id	sid	tid	token	lemma	pos
ejpam-2291	1	1	european	european	PROPN
ejpam-2291	1	2	journal	journal	PROPN
ejpam-2291	1	3	of	of	ADP
ejpam-2291	1	4	pure	pure	ADJ
ejpam-2291	1	5	and	and	CCONJ
ejpam-2291	1	6	applied	apply	VERB
ejpam-2291	1	7	mathematics	mathematic	NOUN
ejpam-2291	1	8	vol	vol	NOUN
ejpam-2291	1	9	.	.	PUNCT
ejpam-2291	2	1	7	7	NUM
ejpam-2291	2	2	,	,	PUNCT
ejpam-2291	2	3	no	no	INTJ
ejpam-2291	2	4	.	.	NOUN
ejpam-2291	2	5	4	4	NUM
ejpam-2291	2	6	,	,	PUNCT
ejpam-2291	2	7	2014	2014	NUM
ejpam-2291	2	8	,	,	PUNCT
ejpam-2291	2	9	429	429	NUM
ejpam-2291	2	10	-	-	SYM
ejpam-2291	2	11	436	436	NUM
ejpam-2291	2	12	issn	issn	PROPN
ejpam-2291	2	13	1307	1307	NUM
ejpam-2291	2	14	-	-	SYM
ejpam-2291	2	15	5543	5543	NUM
ejpam-2291	2	16	–	–	PUNCT
ejpam-2291	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2291	2	18	regularity	regularity	NOUN
ejpam-2291	2	19	of	of	ADP
ejpam-2291	2	20	the	the	DET
ejpam-2291	2	21	rees	ree	NOUN
ejpam-2291	2	22	and	and	CCONJ
ejpam-2291	2	23	associated	associate	VERB
ejpam-2291	2	24	graded	grade	VERB
ejpam-2291	2	25	modules	module	NOUN
ejpam-2291	2	26	naser	naser	PROPN
ejpam-2291	2	27	zamani	zamani	PROPN
ejpam-2291	2	28	faculty	faculty	PROPN
ejpam-2291	2	29	of	of	ADP
ejpam-2291	2	30	mathematical	mathematical	ADJ
ejpam-2291	2	31	sciences	sciences	PROPN
ejpam-2291	2	32	,	,	PUNCT
ejpam-2291	2	33	university	university	NOUN
ejpam-2291	2	34	of	of	ADP
ejpam-2291	2	35	mohaghegh	mohaghegh	PROPN
ejpam-2291	2	36	ardabili	ardabili	PROPN
ejpam-2291	2	37	,	,	PUNCT
ejpam-2291	2	38	ardabil	ardabil	VERB
ejpam-2291	2	39	,	,	PUNCT
ejpam-2291	2	40	iran	iran	PROPN
ejpam-2291	2	41	abstract	abstract	NOUN
ejpam-2291	2	42	.	.	PUNCT
ejpam-2291	3	1	let	let	VERB
ejpam-2291	3	2	a	a	PRON
ejpam-2291	3	3	be	be	AUX
ejpam-2291	3	4	a	a	DET
ejpam-2291	3	5	noetherian	noetherian	ADJ
ejpam-2291	3	6	ring	ring	NOUN
ejpam-2291	3	7	and	and	CCONJ
ejpam-2291	3	8	b	b	NOUN
ejpam-2291	3	9	be	be	AUX
ejpam-2291	3	10	an	an	DET
ejpam-2291	3	11	ideal	ideal	NOUN
ejpam-2291	3	12	of	of	ADP
ejpam-2291	3	13	a.	a.	NOUN
ejpam-2291	3	14	let	let	VERB
ejpam-2291	3	15	e	e	PRON
ejpam-2291	3	16	be	be	AUX
ejpam-2291	3	17	a	a	DET
ejpam-2291	3	18	finitely	finitely	ADV
ejpam-2291	3	19	generated	generate	VERB
ejpam-2291	3	20	a	a	DET
ejpam-2291	3	21	-	-	PUNCT
ejpam-2291	3	22	module	module	NOUN
ejpam-2291	3	23	.	.	PUNCT
ejpam-2291	4	1	it	it	PRON
ejpam-2291	4	2	is	be	AUX
ejpam-2291	4	3	shown	show	VERB
ejpam-2291	4	4	that	that	SCONJ
ejpam-2291	4	5	there	there	PRON
ejpam-2291	4	6	is	be	VERB
ejpam-2291	4	7	a	a	DET
ejpam-2291	4	8	close	close	ADJ
ejpam-2291	4	9	relationship	relationship	NOUN
ejpam-2291	4	10	between	between	ADP
ejpam-2291	4	11	the	the	DET
ejpam-2291	4	12	cohomological	cohomological	ADJ
ejpam-2291	4	13	invariants	invariant	NOUN
ejpam-2291	4	14	of	of	ADP
ejpam-2291	4	15	the	the	DET
ejpam-2291	4	16	associated	associate	VERB
ejpam-2291	4	17	graded	grade	VERB
ejpam-2291	4	18	module	module	NOUN
ejpam-2291	4	19	of	of	ADP
ejpam-2291	4	20	e	e	NOUN
ejpam-2291	4	21	with	with	ADP
ejpam-2291	4	22	respect	respect	NOUN
ejpam-2291	4	23	to	to	ADP
ejpam-2291	4	24	b	b	NOUN
ejpam-2291	4	25	and	and	CCONJ
ejpam-2291	4	26	the	the	DET
ejpam-2291	4	27	rees	ree	NOUN
ejpam-2291	4	28	module	module	NOUN
ejpam-2291	4	29	of	of	ADP
ejpam-2291	4	30	e	e	NOUN
ejpam-2291	4	31	associated	associate	VERB
ejpam-2291	4	32	to	to	ADP
ejpam-2291	4	33	b.	b.	PROPN
ejpam-2291	4	34	also	also	ADV
ejpam-2291	4	35	a	a	DET
ejpam-2291	4	36	formula	formula	NOUN
ejpam-2291	4	37	for	for	ADP
ejpam-2291	4	38	the	the	DET
ejpam-2291	4	39	regularity	regularity	NOUN
ejpam-2291	4	40	of	of	ADP
ejpam-2291	4	41	the	the	DET
ejpam-2291	4	42	rees	rees	PROPN
ejpam-2291	4	43	module	module	NOUN
ejpam-2291	4	44	of	of	ADP
ejpam-2291	4	45	e	e	NOUN
ejpam-2291	4	46	associated	associate	VERB
ejpam-2291	4	47	to	to	ADP
ejpam-2291	4	48	b	b	NOUN
ejpam-2291	4	49	will	will	AUX
ejpam-2291	4	50	be	be	AUX
ejpam-2291	4	51	given	give	VERB
ejpam-2291	4	52	.	.	PUNCT
ejpam-2291	5	1	2010	2010	NUM
ejpam-2291	5	2	mathematics	mathematic	NOUN
ejpam-2291	5	3	subject	subject	NOUN
ejpam-2291	5	4	classifications	classification	NOUN
ejpam-2291	5	5	:	:	PUNCT
ejpam-2291	5	6	13a99	13a99	NUM
ejpam-2291	5	7	,	,	PUNCT
ejpam-2291	5	8	13d45	13d45	NOUN
ejpam-2291	5	9	key	key	ADJ
ejpam-2291	5	10	words	word	NOUN
ejpam-2291	5	11	and	and	CCONJ
ejpam-2291	5	12	phrases	phrase	NOUN
ejpam-2291	5	13	:	:	PUNCT
ejpam-2291	5	14	associated	associate	VERB
ejpam-2291	5	15	graded	grade	VERB
ejpam-2291	5	16	rings	ring	NOUN
ejpam-2291	5	17	and	and	CCONJ
ejpam-2291	5	18	modules	module	NOUN
ejpam-2291	5	19	,	,	PUNCT
ejpam-2291	5	20	graded	grade	VERB
ejpam-2291	5	21	local	local	ADJ
ejpam-2291	5	22	cohomology	cohomology	NOUN
ejpam-2291	5	23	,	,	PUNCT
ejpam-2291	5	24	reduction	reduction	NOUN
ejpam-2291	5	25	number	number	NOUN
ejpam-2291	5	26	,	,	PUNCT
ejpam-2291	5	27	filter	filter	NOUN
ejpam-2291	5	28	regular	regular	ADJ
ejpam-2291	5	29	sequence	sequence	NOUN
ejpam-2291	5	30	1	1	NUM
ejpam-2291	5	31	.	.	PUNCT
ejpam-2291	6	1	introduction	introduction	NOUN
ejpam-2291	6	2	let	let	VERB
ejpam-2291	6	3	s	s	PRON
ejpam-2291	6	4	=	=	PUNCT
ejpam-2291	6	5	⊕n≥0sn	⊕n≥0sn	AUX
ejpam-2291	6	6	be	be	AUX
ejpam-2291	6	7	a	a	DET
ejpam-2291	6	8	finitely	finitely	ADV
ejpam-2291	6	9	generated	generate	VERB
ejpam-2291	6	10	standard	standard	NOUN
ejpam-2291	6	11	graded	grade	VERB
ejpam-2291	6	12	algebra	algebra	NOUN
ejpam-2291	6	13	over	over	ADP
ejpam-2291	6	14	a	a	DET
ejpam-2291	6	15	noetherian	noetherian	ADJ
ejpam-2291	6	16	commutative	commutative	ADJ
ejpam-2291	6	17	ring	ring	NOUN
ejpam-2291	6	18	s0	s0	PROPN
ejpam-2291	6	19	.	.	PUNCT
ejpam-2291	7	1	we	we	PRON
ejpam-2291	7	2	denote	denote	VERB
ejpam-2291	7	3	by	by	ADP
ejpam-2291	7	4	s+	s+	NOUN
ejpam-2291	7	5	=	=	PUNCT
ejpam-2291	7	6	⊕n≥1sn	⊕n≥1sn	NOUN
ejpam-2291	7	7	the	the	DET
ejpam-2291	7	8	ideal	ideal	NOUN
ejpam-2291	7	9	generated	generate	VERB
ejpam-2291	7	10	by	by	ADP
ejpam-2291	7	11	the	the	DET
ejpam-2291	7	12	homogeneous	homogeneous	ADJ
ejpam-2291	7	13	elements	element	NOUN
ejpam-2291	7	14	of	of	ADP
ejpam-2291	7	15	positive	positive	ADJ
ejpam-2291	7	16	degree	degree	NOUN
ejpam-2291	7	17	of	of	ADP
ejpam-2291	7	18	s.	s.	PROPN
ejpam-2291	7	19	for	for	ADP
ejpam-2291	7	20	a	a	DET
ejpam-2291	7	21	graded	grade	VERB
ejpam-2291	7	22	s	s	NOUN
ejpam-2291	7	23	-	-	PUNCT
ejpam-2291	7	24	module	module	NOUN
ejpam-2291	7	25	l	l	NOUN
ejpam-2291	7	26	,	,	PUNCT
ejpam-2291	7	27	the	the	DET
ejpam-2291	7	28	homogeneous	homogeneous	ADJ
ejpam-2291	7	29	part	part	NOUN
ejpam-2291	7	30	of	of	ADP
ejpam-2291	7	31	degree	degree	NOUN
ejpam-2291	7	32	n	n	PROPN
ejpam-2291	7	33	of	of	ADP
ejpam-2291	7	34	l	l	NOUN
ejpam-2291	7	35	,	,	PUNCT
ejpam-2291	7	36	is	be	AUX
ejpam-2291	7	37	denoted	denote	VERB
ejpam-2291	7	38	by	by	ADP
ejpam-2291	7	39	ln	ln	ADJ
ejpam-2291	7	40	,	,	PUNCT
ejpam-2291	7	41	and	and	CCONJ
ejpam-2291	7	42	l(t	l(t	NOUN
ejpam-2291	7	43	)	)	PUNCT
ejpam-2291	7	44	is	be	AUX
ejpam-2291	7	45	the	the	DET
ejpam-2291	7	46	same	same	ADJ
ejpam-2291	7	47	module	module	NOUN
ejpam-2291	7	48	l	l	NOUN
ejpam-2291	7	49	shifted	shift	VERB
ejpam-2291	7	50	by	by	ADP
ejpam-2291	7	51	t.	t.	PROPN
ejpam-2291	7	52	the	the	DET
ejpam-2291	7	53	end	end	NOUN
ejpam-2291	7	54	of	of	ADP
ejpam-2291	7	55	l	l	NOUN
ejpam-2291	7	56	is	be	AUX
ejpam-2291	7	57	defined	define	VERB
ejpam-2291	7	58	by	by	ADP
ejpam-2291	7	59	end(l	end(l	PROPN
ejpam-2291	7	60	)	)	PUNCT
ejpam-2291	7	61	=	=	PRON
ejpam-2291	7	62	max{n	max{n	NOUN
ejpam-2291	7	63	:	:	PUNCT
ejpam-2291	7	64	ln	ln	ADJ
ejpam-2291	7	65	6=	6=	NOUN
ejpam-2291	7	66	0	0	NUM
ejpam-2291	7	67	}	}	PUNCT
ejpam-2291	7	68	,	,	PUNCT
ejpam-2291	7	69	and	and	CCONJ
ejpam-2291	7	70	end(0	end(0	NOUN
ejpam-2291	7	71	)	)	PUNCT
ejpam-2291	8	1	=	=	PUNCT
ejpam-2291	8	2	−∞	−∞	PUNCT
ejpam-2291	8	3	by	by	ADP
ejpam-2291	8	4	convention	convention	NOUN
ejpam-2291	8	5	.	.	PUNCT
ejpam-2291	9	1	for	for	ADP
ejpam-2291	9	2	each	each	DET
ejpam-2291	9	3	i	i	PRON
ejpam-2291	9	4	≥	≥	NOUN
ejpam-2291	9	5	0	0	NUM
ejpam-2291	9	6	,	,	PUNCT
ejpam-2291	9	7	the	the	DET
ejpam-2291	9	8	ith	ith	PROPN
ejpam-2291	9	9	local	local	ADJ
ejpam-2291	9	10	cohomology	cohomology	NOUN
ejpam-2291	9	11	module	module	NOUN
ejpam-2291	9	12	h	h	NOUN
ejpam-2291	9	13	i	i	PRON
ejpam-2291	9	14	s+	s+	ADV
ejpam-2291	9	15	(	(	PUNCT
ejpam-2291	9	16	l	l	NOUN
ejpam-2291	9	17	)	)	PUNCT
ejpam-2291	9	18	of	of	ADP
ejpam-2291	9	19	a	a	DET
ejpam-2291	9	20	graded	grade	VERB
ejpam-2291	9	21	s	s	NOUN
ejpam-2291	9	22	-	-	PUNCT
ejpam-2291	9	23	module	module	NOUN
ejpam-2291	9	24	l	l	NOUN
ejpam-2291	9	25	supported	support	VERB
ejpam-2291	9	26	in	in	ADP
ejpam-2291	9	27	s+	s+	ADV
ejpam-2291	9	28	is	be	AUX
ejpam-2291	9	29	also	also	ADV
ejpam-2291	9	30	a	a	DET
ejpam-2291	9	31	graded	grade	VERB
ejpam-2291	9	32	s	s	NOUN
ejpam-2291	9	33	-	-	NOUN
ejpam-2291	9	34	module	module	NOUN
ejpam-2291	9	35	in	in	ADP
ejpam-2291	9	36	a	a	DET
ejpam-2291	9	37	natural	natural	ADJ
ejpam-2291	9	38	way	way	NOUN
ejpam-2291	9	39	and	and	CCONJ
ejpam-2291	9	40	h	h	NOUN
ejpam-2291	10	1	i	i	PRON
ejpam-2291	10	2	s+	s+	ADV
ejpam-2291	10	3	(	(	PUNCT
ejpam-2291	10	4	l)n	l)n	X
ejpam-2291	10	5	is	be	AUX
ejpam-2291	10	6	a	a	DET
ejpam-2291	10	7	finitely	finitely	ADV
ejpam-2291	10	8	generated	generate	VERB
ejpam-2291	10	9	s0	s0	NOUN
ejpam-2291	10	10	-	-	PUNCT
ejpam-2291	10	11	module	module	NOUN
ejpam-2291	10	12	for	for	ADP
ejpam-2291	10	13	all	all	PRON
ejpam-2291	10	14	i	i	PRON
ejpam-2291	10	15	≥	≥	VERB
ejpam-2291	10	16	0	0	NUM
ejpam-2291	10	17	and	and	CCONJ
ejpam-2291	10	18	all	all	PRON
ejpam-2291	10	19	n	n	CCONJ
ejpam-2291	10	20	,	,	PUNCT
ejpam-2291	10	21	and	and	CCONJ
ejpam-2291	10	22	it	it	PRON
ejpam-2291	10	23	is	be	AUX
ejpam-2291	10	24	zero	zero	NUM
ejpam-2291	10	25	for	for	ADP
ejpam-2291	10	26	for	for	ADP
ejpam-2291	10	27	large	large	ADJ
ejpam-2291	10	28	values	value	NOUN
ejpam-2291	10	29	of	of	ADP
ejpam-2291	10	30	n	n	PROPN
ejpam-2291	10	31	(	(	PUNCT
ejpam-2291	10	32	see	see	VERB
ejpam-2291	10	33	[	[	X
ejpam-2291	10	34	1	1	NUM
ejpam-2291	10	35	,	,	PUNCT
ejpam-2291	10	36	chapter	chapter	NOUN
ejpam-2291	10	37	15	15	NUM
ejpam-2291	10	38	]	]	PUNCT
ejpam-2291	10	39	)	)	PUNCT
ejpam-2291	10	40	.	.	PUNCT
ejpam-2291	11	1	following	follow	VERB
ejpam-2291	11	2	[	[	X
ejpam-2291	11	3	3	3	NUM
ejpam-2291	11	4	]	]	PUNCT
ejpam-2291	11	5	,	,	PUNCT
ejpam-2291	11	6	we	we	PRON
ejpam-2291	11	7	put	put	VERB
ejpam-2291	11	8	ai(l	ai(l	PRON
ejpam-2291	11	9	)	)	PUNCT
ejpam-2291	11	10	=	=	SYM
ejpam-2291	12	1	end(h	end(h	PROPN
ejpam-2291	13	1	i	i	PRON
ejpam-2291	13	2	s+	s+	X
ejpam-2291	13	3	(	(	PUNCT
ejpam-2291	13	4	l	l	NOUN
ejpam-2291	13	5	)	)	PUNCT
ejpam-2291	13	6	)	)	PUNCT
ejpam-2291	13	7	.	.	PUNCT
ejpam-2291	14	1	then	then	ADV
ejpam-2291	14	2	the	the	DET
ejpam-2291	14	3	regularity	regularity	NOUN
ejpam-2291	14	4	of	of	ADP
ejpam-2291	14	5	l	l	NOUN
ejpam-2291	14	6	is	be	AUX
ejpam-2291	14	7	defined	define	VERB
ejpam-2291	14	8	by	by	ADP
ejpam-2291	14	9	reg(l	reg(l	X
ejpam-2291	14	10	)	)	PUNCT
ejpam-2291	15	1	=	=	SYM
ejpam-2291	15	2	max{ai(l	max{ai(l	X
ejpam-2291	15	3	)	)	PUNCT
ejpam-2291	16	1	+	+	CCONJ
ejpam-2291	16	2	i	i	PRON
ejpam-2291	16	3	:	:	PUNCT
ejpam-2291	16	4	i	i	PRON
ejpam-2291	16	5	≥	≥	VERB
ejpam-2291	16	6	0	0	NUM
ejpam-2291	16	7	}	}	PUNCT
ejpam-2291	16	8	.	.	PUNCT
ejpam-2291	17	1	let	let	VERB
ejpam-2291	17	2	a	a	PRON
ejpam-2291	17	3	be	be	AUX
ejpam-2291	17	4	a	a	DET
ejpam-2291	17	5	noetherian	noetherian	ADJ
ejpam-2291	17	6	commutative	commutative	ADJ
ejpam-2291	17	7	ring	ring	NOUN
ejpam-2291	17	8	and	and	CCONJ
ejpam-2291	17	9	b	b	NOUN
ejpam-2291	17	10	an	an	DET
ejpam-2291	17	11	ideal	ideal	NOUN
ejpam-2291	17	12	of	of	ADP
ejpam-2291	17	13	a.	a.	NOUN
ejpam-2291	17	14	let	let	VERB
ejpam-2291	17	15	e	e	PRON
ejpam-2291	17	16	be	be	AUX
ejpam-2291	17	17	a	a	DET
ejpam-2291	17	18	finitely	finitely	ADV
ejpam-2291	17	19	generated	generate	VERB
ejpam-2291	17	20	a	a	DET
ejpam-2291	17	21	-	-	PUNCT
ejpam-2291	17	22	module	module	NOUN
ejpam-2291	17	23	.	.	PUNCT
ejpam-2291	18	1	we	we	PRON
ejpam-2291	18	2	denote	denote	VERB
ejpam-2291	18	3	by	by	ADP
ejpam-2291	18	4	rb(e	rb(e	NOUN
ejpam-2291	18	5	)	)	PUNCT
ejpam-2291	18	6	=	=	SYM
ejpam-2291	19	1	⊕n≥0b	⊕n≥0b	NOUN
ejpam-2291	19	2	ne	ne	X
ejpam-2291	20	1	the	the	DET
ejpam-2291	20	2	rees	rees	PROPN
ejpam-2291	20	3	module	module	NOUN
ejpam-2291	20	4	of	of	ADP
ejpam-2291	20	5	e	e	NOUN
ejpam-2291	20	6	associated	associate	VERB
ejpam-2291	20	7	to	to	ADP
ejpam-2291	20	8	b	b	PROPN
ejpam-2291	20	9	and	and	CCONJ
ejpam-2291	20	10	by	by	ADP
ejpam-2291	20	11	gb(e	gb(e	ADJ
ejpam-2291	20	12	)	)	PUNCT
ejpam-2291	20	13	=	=	SYM
ejpam-2291	20	14	⊕n≥0b	⊕n≥0b	X
ejpam-2291	20	15	ne	ne	PROPN
ejpam-2291	20	16	/	/	SYM
ejpam-2291	20	17	bn+1e	bn+1e	NOUN
ejpam-2291	20	18	=	=	SYM
ejpam-2291	20	19	rb(e)/brb(e	rb(e)/brb(e	PROPN
ejpam-2291	20	20	)	)	PUNCT
ejpam-2291	20	21	the	the	DET
ejpam-2291	20	22	associated	associate	VERB
ejpam-2291	20	23	graded	grade	VERB
ejpam-2291	20	24	module	module	NOUN
ejpam-2291	20	25	of	of	ADP
ejpam-2291	20	26	e	e	NOUN
ejpam-2291	20	27	with	with	ADP
ejpam-2291	20	28	respect	respect	NOUN
ejpam-2291	20	29	to	to	ADP
ejpam-2291	20	30	b.	b.	PROPN
ejpam-2291	20	31	in	in	ADP
ejpam-2291	20	32	the	the	DET
ejpam-2291	20	33	case	case	NOUN
ejpam-2291	20	34	e	e	NOUN
ejpam-2291	20	35	=	=	PUNCT
ejpam-2291	20	36	a	a	X
ejpam-2291	20	37	,	,	PUNCT
ejpam-2291	20	38	these	these	DET
ejpam-2291	20	39	modules	module	NOUN
ejpam-2291	20	40	are	be	AUX
ejpam-2291	20	41	denoted	denote	VERB
ejpam-2291	20	42	by	by	ADP
ejpam-2291	20	43	r(b	r(b	PROPN
ejpam-2291	20	44	)	)	PUNCT
ejpam-2291	20	45	and	and	CCONJ
ejpam-2291	20	46	g(b	g(b	PROPN
ejpam-2291	20	47	)	)	PUNCT
ejpam-2291	20	48	=	=	SYM
ejpam-2291	20	49	r(b)/br(b	r(b)/br(b	PROPN
ejpam-2291	20	50	)	)	PUNCT
ejpam-2291	20	51	respectively	respectively	ADV
ejpam-2291	20	52	.	.	PUNCT
ejpam-2291	21	1	recall	recall	NOUN
ejpam-2291	21	2	from	from	ADP
ejpam-2291	21	3	[	[	X
ejpam-2291	21	4	2	2	NUM
ejpam-2291	21	5	,	,	PUNCT
ejpam-2291	21	6	definition	definition	NOUN
ejpam-2291	21	7	4.6.4	4.6.4	NUM
ejpam-2291	21	8	]	]	PUNCT
ejpam-2291	21	9	that	that	SCONJ
ejpam-2291	21	10	an	an	DET
ejpam-2291	21	11	ideal	ideal	NOUN
ejpam-2291	21	12	a	a	DET
ejpam-2291	21	13	⊆	⊆	NUM
ejpam-2291	21	14	b	b	NOUN
ejpam-2291	21	15	is	be	AUX
ejpam-2291	21	16	called	call	VERB
ejpam-2291	21	17	a	a	DET
ejpam-2291	21	18	reduction	reduction	NOUN
ejpam-2291	21	19	of	of	ADP
ejpam-2291	21	20	b	b	NOUN
ejpam-2291	21	21	with	with	ADP
ejpam-2291	21	22	respect	respect	NOUN
ejpam-2291	21	23	to	to	ADP
ejpam-2291	21	24	e	e	NOUN
ejpam-2291	21	25	if	if	SCONJ
ejpam-2291	21	26	rb(e	rb(e	VERB
ejpam-2291	21	27	)	)	PUNCT
ejpam-2291	21	28	is	be	AUX
ejpam-2291	21	29	a	a	DET
ejpam-2291	21	30	finitely	finitely	ADV
ejpam-2291	21	31	generated	generate	VERB
ejpam-2291	21	32	r(a)-module	r(a)-module	PROPN
ejpam-2291	21	33	,	,	PUNCT
ejpam-2291	21	34	or	or	CCONJ
ejpam-2291	21	35	equivalently	equivalently	ADV
ejpam-2291	21	36	,	,	PUNCT
ejpam-2291	21	37	if	if	SCONJ
ejpam-2291	21	38	br+1e	br+1e	NOUN
ejpam-2291	21	39	=	=	PRON
ejpam-2291	21	40	abr	abr	X
ejpam-2291	21	41	e	e	NOUN
ejpam-2291	21	42	for	for	ADP
ejpam-2291	21	43	some	some	DET
ejpam-2291	21	44	email	email	NOUN
ejpam-2291	21	45	address	address	NOUN
ejpam-2291	21	46	:	:	PUNCT
ejpam-2291	22	1	naserzaka@yahoo.com	naserzaka@yahoo.com	X
ejpam-2291	22	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2291	23	1	429	429	NUM
ejpam-2291	24	1	c	c	X
ejpam-2291	24	2	©	©	PROPN
ejpam-2291	24	3	2014	2014	NUM
ejpam-2291	24	4	ejpam	ejpam	NOUN
ejpam-2291	24	5	all	all	DET
ejpam-2291	24	6	rights	right	NOUN
ejpam-2291	24	7	reserved	reserve	VERB
ejpam-2291	24	8	.	.	PUNCT
ejpam-2291	25	1	n.	n.	PROPN
ejpam-2291	25	2	zamani	zamani	PROPN
ejpam-2291	25	3	/	/	SYM
ejpam-2291	25	4	eur	eur	PROPN
ejpam-2291	25	5	.	.	PUNCT
ejpam-2291	26	1	j.	j.	PROPN
ejpam-2291	26	2	pure	pure	PROPN
ejpam-2291	26	3	appl	appl	PROPN
ejpam-2291	26	4	.	.	PROPN
ejpam-2291	26	5	math	math	PROPN
ejpam-2291	26	6	,	,	PUNCT
ejpam-2291	26	7	7	7	NUM
ejpam-2291	26	8	(	(	PUNCT
ejpam-2291	26	9	2014	2014	NUM
ejpam-2291	26	10	)	)	PUNCT
ejpam-2291	26	11	,	,	PUNCT
ejpam-2291	26	12	429	429	NUM
ejpam-2291	26	13	-	-	SYM
ejpam-2291	26	14	436	436	NUM
ejpam-2291	26	15	430	430	NUM
ejpam-2291	26	16	r	r	NOUN
ejpam-2291	26	17	≥	≥	NOUN
ejpam-2291	26	18	0	0	NUM
ejpam-2291	26	19	.	.	PUNCT
ejpam-2291	27	1	the	the	DET
ejpam-2291	27	2	least	least	ADJ
ejpam-2291	27	3	such	such	ADJ
ejpam-2291	27	4	r	r	NOUN
ejpam-2291	27	5	is	be	AUX
ejpam-2291	27	6	denoted	denote	VERB
ejpam-2291	27	7	by	by	ADP
ejpam-2291	27	8	ra(b	ra(b	NUM
ejpam-2291	27	9	,	,	PUNCT
ejpam-2291	27	10	e	e	NOUN
ejpam-2291	27	11	)	)	PUNCT
ejpam-2291	27	12	.	.	PUNCT
ejpam-2291	28	1	this	this	DET
ejpam-2291	28	2	paper	paper	NOUN
ejpam-2291	28	3	is	be	AUX
ejpam-2291	28	4	divided	divide	VERB
ejpam-2291	28	5	into	into	ADP
ejpam-2291	28	6	3	3	NUM
ejpam-2291	28	7	sections	section	NOUN
ejpam-2291	28	8	.	.	PUNCT
ejpam-2291	29	1	in	in	ADP
ejpam-2291	29	2	section	section	NOUN
ejpam-2291	29	3	2	2	NUM
ejpam-2291	29	4	we	we	PRON
ejpam-2291	29	5	prepare	prepare	VERB
ejpam-2291	29	6	some	some	DET
ejpam-2291	29	7	results	result	NOUN
ejpam-2291	29	8	related	relate	VERB
ejpam-2291	29	9	to	to	ADP
ejpam-2291	29	10	the	the	DET
ejpam-2291	29	11	castelnuovo	castelnuovo	PROPN
ejpam-2291	29	12	regularity	regularity	NOUN
ejpam-2291	29	13	of	of	ADP
ejpam-2291	29	14	a	a	DET
ejpam-2291	29	15	graded	grade	VERB
ejpam-2291	29	16	module	module	NOUN
ejpam-2291	29	17	,	,	PUNCT
ejpam-2291	29	18	from	from	ADP
ejpam-2291	29	19	which	which	PRON
ejpam-2291	29	20	we	we	PRON
ejpam-2291	29	21	prove	prove	VERB
ejpam-2291	29	22	in	in	ADP
ejpam-2291	29	23	theorem	theorem	NOUN
ejpam-2291	29	24	1	1	NUM
ejpam-2291	29	25	that	that	SCONJ
ejpam-2291	29	26	reg(l	reg(l	NOUN
ejpam-2291	29	27	)	)	PUNCT
ejpam-2291	29	28	can	can	AUX
ejpam-2291	29	29	be	be	AUX
ejpam-2291	29	30	characterized	characterize	VERB
ejpam-2291	29	31	in	in	ADP
ejpam-2291	29	32	terms	term	NOUN
ejpam-2291	29	33	of	of	ADP
ejpam-2291	29	34	a	a	DET
ejpam-2291	29	35	minimal	minimal	ADJ
ejpam-2291	29	36	reduction	reduction	NOUN
ejpam-2291	29	37	of	of	ADP
ejpam-2291	29	38	s+	s+	NOUN
ejpam-2291	29	39	with	with	ADP
ejpam-2291	29	40	respect	respect	NOUN
ejpam-2291	29	41	to	to	ADP
ejpam-2291	29	42	l	l	NOUN
ejpam-2291	29	43	,	,	PUNCT
ejpam-2291	29	44	which	which	PRON
ejpam-2291	29	45	is	be	AUX
ejpam-2291	29	46	generated	generate	VERB
ejpam-2291	29	47	by	by	ADP
ejpam-2291	29	48	an	an	DET
ejpam-2291	29	49	s+-filter	s+-filter	NOUN
ejpam-2291	29	50	regular	regular	ADJ
ejpam-2291	29	51	sequence	sequence	NOUN
ejpam-2291	29	52	of	of	ADP
ejpam-2291	29	53	homogeneous	homogeneous	ADJ
ejpam-2291	29	54	elements	element	NOUN
ejpam-2291	29	55	of	of	ADP
ejpam-2291	29	56	degree	degree	NOUN
ejpam-2291	29	57	1	1	NUM
ejpam-2291	29	58	,	,	PUNCT
ejpam-2291	29	59	for	for	ADP
ejpam-2291	29	60	l.	l.	PROPN
ejpam-2291	29	61	in	in	ADP
ejpam-2291	29	62	section	section	NOUN
ejpam-2291	29	63	3	3	NUM
ejpam-2291	29	64	,	,	PUNCT
ejpam-2291	29	65	using	use	VERB
ejpam-2291	29	66	the	the	DET
ejpam-2291	29	67	ideas	idea	NOUN
ejpam-2291	29	68	of	of	ADP
ejpam-2291	29	69	[	[	X
ejpam-2291	29	70	5	5	NUM
ejpam-2291	29	71	]	]	PUNCT
ejpam-2291	29	72	,	,	PUNCT
ejpam-2291	29	73	we	we	PRON
ejpam-2291	29	74	will	will	AUX
ejpam-2291	29	75	show	show	VERB
ejpam-2291	29	76	that	that	SCONJ
ejpam-2291	29	77	there	there	PRON
ejpam-2291	29	78	is	be	VERB
ejpam-2291	29	79	a	a	DET
ejpam-2291	29	80	close	close	ADJ
ejpam-2291	29	81	relationship	relationship	NOUN
ejpam-2291	29	82	between	between	ADP
ejpam-2291	29	83	the	the	DET
ejpam-2291	29	84	invariants	invariant	NOUN
ejpam-2291	29	85	ai(rb(e	ai(rb(e	ADJ
ejpam-2291	29	86	)	)	PUNCT
ejpam-2291	29	87	)	)	PUNCT
ejpam-2291	29	88	and	and	CCONJ
ejpam-2291	29	89	ai(gb(e	ai(gb(e	PROPN
ejpam-2291	29	90	)	)	PUNCT
ejpam-2291	29	91	)	)	PUNCT
ejpam-2291	29	92	,	,	PUNCT
ejpam-2291	29	93	from	from	ADP
ejpam-2291	29	94	which	which	PRON
ejpam-2291	29	95	we	we	PRON
ejpam-2291	29	96	can	can	AUX
ejpam-2291	29	97	easily	easily	ADV
ejpam-2291	29	98	derive	derive	VERB
ejpam-2291	29	99	the	the	DET
ejpam-2291	29	100	formula	formula	NOUN
ejpam-2291	29	101	reg(rb(e	reg(rb(e	PROPN
ejpam-2291	29	102	)	)	PUNCT
ejpam-2291	29	103	)	)	PUNCT
ejpam-2291	30	1	=	=	SYM
ejpam-2291	30	2	reg(gb(e	reg(gb(e	PROPN
ejpam-2291	30	3	)	)	PUNCT
ejpam-2291	30	4	)	)	PUNCT
ejpam-2291	30	5	.	.	PUNCT
ejpam-2291	31	1	also	also	ADV
ejpam-2291	31	2	we	we	PRON
ejpam-2291	31	3	give	give	VERB
ejpam-2291	31	4	a	a	DET
ejpam-2291	31	5	formula	formula	NOUN
ejpam-2291	31	6	for	for	ADP
ejpam-2291	31	7	the	the	DET
ejpam-2291	31	8	number	number	NOUN
ejpam-2291	31	9	reg(rb(e	reg(rb(e	PROPN
ejpam-2291	31	10	)	)	PUNCT
ejpam-2291	31	11	)	)	PUNCT
ejpam-2291	31	12	in	in	ADP
ejpam-2291	31	13	corollary	corollary	ADJ
ejpam-2291	31	14	4	4	NUM
ejpam-2291	31	15	.	.	NOUN
ejpam-2291	31	16	2	2	NUM
ejpam-2291	31	17	.	.	X
ejpam-2291	31	18	preliminaries	preliminary	NOUN
ejpam-2291	31	19	from	from	ADP
ejpam-2291	31	20	now	now	ADV
ejpam-2291	31	21	on	on	ADV
ejpam-2291	31	22	assume	assume	VERB
ejpam-2291	31	23	that	that	SCONJ
ejpam-2291	31	24	l	l	NOUN
ejpam-2291	31	25	is	be	AUX
ejpam-2291	31	26	finitely	finitely	ADV
ejpam-2291	31	27	generated	generate	VERB
ejpam-2291	31	28	.	.	PUNCT
ejpam-2291	32	1	let	let	VERB
ejpam-2291	32	2	f	f	NOUN
ejpam-2291	32	3	=	=	PUNCT
ejpam-2291	32	4	f1	f1	PROPN
ejpam-2291	32	5	,	,	PUNCT
ejpam-2291	32	6	.	.	PUNCT
ejpam-2291	32	7	.	.	PUNCT
ejpam-2291	33	1	.	.	PUNCT
ejpam-2291	34	1	,	,	PUNCT
ejpam-2291	34	2	fh	fh	PROPN
ejpam-2291	34	3	be	be	AUX
ejpam-2291	34	4	a	a	DET
ejpam-2291	34	5	sequence	sequence	NOUN
ejpam-2291	34	6	of	of	ADP
ejpam-2291	34	7	homogeneous	homogeneous	ADJ
ejpam-2291	34	8	elements	element	NOUN
ejpam-2291	34	9	of	of	ADP
ejpam-2291	34	10	s.	s.	PROPN
ejpam-2291	34	11	we	we	PRON
ejpam-2291	34	12	call	call	VERB
ejpam-2291	34	13	f1	f1	NOUN
ejpam-2291	34	14	,	,	PUNCT
ejpam-2291	34	15	.	.	PUNCT
ejpam-2291	34	16	.	.	PUNCT
ejpam-2291	35	1	.	.	PUNCT
ejpam-2291	36	1	,	,	PUNCT
ejpam-2291	36	2	fh	fh	PROPN
ejpam-2291	36	3	an	an	DET
ejpam-2291	36	4	s+-filter	s+-filter	NOUN
ejpam-2291	36	5	regular	regular	ADJ
ejpam-2291	36	6	sequence	sequence	NOUN
ejpam-2291	36	7	for	for	ADP
ejpam-2291	36	8	l	l	NOUN
ejpam-2291	36	9	if	if	SCONJ
ejpam-2291	36	10	for	for	ADP
ejpam-2291	36	11	all	all	DET
ejpam-2291	36	12	i	i	PRON
ejpam-2291	36	13	=	=	NOUN
ejpam-2291	36	14	1	1	NUM
ejpam-2291	36	15	,	,	PUNCT
ejpam-2291	36	16	.	.	PUNCT
ejpam-2291	36	17	.	.	PUNCT
ejpam-2291	36	18	.	.	PUNCT
ejpam-2291	37	1	,	,	PUNCT
ejpam-2291	37	2	h	h	PROPN
ejpam-2291	37	3	fi	fi	NOUN
ejpam-2291	37	4	/∈	/∈	PUNCT
ejpam-2291	38	1	⋃	⋃	NOUN
ejpam-2291	38	2	p∈asss(l/	p∈asss(l/	NOUN
ejpam-2291	38	3	(	(	PUNCT
ejpam-2291	38	4	f1	f1	NOUN
ejpam-2291	38	5	,	,	PUNCT
ejpam-2291	38	6	...	...	PUNCT
ejpam-2291	38	7	,	,	PUNCT
ejpam-2291	38	8	fi−1)l)\v	fi−1)l)\v	PROPN
ejpam-2291	38	9	(	(	PUNCT
ejpam-2291	38	10	s+	s+	X
ejpam-2291	38	11	)	)	PUNCT
ejpam-2291	39	1	p	p	X
ejpam-2291	39	2	,	,	PUNCT
ejpam-2291	39	3	where	where	SCONJ
ejpam-2291	39	4	v	v	NOUN
ejpam-2291	39	5	(	(	PUNCT
ejpam-2291	39	6	s+	s+	ADV
ejpam-2291	39	7	)	)	PUNCT
ejpam-2291	39	8	is	be	AUX
ejpam-2291	39	9	the	the	DET
ejpam-2291	39	10	set	set	NOUN
ejpam-2291	39	11	of	of	ADP
ejpam-2291	39	12	all	all	DET
ejpam-2291	39	13	prime	prime	ADJ
ejpam-2291	39	14	ideals	ideal	NOUN
ejpam-2291	39	15	of	of	ADP
ejpam-2291	39	16	s	s	AUX
ejpam-2291	39	17	containing	contain	VERB
ejpam-2291	39	18	s+	s+	ADV
ejpam-2291	39	19	and	and	CCONJ
ejpam-2291	39	20	for	for	ADP
ejpam-2291	39	21	an	an	DET
ejpam-2291	39	22	s	s	NOUN
ejpam-2291	39	23	-	-	PUNCT
ejpam-2291	39	24	module	module	NOUN
ejpam-2291	39	25	x	x	SYM
ejpam-2291	39	26	,	,	PUNCT
ejpam-2291	39	27	asss(x	asss(x	PROPN
ejpam-2291	39	28	)	)	PUNCT
ejpam-2291	39	29	denotes	denote	VERB
ejpam-2291	39	30	the	the	DET
ejpam-2291	39	31	set	set	NOUN
ejpam-2291	39	32	of	of	ADP
ejpam-2291	39	33	all	all	DET
ejpam-2291	39	34	associated	associate	VERB
ejpam-2291	39	35	prime	prime	ADJ
ejpam-2291	39	36	ideals	ideal	NOUN
ejpam-2291	39	37	of	of	ADP
ejpam-2291	39	38	x	x	X
ejpam-2291	39	39	.	.	PUNCT
ejpam-2291	40	1	we	we	PRON
ejpam-2291	40	2	define	define	VERB
ejpam-2291	40	3	e(f	e(f	PROPN
ejpam-2291	40	4	,	,	PUNCT
ejpam-2291	40	5	l	l	NOUN
ejpam-2291	40	6	)	)	PUNCT
ejpam-2291	40	7	=	=	SYM
ejpam-2291	40	8	sup{end	sup{end	NOUN
ejpam-2291	40	9	(	(	PUNCT
ejpam-2291	40	10	(	(	PUNCT
ejpam-2291	40	11	(	(	PUNCT
ejpam-2291	40	12	f1	f1	NOUN
ejpam-2291	40	13	,	,	PUNCT
ejpam-2291	40	14	.	.	PUNCT
ejpam-2291	40	15	.	.	PUNCT
ejpam-2291	40	16	.	.	PUNCT
ejpam-2291	41	1	,	,	PUNCT
ejpam-2291	41	2	fi−1)l	fi−1)l	PROPN
ejpam-2291	41	3	:	:	PUNCT
ejpam-2291	41	4	l	l	NOUN
ejpam-2291	41	5	fi)/	fi)/	X
ejpam-2291	41	6	(	(	PUNCT
ejpam-2291	41	7	f1	f1	NOUN
ejpam-2291	41	8	,	,	PUNCT
ejpam-2291	41	9	.	.	PUNCT
ejpam-2291	41	10	.	.	PUNCT
ejpam-2291	41	11	.	.	PUNCT
ejpam-2291	42	1	,	,	PUNCT
ejpam-2291	42	2	fi−1)l	fi−1)l	PROPN
ejpam-2291	42	3	)	)	PUNCT
ejpam-2291	42	4	:	:	PUNCT
ejpam-2291	43	1	i	i	NOUN
ejpam-2291	43	2	=	=	NOUN
ejpam-2291	43	3	1	1	NUM
ejpam-2291	43	4	,	,	PUNCT
ejpam-2291	43	5	.	.	PUNCT
ejpam-2291	43	6	.	.	PUNCT
ejpam-2291	43	7	.	.	PUNCT
ejpam-2291	44	1	,	,	PUNCT
ejpam-2291	44	2	h	h	NOUN
ejpam-2291	44	3	}	}	PUNCT
ejpam-2291	44	4	.	.	PUNCT
ejpam-2291	45	1	then	then	ADV
ejpam-2291	45	2	by	by	ADP
ejpam-2291	45	3	[	[	X
ejpam-2291	45	4	1	1	NUM
ejpam-2291	45	5	,	,	PUNCT
ejpam-2291	45	6	18.3.8	18.3.8	NUM
ejpam-2291	45	7	]	]	X
ejpam-2291	45	8	,	,	PUNCT
ejpam-2291	45	9	f1	f1	NOUN
ejpam-2291	45	10	,	,	PUNCT
ejpam-2291	45	11	.	.	PUNCT
ejpam-2291	45	12	.	.	PUNCT
ejpam-2291	45	13	.	.	PUNCT
ejpam-2291	46	1	,	,	PUNCT
ejpam-2291	46	2	fh	fh	PROPN
ejpam-2291	46	3	is	be	AUX
ejpam-2291	46	4	an	an	DET
ejpam-2291	46	5	s+-filter	s+-filter	NOUN
ejpam-2291	46	6	regular	regular	ADJ
ejpam-2291	46	7	sequence	sequence	NOUN
ejpam-2291	46	8	on	on	ADP
ejpam-2291	46	9	l	l	NOUN
ejpam-2291	46	10	if	if	SCONJ
ejpam-2291	47	1	and	and	CCONJ
ejpam-2291	47	2	only	only	ADV
ejpam-2291	47	3	if	if	SCONJ
ejpam-2291	47	4	e(f	e(f	PROPN
ejpam-2291	47	5	,	,	PUNCT
ejpam-2291	47	6	l)<∞.	l)<∞.	NOUN
ejpam-2291	47	7	it	it	PRON
ejpam-2291	47	8	will	will	AUX
ejpam-2291	47	9	be	be	AUX
ejpam-2291	47	10	crucial	crucial	ADJ
ejpam-2291	47	11	to	to	PART
ejpam-2291	47	12	understand	understand	VERB
ejpam-2291	47	13	how	how	SCONJ
ejpam-2291	47	14	the	the	DET
ejpam-2291	47	15	invariants	invariant	NOUN
ejpam-2291	47	16	ai(l	ai(l	PRON
ejpam-2291	47	17	)	)	PUNCT
ejpam-2291	47	18	behave	behave	VERB
ejpam-2291	47	19	with	with	ADP
ejpam-2291	47	20	respect	respect	NOUN
ejpam-2291	47	21	to	to	PART
ejpam-2291	47	22	s+-filter	s+-filter	VERB
ejpam-2291	47	23	regular	regular	ADJ
ejpam-2291	47	24	sequences	sequence	NOUN
ejpam-2291	47	25	for	for	ADP
ejpam-2291	47	26	l.	l.	PROPN
ejpam-2291	47	27	this	this	DET
ejpam-2291	47	28	relationship	relationship	NOUN
ejpam-2291	47	29	was	be	AUX
ejpam-2291	47	30	illuminated	illuminate	VERB
ejpam-2291	47	31	by	by	ADP
ejpam-2291	47	32	trung	trung	VERB
ejpam-2291	47	33	in	in	ADP
ejpam-2291	47	34	the	the	DET
ejpam-2291	47	35	following	follow	VERB
ejpam-2291	47	36	lemma	lemma	PROPN
ejpam-2291	47	37	.	.	PUNCT
ejpam-2291	48	1	because	because	SCONJ
ejpam-2291	48	2	of	of	ADP
ejpam-2291	48	3	its	its	PRON
ejpam-2291	48	4	importance	importance	NOUN
ejpam-2291	48	5	in	in	ADP
ejpam-2291	48	6	our	our	PRON
ejpam-2291	48	7	argument	argument	NOUN
ejpam-2291	48	8	,	,	PUNCT
ejpam-2291	48	9	we	we	PRON
ejpam-2291	48	10	supply	supply	VERB
ejpam-2291	48	11	the	the	DET
ejpam-2291	48	12	proof	proof	NOUN
ejpam-2291	48	13	along	along	ADP
ejpam-2291	48	14	the	the	DET
ejpam-2291	48	15	statement	statement	NOUN
ejpam-2291	48	16	.	.	PUNCT
ejpam-2291	49	1	lemma	lemma	PROPN
ejpam-2291	49	2	1	1	NUM
ejpam-2291	49	3	(	(	PUNCT
ejpam-2291	49	4	[	[	X
ejpam-2291	49	5	6	6	NUM
ejpam-2291	49	6	,	,	PUNCT
ejpam-2291	49	7	lemma	lemma	PROPN
ejpam-2291	49	8	2.3	2.3	NUM
ejpam-2291	49	9	]	]	PUNCT
ejpam-2291	49	10	)	)	PUNCT
ejpam-2291	49	11	.	.	PUNCT
ejpam-2291	50	1	let	let	VERB
ejpam-2291	50	2	f	f	PROPN
ejpam-2291	50	3	∈	∈	PROPN
ejpam-2291	50	4	s1	s1	PROPN
ejpam-2291	50	5	be	be	AUX
ejpam-2291	50	6	a	a	DET
ejpam-2291	50	7	homogeneous	homogeneous	ADJ
ejpam-2291	50	8	s+-filter	s+-filter	NOUN
ejpam-2291	50	9	regular	regular	ADJ
ejpam-2291	50	10	element	element	NOUN
ejpam-2291	50	11	for	for	ADP
ejpam-2291	50	12	l.	l.	PROPN
ejpam-2291	50	13	then	then	ADV
ejpam-2291	50	14	for	for	ADP
ejpam-2291	50	15	all	all	PRON
ejpam-2291	50	16	i	i	PRON
ejpam-2291	50	17	≥	≥	NOUN
ejpam-2291	50	18	0	0	NUM
ejpam-2291	50	19	,	,	PUNCT
ejpam-2291	50	20	ai+1(l	ai+1(l	PROPN
ejpam-2291	50	21	)	)	PUNCT
ejpam-2291	51	1	+	+	NUM
ejpam-2291	51	2	1≤	1≤	NUM
ejpam-2291	51	3	ai(l/	ai(l/	PROPN
ejpam-2291	51	4	f	f	PROPN
ejpam-2291	51	5	l)≤max{ai(l	l)≤max{ai(l	PROPN
ejpam-2291	51	6	)	)	PUNCT
ejpam-2291	51	7	,	,	PUNCT
ejpam-2291	51	8	ai+1(l	ai+1(l	PROPN
ejpam-2291	51	9	)	)	PUNCT
ejpam-2291	51	10	+	+	CCONJ
ejpam-2291	51	11	1	1	NUM
ejpam-2291	51	12	}	}	PUNCT
ejpam-2291	51	13	.	.	PUNCT
ejpam-2291	52	1	proof	proof	NOUN
ejpam-2291	52	2	.	.	PUNCT
ejpam-2291	53	1	note	note	VERB
ejpam-2291	53	2	that	that	SCONJ
ejpam-2291	53	3	by	by	ADP
ejpam-2291	53	4	the	the	DET
ejpam-2291	53	5	statement	statement	NOUN
ejpam-2291	53	6	after	after	ADP
ejpam-2291	53	7	the	the	DET
ejpam-2291	53	8	definition	definition	NOUN
ejpam-2291	53	9	of	of	ADP
ejpam-2291	53	10	an	an	DET
ejpam-2291	53	11	s+-filter	s+-filter	NOUN
ejpam-2291	53	12	regular	regular	ADJ
ejpam-2291	53	13	sequence	sequence	NOUN
ejpam-2291	53	14	for	for	ADP
ejpam-2291	53	15	l	l	NOUN
ejpam-2291	53	16	,	,	PUNCT
ejpam-2291	53	17	h0	h0	PROPN
ejpam-2291	53	18	s+	s+	PUNCT
ejpam-2291	53	19	(	(	PUNCT
ejpam-2291	53	20	0	0	NUM
ejpam-2291	53	21	:	:	PUNCT
ejpam-2291	53	22	l	l	NOUN
ejpam-2291	53	23	f	f	NOUN
ejpam-2291	53	24	)	)	PUNCT
ejpam-2291	53	25	=	=	PUNCT
ejpam-2291	54	1	(	(	PUNCT
ejpam-2291	54	2	0	0	NUM
ejpam-2291	54	3	:	:	PUNCT
ejpam-2291	54	4	l	l	PROPN
ejpam-2291	54	5	f	f	PROPN
ejpam-2291	54	6	)	)	PUNCT
ejpam-2291	54	7	and	and	CCONJ
ejpam-2291	55	1	hence	hence	ADV
ejpam-2291	55	2	h	h	NOUN
ejpam-2291	55	3	i	i	PRON
ejpam-2291	55	4	s+	s+	PUNCT
ejpam-2291	55	5	(	(	PUNCT
ejpam-2291	55	6	0	0	NUM
ejpam-2291	55	7	:	:	PUNCT
ejpam-2291	55	8	l	l	NOUN
ejpam-2291	55	9	f	f	X
ejpam-2291	55	10	)	)	PUNCT
ejpam-2291	56	1	=	=	SYM
ejpam-2291	56	2	0	0	NUM
ejpam-2291	57	1	for	for	ADP
ejpam-2291	57	2	all	all	PRON
ejpam-2291	57	3	i	i	PRON
ejpam-2291	57	4	≥	≥	VERB
ejpam-2291	57	5	1	1	NUM
ejpam-2291	57	6	.	.	PUNCT
ejpam-2291	57	7	then	then	ADV
ejpam-2291	57	8	from	from	ADP
ejpam-2291	57	9	the	the	DET
ejpam-2291	57	10	exact	exact	ADJ
ejpam-2291	57	11	sequence	sequence	NOUN
ejpam-2291	57	12	0	0	X
ejpam-2291	57	13	−→	−→	NOUN
ejpam-2291	57	14	(	(	PUNCT
ejpam-2291	57	15	0	0	NUM
ejpam-2291	57	16	:	:	PUNCT
ejpam-2291	57	17	l	l	NOUN
ejpam-2291	57	18	f	f	X
ejpam-2291	57	19	)	)	PUNCT
ejpam-2291	57	20	−→	−→	NOUN
ejpam-2291	57	21	l	l	NOUN
ejpam-2291	57	22	−→	−→	NOUN
ejpam-2291	57	23	l/(0	l/(0	NOUN
ejpam-2291	57	24	:	:	PUNCT
ejpam-2291	57	25	l	l	PROPN
ejpam-2291	57	26	f	f	X
ejpam-2291	57	27	)	)	PUNCT
ejpam-2291	58	1	−→	−→	NOUN
ejpam-2291	58	2	0	0	NUM
ejpam-2291	58	3	,	,	PUNCT
ejpam-2291	58	4	we	we	PRON
ejpam-2291	58	5	see	see	VERB
ejpam-2291	58	6	that	that	SCONJ
ejpam-2291	58	7	h	h	NOUN
ejpam-2291	59	1	i	i	PRON
ejpam-2291	59	2	s+	s+	PUNCT
ejpam-2291	59	3	(	(	PUNCT
ejpam-2291	59	4	l)∼=	l)∼=	X
ejpam-2291	59	5	h	h	NOUN
ejpam-2291	59	6	i	i	PRON
ejpam-2291	59	7	s+	s+	ADV
ejpam-2291	59	8	(	(	PUNCT
ejpam-2291	59	9	l/(0	l/(0	NOUN
ejpam-2291	59	10	:	:	PUNCT
ejpam-2291	59	11	l	l	PROPN
ejpam-2291	59	12	f	f	PROPN
ejpam-2291	59	13	)	)	PUNCT
ejpam-2291	59	14	)	)	PUNCT
ejpam-2291	59	15	for	for	ADP
ejpam-2291	59	16	all	all	PRON
ejpam-2291	59	17	i	i	PRON
ejpam-2291	59	18	≥	≥	VERB
ejpam-2291	59	19	1	1	NUM
ejpam-2291	59	20	.	.	PUNCT
ejpam-2291	60	1	now	now	ADV
ejpam-2291	60	2	,	,	PUNCT
ejpam-2291	60	3	from	from	ADP
ejpam-2291	60	4	the	the	DET
ejpam-2291	60	5	exact	exact	ADJ
ejpam-2291	60	6	sequence	sequence	NOUN
ejpam-2291	60	7	0	0	NUM
ejpam-2291	60	8	−→	−→	ADJ
ejpam-2291	60	9	l/(0	l/(0	NOUN
ejpam-2291	60	10	:	:	PUNCT
ejpam-2291	60	11	l	l	PROPN
ejpam-2291	60	12	f	f	X
ejpam-2291	60	13	)	)	PUNCT
ejpam-2291	61	1	f	f	PROPN
ejpam-2291	61	2	−→	−→	NOUN
ejpam-2291	61	3	l(1	l(1	PROPN
ejpam-2291	61	4	)	)	PUNCT
ejpam-2291	61	5	−→	−→	NOUN
ejpam-2291	61	6	l(1	l(1	PROPN
ejpam-2291	61	7	)	)	PUNCT
ejpam-2291	61	8	−→	−→	NOUN
ejpam-2291	61	9	0	0	NUM
ejpam-2291	61	10	,	,	PUNCT
ejpam-2291	61	11	we	we	PRON
ejpam-2291	61	12	obtain	obtain	VERB
ejpam-2291	61	13	the	the	DET
ejpam-2291	61	14	exact	exact	ADJ
ejpam-2291	61	15	sequence	sequence	NOUN
ejpam-2291	61	16	h	h	NOUN
ejpam-2291	62	1	i	i	PRON
ejpam-2291	62	2	s+	s+	PUNCT
ejpam-2291	62	3	(	(	PUNCT
ejpam-2291	62	4	l)n+1→	l)n+1→	PROPN
ejpam-2291	62	5	h	h	INTJ
ejpam-2291	63	1	i	i	PRON
ejpam-2291	63	2	s+	s+	PUNCT
ejpam-2291	63	3	(	(	PUNCT
ejpam-2291	63	4	l/	l/	X
ejpam-2291	63	5	f	f	PROPN
ejpam-2291	63	6	l)n+1→	l)n+1→	PROPN
ejpam-2291	63	7	h	h	PROPN
ejpam-2291	63	8	i+1	i+1	NUM
ejpam-2291	63	9	s+	s+	ADV
ejpam-2291	63	10	(	(	PUNCT
ejpam-2291	63	11	l)n→	l)n→	NOUN
ejpam-2291	63	12	h	h	NOUN
ejpam-2291	63	13	i+1	i+1	ADJ
ejpam-2291	63	14	s+	s+	ADV
ejpam-2291	63	15	(	(	PUNCT
ejpam-2291	63	16	l)n+1	l)n+1	ADJ
ejpam-2291	63	17	,	,	PUNCT
ejpam-2291	63	18	for	for	SCONJ
ejpam-2291	63	19	each	each	DET
ejpam-2291	63	20	i	i	PRON
ejpam-2291	63	21	≥	≥	VERB
ejpam-2291	63	22	0	0	NUM
ejpam-2291	63	23	and	and	CCONJ
ejpam-2291	63	24	n	n	PRON
ejpam-2291	63	25	∈	∈	PROPN
ejpam-2291	63	26	z.	z.	NOUN
ejpam-2291	63	27	analyzing	analyze	VERB
ejpam-2291	63	28	these	these	DET
ejpam-2291	63	29	sequences	sequence	NOUN
ejpam-2291	63	30	easily	easily	ADV
ejpam-2291	63	31	yields	yield	VERB
ejpam-2291	63	32	the	the	DET
ejpam-2291	63	33	desired	desire	VERB
ejpam-2291	63	34	inequalities	inequality	NOUN
ejpam-2291	63	35	.	.	PUNCT
ejpam-2291	64	1	n.	n.	PROPN
ejpam-2291	64	2	zamani	zamani	PROPN
ejpam-2291	64	3	/	/	SYM
ejpam-2291	64	4	eur	eur	PROPN
ejpam-2291	64	5	.	.	PUNCT
ejpam-2291	65	1	j.	j.	PROPN
ejpam-2291	65	2	pure	pure	PROPN
ejpam-2291	65	3	appl	appl	PROPN
ejpam-2291	65	4	.	.	PROPN
ejpam-2291	65	5	math	math	PROPN
ejpam-2291	65	6	,	,	PUNCT
ejpam-2291	65	7	7	7	NUM
ejpam-2291	65	8	(	(	PUNCT
ejpam-2291	65	9	2014	2014	NUM
ejpam-2291	65	10	)	)	PUNCT
ejpam-2291	65	11	,	,	PUNCT
ejpam-2291	65	12	429	429	NUM
ejpam-2291	65	13	-	-	SYM
ejpam-2291	65	14	436	436	NUM
ejpam-2291	65	15	431	431	NUM
ejpam-2291	65	16	lemma	lemma	PROPN
ejpam-2291	65	17	2	2	NUM
ejpam-2291	65	18	.	.	PUNCT
ejpam-2291	66	1	let	let	VERB
ejpam-2291	66	2	f=	f=	ADJ
ejpam-2291	66	3	f1	f1	NOUN
ejpam-2291	66	4	,	,	PUNCT
ejpam-2291	66	5	.	.	PUNCT
ejpam-2291	66	6	.	.	PUNCT
ejpam-2291	67	1	.	.	PUNCT
ejpam-2291	68	1	,	,	PUNCT
ejpam-2291	68	2	fh	fh	PROPN
ejpam-2291	68	3	be	be	AUX
ejpam-2291	68	4	an	an	DET
ejpam-2291	68	5	s+-filter	s+-filter	NOUN
ejpam-2291	68	6	regular	regular	ADJ
ejpam-2291	68	7	sequence	sequence	NOUN
ejpam-2291	68	8	of	of	ADP
ejpam-2291	68	9	homogeneous	homogeneous	ADJ
ejpam-2291	68	10	elements	element	NOUN
ejpam-2291	68	11	of	of	ADP
ejpam-2291	68	12	degree	degree	NOUN
ejpam-2291	68	13	1	1	NUM
ejpam-2291	68	14	for	for	ADP
ejpam-2291	68	15	l.	l.	PROPN
ejpam-2291	68	16	then	then	ADV
ejpam-2291	68	17	:	:	PUNCT
ejpam-2291	68	18	(	(	PUNCT
ejpam-2291	68	19	i	i	NOUN
ejpam-2291	68	20	)	)	PUNCT
ejpam-2291	68	21	e(f	e(f	PROPN
ejpam-2291	68	22	,	,	PUNCT
ejpam-2291	68	23	l	l	NOUN
ejpam-2291	68	24	)	)	PUNCT
ejpam-2291	68	25	=	=	NOUN
ejpam-2291	68	26	max{ai(l	max{ai(l	X
ejpam-2291	68	27	)	)	PUNCT
ejpam-2291	69	1	+	+	CCONJ
ejpam-2291	69	2	i	i	PRON
ejpam-2291	69	3	:	:	PUNCT
ejpam-2291	69	4	i	i	NOUN
ejpam-2291	69	5	=	=	NOUN
ejpam-2291	69	6	0	0	NUM
ejpam-2291	69	7	,	,	PUNCT
ejpam-2291	69	8	.	.	PUNCT
ejpam-2291	69	9	.	.	PUNCT
ejpam-2291	69	10	.	.	PUNCT
ejpam-2291	70	1	,	,	PUNCT
ejpam-2291	70	2	h−	h−	PROPN
ejpam-2291	70	3	1	1	NUM
ejpam-2291	70	4	}	}	PUNCT
ejpam-2291	70	5	,	,	PUNCT
ejpam-2291	70	6	(	(	PUNCT
ejpam-2291	70	7	ii	ii	NOUN
ejpam-2291	70	8	)	)	PUNCT
ejpam-2291	70	9	for	for	ADP
ejpam-2291	70	10	all	all	DET
ejpam-2291	70	11	0≤	0≤	NUM
ejpam-2291	70	12	t	t	NOUN
ejpam-2291	70	13	≤	≤	NUM
ejpam-2291	70	14	h	h	NOUN
ejpam-2291	70	15	,	,	PUNCT
ejpam-2291	70	16	max{ai(l)+i	max{ai(l)+i	PROPN
ejpam-2291	70	17	:	:	PUNCT
ejpam-2291	70	18	i	i	NOUN
ejpam-2291	70	19	=	=	NOUN
ejpam-2291	70	20	0	0	NUM
ejpam-2291	70	21	,	,	PUNCT
ejpam-2291	70	22	.	.	PUNCT
ejpam-2291	70	23	.	.	PUNCT
ejpam-2291	70	24	.	.	PUNCT
ejpam-2291	71	1	,	,	PUNCT
ejpam-2291	71	2	t}=max{end	t}=max{end	ADP
ejpam-2291	71	3	(	(	PUNCT
ejpam-2291	71	4	(	(	PUNCT
ejpam-2291	71	5	(	(	PUNCT
ejpam-2291	71	6	f1	f1	NOUN
ejpam-2291	71	7	,	,	PUNCT
ejpam-2291	71	8	.	.	PUNCT
ejpam-2291	71	9	.	.	PUNCT
ejpam-2291	72	1	.	.	PUNCT
ejpam-2291	73	1	,	,	PUNCT
ejpam-2291	73	2	ft)l	ft)l	PROPN
ejpam-2291	73	3	:	:	PUNCT
ejpam-2291	73	4	l	l	PROPN
ejpam-2291	73	5	s+)/	s+)/	PROPN
ejpam-2291	73	6	(	(	PUNCT
ejpam-2291	73	7	f1	f1	NOUN
ejpam-2291	73	8	,	,	PUNCT
ejpam-2291	73	9	.	.	PUNCT
ejpam-2291	73	10	.	.	PUNCT
ejpam-2291	74	1	.	.	PUNCT
ejpam-2291	75	1	,	,	PUNCT
ejpam-2291	75	2	ft)l	ft)l	PROPN
ejpam-2291	75	3	)	)	PUNCT
ejpam-2291	75	4	:	:	PUNCT
ejpam-2291	76	1	i	i	NOUN
ejpam-2291	76	2	=	=	NOUN
ejpam-2291	76	3	0	0	NUM
ejpam-2291	76	4	,	,	PUNCT
ejpam-2291	76	5	.	.	PUNCT
ejpam-2291	76	6	.	.	PUNCT
ejpam-2291	76	7	.	.	PUNCT
ejpam-2291	77	1	,	,	PUNCT
ejpam-2291	77	2	t	t	PROPN
ejpam-2291	77	3	}	}	PUNCT
ejpam-2291	77	4	.	.	PUNCT
ejpam-2291	78	1	proof	proof	NOUN
ejpam-2291	78	2	.	.	PUNCT
ejpam-2291	79	1	(	(	PUNCT
ejpam-2291	79	2	i	i	NOUN
ejpam-2291	79	3	)	)	PUNCT
ejpam-2291	79	4	we	we	PRON
ejpam-2291	79	5	prove	prove	VERB
ejpam-2291	79	6	by	by	ADP
ejpam-2291	79	7	induction	induction	NOUN
ejpam-2291	79	8	on	on	ADP
ejpam-2291	79	9	h≥	h≥	PROPN
ejpam-2291	79	10	1	1	NUM
ejpam-2291	79	11	.	.	PUNCT
ejpam-2291	80	1	since	since	SCONJ
ejpam-2291	80	2	(	(	PUNCT
ejpam-2291	80	3	0	0	NUM
ejpam-2291	80	4	:	:	PUNCT
ejpam-2291	80	5	l	l	NOUN
ejpam-2291	80	6	f1	f1	NOUN
ejpam-2291	80	7	)	)	PUNCT
ejpam-2291	81	1	⊆	⊆	NUM
ejpam-2291	81	2	∪n≥1(0	∪n≥1(0	NOUN
ejpam-2291	81	3	:	:	PUNCT
ejpam-2291	81	4	l	l	NOUN
ejpam-2291	81	5	s+	s+	X
ejpam-2291	81	6	n	n	CCONJ
ejpam-2291	81	7	)	)	PUNCT
ejpam-2291	81	8	and	and	CCONJ
ejpam-2291	81	9	f1h0	f1h0	NUM
ejpam-2291	81	10	s+	s+	X
ejpam-2291	81	11	(	(	PUNCT
ejpam-2291	81	12	l)a0(l	l)a0(l	NOUN
ejpam-2291	81	13	)	)	PUNCT
ejpam-2291	81	14	⊆	⊆	NUM
ejpam-2291	81	15	h0	h0	NOUN
ejpam-2291	81	16	s+	s+	PUNCT
ejpam-2291	81	17	(	(	PUNCT
ejpam-2291	81	18	l)a0(l)+1	l)a0(l)+1	NOUN
ejpam-2291	81	19	=	=	SYM
ejpam-2291	81	20	0	0	NUM
ejpam-2291	81	21	,	,	PUNCT
ejpam-2291	81	22	thus	thus	ADV
ejpam-2291	81	23	e	e	X
ejpam-2291	81	24	(	(	PUNCT
ejpam-2291	81	25	f1	f1	NOUN
ejpam-2291	81	26	,	,	PUNCT
ejpam-2291	81	27	l	l	NOUN
ejpam-2291	81	28	)	)	PUNCT
ejpam-2291	81	29	=	=	SYM
ejpam-2291	81	30	a0(l	a0(l	NOUN
ejpam-2291	81	31	)	)	PUNCT
ejpam-2291	81	32	and	and	CCONJ
ejpam-2291	81	33	the	the	DET
ejpam-2291	81	34	case	case	NOUN
ejpam-2291	81	35	h	h	NOUN
ejpam-2291	81	36	=	=	NOUN
ejpam-2291	81	37	1	1	NUM
ejpam-2291	81	38	is	be	AUX
ejpam-2291	81	39	immediate	immediate	ADJ
ejpam-2291	81	40	.	.	PUNCT
ejpam-2291	82	1	so	so	ADV
ejpam-2291	82	2	let	let	VERB
ejpam-2291	82	3	h	h	PRON
ejpam-2291	82	4	>	>	X
ejpam-2291	83	1	1	1	X
ejpam-2291	83	2	.	.	PUNCT
ejpam-2291	84	1	let	let	VERB
ejpam-2291	84	2	l̄	l̄	NOUN
ejpam-2291	84	3	=	=	SYM
ejpam-2291	84	4	l/	l/	NOUN
ejpam-2291	84	5	f1	f1	NOUN
ejpam-2291	84	6	l	l	PROPN
ejpam-2291	84	7	and	and	CCONJ
ejpam-2291	84	8	f̄=	f̄=	VERB
ejpam-2291	84	9	f̄2	f̄2	PROPN
ejpam-2291	84	10	,	,	PUNCT
ejpam-2291	84	11	.	.	PUNCT
ejpam-2291	84	12	.	.	PUNCT
ejpam-2291	85	1	.	.	PUNCT
ejpam-2291	86	1	,	,	PUNCT
ejpam-2291	86	2	f̄h	f̄h	NOUN
ejpam-2291	86	3	in	in	ADP
ejpam-2291	86	4	s̄	s̄	NOUN
ejpam-2291	86	5	=	=	SYM
ejpam-2291	86	6	s/	s/	PROPN
ejpam-2291	86	7	(	(	PUNCT
ejpam-2291	86	8	f1	f1	NOUN
ejpam-2291	86	9	)	)	PUNCT
ejpam-2291	86	10	.	.	PUNCT
ejpam-2291	87	1	by	by	ADP
ejpam-2291	87	2	induction	induction	NOUN
ejpam-2291	87	3	and	and	CCONJ
ejpam-2291	87	4	using	use	VERB
ejpam-2291	87	5	lemma	lemma	PROPN
ejpam-2291	87	6	1	1	NUM
ejpam-2291	87	7	,	,	PUNCT
ejpam-2291	87	8	we	we	PRON
ejpam-2291	87	9	have	have	VERB
ejpam-2291	87	10	max{ai(l	max{ai(l	PROPN
ejpam-2291	87	11	)	)	PUNCT
ejpam-2291	88	1	+	+	CCONJ
ejpam-2291	88	2	i	i	PRON
ejpam-2291	88	3	:	:	PUNCT
ejpam-2291	88	4	i	i	NOUN
ejpam-2291	88	5	=	=	NOUN
ejpam-2291	88	6	1	1	NUM
ejpam-2291	88	7	,	,	PUNCT
ejpam-2291	88	8	.	.	PUNCT
ejpam-2291	88	9	.	.	PUNCT
ejpam-2291	88	10	.	.	PUNCT
ejpam-2291	89	1	,	,	PUNCT
ejpam-2291	89	2	h−	h−	PROPN
ejpam-2291	89	3	1	1	NUM
ejpam-2291	89	4	}	}	PUNCT
ejpam-2291	89	5	≤e(̄f	≤e(̄f	ADJ
ejpam-2291	89	6	,	,	PUNCT
ejpam-2291	89	7	l̄	l̄	NOUN
ejpam-2291	89	8	)	)	PUNCT
ejpam-2291	90	1	=	=	NOUN
ejpam-2291	90	2	max{ai(l/	max{ai(l/	NOUN
ejpam-2291	90	3	f1	f1	NOUN
ejpam-2291	90	4	l	l	NOUN
ejpam-2291	90	5	)	)	PUNCT
ejpam-2291	91	1	+	+	CCONJ
ejpam-2291	91	2	i	i	PRON
ejpam-2291	91	3	:	:	PUNCT
ejpam-2291	91	4	i	i	NOUN
ejpam-2291	91	5	=	=	NOUN
ejpam-2291	91	6	0	0	NUM
ejpam-2291	91	7	,	,	PUNCT
ejpam-2291	91	8	.	.	PUNCT
ejpam-2291	91	9	.	.	PUNCT
ejpam-2291	91	10	.	.	PUNCT
ejpam-2291	92	1	,	,	PUNCT
ejpam-2291	92	2	h−	h−	PROPN
ejpam-2291	92	3	2	2	X
ejpam-2291	92	4	}	}	PUNCT
ejpam-2291	92	5	≤max{ai(l	≤max{ai(l	PROPN
ejpam-2291	92	6	)	)	PUNCT
ejpam-2291	93	1	+	+	CCONJ
ejpam-2291	93	2	i	i	PRON
ejpam-2291	93	3	:	:	PUNCT
ejpam-2291	93	4	i	i	NOUN
ejpam-2291	93	5	=	=	NOUN
ejpam-2291	93	6	0	0	NUM
ejpam-2291	93	7	,	,	PUNCT
ejpam-2291	93	8	.	.	PUNCT
ejpam-2291	93	9	.	.	PUNCT
ejpam-2291	93	10	.	.	PUNCT
ejpam-2291	94	1	,	,	PUNCT
ejpam-2291	94	2	h−	h−	PROPN
ejpam-2291	94	3	1	1	NUM
ejpam-2291	94	4	}	}	PUNCT
ejpam-2291	94	5	.	.	PUNCT
ejpam-2291	95	1	now	now	ADV
ejpam-2291	95	2	since	since	SCONJ
ejpam-2291	95	3	e(f	e(f	PROPN
ejpam-2291	95	4	,	,	PUNCT
ejpam-2291	95	5	l	l	NOUN
ejpam-2291	95	6	)	)	PUNCT
ejpam-2291	95	7	=	=	SYM
ejpam-2291	95	8	max{e	max{e	X
ejpam-2291	95	9	(	(	PUNCT
ejpam-2291	95	10	f1	f1	NOUN
ejpam-2291	95	11	,	,	PUNCT
ejpam-2291	95	12	l	l	NOUN
ejpam-2291	95	13	)	)	PUNCT
ejpam-2291	95	14	,	,	PUNCT
ejpam-2291	95	15	e(̄f	e(̄f	PROPN
ejpam-2291	95	16	,	,	PUNCT
ejpam-2291	95	17	l̄	l̄	NOUN
ejpam-2291	95	18	)	)	PUNCT
ejpam-2291	95	19	}	}	PUNCT
ejpam-2291	95	20	,	,	PUNCT
ejpam-2291	95	21	the	the	DET
ejpam-2291	95	22	result	result	NOUN
ejpam-2291	95	23	follows	follow	VERB
ejpam-2291	95	24	.	.	PUNCT
ejpam-2291	96	1	(	(	PUNCT
ejpam-2291	96	2	ii	ii	NOUN
ejpam-2291	96	3	)	)	PUNCT
ejpam-2291	96	4	using	use	VERB
ejpam-2291	96	5	lemma	lemma	PROPN
ejpam-2291	96	6	1	1	NUM
ejpam-2291	96	7	repeatedly	repeatedly	ADV
ejpam-2291	96	8	,	,	PUNCT
ejpam-2291	96	9	we	we	PRON
ejpam-2291	96	10	deduce	deduce	VERB
ejpam-2291	96	11	that	that	PRON
ejpam-2291	96	12	ai(l	ai(l	PRON
ejpam-2291	96	13	)	)	PUNCT
ejpam-2291	97	1	+	+	CCONJ
ejpam-2291	97	2	i	i	PRON
ejpam-2291	97	3	≤	≤	NUM
ejpam-2291	97	4	a0(l/	a0(l/	ADJ
ejpam-2291	97	5	(	(	PUNCT
ejpam-2291	97	6	f1	f1	NOUN
ejpam-2291	97	7	,	,	PUNCT
ejpam-2291	97	8	.	.	PUNCT
ejpam-2291	97	9	.	.	PUNCT
ejpam-2291	97	10	.	.	PUNCT
ejpam-2291	98	1	,	,	PUNCT
ejpam-2291	98	2	fi)l)≤max{a	fi)l)≤max{a	PUNCT
ejpam-2291	98	3	j(l	j(l	PROPN
ejpam-2291	98	4	)	)	PUNCT
ejpam-2291	99	1	+	+	CCONJ
ejpam-2291	99	2	j	j	NOUN
ejpam-2291	99	3	:	:	PUNCT
ejpam-2291	99	4	j	j	X
ejpam-2291	99	5	=	=	SYM
ejpam-2291	99	6	0	0	PROPN
ejpam-2291	99	7	,	,	PUNCT
ejpam-2291	99	8	.	.	PUNCT
ejpam-2291	99	9	.	.	PUNCT
ejpam-2291	99	10	.	.	PUNCT
ejpam-2291	100	1	,	,	PUNCT
ejpam-2291	100	2	i	i	PRON
ejpam-2291	100	3	}	}	PUNCT
ejpam-2291	100	4	.	.	PUNCT
ejpam-2291	101	1	from	from	ADP
ejpam-2291	101	2	this	this	PRON
ejpam-2291	101	3	it	it	PRON
ejpam-2291	101	4	follows	follow	VERB
ejpam-2291	101	5	that	that	SCONJ
ejpam-2291	101	6	for	for	ADP
ejpam-2291	101	7	t	t	PROPN
ejpam-2291	101	8	≤	≤	NUM
ejpam-2291	101	9	h	h	NOUN
ejpam-2291	101	10	,	,	PUNCT
ejpam-2291	101	11	max{ai(l	max{ai(l	PROPN
ejpam-2291	101	12	)	)	PUNCT
ejpam-2291	102	1	+	+	CCONJ
ejpam-2291	102	2	i	i	PRON
ejpam-2291	102	3	:	:	PUNCT
ejpam-2291	102	4	i	i	NOUN
ejpam-2291	102	5	=	=	NOUN
ejpam-2291	102	6	0	0	NUM
ejpam-2291	102	7	,	,	PUNCT
ejpam-2291	102	8	.	.	PUNCT
ejpam-2291	102	9	.	.	PUNCT
ejpam-2291	102	10	.	.	PUNCT
ejpam-2291	102	11	,	,	PUNCT
ejpam-2291	102	12	t}=max{a0(l/	t}=max{a0(l/	PROPN
ejpam-2291	102	13	(	(	PUNCT
ejpam-2291	102	14	f1	f1	NOUN
ejpam-2291	102	15	,	,	PUNCT
ejpam-2291	102	16	.	.	PUNCT
ejpam-2291	102	17	.	.	PUNCT
ejpam-2291	102	18	.	.	PUNCT
ejpam-2291	103	1	,	,	PUNCT
ejpam-2291	103	2	fi)l	fi)l	PROPN
ejpam-2291	103	3	)	)	PUNCT
ejpam-2291	103	4	:	:	PUNCT
ejpam-2291	104	1	i	i	NOUN
ejpam-2291	104	2	=	=	NOUN
ejpam-2291	104	3	0	0	NUM
ejpam-2291	104	4	,	,	PUNCT
ejpam-2291	104	5	.	.	PUNCT
ejpam-2291	104	6	.	.	PUNCT
ejpam-2291	104	7	.	.	PUNCT
ejpam-2291	105	1	,	,	PUNCT
ejpam-2291	105	2	t	t	PROPN
ejpam-2291	105	3	}	}	PUNCT
ejpam-2291	105	4	.	.	PUNCT
ejpam-2291	106	1	set	set	VERB
ejpam-2291	106	2	a	a	DET
ejpam-2291	106	3	=	=	SYM
ejpam-2291	106	4	a0(l/	a0(l/	ADJ
ejpam-2291	106	5	(	(	PUNCT
ejpam-2291	106	6	f1	f1	NOUN
ejpam-2291	106	7	,	,	PUNCT
ejpam-2291	106	8	.	.	PUNCT
ejpam-2291	106	9	.	.	PUNCT
ejpam-2291	107	1	.	.	PUNCT
ejpam-2291	108	1	,	,	PUNCT
ejpam-2291	108	2	fi)l	fi)l	PROPN
ejpam-2291	108	3	)	)	PUNCT
ejpam-2291	108	4	.	.	PUNCT
ejpam-2291	109	1	we	we	PRON
ejpam-2291	109	2	have	have	AUX
ejpam-2291	109	3	h0	h0	VERB
ejpam-2291	109	4	s+	s+	PUNCT
ejpam-2291	109	5	(	(	PUNCT
ejpam-2291	109	6	l/	l/	X
ejpam-2291	109	7	(	(	PUNCT
ejpam-2291	109	8	f1	f1	NOUN
ejpam-2291	109	9	,	,	PUNCT
ejpam-2291	109	10	.	.	PUNCT
ejpam-2291	109	11	.	.	PUNCT
ejpam-2291	109	12	.	.	PUNCT
ejpam-2291	110	1	,	,	PUNCT
ejpam-2291	110	2	fi)l	fi)l	NOUN
ejpam-2291	110	3	)	)	PUNCT
ejpam-2291	111	1	=	=	SYM
ejpam-2291	111	2	⋃	⋃	ADP
ejpam-2291	111	3	n≥1	n≥1	NOUN
ejpam-2291	111	4	(	(	PUNCT
ejpam-2291	111	5	(	(	PUNCT
ejpam-2291	111	6	f1	f1	NOUN
ejpam-2291	111	7	,	,	PUNCT
ejpam-2291	111	8	.	.	PUNCT
ejpam-2291	111	9	.	.	PUNCT
ejpam-2291	111	10	.	.	PUNCT
ejpam-2291	112	1	,	,	PUNCT
ejpam-2291	112	2	fi)l	fi)l	NOUN
ejpam-2291	112	3	:	:	PUNCT
ejpam-2291	112	4	l	l	NOUN
ejpam-2291	112	5	s+	s+	PUNCT
ejpam-2291	112	6	n)/	n)/	PROPN
ejpam-2291	112	7	(	(	PUNCT
ejpam-2291	112	8	f1	f1	NOUN
ejpam-2291	112	9	,	,	PUNCT
ejpam-2291	112	10	.	.	PUNCT
ejpam-2291	112	11	.	.	PUNCT
ejpam-2291	112	12	.	.	PUNCT
ejpam-2291	113	1	,	,	PUNCT
ejpam-2291	113	2	fi)l	fi)l	PROPN
ejpam-2291	113	3	.	.	PUNCT
ejpam-2291	114	1	therefore	therefore	ADV
ejpam-2291	114	2	h0	h0	PROPN
ejpam-2291	114	3	s+	s+	ADV
ejpam-2291	114	4	(	(	PUNCT
ejpam-2291	114	5	l/	l/	X
ejpam-2291	114	6	(	(	PUNCT
ejpam-2291	114	7	f1	f1	NOUN
ejpam-2291	114	8	,	,	PUNCT
ejpam-2291	114	9	.	.	PUNCT
ejpam-2291	114	10	.	.	PUNCT
ejpam-2291	114	11	.	.	PUNCT
ejpam-2291	115	1	,	,	PUNCT
ejpam-2291	115	2	fi)l)a	fi)l)a	NOUN
ejpam-2291	115	3	⊆	⊆	NUM
ejpam-2291	115	4	(	(	PUNCT
ejpam-2291	115	5	(	(	PUNCT
ejpam-2291	115	6	f1	f1	NOUN
ejpam-2291	115	7	,	,	PUNCT
ejpam-2291	115	8	.	.	PUNCT
ejpam-2291	115	9	.	.	PUNCT
ejpam-2291	116	1	.	.	PUNCT
ejpam-2291	117	1	,	,	PUNCT
ejpam-2291	117	2	fi)l	fi)l	NOUN
ejpam-2291	117	3	:	:	PUNCT
ejpam-2291	117	4	l	l	PROPN
ejpam-2291	117	5	s+)/	s+)/	PROPN
ejpam-2291	117	6	(	(	PUNCT
ejpam-2291	117	7	f1	f1	NOUN
ejpam-2291	117	8	,	,	PUNCT
ejpam-2291	117	9	.	.	PUNCT
ejpam-2291	117	10	.	.	PUNCT
ejpam-2291	117	11	.	.	PUNCT
ejpam-2291	118	1	,	,	PUNCT
ejpam-2291	118	2	fi)l	fi)l	PROPN
ejpam-2291	118	3	⊆	⊆	NUM
ejpam-2291	118	4	h0	h0	NOUN
ejpam-2291	118	5	s+	s+	PUNCT
ejpam-2291	118	6	(	(	PUNCT
ejpam-2291	118	7	l/	l/	X
ejpam-2291	118	8	(	(	PUNCT
ejpam-2291	118	9	f1	f1	NOUN
ejpam-2291	118	10	,	,	PUNCT
ejpam-2291	118	11	.	.	PUNCT
ejpam-2291	118	12	.	.	PUNCT
ejpam-2291	118	13	.	.	PUNCT
ejpam-2291	119	1	,	,	PUNCT
ejpam-2291	119	2	fi)l	fi)l	PROPN
ejpam-2291	119	3	)	)	PUNCT
ejpam-2291	119	4	.	.	PUNCT
ejpam-2291	120	1	hence	hence	ADV
ejpam-2291	120	2	a	a	DET
ejpam-2291	120	3	(	(	PUNCT
ejpam-2291	120	4	(	(	PUNCT
ejpam-2291	120	5	(	(	PUNCT
ejpam-2291	120	6	f1	f1	NOUN
ejpam-2291	120	7	,	,	PUNCT
ejpam-2291	120	8	.	.	PUNCT
ejpam-2291	120	9	.	.	PUNCT
ejpam-2291	121	1	.	.	PUNCT
ejpam-2291	122	1	,	,	PUNCT
ejpam-2291	122	2	fi)l	fi)l	NOUN
ejpam-2291	122	3	:	:	PUNCT
ejpam-2291	122	4	l	l	PROPN
ejpam-2291	122	5	s+)/	s+)/	PROPN
ejpam-2291	122	6	(	(	PUNCT
ejpam-2291	122	7	f1	f1	NOUN
ejpam-2291	122	8	,	,	PUNCT
ejpam-2291	122	9	.	.	PUNCT
ejpam-2291	122	10	.	.	PUNCT
ejpam-2291	122	11	.	.	PUNCT
ejpam-2291	123	1	,	,	PUNCT
ejpam-2291	123	2	fi)l	fi)l	NOUN
ejpam-2291	123	3	)	)	PUNCT
ejpam-2291	123	4	=	=	SYM
ejpam-2291	124	1	a	a	PRON
ejpam-2291	124	2	,	,	PUNCT
ejpam-2291	124	3	and	and	CCONJ
ejpam-2291	124	4	the	the	DET
ejpam-2291	124	5	result	result	NOUN
ejpam-2291	124	6	follows	follow	VERB
ejpam-2291	124	7	.	.	PUNCT
ejpam-2291	125	1	the	the	DET
ejpam-2291	125	2	following	follow	VERB
ejpam-2291	125	3	corollary	corollary	NOUN
ejpam-2291	125	4	generalizes	generalize	NOUN
ejpam-2291	125	5	[	[	X
ejpam-2291	125	6	5	5	NUM
ejpam-2291	125	7	,	,	PUNCT
ejpam-2291	125	8	corollary	corollary	ADJ
ejpam-2291	125	9	2.3	2.3	NUM
ejpam-2291	125	10	]	]	PUNCT
ejpam-2291	125	11	to	to	ADP
ejpam-2291	125	12	the	the	DET
ejpam-2291	125	13	module	module	NOUN
ejpam-2291	125	14	case	case	NOUN
ejpam-2291	125	15	.	.	PUNCT
ejpam-2291	126	1	corollary	corollary	ADJ
ejpam-2291	126	2	1	1	NUM
ejpam-2291	126	3	.	.	PUNCT
ejpam-2291	127	1	let	let	VERB
ejpam-2291	127	2	g	g	NOUN
ejpam-2291	127	3	=	=	VERB
ejpam-2291	127	4	grade(s+	grade(s+	NOUN
ejpam-2291	127	5	,	,	PUNCT
ejpam-2291	127	6	l	l	NOUN
ejpam-2291	127	7	)	)	PUNCT
ejpam-2291	127	8	.	.	PUNCT
ejpam-2291	128	1	then	then	ADV
ejpam-2291	128	2	:	:	PUNCT
ejpam-2291	128	3	(	(	PUNCT
ejpam-2291	128	4	i	i	NOUN
ejpam-2291	128	5	)	)	PUNCT
ejpam-2291	128	6	ai(l	ai(l	PRON
ejpam-2291	128	7	)	)	PUNCT
ejpam-2291	129	1	=	=	PUNCT
ejpam-2291	129	2	−∞	−∞	X
ejpam-2291	129	3	for	for	ADP
ejpam-2291	129	4	i	i	PRON
ejpam-2291	129	5	<	<	X
ejpam-2291	129	6	g.	g.	PROPN
ejpam-2291	129	7	(	(	PUNCT
ejpam-2291	129	8	ii	ii	PROPN
ejpam-2291	129	9	)	)	PUNCT
ejpam-2291	129	10	ag(l)≥	ag(l)≥	NOUN
ejpam-2291	129	11	−g	−g	NOUN
ejpam-2291	129	12	.	.	PUNCT
ejpam-2291	130	1	(	(	PUNCT
ejpam-2291	130	2	iii	iii	X
ejpam-2291	130	3	)	)	PUNCT
ejpam-2291	130	4	if	if	SCONJ
ejpam-2291	130	5	h1	h1	ADJ
ejpam-2291	130	6	s+	s+	PUNCT
ejpam-2291	130	7	(	(	PUNCT
ejpam-2291	130	8	l	l	NOUN
ejpam-2291	130	9	)	)	PUNCT
ejpam-2291	130	10	6=	6=	ADP
ejpam-2291	130	11	0	0	NUM
ejpam-2291	130	12	,	,	PUNCT
ejpam-2291	130	13	then	then	ADV
ejpam-2291	130	14	a1(l)≥	a1(l)≥	ADP
ejpam-2291	130	15	−1	−1	NOUN
ejpam-2291	130	16	.	.	PUNCT
ejpam-2291	131	1	n.	n.	PROPN
ejpam-2291	131	2	zamani	zamani	PROPN
ejpam-2291	131	3	/	/	SYM
ejpam-2291	131	4	eur	eur	PROPN
ejpam-2291	131	5	.	.	PUNCT
ejpam-2291	132	1	j.	j.	PROPN
ejpam-2291	132	2	pure	pure	PROPN
ejpam-2291	132	3	appl	appl	PROPN
ejpam-2291	132	4	.	.	PROPN
ejpam-2291	132	5	math	math	PROPN
ejpam-2291	132	6	,	,	PUNCT
ejpam-2291	132	7	7	7	NUM
ejpam-2291	132	8	(	(	PUNCT
ejpam-2291	132	9	2014	2014	NUM
ejpam-2291	132	10	)	)	PUNCT
ejpam-2291	132	11	,	,	PUNCT
ejpam-2291	132	12	429	429	NUM
ejpam-2291	132	13	-	-	SYM
ejpam-2291	132	14	436	436	NUM
ejpam-2291	132	15	432	432	NUM
ejpam-2291	132	16	proof	proof	NOUN
ejpam-2291	132	17	.	.	PUNCT
ejpam-2291	133	1	we	we	PRON
ejpam-2291	133	2	may	may	AUX
ejpam-2291	133	3	assume	assume	VERB
ejpam-2291	133	4	that	that	SCONJ
ejpam-2291	133	5	the	the	DET
ejpam-2291	133	6	base	base	NOUN
ejpam-2291	133	7	ring	ring	NOUN
ejpam-2291	133	8	s0	s0	NOUN
ejpam-2291	133	9	is	be	AUX
ejpam-2291	133	10	local	local	ADJ
ejpam-2291	133	11	with	with	ADP
ejpam-2291	133	12	infinite	infinite	ADJ
ejpam-2291	133	13	residue	residue	NOUN
ejpam-2291	133	14	field	field	NOUN
ejpam-2291	133	15	.	.	PUNCT
ejpam-2291	134	1	then	then	ADV
ejpam-2291	134	2	from	from	ADP
ejpam-2291	134	3	the	the	DET
ejpam-2291	134	4	graded	grade	VERB
ejpam-2291	134	5	version	version	NOUN
ejpam-2291	134	6	of	of	ADP
ejpam-2291	134	7	prime	prime	ADJ
ejpam-2291	134	8	avoidance	avoidance	NOUN
ejpam-2291	134	9	theorem	theorem	NOUN
ejpam-2291	134	10	(	(	PUNCT
ejpam-2291	134	11	see	see	VERB
ejpam-2291	134	12	for	for	ADP
ejpam-2291	134	13	example	example	NOUN
ejpam-2291	135	1	[	[	X
ejpam-2291	135	2	2	2	NUM
ejpam-2291	135	3	,	,	PUNCT
ejpam-2291	135	4	proposition	proposition	NOUN
ejpam-2291	135	5	1.5.12	1.5.12	NUM
ejpam-2291	135	6	]	]	PUNCT
ejpam-2291	135	7	)	)	PUNCT
ejpam-2291	135	8	there	there	PRON
ejpam-2291	135	9	exists	exist	VERB
ejpam-2291	135	10	an	an	DET
ejpam-2291	135	11	l	l	ADJ
ejpam-2291	135	12	-	-	PUNCT
ejpam-2291	135	13	sequence	sequence	NOUN
ejpam-2291	135	14	f1	f1	NOUN
ejpam-2291	135	15	,	,	PUNCT
ejpam-2291	135	16	.	.	PUNCT
ejpam-2291	135	17	.	.	PUNCT
ejpam-2291	136	1	.	.	PUNCT
ejpam-2291	137	1	,	,	PUNCT
ejpam-2291	137	2	fg	fg	PROPN
ejpam-2291	137	3	of	of	ADP
ejpam-2291	137	4	homogeneous	homogeneous	ADJ
ejpam-2291	137	5	elements	element	NOUN
ejpam-2291	137	6	of	of	ADP
ejpam-2291	137	7	s1	s1	NOUN
ejpam-2291	137	8	.	.	PUNCT
ejpam-2291	138	1	since	since	SCONJ
ejpam-2291	138	2	(	(	PUNCT
ejpam-2291	138	3	f1	f1	NOUN
ejpam-2291	138	4	,	,	PUNCT
ejpam-2291	138	5	.	.	PUNCT
ejpam-2291	138	6	.	.	PUNCT
ejpam-2291	138	7	.	.	PUNCT
ejpam-2291	139	1	,	,	PUNCT
ejpam-2291	140	1	fg)l	fg)l	NUM
ejpam-2291	140	2	:	:	PUNCT
ejpam-2291	140	3	l	l	NOUN
ejpam-2291	140	4	s+	s+	PUNCT
ejpam-2291	140	5	=	=	SYM
ejpam-2291	140	6	(	(	PUNCT
ejpam-2291	140	7	f1	f1	NOUN
ejpam-2291	140	8	,	,	PUNCT
ejpam-2291	140	9	.	.	PUNCT
ejpam-2291	140	10	.	.	PUNCT
ejpam-2291	141	1	.	.	PUNCT
ejpam-2291	142	1	,	,	PUNCT
ejpam-2291	142	2	fg)l	fg)l	PROPN
ejpam-2291	142	3	for	for	ADP
ejpam-2291	142	4	i	i	PRON
ejpam-2291	142	5	=	=	NOUN
ejpam-2291	142	6	1	1	NUM
ejpam-2291	142	7	,	,	PUNCT
ejpam-2291	142	8	.	.	PUNCT
ejpam-2291	142	9	.	.	PUNCT
ejpam-2291	143	1	.	.	PUNCT
ejpam-2291	144	1	,	,	PUNCT
ejpam-2291	144	2	g	g	NOUN
ejpam-2291	144	3	;	;	PUNCT
ejpam-2291	144	4	hence	hence	ADV
ejpam-2291	144	5	lemma	lemma	PROPN
ejpam-2291	144	6	2(ii	2(ii	NUM
ejpam-2291	144	7	)	)	PUNCT
ejpam-2291	144	8	implies	imply	VERB
ejpam-2291	144	9	that	that	SCONJ
ejpam-2291	144	10	max{a	max{a	NOUN
ejpam-2291	144	11	j(l)+	j(l)+	PROPN
ejpam-2291	144	12	j	j	PROPN
ejpam-2291	144	13	:	:	PUNCT
ejpam-2291	144	14	j	j	PROPN
ejpam-2291	144	15	=	=	SYM
ejpam-2291	144	16	1	1	NUM
ejpam-2291	144	17	,	,	PUNCT
ejpam-2291	144	18	.	.	PUNCT
ejpam-2291	144	19	.	.	PUNCT
ejpam-2291	145	1	.	.	PUNCT
ejpam-2291	146	1	,	,	PUNCT
ejpam-2291	146	2	i−1}=	i−1}=	ADJ
ejpam-2291	146	3	−∞.	−∞.	NOUN
ejpam-2291	146	4	hence	hence	ADV
ejpam-2291	146	5	ai(l	ai(l	PRON
ejpam-2291	146	6	)	)	PUNCT
ejpam-2291	147	1	=	=	PUNCT
ejpam-2291	147	2	−∞	−∞	X
ejpam-2291	147	3	for	for	ADP
ejpam-2291	147	4	i	i	PROPN
ejpam-2291	147	5	=	=	NOUN
ejpam-2291	147	6	0	0	NUM
ejpam-2291	147	7	,	,	PUNCT
ejpam-2291	147	8	.	.	PUNCT
ejpam-2291	147	9	.	.	PUNCT
ejpam-2291	148	1	.	.	PUNCT
ejpam-2291	149	1	,	,	PUNCT
ejpam-2291	149	2	g	g	NOUN
ejpam-2291	149	3	−	−	PROPN
ejpam-2291	149	4	1	1	NUM
ejpam-2291	149	5	.	.	PUNCT
ejpam-2291	150	1	as	as	ADP
ejpam-2291	150	2	a	a	DET
ejpam-2291	150	3	consequence	consequence	NOUN
ejpam-2291	150	4	,	,	PUNCT
ejpam-2291	150	5	ag(l	ag(l	NUM
ejpam-2291	150	6	)	)	PUNCT
ejpam-2291	151	1	+	+	CCONJ
ejpam-2291	151	2	g	g	PROPN
ejpam-2291	151	3	=	=	NOUN
ejpam-2291	151	4	max{ai(l	max{ai(l	X
ejpam-2291	151	5	)	)	PUNCT
ejpam-2291	152	1	+	+	CCONJ
ejpam-2291	152	2	i	i	PRON
ejpam-2291	152	3	:	:	PUNCT
ejpam-2291	152	4	i	i	NOUN
ejpam-2291	152	5	=	=	NOUN
ejpam-2291	152	6	0	0	NUM
ejpam-2291	152	7	,	,	PUNCT
ejpam-2291	152	8	.	.	PUNCT
ejpam-2291	152	9	.	.	PUNCT
ejpam-2291	152	10	.	.	PUNCT
ejpam-2291	153	1	,	,	PUNCT
ejpam-2291	153	2	g}=	g}=	PROPN
ejpam-2291	153	3	a	a	X
ejpam-2291	153	4	(	(	PUNCT
ejpam-2291	153	5	(	(	PUNCT
ejpam-2291	153	6	(	(	PUNCT
ejpam-2291	153	7	f1	f1	NOUN
ejpam-2291	153	8	,	,	PUNCT
ejpam-2291	153	9	.	.	PUNCT
ejpam-2291	153	10	.	.	PUNCT
ejpam-2291	154	1	.	.	PUNCT
ejpam-2291	155	1	,	,	PUNCT
ejpam-2291	155	2	fg)l	fg)l	NUM
ejpam-2291	155	3	:	:	PUNCT
ejpam-2291	155	4	l	l	PROPN
ejpam-2291	155	5	s+)/	s+)/	PROPN
ejpam-2291	155	6	(	(	PUNCT
ejpam-2291	155	7	f1	f1	NOUN
ejpam-2291	155	8	,	,	PUNCT
ejpam-2291	155	9	.	.	PUNCT
ejpam-2291	155	10	.	.	PUNCT
ejpam-2291	155	11	.	.	PUNCT
ejpam-2291	156	1	,	,	PUNCT
ejpam-2291	156	2	fg)l)≥	fg)l)≥	ADJ
ejpam-2291	156	3	0	0	NUM
ejpam-2291	156	4	.	.	PUNCT
ejpam-2291	157	1	therefore	therefore	ADV
ejpam-2291	157	2	,	,	PUNCT
ejpam-2291	157	3	ag(l)≥	ag(l)≥	PROPN
ejpam-2291	157	4	−g	−g	NOUN
ejpam-2291	157	5	and	and	CCONJ
ejpam-2291	157	6	(	(	PUNCT
ejpam-2291	157	7	i	i	NOUN
ejpam-2291	157	8	)	)	PUNCT
ejpam-2291	157	9	and	and	CCONJ
ejpam-2291	157	10	(	(	PUNCT
ejpam-2291	157	11	ii	ii	NOUN
ejpam-2291	157	12	)	)	PUNCT
ejpam-2291	157	13	have	have	AUX
ejpam-2291	157	14	been	be	AUX
ejpam-2291	157	15	proved	prove	VERB
ejpam-2291	157	16	.	.	PUNCT
ejpam-2291	158	1	to	to	PART
ejpam-2291	158	2	prove	prove	VERB
ejpam-2291	158	3	(	(	PUNCT
ejpam-2291	158	4	iii	iii	NOUN
ejpam-2291	158	5	)	)	PUNCT
ejpam-2291	158	6	,	,	PUNCT
ejpam-2291	158	7	set	set	VERB
ejpam-2291	158	8	s̄	s̄	NOUN
ejpam-2291	158	9	=	=	SYM
ejpam-2291	158	10	s	s	X
ejpam-2291	158	11	/	/	SYM
ejpam-2291	158	12	h0	h0	NOUN
ejpam-2291	158	13	s+	s+	PUNCT
ejpam-2291	158	14	(	(	PUNCT
ejpam-2291	158	15	s	s	X
ejpam-2291	158	16	)	)	PUNCT
ejpam-2291	158	17	and	and	CCONJ
ejpam-2291	158	18	l̄	l̄	NOUN
ejpam-2291	159	1	=	=	PUNCT
ejpam-2291	159	2	l	l	NOUN
ejpam-2291	159	3	/	/	SYM
ejpam-2291	159	4	h0	h0	PROPN
ejpam-2291	159	5	s+	s+	PUNCT
ejpam-2291	159	6	(	(	PUNCT
ejpam-2291	159	7	l	l	NOUN
ejpam-2291	159	8	)	)	PUNCT
ejpam-2291	159	9	.	.	PUNCT
ejpam-2291	160	1	then	then	ADV
ejpam-2291	160	2	it	it	PRON
ejpam-2291	160	3	is	be	AUX
ejpam-2291	160	4	easy	easy	ADJ
ejpam-2291	160	5	to	to	PART
ejpam-2291	160	6	see	see	VERB
ejpam-2291	160	7	that	that	DET
ejpam-2291	160	8	grade(s̄+	grade(s̄+	NOUN
ejpam-2291	160	9	,	,	PUNCT
ejpam-2291	160	10	l̄)≥	l̄)≥	ADV
ejpam-2291	160	11	1	1	NUM
ejpam-2291	160	12	and	and	CCONJ
ejpam-2291	160	13	h1	h1	VERB
ejpam-2291	160	14	s̄+	s̄+	NUM
ejpam-2291	160	15	(	(	PUNCT
ejpam-2291	160	16	l̄)∼=	l̄)∼=	NOUN
ejpam-2291	160	17	h1	h1	VERB
ejpam-2291	160	18	s+	s+	PUNCT
ejpam-2291	160	19	(	(	PUNCT
ejpam-2291	160	20	l	l	NOUN
ejpam-2291	160	21	)	)	PUNCT
ejpam-2291	160	22	6=	6=	ADP
ejpam-2291	160	23	0	0	X
ejpam-2291	160	24	.	.	PUNCT
ejpam-2291	161	1	therefore	therefore	ADV
ejpam-2291	161	2	a1(l	a1(l	X
ejpam-2291	161	3	)	)	PUNCT
ejpam-2291	161	4	=	=	PUNCT
ejpam-2291	161	5	a1(l̄)≥	a1(l̄)≥	ADV
ejpam-2291	161	6	−1	−1	NOUN
ejpam-2291	161	7	by	by	ADP
ejpam-2291	161	8	(	(	PUNCT
ejpam-2291	161	9	ii	ii	NOUN
ejpam-2291	161	10	)	)	PUNCT
ejpam-2291	161	11	.	.	PUNCT
ejpam-2291	162	1	theorem	theorem	NOUN
ejpam-2291	162	2	1	1	X
ejpam-2291	162	3	.	.	PUNCT
ejpam-2291	163	1	let	let	VERB
ejpam-2291	163	2	f=	f=	ADJ
ejpam-2291	163	3	f1	f1	PROPN
ejpam-2291	163	4	∈	∈	PROPN
ejpam-2291	163	5	s1	s1	NOUN
ejpam-2291	163	6	,	,	PUNCT
ejpam-2291	163	7	.	.	PUNCT
ejpam-2291	163	8	.	.	PUNCT
ejpam-2291	164	1	.	.	PUNCT
ejpam-2291	165	1	,	,	PUNCT
ejpam-2291	165	2	fh	fh	PROPN
ejpam-2291	165	3	∈	∈	PROPN
ejpam-2291	165	4	s1	s1	PROPN
ejpam-2291	165	5	be	be	AUX
ejpam-2291	165	6	an	an	DET
ejpam-2291	165	7	s+-filter	s+-filter	NOUN
ejpam-2291	165	8	regular	regular	ADJ
ejpam-2291	165	9	sequence	sequence	NOUN
ejpam-2291	165	10	for	for	ADP
ejpam-2291	165	11	l.	l.	PROPN
ejpam-2291	165	12	let	let	VERB
ejpam-2291	165	13	b=	b=	NOUN
ejpam-2291	165	14	(	(	PUNCT
ejpam-2291	165	15	f1	f1	NOUN
ejpam-2291	165	16	,	,	PUNCT
ejpam-2291	165	17	.	.	PUNCT
ejpam-2291	165	18	.	.	PUNCT
ejpam-2291	166	1	.	.	PUNCT
ejpam-2291	167	1	,	,	PUNCT
ejpam-2291	167	2	fh	fh	PROPN
ejpam-2291	167	3	)	)	PUNCT
ejpam-2291	167	4	be	be	VERB
ejpam-2291	167	5	a	a	DET
ejpam-2291	167	6	reduction	reduction	NOUN
ejpam-2291	167	7	of	of	ADP
ejpam-2291	167	8	s+	s+	NOUN
ejpam-2291	167	9	with	with	ADP
ejpam-2291	167	10	respect	respect	NOUN
ejpam-2291	167	11	to	to	ADP
ejpam-2291	167	12	l.	l.	PROPN
ejpam-2291	167	13	then	then	ADV
ejpam-2291	167	14	reg(l	reg(l	PROPN
ejpam-2291	167	15	)	)	PUNCT
ejpam-2291	168	1	=	=	SYM
ejpam-2291	168	2	max{e(f	max{e(f	PROPN
ejpam-2291	168	3	,	,	PUNCT
ejpam-2291	168	4	l	l	NOUN
ejpam-2291	168	5	)	)	PUNCT
ejpam-2291	168	6	,	,	PUNCT
ejpam-2291	168	7	rb(s+	rb(s+	PROPN
ejpam-2291	168	8	,	,	PUNCT
ejpam-2291	168	9	l	l	NOUN
ejpam-2291	168	10	)	)	PUNCT
ejpam-2291	168	11	}	}	PUNCT
ejpam-2291	168	12	.	.	PUNCT
ejpam-2291	169	1	proof	proof	NOUN
ejpam-2291	169	2	.	.	PUNCT
ejpam-2291	170	1	by	by	ADP
ejpam-2291	170	2	lemma	lemma	PROPN
ejpam-2291	170	3	2	2	NUM
ejpam-2291	170	4	we	we	PRON
ejpam-2291	170	5	have	have	VERB
ejpam-2291	170	6	e(f	e(f	PROPN
ejpam-2291	170	7	,	,	PUNCT
ejpam-2291	170	8	l	l	NOUN
ejpam-2291	170	9	)	)	PUNCT
ejpam-2291	170	10	=	=	PRON
ejpam-2291	170	11	max{end	max{end	NOUN
ejpam-2291	170	12	(	(	PUNCT
ejpam-2291	170	13	(	(	PUNCT
ejpam-2291	170	14	(	(	PUNCT
ejpam-2291	170	15	f1	f1	NOUN
ejpam-2291	170	16	,	,	PUNCT
ejpam-2291	170	17	.	.	PUNCT
ejpam-2291	170	18	.	.	PUNCT
ejpam-2291	170	19	.	.	PUNCT
ejpam-2291	171	1	,	,	PUNCT
ejpam-2291	171	2	fi)l	fi)l	NOUN
ejpam-2291	171	3	:	:	PUNCT
ejpam-2291	171	4	l	l	PROPN
ejpam-2291	171	5	s+)/	s+)/	PROPN
ejpam-2291	171	6	(	(	PUNCT
ejpam-2291	171	7	f1	f1	NOUN
ejpam-2291	171	8	,	,	PUNCT
ejpam-2291	171	9	.	.	PUNCT
ejpam-2291	171	10	.	.	PUNCT
ejpam-2291	171	11	.	.	PUNCT
ejpam-2291	172	1	,	,	PUNCT
ejpam-2291	172	2	fi)l	fi)l	PROPN
ejpam-2291	172	3	)	)	PUNCT
ejpam-2291	172	4	:	:	PUNCT
ejpam-2291	173	1	i	i	NOUN
ejpam-2291	173	2	=	=	NOUN
ejpam-2291	173	3	0	0	NUM
ejpam-2291	173	4	,	,	PUNCT
ejpam-2291	173	5	.	.	PUNCT
ejpam-2291	173	6	.	.	PUNCT
ejpam-2291	173	7	.	.	PUNCT
ejpam-2291	174	1	,	,	PUNCT
ejpam-2291	174	2	h−	h−	PROPN
ejpam-2291	174	3	1	1	NUM
ejpam-2291	174	4	}	}	PUNCT
ejpam-2291	174	5	.	.	PUNCT
ejpam-2291	175	1	furthermore	furthermore	ADV
ejpam-2291	175	2	,	,	PUNCT
ejpam-2291	175	3	rb(s+	rb(s+	PROPN
ejpam-2291	175	4	,	,	PUNCT
ejpam-2291	175	5	l	l	NOUN
ejpam-2291	175	6	)	)	PUNCT
ejpam-2291	175	7	=	=	SYM
ejpam-2291	175	8	end(l	end(l	PROPN
ejpam-2291	175	9	/	/	SYM
ejpam-2291	175	10	bl	bl	PROPN
ejpam-2291	175	11	)	)	PUNCT
ejpam-2291	175	12	=	=	SYM
ejpam-2291	175	13	end	end	NOUN
ejpam-2291	175	14	(	(	PUNCT
ejpam-2291	175	15	(	(	PUNCT
ejpam-2291	175	16	(	(	PUNCT
ejpam-2291	175	17	f1	f1	NOUN
ejpam-2291	175	18	,	,	PUNCT
ejpam-2291	175	19	.	.	PUNCT
ejpam-2291	175	20	.	.	PUNCT
ejpam-2291	175	21	.	.	PUNCT
ejpam-2291	176	1	,	,	PUNCT
ejpam-2291	176	2	fh)l	fh)l	PROPN
ejpam-2291	176	3	:	:	PUNCT
ejpam-2291	176	4	l	l	PROPN
ejpam-2291	176	5	s+)/	s+)/	PROPN
ejpam-2291	176	6	(	(	PUNCT
ejpam-2291	176	7	f1	f1	NOUN
ejpam-2291	176	8	,	,	PUNCT
ejpam-2291	176	9	.	.	PUNCT
ejpam-2291	176	10	.	.	PUNCT
ejpam-2291	176	11	.	.	PUNCT
ejpam-2291	177	1	,	,	PUNCT
ejpam-2291	177	2	fh)l	fh)l	PROPN
ejpam-2291	177	3	)	)	PUNCT
ejpam-2291	177	4	.	.	PUNCT
ejpam-2291	178	1	therefore	therefore	ADV
ejpam-2291	178	2	max{e(f	max{e(f	PROPN
ejpam-2291	178	3	,	,	PUNCT
ejpam-2291	178	4	l	l	NOUN
ejpam-2291	178	5	)	)	PUNCT
ejpam-2291	178	6	,	,	PUNCT
ejpam-2291	178	7	rb(s+	rb(s+	PROPN
ejpam-2291	178	8	,	,	PUNCT
ejpam-2291	178	9	l)}=max{end	l)}=max{end	PROPN
ejpam-2291	178	10	(	(	PUNCT
ejpam-2291	178	11	(	(	PUNCT
ejpam-2291	178	12	(	(	PUNCT
ejpam-2291	178	13	f1	f1	NOUN
ejpam-2291	178	14	,	,	PUNCT
ejpam-2291	178	15	.	.	PUNCT
ejpam-2291	178	16	.	.	PUNCT
ejpam-2291	179	1	.	.	PUNCT
ejpam-2291	180	1	,	,	PUNCT
ejpam-2291	180	2	fi)l	fi)l	NOUN
ejpam-2291	180	3	:	:	PUNCT
ejpam-2291	180	4	l	l	PROPN
ejpam-2291	180	5	s+)/	s+)/	PROPN
ejpam-2291	180	6	(	(	PUNCT
ejpam-2291	180	7	f1	f1	NOUN
ejpam-2291	180	8	,	,	PUNCT
ejpam-2291	180	9	.	.	PUNCT
ejpam-2291	180	10	.	.	PUNCT
ejpam-2291	180	11	.	.	PUNCT
ejpam-2291	181	1	,	,	PUNCT
ejpam-2291	181	2	fi)l	fi)l	PROPN
ejpam-2291	181	3	)	)	PUNCT
ejpam-2291	181	4	:	:	PUNCT
ejpam-2291	182	1	i	i	NOUN
ejpam-2291	182	2	=	=	NOUN
ejpam-2291	182	3	0	0	NUM
ejpam-2291	182	4	,	,	PUNCT
ejpam-2291	182	5	.	.	PUNCT
ejpam-2291	182	6	.	.	PUNCT
ejpam-2291	182	7	.	.	PUNCT
ejpam-2291	183	1	,	,	PUNCT
ejpam-2291	183	2	h	h	NOUN
ejpam-2291	183	3	}	}	PUNCT
ejpam-2291	183	4	=	=	ADJ
ejpam-2291	183	5	max{ai(l	max{ai(l	X
ejpam-2291	183	6	)	)	PUNCT
ejpam-2291	184	1	+	+	CCONJ
ejpam-2291	184	2	i	i	PRON
ejpam-2291	184	3	:	:	PUNCT
ejpam-2291	184	4	i	i	NOUN
ejpam-2291	184	5	=	=	NOUN
ejpam-2291	184	6	0	0	NUM
ejpam-2291	184	7	,	,	PUNCT
ejpam-2291	184	8	.	.	PUNCT
ejpam-2291	184	9	.	.	PUNCT
ejpam-2291	184	10	.	.	PUNCT
ejpam-2291	185	1	,	,	PUNCT
ejpam-2291	185	2	h	h	NOUN
ejpam-2291	185	3	}	}	PUNCT
ejpam-2291	185	4	.	.	PUNCT
ejpam-2291	186	1	since	since	SCONJ
ejpam-2291	186	2	reg(l	reg(l	X
ejpam-2291	186	3	)	)	PUNCT
ejpam-2291	186	4	=	=	SYM
ejpam-2291	186	5	max{ai(l	max{ai(l	PROPN
ejpam-2291	186	6	)	)	PUNCT
ejpam-2291	187	1	+	+	CCONJ
ejpam-2291	187	2	i	i	PRON
ejpam-2291	187	3	:	:	PUNCT
ejpam-2291	187	4	i	i	PRON
ejpam-2291	187	5	≥	≥	VERB
ejpam-2291	187	6	0	0	NUM
ejpam-2291	187	7	}	}	PUNCT
ejpam-2291	187	8	,	,	PUNCT
ejpam-2291	187	9	it	it	PRON
ejpam-2291	187	10	is	be	AUX
ejpam-2291	187	11	enough	enough	ADJ
ejpam-2291	187	12	to	to	PART
ejpam-2291	187	13	show	show	VERB
ejpam-2291	187	14	that	that	SCONJ
ejpam-2291	187	15	h	h	NOUN
ejpam-2291	188	1	i	i	PRON
ejpam-2291	188	2	s+	s+	PUNCT
ejpam-2291	188	3	(	(	PUNCT
ejpam-2291	188	4	l	l	NOUN
ejpam-2291	188	5	)	)	PUNCT
ejpam-2291	188	6	=	=	SYM
ejpam-2291	188	7	0	0	NUM
ejpam-2291	188	8	for	for	ADP
ejpam-2291	188	9	all	all	PRON
ejpam-2291	188	10	i	i	PRON
ejpam-2291	188	11	>	>	X
ejpam-2291	188	12	h.	h.	PROPN
ejpam-2291	189	1	if	if	SCONJ
ejpam-2291	189	2	h	h	NOUN
ejpam-2291	189	3	=	=	NOUN
ejpam-2291	189	4	0	0	NUM
ejpam-2291	189	5	,	,	PUNCT
ejpam-2291	189	6	then	then	ADV
ejpam-2291	189	7	l	l	NOUN
ejpam-2291	189	8	is	be	AUX
ejpam-2291	189	9	annihilated	annihilate	VERB
ejpam-2291	189	10	by	by	ADP
ejpam-2291	189	11	some	some	DET
ejpam-2291	189	12	power	power	NOUN
ejpam-2291	189	13	of	of	ADP
ejpam-2291	189	14	s+	s+	NOUN
ejpam-2291	189	15	and	and	CCONJ
ejpam-2291	189	16	so	so	ADV
ejpam-2291	189	17	h	h	VERB
ejpam-2291	190	1	i	i	PRON
ejpam-2291	190	2	s+	s+	ADV
ejpam-2291	190	3	(	(	PUNCT
ejpam-2291	190	4	l	l	NOUN
ejpam-2291	190	5	)	)	PUNCT
ejpam-2291	190	6	=	=	SYM
ejpam-2291	190	7	0	0	NUM
ejpam-2291	190	8	for	for	ADP
ejpam-2291	190	9	all	all	DET
ejpam-2291	190	10	i	i	PRON
ejpam-2291	190	11	>	>	X
ejpam-2291	190	12	0	0	X
ejpam-2291	190	13	.	.	PUNCT
ejpam-2291	191	1	so	so	ADV
ejpam-2291	191	2	let	let	VERB
ejpam-2291	191	3	h	h	PRON
ejpam-2291	191	4	≥	≥	NOUN
ejpam-2291	191	5	1	1	NUM
ejpam-2291	191	6	.	.	PUNCT
ejpam-2291	192	1	by	by	ADP
ejpam-2291	192	2	induction	induction	NOUN
ejpam-2291	192	3	,	,	PUNCT
ejpam-2291	192	4	we	we	PRON
ejpam-2291	192	5	have	have	VERB
ejpam-2291	192	6	h	h	NOUN
ejpam-2291	192	7	i	i	PRON
ejpam-2291	192	8	s+	s+	PUNCT
ejpam-2291	192	9	(	(	PUNCT
ejpam-2291	192	10	l/	l/	PROPN
ejpam-2291	192	11	f1	f1	PROPN
ejpam-2291	192	12	l	l	NOUN
ejpam-2291	192	13	)	)	PUNCT
ejpam-2291	192	14	=	=	SYM
ejpam-2291	192	15	0	0	NUM
ejpam-2291	193	1	for	for	ADP
ejpam-2291	193	2	all	all	PRON
ejpam-2291	193	3	i	i	PRON
ejpam-2291	193	4	>	>	X
ejpam-2291	193	5	h−	h−	PROPN
ejpam-2291	193	6	1	1	NUM
ejpam-2291	193	7	.	.	PUNCT
ejpam-2291	193	8	hence	hence	ADV
ejpam-2291	193	9	ai(l/	ai(l/	PROPN
ejpam-2291	193	10	f1	f1	PROPN
ejpam-2291	193	11	l	l	NOUN
ejpam-2291	193	12	)	)	PUNCT
ejpam-2291	193	13	=	=	NOUN
ejpam-2291	193	14	−∞	−∞	X
ejpam-2291	193	15	for	for	ADP
ejpam-2291	193	16	all	all	DET
ejpam-2291	193	17	i	i	PRON
ejpam-2291	193	18	>	>	X
ejpam-2291	193	19	h−	h−	PROPN
ejpam-2291	193	20	1	1	NUM
ejpam-2291	193	21	.	.	PUNCT
ejpam-2291	193	22	by	by	ADP
ejpam-2291	193	23	lemma	lemma	PROPN
ejpam-2291	193	24	1	1	NUM
ejpam-2291	193	25	,	,	PUNCT
ejpam-2291	193	26	this	this	PRON
ejpam-2291	193	27	implies	imply	VERB
ejpam-2291	193	28	ai+1(l	ai+1(l	NOUN
ejpam-2291	193	29	)	)	PUNCT
ejpam-2291	194	1	=	=	PUNCT
ejpam-2291	195	1	−∞	−∞	NOUN
ejpam-2291	195	2	and	and	CCONJ
ejpam-2291	195	3	h	h	NOUN
ejpam-2291	195	4	i+1	i+1	ADV
ejpam-2291	195	5	s+	s+	ADV
ejpam-2291	195	6	(	(	PUNCT
ejpam-2291	195	7	l	l	NOUN
ejpam-2291	195	8	)	)	PUNCT
ejpam-2291	195	9	=	=	SYM
ejpam-2291	195	10	0	0	NUM
ejpam-2291	196	1	for	for	ADP
ejpam-2291	196	2	all	all	PRON
ejpam-2291	196	3	i	i	PRON
ejpam-2291	196	4	>	>	X
ejpam-2291	196	5	h.	h.	PROPN
ejpam-2291	196	6	3	3	X
ejpam-2291	196	7	.	.	PUNCT
ejpam-2291	196	8	regularity	regularity	NOUN
ejpam-2291	196	9	results	result	NOUN
ejpam-2291	196	10	in	in	ADP
ejpam-2291	196	11	this	this	DET
ejpam-2291	196	12	section	section	NOUN
ejpam-2291	196	13	,	,	PUNCT
ejpam-2291	196	14	using	use	VERB
ejpam-2291	196	15	the	the	DET
ejpam-2291	196	16	ideas	idea	NOUN
ejpam-2291	196	17	of	of	ADP
ejpam-2291	196	18	[	[	X
ejpam-2291	196	19	5	5	NUM
ejpam-2291	196	20	]	]	PUNCT
ejpam-2291	196	21	,	,	PUNCT
ejpam-2291	196	22	we	we	PRON
ejpam-2291	196	23	will	will	AUX
ejpam-2291	196	24	show	show	VERB
ejpam-2291	196	25	that	that	SCONJ
ejpam-2291	196	26	there	there	PRON
ejpam-2291	196	27	is	be	VERB
ejpam-2291	196	28	a	a	DET
ejpam-2291	196	29	close	close	ADJ
ejpam-2291	196	30	relationship	relationship	NOUN
ejpam-2291	196	31	between	between	ADP
ejpam-2291	196	32	the	the	DET
ejpam-2291	196	33	invariants	invariant	NOUN
ejpam-2291	196	34	ai(rb(e	ai(rb(e	ADJ
ejpam-2291	196	35	)	)	PUNCT
ejpam-2291	196	36	)	)	PUNCT
ejpam-2291	196	37	and	and	CCONJ
ejpam-2291	196	38	ai(gb(e	ai(gb(e	PROPN
ejpam-2291	196	39	)	)	PUNCT
ejpam-2291	196	40	)	)	PUNCT
ejpam-2291	196	41	,	,	PUNCT
ejpam-2291	196	42	from	from	ADP
ejpam-2291	196	43	which	which	PRON
ejpam-2291	196	44	we	we	PRON
ejpam-2291	196	45	can	can	AUX
ejpam-2291	196	46	easily	easily	ADV
ejpam-2291	196	47	derive	derive	VERB
ejpam-2291	196	48	the	the	DET
ejpam-2291	196	49	formula	formula	NOUN
ejpam-2291	196	50	reg(r(e	reg(r(e	NOUN
ejpam-2291	196	51	)	)	PUNCT
ejpam-2291	196	52	)	)	PUNCT
ejpam-2291	197	1	=	=	SYM
ejpam-2291	197	2	reg(g(e	reg(g(e	NOUN
ejpam-2291	197	3	)	)	PUNCT
ejpam-2291	197	4	)	)	PUNCT
ejpam-2291	197	5	which	which	PRON
ejpam-2291	197	6	is	be	AUX
ejpam-2291	197	7	a	a	DET
ejpam-2291	197	8	generalization	generalization	NOUN
ejpam-2291	197	9	of	of	ADP
ejpam-2291	197	10	that	that	PRON
ejpam-2291	197	11	of	of	ADP
ejpam-2291	197	12	ooishi	ooishi	NOUN
ejpam-2291	198	1	[	[	X
ejpam-2291	198	2	4	4	NUM
ejpam-2291	198	3	]	]	PUNCT
ejpam-2291	198	4	and	and	CCONJ
ejpam-2291	198	5	[	[	X
ejpam-2291	198	6	5	5	NUM
ejpam-2291	198	7	,	,	PUNCT
ejpam-2291	198	8	theorem	theorem	VERB
ejpam-2291	198	9	3.1	3.1	NUM
ejpam-2291	198	10	]	]	PUNCT
ejpam-2291	198	11	.	.	PUNCT
ejpam-2291	199	1	for	for	ADP
ejpam-2291	199	2	simplicity	simplicity	NOUN
ejpam-2291	199	3	we	we	PRON
ejpam-2291	199	4	shall	shall	AUX
ejpam-2291	199	5	denote	denote	VERB
ejpam-2291	199	6	rb(e	rb(e	VERB
ejpam-2291	199	7	)	)	PUNCT
ejpam-2291	199	8	by	by	ADP
ejpam-2291	199	9	r(e	r(e	NOUN
ejpam-2291	199	10	)	)	PUNCT
ejpam-2291	199	11	,	,	PUNCT
ejpam-2291	199	12	gb(e	gb(e	X
ejpam-2291	199	13	)	)	PUNCT
ejpam-2291	199	14	by	by	ADP
ejpam-2291	199	15	g(e	g(e	PROPN
ejpam-2291	199	16	)	)	PUNCT
ejpam-2291	199	17	,	,	PUNCT
ejpam-2291	199	18	r(b)+	r(b)+	NOUN
ejpam-2291	199	19	by	by	ADP
ejpam-2291	199	20	r+	r+	NOUN
ejpam-2291	199	21	and	and	CCONJ
ejpam-2291	199	22	g(b)+	g(b)+	VERB
ejpam-2291	199	23	by	by	ADP
ejpam-2291	199	24	g+	g+	PROPN
ejpam-2291	199	25	.	.	PUNCT
ejpam-2291	200	1	n.	n.	PROPN
ejpam-2291	200	2	zamani	zamani	PROPN
ejpam-2291	200	3	/	/	SYM
ejpam-2291	200	4	eur	eur	PROPN
ejpam-2291	200	5	.	.	PUNCT
ejpam-2291	201	1	j.	j.	PROPN
ejpam-2291	201	2	pure	pure	PROPN
ejpam-2291	201	3	appl	appl	PROPN
ejpam-2291	201	4	.	.	PROPN
ejpam-2291	201	5	math	math	PROPN
ejpam-2291	201	6	,	,	PUNCT
ejpam-2291	201	7	7	7	NUM
ejpam-2291	201	8	(	(	PUNCT
ejpam-2291	201	9	2014	2014	NUM
ejpam-2291	201	10	)	)	PUNCT
ejpam-2291	201	11	,	,	PUNCT
ejpam-2291	201	12	429	429	NUM
ejpam-2291	201	13	-	-	SYM
ejpam-2291	201	14	436	436	NUM
ejpam-2291	201	15	433	433	NUM
ejpam-2291	201	16	theorem	theorem	NOUN
ejpam-2291	201	17	2	2	NUM
ejpam-2291	201	18	.	.	PUNCT
ejpam-2291	202	1	let	let	VERB
ejpam-2291	202	2	the	the	DET
ejpam-2291	202	3	notation	notation	NOUN
ejpam-2291	202	4	be	be	AUX
ejpam-2291	202	5	as	as	ADP
ejpam-2291	202	6	in	in	ADP
ejpam-2291	202	7	above	above	ADV
ejpam-2291	202	8	.	.	PUNCT
ejpam-2291	203	1	then	then	ADV
ejpam-2291	203	2	:	:	PUNCT
ejpam-2291	203	3	(	(	PUNCT
ejpam-2291	203	4	i	i	NOUN
ejpam-2291	203	5	)	)	PUNCT
ejpam-2291	203	6	for	for	ADP
ejpam-2291	203	7	each	each	DET
ejpam-2291	203	8	i	i	PRON
ejpam-2291	203	9	6=	6=	PROPN
ejpam-2291	203	10	1	1	NUM
ejpam-2291	203	11	,	,	PUNCT
ejpam-2291	203	12	ai(r(e))≤	ai(r(e))≤	X
ejpam-2291	203	13	ai(g(e	ai(g(e	ADJ
ejpam-2291	203	14	)	)	PUNCT
ejpam-2291	203	15	)	)	PUNCT
ejpam-2291	203	16	.	.	PUNCT
ejpam-2291	204	1	(	(	PUNCT
ejpam-2291	204	2	ii	ii	NOUN
ejpam-2291	204	3	)	)	PUNCT
ejpam-2291	204	4	ai(r(e	ai(r(e	NOUN
ejpam-2291	204	5	)	)	PUNCT
ejpam-2291	204	6	)	)	PUNCT
ejpam-2291	205	1	=	=	PUNCT
ejpam-2291	205	2	ai(g(e	ai(g(e	NOUN
ejpam-2291	205	3	)	)	PUNCT
ejpam-2291	205	4	)	)	PUNCT
ejpam-2291	206	1	if	if	SCONJ
ejpam-2291	206	2	ai+1(g(e))≤	ai+1(g(e))≤	NOUN
ejpam-2291	206	3	ai(g(e	ai(g(e	ADV
ejpam-2291	206	4	)	)	PUNCT
ejpam-2291	206	5	)	)	PUNCT
ejpam-2291	206	6	,	,	PUNCT
ejpam-2291	206	7	i	i	PRON
ejpam-2291	206	8	6=	6=	PROPN
ejpam-2291	206	9	1	1	X
ejpam-2291	206	10	.	.	PUNCT
ejpam-2291	206	11	(	(	PUNCT
ejpam-2291	206	12	iii	iii	X
ejpam-2291	206	13	)	)	PUNCT
ejpam-2291	206	14	if	if	SCONJ
ejpam-2291	206	15	h1	h1	ADJ
ejpam-2291	206	16	g+	g+	X
ejpam-2291	206	17	(	(	PUNCT
ejpam-2291	206	18	g(e	g(e	PROPN
ejpam-2291	206	19	)	)	PUNCT
ejpam-2291	206	20	)	)	PUNCT
ejpam-2291	207	1	6=	6=	ADP
ejpam-2291	207	2	0	0	NUM
ejpam-2291	208	1	or	or	CCONJ
ejpam-2291	208	2	if	if	SCONJ
ejpam-2291	208	3	b	b	PROPN
ejpam-2291	208	4	⊆	⊆	NUM
ejpam-2291	208	5	p	p	NOUN
ejpam-2291	208	6	(	(	PUNCT
ejpam-2291	208	7	0	0	NUM
ejpam-2291	208	8	:	:	PUNCT
ejpam-2291	208	9	a	a	DET
ejpam-2291	208	10	e	e	NOUN
ejpam-2291	208	11	)	)	PUNCT
ejpam-2291	208	12	,	,	PUNCT
ejpam-2291	208	13	the	the	DET
ejpam-2291	208	14	statements	statement	NOUN
ejpam-2291	208	15	(	(	PUNCT
ejpam-2291	208	16	i	i	NOUN
ejpam-2291	208	17	)	)	PUNCT
ejpam-2291	208	18	and	and	CCONJ
ejpam-2291	208	19	(	(	PUNCT
ejpam-2291	208	20	ii	ii	NOUN
ejpam-2291	208	21	)	)	PUNCT
ejpam-2291	208	22	hold	hold	VERB
ejpam-2291	208	23	for	for	ADP
ejpam-2291	208	24	i	i	PRON
ejpam-2291	208	25	=	=	NOUN
ejpam-2291	208	26	1	1	X
ejpam-2291	208	27	.	.	PUNCT
ejpam-2291	208	28	(	(	PUNCT
ejpam-2291	208	29	iv	iv	X
ejpam-2291	208	30	)	)	PUNCT
ejpam-2291	208	31	if	if	SCONJ
ejpam-2291	208	32	h1	h1	ADJ
ejpam-2291	208	33	g+	g+	X
ejpam-2291	208	34	(	(	PUNCT
ejpam-2291	208	35	g(e	g(e	PROPN
ejpam-2291	208	36	)	)	PUNCT
ejpam-2291	208	37	)	)	PUNCT
ejpam-2291	209	1	=	=	SYM
ejpam-2291	209	2	0	0	NUM
ejpam-2291	209	3	and	and	CCONJ
ejpam-2291	209	4	b	b	PROPN
ejpam-2291	209	5	6⊆	6⊆	NUM
ejpam-2291	209	6	p	p	NOUN
ejpam-2291	209	7	(	(	PUNCT
ejpam-2291	209	8	0	0	NUM
ejpam-2291	209	9	:	:	PUNCT
ejpam-2291	209	10	a	a	DET
ejpam-2291	209	11	e	e	NOUN
ejpam-2291	209	12	)	)	PUNCT
ejpam-2291	209	13	then	then	ADV
ejpam-2291	209	14	a1(r(e	a1(r(e	NUM
ejpam-2291	209	15	)	)	PUNCT
ejpam-2291	209	16	)	)	PUNCT
ejpam-2291	210	1	=	=	PUNCT
ejpam-2291	210	2	−1	−1	NOUN
ejpam-2291	210	3	.	.	PUNCT
ejpam-2291	211	1	proof	proof	NOUN
ejpam-2291	211	2	.	.	PUNCT
ejpam-2291	212	1	we	we	PRON
ejpam-2291	212	2	consider	consider	VERB
ejpam-2291	212	3	the	the	DET
ejpam-2291	212	4	exact	exact	ADJ
ejpam-2291	212	5	sequence	sequence	NOUN
ejpam-2291	212	6	0	0	NUM
ejpam-2291	212	7	−→	−→	NOUN
ejpam-2291	212	8	r(e)+	r(e)+	PROPN
ejpam-2291	212	9	−→	−→	NOUN
ejpam-2291	212	10	r(e	r(e	NOUN
ejpam-2291	212	11	)	)	PUNCT
ejpam-2291	213	1	−→	−→	NOUN
ejpam-2291	213	2	e	e	NOUN
ejpam-2291	213	3	−→	−→	NOUN
ejpam-2291	213	4	0	0	NUM
ejpam-2291	213	5	,	,	PUNCT
ejpam-2291	213	6	(	(	PUNCT
ejpam-2291	213	7	1	1	X
ejpam-2291	213	8	)	)	PUNCT
ejpam-2291	213	9	where	where	SCONJ
ejpam-2291	213	10	e	e	NOUN
ejpam-2291	213	11	is	be	AUX
ejpam-2291	213	12	considered	consider	VERB
ejpam-2291	213	13	as	as	SCONJ
ejpam-2291	213	14	a	a	DET
ejpam-2291	213	15	graded	grade	VERB
ejpam-2291	213	16	r	r	NOUN
ejpam-2291	213	17	-	-	PUNCT
ejpam-2291	213	18	module	module	NOUN
ejpam-2291	213	19	concentrated	concentrate	VERB
ejpam-2291	213	20	in	in	ADP
ejpam-2291	213	21	degree	degree	NOUN
ejpam-2291	213	22	zero	zero	NUM
ejpam-2291	213	23	.	.	PUNCT
ejpam-2291	214	1	since	since	SCONJ
ejpam-2291	214	2	h0	h0	PROPN
ejpam-2291	214	3	r+	r+	NOUN
ejpam-2291	214	4	(	(	PUNCT
ejpam-2291	214	5	e)n	e)n	X
ejpam-2291	214	6	=	=	X
ejpam-2291	214	7	0	0	NUM
ejpam-2291	214	8	for	for	ADP
ejpam-2291	214	9	n	n	PROPN
ejpam-2291	214	10	6=	6=	NUM
ejpam-2291	214	11	0	0	NUM
ejpam-2291	215	1	and	and	CCONJ
ejpam-2291	215	2	h	h	NOUN
ejpam-2291	216	1	i	i	PRON
ejpam-2291	216	2	r+	r+	PRON
ejpam-2291	216	3	(	(	PUNCT
ejpam-2291	216	4	e	e	NOUN
ejpam-2291	216	5	)	)	PUNCT
ejpam-2291	216	6	=	=	SYM
ejpam-2291	216	7	0	0	NUM
ejpam-2291	216	8	for	for	SCONJ
ejpam-2291	216	9	i	i	PRON
ejpam-2291	216	10	≥	≥	NOUN
ejpam-2291	216	11	1	1	NUM
ejpam-2291	216	12	,	,	PUNCT
ejpam-2291	216	13	so	so	ADV
ejpam-2291	216	14	from	from	ADP
ejpam-2291	216	15	the	the	DET
ejpam-2291	216	16	exact	exact	ADJ
ejpam-2291	216	17	sequence	sequence	NOUN
ejpam-2291	216	18	(	(	PUNCT
ejpam-2291	216	19	1	1	X
ejpam-2291	216	20	)	)	PUNCT
ejpam-2291	216	21	we	we	PRON
ejpam-2291	216	22	deduce	deduce	VERB
ejpam-2291	216	23	that	that	SCONJ
ejpam-2291	216	24	h	h	NOUN
ejpam-2291	217	1	i	i	PRON
ejpam-2291	217	2	r+	r+	PUNCT
ejpam-2291	217	3	(	(	PUNCT
ejpam-2291	217	4	r(e)+)n	r(e)+)n	PROPN
ejpam-2291	217	5	∼=	∼=	PROPN
ejpam-2291	217	6	h	h	NOUN
ejpam-2291	217	7	i	i	PRON
ejpam-2291	217	8	r+	r+	VERB
ejpam-2291	217	9	(	(	PUNCT
ejpam-2291	217	10	r(e))n	r(e))n	VERB
ejpam-2291	217	11	for	for	ADP
ejpam-2291	217	12	n	n	NOUN
ejpam-2291	217	13	=	=	SYM
ejpam-2291	217	14	0	0	NUM
ejpam-2291	217	15	,	,	PUNCT
ejpam-2291	217	16	i	i	PRON
ejpam-2291	217	17	≥	≥	VERB
ejpam-2291	217	18	2	2	NUM
ejpam-2291	217	19	,	,	PUNCT
ejpam-2291	217	20	and	and	CCONJ
ejpam-2291	217	21	for	for	ADP
ejpam-2291	217	22	n	n	PROPN
ejpam-2291	217	23	6=	6=	NUM
ejpam-2291	217	24	0	0	NUM
ejpam-2291	217	25	,	,	PUNCT
ejpam-2291	217	26	i	i	PRON
ejpam-2291	217	27	≥	≥	VERB
ejpam-2291	217	28	0	0	NUM
ejpam-2291	217	29	.	.	PUNCT
ejpam-2291	218	1	since	since	SCONJ
ejpam-2291	218	2	h	h	PROPN
ejpam-2291	218	3	i	i	PRON
ejpam-2291	218	4	g+	g+	VERB
ejpam-2291	218	5	(	(	PUNCT
ejpam-2291	218	6	g(e	g(e	PROPN
ejpam-2291	218	7	)	)	PUNCT
ejpam-2291	218	8	)	)	PUNCT
ejpam-2291	219	1	=	=	PUNCT
ejpam-2291	220	1	h	h	NOUN
ejpam-2291	221	1	i	i	PRON
ejpam-2291	221	2	r+	r+	PUNCT
ejpam-2291	221	3	(	(	PUNCT
ejpam-2291	221	4	g(e	g(e	PROPN
ejpam-2291	221	5	)	)	PUNCT
ejpam-2291	221	6	)	)	PUNCT
ejpam-2291	221	7	,	,	PUNCT
ejpam-2291	221	8	the	the	DET
ejpam-2291	221	9	exact	exact	ADJ
ejpam-2291	221	10	sequence	sequence	NOUN
ejpam-2291	221	11	0	0	NUM
ejpam-2291	221	12	−→	−→	NOUN
ejpam-2291	221	13	r(e)+(1	r(e)+(1	NOUN
ejpam-2291	221	14	)	)	PUNCT
ejpam-2291	221	15	−→	−→	NOUN
ejpam-2291	221	16	r(e	r(e	NOUN
ejpam-2291	221	17	)	)	PUNCT
ejpam-2291	221	18	−→	−→	NOUN
ejpam-2291	221	19	g(e	g(e	PROPN
ejpam-2291	221	20	)	)	PUNCT
ejpam-2291	221	21	−→	−→	NOUN
ejpam-2291	221	22	0	0	NUM
ejpam-2291	221	23	,	,	PUNCT
ejpam-2291	221	24	(	(	PUNCT
ejpam-2291	221	25	2	2	X
ejpam-2291	221	26	)	)	PUNCT
ejpam-2291	221	27	induces	induce	VERB
ejpam-2291	221	28	the	the	DET
ejpam-2291	221	29	exact	exact	ADJ
ejpam-2291	221	30	sequence	sequence	NOUN
ejpam-2291	221	31	h	h	NOUN
ejpam-2291	222	1	i	i	PRON
ejpam-2291	222	2	r+	r+	PUNCT
ejpam-2291	222	3	(	(	PUNCT
ejpam-2291	222	4	r(e)+)n+1→	r(e)+)n+1→	NOUN
ejpam-2291	222	5	h	h	VERB
ejpam-2291	223	1	i	i	PRON
ejpam-2291	223	2	r+	r+	PRON
ejpam-2291	223	3	(	(	PUNCT
ejpam-2291	223	4	r(e))n→	r(e))n→	NOUN
ejpam-2291	223	5	h	h	NOUN
ejpam-2291	224	1	i	i	PRON
ejpam-2291	224	2	r+	r+	PUNCT
ejpam-2291	224	3	(	(	PUNCT
ejpam-2291	224	4	g(e))n→	g(e))n→	NOUN
ejpam-2291	224	5	h	h	NOUN
ejpam-2291	224	6	i+1	i+1	VERB
ejpam-2291	224	7	r+	r+	PRON
ejpam-2291	224	8	(	(	PUNCT
ejpam-2291	224	9	r(e)+)n+1	r(e)+)n+1	NOUN
ejpam-2291	224	10	.	.	PUNCT
ejpam-2291	225	1	(	(	PUNCT
ejpam-2291	225	2	3	3	X
ejpam-2291	225	3	)	)	PUNCT
ejpam-2291	225	4	replacing	replace	VERB
ejpam-2291	225	5	h	h	NOUN
ejpam-2291	226	1	i	i	PRON
ejpam-2291	226	2	r+	r+	VERB
ejpam-2291	226	3	(	(	PUNCT
ejpam-2291	226	4	r(e)+)n+1	r(e)+)n+1	VERB
ejpam-2291	226	5	by	by	ADP
ejpam-2291	226	6	h	h	NOUN
ejpam-2291	226	7	i	i	PRON
ejpam-2291	226	8	r+	r+	VERB
ejpam-2291	226	9	(	(	PUNCT
ejpam-2291	226	10	r(e))n+1	r(e))n+1	NOUN
ejpam-2291	226	11	and	and	CCONJ
ejpam-2291	226	12	setting	set	VERB
ejpam-2291	227	1	h	h	NOUN
ejpam-2291	228	1	i	i	PRON
ejpam-2291	228	2	r+	r+	VERB
ejpam-2291	228	3	(	(	PUNCT
ejpam-2291	228	4	g(e	g(e	PROPN
ejpam-2291	228	5	)	)	PUNCT
ejpam-2291	228	6	)	)	PUNCT
ejpam-2291	229	1	=	=	PUNCT
ejpam-2291	229	2	0	0	PUNCT
ejpam-2291	229	3	whenever	whenever	SCONJ
ejpam-2291	229	4	that	that	PRON
ejpam-2291	229	5	is	be	AUX
ejpam-2291	229	6	possible	possible	ADJ
ejpam-2291	229	7	,	,	PUNCT
ejpam-2291	229	8	we	we	PRON
ejpam-2291	229	9	get	get	VERB
ejpam-2291	229	10	an	an	DET
ejpam-2291	229	11	epimorphism	epimorphism	NOUN
ejpam-2291	229	12	h	h	NOUN
ejpam-2291	230	1	i	i	PRON
ejpam-2291	230	2	r+	r+	PUNCT
ejpam-2291	230	3	(	(	PUNCT
ejpam-2291	230	4	r(e))n+1→	r(e))n+1→	NOUN
ejpam-2291	230	5	h	h	NOUN
ejpam-2291	231	1	i	i	PRON
ejpam-2291	231	2	r+	r+	VERB
ejpam-2291	231	3	(	(	PUNCT
ejpam-2291	231	4	r(e))n	r(e))n	VERB
ejpam-2291	231	5	for	for	ADP
ejpam-2291	231	6	all	all	DET
ejpam-2291	231	7	n≥max{0	n≥max{0	PROPN
ejpam-2291	231	8	,	,	PUNCT
ejpam-2291	231	9	ai(g(e	ai(g(e	NOUN
ejpam-2291	231	10	)	)	PUNCT
ejpam-2291	231	11	)	)	PUNCT
ejpam-2291	232	1	+	+	CCONJ
ejpam-2291	232	2	1	1	X
ejpam-2291	232	3	}	}	PUNCT
ejpam-2291	232	4	if	if	SCONJ
ejpam-2291	232	5	i	i	PRON
ejpam-2291	232	6	=	=	NOUN
ejpam-2291	232	7	0,1	0,1	NUM
ejpam-2291	232	8	,	,	PUNCT
ejpam-2291	232	9	and	and	CCONJ
ejpam-2291	232	10	for	for	ADP
ejpam-2291	232	11	n	n	PRON
ejpam-2291	232	12	≥	≥	NOUN
ejpam-2291	232	13	ai(g(e	ai(g(e	ADV
ejpam-2291	232	14	)	)	PUNCT
ejpam-2291	232	15	)	)	PUNCT
ejpam-2291	233	1	+	+	CCONJ
ejpam-2291	233	2	1	1	NUM
ejpam-2291	233	3	if	if	SCONJ
ejpam-2291	233	4	i	i	PRON
ejpam-2291	233	5	≥	≥	VERB
ejpam-2291	233	6	2	2	NUM
ejpam-2291	233	7	.	.	PUNCT
ejpam-2291	234	1	since	since	SCONJ
ejpam-2291	234	2	h	h	NOUN
ejpam-2291	234	3	i	i	PRON
ejpam-2291	234	4	r+	r+	VERB
ejpam-2291	234	5	(	(	PUNCT
ejpam-2291	234	6	r(e))n	r(e))n	NOUN
ejpam-2291	234	7	=	=	NOUN
ejpam-2291	234	8	0	0	NUM
ejpam-2291	234	9	for	for	ADP
ejpam-2291	234	10	large	large	ADJ
ejpam-2291	234	11	values	value	NOUN
ejpam-2291	234	12	of	of	ADP
ejpam-2291	234	13	n	n	CCONJ
ejpam-2291	234	14	,	,	PUNCT
ejpam-2291	234	15	so	so	SCONJ
ejpam-2291	234	16	we	we	PRON
ejpam-2291	234	17	deduce	deduce	VERB
ejpam-2291	234	18	that	that	SCONJ
ejpam-2291	234	19	h	h	NOUN
ejpam-2291	235	1	i	i	PRON
ejpam-2291	235	2	r+	r+	VERB
ejpam-2291	235	3	(	(	PUNCT
ejpam-2291	235	4	r(e))n	r(e))n	NOUN
ejpam-2291	235	5	=	=	NOUN
ejpam-2291	235	6	0	0	NUM
ejpam-2291	235	7	for	for	ADP
ejpam-2291	235	8	n	n	PRON
ejpam-2291	235	9	≥	≥	NOUN
ejpam-2291	235	10	max{0	max{0	NUM
ejpam-2291	235	11	,	,	PUNCT
ejpam-2291	235	12	ai(g(e	ai(g(e	NOUN
ejpam-2291	235	13	)	)	PUNCT
ejpam-2291	235	14	)	)	PUNCT
ejpam-2291	236	1	+	+	CCONJ
ejpam-2291	236	2	1	1	X
ejpam-2291	236	3	}	}	PUNCT
ejpam-2291	236	4	if	if	SCONJ
ejpam-2291	236	5	i	i	PRON
ejpam-2291	236	6	=	=	NOUN
ejpam-2291	236	7	0	0	NUM
ejpam-2291	236	8	,	,	PUNCT
ejpam-2291	236	9	1	1	NUM
ejpam-2291	236	10	and	and	CCONJ
ejpam-2291	236	11	for	for	ADP
ejpam-2291	236	12	n	n	PRON
ejpam-2291	236	13	≥	≥	NOUN
ejpam-2291	236	14	ai(g(e	ai(g(e	ADV
ejpam-2291	236	15	)	)	PUNCT
ejpam-2291	236	16	)	)	PUNCT
ejpam-2291	237	1	+	+	CCONJ
ejpam-2291	237	2	1	1	NUM
ejpam-2291	237	3	if	if	SCONJ
ejpam-2291	237	4	i	i	PRON
ejpam-2291	237	5	≥	≥	VERB
ejpam-2291	237	6	2	2	NUM
ejpam-2291	237	7	.	.	PUNCT
ejpam-2291	237	8	from	from	ADP
ejpam-2291	237	9	the	the	DET
ejpam-2291	237	10	above	above	ADJ
ejpam-2291	237	11	formula	formula	NOUN
ejpam-2291	237	12	immediately	immediately	ADV
ejpam-2291	237	13	we	we	PRON
ejpam-2291	237	14	have	have	VERB
ejpam-2291	237	15	ai(r(e))≤	ai(r(e))≤	NUM
ejpam-2291	237	16	ai(g(e	ai(g(e	ADV
ejpam-2291	237	17	)	)	PUNCT
ejpam-2291	237	18	)	)	PUNCT
ejpam-2291	238	1	for	for	ADP
ejpam-2291	238	2	i	i	PRON
ejpam-2291	238	3	≥	≥	NOUN
ejpam-2291	238	4	2	2	NUM
ejpam-2291	238	5	.	.	X
ejpam-2291	239	1	for	for	ADP
ejpam-2291	239	2	i	i	PRON
ejpam-2291	239	3	=	=	SYM
ejpam-2291	239	4	0	0	NUM
ejpam-2291	239	5	we	we	PRON
ejpam-2291	239	6	consider	consider	VERB
ejpam-2291	239	7	two	two	NUM
ejpam-2291	239	8	cases	case	NOUN
ejpam-2291	239	9	.	.	PUNCT
ejpam-2291	240	1	if	if	SCONJ
ejpam-2291	240	2	h0	h0	PROPN
ejpam-2291	240	3	r+	r+	PRON
ejpam-2291	240	4	(	(	PUNCT
ejpam-2291	240	5	g(e	g(e	PROPN
ejpam-2291	240	6	)	)	PUNCT
ejpam-2291	240	7	)	)	PUNCT
ejpam-2291	241	1	=	=	PUNCT
ejpam-2291	241	2	0	0	NUM
ejpam-2291	241	3	,	,	PUNCT
ejpam-2291	241	4	then	then	ADV
ejpam-2291	241	5	a0(g(e	a0(g(e	ADV
ejpam-2291	241	6	)	)	PUNCT
ejpam-2291	241	7	)	)	PUNCT
ejpam-2291	242	1	=	=	SYM
ejpam-2291	242	2	−∞.	−∞.	PROPN
ejpam-2291	242	3	therefore	therefore	ADV
ejpam-2291	242	4	by	by	ADP
ejpam-2291	242	5	(	(	PUNCT
ejpam-2291	242	6	4	4	X
ejpam-2291	242	7	)	)	PUNCT
ejpam-2291	242	8	h0	h0	NOUN
ejpam-2291	242	9	r+	r+	NOUN
ejpam-2291	242	10	(	(	PUNCT
ejpam-2291	242	11	r(e))n	r(e))n	NOUN
ejpam-2291	242	12	=	=	NOUN
ejpam-2291	242	13	0	0	NUM
ejpam-2291	242	14	for	for	ADP
ejpam-2291	242	15	all	all	DET
ejpam-2291	242	16	n	n	PRON
ejpam-2291	242	17	≥	≥	NOUN
ejpam-2291	242	18	0	0	NUM
ejpam-2291	242	19	.	.	PUNCT
ejpam-2291	243	1	from	from	ADP
ejpam-2291	243	2	this	this	PRON
ejpam-2291	243	3	it	it	PRON
ejpam-2291	243	4	follows	follow	VERB
ejpam-2291	243	5	that	that	DET
ejpam-2291	243	6	h0	h0	PROPN
ejpam-2291	243	7	r+	r+	NOUN
ejpam-2291	243	8	(	(	PUNCT
ejpam-2291	243	9	r(e	r(e	NOUN
ejpam-2291	243	10	)	)	PUNCT
ejpam-2291	243	11	)	)	PUNCT
ejpam-2291	244	1	=	=	PUNCT
ejpam-2291	244	2	0	0	X
ejpam-2291	244	3	.	.	PUNCT
ejpam-2291	244	4	hence	hence	ADV
ejpam-2291	244	5	a0(r(e	a0(r(e	PROPN
ejpam-2291	244	6	)	)	PUNCT
ejpam-2291	244	7	)	)	PUNCT
ejpam-2291	245	1	=	=	PUNCT
ejpam-2291	246	1	−∞	−∞	X
ejpam-2291	246	2	=	=	NOUN
ejpam-2291	246	3	a0(g(e	a0(g(e	NOUN
ejpam-2291	246	4	)	)	PUNCT
ejpam-2291	246	5	)	)	PUNCT
ejpam-2291	246	6	.	.	PUNCT
ejpam-2291	247	1	if	if	SCONJ
ejpam-2291	247	2	h0	h0	PROPN
ejpam-2291	247	3	r+	r+	PRON
ejpam-2291	247	4	(	(	PUNCT
ejpam-2291	247	5	g(e	g(e	PROPN
ejpam-2291	247	6	)	)	PUNCT
ejpam-2291	247	7	)	)	PUNCT
ejpam-2291	248	1	6=	6=	ADP
ejpam-2291	248	2	0	0	NUM
ejpam-2291	248	3	,	,	PUNCT
ejpam-2291	248	4	a0(g(e	a0(g(e	NOUN
ejpam-2291	248	5	)	)	PUNCT
ejpam-2291	248	6	)	)	PUNCT
ejpam-2291	248	7	≥	≥	NOUN
ejpam-2291	248	8	0	0	NUM
ejpam-2291	248	9	.	.	PUNCT
ejpam-2291	249	1	hence	hence	ADV
ejpam-2291	249	2	h0	h0	PROPN
ejpam-2291	249	3	r+	r+	NOUN
ejpam-2291	249	4	(	(	PUNCT
ejpam-2291	249	5	r(e))n	r(e))n	NOUN
ejpam-2291	249	6	=	=	NOUN
ejpam-2291	249	7	0	0	NUM
ejpam-2291	249	8	for	for	ADP
ejpam-2291	249	9	n≥	n≥	PROPN
ejpam-2291	249	10	a0(g(e	a0(g(e	NOUN
ejpam-2291	249	11	)	)	PUNCT
ejpam-2291	249	12	)	)	PUNCT
ejpam-2291	250	1	+	+	CCONJ
ejpam-2291	250	2	1	1	NUM
ejpam-2291	250	3	by	by	ADP
ejpam-2291	250	4	(	(	PUNCT
ejpam-2291	250	5	4	4	NUM
ejpam-2291	250	6	)	)	PUNCT
ejpam-2291	250	7	,	,	PUNCT
ejpam-2291	250	8	which	which	PRON
ejpam-2291	250	9	implies	imply	VERB
ejpam-2291	250	10	a0(r(e))≤	a0(r(e))≤	ADV
ejpam-2291	250	11	a0(g(e	a0(g(e	PRON
ejpam-2291	250	12	)	)	PUNCT
ejpam-2291	250	13	)	)	PUNCT
ejpam-2291	250	14	.	.	PUNCT
ejpam-2291	251	1	so	so	ADV
ejpam-2291	251	2	(	(	PUNCT
ejpam-2291	251	3	i	i	NOUN
ejpam-2291	251	4	)	)	PUNCT
ejpam-2291	251	5	is	be	AUX
ejpam-2291	251	6	proved	prove	VERB
ejpam-2291	251	7	.	.	PUNCT
ejpam-2291	252	1	if	if	SCONJ
ejpam-2291	252	2	h1	h1	ADJ
ejpam-2291	252	3	r+	r+	PUNCT
ejpam-2291	252	4	(	(	PUNCT
ejpam-2291	252	5	g(e	g(e	PROPN
ejpam-2291	252	6	)	)	PUNCT
ejpam-2291	252	7	)	)	PUNCT
ejpam-2291	253	1	6=	6=	ADP
ejpam-2291	253	2	0	0	NUM
ejpam-2291	253	3	,	,	PUNCT
ejpam-2291	253	4	then	then	ADV
ejpam-2291	253	5	a1(g(e	a1(g(e	NUM
ejpam-2291	253	6	)	)	PUNCT
ejpam-2291	253	7	)	)	PUNCT
ejpam-2291	253	8	≥	≥	X
ejpam-2291	253	9	−1	−1	ADV
ejpam-2291	253	10	by	by	ADP
ejpam-2291	253	11	corollary	corollary	ADJ
ejpam-2291	253	12	1(iii	1(iii	NUM
ejpam-2291	253	13	)	)	PUNCT
ejpam-2291	253	14	.	.	PUNCT
ejpam-2291	254	1	hence	hence	ADV
ejpam-2291	254	2	by	by	ADP
ejpam-2291	254	3	(	(	PUNCT
ejpam-2291	254	4	4	4	X
ejpam-2291	254	5	)	)	PUNCT
ejpam-2291	254	6	h1	h1	NOUN
ejpam-2291	254	7	r+	r+	PRON
ejpam-2291	254	8	(	(	PUNCT
ejpam-2291	254	9	r(e))n	r(e))n	NOUN
ejpam-2291	254	10	=	=	SYM
ejpam-2291	254	11	0	0	NUM
ejpam-2291	254	12	for	for	ADP
ejpam-2291	254	13	n	n	PRON
ejpam-2291	254	14	≥	≥	NOUN
ejpam-2291	254	15	a1(g(e	a1(g(e	NUM
ejpam-2291	254	16	)	)	PUNCT
ejpam-2291	254	17	)	)	PUNCT
ejpam-2291	254	18	which	which	PRON
ejpam-2291	254	19	implies	imply	VERB
ejpam-2291	254	20	a1(r(e	a1(r(e	NOUN
ejpam-2291	254	21	)	)	PUNCT
ejpam-2291	254	22	)	)	PUNCT
ejpam-2291	254	23	≤	≤	NUM
ejpam-2291	254	24	a1(g(e	a1(g(e	NUM
ejpam-2291	254	25	)	)	PUNCT
ejpam-2291	254	26	)	)	PUNCT
ejpam-2291	254	27	.	.	PUNCT
ejpam-2291	255	1	if	if	SCONJ
ejpam-2291	255	2	b	b	PROPN
ejpam-2291	255	3	⊆	⊆	NUM
ejpam-2291	255	4	p	p	NOUN
ejpam-2291	255	5	(	(	PUNCT
ejpam-2291	255	6	0	0	NUM
ejpam-2291	255	7	:	:	PUNCT
ejpam-2291	255	8	a	a	DET
ejpam-2291	255	9	e	e	NOUN
ejpam-2291	255	10	)	)	PUNCT
ejpam-2291	255	11	,	,	PUNCT
ejpam-2291	255	12	then	then	ADV
ejpam-2291	255	13	h	h	NOUN
ejpam-2291	255	14	i	i	PRON
ejpam-2291	255	15	r+	r+	PUNCT
ejpam-2291	255	16	(	(	PUNCT
ejpam-2291	255	17	r(e	r(e	NOUN
ejpam-2291	255	18	)	)	PUNCT
ejpam-2291	255	19	)	)	PUNCT
ejpam-2291	256	1	=	=	SYM
ejpam-2291	256	2	0	0	PUNCT
ejpam-2291	257	1	and	and	CCONJ
ejpam-2291	257	2	h	h	NOUN
ejpam-2291	258	1	i	i	PRON
ejpam-2291	258	2	r+	r+	PUNCT
ejpam-2291	258	3	(	(	PUNCT
ejpam-2291	258	4	g(e	g(e	PROPN
ejpam-2291	258	5	)	)	PUNCT
ejpam-2291	258	6	)	)	PUNCT
ejpam-2291	259	1	=	=	SYM
ejpam-2291	259	2	0	0	NUM
ejpam-2291	260	1	for	for	ADP
ejpam-2291	260	2	all	all	PRON
ejpam-2291	260	3	i	i	PRON
ejpam-2291	260	4	≥	≥	VERB
ejpam-2291	260	5	1	1	NUM
ejpam-2291	260	6	.	.	PUNCT
ejpam-2291	260	7	hence	hence	ADV
ejpam-2291	260	8	a1(r(e	a1(r(e	NUM
ejpam-2291	260	9	)	)	PUNCT
ejpam-2291	260	10	)	)	PUNCT
ejpam-2291	261	1	=	=	SYM
ejpam-2291	261	2	a1(g(e	a1(g(e	NOUN
ejpam-2291	261	3	)	)	PUNCT
ejpam-2291	261	4	)	)	PUNCT
ejpam-2291	262	1	=	=	SYM
ejpam-2291	262	2	−∞.	−∞.	ADJ
ejpam-2291	262	3	so	so	SCONJ
ejpam-2291	262	4	the	the	DET
ejpam-2291	262	5	first	first	ADJ
ejpam-2291	262	6	part	part	NOUN
ejpam-2291	262	7	of	of	ADP
ejpam-2291	262	8	(	(	PUNCT
ejpam-2291	262	9	iii	iii	NOUN
ejpam-2291	262	10	)	)	PUNCT
ejpam-2291	262	11	is	be	AUX
ejpam-2291	262	12	proved	prove	VERB
ejpam-2291	262	13	.	.	PUNCT
ejpam-2291	263	1	n.	n.	PROPN
ejpam-2291	263	2	zamani	zamani	PROPN
ejpam-2291	263	3	/	/	SYM
ejpam-2291	263	4	eur	eur	PROPN
ejpam-2291	263	5	.	.	PUNCT
ejpam-2291	264	1	j.	j.	PROPN
ejpam-2291	264	2	pure	pure	PROPN
ejpam-2291	264	3	appl	appl	PROPN
ejpam-2291	264	4	.	.	PROPN
ejpam-2291	264	5	math	math	PROPN
ejpam-2291	264	6	,	,	PUNCT
ejpam-2291	264	7	7	7	NUM
ejpam-2291	264	8	(	(	PUNCT
ejpam-2291	264	9	2014	2014	NUM
ejpam-2291	264	10	)	)	PUNCT
ejpam-2291	264	11	,	,	PUNCT
ejpam-2291	264	12	429	429	NUM
ejpam-2291	264	13	-	-	SYM
ejpam-2291	264	14	436	436	NUM
ejpam-2291	264	15	434	434	NUM
ejpam-2291	264	16	now	now	ADV
ejpam-2291	264	17	we	we	PRON
ejpam-2291	264	18	prove	prove	VERB
ejpam-2291	264	19	(	(	PUNCT
ejpam-2291	264	20	ii	ii	NOUN
ejpam-2291	264	21	)	)	PUNCT
ejpam-2291	264	22	and	and	CCONJ
ejpam-2291	264	23	the	the	DET
ejpam-2291	264	24	second	second	ADJ
ejpam-2291	264	25	part	part	NOUN
ejpam-2291	264	26	of	of	ADP
ejpam-2291	264	27	(	(	PUNCT
ejpam-2291	264	28	iii	iii	NOUN
ejpam-2291	264	29	)	)	PUNCT
ejpam-2291	264	30	.	.	PUNCT
ejpam-2291	265	1	it	it	PRON
ejpam-2291	265	2	is	be	AUX
ejpam-2291	265	3	sufficient	sufficient	ADJ
ejpam-2291	265	4	to	to	PART
ejpam-2291	265	5	show	show	VERB
ejpam-2291	265	6	that	that	SCONJ
ejpam-2291	265	7	ai(g(e))≤	ai(g(e))≤	NUM
ejpam-2291	265	8	ai(r(e	ai(r(e	NOUN
ejpam-2291	265	9	)	)	PUNCT
ejpam-2291	265	10	)	)	PUNCT
ejpam-2291	265	11	for	for	ADP
ejpam-2291	265	12	i	i	PRON
ejpam-2291	265	13	≥	≥	NOUN
ejpam-2291	265	14	0	0	NUM
ejpam-2291	265	15	.	.	PUNCT
ejpam-2291	266	1	we	we	PRON
ejpam-2291	266	2	may	may	AUX
ejpam-2291	266	3	assume	assume	VERB
ejpam-2291	266	4	that	that	SCONJ
ejpam-2291	266	5	ai(g(e	ai(g(e	VERB
ejpam-2291	266	6	)	)	PUNCT
ejpam-2291	266	7	)	)	PUNCT
ejpam-2291	267	1	6=	6=	ADP
ejpam-2291	267	2	−∞.	−∞.	NOUN
ejpam-2291	267	3	for	for	ADP
ejpam-2291	267	4	i	i	PROPN
ejpam-2291	267	5	=	=	NOUN
ejpam-2291	267	6	0	0	NUM
ejpam-2291	267	7	,	,	PUNCT
ejpam-2291	267	8	we	we	PRON
ejpam-2291	267	9	have	have	VERB
ejpam-2291	267	10	either	either	CCONJ
ejpam-2291	267	11	a1(r(e	a1(r(e	NOUN
ejpam-2291	267	12	)	)	PUNCT
ejpam-2291	267	13	)	)	PUNCT
ejpam-2291	268	1	≤	≤	NUM
ejpam-2291	268	2	−1	−1	NOUN
ejpam-2291	268	3	or	or	CCONJ
ejpam-2291	268	4	a1(r(e	a1(r(e	NUM
ejpam-2291	268	5	)	)	PUNCT
ejpam-2291	268	6	)	)	PUNCT
ejpam-2291	269	1	≤	≤	NUM
ejpam-2291	269	2	a1(g(e	a1(g(e	NUM
ejpam-2291	269	3	)	)	PUNCT
ejpam-2291	269	4	)	)	PUNCT
ejpam-2291	269	5	by	by	ADP
ejpam-2291	269	6	(	(	PUNCT
ejpam-2291	269	7	4	4	NUM
ejpam-2291	269	8	)	)	PUNCT
ejpam-2291	269	9	.	.	PUNCT
ejpam-2291	270	1	for	for	ADP
ejpam-2291	270	2	i	i	PRON
ejpam-2291	270	3	≥	≥	NUM
ejpam-2291	270	4	1	1	NUM
ejpam-2291	270	5	,	,	PUNCT
ejpam-2291	270	6	we	we	PRON
ejpam-2291	270	7	have	have	VERB
ejpam-2291	270	8	ai+1(r(e	ai+1(r(e	NOUN
ejpam-2291	270	9	)	)	PUNCT
ejpam-2291	270	10	)	)	PUNCT
ejpam-2291	270	11	≤	≤	NUM
ejpam-2291	270	12	ai+1(g(e	ai+1(g(e	NOUN
ejpam-2291	270	13	)	)	PUNCT
ejpam-2291	270	14	)	)	PUNCT
ejpam-2291	271	1	by	by	ADP
ejpam-2291	271	2	(	(	PUNCT
ejpam-2291	271	3	i	i	NOUN
ejpam-2291	271	4	)	)	PUNCT
ejpam-2291	271	5	.	.	PUNCT
ejpam-2291	272	1	hence	hence	ADV
ejpam-2291	272	2	the	the	DET
ejpam-2291	272	3	assumption	assumption	NOUN
ejpam-2291	272	4	ai+1(g(e	ai+1(g(e	NOUN
ejpam-2291	272	5	)	)	PUNCT
ejpam-2291	272	6	)	)	PUNCT
ejpam-2291	272	7	≤	≤	NOUN
ejpam-2291	272	8	ai(g(e	ai(g(e	ADV
ejpam-2291	272	9	)	)	PUNCT
ejpam-2291	272	10	)	)	PUNCT
ejpam-2291	272	11	implies	imply	VERB
ejpam-2291	272	12	that	that	DET
ejpam-2291	272	13	ai+1(r(e	ai+1(r(e	NOUN
ejpam-2291	272	14	)	)	PUNCT
ejpam-2291	272	15	)	)	PUNCT
ejpam-2291	272	16	≤	≤	NOUN
ejpam-2291	273	1	ai(g(e	ai(g(e	ADV
ejpam-2291	273	2	)	)	PUNCT
ejpam-2291	273	3	)	)	PUNCT
ejpam-2291	273	4	.	.	PUNCT
ejpam-2291	274	1	put	put	VERB
ejpam-2291	274	2	n	n	NOUN
ejpam-2291	274	3	=	=	PUNCT
ejpam-2291	274	4	ai(g(e	ai(g(e	NOUN
ejpam-2291	274	5	)	)	PUNCT
ejpam-2291	274	6	)	)	PUNCT
ejpam-2291	274	7	.	.	PUNCT
ejpam-2291	275	1	then	then	ADV
ejpam-2291	275	2	h	h	PROPN
ejpam-2291	275	3	i+1	i+1	ADJ
ejpam-2291	275	4	r+	r+	PRON
ejpam-2291	275	5	(	(	PUNCT
ejpam-2291	275	6	r(e)+)n+1	r(e)+)n+1	VERB
ejpam-2291	275	7	∼=	∼=	NOUN
ejpam-2291	275	8	h	h	NOUN
ejpam-2291	275	9	i+1	i+1	VERB
ejpam-2291	275	10	r+	r+	NOUN
ejpam-2291	275	11	(	(	PUNCT
ejpam-2291	275	12	r(e))n+1	r(e))n+1	NOUN
ejpam-2291	275	13	=	=	SYM
ejpam-2291	275	14	0	0	X
ejpam-2291	275	15	.	.	PUNCT
ejpam-2291	276	1	using	use	VERB
ejpam-2291	276	2	this	this	PRON
ejpam-2291	276	3	in	in	ADP
ejpam-2291	276	4	the	the	DET
ejpam-2291	276	5	exact	exact	ADJ
ejpam-2291	276	6	sequence	sequence	NOUN
ejpam-2291	276	7	(	(	PUNCT
ejpam-2291	276	8	3	3	NUM
ejpam-2291	276	9	)	)	PUNCT
ejpam-2291	276	10	,	,	PUNCT
ejpam-2291	276	11	we	we	PRON
ejpam-2291	276	12	get	get	VERB
ejpam-2291	276	13	an	an	DET
ejpam-2291	276	14	epimorphism	epimorphism	NOUN
ejpam-2291	276	15	h	h	NOUN
ejpam-2291	277	1	i	i	PRON
ejpam-2291	277	2	r+	r+	PUNCT
ejpam-2291	277	3	(	(	PUNCT
ejpam-2291	277	4	r(e))n	r(e))n	VERB
ejpam-2291	277	5	−→	−→	ADJ
ejpam-2291	277	6	h	h	NOUN
ejpam-2291	278	1	i	i	PRON
ejpam-2291	278	2	r+	r+	PUNCT
ejpam-2291	278	3	(	(	PUNCT
ejpam-2291	278	4	g(e))n	g(e))n	PROPN
ejpam-2291	278	5	.	.	PUNCT
ejpam-2291	279	1	since	since	SCONJ
ejpam-2291	279	2	h	h	PROPN
ejpam-2291	279	3	i	i	PRON
ejpam-2291	279	4	r+	r+	VERB
ejpam-2291	279	5	(	(	PUNCT
ejpam-2291	279	6	g(e))n	g(e))n	PROPN
ejpam-2291	279	7	6=	6=	ADP
ejpam-2291	279	8	0	0	NUM
ejpam-2291	279	9	,	,	PUNCT
ejpam-2291	279	10	so	so	SCONJ
ejpam-2291	279	11	h	h	NOUN
ejpam-2291	280	1	i	i	PRON
ejpam-2291	280	2	r+	r+	VERB
ejpam-2291	280	3	(	(	PUNCT
ejpam-2291	280	4	r(e))n	r(e))n	VERB
ejpam-2291	280	5	6=	6=	ADP
ejpam-2291	280	6	0	0	NUM
ejpam-2291	280	7	.	.	PUNCT
ejpam-2291	281	1	therefore	therefore	ADV
ejpam-2291	281	2	,	,	PUNCT
ejpam-2291	281	3	ai(g(e))≤	ai(g(e))≤	NUM
ejpam-2291	281	4	ai(r(e	ai(r(e	NOUN
ejpam-2291	281	5	)	)	PUNCT
ejpam-2291	281	6	)	)	PUNCT
ejpam-2291	281	7	.	.	PUNCT
ejpam-2291	282	1	to	to	PART
ejpam-2291	282	2	prove	prove	VERB
ejpam-2291	282	3	(	(	PUNCT
ejpam-2291	282	4	iv	iv	X
ejpam-2291	282	5	)	)	PUNCT
ejpam-2291	282	6	we	we	PRON
ejpam-2291	282	7	assume	assume	VERB
ejpam-2291	282	8	that	that	SCONJ
ejpam-2291	282	9	h1	h1	VERB
ejpam-2291	282	10	r+	r+	PUNCT
ejpam-2291	282	11	(	(	PUNCT
ejpam-2291	282	12	g(e	g(e	PROPN
ejpam-2291	282	13	)	)	PUNCT
ejpam-2291	282	14	)	)	PUNCT
ejpam-2291	283	1	=	=	PUNCT
ejpam-2291	283	2	0	0	X
ejpam-2291	283	3	.	.	PUNCT
ejpam-2291	284	1	then	then	ADV
ejpam-2291	284	2	a1(g(e	a1(g(e	NUM
ejpam-2291	284	3	)	)	PUNCT
ejpam-2291	284	4	)	)	PUNCT
ejpam-2291	285	1	=	=	SYM
ejpam-2291	285	2	−∞.	−∞.	ADJ
ejpam-2291	285	3	hence	hence	ADV
ejpam-2291	285	4	a1(r(e	a1(r(e	PROPN
ejpam-2291	285	5	)	)	PUNCT
ejpam-2291	285	6	)	)	PUNCT
ejpam-2291	286	1	≤	≤	NUM
ejpam-2291	286	2	−1	−1	NOUN
ejpam-2291	286	3	by	by	ADP
ejpam-2291	286	4	(	(	PUNCT
ejpam-2291	286	5	4	4	NUM
ejpam-2291	286	6	)	)	PUNCT
ejpam-2291	286	7	.	.	PUNCT
ejpam-2291	287	1	if	if	SCONJ
ejpam-2291	287	2	a1(r(e	a1(r(e	NUM
ejpam-2291	287	3	)	)	PUNCT
ejpam-2291	287	4	)	)	PUNCT
ejpam-2291	288	1	<	<	X
ejpam-2291	288	2	−1	−1	NOUN
ejpam-2291	288	3	,	,	PUNCT
ejpam-2291	288	4	h1	h1	AUX
ejpam-2291	288	5	r+	r+	PRON
ejpam-2291	288	6	(	(	PUNCT
ejpam-2291	288	7	r(e))−1	r(e))−1	NOUN
ejpam-2291	288	8	=	=	NOUN
ejpam-2291	288	9	0	0	NUM
ejpam-2291	288	10	.	.	PUNCT
ejpam-2291	289	1	since	since	SCONJ
ejpam-2291	289	2	h0	h0	PROPN
ejpam-2291	289	3	r+	r+	NOUN
ejpam-2291	289	4	(	(	PUNCT
ejpam-2291	289	5	g(e))−1	g(e))−1	NOUN
ejpam-2291	289	6	=	=	SYM
ejpam-2291	289	7	0	0	NUM
ejpam-2291	289	8	,	,	PUNCT
ejpam-2291	289	9	from	from	ADP
ejpam-2291	289	10	the	the	DET
ejpam-2291	289	11	exact	exact	ADJ
ejpam-2291	289	12	sequence	sequence	NOUN
ejpam-2291	289	13	(	(	PUNCT
ejpam-2291	289	14	2	2	X
ejpam-2291	289	15	)	)	PUNCT
ejpam-2291	289	16	we	we	PRON
ejpam-2291	289	17	can	can	AUX
ejpam-2291	289	18	deduce	deduce	VERB
ejpam-2291	289	19	that	that	DET
ejpam-2291	289	20	h1	h1	NOUN
ejpam-2291	289	21	r+	r+	PUNCT
ejpam-2291	289	22	(	(	PUNCT
ejpam-2291	289	23	r(e)+)0	r(e)+)0	PROPN
ejpam-2291	289	24	=	=	PUNCT
ejpam-2291	289	25	0	0	X
ejpam-2291	289	26	.	.	PUNCT
ejpam-2291	290	1	now	now	ADV
ejpam-2291	290	2	,	,	PUNCT
ejpam-2291	290	3	using	use	VERB
ejpam-2291	290	4	the	the	DET
ejpam-2291	290	5	exact	exact	ADJ
ejpam-2291	290	6	sequence	sequence	NOUN
ejpam-2291	290	7	(	(	PUNCT
ejpam-2291	290	8	1	1	X
ejpam-2291	290	9	)	)	PUNCT
ejpam-2291	290	10	we	we	PRON
ejpam-2291	290	11	get	get	VERB
ejpam-2291	290	12	the	the	DET
ejpam-2291	290	13	exact	exact	ADJ
ejpam-2291	290	14	sequence	sequence	NOUN
ejpam-2291	290	15	h0	h0	NOUN
ejpam-2291	290	16	r+	r+	PRON
ejpam-2291	290	17	(	(	PUNCT
ejpam-2291	290	18	r(e)+)0	r(e)+)0	PROPN
ejpam-2291	290	19	−→	−→	PROPN
ejpam-2291	290	20	h0	h0	PROPN
ejpam-2291	290	21	r+	r+	PRON
ejpam-2291	290	22	(	(	PUNCT
ejpam-2291	290	23	r(e))0	r(e))0	PROPN
ejpam-2291	290	24	−→	−→	NOUN
ejpam-2291	290	25	h0	h0	NOUN
ejpam-2291	290	26	r+	r+	NOUN
ejpam-2291	290	27	(	(	PUNCT
ejpam-2291	290	28	e	e	NOUN
ejpam-2291	290	29	)	)	PUNCT
ejpam-2291	290	30	−→	−→	NOUN
ejpam-2291	290	31	0	0	NUM
ejpam-2291	290	32	.	.	PUNCT
ejpam-2291	291	1	but	but	CCONJ
ejpam-2291	291	2	since	since	SCONJ
ejpam-2291	291	3	(	(	PUNCT
ejpam-2291	291	4	r(e)+)0	r(e)+)0	PROPN
ejpam-2291	291	5	=	=	SYM
ejpam-2291	291	6	0	0	NUM
ejpam-2291	291	7	,	,	PUNCT
ejpam-2291	291	8	so	so	ADV
ejpam-2291	291	9	h0	h0	ADJ
ejpam-2291	291	10	r+	r+	PRON
ejpam-2291	291	11	(	(	PUNCT
ejpam-2291	291	12	r(e)+)0	r(e)+)0	NOUN
ejpam-2291	291	13	=	=	SYM
ejpam-2291	291	14	0	0	X
ejpam-2291	291	15	.	.	PUNCT
ejpam-2291	292	1	furthermore	furthermore	ADV
ejpam-2291	292	2	,	,	PUNCT
ejpam-2291	292	3	h0	h0	PROPN
ejpam-2291	292	4	r+	r+	NOUN
ejpam-2291	292	5	(	(	PUNCT
ejpam-2291	292	6	r(e))0	r(e))0	PROPN
ejpam-2291	292	7	=	=	SYM
ejpam-2291	292	8	h0	h0	PROPN
ejpam-2291	292	9	b	b	PROPN
ejpam-2291	292	10	(	(	PUNCT
ejpam-2291	292	11	e	e	NOUN
ejpam-2291	292	12	)	)	PUNCT
ejpam-2291	292	13	and	and	CCONJ
ejpam-2291	292	14	h0	h0	PROPN
ejpam-2291	292	15	r+	r+	NOUN
ejpam-2291	292	16	(	(	PUNCT
ejpam-2291	292	17	e	e	NOUN
ejpam-2291	292	18	)	)	PUNCT
ejpam-2291	292	19	=	=	SYM
ejpam-2291	292	20	e.	e.	PROPN
ejpam-2291	292	21	therefore	therefore	ADV
ejpam-2291	292	22	,	,	PUNCT
ejpam-2291	292	23	h0	h0	PROPN
ejpam-2291	292	24	b	b	PROPN
ejpam-2291	292	25	(	(	PUNCT
ejpam-2291	292	26	e	e	NOUN
ejpam-2291	292	27	)	)	PUNCT
ejpam-2291	292	28	=	=	SYM
ejpam-2291	292	29	e	e	NOUN
ejpam-2291	292	30	which	which	PRON
ejpam-2291	292	31	is	be	AUX
ejpam-2291	292	32	equivalent	equivalent	ADJ
ejpam-2291	292	33	to	to	ADP
ejpam-2291	292	34	the	the	DET
ejpam-2291	292	35	condition	condition	NOUN
ejpam-2291	292	36	bt	bt	NOUN
ejpam-2291	292	37	e	e	PROPN
ejpam-2291	292	38	=	=	NOUN
ejpam-2291	292	39	0	0	NUM
ejpam-2291	292	40	for	for	ADP
ejpam-2291	292	41	some	some	DET
ejpam-2291	292	42	t	t	NOUN
ejpam-2291	292	43	≥	≥	NOUN
ejpam-2291	292	44	1	1	NUM
ejpam-2291	292	45	.	.	PUNCT
ejpam-2291	293	1	thus	thus	ADV
ejpam-2291	293	2	if	if	SCONJ
ejpam-2291	293	3	,	,	PUNCT
ejpam-2291	293	4	b	b	PROPN
ejpam-2291	293	5	6⊆	6⊆	NUM
ejpam-2291	293	6	p	p	NOUN
ejpam-2291	293	7	(	(	PUNCT
ejpam-2291	293	8	0	0	NUM
ejpam-2291	293	9	:	:	PUNCT
ejpam-2291	293	10	a	a	DET
ejpam-2291	293	11	e	e	NOUN
ejpam-2291	293	12	)	)	PUNCT
ejpam-2291	293	13	,	,	PUNCT
ejpam-2291	293	14	we	we	PRON
ejpam-2291	293	15	must	must	AUX
ejpam-2291	293	16	have	have	VERB
ejpam-2291	293	17	a1(r(e	a1(r(e	NUM
ejpam-2291	293	18	)	)	PUNCT
ejpam-2291	293	19	)	)	PUNCT
ejpam-2291	294	1	=	=	PUNCT
ejpam-2291	294	2	−1	−1	NOUN
ejpam-2291	294	3	.	.	PUNCT
ejpam-2291	295	1	now	now	ADV
ejpam-2291	295	2	,	,	PUNCT
ejpam-2291	295	3	the	the	DET
ejpam-2291	295	4	proof	proof	NOUN
ejpam-2291	295	5	of	of	ADP
ejpam-2291	295	6	the	the	DET
ejpam-2291	295	7	theorem	theorem	NOUN
ejpam-2291	295	8	is	be	AUX
ejpam-2291	295	9	complete	complete	ADJ
ejpam-2291	295	10	.	.	PUNCT
ejpam-2291	296	1	corollary	corollary	ADJ
ejpam-2291	296	2	2	2	NUM
ejpam-2291	296	3	.	.	PUNCT
ejpam-2291	297	1	let	let	VERB
ejpam-2291	297	2	`	`	PUNCT
ejpam-2291	297	3	:	:	PUNCT
ejpam-2291	297	4	=	=	NOUN
ejpam-2291	297	5	max{i	max{i	X
ejpam-2291	297	6	:	:	PUNCT
ejpam-2291	297	7	h	h	NOUN
ejpam-2291	297	8	i	i	PRON
ejpam-2291	297	9	g+	g+	VERB
ejpam-2291	297	10	(	(	PUNCT
ejpam-2291	297	11	g(e	g(e	PROPN
ejpam-2291	297	12	)	)	PUNCT
ejpam-2291	297	13	)	)	PUNCT
ejpam-2291	298	1	6=	6=	ADP
ejpam-2291	298	2	0	0	NUM
ejpam-2291	298	3	}	}	PUNCT
ejpam-2291	298	4	.	.	PUNCT
ejpam-2291	299	1	then	then	ADV
ejpam-2291	299	2	:	:	PUNCT
ejpam-2291	299	3	(	(	PUNCT
ejpam-2291	299	4	i	i	NOUN
ejpam-2291	299	5	)	)	PUNCT
ejpam-2291	299	6	a`(r(e	a`(r(e	PROPN
ejpam-2291	299	7	)	)	PUNCT
ejpam-2291	299	8	)	)	PUNCT
ejpam-2291	300	1	=	=	PUNCT
ejpam-2291	300	2	a`(g(e	a`(g(e	NOUN
ejpam-2291	300	3	)	)	PUNCT
ejpam-2291	300	4	)	)	PUNCT
ejpam-2291	300	5	,	,	PUNCT
ejpam-2291	300	6	(	(	PUNCT
ejpam-2291	300	7	ii	ii	NOUN
ejpam-2291	300	8	)	)	PUNCT
ejpam-2291	300	9	if	if	SCONJ
ejpam-2291	300	10	b	b	PROPN
ejpam-2291	300	11	⊆	⊆	NUM
ejpam-2291	300	12	p	p	NOUN
ejpam-2291	300	13	(	(	PUNCT
ejpam-2291	300	14	0	0	NUM
ejpam-2291	300	15	:	:	PUNCT
ejpam-2291	300	16	a	a	DET
ejpam-2291	300	17	e	e	NOUN
ejpam-2291	300	18	)	)	PUNCT
ejpam-2291	300	19	or	or	CCONJ
ejpam-2291	300	20	`	`	PUNCT
ejpam-2291	300	21	≥	≥	NUM
ejpam-2291	300	22	1	1	NUM
ejpam-2291	300	23	,	,	PUNCT
ejpam-2291	300	24	then	then	ADV
ejpam-2291	300	25	`	`	PUNCT
ejpam-2291	300	26	=	=	NOUN
ejpam-2291	300	27	max{i	max{i	X
ejpam-2291	300	28	:	:	PUNCT
ejpam-2291	300	29	h	h	NOUN
ejpam-2291	301	1	i	i	PRON
ejpam-2291	301	2	r+	r+	PUNCT
ejpam-2291	301	3	(	(	PUNCT
ejpam-2291	301	4	r(e	r(e	NOUN
ejpam-2291	301	5	)	)	PUNCT
ejpam-2291	301	6	)	)	PUNCT
ejpam-2291	302	1	6=	6=	ADP
ejpam-2291	302	2	0	0	NUM
ejpam-2291	302	3	}	}	PUNCT
ejpam-2291	302	4	.	.	PUNCT
ejpam-2291	303	1	proof	proof	NOUN
ejpam-2291	303	2	.	.	PUNCT
ejpam-2291	304	1	for	for	ADP
ejpam-2291	304	2	i	i	PRON
ejpam-2291	304	3	≥	≥	NOUN
ejpam-2291	304	4	`	`	PUNCT
ejpam-2291	304	5	,	,	PUNCT
ejpam-2291	304	6	we	we	PRON
ejpam-2291	304	7	have	have	VERB
ejpam-2291	304	8	ai(g(e	ai(g(e	ADV
ejpam-2291	304	9	)	)	PUNCT
ejpam-2291	304	10	)	)	PUNCT
ejpam-2291	304	11	≥	≥	PROPN
ejpam-2291	304	12	ai+1(g(e	ai+1(g(e	NOUN
ejpam-2291	304	13	)	)	PUNCT
ejpam-2291	304	14	)	)	PUNCT
ejpam-2291	305	1	=	=	SYM
ejpam-2291	305	2	−∞.	−∞.	PROPN
ejpam-2291	305	3	therefore	therefore	ADV
ejpam-2291	305	4	,	,	PUNCT
ejpam-2291	305	5	ai(r(e	ai(r(e	NOUN
ejpam-2291	305	6	)	)	PUNCT
ejpam-2291	305	7	)	)	PUNCT
ejpam-2291	306	1	=	=	PUNCT
ejpam-2291	306	2	ai(g(e	ai(g(e	NOUN
ejpam-2291	306	3	)	)	PUNCT
ejpam-2291	306	4	)	)	PUNCT
ejpam-2291	307	1	if	if	SCONJ
ejpam-2291	307	2	i	i	PRON
ejpam-2291	307	3	6=	6=	NUM
ejpam-2291	307	4	1	1	NUM
ejpam-2291	307	5	by	by	ADP
ejpam-2291	307	6	theorem	theorem	ADJ
ejpam-2291	307	7	2(ii	2(ii	NUM
ejpam-2291	307	8	)	)	PUNCT
ejpam-2291	307	9	.	.	PUNCT
ejpam-2291	308	1	hence	hence	ADV
ejpam-2291	308	2	(	(	PUNCT
ejpam-2291	308	3	i	i	NOUN
ejpam-2291	308	4	)	)	PUNCT
ejpam-2291	308	5	and(ii	and(ii	NOUN
ejpam-2291	308	6	)	)	PUNCT
ejpam-2291	308	7	are	be	AUX
ejpam-2291	308	8	obvious	obvious	ADJ
ejpam-2291	309	1	if	if	SCONJ
ejpam-2291	309	2	`	`	PUNCT
ejpam-2291	309	3	>	>	X
ejpam-2291	309	4	1	1	X
ejpam-2291	309	5	.	.	PUNCT
ejpam-2291	310	1	it	it	PRON
ejpam-2291	310	2	remains	remain	VERB
ejpam-2291	310	3	to	to	PART
ejpam-2291	310	4	show	show	VERB
ejpam-2291	310	5	that	that	PRON
ejpam-2291	310	6	a1(r(e	a1(r(e	PROPN
ejpam-2291	310	7	)	)	PUNCT
ejpam-2291	310	8	)	)	PUNCT
ejpam-2291	311	1	=	=	SYM
ejpam-2291	311	2	a1(g(e	a1(g(e	NOUN
ejpam-2291	311	3	)	)	PUNCT
ejpam-2291	311	4	)	)	PUNCT
ejpam-2291	312	1	if	if	SCONJ
ejpam-2291	312	2	`	`	PUNCT
ejpam-2291	312	3	=	=	SYM
ejpam-2291	312	4	1	1	NUM
ejpam-2291	312	5	or	or	CCONJ
ejpam-2291	312	6	if	if	SCONJ
ejpam-2291	312	7	`	`	PUNCT
ejpam-2291	312	8	=	=	SYM
ejpam-2291	312	9	0	0	NUM
ejpam-2291	312	10	and	and	CCONJ
ejpam-2291	312	11	b	b	NOUN
ejpam-2291	312	12	⊆	⊆	NUM
ejpam-2291	312	13	p	p	NOUN
ejpam-2291	312	14	(	(	PUNCT
ejpam-2291	312	15	0	0	NUM
ejpam-2291	312	16	:	:	PUNCT
ejpam-2291	312	17	a	a	DET
ejpam-2291	312	18	e	e	NOUN
ejpam-2291	312	19	)	)	PUNCT
ejpam-2291	312	20	.	.	PUNCT
ejpam-2291	313	1	but	but	CCONJ
ejpam-2291	313	2	this	this	PRON
ejpam-2291	313	3	follows	follow	VERB
ejpam-2291	313	4	from	from	ADP
ejpam-2291	313	5	theorem	theorem	ADJ
ejpam-2291	313	6	2(iii	2(iii	NUM
ejpam-2291	313	7	)	)	PUNCT
ejpam-2291	313	8	.	.	PUNCT
ejpam-2291	314	1	corollary	corollary	ADJ
ejpam-2291	314	2	3	3	NUM
ejpam-2291	314	3	.	.	PUNCT
ejpam-2291	314	4	with	with	ADP
ejpam-2291	314	5	the	the	DET
ejpam-2291	314	6	notation	notation	NOUN
ejpam-2291	314	7	as	as	ADP
ejpam-2291	314	8	in	in	ADP
ejpam-2291	314	9	above	above	ADV
ejpam-2291	314	10	we	we	PRON
ejpam-2291	314	11	have	have	VERB
ejpam-2291	314	12	reg(r(e	reg(r(e	NOUN
ejpam-2291	314	13	)	)	PUNCT
ejpam-2291	314	14	)	)	PUNCT
ejpam-2291	315	1	=	=	SYM
ejpam-2291	315	2	reg(g(e	reg(g(e	NOUN
ejpam-2291	315	3	)	)	PUNCT
ejpam-2291	315	4	)	)	PUNCT
ejpam-2291	315	5	.	.	PUNCT
ejpam-2291	316	1	proof	proof	NOUN
ejpam-2291	316	2	.	.	PUNCT
ejpam-2291	317	1	by	by	ADP
ejpam-2291	317	2	theorem	theorem	NOUN
ejpam-2291	317	3	2(i	2(i	NUM
ejpam-2291	317	4	)	)	PUNCT
ejpam-2291	317	5	we	we	PRON
ejpam-2291	317	6	have	have	VERB
ejpam-2291	317	7	ai(r(e	ai(r(e	NOUN
ejpam-2291	317	8	)	)	PUNCT
ejpam-2291	317	9	)	)	PUNCT
ejpam-2291	318	1	+	+	CCONJ
ejpam-2291	318	2	i	i	PRON
ejpam-2291	318	3	≤	≤	X
ejpam-2291	318	4	ai(g(e	ai(g(e	ADV
ejpam-2291	318	5	)	)	PUNCT
ejpam-2291	318	6	)	)	PUNCT
ejpam-2291	319	1	+	+	CCONJ
ejpam-2291	319	2	i	i	PRON
ejpam-2291	319	3	for	for	ADP
ejpam-2291	319	4	i	i	PRON
ejpam-2291	319	5	6=	6=	PROPN
ejpam-2291	319	6	1	1	X
ejpam-2291	319	7	.	.	PUNCT
ejpam-2291	319	8	by	by	ADP
ejpam-2291	319	9	theorem	theorem	ADJ
ejpam-2291	319	10	2(iii	2(iii	NUM
ejpam-2291	319	11	)	)	PUNCT
ejpam-2291	319	12	and	and	CCONJ
ejpam-2291	319	13	(	(	PUNCT
ejpam-2291	319	14	iv	iv	X
ejpam-2291	319	15	)	)	PUNCT
ejpam-2291	319	16	,	,	PUNCT
ejpam-2291	319	17	either	either	CCONJ
ejpam-2291	319	18	a1(r(e	a1(r(e	NOUN
ejpam-2291	319	19	)	)	PUNCT
ejpam-2291	319	20	)	)	PUNCT
ejpam-2291	320	1	+	+	CCONJ
ejpam-2291	320	2	1≤	1≤	NUM
ejpam-2291	320	3	a1(g(e	a1(g(e	NUM
ejpam-2291	320	4	)	)	PUNCT
ejpam-2291	320	5	)	)	PUNCT
ejpam-2291	321	1	+	+	CCONJ
ejpam-2291	321	2	1	1	NUM
ejpam-2291	321	3	or	or	CCONJ
ejpam-2291	321	4	a1(r(e	a1(r(e	NUM
ejpam-2291	321	5	)	)	PUNCT
ejpam-2291	321	6	)	)	PUNCT
ejpam-2291	322	1	+	+	CCONJ
ejpam-2291	322	2	1=	1=	NUM
ejpam-2291	322	3	0≤	0≤	NUM
ejpam-2291	322	4	reg(g(e	reg(g(e	NOUN
ejpam-2291	322	5	)	)	PUNCT
ejpam-2291	322	6	)	)	PUNCT
ejpam-2291	322	7	.	.	PUNCT
ejpam-2291	323	1	therefore	therefore	ADV
ejpam-2291	323	2	,	,	PUNCT
ejpam-2291	323	3	reg(r(e	reg(r(e	NOUN
ejpam-2291	323	4	)	)	PUNCT
ejpam-2291	323	5	)	)	PUNCT
ejpam-2291	324	1	=	=	SYM
ejpam-2291	324	2	max{ai(r(e	max{ai(r(e	PROPN
ejpam-2291	324	3	)	)	PUNCT
ejpam-2291	324	4	)	)	PUNCT
ejpam-2291	325	1	+	+	CCONJ
ejpam-2291	325	2	i	i	PRON
ejpam-2291	325	3	:	:	PUNCT
ejpam-2291	325	4	i	i	PRON
ejpam-2291	325	5	≥	≥	VERB
ejpam-2291	325	6	0	0	NUM
ejpam-2291	325	7	}	}	PUNCT
ejpam-2291	325	8	≤max{ai(g(e	≤max{ai(g(e	NOUN
ejpam-2291	325	9	)	)	PUNCT
ejpam-2291	325	10	)	)	PUNCT
ejpam-2291	326	1	+	+	CCONJ
ejpam-2291	327	1	i	i	PRON
ejpam-2291	327	2	:	:	PUNCT
ejpam-2291	327	3	i	i	PRON
ejpam-2291	327	4	≥	≥	VERB
ejpam-2291	327	5	0}=	0}=	NUM
ejpam-2291	327	6	reg(g(e	reg(g(e	NOUN
ejpam-2291	327	7	)	)	PUNCT
ejpam-2291	327	8	)	)	PUNCT
ejpam-2291	327	9	.	.	PUNCT
ejpam-2291	328	1	to	to	PART
ejpam-2291	328	2	prove	prove	VERB
ejpam-2291	328	3	reg(g(e))≤	reg(g(e))≤	ADJ
ejpam-2291	328	4	reg(r(e	reg(r(e	NOUN
ejpam-2291	328	5	)	)	PUNCT
ejpam-2291	328	6	)	)	PUNCT
ejpam-2291	328	7	,	,	PUNCT
ejpam-2291	328	8	let	let	VERB
ejpam-2291	328	9	i	i	PRON
ejpam-2291	328	10	be	be	AUX
ejpam-2291	328	11	maximal	maximal	ADJ
ejpam-2291	328	12	such	such	ADJ
ejpam-2291	328	13	that	that	DET
ejpam-2291	328	14	reg(g(e	reg(g(e	NOUN
ejpam-2291	328	15	)	)	PUNCT
ejpam-2291	328	16	)	)	PUNCT
ejpam-2291	329	1	=	=	PUNCT
ejpam-2291	329	2	ai(g(e	ai(g(e	NOUN
ejpam-2291	329	3	)	)	PUNCT
ejpam-2291	329	4	)	)	PUNCT
ejpam-2291	330	1	+	+	CCONJ
ejpam-2291	330	2	i.	i.	NOUN
ejpam-2291	330	3	then	then	ADV
ejpam-2291	330	4	h	h	PROPN
ejpam-2291	331	1	i	i	PRON
ejpam-2291	331	2	g+	g+	VERB
ejpam-2291	331	3	(	(	PUNCT
ejpam-2291	331	4	g(e	g(e	PROPN
ejpam-2291	331	5	)	)	PUNCT
ejpam-2291	331	6	)	)	PUNCT
ejpam-2291	332	1	6=	6=	ADP
ejpam-2291	332	2	0	0	NUM
ejpam-2291	332	3	and	and	CCONJ
ejpam-2291	332	4	ai+1(g(e	ai+1(g(e	NOUN
ejpam-2291	332	5	)	)	PUNCT
ejpam-2291	332	6	)	)	PUNCT
ejpam-2291	332	7	<	<	X
ejpam-2291	332	8	ai(g(e	ai(g(e	NOUN
ejpam-2291	332	9	)	)	PUNCT
ejpam-2291	332	10	)	)	PUNCT
ejpam-2291	332	11	.	.	PUNCT
ejpam-2291	333	1	now	now	ADV
ejpam-2291	333	2	,	,	PUNCT
ejpam-2291	333	3	using	use	VERB
ejpam-2291	333	4	theorem	theorem	ADJ
ejpam-2291	333	5	2(ii),(iii	2(ii),(iii	NOUN
ejpam-2291	333	6	)	)	PUNCT
ejpam-2291	333	7	,	,	PUNCT
ejpam-2291	333	8	we	we	PRON
ejpam-2291	333	9	get	get	VERB
ejpam-2291	333	10	ai(r(e	ai(r(e	NOUN
ejpam-2291	333	11	)	)	PUNCT
ejpam-2291	333	12	)	)	PUNCT
ejpam-2291	334	1	=	=	PUNCT
ejpam-2291	334	2	ai(g(e	ai(g(e	NOUN
ejpam-2291	334	3	)	)	PUNCT
ejpam-2291	334	4	)	)	PUNCT
ejpam-2291	334	5	.	.	PUNCT
ejpam-2291	335	1	hence	hence	ADV
ejpam-2291	335	2	reg(g(e	reg(g(e	NOUN
ejpam-2291	335	3	)	)	PUNCT
ejpam-2291	335	4	)	)	PUNCT
ejpam-2291	336	1	=	=	SYM
ejpam-2291	336	2	ai(r(e	ai(r(e	NOUN
ejpam-2291	336	3	)	)	PUNCT
ejpam-2291	336	4	)	)	PUNCT
ejpam-2291	337	1	+	+	CCONJ
ejpam-2291	337	2	i	i	PRON
ejpam-2291	337	3	≤	≤	NUM
ejpam-2291	337	4	reg(r(e	reg(r(e	NOUN
ejpam-2291	337	5	)	)	PUNCT
ejpam-2291	337	6	)	)	PUNCT
ejpam-2291	337	7	.	.	PUNCT
ejpam-2291	338	1	in	in	ADP
ejpam-2291	338	2	the	the	DET
ejpam-2291	338	3	following	following	NOUN
ejpam-2291	338	4	we	we	PRON
ejpam-2291	338	5	consider	consider	VERB
ejpam-2291	338	6	r(b	r(b	NOUN
ejpam-2291	338	7	)	)	PUNCT
ejpam-2291	338	8	as	as	ADP
ejpam-2291	338	9	a	a	DET
ejpam-2291	338	10	subring	subring	NOUN
ejpam-2291	338	11	of	of	ADP
ejpam-2291	338	12	the	the	DET
ejpam-2291	338	13	polynomial	polynomial	ADJ
ejpam-2291	338	14	ring	ring	NOUN
ejpam-2291	338	15	a[t	a[t	NOUN
ejpam-2291	338	16	]	]	PUNCT
ejpam-2291	338	17	.	.	PUNCT
ejpam-2291	339	1	references	reference	NOUN
ejpam-2291	339	2	435	435	NUM
ejpam-2291	339	3	proposition	proposition	NOUN
ejpam-2291	339	4	1	1	NUM
ejpam-2291	339	5	.	.	PUNCT
ejpam-2291	340	1	let	let	VERB
ejpam-2291	340	2	f1	f1	NOUN
ejpam-2291	340	3	,	,	PUNCT
ejpam-2291	340	4	.	.	PUNCT
ejpam-2291	340	5	.	.	PUNCT
ejpam-2291	341	1	.	.	PUNCT
ejpam-2291	342	1	,	,	PUNCT
ejpam-2291	342	2	fh	fh	PROPN
ejpam-2291	342	3	be	be	AUX
ejpam-2291	342	4	a	a	DET
ejpam-2291	342	5	sequence	sequence	NOUN
ejpam-2291	342	6	of	of	ADP
ejpam-2291	342	7	elements	element	NOUN
ejpam-2291	342	8	of	of	ADP
ejpam-2291	342	9	b.	b.	PROPN
ejpam-2291	343	1	then	then	ADV
ejpam-2291	343	2	f	f	X
ejpam-2291	343	3	:	:	PUNCT
ejpam-2291	343	4	=	=	PROPN
ejpam-2291	343	5	f1	f1	PROPN
ejpam-2291	343	6	t	t	PROPN
ejpam-2291	343	7	,	,	PUNCT
ejpam-2291	343	8	.	.	PUNCT
ejpam-2291	343	9	.	.	PUNCT
ejpam-2291	343	10	.	.	PUNCT
ejpam-2291	344	1	,	,	PUNCT
ejpam-2291	344	2	fh	fh	PROPN
ejpam-2291	344	3	t	t	PROPN
ejpam-2291	344	4	is	be	AUX
ejpam-2291	344	5	an	an	DET
ejpam-2291	344	6	r(b)+filter	r(b)+filter	NOUN
ejpam-2291	344	7	regular	regular	ADJ
ejpam-2291	344	8	sequence	sequence	NOUN
ejpam-2291	344	9	for	for	ADP
ejpam-2291	344	10	r(e	r(e	NOUN
ejpam-2291	344	11	)	)	PUNCT
ejpam-2291	345	1	if	if	SCONJ
ejpam-2291	345	2	and	and	CCONJ
ejpam-2291	345	3	only	only	ADV
ejpam-2291	345	4	if	if	SCONJ
ejpam-2291	345	5	for	for	ADP
ejpam-2291	345	6	all	all	DET
ejpam-2291	345	7	large	large	ADJ
ejpam-2291	345	8	n≥	n≥	NOUN
ejpam-2291	345	9	1	1	NUM
ejpam-2291	345	10	,	,	PUNCT
ejpam-2291	345	11	[	[	X
ejpam-2291	345	12	(	(	PUNCT
ejpam-2291	345	13	f1	f1	NOUN
ejpam-2291	345	14	,	,	PUNCT
ejpam-2291	345	15	.	.	PUNCT
ejpam-2291	345	16	.	.	PUNCT
ejpam-2291	346	1	.	.	PUNCT
ejpam-2291	347	1	,	,	PUNCT
ejpam-2291	347	2	fi−1)b	fi−1)b	PUNCT
ejpam-2291	347	3	ne	ne	PROPN
ejpam-2291	347	4	:	:	PUNCT
ejpam-2291	347	5	e	e	X
ejpam-2291	347	6	fi]∩	fi]∩	NOUN
ejpam-2291	347	7	bne	bne	PROPN
ejpam-2291	347	8	=	=	PROPN
ejpam-2291	347	9	(	(	PUNCT
ejpam-2291	347	10	f1	f1	NOUN
ejpam-2291	347	11	,	,	PUNCT
ejpam-2291	347	12	.	.	PUNCT
ejpam-2291	347	13	.	.	PUNCT
ejpam-2291	348	1	.	.	PUNCT
ejpam-2291	349	1	,	,	PUNCT
ejpam-2291	349	2	fi−1)b	fi−1)b	X
ejpam-2291	349	3	n−1e	n−1e	PROPN
ejpam-2291	350	1	for	for	ADP
ejpam-2291	350	2	i	i	PRON
ejpam-2291	350	3	=	=	NOUN
ejpam-2291	350	4	1	1	NUM
ejpam-2291	350	5	,	,	PUNCT
ejpam-2291	350	6	.	.	PUNCT
ejpam-2291	350	7	.	.	PUNCT
ejpam-2291	351	1	.	.	PUNCT
ejpam-2291	352	1	,	,	PUNCT
ejpam-2291	352	2	h.	h.	PROPN
ejpam-2291	352	3	(	(	PUNCT
ejpam-2291	352	4	4	4	NUM
ejpam-2291	352	5	)	)	PUNCT
ejpam-2291	352	6	if	if	SCONJ
ejpam-2291	352	7	this	this	PRON
ejpam-2291	352	8	is	be	AUX
ejpam-2291	352	9	the	the	DET
ejpam-2291	352	10	case	case	NOUN
ejpam-2291	352	11	,	,	PUNCT
ejpam-2291	352	12	then	then	ADV
ejpam-2291	352	13	e(f	e(f	PROPN
ejpam-2291	352	14	,	,	PUNCT
ejpam-2291	352	15	r(e	r(e	PROPN
ejpam-2291	352	16	)	)	PUNCT
ejpam-2291	352	17	)	)	PUNCT
ejpam-2291	352	18	is	be	AUX
ejpam-2291	352	19	the	the	DET
ejpam-2291	352	20	least	least	ADJ
ejpam-2291	352	21	integer	integer	NOUN
ejpam-2291	352	22	r	r	NOUN
ejpam-2291	352	23	such	such	ADJ
ejpam-2291	352	24	that	that	SCONJ
ejpam-2291	352	25	(	(	PUNCT
ejpam-2291	352	26	4	4	X
ejpam-2291	352	27	)	)	PUNCT
ejpam-2291	352	28	holds	hold	VERB
ejpam-2291	352	29	for	for	ADP
ejpam-2291	352	30	all	all	DET
ejpam-2291	352	31	n≥	n≥	NOUN
ejpam-2291	352	32	r	r	NOUN
ejpam-2291	352	33	+	+	NOUN
ejpam-2291	352	34	1	1	NUM
ejpam-2291	352	35	.	.	X
ejpam-2291	352	36	proof	proof	NOUN
ejpam-2291	352	37	.	.	PUNCT
ejpam-2291	353	1	the	the	DET
ejpam-2291	353	2	sequence	sequence	NOUN
ejpam-2291	353	3	f=	f=	PROPN
ejpam-2291	353	4	f1	f1	PROPN
ejpam-2291	353	5	t	t	PROPN
ejpam-2291	353	6	,	,	PUNCT
ejpam-2291	353	7	.	.	PUNCT
ejpam-2291	353	8	.	.	PUNCT
ejpam-2291	353	9	.	.	PUNCT
ejpam-2291	354	1	,	,	PUNCT
ejpam-2291	354	2	fh	fh	PROPN
ejpam-2291	354	3	t	t	PROPN
ejpam-2291	354	4	is	be	AUX
ejpam-2291	354	5	an	an	DET
ejpam-2291	354	6	r(b)+-filter	r(b)+-filter	NOUN
ejpam-2291	354	7	regular	regular	ADJ
ejpam-2291	354	8	sequence	sequence	NOUN
ejpam-2291	354	9	for	for	ADP
ejpam-2291	354	10	r(e	r(e	NOUN
ejpam-2291	354	11	)	)	PUNCT
ejpam-2291	355	1	if	if	SCONJ
ejpam-2291	355	2	and	and	CCONJ
ejpam-2291	355	3	only	only	ADV
ejpam-2291	355	4	if	if	SCONJ
ejpam-2291	355	5	[	[	X
ejpam-2291	355	6	(	(	PUNCT
ejpam-2291	355	7	f1	f1	PROPN
ejpam-2291	355	8	t	t	PROPN
ejpam-2291	355	9	,	,	PUNCT
ejpam-2291	355	10	.	.	PUNCT
ejpam-2291	355	11	.	.	PUNCT
ejpam-2291	355	12	.	.	PUNCT
ejpam-2291	356	1	,	,	PUNCT
ejpam-2291	356	2	fi−1	fi−1	PROPN
ejpam-2291	356	3	t)r(e	t)r(e	PROPN
ejpam-2291	356	4	)	)	PUNCT
ejpam-2291	356	5	:	:	PUNCT
ejpam-2291	356	6	r(e	r(e	NOUN
ejpam-2291	356	7	)	)	PUNCT
ejpam-2291	356	8	fi	fi	NOUN
ejpam-2291	356	9	t]n	t]n	NOUN
ejpam-2291	356	10	is	be	AUX
ejpam-2291	356	11	equal	equal	ADJ
ejpam-2291	356	12	to	to	ADP
ejpam-2291	356	13	[	[	X
ejpam-2291	356	14	(	(	PUNCT
ejpam-2291	356	15	f1	f1	PROPN
ejpam-2291	356	16	t	t	PROPN
ejpam-2291	356	17	,	,	PUNCT
ejpam-2291	356	18	.	.	PUNCT
ejpam-2291	356	19	.	.	PUNCT
ejpam-2291	357	1	.	.	PUNCT
ejpam-2291	358	1	,	,	PUNCT
ejpam-2291	358	2	fi−1	fi−1	PROPN
ejpam-2291	358	3	t)r(e)]n	t)r(e)]n	PROPN
ejpam-2291	358	4	for	for	ADP
ejpam-2291	358	5	all	all	PRON
ejpam-2291	358	6	large	large	ADJ
ejpam-2291	358	7	n	n	PRON
ejpam-2291	358	8	≥	≥	NOUN
ejpam-2291	358	9	1	1	NUM
ejpam-2291	358	10	and	and	CCONJ
ejpam-2291	358	11	all	all	PRON
ejpam-2291	358	12	i	i	PRON
ejpam-2291	358	13	=	=	NOUN
ejpam-2291	358	14	1	1	NUM
ejpam-2291	358	15	,	,	PUNCT
ejpam-2291	358	16	.	.	PUNCT
ejpam-2291	358	17	.	.	PUNCT
ejpam-2291	359	1	.	.	PUNCT
ejpam-2291	360	1	,	,	PUNCT
ejpam-2291	360	2	h.	h.	PROPN
ejpam-2291	360	3	but	but	CCONJ
ejpam-2291	360	4	the	the	DET
ejpam-2291	360	5	first	first	ADJ
ejpam-2291	360	6	module	module	NOUN
ejpam-2291	360	7	is	be	AUX
ejpam-2291	360	8	equal	equal	ADJ
ejpam-2291	360	9	to	to	ADP
ejpam-2291	360	10	[	[	X
ejpam-2291	360	11	(	(	PUNCT
ejpam-2291	360	12	f1	f1	NOUN
ejpam-2291	360	13	,	,	PUNCT
ejpam-2291	360	14	.	.	PUNCT
ejpam-2291	360	15	.	.	PUNCT
ejpam-2291	361	1	.	.	PUNCT
ejpam-2291	362	1	,	,	PUNCT
ejpam-2291	362	2	fi−1)bne	fi−1)bne	ADV
ejpam-2291	362	3	:	:	PUNCT
ejpam-2291	362	4	e	e	NOUN
ejpam-2291	362	5	fi	fi	NOUN
ejpam-2291	362	6	]	]	X
ejpam-2291	362	7	∩	∩	X
ejpam-2291	362	8	bne	bne	PROPN
ejpam-2291	362	9	and	and	CCONJ
ejpam-2291	362	10	the	the	DET
ejpam-2291	362	11	second	second	NOUN
ejpam-2291	362	12	is	be	AUX
ejpam-2291	362	13	equal	equal	ADJ
ejpam-2291	362	14	to	to	ADP
ejpam-2291	362	15	(	(	PUNCT
ejpam-2291	362	16	f1	f1	NOUN
ejpam-2291	362	17	,	,	PUNCT
ejpam-2291	362	18	.	.	PUNCT
ejpam-2291	362	19	.	.	PUNCT
ejpam-2291	363	1	.	.	PUNCT
ejpam-2291	364	1	,	,	PUNCT
ejpam-2291	365	1	fi−1)bn−1e	fi−1)bn−1e	PROPN
ejpam-2291	365	2	.	.	PUNCT
ejpam-2291	366	1	we	we	PRON
ejpam-2291	366	2	note	note	VERB
ejpam-2291	366	3	that	that	SCONJ
ejpam-2291	366	4	e(f	e(f	PROPN
ejpam-2291	366	5	,	,	PUNCT
ejpam-2291	366	6	r(e	r(e	PROPN
ejpam-2291	366	7	)	)	PUNCT
ejpam-2291	366	8	)	)	PUNCT
ejpam-2291	366	9	is	be	AUX
ejpam-2291	366	10	the	the	DET
ejpam-2291	366	11	least	least	ADJ
ejpam-2291	366	12	integer	integer	NOUN
ejpam-2291	366	13	r	r	NOUN
ejpam-2291	366	14	such	such	ADJ
ejpam-2291	366	15	that	that	SCONJ
ejpam-2291	366	16	the	the	DET
ejpam-2291	366	17	equality	equality	NOUN
ejpam-2291	366	18	[	[	X
ejpam-2291	366	19	(	(	PUNCT
ejpam-2291	366	20	f1	f1	PROPN
ejpam-2291	366	21	t	t	PROPN
ejpam-2291	366	22	,	,	PUNCT
ejpam-2291	366	23	.	.	PUNCT
ejpam-2291	366	24	.	.	PUNCT
ejpam-2291	367	1	.	.	PUNCT
ejpam-2291	368	1	,	,	PUNCT
ejpam-2291	368	2	fi−1	fi−1	PROPN
ejpam-2291	368	3	t)r(e	t)r(e	PROPN
ejpam-2291	368	4	)	)	PUNCT
ejpam-2291	368	5	:	:	PUNCT
ejpam-2291	368	6	r(e	r(e	NOUN
ejpam-2291	368	7	)	)	PUNCT
ejpam-2291	368	8	fi	fi	NOUN
ejpam-2291	368	9	t]n	t]n	NOUN
ejpam-2291	368	10	=	=	PUNCT
ejpam-2291	369	1	[	[	X
ejpam-2291	369	2	(	(	PUNCT
ejpam-2291	369	3	f1	f1	PROPN
ejpam-2291	369	4	t	t	PROPN
ejpam-2291	369	5	,	,	PUNCT
ejpam-2291	369	6	.	.	PUNCT
ejpam-2291	369	7	.	.	PUNCT
ejpam-2291	369	8	.	.	PUNCT
ejpam-2291	370	1	,	,	PUNCT
ejpam-2291	370	2	fi−1	fi−1	PROPN
ejpam-2291	370	3	t)r(e)]n	t)r(e)]n	PROPN
ejpam-2291	370	4	holds	hold	VERB
ejpam-2291	370	5	for	for	ADP
ejpam-2291	370	6	all	all	PRON
ejpam-2291	370	7	n≥	n≥	NOUN
ejpam-2291	370	8	r	r	NOUN
ejpam-2291	370	9	+	+	CCONJ
ejpam-2291	370	10	1	1	NUM
ejpam-2291	370	11	.	.	PUNCT
ejpam-2291	370	12	corollary	corollary	ADJ
ejpam-2291	370	13	4	4	NUM
ejpam-2291	370	14	.	.	PUNCT
ejpam-2291	371	1	let	let	VERB
ejpam-2291	371	2	a=	a=	ADV
ejpam-2291	371	3	(	(	PUNCT
ejpam-2291	371	4	f1	f1	NOUN
ejpam-2291	371	5	,	,	PUNCT
ejpam-2291	371	6	.	.	PUNCT
ejpam-2291	371	7	.	.	PUNCT
ejpam-2291	372	1	.	.	PUNCT
ejpam-2291	373	1	,	,	PUNCT
ejpam-2291	373	2	fh	fh	PROPN
ejpam-2291	373	3	)	)	PUNCT
ejpam-2291	373	4	be	be	VERB
ejpam-2291	373	5	a	a	DET
ejpam-2291	373	6	reduction	reduction	NOUN
ejpam-2291	373	7	of	of	ADP
ejpam-2291	373	8	b	b	NOUN
ejpam-2291	373	9	with	with	ADP
ejpam-2291	373	10	respect	respect	NOUN
ejpam-2291	373	11	to	to	ADP
ejpam-2291	373	12	e.	e.	PROPN
ejpam-2291	373	13	suppose	suppose	VERB
ejpam-2291	373	14	that	that	SCONJ
ejpam-2291	373	15	f=	f=	PROPN
ejpam-2291	373	16	f1	f1	PROPN
ejpam-2291	373	17	t	t	PROPN
ejpam-2291	373	18	,	,	PUNCT
ejpam-2291	373	19	.	.	PUNCT
ejpam-2291	373	20	.	.	PUNCT
ejpam-2291	374	1	.	.	PUNCT
ejpam-2291	375	1	,	,	PUNCT
ejpam-2291	375	2	fh	fh	PROPN
ejpam-2291	375	3	t	t	PROPN
ejpam-2291	375	4	is	be	AUX
ejpam-2291	375	5	an	an	DET
ejpam-2291	375	6	r(b)+-filter	r(b)+-filter	NOUN
ejpam-2291	375	7	regular	regular	ADJ
ejpam-2291	375	8	sequence	sequence	NOUN
ejpam-2291	375	9	for	for	ADP
ejpam-2291	375	10	r(e	r(e	NOUN
ejpam-2291	375	11	)	)	PUNCT
ejpam-2291	375	12	.	.	PUNCT
ejpam-2291	376	1	then	then	ADV
ejpam-2291	376	2	reg(r(e	reg(r(e	PROPN
ejpam-2291	376	3	)	)	PUNCT
ejpam-2291	376	4	)	)	PUNCT
ejpam-2291	377	1	=	=	PRON
ejpam-2291	377	2	min{r	min{r	VERB
ejpam-2291	377	3	≥	≥	NOUN
ejpam-2291	377	4	0	0	NUM
ejpam-2291	377	5	:	:	PUNCT
ejpam-2291	378	1	r	r	NOUN
ejpam-2291	378	2	≥	≥	NOUN
ejpam-2291	378	3	ra(b	ra(b	NOUN
ejpam-2291	378	4	,	,	PUNCT
ejpam-2291	378	5	e	e	NOUN
ejpam-2291	378	6	)	)	PUNCT
ejpam-2291	378	7	and	and	CCONJ
ejpam-2291	378	8	(	(	PUNCT
ejpam-2291	378	9	4	4	X
ejpam-2291	378	10	)	)	PUNCT
ejpam-2291	378	11	holds	hold	VERB
ejpam-2291	378	12	for	for	ADP
ejpam-2291	378	13	all	all	DET
ejpam-2291	378	14	n≥	n≥	NOUN
ejpam-2291	378	15	r	r	NOUN
ejpam-2291	378	16	+	+	CCONJ
ejpam-2291	378	17	1	1	NUM
ejpam-2291	378	18	}	}	PUNCT
ejpam-2291	378	19	.	.	PUNCT
ejpam-2291	379	1	proof	proof	NOUN
ejpam-2291	379	2	.	.	PUNCT
ejpam-2291	380	1	let	let	VERB
ejpam-2291	380	2	q	q	NOUN
ejpam-2291	381	1	=	=	PUNCT
ejpam-2291	381	2	(	(	PUNCT
ejpam-2291	381	3	f1	f1	PROPN
ejpam-2291	381	4	t	t	PROPN
ejpam-2291	381	5	,	,	PUNCT
ejpam-2291	381	6	.	.	PUNCT
ejpam-2291	381	7	.	.	PUNCT
ejpam-2291	381	8	.	.	PUNCT
ejpam-2291	382	1	,	,	PUNCT
ejpam-2291	382	2	fh	fh	PROPN
ejpam-2291	382	3	t	t	PROPN
ejpam-2291	382	4	)	)	PUNCT
ejpam-2291	382	5	.	.	PUNCT
ejpam-2291	383	1	since	since	SCONJ
ejpam-2291	383	2	a	a	PRON
ejpam-2291	383	3	is	be	AUX
ejpam-2291	383	4	a	a	DET
ejpam-2291	383	5	reduction	reduction	NOUN
ejpam-2291	383	6	of	of	ADP
ejpam-2291	383	7	b	b	NOUN
ejpam-2291	383	8	relative	relative	ADJ
ejpam-2291	383	9	to	to	ADP
ejpam-2291	383	10	e	e	NOUN
ejpam-2291	383	11	,	,	PUNCT
ejpam-2291	383	12	then	then	ADV
ejpam-2291	383	13	q	q	X
ejpam-2291	383	14	is	be	AUX
ejpam-2291	383	15	a	a	DET
ejpam-2291	383	16	reduction	reduction	NOUN
ejpam-2291	383	17	of	of	ADP
ejpam-2291	383	18	r(b)+	r(b)+	PROPN
ejpam-2291	383	19	relative	relative	NOUN
ejpam-2291	383	20	to	to	ADP
ejpam-2291	383	21	r(e	r(e	NOUN
ejpam-2291	383	22	)	)	PUNCT
ejpam-2291	383	23	.	.	PUNCT
ejpam-2291	384	1	moreover	moreover	ADV
ejpam-2291	384	2	if	if	SCONJ
ejpam-2291	384	3	abne	abne	ADV
ejpam-2291	384	4	=	=	SYM
ejpam-2291	384	5	bn+1	bn+1	PROPN
ejpam-2291	384	6	,	,	PUNCT
ejpam-2291	384	7	then	then	ADV
ejpam-2291	384	8	qr(b)n+r(e	qr(b)n+r(e	ADP
ejpam-2291	384	9	)	)	PUNCT
ejpam-2291	384	10	=	=	PUNCT
ejpam-2291	385	1	r(b)n+1	r(b)n+1	PROPN
ejpam-2291	385	2	+	+	NUM
ejpam-2291	385	3	r(e	r(e	NOUN
ejpam-2291	385	4	)	)	PUNCT
ejpam-2291	385	5	and	and	CCONJ
ejpam-2291	385	6	ra(b	ra(b	ADJ
ejpam-2291	385	7	,	,	PUNCT
ejpam-2291	385	8	e	e	NOUN
ejpam-2291	385	9	)	)	PUNCT
ejpam-2291	385	10	=	=	SYM
ejpam-2291	385	11	rq(r(b)+	rq(r(b)+	NOUN
ejpam-2291	385	12	,	,	PUNCT
ejpam-2291	385	13	r(e	r(e	NOUN
ejpam-2291	385	14	)	)	PUNCT
ejpam-2291	385	15	)	)	PUNCT
ejpam-2291	385	16	.	.	PUNCT
ejpam-2291	386	1	by	by	ADP
ejpam-2291	386	2	theorem	theorem	NOUN
ejpam-2291	386	3	1	1	NUM
ejpam-2291	386	4	,	,	PUNCT
ejpam-2291	386	5	reg(r(e	reg(r(e	NOUN
ejpam-2291	386	6	)	)	PUNCT
ejpam-2291	386	7	)	)	PUNCT
ejpam-2291	387	1	=	=	SYM
ejpam-2291	387	2	max{e(f	max{e(f	PROPN
ejpam-2291	387	3	,	,	PUNCT
ejpam-2291	387	4	r(e	r(e	PROPN
ejpam-2291	387	5	)	)	PUNCT
ejpam-2291	387	6	)	)	PUNCT
ejpam-2291	387	7	,	,	PUNCT
ejpam-2291	387	8	ra(b	ra(b	X
ejpam-2291	387	9	,	,	PUNCT
ejpam-2291	387	10	e	e	NOUN
ejpam-2291	387	11	)	)	PUNCT
ejpam-2291	387	12	}	}	PUNCT
ejpam-2291	387	13	.	.	PUNCT
ejpam-2291	388	1	therefore	therefore	ADV
ejpam-2291	388	2	,	,	PUNCT
ejpam-2291	388	3	the	the	DET
ejpam-2291	388	4	result	result	NOUN
ejpam-2291	388	5	follows	follow	VERB
ejpam-2291	388	6	from	from	ADP
ejpam-2291	388	7	proposition	proposition	NOUN
ejpam-2291	388	8	1	1	NUM
ejpam-2291	388	9	.	.	PUNCT
ejpam-2291	388	10	similarly	similarly	ADV
ejpam-2291	388	11	as	as	ADP
ejpam-2291	388	12	for	for	ADP
ejpam-2291	388	13	proposition	proposition	NOUN
ejpam-2291	388	14	1	1	NUM
ejpam-2291	388	15	,	,	PUNCT
ejpam-2291	388	16	we	we	PRON
ejpam-2291	388	17	can	can	AUX
ejpam-2291	388	18	prove	prove	VERB
ejpam-2291	388	19	the	the	DET
ejpam-2291	388	20	following	follow	VERB
ejpam-2291	388	21	characterization	characterization	NOUN
ejpam-2291	388	22	of	of	ADP
ejpam-2291	388	23	a	a	DET
ejpam-2291	388	24	homogeneous	homogeneous	ADJ
ejpam-2291	388	25	g(b)+	g(b)+	NOUN
ejpam-2291	388	26	filter	filter	NOUN
ejpam-2291	388	27	regular	regular	ADJ
ejpam-2291	388	28	sequence	sequence	NOUN
ejpam-2291	388	29	of	of	ADP
ejpam-2291	388	30	degree	degree	NOUN
ejpam-2291	388	31	1	1	NUM
ejpam-2291	388	32	for	for	ADP
ejpam-2291	388	33	g(e	g(e	PROPN
ejpam-2291	388	34	)	)	PUNCT
ejpam-2291	388	35	.	.	PUNCT
ejpam-2291	389	1	if	if	SCONJ
ejpam-2291	389	2	x	x	SYM
ejpam-2291	389	3	∈	∈	PROPN
ejpam-2291	389	4	a	a	DET
ejpam-2291	389	5	then	then	ADV
ejpam-2291	389	6	x∗	x∗	PROPN
ejpam-2291	389	7	denotes	denote	VERB
ejpam-2291	389	8	the	the	DET
ejpam-2291	389	9	initial	initial	ADJ
ejpam-2291	389	10	form	form	NOUN
ejpam-2291	389	11	of	of	ADP
ejpam-2291	389	12	x	x	PUNCT
ejpam-2291	389	13	in	in	ADP
ejpam-2291	389	14	g(b	g(b	PROPN
ejpam-2291	389	15	)	)	PUNCT
ejpam-2291	389	16	.	.	PUNCT
ejpam-2291	390	1	proposition	proposition	NOUN
ejpam-2291	390	2	2	2	NUM
ejpam-2291	390	3	.	.	PUNCT
ejpam-2291	390	4	let	let	VERB
ejpam-2291	390	5	f1	f1	NOUN
ejpam-2291	390	6	,	,	PUNCT
ejpam-2291	390	7	.	.	PUNCT
ejpam-2291	390	8	.	.	PUNCT
ejpam-2291	391	1	.	.	PUNCT
ejpam-2291	392	1	,	,	PUNCT
ejpam-2291	392	2	fh	fh	PROPN
ejpam-2291	392	3	be	be	VERB
ejpam-2291	392	4	elements	element	NOUN
ejpam-2291	392	5	of	of	ADP
ejpam-2291	392	6	b.	b.	PROPN
ejpam-2291	392	7	then	then	ADV
ejpam-2291	392	8	f∗	f∗	NOUN
ejpam-2291	393	1	=	=	PUNCT
ejpam-2291	393	2	f	f	X
ejpam-2291	393	3	∗1	∗1	INTJ
ejpam-2291	393	4	,	,	PUNCT
ejpam-2291	393	5	.	.	PUNCT
ejpam-2291	393	6	.	.	PUNCT
ejpam-2291	393	7	.	.	PUNCT
ejpam-2291	394	1	,	,	PUNCT
ejpam-2291	394	2	f	f	PROPN
ejpam-2291	394	3	∗h	∗h	NOUN
ejpam-2291	394	4	is	be	AUX
ejpam-2291	394	5	an	an	DET
ejpam-2291	394	6	g(b)+-filter	g(b)+-filter	NOUN
ejpam-2291	394	7	regular	regular	ADJ
ejpam-2291	394	8	sequence	sequence	NOUN
ejpam-2291	394	9	for	for	ADP
ejpam-2291	394	10	g(e	g(e	PROPN
ejpam-2291	394	11	)	)	PUNCT
ejpam-2291	394	12	)	)	PUNCT
ejpam-2291	395	1	if	if	SCONJ
ejpam-2291	395	2	and	and	CCONJ
ejpam-2291	395	3	only	only	ADV
ejpam-2291	395	4	if	if	SCONJ
ejpam-2291	395	5	for	for	ADP
ejpam-2291	395	6	large	large	ADJ
ejpam-2291	395	7	values	value	NOUN
ejpam-2291	395	8	of	of	ADP
ejpam-2291	395	9	n	n	CCONJ
ejpam-2291	395	10	,	,	PUNCT
ejpam-2291	395	11	[	[	X
ejpam-2291	395	12	(	(	PUNCT
ejpam-2291	395	13	f1	f1	NOUN
ejpam-2291	395	14	,	,	PUNCT
ejpam-2291	395	15	.	.	PUNCT
ejpam-2291	395	16	.	.	PUNCT
ejpam-2291	395	17	.	.	PUNCT
ejpam-2291	396	1	,	,	PUNCT
ejpam-2291	396	2	fi−1)b	fi−1)b	X
ejpam-2291	396	3	ne	ne	PROPN
ejpam-2291	396	4	+	+	CCONJ
ejpam-2291	396	5	bn+2e	bn+2e	PROPN
ejpam-2291	396	6	]	]	PUNCT
ejpam-2291	396	7	:	:	PUNCT
ejpam-2291	396	8	e	e	X
ejpam-2291	396	9	fi	fi	NOUN
ejpam-2291	396	10	∩	∩	NOUN
ejpam-2291	396	11	bne	bne	PROPN
ejpam-2291	396	12	=	=	SYM
ejpam-2291	396	13	(	(	PUNCT
ejpam-2291	396	14	(	(	PUNCT
ejpam-2291	396	15	f1	f1	NOUN
ejpam-2291	396	16	,	,	PUNCT
ejpam-2291	396	17	.	.	PUNCT
ejpam-2291	396	18	.	.	PUNCT
ejpam-2291	397	1	.	.	PUNCT
ejpam-2291	398	1	,	,	PUNCT
ejpam-2291	398	2	fi−1)b	fi−1)b	X
ejpam-2291	398	3	n−1e	n−1e	PROPN
ejpam-2291	399	1	+	+	NUM
ejpam-2291	399	2	bn+1e	bn+1e	NOUN
ejpam-2291	399	3	)	)	PUNCT
ejpam-2291	399	4	for	for	ADP
ejpam-2291	399	5	i	i	PROPN
ejpam-2291	399	6	=	=	NOUN
ejpam-2291	399	7	1	1	NUM
ejpam-2291	399	8	,	,	PUNCT
ejpam-2291	399	9	.	.	PUNCT
ejpam-2291	399	10	.	.	PUNCT
ejpam-2291	399	11	.	.	PUNCT
ejpam-2291	400	1	,	,	PUNCT
ejpam-2291	400	2	s.	s.	PROPN
ejpam-2291	400	3	if	if	SCONJ
ejpam-2291	400	4	this	this	PRON
ejpam-2291	400	5	is	be	AUX
ejpam-2291	400	6	the	the	DET
ejpam-2291	400	7	case	case	NOUN
ejpam-2291	400	8	,	,	PUNCT
ejpam-2291	400	9	e(f∗	e(f∗	PROPN
ejpam-2291	400	10	,	,	PUNCT
ejpam-2291	400	11	g(e	g(e	PROPN
ejpam-2291	400	12	)	)	PUNCT
ejpam-2291	400	13	)	)	PUNCT
ejpam-2291	400	14	is	be	AUX
ejpam-2291	400	15	the	the	DET
ejpam-2291	400	16	least	least	ADJ
ejpam-2291	400	17	number	number	NOUN
ejpam-2291	400	18	r	r	NOUN
ejpam-2291	400	19	such	such	ADJ
ejpam-2291	400	20	that	that	SCONJ
ejpam-2291	400	21	the	the	DET
ejpam-2291	400	22	above	above	ADJ
ejpam-2291	400	23	equality	equality	NOUN
ejpam-2291	400	24	holds	hold	VERB
ejpam-2291	400	25	for	for	ADP
ejpam-2291	400	26	n≥	n≥	NOUN
ejpam-2291	400	27	r	r	NOUN
ejpam-2291	400	28	+	+	NOUN
ejpam-2291	400	29	1	1	NUM
ejpam-2291	400	30	.	.	PUNCT
ejpam-2291	400	31	references	reference	NOUN
ejpam-2291	400	32	[	[	X
ejpam-2291	400	33	1	1	NUM
ejpam-2291	400	34	]	]	PUNCT
ejpam-2291	400	35	m	m	NOUN
ejpam-2291	400	36	brodmann	brodmann	NOUN
ejpam-2291	400	37	and	and	CCONJ
ejpam-2291	400	38	r	r	NOUN
ejpam-2291	400	39	sharp	sharp	ADJ
ejpam-2291	400	40	.	.	PUNCT
ejpam-2291	401	1	local	local	ADJ
ejpam-2291	401	2	cohomology	cohomology	NOUN
ejpam-2291	401	3	:	:	PUNCT
ejpam-2291	401	4	an	an	DET
ejpam-2291	401	5	algebraic	algebraic	ADJ
ejpam-2291	401	6	introduction	introduction	NOUN
ejpam-2291	401	7	with	with	ADP
ejpam-2291	401	8	geometric	geometric	ADJ
ejpam-2291	401	9	applications	application	NOUN
ejpam-2291	401	10	.	.	PUNCT
ejpam-2291	402	1	cambridge	cambridge	PROPN
ejpam-2291	402	2	university	university	PROPN
ejpam-2291	402	3	press	press	PROPN
ejpam-2291	402	4	,	,	PUNCT
ejpam-2291	402	5	cambridge	cambridge	PROPN
ejpam-2291	402	6	,	,	PUNCT
ejpam-2291	402	7	1998	1998	NUM
ejpam-2291	402	8	.	.	PUNCT
ejpam-2291	403	1	[	[	X
ejpam-2291	403	2	2	2	NUM
ejpam-2291	403	3	]	]	X
ejpam-2291	403	4	w	w	NOUN
ejpam-2291	403	5	bruns	brun	NOUN
ejpam-2291	403	6	and	and	CCONJ
ejpam-2291	403	7	j	j	PROPN
ejpam-2291	403	8	herzog	herzog	PROPN
ejpam-2291	403	9	.	.	PUNCT
ejpam-2291	403	10	cohen	cohen	PROPN
ejpam-2291	403	11	-	-	PUNCT
ejpam-2291	403	12	macaulay	macaulay	PROPN
ejpam-2291	403	13	rings	ring	NOUN
ejpam-2291	403	14	.	.	PUNCT
ejpam-2291	404	1	cambridge	cambridge	PROPN
ejpam-2291	404	2	university	university	PROPN
ejpam-2291	404	3	press	press	PROPN
ejpam-2291	404	4	,	,	PUNCT
ejpam-2291	404	5	cambridge	cambridge	PROPN
ejpam-2291	404	6	,	,	PUNCT
ejpam-2291	404	7	1993	1993	NUM
ejpam-2291	404	8	.	.	PUNCT
ejpam-2291	405	1	references	reference	NOUN
ejpam-2291	405	2	436	436	NUM
ejpam-2291	406	1	[	[	X
ejpam-2291	406	2	3	3	NUM
ejpam-2291	406	3	]	]	X
ejpam-2291	406	4	s	s	PART
ejpam-2291	406	5	gote	gote	NOUN
ejpam-2291	406	6	and	and	CCONJ
ejpam-2291	406	7	k	k	PROPN
ejpam-2291	406	8	watanabe	watanabe	PROPN
ejpam-2291	406	9	.	.	PUNCT
ejpam-2291	407	1	graded	grade	VERB
ejpam-2291	407	2	rings	ring	NOUN
ejpam-2291	407	3	i.	i.	PROPN
ejpam-2291	407	4	journal	journal	PROPN
ejpam-2291	407	5	of	of	ADP
ejpam-2291	407	6	the	the	DET
ejpam-2291	407	7	mathematical	mathematical	ADJ
ejpam-2291	407	8	society	society	NOUN
ejpam-2291	407	9	of	of	ADP
ejpam-2291	407	10	japan	japan	PROPN
ejpam-2291	407	11	30:179	30:179	PROPN
ejpam-2291	407	12	-	-	PUNCT
ejpam-2291	407	13	213	213	NUM
ejpam-2291	407	14	,	,	PUNCT
ejpam-2291	407	15	1978	1978	NUM
ejpam-2291	407	16	.	.	PUNCT
ejpam-2291	408	1	[	[	X
ejpam-2291	408	2	4	4	X
ejpam-2291	408	3	]	]	PUNCT
ejpam-2291	408	4	a	a	DET
ejpam-2291	408	5	ooishi	ooishi	NOUN
ejpam-2291	408	6	.	.	PUNCT
ejpam-2291	409	1	genera	genera	NOUN
ejpam-2291	409	2	and	and	CCONJ
ejpam-2291	409	3	arithmetic	arithmetic	ADJ
ejpam-2291	409	4	genera	genera	NOUN
ejpam-2291	409	5	of	of	ADP
ejpam-2291	409	6	commutative	commutative	ADJ
ejpam-2291	409	7	rings	ring	NOUN
ejpam-2291	409	8	.	.	PUNCT
ejpam-2291	410	1	hiroshima	hiroshima	PROPN
ejpam-2291	410	2	mathematical	mathematical	PROPN
ejpam-2291	410	3	journal	journal	PROPN
ejpam-2291	410	4	.	.	PUNCT
ejpam-2291	411	1	17:47	17:47	NUM
ejpam-2291	411	2	-	-	SYM
ejpam-2291	411	3	66	66	NUM
ejpam-2291	411	4	,	,	PUNCT
ejpam-2291	411	5	1987	1987	NUM
ejpam-2291	411	6	.	.	PUNCT
ejpam-2291	412	1	[	[	X
ejpam-2291	412	2	5	5	NUM
ejpam-2291	412	3	]	]	PUNCT
ejpam-2291	412	4	n	n	PRON
ejpam-2291	412	5	v	v	NOUN
ejpam-2291	412	6	trung	trung	NOUN
ejpam-2291	412	7	.	.	PUNCT
ejpam-2291	413	1	the	the	DET
ejpam-2291	413	2	castelnuovo	castelnuovo	PROPN
ejpam-2291	413	3	regularity	regularity	NOUN
ejpam-2291	413	4	of	of	ADP
ejpam-2291	413	5	the	the	DET
ejpam-2291	413	6	rees	rees	PROPN
ejpam-2291	413	7	algebra	algebra	NOUN
ejpam-2291	413	8	and	and	CCONJ
ejpam-2291	413	9	the	the	DET
ejpam-2291	413	10	associated	associate	VERB
ejpam-2291	413	11	graded	grade	VERB
ejpam-2291	413	12	ring	ring	NOUN
ejpam-2291	413	13	.	.	PUNCT
ejpam-2291	414	1	transactions	transaction	NOUN
ejpam-2291	414	2	of	of	ADP
ejpam-2291	414	3	the	the	DET
ejpam-2291	414	4	american	american	PROPN
ejpam-2291	414	5	mathematical	mathematical	PROPN
ejpam-2291	414	6	society	society	NOUN
ejpam-2291	414	7	,	,	PUNCT
ejpam-2291	414	8	350	350	NUM
ejpam-2291	414	9	:	:	SYM
ejpam-2291	414	10	2813	2813	NUM
ejpam-2291	414	11	-	-	SYM
ejpam-2291	414	12	2832	2832	NUM
ejpam-2291	414	13	,	,	PUNCT
ejpam-2291	414	14	1998	1998	NUM
ejpam-2291	414	15	.	.	PUNCT
ejpam-2291	415	1	[	[	X
ejpam-2291	415	2	6	6	NUM
ejpam-2291	415	3	]	]	SYM
ejpam-2291	415	4	n	n	PRON
ejpam-2291	415	5	v	v	NOUN
ejpam-2291	415	6	trung	trung	VERB
ejpam-2291	415	7	.	.	PUNCT
ejpam-2291	415	8	reduction	reduction	NOUN
ejpam-2291	415	9	exponents	exponent	NOUN
ejpam-2291	415	10	and	and	CCONJ
ejpam-2291	415	11	degree	degree	NOUN
ejpam-2291	415	12	bound	bind	VERB
ejpam-2291	415	13	for	for	ADP
ejpam-2291	415	14	the	the	DET
ejpam-2291	415	15	defining	define	VERB
ejpam-2291	415	16	equations	equation	NOUN
ejpam-2291	415	17	of	of	ADP
ejpam-2291	415	18	graded	grade	VERB
ejpam-2291	415	19	rings	ring	NOUN
ejpam-2291	415	20	.	.	PUNCT
ejpam-2291	416	1	proceedings	proceeding	NOUN
ejpam-2291	416	2	of	of	ADP
ejpam-2291	416	3	the	the	DET
ejpam-2291	416	4	american	american	PROPN
ejpam-2291	416	5	mathematical	mathematical	PROPN
ejpam-2291	416	6	society	society	NOUN
ejpam-2291	416	7	.	.	PUNCT
ejpam-2291	417	1	101:229	101:229	NUM
ejpam-2291	417	2	-	-	SYM
ejpam-2291	417	3	236	236	NUM
ejpam-2291	417	4	,	,	PUNCT
ejpam-2291	417	5	1987	1987	NUM
ejpam-2291	417	6	.	.	PUNCT