4254	344	16	t	t	PROPN
ejpam-4254	344	17	)	)	PUNCT
ejpam-4254	344	18	̸=	̸=	PROPN
ejpam-4254	344	19	∅.	∅.	ADV
ejpam-4254	344	20	let	let	VERB
ejpam-4254	344	21	a	a	DET
ejpam-4254	344	22	,	,	PUNCT
ejpam-4254	344	23	b	b	X
ejpam-4254	344	24	∈	∈	PROPN
ejpam-4254	344	25	u	u	NOUN
ejpam-4254	344	26	.	.	PUNCT
ejpam-4254	345	1	then	then	ADV
ejpam-4254	345	2	a	a	DET
ejpam-4254	345	3	∈	∈	PROPN
ejpam-4254	345	4	u+(µp	u+(µp	PROPN
ejpam-4254	345	5	,	,	PUNCT
ejpam-4254	345	6	t	t	PROPN
ejpam-4254	345	7	)	)	PUNCT
ejpam-4254	345	8	⇒	⇒	NOUN
ejpam-4254	345	9	µp(a	µp(a	NUM
ejpam-4254	345	10	)	)	PUNCT
ejpam-4254	345	11	>	>	X
ejpam-4254	345	12	t	t	PROPN
ejpam-4254	345	13	⇒	⇒	PROPN
ejpam-4254	345	14	µp(0	µp(0	PROPN
ejpam-4254	345	15	)	)	PUNCT
ejpam-4254	345	16	≥	≥	NOUN
ejpam-4254	345	17	µp(a	µp(a	NUM
ejpam-4254	345	18	)	)	PUNCT
ejpam-4254	345	19	>	>	X
ejpam-4254	345	20	t	t	PROPN
ejpam-4254	345	21	(	(	PUNCT
ejpam-4254	345	22	(	(	PUNCT
ejpam-4254	345	23	1.25	1.25	NUM
ejpam-4254	345	24	)	)	PUNCT
ejpam-4254	345	25	)	)	PUNCT
ejpam-4254	345	26	⇒	⇒	VERB
ejpam-4254	345	27	0	0	NUM
ejpam-4254	345	28	∈	∈	PROPN
ejpam-4254	345	29	u+(µp	u+(µp	PROPN
ejpam-4254	345	30	,	,	PUNCT
ejpam-4254	345	31	t	t	PROPN
ejpam-4254	345	32	)	)	PUNCT
ejpam-4254	345	33	,	,	PUNCT
ejpam-4254	345	34	a	a	DET
ejpam-4254	345	35	⋆	⋆	PROPN
ejpam-4254	345	36	b	b	NOUN
ejpam-4254	345	37	,	,	PUNCT
ejpam-4254	345	38	a	a	DET
ejpam-4254	345	39	∈	∈	NOUN
ejpam-4254	345	40	u+(µp	u+(µp	PROPN
ejpam-4254	345	41	,	,	PUNCT
ejpam-4254	345	42	t	t	PROPN
ejpam-4254	345	43	)	)	PUNCT
ejpam-4254	345	44	⇒	⇒	NOUN
ejpam-4254	345	45	µp(a	µp(a	PUNCT
ejpam-4254	345	46	⋆	⋆	PROPN
ejpam-4254	345	47	b	b	NOUN
ejpam-4254	345	48	)	)	PUNCT
ejpam-4254	345	49	>	>	X
ejpam-4254	345	50	t	t	PROPN
ejpam-4254	345	51	,	,	PUNCT
ejpam-4254	345	52	µp(a	µp(a	NUM
ejpam-4254	345	53	)	)	PUNCT
ejpam-4254	345	54	>	>	X
ejpam-4254	345	55	t	t	PROPN
ejpam-4254	345	56	⇒	⇒	VERB
ejpam-4254	345	57	min{µp(a	min{µp(a	NOUN
ejpam-4254	345	58	⋆	⋆	X
ejpam-4254	345	59	b	b	NOUN
ejpam-4254	345	60	)	)	PUNCT
ejpam-4254	345	61	,	,	PUNCT
ejpam-4254	345	62	µp(a	µp(a	NUM
ejpam-4254	345	63	)	)	PUNCT
ejpam-4254	345	64	}	}	PUNCT
ejpam-4254	345	65	>	>	PUNCT
ejpam-4254	345	66	t	t	PROPN
ejpam-4254	345	67	⇒	⇒	NOUN
ejpam-4254	345	68	µp(b	µp(b	PUNCT
ejpam-4254	345	69	)	)	PUNCT
ejpam-4254	345	70	≥	≥	NOUN
ejpam-4254	345	71	min{µp(a	min{µp(a	NOUN
ejpam-4254	345	72	⋆	⋆	X
ejpam-4254	345	73	b	b	NOUN
ejpam-4254	345	74	)	)	PUNCT
ejpam-4254	345	75	,	,	PUNCT
ejpam-4254	345	76	µp(a	µp(a	NUM
ejpam-4254	345	77	)	)	PUNCT
ejpam-4254	345	78	}	}	PUNCT
ejpam-4254	345	79	>	>	X
ejpam-4254	345	80	t	t	PROPN
ejpam-4254	345	81	(	(	PUNCT
ejpam-4254	345	82	(	(	PUNCT
ejpam-4254	345	83	1.27	1.27	NUM
ejpam-4254	345	84	)	)	PUNCT
ejpam-4254	345	85	)	)	PUNCT
ejpam-4254	345	86	⇒	⇒	PROPN
ejpam-4254	345	87	b	b	PROPN
ejpam-4254	345	88	∈	∈	PROPN
ejpam-4254	345	89	u+(µp	u+(µp	PROPN
ejpam-4254	345	90	,	,	PUNCT
ejpam-4254	345	91	t	t	PROPN
ejpam-4254	345	92	)	)	PUNCT
ejpam-4254	345	93	,	,	PUNCT
ejpam-4254	345	94	a	a	DET
ejpam-4254	345	95	∈	∈	PROPN
ejpam-4254	345	96	l−(νp	l−(νp	PROPN
ejpam-4254	345	97	,	,	PUNCT
ejpam-4254	345	98	t	t	PROPN
ejpam-4254	345	99	)	)	PUNCT
ejpam-4254	345	100	⇒	⇒	NOUN
ejpam-4254	345	101	νp(a	νp(a	NUM
ejpam-4254	345	102	)	)	PUNCT
ejpam-4254	345	103	<	<	X
ejpam-4254	345	104	t	t	PROPN
ejpam-4254	345	105	⇒	⇒	PROPN
ejpam-4254	345	106	νp(0	νp(0	PROPN
ejpam-4254	345	107	)	)	PUNCT
ejpam-4254	345	108	≤	≤	NOUN
ejpam-4254	345	109	νp(a	νp(a	NUM
ejpam-4254	345	110	)	)	PUNCT
ejpam-4254	345	111	<	<	X
ejpam-4254	345	112	t	t	X
ejpam-4254	345	113	(	(	PUNCT
ejpam-4254	345	114	(	(	PUNCT
ejpam-4254	345	115	1.26	1.26	NUM
ejpam-4254	345	116	)	)	PUNCT
ejpam-4254	345	117	)	)	PUNCT
ejpam-4254	345	118	⇒	⇒	VERB
ejpam-4254	345	119	0	0	NUM
ejpam-4254	346	1	∈	∈	PROPN
ejpam-4254	346	2	l−(νp	l−(νp	PROPN
ejpam-4254	346	3	,	,	PUNCT
ejpam-4254	346	4	t	t	PROPN
ejpam-4254	346	5	)	)	PUNCT
ejpam-4254	346	6	,	,	PUNCT
ejpam-4254	346	7	and	and	CCONJ
ejpam-4254	346	8	a	a	DET
ejpam-4254	346	9	⋆	⋆	NOUN
ejpam-4254	346	10	b	b	NOUN
ejpam-4254	346	11	,	,	PUNCT
ejpam-4254	346	12	a	a	DET
ejpam-4254	346	13	∈	∈	PROPN
ejpam-4254	346	14	l−(νp	l−(νp	PROPN
ejpam-4254	346	15	,	,	PUNCT
ejpam-4254	346	16	t	t	PROPN
ejpam-4254	346	17	)	)	PUNCT
ejpam-4254	346	18	⇒	⇒	NOUN
ejpam-4254	346	19	νp(a	νp(a	NUM
ejpam-4254	346	20	⋆	⋆	PUNCT
ejpam-4254	346	21	b	b	NOUN
ejpam-4254	346	22	)	)	PUNCT
ejpam-4254	346	23	<	<	X
ejpam-4254	346	24	t	t	PROPN
ejpam-4254	346	25	,	,	PUNCT
ejpam-4254	346	26	νp(a	νp(a	NUM
ejpam-4254	346	27	)	)	PUNCT
ejpam-4254	346	28	<	<	X
ejpam-4254	346	29	t	t	X
ejpam-4254	346	30	⇒	⇒	X
ejpam-4254	346	31	max{νp(a	max{νp(a	PROPN
ejpam-4254	346	32	⋆	⋆	NOUN
ejpam-4254	346	33	b	b	NOUN
ejpam-4254	346	34	)	)	PUNCT
ejpam-4254	346	35	,	,	PUNCT
ejpam-4254	346	36	νp(a	νp(a	NUM
ejpam-4254	346	37	)	)	PUNCT
ejpam-4254	346	38	}	}	PUNCT
ejpam-4254	346	39	<	<	X
ejpam-4254	346	40	t	t	PROPN
ejpam-4254	346	41	⇒	⇒	PROPN
ejpam-4254	346	42	νp(b	νp(b	PROPN
ejpam-4254	346	43	)	)	PUNCT
ejpam-4254	346	44	≤	≤	NOUN
ejpam-4254	346	45	max{νp(a	max{νp(a	NOUN
ejpam-4254	346	46	⋆	⋆	NOUN
ejpam-4254	346	47	b	b	NOUN
ejpam-4254	346	48	)	)	PUNCT
ejpam-4254	346	49	,	,	PUNCT
ejpam-4254	346	50	νp(a	νp(a	NUM
ejpam-4254	346	51	)	)	PUNCT
ejpam-4254	346	52	}	}	PUNCT
ejpam-4254	346	53	<	<	X
ejpam-4254	346	54	t	t	X
ejpam-4254	346	55	(	(	PUNCT
ejpam-4254	346	56	(	(	PUNCT
ejpam-4254	346	57	1.28	1.28	NUM
ejpam-4254	346	58	)	)	PUNCT
ejpam-4254	346	59	)	)	PUNCT
ejpam-4254	346	60	⇒	⇒	VERB
ejpam-4254	346	61	b	b	X
ejpam-4254	346	62	∈	∈	PROPN
ejpam-4254	346	63	l−(νp	l−(νp	PROPN
ejpam-4254	346	64	,	,	PUNCT
ejpam-4254	346	65	t	t	PROPN
ejpam-4254	346	66	)	)	PUNCT
ejpam-4254	346	67	.	.	PUNCT
ejpam-4254	347	1	hence	hence	ADV
ejpam-4254	347	2	,	,	PUNCT
ejpam-4254	347	3	u+(µp	u+(µp	PROPN
ejpam-4254	347	4	,	,	PUNCT
ejpam-4254	347	5	t	t	PROPN
ejpam-4254	347	6	)	)	PUNCT
ejpam-4254	347	7	and	and	CCONJ
ejpam-4254	347	8	l−(νp	l−(νp	PROPN
ejpam-4254	347	9	,	,	PUNCT
ejpam-4254	347	10	t	t	PROPN
ejpam-4254	347	11	)	)	PUNCT
ejpam-4254	347	12	are	be	AUX
ejpam-4254	347	13	upfs	upf	NOUN
ejpam-4254	347	14	of	of	ADP
ejpam-4254	347	15	u	u	PROPN
ejpam-4254	347	16	.	.	PUNCT
ejpam-4254	348	1	conversely	conversely	ADV
ejpam-4254	348	2	,	,	PUNCT
ejpam-4254	348	3	assume	assume	VERB
ejpam-4254	348	4	for	for	ADP
ejpam-4254	348	5	all	all	DET
ejpam-4254	348	6	t	t	NOUN
ejpam-4254	348	7	∈	∈	PROPN
ejpam-4254	349	1	[	[	X
ejpam-4254	349	2	0	0	NUM
ejpam-4254	349	3	,	,	PUNCT
ejpam-4254	349	4	1	1	NUM
ejpam-4254	349	5	]	]	PUNCT
ejpam-4254	349	6	,	,	PUNCT
ejpam-4254	349	7	u+(µp	u+(µp	PROPN
ejpam-4254	349	8	,	,	PUNCT
ejpam-4254	349	9	t	t	PROPN
ejpam-4254	349	10	)	)	PUNCT
ejpam-4254	349	11	and	and	CCONJ
ejpam-4254	349	12	l−(νp	l−(νp	PROPN
ejpam-4254	349	13	,	,	PUNCT
ejpam-4254	349	14	t	t	PROPN
ejpam-4254	349	15	)	)	PUNCT
ejpam-4254	349	16	are	be	AUX
ejpam-4254	349	17	upfs	upf	NOUN
ejpam-4254	349	18	of	of	ADP
ejpam-4254	349	19	u	u	PRON
ejpam-4254	349	20	if	if	SCONJ
ejpam-4254	349	21	the	the	DET
ejpam-4254	349	22	sets	set	NOUN
ejpam-4254	349	23	are	be	AUX
ejpam-4254	349	24	nonempty	nonempty	ADJ
ejpam-4254	349	25	.	.	PUNCT
ejpam-4254	350	1	suppose	suppose	VERB
ejpam-4254	350	2	there	there	PRON
ejpam-4254	350	3	exists	exist	VERB
ejpam-4254	350	4	a	a	DET
ejpam-4254	350	5	∈	∈	PROPN
ejpam-4254	350	6	u	u	NOUN
ejpam-4254	350	7	such	such	ADJ
ejpam-4254	350	8	that	that	DET
ejpam-4254	350	9	µp(0	µp(0	NOUN
ejpam-4254	350	10	)	)	PUNCT
ejpam-4254	350	11	<	<	X
ejpam-4254	350	12	µp(a	µp(a	NUM
ejpam-4254	350	13	)	)	PUNCT
ejpam-4254	350	14	.	.	PUNCT
ejpam-4254	351	1	choose	choose	VERB
ejpam-4254	351	2	t	t	PROPN
ejpam-4254	351	3	=	=	SYM
ejpam-4254	351	4	µp(0	µp(0	NOUN
ejpam-4254	351	5	)	)	PUNCT
ejpam-4254	351	6	∈	∈	NOUN
ejpam-4254	352	1	[	[	X
ejpam-4254	352	2	0	0	NUM
ejpam-4254	352	3	,	,	PUNCT
ejpam-4254	352	4	1	1	NUM
ejpam-4254	352	5	]	]	PUNCT
ejpam-4254	352	6	.	.	PUNCT
ejpam-4254	353	1	then	then	ADV
ejpam-4254	353	2	µp(a	µp(a	NUM
ejpam-4254	353	3	)	)	PUNCT
ejpam-4254	353	4	>	>	PUNCT
ejpam-4254	354	1	t.	t.	NOUN
ejpam-4254	354	2	thus	thus	ADV
ejpam-4254	354	3	a	a	DET
ejpam-4254	354	4	∈	∈	NOUN
ejpam-4254	354	5	u+(µp	u+(µp	NOUN
ejpam-4254	354	6	,	,	PUNCT
ejpam-4254	354	7	t	t	PROPN
ejpam-4254	354	8	)	)	PUNCT
ejpam-4254	354	9	̸=	̸=	PROPN
ejpam-4254	354	10	∅.	∅.	ADV
ejpam-4254	354	11	as	as	ADP
ejpam-4254	354	12	a	a	DET
ejpam-4254	354	13	hypothesis	hypothesis	NOUN
ejpam-4254	354	14	,	,	PUNCT
ejpam-4254	354	15	we	we	PRON
ejpam-4254	354	16	get	get	VERB
ejpam-4254	354	17	u+(µp	u+(µp	NOUN
ejpam-4254	354	18	,	,	PUNCT
ejpam-4254	354	19	t	t	PROPN
ejpam-4254	354	20	)	)	PUNCT
ejpam-4254	354	21	is	be	AUX
ejpam-4254	354	22	a	a	DET
ejpam-4254	354	23	upf	upf	NOUN
ejpam-4254	354	24	of	of	ADP
ejpam-4254	354	25	u	u	NOUN
ejpam-4254	354	26	and	and	CCONJ
ejpam-4254	354	27	a.	a.	NOUN
ejpam-4254	354	28	iampan	iampan	NOUN
ejpam-4254	354	29	et	et	PROPN
ejpam-4254	355	1	al	al	PROPN
ejpam-4254	355	2	.	.	PUNCT
ejpam-4254	355	3	/	/	SYM
ejpam-4254	355	4	eur	eur	PROPN
ejpam-4254	355	5	.	.	PUNCT
ejpam-4254	356	1	j.	j.	PROPN
ejpam-4254	356	2	pure	pure	PROPN
ejpam-4254	356	3	appl	appl	PROPN
ejpam-4254	356	4	.	.	PROPN
ejpam-4254	356	5	math	math	PROPN
ejpam-4254	356	6	,	,	PUNCT
ejpam-4254	356	7	15	15	NUM
ejpam-4254	356	8	(	(	PUNCT
ejpam-4254	356	9	1	1	NUM
ejpam-4254	356	10	)	)	PUNCT
ejpam-4254	356	11	(	(	PUNCT
ejpam-4254	356	12	2022	2022	NUM
ejpam-4254	356	13	)	)	PUNCT
ejpam-4254	356	14	,	,	PUNCT
ejpam-4254	356	15	169	169	NUM
ejpam-4254	356	16	-	-	SYM
ejpam-4254	356	17	198	198	NUM
ejpam-4254	356	18	186	186	NUM
ejpam-4254	356	19	so	so	ADV
ejpam-4254	356	20	0	0	NUM
ejpam-4254	356	21	∈	∈	PROPN
ejpam-4254	356	22	u+(µp	u+(µp	PROPN
ejpam-4254	356	23	,	,	PUNCT
ejpam-4254	356	24	t	t	PROPN
ejpam-4254	356	25	)	)	PUNCT
ejpam-4254	356	26	.	.	PUNCT
ejpam-4254	357	1	thus	thus	ADV
ejpam-4254	357	2	µp(0	µp(0	VERB
ejpam-4254	357	3	)	)	PUNCT
ejpam-4254	357	4	>	>	X
ejpam-4254	357	5	t	t	NOUN
ejpam-4254	357	6	=	=	SYM
ejpam-4254	357	7	µp(0	µp(0	NOUN
ejpam-4254	357	8	)	)	PUNCT
ejpam-4254	357	9	,	,	PUNCT
ejpam-4254	357	10	a	a	DET
ejpam-4254	357	11	contradiction	contradiction	NOUN
ejpam-4254	357	12	.	.	PUNCT
ejpam-4254	358	1	hence	hence	ADV
ejpam-4254	358	2	,	,	PUNCT
ejpam-4254	358	3	µp(0	µp(0	NOUN
ejpam-4254	358	4	)	)	PUNCT
ejpam-4254	358	5	≥	≥	NOUN
ejpam-4254	358	6	µp(a	µp(a	NUM
ejpam-4254	358	7	)	)	PUNCT
ejpam-4254	358	8	for	for	ADP
ejpam-4254	358	9	all	all	DET
ejpam-4254	358	10	a	a	DET
ejpam-4254	358	11	∈	∈	PROPN
ejpam-4254	358	12	u	u	NOUN
ejpam-4254	358	13	.	.	PUNCT
ejpam-4254	358	14	suppose	suppose	VERB
ejpam-4254	358	15	there	there	PRON
ejpam-4254	358	16	exist	exist	VERB
ejpam-4254	358	17	a	a	DET
ejpam-4254	358	18	,	,	PUNCT
ejpam-4254	358	19	b	b	X
ejpam-4254	358	20	∈	∈	PROPN
ejpam-4254	358	21	u	u	NOUN
ejpam-4254	358	22	such	such	ADJ
ejpam-4254	358	23	that	that	SCONJ
ejpam-4254	358	24	µp(b	µp(b	NOUN
ejpam-4254	358	25	)	)	PUNCT
ejpam-4254	358	26	<	<	X
ejpam-4254	358	27	min{µp(a	min{µp(a	NOUN
ejpam-4254	358	28	⋆	⋆	PUNCT
ejpam-4254	358	29	b	b	NOUN
ejpam-4254	358	30	)	)	PUNCT
ejpam-4254	358	31	,	,	PUNCT
ejpam-4254	358	32	µp(a	µp(a	NUM
ejpam-4254	358	33	)	)	PUNCT
ejpam-4254	358	34	}	}	PUNCT
ejpam-4254	358	35	.	.	PUNCT
ejpam-4254	359	1	choose	choose	VERB
ejpam-4254	359	2	t	t	PROPN
ejpam-4254	359	3	=	=	SYM
ejpam-4254	359	4	µp(b	µp(b	X
ejpam-4254	359	5	)	)	PUNCT
ejpam-4254	359	6	∈	∈	PROPN
ejpam-4254	360	1	[	[	X
ejpam-4254	360	2	0	0	NUM
ejpam-4254	360	3	,	,	PUNCT
ejpam-4254	360	4	1	1	NUM
ejpam-4254	360	5	]	]	PUNCT
ejpam-4254	360	6	.	.	PUNCT
ejpam-4254	361	1	then	then	ADV
ejpam-4254	361	2	µp(a	µp(a	PUNCT
ejpam-4254	361	3	⋆	⋆	PROPN
ejpam-4254	361	4	b	b	NOUN
ejpam-4254	361	5	)	)	PUNCT
ejpam-4254	361	6	>	>	X
ejpam-4254	361	7	t	t	NOUN
ejpam-4254	361	8	and	and	CCONJ
ejpam-4254	361	9	µp(a	µp(a	NUM
ejpam-4254	361	10	)	)	PUNCT
ejpam-4254	361	11	>	>	PUNCT
ejpam-4254	362	1	t.	t.	NOUN
ejpam-4254	362	2	thus	thus	ADV
ejpam-4254	362	3	a	a	DET
ejpam-4254	362	4	⋆	⋆	NOUN
ejpam-4254	362	5	b	b	NOUN
ejpam-4254	362	6	,	,	PUNCT
ejpam-4254	362	7	a	a	DET
ejpam-4254	362	8	∈	∈	NOUN
ejpam-4254	362	9	u+(µp	u+(µp	NOUN
ejpam-4254	362	10	,	,	PUNCT
ejpam-4254	362	11	t	t	PROPN
ejpam-4254	362	12	)	)	PUNCT
ejpam-4254	362	13	̸=	̸=	PROPN
ejpam-4254	362	14	∅.	∅.	ADV
ejpam-4254	362	15	as	as	ADP
ejpam-4254	362	16	a	a	DET
ejpam-4254	362	17	hypothesis	hypothesis	NOUN
ejpam-4254	362	18	,	,	PUNCT
ejpam-4254	362	19	we	we	PRON
ejpam-4254	362	20	get	get	VERB
ejpam-4254	362	21	u+(µp	u+(µp	NOUN
ejpam-4254	362	22	,	,	PUNCT
ejpam-4254	362	23	t	t	PROPN
ejpam-4254	362	24	)	)	PUNCT
ejpam-4254	362	25	is	be	AUX
ejpam-4254	362	26	a	a	DET
ejpam-4254	362	27	upf	upf	NOUN
ejpam-4254	362	28	of	of	ADP
ejpam-4254	362	29	u	u	NOUN
ejpam-4254	362	30	and	and	CCONJ
ejpam-4254	362	31	so	so	ADV
ejpam-4254	362	32	b	b	PROPN
ejpam-4254	362	33	∈	∈	PROPN
ejpam-4254	362	34	u+(µp	u+(µp	PROPN
ejpam-4254	362	35	,	,	PUNCT
ejpam-4254	362	36	t	t	PROPN
ejpam-4254	362	37	)	)	PUNCT
ejpam-4254	362	38	.	.	PUNCT
ejpam-4254	363	1	thus	thus	ADV
ejpam-4254	363	2	µp(b	µp(b	PUNCT
ejpam-4254	363	3	)	)	PUNCT
ejpam-4254	363	4	>	>	X
ejpam-4254	363	5	t	t	PROPN
ejpam-4254	363	6	=	=	SYM
ejpam-4254	363	7	µp(b	µp(b	NOUN
ejpam-4254	363	8	)	)	PUNCT
ejpam-4254	363	9	,	,	PUNCT
ejpam-4254	363	10	a	a	DET
ejpam-4254	363	11	contradiction	contradiction	NOUN
ejpam-4254	363	12	.	.	PUNCT
ejpam-4254	364	1	hence	hence	ADV
ejpam-4254	364	2	,	,	PUNCT
ejpam-4254	364	3	µp(b	µp(b	ADJ
ejpam-4254	364	4	)	)	PUNCT
ejpam-4254	364	5	≥	≥	NOUN
ejpam-4254	364	6	min{µp(a	min{µp(a	NOUN
ejpam-4254	364	7	⋆	⋆	X
ejpam-4254	364	8	b	b	NOUN
ejpam-4254	364	9	)	)	PUNCT
ejpam-4254	364	10	,	,	PUNCT
ejpam-4254	364	11	µp(a	µp(a	NUM
ejpam-4254	364	12	)	)	PUNCT
ejpam-4254	364	13	}	}	PUNCT
ejpam-4254	364	14	for	for	ADP
ejpam-4254	364	15	all	all	DET
ejpam-4254	364	16	a	a	DET
ejpam-4254	364	17	,	,	PUNCT
ejpam-4254	364	18	b	b	X
ejpam-4254	364	19	∈	∈	PROPN
ejpam-4254	364	20	u	u	NOUN
ejpam-4254	364	21	.	.	PUNCT
ejpam-4254	364	22	suppose	suppose	VERB
ejpam-4254	364	23	there	there	PRON
ejpam-4254	364	24	exists	exist	VERB
ejpam-4254	364	25	a	a	DET
ejpam-4254	364	26	∈	∈	PROPN
ejpam-4254	364	27	u	u	NOUN
ejpam-4254	364	28	such	such	ADJ
ejpam-4254	364	29	that	that	DET
ejpam-4254	364	30	νp(0	νp(0	NOUN
ejpam-4254	364	31	)	)	PUNCT
ejpam-4254	364	32	>	>	X
ejpam-4254	364	33	νp(a	νp(a	NUM
ejpam-4254	364	34	)	)	PUNCT
ejpam-4254	364	35	.	.	PUNCT
ejpam-4254	365	1	choose	choose	VERB
ejpam-4254	365	2	t	t	PROPN
ejpam-4254	365	3	=	=	SYM
ejpam-4254	365	4	νp(0	νp(0	NOUN
ejpam-4254	365	5	)	)	PUNCT
ejpam-4254	365	6	∈	∈	PROPN
ejpam-4254	366	1	[	[	X
ejpam-4254	366	2	0	0	NUM
ejpam-4254	366	3	,	,	PUNCT
ejpam-4254	366	4	1	1	NUM
ejpam-4254	366	5	]	]	PUNCT
ejpam-4254	366	6	.	.	PUNCT
ejpam-4254	367	1	then	then	ADV
ejpam-4254	367	2	νp(a	νp(a	NUM
ejpam-4254	367	3	)	)	PUNCT
ejpam-4254	368	1	<	<	X
ejpam-4254	368	2	t.	t.	X
ejpam-4254	368	3	thus	thus	ADV
ejpam-4254	368	4	a	a	DET
ejpam-4254	368	5	∈	∈	PROPN
ejpam-4254	368	6	l−(νp	l−(νp	PROPN
ejpam-4254	368	7	,	,	PUNCT
ejpam-4254	368	8	t	t	PROPN
ejpam-4254	368	9	)	)	PUNCT
ejpam-4254	368	10	̸=	̸=	PROPN
ejpam-4254	368	11	∅.	∅.	ADV
ejpam-4254	368	12	as	as	ADP
ejpam-4254	368	13	a	a	DET
ejpam-4254	368	14	hypothesis	hypothesis	NOUN
ejpam-4254	368	15	,	,	PUNCT
ejpam-4254	368	16	we	we	PRON
ejpam-4254	368	17	get	get	VERB
ejpam-4254	368	18	l−(νp	l−(νp	PROPN
ejpam-4254	368	19	,	,	PUNCT
ejpam-4254	368	20	t	t	PROPN
ejpam-4254	368	21	)	)	PUNCT
ejpam-4254	368	22	is	be	AUX
ejpam-4254	368	23	a	a	DET
ejpam-4254	368	24	upf	upf	NOUN
ejpam-4254	368	25	of	of	ADP
ejpam-4254	368	26	u	u	NOUN
ejpam-4254	368	27	and	and	CCONJ
ejpam-4254	369	1	so	so	ADV
ejpam-4254	369	2	0	0	NUM
ejpam-4254	369	3	∈	∈	PROPN
ejpam-4254	369	4	l−(νp	l−(νp	PROPN
ejpam-4254	369	5	,	,	PUNCT
ejpam-4254	369	6	t	t	PROPN
ejpam-4254	369	7	)	)	PUNCT
ejpam-4254	369	8	.	.	PUNCT
ejpam-4254	370	1	thus	thus	ADV
ejpam-4254	370	2	νp(0	νp(0	VERB
ejpam-4254	370	3	)	)	PUNCT
ejpam-4254	370	4	<	<	X
ejpam-4254	370	5	t	t	PROPN
ejpam-4254	370	6	=	=	SYM
ejpam-4254	370	7	νp(0	νp(0	PROPN
ejpam-4254	370	8	)	)	PUNCT
ejpam-4254	370	9	,	,	PUNCT
ejpam-4254	370	10	a	a	DET
ejpam-4254	370	11	contradiction	contradiction	NOUN
ejpam-4254	370	12	.	.	PUNCT
ejpam-4254	371	1	hence	hence	ADV
ejpam-4254	371	2	,	,	PUNCT
ejpam-4254	371	3	νp(0	νp(0	NOUN
ejpam-4254	371	4	)	)	PUNCT
ejpam-4254	371	5	≤	≤	NOUN
ejpam-4254	371	6	νp(a	νp(a	NUM
ejpam-4254	371	7	)	)	PUNCT
ejpam-4254	371	8	for	for	ADP
ejpam-4254	371	9	all	all	DET
ejpam-4254	371	10	a	a	DET
ejpam-4254	371	11	∈	∈	PROPN
ejpam-4254	371	12	u	u	NOUN
ejpam-4254	371	13	.	.	PUNCT
ejpam-4254	371	14	suppose	suppose	VERB
ejpam-4254	371	15	there	there	PRON
ejpam-4254	371	16	exist	exist	VERB
ejpam-4254	371	17	a	a	DET
ejpam-4254	371	18	,	,	PUNCT
ejpam-4254	371	19	b	b	X
ejpam-4254	371	20	∈	∈	PROPN
ejpam-4254	371	21	u	u	NOUN
ejpam-4254	371	22	such	such	ADJ
ejpam-4254	371	23	that	that	DET
ejpam-4254	371	24	νp(b	νp(b	NOUN
ejpam-4254	371	25	)	)	PUNCT
ejpam-4254	371	26	>	>	X
ejpam-4254	371	27	max{νp(a	max{νp(a	PROPN
ejpam-4254	371	28	⋆	⋆	NOUN
ejpam-4254	371	29	b	b	NOUN
ejpam-4254	371	30	)	)	PUNCT
ejpam-4254	371	31	,	,	PUNCT
ejpam-4254	371	32	νp(a	νp(a	NUM
ejpam-4254	371	33	)	)	PUNCT
ejpam-4254	371	34	}	}	PUNCT
ejpam-4254	371	35	.	.	PUNCT
ejpam-4254	372	1	choose	choose	VERB
ejpam-4254	372	2	t	t	NOUN
ejpam-4254	372	3	=	=	SYM
ejpam-4254	372	4	νp(b	νp(b	NOUN
ejpam-4254	372	5	)	)	PUNCT
ejpam-4254	372	6	∈	∈	PROPN
ejpam-4254	373	1	[	[	X
ejpam-4254	373	2	0	0	NUM
ejpam-4254	373	3	,	,	PUNCT
ejpam-4254	373	4	1	1	NUM
ejpam-4254	373	5	]	]	PUNCT
ejpam-4254	373	6	.	.	PUNCT
ejpam-4254	374	1	then	then	ADV
ejpam-4254	374	2	νp(a	νp(a	NUM
ejpam-4254	374	3	⋆	⋆	ADJ
ejpam-4254	374	4	b	b	NOUN
ejpam-4254	374	5	)	)	PUNCT
ejpam-4254	374	6	<	<	X
ejpam-4254	374	7	t	t	PROPN
ejpam-4254	374	8	and	and	CCONJ
ejpam-4254	374	9	νp(a	νp(a	NUM
ejpam-4254	374	10	)	)	PUNCT
ejpam-4254	375	1	<	<	X
ejpam-4254	375	2	t.	t.	X
ejpam-4254	375	3	thus	thus	ADV
ejpam-4254	375	4	a	a	DET
ejpam-4254	375	5	⋆	⋆	NOUN
ejpam-4254	375	6	b	b	NOUN
ejpam-4254	375	7	,	,	PUNCT
ejpam-4254	375	8	a	a	DET
ejpam-4254	375	9	∈	∈	PROPN
ejpam-4254	375	10	l−(νp	l−(νp	PROPN
ejpam-4254	375	11	,	,	PUNCT
ejpam-4254	375	12	t	t	PROPN
ejpam-4254	375	13	)	)	PUNCT
ejpam-4254	375	14	̸=	̸=	PROPN
ejpam-4254	375	15	∅.	∅.	ADV
ejpam-4254	375	16	as	as	ADP
ejpam-4254	375	17	a	a	DET
ejpam-4254	375	18	hypothesis	hypothesis	NOUN
ejpam-4254	375	19	,	,	PUNCT
ejpam-4254	375	20	we	we	PRON
ejpam-4254	375	21	get	get	VERB
ejpam-4254	375	22	l−(νp	l−(νp	PROPN
ejpam-4254	375	23	,	,	PUNCT
ejpam-4254	375	24	t	t	PROPN
ejpam-4254	375	25	)	)	PUNCT
ejpam-4254	375	26	is	be	AUX
ejpam-4254	375	27	a	a	DET
ejpam-4254	375	28	upf	upf	NOUN
ejpam-4254	375	29	of	of	ADP
ejpam-4254	375	30	u	u	NOUN
ejpam-4254	375	31	and	and	CCONJ
ejpam-4254	376	1	so	so	ADV
ejpam-4254	376	2	b	b	PROPN
ejpam-4254	376	3	∈	∈	PROPN
ejpam-4254	376	4	l−(νp	l−(νp	PROPN
ejpam-4254	376	5	,	,	PUNCT
ejpam-4254	376	6	t	t	PROPN
ejpam-4254	376	7	)	)	PUNCT
ejpam-4254	376	8	.	.	PUNCT
ejpam-4254	377	1	thus	thus	ADV
ejpam-4254	377	2	νp(b	νp(b	VERB
ejpam-4254	377	3	)	)	PUNCT
ejpam-4254	377	4	<	<	X
ejpam-4254	377	5	t	t	NOUN
ejpam-4254	377	6	=	=	SYM
ejpam-4254	377	7	νp(b	νp(b	PROPN
ejpam-4254	377	8	)	)	PUNCT
ejpam-4254	377	9	,	,	PUNCT
ejpam-4254	377	10	a	a	DET
ejpam-4254	377	11	contradiction	contradiction	NOUN
ejpam-4254	377	12	.	.	PUNCT
ejpam-4254	378	1	hence	hence	ADV
ejpam-4254	378	2	,	,	PUNCT
ejpam-4254	378	3	νp(b	νp(b	NOUN
ejpam-4254	378	4	)	)	PUNCT
ejpam-4254	378	5	≤	≤	NOUN
ejpam-4254	378	6	max{νp(a	max{νp(a	NOUN
ejpam-4254	378	7	⋆	⋆	NOUN
ejpam-4254	378	8	b	b	NOUN
ejpam-4254	378	9	)	)	PUNCT
ejpam-4254	378	10	,	,	PUNCT
ejpam-4254	378	11	νp(a	νp(a	NUM
ejpam-4254	378	12	)	)	PUNCT
ejpam-4254	378	13	}	}	PUNCT
ejpam-4254	378	14	for	for	ADP
ejpam-4254	378	15	all	all	DET
ejpam-4254	378	16	a	a	DET
ejpam-4254	378	17	,	,	PUNCT
ejpam-4254	378	18	b	b	X
ejpam-4254	378	19	∈	∈	PROPN
ejpam-4254	378	20	u	u	NOUN
ejpam-4254	378	21	.	.	PUNCT
ejpam-4254	379	1	therefore	therefore	ADV
ejpam-4254	379	2	,	,	PUNCT
ejpam-4254	379	3	p	p	PRON
ejpam-4254	379	4	is	be	AUX
ejpam-4254	379	5	a	a	DET
ejpam-4254	379	6	pfupf	pfupf	NOUN
ejpam-4254	379	7	of	of	ADP
ejpam-4254	379	8	u	u	PROPN
ejpam-4254	379	9	.	.	PUNCT
ejpam-4254	380	1	theorem	theorem	VERB
ejpam-4254	380	2	8	8	NUM
ejpam-4254	380	3	.	.	PUNCT
ejpam-4254	381	1	p	p	NOUN
ejpam-4254	381	2	is	be	AUX
ejpam-4254	381	3	a	a	DET
ejpam-4254	381	4	pfupi	pfupi	NOUN
ejpam-4254	381	5	of	of	ADP
ejpam-4254	381	6	u	u	PRON
ejpam-4254	381	7	if	if	SCONJ
ejpam-4254	381	8	and	and	CCONJ
ejpam-4254	381	9	only	only	ADV
ejpam-4254	381	10	if	if	SCONJ
ejpam-4254	381	11	u(µp	u(µp	NOUN
ejpam-4254	381	12	,	,	PUNCT
ejpam-4254	381	13	t	t	PROPN
ejpam-4254	381	14	)	)	PUNCT
ejpam-4254	381	15	and	and	CCONJ
ejpam-4254	381	16	l(νp	l(νp	PROPN
ejpam-4254	381	17	,	,	PUNCT
ejpam-4254	381	18	t	t	PROPN
ejpam-4254	381	19	)	)	PUNCT
ejpam-4254	381	20	are	be	AUX
ejpam-4254	381	21	,	,	PUNCT
ejpam-4254	381	22	if	if	SCONJ
ejpam-4254	381	23	the	the	DET
ejpam-4254	381	24	sets	set	NOUN
ejpam-4254	381	25	are	be	AUX
ejpam-4254	381	26	nonempty	nonempty	ADJ
ejpam-4254	381	27	,	,	PUNCT
ejpam-4254	381	28	upis	upis	ADJ
ejpam-4254	381	29	for	for	ADP
ejpam-4254	381	30	every	every	DET
ejpam-4254	381	31	t	t	NOUN
ejpam-4254	381	32	∈	∈	PROPN
ejpam-4254	382	1	[	[	X
ejpam-4254	382	2	0	0	NUM
ejpam-4254	382	3	,	,	PUNCT
ejpam-4254	382	4	1	1	NUM
ejpam-4254	382	5	]	]	PUNCT
ejpam-4254	382	6	.	.	PUNCT
ejpam-4254	383	1	proof	proof	NOUN
ejpam-4254	383	2	.	.	PUNCT
ejpam-4254	384	1	assume	assume	VERB
ejpam-4254	384	2	p	p	X
ejpam-4254	384	3	=	=	X
ejpam-4254	384	4	(	(	PUNCT
ejpam-4254	384	5	µp	µp	PROPN
ejpam-4254	384	6	,	,	PUNCT
ejpam-4254	384	7	νp	νp	NOUN
ejpam-4254	384	8	)	)	PUNCT
ejpam-4254	384	9	is	be	AUX
ejpam-4254	384	10	a	a	DET
ejpam-4254	384	11	pfupi	pfupi	NOUN
ejpam-4254	384	12	of	of	ADP
ejpam-4254	384	13	u	u	PROPN
ejpam-4254	384	14	.	.	PUNCT
ejpam-4254	385	1	let	let	VERB
ejpam-4254	385	2	t	t	X
ejpam-4254	385	3	∈	∈	PROPN
ejpam-4254	386	1	[	[	X
ejpam-4254	386	2	0	0	NUM
ejpam-4254	386	3	,	,	PUNCT
ejpam-4254	386	4	1	1	NUM
ejpam-4254	386	5	]	]	PUNCT
ejpam-4254	386	6	be	be	AUX
ejpam-4254	386	7	such	such	ADJ
ejpam-4254	386	8	that	that	SCONJ
ejpam-4254	386	9	u(µp	u(µp	NOUN
ejpam-4254	386	10	,	,	PUNCT
ejpam-4254	386	11	t	t	PROPN
ejpam-4254	386	12	)	)	PUNCT
ejpam-4254	386	13	,	,	PUNCT
ejpam-4254	386	14	l(νp	l(νp	PROPN
ejpam-4254	386	15	,	,	PUNCT
ejpam-4254	386	16	t	t	PROPN
ejpam-4254	386	17	)	)	PUNCT
ejpam-4254	386	18	̸=	̸=	PROPN
ejpam-4254	386	19	∅.	∅.	ADV
ejpam-4254	386	20	let	let	VERB
ejpam-4254	386	21	a	a	DET
ejpam-4254	386	22	,	,	PUNCT
ejpam-4254	386	23	b	b	NOUN
ejpam-4254	386	24	,	,	PUNCT
ejpam-4254	386	25	c	c	PROPN
ejpam-4254	386	26	∈	∈	PROPN
ejpam-4254	386	27	u	u	PROPN
ejpam-4254	386	28	.	.	PUNCT
ejpam-4254	387	1	then	then	ADV
ejpam-4254	387	2	a	a	DET
ejpam-4254	387	3	∈	∈	PROPN
ejpam-4254	387	4	u(µp	u(µp	NOUN
ejpam-4254	387	5	,	,	PUNCT
ejpam-4254	387	6	t	t	PROPN
ejpam-4254	387	7	)	)	PUNCT
ejpam-4254	387	8	⇒	⇒	NOUN
ejpam-4254	387	9	µp(a	µp(a	NUM
ejpam-4254	387	10	)	)	PUNCT
ejpam-4254	387	11	≥	≥	NOUN
ejpam-4254	387	12	t	t	PROPN
ejpam-4254	387	13	⇒	⇒	PROPN
ejpam-4254	387	14	µp(0	µp(0	NOUN
ejpam-4254	387	15	)	)	PUNCT
ejpam-4254	387	16	≥	≥	NOUN
ejpam-4254	387	17	µp(a	µp(a	NUM
ejpam-4254	387	18	)	)	PUNCT
ejpam-4254	387	19	≥	≥	NOUN
ejpam-4254	387	20	t	t	PROPN
ejpam-4254	387	21	(	(	PUNCT
ejpam-4254	387	22	(	(	PUNCT
ejpam-4254	387	23	1.25	1.25	NUM
ejpam-4254	387	24	)	)	PUNCT
ejpam-4254	387	25	)	)	PUNCT
ejpam-4254	387	26	⇒	⇒	VERB
ejpam-4254	387	27	0	0	NUM
ejpam-4254	388	1	∈	∈	PROPN
ejpam-4254	388	2	u(µp	u(µp	NOUN
ejpam-4254	388	3	,	,	PUNCT
ejpam-4254	388	4	t	t	PROPN
ejpam-4254	388	5	)	)	PUNCT
ejpam-4254	388	6	,	,	PUNCT
ejpam-4254	388	7	a	a	DET
ejpam-4254	388	8	⋆	⋆	X
ejpam-4254	388	9	(	(	PUNCT
ejpam-4254	388	10	b	b	NOUN
ejpam-4254	388	11	⋆	⋆	NOUN
ejpam-4254	388	12	c	c	NOUN
ejpam-4254	388	13	)	)	PUNCT
ejpam-4254	388	14	,	,	PUNCT
ejpam-4254	388	15	b	b	X
ejpam-4254	388	16	∈	∈	PROPN
ejpam-4254	388	17	u(µp	u(µp	PROPN
ejpam-4254	388	18	,	,	PUNCT
ejpam-4254	388	19	t	t	PROPN
ejpam-4254	388	20	)	)	PUNCT
ejpam-4254	388	21	⇒	⇒	NOUN
ejpam-4254	388	22	µp(a	µp(a	PUNCT
ejpam-4254	388	23	⋆	⋆	X
ejpam-4254	388	24	(	(	PUNCT
ejpam-4254	388	25	b	b	NOUN
ejpam-4254	388	26	⋆	⋆	ADJ
ejpam-4254	388	27	c	c	NOUN
ejpam-4254	388	28	)	)	PUNCT
ejpam-4254	388	29	)	)	PUNCT
ejpam-4254	388	30	≥	≥	PROPN
ejpam-4254	388	31	t	t	PROPN
ejpam-4254	388	32	,	,	PUNCT
ejpam-4254	388	33	µp(b	µp(b	ADJ
ejpam-4254	388	34	)	)	PUNCT
ejpam-4254	388	35	≥	≥	NOUN
ejpam-4254	388	36	t	t	PROPN
ejpam-4254	388	37	⇒	⇒	NOUN
ejpam-4254	388	38	min{µp(a	min{µp(a	NOUN
ejpam-4254	388	39	⋆	⋆	X
ejpam-4254	388	40	(	(	PUNCT
ejpam-4254	388	41	b	b	X
ejpam-4254	388	42	⋆	⋆	ADJ
ejpam-4254	388	43	c	c	NOUN
ejpam-4254	388	44	)	)	PUNCT
ejpam-4254	388	45	)	)	PUNCT
ejpam-4254	388	46	,	,	PUNCT
ejpam-4254	388	47	µp(b	µp(b	ADJ
ejpam-4254	388	48	)	)	PUNCT
ejpam-4254	388	49	}	}	PUNCT
ejpam-4254	388	50	≥	≥	PROPN
ejpam-4254	388	51	t	t	PROPN
ejpam-4254	388	52	⇒	⇒	NOUN
ejpam-4254	388	53	µp(a	µp(a	PUNCT
ejpam-4254	388	54	⋆	⋆	ADP
ejpam-4254	388	55	c	c	NOUN
ejpam-4254	388	56	)	)	PUNCT
ejpam-4254	388	57	≥	≥	NOUN
ejpam-4254	388	58	min{µp(a	min{µp(a	NOUN
ejpam-4254	388	59	⋆	⋆	X
ejpam-4254	388	60	(	(	PUNCT
ejpam-4254	388	61	b	b	X
ejpam-4254	388	62	⋆	⋆	ADJ
ejpam-4254	388	63	c	c	NOUN
ejpam-4254	388	64	)	)	PUNCT
ejpam-4254	388	65	)	)	PUNCT
ejpam-4254	388	66	,	,	PUNCT
ejpam-4254	388	67	µp(b	µp(b	ADJ
ejpam-4254	388	68	)	)	PUNCT
ejpam-4254	388	69	}	}	PUNCT
ejpam-4254	388	70	≥	≥	PROPN
ejpam-4254	388	71	t	t	PROPN
ejpam-4254	388	72	(	(	PUNCT
ejpam-4254	388	73	(	(	PUNCT
ejpam-4254	388	74	1.29	1.29	NUM
ejpam-4254	388	75	)	)	PUNCT
ejpam-4254	388	76	)	)	PUNCT
ejpam-4254	388	77	⇒	⇒	VERB
ejpam-4254	388	78	a	a	DET
ejpam-4254	388	79	⋆	⋆	NOUN
ejpam-4254	388	80	c	c	PROPN
ejpam-4254	388	81	∈	∈	PROPN
ejpam-4254	388	82	u(µp	u(µp	PROPN
ejpam-4254	388	83	,	,	PUNCT
ejpam-4254	388	84	t	t	PROPN
ejpam-4254	388	85	)	)	PUNCT
ejpam-4254	388	86	,	,	PUNCT
ejpam-4254	388	87	a	a	DET
ejpam-4254	388	88	∈	∈	PROPN
ejpam-4254	388	89	l(νp	l(νp	PROPN
ejpam-4254	388	90	,	,	PUNCT
ejpam-4254	388	91	t	t	PROPN
ejpam-4254	388	92	)	)	PUNCT
ejpam-4254	388	93	⇒	⇒	NOUN
ejpam-4254	388	94	νp(a	νp(a	NUM
ejpam-4254	388	95	)	)	PUNCT
ejpam-4254	388	96	≤	≤	PUNCT
ejpam-4254	388	97	t	t	PROPN
ejpam-4254	388	98	⇒	⇒	PROPN
ejpam-4254	388	99	νp(0	νp(0	PROPN
ejpam-4254	388	100	)	)	PUNCT
ejpam-4254	388	101	≤	≤	NOUN
ejpam-4254	388	102	νp(a	νp(a	NUM
ejpam-4254	388	103	)	)	PUNCT
ejpam-4254	388	104	≤	≤	NUM
ejpam-4254	388	105	t	t	NOUN
ejpam-4254	388	106	(	(	PUNCT
ejpam-4254	388	107	(	(	PUNCT
ejpam-4254	388	108	1.26	1.26	NUM
ejpam-4254	388	109	)	)	PUNCT
ejpam-4254	388	110	)	)	PUNCT
ejpam-4254	388	111	⇒	⇒	VERB
ejpam-4254	388	112	0	0	NUM
ejpam-4254	388	113	∈	∈	PROPN
ejpam-4254	388	114	l(νp	l(νp	PROPN
ejpam-4254	388	115	,	,	PUNCT
ejpam-4254	388	116	t	t	PROPN
ejpam-4254	388	117	)	)	PUNCT
ejpam-4254	388	118	,	,	PUNCT
ejpam-4254	388	119	and	and	CCONJ
ejpam-4254	388	120	a	a	DET
ejpam-4254	388	121	⋆	⋆	X
ejpam-4254	388	122	(	(	PUNCT
ejpam-4254	388	123	b	b	NOUN
ejpam-4254	388	124	⋆	⋆	NOUN
ejpam-4254	388	125	c	c	NOUN
ejpam-4254	388	126	)	)	PUNCT
ejpam-4254	388	127	,	,	PUNCT
ejpam-4254	388	128	b	b	X
ejpam-4254	388	129	∈	∈	PROPN
ejpam-4254	388	130	l(νp	l(νp	PROPN
ejpam-4254	388	131	,	,	PUNCT
ejpam-4254	388	132	t	t	PROPN
ejpam-4254	388	133	)	)	PUNCT
ejpam-4254	388	134	⇒	⇒	NOUN
ejpam-4254	388	135	νp(a	νp(a	ADV
ejpam-4254	389	1	⋆	⋆	X
ejpam-4254	389	2	(	(	PUNCT
ejpam-4254	389	3	b	b	NOUN
ejpam-4254	389	4	⋆	⋆	ADJ
ejpam-4254	389	5	c	c	NOUN
ejpam-4254	389	6	)	)	PUNCT
ejpam-4254	389	7	)	)	PUNCT
ejpam-4254	389	8	≤	≤	PROPN
ejpam-4254	389	9	t	t	PROPN
ejpam-4254	389	10	,	,	PUNCT
ejpam-4254	389	11	νp(b	νp(b	NOUN
ejpam-4254	389	12	)	)	PUNCT
ejpam-4254	389	13	≤	≤	PUNCT
ejpam-4254	390	1	t	t	PROPN
ejpam-4254	390	2	⇒	⇒	NOUN
ejpam-4254	390	3	max{µp(a	max{µp(a	PROPN
ejpam-4254	390	4	⋆	⋆	X
ejpam-4254	390	5	(	(	PUNCT
ejpam-4254	390	6	b	b	NOUN
ejpam-4254	390	7	⋆	⋆	ADJ
ejpam-4254	390	8	c	c	NOUN
ejpam-4254	390	9	)	)	PUNCT
ejpam-4254	390	10	)	)	PUNCT
ejpam-4254	390	11	,	,	PUNCT
ejpam-4254	390	12	νp(b	νp(b	NOUN
ejpam-4254	390	13	)	)	PUNCT
ejpam-4254	390	14	}	}	PUNCT
ejpam-4254	390	15	≤	≤	NUM
ejpam-4254	390	16	t	t	PROPN
ejpam-4254	390	17	⇒	⇒	NOUN
ejpam-4254	390	18	νp(a	νp(a	ADV
ejpam-4254	390	19	⋆	⋆	VERB
ejpam-4254	390	20	c	c	NOUN
ejpam-4254	390	21	)	)	PUNCT
ejpam-4254	390	22	≤	≤	NOUN
ejpam-4254	390	23	max{νp(a	max{νp(a	NOUN
ejpam-4254	390	24	⋆	⋆	X
ejpam-4254	390	25	(	(	PUNCT
ejpam-4254	390	26	b	b	NOUN
ejpam-4254	390	27	⋆	⋆	ADJ
ejpam-4254	390	28	c	c	NOUN
ejpam-4254	390	29	)	)	PUNCT
ejpam-4254	390	30	)	)	PUNCT
ejpam-4254	390	31	,	,	PUNCT
ejpam-4254	390	32	νp(b	νp(b	NOUN
ejpam-4254	390	33	)	)	PUNCT
ejpam-4254	390	34	}	}	PUNCT
ejpam-4254	390	35	≤	≤	PROPN
ejpam-4254	390	36	t	t	NOUN
ejpam-4254	390	37	(	(	PUNCT
ejpam-4254	390	38	(	(	PUNCT
ejpam-4254	390	39	1.30	1.30	NUM
ejpam-4254	390	40	)	)	PUNCT
ejpam-4254	390	41	)	)	PUNCT
ejpam-4254	390	42	⇒	⇒	VERB
ejpam-4254	390	43	a	a	DET
ejpam-4254	390	44	⋆	⋆	NOUN
ejpam-4254	390	45	c	c	PROPN
ejpam-4254	390	46	∈	∈	PROPN
ejpam-4254	390	47	l(νp	l(νp	PROPN
ejpam-4254	390	48	,	,	PUNCT
ejpam-4254	390	49	t	t	PROPN
ejpam-4254	390	50	)	)	PUNCT
ejpam-4254	390	51	.	.	PUNCT
ejpam-4254	391	1	a.	a.	PROPN
ejpam-4254	391	2	iampan	iampan	PROPN
ejpam-4254	391	3	et	et	PROPN
ejpam-4254	391	4	al	al	PROPN
ejpam-4254	391	5	.	.	PUNCT
ejpam-4254	391	6	/	/	SYM
ejpam-4254	391	7	eur	eur	PROPN
ejpam-4254	391	8	.	.	PUNCT
ejpam-4254	392	1	j.	j.	PROPN
ejpam-4254	392	2	pure	pure	PROPN
ejpam-4254	392	3	appl	appl	PROPN
ejpam-4254	392	4	.	.	PROPN
ejpam-4254	392	5	math	math	PROPN
ejpam-4254	392	6	,	,	PUNCT
ejpam-4254	392	7	15	15	NUM
ejpam-4254	392	8	(	(	PUNCT
ejpam-4254	392	9	1	1	NUM
ejpam-4254	392	10	)	)	PUNCT
ejpam-4254	392	11	(	(	PUNCT
ejpam-4254	392	12	2022	2022	NUM
ejpam-4254	392	13	)	)	PUNCT
ejpam-4254	392	14	,	,	PUNCT
ejpam-4254	392	15	169	169	NUM
ejpam-4254	392	16	-	-	SYM
ejpam-4254	392	17	198	198	NUM
ejpam-4254	392	18	187	187	NUM
ejpam-4254	392	19	hence	hence	ADV
ejpam-4254	392	20	,	,	PUNCT
ejpam-4254	392	21	u(µp	u(µp	PROPN
ejpam-4254	392	22	,	,	PUNCT
ejpam-4254	392	23	t	t	PROPN
ejpam-4254	392	24	)	)	PUNCT
ejpam-4254	392	25	and	and	CCONJ
ejpam-4254	392	26	l(νp	l(νp	PROPN
ejpam-4254	392	27	,	,	PUNCT
ejpam-4254	392	28	t	t	PROPN
ejpam-4254	392	29	)	)	PUNCT
ejpam-4254	392	30	are	be	AUX
ejpam-4254	392	31	upis	upis	ADJ
ejpam-4254	392	32	of	of	ADP
ejpam-4254	392	33	u	u	PROPN
ejpam-4254	392	34	.	.	PUNCT
ejpam-4254	393	1	conversely	conversely	ADV
ejpam-4254	393	2	,	,	PUNCT
ejpam-4254	393	3	assume	assume	VERB
ejpam-4254	393	4	for	for	ADP
ejpam-4254	393	5	all	all	DET
ejpam-4254	393	6	t	t	NOUN
ejpam-4254	393	7	∈	∈	PROPN
ejpam-4254	394	1	[	[	X
ejpam-4254	394	2	0	0	NUM
ejpam-4254	394	3	,	,	PUNCT
ejpam-4254	394	4	1	1	NUM
ejpam-4254	394	5	]	]	PUNCT
ejpam-4254	394	6	,	,	PUNCT
ejpam-4254	394	7	u(µp	u(µp	PROPN
ejpam-4254	394	8	,	,	PUNCT
ejpam-4254	394	9	t	t	PROPN
ejpam-4254	394	10	)	)	PUNCT
ejpam-4254	394	11	and	and	CCONJ
ejpam-4254	394	12	l(νp	l(νp	PROPN
ejpam-4254	394	13	,	,	PUNCT
ejpam-4254	394	14	t	t	PROPN
ejpam-4254	394	15	)	)	PUNCT
ejpam-4254	394	16	are	be	AUX
ejpam-4254	394	17	upis	upis	ADJ
ejpam-4254	394	18	of	of	ADP
ejpam-4254	394	19	u	u	PRON
ejpam-4254	394	20	if	if	SCONJ
ejpam-4254	394	21	the	the	DET
ejpam-4254	394	22	sets	set	NOUN
ejpam-4254	394	23	are	be	AUX
ejpam-4254	394	24	nonempty	nonempty	ADJ
ejpam-4254	394	25	.	.	PUNCT
ejpam-4254	395	1	let	let	VERB
ejpam-4254	395	2	a	a	DET
ejpam-4254	395	3	,	,	PUNCT
ejpam-4254	395	4	b	b	NOUN
ejpam-4254	395	5	,	,	PUNCT
ejpam-4254	395	6	c	c	PROPN
ejpam-4254	395	7	∈	∈	PROPN
ejpam-4254	395	8	u	u	PROPN
ejpam-4254	395	9	.	.	PUNCT
ejpam-4254	396	1	choose	choose	VERB
ejpam-4254	396	2	t	t	NOUN
ejpam-4254	396	3	=	=	SYM
ejpam-4254	396	4	µp(a	µp(a	PRON
ejpam-4254	396	5	)	)	PUNCT
ejpam-4254	396	6	∈	∈	NOUN
ejpam-4254	397	1	[	[	X
ejpam-4254	397	2	0	0	NUM
ejpam-4254	397	3	,	,	PUNCT
ejpam-4254	397	4	1	1	NUM
ejpam-4254	397	5	]	]	PUNCT
ejpam-4254	397	6	.	.	PUNCT
ejpam-4254	398	1	then	then	ADV
ejpam-4254	398	2	µp(a	µp(a	NUM
ejpam-4254	398	3	)	)	PUNCT
ejpam-4254	398	4	≥	≥	NOUN
ejpam-4254	398	5	t.	t.	NOUN
ejpam-4254	398	6	thus	thus	ADV
ejpam-4254	398	7	a	a	DET
ejpam-4254	398	8	∈	∈	NOUN
ejpam-4254	398	9	u(µp	u(µp	NOUN
ejpam-4254	398	10	,	,	PUNCT
ejpam-4254	398	11	t	t	PROPN
ejpam-4254	398	12	)	)	PUNCT
ejpam-4254	398	13	̸=	̸=	PROPN
ejpam-4254	398	14	∅.	∅.	ADV
ejpam-4254	398	15	as	as	ADP
ejpam-4254	398	16	a	a	DET
ejpam-4254	398	17	hypothesis	hypothesis	NOUN
ejpam-4254	398	18	,	,	PUNCT
ejpam-4254	398	19	we	we	PRON
ejpam-4254	398	20	get	get	VERB
ejpam-4254	398	21	u(µp	u(µp	NOUN
ejpam-4254	398	22	,	,	PUNCT
ejpam-4254	398	23	t	t	PROPN
ejpam-4254	398	24	)	)	PUNCT
ejpam-4254	398	25	is	be	AUX
ejpam-4254	398	26	a	a	DET
ejpam-4254	398	27	upi	upi	NOUN
ejpam-4254	398	28	of	of	ADP
ejpam-4254	398	29	u	u	NOUN
ejpam-4254	398	30	and	and	CCONJ
ejpam-4254	398	31	so	so	ADV
ejpam-4254	398	32	0	0	NUM
ejpam-4254	398	33	∈	∈	PROPN
ejpam-4254	398	34	u(µp	u(µp	NOUN
ejpam-4254	398	35	,	,	PUNCT
ejpam-4254	398	36	t	t	PROPN
ejpam-4254	398	37	)	)	PUNCT
ejpam-4254	398	38	.	.	PUNCT
ejpam-4254	399	1	thus	thus	ADV
ejpam-4254	399	2	µp(0	µp(0	NOUN
ejpam-4254	399	3	)	)	PUNCT
ejpam-4254	399	4	≥	≥	NOUN
ejpam-4254	399	5	t	t	NOUN
ejpam-4254	399	6	=	=	PUNCT
ejpam-4254	399	7	µp(a	µp(a	NUM
ejpam-4254	399	8	)	)	PUNCT
ejpam-4254	399	9	.	.	PUNCT
ejpam-4254	400	1	choose	choose	VERB
ejpam-4254	400	2	t	t	PROPN
ejpam-4254	400	3	=	=	PUNCT
ejpam-4254	401	1	min{µp(a	min{µp(a	NOUN
ejpam-4254	401	2	⋆	⋆	X
ejpam-4254	401	3	(	(	PUNCT
ejpam-4254	401	4	b	b	NOUN
ejpam-4254	401	5	⋆	⋆	ADJ
ejpam-4254	401	6	c	c	NOUN
ejpam-4254	401	7	)	)	PUNCT
ejpam-4254	401	8	)	)	PUNCT
ejpam-4254	401	9	,	,	PUNCT
ejpam-4254	401	10	µp(b	µp(b	ADJ
ejpam-4254	401	11	)	)	PUNCT
ejpam-4254	401	12	}	}	PUNCT
ejpam-4254	401	13	∈	∈	PROPN
ejpam-4254	402	1	[	[	X
ejpam-4254	402	2	0	0	NUM
ejpam-4254	402	3	,	,	PUNCT
ejpam-4254	402	4	1	1	NUM
ejpam-4254	402	5	]	]	PUNCT
ejpam-4254	402	6	.	.	PUNCT
ejpam-4254	403	1	then	then	ADV
ejpam-4254	403	2	µp(a	µp(a	PUNCT
ejpam-4254	403	3	⋆	⋆	X
ejpam-4254	403	4	(	(	PUNCT
ejpam-4254	403	5	b	b	NOUN
ejpam-4254	403	6	⋆	⋆	ADJ
ejpam-4254	403	7	c	c	NOUN
ejpam-4254	403	8	)	)	PUNCT
ejpam-4254	403	9	)	)	PUNCT
ejpam-4254	403	10	≥	≥	PROPN
ejpam-4254	403	11	t	t	NOUN
ejpam-4254	403	12	and	and	CCONJ
ejpam-4254	403	13	µp(b	µp(b	ADJ
ejpam-4254	403	14	)	)	PUNCT
ejpam-4254	403	15	≥	≥	NOUN
ejpam-4254	403	16	t.	t.	NOUN
ejpam-4254	403	17	thus	thus	ADV
ejpam-4254	403	18	a	a	DET
ejpam-4254	403	19	⋆	⋆	X
ejpam-4254	403	20	(	(	PUNCT
ejpam-4254	403	21	b	b	NOUN
ejpam-4254	403	22	⋆	⋆	NOUN
ejpam-4254	403	23	c	c	NOUN
ejpam-4254	403	24	)	)	PUNCT
ejpam-4254	403	25	,	,	PUNCT
ejpam-4254	403	26	b	b	X
ejpam-4254	403	27	∈	∈	PROPN
ejpam-4254	403	28	u(µp	u(µp	PROPN
ejpam-4254	403	29	,	,	PUNCT
ejpam-4254	403	30	t	t	PROPN
ejpam-4254	403	31	)	)	PUNCT
ejpam-4254	403	32	̸=	̸=	PROPN
ejpam-4254	403	33	∅.	∅.	ADV
ejpam-4254	403	34	as	as	ADP
ejpam-4254	403	35	a	a	DET
ejpam-4254	403	36	hypothesis	hypothesis	NOUN
ejpam-4254	403	37	,	,	PUNCT
ejpam-4254	403	38	we	we	PRON
ejpam-4254	403	39	get	get	VERB
ejpam-4254	403	40	u(µp	u(µp	NOUN
ejpam-4254	403	41	,	,	PUNCT
ejpam-4254	403	42	t	t	PROPN
ejpam-4254	403	43	)	)	PUNCT
ejpam-4254	403	44	is	be	AUX
ejpam-4254	403	45	a	a	DET
ejpam-4254	403	46	upi	upi	NOUN
ejpam-4254	403	47	of	of	ADP
ejpam-4254	403	48	u	u	PROPN
ejpam-4254	404	1	and	and	CCONJ
ejpam-4254	404	2	so	so	ADV
ejpam-4254	404	3	a	a	DET
ejpam-4254	404	4	⋆	⋆	NOUN
ejpam-4254	404	5	c	c	NOUN
ejpam-4254	404	6	∈	∈	PROPN
ejpam-4254	404	7	u(µp	u(µp	PROPN
ejpam-4254	404	8	,	,	PUNCT
ejpam-4254	404	9	t	t	PROPN
ejpam-4254	404	10	)	)	PUNCT
ejpam-4254	404	11	.	.	PUNCT
ejpam-4254	405	1	thus	thus	ADV
ejpam-4254	405	2	µp(a	µp(a	PUNCT
ejpam-4254	405	3	⋆	⋆	ADP
ejpam-4254	405	4	c	c	NOUN
ejpam-4254	405	5	)	)	PUNCT
ejpam-4254	405	6	≥	≥	NOUN
ejpam-4254	405	7	t	t	NOUN
ejpam-4254	405	8	=	=	SYM
ejpam-4254	405	9	min{µp(a	min{µp(a	NOUN
ejpam-4254	405	10	⋆	⋆	X
ejpam-4254	405	11	(	(	PUNCT
ejpam-4254	405	12	b	b	NOUN
ejpam-4254	405	13	⋆	⋆	ADJ
ejpam-4254	405	14	c	c	NOUN
ejpam-4254	405	15	)	)	PUNCT
ejpam-4254	405	16	)	)	PUNCT
ejpam-4254	405	17	,	,	PUNCT
ejpam-4254	405	18	µp(b	µp(b	ADJ
ejpam-4254	405	19	)	)	PUNCT
ejpam-4254	405	20	}	}	PUNCT
ejpam-4254	405	21	.	.	PUNCT
ejpam-4254	406	1	choose	choose	VERB
ejpam-4254	406	2	t	t	NOUN
ejpam-4254	406	3	=	=	SYM
ejpam-4254	406	4	νp(a	νp(a	X
ejpam-4254	406	5	)	)	PUNCT
ejpam-4254	406	6	∈	∈	NOUN
ejpam-4254	407	1	[	[	X
ejpam-4254	407	2	0	0	NUM
ejpam-4254	407	3	,	,	PUNCT
ejpam-4254	407	4	1	1	NUM
ejpam-4254	407	5	]	]	PUNCT
ejpam-4254	407	6	.	.	PUNCT
ejpam-4254	408	1	the	the	DET
ejpam-4254	408	2	νp(a	νp(a	NUM
ejpam-4254	408	3	)	)	PUNCT
ejpam-4254	408	4	≤	≤	NOUN
ejpam-4254	408	5	t.	t.	NOUN
ejpam-4254	408	6	thus	thus	ADV
ejpam-4254	408	7	a	a	DET
ejpam-4254	408	8	∈	∈	PROPN
ejpam-4254	408	9	l(νp	l(νp	PROPN
ejpam-4254	408	10	,	,	PUNCT
ejpam-4254	408	11	t	t	PROPN
ejpam-4254	408	12	)	)	PUNCT
ejpam-4254	408	13	̸=	̸=	PROPN
ejpam-4254	408	14	∅.	∅.	ADV
ejpam-4254	408	15	as	as	ADP
ejpam-4254	408	16	a	a	DET
ejpam-4254	408	17	hypothesis	hypothesis	NOUN
ejpam-4254	408	18	,	,	PUNCT
ejpam-4254	408	19	we	we	PRON
ejpam-4254	408	20	get	get	VERB
ejpam-4254	408	21	l(νp	l(νp	PROPN
ejpam-4254	408	22	,	,	PUNCT
ejpam-4254	408	23	t	t	PROPN
ejpam-4254	408	24	)	)	PUNCT
ejpam-4254	408	25	is	be	AUX
ejpam-4254	408	26	a	a	DET
ejpam-4254	408	27	upi	upi	NOUN
ejpam-4254	408	28	of	of	ADP
ejpam-4254	408	29	u	u	NOUN
ejpam-4254	408	30	and	and	CCONJ
ejpam-4254	408	31	so	so	ADV
ejpam-4254	408	32	0	0	NUM
ejpam-4254	408	33	∈	∈	PROPN
ejpam-4254	408	34	u(νp	u(νp	PROPN
ejpam-4254	408	35	,	,	PUNCT
ejpam-4254	408	36	t	t	PROPN
ejpam-4254	408	37	)	)	PUNCT
ejpam-4254	408	38	.	.	PUNCT
ejpam-4254	409	1	thus	thus	ADV
ejpam-4254	409	2	νp(0	νp(0	NOUN
ejpam-4254	409	3	)	)	PUNCT
ejpam-4254	409	4	≤	≤	NOUN
ejpam-4254	409	5	t	t	NOUN
ejpam-4254	409	6	=	=	PUNCT
ejpam-4254	409	7	νp(a	νp(a	NUM
ejpam-4254	409	8	)	)	PUNCT
ejpam-4254	409	9	.	.	PUNCT
ejpam-4254	410	1	choose	choose	VERB
ejpam-4254	410	2	t	t	PROPN
ejpam-4254	410	3	=	=	SYM
ejpam-4254	410	4	max{νp(a	max{νp(a	NOUN
ejpam-4254	410	5	⋆	⋆	X
ejpam-4254	410	6	(	(	PUNCT
ejpam-4254	410	7	b	b	NOUN
ejpam-4254	410	8	⋆	⋆	ADJ
ejpam-4254	410	9	c	c	NOUN
ejpam-4254	410	10	)	)	PUNCT
ejpam-4254	410	11	)	)	PUNCT
ejpam-4254	410	12	,	,	PUNCT
ejpam-4254	410	13	νp(b	νp(b	NOUN
ejpam-4254	410	14	)	)	PUNCT
ejpam-4254	410	15	}	}	PUNCT
ejpam-4254	410	16	∈	∈	PROPN
ejpam-4254	411	1	[	[	X
ejpam-4254	411	2	0	0	NUM
ejpam-4254	411	3	,	,	PUNCT
ejpam-4254	411	4	1	1	NUM
ejpam-4254	411	5	]	]	PUNCT
ejpam-4254	411	6	.	.	PUNCT
ejpam-4254	412	1	then	then	ADV
ejpam-4254	412	2	νp(a	νp(a	NUM
ejpam-4254	412	3	⋆	⋆	X
ejpam-4254	412	4	(	(	PUNCT
ejpam-4254	412	5	b	b	NOUN
ejpam-4254	412	6	⋆	⋆	ADJ
ejpam-4254	412	7	c	c	NOUN
ejpam-4254	412	8	)	)	PUNCT
ejpam-4254	412	9	)	)	PUNCT
ejpam-4254	412	10	≤	≤	PROPN
ejpam-4254	412	11	t	t	NOUN
ejpam-4254	412	12	and	and	CCONJ
ejpam-4254	412	13	νp(b	νp(b	NOUN
ejpam-4254	412	14	)	)	PUNCT
ejpam-4254	412	15	≤	≤	NOUN
ejpam-4254	413	1	t.	t.	NOUN
ejpam-4254	413	2	thus	thus	ADV
ejpam-4254	413	3	a	a	DET
ejpam-4254	413	4	⋆	⋆	X
ejpam-4254	413	5	(	(	PUNCT
ejpam-4254	413	6	b	b	NOUN
ejpam-4254	413	7	⋆	⋆	NOUN
ejpam-4254	413	8	c	c	NOUN
ejpam-4254	413	9	)	)	PUNCT
ejpam-4254	413	10	,	,	PUNCT
ejpam-4254	413	11	b	b	X
ejpam-4254	413	12	∈	∈	PROPN
ejpam-4254	413	13	l(µp	l(µp	NOUN
ejpam-4254	413	14	,	,	PUNCT
ejpam-4254	413	15	t	t	PROPN
ejpam-4254	413	16	)	)	PUNCT
ejpam-4254	413	17	̸=	̸=	PROPN
ejpam-4254	413	18	∅.	∅.	ADV
ejpam-4254	413	19	as	as	ADP
ejpam-4254	413	20	a	a	DET
ejpam-4254	413	21	hypothesis	hypothesis	NOUN
ejpam-4254	413	22	,	,	PUNCT
ejpam-4254	413	23	we	we	PRON
ejpam-4254	413	24	get	get	VERB
ejpam-4254	413	25	l(µp	l(µp	NOUN
ejpam-4254	413	26	,	,	PUNCT
ejpam-4254	413	27	t	t	PROPN
ejpam-4254	413	28	)	)	PUNCT
ejpam-4254	413	29	is	be	AUX
ejpam-4254	413	30	a	a	DET
ejpam-4254	413	31	upi	upi	NOUN
ejpam-4254	413	32	of	of	ADP
ejpam-4254	413	33	u	u	PROPN
ejpam-4254	413	34	and	and	CCONJ
ejpam-4254	413	35	so	so	ADV
ejpam-4254	413	36	a	a	DET
ejpam-4254	413	37	⋆	⋆	NOUN
ejpam-4254	413	38	c	c	NOUN
ejpam-4254	413	39	∈	∈	PROPN
ejpam-4254	413	40	l(µp	l(µp	PROPN
ejpam-4254	413	41	,	,	PUNCT
ejpam-4254	413	42	t	t	PROPN
ejpam-4254	413	43	)	)	PUNCT
ejpam-4254	413	44	.	.	PUNCT
ejpam-4254	414	1	thus	thus	ADV
ejpam-4254	414	2	νp(a	νp(a	NUM
ejpam-4254	414	3	⋆	⋆	ADP
ejpam-4254	414	4	c	c	NOUN
ejpam-4254	414	5	)	)	PUNCT
ejpam-4254	414	6	≤	≤	NOUN
ejpam-4254	414	7	t	t	NOUN
ejpam-4254	414	8	=	=	SYM
ejpam-4254	414	9	max{νp(a	max{νp(a	NOUN
ejpam-4254	414	10	⋆	⋆	X
ejpam-4254	414	11	(	(	PUNCT
ejpam-4254	414	12	b	b	NOUN
ejpam-4254	414	13	⋆	⋆	ADJ
ejpam-4254	414	14	c	c	NOUN
ejpam-4254	414	15	)	)	PUNCT
ejpam-4254	414	16	)	)	PUNCT
ejpam-4254	414	17	,	,	PUNCT
ejpam-4254	414	18	νp(b	νp(b	NOUN
ejpam-4254	414	19	)	)	PUNCT
ejpam-4254	414	20	}	}	PUNCT
ejpam-4254	414	21	.	.	PUNCT
ejpam-4254	415	1	hence	hence	ADV
ejpam-4254	415	2	,	,	PUNCT
ejpam-4254	415	3	p	p	PROPN
ejpam-4254	415	4	is	be	AUX
ejpam-4254	415	5	a	a	DET
ejpam-4254	415	6	pfupi	pfupi	NOUN
ejpam-4254	415	7	of	of	ADP
ejpam-4254	415	8	u	u	PROPN
ejpam-4254	415	9	.	.	PUNCT
ejpam-4254	416	1	theorem	theorem	VERB
ejpam-4254	416	2	9	9	NUM
ejpam-4254	416	3	.	.	PUNCT
ejpam-4254	417	1	p	p	NOUN
ejpam-4254	417	2	is	be	AUX
ejpam-4254	417	3	a	a	DET
ejpam-4254	417	4	pfupi	pfupi	NOUN
ejpam-4254	417	5	of	of	ADP
ejpam-4254	417	6	u	u	PRON
ejpam-4254	417	7	if	if	SCONJ
ejpam-4254	417	8	and	and	CCONJ
ejpam-4254	417	9	only	only	ADV
ejpam-4254	417	10	if	if	SCONJ
ejpam-4254	417	11	u+(µp	u+(µp	NOUN
ejpam-4254	417	12	,	,	PUNCT
ejpam-4254	417	13	t	t	PROPN
ejpam-4254	417	14	)	)	PUNCT
ejpam-4254	417	15	and	and	CCONJ
ejpam-4254	417	16	l−(νp	l−(νp	PROPN
ejpam-4254	417	17	,	,	PUNCT
ejpam-4254	417	18	t	t	PROPN
ejpam-4254	417	19	)	)	PUNCT
ejpam-4254	417	20	are	be	AUX
ejpam-4254	417	21	,	,	PUNCT
ejpam-4254	417	22	if	if	SCONJ
ejpam-4254	417	23	the	the	DET
ejpam-4254	417	24	sets	set	NOUN
ejpam-4254	417	25	are	be	AUX
ejpam-4254	417	26	nonempty	nonempty	ADJ
ejpam-4254	417	27	,	,	PUNCT
ejpam-4254	417	28	upis	upis	ADJ
ejpam-4254	417	29	of	of	ADP
ejpam-4254	417	30	u	u	NOUN
ejpam-4254	417	31	for	for	ADP
ejpam-4254	417	32	every	every	DET
ejpam-4254	417	33	t	t	NOUN
ejpam-4254	417	34	∈	∈	PROPN
ejpam-4254	418	1	[	[	X
ejpam-4254	418	2	0	0	NUM
ejpam-4254	418	3	,	,	PUNCT
ejpam-4254	418	4	1	1	NUM
ejpam-4254	418	5	]	]	PUNCT
ejpam-4254	418	6	.	.	PUNCT
ejpam-4254	419	1	proof	proof	NOUN
ejpam-4254	419	2	.	.	PUNCT
ejpam-4254	420	1	assume	assume	VERB
ejpam-4254	420	2	p	p	X
ejpam-4254	420	3	=	=	X
ejpam-4254	420	4	(	(	PUNCT
ejpam-4254	420	5	µp	µp	PROPN
ejpam-4254	420	6	,	,	PUNCT
ejpam-4254	420	7	νp	νp	NOUN
ejpam-4254	420	8	)	)	PUNCT
ejpam-4254	420	9	is	be	AUX
ejpam-4254	420	10	a	a	DET
ejpam-4254	420	11	pfupi	pfupi	NOUN
ejpam-4254	420	12	of	of	ADP
ejpam-4254	420	13	u	u	PROPN
ejpam-4254	420	14	.	.	PUNCT
ejpam-4254	421	1	let	let	VERB
ejpam-4254	421	2	t	t	X
ejpam-4254	421	3	∈	∈	PROPN
ejpam-4254	422	1	[	[	X
ejpam-4254	422	2	0	0	NUM
ejpam-4254	422	3	,	,	PUNCT
ejpam-4254	422	4	1	1	NUM
ejpam-4254	422	5	]	]	PUNCT
ejpam-4254	422	6	be	be	AUX
ejpam-4254	422	7	such	such	ADJ
ejpam-4254	422	8	that	that	SCONJ
ejpam-4254	422	9	u+(µp	u+(µp	NOUN
ejpam-4254	422	10	,	,	PUNCT
ejpam-4254	422	11	t	t	PROPN
ejpam-4254	422	12	)	)	PUNCT
ejpam-4254	422	13	,	,	PUNCT
ejpam-4254	422	14	l−(νp	l−(νp	PROPN
ejpam-4254	422	15	,	,	PUNCT
ejpam-4254	422	16	t	t	PROPN
ejpam-4254	422	17	)	)	PUNCT
ejpam-4254	422	18	̸=	̸=	PROPN
ejpam-4254	422	19	∅.	∅.	ADV
ejpam-4254	422	20	let	let	VERB
ejpam-4254	422	21	a	a	DET
ejpam-4254	422	22	,	,	PUNCT
ejpam-4254	422	23	b	b	NOUN
ejpam-4254	422	24	,	,	PUNCT
ejpam-4254	422	25	c	c	PROPN
ejpam-4254	422	26	∈	∈	PROPN
ejpam-4254	422	27	u	u	PROPN
ejpam-4254	422	28	.	.	PUNCT
ejpam-4254	423	1	then	then	ADV
ejpam-4254	423	2	a	a	DET
ejpam-4254	423	3	∈	∈	PROPN
ejpam-4254	423	4	u+(µp	u+(µp	PROPN
ejpam-4254	423	5	,	,	PUNCT
ejpam-4254	423	6	t	t	PROPN
ejpam-4254	423	7	)	)	PUNCT
ejpam-4254	423	8	⇒	⇒	NOUN
ejpam-4254	423	9	µp(a	µp(a	NUM
ejpam-4254	423	10	)	)	PUNCT
ejpam-4254	423	11	>	>	X
ejpam-4254	423	12	t	t	PROPN
ejpam-4254	423	13	⇒	⇒	PROPN
ejpam-4254	423	14	µp(0	µp(0	PROPN
ejpam-4254	423	15	)	)	PUNCT
ejpam-4254	423	16	≥	≥	NOUN
ejpam-4254	423	17	µp(a	µp(a	NUM
ejpam-4254	423	18	)	)	PUNCT
ejpam-4254	423	19	>	>	X
ejpam-4254	423	20	t	t	PROPN
ejpam-4254	423	21	(	(	PUNCT
ejpam-4254	423	22	(	(	PUNCT
ejpam-4254	423	23	1.25	1.25	NUM
ejpam-4254	423	24	)	)	PUNCT
ejpam-4254	423	25	)	)	PUNCT
ejpam-4254	423	26	⇒	⇒	VERB
ejpam-4254	423	27	0	0	NUM
ejpam-4254	423	28	∈	∈	PROPN
ejpam-4254	423	29	u+(µp	u+(µp	PROPN
ejpam-4254	423	30	,	,	PUNCT
ejpam-4254	423	31	t	t	PROPN
ejpam-4254	423	32	)	)	PUNCT
ejpam-4254	423	33	,	,	PUNCT
ejpam-4254	423	34	a	a	DET
ejpam-4254	423	35	⋆	⋆	X
ejpam-4254	423	36	(	(	PUNCT
ejpam-4254	423	37	b	b	NOUN
ejpam-4254	423	38	⋆	⋆	NOUN
ejpam-4254	423	39	c	c	NOUN
ejpam-4254	423	40	)	)	PUNCT
ejpam-4254	423	41	,	,	PUNCT
ejpam-4254	423	42	b	b	X
ejpam-4254	423	43	∈	∈	PROPN
ejpam-4254	423	44	u+(µp	u+(µp	PROPN
ejpam-4254	423	45	,	,	PUNCT
ejpam-4254	423	46	t	t	PROPN
ejpam-4254	423	47	)	)	PUNCT
ejpam-4254	423	48	⇒	⇒	NOUN
ejpam-4254	423	49	µp(a	µp(a	PUNCT
ejpam-4254	423	50	⋆	⋆	X
ejpam-4254	423	51	(	(	PUNCT
ejpam-4254	423	52	b	b	NOUN
ejpam-4254	423	53	⋆	⋆	ADJ
ejpam-4254	423	54	c	c	NOUN
ejpam-4254	423	55	)	)	PUNCT
ejpam-4254	423	56	)	)	PUNCT
ejpam-4254	424	1	>	>	X
ejpam-4254	424	2	t	t	PROPN
ejpam-4254	424	3	,	,	PUNCT
ejpam-4254	424	4	µp(b	µp(b	ADJ
ejpam-4254	424	5	)	)	PUNCT
ejpam-4254	424	6	>	>	X
ejpam-4254	424	7	t	t	PROPN
ejpam-4254	424	8	⇒	⇒	NOUN
ejpam-4254	425	1	min{µp(a	min{µp(a	NOUN
ejpam-4254	425	2	⋆	⋆	X
ejpam-4254	425	3	(	(	PUNCT
ejpam-4254	425	4	b	b	X
ejpam-4254	425	5	⋆	⋆	ADJ
ejpam-4254	425	6	c	c	NOUN
ejpam-4254	425	7	)	)	PUNCT
ejpam-4254	425	8	)	)	PUNCT
ejpam-4254	425	9	,	,	PUNCT
ejpam-4254	425	10	µp(b	µp(b	ADJ
ejpam-4254	425	11	)	)	PUNCT
ejpam-4254	425	12	}	}	PUNCT
ejpam-4254	425	13	>	>	PUNCT
ejpam-4254	425	14	t	t	PROPN
ejpam-4254	425	15	⇒	⇒	NOUN
ejpam-4254	425	16	µp(a	µp(a	PUNCT
ejpam-4254	425	17	⋆	⋆	ADP
ejpam-4254	425	18	c	c	NOUN
ejpam-4254	425	19	)	)	PUNCT
ejpam-4254	425	20	≥	≥	NOUN
ejpam-4254	425	21	min{µp(a	min{µp(a	NOUN
ejpam-4254	425	22	⋆	⋆	X
ejpam-4254	425	23	(	(	PUNCT
ejpam-4254	425	24	b	b	X
ejpam-4254	425	25	⋆	⋆	ADJ
ejpam-4254	425	26	c	c	NOUN
ejpam-4254	425	27	)	)	PUNCT
ejpam-4254	425	28	)	)	PUNCT
ejpam-4254	425	29	,	,	PUNCT
ejpam-4254	425	30	µp(b	µp(b	ADJ
ejpam-4254	425	31	)	)	PUNCT
ejpam-4254	425	32	}	}	PUNCT
ejpam-4254	425	33	>	>	X
ejpam-4254	425	34	t	t	PROPN
ejpam-4254	425	35	(	(	PUNCT
ejpam-4254	425	36	(	(	PUNCT
ejpam-4254	425	37	1.29	1.29	NUM
ejpam-4254	425	38	)	)	PUNCT
ejpam-4254	425	39	)	)	PUNCT
ejpam-4254	425	40	⇒	⇒	VERB
ejpam-4254	425	41	a	a	DET
ejpam-4254	425	42	⋆	⋆	NOUN
ejpam-4254	425	43	c	c	PROPN
ejpam-4254	425	44	∈	∈	PROPN
ejpam-4254	425	45	u+(µp	u+(µp	PROPN
ejpam-4254	425	46	,	,	PUNCT
ejpam-4254	425	47	t	t	PROPN
ejpam-4254	425	48	)	)	PUNCT
ejpam-4254	425	49	,	,	PUNCT
ejpam-4254	425	50	a	a	DET
ejpam-4254	425	51	∈	∈	PROPN
ejpam-4254	425	52	l−(νp	l−(νp	PROPN
ejpam-4254	425	53	,	,	PUNCT
ejpam-4254	425	54	t	t	PROPN
ejpam-4254	425	55	)	)	PUNCT
ejpam-4254	425	56	⇒	⇒	NOUN
ejpam-4254	425	57	νp(a	νp(a	NUM
ejpam-4254	425	58	)	)	PUNCT
ejpam-4254	425	59	<	<	X
ejpam-4254	425	60	t	t	PROPN
ejpam-4254	425	61	⇒	⇒	PROPN
ejpam-4254	425	62	νp(0	νp(0	PROPN
ejpam-4254	425	63	)	)	PUNCT
ejpam-4254	425	64	≤	≤	NOUN
ejpam-4254	425	65	νp(a	νp(a	NUM
ejpam-4254	425	66	)	)	PUNCT
ejpam-4254	425	67	<	<	X
ejpam-4254	425	68	t	t	X
ejpam-4254	425	69	(	(	PUNCT
ejpam-4254	425	70	(	(	PUNCT
ejpam-4254	425	71	1.26	1.26	NUM
ejpam-4254	425	72	)	)	PUNCT
ejpam-4254	425	73	)	)	PUNCT
ejpam-4254	425	74	⇒	⇒	VERB
ejpam-4254	425	75	0	0	NUM
ejpam-4254	426	1	∈	∈	PROPN
ejpam-4254	426	2	l−(νp	l−(νp	PROPN
ejpam-4254	426	3	,	,	PUNCT
ejpam-4254	426	4	t	t	PROPN
ejpam-4254	426	5	)	)	PUNCT
ejpam-4254	426	6	,	,	PUNCT
ejpam-4254	426	7	and	and	CCONJ
ejpam-4254	426	8	a	a	DET
ejpam-4254	426	9	⋆	⋆	X
ejpam-4254	426	10	(	(	PUNCT
ejpam-4254	426	11	b	b	NOUN
ejpam-4254	426	12	⋆	⋆	NOUN
ejpam-4254	426	13	c	c	NOUN
ejpam-4254	426	14	)	)	PUNCT
ejpam-4254	426	15	,	,	PUNCT
ejpam-4254	426	16	b	b	X
ejpam-4254	426	17	∈	∈	PROPN
ejpam-4254	426	18	l−(νp	l−(νp	PROPN
ejpam-4254	426	19	,	,	PUNCT
ejpam-4254	426	20	t	t	PROPN
ejpam-4254	426	21	)	)	PUNCT
ejpam-4254	426	22	⇒	⇒	NOUN
ejpam-4254	426	23	νp(a	νp(a	ADV
ejpam-4254	426	24	⋆	⋆	X
ejpam-4254	426	25	(	(	PUNCT
ejpam-4254	426	26	b	b	NOUN
ejpam-4254	426	27	⋆	⋆	ADJ
ejpam-4254	426	28	c	c	NOUN
ejpam-4254	426	29	)	)	PUNCT
ejpam-4254	426	30	)	)	PUNCT
ejpam-4254	426	31	<	<	X
ejpam-4254	426	32	t	t	PROPN
ejpam-4254	426	33	,	,	PUNCT
ejpam-4254	426	34	νp(b	νp(b	NOUN
ejpam-4254	426	35	)	)	PUNCT
ejpam-4254	426	36	<	<	X
ejpam-4254	426	37	t	t	X
ejpam-4254	426	38	⇒	⇒	X
ejpam-4254	426	39	max{νp(a	max{νp(a	ADJ
ejpam-4254	426	40	⋆	⋆	X
ejpam-4254	426	41	(	(	PUNCT
ejpam-4254	426	42	b	b	NOUN
ejpam-4254	426	43	⋆	⋆	ADJ
ejpam-4254	426	44	c	c	NOUN
ejpam-4254	426	45	)	)	PUNCT
ejpam-4254	426	46	)	)	PUNCT
ejpam-4254	426	47	,	,	PUNCT
ejpam-4254	426	48	νp(b	νp(b	NOUN
ejpam-4254	426	49	)	)	PUNCT
ejpam-4254	426	50	}	}	PUNCT
ejpam-4254	426	51	<	<	X
ejpam-4254	426	52	t	t	PROPN
ejpam-4254	426	53	⇒	⇒	NOUN
ejpam-4254	426	54	νp(a	νp(a	ADV
ejpam-4254	426	55	⋆	⋆	VERB
ejpam-4254	426	56	c	c	NOUN
ejpam-4254	426	57	)	)	PUNCT
ejpam-4254	426	58	≤	≤	NOUN
ejpam-4254	426	59	max{νp(a	max{νp(a	NOUN
ejpam-4254	426	60	⋆	⋆	X
ejpam-4254	426	61	(	(	PUNCT
ejpam-4254	426	62	b	b	NOUN
ejpam-4254	426	63	⋆	⋆	ADJ
ejpam-4254	426	64	c	c	NOUN
ejpam-4254	426	65	)	)	PUNCT
ejpam-4254	426	66	)	)	PUNCT
ejpam-4254	426	67	,	,	PUNCT
ejpam-4254	426	68	νp(b	νp(b	NOUN
ejpam-4254	426	69	)	)	PUNCT
ejpam-4254	426	70	}	}	PUNCT
ejpam-4254	426	71	<	<	X
ejpam-4254	426	72	t	t	X
ejpam-4254	426	73	(	(	PUNCT
ejpam-4254	426	74	(	(	PUNCT
ejpam-4254	426	75	1.30	1.30	NUM
ejpam-4254	426	76	)	)	PUNCT
ejpam-4254	426	77	)	)	PUNCT
ejpam-4254	426	78	⇒	⇒	VERB
ejpam-4254	426	79	a	a	DET
ejpam-4254	426	80	⋆	⋆	NOUN
ejpam-4254	426	81	c	c	NOUN
ejpam-4254	426	82	∈	∈	PROPN
ejpam-4254	426	83	l−(νp	l−(νp	PROPN
ejpam-4254	426	84	,	,	PUNCT
ejpam-4254	426	85	t	t	PROPN
ejpam-4254	426	86	)	)	PUNCT
ejpam-4254	426	87	.	.	PUNCT
ejpam-4254	427	1	a.	a.	PROPN
ejpam-4254	427	2	iampan	iampan	PROPN
ejpam-4254	427	3	et	et	PROPN
ejpam-4254	427	4	al	al	PROPN
ejpam-4254	427	5	.	.	PUNCT
ejpam-4254	427	6	/	/	SYM
ejpam-4254	427	7	eur	eur	PROPN
ejpam-4254	427	8	.	.	PUNCT
ejpam-4254	428	1	j.	j.	PROPN
ejpam-4254	428	2	pure	pure	PROPN
ejpam-4254	428	3	appl	appl	PROPN
ejpam-4254	428	4	.	.	PROPN
ejpam-4254	428	5	math	math	PROPN
ejpam-4254	428	6	,	,	PUNCT
ejpam-4254	428	7	15	15	NUM
ejpam-4254	428	8	(	(	PUNCT
ejpam-4254	428	9	1	1	NUM
ejpam-4254	428	10	)	)	PUNCT
ejpam-4254	428	11	(	(	PUNCT
ejpam-4254	428	12	2022	2022	NUM
ejpam-4254	428	13	)	)	PUNCT
ejpam-4254	428	14	,	,	PUNCT
ejpam-4254	428	15	169	169	NUM
ejpam-4254	428	16	-	-	SYM
ejpam-4254	428	17	198	198	NUM
ejpam-4254	428	18	188	188	NUM
ejpam-4254	428	19	hence	hence	ADV
ejpam-4254	428	20	,	,	PUNCT
ejpam-4254	428	21	u+(µp	u+(µp	PROPN
ejpam-4254	428	22	,	,	PUNCT
ejpam-4254	428	23	t	t	PROPN
ejpam-4254	428	24	)	)	PUNCT
ejpam-4254	428	25	and	and	CCONJ
ejpam-4254	428	26	l−(νp	l−(νp	PROPN
ejpam-4254	428	27	,	,	PUNCT
ejpam-4254	428	28	t	t	PROPN
ejpam-4254	428	29	)	)	PUNCT
ejpam-4254	428	30	are	be	AUX
ejpam-4254	428	31	upis	upis	ADJ
ejpam-4254	428	32	of	of	ADP
ejpam-4254	428	33	u	u	PROPN
ejpam-4254	428	34	.	.	PUNCT
ejpam-4254	429	1	conversely	conversely	ADV
ejpam-4254	429	2	,	,	PUNCT
ejpam-4254	429	3	assume	assume	VERB
ejpam-4254	429	4	for	for	ADP
ejpam-4254	429	5	all	all	DET
ejpam-4254	429	6	t	t	NOUN
ejpam-4254	429	7	∈	∈	PROPN
ejpam-4254	430	1	[	[	X
ejpam-4254	430	2	0	0	NUM
ejpam-4254	430	3	,	,	PUNCT
ejpam-4254	430	4	1	1	NUM
ejpam-4254	430	5	]	]	PUNCT
ejpam-4254	430	6	,	,	PUNCT
ejpam-4254	430	7	u+(µp	u+(µp	PROPN
ejpam-4254	430	8	,	,	PUNCT
ejpam-4254	430	9	t	t	PROPN
ejpam-4254	430	10	)	)	PUNCT
ejpam-4254	430	11	and	and	CCONJ
ejpam-4254	430	12	l−(νp	l−(νp	PROPN
ejpam-4254	430	13	,	,	PUNCT
ejpam-4254	430	14	t	t	PROPN
ejpam-4254	430	15	)	)	PUNCT
ejpam-4254	430	16	are	be	AUX
ejpam-4254	430	17	upis	upis	ADJ
ejpam-4254	430	18	of	of	ADP
ejpam-4254	430	19	u	u	PRON
ejpam-4254	430	20	if	if	SCONJ
ejpam-4254	430	21	the	the	DET
ejpam-4254	430	22	sets	set	NOUN
ejpam-4254	430	23	are	be	AUX
ejpam-4254	430	24	nonempty	nonempty	ADJ
ejpam-4254	430	25	.	.	PUNCT
ejpam-4254	431	1	suppose	suppose	VERB
ejpam-4254	431	2	there	there	PRON
ejpam-4254	431	3	exists	exist	VERB
ejpam-4254	431	4	a	a	DET
ejpam-4254	431	5	∈	∈	PROPN
ejpam-4254	431	6	u	u	NOUN
ejpam-4254	431	7	such	such	ADJ
ejpam-4254	431	8	that	that	DET
ejpam-4254	431	9	µp(0	µp(0	NOUN
ejpam-4254	431	10	)	)	PUNCT
ejpam-4254	431	11	<	<	X
ejpam-4254	431	12	µp(a	µp(a	NUM
ejpam-4254	431	13	)	)	PUNCT
ejpam-4254	431	14	.	.	PUNCT
ejpam-4254	432	1	choose	choose	VERB
ejpam-4254	432	2	t	t	PROPN
ejpam-4254	432	3	=	=	SYM
ejpam-4254	432	4	µp(0	µp(0	NOUN
ejpam-4254	432	5	)	)	PUNCT
ejpam-4254	432	6	∈	∈	NOUN
ejpam-4254	433	1	[	[	X
ejpam-4254	433	2	0	0	NUM
ejpam-4254	433	3	,	,	PUNCT
ejpam-4254	433	4	1	1	NUM
ejpam-4254	433	5	]	]	PUNCT
ejpam-4254	433	6	.	.	PUNCT
ejpam-4254	434	1	then	then	ADV
ejpam-4254	434	2	µp(a	µp(a	NUM
ejpam-4254	434	3	)	)	PUNCT
ejpam-4254	434	4	>	>	PUNCT
ejpam-4254	435	1	t.	t.	NOUN
ejpam-4254	435	2	thus	thus	ADV
ejpam-4254	435	3	a	a	DET
ejpam-4254	435	4	∈	∈	NOUN
ejpam-4254	435	5	u+(µp	u+(µp	NOUN
ejpam-4254	435	6	,	,	PUNCT
ejpam-4254	435	7	t	t	PROPN
ejpam-4254	435	8	)	)	PUNCT
ejpam-4254	435	9	̸=	̸=	PROPN
ejpam-4254	435	10	∅.	∅.	ADV
ejpam-4254	435	11	as	as	ADP
ejpam-4254	435	12	a	a	DET
ejpam-4254	435	13	hypothesis	hypothesis	NOUN
ejpam-4254	435	14	,	,	PUNCT
ejpam-4254	435	15	we	we	PRON
ejpam-4254	435	16	get	get	VERB
ejpam-4254	435	17	u+(µp	u+(µp	NOUN
ejpam-4254	435	18	,	,	PUNCT
ejpam-4254	435	19	t	t	PROPN
ejpam-4254	435	20	)	)	PUNCT
ejpam-4254	435	21	is	be	AUX
ejpam-4254	435	22	a	a	DET
ejpam-4254	435	23	upi	upi	NOUN
ejpam-4254	435	24	of	of	ADP
ejpam-4254	435	25	u	u	NOUN
ejpam-4254	435	26	and	and	CCONJ
ejpam-4254	435	27	so	so	ADV
ejpam-4254	435	28	0	0	NUM
ejpam-4254	435	29	∈	∈	PROPN
ejpam-4254	435	30	u+(µp	u+(µp	PROPN
ejpam-4254	435	31	,	,	PUNCT
ejpam-4254	435	32	t	t	PROPN
ejpam-4254	435	33	)	)	PUNCT
ejpam-4254	435	34	.	.	PUNCT
ejpam-4254	436	1	thus	thus	ADV
ejpam-4254	436	2	µp(0	µp(0	VERB
ejpam-4254	436	3	)	)	PUNCT
ejpam-4254	436	4	>	>	X
ejpam-4254	436	5	t	t	NOUN
ejpam-4254	436	6	=	=	SYM
ejpam-4254	436	7	µp(0	µp(0	NOUN
ejpam-4254	436	8	)	)	PUNCT
ejpam-4254	436	9	,	,	PUNCT
ejpam-4254	436	10	a	a	DET
ejpam-4254	436	11	contradiction	contradiction	NOUN
ejpam-4254	436	12	.	.	PUNCT
ejpam-4254	437	1	hence	hence	ADV
ejpam-4254	437	2	,	,	PUNCT
ejpam-4254	437	3	µp(0	µp(0	NOUN
ejpam-4254	437	4	)	)	PUNCT
ejpam-4254	437	5	≥	≥	NOUN
ejpam-4254	437	6	µp(a	µp(a	NUM
ejpam-4254	437	7	)	)	PUNCT
ejpam-4254	437	8	for	for	ADP
ejpam-4254	437	9	all	all	DET
ejpam-4254	437	10	a	a	DET
ejpam-4254	437	11	∈	∈	PROPN
ejpam-4254	437	12	u	u	NOUN
ejpam-4254	437	13	.	.	PUNCT
ejpam-4254	437	14	suppose	suppose	VERB
ejpam-4254	437	15	there	there	PRON
ejpam-4254	437	16	exist	exist	VERB
ejpam-4254	437	17	a	a	DET
ejpam-4254	437	18	,	,	PUNCT
ejpam-4254	437	19	b	b	NOUN
ejpam-4254	437	20	,	,	PUNCT
ejpam-4254	437	21	c	c	PROPN
ejpam-4254	437	22	∈	∈	PROPN
ejpam-4254	437	23	u	u	NOUN
ejpam-4254	437	24	such	such	ADJ
ejpam-4254	437	25	that	that	DET
ejpam-4254	437	26	µp(a⋆c	µp(a⋆c	NUM
ejpam-4254	437	27	)	)	PUNCT
ejpam-4254	437	28	<	<	X
ejpam-4254	437	29	min{µp(a⋆(b⋆c	min{µp(a⋆(b⋆c	PROPN
ejpam-4254	437	30	)	)	PUNCT
ejpam-4254	437	31	)	)	PUNCT
ejpam-4254	437	32	,	,	PUNCT
ejpam-4254	437	33	µp(b	µp(b	ADJ
ejpam-4254	437	34	)	)	PUNCT
ejpam-4254	437	35	}	}	PUNCT
ejpam-4254	437	36	.	.	PUNCT
ejpam-4254	438	1	choose	choose	VERB
ejpam-4254	438	2	t	t	NOUN
ejpam-4254	438	3	=	=	PUNCT
ejpam-4254	438	4	µp(a	µp(a	PUNCT
ejpam-4254	438	5	⋆	⋆	PUNCT
ejpam-4254	438	6	c	c	NOUN
ejpam-4254	438	7	)	)	PUNCT
ejpam-4254	438	8	∈	∈	PROPN
ejpam-4254	439	1	[	[	X
ejpam-4254	439	2	0	0	NUM
ejpam-4254	439	3	,	,	PUNCT
ejpam-4254	439	4	1	1	NUM
ejpam-4254	439	5	]	]	PUNCT
ejpam-4254	439	6	.	.	PUNCT
ejpam-4254	440	1	then	then	ADV
ejpam-4254	440	2	µp(a	µp(a	PUNCT
ejpam-4254	440	3	⋆	⋆	X
ejpam-4254	440	4	(	(	PUNCT
ejpam-4254	440	5	b	b	NOUN
ejpam-4254	440	6	⋆	⋆	ADJ
ejpam-4254	440	7	c	c	NOUN
ejpam-4254	440	8	)	)	PUNCT
ejpam-4254	440	9	)	)	PUNCT
ejpam-4254	440	10	>	>	X
ejpam-4254	440	11	t	t	PROPN
ejpam-4254	440	12	and	and	CCONJ
ejpam-4254	440	13	µp(b	µp(b	ADP
ejpam-4254	440	14	)	)	PUNCT
ejpam-4254	440	15	>	>	PUNCT
ejpam-4254	441	1	t.	t.	NOUN
ejpam-4254	441	2	thus	thus	ADV
ejpam-4254	441	3	a	a	DET
ejpam-4254	441	4	⋆	⋆	X
ejpam-4254	441	5	(	(	PUNCT
ejpam-4254	441	6	b	b	NOUN
ejpam-4254	441	7	⋆	⋆	NOUN
ejpam-4254	441	8	c	c	NOUN
ejpam-4254	441	9	)	)	PUNCT
ejpam-4254	441	10	,	,	PUNCT
ejpam-4254	441	11	b	b	X
ejpam-4254	441	12	∈	∈	PROPN
ejpam-4254	441	13	u+(µp	u+(µp	PROPN
ejpam-4254	441	14	,	,	PUNCT
ejpam-4254	441	15	t	t	PROPN
ejpam-4254	441	16	)	)	PUNCT
ejpam-4254	441	17	̸=	̸=	PROPN
ejpam-4254	441	18	∅.	∅.	ADV
ejpam-4254	441	19	as	as	ADP
ejpam-4254	441	20	a	a	DET
ejpam-4254	441	21	hypothesis	hypothesis	NOUN
ejpam-4254	441	22	,	,	PUNCT
ejpam-4254	441	23	we	we	PRON
ejpam-4254	441	24	get	get	VERB
ejpam-4254	441	25	u+(µp	u+(µp	NOUN
ejpam-4254	441	26	,	,	PUNCT
ejpam-4254	441	27	t	t	PROPN
ejpam-4254	441	28	)	)	PUNCT
ejpam-4254	441	29	is	be	AUX
ejpam-4254	441	30	a	a	DET
ejpam-4254	441	31	upi	upi	NOUN
ejpam-4254	441	32	of	of	ADP
ejpam-4254	441	33	u	u	PROPN
ejpam-4254	441	34	and	and	CCONJ
ejpam-4254	441	35	so	so	ADV
ejpam-4254	441	36	a	a	DET
ejpam-4254	441	37	⋆	⋆	NOUN
ejpam-4254	441	38	c	c	PROPN
ejpam-4254	441	39	∈	∈	PROPN
ejpam-4254	441	40	u+(µp	u+(µp	PROPN
ejpam-4254	441	41	,	,	PUNCT
ejpam-4254	441	42	t	t	PROPN
ejpam-4254	441	43	)	)	PUNCT
ejpam-4254	441	44	.	.	PUNCT
ejpam-4254	442	1	thus	thus	ADV
ejpam-4254	442	2	µp(a⋆c	µp(a⋆c	NUM
ejpam-4254	442	3	)	)	PUNCT
ejpam-4254	442	4	>	>	X
ejpam-4254	442	5	t	t	NOUN
ejpam-4254	442	6	=	=	SYM
ejpam-4254	442	7	µp(a⋆c	µp(a⋆c	NUM
ejpam-4254	442	8	)	)	PUNCT
ejpam-4254	442	9	,	,	PUNCT
ejpam-4254	442	10	a	a	DET
ejpam-4254	442	11	contradiction	contradiction	NOUN
ejpam-4254	442	12	.	.	PUNCT
ejpam-4254	443	1	hence	hence	ADV
ejpam-4254	443	2	,	,	PUNCT
ejpam-4254	443	3	µp(a⋆c	µp(a⋆c	NUM
ejpam-4254	443	4	)	)	PUNCT
ejpam-4254	443	5	≥	≥	NOUN
ejpam-4254	443	6	min{µp(a⋆(b⋆c	min{µp(a⋆(b⋆c	PROPN
ejpam-4254	443	7	)	)	PUNCT
ejpam-4254	443	8	)	)	PUNCT
ejpam-4254	443	9	,	,	PUNCT
ejpam-4254	443	10	µp(b	µp(b	ADJ
ejpam-4254	443	11	)	)	PUNCT
ejpam-4254	443	12	}	}	PUNCT
ejpam-4254	443	13	for	for	ADP
ejpam-4254	443	14	all	all	DET
ejpam-4254	443	15	a	a	DET
ejpam-4254	443	16	,	,	PUNCT
ejpam-4254	443	17	b	b	NOUN
ejpam-4254	443	18	,	,	PUNCT
ejpam-4254	443	19	c	c	PROPN
ejpam-4254	443	20	∈	∈	PROPN
ejpam-4254	443	21	u	u	PROPN
ejpam-4254	443	22	.	.	PUNCT
ejpam-4254	443	23	suppose	suppose	VERB
ejpam-4254	443	24	there	there	PRON
ejpam-4254	443	25	exists	exist	VERB
ejpam-4254	443	26	a	a	DET
ejpam-4254	443	27	∈	∈	PROPN
ejpam-4254	443	28	u	u	NOUN
ejpam-4254	443	29	such	such	ADJ
ejpam-4254	443	30	that	that	DET
ejpam-4254	443	31	νp(0	νp(0	NOUN
ejpam-4254	443	32	)	)	PUNCT
ejpam-4254	443	33	>	>	X
ejpam-4254	443	34	νp(a	νp(a	NUM
ejpam-4254	443	35	)	)	PUNCT
ejpam-4254	443	36	.	.	PUNCT
ejpam-4254	444	1	choose	choose	VERB
ejpam-4254	444	2	t	t	PROPN
ejpam-4254	444	3	=	=	SYM
ejpam-4254	444	4	νp(0	νp(0	NOUN
ejpam-4254	444	5	)	)	PUNCT
ejpam-4254	444	6	∈	∈	PROPN
ejpam-4254	445	1	[	[	X
ejpam-4254	445	2	0	0	NUM
ejpam-4254	445	3	,	,	PUNCT
ejpam-4254	445	4	1	1	NUM
ejpam-4254	445	5	]	]	PUNCT
ejpam-4254	445	6	.	.	PUNCT
ejpam-4254	446	1	then	then	ADV
ejpam-4254	446	2	νp(a	νp(a	NUM
ejpam-4254	446	3	)	)	PUNCT
ejpam-4254	447	1	<	<	X
ejpam-4254	447	2	t.	t.	X
ejpam-4254	447	3	thus	thus	ADV
ejpam-4254	447	4	a	a	DET
ejpam-4254	447	5	∈	∈	PROPN
ejpam-4254	447	6	l−(νp	l−(νp	PROPN
ejpam-4254	447	7	,	,	PUNCT
ejpam-4254	447	8	t	t	PROPN
ejpam-4254	447	9	)	)	PUNCT
ejpam-4254	447	10	̸=	̸=	PROPN
ejpam-4254	447	11	∅.	∅.	ADV
ejpam-4254	447	12	as	as	ADP
ejpam-4254	447	13	a	a	DET
ejpam-4254	447	14	hypothesis	hypothesis	NOUN
ejpam-4254	447	15	,	,	PUNCT
ejpam-4254	447	16	we	we	PRON
ejpam-4254	447	17	get	get	VERB
ejpam-4254	447	18	l−(νp	l−(νp	PROPN
ejpam-4254	447	19	,	,	PUNCT
ejpam-4254	447	20	t	t	PROPN
ejpam-4254	447	21	)	)	PUNCT
ejpam-4254	447	22	is	be	AUX
ejpam-4254	447	23	a	a	DET
ejpam-4254	447	24	upi	upi	NOUN
ejpam-4254	447	25	of	of	ADP
ejpam-4254	447	26	u	u	NOUN
ejpam-4254	447	27	and	and	CCONJ
ejpam-4254	447	28	so	so	ADV
ejpam-4254	447	29	0	0	NUM
ejpam-4254	447	30	∈	∈	PROPN
ejpam-4254	447	31	l−(νp	l−(νp	PROPN
ejpam-4254	447	32	,	,	PUNCT
ejpam-4254	447	33	t	t	PROPN
ejpam-4254	447	34	)	)	PUNCT
ejpam-4254	447	35	.	.	PUNCT
ejpam-4254	448	1	thus	thus	ADV
ejpam-4254	448	2	νp(0	νp(0	VERB
ejpam-4254	448	3	)	)	PUNCT
ejpam-4254	448	4	<	<	X
ejpam-4254	448	5	t	t	PROPN
ejpam-4254	448	6	=	=	SYM
ejpam-4254	448	7	νp(0	νp(0	PROPN
ejpam-4254	448	8	)	)	PUNCT
ejpam-4254	448	9	,	,	PUNCT
ejpam-4254	448	10	a	a	DET
ejpam-4254	448	11	contradiction	contradiction	NOUN
ejpam-4254	448	12	.	.	PUNCT
ejpam-4254	449	1	hence	hence	ADV
ejpam-4254	449	2	,	,	PUNCT
ejpam-4254	449	3	νp(0	νp(0	NOUN
ejpam-4254	449	4	)	)	PUNCT
ejpam-4254	449	5	≤	≤	NOUN
ejpam-4254	449	6	νp(a	νp(a	NUM
ejpam-4254	449	7	)	)	PUNCT
ejpam-4254	449	8	for	for	ADP
ejpam-4254	449	9	all	all	DET
ejpam-4254	449	10	a	a	DET
ejpam-4254	449	11	∈	∈	PROPN
ejpam-4254	449	12	u	u	NOUN
ejpam-4254	449	13	.	.	PUNCT
ejpam-4254	449	14	suppose	suppose	VERB
ejpam-4254	449	15	there	there	PRON
ejpam-4254	449	16	exist	exist	VERB
ejpam-4254	449	17	a	a	DET
ejpam-4254	449	18	,	,	PUNCT
ejpam-4254	449	19	b	b	NOUN
ejpam-4254	449	20	,	,	PUNCT
ejpam-4254	449	21	c	c	PROPN
ejpam-4254	449	22	∈	∈	PROPN
ejpam-4254	449	23	u	u	NOUN
ejpam-4254	449	24	such	such	ADJ
ejpam-4254	449	25	that	that	DET
ejpam-4254	449	26	νp(a⋆c	νp(a⋆c	NOUN
ejpam-4254	449	27	)	)	PUNCT
ejpam-4254	449	28	>	>	PUNCT
ejpam-4254	450	1	max{νp(a⋆	max{νp(a⋆	PRON
ejpam-4254	450	2	(	(	PUNCT
ejpam-4254	450	3	b⋆c	b⋆c	PROPN
ejpam-4254	450	4	)	)	PUNCT
ejpam-4254	450	5	)	)	PUNCT
ejpam-4254	450	6	,	,	PUNCT
ejpam-4254	450	7	νp(b	νp(b	NOUN
ejpam-4254	450	8	)	)	PUNCT
ejpam-4254	450	9	}	}	PUNCT
ejpam-4254	450	10	.	.	PUNCT
ejpam-4254	451	1	choose	choose	VERB
ejpam-4254	451	2	t	t	NOUN
ejpam-4254	451	3	=	=	SYM
ejpam-4254	451	4	νp(a	νp(a	X
ejpam-4254	451	5	)	)	PUNCT
ejpam-4254	451	6	∈	∈	NOUN
ejpam-4254	452	1	[	[	X
ejpam-4254	452	2	0	0	NUM
ejpam-4254	452	3	,	,	PUNCT
ejpam-4254	452	4	1	1	NUM
ejpam-4254	452	5	]	]	PUNCT
ejpam-4254	452	6	.	.	PUNCT
ejpam-4254	453	1	then	then	ADV
ejpam-4254	453	2	νp(a⋆	νp(a⋆	PROPN
ejpam-4254	453	3	(	(	PUNCT
ejpam-4254	453	4	b⋆c	b⋆c	PROPN
ejpam-4254	453	5	)	)	PUNCT
ejpam-4254	453	6	)	)	PUNCT
ejpam-4254	453	7	<	<	X
ejpam-4254	453	8	t	t	PROPN
ejpam-4254	453	9	and	and	CCONJ
ejpam-4254	453	10	νp(b	νp(b	NOUN
ejpam-4254	453	11	)	)	PUNCT
ejpam-4254	454	1	<	<	X
ejpam-4254	454	2	t.	t.	X
ejpam-4254	454	3	thus	thus	ADV
ejpam-4254	454	4	a⋆	a⋆	CCONJ
ejpam-4254	454	5	(	(	PUNCT
ejpam-4254	454	6	b⋆c	b⋆c	PROPN
ejpam-4254	454	7	)	)	PUNCT
ejpam-4254	454	8	,	,	PUNCT
ejpam-4254	454	9	b	b	X
ejpam-4254	454	10	∈	∈	PROPN
ejpam-4254	454	11	l−(νp	l−(νp	PROPN
ejpam-4254	454	12	,	,	PUNCT
ejpam-4254	454	13	t	t	PROPN
ejpam-4254	454	14	)	)	PUNCT
ejpam-4254	454	15	̸=	̸=	PROPN
ejpam-4254	454	16	∅.	∅.	ADV
ejpam-4254	454	17	as	as	ADP
ejpam-4254	454	18	a	a	DET
ejpam-4254	454	19	hypothesis	hypothesis	NOUN
ejpam-4254	454	20	,	,	PUNCT
ejpam-4254	454	21	we	we	PRON
ejpam-4254	454	22	get	get	VERB
ejpam-4254	454	23	l−(νp	l−(νp	PROPN
ejpam-4254	454	24	,	,	PUNCT
ejpam-4254	454	25	t	t	PROPN
ejpam-4254	454	26	)	)	PUNCT
ejpam-4254	454	27	is	be	AUX
ejpam-4254	454	28	a	a	DET
ejpam-4254	454	29	upi	upi	NOUN
ejpam-4254	454	30	of	of	ADP
ejpam-4254	454	31	u	u	PROPN
ejpam-4254	454	32	and	and	CCONJ
ejpam-4254	454	33	so	so	ADV
ejpam-4254	454	34	a	a	DET
ejpam-4254	454	35	⋆	⋆	NOUN
ejpam-4254	454	36	c	c	NOUN
ejpam-4254	454	37	∈	∈	PROPN
ejpam-4254	454	38	l−(νp	l−(νp	PROPN
ejpam-4254	454	39	,	,	PUNCT
ejpam-4254	454	40	t	t	PROPN
ejpam-4254	454	41	)	)	PUNCT
ejpam-4254	454	42	.	.	PUNCT
ejpam-4254	455	1	thus	thus	ADV
ejpam-4254	455	2	νp(a	νp(a	NUM
ejpam-4254	455	3	⋆	⋆	VERB
ejpam-4254	455	4	c	c	NOUN
ejpam-4254	455	5	)	)	PUNCT
ejpam-4254	455	6	<	<	X
ejpam-4254	455	7	t	t	PROPN
ejpam-4254	455	8	=	=	PUNCT
ejpam-4254	455	9	νp(a⋆c	νp(a⋆c	NUM
ejpam-4254	455	10	)	)	PUNCT
ejpam-4254	455	11	,	,	PUNCT
ejpam-4254	455	12	a	a	DET
ejpam-4254	455	13	contradiction	contradiction	NOUN
ejpam-4254	455	14	.	.	PUNCT
ejpam-4254	456	1	hence	hence	ADV
ejpam-4254	456	2	,	,	PUNCT
ejpam-4254	456	3	νp(a⋆c	νp(a⋆c	PRON
ejpam-4254	456	4	)	)	PUNCT
ejpam-4254	456	5	≤	≤	NUM
ejpam-4254	456	6	max{νp(a⋆(b⋆c	max{νp(a⋆(b⋆c	NOUN
ejpam-4254	456	7	)	)	PUNCT
ejpam-4254	456	8	)	)	PUNCT
ejpam-4254	456	9	,	,	PUNCT
ejpam-4254	456	10	νp(b	νp(b	NOUN
ejpam-4254	456	11	)	)	PUNCT
ejpam-4254	456	12	}	}	PUNCT
ejpam-4254	456	13	for	for	ADP
ejpam-4254	456	14	all	all	DET
ejpam-4254	456	15	a	a	DET
ejpam-4254	456	16	,	,	PUNCT
ejpam-4254	456	17	b	b	NOUN
ejpam-4254	456	18	,	,	PUNCT
ejpam-4254	456	19	c	c	PROPN
ejpam-4254	456	20	∈	∈	PROPN
ejpam-4254	456	21	u	u	PROPN
ejpam-4254	456	22	.	.	PUNCT
ejpam-4254	457	1	therefore	therefore	ADV
ejpam-4254	457	2	,	,	PUNCT
ejpam-4254	457	3	p	p	PRON
ejpam-4254	457	4	is	be	AUX
ejpam-4254	457	5	a	a	DET
ejpam-4254	457	6	pfupi	pfupi	NOUN
ejpam-4254	457	7	of	of	ADP
ejpam-4254	457	8	u	u	PROPN
ejpam-4254	457	9	.	.	PUNCT
ejpam-4254	458	1	theorem	theorem	VERB
ejpam-4254	458	2	10	10	NUM
ejpam-4254	458	3	.	.	PUNCT
ejpam-4254	459	1	p	p	NOUN
ejpam-4254	459	2	is	be	AUX
ejpam-4254	459	3	a	a	DET
ejpam-4254	459	4	pfsupi	pfsupi	NOUN
ejpam-4254	459	5	of	of	ADP
ejpam-4254	459	6	u	u	PRON
ejpam-4254	459	7	if	if	SCONJ
ejpam-4254	459	8	and	and	CCONJ
ejpam-4254	459	9	only	only	ADV
ejpam-4254	459	10	if	if	SCONJ
ejpam-4254	459	11	u(µp	u(µp	NOUN
ejpam-4254	459	12	,	,	PUNCT
ejpam-4254	459	13	t	t	PROPN
ejpam-4254	459	14	)	)	PUNCT
ejpam-4254	459	15	and	and	CCONJ
ejpam-4254	459	16	l(νp	l(νp	PROPN
ejpam-4254	459	17	,	,	PUNCT
ejpam-4254	459	18	t	t	PROPN
ejpam-4254	459	19	)	)	PUNCT
ejpam-4254	459	20	are	be	AUX
ejpam-4254	459	21	,	,	PUNCT
ejpam-4254	459	22	if	if	SCONJ
ejpam-4254	459	23	the	the	DET
ejpam-4254	459	24	sets	set	NOUN
ejpam-4254	459	25	are	be	AUX
ejpam-4254	459	26	nonempty	nonempty	ADJ
ejpam-4254	459	27	,	,	PUNCT
ejpam-4254	459	28	supis	supi	VERB
ejpam-4254	459	29	for	for	ADP
ejpam-4254	459	30	every	every	DET
ejpam-4254	459	31	t	t	NOUN
ejpam-4254	459	32	∈	∈	PROPN
ejpam-4254	460	1	[	[	X
ejpam-4254	460	2	0	0	NUM
ejpam-4254	460	3	,	,	PUNCT
ejpam-4254	460	4	1	1	NUM
ejpam-4254	460	5	]	]	PUNCT
ejpam-4254	460	6	.	.	PUNCT
ejpam-4254	461	1	proof	proof	NOUN
ejpam-4254	461	2	.	.	PUNCT
ejpam-4254	462	1	assume	assume	VERB
ejpam-4254	462	2	p	p	X
ejpam-4254	462	3	=	=	X
ejpam-4254	462	4	(	(	PUNCT
ejpam-4254	462	5	µp	µp	PROPN
ejpam-4254	462	6	,	,	PUNCT
ejpam-4254	462	7	νp	νp	NOUN
ejpam-4254	462	8	)	)	PUNCT
ejpam-4254	462	9	is	be	AUX
ejpam-4254	462	10	a	a	DET
ejpam-4254	462	11	pfsupi	pfsupi	NOUN
ejpam-4254	462	12	of	of	ADP
ejpam-4254	462	13	u	u	PROPN
ejpam-4254	462	14	.	.	PUNCT
ejpam-4254	463	1	let	let	VERB
ejpam-4254	463	2	t	t	X
ejpam-4254	463	3	∈	∈	PROPN
ejpam-4254	464	1	[	[	X
ejpam-4254	464	2	0	0	NUM
ejpam-4254	464	3	,	,	PUNCT
ejpam-4254	464	4	1	1	NUM
ejpam-4254	464	5	]	]	PUNCT
ejpam-4254	464	6	be	be	AUX
ejpam-4254	464	7	such	such	ADJ
ejpam-4254	464	8	that	that	SCONJ
ejpam-4254	464	9	u(µp	u(µp	NOUN
ejpam-4254	464	10	,	,	PUNCT
ejpam-4254	464	11	t	t	PROPN
ejpam-4254	464	12	)	)	PUNCT
ejpam-4254	464	13	,	,	PUNCT
ejpam-4254	464	14	l(νp	l(νp	PROPN
ejpam-4254	464	15	,	,	PUNCT
ejpam-4254	464	16	t	t	PROPN
ejpam-4254	464	17	)	)	PUNCT
ejpam-4254	464	18	̸=	̸=	PROPN
ejpam-4254	464	19	∅.	∅.	ADV
ejpam-4254	464	20	let	let	VERB
ejpam-4254	464	21	a	a	DET
ejpam-4254	464	22	,	,	PUNCT
ejpam-4254	464	23	b	b	NOUN
ejpam-4254	464	24	,	,	PUNCT
ejpam-4254	464	25	c	c	PROPN
ejpam-4254	464	26	∈	∈	PROPN
ejpam-4254	464	27	u	u	PROPN
ejpam-4254	464	28	.	.	PUNCT
ejpam-4254	465	1	then	then	ADV
ejpam-4254	465	2	a	a	DET
ejpam-4254	465	3	∈	∈	PROPN
ejpam-4254	465	4	u(µp	u(µp	NOUN
ejpam-4254	465	5	,	,	PUNCT
ejpam-4254	465	6	t	t	PROPN
ejpam-4254	465	7	)	)	PUNCT
ejpam-4254	465	8	⇒	⇒	NOUN
ejpam-4254	465	9	µp(a	µp(a	NUM
ejpam-4254	465	10	)	)	PUNCT
ejpam-4254	465	11	≥	≥	NOUN
ejpam-4254	465	12	t	t	PROPN
ejpam-4254	465	13	⇒	⇒	PROPN
ejpam-4254	465	14	µp(0	µp(0	NOUN
ejpam-4254	465	15	)	)	PUNCT
ejpam-4254	465	16	≥	≥	NOUN
ejpam-4254	465	17	µp(a	µp(a	NUM
ejpam-4254	465	18	)	)	PUNCT
ejpam-4254	465	19	≥	≥	NOUN
ejpam-4254	465	20	t	t	PROPN
ejpam-4254	465	21	(	(	PUNCT
ejpam-4254	465	22	(	(	PUNCT
ejpam-4254	465	23	1.25	1.25	NUM
ejpam-4254	465	24	)	)	PUNCT
ejpam-4254	465	25	)	)	PUNCT
ejpam-4254	465	26	⇒	⇒	VERB
ejpam-4254	465	27	0	0	NUM
ejpam-4254	466	1	∈	∈	PROPN
ejpam-4254	466	2	u(µp	u(µp	NOUN
ejpam-4254	466	3	,	,	PUNCT
ejpam-4254	466	4	t	t	PROPN
ejpam-4254	466	5	)	)	PUNCT
ejpam-4254	466	6	,	,	PUNCT
ejpam-4254	466	7	(	(	PUNCT
ejpam-4254	466	8	c	c	NOUN
ejpam-4254	466	9	⋆	⋆	NOUN
ejpam-4254	466	10	b	b	NOUN
ejpam-4254	466	11	)	)	PUNCT
ejpam-4254	466	12	⋆	⋆	X
ejpam-4254	466	13	(	(	PUNCT
ejpam-4254	466	14	c	c	NOUN
ejpam-4254	466	15	⋆	⋆	VERB
ejpam-4254	466	16	a	a	NOUN
ejpam-4254	466	17	)	)	PUNCT
ejpam-4254	466	18	,	,	PUNCT
ejpam-4254	466	19	b	b	X
ejpam-4254	466	20	∈	∈	PROPN
ejpam-4254	466	21	u(µp	u(µp	PROPN
ejpam-4254	466	22	,	,	PUNCT
ejpam-4254	466	23	t	t	PROPN
ejpam-4254	466	24	)	)	PUNCT
ejpam-4254	466	25	⇒	⇒	PROPN
ejpam-4254	466	26	µp((c	µp((c	NOUN
ejpam-4254	466	27	⋆	⋆	PROPN
ejpam-4254	466	28	b	b	NOUN
ejpam-4254	466	29	)	)	PUNCT
ejpam-4254	466	30	⋆	⋆	NOUN
ejpam-4254	466	31	(	(	PUNCT
ejpam-4254	466	32	c	c	NOUN
ejpam-4254	466	33	⋆	⋆	NOUN
ejpam-4254	466	34	a	a	NOUN
ejpam-4254	466	35	)	)	PUNCT
ejpam-4254	466	36	)	)	PUNCT
ejpam-4254	466	37	≥	≥	PROPN
ejpam-4254	466	38	t	t	PROPN
ejpam-4254	466	39	,	,	PUNCT
ejpam-4254	466	40	µp(b	µp(b	ADJ
ejpam-4254	466	41	)	)	PUNCT
ejpam-4254	466	42	≥	≥	PROPN
ejpam-4254	466	43	t	t	PROPN
ejpam-4254	466	44	⇒	⇒	PROPN
ejpam-4254	466	45	min{µp((c	min{µp((c	PROPN
ejpam-4254	466	46	⋆	⋆	NOUN
ejpam-4254	466	47	b	b	NOUN
ejpam-4254	466	48	)	)	PUNCT
ejpam-4254	466	49	⋆	⋆	NOUN
ejpam-4254	466	50	(	(	PUNCT
ejpam-4254	466	51	c	c	NOUN
ejpam-4254	466	52	⋆	⋆	VERB
ejpam-4254	466	53	a	a	NOUN
ejpam-4254	466	54	)	)	PUNCT
ejpam-4254	466	55	)	)	PUNCT
ejpam-4254	466	56	,	,	PUNCT
ejpam-4254	466	57	µp(b	µp(b	ADJ
ejpam-4254	466	58	)	)	PUNCT
ejpam-4254	466	59	}	}	PUNCT
ejpam-4254	466	60	≥	≥	X
ejpam-4254	466	61	t	t	PROPN
ejpam-4254	466	62	⇒	⇒	NOUN
ejpam-4254	466	63	µp(a	µp(a	NUM
ejpam-4254	466	64	)	)	PUNCT
ejpam-4254	466	65	≥	≥	X
ejpam-4254	466	66	min{µp((c	min{µp((c	INTJ
ejpam-4254	466	67	⋆	⋆	NOUN
ejpam-4254	466	68	b	b	NOUN
ejpam-4254	466	69	)	)	PUNCT
ejpam-4254	466	70	⋆	⋆	NOUN
ejpam-4254	466	71	(	(	PUNCT
ejpam-4254	466	72	c	c	NOUN
ejpam-4254	466	73	⋆	⋆	VERB
ejpam-4254	466	74	a	a	NOUN
ejpam-4254	466	75	)	)	PUNCT
ejpam-4254	466	76	)	)	PUNCT
ejpam-4254	466	77	,	,	PUNCT
ejpam-4254	466	78	µp(b	µp(b	ADJ
ejpam-4254	466	79	)	)	PUNCT
ejpam-4254	466	80	}	}	PUNCT
ejpam-4254	466	81	≥	≥	PROPN
ejpam-4254	466	82	t	t	PROPN
ejpam-4254	466	83	(	(	PUNCT
ejpam-4254	466	84	(	(	PUNCT
ejpam-4254	466	85	1.31	1.31	NUM
ejpam-4254	466	86	)	)	PUNCT
ejpam-4254	466	87	)	)	PUNCT
ejpam-4254	466	88	⇒	⇒	VERB
ejpam-4254	466	89	a	a	DET
ejpam-4254	466	90	∈	∈	PROPN
ejpam-4254	466	91	u(µp	u(µp	NOUN
ejpam-4254	466	92	,	,	PUNCT
ejpam-4254	466	93	t	t	PROPN
ejpam-4254	466	94	)	)	PUNCT
ejpam-4254	466	95	,	,	PUNCT
ejpam-4254	466	96	a	a	DET
ejpam-4254	466	97	∈	∈	PROPN
ejpam-4254	466	98	l(νp	l(νp	PROPN
ejpam-4254	466	99	,	,	PUNCT
ejpam-4254	466	100	t	t	PROPN
ejpam-4254	466	101	)	)	PUNCT
ejpam-4254	466	102	⇒	⇒	NOUN
ejpam-4254	466	103	νp(a	νp(a	NUM
ejpam-4254	466	104	)	)	PUNCT
ejpam-4254	466	105	≤	≤	PUNCT
ejpam-4254	466	106	t	t	PROPN
ejpam-4254	466	107	⇒	⇒	PROPN
ejpam-4254	466	108	νp(0	νp(0	PROPN
ejpam-4254	466	109	)	)	PUNCT
ejpam-4254	466	110	≤	≤	NOUN
ejpam-4254	466	111	νp(a	νp(a	NUM
ejpam-4254	466	112	)	)	PUNCT
ejpam-4254	466	113	≤	≤	NUM
ejpam-4254	466	114	t	t	NOUN
ejpam-4254	466	115	(	(	PUNCT
ejpam-4254	466	116	(	(	PUNCT
ejpam-4254	466	117	1.26	1.26	NUM
ejpam-4254	466	118	)	)	PUNCT
ejpam-4254	466	119	)	)	PUNCT
ejpam-4254	466	120	⇒	⇒	VERB
ejpam-4254	466	121	0	0	NUM
ejpam-4254	466	122	∈	∈	PROPN
ejpam-4254	466	123	l(νp	l(νp	PROPN
ejpam-4254	466	124	,	,	PUNCT
ejpam-4254	466	125	t	t	PROPN
ejpam-4254	466	126	)	)	PUNCT
ejpam-4254	466	127	,	,	PUNCT
ejpam-4254	467	1	a.	a.	NOUN
ejpam-4254	467	2	iampan	iampan	NOUN
ejpam-4254	467	3	et	et	PROPN
ejpam-4254	467	4	al	al	PROPN
ejpam-4254	467	5	.	.	PUNCT
ejpam-4254	467	6	/	/	SYM
ejpam-4254	467	7	eur	eur	PROPN
ejpam-4254	467	8	.	.	PUNCT
ejpam-4254	468	1	j.	j.	PROPN
ejpam-4254	468	2	pure	pure	PROPN
ejpam-4254	468	3	appl	appl	PROPN
ejpam-4254	468	4	.	.	PROPN
ejpam-4254	468	5	math	math	PROPN
ejpam-4254	468	6	,	,	PUNCT
ejpam-4254	468	7	15	15	NUM
ejpam-4254	468	8	(	(	PUNCT
ejpam-4254	468	9	1	1	NUM
ejpam-4254	468	10	)	)	PUNCT
ejpam-4254	468	11	(	(	PUNCT
ejpam-4254	468	12	2022	2022	NUM
ejpam-4254	468	13	)	)	PUNCT
ejpam-4254	468	14	,	,	PUNCT
ejpam-4254	468	15	169	169	NUM
ejpam-4254	468	16	-	-	SYM
ejpam-4254	468	17	198	198	NUM
ejpam-4254	468	18	189	189	NUM
ejpam-4254	468	19	and	and	CCONJ
ejpam-4254	468	20	(	(	PUNCT
ejpam-4254	468	21	c	c	PROPN
ejpam-4254	468	22	⋆	⋆	NOUN
ejpam-4254	468	23	b	b	NOUN
ejpam-4254	468	24	)	)	PUNCT
ejpam-4254	468	25	⋆	⋆	X
ejpam-4254	468	26	(	(	PUNCT
ejpam-4254	468	27	c	c	NOUN
ejpam-4254	468	28	⋆	⋆	VERB
ejpam-4254	468	29	a	a	NOUN
ejpam-4254	468	30	)	)	PUNCT
ejpam-4254	468	31	,	,	PUNCT
ejpam-4254	468	32	b	b	X
ejpam-4254	468	33	∈	∈	PROPN
ejpam-4254	468	34	l(νp	l(νp	PROPN
ejpam-4254	468	35	,	,	PUNCT
ejpam-4254	468	36	t	t	PROPN
ejpam-4254	468	37	)	)	PUNCT
ejpam-4254	468	38	⇒	⇒	NOUN
ejpam-4254	468	39	νp((c	νp((c	NOUN
ejpam-4254	468	40	⋆	⋆	X
ejpam-4254	468	41	b	b	NOUN
ejpam-4254	468	42	)	)	PUNCT
ejpam-4254	468	43	⋆	⋆	NOUN
ejpam-4254	468	44	(	(	PUNCT
ejpam-4254	468	45	c	c	NOUN
ejpam-4254	468	46	⋆	⋆	VERB
ejpam-4254	468	47	a	a	NOUN
ejpam-4254	468	48	)	)	PUNCT
ejpam-4254	468	49	)	)	PUNCT
ejpam-4254	468	50	≤	≤	NOUN
ejpam-4254	468	51	t	t	PROPN
ejpam-4254	468	52	,	,	PUNCT
ejpam-4254	468	53	νp(b	νp(b	NOUN
ejpam-4254	468	54	)	)	PUNCT
ejpam-4254	468	55	≤	≤	PUNCT
ejpam-4254	468	56	t	t	NOUN
ejpam-4254	468	57	⇒	⇒	NOUN
ejpam-4254	469	1	max{µp((c	max{µp((c	PROPN
ejpam-4254	469	2	⋆	⋆	PUNCT
ejpam-4254	469	3	b	b	NOUN
ejpam-4254	469	4	)	)	PUNCT
ejpam-4254	469	5	⋆	⋆	X
ejpam-4254	469	6	(	(	PUNCT
ejpam-4254	469	7	c	c	NOUN
ejpam-4254	469	8	⋆	⋆	VERB
ejpam-4254	469	9	a	a	NOUN
ejpam-4254	469	10	)	)	PUNCT
ejpam-4254	469	11	)	)	PUNCT
ejpam-4254	469	12	,	,	PUNCT
ejpam-4254	469	13	νp(b	νp(b	NOUN
ejpam-4254	469	14	)	)	PUNCT
ejpam-4254	469	15	}	}	PUNCT
ejpam-4254	469	16	≤	≤	NUM
ejpam-4254	469	17	t	t	PROPN
ejpam-4254	469	18	⇒	⇒	NOUN
ejpam-4254	469	19	νp(a	νp(a	NUM
ejpam-4254	469	20	)	)	PUNCT
ejpam-4254	469	21	≤	≤	NOUN
ejpam-4254	469	22	max{νp((c	max{νp((c	PROPN
ejpam-4254	469	23	⋆	⋆	PUNCT
ejpam-4254	469	24	b	b	NOUN
ejpam-4254	469	25	)	)	PUNCT
ejpam-4254	469	26	⋆	⋆	X
ejpam-4254	469	27	(	(	PUNCT
ejpam-4254	469	28	c	c	NOUN
ejpam-4254	469	29	⋆	⋆	VERB
ejpam-4254	469	30	a	a	NOUN
ejpam-4254	469	31	)	)	PUNCT
ejpam-4254	469	32	)	)	PUNCT
ejpam-4254	469	33	,	,	PUNCT
ejpam-4254	469	34	νp(b	νp(b	NOUN
ejpam-4254	469	35	)	)	PUNCT
ejpam-4254	469	36	}	}	PUNCT
ejpam-4254	469	37	≤	≤	PROPN
ejpam-4254	469	38	t	t	NOUN
ejpam-4254	469	39	(	(	PUNCT
ejpam-4254	469	40	(	(	PUNCT
ejpam-4254	469	41	1.32	1.32	NUM
ejpam-4254	469	42	)	)	PUNCT
ejpam-4254	469	43	)	)	PUNCT
ejpam-4254	469	44	⇒	⇒	VERB
ejpam-4254	469	45	a	a	DET
ejpam-4254	469	46	∈	∈	PROPN
ejpam-4254	469	47	l(νp	l(νp	PROPN
ejpam-4254	469	48	,	,	PUNCT
ejpam-4254	469	49	t	t	PROPN
ejpam-4254	469	50	)	)	PUNCT
ejpam-4254	469	51	.	.	PUNCT
ejpam-4254	470	1	hence	hence	ADV
ejpam-4254	470	2	,	,	PUNCT
ejpam-4254	470	3	u(µp	u(µp	PROPN
ejpam-4254	470	4	,	,	PUNCT
ejpam-4254	470	5	t	t	PROPN
ejpam-4254	470	6	)	)	PUNCT
ejpam-4254	470	7	and	and	CCONJ
ejpam-4254	470	8	l(νp	l(νp	PROPN
ejpam-4254	470	9	,	,	PUNCT
ejpam-4254	470	10	t	t	PROPN
ejpam-4254	470	11	)	)	PUNCT
ejpam-4254	470	12	are	be	AUX
ejpam-4254	470	13	supis	supi	VERB
ejpam-4254	470	14	of	of	ADP
ejpam-4254	470	15	u	u	PROPN
ejpam-4254	470	16	.	.	PUNCT
ejpam-4254	471	1	conversely	conversely	ADV
ejpam-4254	471	2	,	,	PUNCT
ejpam-4254	471	3	assume	assume	VERB
ejpam-4254	471	4	for	for	ADP
ejpam-4254	471	5	all	all	DET
ejpam-4254	471	6	t	t	NOUN
ejpam-4254	471	7	∈	∈	PROPN
ejpam-4254	472	1	[	[	X
ejpam-4254	472	2	0	0	NUM
ejpam-4254	472	3	,	,	PUNCT
ejpam-4254	472	4	1	1	NUM
ejpam-4254	472	5	]	]	PUNCT
ejpam-4254	472	6	,	,	PUNCT
ejpam-4254	472	7	u(µp	u(µp	PROPN
ejpam-4254	472	8	,	,	PUNCT
ejpam-4254	472	9	t	t	PROPN
ejpam-4254	472	10	)	)	PUNCT
ejpam-4254	472	11	and	and	CCONJ
ejpam-4254	472	12	l(νp	l(νp	PROPN
ejpam-4254	472	13	,	,	PUNCT
ejpam-4254	472	14	t	t	PROPN
ejpam-4254	472	15	)	)	PUNCT
ejpam-4254	472	16	are	be	AUX
ejpam-4254	472	17	supis	supi	VERB
ejpam-4254	472	18	of	of	ADP
ejpam-4254	472	19	u	u	PRON
ejpam-4254	472	20	if	if	SCONJ
ejpam-4254	472	21	the	the	DET
ejpam-4254	472	22	sets	set	NOUN
ejpam-4254	472	23	are	be	AUX
ejpam-4254	472	24	nonempty	nonempty	ADJ
ejpam-4254	472	25	.	.	PUNCT
ejpam-4254	473	1	let	let	VERB
ejpam-4254	473	2	a	a	DET
ejpam-4254	473	3	,	,	PUNCT
ejpam-4254	473	4	b	b	NOUN
ejpam-4254	473	5	,	,	PUNCT
ejpam-4254	473	6	c	c	PROPN
ejpam-4254	473	7	∈	∈	PROPN
ejpam-4254	473	8	u	u	PROPN
ejpam-4254	473	9	.	.	PUNCT
ejpam-4254	474	1	choose	choose	VERB
ejpam-4254	474	2	t	t	NOUN
ejpam-4254	474	3	=	=	SYM
ejpam-4254	474	4	µp(a	µp(a	PRON
ejpam-4254	474	5	)	)	PUNCT
ejpam-4254	474	6	∈	∈	NOUN
ejpam-4254	475	1	[	[	X
ejpam-4254	475	2	0	0	NUM
ejpam-4254	475	3	,	,	PUNCT
ejpam-4254	475	4	1	1	NUM
ejpam-4254	475	5	]	]	PUNCT
ejpam-4254	475	6	.	.	PUNCT
ejpam-4254	476	1	then	then	ADV
ejpam-4254	476	2	µp(a	µp(a	NUM
ejpam-4254	476	3	)	)	PUNCT
ejpam-4254	476	4	≥	≥	NOUN
ejpam-4254	476	5	t.	t.	NOUN
ejpam-4254	476	6	thus	thus	ADV
ejpam-4254	476	7	a	a	DET
ejpam-4254	476	8	∈	∈	NOUN
ejpam-4254	476	9	u(µp	u(µp	NOUN
ejpam-4254	476	10	,	,	PUNCT
ejpam-4254	476	11	t	t	PROPN
ejpam-4254	476	12	)	)	PUNCT
ejpam-4254	476	13	̸=	̸=	PROPN
ejpam-4254	476	14	∅.	∅.	ADV
ejpam-4254	476	15	as	as	ADP
ejpam-4254	476	16	a	a	DET
ejpam-4254	476	17	hypothesis	hypothesis	NOUN
ejpam-4254	476	18	,	,	PUNCT
ejpam-4254	476	19	we	we	PRON
ejpam-4254	476	20	get	get	VERB
ejpam-4254	476	21	u(µp	u(µp	NOUN
ejpam-4254	476	22	,	,	PUNCT
ejpam-4254	476	23	t	t	PROPN
ejpam-4254	476	24	)	)	PUNCT
ejpam-4254	476	25	is	be	AUX
ejpam-4254	476	26	a	a	DET
ejpam-4254	476	27	supi	supi	NOUN
ejpam-4254	476	28	of	of	ADP
ejpam-4254	476	29	u	u	NOUN
ejpam-4254	476	30	and	and	CCONJ
ejpam-4254	476	31	so	so	ADV
ejpam-4254	476	32	0	0	NUM
ejpam-4254	476	33	∈	∈	PROPN
ejpam-4254	476	34	u(µp	u(µp	NOUN
ejpam-4254	476	35	,	,	PUNCT
ejpam-4254	476	36	t	t	PROPN
ejpam-4254	476	37	)	)	PUNCT
ejpam-4254	476	38	.	.	PUNCT
ejpam-4254	477	1	thus	thus	ADV
ejpam-4254	477	2	µp(0	µp(0	NOUN
ejpam-4254	477	3	)	)	PUNCT
ejpam-4254	477	4	≥	≥	NOUN
ejpam-4254	477	5	t	t	NOUN
ejpam-4254	477	6	=	=	PUNCT
ejpam-4254	477	7	µp(a	µp(a	NUM
ejpam-4254	477	8	)	)	PUNCT
ejpam-4254	477	9	.	.	PUNCT
ejpam-4254	478	1	choose	choose	VERB
ejpam-4254	478	2	t	t	PROPN
ejpam-4254	478	3	=	=	SYM
ejpam-4254	478	4	min{µp((c	min{µp((c	PROPN
ejpam-4254	478	5	⋆	⋆	NOUN
ejpam-4254	478	6	b	b	NOUN
ejpam-4254	478	7	)	)	PUNCT
ejpam-4254	478	8	⋆	⋆	NOUN
ejpam-4254	478	9	(	(	PUNCT
ejpam-4254	478	10	c	c	NOUN
ejpam-4254	478	11	⋆	⋆	VERB
ejpam-4254	478	12	a	a	NOUN
ejpam-4254	478	13	)	)	PUNCT
ejpam-4254	478	14	)	)	PUNCT
ejpam-4254	478	15	,	,	PUNCT
ejpam-4254	478	16	µp(b	µp(b	ADJ
ejpam-4254	478	17	)	)	PUNCT
ejpam-4254	478	18	}	}	PUNCT
ejpam-4254	478	19	∈	∈	PROPN
ejpam-4254	479	1	[	[	X
ejpam-4254	479	2	0	0	NUM
ejpam-4254	479	3	,	,	PUNCT
ejpam-4254	479	4	1	1	NUM
ejpam-4254	479	5	]	]	PUNCT
ejpam-4254	479	6	.	.	PUNCT
ejpam-4254	480	1	then	then	ADV
ejpam-4254	480	2	µp((c	µp((c	ADP
ejpam-4254	480	3	⋆	⋆	PROPN
ejpam-4254	480	4	b	b	NOUN
ejpam-4254	480	5	)	)	PUNCT
ejpam-4254	480	6	⋆	⋆	NOUN
ejpam-4254	480	7	(	(	PUNCT
ejpam-4254	480	8	c	c	NOUN
ejpam-4254	480	9	⋆	⋆	NOUN
ejpam-4254	480	10	a	a	NOUN
ejpam-4254	480	11	)	)	PUNCT
ejpam-4254	480	12	)	)	PUNCT
ejpam-4254	480	13	≥	≥	PROPN
ejpam-4254	480	14	t	t	NOUN
ejpam-4254	480	15	and	and	CCONJ
ejpam-4254	480	16	µp(b	µp(b	ADJ
ejpam-4254	480	17	)	)	PUNCT
ejpam-4254	480	18	≥	≥	NOUN
ejpam-4254	480	19	t.	t.	NOUN
ejpam-4254	480	20	thus	thus	ADV
ejpam-4254	480	21	(	(	PUNCT
ejpam-4254	480	22	c	c	NOUN
ejpam-4254	480	23	⋆	⋆	NOUN
ejpam-4254	480	24	b	b	NOUN
ejpam-4254	480	25	)	)	PUNCT
ejpam-4254	480	26	⋆	⋆	X
ejpam-4254	480	27	(	(	PUNCT
ejpam-4254	480	28	c	c	NOUN
ejpam-4254	480	29	⋆	⋆	VERB
ejpam-4254	480	30	a	a	NOUN
ejpam-4254	480	31	)	)	PUNCT
ejpam-4254	480	32	,	,	PUNCT
ejpam-4254	480	33	b	b	X
ejpam-4254	480	34	∈	∈	PROPN
ejpam-4254	480	35	u(µp	u(µp	PROPN
ejpam-4254	480	36	,	,	PUNCT
ejpam-4254	480	37	t	t	PROPN
ejpam-4254	480	38	)	)	PUNCT
ejpam-4254	480	39	̸=	̸=	PROPN
ejpam-4254	480	40	∅.	∅.	ADV
ejpam-4254	480	41	as	as	ADP
ejpam-4254	480	42	a	a	DET
ejpam-4254	480	43	hypothesis	hypothesis	NOUN
ejpam-4254	480	44	,	,	PUNCT
ejpam-4254	480	45	we	we	PRON
ejpam-4254	480	46	get	get	VERB
ejpam-4254	480	47	u(µp	u(µp	NOUN
ejpam-4254	480	48	,	,	PUNCT
ejpam-4254	480	49	t	t	PROPN
ejpam-4254	480	50	)	)	PUNCT
ejpam-4254	480	51	is	be	AUX
ejpam-4254	480	52	a	a	DET
ejpam-4254	480	53	supi	supi	NOUN
ejpam-4254	480	54	of	of	ADP
ejpam-4254	480	55	u	u	NOUN
ejpam-4254	480	56	and	and	CCONJ
ejpam-4254	480	57	so	so	ADV
ejpam-4254	480	58	a	a	DET
ejpam-4254	480	59	∈	∈	PROPN
ejpam-4254	480	60	u(µp	u(µp	NOUN
ejpam-4254	480	61	,	,	PUNCT
ejpam-4254	480	62	t	t	PROPN
ejpam-4254	480	63	)	)	PUNCT
ejpam-4254	480	64	.	.	PUNCT
ejpam-4254	481	1	thus	thus	ADV
ejpam-4254	481	2	µp(a	µp(a	NUM
ejpam-4254	481	3	)	)	PUNCT
ejpam-4254	481	4	≥	≥	NOUN
ejpam-4254	481	5	t	t	NOUN
ejpam-4254	481	6	=	=	SYM
ejpam-4254	481	7	min{µp((c	min{µp((c	PROPN
ejpam-4254	481	8	⋆	⋆	NOUN
ejpam-4254	481	9	b	b	NOUN
ejpam-4254	481	10	)	)	PUNCT
ejpam-4254	481	11	⋆	⋆	NOUN
ejpam-4254	481	12	(	(	PUNCT
ejpam-4254	481	13	c	c	NOUN
ejpam-4254	481	14	⋆	⋆	VERB
ejpam-4254	481	15	a	a	NOUN
ejpam-4254	481	16	)	)	PUNCT
ejpam-4254	481	17	)	)	PUNCT
ejpam-4254	481	18	,	,	PUNCT
ejpam-4254	481	19	µp(b	µp(b	ADJ
ejpam-4254	481	20	)	)	PUNCT
ejpam-4254	481	21	}	}	PUNCT
ejpam-4254	481	22	.	.	PUNCT
ejpam-4254	482	1	choose	choose	VERB
ejpam-4254	482	2	t	t	NOUN
ejpam-4254	482	3	=	=	SYM
ejpam-4254	482	4	νp(a	νp(a	X
ejpam-4254	482	5	)	)	PUNCT
ejpam-4254	482	6	∈	∈	NOUN
ejpam-4254	483	1	[	[	X
ejpam-4254	483	2	0	0	NUM
ejpam-4254	483	3	,	,	PUNCT
ejpam-4254	483	4	1	1	NUM
ejpam-4254	483	5	]	]	PUNCT
ejpam-4254	483	6	.	.	PUNCT
ejpam-4254	484	1	the	the	DET
ejpam-4254	484	2	νp(a	νp(a	NUM
ejpam-4254	484	3	)	)	PUNCT
ejpam-4254	484	4	≤	≤	NOUN
ejpam-4254	484	5	t.	t.	NOUN
ejpam-4254	484	6	thus	thus	ADV
ejpam-4254	484	7	a	a	DET
ejpam-4254	484	8	∈	∈	PROPN
ejpam-4254	484	9	l(νp	l(νp	PROPN
ejpam-4254	484	10	,	,	PUNCT
ejpam-4254	484	11	t	t	PROPN
ejpam-4254	484	12	)	)	PUNCT
ejpam-4254	484	13	̸=	̸=	PROPN
ejpam-4254	484	14	∅.	∅.	ADV
ejpam-4254	484	15	as	as	ADP
ejpam-4254	484	16	a	a	DET
ejpam-4254	484	17	hypothesis	hypothesis	NOUN
ejpam-4254	484	18	,	,	PUNCT
ejpam-4254	484	19	we	we	PRON
ejpam-4254	484	20	get	get	VERB
ejpam-4254	484	21	l(νp	l(νp	PROPN
ejpam-4254	484	22	,	,	PUNCT
ejpam-4254	484	23	t	t	PROPN
ejpam-4254	484	24	)	)	PUNCT
ejpam-4254	484	25	is	be	AUX
ejpam-4254	484	26	a	a	DET
ejpam-4254	484	27	supi	supi	NOUN
ejpam-4254	484	28	of	of	ADP
ejpam-4254	484	29	u	u	NOUN
ejpam-4254	484	30	and	and	CCONJ
ejpam-4254	484	31	so	so	ADV
ejpam-4254	484	32	0	0	NUM
ejpam-4254	484	33	∈	∈	PROPN
ejpam-4254	484	34	u(νp	u(νp	PROPN
ejpam-4254	484	35	,	,	PUNCT
ejpam-4254	484	36	t	t	PROPN
ejpam-4254	484	37	)	)	PUNCT
ejpam-4254	484	38	.	.	PUNCT
ejpam-4254	485	1	thus	thus	ADV
ejpam-4254	485	2	νp(0	νp(0	NOUN
ejpam-4254	485	3	)	)	PUNCT
ejpam-4254	485	4	≤	≤	NOUN
ejpam-4254	485	5	t	t	NOUN
ejpam-4254	485	6	=	=	PUNCT
ejpam-4254	485	7	νp(a	νp(a	NUM
ejpam-4254	485	8	)	)	PUNCT
ejpam-4254	485	9	.	.	PUNCT
ejpam-4254	486	1	choose	choose	VERB
ejpam-4254	486	2	t	t	PROPN
ejpam-4254	486	3	=	=	SYM
ejpam-4254	486	4	max{νp((c	max{νp((c	PROPN
ejpam-4254	486	5	⋆	⋆	PUNCT
ejpam-4254	486	6	b	b	NOUN
ejpam-4254	486	7	)	)	PUNCT
ejpam-4254	486	8	⋆	⋆	X
ejpam-4254	486	9	(	(	PUNCT
ejpam-4254	486	10	c	c	NOUN
ejpam-4254	486	11	⋆	⋆	VERB
ejpam-4254	486	12	a	a	NOUN
ejpam-4254	486	13	)	)	PUNCT
ejpam-4254	486	14	)	)	PUNCT
ejpam-4254	486	15	,	,	PUNCT
ejpam-4254	486	16	νp(b	νp(b	NOUN
ejpam-4254	486	17	)	)	PUNCT
ejpam-4254	486	18	}	}	PUNCT
ejpam-4254	486	19	∈	∈	PROPN
ejpam-4254	487	1	[	[	X
ejpam-4254	487	2	0	0	NUM
ejpam-4254	487	3	,	,	PUNCT
ejpam-4254	487	4	1	1	NUM
ejpam-4254	487	5	]	]	PUNCT
ejpam-4254	487	6	.	.	PUNCT
ejpam-4254	488	1	then	then	ADV
ejpam-4254	488	2	νp((c	νp((c	ADV
ejpam-4254	488	3	⋆	⋆	PUNCT
ejpam-4254	488	4	b	b	NOUN
ejpam-4254	488	5	)	)	PUNCT
ejpam-4254	488	6	⋆	⋆	NOUN
ejpam-4254	488	7	(	(	PUNCT
ejpam-4254	488	8	c	c	NOUN
ejpam-4254	488	9	⋆	⋆	VERB
ejpam-4254	488	10	a	a	NOUN
ejpam-4254	488	11	)	)	PUNCT
ejpam-4254	488	12	)	)	PUNCT
ejpam-4254	488	13	≤	≤	NOUN
ejpam-4254	488	14	t	t	NOUN
ejpam-4254	488	15	and	and	CCONJ
ejpam-4254	488	16	νp(b	νp(b	NOUN
ejpam-4254	488	17	)	)	PUNCT
ejpam-4254	488	18	≤	≤	NOUN
ejpam-4254	488	19	t.	t.	NOUN
ejpam-4254	489	1	thus	thus	ADV
ejpam-4254	489	2	(	(	PUNCT
ejpam-4254	489	3	c	c	NOUN
ejpam-4254	489	4	⋆	⋆	NOUN
ejpam-4254	489	5	b	b	NOUN
ejpam-4254	489	6	)	)	PUNCT
ejpam-4254	489	7	⋆	⋆	X
ejpam-4254	489	8	(	(	PUNCT
ejpam-4254	489	9	c	c	NOUN
ejpam-4254	489	10	⋆	⋆	VERB
ejpam-4254	489	11	a	a	NOUN
ejpam-4254	489	12	)	)	PUNCT
ejpam-4254	489	13	,	,	PUNCT
ejpam-4254	489	14	b	b	X
ejpam-4254	489	15	∈	∈	PROPN
ejpam-4254	489	16	l(µp	l(µp	NOUN
ejpam-4254	489	17	,	,	PUNCT
ejpam-4254	489	18	t	t	PROPN
ejpam-4254	489	19	)	)	PUNCT
ejpam-4254	489	20	̸=	̸=	PROPN
ejpam-4254	489	21	∅.	∅.	ADV
ejpam-4254	489	22	as	as	ADP
ejpam-4254	489	23	a	a	DET
ejpam-4254	489	24	hypothesis	hypothesis	NOUN
ejpam-4254	489	25	,	,	PUNCT
ejpam-4254	489	26	we	we	PRON
ejpam-4254	489	27	get	get	VERB
ejpam-4254	489	28	l(µp	l(µp	NOUN
ejpam-4254	489	29	,	,	PUNCT
ejpam-4254	489	30	t	t	PROPN
ejpam-4254	489	31	)	)	PUNCT
ejpam-4254	489	32	is	be	AUX
ejpam-4254	489	33	a	a	DET
ejpam-4254	489	34	supi	supi	NOUN
ejpam-4254	489	35	of	of	ADP
ejpam-4254	489	36	u	u	NOUN
ejpam-4254	489	37	and	and	CCONJ
ejpam-4254	489	38	so	so	ADV
ejpam-4254	489	39	a	a	DET
ejpam-4254	489	40	∈	∈	NOUN
ejpam-4254	489	41	l(µp	l(µp	NOUN
ejpam-4254	489	42	,	,	PUNCT
ejpam-4254	489	43	t	t	PROPN
ejpam-4254	489	44	)	)	PUNCT
ejpam-4254	489	45	.	.	PUNCT
ejpam-4254	490	1	thus	thus	ADV
ejpam-4254	490	2	νp(a	νp(a	NUM
ejpam-4254	490	3	)	)	PUNCT
ejpam-4254	490	4	≥	≥	NOUN
ejpam-4254	490	5	t	t	NOUN
ejpam-4254	490	6	=	=	SYM
ejpam-4254	490	7	max{νp((c	max{νp((c	PROPN
ejpam-4254	490	8	⋆	⋆	PUNCT
ejpam-4254	490	9	b	b	NOUN
ejpam-4254	490	10	)	)	PUNCT
ejpam-4254	490	11	⋆	⋆	X
ejpam-4254	490	12	(	(	PUNCT
ejpam-4254	490	13	c	c	NOUN
ejpam-4254	490	14	⋆	⋆	VERB
ejpam-4254	490	15	a	a	NOUN
ejpam-4254	490	16	)	)	PUNCT
ejpam-4254	490	17	)	)	PUNCT
ejpam-4254	490	18	,	,	PUNCT
ejpam-4254	490	19	νp(b	νp(b	NOUN
ejpam-4254	490	20	)	)	PUNCT
ejpam-4254	490	21	}	}	PUNCT
ejpam-4254	490	22	.	.	PUNCT
ejpam-4254	491	1	hence	hence	ADV
ejpam-4254	491	2	,	,	PUNCT
ejpam-4254	491	3	p	p	PROPN
ejpam-4254	491	4	is	be	AUX
ejpam-4254	491	5	a	a	DET
ejpam-4254	491	6	pfsupi	pfsupi	NOUN
ejpam-4254	491	7	of	of	ADP
ejpam-4254	491	8	u	u	PROPN
ejpam-4254	491	9	.	.	PUNCT
ejpam-4254	492	1	theorem	theorem	VERB
ejpam-4254	492	2	11	11	NUM
ejpam-4254	492	3	.	.	PUNCT
ejpam-4254	493	1	p	p	NOUN
ejpam-4254	493	2	is	be	AUX
ejpam-4254	493	3	a	a	DET
ejpam-4254	493	4	pfsupi	pfsupi	NOUN
ejpam-4254	493	5	of	of	ADP
ejpam-4254	493	6	u	u	PRON
ejpam-4254	493	7	if	if	SCONJ
ejpam-4254	493	8	and	and	CCONJ
ejpam-4254	493	9	only	only	ADV
ejpam-4254	493	10	if	if	SCONJ
ejpam-4254	493	11	u+(µp	u+(µp	NOUN
ejpam-4254	493	12	,	,	PUNCT
ejpam-4254	493	13	t	t	PROPN
ejpam-4254	493	14	)	)	PUNCT
ejpam-4254	493	15	and	and	CCONJ
ejpam-4254	493	16	l−(νp	l−(νp	PROPN
ejpam-4254	493	17	,	,	PUNCT
ejpam-4254	493	18	t	t	PROPN
ejpam-4254	493	19	)	)	PUNCT
ejpam-4254	493	20	are	be	AUX
ejpam-4254	493	21	,	,	PUNCT
ejpam-4254	493	22	if	if	SCONJ
ejpam-4254	493	23	the	the	DET
ejpam-4254	493	24	sets	set	NOUN
ejpam-4254	493	25	are	be	AUX
ejpam-4254	493	26	nonempty	nonempty	ADJ
ejpam-4254	493	27	,	,	PUNCT
ejpam-4254	493	28	supis	supis	NOUN
ejpam-4254	493	29	of	of	ADP
ejpam-4254	493	30	u	u	NOUN
ejpam-4254	493	31	for	for	ADP
ejpam-4254	493	32	every	every	DET
ejpam-4254	493	33	t	t	NOUN
ejpam-4254	493	34	∈	∈	PROPN
ejpam-4254	494	1	[	[	X
ejpam-4254	494	2	0	0	NUM
ejpam-4254	494	3	,	,	PUNCT
ejpam-4254	494	4	1	1	NUM
ejpam-4254	494	5	]	]	PUNCT
ejpam-4254	494	6	.	.	PUNCT
ejpam-4254	495	1	proof	proof	NOUN
ejpam-4254	495	2	.	.	PUNCT
ejpam-4254	496	1	assume	assume	VERB
ejpam-4254	496	2	p	p	X
ejpam-4254	496	3	=	=	X
ejpam-4254	496	4	(	(	PUNCT
ejpam-4254	496	5	µp	µp	PROPN
ejpam-4254	496	6	,	,	PUNCT
ejpam-4254	496	7	νp	νp	NOUN
ejpam-4254	496	8	)	)	PUNCT
ejpam-4254	496	9	is	be	AUX
ejpam-4254	496	10	a	a	DET
ejpam-4254	496	11	pfsupi	pfsupi	NOUN
ejpam-4254	496	12	of	of	ADP
ejpam-4254	496	13	u	u	PROPN
ejpam-4254	496	14	.	.	PUNCT
ejpam-4254	497	1	let	let	VERB
ejpam-4254	497	2	t	t	X
ejpam-4254	497	3	∈	∈	PROPN
ejpam-4254	498	1	[	[	X
ejpam-4254	498	2	0	0	NUM
ejpam-4254	498	3	,	,	PUNCT
ejpam-4254	498	4	1	1	NUM
ejpam-4254	498	5	]	]	PUNCT
ejpam-4254	498	6	be	be	AUX
ejpam-4254	498	7	such	such	ADJ
ejpam-4254	498	8	that	that	SCONJ
ejpam-4254	498	9	u+(µp	u+(µp	NOUN
ejpam-4254	498	10	,	,	PUNCT
ejpam-4254	498	11	t	t	PROPN
ejpam-4254	498	12	)	)	PUNCT
ejpam-4254	498	13	,	,	PUNCT
ejpam-4254	498	14	l−(νp	l−(νp	PROPN
ejpam-4254	498	15	,	,	PUNCT
ejpam-4254	498	16	t	t	PROPN
ejpam-4254	498	17	)	)	PUNCT
ejpam-4254	498	18	̸=	̸=	PROPN
ejpam-4254	498	19	∅.	∅.	ADV
ejpam-4254	498	20	let	let	VERB
ejpam-4254	498	21	a	a	DET
ejpam-4254	498	22	,	,	PUNCT
ejpam-4254	498	23	b	b	NOUN
ejpam-4254	498	24	,	,	PUNCT
ejpam-4254	498	25	c	c	PROPN
ejpam-4254	498	26	∈	∈	PROPN
ejpam-4254	498	27	u	u	PROPN
ejpam-4254	498	28	.	.	PUNCT
ejpam-4254	499	1	then	then	ADV
ejpam-4254	499	2	a	a	DET
ejpam-4254	499	3	∈	∈	PROPN
ejpam-4254	499	4	u+(µp	u+(µp	PROPN
ejpam-4254	499	5	,	,	PUNCT
ejpam-4254	499	6	t	t	PROPN
ejpam-4254	499	7	)	)	PUNCT
ejpam-4254	499	8	⇒	⇒	NOUN
ejpam-4254	499	9	µp(a	µp(a	NUM
ejpam-4254	499	10	)	)	PUNCT
ejpam-4254	499	11	>	>	X
ejpam-4254	499	12	t	t	PROPN
ejpam-4254	499	13	⇒	⇒	PROPN
ejpam-4254	499	14	µp(0	µp(0	PROPN
ejpam-4254	499	15	)	)	PUNCT
ejpam-4254	499	16	≥	≥	NOUN
ejpam-4254	499	17	µp(a	µp(a	NUM
ejpam-4254	499	18	)	)	PUNCT
ejpam-4254	499	19	>	>	X
ejpam-4254	499	20	t	t	PROPN
ejpam-4254	499	21	(	(	PUNCT
ejpam-4254	499	22	(	(	PUNCT
ejpam-4254	499	23	1.25	1.25	NUM
ejpam-4254	499	24	)	)	PUNCT
ejpam-4254	499	25	)	)	PUNCT
ejpam-4254	499	26	⇒	⇒	VERB
ejpam-4254	499	27	0	0	NUM
ejpam-4254	499	28	∈	∈	PROPN
ejpam-4254	499	29	u+(µp	u+(µp	PROPN
ejpam-4254	499	30	,	,	PUNCT
ejpam-4254	499	31	t	t	PROPN
ejpam-4254	499	32	)	)	PUNCT
ejpam-4254	499	33	,	,	PUNCT
ejpam-4254	499	34	(	(	PUNCT
ejpam-4254	499	35	c	c	NOUN
ejpam-4254	499	36	⋆	⋆	NOUN
ejpam-4254	499	37	b	b	NOUN
ejpam-4254	499	38	)	)	PUNCT
ejpam-4254	499	39	⋆	⋆	X
ejpam-4254	499	40	(	(	PUNCT
ejpam-4254	499	41	c	c	NOUN
ejpam-4254	499	42	⋆	⋆	VERB
ejpam-4254	499	43	a	a	NOUN
ejpam-4254	499	44	)	)	PUNCT
ejpam-4254	499	45	,	,	PUNCT
ejpam-4254	499	46	b	b	X
ejpam-4254	499	47	∈	∈	PROPN
ejpam-4254	499	48	u+(µp	u+(µp	PROPN
ejpam-4254	499	49	,	,	PUNCT
ejpam-4254	499	50	t	t	PROPN
ejpam-4254	499	51	)	)	PUNCT
ejpam-4254	499	52	⇒	⇒	PROPN
ejpam-4254	499	53	µp((c	µp((c	NOUN
ejpam-4254	499	54	⋆	⋆	PROPN
ejpam-4254	499	55	b	b	NOUN
ejpam-4254	499	56	)	)	PUNCT
ejpam-4254	499	57	⋆	⋆	NOUN
ejpam-4254	499	58	(	(	PUNCT
ejpam-4254	499	59	c	c	NOUN
ejpam-4254	499	60	⋆	⋆	NOUN
ejpam-4254	499	61	a	a	NOUN
ejpam-4254	499	62	)	)	PUNCT
ejpam-4254	499	63	)	)	PUNCT
ejpam-4254	499	64	>	>	X
ejpam-4254	500	1	t	t	PROPN
ejpam-4254	500	2	,	,	PUNCT
ejpam-4254	500	3	µp(b	µp(b	ADJ
ejpam-4254	500	4	)	)	PUNCT
ejpam-4254	500	5	>	>	X
ejpam-4254	500	6	t	t	PROPN
ejpam-4254	500	7	⇒	⇒	PROPN
ejpam-4254	500	8	min{µp((c	min{µp((c	PROPN
ejpam-4254	500	9	⋆	⋆	NOUN
ejpam-4254	500	10	b	b	NOUN
ejpam-4254	500	11	)	)	PUNCT
ejpam-4254	500	12	⋆	⋆	NOUN
ejpam-4254	500	13	(	(	PUNCT
ejpam-4254	500	14	c	c	NOUN
ejpam-4254	500	15	⋆	⋆	VERB
ejpam-4254	500	16	a	a	NOUN
ejpam-4254	500	17	)	)	PUNCT
ejpam-4254	500	18	)	)	PUNCT
ejpam-4254	500	19	,	,	PUNCT
ejpam-4254	500	20	µp(b	µp(b	ADJ
ejpam-4254	500	21	)	)	PUNCT
ejpam-4254	500	22	}	}	PUNCT
ejpam-4254	500	23	>	>	PUNCT
ejpam-4254	500	24	t	t	PROPN
ejpam-4254	500	25	⇒	⇒	NOUN
ejpam-4254	500	26	µp(a	µp(a	NUM
ejpam-4254	500	27	)	)	PUNCT
ejpam-4254	500	28	≥	≥	X
ejpam-4254	500	29	min{µp((c	min{µp((c	INTJ
ejpam-4254	500	30	⋆	⋆	NOUN
ejpam-4254	500	31	b	b	NOUN
ejpam-4254	500	32	)	)	PUNCT
ejpam-4254	500	33	⋆	⋆	NOUN
ejpam-4254	500	34	(	(	PUNCT
ejpam-4254	500	35	c	c	NOUN
ejpam-4254	500	36	⋆	⋆	VERB
ejpam-4254	500	37	a	a	NOUN
ejpam-4254	500	38	)	)	PUNCT
ejpam-4254	500	39	)	)	PUNCT
ejpam-4254	500	40	,	,	PUNCT
ejpam-4254	500	41	µp(b	µp(b	ADJ
ejpam-4254	500	42	)	)	PUNCT
ejpam-4254	500	43	}	}	PUNCT
ejpam-4254	500	44	>	>	X
ejpam-4254	500	45	t	t	PROPN
ejpam-4254	500	46	(	(	PUNCT
ejpam-4254	500	47	(	(	PUNCT
ejpam-4254	500	48	1.31	1.31	NUM
ejpam-4254	500	49	)	)	PUNCT
ejpam-4254	500	50	)	)	PUNCT
ejpam-4254	500	51	⇒	⇒	VERB
ejpam-4254	500	52	a	a	DET
ejpam-4254	500	53	∈	∈	PROPN
ejpam-4254	500	54	u+(µp	u+(µp	NOUN
ejpam-4254	500	55	,	,	PUNCT
ejpam-4254	500	56	t	t	PROPN
ejpam-4254	500	57	)	)	PUNCT
ejpam-4254	500	58	,	,	PUNCT
ejpam-4254	500	59	a	a	DET
ejpam-4254	500	60	∈	∈	PROPN
ejpam-4254	500	61	l−(νp	l−(νp	PROPN
ejpam-4254	500	62	,	,	PUNCT
ejpam-4254	500	63	t	t	PROPN
ejpam-4254	500	64	)	)	PUNCT
ejpam-4254	500	65	⇒	⇒	NOUN
ejpam-4254	500	66	νp(a	νp(a	NUM
ejpam-4254	500	67	)	)	PUNCT
ejpam-4254	500	68	<	<	X
ejpam-4254	500	69	t	t	PROPN
ejpam-4254	500	70	⇒	⇒	PROPN
ejpam-4254	500	71	νp(0	νp(0	PROPN
ejpam-4254	500	72	)	)	PUNCT
ejpam-4254	500	73	≤	≤	NOUN
ejpam-4254	500	74	νp(a	νp(a	NUM
ejpam-4254	500	75	)	)	PUNCT
ejpam-4254	500	76	<	<	X
ejpam-4254	500	77	t	t	X
ejpam-4254	500	78	(	(	PUNCT
ejpam-4254	500	79	(	(	PUNCT
ejpam-4254	500	80	1.26	1.26	NUM
ejpam-4254	500	81	)	)	PUNCT
ejpam-4254	500	82	)	)	PUNCT
ejpam-4254	500	83	⇒	⇒	VERB
ejpam-4254	500	84	0	0	NUM
ejpam-4254	501	1	∈	∈	PROPN
ejpam-4254	501	2	l−(νp	l−(νp	PROPN
ejpam-4254	501	3	,	,	PUNCT
ejpam-4254	501	4	t	t	PROPN
ejpam-4254	501	5	)	)	PUNCT
ejpam-4254	501	6	,	,	PUNCT
ejpam-4254	501	7	a.	a.	NOUN
ejpam-4254	501	8	iampan	iampan	NOUN
ejpam-4254	501	9	et	et	PROPN
ejpam-4254	501	10	al	al	PROPN
ejpam-4254	501	11	.	.	PUNCT
ejpam-4254	501	12	/	/	SYM
ejpam-4254	501	13	eur	eur	PROPN
ejpam-4254	501	14	.	.	PUNCT
ejpam-4254	502	1	j.	j.	PROPN
ejpam-4254	502	2	pure	pure	PROPN
ejpam-4254	502	3	appl	appl	PROPN
ejpam-4254	502	4	.	.	PROPN
ejpam-4254	502	5	math	math	PROPN
ejpam-4254	502	6	,	,	PUNCT
ejpam-4254	502	7	15	15	NUM
ejpam-4254	502	8	(	(	PUNCT
ejpam-4254	502	9	1	1	NUM
ejpam-4254	502	10	)	)	PUNCT
ejpam-4254	502	11	(	(	PUNCT
ejpam-4254	502	12	2022	2022	NUM
ejpam-4254	502	13	)	)	PUNCT
ejpam-4254	502	14	,	,	PUNCT
ejpam-4254	502	15	169	169	NUM
ejpam-4254	502	16	-	-	SYM
ejpam-4254	502	17	198	198	NUM
ejpam-4254	502	18	190	190	NUM
ejpam-4254	502	19	and	and	CCONJ
ejpam-4254	502	20	(	(	PUNCT
ejpam-4254	502	21	c	c	PROPN
ejpam-4254	502	22	⋆	⋆	NOUN
ejpam-4254	502	23	b	b	NOUN
ejpam-4254	502	24	)	)	PUNCT
ejpam-4254	502	25	⋆	⋆	X
ejpam-4254	502	26	(	(	PUNCT
ejpam-4254	502	27	c	c	NOUN
ejpam-4254	502	28	⋆	⋆	VERB
ejpam-4254	502	29	a	a	NOUN
ejpam-4254	502	30	)	)	PUNCT
ejpam-4254	502	31	,	,	PUNCT
ejpam-4254	502	32	b	b	X
ejpam-4254	502	33	∈	∈	PROPN
ejpam-4254	502	34	l−(νp	l−(νp	PROPN
ejpam-4254	502	35	,	,	PUNCT
ejpam-4254	502	36	t	t	PROPN
ejpam-4254	502	37	)	)	PUNCT
ejpam-4254	502	38	⇒	⇒	NOUN
ejpam-4254	502	39	νp((c	νp((c	NOUN
ejpam-4254	502	40	⋆	⋆	X
ejpam-4254	502	41	b	b	NOUN
ejpam-4254	502	42	)	)	PUNCT
ejpam-4254	502	43	⋆	⋆	NOUN
ejpam-4254	502	44	(	(	PUNCT
ejpam-4254	502	45	c	c	NOUN
ejpam-4254	502	46	⋆	⋆	NOUN
ejpam-4254	502	47	a	a	NOUN
ejpam-4254	502	48	)	)	PUNCT
ejpam-4254	502	49	)	)	PUNCT
ejpam-4254	502	50	<	<	X
ejpam-4254	502	51	t	t	PROPN
ejpam-4254	502	52	,	,	PUNCT
ejpam-4254	502	53	νp(b	νp(b	NOUN
ejpam-4254	502	54	)	)	PUNCT
ejpam-4254	502	55	<	<	X
ejpam-4254	502	56	t	t	X
ejpam-4254	502	57	⇒	⇒	X
ejpam-4254	502	58	max{νp((c	max{νp((c	PROPN
ejpam-4254	502	59	⋆	⋆	PROPN
ejpam-4254	502	60	b	b	NOUN
ejpam-4254	502	61	)	)	PUNCT
ejpam-4254	502	62	⋆	⋆	X
ejpam-4254	502	63	(	(	PUNCT
ejpam-4254	502	64	c	c	NOUN
ejpam-4254	502	65	⋆	⋆	VERB
ejpam-4254	502	66	a	a	NOUN
ejpam-4254	502	67	)	)	PUNCT
ejpam-4254	502	68	)	)	PUNCT
ejpam-4254	502	69	,	,	PUNCT
ejpam-4254	502	70	νp(b	νp(b	NOUN
ejpam-4254	502	71	)	)	PUNCT
ejpam-4254	502	72	}	}	PUNCT
ejpam-4254	503	1	<	<	X
ejpam-4254	503	2	t	t	PROPN
ejpam-4254	503	3	⇒	⇒	NOUN
ejpam-4254	503	4	νp(a	νp(a	NUM
ejpam-4254	503	5	)	)	PUNCT
ejpam-4254	503	6	≤	≤	NOUN
ejpam-4254	503	7	max{νp((c	max{νp((c	PROPN
ejpam-4254	503	8	⋆	⋆	PUNCT
ejpam-4254	503	9	b	b	NOUN
ejpam-4254	503	10	)	)	PUNCT
ejpam-4254	503	11	⋆	⋆	X
ejpam-4254	503	12	(	(	PUNCT
ejpam-4254	503	13	c	c	NOUN
ejpam-4254	503	14	⋆	⋆	VERB
ejpam-4254	503	15	a	a	NOUN
ejpam-4254	503	16	)	)	PUNCT
ejpam-4254	503	17	)	)	PUNCT
ejpam-4254	503	18	,	,	PUNCT
ejpam-4254	503	19	νp(b	νp(b	NOUN
ejpam-4254	503	20	)	)	PUNCT
ejpam-4254	503	21	}	}	PUNCT
ejpam-4254	503	22	<	<	X
ejpam-4254	503	23	t	t	X
ejpam-4254	503	24	(	(	PUNCT
ejpam-4254	503	25	(	(	PUNCT
ejpam-4254	503	26	1.32	1.32	NUM
ejpam-4254	503	27	)	)	PUNCT
ejpam-4254	503	28	)	)	PUNCT
ejpam-4254	503	29	⇒	⇒	VERB
ejpam-4254	503	30	a	a	DET
ejpam-4254	503	31	∈	∈	PROPN
ejpam-4254	503	32	l−(νp	l−(νp	PROPN
ejpam-4254	503	33	,	,	PUNCT
ejpam-4254	503	34	t	t	PROPN
ejpam-4254	503	35	)	)	PUNCT
ejpam-4254	503	36	.	.	PUNCT
ejpam-4254	504	1	hence	hence	ADV
ejpam-4254	504	2	,	,	PUNCT
ejpam-4254	504	3	u+(µp	u+(µp	PROPN
ejpam-4254	504	4	,	,	PUNCT
ejpam-4254	504	5	t	t	PROPN
ejpam-4254	504	6	)	)	PUNCT
ejpam-4254	504	7	and	and	CCONJ
ejpam-4254	504	8	l−(νp	l−(νp	PROPN
ejpam-4254	504	9	,	,	PUNCT
ejpam-4254	504	10	t	t	PROPN
ejpam-4254	504	11	)	)	PUNCT
ejpam-4254	504	12	are	be	AUX
ejpam-4254	504	13	supis	supi	VERB
ejpam-4254	504	14	of	of	ADP
ejpam-4254	504	15	u	u	PROPN
ejpam-4254	504	16	.	.	PUNCT
ejpam-4254	505	1	conversely	conversely	ADV
ejpam-4254	505	2	,	,	PUNCT
ejpam-4254	505	3	assume	assume	VERB
ejpam-4254	505	4	for	for	ADP
ejpam-4254	505	5	all	all	DET
ejpam-4254	505	6	t	t	NOUN
ejpam-4254	505	7	∈	∈	PROPN
ejpam-4254	506	1	[	[	X
ejpam-4254	506	2	0	0	NUM
ejpam-4254	506	3	,	,	PUNCT
ejpam-4254	506	4	1	1	NUM
ejpam-4254	506	5	]	]	PUNCT
ejpam-4254	506	6	,	,	PUNCT
ejpam-4254	506	7	u+(µp	u+(µp	PROPN
ejpam-4254	506	8	,	,	PUNCT
ejpam-4254	506	9	t	t	PROPN
ejpam-4254	506	10	)	)	PUNCT
ejpam-4254	506	11	and	and	CCONJ
ejpam-4254	506	12	l−(νp	l−(νp	PROPN
ejpam-4254	506	13	,	,	PUNCT
ejpam-4254	506	14	t	t	PROPN
ejpam-4254	506	15	)	)	PUNCT
ejpam-4254	506	16	are	be	AUX
ejpam-4254	506	17	supis	supi	VERB
ejpam-4254	506	18	of	of	ADP
ejpam-4254	506	19	u	u	PRON
ejpam-4254	506	20	if	if	SCONJ
ejpam-4254	506	21	the	the	DET
ejpam-4254	506	22	sets	set	NOUN
ejpam-4254	506	23	are	be	AUX
ejpam-4254	506	24	nonempty	nonempty	ADJ
ejpam-4254	506	25	.	.	PUNCT
ejpam-4254	507	1	suppose	suppose	VERB
ejpam-4254	507	2	there	there	PRON
ejpam-4254	507	3	exists	exist	VERB
ejpam-4254	507	4	a	a	DET
ejpam-4254	507	5	∈	∈	PROPN
ejpam-4254	507	6	u	u	NOUN
ejpam-4254	507	7	such	such	ADJ
ejpam-4254	507	8	that	that	DET
ejpam-4254	507	9	µp(0	µp(0	NOUN
ejpam-4254	507	10	)	)	PUNCT
ejpam-4254	507	11	<	<	X
ejpam-4254	507	12	µp(a	µp(a	NUM
ejpam-4254	507	13	)	)	PUNCT
ejpam-4254	507	14	.	.	PUNCT
ejpam-4254	508	1	choose	choose	VERB
ejpam-4254	508	2	t	t	PROPN
ejpam-4254	508	3	=	=	SYM
ejpam-4254	508	4	µp(0	µp(0	NOUN
ejpam-4254	508	5	)	)	PUNCT
ejpam-4254	508	6	∈	∈	NOUN
ejpam-4254	509	1	[	[	X
ejpam-4254	509	2	0	0	NUM
ejpam-4254	509	3	,	,	PUNCT
ejpam-4254	509	4	1	1	NUM
ejpam-4254	509	5	]	]	PUNCT
ejpam-4254	509	6	.	.	PUNCT
ejpam-4254	510	1	then	then	ADV
ejpam-4254	510	2	µp(a	µp(a	NUM
ejpam-4254	510	3	)	)	PUNCT
ejpam-4254	510	4	>	>	PUNCT
ejpam-4254	511	1	t.	t.	NOUN
ejpam-4254	511	2	thus	thus	ADV
ejpam-4254	511	3	a	a	DET
ejpam-4254	511	4	∈	∈	NOUN
ejpam-4254	511	5	u+(µp	u+(µp	NOUN
ejpam-4254	511	6	,	,	PUNCT
ejpam-4254	511	7	t	t	PROPN
ejpam-4254	511	8	)	)	PUNCT
ejpam-4254	511	9	̸=	̸=	PROPN
ejpam-4254	511	10	∅.	∅.	ADV
ejpam-4254	511	11	as	as	ADP
ejpam-4254	511	12	a	a	DET
ejpam-4254	511	13	hypothesis	hypothesis	NOUN
ejpam-4254	511	14	,	,	PUNCT
ejpam-4254	511	15	we	we	PRON
ejpam-4254	511	16	get	get	VERB
ejpam-4254	511	17	u+(µp	u+(µp	NOUN
ejpam-4254	511	18	,	,	PUNCT
ejpam-4254	511	19	t	t	PROPN
ejpam-4254	511	20	)	)	PUNCT
ejpam-4254	511	21	is	be	AUX
ejpam-4254	511	22	a	a	DET
ejpam-4254	511	23	supi	supi	NOUN
ejpam-4254	511	24	of	of	ADP
ejpam-4254	511	25	u	u	NOUN
ejpam-4254	511	26	and	and	CCONJ
ejpam-4254	511	27	so	so	ADV
ejpam-4254	511	28	0	0	NUM
ejpam-4254	511	29	∈	∈	PROPN
ejpam-4254	511	30	u+(µp	u+(µp	PROPN
ejpam-4254	511	31	,	,	PUNCT
ejpam-4254	511	32	t	t	PROPN
ejpam-4254	511	33	)	)	PUNCT
ejpam-4254	511	34	.	.	PUNCT
ejpam-4254	512	1	thus	thus	ADV
ejpam-4254	512	2	µp(0	µp(0	VERB
ejpam-4254	512	3	)	)	PUNCT
ejpam-4254	512	4	>	>	X
ejpam-4254	512	5	t	t	NOUN
ejpam-4254	512	6	=	=	SYM
ejpam-4254	512	7	µp(0	µp(0	NOUN
ejpam-4254	512	8	)	)	PUNCT
ejpam-4254	512	9	,	,	PUNCT
ejpam-4254	512	10	a	a	DET
ejpam-4254	512	11	contradiction	contradiction	NOUN
ejpam-4254	512	12	.	.	PUNCT
ejpam-4254	513	1	hence	hence	ADV
ejpam-4254	513	2	,	,	PUNCT
ejpam-4254	513	3	µp(0	µp(0	NOUN
ejpam-4254	513	4	)	)	PUNCT
ejpam-4254	513	5	≥	≥	NOUN
ejpam-4254	513	6	µp(a	µp(a	NUM
ejpam-4254	513	7	)	)	PUNCT
ejpam-4254	513	8	for	for	ADP
ejpam-4254	513	9	all	all	DET
ejpam-4254	513	10	a	a	DET
ejpam-4254	513	11	∈	∈	PROPN
ejpam-4254	513	12	u	u	NOUN
ejpam-4254	513	13	.	.	PUNCT
ejpam-4254	513	14	suppose	suppose	VERB
ejpam-4254	513	15	there	there	PRON
ejpam-4254	513	16	exist	exist	VERB
ejpam-4254	513	17	a	a	DET
ejpam-4254	513	18	,	,	PUNCT
ejpam-4254	513	19	b	b	NOUN
ejpam-4254	513	20	,	,	PUNCT
ejpam-4254	513	21	c	c	PROPN
ejpam-4254	513	22	∈	∈	PROPN
ejpam-4254	513	23	u	u	NOUN
ejpam-4254	513	24	such	such	ADJ
ejpam-4254	513	25	that	that	DET
ejpam-4254	513	26	µp(a	µp(a	NUM
ejpam-4254	513	27	)	)	PUNCT
ejpam-4254	513	28	<	<	X
ejpam-4254	513	29	min{µp((c⋆b)⋆(c⋆a	min{µp((c⋆b)⋆(c⋆a	NOUN
ejpam-4254	513	30	)	)	PUNCT
ejpam-4254	513	31	)	)	PUNCT
ejpam-4254	513	32	,	,	PUNCT
ejpam-4254	513	33	µp(b	µp(b	ADJ
ejpam-4254	513	34	)	)	PUNCT
ejpam-4254	513	35	}	}	PUNCT
ejpam-4254	513	36	.	.	PUNCT
ejpam-4254	514	1	choose	choose	VERB
ejpam-4254	514	2	t	t	NOUN
ejpam-4254	514	3	=	=	SYM
ejpam-4254	514	4	µp(a	µp(a	PRON
ejpam-4254	514	5	)	)	PUNCT
ejpam-4254	514	6	∈	∈	NOUN
ejpam-4254	515	1	[	[	X
ejpam-4254	515	2	0	0	NUM
ejpam-4254	515	3	,	,	PUNCT
ejpam-4254	515	4	1	1	NUM
ejpam-4254	515	5	]	]	PUNCT
ejpam-4254	515	6	.	.	PUNCT
ejpam-4254	516	1	then	then	ADV
ejpam-4254	516	2	µp((c	µp((c	ADP
ejpam-4254	516	3	⋆	⋆	PROPN
ejpam-4254	516	4	b	b	NOUN
ejpam-4254	516	5	)	)	PUNCT
ejpam-4254	516	6	⋆	⋆	NOUN
ejpam-4254	516	7	(	(	PUNCT
ejpam-4254	516	8	c	c	NOUN
ejpam-4254	516	9	⋆	⋆	NOUN
ejpam-4254	516	10	a	a	NOUN
ejpam-4254	516	11	)	)	PUNCT
ejpam-4254	516	12	)	)	PUNCT
ejpam-4254	516	13	>	>	X
ejpam-4254	516	14	t	t	PROPN
ejpam-4254	516	15	and	and	CCONJ
ejpam-4254	516	16	µp(b	µp(b	ADP
ejpam-4254	516	17	)	)	PUNCT
ejpam-4254	516	18	>	>	PUNCT
ejpam-4254	517	1	t.	t.	PROPN
ejpam-4254	517	2	thus	thus	ADV
ejpam-4254	517	3	(	(	PUNCT
ejpam-4254	517	4	c	c	NOUN
ejpam-4254	517	5	⋆	⋆	NOUN
ejpam-4254	517	6	b	b	NOUN
ejpam-4254	517	7	)	)	PUNCT
ejpam-4254	517	8	⋆	⋆	X
ejpam-4254	517	9	(	(	PUNCT
ejpam-4254	517	10	c	c	NOUN
ejpam-4254	517	11	⋆	⋆	VERB
ejpam-4254	517	12	a	a	NOUN
ejpam-4254	517	13	)	)	PUNCT
ejpam-4254	517	14	,	,	PUNCT
ejpam-4254	517	15	b	b	X
ejpam-4254	517	16	∈	∈	PROPN
ejpam-4254	517	17	u+(µp	u+(µp	PROPN
ejpam-4254	517	18	,	,	PUNCT
ejpam-4254	517	19	t	t	PROPN
ejpam-4254	517	20	)	)	PUNCT
ejpam-4254	517	21	̸=	̸=	PROPN
ejpam-4254	517	22	∅.	∅.	ADV
ejpam-4254	517	23	as	as	ADP
ejpam-4254	517	24	a	a	DET
ejpam-4254	517	25	hypothesis	hypothesis	NOUN
ejpam-4254	517	26	,	,	PUNCT
ejpam-4254	517	27	we	we	PRON
ejpam-4254	517	28	get	get	VERB
ejpam-4254	517	29	u+(µp	u+(µp	NOUN
ejpam-4254	517	30	,	,	PUNCT
ejpam-4254	517	31	t	t	PROPN
ejpam-4254	517	32	)	)	PUNCT
ejpam-4254	517	33	is	be	AUX
ejpam-4254	517	34	a	a	DET
ejpam-4254	517	35	supi	supi	NOUN
ejpam-4254	517	36	of	of	ADP
ejpam-4254	517	37	u	u	NOUN
ejpam-4254	517	38	and	and	CCONJ
ejpam-4254	517	39	so	so	ADV
ejpam-4254	517	40	a	a	DET
ejpam-4254	517	41	∈	∈	PROPN
ejpam-4254	517	42	u+(µp	u+(µp	PROPN
ejpam-4254	517	43	,	,	PUNCT
ejpam-4254	517	44	t	t	PROPN
ejpam-4254	517	45	)	)	PUNCT
ejpam-4254	517	46	.	.	PUNCT
ejpam-4254	518	1	thus	thus	ADV
ejpam-4254	518	2	µp(a	µp(a	NUM
ejpam-4254	518	3	)	)	PUNCT
ejpam-4254	518	4	>	>	X
ejpam-4254	518	5	t	t	NOUN
ejpam-4254	518	6	=	=	SYM
ejpam-4254	518	7	µp(a	µp(a	PROPN
ejpam-4254	518	8	)	)	PUNCT
ejpam-4254	518	9	,	,	PUNCT
ejpam-4254	518	10	a	a	DET
ejpam-4254	518	11	contradiction	contradiction	NOUN
ejpam-4254	518	12	.	.	PUNCT
ejpam-4254	519	1	hence	hence	ADV
ejpam-4254	519	2	,	,	PUNCT
ejpam-4254	519	3	µp(a	µp(a	PROPN
ejpam-4254	519	4	)	)	PUNCT
ejpam-4254	519	5	≥	≥	X
ejpam-4254	519	6	min{µp((c	min{µp((c	INTJ
ejpam-4254	519	7	⋆	⋆	NOUN
ejpam-4254	519	8	b	b	NOUN
ejpam-4254	519	9	)	)	PUNCT
ejpam-4254	519	10	⋆	⋆	NOUN
ejpam-4254	520	1	(	(	PUNCT
ejpam-4254	520	2	c	c	NOUN
ejpam-4254	520	3	⋆	⋆	VERB
ejpam-4254	520	4	a	a	NOUN
ejpam-4254	520	5	)	)	PUNCT
ejpam-4254	520	6	)	)	PUNCT
ejpam-4254	520	7	,	,	PUNCT
ejpam-4254	520	8	µp(b	µp(b	ADJ
ejpam-4254	520	9	)	)	PUNCT
ejpam-4254	520	10	}	}	PUNCT
ejpam-4254	520	11	for	for	ADP
ejpam-4254	520	12	all	all	DET
ejpam-4254	520	13	a	a	DET
ejpam-4254	520	14	,	,	PUNCT
ejpam-4254	520	15	b	b	NOUN
ejpam-4254	520	16	,	,	PUNCT
ejpam-4254	520	17	c	c	PROPN
ejpam-4254	520	18	∈	∈	PROPN
ejpam-4254	520	19	u	u	PROPN
ejpam-4254	520	20	.	.	PUNCT
ejpam-4254	520	21	suppose	suppose	VERB
ejpam-4254	520	22	there	there	PRON
ejpam-4254	520	23	exists	exist	VERB
ejpam-4254	520	24	a	a	DET
ejpam-4254	520	25	∈	∈	PROPN
ejpam-4254	520	26	u	u	NOUN
ejpam-4254	520	27	such	such	ADJ
ejpam-4254	520	28	that	that	DET
ejpam-4254	520	29	νp(0	νp(0	NOUN
ejpam-4254	520	30	)	)	PUNCT
ejpam-4254	520	31	>	>	X
ejpam-4254	520	32	νp(a	νp(a	NUM
ejpam-4254	520	33	)	)	PUNCT
ejpam-4254	520	34	.	.	PUNCT
ejpam-4254	521	1	choose	choose	VERB
ejpam-4254	521	2	t	t	PROPN
ejpam-4254	521	3	=	=	SYM
ejpam-4254	521	4	νp(0	νp(0	NOUN
ejpam-4254	521	5	)	)	PUNCT
ejpam-4254	521	6	∈	∈	PROPN
ejpam-4254	522	1	[	[	X
ejpam-4254	522	2	0	0	NUM
ejpam-4254	522	3	,	,	PUNCT
ejpam-4254	522	4	1	1	NUM
ejpam-4254	522	5	]	]	PUNCT
ejpam-4254	522	6	.	.	PUNCT
ejpam-4254	523	1	then	then	ADV
ejpam-4254	523	2	νp(a	νp(a	NUM
ejpam-4254	523	3	)	)	PUNCT
ejpam-4254	524	1	<	<	X
ejpam-4254	524	2	t.	t.	X
ejpam-4254	524	3	thus	thus	ADV
ejpam-4254	524	4	a	a	DET
ejpam-4254	524	5	∈	∈	PROPN
ejpam-4254	524	6	l−(νp	l−(νp	PROPN
ejpam-4254	524	7	,	,	PUNCT
ejpam-4254	524	8	t	t	PROPN
ejpam-4254	524	9	)	)	PUNCT
ejpam-4254	524	10	̸=	̸=	PROPN
ejpam-4254	524	11	∅.	∅.	ADV
ejpam-4254	524	12	as	as	ADP
ejpam-4254	524	13	a	a	DET
ejpam-4254	524	14	hypothesis	hypothesis	NOUN
ejpam-4254	524	15	,	,	PUNCT
ejpam-4254	524	16	we	we	PRON
ejpam-4254	524	17	get	get	VERB
ejpam-4254	524	18	l−(νp	l−(νp	PROPN
ejpam-4254	524	19	,	,	PUNCT
ejpam-4254	524	20	t	t	PROPN
ejpam-4254	524	21	)	)	PUNCT
ejpam-4254	524	22	is	be	AUX
ejpam-4254	524	23	a	a	DET
ejpam-4254	524	24	supi	supi	NOUN
ejpam-4254	524	25	of	of	ADP
ejpam-4254	524	26	u	u	NOUN
ejpam-4254	524	27	and	and	CCONJ
ejpam-4254	524	28	so	so	ADV
ejpam-4254	524	29	0	0	NUM
ejpam-4254	524	30	∈	∈	PROPN
ejpam-4254	524	31	l−(νp	l−(νp	PROPN
ejpam-4254	524	32	,	,	PUNCT
ejpam-4254	524	33	t	t	PROPN
ejpam-4254	524	34	)	)	PUNCT
ejpam-4254	524	35	.	.	PUNCT
ejpam-4254	525	1	thus	thus	ADV
ejpam-4254	525	2	νp(0	νp(0	VERB
ejpam-4254	525	3	)	)	PUNCT
ejpam-4254	525	4	<	<	X
ejpam-4254	525	5	t	t	PROPN
ejpam-4254	525	6	=	=	SYM
ejpam-4254	525	7	νp(0	νp(0	PROPN
ejpam-4254	525	8	)	)	PUNCT
ejpam-4254	525	9	,	,	PUNCT
ejpam-4254	525	10	a	a	DET
ejpam-4254	525	11	contradiction	contradiction	NOUN
ejpam-4254	525	12	.	.	PUNCT
ejpam-4254	526	1	hence	hence	ADV
ejpam-4254	526	2	,	,	PUNCT
ejpam-4254	526	3	νp(0	νp(0	NOUN
ejpam-4254	526	4	)	)	PUNCT
ejpam-4254	526	5	≤	≤	NOUN
ejpam-4254	526	6	νp(a	νp(a	NUM
ejpam-4254	526	7	)	)	PUNCT
ejpam-4254	526	8	for	for	ADP
ejpam-4254	526	9	all	all	DET
ejpam-4254	526	10	a	a	DET
ejpam-4254	526	11	∈	∈	PROPN
ejpam-4254	526	12	u	u	NOUN
ejpam-4254	526	13	.	.	PUNCT
ejpam-4254	526	14	suppose	suppose	VERB
ejpam-4254	526	15	there	there	PRON
ejpam-4254	526	16	exist	exist	VERB
ejpam-4254	526	17	a	a	DET
ejpam-4254	526	18	,	,	PUNCT
ejpam-4254	526	19	b	b	NOUN
ejpam-4254	526	20	,	,	PUNCT
ejpam-4254	526	21	c	c	PROPN
ejpam-4254	526	22	∈	∈	PROPN
ejpam-4254	526	23	u	u	NOUN
ejpam-4254	526	24	such	such	ADJ
ejpam-4254	526	25	that	that	DET
ejpam-4254	526	26	νp(a	νp(a	NUM
ejpam-4254	526	27	)	)	PUNCT
ejpam-4254	526	28	>	>	X
ejpam-4254	526	29	max{νp((c⋆b)⋆(c⋆a	max{νp((c⋆b)⋆(c⋆a	NOUN
ejpam-4254	526	30	)	)	PUNCT
ejpam-4254	526	31	)	)	PUNCT
ejpam-4254	526	32	,	,	PUNCT
ejpam-4254	526	33	νp(b	νp(b	NOUN
ejpam-4254	526	34	)	)	PUNCT
ejpam-4254	526	35	}	}	PUNCT
ejpam-4254	526	36	.	.	PUNCT
ejpam-4254	527	1	choose	choose	VERB
ejpam-4254	527	2	t	t	NOUN
ejpam-4254	527	3	=	=	SYM
ejpam-4254	527	4	νp(a	νp(a	X
ejpam-4254	527	5	)	)	PUNCT
ejpam-4254	527	6	∈	∈	NOUN
ejpam-4254	528	1	[	[	X
ejpam-4254	528	2	0	0	NUM
ejpam-4254	528	3	,	,	PUNCT
ejpam-4254	528	4	1	1	NUM
ejpam-4254	528	5	]	]	PUNCT
ejpam-4254	528	6	.	.	PUNCT
ejpam-4254	529	1	then	then	ADV
ejpam-4254	529	2	νp((c	νp((c	ADV
ejpam-4254	529	3	⋆	⋆	PUNCT
ejpam-4254	529	4	b	b	NOUN
ejpam-4254	529	5	)	)	PUNCT
ejpam-4254	529	6	⋆	⋆	NOUN
ejpam-4254	529	7	(	(	PUNCT
ejpam-4254	529	8	c	c	NOUN
ejpam-4254	529	9	⋆	⋆	NOUN
ejpam-4254	529	10	a	a	NOUN
ejpam-4254	529	11	)	)	PUNCT
ejpam-4254	529	12	)	)	PUNCT
ejpam-4254	529	13	<	<	X
ejpam-4254	529	14	t	t	NOUN
ejpam-4254	529	15	and	and	CCONJ
ejpam-4254	529	16	νp(b	νp(b	NOUN
ejpam-4254	529	17	)	)	PUNCT
ejpam-4254	529	18	<	<	X
ejpam-4254	529	19	t.	t.	X
ejpam-4254	529	20	thus	thus	ADV
ejpam-4254	529	21	(	(	PUNCT
ejpam-4254	529	22	c	c	NOUN
ejpam-4254	529	23	⋆	⋆	NOUN
ejpam-4254	529	24	b	b	NOUN
ejpam-4254	529	25	)	)	PUNCT
ejpam-4254	529	26	⋆	⋆	X
ejpam-4254	529	27	(	(	PUNCT
ejpam-4254	529	28	c	c	NOUN
ejpam-4254	529	29	⋆	⋆	VERB
ejpam-4254	529	30	a	a	NOUN
ejpam-4254	529	31	)	)	PUNCT
ejpam-4254	529	32	,	,	PUNCT
ejpam-4254	529	33	b	b	X
ejpam-4254	529	34	∈	∈	PROPN
ejpam-4254	529	35	l−(νp	l−(νp	PROPN
ejpam-4254	529	36	,	,	PUNCT
ejpam-4254	529	37	t	t	PROPN
ejpam-4254	529	38	)	)	PUNCT
ejpam-4254	529	39	̸=	̸=	PROPN
ejpam-4254	529	40	∅.	∅.	ADV
ejpam-4254	529	41	as	as	ADP
ejpam-4254	529	42	a	a	DET
ejpam-4254	529	43	hypothesis	hypothesis	NOUN
ejpam-4254	529	44	,	,	PUNCT
ejpam-4254	529	45	we	we	PRON
ejpam-4254	529	46	get	get	VERB
ejpam-4254	529	47	l−(νp	l−(νp	PROPN
ejpam-4254	529	48	,	,	PUNCT
ejpam-4254	529	49	t	t	PROPN
ejpam-4254	529	50	)	)	PUNCT
ejpam-4254	529	51	is	be	AUX
ejpam-4254	529	52	a	a	DET
ejpam-4254	529	53	supi	supi	NOUN
ejpam-4254	529	54	of	of	ADP
ejpam-4254	529	55	u	u	NOUN
ejpam-4254	529	56	and	and	CCONJ
ejpam-4254	529	57	so	so	ADV
ejpam-4254	529	58	a	a	DET
ejpam-4254	529	59	∈	∈	PROPN
ejpam-4254	529	60	l−(νp	l−(νp	PROPN
ejpam-4254	529	61	,	,	PUNCT
ejpam-4254	529	62	t	t	PROPN
ejpam-4254	529	63	)	)	PUNCT
ejpam-4254	529	64	.	.	PUNCT
ejpam-4254	530	1	thus	thus	ADV
ejpam-4254	530	2	νp(a	νp(a	NUM
ejpam-4254	530	3	)	)	PUNCT
ejpam-4254	530	4	<	<	X
ejpam-4254	530	5	t	t	NOUN
ejpam-4254	530	6	=	=	PUNCT
ejpam-4254	530	7	νp(a	νp(a	NUM
ejpam-4254	530	8	)	)	PUNCT
ejpam-4254	530	9	,	,	PUNCT
ejpam-4254	530	10	a	a	DET
ejpam-4254	530	11	contradiction	contradiction	NOUN
ejpam-4254	530	12	.	.	PUNCT
ejpam-4254	531	1	hence	hence	ADV
ejpam-4254	531	2	,	,	PUNCT
ejpam-4254	531	3	νp(a	νp(a	NUM
ejpam-4254	531	4	)	)	PUNCT
ejpam-4254	531	5	≤	≤	NOUN
ejpam-4254	531	6	max{νp((c	max{νp((c	PROPN
ejpam-4254	531	7	⋆	⋆	PUNCT
ejpam-4254	531	8	b	b	NOUN
ejpam-4254	531	9	)	)	PUNCT
ejpam-4254	531	10	⋆	⋆	X
ejpam-4254	531	11	(	(	PUNCT
ejpam-4254	531	12	c	c	NOUN
ejpam-4254	531	13	⋆	⋆	VERB
ejpam-4254	531	14	a	a	NOUN
ejpam-4254	531	15	)	)	PUNCT
ejpam-4254	531	16	)	)	PUNCT
ejpam-4254	531	17	,	,	PUNCT
ejpam-4254	531	18	νp(b	νp(b	NOUN
ejpam-4254	531	19	)	)	PUNCT
ejpam-4254	531	20	}	}	PUNCT
ejpam-4254	531	21	for	for	ADP
ejpam-4254	531	22	all	all	DET
ejpam-4254	531	23	a	a	DET
ejpam-4254	531	24	,	,	PUNCT
ejpam-4254	531	25	b	b	NOUN
ejpam-4254	531	26	,	,	PUNCT
ejpam-4254	531	27	c	c	PROPN
ejpam-4254	531	28	∈	∈	PROPN
ejpam-4254	531	29	u	u	PROPN
ejpam-4254	531	30	.	.	PUNCT
ejpam-4254	532	1	therefore	therefore	ADV
ejpam-4254	532	2	,	,	PUNCT
ejpam-4254	532	3	p	p	PRON
ejpam-4254	532	4	is	be	AUX
ejpam-4254	532	5	a	a	DET
ejpam-4254	532	6	pfsupi	pfsupi	NOUN
ejpam-4254	532	7	of	of	ADP
ejpam-4254	532	8	u	u	PROPN
ejpam-4254	532	9	.	.	PUNCT
ejpam-4254	533	1	theorem	theorem	NOUN
ejpam-4254	533	2	12	12	NUM
ejpam-4254	533	3	.	.	PUNCT
ejpam-4254	534	1	p	p	NOUN
ejpam-4254	534	2	is	be	AUX
ejpam-4254	534	3	a	a	DET
ejpam-4254	534	4	pfsupi	pfsupi	NOUN
ejpam-4254	534	5	of	of	ADP
ejpam-4254	534	6	u	u	PRON
ejpam-4254	534	7	if	if	SCONJ
ejpam-4254	534	8	and	and	CCONJ
ejpam-4254	534	9	only	only	ADV
ejpam-4254	534	10	if	if	SCONJ
ejpam-4254	534	11	e(µp	e(µp	NOUN
ejpam-4254	534	12	,	,	PUNCT
ejpam-4254	534	13	µp(0	µp(0	NOUN
ejpam-4254	534	14	)	)	PUNCT
ejpam-4254	534	15	)	)	PUNCT
ejpam-4254	534	16	and	and	CCONJ
ejpam-4254	534	17	e(νp	e(νp	PROPN
ejpam-4254	534	18	,	,	PUNCT
ejpam-4254	534	19	νp(0	νp(0	NOUN
ejpam-4254	534	20	)	)	PUNCT
ejpam-4254	534	21	)	)	PUNCT
ejpam-4254	534	22	are	be	AUX
ejpam-4254	534	23	supis	supi	VERB
ejpam-4254	534	24	of	of	ADP
ejpam-4254	534	25	u	u	PROPN
ejpam-4254	534	26	.	.	PUNCT
ejpam-4254	535	1	proof	proof	NOUN
ejpam-4254	535	2	.	.	PUNCT
ejpam-4254	536	1	assume	assume	VERB
ejpam-4254	536	2	p	p	X
ejpam-4254	536	3	=	=	X
ejpam-4254	536	4	(	(	PUNCT
ejpam-4254	536	5	µp	µp	PROPN
ejpam-4254	536	6	,	,	PUNCT
ejpam-4254	536	7	νp	νp	NOUN
ejpam-4254	536	8	)	)	PUNCT
ejpam-4254	536	9	is	be	AUX
ejpam-4254	536	10	a	a	DET
ejpam-4254	536	11	pfsupi	pfsupi	NOUN
ejpam-4254	536	12	of	of	ADP
ejpam-4254	536	13	u	u	NOUN
ejpam-4254	536	14	.	.	PUNCT
ejpam-4254	537	1	since	since	SCONJ
ejpam-4254	537	2	p	p	NOUN
ejpam-4254	537	3	is	be	AUX
ejpam-4254	537	4	constant	constant	ADJ
ejpam-4254	537	5	,	,	PUNCT
ejpam-4254	537	6	we	we	PRON
ejpam-4254	537	7	have	have	VERB
ejpam-4254	537	8	(	(	PUNCT
ejpam-4254	537	9	∀a	∀a	NOUN
ejpam-4254	537	10	∈	∈	PROPN
ejpam-4254	537	11	u	u	NOUN
ejpam-4254	537	12	)	)	PUNCT
ejpam-4254	537	13	(	(	PUNCT
ejpam-4254	537	14	µp(a	µp(a	NUM
ejpam-4254	537	15	)	)	PUNCT
ejpam-4254	537	16	=	=	SYM
ejpam-4254	537	17	µp(0	µp(0	NOUN
ejpam-4254	537	18	)	)	PUNCT
ejpam-4254	537	19	νp(a	νp(a	NUM
ejpam-4254	537	20	)	)	PUNCT
ejpam-4254	537	21	=	=	SYM
ejpam-4254	537	22	νp(0	νp(0	NOUN
ejpam-4254	537	23	)	)	PUNCT
ejpam-4254	537	24	)	)	PUNCT
ejpam-4254	537	25	.	.	PUNCT
ejpam-4254	538	1	thus	thus	ADV
ejpam-4254	538	2	a	a	DET
ejpam-4254	538	3	∈	∈	PROPN
ejpam-4254	538	4	e(µp	e(µp	NOUN
ejpam-4254	538	5	,	,	PUNCT
ejpam-4254	538	6	µp(0	µp(0	NOUN
ejpam-4254	538	7	)	)	PUNCT
ejpam-4254	538	8	)	)	PUNCT
ejpam-4254	538	9	and	and	CCONJ
ejpam-4254	538	10	a	a	DET
ejpam-4254	538	11	∈	∈	PROPN
ejpam-4254	538	12	e(νp	e(νp	PROPN
ejpam-4254	538	13	,	,	PUNCT
ejpam-4254	538	14	νp(0	νp(0	NOUN
ejpam-4254	538	15	)	)	PUNCT
ejpam-4254	538	16	)	)	PUNCT
ejpam-4254	538	17	and	and	CCONJ
ejpam-4254	538	18	so	so	ADV
ejpam-4254	538	19	e(µp	e(µp	NOUN
ejpam-4254	538	20	,	,	PUNCT
ejpam-4254	538	21	µp(0	µp(0	NOUN
ejpam-4254	538	22	)	)	PUNCT
ejpam-4254	538	23	)	)	PUNCT
ejpam-4254	539	1	=	=	SYM
ejpam-4254	539	2	u	u	NOUN
ejpam-4254	539	3	and	and	CCONJ
ejpam-4254	539	4	e(νp	e(νp	PROPN
ejpam-4254	539	5	,	,	PUNCT
ejpam-4254	539	6	νp(0	νp(0	NOUN
ejpam-4254	539	7	)	)	PUNCT
ejpam-4254	539	8	)	)	PUNCT
ejpam-4254	540	1	=	=	SYM
ejpam-4254	540	2	u	u	PROPN
ejpam-4254	540	3	.	.	PUNCT
ejpam-4254	541	1	hence	hence	ADV
ejpam-4254	541	2	,	,	PUNCT
ejpam-4254	541	3	e(µp	e(µp	NOUN
ejpam-4254	541	4	,	,	PUNCT
ejpam-4254	541	5	µp(0	µp(0	NOUN
ejpam-4254	541	6	)	)	PUNCT
ejpam-4254	541	7	)	)	PUNCT
ejpam-4254	541	8	and	and	CCONJ
ejpam-4254	541	9	e(νp	e(νp	PROPN
ejpam-4254	541	10	,	,	PUNCT
ejpam-4254	541	11	νp(0	νp(0	NOUN
ejpam-4254	541	12	)	)	PUNCT
ejpam-4254	541	13	)	)	PUNCT
ejpam-4254	541	14	are	be	AUX
ejpam-4254	541	15	supis	supi	VERB
ejpam-4254	541	16	of	of	ADP
ejpam-4254	541	17	u	u	PROPN
ejpam-4254	541	18	.	.	PUNCT
ejpam-4254	542	1	conversely	conversely	ADV
ejpam-4254	542	2	,	,	PUNCT
ejpam-4254	542	3	assume	assume	VERB
ejpam-4254	542	4	e(µp	e(µp	NOUN
ejpam-4254	542	5	,	,	PUNCT
ejpam-4254	542	6	µp(0	µp(0	NOUN
ejpam-4254	542	7	)	)	PUNCT
ejpam-4254	542	8	)	)	PUNCT
ejpam-4254	542	9	and	and	CCONJ
ejpam-4254	542	10	e(νp	e(νp	PROPN
ejpam-4254	542	11	,	,	PUNCT
ejpam-4254	542	12	νp(0	νp(0	NOUN
ejpam-4254	542	13	)	)	PUNCT
ejpam-4254	542	14	)	)	PUNCT
ejpam-4254	542	15	are	be	AUX
ejpam-4254	542	16	supis	supi	VERB
ejpam-4254	542	17	of	of	ADP
ejpam-4254	542	18	u	u	PROPN
ejpam-4254	542	19	.	.	PUNCT
ejpam-4254	543	1	then	then	ADV
ejpam-4254	543	2	e(µp	e(µp	NOUN
ejpam-4254	543	3	,	,	PUNCT
ejpam-4254	543	4	µp(0	µp(0	NOUN
ejpam-4254	543	5	)	)	PUNCT
ejpam-4254	543	6	)	)	PUNCT
ejpam-4254	544	1	=	=	SYM
ejpam-4254	544	2	u	u	NOUN
ejpam-4254	544	3	and	and	CCONJ
ejpam-4254	544	4	e(νp	e(νp	PROPN
ejpam-4254	544	5	,	,	PUNCT
ejpam-4254	544	6	νp(0	νp(0	NOUN
ejpam-4254	544	7	)	)	PUNCT
ejpam-4254	544	8	)	)	PUNCT
ejpam-4254	545	1	=	=	SYM
ejpam-4254	545	2	u	u	NOUN
ejpam-4254	545	3	.	.	PUNCT
ejpam-4254	546	1	we	we	PRON
ejpam-4254	546	2	consider	consider	VERB
ejpam-4254	546	3	(	(	PUNCT
ejpam-4254	546	4	∀a	∀a	NOUN
ejpam-4254	546	5	∈	∈	PROPN
ejpam-4254	546	6	u	u	NOUN
ejpam-4254	546	7	)	)	PUNCT
ejpam-4254	546	8	(	(	PUNCT
ejpam-4254	546	9	µp(a	µp(a	NUM
ejpam-4254	546	10	)	)	PUNCT
ejpam-4254	546	11	=	=	SYM
ejpam-4254	546	12	µp(0	µp(0	NOUN
ejpam-4254	546	13	)	)	PUNCT
ejpam-4254	546	14	νp(a	νp(a	NUM
ejpam-4254	546	15	)	)	PUNCT
ejpam-4254	546	16	=	=	SYM
ejpam-4254	546	17	νp(0	νp(0	NOUN
ejpam-4254	546	18	)	)	PUNCT
ejpam-4254	546	19	)	)	PUNCT
ejpam-4254	546	20	.	.	PUNCT
ejpam-4254	547	1	a.	a.	PROPN
ejpam-4254	547	2	iampan	iampan	PROPN
ejpam-4254	547	3	et	et	PROPN
ejpam-4254	547	4	al	al	PROPN
ejpam-4254	547	5	.	.	PUNCT
ejpam-4254	547	6	/	/	SYM
ejpam-4254	547	7	eur	eur	PROPN
ejpam-4254	547	8	.	.	PUNCT
ejpam-4254	548	1	j.	j.	PROPN
ejpam-4254	548	2	pure	pure	PROPN
ejpam-4254	548	3	appl	appl	PROPN
ejpam-4254	548	4	.	.	PROPN
ejpam-4254	548	5	math	math	PROPN
ejpam-4254	548	6	,	,	PUNCT
ejpam-4254	548	7	15	15	NUM
ejpam-4254	548	8	(	(	PUNCT
ejpam-4254	548	9	1	1	NUM
ejpam-4254	548	10	)	)	PUNCT
ejpam-4254	548	11	(	(	PUNCT
ejpam-4254	548	12	2022	2022	NUM
ejpam-4254	548	13	)	)	PUNCT
ejpam-4254	548	14	,	,	PUNCT
ejpam-4254	548	15	169	169	NUM
ejpam-4254	548	16	-	-	SYM
ejpam-4254	548	17	198	198	NUM
ejpam-4254	548	18	191	191	NUM
ejpam-4254	548	19	thus	thus	ADV
ejpam-4254	548	20	p	p	NOUN
ejpam-4254	548	21	is	be	AUX
ejpam-4254	548	22	constant	constant	ADJ
ejpam-4254	548	23	,	,	PUNCT
ejpam-4254	548	24	that	that	ADV
ejpam-4254	548	25	is	is	ADV
ejpam-4254	548	26	,	,	PUNCT
ejpam-4254	548	27	p	p	PRON
ejpam-4254	548	28	is	be	AUX
ejpam-4254	548	29	a	a	DET
ejpam-4254	548	30	pfsupi	pfsupi	NOUN
ejpam-4254	548	31	of	of	ADP
ejpam-4254	548	32	u	u	NOUN
ejpam-4254	548	33	.	.	PUNCT
ejpam-4254	549	1	the	the	DET
ejpam-4254	549	2	following	follow	VERB
ejpam-4254	549	3	lemma	lemma	PROPN
ejpam-4254	549	4	shows	show	VERB
ejpam-4254	549	5	the	the	DET
ejpam-4254	549	6	relationships	relationship	NOUN
ejpam-4254	549	7	between	between	ADP
ejpam-4254	549	8	t	t	NOUN
ejpam-4254	549	9	-	-	PUNCT
ejpam-4254	549	10	level	level	NOUN
ejpam-4254	549	11	subsets	subset	NOUN
ejpam-4254	549	12	of	of	ADP
ejpam-4254	549	13	approximations	approximation	NOUN
ejpam-4254	549	14	and	and	CCONJ
ejpam-4254	549	15	approximations	approximation	NOUN
ejpam-4254	549	16	of	of	ADP
ejpam-4254	549	17	t	t	NOUN
ejpam-4254	549	18	-	-	PUNCT
ejpam-4254	549	19	level	level	NOUN
ejpam-4254	549	20	subsets	subset	NOUN
ejpam-4254	549	21	.	.	PUNCT
ejpam-4254	550	1	lemma	lemma	PROPN
ejpam-4254	550	2	1	1	X
ejpam-4254	550	3	.	.	PUNCT
ejpam-4254	551	1	let	let	VERB
ejpam-4254	551	2	ρ	ρ	NOUN
ejpam-4254	551	3	be	be	AUX
ejpam-4254	551	4	a	a	DET
ejpam-4254	551	5	cr	cr	NOUN
ejpam-4254	551	6	on	on	ADP
ejpam-4254	551	7	u	u	PROPN
ejpam-4254	551	8	and	and	CCONJ
ejpam-4254	551	9	t	t	PROPN
ejpam-4254	551	10	∈	∈	PROPN
ejpam-4254	552	1	[	[	X
ejpam-4254	552	2	0	0	NUM
ejpam-4254	552	3	,	,	PUNCT
ejpam-4254	552	4	1	1	NUM
ejpam-4254	552	5	]	]	PUNCT
ejpam-4254	552	6	.	.	PUNCT
ejpam-4254	553	1	then	then	ADV
ejpam-4254	553	2	the	the	DET
ejpam-4254	553	3	following	following	ADJ
ejpam-4254	553	4	statements	statement	NOUN
ejpam-4254	553	5	hold	hold	VERB
ejpam-4254	553	6	:	:	PUNCT
ejpam-4254	553	7	(	(	PUNCT
ejpam-4254	553	8	1	1	X
ejpam-4254	553	9	)	)	PUNCT
ejpam-4254	553	10	u(µp	u(µp	PROPN
ejpam-4254	553	11	,	,	PUNCT
ejpam-4254	553	12	t	t	PROPN
ejpam-4254	553	13	)	)	PUNCT
ejpam-4254	553	14	=	=	PUNCT
ejpam-4254	554	1	ρ−(u(µp	ρ−(u(µp	PROPN
ejpam-4254	554	2	,	,	PUNCT
ejpam-4254	554	3	t	t	PROPN
ejpam-4254	554	4	)	)	PUNCT
ejpam-4254	554	5	)	)	PUNCT
ejpam-4254	554	6	,	,	PUNCT
ejpam-4254	554	7	(	(	PUNCT
ejpam-4254	554	8	2	2	X
ejpam-4254	554	9	)	)	PUNCT
ejpam-4254	554	10	u+(µp	u+(µp	NOUN
ejpam-4254	554	11	,	,	PUNCT
ejpam-4254	554	12	t	t	PROPN
ejpam-4254	554	13	)	)	PUNCT
ejpam-4254	554	14	=	=	SYM
ejpam-4254	555	1	ρ−(u+(µp	ρ−(u+(µp	PROPN
ejpam-4254	555	2	,	,	PUNCT
ejpam-4254	555	3	t	t	PROPN
ejpam-4254	555	4	)	)	PUNCT
ejpam-4254	555	5	)	)	PUNCT
ejpam-4254	555	6	,	,	PUNCT
ejpam-4254	555	7	(	(	PUNCT
ejpam-4254	555	8	3	3	X
ejpam-4254	555	9	)	)	PUNCT
ejpam-4254	555	10	l(νp	l(νp	PROPN
ejpam-4254	555	11	,	,	PUNCT
ejpam-4254	555	12	t	t	PROPN
ejpam-4254	555	13	)	)	PUNCT
ejpam-4254	555	14	=	=	SYM
ejpam-4254	556	1	ρ+(l(νp	ρ+(l(νp	PROPN
ejpam-4254	556	2	,	,	PUNCT
ejpam-4254	556	3	t	t	PROPN
ejpam-4254	556	4	)	)	PUNCT
ejpam-4254	556	5	)	)	PUNCT
ejpam-4254	556	6	,	,	PUNCT
ejpam-4254	556	7	(	(	PUNCT
ejpam-4254	556	8	4	4	X
ejpam-4254	556	9	)	)	PUNCT
ejpam-4254	556	10	l−(νp	l−(νp	PROPN
ejpam-4254	556	11	,	,	PUNCT
ejpam-4254	556	12	t	t	PROPN
ejpam-4254	556	13	)	)	PUNCT
ejpam-4254	556	14	=	=	SYM
ejpam-4254	557	1	ρ+(l−(νp	ρ+(l−(νp	PROPN
ejpam-4254	557	2	,	,	PUNCT
ejpam-4254	557	3	t	t	PROPN
ejpam-4254	557	4	)	)	PUNCT
ejpam-4254	557	5	)	)	PUNCT
ejpam-4254	557	6	,	,	PUNCT
ejpam-4254	557	7	(	(	PUNCT
ejpam-4254	557	8	5	5	X
ejpam-4254	557	9	)	)	PUNCT
ejpam-4254	557	10	u(µ	u(µ	PROPN
ejpam-4254	557	11	p	p	NOUN
ejpam-4254	557	12	,	,	PUNCT
ejpam-4254	557	13	t	t	PROPN
ejpam-4254	557	14	)	)	PUNCT
ejpam-4254	557	15	=	=	PUNCT
ejpam-4254	558	1	ρ+(u(µp	ρ+(u(µp	NOUN
ejpam-4254	558	2	,	,	PUNCT
ejpam-4254	558	3	t	t	NOUN
ejpam-4254	558	4	)	)	PUNCT
ejpam-4254	558	5	)	)	PUNCT
ejpam-4254	558	6	,	,	PUNCT
ejpam-4254	558	7	(	(	PUNCT
ejpam-4254	558	8	6	6	X
ejpam-4254	558	9	)	)	PUNCT
ejpam-4254	558	10	u+(µ	u+(µ	PROPN
ejpam-4254	558	11	p	p	PROPN
ejpam-4254	558	12	,	,	PUNCT
ejpam-4254	558	13	t	t	PROPN
ejpam-4254	558	14	)	)	PUNCT
ejpam-4254	558	15	=	=	SYM
ejpam-4254	559	1	ρ+(u+(µp	ρ+(u+(µp	PROPN
ejpam-4254	559	2	,	,	PUNCT
ejpam-4254	559	3	t	t	PROPN
ejpam-4254	559	4	)	)	PUNCT
ejpam-4254	559	5	)	)	PUNCT
ejpam-4254	559	6	,	,	PUNCT
ejpam-4254	559	7	(	(	PUNCT
ejpam-4254	559	8	7	7	X
ejpam-4254	559	9	)	)	PUNCT
ejpam-4254	559	10	l(νp	l(νp	PROPN
ejpam-4254	559	11	,	,	PUNCT
ejpam-4254	559	12	t	t	PROPN
ejpam-4254	559	13	)	)	PUNCT
ejpam-4254	559	14	=	=	SYM
ejpam-4254	560	1	ρ−(l(νp	ρ−(l(νp	PROPN
ejpam-4254	560	2	,	,	PUNCT
ejpam-4254	560	3	t	t	PROPN
ejpam-4254	560	4	)	)	PUNCT
ejpam-4254	560	5	)	)	PUNCT
ejpam-4254	560	6	,	,	PUNCT
ejpam-4254	560	7	and	and	CCONJ
ejpam-4254	560	8	(	(	PUNCT
ejpam-4254	560	9	8)	8)	NUM
ejpam-4254	560	10	l−(νp	l−(νp	PROPN
ejpam-4254	560	11	,	,	PUNCT
ejpam-4254	560	12	t	t	PROPN
ejpam-4254	560	13	)	)	PUNCT
ejpam-4254	560	14	=	=	SYM
ejpam-4254	561	1	ρ−(l−(νp	ρ−(l−(νp	X
ejpam-4254	561	2	,	,	PUNCT
ejpam-4254	561	3	t	t	PROPN
ejpam-4254	561	4	)	)	PUNCT
ejpam-4254	561	5	)	)	PUNCT
ejpam-4254	561	6	.	.	PUNCT
ejpam-4254	562	1	proof	proof	NOUN
ejpam-4254	562	2	.	.	PUNCT
ejpam-4254	563	1	(	(	PUNCT
ejpam-4254	563	2	1	1	X
ejpam-4254	563	3	)	)	PUNCT
ejpam-4254	563	4	let	let	VERB
ejpam-4254	563	5	a	a	DET
ejpam-4254	563	6	∈	∈	PROPN
ejpam-4254	563	7	u	u	NOUN
ejpam-4254	563	8	.	.	PUNCT
ejpam-4254	564	1	then	then	ADV
ejpam-4254	564	2	a	a	DET
ejpam-4254	564	3	∈	∈	PROPN
ejpam-4254	564	4	u(µp	u(µp	NOUN
ejpam-4254	564	5	,	,	PUNCT
ejpam-4254	564	6	t	t	PROPN
ejpam-4254	564	7	)	)	PUNCT
ejpam-4254	564	8	⇔	⇔	NOUN
ejpam-4254	564	9	µp(a	µp(a	NUM
ejpam-4254	564	10	)	)	PUNCT
ejpam-4254	564	11	≥	≥	NOUN
ejpam-4254	564	12	t	t	PROPN
ejpam-4254	564	13	(	(	PUNCT
ejpam-4254	564	14	definition	definition	NOUN
ejpam-4254	564	15	12	12	NUM
ejpam-4254	564	16	)	)	PUNCT
ejpam-4254	564	17	⇔	⇔	PROPN
ejpam-4254	564	18	sup	sup	NOUN
ejpam-4254	564	19	u∈(a)ρ	u∈(a)ρ	PROPN
ejpam-4254	564	20	{	{	PUNCT
ejpam-4254	564	21	µp(u	µp(u	NOUN
ejpam-4254	564	22	)	)	PUNCT
ejpam-4254	564	23	}	}	PUNCT
ejpam-4254	564	24	≥	≥	PROPN
ejpam-4254	564	25	t	t	PROPN
ejpam-4254	564	26	(	(	PUNCT
ejpam-4254	564	27	definition	definition	NOUN
ejpam-4254	564	28	9	9	NUM
ejpam-4254	564	29	)	)	PUNCT
ejpam-4254	564	30	⇔	⇔	PROPN
ejpam-4254	564	31	∃a	∃a	NOUN
ejpam-4254	564	32	∈	∈	PROPN
ejpam-4254	564	33	(	(	PUNCT
ejpam-4254	564	34	a)ρ	a)ρ	NOUN
ejpam-4254	564	35	,	,	PUNCT
ejpam-4254	564	36	µp(u	µp(u	NOUN
ejpam-4254	564	37	)	)	PUNCT
ejpam-4254	564	38	≥	≥	PROPN
ejpam-4254	564	39	t	t	PROPN
ejpam-4254	564	40	⇔	⇔	PROPN
ejpam-4254	564	41	∃a	∃a	PROPN
ejpam-4254	564	42	∈	∈	PROPN
ejpam-4254	564	43	(	(	PUNCT
ejpam-4254	564	44	a)ρ	a)ρ	NOUN
ejpam-4254	564	45	∩	∩	NOUN
ejpam-4254	564	46	u(µp	u(µp	NOUN
ejpam-4254	564	47	,	,	PUNCT
ejpam-4254	564	48	t	t	PROPN
ejpam-4254	564	49	)	)	PUNCT
ejpam-4254	564	50	̸=	̸=	PROPN
ejpam-4254	564	51	∅	∅	NOUN
ejpam-4254	564	52	(	(	PUNCT
ejpam-4254	564	53	definition	definition	NOUN
ejpam-4254	564	54	12	12	NUM
ejpam-4254	564	55	)	)	PUNCT
ejpam-4254	564	56	⇔	⇔	NOUN
ejpam-4254	564	57	a	a	DET
ejpam-4254	564	58	∈	∈	PROPN
ejpam-4254	564	59	ρ−(u(µp	ρ−(u(µp	NUM
ejpam-4254	564	60	,	,	PUNCT
ejpam-4254	564	61	t	t	PROPN
ejpam-4254	564	62	)	)	PUNCT
ejpam-4254	564	63	)	)	PUNCT
ejpam-4254	564	64	.	.	PUNCT
ejpam-4254	565	1	(	(	PUNCT
ejpam-4254	565	2	definition	definition	NOUN
ejpam-4254	565	3	7	7	NUM
ejpam-4254	565	4	)	)	PUNCT
ejpam-4254	565	5	(	(	PUNCT
ejpam-4254	565	6	2	2	X
ejpam-4254	565	7	)	)	PUNCT
ejpam-4254	565	8	let	let	VERB
ejpam-4254	565	9	a	a	DET
ejpam-4254	565	10	∈	∈	PROPN
ejpam-4254	565	11	u	u	NOUN
ejpam-4254	565	12	.	.	PUNCT
ejpam-4254	566	1	then	then	ADV
ejpam-4254	566	2	a	a	DET
ejpam-4254	566	3	∈	∈	PROPN
ejpam-4254	566	4	u+(µp	u+(µp	PROPN
ejpam-4254	566	5	,	,	PUNCT
ejpam-4254	566	6	t	t	PROPN
ejpam-4254	566	7	)	)	PUNCT
ejpam-4254	566	8	⇔	⇔	NOUN
ejpam-4254	566	9	µp(a	µp(a	NUM
ejpam-4254	566	10	)	)	PUNCT
ejpam-4254	566	11	>	>	X
ejpam-4254	566	12	t	t	PROPN
ejpam-4254	566	13	(	(	PUNCT
ejpam-4254	566	14	definition	definition	NOUN
ejpam-4254	566	15	12	12	NUM
ejpam-4254	566	16	)	)	PUNCT
ejpam-4254	566	17	⇔	⇔	PROPN
ejpam-4254	566	18	sup	sup	NOUN
ejpam-4254	566	19	u∈(a)ρ	u∈(a)ρ	PROPN
ejpam-4254	566	20	{	{	PUNCT
ejpam-4254	566	21	µp(u	µp(u	NOUN
ejpam-4254	566	22	)	)	PUNCT
ejpam-4254	566	23	}	}	PUNCT
ejpam-4254	566	24	>	>	X
ejpam-4254	566	25	t	t	PROPN
ejpam-4254	566	26	(	(	PUNCT
ejpam-4254	566	27	definition	definition	NOUN
ejpam-4254	566	28	9	9	NUM
ejpam-4254	566	29	)	)	PUNCT
ejpam-4254	566	30	⇔	⇔	PROPN
ejpam-4254	566	31	∃a	∃a	NOUN
ejpam-4254	566	32	∈	∈	PROPN
ejpam-4254	566	33	(	(	PUNCT
ejpam-4254	566	34	a)ρ	a)ρ	NOUN
ejpam-4254	566	35	,	,	PUNCT
ejpam-4254	566	36	µp(u	µp(u	NOUN
ejpam-4254	566	37	)	)	PUNCT
ejpam-4254	566	38	>	>	PUNCT
ejpam-4254	566	39	t	t	PROPN
ejpam-4254	566	40	⇔	⇔	PROPN
ejpam-4254	566	41	∃a	∃a	PROPN
ejpam-4254	566	42	∈	∈	PROPN
ejpam-4254	566	43	(	(	PUNCT
ejpam-4254	566	44	a)ρ	a)ρ	NOUN
ejpam-4254	566	45	∩	∩	NOUN
ejpam-4254	566	46	u+(µp	u+(µp	NOUN
ejpam-4254	566	47	,	,	PUNCT
ejpam-4254	566	48	t	t	PROPN
ejpam-4254	566	49	)	)	PUNCT
ejpam-4254	566	50	̸=	̸=	PROPN
ejpam-4254	566	51	∅	∅	NOUN
ejpam-4254	566	52	(	(	PUNCT
ejpam-4254	566	53	definition	definition	NOUN
ejpam-4254	566	54	12	12	NUM
ejpam-4254	566	55	)	)	PUNCT
ejpam-4254	566	56	⇔	⇔	NOUN
ejpam-4254	566	57	a	a	DET
ejpam-4254	566	58	∈	∈	PROPN
ejpam-4254	566	59	ρ−(u+(µp	ρ−(u+(µp	PROPN
ejpam-4254	566	60	,	,	PUNCT
ejpam-4254	566	61	t	t	PROPN
ejpam-4254	566	62	)	)	PUNCT
ejpam-4254	566	63	)	)	PUNCT
ejpam-4254	566	64	.	.	PUNCT
ejpam-4254	567	1	(	(	PUNCT
ejpam-4254	567	2	definition	definition	NOUN
ejpam-4254	567	3	7	7	NUM
ejpam-4254	567	4	)	)	PUNCT
ejpam-4254	567	5	(	(	PUNCT
ejpam-4254	567	6	3	3	X
ejpam-4254	567	7	)	)	PUNCT
ejpam-4254	567	8	let	let	VERB
ejpam-4254	567	9	a	a	DET
ejpam-4254	567	10	∈	∈	PROPN
ejpam-4254	567	11	u	u	NOUN
ejpam-4254	567	12	.	.	PUNCT
ejpam-4254	568	1	then	then	ADV
ejpam-4254	568	2	a	a	DET
ejpam-4254	568	3	∈	∈	PROPN
ejpam-4254	568	4	l(νp	l(νp	PROPN
ejpam-4254	568	5	,	,	PUNCT
ejpam-4254	568	6	t	t	PROPN
ejpam-4254	568	7	)	)	PUNCT
ejpam-4254	568	8	⇔	⇔	NOUN
ejpam-4254	568	9	νp(a	νp(a	NUM
ejpam-4254	568	10	)	)	PUNCT
ejpam-4254	568	11	≤	≤	NOUN
ejpam-4254	568	12	t	t	NOUN
ejpam-4254	568	13	(	(	PUNCT
ejpam-4254	568	14	definition	definition	NOUN
ejpam-4254	568	15	12	12	NUM
ejpam-4254	568	16	)	)	PUNCT
ejpam-4254	568	17	⇔	⇔	PROPN
ejpam-4254	568	18	inf	inf	PROPN
ejpam-4254	568	19	u∈(a)ρ	u∈(a)ρ	X
ejpam-4254	568	20	{	{	PUNCT
ejpam-4254	568	21	νp(u	νp(u	NOUN
ejpam-4254	568	22	)	)	PUNCT
ejpam-4254	568	23	}	}	PUNCT
ejpam-4254	568	24	≤	≤	PROPN
ejpam-4254	568	25	t	t	NOUN
ejpam-4254	568	26	(	(	PUNCT
ejpam-4254	568	27	definition	definition	NOUN
ejpam-4254	568	28	9	9	NUM
ejpam-4254	568	29	)	)	PUNCT
ejpam-4254	568	30	⇔	⇔	X
ejpam-4254	568	31	∀a	∀a	X
ejpam-4254	568	32	∈	∈	PROPN
ejpam-4254	568	33	(	(	PUNCT
ejpam-4254	568	34	a)ρ	a)ρ	NOUN
ejpam-4254	568	35	,	,	PUNCT
ejpam-4254	568	36	νp(u	νp(u	NUM
ejpam-4254	568	37	)	)	PUNCT
ejpam-4254	568	38	≤	≤	NOUN
ejpam-4254	569	1	t	t	PROPN
ejpam-4254	569	2	a.	a.	NOUN
ejpam-4254	569	3	iampan	iampan	PROPN
ejpam-4254	569	4	et	et	PROPN
ejpam-4254	569	5	al	al	PROPN
ejpam-4254	569	6	.	.	PUNCT
ejpam-4254	569	7	/	/	SYM
ejpam-4254	569	8	eur	eur	PROPN
ejpam-4254	569	9	.	.	PUNCT
ejpam-4254	570	1	j.	j.	PROPN
ejpam-4254	570	2	pure	pure	PROPN
ejpam-4254	570	3	appl	appl	PROPN
ejpam-4254	570	4	.	.	PROPN
ejpam-4254	570	5	math	math	PROPN
ejpam-4254	570	6	,	,	PUNCT
ejpam-4254	570	7	15	15	NUM
ejpam-4254	570	8	(	(	PUNCT
ejpam-4254	570	9	1	1	NUM
ejpam-4254	570	10	)	)	PUNCT
ejpam-4254	570	11	(	(	PUNCT
ejpam-4254	570	12	2022	2022	NUM
ejpam-4254	570	13	)	)	PUNCT
ejpam-4254	570	14	,	,	PUNCT
ejpam-4254	570	15	169	169	NUM
ejpam-4254	570	16	-	-	SYM
ejpam-4254	570	17	198	198	NUM
ejpam-4254	570	18	192	192	NUM
ejpam-4254	570	19	⇔	⇔	NUM
ejpam-4254	570	20	∀a	∀a	NOUN
ejpam-4254	570	21	∈	∈	NOUN
ejpam-4254	570	22	(	(	PUNCT
ejpam-4254	570	23	a)ρ	a)ρ	NOUN
ejpam-4254	570	24	,	,	PUNCT
ejpam-4254	570	25	a	a	DET
ejpam-4254	570	26	∈	∈	PROPN
ejpam-4254	570	27	l(νp	l(νp	PROPN
ejpam-4254	570	28	,	,	PUNCT
ejpam-4254	570	29	t	t	PROPN
ejpam-4254	570	30	)	)	PUNCT
ejpam-4254	570	31	(	(	PUNCT
ejpam-4254	570	32	definition	definition	NOUN
ejpam-4254	570	33	12	12	NUM
ejpam-4254	570	34	)	)	PUNCT
ejpam-4254	570	35	⇔	⇔	NOUN
ejpam-4254	570	36	(	(	PUNCT
ejpam-4254	570	37	a)ρ	a)ρ	NOUN
ejpam-4254	570	38	⊆	⊆	NUM
ejpam-4254	570	39	l(νp	l(νp	ADJ
ejpam-4254	570	40	,	,	PUNCT
ejpam-4254	570	41	t	t	PROPN
ejpam-4254	570	42	)	)	PUNCT
ejpam-4254	570	43	⇔	⇔	NOUN
ejpam-4254	570	44	a	a	DET
ejpam-4254	570	45	∈	∈	PROPN
ejpam-4254	570	46	ρ+(l(νp	ρ+(l(νp	PROPN
ejpam-4254	570	47	,	,	PUNCT
ejpam-4254	570	48	t	t	PROPN
ejpam-4254	570	49	)	)	PUNCT
ejpam-4254	570	50	)	)	PUNCT
ejpam-4254	570	51	.	.	PUNCT
ejpam-4254	571	1	(	(	PUNCT
ejpam-4254	571	2	definition	definition	NOUN
ejpam-4254	571	3	7	7	NUM
ejpam-4254	571	4	)	)	PUNCT
ejpam-4254	571	5	(	(	PUNCT
ejpam-4254	571	6	4	4	X
ejpam-4254	571	7	)	)	PUNCT
ejpam-4254	571	8	let	let	VERB
ejpam-4254	571	9	a	a	DET
ejpam-4254	571	10	∈	∈	PROPN
ejpam-4254	571	11	u	u	NOUN
ejpam-4254	571	12	.	.	PUNCT
ejpam-4254	572	1	then	then	ADV
ejpam-4254	572	2	a	a	DET
ejpam-4254	572	3	∈	∈	PROPN
ejpam-4254	572	4	l−(νp	l−(νp	PROPN
ejpam-4254	572	5	,	,	PUNCT
ejpam-4254	572	6	t	t	PROPN
ejpam-4254	572	7	)	)	PUNCT
ejpam-4254	572	8	⇔	⇔	NOUN
ejpam-4254	572	9	νp(a	νp(a	NUM
ejpam-4254	572	10	)	)	PUNCT
ejpam-4254	572	11	<	<	X
ejpam-4254	572	12	t	t	PROPN
ejpam-4254	572	13	(	(	PUNCT
ejpam-4254	572	14	definition	definition	NOUN
ejpam-4254	572	15	12	12	NUM
ejpam-4254	572	16	)	)	PUNCT
ejpam-4254	572	17	⇔	⇔	PROPN
ejpam-4254	572	18	inf	inf	PROPN
ejpam-4254	572	19	u∈(a)ρ	u∈(a)ρ	X
ejpam-4254	572	20	{	{	PUNCT
ejpam-4254	572	21	νp(u	νp(u	NOUN
ejpam-4254	572	22	)	)	PUNCT
ejpam-4254	572	23	}	}	PUNCT
ejpam-4254	572	24	<	<	X
ejpam-4254	572	25	t	t	PROPN
ejpam-4254	572	26	(	(	PUNCT
ejpam-4254	572	27	definition	definition	NOUN
ejpam-4254	572	28	9	9	NUM
ejpam-4254	572	29	)	)	PUNCT
ejpam-4254	572	30	⇔	⇔	X
ejpam-4254	572	31	∀a	∀a	X
ejpam-4254	572	32	∈	∈	PROPN
ejpam-4254	572	33	(	(	PUNCT
ejpam-4254	572	34	a)ρ	a)ρ	NOUN
ejpam-4254	572	35	,	,	PUNCT
ejpam-4254	572	36	νp(u	νp(u	NUM
ejpam-4254	572	37	)	)	PUNCT
ejpam-4254	572	38	<	<	X
ejpam-4254	572	39	t	t	PROPN
ejpam-4254	572	40	⇔	⇔	X
ejpam-4254	572	41	∀a	∀a	X
ejpam-4254	572	42	∈	∈	PROPN
ejpam-4254	572	43	(	(	PUNCT
ejpam-4254	572	44	a)ρ	a)ρ	NOUN
ejpam-4254	572	45	,	,	PUNCT
ejpam-4254	572	46	a	a	DET
ejpam-4254	572	47	∈	∈	PROPN
ejpam-4254	572	48	l−(νp	l−(νp	PROPN
ejpam-4254	572	49	,	,	PUNCT
ejpam-4254	572	50	t	t	PROPN
ejpam-4254	572	51	)	)	PUNCT
ejpam-4254	572	52	(	(	PUNCT
ejpam-4254	572	53	definition	definition	NOUN
ejpam-4254	572	54	12	12	NUM
ejpam-4254	572	55	)	)	PUNCT
ejpam-4254	572	56	⇔	⇔	NOUN
ejpam-4254	572	57	(	(	PUNCT
ejpam-4254	572	58	a)ρ	a)ρ	NOUN
ejpam-4254	572	59	⊆	⊆	NUM
ejpam-4254	572	60	l−(νp	l−(νp	PROPN
ejpam-4254	572	61	,	,	PUNCT
ejpam-4254	572	62	t	t	PROPN
ejpam-4254	572	63	)	)	PUNCT
ejpam-4254	572	64	⇔	⇔	NOUN
ejpam-4254	572	65	a	a	DET
ejpam-4254	572	66	∈	∈	PROPN
ejpam-4254	572	67	ρ+(l−(νp	ρ+(l−(νp	PROPN
ejpam-4254	572	68	,	,	PUNCT
ejpam-4254	572	69	t	t	PROPN
ejpam-4254	572	70	)	)	PUNCT
ejpam-4254	572	71	)	)	PUNCT
ejpam-4254	572	72	.	.	PUNCT
ejpam-4254	573	1	(	(	PUNCT
ejpam-4254	573	2	definition	definition	NOUN
ejpam-4254	573	3	7	7	NUM
ejpam-4254	573	4	)	)	PUNCT
ejpam-4254	573	5	(	(	PUNCT
ejpam-4254	573	6	5	5	X
ejpam-4254	573	7	)	)	PUNCT
ejpam-4254	573	8	let	let	VERB
ejpam-4254	573	9	a	a	DET
ejpam-4254	573	10	∈	∈	PROPN
ejpam-4254	573	11	u	u	NOUN
ejpam-4254	573	12	.	.	PUNCT
ejpam-4254	574	1	then	then	ADV
ejpam-4254	574	2	a	a	DET
ejpam-4254	574	3	∈	∈	PROPN
ejpam-4254	574	4	u(µ	u(µ	PROPN
ejpam-4254	574	5	p	p	NOUN
ejpam-4254	574	6	,	,	PUNCT
ejpam-4254	574	7	t	t	PROPN
ejpam-4254	574	8	)	)	PUNCT
ejpam-4254	574	9	⇔	⇔	PROPN
ejpam-4254	574	10	µ	µ	X
ejpam-4254	574	11	p	p	X
ejpam-4254	574	12	(	(	PUNCT
ejpam-4254	574	13	a	a	NOUN
ejpam-4254	574	14	)	)	PUNCT
ejpam-4254	574	15	≥	≥	NOUN
ejpam-4254	574	16	t	t	PROPN
ejpam-4254	574	17	(	(	PUNCT
ejpam-4254	574	18	definition	definition	NOUN
ejpam-4254	574	19	12	12	NUM
ejpam-4254	574	20	)	)	PUNCT
ejpam-4254	574	21	⇔	⇔	PROPN
ejpam-4254	574	22	inf	inf	PROPN
ejpam-4254	574	23	u∈(a)ρ	u∈(a)ρ	X
ejpam-4254	574	24	{	{	PUNCT
ejpam-4254	574	25	µp(u	µp(u	NOUN
ejpam-4254	574	26	)	)	PUNCT
ejpam-4254	574	27	}	}	PUNCT
ejpam-4254	574	28	≥	≥	PROPN
ejpam-4254	574	29	t	t	PROPN
ejpam-4254	574	30	(	(	PUNCT
ejpam-4254	574	31	definition	definition	NOUN
ejpam-4254	574	32	9	9	NUM
ejpam-4254	574	33	)	)	PUNCT
ejpam-4254	574	34	⇔	⇔	X
ejpam-4254	574	35	∀a	∀a	X
ejpam-4254	574	36	∈	∈	PROPN
ejpam-4254	574	37	(	(	PUNCT
ejpam-4254	574	38	a)ρ	a)ρ	NOUN
ejpam-4254	574	39	,	,	PUNCT
ejpam-4254	574	40	µp(u	µp(u	NOUN
ejpam-4254	574	41	)	)	PUNCT
ejpam-4254	574	42	≥	≥	PROPN
ejpam-4254	574	43	t	t	PROPN
ejpam-4254	574	44	⇔	⇔	X
ejpam-4254	574	45	∀a	∀a	X
ejpam-4254	574	46	∈	∈	PROPN
ejpam-4254	574	47	(	(	PUNCT
ejpam-4254	574	48	a)ρ	a)ρ	NOUN
ejpam-4254	574	49	,	,	PUNCT
ejpam-4254	574	50	a	a	DET
ejpam-4254	574	51	∈	∈	PROPN
ejpam-4254	574	52	u(µp	u(µp	NOUN
ejpam-4254	574	53	,	,	PUNCT
ejpam-4254	574	54	t	t	PROPN
ejpam-4254	574	55	)	)	PUNCT
ejpam-4254	574	56	(	(	PUNCT
ejpam-4254	574	57	definition	definition	NOUN
ejpam-4254	574	58	12	12	NUM
ejpam-4254	574	59	)	)	PUNCT
ejpam-4254	574	60	⇔	⇔	NOUN
ejpam-4254	574	61	(	(	PUNCT
ejpam-4254	574	62	a)ρ	a)ρ	NOUN
ejpam-4254	574	63	⊆	⊆	NUM
ejpam-4254	574	64	u(µp	u(µp	NOUN
ejpam-4254	574	65	,	,	PUNCT
ejpam-4254	574	66	t	t	PROPN
ejpam-4254	574	67	)	)	PUNCT
ejpam-4254	574	68	⇔	⇔	NOUN
ejpam-4254	574	69	a	a	DET
ejpam-4254	574	70	∈	∈	PROPN
ejpam-4254	574	71	ρ+(u(µp	ρ+(u(µp	NOUN
ejpam-4254	574	72	,	,	PUNCT
ejpam-4254	574	73	t	t	PROPN
ejpam-4254	574	74	)	)	PUNCT
ejpam-4254	574	75	)	)	PUNCT
ejpam-4254	574	76	.	.	PUNCT
ejpam-4254	575	1	(	(	PUNCT
ejpam-4254	575	2	definition	definition	NOUN
ejpam-4254	575	3	7	7	NUM
ejpam-4254	575	4	)	)	PUNCT
ejpam-4254	575	5	(	(	PUNCT
ejpam-4254	575	6	6	6	X
ejpam-4254	575	7	)	)	PUNCT
ejpam-4254	575	8	let	let	VERB
ejpam-4254	575	9	a	a	DET
ejpam-4254	575	10	∈	∈	PROPN
ejpam-4254	575	11	u	u	NOUN
ejpam-4254	575	12	.	.	PUNCT
ejpam-4254	576	1	then	then	ADV
ejpam-4254	576	2	a	a	DET
ejpam-4254	576	3	∈	∈	PROPN
ejpam-4254	576	4	u+(µ	u+(µ	X
ejpam-4254	576	5	p	p	X
ejpam-4254	576	6	,	,	PUNCT
ejpam-4254	576	7	t	t	PROPN
ejpam-4254	576	8	)	)	PUNCT
ejpam-4254	576	9	⇔	⇔	PROPN
ejpam-4254	576	10	µ	µ	X
ejpam-4254	576	11	p	p	X
ejpam-4254	576	12	(	(	PUNCT
ejpam-4254	576	13	a	a	NOUN
ejpam-4254	576	14	)	)	PUNCT
ejpam-4254	576	15	>	>	X
ejpam-4254	577	1	t	t	PROPN
ejpam-4254	577	2	(	(	PUNCT
ejpam-4254	577	3	definition	definition	NOUN
ejpam-4254	577	4	12	12	NUM
ejpam-4254	577	5	)	)	PUNCT
ejpam-4254	577	6	⇔	⇔	PROPN
ejpam-4254	577	7	inf	inf	PROPN
ejpam-4254	577	8	u∈(a)ρ	u∈(a)ρ	X
ejpam-4254	577	9	{	{	PUNCT
ejpam-4254	577	10	µp(u	µp(u	NOUN
ejpam-4254	577	11	)	)	PUNCT
ejpam-4254	577	12	}	}	PUNCT
ejpam-4254	577	13	>	>	X
ejpam-4254	577	14	t	t	PROPN
ejpam-4254	577	15	(	(	PUNCT
ejpam-4254	577	16	definition	definition	NOUN
ejpam-4254	577	17	9	9	NUM
ejpam-4254	577	18	)	)	PUNCT
ejpam-4254	577	19	⇔	⇔	X
ejpam-4254	577	20	∀a	∀a	X
ejpam-4254	577	21	∈	∈	PROPN
ejpam-4254	577	22	(	(	PUNCT
ejpam-4254	577	23	a)ρ	a)ρ	NOUN
ejpam-4254	577	24	,	,	PUNCT
ejpam-4254	577	25	µp(u	µp(u	NOUN
ejpam-4254	577	26	)	)	PUNCT
ejpam-4254	577	27	>	>	PUNCT
ejpam-4254	577	28	t	t	PROPN
ejpam-4254	577	29	⇔	⇔	X
ejpam-4254	577	30	∀a	∀a	X
ejpam-4254	577	31	∈	∈	PROPN
ejpam-4254	577	32	(	(	PUNCT
ejpam-4254	577	33	a)ρ	a)ρ	NOUN
ejpam-4254	577	34	,	,	PUNCT
ejpam-4254	577	35	a	a	DET
ejpam-4254	577	36	∈	∈	NOUN
ejpam-4254	577	37	u+(µp	u+(µp	PROPN
ejpam-4254	577	38	,	,	PUNCT
ejpam-4254	577	39	t	t	PROPN
ejpam-4254	577	40	)	)	PUNCT
ejpam-4254	577	41	(	(	PUNCT
ejpam-4254	577	42	definition	definition	NOUN
ejpam-4254	577	43	12	12	NUM
ejpam-4254	577	44	)	)	PUNCT
ejpam-4254	577	45	⇔	⇔	NOUN
ejpam-4254	577	46	(	(	PUNCT
ejpam-4254	577	47	a)ρ	a)ρ	NOUN
ejpam-4254	577	48	⊆	⊆	NUM
ejpam-4254	577	49	u+(µp	u+(µp	NOUN
ejpam-4254	577	50	,	,	PUNCT
ejpam-4254	577	51	t	t	PROPN
ejpam-4254	577	52	)	)	PUNCT
ejpam-4254	577	53	⇔	⇔	NOUN
ejpam-4254	577	54	a	a	DET
ejpam-4254	577	55	∈	∈	PROPN
ejpam-4254	577	56	ρ+(u+(µp	ρ+(u+(µp	PROPN
ejpam-4254	577	57	,	,	PUNCT
ejpam-4254	577	58	t	t	PROPN
ejpam-4254	577	59	)	)	PUNCT
ejpam-4254	577	60	)	)	PUNCT
ejpam-4254	577	61	.	.	PUNCT
ejpam-4254	578	1	(	(	PUNCT
ejpam-4254	578	2	definition	definition	NOUN
ejpam-4254	578	3	7	7	NUM
ejpam-4254	578	4	)	)	PUNCT
ejpam-4254	578	5	(	(	PUNCT
ejpam-4254	578	6	7	7	X
ejpam-4254	578	7	)	)	PUNCT
ejpam-4254	578	8	let	let	VERB
ejpam-4254	578	9	a	a	DET
ejpam-4254	578	10	∈	∈	PROPN
ejpam-4254	578	11	u	u	NOUN
ejpam-4254	578	12	.	.	PUNCT
ejpam-4254	579	1	then	then	ADV
ejpam-4254	579	2	a	a	DET
ejpam-4254	579	3	∈	∈	PROPN
ejpam-4254	579	4	l(νp	l(νp	PROPN
ejpam-4254	579	5	,	,	PUNCT
ejpam-4254	579	6	t	t	PROPN
ejpam-4254	579	7	)	)	PUNCT
ejpam-4254	579	8	⇔	⇔	NOUN
ejpam-4254	579	9	νp(a	νp(a	NUM
ejpam-4254	579	10	)	)	PUNCT
ejpam-4254	579	11	≤	≤	NOUN
ejpam-4254	579	12	t	t	NOUN
ejpam-4254	579	13	(	(	PUNCT
ejpam-4254	579	14	definition	definition	NOUN
ejpam-4254	579	15	12	12	NUM
ejpam-4254	579	16	)	)	PUNCT
ejpam-4254	579	17	⇔	⇔	PROPN
ejpam-4254	579	18	sup	sup	NOUN
ejpam-4254	579	19	u∈(a)ρ	u∈(a)ρ	PROPN
ejpam-4254	579	20	{	{	PUNCT
ejpam-4254	579	21	νp(u	νp(u	NOUN
ejpam-4254	579	22	)	)	PUNCT
ejpam-4254	579	23	}	}	PUNCT
ejpam-4254	579	24	≤	≤	PROPN
ejpam-4254	579	25	t	t	NOUN
ejpam-4254	579	26	(	(	PUNCT
ejpam-4254	579	27	definition	definition	NOUN
ejpam-4254	579	28	9	9	NUM
ejpam-4254	579	29	)	)	PUNCT
ejpam-4254	579	30	⇔	⇔	PROPN
ejpam-4254	579	31	∃a	∃a	NOUN
ejpam-4254	579	32	∈	∈	PROPN
ejpam-4254	579	33	(	(	PUNCT
ejpam-4254	579	34	a)ρ	a)ρ	NOUN
ejpam-4254	579	35	,	,	PUNCT
ejpam-4254	579	36	νp(u	νp(u	NUM
ejpam-4254	579	37	)	)	PUNCT
ejpam-4254	579	38	≤	≤	NOUN
ejpam-4254	579	39	t	t	PROPN
ejpam-4254	579	40	⇔	⇔	X
ejpam-4254	579	41	∃a	∃a	PROPN
ejpam-4254	579	42	∈	∈	PROPN
ejpam-4254	579	43	(	(	PUNCT
ejpam-4254	579	44	a)ρ	a)ρ	NOUN
ejpam-4254	579	45	∩	∩	NOUN
ejpam-4254	579	46	l(νp	l(νp	PROPN
ejpam-4254	579	47	,	,	PUNCT
ejpam-4254	579	48	t	t	PROPN
ejpam-4254	579	49	)	)	PUNCT
ejpam-4254	579	50	̸=	̸=	PROPN
ejpam-4254	579	51	∅	∅	NOUN
ejpam-4254	579	52	(	(	PUNCT
ejpam-4254	579	53	definition	definition	NOUN
ejpam-4254	579	54	12	12	NUM
ejpam-4254	579	55	)	)	PUNCT
ejpam-4254	579	56	⇔	⇔	NOUN
ejpam-4254	579	57	a	a	DET
ejpam-4254	579	58	∈	∈	PROPN
ejpam-4254	579	59	ρ−(l(νp	ρ−(l(νp	PROPN
ejpam-4254	579	60	,	,	PUNCT
ejpam-4254	579	61	t	t	PROPN
ejpam-4254	579	62	)	)	PUNCT
ejpam-4254	579	63	)	)	PUNCT
ejpam-4254	579	64	.	.	PUNCT
ejpam-4254	580	1	(	(	PUNCT
ejpam-4254	580	2	definition	definition	NOUN
ejpam-4254	580	3	7	7	NUM
ejpam-4254	580	4	)	)	PUNCT
ejpam-4254	580	5	a.	a.	NOUN
ejpam-4254	580	6	iampan	iampan	NOUN
ejpam-4254	580	7	et	et	PROPN
ejpam-4254	580	8	al	al	PROPN
ejpam-4254	580	9	.	.	PUNCT
ejpam-4254	580	10	/	/	SYM
ejpam-4254	580	11	eur	eur	PROPN
ejpam-4254	580	12	.	.	PUNCT
ejpam-4254	581	1	j.	j.	PROPN
ejpam-4254	581	2	pure	pure	PROPN
ejpam-4254	581	3	appl	appl	PROPN
ejpam-4254	581	4	.	.	PROPN
ejpam-4254	581	5	math	math	PROPN
ejpam-4254	581	6	,	,	PUNCT
ejpam-4254	581	7	15	15	NUM
ejpam-4254	581	8	(	(	PUNCT
ejpam-4254	581	9	1	1	NUM
ejpam-4254	581	10	)	)	PUNCT
ejpam-4254	581	11	(	(	PUNCT
ejpam-4254	581	12	2022	2022	NUM
ejpam-4254	581	13	)	)	PUNCT
ejpam-4254	581	14	,	,	PUNCT
ejpam-4254	581	15	169	169	NUM
ejpam-4254	581	16	-	-	SYM
ejpam-4254	581	17	198	198	NUM
ejpam-4254	581	18	193	193	NUM
ejpam-4254	581	19	(	(	PUNCT
ejpam-4254	581	20	8)	8)	NUM
ejpam-4254	581	21	let	let	VERB
ejpam-4254	581	22	a	a	DET
ejpam-4254	581	23	∈	∈	PROPN
ejpam-4254	581	24	u	u	NOUN
ejpam-4254	581	25	.	.	PUNCT
ejpam-4254	582	1	then	then	ADV
ejpam-4254	582	2	a	a	DET
ejpam-4254	582	3	∈	∈	PROPN
ejpam-4254	582	4	l−(νp	l−(νp	PROPN
ejpam-4254	582	5	,	,	PUNCT
ejpam-4254	582	6	t	t	PROPN
ejpam-4254	582	7	)	)	PUNCT
ejpam-4254	582	8	⇔	⇔	NOUN
ejpam-4254	582	9	νp(a	νp(a	NUM
ejpam-4254	582	10	)	)	PUNCT
ejpam-4254	582	11	<	<	X
ejpam-4254	582	12	t	t	PROPN
ejpam-4254	582	13	(	(	PUNCT
ejpam-4254	582	14	definition	definition	NOUN
ejpam-4254	582	15	12	12	NUM
ejpam-4254	582	16	)	)	PUNCT
ejpam-4254	582	17	⇔	⇔	PROPN
ejpam-4254	582	18	sup	sup	NOUN
ejpam-4254	582	19	u∈(a)ρ	u∈(a)ρ	PROPN
ejpam-4254	582	20	{	{	PUNCT
ejpam-4254	582	21	νp(u	νp(u	NOUN
ejpam-4254	582	22	)	)	PUNCT
ejpam-4254	582	23	}	}	PUNCT
ejpam-4254	582	24	<	<	X
ejpam-4254	582	25	t	t	PROPN
ejpam-4254	582	26	(	(	PUNCT
ejpam-4254	582	27	definition	definition	NOUN
ejpam-4254	582	28	9	9	NUM
ejpam-4254	582	29	)	)	PUNCT
ejpam-4254	582	30	⇔	⇔	PROPN
ejpam-4254	582	31	∃a	∃a	NOUN
ejpam-4254	582	32	∈	∈	PROPN
ejpam-4254	582	33	(	(	PUNCT
ejpam-4254	582	34	a)ρ	a)ρ	NOUN
ejpam-4254	582	35	,	,	PUNCT
ejpam-4254	582	36	νp(u	νp(u	NUM
ejpam-4254	582	37	)	)	PUNCT
ejpam-4254	582	38	<	<	X
ejpam-4254	582	39	t	t	PROPN
ejpam-4254	582	40	⇔	⇔	PROPN
ejpam-4254	582	41	∃a	∃a	PROPN
ejpam-4254	582	42	∈	∈	PROPN
ejpam-4254	582	43	(	(	PUNCT
ejpam-4254	582	44	a)ρ	a)ρ	X
ejpam-4254	582	45	∩	∩	ADJ
ejpam-4254	582	46	l−(νp	l−(νp	PROPN
ejpam-4254	582	47	,	,	PUNCT
ejpam-4254	582	48	t	t	PROPN
ejpam-4254	582	49	)	)	PUNCT
ejpam-4254	582	50	̸=	̸=	PROPN
ejpam-4254	582	51	∅	∅	NOUN
ejpam-4254	582	52	(	(	PUNCT
ejpam-4254	582	53	definition	definition	NOUN
ejpam-4254	582	54	12	12	NUM
ejpam-4254	582	55	)	)	PUNCT
ejpam-4254	582	56	⇔	⇔	NOUN
ejpam-4254	582	57	a	a	DET
ejpam-4254	582	58	∈	∈	PROPN
ejpam-4254	582	59	ρ−(l−(νp	ρ−(l−(νp	NOUN
ejpam-4254	582	60	,	,	PUNCT
ejpam-4254	582	61	t	t	PROPN
ejpam-4254	582	62	)	)	PUNCT
ejpam-4254	582	63	)	)	PUNCT
ejpam-4254	582	64	.	.	PUNCT
ejpam-4254	583	1	(	(	PUNCT
ejpam-4254	583	2	definition	definition	NOUN
ejpam-4254	583	3	7	7	NUM
ejpam-4254	583	4	)	)	PUNCT
ejpam-4254	583	5	the	the	DET
ejpam-4254	583	6	following	follow	VERB
ejpam-4254	583	7	theorems	theorem	NOUN
ejpam-4254	583	8	show	show	VERB
ejpam-4254	583	9	the	the	DET
ejpam-4254	583	10	relationships	relationship	NOUN
ejpam-4254	583	11	between	between	ADP
ejpam-4254	583	12	rpfss	rpfss	NOUN
ejpam-4254	583	13	and	and	CCONJ
ejpam-4254	583	14	their	their	PRON
ejpam-4254	583	15	t	t	NOUN
ejpam-4254	583	16	-	-	PUNCT
ejpam-4254	583	17	level	level	NOUN
ejpam-4254	583	18	subsets	subset	NOUN
ejpam-4254	583	19	.	.	PUNCT
ejpam-4254	584	1	theorem	theorem	NOUN
ejpam-4254	584	2	13	13	NUM
ejpam-4254	584	3	.	.	PUNCT
ejpam-4254	585	1	let	let	VERB
ejpam-4254	585	2	ρ	ρ	NOUN
ejpam-4254	585	3	be	be	AUX
ejpam-4254	585	4	a	a	DET
ejpam-4254	585	5	cr	cr	NOUN
ejpam-4254	585	6	on	on	ADP
ejpam-4254	585	7	u	u	PROPN
ejpam-4254	585	8	.	.	PUNCT
ejpam-4254	586	1	then	then	ADV
ejpam-4254	586	2	p	p	PROPN
ejpam-4254	586	3	is	be	AUX
ejpam-4254	586	4	an	an	DET
ejpam-4254	586	5	uprpfups	uprpfup	NOUN
ejpam-4254	586	6	of	of	ADP
ejpam-4254	586	7	u	u	PRON
ejpam-4254	586	8	if	if	SCONJ
ejpam-4254	586	9	and	and	CCONJ
ejpam-4254	586	10	only	only	ADV
ejpam-4254	586	11	if	if	SCONJ
ejpam-4254	586	12	u(µp	u(µp	NOUN
ejpam-4254	586	13	,	,	PUNCT
ejpam-4254	586	14	t	t	PROPN
ejpam-4254	586	15	)	)	PUNCT
ejpam-4254	586	16	and	and	CCONJ
ejpam-4254	586	17	l(νp	l(νp	PROPN
ejpam-4254	586	18	,	,	PUNCT
ejpam-4254	586	19	t	t	PROPN
ejpam-4254	586	20	)	)	PUNCT
ejpam-4254	586	21	are	be	AUX
ejpam-4254	586	22	,	,	PUNCT
ejpam-4254	586	23	if	if	SCONJ
ejpam-4254	586	24	the	the	DET
ejpam-4254	586	25	sets	set	NOUN
ejpam-4254	586	26	are	be	AUX
ejpam-4254	586	27	nonempty	nonempty	ADJ
ejpam-4254	586	28	,	,	PUNCT
ejpam-4254	586	29	an	an	DET
ejpam-4254	586	30	uprups	uprup	NOUN
ejpam-4254	586	31	and	and	CCONJ
ejpam-4254	586	32	a	a	DET
ejpam-4254	586	33	lorups	lorup	NOUN
ejpam-4254	586	34	of	of	ADP
ejpam-4254	586	35	u	u	NOUN
ejpam-4254	586	36	for	for	ADP
ejpam-4254	586	37	every	every	DET
ejpam-4254	586	38	t	t	NOUN
ejpam-4254	586	39	∈	∈	PROPN
ejpam-4254	587	1	[	[	X
ejpam-4254	587	2	0	0	NUM
ejpam-4254	587	3	,	,	PUNCT
ejpam-4254	587	4	1	1	NUM
ejpam-4254	587	5	]	]	NUM
ejpam-4254	587	6	,	,	PUNCT
ejpam-4254	587	7	respectively	respectively	ADV
ejpam-4254	587	8	.	.	PUNCT
ejpam-4254	588	1	proof	proof	NOUN
ejpam-4254	588	2	.	.	PUNCT
ejpam-4254	589	1	it	it	PRON
ejpam-4254	589	2	is	be	AUX
ejpam-4254	589	3	straightforward	straightforward	ADJ
ejpam-4254	589	4	by	by	ADP
ejpam-4254	589	5	theorem	theorem	ADJ
ejpam-4254	589	6	2	2	NUM
ejpam-4254	589	7	and	and	CCONJ
ejpam-4254	589	8	lemmas	lemmas	PROPN
ejpam-4254	589	9	1	1	NUM
ejpam-4254	589	10	(	(	PUNCT
ejpam-4254	589	11	1	1	NUM
ejpam-4254	589	12	)	)	PUNCT
ejpam-4254	589	13	and	and	CCONJ
ejpam-4254	589	14	(	(	PUNCT
ejpam-4254	589	15	3	3	NUM
ejpam-4254	589	16	)	)	PUNCT
ejpam-4254	589	17	.	.	PUNCT
ejpam-4254	590	1	theorem	theorem	NOUN
ejpam-4254	590	2	14	14	NUM
ejpam-4254	590	3	.	.	PUNCT
ejpam-4254	591	1	let	let	VERB
ejpam-4254	591	2	ρ	ρ	NOUN
ejpam-4254	591	3	be	be	AUX
ejpam-4254	591	4	a	a	DET
ejpam-4254	591	5	cr	cr	NOUN
ejpam-4254	591	6	on	on	ADP
ejpam-4254	591	7	u	u	PROPN
ejpam-4254	591	8	.	.	PUNCT
ejpam-4254	592	1	then	then	ADV
ejpam-4254	592	2	p	p	PROPN
ejpam-4254	592	3	is	be	AUX
ejpam-4254	592	4	an	an	DET
ejpam-4254	592	5	uprpfups	uprpfup	NOUN
ejpam-4254	592	6	of	of	ADP
ejpam-4254	592	7	u	u	PRON
ejpam-4254	592	8	if	if	SCONJ
ejpam-4254	593	1	and	and	CCONJ
ejpam-4254	593	2	only	only	ADV
ejpam-4254	593	3	if	if	SCONJ
ejpam-4254	593	4	u+(µp	u+(µp	NOUN
ejpam-4254	593	5	,	,	PUNCT
ejpam-4254	593	6	t	t	PROPN
ejpam-4254	593	7	)	)	PUNCT
ejpam-4254	593	8	and	and	CCONJ
ejpam-4254	593	9	l−(νp	l−(νp	PROPN
ejpam-4254	593	10	,	,	PUNCT
ejpam-4254	593	11	t	t	PROPN
ejpam-4254	593	12	)	)	PUNCT
ejpam-4254	593	13	are	be	AUX
ejpam-4254	593	14	,	,	PUNCT
ejpam-4254	593	15	if	if	SCONJ
ejpam-4254	593	16	the	the	DET
ejpam-4254	593	17	sets	set	NOUN
ejpam-4254	593	18	are	be	AUX
ejpam-4254	593	19	nonempty	nonempty	ADJ
ejpam-4254	593	20	,	,	PUNCT
ejpam-4254	593	21	an	an	DET
ejpam-4254	593	22	uprups	uprup	NOUN
ejpam-4254	593	23	and	and	CCONJ
ejpam-4254	593	24	a	a	DET
ejpam-4254	593	25	lorups	lorup	NOUN
ejpam-4254	593	26	of	of	ADP
ejpam-4254	593	27	u	u	NOUN
ejpam-4254	593	28	for	for	ADP
ejpam-4254	593	29	every	every	DET
ejpam-4254	593	30	t	t	NOUN
ejpam-4254	593	31	∈	∈	PROPN
ejpam-4254	594	1	[	[	X
ejpam-4254	594	2	0	0	NUM
ejpam-4254	594	3	,	,	PUNCT
ejpam-4254	594	4	1	1	NUM
ejpam-4254	594	5	]	]	NUM
ejpam-4254	594	6	,	,	PUNCT
ejpam-4254	594	7	respectively	respectively	ADV
ejpam-4254	594	8	.	.	PUNCT
ejpam-4254	595	1	proof	proof	NOUN
ejpam-4254	595	2	.	.	PUNCT
ejpam-4254	596	1	it	it	PRON
ejpam-4254	596	2	is	be	AUX
ejpam-4254	596	3	straightforward	straightforward	ADJ
ejpam-4254	596	4	by	by	ADP
ejpam-4254	596	5	theorem	theorem	ADJ
ejpam-4254	596	6	3	3	NUM
ejpam-4254	596	7	and	and	CCONJ
ejpam-4254	596	8	lemmas	lemmas	PROPN
ejpam-4254	596	9	1	1	NUM
ejpam-4254	596	10	(	(	PUNCT
ejpam-4254	596	11	2	2	NUM
ejpam-4254	596	12	)	)	PUNCT
ejpam-4254	596	13	and	and	CCONJ
ejpam-4254	596	14	(	(	PUNCT
ejpam-4254	596	15	4	4	NUM
ejpam-4254	596	16	)	)	PUNCT
ejpam-4254	596	17	.	.	PUNCT
ejpam-4254	597	1	theorem	theorem	NOUN
ejpam-4254	597	2	15	15	NUM
ejpam-4254	597	3	.	.	PUNCT
ejpam-4254	598	1	let	let	VERB
ejpam-4254	598	2	ρ	ρ	NOUN
ejpam-4254	598	3	be	be	AUX
ejpam-4254	598	4	a	a	DET
ejpam-4254	598	5	cr	cr	NOUN
ejpam-4254	598	6	on	on	ADP
ejpam-4254	598	7	u	u	PROPN
ejpam-4254	598	8	.	.	PUNCT
ejpam-4254	599	1	then	then	ADV
ejpam-4254	599	2	p	p	PROPN
ejpam-4254	599	3	is	be	AUX
ejpam-4254	599	4	an	an	DET
ejpam-4254	599	5	uprpfnupf	uprpfnupf	NOUN
ejpam-4254	599	6	of	of	ADP
ejpam-4254	599	7	u	u	PRON
ejpam-4254	599	8	if	if	SCONJ
ejpam-4254	599	9	and	and	CCONJ
ejpam-4254	599	10	only	only	ADV
ejpam-4254	599	11	if	if	SCONJ
ejpam-4254	599	12	u(µp	u(µp	NOUN
ejpam-4254	599	13	,	,	PUNCT
ejpam-4254	599	14	t	t	PROPN
ejpam-4254	599	15	)	)	PUNCT
ejpam-4254	599	16	and	and	CCONJ
ejpam-4254	599	17	l(νp	l(νp	PROPN
ejpam-4254	599	18	,	,	PUNCT
ejpam-4254	599	19	t	t	PROPN
ejpam-4254	599	20	)	)	PUNCT
ejpam-4254	599	21	are	be	AUX
ejpam-4254	599	22	,	,	PUNCT
ejpam-4254	599	23	if	if	SCONJ
ejpam-4254	599	24	the	the	DET
ejpam-4254	599	25	sets	set	NOUN
ejpam-4254	599	26	are	be	AUX
ejpam-4254	599	27	nonempty	nonempty	ADJ
ejpam-4254	599	28	,	,	PUNCT
ejpam-4254	599	29	an	an	DET
ejpam-4254	599	30	uprnupf	uprnupf	NOUN
ejpam-4254	599	31	and	and	CCONJ
ejpam-4254	599	32	a	a	DET
ejpam-4254	599	33	lornupf	lornupf	NOUN
ejpam-4254	599	34	of	of	ADP
ejpam-4254	599	35	u	u	NOUN
ejpam-4254	599	36	for	for	ADP
ejpam-4254	599	37	every	every	DET
ejpam-4254	599	38	t	t	NOUN
ejpam-4254	599	39	∈	∈	PROPN
ejpam-4254	600	1	[	[	X
ejpam-4254	600	2	0	0	NUM
ejpam-4254	600	3	,	,	PUNCT
ejpam-4254	600	4	1	1	NUM
ejpam-4254	600	5	]	]	NUM
ejpam-4254	600	6	,	,	PUNCT
ejpam-4254	600	7	respectively	respectively	ADV
ejpam-4254	600	8	.	.	PUNCT
ejpam-4254	601	1	proof	proof	NOUN
ejpam-4254	601	2	.	.	PUNCT
ejpam-4254	602	1	it	it	PRON
ejpam-4254	602	2	is	be	AUX
ejpam-4254	602	3	straightforward	straightforward	ADJ
ejpam-4254	602	4	by	by	ADP
ejpam-4254	602	5	theorem	theorem	ADJ
ejpam-4254	602	6	4	4	NUM
ejpam-4254	602	7	and	and	CCONJ
ejpam-4254	602	8	lemmas	lemmas	PROPN
ejpam-4254	602	9	1	1	NUM
ejpam-4254	602	10	(	(	PUNCT
ejpam-4254	602	11	1	1	NUM
ejpam-4254	602	12	)	)	PUNCT
ejpam-4254	602	13	and	and	CCONJ
ejpam-4254	602	14	(	(	PUNCT
ejpam-4254	602	15	3	3	NUM
ejpam-4254	602	16	)	)	PUNCT
ejpam-4254	602	17	.	.	PUNCT
ejpam-4254	603	1	theorem	theorem	VERB
ejpam-4254	603	2	16	16	NUM
ejpam-4254	603	3	.	.	PUNCT
ejpam-4254	604	1	let	let	VERB
ejpam-4254	604	2	ρ	ρ	NOUN
ejpam-4254	604	3	be	be	AUX
ejpam-4254	604	4	a	a	DET
ejpam-4254	604	5	cr	cr	NOUN
ejpam-4254	604	6	on	on	ADP
ejpam-4254	604	7	u	u	PROPN
ejpam-4254	604	8	.	.	PUNCT
ejpam-4254	605	1	then	then	ADV
ejpam-4254	605	2	p	p	PROPN
ejpam-4254	605	3	is	be	AUX
ejpam-4254	605	4	an	an	DET
ejpam-4254	605	5	uprpfnupf	uprpfnupf	NOUN
ejpam-4254	605	6	of	of	ADP
ejpam-4254	605	7	u	u	PRON
ejpam-4254	605	8	if	if	SCONJ
ejpam-4254	606	1	and	and	CCONJ
ejpam-4254	606	2	only	only	ADV
ejpam-4254	606	3	if	if	SCONJ
ejpam-4254	606	4	u+(µp	u+(µp	NOUN
ejpam-4254	606	5	,	,	PUNCT
ejpam-4254	606	6	t	t	PROPN
ejpam-4254	606	7	)	)	PUNCT
ejpam-4254	606	8	and	and	CCONJ
ejpam-4254	606	9	l−(νp	l−(νp	PROPN
ejpam-4254	606	10	,	,	PUNCT
ejpam-4254	606	11	t	t	PROPN
ejpam-4254	606	12	)	)	PUNCT
ejpam-4254	606	13	are	be	AUX
ejpam-4254	606	14	,	,	PUNCT
ejpam-4254	606	15	if	if	SCONJ
ejpam-4254	606	16	the	the	DET
ejpam-4254	606	17	sets	set	NOUN
ejpam-4254	606	18	are	be	AUX
ejpam-4254	606	19	nonempty	nonempty	ADJ
ejpam-4254	606	20	,	,	PUNCT
ejpam-4254	606	21	an	an	DET
ejpam-4254	606	22	uprnupf	uprnupf	NOUN
ejpam-4254	606	23	and	and	CCONJ
ejpam-4254	606	24	a	a	DET
ejpam-4254	606	25	lornupf	lornupf	NOUN
ejpam-4254	606	26	of	of	ADP
ejpam-4254	606	27	u	u	NOUN
ejpam-4254	606	28	for	for	ADP
ejpam-4254	606	29	every	every	DET
ejpam-4254	606	30	t	t	NOUN
ejpam-4254	606	31	∈	∈	PROPN
ejpam-4254	607	1	[	[	X
ejpam-4254	607	2	0	0	NUM
ejpam-4254	607	3	,	,	PUNCT
ejpam-4254	607	4	1	1	NUM
ejpam-4254	607	5	]	]	NUM
ejpam-4254	607	6	,	,	PUNCT
ejpam-4254	607	7	respectively	respectively	ADV
ejpam-4254	607	8	.	.	PUNCT
ejpam-4254	608	1	proof	proof	NOUN
ejpam-4254	608	2	.	.	PUNCT
ejpam-4254	609	1	it	it	PRON
ejpam-4254	609	2	is	be	AUX
ejpam-4254	609	3	straightforward	straightforward	ADJ
ejpam-4254	609	4	by	by	ADP
ejpam-4254	609	5	theorem	theorem	ADJ
ejpam-4254	609	6	4	4	NUM
ejpam-4254	609	7	and	and	CCONJ
ejpam-4254	609	8	lemmas	lemmas	PROPN
ejpam-4254	609	9	1	1	NUM
ejpam-4254	609	10	(	(	PUNCT
ejpam-4254	609	11	1	1	NUM
ejpam-4254	609	12	)	)	PUNCT
ejpam-4254	609	13	and	and	CCONJ
ejpam-4254	609	14	(	(	PUNCT
ejpam-4254	609	15	3	3	NUM
ejpam-4254	609	16	)	)	PUNCT
ejpam-4254	609	17	.	.	PUNCT
ejpam-4254	610	1	theorem	theorem	NOUN
ejpam-4254	610	2	17	17	NUM
ejpam-4254	610	3	.	.	PUNCT
ejpam-4254	611	1	let	let	VERB
ejpam-4254	611	2	ρ	ρ	NOUN
ejpam-4254	611	3	be	be	AUX
ejpam-4254	611	4	a	a	DET
ejpam-4254	611	5	cr	cr	NOUN
ejpam-4254	611	6	on	on	ADP
ejpam-4254	611	7	u	u	PROPN
ejpam-4254	611	8	.	.	PUNCT
ejpam-4254	612	1	then	then	ADV
ejpam-4254	612	2	p	p	PROPN
ejpam-4254	612	3	is	be	AUX
ejpam-4254	612	4	an	an	DET
ejpam-4254	612	5	uprpfupf	uprpfupf	ADJ
ejpam-4254	612	6	of	of	ADP
ejpam-4254	612	7	u	u	PRON
ejpam-4254	612	8	if	if	SCONJ
ejpam-4254	613	1	and	and	CCONJ
ejpam-4254	613	2	only	only	ADV
ejpam-4254	613	3	if	if	SCONJ
ejpam-4254	613	4	u(µp	u(µp	NOUN
ejpam-4254	613	5	,	,	PUNCT
ejpam-4254	613	6	t	t	PROPN
ejpam-4254	613	7	)	)	PUNCT
ejpam-4254	613	8	and	and	CCONJ
ejpam-4254	613	9	l(νp	l(νp	PROPN
ejpam-4254	613	10	,	,	PUNCT
ejpam-4254	613	11	t	t	PROPN
ejpam-4254	613	12	)	)	PUNCT
ejpam-4254	613	13	are	be	AUX
ejpam-4254	613	14	,	,	PUNCT
ejpam-4254	613	15	if	if	SCONJ
ejpam-4254	613	16	the	the	DET
ejpam-4254	613	17	sets	set	NOUN
ejpam-4254	613	18	are	be	AUX
ejpam-4254	613	19	nonempty	nonempty	ADJ
ejpam-4254	613	20	,	,	PUNCT
ejpam-4254	613	21	an	an	DET
ejpam-4254	613	22	uprupf	uprupf	NOUN
ejpam-4254	613	23	and	and	CCONJ
ejpam-4254	613	24	a	a	DET
ejpam-4254	613	25	lorupf	lorupf	NOUN
ejpam-4254	613	26	of	of	ADP
ejpam-4254	613	27	u	u	NOUN
ejpam-4254	613	28	for	for	ADP
ejpam-4254	613	29	every	every	DET
ejpam-4254	613	30	t	t	NOUN
ejpam-4254	613	31	∈	∈	PROPN
ejpam-4254	614	1	[	[	X
ejpam-4254	614	2	0	0	NUM
ejpam-4254	614	3	,	,	PUNCT
ejpam-4254	614	4	1	1	NUM
ejpam-4254	614	5	]	]	NUM
ejpam-4254	614	6	,	,	PUNCT
ejpam-4254	614	7	respectively	respectively	ADV
ejpam-4254	614	8	.	.	PUNCT
ejpam-4254	615	1	proof	proof	NOUN
ejpam-4254	615	2	.	.	PUNCT
ejpam-4254	616	1	it	it	PRON
ejpam-4254	616	2	is	be	AUX
ejpam-4254	616	3	straightforward	straightforward	ADJ
ejpam-4254	616	4	by	by	ADP
ejpam-4254	616	5	theorem	theorem	NOUN
ejpam-4254	616	6	6	6	NUM
ejpam-4254	616	7	and	and	CCONJ
ejpam-4254	616	8	lemmas	lemmas	PROPN
ejpam-4254	616	9	1	1	NUM
ejpam-4254	616	10	(	(	PUNCT
ejpam-4254	616	11	1	1	NUM
ejpam-4254	616	12	)	)	PUNCT
ejpam-4254	616	13	and	and	CCONJ
ejpam-4254	616	14	(	(	PUNCT
ejpam-4254	616	15	3	3	NUM
ejpam-4254	616	16	)	)	PUNCT
ejpam-4254	616	17	.	.	PUNCT
ejpam-4254	617	1	theorem	theorem	NOUN
ejpam-4254	617	2	18	18	NUM
ejpam-4254	617	3	.	.	PUNCT
ejpam-4254	618	1	let	let	VERB
ejpam-4254	618	2	ρ	ρ	NOUN
ejpam-4254	618	3	be	be	AUX
ejpam-4254	618	4	a	a	DET
ejpam-4254	618	5	cr	cr	NOUN
ejpam-4254	618	6	on	on	ADP
ejpam-4254	618	7	u	u	PROPN
ejpam-4254	618	8	.	.	PUNCT
ejpam-4254	619	1	then	then	ADV
ejpam-4254	619	2	p	p	PROPN
ejpam-4254	619	3	is	be	AUX
ejpam-4254	619	4	an	an	DET
ejpam-4254	619	5	uprpfupf	uprpfupf	ADJ
ejpam-4254	619	6	of	of	ADP
ejpam-4254	619	7	u	u	PRON
ejpam-4254	619	8	if	if	SCONJ
ejpam-4254	620	1	and	and	CCONJ
ejpam-4254	620	2	only	only	ADV
ejpam-4254	620	3	if	if	SCONJ
ejpam-4254	620	4	u+(µp	u+(µp	NOUN
ejpam-4254	620	5	,	,	PUNCT
ejpam-4254	620	6	t	t	PROPN
ejpam-4254	620	7	)	)	PUNCT
ejpam-4254	620	8	and	and	CCONJ
ejpam-4254	620	9	l−(νp	l−(νp	PROPN
ejpam-4254	620	10	,	,	PUNCT
ejpam-4254	620	11	t	t	PROPN
ejpam-4254	620	12	)	)	PUNCT
ejpam-4254	620	13	are	be	AUX
ejpam-4254	620	14	,	,	PUNCT
ejpam-4254	620	15	if	if	SCONJ
ejpam-4254	620	16	the	the	DET
ejpam-4254	620	17	sets	set	NOUN
ejpam-4254	620	18	are	be	AUX
ejpam-4254	620	19	nonempty	nonempty	ADJ
ejpam-4254	620	20	,	,	PUNCT
ejpam-4254	620	21	an	an	DET
ejpam-4254	620	22	uprupf	uprupf	NOUN
ejpam-4254	620	23	and	and	CCONJ
ejpam-4254	620	24	a	a	DET
ejpam-4254	620	25	lorupf	lorupf	NOUN
ejpam-4254	620	26	of	of	ADP
ejpam-4254	620	27	u	u	NOUN
ejpam-4254	620	28	for	for	ADP
ejpam-4254	620	29	every	every	DET
ejpam-4254	620	30	t	t	NOUN
ejpam-4254	620	31	∈	∈	PROPN
ejpam-4254	621	1	[	[	X
ejpam-4254	621	2	0	0	NUM
ejpam-4254	621	3	,	,	PUNCT
ejpam-4254	621	4	1	1	NUM
ejpam-4254	621	5	]	]	NUM
ejpam-4254	621	6	,	,	PUNCT
ejpam-4254	621	7	respectively	respectively	ADV
ejpam-4254	621	8	.	.	PUNCT
ejpam-4254	622	1	a.	a.	PROPN
ejpam-4254	622	2	iampan	iampan	PROPN
ejpam-4254	622	3	et	et	PROPN
ejpam-4254	622	4	al	al	PROPN
ejpam-4254	622	5	.	.	PUNCT
ejpam-4254	622	6	/	/	SYM
ejpam-4254	622	7	eur	eur	PROPN
ejpam-4254	622	8	.	.	PUNCT
ejpam-4254	623	1	j.	j.	PROPN
ejpam-4254	623	2	pure	pure	PROPN
ejpam-4254	623	3	appl	appl	PROPN
ejpam-4254	623	4	.	.	PROPN
ejpam-4254	623	5	math	math	PROPN
ejpam-4254	623	6	,	,	PUNCT
ejpam-4254	623	7	15	15	NUM
ejpam-4254	623	8	(	(	PUNCT
ejpam-4254	623	9	1	1	NUM
ejpam-4254	623	10	)	)	PUNCT
ejpam-4254	623	11	(	(	PUNCT
ejpam-4254	623	12	2022	2022	NUM
ejpam-4254	623	13	)	)	PUNCT
ejpam-4254	623	14	,	,	PUNCT
ejpam-4254	623	15	169	169	NUM
ejpam-4254	623	16	-	-	SYM
ejpam-4254	623	17	198	198	NUM
ejpam-4254	623	18	194	194	NUM
ejpam-4254	623	19	proof	proof	NOUN
ejpam-4254	623	20	.	.	PUNCT
ejpam-4254	624	1	it	it	PRON
ejpam-4254	624	2	is	be	AUX
ejpam-4254	624	3	straightforward	straightforward	ADJ
ejpam-4254	624	4	by	by	ADP
ejpam-4254	624	5	theorem	theorem	ADJ
ejpam-4254	624	6	7	7	NUM
ejpam-4254	624	7	and	and	CCONJ
ejpam-4254	624	8	lemmas	lemmas	PROPN
ejpam-4254	624	9	1	1	NUM
ejpam-4254	624	10	(	(	PUNCT
ejpam-4254	624	11	2	2	NUM
ejpam-4254	624	12	)	)	PUNCT
ejpam-4254	624	13	and	and	CCONJ
ejpam-4254	624	14	(	(	PUNCT
ejpam-4254	624	15	4	4	NUM
ejpam-4254	624	16	)	)	PUNCT
ejpam-4254	624	17	.	.	PUNCT
ejpam-4254	625	1	theorem	theorem	NOUN
ejpam-4254	625	2	19	19	NUM
ejpam-4254	625	3	.	.	PUNCT
ejpam-4254	626	1	let	let	VERB
ejpam-4254	626	2	ρ	ρ	NOUN
ejpam-4254	626	3	be	be	AUX
ejpam-4254	626	4	a	a	DET
ejpam-4254	626	5	cr	cr	NOUN
ejpam-4254	626	6	on	on	ADP
ejpam-4254	626	7	u	u	PROPN
ejpam-4254	626	8	.	.	PUNCT
ejpam-4254	627	1	then	then	ADV
ejpam-4254	627	2	p	p	PROPN
ejpam-4254	627	3	is	be	AUX
ejpam-4254	627	4	an	an	DET
ejpam-4254	627	5	uprpfupi	uprpfupi	NOUN
ejpam-4254	627	6	of	of	ADP
ejpam-4254	627	7	u	u	PRON
ejpam-4254	627	8	if	if	SCONJ
ejpam-4254	627	9	and	and	CCONJ
ejpam-4254	627	10	only	only	ADV
ejpam-4254	627	11	if	if	SCONJ
ejpam-4254	627	12	u(µp	u(µp	NOUN
ejpam-4254	627	13	,	,	PUNCT
ejpam-4254	627	14	t	t	PROPN
ejpam-4254	627	15	)	)	PUNCT
ejpam-4254	627	16	and	and	CCONJ
ejpam-4254	627	17	l(νp	l(νp	PROPN
ejpam-4254	627	18	,	,	PUNCT
ejpam-4254	627	19	t	t	PROPN
ejpam-4254	627	20	)	)	PUNCT
ejpam-4254	627	21	are	be	AUX
ejpam-4254	627	22	,	,	PUNCT
ejpam-4254	627	23	if	if	SCONJ
ejpam-4254	627	24	the	the	DET
ejpam-4254	627	25	sets	set	NOUN
ejpam-4254	627	26	are	be	AUX
ejpam-4254	627	27	nonempty	nonempty	ADJ
ejpam-4254	627	28	,	,	PUNCT
ejpam-4254	627	29	an	an	DET
ejpam-4254	627	30	uprupi	uprupi	NOUN
ejpam-4254	627	31	and	and	CCONJ
ejpam-4254	627	32	a	a	DET
ejpam-4254	627	33	lorupi	lorupi	NOUN
ejpam-4254	627	34	of	of	ADP
ejpam-4254	627	35	u	u	NOUN
ejpam-4254	627	36	for	for	ADP
ejpam-4254	627	37	every	every	DET
ejpam-4254	627	38	t	t	NOUN
ejpam-4254	627	39	∈	∈	PROPN
ejpam-4254	628	1	[	[	X
ejpam-4254	628	2	0	0	NUM
ejpam-4254	628	3	,	,	PUNCT
ejpam-4254	628	4	1	1	NUM
ejpam-4254	628	5	]	]	NUM
ejpam-4254	628	6	,	,	PUNCT
ejpam-4254	628	7	respectively	respectively	ADV
ejpam-4254	628	8	.	.	PUNCT
ejpam-4254	629	1	proof	proof	NOUN
ejpam-4254	629	2	.	.	PUNCT
ejpam-4254	630	1	it	it	PRON
ejpam-4254	630	2	is	be	AUX
ejpam-4254	630	3	straightforward	straightforward	ADJ
ejpam-4254	630	4	by	by	ADP
ejpam-4254	630	5	theorem	theorem	ADJ
ejpam-4254	630	6	8	8	NUM
ejpam-4254	630	7	and	and	CCONJ
ejpam-4254	630	8	lemmas	lemmas	PROPN
ejpam-4254	630	9	1	1	NUM
ejpam-4254	630	10	(	(	PUNCT
ejpam-4254	630	11	1	1	NUM
ejpam-4254	630	12	)	)	PUNCT
ejpam-4254	630	13	and	and	CCONJ
ejpam-4254	630	14	(	(	PUNCT
ejpam-4254	630	15	3	3	NUM
ejpam-4254	630	16	)	)	PUNCT
ejpam-4254	630	17	.	.	PUNCT
ejpam-4254	631	1	theorem	theorem	NOUN
ejpam-4254	631	2	20	20	NUM
ejpam-4254	631	3	.	.	PUNCT
ejpam-4254	632	1	let	let	VERB
ejpam-4254	632	2	ρ	ρ	NOUN
ejpam-4254	632	3	be	be	AUX
ejpam-4254	632	4	a	a	DET
ejpam-4254	632	5	cr	cr	NOUN
ejpam-4254	632	6	on	on	ADP
ejpam-4254	632	7	u	u	PROPN
ejpam-4254	632	8	.	.	PUNCT
ejpam-4254	633	1	then	then	ADV
ejpam-4254	633	2	p	p	PROPN
ejpam-4254	633	3	is	be	AUX
ejpam-4254	633	4	an	an	DET
ejpam-4254	633	5	uprpfupi	uprpfupi	NOUN
ejpam-4254	633	6	of	of	ADP
ejpam-4254	633	7	u	u	PRON
ejpam-4254	633	8	if	if	SCONJ
ejpam-4254	634	1	and	and	CCONJ
ejpam-4254	634	2	only	only	ADV
ejpam-4254	634	3	if	if	SCONJ
ejpam-4254	634	4	u+(µp	u+(µp	NOUN
ejpam-4254	634	5	,	,	PUNCT
ejpam-4254	634	6	t	t	PROPN
ejpam-4254	634	7	)	)	PUNCT
ejpam-4254	634	8	and	and	CCONJ
ejpam-4254	634	9	l−(νp	l−(νp	PROPN
ejpam-4254	634	10	,	,	PUNCT
ejpam-4254	634	11	t	t	PROPN
ejpam-4254	634	12	)	)	PUNCT
ejpam-4254	634	13	are	be	AUX
ejpam-4254	634	14	,	,	PUNCT
ejpam-4254	634	15	if	if	SCONJ
ejpam-4254	634	16	the	the	DET
ejpam-4254	634	17	sets	set	NOUN
ejpam-4254	634	18	are	be	AUX
ejpam-4254	634	19	nonempty	nonempty	ADJ
ejpam-4254	634	20	,	,	PUNCT
ejpam-4254	634	21	an	an	DET
ejpam-4254	634	22	uprupi	uprupi	NOUN
ejpam-4254	634	23	and	and	CCONJ
ejpam-4254	634	24	a	a	DET
ejpam-4254	634	25	lorupi	lorupi	NOUN
ejpam-4254	634	26	of	of	ADP
ejpam-4254	634	27	u	u	NOUN
ejpam-4254	634	28	for	for	ADP
ejpam-4254	634	29	every	every	DET
ejpam-4254	634	30	t	t	NOUN
ejpam-4254	634	31	∈	∈	PROPN
ejpam-4254	635	1	[	[	X
ejpam-4254	635	2	0	0	NUM
ejpam-4254	635	3	,	,	PUNCT
ejpam-4254	635	4	1	1	NUM
ejpam-4254	635	5	]	]	NUM
ejpam-4254	635	6	,	,	PUNCT
ejpam-4254	635	7	respectively	respectively	ADV
ejpam-4254	635	8	.	.	PUNCT
ejpam-4254	636	1	proof	proof	NOUN
ejpam-4254	636	2	.	.	PUNCT
ejpam-4254	637	1	it	it	PRON
ejpam-4254	637	2	is	be	AUX
ejpam-4254	637	3	straightforward	straightforward	ADJ
ejpam-4254	637	4	by	by	ADP
ejpam-4254	637	5	theorem	theorem	ADJ
ejpam-4254	637	6	9	9	NUM
ejpam-4254	637	7	and	and	CCONJ
ejpam-4254	637	8	lemmas	lemmas	PROPN
ejpam-4254	637	9	1	1	NUM
ejpam-4254	637	10	(	(	PUNCT
ejpam-4254	637	11	2	2	NUM
ejpam-4254	637	12	)	)	PUNCT
ejpam-4254	637	13	and	and	CCONJ
ejpam-4254	637	14	(	(	PUNCT
ejpam-4254	637	15	4	4	NUM
ejpam-4254	637	16	)	)	PUNCT
ejpam-4254	637	17	.	.	PUNCT
ejpam-4254	638	1	theorem	theorem	NOUN
ejpam-4254	638	2	21	21	NUM
ejpam-4254	638	3	.	.	PUNCT
ejpam-4254	639	1	let	let	VERB
ejpam-4254	639	2	ρ	ρ	NOUN
ejpam-4254	639	3	be	be	AUX
ejpam-4254	639	4	a	a	DET
ejpam-4254	639	5	cr	cr	NOUN
ejpam-4254	639	6	on	on	ADP
ejpam-4254	639	7	u	u	PROPN
ejpam-4254	639	8	.	.	PUNCT
ejpam-4254	640	1	then	then	ADV
ejpam-4254	640	2	p	p	PROPN
ejpam-4254	640	3	is	be	AUX
ejpam-4254	640	4	an	an	DET
ejpam-4254	640	5	uprpfsupi	uprpfsupi	NOUN
ejpam-4254	640	6	of	of	ADP
ejpam-4254	640	7	u	u	PRON
ejpam-4254	640	8	if	if	SCONJ
ejpam-4254	640	9	and	and	CCONJ
ejpam-4254	640	10	only	only	ADV
ejpam-4254	640	11	if	if	SCONJ
ejpam-4254	640	12	u(µp	u(µp	NOUN
ejpam-4254	640	13	,	,	PUNCT
ejpam-4254	640	14	t	t	PROPN
ejpam-4254	640	15	)	)	PUNCT
ejpam-4254	640	16	and	and	CCONJ
ejpam-4254	640	17	l(νp	l(νp	PROPN
ejpam-4254	640	18	,	,	PUNCT
ejpam-4254	640	19	t	t	PROPN
ejpam-4254	640	20	)	)	PUNCT
ejpam-4254	640	21	are	be	AUX
ejpam-4254	640	22	,	,	PUNCT
ejpam-4254	640	23	if	if	SCONJ
ejpam-4254	640	24	the	the	DET
ejpam-4254	640	25	sets	set	NOUN
ejpam-4254	640	26	are	be	AUX
ejpam-4254	640	27	nonempty	nonempty	ADJ
ejpam-4254	640	28	,	,	PUNCT
ejpam-4254	640	29	an	an	DET
ejpam-4254	640	30	uprsupi	uprsupi	NOUN
ejpam-4254	640	31	and	and	CCONJ
ejpam-4254	640	32	a	a	DET
ejpam-4254	640	33	lorsupi	lorsupi	NOUN
ejpam-4254	640	34	of	of	ADP
ejpam-4254	640	35	u	u	NOUN
ejpam-4254	640	36	for	for	ADP
ejpam-4254	640	37	every	every	DET
ejpam-4254	640	38	t	t	NOUN
ejpam-4254	640	39	∈	∈	PROPN
ejpam-4254	641	1	[	[	X
ejpam-4254	641	2	0	0	NUM
ejpam-4254	641	3	,	,	PUNCT
ejpam-4254	641	4	1	1	NUM
ejpam-4254	641	5	]	]	NUM
ejpam-4254	641	6	,	,	PUNCT
ejpam-4254	641	7	respectively	respectively	ADV
ejpam-4254	641	8	.	.	PUNCT
ejpam-4254	642	1	proof	proof	NOUN
ejpam-4254	642	2	.	.	PUNCT
ejpam-4254	643	1	it	it	PRON
ejpam-4254	643	2	is	be	AUX
ejpam-4254	643	3	straightforward	straightforward	ADJ
ejpam-4254	643	4	by	by	ADP
ejpam-4254	643	5	theorem	theorem	ADJ
ejpam-4254	643	6	10	10	NUM
ejpam-4254	643	7	and	and	CCONJ
ejpam-4254	643	8	lemmas	lemmas	PROPN
ejpam-4254	643	9	1	1	NUM
ejpam-4254	643	10	(	(	PUNCT
ejpam-4254	643	11	1	1	NUM
ejpam-4254	643	12	)	)	PUNCT
ejpam-4254	643	13	and	and	CCONJ
ejpam-4254	643	14	(	(	PUNCT
ejpam-4254	643	15	3	3	NUM
ejpam-4254	643	16	)	)	PUNCT
ejpam-4254	643	17	.	.	PUNCT
ejpam-4254	644	1	theorem	theorem	NOUN
ejpam-4254	644	2	22	22	NUM
ejpam-4254	644	3	.	.	PUNCT
ejpam-4254	645	1	let	let	VERB
ejpam-4254	645	2	ρ	ρ	NOUN
ejpam-4254	645	3	be	be	AUX
ejpam-4254	645	4	a	a	DET
ejpam-4254	645	5	cr	cr	NOUN
ejpam-4254	645	6	on	on	ADP
ejpam-4254	645	7	u	u	PROPN
ejpam-4254	645	8	.	.	PUNCT
ejpam-4254	646	1	then	then	ADV
ejpam-4254	646	2	p	p	PROPN
ejpam-4254	646	3	is	be	AUX
ejpam-4254	646	4	an	an	DET
ejpam-4254	646	5	uprpfsupi	uprpfsupi	NOUN
ejpam-4254	646	6	of	of	ADP
ejpam-4254	646	7	u	u	PRON
ejpam-4254	646	8	if	if	SCONJ
ejpam-4254	647	1	and	and	CCONJ
ejpam-4254	647	2	only	only	ADV
ejpam-4254	647	3	if	if	SCONJ
ejpam-4254	647	4	u+(µp	u+(µp	NOUN
ejpam-4254	647	5	,	,	PUNCT
ejpam-4254	647	6	t	t	PROPN
ejpam-4254	647	7	)	)	PUNCT
ejpam-4254	647	8	and	and	CCONJ
ejpam-4254	647	9	l−(νp	l−(νp	PROPN
ejpam-4254	647	10	,	,	PUNCT
ejpam-4254	647	11	t	t	PROPN
ejpam-4254	647	12	)	)	PUNCT
ejpam-4254	647	13	are	be	AUX
ejpam-4254	647	14	,	,	PUNCT
ejpam-4254	647	15	if	if	SCONJ
ejpam-4254	647	16	the	the	DET
ejpam-4254	647	17	sets	set	NOUN
ejpam-4254	647	18	are	be	AUX
ejpam-4254	647	19	nonempty	nonempty	ADJ
ejpam-4254	647	20	,	,	PUNCT
ejpam-4254	647	21	an	an	DET
ejpam-4254	647	22	uprsupi	uprsupi	NOUN
ejpam-4254	647	23	and	and	CCONJ
ejpam-4254	647	24	a	a	DET
ejpam-4254	647	25	lorsupi	lorsupi	NOUN
ejpam-4254	647	26	of	of	ADP
ejpam-4254	647	27	u	u	NOUN
ejpam-4254	647	28	for	for	ADP
ejpam-4254	647	29	every	every	DET
ejpam-4254	647	30	t	t	NOUN
ejpam-4254	647	31	∈	∈	PROPN
ejpam-4254	648	1	[	[	X
ejpam-4254	648	2	0	0	NUM
ejpam-4254	648	3	,	,	PUNCT
ejpam-4254	648	4	1	1	NUM
ejpam-4254	648	5	]	]	NUM
ejpam-4254	648	6	,	,	PUNCT
ejpam-4254	648	7	respectively	respectively	ADV
ejpam-4254	648	8	.	.	PUNCT
ejpam-4254	649	1	proof	proof	NOUN
ejpam-4254	649	2	.	.	PUNCT
ejpam-4254	650	1	it	it	PRON
ejpam-4254	650	2	is	be	AUX
ejpam-4254	650	3	straightforward	straightforward	ADJ
ejpam-4254	650	4	by	by	ADP
ejpam-4254	650	5	theorem	theorem	ADJ
ejpam-4254	650	6	11	11	NUM
ejpam-4254	650	7	and	and	CCONJ
ejpam-4254	650	8	lemmas	lemmas	PROPN
ejpam-4254	650	9	1	1	NUM
ejpam-4254	650	10	(	(	PUNCT
ejpam-4254	650	11	2	2	NUM
ejpam-4254	650	12	)	)	PUNCT
ejpam-4254	650	13	and	and	CCONJ
ejpam-4254	650	14	(	(	PUNCT
ejpam-4254	650	15	4	4	NUM
ejpam-4254	650	16	)	)	PUNCT
ejpam-4254	650	17	.	.	PUNCT
ejpam-4254	651	1	theorem	theorem	VERB
ejpam-4254	651	2	23	23	NUM
ejpam-4254	651	3	.	.	PUNCT
ejpam-4254	652	1	let	let	VERB
ejpam-4254	652	2	ρ	ρ	NOUN
ejpam-4254	652	3	be	be	AUX
ejpam-4254	652	4	a	a	DET
ejpam-4254	652	5	cr	cr	NOUN
ejpam-4254	652	6	on	on	ADP
ejpam-4254	652	7	u	u	PROPN
ejpam-4254	652	8	.	.	PUNCT
ejpam-4254	653	1	then	then	ADV
ejpam-4254	653	2	p	p	PROPN
ejpam-4254	653	3	is	be	AUX
ejpam-4254	653	4	a	a	DET
ejpam-4254	653	5	lorpfups	lorpfup	NOUN
ejpam-4254	653	6	of	of	ADP
ejpam-4254	653	7	u	u	PRON
ejpam-4254	653	8	if	if	SCONJ
ejpam-4254	653	9	and	and	CCONJ
ejpam-4254	653	10	only	only	ADV
ejpam-4254	653	11	if	if	SCONJ
ejpam-4254	653	12	u(µp	u(µp	NOUN
ejpam-4254	653	13	,	,	PUNCT
ejpam-4254	653	14	t	t	PROPN
ejpam-4254	653	15	)	)	PUNCT
ejpam-4254	653	16	and	and	CCONJ
ejpam-4254	653	17	l(νp	l(νp	PROPN
ejpam-4254	653	18	,	,	PUNCT
ejpam-4254	653	19	t	t	PROPN
ejpam-4254	653	20	)	)	PUNCT
ejpam-4254	653	21	are	be	AUX
ejpam-4254	653	22	,	,	PUNCT
ejpam-4254	653	23	if	if	SCONJ
ejpam-4254	653	24	the	the	DET
ejpam-4254	653	25	sets	set	NOUN
ejpam-4254	653	26	are	be	AUX
ejpam-4254	653	27	nonempty	nonempty	ADJ
ejpam-4254	653	28	,	,	PUNCT
ejpam-4254	653	29	an	an	DET
ejpam-4254	653	30	uprups	uprup	NOUN
ejpam-4254	653	31	and	and	CCONJ
ejpam-4254	653	32	a	a	DET
ejpam-4254	653	33	lorups	lorup	NOUN
ejpam-4254	653	34	of	of	ADP
ejpam-4254	653	35	u	u	NOUN
ejpam-4254	653	36	for	for	ADP
ejpam-4254	653	37	every	every	DET
ejpam-4254	653	38	t	t	NOUN
ejpam-4254	653	39	∈	∈	PROPN
ejpam-4254	654	1	[	[	X
ejpam-4254	654	2	0	0	NUM
ejpam-4254	654	3	,	,	PUNCT
ejpam-4254	654	4	1	1	NUM
ejpam-4254	654	5	]	]	NUM
ejpam-4254	654	6	,	,	PUNCT
ejpam-4254	654	7	respectively	respectively	ADV
ejpam-4254	654	8	.	.	PUNCT
ejpam-4254	655	1	proof	proof	NOUN
ejpam-4254	655	2	.	.	PUNCT
ejpam-4254	656	1	it	it	PRON
ejpam-4254	656	2	is	be	AUX
ejpam-4254	656	3	straightforward	straightforward	ADJ
ejpam-4254	656	4	by	by	ADP
ejpam-4254	656	5	theorem	theorem	ADJ
ejpam-4254	656	6	2	2	NUM
ejpam-4254	656	7	and	and	CCONJ
ejpam-4254	656	8	lemmas	lemmas	PROPN
ejpam-4254	656	9	1	1	NUM
ejpam-4254	656	10	(	(	PUNCT
ejpam-4254	656	11	5	5	NUM
ejpam-4254	656	12	)	)	PUNCT
ejpam-4254	656	13	and	and	CCONJ
ejpam-4254	656	14	(	(	PUNCT
ejpam-4254	656	15	7	7	NUM
ejpam-4254	656	16	)	)	PUNCT
ejpam-4254	656	17	.	.	PUNCT
ejpam-4254	657	1	theorem	theorem	NOUN
ejpam-4254	657	2	24	24	NUM
ejpam-4254	657	3	.	.	PUNCT
ejpam-4254	658	1	let	let	VERB
ejpam-4254	658	2	ρ	ρ	NOUN
ejpam-4254	658	3	be	be	AUX
ejpam-4254	658	4	a	a	DET
ejpam-4254	658	5	cr	cr	NOUN
ejpam-4254	658	6	on	on	ADP
ejpam-4254	658	7	u	u	PROPN
ejpam-4254	658	8	.	.	PUNCT
ejpam-4254	659	1	then	then	ADV
ejpam-4254	659	2	p	p	PROPN
ejpam-4254	659	3	is	be	AUX
ejpam-4254	659	4	a	a	DET
ejpam-4254	659	5	lorpfups	lorpfup	NOUN
ejpam-4254	659	6	of	of	ADP
ejpam-4254	659	7	u	u	PRON
ejpam-4254	659	8	if	if	SCONJ
ejpam-4254	660	1	and	and	CCONJ
ejpam-4254	660	2	only	only	ADV
ejpam-4254	660	3	if	if	SCONJ
ejpam-4254	660	4	u+(µp	u+(µp	NOUN
ejpam-4254	660	5	,	,	PUNCT
ejpam-4254	660	6	t	t	PROPN
ejpam-4254	660	7	)	)	PUNCT
ejpam-4254	660	8	and	and	CCONJ
ejpam-4254	660	9	l−(νp	l−(νp	PROPN
ejpam-4254	660	10	,	,	PUNCT
ejpam-4254	660	11	t	t	PROPN
ejpam-4254	660	12	)	)	PUNCT
ejpam-4254	660	13	are	be	AUX
ejpam-4254	660	14	,	,	PUNCT
ejpam-4254	660	15	if	if	SCONJ
ejpam-4254	660	16	the	the	DET
ejpam-4254	660	17	sets	set	NOUN
ejpam-4254	660	18	are	be	AUX
ejpam-4254	660	19	nonempty	nonempty	ADJ
ejpam-4254	660	20	,	,	PUNCT
ejpam-4254	660	21	an	an	DET
ejpam-4254	660	22	uprups	uprup	NOUN
ejpam-4254	660	23	and	and	CCONJ
ejpam-4254	660	24	a	a	DET
ejpam-4254	660	25	lorups	lorup	NOUN
ejpam-4254	660	26	of	of	ADP
ejpam-4254	660	27	u	u	NOUN
ejpam-4254	660	28	for	for	ADP
ejpam-4254	660	29	every	every	DET
ejpam-4254	660	30	t	t	NOUN
ejpam-4254	660	31	∈	∈	PROPN
ejpam-4254	661	1	[	[	X
ejpam-4254	661	2	0	0	NUM
ejpam-4254	661	3	,	,	PUNCT
ejpam-4254	661	4	1	1	NUM
ejpam-4254	661	5	]	]	NUM
ejpam-4254	661	6	,	,	PUNCT
ejpam-4254	661	7	respectively	respectively	ADV
ejpam-4254	661	8	.	.	PUNCT
ejpam-4254	662	1	proof	proof	NOUN
ejpam-4254	662	2	.	.	PUNCT
ejpam-4254	663	1	it	it	PRON
ejpam-4254	663	2	is	be	AUX
ejpam-4254	663	3	straightforward	straightforward	ADJ
ejpam-4254	663	4	by	by	ADP
ejpam-4254	663	5	theorem	theorem	ADJ
ejpam-4254	663	6	3	3	NUM
ejpam-4254	663	7	and	and	CCONJ
ejpam-4254	663	8	lemmas	lemmas	PROPN
ejpam-4254	663	9	1	1	NUM
ejpam-4254	663	10	(	(	PUNCT
ejpam-4254	663	11	6	6	NUM
ejpam-4254	663	12	)	)	PUNCT
ejpam-4254	663	13	and	and	CCONJ
ejpam-4254	663	14	(	(	PUNCT
ejpam-4254	663	15	8)	8)	NUM
ejpam-4254	663	16	.	.	PUNCT
ejpam-4254	663	17	theorem	theorem	NOUN
ejpam-4254	663	18	25	25	NUM
ejpam-4254	663	19	.	.	PUNCT
ejpam-4254	664	1	let	let	VERB
ejpam-4254	664	2	ρ	ρ	NOUN
ejpam-4254	664	3	be	be	AUX
ejpam-4254	664	4	a	a	DET
ejpam-4254	664	5	cr	cr	NOUN
ejpam-4254	664	6	on	on	ADP
ejpam-4254	664	7	u	u	PROPN
ejpam-4254	664	8	.	.	PUNCT
ejpam-4254	665	1	then	then	ADV
ejpam-4254	665	2	p	p	PROPN
ejpam-4254	665	3	is	be	AUX
ejpam-4254	665	4	a	a	DET
ejpam-4254	665	5	lorpfnupf	lorpfnupf	NOUN
ejpam-4254	665	6	of	of	ADP
ejpam-4254	665	7	u	u	PRON
ejpam-4254	665	8	if	if	SCONJ
ejpam-4254	666	1	and	and	CCONJ
ejpam-4254	666	2	only	only	ADV
ejpam-4254	666	3	if	if	SCONJ
ejpam-4254	666	4	u(µp	u(µp	NOUN
ejpam-4254	666	5	,	,	PUNCT
ejpam-4254	666	6	t	t	PROPN
ejpam-4254	666	7	)	)	PUNCT
ejpam-4254	666	8	and	and	CCONJ
ejpam-4254	666	9	l(νp	l(νp	PROPN
ejpam-4254	666	10	,	,	PUNCT
ejpam-4254	666	11	t	t	PROPN
ejpam-4254	666	12	)	)	PUNCT
ejpam-4254	666	13	are	be	AUX
ejpam-4254	666	14	,	,	PUNCT
ejpam-4254	666	15	if	if	SCONJ
ejpam-4254	666	16	the	the	DET
ejpam-4254	666	17	sets	set	NOUN
ejpam-4254	666	18	are	be	AUX
ejpam-4254	666	19	nonempty	nonempty	ADJ
ejpam-4254	666	20	,	,	PUNCT
ejpam-4254	666	21	an	an	DET
ejpam-4254	666	22	uprnupf	uprnupf	NOUN
ejpam-4254	666	23	and	and	CCONJ
ejpam-4254	666	24	a	a	DET
ejpam-4254	666	25	lornupf	lornupf	NOUN
ejpam-4254	666	26	of	of	ADP
ejpam-4254	666	27	u	u	NOUN
ejpam-4254	666	28	for	for	ADP
ejpam-4254	666	29	every	every	DET
ejpam-4254	666	30	t	t	NOUN
ejpam-4254	666	31	∈	∈	PROPN
ejpam-4254	667	1	[	[	X
ejpam-4254	667	2	0	0	NUM
ejpam-4254	667	3	,	,	PUNCT
ejpam-4254	667	4	1	1	NUM
ejpam-4254	667	5	]	]	NUM
ejpam-4254	667	6	,	,	PUNCT
ejpam-4254	667	7	respectively	respectively	ADV
ejpam-4254	667	8	.	.	PUNCT
ejpam-4254	668	1	proof	proof	NOUN
ejpam-4254	668	2	.	.	PUNCT
ejpam-4254	669	1	it	it	PRON
ejpam-4254	669	2	is	be	AUX
ejpam-4254	669	3	straightforward	straightforward	ADJ
ejpam-4254	669	4	by	by	ADP
ejpam-4254	669	5	theorem	theorem	ADJ
ejpam-4254	669	6	4	4	NUM
ejpam-4254	669	7	and	and	CCONJ
ejpam-4254	669	8	lemmas	lemmas	PROPN
ejpam-4254	669	9	1	1	NUM
ejpam-4254	669	10	(	(	PUNCT
ejpam-4254	669	11	5	5	NUM
ejpam-4254	669	12	)	)	PUNCT
ejpam-4254	669	13	and	and	CCONJ
ejpam-4254	669	14	(	(	PUNCT
ejpam-4254	669	15	7	7	NUM
ejpam-4254	669	16	)	)	PUNCT
ejpam-4254	669	17	.	.	PUNCT
ejpam-4254	670	1	a.	a.	PROPN
ejpam-4254	670	2	iampan	iampan	PROPN
ejpam-4254	670	3	et	et	PROPN
ejpam-4254	670	4	al	al	PROPN
ejpam-4254	670	5	.	.	PUNCT
ejpam-4254	670	6	/	/	SYM
ejpam-4254	670	7	eur	eur	PROPN
ejpam-4254	670	8	.	.	PUNCT
ejpam-4254	671	1	j.	j.	PROPN
ejpam-4254	671	2	pure	pure	PROPN
ejpam-4254	671	3	appl	appl	PROPN
ejpam-4254	671	4	.	.	PROPN
ejpam-4254	671	5	math	math	PROPN
ejpam-4254	671	6	,	,	PUNCT
ejpam-4254	671	7	15	15	NUM
ejpam-4254	671	8	(	(	PUNCT
ejpam-4254	671	9	1	1	NUM
ejpam-4254	671	10	)	)	PUNCT
ejpam-4254	671	11	(	(	PUNCT
ejpam-4254	671	12	2022	2022	NUM
ejpam-4254	671	13	)	)	PUNCT
ejpam-4254	671	14	,	,	PUNCT
ejpam-4254	671	15	169	169	NUM
ejpam-4254	671	16	-	-	SYM
ejpam-4254	671	17	198	198	NUM
ejpam-4254	671	18	195	195	NUM
ejpam-4254	671	19	theorem	theorem	NOUN
ejpam-4254	671	20	26	26	NUM
ejpam-4254	671	21	.	.	PUNCT
ejpam-4254	672	1	let	let	VERB
ejpam-4254	672	2	ρ	ρ	NOUN
ejpam-4254	672	3	be	be	AUX
ejpam-4254	672	4	a	a	DET
ejpam-4254	672	5	cr	cr	NOUN
ejpam-4254	672	6	on	on	ADP
ejpam-4254	672	7	u	u	PROPN
ejpam-4254	672	8	.	.	PUNCT
ejpam-4254	673	1	then	then	ADV
ejpam-4254	673	2	p	p	PROPN
ejpam-4254	673	3	is	be	AUX
ejpam-4254	673	4	a	a	DET
ejpam-4254	673	5	lorpfnupf	lorpfnupf	NOUN
ejpam-4254	673	6	of	of	ADP
ejpam-4254	673	7	u	u	PRON
ejpam-4254	673	8	if	if	SCONJ
ejpam-4254	674	1	and	and	CCONJ
ejpam-4254	674	2	only	only	ADV
ejpam-4254	674	3	if	if	SCONJ
ejpam-4254	674	4	u+(µp	u+(µp	NOUN
ejpam-4254	674	5	,	,	PUNCT
ejpam-4254	674	6	t	t	PROPN
ejpam-4254	674	7	)	)	PUNCT
ejpam-4254	674	8	and	and	CCONJ
ejpam-4254	674	9	l−(νp	l−(νp	PROPN
ejpam-4254	674	10	,	,	PUNCT
ejpam-4254	674	11	t	t	PROPN
ejpam-4254	674	12	)	)	PUNCT
ejpam-4254	674	13	are	be	AUX
ejpam-4254	674	14	,	,	PUNCT
ejpam-4254	674	15	if	if	SCONJ
ejpam-4254	674	16	the	the	DET
ejpam-4254	674	17	sets	set	NOUN
ejpam-4254	674	18	are	be	AUX
ejpam-4254	674	19	nonempty	nonempty	ADJ
ejpam-4254	674	20	,	,	PUNCT
ejpam-4254	674	21	an	an	DET
ejpam-4254	674	22	uprnupf	uprnupf	NOUN
ejpam-4254	674	23	and	and	CCONJ
ejpam-4254	674	24	a	a	DET
ejpam-4254	674	25	lornupf	lornupf	NOUN
ejpam-4254	674	26	of	of	ADP
ejpam-4254	674	27	u	u	NOUN
ejpam-4254	674	28	for	for	ADP
ejpam-4254	674	29	every	every	DET
ejpam-4254	674	30	t	t	NOUN
ejpam-4254	674	31	∈	∈	PROPN
ejpam-4254	675	1	[	[	X
ejpam-4254	675	2	0	0	NUM
ejpam-4254	675	3	,	,	PUNCT
ejpam-4254	675	4	1	1	NUM
ejpam-4254	675	5	]	]	NUM
ejpam-4254	675	6	,	,	PUNCT
ejpam-4254	675	7	respectively	respectively	ADV
ejpam-4254	675	8	.	.	PUNCT
ejpam-4254	676	1	proof	proof	NOUN
ejpam-4254	676	2	.	.	PUNCT
ejpam-4254	677	1	it	it	PRON
ejpam-4254	677	2	is	be	AUX
ejpam-4254	677	3	straightforward	straightforward	ADJ
ejpam-4254	677	4	by	by	ADP
ejpam-4254	677	5	theorem	theorem	NOUN
ejpam-4254	677	6	5	5	NUM
ejpam-4254	677	7	and	and	CCONJ
ejpam-4254	677	8	lemmas	lemmas	PROPN
ejpam-4254	677	9	1	1	NUM
ejpam-4254	677	10	(	(	PUNCT
ejpam-4254	677	11	6	6	NUM
ejpam-4254	677	12	)	)	PUNCT
ejpam-4254	677	13	and	and	CCONJ
ejpam-4254	677	14	(	(	PUNCT
ejpam-4254	677	15	8)	8)	NUM
ejpam-4254	677	16	.	.	PUNCT
ejpam-4254	677	17	theorem	theorem	NOUN
ejpam-4254	677	18	27	27	NUM
ejpam-4254	677	19	.	.	PUNCT
ejpam-4254	678	1	let	let	VERB
ejpam-4254	678	2	ρ	ρ	NOUN
ejpam-4254	678	3	be	be	AUX
ejpam-4254	678	4	a	a	DET
ejpam-4254	678	5	cr	cr	NOUN
ejpam-4254	678	6	on	on	ADP
ejpam-4254	678	7	u	u	PROPN
ejpam-4254	678	8	.	.	PUNCT
ejpam-4254	679	1	then	then	ADV
ejpam-4254	679	2	p	p	PROPN
ejpam-4254	679	3	is	be	AUX
ejpam-4254	679	4	a	a	DET
ejpam-4254	679	5	lorpfupf	lorpfupf	NOUN
ejpam-4254	679	6	of	of	ADP
ejpam-4254	679	7	u	u	PRON
ejpam-4254	679	8	if	if	SCONJ
ejpam-4254	679	9	and	and	CCONJ
ejpam-4254	679	10	only	only	ADV
ejpam-4254	679	11	if	if	SCONJ
ejpam-4254	679	12	u(µp	u(µp	NOUN
ejpam-4254	679	13	,	,	PUNCT
ejpam-4254	679	14	t	t	PROPN
ejpam-4254	679	15	)	)	PUNCT
ejpam-4254	679	16	and	and	CCONJ
ejpam-4254	679	17	l(νp	l(νp	PROPN
ejpam-4254	679	18	,	,	PUNCT
ejpam-4254	679	19	t	t	PROPN
ejpam-4254	679	20	)	)	PUNCT
ejpam-4254	679	21	are	be	AUX
ejpam-4254	679	22	,	,	PUNCT
ejpam-4254	679	23	if	if	SCONJ
ejpam-4254	679	24	the	the	DET
ejpam-4254	679	25	sets	set	NOUN
ejpam-4254	679	26	are	be	AUX
ejpam-4254	679	27	nonempty	nonempty	ADJ
ejpam-4254	679	28	,	,	PUNCT
ejpam-4254	679	29	an	an	DET
ejpam-4254	679	30	uprupf	uprupf	NOUN
ejpam-4254	679	31	and	and	CCONJ
ejpam-4254	679	32	a	a	DET
ejpam-4254	679	33	lorupf	lorupf	NOUN
ejpam-4254	679	34	of	of	ADP
ejpam-4254	679	35	u	u	NOUN
ejpam-4254	679	36	for	for	ADP
ejpam-4254	679	37	every	every	DET
ejpam-4254	679	38	t	t	NOUN
ejpam-4254	679	39	∈	∈	PROPN
ejpam-4254	680	1	[	[	X
ejpam-4254	680	2	0	0	NUM
ejpam-4254	680	3	,	,	PUNCT
ejpam-4254	680	4	1	1	NUM
ejpam-4254	680	5	]	]	NUM
ejpam-4254	680	6	,	,	PUNCT
ejpam-4254	680	7	respectively	respectively	ADV
ejpam-4254	680	8	.	.	PUNCT
ejpam-4254	681	1	proof	proof	NOUN
ejpam-4254	681	2	.	.	PUNCT
ejpam-4254	682	1	it	it	PRON
ejpam-4254	682	2	is	be	AUX
ejpam-4254	682	3	straightforward	straightforward	ADJ
ejpam-4254	682	4	by	by	ADP
ejpam-4254	682	5	theorem	theorem	NOUN
ejpam-4254	682	6	6	6	NUM
ejpam-4254	682	7	and	and	CCONJ
ejpam-4254	682	8	lemmas	lemmas	PROPN
ejpam-4254	682	9	1	1	NUM
ejpam-4254	682	10	(	(	PUNCT
ejpam-4254	682	11	5	5	NUM
ejpam-4254	682	12	)	)	PUNCT
ejpam-4254	682	13	and	and	CCONJ
ejpam-4254	682	14	(	(	PUNCT
ejpam-4254	682	15	7	7	NUM
ejpam-4254	682	16	)	)	PUNCT
ejpam-4254	682	17	.	.	PUNCT
ejpam-4254	683	1	theorem	theorem	PROPN
ejpam-4254	683	2	28	28	NUM
ejpam-4254	683	3	.	.	PUNCT
ejpam-4254	684	1	let	let	VERB
ejpam-4254	684	2	ρ	ρ	NOUN
ejpam-4254	684	3	be	be	AUX
ejpam-4254	684	4	a	a	DET
ejpam-4254	684	5	cr	cr	NOUN
ejpam-4254	684	6	on	on	ADP
ejpam-4254	684	7	u	u	PROPN
ejpam-4254	684	8	.	.	PUNCT
ejpam-4254	685	1	then	then	ADV
ejpam-4254	685	2	p	p	PROPN
ejpam-4254	685	3	is	be	AUX
ejpam-4254	685	4	a	a	DET
ejpam-4254	685	5	lorpfupf	lorpfupf	NOUN
ejpam-4254	685	6	of	of	ADP
ejpam-4254	685	7	u	u	PRON
ejpam-4254	685	8	if	if	SCONJ
ejpam-4254	686	1	and	and	CCONJ
ejpam-4254	686	2	only	only	ADV
ejpam-4254	686	3	if	if	SCONJ
ejpam-4254	686	4	u+(µp	u+(µp	NOUN
ejpam-4254	686	5	,	,	PUNCT
ejpam-4254	686	6	t	t	PROPN
ejpam-4254	686	7	)	)	PUNCT
ejpam-4254	686	8	and	and	CCONJ
ejpam-4254	686	9	l−(νp	l−(νp	PROPN
ejpam-4254	686	10	,	,	PUNCT
ejpam-4254	686	11	t	t	PROPN
ejpam-4254	686	12	)	)	PUNCT
ejpam-4254	686	13	are	be	AUX
ejpam-4254	686	14	,	,	PUNCT
ejpam-4254	686	15	if	if	SCONJ
ejpam-4254	686	16	the	the	DET
ejpam-4254	686	17	sets	set	NOUN
ejpam-4254	686	18	are	be	AUX
ejpam-4254	686	19	nonempty	nonempty	ADJ
ejpam-4254	686	20	,	,	PUNCT
ejpam-4254	686	21	an	an	DET
ejpam-4254	686	22	uprupf	uprupf	NOUN
ejpam-4254	686	23	and	and	CCONJ
ejpam-4254	686	24	a	a	DET
ejpam-4254	686	25	lorupf	lorupf	NOUN
ejpam-4254	686	26	of	of	ADP
ejpam-4254	686	27	u	u	NOUN
ejpam-4254	686	28	for	for	ADP
ejpam-4254	686	29	every	every	DET
ejpam-4254	686	30	t	t	NOUN
ejpam-4254	686	31	∈	∈	PROPN
ejpam-4254	687	1	[	[	X
ejpam-4254	687	2	0	0	NUM
ejpam-4254	687	3	,	,	PUNCT
ejpam-4254	687	4	1	1	NUM
ejpam-4254	687	5	]	]	NUM
ejpam-4254	687	6	,	,	PUNCT
ejpam-4254	687	7	respectively	respectively	ADV
ejpam-4254	687	8	.	.	PUNCT
ejpam-4254	688	1	proof	proof	NOUN
ejpam-4254	688	2	.	.	PUNCT
ejpam-4254	689	1	it	it	PRON
ejpam-4254	689	2	is	be	AUX
ejpam-4254	689	3	straightforward	straightforward	ADJ
ejpam-4254	689	4	by	by	ADP
ejpam-4254	689	5	theorem	theorem	ADJ
ejpam-4254	689	6	7	7	NUM
ejpam-4254	689	7	and	and	CCONJ
ejpam-4254	689	8	lemmas	lemmas	PROPN
ejpam-4254	689	9	1	1	NUM
ejpam-4254	689	10	(	(	PUNCT
ejpam-4254	689	11	6	6	NUM
ejpam-4254	689	12	)	)	PUNCT
ejpam-4254	689	13	and	and	CCONJ
ejpam-4254	689	14	(	(	PUNCT
ejpam-4254	689	15	8)	8)	NUM
ejpam-4254	689	16	.	.	PUNCT
ejpam-4254	689	17	theorem	theorem	NOUN
ejpam-4254	689	18	29	29	NUM
ejpam-4254	689	19	.	.	PUNCT
ejpam-4254	690	1	let	let	VERB
ejpam-4254	690	2	ρ	ρ	NOUN
ejpam-4254	690	3	be	be	AUX
ejpam-4254	690	4	a	a	DET
ejpam-4254	690	5	cr	cr	NOUN
ejpam-4254	690	6	on	on	ADP
ejpam-4254	690	7	u	u	PROPN
ejpam-4254	690	8	.	.	PUNCT
ejpam-4254	691	1	then	then	ADV
ejpam-4254	691	2	p	p	PROPN
ejpam-4254	691	3	is	be	AUX
ejpam-4254	691	4	a	a	DET
ejpam-4254	691	5	lorpfupi	lorpfupi	NOUN
ejpam-4254	691	6	of	of	ADP
ejpam-4254	691	7	u	u	PRON
ejpam-4254	691	8	if	if	SCONJ
ejpam-4254	691	9	and	and	CCONJ
ejpam-4254	691	10	only	only	ADV
ejpam-4254	691	11	if	if	SCONJ
ejpam-4254	691	12	u(µp	u(µp	NOUN
ejpam-4254	691	13	,	,	PUNCT
ejpam-4254	691	14	t	t	PROPN
ejpam-4254	691	15	)	)	PUNCT
ejpam-4254	691	16	and	and	CCONJ
ejpam-4254	691	17	l(νp	l(νp	PROPN
ejpam-4254	691	18	,	,	PUNCT
ejpam-4254	691	19	t	t	PROPN
ejpam-4254	691	20	)	)	PUNCT
ejpam-4254	691	21	are	be	AUX
ejpam-4254	691	22	,	,	PUNCT
ejpam-4254	691	23	if	if	SCONJ
ejpam-4254	691	24	the	the	DET
ejpam-4254	691	25	sets	set	NOUN
ejpam-4254	691	26	are	be	AUX
ejpam-4254	691	27	nonempty	nonempty	ADJ
ejpam-4254	691	28	,	,	PUNCT
ejpam-4254	691	29	an	an	DET
ejpam-4254	691	30	uprupi	uprupi	NOUN
ejpam-4254	691	31	and	and	CCONJ
ejpam-4254	691	32	a	a	DET
ejpam-4254	691	33	lorupi	lorupi	NOUN
ejpam-4254	691	34	of	of	ADP
ejpam-4254	691	35	u	u	NOUN
ejpam-4254	691	36	for	for	ADP
ejpam-4254	691	37	every	every	DET
ejpam-4254	691	38	t	t	NOUN
ejpam-4254	691	39	∈	∈	PROPN
ejpam-4254	692	1	[	[	X
ejpam-4254	692	2	0	0	NUM
ejpam-4254	692	3	,	,	PUNCT
ejpam-4254	692	4	1	1	NUM
ejpam-4254	692	5	]	]	NUM
ejpam-4254	692	6	,	,	PUNCT
ejpam-4254	692	7	respectively	respectively	ADV
ejpam-4254	692	8	.	.	PUNCT
ejpam-4254	693	1	proof	proof	NOUN
ejpam-4254	693	2	.	.	PUNCT
ejpam-4254	694	1	it	it	PRON
ejpam-4254	694	2	is	be	AUX
ejpam-4254	694	3	straightforward	straightforward	ADJ
ejpam-4254	694	4	by	by	ADP
ejpam-4254	694	5	theorem	theorem	ADJ
ejpam-4254	694	6	8	8	NUM
ejpam-4254	694	7	and	and	CCONJ
ejpam-4254	694	8	lemmas	lemmas	PROPN
ejpam-4254	694	9	1	1	NUM
ejpam-4254	694	10	(	(	PUNCT
ejpam-4254	694	11	5	5	NUM
ejpam-4254	694	12	)	)	PUNCT
ejpam-4254	694	13	and	and	CCONJ
ejpam-4254	694	14	(	(	PUNCT
ejpam-4254	694	15	7	7	NUM
ejpam-4254	694	16	)	)	PUNCT
ejpam-4254	694	17	.	.	PUNCT
ejpam-4254	695	1	theorem	theorem	NOUN
ejpam-4254	695	2	30	30	NUM
ejpam-4254	695	3	.	.	PUNCT
ejpam-4254	696	1	let	let	VERB
ejpam-4254	696	2	ρ	ρ	NOUN
ejpam-4254	696	3	be	be	AUX
ejpam-4254	696	4	a	a	DET
ejpam-4254	696	5	cr	cr	NOUN
ejpam-4254	696	6	on	on	ADP
ejpam-4254	696	7	u	u	PROPN
ejpam-4254	696	8	.	.	PUNCT
ejpam-4254	697	1	then	then	ADV
ejpam-4254	697	2	p	p	PROPN
ejpam-4254	697	3	is	be	AUX
ejpam-4254	697	4	a	a	DET
ejpam-4254	697	5	lorpfupi	lorpfupi	NOUN
ejpam-4254	697	6	of	of	ADP
ejpam-4254	697	7	u	u	PRON
ejpam-4254	697	8	if	if	SCONJ
ejpam-4254	698	1	and	and	CCONJ
ejpam-4254	698	2	only	only	ADV
ejpam-4254	698	3	if	if	SCONJ
ejpam-4254	698	4	u+(µp	u+(µp	NOUN
ejpam-4254	698	5	,	,	PUNCT
ejpam-4254	698	6	t	t	PROPN
ejpam-4254	698	7	)	)	PUNCT
ejpam-4254	698	8	and	and	CCONJ
ejpam-4254	698	9	l−(νp	l−(νp	PROPN
ejpam-4254	698	10	,	,	PUNCT
ejpam-4254	698	11	t	t	PROPN
ejpam-4254	698	12	)	)	PUNCT
ejpam-4254	698	13	are	be	AUX
ejpam-4254	698	14	,	,	PUNCT
ejpam-4254	698	15	if	if	SCONJ
ejpam-4254	698	16	the	the	DET
ejpam-4254	698	17	sets	set	NOUN
ejpam-4254	698	18	are	be	AUX
ejpam-4254	698	19	nonempty	nonempty	ADJ
ejpam-4254	698	20	,	,	PUNCT
ejpam-4254	698	21	an	an	DET
ejpam-4254	698	22	uprupi	uprupi	NOUN
ejpam-4254	698	23	and	and	CCONJ
ejpam-4254	698	24	a	a	DET
ejpam-4254	698	25	lorupi	lorupi	NOUN
ejpam-4254	698	26	of	of	ADP
ejpam-4254	698	27	u	u	NOUN
ejpam-4254	698	28	for	for	ADP
ejpam-4254	698	29	every	every	DET
ejpam-4254	698	30	t	t	NOUN
ejpam-4254	698	31	∈	∈	PROPN
ejpam-4254	699	1	[	[	X
ejpam-4254	699	2	0	0	NUM
ejpam-4254	699	3	,	,	PUNCT
ejpam-4254	699	4	1	1	NUM
ejpam-4254	699	5	]	]	NUM
ejpam-4254	699	6	,	,	PUNCT
ejpam-4254	699	7	respectively	respectively	ADV
ejpam-4254	699	8	.	.	PUNCT
ejpam-4254	700	1	proof	proof	NOUN
ejpam-4254	700	2	.	.	PUNCT
ejpam-4254	701	1	it	it	PRON
ejpam-4254	701	2	is	be	AUX
ejpam-4254	701	3	straightforward	straightforward	ADJ
ejpam-4254	701	4	by	by	ADP
ejpam-4254	701	5	theorem	theorem	ADJ
ejpam-4254	701	6	9	9	NUM
ejpam-4254	701	7	and	and	CCONJ
ejpam-4254	701	8	lemmas	lemmas	PROPN
ejpam-4254	701	9	1	1	NUM
ejpam-4254	701	10	(	(	PUNCT
ejpam-4254	701	11	6	6	NUM
ejpam-4254	701	12	)	)	PUNCT
ejpam-4254	701	13	and	and	CCONJ
ejpam-4254	701	14	(	(	PUNCT
ejpam-4254	701	15	8)	8)	NUM
ejpam-4254	701	16	.	.	PUNCT
ejpam-4254	701	17	theorem	theorem	NOUN
ejpam-4254	701	18	31	31	NUM
ejpam-4254	701	19	.	.	PUNCT
ejpam-4254	702	1	let	let	VERB
ejpam-4254	702	2	ρ	ρ	NOUN
ejpam-4254	702	3	be	be	AUX
ejpam-4254	702	4	a	a	DET
ejpam-4254	702	5	cr	cr	NOUN
ejpam-4254	702	6	on	on	ADP
ejpam-4254	702	7	u	u	PROPN
ejpam-4254	702	8	.	.	PUNCT
ejpam-4254	703	1	then	then	ADV
ejpam-4254	703	2	p	p	PROPN
ejpam-4254	703	3	is	be	AUX
ejpam-4254	703	4	a	a	DET
ejpam-4254	703	5	lorpfsupi	lorpfsupi	NOUN
ejpam-4254	703	6	of	of	ADP
ejpam-4254	703	7	u	u	PRON
ejpam-4254	703	8	if	if	SCONJ
ejpam-4254	703	9	and	and	CCONJ
ejpam-4254	703	10	only	only	ADV
ejpam-4254	703	11	if	if	SCONJ
ejpam-4254	703	12	u(µp	u(µp	NOUN
ejpam-4254	703	13	,	,	PUNCT
ejpam-4254	703	14	t	t	PROPN
ejpam-4254	703	15	)	)	PUNCT
ejpam-4254	703	16	and	and	CCONJ
ejpam-4254	703	17	l(νp	l(νp	PROPN
ejpam-4254	703	18	,	,	PUNCT
ejpam-4254	703	19	t	t	PROPN
ejpam-4254	703	20	)	)	PUNCT
ejpam-4254	703	21	are	be	AUX
ejpam-4254	703	22	,	,	PUNCT
ejpam-4254	703	23	if	if	SCONJ
ejpam-4254	703	24	the	the	DET
ejpam-4254	703	25	sets	set	NOUN
ejpam-4254	703	26	are	be	AUX
ejpam-4254	703	27	nonempty	nonempty	ADJ
ejpam-4254	703	28	,	,	PUNCT
ejpam-4254	703	29	an	an	DET
ejpam-4254	703	30	uprsupi	uprsupi	NOUN
ejpam-4254	703	31	and	and	CCONJ
ejpam-4254	703	32	a	a	DET
ejpam-4254	703	33	lorsupi	lorsupi	NOUN
ejpam-4254	703	34	of	of	ADP
ejpam-4254	703	35	u	u	NOUN
ejpam-4254	703	36	for	for	ADP
ejpam-4254	703	37	every	every	DET
ejpam-4254	703	38	t	t	NOUN
ejpam-4254	703	39	∈	∈	PROPN
ejpam-4254	704	1	[	[	X
ejpam-4254	704	2	0	0	NUM
ejpam-4254	704	3	,	,	PUNCT
ejpam-4254	704	4	1	1	NUM
ejpam-4254	704	5	]	]	NUM
ejpam-4254	704	6	,	,	PUNCT
ejpam-4254	704	7	respectively	respectively	ADV
ejpam-4254	704	8	.	.	PUNCT
ejpam-4254	705	1	proof	proof	NOUN
ejpam-4254	705	2	.	.	PUNCT
ejpam-4254	706	1	it	it	PRON
ejpam-4254	706	2	is	be	AUX
ejpam-4254	706	3	straightforward	straightforward	ADJ
ejpam-4254	706	4	by	by	ADP
ejpam-4254	706	5	theorem	theorem	ADJ
ejpam-4254	706	6	10	10	NUM
ejpam-4254	706	7	and	and	CCONJ
ejpam-4254	706	8	lemmas	lemmas	PROPN
ejpam-4254	706	9	1	1	NUM
ejpam-4254	706	10	(	(	PUNCT
ejpam-4254	706	11	5	5	NUM
ejpam-4254	706	12	)	)	PUNCT
ejpam-4254	706	13	and	and	CCONJ
ejpam-4254	706	14	(	(	PUNCT
ejpam-4254	706	15	7	7	NUM
ejpam-4254	706	16	)	)	PUNCT
ejpam-4254	706	17	.	.	PUNCT
ejpam-4254	707	1	theorem	theorem	ADJ
ejpam-4254	707	2	32	32	NUM
ejpam-4254	707	3	.	.	PUNCT
ejpam-4254	708	1	let	let	VERB
ejpam-4254	708	2	ρ	ρ	NOUN
ejpam-4254	708	3	be	be	AUX
ejpam-4254	708	4	a	a	DET
ejpam-4254	708	5	cr	cr	NOUN
ejpam-4254	708	6	on	on	ADP
ejpam-4254	708	7	u	u	PROPN
ejpam-4254	708	8	.	.	PUNCT
ejpam-4254	709	1	then	then	ADV
ejpam-4254	709	2	p	p	PROPN
ejpam-4254	709	3	is	be	AUX
ejpam-4254	709	4	a	a	DET
ejpam-4254	709	5	lorpfsupi	lorpfsupi	NOUN
ejpam-4254	709	6	of	of	ADP
ejpam-4254	709	7	u	u	PRON
ejpam-4254	709	8	if	if	SCONJ
ejpam-4254	710	1	and	and	CCONJ
ejpam-4254	710	2	only	only	ADV
ejpam-4254	710	3	if	if	SCONJ
ejpam-4254	710	4	u+(µp	u+(µp	NOUN
ejpam-4254	710	5	,	,	PUNCT
ejpam-4254	710	6	t	t	PROPN
ejpam-4254	710	7	)	)	PUNCT
ejpam-4254	710	8	and	and	CCONJ
ejpam-4254	710	9	l−(νp	l−(νp	PROPN
ejpam-4254	710	10	,	,	PUNCT
ejpam-4254	710	11	t	t	PROPN
ejpam-4254	710	12	)	)	PUNCT
ejpam-4254	710	13	are	be	AUX
ejpam-4254	710	14	,	,	PUNCT
ejpam-4254	710	15	if	if	SCONJ
ejpam-4254	710	16	the	the	DET
ejpam-4254	710	17	sets	set	NOUN
ejpam-4254	710	18	are	be	AUX
ejpam-4254	710	19	nonempty	nonempty	ADJ
ejpam-4254	710	20	,	,	PUNCT
ejpam-4254	710	21	an	an	DET
ejpam-4254	710	22	uprsupi	uprsupi	NOUN
ejpam-4254	710	23	and	and	CCONJ
ejpam-4254	710	24	a	a	DET
ejpam-4254	710	25	lorsupi	lorsupi	NOUN
ejpam-4254	710	26	of	of	ADP
ejpam-4254	710	27	u	u	NOUN
ejpam-4254	710	28	for	for	ADP
ejpam-4254	710	29	every	every	DET
ejpam-4254	710	30	t	t	NOUN
ejpam-4254	710	31	∈	∈	PROPN
ejpam-4254	711	1	[	[	X
ejpam-4254	711	2	0	0	NUM
ejpam-4254	711	3	,	,	PUNCT
ejpam-4254	711	4	1	1	NUM
ejpam-4254	711	5	]	]	NUM
ejpam-4254	711	6	,	,	PUNCT
ejpam-4254	711	7	respectively	respectively	ADV
ejpam-4254	711	8	.	.	PUNCT
ejpam-4254	712	1	proof	proof	NOUN
ejpam-4254	712	2	.	.	PUNCT
ejpam-4254	713	1	it	it	PRON
ejpam-4254	713	2	is	be	AUX
ejpam-4254	713	3	straightforward	straightforward	ADJ
ejpam-4254	713	4	by	by	ADP
ejpam-4254	713	5	theorem	theorem	ADJ
ejpam-4254	713	6	11	11	NUM
ejpam-4254	713	7	and	and	CCONJ
ejpam-4254	713	8	lemmas	lemmas	PROPN
ejpam-4254	713	9	1	1	NUM
ejpam-4254	713	10	(	(	PUNCT
ejpam-4254	713	11	6	6	NUM
ejpam-4254	713	12	)	)	PUNCT
ejpam-4254	713	13	and	and	CCONJ
ejpam-4254	713	14	(	(	PUNCT
ejpam-4254	713	15	8)	8)	NUM
ejpam-4254	713	16	.	.	PUNCT
ejpam-4254	713	17	theorem	theorem	NOUN
ejpam-4254	713	18	33	33	NUM
ejpam-4254	713	19	.	.	PUNCT
ejpam-4254	714	1	let	let	VERB
ejpam-4254	714	2	ρ	ρ	NOUN
ejpam-4254	714	3	be	be	AUX
ejpam-4254	714	4	a	a	DET
ejpam-4254	714	5	cr	cr	NOUN
ejpam-4254	714	6	on	on	ADP
ejpam-4254	714	7	u	u	PROPN
ejpam-4254	714	8	.	.	PUNCT
ejpam-4254	715	1	then	then	ADV
ejpam-4254	715	2	p	p	PROPN
ejpam-4254	715	3	is	be	AUX
ejpam-4254	715	4	a	a	DET
ejpam-4254	715	5	rpfups	rpfup	NOUN
ejpam-4254	715	6	(	(	PUNCT
ejpam-4254	715	7	resp	resp	NOUN
ejpam-4254	715	8	.	.	PUNCT
ejpam-4254	715	9	,	,	PUNCT
ejpam-4254	715	10	rpfnupf	rpfnupf	PROPN
ejpam-4254	715	11	,	,	PUNCT
ejpam-4254	715	12	rpfupf	rpfupf	PROPN
ejpam-4254	715	13	,	,	PUNCT
ejpam-4254	715	14	rpfupi	rpfupi	NOUN
ejpam-4254	715	15	,	,	PUNCT
ejpam-4254	715	16	and	and	CCONJ
ejpam-4254	715	17	rpfsupi	rpfsupi	NOUN
ejpam-4254	715	18	)	)	PUNCT
ejpam-4254	715	19	of	of	ADP
ejpam-4254	715	20	u	u	PRON
ejpam-4254	715	21	if	if	SCONJ
ejpam-4254	715	22	and	and	CCONJ
ejpam-4254	715	23	only	only	ADV
ejpam-4254	715	24	if	if	SCONJ
ejpam-4254	715	25	u(µp	u(µp	NOUN
ejpam-4254	715	26	,	,	PUNCT
ejpam-4254	715	27	t	t	PROPN
ejpam-4254	715	28	)	)	PUNCT
ejpam-4254	715	29	and	and	CCONJ
ejpam-4254	715	30	l(νp	l(νp	PROPN
ejpam-4254	715	31	,	,	PUNCT
ejpam-4254	715	32	t	t	PROPN
ejpam-4254	715	33	)	)	PUNCT
ejpam-4254	715	34	are	be	AUX
ejpam-4254	715	35	,	,	PUNCT
ejpam-4254	715	36	if	if	SCONJ
ejpam-4254	715	37	the	the	DET
ejpam-4254	715	38	sets	set	NOUN
ejpam-4254	715	39	are	be	AUX
ejpam-4254	715	40	nonempty	nonempty	ADJ
ejpam-4254	715	41	,	,	PUNCT
ejpam-4254	715	42	rupss	rupss	PROPN
ejpam-4254	715	43	(	(	PUNCT
ejpam-4254	715	44	resp	resp	PROPN
ejpam-4254	715	45	.	.	PUNCT
ejpam-4254	715	46	,	,	PUNCT
ejpam-4254	715	47	rnupfs	rnupf	NOUN
ejpam-4254	715	48	,	,	PUNCT
ejpam-4254	715	49	rupfs	rupf	NOUN
ejpam-4254	715	50	,	,	PUNCT
ejpam-4254	715	51	rupis	rupis	ADJ
ejpam-4254	715	52	,	,	PUNCT
ejpam-4254	715	53	and	and	CCONJ
ejpam-4254	715	54	rsupis	rsupi	VERB
ejpam-4254	715	55	)	)	PUNCT
ejpam-4254	715	56	of	of	ADP
ejpam-4254	715	57	u	u	NOUN
ejpam-4254	715	58	for	for	ADP
ejpam-4254	715	59	every	every	DET
ejpam-4254	715	60	t	t	NOUN
ejpam-4254	715	61	∈	∈	PROPN
ejpam-4254	716	1	[	[	X
ejpam-4254	716	2	0	0	NUM
ejpam-4254	716	3	,	,	PUNCT
ejpam-4254	716	4	1	1	NUM
ejpam-4254	716	5	]	]	PUNCT
ejpam-4254	716	6	.	.	PUNCT
ejpam-4254	717	1	references	reference	NOUN
ejpam-4254	717	2	196	196	NUM
ejpam-4254	717	3	proof	proof	NOUN
ejpam-4254	717	4	.	.	PUNCT
ejpam-4254	718	1	it	it	PRON
ejpam-4254	718	2	is	be	AUX
ejpam-4254	718	3	straightforward	straightforward	ADJ
ejpam-4254	718	4	by	by	ADP
ejpam-4254	718	5	theorems	theorem	NOUN
ejpam-4254	718	6	13	13	NUM
ejpam-4254	718	7	(	(	PUNCT
ejpam-4254	718	8	resp	resp	NOUN
ejpam-4254	718	9	.	.	PUNCT
ejpam-4254	718	10	,	,	PUNCT
ejpam-4254	718	11	theorems	theorems	PROPN
ejpam-4254	718	12	15	15	NUM
ejpam-4254	718	13	,	,	PUNCT
ejpam-4254	718	14	17	17	NUM
ejpam-4254	718	15	,	,	PUNCT
ejpam-4254	718	16	19	19	NUM
ejpam-4254	718	17	,	,	PUNCT
ejpam-4254	718	18	21	21	NUM
ejpam-4254	718	19	)	)	PUNCT
ejpam-4254	718	20	and	and	CCONJ
ejpam-4254	718	21	23	23	NUM
ejpam-4254	718	22	(	(	PUNCT
ejpam-4254	718	23	resp	resp	NOUN
ejpam-4254	718	24	.	.	PUNCT
ejpam-4254	718	25	,	,	PUNCT
ejpam-4254	718	26	theorems	theorem	VERB
ejpam-4254	718	27	25	25	NUM
ejpam-4254	718	28	,	,	PUNCT
ejpam-4254	718	29	27	27	NUM
ejpam-4254	718	30	,	,	PUNCT
ejpam-4254	718	31	29	29	NUM
ejpam-4254	718	32	,	,	PUNCT
ejpam-4254	718	33	31	31	NUM
ejpam-4254	718	34	)	)	PUNCT
ejpam-4254	718	35	.	.	PUNCT
ejpam-4254	719	1	theorem	theorem	VERB
ejpam-4254	719	2	34	34	NUM
ejpam-4254	719	3	.	.	PUNCT
ejpam-4254	720	1	let	let	VERB
ejpam-4254	720	2	ρ	ρ	NOUN
ejpam-4254	720	3	be	be	AUX
ejpam-4254	720	4	a	a	DET
ejpam-4254	720	5	cr	cr	NOUN
ejpam-4254	720	6	on	on	ADP
ejpam-4254	720	7	u	u	PROPN
ejpam-4254	720	8	.	.	PUNCT
ejpam-4254	721	1	then	then	ADV
ejpam-4254	721	2	p	p	PROPN
ejpam-4254	721	3	is	be	AUX
ejpam-4254	721	4	a	a	DET
ejpam-4254	721	5	rpfups	rpfup	NOUN
ejpam-4254	721	6	(	(	PUNCT
ejpam-4254	721	7	resp	resp	NOUN
ejpam-4254	721	8	.	.	PUNCT
ejpam-4254	721	9	,	,	PUNCT
ejpam-4254	721	10	rpfnupf	rpfnupf	PROPN
ejpam-4254	721	11	,	,	PUNCT
ejpam-4254	721	12	rpfupf	rpfupf	PROPN
ejpam-4254	721	13	,	,	PUNCT
ejpam-4254	721	14	rpfupi	rpfupi	NOUN
ejpam-4254	721	15	,	,	PUNCT
ejpam-4254	721	16	and	and	CCONJ
ejpam-4254	721	17	rpfsupi	rpfsupi	NOUN
ejpam-4254	721	18	)	)	PUNCT
ejpam-4254	721	19	of	of	ADP
ejpam-4254	721	20	u	u	PRON
ejpam-4254	721	21	if	if	SCONJ
ejpam-4254	722	1	and	and	CCONJ
ejpam-4254	722	2	only	only	ADV
ejpam-4254	722	3	if	if	SCONJ
ejpam-4254	722	4	u+(µp	u+(µp	NOUN
ejpam-4254	722	5	,	,	PUNCT
ejpam-4254	722	6	t	t	PROPN
ejpam-4254	722	7	)	)	PUNCT
ejpam-4254	722	8	and	and	CCONJ
ejpam-4254	722	9	l−(νp	l−(νp	PROPN
ejpam-4254	722	10	,	,	PUNCT
ejpam-4254	722	11	t	t	PROPN
ejpam-4254	722	12	)	)	PUNCT
ejpam-4254	722	13	are	be	AUX
ejpam-4254	722	14	,	,	PUNCT
ejpam-4254	722	15	if	if	SCONJ
ejpam-4254	722	16	the	the	DET
ejpam-4254	722	17	sets	set	NOUN
ejpam-4254	722	18	are	be	AUX
ejpam-4254	722	19	nonempty	nonempty	ADJ
ejpam-4254	722	20	,	,	PUNCT
ejpam-4254	722	21	rupss	rupss	PROPN
ejpam-4254	722	22	(	(	PUNCT
ejpam-4254	722	23	resp	resp	PROPN
ejpam-4254	722	24	.	.	PUNCT
ejpam-4254	722	25	,	,	PUNCT
ejpam-4254	722	26	rnupfs	rnupf	NOUN
ejpam-4254	722	27	,	,	PUNCT
ejpam-4254	722	28	rupfs	rupf	NOUN
ejpam-4254	722	29	,	,	PUNCT
ejpam-4254	722	30	rupis	rupis	ADJ
ejpam-4254	722	31	,	,	PUNCT
ejpam-4254	722	32	and	and	CCONJ
ejpam-4254	722	33	rsupis	rsupi	VERB
ejpam-4254	722	34	)	)	PUNCT
ejpam-4254	722	35	of	of	ADP
ejpam-4254	722	36	u	u	NOUN
ejpam-4254	722	37	for	for	ADP
ejpam-4254	722	38	every	every	DET
ejpam-4254	722	39	t	t	NOUN
ejpam-4254	722	40	∈	∈	PROPN
ejpam-4254	723	1	[	[	X
ejpam-4254	723	2	0	0	NUM
ejpam-4254	723	3	,	,	PUNCT
ejpam-4254	723	4	1	1	NUM
ejpam-4254	723	5	]	]	PUNCT
ejpam-4254	723	6	.	.	PUNCT
ejpam-4254	724	1	proof	proof	NOUN
ejpam-4254	724	2	.	.	PUNCT
ejpam-4254	725	1	it	it	PRON
ejpam-4254	725	2	is	be	AUX
ejpam-4254	725	3	straightforward	straightforward	ADJ
ejpam-4254	725	4	by	by	ADP
ejpam-4254	725	5	theorems	theorem	NOUN
ejpam-4254	725	6	14	14	NUM
ejpam-4254	725	7	(	(	PUNCT
ejpam-4254	725	8	resp	resp	NOUN
ejpam-4254	725	9	.	.	PUNCT
ejpam-4254	725	10	,	,	PUNCT
ejpam-4254	725	11	theorems	theorem	VERB
ejpam-4254	725	12	16	16	NUM
ejpam-4254	725	13	,	,	PUNCT
ejpam-4254	725	14	18	18	NUM
ejpam-4254	725	15	,	,	PUNCT
ejpam-4254	725	16	20	20	NUM
ejpam-4254	725	17	,	,	PUNCT
ejpam-4254	725	18	22	22	NUM
ejpam-4254	725	19	)	)	PUNCT
ejpam-4254	725	20	and	and	CCONJ
ejpam-4254	725	21	24	24	NUM
ejpam-4254	725	22	(	(	PUNCT
ejpam-4254	725	23	resp	resp	NOUN
ejpam-4254	725	24	.	.	PUNCT
ejpam-4254	725	25	,	,	PUNCT
ejpam-4254	725	26	theorems	theorem	VERB
ejpam-4254	725	27	26	26	NUM
ejpam-4254	725	28	,	,	PUNCT
ejpam-4254	725	29	28	28	NUM
ejpam-4254	725	30	,	,	PUNCT
ejpam-4254	725	31	30	30	NUM
ejpam-4254	725	32	,	,	PUNCT
ejpam-4254	725	33	32	32	NUM
ejpam-4254	725	34	)	)	PUNCT
ejpam-4254	725	35	.	.	PUNCT
ejpam-4254	726	1	4	4	X
ejpam-4254	726	2	.	.	X
ejpam-4254	726	3	conclusions	conclusion	NOUN
ejpam-4254	726	4	and	and	CCONJ
ejpam-4254	726	5	future	future	ADJ
ejpam-4254	726	6	works	work	NOUN
ejpam-4254	726	7	in	in	ADP
ejpam-4254	726	8	this	this	DET
ejpam-4254	726	9	paper	paper	NOUN
ejpam-4254	726	10	,	,	PUNCT
ejpam-4254	726	11	we	we	PRON
ejpam-4254	726	12	have	have	AUX
ejpam-4254	726	13	introduced	introduce	VERB
ejpam-4254	726	14	the	the	DET
ejpam-4254	726	15	concept	concept	NOUN
ejpam-4254	726	16	of	of	ADP
ejpam-4254	726	17	rss	rss	NOUN
ejpam-4254	726	18	to	to	PART
ejpam-4254	726	19	pfss	pfss	VERB
ejpam-4254	726	20	in	in	ADP
ejpam-4254	726	21	up	up	ADV
ejpam-4254	726	22	-	-	PUNCT
ejpam-4254	726	23	algebras	algebras	X
ejpam-4254	726	24	.	.	PUNCT
ejpam-4254	727	1	then	then	ADV
ejpam-4254	727	2	we	we	PRON
ejpam-4254	727	3	have	have	AUX
ejpam-4254	727	4	introduced	introduce	VERB
ejpam-4254	727	5	fifteen	fifteen	NUM
ejpam-4254	727	6	types	type	NOUN
ejpam-4254	727	7	of	of	ADP
ejpam-4254	727	8	rpfss	rpfss	NOUN
ejpam-4254	727	9	in	in	ADP
ejpam-4254	727	10	up	up	ADP
ejpam-4254	727	11	-	-	PUNCT
ejpam-4254	727	12	algebras	algebras	X
ejpam-4254	727	13	,	,	PUNCT
ejpam-4254	727	14	namely	namely	ADV
ejpam-4254	727	15	uprpfupss	uprpfupss	PROPN
ejpam-4254	727	16	,	,	PUNCT
ejpam-4254	727	17	uprpfnupfs	uprpfnupf	NOUN
ejpam-4254	727	18	,	,	PUNCT
ejpam-4254	727	19	uprpfupfs	uprpfupf	NOUN
ejpam-4254	727	20	,	,	PUNCT
ejpam-4254	727	21	uprpfupis	uprpfupis	ADJ
ejpam-4254	727	22	,	,	PUNCT
ejpam-4254	727	23	uprpfsupis	uprpfsupis	ADJ
ejpam-4254	727	24	,	,	PUNCT
ejpam-4254	727	25	lorpfupss	lorpfupss	PROPN
ejpam-4254	727	26	,	,	PUNCT
ejpam-4254	727	27	lorpfnupfs	lorpfnupf	NOUN
ejpam-4254	727	28	,	,	PUNCT
ejpam-4254	727	29	lorpfupfs	lorpfupf	NOUN
ejpam-4254	727	30	,	,	PUNCT
ejpam-4254	727	31	lorpfupis	lorpfupis	NOUN
ejpam-4254	727	32	,	,	PUNCT
ejpam-4254	727	33	lorpfsupis	lorpfsupis	ADJ
ejpam-4254	727	34	,	,	PUNCT
ejpam-4254	727	35	rpfupss	rpfupss	PROPN
ejpam-4254	727	36	,	,	PUNCT
ejpam-4254	727	37	rpfnupfs	rpfnupfs	PROPN
ejpam-4254	727	38	,	,	PUNCT
ejpam-4254	727	39	rpfupfs	rpfupf	NOUN
ejpam-4254	727	40	,	,	PUNCT
ejpam-4254	727	41	rpfupis	rpfupis	NOUN
ejpam-4254	727	42	,	,	PUNCT
ejpam-4254	727	43	and	and	CCONJ
ejpam-4254	727	44	rpfsupis	rpfsupis	PROPN
ejpam-4254	727	45	and	and	CCONJ
ejpam-4254	727	46	so	so	ADV
ejpam-4254	727	47	proved	prove	VERB
ejpam-4254	727	48	their	their	PRON
ejpam-4254	727	49	generalizations	generalization	NOUN
ejpam-4254	727	50	.	.	PUNCT
ejpam-4254	728	1	in	in	ADP
ejpam-4254	728	2	addition	addition	NOUN
ejpam-4254	728	3	,	,	PUNCT
ejpam-4254	728	4	we	we	PRON
ejpam-4254	728	5	investigated	investigate	VERB
ejpam-4254	728	6	t	t	NOUN
ejpam-4254	728	7	-	-	PUNCT
ejpam-4254	728	8	level	level	NOUN
ejpam-4254	728	9	subsets	subset	NOUN
ejpam-4254	728	10	of	of	ADP
ejpam-4254	728	11	rpfss	rpfss	NOUN
ejpam-4254	728	12	in	in	ADP
ejpam-4254	728	13	up	up	ADV
ejpam-4254	728	14	-	-	PUNCT
ejpam-4254	728	15	algebras	algebras	NOUN
ejpam-4254	728	16	in	in	ADP
ejpam-4254	728	17	order	order	NOUN
ejpam-4254	728	18	to	to	PART
ejpam-4254	728	19	discuss	discuss	VERB
ejpam-4254	728	20	the	the	DET
ejpam-4254	728	21	relationships	relationship	NOUN
ejpam-4254	728	22	between	between	ADP
ejpam-4254	728	23	rpfss	rpfss	NOUN
ejpam-4254	728	24	and	and	CCONJ
ejpam-4254	728	25	rss	rss	VERB
ejpam-4254	728	26	in	in	ADP
ejpam-4254	728	27	up	up	ADP
ejpam-4254	728	28	-	-	PUNCT
ejpam-4254	728	29	algebras	algebras	X
ejpam-4254	728	30	.	.	PUNCT
ejpam-4254	729	1	the	the	DET
ejpam-4254	729	2	following	follow	VERB
ejpam-4254	729	3	are	be	AUX
ejpam-4254	729	4	some	some	DET
ejpam-4254	729	5	essential	essential	ADJ
ejpam-4254	729	6	subjects	subject	NOUN
ejpam-4254	729	7	for	for	ADP
ejpam-4254	729	8	our	our	PRON
ejpam-4254	729	9	future	future	ADJ
ejpam-4254	729	10	research	research	NOUN
ejpam-4254	729	11	of	of	ADP
ejpam-4254	729	12	up	up	ADP
ejpam-4254	729	13	-	-	PUNCT
ejpam-4254	729	14	algebras	algebras	X
ejpam-4254	729	15	:	:	PUNCT
ejpam-4254	729	16	(	(	PUNCT
ejpam-4254	729	17	1	1	X
ejpam-4254	729	18	)	)	PUNCT
ejpam-4254	729	19	to	to	PART
ejpam-4254	729	20	get	get	VERB
ejpam-4254	729	21	more	more	ADJ
ejpam-4254	729	22	results	result	NOUN
ejpam-4254	729	23	in	in	ADP
ejpam-4254	729	24	rpfss	rpfss	NOUN
ejpam-4254	729	25	,	,	PUNCT
ejpam-4254	729	26	(	(	PUNCT
ejpam-4254	729	27	2	2	X
ejpam-4254	729	28	)	)	PUNCT
ejpam-4254	729	29	to	to	PART
ejpam-4254	729	30	define	define	VERB
ejpam-4254	729	31	more	more	ADJ
ejpam-4254	729	32	types	type	NOUN
ejpam-4254	729	33	of	of	ADP
ejpam-4254	729	34	rpfss	rpfss	NOUN
ejpam-4254	729	35	,	,	PUNCT
ejpam-4254	729	36	and	and	CCONJ
ejpam-4254	729	37	(	(	PUNCT
ejpam-4254	729	38	3	3	X
ejpam-4254	729	39	)	)	PUNCT
ejpam-4254	729	40	to	to	PART
ejpam-4254	729	41	study	study	VERB
ejpam-4254	729	42	the	the	DET
ejpam-4254	729	43	soft	soft	ADJ
ejpam-4254	729	44	set	set	NOUN
ejpam-4254	729	45	theory	theory	NOUN
ejpam-4254	729	46	of	of	ADP
ejpam-4254	729	47	pfss	pfss	NOUN
ejpam-4254	729	48	.	.	PUNCT
ejpam-4254	730	1	acknowledgements	acknowledgement	VERB
ejpam-4254	730	2	this	this	DET
ejpam-4254	730	3	research	research	NOUN
ejpam-4254	730	4	and	and	CCONJ
ejpam-4254	730	5	innovation	innovation	NOUN
ejpam-4254	730	6	activity	activity	NOUN
ejpam-4254	730	7	is	be	AUX
ejpam-4254	730	8	funded	fund	VERB
ejpam-4254	730	9	by	by	ADP
ejpam-4254	730	10	national	national	PROPN
ejpam-4254	730	11	research	research	PROPN
ejpam-4254	730	12	council	council	PROPN
ejpam-4254	730	13	of	of	ADP
ejpam-4254	730	14	thailand	thailand	PROPN
ejpam-4254	730	15	(	(	PUNCT
ejpam-4254	730	16	nrct	nrct	PROPN
ejpam-4254	730	17	)	)	PUNCT
ejpam-4254	730	18	.	.	PUNCT
ejpam-4254	731	1	references	reference	NOUN
ejpam-4254	731	2	[	[	X
ejpam-4254	731	3	1	1	X
ejpam-4254	731	4	]	]	PUNCT
ejpam-4254	731	5	s.	s.	PROPN
ejpam-4254	731	6	s.	s.	PROPN
ejpam-4254	731	7	ahn	ahn	PROPN
ejpam-4254	731	8	and	and	CCONJ
ejpam-4254	731	9	c.	c.	PROPN
ejpam-4254	731	10	kim	kim	PROPN
ejpam-4254	731	11	.	.	PUNCT
ejpam-4254	732	1	rough	rough	ADJ
ejpam-4254	732	2	set	set	NOUN
ejpam-4254	732	3	theory	theory	NOUN
ejpam-4254	732	4	applied	apply	VERB
ejpam-4254	732	5	to	to	ADP
ejpam-4254	732	6	fuzzy	fuzzy	ADJ
ejpam-4254	732	7	filters	filter	NOUN
ejpam-4254	732	8	in	in	ADP
ejpam-4254	732	9	be	be	AUX
ejpam-4254	732	10	-	-	PUNCT
ejpam-4254	732	11	algebras	algebra	NOUN
ejpam-4254	732	12	.	.	PUNCT
ejpam-4254	733	1	commun	commun	PROPN
ejpam-4254	733	2	.	.	PUNCT
ejpam-4254	734	1	korean	korean	ADJ
ejpam-4254	734	2	math	math	PROPN
ejpam-4254	734	3	.	.	PUNCT
ejpam-4254	735	1	soc	soc	PROPN
ejpam-4254	735	2	.	.	PUNCT
ejpam-4254	735	3	,	,	PUNCT
ejpam-4254	735	4	31(3):451–460	31(3):451–460	NUM
ejpam-4254	735	5	,	,	PUNCT
ejpam-4254	735	6	2016	2016	NUM
ejpam-4254	735	7	.	.	PUNCT
ejpam-4254	736	1	[	[	X
ejpam-4254	736	2	2	2	X
ejpam-4254	736	3	]	]	PUNCT
ejpam-4254	736	4	s.	s.	PROPN
ejpam-4254	736	5	s.	s.	PROPN
ejpam-4254	736	6	ahn	ahn	PROPN
ejpam-4254	736	7	and	and	CCONJ
ejpam-4254	736	8	j.	j.	PROPN
ejpam-4254	736	9	m.	m.	PROPN
ejpam-4254	736	10	ko	ko	PROPN
ejpam-4254	736	11	.	.	PUNCT
ejpam-4254	737	1	rough	rough	ADJ
ejpam-4254	737	2	fuzzy	fuzzy	ADJ
ejpam-4254	737	3	ideals	ideal	NOUN
ejpam-4254	737	4	in	in	ADP
ejpam-4254	737	5	bck	bck	PROPN
ejpam-4254	737	6	/	/	SYM
ejpam-4254	737	7	bci	bci	NOUN
ejpam-4254	737	8	-	-	PUNCT
ejpam-4254	737	9	algebras	algebras	X
ejpam-4254	737	10	.	.	PUNCT
ejpam-4254	738	1	j.	j.	PROPN
ejpam-4254	738	2	comput	comput	PROPN
ejpam-4254	738	3	.	.	PUNCT
ejpam-4254	739	1	anal	anal	PROPN
ejpam-4254	739	2	.	.	PUNCT
ejpam-4254	739	3	appl	appl	PROPN
ejpam-4254	739	4	.	.	PROPN
ejpam-4254	739	5	,	,	PUNCT
ejpam-4254	739	6	25(1):75–84	25(1):75–84	NOUN
ejpam-4254	739	7	,	,	PUNCT
ejpam-4254	739	8	2018	2018	NUM
ejpam-4254	739	9	.	.	PUNCT
ejpam-4254	740	1	[	[	X
ejpam-4254	740	2	3	3	X
ejpam-4254	740	3	]	]	PUNCT
ejpam-4254	740	4	m.	m.	NOUN
ejpam-4254	740	5	a.	a.	NOUN
ejpam-4254	740	6	ansari	ansari	PROPN
ejpam-4254	740	7	,	,	PUNCT
ejpam-4254	740	8	a.	a.	PROPN
ejpam-4254	740	9	haidar	haidar	NOUN
ejpam-4254	740	10	,	,	PUNCT
ejpam-4254	740	11	and	and	CCONJ
ejpam-4254	740	12	a.	a.	PROPN
ejpam-4254	740	13	n.	n.	PROPN
ejpam-4254	740	14	a.	a.	PROPN
ejpam-4254	740	15	koam	koam	PROPN
ejpam-4254	740	16	.	.	PUNCT
ejpam-4254	741	1	on	on	ADP
ejpam-4254	741	2	a	a	DET
ejpam-4254	741	3	graph	graph	NOUN
ejpam-4254	741	4	associated	associate	VERB
ejpam-4254	741	5	to	to	ADP
ejpam-4254	741	6	up	up	ADV
ejpam-4254	741	7	-	-	PUNCT
ejpam-4254	741	8	algebras	algebras	PROPN
ejpam-4254	741	9	.	.	PUNCT
ejpam-4254	741	10	math	math	NOUN
ejpam-4254	741	11	.	.	PUNCT
ejpam-4254	742	1	comput	comput	NOUN
ejpam-4254	742	2	.	.	PUNCT
ejpam-4254	743	1	appl	appl	PROPN
ejpam-4254	743	2	.	.	PROPN
ejpam-4254	744	1	,	,	PUNCT
ejpam-4254	744	2	23(4):61	23(4):61	NUM
ejpam-4254	744	3	,	,	PUNCT
ejpam-4254	744	4	2018	2018	NUM
ejpam-4254	744	5	.	.	PUNCT
ejpam-4254	745	1	references	reference	NOUN
ejpam-4254	745	2	197	197	NUM
ejpam-4254	745	3	[	[	SYM
ejpam-4254	745	4	4	4	NUM
ejpam-4254	745	5	]	]	PUNCT
ejpam-4254	745	6	m.	m.	NOUN
ejpam-4254	745	7	a.	a.	NOUN
ejpam-4254	745	8	ansari	ansari	PROPN
ejpam-4254	745	9	,	,	PUNCT
ejpam-4254	745	10	a.	a.	PROPN
ejpam-4254	745	11	n.	n.	PROPN
ejpam-4254	745	12	a.	a.	PROPN
ejpam-4254	745	13	koam	koam	PROPN
ejpam-4254	745	14	,	,	PUNCT
ejpam-4254	745	15	and	and	CCONJ
ejpam-4254	745	16	a.	a.	NOUN
ejpam-4254	745	17	haider	haider	PROPN
ejpam-4254	745	18	.	.	PUNCT
ejpam-4254	746	1	rough	rough	ADJ
ejpam-4254	746	2	set	set	NOUN
ejpam-4254	746	3	theory	theory	NOUN
ejpam-4254	746	4	applied	apply	VERB
ejpam-4254	746	5	to	to	ADP
ejpam-4254	746	6	upalgebras	upalgebra	NOUN
ejpam-4254	746	7	.	.	PUNCT
ejpam-4254	747	1	ital	ital	PROPN
ejpam-4254	747	2	.	.	PUNCT
ejpam-4254	748	1	j.	j.	PROPN
ejpam-4254	748	2	pure	pure	PROPN
ejpam-4254	748	3	appl	appl	PROPN
ejpam-4254	748	4	.	.	PUNCT
ejpam-4254	748	5	math	math	PROPN
ejpam-4254	748	6	.	.	PUNCT
ejpam-4254	748	7	,	,	PUNCT
ejpam-4254	748	8	42:388–402	42:388–402	PROPN
ejpam-4254	748	9	,	,	PUNCT
ejpam-4254	748	10	2019	2019	NUM
ejpam-4254	748	11	.	.	PUNCT
ejpam-4254	749	1	[	[	X
ejpam-4254	749	2	5	5	X
ejpam-4254	749	3	]	]	PUNCT
ejpam-4254	749	4	k.	k.	PROPN
ejpam-4254	749	5	t.	t.	PROPN
ejpam-4254	749	6	atanassov	atanassov	PROPN
ejpam-4254	749	7	.	.	PUNCT
ejpam-4254	750	1	intuitionistic	intuitionistic	ADJ
ejpam-4254	750	2	fuzzy	fuzzy	ADJ
ejpam-4254	750	3	sets	set	NOUN
ejpam-4254	750	4	.	.	PUNCT
ejpam-4254	751	1	fuzzy	fuzzy	ADJ
ejpam-4254	751	2	sets	set	NOUN
ejpam-4254	751	3	syst	syst	PROPN
ejpam-4254	751	4	.	.	PUNCT
ejpam-4254	751	5	,	,	PUNCT
ejpam-4254	751	6	20:87–96	20:87–96	NUM
ejpam-4254	751	7	,	,	PUNCT
ejpam-4254	751	8	1986	1986	NUM
ejpam-4254	751	9	.	.	PUNCT
ejpam-4254	752	1	[	[	X
ejpam-4254	752	2	6	6	NUM
ejpam-4254	752	3	]	]	PUNCT
ejpam-4254	752	4	l.	l.	PROPN
ejpam-4254	752	5	chen	chen	PROPN
ejpam-4254	752	6	and	and	CCONJ
ejpam-4254	752	7	f.	f.	PROPN
ejpam-4254	752	8	wang	wang	PROPN
ejpam-4254	752	9	.	.	PUNCT
ejpam-4254	753	1	on	on	ADP
ejpam-4254	753	2	rough	rough	ADJ
ejpam-4254	753	3	ideals	ideal	NOUN
ejpam-4254	753	4	and	and	CCONJ
ejpam-4254	753	5	rough	rough	ADJ
ejpam-4254	753	6	fuzzy	fuzzy	ADJ
ejpam-4254	753	7	ideals	ideal	NOUN
ejpam-4254	753	8	of	of	ADP
ejpam-4254	753	9	bci	bci	NOUN
ejpam-4254	753	10	-	-	PUNCT
ejpam-4254	753	11	algebras	algebras	ADJ
ejpam-4254	753	12	.	.	PUNCT
ejpam-4254	753	13	fifth	fifth	ADJ
ejpam-4254	753	14	international	international	ADJ
ejpam-4254	753	15	conference	conference	NOUN
ejpam-4254	753	16	on	on	ADP
ejpam-4254	753	17	fuzzy	fuzzy	ADJ
ejpam-4254	753	18	systems	system	NOUN
ejpam-4254	753	19	and	and	CCONJ
ejpam-4254	753	20	knowledge	knowledge	NOUN
ejpam-4254	753	21	discovery	discovery	PROPN
ejpam-4254	753	22	,	,	PUNCT
ejpam-4254	753	23	5:281–284	5:281–284	NUM
ejpam-4254	753	24	,	,	PUNCT
ejpam-4254	753	25	2008	2008	NUM
ejpam-4254	753	26	.	.	PUNCT
ejpam-4254	754	1	[	[	X
ejpam-4254	754	2	7	7	X
ejpam-4254	754	3	]	]	X
ejpam-4254	754	4	r.	r.	PROPN
ejpam-4254	754	5	chinram	chinram	PROPN
ejpam-4254	754	6	and	and	CCONJ
ejpam-4254	754	7	t.	t.	NOUN
ejpam-4254	754	8	panityakul	panityakul	NOUN
ejpam-4254	754	9	.	.	PUNCT
ejpam-4254	755	1	rough	rough	ADJ
ejpam-4254	755	2	pythagorean	pythagorean	PROPN
ejpam-4254	755	3	fuzzy	fuzzy	ADJ
ejpam-4254	755	4	ideals	ideal	NOUN
ejpam-4254	755	5	in	in	ADP
ejpam-4254	755	6	ternary	ternary	ADJ
ejpam-4254	755	7	semigroups	semigroup	NOUN
ejpam-4254	755	8	.	.	PUNCT
ejpam-4254	756	1	j.	j.	PROPN
ejpam-4254	756	2	math	math	PROPN
ejpam-4254	756	3	.	.	PUNCT
ejpam-4254	757	1	computer	computer	NOUN
ejpam-4254	757	2	sci	sci	PROPN
ejpam-4254	757	3	.	.	PROPN
ejpam-4254	757	4	,	,	PUNCT
ejpam-4254	757	5	20:303–312	20:303–312	PROPN
ejpam-4254	757	6	,	,	PUNCT
ejpam-4254	757	7	2020	2020	NUM
ejpam-4254	757	8	.	.	PUNCT
ejpam-4254	758	1	[	[	X
ejpam-4254	758	2	8	8	NUM
ejpam-4254	758	3	]	]	X
ejpam-4254	758	4	n.	n.	PROPN
ejpam-4254	758	5	dokkhamdang	dokkhamdang	PROPN
ejpam-4254	758	6	,	,	PUNCT
ejpam-4254	758	7	a.	a.	PROPN
ejpam-4254	758	8	kesorn	kesorn	PROPN
ejpam-4254	758	9	,	,	PUNCT
ejpam-4254	758	10	and	and	CCONJ
ejpam-4254	758	11	a.	a.	NOUN
ejpam-4254	758	12	iampan	iampan	PROPN
ejpam-4254	758	13	.	.	PUNCT
ejpam-4254	759	1	generalized	generalize	VERB
ejpam-4254	759	2	fuzzy	fuzzy	ADJ
ejpam-4254	759	3	sets	set	NOUN
ejpam-4254	759	4	in	in	ADP
ejpam-4254	759	5	up	up	ADP
ejpam-4254	759	6	-	-	PUNCT
ejpam-4254	759	7	algebras	algebras	X
ejpam-4254	759	8	.	.	PUNCT
ejpam-4254	760	1	ann	ann	PROPN
ejpam-4254	760	2	.	.	PUNCT
ejpam-4254	760	3	fuzzy	fuzzy	ADJ
ejpam-4254	760	4	math	math	NOUN
ejpam-4254	760	5	.	.	PUNCT
ejpam-4254	761	1	inform	inform	NOUN
ejpam-4254	761	2	.	.	PUNCT
ejpam-4254	761	3	,	,	PUNCT
ejpam-4254	761	4	16(2):171–190	16(2):171–190	NUM
ejpam-4254	761	5	,	,	PUNCT
ejpam-4254	761	6	2018	2018	NUM
ejpam-4254	761	7	.	.	PUNCT
ejpam-4254	762	1	[	[	X
ejpam-4254	762	2	9	9	NUM
ejpam-4254	762	3	]	]	X
ejpam-4254	762	4	t.	t.	NOUN
ejpam-4254	762	5	guntasow	guntasow	NOUN
ejpam-4254	762	6	,	,	PUNCT
ejpam-4254	762	7	s.	s.	PROPN
ejpam-4254	762	8	sajak	sajak	PROPN
ejpam-4254	762	9	,	,	PUNCT
ejpam-4254	762	10	a.	a.	PROPN
ejpam-4254	762	11	jomkham	jomkham	PROPN
ejpam-4254	762	12	,	,	PUNCT
ejpam-4254	762	13	and	and	CCONJ
ejpam-4254	762	14	a.	a.	NOUN
ejpam-4254	762	15	iampan	iampan	PROPN
ejpam-4254	762	16	.	.	PUNCT
ejpam-4254	763	1	fuzzy	fuzzy	ADJ
ejpam-4254	763	2	translations	translation	NOUN
ejpam-4254	763	3	of	of	ADP
ejpam-4254	763	4	a	a	DET
ejpam-4254	763	5	fuzzy	fuzzy	ADJ
ejpam-4254	763	6	set	set	NOUN
ejpam-4254	763	7	in	in	ADP
ejpam-4254	763	8	up	up	ADP
ejpam-4254	763	9	-	-	PUNCT
ejpam-4254	763	10	algebras	algebras	X
ejpam-4254	763	11	.	.	PUNCT
ejpam-4254	764	1	j.	j.	PROPN
ejpam-4254	764	2	indones	indones	PROPN
ejpam-4254	764	3	.	.	PUNCT
ejpam-4254	765	1	math	math	NOUN
ejpam-4254	765	2	.	.	PUNCT
ejpam-4254	766	1	soc	soc	PROPN
ejpam-4254	766	2	.	.	PROPN
ejpam-4254	766	3	,	,	PUNCT
ejpam-4254	766	4	23(2):1–19	23(2):1–19	NUM
ejpam-4254	766	5	,	,	PUNCT
ejpam-4254	766	6	2017	2017	NUM
ejpam-4254	766	7	.	.	PUNCT
ejpam-4254	767	1	[	[	X
ejpam-4254	767	2	10	10	NUM
ejpam-4254	767	3	]	]	PUNCT
ejpam-4254	767	4	a.	a.	NOUN
ejpam-4254	767	5	hussain	hussain	PROPN
ejpam-4254	767	6	,	,	PUNCT
ejpam-4254	767	7	t.	t.	PROPN
ejpam-4254	767	8	mahmood	mahmood	PROPN
ejpam-4254	767	9	,	,	PUNCT
ejpam-4254	767	10	and	and	CCONJ
ejpam-4254	767	11	m.	m.	PROPN
ejpam-4254	767	12	i.	i.	PROPN
ejpam-4254	767	13	ali	ali	PROPN
ejpam-4254	767	14	.	.	PUNCT
ejpam-4254	768	1	rough	rough	ADJ
ejpam-4254	768	2	pythagorean	pythagorean	PROPN
ejpam-4254	768	3	fuzzy	fuzzy	ADJ
ejpam-4254	768	4	ideals	ideal	NOUN
ejpam-4254	768	5	in	in	ADP
ejpam-4254	768	6	semigroups	semigroup	NOUN
ejpam-4254	768	7	.	.	PUNCT
ejpam-4254	769	1	comput	comput	NOUN
ejpam-4254	769	2	.	.	PUNCT
ejpam-4254	770	1	appl	appl	PROPN
ejpam-4254	770	2	.	.	PROPN
ejpam-4254	770	3	math	math	PROPN
ejpam-4254	770	4	.	.	PUNCT
ejpam-4254	770	5	,	,	PUNCT
ejpam-4254	770	6	38(15	38(15	NUM
ejpam-4254	770	7	)	)	PUNCT
ejpam-4254	770	8	,	,	PUNCT
ejpam-4254	770	9	1986	1986	NUM
ejpam-4254	770	10	.	.	PUNCT
ejpam-4254	771	1	[	[	X
ejpam-4254	771	2	11	11	NUM
ejpam-4254	771	3	]	]	PUNCT
ejpam-4254	771	4	a.	a.	NOUN
ejpam-4254	771	5	iampan	iampan	PROPN
ejpam-4254	771	6	.	.	PUNCT
ejpam-4254	772	1	a	a	DET
ejpam-4254	772	2	new	new	ADJ
ejpam-4254	772	3	branch	branch	NOUN
ejpam-4254	772	4	of	of	ADP
ejpam-4254	772	5	the	the	DET
ejpam-4254	772	6	logical	logical	ADJ
ejpam-4254	772	7	algebra	algebra	NOUN
ejpam-4254	772	8	:	:	PUNCT
ejpam-4254	772	9	up	up	ADP
ejpam-4254	772	10	-	-	PUNCT
ejpam-4254	772	11	algebras	algebras	X
ejpam-4254	772	12	.	.	PUNCT
ejpam-4254	773	1	j.	j.	PROPN
ejpam-4254	773	2	algebra	algebra	PROPN
ejpam-4254	773	3	relat	relat	PROPN
ejpam-4254	773	4	.	.	PUNCT
ejpam-4254	774	1	top	top	PROPN
ejpam-4254	774	2	.	.	PROPN
ejpam-4254	774	3	,	,	PUNCT
ejpam-4254	774	4	5(1):35–54	5(1):35–54	NUM
ejpam-4254	774	5	,	,	PUNCT
ejpam-4254	774	6	2017	2017	NUM
ejpam-4254	774	7	.	.	PUNCT
ejpam-4254	775	1	[	[	X
ejpam-4254	775	2	12	12	NUM
ejpam-4254	775	3	]	]	PUNCT
ejpam-4254	775	4	a.	a.	NOUN
ejpam-4254	775	5	iampan	iampan	PROPN
ejpam-4254	775	6	.	.	PUNCT
ejpam-4254	776	1	introducing	introduce	VERB
ejpam-4254	776	2	fully	fully	ADV
ejpam-4254	776	3	up	up	ADP
ejpam-4254	776	4	-	-	PUNCT
ejpam-4254	776	5	semigroups	semigroup	NOUN
ejpam-4254	776	6	.	.	PUNCT
ejpam-4254	777	1	discuss	discuss	PROPN
ejpam-4254	777	2	.	.	PUNCT
ejpam-4254	777	3	math	math	PROPN
ejpam-4254	777	4	.	.	PUNCT
ejpam-4254	777	5	,	,	PUNCT
ejpam-4254	778	1	gen	gen	PROPN
ejpam-4254	778	2	.	.	PROPN
ejpam-4254	778	3	algebra	algebra	PROPN
ejpam-4254	778	4	appl	appl	PROPN
ejpam-4254	778	5	.	.	PROPN
ejpam-4254	778	6	,	,	PUNCT
ejpam-4254	778	7	38(2):297–306	38(2):297–306	NUM
ejpam-4254	778	8	,	,	PUNCT
ejpam-4254	778	9	2018	2018	NUM
ejpam-4254	778	10	.	.	PUNCT
ejpam-4254	779	1	[	[	X
ejpam-4254	779	2	13	13	NUM
ejpam-4254	779	3	]	]	PUNCT
ejpam-4254	779	4	a.	a.	NOUN
ejpam-4254	779	5	iampan	iampan	PROPN
ejpam-4254	779	6	.	.	PUNCT
ejpam-4254	780	1	multipliers	multiplier	NOUN
ejpam-4254	780	2	and	and	CCONJ
ejpam-4254	780	3	near	near	ADP
ejpam-4254	780	4	up	up	ADP
ejpam-4254	780	5	-	-	PUNCT
ejpam-4254	780	6	filters	filter	NOUN
ejpam-4254	780	7	of	of	ADP
ejpam-4254	780	8	up	up	ADP
ejpam-4254	780	9	-	-	PUNCT
ejpam-4254	780	10	algebras	algebras	X
ejpam-4254	780	11	.	.	PUNCT
ejpam-4254	781	1	j.	j.	PROPN
ejpam-4254	781	2	discrete	discrete	PROPN
ejpam-4254	781	3	math	math	PROPN
ejpam-4254	781	4	.	.	PUNCT
ejpam-4254	782	1	sci	sci	PROPN
ejpam-4254	782	2	.	.	PUNCT
ejpam-4254	782	3	cryptography	cryptography	PROPN
ejpam-4254	782	4	,	,	PUNCT
ejpam-4254	782	5	24(3):667–680	24(3):667–680	PROPN
ejpam-4254	782	6	,	,	PUNCT
ejpam-4254	782	7	2021	2021	NUM
ejpam-4254	782	8	.	.	PUNCT
ejpam-4254	783	1	[	[	X
ejpam-4254	783	2	14	14	NUM
ejpam-4254	783	3	]	]	PUNCT
ejpam-4254	783	4	a.	a.	NOUN
ejpam-4254	783	5	iampan	iampan	PROPN
ejpam-4254	783	6	,	,	PUNCT
ejpam-4254	783	7	m.	m.	NOUN
ejpam-4254	783	8	songsaeng	songsaeng	PROPN
ejpam-4254	783	9	,	,	PUNCT
ejpam-4254	783	10	and	and	CCONJ
ejpam-4254	783	11	g.	g.	PROPN
ejpam-4254	783	12	muhiuddin	muhiuddin	PROPN
ejpam-4254	783	13	.	.	PUNCT
ejpam-4254	784	1	fuzzy	fuzzy	ADJ
ejpam-4254	784	2	duplex	duplex	PROPN
ejpam-4254	784	3	up	up	ADP
ejpam-4254	784	4	-	-	PUNCT
ejpam-4254	784	5	algebras	algebras	X
ejpam-4254	784	6	.	.	PUNCT
ejpam-4254	785	1	eur	eur	PROPN
ejpam-4254	785	2	.	.	PUNCT
ejpam-4254	786	1	j.	j.	PROPN
ejpam-4254	786	2	pure	pure	PROPN
ejpam-4254	786	3	appl	appl	PROPN
ejpam-4254	786	4	.	.	PUNCT
ejpam-4254	786	5	math	math	PROPN
ejpam-4254	786	6	.	.	PUNCT
ejpam-4254	786	7	,	,	PUNCT
ejpam-4254	786	8	13(3):459–471	13(3):459–471	PROPN
ejpam-4254	786	9	,	,	PUNCT
ejpam-4254	786	10	2020	2020	NUM
ejpam-4254	786	11	.	.	PUNCT
ejpam-4254	787	1	[	[	X
ejpam-4254	787	2	15	15	NUM
ejpam-4254	787	3	]	]	X
ejpam-4254	787	4	y.	y.	PROPN
ejpam-4254	787	5	b.	b.	PROPN
ejpam-4254	787	6	jun	jun	PROPN
ejpam-4254	787	7	,	,	PUNCT
ejpam-4254	787	8	s.-z	s.-z	PROPN
ejpam-4254	787	9	.	.	PUNCT
ejpam-4254	788	1	song	song	NOUN
ejpam-4254	788	2	,	,	PUNCT
ejpam-4254	788	3	and	and	CCONJ
ejpam-4254	788	4	e.	e.	PROPN
ejpam-4254	788	5	h.	h.	PROPN
ejpam-4254	788	6	roh	roh	PROPN
ejpam-4254	788	7	.	.	PUNCT
ejpam-4254	789	1	generalized	generalize	VERB
ejpam-4254	789	2	rough	rough	ADJ
ejpam-4254	789	3	sets	set	NOUN
ejpam-4254	789	4	applied	apply	VERB
ejpam-4254	789	5	to	to	PART
ejpam-4254	789	6	bck	bck	VERB
ejpam-4254	789	7	/	/	SYM
ejpam-4254	789	8	bcialgebras	bcialgebra	NOUN
ejpam-4254	789	9	.	.	PUNCT
ejpam-4254	790	1	discuss	discuss	PROPN
ejpam-4254	790	2	.	.	PUNCT
ejpam-4254	790	3	math	math	PROPN
ejpam-4254	790	4	.	.	PUNCT
ejpam-4254	790	5	,	,	PUNCT
ejpam-4254	790	6	gen	gen	PROPN
ejpam-4254	790	7	.	.	PROPN
ejpam-4254	790	8	algebra	algebra	PROPN
ejpam-4254	790	9	appl	appl	PROPN
ejpam-4254	790	10	.	.	PROPN
ejpam-4254	790	11	,	,	PUNCT
ejpam-4254	790	12	41(2):343–360	41(2):343–360	PROPN
ejpam-4254	790	13	,	,	PUNCT
ejpam-4254	790	14	2021	2021	NUM
ejpam-4254	790	15	.	.	PUNCT
ejpam-4254	791	1	[	[	X
ejpam-4254	791	2	16	16	NUM
ejpam-4254	791	3	]	]	PUNCT
ejpam-4254	791	4	t.	t.	PROPN
ejpam-4254	791	5	klinseesook	klinseesook	PROPN
ejpam-4254	791	6	,	,	PUNCT
ejpam-4254	791	7	s.	s.	PROPN
ejpam-4254	791	8	bukok	bukok	PROPN
ejpam-4254	791	9	,	,	PUNCT
ejpam-4254	791	10	and	and	CCONJ
ejpam-4254	791	11	a.	a.	NOUN
ejpam-4254	791	12	iampan	iampan	PROPN
ejpam-4254	791	13	.	.	PUNCT
ejpam-4254	792	1	rough	rough	ADJ
ejpam-4254	792	2	set	set	NOUN
ejpam-4254	792	3	theory	theory	NOUN
ejpam-4254	792	4	applied	apply	VERB
ejpam-4254	792	5	to	to	ADP
ejpam-4254	792	6	up	up	ADV
ejpam-4254	792	7	-	-	PUNCT
ejpam-4254	792	8	algebras	algebras	X
ejpam-4254	792	9	.	.	PUNCT
ejpam-4254	793	1	j.	j.	PROPN
ejpam-4254	793	2	inf	inf	PROPN
ejpam-4254	793	3	.	.	PROPN
ejpam-4254	793	4	optim	optim	PROPN
ejpam-4254	793	5	.	.	PUNCT
ejpam-4254	794	1	sci	sci	PROPN
ejpam-4254	794	2	.	.	PROPN
ejpam-4254	794	3	,	,	PUNCT
ejpam-4254	794	4	41(3):705–722	41(3):705–722	NUM
ejpam-4254	794	5	,	,	PUNCT
ejpam-4254	794	6	2020	2020	NUM
ejpam-4254	794	7	.	.	PUNCT
ejpam-4254	795	1	[	[	X
ejpam-4254	795	2	17	17	NUM
ejpam-4254	795	3	]	]	X
ejpam-4254	795	4	r.	r.	PROPN
ejpam-4254	795	5	moradiana	moradiana	PROPN
ejpam-4254	795	6	,	,	PUNCT
ejpam-4254	795	7	.	.	PUNCT
ejpam-4254	795	8	s.	s.	PROPN
ejpam-4254	795	9	k.	k.	PROPN
ejpam-4254	795	10	shoarb	shoarb	PROPN
ejpam-4254	795	11	,	,	PUNCT
ejpam-4254	795	12	and	and	CCONJ
ejpam-4254	795	13	a.	a.	NOUN
ejpam-4254	795	14	radfarc	radfarc	PROPN
ejpam-4254	795	15	.	.	PUNCT
ejpam-4254	796	1	rough	rough	ADJ
ejpam-4254	796	2	sets	set	NOUN
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ejpam-4254	796	4	by	by	ADP
ejpam-4254	796	5	fuzzy	fuzzy	ADJ
ejpam-4254	796	6	ideals	ideal	NOUN
ejpam-4254	796	7	in	in	ADP
ejpam-4254	796	8	bck	bck	NOUN
ejpam-4254	796	9	-	-	PUNCT
ejpam-4254	796	10	algebras	algebras	PROPN
ejpam-4254	796	11	.	.	PUNCT
ejpam-4254	797	1	j.	j.	PROPN
ejpam-4254	797	2	intell	intell	PROPN
ejpam-4254	797	3	.	.	PUNCT
ejpam-4254	798	1	fuzzy	fuzzy	ADJ
ejpam-4254	798	2	syst	syst	PROPN
ejpam-4254	798	3	.	.	PROPN
ejpam-4254	798	4	,	,	PUNCT
ejpam-4254	798	5	30:2397–2404	30:2397–2404	PROPN
ejpam-4254	798	6	,	,	PUNCT
ejpam-4254	798	7	2016	2016	NUM
ejpam-4254	798	8	.	.	PUNCT
ejpam-4254	799	1	[	[	X
ejpam-4254	799	2	18	18	NUM
ejpam-4254	799	3	]	]	PUNCT
ejpam-4254	799	4	z.	z.	PROPN
ejpam-4254	799	5	pawlak	pawlak	PROPN
ejpam-4254	799	6	.	.	PUNCT
ejpam-4254	800	1	rough	rough	ADJ
ejpam-4254	800	2	sets	set	NOUN
ejpam-4254	800	3	.	.	PUNCT
ejpam-4254	801	1	int	int	NOUN
ejpam-4254	801	2	.	.	PUNCT
ejpam-4254	802	1	j.	j.	PROPN
ejpam-4254	802	2	inform	inform	PROPN
ejpam-4254	802	3	.	.	PUNCT
ejpam-4254	803	1	comp	comp	PROPN
ejpam-4254	803	2	.	.	PUNCT
ejpam-4254	804	1	sci	sci	PROPN
ejpam-4254	804	2	.	.	PROPN
ejpam-4254	804	3	,	,	PUNCT
ejpam-4254	804	4	11:341–356	11:341–356	NUM
ejpam-4254	804	5	,	,	PUNCT
ejpam-4254	804	6	1982	1982	NUM
ejpam-4254	804	7	.	.	PUNCT
ejpam-4254	805	1	[	[	X
ejpam-4254	805	2	19	19	NUM
ejpam-4254	805	3	]	]	X
ejpam-4254	805	4	c.	c.	NOUN
ejpam-4254	805	5	prabpayak	prabpayak	NOUN
ejpam-4254	805	6	and	and	CCONJ
ejpam-4254	805	7	u.	u.	NOUN
ejpam-4254	805	8	leerawat	leerawat	PROPN
ejpam-4254	805	9	.	.	PUNCT
ejpam-4254	806	1	on	on	ADP
ejpam-4254	806	2	ideals	ideal	NOUN
ejpam-4254	806	3	and	and	CCONJ
ejpam-4254	806	4	congruences	congruence	NOUN
ejpam-4254	806	5	in	in	ADP
ejpam-4254	806	6	ku	ku	PROPN
ejpam-4254	806	7	-	-	PUNCT
ejpam-4254	806	8	algebras	algebras	PROPN
ejpam-4254	806	9	.	.	PUNCT
ejpam-4254	807	1	sci	sci	PROPN
ejpam-4254	807	2	.	.	PROPN
ejpam-4254	807	3	magna	magna	PROPN
ejpam-4254	807	4	,	,	PUNCT
ejpam-4254	807	5	5(1):54–57	5(1):54–57	NUM
ejpam-4254	807	6	,	,	PUNCT
ejpam-4254	807	7	2009	2009	NUM
ejpam-4254	807	8	.	.	PUNCT
ejpam-4254	808	1	[	[	X
ejpam-4254	808	2	20	20	NUM
ejpam-4254	808	3	]	]	PUNCT
ejpam-4254	808	4	a.	a.	NOUN
ejpam-4254	808	5	satirad	satirad	PROPN
ejpam-4254	808	6	,	,	PUNCT
ejpam-4254	808	7	r.	r.	PROPN
ejpam-4254	808	8	chinram	chinram	PROPN
ejpam-4254	808	9	,	,	PUNCT
ejpam-4254	808	10	and	and	CCONJ
ejpam-4254	808	11	a.	a.	NOUN
ejpam-4254	808	12	iampan	iampan	PROPN
ejpam-4254	808	13	.	.	PUNCT
ejpam-4254	809	1	pythagorean	pythagorean	PROPN
ejpam-4254	809	2	fuzzy	fuzzy	ADJ
ejpam-4254	809	3	sets	set	NOUN
ejpam-4254	809	4	in	in	ADP
ejpam-4254	809	5	up	up	ADV
ejpam-4254	809	6	-	-	PUNCT
ejpam-4254	809	7	algebras	algebra	NOUN
ejpam-4254	809	8	and	and	CCONJ
ejpam-4254	809	9	approximations	approximation	NOUN
ejpam-4254	809	10	.	.	PUNCT
ejpam-4254	810	1	aims	aim	VERB
ejpam-4254	810	2	math	math	NOUN
ejpam-4254	810	3	.	.	PUNCT
ejpam-4254	810	4	,	,	PUNCT
ejpam-4254	810	5	6(6):6002–6032	6(6):6002–6032	PROPN
ejpam-4254	810	6	,	,	PUNCT
ejpam-4254	810	7	2021	2021	NUM
ejpam-4254	810	8	.	.	PUNCT
ejpam-4254	811	1	references	reference	NOUN
ejpam-4254	811	2	198	198	NUM
ejpam-4254	811	3	[	[	X
ejpam-4254	811	4	21	21	NUM
ejpam-4254	811	5	]	]	PUNCT
ejpam-4254	811	6	a.	a.	NOUN
ejpam-4254	811	7	satirad	satirad	PROPN
ejpam-4254	811	8	,	,	PUNCT
ejpam-4254	811	9	r.	r.	PROPN
ejpam-4254	811	10	chinram	chinram	PROPN
ejpam-4254	811	11	,	,	PUNCT
ejpam-4254	811	12	p.	p.	PROPN
ejpam-4254	811	13	julatha	julatha	PROPN
ejpam-4254	811	14	,	,	PUNCT
ejpam-4254	811	15	and	and	CCONJ
ejpam-4254	811	16	a.	a.	NOUN
ejpam-4254	811	17	iampan	iampan	PROPN
ejpam-4254	811	18	.	.	PUNCT
ejpam-4254	812	1	some	some	DET
ejpam-4254	812	2	pythagorean	pythagorean	ADJ
ejpam-4254	812	3	fuzzy	fuzzy	ADJ
ejpam-4254	812	4	upfilters	upfilter	NOUN
ejpam-4254	812	5	of	of	ADP
ejpam-4254	812	6	up	up	ADV
ejpam-4254	812	7	-	-	PUNCT
ejpam-4254	812	8	algebras	algebras	NOUN
ejpam-4254	812	9	with	with	ADP
ejpam-4254	812	10	approximations	approximation	NOUN
ejpam-4254	812	11	.	.	PUNCT
ejpam-4254	813	1	manuscript	manuscript	NOUN
ejpam-4254	813	2	submitted	submit	VERB
ejpam-4254	813	3	for	for	ADP
ejpam-4254	813	4	publication	publication	NOUN
ejpam-4254	813	5	,	,	PUNCT
ejpam-4254	813	6	november	november	PROPN
ejpam-4254	813	7	2021	2021	NUM
ejpam-4254	813	8	.	.	PUNCT
ejpam-4254	814	1	[	[	X
ejpam-4254	814	2	22	22	NUM
ejpam-4254	814	3	]	]	PUNCT
ejpam-4254	814	4	a.	a.	NOUN
ejpam-4254	814	5	satirad	satirad	PROPN
ejpam-4254	814	6	,	,	PUNCT
ejpam-4254	814	7	p.	p.	PROPN
ejpam-4254	814	8	mosrijai	mosrijai	PROPN
ejpam-4254	814	9	,	,	PUNCT
ejpam-4254	814	10	and	and	CCONJ
ejpam-4254	814	11	a.	a.	NOUN
ejpam-4254	814	12	iampan	iampan	PROPN
ejpam-4254	814	13	.	.	PUNCT
ejpam-4254	815	1	formulas	formula	NOUN
ejpam-4254	815	2	for	for	ADP
ejpam-4254	815	3	finding	find	VERB
ejpam-4254	815	4	up	up	ADP
ejpam-4254	815	5	-	-	PUNCT
ejpam-4254	815	6	algebras	algebras	X
ejpam-4254	815	7	.	.	PUNCT
ejpam-4254	816	1	int	int	NOUN
ejpam-4254	816	2	.	.	PUNCT
ejpam-4254	817	1	j.	j.	PROPN
ejpam-4254	817	2	math	math	PROPN
ejpam-4254	817	3	.	.	PUNCT
ejpam-4254	818	1	comput	comput	NOUN
ejpam-4254	818	2	.	.	PUNCT
ejpam-4254	819	1	sci	sci	PROPN
ejpam-4254	819	2	.	.	PROPN
ejpam-4254	819	3	,	,	PUNCT
ejpam-4254	819	4	14(2):403–409	14(2):403–409	PROPN
ejpam-4254	819	5	,	,	PUNCT
ejpam-4254	819	6	2019	2019	NUM
ejpam-4254	819	7	.	.	PUNCT
ejpam-4254	820	1	[	[	X
ejpam-4254	820	2	23	23	NUM
ejpam-4254	820	3	]	]	PUNCT
ejpam-4254	820	4	a.	a.	NOUN
ejpam-4254	820	5	satirad	satirad	PROPN
ejpam-4254	820	6	,	,	PUNCT
ejpam-4254	820	7	p.	p.	PROPN
ejpam-4254	820	8	mosrijai	mosrijai	PROPN
ejpam-4254	820	9	,	,	PUNCT
ejpam-4254	820	10	and	and	CCONJ
ejpam-4254	820	11	a.	a.	NOUN
ejpam-4254	820	12	iampan	iampan	PROPN
ejpam-4254	820	13	.	.	PUNCT
ejpam-4254	821	1	generalized	generalized	ADJ
ejpam-4254	821	2	power	power	NOUN
ejpam-4254	821	3	up	up	ADP
ejpam-4254	821	4	-	-	PUNCT
ejpam-4254	821	5	algebras	algebras	PROPN
ejpam-4254	821	6	.	.	PUNCT
ejpam-4254	822	1	int	int	NOUN
ejpam-4254	822	2	.	.	PUNCT
ejpam-4254	823	1	j.	j.	PROPN
ejpam-4254	823	2	math	math	PROPN
ejpam-4254	823	3	.	.	PUNCT
ejpam-4254	824	1	comput	comput	NOUN
ejpam-4254	824	2	.	.	PUNCT
ejpam-4254	825	1	sci	sci	PROPN
ejpam-4254	825	2	.	.	PROPN
ejpam-4254	825	3	,	,	PUNCT
ejpam-4254	825	4	14(1):17–25	14(1):17–25	NUM
ejpam-4254	825	5	,	,	PUNCT
ejpam-4254	825	6	2019	2019	NUM
ejpam-4254	825	7	.	.	PUNCT
ejpam-4254	826	1	[	[	X
ejpam-4254	826	2	24	24	NUM
ejpam-4254	826	3	]	]	PUNCT
ejpam-4254	826	4	t.	t.	NOUN
ejpam-4254	826	5	senapati	senapati	PROPN
ejpam-4254	826	6	,	,	PUNCT
ejpam-4254	826	7	y.	y.	PROPN
ejpam-4254	826	8	b.	b.	PROPN
ejpam-4254	826	9	jun	jun	PROPN
ejpam-4254	826	10	,	,	PUNCT
ejpam-4254	826	11	and	and	CCONJ
ejpam-4254	826	12	k.	k.	PROPN
ejpam-4254	826	13	p.	p.	PROPN
ejpam-4254	826	14	shum	shum	PROPN
ejpam-4254	826	15	.	.	PUNCT
ejpam-4254	827	1	cubic	cubic	ADJ
ejpam-4254	827	2	set	set	VERB
ejpam-4254	827	3	structure	structure	NOUN
ejpam-4254	827	4	applied	apply	VERB
ejpam-4254	827	5	in	in	ADP
ejpam-4254	827	6	up	up	ADP
ejpam-4254	827	7	-	-	PUNCT
ejpam-4254	827	8	algebras	algebras	X
ejpam-4254	827	9	.	.	PUNCT
ejpam-4254	828	1	discrete	discrete	ADJ
ejpam-4254	828	2	math	math	NOUN
ejpam-4254	828	3	.	.	PUNCT
ejpam-4254	829	1	algorithms	algorithms	PROPN
ejpam-4254	829	2	appl	appl	PROPN
ejpam-4254	829	3	.	.	PROPN
ejpam-4254	829	4	,	,	PUNCT
ejpam-4254	829	5	10(4):1850049	10(4):1850049	NUM
ejpam-4254	829	6	,	,	PUNCT
ejpam-4254	829	7	2018	2018	NUM
ejpam-4254	829	8	.	.	PUNCT
ejpam-4254	830	1	[	[	X
ejpam-4254	830	2	25	25	NUM
ejpam-4254	830	3	]	]	PUNCT
ejpam-4254	830	4	t.	t.	NOUN
ejpam-4254	830	5	senapati	senapati	PROPN
ejpam-4254	830	6	,	,	PUNCT
ejpam-4254	830	7	g.	g.	PROPN
ejpam-4254	830	8	muhiuddin	muhiuddin	PROPN
ejpam-4254	830	9	,	,	PUNCT
ejpam-4254	830	10	and	and	CCONJ
ejpam-4254	830	11	k.	k.	PROPN
ejpam-4254	830	12	p.	p.	PROPN
ejpam-4254	830	13	shum	shum	PROPN
ejpam-4254	830	14	.	.	PUNCT
ejpam-4254	831	1	representation	representation	NOUN
ejpam-4254	831	2	of	of	ADP
ejpam-4254	831	3	up	up	ADV
ejpam-4254	831	4	-	-	PUNCT
ejpam-4254	831	5	algebras	algebras	NOUN
ejpam-4254	831	6	in	in	ADP
ejpam-4254	831	7	interval	interval	NOUN
ejpam-4254	831	8	-	-	PUNCT
ejpam-4254	831	9	valued	value	VERB
ejpam-4254	831	10	intuitionistic	intuitionistic	ADJ
ejpam-4254	831	11	fuzzy	fuzzy	ADJ
ejpam-4254	831	12	environment	environment	NOUN
ejpam-4254	831	13	.	.	PUNCT
ejpam-4254	832	1	ital	ital	PROPN
ejpam-4254	832	2	.	.	PUNCT
ejpam-4254	833	1	j.	j.	PROPN
ejpam-4254	833	2	pure	pure	PROPN
ejpam-4254	833	3	appl	appl	PROPN
ejpam-4254	833	4	.	.	PUNCT
ejpam-4254	833	5	math	math	PROPN
ejpam-4254	833	6	.	.	PUNCT
ejpam-4254	833	7	,	,	PUNCT
ejpam-4254	833	8	38:497	38:497	NUM
ejpam-4254	833	9	–	–	PUNCT
ejpam-4254	833	10	517	517	NUM
ejpam-4254	833	11	,	,	PUNCT
ejpam-4254	833	12	2017	2017	NUM
ejpam-4254	833	13	.	.	PUNCT
ejpam-4254	834	1	[	[	X
ejpam-4254	834	2	26	26	NUM
ejpam-4254	834	3	]	]	PUNCT
ejpam-4254	834	4	j.	j.	PROPN
ejpam-4254	834	5	somjanta	somjanta	PROPN
ejpam-4254	834	6	,	,	PUNCT
ejpam-4254	834	7	n.	n.	PROPN
ejpam-4254	834	8	thuekaew	thuekaew	PROPN
ejpam-4254	834	9	,	,	PUNCT
ejpam-4254	834	10	p.	p.	NOUN
ejpam-4254	834	11	kumpeangkeaw	kumpeangkeaw	PROPN
ejpam-4254	834	12	,	,	PUNCT
ejpam-4254	834	13	and	and	CCONJ
ejpam-4254	834	14	a.	a.	NOUN
ejpam-4254	834	15	iampan	iampan	PROPN
ejpam-4254	834	16	.	.	PUNCT
ejpam-4254	835	1	fuzzy	fuzzy	ADJ
ejpam-4254	835	2	sets	set	NOUN
ejpam-4254	835	3	in	in	ADP
ejpam-4254	835	4	upalgebras	upalgebra	NOUN
ejpam-4254	835	5	.	.	PUNCT
ejpam-4254	836	1	ann	ann	PROPN
ejpam-4254	836	2	.	.	PUNCT
ejpam-4254	836	3	fuzzy	fuzzy	ADJ
ejpam-4254	836	4	math	math	NOUN
ejpam-4254	836	5	.	.	PUNCT
ejpam-4254	837	1	inform	inform	NOUN
ejpam-4254	837	2	.	.	PUNCT
ejpam-4254	837	3	,	,	PUNCT
ejpam-4254	837	4	12(6):739–756	12(6):739–756	PROPN
ejpam-4254	837	5	,	,	PUNCT
ejpam-4254	837	6	2016	2016	NUM
ejpam-4254	837	7	.	.	PUNCT
ejpam-4254	838	1	[	[	X
ejpam-4254	838	2	27	27	NUM
ejpam-4254	838	3	]	]	X
ejpam-4254	838	4	r.	r.	PROPN
ejpam-4254	838	5	r.	r.	PROPN
ejpam-4254	838	6	yager	yager	PROPN
ejpam-4254	838	7	.	.	PUNCT
ejpam-4254	839	1	pythagorean	pythagorean	PROPN
ejpam-4254	839	2	fuzzy	fuzzy	ADJ
ejpam-4254	839	3	subsets	subset	NOUN
ejpam-4254	839	4	.	.	PUNCT
ejpam-4254	840	1	in	in	ADP
ejpam-4254	840	2	:	:	PUNCT
ejpam-4254	840	3	proc	proc	NOUN
ejpam-4254	840	4	joint	joint	PROPN
ejpam-4254	840	5	ifsa	ifsa	PROPN
ejpam-4254	840	6	world	world	PROPN
ejpam-4254	840	7	congress	congress	PROPN
ejpam-4254	840	8	and	and	CCONJ
ejpam-4254	840	9	nafips	nafip	NOUN
ejpam-4254	840	10	annual	annual	ADJ
ejpam-4254	840	11	meeting	meeting	NOUN
ejpam-4254	840	12	,	,	PUNCT
ejpam-4254	840	13	edmomton	edmomton	PROPN
ejpam-4254	840	14	,	,	PUNCT
ejpam-4254	840	15	canada	canada	PROPN
ejpam-4254	840	16	,	,	PUNCT
ejpam-4254	840	17	pages	page	NOUN
ejpam-4254	840	18	57–61	57–61	NUM
ejpam-4254	840	19	,	,	PUNCT
ejpam-4254	840	20	2013	2013	NUM
ejpam-4254	840	21	.	.	PUNCT
ejpam-4254	841	1	[	[	X
ejpam-4254	841	2	28	28	NUM
ejpam-4254	841	3	]	]	X
ejpam-4254	841	4	r.	r.	PROPN
ejpam-4254	841	5	r.	r.	PROPN
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ejpam-4254	841	8	a.	a.	NOUN
ejpam-4254	841	9	m.	m.	NOUN
ejpam-4254	841	10	abbasov	abbasov	PROPN
ejpam-4254	841	11	.	.	PUNCT
ejpam-4254	842	1	pythagorean	pythagorean	PROPN
ejpam-4254	842	2	member	member	NOUN
ejpam-4254	842	3	grades	grade	NOUN
ejpam-4254	842	4	,	,	PUNCT
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ejpam-4254	842	6	numbers	number	NOUN
ejpam-4254	842	7	,	,	PUNCT
ejpam-4254	842	8	and	and	CCONJ
ejpam-4254	842	9	decision	decision	NOUN
ejpam-4254	842	10	making	making	NOUN
ejpam-4254	842	11	.	.	PUNCT
ejpam-4254	843	1	int	int	NOUN
ejpam-4254	843	2	.	.	PUNCT
ejpam-4254	844	1	j.	j.	PROPN
ejpam-4254	844	2	intell	intell	PROPN
ejpam-4254	844	3	.	.	PUNCT
ejpam-4254	845	1	syst	syst	PROPN
ejpam-4254	845	2	.	.	PROPN
ejpam-4254	845	3	,	,	PUNCT
ejpam-4254	845	4	28:436–452	28:436–452	NOUN
ejpam-4254	845	5	,	,	PUNCT
ejpam-4254	845	6	2013	2013	NUM
ejpam-4254	845	7	.	.	PUNCT
ejpam-4254	846	1	[	[	X
ejpam-4254	846	2	29	29	NUM
ejpam-4254	846	3	]	]	X
ejpam-4254	846	4	l.	l.	PROPN
ejpam-4254	846	5	a.	a.	PROPN
ejpam-4254	846	6	zadeh	zadeh	PROPN
ejpam-4254	846	7	.	.	PUNCT
ejpam-4254	846	8	fuzzy	fuzzy	ADJ
ejpam-4254	846	9	sets	set	NOUN
ejpam-4254	846	10	.	.	PUNCT
ejpam-4254	847	1	inf	inf	PROPN
ejpam-4254	847	2	.	.	PUNCT
ejpam-4254	847	3	cont	cont	PROPN
ejpam-4254	847	4	.	.	PROPN
ejpam-4254	847	5	,	,	PUNCT
ejpam-4254	847	6	8:338–353	8:338–353	NUM
ejpam-4254	847	7	,	,	PUNCT
ejpam-4254	847	8	1965	1965	NUM
ejpam-4254	847	9	.	.	PUNCT