id	sid	tid	token	lemma	pos
ejpam-3421	1	1	european	european	PROPN
ejpam-3421	1	2	journal	journal	PROPN
ejpam-3421	1	3	of	of	ADP
ejpam-3421	1	4	pure	pure	ADJ
ejpam-3421	1	5	and	and	CCONJ
ejpam-3421	1	6	applied	apply	VERB
ejpam-3421	1	7	mathematics	mathematic	NOUN
ejpam-3421	1	8	vol	vol	NOUN
ejpam-3421	1	9	.	.	PROPN
ejpam-3421	2	1	12	12	NUM
ejpam-3421	2	2	,	,	PUNCT
ejpam-3421	2	3	no	no	INTJ
ejpam-3421	2	4	.	.	NOUN
ejpam-3421	2	5	2	2	NUM
ejpam-3421	2	6	,	,	PUNCT
ejpam-3421	2	7	2019	2019	NUM
ejpam-3421	2	8	,	,	PUNCT
ejpam-3421	2	9	499	499	NUM
ejpam-3421	2	10	-	-	SYM
ejpam-3421	2	11	505	505	NUM
ejpam-3421	2	12	issn	issn	PROPN
ejpam-3421	2	13	1307	1307	NUM
ejpam-3421	2	14	-	-	SYM
ejpam-3421	2	15	5543	5543	NUM
ejpam-3421	2	16	–	–	PUNCT
ejpam-3421	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3421	2	18	published	publish	VERB
ejpam-3421	2	19	by	by	ADP
ejpam-3421	2	20	new	new	PROPN
ejpam-3421	2	21	york	york	PROPN
ejpam-3421	2	22	business	business	PROPN
ejpam-3421	2	23	global	global	PROPN
ejpam-3421	2	24	on	on	ADP
ejpam-3421	2	25	topologies	topology	NOUN
ejpam-3421	2	26	induced	induce	VERB
ejpam-3421	2	27	by	by	ADP
ejpam-3421	2	28	graphs	graph	NOUN
ejpam-3421	2	29	under	under	ADP
ejpam-3421	2	30	some	some	DET
ejpam-3421	2	31	unary	unary	ADJ
ejpam-3421	2	32	and	and	CCONJ
ejpam-3421	2	33	binary	binary	ADJ
ejpam-3421	2	34	operations	operation	NOUN
ejpam-3421	2	35	caen	caen	PROPN
ejpam-3421	2	36	grace	grace	PROPN
ejpam-3421	2	37	s.	s.	PROPN
ejpam-3421	2	38	nianga1,∗	nianga1,∗	PROPN
ejpam-3421	2	39	,	,	PUNCT
ejpam-3421	2	40	sergio	sergio	PROPN
ejpam-3421	2	41	r.	r.	PROPN
ejpam-3421	2	42	canoy	canoy	PROPN
ejpam-3421	2	43	jr.1	jr.1	PROPN
ejpam-3421	2	44	1	1	NUM
ejpam-3421	2	45	department	department	NOUN
ejpam-3421	2	46	of	of	ADP
ejpam-3421	2	47	mathematics	mathematic	NOUN
ejpam-3421	2	48	and	and	CCONJ
ejpam-3421	2	49	statistics	statistic	NOUN
ejpam-3421	2	50	,	,	PUNCT
ejpam-3421	2	51	college	college	NOUN
ejpam-3421	2	52	of	of	ADP
ejpam-3421	2	53	science	science	NOUN
ejpam-3421	2	54	and	and	CCONJ
ejpam-3421	2	55	mathematics	mathematic	NOUN
ejpam-3421	2	56	,	,	PUNCT
ejpam-3421	2	57	center	center	NOUN
ejpam-3421	2	58	of	of	ADP
ejpam-3421	2	59	graph	graph	NOUN
ejpam-3421	2	60	theory	theory	NOUN
ejpam-3421	2	61	,	,	PUNCT
ejpam-3421	2	62	algebra	algebra	NOUN
ejpam-3421	2	63	,	,	PUNCT
ejpam-3421	2	64	and	and	CCONJ
ejpam-3421	2	65	analysis	analysis	NOUN
ejpam-3421	2	66	-	-	PUNCT
ejpam-3421	2	67	prism	prism	NOUN
ejpam-3421	2	68	,	,	PUNCT
ejpam-3421	2	69	mindanao	mindanao	PROPN
ejpam-3421	2	70	state	state	PROPN
ejpam-3421	2	71	university	university	PROPN
ejpam-3421	2	72	-	-	PUNCT
ejpam-3421	2	73	iligan	iligan	PROPN
ejpam-3421	2	74	institute	institute	PROPN
ejpam-3421	2	75	of	of	ADP
ejpam-3421	2	76	technology	technology	PROPN
ejpam-3421	2	77	,	,	PUNCT
ejpam-3421	2	78	9200	9200	NUM
ejpam-3421	2	79	iligan	iligan	ADJ
ejpam-3421	2	80	city	city	NOUN
ejpam-3421	2	81	,	,	PUNCT
ejpam-3421	2	82	philippines	philippine	NOUN
ejpam-3421	2	83	abstract	abstract	ADJ
ejpam-3421	2	84	.	.	PUNCT
ejpam-3421	3	1	let	let	VERB
ejpam-3421	3	2	g	g	PROPN
ejpam-3421	3	3	=	=	SYM
ejpam-3421	3	4	(	(	PUNCT
ejpam-3421	3	5	v	v	NOUN
ejpam-3421	3	6	(	(	PUNCT
ejpam-3421	3	7	g	g	NOUN
ejpam-3421	3	8	)	)	PUNCT
ejpam-3421	3	9	,	,	PUNCT
ejpam-3421	3	10	e(g	e(g	PROPN
ejpam-3421	3	11	)	)	PUNCT
ejpam-3421	3	12	)	)	PUNCT
ejpam-3421	4	1	be	be	AUX
ejpam-3421	4	2	any	any	DET
ejpam-3421	4	3	simple	simple	ADJ
ejpam-3421	4	4	undirected	undirected	ADJ
ejpam-3421	4	5	graph	graph	NOUN
ejpam-3421	4	6	.	.	PUNCT
ejpam-3421	5	1	the	the	DET
ejpam-3421	5	2	open	open	ADJ
ejpam-3421	5	3	hop	hop	NOUN
ejpam-3421	5	4	neighborhood	neighborhood	NOUN
ejpam-3421	5	5	of	of	ADP
ejpam-3421	5	6	v	v	NUM
ejpam-3421	5	7	∈	∈	NOUN
ejpam-3421	5	8	v	v	NOUN
ejpam-3421	5	9	(	(	PUNCT
ejpam-3421	5	10	g	g	NOUN
ejpam-3421	5	11	)	)	PUNCT
ejpam-3421	5	12	is	be	AUX
ejpam-3421	5	13	the	the	DET
ejpam-3421	5	14	set	set	ADJ
ejpam-3421	5	15	n2	n2	ADJ
ejpam-3421	5	16	g(v	g(v	PROPN
ejpam-3421	5	17	)	)	PUNCT
ejpam-3421	5	18	=	=	PRON
ejpam-3421	5	19	{	{	PUNCT
ejpam-3421	5	20	u	u	NOUN
ejpam-3421	5	21	∈	∈	PROPN
ejpam-3421	5	22	v	v	NOUN
ejpam-3421	5	23	(	(	PUNCT
ejpam-3421	5	24	g	g	NOUN
ejpam-3421	5	25	)	)	PUNCT
ejpam-3421	5	26	:	:	PUNCT
ejpam-3421	5	27	dg(u	dg(u	X
ejpam-3421	5	28	,	,	PUNCT
ejpam-3421	5	29	v	v	NOUN
ejpam-3421	5	30	)	)	PUNCT
ejpam-3421	5	31	=	=	SYM
ejpam-3421	5	32	2	2	NUM
ejpam-3421	5	33	}	}	PUNCT
ejpam-3421	5	34	.	.	PUNCT
ejpam-3421	6	1	then	then	ADV
ejpam-3421	6	2	g	g	PROPN
ejpam-3421	6	3	induces	induce	VERB
ejpam-3421	6	4	a	a	DET
ejpam-3421	6	5	topology	topology	NOUN
ejpam-3421	6	6	τg	τg	NOUN
ejpam-3421	6	7	on	on	ADP
ejpam-3421	6	8	v	v	ADP
ejpam-3421	6	9	(	(	PUNCT
ejpam-3421	6	10	g	g	NOUN
ejpam-3421	6	11	)	)	PUNCT
ejpam-3421	6	12	with	with	ADP
ejpam-3421	6	13	base	base	NOUN
ejpam-3421	6	14	consisting	consist	VERB
ejpam-3421	6	15	of	of	ADP
ejpam-3421	6	16	sets	set	NOUN
ejpam-3421	6	17	of	of	ADP
ejpam-3421	6	18	the	the	DET
ejpam-3421	6	19	form	form	NOUN
ejpam-3421	6	20	f	f	PROPN
ejpam-3421	6	21	2	2	NUM
ejpam-3421	6	22	g[a	g[a	NOUN
ejpam-3421	6	23	]	]	X
ejpam-3421	6	24	=	=	SYM
ejpam-3421	6	25	v	v	X
ejpam-3421	6	26	(	(	PUNCT
ejpam-3421	6	27	g)\n2	g)\n2	NOUN
ejpam-3421	6	28	g[a	g[a	PROPN
ejpam-3421	6	29	]	]	X
ejpam-3421	6	30	,	,	PUNCT
ejpam-3421	6	31	where	where	SCONJ
ejpam-3421	6	32	n2	n2	ADJ
ejpam-3421	6	33	g[a	g[a	NOUN
ejpam-3421	6	34	]	]	X
ejpam-3421	6	35	=	=	PUNCT
ejpam-3421	6	36	a	a	PRON
ejpam-3421	6	37	∪	∪	X
ejpam-3421	6	38	{	{	PUNCT
ejpam-3421	6	39	v	v	NOUN
ejpam-3421	6	40	∈	∈	NOUN
ejpam-3421	6	41	v	v	NOUN
ejpam-3421	6	42	(	(	PUNCT
ejpam-3421	6	43	g	g	NOUN
ejpam-3421	6	44	)	)	PUNCT
ejpam-3421	6	45	:	:	PUNCT
ejpam-3421	6	46	n2	n2	ADJ
ejpam-3421	6	47	g(v	g(v	PROPN
ejpam-3421	6	48	)	)	PUNCT
ejpam-3421	6	49	∩	∩	NOUN
ejpam-3421	6	50	a	a	DET
ejpam-3421	6	51	6=	6=	ADP
ejpam-3421	6	52	∅	∅	NOUN
ejpam-3421	6	53	}	}	PUNCT
ejpam-3421	6	54	and	and	CCONJ
ejpam-3421	6	55	a	a	DET
ejpam-3421	6	56	ranges	range	NOUN
ejpam-3421	6	57	over	over	ADP
ejpam-3421	6	58	all	all	DET
ejpam-3421	6	59	subsets	subset	NOUN
ejpam-3421	6	60	of	of	ADP
ejpam-3421	6	61	v	v	NOUN
ejpam-3421	6	62	(	(	PUNCT
ejpam-3421	6	63	g	g	NOUN
ejpam-3421	6	64	)	)	PUNCT
ejpam-3421	6	65	.	.	PUNCT
ejpam-3421	7	1	in	in	ADP
ejpam-3421	7	2	this	this	DET
ejpam-3421	7	3	paper	paper	NOUN
ejpam-3421	7	4	,	,	PUNCT
ejpam-3421	7	5	we	we	PRON
ejpam-3421	7	6	describe	describe	VERB
ejpam-3421	7	7	the	the	DET
ejpam-3421	7	8	topologies	topology	NOUN
ejpam-3421	7	9	induced	induce	VERB
ejpam-3421	7	10	by	by	ADP
ejpam-3421	7	11	the	the	DET
ejpam-3421	7	12	complement	complement	NOUN
ejpam-3421	7	13	of	of	ADP
ejpam-3421	7	14	a	a	DET
ejpam-3421	7	15	graph	graph	NOUN
ejpam-3421	7	16	,	,	PUNCT
ejpam-3421	7	17	the	the	DET
ejpam-3421	7	18	join	join	NOUN
ejpam-3421	7	19	,	,	PUNCT
ejpam-3421	7	20	the	the	DET
ejpam-3421	7	21	corona	corona	NOUN
ejpam-3421	7	22	,	,	PUNCT
ejpam-3421	7	23	the	the	DET
ejpam-3421	7	24	composition	composition	NOUN
ejpam-3421	7	25	and	and	CCONJ
ejpam-3421	7	26	the	the	DET
ejpam-3421	7	27	cartesian	cartesian	ADJ
ejpam-3421	7	28	product	product	NOUN
ejpam-3421	7	29	of	of	ADP
ejpam-3421	7	30	graphs	graph	NOUN
ejpam-3421	7	31	.	.	PUNCT
ejpam-3421	8	1	2010	2010	NUM
ejpam-3421	8	2	mathematics	mathematic	NOUN
ejpam-3421	8	3	subject	subject	NOUN
ejpam-3421	8	4	classifications	classification	NOUN
ejpam-3421	8	5	:	:	PUNCT
ejpam-3421	8	6	05c76	05c76	NUM
ejpam-3421	8	7	key	key	ADJ
ejpam-3421	8	8	words	word	NOUN
ejpam-3421	8	9	and	and	CCONJ
ejpam-3421	8	10	phrases	phrase	NOUN
ejpam-3421	8	11	:	:	PUNCT
ejpam-3421	8	12	join	join	VERB
ejpam-3421	8	13	,	,	PUNCT
ejpam-3421	8	14	corona	corona	PROPN
ejpam-3421	8	15	,	,	PUNCT
ejpam-3421	8	16	lexicographic	lexicographic	ADJ
ejpam-3421	8	17	product	product	NOUN
ejpam-3421	8	18	,	,	PUNCT
ejpam-3421	8	19	cartesian	cartesian	ADJ
ejpam-3421	8	20	product	product	NOUN
ejpam-3421	8	21	,	,	PUNCT
ejpam-3421	8	22	open	open	ADJ
ejpam-3421	8	23	hop	hop	NOUN
ejpam-3421	8	24	neighborhood	neighborhood	NOUN
ejpam-3421	8	25	1	1	NUM
ejpam-3421	8	26	.	.	PUNCT
ejpam-3421	9	1	introduction	introduction	NOUN
ejpam-3421	9	2	let	let	VERB
ejpam-3421	9	3	g	g	NOUN
ejpam-3421	9	4	=	=	SYM
ejpam-3421	9	5	(	(	PUNCT
ejpam-3421	9	6	v	v	NOUN
ejpam-3421	9	7	(	(	PUNCT
ejpam-3421	9	8	g	g	NOUN
ejpam-3421	9	9	)	)	PUNCT
ejpam-3421	9	10	,	,	PUNCT
ejpam-3421	9	11	v	v	X
ejpam-3421	9	12	(	(	PUNCT
ejpam-3421	9	13	h	h	NOUN
ejpam-3421	9	14	)	)	PUNCT
ejpam-3421	9	15	)	)	PUNCT
ejpam-3421	9	16	be	be	AUX
ejpam-3421	9	17	any	any	DET
ejpam-3421	9	18	simple	simple	ADJ
ejpam-3421	9	19	undirected	undirected	ADJ
ejpam-3421	9	20	graph	graph	NOUN
ejpam-3421	9	21	.	.	PUNCT
ejpam-3421	10	1	the	the	DET
ejpam-3421	10	2	distance	distance	NOUN
ejpam-3421	10	3	d(u	d(u	PROPN
ejpam-3421	10	4	,	,	PUNCT
ejpam-3421	10	5	v	v	NOUN
ejpam-3421	10	6	)	)	PUNCT
ejpam-3421	10	7	between	between	ADP
ejpam-3421	10	8	two	two	NUM
ejpam-3421	10	9	vertices	vertex	NOUN
ejpam-3421	10	10	u	u	NOUN
ejpam-3421	10	11	and	and	CCONJ
ejpam-3421	10	12	v	v	NOUN
ejpam-3421	10	13	in	in	ADP
ejpam-3421	10	14	g	g	PROPN
ejpam-3421	10	15	is	be	AUX
ejpam-3421	10	16	the	the	DET
ejpam-3421	10	17	length	length	NOUN
ejpam-3421	10	18	of	of	ADP
ejpam-3421	10	19	a	a	DET
ejpam-3421	10	20	shortest	short	ADJ
ejpam-3421	10	21	path	path	NOUN
ejpam-3421	10	22	joining	join	VERB
ejpam-3421	10	23	u	u	NOUN
ejpam-3421	10	24	and	and	CCONJ
ejpam-3421	10	25	v.	v.	CCONJ
ejpam-3421	10	26	let	let	VERB
ejpam-3421	10	27	v	v	NUM
ejpam-3421	10	28	∈	∈	PROPN
ejpam-3421	10	29	v	v	NOUN
ejpam-3421	10	30	(	(	PUNCT
ejpam-3421	10	31	g	g	NOUN
ejpam-3421	10	32	)	)	PUNCT
ejpam-3421	10	33	.	.	PUNCT
ejpam-3421	11	1	the	the	DET
ejpam-3421	11	2	neighborhood	neighborhood	NOUN
ejpam-3421	11	3	of	of	ADP
ejpam-3421	11	4	v	v	NOUN
ejpam-3421	11	5	is	be	AUX
ejpam-3421	11	6	the	the	DET
ejpam-3421	11	7	set	set	NOUN
ejpam-3421	11	8	n(v	n(v	PROPN
ejpam-3421	11	9	)	)	PUNCT
ejpam-3421	11	10	consisting	consist	VERB
ejpam-3421	11	11	of	of	ADP
ejpam-3421	11	12	all	all	DET
ejpam-3421	11	13	u	u	NOUN
ejpam-3421	11	14	∈	∈	PROPN
ejpam-3421	11	15	v	v	NOUN
ejpam-3421	11	16	(	(	PUNCT
ejpam-3421	11	17	g	g	NOUN
ejpam-3421	11	18	)	)	PUNCT
ejpam-3421	11	19	which	which	PRON
ejpam-3421	11	20	are	be	AUX
ejpam-3421	11	21	adjacent	adjacent	ADJ
ejpam-3421	11	22	with	with	ADP
ejpam-3421	11	23	v	v	NUM
ejpam-3421	11	24	and	and	CCONJ
ejpam-3421	11	25	the	the	DET
ejpam-3421	11	26	closed	closed	ADJ
ejpam-3421	11	27	neighborhood	neighborhood	NOUN
ejpam-3421	11	28	is	be	AUX
ejpam-3421	11	29	n	n	PRON
ejpam-3421	11	30	[	[	X
ejpam-3421	11	31	v	v	X
ejpam-3421	11	32	]	]	X
ejpam-3421	11	33	=	=	PUNCT
ejpam-3421	11	34	n(v	n(v	PROPN
ejpam-3421	11	35	)	)	PUNCT
ejpam-3421	11	36	∪	∪	NOUN
ejpam-3421	11	37	{	{	PUNCT
ejpam-3421	11	38	v	v	NOUN
ejpam-3421	11	39	}	}	PUNCT
ejpam-3421	11	40	.	.	PUNCT
ejpam-3421	12	1	for	for	ADP
ejpam-3421	12	2	any	any	DET
ejpam-3421	12	3	a	a	DET
ejpam-3421	12	4	⊆	⊆	NUM
ejpam-3421	12	5	v	v	NOUN
ejpam-3421	12	6	(	(	PUNCT
ejpam-3421	12	7	g	g	NOUN
ejpam-3421	12	8	)	)	PUNCT
ejpam-3421	12	9	,	,	PUNCT
ejpam-3421	12	10	n(a	n(a	X
ejpam-3421	12	11	)	)	PUNCT
ejpam-3421	12	12	=	=	PRON
ejpam-3421	13	1	{	{	PUNCT
ejpam-3421	13	2	x	x	X
ejpam-3421	13	3	:	:	PUNCT
ejpam-3421	13	4	xa	xa	PROPN
ejpam-3421	13	5	∈	∈	PROPN
ejpam-3421	13	6	e(g	e(g	PROPN
ejpam-3421	13	7	)	)	PUNCT
ejpam-3421	13	8	for	for	ADP
ejpam-3421	13	9	some	some	DET
ejpam-3421	13	10	a	a	DET
ejpam-3421	13	11	∈	∈	PROPN
ejpam-3421	13	12	a	a	PRON
ejpam-3421	13	13	}	}	PUNCT
ejpam-3421	13	14	is	be	AUX
ejpam-3421	13	15	called	call	VERB
ejpam-3421	13	16	the	the	DET
ejpam-3421	13	17	neighborhood	neighborhood	NOUN
ejpam-3421	13	18	of	of	ADP
ejpam-3421	13	19	a	a	PRON
ejpam-3421	13	20	and	and	CCONJ
ejpam-3421	13	21	n	n	CCONJ
ejpam-3421	14	1	[	[	X
ejpam-3421	14	2	a	a	X
ejpam-3421	14	3	]	]	X
ejpam-3421	14	4	=	=	SYM
ejpam-3421	14	5	n(a	n(a	NOUN
ejpam-3421	14	6	)	)	PUNCT
ejpam-3421	14	7	∪	∪	ADP
ejpam-3421	14	8	a	a	PRON
ejpam-3421	14	9	is	be	AUX
ejpam-3421	14	10	called	call	VERB
ejpam-3421	14	11	the	the	DET
ejpam-3421	14	12	closed	closed	ADJ
ejpam-3421	14	13	neighborhood	neighborhood	NOUN
ejpam-3421	14	14	of	of	ADP
ejpam-3421	14	15	a.	a.	NOUN
ejpam-3421	14	16	moreover	moreover	ADV
ejpam-3421	14	17	,	,	PUNCT
ejpam-3421	14	18	for	for	ADP
ejpam-3421	14	19	each	each	DET
ejpam-3421	14	20	v	v	NUM
ejpam-3421	14	21	∈	∈	PROPN
ejpam-3421	14	22	v	v	NOUN
ejpam-3421	14	23	(	(	PUNCT
ejpam-3421	14	24	g	g	NOUN
ejpam-3421	14	25	)	)	PUNCT
ejpam-3421	14	26	,	,	PUNCT
ejpam-3421	14	27	the	the	DET
ejpam-3421	14	28	open	open	ADJ
ejpam-3421	14	29	hop	hop	NOUN
ejpam-3421	14	30	neighborhood	neighborhood	NOUN
ejpam-3421	14	31	of	of	ADP
ejpam-3421	14	32	v	v	NOUN
ejpam-3421	14	33	is	be	AUX
ejpam-3421	14	34	the	the	DET
ejpam-3421	14	35	set	set	ADJ
ejpam-3421	14	36	n2	n2	ADJ
ejpam-3421	14	37	g(v	g(v	PROPN
ejpam-3421	14	38	)	)	PUNCT
ejpam-3421	14	39	=	=	PRON
ejpam-3421	14	40	{	{	PUNCT
ejpam-3421	14	41	u	u	NOUN
ejpam-3421	14	42	∈	∈	PROPN
ejpam-3421	14	43	v	v	NOUN
ejpam-3421	14	44	(	(	PUNCT
ejpam-3421	14	45	g	g	NOUN
ejpam-3421	14	46	)	)	PUNCT
ejpam-3421	14	47	:	:	PUNCT
ejpam-3421	14	48	dg(u	dg(u	X
ejpam-3421	14	49	,	,	PUNCT
ejpam-3421	14	50	v	v	NOUN
ejpam-3421	14	51	)	)	PUNCT
ejpam-3421	14	52	=	=	SYM
ejpam-3421	14	53	2	2	X
ejpam-3421	14	54	}	}	PUNCT
ejpam-3421	14	55	and	and	CCONJ
ejpam-3421	14	56	the	the	DET
ejpam-3421	14	57	closed	closed	ADJ
ejpam-3421	14	58	hop	hop	NOUN
ejpam-3421	14	59	neighborhood	neighborhood	NOUN
ejpam-3421	14	60	of	of	ADP
ejpam-3421	14	61	v	v	NOUN
ejpam-3421	14	62	is	be	AUX
ejpam-3421	14	63	the	the	DET
ejpam-3421	14	64	set	set	ADJ
ejpam-3421	14	65	n2	n2	ADJ
ejpam-3421	14	66	g[v	g[v	NOUN
ejpam-3421	14	67	]	]	X
ejpam-3421	14	68	=	=	SYM
ejpam-3421	14	69	{	{	PUNCT
ejpam-3421	14	70	v	v	NOUN
ejpam-3421	14	71	}	}	PUNCT
ejpam-3421	14	72	∪	∪	ADJ
ejpam-3421	14	73	n2	n2	ADJ
ejpam-3421	14	74	g(v	g(v	PROPN
ejpam-3421	14	75	)	)	PUNCT
ejpam-3421	14	76	.	.	PUNCT
ejpam-3421	15	1	also	also	ADV
ejpam-3421	15	2	,	,	PUNCT
ejpam-3421	15	3	for	for	ADP
ejpam-3421	15	4	any	any	DET
ejpam-3421	15	5	a	a	DET
ejpam-3421	15	6	⊆	⊆	NUM
ejpam-3421	15	7	v	v	NOUN
ejpam-3421	15	8	(	(	PUNCT
ejpam-3421	15	9	g	g	NOUN
ejpam-3421	15	10	)	)	PUNCT
ejpam-3421	15	11	,	,	PUNCT
ejpam-3421	15	12	n2	n2	PROPN
ejpam-3421	15	13	g(a	g(a	PROPN
ejpam-3421	15	14	)	)	PUNCT
ejpam-3421	15	15	=	=	PRON
ejpam-3421	16	1	{	{	PUNCT
ejpam-3421	16	2	v	v	NUM
ejpam-3421	16	3	∈	∈	NOUN
ejpam-3421	16	4	v	v	NOUN
ejpam-3421	16	5	(	(	PUNCT
ejpam-3421	16	6	g	g	NOUN
ejpam-3421	16	7	)	)	PUNCT
ejpam-3421	16	8	:	:	PUNCT
ejpam-3421	16	9	n2	n2	ADJ
ejpam-3421	16	10	g(v	g(v	PROPN
ejpam-3421	16	11	)	)	PUNCT
ejpam-3421	16	12	∩	∩	NOUN
ejpam-3421	16	13	a	a	DET
ejpam-3421	16	14	6=	6=	NOUN
ejpam-3421	16	15	∅	∅	NOUN
ejpam-3421	16	16	}	}	PUNCT
ejpam-3421	16	17	is	be	AUX
ejpam-3421	16	18	called	call	VERB
ejpam-3421	16	19	the	the	DET
ejpam-3421	16	20	open	open	ADJ
ejpam-3421	16	21	hop	hop	NOUN
ejpam-3421	16	22	neighborhood	neighborhood	NOUN
ejpam-3421	16	23	of	of	ADP
ejpam-3421	16	24	a	a	PRON
ejpam-3421	16	25	and	and	CCONJ
ejpam-3421	16	26	the	the	DET
ejpam-3421	16	27	set	set	ADJ
ejpam-3421	16	28	n2	n2	NOUN
ejpam-3421	16	29	g[a	g[a	PROPN
ejpam-3421	16	30	]	]	X
ejpam-3421	16	31	=	=	PUNCT
ejpam-3421	16	32	a	a	DET
ejpam-3421	16	33	∪n2	∪n2	PROPN
ejpam-3421	16	34	g(a	g(a	PROPN
ejpam-3421	16	35	)	)	PUNCT
ejpam-3421	16	36	is	be	AUX
ejpam-3421	16	37	the	the	DET
ejpam-3421	16	38	called	call	VERB
ejpam-3421	16	39	closed	closed	ADJ
ejpam-3421	16	40	hop	hop	NOUN
ejpam-3421	16	41	neighborhood	neighborhood	NOUN
ejpam-3421	16	42	of	of	ADP
ejpam-3421	16	43	a.	a.	NOUN
ejpam-3421	16	44	denote	denote	NOUN
ejpam-3421	16	45	by	by	ADP
ejpam-3421	16	46	f	f	PROPN
ejpam-3421	16	47	2	2	NUM
ejpam-3421	16	48	g[a	g[a	NOUN
ejpam-3421	16	49	]	]	X
ejpam-3421	16	50	the	the	DET
ejpam-3421	16	51	complement	complement	NOUN
ejpam-3421	16	52	of	of	ADP
ejpam-3421	16	53	n2	n2	ADJ
ejpam-3421	16	54	g[a	g[a	PROPN
ejpam-3421	16	55	]	]	X
ejpam-3421	16	56	,	,	PUNCT
ejpam-3421	16	57	i.e.	i.e.	X
ejpam-3421	16	58	,	,	PUNCT
ejpam-3421	16	59	f	f	PROPN
ejpam-3421	16	60	2	2	NUM
ejpam-3421	16	61	g[a	g[a	NOUN
ejpam-3421	16	62	]	]	X
ejpam-3421	16	63	=	=	SYM
ejpam-3421	16	64	v	v	X
ejpam-3421	16	65	(	(	PUNCT
ejpam-3421	16	66	g)\n2	g)\n2	NOUN
ejpam-3421	16	67	g[a	g[a	NOUN
ejpam-3421	16	68	]	]	X
ejpam-3421	16	69	.	.	PUNCT
ejpam-3421	17	1	in	in	ADP
ejpam-3421	17	2	1983	1983	NUM
ejpam-3421	17	3	,	,	PUNCT
ejpam-3421	17	4	diesto	diesto	NOUN
ejpam-3421	17	5	and	and	CCONJ
ejpam-3421	17	6	gervacio	gervacio	NOUN
ejpam-3421	17	7	in	in	ADP
ejpam-3421	17	8	[	[	X
ejpam-3421	17	9	5	5	NUM
ejpam-3421	17	10	]	]	PUNCT
ejpam-3421	17	11	proved	prove	VERB
ejpam-3421	17	12	that	that	SCONJ
ejpam-3421	17	13	given	give	VERB
ejpam-3421	17	14	a	a	DET
ejpam-3421	17	15	simple	simple	ADJ
ejpam-3421	17	16	graphg	graphg	NOUN
ejpam-3421	17	17	=	=	SYM
ejpam-3421	17	18	(	(	PUNCT
ejpam-3421	17	19	v	v	NOUN
ejpam-3421	17	20	(	(	PUNCT
ejpam-3421	17	21	g	g	NOUN
ejpam-3421	17	22	)	)	PUNCT
ejpam-3421	17	23	,	,	PUNCT
ejpam-3421	17	24	e(g	e(g	PROPN
ejpam-3421	17	25	)	)	PUNCT
ejpam-3421	17	26	)	)	PUNCT
ejpam-3421	17	27	,	,	PUNCT
ejpam-3421	17	28	g	g	PROPN
ejpam-3421	17	29	induces	induce	VERB
ejpam-3421	17	30	a	a	DET
ejpam-3421	17	31	topology	topology	NOUN
ejpam-3421	17	32	on	on	ADP
ejpam-3421	17	33	v	v	ADP
ejpam-3421	17	34	(	(	PUNCT
ejpam-3421	17	35	g	g	NOUN
ejpam-3421	17	36	)	)	PUNCT
ejpam-3421	17	37	,	,	PUNCT
ejpam-3421	17	38	denoted	denote	VERB
ejpam-3421	17	39	by	by	ADP
ejpam-3421	17	40	τg	τg	ADP
ejpam-3421	17	41	,	,	PUNCT
ejpam-3421	17	42	with	with	ADP
ejpam-3421	17	43	base	base	NOUN
ejpam-3421	17	44	consisting	consist	VERB
ejpam-3421	17	45	of	of	ADP
ejpam-3421	17	46	sets	set	NOUN
ejpam-3421	17	47	of	of	ADP
ejpam-3421	17	48	the	the	DET
ejpam-3421	17	49	form	form	NOUN
ejpam-3421	17	50	∗corresponding	∗corresponde	VERB
ejpam-3421	17	51	author	author	NOUN
ejpam-3421	17	52	.	.	PUNCT
ejpam-3421	18	1	doi	doi	NOUN
ejpam-3421	18	2	:	:	PUNCT
ejpam-3421	18	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3421	https://doi.org/10.29020/nybg.ejpam.v12i2.3421	ADP
ejpam-3421	18	4	email	email	NOUN
ejpam-3421	18	5	addresses	address	NOUN
ejpam-3421	18	6	:	:	PUNCT
ejpam-3421	18	7	caengrace1997@gmail.com	caengrace1997@gmail.com	X
ejpam-3421	18	8	(	(	PUNCT
ejpam-3421	18	9	c.	c.	PROPN
ejpam-3421	18	10	nianga	nianga	PROPN
ejpam-3421	18	11	)	)	PUNCT
ejpam-3421	18	12	,	,	PUNCT
ejpam-3421	18	13	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-3421	18	14	(	(	PUNCT
ejpam-3421	18	15	s.	s.	PROPN
ejpam-3421	18	16	canoy	canoy	PROPN
ejpam-3421	18	17	jr	jr	PROPN
ejpam-3421	18	18	.	.	PUNCT
ejpam-3421	18	19	)	)	PUNCT
ejpam-3421	18	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3421	19	1	499	499	NUM
ejpam-3421	19	2	c	c	NOUN
ejpam-3421	19	3	©	©	PROPN
ejpam-3421	19	4	2019	2019	NUM
ejpam-3421	19	5	ejpam	ejpam	NOUN
ejpam-3421	19	6	all	all	DET
ejpam-3421	19	7	rights	right	NOUN
ejpam-3421	19	8	reserved	reserve	VERB
ejpam-3421	19	9	.	.	PUNCT
ejpam-3421	20	1	c.	c.	PROPN
ejpam-3421	20	2	nianga	nianga	PROPN
ejpam-3421	20	3	,	,	PUNCT
ejpam-3421	20	4	s.	s.	PROPN
ejpam-3421	20	5	canoy	canoy	PROPN
ejpam-3421	20	6	/	/	SYM
ejpam-3421	20	7	eur	eur	PROPN
ejpam-3421	20	8	.	.	PUNCT
ejpam-3421	21	1	j.	j.	PROPN
ejpam-3421	21	2	pure	pure	PROPN
ejpam-3421	21	3	appl	appl	PROPN
ejpam-3421	21	4	.	.	PROPN
ejpam-3421	21	5	math	math	PROPN
ejpam-3421	21	6	,	,	PUNCT
ejpam-3421	21	7	12	12	NUM
ejpam-3421	21	8	(	(	PUNCT
ejpam-3421	21	9	2	2	NUM
ejpam-3421	21	10	)	)	PUNCT
ejpam-3421	21	11	(	(	PUNCT
ejpam-3421	21	12	2019	2019	NUM
ejpam-3421	21	13	)	)	PUNCT
ejpam-3421	21	14	,	,	PUNCT
ejpam-3421	21	15	499	499	NUM
ejpam-3421	21	16	-	-	SYM
ejpam-3421	21	17	505	505	NUM
ejpam-3421	21	18	500	500	NUM
ejpam-3421	21	19	fg(a	fg(a	NOUN
ejpam-3421	21	20	)	)	PUNCT
ejpam-3421	21	21	=	=	SYM
ejpam-3421	21	22	v	v	X
ejpam-3421	21	23	(	(	PUNCT
ejpam-3421	21	24	g)\ng(a	g)\ng(a	PROPN
ejpam-3421	21	25	)	)	PUNCT
ejpam-3421	21	26	,	,	PUNCT
ejpam-3421	21	27	where	where	SCONJ
ejpam-3421	21	28	ng(a	ng(a	NOUN
ejpam-3421	21	29	)	)	PUNCT
ejpam-3421	21	30	=	=	PUNCT
ejpam-3421	21	31	a	a	DET
ejpam-3421	21	32	∪	∪	X
ejpam-3421	21	33	{	{	PUNCT
ejpam-3421	21	34	x	x	NOUN
ejpam-3421	21	35	:	:	PUNCT
ejpam-3421	21	36	xa	xa	PROPN
ejpam-3421	21	37	∈	∈	PROPN
ejpam-3421	21	38	e	e	PROPN
ejpam-3421	21	39	for	for	ADP
ejpam-3421	21	40	some	some	DET
ejpam-3421	21	41	a	a	DET
ejpam-3421	21	42	∈	∈	PROPN
ejpam-3421	21	43	a	a	PRON
ejpam-3421	21	44	}	}	PUNCT
ejpam-3421	21	45	and	and	CCONJ
ejpam-3421	21	46	a	a	DET
ejpam-3421	21	47	ranges	range	NOUN
ejpam-3421	21	48	over	over	ADP
ejpam-3421	21	49	all	all	DET
ejpam-3421	21	50	subsets	subset	NOUN
ejpam-3421	21	51	of	of	ADP
ejpam-3421	21	52	v	v	NOUN
ejpam-3421	21	53	(	(	PUNCT
ejpam-3421	21	54	g	g	NOUN
ejpam-3421	21	55	)	)	PUNCT
ejpam-3421	21	56	.	.	PUNCT
ejpam-3421	22	1	their	their	PRON
ejpam-3421	22	2	construction	construction	NOUN
ejpam-3421	22	3	was	be	AUX
ejpam-3421	22	4	further	far	ADV
ejpam-3421	22	5	investigated	investigate	VERB
ejpam-3421	22	6	in	in	ADP
ejpam-3421	22	7	[	[	X
ejpam-3421	22	8	2	2	NUM
ejpam-3421	22	9	]	]	PUNCT
ejpam-3421	22	10	,	,	PUNCT
ejpam-3421	22	11	[	[	X
ejpam-3421	22	12	3	3	NUM
ejpam-3421	22	13	]	]	PUNCT
ejpam-3421	22	14	and	and	CCONJ
ejpam-3421	22	15	[	[	X
ejpam-3421	22	16	6	6	NUM
ejpam-3421	22	17	]	]	PUNCT
ejpam-3421	22	18	.	.	PUNCT
ejpam-3421	23	1	in	in	ADP
ejpam-3421	23	2	particular	particular	ADJ
ejpam-3421	23	3	,	,	PUNCT
ejpam-3421	23	4	canoy	canoy	ADJ
ejpam-3421	23	5	and	and	CCONJ
ejpam-3421	23	6	lemence	lemence	ADV
ejpam-3421	23	7	in	in	ADP
ejpam-3421	23	8	[	[	X
ejpam-3421	23	9	2	2	NUM
ejpam-3421	23	10	]	]	PUNCT
ejpam-3421	23	11	described	describe	VERB
ejpam-3421	23	12	the	the	DET
ejpam-3421	23	13	topologies	topology	NOUN
ejpam-3421	23	14	induced	induce	VERB
ejpam-3421	23	15	by	by	ADP
ejpam-3421	23	16	the	the	DET
ejpam-3421	23	17	complement	complement	NOUN
ejpam-3421	23	18	of	of	ADP
ejpam-3421	23	19	a	a	DET
ejpam-3421	23	20	graph	graph	NOUN
ejpam-3421	23	21	,	,	PUNCT
ejpam-3421	23	22	the	the	DET
ejpam-3421	23	23	join	join	NOUN
ejpam-3421	23	24	of	of	ADP
ejpam-3421	23	25	graphs	graph	NOUN
ejpam-3421	23	26	,	,	PUNCT
ejpam-3421	23	27	composition	composition	NOUN
ejpam-3421	23	28	and	and	CCONJ
ejpam-3421	23	29	cartesian	cartesian	ADJ
ejpam-3421	23	30	product	product	NOUN
ejpam-3421	23	31	of	of	ADP
ejpam-3421	23	32	graphs	graph	NOUN
ejpam-3421	23	33	.	.	PUNCT
ejpam-3421	24	1	in	in	ADP
ejpam-3421	24	2	[	[	X
ejpam-3421	24	3	1	1	NUM
ejpam-3421	24	4	]	]	PUNCT
ejpam-3421	24	5	,	,	PUNCT
ejpam-3421	24	6	canoy	canoy	ADJ
ejpam-3421	24	7	and	and	CCONJ
ejpam-3421	24	8	gimeno	gimeno	PROPN
ejpam-3421	24	9	presented	present	VERB
ejpam-3421	24	10	another	another	DET
ejpam-3421	24	11	way	way	NOUN
ejpam-3421	24	12	of	of	ADP
ejpam-3421	24	13	constructing	construct	VERB
ejpam-3421	24	14	a	a	DET
ejpam-3421	24	15	topology	topology	NOUN
ejpam-3421	24	16	τg	τg	NOUN
ejpam-3421	24	17	from	from	ADP
ejpam-3421	24	18	a	a	DET
ejpam-3421	24	19	connected	connected	ADJ
ejpam-3421	24	20	graph	graph	NOUN
ejpam-3421	24	21	g	g	NOUN
ejpam-3421	24	22	by	by	ADP
ejpam-3421	24	23	considering	consider	VERB
ejpam-3421	24	24	the	the	DET
ejpam-3421	24	25	family	family	NOUN
ejpam-3421	24	26	ω(g	ω(g	NOUN
ejpam-3421	24	27	)	)	PUNCT
ejpam-3421	24	28	=	=	PRON
ejpam-3421	24	29	{	{	PUNCT
ejpam-3421	24	30	f	f	PROPN
ejpam-3421	24	31	2	2	NUM
ejpam-3421	24	32	g[a	g[a	NOUN
ejpam-3421	24	33	]	]	X
ejpam-3421	24	34	:	:	PUNCT
ejpam-3421	24	35	a	a	DET
ejpam-3421	24	36	⊆	⊆	NUM
ejpam-3421	24	37	v	v	NOUN
ejpam-3421	24	38	(	(	PUNCT
ejpam-3421	24	39	g	g	NOUN
ejpam-3421	24	40	)	)	PUNCT
ejpam-3421	24	41	}	}	PUNCT
ejpam-3421	24	42	where	where	SCONJ
ejpam-3421	24	43	f	f	PROPN
ejpam-3421	24	44	2	2	NUM
ejpam-3421	24	45	g[a	g[a	NOUN
ejpam-3421	24	46	]	]	X
ejpam-3421	24	47	=	=	SYM
ejpam-3421	24	48	{	{	PUNCT
ejpam-3421	24	49	x	x	PROPN
ejpam-3421	24	50	∈	∈	PROPN
ejpam-3421	24	51	v	v	NOUN
ejpam-3421	24	52	(	(	PUNCT
ejpam-3421	24	53	g	g	NOUN
ejpam-3421	24	54	)	)	PUNCT
ejpam-3421	24	55	:	:	PUNCT
ejpam-3421	24	56	x	x	X
ejpam-3421	24	57	/∈	/∈	PUNCT
ejpam-3421	24	58	a	a	PRON
ejpam-3421	24	59	and	and	CCONJ
ejpam-3421	24	60	dg(x	dg(x	NUM
ejpam-3421	24	61	,	,	PUNCT
ejpam-3421	24	62	a	a	PRON
ejpam-3421	24	63	)	)	PUNCT
ejpam-3421	24	64	6=	6=	ADP
ejpam-3421	24	65	2	2	NUM
ejpam-3421	24	66	for	for	ADP
ejpam-3421	24	67	all	all	DET
ejpam-3421	24	68	a	a	DET
ejpam-3421	24	69	∈	∈	PROPN
ejpam-3421	24	70	a	a	PRON
ejpam-3421	24	71	}	}	PUNCT
ejpam-3421	24	72	.	.	PUNCT
ejpam-3421	25	1	they	they	PRON
ejpam-3421	25	2	showed	show	VERB
ejpam-3421	25	3	that	that	SCONJ
ejpam-3421	25	4	this	this	DET
ejpam-3421	25	5	family	family	NOUN
ejpam-3421	25	6	is	be	AUX
ejpam-3421	25	7	a	a	DET
ejpam-3421	25	8	base	base	NOUN
ejpam-3421	25	9	for	for	ADP
ejpam-3421	25	10	some	some	DET
ejpam-3421	25	11	topology	topology	NOUN
ejpam-3421	25	12	τg	τg	NOUN
ejpam-3421	25	13	on	on	ADP
ejpam-3421	25	14	v	v	ADP
ejpam-3421	25	15	(	(	PUNCT
ejpam-3421	25	16	g	g	NOUN
ejpam-3421	25	17	)	)	PUNCT
ejpam-3421	25	18	.	.	PUNCT
ejpam-3421	26	1	this	this	DET
ejpam-3421	26	2	construction	construction	NOUN
ejpam-3421	26	3	is	be	AUX
ejpam-3421	26	4	also	also	ADV
ejpam-3421	26	5	studied	study	VERB
ejpam-3421	26	6	by	by	ADP
ejpam-3421	26	7	nianga	nianga	PROPN
ejpam-3421	26	8	et	et	PROPN
ejpam-3421	26	9	al	al	PROPN
ejpam-3421	26	10	,	,	PUNCT
ejpam-3421	26	11	in	in	ADP
ejpam-3421	26	12	[	[	X
ejpam-3421	26	13	4	4	X
ejpam-3421	26	14	]	]	PUNCT
ejpam-3421	26	15	for	for	ADP
ejpam-3421	26	16	any	any	DET
ejpam-3421	26	17	graph	graph	NOUN
ejpam-3421	26	18	g.	g.	NOUN
ejpam-3421	27	1	it	it	PRON
ejpam-3421	27	2	is	be	AUX
ejpam-3421	27	3	also	also	ADV
ejpam-3421	27	4	shown	show	VERB
ejpam-3421	27	5	that	that	SCONJ
ejpam-3421	27	6	the	the	DET
ejpam-3421	27	7	family	family	NOUN
ejpam-3421	27	8	bg	bg	PROPN
ejpam-3421	27	9	=	=	PUNCT
ejpam-3421	27	10	{	{	PUNCT
ejpam-3421	27	11	f	f	PROPN
ejpam-3421	27	12	2	2	NUM
ejpam-3421	27	13	g[a	g[a	NOUN
ejpam-3421	27	14	]	]	X
ejpam-3421	27	15	:	:	PUNCT
ejpam-3421	27	16	a	a	DET
ejpam-3421	27	17	⊆	⊆	NUM
ejpam-3421	27	18	v	v	NOUN
ejpam-3421	27	19	(	(	PUNCT
ejpam-3421	27	20	g	g	NOUN
ejpam-3421	27	21	)	)	PUNCT
ejpam-3421	27	22	}	}	PUNCT
ejpam-3421	27	23	and	and	CCONJ
ejpam-3421	27	24	sg	sg	X
ejpam-3421	27	25	=	=	SYM
ejpam-3421	27	26	{	{	PUNCT
ejpam-3421	27	27	f	f	PROPN
ejpam-3421	27	28	2	2	NUM
ejpam-3421	27	29	g[v	g[v	NOUN
ejpam-3421	27	30	]	]	PUNCT
ejpam-3421	27	31	:	:	PUNCT
ejpam-3421	27	32	v	v	X
ejpam-3421	27	33	∈	∈	PROPN
ejpam-3421	27	34	v	v	NOUN
ejpam-3421	27	35	(	(	PUNCT
ejpam-3421	27	36	g	g	NOUN
ejpam-3421	27	37	)	)	PUNCT
ejpam-3421	27	38	}	}	PUNCT
ejpam-3421	27	39	are	be	AUX
ejpam-3421	27	40	,	,	PUNCT
ejpam-3421	27	41	respectively	respectively	ADV
ejpam-3421	27	42	,	,	PUNCT
ejpam-3421	27	43	base	base	NOUN
ejpam-3421	27	44	and	and	CCONJ
ejpam-3421	27	45	subbase	subbase	VERB
ejpam-3421	27	46	for	for	ADP
ejpam-3421	27	47	the	the	DET
ejpam-3421	27	48	topology	topology	NOUN
ejpam-3421	27	49	τg	τg	NOUN
ejpam-3421	27	50	on	on	ADP
ejpam-3421	27	51	v	v	ADP
ejpam-3421	27	52	(	(	PUNCT
ejpam-3421	27	53	g	g	NOUN
ejpam-3421	27	54	)	)	PUNCT
ejpam-3421	27	55	.	.	PUNCT
ejpam-3421	28	1	concepts	concept	NOUN
ejpam-3421	28	2	on	on	ADP
ejpam-3421	28	3	graph	graph	NOUN
ejpam-3421	28	4	theory	theory	NOUN
ejpam-3421	28	5	and	and	CCONJ
ejpam-3421	28	6	topology	topology	NOUN
ejpam-3421	28	7	are	be	AUX
ejpam-3421	28	8	taken	take	VERB
ejpam-3421	28	9	from	from	ADP
ejpam-3421	28	10	[	[	X
ejpam-3421	28	11	7	7	NUM
ejpam-3421	28	12	]	]	PUNCT
ejpam-3421	28	13	and	and	CCONJ
ejpam-3421	28	14	[	[	X
ejpam-3421	28	15	8	8	NUM
ejpam-3421	28	16	]	]	PUNCT
ejpam-3421	28	17	,	,	PUNCT
ejpam-3421	28	18	respectively	respectively	ADV
ejpam-3421	28	19	.	.	PUNCT
ejpam-3421	29	1	2	2	X
ejpam-3421	29	2	.	.	NOUN
ejpam-3421	29	3	results	result	VERB
ejpam-3421	29	4	definition	definition	NOUN
ejpam-3421	29	5	1	1	NUM
ejpam-3421	29	6	.	.	PUNCT
ejpam-3421	30	1	the	the	DET
ejpam-3421	30	2	complement	complement	NOUN
ejpam-3421	30	3	of	of	ADP
ejpam-3421	30	4	graph	graph	NOUN
ejpam-3421	30	5	g	g	NOUN
ejpam-3421	30	6	,	,	PUNCT
ejpam-3421	30	7	denoted	denote	VERB
ejpam-3421	30	8	by	by	ADP
ejpam-3421	30	9	g	g	PROPN
ejpam-3421	30	10	is	be	AUX
ejpam-3421	30	11	the	the	DET
ejpam-3421	30	12	graph	graph	NOUN
ejpam-3421	30	13	with	with	ADP
ejpam-3421	30	14	v	v	NOUN
ejpam-3421	30	15	(	(	PUNCT
ejpam-3421	30	16	g	g	NOUN
ejpam-3421	30	17	)	)	PUNCT
ejpam-3421	30	18	=	=	NOUN
ejpam-3421	30	19	v	v	X
ejpam-3421	30	20	(	(	PUNCT
ejpam-3421	30	21	g	g	NOUN
ejpam-3421	30	22	)	)	PUNCT
ejpam-3421	30	23	and	and	CCONJ
ejpam-3421	30	24	uv	uv	NOUN
ejpam-3421	30	25	∈	∈	PROPN
ejpam-3421	30	26	e(g	e(g	PROPN
ejpam-3421	30	27	)	)	PUNCT
ejpam-3421	31	1	if	if	SCONJ
ejpam-3421	31	2	and	and	CCONJ
ejpam-3421	31	3	only	only	ADV
ejpam-3421	31	4	if	if	SCONJ
ejpam-3421	31	5	uv	uv	PROPN
ejpam-3421	31	6	/∈	/∈	PUNCT
ejpam-3421	31	7	e(g	e(g	PROPN
ejpam-3421	31	8	)	)	PUNCT
ejpam-3421	31	9	,	,	PUNCT
ejpam-3421	31	10	where	where	SCONJ
ejpam-3421	31	11	u	u	NOUN
ejpam-3421	31	12	,	,	PUNCT
ejpam-3421	31	13	v	v	PROPN
ejpam-3421	31	14	∈	∈	PROPN
ejpam-3421	31	15	v	v	NOUN
ejpam-3421	31	16	(	(	PUNCT
ejpam-3421	31	17	g	g	NOUN
ejpam-3421	31	18	)	)	PUNCT
ejpam-3421	31	19	=	=	NOUN
ejpam-3421	31	20	v	v	X
ejpam-3421	31	21	(	(	PUNCT
ejpam-3421	31	22	g	g	NOUN
ejpam-3421	31	23	)	)	PUNCT
ejpam-3421	31	24	.	.	PUNCT
ejpam-3421	32	1	theorem	theorem	NOUN
ejpam-3421	32	2	1	1	X
ejpam-3421	32	3	.	.	PUNCT
ejpam-3421	33	1	let	let	VERB
ejpam-3421	33	2	g	g	NOUN
ejpam-3421	33	3	be	be	AUX
ejpam-3421	33	4	any	any	DET
ejpam-3421	33	5	graph	graph	NOUN
ejpam-3421	33	6	and	and	CCONJ
ejpam-3421	33	7	g	g	ADP
ejpam-3421	33	8	its	its	PRON
ejpam-3421	33	9	complement	complement	NOUN
ejpam-3421	33	10	.	.	PUNCT
ejpam-3421	34	1	then	then	ADV
ejpam-3421	34	2	for	for	ADP
ejpam-3421	34	3	each	each	PRON
ejpam-3421	34	4	v	v	NUM
ejpam-3421	34	5	∈	∈	PROPN
ejpam-3421	34	6	v	v	NOUN
ejpam-3421	34	7	(	(	PUNCT
ejpam-3421	34	8	g	g	NOUN
ejpam-3421	34	9	)	)	PUNCT
ejpam-3421	34	10	,	,	PUNCT
ejpam-3421	34	11	f	f	PROPN
ejpam-3421	34	12	2	2	NUM
ejpam-3421	34	13	g	g	NOUN
ejpam-3421	34	14	[	[	X
ejpam-3421	34	15	v	v	X
ejpam-3421	34	16	]	]	X
ejpam-3421	34	17	=	=	SYM
ejpam-3421	34	18			PUNCT
ejpam-3421	34	19	fg[v	fg[v	PROPN
ejpam-3421	34	20	]	]	PUNCT
ejpam-3421	34	21	∪	∪	ADP
ejpam-3421	34	22			PROPN
ejpam-3421	34	23	⋂	⋂	PROPN
ejpam-3421	34	24	u∈fg[v	u∈fg[v	PROPN
ejpam-3421	34	25	]	]	X
ejpam-3421	34	26	ng(u	ng(u	NOUN
ejpam-3421	34	27	)	)	PUNCT
ejpam-3421	34	28			NOUN
ejpam-3421	34	29	,	,	PUNCT
ejpam-3421	34	30	if	if	SCONJ
ejpam-3421	34	31	fg[v	fg[v	PROPN
ejpam-3421	34	32	]	]	PUNCT
ejpam-3421	34	33	6=	6=	ADP
ejpam-3421	34	34	∅	∅	NOUN
ejpam-3421	34	35	ng(v	ng(v	NOUN
ejpam-3421	34	36	)	)	PUNCT
ejpam-3421	34	37	,	,	PUNCT
ejpam-3421	34	38	if	if	SCONJ
ejpam-3421	34	39	fg[v	fg[v	PROPN
ejpam-3421	34	40	]	]	X
ejpam-3421	34	41	=	=	X
ejpam-3421	34	42	∅.	∅.	X
ejpam-3421	34	43	(	(	PUNCT
ejpam-3421	34	44	1	1	NUM
ejpam-3421	34	45	)	)	PUNCT
ejpam-3421	34	46	proof	proof	NOUN
ejpam-3421	34	47	.	.	PUNCT
ejpam-3421	35	1	let	let	VERB
ejpam-3421	35	2	g	g	NOUN
ejpam-3421	35	3	be	be	AUX
ejpam-3421	35	4	any	any	DET
ejpam-3421	35	5	graph	graph	NOUN
ejpam-3421	35	6	and	and	CCONJ
ejpam-3421	35	7	g	g	ADP
ejpam-3421	35	8	its	its	PRON
ejpam-3421	35	9	complement	complement	NOUN
ejpam-3421	35	10	.	.	PUNCT
ejpam-3421	36	1	let	let	VERB
ejpam-3421	36	2	v	v	NUM
ejpam-3421	36	3	∈	∈	PROPN
ejpam-3421	36	4	v	v	NOUN
ejpam-3421	36	5	(	(	PUNCT
ejpam-3421	36	6	g	g	NOUN
ejpam-3421	36	7	)	)	PUNCT
ejpam-3421	36	8	and	and	CCONJ
ejpam-3421	36	9	set	set	VERB
ejpam-3421	36	10	a	a	DET
ejpam-3421	36	11	=	=	PUNCT
ejpam-3421	36	12	∩u∈fg[v]ng(u	∩u∈fg[v]ng(u	NOUN
ejpam-3421	36	13	)	)	PUNCT
ejpam-3421	36	14	.	.	PUNCT
ejpam-3421	37	1	suppose	suppose	VERB
ejpam-3421	37	2	fg[v	fg[v	PROPN
ejpam-3421	37	3	]	]	X
ejpam-3421	37	4	=	=	PUNCT
ejpam-3421	37	5	∅.	∅.	PROPN
ejpam-3421	37	6	then	then	ADV
ejpam-3421	37	7	ng(v	ng(v	PUNCT
ejpam-3421	37	8	)	)	PUNCT
ejpam-3421	37	9	=	=	SYM
ejpam-3421	37	10	v	v	X
ejpam-3421	37	11	(	(	PUNCT
ejpam-3421	37	12	g)\{v	g)\{v	PROPN
ejpam-3421	37	13	}	}	PUNCT
ejpam-3421	37	14	.	.	PUNCT
ejpam-3421	38	1	hence	hence	ADV
ejpam-3421	38	2	,	,	PUNCT
ejpam-3421	38	3	v	v	PRON
ejpam-3421	38	4	is	be	AUX
ejpam-3421	38	5	an	an	DET
ejpam-3421	38	6	isolated	isolated	ADJ
ejpam-3421	38	7	vertex	vertex	NOUN
ejpam-3421	38	8	in	in	ADP
ejpam-3421	38	9	g.	g.	PROPN
ejpam-3421	38	10	thus	thus	ADV
ejpam-3421	38	11	,	,	PUNCT
ejpam-3421	38	12	f	f	PROPN
ejpam-3421	38	13	2	2	NUM
ejpam-3421	38	14	g	g	NOUN
ejpam-3421	38	15	[	[	X
ejpam-3421	38	16	v	v	X
ejpam-3421	38	17	]	]	X
ejpam-3421	38	18	=	=	PUNCT
ejpam-3421	38	19	ng(v	ng(v	X
ejpam-3421	38	20	)	)	PUNCT
ejpam-3421	38	21	.	.	PUNCT
ejpam-3421	39	1	suppose	suppose	VERB
ejpam-3421	39	2	fg[v	fg[v	PROPN
ejpam-3421	39	3	]	]	PUNCT
ejpam-3421	39	4	6=	6=	ADP
ejpam-3421	39	5	∅.	∅.	ADV
ejpam-3421	39	6	let	let	VERB
ejpam-3421	39	7	u	u	PROPN
ejpam-3421	39	8	∈	∈	PROPN
ejpam-3421	39	9	fg[v	fg[v	PROPN
ejpam-3421	39	10	]	]	PUNCT
ejpam-3421	39	11	.	.	PUNCT
ejpam-3421	40	1	then	then	ADV
ejpam-3421	40	2	u	u	PROPN
ejpam-3421	40	3	6=	6=	PROPN
ejpam-3421	40	4	v	v	NOUN
ejpam-3421	40	5	and	and	CCONJ
ejpam-3421	40	6	u	u	NOUN
ejpam-3421	40	7	/∈	/∈	PUNCT
ejpam-3421	40	8	ng(v	ng(v	NUM
ejpam-3421	40	9	)	)	PUNCT
ejpam-3421	40	10	.	.	PUNCT
ejpam-3421	41	1	hence	hence	ADV
ejpam-3421	41	2	,	,	PUNCT
ejpam-3421	41	3	u	u	PROPN
ejpam-3421	41	4	6=	6=	PROPN
ejpam-3421	41	5	v	v	NOUN
ejpam-3421	41	6	and	and	CCONJ
ejpam-3421	41	7	u	u	NOUN
ejpam-3421	41	8	∈	∈	PROPN
ejpam-3421	41	9	ng(v	ng(v	PRON
ejpam-3421	41	10	)	)	PUNCT
ejpam-3421	41	11	.	.	PUNCT
ejpam-3421	42	1	thus	thus	ADV
ejpam-3421	42	2	,	,	PUNCT
ejpam-3421	42	3	u	u	PROPN
ejpam-3421	42	4	∈	∈	PROPN
ejpam-3421	42	5	f	f	NOUN
ejpam-3421	42	6	2	2	NUM
ejpam-3421	42	7	g	g	NOUN
ejpam-3421	42	8	[	[	X
ejpam-3421	42	9	v	v	X
ejpam-3421	42	10	]	]	PUNCT
ejpam-3421	42	11	.	.	PUNCT
ejpam-3421	43	1	next	next	ADJ
ejpam-3421	43	2	,	,	PUNCT
ejpam-3421	43	3	let	let	VERB
ejpam-3421	43	4	w	w	PROPN
ejpam-3421	43	5	∈	∈	VERB
ejpam-3421	43	6	a.	a.	NOUN
ejpam-3421	43	7	then	then	ADV
ejpam-3421	43	8	w	w	PROPN
ejpam-3421	43	9	∈	∈	PROPN
ejpam-3421	43	10	ng(u	ng(u	NOUN
ejpam-3421	43	11	)	)	PUNCT
ejpam-3421	43	12	for	for	ADP
ejpam-3421	43	13	all	all	DET
ejpam-3421	43	14	u	u	PROPN
ejpam-3421	43	15	∈	∈	PROPN
ejpam-3421	43	16	fg[v	fg[v	PROPN
ejpam-3421	43	17	]	]	X
ejpam-3421	43	18	.	.	PUNCT
ejpam-3421	44	1	since	since	SCONJ
ejpam-3421	44	2	u	u	PROPN
ejpam-3421	44	3	/∈	/∈	PUNCT
ejpam-3421	44	4	ng(v	ng(v	NUM
ejpam-3421	44	5	)	)	PUNCT
ejpam-3421	44	6	,	,	PUNCT
ejpam-3421	44	7	it	it	PRON
ejpam-3421	44	8	follows	follow	VERB
ejpam-3421	44	9	that	that	PRON
ejpam-3421	44	10	w	w	PROPN
ejpam-3421	44	11	6=	6=	PROPN
ejpam-3421	44	12	v.	v.	ADP
ejpam-3421	44	13	also	also	ADV
ejpam-3421	44	14	,	,	PUNCT
ejpam-3421	44	15	w	w	PROPN
ejpam-3421	44	16	/∈	/∈	PROPN
ejpam-3421	44	17	ng(u	ng(u	NOUN
ejpam-3421	44	18	)	)	PUNCT
ejpam-3421	44	19	for	for	ADP
ejpam-3421	44	20	all	all	DET
ejpam-3421	44	21	u	u	PROPN
ejpam-3421	44	22	∈	∈	PROPN
ejpam-3421	44	23	ng(v	ng(v	PUNCT
ejpam-3421	44	24	)	)	PUNCT
ejpam-3421	44	25	.	.	PUNCT
ejpam-3421	45	1	it	it	PRON
ejpam-3421	45	2	implies	imply	VERB
ejpam-3421	45	3	that	that	SCONJ
ejpam-3421	45	4	dg(w	dg(w	NUM
ejpam-3421	45	5	,	,	PUNCT
ejpam-3421	45	6	v	v	NOUN
ejpam-3421	45	7	)	)	PUNCT
ejpam-3421	45	8	6=	6=	ADP
ejpam-3421	45	9	2	2	NUM
ejpam-3421	45	10	.	.	X
ejpam-3421	46	1	hence	hence	ADV
ejpam-3421	46	2	,	,	PUNCT
ejpam-3421	46	3	w	w	PROPN
ejpam-3421	46	4	∈	∈	PROPN
ejpam-3421	46	5	f	f	NOUN
ejpam-3421	46	6	2	2	NUM
ejpam-3421	46	7	g	g	NOUN
ejpam-3421	46	8	[	[	X
ejpam-3421	46	9	v	v	X
ejpam-3421	46	10	]	]	X
ejpam-3421	46	11	.	.	PUNCT
ejpam-3421	47	1	consequently	consequently	ADV
ejpam-3421	47	2	,	,	PUNCT
ejpam-3421	47	3	fg[v	fg[v	PROPN
ejpam-3421	47	4	]	]	PUNCT
ejpam-3421	47	5	∪	∪	ADP
ejpam-3421	47	6	[	[	X
ejpam-3421	47	7	∩u∈fg[v]ng(u	∩u∈fg[v]ng(u	NOUN
ejpam-3421	47	8	)	)	PUNCT
ejpam-3421	47	9	]	]	PUNCT
ejpam-3421	48	1	⊆	⊆	NUM
ejpam-3421	48	2	f	f	SYM
ejpam-3421	48	3	2	2	NUM
ejpam-3421	48	4	g	g	NOUN
ejpam-3421	48	5	[	[	X
ejpam-3421	48	6	v	v	X
ejpam-3421	48	7	]	]	PUNCT
ejpam-3421	48	8	.	.	PUNCT
ejpam-3421	49	1	next	next	ADJ
ejpam-3421	49	2	,	,	PUNCT
ejpam-3421	49	3	let	let	VERB
ejpam-3421	49	4	x	x	PUNCT
ejpam-3421	49	5	∈	∈	NOUN
ejpam-3421	49	6	f	f	NOUN
ejpam-3421	49	7	2	2	NUM
ejpam-3421	49	8	g	g	NOUN
ejpam-3421	49	9	[	[	X
ejpam-3421	49	10	v	v	NOUN
ejpam-3421	49	11	]	]	PUNCT
ejpam-3421	49	12	.	.	PUNCT
ejpam-3421	50	1	then	then	ADV
ejpam-3421	50	2	x	x	X
ejpam-3421	50	3	6=	6=	ADP
ejpam-3421	50	4	v	v	NOUN
ejpam-3421	50	5	and	and	CCONJ
ejpam-3421	50	6	x	x	ADJ
ejpam-3421	50	7	/∈	/∈	PUNCT
ejpam-3421	50	8	n2	n2	PROPN
ejpam-3421	50	9	g	g	PROPN
ejpam-3421	50	10	(	(	PUNCT
ejpam-3421	50	11	v	v	NOUN
ejpam-3421	50	12	)	)	PUNCT
ejpam-3421	50	13	.	.	PUNCT
ejpam-3421	51	1	if	if	SCONJ
ejpam-3421	51	2	x	x	PROPN
ejpam-3421	51	3	∈	∈	PROPN
ejpam-3421	51	4	fg[v	fg[v	PROPN
ejpam-3421	51	5	]	]	X
ejpam-3421	51	6	,	,	PUNCT
ejpam-3421	51	7	then	then	ADV
ejpam-3421	51	8	we	we	PRON
ejpam-3421	51	9	are	be	AUX
ejpam-3421	51	10	done	do	VERB
ejpam-3421	51	11	.	.	PUNCT
ejpam-3421	52	1	suppose	suppose	VERB
ejpam-3421	52	2	x	x	X
ejpam-3421	52	3	/∈	/∈	PUNCT
ejpam-3421	52	4	fg[v	fg[v	PROPN
ejpam-3421	52	5	]	]	PUNCT
ejpam-3421	52	6	.	.	PUNCT
ejpam-3421	53	1	then	then	ADV
ejpam-3421	53	2	x	x	SYM
ejpam-3421	53	3	∈	∈	NOUN
ejpam-3421	53	4	ng(v	ng(v	NOUN
ejpam-3421	53	5	)	)	PUNCT
ejpam-3421	53	6	.	.	PUNCT
ejpam-3421	54	1	suppose	suppose	VERB
ejpam-3421	54	2	further	far	ADV
ejpam-3421	54	3	that	that	SCONJ
ejpam-3421	54	4	there	there	PRON
ejpam-3421	54	5	exists	exist	VERB
ejpam-3421	54	6	u	u	PROPN
ejpam-3421	54	7	∈	∈	PROPN
ejpam-3421	54	8	fg[v	fg[v	PROPN
ejpam-3421	54	9	]	]	X
ejpam-3421	54	10	such	such	ADJ
ejpam-3421	54	11	that	that	SCONJ
ejpam-3421	54	12	x	x	SYM
ejpam-3421	54	13	/∈	/∈	PUNCT
ejpam-3421	54	14	ng(u	ng(u	NOUN
ejpam-3421	54	15	)	)	PUNCT
ejpam-3421	54	16	.	.	PUNCT
ejpam-3421	55	1	thus	thus	ADV
ejpam-3421	55	2	,	,	PUNCT
ejpam-3421	55	3	u	u	PROPN
ejpam-3421	55	4	∈	∈	PROPN
ejpam-3421	55	5	ng(v	ng(v	PUNCT
ejpam-3421	55	6	)	)	PUNCT
ejpam-3421	55	7	and	and	CCONJ
ejpam-3421	55	8	x	x	PROPN
ejpam-3421	55	9	∈	∈	PROPN
ejpam-3421	55	10	ng(u	ng(u	NOUN
ejpam-3421	55	11	)	)	PUNCT
ejpam-3421	55	12	.	.	PUNCT
ejpam-3421	56	1	also	also	ADV
ejpam-3421	56	2	,	,	PUNCT
ejpam-3421	56	3	since	since	SCONJ
ejpam-3421	56	4	x	x	PROPN
ejpam-3421	56	5	∈	∈	PROPN
ejpam-3421	56	6	ng(v	ng(v	NOUN
ejpam-3421	56	7	)	)	PUNCT
ejpam-3421	56	8	,	,	PUNCT
ejpam-3421	56	9	x	x	X
ejpam-3421	56	10	/∈	/∈	PUNCT
ejpam-3421	56	11	ng(v	ng(v	NUM
ejpam-3421	56	12	)	)	PUNCT
ejpam-3421	56	13	.	.	PUNCT
ejpam-3421	57	1	thus	thus	ADV
ejpam-3421	57	2	,	,	PUNCT
ejpam-3421	57	3	dg(x	dg(x	X
ejpam-3421	57	4	,	,	PUNCT
ejpam-3421	57	5	v	v	NOUN
ejpam-3421	57	6	)	)	PUNCT
ejpam-3421	57	7	=	=	SYM
ejpam-3421	57	8	2	2	NUM
ejpam-3421	57	9	,	,	PUNCT
ejpam-3421	57	10	that	that	ADV
ejpam-3421	57	11	is	is	ADV
ejpam-3421	57	12	,	,	PUNCT
ejpam-3421	57	13	x	x	SYM
ejpam-3421	57	14	∈	∈	PROPN
ejpam-3421	57	15	n2	n2	NOUN
ejpam-3421	57	16	g	g	PROPN
ejpam-3421	57	17	(	(	PUNCT
ejpam-3421	57	18	v	v	NOUN
ejpam-3421	57	19	)	)	PUNCT
ejpam-3421	57	20	,	,	PUNCT
ejpam-3421	57	21	a	a	DET
ejpam-3421	57	22	contradiction	contradiction	NOUN
ejpam-3421	57	23	.	.	PUNCT
ejpam-3421	58	1	therefore	therefore	ADV
ejpam-3421	58	2	,	,	PUNCT
ejpam-3421	58	3	x	x	PROPN
ejpam-3421	58	4	∈	∈	PROPN
ejpam-3421	58	5	ng(u	ng(u	NOUN
ejpam-3421	58	6	)	)	PUNCT
ejpam-3421	58	7	for	for	ADP
ejpam-3421	58	8	all	all	DET
ejpam-3421	58	9	u	u	PROPN
ejpam-3421	58	10	∈	∈	PROPN
ejpam-3421	58	11	fg[v	fg[v	PROPN
ejpam-3421	58	12	]	]	PUNCT
ejpam-3421	58	13	.	.	PUNCT
ejpam-3421	59	1	this	this	PRON
ejpam-3421	59	2	shows	show	VERB
ejpam-3421	59	3	that	that	SCONJ
ejpam-3421	59	4	x	x	SYM
ejpam-3421	59	5	∈	∈	NOUN
ejpam-3421	59	6	a.	a.	NOUN
ejpam-3421	59	7	accordingly	accordingly	ADV
ejpam-3421	59	8	,	,	PUNCT
ejpam-3421	59	9	f	f	PROPN
ejpam-3421	59	10	2	2	NUM
ejpam-3421	59	11	g	g	NOUN
ejpam-3421	59	12	[	[	X
ejpam-3421	59	13	v	v	X
ejpam-3421	59	14	]	]	X
ejpam-3421	59	15	⊆	⊆	NUM
ejpam-3421	59	16	fg[v	fg[v	NOUN
ejpam-3421	59	17	]	]	PUNCT
ejpam-3421	59	18	∪	∪	ADP
ejpam-3421	59	19	[	[	X
ejpam-3421	59	20	∩u∈fg[v]ng(u	∩u∈fg[v]ng(u	X
ejpam-3421	59	21	)	)	PUNCT
ejpam-3421	59	22	]	]	PUNCT
ejpam-3421	59	23	.	.	PUNCT
ejpam-3421	60	1	this	this	PRON
ejpam-3421	60	2	establishes	establish	VERB
ejpam-3421	60	3	the	the	DET
ejpam-3421	60	4	desired	desire	VERB
ejpam-3421	60	5	equality	equality	NOUN
ejpam-3421	60	6	.	.	PUNCT
ejpam-3421	61	1	theorem	theorem	NOUN
ejpam-3421	61	2	2	2	NUM
ejpam-3421	61	3	.	.	PUNCT
ejpam-3421	62	1	let	let	VERB
ejpam-3421	62	2	g	g	NOUN
ejpam-3421	62	3	be	be	AUX
ejpam-3421	62	4	any	any	DET
ejpam-3421	62	5	graph	graph	NOUN
ejpam-3421	62	6	and	and	CCONJ
ejpam-3421	62	7	g	g	ADP
ejpam-3421	62	8	its	its	PRON
ejpam-3421	62	9	complement	complement	NOUN
ejpam-3421	62	10	.	.	PUNCT
ejpam-3421	63	1	if	if	SCONJ
ejpam-3421	63	2	v	v	NOUN
ejpam-3421	63	3	is	be	AUX
ejpam-3421	63	4	an	an	DET
ejpam-3421	63	5	isolated	isolated	ADJ
ejpam-3421	63	6	vertex	vertex	NOUN
ejpam-3421	63	7	of	of	ADP
ejpam-3421	63	8	g	g	PROPN
ejpam-3421	63	9	(	(	PUNCT
ejpam-3421	63	10	or	or	CCONJ
ejpam-3421	63	11	of	of	ADP
ejpam-3421	63	12	g	g	NOUN
ejpam-3421	63	13	)	)	PUNCT
ejpam-3421	63	14	,	,	PUNCT
ejpam-3421	63	15	then	then	ADV
ejpam-3421	63	16	{	{	PUNCT
ejpam-3421	63	17	v	v	NOUN
ejpam-3421	63	18	}	}	PUNCT
ejpam-3421	63	19	∈	∈	PROPN
ejpam-3421	63	20	τg	τg	NOUN
ejpam-3421	63	21	∩	∩	PROPN
ejpam-3421	63	22	τg	τg	PROPN
ejpam-3421	63	23	.	.	PUNCT
ejpam-3421	63	24	proof	proof	NOUN
ejpam-3421	63	25	.	.	PUNCT
ejpam-3421	64	1	suppose	suppose	VERB
ejpam-3421	64	2	v	v	NOUN
ejpam-3421	64	3	is	be	AUX
ejpam-3421	64	4	an	an	DET
ejpam-3421	64	5	isolated	isolated	ADJ
ejpam-3421	64	6	vertex	vertex	NOUN
ejpam-3421	64	7	of	of	ADP
ejpam-3421	64	8	g	g	PROPN
ejpam-3421	64	9	(	(	PUNCT
ejpam-3421	64	10	or	or	CCONJ
ejpam-3421	64	11	of	of	ADP
ejpam-3421	64	12	g	g	NOUN
ejpam-3421	64	13	)	)	PUNCT
ejpam-3421	64	14	.	.	PUNCT
ejpam-3421	65	1	then	then	ADV
ejpam-3421	65	2	{	{	PUNCT
ejpam-3421	65	3	v	v	NOUN
ejpam-3421	65	4	}	}	PUNCT
ejpam-3421	65	5	=	=	SYM
ejpam-3421	65	6	f	f	PROPN
ejpam-3421	65	7	2	2	NUM
ejpam-3421	65	8	g[v	g[v	NOUN
ejpam-3421	65	9	(	(	PUNCT
ejpam-3421	65	10	g)\{v	g)\{v	PROPN
ejpam-3421	65	11	}	}	PUNCT
ejpam-3421	65	12	]	]	PUNCT
ejpam-3421	66	1	=	=	SYM
ejpam-3421	66	2	f	f	PROPN
ejpam-3421	66	3	2	2	NUM
ejpam-3421	66	4	g[v	g[v	NOUN
ejpam-3421	66	5	(	(	PUNCT
ejpam-3421	66	6	g)\{v	g)\{v	PROPN
ejpam-3421	66	7	}	}	PUNCT
ejpam-3421	66	8	]	]	PUNCT
ejpam-3421	66	9	and	and	CCONJ
ejpam-3421	66	10	so	so	ADV
ejpam-3421	66	11	,	,	PUNCT
ejpam-3421	66	12	{	{	PUNCT
ejpam-3421	66	13	v	v	NOUN
ejpam-3421	66	14	}	}	PUNCT
ejpam-3421	66	15	∈	∈	PROPN
ejpam-3421	66	16	bg	bg	PROPN
ejpam-3421	66	17	and	and	CCONJ
ejpam-3421	66	18	{	{	PUNCT
ejpam-3421	66	19	v	v	NOUN
ejpam-3421	66	20	}	}	PUNCT
ejpam-3421	66	21	∈	∈	PROPN
ejpam-3421	66	22	bg	bg	PROPN
ejpam-3421	66	23	.	.	PUNCT
ejpam-3421	67	1	thus	thus	ADV
ejpam-3421	67	2	,	,	PUNCT
ejpam-3421	67	3	{	{	PUNCT
ejpam-3421	67	4	v	v	NOUN
ejpam-3421	67	5	}	}	PUNCT
ejpam-3421	67	6	∈	∈	PROPN
ejpam-3421	67	7	τg	τg	NOUN
ejpam-3421	67	8	and	and	CCONJ
ejpam-3421	67	9	{	{	PUNCT
ejpam-3421	67	10	v	v	NOUN
ejpam-3421	67	11	}	}	PUNCT
ejpam-3421	67	12	∈	∈	PROPN
ejpam-3421	67	13	τg	τg	NOUN
ejpam-3421	67	14	.	.	PUNCT
ejpam-3421	68	1	therefore	therefore	ADV
ejpam-3421	68	2	,	,	PUNCT
ejpam-3421	68	3	{	{	PUNCT
ejpam-3421	68	4	v	v	NOUN
ejpam-3421	68	5	}	}	PUNCT
ejpam-3421	68	6	∈	∈	PROPN
ejpam-3421	68	7	τg	τg	NOUN
ejpam-3421	68	8	∩	∩	PROPN
ejpam-3421	68	9	τg	τg	PROPN
ejpam-3421	68	10	.	.	PUNCT
ejpam-3421	68	11	c.	c.	PROPN
ejpam-3421	68	12	nianga	nianga	PROPN
ejpam-3421	68	13	,	,	PUNCT
ejpam-3421	68	14	s.	s.	PROPN
ejpam-3421	68	15	canoy	canoy	PROPN
ejpam-3421	68	16	/	/	SYM
ejpam-3421	68	17	eur	eur	PROPN
ejpam-3421	68	18	.	.	PUNCT
ejpam-3421	69	1	j.	j.	PROPN
ejpam-3421	69	2	pure	pure	PROPN
ejpam-3421	69	3	appl	appl	PROPN
ejpam-3421	69	4	.	.	PROPN
ejpam-3421	69	5	math	math	PROPN
ejpam-3421	69	6	,	,	PUNCT
ejpam-3421	69	7	12	12	NUM
ejpam-3421	69	8	(	(	PUNCT
ejpam-3421	69	9	2	2	NUM
ejpam-3421	69	10	)	)	PUNCT
ejpam-3421	69	11	(	(	PUNCT
ejpam-3421	69	12	2019	2019	NUM
ejpam-3421	69	13	)	)	PUNCT
ejpam-3421	69	14	,	,	PUNCT
ejpam-3421	69	15	499	499	NUM
ejpam-3421	69	16	-	-	SYM
ejpam-3421	69	17	505	505	NUM
ejpam-3421	69	18	501	501	NUM
ejpam-3421	69	19	remark	remark	NOUN
ejpam-3421	69	20	1	1	NUM
ejpam-3421	69	21	.	.	PUNCT
ejpam-3421	70	1	the	the	DET
ejpam-3421	70	2	converse	converse	NOUN
ejpam-3421	70	3	of	of	ADP
ejpam-3421	70	4	theorem	theorem	NOUN
ejpam-3421	70	5	17	17	NUM
ejpam-3421	70	6	is	be	AUX
ejpam-3421	70	7	not	not	PART
ejpam-3421	70	8	true	true	ADJ
ejpam-3421	70	9	.	.	PUNCT
ejpam-3421	71	1	consider	consider	VERB
ejpam-3421	71	2	g	g	NOUN
ejpam-3421	71	3	=	=	SYM
ejpam-3421	71	4	p5	p5	PROPN
ejpam-3421	71	5	=	=	PUNCT
ejpam-3421	72	1	[	[	X
ejpam-3421	72	2	a	a	PRON
ejpam-3421	72	3	,	,	PUNCT
ejpam-3421	72	4	b	b	NOUN
ejpam-3421	72	5	,	,	PUNCT
ejpam-3421	72	6	c	c	NOUN
ejpam-3421	72	7	,	,	PUNCT
ejpam-3421	72	8	d	d	NOUN
ejpam-3421	72	9	,	,	PUNCT
ejpam-3421	72	10	e	e	NOUN
ejpam-3421	72	11	]	]	PUNCT
ejpam-3421	72	12	.	.	PUNCT
ejpam-3421	73	1	then	then	ADV
ejpam-3421	73	2	{	{	PUNCT
ejpam-3421	73	3	e	e	NOUN
ejpam-3421	73	4	}	}	PUNCT
ejpam-3421	73	5	=	=	SYM
ejpam-3421	73	6	f	f	PROPN
ejpam-3421	73	7	2	2	NUM
ejpam-3421	73	8	g[a	g[a	ADJ
ejpam-3421	73	9	,	,	PUNCT
ejpam-3421	73	10	b	b	NOUN
ejpam-3421	73	11	]	]	PUNCT
ejpam-3421	73	12	and	and	CCONJ
ejpam-3421	73	13	{	{	PUNCT
ejpam-3421	73	14	e	e	NOUN
ejpam-3421	73	15	}	}	PUNCT
ejpam-3421	73	16	=	=	SYM
ejpam-3421	73	17	fg[a	fg[a	PROPN
ejpam-3421	73	18	,	,	PUNCT
ejpam-3421	73	19	c	c	NOUN
ejpam-3421	73	20	]	]	PUNCT
ejpam-3421	73	21	.	.	PUNCT
ejpam-3421	74	1	however	however	ADV
ejpam-3421	74	2	,	,	PUNCT
ejpam-3421	74	3	e	e	PROPN
ejpam-3421	74	4	is	be	AUX
ejpam-3421	74	5	not	not	PART
ejpam-3421	74	6	an	an	DET
ejpam-3421	74	7	isolated	isolated	ADJ
ejpam-3421	74	8	vertex	vertex	NOUN
ejpam-3421	74	9	of	of	ADP
ejpam-3421	74	10	g	g	NOUN
ejpam-3421	74	11	nor	nor	CCONJ
ejpam-3421	74	12	of	of	ADP
ejpam-3421	74	13	g.	g.	NOUN
ejpam-3421	74	14	definition	definition	NOUN
ejpam-3421	74	15	2	2	NUM
ejpam-3421	74	16	.	.	PUNCT
ejpam-3421	75	1	the	the	DET
ejpam-3421	75	2	join	join	NOUN
ejpam-3421	75	3	g1	g1	PROPN
ejpam-3421	75	4	+	+	CCONJ
ejpam-3421	75	5	g2	g2	NOUN
ejpam-3421	75	6	of	of	ADP
ejpam-3421	75	7	graphs	graph	NOUN
ejpam-3421	75	8	g1	g1	PROPN
ejpam-3421	75	9	and	and	CCONJ
ejpam-3421	75	10	g2	g2	PROPN
ejpam-3421	75	11	is	be	AUX
ejpam-3421	75	12	the	the	DET
ejpam-3421	75	13	graph	graph	NOUN
ejpam-3421	75	14	g	g	NOUN
ejpam-3421	75	15	with	with	ADP
ejpam-3421	75	16	v	v	NOUN
ejpam-3421	75	17	(	(	PUNCT
ejpam-3421	75	18	g	g	NOUN
ejpam-3421	75	19	)	)	PUNCT
ejpam-3421	75	20	=	=	NOUN
ejpam-3421	75	21	v	v	X
ejpam-3421	75	22	(	(	PUNCT
ejpam-3421	75	23	g1	g1	PROPN
ejpam-3421	75	24	)	)	PUNCT
ejpam-3421	75	25	∪	∪	NOUN
ejpam-3421	75	26	v	v	PROPN
ejpam-3421	75	27	(	(	PUNCT
ejpam-3421	75	28	g2	g2	PROPN
ejpam-3421	75	29	)	)	PUNCT
ejpam-3421	75	30	and	and	CCONJ
ejpam-3421	75	31	e(g	e(g	PROPN
ejpam-3421	75	32	)	)	PUNCT
ejpam-3421	75	33	=	=	SYM
ejpam-3421	75	34	e(g1	e(g1	X
ejpam-3421	75	35	)	)	PUNCT
ejpam-3421	75	36	∪	∪	ADP
ejpam-3421	75	37	e(g2	e(g2	ADV
ejpam-3421	75	38	)	)	PUNCT
ejpam-3421	75	39	∪	∪	NOUN
ejpam-3421	75	40	{	{	PUNCT
ejpam-3421	75	41	uv	uv	NOUN
ejpam-3421	75	42	:	:	PUNCT
ejpam-3421	75	43	u	u	PROPN
ejpam-3421	75	44	∈	∈	PROPN
ejpam-3421	75	45	v	v	NOUN
ejpam-3421	75	46	(	(	PUNCT
ejpam-3421	75	47	g1	g1	PROPN
ejpam-3421	75	48	)	)	PUNCT
ejpam-3421	75	49	and	and	CCONJ
ejpam-3421	75	50	v	v	ADP
ejpam-3421	75	51	∈	∈	PROPN
ejpam-3421	75	52	v(g2	v(g2	X
ejpam-3421	75	53	)	)	PUNCT
ejpam-3421	75	54	}	}	PUNCT
ejpam-3421	75	55	.	.	PUNCT
ejpam-3421	76	1	theorem	theorem	NOUN
ejpam-3421	76	2	3	3	X
ejpam-3421	76	3	.	.	PUNCT
ejpam-3421	77	1	let	let	VERB
ejpam-3421	77	2	g	g	PROPN
ejpam-3421	77	3	=	=	SYM
ejpam-3421	77	4	(	(	PUNCT
ejpam-3421	77	5	v	v	NOUN
ejpam-3421	77	6	(	(	PUNCT
ejpam-3421	77	7	g	g	NOUN
ejpam-3421	77	8	)	)	PUNCT
ejpam-3421	77	9	,	,	PUNCT
ejpam-3421	77	10	e(g	e(g	PROPN
ejpam-3421	77	11	)	)	PUNCT
ejpam-3421	77	12	)	)	PUNCT
ejpam-3421	78	1	and	and	CCONJ
ejpam-3421	78	2	h	h	NOUN
ejpam-3421	78	3	=	=	SYM
ejpam-3421	78	4	(	(	PUNCT
ejpam-3421	78	5	v	v	NOUN
ejpam-3421	78	6	(	(	PUNCT
ejpam-3421	78	7	h	h	NOUN
ejpam-3421	78	8	)	)	PUNCT
ejpam-3421	78	9	,	,	PUNCT
ejpam-3421	78	10	e(h	e(h	PROPN
ejpam-3421	78	11	)	)	PUNCT
ejpam-3421	78	12	)	)	PUNCT
ejpam-3421	78	13	be	be	AUX
ejpam-3421	78	14	graphs	graph	NOUN
ejpam-3421	78	15	and	and	CCONJ
ejpam-3421	78	16	let	let	VERB
ejpam-3421	78	17	∅	∅	NOUN
ejpam-3421	78	18	6=	6=	ADP
ejpam-3421	78	19	a	a	DET
ejpam-3421	78	20	⊆	⊆	NUM
ejpam-3421	78	21	v	v	NOUN
ejpam-3421	78	22	(	(	PUNCT
ejpam-3421	78	23	g	g	NOUN
ejpam-3421	78	24	)	)	PUNCT
ejpam-3421	78	25	and	and	CCONJ
ejpam-3421	78	26	∅	∅	NOUN
ejpam-3421	78	27	6=	6=	ADP
ejpam-3421	78	28	b	b	X
ejpam-3421	78	29	⊆	⊆	NUM
ejpam-3421	78	30	v	v	NOUN
ejpam-3421	78	31	(	(	PUNCT
ejpam-3421	78	32	h	h	NOUN
ejpam-3421	78	33	)	)	PUNCT
ejpam-3421	78	34	.	.	PUNCT
ejpam-3421	79	1	then	then	ADV
ejpam-3421	79	2	(	(	PUNCT
ejpam-3421	79	3	i	i	NOUN
ejpam-3421	79	4	)	)	PUNCT
ejpam-3421	79	5	f	f	PROPN
ejpam-3421	79	6	2	2	NUM
ejpam-3421	79	7	g+h	g+h	PROPN
ejpam-3421	80	1	[	[	X
ejpam-3421	80	2	a	a	X
ejpam-3421	80	3	]	]	X
ejpam-3421	80	4	=	=	SYM
ejpam-3421	80	5	v	v	ADJ
ejpam-3421	80	6	(	(	PUNCT
ejpam-3421	80	7	h	h	NOUN
ejpam-3421	80	8	)	)	PUNCT
ejpam-3421	80	9	∪	∪	ADP
ejpam-3421	80	10	[	[	X
ejpam-3421	80	11	∩a∈ang(a	∩a∈ang(a	PROPN
ejpam-3421	80	12	)	)	PUNCT
ejpam-3421	80	13	]	]	PUNCT
ejpam-3421	80	14	;	;	PUNCT
ejpam-3421	80	15	(	(	PUNCT
ejpam-3421	80	16	ii	ii	NOUN
ejpam-3421	80	17	)	)	PUNCT
ejpam-3421	80	18	f	f	PROPN
ejpam-3421	80	19	2	2	NUM
ejpam-3421	80	20	g+h	g+h	PROPN
ejpam-3421	81	1	[	[	X
ejpam-3421	81	2	b	b	X
ejpam-3421	81	3	]	]	X
ejpam-3421	81	4	=	=	SYM
ejpam-3421	81	5	v	v	X
ejpam-3421	81	6	(	(	PUNCT
ejpam-3421	81	7	g	g	NOUN
ejpam-3421	81	8	)	)	PUNCT
ejpam-3421	81	9	∪	∪	ADP
ejpam-3421	81	10	[	[	X
ejpam-3421	81	11	∩b∈bnh(b	∩b∈bnh(b	ADJ
ejpam-3421	81	12	)	)	PUNCT
ejpam-3421	81	13	]	]	PUNCT
ejpam-3421	81	14	and	and	CCONJ
ejpam-3421	81	15	(	(	PUNCT
ejpam-3421	81	16	iii	iii	X
ejpam-3421	81	17	)	)	PUNCT
ejpam-3421	81	18	f	f	PROPN
ejpam-3421	81	19	2	2	NUM
ejpam-3421	81	20	g[∅	g[∅	PROPN
ejpam-3421	81	21	]	]	X
ejpam-3421	81	22	=	=	SYM
ejpam-3421	81	23	v	v	X
ejpam-3421	81	24	(	(	PUNCT
ejpam-3421	81	25	g	g	NOUN
ejpam-3421	81	26	)	)	PUNCT
ejpam-3421	81	27	∪	∪	NOUN
ejpam-3421	81	28	v	v	NOUN
ejpam-3421	81	29	(	(	PUNCT
ejpam-3421	81	30	h	h	NOUN
ejpam-3421	81	31	)	)	PUNCT
ejpam-3421	81	32	.	.	PUNCT
ejpam-3421	82	1	proof	proof	NOUN
ejpam-3421	82	2	.	.	PUNCT
ejpam-3421	83	1	let	let	VERB
ejpam-3421	83	2	g	g	PROPN
ejpam-3421	83	3	=	=	SYM
ejpam-3421	83	4	(	(	PUNCT
ejpam-3421	83	5	v	v	NOUN
ejpam-3421	83	6	(	(	PUNCT
ejpam-3421	83	7	g	g	NOUN
ejpam-3421	83	8	)	)	PUNCT
ejpam-3421	83	9	,	,	PUNCT
ejpam-3421	83	10	e(g	e(g	PROPN
ejpam-3421	83	11	)	)	PUNCT
ejpam-3421	83	12	)	)	PUNCT
ejpam-3421	83	13	and	and	CCONJ
ejpam-3421	83	14	h	h	NOUN
ejpam-3421	83	15	=	=	SYM
ejpam-3421	83	16	(	(	PUNCT
ejpam-3421	83	17	v	v	NOUN
ejpam-3421	83	18	(	(	PUNCT
ejpam-3421	83	19	h	h	NOUN
ejpam-3421	83	20	)	)	PUNCT
ejpam-3421	83	21	,	,	PUNCT
ejpam-3421	83	22	e(h	e(h	PROPN
ejpam-3421	83	23	)	)	PUNCT
ejpam-3421	83	24	)	)	PUNCT
ejpam-3421	83	25	be	be	AUX
ejpam-3421	83	26	graphs	graph	NOUN
ejpam-3421	83	27	.	.	PUNCT
ejpam-3421	84	1	let	let	VERB
ejpam-3421	84	2	∅	∅	NOUN
ejpam-3421	84	3	6=	6=	ADP
ejpam-3421	84	4	a	a	DET
ejpam-3421	84	5	⊆	⊆	NUM
ejpam-3421	84	6	v	v	NOUN
ejpam-3421	84	7	(	(	PUNCT
ejpam-3421	84	8	g	g	NOUN
ejpam-3421	84	9	)	)	PUNCT
ejpam-3421	84	10	and	and	CCONJ
ejpam-3421	84	11	∅	∅	NOUN
ejpam-3421	84	12	6=	6=	ADP
ejpam-3421	84	13	b	b	X
ejpam-3421	84	14	⊆	⊆	NUM
ejpam-3421	84	15	v	v	NOUN
ejpam-3421	84	16	(	(	PUNCT
ejpam-3421	84	17	h	h	NOUN
ejpam-3421	84	18	)	)	PUNCT
ejpam-3421	84	19	.	.	PUNCT
ejpam-3421	85	1	(	(	PUNCT
ejpam-3421	85	2	i	i	NOUN
ejpam-3421	85	3	)	)	PUNCT
ejpam-3421	85	4	note	note	VERB
ejpam-3421	85	5	that	that	DET
ejpam-3421	85	6	n2	n2	NOUN
ejpam-3421	85	7	g+h	g+h	PROPN
ejpam-3421	86	1	[	[	X
ejpam-3421	86	2	a	a	X
ejpam-3421	86	3	]	]	X
ejpam-3421	86	4	=	=	PUNCT
ejpam-3421	86	5	a	a	DET
ejpam-3421	86	6	∪	∪	X
ejpam-3421	86	7	{	{	PUNCT
ejpam-3421	86	8	v	v	NOUN
ejpam-3421	86	9	∈	∈	NOUN
ejpam-3421	86	10	v	v	NOUN
ejpam-3421	86	11	(	(	PUNCT
ejpam-3421	86	12	g+h	g+h	PROPN
ejpam-3421	86	13	)	)	PUNCT
ejpam-3421	86	14	:	:	PUNCT
ejpam-3421	87	1	dg+h(v	dg+h(v	VERB
ejpam-3421	87	2	,	,	PUNCT
ejpam-3421	87	3	a	a	PRON
ejpam-3421	87	4	)	)	PUNCT
ejpam-3421	87	5	=	=	SYM
ejpam-3421	87	6	2	2	NUM
ejpam-3421	87	7	for	for	ADP
ejpam-3421	87	8	some	some	DET
ejpam-3421	87	9	a	a	DET
ejpam-3421	87	10	∈	∈	PROPN
ejpam-3421	87	11	a	a	PRON
ejpam-3421	87	12	}	}	PUNCT
ejpam-3421	87	13	.	.	PUNCT
ejpam-3421	88	1	since	since	SCONJ
ejpam-3421	88	2	v	v	NOUN
ejpam-3421	88	3	(	(	PUNCT
ejpam-3421	88	4	h	h	NOUN
ejpam-3421	88	5	)	)	PUNCT
ejpam-3421	88	6	⊆	⊆	NUM
ejpam-3421	88	7	ng+h(a	ng+h(a	NUM
ejpam-3421	88	8	)	)	PUNCT
ejpam-3421	88	9	,	,	PUNCT
ejpam-3421	88	10	n2	n2	NOUN
ejpam-3421	88	11	g+h	g+h	PROPN
ejpam-3421	89	1	[	[	X
ejpam-3421	89	2	a	a	X
ejpam-3421	89	3	]	]	X
ejpam-3421	89	4	=	=	PUNCT
ejpam-3421	89	5	a	a	DET
ejpam-3421	89	6	∪	∪	X
ejpam-3421	89	7	{	{	PUNCT
ejpam-3421	89	8	v	v	NOUN
ejpam-3421	89	9	∈	∈	NOUN
ejpam-3421	89	10	v	v	NOUN
ejpam-3421	89	11	(	(	PUNCT
ejpam-3421	89	12	g	g	NOUN
ejpam-3421	89	13	)	)	PUNCT
ejpam-3421	89	14	:	:	PUNCT
ejpam-3421	90	1	dg+h(v	dg+h(v	VERB
ejpam-3421	90	2	,	,	PUNCT
ejpam-3421	90	3	a	a	PRON
ejpam-3421	90	4	)	)	PUNCT
ejpam-3421	90	5	=	=	SYM
ejpam-3421	90	6	2	2	NUM
ejpam-3421	90	7	for	for	ADP
ejpam-3421	90	8	some	some	DET
ejpam-3421	90	9	a	a	DET
ejpam-3421	90	10	∈	∈	PROPN
ejpam-3421	90	11	a	a	PRON
ejpam-3421	90	12	}	}	PUNCT
ejpam-3421	90	13	=	=	PUNCT
ejpam-3421	90	14	a	a	DET
ejpam-3421	90	15	∪	∪	ADJ
ejpam-3421	90	16	{	{	PUNCT
ejpam-3421	90	17	v	v	NOUN
ejpam-3421	90	18	∈	∈	NOUN
ejpam-3421	90	19	v	v	NOUN
ejpam-3421	90	20	(	(	PUNCT
ejpam-3421	90	21	g	g	NOUN
ejpam-3421	90	22	)	)	PUNCT
ejpam-3421	90	23	:	:	PUNCT
ejpam-3421	90	24	dg(v	dg(v	X
ejpam-3421	90	25	,	,	PUNCT
ejpam-3421	90	26	a	a	PRON
ejpam-3421	90	27	)	)	PUNCT
ejpam-3421	90	28	6=	6=	ADP
ejpam-3421	90	29	1	1	NUM
ejpam-3421	90	30	for	for	ADP
ejpam-3421	90	31	some	some	DET
ejpam-3421	90	32	a	a	DET
ejpam-3421	90	33	∈	∈	PROPN
ejpam-3421	90	34	a	a	PRON
ejpam-3421	90	35	}	}	PUNCT
ejpam-3421	90	36	.	.	PUNCT
ejpam-3421	91	1	hence	hence	ADV
ejpam-3421	91	2	,	,	PUNCT
ejpam-3421	91	3	f	f	PROPN
ejpam-3421	91	4	2	2	NUM
ejpam-3421	91	5	g+h	g+h	PROPN
ejpam-3421	92	1	[	[	X
ejpam-3421	92	2	a	a	X
ejpam-3421	92	3	]	]	X
ejpam-3421	92	4	=	=	SYM
ejpam-3421	92	5	v	v	ADJ
ejpam-3421	92	6	(	(	PUNCT
ejpam-3421	92	7	h	h	NOUN
ejpam-3421	92	8	)	)	PUNCT
ejpam-3421	92	9	∪	∪	ADP
ejpam-3421	92	10	[	[	X
ejpam-3421	92	11	∩a∈ang(a	∩a∈ang(a	PROPN
ejpam-3421	92	12	)	)	PUNCT
ejpam-3421	92	13	]	]	PUNCT
ejpam-3421	92	14	.	.	PUNCT
ejpam-3421	93	1	(	(	PUNCT
ejpam-3421	93	2	ii	ii	NOUN
ejpam-3421	93	3	)	)	PUNCT
ejpam-3421	93	4	similarly	similarly	ADV
ejpam-3421	93	5	,	,	PUNCT
ejpam-3421	93	6	f	f	PROPN
ejpam-3421	93	7	2	2	NUM
ejpam-3421	93	8	g+h	g+h	PROPN
ejpam-3421	94	1	[	[	X
ejpam-3421	94	2	b	b	X
ejpam-3421	94	3	]	]	X
ejpam-3421	94	4	=	=	SYM
ejpam-3421	94	5	v	v	X
ejpam-3421	94	6	(	(	PUNCT
ejpam-3421	94	7	g	g	NOUN
ejpam-3421	94	8	)	)	PUNCT
ejpam-3421	94	9	∪	∪	ADP
ejpam-3421	94	10	[	[	X
ejpam-3421	94	11	∩b∈bnh(b	∩b∈bnh(b	ADJ
ejpam-3421	94	12	)	)	PUNCT
ejpam-3421	94	13	]	]	PUNCT
ejpam-3421	94	14	.	.	PUNCT
ejpam-3421	95	1	(	(	PUNCT
ejpam-3421	95	2	iii	iii	X
ejpam-3421	95	3	)	)	PUNCT
ejpam-3421	95	4	clearly	clearly	ADV
ejpam-3421	95	5	,	,	PUNCT
ejpam-3421	95	6	f	f	PROPN
ejpam-3421	95	7	2	2	NUM
ejpam-3421	95	8	g+h	g+h	NOUN
ejpam-3421	96	1	[	[	X
ejpam-3421	96	2	∅	∅	NOUN
ejpam-3421	96	3	]	]	PUNCT
ejpam-3421	96	4	=	=	SYM
ejpam-3421	96	5	v	v	X
ejpam-3421	96	6	(	(	PUNCT
ejpam-3421	96	7	g	g	NOUN
ejpam-3421	96	8	)	)	PUNCT
ejpam-3421	96	9	∪	∪	NOUN
ejpam-3421	96	10	v	v	NOUN
ejpam-3421	96	11	(	(	PUNCT
ejpam-3421	96	12	h	h	NOUN
ejpam-3421	96	13	)	)	PUNCT
ejpam-3421	96	14	.	.	PUNCT
ejpam-3421	97	1	remark	remark	PROPN
ejpam-3421	97	2	2	2	NUM
ejpam-3421	97	3	.	.	PUNCT
ejpam-3421	98	1	let	let	VERB
ejpam-3421	98	2	g	g	NOUN
ejpam-3421	98	3	be	be	AUX
ejpam-3421	98	4	any	any	DET
ejpam-3421	98	5	graph	graph	NOUN
ejpam-3421	98	6	and	and	CCONJ
ejpam-3421	98	7	let	let	VERB
ejpam-3421	98	8	a1	a1	NOUN
ejpam-3421	98	9	,	,	PUNCT
ejpam-3421	98	10	a2	a2	PROPN
ejpam-3421	98	11	⊆	⊆	NUM
ejpam-3421	98	12	v	v	NOUN
ejpam-3421	98	13	(	(	PUNCT
ejpam-3421	98	14	g	g	NOUN
ejpam-3421	98	15	)	)	PUNCT
ejpam-3421	98	16	.	.	PUNCT
ejpam-3421	99	1	then	then	ADV
ejpam-3421	99	2	n2	n2	PROPN
ejpam-3421	99	3	g[a1	g[a1	NOUN
ejpam-3421	99	4	∪a2	∪a2	X
ejpam-3421	99	5	]	]	X
ejpam-3421	99	6	=	=	SYM
ejpam-3421	99	7	n2	n2	ADJ
ejpam-3421	99	8	g[a1	g[a1	NOUN
ejpam-3421	99	9	]	]	X
ejpam-3421	99	10	∪n2	∪n2	PROPN
ejpam-3421	99	11	g[a2	g[a2	PROPN
ejpam-3421	99	12	]	]	PUNCT
ejpam-3421	99	13	.	.	PUNCT
ejpam-3421	100	1	theorem	theorem	ADJ
ejpam-3421	100	2	4	4	NUM
ejpam-3421	100	3	.	.	PUNCT
ejpam-3421	101	1	let	let	VERB
ejpam-3421	101	2	g	g	PROPN
ejpam-3421	101	3	=	=	SYM
ejpam-3421	101	4	(	(	PUNCT
ejpam-3421	101	5	v	v	NOUN
ejpam-3421	101	6	(	(	PUNCT
ejpam-3421	101	7	g	g	NOUN
ejpam-3421	101	8	)	)	PUNCT
ejpam-3421	101	9	,	,	PUNCT
ejpam-3421	101	10	e(g	e(g	PROPN
ejpam-3421	101	11	)	)	PUNCT
ejpam-3421	101	12	)	)	PUNCT
ejpam-3421	102	1	and	and	CCONJ
ejpam-3421	102	2	h	h	NOUN
ejpam-3421	102	3	=	=	SYM
ejpam-3421	102	4	(	(	PUNCT
ejpam-3421	102	5	v	v	NOUN
ejpam-3421	102	6	(	(	PUNCT
ejpam-3421	102	7	h	h	NOUN
ejpam-3421	102	8	)	)	PUNCT
ejpam-3421	102	9	,	,	PUNCT
ejpam-3421	102	10	e(h	e(h	PROPN
ejpam-3421	102	11	)	)	PUNCT
ejpam-3421	102	12	)	)	PUNCT
ejpam-3421	102	13	be	be	AUX
ejpam-3421	102	14	graphs	graph	NOUN
ejpam-3421	102	15	.	.	PUNCT
ejpam-3421	103	1	then	then	ADV
ejpam-3421	103	2	for	for	ADP
ejpam-3421	103	3	any	any	DET
ejpam-3421	103	4	a	a	DET
ejpam-3421	103	5	⊆	⊆	NUM
ejpam-3421	103	6	v	v	NOUN
ejpam-3421	103	7	(	(	PUNCT
ejpam-3421	103	8	g+h	g+h	NOUN
ejpam-3421	103	9	)	)	PUNCT
ejpam-3421	103	10	such	such	ADJ
ejpam-3421	103	11	that	that	SCONJ
ejpam-3421	103	12	a	a	DET
ejpam-3421	103	13	∩	∩	ADJ
ejpam-3421	103	14	v	v	NOUN
ejpam-3421	103	15	(	(	PUNCT
ejpam-3421	103	16	g	g	NOUN
ejpam-3421	103	17	)	)	PUNCT
ejpam-3421	103	18	=	=	SYM
ejpam-3421	103	19	ag	ag	PROPN
ejpam-3421	103	20	6=	6=	NUM
ejpam-3421	103	21	∅	∅	NOUN
ejpam-3421	103	22	and	and	CCONJ
ejpam-3421	103	23	a	a	DET
ejpam-3421	103	24	∩	∩	ADJ
ejpam-3421	103	25	v	v	NOUN
ejpam-3421	103	26	(	(	PUNCT
ejpam-3421	103	27	h	h	NOUN
ejpam-3421	103	28	)	)	PUNCT
ejpam-3421	103	29	=	=	PUNCT
ejpam-3421	103	30	ah	ah	INTJ
ejpam-3421	103	31	6=	6=	ADP
ejpam-3421	103	32	∅	∅	NOUN
ejpam-3421	103	33	,	,	PUNCT
ejpam-3421	103	34	f	f	PROPN
ejpam-3421	103	35	2	2	NUM
ejpam-3421	103	36	g+h	g+h	PROPN
ejpam-3421	104	1	[	[	X
ejpam-3421	104	2	a	a	X
ejpam-3421	104	3	]	]	X
ejpam-3421	104	4	=	=	SYM
ejpam-3421	104	5	f	f	PROPN
ejpam-3421	104	6	2	2	NUM
ejpam-3421	104	7	g+h	g+h	PROPN
ejpam-3421	105	1	[	[	X
ejpam-3421	105	2	ag	ag	X
ejpam-3421	105	3	]	]	X
ejpam-3421	105	4	∩	∩	PROPN
ejpam-3421	105	5	f	f	PROPN
ejpam-3421	105	6	2	2	NUM
ejpam-3421	105	7	g+h	g+h	PROPN
ejpam-3421	106	1	[	[	X
ejpam-3421	106	2	ah	ah	INTJ
ejpam-3421	106	3	]	]	X
ejpam-3421	106	4	.	.	PUNCT
ejpam-3421	107	1	c.	c.	PROPN
ejpam-3421	107	2	nianga	nianga	PROPN
ejpam-3421	107	3	,	,	PUNCT
ejpam-3421	107	4	s.	s.	PROPN
ejpam-3421	107	5	canoy	canoy	PROPN
ejpam-3421	107	6	/	/	SYM
ejpam-3421	107	7	eur	eur	PROPN
ejpam-3421	107	8	.	.	PUNCT
ejpam-3421	108	1	j.	j.	PROPN
ejpam-3421	108	2	pure	pure	PROPN
ejpam-3421	108	3	appl	appl	PROPN
ejpam-3421	108	4	.	.	PROPN
ejpam-3421	108	5	math	math	PROPN
ejpam-3421	108	6	,	,	PUNCT
ejpam-3421	108	7	12	12	NUM
ejpam-3421	108	8	(	(	PUNCT
ejpam-3421	108	9	2	2	NUM
ejpam-3421	108	10	)	)	PUNCT
ejpam-3421	108	11	(	(	PUNCT
ejpam-3421	108	12	2019	2019	NUM
ejpam-3421	108	13	)	)	PUNCT
ejpam-3421	108	14	,	,	PUNCT
ejpam-3421	108	15	499	499	NUM
ejpam-3421	108	16	-	-	SYM
ejpam-3421	108	17	505	505	NUM
ejpam-3421	108	18	502	502	NUM
ejpam-3421	108	19	proof	proof	NOUN
ejpam-3421	108	20	.	.	PUNCT
ejpam-3421	109	1	let	let	VERB
ejpam-3421	109	2	a	a	DET
ejpam-3421	109	3	⊆	⊆	NUM
ejpam-3421	109	4	v	v	NOUN
ejpam-3421	109	5	(	(	PUNCT
ejpam-3421	109	6	g	g	PROPN
ejpam-3421	109	7	+	+	NOUN
ejpam-3421	109	8	h	h	NOUN
ejpam-3421	109	9	)	)	PUNCT
ejpam-3421	109	10	.	.	PUNCT
ejpam-3421	110	1	suppose	suppose	VERB
ejpam-3421	110	2	a	a	DET
ejpam-3421	110	3	∩	∩	ADJ
ejpam-3421	110	4	v	v	NOUN
ejpam-3421	110	5	(	(	PUNCT
ejpam-3421	110	6	g	g	NOUN
ejpam-3421	110	7	)	)	PUNCT
ejpam-3421	110	8	=	=	SYM
ejpam-3421	110	9	ag	ag	PROPN
ejpam-3421	110	10	6=	6=	NUM
ejpam-3421	110	11	∅	∅	NOUN
ejpam-3421	110	12	and	and	CCONJ
ejpam-3421	110	13	a	a	DET
ejpam-3421	110	14	∩	∩	ADJ
ejpam-3421	110	15	v	v	NOUN
ejpam-3421	110	16	(	(	PUNCT
ejpam-3421	110	17	h	h	NOUN
ejpam-3421	110	18	)	)	PUNCT
ejpam-3421	110	19	=	=	PUNCT
ejpam-3421	111	1	ah	ah	INTJ
ejpam-3421	111	2	6=	6=	ADP
ejpam-3421	111	3	∅.	∅.	VERB
ejpam-3421	111	4	then	then	ADV
ejpam-3421	111	5	x	x	SYM
ejpam-3421	111	6	∈	∈	PROPN
ejpam-3421	111	7	f	f	PROPN
ejpam-3421	111	8	2	2	NUM
ejpam-3421	111	9	g+h	g+h	PROPN
ejpam-3421	112	1	[	[	X
ejpam-3421	112	2	a	a	X
ejpam-3421	112	3	]	]	X
ejpam-3421	112	4	if	if	SCONJ
ejpam-3421	112	5	and	and	CCONJ
ejpam-3421	112	6	only	only	ADV
ejpam-3421	112	7	if	if	SCONJ
ejpam-3421	112	8	x	x	PROPN
ejpam-3421	112	9	/∈	/∈	PUNCT
ejpam-3421	112	10	n2	n2	PROPN
ejpam-3421	112	11	g+h	g+h	PROPN
ejpam-3421	113	1	[	[	X
ejpam-3421	113	2	a	a	X
ejpam-3421	113	3	]	]	X
ejpam-3421	113	4	.	.	PUNCT
ejpam-3421	114	1	by	by	ADP
ejpam-3421	114	2	remark	remark	NOUN
ejpam-3421	114	3	2	2	NUM
ejpam-3421	114	4	,	,	PUNCT
ejpam-3421	114	5	x	x	SYM
ejpam-3421	114	6	∈	∈	PROPN
ejpam-3421	114	7	f	f	PROPN
ejpam-3421	114	8	2	2	NUM
ejpam-3421	114	9	g+h	g+h	PROPN
ejpam-3421	115	1	[	[	X
ejpam-3421	115	2	a	a	X
ejpam-3421	115	3	]	]	X
ejpam-3421	115	4	if	if	SCONJ
ejpam-3421	115	5	and	and	CCONJ
ejpam-3421	115	6	only	only	ADV
ejpam-3421	115	7	if	if	SCONJ
ejpam-3421	115	8	x	x	SYM
ejpam-3421	115	9	∈	∈	NOUN
ejpam-3421	115	10	f	f	PROPN
ejpam-3421	115	11	2	2	NUM
ejpam-3421	115	12	g+h	g+h	PROPN
ejpam-3421	116	1	[	[	X
ejpam-3421	116	2	ag	ag	X
ejpam-3421	116	3	]	]	X
ejpam-3421	116	4	∩	∩	PROPN
ejpam-3421	116	5	f	f	PROPN
ejpam-3421	116	6	2	2	NUM
ejpam-3421	116	7	g+h	g+h	PROPN
ejpam-3421	117	1	[	[	X
ejpam-3421	117	2	ah	ah	INTJ
ejpam-3421	117	3	]	]	X
ejpam-3421	117	4	.	.	PUNCT
ejpam-3421	118	1	the	the	DET
ejpam-3421	118	2	next	next	ADJ
ejpam-3421	118	3	theorem	theorem	NOUN
ejpam-3421	118	4	follows	follow	VERB
ejpam-3421	118	5	from	from	ADP
ejpam-3421	118	6	theorem	theorem	ADJ
ejpam-3421	118	7	3	3	NUM
ejpam-3421	118	8	(	(	PUNCT
ejpam-3421	118	9	i	i	NOUN
ejpam-3421	118	10	)	)	PUNCT
ejpam-3421	118	11	and	and	CCONJ
ejpam-3421	118	12	(	(	PUNCT
ejpam-3421	118	13	ii	ii	NOUN
ejpam-3421	118	14	)	)	PUNCT
ejpam-3421	118	15	.	.	PUNCT
ejpam-3421	119	1	corollary	corollary	ADJ
ejpam-3421	119	2	1	1	NUM
ejpam-3421	119	3	.	.	PUNCT
ejpam-3421	120	1	let	let	VERB
ejpam-3421	120	2	g	g	PROPN
ejpam-3421	120	3	=	=	SYM
ejpam-3421	120	4	(	(	PUNCT
ejpam-3421	120	5	v	v	NOUN
ejpam-3421	120	6	(	(	PUNCT
ejpam-3421	120	7	g	g	NOUN
ejpam-3421	120	8	)	)	PUNCT
ejpam-3421	120	9	,	,	PUNCT
ejpam-3421	120	10	e(g	e(g	PROPN
ejpam-3421	120	11	)	)	PUNCT
ejpam-3421	120	12	)	)	PUNCT
ejpam-3421	121	1	and	and	CCONJ
ejpam-3421	121	2	h	h	NOUN
ejpam-3421	121	3	=	=	SYM
ejpam-3421	121	4	(	(	PUNCT
ejpam-3421	121	5	v	v	NOUN
ejpam-3421	121	6	(	(	PUNCT
ejpam-3421	121	7	h	h	NOUN
ejpam-3421	121	8	)	)	PUNCT
ejpam-3421	121	9	,	,	PUNCT
ejpam-3421	121	10	e(h	e(h	PROPN
ejpam-3421	121	11	)	)	PUNCT
ejpam-3421	121	12	)	)	PUNCT
ejpam-3421	121	13	be	be	AUX
ejpam-3421	121	14	graphs	graph	NOUN
ejpam-3421	121	15	.	.	PUNCT
ejpam-3421	122	1	then	then	ADV
ejpam-3421	122	2	for	for	ADP
ejpam-3421	122	3	any	any	DET
ejpam-3421	122	4	v	v	NUM
ejpam-3421	122	5	∈	∈	NOUN
ejpam-3421	122	6	v	v	NOUN
ejpam-3421	122	7	(	(	PUNCT
ejpam-3421	122	8	g	g	NOUN
ejpam-3421	122	9	)	)	PUNCT
ejpam-3421	122	10	∪	∪	NOUN
ejpam-3421	122	11	v	v	NOUN
ejpam-3421	122	12	(	(	PUNCT
ejpam-3421	122	13	h	h	NOUN
ejpam-3421	122	14	)	)	PUNCT
ejpam-3421	122	15	,	,	PUNCT
ejpam-3421	122	16	f	f	PROPN
ejpam-3421	122	17	2	2	NUM
ejpam-3421	122	18	g+h	g+h	PROPN
ejpam-3421	123	1	[	[	X
ejpam-3421	123	2	v	v	X
ejpam-3421	123	3	]	]	X
ejpam-3421	123	4	=	=	SYM
ejpam-3421	123	5	{	{	PUNCT
ejpam-3421	123	6	v	v	NOUN
ejpam-3421	123	7	(	(	PUNCT
ejpam-3421	123	8	h	h	NOUN
ejpam-3421	123	9	)	)	PUNCT
ejpam-3421	123	10	∪ng(v	∪ng(v	ADJ
ejpam-3421	123	11	)	)	PUNCT
ejpam-3421	123	12	,	,	PUNCT
ejpam-3421	123	13	if	if	SCONJ
ejpam-3421	123	14	v	v	NUM
ejpam-3421	123	15	∈	∈	PROPN
ejpam-3421	123	16	v	v	NOUN
ejpam-3421	123	17	(	(	PUNCT
ejpam-3421	123	18	g	g	NOUN
ejpam-3421	123	19	)	)	PUNCT
ejpam-3421	123	20	v	v	NOUN
ejpam-3421	123	21	(	(	PUNCT
ejpam-3421	123	22	g	g	NOUN
ejpam-3421	123	23	)	)	PUNCT
ejpam-3421	123	24	∪ng(v	∪ng(v	ADJ
ejpam-3421	123	25	)	)	PUNCT
ejpam-3421	123	26	,	,	PUNCT
ejpam-3421	123	27	if	if	SCONJ
ejpam-3421	123	28	v	v	NUM
ejpam-3421	123	29	∈	∈	PROPN
ejpam-3421	123	30	v	v	NOUN
ejpam-3421	123	31	(	(	PUNCT
ejpam-3421	123	32	h	h	NOUN
ejpam-3421	123	33	)	)	PUNCT
ejpam-3421	123	34	.	.	PUNCT
ejpam-3421	124	1	(	(	PUNCT
ejpam-3421	124	2	2	2	X
ejpam-3421	124	3	)	)	PUNCT
ejpam-3421	124	4	definition	definition	NOUN
ejpam-3421	124	5	3	3	NUM
ejpam-3421	124	6	.	.	PUNCT
ejpam-3421	125	1	the	the	DET
ejpam-3421	125	2	corona	corona	NOUN
ejpam-3421	125	3	g	g	PROPN
ejpam-3421	125	4	◦	◦	NOUN
ejpam-3421	125	5	h	h	NOUN
ejpam-3421	125	6	of	of	ADP
ejpam-3421	125	7	graphs	graph	NOUN
ejpam-3421	125	8	g	g	NOUN
ejpam-3421	125	9	and	and	CCONJ
ejpam-3421	125	10	h	h	NOUN
ejpam-3421	125	11	is	be	AUX
ejpam-3421	125	12	the	the	DET
ejpam-3421	125	13	graph	graph	NOUN
ejpam-3421	125	14	obtained	obtain	VERB
ejpam-3421	125	15	by	by	ADP
ejpam-3421	125	16	taking	take	VERB
ejpam-3421	125	17	one	one	NUM
ejpam-3421	125	18	copy	copy	NOUN
ejpam-3421	125	19	of	of	ADP
ejpam-3421	125	20	g	g	PROPN
ejpam-3421	125	21	and	and	CCONJ
ejpam-3421	125	22	|v	|v	PROPN
ejpam-3421	125	23	(	(	PUNCT
ejpam-3421	125	24	g)|	g)|	PROPN
ejpam-3421	125	25	copies	copy	NOUN
ejpam-3421	125	26	h	h	NOUN
ejpam-3421	125	27	and	and	CCONJ
ejpam-3421	125	28	then	then	ADV
ejpam-3421	125	29	forming	form	VERB
ejpam-3421	125	30	the	the	DET
ejpam-3421	125	31	sum	sum	NOUN
ejpam-3421	125	32	〈	〈	PROPN
ejpam-3421	125	33	v	v	NOUN
ejpam-3421	125	34	〉	〉	NOUN
ejpam-3421	125	35	+	+	NUM
ejpam-3421	125	36	hv	hv	NOUN
ejpam-3421	125	37	=	=	SYM
ejpam-3421	125	38	v	v	PROPN
ejpam-3421	125	39	+	+	CCONJ
ejpam-3421	125	40	hv	hv	NOUN
ejpam-3421	125	41	for	for	ADP
ejpam-3421	125	42	each	each	PRON
ejpam-3421	125	43	v	v	NUM
ejpam-3421	125	44	∈	∈	PROPN
ejpam-3421	125	45	v	v	NOUN
ejpam-3421	125	46	(	(	PUNCT
ejpam-3421	125	47	g	g	NOUN
ejpam-3421	125	48	)	)	PUNCT
ejpam-3421	125	49	,	,	PUNCT
ejpam-3421	125	50	where	where	SCONJ
ejpam-3421	125	51	hv	hv	PROPN
ejpam-3421	125	52	is	be	AUX
ejpam-3421	125	53	a	a	DET
ejpam-3421	125	54	copy	copy	NOUN
ejpam-3421	125	55	of	of	ADP
ejpam-3421	125	56	h	h	NOUN
ejpam-3421	125	57	corresponding	correspond	VERB
ejpam-3421	125	58	to	to	ADP
ejpam-3421	125	59	the	the	DET
ejpam-3421	125	60	vertex	vertex	NOUN
ejpam-3421	125	61	v.	v.	ADP
ejpam-3421	125	62	theorem	theorem	NOUN
ejpam-3421	125	63	5	5	X
ejpam-3421	125	64	.	.	PUNCT
ejpam-3421	126	1	let	let	VERB
ejpam-3421	126	2	g	g	PROPN
ejpam-3421	126	3	=	=	SYM
ejpam-3421	126	4	(	(	PUNCT
ejpam-3421	126	5	v	v	NOUN
ejpam-3421	126	6	(	(	PUNCT
ejpam-3421	126	7	g	g	NOUN
ejpam-3421	126	8	)	)	PUNCT
ejpam-3421	126	9	,	,	PUNCT
ejpam-3421	126	10	e(g	e(g	PROPN
ejpam-3421	126	11	)	)	PUNCT
ejpam-3421	126	12	)	)	PUNCT
ejpam-3421	127	1	and	and	CCONJ
ejpam-3421	127	2	h	h	NOUN
ejpam-3421	127	3	=	=	SYM
ejpam-3421	127	4	(	(	PUNCT
ejpam-3421	127	5	v	v	NOUN
ejpam-3421	127	6	(	(	PUNCT
ejpam-3421	127	7	h	h	NOUN
ejpam-3421	127	8	)	)	PUNCT
ejpam-3421	127	9	,	,	PUNCT
ejpam-3421	127	10	e(h	e(h	PROPN
ejpam-3421	127	11	)	)	PUNCT
ejpam-3421	127	12	)	)	PUNCT
ejpam-3421	127	13	be	be	AUX
ejpam-3421	127	14	graphs	graph	NOUN
ejpam-3421	127	15	.	.	PUNCT
ejpam-3421	128	1	then	then	ADV
ejpam-3421	128	2	for	for	ADP
ejpam-3421	128	3	any	any	DET
ejpam-3421	128	4	a	a	DET
ejpam-3421	128	5	∈	∈	PROPN
ejpam-3421	128	6	v	v	NOUN
ejpam-3421	128	7	(	(	PUNCT
ejpam-3421	128	8	g	g	PROPN
ejpam-3421	128	9	◦	◦	NOUN
ejpam-3421	128	10	h	h	NOUN
ejpam-3421	128	11	)	)	PUNCT
ejpam-3421	128	12	,	,	PUNCT
ejpam-3421	128	13	f	f	PROPN
ejpam-3421	128	14	2	2	NUM
ejpam-3421	128	15	g	g	NOUN
ejpam-3421	128	16	◦	◦	NOUN
ejpam-3421	128	17	h	h	NOUN
ejpam-3421	129	1	[	[	X
ejpam-3421	129	2	a	a	X
ejpam-3421	129	3	]	]	X
ejpam-3421	129	4	=	=	PUNCT
ejpam-3421	129	5			NUM
ejpam-3421	129	6	f	f	NOUN
ejpam-3421	129	7	2	2	NUM
ejpam-3421	129	8	g[a	g[a	NOUN
ejpam-3421	129	9	]	]	PUNCT
ejpam-3421	129	10	∪	∪	ADP
ejpam-3421	129	11			NOUN
ejpam-3421	129	12	⋃	⋃	NOUN
ejpam-3421	129	13	v∈v	v∈v	NOUN
ejpam-3421	129	14	(	(	PUNCT
ejpam-3421	129	15	g)\ng(a	g)\ng(a	NOUN
ejpam-3421	129	16	)	)	PUNCT
ejpam-3421	129	17	v	v	NOUN
ejpam-3421	129	18	(	(	PUNCT
ejpam-3421	129	19	hv	hv	NOUN
ejpam-3421	129	20	)	)	PUNCT
ejpam-3421	129	21			NOUN
ejpam-3421	129	22	,	,	PUNCT
ejpam-3421	129	23	if	if	SCONJ
ejpam-3421	129	24	a	a	DET
ejpam-3421	129	25	∈	∈	PROPN
ejpam-3421	129	26	v	v	NOUN
ejpam-3421	129	27	(	(	PUNCT
ejpam-3421	129	28	g	g	NOUN
ejpam-3421	129	29	)	)	PUNCT
ejpam-3421	129	30	nhw(a	nhw(a	PROPN
ejpam-3421	129	31	)	)	PUNCT
ejpam-3421	129	32	∪	∪	ADP
ejpam-3421	129	33	[	[	X
ejpam-3421	129	34	v	v	X
ejpam-3421	129	35	(	(	PUNCT
ejpam-3421	129	36	g)\ng(w	g)\ng(w	PROPN
ejpam-3421	129	37	)	)	PUNCT
ejpam-3421	129	38	]	]	PUNCT
ejpam-3421	129	39	∪	∪	ADP
ejpam-3421	129	40			PROPN
ejpam-3421	129	41	⋃	⋃	NOUN
ejpam-3421	129	42	v∈v	v∈v	NOUN
ejpam-3421	129	43	(	(	PUNCT
ejpam-3421	129	44	g)\{w	g)\{w	NOUN
ejpam-3421	129	45	}	}	PUNCT
ejpam-3421	129	46	v	v	NOUN
ejpam-3421	129	47	(	(	PUNCT
ejpam-3421	129	48	hv	hv	NOUN
ejpam-3421	129	49	)	)	PUNCT
ejpam-3421	129	50			NOUN
ejpam-3421	129	51	,	,	PUNCT
ejpam-3421	129	52	if	if	SCONJ
ejpam-3421	129	53	a	a	DET
ejpam-3421	129	54	∈	∈	PROPN
ejpam-3421	129	55	v	v	NOUN
ejpam-3421	129	56	(	(	PUNCT
ejpam-3421	129	57	hw	hw	NOUN
ejpam-3421	129	58	)	)	PUNCT
ejpam-3421	129	59	(	(	PUNCT
ejpam-3421	129	60	3	3	X
ejpam-3421	129	61	)	)	PUNCT
ejpam-3421	129	62	proof	proof	NOUN
ejpam-3421	129	63	.	.	PUNCT
ejpam-3421	130	1	let	let	VERB
ejpam-3421	130	2	x	x	SYM
ejpam-3421	130	3	∈	∈	NOUN
ejpam-3421	130	4	f	f	NOUN
ejpam-3421	130	5	2	2	NUM
ejpam-3421	130	6	g	g	NOUN
ejpam-3421	130	7	◦	◦	NOUN
ejpam-3421	130	8	h	h	NOUN
ejpam-3421	131	1	[	[	X
ejpam-3421	131	2	a	a	X
ejpam-3421	131	3	]	]	X
ejpam-3421	131	4	.	.	PUNCT
ejpam-3421	132	1	then	then	ADV
ejpam-3421	132	2	x	x	X
ejpam-3421	132	3	6=	6=	ADP
ejpam-3421	132	4	a	a	PRON
ejpam-3421	132	5	and	and	CCONJ
ejpam-3421	132	6	x	x	ADJ
ejpam-3421	132	7	/∈	/∈	SYM
ejpam-3421	132	8	n2	n2	PROPN
ejpam-3421	132	9	g	g	PROPN
ejpam-3421	132	10	◦	◦	PROPN
ejpam-3421	132	11	h(a	h(a	PROPN
ejpam-3421	132	12	)	)	PUNCT
ejpam-3421	132	13	.	.	PUNCT
ejpam-3421	133	1	consider	consider	VERB
ejpam-3421	133	2	the	the	DET
ejpam-3421	133	3	following	follow	VERB
ejpam-3421	133	4	cases	case	NOUN
ejpam-3421	133	5	:	:	PUNCT
ejpam-3421	133	6	case	case	NOUN
ejpam-3421	133	7	1	1	NUM
ejpam-3421	133	8	.	.	PUNCT
ejpam-3421	133	9	suppose	suppose	VERB
ejpam-3421	133	10	a	a	DET
ejpam-3421	133	11	∈	∈	PROPN
ejpam-3421	133	12	v	v	NOUN
ejpam-3421	133	13	(	(	PUNCT
ejpam-3421	133	14	g	g	NOUN
ejpam-3421	133	15	)	)	PUNCT
ejpam-3421	133	16	.	.	PUNCT
ejpam-3421	134	1	if	if	SCONJ
ejpam-3421	134	2	x	x	SYM
ejpam-3421	134	3	∈	∈	PROPN
ejpam-3421	134	4	v	v	X
ejpam-3421	134	5	(	(	PUNCT
ejpam-3421	134	6	g	g	NOUN
ejpam-3421	134	7	)	)	PUNCT
ejpam-3421	134	8	,	,	PUNCT
ejpam-3421	134	9	then	then	ADV
ejpam-3421	134	10	x	x	SYM
ejpam-3421	134	11	/∈	/∈	PROPN
ejpam-3421	134	12	n2	n2	PROPN
ejpam-3421	134	13	g(a	g(a	PROPN
ejpam-3421	134	14	)	)	PUNCT
ejpam-3421	134	15	since	since	SCONJ
ejpam-3421	134	16	x	x	PROPN
ejpam-3421	134	17	/∈	/∈	PROPN
ejpam-3421	134	18	n2	n2	PROPN
ejpam-3421	134	19	g	g	PROPN
ejpam-3421	134	20	◦	◦	NOUN
ejpam-3421	134	21	h(a	h(a	PROPN
ejpam-3421	134	22	)	)	PUNCT
ejpam-3421	134	23	.	.	PUNCT
ejpam-3421	135	1	hence	hence	ADV
ejpam-3421	135	2	,	,	PUNCT
ejpam-3421	135	3	x	x	PUNCT
ejpam-3421	135	4	∈	∈	PROPN
ejpam-3421	135	5	f	f	PROPN
ejpam-3421	135	6	2	2	NUM
ejpam-3421	135	7	g[a	g[a	NOUN
ejpam-3421	135	8	]	]	PUNCT
ejpam-3421	135	9	.	.	PUNCT
ejpam-3421	135	10	suppose	suppose	VERB
ejpam-3421	135	11	x	x	X
ejpam-3421	135	12	/∈	/∈	PUNCT
ejpam-3421	136	1	v	v	INTJ
ejpam-3421	136	2	(	(	PUNCT
ejpam-3421	136	3	g	g	NOUN
ejpam-3421	136	4	)	)	PUNCT
ejpam-3421	136	5	.	.	PUNCT
ejpam-3421	137	1	let	let	VERB
ejpam-3421	137	2	u	u	PRON
ejpam-3421	137	3	∈	∈	PROPN
ejpam-3421	137	4	v	v	ADP
ejpam-3421	137	5	(	(	PUNCT
ejpam-3421	137	6	g	g	NOUN
ejpam-3421	137	7	)	)	PUNCT
ejpam-3421	137	8	such	such	ADJ
ejpam-3421	137	9	that	that	SCONJ
ejpam-3421	137	10	x	x	SYM
ejpam-3421	137	11	∈	∈	PROPN
ejpam-3421	137	12	v	v	X
ejpam-3421	137	13	(	(	PUNCT
ejpam-3421	137	14	hu	hu	PROPN
ejpam-3421	137	15	)	)	PUNCT
ejpam-3421	137	16	.	.	PUNCT
ejpam-3421	138	1	if	if	SCONJ
ejpam-3421	138	2	u	u	PROPN
ejpam-3421	138	3	=	=	X
ejpam-3421	138	4	a	a	PROPN
ejpam-3421	138	5	,	,	PUNCT
ejpam-3421	138	6	then	then	ADV
ejpam-3421	138	7	x	x	SYM
ejpam-3421	138	8	∈	∈	PROPN
ejpam-3421	138	9	v	v	X
ejpam-3421	138	10	(	(	PUNCT
ejpam-3421	138	11	hu	hu	PROPN
ejpam-3421	138	12	)	)	PUNCT
ejpam-3421	138	13	and	and	CCONJ
ejpam-3421	138	14	u	u	PROPN
ejpam-3421	138	15	∈	∈	PROPN
ejpam-3421	138	16	v	v	NOUN
ejpam-3421	138	17	(	(	PUNCT
ejpam-3421	138	18	g)\ng(a	g)\ng(a	NOUN
ejpam-3421	138	19	)	)	PUNCT
ejpam-3421	138	20	.	.	PUNCT
ejpam-3421	138	21	suppose	suppose	VERB
ejpam-3421	138	22	u	u	PROPN
ejpam-3421	138	23	6=	6=	NOUN
ejpam-3421	138	24	a.	a.	NOUN
ejpam-3421	138	25	since	since	SCONJ
ejpam-3421	138	26	x	x	PROPN
ejpam-3421	138	27	/∈	/∈	PROPN
ejpam-3421	138	28	n2	n2	PROPN
ejpam-3421	138	29	g(a	g(a	PROPN
ejpam-3421	138	30	)	)	PUNCT
ejpam-3421	138	31	and	and	CCONJ
ejpam-3421	138	32	dg	dg	PROPN
ejpam-3421	138	33	◦	◦	PROPN
ejpam-3421	138	34	h(a	h(a	PROPN
ejpam-3421	138	35	,	,	PUNCT
ejpam-3421	138	36	y	y	PROPN
ejpam-3421	138	37	)	)	PUNCT
ejpam-3421	138	38	=	=	SYM
ejpam-3421	138	39	2	2	NUM
ejpam-3421	138	40	for	for	ADP
ejpam-3421	138	41	all	all	DET
ejpam-3421	138	42	y	y	PROPN
ejpam-3421	138	43	∈	∈	PROPN
ejpam-3421	138	44	v	v	NOUN
ejpam-3421	138	45	(	(	PUNCT
ejpam-3421	138	46	hz	hz	PROPN
ejpam-3421	138	47	)	)	PUNCT
ejpam-3421	138	48	with	with	ADP
ejpam-3421	138	49	z	z	PROPN
ejpam-3421	138	50	∈	∈	PROPN
ejpam-3421	138	51	ng(a	ng(a	NOUN
ejpam-3421	138	52	)	)	PUNCT
ejpam-3421	138	53	,	,	PUNCT
ejpam-3421	138	54	it	it	PRON
ejpam-3421	138	55	follows	follow	VERB
ejpam-3421	138	56	that	that	SCONJ
ejpam-3421	138	57	u	u	PROPN
ejpam-3421	138	58	∈	∈	PROPN
ejpam-3421	138	59	v	v	NOUN
ejpam-3421	138	60	(	(	PUNCT
ejpam-3421	138	61	g)\ng(a	g)\ng(a	NOUN
ejpam-3421	138	62	)	)	PUNCT
ejpam-3421	138	63	.	.	PUNCT
ejpam-3421	139	1	thus	thus	ADV
ejpam-3421	139	2	,	,	PUNCT
ejpam-3421	139	3	f	f	PROPN
ejpam-3421	139	4	2	2	NUM
ejpam-3421	139	5	g	g	NOUN
ejpam-3421	139	6	◦	◦	NOUN
ejpam-3421	139	7	h	h	NOUN
ejpam-3421	140	1	[	[	X
ejpam-3421	140	2	a	a	X
ejpam-3421	140	3	]	]	X
ejpam-3421	140	4	⊆	⊆	NUM
ejpam-3421	140	5	f	f	SYM
ejpam-3421	140	6	2	2	NUM
ejpam-3421	140	7	g[a	g[a	NOUN
ejpam-3421	140	8	]	]	PUNCT
ejpam-3421	140	9	∪	∪	ADP
ejpam-3421	140	10	[	[	PUNCT
ejpam-3421	140	11	∪v∈v	∪v∈v	X
ejpam-3421	140	12	(	(	PUNCT
ejpam-3421	140	13	g)\ng(a)v	g)\ng(a)v	PROPN
ejpam-3421	140	14	(	(	PUNCT
ejpam-3421	140	15	hv	hv	PROPN
ejpam-3421	140	16	)	)	PUNCT
ejpam-3421	140	17	]	]	PUNCT
ejpam-3421	141	1	=	=	PUNCT
ejpam-3421	141	2	x.	x.	NOUN
ejpam-3421	141	3	now	now	ADV
ejpam-3421	141	4	,	,	PUNCT
ejpam-3421	141	5	let	let	VERB
ejpam-3421	141	6	w	w	PROPN
ejpam-3421	141	7	∈	∈	PROPN
ejpam-3421	141	8	x.	x.	NOUN
ejpam-3421	142	1	if	if	SCONJ
ejpam-3421	142	2	w	w	PROPN
ejpam-3421	142	3	∈	∈	PROPN
ejpam-3421	142	4	f	f	PROPN
ejpam-3421	142	5	2	2	NUM
ejpam-3421	142	6	g[a	g[a	NOUN
ejpam-3421	142	7	]	]	X
ejpam-3421	142	8	,	,	PUNCT
ejpam-3421	142	9	then	then	ADV
ejpam-3421	142	10	w	w	PROPN
ejpam-3421	142	11	/∈	/∈	PUNCT
ejpam-3421	142	12	n2	n2	ADJ
ejpam-3421	142	13	g[a	g[a	PROPN
ejpam-3421	142	14	]	]	X
ejpam-3421	142	15	.	.	PUNCT
ejpam-3421	143	1	hence	hence	ADV
ejpam-3421	143	2	,	,	PUNCT
ejpam-3421	143	3	w	w	PROPN
ejpam-3421	143	4	/∈	/∈	PROPN
ejpam-3421	143	5	n2	n2	NOUN
ejpam-3421	144	1	g	g	PROPN
ejpam-3421	144	2	◦	◦	NOUN
ejpam-3421	144	3	h	h	NOUN
ejpam-3421	145	1	[	[	X
ejpam-3421	145	2	a	a	X
ejpam-3421	145	3	]	]	X
ejpam-3421	145	4	.	.	PUNCT
ejpam-3421	146	1	this	this	PRON
ejpam-3421	146	2	implies	imply	VERB
ejpam-3421	146	3	that	that	SCONJ
ejpam-3421	146	4	w	w	PROPN
ejpam-3421	146	5	∈	∈	PROPN
ejpam-3421	146	6	f	f	PROPN
ejpam-3421	146	7	2	2	NUM
ejpam-3421	146	8	g	g	NOUN
ejpam-3421	146	9	◦	◦	NOUN
ejpam-3421	146	10	h	h	NOUN
ejpam-3421	147	1	[	[	X
ejpam-3421	147	2	a	a	X
ejpam-3421	147	3	]	]	X
ejpam-3421	147	4	.	.	PUNCT
ejpam-3421	147	5	suppose	suppose	VERB
ejpam-3421	147	6	w	w	PROPN
ejpam-3421	147	7	∈	∈	PROPN
ejpam-3421	147	8	∪v∈v	∪v∈v	X
ejpam-3421	147	9	(	(	PUNCT
ejpam-3421	147	10	g)\ng(a)v	g)\ng(a)v	PROPN
ejpam-3421	147	11	(	(	PUNCT
ejpam-3421	147	12	hv	hv	PROPN
ejpam-3421	147	13	)	)	PUNCT
ejpam-3421	147	14	.	.	PUNCT
ejpam-3421	148	1	then	then	ADV
ejpam-3421	148	2	there	there	PRON
ejpam-3421	148	3	exists	exist	VERB
ejpam-3421	148	4	v	v	ADP
ejpam-3421	148	5	∈	∈	PROPN
ejpam-3421	148	6	v	v	NOUN
ejpam-3421	148	7	(	(	PUNCT
ejpam-3421	148	8	g)\ng(a	g)\ng(a	NOUN
ejpam-3421	148	9	)	)	PUNCT
ejpam-3421	148	10	such	such	ADJ
ejpam-3421	148	11	that	that	SCONJ
ejpam-3421	148	12	w	w	PROPN
ejpam-3421	148	13	∈	∈	PROPN
ejpam-3421	148	14	v	v	ADP
ejpam-3421	148	15	(	(	PUNCT
ejpam-3421	148	16	hv	hv	PROPN
ejpam-3421	148	17	)	)	PUNCT
ejpam-3421	148	18	.	.	PUNCT
ejpam-3421	149	1	it	it	PRON
ejpam-3421	149	2	follows	follow	VERB
ejpam-3421	149	3	that	that	PRON
ejpam-3421	149	4	w	w	ADP
ejpam-3421	149	5	6=	6=	ADP
ejpam-3421	149	6	a	a	PRON
ejpam-3421	149	7	and	and	CCONJ
ejpam-3421	149	8	dg	dg	NOUN
ejpam-3421	149	9	◦	◦	NOUN
ejpam-3421	149	10	h(w	h(w	PROPN
ejpam-3421	149	11	,	,	PUNCT
ejpam-3421	149	12	a	a	PRON
ejpam-3421	149	13	)	)	PUNCT
ejpam-3421	149	14	6=	6=	ADP
ejpam-3421	149	15	2	2	NUM
ejpam-3421	149	16	.	.	PUNCT
ejpam-3421	150	1	thus	thus	ADV
ejpam-3421	150	2	,	,	PUNCT
ejpam-3421	150	3	w	w	PROPN
ejpam-3421	150	4	∈	∈	PROPN
ejpam-3421	150	5	f	f	NOUN
ejpam-3421	150	6	2	2	NUM
ejpam-3421	150	7	g	g	NOUN
ejpam-3421	150	8	◦	◦	NOUN
ejpam-3421	150	9	h	h	NOUN
ejpam-3421	151	1	[	[	X
ejpam-3421	151	2	a	a	X
ejpam-3421	151	3	]	]	X
ejpam-3421	151	4	.	.	PUNCT
ejpam-3421	152	1	therefore	therefore	ADV
ejpam-3421	152	2	,	,	PUNCT
ejpam-3421	152	3	f	f	PROPN
ejpam-3421	152	4	2	2	NUM
ejpam-3421	152	5	g[a	g[a	NOUN
ejpam-3421	152	6	]	]	PUNCT
ejpam-3421	152	7	∪	∪	ADP
ejpam-3421	152	8	[	[	PUNCT
ejpam-3421	152	9	∪v∈v	∪v∈v	X
ejpam-3421	152	10	(	(	PUNCT
ejpam-3421	152	11	g)\ng(a)v	g)\ng(a)v	PROPN
ejpam-3421	152	12	(	(	PUNCT
ejpam-3421	152	13	hv	hv	PROPN
ejpam-3421	152	14	)	)	PUNCT
ejpam-3421	152	15	]	]	PUNCT
ejpam-3421	152	16	⊆	⊆	NUM
ejpam-3421	152	17	f	f	SYM
ejpam-3421	152	18	2	2	NUM
ejpam-3421	152	19	g	g	NOUN
ejpam-3421	152	20	◦	◦	NOUN
ejpam-3421	152	21	h	h	NOUN
ejpam-3421	153	1	[	[	X
ejpam-3421	153	2	a	a	X
ejpam-3421	153	3	]	]	X
ejpam-3421	153	4	.	.	PUNCT
ejpam-3421	154	1	case	case	NOUN
ejpam-3421	154	2	2	2	X
ejpam-3421	154	3	.	.	PUNCT
ejpam-3421	154	4	suppose	suppose	VERB
ejpam-3421	154	5	a	a	DET
ejpam-3421	154	6	∈	∈	PROPN
ejpam-3421	154	7	v	v	NOUN
ejpam-3421	154	8	(	(	PUNCT
ejpam-3421	154	9	hw	hw	NOUN
ejpam-3421	154	10	)	)	PUNCT
ejpam-3421	154	11	for	for	ADP
ejpam-3421	154	12	some	some	DET
ejpam-3421	154	13	w	w	PROPN
ejpam-3421	154	14	∈	∈	PROPN
ejpam-3421	154	15	v	v	ADP
ejpam-3421	154	16	(	(	PUNCT
ejpam-3421	154	17	g	g	NOUN
ejpam-3421	154	18	)	)	PUNCT
ejpam-3421	154	19	.	.	PUNCT
ejpam-3421	155	1	if	if	SCONJ
ejpam-3421	155	2	x	x	X
ejpam-3421	155	3	=	=	SYM
ejpam-3421	155	4	w	w	PROPN
ejpam-3421	155	5	,	,	PUNCT
ejpam-3421	155	6	then	then	ADV
ejpam-3421	155	7	x	x	SYM
ejpam-3421	155	8	∈	∈	PROPN
ejpam-3421	155	9	v	v	X
ejpam-3421	155	10	(	(	PUNCT
ejpam-3421	155	11	g)\ng(w	g)\ng(w	PROPN
ejpam-3421	155	12	)	)	PUNCT
ejpam-3421	155	13	.	.	PUNCT
ejpam-3421	156	1	suppose	suppose	VERB
ejpam-3421	156	2	x	x	SYM
ejpam-3421	156	3	6=	6=	ADP
ejpam-3421	156	4	w.	w.	NOUN
ejpam-3421	156	5	if	if	SCONJ
ejpam-3421	156	6	x	x	PROPN
ejpam-3421	156	7	∈	∈	PROPN
ejpam-3421	156	8	v	v	X
ejpam-3421	156	9	(	(	PUNCT
ejpam-3421	156	10	g	g	NOUN
ejpam-3421	156	11	)	)	PUNCT
ejpam-3421	156	12	,	,	PUNCT
ejpam-3421	156	13	then	then	ADV
ejpam-3421	156	14	dg(x	dg(x	NUM
ejpam-3421	156	15	,	,	PUNCT
ejpam-3421	156	16	w	w	NOUN
ejpam-3421	156	17	)	)	PUNCT
ejpam-3421	156	18	6=	6=	ADP
ejpam-3421	156	19	1	1	NUM
ejpam-3421	156	20	because	because	SCONJ
ejpam-3421	156	21	dg	dg	NOUN
ejpam-3421	156	22	◦	◦	NOUN
ejpam-3421	156	23	h(x	h(x	PROPN
ejpam-3421	156	24	,	,	PUNCT
ejpam-3421	156	25	a	a	PRON
ejpam-3421	156	26	)	)	PUNCT
ejpam-3421	156	27	6=	6=	ADP
ejpam-3421	156	28	2	2	NUM
ejpam-3421	156	29	.	.	PUNCT
ejpam-3421	156	30	hence	hence	ADV
ejpam-3421	156	31	,	,	PUNCT
ejpam-3421	156	32	x	x	PUNCT
ejpam-3421	156	33	∈	∈	PROPN
ejpam-3421	156	34	v	v	X
ejpam-3421	156	35	(	(	PUNCT
ejpam-3421	156	36	g)\ng(w	g)\ng(w	PROPN
ejpam-3421	156	37	)	)	PUNCT
ejpam-3421	156	38	.	.	PUNCT
ejpam-3421	157	1	suppose	suppose	VERB
ejpam-3421	157	2	x	x	SYM
ejpam-3421	157	3	∈	∈	PROPN
ejpam-3421	157	4	v	v	ADP
ejpam-3421	157	5	(	(	PUNCT
ejpam-3421	157	6	hq	hq	NOUN
ejpam-3421	157	7	)	)	PUNCT
ejpam-3421	157	8	for	for	ADP
ejpam-3421	157	9	some	some	DET
ejpam-3421	157	10	q	q	PROPN
ejpam-3421	157	11	∈	∈	PROPN
ejpam-3421	157	12	v	v	NOUN
ejpam-3421	157	13	(	(	PUNCT
ejpam-3421	157	14	g	g	NOUN
ejpam-3421	157	15	)	)	PUNCT
ejpam-3421	157	16	.	.	PUNCT
ejpam-3421	158	1	if	if	SCONJ
ejpam-3421	158	2	q	q	NOUN
ejpam-3421	158	3	=	=	SYM
ejpam-3421	158	4	w	w	NOUN
ejpam-3421	158	5	,	,	PUNCT
ejpam-3421	158	6	then	then	ADV
ejpam-3421	158	7	x	x	PART
ejpam-3421	158	8	∈	∈	PROPN
ejpam-3421	158	9	v	v	X
ejpam-3421	158	10	(	(	PUNCT
ejpam-3421	158	11	hw	hw	NOUN
ejpam-3421	158	12	)	)	PUNCT
ejpam-3421	158	13	.	.	PUNCT
ejpam-3421	159	1	since	since	SCONJ
ejpam-3421	159	2	x	x	PROPN
ejpam-3421	159	3	6=	6=	ADP
ejpam-3421	159	4	a	a	PRON
ejpam-3421	159	5	and	and	CCONJ
ejpam-3421	159	6	a	a	DET
ejpam-3421	159	7	∈	∈	NOUN
ejpam-3421	159	8	v	v	NOUN
ejpam-3421	159	9	(	(	PUNCT
ejpam-3421	159	10	hw	hw	NOUN
ejpam-3421	159	11	)	)	PUNCT
ejpam-3421	159	12	,	,	PUNCT
ejpam-3421	159	13	x	x	PUNCT
ejpam-3421	159	14	∈	∈	PROPN
ejpam-3421	159	15	nhw(a	nhw(a	PROPN
ejpam-3421	159	16	)	)	PUNCT
ejpam-3421	159	17	(	(	PUNCT
ejpam-3421	159	18	otherwise	otherwise	ADV
ejpam-3421	159	19	,	,	PUNCT
ejpam-3421	159	20	dg	dg	PROPN
ejpam-3421	159	21	◦	◦	PROPN
ejpam-3421	159	22	h(a	h(a	PROPN
ejpam-3421	159	23	,	,	PUNCT
ejpam-3421	159	24	x	x	NOUN
ejpam-3421	159	25	)	)	PUNCT
ejpam-3421	159	26	=	=	SYM
ejpam-3421	159	27	2	2	NUM
ejpam-3421	159	28	)	)	PUNCT
ejpam-3421	159	29	.	.	PUNCT
ejpam-3421	159	30	suppose	suppose	VERB
ejpam-3421	159	31	q	q	PROPN
ejpam-3421	160	1	6=	6=	ADP
ejpam-3421	160	2	w.	w.	PROPN
ejpam-3421	160	3	then	then	ADV
ejpam-3421	160	4	x	x	SYM
ejpam-3421	160	5	∈	∈	PROPN
ejpam-3421	160	6	v	v	ADP
ejpam-3421	160	7	(	(	PUNCT
ejpam-3421	160	8	hq	hq	NOUN
ejpam-3421	160	9	)	)	PUNCT
ejpam-3421	160	10	and	and	CCONJ
ejpam-3421	160	11	q	q	PROPN
ejpam-3421	160	12	∈	∈	PROPN
ejpam-3421	160	13	v	v	NOUN
ejpam-3421	160	14	(	(	PUNCT
ejpam-3421	160	15	g)\{w	g)\{w	NOUN
ejpam-3421	160	16	}	}	PUNCT
ejpam-3421	160	17	.	.	PUNCT
ejpam-3421	161	1	thus	thus	ADV
ejpam-3421	161	2	,	,	PUNCT
ejpam-3421	161	3	z	z	PROPN
ejpam-3421	161	4	∈	∈	PROPN
ejpam-3421	161	5	nhw(a	nhw(a	PROPN
ejpam-3421	161	6	)	)	PUNCT
ejpam-3421	161	7	∪	∪	ADP
ejpam-3421	161	8	[	[	X
ejpam-3421	161	9	v	v	X
ejpam-3421	161	10	(	(	PUNCT
ejpam-3421	161	11	g)\ng(w	g)\ng(w	PROPN
ejpam-3421	161	12	)	)	PUNCT
ejpam-3421	161	13	]	]	PUNCT
ejpam-3421	161	14	∪	∪	ADP
ejpam-3421	161	15	[	[	PUNCT
ejpam-3421	161	16	∪v∈v	∪v∈v	NOUN
ejpam-3421	161	17	(	(	PUNCT
ejpam-3421	161	18	g)\{w}v	g)\{w}v	PROPN
ejpam-3421	161	19	(	(	PUNCT
ejpam-3421	161	20	hv	hv	PROPN
ejpam-3421	161	21	)	)	PUNCT
ejpam-3421	161	22	]	]	PUNCT
ejpam-3421	162	1	=	=	PUNCT
ejpam-3421	162	2	y.	y.	PROPN
ejpam-3421	162	3	c.	c.	PROPN
ejpam-3421	162	4	nianga	nianga	PROPN
ejpam-3421	162	5	,	,	PUNCT
ejpam-3421	162	6	s.	s.	PROPN
ejpam-3421	162	7	canoy	canoy	PROPN
ejpam-3421	162	8	/	/	SYM
ejpam-3421	162	9	eur	eur	PROPN
ejpam-3421	162	10	.	.	PUNCT
ejpam-3421	163	1	j.	j.	PROPN
ejpam-3421	163	2	pure	pure	PROPN
ejpam-3421	163	3	appl	appl	PROPN
ejpam-3421	163	4	.	.	PROPN
ejpam-3421	163	5	math	math	PROPN
ejpam-3421	163	6	,	,	PUNCT
ejpam-3421	163	7	12	12	NUM
ejpam-3421	163	8	(	(	PUNCT
ejpam-3421	163	9	2	2	NUM
ejpam-3421	163	10	)	)	PUNCT
ejpam-3421	163	11	(	(	PUNCT
ejpam-3421	163	12	2019	2019	NUM
ejpam-3421	163	13	)	)	PUNCT
ejpam-3421	163	14	,	,	PUNCT
ejpam-3421	163	15	499	499	NUM
ejpam-3421	163	16	-	-	SYM
ejpam-3421	163	17	505	505	NUM
ejpam-3421	163	18	503	503	NUM
ejpam-3421	163	19	suppose	suppose	VERB
ejpam-3421	163	20	now	now	ADV
ejpam-3421	163	21	that	that	SCONJ
ejpam-3421	163	22	p	p	PROPN
ejpam-3421	163	23	∈	∈	PROPN
ejpam-3421	163	24	y.	y.	NOUN
ejpam-3421	163	25	if	if	SCONJ
ejpam-3421	163	26	p	p	PROPN
ejpam-3421	163	27	∈	∈	PROPN
ejpam-3421	163	28	nhw(a	nhw(a	PROPN
ejpam-3421	163	29	)	)	PUNCT
ejpam-3421	163	30	,	,	PUNCT
ejpam-3421	163	31	then	then	ADV
ejpam-3421	163	32	dg	dg	VERB
ejpam-3421	163	33	◦	◦	NOUN
ejpam-3421	163	34	h(p	h(p	NOUN
ejpam-3421	163	35	,	,	PUNCT
ejpam-3421	163	36	a	a	PRON
ejpam-3421	163	37	)	)	PUNCT
ejpam-3421	163	38	=	=	SYM
ejpam-3421	163	39	dhw(p	dhw(p	PROPN
ejpam-3421	163	40	,	,	PUNCT
ejpam-3421	163	41	a	a	PRON
ejpam-3421	163	42	)	)	PUNCT
ejpam-3421	163	43	=	=	SYM
ejpam-3421	163	44	1	1	X
ejpam-3421	163	45	.	.	PUNCT
ejpam-3421	164	1	hence	hence	ADV
ejpam-3421	164	2	,	,	PUNCT
ejpam-3421	164	3	p	p	PROPN
ejpam-3421	164	4	∈	∈	PROPN
ejpam-3421	164	5	f	f	NOUN
ejpam-3421	164	6	2	2	NUM
ejpam-3421	164	7	g	g	NOUN
ejpam-3421	164	8	◦	◦	NOUN
ejpam-3421	164	9	h	h	NOUN
ejpam-3421	165	1	[	[	X
ejpam-3421	165	2	a	a	X
ejpam-3421	165	3	]	]	X
ejpam-3421	165	4	.	.	PUNCT
ejpam-3421	166	1	if	if	SCONJ
ejpam-3421	166	2	p	p	PROPN
ejpam-3421	166	3	∈	∈	PROPN
ejpam-3421	166	4	v	v	ADP
ejpam-3421	166	5	(	(	PUNCT
ejpam-3421	166	6	g)\ng(w	g)\ng(w	PROPN
ejpam-3421	166	7	)	)	PUNCT
ejpam-3421	166	8	,	,	PUNCT
ejpam-3421	166	9	then	then	ADV
ejpam-3421	166	10	dg	dg	VERB
ejpam-3421	166	11	◦	◦	NOUN
ejpam-3421	166	12	h(p	h(p	NOUN
ejpam-3421	166	13	,	,	PUNCT
ejpam-3421	166	14	w	w	NOUN
ejpam-3421	166	15	)	)	PUNCT
ejpam-3421	166	16	=	=	NOUN
ejpam-3421	166	17	dg(p	dg(p	X
ejpam-3421	166	18	,	,	PUNCT
ejpam-3421	166	19	w	w	NOUN
ejpam-3421	166	20	)	)	PUNCT
ejpam-3421	166	21	6=	6=	ADP
ejpam-3421	166	22	1	1	NUM
ejpam-3421	166	23	.	.	PUNCT
ejpam-3421	167	1	hence	hence	ADV
ejpam-3421	167	2	,	,	PUNCT
ejpam-3421	167	3	p	p	PROPN
ejpam-3421	167	4	6=	6=	ADP
ejpam-3421	167	5	a	a	DET
ejpam-3421	167	6	and	and	CCONJ
ejpam-3421	167	7	dg	dg	NOUN
ejpam-3421	167	8	◦	◦	PROPN
ejpam-3421	167	9	h(a	h(a	PROPN
ejpam-3421	167	10	,	,	PUNCT
ejpam-3421	167	11	p	p	NOUN
ejpam-3421	167	12	)	)	PUNCT
ejpam-3421	167	13	6=	6=	ADP
ejpam-3421	167	14	2	2	X
ejpam-3421	167	15	.	.	PUNCT
ejpam-3421	168	1	this	this	PRON
ejpam-3421	168	2	implies	imply	VERB
ejpam-3421	168	3	that	that	SCONJ
ejpam-3421	168	4	p	p	PROPN
ejpam-3421	168	5	∈	∈	PROPN
ejpam-3421	168	6	f	f	NOUN
ejpam-3421	168	7	2	2	NUM
ejpam-3421	168	8	g	g	NOUN
ejpam-3421	168	9	◦	◦	NOUN
ejpam-3421	168	10	h	h	NOUN
ejpam-3421	169	1	[	[	X
ejpam-3421	169	2	a	a	X
ejpam-3421	169	3	]	]	X
ejpam-3421	169	4	.	.	PUNCT
ejpam-3421	170	1	finally	finally	ADV
ejpam-3421	170	2	,	,	PUNCT
ejpam-3421	170	3	if	if	SCONJ
ejpam-3421	170	4	p	p	PROPN
ejpam-3421	170	5	∈	∈	PROPN
ejpam-3421	170	6	∪v∈v	∪v∈v	X
ejpam-3421	170	7	(	(	PUNCT
ejpam-3421	170	8	g)\{w}v	g)\{w}v	PROPN
ejpam-3421	170	9	(	(	PUNCT
ejpam-3421	170	10	hv	hv	PROPN
ejpam-3421	170	11	)	)	PUNCT
ejpam-3421	170	12	,	,	PUNCT
ejpam-3421	170	13	then	then	ADV
ejpam-3421	170	14	there	there	PRON
ejpam-3421	170	15	exists	exist	VERB
ejpam-3421	170	16	r	r	NOUN
ejpam-3421	170	17	∈	∈	PROPN
ejpam-3421	170	18	v	v	NOUN
ejpam-3421	170	19	(	(	PUNCT
ejpam-3421	170	20	g)\{w	g)\{w	NOUN
ejpam-3421	170	21	}	}	PUNCT
ejpam-3421	170	22	such	such	ADJ
ejpam-3421	170	23	that	that	SCONJ
ejpam-3421	170	24	p	p	PROPN
ejpam-3421	170	25	∈	∈	PROPN
ejpam-3421	170	26	v	v	ADP
ejpam-3421	170	27	(	(	PUNCT
ejpam-3421	170	28	hr	hr	NOUN
ejpam-3421	170	29	)	)	PUNCT
ejpam-3421	170	30	.	.	PUNCT
ejpam-3421	171	1	since	since	SCONJ
ejpam-3421	171	2	dg	dg	PROPN
ejpam-3421	171	3	◦	◦	PROPN
ejpam-3421	171	4	h(a	h(a	PROPN
ejpam-3421	171	5	,	,	PUNCT
ejpam-3421	171	6	p	p	NOUN
ejpam-3421	171	7	)	)	PUNCT
ejpam-3421	171	8	=	=	SYM
ejpam-3421	171	9	dg	dg	PROPN
ejpam-3421	171	10	◦	◦	PROPN
ejpam-3421	171	11	h(a	h(a	PROPN
ejpam-3421	171	12	,	,	PUNCT
ejpam-3421	171	13	w	w	PROPN
ejpam-3421	171	14	)	)	PUNCT
ejpam-3421	171	15	+	+	NUM
ejpam-3421	171	16	dg	dg	NOUN
ejpam-3421	171	17	◦	◦	NOUN
ejpam-3421	171	18	h(r	h(r	NOUN
ejpam-3421	171	19	,	,	PUNCT
ejpam-3421	171	20	w	w	PROPN
ejpam-3421	171	21	)	)	PUNCT
ejpam-3421	171	22	+	+	NUM
ejpam-3421	171	23	dg	dg	NOUN
ejpam-3421	171	24	◦	◦	NOUN
ejpam-3421	171	25	h(r	h(r	NOUN
ejpam-3421	171	26	,	,	PUNCT
ejpam-3421	171	27	p	p	NOUN
ejpam-3421	171	28	)	)	PUNCT
ejpam-3421	171	29	=	=	SYM
ejpam-3421	171	30	2	2	NUM
ejpam-3421	171	31	+	+	NUM
ejpam-3421	171	32	dg	dg	NOUN
ejpam-3421	171	33	◦	◦	NOUN
ejpam-3421	171	34	h(r	h(r	NOUN
ejpam-3421	171	35	,	,	PUNCT
ejpam-3421	171	36	w	w	PROPN
ejpam-3421	171	37	)	)	PUNCT
ejpam-3421	171	38	≥	≥	NOUN
ejpam-3421	171	39	3	3	NUM
ejpam-3421	171	40	,	,	PUNCT
ejpam-3421	171	41	it	it	PRON
ejpam-3421	171	42	follows	follow	VERB
ejpam-3421	171	43	that	that	SCONJ
ejpam-3421	171	44	p	p	PROPN
ejpam-3421	171	45	∈	∈	PROPN
ejpam-3421	171	46	f	f	NOUN
ejpam-3421	171	47	2	2	NUM
ejpam-3421	171	48	g	g	NOUN
ejpam-3421	171	49	◦	◦	NOUN
ejpam-3421	171	50	h	h	NOUN
ejpam-3421	172	1	[	[	X
ejpam-3421	172	2	a	a	X
ejpam-3421	172	3	]	]	X
ejpam-3421	172	4	.	.	PUNCT
ejpam-3421	173	1	therefore	therefore	ADV
ejpam-3421	173	2	,	,	PUNCT
ejpam-3421	173	3	nhw(a	nhw(a	PROPN
ejpam-3421	173	4	)	)	PUNCT
ejpam-3421	173	5	∪	∪	ADP
ejpam-3421	173	6	[	[	X
ejpam-3421	173	7	v	v	X
ejpam-3421	173	8	(	(	PUNCT
ejpam-3421	173	9	g)\ng(w	g)\ng(w	PROPN
ejpam-3421	173	10	)	)	PUNCT
ejpam-3421	173	11	]	]	PUNCT
ejpam-3421	173	12	∪	∪	ADP
ejpam-3421	173	13	[	[	PUNCT
ejpam-3421	173	14	∪v∈v	∪v∈v	NOUN
ejpam-3421	173	15	(	(	PUNCT
ejpam-3421	173	16	g)\{w}v	g)\{w}v	PROPN
ejpam-3421	173	17	(	(	PUNCT
ejpam-3421	173	18	hv	hv	PROPN
ejpam-3421	173	19	)	)	PUNCT
ejpam-3421	173	20	]	]	PUNCT
ejpam-3421	174	1	⊆	⊆	NUM
ejpam-3421	174	2	f	f	SYM
ejpam-3421	174	3	2	2	NUM
ejpam-3421	174	4	g	g	NOUN
ejpam-3421	174	5	◦	◦	NOUN
ejpam-3421	174	6	h	h	NOUN
ejpam-3421	175	1	[	[	X
ejpam-3421	175	2	a	a	X
ejpam-3421	175	3	]	]	X
ejpam-3421	175	4	.	.	PUNCT
ejpam-3421	176	1	accordingly	accordingly	ADV
ejpam-3421	176	2	,	,	PUNCT
ejpam-3421	176	3	the	the	DET
ejpam-3421	176	4	desired	desire	VERB
ejpam-3421	176	5	equality	equality	NOUN
ejpam-3421	176	6	follows	follow	VERB
ejpam-3421	176	7	.	.	PUNCT
ejpam-3421	177	1	definition	definition	NOUN
ejpam-3421	177	2	4	4	NUM
ejpam-3421	177	3	.	.	PUNCT
ejpam-3421	178	1	the	the	DET
ejpam-3421	178	2	lexicographic	lexicographic	ADJ
ejpam-3421	178	3	product	product	NOUN
ejpam-3421	178	4	(	(	PUNCT
ejpam-3421	178	5	composition	composition	NOUN
ejpam-3421	178	6	)	)	PUNCT
ejpam-3421	178	7	of	of	ADP
ejpam-3421	178	8	graphs	graph	NOUN
ejpam-3421	178	9	g	g	PROPN
ejpam-3421	178	10	and	and	CCONJ
ejpam-3421	178	11	h	h	NOUN
ejpam-3421	178	12	,	,	PUNCT
ejpam-3421	178	13	denoted	denote	VERB
ejpam-3421	178	14	by	by	ADP
ejpam-3421	178	15	g[h	g[h	NOUN
ejpam-3421	178	16	]	]	PUNCT
ejpam-3421	178	17	,	,	PUNCT
ejpam-3421	178	18	is	be	AUX
ejpam-3421	178	19	the	the	DET
ejpam-3421	178	20	graph	graph	NOUN
ejpam-3421	178	21	with	with	ADP
ejpam-3421	178	22	v	v	NOUN
ejpam-3421	178	23	(	(	PUNCT
ejpam-3421	178	24	g[h	g[h	PROPN
ejpam-3421	178	25	]	]	PUNCT
ejpam-3421	178	26	)	)	PUNCT
ejpam-3421	178	27	=	=	SYM
ejpam-3421	178	28	v	v	X
ejpam-3421	178	29	(	(	PUNCT
ejpam-3421	178	30	g)×v	g)×v	PROPN
ejpam-3421	178	31	(	(	PUNCT
ejpam-3421	178	32	h	h	NOUN
ejpam-3421	178	33	)	)	PUNCT
ejpam-3421	178	34	and	and	CCONJ
ejpam-3421	178	35	(	(	PUNCT
ejpam-3421	178	36	u	u	NOUN
ejpam-3421	178	37	,	,	PUNCT
ejpam-3421	178	38	v)(u′	v)(u′	NOUN
ejpam-3421	178	39	,	,	PUNCT
ejpam-3421	178	40	v′	v′	NOUN
ejpam-3421	178	41	)	)	PUNCT
ejpam-3421	178	42	∈	∈	NOUN
ejpam-3421	178	43	e(g[h	e(g[h	NOUN
ejpam-3421	178	44	]	]	PUNCT
ejpam-3421	178	45	)	)	PUNCT
ejpam-3421	179	1	if	if	SCONJ
ejpam-3421	179	2	and	and	CCONJ
ejpam-3421	179	3	only	only	ADV
ejpam-3421	179	4	if	if	SCONJ
ejpam-3421	179	5	either	either	CCONJ
ejpam-3421	179	6	uu′	uu′	PROPN
ejpam-3421	179	7	∈	∈	PROPN
ejpam-3421	179	8	e(g	e(g	PROPN
ejpam-3421	179	9	)	)	PUNCT
ejpam-3421	179	10	or	or	CCONJ
ejpam-3421	179	11	u	u	X
ejpam-3421	179	12	=	=	PUNCT
ejpam-3421	179	13	u′	u′	PROPN
ejpam-3421	179	14	and	and	CCONJ
ejpam-3421	179	15	vv′	vv′	NOUN
ejpam-3421	179	16	∈	∈	PROPN
ejpam-3421	179	17	e(h	e(h	PROPN
ejpam-3421	179	18	)	)	PUNCT
ejpam-3421	179	19	.	.	PUNCT
ejpam-3421	180	1	theorem	theorem	VERB
ejpam-3421	180	2	6	6	NUM
ejpam-3421	180	3	.	.	PUNCT
ejpam-3421	181	1	let	let	VERB
ejpam-3421	181	2	g	g	PROPN
ejpam-3421	181	3	=	=	SYM
ejpam-3421	181	4	(	(	PUNCT
ejpam-3421	181	5	v	v	NOUN
ejpam-3421	181	6	(	(	PUNCT
ejpam-3421	181	7	g	g	NOUN
ejpam-3421	181	8	)	)	PUNCT
ejpam-3421	181	9	,	,	PUNCT
ejpam-3421	181	10	e(g	e(g	PROPN
ejpam-3421	181	11	)	)	PUNCT
ejpam-3421	181	12	)	)	PUNCT
ejpam-3421	182	1	and	and	CCONJ
ejpam-3421	182	2	h	h	NOUN
ejpam-3421	182	3	=	=	SYM
ejpam-3421	182	4	(	(	PUNCT
ejpam-3421	182	5	v	v	NOUN
ejpam-3421	182	6	(	(	PUNCT
ejpam-3421	182	7	h	h	NOUN
ejpam-3421	182	8	)	)	PUNCT
ejpam-3421	182	9	,	,	PUNCT
ejpam-3421	182	10	e(h	e(h	PROPN
ejpam-3421	182	11	)	)	PUNCT
ejpam-3421	182	12	)	)	PUNCT
ejpam-3421	182	13	be	be	AUX
ejpam-3421	182	14	any	any	DET
ejpam-3421	182	15	two	two	NUM
ejpam-3421	182	16	graphs	graph	NOUN
ejpam-3421	182	17	and	and	CCONJ
ejpam-3421	182	18	let	let	VERB
ejpam-3421	182	19	(	(	PUNCT
ejpam-3421	182	20	v	v	NOUN
ejpam-3421	182	21	,	,	PUNCT
ejpam-3421	182	22	a	a	PRON
ejpam-3421	182	23	)	)	PUNCT
ejpam-3421	182	24	∈	∈	NOUN
ejpam-3421	182	25	v	v	NOUN
ejpam-3421	182	26	(	(	PUNCT
ejpam-3421	182	27	g[h	g[h	PROPN
ejpam-3421	182	28	]	]	PUNCT
ejpam-3421	182	29	)	)	PUNCT
ejpam-3421	182	30	.	.	PUNCT
ejpam-3421	183	1	then	then	ADV
ejpam-3421	183	2	f	f	PROPN
ejpam-3421	183	3	2	2	NUM
ejpam-3421	183	4	g[h][(v	g[h][(v	VERB
ejpam-3421	183	5	,	,	PUNCT
ejpam-3421	183	6	a	a	PRON
ejpam-3421	183	7	)	)	PUNCT
ejpam-3421	183	8	]	]	PUNCT
ejpam-3421	184	1	=	=	PUNCT
ejpam-3421	184	2	(	(	PUNCT
ejpam-3421	184	3	f	f	PROPN
ejpam-3421	184	4	2	2	NUM
ejpam-3421	184	5	g[v]×	g[v]×	NOUN
ejpam-3421	184	6	v	v	X
ejpam-3421	184	7	(	(	PUNCT
ejpam-3421	184	8	h	h	NOUN
ejpam-3421	184	9	)	)	PUNCT
ejpam-3421	184	10	)	)	PUNCT
ejpam-3421	184	11	∪	∪	ADP
ejpam-3421	184	12	(	(	PUNCT
ejpam-3421	184	13	{	{	PUNCT
ejpam-3421	184	14	v	v	NOUN
ejpam-3421	184	15	}	}	PUNCT
ejpam-3421	184	16	×	×	PROPN
ejpam-3421	184	17	f	f	NOUN
ejpam-3421	184	18	2	2	NUM
ejpam-3421	184	19	h	h	NOUN
ejpam-3421	185	1	[	[	X
ejpam-3421	185	2	a	a	X
ejpam-3421	185	3	]	]	X
ejpam-3421	185	4	)	)	PUNCT
ejpam-3421	185	5	.	.	PUNCT
ejpam-3421	186	1	proof	proof	NOUN
ejpam-3421	186	2	.	.	PUNCT
ejpam-3421	187	1	note	note	VERB
ejpam-3421	187	2	that	that	SCONJ
ejpam-3421	187	3	(	(	PUNCT
ejpam-3421	187	4	x	x	X
ejpam-3421	187	5	,	,	PUNCT
ejpam-3421	187	6	q	q	X
ejpam-3421	187	7	)	)	PUNCT
ejpam-3421	187	8	∈	∈	PROPN
ejpam-3421	187	9	f	f	PROPN
ejpam-3421	187	10	2	2	NUM
ejpam-3421	187	11	g[h][(v	g[h][(v	VERB
ejpam-3421	187	12	,	,	PUNCT
ejpam-3421	187	13	a	a	X
ejpam-3421	187	14	)	)	PUNCT
ejpam-3421	187	15	]	]	PUNCT
ejpam-3421	187	16	if	if	SCONJ
ejpam-3421	187	17	and	and	CCONJ
ejpam-3421	187	18	only	only	ADV
ejpam-3421	187	19	if	if	SCONJ
ejpam-3421	187	20	(	(	PUNCT
ejpam-3421	187	21	x	x	NOUN
ejpam-3421	187	22	,	,	PUNCT
ejpam-3421	187	23	q	q	NOUN
ejpam-3421	187	24	)	)	PUNCT
ejpam-3421	187	25	6=	6=	ADP
ejpam-3421	187	26	(	(	PUNCT
ejpam-3421	187	27	v	v	NOUN
ejpam-3421	187	28	,	,	PUNCT
ejpam-3421	187	29	a	a	PRON
ejpam-3421	187	30	)	)	PUNCT
ejpam-3421	187	31	and	and	CCONJ
ejpam-3421	187	32	dg[h]((x	dg[h]((x	NOUN
ejpam-3421	187	33	,	,	PUNCT
ejpam-3421	187	34	q	q	NOUN
ejpam-3421	187	35	)	)	PUNCT
ejpam-3421	187	36	,	,	PUNCT
ejpam-3421	187	37	(	(	PUNCT
ejpam-3421	187	38	v	v	NOUN
ejpam-3421	187	39	,	,	PUNCT
ejpam-3421	187	40	a	a	PRON
ejpam-3421	187	41	)	)	PUNCT
ejpam-3421	187	42	)	)	PUNCT
ejpam-3421	187	43	6=	6=	ADP
ejpam-3421	188	1	2	2	X
ejpam-3421	188	2	.	.	X
ejpam-3421	188	3	consider	consider	VERB
ejpam-3421	188	4	the	the	DET
ejpam-3421	188	5	following	follow	VERB
ejpam-3421	188	6	cases	case	NOUN
ejpam-3421	188	7	:	:	PUNCT
ejpam-3421	188	8	case	case	NOUN
ejpam-3421	188	9	1	1	X
ejpam-3421	188	10	.	.	PUNCT
ejpam-3421	188	11	suppose	suppose	VERB
ejpam-3421	188	12	x	x	PUNCT
ejpam-3421	188	13	=	=	PUNCT
ejpam-3421	189	1	v.	v.	ADP
ejpam-3421	189	2	then	then	ADV
ejpam-3421	189	3	q	q	X
ejpam-3421	189	4	6=	6=	NUM
ejpam-3421	189	5	a.	a.	NOUN
ejpam-3421	189	6	since	since	SCONJ
ejpam-3421	189	7	dg[h]((v	dg[h]((v	NOUN
ejpam-3421	189	8	,	,	PUNCT
ejpam-3421	189	9	q	q	NOUN
ejpam-3421	189	10	)	)	PUNCT
ejpam-3421	189	11	,	,	PUNCT
ejpam-3421	189	12	(	(	PUNCT
ejpam-3421	189	13	v	v	NOUN
ejpam-3421	189	14	,	,	PUNCT
ejpam-3421	189	15	a	a	PRON
ejpam-3421	189	16	)	)	PUNCT
ejpam-3421	189	17	)	)	PUNCT
ejpam-3421	189	18	=	=	PUNCT
ejpam-3421	190	1	dh(a	dh(a	ADJ
ejpam-3421	190	2	,	,	PUNCT
ejpam-3421	190	3	q	q	NOUN
ejpam-3421	190	4	)	)	PUNCT
ejpam-3421	190	5	6=	6=	ADP
ejpam-3421	190	6	2	2	NUM
ejpam-3421	190	7	,	,	PUNCT
ejpam-3421	190	8	q	q	PROPN
ejpam-3421	190	9	∈	∈	PROPN
ejpam-3421	190	10	f	f	PROPN
ejpam-3421	190	11	2	2	NUM
ejpam-3421	190	12	h	h	NOUN
ejpam-3421	191	1	[	[	X
ejpam-3421	191	2	a	a	X
ejpam-3421	191	3	]	]	X
ejpam-3421	191	4	,	,	PUNCT
ejpam-3421	191	5	q	q	PROPN
ejpam-3421	191	6	∈	∈	PROPN
ejpam-3421	191	7	f	f	PROPN
ejpam-3421	191	8	2	2	NUM
ejpam-3421	191	9	h	h	NOUN
ejpam-3421	192	1	[	[	X
ejpam-3421	192	2	a	a	X
ejpam-3421	192	3	]	]	X
ejpam-3421	192	4	.	.	PUNCT
ejpam-3421	193	1	hence	hence	ADV
ejpam-3421	193	2	,	,	PUNCT
ejpam-3421	193	3	(	(	PUNCT
ejpam-3421	193	4	x	x	X
ejpam-3421	193	5	,	,	PUNCT
ejpam-3421	193	6	q	q	ADJ
ejpam-3421	193	7	)	)	PUNCT
ejpam-3421	193	8	∈	∈	PROPN
ejpam-3421	193	9	{	{	PUNCT
ejpam-3421	193	10	v	v	NOUN
ejpam-3421	193	11	}	}	PUNCT
ejpam-3421	193	12	×	×	PROPN
ejpam-3421	193	13	f	f	NOUN
ejpam-3421	193	14	2	2	NUM
ejpam-3421	193	15	h	h	NOUN
ejpam-3421	194	1	[	[	X
ejpam-3421	194	2	a	a	X
ejpam-3421	194	3	]	]	X
ejpam-3421	194	4	.	.	PUNCT
ejpam-3421	195	1	case	case	NOUN
ejpam-3421	195	2	2	2	X
ejpam-3421	195	3	.	.	PUNCT
ejpam-3421	195	4	suppose	suppose	VERB
ejpam-3421	195	5	x	x	PUNCT
ejpam-3421	195	6	6=	6=	ADP
ejpam-3421	195	7	v.	v.	CCONJ
ejpam-3421	195	8	then	then	ADV
ejpam-3421	195	9	dg(x	dg(x	NUM
ejpam-3421	195	10	,	,	PUNCT
ejpam-3421	195	11	v	v	NOUN
ejpam-3421	195	12	)	)	PUNCT
ejpam-3421	195	13	=	=	PUNCT
ejpam-3421	196	1	dg[h]((x	dg[h]((x	NOUN
ejpam-3421	196	2	,	,	PUNCT
ejpam-3421	196	3	q	q	NOUN
ejpam-3421	196	4	)	)	PUNCT
ejpam-3421	196	5	,	,	PUNCT
ejpam-3421	196	6	(	(	PUNCT
ejpam-3421	196	7	v	v	NOUN
ejpam-3421	196	8	,	,	PUNCT
ejpam-3421	196	9	a	a	PRON
ejpam-3421	196	10	)	)	PUNCT
ejpam-3421	196	11	)	)	PUNCT
ejpam-3421	196	12	6=	6=	ADP
ejpam-3421	197	1	2	2	X
ejpam-3421	197	2	.	.	PUNCT
ejpam-3421	198	1	hence	hence	ADV
ejpam-3421	198	2	,	,	PUNCT
ejpam-3421	198	3	x	x	PUNCT
ejpam-3421	198	4	∈	∈	PROPN
ejpam-3421	198	5	f	f	PROPN
ejpam-3421	198	6	2	2	NUM
ejpam-3421	198	7	g[v	g[v	NOUN
ejpam-3421	198	8	]	]	PUNCT
ejpam-3421	198	9	and	and	CCONJ
ejpam-3421	198	10	(	(	PUNCT
ejpam-3421	198	11	x	x	NOUN
ejpam-3421	198	12	,	,	PUNCT
ejpam-3421	198	13	q	q	X
ejpam-3421	198	14	)	)	PUNCT
ejpam-3421	198	15	∈	∈	PROPN
ejpam-3421	198	16	f	f	NOUN
ejpam-3421	198	17	2	2	NUM
ejpam-3421	198	18	g[v]×	g[v]×	NOUN
ejpam-3421	198	19	v	v	X
ejpam-3421	198	20	(	(	PUNCT
ejpam-3421	198	21	h	h	NOUN
ejpam-3421	198	22	)	)	PUNCT
ejpam-3421	198	23	.	.	PUNCT
ejpam-3421	199	1	therefore	therefore	ADV
ejpam-3421	199	2	,	,	PUNCT
ejpam-3421	199	3	f	f	PROPN
ejpam-3421	199	4	2	2	NUM
ejpam-3421	199	5	g[h][(v	g[h][(v	VERB
ejpam-3421	199	6	,	,	PUNCT
ejpam-3421	199	7	a	a	NOUN
ejpam-3421	199	8	)	)	PUNCT
ejpam-3421	199	9	]	]	PUNCT
ejpam-3421	200	1	⊆	⊆	X
ejpam-3421	200	2	(	(	PUNCT
ejpam-3421	200	3	f	f	PROPN
ejpam-3421	200	4	2	2	NUM
ejpam-3421	200	5	g[v]×	g[v]×	NOUN
ejpam-3421	200	6	v	v	X
ejpam-3421	200	7	(	(	PUNCT
ejpam-3421	200	8	h	h	NOUN
ejpam-3421	200	9	)	)	PUNCT
ejpam-3421	200	10	)	)	PUNCT
ejpam-3421	200	11	∪	∪	ADP
ejpam-3421	200	12	(	(	PUNCT
ejpam-3421	200	13	{	{	PUNCT
ejpam-3421	200	14	v	v	NOUN
ejpam-3421	200	15	}	}	PUNCT
ejpam-3421	200	16	×	×	PROPN
ejpam-3421	200	17	f	f	NOUN
ejpam-3421	200	18	2	2	NUM
ejpam-3421	200	19	h	h	NOUN
ejpam-3421	201	1	[	[	X
ejpam-3421	201	2	a	a	X
ejpam-3421	201	3	]	]	X
ejpam-3421	201	4	)	)	PUNCT
ejpam-3421	201	5	.	.	PUNCT
ejpam-3421	202	1	next	next	ADV
ejpam-3421	202	2	,	,	PUNCT
ejpam-3421	202	3	let	let	VERB
ejpam-3421	202	4	(	(	PUNCT
ejpam-3421	202	5	w	w	NOUN
ejpam-3421	202	6	,	,	PUNCT
ejpam-3421	202	7	p	p	NOUN
ejpam-3421	202	8	)	)	PUNCT
ejpam-3421	202	9	∈	∈	PROPN
ejpam-3421	202	10	f	f	PROPN
ejpam-3421	202	11	2	2	NUM
ejpam-3421	202	12	g[v	g[v	NOUN
ejpam-3421	202	13	]	]	X
ejpam-3421	202	14	×	×	NOUN
ejpam-3421	202	15	v	v	NOUN
ejpam-3421	202	16	(	(	PUNCT
ejpam-3421	202	17	h	h	NOUN
ejpam-3421	202	18	)	)	PUNCT
ejpam-3421	202	19	.	.	PUNCT
ejpam-3421	203	1	then	then	ADV
ejpam-3421	203	2	w	w	PROPN
ejpam-3421	203	3	∈	∈	PROPN
ejpam-3421	203	4	f	f	PROPN
ejpam-3421	203	5	2	2	NUM
ejpam-3421	203	6	g[v	g[v	NOUN
ejpam-3421	203	7	]	]	PUNCT
ejpam-3421	203	8	,	,	PUNCT
ejpam-3421	203	9	that	that	ADV
ejpam-3421	203	10	is	is	ADV
ejpam-3421	203	11	,	,	PUNCT
ejpam-3421	203	12	w	w	PROPN
ejpam-3421	203	13	6=	6=	PROPN
ejpam-3421	203	14	v	v	NOUN
ejpam-3421	203	15	and	and	CCONJ
ejpam-3421	203	16	dg(w	dg(w	NOUN
ejpam-3421	203	17	,	,	PUNCT
ejpam-3421	203	18	v	v	NOUN
ejpam-3421	203	19	)	)	PUNCT
ejpam-3421	203	20	6=	6=	ADP
ejpam-3421	203	21	2	2	X
ejpam-3421	203	22	.	.	PUNCT
ejpam-3421	204	1	it	it	PRON
ejpam-3421	204	2	follows	follow	VERB
ejpam-3421	204	3	that	that	SCONJ
ejpam-3421	204	4	(	(	PUNCT
ejpam-3421	204	5	w	w	PROPN
ejpam-3421	204	6	,	,	PUNCT
ejpam-3421	204	7	p	p	NOUN
ejpam-3421	204	8	)	)	PUNCT
ejpam-3421	204	9	6=	6=	ADP
ejpam-3421	204	10	(	(	PUNCT
ejpam-3421	204	11	v	v	NOUN
ejpam-3421	204	12	,	,	PUNCT
ejpam-3421	204	13	a	a	PRON
ejpam-3421	204	14	)	)	PUNCT
ejpam-3421	204	15	and	and	CCONJ
ejpam-3421	204	16	dg[h]((w	dg[h]((w	NOUN
ejpam-3421	204	17	,	,	PUNCT
ejpam-3421	204	18	p	p	NOUN
ejpam-3421	204	19	)	)	PUNCT
ejpam-3421	204	20	,	,	PUNCT
ejpam-3421	204	21	(	(	PUNCT
ejpam-3421	204	22	v	v	NOUN
ejpam-3421	204	23	,	,	PUNCT
ejpam-3421	204	24	a	a	PRON
ejpam-3421	204	25	)	)	PUNCT
ejpam-3421	204	26	)	)	PUNCT
ejpam-3421	205	1	=	=	SYM
ejpam-3421	205	2	dg(w	dg(w	X
ejpam-3421	205	3	,	,	PUNCT
ejpam-3421	205	4	v	v	NOUN
ejpam-3421	205	5	)	)	PUNCT
ejpam-3421	205	6	6=	6=	ADP
ejpam-3421	205	7	2	2	X
ejpam-3421	205	8	.	.	PUNCT
ejpam-3421	206	1	this	this	PRON
ejpam-3421	206	2	shows	show	VERB
ejpam-3421	206	3	that	that	SCONJ
ejpam-3421	206	4	(	(	PUNCT
ejpam-3421	206	5	w	w	PROPN
ejpam-3421	206	6	,	,	PUNCT
ejpam-3421	206	7	p	p	NOUN
ejpam-3421	206	8	)	)	PUNCT
ejpam-3421	206	9	∈	∈	PROPN
ejpam-3421	206	10	f	f	PROPN
ejpam-3421	206	11	2	2	NUM
ejpam-3421	206	12	g[h][(v	g[h][(v	VERB
ejpam-3421	206	13	,	,	PUNCT
ejpam-3421	206	14	a	a	PRON
ejpam-3421	206	15	)	)	PUNCT
ejpam-3421	206	16	]	]	PUNCT
ejpam-3421	206	17	.	.	PUNCT
ejpam-3421	207	1	hence	hence	ADV
ejpam-3421	207	2	,	,	PUNCT
ejpam-3421	207	3	f	f	PROPN
ejpam-3421	207	4	2	2	NUM
ejpam-3421	207	5	g[v	g[v	NOUN
ejpam-3421	207	6	]	]	X
ejpam-3421	207	7	×	×	NOUN
ejpam-3421	207	8	v	v	NOUN
ejpam-3421	207	9	(	(	PUNCT
ejpam-3421	207	10	h	h	NOUN
ejpam-3421	207	11	)	)	PUNCT
ejpam-3421	207	12	⊆	⊆	NUM
ejpam-3421	207	13	fg[h][(v	fg[h][(v	PROPN
ejpam-3421	207	14	,	,	PUNCT
ejpam-3421	207	15	a	a	PRON
ejpam-3421	207	16	)	)	PUNCT
ejpam-3421	207	17	]	]	PUNCT
ejpam-3421	207	18	.	.	PUNCT
ejpam-3421	208	1	finally	finally	ADV
ejpam-3421	208	2	,	,	PUNCT
ejpam-3421	208	3	let	let	VERB
ejpam-3421	208	4	(	(	PUNCT
ejpam-3421	208	5	z	z	NOUN
ejpam-3421	208	6	,	,	PUNCT
ejpam-3421	208	7	t	t	PROPN
ejpam-3421	208	8	)	)	PUNCT
ejpam-3421	208	9	∈	∈	PROPN
ejpam-3421	208	10	{	{	PUNCT
ejpam-3421	208	11	v	v	NOUN
ejpam-3421	208	12	}	}	PUNCT
ejpam-3421	208	13	×	×	PROPN
ejpam-3421	208	14	f	f	NOUN
ejpam-3421	208	15	2	2	NUM
ejpam-3421	208	16	h	h	NOUN
ejpam-3421	209	1	[	[	X
ejpam-3421	209	2	a	a	X
ejpam-3421	209	3	]	]	X
ejpam-3421	209	4	.	.	PUNCT
ejpam-3421	210	1	then	then	ADV
ejpam-3421	210	2	z	z	NOUN
ejpam-3421	210	3	=	=	SYM
ejpam-3421	210	4	v	v	PROPN
ejpam-3421	210	5	and	and	CCONJ
ejpam-3421	210	6	t	t	NOUN
ejpam-3421	210	7	∈	∈	PROPN
ejpam-3421	211	1	f	f	PROPN
ejpam-3421	211	2	2	2	NUM
ejpam-3421	211	3	h	h	NOUN
ejpam-3421	212	1	[	[	X
ejpam-3421	212	2	a	a	X
ejpam-3421	212	3	]	]	X
ejpam-3421	212	4	.	.	PUNCT
ejpam-3421	213	1	hence	hence	ADV
ejpam-3421	213	2	,	,	PUNCT
ejpam-3421	213	3	t	t	PROPN
ejpam-3421	213	4	6=	6=	PROPN
ejpam-3421	213	5	a	a	PRON
ejpam-3421	213	6	and	and	CCONJ
ejpam-3421	213	7	dh(a	dh(a	ADJ
ejpam-3421	213	8	,	,	PUNCT
ejpam-3421	213	9	t	t	PROPN
ejpam-3421	213	10	)	)	PUNCT
ejpam-3421	213	11	6=	6=	ADP
ejpam-3421	213	12	2	2	NUM
ejpam-3421	213	13	.	.	PUNCT
ejpam-3421	213	14	consequently	consequently	ADV
ejpam-3421	213	15	,	,	PUNCT
ejpam-3421	213	16	(	(	PUNCT
ejpam-3421	213	17	z	z	NOUN
ejpam-3421	213	18	,	,	PUNCT
ejpam-3421	213	19	t	t	PROPN
ejpam-3421	213	20	)	)	PUNCT
ejpam-3421	213	21	6=	6=	ADP
ejpam-3421	213	22	(	(	PUNCT
ejpam-3421	213	23	v	v	NOUN
ejpam-3421	213	24	,	,	PUNCT
ejpam-3421	213	25	a	a	PRON
ejpam-3421	213	26	)	)	PUNCT
ejpam-3421	213	27	and	and	CCONJ
ejpam-3421	213	28	dg[h]((z	dg[h]((z	PROPN
ejpam-3421	213	29	,	,	PUNCT
ejpam-3421	213	30	t	t	PROPN
ejpam-3421	213	31	)	)	PUNCT
ejpam-3421	213	32	,	,	PUNCT
ejpam-3421	213	33	(	(	PUNCT
ejpam-3421	213	34	v	v	NOUN
ejpam-3421	213	35	,	,	PUNCT
ejpam-3421	213	36	a	a	PRON
ejpam-3421	213	37	)	)	PUNCT
ejpam-3421	213	38	)	)	PUNCT
ejpam-3421	214	1	=	=	SYM
ejpam-3421	214	2	dh(a	dh(a	ADJ
ejpam-3421	214	3	,	,	PUNCT
ejpam-3421	214	4	t	t	PROPN
ejpam-3421	214	5	)	)	PUNCT
ejpam-3421	214	6	6=	6=	ADP
ejpam-3421	214	7	2	2	NUM
ejpam-3421	214	8	,	,	PUNCT
ejpam-3421	214	9	showing	show	VERB
ejpam-3421	214	10	that	that	SCONJ
ejpam-3421	214	11	(	(	PUNCT
ejpam-3421	214	12	z	z	NOUN
ejpam-3421	214	13	,	,	PUNCT
ejpam-3421	214	14	t	t	PROPN
ejpam-3421	214	15	)	)	PUNCT
ejpam-3421	214	16	∈	∈	PROPN
ejpam-3421	214	17	f	f	PROPN
ejpam-3421	214	18	2	2	NUM
ejpam-3421	214	19	g[h][a	g[h][a	PROPN
ejpam-3421	214	20	]	]	PUNCT
ejpam-3421	214	21	.	.	PUNCT
ejpam-3421	215	1	thus	thus	ADV
ejpam-3421	215	2	,	,	PUNCT
ejpam-3421	215	3	{	{	PUNCT
ejpam-3421	215	4	v	v	NOUN
ejpam-3421	215	5	}	}	PUNCT
ejpam-3421	215	6	×	×	PROPN
ejpam-3421	215	7	f	f	NOUN
ejpam-3421	215	8	2	2	NUM
ejpam-3421	215	9	h	h	NOUN
ejpam-3421	216	1	[	[	X
ejpam-3421	216	2	a	a	X
ejpam-3421	216	3	]	]	X
ejpam-3421	216	4	⊆	⊆	NUM
ejpam-3421	216	5	f	f	SYM
ejpam-3421	216	6	2	2	NUM
ejpam-3421	216	7	g[h][(v	g[h][(v	VERB
ejpam-3421	216	8	,	,	PUNCT
ejpam-3421	216	9	a	a	PRON
ejpam-3421	216	10	)	)	PUNCT
ejpam-3421	216	11	]	]	PUNCT
ejpam-3421	216	12	.	.	PUNCT
ejpam-3421	217	1	this	this	PRON
ejpam-3421	217	2	establishes	establish	VERB
ejpam-3421	217	3	the	the	DET
ejpam-3421	217	4	desired	desire	VERB
ejpam-3421	217	5	equality	equality	NOUN
ejpam-3421	217	6	.	.	PUNCT
ejpam-3421	218	1	c.	c.	PROPN
ejpam-3421	218	2	nianga	nianga	PROPN
ejpam-3421	218	3	,	,	PUNCT
ejpam-3421	218	4	s.	s.	PROPN
ejpam-3421	218	5	canoy	canoy	PROPN
ejpam-3421	218	6	/	/	SYM
ejpam-3421	218	7	eur	eur	PROPN
ejpam-3421	218	8	.	.	PUNCT
ejpam-3421	219	1	j.	j.	PROPN
ejpam-3421	219	2	pure	pure	PROPN
ejpam-3421	219	3	appl	appl	PROPN
ejpam-3421	219	4	.	.	PROPN
ejpam-3421	219	5	math	math	PROPN
ejpam-3421	219	6	,	,	PUNCT
ejpam-3421	219	7	12	12	NUM
ejpam-3421	219	8	(	(	PUNCT
ejpam-3421	219	9	2	2	NUM
ejpam-3421	219	10	)	)	PUNCT
ejpam-3421	219	11	(	(	PUNCT
ejpam-3421	219	12	2019	2019	NUM
ejpam-3421	219	13	)	)	PUNCT
ejpam-3421	219	14	,	,	PUNCT
ejpam-3421	219	15	499	499	NUM
ejpam-3421	219	16	-	-	SYM
ejpam-3421	219	17	505	505	NUM
ejpam-3421	219	18	504	504	NUM
ejpam-3421	219	19	definition	definition	NOUN
ejpam-3421	219	20	5	5	NUM
ejpam-3421	219	21	.	.	PUNCT
ejpam-3421	220	1	the	the	DET
ejpam-3421	220	2	cartesian	cartesian	ADJ
ejpam-3421	220	3	product	product	NOUN
ejpam-3421	220	4	of	of	ADP
ejpam-3421	220	5	two	two	NUM
ejpam-3421	220	6	graphs	graph	NOUN
ejpam-3421	220	7	g1	g1	NOUN
ejpam-3421	220	8	and	and	CCONJ
ejpam-3421	220	9	g2	g2	PROPN
ejpam-3421	220	10	denoted	denote	VERB
ejpam-3421	220	11	by	by	ADP
ejpam-3421	220	12	g1	g1	PROPN
ejpam-3421	220	13	�	�	PROPN
ejpam-3421	220	14	g2	g2	PROPN
ejpam-3421	220	15	is	be	AUX
ejpam-3421	220	16	a	a	DET
ejpam-3421	220	17	graph	graph	NOUN
ejpam-3421	220	18	with	with	ADP
ejpam-3421	220	19	v	v	NOUN
ejpam-3421	220	20	(	(	PUNCT
ejpam-3421	220	21	g1	g1	PROPN
ejpam-3421	220	22	�	�	PROPN
ejpam-3421	220	23	g2	g2	PROPN
ejpam-3421	220	24	)	)	PUNCT
ejpam-3421	221	1	=	=	SYM
ejpam-3421	221	2	v	v	X
ejpam-3421	221	3	(	(	PUNCT
ejpam-3421	221	4	g1	g1	PROPN
ejpam-3421	221	5	)	)	PUNCT
ejpam-3421	221	6	×	×	NOUN
ejpam-3421	221	7	v	v	NOUN
ejpam-3421	221	8	(	(	PUNCT
ejpam-3421	221	9	g2	g2	PROPN
ejpam-3421	221	10	)	)	PUNCT
ejpam-3421	221	11	and	and	CCONJ
ejpam-3421	221	12	two	two	NUM
ejpam-3421	221	13	vertices	vertice	VERB
ejpam-3421	221	14	a	a	DET
ejpam-3421	221	15	=	=	PUNCT
ejpam-3421	221	16	(	(	PUNCT
ejpam-3421	221	17	u1	u1	PROPN
ejpam-3421	221	18	,	,	PUNCT
ejpam-3421	221	19	u2	u2	PROPN
ejpam-3421	221	20	)	)	PUNCT
ejpam-3421	221	21	and	and	CCONJ
ejpam-3421	221	22	b	b	X
ejpam-3421	221	23	=	=	SYM
ejpam-3421	221	24	(	(	PUNCT
ejpam-3421	221	25	v1	v1	PROPN
ejpam-3421	221	26	,	,	PUNCT
ejpam-3421	221	27	v2	v2	PROPN
ejpam-3421	221	28	)	)	PUNCT
ejpam-3421	221	29	are	be	AUX
ejpam-3421	221	30	adjacent	adjacent	ADJ
ejpam-3421	221	31	in	in	ADP
ejpam-3421	221	32	g1	g1	PROPN
ejpam-3421	221	33	�	�	PROPN
ejpam-3421	221	34	g2	g2	PROPN
ejpam-3421	221	35	if	if	SCONJ
ejpam-3421	221	36	and	and	CCONJ
ejpam-3421	221	37	only	only	ADV
ejpam-3421	221	38	if	if	SCONJ
ejpam-3421	221	39	either	either	PRON
ejpam-3421	221	40	u1	u1	NOUN
ejpam-3421	221	41	=	=	SYM
ejpam-3421	221	42	v1	v1	NOUN
ejpam-3421	221	43	and	and	CCONJ
ejpam-3421	221	44	u2v2	u2v2	PROPN
ejpam-3421	221	45	∈	∈	PROPN
ejpam-3421	221	46	e(g2	e(g2	X
ejpam-3421	221	47	)	)	PUNCT
ejpam-3421	221	48	or	or	CCONJ
ejpam-3421	221	49	u2	u2	NOUN
ejpam-3421	221	50	=	=	PUNCT
ejpam-3421	221	51	v2	v2	PROPN
ejpam-3421	221	52	and	and	CCONJ
ejpam-3421	221	53	u1v1	u1v1	NOUN
ejpam-3421	221	54	∈	∈	PROPN
ejpam-3421	221	55	e(g1	e(g1	NOUN
ejpam-3421	221	56	)	)	PUNCT
ejpam-3421	221	57	.	.	PUNCT
ejpam-3421	222	1	theorem	theorem	ADJ
ejpam-3421	222	2	7	7	NUM
ejpam-3421	222	3	.	.	PUNCT
ejpam-3421	223	1	let	let	VERB
ejpam-3421	223	2	k	k	NOUN
ejpam-3421	223	3	=	=	PUNCT
ejpam-3421	223	4	g	g	PROPN
ejpam-3421	223	5	�	�	NOUN
ejpam-3421	223	6	h	h	NOUN
ejpam-3421	223	7	=	=	SYM
ejpam-3421	223	8	(	(	PUNCT
ejpam-3421	223	9	v	v	NOUN
ejpam-3421	223	10	(	(	PUNCT
ejpam-3421	223	11	k	k	NOUN
ejpam-3421	223	12	)	)	PUNCT
ejpam-3421	223	13	,	,	PUNCT
ejpam-3421	223	14	e(k	e(k	NOUN
ejpam-3421	223	15	)	)	PUNCT
ejpam-3421	223	16	)	)	PUNCT
ejpam-3421	223	17	,	,	PUNCT
ejpam-3421	223	18	where	where	SCONJ
ejpam-3421	223	19	g	g	NOUN
ejpam-3421	223	20	=	=	SYM
ejpam-3421	223	21	(	(	PUNCT
ejpam-3421	223	22	v	v	NOUN
ejpam-3421	223	23	(	(	PUNCT
ejpam-3421	223	24	g	g	NOUN
ejpam-3421	223	25	)	)	PUNCT
ejpam-3421	223	26	,	,	PUNCT
ejpam-3421	223	27	e(g	e(g	PROPN
ejpam-3421	223	28	)	)	PUNCT
ejpam-3421	223	29	)	)	PUNCT
ejpam-3421	223	30	and	and	CCONJ
ejpam-3421	223	31	h	h	NOUN
ejpam-3421	223	32	=	=	SYM
ejpam-3421	223	33	(	(	PUNCT
ejpam-3421	223	34	v	v	NOUN
ejpam-3421	223	35	(	(	PUNCT
ejpam-3421	223	36	h	h	NOUN
ejpam-3421	223	37	)	)	PUNCT
ejpam-3421	223	38	,	,	PUNCT
ejpam-3421	223	39	e(h	e(h	PROPN
ejpam-3421	223	40	)	)	PUNCT
ejpam-3421	223	41	)	)	PUNCT
ejpam-3421	223	42	.	.	PUNCT
ejpam-3421	224	1	then	then	ADV
ejpam-3421	224	2	for	for	SCONJ
ejpam-3421	224	3	each	each	DET
ejpam-3421	224	4	(	(	PUNCT
ejpam-3421	224	5	v	v	NOUN
ejpam-3421	224	6	,	,	PUNCT
ejpam-3421	224	7	a	a	PRON
ejpam-3421	224	8	)	)	PUNCT
ejpam-3421	224	9	∈	∈	NOUN
ejpam-3421	224	10	v	v	NOUN
ejpam-3421	224	11	(	(	PUNCT
ejpam-3421	224	12	k	k	NOUN
ejpam-3421	224	13	)	)	PUNCT
ejpam-3421	224	14	,	,	PUNCT
ejpam-3421	224	15	f	f	PROPN
ejpam-3421	224	16	2	2	NUM
ejpam-3421	224	17	k	k	X
ejpam-3421	224	18	[	[	X
ejpam-3421	224	19	(	(	PUNCT
ejpam-3421	224	20	v	v	NOUN
ejpam-3421	224	21	,	,	PUNCT
ejpam-3421	224	22	a	a	NOUN
ejpam-3421	224	23	)	)	PUNCT
ejpam-3421	224	24	]	]	PUNCT
ejpam-3421	225	1	=	=	PUNCT
ejpam-3421	225	2	[	[	PUNCT
ejpam-3421	225	3	f	f	NOUN
ejpam-3421	225	4	2	2	NUM
ejpam-3421	225	5	g[v]×	g[v]×	ADV
ejpam-3421	225	6	{	{	PUNCT
ejpam-3421	225	7	a	a	NOUN
ejpam-3421	225	8	}	}	PUNCT
ejpam-3421	225	9	]	]	PUNCT
ejpam-3421	225	10	∪	∪	X
ejpam-3421	225	11	[	[	PUNCT
ejpam-3421	225	12	{	{	PUNCT
ejpam-3421	225	13	v	v	NOUN
ejpam-3421	225	14	}	}	PUNCT
ejpam-3421	225	15	×	×	PROPN
ejpam-3421	225	16	f	f	NOUN
ejpam-3421	225	17	2	2	NUM
ejpam-3421	225	18	h	h	NOUN
ejpam-3421	226	1	[	[	X
ejpam-3421	226	2	a	a	X
ejpam-3421	226	3	]	]	X
ejpam-3421	226	4	]	]	PUNCT
ejpam-3421	226	5	∪	∪	ADP
ejpam-3421	226	6	[	[	X
ejpam-3421	226	7	fg[v]×	fg[v]×	ADJ
ejpam-3421	226	8	v	v	NOUN
ejpam-3421	226	9	(	(	PUNCT
ejpam-3421	226	10	h)\{a	h)\{a	NOUN
ejpam-3421	226	11	}	}	PUNCT
ejpam-3421	226	12	]	]	PUNCT
ejpam-3421	226	13	∪	∪	ADP
ejpam-3421	226	14	[	[	X
ejpam-3421	226	15	ng(v)×	ng(v)×	PROPN
ejpam-3421	226	16	fg[a	fg[a	PROPN
ejpam-3421	226	17	]	]	X
ejpam-3421	226	18	]	]	PUNCT
ejpam-3421	226	19	.	.	PUNCT
ejpam-3421	227	1	proof	proof	NOUN
ejpam-3421	227	2	.	.	PUNCT
ejpam-3421	228	1	let	let	VERB
ejpam-3421	228	2	(	(	PUNCT
ejpam-3421	228	3	v	v	NOUN
ejpam-3421	228	4	,	,	PUNCT
ejpam-3421	228	5	a	a	PRON
ejpam-3421	228	6	)	)	PUNCT
ejpam-3421	228	7	∈	∈	NOUN
ejpam-3421	228	8	v	v	NOUN
ejpam-3421	228	9	(	(	PUNCT
ejpam-3421	228	10	k	k	NOUN
ejpam-3421	228	11	)	)	PUNCT
ejpam-3421	228	12	=	=	NOUN
ejpam-3421	228	13	v	v	X
ejpam-3421	228	14	(	(	PUNCT
ejpam-3421	228	15	g	g	PROPN
ejpam-3421	228	16	�	�	NOUN
ejpam-3421	228	17	h	h	NOUN
ejpam-3421	228	18	)	)	PUNCT
ejpam-3421	228	19	and	and	CCONJ
ejpam-3421	228	20	(	(	PUNCT
ejpam-3421	228	21	x	x	X
ejpam-3421	228	22	,	,	PUNCT
ejpam-3421	228	23	q	q	X
ejpam-3421	228	24	)	)	PUNCT
ejpam-3421	228	25	∈	∈	PROPN
ejpam-3421	229	1	f	f	NOUN
ejpam-3421	229	2	2	2	NUM
ejpam-3421	229	3	k	k	NOUN
ejpam-3421	229	4	[	[	X
ejpam-3421	229	5	(	(	PUNCT
ejpam-3421	229	6	v	v	NOUN
ejpam-3421	229	7	,	,	PUNCT
ejpam-3421	229	8	a	a	NOUN
ejpam-3421	229	9	)	)	PUNCT
ejpam-3421	229	10	]	]	PUNCT
ejpam-3421	229	11	.	.	PUNCT
ejpam-3421	230	1	then	then	ADV
ejpam-3421	230	2	(	(	PUNCT
ejpam-3421	230	3	v	v	NOUN
ejpam-3421	230	4	,	,	PUNCT
ejpam-3421	230	5	a	a	PRON
ejpam-3421	230	6	)	)	PUNCT
ejpam-3421	230	7	6=	6=	NUM
ejpam-3421	230	8	(	(	PUNCT
ejpam-3421	230	9	x	x	X
ejpam-3421	230	10	,	,	PUNCT
ejpam-3421	230	11	q	q	NOUN
ejpam-3421	230	12	)	)	PUNCT
ejpam-3421	230	13	and	and	CCONJ
ejpam-3421	230	14	dk((v	dk((v	PROPN
ejpam-3421	230	15	,	,	PUNCT
ejpam-3421	230	16	a	a	PRON
ejpam-3421	230	17	)	)	PUNCT
ejpam-3421	230	18	,	,	PUNCT
ejpam-3421	230	19	(	(	PUNCT
ejpam-3421	230	20	x	x	X
ejpam-3421	230	21	,	,	PUNCT
ejpam-3421	230	22	q	q	NOUN
ejpam-3421	230	23	)	)	PUNCT
ejpam-3421	230	24	)	)	PUNCT
ejpam-3421	230	25	6=	6=	ADP
ejpam-3421	230	26	2	2	X
ejpam-3421	230	27	.	.	PUNCT
ejpam-3421	231	1	now	now	ADV
ejpam-3421	231	2	,	,	PUNCT
ejpam-3421	231	3	consider	consider	VERB
ejpam-3421	231	4	the	the	DET
ejpam-3421	231	5	following	follow	VERB
ejpam-3421	231	6	cases	case	NOUN
ejpam-3421	231	7	:	:	PUNCT
ejpam-3421	231	8	case	case	NOUN
ejpam-3421	231	9	1	1	NUM
ejpam-3421	231	10	.	.	X
ejpam-3421	231	11	assume	assume	VERB
ejpam-3421	231	12	that	that	SCONJ
ejpam-3421	231	13	x	x	PRON
ejpam-3421	231	14	=	=	PUNCT
ejpam-3421	231	15	v.	v.	ADP
ejpam-3421	231	16	then	then	ADV
ejpam-3421	231	17	q	q	X
ejpam-3421	232	1	6=	6=	ADP
ejpam-3421	232	2	a	a	PRON
ejpam-3421	232	3	and	and	CCONJ
ejpam-3421	232	4	dh(q	dh(q	ADV
ejpam-3421	232	5	,	,	PUNCT
ejpam-3421	232	6	a	a	PRON
ejpam-3421	232	7	)	)	PUNCT
ejpam-3421	232	8	=	=	SYM
ejpam-3421	232	9	dk((x	dk((x	ADJ
ejpam-3421	232	10	,	,	PUNCT
ejpam-3421	232	11	q	q	NOUN
ejpam-3421	232	12	)	)	PUNCT
ejpam-3421	232	13	,	,	PUNCT
ejpam-3421	232	14	(	(	PUNCT
ejpam-3421	232	15	x	x	X
ejpam-3421	232	16	,	,	PUNCT
ejpam-3421	232	17	a	a	NOUN
ejpam-3421	232	18	)	)	PUNCT
ejpam-3421	232	19	)	)	PUNCT
ejpam-3421	233	1	6=	6=	ADP
ejpam-3421	233	2	2	2	NUM
ejpam-3421	233	3	and	and	CCONJ
ejpam-3421	233	4	so	so	ADV
ejpam-3421	233	5	,	,	PUNCT
ejpam-3421	233	6	q	q	PROPN
ejpam-3421	233	7	∈	∈	PROPN
ejpam-3421	233	8	f	f	PROPN
ejpam-3421	233	9	2	2	NUM
ejpam-3421	233	10	h	h	NOUN
ejpam-3421	234	1	[	[	X
ejpam-3421	234	2	a	a	X
ejpam-3421	234	3	]	]	X
ejpam-3421	234	4	.	.	PUNCT
ejpam-3421	235	1	hence	hence	ADV
ejpam-3421	235	2	,	,	PUNCT
ejpam-3421	235	3	(	(	PUNCT
ejpam-3421	235	4	x	x	X
ejpam-3421	235	5	,	,	PUNCT
ejpam-3421	235	6	q	q	ADJ
ejpam-3421	235	7	)	)	PUNCT
ejpam-3421	235	8	∈	∈	PROPN
ejpam-3421	235	9	{	{	PUNCT
ejpam-3421	235	10	v	v	NOUN
ejpam-3421	235	11	}	}	PUNCT
ejpam-3421	235	12	×	×	PROPN
ejpam-3421	235	13	f	f	NOUN
ejpam-3421	235	14	2	2	NUM
ejpam-3421	235	15	h	h	NOUN
ejpam-3421	236	1	[	[	X
ejpam-3421	236	2	a	a	X
ejpam-3421	236	3	]	]	X
ejpam-3421	236	4	.	.	PUNCT
ejpam-3421	237	1	case	case	NOUN
ejpam-3421	237	2	2	2	NUM
ejpam-3421	237	3	.	.	X
ejpam-3421	237	4	assume	assume	VERB
ejpam-3421	237	5	that	that	SCONJ
ejpam-3421	237	6	x	x	PROPN
ejpam-3421	237	7	6=	6=	ADP
ejpam-3421	237	8	v.	v.	ADP
ejpam-3421	237	9	subcase	subcase	PROPN
ejpam-3421	237	10	1	1	X
ejpam-3421	237	11	.	.	PUNCT
ejpam-3421	238	1	let	let	VERB
ejpam-3421	238	2	q	q	NOUN
ejpam-3421	238	3	=	=	PUNCT
ejpam-3421	238	4	a.	a.	NOUN
ejpam-3421	238	5	then	then	ADV
ejpam-3421	238	6	dg(x	dg(x	NUM
ejpam-3421	238	7	,	,	PUNCT
ejpam-3421	238	8	v	v	NOUN
ejpam-3421	238	9	)	)	PUNCT
ejpam-3421	238	10	=	=	PUNCT
ejpam-3421	238	11	dk((x	dk((x	ADJ
ejpam-3421	238	12	,	,	PUNCT
ejpam-3421	238	13	q	q	NOUN
ejpam-3421	238	14	)	)	PUNCT
ejpam-3421	238	15	,	,	PUNCT
ejpam-3421	238	16	(	(	PUNCT
ejpam-3421	238	17	v	v	NOUN
ejpam-3421	238	18	,	,	PUNCT
ejpam-3421	238	19	q	q	NOUN
ejpam-3421	238	20	)	)	PUNCT
ejpam-3421	238	21	)	)	PUNCT
ejpam-3421	239	1	6=	6=	ADP
ejpam-3421	239	2	2	2	NUM
ejpam-3421	239	3	and	and	CCONJ
ejpam-3421	239	4	thus	thus	ADV
ejpam-3421	239	5	,	,	PUNCT
ejpam-3421	239	6	x	x	PROPN
ejpam-3421	239	7	∈	∈	PROPN
ejpam-3421	239	8	f	f	PROPN
ejpam-3421	239	9	2	2	NUM
ejpam-3421	239	10	g[v	g[v	NOUN
ejpam-3421	239	11	]	]	PUNCT
ejpam-3421	239	12	.	.	PUNCT
ejpam-3421	240	1	it	it	PRON
ejpam-3421	240	2	follows	follow	VERB
ejpam-3421	240	3	that	that	SCONJ
ejpam-3421	240	4	(	(	PUNCT
ejpam-3421	240	5	x	x	X
ejpam-3421	240	6	,	,	PUNCT
ejpam-3421	240	7	q	q	X
ejpam-3421	240	8	)	)	PUNCT
ejpam-3421	240	9	∈	∈	PROPN
ejpam-3421	240	10	f	f	NOUN
ejpam-3421	240	11	2	2	NUM
ejpam-3421	240	12	g[v]×	g[v]×	ADV
ejpam-3421	240	13	{	{	PUNCT
ejpam-3421	240	14	a	a	X
ejpam-3421	240	15	}	}	PUNCT
ejpam-3421	240	16	.	.	PUNCT
ejpam-3421	241	1	subcase	subcase	PROPN
ejpam-3421	241	2	2	2	NUM
ejpam-3421	241	3	.	.	PUNCT
ejpam-3421	242	1	let	let	VERB
ejpam-3421	242	2	q	q	PROPN
ejpam-3421	242	3	6=	6=	NOUN
ejpam-3421	242	4	a.	a.	NOUN
ejpam-3421	242	5	suppose	suppose	VERB
ejpam-3421	242	6	that	that	SCONJ
ejpam-3421	242	7	x	x	SYM
ejpam-3421	242	8	∈	∈	NOUN
ejpam-3421	242	9	ng(v	ng(v	NOUN
ejpam-3421	242	10	)	)	PUNCT
ejpam-3421	242	11	.	.	PUNCT
ejpam-3421	243	1	if	if	SCONJ
ejpam-3421	243	2	q	q	PROPN
ejpam-3421	243	3	∈	∈	PROPN
ejpam-3421	243	4	nh(a	nh(a	NUM
ejpam-3421	243	5	)	)	PUNCT
ejpam-3421	243	6	,	,	PUNCT
ejpam-3421	243	7	then	then	ADV
ejpam-3421	243	8	dk((x	dk((x	ADV
ejpam-3421	243	9	,	,	PUNCT
ejpam-3421	243	10	q	q	NOUN
ejpam-3421	243	11	)	)	PUNCT
ejpam-3421	243	12	,	,	PUNCT
ejpam-3421	243	13	(	(	PUNCT
ejpam-3421	243	14	v	v	NOUN
ejpam-3421	243	15	,	,	PUNCT
ejpam-3421	243	16	a	a	PRON
ejpam-3421	243	17	)	)	PUNCT
ejpam-3421	243	18	)	)	PUNCT
ejpam-3421	243	19	=	=	SYM
ejpam-3421	243	20	dg(x	dg(x	X
ejpam-3421	243	21	,	,	PUNCT
ejpam-3421	243	22	v	v	NOUN
ejpam-3421	243	23	)	)	PUNCT
ejpam-3421	243	24	+	+	CCONJ
ejpam-3421	244	1	dh(q	dh(q	ADV
ejpam-3421	244	2	,	,	PUNCT
ejpam-3421	244	3	a	a	X
ejpam-3421	244	4	)	)	PUNCT
ejpam-3421	244	5	=	=	SYM
ejpam-3421	244	6	2	2	NUM
ejpam-3421	244	7	,	,	PUNCT
ejpam-3421	244	8	a	a	DET
ejpam-3421	244	9	contradiction	contradiction	NOUN
ejpam-3421	244	10	.	.	PUNCT
ejpam-3421	245	1	thus	thus	ADV
ejpam-3421	245	2	,	,	PUNCT
ejpam-3421	245	3	q	q	PROPN
ejpam-3421	245	4	∈	∈	PROPN
ejpam-3421	245	5	v	v	X
ejpam-3421	245	6	(	(	PUNCT
ejpam-3421	245	7	h)\nh	h)\nh	PROPN
ejpam-3421	246	1	[	[	X
ejpam-3421	246	2	a	a	X
ejpam-3421	246	3	]	]	X
ejpam-3421	246	4	.	.	PUNCT
ejpam-3421	247	1	hence	hence	ADV
ejpam-3421	247	2	,	,	PUNCT
ejpam-3421	247	3	(	(	PUNCT
ejpam-3421	247	4	x	x	X
ejpam-3421	247	5	,	,	PUNCT
ejpam-3421	247	6	q	q	ADJ
ejpam-3421	247	7	)	)	PUNCT
ejpam-3421	247	8	∈	∈	NOUN
ejpam-3421	247	9	ng(v	ng(v	PUNCT
ejpam-3421	247	10	)	)	PUNCT
ejpam-3421	247	11	×	×	PROPN
ejpam-3421	247	12	fg[a	fg[a	PROPN
ejpam-3421	247	13	]	]	PUNCT
ejpam-3421	247	14	.	.	PUNCT
ejpam-3421	248	1	suppose	suppose	VERB
ejpam-3421	248	2	x	x	X
ejpam-3421	248	3	/∈	/∈	PUNCT
ejpam-3421	248	4	ng(v	ng(v	NUM
ejpam-3421	248	5	)	)	PUNCT
ejpam-3421	248	6	.	.	PUNCT
ejpam-3421	249	1	then	then	ADV
ejpam-3421	249	2	x	x	X
ejpam-3421	249	3	∈	∈	PROPN
ejpam-3421	249	4	fg[v	fg[v	PROPN
ejpam-3421	249	5	]	]	PUNCT
ejpam-3421	249	6	.	.	PUNCT
ejpam-3421	250	1	hence	hence	ADV
ejpam-3421	250	2	,	,	PUNCT
ejpam-3421	250	3	(	(	PUNCT
ejpam-3421	250	4	x	x	X
ejpam-3421	250	5	,	,	PUNCT
ejpam-3421	250	6	q	q	ADJ
ejpam-3421	250	7	)	)	PUNCT
ejpam-3421	250	8	∈	∈	PROPN
ejpam-3421	250	9	fg[v]×	fg[v]×	ADP
ejpam-3421	250	10	v	v	NOUN
ejpam-3421	250	11	(	(	PUNCT
ejpam-3421	250	12	h)\{a	h)\{a	NOUN
ejpam-3421	250	13	}	}	PUNCT
ejpam-3421	250	14	.	.	PUNCT
ejpam-3421	251	1	therefore	therefore	ADV
ejpam-3421	251	2	,	,	PUNCT
ejpam-3421	251	3	f	f	PROPN
ejpam-3421	251	4	2	2	NUM
ejpam-3421	251	5	k	k	X
ejpam-3421	251	6	[	[	X
ejpam-3421	251	7	(	(	PUNCT
ejpam-3421	251	8	v	v	NOUN
ejpam-3421	251	9	,	,	PUNCT
ejpam-3421	251	10	a	a	NOUN
ejpam-3421	251	11	)	)	PUNCT
ejpam-3421	251	12	]	]	PUNCT
ejpam-3421	252	1	⊆	⊆	NUM
ejpam-3421	252	2	[	[	PUNCT
ejpam-3421	252	3	f	f	NOUN
ejpam-3421	252	4	2	2	NUM
ejpam-3421	252	5	g[v]×	g[v]×	ADV
ejpam-3421	252	6	{	{	PUNCT
ejpam-3421	252	7	a	a	NOUN
ejpam-3421	252	8	}	}	PUNCT
ejpam-3421	252	9	]	]	PUNCT
ejpam-3421	252	10	∪	∪	X
ejpam-3421	252	11	[	[	PUNCT
ejpam-3421	252	12	{	{	PUNCT
ejpam-3421	252	13	v	v	NOUN
ejpam-3421	252	14	}	}	PUNCT
ejpam-3421	252	15	×	×	PROPN
ejpam-3421	252	16	f	f	NOUN
ejpam-3421	252	17	2	2	NUM
ejpam-3421	252	18	h	h	NOUN
ejpam-3421	253	1	[	[	X
ejpam-3421	253	2	a	a	X
ejpam-3421	253	3	]	]	X
ejpam-3421	253	4	]	]	PUNCT
ejpam-3421	253	5	∪	∪	ADP
ejpam-3421	253	6	[	[	X
ejpam-3421	253	7	fg[v]×	fg[v]×	ADJ
ejpam-3421	253	8	v	v	NOUN
ejpam-3421	253	9	(	(	PUNCT
ejpam-3421	253	10	h)\{a	h)\{a	NOUN
ejpam-3421	253	11	}	}	PUNCT
ejpam-3421	253	12	]	]	PUNCT
ejpam-3421	253	13	∪	∪	ADP
ejpam-3421	253	14	[	[	X
ejpam-3421	253	15	ng(v)×	ng(v)×	PROPN
ejpam-3421	253	16	fg[a	fg[a	PROPN
ejpam-3421	253	17	]	]	X
ejpam-3421	253	18	]	]	PUNCT
ejpam-3421	253	19	.	.	PUNCT
ejpam-3421	254	1	next	next	ADV
ejpam-3421	254	2	,	,	PUNCT
ejpam-3421	254	3	let	let	VERB
ejpam-3421	254	4	(	(	PUNCT
ejpam-3421	254	5	v	v	NOUN
ejpam-3421	254	6	,	,	PUNCT
ejpam-3421	254	7	p	p	NOUN
ejpam-3421	254	8	)	)	PUNCT
ejpam-3421	254	9	∈	∈	PROPN
ejpam-3421	254	10	{	{	PUNCT
ejpam-3421	254	11	v	v	NOUN
ejpam-3421	254	12	}	}	PUNCT
ejpam-3421	254	13	×	×	PROPN
ejpam-3421	254	14	f	f	NOUN
ejpam-3421	254	15	2	2	NUM
ejpam-3421	254	16	h	h	NOUN
ejpam-3421	255	1	[	[	X
ejpam-3421	255	2	a	a	X
ejpam-3421	255	3	]	]	X
ejpam-3421	255	4	.	.	PUNCT
ejpam-3421	256	1	then	then	ADV
ejpam-3421	256	2	p	p	X
ejpam-3421	256	3	6=	6=	PROPN
ejpam-3421	256	4	a	a	PRON
ejpam-3421	256	5	and	and	CCONJ
ejpam-3421	256	6	dh(a	dh(a	ADJ
ejpam-3421	256	7	,	,	PUNCT
ejpam-3421	256	8	p	p	NOUN
ejpam-3421	256	9	)	)	PUNCT
ejpam-3421	256	10	6=	6=	ADP
ejpam-3421	256	11	2	2	NUM
ejpam-3421	256	12	.	.	PUNCT
ejpam-3421	257	1	hence	hence	ADV
ejpam-3421	257	2	,	,	PUNCT
ejpam-3421	257	3	(	(	PUNCT
ejpam-3421	257	4	v	v	NOUN
ejpam-3421	257	5	,	,	PUNCT
ejpam-3421	257	6	p	p	NOUN
ejpam-3421	257	7	)	)	PUNCT
ejpam-3421	257	8	6=	6=	ADP
ejpam-3421	257	9	(	(	PUNCT
ejpam-3421	257	10	v	v	NOUN
ejpam-3421	257	11	,	,	PUNCT
ejpam-3421	257	12	a	a	PRON
ejpam-3421	257	13	)	)	PUNCT
ejpam-3421	257	14	and	and	CCONJ
ejpam-3421	257	15	dk((v	dk((v	NOUN
ejpam-3421	257	16	,	,	PUNCT
ejpam-3421	257	17	p	p	NOUN
ejpam-3421	257	18	)	)	PUNCT
ejpam-3421	257	19	,	,	PUNCT
ejpam-3421	257	20	(	(	PUNCT
ejpam-3421	257	21	v	v	NOUN
ejpam-3421	257	22	,	,	PUNCT
ejpam-3421	257	23	a	a	PRON
ejpam-3421	257	24	)	)	PUNCT
ejpam-3421	257	25	)	)	PUNCT
ejpam-3421	257	26	=	=	SYM
ejpam-3421	258	1	dh(a	dh(a	ADJ
ejpam-3421	258	2	,	,	PUNCT
ejpam-3421	258	3	p	p	NOUN
ejpam-3421	258	4	)	)	PUNCT
ejpam-3421	258	5	6=	6=	ADP
ejpam-3421	258	6	2	2	NUM
ejpam-3421	258	7	,	,	PUNCT
ejpam-3421	258	8	that	that	ADV
ejpam-3421	258	9	is	is	ADV
ejpam-3421	258	10	,	,	PUNCT
ejpam-3421	258	11	(	(	PUNCT
ejpam-3421	258	12	v	v	NOUN
ejpam-3421	258	13	,	,	PUNCT
ejpam-3421	258	14	p	p	NOUN
ejpam-3421	258	15	)	)	PUNCT
ejpam-3421	258	16	∈	∈	PROPN
ejpam-3421	259	1	f	f	NOUN
ejpam-3421	259	2	2	2	NUM
ejpam-3421	259	3	k	k	NOUN
ejpam-3421	259	4	[	[	X
ejpam-3421	259	5	(	(	PUNCT
ejpam-3421	259	6	v	v	NOUN
ejpam-3421	259	7	,	,	PUNCT
ejpam-3421	259	8	a	a	NOUN
ejpam-3421	259	9	)	)	PUNCT
ejpam-3421	259	10	]	]	PUNCT
ejpam-3421	259	11	.	.	PUNCT
ejpam-3421	260	1	if	if	SCONJ
ejpam-3421	260	2	(	(	PUNCT
ejpam-3421	260	3	x	x	NOUN
ejpam-3421	260	4	,	,	PUNCT
ejpam-3421	260	5	a	a	PRON
ejpam-3421	260	6	)	)	PUNCT
ejpam-3421	260	7	∈	∈	PROPN
ejpam-3421	260	8	f	f	PROPN
ejpam-3421	260	9	2	2	NUM
ejpam-3421	260	10	g[v	g[v	NOUN
ejpam-3421	260	11	]	]	X
ejpam-3421	260	12	×	×	NOUN
ejpam-3421	260	13	{	{	PUNCT
ejpam-3421	260	14	a	a	NOUN
ejpam-3421	260	15	}	}	PUNCT
ejpam-3421	260	16	,	,	PUNCT
ejpam-3421	260	17	then	then	ADV
ejpam-3421	260	18	x	x	X
ejpam-3421	260	19	6=	6=	ADP
ejpam-3421	260	20	v	v	NOUN
ejpam-3421	260	21	and	and	CCONJ
ejpam-3421	260	22	dg(x	dg(x	NUM
ejpam-3421	260	23	,	,	PUNCT
ejpam-3421	260	24	v	v	NOUN
ejpam-3421	260	25	)	)	PUNCT
ejpam-3421	260	26	6=	6=	ADP
ejpam-3421	260	27	2	2	NUM
ejpam-3421	260	28	.	.	PUNCT
ejpam-3421	260	29	hence	hence	ADV
ejpam-3421	260	30	,	,	PUNCT
ejpam-3421	260	31	(	(	PUNCT
ejpam-3421	260	32	x	x	X
ejpam-3421	260	33	,	,	PUNCT
ejpam-3421	260	34	a	a	PRON
ejpam-3421	260	35	)	)	PUNCT
ejpam-3421	260	36	6=	6=	ADP
ejpam-3421	260	37	(	(	PUNCT
ejpam-3421	260	38	v	v	NOUN
ejpam-3421	260	39	,	,	PUNCT
ejpam-3421	260	40	a	a	PRON
ejpam-3421	260	41	)	)	PUNCT
ejpam-3421	260	42	and	and	CCONJ
ejpam-3421	260	43	dk((v	dk((v	NOUN
ejpam-3421	260	44	,	,	PUNCT
ejpam-3421	260	45	a	a	PRON
ejpam-3421	260	46	)	)	PUNCT
ejpam-3421	260	47	,	,	PUNCT
ejpam-3421	260	48	(	(	PUNCT
ejpam-3421	260	49	x	x	X
ejpam-3421	260	50	,	,	PUNCT
ejpam-3421	260	51	a	a	NOUN
ejpam-3421	260	52	)	)	PUNCT
ejpam-3421	260	53	)	)	PUNCT
ejpam-3421	260	54	=	=	SYM
ejpam-3421	260	55	dg(x	dg(x	X
ejpam-3421	260	56	,	,	PUNCT
ejpam-3421	260	57	v	v	NOUN
ejpam-3421	260	58	)	)	PUNCT
ejpam-3421	260	59	6=	6=	ADP
ejpam-3421	260	60	2	2	NUM
ejpam-3421	260	61	,	,	PUNCT
ejpam-3421	260	62	that	that	ADV
ejpam-3421	260	63	is	is	ADV
ejpam-3421	260	64	,	,	PUNCT
ejpam-3421	260	65	(	(	PUNCT
ejpam-3421	260	66	x	x	NOUN
ejpam-3421	260	67	,	,	PUNCT
ejpam-3421	260	68	a	a	PRON
ejpam-3421	260	69	)	)	PUNCT
ejpam-3421	260	70	∈	∈	PROPN
ejpam-3421	260	71	f	f	NOUN
ejpam-3421	260	72	2	2	NUM
ejpam-3421	260	73	k	k	NOUN
ejpam-3421	260	74	[	[	X
ejpam-3421	260	75	(	(	PUNCT
ejpam-3421	260	76	v	v	NOUN
ejpam-3421	260	77	,	,	PUNCT
ejpam-3421	260	78	a	a	NOUN
ejpam-3421	260	79	)	)	PUNCT
ejpam-3421	260	80	]	]	PUNCT
ejpam-3421	260	81	.	.	PUNCT
ejpam-3421	261	1	now	now	ADV
ejpam-3421	261	2	,	,	PUNCT
ejpam-3421	261	3	(	(	PUNCT
ejpam-3421	261	4	y	y	PROPN
ejpam-3421	261	5	,	,	PUNCT
ejpam-3421	261	6	b	b	NOUN
ejpam-3421	261	7	)	)	PUNCT
ejpam-3421	261	8	∈	∈	PROPN
ejpam-3421	261	9	ng(v)×	ng(v)×	PROPN
ejpam-3421	261	10	fh	fh	PROPN
ejpam-3421	262	1	[	[	X
ejpam-3421	262	2	a	a	X
ejpam-3421	262	3	]	]	PUNCT
ejpam-3421	262	4	implies	imply	VERB
ejpam-3421	262	5	dg(y	dg(y	ADJ
ejpam-3421	262	6	,	,	PUNCT
ejpam-3421	262	7	v	v	NOUN
ejpam-3421	262	8	)	)	PUNCT
ejpam-3421	262	9	=	=	SYM
ejpam-3421	262	10	1	1	NUM
ejpam-3421	262	11	and	and	CCONJ
ejpam-3421	262	12	dh(b	dh(b	PROPN
ejpam-3421	262	13	,	,	PUNCT
ejpam-3421	262	14	a	a	PRON
ejpam-3421	262	15	)	)	PUNCT
ejpam-3421	262	16	≥	≥	NOUN
ejpam-3421	262	17	2	2	NUM
ejpam-3421	262	18	.	.	PUNCT
ejpam-3421	263	1	it	it	PRON
ejpam-3421	263	2	follows	follow	VERB
ejpam-3421	263	3	that	that	SCONJ
ejpam-3421	263	4	(	(	PUNCT
ejpam-3421	263	5	y	y	PROPN
ejpam-3421	263	6	,	,	PUNCT
ejpam-3421	263	7	b	b	NOUN
ejpam-3421	263	8	)	)	PUNCT
ejpam-3421	263	9	6=	6=	ADP
ejpam-3421	263	10	(	(	PUNCT
ejpam-3421	263	11	v	v	NOUN
ejpam-3421	263	12	,	,	PUNCT
ejpam-3421	263	13	a	a	PRON
ejpam-3421	263	14	)	)	PUNCT
ejpam-3421	263	15	and	and	CCONJ
ejpam-3421	263	16	dk((y	dk((y	PROPN
ejpam-3421	263	17	,	,	PUNCT
ejpam-3421	263	18	b	b	NOUN
ejpam-3421	263	19	)	)	PUNCT
ejpam-3421	263	20	,	,	PUNCT
ejpam-3421	263	21	(	(	PUNCT
ejpam-3421	263	22	v	v	NOUN
ejpam-3421	263	23	,	,	PUNCT
ejpam-3421	263	24	a	a	PRON
ejpam-3421	263	25	)	)	PUNCT
ejpam-3421	263	26	)	)	PUNCT
ejpam-3421	263	27	=	=	SYM
ejpam-3421	264	1	dg(y	dg(y	ADJ
ejpam-3421	264	2	,	,	PUNCT
ejpam-3421	264	3	v	v	NOUN
ejpam-3421	264	4	)	)	PUNCT
ejpam-3421	264	5	+	+	CCONJ
ejpam-3421	264	6	dh(b	dh(b	PROPN
ejpam-3421	264	7	,	,	PUNCT
ejpam-3421	264	8	a	a	PRON
ejpam-3421	264	9	)	)	PUNCT
ejpam-3421	264	10	≥	≥	NOUN
ejpam-3421	264	11	3	3	NUM
ejpam-3421	264	12	.	.	PUNCT
ejpam-3421	265	1	hence	hence	ADV
ejpam-3421	265	2	,	,	PUNCT
ejpam-3421	265	3	(	(	PUNCT
ejpam-3421	265	4	y	y	PROPN
ejpam-3421	265	5	,	,	PUNCT
ejpam-3421	265	6	b	b	NOUN
ejpam-3421	265	7	)	)	PUNCT
ejpam-3421	265	8	∈	∈	PROPN
ejpam-3421	265	9	f	f	NOUN
ejpam-3421	265	10	2	2	NUM
ejpam-3421	265	11	k	k	NOUN
ejpam-3421	265	12	[	[	X
ejpam-3421	265	13	(	(	PUNCT
ejpam-3421	265	14	v	v	NOUN
ejpam-3421	265	15	,	,	PUNCT
ejpam-3421	265	16	a	a	NOUN
ejpam-3421	265	17	)	)	PUNCT
ejpam-3421	265	18	]	]	PUNCT
ejpam-3421	265	19	.	.	PUNCT
ejpam-3421	266	1	finally	finally	ADV
ejpam-3421	266	2	,	,	PUNCT
ejpam-3421	266	3	(	(	PUNCT
ejpam-3421	266	4	z	z	X
ejpam-3421	266	5	,	,	PUNCT
ejpam-3421	266	6	t	t	PROPN
ejpam-3421	266	7	)	)	PUNCT
ejpam-3421	266	8	∈	∈	PROPN
ejpam-3421	267	1	[	[	X
ejpam-3421	267	2	fg[v]×	fg[v]×	ADP
ejpam-3421	267	3	v	v	NOUN
ejpam-3421	267	4	(	(	PUNCT
ejpam-3421	267	5	h)\{a	h)\{a	NOUN
ejpam-3421	267	6	}	}	PUNCT
ejpam-3421	267	7	]	]	PUNCT
ejpam-3421	267	8	implies	imply	VERB
ejpam-3421	267	9	dg(z	dg(z	NUM
ejpam-3421	267	10	,	,	PUNCT
ejpam-3421	267	11	v	v	NOUN
ejpam-3421	267	12	)	)	PUNCT
ejpam-3421	267	13	≥	≥	NOUN
ejpam-3421	267	14	2	2	NUM
ejpam-3421	267	15	and	and	CCONJ
ejpam-3421	267	16	dh(t	dh(t	NUM
ejpam-3421	267	17	,	,	PUNCT
ejpam-3421	267	18	a	a	PRON
ejpam-3421	267	19	)	)	PUNCT
ejpam-3421	267	20	≥	≥	NOUN
ejpam-3421	267	21	1	1	NUM
ejpam-3421	267	22	.	.	PUNCT
ejpam-3421	268	1	this	this	PRON
ejpam-3421	268	2	means	mean	VERB
ejpam-3421	268	3	that	that	SCONJ
ejpam-3421	268	4	(	(	PUNCT
ejpam-3421	268	5	z	z	NOUN
ejpam-3421	268	6	,	,	PUNCT
ejpam-3421	268	7	t	t	PROPN
ejpam-3421	268	8	)	)	PUNCT
ejpam-3421	268	9	6=	6=	ADP
ejpam-3421	268	10	(	(	PUNCT
ejpam-3421	268	11	v	v	NOUN
ejpam-3421	268	12	,	,	PUNCT
ejpam-3421	268	13	a	a	PRON
ejpam-3421	268	14	)	)	PUNCT
ejpam-3421	268	15	and	and	CCONJ
ejpam-3421	268	16	dk((z	dk((z	PROPN
ejpam-3421	268	17	,	,	PUNCT
ejpam-3421	268	18	t	t	PROPN
ejpam-3421	268	19	)	)	PUNCT
ejpam-3421	268	20	,	,	PUNCT
ejpam-3421	268	21	(	(	PUNCT
ejpam-3421	268	22	v	v	NOUN
ejpam-3421	268	23	,	,	PUNCT
ejpam-3421	268	24	a	a	PRON
ejpam-3421	268	25	)	)	PUNCT
ejpam-3421	268	26	)	)	PUNCT
ejpam-3421	269	1	=	=	SYM
ejpam-3421	269	2	dg(z	dg(z	NUM
ejpam-3421	269	3	,	,	PUNCT
ejpam-3421	269	4	v	v	NOUN
ejpam-3421	269	5	)	)	PUNCT
ejpam-3421	269	6	+	+	CCONJ
ejpam-3421	269	7	dh(t	dh(t	NOUN
ejpam-3421	269	8	,	,	PUNCT
ejpam-3421	269	9	a	a	PRON
ejpam-3421	269	10	)	)	PUNCT
ejpam-3421	269	11	≥	≥	NOUN
ejpam-3421	269	12	3	3	NUM
ejpam-3421	269	13	.	.	PUNCT
ejpam-3421	270	1	thus	thus	ADV
ejpam-3421	270	2	,	,	PUNCT
ejpam-3421	270	3	(	(	PUNCT
ejpam-3421	270	4	z	z	X
ejpam-3421	270	5	,	,	PUNCT
ejpam-3421	270	6	t	t	PROPN
ejpam-3421	270	7	)	)	PUNCT
ejpam-3421	270	8	∈	∈	PROPN
ejpam-3421	270	9	f	f	NOUN
ejpam-3421	270	10	2	2	NUM
ejpam-3421	270	11	k	k	NOUN
ejpam-3421	270	12	[	[	X
ejpam-3421	270	13	(	(	PUNCT
ejpam-3421	270	14	v	v	NOUN
ejpam-3421	270	15	,	,	PUNCT
ejpam-3421	270	16	a	a	NOUN
ejpam-3421	270	17	)	)	PUNCT
ejpam-3421	270	18	]	]	PUNCT
ejpam-3421	270	19	.	.	PUNCT
ejpam-3421	271	1	therefore	therefore	ADV
ejpam-3421	271	2	,	,	PUNCT
ejpam-3421	271	3	[	[	PUNCT
ejpam-3421	271	4	f	f	X
ejpam-3421	271	5	2	2	NUM
ejpam-3421	271	6	g[v]×	g[v]×	ADV
ejpam-3421	271	7	{	{	PUNCT
ejpam-3421	271	8	a	a	NOUN
ejpam-3421	271	9	}	}	PUNCT
ejpam-3421	271	10	]	]	PUNCT
ejpam-3421	271	11	∪	∪	X
ejpam-3421	271	12	[	[	PUNCT
ejpam-3421	271	13	{	{	PUNCT
ejpam-3421	271	14	v	v	NOUN
ejpam-3421	271	15	}	}	PUNCT
ejpam-3421	271	16	×	×	PROPN
ejpam-3421	271	17	f	f	NOUN
ejpam-3421	271	18	2	2	NUM
ejpam-3421	271	19	h	h	NOUN
ejpam-3421	272	1	[	[	X
ejpam-3421	272	2	a	a	X
ejpam-3421	272	3	]	]	X
ejpam-3421	272	4	]	]	PUNCT
ejpam-3421	272	5	∪	∪	ADP
ejpam-3421	272	6	[	[	X
ejpam-3421	272	7	fg[v]×	fg[v]×	ADJ
ejpam-3421	272	8	v	v	NOUN
ejpam-3421	272	9	(	(	PUNCT
ejpam-3421	272	10	h)\{a	h)\{a	NOUN
ejpam-3421	272	11	}	}	PUNCT
ejpam-3421	272	12	]	]	PUNCT
ejpam-3421	272	13	∪	∪	ADP
ejpam-3421	272	14	[	[	X
ejpam-3421	272	15	ng(v)×	ng(v)×	PROPN
ejpam-3421	272	16	fg[a	fg[a	PROPN
ejpam-3421	272	17	]	]	X
ejpam-3421	272	18	]	]	X
ejpam-3421	272	19	⊆	⊆	NUM
ejpam-3421	272	20	f	f	SYM
ejpam-3421	272	21	2	2	NUM
ejpam-3421	272	22	k	k	NOUN
ejpam-3421	272	23	[	[	X
ejpam-3421	272	24	(	(	PUNCT
ejpam-3421	272	25	v	v	NOUN
ejpam-3421	272	26	,	,	PUNCT
ejpam-3421	272	27	a	a	NOUN
ejpam-3421	272	28	)	)	PUNCT
ejpam-3421	272	29	]	]	PUNCT
ejpam-3421	272	30	.	.	PUNCT
ejpam-3421	273	1	this	this	PRON
ejpam-3421	273	2	establishes	establish	VERB
ejpam-3421	273	3	the	the	DET
ejpam-3421	273	4	desired	desire	VERB
ejpam-3421	273	5	equality	equality	NOUN
ejpam-3421	273	6	.	.	PUNCT
ejpam-3421	274	1	references	reference	NOUN
ejpam-3421	274	2	505	505	NUM
ejpam-3421	274	3	acknowledgements	acknowledgement	NOUN
ejpam-3421	274	4	this	this	DET
ejpam-3421	274	5	research	research	NOUN
ejpam-3421	274	6	is	be	AUX
ejpam-3421	274	7	funded	fund	VERB
ejpam-3421	274	8	by	by	ADP
ejpam-3421	274	9	the	the	DET
ejpam-3421	274	10	philippine	philippine	PROPN
ejpam-3421	274	11	department	department	PROPN
ejpam-3421	274	12	of	of	ADP
ejpam-3421	274	13	science	science	NOUN
ejpam-3421	274	14	and	and	CCONJ
ejpam-3421	274	15	technologyaccelerated	technologyaccelerated	ADJ
ejpam-3421	274	16	science	science	NOUN
ejpam-3421	274	17	and	and	CCONJ
ejpam-3421	274	18	technology	technology	NOUN
ejpam-3421	274	19	human	human	ADJ
ejpam-3421	274	20	resource	resource	NOUN
ejpam-3421	274	21	development	development	NOUN
ejpam-3421	274	22	program	program	NOUN
ejpam-3421	274	23	(	(	PUNCT
ejpam-3421	274	24	dostasthrdp	dostasthrdp	PROPN
ejpam-3421	274	25	)	)	PUNCT
ejpam-3421	274	26	and	and	CCONJ
ejpam-3421	274	27	mindanao	mindanao	PROPN
ejpam-3421	274	28	state	state	PROPN
ejpam-3421	274	29	university	university	PROPN
ejpam-3421	274	30	-	-	PUNCT
ejpam-3421	274	31	iligan	iligan	PROPN
ejpam-3421	274	32	institute	institute	PROPN
ejpam-3421	274	33	of	of	ADP
ejpam-3421	274	34	technology	technology	PROPN
ejpam-3421	274	35	.	.	PUNCT
ejpam-3421	275	1	references	reference	NOUN
ejpam-3421	275	2	[	[	X
ejpam-3421	275	3	1	1	X
ejpam-3421	275	4	]	]	PUNCT
ejpam-3421	275	5	s.	s.	PROPN
ejpam-3421	275	6	canoy	canoy	PROPN
ejpam-3421	275	7	and	and	CCONJ
ejpam-3421	275	8	j.	j.	PROPN
ejpam-3421	275	9	gimeno	gimeno	PROPN
ejpam-3421	275	10	.	.	PUNCT
ejpam-3421	276	1	which	which	DET
ejpam-3421	276	2	connected	connect	VERB
ejpam-3421	276	3	graphs	graph	NOUN
ejpam-3421	276	4	induce	induce	VERB
ejpam-3421	276	5	the	the	DET
ejpam-3421	276	6	indiscrete	indiscrete	ADJ
ejpam-3421	276	7	and	and	CCONJ
ejpam-3421	276	8	the	the	DET
ejpam-3421	276	9	discrete	discrete	ADJ
ejpam-3421	276	10	topologies	topology	NOUN
ejpam-3421	276	11	?	?	PUNCT
ejpam-3421	277	1	journal	journal	NOUN
ejpam-3421	277	2	of	of	ADP
ejpam-3421	277	3	research	research	NOUN
ejpam-3421	277	4	in	in	ADP
ejpam-3421	277	5	science	science	NOUN
ejpam-3421	277	6	and	and	CCONJ
ejpam-3421	277	7	engineering	engineering	NOUN
ejpam-3421	277	8	,	,	PUNCT
ejpam-3421	277	9	1:17–19	1:17–19	NOUN
ejpam-3421	277	10	,	,	PUNCT
ejpam-3421	277	11	2004	2004	NUM
ejpam-3421	277	12	.	.	PUNCT
ejpam-3421	278	1	[	[	X
ejpam-3421	278	2	2	2	X
ejpam-3421	278	3	]	]	PUNCT
ejpam-3421	278	4	s.	s.	PROPN
ejpam-3421	278	5	canoy	canoy	PROPN
ejpam-3421	278	6	and	and	CCONJ
ejpam-3421	278	7	r.	r.	PROPN
ejpam-3421	278	8	lemence	lemence	PROPN
ejpam-3421	278	9	.	.	PUNCT
ejpam-3421	279	1	another	another	DET
ejpam-3421	279	2	look	look	NOUN
ejpam-3421	279	3	at	at	ADP
ejpam-3421	279	4	the	the	DET
ejpam-3421	279	5	topologies	topology	NOUN
ejpam-3421	279	6	induced	induce	VERB
ejpam-3421	279	7	by	by	ADP
ejpam-3421	279	8	graphs	graph	NOUN
ejpam-3421	279	9	.	.	PUNCT
ejpam-3421	280	1	matimyas	matimyas	PROPN
ejpam-3421	280	2	matematika	matematika	PROPN
ejpam-3421	280	3	,	,	PUNCT
ejpam-3421	280	4	21:1–7	21:1–7	NUM
ejpam-3421	280	5	,	,	PUNCT
ejpam-3421	280	6	1998	1998	NUM
ejpam-3421	280	7	.	.	PUNCT
ejpam-3421	281	1	[	[	X
ejpam-3421	281	2	3	3	X
ejpam-3421	281	3	]	]	X
ejpam-3421	281	4	s.	s.	PROPN
ejpam-3421	281	5	canoy	canoy	PROPN
ejpam-3421	281	6	and	and	CCONJ
ejpam-3421	281	7	r.	r.	PROPN
ejpam-3421	281	8	lemence	lemence	PROPN
ejpam-3421	281	9	.	.	PUNCT
ejpam-3421	282	1	topologies	topology	NOUN
ejpam-3421	282	2	induced	induce	VERB
ejpam-3421	282	3	by	by	ADP
ejpam-3421	282	4	some	some	DET
ejpam-3421	282	5	special	special	ADJ
ejpam-3421	282	6	graphs	graph	NOUN
ejpam-3421	282	7	.	.	PUNCT
ejpam-3421	283	1	journal	journal	NOUN
ejpam-3421	283	2	of	of	ADP
ejpam-3421	283	3	mathematics	mathematic	NOUN
ejpam-3421	283	4	,	,	PUNCT
ejpam-3421	283	5	2:45–50	2:45–50	NUM
ejpam-3421	283	6	,	,	PUNCT
ejpam-3421	283	7	1999	1999	NUM
ejpam-3421	283	8	.	.	PUNCT
ejpam-3421	284	1	[	[	X
ejpam-3421	284	2	4	4	X
ejpam-3421	284	3	]	]	X
ejpam-3421	284	4	s.	s.	PROPN
ejpam-3421	284	5	canoy	canoy	PROPN
ejpam-3421	284	6	and	and	CCONJ
ejpam-3421	284	7	c.	c.	PROPN
ejpam-3421	284	8	g.	g.	PROPN
ejpam-3421	284	9	nianga	nianga	PROPN
ejpam-3421	284	10	.	.	PUNCT
ejpam-3421	285	1	on	on	ADP
ejpam-3421	285	2	a	a	DET
ejpam-3421	285	3	finite	finite	ADJ
ejpam-3421	285	4	topological	topological	ADJ
ejpam-3421	285	5	space	space	NOUN
ejpam-3421	285	6	induced	induce	VERB
ejpam-3421	285	7	by	by	ADP
ejpam-3421	285	8	hop	hop	NOUN
ejpam-3421	285	9	neighborhoods	neighborhood	NOUN
ejpam-3421	285	10	of	of	ADP
ejpam-3421	285	11	a	a	DET
ejpam-3421	285	12	graph	graph	NOUN
ejpam-3421	285	13	.	.	PUNCT
ejpam-3421	285	14	advances	advance	NOUN
ejpam-3421	285	15	and	and	CCONJ
ejpam-3421	285	16	applications	application	NOUN
ejpam-3421	285	17	in	in	ADP
ejpam-3421	285	18	discrete	discrete	ADJ
ejpam-3421	285	19	mathematics	mathematic	NOUN
ejpam-3421	285	20	,	,	PUNCT
ejpam-3421	285	21	submitted	submit	VERB
ejpam-3421	285	22	.	.	PUNCT
ejpam-3421	286	1	[	[	X
ejpam-3421	286	2	5	5	X
ejpam-3421	286	3	]	]	PUNCT
ejpam-3421	286	4	s.	s.	PROPN
ejpam-3421	286	5	diesto	diesto	PROPN
ejpam-3421	286	6	and	and	CCONJ
ejpam-3421	286	7	s.	s.	PROPN
ejpam-3421	286	8	gervacio	gervacio	PROPN
ejpam-3421	286	9	.	.	PUNCT
ejpam-3421	287	1	finite	finite	PROPN
ejpam-3421	287	2	topological	topological	ADJ
ejpam-3421	287	3	graphs	graph	NOUN
ejpam-3421	287	4	.	.	PUNCT
ejpam-3421	288	1	journal	journal	NOUN
ejpam-3421	288	2	of	of	ADP
ejpam-3421	288	3	research	research	NOUN
ejpam-3421	288	4	and	and	CCONJ
ejpam-3421	288	5	development	development	NOUN
ejpam-3421	288	6	,	,	PUNCT
ejpam-3421	288	7	msu	msu	PROPN
ejpam-3421	288	8	-	-	PUNCT
ejpam-3421	288	9	iit	iit	NOUN
ejpam-3421	288	10	,	,	PUNCT
ejpam-3421	288	11	1:76–81	1:76–81	NUM
ejpam-3421	288	12	,	,	PUNCT
ejpam-3421	288	13	1983	1983	NUM
ejpam-3421	288	14	.	.	PUNCT
ejpam-3421	289	1	[	[	X
ejpam-3421	289	2	6	6	NUM
ejpam-3421	289	3	]	]	PUNCT
ejpam-3421	289	4	r.	r.	PROPN
ejpam-3421	289	5	guerrero	guerrero	PROPN
ejpam-3421	289	6	and	and	CCONJ
ejpam-3421	289	7	s.	s.	PROPN
ejpam-3421	289	8	gervacio	gervacio	PROPN
ejpam-3421	289	9	.	.	PUNCT
ejpam-3421	290	1	characterization	characterization	NOUN
ejpam-3421	290	2	of	of	ADP
ejpam-3421	290	3	graphs	graph	NOUN
ejpam-3421	290	4	which	which	PRON
ejpam-3421	290	5	induce	induce	VERB
ejpam-3421	290	6	the	the	DET
ejpam-3421	290	7	discrete	discrete	ADJ
ejpam-3421	290	8	and	and	CCONJ
ejpam-3421	290	9	indiscrete	indiscrete	ADJ
ejpam-3421	290	10	topological	topological	ADJ
ejpam-3421	290	11	spaces	space	NOUN
ejpam-3421	290	12	.	.	PUNCT
ejpam-3421	291	1	matimyas	matimyas	PROPN
ejpam-3421	291	2	matematika	matematika	PROPN
ejpam-3421	291	3	,	,	PUNCT
ejpam-3421	291	4	special	special	ADJ
ejpam-3421	291	5	issue	issue	NOUN
ejpam-3421	291	6	,	,	PUNCT
ejpam-3421	291	7	1:11–15	1:11–15	NUM
ejpam-3421	291	8	,	,	PUNCT
ejpam-3421	291	9	1989	1989	NUM
ejpam-3421	291	10	.	.	PUNCT
ejpam-3421	292	1	[	[	X
ejpam-3421	292	2	7	7	X
ejpam-3421	292	3	]	]	X
ejpam-3421	292	4	f.	f.	PROPN
ejpam-3421	292	5	harary	harary	PROPN
ejpam-3421	292	6	.	.	PUNCT
ejpam-3421	293	1	graph	graph	NOUN
ejpam-3421	293	2	theory	theory	NOUN
ejpam-3421	293	3	.	.	PUNCT
ejpam-3421	294	1	addison	addison	PROPN
ejpam-3421	294	2	-	-	PUNCT
ejpam-3421	294	3	wesley	wesley	PROPN
ejpam-3421	294	4	publishing	publishing	PROPN
ejpam-3421	294	5	company	company	NOUN
ejpam-3421	294	6	,	,	PUNCT
ejpam-3421	294	7	usa	usa	PROPN
ejpam-3421	294	8	,	,	PUNCT
ejpam-3421	294	9	1969	1969	NUM
ejpam-3421	294	10	.	.	PUNCT
ejpam-3421	295	1	[	[	X
ejpam-3421	295	2	8	8	X
ejpam-3421	295	3	]	]	X
ejpam-3421	295	4	s.	s.	PROPN
ejpam-3421	295	5	lipschutz	lipschutz	PROPN
ejpam-3421	295	6	.	.	PUNCT
ejpam-3421	296	1	general	general	ADJ
ejpam-3421	296	2	topology	topology	PROPN
ejpam-3421	296	3	,	,	PUNCT
ejpam-3421	296	4	schaum	schaum	PROPN
ejpam-3421	296	5	’s	’s	PART
ejpam-3421	296	6	outline	outline	PROPN
ejpam-3421	296	7	series	series	PROPN
ejpam-3421	296	8	.	.	PUNCT
ejpam-3421	297	1	mcgraw	mcgraw	PROPN
ejpam-3421	297	2	hill	hill	PROPN
ejpam-3421	297	3	international	international	PROPN
ejpam-3421	297	4	publishing	publishing	PROPN
ejpam-3421	297	5	co.	co.	PROPN
ejpam-3421	297	6	,	,	PUNCT
ejpam-3421	297	7	1987	1987	NUM
ejpam-3421	297	8	.	.	PUNCT