id	sid	tid	token	lemma	pos
ejpam-3990	1	1	european	european	PROPN
ejpam-3990	1	2	journal	journal	PROPN
ejpam-3990	1	3	of	of	ADP
ejpam-3990	1	4	pure	pure	ADJ
ejpam-3990	1	5	and	and	CCONJ
ejpam-3990	1	6	applied	apply	VERB
ejpam-3990	1	7	mathematics	mathematic	NOUN
ejpam-3990	1	8	vol	vol	NOUN
ejpam-3990	1	9	.	.	PUNCT
ejpam-3990	2	1	14	14	NUM
ejpam-3990	2	2	,	,	PUNCT
ejpam-3990	2	3	no	no	INTJ
ejpam-3990	2	4	.	.	NOUN
ejpam-3990	2	5	3	3	NUM
ejpam-3990	2	6	,	,	PUNCT
ejpam-3990	2	7	2021	2021	NUM
ejpam-3990	2	8	,	,	PUNCT
ejpam-3990	2	9	695	695	NUM
ejpam-3990	2	10	-	-	SYM
ejpam-3990	2	11	705	705	NUM
ejpam-3990	2	12	issn	issn	PROPN
ejpam-3990	2	13	1307	1307	NUM
ejpam-3990	2	14	-	-	SYM
ejpam-3990	2	15	5543	5543	NUM
ejpam-3990	2	16	–	–	PUNCT
ejpam-3990	2	17	ejpam.com	ejpam.com	X
ejpam-3990	2	18	published	publish	VERB
ejpam-3990	2	19	by	by	ADP
ejpam-3990	2	20	new	new	PROPN
ejpam-3990	2	21	york	york	PROPN
ejpam-3990	2	22	business	business	PROPN
ejpam-3990	2	23	global	global	PROPN
ejpam-3990	2	24	on	on	ADP
ejpam-3990	2	25	a	a	DET
ejpam-3990	2	26	topological	topological	ADJ
ejpam-3990	2	27	space	space	NOUN
ejpam-3990	2	28	generated	generate	VERB
ejpam-3990	2	29	by	by	ADP
ejpam-3990	2	30	monophonic	monophonic	ADJ
ejpam-3990	2	31	eccentric	eccentric	ADJ
ejpam-3990	2	32	neighborhoods	neighborhood	NOUN
ejpam-3990	2	33	of	of	ADP
ejpam-3990	2	34	a	a	DET
ejpam-3990	2	35	graph	graph	NOUN
ejpam-3990	2	36	anabel	anabel	PROPN
ejpam-3990	2	37	e.	e.	PROPN
ejpam-3990	2	38	gamorez1,∗	gamorez1,∗	PROPN
ejpam-3990	2	39	,	,	PUNCT
ejpam-3990	2	40	sergio	sergio	PROPN
ejpam-3990	2	41	r.	r.	PROPN
ejpam-3990	2	42	canoy	canoy	PROPN
ejpam-3990	2	43	jr.2	jr.2	PROPN
ejpam-3990	2	44	1	1	NUM
ejpam-3990	2	45	department	department	NOUN
ejpam-3990	2	46	of	of	ADP
ejpam-3990	2	47	mathematics	mathematic	NOUN
ejpam-3990	2	48	and	and	CCONJ
ejpam-3990	2	49	statistics	statistic	NOUN
ejpam-3990	2	50	,	,	PUNCT
ejpam-3990	2	51	college	college	NOUN
ejpam-3990	2	52	of	of	ADP
ejpam-3990	2	53	science	science	NOUN
ejpam-3990	2	54	and	and	CCONJ
ejpam-3990	2	55	mathematics	mathematic	NOUN
ejpam-3990	2	56	,	,	PUNCT
ejpam-3990	2	57	western	western	ADJ
ejpam-3990	2	58	mindanao	mindanao	PROPN
ejpam-3990	2	59	state	state	PROPN
ejpam-3990	2	60	university	university	PROPN
ejpam-3990	2	61	,	,	PUNCT
ejpam-3990	2	62	7000	7000	NUM
ejpam-3990	2	63	,	,	PUNCT
ejpam-3990	2	64	zamboanga	zamboanga	PROPN
ejpam-3990	2	65	city	city	PROPN
ejpam-3990	2	66	,	,	PUNCT
ejpam-3990	2	67	philippines	philippines	PROPN
ejpam-3990	2	68	2	2	NUM
ejpam-3990	2	69	department	department	NOUN
ejpam-3990	2	70	of	of	ADP
ejpam-3990	2	71	mathematics	mathematic	NOUN
ejpam-3990	2	72	and	and	CCONJ
ejpam-3990	2	73	statistics	statistic	NOUN
ejpam-3990	2	74	,	,	PUNCT
ejpam-3990	2	75	college	college	NOUN
ejpam-3990	2	76	of	of	ADP
ejpam-3990	2	77	science	science	NOUN
ejpam-3990	2	78	and	and	CCONJ
ejpam-3990	2	79	mathematics	mathematic	NOUN
ejpam-3990	2	80	,	,	PUNCT
ejpam-3990	2	81	center	center	NOUN
ejpam-3990	2	82	of	of	ADP
ejpam-3990	2	83	graph	graph	NOUN
ejpam-3990	2	84	theory	theory	NOUN
ejpam-3990	2	85	,	,	PUNCT
ejpam-3990	2	86	algebra	algebra	NOUN
ejpam-3990	2	87	,	,	PUNCT
ejpam-3990	2	88	and	and	CCONJ
ejpam-3990	2	89	analysis	analysis	NOUN
ejpam-3990	2	90	-	-	PUNCT
ejpam-3990	2	91	premier	premier	NOUN
ejpam-3990	2	92	research	research	NOUN
ejpam-3990	2	93	institute	institute	PROPN
ejpam-3990	2	94	of	of	ADP
ejpam-3990	2	95	science	science	NOUN
ejpam-3990	2	96	and	and	CCONJ
ejpam-3990	2	97	mathematics	mathematic	NOUN
ejpam-3990	2	98	,	,	PUNCT
ejpam-3990	2	99	mindanao	mindanao	PROPN
ejpam-3990	2	100	state	state	PROPN
ejpam-3990	2	101	university	university	PROPN
ejpam-3990	2	102	-	-	PUNCT
ejpam-3990	2	103	iligan	iligan	PROPN
ejpam-3990	2	104	institute	institute	PROPN
ejpam-3990	2	105	of	of	ADP
ejpam-3990	2	106	technology	technology	PROPN
ejpam-3990	2	107	,	,	PUNCT
ejpam-3990	2	108	9200	9200	NUM
ejpam-3990	2	109	,	,	PUNCT
ejpam-3990	2	110	iligan	iligan	ADJ
ejpam-3990	2	111	city	city	NOUN
ejpam-3990	2	112	,	,	PUNCT
ejpam-3990	2	113	philippines	philippine	NOUN
ejpam-3990	2	114	abstract	abstract	ADJ
ejpam-3990	2	115	.	.	PUNCT
ejpam-3990	3	1	in	in	ADP
ejpam-3990	3	2	this	this	DET
ejpam-3990	3	3	paper	paper	NOUN
ejpam-3990	3	4	,	,	PUNCT
ejpam-3990	3	5	we	we	PRON
ejpam-3990	3	6	present	present	VERB
ejpam-3990	3	7	a	a	DET
ejpam-3990	3	8	way	way	NOUN
ejpam-3990	3	9	of	of	ADP
ejpam-3990	3	10	constructing	construct	VERB
ejpam-3990	3	11	a	a	DET
ejpam-3990	3	12	topology	topology	NOUN
ejpam-3990	3	13	on	on	ADP
ejpam-3990	3	14	a	a	DET
ejpam-3990	3	15	vertex	vertex	NOUN
ejpam-3990	3	16	set	set	NOUN
ejpam-3990	3	17	of	of	ADP
ejpam-3990	3	18	a	a	DET
ejpam-3990	3	19	graph	graph	NOUN
ejpam-3990	3	20	using	use	VERB
ejpam-3990	3	21	monophonic	monophonic	ADJ
ejpam-3990	3	22	eccentric	eccentric	ADJ
ejpam-3990	3	23	neighborhoods	neighborhood	NOUN
ejpam-3990	3	24	of	of	ADP
ejpam-3990	3	25	the	the	DET
ejpam-3990	3	26	graph	graph	NOUN
ejpam-3990	3	27	g.	g.	NOUN
ejpam-3990	3	28	in	in	ADP
ejpam-3990	3	29	this	this	DET
ejpam-3990	3	30	type	type	NOUN
ejpam-3990	3	31	of	of	ADP
ejpam-3990	3	32	construction	construction	NOUN
ejpam-3990	3	33	,	,	PUNCT
ejpam-3990	3	34	we	we	PRON
ejpam-3990	3	35	characterize	characterize	VERB
ejpam-3990	3	36	those	those	DET
ejpam-3990	3	37	graphs	graph	NOUN
ejpam-3990	3	38	that	that	PRON
ejpam-3990	3	39	induce	induce	VERB
ejpam-3990	3	40	the	the	DET
ejpam-3990	3	41	indiscrete	indiscrete	ADJ
ejpam-3990	3	42	topology	topology	NOUN
ejpam-3990	3	43	,	,	PUNCT
ejpam-3990	3	44	the	the	DET
ejpam-3990	3	45	discrete	discrete	ADJ
ejpam-3990	3	46	topology	topology	NOUN
ejpam-3990	3	47	,	,	PUNCT
ejpam-3990	3	48	and	and	CCONJ
ejpam-3990	3	49	a	a	DET
ejpam-3990	3	50	particular	particular	ADJ
ejpam-3990	3	51	point	point	NOUN
ejpam-3990	3	52	topology	topology	NOUN
ejpam-3990	3	53	.	.	PUNCT
ejpam-3990	4	1	2020	2020	NUM
ejpam-3990	4	2	mathematics	mathematic	NOUN
ejpam-3990	4	3	subject	subject	NOUN
ejpam-3990	4	4	classifications	classification	NOUN
ejpam-3990	4	5	:	:	PUNCT
ejpam-3990	4	6	05c12	05c12	NOUN
ejpam-3990	4	7	,	,	PUNCT
ejpam-3990	4	8	54b05	54b05	CCONJ
ejpam-3990	4	9	key	key	ADJ
ejpam-3990	4	10	words	word	NOUN
ejpam-3990	4	11	and	and	CCONJ
ejpam-3990	4	12	phrases	phrase	NOUN
ejpam-3990	4	13	:	:	PUNCT
ejpam-3990	4	14	topology	topology	NOUN
ejpam-3990	4	15	,	,	PUNCT
ejpam-3990	4	16	graph	graph	NOUN
ejpam-3990	4	17	,	,	PUNCT
ejpam-3990	4	18	monophonic	monophonic	ADJ
ejpam-3990	4	19	distance	distance	NOUN
ejpam-3990	4	20	,	,	PUNCT
ejpam-3990	4	21	monophonic	monophonic	ADJ
ejpam-3990	4	22	eccentric	eccentric	ADJ
ejpam-3990	4	23	neighborhood	neighborhood	NOUN
ejpam-3990	4	24	1	1	NUM
ejpam-3990	4	25	.	.	X
ejpam-3990	4	26	introduction	introduction	NOUN
ejpam-3990	4	27	a	a	DET
ejpam-3990	4	28	metric	metric	ADJ
ejpam-3990	4	29	or	or	CCONJ
ejpam-3990	4	30	distance	distance	NOUN
ejpam-3990	4	31	function	function	NOUN
ejpam-3990	4	32	in	in	ADP
ejpam-3990	4	33	a	a	DET
ejpam-3990	4	34	non	non	ADJ
ejpam-3990	4	35	-	-	ADJ
ejpam-3990	4	36	empty	empty	ADJ
ejpam-3990	4	37	set	set	NOUN
ejpam-3990	4	38	is	be	AUX
ejpam-3990	4	39	known	know	VERB
ejpam-3990	4	40	to	to	PART
ejpam-3990	4	41	generate	generate	VERB
ejpam-3990	4	42	a	a	DET
ejpam-3990	4	43	topology	topology	NOUN
ejpam-3990	4	44	on	on	ADP
ejpam-3990	4	45	the	the	DET
ejpam-3990	4	46	set	set	NOUN
ejpam-3990	4	47	via	via	ADP
ejpam-3990	4	48	the	the	DET
ejpam-3990	4	49	family	family	NOUN
ejpam-3990	4	50	of	of	ADP
ejpam-3990	4	51	open	open	ADJ
ejpam-3990	4	52	balls	ball	NOUN
ejpam-3990	4	53	the	the	DET
ejpam-3990	4	54	metric	metric	ADJ
ejpam-3990	4	55	induces	induce	NOUN
ejpam-3990	4	56	.	.	PUNCT
ejpam-3990	5	1	indeed	indeed	ADV
ejpam-3990	5	2	,	,	PUNCT
ejpam-3990	5	3	it	it	PRON
ejpam-3990	5	4	is	be	AUX
ejpam-3990	5	5	well	well	ADV
ejpam-3990	5	6	known	know	VERB
ejpam-3990	5	7	that	that	SCONJ
ejpam-3990	5	8	every	every	DET
ejpam-3990	5	9	metric	metric	ADJ
ejpam-3990	5	10	space	space	NOUN
ejpam-3990	5	11	is	be	AUX
ejpam-3990	5	12	a	a	DET
ejpam-3990	5	13	topological	topological	ADJ
ejpam-3990	5	14	space	space	NOUN
ejpam-3990	5	15	.	.	PUNCT
ejpam-3990	6	1	topologizing	topologize	VERB
ejpam-3990	6	2	a	a	DET
ejpam-3990	6	3	non	non	ADJ
ejpam-3990	6	4	-	-	ADJ
ejpam-3990	6	5	empty	empty	ADJ
ejpam-3990	6	6	set	set	NOUN
ejpam-3990	6	7	can	can	AUX
ejpam-3990	6	8	well	well	ADV
ejpam-3990	6	9	be	be	AUX
ejpam-3990	6	10	done	do	VERB
ejpam-3990	6	11	by	by	ADP
ejpam-3990	6	12	using	use	VERB
ejpam-3990	6	13	a	a	DET
ejpam-3990	6	14	family	family	NOUN
ejpam-3990	6	15	of	of	ADP
ejpam-3990	6	16	subsets	subset	NOUN
ejpam-3990	6	17	of	of	ADP
ejpam-3990	6	18	the	the	DET
ejpam-3990	6	19	set	set	NOUN
ejpam-3990	6	20	(	(	PUNCT
ejpam-3990	6	21	as	as	SCONJ
ejpam-3990	6	22	done	do	VERB
ejpam-3990	6	23	in	in	ADP
ejpam-3990	6	24	a	a	DET
ejpam-3990	6	25	metric	metric	ADJ
ejpam-3990	6	26	space	space	NOUN
ejpam-3990	6	27	)	)	PUNCT
ejpam-3990	6	28	that	that	PRON
ejpam-3990	6	29	will	will	AUX
ejpam-3990	6	30	serve	serve	VERB
ejpam-3990	6	31	as	as	ADP
ejpam-3990	6	32	a	a	DET
ejpam-3990	6	33	base	base	NOUN
ejpam-3990	6	34	of	of	ADP
ejpam-3990	6	35	some	some	DET
ejpam-3990	6	36	topology	topology	NOUN
ejpam-3990	6	37	on	on	ADP
ejpam-3990	6	38	the	the	DET
ejpam-3990	6	39	given	give	VERB
ejpam-3990	6	40	set	set	NOUN
ejpam-3990	6	41	.	.	PUNCT
ejpam-3990	7	1	recently	recently	ADV
ejpam-3990	7	2	,	,	PUNCT
ejpam-3990	7	3	topologizing	topologize	VERB
ejpam-3990	7	4	the	the	DET
ejpam-3990	7	5	vertex	vertex	NOUN
ejpam-3990	7	6	set	set	NOUN
ejpam-3990	7	7	of	of	ADP
ejpam-3990	7	8	a	a	DET
ejpam-3990	7	9	given	give	VERB
ejpam-3990	7	10	graph	graph	NOUN
ejpam-3990	7	11	was	be	AUX
ejpam-3990	7	12	done	do	VERB
ejpam-3990	7	13	to	to	PART
ejpam-3990	7	14	obtain	obtain	VERB
ejpam-3990	7	15	topological	topological	ADJ
ejpam-3990	7	16	spaces	space	NOUN
ejpam-3990	7	17	from	from	ADP
ejpam-3990	7	18	a	a	DET
ejpam-3990	7	19	given	give	VERB
ejpam-3990	7	20	graph	graph	NOUN
ejpam-3990	7	21	.	.	PUNCT
ejpam-3990	7	22	gervacio	gervacio	NOUN
ejpam-3990	7	23	and	and	CCONJ
ejpam-3990	7	24	diesto	diesto	ADJ
ejpam-3990	8	1	[	[	X
ejpam-3990	8	2	2	2	NUM
ejpam-3990	8	3	]	]	PUNCT
ejpam-3990	8	4	used	use	VERB
ejpam-3990	8	5	the	the	DET
ejpam-3990	8	6	standard	standard	ADJ
ejpam-3990	8	7	neighborhoods	neighborhood	NOUN
ejpam-3990	8	8	of	of	ADP
ejpam-3990	8	9	a	a	DET
ejpam-3990	8	10	graph	graph	NOUN
ejpam-3990	8	11	to	to	PART
ejpam-3990	8	12	construct	construct	VERB
ejpam-3990	8	13	a	a	DET
ejpam-3990	8	14	topology	topology	NOUN
ejpam-3990	8	15	on	on	ADP
ejpam-3990	8	16	its	its	PRON
ejpam-3990	8	17	vertex	vertex	NOUN
ejpam-3990	8	18	set	set	NOUN
ejpam-3990	8	19	.	.	PUNCT
ejpam-3990	9	1	admittedly	admittedly	ADV
ejpam-3990	9	2	,	,	PUNCT
ejpam-3990	9	3	due	due	ADP
ejpam-3990	9	4	to	to	ADP
ejpam-3990	9	5	its	its	PRON
ejpam-3990	9	6	limited	limited	ADJ
ejpam-3990	9	7	circulation	circulation	NOUN
ejpam-3990	9	8	,	,	PUNCT
ejpam-3990	9	9	the	the	DET
ejpam-3990	9	10	work	work	NOUN
ejpam-3990	9	11	is	be	AUX
ejpam-3990	9	12	not	not	PART
ejpam-3990	9	13	so	so	ADV
ejpam-3990	9	14	popular	popular	ADJ
ejpam-3990	9	15	.	.	PUNCT
ejpam-3990	10	1	this	this	DET
ejpam-3990	10	2	construction	construction	NOUN
ejpam-3990	10	3	,	,	PUNCT
ejpam-3990	10	4	however	however	ADV
ejpam-3990	10	5	,	,	PUNCT
ejpam-3990	10	6	was	be	AUX
ejpam-3990	10	7	further	far	ADV
ejpam-3990	10	8	studied	study	VERB
ejpam-3990	10	9	in	in	ADP
ejpam-3990	10	10	[	[	X
ejpam-3990	10	11	3	3	NUM
ejpam-3990	10	12	]	]	PUNCT
ejpam-3990	10	13	,	,	PUNCT
ejpam-3990	10	14	[	[	X
ejpam-3990	10	15	6	6	NUM
ejpam-3990	10	16	]	]	PUNCT
ejpam-3990	10	17	and	and	CCONJ
ejpam-3990	10	18	[	[	X
ejpam-3990	10	19	1	1	NUM
ejpam-3990	10	20	]	]	PUNCT
ejpam-3990	10	21	.	.	PUNCT
ejpam-3990	11	1	nianga	nianga	PROPN
ejpam-3990	11	2	and	and	CCONJ
ejpam-3990	11	3	canoy	canoy	ADJ
ejpam-3990	11	4	in	in	ADP
ejpam-3990	11	5	[	[	X
ejpam-3990	11	6	8	8	NUM
ejpam-3990	11	7	]	]	PUNCT
ejpam-3990	11	8	presented	present	VERB
ejpam-3990	11	9	another	another	DET
ejpam-3990	11	10	way	way	NOUN
ejpam-3990	11	11	of	of	ADP
ejpam-3990	11	12	generating	generate	VERB
ejpam-3990	11	13	a	a	DET
ejpam-3990	11	14	topology	topology	NOUN
ejpam-3990	11	15	on	on	ADP
ejpam-3990	11	16	a	a	DET
ejpam-3990	11	17	graph	graph	NOUN
ejpam-3990	11	18	using	use	VERB
ejpam-3990	11	19	the	the	DET
ejpam-3990	11	20	hop	hop	NOUN
ejpam-3990	11	21	or	or	CCONJ
ejpam-3990	11	22	2	2	NUM
ejpam-3990	11	23	-	-	PUNCT
ejpam-3990	11	24	step	step	NOUN
ejpam-3990	11	25	neighborhoods	neighborhood	NOUN
ejpam-3990	11	26	of	of	ADP
ejpam-3990	11	27	a	a	DET
ejpam-3990	11	28	graph	graph	NOUN
ejpam-3990	11	29	.	.	PUNCT
ejpam-3990	12	1	they	they	PRON
ejpam-3990	12	2	further	far	ADV
ejpam-3990	12	3	investigated	investigate	VERB
ejpam-3990	12	4	in	in	ADP
ejpam-3990	12	5	[	[	X
ejpam-3990	12	6	9	9	NUM
ejpam-3990	12	7	]	]	PUNCT
ejpam-3990	12	8	,	,	PUNCT
ejpam-3990	12	9	the	the	DET
ejpam-3990	12	10	topologies	topology	NOUN
ejpam-3990	12	11	induced	induce	VERB
ejpam-3990	12	12	by	by	ADP
ejpam-3990	12	13	the	the	DET
ejpam-3990	12	14	complement	complement	NOUN
ejpam-3990	12	15	of	of	ADP
ejpam-3990	12	16	a	a	DET
ejpam-3990	12	17	graph	graph	NOUN
ejpam-3990	12	18	,	,	PUNCT
ejpam-3990	12	19	the	the	DET
ejpam-3990	12	20	join	join	NOUN
ejpam-3990	12	21	,	,	PUNCT
ejpam-3990	12	22	corona	corona	NOUN
ejpam-3990	12	23	,	,	PUNCT
ejpam-3990	12	24	composition	composition	NOUN
ejpam-3990	12	25	and	and	CCONJ
ejpam-3990	12	26	the	the	DET
ejpam-3990	12	27	∗corresponding	∗corresponde	VERB
ejpam-3990	12	28	author	author	NOUN
ejpam-3990	12	29	.	.	PUNCT
ejpam-3990	13	1	doi	doi	NOUN
ejpam-3990	13	2	:	:	PUNCT
ejpam-3990	13	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3990	https://doi.org/10.29020/nybg.ejpam.v14i3.3990	ADP
ejpam-3990	13	4	email	email	NOUN
ejpam-3990	13	5	addresses	address	NOUN
ejpam-3990	13	6	:	:	PUNCT
ejpam-3990	13	7	anabel.gamorez@wmsu.edu.ph	anabel.gamorez@wmsu.edu.ph	X
ejpam-3990	13	8	(	(	PUNCT
ejpam-3990	13	9	a.	a.	NOUN
ejpam-3990	13	10	gamorez	gamorez	PROPN
ejpam-3990	13	11	)	)	PUNCT
ejpam-3990	13	12	,	,	PUNCT
ejpam-3990	13	13	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-3990	13	14	(	(	PUNCT
ejpam-3990	13	15	s.	s.	PROPN
ejpam-3990	13	16	canoy	canoy	PROPN
ejpam-3990	13	17	jr	jr	PROPN
ejpam-3990	13	18	.	.	PUNCT
ejpam-3990	13	19	)	)	PUNCT
ejpam-3990	13	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3990	14	1	695	695	NUM
ejpam-3990	14	2	©	©	ADP
ejpam-3990	14	3	2021	2021	NUM
ejpam-3990	14	4	ejpam	ejpam	VERB
ejpam-3990	14	5	all	all	DET
ejpam-3990	14	6	rights	right	NOUN
ejpam-3990	14	7	reserved	reserve	VERB
ejpam-3990	14	8	.	.	PUNCT
ejpam-3990	15	1	a.	a.	PROPN
ejpam-3990	15	2	gamorez	gamorez	PROPN
ejpam-3990	15	3	,	,	PUNCT
ejpam-3990	15	4	s.	s.	PROPN
ejpam-3990	15	5	canoy	canoy	PROPN
ejpam-3990	15	6	jr	jr	PROPN
ejpam-3990	15	7	.	.	PROPN
ejpam-3990	15	8	/	/	SYM
ejpam-3990	15	9	eur	eur	PROPN
ejpam-3990	15	10	.	.	PUNCT
ejpam-3990	16	1	j.	j.	PROPN
ejpam-3990	16	2	pure	pure	PROPN
ejpam-3990	16	3	appl	appl	PROPN
ejpam-3990	16	4	.	.	PROPN
ejpam-3990	16	5	math	math	PROPN
ejpam-3990	16	6	,	,	PUNCT
ejpam-3990	16	7	14	14	NUM
ejpam-3990	16	8	(	(	PUNCT
ejpam-3990	16	9	3	3	NUM
ejpam-3990	16	10	)	)	PUNCT
ejpam-3990	16	11	(	(	PUNCT
ejpam-3990	16	12	2021	2021	NUM
ejpam-3990	16	13	)	)	PUNCT
ejpam-3990	16	14	,	,	PUNCT
ejpam-3990	16	15	695	695	NUM
ejpam-3990	16	16	-	-	SYM
ejpam-3990	16	17	705	705	NUM
ejpam-3990	16	18	696	696	NUM
ejpam-3990	16	19	cartesian	cartesian	ADJ
ejpam-3990	16	20	product	product	NOUN
ejpam-3990	16	21	of	of	ADP
ejpam-3990	16	22	graphs	graph	NOUN
ejpam-3990	16	23	.	.	PUNCT
ejpam-3990	17	1	the	the	DET
ejpam-3990	17	2	same	same	ADJ
ejpam-3990	17	3	construction	construction	NOUN
ejpam-3990	17	4	was	be	AUX
ejpam-3990	17	5	also	also	ADV
ejpam-3990	17	6	studied	study	VERB
ejpam-3990	17	7	by	by	ADP
ejpam-3990	17	8	canoy	canoy	NOUN
ejpam-3990	17	9	and	and	CCONJ
ejpam-3990	17	10	gimeno	gimeno	VERB
ejpam-3990	17	11	[	[	X
ejpam-3990	17	12	4	4	NUM
ejpam-3990	17	13	]	]	PUNCT
ejpam-3990	17	14	.	.	PUNCT
ejpam-3990	18	1	in	in	ADP
ejpam-3990	18	2	this	this	DET
ejpam-3990	18	3	paper	paper	NOUN
ejpam-3990	18	4	we	we	PRON
ejpam-3990	18	5	construct	construct	VERB
ejpam-3990	18	6	a	a	DET
ejpam-3990	18	7	topology	topology	NOUN
ejpam-3990	18	8	on	on	ADP
ejpam-3990	18	9	a	a	DET
ejpam-3990	18	10	vertex	vertex	NOUN
ejpam-3990	18	11	set	set	NOUN
ejpam-3990	18	12	of	of	ADP
ejpam-3990	18	13	a	a	DET
ejpam-3990	18	14	graph	graph	NOUN
ejpam-3990	18	15	using	use	VERB
ejpam-3990	18	16	its	its	PRON
ejpam-3990	18	17	monophonic	monophonic	ADJ
ejpam-3990	18	18	eccentric	eccentric	ADJ
ejpam-3990	18	19	neigbhorhoods	neigbhorhood	NOUN
ejpam-3990	18	20	and	and	CCONJ
ejpam-3990	18	21	investigate	investigate	VERB
ejpam-3990	18	22	some	some	PRON
ejpam-3990	18	23	of	of	ADP
ejpam-3990	18	24	the	the	DET
ejpam-3990	18	25	topological	topological	ADJ
ejpam-3990	18	26	structures	structure	NOUN
ejpam-3990	18	27	and	and	CCONJ
ejpam-3990	18	28	properties	property	NOUN
ejpam-3990	18	29	of	of	ADP
ejpam-3990	18	30	the	the	DET
ejpam-3990	18	31	space	space	NOUN
ejpam-3990	18	32	generated	generate	VERB
ejpam-3990	18	33	.	.	PUNCT
ejpam-3990	19	1	under	under	ADP
ejpam-3990	19	2	this	this	DET
ejpam-3990	19	3	construction	construction	NOUN
ejpam-3990	19	4	we	we	PRON
ejpam-3990	19	5	,	,	PUNCT
ejpam-3990	19	6	among	among	ADP
ejpam-3990	19	7	others	other	NOUN
ejpam-3990	19	8	,	,	PUNCT
ejpam-3990	19	9	characterize	characterize	VERB
ejpam-3990	19	10	those	those	DET
ejpam-3990	19	11	graphs	graph	NOUN
ejpam-3990	19	12	that	that	PRON
ejpam-3990	19	13	induced	induce	VERB
ejpam-3990	19	14	the	the	DET
ejpam-3990	19	15	indiscrete	indiscrete	ADJ
ejpam-3990	19	16	topology	topology	NOUN
ejpam-3990	19	17	,	,	PUNCT
ejpam-3990	19	18	the	the	DET
ejpam-3990	19	19	discrete	discrete	ADJ
ejpam-3990	19	20	topology	topology	NOUN
ejpam-3990	19	21	and	and	CCONJ
ejpam-3990	19	22	a	a	DET
ejpam-3990	19	23	particular	particular	ADJ
ejpam-3990	19	24	point	point	NOUN
ejpam-3990	19	25	topology	topology	NOUN
ejpam-3990	19	26	.	.	PUNCT
ejpam-3990	20	1	for	for	ADP
ejpam-3990	20	2	any	any	DET
ejpam-3990	20	3	two	two	NUM
ejpam-3990	20	4	vertices	vertex	NOUN
ejpam-3990	20	5	u	u	NOUN
ejpam-3990	20	6	and	and	CCONJ
ejpam-3990	20	7	v	v	NOUN
ejpam-3990	20	8	in	in	ADP
ejpam-3990	20	9	a	a	DET
ejpam-3990	20	10	graph	graph	NOUN
ejpam-3990	20	11	g	g	NOUN
ejpam-3990	20	12	,	,	PUNCT
ejpam-3990	20	13	the	the	DET
ejpam-3990	20	14	distance	distance	NOUN
ejpam-3990	20	15	dg(u	dg(u	X
ejpam-3990	20	16	,	,	PUNCT
ejpam-3990	20	17	v	v	NOUN
ejpam-3990	20	18	)	)	PUNCT
ejpam-3990	20	19	is	be	AUX
ejpam-3990	20	20	the	the	DET
ejpam-3990	20	21	length	length	NOUN
ejpam-3990	20	22	of	of	ADP
ejpam-3990	20	23	a	a	DET
ejpam-3990	20	24	shortest	short	ADJ
ejpam-3990	20	25	path	path	NOUN
ejpam-3990	20	26	joining	join	VERB
ejpam-3990	20	27	u	u	PROPN
ejpam-3990	20	28	and	and	CCONJ
ejpam-3990	20	29	v.	v.	ADP
ejpam-3990	20	30	the	the	DET
ejpam-3990	20	31	open	open	ADJ
ejpam-3990	20	32	neighborhood	neighborhood	NOUN
ejpam-3990	20	33	of	of	ADP
ejpam-3990	20	34	a	a	DET
ejpam-3990	20	35	point	point	NOUN
ejpam-3990	20	36	u	u	NOUN
ejpam-3990	20	37	is	be	AUX
ejpam-3990	20	38	the	the	DET
ejpam-3990	20	39	set	set	NOUN
ejpam-3990	20	40	ng(u	ng(u	NOUN
ejpam-3990	20	41	)	)	PUNCT
ejpam-3990	20	42	consisting	consist	VERB
ejpam-3990	20	43	of	of	ADP
ejpam-3990	20	44	all	all	DET
ejpam-3990	20	45	points	point	NOUN
ejpam-3990	20	46	v	v	NUM
ejpam-3990	20	47	which	which	PRON
ejpam-3990	20	48	are	be	AUX
ejpam-3990	20	49	adjacent	adjacent	ADJ
ejpam-3990	20	50	to	to	PART
ejpam-3990	20	51	u.	u.	VERB
ejpam-3990	20	52	the	the	DET
ejpam-3990	20	53	closed	closed	ADJ
ejpam-3990	20	54	neighborhood	neighborhood	NOUN
ejpam-3990	20	55	of	of	ADP
ejpam-3990	20	56	u	u	NOUN
ejpam-3990	20	57	is	be	AUX
ejpam-3990	20	58	ng[u	ng[u	PROPN
ejpam-3990	20	59	]	]	X
ejpam-3990	20	60	=	=	PUNCT
ejpam-3990	20	61	ng(u)∪{u	ng(u)∪{u	VERB
ejpam-3990	20	62	}	}	PUNCT
ejpam-3990	20	63	.	.	PUNCT
ejpam-3990	21	1	for	for	ADP
ejpam-3990	21	2	any	any	DET
ejpam-3990	21	3	a	a	DET
ejpam-3990	21	4	⊆	⊆	NUM
ejpam-3990	21	5	v	v	NOUN
ejpam-3990	21	6	(	(	PUNCT
ejpam-3990	21	7	g	g	NOUN
ejpam-3990	21	8	)	)	PUNCT
ejpam-3990	21	9	,	,	PUNCT
ejpam-3990	21	10	ng(a	ng(a	X
ejpam-3990	21	11	)	)	PUNCT
ejpam-3990	21	12	=	=	PUNCT
ejpam-3990	21	13	⋃	⋃	NOUN
ejpam-3990	21	14	v∈a	v∈a	NOUN
ejpam-3990	21	15	ng(v	ng(v	PUNCT
ejpam-3990	21	16	)	)	PUNCT
ejpam-3990	21	17	is	be	AUX
ejpam-3990	21	18	called	call	VERB
ejpam-3990	21	19	the	the	DET
ejpam-3990	21	20	open	open	ADJ
ejpam-3990	21	21	neighborhood	neighborhood	NOUN
ejpam-3990	21	22	of	of	ADP
ejpam-3990	21	23	a	a	PRON
ejpam-3990	21	24	and	and	CCONJ
ejpam-3990	21	25	ng[a	ng[a	NOUN
ejpam-3990	21	26	]	]	X
ejpam-3990	22	1	=	=	SYM
ejpam-3990	22	2	ng(a)∪a	ng(a)∪a	PROPN
ejpam-3990	22	3	is	be	AUX
ejpam-3990	22	4	called	call	VERB
ejpam-3990	22	5	the	the	DET
ejpam-3990	22	6	closed	closed	ADJ
ejpam-3990	22	7	neighborhood	neighborhood	NOUN
ejpam-3990	22	8	of	of	ADP
ejpam-3990	22	9	a.	a.	NOUN
ejpam-3990	22	10	the	the	DET
ejpam-3990	22	11	complement	complement	NOUN
ejpam-3990	22	12	of	of	ADP
ejpam-3990	22	13	ng[a	ng[a	PROPN
ejpam-3990	22	14	]	]	PUNCT
ejpam-3990	22	15	is	be	AUX
ejpam-3990	22	16	denoted	denote	VERB
ejpam-3990	22	17	by	by	ADP
ejpam-3990	22	18	fg[a	fg[a	PROPN
ejpam-3990	22	19	]	]	PUNCT
ejpam-3990	22	20	that	that	ADV
ejpam-3990	22	21	is	be	AUX
ejpam-3990	22	22	,	,	PUNCT
ejpam-3990	22	23	fg[a	fg[a	PROPN
ejpam-3990	22	24	]	]	X
ejpam-3990	23	1	=	=	SYM
ejpam-3990	23	2	v	v	X
ejpam-3990	23	3	(	(	PUNCT
ejpam-3990	23	4	g)\ng[a	g)\ng[a	PROPN
ejpam-3990	23	5	]	]	PUNCT
ejpam-3990	23	6	.	.	PUNCT
ejpam-3990	24	1	if	if	SCONJ
ejpam-3990	24	2	a	a	DET
ejpam-3990	24	3	=	=	X
ejpam-3990	24	4	{	{	PUNCT
ejpam-3990	24	5	v	v	NOUN
ejpam-3990	24	6	}	}	PUNCT
ejpam-3990	24	7	,	,	PUNCT
ejpam-3990	24	8	then	then	ADV
ejpam-3990	24	9	we	we	PRON
ejpam-3990	24	10	write	write	VERB
ejpam-3990	24	11	fg[a	fg[a	PROPN
ejpam-3990	24	12	]	]	X
ejpam-3990	25	1	=	=	PUNCT
ejpam-3990	25	2	fg[v	fg[v	PROPN
ejpam-3990	25	3	]	]	X
ejpam-3990	25	4	.	.	PUNCT
ejpam-3990	26	1	for	for	ADP
ejpam-3990	26	2	each	each	DET
ejpam-3990	26	3	v	v	NUM
ejpam-3990	26	4	∈	∈	PROPN
ejpam-3990	26	5	v	v	NOUN
ejpam-3990	26	6	(	(	PUNCT
ejpam-3990	26	7	g	g	NOUN
ejpam-3990	26	8	)	)	PUNCT
ejpam-3990	26	9	,	,	PUNCT
ejpam-3990	26	10	n2	n2	ADJ
ejpam-3990	26	11	g(v	g(v	X
ejpam-3990	26	12	)	)	PUNCT
ejpam-3990	26	13	=	=	PRON
ejpam-3990	26	14	{	{	PUNCT
ejpam-3990	26	15	u	u	NOUN
ejpam-3990	26	16	∈	∈	PROPN
ejpam-3990	26	17	v	v	NOUN
ejpam-3990	26	18	(	(	PUNCT
ejpam-3990	26	19	g	g	NOUN
ejpam-3990	26	20	)	)	PUNCT
ejpam-3990	26	21	:	:	PUNCT
ejpam-3990	26	22	dg(u	dg(u	X
ejpam-3990	26	23	,	,	PUNCT
ejpam-3990	26	24	v	v	NOUN
ejpam-3990	26	25	)	)	PUNCT
ejpam-3990	26	26	=	=	SYM
ejpam-3990	27	1	2	2	X
ejpam-3990	27	2	}	}	PUNCT
ejpam-3990	27	3	is	be	AUX
ejpam-3990	27	4	called	call	VERB
ejpam-3990	27	5	the	the	DET
ejpam-3990	27	6	open	open	ADJ
ejpam-3990	27	7	hop	hop	NOUN
ejpam-3990	27	8	neighborhood	neighborhood	NOUN
ejpam-3990	27	9	of	of	ADP
ejpam-3990	27	10	v	v	NOUN
ejpam-3990	27	11	and	and	CCONJ
ejpam-3990	27	12	n2	n2	ADJ
ejpam-3990	27	13	g[v	g[v	NOUN
ejpam-3990	27	14	]	]	X
ejpam-3990	27	15	=	=	SYM
ejpam-3990	27	16	{	{	PUNCT
ejpam-3990	27	17	v	v	NOUN
ejpam-3990	27	18	}	}	PUNCT
ejpam-3990	27	19	∪n2	∪n2	ADJ
ejpam-3990	27	20	g(v	g(v	NOUN
ejpam-3990	27	21	)	)	PUNCT
ejpam-3990	27	22	is	be	AUX
ejpam-3990	27	23	called	call	VERB
ejpam-3990	27	24	the	the	DET
ejpam-3990	27	25	closed	closed	ADJ
ejpam-3990	27	26	hop	hop	NOUN
ejpam-3990	27	27	neighborhood	neighborhood	NOUN
ejpam-3990	27	28	of	of	ADP
ejpam-3990	27	29	v.	v.	NOUN
ejpam-3990	27	30	for	for	ADP
ejpam-3990	27	31	any	any	DET
ejpam-3990	27	32	a	a	DET
ejpam-3990	27	33	⊆	⊆	NUM
ejpam-3990	27	34	v	v	NOUN
ejpam-3990	27	35	(	(	PUNCT
ejpam-3990	27	36	g	g	NOUN
ejpam-3990	27	37	)	)	PUNCT
ejpam-3990	27	38	,	,	PUNCT
ejpam-3990	27	39	n2	n2	PROPN
ejpam-3990	27	40	g(a	g(a	PROPN
ejpam-3990	27	41	)	)	PUNCT
ejpam-3990	28	1	=	=	PUNCT
ejpam-3990	28	2	⋃	⋃	ADP
ejpam-3990	28	3	a∈a	a∈a	ADJ
ejpam-3990	28	4	n2	n2	PROPN
ejpam-3990	28	5	g(a	g(a	PROPN
ejpam-3990	28	6	)	)	PUNCT
ejpam-3990	28	7	=	=	PRON
ejpam-3990	28	8	{	{	PUNCT
ejpam-3990	28	9	v	v	NUM
ejpam-3990	28	10	∈	∈	NOUN
ejpam-3990	28	11	v	v	NOUN
ejpam-3990	28	12	(	(	PUNCT
ejpam-3990	28	13	g	g	NOUN
ejpam-3990	28	14	)	)	PUNCT
ejpam-3990	28	15	:	:	PUNCT
ejpam-3990	28	16	n2	n2	ADJ
ejpam-3990	28	17	g(v	g(v	PROPN
ejpam-3990	28	18	)	)	PUNCT
ejpam-3990	28	19	∩	∩	NOUN
ejpam-3990	28	20	a	a	DET
ejpam-3990	28	21	6=	6=	NOUN
ejpam-3990	28	22	∅	∅	NOUN
ejpam-3990	28	23	}	}	PUNCT
ejpam-3990	28	24	is	be	AUX
ejpam-3990	28	25	called	call	VERB
ejpam-3990	28	26	the	the	DET
ejpam-3990	28	27	open	open	ADJ
ejpam-3990	28	28	hop	hop	NOUN
ejpam-3990	28	29	neighborhood	neighborhood	NOUN
ejpam-3990	28	30	of	of	ADP
ejpam-3990	28	31	a	a	DET
ejpam-3990	28	32	and	and	CCONJ
ejpam-3990	28	33	n2	n2	ADJ
ejpam-3990	28	34	g[a	g[a	NOUN
ejpam-3990	28	35	]	]	X
ejpam-3990	28	36	=	=	PUNCT
ejpam-3990	28	37	a	a	DET
ejpam-3990	28	38	∪	∪	ADJ
ejpam-3990	28	39	n2	n2	PROPN
ejpam-3990	28	40	g(a	g(a	PROPN
ejpam-3990	28	41	)	)	PUNCT
ejpam-3990	28	42	is	be	AUX
ejpam-3990	28	43	the	the	DET
ejpam-3990	28	44	closed	closed	ADJ
ejpam-3990	28	45	hop	hop	NOUN
ejpam-3990	28	46	neighborhood	neighborhood	NOUN
ejpam-3990	28	47	of	of	ADP
ejpam-3990	28	48	a.	a.	NOUN
ejpam-3990	28	49	denote	denote	NOUN
ejpam-3990	28	50	by	by	ADP
ejpam-3990	28	51	f	f	PROPN
ejpam-3990	28	52	2	2	NUM
ejpam-3990	28	53	g[a	g[a	NOUN
ejpam-3990	28	54	]	]	X
ejpam-3990	28	55	the	the	DET
ejpam-3990	28	56	complement	complement	NOUN
ejpam-3990	28	57	of	of	ADP
ejpam-3990	28	58	n2	n2	ADJ
ejpam-3990	28	59	g[a	g[a	PROPN
ejpam-3990	28	60	]	]	X
ejpam-3990	28	61	,	,	PUNCT
ejpam-3990	28	62	that	that	ADV
ejpam-3990	28	63	is	is	ADV
ejpam-3990	28	64	,	,	PUNCT
ejpam-3990	28	65	f	f	PROPN
ejpam-3990	28	66	2	2	NUM
ejpam-3990	28	67	g[a	g[a	NOUN
ejpam-3990	28	68	]	]	X
ejpam-3990	28	69	=	=	SYM
ejpam-3990	28	70	v	v	X
ejpam-3990	28	71	(	(	PUNCT
ejpam-3990	28	72	g)\n2	g)\n2	NOUN
ejpam-3990	28	73	g[a	g[a	NOUN
ejpam-3990	28	74	]	]	X
ejpam-3990	28	75	.	.	PUNCT
ejpam-3990	29	1	recently	recently	ADV
ejpam-3990	29	2	,	,	PUNCT
ejpam-3990	29	3	titus	titus	PROPN
ejpam-3990	30	1	[	[	X
ejpam-3990	30	2	10	10	NUM
ejpam-3990	30	3	]	]	PUNCT
ejpam-3990	30	4	introduced	introduce	VERB
ejpam-3990	30	5	some	some	DET
ejpam-3990	30	6	concepts	concept	NOUN
ejpam-3990	30	7	related	relate	VERB
ejpam-3990	30	8	to	to	ADP
ejpam-3990	30	9	monophonic	monophonic	ADJ
ejpam-3990	30	10	paths	path	NOUN
ejpam-3990	30	11	in	in	ADP
ejpam-3990	30	12	a	a	DET
ejpam-3990	30	13	graph	graph	NOUN
ejpam-3990	30	14	.	.	PUNCT
ejpam-3990	31	1	a	a	DET
ejpam-3990	31	2	chord	chord	NOUN
ejpam-3990	31	3	of	of	ADP
ejpam-3990	31	4	a	a	DET
ejpam-3990	31	5	path	path	NOUN
ejpam-3990	31	6	p	p	NOUN
ejpam-3990	31	7	in	in	ADP
ejpam-3990	31	8	a	a	DET
ejpam-3990	31	9	graph	graph	NOUN
ejpam-3990	31	10	g	g	NOUN
ejpam-3990	31	11	is	be	AUX
ejpam-3990	31	12	an	an	DET
ejpam-3990	31	13	edge	edge	NOUN
ejpam-3990	31	14	joining	join	VERB
ejpam-3990	31	15	two	two	NUM
ejpam-3990	31	16	non	non	ADJ
ejpam-3990	31	17	-	-	ADJ
ejpam-3990	31	18	adjacent	adjacent	ADJ
ejpam-3990	31	19	vertices	vertex	NOUN
ejpam-3990	31	20	of	of	ADP
ejpam-3990	31	21	p	p	NOUN
ejpam-3990	31	22	.	.	PUNCT
ejpam-3990	32	1	a	a	DET
ejpam-3990	32	2	p	p	NOUN
ejpam-3990	32	3	in	in	ADP
ejpam-3990	32	4	a	a	DET
ejpam-3990	32	5	graph	graph	NOUN
ejpam-3990	32	6	g	g	NOUN
ejpam-3990	32	7	is	be	AUX
ejpam-3990	32	8	called	call	VERB
ejpam-3990	32	9	a	a	DET
ejpam-3990	32	10	monophonic	monophonic	ADJ
ejpam-3990	32	11	path	path	NOUN
ejpam-3990	32	12	if	if	SCONJ
ejpam-3990	32	13	it	it	PRON
ejpam-3990	32	14	is	be	AUX
ejpam-3990	32	15	chordless	chordless	ADJ
ejpam-3990	32	16	.	.	PUNCT
ejpam-3990	33	1	for	for	ADP
ejpam-3990	33	2	any	any	DET
ejpam-3990	33	3	two	two	NUM
ejpam-3990	33	4	vertices	vertex	NOUN
ejpam-3990	33	5	u	u	NOUN
ejpam-3990	33	6	and	and	CCONJ
ejpam-3990	33	7	v	v	NOUN
ejpam-3990	33	8	in	in	ADP
ejpam-3990	33	9	a	a	DET
ejpam-3990	33	10	connected	connected	ADJ
ejpam-3990	33	11	graph	graph	NOUN
ejpam-3990	33	12	g	g	NOUN
ejpam-3990	33	13	,	,	PUNCT
ejpam-3990	33	14	the	the	DET
ejpam-3990	33	15	monophonic	monophonic	ADJ
ejpam-3990	33	16	distance	distance	NOUN
ejpam-3990	33	17	dmg	dmg	NOUN
ejpam-3990	33	18	(	(	PUNCT
ejpam-3990	33	19	u	u	NOUN
ejpam-3990	33	20	,	,	PUNCT
ejpam-3990	33	21	v	v	NOUN
ejpam-3990	33	22	)	)	PUNCT
ejpam-3990	33	23	from	from	ADP
ejpam-3990	33	24	u	u	PRON
ejpam-3990	33	25	to	to	ADP
ejpam-3990	33	26	v	v	NOUN
ejpam-3990	33	27	is	be	AUX
ejpam-3990	33	28	defined	define	VERB
ejpam-3990	33	29	as	as	ADP
ejpam-3990	33	30	the	the	DET
ejpam-3990	33	31	length	length	NOUN
ejpam-3990	33	32	of	of	ADP
ejpam-3990	33	33	a	a	DET
ejpam-3990	33	34	longest	long	ADJ
ejpam-3990	33	35	u	u	NOUN
ejpam-3990	33	36	-	-	ADJ
ejpam-3990	33	37	v	v	ADJ
ejpam-3990	33	38	monophonic	monophonic	ADJ
ejpam-3990	33	39	path	path	NOUN
ejpam-3990	33	40	in	in	ADP
ejpam-3990	33	41	g.	g.	PROPN
ejpam-3990	33	42	the	the	DET
ejpam-3990	33	43	monophonic	monophonic	ADJ
ejpam-3990	33	44	eccentricity	eccentricity	NOUN
ejpam-3990	33	45	emg	emg	NOUN
ejpam-3990	33	46	(	(	PUNCT
ejpam-3990	33	47	v	v	NOUN
ejpam-3990	33	48	)	)	PUNCT
ejpam-3990	33	49	of	of	ADP
ejpam-3990	33	50	a	a	DET
ejpam-3990	33	51	vertex	vertex	NOUN
ejpam-3990	33	52	v	v	NOUN
ejpam-3990	33	53	in	in	ADP
ejpam-3990	33	54	g	g	PROPN
ejpam-3990	33	55	is	be	AUX
ejpam-3990	33	56	the	the	DET
ejpam-3990	33	57	maximum	maximum	ADJ
ejpam-3990	33	58	monophonic	monophonic	ADJ
ejpam-3990	33	59	distance	distance	NOUN
ejpam-3990	33	60	from	from	ADP
ejpam-3990	33	61	v	v	NUM
ejpam-3990	33	62	to	to	ADP
ejpam-3990	33	63	a	a	DET
ejpam-3990	33	64	vertex	vertex	NOUN
ejpam-3990	33	65	of	of	ADP
ejpam-3990	33	66	g.	g.	PROPN
ejpam-3990	33	67	the	the	DET
ejpam-3990	33	68	monophonic	monophonic	ADJ
ejpam-3990	33	69	radius	radius	PROPN
ejpam-3990	33	70	radm(g	radm(g	PROPN
ejpam-3990	33	71	)	)	PUNCT
ejpam-3990	33	72	of	of	ADP
ejpam-3990	33	73	graph	graph	NOUN
ejpam-3990	33	74	g	g	PROPN
ejpam-3990	33	75	is	be	AUX
ejpam-3990	33	76	radm(g	radm(g	NOUN
ejpam-3990	33	77	)	)	PUNCT
ejpam-3990	34	1	=	=	VERB
ejpam-3990	34	2	min{emg	min{emg	NOUN
ejpam-3990	34	3	(	(	PUNCT
ejpam-3990	34	4	v	v	NOUN
ejpam-3990	34	5	)	)	PUNCT
ejpam-3990	34	6	:	:	PUNCT
ejpam-3990	35	1	v	v	X
ejpam-3990	35	2	∈	∈	PROPN
ejpam-3990	35	3	v	v	NOUN
ejpam-3990	35	4	(	(	PUNCT
ejpam-3990	35	5	g	g	NOUN
ejpam-3990	35	6	)	)	PUNCT
ejpam-3990	35	7	}	}	PUNCT
ejpam-3990	35	8	.	.	PUNCT
ejpam-3990	36	1	a	a	DET
ejpam-3990	36	2	vertex	vertex	NOUN
ejpam-3990	36	3	w	w	NOUN
ejpam-3990	36	4	in	in	ADP
ejpam-3990	36	5	g	g	PROPN
ejpam-3990	36	6	is	be	AUX
ejpam-3990	36	7	a	a	DET
ejpam-3990	36	8	monophonic	monophonic	ADJ
ejpam-3990	36	9	eccentric	eccentric	ADJ
ejpam-3990	36	10	vertex	vertex	NOUN
ejpam-3990	36	11	of	of	ADP
ejpam-3990	36	12	a	a	DET
ejpam-3990	36	13	vertex	vertex	NOUN
ejpam-3990	36	14	v	v	NOUN
ejpam-3990	36	15	in	in	ADP
ejpam-3990	36	16	g	g	PROPN
ejpam-3990	36	17	if	if	SCONJ
ejpam-3990	36	18	emg	emg	PROPN
ejpam-3990	36	19	(	(	PUNCT
ejpam-3990	36	20	v	v	NOUN
ejpam-3990	36	21	)	)	PUNCT
ejpam-3990	36	22	=	=	PUNCT
ejpam-3990	36	23	dmg	dmg	X
ejpam-3990	36	24	(	(	PUNCT
ejpam-3990	36	25	w	w	PROPN
ejpam-3990	36	26	,	,	PUNCT
ejpam-3990	36	27	v	v	NOUN
ejpam-3990	36	28	)	)	PUNCT
ejpam-3990	36	29	.	.	PUNCT
ejpam-3990	37	1	in	in	ADP
ejpam-3990	37	2	this	this	DET
ejpam-3990	37	3	case	case	NOUN
ejpam-3990	37	4	,	,	PUNCT
ejpam-3990	37	5	we	we	PRON
ejpam-3990	37	6	say	say	VERB
ejpam-3990	37	7	that	that	SCONJ
ejpam-3990	37	8	w	w	NOUN
ejpam-3990	37	9	is	be	AUX
ejpam-3990	37	10	a	a	DET
ejpam-3990	37	11	monophonic	monophonic	ADJ
ejpam-3990	37	12	eccentric	eccentric	ADJ
ejpam-3990	37	13	neighbor	neighbor	NOUN
ejpam-3990	37	14	of	of	ADP
ejpam-3990	37	15	v.	v.	ADP
ejpam-3990	37	16	the	the	DET
ejpam-3990	37	17	set	set	NOUN
ejpam-3990	37	18	of	of	ADP
ejpam-3990	37	19	all	all	DET
ejpam-3990	37	20	monophonic	monophonic	ADJ
ejpam-3990	37	21	eccentric	eccentric	ADJ
ejpam-3990	37	22	vertices	vertex	NOUN
ejpam-3990	37	23	(	(	PUNCT
ejpam-3990	37	24	neighbors	neighbor	NOUN
ejpam-3990	37	25	)	)	PUNCT
ejpam-3990	37	26	of	of	ADP
ejpam-3990	37	27	v	v	NOUN
ejpam-3990	37	28	is	be	AUX
ejpam-3990	37	29	denoted	denote	VERB
ejpam-3990	37	30	by	by	ADP
ejpam-3990	37	31	n	n	PRON
ejpam-3990	37	32	em	em	PRON
ejpam-3990	37	33	g	g	PROPN
ejpam-3990	37	34	(	(	PUNCT
ejpam-3990	37	35	v	v	NOUN
ejpam-3990	37	36	)	)	PUNCT
ejpam-3990	37	37	.	.	PUNCT
ejpam-3990	38	1	that	that	PRON
ejpam-3990	38	2	is	be	AUX
ejpam-3990	38	3	,	,	PUNCT
ejpam-3990	38	4	n	n	CCONJ
ejpam-3990	38	5	em	em	PRON
ejpam-3990	38	6	g	g	PROPN
ejpam-3990	38	7	(	(	PUNCT
ejpam-3990	38	8	v	v	NOUN
ejpam-3990	38	9	)	)	PUNCT
ejpam-3990	38	10	=	=	PRON
ejpam-3990	39	1	{	{	PUNCT
ejpam-3990	39	2	w	w	NOUN
ejpam-3990	39	3	∈	∈	PROPN
ejpam-3990	39	4	v	v	ADP
ejpam-3990	39	5	(	(	PUNCT
ejpam-3990	39	6	g	g	NOUN
ejpam-3990	39	7	)	)	PUNCT
ejpam-3990	39	8	:	:	PUNCT
ejpam-3990	40	1	dmg	dmg	VERB
ejpam-3990	40	2	(	(	PUNCT
ejpam-3990	40	3	w	w	PROPN
ejpam-3990	40	4	,	,	PUNCT
ejpam-3990	40	5	v	v	NOUN
ejpam-3990	40	6	)	)	PUNCT
ejpam-3990	40	7	=	=	SYM
ejpam-3990	40	8	emg	emg	NOUN
ejpam-3990	40	9	(	(	PUNCT
ejpam-3990	40	10	v	v	NOUN
ejpam-3990	40	11	)	)	PUNCT
ejpam-3990	40	12	}	}	PUNCT
ejpam-3990	40	13	.	.	PUNCT
ejpam-3990	41	1	the	the	DET
ejpam-3990	41	2	monophonic	monophonic	ADJ
ejpam-3990	41	3	eccentric	eccentric	ADJ
ejpam-3990	41	4	open	open	ADJ
ejpam-3990	41	5	neighborhood	neighborhood	NOUN
ejpam-3990	41	6	of	of	ADP
ejpam-3990	41	7	a	a	DET
ejpam-3990	41	8	⊆	⊆	NUM
ejpam-3990	41	9	v	v	NOUN
ejpam-3990	41	10	(	(	PUNCT
ejpam-3990	41	11	g	g	NOUN
ejpam-3990	41	12	)	)	PUNCT
ejpam-3990	41	13	given	give	VERB
ejpam-3990	41	14	by	by	ADP
ejpam-3990	41	15	n	n	PRON
ejpam-3990	41	16	em	em	PRON
ejpam-3990	41	17	g	g	PROPN
ejpam-3990	41	18	(	(	PUNCT
ejpam-3990	41	19	a	a	NOUN
ejpam-3990	41	20	)	)	PUNCT
ejpam-3990	41	21	=	=	NOUN
ejpam-3990	42	1	⋃	⋃	NOUN
ejpam-3990	42	2	a∈a	a∈a	NOUN
ejpam-3990	42	3	n	n	PRON
ejpam-3990	42	4	em	em	PRON
ejpam-3990	42	5	g	g	PROPN
ejpam-3990	42	6	(	(	PUNCT
ejpam-3990	42	7	a	a	NOUN
ejpam-3990	42	8	)	)	PUNCT
ejpam-3990	42	9	.	.	PUNCT
ejpam-3990	43	1	the	the	DET
ejpam-3990	43	2	monophonic	monophonic	ADJ
ejpam-3990	43	3	eccentric	eccentric	ADJ
ejpam-3990	43	4	closed	closed	ADJ
ejpam-3990	43	5	neighborhood	neighborhood	NOUN
ejpam-3990	43	6	of	of	ADP
ejpam-3990	43	7	a	a	PRON
ejpam-3990	43	8	is	be	AUX
ejpam-3990	43	9	n	n	PRON
ejpam-3990	43	10	em	em	PRON
ejpam-3990	43	11	g	g	PROPN
ejpam-3990	44	1	[	[	X
ejpam-3990	44	2	a	a	X
ejpam-3990	44	3	]	]	X
ejpam-3990	44	4	=	=	SYM
ejpam-3990	45	1	a	a	PRON
ejpam-3990	45	2	∪n	∪n	NUM
ejpam-3990	45	3	em	em	PRON
ejpam-3990	45	4	g	g	PROPN
ejpam-3990	45	5	(	(	PUNCT
ejpam-3990	45	6	a	a	NOUN
ejpam-3990	45	7	)	)	PUNCT
ejpam-3990	45	8	.	.	PUNCT
ejpam-3990	46	1	the	the	DET
ejpam-3990	46	2	complement	complement	NOUN
ejpam-3990	46	3	of	of	ADP
ejpam-3990	46	4	n	n	PRON
ejpam-3990	46	5	em	em	PRON
ejpam-3990	46	6	g	g	PROPN
ejpam-3990	47	1	[	[	X
ejpam-3990	47	2	a	a	X
ejpam-3990	47	3	]	]	X
ejpam-3990	47	4	is	be	AUX
ejpam-3990	47	5	f	f	X
ejpam-3990	47	6	em	em	PRON
ejpam-3990	47	7	g	g	PROPN
ejpam-3990	48	1	[	[	X
ejpam-3990	48	2	a	a	X
ejpam-3990	48	3	]	]	X
ejpam-3990	48	4	=	=	SYM
ejpam-3990	48	5	v	v	X
ejpam-3990	48	6	(	(	PUNCT
ejpam-3990	48	7	g)\n	g)\n	VERB
ejpam-3990	48	8	em	em	PRON
ejpam-3990	48	9	g	g	PROPN
ejpam-3990	49	1	[	[	X
ejpam-3990	49	2	a	a	X
ejpam-3990	49	3	]	]	X
ejpam-3990	49	4	.	.	PUNCT
ejpam-3990	50	1	if	if	SCONJ
ejpam-3990	50	2	a	a	DET
ejpam-3990	50	3	=	=	X
ejpam-3990	50	4	{	{	PUNCT
ejpam-3990	50	5	v	v	NOUN
ejpam-3990	50	6	}	}	PUNCT
ejpam-3990	50	7	,	,	PUNCT
ejpam-3990	50	8	we	we	PRON
ejpam-3990	50	9	write	write	VERB
ejpam-3990	50	10	f	f	PROPN
ejpam-3990	50	11	em	em	PRON
ejpam-3990	50	12	g	g	PROPN
ejpam-3990	51	1	[	[	X
ejpam-3990	51	2	a	a	X
ejpam-3990	51	3	]	]	X
ejpam-3990	51	4	=	=	PUNCT
ejpam-3990	51	5	f	f	X
ejpam-3990	51	6	em	em	PRON
ejpam-3990	51	7	g	g	PROPN
ejpam-3990	52	1	[	[	X
ejpam-3990	52	2	v	v	X
ejpam-3990	52	3	]	]	X
ejpam-3990	52	4	.	.	PUNCT
ejpam-3990	53	1	for	for	ADP
ejpam-3990	53	2	other	other	ADJ
ejpam-3990	53	3	basic	basic	ADJ
ejpam-3990	53	4	concepts	concept	NOUN
ejpam-3990	53	5	not	not	PART
ejpam-3990	53	6	defined	define	VERB
ejpam-3990	53	7	here	here	ADV
ejpam-3990	53	8	,	,	PUNCT
ejpam-3990	53	9	we	we	PRON
ejpam-3990	53	10	refer	refer	VERB
ejpam-3990	53	11	the	the	DET
ejpam-3990	53	12	readers	reader	NOUN
ejpam-3990	53	13	to	to	ADP
ejpam-3990	53	14	[	[	X
ejpam-3990	53	15	5	5	NUM
ejpam-3990	53	16	]	]	PUNCT
ejpam-3990	53	17	and	and	CCONJ
ejpam-3990	53	18	[	[	X
ejpam-3990	53	19	7	7	NUM
ejpam-3990	53	20	]	]	SYM
ejpam-3990	53	21	.	.	PUNCT
ejpam-3990	54	1	2	2	X
ejpam-3990	54	2	.	.	X
ejpam-3990	54	3	results	result	VERB
ejpam-3990	54	4	the	the	DET
ejpam-3990	54	5	first	first	ADJ
ejpam-3990	54	6	few	few	ADJ
ejpam-3990	54	7	results	result	NOUN
ejpam-3990	54	8	show	show	VERB
ejpam-3990	54	9	how	how	SCONJ
ejpam-3990	54	10	a	a	DET
ejpam-3990	54	11	topological	topological	ADJ
ejpam-3990	54	12	space	space	NOUN
ejpam-3990	54	13	from	from	ADP
ejpam-3990	54	14	a	a	DET
ejpam-3990	54	15	given	give	VERB
ejpam-3990	54	16	graph	graph	NOUN
ejpam-3990	54	17	g	g	PROPN
ejpam-3990	54	18	is	be	AUX
ejpam-3990	54	19	being	be	AUX
ejpam-3990	54	20	constructed	construct	VERB
ejpam-3990	54	21	using	use	VERB
ejpam-3990	54	22	the	the	DET
ejpam-3990	54	23	monophonic	monophonic	ADJ
ejpam-3990	54	24	eccentric	eccentric	ADJ
ejpam-3990	54	25	neighborhoods	neighborhood	NOUN
ejpam-3990	54	26	of	of	ADP
ejpam-3990	54	27	the	the	DET
ejpam-3990	54	28	graph	graph	NOUN
ejpam-3990	54	29	.	.	PUNCT
ejpam-3990	55	1	lemma	lemma	PROPN
ejpam-3990	55	2	1	1	X
ejpam-3990	55	3	.	.	PUNCT
ejpam-3990	56	1	let	let	VERB
ejpam-3990	56	2	g	g	NOUN
ejpam-3990	56	3	be	be	AUX
ejpam-3990	56	4	any	any	DET
ejpam-3990	56	5	graph	graph	NOUN
ejpam-3990	56	6	and	and	CCONJ
ejpam-3990	56	7	let	let	VERB
ejpam-3990	56	8	a	a	DET
ejpam-3990	56	9	,	,	PUNCT
ejpam-3990	56	10	b	b	PROPN
ejpam-3990	56	11	⊆	⊆	NUM
ejpam-3990	56	12	v	v	NOUN
ejpam-3990	56	13	(	(	PUNCT
ejpam-3990	56	14	g	g	NOUN
ejpam-3990	56	15	)	)	PUNCT
ejpam-3990	56	16	.	.	PUNCT
ejpam-3990	57	1	then	then	ADV
ejpam-3990	57	2	n	n	CCONJ
ejpam-3990	57	3	em	em	PRON
ejpam-3990	57	4	g	g	PROPN
ejpam-3990	57	5	(	(	PUNCT
ejpam-3990	57	6	a	a	DET
ejpam-3990	57	7	∪b	∪b	NOUN
ejpam-3990	57	8	)	)	PUNCT
ejpam-3990	57	9	=	=	SYM
ejpam-3990	58	1	n	n	CCONJ
ejpam-3990	58	2	em	em	PRON
ejpam-3990	58	3	g	g	PROPN
ejpam-3990	58	4	(	(	PUNCT
ejpam-3990	58	5	a	a	NOUN
ejpam-3990	58	6	)	)	PUNCT
ejpam-3990	58	7	∪n	∪n	PROPN
ejpam-3990	58	8	em	em	PRON
ejpam-3990	59	1	g	g	PROPN
ejpam-3990	59	2	(	(	PUNCT
ejpam-3990	59	3	b	b	NOUN
ejpam-3990	59	4	)	)	PUNCT
ejpam-3990	59	5	.	.	PUNCT
ejpam-3990	60	1	a.	a.	PROPN
ejpam-3990	60	2	gamorez	gamorez	PROPN
ejpam-3990	60	3	,	,	PUNCT
ejpam-3990	60	4	s.	s.	PROPN
ejpam-3990	60	5	canoy	canoy	PROPN
ejpam-3990	60	6	jr	jr	PROPN
ejpam-3990	60	7	.	.	PROPN
ejpam-3990	60	8	/	/	SYM
ejpam-3990	60	9	eur	eur	PROPN
ejpam-3990	60	10	.	.	PUNCT
ejpam-3990	61	1	j.	j.	PROPN
ejpam-3990	61	2	pure	pure	PROPN
ejpam-3990	61	3	appl	appl	PROPN
ejpam-3990	61	4	.	.	PROPN
ejpam-3990	61	5	math	math	PROPN
ejpam-3990	61	6	,	,	PUNCT
ejpam-3990	61	7	14	14	NUM
ejpam-3990	61	8	(	(	PUNCT
ejpam-3990	61	9	3	3	NUM
ejpam-3990	61	10	)	)	PUNCT
ejpam-3990	61	11	(	(	PUNCT
ejpam-3990	61	12	2021	2021	NUM
ejpam-3990	61	13	)	)	PUNCT
ejpam-3990	61	14	,	,	PUNCT
ejpam-3990	61	15	695	695	NUM
ejpam-3990	61	16	-	-	SYM
ejpam-3990	61	17	705	705	NUM
ejpam-3990	61	18	697	697	NUM
ejpam-3990	61	19	proof	proof	NOUN
ejpam-3990	61	20	.	.	PUNCT
ejpam-3990	62	1	clearly	clearly	ADV
ejpam-3990	62	2	,	,	PUNCT
ejpam-3990	62	3	n	n	CCONJ
ejpam-3990	62	4	em	em	PRON
ejpam-3990	62	5	g	g	PROPN
ejpam-3990	62	6	(	(	PUNCT
ejpam-3990	62	7	a	a	NOUN
ejpam-3990	62	8	)	)	PUNCT
ejpam-3990	62	9	⊆	⊆	NUM
ejpam-3990	62	10	n	n	NUM
ejpam-3990	62	11	em	em	PRON
ejpam-3990	62	12	g	g	PROPN
ejpam-3990	62	13	(	(	PUNCT
ejpam-3990	62	14	a∪b	a∪b	ADJ
ejpam-3990	62	15	)	)	PUNCT
ejpam-3990	62	16	and	and	CCONJ
ejpam-3990	62	17	n	n	PRON
ejpam-3990	62	18	em	em	PRON
ejpam-3990	62	19	g	g	PROPN
ejpam-3990	62	20	(	(	PUNCT
ejpam-3990	62	21	b	b	NOUN
ejpam-3990	62	22	)	)	PUNCT
ejpam-3990	62	23	⊆	⊆	NUM
ejpam-3990	62	24	n	n	NUM
ejpam-3990	62	25	em	em	PRON
ejpam-3990	62	26	g	g	PROPN
ejpam-3990	62	27	(	(	PUNCT
ejpam-3990	62	28	a∪b	a∪b	ADJ
ejpam-3990	62	29	)	)	PUNCT
ejpam-3990	62	30	.	.	PUNCT
ejpam-3990	63	1	hence	hence	ADV
ejpam-3990	63	2	,	,	PUNCT
ejpam-3990	63	3	n	n	CCONJ
ejpam-3990	63	4	em	em	PRON
ejpam-3990	63	5	g	g	PROPN
ejpam-3990	63	6	(	(	PUNCT
ejpam-3990	63	7	a)∪	a)∪	ADV
ejpam-3990	63	8	n	n	CCONJ
ejpam-3990	63	9	em	em	PRON
ejpam-3990	63	10	g	g	PROPN
ejpam-3990	63	11	(	(	PUNCT
ejpam-3990	63	12	b	b	NOUN
ejpam-3990	63	13	)	)	PUNCT
ejpam-3990	63	14	⊆	⊆	NUM
ejpam-3990	63	15	n	n	NUM
ejpam-3990	63	16	em	em	PRON
ejpam-3990	63	17	g	g	PROPN
ejpam-3990	63	18	(	(	PUNCT
ejpam-3990	63	19	a	a	DET
ejpam-3990	63	20	∪	∪	ADJ
ejpam-3990	63	21	b	b	NOUN
ejpam-3990	63	22	)	)	PUNCT
ejpam-3990	63	23	.	.	PUNCT
ejpam-3990	64	1	next	next	ADV
ejpam-3990	64	2	,	,	PUNCT
ejpam-3990	64	3	let	let	VERB
ejpam-3990	64	4	w	w	NOUN
ejpam-3990	64	5	∈	∈	PROPN
ejpam-3990	65	1	n	n	CCONJ
ejpam-3990	65	2	em	em	PRON
ejpam-3990	65	3	g	g	PROPN
ejpam-3990	65	4	(	(	PUNCT
ejpam-3990	65	5	a	a	DET
ejpam-3990	65	6	∪	∪	ADJ
ejpam-3990	65	7	b	b	NOUN
ejpam-3990	65	8	)	)	PUNCT
ejpam-3990	65	9	.	.	PUNCT
ejpam-3990	66	1	then	then	ADV
ejpam-3990	66	2	there	there	PRON
ejpam-3990	66	3	exists	exist	VERB
ejpam-3990	66	4	v	v	ADP
ejpam-3990	66	5	∈	∈	PROPN
ejpam-3990	66	6	a	a	DET
ejpam-3990	66	7	∪	∪	NOUN
ejpam-3990	66	8	b	b	NOUN
ejpam-3990	66	9	such	such	ADJ
ejpam-3990	66	10	that	that	DET
ejpam-3990	66	11	dmg	dmg	NOUN
ejpam-3990	66	12	(	(	PUNCT
ejpam-3990	66	13	w	w	PROPN
ejpam-3990	66	14	,	,	PUNCT
ejpam-3990	66	15	v	v	NOUN
ejpam-3990	66	16	)	)	PUNCT
ejpam-3990	66	17	=	=	SYM
ejpam-3990	66	18	emg	emg	NOUN
ejpam-3990	66	19	(	(	PUNCT
ejpam-3990	66	20	v	v	NOUN
ejpam-3990	66	21	)	)	PUNCT
ejpam-3990	66	22	.	.	PUNCT
ejpam-3990	67	1	thus	thus	ADV
ejpam-3990	67	2	,	,	PUNCT
ejpam-3990	67	3	w	w	PROPN
ejpam-3990	67	4	∈	∈	PROPN
ejpam-3990	67	5	n	n	CCONJ
ejpam-3990	67	6	em	em	PRON
ejpam-3990	67	7	g	g	PROPN
ejpam-3990	67	8	(	(	PUNCT
ejpam-3990	67	9	a	a	NOUN
ejpam-3990	67	10	)	)	PUNCT
ejpam-3990	67	11	or	or	CCONJ
ejpam-3990	67	12	w	w	PROPN
ejpam-3990	67	13	∈	∈	PROPN
ejpam-3990	67	14	n	n	CCONJ
ejpam-3990	67	15	em	em	PRON
ejpam-3990	67	16	g	g	PROPN
ejpam-3990	67	17	(	(	PUNCT
ejpam-3990	67	18	b	b	NOUN
ejpam-3990	67	19	)	)	PUNCT
ejpam-3990	67	20	showing	show	VERB
ejpam-3990	67	21	that	that	SCONJ
ejpam-3990	67	22	n	n	VERB
ejpam-3990	67	23	em	em	PRON
ejpam-3990	67	24	g	g	PROPN
ejpam-3990	67	25	(	(	PUNCT
ejpam-3990	67	26	a	a	DET
ejpam-3990	67	27	∪	∪	ADJ
ejpam-3990	67	28	b	b	NOUN
ejpam-3990	67	29	)	)	PUNCT
ejpam-3990	67	30	⊆	⊆	NUM
ejpam-3990	67	31	n	n	NUM
ejpam-3990	67	32	em	em	PRON
ejpam-3990	67	33	g	g	PROPN
ejpam-3990	67	34	(	(	PUNCT
ejpam-3990	67	35	a	a	NOUN
ejpam-3990	67	36	)	)	PUNCT
ejpam-3990	67	37	∪n	∪n	PROPN
ejpam-3990	67	38	em	em	PRON
ejpam-3990	67	39	g	g	PROPN
ejpam-3990	67	40	(	(	PUNCT
ejpam-3990	67	41	b	b	NOUN
ejpam-3990	67	42	)	)	PUNCT
ejpam-3990	67	43	.	.	PUNCT
ejpam-3990	68	1	therefore	therefore	ADV
ejpam-3990	68	2	,	,	PUNCT
ejpam-3990	68	3	equality	equality	NOUN
ejpam-3990	68	4	holds	hold	VERB
ejpam-3990	68	5	.	.	PUNCT
ejpam-3990	69	1	lemma	lemma	PROPN
ejpam-3990	69	2	2	2	X
ejpam-3990	69	3	.	.	PUNCT
ejpam-3990	70	1	let	let	VERB
ejpam-3990	70	2	g	g	NOUN
ejpam-3990	70	3	be	be	AUX
ejpam-3990	70	4	any	any	DET
ejpam-3990	70	5	graph	graph	NOUN
ejpam-3990	70	6	.	.	PUNCT
ejpam-3990	71	1	if	if	SCONJ
ejpam-3990	71	2	a	a	PRON
ejpam-3990	71	3	,	,	PUNCT
ejpam-3990	71	4	b	b	PROPN
ejpam-3990	71	5	⊆	⊆	NUM
ejpam-3990	71	6	v	v	NOUN
ejpam-3990	71	7	(	(	PUNCT
ejpam-3990	71	8	g	g	NOUN
ejpam-3990	71	9	)	)	PUNCT
ejpam-3990	71	10	and	and	CCONJ
ejpam-3990	71	11	a	a	DET
ejpam-3990	71	12	⊆	⊆	NUM
ejpam-3990	71	13	b	b	NOUN
ejpam-3990	71	14	,	,	PUNCT
ejpam-3990	71	15	then	then	ADV
ejpam-3990	71	16	f	f	PROPN
ejpam-3990	71	17	em	em	PRON
ejpam-3990	71	18	g	g	PROPN
ejpam-3990	72	1	[	[	X
ejpam-3990	72	2	b	b	X
ejpam-3990	72	3	]	]	X
ejpam-3990	72	4	⊆	⊆	NUM
ejpam-3990	72	5	f	f	X
ejpam-3990	72	6	em	em	PRON
ejpam-3990	72	7	g	g	PROPN
ejpam-3990	73	1	[	[	X
ejpam-3990	73	2	a	a	X
ejpam-3990	73	3	]	]	X
ejpam-3990	73	4	.	.	PUNCT
ejpam-3990	74	1	proof	proof	NOUN
ejpam-3990	74	2	.	.	PUNCT
ejpam-3990	75	1	let	let	VERB
ejpam-3990	75	2	v	v	X
ejpam-3990	75	3	∈	∈	PRON
ejpam-3990	76	1	f	f	NOUN
ejpam-3990	76	2	em	em	PRON
ejpam-3990	76	3	g	g	PROPN
ejpam-3990	77	1	[	[	X
ejpam-3990	78	1	b	b	X
ejpam-3990	78	2	]	]	X
ejpam-3990	78	3	.	.	PUNCT
ejpam-3990	79	1	then	then	ADV
ejpam-3990	79	2	v	v	ADP
ejpam-3990	79	3	/∈	/∈	PROPN
ejpam-3990	80	1	b	b	NOUN
ejpam-3990	80	2	and	and	CCONJ
ejpam-3990	80	3	v	v	NOUN
ejpam-3990	80	4	is	be	AUX
ejpam-3990	80	5	not	not	PART
ejpam-3990	80	6	a	a	DET
ejpam-3990	80	7	monophonic	monophonic	ADJ
ejpam-3990	80	8	eccentric	eccentric	ADJ
ejpam-3990	80	9	vertex	vertex	NOUN
ejpam-3990	80	10	of	of	ADP
ejpam-3990	80	11	any	any	DET
ejpam-3990	80	12	vertex	vertex	NOUN
ejpam-3990	80	13	in	in	ADP
ejpam-3990	80	14	b	b	NOUN
ejpam-3990	80	15	,	,	PUNCT
ejpam-3990	80	16	that	that	PRON
ejpam-3990	80	17	is	be	AUX
ejpam-3990	80	18	dmg	dmg	ADJ
ejpam-3990	80	19	(	(	PUNCT
ejpam-3990	80	20	v	v	NOUN
ejpam-3990	80	21	,	,	PUNCT
ejpam-3990	80	22	b	b	NOUN
ejpam-3990	80	23	)	)	PUNCT
ejpam-3990	80	24	6=	6=	ADP
ejpam-3990	80	25	emg	emg	NOUN
ejpam-3990	80	26	(	(	PUNCT
ejpam-3990	80	27	b	b	NOUN
ejpam-3990	80	28	)	)	PUNCT
ejpam-3990	80	29	for	for	ADP
ejpam-3990	80	30	all	all	DET
ejpam-3990	80	31	b	b	PROPN
ejpam-3990	80	32	∈	∈	PROPN
ejpam-3990	80	33	b.	b.	PROPN
ejpam-3990	80	34	since	since	SCONJ
ejpam-3990	80	35	a	a	DET
ejpam-3990	80	36	⊆	⊆	NUM
ejpam-3990	80	37	b	b	NOUN
ejpam-3990	80	38	,	,	PUNCT
ejpam-3990	80	39	v	v	NOUN
ejpam-3990	80	40	/∈	/∈	PUNCT
ejpam-3990	80	41	a	a	PRON
ejpam-3990	80	42	and	and	CCONJ
ejpam-3990	80	43	v	v	NOUN
ejpam-3990	80	44	is	be	AUX
ejpam-3990	80	45	not	not	PART
ejpam-3990	80	46	a	a	DET
ejpam-3990	80	47	monophonic	monophonic	ADJ
ejpam-3990	80	48	eccentric	eccentric	ADJ
ejpam-3990	80	49	vertex	vertex	NOUN
ejpam-3990	80	50	of	of	ADP
ejpam-3990	80	51	a	a	PRON
ejpam-3990	80	52	,	,	PUNCT
ejpam-3990	80	53	that	that	ADV
ejpam-3990	80	54	is	is	ADV
ejpam-3990	80	55	,	,	PUNCT
ejpam-3990	80	56	dmg	dmg	X
ejpam-3990	80	57	(	(	PUNCT
ejpam-3990	80	58	v	v	NOUN
ejpam-3990	80	59	,	,	PUNCT
ejpam-3990	80	60	a	a	PRON
ejpam-3990	80	61	)	)	PUNCT
ejpam-3990	80	62	6=	6=	ADP
ejpam-3990	80	63	emg	emg	NOUN
ejpam-3990	80	64	(	(	PUNCT
ejpam-3990	80	65	a	a	NOUN
ejpam-3990	80	66	)	)	PUNCT
ejpam-3990	80	67	for	for	ADP
ejpam-3990	80	68	all	all	DET
ejpam-3990	80	69	a	a	DET
ejpam-3990	80	70	∈	∈	PROPN
ejpam-3990	80	71	a.	a.	NOUN
ejpam-3990	80	72	thus	thus	ADV
ejpam-3990	80	73	,	,	PUNCT
ejpam-3990	80	74	v	v	X
ejpam-3990	80	75	∈	∈	PROPN
ejpam-3990	80	76	f	f	X
ejpam-3990	80	77	em	em	PRON
ejpam-3990	81	1	g	g	PROPN
ejpam-3990	81	2	[	[	X
ejpam-3990	81	3	a	a	X
ejpam-3990	81	4	]	]	X
ejpam-3990	81	5	.	.	PUNCT
ejpam-3990	82	1	therefore	therefore	ADV
ejpam-3990	82	2	,	,	PUNCT
ejpam-3990	82	3	f	f	PROPN
ejpam-3990	82	4	em	em	PRON
ejpam-3990	82	5	g	g	PROPN
ejpam-3990	83	1	[	[	X
ejpam-3990	83	2	b	b	X
ejpam-3990	83	3	]	]	X
ejpam-3990	83	4	⊆	⊆	NUM
ejpam-3990	83	5	f	f	X
ejpam-3990	83	6	em	em	PRON
ejpam-3990	83	7	g	g	PROPN
ejpam-3990	84	1	[	[	X
ejpam-3990	84	2	a	a	X
ejpam-3990	84	3	]	]	X
ejpam-3990	84	4	.	.	PUNCT
ejpam-3990	85	1	lemma	lemma	PROPN
ejpam-3990	85	2	3	3	X
ejpam-3990	85	3	.	.	PUNCT
ejpam-3990	86	1	let	let	VERB
ejpam-3990	86	2	g	g	NOUN
ejpam-3990	86	3	be	be	AUX
ejpam-3990	86	4	any	any	DET
ejpam-3990	86	5	graph	graph	NOUN
ejpam-3990	86	6	.	.	PUNCT
ejpam-3990	87	1	if	if	SCONJ
ejpam-3990	87	2	a	a	DET
ejpam-3990	87	3	,	,	PUNCT
ejpam-3990	87	4	b	b	PROPN
ejpam-3990	87	5	⊆	⊆	NUM
ejpam-3990	87	6	v	v	NOUN
ejpam-3990	87	7	(	(	PUNCT
ejpam-3990	87	8	g	g	NOUN
ejpam-3990	87	9	)	)	PUNCT
ejpam-3990	87	10	then	then	ADV
ejpam-3990	87	11	f	f	VERB
ejpam-3990	87	12	em	em	PRON
ejpam-3990	87	13	g	g	PROPN
ejpam-3990	88	1	[	[	X
ejpam-3990	88	2	a	a	DET
ejpam-3990	88	3	∪b	∪b	NOUN
ejpam-3990	88	4	]	]	X
ejpam-3990	88	5	=	=	SYM
ejpam-3990	88	6	f	f	X
ejpam-3990	88	7	em	em	PRON
ejpam-3990	88	8	g	g	PROPN
ejpam-3990	89	1	[	[	X
ejpam-3990	89	2	a	a	X
ejpam-3990	89	3	]	]	X
ejpam-3990	89	4	∩	∩	PROPN
ejpam-3990	89	5	f	f	PROPN
ejpam-3990	89	6	em	em	PRON
ejpam-3990	89	7	g	g	PROPN
ejpam-3990	89	8	[	[	X
ejpam-3990	89	9	b	b	X
ejpam-3990	89	10	]	]	PUNCT
ejpam-3990	89	11	.	.	PUNCT
ejpam-3990	90	1	proof	proof	NOUN
ejpam-3990	90	2	.	.	PUNCT
ejpam-3990	91	1	since	since	SCONJ
ejpam-3990	91	2	a	a	DET
ejpam-3990	91	3	⊆	⊆	NUM
ejpam-3990	91	4	a∪b	a∪b	NOUN
ejpam-3990	91	5	and	and	CCONJ
ejpam-3990	91	6	b	b	NOUN
ejpam-3990	91	7	⊆	⊆	NUM
ejpam-3990	91	8	a∪b	a∪b	NOUN
ejpam-3990	91	9	,	,	PUNCT
ejpam-3990	91	10	f	f	PROPN
ejpam-3990	91	11	em	em	PRON
ejpam-3990	91	12	g	g	X
ejpam-3990	92	1	[	[	X
ejpam-3990	92	2	a∪b	a∪b	X
ejpam-3990	92	3	]	]	X
ejpam-3990	92	4	⊆	⊆	NUM
ejpam-3990	92	5	f	f	X
ejpam-3990	92	6	em	em	PRON
ejpam-3990	92	7	g	g	PROPN
ejpam-3990	93	1	[	[	X
ejpam-3990	93	2	a	a	X
ejpam-3990	93	3	]	]	X
ejpam-3990	93	4	and	and	CCONJ
ejpam-3990	93	5	f	f	PRON
ejpam-3990	94	1	em	em	PRON
ejpam-3990	94	2	g	g	PROPN
ejpam-3990	95	1	[	[	X
ejpam-3990	95	2	a∪b	a∪b	X
ejpam-3990	95	3	]	]	X
ejpam-3990	95	4	⊆	⊆	NUM
ejpam-3990	95	5	f	f	X
ejpam-3990	95	6	em	em	PRON
ejpam-3990	95	7	g	g	PROPN
ejpam-3990	96	1	[	[	X
ejpam-3990	96	2	b	b	X
ejpam-3990	96	3	]	]	X
ejpam-3990	96	4	by	by	ADP
ejpam-3990	96	5	lemma	lemma	PROPN
ejpam-3990	96	6	2	2	NUM
ejpam-3990	96	7	.	.	PUNCT
ejpam-3990	97	1	thus	thus	ADV
ejpam-3990	97	2	,	,	PUNCT
ejpam-3990	97	3	f	f	PROPN
ejpam-3990	97	4	em	em	PRON
ejpam-3990	97	5	g	g	PROPN
ejpam-3990	97	6	[	[	X
ejpam-3990	97	7	a	a	PRON
ejpam-3990	97	8	∪b	∪b	NOUN
ejpam-3990	97	9	]	]	X
ejpam-3990	97	10	⊆	⊆	NUM
ejpam-3990	97	11	f	f	X
ejpam-3990	97	12	em	em	PRON
ejpam-3990	97	13	g	g	PROPN
ejpam-3990	98	1	[	[	X
ejpam-3990	98	2	a	a	X
ejpam-3990	98	3	]	]	X
ejpam-3990	98	4	∩	∩	PROPN
ejpam-3990	98	5	f	f	PROPN
ejpam-3990	98	6	em	em	PRON
ejpam-3990	98	7	g	g	PROPN
ejpam-3990	98	8	[	[	X
ejpam-3990	98	9	b	b	X
ejpam-3990	98	10	]	]	X
ejpam-3990	98	11	.	.	PUNCT
ejpam-3990	99	1	now	now	ADV
ejpam-3990	99	2	,	,	PUNCT
ejpam-3990	99	3	let	let	VERB
ejpam-3990	99	4	v	v	X
ejpam-3990	99	5	∈	∈	NOUN
ejpam-3990	100	1	f	f	NOUN
ejpam-3990	100	2	em	em	PRON
ejpam-3990	100	3	g	g	PROPN
ejpam-3990	101	1	[	[	X
ejpam-3990	101	2	a	a	X
ejpam-3990	101	3	]	]	X
ejpam-3990	101	4	∩	∩	PROPN
ejpam-3990	101	5	f	f	PROPN
ejpam-3990	101	6	em	em	PRON
ejpam-3990	101	7	g	g	PROPN
ejpam-3990	101	8	[	[	X
ejpam-3990	101	9	b	b	X
ejpam-3990	101	10	]	]	X
ejpam-3990	101	11	.	.	PUNCT
ejpam-3990	102	1	then	then	ADV
ejpam-3990	102	2	v	v	X
ejpam-3990	102	3	∈	∈	NOUN
ejpam-3990	103	1	f	f	X
ejpam-3990	104	1	em	em	PRON
ejpam-3990	104	2	g	g	PROPN
ejpam-3990	105	1	[	[	X
ejpam-3990	105	2	a	a	X
ejpam-3990	105	3	]	]	X
ejpam-3990	105	4	and	and	CCONJ
ejpam-3990	105	5	v	v	ADP
ejpam-3990	105	6	∈	∈	NOUN
ejpam-3990	106	1	f	f	X
ejpam-3990	106	2	em	em	PRON
ejpam-3990	106	3	g	g	PROPN
ejpam-3990	107	1	[	[	X
ejpam-3990	108	1	b	b	X
ejpam-3990	108	2	]	]	X
ejpam-3990	108	3	.	.	PUNCT
ejpam-3990	109	1	it	it	PRON
ejpam-3990	109	2	follows	follow	VERB
ejpam-3990	109	3	that	that	PRON
ejpam-3990	109	4	v	v	ADP
ejpam-3990	109	5	/∈	/∈	PROPN
ejpam-3990	109	6	a	a	PRON
ejpam-3990	109	7	,	,	PUNCT
ejpam-3990	109	8	v	v	NOUN
ejpam-3990	109	9	/∈	/∈	SYM
ejpam-3990	109	10	b	b	NOUN
ejpam-3990	109	11	,	,	PUNCT
ejpam-3990	109	12	v	v	NOUN
ejpam-3990	109	13	/∈	/∈	PUNCT
ejpam-3990	110	1	n	n	CCONJ
ejpam-3990	110	2	em	em	PRON
ejpam-3990	110	3	g	g	PROPN
ejpam-3990	110	4	(	(	PUNCT
ejpam-3990	110	5	a	a	NOUN
ejpam-3990	110	6	)	)	PUNCT
ejpam-3990	110	7	and	and	CCONJ
ejpam-3990	110	8	v	v	NOUN
ejpam-3990	110	9	/∈	/∈	PUNCT
ejpam-3990	111	1	n	n	CCONJ
ejpam-3990	111	2	em	em	PRON
ejpam-3990	111	3	g	g	PROPN
ejpam-3990	111	4	(	(	PUNCT
ejpam-3990	111	5	b	b	NOUN
ejpam-3990	111	6	)	)	PUNCT
ejpam-3990	111	7	.	.	PUNCT
ejpam-3990	112	1	hence	hence	ADV
ejpam-3990	112	2	,	,	PUNCT
ejpam-3990	112	3	by	by	ADP
ejpam-3990	112	4	lemma	lemma	PROPN
ejpam-3990	112	5	1	1	NUM
ejpam-3990	112	6	,	,	PUNCT
ejpam-3990	112	7	v	v	NOUN
ejpam-3990	112	8	/∈	/∈	SYM
ejpam-3990	112	9	a∪b	a∪b	NOUN
ejpam-3990	112	10	and	and	CCONJ
ejpam-3990	112	11	v	v	NOUN
ejpam-3990	112	12	/∈	/∈	PUNCT
ejpam-3990	113	1	n	n	CCONJ
ejpam-3990	113	2	em	em	PRON
ejpam-3990	113	3	g	g	PROPN
ejpam-3990	113	4	(	(	PUNCT
ejpam-3990	113	5	a∪b	a∪b	ADJ
ejpam-3990	113	6	)	)	PUNCT
ejpam-3990	113	7	.	.	PUNCT
ejpam-3990	114	1	therefore	therefore	ADV
ejpam-3990	114	2	,	,	PUNCT
ejpam-3990	114	3	v	v	X
ejpam-3990	114	4	∈	∈	PROPN
ejpam-3990	114	5	f	f	X
ejpam-3990	114	6	em	em	PRON
ejpam-3990	114	7	g	g	PROPN
ejpam-3990	115	1	[	[	X
ejpam-3990	115	2	a	a	PRON
ejpam-3990	115	3	∪b	∪b	NOUN
ejpam-3990	115	4	]	]	X
ejpam-3990	115	5	and	and	CCONJ
ejpam-3990	115	6	f	f	PRON
ejpam-3990	115	7	em	em	PRON
ejpam-3990	115	8	g	g	PROPN
ejpam-3990	115	9	[	[	X
ejpam-3990	115	10	a	a	X
ejpam-3990	115	11	]	]	X
ejpam-3990	115	12	∩	∩	PROPN
ejpam-3990	115	13	f	f	PROPN
ejpam-3990	115	14	em	em	PRON
ejpam-3990	115	15	g	g	PROPN
ejpam-3990	116	1	[	[	X
ejpam-3990	116	2	b	b	X
ejpam-3990	116	3	]	]	X
ejpam-3990	116	4	⊆	⊆	NUM
ejpam-3990	116	5	f	f	X
ejpam-3990	116	6	em	em	PRON
ejpam-3990	116	7	g	g	PROPN
ejpam-3990	117	1	[	[	X
ejpam-3990	117	2	a	a	PRON
ejpam-3990	117	3	∪b	∪b	NOUN
ejpam-3990	117	4	]	]	PUNCT
ejpam-3990	117	5	.	.	PUNCT
ejpam-3990	118	1	accordingly	accordingly	ADV
ejpam-3990	118	2	,	,	PUNCT
ejpam-3990	118	3	f	f	PROPN
ejpam-3990	118	4	em	em	PRON
ejpam-3990	118	5	g	g	PROPN
ejpam-3990	119	1	[	[	X
ejpam-3990	119	2	a	a	DET
ejpam-3990	119	3	∪b	∪b	NOUN
ejpam-3990	119	4	]	]	X
ejpam-3990	119	5	=	=	SYM
ejpam-3990	119	6	f	f	X
ejpam-3990	119	7	em	em	PRON
ejpam-3990	119	8	g	g	PROPN
ejpam-3990	120	1	[	[	X
ejpam-3990	120	2	a	a	X
ejpam-3990	120	3	]	]	X
ejpam-3990	120	4	∩	∩	PROPN
ejpam-3990	120	5	f	f	PROPN
ejpam-3990	120	6	em	em	PRON
ejpam-3990	120	7	g	g	PROPN
ejpam-3990	120	8	[	[	X
ejpam-3990	120	9	b	b	X
ejpam-3990	120	10	]	]	PUNCT
ejpam-3990	120	11	.	.	PUNCT
ejpam-3990	121	1	note	note	VERB
ejpam-3990	121	2	that	that	SCONJ
ejpam-3990	121	3	lemma	lemma	PROPN
ejpam-3990	121	4	3	3	NUM
ejpam-3990	121	5	can	can	AUX
ejpam-3990	121	6	also	also	ADV
ejpam-3990	121	7	be	be	AUX
ejpam-3990	121	8	proved	prove	VERB
ejpam-3990	121	9	using	use	VERB
ejpam-3990	121	10	lemma	lemma	PROPN
ejpam-3990	121	11	1	1	NUM
ejpam-3990	121	12	.	.	PUNCT
ejpam-3990	121	13	by	by	ADP
ejpam-3990	121	14	induction	induction	NOUN
ejpam-3990	121	15	on	on	ADP
ejpam-3990	121	16	the	the	DET
ejpam-3990	121	17	number	number	NOUN
ejpam-3990	121	18	of	of	ADP
ejpam-3990	121	19	sets	set	NOUN
ejpam-3990	121	20	involved	involve	VERB
ejpam-3990	121	21	,	,	PUNCT
ejpam-3990	121	22	the	the	DET
ejpam-3990	121	23	next	next	ADJ
ejpam-3990	121	24	is	be	AUX
ejpam-3990	121	25	immediate	immediate	ADJ
ejpam-3990	121	26	.	.	PUNCT
ejpam-3990	122	1	theorem	theorem	NOUN
ejpam-3990	122	2	1	1	X
ejpam-3990	122	3	.	.	PUNCT
ejpam-3990	123	1	let	let	VERB
ejpam-3990	123	2	g	g	NOUN
ejpam-3990	123	3	be	be	AUX
ejpam-3990	123	4	any	any	DET
ejpam-3990	123	5	graph	graph	NOUN
ejpam-3990	123	6	.	.	PUNCT
ejpam-3990	124	1	if	if	SCONJ
ejpam-3990	124	2	a1	a1	PROPN
ejpam-3990	124	3	,	,	PUNCT
ejpam-3990	124	4	a2	a2	PROPN
ejpam-3990	124	5	,	,	PUNCT
ejpam-3990	124	6	...	...	PUNCT
ejpam-3990	124	7	,	,	PUNCT
ejpam-3990	124	8	an	an	PRON
ejpam-3990	124	9	are	be	AUX
ejpam-3990	124	10	subsets	subset	NOUN
ejpam-3990	124	11	of	of	ADP
ejpam-3990	124	12	v	v	NOUN
ejpam-3990	124	13	(	(	PUNCT
ejpam-3990	124	14	g	g	NOUN
ejpam-3990	124	15	)	)	PUNCT
ejpam-3990	124	16	,	,	PUNCT
ejpam-3990	124	17	then	then	ADV
ejpam-3990	124	18	f	f	PROPN
ejpam-3990	124	19	em	em	PRON
ejpam-3990	124	20	g	g	PROPN
ejpam-3990	124	21	[	[	PUNCT
ejpam-3990	124	22	n⋃	n⋃	PROPN
ejpam-3990	124	23	i=1	i=1	PROPN
ejpam-3990	124	24	ai	ai	VERB
ejpam-3990	124	25	]	]	PUNCT
ejpam-3990	124	26	=	=	PUNCT
ejpam-3990	124	27	n⋂	n⋂	VERB
ejpam-3990	124	28	i=1	i=1	PROPN
ejpam-3990	125	1	f	f	X
ejpam-3990	125	2	em	em	PRON
ejpam-3990	125	3	g	g	PROPN
ejpam-3990	126	1	[	[	X
ejpam-3990	126	2	ai	ai	ADP
ejpam-3990	126	3	]	]	PUNCT
ejpam-3990	126	4	.	.	PUNCT
ejpam-3990	127	1	theorem	theorem	NOUN
ejpam-3990	127	2	2	2	NUM
ejpam-3990	127	3	.	.	PUNCT
ejpam-3990	128	1	let	let	VERB
ejpam-3990	128	2	g	g	NOUN
ejpam-3990	128	3	be	be	AUX
ejpam-3990	128	4	any	any	DET
ejpam-3990	128	5	graph	graph	NOUN
ejpam-3990	128	6	.	.	PUNCT
ejpam-3990	129	1	the	the	DET
ejpam-3990	129	2	family	family	NOUN
ejpam-3990	129	3	bemg	bemg	VERB
ejpam-3990	129	4	=	=	PUNCT
ejpam-3990	130	1	{	{	PUNCT
ejpam-3990	130	2	f	f	X
ejpam-3990	130	3	em	em	PRON
ejpam-3990	130	4	g	g	PROPN
ejpam-3990	131	1	[	[	X
ejpam-3990	131	2	a	a	X
ejpam-3990	131	3	]	]	X
ejpam-3990	131	4	:	:	PUNCT
ejpam-3990	131	5	a	a	DET
ejpam-3990	131	6	⊆	⊆	NUM
ejpam-3990	131	7	v	v	NOUN
ejpam-3990	131	8	(	(	PUNCT
ejpam-3990	131	9	g	g	NOUN
ejpam-3990	131	10	)	)	PUNCT
ejpam-3990	131	11	}	}	PUNCT
ejpam-3990	131	12	is	be	AUX
ejpam-3990	131	13	a	a	DET
ejpam-3990	131	14	base	base	NOUN
ejpam-3990	131	15	for	for	ADP
ejpam-3990	131	16	some	some	DET
ejpam-3990	131	17	topology	topology	NOUN
ejpam-3990	131	18	on	on	ADP
ejpam-3990	131	19	v	v	ADP
ejpam-3990	131	20	(	(	PUNCT
ejpam-3990	131	21	g	g	NOUN
ejpam-3990	131	22	)	)	PUNCT
ejpam-3990	131	23	.	.	PUNCT
ejpam-3990	132	1	proof	proof	NOUN
ejpam-3990	132	2	.	.	PUNCT
ejpam-3990	133	1	note	note	VERB
ejpam-3990	133	2	that	that	SCONJ
ejpam-3990	133	3	n	n	PRON
ejpam-3990	133	4	em	em	PRON
ejpam-3990	133	5	g	g	NOUN
ejpam-3990	134	1	[	[	X
ejpam-3990	134	2	∅	∅	NOUN
ejpam-3990	134	3	]	]	PUNCT
ejpam-3990	134	4	=	=	SYM
ejpam-3990	134	5	∅	∅	NOUN
ejpam-3990	135	1	and	and	CCONJ
ejpam-3990	135	2	so	so	ADV
ejpam-3990	135	3	f	f	PROPN
ejpam-3990	135	4	em	em	PRON
ejpam-3990	135	5	g	g	PROPN
ejpam-3990	136	1	[	[	X
ejpam-3990	136	2	∅	∅	NOUN
ejpam-3990	136	3	]	]	PUNCT
ejpam-3990	136	4	=	=	SYM
ejpam-3990	136	5	v	v	X
ejpam-3990	136	6	(	(	PUNCT
ejpam-3990	136	7	g	g	NOUN
ejpam-3990	136	8	)	)	PUNCT
ejpam-3990	136	9	∈	∈	NOUN
ejpam-3990	136	10	bemg	bemg	VERB
ejpam-3990	136	11	.	.	PUNCT
ejpam-3990	137	1	now	now	ADV
ejpam-3990	137	2	let	let	VERB
ejpam-3990	137	3	a	a	DET
ejpam-3990	137	4	,	,	PUNCT
ejpam-3990	137	5	b	b	PROPN
ejpam-3990	137	6	⊆	⊆	NUM
ejpam-3990	137	7	v	v	NOUN
ejpam-3990	137	8	(	(	PUNCT
ejpam-3990	137	9	g	g	NOUN
ejpam-3990	137	10	)	)	PUNCT
ejpam-3990	137	11	.	.	PUNCT
ejpam-3990	138	1	by	by	ADP
ejpam-3990	138	2	lemma	lemma	PROPN
ejpam-3990	138	3	3	3	NUM
ejpam-3990	138	4	,	,	PUNCT
ejpam-3990	138	5	f	f	PROPN
ejpam-3990	138	6	em	em	PRON
ejpam-3990	138	7	g	g	PROPN
ejpam-3990	138	8	[	[	X
ejpam-3990	138	9	a	a	X
ejpam-3990	138	10	]	]	X
ejpam-3990	138	11	∩	∩	PROPN
ejpam-3990	138	12	f	f	PROPN
ejpam-3990	138	13	em	em	PRON
ejpam-3990	138	14	g	g	PROPN
ejpam-3990	139	1	[	[	X
ejpam-3990	139	2	b	b	X
ejpam-3990	139	3	]	]	X
ejpam-3990	139	4	=	=	PUNCT
ejpam-3990	139	5	f	f	X
ejpam-3990	139	6	em	em	PRON
ejpam-3990	139	7	g	g	PROPN
ejpam-3990	140	1	[	[	X
ejpam-3990	140	2	a	a	DET
ejpam-3990	140	3	∪	∪	X
ejpam-3990	140	4	b	b	NOUN
ejpam-3990	140	5	]	]	PUNCT
ejpam-3990	140	6	∈	∈	PROPN
ejpam-3990	140	7	bem	bem	PROPN
ejpam-3990	140	8	g	g	PROPN
ejpam-3990	140	9	.	.	PUNCT
ejpam-3990	141	1	therefore	therefore	ADV
ejpam-3990	141	2	,	,	PUNCT
ejpam-3990	141	3	bemg	bemg	PROPN
ejpam-3990	141	4	is	be	AUX
ejpam-3990	141	5	a	a	DET
ejpam-3990	141	6	base	base	NOUN
ejpam-3990	141	7	for	for	ADP
ejpam-3990	141	8	some	some	DET
ejpam-3990	141	9	topology	topology	NOUN
ejpam-3990	141	10	on	on	ADP
ejpam-3990	141	11	v	v	ADP
ejpam-3990	141	12	(	(	PUNCT
ejpam-3990	141	13	g	g	NOUN
ejpam-3990	141	14	)	)	PUNCT
ejpam-3990	141	15	.	.	PUNCT
ejpam-3990	142	1	henceforth	henceforth	ADV
ejpam-3990	142	2	,	,	PUNCT
ejpam-3990	142	3	we	we	PRON
ejpam-3990	142	4	denote	denote	VERB
ejpam-3990	142	5	by	by	ADP
ejpam-3990	142	6	τ	τ	PROPN
ejpam-3990	142	7	emg	emg	NOUN
ejpam-3990	142	8	the	the	DET
ejpam-3990	142	9	topology	topology	NOUN
ejpam-3990	142	10	generated	generate	VERB
ejpam-3990	142	11	by	by	ADP
ejpam-3990	142	12	bemg	bemg	PROPN
ejpam-3990	142	13	.	.	PUNCT
ejpam-3990	143	1	also	also	ADV
ejpam-3990	143	2	we	we	PRON
ejpam-3990	143	3	denote	denote	VERB
ejpam-3990	143	4	by	by	ADP
ejpam-3990	143	5	ig	ig	PRON
ejpam-3990	143	6	and	and	CCONJ
ejpam-3990	143	7	dg	dg	VERB
ejpam-3990	143	8	the	the	DET
ejpam-3990	143	9	indiscrete	indiscrete	ADJ
ejpam-3990	143	10	and	and	CCONJ
ejpam-3990	143	11	the	the	DET
ejpam-3990	143	12	discrete	discrete	ADJ
ejpam-3990	143	13	topologies	topology	NOUN
ejpam-3990	143	14	on	on	ADP
ejpam-3990	143	15	v	v	ADP
ejpam-3990	143	16	(	(	PUNCT
ejpam-3990	143	17	g	g	NOUN
ejpam-3990	143	18	)	)	PUNCT
ejpam-3990	143	19	,	,	PUNCT
ejpam-3990	143	20	respectively	respectively	ADV
ejpam-3990	143	21	.	.	PUNCT
ejpam-3990	144	1	theorem	theorem	NOUN
ejpam-3990	144	2	3	3	X
ejpam-3990	144	3	.	.	PUNCT
ejpam-3990	145	1	let	let	VERB
ejpam-3990	145	2	g	g	NOUN
ejpam-3990	145	3	be	be	AUX
ejpam-3990	145	4	any	any	DET
ejpam-3990	145	5	graph	graph	NOUN
ejpam-3990	145	6	.	.	PUNCT
ejpam-3990	146	1	the	the	DET
ejpam-3990	146	2	family	family	NOUN
ejpam-3990	146	3	semg	semg	NOUN
ejpam-3990	146	4	=	=	PUNCT
ejpam-3990	146	5	{	{	PUNCT
ejpam-3990	146	6	f	f	X
ejpam-3990	146	7	em	em	PRON
ejpam-3990	146	8	g	g	PROPN
ejpam-3990	147	1	[	[	X
ejpam-3990	147	2	v	v	X
ejpam-3990	147	3	]	]	X
ejpam-3990	147	4	:	:	PUNCT
ejpam-3990	147	5	v	v	NUM
ejpam-3990	147	6	∈	∈	PROPN
ejpam-3990	147	7	v	v	NOUN
ejpam-3990	147	8	(	(	PUNCT
ejpam-3990	147	9	g	g	NOUN
ejpam-3990	147	10	)	)	PUNCT
ejpam-3990	147	11	}	}	PUNCT
ejpam-3990	147	12	forms	form	VERB
ejpam-3990	147	13	a	a	DET
ejpam-3990	147	14	subbase	subbase	NOUN
ejpam-3990	147	15	for	for	ADP
ejpam-3990	147	16	τ	τ	PROPN
ejpam-3990	147	17	emg	emg	PROPN
ejpam-3990	147	18	.	.	PUNCT
ejpam-3990	148	1	a.	a.	PROPN
ejpam-3990	148	2	gamorez	gamorez	PROPN
ejpam-3990	148	3	,	,	PUNCT
ejpam-3990	148	4	s.	s.	PROPN
ejpam-3990	148	5	canoy	canoy	PROPN
ejpam-3990	148	6	jr	jr	PROPN
ejpam-3990	148	7	.	.	PROPN
ejpam-3990	148	8	/	/	SYM
ejpam-3990	148	9	eur	eur	PROPN
ejpam-3990	148	10	.	.	PUNCT
ejpam-3990	149	1	j.	j.	PROPN
ejpam-3990	149	2	pure	pure	PROPN
ejpam-3990	149	3	appl	appl	PROPN
ejpam-3990	149	4	.	.	PROPN
ejpam-3990	149	5	math	math	PROPN
ejpam-3990	149	6	,	,	PUNCT
ejpam-3990	149	7	14	14	NUM
ejpam-3990	149	8	(	(	PUNCT
ejpam-3990	149	9	3	3	NUM
ejpam-3990	149	10	)	)	PUNCT
ejpam-3990	149	11	(	(	PUNCT
ejpam-3990	149	12	2021	2021	NUM
ejpam-3990	149	13	)	)	PUNCT
ejpam-3990	149	14	,	,	PUNCT
ejpam-3990	149	15	695	695	NUM
ejpam-3990	149	16	-	-	SYM
ejpam-3990	149	17	705	705	NUM
ejpam-3990	149	18	698	698	NUM
ejpam-3990	149	19	proof	proof	NOUN
ejpam-3990	149	20	.	.	PUNCT
ejpam-3990	150	1	let	let	VERB
ejpam-3990	150	2	semg	semg	NOUN
ejpam-3990	150	3	=	=	PRON
ejpam-3990	150	4	{	{	PUNCT
ejpam-3990	150	5	f	f	X
ejpam-3990	150	6	em	em	PRON
ejpam-3990	151	1	g	g	PROPN
ejpam-3990	151	2	[	[	X
ejpam-3990	151	3	v	v	X
ejpam-3990	151	4	]	]	X
ejpam-3990	151	5	:	:	PUNCT
ejpam-3990	151	6	v	v	NUM
ejpam-3990	151	7	∈	∈	PROPN
ejpam-3990	151	8	v	v	NOUN
ejpam-3990	151	9	(	(	PUNCT
ejpam-3990	151	10	g	g	NOUN
ejpam-3990	151	11	)	)	PUNCT
ejpam-3990	151	12	}	}	PUNCT
ejpam-3990	151	13	and	and	CCONJ
ejpam-3990	151	14	let	let	VERB
ejpam-3990	151	15	a	a	DET
ejpam-3990	151	16	=	=	PUNCT
ejpam-3990	151	17	{	{	PUNCT
ejpam-3990	151	18	a1	a1	PROPN
ejpam-3990	151	19	,	,	PUNCT
ejpam-3990	151	20	a2	a2	PROPN
ejpam-3990	151	21	,	,	PUNCT
ejpam-3990	151	22	...	...	PUNCT
ejpam-3990	151	23	,	,	PUNCT
ejpam-3990	151	24	an	an	PRON
ejpam-3990	151	25	}	}	PUNCT
ejpam-3990	151	26	.	.	PUNCT
ejpam-3990	152	1	by	by	ADP
ejpam-3990	152	2	lemma	lemma	PROPN
ejpam-3990	152	3	3	3	NUM
ejpam-3990	152	4	,	,	PUNCT
ejpam-3990	152	5	f	f	PROPN
ejpam-3990	152	6	em	em	PRON
ejpam-3990	152	7	g	g	PROPN
ejpam-3990	152	8	[	[	X
ejpam-3990	152	9	a1	a1	X
ejpam-3990	152	10	]	]	PUNCT
ejpam-3990	152	11	∩	∩	NOUN
ejpam-3990	152	12	f	f	PROPN
ejpam-3990	152	13	em	em	PRON
ejpam-3990	152	14	g	g	PROPN
ejpam-3990	152	15	[	[	X
ejpam-3990	152	16	a2	a2	X
ejpam-3990	152	17	]	]	X
ejpam-3990	152	18	∩	∩	NOUN
ejpam-3990	152	19	...	...	PUNCT
ejpam-3990	152	20	∩	∩	PROPN
ejpam-3990	152	21	f	f	X
ejpam-3990	152	22	em	em	PRON
ejpam-3990	152	23	g	g	PROPN
ejpam-3990	153	1	[	[	X
ejpam-3990	153	2	an	an	X
ejpam-3990	153	3	]	]	X
ejpam-3990	153	4	=	=	PUNCT
ejpam-3990	153	5	f	f	X
ejpam-3990	153	6	em	em	PRON
ejpam-3990	153	7	g	g	PROPN
ejpam-3990	154	1	[	[	X
ejpam-3990	154	2	a	a	X
ejpam-3990	154	3	]	]	X
ejpam-3990	154	4	.	.	PUNCT
ejpam-3990	155	1	thus	thus	ADV
ejpam-3990	155	2	,	,	PUNCT
ejpam-3990	155	3	every	every	DET
ejpam-3990	155	4	element	element	NOUN
ejpam-3990	155	5	of	of	ADP
ejpam-3990	155	6	bemg	bemg	PROPN
ejpam-3990	155	7	is	be	AUX
ejpam-3990	155	8	a	a	DET
ejpam-3990	155	9	finite	finite	ADJ
ejpam-3990	155	10	intersection	intersection	NOUN
ejpam-3990	155	11	of	of	ADP
ejpam-3990	155	12	members	member	NOUN
ejpam-3990	155	13	of	of	ADP
ejpam-3990	155	14	semg	semg	NOUN
ejpam-3990	155	15	.	.	PUNCT
ejpam-3990	156	1	therefore	therefore	ADV
ejpam-3990	156	2	,	,	PUNCT
ejpam-3990	156	3	bemg	bemg	PROPN
ejpam-3990	156	4	is	be	AUX
ejpam-3990	156	5	a	a	DET
ejpam-3990	156	6	subbase	subbase	NOUN
ejpam-3990	156	7	of	of	ADP
ejpam-3990	156	8	τ	τ	PROPN
ejpam-3990	156	9	emg	emg	PROPN
ejpam-3990	156	10	.	.	PUNCT
ejpam-3990	157	1	theorem	theorem	VERB
ejpam-3990	157	2	4	4	NUM
ejpam-3990	157	3	.	.	PUNCT
ejpam-3990	158	1	let	let	VERB
ejpam-3990	158	2	g	g	NOUN
ejpam-3990	158	3	be	be	AUX
ejpam-3990	158	4	any	any	DET
ejpam-3990	158	5	graph	graph	NOUN
ejpam-3990	158	6	of	of	ADP
ejpam-3990	158	7	order	order	NOUN
ejpam-3990	158	8	n	n	PRON
ejpam-3990	158	9	≥	≥	NOUN
ejpam-3990	158	10	1	1	NUM
ejpam-3990	158	11	.	.	PUNCT
ejpam-3990	159	1	then	then	ADV
ejpam-3990	159	2	τ	τ	PROPN
ejpam-3990	159	3	emg	emg	NOUN
ejpam-3990	159	4	is	be	AUX
ejpam-3990	159	5	the	the	DET
ejpam-3990	159	6	indiscrete	indiscrete	ADJ
ejpam-3990	159	7	topology	topology	NOUN
ejpam-3990	159	8	if	if	SCONJ
ejpam-3990	159	9	and	and	CCONJ
ejpam-3990	159	10	only	only	ADV
ejpam-3990	159	11	if	if	SCONJ
ejpam-3990	159	12	g	g	PROPN
ejpam-3990	159	13	=	=	PROPN
ejpam-3990	159	14	kn	kn	PROPN
ejpam-3990	159	15	.	.	PUNCT
ejpam-3990	159	16	proof	proof	PROPN
ejpam-3990	159	17	.	.	PUNCT
ejpam-3990	160	1	suppose	suppose	VERB
ejpam-3990	160	2	that	that	SCONJ
ejpam-3990	160	3	τ	τ	PROPN
ejpam-3990	160	4	emg	emg	NOUN
ejpam-3990	160	5	is	be	AUX
ejpam-3990	160	6	the	the	DET
ejpam-3990	160	7	indiscrete	indiscrete	ADJ
ejpam-3990	160	8	topology	topology	NOUN
ejpam-3990	160	9	.	.	PUNCT
ejpam-3990	161	1	suppose	suppose	VERB
ejpam-3990	161	2	further	far	ADV
ejpam-3990	161	3	that	that	PRON
ejpam-3990	161	4	g	g	PROPN
ejpam-3990	161	5	6=	6=	PROPN
ejpam-3990	162	1	kn	kn	PROPN
ejpam-3990	162	2	.	.	PUNCT
ejpam-3990	163	1	then	then	ADV
ejpam-3990	163	2	there	there	PRON
ejpam-3990	163	3	exist	exist	VERB
ejpam-3990	163	4	x	x	NOUN
ejpam-3990	163	5	,	,	PUNCT
ejpam-3990	163	6	y	y	PROPN
ejpam-3990	163	7	∈	∈	PROPN
ejpam-3990	163	8	v	v	ADP
ejpam-3990	163	9	(	(	PUNCT
ejpam-3990	163	10	g	g	NOUN
ejpam-3990	163	11	)	)	PUNCT
ejpam-3990	163	12	such	such	ADJ
ejpam-3990	163	13	that	that	PRON
ejpam-3990	163	14	dmg	dmg	NOUN
ejpam-3990	163	15	(	(	PUNCT
ejpam-3990	163	16	x	x	NOUN
ejpam-3990	163	17	,	,	PUNCT
ejpam-3990	163	18	y	y	NOUN
ejpam-3990	163	19	)	)	PUNCT
ejpam-3990	163	20	=	=	SYM
ejpam-3990	163	21	emg	emg	NOUN
ejpam-3990	163	22	(	(	PUNCT
ejpam-3990	163	23	x	x	NOUN
ejpam-3990	163	24	)	)	PUNCT
ejpam-3990	163	25	≥	≥	NOUN
ejpam-3990	163	26	2	2	NUM
ejpam-3990	163	27	.	.	PUNCT
ejpam-3990	163	28	let	let	VERB
ejpam-3990	163	29	p	p	NOUN
ejpam-3990	163	30	=	=	PUNCT
ejpam-3990	164	1	[	[	X
ejpam-3990	164	2	x1	x1	PROPN
ejpam-3990	164	3	,	,	PUNCT
ejpam-3990	164	4	x2	x2	PROPN
ejpam-3990	164	5	,	,	PUNCT
ejpam-3990	164	6	...	...	PUNCT
ejpam-3990	164	7	,	,	PUNCT
ejpam-3990	164	8	xk	xk	PROPN
ejpam-3990	164	9	]	]	X
ejpam-3990	164	10	,	,	PUNCT
ejpam-3990	164	11	where	where	SCONJ
ejpam-3990	164	12	x1	x1	ADJ
ejpam-3990	164	13	=	=	PUNCT
ejpam-3990	164	14	x	x	X
ejpam-3990	164	15	and	and	CCONJ
ejpam-3990	164	16	xk	xk	PROPN
ejpam-3990	164	17	=	=	SYM
ejpam-3990	164	18	y	y	PROPN
ejpam-3990	164	19	,	,	PUNCT
ejpam-3990	164	20	be	be	AUX
ejpam-3990	164	21	an	an	DET
ejpam-3990	164	22	x	x	ADJ
ejpam-3990	164	23	-	-	ADJ
ejpam-3990	164	24	y	y	ADJ
ejpam-3990	164	25	monophonic	monophonic	ADJ
ejpam-3990	164	26	path	path	NOUN
ejpam-3990	164	27	.	.	PUNCT
ejpam-3990	165	1	then	then	ADV
ejpam-3990	165	2	k	k	PROPN
ejpam-3990	165	3	≥	≥	NUM
ejpam-3990	165	4	3	3	NUM
ejpam-3990	165	5	and	and	CCONJ
ejpam-3990	165	6	x2	x2	NOUN
ejpam-3990	165	7	/∈	/∈	PUNCT
ejpam-3990	165	8	n	n	CCONJ
ejpam-3990	165	9	em	em	PRON
ejpam-3990	165	10	g	g	PROPN
ejpam-3990	166	1	[	[	X
ejpam-3990	167	1	x	x	X
ejpam-3990	167	2	]	]	X
ejpam-3990	167	3	.	.	PUNCT
ejpam-3990	168	1	hence	hence	ADV
ejpam-3990	168	2	,	,	PUNCT
ejpam-3990	168	3	x2	x2	PROPN
ejpam-3990	168	4	∈	∈	PROPN
ejpam-3990	168	5	f	f	X
ejpam-3990	168	6	em	em	PRON
ejpam-3990	168	7	g	g	PROPN
ejpam-3990	169	1	[	[	X
ejpam-3990	170	1	x	x	X
ejpam-3990	170	2	]	]	X
ejpam-3990	170	3	6=	6=	ADP
ejpam-3990	170	4	∅.	∅.	NOUN
ejpam-3990	170	5	since	since	SCONJ
ejpam-3990	170	6	x	x	X
ejpam-3990	170	7	,	,	PUNCT
ejpam-3990	170	8	y	y	PROPN
ejpam-3990	170	9	/∈	/∈	PUNCT
ejpam-3990	171	1	f	f	VERB
ejpam-3990	171	2	em	em	PRON
ejpam-3990	172	1	g	g	X
ejpam-3990	173	1	[	[	X
ejpam-3990	173	2	x	x	X
ejpam-3990	173	3	]	]	X
ejpam-3990	173	4	,	,	PUNCT
ejpam-3990	173	5	it	it	PRON
ejpam-3990	173	6	follows	follow	VERB
ejpam-3990	173	7	that	that	SCONJ
ejpam-3990	173	8	f	f	PROPN
ejpam-3990	173	9	em	em	PRON
ejpam-3990	173	10	g	g	PROPN
ejpam-3990	174	1	[	[	X
ejpam-3990	174	2	x	x	X
ejpam-3990	174	3	]	]	X
ejpam-3990	174	4	6=	6=	NUM
ejpam-3990	174	5	v	v	ADP
ejpam-3990	174	6	(	(	PUNCT
ejpam-3990	174	7	g	g	NOUN
ejpam-3990	174	8	)	)	PUNCT
ejpam-3990	174	9	.	.	PUNCT
ejpam-3990	175	1	therefore	therefore	ADV
ejpam-3990	175	2	,	,	PUNCT
ejpam-3990	175	3	τ	τ	PROPN
ejpam-3990	175	4	emg	emg	NOUN
ejpam-3990	175	5	is	be	AUX
ejpam-3990	175	6	not	not	PART
ejpam-3990	175	7	the	the	DET
ejpam-3990	175	8	indiscrete	indiscrete	ADJ
ejpam-3990	175	9	topology	topology	NOUN
ejpam-3990	175	10	,	,	PUNCT
ejpam-3990	175	11	a	a	DET
ejpam-3990	175	12	contradiction	contradiction	NOUN
ejpam-3990	175	13	.	.	PUNCT
ejpam-3990	176	1	thus	thus	ADV
ejpam-3990	176	2	,	,	PUNCT
ejpam-3990	176	3	g	g	PROPN
ejpam-3990	176	4	=	=	SYM
ejpam-3990	176	5	kn	kn	PROPN
ejpam-3990	176	6	.	.	PUNCT
ejpam-3990	177	1	let	let	VERB
ejpam-3990	177	2	g	g	PROPN
ejpam-3990	177	3	=	=	PROPN
ejpam-3990	177	4	kn	kn	PROPN
ejpam-3990	177	5	and	and	CCONJ
ejpam-3990	177	6	let	let	VERB
ejpam-3990	177	7	a	a	PRON
ejpam-3990	177	8	be	be	AUX
ejpam-3990	177	9	a	a	DET
ejpam-3990	177	10	non	non	X
ejpam-3990	177	11	empty	empty	ADJ
ejpam-3990	177	12	subset	subset	NOUN
ejpam-3990	177	13	of	of	ADP
ejpam-3990	177	14	v	v	NOUN
ejpam-3990	177	15	(	(	PUNCT
ejpam-3990	177	16	g	g	NOUN
ejpam-3990	177	17	)	)	PUNCT
ejpam-3990	177	18	.	.	PUNCT
ejpam-3990	178	1	then	then	ADV
ejpam-3990	178	2	n	n	CCONJ
ejpam-3990	178	3	em	em	PRON
ejpam-3990	178	4	g	g	VERB
ejpam-3990	179	1	[	[	X
ejpam-3990	179	2	a	a	X
ejpam-3990	179	3	]	]	X
ejpam-3990	179	4	=	=	SYM
ejpam-3990	179	5	v	v	NOUN
ejpam-3990	179	6	(	(	PUNCT
ejpam-3990	179	7	g	g	NOUN
ejpam-3990	179	8	)	)	PUNCT
ejpam-3990	179	9	.	.	PUNCT
ejpam-3990	180	1	hence	hence	ADV
ejpam-3990	180	2	,	,	PUNCT
ejpam-3990	180	3	f	f	PROPN
ejpam-3990	180	4	em	em	PRON
ejpam-3990	180	5	g	g	PROPN
ejpam-3990	181	1	[	[	X
ejpam-3990	181	2	a	a	X
ejpam-3990	181	3	]	]	X
ejpam-3990	181	4	=	=	PUNCT
ejpam-3990	181	5	∅.	∅.	VERB
ejpam-3990	181	6	therefore	therefore	ADV
ejpam-3990	181	7	,	,	PUNCT
ejpam-3990	181	8	τ	τ	PROPN
ejpam-3990	181	9	emg	emg	NOUN
ejpam-3990	181	10	is	be	AUX
ejpam-3990	181	11	the	the	DET
ejpam-3990	181	12	indiscrete	indiscrete	ADJ
ejpam-3990	181	13	topology	topology	NOUN
ejpam-3990	181	14	on	on	ADP
ejpam-3990	181	15	v	v	ADP
ejpam-3990	181	16	(	(	PUNCT
ejpam-3990	181	17	g	g	NOUN
ejpam-3990	181	18	)	)	PUNCT
ejpam-3990	181	19	.	.	PUNCT
ejpam-3990	182	1	theorem	theorem	NOUN
ejpam-3990	182	2	5	5	NUM
ejpam-3990	182	3	.	.	PUNCT
ejpam-3990	183	1	let	let	VERB
ejpam-3990	183	2	g	g	NOUN
ejpam-3990	183	3	be	be	AUX
ejpam-3990	183	4	any	any	DET
ejpam-3990	183	5	graph	graph	NOUN
ejpam-3990	183	6	.	.	PUNCT
ejpam-3990	184	1	then	then	ADV
ejpam-3990	184	2	τ	τ	PROPN
ejpam-3990	184	3	emg	emg	NOUN
ejpam-3990	184	4	is	be	AUX
ejpam-3990	184	5	the	the	DET
ejpam-3990	184	6	discrete	discrete	ADJ
ejpam-3990	184	7	topology	topology	NOUN
ejpam-3990	184	8	on	on	ADP
ejpam-3990	184	9	v	v	ADP
ejpam-3990	184	10	(	(	PUNCT
ejpam-3990	184	11	g	g	NOUN
ejpam-3990	184	12	)	)	PUNCT
ejpam-3990	184	13	if	if	SCONJ
ejpam-3990	184	14	and	and	CCONJ
ejpam-3990	184	15	only	only	ADV
ejpam-3990	184	16	if	if	SCONJ
ejpam-3990	184	17	for	for	ADP
ejpam-3990	184	18	each	each	PRON
ejpam-3990	184	19	a	a	DET
ejpam-3990	184	20	∈	∈	PROPN
ejpam-3990	184	21	v	v	NOUN
ejpam-3990	184	22	(	(	PUNCT
ejpam-3990	184	23	g	g	NOUN
ejpam-3990	184	24	)	)	PUNCT
ejpam-3990	184	25	and	and	CCONJ
ejpam-3990	184	26	for	for	ADP
ejpam-3990	184	27	each	each	DET
ejpam-3990	184	28	v	v	NUM
ejpam-3990	184	29	∈	∈	PROPN
ejpam-3990	184	30	v	v	NOUN
ejpam-3990	184	31	(	(	PUNCT
ejpam-3990	184	32	g	g	NOUN
ejpam-3990	184	33	)	)	PUNCT
ejpam-3990	184	34	with	with	ADP
ejpam-3990	184	35	a	a	DET
ejpam-3990	184	36	∈	∈	NOUN
ejpam-3990	184	37	n	n	CCONJ
ejpam-3990	184	38	em	em	PRON
ejpam-3990	184	39	g	g	PROPN
ejpam-3990	184	40	(	(	PUNCT
ejpam-3990	184	41	v	v	NOUN
ejpam-3990	184	42	)	)	PUNCT
ejpam-3990	184	43	,	,	PUNCT
ejpam-3990	184	44	there	there	PRON
ejpam-3990	184	45	exists	exist	VERB
ejpam-3990	184	46	w	w	PROPN
ejpam-3990	184	47	∈	∈	PROPN
ejpam-3990	184	48	v	v	NOUN
ejpam-3990	184	49	(	(	PUNCT
ejpam-3990	184	50	g)\{a	g)\{a	PROPN
ejpam-3990	184	51	}	}	PUNCT
ejpam-3990	184	52	such	such	ADJ
ejpam-3990	184	53	that	that	SCONJ
ejpam-3990	184	54	v	v	NUM
ejpam-3990	184	55	∈	∈	PROPN
ejpam-3990	185	1	n	n	PRON
ejpam-3990	185	2	em	em	PRON
ejpam-3990	185	3	g	g	PROPN
ejpam-3990	185	4	(	(	PUNCT
ejpam-3990	185	5	w	w	NOUN
ejpam-3990	185	6	)	)	PUNCT
ejpam-3990	185	7	but	but	CCONJ
ejpam-3990	185	8	a	a	DET
ejpam-3990	185	9	/∈	/∈	NOUN
ejpam-3990	186	1	n	n	VERB
ejpam-3990	186	2	em	em	PRON
ejpam-3990	186	3	g	g	PROPN
ejpam-3990	186	4	(	(	PUNCT
ejpam-3990	186	5	w	w	NOUN
ejpam-3990	186	6	)	)	PUNCT
ejpam-3990	186	7	.	.	PUNCT
ejpam-3990	187	1	proof	proof	NOUN
ejpam-3990	187	2	.	.	PUNCT
ejpam-3990	188	1	suppose	suppose	VERB
ejpam-3990	188	2	that	that	SCONJ
ejpam-3990	188	3	τ	τ	PROPN
ejpam-3990	188	4	emg	emg	NOUN
ejpam-3990	188	5	is	be	AUX
ejpam-3990	188	6	the	the	DET
ejpam-3990	188	7	discrete	discrete	ADJ
ejpam-3990	188	8	topology	topology	NOUN
ejpam-3990	188	9	dg	dg	VERB
ejpam-3990	188	10	on	on	ADP
ejpam-3990	188	11	v	v	ADP
ejpam-3990	188	12	(	(	PUNCT
ejpam-3990	188	13	g	g	NOUN
ejpam-3990	188	14	)	)	PUNCT
ejpam-3990	188	15	.	.	PUNCT
ejpam-3990	189	1	let	let	VERB
ejpam-3990	189	2	a	a	DET
ejpam-3990	189	3	∈	∈	PROPN
ejpam-3990	189	4	v	v	NOUN
ejpam-3990	189	5	(	(	PUNCT
ejpam-3990	189	6	g	g	NOUN
ejpam-3990	189	7	)	)	PUNCT
ejpam-3990	189	8	and	and	CCONJ
ejpam-3990	189	9	let	let	VERB
ejpam-3990	189	10	v	v	NUM
ejpam-3990	189	11	∈	∈	PROPN
ejpam-3990	189	12	v	v	NOUN
ejpam-3990	189	13	(	(	PUNCT
ejpam-3990	189	14	g	g	NOUN
ejpam-3990	189	15	)	)	PUNCT
ejpam-3990	189	16	with	with	ADP
ejpam-3990	189	17	a	a	DET
ejpam-3990	189	18	∈	∈	NOUN
ejpam-3990	189	19	n	n	CCONJ
ejpam-3990	189	20	em	em	PRON
ejpam-3990	189	21	g	g	PROPN
ejpam-3990	189	22	(	(	PUNCT
ejpam-3990	189	23	v	v	NOUN
ejpam-3990	189	24	)	)	PUNCT
ejpam-3990	189	25	.	.	PUNCT
ejpam-3990	190	1	since	since	SCONJ
ejpam-3990	190	2	τ	τ	PROPN
ejpam-3990	190	3	emg	emg	NOUN
ejpam-3990	190	4	is	be	AUX
ejpam-3990	190	5	the	the	DET
ejpam-3990	190	6	discrete	discrete	ADJ
ejpam-3990	190	7	topology	topology	NOUN
ejpam-3990	190	8	,	,	PUNCT
ejpam-3990	190	9	{	{	PUNCT
ejpam-3990	190	10	a	a	DET
ejpam-3990	190	11	}	}	PUNCT
ejpam-3990	190	12	∈	∈	NOUN
ejpam-3990	190	13	bemg	bemg	NOUN
ejpam-3990	190	14	,	,	PUNCT
ejpam-3990	190	15	that	that	ADV
ejpam-3990	190	16	is	is	ADV
ejpam-3990	190	17	,	,	PUNCT
ejpam-3990	190	18	there	there	PRON
ejpam-3990	190	19	exists	exist	VERB
ejpam-3990	190	20	a	a	DET
ejpam-3990	190	21	⊆	⊆	NUM
ejpam-3990	190	22	v	v	NOUN
ejpam-3990	190	23	(	(	PUNCT
ejpam-3990	190	24	g	g	NOUN
ejpam-3990	190	25	)	)	PUNCT
ejpam-3990	190	26	such	such	ADJ
ejpam-3990	190	27	that	that	SCONJ
ejpam-3990	190	28	f	f	PROPN
ejpam-3990	190	29	em	em	PRON
ejpam-3990	190	30	g	g	PROPN
ejpam-3990	191	1	[	[	X
ejpam-3990	191	2	a	a	X
ejpam-3990	191	3	]	]	X
ejpam-3990	191	4	=	=	X
ejpam-3990	191	5	{	{	PUNCT
ejpam-3990	191	6	a	a	NOUN
ejpam-3990	191	7	}	}	PUNCT
ejpam-3990	191	8	.	.	PUNCT
ejpam-3990	192	1	since	since	SCONJ
ejpam-3990	192	2	a	a	DET
ejpam-3990	192	3	∈	∈	NOUN
ejpam-3990	192	4	n	n	CCONJ
ejpam-3990	192	5	em	em	PRON
ejpam-3990	192	6	g	g	PROPN
ejpam-3990	192	7	(	(	PUNCT
ejpam-3990	192	8	v	v	NOUN
ejpam-3990	192	9	)	)	PUNCT
ejpam-3990	192	10	,	,	PUNCT
ejpam-3990	192	11	v	v	X
ejpam-3990	192	12	/∈	/∈	PUNCT
ejpam-3990	192	13	a.	a.	NOUN
ejpam-3990	192	14	also	also	ADV
ejpam-3990	192	15	,	,	PUNCT
ejpam-3990	192	16	v	v	X
ejpam-3990	192	17	/∈	/∈	PUNCT
ejpam-3990	193	1	f	f	VERB
ejpam-3990	193	2	em	em	PRON
ejpam-3990	194	1	g	g	PROPN
ejpam-3990	195	1	[	[	X
ejpam-3990	195	2	a	a	X
ejpam-3990	195	3	]	]	PUNCT
ejpam-3990	195	4	implies	imply	VERB
ejpam-3990	195	5	that	that	SCONJ
ejpam-3990	195	6	there	there	PRON
ejpam-3990	195	7	exists	exist	VERB
ejpam-3990	195	8	w	w	PROPN
ejpam-3990	195	9	∈	∈	PROPN
ejpam-3990	195	10	a	a	DET
ejpam-3990	195	11	such	such	ADJ
ejpam-3990	195	12	that	that	DET
ejpam-3990	195	13	dmg	dmg	NOUN
ejpam-3990	195	14	(	(	PUNCT
ejpam-3990	195	15	w	w	PROPN
ejpam-3990	195	16	,	,	PUNCT
ejpam-3990	195	17	v	v	NOUN
ejpam-3990	195	18	)	)	PUNCT
ejpam-3990	195	19	=	=	SYM
ejpam-3990	195	20	emg	emg	NOUN
ejpam-3990	195	21	(	(	PUNCT
ejpam-3990	195	22	w	w	NOUN
ejpam-3990	195	23	)	)	PUNCT
ejpam-3990	195	24	,	,	PUNCT
ejpam-3990	195	25	that	that	ADV
ejpam-3990	195	26	is	is	ADV
ejpam-3990	195	27	,	,	PUNCT
ejpam-3990	195	28	v	v	X
ejpam-3990	195	29	∈	∈	PROPN
ejpam-3990	195	30	n	n	CCONJ
ejpam-3990	195	31	em	em	PRON
ejpam-3990	195	32	g	g	PROPN
ejpam-3990	195	33	(	(	PUNCT
ejpam-3990	195	34	w	w	NOUN
ejpam-3990	195	35	)	)	PUNCT
ejpam-3990	195	36	.	.	PUNCT
ejpam-3990	196	1	moreover	moreover	ADV
ejpam-3990	196	2	,	,	PUNCT
ejpam-3990	196	3	because	because	SCONJ
ejpam-3990	196	4	a	a	DET
ejpam-3990	196	5	∈	∈	NOUN
ejpam-3990	196	6	f	f	X
ejpam-3990	196	7	em	em	PRON
ejpam-3990	196	8	g	g	PROPN
ejpam-3990	197	1	[	[	X
ejpam-3990	197	2	a	a	X
ejpam-3990	197	3	]	]	X
ejpam-3990	197	4	,	,	PUNCT
ejpam-3990	197	5	a	a	PRON
ejpam-3990	197	6	/∈	/∈	NOUN
ejpam-3990	198	1	n	n	VERB
ejpam-3990	198	2	em	em	PRON
ejpam-3990	198	3	g	g	PROPN
ejpam-3990	198	4	(	(	PUNCT
ejpam-3990	198	5	w	w	NOUN
ejpam-3990	198	6	)	)	PUNCT
ejpam-3990	198	7	.	.	PUNCT
ejpam-3990	199	1	thus	thus	ADV
ejpam-3990	199	2	,	,	PUNCT
ejpam-3990	199	3	g	g	PROPN
ejpam-3990	199	4	satisfies	satisfy	VERB
ejpam-3990	199	5	the	the	DET
ejpam-3990	199	6	desired	desire	VERB
ejpam-3990	199	7	property	property	NOUN
ejpam-3990	199	8	.	.	PUNCT
ejpam-3990	200	1	for	for	ADP
ejpam-3990	200	2	the	the	DET
ejpam-3990	200	3	converse	converse	NOUN
ejpam-3990	200	4	,	,	PUNCT
ejpam-3990	200	5	suppose	suppose	VERB
ejpam-3990	200	6	that	that	SCONJ
ejpam-3990	200	7	the	the	DET
ejpam-3990	200	8	given	give	VERB
ejpam-3990	200	9	condition	condition	NOUN
ejpam-3990	200	10	is	be	AUX
ejpam-3990	200	11	satisfied	satisfied	ADJ
ejpam-3990	200	12	by	by	ADP
ejpam-3990	200	13	g.	g.	PROPN
ejpam-3990	200	14	if	if	SCONJ
ejpam-3990	200	15	g	g	PROPN
ejpam-3990	200	16	=	=	PROPN
ejpam-3990	200	17	k1	k1	PROPN
ejpam-3990	200	18	,	,	PUNCT
ejpam-3990	200	19	then	then	ADV
ejpam-3990	200	20	clearly	clearly	ADV
ejpam-3990	200	21	,	,	PUNCT
ejpam-3990	200	22	τ	τ	PROPN
ejpam-3990	200	23	emg	emg	NOUN
ejpam-3990	200	24	=	=	PUNCT
ejpam-3990	200	25	dg	dg	PROPN
ejpam-3990	200	26	.	.	PUNCT
ejpam-3990	201	1	suppose	suppose	VERB
ejpam-3990	201	2	g	g	PROPN
ejpam-3990	201	3	6=	6=	PROPN
ejpam-3990	201	4	k1	k1	PROPN
ejpam-3990	201	5	.	.	PUNCT
ejpam-3990	202	1	let	let	VERB
ejpam-3990	202	2	a	a	DET
ejpam-3990	202	3	∈	∈	PROPN
ejpam-3990	202	4	v	v	NOUN
ejpam-3990	202	5	(	(	PUNCT
ejpam-3990	202	6	g	g	NOUN
ejpam-3990	202	7	)	)	PUNCT
ejpam-3990	202	8	and	and	CCONJ
ejpam-3990	202	9	let	let	VERB
ejpam-3990	202	10	aa	aa	NOUN
ejpam-3990	202	11	=	=	PUNCT
ejpam-3990	202	12	{	{	PUNCT
ejpam-3990	202	13	v	v	NUM
ejpam-3990	202	14	∈	∈	NOUN
ejpam-3990	202	15	v	v	NOUN
ejpam-3990	202	16	(	(	PUNCT
ejpam-3990	202	17	g	g	NOUN
ejpam-3990	202	18	)	)	PUNCT
ejpam-3990	202	19	:	:	PUNCT
ejpam-3990	202	20	a	a	DET
ejpam-3990	202	21	∈	∈	PROPN
ejpam-3990	202	22	n	n	CCONJ
ejpam-3990	202	23	em	em	PRON
ejpam-3990	202	24	g	g	PROPN
ejpam-3990	202	25	(	(	PUNCT
ejpam-3990	202	26	v	v	NOUN
ejpam-3990	202	27	)	)	PUNCT
ejpam-3990	202	28	}	}	PUNCT
ejpam-3990	202	29	.	.	PUNCT
ejpam-3990	203	1	set	set	VERB
ejpam-3990	203	2	a	a	DET
ejpam-3990	203	3	=	=	SYM
ejpam-3990	203	4	v	v	NOUN
ejpam-3990	203	5	(	(	PUNCT
ejpam-3990	203	6	g)\(aa	g)\(aa	PROPN
ejpam-3990	203	7	∪	∪	X
ejpam-3990	203	8	{	{	PUNCT
ejpam-3990	203	9	a	a	NOUN
ejpam-3990	203	10	}	}	PUNCT
ejpam-3990	203	11	)	)	PUNCT
ejpam-3990	203	12	.	.	PUNCT
ejpam-3990	204	1	then	then	ADV
ejpam-3990	204	2	,	,	PUNCT
ejpam-3990	204	3	by	by	ADP
ejpam-3990	204	4	assumption	assumption	NOUN
ejpam-3990	204	5	,	,	PUNCT
ejpam-3990	204	6	a	a	DET
ejpam-3990	204	7	6=	6=	NUM
ejpam-3990	204	8	∅.	∅.	NOUN
ejpam-3990	204	9	since	since	SCONJ
ejpam-3990	204	10	a	a	DET
ejpam-3990	204	11	/∈	/∈	NOUN
ejpam-3990	204	12	a	a	NOUN
ejpam-3990	204	13	and	and	CCONJ
ejpam-3990	204	14	a	a	PRON
ejpam-3990	204	15	/∈	/∈	NOUN
ejpam-3990	204	16	n	n	VERB
ejpam-3990	204	17	em	em	PRON
ejpam-3990	204	18	g	g	PROPN
ejpam-3990	204	19	(	(	PUNCT
ejpam-3990	204	20	w	w	NOUN
ejpam-3990	204	21	)	)	PUNCT
ejpam-3990	204	22	for	for	ADP
ejpam-3990	204	23	all	all	DET
ejpam-3990	204	24	w	w	PROPN
ejpam-3990	204	25	∈	∈	PROPN
ejpam-3990	204	26	a	a	PRON
ejpam-3990	204	27	,	,	PUNCT
ejpam-3990	204	28	it	it	PRON
ejpam-3990	204	29	follows	follow	VERB
ejpam-3990	204	30	that	that	SCONJ
ejpam-3990	204	31	a	a	DET
ejpam-3990	204	32	∈	∈	NOUN
ejpam-3990	204	33	f	f	X
ejpam-3990	204	34	em	em	PRON
ejpam-3990	204	35	g	g	PROPN
ejpam-3990	205	1	[	[	X
ejpam-3990	205	2	a	a	X
ejpam-3990	205	3	]	]	X
ejpam-3990	205	4	.	.	PUNCT
ejpam-3990	205	5	suppose	suppose	VERB
ejpam-3990	205	6	there	there	PRON
ejpam-3990	205	7	exists	exist	VERB
ejpam-3990	205	8	q	q	PROPN
ejpam-3990	205	9	∈	∈	PROPN
ejpam-3990	205	10	f	f	X
ejpam-3990	205	11	em	em	PRON
ejpam-3990	205	12	g	g	PROPN
ejpam-3990	205	13	[	[	X
ejpam-3990	205	14	a]\{a	a]\{a	X
ejpam-3990	205	15	}	}	PUNCT
ejpam-3990	205	16	.	.	PUNCT
ejpam-3990	206	1	then	then	ADV
ejpam-3990	206	2	q	q	X
ejpam-3990	206	3	/∈	/∈	PUNCT
ejpam-3990	206	4	a∪{a	a∪{a	NUM
ejpam-3990	206	5	}	}	PUNCT
ejpam-3990	206	6	.	.	PUNCT
ejpam-3990	207	1	hence	hence	ADV
ejpam-3990	207	2	,	,	PUNCT
ejpam-3990	207	3	q	q	PROPN
ejpam-3990	207	4	∈	∈	PROPN
ejpam-3990	207	5	aa	aa	NOUN
ejpam-3990	207	6	,	,	PUNCT
ejpam-3990	207	7	that	that	ADV
ejpam-3990	207	8	is	is	ADV
ejpam-3990	207	9	,	,	PUNCT
ejpam-3990	207	10	a	a	DET
ejpam-3990	207	11	∈	∈	NOUN
ejpam-3990	208	1	n	n	CCONJ
ejpam-3990	208	2	em	em	PRON
ejpam-3990	208	3	g	g	PROPN
ejpam-3990	208	4	(	(	PUNCT
ejpam-3990	208	5	q	q	NOUN
ejpam-3990	208	6	)	)	PUNCT
ejpam-3990	208	7	.	.	PUNCT
ejpam-3990	209	1	by	by	ADP
ejpam-3990	209	2	assumption	assumption	NOUN
ejpam-3990	209	3	,	,	PUNCT
ejpam-3990	209	4	there	there	PRON
ejpam-3990	209	5	exists	exist	VERB
ejpam-3990	209	6	w	w	PROPN
ejpam-3990	209	7	/∈	/∈	PUNCT
ejpam-3990	209	8	aa	aa	NOUN
ejpam-3990	209	9	∪	∪	ADV
ejpam-3990	209	10	{	{	PUNCT
ejpam-3990	209	11	a	a	PRON
ejpam-3990	209	12	}	}	PUNCT
ejpam-3990	209	13	such	such	ADJ
ejpam-3990	209	14	that	that	SCONJ
ejpam-3990	209	15	q	q	PUNCT
ejpam-3990	209	16	∈	∈	PROPN
ejpam-3990	209	17	n	n	CCONJ
ejpam-3990	209	18	em	em	PRON
ejpam-3990	209	19	g	g	PROPN
ejpam-3990	209	20	(	(	PUNCT
ejpam-3990	209	21	w	w	PROPN
ejpam-3990	209	22	)	)	PUNCT
ejpam-3990	209	23	,	,	PUNCT
ejpam-3990	209	24	that	that	ADV
ejpam-3990	209	25	is	is	ADV
ejpam-3990	209	26	,	,	PUNCT
ejpam-3990	209	27	dmg	dmg	INTJ
ejpam-3990	209	28	(	(	PUNCT
ejpam-3990	209	29	q	q	NOUN
ejpam-3990	209	30	,	,	PUNCT
ejpam-3990	209	31	w	w	NOUN
ejpam-3990	209	32	)	)	PUNCT
ejpam-3990	209	33	=	=	SYM
ejpam-3990	209	34	emg	emg	NOUN
ejpam-3990	209	35	(	(	PUNCT
ejpam-3990	209	36	w	w	NOUN
ejpam-3990	209	37	)	)	PUNCT
ejpam-3990	209	38	.	.	PUNCT
ejpam-3990	210	1	this	this	PRON
ejpam-3990	210	2	contradicts	contradict	VERB
ejpam-3990	210	3	the	the	DET
ejpam-3990	210	4	fact	fact	NOUN
ejpam-3990	210	5	that	that	SCONJ
ejpam-3990	210	6	q	q	PUNCT
ejpam-3990	210	7	∈	∈	PROPN
ejpam-3990	211	1	f	f	X
ejpam-3990	212	1	em	em	PRON
ejpam-3990	212	2	g	g	PROPN
ejpam-3990	213	1	[	[	X
ejpam-3990	213	2	a	a	X
ejpam-3990	213	3	]	]	X
ejpam-3990	213	4	.	.	PUNCT
ejpam-3990	214	1	therefore	therefore	ADV
ejpam-3990	214	2	,	,	PUNCT
ejpam-3990	214	3	f	f	PROPN
ejpam-3990	214	4	em	em	PRON
ejpam-3990	214	5	g	g	PROPN
ejpam-3990	215	1	[	[	X
ejpam-3990	215	2	a	a	X
ejpam-3990	215	3	]	]	X
ejpam-3990	215	4	=	=	X
ejpam-3990	215	5	{	{	PUNCT
ejpam-3990	215	6	a	a	NOUN
ejpam-3990	215	7	}	}	PUNCT
ejpam-3990	215	8	.	.	PUNCT
ejpam-3990	216	1	since	since	SCONJ
ejpam-3990	216	2	a	a	PRON
ejpam-3990	216	3	was	be	AUX
ejpam-3990	216	4	arbitrarily	arbitrarily	ADV
ejpam-3990	216	5	chosen	choose	VERB
ejpam-3990	216	6	,	,	PUNCT
ejpam-3990	216	7	it	it	PRON
ejpam-3990	216	8	follows	follow	VERB
ejpam-3990	216	9	that	that	SCONJ
ejpam-3990	216	10	{	{	PUNCT
ejpam-3990	216	11	a	a	PRON
ejpam-3990	216	12	}	}	PUNCT
ejpam-3990	216	13	∈	∈	PROPN
ejpam-3990	216	14	τ	τ	PROPN
ejpam-3990	216	15	emg	emg	NOUN
ejpam-3990	216	16	for	for	ADP
ejpam-3990	216	17	all	all	DET
ejpam-3990	216	18	a	a	DET
ejpam-3990	216	19	∈	∈	PROPN
ejpam-3990	216	20	v	v	NOUN
ejpam-3990	216	21	(	(	PUNCT
ejpam-3990	216	22	g	g	NOUN
ejpam-3990	216	23	)	)	PUNCT
ejpam-3990	216	24	.	.	PUNCT
ejpam-3990	217	1	thus	thus	ADV
ejpam-3990	217	2	,	,	PUNCT
ejpam-3990	217	3	τ	τ	PROPN
ejpam-3990	217	4	emg	emg	NOUN
ejpam-3990	217	5	is	be	AUX
ejpam-3990	217	6	the	the	DET
ejpam-3990	217	7	discrete	discrete	ADJ
ejpam-3990	217	8	topology	topology	NOUN
ejpam-3990	217	9	.	.	PUNCT
ejpam-3990	218	1	corollary	corollary	ADJ
ejpam-3990	218	2	1	1	NUM
ejpam-3990	218	3	.	.	PUNCT
ejpam-3990	219	1	let	let	VERB
ejpam-3990	219	2	g1	g1	PROPN
ejpam-3990	219	3	,	,	PUNCT
ejpam-3990	219	4	g2	g2	PROPN
ejpam-3990	219	5	,	,	PUNCT
ejpam-3990	219	6	...	...	PUNCT
ejpam-3990	219	7	,	,	PUNCT
ejpam-3990	219	8	gn	gn	PROPN
ejpam-3990	219	9	be	be	AUX
ejpam-3990	219	10	graphs	graph	NOUN
ejpam-3990	219	11	such	such	ADJ
ejpam-3990	219	12	that	that	SCONJ
ejpam-3990	219	13	τ	τ	PROPN
ejpam-3990	219	14	emgi	emgi	NOUN
ejpam-3990	219	15	=	=	SYM
ejpam-3990	219	16	dgi	dgi	PROPN
ejpam-3990	219	17	for	for	ADP
ejpam-3990	219	18	each	each	DET
ejpam-3990	219	19	i	i	PRON
ejpam-3990	219	20	∈	∈	PROPN
ejpam-3990	219	21	{	{	PUNCT
ejpam-3990	219	22	1	1	NUM
ejpam-3990	219	23	,	,	PUNCT
ejpam-3990	219	24	2	2	NUM
ejpam-3990	219	25	,	,	PUNCT
ejpam-3990	219	26	...	...	PUNCT
ejpam-3990	219	27	,	,	PUNCT
ejpam-3990	219	28	n	n	CCONJ
ejpam-3990	219	29	}	}	PUNCT
ejpam-3990	219	30	.	.	PUNCT
ejpam-3990	220	1	if	if	SCONJ
ejpam-3990	220	2	g	g	PROPN
ejpam-3990	220	3	=	=	SYM
ejpam-3990	220	4	n⋃	n⋃	X
ejpam-3990	220	5	i=1	i=1	PROPN
ejpam-3990	220	6	gi	gi	PROPN
ejpam-3990	220	7	,	,	PUNCT
ejpam-3990	220	8	then	then	ADV
ejpam-3990	220	9	τ	τ	PROPN
ejpam-3990	220	10	em	em	PRON
ejpam-3990	220	11	g	g	PROPN
ejpam-3990	220	12	=	=	PUNCT
ejpam-3990	220	13	dg	dg	PROPN
ejpam-3990	220	14	.	.	PUNCT
ejpam-3990	221	1	proof	proof	NOUN
ejpam-3990	221	2	.	.	PUNCT
ejpam-3990	222	1	let	let	VERB
ejpam-3990	222	2	g	g	PROPN
ejpam-3990	222	3	=	=	VERB
ejpam-3990	222	4	n⋃	n⋃	X
ejpam-3990	222	5	i=1	i=1	PROPN
ejpam-3990	222	6	gi	gi	X
ejpam-3990	222	7	and	and	CCONJ
ejpam-3990	222	8	let	let	VERB
ejpam-3990	222	9	a	a	DET
ejpam-3990	222	10	,	,	PUNCT
ejpam-3990	222	11	v	v	NOUN
ejpam-3990	222	12	∈	∈	PROPN
ejpam-3990	222	13	v	v	NOUN
ejpam-3990	222	14	(	(	PUNCT
ejpam-3990	222	15	g	g	NOUN
ejpam-3990	222	16	)	)	PUNCT
ejpam-3990	222	17	such	such	ADJ
ejpam-3990	222	18	that	that	SCONJ
ejpam-3990	222	19	a	a	DET
ejpam-3990	222	20	∈	∈	NOUN
ejpam-3990	222	21	n	n	CCONJ
ejpam-3990	222	22	em	em	PRON
ejpam-3990	222	23	g	g	PROPN
ejpam-3990	222	24	(	(	PUNCT
ejpam-3990	222	25	v	v	NOUN
ejpam-3990	222	26	)	)	PUNCT
ejpam-3990	222	27	.	.	PUNCT
ejpam-3990	223	1	then	then	ADV
ejpam-3990	223	2	there	there	PRON
ejpam-3990	223	3	exists	exist	VERB
ejpam-3990	223	4	a	a	DET
ejpam-3990	223	5	unique	unique	ADJ
ejpam-3990	223	6	i	i	PRON
ejpam-3990	223	7	∈	∈	PROPN
ejpam-3990	223	8	{	{	PUNCT
ejpam-3990	223	9	1	1	NUM
ejpam-3990	223	10	,	,	PUNCT
ejpam-3990	223	11	2	2	NUM
ejpam-3990	223	12	,	,	PUNCT
ejpam-3990	223	13	...	...	PUNCT
ejpam-3990	223	14	,	,	PUNCT
ejpam-3990	223	15	n	n	CCONJ
ejpam-3990	223	16	}	}	PUNCT
ejpam-3990	223	17	such	such	ADJ
ejpam-3990	223	18	that	that	SCONJ
ejpam-3990	223	19	a	a	DET
ejpam-3990	223	20	,	,	PUNCT
ejpam-3990	223	21	v	v	NOUN
ejpam-3990	223	22	∈	∈	PROPN
ejpam-3990	223	23	v	v	NOUN
ejpam-3990	223	24	(	(	PUNCT
ejpam-3990	223	25	gi	gi	NOUN
ejpam-3990	223	26	)	)	PUNCT
ejpam-3990	223	27	.	.	PUNCT
ejpam-3990	224	1	hence	hence	ADV
ejpam-3990	224	2	,	,	PUNCT
ejpam-3990	224	3	a	a	DET
ejpam-3990	224	4	∈	∈	NOUN
ejpam-3990	224	5	n	n	CCONJ
ejpam-3990	224	6	em	em	PRON
ejpam-3990	224	7	gi	gi	INTJ
ejpam-3990	224	8	(	(	PUNCT
ejpam-3990	224	9	v	v	NOUN
ejpam-3990	224	10	)	)	PUNCT
ejpam-3990	224	11	.	.	PUNCT
ejpam-3990	225	1	since	since	SCONJ
ejpam-3990	225	2	τ	τ	PROPN
ejpam-3990	225	3	emgi	emgi	NOUN
ejpam-3990	225	4	=	=	SYM
ejpam-3990	225	5	dgi	dgi	PROPN
ejpam-3990	225	6	,	,	PUNCT
ejpam-3990	225	7	there	there	PRON
ejpam-3990	225	8	exists	exist	VERB
ejpam-3990	225	9	w	w	PROPN
ejpam-3990	225	10	∈	∈	PROPN
ejpam-3990	225	11	v	v	NOUN
ejpam-3990	225	12	(	(	PUNCT
ejpam-3990	225	13	gi)\{a	gi)\{a	PROPN
ejpam-3990	225	14	}	}	PUNCT
ejpam-3990	225	15	such	such	ADJ
ejpam-3990	225	16	that	that	SCONJ
ejpam-3990	225	17	v	v	NUM
ejpam-3990	225	18	∈	∈	PROPN
ejpam-3990	226	1	n	n	CCONJ
ejpam-3990	226	2	em	em	PRON
ejpam-3990	226	3	gi	gi	INTJ
ejpam-3990	226	4	(	(	PUNCT
ejpam-3990	226	5	w	w	NOUN
ejpam-3990	226	6	)	)	PUNCT
ejpam-3990	226	7	and	and	CCONJ
ejpam-3990	226	8	a	a	DET
ejpam-3990	226	9	/∈	/∈	NOUN
ejpam-3990	227	1	n	n	VERB
ejpam-3990	227	2	em	em	PRON
ejpam-3990	227	3	gi	gi	INTJ
ejpam-3990	227	4	(	(	PUNCT
ejpam-3990	227	5	w	w	NOUN
ejpam-3990	227	6	)	)	PUNCT
ejpam-3990	227	7	by	by	ADP
ejpam-3990	227	8	theorem	theorem	NOUN
ejpam-3990	227	9	5	5	NUM
ejpam-3990	227	10	.	.	PUNCT
ejpam-3990	227	11	thus	thus	ADV
ejpam-3990	227	12	,	,	PUNCT
ejpam-3990	227	13	there	there	PRON
ejpam-3990	227	14	exists	exist	VERB
ejpam-3990	227	15	w	w	PROPN
ejpam-3990	227	16	∈	∈	PROPN
ejpam-3990	227	17	v	v	NOUN
ejpam-3990	227	18	(	(	PUNCT
ejpam-3990	227	19	g)\{a	g)\{a	PROPN
ejpam-3990	227	20	}	}	PUNCT
ejpam-3990	227	21	such	such	ADJ
ejpam-3990	227	22	that	that	SCONJ
ejpam-3990	227	23	v	v	NUM
ejpam-3990	227	24	∈	∈	PROPN
ejpam-3990	228	1	n	n	PRON
ejpam-3990	228	2	em	em	PRON
ejpam-3990	228	3	g	g	PROPN
ejpam-3990	228	4	(	(	PUNCT
ejpam-3990	228	5	w	w	NOUN
ejpam-3990	228	6	)	)	PUNCT
ejpam-3990	228	7	and	and	CCONJ
ejpam-3990	228	8	a	a	DET
ejpam-3990	228	9	/∈	/∈	NOUN
ejpam-3990	229	1	n	n	VERB
ejpam-3990	229	2	em	em	PRON
ejpam-3990	229	3	g	g	PROPN
ejpam-3990	229	4	(	(	PUNCT
ejpam-3990	229	5	w	w	NOUN
ejpam-3990	229	6	)	)	PUNCT
ejpam-3990	229	7	.	.	PUNCT
ejpam-3990	230	1	therefore	therefore	ADV
ejpam-3990	230	2	,	,	PUNCT
ejpam-3990	230	3	τ	τ	PROPN
ejpam-3990	230	4	emg	emg	NOUN
ejpam-3990	230	5	=	=	PUNCT
ejpam-3990	230	6	dg	dg	PROPN
ejpam-3990	230	7	.	.	PUNCT
ejpam-3990	231	1	a.	a.	PROPN
ejpam-3990	231	2	gamorez	gamorez	PROPN
ejpam-3990	231	3	,	,	PUNCT
ejpam-3990	231	4	s.	s.	PROPN
ejpam-3990	231	5	canoy	canoy	PROPN
ejpam-3990	231	6	jr	jr	PROPN
ejpam-3990	231	7	.	.	PROPN
ejpam-3990	231	8	/	/	SYM
ejpam-3990	231	9	eur	eur	PROPN
ejpam-3990	231	10	.	.	PUNCT
ejpam-3990	232	1	j.	j.	PROPN
ejpam-3990	232	2	pure	pure	PROPN
ejpam-3990	232	3	appl	appl	PROPN
ejpam-3990	232	4	.	.	PROPN
ejpam-3990	232	5	math	math	PROPN
ejpam-3990	232	6	,	,	PUNCT
ejpam-3990	232	7	14	14	NUM
ejpam-3990	232	8	(	(	PUNCT
ejpam-3990	232	9	3	3	NUM
ejpam-3990	232	10	)	)	PUNCT
ejpam-3990	232	11	(	(	PUNCT
ejpam-3990	232	12	2021	2021	NUM
ejpam-3990	232	13	)	)	PUNCT
ejpam-3990	232	14	,	,	PUNCT
ejpam-3990	232	15	695	695	NUM
ejpam-3990	232	16	-	-	SYM
ejpam-3990	232	17	705	705	NUM
ejpam-3990	232	18	699	699	NUM
ejpam-3990	232	19	corollary	corollary	ADJ
ejpam-3990	232	20	2	2	NUM
ejpam-3990	232	21	.	.	PUNCT
ejpam-3990	233	1	if	if	SCONJ
ejpam-3990	233	2	g	g	PROPN
ejpam-3990	233	3	=	=	SYM
ejpam-3990	233	4	kn	kn	PROPN
ejpam-3990	233	5	,	,	PUNCT
ejpam-3990	233	6	then	then	ADV
ejpam-3990	233	7	τ	τ	PROPN
ejpam-3990	233	8	em	em	PRON
ejpam-3990	233	9	g	g	PROPN
ejpam-3990	233	10	=	=	PUNCT
ejpam-3990	233	11	dg	dg	PROPN
ejpam-3990	233	12	.	.	PUNCT
ejpam-3990	234	1	proof	proof	NOUN
ejpam-3990	234	2	.	.	PUNCT
ejpam-3990	235	1	let	let	VERB
ejpam-3990	235	2	a	a	DET
ejpam-3990	235	3	∈	∈	PROPN
ejpam-3990	235	4	v	v	NOUN
ejpam-3990	235	5	(	(	PUNCT
ejpam-3990	235	6	g	g	NOUN
ejpam-3990	235	7	)	)	PUNCT
ejpam-3990	235	8	.	.	PUNCT
ejpam-3990	236	1	then	then	ADV
ejpam-3990	236	2	aa	aa	INTJ
ejpam-3990	236	3	=	=	PUNCT
ejpam-3990	236	4	{	{	PUNCT
ejpam-3990	236	5	v	v	NUM
ejpam-3990	236	6	∈	∈	NOUN
ejpam-3990	236	7	v	v	NOUN
ejpam-3990	236	8	(	(	PUNCT
ejpam-3990	236	9	g	g	NOUN
ejpam-3990	236	10	)	)	PUNCT
ejpam-3990	236	11	:	:	PUNCT
ejpam-3990	236	12	a	a	DET
ejpam-3990	236	13	∈	∈	PROPN
ejpam-3990	236	14	n	n	CCONJ
ejpam-3990	236	15	em	em	PRON
ejpam-3990	236	16	g	g	PROPN
ejpam-3990	236	17	(	(	PUNCT
ejpam-3990	236	18	v	v	NOUN
ejpam-3990	236	19	)	)	PUNCT
ejpam-3990	236	20	}	}	PUNCT
ejpam-3990	236	21	=	=	PUNCT
ejpam-3990	236	22	∅.	∅.	AUX
ejpam-3990	236	23	let	let	VERB
ejpam-3990	236	24	a	a	DET
ejpam-3990	236	25	=	=	SYM
ejpam-3990	236	26	v	v	NOUN
ejpam-3990	236	27	(	(	PUNCT
ejpam-3990	236	28	g)\[aa	g)\[aa	NOUN
ejpam-3990	236	29	∪	∪	VERB
ejpam-3990	236	30	{	{	PUNCT
ejpam-3990	236	31	a	a	NOUN
ejpam-3990	236	32	}	}	PUNCT
ejpam-3990	236	33	]	]	PUNCT
ejpam-3990	236	34	=	=	SYM
ejpam-3990	236	35	v	v	X
ejpam-3990	236	36	(	(	PUNCT
ejpam-3990	236	37	g)\{a	g)\{a	PROPN
ejpam-3990	236	38	}	}	PUNCT
ejpam-3990	236	39	.	.	PUNCT
ejpam-3990	237	1	then	then	ADV
ejpam-3990	237	2	,	,	PUNCT
ejpam-3990	237	3	f	f	PROPN
ejpam-3990	237	4	em	em	PRON
ejpam-3990	237	5	g	g	PROPN
ejpam-3990	238	1	[	[	X
ejpam-3990	238	2	a	a	X
ejpam-3990	238	3	]	]	X
ejpam-3990	238	4	=	=	X
ejpam-3990	238	5	{	{	PUNCT
ejpam-3990	238	6	a	a	PRON
ejpam-3990	238	7	}	}	PUNCT
ejpam-3990	238	8	∈	∈	PROPN
ejpam-3990	238	9	τ	τ	PROPN
ejpam-3990	238	10	emg	emg	NOUN
ejpam-3990	238	11	.	.	PUNCT
ejpam-3990	239	1	thus	thus	ADV
ejpam-3990	239	2	,	,	PUNCT
ejpam-3990	239	3	τ	τ	PROPN
ejpam-3990	239	4	emg	emg	NOUN
ejpam-3990	239	5	=	=	SYM
ejpam-3990	239	6	dg	dg	PROPN
ejpam-3990	239	7	.	.	PUNCT
ejpam-3990	240	1	lemma	lemma	PROPN
ejpam-3990	240	2	4	4	X
ejpam-3990	240	3	.	.	PUNCT
ejpam-3990	241	1	let	let	VERB
ejpam-3990	241	2	g	g	NOUN
ejpam-3990	241	3	=	=	PUNCT
ejpam-3990	241	4	cn	cn	PROPN
ejpam-3990	242	1	=	=	PUNCT
ejpam-3990	243	1	[	[	X
ejpam-3990	243	2	v1	v1	NOUN
ejpam-3990	243	3	,	,	PUNCT
ejpam-3990	243	4	v2	v2	PROPN
ejpam-3990	243	5	,	,	PUNCT
ejpam-3990	243	6	...	...	PUNCT
ejpam-3990	243	7	vn	vn	NOUN
ejpam-3990	243	8	,	,	PUNCT
ejpam-3990	243	9	v1	v1	PROPN
ejpam-3990	243	10	]	]	PUNCT
ejpam-3990	243	11	be	be	VERB
ejpam-3990	243	12	a	a	DET
ejpam-3990	243	13	cycle	cycle	NOUN
ejpam-3990	243	14	with	with	ADP
ejpam-3990	243	15	n	n	PRON
ejpam-3990	243	16	≥	≥	NUM
ejpam-3990	243	17	3	3	NUM
ejpam-3990	243	18	.	.	PUNCT
ejpam-3990	244	1	then	then	ADV
ejpam-3990	244	2	emg	emg	NOUN
ejpam-3990	244	3	(	(	PUNCT
ejpam-3990	244	4	v	v	NOUN
ejpam-3990	244	5	)	)	PUNCT
ejpam-3990	244	6	=	=	PUNCT
ejpam-3990	244	7	n−	n−	NOUN
ejpam-3990	244	8	2	2	NUM
ejpam-3990	244	9	for	for	ADP
ejpam-3990	244	10	all	all	DET
ejpam-3990	244	11	v	v	ADP
ejpam-3990	244	12	∈	∈	NOUN
ejpam-3990	244	13	v	v	NOUN
ejpam-3990	244	14	(	(	PUNCT
ejpam-3990	244	15	g	g	NOUN
ejpam-3990	244	16	)	)	PUNCT
ejpam-3990	244	17	.	.	PUNCT
ejpam-3990	245	1	proof	proof	NOUN
ejpam-3990	245	2	.	.	PUNCT
ejpam-3990	246	1	suppose	suppose	VERB
ejpam-3990	246	2	w	w	PROPN
ejpam-3990	246	3	∈	∈	PROPN
ejpam-3990	246	4	v	v	ADP
ejpam-3990	246	5	(	(	PUNCT
ejpam-3990	246	6	cn	cn	PROPN
ejpam-3990	246	7	)	)	PUNCT
ejpam-3990	246	8	.	.	PUNCT
ejpam-3990	247	1	without	without	ADP
ejpam-3990	247	2	loss	loss	NOUN
ejpam-3990	247	3	of	of	ADP
ejpam-3990	247	4	generality	generality	NOUN
ejpam-3990	247	5	,	,	PUNCT
ejpam-3990	247	6	let	let	VERB
ejpam-3990	247	7	w	w	NOUN
ejpam-3990	247	8	=	=	PUNCT
ejpam-3990	247	9	v1	v1	NOUN
ejpam-3990	247	10	.	.	PUNCT
ejpam-3990	248	1	since	since	SCONJ
ejpam-3990	248	2	emcn	emcn	PROPN
ejpam-3990	248	3	(	(	PUNCT
ejpam-3990	248	4	w	w	NOUN
ejpam-3990	248	5	)	)	PUNCT
ejpam-3990	248	6	=	=	SYM
ejpam-3990	248	7	max{dmcn	max{dmcn	PROPN
ejpam-3990	248	8	(	(	PUNCT
ejpam-3990	248	9	w	w	PROPN
ejpam-3990	248	10	,	,	PUNCT
ejpam-3990	248	11	v	v	NOUN
ejpam-3990	248	12	)	)	PUNCT
ejpam-3990	248	13	:	:	PUNCT
ejpam-3990	248	14	v	v	X
ejpam-3990	248	15	∈	∈	PROPN
ejpam-3990	248	16	v	v	NOUN
ejpam-3990	248	17	(	(	PUNCT
ejpam-3990	248	18	cn	cn	NOUN
ejpam-3990	248	19	)	)	PUNCT
ejpam-3990	248	20	}	}	PUNCT
ejpam-3990	248	21	,	,	PUNCT
ejpam-3990	248	22	it	it	PRON
ejpam-3990	248	23	follows	follow	VERB
ejpam-3990	248	24	that	that	SCONJ
ejpam-3990	248	25	emcn	emcn	PROPN
ejpam-3990	248	26	(	(	PUNCT
ejpam-3990	248	27	w	w	NOUN
ejpam-3990	248	28	)	)	PUNCT
ejpam-3990	248	29	=	=	SYM
ejpam-3990	248	30	n−	n−	NOUN
ejpam-3990	248	31	2	2	NUM
ejpam-3990	248	32	.	.	NOUN
ejpam-3990	248	33	example	example	NOUN
ejpam-3990	249	1	1	1	NUM
ejpam-3990	249	2	.	.	PUNCT
ejpam-3990	250	1	let	let	VERB
ejpam-3990	250	2	c5	c5	PROPN
ejpam-3990	250	3	=	=	PUNCT
ejpam-3990	251	1	[	[	X
ejpam-3990	251	2	v1	v1	NOUN
ejpam-3990	251	3	,	,	PUNCT
ejpam-3990	251	4	v2	v2	PROPN
ejpam-3990	251	5	,	,	PUNCT
ejpam-3990	251	6	v3	v3	PROPN
ejpam-3990	251	7	,	,	PUNCT
ejpam-3990	251	8	v4	v4	PROPN
ejpam-3990	251	9	,	,	PUNCT
ejpam-3990	251	10	v5	v5	NOUN
ejpam-3990	251	11	,	,	PUNCT
ejpam-3990	251	12	v1	v1	NOUN
ejpam-3990	251	13	]	]	PUNCT
ejpam-3990	251	14	.	.	PUNCT
ejpam-3990	252	1	then	then	ADV
ejpam-3990	252	2	by	by	ADP
ejpam-3990	252	3	lemma	lemma	PROPN
ejpam-3990	252	4	4	4	NUM
ejpam-3990	252	5	,	,	PUNCT
ejpam-3990	252	6	we	we	PRON
ejpam-3990	252	7	have	have	VERB
ejpam-3990	252	8	n	n	NUM
ejpam-3990	252	9	em	em	PRON
ejpam-3990	252	10	c5	c5	PROPN
ejpam-3990	253	1	[	[	X
ejpam-3990	253	2	v1	v1	X
ejpam-3990	253	3	]	]	X
ejpam-3990	253	4	=	=	SYM
ejpam-3990	253	5	{	{	PUNCT
ejpam-3990	253	6	v1	v1	PROPN
ejpam-3990	253	7	,	,	PUNCT
ejpam-3990	253	8	v3	v3	PROPN
ejpam-3990	253	9	,	,	PUNCT
ejpam-3990	253	10	v4	v4	PROPN
ejpam-3990	253	11	}	}	PUNCT
ejpam-3990	253	12	f	f	PROPN
ejpam-3990	253	13	em	em	PROPN
ejpam-3990	253	14	c5	c5	PROPN
ejpam-3990	254	1	[	[	X
ejpam-3990	254	2	v1	v1	X
ejpam-3990	254	3	]	]	X
ejpam-3990	254	4	=	=	SYM
ejpam-3990	254	5	{	{	PUNCT
ejpam-3990	254	6	v2	v2	PROPN
ejpam-3990	254	7	,	,	PUNCT
ejpam-3990	254	8	v5	v5	PROPN
ejpam-3990	254	9	}	}	PUNCT
ejpam-3990	254	10	n	n	PROPN
ejpam-3990	254	11	em	em	PRON
ejpam-3990	254	12	c5	c5	PROPN
ejpam-3990	255	1	[	[	X
ejpam-3990	255	2	v2	v2	X
ejpam-3990	255	3	]	]	X
ejpam-3990	255	4	=	=	SYM
ejpam-3990	255	5	{	{	PUNCT
ejpam-3990	255	6	v2	v2	PROPN
ejpam-3990	255	7	,	,	PUNCT
ejpam-3990	255	8	v4	v4	NOUN
ejpam-3990	255	9	,	,	PUNCT
ejpam-3990	255	10	v5	v5	PROPN
ejpam-3990	255	11	}	}	PUNCT
ejpam-3990	255	12	f	f	NOUN
ejpam-3990	255	13	em	em	PROPN
ejpam-3990	255	14	c5	c5	PROPN
ejpam-3990	256	1	[	[	X
ejpam-3990	256	2	v2	v2	X
ejpam-3990	256	3	]	]	X
ejpam-3990	256	4	=	=	SYM
ejpam-3990	256	5	{	{	PUNCT
ejpam-3990	256	6	v1	v1	PROPN
ejpam-3990	256	7	,	,	PUNCT
ejpam-3990	256	8	v3	v3	PROPN
ejpam-3990	256	9	}	}	PUNCT
ejpam-3990	256	10	n	n	PROPN
ejpam-3990	256	11	em	em	PRON
ejpam-3990	256	12	c5	c5	PROPN
ejpam-3990	257	1	[	[	X
ejpam-3990	257	2	v3	v3	PROPN
ejpam-3990	257	3	]	]	X
ejpam-3990	257	4	=	=	SYM
ejpam-3990	257	5	{	{	PUNCT
ejpam-3990	257	6	v1	v1	PROPN
ejpam-3990	257	7	,	,	PUNCT
ejpam-3990	257	8	v3	v3	PROPN
ejpam-3990	257	9	,	,	PUNCT
ejpam-3990	257	10	v5	v5	PROPN
ejpam-3990	257	11	}	}	PUNCT
ejpam-3990	257	12	f	f	NOUN
ejpam-3990	257	13	em	em	PROPN
ejpam-3990	257	14	c5	c5	PROPN
ejpam-3990	258	1	[	[	X
ejpam-3990	258	2	v3	v3	PROPN
ejpam-3990	258	3	]	]	X
ejpam-3990	258	4	=	=	PRON
ejpam-3990	258	5	{	{	PUNCT
ejpam-3990	258	6	v2	v2	PROPN
ejpam-3990	258	7	,	,	PUNCT
ejpam-3990	258	8	v4	v4	NOUN
ejpam-3990	258	9	}	}	PUNCT
ejpam-3990	258	10	n	n	CCONJ
ejpam-3990	258	11	em	em	PRON
ejpam-3990	258	12	c5	c5	PROPN
ejpam-3990	259	1	[	[	X
ejpam-3990	259	2	v4	v4	X
ejpam-3990	259	3	]	]	X
ejpam-3990	259	4	=	=	SYM
ejpam-3990	259	5	{	{	PUNCT
ejpam-3990	259	6	v1	v1	PROPN
ejpam-3990	259	7	,	,	PUNCT
ejpam-3990	259	8	v2	v2	PROPN
ejpam-3990	259	9	,	,	PUNCT
ejpam-3990	259	10	v4	v4	PROPN
ejpam-3990	259	11	}	}	PUNCT
ejpam-3990	259	12	f	f	PROPN
ejpam-3990	259	13	em	em	PROPN
ejpam-3990	259	14	c5	c5	PROPN
ejpam-3990	260	1	[	[	X
ejpam-3990	260	2	v4	v4	X
ejpam-3990	260	3	]	]	X
ejpam-3990	260	4	=	=	SYM
ejpam-3990	260	5	{	{	PUNCT
ejpam-3990	260	6	v3	v3	PROPN
ejpam-3990	260	7	,	,	PUNCT
ejpam-3990	260	8	v5	v5	PROPN
ejpam-3990	260	9	}	}	PUNCT
ejpam-3990	260	10	n	n	PROPN
ejpam-3990	260	11	em	em	PRON
ejpam-3990	260	12	c5	c5	PROPN
ejpam-3990	261	1	[	[	X
ejpam-3990	261	2	v5	v5	X
ejpam-3990	261	3	]	]	X
ejpam-3990	261	4	=	=	SYM
ejpam-3990	261	5	{	{	PUNCT
ejpam-3990	261	6	v2	v2	PROPN
ejpam-3990	261	7	,	,	PUNCT
ejpam-3990	261	8	v3	v3	PROPN
ejpam-3990	261	9	,	,	PUNCT
ejpam-3990	261	10	v5	v5	PROPN
ejpam-3990	261	11	}	}	PUNCT
ejpam-3990	261	12	f	f	NOUN
ejpam-3990	261	13	em	em	PROPN
ejpam-3990	261	14	c5	c5	PROPN
ejpam-3990	262	1	[	[	X
ejpam-3990	262	2	v5	v5	X
ejpam-3990	262	3	]	]	X
ejpam-3990	262	4	=	=	SYM
ejpam-3990	262	5	{	{	PUNCT
ejpam-3990	262	6	v1	v1	PROPN
ejpam-3990	262	7	,	,	PUNCT
ejpam-3990	262	8	v4	v4	NOUN
ejpam-3990	262	9	}	}	PUNCT
ejpam-3990	262	10	.	.	PUNCT
ejpam-3990	263	1	note	note	VERB
ejpam-3990	263	2	that	that	SCONJ
ejpam-3990	263	3	f	f	PROPN
ejpam-3990	263	4	em	em	PRON
ejpam-3990	263	5	c5	c5	PROPN
ejpam-3990	264	1	[	[	X
ejpam-3990	264	2	v2	v2	X
ejpam-3990	264	3	]	]	PUNCT
ejpam-3990	264	4	∩	∩	PROPN
ejpam-3990	264	5	f	f	PROPN
ejpam-3990	264	6	em	em	PROPN
ejpam-3990	264	7	c5	c5	PROPN
ejpam-3990	265	1	[	[	X
ejpam-3990	265	2	v5	v5	X
ejpam-3990	265	3	]	]	X
ejpam-3990	265	4	=	=	SYM
ejpam-3990	265	5	{	{	PUNCT
ejpam-3990	265	6	v1	v1	NOUN
ejpam-3990	265	7	}	}	PUNCT
ejpam-3990	265	8	f	f	PROPN
ejpam-3990	265	9	em	em	PROPN
ejpam-3990	265	10	c5	c5	PROPN
ejpam-3990	265	11	[	[	X
ejpam-3990	265	12	v3	v3	PROPN
ejpam-3990	265	13	]	]	PUNCT
ejpam-3990	265	14	∩	∩	PROPN
ejpam-3990	265	15	f	f	PROPN
ejpam-3990	265	16	em	em	PROPN
ejpam-3990	265	17	c5	c5	PROPN
ejpam-3990	266	1	[	[	X
ejpam-3990	266	2	v5	v5	X
ejpam-3990	266	3	]	]	X
ejpam-3990	266	4	=	=	SYM
ejpam-3990	266	5	{	{	PUNCT
ejpam-3990	266	6	v4	v4	PROPN
ejpam-3990	266	7	}	}	PUNCT
ejpam-3990	266	8	f	f	PROPN
ejpam-3990	266	9	em	em	PROPN
ejpam-3990	266	10	c5	c5	PROPN
ejpam-3990	267	1	[	[	X
ejpam-3990	267	2	v1	v1	X
ejpam-3990	267	3	]	]	PUNCT
ejpam-3990	267	4	∩	∩	PROPN
ejpam-3990	267	5	f	f	PROPN
ejpam-3990	267	6	em	em	PROPN
ejpam-3990	267	7	c5	c5	PROPN
ejpam-3990	268	1	[	[	X
ejpam-3990	268	2	v3	v3	PROPN
ejpam-3990	268	3	]	]	X
ejpam-3990	268	4	=	=	SYM
ejpam-3990	268	5	{	{	PUNCT
ejpam-3990	268	6	v2	v2	PROPN
ejpam-3990	268	7	}	}	PUNCT
ejpam-3990	268	8	f	f	NOUN
ejpam-3990	268	9	em	em	PROPN
ejpam-3990	268	10	c5	c5	PROPN
ejpam-3990	269	1	[	[	X
ejpam-3990	269	2	v1	v1	X
ejpam-3990	269	3	]	]	PUNCT
ejpam-3990	269	4	∩	∩	PROPN
ejpam-3990	269	5	f	f	PROPN
ejpam-3990	269	6	em	em	PROPN
ejpam-3990	269	7	c5	c5	PROPN
ejpam-3990	270	1	[	[	X
ejpam-3990	270	2	v4	v4	X
ejpam-3990	270	3	]	]	X
ejpam-3990	270	4	=	=	PUNCT
ejpam-3990	270	5	{	{	PUNCT
ejpam-3990	270	6	v5	v5	PROPN
ejpam-3990	270	7	}	}	PUNCT
ejpam-3990	270	8	.	.	PUNCT
ejpam-3990	271	1	f	f	X
ejpam-3990	272	1	em	em	PRON
ejpam-3990	272	2	c5	c5	PROPN
ejpam-3990	273	1	[	[	X
ejpam-3990	273	2	v1	v1	X
ejpam-3990	273	3	]	]	PUNCT
ejpam-3990	273	4	∩	∩	PROPN
ejpam-3990	273	5	f	f	PROPN
ejpam-3990	273	6	em	em	PROPN
ejpam-3990	273	7	c5	c5	PROPN
ejpam-3990	274	1	[	[	X
ejpam-3990	274	2	v2	v2	X
ejpam-3990	274	3	]	]	X
ejpam-3990	274	4	=	=	SYM
ejpam-3990	274	5	{	{	PUNCT
ejpam-3990	274	6	v3	v3	PROPN
ejpam-3990	274	7	}	}	PUNCT
ejpam-3990	274	8	since	since	SCONJ
ejpam-3990	274	9	{	{	PUNCT
ejpam-3990	274	10	v1	v1	NOUN
ejpam-3990	274	11	}	}	PUNCT
ejpam-3990	274	12	,	,	PUNCT
ejpam-3990	274	13	{	{	PUNCT
ejpam-3990	274	14	v2	v2	NOUN
ejpam-3990	274	15	}	}	PUNCT
ejpam-3990	274	16	,	,	PUNCT
ejpam-3990	274	17	{	{	PUNCT
ejpam-3990	274	18	v3	v3	NOUN
ejpam-3990	274	19	}	}	PUNCT
ejpam-3990	274	20	,	,	PUNCT
ejpam-3990	274	21	{	{	PUNCT
ejpam-3990	274	22	v4	v4	NOUN
ejpam-3990	274	23	}	}	PUNCT
ejpam-3990	274	24	,	,	PUNCT
ejpam-3990	274	25	{	{	PUNCT
ejpam-3990	274	26	v5	v5	NOUN
ejpam-3990	274	27	}	}	PUNCT
ejpam-3990	274	28	,	,	PUNCT
ejpam-3990	274	29	{	{	PUNCT
ejpam-3990	274	30	v6	v6	NOUN
ejpam-3990	274	31	}	}	PUNCT
ejpam-3990	274	32	∈	∈	PROPN
ejpam-3990	274	33	bemc5	bemc5	NOUN
ejpam-3990	274	34	,	,	PUNCT
ejpam-3990	274	35	it	it	PRON
ejpam-3990	274	36	follows	follow	VERB
ejpam-3990	274	37	that	that	SCONJ
ejpam-3990	274	38	τ	τ	PROPN
ejpam-3990	274	39	emc5	emc5	PROPN
ejpam-3990	274	40	=	=	SYM
ejpam-3990	274	41	dc5	dc5	PROPN
ejpam-3990	274	42	.	.	PROPN
ejpam-3990	274	43	example	example	NOUN
ejpam-3990	274	44	2	2	NUM
ejpam-3990	274	45	.	.	X
ejpam-3990	275	1	consider	consider	VERB
ejpam-3990	275	2	now	now	ADV
ejpam-3990	275	3	c6	c6	PROPN
ejpam-3990	275	4	=	=	PUNCT
ejpam-3990	276	1	[	[	X
ejpam-3990	276	2	v1	v1	NOUN
ejpam-3990	276	3	,	,	PUNCT
ejpam-3990	276	4	v2	v2	PROPN
ejpam-3990	276	5	,	,	PUNCT
ejpam-3990	276	6	v3	v3	PROPN
ejpam-3990	276	7	,	,	PUNCT
ejpam-3990	276	8	v4	v4	PROPN
ejpam-3990	276	9	,	,	PUNCT
ejpam-3990	276	10	v5	v5	PROPN
ejpam-3990	276	11	,	,	PUNCT
ejpam-3990	276	12	v6	v6	NOUN
ejpam-3990	276	13	,	,	PUNCT
ejpam-3990	276	14	v1	v1	PROPN
ejpam-3990	276	15	]	]	PUNCT
ejpam-3990	276	16	.	.	PUNCT
ejpam-3990	277	1	then	then	ADV
ejpam-3990	277	2	by	by	ADP
ejpam-3990	277	3	lemma	lemma	PROPN
ejpam-3990	277	4	4	4	NUM
ejpam-3990	277	5	,	,	PUNCT
ejpam-3990	277	6	we	we	PRON
ejpam-3990	277	7	have	have	VERB
ejpam-3990	277	8	n	n	NUM
ejpam-3990	277	9	em	em	PRON
ejpam-3990	277	10	c6	c6	PROPN
ejpam-3990	278	1	[	[	X
ejpam-3990	278	2	v1	v1	X
ejpam-3990	278	3	]	]	X
ejpam-3990	278	4	=	=	SYM
ejpam-3990	278	5	{	{	PUNCT
ejpam-3990	278	6	v1	v1	PROPN
ejpam-3990	278	7	,	,	PUNCT
ejpam-3990	278	8	v3	v3	PROPN
ejpam-3990	278	9	,	,	PUNCT
ejpam-3990	278	10	v5	v5	PROPN
ejpam-3990	278	11	}	}	PUNCT
ejpam-3990	278	12	f	f	PROPN
ejpam-3990	279	1	em	em	PROPN
ejpam-3990	279	2	c6	c6	PROPN
ejpam-3990	280	1	[	[	X
ejpam-3990	280	2	v1	v1	X
ejpam-3990	280	3	]	]	X
ejpam-3990	280	4	=	=	SYM
ejpam-3990	280	5	{	{	PUNCT
ejpam-3990	280	6	v2	v2	PROPN
ejpam-3990	280	7	,	,	PUNCT
ejpam-3990	280	8	v4	v4	PROPN
ejpam-3990	280	9	,	,	PUNCT
ejpam-3990	280	10	v6	v6	PROPN
ejpam-3990	280	11	}	}	PUNCT
ejpam-3990	280	12	n	n	PROPN
ejpam-3990	280	13	em	em	PRON
ejpam-3990	280	14	c6	c6	PROPN
ejpam-3990	281	1	[	[	X
ejpam-3990	281	2	v2	v2	X
ejpam-3990	281	3	]	]	X
ejpam-3990	281	4	=	=	SYM
ejpam-3990	281	5	{	{	PUNCT
ejpam-3990	281	6	v2	v2	PROPN
ejpam-3990	281	7	,	,	PUNCT
ejpam-3990	281	8	v4	v4	PROPN
ejpam-3990	281	9	,	,	PUNCT
ejpam-3990	281	10	v6	v6	PROPN
ejpam-3990	281	11	}	}	PUNCT
ejpam-3990	281	12	f	f	PROPN
ejpam-3990	282	1	em	em	PROPN
ejpam-3990	282	2	c6	c6	PROPN
ejpam-3990	283	1	[	[	X
ejpam-3990	283	2	v2	v2	X
ejpam-3990	283	3	]	]	X
ejpam-3990	283	4	=	=	SYM
ejpam-3990	283	5	{	{	PUNCT
ejpam-3990	283	6	v1	v1	PROPN
ejpam-3990	283	7	,	,	PUNCT
ejpam-3990	283	8	v3	v3	PROPN
ejpam-3990	283	9	,	,	PUNCT
ejpam-3990	283	10	v5	v5	PROPN
ejpam-3990	283	11	}	}	PUNCT
ejpam-3990	283	12	n	n	PROPN
ejpam-3990	283	13	em	em	PRON
ejpam-3990	283	14	c6	c6	PROPN
ejpam-3990	284	1	[	[	X
ejpam-3990	284	2	v3	v3	X
ejpam-3990	284	3	]	]	X
ejpam-3990	284	4	=	=	SYM
ejpam-3990	284	5	{	{	PUNCT
ejpam-3990	284	6	v1	v1	PROPN
ejpam-3990	284	7	,	,	PUNCT
ejpam-3990	284	8	v3	v3	PROPN
ejpam-3990	284	9	,	,	PUNCT
ejpam-3990	284	10	v5	v5	PROPN
ejpam-3990	284	11	}	}	PUNCT
ejpam-3990	284	12	f	f	PROPN
ejpam-3990	285	1	em	em	PROPN
ejpam-3990	285	2	c6	c6	PROPN
ejpam-3990	286	1	[	[	X
ejpam-3990	286	2	v3	v3	X
ejpam-3990	286	3	]	]	X
ejpam-3990	286	4	=	=	PRON
ejpam-3990	286	5	{	{	PUNCT
ejpam-3990	286	6	v2	v2	PROPN
ejpam-3990	286	7	,	,	PUNCT
ejpam-3990	286	8	v4	v4	PROPN
ejpam-3990	286	9	,	,	PUNCT
ejpam-3990	286	10	v6	v6	PROPN
ejpam-3990	286	11	}	}	PUNCT
ejpam-3990	286	12	n	n	PROPN
ejpam-3990	286	13	em	em	PRON
ejpam-3990	286	14	c6	c6	PROPN
ejpam-3990	287	1	[	[	X
ejpam-3990	287	2	v4	v4	X
ejpam-3990	287	3	]	]	X
ejpam-3990	287	4	=	=	SYM
ejpam-3990	287	5	{	{	PUNCT
ejpam-3990	287	6	v2	v2	PROPN
ejpam-3990	287	7	,	,	PUNCT
ejpam-3990	287	8	v4	v4	PROPN
ejpam-3990	287	9	,	,	PUNCT
ejpam-3990	287	10	v6	v6	PROPN
ejpam-3990	287	11	}	}	PUNCT
ejpam-3990	287	12	f	f	PROPN
ejpam-3990	288	1	em	em	PROPN
ejpam-3990	288	2	c6	c6	PROPN
ejpam-3990	289	1	[	[	X
ejpam-3990	289	2	v4	v4	X
ejpam-3990	289	3	]	]	X
ejpam-3990	289	4	=	=	SYM
ejpam-3990	289	5	{	{	PUNCT
ejpam-3990	289	6	v1	v1	PROPN
ejpam-3990	289	7	,	,	PUNCT
ejpam-3990	289	8	v3	v3	PROPN
ejpam-3990	289	9	,	,	PUNCT
ejpam-3990	289	10	v5	v5	PROPN
ejpam-3990	289	11	}	}	PUNCT
ejpam-3990	289	12	n	n	PROPN
ejpam-3990	289	13	em	em	PRON
ejpam-3990	289	14	c6	c6	PROPN
ejpam-3990	290	1	[	[	X
ejpam-3990	290	2	v5	v5	X
ejpam-3990	290	3	]	]	X
ejpam-3990	290	4	=	=	SYM
ejpam-3990	290	5	{	{	PUNCT
ejpam-3990	290	6	v1	v1	PROPN
ejpam-3990	290	7	,	,	PUNCT
ejpam-3990	290	8	v3	v3	PROPN
ejpam-3990	290	9	,	,	PUNCT
ejpam-3990	290	10	v5	v5	PROPN
ejpam-3990	290	11	}	}	PUNCT
ejpam-3990	290	12	f	f	PROPN
ejpam-3990	290	13	em	em	PROPN
ejpam-3990	290	14	c6	c6	PROPN
ejpam-3990	291	1	[	[	X
ejpam-3990	291	2	v5	v5	X
ejpam-3990	291	3	]	]	X
ejpam-3990	291	4	=	=	SYM
ejpam-3990	291	5	{	{	PUNCT
ejpam-3990	291	6	v2	v2	PROPN
ejpam-3990	291	7	,	,	PUNCT
ejpam-3990	291	8	v4	v4	PROPN
ejpam-3990	291	9	,	,	PUNCT
ejpam-3990	291	10	v6	v6	PROPN
ejpam-3990	291	11	}	}	PUNCT
ejpam-3990	291	12	n	n	PROPN
ejpam-3990	291	13	em	em	PROPN
ejpam-3990	291	14	c6	c6	PROPN
ejpam-3990	292	1	[	[	X
ejpam-3990	292	2	v6	v6	X
ejpam-3990	292	3	]	]	X
ejpam-3990	292	4	=	=	PUNCT
ejpam-3990	292	5	{	{	PUNCT
ejpam-3990	292	6	v2	v2	PROPN
ejpam-3990	292	7	,	,	PUNCT
ejpam-3990	292	8	v4	v4	PROPN
ejpam-3990	292	9	,	,	PUNCT
ejpam-3990	292	10	v6	v6	PROPN
ejpam-3990	292	11	}	}	PUNCT
ejpam-3990	292	12	f	f	PROPN
ejpam-3990	293	1	em	em	PROPN
ejpam-3990	293	2	c6	c6	PROPN
ejpam-3990	294	1	[	[	X
ejpam-3990	294	2	v6	v6	X
ejpam-3990	294	3	]	]	X
ejpam-3990	294	4	=	=	PUNCT
ejpam-3990	294	5	{	{	PUNCT
ejpam-3990	294	6	v1	v1	PROPN
ejpam-3990	294	7	,	,	PUNCT
ejpam-3990	294	8	v3	v3	PROPN
ejpam-3990	294	9	,	,	PUNCT
ejpam-3990	294	10	v5	v5	PROPN
ejpam-3990	294	11	}	}	PUNCT
ejpam-3990	294	12	.	.	PUNCT
ejpam-3990	295	1	note	note	VERB
ejpam-3990	295	2	that	that	SCONJ
ejpam-3990	295	3	{	{	PUNCT
ejpam-3990	295	4	v1	v1	NOUN
ejpam-3990	295	5	}	}	PUNCT
ejpam-3990	295	6	,	,	PUNCT
ejpam-3990	295	7	{	{	PUNCT
ejpam-3990	295	8	v2	v2	NOUN
ejpam-3990	295	9	}	}	PUNCT
ejpam-3990	295	10	,	,	PUNCT
ejpam-3990	295	11	{	{	PUNCT
ejpam-3990	295	12	v3	v3	NOUN
ejpam-3990	295	13	}	}	PUNCT
ejpam-3990	295	14	,	,	PUNCT
ejpam-3990	295	15	{	{	PUNCT
ejpam-3990	295	16	v4	v4	NOUN
ejpam-3990	295	17	}	}	PUNCT
ejpam-3990	295	18	,	,	PUNCT
ejpam-3990	295	19	{	{	PUNCT
ejpam-3990	295	20	v5	v5	NOUN
ejpam-3990	295	21	}	}	PUNCT
ejpam-3990	295	22	,	,	PUNCT
ejpam-3990	295	23	{	{	PUNCT
ejpam-3990	295	24	v6	v6	NOUN
ejpam-3990	295	25	}	}	PUNCT
ejpam-3990	295	26	/∈	/∈	PUNCT
ejpam-3990	296	1	bemc6	bemc6	NOUN
ejpam-3990	296	2	.	.	PUNCT
ejpam-3990	297	1	hence	hence	ADV
ejpam-3990	297	2	,	,	PUNCT
ejpam-3990	297	3	τ	τ	PROPN
ejpam-3990	297	4	emc6	emc6	PROPN
ejpam-3990	297	5	6=	6=	NUM
ejpam-3990	297	6	dc6	dc6	PROPN
ejpam-3990	297	7	.	.	PUNCT
ejpam-3990	298	1	a.	a.	PROPN
ejpam-3990	298	2	gamorez	gamorez	PROPN
ejpam-3990	298	3	,	,	PUNCT
ejpam-3990	298	4	s.	s.	PROPN
ejpam-3990	298	5	canoy	canoy	PROPN
ejpam-3990	298	6	jr	jr	PROPN
ejpam-3990	298	7	.	.	PROPN
ejpam-3990	298	8	/	/	SYM
ejpam-3990	298	9	eur	eur	PROPN
ejpam-3990	298	10	.	.	PUNCT
ejpam-3990	299	1	j.	j.	PROPN
ejpam-3990	299	2	pure	pure	PROPN
ejpam-3990	299	3	appl	appl	PROPN
ejpam-3990	299	4	.	.	PROPN
ejpam-3990	299	5	math	math	PROPN
ejpam-3990	299	6	,	,	PUNCT
ejpam-3990	299	7	14	14	NUM
ejpam-3990	299	8	(	(	PUNCT
ejpam-3990	299	9	3	3	NUM
ejpam-3990	299	10	)	)	PUNCT
ejpam-3990	299	11	(	(	PUNCT
ejpam-3990	299	12	2021	2021	NUM
ejpam-3990	299	13	)	)	PUNCT
ejpam-3990	299	14	,	,	PUNCT
ejpam-3990	299	15	695	695	NUM
ejpam-3990	299	16	-	-	SYM
ejpam-3990	299	17	705	705	NUM
ejpam-3990	299	18	700	700	NUM
ejpam-3990	299	19	theorem	theorem	NOUN
ejpam-3990	299	20	6	6	NUM
ejpam-3990	299	21	.	.	PUNCT
ejpam-3990	300	1	τ	τ	PROPN
ejpam-3990	300	2	emcn	emcn	PROPN
ejpam-3990	300	3	6=	6=	NUM
ejpam-3990	300	4	dcn	dcn	PROPN
ejpam-3990	300	5	for	for	ADP
ejpam-3990	300	6	n	n	NOUN
ejpam-3990	300	7	=	=	SYM
ejpam-3990	300	8	3	3	NUM
ejpam-3990	300	9	,	,	PUNCT
ejpam-3990	300	10	4	4	NUM
ejpam-3990	300	11	,	,	PUNCT
ejpam-3990	300	12	6	6	NUM
ejpam-3990	300	13	and	and	CCONJ
ejpam-3990	300	14	τ	τ	PROPN
ejpam-3990	300	15	emcn	emcn	PROPN
ejpam-3990	300	16	=	=	SYM
ejpam-3990	300	17	dcn	dcn	PROPN
ejpam-3990	300	18	for	for	ADP
ejpam-3990	300	19	n	n	PRON
ejpam-3990	300	20	∈	∈	PROPN
ejpam-3990	300	21	{	{	PUNCT
ejpam-3990	300	22	5	5	NUM
ejpam-3990	300	23	,	,	PUNCT
ejpam-3990	300	24	7	7	NUM
ejpam-3990	300	25	,	,	PUNCT
ejpam-3990	300	26	8	8	NUM
ejpam-3990	300	27	,	,	PUNCT
ejpam-3990	300	28	...	...	PUNCT
ejpam-3990	300	29	}	}	PUNCT
ejpam-3990	300	30	.	.	PUNCT
ejpam-3990	301	1	proof	proof	NOUN
ejpam-3990	301	2	.	.	PUNCT
ejpam-3990	302	1	since	since	SCONJ
ejpam-3990	302	2	c3	c3	PROPN
ejpam-3990	302	3	∼=	∼=	PROPN
ejpam-3990	302	4	k3	k3	VERB
ejpam-3990	302	5	,	,	PUNCT
ejpam-3990	302	6	τ	τ	PROPN
ejpam-3990	302	7	em	em	PROPN
ejpam-3990	302	8	c3	c3	PROPN
ejpam-3990	302	9	=	=	PROPN
ejpam-3990	302	10	ic3	ic3	PROPN
ejpam-3990	302	11	6=	6=	PROPN
ejpam-3990	302	12	dc3	dc3	NOUN
ejpam-3990	302	13	by	by	ADP
ejpam-3990	302	14	theorem	theorem	NOUN
ejpam-3990	302	15	4	4	NUM
ejpam-3990	302	16	.	.	PUNCT
ejpam-3990	302	17	let	let	VERB
ejpam-3990	302	18	c4	c4	NOUN
ejpam-3990	302	19	=	=	PUNCT
ejpam-3990	303	1	[	[	X
ejpam-3990	303	2	v1	v1	NOUN
ejpam-3990	303	3	,	,	PUNCT
ejpam-3990	303	4	v2	v2	PROPN
ejpam-3990	303	5	,	,	PUNCT
ejpam-3990	303	6	v3	v3	PROPN
ejpam-3990	303	7	,	,	PUNCT
ejpam-3990	303	8	v4	v4	NOUN
ejpam-3990	303	9	,	,	PUNCT
ejpam-3990	303	10	v1	v1	NOUN
ejpam-3990	303	11	]	]	PUNCT
ejpam-3990	303	12	and	and	CCONJ
ejpam-3990	303	13	let	let	VERB
ejpam-3990	303	14	a	a	DET
ejpam-3990	303	15	=	=	PUNCT
ejpam-3990	303	16	v1	v1	NOUN
ejpam-3990	303	17	.	.	PUNCT
ejpam-3990	304	1	set	set	VERB
ejpam-3990	304	2	aa	aa	NOUN
ejpam-3990	304	3	=	=	PUNCT
ejpam-3990	304	4	{	{	PUNCT
ejpam-3990	304	5	v	v	NUM
ejpam-3990	304	6	∈	∈	NOUN
ejpam-3990	304	7	v	v	NOUN
ejpam-3990	304	8	(	(	PUNCT
ejpam-3990	304	9	c4	c4	NOUN
ejpam-3990	304	10	)	)	PUNCT
ejpam-3990	304	11	:	:	PUNCT
ejpam-3990	304	12	a	a	DET
ejpam-3990	304	13	∈	∈	PROPN
ejpam-3990	304	14	n	n	CCONJ
ejpam-3990	304	15	em	em	PRON
ejpam-3990	304	16	c4	c4	NOUN
ejpam-3990	304	17	(	(	PUNCT
ejpam-3990	304	18	v	v	NOUN
ejpam-3990	304	19	)	)	PUNCT
ejpam-3990	304	20	}	}	PUNCT
ejpam-3990	304	21	.	.	PUNCT
ejpam-3990	305	1	then	then	ADV
ejpam-3990	305	2	by	by	ADP
ejpam-3990	305	3	lemma	lemma	PROPN
ejpam-3990	305	4	4	4	NUM
ejpam-3990	305	5	,	,	PUNCT
ejpam-3990	305	6	aa	aa	NOUN
ejpam-3990	305	7	=	=	PUNCT
ejpam-3990	305	8	{	{	PUNCT
ejpam-3990	305	9	v3	v3	PROPN
ejpam-3990	305	10	}	}	PUNCT
ejpam-3990	305	11	.	.	PUNCT
ejpam-3990	306	1	note	note	VERB
ejpam-3990	306	2	that	that	SCONJ
ejpam-3990	306	3	v3	v3	PROPN
ejpam-3990	306	4	/∈	/∈	PUNCT
ejpam-3990	307	1	n	n	CCONJ
ejpam-3990	307	2	em	em	PRON
ejpam-3990	307	3	g	g	PROPN
ejpam-3990	307	4	(	(	PUNCT
ejpam-3990	307	5	v2)∩n	v2)∩n	ADP
ejpam-3990	307	6	em	em	PRON
ejpam-3990	307	7	g	g	PROPN
ejpam-3990	307	8	(	(	PUNCT
ejpam-3990	307	9	v4	v4	PROPN
ejpam-3990	307	10	)	)	PUNCT
ejpam-3990	307	11	.	.	PUNCT
ejpam-3990	308	1	hence	hence	ADV
ejpam-3990	308	2	,	,	PUNCT
ejpam-3990	308	3	we	we	PRON
ejpam-3990	308	4	could	could	AUX
ejpam-3990	308	5	not	not	PART
ejpam-3990	308	6	find	find	VERB
ejpam-3990	308	7	w	w	ADP
ejpam-3990	308	8	6=	6=	ADP
ejpam-3990	308	9	a	a	DET
ejpam-3990	308	10	such	such	ADJ
ejpam-3990	308	11	that	that	SCONJ
ejpam-3990	308	12	v3	v3	PROPN
ejpam-3990	308	13	∈	∈	PROPN
ejpam-3990	308	14	n	n	CCONJ
ejpam-3990	308	15	em	em	PRON
ejpam-3990	308	16	c4	c4	NOUN
ejpam-3990	308	17	(	(	PUNCT
ejpam-3990	308	18	w	w	NOUN
ejpam-3990	308	19	)	)	PUNCT
ejpam-3990	308	20	.	.	PUNCT
ejpam-3990	309	1	therefore	therefore	ADV
ejpam-3990	309	2	,	,	PUNCT
ejpam-3990	309	3	c4	c4	NOUN
ejpam-3990	309	4	does	do	AUX
ejpam-3990	309	5	not	not	PART
ejpam-3990	309	6	induce	induce	VERB
ejpam-3990	309	7	the	the	DET
ejpam-3990	309	8	discrete	discrete	ADJ
ejpam-3990	309	9	topology	topology	NOUN
ejpam-3990	309	10	.	.	PUNCT
ejpam-3990	310	1	suppose	suppose	VERB
ejpam-3990	310	2	c6	c6	PROPN
ejpam-3990	310	3	=	=	PUNCT
ejpam-3990	311	1	[	[	X
ejpam-3990	311	2	v1	v1	NOUN
ejpam-3990	311	3	,	,	PUNCT
ejpam-3990	311	4	v2	v2	PROPN
ejpam-3990	311	5	,	,	PUNCT
ejpam-3990	311	6	v3	v3	PROPN
ejpam-3990	311	7	,	,	PUNCT
ejpam-3990	311	8	v4	v4	PROPN
ejpam-3990	311	9	,	,	PUNCT
ejpam-3990	311	10	v5	v5	PROPN
ejpam-3990	311	11	,	,	PUNCT
ejpam-3990	311	12	v6	v6	NOUN
ejpam-3990	311	13	,	,	PUNCT
ejpam-3990	311	14	v1	v1	PROPN
ejpam-3990	311	15	]	]	PUNCT
ejpam-3990	311	16	and	and	CCONJ
ejpam-3990	311	17	let	let	VERB
ejpam-3990	311	18	a	a	DET
ejpam-3990	311	19	=	=	PUNCT
ejpam-3990	311	20	v1	v1	NOUN
ejpam-3990	311	21	.	.	PUNCT
ejpam-3990	312	1	set	set	VERB
ejpam-3990	312	2	aa	aa	NOUN
ejpam-3990	312	3	=	=	PUNCT
ejpam-3990	312	4	{	{	PUNCT
ejpam-3990	312	5	v	v	NUM
ejpam-3990	312	6	∈	∈	NOUN
ejpam-3990	312	7	v	v	NOUN
ejpam-3990	312	8	(	(	PUNCT
ejpam-3990	312	9	c6	c6	PROPN
ejpam-3990	312	10	)	)	PUNCT
ejpam-3990	312	11	:	:	PUNCT
ejpam-3990	312	12	a	a	DET
ejpam-3990	312	13	∈	∈	PROPN
ejpam-3990	312	14	n	n	CCONJ
ejpam-3990	312	15	em	em	PROPN
ejpam-3990	312	16	c6	c6	PROPN
ejpam-3990	312	17	(	(	PUNCT
ejpam-3990	312	18	v	v	NOUN
ejpam-3990	312	19	)	)	PUNCT
ejpam-3990	312	20	}	}	PUNCT
ejpam-3990	312	21	.	.	PUNCT
ejpam-3990	313	1	again	again	ADV
ejpam-3990	313	2	,	,	PUNCT
ejpam-3990	313	3	by	by	ADP
ejpam-3990	313	4	lemma	lemma	PROPN
ejpam-3990	313	5	4	4	NUM
ejpam-3990	313	6	,	,	PUNCT
ejpam-3990	313	7	aa	aa	NOUN
ejpam-3990	313	8	=	=	PUNCT
ejpam-3990	313	9	{	{	PUNCT
ejpam-3990	313	10	v3	v3	PROPN
ejpam-3990	313	11	,	,	PUNCT
ejpam-3990	313	12	v5	v5	PROPN
ejpam-3990	313	13	}	}	PUNCT
ejpam-3990	313	14	.	.	PUNCT
ejpam-3990	314	1	note	note	VERB
ejpam-3990	314	2	that	that	SCONJ
ejpam-3990	314	3	the	the	DET
ejpam-3990	314	4	only	only	ADJ
ejpam-3990	314	5	vertex	vertex	NOUN
ejpam-3990	314	6	w	w	ADP
ejpam-3990	314	7	6=	6=	ADP
ejpam-3990	314	8	a	a	PRON
ejpam-3990	314	9	with	with	ADP
ejpam-3990	314	10	v3	v3	PROPN
ejpam-3990	314	11	∈	∈	PROPN
ejpam-3990	314	12	n	n	CCONJ
ejpam-3990	314	13	em	em	PROPN
ejpam-3990	314	14	c6	c6	PROPN
ejpam-3990	314	15	(	(	PUNCT
ejpam-3990	314	16	w	w	NOUN
ejpam-3990	314	17	)	)	PUNCT
ejpam-3990	314	18	is	be	AUX
ejpam-3990	314	19	v5	v5	PROPN
ejpam-3990	314	20	.	.	PUNCT
ejpam-3990	315	1	however	however	ADV
ejpam-3990	315	2	,	,	PUNCT
ejpam-3990	315	3	a	a	DET
ejpam-3990	315	4	=	=	NOUN
ejpam-3990	315	5	v1	v1	NOUN
ejpam-3990	315	6	∈	∈	PROPN
ejpam-3990	315	7	n	n	CCONJ
ejpam-3990	315	8	em	em	PROPN
ejpam-3990	315	9	c6	c6	PROPN
ejpam-3990	315	10	(	(	PUNCT
ejpam-3990	315	11	v5	v5	PROPN
ejpam-3990	315	12	)	)	PUNCT
ejpam-3990	315	13	.	.	PUNCT
ejpam-3990	316	1	thus	thus	ADV
ejpam-3990	316	2	,	,	PUNCT
ejpam-3990	316	3	by	by	ADP
ejpam-3990	316	4	theorem	theorem	NOUN
ejpam-3990	316	5	5	5	NUM
ejpam-3990	316	6	,	,	PUNCT
ejpam-3990	316	7	c6	c6	PROPN
ejpam-3990	316	8	does	do	AUX
ejpam-3990	316	9	not	not	PART
ejpam-3990	316	10	induce	induce	VERB
ejpam-3990	316	11	the	the	DET
ejpam-3990	316	12	discrete	discrete	ADJ
ejpam-3990	316	13	topology	topology	NOUN
ejpam-3990	316	14	.	.	PUNCT
ejpam-3990	317	1	next	next	ADV
ejpam-3990	317	2	let	let	VERB
ejpam-3990	317	3	n	n	PROPN
ejpam-3990	317	4	=	=	SYM
ejpam-3990	317	5	5	5	NUM
ejpam-3990	317	6	and	and	CCONJ
ejpam-3990	317	7	let	let	VERB
ejpam-3990	317	8	a	a	DET
ejpam-3990	317	9	∈	∈	PROPN
ejpam-3990	317	10	v	v	NOUN
ejpam-3990	317	11	(	(	PUNCT
ejpam-3990	317	12	c5	c5	PROPN
ejpam-3990	317	13	)	)	PUNCT
ejpam-3990	317	14	.	.	PUNCT
ejpam-3990	318	1	we	we	PRON
ejpam-3990	318	2	may	may	AUX
ejpam-3990	318	3	assume	assume	VERB
ejpam-3990	318	4	that	that	SCONJ
ejpam-3990	318	5	a	a	DET
ejpam-3990	318	6	=	=	SYM
ejpam-3990	318	7	v1	v1	NOUN
ejpam-3990	318	8	.	.	PUNCT
ejpam-3990	319	1	let	let	VERB
ejpam-3990	319	2	aa	aa	NOUN
ejpam-3990	319	3	=	=	PUNCT
ejpam-3990	319	4	{	{	PUNCT
ejpam-3990	319	5	v	v	NUM
ejpam-3990	319	6	∈	∈	NOUN
ejpam-3990	319	7	v	v	NOUN
ejpam-3990	319	8	(	(	PUNCT
ejpam-3990	319	9	cn	cn	PROPN
ejpam-3990	319	10	)	)	PUNCT
ejpam-3990	319	11	:	:	PUNCT
ejpam-3990	319	12	a	a	DET
ejpam-3990	319	13	∈	∈	PROPN
ejpam-3990	319	14	n	n	CCONJ
ejpam-3990	319	15	em	em	PRON
ejpam-3990	319	16	cn	cn	INTJ
ejpam-3990	319	17	(	(	PUNCT
ejpam-3990	319	18	v	v	NOUN
ejpam-3990	319	19	)	)	PUNCT
ejpam-3990	319	20	}	}	PUNCT
ejpam-3990	319	21	.	.	PUNCT
ejpam-3990	320	1	then	then	ADV
ejpam-3990	320	2	aa	aa	INTJ
ejpam-3990	320	3	=	=	PUNCT
ejpam-3990	320	4	{	{	PUNCT
ejpam-3990	320	5	v3	v3	PROPN
ejpam-3990	320	6	,	,	PUNCT
ejpam-3990	320	7	v4	v4	PROPN
ejpam-3990	320	8	}	}	PUNCT
ejpam-3990	320	9	.	.	PUNCT
ejpam-3990	321	1	since	since	SCONJ
ejpam-3990	321	2	v3	v3	PROPN
ejpam-3990	321	3	∈	∈	PROPN
ejpam-3990	321	4	n	n	PRON
ejpam-3990	321	5	em	em	PRON
ejpam-3990	321	6	cn	cn	PROPN
ejpam-3990	321	7	(	(	PUNCT
ejpam-3990	321	8	v5	v5	PROPN
ejpam-3990	321	9	)	)	PUNCT
ejpam-3990	321	10	,	,	PUNCT
ejpam-3990	321	11	v4	v4	PROPN
ejpam-3990	321	12	∈	∈	PROPN
ejpam-3990	322	1	n	n	CCONJ
ejpam-3990	322	2	em	em	PRON
ejpam-3990	322	3	cn	cn	PROPN
ejpam-3990	322	4	(	(	PUNCT
ejpam-3990	322	5	v2	v2	PROPN
ejpam-3990	322	6	)	)	PUNCT
ejpam-3990	322	7	where	where	SCONJ
ejpam-3990	322	8	v2	v2	NOUN
ejpam-3990	322	9	,	,	PUNCT
ejpam-3990	322	10	v5	v5	PROPN
ejpam-3990	322	11	/∈	/∈	PUNCT
ejpam-3990	323	1	aa	aa	PROPN
ejpam-3990	323	2	,	,	PUNCT
ejpam-3990	323	3	it	it	PRON
ejpam-3990	323	4	follows	follow	VERB
ejpam-3990	323	5	from	from	ADP
ejpam-3990	323	6	theorem	theorem	ADJ
ejpam-3990	323	7	5	5	NUM
ejpam-3990	323	8	that	that	PRON
ejpam-3990	323	9	τ	τ	PROPN
ejpam-3990	323	10	emc5	emc5	PROPN
ejpam-3990	323	11	=	=	PROPN
ejpam-3990	323	12	dc5	dc5	PROPN
ejpam-3990	323	13	.	.	PUNCT
ejpam-3990	324	1	suppose	suppose	VERB
ejpam-3990	324	2	n	n	PRON
ejpam-3990	324	3	≥	≥	NUM
ejpam-3990	324	4	7	7	NUM
ejpam-3990	324	5	.	.	PUNCT
ejpam-3990	325	1	let	let	VERB
ejpam-3990	325	2	a	a	DET
ejpam-3990	325	3	=	=	NOUN
ejpam-3990	325	4	v1	v1	NOUN
ejpam-3990	325	5	.	.	PUNCT
ejpam-3990	326	1	then	then	ADV
ejpam-3990	326	2	,	,	PUNCT
ejpam-3990	326	3	aa	aa	NOUN
ejpam-3990	326	4	=	=	PUNCT
ejpam-3990	326	5	{	{	PUNCT
ejpam-3990	326	6	v	v	NUM
ejpam-3990	326	7	∈	∈	NOUN
ejpam-3990	326	8	v	v	NOUN
ejpam-3990	326	9	(	(	PUNCT
ejpam-3990	326	10	cn	cn	PROPN
ejpam-3990	326	11	)	)	PUNCT
ejpam-3990	326	12	:	:	PUNCT
ejpam-3990	326	13	a	a	DET
ejpam-3990	326	14	∈	∈	PROPN
ejpam-3990	326	15	n	n	CCONJ
ejpam-3990	326	16	em	em	PRON
ejpam-3990	326	17	cn	cn	INTJ
ejpam-3990	326	18	(	(	PUNCT
ejpam-3990	326	19	v	v	NOUN
ejpam-3990	326	20	)	)	PUNCT
ejpam-3990	326	21	}	}	PUNCT
ejpam-3990	326	22	.	.	PUNCT
ejpam-3990	327	1	thus	thus	ADV
ejpam-3990	327	2	,	,	PUNCT
ejpam-3990	327	3	aa	aa	NOUN
ejpam-3990	327	4	=	=	PUNCT
ejpam-3990	327	5	{	{	PUNCT
ejpam-3990	327	6	v3	v3	PROPN
ejpam-3990	327	7	,	,	PUNCT
ejpam-3990	327	8	vn−1	vn−1	PROPN
ejpam-3990	327	9	}	}	PUNCT
ejpam-3990	327	10	.	.	PUNCT
ejpam-3990	328	1	note	note	VERB
ejpam-3990	328	2	that	that	SCONJ
ejpam-3990	328	3	v3	v3	PROPN
ejpam-3990	328	4	∈	∈	PROPN
ejpam-3990	328	5	n	n	PRON
ejpam-3990	328	6	em	em	PRON
ejpam-3990	328	7	cn	cn	PROPN
ejpam-3990	328	8	(	(	PUNCT
ejpam-3990	328	9	v5	v5	PROPN
ejpam-3990	328	10	)	)	PUNCT
ejpam-3990	328	11	and	and	CCONJ
ejpam-3990	328	12	vn−1	vn−1	PROPN
ejpam-3990	328	13	∈	∈	PROPN
ejpam-3990	329	1	n	n	CCONJ
ejpam-3990	329	2	em	em	PRON
ejpam-3990	329	3	cn	cn	PROPN
ejpam-3990	329	4	(	(	PUNCT
ejpam-3990	329	5	vn−3	vn−3	PROPN
ejpam-3990	329	6	)	)	PUNCT
ejpam-3990	329	7	but	but	CCONJ
ejpam-3990	329	8	v1	v1	NOUN
ejpam-3990	329	9	/∈	/∈	PUNCT
ejpam-3990	330	1	n	n	CCONJ
ejpam-3990	330	2	em	em	PRON
ejpam-3990	330	3	cn	cn	PROPN
ejpam-3990	330	4	(	(	PUNCT
ejpam-3990	330	5	v5	v5	PROPN
ejpam-3990	330	6	)	)	PUNCT
ejpam-3990	330	7	∩n	∩n	NOUN
ejpam-3990	330	8	em	em	PRON
ejpam-3990	330	9	cn	cn	PROPN
ejpam-3990	330	10	(	(	PUNCT
ejpam-3990	330	11	vn−3	vn−3	PROPN
ejpam-3990	330	12	)	)	PUNCT
ejpam-3990	330	13	.	.	PUNCT
ejpam-3990	331	1	thus	thus	ADV
ejpam-3990	331	2	,	,	PUNCT
ejpam-3990	331	3	by	by	ADP
ejpam-3990	331	4	theorem	theorem	NOUN
ejpam-3990	331	5	5	5	NUM
ejpam-3990	331	6	,	,	PUNCT
ejpam-3990	331	7	τ	τ	PROPN
ejpam-3990	331	8	emcn	emcn	PROPN
ejpam-3990	331	9	=	=	SYM
ejpam-3990	331	10	dcn	dcn	PROPN
ejpam-3990	331	11	.	.	PUNCT
ejpam-3990	331	12	theorem	theorem	VERB
ejpam-3990	331	13	7	7	NUM
ejpam-3990	331	14	.	.	PUNCT
ejpam-3990	332	1	let	let	VERB
ejpam-3990	332	2	g	g	PROPN
ejpam-3990	332	3	=	=	VERB
ejpam-3990	332	4	cn	cn	PROPN
ejpam-3990	332	5	be	be	AUX
ejpam-3990	332	6	a	a	DET
ejpam-3990	332	7	cycle	cycle	NOUN
ejpam-3990	332	8	with	with	ADP
ejpam-3990	332	9	≥	≥	NOUN
ejpam-3990	332	10	4	4	NUM
ejpam-3990	332	11	.	.	PUNCT
ejpam-3990	333	1	then	then	ADV
ejpam-3990	333	2	f	f	PROPN
ejpam-3990	333	3	em	em	PRON
ejpam-3990	333	4	g	g	PROPN
ejpam-3990	334	1	[	[	X
ejpam-3990	334	2	vi	vi	X
ejpam-3990	334	3	]	]	X
ejpam-3990	334	4	=	=	PUNCT
ejpam-3990	334	5			PUNCT
ejpam-3990	334	6	v	v	NOUN
ejpam-3990	334	7	(	(	PUNCT
ejpam-3990	334	8	g)\{vi	g)\{vi	PROPN
ejpam-3990	334	9	,	,	PUNCT
ejpam-3990	334	10	vi+2	vi+2	PROPN
ejpam-3990	334	11	,	,	PUNCT
ejpam-3990	334	12	vi+n−2	vi+n−2	PROPN
ejpam-3990	334	13	}	}	PUNCT
ejpam-3990	334	14	,	,	PUNCT
ejpam-3990	334	15	if	if	SCONJ
ejpam-3990	334	16	i	i	PRON
ejpam-3990	334	17	=	=	NOUN
ejpam-3990	334	18	1	1	NUM
ejpam-3990	334	19	,	,	PUNCT
ejpam-3990	334	20	2	2	NUM
ejpam-3990	334	21	v	v	NOUN
ejpam-3990	334	22	(	(	PUNCT
ejpam-3990	334	23	g)\{vi−2	g)\{vi−2	NOUN
ejpam-3990	334	24	,	,	PUNCT
ejpam-3990	334	25	vi	vi	NOUN
ejpam-3990	334	26	,	,	PUNCT
ejpam-3990	334	27	vi+2	vi+2	NUM
ejpam-3990	334	28	}	}	PUNCT
ejpam-3990	334	29	,	,	PUNCT
ejpam-3990	334	30	if	if	SCONJ
ejpam-3990	334	31	3	3	NUM
ejpam-3990	334	32	≤	≤	NUM
ejpam-3990	334	33	i	i	NOUN
ejpam-3990	334	34	≤	≤	ADJ
ejpam-3990	334	35	n−	n−	NOUN
ejpam-3990	334	36	2	2	NUM
ejpam-3990	334	37	v	v	NOUN
ejpam-3990	334	38	(	(	PUNCT
ejpam-3990	334	39	g)\{vi−n+2	g)\{vi−n+2	PROPN
ejpam-3990	334	40	,	,	PUNCT
ejpam-3990	334	41	vi−2	vi−2	PROPN
ejpam-3990	334	42	,	,	PUNCT
ejpam-3990	334	43	vi	vi	NOUN
ejpam-3990	334	44	}	}	PUNCT
ejpam-3990	334	45	,	,	PUNCT
ejpam-3990	334	46	if	if	SCONJ
ejpam-3990	334	47	i	i	PRON
ejpam-3990	334	48	=	=	SYM
ejpam-3990	334	49	n	n	CCONJ
ejpam-3990	334	50	,	,	PUNCT
ejpam-3990	334	51	n−	n−	NOUN
ejpam-3990	334	52	1	1	NUM
ejpam-3990	334	53	where	where	SCONJ
ejpam-3990	334	54	vi+2	vi+2	NUM
ejpam-3990	334	55	=	=	SYM
ejpam-3990	334	56	vi+n−2	vi+n−2	PROPN
ejpam-3990	334	57	and	and	CCONJ
ejpam-3990	334	58	vi−2	vi−2	PROPN
ejpam-3990	334	59	=	=	SYM
ejpam-3990	334	60	vi−n+2	vi−n+2	NOUN
ejpam-3990	334	61	if	if	SCONJ
ejpam-3990	334	62	n	n	NOUN
ejpam-3990	334	63	=	=	SYM
ejpam-3990	334	64	4	4	X
ejpam-3990	334	65	.	.	PUNCT
ejpam-3990	334	66	proof	proof	NOUN
ejpam-3990	334	67	.	.	PUNCT
ejpam-3990	335	1	let	let	VERB
ejpam-3990	335	2	i	i	PRON
ejpam-3990	335	3	=	=	NOUN
ejpam-3990	335	4	1	1	X
ejpam-3990	335	5	.	.	PUNCT
ejpam-3990	335	6	by	by	ADP
ejpam-3990	335	7	lemma	lemma	PROPN
ejpam-3990	335	8	4	4	NUM
ejpam-3990	335	9	,	,	PUNCT
ejpam-3990	335	10	emg	emg	NOUN
ejpam-3990	335	11	(	(	PUNCT
ejpam-3990	335	12	v	v	NOUN
ejpam-3990	335	13	)	)	PUNCT
ejpam-3990	335	14	=	=	SYM
ejpam-3990	335	15	2	2	X
ejpam-3990	335	16	.	.	PUNCT
ejpam-3990	336	1	thus	thus	ADV
ejpam-3990	336	2	,	,	PUNCT
ejpam-3990	336	3	n	n	PRON
ejpam-3990	336	4	em	em	PRON
ejpam-3990	336	5	c4	c4	NOUN
ejpam-3990	336	6	[	[	X
ejpam-3990	336	7	v1	v1	NOUN
ejpam-3990	336	8	]	]	X
ejpam-3990	336	9	=	=	SYM
ejpam-3990	336	10	{	{	PUNCT
ejpam-3990	336	11	v1	v1	PROPN
ejpam-3990	336	12	,	,	PUNCT
ejpam-3990	336	13	v3	v3	PROPN
ejpam-3990	336	14	}	}	PUNCT
ejpam-3990	336	15	.	.	PUNCT
ejpam-3990	337	1	hence	hence	ADV
ejpam-3990	337	2	,	,	PUNCT
ejpam-3990	337	3	f	f	PROPN
ejpam-3990	337	4	em	em	PRON
ejpam-3990	337	5	c4	c4	VERB
ejpam-3990	337	6	[	[	X
ejpam-3990	337	7	v1	v1	NOUN
ejpam-3990	337	8	]	]	X
ejpam-3990	337	9	=	=	SYM
ejpam-3990	337	10	v	v	NOUN
ejpam-3990	337	11	(	(	PUNCT
ejpam-3990	337	12	c4)\{vi	c4)\{vi	NOUN
ejpam-3990	337	13	,	,	PUNCT
ejpam-3990	337	14	vi+2	vi+2	NUM
ejpam-3990	337	15	}	}	PUNCT
ejpam-3990	337	16	.	.	PUNCT
ejpam-3990	338	1	similarly	similarly	ADV
ejpam-3990	338	2	,	,	PUNCT
ejpam-3990	338	3	if	if	SCONJ
ejpam-3990	338	4	i	i	PRON
ejpam-3990	338	5	=	=	SYM
ejpam-3990	338	6	2	2	NUM
ejpam-3990	338	7	,	,	PUNCT
ejpam-3990	338	8	then	then	ADV
ejpam-3990	338	9	f	f	PROPN
ejpam-3990	338	10	em	em	PRON
ejpam-3990	338	11	c4	c4	NOUN
ejpam-3990	338	12	[	[	X
ejpam-3990	338	13	v2	v2	X
ejpam-3990	338	14	]	]	X
ejpam-3990	338	15	=	=	SYM
ejpam-3990	338	16	v	v	NOUN
ejpam-3990	338	17	(	(	PUNCT
ejpam-3990	338	18	c4)\{vi	c4)\{vi	NOUN
ejpam-3990	338	19	,	,	PUNCT
ejpam-3990	338	20	vi+2	vi+2	ADP
ejpam-3990	338	21	}	}	PUNCT
ejpam-3990	338	22	.	.	PUNCT
ejpam-3990	339	1	if	if	SCONJ
ejpam-3990	339	2	i	i	PRON
ejpam-3990	339	3	=	=	SYM
ejpam-3990	339	4	n	n	CCONJ
ejpam-3990	339	5	,	,	PUNCT
ejpam-3990	339	6	then	then	ADV
ejpam-3990	339	7	n	n	CCONJ
ejpam-3990	339	8	em	em	PRON
ejpam-3990	339	9	c4	c4	NOUN
ejpam-3990	340	1	[	[	X
ejpam-3990	340	2	v4	v4	X
ejpam-3990	340	3	]	]	X
ejpam-3990	340	4	=	=	SYM
ejpam-3990	340	5	{	{	PUNCT
ejpam-3990	340	6	v2	v2	PROPN
ejpam-3990	340	7	,	,	PUNCT
ejpam-3990	340	8	v4	v4	PROPN
ejpam-3990	340	9	}	}	PUNCT
ejpam-3990	340	10	.	.	PUNCT
ejpam-3990	341	1	thus	thus	ADV
ejpam-3990	341	2	,	,	PUNCT
ejpam-3990	341	3	f	f	PROPN
ejpam-3990	341	4	em	em	PRON
ejpam-3990	341	5	c4	c4	VERB
ejpam-3990	341	6	[	[	X
ejpam-3990	341	7	v4	v4	X
ejpam-3990	341	8	]	]	X
ejpam-3990	341	9	=	=	SYM
ejpam-3990	341	10	v	v	X
ejpam-3990	341	11	(	(	PUNCT
ejpam-3990	341	12	c4)\{vi	c4)\{vi	NOUN
ejpam-3990	341	13	,	,	PUNCT
ejpam-3990	341	14	vi−2	vi−2	NOUN
ejpam-3990	341	15	}	}	PUNCT
ejpam-3990	341	16	.	.	PUNCT
ejpam-3990	342	1	similarly	similarly	ADV
ejpam-3990	342	2	,	,	PUNCT
ejpam-3990	342	3	if	if	SCONJ
ejpam-3990	342	4	i	i	PRON
ejpam-3990	342	5	=	=	VERB
ejpam-3990	342	6	n−	n−	NOUN
ejpam-3990	342	7	1	1	NUM
ejpam-3990	342	8	,	,	PUNCT
ejpam-3990	342	9	then	then	ADV
ejpam-3990	342	10	f	f	PROPN
ejpam-3990	342	11	em	em	PROPN
ejpam-3990	342	12	c4	c4	NOUN
ejpam-3990	342	13	[	[	X
ejpam-3990	342	14	v3	v3	X
ejpam-3990	342	15	]	]	X
ejpam-3990	342	16	=	=	SYM
ejpam-3990	342	17	v	v	X
ejpam-3990	342	18	(	(	PUNCT
ejpam-3990	342	19	c4)\{vi	c4)\{vi	NOUN
ejpam-3990	342	20	,	,	PUNCT
ejpam-3990	342	21	vi−2	vi−2	NOUN
ejpam-3990	342	22	}	}	PUNCT
ejpam-3990	342	23	.	.	PUNCT
ejpam-3990	343	1	let	let	VERB
ejpam-3990	343	2	i	i	PRON
ejpam-3990	343	3	∈	∈	PROPN
ejpam-3990	343	4	{	{	PUNCT
ejpam-3990	343	5	1	1	NUM
ejpam-3990	343	6	,	,	PUNCT
ejpam-3990	343	7	2	2	NUM
ejpam-3990	343	8	}	}	PUNCT
ejpam-3990	343	9	.	.	PUNCT
ejpam-3990	344	1	by	by	ADP
ejpam-3990	344	2	lemma	lemma	PROPN
ejpam-3990	344	3	4	4	NUM
ejpam-3990	344	4	,	,	PUNCT
ejpam-3990	344	5	n	n	PRON
ejpam-3990	344	6	em	em	PRON
ejpam-3990	344	7	cn	cn	X
ejpam-3990	345	1	[	[	X
ejpam-3990	345	2	v1	v1	X
ejpam-3990	345	3	]	]	X
ejpam-3990	345	4	=	=	SYM
ejpam-3990	345	5	{	{	PUNCT
ejpam-3990	345	6	v1	v1	PROPN
ejpam-3990	345	7	,	,	PUNCT
ejpam-3990	345	8	v3	v3	PROPN
ejpam-3990	345	9	,	,	PUNCT
ejpam-3990	345	10	vn−1	vn−1	ADJ
ejpam-3990	345	11	}	}	PUNCT
ejpam-3990	345	12	and	and	CCONJ
ejpam-3990	345	13	n	n	PRON
ejpam-3990	345	14	em	em	PRON
ejpam-3990	345	15	cn	cn	PROPN
ejpam-3990	346	1	[	[	X
ejpam-3990	346	2	v2	v2	X
ejpam-3990	346	3	]	]	X
ejpam-3990	346	4	=	=	SYM
ejpam-3990	346	5	{	{	PUNCT
ejpam-3990	346	6	v2	v2	PROPN
ejpam-3990	346	7	,	,	PUNCT
ejpam-3990	346	8	v4	v4	NOUN
ejpam-3990	346	9	,	,	PUNCT
ejpam-3990	346	10	vn	vn	PROPN
ejpam-3990	346	11	}	}	PUNCT
ejpam-3990	346	12	.	.	PUNCT
ejpam-3990	347	1	thus	thus	ADV
ejpam-3990	347	2	,	,	PUNCT
ejpam-3990	347	3	f	f	PROPN
ejpam-3990	347	4	em	em	PRON
ejpam-3990	347	5	cn	cn	PROPN
ejpam-3990	348	1	[	[	X
ejpam-3990	348	2	vi	vi	X
ejpam-3990	348	3	]	]	X
ejpam-3990	348	4	=	=	SYM
ejpam-3990	348	5	v	v	X
ejpam-3990	348	6	(	(	PUNCT
ejpam-3990	348	7	cn)\{vi	cn)\{vi	PROPN
ejpam-3990	348	8	,	,	PUNCT
ejpam-3990	348	9	vi+2	vi+2	NUM
ejpam-3990	348	10	,	,	PUNCT
ejpam-3990	348	11	vi+n−2	vi+n−2	PROPN
ejpam-3990	348	12	}	}	PUNCT
ejpam-3990	348	13	.	.	PUNCT
ejpam-3990	349	1	suppose	suppose	VERB
ejpam-3990	349	2	that	that	SCONJ
ejpam-3990	349	3	i	i	PRON
ejpam-3990	349	4	∈	∈	PROPN
ejpam-3990	349	5	{	{	PUNCT
ejpam-3990	349	6	3	3	NUM
ejpam-3990	349	7	,	,	PUNCT
ejpam-3990	349	8	4	4	NUM
ejpam-3990	349	9	,	,	PUNCT
ejpam-3990	349	10	...	...	PUNCT
ejpam-3990	349	11	,	,	PUNCT
ejpam-3990	349	12	n−	n−	NOUN
ejpam-3990	349	13	2	2	NUM
ejpam-3990	349	14	}	}	PUNCT
ejpam-3990	349	15	.	.	PUNCT
ejpam-3990	350	1	then	then	ADV
ejpam-3990	350	2	,	,	PUNCT
ejpam-3990	350	3	n	n	PRON
ejpam-3990	350	4	em	em	PRON
ejpam-3990	350	5	cn	cn	X
ejpam-3990	351	1	[	[	X
ejpam-3990	351	2	vi	vi	X
ejpam-3990	351	3	]	]	X
ejpam-3990	351	4	=	=	SYM
ejpam-3990	351	5	{	{	PUNCT
ejpam-3990	351	6	vi−2	vi−2	PROPN
ejpam-3990	351	7	,	,	PUNCT
ejpam-3990	351	8	vi	vi	NOUN
ejpam-3990	351	9	,	,	PUNCT
ejpam-3990	351	10	vi+2	vi+2	NUM
ejpam-3990	351	11	}	}	PUNCT
ejpam-3990	351	12	.	.	PUNCT
ejpam-3990	352	1	it	it	PRON
ejpam-3990	352	2	follows	follow	VERB
ejpam-3990	352	3	that	that	SCONJ
ejpam-3990	352	4	f	f	PROPN
ejpam-3990	353	1	em	em	PRON
ejpam-3990	353	2	cn	cn	PROPN
ejpam-3990	354	1	[	[	X
ejpam-3990	354	2	vi	vi	X
ejpam-3990	354	3	]	]	X
ejpam-3990	354	4	=	=	SYM
ejpam-3990	354	5	v	v	NOUN
ejpam-3990	354	6	(	(	PUNCT
ejpam-3990	354	7	cn)\{vi−2	cn)\{vi−2	X
ejpam-3990	354	8	,	,	PUNCT
ejpam-3990	354	9	vi	vi	NOUN
ejpam-3990	354	10	,	,	PUNCT
ejpam-3990	354	11	vi+2	vi+2	NUM
ejpam-3990	354	12	}	}	PUNCT
ejpam-3990	354	13	.	.	PUNCT
ejpam-3990	355	1	next	next	ADV
ejpam-3990	355	2	,	,	PUNCT
ejpam-3990	355	3	suppose	suppose	VERB
ejpam-3990	355	4	,	,	PUNCT
ejpam-3990	355	5	i	i	PRON
ejpam-3990	355	6	∈	∈	PROPN
ejpam-3990	355	7	{	{	PUNCT
ejpam-3990	355	8	n	n	CCONJ
ejpam-3990	355	9	,	,	PUNCT
ejpam-3990	355	10	n	n	CCONJ
ejpam-3990	355	11	−	−	PROPN
ejpam-3990	355	12	1	1	NUM
ejpam-3990	355	13	}	}	PUNCT
ejpam-3990	355	14	.	.	PUNCT
ejpam-3990	356	1	by	by	ADP
ejpam-3990	356	2	lemma	lemma	PROPN
ejpam-3990	356	3	4	4	NUM
ejpam-3990	356	4	,	,	PUNCT
ejpam-3990	356	5	n	n	PRON
ejpam-3990	356	6	em	em	PRON
ejpam-3990	356	7	cn	cn	PROPN
ejpam-3990	357	1	[	[	X
ejpam-3990	357	2	vn	vn	X
ejpam-3990	357	3	]	]	X
ejpam-3990	357	4	=	=	SYM
ejpam-3990	357	5	{	{	PUNCT
ejpam-3990	357	6	v2	v2	PROPN
ejpam-3990	357	7	,	,	PUNCT
ejpam-3990	357	8	vn−2	vn−2	PROPN
ejpam-3990	357	9	,	,	PUNCT
ejpam-3990	357	10	vn	vn	NOUN
ejpam-3990	357	11	}	}	PUNCT
ejpam-3990	357	12	and	and	CCONJ
ejpam-3990	357	13	n	n	PRON
ejpam-3990	358	1	em	em	PRON
ejpam-3990	358	2	cn	cn	PROPN
ejpam-3990	359	1	[	[	X
ejpam-3990	359	2	vn−1	vn−1	PROPN
ejpam-3990	359	3	]	]	X
ejpam-3990	359	4	=	=	SYM
ejpam-3990	359	5	{	{	PUNCT
ejpam-3990	359	6	v1	v1	PROPN
ejpam-3990	359	7	,	,	PUNCT
ejpam-3990	359	8	vn−3	vn−3	PROPN
ejpam-3990	359	9	,	,	PUNCT
ejpam-3990	359	10	vn−1	vn−1	ADJ
ejpam-3990	359	11	}	}	PUNCT
ejpam-3990	359	12	.	.	PUNCT
ejpam-3990	360	1	therefore	therefore	ADV
ejpam-3990	360	2	,	,	PUNCT
ejpam-3990	360	3	f	f	PROPN
ejpam-3990	360	4	em	em	PRON
ejpam-3990	360	5	cn	cn	PROPN
ejpam-3990	361	1	[	[	X
ejpam-3990	361	2	vi	vi	X
ejpam-3990	361	3	]	]	X
ejpam-3990	361	4	=	=	SYM
ejpam-3990	361	5	v	v	NOUN
ejpam-3990	361	6	(	(	PUNCT
ejpam-3990	361	7	cn)\{vi−2	cn)\{vi−2	X
ejpam-3990	361	8	,	,	PUNCT
ejpam-3990	361	9	vi	vi	PROPN
ejpam-3990	361	10	,	,	PUNCT
ejpam-3990	361	11	vi−n+2	vi−n+2	NOUN
ejpam-3990	361	12	}	}	PUNCT
ejpam-3990	361	13	.	.	PUNCT
ejpam-3990	362	1	this	this	PRON
ejpam-3990	362	2	proves	prove	VERB
ejpam-3990	362	3	the	the	DET
ejpam-3990	362	4	assertion	assertion	NOUN
ejpam-3990	362	5	.	.	PUNCT
ejpam-3990	363	1	lemma	lemma	PROPN
ejpam-3990	363	2	5	5	NUM
ejpam-3990	363	3	.	.	PUNCT
ejpam-3990	364	1	f	f	PROPN
ejpam-3990	365	1	em	em	PRON
ejpam-3990	365	2	c3	c3	X
ejpam-3990	366	1	[	[	X
ejpam-3990	366	2	v	v	X
ejpam-3990	366	3	]	]	X
ejpam-3990	366	4	=	=	SYM
ejpam-3990	366	5	∅	∅	NOUN
ejpam-3990	366	6	for	for	ADP
ejpam-3990	366	7	all	all	PRON
ejpam-3990	366	8	v	v	ADP
ejpam-3990	366	9	∈	∈	NOUN
ejpam-3990	366	10	v	v	NOUN
ejpam-3990	366	11	(	(	PUNCT
ejpam-3990	366	12	c3	c3	PROPN
ejpam-3990	366	13	)	)	PUNCT
ejpam-3990	366	14	.	.	PUNCT
ejpam-3990	367	1	theorem	theorem	ADJ
ejpam-3990	367	2	8	8	NUM
ejpam-3990	367	3	.	.	PUNCT
ejpam-3990	368	1	let	let	VERB
ejpam-3990	368	2	g	g	NOUN
ejpam-3990	368	3	=	=	PUNCT
ejpam-3990	368	4	pn	pn	PROPN
ejpam-3990	369	1	=	=	PUNCT
ejpam-3990	370	1	[	[	X
ejpam-3990	370	2	v1	v1	NOUN
ejpam-3990	370	3	,	,	PUNCT
ejpam-3990	370	4	v2	v2	PROPN
ejpam-3990	370	5	,	,	PUNCT
ejpam-3990	370	6	...	...	PUNCT
ejpam-3990	370	7	vn	vn	PART
ejpam-3990	370	8	]	]	X
ejpam-3990	370	9	be	be	AUX
ejpam-3990	370	10	a	a	DET
ejpam-3990	370	11	path	path	NOUN
ejpam-3990	370	12	of	of	ADP
ejpam-3990	370	13	order	order	NOUN
ejpam-3990	370	14	n	n	PRON
ejpam-3990	370	15	≥	≥	NOUN
ejpam-3990	370	16	3	3	NUM
ejpam-3990	370	17	.	.	PUNCT
ejpam-3990	371	1	(	(	PUNCT
ejpam-3990	371	2	a	a	X
ejpam-3990	371	3	)	)	PUNCT
ejpam-3990	371	4	if	if	SCONJ
ejpam-3990	371	5	n	n	PRON
ejpam-3990	371	6	is	be	AUX
ejpam-3990	371	7	even	even	ADV
ejpam-3990	371	8	,	,	PUNCT
ejpam-3990	371	9	then	then	ADV
ejpam-3990	371	10	τ	τ	PROPN
ejpam-3990	371	11	emg	emg	NOUN
ejpam-3990	371	12	has	have	VERB
ejpam-3990	371	13	a	a	DET
ejpam-3990	371	14	subbase	subbase	NOUN
ejpam-3990	371	15	consisting	consist	VERB
ejpam-3990	371	16	of	of	ADP
ejpam-3990	371	17	all	all	DET
ejpam-3990	371	18	sets	set	NOUN
ejpam-3990	371	19	of	of	ADP
ejpam-3990	371	20	the	the	DET
ejpam-3990	371	21	form	form	NOUN
ejpam-3990	372	1	f	f	X
ejpam-3990	372	2	em	em	PRON
ejpam-3990	372	3	g	g	PROPN
ejpam-3990	373	1	[	[	X
ejpam-3990	373	2	vi	vi	X
ejpam-3990	373	3	]	]	X
ejpam-3990	373	4	=	=	SYM
ejpam-3990	373	5	{	{	PUNCT
ejpam-3990	373	6	v	v	NOUN
ejpam-3990	373	7	(	(	PUNCT
ejpam-3990	373	8	g)\{vi	g)\{vi	PROPN
ejpam-3990	373	9	,	,	PUNCT
ejpam-3990	373	10	vn	vn	VERB
ejpam-3990	373	11	}	}	PUNCT
ejpam-3990	373	12	if	if	SCONJ
ejpam-3990	373	13	i	i	PRON
ejpam-3990	373	14	≤	≤	VERB
ejpam-3990	374	1	n	n	PRON
ejpam-3990	374	2	2	2	NUM
ejpam-3990	374	3	v	v	NOUN
ejpam-3990	374	4	(	(	PUNCT
ejpam-3990	374	5	g)\{v1	g)\{v1	NOUN
ejpam-3990	374	6	,	,	PUNCT
ejpam-3990	374	7	vi	vi	NOUN
ejpam-3990	374	8	}	}	PUNCT
ejpam-3990	374	9	if	if	SCONJ
ejpam-3990	374	10	i	i	PRON
ejpam-3990	374	11	>	>	X
ejpam-3990	374	12	n	n	PROPN
ejpam-3990	374	13	2	2	NUM
ejpam-3990	374	14	.	.	PUNCT
ejpam-3990	375	1	a.	a.	NOUN
ejpam-3990	375	2	gamorez	gamorez	PROPN
ejpam-3990	375	3	,	,	PUNCT
ejpam-3990	375	4	s.	s.	PROPN
ejpam-3990	375	5	canoy	canoy	PROPN
ejpam-3990	375	6	jr	jr	PROPN
ejpam-3990	375	7	.	.	PROPN
ejpam-3990	375	8	/	/	SYM
ejpam-3990	375	9	eur	eur	PROPN
ejpam-3990	375	10	.	.	PUNCT
ejpam-3990	376	1	j.	j.	PROPN
ejpam-3990	376	2	pure	pure	PROPN
ejpam-3990	376	3	appl	appl	PROPN
ejpam-3990	376	4	.	.	PROPN
ejpam-3990	376	5	math	math	PROPN
ejpam-3990	376	6	,	,	PUNCT
ejpam-3990	376	7	14	14	NUM
ejpam-3990	376	8	(	(	PUNCT
ejpam-3990	376	9	3	3	NUM
ejpam-3990	376	10	)	)	PUNCT
ejpam-3990	376	11	(	(	PUNCT
ejpam-3990	376	12	2021	2021	NUM
ejpam-3990	376	13	)	)	PUNCT
ejpam-3990	376	14	,	,	PUNCT
ejpam-3990	376	15	695	695	NUM
ejpam-3990	376	16	-	-	SYM
ejpam-3990	376	17	705	705	NUM
ejpam-3990	376	18	701	701	NUM
ejpam-3990	376	19	(	(	PUNCT
ejpam-3990	376	20	b	b	NOUN
ejpam-3990	376	21	)	)	PUNCT
ejpam-3990	376	22	if	if	SCONJ
ejpam-3990	376	23	n	n	NOUN
ejpam-3990	376	24	is	be	AUX
ejpam-3990	376	25	odd	odd	ADJ
ejpam-3990	376	26	,	,	PUNCT
ejpam-3990	376	27	then	then	ADV
ejpam-3990	376	28	τ	τ	PROPN
ejpam-3990	376	29	emg	emg	NOUN
ejpam-3990	376	30	has	have	VERB
ejpam-3990	376	31	a	a	DET
ejpam-3990	376	32	subbase	subbase	NOUN
ejpam-3990	376	33	consisting	consist	VERB
ejpam-3990	376	34	of	of	ADP
ejpam-3990	376	35	all	all	DET
ejpam-3990	376	36	sets	set	NOUN
ejpam-3990	376	37	of	of	ADP
ejpam-3990	376	38	the	the	DET
ejpam-3990	376	39	form	form	NOUN
ejpam-3990	376	40	f	f	X
ejpam-3990	376	41	em	em	PRON
ejpam-3990	376	42	g	g	PROPN
ejpam-3990	377	1	[	[	X
ejpam-3990	377	2	vi	vi	X
ejpam-3990	377	3	]	]	X
ejpam-3990	377	4	=	=	PUNCT
ejpam-3990	377	5			PUNCT
ejpam-3990	377	6	v	v	NOUN
ejpam-3990	377	7	(	(	PUNCT
ejpam-3990	377	8	g)\{vi	g)\{vi	PROPN
ejpam-3990	377	9	,	,	PUNCT
ejpam-3990	377	10	vn	vn	VERB
ejpam-3990	377	11	}	}	PUNCT
ejpam-3990	377	12	if	if	SCONJ
ejpam-3990	377	13	i	i	PRON
ejpam-3990	377	14	<	<	X
ejpam-3990	377	15	n+1	n+1	PROPN
ejpam-3990	377	16	2	2	NUM
ejpam-3990	377	17	v	v	NOUN
ejpam-3990	377	18	(	(	PUNCT
ejpam-3990	377	19	g)\{v1	g)\{v1	NOUN
ejpam-3990	377	20	,	,	PUNCT
ejpam-3990	377	21	vi	vi	PROPN
ejpam-3990	377	22	,	,	PUNCT
ejpam-3990	377	23	vn	vn	VERB
ejpam-3990	377	24	}	}	PUNCT
ejpam-3990	377	25	if	if	SCONJ
ejpam-3990	377	26	i	i	PRON
ejpam-3990	377	27	=	=	SYM
ejpam-3990	377	28	n+1	n+1	PROPN
ejpam-3990	377	29	2	2	NUM
ejpam-3990	377	30	v	v	NOUN
ejpam-3990	377	31	(	(	PUNCT
ejpam-3990	377	32	g)\{v1	g)\{v1	NOUN
ejpam-3990	377	33	,	,	PUNCT
ejpam-3990	377	34	vi	vi	NOUN
ejpam-3990	377	35	}	}	PUNCT
ejpam-3990	377	36	if	if	SCONJ
ejpam-3990	377	37	i	i	PRON
ejpam-3990	377	38	>	>	X
ejpam-3990	377	39	n+1	n+1	PROPN
ejpam-3990	377	40	2	2	NUM
ejpam-3990	377	41	.	.	PUNCT
ejpam-3990	378	1	proof	proof	NOUN
ejpam-3990	378	2	.	.	PUNCT
ejpam-3990	379	1	suppose	suppose	VERB
ejpam-3990	379	2	n	n	PRON
ejpam-3990	379	3	is	be	AUX
ejpam-3990	379	4	even	even	ADV
ejpam-3990	379	5	.	.	PUNCT
ejpam-3990	380	1	let	let	VERB
ejpam-3990	380	2	i	i	PRON
ejpam-3990	380	3	≤	≤	NOUN
ejpam-3990	381	1	n	n	PRON
ejpam-3990	381	2	2	2	NUM
ejpam-3990	381	3	.	.	PUNCT
ejpam-3990	382	1	then	then	ADV
ejpam-3990	382	2	n	n	ADV
ejpam-3990	382	3	em	em	PRON
ejpam-3990	382	4	g	g	PROPN
ejpam-3990	383	1	[	[	X
ejpam-3990	384	1	vi	vi	X
ejpam-3990	384	2	]	]	X
ejpam-3990	384	3	=	=	SYM
ejpam-3990	384	4	{	{	PUNCT
ejpam-3990	384	5	vi	vi	PROPN
ejpam-3990	384	6	,	,	PUNCT
ejpam-3990	384	7	vn	vn	NOUN
ejpam-3990	384	8	}	}	PUNCT
ejpam-3990	384	9	.	.	PUNCT
ejpam-3990	385	1	hence	hence	ADV
ejpam-3990	385	2	,	,	PUNCT
ejpam-3990	385	3	f	f	PROPN
ejpam-3990	385	4	em	em	PRON
ejpam-3990	385	5	g	g	PROPN
ejpam-3990	386	1	[	[	X
ejpam-3990	386	2	vi	vi	X
ejpam-3990	386	3	]	]	X
ejpam-3990	386	4	=	=	SYM
ejpam-3990	386	5	v	v	X
ejpam-3990	386	6	(	(	PUNCT
ejpam-3990	386	7	g)\{vi	g)\{vi	PROPN
ejpam-3990	386	8	,	,	PUNCT
ejpam-3990	386	9	vn	vn	NOUN
ejpam-3990	386	10	}	}	PUNCT
ejpam-3990	386	11	.	.	PUNCT
ejpam-3990	387	1	if	if	SCONJ
ejpam-3990	387	2	i	i	PRON
ejpam-3990	387	3	>	>	X
ejpam-3990	387	4	n	n	NUM
ejpam-3990	387	5	2	2	NUM
ejpam-3990	387	6	,	,	PUNCT
ejpam-3990	387	7	then	then	ADV
ejpam-3990	387	8	n	n	CCONJ
ejpam-3990	387	9	em	em	PRON
ejpam-3990	387	10	g	g	PROPN
ejpam-3990	387	11	[	[	X
ejpam-3990	387	12	vi	vi	X
ejpam-3990	387	13	]	]	X
ejpam-3990	387	14	=	=	SYM
ejpam-3990	387	15	{	{	PUNCT
ejpam-3990	387	16	v1	v1	PROPN
ejpam-3990	387	17	,	,	PUNCT
ejpam-3990	387	18	vi	vi	NOUN
ejpam-3990	387	19	}	}	PUNCT
ejpam-3990	387	20	.	.	PUNCT
ejpam-3990	388	1	thus	thus	ADV
ejpam-3990	388	2	,	,	PUNCT
ejpam-3990	388	3	f	f	PROPN
ejpam-3990	388	4	em	em	PRON
ejpam-3990	388	5	g	g	PROPN
ejpam-3990	388	6	[	[	X
ejpam-3990	388	7	vi	vi	X
ejpam-3990	388	8	]	]	X
ejpam-3990	388	9	=	=	SYM
ejpam-3990	388	10	v	v	NOUN
ejpam-3990	388	11	(	(	PUNCT
ejpam-3990	388	12	g)\{v1	g)\{v1	NOUN
ejpam-3990	388	13	,	,	PUNCT
ejpam-3990	388	14	vi	vi	NOUN
ejpam-3990	388	15	}	}	PUNCT
ejpam-3990	388	16	.	.	PUNCT
ejpam-3990	389	1	suppose	suppose	VERB
ejpam-3990	389	2	n	n	PRON
ejpam-3990	389	3	is	be	AUX
ejpam-3990	389	4	odd	odd	ADJ
ejpam-3990	389	5	.	.	PUNCT
ejpam-3990	390	1	let	let	VERB
ejpam-3990	390	2	i	i	PRON
ejpam-3990	390	3	<	<	X
ejpam-3990	390	4	n+1	n+1	PROPN
ejpam-3990	390	5	2	2	NUM
ejpam-3990	390	6	.	.	PUNCT
ejpam-3990	391	1	then	then	ADV
ejpam-3990	391	2	n	n	ADV
ejpam-3990	391	3	em	em	PRON
ejpam-3990	391	4	g	g	PROPN
ejpam-3990	392	1	[	[	X
ejpam-3990	393	1	vi	vi	X
ejpam-3990	393	2	]	]	X
ejpam-3990	393	3	=	=	SYM
ejpam-3990	393	4	{	{	PUNCT
ejpam-3990	393	5	vi	vi	PROPN
ejpam-3990	393	6	,	,	PUNCT
ejpam-3990	393	7	vn	vn	NOUN
ejpam-3990	393	8	}	}	PUNCT
ejpam-3990	393	9	.	.	PUNCT
ejpam-3990	394	1	thus	thus	ADV
ejpam-3990	394	2	,	,	PUNCT
ejpam-3990	394	3	f	f	PROPN
ejpam-3990	394	4	em	em	PRON
ejpam-3990	394	5	g	g	PROPN
ejpam-3990	394	6	[	[	X
ejpam-3990	394	7	vi	vi	X
ejpam-3990	394	8	]	]	X
ejpam-3990	394	9	=	=	SYM
ejpam-3990	394	10	v	v	X
ejpam-3990	394	11	(	(	PUNCT
ejpam-3990	394	12	g)\{vi	g)\{vi	PROPN
ejpam-3990	394	13	,	,	PUNCT
ejpam-3990	394	14	vn	vn	PROPN
ejpam-3990	394	15	}	}	PUNCT
ejpam-3990	394	16	.	.	PUNCT
ejpam-3990	395	1	suppose	suppose	VERB
ejpam-3990	395	2	i	i	PRON
ejpam-3990	395	3	=	=	SYM
ejpam-3990	395	4	n+1	n+1	PROPN
ejpam-3990	395	5	2	2	NUM
ejpam-3990	395	6	.	.	PUNCT
ejpam-3990	396	1	then	then	ADV
ejpam-3990	396	2	n	n	ADV
ejpam-3990	396	3	em	em	PRON
ejpam-3990	396	4	g	g	PROPN
ejpam-3990	397	1	[	[	X
ejpam-3990	397	2	vi	vi	X
ejpam-3990	397	3	]	]	X
ejpam-3990	397	4	=	=	SYM
ejpam-3990	397	5	{	{	PUNCT
ejpam-3990	397	6	v1	v1	PROPN
ejpam-3990	397	7	,	,	PUNCT
ejpam-3990	397	8	vi	vi	PROPN
ejpam-3990	397	9	,	,	PUNCT
ejpam-3990	397	10	vn	vn	NOUN
ejpam-3990	397	11	}	}	PUNCT
ejpam-3990	397	12	.	.	PUNCT
ejpam-3990	398	1	hence	hence	ADV
ejpam-3990	398	2	,	,	PUNCT
ejpam-3990	398	3	f	f	PROPN
ejpam-3990	398	4	em	em	PRON
ejpam-3990	398	5	g	g	PROPN
ejpam-3990	399	1	[	[	X
ejpam-3990	399	2	vi	vi	X
ejpam-3990	399	3	]	]	X
ejpam-3990	399	4	=	=	SYM
ejpam-3990	399	5	v	v	NOUN
ejpam-3990	399	6	(	(	PUNCT
ejpam-3990	399	7	g)\{v1	g)\{v1	PROPN
ejpam-3990	399	8	,	,	PUNCT
ejpam-3990	399	9	vi	vi	PROPN
ejpam-3990	399	10	,	,	PUNCT
ejpam-3990	399	11	vn	vn	NOUN
ejpam-3990	399	12	}	}	PUNCT
ejpam-3990	399	13	.	.	PUNCT
ejpam-3990	400	1	let	let	VERB
ejpam-3990	400	2	i	i	PRON
ejpam-3990	400	3	>	>	X
ejpam-3990	400	4	n+1	n+1	PROPN
ejpam-3990	400	5	2	2	NUM
ejpam-3990	400	6	.	.	PUNCT
ejpam-3990	401	1	then	then	ADV
ejpam-3990	401	2	n	n	ADV
ejpam-3990	401	3	em	em	PRON
ejpam-3990	401	4	g	g	PROPN
ejpam-3990	402	1	[	[	X
ejpam-3990	403	1	vi	vi	X
ejpam-3990	403	2	]	]	X
ejpam-3990	403	3	=	=	SYM
ejpam-3990	403	4	{	{	PUNCT
ejpam-3990	403	5	v1	v1	PROPN
ejpam-3990	403	6	,	,	PUNCT
ejpam-3990	403	7	vi	vi	NOUN
ejpam-3990	403	8	}	}	PUNCT
ejpam-3990	403	9	.	.	PUNCT
ejpam-3990	404	1	therefore	therefore	ADV
ejpam-3990	404	2	,	,	PUNCT
ejpam-3990	404	3	f	f	PROPN
ejpam-3990	404	4	em	em	PRON
ejpam-3990	404	5	g	g	PROPN
ejpam-3990	404	6	[	[	X
ejpam-3990	404	7	vi	vi	X
ejpam-3990	404	8	]	]	X
ejpam-3990	404	9	=	=	SYM
ejpam-3990	404	10	v	v	NOUN
ejpam-3990	404	11	(	(	PUNCT
ejpam-3990	404	12	g)\{v1	g)\{v1	NOUN
ejpam-3990	404	13	,	,	PUNCT
ejpam-3990	404	14	vi	vi	NOUN
ejpam-3990	404	15	}	}	PUNCT
ejpam-3990	404	16	.	.	PUNCT
ejpam-3990	405	1	theorem	theorem	NOUN
ejpam-3990	405	2	9	9	NUM
ejpam-3990	405	3	.	.	PUNCT
ejpam-3990	406	1	let	let	VERB
ejpam-3990	406	2	g	g	NOUN
ejpam-3990	406	3	=	=	PUNCT
ejpam-3990	406	4	pn	pn	PROPN
ejpam-3990	407	1	=	=	PUNCT
ejpam-3990	408	1	[	[	X
ejpam-3990	408	2	v1	v1	NOUN
ejpam-3990	408	3	,	,	PUNCT
ejpam-3990	408	4	v2	v2	PROPN
ejpam-3990	408	5	,	,	PUNCT
ejpam-3990	408	6	...	...	PUNCT
ejpam-3990	408	7	vn	vn	PART
ejpam-3990	408	8	]	]	X
ejpam-3990	408	9	be	be	AUX
ejpam-3990	408	10	a	a	DET
ejpam-3990	408	11	path	path	NOUN
ejpam-3990	408	12	of	of	ADP
ejpam-3990	408	13	order	order	NOUN
ejpam-3990	408	14	n	n	PRON
ejpam-3990	408	15	≥	≥	NOUN
ejpam-3990	408	16	3	3	NUM
ejpam-3990	408	17	.	.	PUNCT
ejpam-3990	409	1	then	then	ADV
ejpam-3990	409	2	{	{	PUNCT
ejpam-3990	409	3	v	v	NOUN
ejpam-3990	409	4	}	}	PUNCT
ejpam-3990	409	5	∈	∈	PROPN
ejpam-3990	409	6	τ	τ	PROPN
ejpam-3990	409	7	emg	emg	NOUN
ejpam-3990	409	8	if	if	SCONJ
ejpam-3990	409	9	and	and	CCONJ
ejpam-3990	409	10	only	only	ADV
ejpam-3990	409	11	if	if	SCONJ
ejpam-3990	409	12	v	v	NUM
ejpam-3990	409	13	6=	6=	X
ejpam-3990	409	14	v1	v1	NOUN
ejpam-3990	409	15	,	,	PUNCT
ejpam-3990	409	16	vn	vn	NOUN
ejpam-3990	409	17	.	.	PUNCT
ejpam-3990	410	1	proof	proof	NOUN
ejpam-3990	410	2	.	.	PUNCT
ejpam-3990	411	1	suppose	suppose	VERB
ejpam-3990	411	2	{	{	PUNCT
ejpam-3990	411	3	v	v	NOUN
ejpam-3990	411	4	}	}	PUNCT
ejpam-3990	411	5	∈	∈	PROPN
ejpam-3990	411	6	τ	τ	PROPN
ejpam-3990	411	7	emg	emg	NOUN
ejpam-3990	411	8	.	.	PUNCT
ejpam-3990	412	1	suppose	suppose	VERB
ejpam-3990	412	2	further	far	ADV
ejpam-3990	412	3	that	that	DET
ejpam-3990	412	4	v	v	X
ejpam-3990	412	5	=	=	SYM
ejpam-3990	412	6	v1	v1	NOUN
ejpam-3990	412	7	.	.	PUNCT
ejpam-3990	413	1	then	then	ADV
ejpam-3990	413	2	there	there	PRON
ejpam-3990	413	3	exists	exist	VERB
ejpam-3990	413	4	∅	∅	NOUN
ejpam-3990	413	5	6=	6=	ADP
ejpam-3990	413	6	a	a	DET
ejpam-3990	413	7	⊆	⊆	NUM
ejpam-3990	413	8	v	v	NOUN
ejpam-3990	413	9	(	(	PUNCT
ejpam-3990	413	10	g	g	NOUN
ejpam-3990	413	11	)	)	PUNCT
ejpam-3990	413	12	such	such	ADJ
ejpam-3990	413	13	that	that	SCONJ
ejpam-3990	413	14	f	f	PROPN
ejpam-3990	413	15	em	em	PRON
ejpam-3990	413	16	g	g	PROPN
ejpam-3990	414	1	[	[	X
ejpam-3990	414	2	a	a	X
ejpam-3990	414	3	]	]	X
ejpam-3990	414	4	=	=	SYM
ejpam-3990	414	5	{	{	PUNCT
ejpam-3990	414	6	v1	v1	NOUN
ejpam-3990	414	7	}	}	PUNCT
ejpam-3990	414	8	.	.	PUNCT
ejpam-3990	415	1	this	this	PRON
ejpam-3990	415	2	means	mean	VERB
ejpam-3990	415	3	that	that	SCONJ
ejpam-3990	415	4	v1	v1	NOUN
ejpam-3990	415	5	/∈	/∈	PUNCT
ejpam-3990	416	1	a	a	DET
ejpam-3990	416	2	and	and	CCONJ
ejpam-3990	416	3	dmg	dmg	ADJ
ejpam-3990	416	4	(	(	PUNCT
ejpam-3990	416	5	v1	v1	PROPN
ejpam-3990	416	6	,	,	PUNCT
ejpam-3990	416	7	a	a	PRON
ejpam-3990	416	8	)	)	PUNCT
ejpam-3990	416	9	6=	6=	ADP
ejpam-3990	416	10	emg	emg	NOUN
ejpam-3990	416	11	(	(	PUNCT
ejpam-3990	416	12	a	a	NOUN
ejpam-3990	416	13	)	)	PUNCT
ejpam-3990	416	14	for	for	ADP
ejpam-3990	416	15	all	all	DET
ejpam-3990	416	16	a	a	DET
ejpam-3990	416	17	∈	∈	NOUN
ejpam-3990	416	18	a.	a.	NOUN
ejpam-3990	416	19	since	since	SCONJ
ejpam-3990	416	20	n	n	PROPN
ejpam-3990	416	21	em	em	PRON
ejpam-3990	416	22	g	g	PROPN
ejpam-3990	416	23	(	(	PUNCT
ejpam-3990	416	24	vn	vn	PROPN
ejpam-3990	416	25	)	)	PUNCT
ejpam-3990	416	26	=	=	SYM
ejpam-3990	416	27	{	{	PUNCT
ejpam-3990	416	28	v1	v1	NOUN
ejpam-3990	416	29	}	}	PUNCT
ejpam-3990	416	30	,	,	PUNCT
ejpam-3990	416	31	vn	vn	PROPN
ejpam-3990	416	32	/∈	/∈	PUNCT
ejpam-3990	417	1	a.	a.	PROPN
ejpam-3990	417	2	first	first	ADV
ejpam-3990	417	3	,	,	PUNCT
ejpam-3990	417	4	suppose	suppose	VERB
ejpam-3990	417	5	that	that	SCONJ
ejpam-3990	417	6	n	n	PRON
ejpam-3990	417	7	is	be	AUX
ejpam-3990	417	8	odd	odd	ADJ
ejpam-3990	417	9	.	.	PUNCT
ejpam-3990	418	1	from	from	ADP
ejpam-3990	418	2	theorem	theorem	ADJ
ejpam-3990	418	3	8	8	NUM
ejpam-3990	418	4	(	(	PUNCT
ejpam-3990	418	5	b	b	X
ejpam-3990	418	6	)	)	PUNCT
ejpam-3990	418	7	it	it	PRON
ejpam-3990	418	8	follows	follow	VERB
ejpam-3990	418	9	that	that	PRON
ejpam-3990	418	10	vi	vi	PROPN
ejpam-3990	418	11	/∈	/∈	PUNCT
ejpam-3990	419	1	a	a	PRON
ejpam-3990	419	2	for	for	ADP
ejpam-3990	419	3	all	all	PRON
ejpam-3990	419	4	i	i	PRON
ejpam-3990	419	5	≥	≥	VERB
ejpam-3990	419	6	n+1	n+1	ADV
ejpam-3990	419	7	2	2	NUM
ejpam-3990	419	8	.	.	PUNCT
ejpam-3990	420	1	hence	hence	ADV
ejpam-3990	420	2	,	,	PUNCT
ejpam-3990	420	3	a	a	DET
ejpam-3990	420	4	⊆	⊆	NUM
ejpam-3990	420	5	{	{	PUNCT
ejpam-3990	420	6	vj	vj	NOUN
ejpam-3990	420	7	:	:	PUNCT
ejpam-3990	420	8	1	1	NUM
ejpam-3990	420	9	<	<	X
ejpam-3990	420	10	j	j	X
ejpam-3990	420	11	<	<	X
ejpam-3990	420	12	n+	n+	PROPN
ejpam-3990	420	13	1	1	NUM
ejpam-3990	420	14	2	2	NUM
ejpam-3990	420	15	}	}	PUNCT
ejpam-3990	420	16	.	.	PUNCT
ejpam-3990	421	1	thus	thus	ADV
ejpam-3990	421	2	,	,	PUNCT
ejpam-3990	421	3	by	by	ADP
ejpam-3990	421	4	theorem	theorem	NOUN
ejpam-3990	421	5	8	8	NUM
ejpam-3990	421	6	,	,	PUNCT
ejpam-3990	421	7	vn+1	vn+1	PROPN
ejpam-3990	421	8	2	2	NUM
ejpam-3990	421	9	∈	∈	NOUN
ejpam-3990	421	10	f	f	NOUN
ejpam-3990	421	11	em	em	PRON
ejpam-3990	421	12	g	g	PROPN
ejpam-3990	422	1	[	[	X
ejpam-3990	422	2	a	a	X
ejpam-3990	422	3	]	]	X
ejpam-3990	422	4	,	,	PUNCT
ejpam-3990	422	5	a	a	DET
ejpam-3990	422	6	contradiction	contradiction	NOUN
ejpam-3990	422	7	.	.	PUNCT
ejpam-3990	423	1	suppose	suppose	VERB
ejpam-3990	423	2	n	n	PRON
ejpam-3990	423	3	is	be	AUX
ejpam-3990	423	4	even	even	ADV
ejpam-3990	423	5	.	.	PUNCT
ejpam-3990	424	1	from	from	ADP
ejpam-3990	424	2	theorem	theorem	ADJ
ejpam-3990	424	3	8	8	NUM
ejpam-3990	424	4	(	(	PUNCT
ejpam-3990	424	5	a	a	NOUN
ejpam-3990	424	6	)	)	PUNCT
ejpam-3990	424	7	,	,	PUNCT
ejpam-3990	424	8	vi	vi	PROPN
ejpam-3990	424	9	/∈	/∈	PUNCT
ejpam-3990	425	1	a	a	PRON
ejpam-3990	425	2	for	for	ADP
ejpam-3990	425	3	all	all	DET
ejpam-3990	425	4	i	i	PRON
ejpam-3990	425	5	>	>	X
ejpam-3990	425	6	n	n	PROPN
ejpam-3990	425	7	2	2	NUM
ejpam-3990	425	8	.	.	PUNCT
ejpam-3990	426	1	thus	thus	ADV
ejpam-3990	426	2	,	,	PUNCT
ejpam-3990	426	3	a	a	DET
ejpam-3990	426	4	⊆	⊆	NUM
ejpam-3990	426	5	{	{	PUNCT
ejpam-3990	426	6	vj	vj	NOUN
ejpam-3990	426	7	:	:	PUNCT
ejpam-3990	426	8	1	1	NUM
ejpam-3990	426	9	<	<	X
ejpam-3990	426	10	j	j	PROPN
ejpam-3990	426	11	≤	≤	PROPN
ejpam-3990	426	12	n	n	PRON
ejpam-3990	426	13	2	2	NUM
ejpam-3990	426	14	}	}	PUNCT
ejpam-3990	426	15	.	.	PUNCT
ejpam-3990	427	1	hence	hence	ADV
ejpam-3990	427	2	,	,	PUNCT
ejpam-3990	427	3	by	by	ADP
ejpam-3990	427	4	theorem	theorem	NOUN
ejpam-3990	427	5	8	8	NUM
ejpam-3990	427	6	,	,	PUNCT
ejpam-3990	427	7	vn	vn	NOUN
ejpam-3990	427	8	2	2	NUM
ejpam-3990	427	9	+1	+1	NOUN
ejpam-3990	427	10	∈	∈	PROPN
ejpam-3990	428	1	f	f	X
ejpam-3990	428	2	em	em	PRON
ejpam-3990	428	3	g	g	PROPN
ejpam-3990	429	1	[	[	X
ejpam-3990	429	2	a	a	X
ejpam-3990	429	3	]	]	X
ejpam-3990	429	4	,	,	PUNCT
ejpam-3990	429	5	a	a	DET
ejpam-3990	429	6	contradiction	contradiction	NOUN
ejpam-3990	429	7	.	.	PUNCT
ejpam-3990	430	1	therefore	therefore	ADV
ejpam-3990	430	2	,	,	PUNCT
ejpam-3990	430	3	{	{	PUNCT
ejpam-3990	430	4	v1	v1	NOUN
ejpam-3990	430	5	}	}	PUNCT
ejpam-3990	430	6	/∈	/∈	PUNCT
ejpam-3990	431	1	τ	τ	PROPN
ejpam-3990	431	2	emg	emg	NOUN
ejpam-3990	431	3	.	.	PUNCT
ejpam-3990	432	1	similarly	similarly	ADV
ejpam-3990	432	2	,	,	PUNCT
ejpam-3990	432	3	{	{	PUNCT
ejpam-3990	432	4	vn	vn	NOUN
ejpam-3990	432	5	}	}	PUNCT
ejpam-3990	432	6	/∈	/∈	PUNCT
ejpam-3990	433	1	τ	τ	PROPN
ejpam-3990	433	2	emg	emg	NOUN
ejpam-3990	433	3	.	.	PUNCT
ejpam-3990	434	1	for	for	ADP
ejpam-3990	434	2	the	the	DET
ejpam-3990	434	3	converse	converse	NOUN
ejpam-3990	434	4	,	,	PUNCT
ejpam-3990	434	5	suppose	suppose	VERB
ejpam-3990	434	6	that	that	SCONJ
ejpam-3990	434	7	v	v	PROPN
ejpam-3990	434	8	6=	6=	X
ejpam-3990	434	9	v1	v1	NOUN
ejpam-3990	434	10	,	,	PUNCT
ejpam-3990	434	11	vn	vn	NOUN
ejpam-3990	434	12	and	and	CCONJ
ejpam-3990	434	13	let	let	VERB
ejpam-3990	434	14	vj	vj	PROPN
ejpam-3990	434	15	∈	∈	PROPN
ejpam-3990	434	16	pn	pn	PROPN
ejpam-3990	434	17	.	.	PROPN
ejpam-3990	434	18	consider	consider	VERB
ejpam-3990	434	19	the	the	DET
ejpam-3990	434	20	following	follow	VERB
ejpam-3990	434	21	cases	case	NOUN
ejpam-3990	434	22	:	:	PUNCT
ejpam-3990	434	23	case	case	NOUN
ejpam-3990	434	24	1	1	NUM
ejpam-3990	434	25	.	.	NOUN
ejpam-3990	434	26	1	1	NUM
ejpam-3990	434	27	<	<	X
ejpam-3990	434	28	j	j	X
ejpam-3990	434	29	<	<	X
ejpam-3990	434	30	dn2	dn2	PROPN
ejpam-3990	434	31	e.	e.	PROPN
ejpam-3990	434	32	let	let	VERB
ejpam-3990	434	33	a	a	DET
ejpam-3990	434	34	=	=	X
ejpam-3990	434	35	v	v	NOUN
ejpam-3990	434	36	(	(	PUNCT
ejpam-3990	434	37	g)\{vj	g)\{vj	PROPN
ejpam-3990	434	38	,	,	PUNCT
ejpam-3990	434	39	vn	vn	PROPN
ejpam-3990	434	40	}	}	PUNCT
ejpam-3990	434	41	.	.	PUNCT
ejpam-3990	435	1	then	then	ADV
ejpam-3990	435	2	f	f	PROPN
ejpam-3990	435	3	em	em	PRON
ejpam-3990	435	4	g	g	PROPN
ejpam-3990	436	1	[	[	X
ejpam-3990	436	2	a	a	X
ejpam-3990	436	3	]	]	X
ejpam-3990	436	4	=	=	SYM
ejpam-3990	436	5	{	{	PUNCT
ejpam-3990	436	6	vj	vj	INTJ
ejpam-3990	436	7	}	}	PUNCT
ejpam-3990	436	8	.	.	PUNCT
ejpam-3990	437	1	case	case	NOUN
ejpam-3990	437	2	2	2	NUM
ejpam-3990	437	3	.	.	PUNCT
ejpam-3990	438	1	j	j	PROPN
ejpam-3990	438	2	=	=	PRON
ejpam-3990	438	3	dn2	dn2	PROPN
ejpam-3990	438	4	e.	e.	PROPN
ejpam-3990	438	5	if	if	SCONJ
ejpam-3990	438	6	n	n	PROPN
ejpam-3990	438	7	is	be	AUX
ejpam-3990	438	8	odd	odd	ADJ
ejpam-3990	438	9	and	and	CCONJ
ejpam-3990	438	10	j	j	PROPN
ejpam-3990	438	11	=	=	SYM
ejpam-3990	438	12	n+1	n+1	PROPN
ejpam-3990	438	13	2	2	NUM
ejpam-3990	438	14	,	,	PUNCT
ejpam-3990	438	15	then	then	ADV
ejpam-3990	438	16	set	set	VERB
ejpam-3990	438	17	b	b	PROPN
ejpam-3990	438	18	=	=	SYM
ejpam-3990	438	19	v	v	PROPN
ejpam-3990	438	20	(	(	PUNCT
ejpam-3990	438	21	g)\{v1	g)\{v1	PROPN
ejpam-3990	438	22	,	,	PUNCT
ejpam-3990	438	23	vj	vj	INTJ
ejpam-3990	438	24	,	,	PUNCT
ejpam-3990	438	25	vn	vn	PROPN
ejpam-3990	438	26	}	}	PUNCT
ejpam-3990	438	27	.	.	PUNCT
ejpam-3990	439	1	then	then	ADV
ejpam-3990	439	2	f	f	PROPN
ejpam-3990	439	3	em	em	PRON
ejpam-3990	439	4	g	g	PROPN
ejpam-3990	440	1	[	[	X
ejpam-3990	440	2	b	b	X
ejpam-3990	440	3	]	]	X
ejpam-3990	440	4	=	=	SYM
ejpam-3990	440	5	{	{	PUNCT
ejpam-3990	440	6	vj	vj	INTJ
ejpam-3990	440	7	}	}	PUNCT
ejpam-3990	440	8	.	.	PUNCT
ejpam-3990	441	1	if	if	SCONJ
ejpam-3990	441	2	n	n	PRON
ejpam-3990	441	3	is	be	AUX
ejpam-3990	441	4	even	even	ADV
ejpam-3990	441	5	,	,	PUNCT
ejpam-3990	441	6	set	set	VERB
ejpam-3990	441	7	b	b	NOUN
ejpam-3990	441	8	=	=	SYM
ejpam-3990	441	9	v	v	PROPN
ejpam-3990	441	10	(	(	PUNCT
ejpam-3990	441	11	g)\{vj	g)\{vj	PROPN
ejpam-3990	441	12	,	,	PUNCT
ejpam-3990	441	13	vn	vn	NOUN
ejpam-3990	441	14	}	}	PUNCT
ejpam-3990	441	15	.	.	PUNCT
ejpam-3990	442	1	case	case	NOUN
ejpam-3990	442	2	3	3	X
ejpam-3990	442	3	.	.	PUNCT
ejpam-3990	442	4	dn2	dn2	PROPN
ejpam-3990	442	5	e	e	PROPN
ejpam-3990	442	6	<	<	X
ejpam-3990	442	7	j	j	X
ejpam-3990	442	8	<	<	X
ejpam-3990	442	9	n.	n.	PROPN
ejpam-3990	442	10	let	let	VERB
ejpam-3990	442	11	d	d	PROPN
ejpam-3990	442	12	=	=	SYM
ejpam-3990	442	13	v	v	PROPN
ejpam-3990	442	14	(	(	PUNCT
ejpam-3990	442	15	g)\{v1	g)\{v1	NOUN
ejpam-3990	442	16	,	,	PUNCT
ejpam-3990	442	17	vj	vj	PROPN
ejpam-3990	442	18	}	}	PUNCT
ejpam-3990	442	19	.	.	PUNCT
ejpam-3990	443	1	then	then	ADV
ejpam-3990	443	2	f	f	PROPN
ejpam-3990	443	3	em	em	PRON
ejpam-3990	443	4	g	g	PROPN
ejpam-3990	444	1	[	[	X
ejpam-3990	444	2	d	d	X
ejpam-3990	444	3	]	]	X
ejpam-3990	444	4	=	=	X
ejpam-3990	444	5	{	{	PUNCT
ejpam-3990	444	6	vj	vj	INTJ
ejpam-3990	444	7	}	}	PUNCT
ejpam-3990	444	8	.	.	PUNCT
ejpam-3990	445	1	therefore	therefore	ADV
ejpam-3990	445	2	,	,	PUNCT
ejpam-3990	445	3	{	{	PUNCT
ejpam-3990	445	4	vj	vj	INTJ
ejpam-3990	445	5	}	}	PUNCT
ejpam-3990	445	6	∈	∈	PROPN
ejpam-3990	445	7	τ	τ	PROPN
ejpam-3990	445	8	emg	emg	NOUN
ejpam-3990	445	9	for	for	ADP
ejpam-3990	445	10	all	all	DET
ejpam-3990	445	11	j	j	PROPN
ejpam-3990	445	12	∈	∈	PROPN
ejpam-3990	445	13	{	{	PUNCT
ejpam-3990	445	14	2	2	NUM
ejpam-3990	445	15	,	,	PUNCT
ejpam-3990	445	16	3	3	NUM
ejpam-3990	445	17	,	,	PUNCT
ejpam-3990	445	18	...	...	PUNCT
ejpam-3990	445	19	,	,	PUNCT
ejpam-3990	445	20	n−	n−	NOUN
ejpam-3990	445	21	1	1	NUM
ejpam-3990	445	22	}	}	PUNCT
ejpam-3990	445	23	.	.	PUNCT
ejpam-3990	446	1	definition	definition	NOUN
ejpam-3990	446	2	1	1	NUM
ejpam-3990	446	3	.	.	PUNCT
ejpam-3990	447	1	the	the	DET
ejpam-3990	447	2	join	join	PROPN
ejpam-3990	447	3	g+h	g+h	PROPN
ejpam-3990	447	4	of	of	ADP
ejpam-3990	447	5	graphs	graph	NOUN
ejpam-3990	447	6	g	g	PROPN
ejpam-3990	447	7	and	and	CCONJ
ejpam-3990	447	8	h	h	NOUN
ejpam-3990	447	9	is	be	AUX
ejpam-3990	447	10	the	the	DET
ejpam-3990	447	11	graph	graph	NOUN
ejpam-3990	447	12	k	k	PROPN
ejpam-3990	447	13	with	with	ADP
ejpam-3990	447	14	v	v	PROPN
ejpam-3990	447	15	(	(	PUNCT
ejpam-3990	447	16	k	k	NOUN
ejpam-3990	447	17	)	)	PUNCT
ejpam-3990	447	18	=	=	NOUN
ejpam-3990	447	19	v	v	X
ejpam-3990	447	20	(	(	PUNCT
ejpam-3990	447	21	g	g	NOUN
ejpam-3990	447	22	)	)	PUNCT
ejpam-3990	447	23	∪	∪	NOUN
ejpam-3990	447	24	v	v	NOUN
ejpam-3990	447	25	(	(	PUNCT
ejpam-3990	447	26	h	h	NOUN
ejpam-3990	447	27	)	)	PUNCT
ejpam-3990	447	28	and	and	CCONJ
ejpam-3990	447	29	e(k	e(k	NOUN
ejpam-3990	447	30	)	)	PUNCT
ejpam-3990	447	31	=	=	SYM
ejpam-3990	447	32	e(g	e(g	NOUN
ejpam-3990	447	33	)	)	PUNCT
ejpam-3990	447	34	∪	∪	ADP
ejpam-3990	447	35	e(h	e(h	PROPN
ejpam-3990	447	36	)	)	PUNCT
ejpam-3990	447	37	∪	∪	NOUN
ejpam-3990	447	38	{	{	PUNCT
ejpam-3990	447	39	uv	uv	NOUN
ejpam-3990	447	40	:	:	PUNCT
ejpam-3990	447	41	u	u	PROPN
ejpam-3990	447	42	∈	∈	PROPN
ejpam-3990	447	43	v	v	ADP
ejpam-3990	447	44	(	(	PUNCT
ejpam-3990	447	45	g	g	NOUN
ejpam-3990	447	46	)	)	PUNCT
ejpam-3990	447	47	and	and	CCONJ
ejpam-3990	447	48	v	v	ADP
ejpam-3990	447	49	∈	∈	PROPN
ejpam-3990	447	50	v	v	NOUN
ejpam-3990	447	51	(	(	PUNCT
ejpam-3990	447	52	h	h	NOUN
ejpam-3990	447	53	)	)	PUNCT
ejpam-3990	447	54	}	}	PUNCT
ejpam-3990	447	55	.	.	PUNCT
ejpam-3990	448	1	theorem	theorem	ADJ
ejpam-3990	448	2	10	10	NUM
ejpam-3990	448	3	.	.	PUNCT
ejpam-3990	449	1	let	let	VERB
ejpam-3990	449	2	g	g	NOUN
ejpam-3990	449	3	be	be	AUX
ejpam-3990	449	4	any	any	DET
ejpam-3990	449	5	graph	graph	NOUN
ejpam-3990	449	6	and	and	CCONJ
ejpam-3990	449	7	let	let	VERB
ejpam-3990	449	8	k1	k1	NOUN
ejpam-3990	449	9	=	=	PUNCT
ejpam-3990	449	10	〈	〈	PROPN
ejpam-3990	449	11	v	v	NOUN
ejpam-3990	449	12	〉	〉	PROPN
ejpam-3990	449	13	.	.	PUNCT
ejpam-3990	450	1	(	(	PUNCT
ejpam-3990	450	2	i	i	NOUN
ejpam-3990	450	3	)	)	PUNCT
ejpam-3990	450	4	if	if	SCONJ
ejpam-3990	450	5	g	g	PROPN
ejpam-3990	450	6	is	be	AUX
ejpam-3990	450	7	connected	connect	VERB
ejpam-3990	450	8	,	,	PUNCT
ejpam-3990	450	9	then	then	ADV
ejpam-3990	450	10	f	f	PROPN
ejpam-3990	450	11	em	em	PROPN
ejpam-3990	450	12	k1+g[w	k1+g[w	PROPN
ejpam-3990	450	13	]	]	X
ejpam-3990	451	1	=	=	PUNCT
ejpam-3990	451	2			PUNCT
ejpam-3990	451	3	∅	∅	NOUN
ejpam-3990	451	4	,	,	PUNCT
ejpam-3990	451	5	if	if	SCONJ
ejpam-3990	451	6	[	[	X
ejpam-3990	451	7	w	w	NOUN
ejpam-3990	451	8	∈	∈	ADJ
ejpam-3990	451	9	v	v	ADP
ejpam-3990	451	10	(	(	PUNCT
ejpam-3990	451	11	g	g	NOUN
ejpam-3990	451	12	)	)	PUNCT
ejpam-3990	451	13	and	and	CCONJ
ejpam-3990	451	14	emg	emg	NOUN
ejpam-3990	451	15	(	(	PUNCT
ejpam-3990	451	16	w	w	PROPN
ejpam-3990	451	17	)	)	PUNCT
ejpam-3990	451	18	=	=	SYM
ejpam-3990	451	19	1	1	X
ejpam-3990	451	20	]	]	PUNCT
ejpam-3990	451	21	or	or	CCONJ
ejpam-3990	451	22	w	w	PROPN
ejpam-3990	451	23	=	=	SYM
ejpam-3990	451	24	v	v	PROPN
ejpam-3990	451	25	f	f	NOUN
ejpam-3990	451	26	em	em	PRON
ejpam-3990	451	27	g	g	PROPN
ejpam-3990	452	1	[	[	X
ejpam-3990	452	2	w	w	X
ejpam-3990	452	3	]	]	X
ejpam-3990	452	4	∪	∪	X
ejpam-3990	452	5	{	{	PUNCT
ejpam-3990	452	6	v	v	NOUN
ejpam-3990	452	7	}	}	PUNCT
ejpam-3990	452	8	,	,	PUNCT
ejpam-3990	452	9	if	if	SCONJ
ejpam-3990	452	10	w	w	PROPN
ejpam-3990	452	11	∈	∈	PROPN
ejpam-3990	452	12	v	v	NOUN
ejpam-3990	452	13	(	(	PUNCT
ejpam-3990	452	14	g)andemg	g)andemg	NOUN
ejpam-3990	452	15	(	(	PUNCT
ejpam-3990	452	16	w	w	NOUN
ejpam-3990	452	17	)	)	PUNCT
ejpam-3990	452	18	≥	≥	NOUN
ejpam-3990	452	19	2	2	NUM
ejpam-3990	452	20	.	.	PUNCT
ejpam-3990	452	21	a.	a.	NOUN
ejpam-3990	452	22	gamorez	gamorez	PROPN
ejpam-3990	452	23	,	,	PUNCT
ejpam-3990	452	24	s.	s.	PROPN
ejpam-3990	452	25	canoy	canoy	PROPN
ejpam-3990	452	26	jr	jr	PROPN
ejpam-3990	452	27	.	.	PROPN
ejpam-3990	452	28	/	/	SYM
ejpam-3990	452	29	eur	eur	PROPN
ejpam-3990	452	30	.	.	PUNCT
ejpam-3990	453	1	j.	j.	PROPN
ejpam-3990	453	2	pure	pure	PROPN
ejpam-3990	453	3	appl	appl	PROPN
ejpam-3990	453	4	.	.	PROPN
ejpam-3990	453	5	math	math	PROPN
ejpam-3990	453	6	,	,	PUNCT
ejpam-3990	453	7	14	14	NUM
ejpam-3990	453	8	(	(	PUNCT
ejpam-3990	453	9	3	3	NUM
ejpam-3990	453	10	)	)	PUNCT
ejpam-3990	453	11	(	(	PUNCT
ejpam-3990	453	12	2021	2021	NUM
ejpam-3990	453	13	)	)	PUNCT
ejpam-3990	453	14	,	,	PUNCT
ejpam-3990	453	15	695	695	NUM
ejpam-3990	453	16	-	-	SYM
ejpam-3990	453	17	705	705	NUM
ejpam-3990	453	18	702	702	NUM
ejpam-3990	453	19	(	(	PUNCT
ejpam-3990	453	20	ii	ii	NOUN
ejpam-3990	453	21	)	)	PUNCT
ejpam-3990	453	22	if	if	SCONJ
ejpam-3990	453	23	g	g	PROPN
ejpam-3990	453	24	is	be	AUX
ejpam-3990	453	25	disconnected	disconnect	VERB
ejpam-3990	453	26	,	,	PUNCT
ejpam-3990	453	27	then	then	ADV
ejpam-3990	453	28	f	f	PROPN
ejpam-3990	453	29	em	em	PROPN
ejpam-3990	453	30	k1+g[w	k1+g[w	PROPN
ejpam-3990	453	31	]	]	X
ejpam-3990	454	1	=	=	SYM
ejpam-3990	454	2			PUNCT
ejpam-3990	454	3	∅	∅	NOUN
ejpam-3990	454	4	,	,	PUNCT
ejpam-3990	454	5	if	if	SCONJ
ejpam-3990	454	6	w	w	PROPN
ejpam-3990	454	7	=	=	SYM
ejpam-3990	454	8	v	v	NOUN
ejpam-3990	454	9	ng(w	ng(w	NOUN
ejpam-3990	454	10	)	)	PUNCT
ejpam-3990	454	11	∪	∪	ADP
ejpam-3990	454	12	{	{	PUNCT
ejpam-3990	454	13	v	v	NOUN
ejpam-3990	454	14	}	}	PUNCT
ejpam-3990	454	15	if	if	SCONJ
ejpam-3990	454	16	w	w	PROPN
ejpam-3990	454	17	∈	∈	PROPN
ejpam-3990	454	18	v	v	ADP
ejpam-3990	454	19	(	(	PUNCT
ejpam-3990	454	20	g	g	NOUN
ejpam-3990	454	21	)	)	PUNCT
ejpam-3990	454	22	and	and	CCONJ
ejpam-3990	454	23	1	1	NUM
ejpam-3990	454	24	≤	≤	NOUN
ejpam-3990	454	25	emg	emg	NOUN
ejpam-3990	454	26	(	(	PUNCT
ejpam-3990	454	27	w	w	NOUN
ejpam-3990	454	28	)	)	PUNCT
ejpam-3990	454	29	≤	≤	NUM
ejpam-3990	454	30	2	2	NUM
ejpam-3990	454	31	f	f	NOUN
ejpam-3990	454	32	em	em	PRON
ejpam-3990	454	33	g	g	PROPN
ejpam-3990	455	1	[	[	X
ejpam-3990	455	2	w	w	X
ejpam-3990	455	3	]	]	X
ejpam-3990	455	4	∪	∪	X
ejpam-3990	455	5	{	{	PUNCT
ejpam-3990	455	6	v	v	NOUN
ejpam-3990	455	7	}	}	PUNCT
ejpam-3990	455	8	,	,	PUNCT
ejpam-3990	455	9	if	if	SCONJ
ejpam-3990	455	10	w	w	PROPN
ejpam-3990	455	11	∈	∈	PROPN
ejpam-3990	455	12	v	v	ADP
ejpam-3990	455	13	(	(	PUNCT
ejpam-3990	455	14	g	g	NOUN
ejpam-3990	455	15	)	)	PUNCT
ejpam-3990	455	16	and	and	CCONJ
ejpam-3990	455	17	emg	emg	NOUN
ejpam-3990	455	18	(	(	PUNCT
ejpam-3990	455	19	w	w	PROPN
ejpam-3990	455	20	)	)	PUNCT
ejpam-3990	455	21	≥	≥	NOUN
ejpam-3990	455	22	3	3	NUM
ejpam-3990	455	23	.	.	PUNCT
ejpam-3990	456	1	proof	proof	NOUN
ejpam-3990	456	2	.	.	PUNCT
ejpam-3990	457	1	(	(	PUNCT
ejpam-3990	457	2	i	i	NOUN
ejpam-3990	457	3	)	)	PUNCT
ejpam-3990	457	4	let	let	VERB
ejpam-3990	457	5	g	g	NOUN
ejpam-3990	457	6	be	be	AUX
ejpam-3990	457	7	a	a	DET
ejpam-3990	457	8	connected	connected	ADJ
ejpam-3990	457	9	graph	graph	NOUN
ejpam-3990	457	10	.	.	PUNCT
ejpam-3990	458	1	suppose	suppose	VERB
ejpam-3990	458	2	w	w	PROPN
ejpam-3990	458	3	∈	∈	PROPN
ejpam-3990	458	4	v	v	ADP
ejpam-3990	458	5	(	(	PUNCT
ejpam-3990	458	6	g	g	NOUN
ejpam-3990	458	7	)	)	PUNCT
ejpam-3990	458	8	and	and	CCONJ
ejpam-3990	458	9	emg	emg	NOUN
ejpam-3990	458	10	(	(	PUNCT
ejpam-3990	458	11	w	w	PROPN
ejpam-3990	458	12	)	)	PUNCT
ejpam-3990	458	13	=	=	SYM
ejpam-3990	459	1	1	1	X
ejpam-3990	459	2	.	.	PUNCT
ejpam-3990	460	1	then	then	ADV
ejpam-3990	460	2	,	,	PUNCT
ejpam-3990	460	3	n	n	PRON
ejpam-3990	460	4	em	em	PRON
ejpam-3990	460	5	k1+g[w	k1+g[w	PROPN
ejpam-3990	460	6	]	]	X
ejpam-3990	460	7	=	=	SYM
ejpam-3990	460	8	v	v	X
ejpam-3990	460	9	(	(	PUNCT
ejpam-3990	460	10	k1+g	k1+g	NOUN
ejpam-3990	460	11	)	)	PUNCT
ejpam-3990	460	12	.	.	PUNCT
ejpam-3990	461	1	it	it	PRON
ejpam-3990	461	2	follows	follow	VERB
ejpam-3990	461	3	that	that	SCONJ
ejpam-3990	461	4	f	f	PROPN
ejpam-3990	461	5	em	em	PRON
ejpam-3990	461	6	k1+g[w	k1+g[w	PROPN
ejpam-3990	461	7	]	]	X
ejpam-3990	461	8	=	=	PUNCT
ejpam-3990	461	9	∅.	∅.	VERB
ejpam-3990	461	10	clearly	clearly	ADV
ejpam-3990	461	11	,	,	PUNCT
ejpam-3990	461	12	if	if	SCONJ
ejpam-3990	461	13	w	w	PROPN
ejpam-3990	461	14	=	=	SYM
ejpam-3990	461	15	v	v	NOUN
ejpam-3990	461	16	then	then	ADV
ejpam-3990	461	17	f	f	PROPN
ejpam-3990	461	18	em	em	PROPN
ejpam-3990	461	19	k1+g[w	k1+g[w	PROPN
ejpam-3990	461	20	]	]	X
ejpam-3990	462	1	=	=	PUNCT
ejpam-3990	462	2	∅.	∅.	PRON
ejpam-3990	462	3	next	next	ADV
ejpam-3990	462	4	,	,	PUNCT
ejpam-3990	462	5	suppose	suppose	VERB
ejpam-3990	462	6	w	w	ADP
ejpam-3990	462	7	∈	∈	PROPN
ejpam-3990	462	8	v	v	ADP
ejpam-3990	462	9	(	(	PUNCT
ejpam-3990	462	10	g	g	NOUN
ejpam-3990	462	11	)	)	PUNCT
ejpam-3990	462	12	and	and	CCONJ
ejpam-3990	462	13	emg	emg	NOUN
ejpam-3990	462	14	(	(	PUNCT
ejpam-3990	462	15	w	w	PROPN
ejpam-3990	462	16	)	)	PUNCT
ejpam-3990	462	17	≥	≥	NOUN
ejpam-3990	462	18	2	2	NUM
ejpam-3990	462	19	.	.	PUNCT
ejpam-3990	463	1	then	then	ADV
ejpam-3990	463	2	[	[	X
ejpam-3990	463	3	w	w	X
ejpam-3990	463	4	,	,	PUNCT
ejpam-3990	463	5	v	v	NOUN
ejpam-3990	463	6	,	,	PUNCT
ejpam-3990	463	7	g	g	NOUN
ejpam-3990	463	8	]	]	PUNCT
ejpam-3990	463	9	is	be	AUX
ejpam-3990	463	10	a	a	DET
ejpam-3990	463	11	monophonic	monophonic	ADJ
ejpam-3990	463	12	path	path	NOUN
ejpam-3990	463	13	in	in	ADP
ejpam-3990	463	14	k1+g	k1+g	NOUN
ejpam-3990	463	15	for	for	ADP
ejpam-3990	463	16	all	all	DET
ejpam-3990	463	17	g	g	NOUN
ejpam-3990	463	18	/∈	/∈	PUNCT
ejpam-3990	463	19	ng(w	ng(w	NOUN
ejpam-3990	463	20	)	)	PUNCT
ejpam-3990	463	21	.	.	PUNCT
ejpam-3990	464	1	moreover	moreover	ADV
ejpam-3990	464	2	,	,	PUNCT
ejpam-3990	464	3	since	since	SCONJ
ejpam-3990	464	4	every	every	DET
ejpam-3990	464	5	monophonic	monophonic	ADJ
ejpam-3990	464	6	path	path	NOUN
ejpam-3990	464	7	in	in	ADP
ejpam-3990	464	8	g	g	PROPN
ejpam-3990	464	9	is	be	AUX
ejpam-3990	464	10	a	a	DET
ejpam-3990	464	11	monophonic	monophonic	ADJ
ejpam-3990	464	12	path	path	NOUN
ejpam-3990	464	13	in	in	ADP
ejpam-3990	464	14	k1	k1	PROPN
ejpam-3990	464	15	+	+	PROPN
ejpam-3990	464	16	g.	g.	PROPN
ejpam-3990	464	17	it	it	PRON
ejpam-3990	464	18	follows	follow	VERB
ejpam-3990	464	19	that	that	SCONJ
ejpam-3990	464	20	n	n	PRON
ejpam-3990	464	21	em	em	PRON
ejpam-3990	464	22	k1+g[w	k1+g[w	PROPN
ejpam-3990	464	23	]	]	X
ejpam-3990	465	1	=	=	PUNCT
ejpam-3990	465	2	n	n	CCONJ
ejpam-3990	465	3	em	em	PRON
ejpam-3990	465	4	g	g	PROPN
ejpam-3990	465	5	[	[	X
ejpam-3990	465	6	w	w	X
ejpam-3990	465	7	]	]	X
ejpam-3990	465	8	.	.	PUNCT
ejpam-3990	466	1	thus	thus	ADV
ejpam-3990	466	2	,	,	PUNCT
ejpam-3990	466	3	f	f	PROPN
ejpam-3990	466	4	em	em	PROPN
ejpam-3990	466	5	k1+g[w	k1+g[w	PROPN
ejpam-3990	466	6	]	]	PUNCT
ejpam-3990	467	1	=	=	PUNCT
ejpam-3990	467	2	f	f	X
ejpam-3990	467	3	em	em	PRON
ejpam-3990	467	4	g	g	PROPN
ejpam-3990	468	1	[	[	X
ejpam-3990	468	2	w	w	X
ejpam-3990	468	3	]	]	X
ejpam-3990	468	4	∪	∪	X
ejpam-3990	468	5	{	{	PUNCT
ejpam-3990	468	6	v	v	NOUN
ejpam-3990	468	7	}	}	PUNCT
ejpam-3990	468	8	.	.	PUNCT
ejpam-3990	469	1	(	(	PUNCT
ejpam-3990	469	2	ii	ii	NOUN
ejpam-3990	469	3	)	)	PUNCT
ejpam-3990	469	4	let	let	VERB
ejpam-3990	469	5	g	g	NOUN
ejpam-3990	469	6	be	be	AUX
ejpam-3990	469	7	a	a	DET
ejpam-3990	469	8	disconnected	disconnected	ADJ
ejpam-3990	469	9	graph	graph	NOUN
ejpam-3990	469	10	.	.	PUNCT
ejpam-3990	470	1	clearly	clearly	ADV
ejpam-3990	470	2	,	,	PUNCT
ejpam-3990	470	3	if	if	SCONJ
ejpam-3990	470	4	w	w	PROPN
ejpam-3990	470	5	=	=	SYM
ejpam-3990	470	6	v	v	NOUN
ejpam-3990	470	7	,	,	PUNCT
ejpam-3990	470	8	then	then	ADV
ejpam-3990	470	9	n	n	CCONJ
ejpam-3990	470	10	em	em	PRON
ejpam-3990	470	11	k1+g[w	k1+g[w	PROPN
ejpam-3990	470	12	]	]	X
ejpam-3990	471	1	=	=	SYM
ejpam-3990	471	2	v	v	X
ejpam-3990	471	3	(	(	PUNCT
ejpam-3990	471	4	k1	k1	NOUN
ejpam-3990	471	5	+	+	CCONJ
ejpam-3990	471	6	g	g	NOUN
ejpam-3990	471	7	)	)	PUNCT
ejpam-3990	471	8	and	and	CCONJ
ejpam-3990	471	9	f	f	PRON
ejpam-3990	471	10	em	em	PRON
ejpam-3990	471	11	k1+g[w	k1+g[w	PROPN
ejpam-3990	471	12	]	]	X
ejpam-3990	471	13	=	=	PUNCT
ejpam-3990	471	14	∅.	∅.	AUX
ejpam-3990	471	15	suppose	suppose	VERB
ejpam-3990	471	16	w	w	PROPN
ejpam-3990	471	17	∈	∈	PROPN
ejpam-3990	471	18	v	v	ADP
ejpam-3990	471	19	(	(	PUNCT
ejpam-3990	471	20	g	g	NOUN
ejpam-3990	471	21	)	)	PUNCT
ejpam-3990	471	22	and	and	CCONJ
ejpam-3990	471	23	1	1	NUM
ejpam-3990	471	24	≤	≤	NOUN
ejpam-3990	471	25	emg	emg	NOUN
ejpam-3990	471	26	(	(	PUNCT
ejpam-3990	471	27	w	w	NOUN
ejpam-3990	471	28	)	)	PUNCT
ejpam-3990	471	29	≤	≤	NOUN
ejpam-3990	471	30	2	2	NUM
ejpam-3990	471	31	.	.	X
ejpam-3990	471	32	observe	observe	VERB
ejpam-3990	471	33	that	that	SCONJ
ejpam-3990	471	34	n	n	PRON
ejpam-3990	471	35	em	em	PRON
ejpam-3990	471	36	k1+g[w	k1+g[w	PROPN
ejpam-3990	471	37	]	]	X
ejpam-3990	472	1	=	=	SYM
ejpam-3990	472	2	v	v	X
ejpam-3990	472	3	(	(	PUNCT
ejpam-3990	472	4	g)\ng(w	g)\ng(w	PROPN
ejpam-3990	472	5	)	)	PUNCT
ejpam-3990	472	6	.	.	PUNCT
ejpam-3990	473	1	hence	hence	ADV
ejpam-3990	473	2	,	,	PUNCT
ejpam-3990	473	3	f	f	PROPN
ejpam-3990	473	4	em	em	PROPN
ejpam-3990	473	5	k1+g[w	k1+g[w	PROPN
ejpam-3990	473	6	]	]	X
ejpam-3990	473	7	=	=	PUNCT
ejpam-3990	473	8	ng(w)∪{v	ng(w)∪{v	NUM
ejpam-3990	473	9	}	}	PUNCT
ejpam-3990	473	10	.	.	PUNCT
ejpam-3990	473	11	suppose	suppose	VERB
ejpam-3990	473	12	w	w	PROPN
ejpam-3990	473	13	∈	∈	PROPN
ejpam-3990	473	14	v	v	ADP
ejpam-3990	473	15	(	(	PUNCT
ejpam-3990	473	16	g	g	NOUN
ejpam-3990	473	17	)	)	PUNCT
ejpam-3990	473	18	and	and	CCONJ
ejpam-3990	473	19	emg	emg	NOUN
ejpam-3990	473	20	(	(	PUNCT
ejpam-3990	473	21	w	w	PROPN
ejpam-3990	473	22	)	)	PUNCT
ejpam-3990	473	23	≥	≥	NOUN
ejpam-3990	473	24	3	3	NUM
ejpam-3990	473	25	.	.	PUNCT
ejpam-3990	474	1	since	since	SCONJ
ejpam-3990	474	2	every	every	DET
ejpam-3990	474	3	monophonic	monophonic	ADJ
ejpam-3990	474	4	path	path	NOUN
ejpam-3990	474	5	in	in	ADP
ejpam-3990	474	6	g	g	PROPN
ejpam-3990	474	7	is	be	AUX
ejpam-3990	474	8	a	a	DET
ejpam-3990	474	9	monophonic	monophonic	ADJ
ejpam-3990	474	10	path	path	NOUN
ejpam-3990	474	11	in	in	ADP
ejpam-3990	474	12	k1	k1	PROPN
ejpam-3990	474	13	+	+	PROPN
ejpam-3990	474	14	g.	g.	PROPN
ejpam-3990	474	15	it	it	PRON
ejpam-3990	474	16	follows	follow	VERB
ejpam-3990	474	17	that	that	SCONJ
ejpam-3990	474	18	n	n	PRON
ejpam-3990	474	19	em	em	PRON
ejpam-3990	474	20	k1+g[w	k1+g[w	PROPN
ejpam-3990	474	21	]	]	X
ejpam-3990	475	1	=	=	PUNCT
ejpam-3990	475	2	n	n	CCONJ
ejpam-3990	475	3	em	em	PRON
ejpam-3990	475	4	g	g	PROPN
ejpam-3990	475	5	[	[	X
ejpam-3990	475	6	w	w	X
ejpam-3990	475	7	]	]	X
ejpam-3990	475	8	.	.	PUNCT
ejpam-3990	476	1	therefore	therefore	ADV
ejpam-3990	476	2	,	,	PUNCT
ejpam-3990	476	3	f	f	PROPN
ejpam-3990	476	4	em	em	PRON
ejpam-3990	476	5	g	g	PROPN
ejpam-3990	476	6	[	[	X
ejpam-3990	476	7	w	w	X
ejpam-3990	476	8	]	]	X
ejpam-3990	476	9	∪	∪	X
ejpam-3990	476	10	{	{	PUNCT
ejpam-3990	476	11	v	v	NOUN
ejpam-3990	476	12	}	}	PUNCT
ejpam-3990	476	13	.	.	PUNCT
ejpam-3990	477	1	corollary	corollary	ADJ
ejpam-3990	477	2	3	3	X
ejpam-3990	477	3	.	.	PUNCT
ejpam-3990	478	1	let	let	VERB
ejpam-3990	478	2	k1	k1	NOUN
ejpam-3990	478	3	=	=	SYM
ejpam-3990	478	4	〈	〈	PROPN
ejpam-3990	478	5	v0	v0	NOUN
ejpam-3990	478	6	〉	〉	PROPN
ejpam-3990	478	7	and	and	CCONJ
ejpam-3990	478	8	let	let	VERB
ejpam-3990	478	9	g	g	NOUN
ejpam-3990	478	10	be	be	AUX
ejpam-3990	478	11	any	any	DET
ejpam-3990	478	12	graph	graph	NOUN
ejpam-3990	478	13	.	.	PUNCT
ejpam-3990	479	1	then	then	ADV
ejpam-3990	479	2	,	,	PUNCT
ejpam-3990	479	3	(	(	PUNCT
ejpam-3990	479	4	i	i	NOUN
ejpam-3990	479	5	)	)	PUNCT
ejpam-3990	479	6	sk1+g	sk1+g	NOUN
ejpam-3990	479	7	=	=	NOUN
ejpam-3990	479	8	{	{	PUNCT
ejpam-3990	479	9	∅	∅	NOUN
ejpam-3990	479	10	}	}	PUNCT
ejpam-3990	479	11	∪	∪	NOUN
ejpam-3990	479	12	{	{	PUNCT
ejpam-3990	479	13	f	f	NOUN
ejpam-3990	479	14	em	em	PRON
ejpam-3990	479	15	g	g	PROPN
ejpam-3990	480	1	[	[	X
ejpam-3990	480	2	w	w	X
ejpam-3990	480	3	]	]	X
ejpam-3990	480	4	∪	∪	ADJ
ejpam-3990	480	5	{	{	PUNCT
ejpam-3990	480	6	v0	v0	NOUN
ejpam-3990	480	7	}	}	PUNCT
ejpam-3990	480	8	:	:	PUNCT
ejpam-3990	480	9	w	w	X
ejpam-3990	480	10	∈	∈	PROPN
ejpam-3990	480	11	v	v	ADP
ejpam-3990	480	12	(	(	PUNCT
ejpam-3990	480	13	g	g	NOUN
ejpam-3990	480	14	)	)	PUNCT
ejpam-3990	480	15	and	and	CCONJ
ejpam-3990	480	16	emg	emg	NOUN
ejpam-3990	480	17	(	(	PUNCT
ejpam-3990	480	18	w	w	PROPN
ejpam-3990	480	19	)	)	PUNCT
ejpam-3990	480	20	≥	≥	NOUN
ejpam-3990	480	21	2	2	NUM
ejpam-3990	480	22	}	}	PUNCT
ejpam-3990	480	23	if	if	SCONJ
ejpam-3990	480	24	g	g	PROPN
ejpam-3990	480	25	is	be	AUX
ejpam-3990	480	26	connected	connect	VERB
ejpam-3990	480	27	,	,	PUNCT
ejpam-3990	480	28	(	(	PUNCT
ejpam-3990	480	29	ii	ii	NOUN
ejpam-3990	480	30	)	)	PUNCT
ejpam-3990	480	31	sk1+g	sk1+g	NOUN
ejpam-3990	480	32	=	=	NOUN
ejpam-3990	480	33	{	{	PUNCT
ejpam-3990	480	34	∅	∅	NOUN
ejpam-3990	480	35	}	}	PUNCT
ejpam-3990	480	36	∪	∪	NOUN
ejpam-3990	480	37	{	{	PUNCT
ejpam-3990	480	38	ng(w	ng(w	NOUN
ejpam-3990	480	39	)	)	PUNCT
ejpam-3990	480	40	∪	∪	NOUN
ejpam-3990	480	41	{	{	PUNCT
ejpam-3990	480	42	v0	v0	NOUN
ejpam-3990	480	43	}	}	PUNCT
ejpam-3990	480	44	:	:	PUNCT
ejpam-3990	481	1	w	w	X
ejpam-3990	481	2	∈	∈	PROPN
ejpam-3990	481	3	v	v	ADP
ejpam-3990	481	4	(	(	PUNCT
ejpam-3990	481	5	g	g	NOUN
ejpam-3990	481	6	)	)	PUNCT
ejpam-3990	481	7	and	and	CCONJ
ejpam-3990	481	8	degg(w	degg(w	PROPN
ejpam-3990	481	9	)	)	PUNCT
ejpam-3990	481	10	=	=	SYM
ejpam-3990	481	11	0	0	NUM
ejpam-3990	481	12	or	or	CCONJ
ejpam-3990	481	13	1	1	NUM
ejpam-3990	481	14	≤	≤	NOUN
ejpam-3990	481	15	emg	emg	NOUN
ejpam-3990	481	16	(	(	PUNCT
ejpam-3990	481	17	w	w	NOUN
ejpam-3990	481	18	)	)	PUNCT
ejpam-3990	481	19	≤	≤	NOUN
ejpam-3990	481	20	2	2	NUM
ejpam-3990	481	21	}	}	PUNCT
ejpam-3990	481	22	∪	∪	NOUN
ejpam-3990	481	23	{	{	PUNCT
ejpam-3990	481	24	f	f	NOUN
ejpam-3990	481	25	em	em	PRON
ejpam-3990	481	26	g	g	PROPN
ejpam-3990	481	27	[	[	X
ejpam-3990	481	28	w	w	X
ejpam-3990	481	29	]	]	X
ejpam-3990	481	30	∪	∪	ADJ
ejpam-3990	481	31	{	{	PUNCT
ejpam-3990	481	32	v0	v0	NOUN
ejpam-3990	481	33	}	}	PUNCT
ejpam-3990	481	34	:	:	PUNCT
ejpam-3990	481	35	w	w	X
ejpam-3990	481	36	∈	∈	PROPN
ejpam-3990	481	37	v	v	ADP
ejpam-3990	481	38	(	(	PUNCT
ejpam-3990	481	39	g	g	NOUN
ejpam-3990	481	40	)	)	PUNCT
ejpam-3990	481	41	and	and	CCONJ
ejpam-3990	481	42	emg	emg	NOUN
ejpam-3990	481	43	(	(	PUNCT
ejpam-3990	481	44	w	w	PROPN
ejpam-3990	481	45	)	)	PUNCT
ejpam-3990	481	46	≥	≥	NOUN
ejpam-3990	481	47	3	3	NUM
ejpam-3990	481	48	}	}	PUNCT
ejpam-3990	481	49	if	if	SCONJ
ejpam-3990	481	50	g	g	PROPN
ejpam-3990	481	51	is	be	AUX
ejpam-3990	481	52	disconnected	disconnect	VERB
ejpam-3990	481	53	.	.	PUNCT
ejpam-3990	482	1	(	(	PUNCT
ejpam-3990	482	2	iii	iii	NOUN
ejpam-3990	482	3	)	)	PUNCT
ejpam-3990	482	4	{	{	PUNCT
ejpam-3990	482	5	v	v	NOUN
ejpam-3990	482	6	}	}	PUNCT
ejpam-3990	482	7	/∈	/∈	PUNCT
ejpam-3990	483	1	τ	τ	PROPN
ejpam-3990	483	2	emk1+g	emk1+g	PROPN
ejpam-3990	483	3	for	for	ADP
ejpam-3990	483	4	all	all	DET
ejpam-3990	483	5	v	v	ADP
ejpam-3990	483	6	∈	∈	NOUN
ejpam-3990	483	7	v	v	NOUN
ejpam-3990	483	8	(	(	PUNCT
ejpam-3990	483	9	g	g	NOUN
ejpam-3990	483	10	)	)	PUNCT
ejpam-3990	483	11	.	.	PUNCT
ejpam-3990	484	1	proof	proof	NOUN
ejpam-3990	484	2	.	.	PUNCT
ejpam-3990	485	1	set	set	VERB
ejpam-3990	485	2	h	h	NOUN
ejpam-3990	485	3	=	=	SYM
ejpam-3990	485	4	k1	k1	PROPN
ejpam-3990	485	5	.	.	PUNCT
ejpam-3990	486	1	by	by	ADP
ejpam-3990	486	2	theorem	theorem	NOUN
ejpam-3990	486	3	10	10	NUM
ejpam-3990	486	4	(	(	PUNCT
ejpam-3990	486	5	i	i	NOUN
ejpam-3990	486	6	)	)	PUNCT
ejpam-3990	486	7	and	and	CCONJ
ejpam-3990	486	8	theorem	theorem	VERB
ejpam-3990	486	9	10	10	NUM
ejpam-3990	486	10	(	(	PUNCT
ejpam-3990	486	11	ii	ii	NOUN
ejpam-3990	486	12	)	)	PUNCT
ejpam-3990	486	13	,	,	PUNCT
ejpam-3990	486	14	(	(	PUNCT
ejpam-3990	486	15	i	i	NOUN
ejpam-3990	486	16	)	)	PUNCT
ejpam-3990	486	17	and	and	CCONJ
ejpam-3990	486	18	(	(	PUNCT
ejpam-3990	486	19	ii	ii	NOUN
ejpam-3990	486	20	)	)	PUNCT
ejpam-3990	486	21	hold	hold	VERB
ejpam-3990	486	22	.	.	PUNCT
ejpam-3990	487	1	by	by	ADP
ejpam-3990	487	2	(	(	PUNCT
ejpam-3990	487	3	i	i	NOUN
ejpam-3990	487	4	)	)	PUNCT
ejpam-3990	487	5	and	and	CCONJ
ejpam-3990	487	6	(	(	PUNCT
ejpam-3990	487	7	ii	ii	NOUN
ejpam-3990	487	8	)	)	PUNCT
ejpam-3990	487	9	,	,	PUNCT
ejpam-3990	487	10	(	(	PUNCT
ejpam-3990	487	11	iii	iii	X
ejpam-3990	487	12	)	)	PUNCT
ejpam-3990	487	13	holds	hold	VERB
ejpam-3990	487	14	.	.	PUNCT
ejpam-3990	488	1	lemma	lemma	PROPN
ejpam-3990	488	2	6	6	NUM
ejpam-3990	488	3	.	.	PUNCT
ejpam-3990	489	1	let	let	VERB
ejpam-3990	489	2	k1	k1	NOUN
ejpam-3990	489	3	=	=	SYM
ejpam-3990	489	4	〈	〈	PROPN
ejpam-3990	489	5	v0	v0	NOUN
ejpam-3990	489	6	〉	〉	PROPN
ejpam-3990	489	7	and	and	CCONJ
ejpam-3990	489	8	let	let	VERB
ejpam-3990	489	9	g	g	NOUN
ejpam-3990	489	10	be	be	AUX
ejpam-3990	489	11	any	any	DET
ejpam-3990	489	12	graph	graph	NOUN
ejpam-3990	489	13	with	with	ADP
ejpam-3990	489	14	radm(g	radm(g	NOUN
ejpam-3990	489	15	)	)	PUNCT
ejpam-3990	489	16	≥	≥	NOUN
ejpam-3990	490	1	2	2	NUM
ejpam-3990	490	2	.	.	PUNCT
ejpam-3990	490	3	then	then	ADV
ejpam-3990	490	4	{	{	PUNCT
ejpam-3990	490	5	v0	v0	NOUN
ejpam-3990	490	6	}	}	PUNCT
ejpam-3990	490	7	∈	∈	PROPN
ejpam-3990	490	8	τ	τ	X
ejpam-3990	490	9	emk1+g	emk1+g	PROPN
ejpam-3990	490	10	.	.	PUNCT
ejpam-3990	491	1	proof	proof	NOUN
ejpam-3990	491	2	.	.	PUNCT
ejpam-3990	492	1	suppose	suppose	VERB
ejpam-3990	492	2	g	g	PROPN
ejpam-3990	492	3	is	be	AUX
ejpam-3990	492	4	any	any	DET
ejpam-3990	492	5	graph	graph	NOUN
ejpam-3990	492	6	with	with	ADP
ejpam-3990	492	7	radm(g	radm(g	NOUN
ejpam-3990	492	8	)	)	PUNCT
ejpam-3990	492	9	≥	≥	NOUN
ejpam-3990	493	1	2	2	NUM
ejpam-3990	493	2	.	.	PUNCT
ejpam-3990	494	1	then	then	ADV
ejpam-3990	494	2	,	,	PUNCT
ejpam-3990	494	3	emg	emg	NOUN
ejpam-3990	494	4	(	(	PUNCT
ejpam-3990	494	5	z	z	NOUN
ejpam-3990	494	6	)	)	PUNCT
ejpam-3990	494	7	≥	≥	NOUN
ejpam-3990	494	8	2	2	NUM
ejpam-3990	494	9	for	for	ADP
ejpam-3990	494	10	all	all	DET
ejpam-3990	494	11	z	z	NOUN
ejpam-3990	494	12	∈	∈	PROPN
ejpam-3990	494	13	v	v	NOUN
ejpam-3990	494	14	(	(	PUNCT
ejpam-3990	494	15	g	g	NOUN
ejpam-3990	494	16	)	)	PUNCT
ejpam-3990	494	17	.	.	PUNCT
ejpam-3990	495	1	let	let	VERB
ejpam-3990	495	2	v	v	NUM
ejpam-3990	495	3	∈	∈	PROPN
ejpam-3990	495	4	v	v	NOUN
ejpam-3990	495	5	(	(	PUNCT
ejpam-3990	495	6	g	g	NOUN
ejpam-3990	495	7	)	)	PUNCT
ejpam-3990	495	8	.	.	PUNCT
ejpam-3990	496	1	since	since	SCONJ
ejpam-3990	496	2	v	v	NUM
ejpam-3990	496	3	/∈	/∈	PUNCT
ejpam-3990	496	4	(	(	PUNCT
ejpam-3990	496	5	f	f	VERB
ejpam-3990	496	6	em	em	PRON
ejpam-3990	496	7	g	g	PROPN
ejpam-3990	496	8	[	[	X
ejpam-3990	496	9	v	v	X
ejpam-3990	496	10	]	]	X
ejpam-3990	496	11	∩	∩	NOUN
ejpam-3990	496	12	{	{	PUNCT
ejpam-3990	496	13	v0	v0	NOUN
ejpam-3990	496	14	}	}	PUNCT
ejpam-3990	496	15	)	)	PUNCT
ejpam-3990	496	16	,	,	PUNCT
ejpam-3990	496	17	it	it	PRON
ejpam-3990	496	18	follows	follow	VERB
ejpam-3990	496	19	that	that	PRON
ejpam-3990	496	20	v	v	ADP
ejpam-3990	496	21	/∈	/∈	PUNCT
ejpam-3990	497	1	⋂	⋂	PROPN
ejpam-3990	497	2	z∈v	z∈v	NOUN
ejpam-3990	497	3	(	(	PUNCT
ejpam-3990	497	4	g	g	NOUN
ejpam-3990	497	5	)	)	PUNCT
ejpam-3990	497	6	(	(	PUNCT
ejpam-3990	497	7	f	f	VERB
ejpam-3990	497	8	em	em	PRON
ejpam-3990	497	9	g	g	PROPN
ejpam-3990	498	1	[	[	X
ejpam-3990	498	2	z	z	X
ejpam-3990	498	3	]	]	X
ejpam-3990	498	4	∩	∩	X
ejpam-3990	498	5	{	{	PUNCT
ejpam-3990	498	6	v0	v0	NOUN
ejpam-3990	498	7	}	}	PUNCT
ejpam-3990	498	8	)	)	PUNCT
ejpam-3990	498	9	.	.	PUNCT
ejpam-3990	499	1	since	since	SCONJ
ejpam-3990	499	2	v	v	NOUN
ejpam-3990	499	3	was	be	AUX
ejpam-3990	499	4	arbitrarily	arbitrarily	ADV
ejpam-3990	499	5	chosen	choose	VERB
ejpam-3990	499	6	,	,	PUNCT
ejpam-3990	499	7	{	{	PUNCT
ejpam-3990	499	8	v0	v0	NOUN
ejpam-3990	499	9	}	}	PUNCT
ejpam-3990	499	10	=	=	SYM
ejpam-3990	499	11	⋂	⋂	PROPN
ejpam-3990	499	12	z∈v	z∈v	NOUN
ejpam-3990	499	13	(	(	PUNCT
ejpam-3990	499	14	g	g	NOUN
ejpam-3990	499	15	)	)	PUNCT
ejpam-3990	499	16	(	(	PUNCT
ejpam-3990	499	17	f	f	VERB
ejpam-3990	499	18	em	em	PRON
ejpam-3990	499	19	g	g	PROPN
ejpam-3990	499	20	[	[	X
ejpam-3990	499	21	z	z	X
ejpam-3990	499	22	]	]	X
ejpam-3990	499	23	∪	∪	X
ejpam-3990	499	24	{	{	PUNCT
ejpam-3990	499	25	v0	v0	NOUN
ejpam-3990	499	26	}	}	PUNCT
ejpam-3990	499	27	)	)	PUNCT
ejpam-3990	499	28	.	.	PUNCT
ejpam-3990	500	1	by	by	ADP
ejpam-3990	500	2	corollary	corollary	ADJ
ejpam-3990	500	3	3	3	NUM
ejpam-3990	500	4	,	,	PUNCT
ejpam-3990	500	5	(	(	PUNCT
ejpam-3990	500	6	f	f	VERB
ejpam-3990	500	7	em	em	PRON
ejpam-3990	500	8	g	g	PROPN
ejpam-3990	500	9	[	[	X
ejpam-3990	500	10	z	z	X
ejpam-3990	500	11	]	]	X
ejpam-3990	500	12	∪	∪	X
ejpam-3990	500	13	{	{	PUNCT
ejpam-3990	500	14	v0	v0	NOUN
ejpam-3990	500	15	}	}	PUNCT
ejpam-3990	500	16	)	)	PUNCT
ejpam-3990	500	17	∈	∈	PROPN
ejpam-3990	500	18	semk1+g	semk1+g	NOUN
ejpam-3990	500	19	⊆	⊆	NUM
ejpam-3990	500	20	τ	τ	X
ejpam-3990	500	21	em	em	PRON
ejpam-3990	500	22	k1+g	k1+g	PROPN
ejpam-3990	500	23	.	.	PUNCT
ejpam-3990	501	1	therefore	therefore	ADV
ejpam-3990	501	2	,	,	PUNCT
ejpam-3990	501	3	{	{	PUNCT
ejpam-3990	501	4	v0	v0	NOUN
ejpam-3990	501	5	}	}	PUNCT
ejpam-3990	501	6	∈	∈	PROPN
ejpam-3990	501	7	τ	τ	X
ejpam-3990	501	8	emk1+g	emk1+g	PROPN
ejpam-3990	501	9	.	.	PUNCT
ejpam-3990	502	1	definition	definition	NOUN
ejpam-3990	502	2	2	2	NUM
ejpam-3990	502	3	.	.	PUNCT
ejpam-3990	503	1	let	let	VERB
ejpam-3990	503	2	x	x	SYM
ejpam-3990	503	3	6=	6=	ADP
ejpam-3990	503	4	∅	∅	NOUN
ejpam-3990	503	5	and	and	CCONJ
ejpam-3990	503	6	p	p	NOUN
ejpam-3990	503	7	∈	∈	PROPN
ejpam-3990	503	8	x.	x.	NOUN
ejpam-3990	504	1	the	the	DET
ejpam-3990	504	2	particular	particular	ADJ
ejpam-3990	504	3	point	point	NOUN
ejpam-3990	504	4	p	p	PRON
ejpam-3990	504	5	topology	topology	NOUN
ejpam-3990	504	6	on	on	ADP
ejpam-3990	504	7	x	x	X
ejpam-3990	504	8	is	be	AUX
ejpam-3990	504	9	the	the	DET
ejpam-3990	504	10	class	class	NOUN
ejpam-3990	504	11	τp	τp	NOUN
ejpam-3990	504	12	=	=	PUNCT
ejpam-3990	504	13	{	{	PUNCT
ejpam-3990	504	14	∅	∅	NOUN
ejpam-3990	504	15	}	}	PUNCT
ejpam-3990	504	16	∪	∪	X
ejpam-3990	504	17	{	{	PUNCT
ejpam-3990	504	18	a	a	DET
ejpam-3990	504	19	⊆	⊆	NUM
ejpam-3990	504	20	x	x	SYM
ejpam-3990	504	21	:	:	PUNCT
ejpam-3990	504	22	p	p	X
ejpam-3990	504	23	∈	∈	PROPN
ejpam-3990	504	24	a	a	PRON
ejpam-3990	504	25	}	}	PUNCT
ejpam-3990	504	26	.	.	PUNCT
ejpam-3990	505	1	a.	a.	PROPN
ejpam-3990	505	2	gamorez	gamorez	PROPN
ejpam-3990	505	3	,	,	PUNCT
ejpam-3990	505	4	s.	s.	PROPN
ejpam-3990	505	5	canoy	canoy	PROPN
ejpam-3990	505	6	jr	jr	PROPN
ejpam-3990	505	7	.	.	PROPN
ejpam-3990	505	8	/	/	SYM
ejpam-3990	505	9	eur	eur	PROPN
ejpam-3990	505	10	.	.	PUNCT
ejpam-3990	506	1	j.	j.	PROPN
ejpam-3990	506	2	pure	pure	PROPN
ejpam-3990	506	3	appl	appl	PROPN
ejpam-3990	506	4	.	.	PROPN
ejpam-3990	506	5	math	math	PROPN
ejpam-3990	506	6	,	,	PUNCT
ejpam-3990	506	7	14	14	NUM
ejpam-3990	506	8	(	(	PUNCT
ejpam-3990	506	9	3	3	NUM
ejpam-3990	506	10	)	)	PUNCT
ejpam-3990	506	11	(	(	PUNCT
ejpam-3990	506	12	2021	2021	NUM
ejpam-3990	506	13	)	)	PUNCT
ejpam-3990	506	14	,	,	PUNCT
ejpam-3990	506	15	695	695	NUM
ejpam-3990	506	16	-	-	SYM
ejpam-3990	506	17	705	705	NUM
ejpam-3990	506	18	703	703	NUM
ejpam-3990	506	19	theorem	theorem	NOUN
ejpam-3990	506	20	11	11	NUM
ejpam-3990	506	21	.	.	PUNCT
ejpam-3990	507	1	let	let	VERB
ejpam-3990	507	2	k1	k1	NOUN
ejpam-3990	507	3	=	=	SYM
ejpam-3990	507	4	〈	〈	PROPN
ejpam-3990	507	5	v0	v0	NOUN
ejpam-3990	507	6	〉	〉	PROPN
ejpam-3990	507	7	and	and	CCONJ
ejpam-3990	507	8	let	let	VERB
ejpam-3990	507	9	g	g	PRON
ejpam-3990	507	10	be	be	AUX
ejpam-3990	507	11	a	a	DET
ejpam-3990	507	12	connected	connected	ADJ
ejpam-3990	507	13	graph	graph	NOUN
ejpam-3990	507	14	with	with	ADP
ejpam-3990	507	15	radm(g	radm(g	NOUN
ejpam-3990	507	16	)	)	PUNCT
ejpam-3990	507	17	≥	≥	NOUN
ejpam-3990	508	1	2	2	NUM
ejpam-3990	508	2	.	.	PUNCT
ejpam-3990	508	3	then	then	ADV
ejpam-3990	508	4	τ	τ	PROPN
ejpam-3990	508	5	emk1+g	emk1+g	PROPN
ejpam-3990	508	6	is	be	AUX
ejpam-3990	508	7	the	the	DET
ejpam-3990	508	8	particular	particular	ADJ
ejpam-3990	508	9	point	point	NOUN
ejpam-3990	508	10	topology	topology	NOUN
ejpam-3990	508	11	τv0	τv0	NOUN
ejpam-3990	509	1	if	if	SCONJ
ejpam-3990	509	2	and	and	CCONJ
ejpam-3990	509	3	only	only	ADV
ejpam-3990	509	4	if	if	SCONJ
ejpam-3990	509	5	τ	τ	PROPN
ejpam-3990	509	6	emg	emg	NOUN
ejpam-3990	509	7	is	be	AUX
ejpam-3990	509	8	the	the	DET
ejpam-3990	509	9	discrete	discrete	ADJ
ejpam-3990	509	10	topology	topology	NOUN
ejpam-3990	509	11	on	on	ADP
ejpam-3990	509	12	v	v	ADP
ejpam-3990	509	13	(	(	PUNCT
ejpam-3990	509	14	g	g	NOUN
ejpam-3990	509	15	)	)	PUNCT
ejpam-3990	509	16	.	.	PUNCT
ejpam-3990	510	1	proof	proof	NOUN
ejpam-3990	510	2	.	.	PUNCT
ejpam-3990	511	1	suppose	suppose	VERB
ejpam-3990	511	2	τ	τ	PROPN
ejpam-3990	511	3	emg	emg	NOUN
ejpam-3990	511	4	is	be	AUX
ejpam-3990	511	5	the	the	DET
ejpam-3990	511	6	discrete	discrete	ADJ
ejpam-3990	511	7	topology	topology	NOUN
ejpam-3990	511	8	on	on	ADP
ejpam-3990	511	9	v	v	ADP
ejpam-3990	511	10	(	(	PUNCT
ejpam-3990	511	11	g	g	NOUN
ejpam-3990	511	12	)	)	PUNCT
ejpam-3990	511	13	.	.	PUNCT
ejpam-3990	512	1	note	note	VERB
ejpam-3990	512	2	that	that	SCONJ
ejpam-3990	512	3	{	{	PUNCT
ejpam-3990	512	4	v0	v0	NOUN
ejpam-3990	512	5	}	}	PUNCT
ejpam-3990	512	6	∈	∈	PROPN
ejpam-3990	512	7	τ	τ	X
ejpam-3990	512	8	emk1+g	emk1+g	PROPN
ejpam-3990	512	9	.	.	PUNCT
ejpam-3990	513	1	now	now	ADV
ejpam-3990	513	2	,	,	PUNCT
ejpam-3990	513	3	since	since	SCONJ
ejpam-3990	513	4	{	{	PUNCT
ejpam-3990	513	5	v0	v0	NOUN
ejpam-3990	513	6	}	}	PUNCT
ejpam-3990	513	7	∈	∈	PROPN
ejpam-3990	513	8	(	(	PUNCT
ejpam-3990	513	9	f	f	NOUN
ejpam-3990	513	10	em	em	PRON
ejpam-3990	513	11	g	g	PROPN
ejpam-3990	513	12	[	[	X
ejpam-3990	513	13	w	w	X
ejpam-3990	513	14	]	]	X
ejpam-3990	513	15	∩	∩	ADJ
ejpam-3990	513	16	{	{	PUNCT
ejpam-3990	513	17	v0	v0	NOUN
ejpam-3990	513	18	}	}	PUNCT
ejpam-3990	513	19	)	)	PUNCT
ejpam-3990	513	20	for	for	ADP
ejpam-3990	513	21	all	all	DET
ejpam-3990	513	22	w	w	PROPN
ejpam-3990	513	23	∈	∈	PROPN
ejpam-3990	513	24	v	v	ADP
ejpam-3990	513	25	(	(	PUNCT
ejpam-3990	513	26	g	g	NOUN
ejpam-3990	513	27	)	)	PUNCT
ejpam-3990	513	28	,	,	PUNCT
ejpam-3990	513	29	it	it	PRON
ejpam-3990	513	30	follows	follow	VERB
ejpam-3990	513	31	that	that	SCONJ
ejpam-3990	513	32	{	{	PUNCT
ejpam-3990	513	33	v	v	NOUN
ejpam-3990	513	34	}	}	PUNCT
ejpam-3990	513	35	/∈	/∈	PUNCT
ejpam-3990	513	36	bemk1+g	bemk1+g	NOUN
ejpam-3990	513	37	⊆	⊆	NUM
ejpam-3990	513	38	τ	τ	PUNCT
ejpam-3990	513	39	emk1+g	emk1+g	PROPN
ejpam-3990	513	40	.	.	PUNCT
ejpam-3990	514	1	next	next	ADV
ejpam-3990	514	2	,	,	PUNCT
ejpam-3990	514	3	since	since	SCONJ
ejpam-3990	514	4	τ	τ	PROPN
ejpam-3990	514	5	emg	emg	NOUN
ejpam-3990	514	6	is	be	AUX
ejpam-3990	514	7	a	a	DET
ejpam-3990	514	8	discrete	discrete	ADJ
ejpam-3990	514	9	topology	topology	NOUN
ejpam-3990	514	10	,	,	PUNCT
ejpam-3990	514	11	{	{	PUNCT
ejpam-3990	514	12	v	v	NOUN
ejpam-3990	514	13	}	}	PUNCT
ejpam-3990	514	14	∈	∈	NOUN
ejpam-3990	514	15	bemg	bemg	VERB
ejpam-3990	514	16	for	for	ADP
ejpam-3990	514	17	all	all	PRON
ejpam-3990	514	18	v	v	ADP
ejpam-3990	514	19	∈	∈	NUM
ejpam-3990	514	20	v	v	NOUN
ejpam-3990	514	21	(	(	PUNCT
ejpam-3990	514	22	g	g	NOUN
ejpam-3990	514	23	)	)	PUNCT
ejpam-3990	514	24	.	.	PUNCT
ejpam-3990	515	1	hence	hence	ADV
ejpam-3990	515	2	,	,	PUNCT
ejpam-3990	515	3	there	there	PRON
ejpam-3990	515	4	exist	exist	VERB
ejpam-3990	515	5	vj1	vj1	NOUN
ejpam-3990	515	6	,	,	PUNCT
ejpam-3990	515	7	vj2	vj2	ADJ
ejpam-3990	515	8	,	,	PUNCT
ejpam-3990	515	9	...	...	PUNCT
ejpam-3990	515	10	,	,	PUNCT
ejpam-3990	515	11	vjk	vjk	VERB
ejpam-3990	515	12	∈	∈	PROPN
ejpam-3990	515	13	v	v	ADP
ejpam-3990	515	14	(	(	PUNCT
ejpam-3990	515	15	g	g	NOUN
ejpam-3990	515	16	)	)	PUNCT
ejpam-3990	515	17	such	such	ADJ
ejpam-3990	515	18	that	that	SCONJ
ejpam-3990	515	19	{	{	PUNCT
ejpam-3990	515	20	v	v	NOUN
ejpam-3990	515	21	}	}	PUNCT
ejpam-3990	515	22	=	=	PUNCT
ejpam-3990	515	23	k⋂	k⋂	NOUN
ejpam-3990	516	1	s=1	s=1	X
ejpam-3990	516	2	f	f	X
ejpam-3990	516	3	em	em	PRON
ejpam-3990	516	4	g	g	PROPN
ejpam-3990	517	1	[	[	X
ejpam-3990	517	2	vjs	vjs	X
ejpam-3990	517	3	]	]	PUNCT
ejpam-3990	517	4	.	.	PUNCT
ejpam-3990	518	1	therefore	therefore	ADV
ejpam-3990	518	2	,	,	PUNCT
ejpam-3990	518	3	{	{	PUNCT
ejpam-3990	518	4	v0	v0	NOUN
ejpam-3990	518	5	,	,	PUNCT
ejpam-3990	518	6	v	v	NOUN
ejpam-3990	518	7	}	}	PUNCT
ejpam-3990	518	8	=	=	SYM
ejpam-3990	518	9	(	(	PUNCT
ejpam-3990	518	10	k⋂	k⋂	X
ejpam-3990	518	11	s=1	s=1	X
ejpam-3990	518	12	f	f	X
ejpam-3990	519	1	em	em	PRON
ejpam-3990	519	2	g	g	PROPN
ejpam-3990	520	1	[	[	X
ejpam-3990	520	2	vjs	vjs	X
ejpam-3990	520	3	]	]	PUNCT
ejpam-3990	520	4	)	)	PUNCT
ejpam-3990	520	5	∪	∪	ADP
ejpam-3990	520	6	{	{	PUNCT
ejpam-3990	520	7	v0	v0	NOUN
ejpam-3990	520	8	}	}	PUNCT
ejpam-3990	520	9	=	=	SYM
ejpam-3990	520	10	k⋂	k⋂	X
ejpam-3990	520	11	s=1	s=1	X
ejpam-3990	521	1	(	(	PUNCT
ejpam-3990	521	2	f	f	X
ejpam-3990	521	3	em	em	PRON
ejpam-3990	521	4	g	g	PROPN
ejpam-3990	521	5	[	[	X
ejpam-3990	521	6	vjs	vjs	X
ejpam-3990	521	7	]	]	PUNCT
ejpam-3990	521	8	∪	∪	X
ejpam-3990	521	9	{	{	PUNCT
ejpam-3990	521	10	v0	v0	NOUN
ejpam-3990	521	11	}	}	PUNCT
ejpam-3990	521	12	)	)	PUNCT
ejpam-3990	521	13	∈	∈	NOUN
ejpam-3990	521	14	bemk1+g	bemk1+g	NOUN
ejpam-3990	521	15	⊆	⊆	NUM
ejpam-3990	521	16	τ	τ	X
ejpam-3990	521	17	em	em	PRON
ejpam-3990	521	18	k1+g	k1+g	PROPN
ejpam-3990	521	19	.	.	PUNCT
ejpam-3990	521	20	accordingly	accordingly	ADV
ejpam-3990	521	21	,	,	PUNCT
ejpam-3990	521	22	τ	τ	PROPN
ejpam-3990	521	23	emk1+g	emk1+g	PROPN
ejpam-3990	521	24	=	=	SYM
ejpam-3990	521	25	τv0	τv0	PROPN
ejpam-3990	521	26	.	.	PUNCT
ejpam-3990	522	1	for	for	ADP
ejpam-3990	522	2	the	the	DET
ejpam-3990	522	3	converse	converse	NOUN
ejpam-3990	522	4	,	,	PUNCT
ejpam-3990	522	5	suppose	suppose	VERB
ejpam-3990	522	6	that	that	SCONJ
ejpam-3990	522	7	τ	τ	PROPN
ejpam-3990	522	8	emk1+g	emk1+g	PROPN
ejpam-3990	522	9	=	=	SYM
ejpam-3990	522	10	τv0	τv0	PROPN
ejpam-3990	522	11	.	.	PUNCT
ejpam-3990	523	1	let	let	VERB
ejpam-3990	523	2	v	v	NUM
ejpam-3990	523	3	∈	∈	PROPN
ejpam-3990	523	4	v	v	NOUN
ejpam-3990	523	5	(	(	PUNCT
ejpam-3990	523	6	g	g	NOUN
ejpam-3990	523	7	)	)	PUNCT
ejpam-3990	523	8	.	.	PUNCT
ejpam-3990	524	1	since	since	SCONJ
ejpam-3990	524	2	τ	τ	X
ejpam-3990	524	3	emk1+g	emk1+g	PROPN
ejpam-3990	524	4	=	=	SYM
ejpam-3990	524	5	τv0	τv0	PROPN
ejpam-3990	524	6	,	,	PUNCT
ejpam-3990	524	7	{	{	PUNCT
ejpam-3990	524	8	v0	v0	NOUN
ejpam-3990	524	9	,	,	PUNCT
ejpam-3990	524	10	v	v	NOUN
ejpam-3990	524	11	}	}	PUNCT
ejpam-3990	524	12	∈	∈	PROPN
ejpam-3990	524	13	τ	τ	X
ejpam-3990	524	14	emk1+g	emk1+g	PROPN
ejpam-3990	524	15	.	.	PUNCT
ejpam-3990	524	16	hence	hence	ADV
ejpam-3990	524	17	,	,	PUNCT
ejpam-3990	524	18	there	there	PRON
ejpam-3990	524	19	exists	exist	VERB
ejpam-3990	524	20	a	a	DET
ejpam-3990	524	21	basic	basic	ADJ
ejpam-3990	524	22	open	open	ADJ
ejpam-3990	524	23	set	set	NOUN
ejpam-3990	524	24	b	b	PROPN
ejpam-3990	524	25	∈	∈	NOUN
ejpam-3990	524	26	bemk1+g	bemk1+g	NOUN
ejpam-3990	524	27	such	such	ADJ
ejpam-3990	524	28	that	that	DET
ejpam-3990	524	29	v	v	NUM
ejpam-3990	524	30	∈	∈	PROPN
ejpam-3990	524	31	b	b	NOUN
ejpam-3990	524	32	⊆	⊆	NUM
ejpam-3990	524	33	{	{	PUNCT
ejpam-3990	524	34	v0	v0	NOUN
ejpam-3990	524	35	,	,	PUNCT
ejpam-3990	524	36	v	v	NOUN
ejpam-3990	524	37	}	}	PUNCT
ejpam-3990	524	38	.	.	PUNCT
ejpam-3990	525	1	since	since	SCONJ
ejpam-3990	525	2	{	{	PUNCT
ejpam-3990	525	3	v	v	AUX
ejpam-3990	525	4	}	}	PUNCT
ejpam-3990	525	5	can	can	AUX
ejpam-3990	525	6	not	not	PART
ejpam-3990	525	7	be	be	AUX
ejpam-3990	525	8	a	a	DET
ejpam-3990	525	9	finite	finite	ADJ
ejpam-3990	525	10	intersection	intersection	NOUN
ejpam-3990	525	11	of	of	ADP
ejpam-3990	525	12	subbasic	subbasic	ADJ
ejpam-3990	525	13	open	open	ADJ
ejpam-3990	525	14	sets	set	NOUN
ejpam-3990	525	15	of	of	ADP
ejpam-3990	525	16	the	the	DET
ejpam-3990	525	17	form	form	NOUN
ejpam-3990	526	1	f	f	X
ejpam-3990	526	2	em	em	PRON
ejpam-3990	526	3	g	g	PROPN
ejpam-3990	527	1	[	[	X
ejpam-3990	527	2	w	w	X
ejpam-3990	527	3	]	]	X
ejpam-3990	527	4	∪	∪	ADJ
ejpam-3990	527	5	{	{	PUNCT
ejpam-3990	527	6	v0	v0	NOUN
ejpam-3990	527	7	}	}	PUNCT
ejpam-3990	527	8	,	,	PUNCT
ejpam-3990	527	9	it	it	PRON
ejpam-3990	527	10	follows	follow	VERB
ejpam-3990	527	11	that	that	PRON
ejpam-3990	527	12	b	b	PROPN
ejpam-3990	527	13	6=	6=	NUM
ejpam-3990	527	14	{	{	PUNCT
ejpam-3990	527	15	v	v	NOUN
ejpam-3990	527	16	}	}	PUNCT
ejpam-3990	527	17	.	.	PUNCT
ejpam-3990	528	1	thus	thus	ADV
ejpam-3990	528	2	,	,	PUNCT
ejpam-3990	528	3	b	b	X
ejpam-3990	528	4	=	=	SYM
ejpam-3990	528	5	{	{	PUNCT
ejpam-3990	528	6	v0	v0	PROPN
ejpam-3990	528	7	,	,	PUNCT
ejpam-3990	528	8	v	v	NOUN
ejpam-3990	528	9	}	}	PUNCT
ejpam-3990	528	10	.	.	PUNCT
ejpam-3990	529	1	this	this	PRON
ejpam-3990	529	2	means	mean	VERB
ejpam-3990	529	3	that	that	SCONJ
ejpam-3990	529	4	there	there	PRON
ejpam-3990	529	5	exist	exist	VERB
ejpam-3990	529	6	vj1	vj1	NOUN
ejpam-3990	529	7	,	,	PUNCT
ejpam-3990	529	8	vj2	vj2	ADJ
ejpam-3990	529	9	,	,	PUNCT
ejpam-3990	529	10	...	...	PUNCT
ejpam-3990	529	11	,	,	PUNCT
ejpam-3990	529	12	vjk	vjk	VERB
ejpam-3990	529	13	∈	∈	PROPN
ejpam-3990	529	14	v	v	ADP
ejpam-3990	529	15	(	(	PUNCT
ejpam-3990	529	16	g	g	NOUN
ejpam-3990	529	17	)	)	PUNCT
ejpam-3990	529	18	such	such	ADJ
ejpam-3990	529	19	that	that	SCONJ
ejpam-3990	529	20	{	{	PUNCT
ejpam-3990	529	21	v0	v0	NOUN
ejpam-3990	529	22	,	,	PUNCT
ejpam-3990	529	23	v	v	NOUN
ejpam-3990	529	24	}	}	PUNCT
ejpam-3990	529	25	=	=	SYM
ejpam-3990	529	26	t⋂	t⋂	NOUN
ejpam-3990	529	27	k=1	k=1	PUNCT
ejpam-3990	530	1	(	(	PUNCT
ejpam-3990	530	2	f	f	VERB
ejpam-3990	530	3	em	em	PRON
ejpam-3990	530	4	g	g	X
ejpam-3990	531	1	[	[	X
ejpam-3990	531	2	vjk	vjk	X
ejpam-3990	531	3	]	]	X
ejpam-3990	531	4	∪{v0	∪{v0	NOUN
ejpam-3990	531	5	}	}	PUNCT
ejpam-3990	531	6	)	)	PUNCT
ejpam-3990	531	7	.	.	PUNCT
ejpam-3990	532	1	therefore	therefore	ADV
ejpam-3990	532	2	,	,	PUNCT
ejpam-3990	532	3	{	{	PUNCT
ejpam-3990	532	4	v	v	NOUN
ejpam-3990	532	5	}	}	PUNCT
ejpam-3990	532	6	=	=	SYM
ejpam-3990	532	7	t⋂	t⋂	NOUN
ejpam-3990	533	1	k=1	k=1	PROPN
ejpam-3990	534	1	f	f	X
ejpam-3990	535	1	em	em	PRON
ejpam-3990	535	2	g	g	PROPN
ejpam-3990	536	1	[	[	X
ejpam-3990	536	2	vjk	vjk	X
ejpam-3990	536	3	]	]	PUNCT
ejpam-3990	536	4	,	,	PUNCT
ejpam-3990	536	5	that	that	ADV
ejpam-3990	536	6	is	is	ADV
ejpam-3990	536	7	,	,	PUNCT
ejpam-3990	536	8	{	{	PUNCT
ejpam-3990	536	9	v	v	NOUN
ejpam-3990	536	10	}	}	PUNCT
ejpam-3990	536	11	∈	∈	NOUN
ejpam-3990	536	12	bemg	bemg	VERB
ejpam-3990	536	13	⊆	⊆	NUM
ejpam-3990	536	14	τ	τ	PROPN
ejpam-3990	536	15	emg	emg	NOUN
ejpam-3990	536	16	.	.	PUNCT
ejpam-3990	537	1	this	this	PRON
ejpam-3990	537	2	shows	show	VERB
ejpam-3990	537	3	that	that	SCONJ
ejpam-3990	537	4	τ	τ	PROPN
ejpam-3990	537	5	emg	emg	NOUN
ejpam-3990	537	6	is	be	AUX
ejpam-3990	537	7	the	the	DET
ejpam-3990	537	8	discrete	discrete	ADJ
ejpam-3990	537	9	topology	topology	NOUN
ejpam-3990	537	10	on	on	ADP
ejpam-3990	537	11	v	v	ADP
ejpam-3990	537	12	(	(	PUNCT
ejpam-3990	537	13	g	g	NOUN
ejpam-3990	537	14	)	)	PUNCT
ejpam-3990	537	15	.	.	PUNCT
ejpam-3990	538	1	theorem	theorem	NOUN
ejpam-3990	538	2	12	12	NUM
ejpam-3990	538	3	.	.	PUNCT
ejpam-3990	539	1	let	let	VERB
ejpam-3990	539	2	h	h	PRON
ejpam-3990	539	3	be	be	AUX
ejpam-3990	539	4	a	a	DET
ejpam-3990	539	5	graph	graph	NOUN
ejpam-3990	539	6	with	with	ADP
ejpam-3990	539	7	radm(〈v	radm(〈v	NOUN
ejpam-3990	539	8	(	(	PUNCT
ejpam-3990	539	9	h)\{v0	h)\{v0	ADJ
ejpam-3990	539	10	}	}	SYM
ejpam-3990	539	11	〉	〉	PROPN
ejpam-3990	539	12	)	)	PUNCT
ejpam-3990	539	13	≥	≥	NOUN
ejpam-3990	539	14	2	2	NUM
ejpam-3990	539	15	and	and	CCONJ
ejpam-3990	539	16	let	let	VERB
ejpam-3990	539	17	v0	v0	NOUN
ejpam-3990	539	18	∈	∈	PROPN
ejpam-3990	539	19	v	v	ADP
ejpam-3990	539	20	(	(	PUNCT
ejpam-3990	539	21	h	h	NOUN
ejpam-3990	539	22	)	)	PUNCT
ejpam-3990	539	23	.	.	PUNCT
ejpam-3990	540	1	then	then	ADV
ejpam-3990	540	2	τ	τ	PROPN
ejpam-3990	540	3	emh	emh	PROPN
ejpam-3990	540	4	=	=	PUNCT
ejpam-3990	540	5	τv0	τv0	PROPN
ejpam-3990	540	6	if	if	SCONJ
ejpam-3990	541	1	and	and	CCONJ
ejpam-3990	541	2	only	only	ADV
ejpam-3990	541	3	if	if	SCONJ
ejpam-3990	541	4	h	h	NOUN
ejpam-3990	541	5	=	=	PUNCT
ejpam-3990	542	1	〈	〈	PROPN
ejpam-3990	542	2	v0〉+g	v0〉+g	NOUN
ejpam-3990	542	3	for	for	ADP
ejpam-3990	542	4	some	some	DET
ejpam-3990	542	5	graph	graph	NOUN
ejpam-3990	542	6	g	g	ADP
ejpam-3990	542	7	such	such	ADJ
ejpam-3990	542	8	that	that	DET
ejpam-3990	542	9	radm(g	radm(g	NOUN
ejpam-3990	542	10	)	)	PUNCT
ejpam-3990	542	11	≥	≥	NOUN
ejpam-3990	542	12	2	2	NUM
ejpam-3990	542	13	and	and	CCONJ
ejpam-3990	542	14	τ	τ	PROPN
ejpam-3990	542	15	emg	emg	NOUN
ejpam-3990	542	16	is	be	AUX
ejpam-3990	542	17	the	the	DET
ejpam-3990	542	18	discrete	discrete	ADJ
ejpam-3990	542	19	topology	topology	NOUN
ejpam-3990	542	20	on	on	ADP
ejpam-3990	542	21	v	v	ADP
ejpam-3990	542	22	(	(	PUNCT
ejpam-3990	542	23	g	g	NOUN
ejpam-3990	542	24	)	)	PUNCT
ejpam-3990	542	25	.	.	PUNCT
ejpam-3990	543	1	proof	proof	NOUN
ejpam-3990	543	2	.	.	PUNCT
ejpam-3990	544	1	suppose	suppose	VERB
ejpam-3990	544	2	τ	τ	PROPN
ejpam-3990	544	3	emh	emh	PROPN
ejpam-3990	544	4	=	=	PROPN
ejpam-3990	544	5	τv0	τv0	PROPN
ejpam-3990	544	6	.	.	PUNCT
ejpam-3990	545	1	suppose	suppose	VERB
ejpam-3990	545	2	further	far	ADV
ejpam-3990	545	3	that	that	SCONJ
ejpam-3990	545	4	there	there	PRON
ejpam-3990	545	5	exists	exist	VERB
ejpam-3990	545	6	v	v	ADP
ejpam-3990	545	7	∈	∈	PROPN
ejpam-3990	545	8	v	v	NOUN
ejpam-3990	545	9	(	(	PUNCT
ejpam-3990	545	10	h)\{v0	h)\{v0	ADV
ejpam-3990	545	11	}	}	PUNCT
ejpam-3990	545	12	such	such	ADJ
ejpam-3990	545	13	that	that	DET
ejpam-3990	545	14	v0v	v0v	NOUN
ejpam-3990	545	15	/∈	/∈	PUNCT
ejpam-3990	545	16	e(h	e(h	PROPN
ejpam-3990	545	17	)	)	PUNCT
ejpam-3990	545	18	.	.	PUNCT
ejpam-3990	546	1	then	then	ADV
ejpam-3990	546	2	emh(v0	emh(v0	PROPN
ejpam-3990	546	3	)	)	PUNCT
ejpam-3990	546	4	≥	≥	NOUN
ejpam-3990	546	5	2	2	NUM
ejpam-3990	546	6	.	.	PUNCT
ejpam-3990	547	1	this	this	PRON
ejpam-3990	547	2	implies	imply	VERB
ejpam-3990	547	3	that	that	SCONJ
ejpam-3990	547	4	nh(v0	nh(v0	PROPN
ejpam-3990	547	5	)	)	PUNCT
ejpam-3990	547	6	6=	6=	ADP
ejpam-3990	547	7	∅	∅	NOUN
ejpam-3990	547	8	and	and	CCONJ
ejpam-3990	547	9	nh(v0)∩n	nh(v0)∩n	PROPN
ejpam-3990	547	10	em	em	PRON
ejpam-3990	547	11	h	h	PROPN
ejpam-3990	547	12	(	(	PUNCT
ejpam-3990	547	13	v0	v0	NOUN
ejpam-3990	547	14	)	)	PUNCT
ejpam-3990	547	15	=	=	PUNCT
ejpam-3990	547	16	∅.	∅.	VERB
ejpam-3990	547	17	hence	hence	ADV
ejpam-3990	547	18	,	,	PUNCT
ejpam-3990	547	19	nh(v0	nh(v0	PROPN
ejpam-3990	547	20	)	)	PUNCT
ejpam-3990	548	1	⊆	⊆	NUM
ejpam-3990	548	2	f	f	X
ejpam-3990	548	3	em	em	PRON
ejpam-3990	548	4	h	h	PROPN
ejpam-3990	549	1	[	[	X
ejpam-3990	549	2	v0	v0	X
ejpam-3990	549	3	]	]	X
ejpam-3990	549	4	.	.	PUNCT
ejpam-3990	550	1	this	this	PRON
ejpam-3990	550	2	gives	give	VERB
ejpam-3990	550	3	a	a	DET
ejpam-3990	550	4	contradiction	contradiction	NOUN
ejpam-3990	550	5	because	because	SCONJ
ejpam-3990	550	6	v0	v0	NOUN
ejpam-3990	550	7	/∈	/∈	PUNCT
ejpam-3990	551	1	f	f	VERB
ejpam-3990	552	1	em	em	PRON
ejpam-3990	552	2	h	h	PROPN
ejpam-3990	553	1	[	[	X
ejpam-3990	553	2	v0	v0	X
ejpam-3990	553	3	]	]	PUNCT
ejpam-3990	553	4	and	and	CCONJ
ejpam-3990	553	5	f	f	PRON
ejpam-3990	554	1	em	em	PRON
ejpam-3990	554	2	h	h	PROPN
ejpam-3990	555	1	[	[	X
ejpam-3990	555	2	v0	v0	X
ejpam-3990	555	3	]	]	X
ejpam-3990	555	4	∈	∈	PROPN
ejpam-3990	555	5	τ	τ	PROPN
ejpam-3990	555	6	emh	emh	PROPN
ejpam-3990	555	7	.	.	PUNCT
ejpam-3990	556	1	therefore	therefore	ADV
ejpam-3990	556	2	,	,	PUNCT
ejpam-3990	556	3	v0v	v0v	ADP
ejpam-3990	556	4	∈	∈	PROPN
ejpam-3990	556	5	e(h	e(h	PROPN
ejpam-3990	556	6	)	)	PUNCT
ejpam-3990	556	7	for	for	ADP
ejpam-3990	556	8	all	all	DET
ejpam-3990	556	9	v	v	ADP
ejpam-3990	556	10	∈	∈	NOUN
ejpam-3990	556	11	v	v	NOUN
ejpam-3990	556	12	(	(	PUNCT
ejpam-3990	556	13	h)\{v0	h)\{v0	ADJ
ejpam-3990	556	14	}	}	PUNCT
ejpam-3990	556	15	.	.	PUNCT
ejpam-3990	557	1	let	let	VERB
ejpam-3990	557	2	g	g	NOUN
ejpam-3990	557	3	=	=	PUNCT
ejpam-3990	557	4	〈	〈	PROPN
ejpam-3990	557	5	v	v	NOUN
ejpam-3990	557	6	(	(	PUNCT
ejpam-3990	557	7	h)\{v0	h)\{v0	ADJ
ejpam-3990	557	8	}	}	SYM
ejpam-3990	557	9	〉	〉	NUM
ejpam-3990	557	10	.	.	PUNCT
ejpam-3990	558	1	then	then	ADV
ejpam-3990	558	2	h	h	NOUN
ejpam-3990	559	1	=	=	PUNCT
ejpam-3990	559	2	〈	〈	PROPN
ejpam-3990	559	3	v0〉+g	v0〉+g	NOUN
ejpam-3990	559	4	.	.	PUNCT
ejpam-3990	560	1	by	by	ADP
ejpam-3990	560	2	theorem	theorem	NOUN
ejpam-3990	560	3	11	11	NUM
ejpam-3990	560	4	,	,	PUNCT
ejpam-3990	560	5	τ	τ	PROPN
ejpam-3990	560	6	emg	emg	NOUN
ejpam-3990	560	7	is	be	AUX
ejpam-3990	560	8	the	the	DET
ejpam-3990	560	9	discrete	discrete	ADJ
ejpam-3990	560	10	topology	topology	NOUN
ejpam-3990	560	11	on	on	ADP
ejpam-3990	560	12	v	v	ADP
ejpam-3990	560	13	(	(	PUNCT
ejpam-3990	560	14	g	g	NOUN
ejpam-3990	560	15	)	)	PUNCT
ejpam-3990	560	16	.	.	PUNCT
ejpam-3990	561	1	for	for	ADP
ejpam-3990	561	2	the	the	DET
ejpam-3990	561	3	converse	converse	NOUN
ejpam-3990	561	4	,	,	PUNCT
ejpam-3990	561	5	suppose	suppose	VERB
ejpam-3990	561	6	h	h	NOUN
ejpam-3990	561	7	=	=	PUNCT
ejpam-3990	561	8	〈	〈	PROPN
ejpam-3990	561	9	v0〉+g	v0〉+g	NOUN
ejpam-3990	561	10	for	for	ADP
ejpam-3990	561	11	some	some	DET
ejpam-3990	561	12	graph	graph	NOUN
ejpam-3990	561	13	g	g	ADP
ejpam-3990	561	14	such	such	ADJ
ejpam-3990	561	15	that	that	DET
ejpam-3990	561	16	radm(g	radm(g	NOUN
ejpam-3990	561	17	)	)	PUNCT
ejpam-3990	561	18	≥	≥	NOUN
ejpam-3990	561	19	2	2	NUM
ejpam-3990	561	20	and	and	CCONJ
ejpam-3990	561	21	τ	τ	PROPN
ejpam-3990	561	22	emg	emg	NOUN
ejpam-3990	561	23	is	be	AUX
ejpam-3990	561	24	the	the	DET
ejpam-3990	561	25	discrete	discrete	ADJ
ejpam-3990	561	26	topology	topology	NOUN
ejpam-3990	561	27	on	on	ADP
ejpam-3990	561	28	v	v	ADP
ejpam-3990	561	29	(	(	PUNCT
ejpam-3990	561	30	g	g	NOUN
ejpam-3990	561	31	)	)	PUNCT
ejpam-3990	561	32	.	.	PUNCT
ejpam-3990	562	1	then	then	ADV
ejpam-3990	562	2	by	by	ADP
ejpam-3990	562	3	theorem	theorem	NOUN
ejpam-3990	562	4	11	11	NUM
ejpam-3990	562	5	,	,	PUNCT
ejpam-3990	562	6	τ	τ	PROPN
ejpam-3990	562	7	emh	emh	NOUN
ejpam-3990	562	8	=	=	PROPN
ejpam-3990	562	9	τv0	τv0	PROPN
ejpam-3990	562	10	.	.	PUNCT
ejpam-3990	563	1	corollary	corollary	ADJ
ejpam-3990	563	2	4	4	NUM
ejpam-3990	563	3	.	.	PUNCT
ejpam-3990	564	1	let	let	VERB
ejpam-3990	564	2	g	g	PROPN
ejpam-3990	564	3	=	=	SYM
ejpam-3990	564	4	wn	wn	PROPN
ejpam-3990	564	5	=	=	SYM
ejpam-3990	564	6	〈	〈	PROPN
ejpam-3990	564	7	v0〉+cn	v0〉+cn	NUM
ejpam-3990	564	8	,	,	PUNCT
ejpam-3990	564	9	where	where	SCONJ
ejpam-3990	564	10	n	n	X
ejpam-3990	564	11	∈	∈	PROPN
ejpam-3990	564	12	{	{	PUNCT
ejpam-3990	564	13	5	5	NUM
ejpam-3990	564	14	,	,	PUNCT
ejpam-3990	564	15	7	7	NUM
ejpam-3990	564	16	,	,	PUNCT
ejpam-3990	564	17	8	8	NUM
ejpam-3990	564	18	,	,	PUNCT
ejpam-3990	564	19	...	...	PUNCT
ejpam-3990	564	20	}	}	PUNCT
ejpam-3990	564	21	.	.	PUNCT
ejpam-3990	565	1	then	then	ADV
ejpam-3990	565	2	τ	τ	PROPN
ejpam-3990	565	3	emwn	emwn	NOUN
ejpam-3990	565	4	is	be	AUX
ejpam-3990	565	5	the	the	DET
ejpam-3990	565	6	particular	particular	ADJ
ejpam-3990	565	7	point	point	NOUN
ejpam-3990	565	8	topology	topology	NOUN
ejpam-3990	565	9	τv0	τv0	NOUN
ejpam-3990	565	10	.	.	PUNCT
ejpam-3990	566	1	proof	proof	NOUN
ejpam-3990	566	2	.	.	PUNCT
ejpam-3990	567	1	let	let	VERB
ejpam-3990	567	2	n	n	PRON
ejpam-3990	567	3	∈	∈	PROPN
ejpam-3990	567	4	{	{	PUNCT
ejpam-3990	567	5	5	5	NUM
ejpam-3990	567	6	,	,	PUNCT
ejpam-3990	567	7	7	7	NUM
ejpam-3990	567	8	,	,	PUNCT
ejpam-3990	567	9	8	8	NUM
ejpam-3990	567	10	,	,	PUNCT
ejpam-3990	567	11	...	...	PUNCT
ejpam-3990	567	12	}	}	PUNCT
ejpam-3990	567	13	.	.	PUNCT
ejpam-3990	568	1	then	then	ADV
ejpam-3990	568	2	τ	τ	PROPN
ejpam-3990	568	3	emcn	emcn	PROPN
ejpam-3990	568	4	is	be	AUX
ejpam-3990	568	5	the	the	DET
ejpam-3990	568	6	discrete	discrete	ADJ
ejpam-3990	568	7	topology	topology	NOUN
ejpam-3990	568	8	on	on	ADP
ejpam-3990	568	9	v	v	PROPN
ejpam-3990	568	10	(	(	PUNCT
ejpam-3990	568	11	cn	cn	PROPN
ejpam-3990	568	12	)	)	PUNCT
ejpam-3990	568	13	by	by	ADP
ejpam-3990	568	14	theorem	theorem	NOUN
ejpam-3990	568	15	6	6	NUM
ejpam-3990	568	16	.	.	PUNCT
ejpam-3990	568	17	thus	thus	ADV
ejpam-3990	568	18	,	,	PUNCT
ejpam-3990	568	19	by	by	ADP
ejpam-3990	568	20	theorem	theorem	NOUN
ejpam-3990	568	21	11	11	NUM
ejpam-3990	568	22	,	,	PUNCT
ejpam-3990	568	23	τ	τ	PROPN
ejpam-3990	568	24	emwn	emwn	NOUN
ejpam-3990	568	25	is	be	AUX
ejpam-3990	568	26	the	the	DET
ejpam-3990	568	27	particular	particular	ADJ
ejpam-3990	568	28	point	point	NOUN
ejpam-3990	568	29	topology	topology	NOUN
ejpam-3990	568	30	τv0	τv0	NOUN
ejpam-3990	568	31	.	.	PUNCT
ejpam-3990	569	1	theorem	theorem	VERB
ejpam-3990	569	2	13	13	NUM
ejpam-3990	569	3	.	.	PUNCT
ejpam-3990	570	1	let	let	VERB
ejpam-3990	570	2	g	g	NOUN
ejpam-3990	570	3	=	=	PUNCT
ejpam-3990	570	4	fn	fn	PROPN
ejpam-3990	570	5	=	=	PUNCT
ejpam-3990	570	6	〈	〈	PROPN
ejpam-3990	570	7	v0〉+	v0〉+	PROPN
ejpam-3990	570	8	pn	pn	PROPN
ejpam-3990	570	9	(	(	PUNCT
ejpam-3990	570	10	n	n	CCONJ
ejpam-3990	570	11	≥	≥	NOUN
ejpam-3990	570	12	4	4	NUM
ejpam-3990	570	13	)	)	PUNCT
ejpam-3990	570	14	.	.	PUNCT
ejpam-3990	571	1	then	then	ADV
ejpam-3990	571	2	{	{	PUNCT
ejpam-3990	571	3	v0	v0	PROPN
ejpam-3990	571	4	,	,	PUNCT
ejpam-3990	571	5	v	v	NOUN
ejpam-3990	571	6	}	}	PUNCT
ejpam-3990	571	7	∈	∈	PROPN
ejpam-3990	571	8	τ	τ	X
ejpam-3990	571	9	emfn	emfn	NOUN
ejpam-3990	571	10	for	for	ADP
ejpam-3990	571	11	all	all	DET
ejpam-3990	571	12	v	v	ADP
ejpam-3990	571	13	∈	∈	NOUN
ejpam-3990	571	14	v	v	NOUN
ejpam-3990	571	15	(	(	PUNCT
ejpam-3990	571	16	pn)\{v1	pn)\{v1	PROPN
ejpam-3990	571	17	,	,	PUNCT
ejpam-3990	571	18	vn	vn	NOUN
ejpam-3990	571	19	}	}	PUNCT
ejpam-3990	571	20	.	.	PUNCT
ejpam-3990	572	1	references	reference	NOUN
ejpam-3990	572	2	704	704	NUM
ejpam-3990	572	3	proof	proof	NOUN
ejpam-3990	572	4	.	.	PUNCT
ejpam-3990	573	1	suppose	suppose	VERB
ejpam-3990	573	2	v	v	ADP
ejpam-3990	573	3	∈	∈	PROPN
ejpam-3990	573	4	v	v	NOUN
ejpam-3990	573	5	(	(	PUNCT
ejpam-3990	573	6	pn)\{v1	pn)\{v1	PROPN
ejpam-3990	573	7	,	,	PUNCT
ejpam-3990	573	8	vn	vn	NOUN
ejpam-3990	573	9	}	}	PUNCT
ejpam-3990	573	10	.	.	PUNCT
ejpam-3990	574	1	by	by	ADP
ejpam-3990	574	2	theorem	theorem	NOUN
ejpam-3990	574	3	9	9	NUM
ejpam-3990	574	4	,	,	PUNCT
ejpam-3990	574	5	{	{	PUNCT
ejpam-3990	574	6	v	v	NOUN
ejpam-3990	574	7	}	}	PUNCT
ejpam-3990	574	8	∈	∈	PROPN
ejpam-3990	574	9	τ	τ	PROPN
ejpam-3990	574	10	empn	empn	NOUN
ejpam-3990	574	11	.	.	PUNCT
ejpam-3990	575	1	thus	thus	ADV
ejpam-3990	575	2	,	,	PUNCT
ejpam-3990	575	3	{	{	PUNCT
ejpam-3990	575	4	v	v	NOUN
ejpam-3990	575	5	}	}	PUNCT
ejpam-3990	575	6	∈	∈	NOUN
ejpam-3990	575	7	bempn	bempn	NOUN
ejpam-3990	575	8	.	.	PUNCT
ejpam-3990	576	1	hence	hence	ADV
ejpam-3990	576	2	,	,	PUNCT
ejpam-3990	576	3	there	there	PRON
ejpam-3990	576	4	exist	exist	VERB
ejpam-3990	576	5	vi1	vi1	ADV
ejpam-3990	576	6	,	,	PUNCT
ejpam-3990	576	7	vi2	vi2	INTJ
ejpam-3990	576	8	,	,	PUNCT
ejpam-3990	576	9	...	...	PUNCT
ejpam-3990	576	10	,	,	PUNCT
ejpam-3990	576	11	vik	vik	PROPN
ejpam-3990	576	12	∈	∈	NOUN
ejpam-3990	576	13	v	v	NOUN
ejpam-3990	576	14	(	(	PUNCT
ejpam-3990	576	15	pn	pn	NOUN
ejpam-3990	576	16	)	)	PUNCT
ejpam-3990	576	17	such	such	ADJ
ejpam-3990	576	18	that	that	SCONJ
ejpam-3990	576	19	{	{	PUNCT
ejpam-3990	576	20	v	v	NOUN
ejpam-3990	576	21	}	}	PUNCT
ejpam-3990	576	22	=	=	PUNCT
ejpam-3990	576	23	k⋂	k⋂	NOUN
ejpam-3990	577	1	s=1	s=1	X
ejpam-3990	577	2	f	f	X
ejpam-3990	578	1	em	em	PRON
ejpam-3990	578	2	pn	pn	PROPN
ejpam-3990	579	1	[	[	X
ejpam-3990	579	2	vis	vis	X
ejpam-3990	579	3	]	]	PUNCT
ejpam-3990	579	4	.	.	PUNCT
ejpam-3990	580	1	therefore	therefore	ADV
ejpam-3990	580	2	,	,	PUNCT
ejpam-3990	580	3	{	{	PUNCT
ejpam-3990	580	4	v0	v0	NOUN
ejpam-3990	580	5	,	,	PUNCT
ejpam-3990	580	6	v	v	NOUN
ejpam-3990	580	7	}	}	PUNCT
ejpam-3990	580	8	=	=	PUNCT
ejpam-3990	580	9	k⋂	k⋂	X
ejpam-3990	580	10	s=1	s=1	X
ejpam-3990	581	1	(	(	PUNCT
ejpam-3990	581	2	f	f	X
ejpam-3990	581	3	em	em	PRON
ejpam-3990	581	4	pn	pn	PROPN
ejpam-3990	582	1	[	[	X
ejpam-3990	582	2	vis	vis	X
ejpam-3990	582	3	]	]	PUNCT
ejpam-3990	582	4	∪	∪	X
ejpam-3990	582	5	{	{	PUNCT
ejpam-3990	582	6	v0	v0	NOUN
ejpam-3990	582	7	}	}	PUNCT
ejpam-3990	582	8	)	)	PUNCT
ejpam-3990	582	9	∈	∈	NOUN
ejpam-3990	582	10	bempn	bempn	VERB
ejpam-3990	582	11	⊆	⊆	NUM
ejpam-3990	582	12	τ	τ	X
ejpam-3990	582	13	emfn	emfn	NOUN
ejpam-3990	582	14	,	,	PUNCT
ejpam-3990	582	15	proving	prove	VERB
ejpam-3990	582	16	our	our	PRON
ejpam-3990	582	17	assertion	assertion	NOUN
ejpam-3990	582	18	.	.	PUNCT
ejpam-3990	583	1	theorem	theorem	VERB
ejpam-3990	583	2	14	14	NUM
ejpam-3990	583	3	.	.	PUNCT
ejpam-3990	584	1	if	if	SCONJ
ejpam-3990	584	2	n	n	PRON
ejpam-3990	584	3	is	be	AUX
ejpam-3990	584	4	a	a	DET
ejpam-3990	584	5	positive	positive	ADJ
ejpam-3990	584	6	integer	integer	NOUN
ejpam-3990	584	7	and	and	CCONJ
ejpam-3990	584	8	k1	k1	NOUN
ejpam-3990	584	9	=	=	SYM
ejpam-3990	584	10	〈	〈	PROPN
ejpam-3990	584	11	v0	v0	PROPN
ejpam-3990	584	12	〉	〉	PROPN
ejpam-3990	584	13	,	,	PUNCT
ejpam-3990	584	14	then	then	ADV
ejpam-3990	584	15	τ	τ	PROPN
ejpam-3990	584	16	emk1,n	emk1,n	PROPN
ejpam-3990	584	17	=	=	PRON
ejpam-3990	584	18	{	{	PUNCT
ejpam-3990	584	19	{	{	PUNCT
ejpam-3990	584	20	∅	∅	NOUN
ejpam-3990	584	21	,	,	PUNCT
ejpam-3990	584	22	v	v	PROPN
ejpam-3990	584	23	(	(	PUNCT
ejpam-3990	584	24	k1,n	k1,n	PROPN
ejpam-3990	584	25	)	)	PUNCT
ejpam-3990	584	26	}	}	PUNCT
ejpam-3990	584	27	if	if	SCONJ
ejpam-3990	584	28	n	n	NUM
ejpam-3990	584	29	=	=	SYM
ejpam-3990	584	30	1	1	NUM
ejpam-3990	584	31	{	{	PUNCT
ejpam-3990	584	32	∅	∅	NOUN
ejpam-3990	584	33	,	,	PUNCT
ejpam-3990	584	34	{	{	PUNCT
ejpam-3990	584	35	v0	v0	NOUN
ejpam-3990	584	36	}	}	PUNCT
ejpam-3990	584	37	,	,	PUNCT
ejpam-3990	584	38	v	v	X
ejpam-3990	584	39	(	(	PUNCT
ejpam-3990	584	40	k1,n	k1,n	PROPN
ejpam-3990	584	41	)	)	PUNCT
ejpam-3990	584	42	}	}	PUNCT
ejpam-3990	584	43	if	if	SCONJ
ejpam-3990	584	44	n	n	PRON
ejpam-3990	584	45	≥	≥	NOUN
ejpam-3990	584	46	2	2	NUM
ejpam-3990	584	47	.	.	PUNCT
ejpam-3990	584	48	proof	proof	NOUN
ejpam-3990	584	49	.	.	PUNCT
ejpam-3990	585	1	by	by	ADP
ejpam-3990	585	2	corollary	corollary	ADJ
ejpam-3990	585	3	3	3	NUM
ejpam-3990	585	4	,	,	PUNCT
ejpam-3990	585	5	semk1,n	semk1,n	NOUN
ejpam-3990	585	6	=	=	PRON
ejpam-3990	585	7	{	{	PUNCT
ejpam-3990	585	8	{	{	PUNCT
ejpam-3990	585	9	∅	∅	NOUN
ejpam-3990	585	10	}	}	PUNCT
ejpam-3990	585	11	if	if	SCONJ
ejpam-3990	585	12	n	n	NOUN
ejpam-3990	585	13	=	=	SYM
ejpam-3990	585	14	1	1	NUM
ejpam-3990	585	15	{	{	PUNCT
ejpam-3990	585	16	∅	∅	NOUN
ejpam-3990	585	17	}	}	PUNCT
ejpam-3990	585	18	∪	∪	ADJ
ejpam-3990	585	19	{	{	PUNCT
ejpam-3990	585	20	v0	v0	NOUN
ejpam-3990	585	21	}	}	PUNCT
ejpam-3990	585	22	otherwise	otherwise	ADV
ejpam-3990	585	23	.	.	PUNCT
ejpam-3990	586	1	hence	hence	ADV
ejpam-3990	586	2	,	,	PUNCT
ejpam-3990	586	3	τ	τ	PROPN
ejpam-3990	586	4	emk1,n	emk1,n	PROPN
ejpam-3990	586	5	=	=	PRON
ejpam-3990	586	6	{	{	PUNCT
ejpam-3990	586	7	{	{	PUNCT
ejpam-3990	586	8	∅	∅	NOUN
ejpam-3990	586	9	,	,	PUNCT
ejpam-3990	586	10	v	v	PROPN
ejpam-3990	586	11	(	(	PUNCT
ejpam-3990	586	12	k1,n	k1,n	PROPN
ejpam-3990	586	13	)	)	PUNCT
ejpam-3990	586	14	}	}	PUNCT
ejpam-3990	586	15	if	if	SCONJ
ejpam-3990	586	16	n	n	NUM
ejpam-3990	586	17	=	=	SYM
ejpam-3990	586	18	1	1	NUM
ejpam-3990	586	19	{	{	PUNCT
ejpam-3990	586	20	∅	∅	NOUN
ejpam-3990	586	21	,	,	PUNCT
ejpam-3990	586	22	{	{	PUNCT
ejpam-3990	586	23	v0	v0	NOUN
ejpam-3990	586	24	}	}	PUNCT
ejpam-3990	586	25	,	,	PUNCT
ejpam-3990	586	26	v	v	X
ejpam-3990	586	27	(	(	PUNCT
ejpam-3990	586	28	k1,n	k1,n	PROPN
ejpam-3990	586	29	)	)	PUNCT
ejpam-3990	586	30	}	}	PUNCT
ejpam-3990	586	31	if	if	SCONJ
ejpam-3990	586	32	n	n	PRON
ejpam-3990	586	33	≥	≥	NOUN
ejpam-3990	586	34	2	2	NUM
ejpam-3990	586	35	.	.	PUNCT
ejpam-3990	587	1	this	this	PRON
ejpam-3990	587	2	proves	prove	VERB
ejpam-3990	587	3	the	the	DET
ejpam-3990	587	4	assertion	assertion	NOUN
ejpam-3990	587	5	.	.	PUNCT
ejpam-3990	588	1	acknowledgements	acknowledgement	NOUN
ejpam-3990	588	2	the	the	DET
ejpam-3990	588	3	authors	author	NOUN
ejpam-3990	588	4	would	would	AUX
ejpam-3990	588	5	like	like	VERB
ejpam-3990	588	6	to	to	PART
ejpam-3990	588	7	thank	thank	VERB
ejpam-3990	588	8	western	western	ADJ
ejpam-3990	588	9	mindanao	mindanao	PROPN
ejpam-3990	588	10	state	state	PROPN
ejpam-3990	588	11	university	university	PROPN
ejpam-3990	588	12	(	(	PUNCT
ejpam-3990	588	13	wmsu	wmsu	NOUN
ejpam-3990	588	14	)	)	PUNCT
ejpam-3990	588	15	and	and	CCONJ
ejpam-3990	588	16	mindanao	mindanao	PROPN
ejpam-3990	588	17	state	state	PROPN
ejpam-3990	588	18	university	university	PROPN
ejpam-3990	588	19	-	-	PUNCT
ejpam-3990	588	20	iligan	iligan	PROPN
ejpam-3990	588	21	institute	institute	PROPN
ejpam-3990	588	22	of	of	ADP
ejpam-3990	588	23	technology	technology	PROPN
ejpam-3990	588	24	(	(	PUNCT
ejpam-3990	588	25	msu	msu	PROPN
ejpam-3990	588	26	-	-	PUNCT
ejpam-3990	588	27	iit)for	iit)for	PROPN
ejpam-3990	588	28	funding	fund	VERB
ejpam-3990	588	29	this	this	DET
ejpam-3990	588	30	research	research	NOUN
ejpam-3990	588	31	.	.	PUNCT
ejpam-3990	589	1	references	reference	NOUN
ejpam-3990	589	2	[	[	X
ejpam-3990	589	3	1	1	X
ejpam-3990	589	4	]	]	PUNCT
ejpam-3990	589	5	s.	s.	PROPN
ejpam-3990	589	6	canoy	canoy	PROPN
ejpam-3990	589	7	jr	jr	PROPN
ejpam-3990	589	8	.	.	PUNCT
ejpam-3990	589	9	a.	a.	NOUN
ejpam-3990	589	10	gamorez	gamorez	PROPN
ejpam-3990	589	11	and	and	CCONJ
ejpam-3990	589	12	c.	c.	PROPN
ejpam-3990	589	13	g.	g.	PROPN
ejpam-3990	589	14	nianga	nianga	PROPN
ejpam-3990	589	15	.	.	PUNCT
ejpam-3990	590	1	topologies	topology	NOUN
ejpam-3990	590	2	induced	induce	VERB
ejpam-3990	590	3	by	by	ADP
ejpam-3990	590	4	neighborhoods	neighborhood	NOUN
ejpam-3990	590	5	of	of	ADP
ejpam-3990	590	6	a	a	DET
ejpam-3990	590	7	graphs	graph	NOUN
ejpam-3990	590	8	under	under	ADP
ejpam-3990	590	9	some	some	DET
ejpam-3990	590	10	binary	binary	ADJ
ejpam-3990	590	11	operation	operation	NOUN
ejpam-3990	590	12	.	.	PUNCT
ejpam-3990	591	1	european	european	ADJ
ejpam-3990	591	2	journal	journal	PROPN
ejpam-3990	591	3	of	of	ADP
ejpam-3990	591	4	pure	pure	ADJ
ejpam-3990	591	5	and	and	CCONJ
ejpam-3990	591	6	applied	applied	ADJ
ejpam-3990	591	7	mathematics	mathematic	NOUN
ejpam-3990	591	8	,	,	PUNCT
ejpam-3990	591	9	12(3):749–755	12(3):749–755	NUM
ejpam-3990	591	10	,	,	PUNCT
ejpam-3990	591	11	2019	2019	NUM
ejpam-3990	591	12	.	.	PUNCT
ejpam-3990	592	1	[	[	X
ejpam-3990	592	2	2	2	X
ejpam-3990	592	3	]	]	PUNCT
ejpam-3990	592	4	s.	s.	PROPN
ejpam-3990	592	5	diesto	diesto	PROPN
ejpam-3990	592	6	and	and	CCONJ
ejpam-3990	592	7	s.	s.	PROPN
ejpam-3990	592	8	gervacio	gervacio	PROPN
ejpam-3990	592	9	.	.	PUNCT
ejpam-3990	593	1	finite	finite	PROPN
ejpam-3990	593	2	topological	topological	ADJ
ejpam-3990	593	3	graphs	graph	NOUN
ejpam-3990	593	4	.	.	PUNCT
ejpam-3990	594	1	journal	journal	NOUN
ejpam-3990	594	2	of	of	ADP
ejpam-3990	594	3	research	research	NOUN
ejpam-3990	594	4	and	and	CCONJ
ejpam-3990	594	5	development	development	NOUN
ejpam-3990	594	6	,	,	PUNCT
ejpam-3990	594	7	msu	msu	PROPN
ejpam-3990	594	8	-	-	PUNCT
ejpam-3990	594	9	iit	iit	PROPN
ejpam-3990	594	10	,	,	PUNCT
ejpam-3990	594	11	1(1):76–81	1(1):76–81	NUM
ejpam-3990	594	12	,	,	PUNCT
ejpam-3990	594	13	1983	1983	NUM
ejpam-3990	594	14	.	.	PUNCT
ejpam-3990	595	1	[	[	X
ejpam-3990	595	2	3	3	X
ejpam-3990	595	3	]	]	X
ejpam-3990	595	4	s.	s.	PROPN
ejpam-3990	595	5	gervacio	gervacio	PROPN
ejpam-3990	595	6	and	and	CCONJ
ejpam-3990	595	7	r.	r.	PROPN
ejpam-3990	595	8	guerrero	guerrero	PROPN
ejpam-3990	595	9	.	.	PUNCT
ejpam-3990	596	1	characterization	characterization	NOUN
ejpam-3990	596	2	of	of	ADP
ejpam-3990	596	3	graphs	graph	NOUN
ejpam-3990	596	4	which	which	PRON
ejpam-3990	596	5	induce	induce	VERB
ejpam-3990	596	6	the	the	DET
ejpam-3990	596	7	discrete	discrete	ADJ
ejpam-3990	596	8	and	and	CCONJ
ejpam-3990	596	9	indiscrete	indiscrete	ADJ
ejpam-3990	596	10	topological	topological	ADJ
ejpam-3990	596	11	spaces	space	NOUN
ejpam-3990	596	12	.	.	PUNCT
ejpam-3990	597	1	matimyas	matimyas	PROPN
ejpam-3990	597	2	matematika	matematika	PROPN
ejpam-3990	597	3	,	,	PUNCT
ejpam-3990	597	4	pages	page	NOUN
ejpam-3990	597	5	1–8	1–8	NUM
ejpam-3990	597	6	,	,	PUNCT
ejpam-3990	597	7	1986	1986	NUM
ejpam-3990	597	8	.	.	PUNCT
ejpam-3990	598	1	[	[	X
ejpam-3990	598	2	4	4	X
ejpam-3990	598	3	]	]	X
ejpam-3990	598	4	j.	j.	PROPN
ejpam-3990	598	5	gimeno	gimeno	PROPN
ejpam-3990	598	6	and	and	CCONJ
ejpam-3990	598	7	s.	s.	PROPN
ejpam-3990	598	8	canoy	canoy	PROPN
ejpam-3990	598	9	jr	jr	PROPN
ejpam-3990	598	10	.	.	PROPN
ejpam-3990	598	11	which	which	DET
ejpam-3990	598	12	connected	connect	VERB
ejpam-3990	598	13	graphs	graph	NOUN
ejpam-3990	598	14	induce	induce	VERB
ejpam-3990	598	15	the	the	DET
ejpam-3990	598	16	indiscrete	indiscrete	ADJ
ejpam-3990	598	17	and	and	CCONJ
ejpam-3990	598	18	the	the	DET
ejpam-3990	598	19	discrete	discrete	ADJ
ejpam-3990	598	20	topologies	topology	NOUN
ejpam-3990	598	21	?	?	PUNCT
ejpam-3990	599	1	journal	journal	NOUN
ejpam-3990	599	2	of	of	ADP
ejpam-3990	599	3	research	research	NOUN
ejpam-3990	599	4	in	in	ADP
ejpam-3990	599	5	science	science	NOUN
ejpam-3990	599	6	and	and	CCONJ
ejpam-3990	599	7	engineering	engineering	NOUN
ejpam-3990	599	8	,	,	PUNCT
ejpam-3990	599	9	2:17–19	2:17–19	NUM
ejpam-3990	599	10	,	,	PUNCT
ejpam-3990	599	11	2004	2004	NUM
ejpam-3990	599	12	.	.	PUNCT
ejpam-3990	600	1	references	reference	NOUN
ejpam-3990	600	2	705	705	NUM
ejpam-3990	600	3	[	[	SYM
ejpam-3990	600	4	5	5	NUM
ejpam-3990	600	5	]	]	PUNCT
ejpam-3990	600	6	f.	f.	PROPN
ejpam-3990	600	7	harary	harary	PROPN
ejpam-3990	600	8	.	.	PUNCT
ejpam-3990	601	1	graph	graph	NOUN
ejpam-3990	601	2	theory	theory	NOUN
ejpam-3990	601	3	.	.	PUNCT
ejpam-3990	602	1	addison	addison	PROPN
ejpam-3990	602	2	-	-	PUNCT
ejpam-3990	602	3	wesley	wesley	PROPN
ejpam-3990	602	4	publishing	publishing	PROPN
ejpam-3990	602	5	company	company	NOUN
ejpam-3990	602	6	,	,	PUNCT
ejpam-3990	602	7	usa	usa	PROPN
ejpam-3990	602	8	,	,	PUNCT
ejpam-3990	602	9	1969	1969	NUM
ejpam-3990	602	10	.	.	PUNCT
ejpam-3990	603	1	[	[	X
ejpam-3990	603	2	6	6	NUM
ejpam-3990	603	3	]	]	PUNCT
ejpam-3990	603	4	r.	r.	PROPN
ejpam-3990	603	5	lemence	lemence	PROPN
ejpam-3990	603	6	and	and	CCONJ
ejpam-3990	603	7	s.	s.	PROPN
ejpam-3990	603	8	canoy	canoy	PROPN
ejpam-3990	603	9	jr	jr	PROPN
ejpam-3990	603	10	.	.	PUNCT
ejpam-3990	603	11	another	another	DET
ejpam-3990	603	12	look	look	NOUN
ejpam-3990	603	13	at	at	ADP
ejpam-3990	603	14	the	the	DET
ejpam-3990	603	15	topologies	topology	NOUN
ejpam-3990	603	16	induce	induce	VERB
ejpam-3990	603	17	by	by	ADP
ejpam-3990	603	18	the	the	DET
ejpam-3990	603	19	graphs	graph	NOUN
ejpam-3990	603	20	.	.	PUNCT
ejpam-3990	604	1	matimyas	matimyas	PROPN
ejpam-3990	604	2	matematika	matematika	PROPN
ejpam-3990	604	3	,	,	PUNCT
ejpam-3990	604	4	21(2):1–7	21(2):1–7	NUM
ejpam-3990	604	5	,	,	PUNCT
ejpam-3990	604	6	1998	1998	NUM
ejpam-3990	604	7	.	.	PUNCT
ejpam-3990	605	1	[	[	X
ejpam-3990	605	2	7	7	X
ejpam-3990	605	3	]	]	X
ejpam-3990	605	4	s.	s.	PROPN
ejpam-3990	605	5	lipschutz	lipschutz	PROPN
ejpam-3990	605	6	.	.	PUNCT
ejpam-3990	606	1	general	general	ADJ
ejpam-3990	606	2	topology	topology	PROPN
ejpam-3990	606	3	,	,	PUNCT
ejpam-3990	606	4	schaum	schaum	PROPN
ejpam-3990	606	5	’s	’s	PART
ejpam-3990	606	6	outline	outline	PROPN
ejpam-3990	606	7	series	series	PROPN
ejpam-3990	606	8	.	.	PUNCT
ejpam-3990	607	1	mcgraw	mcgraw	PROPN
ejpam-3990	607	2	hill	hill	PROPN
ejpam-3990	607	3	international	international	PROPN
ejpam-3990	607	4	publishing	publishing	PROPN
ejpam-3990	607	5	co.	co.	PROPN
ejpam-3990	607	6	,	,	PUNCT
ejpam-3990	607	7	1987	1987	NUM
ejpam-3990	607	8	.	.	PUNCT
ejpam-3990	608	1	[	[	X
ejpam-3990	608	2	8	8	NUM
ejpam-3990	608	3	]	]	X
ejpam-3990	608	4	c.	c.	PROPN
ejpam-3990	608	5	g.	g.	PROPN
ejpam-3990	608	6	nianga	nianga	PROPN
ejpam-3990	608	7	and	and	CCONJ
ejpam-3990	608	8	s.	s.	PROPN
ejpam-3990	608	9	canoy	canoy	PROPN
ejpam-3990	608	10	jr	jr	PROPN
ejpam-3990	608	11	.	.	PROPN
ejpam-3990	608	12	on	on	ADP
ejpam-3990	608	13	a	a	DET
ejpam-3990	608	14	finite	finite	ADJ
ejpam-3990	608	15	topological	topological	ADJ
ejpam-3990	608	16	space	space	NOUN
ejpam-3990	608	17	induced	induce	VERB
ejpam-3990	608	18	by	by	ADP
ejpam-3990	608	19	hop	hop	NOUN
ejpam-3990	608	20	neighborhoods	neighborhood	NOUN
ejpam-3990	608	21	of	of	ADP
ejpam-3990	608	22	a	a	DET
ejpam-3990	608	23	graph	graph	NOUN
ejpam-3990	608	24	.	.	PUNCT
ejpam-3990	609	1	advances	advance	NOUN
ejpam-3990	609	2	and	and	CCONJ
ejpam-3990	609	3	applications	application	NOUN
ejpam-3990	609	4	in	in	ADP
ejpam-3990	609	5	discrete	discrete	ADJ
ejpam-3990	609	6	mathematics	mathematic	NOUN
ejpam-3990	609	7	,	,	PUNCT
ejpam-3990	609	8	21(1):79–89	21(1):79–89	NUM
ejpam-3990	609	9	,	,	PUNCT
ejpam-3990	609	10	2019	2019	NUM
ejpam-3990	609	11	.	.	PUNCT
ejpam-3990	610	1	[	[	X
ejpam-3990	610	2	9	9	NUM
ejpam-3990	610	3	]	]	PUNCT
ejpam-3990	610	4	c.	c.	PROPN
ejpam-3990	610	5	g.	g.	PROPN
ejpam-3990	610	6	nianga	nianga	PROPN
ejpam-3990	610	7	and	and	CCONJ
ejpam-3990	610	8	s.	s.	PROPN
ejpam-3990	610	9	canoy	canoy	PROPN
ejpam-3990	610	10	jr	jr	PROPN
ejpam-3990	610	11	.	.	PROPN
ejpam-3990	610	12	on	on	ADP
ejpam-3990	610	13	topologies	topology	NOUN
ejpam-3990	610	14	induced	induce	VERB
ejpam-3990	610	15	by	by	ADP
ejpam-3990	610	16	some	some	DET
ejpam-3990	610	17	unary	unary	ADJ
ejpam-3990	610	18	and	and	CCONJ
ejpam-3990	610	19	binary	binary	ADJ
ejpam-3990	610	20	operations	operation	NOUN
ejpam-3990	610	21	.	.	PUNCT
ejpam-3990	611	1	european	european	ADJ
ejpam-3990	611	2	journal	journal	PROPN
ejpam-3990	611	3	of	of	ADP
ejpam-3990	611	4	pure	pure	ADJ
ejpam-3990	611	5	and	and	CCONJ
ejpam-3990	611	6	applied	applied	ADJ
ejpam-3990	611	7	mathematics	mathematic	NOUN
ejpam-3990	611	8	,	,	PUNCT
ejpam-3990	611	9	12(2):499–505	12(2):499–505	NUM
ejpam-3990	611	10	,	,	PUNCT
ejpam-3990	611	11	2019	2019	NUM
ejpam-3990	611	12	.	.	PUNCT
ejpam-3990	612	1	[	[	X
ejpam-3990	612	2	10	10	NUM
ejpam-3990	612	3	]	]	PUNCT
ejpam-3990	612	4	p.	p.	NOUN
ejpam-3990	612	5	titus	titus	PROPN
ejpam-3990	612	6	and	and	CCONJ
ejpam-3990	612	7	a.	a.	NOUN
ejpam-3990	612	8	santhakumaran	santhakumaran	PROPN
ejpam-3990	612	9	.	.	PUNCT
ejpam-3990	613	1	monophonic	monophonic	ADJ
ejpam-3990	613	2	eccentric	eccentric	ADJ
ejpam-3990	613	3	domination	domination	NOUN
ejpam-3990	613	4	on	on	ADP
ejpam-3990	613	5	graphs	graph	NOUN
ejpam-3990	613	6	,	,	PUNCT
ejpam-3990	613	7	preprint	preprint	NOUN
ejpam-3990	613	8	.	.	PUNCT