id	sid	tid	token	lemma	pos
ejpam-3916	1	1	european	european	PROPN
ejpam-3916	1	2	journal	journal	PROPN
ejpam-3916	1	3	of	of	ADP
ejpam-3916	1	4	pure	pure	ADJ
ejpam-3916	1	5	and	and	CCONJ
ejpam-3916	1	6	applied	apply	VERB
ejpam-3916	1	7	mathematics	mathematic	NOUN
ejpam-3916	1	8	vol	vol	NOUN
ejpam-3916	1	9	.	.	PUNCT
ejpam-3916	2	1	14	14	NUM
ejpam-3916	2	2	,	,	PUNCT
ejpam-3916	2	3	no	no	INTJ
ejpam-3916	2	4	.	.	NOUN
ejpam-3916	2	5	1	1	NUM
ejpam-3916	2	6	,	,	PUNCT
ejpam-3916	2	7	2021	2021	NUM
ejpam-3916	2	8	,	,	PUNCT
ejpam-3916	2	9	112	112	NUM
ejpam-3916	2	10	-	-	SYM
ejpam-3916	2	11	125	125	NUM
ejpam-3916	2	12	issn	issn	PROPN
ejpam-3916	2	13	1307	1307	NUM
ejpam-3916	2	14	-	-	SYM
ejpam-3916	2	15	5543	5543	NUM
ejpam-3916	2	16	–	–	PUNCT
ejpam-3916	2	17	ejpam.com	ejpam.com	X
ejpam-3916	2	18	published	publish	VERB
ejpam-3916	2	19	by	by	ADP
ejpam-3916	2	20	new	new	PROPN
ejpam-3916	2	21	york	york	PROPN
ejpam-3916	2	22	business	business	PROPN
ejpam-3916	2	23	global	global	PROPN
ejpam-3916	2	24	global	global	PROPN
ejpam-3916	2	25	hop	hop	PROPN
ejpam-3916	2	26	domination	domination	PROPN
ejpam-3916	2	27	numbers	number	NOUN
ejpam-3916	2	28	of	of	ADP
ejpam-3916	2	29	graphs	graph	NOUN
ejpam-3916	2	30	gemma	gemma	PROPN
ejpam-3916	2	31	p.	p.	PROPN
ejpam-3916	2	32	salasalan	salasalan	PROPN
ejpam-3916	2	33	1,∗	1,∗	PROPN
ejpam-3916	2	34	,	,	PUNCT
ejpam-3916	2	35	sergio	sergio	PROPN
ejpam-3916	2	36	r.	r.	PROPN
ejpam-3916	2	37	canoy	canoy	PROPN
ejpam-3916	2	38	,	,	PUNCT
ejpam-3916	2	39	jr.1	jr.1	PROPN
ejpam-3916	2	40	1	1	NUM
ejpam-3916	2	41	department	department	NOUN
ejpam-3916	2	42	of	of	ADP
ejpam-3916	2	43	mathematics	mathematic	NOUN
ejpam-3916	2	44	and	and	CCONJ
ejpam-3916	2	45	statistics	statistic	NOUN
ejpam-3916	2	46	,	,	PUNCT
ejpam-3916	2	47	college	college	NOUN
ejpam-3916	2	48	of	of	ADP
ejpam-3916	2	49	science	science	NOUN
ejpam-3916	2	50	and	and	CCONJ
ejpam-3916	2	51	mathematics	mathematic	NOUN
ejpam-3916	2	52	,	,	PUNCT
ejpam-3916	2	53	center	center	NOUN
ejpam-3916	2	54	for	for	ADP
ejpam-3916	2	55	graph	graph	NOUN
ejpam-3916	2	56	theory	theory	NOUN
ejpam-3916	2	57	,	,	PUNCT
ejpam-3916	2	58	algebra	algebra	NOUN
ejpam-3916	2	59	and	and	CCONJ
ejpam-3916	2	60	analysis	analysis	NOUN
ejpam-3916	2	61	,	,	PUNCT
ejpam-3916	2	62	premier	premier	PROPN
ejpam-3916	2	63	research	research	PROPN
ejpam-3916	2	64	institute	institute	PROPN
ejpam-3916	2	65	of	of	ADP
ejpam-3916	2	66	science	science	NOUN
ejpam-3916	2	67	and	and	CCONJ
ejpam-3916	2	68	mathematics	mathematic	NOUN
ejpam-3916	2	69	,	,	PUNCT
ejpam-3916	2	70	msu	msu	PROPN
ejpam-3916	2	71	-	-	PUNCT
ejpam-3916	2	72	iligan	iligan	PROPN
ejpam-3916	2	73	institute	institute	PROPN
ejpam-3916	2	74	of	of	ADP
ejpam-3916	2	75	technology	technology	PROPN
ejpam-3916	2	76	,	,	PUNCT
ejpam-3916	2	77	9200	9200	NUM
ejpam-3916	2	78	iligan	iligan	ADJ
ejpam-3916	2	79	city	city	NOUN
ejpam-3916	2	80	,	,	PUNCT
ejpam-3916	2	81	philippines	philippine	NOUN
ejpam-3916	2	82	abstract	abstract	ADJ
ejpam-3916	2	83	.	.	PUNCT
ejpam-3916	3	1	a	a	DET
ejpam-3916	3	2	set	set	NOUN
ejpam-3916	3	3	s	s	NOUN
ejpam-3916	3	4	⊆	⊆	NUM
ejpam-3916	3	5	v	v	NOUN
ejpam-3916	3	6	(	(	PUNCT
ejpam-3916	3	7	g	g	NOUN
ejpam-3916	3	8	)	)	PUNCT
ejpam-3916	3	9	is	be	AUX
ejpam-3916	3	10	a	a	DET
ejpam-3916	3	11	hop	hop	NOUN
ejpam-3916	3	12	dominating	dominating	NOUN
ejpam-3916	3	13	set	set	NOUN
ejpam-3916	3	14	of	of	ADP
ejpam-3916	3	15	g	g	PROPN
ejpam-3916	3	16	if	if	SCONJ
ejpam-3916	3	17	for	for	ADP
ejpam-3916	3	18	each	each	PRON
ejpam-3916	3	19	v	v	NUM
ejpam-3916	3	20	∈	∈	PROPN
ejpam-3916	3	21	v	v	NOUN
ejpam-3916	3	22	(	(	PUNCT
ejpam-3916	3	23	g	g	NOUN
ejpam-3916	3	24	)	)	PUNCT
ejpam-3916	3	25	\	\	PROPN
ejpam-3916	4	1	s	s	X
ejpam-3916	4	2	,	,	PUNCT
ejpam-3916	4	3	there	there	PRON
ejpam-3916	4	4	exists	exist	VERB
ejpam-3916	4	5	w	w	PROPN
ejpam-3916	4	6	∈	∈	PROPN
ejpam-3916	4	7	s	s	VERB
ejpam-3916	5	1	such	such	ADJ
ejpam-3916	5	2	that	that	PRON
ejpam-3916	5	3	dg(v	dg(v	ADJ
ejpam-3916	5	4	,	,	PUNCT
ejpam-3916	5	5	w	w	NOUN
ejpam-3916	5	6	)	)	PUNCT
ejpam-3916	5	7	=	=	SYM
ejpam-3916	5	8	2	2	X
ejpam-3916	5	9	.	.	PUNCT
ejpam-3916	6	1	it	it	PRON
ejpam-3916	6	2	is	be	AUX
ejpam-3916	6	3	a	a	DET
ejpam-3916	6	4	global	global	ADJ
ejpam-3916	6	5	hop	hop	NOUN
ejpam-3916	6	6	dominating	dominating	NOUN
ejpam-3916	6	7	set	set	NOUN
ejpam-3916	6	8	of	of	ADP
ejpam-3916	6	9	g	g	PROPN
ejpam-3916	6	10	if	if	SCONJ
ejpam-3916	6	11	it	it	PRON
ejpam-3916	6	12	is	be	AUX
ejpam-3916	6	13	a	a	DET
ejpam-3916	6	14	hop	hop	NOUN
ejpam-3916	6	15	dominating	dominating	NOUN
ejpam-3916	6	16	set	set	NOUN
ejpam-3916	6	17	of	of	ADP
ejpam-3916	6	18	both	both	CCONJ
ejpam-3916	6	19	g	g	PROPN
ejpam-3916	6	20	and	and	CCONJ
ejpam-3916	6	21	the	the	DET
ejpam-3916	6	22	complement	complement	NOUN
ejpam-3916	6	23	g	g	PROPN
ejpam-3916	6	24	of	of	ADP
ejpam-3916	6	25	g.	g.	PROPN
ejpam-3916	6	26	the	the	DET
ejpam-3916	6	27	minimum	minimum	ADJ
ejpam-3916	6	28	cardinality	cardinality	NOUN
ejpam-3916	6	29	of	of	ADP
ejpam-3916	6	30	a	a	DET
ejpam-3916	6	31	global	global	ADJ
ejpam-3916	6	32	hop	hop	NOUN
ejpam-3916	6	33	dominating	dominating	NOUN
ejpam-3916	6	34	set	set	NOUN
ejpam-3916	6	35	of	of	ADP
ejpam-3916	6	36	g	g	NOUN
ejpam-3916	6	37	,	,	PUNCT
ejpam-3916	6	38	denoted	denote	VERB
ejpam-3916	6	39	by	by	ADP
ejpam-3916	6	40	γgh(g	γgh(g	NOUN
ejpam-3916	6	41	)	)	PUNCT
ejpam-3916	6	42	,	,	PUNCT
ejpam-3916	6	43	is	be	AUX
ejpam-3916	6	44	called	call	VERB
ejpam-3916	6	45	the	the	DET
ejpam-3916	6	46	global	global	ADJ
ejpam-3916	6	47	hop	hop	NOUN
ejpam-3916	6	48	domination	domination	NOUN
ejpam-3916	6	49	number	number	NOUN
ejpam-3916	6	50	of	of	ADP
ejpam-3916	6	51	g.	g.	PROPN
ejpam-3916	6	52	in	in	ADP
ejpam-3916	6	53	this	this	DET
ejpam-3916	6	54	paper	paper	NOUN
ejpam-3916	6	55	,	,	PUNCT
ejpam-3916	6	56	we	we	PRON
ejpam-3916	6	57	study	study	VERB
ejpam-3916	6	58	the	the	DET
ejpam-3916	6	59	concept	concept	NOUN
ejpam-3916	6	60	of	of	ADP
ejpam-3916	6	61	global	global	ADJ
ejpam-3916	6	62	hop	hop	NOUN
ejpam-3916	6	63	domination	domination	NOUN
ejpam-3916	6	64	in	in	ADP
ejpam-3916	6	65	graphs	graph	NOUN
ejpam-3916	6	66	resulting	result	VERB
ejpam-3916	6	67	from	from	ADP
ejpam-3916	6	68	some	some	DET
ejpam-3916	6	69	binary	binary	ADJ
ejpam-3916	6	70	operations	operation	NOUN
ejpam-3916	6	71	.	.	PUNCT
ejpam-3916	7	1	2020	2020	NUM
ejpam-3916	7	2	mathematics	mathematic	NOUN
ejpam-3916	7	3	subject	subject	NOUN
ejpam-3916	7	4	classifications	classification	NOUN
ejpam-3916	7	5	:	:	PUNCT
ejpam-3916	7	6	05c69	05c69	X
ejpam-3916	7	7	key	key	ADJ
ejpam-3916	7	8	words	word	NOUN
ejpam-3916	7	9	and	and	CCONJ
ejpam-3916	7	10	phrases	phrase	NOUN
ejpam-3916	7	11	:	:	PUNCT
ejpam-3916	7	12	hop	hop	NOUN
ejpam-3916	7	13	domination	domination	NOUN
ejpam-3916	7	14	,	,	PUNCT
ejpam-3916	7	15	global	global	ADJ
ejpam-3916	7	16	hop	hop	PROPN
ejpam-3916	7	17	domination	domination	PROPN
ejpam-3916	7	18	,	,	PUNCT
ejpam-3916	7	19	join	join	NOUN
ejpam-3916	7	20	,	,	PUNCT
ejpam-3916	7	21	corona	corona	PROPN
ejpam-3916	7	22	,	,	PUNCT
ejpam-3916	7	23	lexicographic	lexicographic	ADJ
ejpam-3916	7	24	product	product	NOUN
ejpam-3916	7	25	,	,	PUNCT
ejpam-3916	7	26	and	and	CCONJ
ejpam-3916	7	27	cartesian	cartesian	ADJ
ejpam-3916	7	28	product	product	NOUN
ejpam-3916	7	29	1	1	NUM
ejpam-3916	7	30	.	.	PUNCT
ejpam-3916	8	1	introduction	introduction	NOUN
ejpam-3916	8	2	domination	domination	NOUN
ejpam-3916	8	3	is	be	AUX
ejpam-3916	8	4	a	a	DET
ejpam-3916	8	5	well	well	ADV
ejpam-3916	8	6	-	-	PUNCT
ejpam-3916	8	7	studied	study	VERB
ejpam-3916	8	8	topic	topic	NOUN
ejpam-3916	8	9	in	in	ADP
ejpam-3916	8	10	graph	graph	NOUN
ejpam-3916	8	11	theory	theory	NOUN
ejpam-3916	8	12	.	.	PUNCT
ejpam-3916	9	1	from	from	ADP
ejpam-3916	9	2	the	the	DET
ejpam-3916	9	3	standard	standard	ADJ
ejpam-3916	9	4	concept	concept	NOUN
ejpam-3916	9	5	,	,	PUNCT
ejpam-3916	9	6	many	many	ADJ
ejpam-3916	9	7	other	other	ADJ
ejpam-3916	9	8	variations	variation	NOUN
ejpam-3916	9	9	of	of	ADP
ejpam-3916	9	10	domination	domination	NOUN
ejpam-3916	9	11	have	have	AUX
ejpam-3916	9	12	been	be	AUX
ejpam-3916	9	13	investigated	investigate	VERB
ejpam-3916	9	14	by	by	ADP
ejpam-3916	9	15	researchers	researcher	NOUN
ejpam-3916	9	16	.	.	PUNCT
ejpam-3916	10	1	connected	connect	VERB
ejpam-3916	10	2	,	,	PUNCT
ejpam-3916	10	3	total	total	ADJ
ejpam-3916	10	4	,	,	PUNCT
ejpam-3916	10	5	independent	independent	ADJ
ejpam-3916	10	6	,	,	PUNCT
ejpam-3916	10	7	and	and	CCONJ
ejpam-3916	10	8	global	global	ADJ
ejpam-3916	10	9	domination	domination	NOUN
ejpam-3916	10	10	are	be	AUX
ejpam-3916	10	11	among	among	ADP
ejpam-3916	10	12	the	the	DET
ejpam-3916	10	13	numerous	numerous	ADJ
ejpam-3916	10	14	well	well	ADV
ejpam-3916	10	15	-	-	PUNCT
ejpam-3916	10	16	known	know	VERB
ejpam-3916	10	17	variants	variant	NOUN
ejpam-3916	10	18	of	of	ADP
ejpam-3916	10	19	the	the	DET
ejpam-3916	10	20	standard	standard	ADJ
ejpam-3916	10	21	domination	domination	NOUN
ejpam-3916	10	22	concept	concept	NOUN
ejpam-3916	10	23	.	.	PUNCT
ejpam-3916	11	1	other	other	ADJ
ejpam-3916	11	2	variants	variant	NOUN
ejpam-3916	11	3	may	may	AUX
ejpam-3916	11	4	be	be	AUX
ejpam-3916	11	5	found	find	VERB
ejpam-3916	11	6	in	in	ADP
ejpam-3916	11	7	the	the	DET
ejpam-3916	11	8	two	two	NUM
ejpam-3916	11	9	books	book	NOUN
ejpam-3916	11	10	authored	author	VERB
ejpam-3916	11	11	by	by	ADP
ejpam-3916	11	12	haynes	hayne	NOUN
ejpam-3916	11	13	et	et	PROPN
ejpam-3916	11	14	al	al	PROPN
ejpam-3916	11	15	.	.	PUNCT
ejpam-3916	12	1	(	(	PUNCT
ejpam-3916	12	2	see	see	VERB
ejpam-3916	12	3	[	[	X
ejpam-3916	12	4	5	5	NUM
ejpam-3916	12	5	]	]	PUNCT
ejpam-3916	12	6	and	and	CCONJ
ejpam-3916	12	7	[	[	X
ejpam-3916	12	8	6	6	NUM
ejpam-3916	12	9	]	]	NUM
ejpam-3916	12	10	)	)	PUNCT
ejpam-3916	12	11	.	.	PUNCT
ejpam-3916	13	1	recently	recently	ADV
ejpam-3916	13	2	,	,	PUNCT
ejpam-3916	13	3	natarajan	natarajan	PROPN
ejpam-3916	13	4	and	and	CCONJ
ejpam-3916	13	5	ayyaswamy	ayyaswamy	PROPN
ejpam-3916	13	6	[	[	X
ejpam-3916	13	7	10	10	NUM
ejpam-3916	13	8	]	]	PUNCT
ejpam-3916	13	9	introduced	introduce	VERB
ejpam-3916	13	10	and	and	CCONJ
ejpam-3916	13	11	studied	study	VERB
ejpam-3916	13	12	the	the	DET
ejpam-3916	13	13	concept	concept	NOUN
ejpam-3916	13	14	of	of	ADP
ejpam-3916	13	15	hop	hop	NOUN
ejpam-3916	13	16	domination	domination	NOUN
ejpam-3916	13	17	in	in	ADP
ejpam-3916	13	18	a	a	DET
ejpam-3916	13	19	graph	graph	NOUN
ejpam-3916	13	20	.	.	PUNCT
ejpam-3916	14	1	in	in	ADP
ejpam-3916	14	2	another	another	DET
ejpam-3916	14	3	study	study	NOUN
ejpam-3916	14	4	,	,	PUNCT
ejpam-3916	14	5	ayyaswamy	ayyaswamy	PROPN
ejpam-3916	14	6	et	et	PROPN
ejpam-3916	14	7	al	al	PROPN
ejpam-3916	14	8	.	.	PUNCT
ejpam-3916	15	1	[	[	X
ejpam-3916	15	2	1	1	X
ejpam-3916	15	3	]	]	PUNCT
ejpam-3916	15	4	investigated	investigate	VERB
ejpam-3916	15	5	the	the	DET
ejpam-3916	15	6	same	same	ADJ
ejpam-3916	15	7	concept	concept	NOUN
ejpam-3916	15	8	and	and	CCONJ
ejpam-3916	15	9	gave	give	VERB
ejpam-3916	15	10	bounds	bound	NOUN
ejpam-3916	15	11	of	of	ADP
ejpam-3916	15	12	the	the	DET
ejpam-3916	15	13	hop	hop	NOUN
ejpam-3916	15	14	domination	domination	NOUN
ejpam-3916	15	15	number	number	NOUN
ejpam-3916	15	16	of	of	ADP
ejpam-3916	15	17	some	some	DET
ejpam-3916	15	18	graphs	graph	NOUN
ejpam-3916	15	19	.	.	PUNCT
ejpam-3916	16	1	henning	henning	NOUN
ejpam-3916	16	2	and	and	CCONJ
ejpam-3916	16	3	rad	rad	NOUN
ejpam-3916	17	1	[	[	X
ejpam-3916	17	2	7	7	NUM
ejpam-3916	17	3	]	]	PUNCT
ejpam-3916	17	4	also	also	ADV
ejpam-3916	17	5	studied	study	VERB
ejpam-3916	17	6	the	the	DET
ejpam-3916	17	7	concept	concept	NOUN
ejpam-3916	17	8	and	and	CCONJ
ejpam-3916	17	9	answered	answer	VERB
ejpam-3916	17	10	a	a	DET
ejpam-3916	17	11	question	question	NOUN
ejpam-3916	17	12	posed	pose	VERB
ejpam-3916	17	13	by	by	ADP
ejpam-3916	17	14	ayyaswamy	ayyaswamy	ADJ
ejpam-3916	17	15	and	and	CCONJ
ejpam-3916	17	16	natarajan	natarajan	PROPN
ejpam-3916	17	17	in	in	ADP
ejpam-3916	17	18	[	[	X
ejpam-3916	17	19	10	10	NUM
ejpam-3916	17	20	]	]	PUNCT
ejpam-3916	17	21	.	.	PUNCT
ejpam-3916	18	1	they	they	PRON
ejpam-3916	18	2	showed	show	VERB
ejpam-3916	18	3	that	that	SCONJ
ejpam-3916	18	4	the	the	DET
ejpam-3916	18	5	hop	hop	NOUN
ejpam-3916	18	6	dominating	dominating	NOUN
ejpam-3916	18	7	set	set	NOUN
ejpam-3916	18	8	problem	problem	NOUN
ejpam-3916	18	9	is	be	AUX
ejpam-3916	18	10	np	np	INTJ
ejpam-3916	18	11	-	-	NOUN
ejpam-3916	18	12	complete	complete	ADJ
ejpam-3916	18	13	for	for	ADP
ejpam-3916	18	14	planar	planar	ADJ
ejpam-3916	18	15	bipartite	bipartite	ADJ
ejpam-3916	18	16	graphs	graph	NOUN
ejpam-3916	18	17	and	and	CCONJ
ejpam-3916	18	18	planar	planar	ADJ
ejpam-3916	18	19	chordal	chordal	ADJ
ejpam-3916	18	20	graphs	graph	NOUN
ejpam-3916	18	21	.	.	PUNCT
ejpam-3916	19	1	hop	hop	NOUN
ejpam-3916	19	2	domination	domination	NOUN
ejpam-3916	19	3	and	and	CCONJ
ejpam-3916	19	4	some	some	PRON
ejpam-3916	19	5	of	of	ADP
ejpam-3916	19	6	its	its	PRON
ejpam-3916	19	7	variants	variant	NOUN
ejpam-3916	19	8	are	be	AUX
ejpam-3916	19	9	studied	study	VERB
ejpam-3916	19	10	in	in	ADP
ejpam-3916	19	11	[	[	X
ejpam-3916	19	12	3	3	NUM
ejpam-3916	19	13	]	]	PUNCT
ejpam-3916	19	14	,	,	PUNCT
ejpam-3916	20	1	[	[	X
ejpam-3916	20	2	8	8	NUM
ejpam-3916	20	3	]	]	PUNCT
ejpam-3916	20	4	,	,	PUNCT
ejpam-3916	20	5	[	[	X
ejpam-3916	20	6	9	9	NUM
ejpam-3916	20	7	]	]	PUNCT
ejpam-3916	20	8	,	,	PUNCT
ejpam-3916	20	9	and	and	CCONJ
ejpam-3916	20	10	[	[	X
ejpam-3916	20	11	11	11	NUM
ejpam-3916	20	12	]	]	PUNCT
ejpam-3916	20	13	.	.	PUNCT
ejpam-3916	21	1	in	in	ADP
ejpam-3916	21	2	this	this	DET
ejpam-3916	21	3	paper	paper	NOUN
ejpam-3916	21	4	,	,	PUNCT
ejpam-3916	21	5	we	we	PRON
ejpam-3916	21	6	study	study	VERB
ejpam-3916	21	7	another	another	DET
ejpam-3916	21	8	variation	variation	NOUN
ejpam-3916	21	9	of	of	ADP
ejpam-3916	21	10	hop	hop	NOUN
ejpam-3916	21	11	domination	domination	NOUN
ejpam-3916	21	12	called	call	VERB
ejpam-3916	21	13	global	global	ADJ
ejpam-3916	21	14	hop	hop	PROPN
ejpam-3916	21	15	domination	domination	NOUN
ejpam-3916	21	16	.	.	PUNCT
ejpam-3916	22	1	this	this	PRON
ejpam-3916	22	2	is	be	AUX
ejpam-3916	22	3	obviously	obviously	ADV
ejpam-3916	22	4	the	the	DET
ejpam-3916	22	5	analogue	analogue	NOUN
ejpam-3916	22	6	to	to	ADP
ejpam-3916	22	7	global	global	ADJ
ejpam-3916	22	8	domination	domination	NOUN
ejpam-3916	22	9	studied	study	VERB
ejpam-3916	22	10	in	in	ADP
ejpam-3916	22	11	[	[	X
ejpam-3916	22	12	2	2	NUM
ejpam-3916	22	13	]	]	PUNCT
ejpam-3916	22	14	and	and	CCONJ
ejpam-3916	22	15	[	[	X
ejpam-3916	22	16	4	4	NUM
ejpam-3916	22	17	]	]	PUNCT
ejpam-3916	22	18	.	.	PUNCT
ejpam-3916	23	1	∗corresponding	∗corresponde	VERB
ejpam-3916	23	2	author	author	NOUN
ejpam-3916	23	3	.	.	PUNCT
ejpam-3916	24	1	doi	doi	NOUN
ejpam-3916	24	2	:	:	PUNCT
ejpam-3916	24	3	https://doi.org/10.29020/nybg.ejpam.v14i1.3916	https://doi.org/10.29020/nybg.ejpam.v14i1.3916	ADJ
ejpam-3916	24	4	email	email	NOUN
ejpam-3916	24	5	addresses	address	VERB
ejpam-3916	24	6	:	:	PUNCT
ejpam-3916	24	7	gemma.salasalan@g.msuiit.edu.ph	gemma.salasalan@g.msuiit.edu.ph	PROPN
ejpam-3916	24	8	(	(	PUNCT
ejpam-3916	24	9	g.	g.	PROPN
ejpam-3916	24	10	salasalan	salasalan	NOUN
ejpam-3916	24	11	)	)	PUNCT
ejpam-3916	24	12	,	,	PUNCT
ejpam-3916	24	13	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-3916	24	14	(	(	PUNCT
ejpam-3916	24	15	s.	s.	PROPN
ejpam-3916	24	16	canoy	canoy	PROPN
ejpam-3916	24	17	,	,	PUNCT
ejpam-3916	24	18	jr	jr	PROPN
ejpam-3916	24	19	.	.	PUNCT
ejpam-3916	24	20	)	)	PUNCT
ejpam-3916	24	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3916	25	1	112	112	NUM
ejpam-3916	25	2	c	c	AUX
ejpam-3916	25	3	©	©	PROPN
ejpam-3916	25	4	2021	2021	NUM
ejpam-3916	25	5	ejpam	ejpam	VERB
ejpam-3916	25	6	all	all	DET
ejpam-3916	25	7	rights	right	NOUN
ejpam-3916	25	8	reserved	reserve	VERB
ejpam-3916	25	9	.	.	PUNCT
ejpam-3916	26	1	g.	g.	PROPN
ejpam-3916	26	2	salasalan	salasalan	PROPN
ejpam-3916	26	3	,	,	PUNCT
ejpam-3916	26	4	s.	s.	PROPN
ejpam-3916	26	5	canoy	canoy	PROPN
ejpam-3916	26	6	,	,	PUNCT
ejpam-3916	26	7	jr	jr	PROPN
ejpam-3916	26	8	.	.	PROPN
ejpam-3916	26	9	/	/	SYM
ejpam-3916	26	10	eur	eur	PROPN
ejpam-3916	26	11	.	.	PUNCT
ejpam-3916	27	1	j.	j.	PROPN
ejpam-3916	27	2	pure	pure	PROPN
ejpam-3916	27	3	appl	appl	PROPN
ejpam-3916	27	4	.	.	PROPN
ejpam-3916	27	5	math	math	PROPN
ejpam-3916	27	6	,	,	PUNCT
ejpam-3916	27	7	14	14	NUM
ejpam-3916	27	8	(	(	PUNCT
ejpam-3916	27	9	1	1	NUM
ejpam-3916	27	10	)	)	PUNCT
ejpam-3916	27	11	(	(	PUNCT
ejpam-3916	27	12	2021	2021	NUM
ejpam-3916	27	13	)	)	PUNCT
ejpam-3916	27	14	,	,	PUNCT
ejpam-3916	27	15	112	112	NUM
ejpam-3916	27	16	-	-	SYM
ejpam-3916	27	17	125	125	NUM
ejpam-3916	27	18	113	113	NUM
ejpam-3916	27	19	let	let	VERB
ejpam-3916	27	20	g	g	NOUN
ejpam-3916	27	21	=	=	SYM
ejpam-3916	27	22	(	(	PUNCT
ejpam-3916	27	23	v	v	NOUN
ejpam-3916	27	24	(	(	PUNCT
ejpam-3916	27	25	g	g	NOUN
ejpam-3916	27	26	)	)	PUNCT
ejpam-3916	27	27	,	,	PUNCT
ejpam-3916	27	28	e(g	e(g	PROPN
ejpam-3916	27	29	)	)	PUNCT
ejpam-3916	27	30	)	)	PUNCT
ejpam-3916	27	31	be	be	AUX
ejpam-3916	27	32	a	a	DET
ejpam-3916	27	33	simple	simple	ADJ
ejpam-3916	27	34	graph	graph	NOUN
ejpam-3916	27	35	.	.	PUNCT
ejpam-3916	28	1	the	the	DET
ejpam-3916	28	2	distance	distance	NOUN
ejpam-3916	28	3	between	between	ADP
ejpam-3916	28	4	two	two	NUM
ejpam-3916	28	5	vertices	vertex	NOUN
ejpam-3916	28	6	u	u	NOUN
ejpam-3916	28	7	and	and	CCONJ
ejpam-3916	28	8	v	v	NOUN
ejpam-3916	28	9	of	of	ADP
ejpam-3916	28	10	g	g	NOUN
ejpam-3916	28	11	,	,	PUNCT
ejpam-3916	28	12	denoted	denote	VERB
ejpam-3916	28	13	by	by	ADP
ejpam-3916	28	14	dg(u	dg(u	NOUN
ejpam-3916	28	15	,	,	PUNCT
ejpam-3916	28	16	v	v	NOUN
ejpam-3916	28	17	)	)	PUNCT
ejpam-3916	28	18	,	,	PUNCT
ejpam-3916	28	19	is	be	AUX
ejpam-3916	28	20	equal	equal	ADJ
ejpam-3916	28	21	to	to	ADP
ejpam-3916	28	22	the	the	DET
ejpam-3916	28	23	length	length	NOUN
ejpam-3916	28	24	of	of	ADP
ejpam-3916	28	25	a	a	DET
ejpam-3916	28	26	shortest	short	ADJ
ejpam-3916	28	27	path	path	NOUN
ejpam-3916	28	28	connecting	connect	VERB
ejpam-3916	28	29	u	u	NOUN
ejpam-3916	28	30	and	and	CCONJ
ejpam-3916	28	31	v.	v.	ADP
ejpam-3916	28	32	any	any	DET
ejpam-3916	28	33	path	path	NOUN
ejpam-3916	28	34	connecting	connect	VERB
ejpam-3916	28	35	u	u	NOUN
ejpam-3916	28	36	and	and	CCONJ
ejpam-3916	28	37	v	v	NOUN
ejpam-3916	28	38	of	of	ADP
ejpam-3916	28	39	length	length	NOUN
ejpam-3916	28	40	dg(u	dg(u	ADJ
ejpam-3916	28	41	,	,	PUNCT
ejpam-3916	28	42	v	v	NOUN
ejpam-3916	28	43	)	)	PUNCT
ejpam-3916	28	44	is	be	AUX
ejpam-3916	28	45	called	call	VERB
ejpam-3916	28	46	a	a	DET
ejpam-3916	28	47	u	u	NOUN
ejpam-3916	28	48	-	-	NOUN
ejpam-3916	28	49	v	v	ADJ
ejpam-3916	28	50	geodesic	geodesic	NOUN
ejpam-3916	28	51	.	.	PUNCT
ejpam-3916	29	1	the	the	DET
ejpam-3916	29	2	open	open	ADJ
ejpam-3916	29	3	neighbourhood	neighbourhood	NOUN
ejpam-3916	29	4	of	of	ADP
ejpam-3916	29	5	a	a	DET
ejpam-3916	29	6	vertex	vertex	NOUN
ejpam-3916	29	7	v	v	NOUN
ejpam-3916	29	8	of	of	ADP
ejpam-3916	29	9	g	g	PROPN
ejpam-3916	29	10	is	be	AUX
ejpam-3916	29	11	the	the	DET
ejpam-3916	29	12	set	set	NOUN
ejpam-3916	29	13	ng(v	ng(v	PUNCT
ejpam-3916	29	14	)	)	PUNCT
ejpam-3916	29	15	=	=	SYM
ejpam-3916	30	1	{	{	PUNCT
ejpam-3916	30	2	u	u	NOUN
ejpam-3916	30	3	∈	∈	PROPN
ejpam-3916	30	4	v	v	NOUN
ejpam-3916	30	5	(	(	PUNCT
ejpam-3916	30	6	g	g	NOUN
ejpam-3916	30	7	)	)	PUNCT
ejpam-3916	30	8	:	:	PUNCT
ejpam-3916	30	9	uv	uv	PROPN
ejpam-3916	30	10	∈	∈	PROPN
ejpam-3916	30	11	e(g	e(g	PROPN
ejpam-3916	30	12	)	)	PUNCT
ejpam-3916	30	13	}	}	PUNCT
ejpam-3916	30	14	and	and	CCONJ
ejpam-3916	30	15	its	its	PRON
ejpam-3916	30	16	closed	closed	ADJ
ejpam-3916	30	17	neighbourhood	neighbourhood	NOUN
ejpam-3916	30	18	is	be	AUX
ejpam-3916	30	19	the	the	DET
ejpam-3916	30	20	set	set	NOUN
ejpam-3916	30	21	ng[v	ng[v	NOUN
ejpam-3916	30	22	]	]	X
ejpam-3916	30	23	=	=	SYM
ejpam-3916	30	24	ng(v	ng(v	X
ejpam-3916	30	25	)	)	PUNCT
ejpam-3916	30	26	∪	∪	ADP
ejpam-3916	30	27	{	{	PUNCT
ejpam-3916	30	28	v	v	NOUN
ejpam-3916	30	29	}	}	PUNCT
ejpam-3916	30	30	.	.	PUNCT
ejpam-3916	31	1	the	the	DET
ejpam-3916	31	2	open	open	ADJ
ejpam-3916	31	3	neighbourhood	neighbourhood	NOUN
ejpam-3916	31	4	of	of	ADP
ejpam-3916	31	5	a	a	DET
ejpam-3916	31	6	subset	subset	NOUN
ejpam-3916	31	7	s	s	NOUN
ejpam-3916	31	8	of	of	ADP
ejpam-3916	31	9	v	v	NOUN
ejpam-3916	31	10	(	(	PUNCT
ejpam-3916	31	11	g	g	NOUN
ejpam-3916	31	12	)	)	PUNCT
ejpam-3916	31	13	is	be	AUX
ejpam-3916	31	14	the	the	DET
ejpam-3916	31	15	set	set	NOUN
ejpam-3916	31	16	ng(s	ng(s	NOUN
ejpam-3916	31	17	)	)	PUNCT
ejpam-3916	31	18	=	=	SYM
ejpam-3916	31	19	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-3916	31	20	)	)	PUNCT
ejpam-3916	31	21	and	and	CCONJ
ejpam-3916	31	22	its	its	PRON
ejpam-3916	31	23	closed	closed	ADJ
ejpam-3916	31	24	neighbourhood	neighbourhood	NOUN
ejpam-3916	31	25	is	be	AUX
ejpam-3916	31	26	the	the	DET
ejpam-3916	31	27	set	set	VERB
ejpam-3916	31	28	ng[s	ng[	NOUN
ejpam-3916	31	29	]	]	PUNCT
ejpam-3916	31	30	=	=	SYM
ejpam-3916	31	31	ng(s	ng(s	X
ejpam-3916	31	32	)	)	PUNCT
ejpam-3916	31	33	∪	∪	ADP
ejpam-3916	31	34	s.	s.	PROPN
ejpam-3916	31	35	the	the	DET
ejpam-3916	31	36	degree	degree	NOUN
ejpam-3916	31	37	of	of	ADP
ejpam-3916	31	38	v	v	NOUN
ejpam-3916	31	39	,	,	PUNCT
ejpam-3916	31	40	denoted	denote	VERB
ejpam-3916	31	41	by	by	ADP
ejpam-3916	31	42	degg(v	degg(v	PROPN
ejpam-3916	31	43	)	)	PUNCT
ejpam-3916	31	44	,	,	PUNCT
ejpam-3916	31	45	is	be	AUX
ejpam-3916	31	46	equal	equal	ADJ
ejpam-3916	31	47	to	to	ADP
ejpam-3916	31	48	|ng(v)|	|ng(v)|	NOUN
ejpam-3916	31	49	.	.	PUNCT
ejpam-3916	32	1	the	the	DET
ejpam-3916	32	2	minimum	minimum	NOUN
ejpam-3916	32	3	degree	degree	NOUN
ejpam-3916	32	4	of	of	ADP
ejpam-3916	32	5	g	g	PROPN
ejpam-3916	32	6	is	be	AUX
ejpam-3916	32	7	δ(g	δ(g	ADV
ejpam-3916	32	8	)	)	PUNCT
ejpam-3916	32	9	=	=	SYM
ejpam-3916	32	10	min{degg(v	min{degg(v	PROPN
ejpam-3916	32	11	)	)	PUNCT
ejpam-3916	32	12	:	:	PUNCT
ejpam-3916	32	13	v	v	X
ejpam-3916	32	14	∈	∈	PROPN
ejpam-3916	32	15	v	v	NOUN
ejpam-3916	32	16	(	(	PUNCT
ejpam-3916	32	17	g	g	NOUN
ejpam-3916	32	18	)	)	PUNCT
ejpam-3916	32	19	}	}	PUNCT
ejpam-3916	32	20	and	and	CCONJ
ejpam-3916	32	21	its	its	PRON
ejpam-3916	32	22	maximum	maximum	ADJ
ejpam-3916	32	23	degree	degree	NOUN
ejpam-3916	32	24	is	be	AUX
ejpam-3916	32	25	∆(g	∆(g	NOUN
ejpam-3916	32	26	)	)	PUNCT
ejpam-3916	32	27	=	=	PUNCT
ejpam-3916	32	28	max{degg(v	max{degg(v	NOUN
ejpam-3916	32	29	)	)	PUNCT
ejpam-3916	32	30	:	:	PUNCT
ejpam-3916	32	31	v	v	X
ejpam-3916	32	32	∈	∈	PROPN
ejpam-3916	32	33	v	v	NOUN
ejpam-3916	32	34	(	(	PUNCT
ejpam-3916	32	35	g	g	NOUN
ejpam-3916	32	36	)	)	PUNCT
ejpam-3916	32	37	}	}	PUNCT
ejpam-3916	32	38	.	.	PUNCT
ejpam-3916	33	1	the	the	DET
ejpam-3916	33	2	open	open	ADJ
ejpam-3916	33	3	hop	hop	NOUN
ejpam-3916	33	4	neighbourhood	neighbourhood	NOUN
ejpam-3916	33	5	of	of	ADP
ejpam-3916	33	6	vertex	vertex	NOUN
ejpam-3916	33	7	v	v	NOUN
ejpam-3916	33	8	of	of	ADP
ejpam-3916	33	9	g	g	PROPN
ejpam-3916	33	10	is	be	AUX
ejpam-3916	33	11	the	the	DET
ejpam-3916	33	12	setng(v	setng(v	PROPN
ejpam-3916	33	13	,	,	PUNCT
ejpam-3916	33	14	2	2	X
ejpam-3916	33	15	)	)	PUNCT
ejpam-3916	33	16	=	=	PRON
ejpam-3916	33	17	{	{	PUNCT
ejpam-3916	33	18	w	w	NOUN
ejpam-3916	33	19	∈	∈	PROPN
ejpam-3916	33	20	v	v	ADP
ejpam-3916	33	21	(	(	PUNCT
ejpam-3916	33	22	g	g	NOUN
ejpam-3916	33	23	)	)	PUNCT
ejpam-3916	33	24	:	:	PUNCT
ejpam-3916	33	25	dg(v	dg(v	X
ejpam-3916	33	26	,	,	PUNCT
ejpam-3916	33	27	w	w	NOUN
ejpam-3916	33	28	)	)	PUNCT
ejpam-3916	33	29	=	=	SYM
ejpam-3916	33	30	2	2	NUM
ejpam-3916	33	31	}	}	PUNCT
ejpam-3916	33	32	.	.	PUNCT
ejpam-3916	34	1	a	a	DET
ejpam-3916	34	2	set	set	NOUN
ejpam-3916	34	3	s	s	NOUN
ejpam-3916	34	4	⊆	⊆	NUM
ejpam-3916	34	5	v	v	NOUN
ejpam-3916	34	6	(	(	PUNCT
ejpam-3916	34	7	g	g	NOUN
ejpam-3916	34	8	)	)	PUNCT
ejpam-3916	34	9	is	be	AUX
ejpam-3916	34	10	a	a	DET
ejpam-3916	34	11	dominating	dominating	NOUN
ejpam-3916	34	12	set	set	NOUN
ejpam-3916	34	13	(	(	PUNCT
ejpam-3916	34	14	resp	resp	NOUN
ejpam-3916	34	15	.	.	PUNCT
ejpam-3916	35	1	total	total	ADJ
ejpam-3916	35	2	dominating	dominating	NOUN
ejpam-3916	35	3	set	set	NOUN
ejpam-3916	35	4	)	)	PUNCT
ejpam-3916	35	5	of	of	ADP
ejpam-3916	35	6	g	g	PROPN
ejpam-3916	35	7	if	if	SCONJ
ejpam-3916	35	8	ng[s	ng[	NOUN
ejpam-3916	35	9	]	]	PUNCT
ejpam-3916	35	10	=	=	SYM
ejpam-3916	35	11	v	v	X
ejpam-3916	35	12	(	(	PUNCT
ejpam-3916	35	13	g	g	NOUN
ejpam-3916	35	14	)	)	PUNCT
ejpam-3916	35	15	(	(	PUNCT
ejpam-3916	35	16	resp	resp	NOUN
ejpam-3916	35	17	.	.	PUNCT
ejpam-3916	35	18	ng(s	ng(s	NUM
ejpam-3916	35	19	)	)	PUNCT
ejpam-3916	36	1	=	=	SYM
ejpam-3916	36	2	v	v	X
ejpam-3916	36	3	(	(	PUNCT
ejpam-3916	36	4	g	g	NOUN
ejpam-3916	36	5	)	)	PUNCT
ejpam-3916	36	6	)	)	PUNCT
ejpam-3916	36	7	.	.	PUNCT
ejpam-3916	37	1	the	the	DET
ejpam-3916	37	2	smallest	small	ADJ
ejpam-3916	37	3	cardinality	cardinality	NOUN
ejpam-3916	37	4	of	of	ADP
ejpam-3916	37	5	a	a	DET
ejpam-3916	37	6	dominating	dominating	NOUN
ejpam-3916	37	7	(	(	PUNCT
ejpam-3916	37	8	resp	resp	NOUN
ejpam-3916	37	9	.	.	PUNCT
ejpam-3916	38	1	total	total	ADJ
ejpam-3916	38	2	dominating	dominating	NOUN
ejpam-3916	38	3	)	)	PUNCT
ejpam-3916	38	4	set	set	NOUN
ejpam-3916	38	5	of	of	ADP
ejpam-3916	38	6	g	g	NOUN
ejpam-3916	38	7	,	,	PUNCT
ejpam-3916	38	8	denoted	denote	VERB
ejpam-3916	38	9	by	by	ADP
ejpam-3916	38	10	γ(g	γ(g	PROPN
ejpam-3916	38	11	)	)	PUNCT
ejpam-3916	38	12	(	(	PUNCT
ejpam-3916	38	13	resp	resp	NOUN
ejpam-3916	38	14	.	.	PUNCT
ejpam-3916	38	15	γt(g	γt(g	PUNCT
ejpam-3916	38	16	)	)	PUNCT
ejpam-3916	38	17	)	)	PUNCT
ejpam-3916	38	18	,	,	PUNCT
ejpam-3916	38	19	is	be	AUX
ejpam-3916	38	20	called	call	VERB
ejpam-3916	38	21	the	the	DET
ejpam-3916	38	22	domination	domination	NOUN
ejpam-3916	38	23	number	number	NOUN
ejpam-3916	38	24	(	(	PUNCT
ejpam-3916	38	25	resp	resp	NOUN
ejpam-3916	38	26	.	.	PUNCT
ejpam-3916	39	1	total	total	ADJ
ejpam-3916	39	2	domination	domination	NOUN
ejpam-3916	39	3	number	number	NOUN
ejpam-3916	39	4	)	)	PUNCT
ejpam-3916	39	5	of	of	ADP
ejpam-3916	39	6	g.	g.	PROPN
ejpam-3916	39	7	a	a	DET
ejpam-3916	39	8	dominating	dominating	NOUN
ejpam-3916	39	9	(	(	PUNCT
ejpam-3916	39	10	resp	resp	NOUN
ejpam-3916	39	11	.	.	PUNCT
ejpam-3916	40	1	total	total	ADJ
ejpam-3916	40	2	dominating	dominating	NOUN
ejpam-3916	40	3	)	)	PUNCT
ejpam-3916	40	4	set	set	NOUN
ejpam-3916	40	5	of	of	ADP
ejpam-3916	40	6	g	g	NOUN
ejpam-3916	40	7	with	with	ADP
ejpam-3916	40	8	cardinality	cardinality	PROPN
ejpam-3916	40	9	γ(g	γ(g	PROPN
ejpam-3916	40	10	)	)	PUNCT
ejpam-3916	40	11	(	(	PUNCT
ejpam-3916	40	12	resp	resp	NOUN
ejpam-3916	40	13	.	.	PUNCT
ejpam-3916	40	14	γt(g	γt(g	PUNCT
ejpam-3916	40	15	)	)	PUNCT
ejpam-3916	40	16	)	)	PUNCT
ejpam-3916	40	17	,	,	PUNCT
ejpam-3916	40	18	is	be	AUX
ejpam-3916	40	19	called	call	VERB
ejpam-3916	40	20	a	a	DET
ejpam-3916	40	21	γ	γ	NOUN
ejpam-3916	40	22	-	-	PUNCT
ejpam-3916	40	23	set	set	ADJ
ejpam-3916	40	24	(	(	PUNCT
ejpam-3916	40	25	resp	resp	NOUN
ejpam-3916	40	26	.	.	PUNCT
ejpam-3916	41	1	γt	γt	NOUN
ejpam-3916	41	2	-	-	PUNCT
ejpam-3916	41	3	set	set	NOUN
ejpam-3916	41	4	)	)	PUNCT
ejpam-3916	41	5	of	of	ADP
ejpam-3916	41	6	g.	g.	PROPN
ejpam-3916	42	1	it	it	PRON
ejpam-3916	42	2	should	should	AUX
ejpam-3916	42	3	be	be	AUX
ejpam-3916	42	4	noted	note	VERB
ejpam-3916	42	5	that	that	SCONJ
ejpam-3916	42	6	only	only	ADJ
ejpam-3916	42	7	graphs	graph	NOUN
ejpam-3916	42	8	without	without	ADP
ejpam-3916	42	9	isolated	isolated	ADJ
ejpam-3916	42	10	vertices	vertex	NOUN
ejpam-3916	42	11	admit	admit	VERB
ejpam-3916	42	12	total	total	ADJ
ejpam-3916	42	13	dominating	dominating	NOUN
ejpam-3916	42	14	sets	set	NOUN
ejpam-3916	42	15	.	.	PUNCT
ejpam-3916	43	1	a	a	DET
ejpam-3916	43	2	set	set	NOUN
ejpam-3916	43	3	s	s	NOUN
ejpam-3916	43	4	⊆	⊆	NUM
ejpam-3916	43	5	v	v	NOUN
ejpam-3916	43	6	(	(	PUNCT
ejpam-3916	43	7	g	g	NOUN
ejpam-3916	43	8	)	)	PUNCT
ejpam-3916	43	9	is	be	AUX
ejpam-3916	43	10	a	a	DET
ejpam-3916	43	11	hop	hop	NOUN
ejpam-3916	43	12	dominating	dominating	NOUN
ejpam-3916	43	13	set	set	NOUN
ejpam-3916	43	14	of	of	ADP
ejpam-3916	43	15	g	g	PROPN
ejpam-3916	43	16	if	if	SCONJ
ejpam-3916	43	17	for	for	ADP
ejpam-3916	43	18	each	each	DET
ejpam-3916	43	19	x	x	SYM
ejpam-3916	43	20	∈	∈	PROPN
ejpam-3916	43	21	v	v	ADP
ejpam-3916	43	22	(	(	PUNCT
ejpam-3916	43	23	g	g	NOUN
ejpam-3916	43	24	)	)	PUNCT
ejpam-3916	43	25	\	\	PROPN
ejpam-3916	44	1	s	s	X
ejpam-3916	44	2	,	,	PUNCT
ejpam-3916	44	3	there	there	PRON
ejpam-3916	44	4	exists	exist	VERB
ejpam-3916	44	5	z	z	PROPN
ejpam-3916	44	6	∈	∈	PROPN
ejpam-3916	44	7	s	s	VERB
ejpam-3916	44	8	such	such	ADJ
ejpam-3916	44	9	that	that	PRON
ejpam-3916	44	10	dg(x	dg(x	NOUN
ejpam-3916	44	11	,	,	PUNCT
ejpam-3916	44	12	z	z	NOUN
ejpam-3916	44	13	)	)	PUNCT
ejpam-3916	44	14	=	=	SYM
ejpam-3916	44	15	2	2	X
ejpam-3916	44	16	.	.	X
ejpam-3916	44	17	the	the	DET
ejpam-3916	44	18	smallest	small	ADJ
ejpam-3916	44	19	cardinality	cardinality	NOUN
ejpam-3916	44	20	of	of	ADP
ejpam-3916	44	21	a	a	DET
ejpam-3916	44	22	hop	hop	NOUN
ejpam-3916	44	23	dominating	dominating	NOUN
ejpam-3916	44	24	set	set	NOUN
ejpam-3916	44	25	of	of	ADP
ejpam-3916	44	26	g	g	NOUN
ejpam-3916	44	27	,	,	PUNCT
ejpam-3916	44	28	denoted	denote	VERB
ejpam-3916	44	29	by	by	ADP
ejpam-3916	44	30	γh(g	γh(g	NOUN
ejpam-3916	44	31	)	)	PUNCT
ejpam-3916	44	32	,	,	PUNCT
ejpam-3916	44	33	is	be	AUX
ejpam-3916	44	34	called	call	VERB
ejpam-3916	44	35	the	the	DET
ejpam-3916	44	36	hop	hop	NOUN
ejpam-3916	44	37	domination	domination	NOUN
ejpam-3916	44	38	number	number	NOUN
ejpam-3916	44	39	of	of	ADP
ejpam-3916	44	40	g.	g.	PROPN
ejpam-3916	44	41	a	a	DET
ejpam-3916	44	42	hop	hop	NOUN
ejpam-3916	44	43	dominating	dominating	NOUN
ejpam-3916	44	44	set	set	NOUN
ejpam-3916	44	45	of	of	ADP
ejpam-3916	44	46	g	g	PROPN
ejpam-3916	44	47	with	with	ADP
ejpam-3916	44	48	cardinality	cardinality	NOUN
ejpam-3916	44	49	γh(g	γh(g	NOUN
ejpam-3916	44	50	)	)	PUNCT
ejpam-3916	44	51	is	be	AUX
ejpam-3916	44	52	called	call	VERB
ejpam-3916	44	53	a	a	DET
ejpam-3916	44	54	γh	γh	ADV
ejpam-3916	44	55	-	-	PUNCT
ejpam-3916	44	56	set	set	NOUN
ejpam-3916	44	57	of	of	ADP
ejpam-3916	44	58	g.	g.	PROPN
ejpam-3916	44	59	a	a	DET
ejpam-3916	44	60	set	set	NOUN
ejpam-3916	44	61	s	s	PROPN
ejpam-3916	44	62	⊆	⊆	NUM
ejpam-3916	44	63	v	v	NOUN
ejpam-3916	44	64	(	(	PUNCT
ejpam-3916	44	65	g	g	NOUN
ejpam-3916	44	66	)	)	PUNCT
ejpam-3916	44	67	is	be	AUX
ejpam-3916	44	68	a	a	DET
ejpam-3916	44	69	global	global	ADJ
ejpam-3916	44	70	hop	hop	NOUN
ejpam-3916	44	71	dominating	dominating	NOUN
ejpam-3916	44	72	set	set	NOUN
ejpam-3916	44	73	of	of	ADP
ejpam-3916	44	74	g	g	PROPN
ejpam-3916	44	75	if	if	SCONJ
ejpam-3916	44	76	it	it	PRON
ejpam-3916	44	77	is	be	AUX
ejpam-3916	44	78	a	a	DET
ejpam-3916	44	79	hop	hop	NOUN
ejpam-3916	44	80	dominating	dominating	NOUN
ejpam-3916	44	81	set	set	NOUN
ejpam-3916	44	82	of	of	ADP
ejpam-3916	44	83	g	g	PROPN
ejpam-3916	44	84	and	and	CCONJ
ejpam-3916	44	85	g.	g.	NOUN
ejpam-3916	44	86	the	the	DET
ejpam-3916	44	87	smallest	small	ADJ
ejpam-3916	44	88	cardinality	cardinality	NOUN
ejpam-3916	44	89	of	of	ADP
ejpam-3916	44	90	a	a	DET
ejpam-3916	44	91	global	global	ADJ
ejpam-3916	44	92	hop	hop	NOUN
ejpam-3916	44	93	dominating	dominating	NOUN
ejpam-3916	44	94	set	set	NOUN
ejpam-3916	44	95	of	of	ADP
ejpam-3916	44	96	g	g	NOUN
ejpam-3916	44	97	,	,	PUNCT
ejpam-3916	44	98	denoted	denote	VERB
ejpam-3916	44	99	by	by	ADP
ejpam-3916	44	100	γgh(g	γgh(g	NOUN
ejpam-3916	44	101	)	)	PUNCT
ejpam-3916	44	102	,	,	PUNCT
ejpam-3916	44	103	is	be	AUX
ejpam-3916	44	104	called	call	VERB
ejpam-3916	44	105	the	the	DET
ejpam-3916	44	106	global	global	ADJ
ejpam-3916	44	107	hop	hop	NOUN
ejpam-3916	44	108	domination	domination	NOUN
ejpam-3916	44	109	number	number	NOUN
ejpam-3916	44	110	of	of	ADP
ejpam-3916	44	111	g.	g.	PROPN
ejpam-3916	44	112	a	a	DET
ejpam-3916	44	113	global	global	ADJ
ejpam-3916	44	114	hop	hop	NOUN
ejpam-3916	44	115	dominating	dominating	NOUN
ejpam-3916	44	116	set	set	NOUN
ejpam-3916	44	117	of	of	ADP
ejpam-3916	44	118	g	g	NOUN
ejpam-3916	44	119	with	with	ADP
ejpam-3916	44	120	cardinality	cardinality	NOUN
ejpam-3916	44	121	γgh(g	γgh(g	NOUN
ejpam-3916	44	122	)	)	PUNCT
ejpam-3916	44	123	is	be	AUX
ejpam-3916	44	124	called	call	VERB
ejpam-3916	44	125	a	a	DET
ejpam-3916	44	126	γgh	γgh	PROPN
ejpam-3916	44	127	-	-	PUNCT
ejpam-3916	44	128	set	set	NOUN
ejpam-3916	44	129	of	of	ADP
ejpam-3916	44	130	g.	g.	PROPN
ejpam-3916	44	131	a	a	DET
ejpam-3916	44	132	set	set	NOUN
ejpam-3916	45	1	d	d	PROPN
ejpam-3916	45	2	⊆	⊆	NUM
ejpam-3916	45	3	v	v	ADP
ejpam-3916	45	4	(	(	PUNCT
ejpam-3916	45	5	g	g	NOUN
ejpam-3916	45	6	)	)	PUNCT
ejpam-3916	45	7	is	be	AUX
ejpam-3916	45	8	a	a	DET
ejpam-3916	45	9	pointwise	pointwise	ADJ
ejpam-3916	45	10	non	non	ADJ
ejpam-3916	45	11	-	-	ADJ
ejpam-3916	45	12	dominating	dominating	ADJ
ejpam-3916	45	13	set	set	NOUN
ejpam-3916	45	14	of	of	ADP
ejpam-3916	45	15	g	g	PROPN
ejpam-3916	45	16	if	if	SCONJ
ejpam-3916	45	17	for	for	ADP
ejpam-3916	45	18	each	each	DET
ejpam-3916	45	19	v	v	NUM
ejpam-3916	45	20	∈	∈	PROPN
ejpam-3916	45	21	v	v	NOUN
ejpam-3916	45	22	(	(	PUNCT
ejpam-3916	45	23	g)\d	g)\d	NOUN
ejpam-3916	45	24	,	,	PUNCT
ejpam-3916	45	25	there	there	PRON
ejpam-3916	45	26	exists	exist	VERB
ejpam-3916	45	27	u	u	NOUN
ejpam-3916	45	28	∈	∈	PROPN
ejpam-3916	45	29	d	d	ADP
ejpam-3916	45	30	such	such	ADJ
ejpam-3916	45	31	that	that	DET
ejpam-3916	45	32	v	v	NOUN
ejpam-3916	45	33	/∈	/∈	PUNCT
ejpam-3916	45	34	ng(u	ng(u	NOUN
ejpam-3916	45	35	)	)	PUNCT
ejpam-3916	45	36	.	.	PUNCT
ejpam-3916	46	1	the	the	DET
ejpam-3916	46	2	smallest	small	ADJ
ejpam-3916	46	3	cardinality	cardinality	NOUN
ejpam-3916	46	4	of	of	ADP
ejpam-3916	46	5	a	a	DET
ejpam-3916	46	6	pointwise	pointwise	ADJ
ejpam-3916	46	7	non	non	ADJ
ejpam-3916	46	8	-	-	ADJ
ejpam-3916	46	9	dominating	dominating	ADJ
ejpam-3916	46	10	set	set	NOUN
ejpam-3916	46	11	of	of	ADP
ejpam-3916	46	12	g	g	NOUN
ejpam-3916	46	13	,	,	PUNCT
ejpam-3916	46	14	denoted	denote	VERB
ejpam-3916	46	15	by	by	ADP
ejpam-3916	46	16	pnd(g	pnd(g	PROPN
ejpam-3916	46	17	)	)	PUNCT
ejpam-3916	46	18	,	,	PUNCT
ejpam-3916	46	19	is	be	AUX
ejpam-3916	46	20	called	call	VERB
ejpam-3916	46	21	the	the	DET
ejpam-3916	46	22	pointwise	pointwise	ADJ
ejpam-3916	46	23	non	non	ADJ
ejpam-3916	46	24	-	-	ADJ
ejpam-3916	46	25	domination	domination	ADJ
ejpam-3916	46	26	number	number	NOUN
ejpam-3916	46	27	of	of	ADP
ejpam-3916	46	28	g.	g.	PROPN
ejpam-3916	46	29	a	a	DET
ejpam-3916	46	30	dominating	dominating	NOUN
ejpam-3916	46	31	set	set	NOUN
ejpam-3916	46	32	s	s	PRON
ejpam-3916	46	33	which	which	PRON
ejpam-3916	46	34	is	be	AUX
ejpam-3916	46	35	also	also	ADV
ejpam-3916	46	36	a	a	DET
ejpam-3916	46	37	pointwise	pointwise	ADJ
ejpam-3916	46	38	non	non	ADJ
ejpam-3916	46	39	-	-	ADJ
ejpam-3916	46	40	dominating	dominating	ADJ
ejpam-3916	46	41	set	set	NOUN
ejpam-3916	46	42	of	of	ADP
ejpam-3916	46	43	g	g	PROPN
ejpam-3916	46	44	is	be	AUX
ejpam-3916	46	45	called	call	VERB
ejpam-3916	46	46	a	a	DET
ejpam-3916	46	47	dominating	dominating	NOUN
ejpam-3916	46	48	pointwise	pointwise	ADV
ejpam-3916	46	49	non	non	ADJ
ejpam-3916	46	50	-	-	ADJ
ejpam-3916	46	51	dominating	dominating	ADJ
ejpam-3916	46	52	set	set	NOUN
ejpam-3916	46	53	of	of	ADP
ejpam-3916	46	54	g.	g.	PROPN
ejpam-3916	46	55	the	the	DET
ejpam-3916	46	56	smallest	small	ADJ
ejpam-3916	46	57	cardinality	cardinality	NOUN
ejpam-3916	46	58	of	of	ADP
ejpam-3916	46	59	a	a	DET
ejpam-3916	46	60	dominating	dominating	NOUN
ejpam-3916	46	61	pointwise	pointwise	ADV
ejpam-3916	46	62	non	non	ADJ
ejpam-3916	46	63	-	-	ADJ
ejpam-3916	46	64	dominating	dominating	ADJ
ejpam-3916	46	65	set	set	NOUN
ejpam-3916	46	66	of	of	ADP
ejpam-3916	46	67	g	g	NOUN
ejpam-3916	46	68	will	will	AUX
ejpam-3916	46	69	be	be	AUX
ejpam-3916	46	70	denoted	denote	VERB
ejpam-3916	46	71	by	by	ADP
ejpam-3916	46	72	γpnd(g	γpnd(g	PROPN
ejpam-3916	46	73	)	)	PUNCT
ejpam-3916	46	74	.	.	PUNCT
ejpam-3916	47	1	any	any	DET
ejpam-3916	47	2	pointwise	pointwise	ADJ
ejpam-3916	47	3	non	non	ADJ
ejpam-3916	47	4	-	-	ADJ
ejpam-3916	47	5	dominating	dominating	ADJ
ejpam-3916	47	6	(	(	PUNCT
ejpam-3916	47	7	resp	resp	NOUN
ejpam-3916	47	8	.	.	PUNCT
ejpam-3916	48	1	dominating	dominate	VERB
ejpam-3916	48	2	pointwise	pointwise	PROPN
ejpam-3916	48	3	non	non	ADJ
ejpam-3916	48	4	-	-	ADJ
ejpam-3916	48	5	dominating	dominating	ADJ
ejpam-3916	48	6	)	)	PUNCT
ejpam-3916	48	7	set	set	NOUN
ejpam-3916	48	8	of	of	ADP
ejpam-3916	48	9	g	g	NOUN
ejpam-3916	48	10	with	with	ADP
ejpam-3916	48	11	cardinality	cardinality	NOUN
ejpam-3916	48	12	pnd(g	pnd(g	PROPN
ejpam-3916	48	13	)	)	PUNCT
ejpam-3916	48	14	(	(	PUNCT
ejpam-3916	48	15	resp	resp	NOUN
ejpam-3916	48	16	.	.	PUNCT
ejpam-3916	49	1	γpnd(g	γpnd(g	NOUN
ejpam-3916	49	2	)	)	PUNCT
ejpam-3916	49	3	)	)	PUNCT
ejpam-3916	49	4	,	,	PUNCT
ejpam-3916	49	5	is	be	AUX
ejpam-3916	49	6	called	call	VERB
ejpam-3916	49	7	a	a	DET
ejpam-3916	49	8	pnd	pnd	NOUN
ejpam-3916	49	9	-	-	PUNCT
ejpam-3916	49	10	set	set	VERB
ejpam-3916	49	11	(	(	PUNCT
ejpam-3916	49	12	resp	resp	NOUN
ejpam-3916	49	13	.	.	PUNCT
ejpam-3916	50	1	γpnd	γpnd	NOUN
ejpam-3916	50	2	-	-	PUNCT
ejpam-3916	50	3	set	set	NOUN
ejpam-3916	50	4	)	)	PUNCT
ejpam-3916	50	5	of	of	ADP
ejpam-3916	50	6	g.	g.	PROPN
ejpam-3916	50	7	these	these	DET
ejpam-3916	50	8	concepts	concept	NOUN
ejpam-3916	50	9	and	and	CCONJ
ejpam-3916	50	10	parameters	parameter	NOUN
ejpam-3916	50	11	have	have	AUX
ejpam-3916	50	12	been	be	AUX
ejpam-3916	50	13	defined	define	VERB
ejpam-3916	50	14	and	and	CCONJ
ejpam-3916	50	15	used	use	VERB
ejpam-3916	50	16	in	in	ADP
ejpam-3916	50	17	[	[	X
ejpam-3916	50	18	3	3	NUM
ejpam-3916	50	19	]	]	PUNCT
ejpam-3916	50	20	and	and	CCONJ
ejpam-3916	51	1	[	[	X
ejpam-3916	51	2	9	9	NUM
ejpam-3916	51	3	]	]	SYM
ejpam-3916	51	4	.	.	PUNCT
ejpam-3916	51	5	2	2	X
ejpam-3916	51	6	.	.	X
ejpam-3916	51	7	results	result	NOUN
ejpam-3916	51	8	it	it	PRON
ejpam-3916	51	9	is	be	AUX
ejpam-3916	51	10	worth	worth	ADJ
ejpam-3916	51	11	mentioning	mention	VERB
ejpam-3916	51	12	here	here	ADV
ejpam-3916	51	13	that	that	SCONJ
ejpam-3916	51	14	every	every	DET
ejpam-3916	51	15	graph	graph	NOUN
ejpam-3916	51	16	g	g	PROPN
ejpam-3916	51	17	admits	admit	VERB
ejpam-3916	51	18	a	a	DET
ejpam-3916	51	19	global	global	ADJ
ejpam-3916	51	20	hop	hop	NOUN
ejpam-3916	51	21	dominating	dominating	NOUN
ejpam-3916	51	22	set	set	NOUN
ejpam-3916	51	23	.	.	PUNCT
ejpam-3916	52	1	indeed	indeed	ADV
ejpam-3916	52	2	,	,	PUNCT
ejpam-3916	52	3	the	the	DET
ejpam-3916	52	4	vertex	vertex	NOUN
ejpam-3916	52	5	set	set	VERB
ejpam-3916	52	6	v	v	NOUN
ejpam-3916	52	7	(	(	PUNCT
ejpam-3916	52	8	g	g	NOUN
ejpam-3916	52	9	)	)	PUNCT
ejpam-3916	52	10	of	of	ADP
ejpam-3916	52	11	g	g	PROPN
ejpam-3916	52	12	is	be	AUX
ejpam-3916	52	13	a	a	DET
ejpam-3916	52	14	global	global	ADJ
ejpam-3916	52	15	hop	hop	NOUN
ejpam-3916	52	16	dominating	dominating	NOUN
ejpam-3916	52	17	set	set	NOUN
ejpam-3916	52	18	.	.	PUNCT
ejpam-3916	53	1	further	far	ADV
ejpam-3916	53	2	,	,	PUNCT
ejpam-3916	53	3	we	we	PRON
ejpam-3916	53	4	have	have	VERB
ejpam-3916	53	5	remark	remark	NOUN
ejpam-3916	53	6	1	1	NUM
ejpam-3916	53	7	.	.	NOUN
ejpam-3916	53	8	1	1	NUM
ejpam-3916	53	9	≤	≤	NUM
ejpam-3916	53	10	γgh(g	γgh(g	NOUN
ejpam-3916	53	11	)	)	PUNCT
ejpam-3916	54	1	≤	≤	NOUN
ejpam-3916	54	2	|v	|v	X
ejpam-3916	54	3	(	(	PUNCT
ejpam-3916	54	4	g)|	g)|	NOUN
ejpam-3916	54	5	for	for	ADP
ejpam-3916	54	6	any	any	DET
ejpam-3916	54	7	graph	graph	NOUN
ejpam-3916	54	8	g.	g.	PROPN
ejpam-3916	54	9	moreover	moreover	ADV
ejpam-3916	54	10	,	,	PUNCT
ejpam-3916	54	11	γgh(g	γgh(g	NOUN
ejpam-3916	54	12	)	)	PUNCT
ejpam-3916	54	13	=	=	SYM
ejpam-3916	54	14	1	1	NUM
ejpam-3916	54	15	if	if	SCONJ
ejpam-3916	54	16	and	and	CCONJ
ejpam-3916	54	17	only	only	ADV
ejpam-3916	54	18	if	if	SCONJ
ejpam-3916	54	19	g	g	PROPN
ejpam-3916	54	20	=	=	SYM
ejpam-3916	54	21	k1	k1	PROPN
ejpam-3916	54	22	.	.	PUNCT
ejpam-3916	54	23	theorem	theorem	NOUN
ejpam-3916	54	24	1	1	NUM
ejpam-3916	54	25	.	.	PUNCT
ejpam-3916	55	1	let	let	VERB
ejpam-3916	55	2	g	g	PRON
ejpam-3916	55	3	be	be	AUX
ejpam-3916	55	4	a	a	DET
ejpam-3916	55	5	non	non	ADJ
ejpam-3916	55	6	-	-	ADJ
ejpam-3916	55	7	trivial	trivial	ADJ
ejpam-3916	55	8	graph	graph	NOUN
ejpam-3916	55	9	.	.	PUNCT
ejpam-3916	56	1	then	then	ADV
ejpam-3916	56	2	γgh(g	γgh(g	NOUN
ejpam-3916	56	3	)	)	PUNCT
ejpam-3916	56	4	=	=	SYM
ejpam-3916	56	5	2	2	NUM
ejpam-3916	56	6	if	if	SCONJ
ejpam-3916	56	7	and	and	CCONJ
ejpam-3916	56	8	only	only	ADV
ejpam-3916	56	9	if	if	SCONJ
ejpam-3916	56	10	there	there	PRON
ejpam-3916	56	11	exist	exist	VERB
ejpam-3916	56	12	distinct	distinct	ADJ
ejpam-3916	56	13	vertices	vertex	NOUN
ejpam-3916	56	14	x	x	PUNCT
ejpam-3916	56	15	and	and	CCONJ
ejpam-3916	56	16	y	y	PROPN
ejpam-3916	56	17	of	of	ADP
ejpam-3916	56	18	g	g	PROPN
ejpam-3916	56	19	satisfying	satisfy	VERB
ejpam-3916	56	20	the	the	DET
ejpam-3916	56	21	following	follow	VERB
ejpam-3916	56	22	conditions	condition	NOUN
ejpam-3916	56	23	:	:	PUNCT
ejpam-3916	56	24	g.	g.	PROPN
ejpam-3916	56	25	salasalan	salasalan	NOUN
ejpam-3916	56	26	,	,	PUNCT
ejpam-3916	56	27	s.	s.	PROPN
ejpam-3916	56	28	canoy	canoy	PROPN
ejpam-3916	56	29	,	,	PUNCT
ejpam-3916	56	30	jr	jr	PROPN
ejpam-3916	56	31	.	.	PROPN
ejpam-3916	56	32	/	/	SYM
ejpam-3916	56	33	eur	eur	PROPN
ejpam-3916	56	34	.	.	PUNCT
ejpam-3916	57	1	j.	j.	PROPN
ejpam-3916	57	2	pure	pure	PROPN
ejpam-3916	57	3	appl	appl	PROPN
ejpam-3916	57	4	.	.	PROPN
ejpam-3916	57	5	math	math	PROPN
ejpam-3916	57	6	,	,	PUNCT
ejpam-3916	57	7	14	14	NUM
ejpam-3916	57	8	(	(	PUNCT
ejpam-3916	57	9	1	1	NUM
ejpam-3916	57	10	)	)	PUNCT
ejpam-3916	57	11	(	(	PUNCT
ejpam-3916	57	12	2021	2021	NUM
ejpam-3916	57	13	)	)	PUNCT
ejpam-3916	57	14	,	,	PUNCT
ejpam-3916	57	15	112	112	NUM
ejpam-3916	57	16	-	-	SYM
ejpam-3916	57	17	125	125	NUM
ejpam-3916	57	18	114	114	NUM
ejpam-3916	57	19	(	(	PUNCT
ejpam-3916	57	20	i	i	NOUN
ejpam-3916	57	21	)	)	PUNCT
ejpam-3916	57	22	ng(x	ng(x	NUM
ejpam-3916	57	23	,	,	PUNCT
ejpam-3916	57	24	2	2	X
ejpam-3916	57	25	)	)	PUNCT
ejpam-3916	57	26	∩ng(y	∩ng(y	PROPN
ejpam-3916	57	27	,	,	PUNCT
ejpam-3916	57	28	2	2	NUM
ejpam-3916	57	29	)	)	PUNCT
ejpam-3916	57	30	=	=	NOUN
ejpam-3916	57	31	∅	∅	NOUN
ejpam-3916	57	32	and	and	CCONJ
ejpam-3916	57	33	v	v	NOUN
ejpam-3916	57	34	(	(	PUNCT
ejpam-3916	57	35	g	g	NOUN
ejpam-3916	57	36	)	)	PUNCT
ejpam-3916	57	37	\	\	NOUN
ejpam-3916	57	38	{	{	PUNCT
ejpam-3916	57	39	x	x	NOUN
ejpam-3916	57	40	,	,	PUNCT
ejpam-3916	57	41	y	y	PROPN
ejpam-3916	57	42	}	}	PUNCT
ejpam-3916	57	43	=	=	SYM
ejpam-3916	57	44	ng(x	ng(x	NUM
ejpam-3916	57	45	,	,	PUNCT
ejpam-3916	57	46	2	2	X
ejpam-3916	57	47	)	)	PUNCT
ejpam-3916	57	48	∪ng(y	∪ng(y	PROPN
ejpam-3916	57	49	,	,	PUNCT
ejpam-3916	57	50	2	2	NUM
ejpam-3916	57	51	)	)	PUNCT
ejpam-3916	57	52	;	;	PUNCT
ejpam-3916	57	53	(	(	PUNCT
ejpam-3916	57	54	ii	ii	NOUN
ejpam-3916	57	55	)	)	PUNCT
ejpam-3916	57	56	ng(x	ng(x	NUM
ejpam-3916	57	57	,	,	PUNCT
ejpam-3916	57	58	2	2	X
ejpam-3916	57	59	)	)	PUNCT
ejpam-3916	57	60	=	=	SYM
ejpam-3916	57	61	ng(y	ng(y	NOUN
ejpam-3916	57	62	)	)	PUNCT
ejpam-3916	57	63	\	\	NOUN
ejpam-3916	57	64	{	{	PUNCT
ejpam-3916	57	65	x	x	NOUN
ejpam-3916	57	66	}	}	PUNCT
ejpam-3916	57	67	and	and	CCONJ
ejpam-3916	57	68	ng(y	ng(y	NOUN
ejpam-3916	57	69	,	,	PUNCT
ejpam-3916	57	70	2	2	X
ejpam-3916	57	71	)	)	PUNCT
ejpam-3916	57	72	=	=	SYM
ejpam-3916	57	73	ng(x	ng(x	NUM
ejpam-3916	57	74	)	)	PUNCT
ejpam-3916	57	75	\	\	NOUN
ejpam-3916	58	1	{	{	PUNCT
ejpam-3916	58	2	y	y	NOUN
ejpam-3916	58	3	}	}	PUNCT
ejpam-3916	58	4	;	;	PUNCT
ejpam-3916	58	5	and	and	CCONJ
ejpam-3916	58	6	(	(	PUNCT
ejpam-3916	58	7	iii	iii	X
ejpam-3916	58	8	)	)	PUNCT
ejpam-3916	58	9	if	if	SCONJ
ejpam-3916	58	10	xy	xy	PROPN
ejpam-3916	58	11	∈	∈	PROPN
ejpam-3916	58	12	e(g	e(g	PROPN
ejpam-3916	58	13	)	)	PUNCT
ejpam-3916	58	14	,	,	PUNCT
ejpam-3916	58	15	then	then	ADV
ejpam-3916	58	16	ng(x)\ng(w	ng(x)\ng(w	ADJ
ejpam-3916	58	17	)	)	PUNCT
ejpam-3916	58	18	6=	6=	ADP
ejpam-3916	58	19	∅	∅	NOUN
ejpam-3916	58	20	for	for	ADP
ejpam-3916	58	21	each	each	DET
ejpam-3916	58	22	w	w	PROPN
ejpam-3916	58	23	∈	∈	PROPN
ejpam-3916	58	24	ng(x	ng(x	NUM
ejpam-3916	58	25	,	,	PUNCT
ejpam-3916	58	26	2	2	NUM
ejpam-3916	58	27	)	)	PUNCT
ejpam-3916	58	28	and	and	CCONJ
ejpam-3916	58	29	ng(y)\ng(v	ng(y)\ng(v	VERB
ejpam-3916	58	30	)	)	PUNCT
ejpam-3916	58	31	6=	6=	ADP
ejpam-3916	58	32	∅	∅	NOUN
ejpam-3916	58	33	for	for	ADP
ejpam-3916	58	34	each	each	DET
ejpam-3916	58	35	v	v	NOUN
ejpam-3916	58	36	∈	∈	PROPN
ejpam-3916	58	37	ng(y	ng(y	NOUN
ejpam-3916	58	38	,	,	PUNCT
ejpam-3916	58	39	2	2	NUM
ejpam-3916	58	40	)	)	PUNCT
ejpam-3916	58	41	.	.	PUNCT
ejpam-3916	59	1	proof	proof	NOUN
ejpam-3916	59	2	.	.	PUNCT
ejpam-3916	60	1	suppose	suppose	VERB
ejpam-3916	60	2	γgh(g	γgh(g	NOUN
ejpam-3916	60	3	)	)	PUNCT
ejpam-3916	60	4	=	=	SYM
ejpam-3916	60	5	2	2	X
ejpam-3916	60	6	.	.	X
ejpam-3916	60	7	let	let	VERB
ejpam-3916	60	8	s	s	AUX
ejpam-3916	60	9	=	=	PUNCT
ejpam-3916	60	10	{	{	PUNCT
ejpam-3916	60	11	x	x	PROPN
ejpam-3916	60	12	,	,	PUNCT
ejpam-3916	60	13	y	y	PROPN
ejpam-3916	60	14	}	}	PUNCT
ejpam-3916	60	15	be	be	AUX
ejpam-3916	60	16	γgh	γgh	NOUN
ejpam-3916	60	17	-	-	PUNCT
ejpam-3916	60	18	set	set	NOUN
ejpam-3916	60	19	of	of	ADP
ejpam-3916	60	20	g.	g.	PROPN
ejpam-3916	60	21	suppose	suppose	VERB
ejpam-3916	60	22	there	there	PRON
ejpam-3916	60	23	exists	exist	VERB
ejpam-3916	60	24	z	z	PROPN
ejpam-3916	60	25	∈	∈	PROPN
ejpam-3916	60	26	ng(x	ng(x	NUM
ejpam-3916	60	27	,	,	PUNCT
ejpam-3916	60	28	2)∩ng(y	2)∩ng(y	NUM
ejpam-3916	60	29	,	,	PUNCT
ejpam-3916	60	30	2	2	NUM
ejpam-3916	60	31	)	)	PUNCT
ejpam-3916	60	32	.	.	PUNCT
ejpam-3916	61	1	then	then	ADV
ejpam-3916	61	2	xz	xz	PROPN
ejpam-3916	61	3	,	,	PUNCT
ejpam-3916	61	4	yz	yz	PROPN
ejpam-3916	61	5	∈	∈	PROPN
ejpam-3916	61	6	e(g	e(g	PROPN
ejpam-3916	61	7	)	)	PUNCT
ejpam-3916	61	8	.	.	PUNCT
ejpam-3916	62	1	this	this	PRON
ejpam-3916	62	2	implies	imply	VERB
ejpam-3916	62	3	that	that	SCONJ
ejpam-3916	62	4	dg(x	dg(x	PROPN
ejpam-3916	62	5	,	,	PUNCT
ejpam-3916	62	6	z	z	NOUN
ejpam-3916	62	7	)	)	PUNCT
ejpam-3916	62	8	6=	6=	ADP
ejpam-3916	62	9	2	2	NUM
ejpam-3916	62	10	and	and	CCONJ
ejpam-3916	62	11	dg(y	dg(y	ADJ
ejpam-3916	62	12	,	,	PUNCT
ejpam-3916	62	13	z	z	NOUN
ejpam-3916	62	14	)	)	PUNCT
ejpam-3916	62	15	6=	6=	ADP
ejpam-3916	62	16	2	2	NUM
ejpam-3916	62	17	.	.	X
ejpam-3916	62	18	hence	hence	ADV
ejpam-3916	62	19	,	,	PUNCT
ejpam-3916	62	20	s	s	VERB
ejpam-3916	62	21	is	be	AUX
ejpam-3916	62	22	not	not	PART
ejpam-3916	62	23	hop	hop	NOUN
ejpam-3916	62	24	dominating	dominate	VERB
ejpam-3916	62	25	set	set	NOUN
ejpam-3916	62	26	of	of	ADP
ejpam-3916	62	27	g	g	PROPN
ejpam-3916	62	28	,	,	PUNCT
ejpam-3916	62	29	a	a	DET
ejpam-3916	62	30	contradiction	contradiction	NOUN
ejpam-3916	62	31	.	.	PUNCT
ejpam-3916	63	1	thus	thus	ADV
ejpam-3916	63	2	,	,	PUNCT
ejpam-3916	63	3	ng(x	ng(x	NUM
ejpam-3916	63	4	,	,	PUNCT
ejpam-3916	63	5	2)∩ng(y	2)∩ng(y	NUM
ejpam-3916	63	6	,	,	PUNCT
ejpam-3916	63	7	2	2	NUM
ejpam-3916	63	8	)	)	PUNCT
ejpam-3916	63	9	=	=	NOUN
ejpam-3916	63	10	∅.	∅.	PRON
ejpam-3916	63	11	further	far	ADV
ejpam-3916	63	12	,	,	PUNCT
ejpam-3916	63	13	v	v	X
ejpam-3916	63	14	(	(	PUNCT
ejpam-3916	63	15	g)\{x	g)\{x	PROPN
ejpam-3916	63	16	,	,	PUNCT
ejpam-3916	63	17	y	y	NOUN
ejpam-3916	63	18	}	}	PUNCT
ejpam-3916	63	19	=	=	SYM
ejpam-3916	63	20	ng(x	ng(x	X
ejpam-3916	63	21	,	,	PUNCT
ejpam-3916	63	22	2)∪ng(y	2)∪ng(y	NUM
ejpam-3916	63	23	,	,	PUNCT
ejpam-3916	63	24	2	2	NUM
ejpam-3916	63	25	)	)	PUNCT
ejpam-3916	63	26	because	because	SCONJ
ejpam-3916	63	27	s	s	NOUN
ejpam-3916	63	28	is	be	AUX
ejpam-3916	63	29	a	a	DET
ejpam-3916	63	30	hop	hop	NOUN
ejpam-3916	63	31	dominating	dominating	NOUN
ejpam-3916	63	32	of	of	ADP
ejpam-3916	63	33	set	set	ADJ
ejpam-3916	63	34	g.	g.	PROPN
ejpam-3916	63	35	this	this	PRON
ejpam-3916	63	36	shows	show	VERB
ejpam-3916	63	37	that	that	SCONJ
ejpam-3916	63	38	(	(	PUNCT
ejpam-3916	63	39	i	i	NOUN
ejpam-3916	63	40	)	)	PUNCT
ejpam-3916	63	41	holds	hold	VERB
ejpam-3916	63	42	.	.	PUNCT
ejpam-3916	64	1	now	now	ADV
ejpam-3916	64	2	let	let	VERB
ejpam-3916	64	3	z	z	NOUN
ejpam-3916	64	4	∈	∈	PROPN
ejpam-3916	64	5	ng(x	ng(x	NUM
ejpam-3916	64	6	,	,	PUNCT
ejpam-3916	64	7	2	2	NUM
ejpam-3916	64	8	)	)	PUNCT
ejpam-3916	64	9	.	.	PUNCT
ejpam-3916	65	1	then	then	ADV
ejpam-3916	65	2	z	z	NOUN
ejpam-3916	65	3	/∈	/∈	PUNCT
ejpam-3916	66	1	s	s	PART
ejpam-3916	66	2	and	and	CCONJ
ejpam-3916	66	3	xz	xz	PROPN
ejpam-3916	66	4	∈	∈	PROPN
ejpam-3916	66	5	v	v	ADP
ejpam-3916	66	6	(	(	PUNCT
ejpam-3916	66	7	g	g	NOUN
ejpam-3916	66	8	)	)	PUNCT
ejpam-3916	66	9	.	.	PUNCT
ejpam-3916	67	1	since	since	SCONJ
ejpam-3916	67	2	s	s	PROPN
ejpam-3916	67	3	is	be	AUX
ejpam-3916	67	4	hop	hop	NOUN
ejpam-3916	67	5	dominating	dominate	VERB
ejpam-3916	67	6	set	set	NOUN
ejpam-3916	67	7	of	of	ADP
ejpam-3916	67	8	g	g	PROPN
ejpam-3916	67	9	,	,	PUNCT
ejpam-3916	67	10	it	it	PRON
ejpam-3916	67	11	follows	follow	VERB
ejpam-3916	67	12	that	that	SCONJ
ejpam-3916	67	13	z	z	PROPN
ejpam-3916	67	14	∈	∈	PROPN
ejpam-3916	67	15	ng(y	ng(y	NOUN
ejpam-3916	67	16	,	,	PUNCT
ejpam-3916	67	17	2	2	NUM
ejpam-3916	67	18	)	)	PUNCT
ejpam-3916	67	19	.	.	PUNCT
ejpam-3916	68	1	this	this	PRON
ejpam-3916	68	2	implies	imply	VERB
ejpam-3916	68	3	that	that	SCONJ
ejpam-3916	68	4	z	z	PROPN
ejpam-3916	68	5	∈	∈	PROPN
ejpam-3916	68	6	ng(y	ng(y	NOUN
ejpam-3916	68	7	)	)	PUNCT
ejpam-3916	68	8	\	\	NOUN
ejpam-3916	68	9	{	{	PUNCT
ejpam-3916	68	10	x	x	NOUN
ejpam-3916	68	11	}	}	PUNCT
ejpam-3916	68	12	.	.	PUNCT
ejpam-3916	69	1	on	on	ADP
ejpam-3916	69	2	the	the	DET
ejpam-3916	69	3	other	other	ADJ
ejpam-3916	69	4	hand	hand	NOUN
ejpam-3916	69	5	,	,	PUNCT
ejpam-3916	69	6	if	if	SCONJ
ejpam-3916	69	7	u	u	PROPN
ejpam-3916	69	8	∈	∈	PROPN
ejpam-3916	69	9	ng(y	ng(y	NOUN
ejpam-3916	69	10	)	)	PUNCT
ejpam-3916	69	11	\	\	NOUN
ejpam-3916	69	12	{	{	PUNCT
ejpam-3916	69	13	x	x	X
ejpam-3916	69	14	}	}	PUNCT
ejpam-3916	69	15	,	,	PUNCT
ejpam-3916	69	16	then	then	ADV
ejpam-3916	69	17	u	u	PROPN
ejpam-3916	69	18	∈	∈	PROPN
ejpam-3916	69	19	ng(x	ng(x	NUM
ejpam-3916	69	20	,	,	PUNCT
ejpam-3916	69	21	2	2	NUM
ejpam-3916	69	22	)	)	PUNCT
ejpam-3916	69	23	since	since	SCONJ
ejpam-3916	69	24	s	s	NOUN
ejpam-3916	69	25	is	be	AUX
ejpam-3916	69	26	a	a	DET
ejpam-3916	69	27	hop	hop	NOUN
ejpam-3916	69	28	dominating	dominating	NOUN
ejpam-3916	69	29	of	of	ADP
ejpam-3916	69	30	set	set	ADJ
ejpam-3916	69	31	g.	g.	PROPN
ejpam-3916	69	32	therefore	therefore	ADV
ejpam-3916	69	33	,	,	PUNCT
ejpam-3916	69	34	ng(x	ng(x	NUM
ejpam-3916	69	35	,	,	PUNCT
ejpam-3916	69	36	2	2	X
ejpam-3916	69	37	)	)	PUNCT
ejpam-3916	69	38	=	=	SYM
ejpam-3916	69	39	ng(y	ng(y	NOUN
ejpam-3916	69	40	)	)	PUNCT
ejpam-3916	69	41	\	\	NOUN
ejpam-3916	69	42	{	{	PUNCT
ejpam-3916	69	43	x	x	NOUN
ejpam-3916	69	44	}	}	PUNCT
ejpam-3916	69	45	.	.	PUNCT
ejpam-3916	70	1	similarly	similarly	ADV
ejpam-3916	70	2	,	,	PUNCT
ejpam-3916	70	3	ng(y	ng(y	NOUN
ejpam-3916	70	4	,	,	PUNCT
ejpam-3916	70	5	2	2	NUM
ejpam-3916	70	6	)	)	PUNCT
ejpam-3916	70	7	=	=	SYM
ejpam-3916	70	8	ng(x	ng(x	NUM
ejpam-3916	70	9	)	)	PUNCT
ejpam-3916	70	10	\	\	NOUN
ejpam-3916	70	11	{	{	PUNCT
ejpam-3916	70	12	y	y	NOUN
ejpam-3916	70	13	}	}	PUNCT
ejpam-3916	70	14	,	,	PUNCT
ejpam-3916	70	15	showing	show	VERB
ejpam-3916	70	16	that	that	SCONJ
ejpam-3916	70	17	(	(	PUNCT
ejpam-3916	70	18	ii	ii	NOUN
ejpam-3916	70	19	)	)	PUNCT
ejpam-3916	70	20	holds	hold	VERB
ejpam-3916	70	21	.	.	PUNCT
ejpam-3916	71	1	next	next	ADV
ejpam-3916	71	2	,	,	PUNCT
ejpam-3916	71	3	suppose	suppose	VERB
ejpam-3916	71	4	that	that	SCONJ
ejpam-3916	71	5	xy	xy	PROPN
ejpam-3916	71	6	∈	∈	PROPN
ejpam-3916	71	7	e(g	e(g	PROPN
ejpam-3916	71	8	)	)	PUNCT
ejpam-3916	71	9	and	and	CCONJ
ejpam-3916	71	10	let	let	VERB
ejpam-3916	71	11	w	w	PROPN
ejpam-3916	71	12	∈	∈	PROPN
ejpam-3916	71	13	ng(x	ng(x	NUM
ejpam-3916	71	14	,	,	PUNCT
ejpam-3916	71	15	2	2	NUM
ejpam-3916	71	16	)	)	PUNCT
ejpam-3916	71	17	.	.	PUNCT
ejpam-3916	72	1	then	then	ADV
ejpam-3916	72	2	w	w	PROPN
ejpam-3916	72	3	/∈	/∈	PROPN
ejpam-3916	72	4	s	s	PROPN
ejpam-3916	72	5	and	and	CCONJ
ejpam-3916	72	6	xw	xw	PROPN
ejpam-3916	72	7	∈	∈	PROPN
ejpam-3916	72	8	e(g	e(g	PROPN
ejpam-3916	72	9	)	)	PUNCT
ejpam-3916	72	10	.	.	PUNCT
ejpam-3916	73	1	since	since	SCONJ
ejpam-3916	73	2	s	s	PROPN
ejpam-3916	73	3	is	be	AUX
ejpam-3916	73	4	a	a	DET
ejpam-3916	73	5	hop	hop	NOUN
ejpam-3916	73	6	dominating	dominating	NOUN
ejpam-3916	73	7	set	set	NOUN
ejpam-3916	73	8	of	of	ADP
ejpam-3916	73	9	g	g	PROPN
ejpam-3916	73	10	,	,	PUNCT
ejpam-3916	73	11	w	w	PROPN
ejpam-3916	73	12	∈	∈	PROPN
ejpam-3916	73	13	ng(y	ng(y	NOUN
ejpam-3916	73	14	,	,	PUNCT
ejpam-3916	73	15	2	2	NUM
ejpam-3916	73	16	)	)	PUNCT
ejpam-3916	73	17	.	.	PUNCT
ejpam-3916	74	1	hence	hence	ADV
ejpam-3916	74	2	,	,	PUNCT
ejpam-3916	74	3	there	there	PRON
ejpam-3916	74	4	exists	exist	VERB
ejpam-3916	74	5	z	z	PROPN
ejpam-3916	74	6	∈	∈	PROPN
ejpam-3916	74	7	v	v	NOUN
ejpam-3916	74	8	(	(	PUNCT
ejpam-3916	74	9	g)\s	g)\s	VERB
ejpam-3916	74	10	such	such	ADJ
ejpam-3916	74	11	that	that	SCONJ
ejpam-3916	74	12	z	z	PROPN
ejpam-3916	74	13	∈	∈	PROPN
ejpam-3916	74	14	ng(w	ng(w	NOUN
ejpam-3916	74	15	)	)	PUNCT
ejpam-3916	74	16	∩	∩	NOUN
ejpam-3916	74	17	ng(y	ng(y	NOUN
ejpam-3916	74	18	)	)	PUNCT
ejpam-3916	74	19	.	.	PUNCT
ejpam-3916	75	1	it	it	PRON
ejpam-3916	75	2	follows	follow	VERB
ejpam-3916	75	3	that	that	SCONJ
ejpam-3916	75	4	z	z	PROPN
ejpam-3916	75	5	∈	∈	PROPN
ejpam-3916	75	6	ng(x	ng(x	NUM
ejpam-3916	75	7	)	)	PUNCT
ejpam-3916	75	8	\	\	NOUN
ejpam-3916	75	9	ng(w	ng(w	NOUN
ejpam-3916	75	10	)	)	PUNCT
ejpam-3916	75	11	,	,	PUNCT
ejpam-3916	75	12	i.e.	i.e.	X
ejpam-3916	75	13	,	,	PUNCT
ejpam-3916	75	14	ng(x	ng(x	NUM
ejpam-3916	75	15	)	)	PUNCT
ejpam-3916	75	16	\	\	NOUN
ejpam-3916	75	17	ng(w	ng(w	NOUN
ejpam-3916	75	18	)	)	PUNCT
ejpam-3916	75	19	6=	6=	ADP
ejpam-3916	75	20	∅.	∅.	ADP
ejpam-3916	75	21	similarly	similarly	ADV
ejpam-3916	75	22	,	,	PUNCT
ejpam-3916	75	23	ng(y	ng(y	NOUN
ejpam-3916	75	24	)	)	PUNCT
ejpam-3916	75	25	\ng(v	\ng(v	NOUN
ejpam-3916	75	26	)	)	PUNCT
ejpam-3916	75	27	6=	6=	ADP
ejpam-3916	75	28	∅	∅	NOUN
ejpam-3916	75	29	for	for	ADP
ejpam-3916	75	30	each	each	DET
ejpam-3916	75	31	v	v	NOUN
ejpam-3916	75	32	∈	∈	PROPN
ejpam-3916	75	33	ng(y	ng(y	NOUN
ejpam-3916	75	34	,	,	PUNCT
ejpam-3916	75	35	2	2	NUM
ejpam-3916	75	36	)	)	PUNCT
ejpam-3916	75	37	,	,	PUNCT
ejpam-3916	75	38	showing	show	VERB
ejpam-3916	75	39	that	that	SCONJ
ejpam-3916	75	40	(	(	PUNCT
ejpam-3916	75	41	iii	iii	NOUN
ejpam-3916	75	42	)	)	PUNCT
ejpam-3916	75	43	holds	hold	VERB
ejpam-3916	75	44	.	.	PUNCT
ejpam-3916	76	1	conversely	conversely	ADV
ejpam-3916	76	2	,	,	PUNCT
ejpam-3916	76	3	suppose	suppose	VERB
ejpam-3916	76	4	that	that	SCONJ
ejpam-3916	76	5	there	there	PRON
ejpam-3916	76	6	exist	exist	VERB
ejpam-3916	76	7	distinct	distinct	ADJ
ejpam-3916	76	8	vertices	vertex	NOUN
ejpam-3916	76	9	x	x	PUNCT
ejpam-3916	76	10	and	and	CCONJ
ejpam-3916	76	11	y	y	PROPN
ejpam-3916	76	12	of	of	ADP
ejpam-3916	76	13	g	g	NOUN
ejpam-3916	76	14	satisfying	satisfy	VERB
ejpam-3916	76	15	conditions	condition	NOUN
ejpam-3916	76	16	(	(	PUNCT
ejpam-3916	76	17	i	i	NOUN
ejpam-3916	76	18	)	)	PUNCT
ejpam-3916	76	19	,	,	PUNCT
ejpam-3916	76	20	(	(	PUNCT
ejpam-3916	76	21	ii	ii	NOUN
ejpam-3916	76	22	)	)	PUNCT
ejpam-3916	76	23	,	,	PUNCT
ejpam-3916	76	24	and	and	CCONJ
ejpam-3916	76	25	(	(	PUNCT
ejpam-3916	76	26	iii	iii	NOUN
ejpam-3916	76	27	)	)	PUNCT
ejpam-3916	76	28	.	.	PUNCT
ejpam-3916	77	1	let	let	VERB
ejpam-3916	77	2	s	s	PRON
ejpam-3916	77	3	=	=	PUNCT
ejpam-3916	77	4	{	{	PUNCT
ejpam-3916	77	5	x	x	PROPN
ejpam-3916	77	6	,	,	PUNCT
ejpam-3916	77	7	y	y	NOUN
ejpam-3916	77	8	}	}	PUNCT
ejpam-3916	77	9	.	.	PUNCT
ejpam-3916	78	1	by	by	ADP
ejpam-3916	78	2	(	(	PUNCT
ejpam-3916	78	3	i	i	NOUN
ejpam-3916	78	4	)	)	PUNCT
ejpam-3916	78	5	,	,	PUNCT
ejpam-3916	78	6	s	s	VERB
ejpam-3916	78	7	is	be	AUX
ejpam-3916	78	8	a	a	DET
ejpam-3916	78	9	hop	hop	NOUN
ejpam-3916	78	10	dominating	dominating	NOUN
ejpam-3916	78	11	set	set	NOUN
ejpam-3916	78	12	of	of	ADP
ejpam-3916	78	13	g.	g.	PROPN
ejpam-3916	78	14	let	let	VERB
ejpam-3916	78	15	v	v	NUM
ejpam-3916	78	16	∈	∈	PROPN
ejpam-3916	78	17	v	v	NOUN
ejpam-3916	78	18	(	(	PUNCT
ejpam-3916	78	19	g)\s	g)\s	NOUN
ejpam-3916	78	20	.	.	PUNCT
ejpam-3916	79	1	assume	assume	VERB
ejpam-3916	79	2	,	,	PUNCT
ejpam-3916	79	3	without	without	ADP
ejpam-3916	79	4	loss	loss	NOUN
ejpam-3916	79	5	of	of	ADP
ejpam-3916	79	6	generality	generality	NOUN
ejpam-3916	79	7	,	,	PUNCT
ejpam-3916	79	8	that	that	PRON
ejpam-3916	79	9	v	v	ADP
ejpam-3916	79	10	∈	∈	PROPN
ejpam-3916	79	11	ng(x	ng(x	NUM
ejpam-3916	79	12	,	,	PUNCT
ejpam-3916	79	13	2	2	NUM
ejpam-3916	79	14	)	)	PUNCT
ejpam-3916	79	15	.	.	PUNCT
ejpam-3916	80	1	then	then	ADV
ejpam-3916	80	2	v	v	X
ejpam-3916	80	3	∈	∈	PROPN
ejpam-3916	80	4	ng(y	ng(y	NOUN
ejpam-3916	80	5	)	)	PUNCT
ejpam-3916	80	6	\	\	NOUN
ejpam-3916	80	7	{	{	PUNCT
ejpam-3916	80	8	x	x	NOUN
ejpam-3916	80	9	}	}	PUNCT
ejpam-3916	80	10	by	by	ADP
ejpam-3916	80	11	(	(	PUNCT
ejpam-3916	80	12	ii	ii	NOUN
ejpam-3916	80	13	)	)	PUNCT
ejpam-3916	80	14	.	.	PUNCT
ejpam-3916	81	1	suppose	suppose	VERB
ejpam-3916	81	2	xy	xy	PROPN
ejpam-3916	81	3	/∈	/∈	PUNCT
ejpam-3916	81	4	e(g	e(g	PROPN
ejpam-3916	81	5	)	)	PUNCT
ejpam-3916	81	6	.	.	PUNCT
ejpam-3916	82	1	then	then	ADV
ejpam-3916	82	2	xy	xy	PROPN
ejpam-3916	82	3	,	,	PUNCT
ejpam-3916	82	4	xv	xv	PROPN
ejpam-3916	82	5	∈	∈	PROPN
ejpam-3916	82	6	e(g	e(g	PROPN
ejpam-3916	82	7	)	)	PUNCT
ejpam-3916	82	8	.	.	PUNCT
ejpam-3916	83	1	thus	thus	ADV
ejpam-3916	83	2	,	,	PUNCT
ejpam-3916	83	3	dg(y	dg(y	ADJ
ejpam-3916	83	4	,	,	PUNCT
ejpam-3916	83	5	v	v	NOUN
ejpam-3916	83	6	)	)	PUNCT
ejpam-3916	83	7	=	=	SYM
ejpam-3916	83	8	2	2	X
ejpam-3916	83	9	.	.	PUNCT
ejpam-3916	84	1	next	next	ADV
ejpam-3916	84	2	,	,	PUNCT
ejpam-3916	84	3	suppose	suppose	VERB
ejpam-3916	84	4	that	that	SCONJ
ejpam-3916	84	5	xy	xy	PROPN
ejpam-3916	84	6	∈	∈	PROPN
ejpam-3916	84	7	e(g	e(g	PROPN
ejpam-3916	84	8	)	)	PUNCT
ejpam-3916	84	9	.	.	PUNCT
ejpam-3916	85	1	then	then	ADV
ejpam-3916	85	2	by	by	ADP
ejpam-3916	85	3	(	(	PUNCT
ejpam-3916	85	4	iii	iii	NOUN
ejpam-3916	85	5	)	)	PUNCT
ejpam-3916	85	6	,	,	PUNCT
ejpam-3916	85	7	there	there	PRON
ejpam-3916	85	8	exists	exist	VERB
ejpam-3916	85	9	z	z	PROPN
ejpam-3916	85	10	∈	∈	PROPN
ejpam-3916	85	11	ng(x	ng(x	NUM
ejpam-3916	85	12	)	)	PUNCT
ejpam-3916	85	13	\	\	NOUN
ejpam-3916	85	14	ng(v	ng(v	NOUN
ejpam-3916	85	15	)	)	PUNCT
ejpam-3916	85	16	.	.	PUNCT
ejpam-3916	86	1	hence	hence	ADV
ejpam-3916	86	2	,	,	PUNCT
ejpam-3916	86	3	z	z	PROPN
ejpam-3916	86	4	∈	∈	PROPN
ejpam-3916	86	5	ng(v	ng(v	PUNCT
ejpam-3916	86	6	)	)	PUNCT
ejpam-3916	86	7	∩	∩	NOUN
ejpam-3916	86	8	ng(y	ng(y	NOUN
ejpam-3916	86	9	)	)	PUNCT
ejpam-3916	86	10	,	,	PUNCT
ejpam-3916	86	11	i.e.	i.e.	X
ejpam-3916	86	12	,	,	PUNCT
ejpam-3916	86	13	dg(y	dg(y	ADJ
ejpam-3916	86	14	,	,	PUNCT
ejpam-3916	86	15	v	v	NOUN
ejpam-3916	86	16	)	)	PUNCT
ejpam-3916	86	17	=	=	SYM
ejpam-3916	86	18	2	2	X
ejpam-3916	86	19	.	.	X
ejpam-3916	86	20	therefore	therefore	ADV
ejpam-3916	86	21	,	,	PUNCT
ejpam-3916	86	22	s	s	VERB
ejpam-3916	86	23	is	be	AUX
ejpam-3916	86	24	a	a	DET
ejpam-3916	86	25	global	global	ADJ
ejpam-3916	86	26	hop	hop	NOUN
ejpam-3916	86	27	dominating	dominating	NOUN
ejpam-3916	86	28	set	set	NOUN
ejpam-3916	86	29	of	of	ADP
ejpam-3916	86	30	g.	g.	PROPN
ejpam-3916	86	31	accordingly	accordingly	ADV
ejpam-3916	86	32	,	,	PUNCT
ejpam-3916	86	33	γgh(g	γgh(g	PROPN
ejpam-3916	86	34	)	)	PUNCT
ejpam-3916	86	35	=	=	SYM
ejpam-3916	86	36	2	2	X
ejpam-3916	86	37	.	.	X
ejpam-3916	86	38	theorem	theorem	NOUN
ejpam-3916	86	39	2	2	NUM
ejpam-3916	86	40	.	.	PUNCT
ejpam-3916	87	1	let	let	VERB
ejpam-3916	87	2	g	g	PRON
ejpam-3916	87	3	be	be	AUX
ejpam-3916	87	4	a	a	DET
ejpam-3916	87	5	graph	graph	NOUN
ejpam-3916	87	6	of	of	ADP
ejpam-3916	87	7	order	order	NOUN
ejpam-3916	87	8	n	n	PRON
ejpam-3916	87	9	≥	≥	NOUN
ejpam-3916	87	10	2	2	NUM
ejpam-3916	87	11	.	.	PUNCT
ejpam-3916	88	1	then	then	ADV
ejpam-3916	88	2	γgh(g	γgh(g	NOUN
ejpam-3916	88	3	)	)	PUNCT
ejpam-3916	88	4	=	=	SYM
ejpam-3916	89	1	n	n	NOUN
ejpam-3916	89	2	if	if	SCONJ
ejpam-3916	89	3	and	and	CCONJ
ejpam-3916	89	4	only	only	ADV
ejpam-3916	89	5	if	if	SCONJ
ejpam-3916	89	6	one	one	NUM
ejpam-3916	89	7	of	of	ADP
ejpam-3916	89	8	the	the	DET
ejpam-3916	89	9	following	following	ADJ
ejpam-3916	89	10	statements	statement	NOUN
ejpam-3916	89	11	holds	hold	VERB
ejpam-3916	89	12	:	:	PUNCT
ejpam-3916	89	13	(	(	PUNCT
ejpam-3916	89	14	i	i	NOUN
ejpam-3916	89	15	)	)	PUNCT
ejpam-3916	89	16	every	every	DET
ejpam-3916	89	17	component	component	NOUN
ejpam-3916	89	18	of	of	ADP
ejpam-3916	89	19	g	g	PROPN
ejpam-3916	89	20	is	be	AUX
ejpam-3916	89	21	complete	complete	ADJ
ejpam-3916	89	22	.	.	PUNCT
ejpam-3916	90	1	(	(	PUNCT
ejpam-3916	90	2	ii	ii	NOUN
ejpam-3916	90	3	)	)	PUNCT
ejpam-3916	90	4	for	for	ADP
ejpam-3916	90	5	each	each	DET
ejpam-3916	90	6	v	v	NUM
ejpam-3916	90	7	∈	∈	PROPN
ejpam-3916	90	8	v	v	NOUN
ejpam-3916	90	9	(	(	PUNCT
ejpam-3916	90	10	g	g	NOUN
ejpam-3916	90	11	)	)	PUNCT
ejpam-3916	90	12	,	,	PUNCT
ejpam-3916	90	13	v	v	X
ejpam-3916	90	14	(	(	PUNCT
ejpam-3916	90	15	g	g	NOUN
ejpam-3916	90	16	)	)	PUNCT
ejpam-3916	90	17	\	\	NOUN
ejpam-3916	90	18	ng(v	ng(v	PUNCT
ejpam-3916	90	19	)	)	PUNCT
ejpam-3916	90	20	is	be	AUX
ejpam-3916	90	21	an	an	DET
ejpam-3916	90	22	independent	independent	ADJ
ejpam-3916	90	23	set	set	NOUN
ejpam-3916	90	24	and	and	CCONJ
ejpam-3916	90	25	ng(v	ng(v	NUM
ejpam-3916	90	26	)	)	PUNCT
ejpam-3916	90	27	=	=	SYM
ejpam-3916	90	28	ng(a	ng(a	NOUN
ejpam-3916	90	29	)	)	PUNCT
ejpam-3916	90	30	for	for	ADP
ejpam-3916	90	31	each	each	DET
ejpam-3916	90	32	a	a	DET
ejpam-3916	90	33	∈	∈	PROPN
ejpam-3916	90	34	v	v	NOUN
ejpam-3916	90	35	(	(	PUNCT
ejpam-3916	90	36	g	g	NOUN
ejpam-3916	90	37	)	)	PUNCT
ejpam-3916	90	38	\ng(v	\ng(v	NOUN
ejpam-3916	90	39	)	)	PUNCT
ejpam-3916	90	40	.	.	PUNCT
ejpam-3916	91	1	proof	proof	NOUN
ejpam-3916	91	2	.	.	PUNCT
ejpam-3916	92	1	suppose	suppose	VERB
ejpam-3916	92	2	γgh(g	γgh(g	NOUN
ejpam-3916	92	3	)	)	PUNCT
ejpam-3916	92	4	=	=	SYM
ejpam-3916	92	5	n.	n.	NOUN
ejpam-3916	92	6	suppose	suppose	VERB
ejpam-3916	92	7	first	first	ADV
ejpam-3916	92	8	that	that	SCONJ
ejpam-3916	92	9	g	g	PROPN
ejpam-3916	92	10	is	be	AUX
ejpam-3916	92	11	disconnected	disconnect	VERB
ejpam-3916	92	12	and	and	CCONJ
ejpam-3916	92	13	suppose	suppose	VERB
ejpam-3916	92	14	that	that	SCONJ
ejpam-3916	92	15	g	g	PROPN
ejpam-3916	92	16	has	have	VERB
ejpam-3916	92	17	a	a	DET
ejpam-3916	92	18	component	component	NOUN
ejpam-3916	92	19	c	c	NOUN
ejpam-3916	92	20	which	which	PRON
ejpam-3916	92	21	is	be	AUX
ejpam-3916	92	22	not	not	PART
ejpam-3916	92	23	complete	complete	ADJ
ejpam-3916	92	24	.	.	PUNCT
ejpam-3916	93	1	then	then	ADV
ejpam-3916	93	2	there	there	PRON
ejpam-3916	93	3	exist	exist	VERB
ejpam-3916	93	4	distinct	distinct	ADJ
ejpam-3916	93	5	vertices	vertex	NOUN
ejpam-3916	93	6	x	x	X
ejpam-3916	93	7	,	,	PUNCT
ejpam-3916	93	8	y	y	PROPN
ejpam-3916	93	9	∈	∈	PROPN
ejpam-3916	93	10	v	v	NOUN
ejpam-3916	93	11	(	(	PUNCT
ejpam-3916	93	12	c	c	NOUN
ejpam-3916	93	13	)	)	PUNCT
ejpam-3916	93	14	such	such	ADJ
ejpam-3916	93	15	that	that	DET
ejpam-3916	93	16	dg(x	dg(x	PROPN
ejpam-3916	93	17	,	,	PUNCT
ejpam-3916	93	18	y	y	NOUN
ejpam-3916	93	19	)	)	PUNCT
ejpam-3916	93	20	=	=	SYM
ejpam-3916	93	21	dc(x	dc(x	NOUN
ejpam-3916	93	22	,	,	PUNCT
ejpam-3916	93	23	y	y	NOUN
ejpam-3916	93	24	)	)	PUNCT
ejpam-3916	93	25	=	=	SYM
ejpam-3916	94	1	2	2	X
ejpam-3916	94	2	.	.	X
ejpam-3916	94	3	let	let	VERB
ejpam-3916	94	4	s	s	NOUN
ejpam-3916	94	5	=	=	X
ejpam-3916	94	6	v	v	ADJ
ejpam-3916	94	7	(	(	PUNCT
ejpam-3916	94	8	g	g	NOUN
ejpam-3916	94	9	)	)	PUNCT
ejpam-3916	94	10	\	\	NOUN
ejpam-3916	94	11	{	{	PUNCT
ejpam-3916	94	12	x	x	NOUN
ejpam-3916	94	13	}	}	PUNCT
ejpam-3916	94	14	.	.	PUNCT
ejpam-3916	95	1	then	then	ADV
ejpam-3916	95	2	s	s	VERB
ejpam-3916	95	3	is	be	AUX
ejpam-3916	95	4	a	a	DET
ejpam-3916	95	5	hop	hop	NOUN
ejpam-3916	95	6	dominating	dominating	NOUN
ejpam-3916	95	7	set	set	NOUN
ejpam-3916	95	8	of	of	ADP
ejpam-3916	95	9	g.	g.	PROPN
ejpam-3916	95	10	let	let	VERB
ejpam-3916	95	11	z	z	NOUN
ejpam-3916	95	12	∈	∈	PROPN
ejpam-3916	95	13	c	c	NOUN
ejpam-3916	95	14	such	such	ADJ
ejpam-3916	95	15	that	that	SCONJ
ejpam-3916	95	16	[	[	X
ejpam-3916	95	17	x	x	X
ejpam-3916	95	18	,	,	PUNCT
ejpam-3916	95	19	z	z	PROPN
ejpam-3916	95	20	,	,	PUNCT
ejpam-3916	95	21	y	y	PROPN
ejpam-3916	95	22	]	]	X
ejpam-3916	95	23	is	be	AUX
ejpam-3916	95	24	an	an	DET
ejpam-3916	95	25	x	x	NOUN
ejpam-3916	95	26	-	-	NOUN
ejpam-3916	95	27	y	y	ADJ
ejpam-3916	95	28	geodesic	geodesic	NOUN
ejpam-3916	95	29	in	in	ADP
ejpam-3916	95	30	g.	g.	PROPN
ejpam-3916	95	31	let	let	VERB
ejpam-3916	95	32	c	c	NOUN
ejpam-3916	95	33	′	′	VERB
ejpam-3916	95	34	be	be	AUX
ejpam-3916	95	35	a	a	DET
ejpam-3916	95	36	component	component	NOUN
ejpam-3916	95	37	of	of	ADP
ejpam-3916	95	38	g	g	NOUN
ejpam-3916	95	39	with	with	ADP
ejpam-3916	95	40	c	c	NOUN
ejpam-3916	95	41	′	′	NUM
ejpam-3916	95	42	6=	6=	NUM
ejpam-3916	95	43	c	c	NOUN
ejpam-3916	95	44	and	and	CCONJ
ejpam-3916	95	45	pick	pick	VERB
ejpam-3916	95	46	any	any	DET
ejpam-3916	95	47	w	w	PROPN
ejpam-3916	95	48	∈	∈	PROPN
ejpam-3916	95	49	c	c	NOUN
ejpam-3916	95	50	′.	′.	NOUN
ejpam-3916	95	51	then	then	ADV
ejpam-3916	95	52	[	[	X
ejpam-3916	95	53	x	x	X
ejpam-3916	95	54	,	,	PUNCT
ejpam-3916	95	55	w	w	PROPN
ejpam-3916	95	56	,	,	PUNCT
ejpam-3916	95	57	z	z	X
ejpam-3916	95	58	]	]	X
ejpam-3916	95	59	is	be	AUX
ejpam-3916	95	60	an	an	DET
ejpam-3916	95	61	x	x	ADJ
ejpam-3916	95	62	-	-	NOUN
ejpam-3916	95	63	z	z	ADJ
ejpam-3916	95	64	geodesic	geodesic	NOUN
ejpam-3916	95	65	in	in	ADP
ejpam-3916	95	66	g.	g.	PROPN
ejpam-3916	95	67	it	it	PRON
ejpam-3916	95	68	follows	follow	VERB
ejpam-3916	95	69	that	that	SCONJ
ejpam-3916	95	70	dg(x	dg(x	ADV
ejpam-3916	95	71	,	,	PUNCT
ejpam-3916	95	72	z	z	NOUN
ejpam-3916	95	73	)	)	PUNCT
ejpam-3916	95	74	=	=	SYM
ejpam-3916	95	75	2	2	X
ejpam-3916	95	76	.	.	PUNCT
ejpam-3916	96	1	thus	thus	ADV
ejpam-3916	96	2	,	,	PUNCT
ejpam-3916	96	3	s	s	VERB
ejpam-3916	96	4	is	be	AUX
ejpam-3916	96	5	a	a	DET
ejpam-3916	96	6	hop	hop	NOUN
ejpam-3916	96	7	dominating	dominating	NOUN
ejpam-3916	96	8	set	set	NOUN
ejpam-3916	96	9	of	of	ADP
ejpam-3916	96	10	g	g	NOUN
ejpam-3916	96	11	,	,	PUNCT
ejpam-3916	96	12	showing	show	VERB
ejpam-3916	96	13	that	that	SCONJ
ejpam-3916	96	14	s	s	VERB
ejpam-3916	96	15	is	be	AUX
ejpam-3916	96	16	a	a	DET
ejpam-3916	96	17	global	global	ADJ
ejpam-3916	96	18	hop	hop	NOUN
ejpam-3916	96	19	dominating	dominating	NOUN
ejpam-3916	96	20	set	set	NOUN
ejpam-3916	96	21	of	of	ADP
ejpam-3916	96	22	g.	g.	PROPN
ejpam-3916	96	23	therefore	therefore	ADV
ejpam-3916	96	24	,	,	PUNCT
ejpam-3916	96	25	γgh(g	γgh(g	PROPN
ejpam-3916	96	26	)	)	PUNCT
ejpam-3916	96	27	≤	≤	NUM
ejpam-3916	96	28	|s|	|s|	PROPN
ejpam-3916	96	29	=	=	SYM
ejpam-3916	96	30	n−1	n−1	PROPN
ejpam-3916	96	31	,	,	PUNCT
ejpam-3916	96	32	a	a	DET
ejpam-3916	96	33	contradiction	contradiction	NOUN
ejpam-3916	96	34	.	.	PUNCT
ejpam-3916	97	1	accordingly	accordingly	ADV
ejpam-3916	97	2	,	,	PUNCT
ejpam-3916	97	3	every	every	DET
ejpam-3916	97	4	component	component	NOUN
ejpam-3916	97	5	of	of	ADP
ejpam-3916	97	6	g	g	PROPN
ejpam-3916	97	7	is	be	AUX
ejpam-3916	97	8	complete	complete	ADJ
ejpam-3916	97	9	.	.	PUNCT
ejpam-3916	98	1	next	next	ADV
ejpam-3916	98	2	,	,	PUNCT
ejpam-3916	98	3	suppose	suppose	VERB
ejpam-3916	98	4	that	that	SCONJ
ejpam-3916	98	5	g	g	PROPN
ejpam-3916	98	6	is	be	AUX
ejpam-3916	98	7	connected	connect	VERB
ejpam-3916	98	8	.	.	PUNCT
ejpam-3916	99	1	suppose	suppose	VERB
ejpam-3916	99	2	further	far	ADV
ejpam-3916	99	3	that	that	SCONJ
ejpam-3916	99	4	g	g	PROPN
ejpam-3916	99	5	is	be	AUX
ejpam-3916	99	6	connected	connect	VERB
ejpam-3916	99	7	.	.	PUNCT
ejpam-3916	100	1	then	then	ADV
ejpam-3916	100	2	,	,	PUNCT
ejpam-3916	100	3	clearly	clearly	ADV
ejpam-3916	100	4	,	,	PUNCT
ejpam-3916	100	5	g	g	PROPN
ejpam-3916	100	6	6=	6=	PROPN
ejpam-3916	100	7	kn	kn	PROPN
ejpam-3916	100	8	.	.	PUNCT
ejpam-3916	101	1	let	let	VERB
ejpam-3916	101	2	u	u	NOUN
ejpam-3916	101	3	,	,	PUNCT
ejpam-3916	101	4	v	v	PROPN
ejpam-3916	101	5	∈	∈	PROPN
ejpam-3916	101	6	v	v	NOUN
ejpam-3916	101	7	(	(	PUNCT
ejpam-3916	101	8	g	g	NOUN
ejpam-3916	101	9	)	)	PUNCT
ejpam-3916	101	10	such	such	ADJ
ejpam-3916	101	11	that	that	SCONJ
ejpam-3916	101	12	dg(u	dg(u	ADJ
ejpam-3916	101	13	,	,	PUNCT
ejpam-3916	101	14	v	v	NOUN
ejpam-3916	101	15	)	)	PUNCT
ejpam-3916	101	16	=	=	SYM
ejpam-3916	101	17	2	2	NUM
ejpam-3916	101	18	and	and	CCONJ
ejpam-3916	101	19	let	let	VERB
ejpam-3916	101	20	[	[	X
ejpam-3916	101	21	u	u	NOUN
ejpam-3916	101	22	,	,	PUNCT
ejpam-3916	101	23	p	p	X
ejpam-3916	101	24	,	,	PUNCT
ejpam-3916	101	25	v	v	NOUN
ejpam-3916	101	26	]	]	PUNCT
ejpam-3916	101	27	be	be	AUX
ejpam-3916	101	28	a	a	DET
ejpam-3916	101	29	u	u	NOUN
ejpam-3916	101	30	-	-	NOUN
ejpam-3916	101	31	v	v	ADJ
ejpam-3916	101	32	g.	g.	NOUN
ejpam-3916	101	33	salasalan	salasalan	NOUN
ejpam-3916	101	34	,	,	PUNCT
ejpam-3916	101	35	s.	s.	PROPN
ejpam-3916	101	36	canoy	canoy	PROPN
ejpam-3916	101	37	,	,	PUNCT
ejpam-3916	101	38	jr	jr	PROPN
ejpam-3916	101	39	.	.	PROPN
ejpam-3916	101	40	/	/	SYM
ejpam-3916	101	41	eur	eur	PROPN
ejpam-3916	101	42	.	.	PUNCT
ejpam-3916	102	1	j.	j.	PROPN
ejpam-3916	102	2	pure	pure	PROPN
ejpam-3916	102	3	appl	appl	PROPN
ejpam-3916	102	4	.	.	PROPN
ejpam-3916	102	5	math	math	PROPN
ejpam-3916	102	6	,	,	PUNCT
ejpam-3916	102	7	14	14	NUM
ejpam-3916	102	8	(	(	PUNCT
ejpam-3916	102	9	1	1	NUM
ejpam-3916	102	10	)	)	PUNCT
ejpam-3916	102	11	(	(	PUNCT
ejpam-3916	102	12	2021	2021	NUM
ejpam-3916	102	13	)	)	PUNCT
ejpam-3916	102	14	,	,	PUNCT
ejpam-3916	102	15	112	112	NUM
ejpam-3916	102	16	-	-	SYM
ejpam-3916	102	17	125	125	NUM
ejpam-3916	102	18	115	115	NUM
ejpam-3916	102	19	geodesic	geodesic	NOUN
ejpam-3916	102	20	in	in	ADP
ejpam-3916	102	21	g.	g.	PROPN
ejpam-3916	103	1	then	then	ADV
ejpam-3916	103	2	s∗	s∗	PROPN
ejpam-3916	103	3	=	=	SYM
ejpam-3916	103	4	v	v	PROPN
ejpam-3916	103	5	(	(	PUNCT
ejpam-3916	103	6	g	g	NOUN
ejpam-3916	103	7	)	)	PUNCT
ejpam-3916	103	8	\	\	NOUN
ejpam-3916	104	1	{	{	PUNCT
ejpam-3916	104	2	u	u	NOUN
ejpam-3916	104	3	}	}	PUNCT
ejpam-3916	104	4	is	be	AUX
ejpam-3916	104	5	a	a	DET
ejpam-3916	104	6	hop	hop	NOUN
ejpam-3916	104	7	dominating	dominating	NOUN
ejpam-3916	104	8	set	set	NOUN
ejpam-3916	104	9	of	of	ADP
ejpam-3916	104	10	g.	g.	PROPN
ejpam-3916	104	11	since	since	SCONJ
ejpam-3916	104	12	up	up	ADV
ejpam-3916	104	13	/∈	/∈	PUNCT
ejpam-3916	105	1	e(g	e(g	PROPN
ejpam-3916	105	2	)	)	PUNCT
ejpam-3916	105	3	,	,	PUNCT
ejpam-3916	105	4	it	it	PRON
ejpam-3916	105	5	follows	follow	VERB
ejpam-3916	105	6	that	that	SCONJ
ejpam-3916	105	7	dg(u	dg(u	ADJ
ejpam-3916	105	8	,	,	PUNCT
ejpam-3916	105	9	p	p	NOUN
ejpam-3916	105	10	)	)	PUNCT
ejpam-3916	105	11	≥	≥	NOUN
ejpam-3916	105	12	2	2	NUM
ejpam-3916	105	13	.	.	PUNCT
ejpam-3916	106	1	it	it	PRON
ejpam-3916	106	2	follows	follow	VERB
ejpam-3916	106	3	that	that	SCONJ
ejpam-3916	106	4	there	there	PRON
ejpam-3916	106	5	exists	exist	VERB
ejpam-3916	106	6	q	q	PROPN
ejpam-3916	106	7	∈	∈	PROPN
ejpam-3916	106	8	s	s	VERB
ejpam-3916	106	9	such	such	ADJ
ejpam-3916	107	1	that	that	PRON
ejpam-3916	107	2	dg(u	dg(u	ADJ
ejpam-3916	107	3	,	,	PUNCT
ejpam-3916	107	4	q	q	X
ejpam-3916	107	5	)	)	PUNCT
ejpam-3916	107	6	=	=	SYM
ejpam-3916	107	7	2	2	X
ejpam-3916	107	8	.	.	PUNCT
ejpam-3916	107	9	this	this	PRON
ejpam-3916	107	10	shows	show	VERB
ejpam-3916	107	11	that	that	SCONJ
ejpam-3916	107	12	s∗	s∗	PROPN
ejpam-3916	107	13	is	be	AUX
ejpam-3916	107	14	hop	hop	NOUN
ejpam-3916	107	15	dominating	dominate	VERB
ejpam-3916	107	16	set	set	NOUN
ejpam-3916	107	17	of	of	ADP
ejpam-3916	107	18	g.	g.	PROPN
ejpam-3916	107	19	thus	thus	ADV
ejpam-3916	107	20	,	,	PUNCT
ejpam-3916	107	21	s∗	s∗	PROPN
ejpam-3916	107	22	is	be	AUX
ejpam-3916	107	23	a	a	DET
ejpam-3916	107	24	global	global	ADJ
ejpam-3916	107	25	hop	hop	NOUN
ejpam-3916	107	26	dominating	dominating	NOUN
ejpam-3916	107	27	set	set	NOUN
ejpam-3916	107	28	of	of	ADP
ejpam-3916	107	29	g	g	NOUN
ejpam-3916	107	30	and	and	CCONJ
ejpam-3916	107	31	γgh(g	γgh(g	NOUN
ejpam-3916	107	32	)	)	PUNCT
ejpam-3916	107	33	≤	≤	NOUN
ejpam-3916	107	34	|s∗|	|s∗|	NUM
ejpam-3916	108	1	=	=	SYM
ejpam-3916	108	2	n	n	PRON
ejpam-3916	108	3	−	−	PROPN
ejpam-3916	108	4	1	1	NUM
ejpam-3916	108	5	,	,	PUNCT
ejpam-3916	108	6	a	a	DET
ejpam-3916	108	7	contradiction	contradiction	NOUN
ejpam-3916	108	8	.	.	PUNCT
ejpam-3916	109	1	therefore	therefore	ADV
ejpam-3916	109	2	g	g	PROPN
ejpam-3916	109	3	is	be	AUX
ejpam-3916	109	4	disconnected	disconnect	VERB
ejpam-3916	109	5	.	.	PUNCT
ejpam-3916	110	1	since	since	SCONJ
ejpam-3916	110	2	γgh(g	γgh(g	NOUN
ejpam-3916	110	3	)	)	PUNCT
ejpam-3916	110	4	=	=	SYM
ejpam-3916	110	5	γgh(g	γgh(g	PROPN
ejpam-3916	110	6	)	)	PUNCT
ejpam-3916	110	7	=	=	SYM
ejpam-3916	110	8	n	n	CCONJ
ejpam-3916	110	9	,	,	PUNCT
ejpam-3916	110	10	this	this	PRON
ejpam-3916	110	11	would	would	AUX
ejpam-3916	110	12	imply	imply	VERB
ejpam-3916	110	13	that	that	SCONJ
ejpam-3916	110	14	every	every	DET
ejpam-3916	110	15	component	component	NOUN
ejpam-3916	110	16	of	of	ADP
ejpam-3916	110	17	g	g	PROPN
ejpam-3916	110	18	is	be	AUX
ejpam-3916	110	19	complete	complete	ADJ
ejpam-3916	110	20	(	(	PUNCT
ejpam-3916	110	21	as	as	ADP
ejpam-3916	110	22	in	in	ADP
ejpam-3916	110	23	the	the	DET
ejpam-3916	110	24	first	first	ADJ
ejpam-3916	110	25	case	case	NOUN
ejpam-3916	110	26	applied	apply	VERB
ejpam-3916	110	27	to	to	ADP
ejpam-3916	110	28	g	g	NOUN
ejpam-3916	110	29	)	)	PUNCT
ejpam-3916	110	30	.	.	PUNCT
ejpam-3916	111	1	let	let	VERB
ejpam-3916	111	2	v	v	NUM
ejpam-3916	111	3	∈	∈	PROPN
ejpam-3916	111	4	v	v	NOUN
ejpam-3916	111	5	(	(	PUNCT
ejpam-3916	111	6	g	g	NOUN
ejpam-3916	111	7	)	)	PUNCT
ejpam-3916	111	8	=	=	NOUN
ejpam-3916	111	9	v	v	X
ejpam-3916	111	10	(	(	PUNCT
ejpam-3916	111	11	g	g	NOUN
ejpam-3916	111	12	)	)	PUNCT
ejpam-3916	111	13	and	and	CCONJ
ejpam-3916	111	14	suppose	suppose	VERB
ejpam-3916	111	15	there	there	PRON
ejpam-3916	111	16	exist	exist	VERB
ejpam-3916	111	17	distinct	distinct	ADJ
ejpam-3916	111	18	vertices	vertex	NOUN
ejpam-3916	111	19	a	a	PRON
ejpam-3916	111	20	,	,	PUNCT
ejpam-3916	111	21	b	b	PROPN
ejpam-3916	111	22	∈	∈	PROPN
ejpam-3916	111	23	v	v	NOUN
ejpam-3916	111	24	(	(	PUNCT
ejpam-3916	111	25	g	g	NOUN
ejpam-3916	111	26	)	)	PUNCT
ejpam-3916	111	27	\ng(v	\ng(v	NOUN
ejpam-3916	111	28	)	)	PUNCT
ejpam-3916	111	29	such	such	ADJ
ejpam-3916	111	30	that	that	SCONJ
ejpam-3916	111	31	ab	ab	PROPN
ejpam-3916	111	32	∈	∈	PROPN
ejpam-3916	111	33	e(g	e(g	PROPN
ejpam-3916	111	34	)	)	PUNCT
ejpam-3916	111	35	.	.	PUNCT
ejpam-3916	112	1	then	then	ADV
ejpam-3916	112	2	[	[	X
ejpam-3916	112	3	a	a	X
ejpam-3916	112	4	,	,	PUNCT
ejpam-3916	112	5	v	v	NOUN
ejpam-3916	112	6	,	,	PUNCT
ejpam-3916	112	7	b	b	AUX
ejpam-3916	112	8	]	]	X
ejpam-3916	112	9	is	be	AUX
ejpam-3916	112	10	an	an	DET
ejpam-3916	112	11	a	a	PRON
ejpam-3916	112	12	-	-	PUNCT
ejpam-3916	112	13	b	b	NOUN
ejpam-3916	112	14	geodesic	geodesic	NOUN
ejpam-3916	112	15	in	in	ADP
ejpam-3916	112	16	g	g	NOUN
ejpam-3916	112	17	,	,	PUNCT
ejpam-3916	112	18	implying	imply	VERB
ejpam-3916	112	19	that	that	PRON
ejpam-3916	112	20	sa	sa	PROPN
ejpam-3916	112	21	=	=	SYM
ejpam-3916	112	22	v	v	PROPN
ejpam-3916	112	23	(	(	PUNCT
ejpam-3916	112	24	g)\{a	g)\{a	PROPN
ejpam-3916	112	25	}	}	PUNCT
ejpam-3916	112	26	is	be	AUX
ejpam-3916	112	27	a	a	DET
ejpam-3916	112	28	hop	hop	NOUN
ejpam-3916	112	29	dominating	dominating	NOUN
ejpam-3916	112	30	set	set	NOUN
ejpam-3916	112	31	of	of	ADP
ejpam-3916	112	32	g.	g.	PROPN
ejpam-3916	112	33	now	now	ADV
ejpam-3916	112	34	,	,	PUNCT
ejpam-3916	112	35	since	since	SCONJ
ejpam-3916	112	36	a	a	DET
ejpam-3916	112	37	∈	∈	PROPN
ejpam-3916	112	38	v	v	NOUN
ejpam-3916	112	39	(	(	PUNCT
ejpam-3916	112	40	g)\ng(v	g)\ng(v	PROPN
ejpam-3916	112	41	)	)	PUNCT
ejpam-3916	112	42	,	,	PUNCT
ejpam-3916	112	43	it	it	PRON
ejpam-3916	112	44	follows	follow	VERB
ejpam-3916	112	45	that	that	SCONJ
ejpam-3916	112	46	dg(a	dg(a	X
ejpam-3916	112	47	,	,	PUNCT
ejpam-3916	112	48	v	v	NOUN
ejpam-3916	112	49	)	)	PUNCT
ejpam-3916	112	50	≥	≥	NOUN
ejpam-3916	112	51	2	2	NUM
ejpam-3916	112	52	.	.	PUNCT
ejpam-3916	113	1	this	this	PRON
ejpam-3916	113	2	implies	imply	VERB
ejpam-3916	113	3	that	that	SCONJ
ejpam-3916	113	4	there	there	PRON
ejpam-3916	113	5	exists	exist	VERB
ejpam-3916	113	6	w	w	PROPN
ejpam-3916	113	7	∈	∈	PROPN
ejpam-3916	113	8	sa	sa	NOUN
ejpam-3916	113	9	such	such	ADJ
ejpam-3916	113	10	that	that	PRON
ejpam-3916	113	11	dg(a	dg(a	PROPN
ejpam-3916	113	12	,	,	PUNCT
ejpam-3916	113	13	w	w	NOUN
ejpam-3916	113	14	)	)	PUNCT
ejpam-3916	113	15	=	=	SYM
ejpam-3916	113	16	2	2	NUM
ejpam-3916	113	17	,	,	PUNCT
ejpam-3916	113	18	showing	show	VERB
ejpam-3916	113	19	that	that	PRON
ejpam-3916	113	20	sa	sa	PROPN
ejpam-3916	113	21	is	be	AUX
ejpam-3916	113	22	also	also	ADV
ejpam-3916	113	23	a	a	DET
ejpam-3916	113	24	hop	hop	NOUN
ejpam-3916	113	25	dominating	dominating	NOUN
ejpam-3916	113	26	set	set	NOUN
ejpam-3916	113	27	of	of	ADP
ejpam-3916	113	28	g.	g.	PROPN
ejpam-3916	113	29	hence	hence	ADV
ejpam-3916	113	30	,	,	PUNCT
ejpam-3916	113	31	γgh(g	γgh(g	PROPN
ejpam-3916	113	32	)	)	PUNCT
ejpam-3916	113	33	≤	≤	NOUN
ejpam-3916	114	1	|sa|	|sa|	NUM
ejpam-3916	115	1	=	=	SYM
ejpam-3916	115	2	n−	n−	NOUN
ejpam-3916	115	3	1	1	NUM
ejpam-3916	115	4	,	,	PUNCT
ejpam-3916	115	5	a	a	DET
ejpam-3916	115	6	contradiction	contradiction	NOUN
ejpam-3916	115	7	.	.	PUNCT
ejpam-3916	116	1	therefore	therefore	ADV
ejpam-3916	116	2	,	,	PUNCT
ejpam-3916	116	3	v	v	X
ejpam-3916	116	4	(	(	PUNCT
ejpam-3916	116	5	g	g	NOUN
ejpam-3916	116	6	)	)	PUNCT
ejpam-3916	116	7	\	\	NOUN
ejpam-3916	116	8	ng(v	ng(v	PUNCT
ejpam-3916	116	9	)	)	PUNCT
ejpam-3916	116	10	is	be	AUX
ejpam-3916	116	11	an	an	DET
ejpam-3916	116	12	independent	independent	ADJ
ejpam-3916	116	13	set	set	NOUN
ejpam-3916	116	14	.	.	PUNCT
ejpam-3916	117	1	let	let	VERB
ejpam-3916	117	2	a	a	DET
ejpam-3916	117	3	∈	∈	PROPN
ejpam-3916	117	4	v	v	NOUN
ejpam-3916	117	5	(	(	PUNCT
ejpam-3916	117	6	g	g	NOUN
ejpam-3916	117	7	)	)	PUNCT
ejpam-3916	117	8	\	\	NOUN
ejpam-3916	117	9	ng(v	ng(v	PUNCT
ejpam-3916	117	10	)	)	PUNCT
ejpam-3916	117	11	.	.	PUNCT
ejpam-3916	118	1	let	let	VERB
ejpam-3916	118	2	cv	cv	PROPN
ejpam-3916	118	3	be	be	AUX
ejpam-3916	118	4	the	the	DET
ejpam-3916	118	5	component	component	NOUN
ejpam-3916	118	6	of	of	ADP
ejpam-3916	118	7	g	g	NOUN
ejpam-3916	118	8	with	with	ADP
ejpam-3916	118	9	v	v	PROPN
ejpam-3916	118	10	∈	∈	PROPN
ejpam-3916	118	11	cv	cv	PROPN
ejpam-3916	118	12	.	.	PROPN
ejpam-3916	119	1	since	since	SCONJ
ejpam-3916	119	2	a	a	DET
ejpam-3916	119	3	∈	∈	NOUN
ejpam-3916	119	4	ng(v	ng(v	PUNCT
ejpam-3916	119	5	)	)	PUNCT
ejpam-3916	119	6	and	and	CCONJ
ejpam-3916	119	7	cv	cv	PROPN
ejpam-3916	119	8	is	be	AUX
ejpam-3916	119	9	complete	complete	ADJ
ejpam-3916	119	10	,	,	PUNCT
ejpam-3916	119	11	ng(a	ng(a	PRON
ejpam-3916	119	12	)	)	PUNCT
ejpam-3916	119	13	=	=	PUNCT
ejpam-3916	119	14	ng(v	ng(v	X
ejpam-3916	119	15	)	)	PUNCT
ejpam-3916	119	16	,	,	PUNCT
ejpam-3916	119	17	that	that	ADV
ejpam-3916	119	18	is	is	ADV
ejpam-3916	119	19	,	,	PUNCT
ejpam-3916	119	20	az	az	PROPN
ejpam-3916	119	21	∈	∈	PROPN
ejpam-3916	119	22	e(g	e(g	PROPN
ejpam-3916	119	23	)	)	PUNCT
ejpam-3916	119	24	for	for	ADP
ejpam-3916	119	25	every	every	DET
ejpam-3916	119	26	z	z	PROPN
ejpam-3916	119	27	∈	∈	PROPN
ejpam-3916	119	28	ng(v	ng(v	NOUN
ejpam-3916	119	29	)	)	PUNCT
ejpam-3916	119	30	.	.	PUNCT
ejpam-3916	120	1	this	this	PRON
ejpam-3916	120	2	shows	show	VERB
ejpam-3916	120	3	that	that	SCONJ
ejpam-3916	120	4	(	(	PUNCT
ejpam-3916	120	5	ii	ii	NOUN
ejpam-3916	120	6	)	)	PUNCT
ejpam-3916	120	7	holds	hold	VERB
ejpam-3916	120	8	.	.	PUNCT
ejpam-3916	121	1	for	for	ADP
ejpam-3916	121	2	the	the	DET
ejpam-3916	121	3	converse	converse	NOUN
ejpam-3916	121	4	,	,	PUNCT
ejpam-3916	121	5	suppose	suppose	VERB
ejpam-3916	121	6	first	first	ADV
ejpam-3916	121	7	that	that	SCONJ
ejpam-3916	121	8	(	(	PUNCT
ejpam-3916	121	9	i	i	NOUN
ejpam-3916	121	10	)	)	PUNCT
ejpam-3916	121	11	holds	hold	VERB
ejpam-3916	121	12	.	.	PUNCT
ejpam-3916	122	1	then	then	ADV
ejpam-3916	122	2	,	,	PUNCT
ejpam-3916	122	3	clearly	clearly	ADV
ejpam-3916	122	4	,	,	PUNCT
ejpam-3916	122	5	s	s	NOUN
ejpam-3916	122	6	=	=	SYM
ejpam-3916	122	7	v	v	X
ejpam-3916	122	8	(	(	PUNCT
ejpam-3916	122	9	g	g	NOUN
ejpam-3916	122	10	)	)	PUNCT
ejpam-3916	122	11	is	be	AUX
ejpam-3916	122	12	the	the	DET
ejpam-3916	122	13	only	only	ADJ
ejpam-3916	122	14	hop	hop	NOUN
ejpam-3916	122	15	dominating	dominating	NOUN
ejpam-3916	122	16	set	set	NOUN
ejpam-3916	122	17	of	of	ADP
ejpam-3916	122	18	g.	g.	PROPN
ejpam-3916	122	19	it	it	PRON
ejpam-3916	122	20	follows	follow	VERB
ejpam-3916	122	21	that	that	SCONJ
ejpam-3916	122	22	s	s	VERB
ejpam-3916	122	23	is	be	AUX
ejpam-3916	122	24	the	the	DET
ejpam-3916	122	25	only	only	ADJ
ejpam-3916	122	26	global	global	ADJ
ejpam-3916	122	27	hop	hop	NOUN
ejpam-3916	122	28	dominating	dominating	NOUN
ejpam-3916	122	29	set	set	NOUN
ejpam-3916	122	30	of	of	ADP
ejpam-3916	122	31	g.	g.	PROPN
ejpam-3916	122	32	thus	thus	ADV
ejpam-3916	122	33	,	,	PUNCT
ejpam-3916	122	34	γgh(g	γgh(g	NOUN
ejpam-3916	122	35	)	)	PUNCT
ejpam-3916	123	1	=	=	VERB
ejpam-3916	123	2	n.	n.	PROPN
ejpam-3916	123	3	next	next	ADV
ejpam-3916	123	4	,	,	PUNCT
ejpam-3916	123	5	suppose	suppose	VERB
ejpam-3916	123	6	that	that	SCONJ
ejpam-3916	123	7	(	(	PUNCT
ejpam-3916	123	8	ii	ii	NOUN
ejpam-3916	123	9	)	)	PUNCT
ejpam-3916	123	10	holds	hold	VERB
ejpam-3916	123	11	.	.	PUNCT
ejpam-3916	124	1	then	then	ADV
ejpam-3916	124	2	every	every	DET
ejpam-3916	124	3	component	component	NOUN
ejpam-3916	124	4	of	of	ADP
ejpam-3916	124	5	g	g	PROPN
ejpam-3916	124	6	is	be	AUX
ejpam-3916	124	7	complete	complete	ADJ
ejpam-3916	124	8	.	.	PUNCT
ejpam-3916	125	1	since	since	SCONJ
ejpam-3916	125	2	v	v	NOUN
ejpam-3916	125	3	(	(	PUNCT
ejpam-3916	125	4	g	g	NOUN
ejpam-3916	125	5	)	)	PUNCT
ejpam-3916	125	6	=	=	NOUN
ejpam-3916	125	7	v	v	X
ejpam-3916	125	8	(	(	PUNCT
ejpam-3916	125	9	g	g	NOUN
ejpam-3916	125	10	)	)	PUNCT
ejpam-3916	125	11	is	be	AUX
ejpam-3916	125	12	the	the	DET
ejpam-3916	125	13	only	only	ADJ
ejpam-3916	125	14	hop	hop	NOUN
ejpam-3916	125	15	dominating	dominating	NOUN
ejpam-3916	125	16	set	set	NOUN
ejpam-3916	125	17	of	of	ADP
ejpam-3916	125	18	g	g	PROPN
ejpam-3916	125	19	,	,	PUNCT
ejpam-3916	125	20	it	it	PRON
ejpam-3916	125	21	follows	follow	VERB
ejpam-3916	125	22	that	that	SCONJ
ejpam-3916	125	23	v	v	X
ejpam-3916	125	24	(	(	PUNCT
ejpam-3916	125	25	g	g	NOUN
ejpam-3916	125	26	)	)	PUNCT
ejpam-3916	125	27	is	be	AUX
ejpam-3916	125	28	the	the	DET
ejpam-3916	125	29	only	only	ADJ
ejpam-3916	125	30	global	global	ADJ
ejpam-3916	125	31	hop	hop	NOUN
ejpam-3916	125	32	dominating	dominating	NOUN
ejpam-3916	125	33	set	set	NOUN
ejpam-3916	125	34	of	of	ADP
ejpam-3916	125	35	g.	g.	PROPN
ejpam-3916	125	36	therefore	therefore	ADV
ejpam-3916	125	37	,	,	PUNCT
ejpam-3916	125	38	γgh(g	γgh(g	NOUN
ejpam-3916	125	39	)	)	PUNCT
ejpam-3916	125	40	=	=	VERB
ejpam-3916	126	1	n.	n.	NOUN
ejpam-3916	126	2	the	the	DET
ejpam-3916	126	3	next	next	ADJ
ejpam-3916	126	4	result	result	NOUN
ejpam-3916	126	5	is	be	AUX
ejpam-3916	126	6	a	a	DET
ejpam-3916	126	7	consequence	consequence	NOUN
ejpam-3916	126	8	of	of	ADP
ejpam-3916	126	9	theorem	theorem	ADJ
ejpam-3916	126	10	2	2	NUM
ejpam-3916	126	11	.	.	PUNCT
ejpam-3916	126	12	corollary	corollary	ADJ
ejpam-3916	126	13	1	1	NUM
ejpam-3916	126	14	.	.	NUM
ejpam-3916	126	15	γgh(kn	γgh(kn	NOUN
ejpam-3916	126	16	)	)	PUNCT
ejpam-3916	126	17	=	=	PUNCT
ejpam-3916	126	18	γgh(k1,n−1	γgh(k1,n−1	X
ejpam-3916	126	19	)	)	PUNCT
ejpam-3916	126	20	=	=	SYM
ejpam-3916	127	1	n	n	PROPN
ejpam-3916	127	2	for	for	ADP
ejpam-3916	127	3	all	all	DET
ejpam-3916	127	4	integer	integer	NOUN
ejpam-3916	127	5	n	n	PRON
ejpam-3916	127	6	≥	≥	NOUN
ejpam-3916	127	7	2	2	NUM
ejpam-3916	127	8	.	.	PUNCT
ejpam-3916	128	1	a	a	DET
ejpam-3916	128	2	set	set	NOUN
ejpam-3916	128	3	s	s	NOUN
ejpam-3916	128	4	⊆	⊆	NUM
ejpam-3916	128	5	v	v	NOUN
ejpam-3916	128	6	(	(	PUNCT
ejpam-3916	128	7	g	g	NOUN
ejpam-3916	128	8	)	)	PUNCT
ejpam-3916	128	9	is	be	AUX
ejpam-3916	128	10	a	a	DET
ejpam-3916	128	11	pairwise	pairwise	NOUN
ejpam-3916	128	12	non	non	ADJ
ejpam-3916	128	13	-	-	ADJ
ejpam-3916	128	14	dominating	dominating	ADJ
ejpam-3916	128	15	set	set	NOUN
ejpam-3916	128	16	of	of	ADP
ejpam-3916	128	17	g	g	PROPN
ejpam-3916	128	18	if	if	SCONJ
ejpam-3916	128	19	for	for	ADP
ejpam-3916	128	20	each	each	PRON
ejpam-3916	128	21	v	v	NUM
ejpam-3916	128	22	∈	∈	PROPN
ejpam-3916	128	23	v	v	NOUN
ejpam-3916	128	24	(	(	PUNCT
ejpam-3916	128	25	g	g	NOUN
ejpam-3916	128	26	)	)	PUNCT
ejpam-3916	128	27	\	\	PROPN
ejpam-3916	129	1	s	s	X
ejpam-3916	129	2	,	,	PUNCT
ejpam-3916	129	3	there	there	PRON
ejpam-3916	129	4	exists	exist	VERB
ejpam-3916	129	5	vertex	vertex	NOUN
ejpam-3916	129	6	w	w	PROPN
ejpam-3916	129	7	∈	∈	PROPN
ejpam-3916	129	8	s	s	PART
ejpam-3916	129	9	∩ng(v	∩ng(v	PROPN
ejpam-3916	129	10	)	)	PUNCT
ejpam-3916	129	11	such	such	ADJ
ejpam-3916	129	12	that	that	SCONJ
ejpam-3916	129	13	ng({w	ng({w	NOUN
ejpam-3916	129	14	,	,	PUNCT
ejpam-3916	129	15	v	v	NOUN
ejpam-3916	129	16	}	}	PUNCT
ejpam-3916	129	17	)	)	PUNCT
ejpam-3916	129	18	6=	6=	X
ejpam-3916	129	19	v	v	X
ejpam-3916	129	20	(	(	PUNCT
ejpam-3916	129	21	g	g	NOUN
ejpam-3916	129	22	)	)	PUNCT
ejpam-3916	129	23	.	.	PUNCT
ejpam-3916	130	1	a	a	DET
ejpam-3916	130	2	set	set	NOUN
ejpam-3916	130	3	s	s	NOUN
ejpam-3916	130	4	⊆	⊆	NUM
ejpam-3916	130	5	v	v	NOUN
ejpam-3916	130	6	(	(	PUNCT
ejpam-3916	130	7	g	g	NOUN
ejpam-3916	130	8	)	)	PUNCT
ejpam-3916	130	9	is	be	AUX
ejpam-3916	130	10	a	a	DET
ejpam-3916	130	11	pairwise	pairwise	NOUN
ejpam-3916	130	12	and	and	CCONJ
ejpam-3916	130	13	pointwise	pointwise	VERB
ejpam-3916	130	14	non	non	ADJ
ejpam-3916	130	15	-	-	ADJ
ejpam-3916	130	16	dominating	dominating	ADJ
ejpam-3916	130	17	(	(	PUNCT
ejpam-3916	130	18	ppnd	ppnd	NOUN
ejpam-3916	130	19	)	)	PUNCT
ejpam-3916	130	20	set	set	NOUN
ejpam-3916	130	21	of	of	ADP
ejpam-3916	130	22	g	g	PROPN
ejpam-3916	130	23	if	if	SCONJ
ejpam-3916	130	24	it	it	PRON
ejpam-3916	130	25	is	be	AUX
ejpam-3916	130	26	both	both	CCONJ
ejpam-3916	130	27	a	a	DET
ejpam-3916	130	28	pairwise	pairwise	NOUN
ejpam-3916	130	29	non	non	ADJ
ejpam-3916	130	30	-	-	ADJ
ejpam-3916	130	31	dominating	dominating	ADJ
ejpam-3916	130	32	and	and	CCONJ
ejpam-3916	130	33	pointwise	pointwise	VERB
ejpam-3916	130	34	non	non	ADJ
ejpam-3916	130	35	-	-	ADJ
ejpam-3916	130	36	dominating	dominating	ADJ
ejpam-3916	130	37	set	set	NOUN
ejpam-3916	130	38	of	of	ADP
ejpam-3916	130	39	g.	g.	PROPN
ejpam-3916	130	40	the	the	DET
ejpam-3916	130	41	minimum	minimum	ADJ
ejpam-3916	130	42	cardinality	cardinality	NOUN
ejpam-3916	130	43	of	of	ADP
ejpam-3916	130	44	a	a	DET
ejpam-3916	130	45	ppnd	ppnd	NOUN
ejpam-3916	130	46	set	set	NOUN
ejpam-3916	130	47	of	of	ADP
ejpam-3916	130	48	g	g	PROPN
ejpam-3916	130	49	is	be	AUX
ejpam-3916	130	50	denoted	denote	VERB
ejpam-3916	130	51	by	by	ADP
ejpam-3916	130	52	γppnd(g	γppnd(g	NOUN
ejpam-3916	130	53	)	)	PUNCT
ejpam-3916	130	54	.	.	PUNCT
ejpam-3916	131	1	any	any	DET
ejpam-3916	131	2	pairwise	pairwise	NOUN
ejpam-3916	131	3	and	and	CCONJ
ejpam-3916	131	4	pointwise	pointwise	VERB
ejpam-3916	131	5	non	non	ADJ
ejpam-3916	131	6	-	-	ADJ
ejpam-3916	131	7	dominating	dominating	ADJ
ejpam-3916	131	8	set	set	NOUN
ejpam-3916	131	9	of	of	ADP
ejpam-3916	131	10	g	g	PROPN
ejpam-3916	131	11	with	with	ADP
ejpam-3916	131	12	cardinality	cardinality	NOUN
ejpam-3916	131	13	equal	equal	ADJ
ejpam-3916	131	14	to	to	PART
ejpam-3916	131	15	γppnd(g	γppnd(g	VERB
ejpam-3916	131	16	)	)	PUNCT
ejpam-3916	131	17	is	be	AUX
ejpam-3916	131	18	called	call	VERB
ejpam-3916	131	19	a	a	DET
ejpam-3916	131	20	γppnd	γppnd	NOUN
ejpam-3916	131	21	-	-	PUNCT
ejpam-3916	131	22	set	set	NOUN
ejpam-3916	131	23	of	of	ADP
ejpam-3916	131	24	g.	g.	PROPN
ejpam-3916	131	25	remark	remark	PROPN
ejpam-3916	131	26	2	2	NUM
ejpam-3916	131	27	.	.	PUNCT
ejpam-3916	132	1	a	a	DET
ejpam-3916	132	2	pairwise	pairwise	NOUN
ejpam-3916	132	3	non	non	ADJ
ejpam-3916	132	4	-	-	ADJ
ejpam-3916	132	5	dominating	dominating	ADJ
ejpam-3916	132	6	set	set	NOUN
ejpam-3916	132	7	of	of	ADP
ejpam-3916	132	8	g	g	PROPN
ejpam-3916	132	9	is	be	AUX
ejpam-3916	132	10	a	a	DET
ejpam-3916	132	11	dominating	dominating	NOUN
ejpam-3916	132	12	set	set	NOUN
ejpam-3916	132	13	of	of	ADP
ejpam-3916	132	14	g.	g.	PROPN
ejpam-3916	132	15	theorem	theorem	VERB
ejpam-3916	132	16	3	3	X
ejpam-3916	132	17	.	.	PUNCT
ejpam-3916	133	1	let	let	VERB
ejpam-3916	133	2	g	g	NOUN
ejpam-3916	133	3	be	be	AUX
ejpam-3916	133	4	any	any	DET
ejpam-3916	133	5	graph	graph	NOUN
ejpam-3916	133	6	of	of	ADP
ejpam-3916	133	7	order	order	NOUN
ejpam-3916	133	8	n.	n.	NOUN
ejpam-3916	133	9	then	then	ADV
ejpam-3916	133	10	1	1	NUM
ejpam-3916	133	11	≤	≤	NUM
ejpam-3916	133	12	ppnd(g	ppnd(g	NOUN
ejpam-3916	133	13	)	)	PUNCT
ejpam-3916	133	14	≤	≤	NOUN
ejpam-3916	133	15	n.	n.	NOUN
ejpam-3916	133	16	moreover	moreover	ADV
ejpam-3916	133	17	,	,	PUNCT
ejpam-3916	133	18	(	(	PUNCT
ejpam-3916	133	19	i	i	NOUN
ejpam-3916	133	20	)	)	PUNCT
ejpam-3916	133	21	γppnd(g	γppnd(g	PROPN
ejpam-3916	133	22	)	)	PUNCT
ejpam-3916	133	23	=	=	SYM
ejpam-3916	134	1	1	1	NUM
ejpam-3916	134	2	if	if	SCONJ
ejpam-3916	134	3	and	and	CCONJ
ejpam-3916	134	4	only	only	ADV
ejpam-3916	134	5	if	if	SCONJ
ejpam-3916	134	6	g	g	PROPN
ejpam-3916	134	7	=	=	SYM
ejpam-3916	134	8	k1	k1	PROPN
ejpam-3916	134	9	,	,	PUNCT
ejpam-3916	134	10	(	(	PUNCT
ejpam-3916	134	11	ii	ii	NOUN
ejpam-3916	134	12	)	)	PUNCT
ejpam-3916	134	13	γppnd(g	γppnd(g	PROPN
ejpam-3916	134	14	)	)	PUNCT
ejpam-3916	134	15	=	=	SYM
ejpam-3916	134	16	2	2	NUM
ejpam-3916	134	17	if	if	SCONJ
ejpam-3916	134	18	and	and	CCONJ
ejpam-3916	134	19	only	only	ADV
ejpam-3916	134	20	if	if	SCONJ
ejpam-3916	134	21	one	one	NUM
ejpam-3916	134	22	of	of	ADP
ejpam-3916	134	23	the	the	DET
ejpam-3916	134	24	following	following	ADJ
ejpam-3916	134	25	statements	statement	NOUN
ejpam-3916	134	26	holds	hold	VERB
ejpam-3916	134	27	:	:	PUNCT
ejpam-3916	134	28	(	(	PUNCT
ejpam-3916	134	29	a	a	X
ejpam-3916	134	30	)	)	PUNCT
ejpam-3916	134	31	g	g	NOUN
ejpam-3916	134	32	=	=	SYM
ejpam-3916	134	33	k2	k2	PROPN
ejpam-3916	134	34	(	(	PUNCT
ejpam-3916	134	35	b	b	NOUN
ejpam-3916	134	36	)	)	PUNCT
ejpam-3916	134	37	g	g	PROPN
ejpam-3916	134	38	=	=	SYM
ejpam-3916	134	39	k2	k2	PROPN
ejpam-3916	134	40	(	(	PUNCT
ejpam-3916	134	41	c	c	NOUN
ejpam-3916	134	42	)	)	PUNCT
ejpam-3916	134	43	there	there	PRON
ejpam-3916	134	44	exist	exist	VERB
ejpam-3916	134	45	non	non	ADJ
ejpam-3916	134	46	-	-	ADJ
ejpam-3916	134	47	adjacent	adjacent	ADJ
ejpam-3916	134	48	vertices	vertex	NOUN
ejpam-3916	134	49	x	x	X
ejpam-3916	134	50	,	,	PUNCT
ejpam-3916	134	51	y	y	PROPN
ejpam-3916	134	52	∈	∈	PROPN
ejpam-3916	134	53	v	v	ADP
ejpam-3916	134	54	(	(	PUNCT
ejpam-3916	134	55	g	g	NOUN
ejpam-3916	134	56	)	)	PUNCT
ejpam-3916	134	57	such	such	ADJ
ejpam-3916	134	58	that	that	DET
ejpam-3916	134	59	ng(x	ng(x	NUM
ejpam-3916	134	60	)	)	PUNCT
ejpam-3916	134	61	∩	∩	NOUN
ejpam-3916	134	62	ng(y	ng(y	NOUN
ejpam-3916	134	63	)	)	PUNCT
ejpam-3916	134	64	=	=	NOUN
ejpam-3916	134	65	∅	∅	NOUN
ejpam-3916	134	66	and	and	CCONJ
ejpam-3916	134	67	ng[x	ng[x	PROPN
ejpam-3916	134	68	]	]	X
ejpam-3916	134	69	∪ng[y	∪ng[y	PROPN
ejpam-3916	134	70	]	]	X
ejpam-3916	134	71	=	=	SYM
ejpam-3916	134	72	v	v	X
ejpam-3916	134	73	(	(	PUNCT
ejpam-3916	134	74	g	g	NOUN
ejpam-3916	134	75	)	)	PUNCT
ejpam-3916	134	76	.	.	PUNCT
ejpam-3916	135	1	(	(	PUNCT
ejpam-3916	135	2	d	d	X
ejpam-3916	135	3	)	)	PUNCT
ejpam-3916	135	4	there	there	PRON
ejpam-3916	135	5	exist	exist	VERB
ejpam-3916	135	6	adjacent	adjacent	ADJ
ejpam-3916	135	7	vertices	vertex	NOUN
ejpam-3916	135	8	x	x	X
ejpam-3916	135	9	,	,	PUNCT
ejpam-3916	135	10	y	y	PROPN
ejpam-3916	135	11	∈	∈	PROPN
ejpam-3916	135	12	v	v	ADP
ejpam-3916	135	13	(	(	PUNCT
ejpam-3916	135	14	g	g	NOUN
ejpam-3916	135	15	)	)	PUNCT
ejpam-3916	135	16	such	such	ADJ
ejpam-3916	135	17	that	that	DET
ejpam-3916	135	18	ng(x)∩ng(y	ng(x)∩ng(y	NOUN
ejpam-3916	135	19	)	)	PUNCT
ejpam-3916	135	20	=	=	SYM
ejpam-3916	135	21	∅	∅	NOUN
ejpam-3916	135	22	,	,	PUNCT
ejpam-3916	135	23	ng(x)∪	ng(x)∪	ADJ
ejpam-3916	135	24	ng(y	ng(y	NOUN
ejpam-3916	135	25	)	)	PUNCT
ejpam-3916	135	26	=	=	SYM
ejpam-3916	135	27	v	v	NOUN
ejpam-3916	135	28	(	(	PUNCT
ejpam-3916	135	29	g	g	NOUN
ejpam-3916	135	30	)	)	PUNCT
ejpam-3916	135	31	,	,	PUNCT
ejpam-3916	135	32	and	and	CCONJ
ejpam-3916	135	33	for	for	ADP
ejpam-3916	135	34	each	each	PRON
ejpam-3916	135	35	v	v	X
ejpam-3916	135	36	∈	∈	PROPN
ejpam-3916	135	37	ng(x	ng(x	NUM
ejpam-3916	135	38	)	)	PUNCT
ejpam-3916	135	39	\	\	NOUN
ejpam-3916	135	40	{	{	PUNCT
ejpam-3916	135	41	y	y	NOUN
ejpam-3916	135	42	}	}	PUNCT
ejpam-3916	135	43	and	and	CCONJ
ejpam-3916	135	44	w	w	PROPN
ejpam-3916	135	45	∈	∈	PROPN
ejpam-3916	135	46	ng(y	ng(y	NOUN
ejpam-3916	135	47	)	)	PUNCT
ejpam-3916	135	48	\	\	NOUN
ejpam-3916	135	49	{	{	PUNCT
ejpam-3916	135	50	x	x	X
ejpam-3916	135	51	}	}	PUNCT
ejpam-3916	135	52	,	,	PUNCT
ejpam-3916	135	53	there	there	PRON
ejpam-3916	135	54	exist	exist	VERB
ejpam-3916	135	55	p	p	PROPN
ejpam-3916	135	56	∈	∈	PROPN
ejpam-3916	135	57	ng(y	ng(y	NOUN
ejpam-3916	135	58	)	)	PUNCT
ejpam-3916	135	59	\ng(v	\ng(v	NOUN
ejpam-3916	135	60	)	)	PUNCT
ejpam-3916	135	61	and	and	CCONJ
ejpam-3916	135	62	q	q	NOUN
ejpam-3916	135	63	∈	∈	PROPN
ejpam-3916	135	64	ng(x	ng(x	NUM
ejpam-3916	135	65	)	)	PUNCT
ejpam-3916	135	66	\ng(w	\ng(w	NOUN
ejpam-3916	135	67	)	)	PUNCT
ejpam-3916	135	68	.	.	PUNCT
ejpam-3916	136	1	g.	g.	PROPN
ejpam-3916	136	2	salasalan	salasalan	PROPN
ejpam-3916	136	3	,	,	PUNCT
ejpam-3916	136	4	s.	s.	PROPN
ejpam-3916	136	5	canoy	canoy	PROPN
ejpam-3916	136	6	,	,	PUNCT
ejpam-3916	136	7	jr	jr	PROPN
ejpam-3916	136	8	.	.	PROPN
ejpam-3916	136	9	/	/	SYM
ejpam-3916	136	10	eur	eur	PROPN
ejpam-3916	136	11	.	.	PUNCT
ejpam-3916	137	1	j.	j.	PROPN
ejpam-3916	137	2	pure	pure	PROPN
ejpam-3916	137	3	appl	appl	PROPN
ejpam-3916	137	4	.	.	PROPN
ejpam-3916	137	5	math	math	PROPN
ejpam-3916	137	6	,	,	PUNCT
ejpam-3916	137	7	14	14	NUM
ejpam-3916	137	8	(	(	PUNCT
ejpam-3916	137	9	1	1	NUM
ejpam-3916	137	10	)	)	PUNCT
ejpam-3916	137	11	(	(	PUNCT
ejpam-3916	137	12	2021	2021	NUM
ejpam-3916	137	13	)	)	PUNCT
ejpam-3916	137	14	,	,	PUNCT
ejpam-3916	137	15	112	112	NUM
ejpam-3916	137	16	-	-	SYM
ejpam-3916	137	17	125	125	NUM
ejpam-3916	137	18	116	116	NUM
ejpam-3916	137	19	(	(	PUNCT
ejpam-3916	137	20	iii	iii	NOUN
ejpam-3916	137	21	)	)	PUNCT
ejpam-3916	137	22	γppnd(g	γppnd(g	PROPN
ejpam-3916	137	23	)	)	PUNCT
ejpam-3916	137	24	=	=	SYM
ejpam-3916	138	1	n	n	NOUN
ejpam-3916	138	2	if	if	SCONJ
ejpam-3916	139	1	and	and	CCONJ
ejpam-3916	139	2	only	only	ADV
ejpam-3916	139	3	if	if	SCONJ
ejpam-3916	139	4	g	g	PROPN
ejpam-3916	139	5	=	=	VERB
ejpam-3916	139	6	kn	kn	PROPN
ejpam-3916	139	7	or	or	CCONJ
ejpam-3916	139	8	g	g	PROPN
ejpam-3916	139	9	is	be	AUX
ejpam-3916	139	10	connected	connect	VERB
ejpam-3916	139	11	such	such	ADJ
ejpam-3916	139	12	that	that	DET
ejpam-3916	139	13	ng({u	ng({u	NOUN
ejpam-3916	139	14	,	,	PUNCT
ejpam-3916	139	15	v	v	NOUN
ejpam-3916	139	16	}	}	PUNCT
ejpam-3916	139	17	)	)	PUNCT
ejpam-3916	140	1	=	=	SYM
ejpam-3916	140	2	v	v	X
ejpam-3916	140	3	(	(	PUNCT
ejpam-3916	140	4	g	g	NOUN
ejpam-3916	140	5	)	)	PUNCT
ejpam-3916	140	6	for	for	ADP
ejpam-3916	140	7	each	each	DET
ejpam-3916	140	8	pair	pair	NOUN
ejpam-3916	140	9	of	of	ADP
ejpam-3916	140	10	adjacent	adjacent	ADJ
ejpam-3916	140	11	vertices	vertex	NOUN
ejpam-3916	140	12	u	u	NOUN
ejpam-3916	140	13	,	,	PUNCT
ejpam-3916	140	14	v	v	NOUN
ejpam-3916	140	15	∈	∈	PROPN
ejpam-3916	140	16	v	v	NOUN
ejpam-3916	140	17	(	(	PUNCT
ejpam-3916	140	18	g	g	NOUN
ejpam-3916	140	19	)	)	PUNCT
ejpam-3916	140	20	.	.	PUNCT
ejpam-3916	141	1	proof	proof	NOUN
ejpam-3916	141	2	.	.	PUNCT
ejpam-3916	142	1	clearly	clearly	ADV
ejpam-3916	142	2	,	,	PUNCT
ejpam-3916	142	3	by	by	ADP
ejpam-3916	142	4	definition	definition	NOUN
ejpam-3916	142	5	,	,	PUNCT
ejpam-3916	142	6	a	a	DET
ejpam-3916	142	7	pairwise	pairwise	NOUN
ejpam-3916	142	8	and	and	CCONJ
ejpam-3916	142	9	pointwise	pointwise	VERB
ejpam-3916	142	10	non	non	ADJ
ejpam-3916	142	11	-	-	ADJ
ejpam-3916	142	12	dominating	dominating	ADJ
ejpam-3916	142	13	set	set	NOUN
ejpam-3916	142	14	of	of	ADP
ejpam-3916	142	15	g	g	PROPN
ejpam-3916	142	16	is	be	AUX
ejpam-3916	142	17	nonempty	nonempty	ADJ
ejpam-3916	142	18	.	.	PUNCT
ejpam-3916	143	1	thus	thus	ADV
ejpam-3916	143	2	,	,	PUNCT
ejpam-3916	143	3	ppnd(g	ppnd(g	NUM
ejpam-3916	143	4	)	)	PUNCT
ejpam-3916	143	5	≥	≥	NOUN
ejpam-3916	143	6	1	1	NUM
ejpam-3916	143	7	.	.	PUNCT
ejpam-3916	144	1	also	also	ADV
ejpam-3916	144	2	,	,	PUNCT
ejpam-3916	144	3	since	since	SCONJ
ejpam-3916	144	4	v	v	NOUN
ejpam-3916	144	5	(	(	PUNCT
ejpam-3916	144	6	g	g	NOUN
ejpam-3916	144	7	)	)	PUNCT
ejpam-3916	144	8	is	be	AUX
ejpam-3916	144	9	a	a	DET
ejpam-3916	144	10	pairwise	pairwise	NOUN
ejpam-3916	144	11	and	and	CCONJ
ejpam-3916	144	12	pointwise	pointwise	VERB
ejpam-3916	144	13	nondominating	nondominate	VERB
ejpam-3916	144	14	set	set	NOUN
ejpam-3916	144	15	of	of	ADP
ejpam-3916	144	16	g	g	PROPN
ejpam-3916	144	17	,	,	PUNCT
ejpam-3916	144	18	it	it	PRON
ejpam-3916	144	19	follows	follow	VERB
ejpam-3916	144	20	that	that	PRON
ejpam-3916	144	21	γppnd(g	γppnd(g	ADJ
ejpam-3916	144	22	)	)	PUNCT
ejpam-3916	144	23	≤	≤	NOUN
ejpam-3916	144	24	n.	n.	NOUN
ejpam-3916	144	25	(	(	PUNCT
ejpam-3916	144	26	i	i	NOUN
ejpam-3916	144	27	)	)	PUNCT
ejpam-3916	144	28	next	next	ADV
ejpam-3916	144	29	,	,	PUNCT
ejpam-3916	144	30	suppose	suppose	VERB
ejpam-3916	144	31	that	that	SCONJ
ejpam-3916	144	32	γppnd(g	γppnd(g	VERB
ejpam-3916	144	33	)	)	PUNCT
ejpam-3916	144	34	=	=	SYM
ejpam-3916	145	1	1	1	NUM
ejpam-3916	145	2	,	,	PUNCT
ejpam-3916	145	3	say	say	VERB
ejpam-3916	145	4	s	s	X
ejpam-3916	145	5	=	=	VERB
ejpam-3916	145	6	{	{	PUNCT
ejpam-3916	145	7	v	v	NOUN
ejpam-3916	145	8	}	}	PUNCT
ejpam-3916	145	9	is	be	AUX
ejpam-3916	145	10	a	a	DET
ejpam-3916	145	11	γppnd	γppnd	NOUN
ejpam-3916	145	12	-	-	PUNCT
ejpam-3916	145	13	set	set	NOUN
ejpam-3916	145	14	of	of	ADP
ejpam-3916	145	15	g.	g.	PROPN
ejpam-3916	145	16	if	if	SCONJ
ejpam-3916	145	17	such	such	DET
ejpam-3916	145	18	a	a	DET
ejpam-3916	145	19	vertex	vertex	NOUN
ejpam-3916	145	20	outside	outside	ADP
ejpam-3916	145	21	s	s	PART
ejpam-3916	145	22	exists	exist	VERB
ejpam-3916	145	23	,	,	PUNCT
ejpam-3916	145	24	then	then	ADV
ejpam-3916	145	25	this	this	PRON
ejpam-3916	145	26	would	would	AUX
ejpam-3916	145	27	require	require	VERB
ejpam-3916	145	28	two	two	NUM
ejpam-3916	145	29	distinct	distinct	ADJ
ejpam-3916	145	30	vertices	vertex	NOUN
ejpam-3916	145	31	from	from	ADP
ejpam-3916	145	32	s	s	PRON
ejpam-3916	145	33	to	to	PART
ejpam-3916	145	34	satisfy	satisfy	VERB
ejpam-3916	145	35	the	the	DET
ejpam-3916	145	36	property	property	NOUN
ejpam-3916	145	37	of	of	ADP
ejpam-3916	145	38	s.	s.	PROPN
ejpam-3916	145	39	this	this	PRON
ejpam-3916	145	40	forces	force	VERB
ejpam-3916	145	41	us	we	PRON
ejpam-3916	145	42	to	to	PART
ejpam-3916	145	43	conclude	conclude	VERB
ejpam-3916	145	44	that	that	DET
ejpam-3916	145	45	g	g	PROPN
ejpam-3916	145	46	=	=	SYM
ejpam-3916	145	47	k1	k1	PROPN
ejpam-3916	145	48	.	.	PUNCT
ejpam-3916	146	1	further	far	ADV
ejpam-3916	146	2	,	,	PUNCT
ejpam-3916	146	3	since	since	SCONJ
ejpam-3916	146	4	γppnd(k1	γppnd(k1	PROPN
ejpam-3916	146	5	)	)	PUNCT
ejpam-3916	146	6	=	=	SYM
ejpam-3916	146	7	1	1	NUM
ejpam-3916	146	8	,	,	PUNCT
ejpam-3916	146	9	(	(	PUNCT
ejpam-3916	146	10	i	i	NOUN
ejpam-3916	146	11	)	)	PUNCT
ejpam-3916	146	12	holds	hold	VERB
ejpam-3916	146	13	.	.	PUNCT
ejpam-3916	147	1	(	(	PUNCT
ejpam-3916	147	2	ii	ii	NOUN
ejpam-3916	147	3	)	)	PUNCT
ejpam-3916	147	4	suppose	suppose	VERB
ejpam-3916	147	5	now	now	ADV
ejpam-3916	147	6	that	that	PRON
ejpam-3916	147	7	γppnd(g	γppnd(g	VERB
ejpam-3916	147	8	)	)	PUNCT
ejpam-3916	147	9	=	=	SYM
ejpam-3916	147	10	2	2	NUM
ejpam-3916	147	11	,	,	PUNCT
ejpam-3916	147	12	say	say	VERB
ejpam-3916	147	13	s	s	X
ejpam-3916	147	14	=	=	PUNCT
ejpam-3916	147	15	{	{	PUNCT
ejpam-3916	147	16	x	x	PROPN
ejpam-3916	147	17	,	,	PUNCT
ejpam-3916	147	18	y	y	PRON
ejpam-3916	147	19	}	}	PUNCT
ejpam-3916	147	20	is	be	AUX
ejpam-3916	147	21	a	a	DET
ejpam-3916	147	22	γppnd	γppnd	NOUN
ejpam-3916	147	23	-	-	PUNCT
ejpam-3916	147	24	set	set	NOUN
ejpam-3916	147	25	of	of	ADP
ejpam-3916	147	26	g.	g.	PROPN
ejpam-3916	147	27	if	if	SCONJ
ejpam-3916	147	28	n	n	PROPN
ejpam-3916	147	29	=	=	SYM
ejpam-3916	147	30	2	2	NUM
ejpam-3916	147	31	,	,	PUNCT
ejpam-3916	147	32	then	then	ADV
ejpam-3916	147	33	g	g	PROPN
ejpam-3916	147	34	=	=	PROPN
ejpam-3916	147	35	k2	k2	PROPN
ejpam-3916	147	36	or	or	CCONJ
ejpam-3916	147	37	g	g	NOUN
ejpam-3916	147	38	=	=	SYM
ejpam-3916	147	39	k2	k2	PROPN
ejpam-3916	147	40	.	.	PUNCT
ejpam-3916	148	1	suppose	suppose	VERB
ejpam-3916	148	2	n	n	PRON
ejpam-3916	148	3	≥	≥	X
ejpam-3916	148	4	3	3	NUM
ejpam-3916	148	5	and	and	CCONJ
ejpam-3916	148	6	assume	assume	VERB
ejpam-3916	148	7	first	first	ADV
ejpam-3916	148	8	that	that	SCONJ
ejpam-3916	148	9	xy	xy	PROPN
ejpam-3916	148	10	/∈	/∈	PUNCT
ejpam-3916	148	11	e(g	e(g	PROPN
ejpam-3916	148	12	)	)	PUNCT
ejpam-3916	148	13	.	.	PUNCT
ejpam-3916	149	1	since	since	SCONJ
ejpam-3916	149	2	s	s	PROPN
ejpam-3916	149	3	is	be	AUX
ejpam-3916	149	4	a	a	DET
ejpam-3916	149	5	ppnd	ppnd	NOUN
ejpam-3916	149	6	set	set	NOUN
ejpam-3916	149	7	of	of	ADP
ejpam-3916	149	8	g	g	NOUN
ejpam-3916	149	9	,	,	PUNCT
ejpam-3916	149	10	ng(x	ng(x	NUM
ejpam-3916	149	11	)	)	PUNCT
ejpam-3916	149	12	∩	∩	NOUN
ejpam-3916	149	13	ng(y	ng(y	NOUN
ejpam-3916	149	14	)	)	PUNCT
ejpam-3916	149	15	=	=	NOUN
ejpam-3916	149	16	∅	∅	NOUN
ejpam-3916	149	17	and	and	CCONJ
ejpam-3916	149	18	ng[x	ng[x	PROPN
ejpam-3916	149	19	]	]	PUNCT
ejpam-3916	149	20	∪	∪	ADP
ejpam-3916	149	21	ng[y	ng[y	PROPN
ejpam-3916	149	22	]	]	X
ejpam-3916	149	23	=	=	SYM
ejpam-3916	149	24	v	v	X
ejpam-3916	149	25	(	(	PUNCT
ejpam-3916	149	26	g	g	NOUN
ejpam-3916	149	27	)	)	PUNCT
ejpam-3916	149	28	.	.	PUNCT
ejpam-3916	150	1	hence	hence	ADV
ejpam-3916	150	2	,	,	PUNCT
ejpam-3916	150	3	(	(	PUNCT
ejpam-3916	150	4	c	c	X
ejpam-3916	150	5	)	)	PUNCT
ejpam-3916	150	6	holds	hold	NOUN
ejpam-3916	150	7	.	.	PUNCT
ejpam-3916	151	1	suppose	suppose	VERB
ejpam-3916	151	2	xy	xy	PROPN
ejpam-3916	151	3	∈	∈	PROPN
ejpam-3916	151	4	e(g	e(g	PROPN
ejpam-3916	151	5	)	)	PUNCT
ejpam-3916	151	6	.	.	PUNCT
ejpam-3916	152	1	again	again	ADV
ejpam-3916	152	2	,	,	PUNCT
ejpam-3916	152	3	since	since	SCONJ
ejpam-3916	152	4	s	s	PRON
ejpam-3916	152	5	a	a	DET
ejpam-3916	152	6	ppnd	ppnd	NOUN
ejpam-3916	152	7	set	set	NOUN
ejpam-3916	152	8	of	of	ADP
ejpam-3916	152	9	g	g	NOUN
ejpam-3916	152	10	,	,	PUNCT
ejpam-3916	152	11	ng(x	ng(x	NUM
ejpam-3916	152	12	)	)	PUNCT
ejpam-3916	152	13	∩	∩	NOUN
ejpam-3916	152	14	ng(y	ng(y	NOUN
ejpam-3916	152	15	)	)	PUNCT
ejpam-3916	152	16	=	=	NOUN
ejpam-3916	152	17	∅	∅	NOUN
ejpam-3916	152	18	and	and	CCONJ
ejpam-3916	152	19	ng(x	ng(x	NUM
ejpam-3916	152	20	)	)	PUNCT
ejpam-3916	152	21	∪	∪	ADP
ejpam-3916	152	22	ng(y	ng(y	NOUN
ejpam-3916	152	23	)	)	PUNCT
ejpam-3916	152	24	=	=	SYM
ejpam-3916	152	25	v	v	NOUN
ejpam-3916	152	26	(	(	PUNCT
ejpam-3916	152	27	g	g	NOUN
ejpam-3916	152	28	)	)	PUNCT
ejpam-3916	152	29	.	.	PUNCT
ejpam-3916	153	1	let	let	VERB
ejpam-3916	153	2	v	v	ADP
ejpam-3916	153	3	∈	∈	PROPN
ejpam-3916	153	4	ng(x	ng(x	NUM
ejpam-3916	153	5	)	)	PUNCT
ejpam-3916	153	6	\	\	NOUN
ejpam-3916	153	7	{	{	PUNCT
ejpam-3916	153	8	y	y	NOUN
ejpam-3916	153	9	}	}	PUNCT
ejpam-3916	153	10	.	.	PUNCT
ejpam-3916	154	1	since	since	SCONJ
ejpam-3916	154	2	ng({x	ng({x	PRON
ejpam-3916	154	3	,	,	PUNCT
ejpam-3916	154	4	v	v	NOUN
ejpam-3916	154	5	}	}	PUNCT
ejpam-3916	154	6	)	)	PUNCT
ejpam-3916	154	7	6=	6=	X
ejpam-3916	154	8	v	v	X
ejpam-3916	154	9	(	(	PUNCT
ejpam-3916	154	10	g	g	NOUN
ejpam-3916	154	11	)	)	PUNCT
ejpam-3916	154	12	,	,	PUNCT
ejpam-3916	154	13	there	there	PRON
ejpam-3916	154	14	exists	exist	VERB
ejpam-3916	154	15	p	p	PROPN
ejpam-3916	154	16	∈	∈	PROPN
ejpam-3916	154	17	v	v	ADP
ejpam-3916	154	18	(	(	PUNCT
ejpam-3916	154	19	g	g	NOUN
ejpam-3916	154	20	)	)	PUNCT
ejpam-3916	154	21	\	\	PROPN
ejpam-3916	154	22	ng({x	ng({x	PROPN
ejpam-3916	154	23	,	,	PUNCT
ejpam-3916	154	24	v	v	NOUN
ejpam-3916	154	25	}	}	PUNCT
ejpam-3916	154	26	)	)	PUNCT
ejpam-3916	154	27	.	.	PUNCT
ejpam-3916	155	1	since	since	SCONJ
ejpam-3916	155	2	ng(x	ng(x	NUM
ejpam-3916	155	3	)	)	PUNCT
ejpam-3916	155	4	∩	∩	NOUN
ejpam-3916	155	5	ng(y	ng(y	NOUN
ejpam-3916	155	6	)	)	PUNCT
ejpam-3916	155	7	=	=	NOUN
ejpam-3916	155	8	∅	∅	NOUN
ejpam-3916	155	9	,	,	PUNCT
ejpam-3916	155	10	it	it	PRON
ejpam-3916	155	11	follows	follow	VERB
ejpam-3916	155	12	that	that	SCONJ
ejpam-3916	155	13	p	p	PROPN
ejpam-3916	155	14	∈	∈	PROPN
ejpam-3916	155	15	ng(y	ng(y	NOUN
ejpam-3916	155	16	)	)	PUNCT
ejpam-3916	155	17	\	\	NOUN
ejpam-3916	155	18	ng(v	ng(v	PUNCT
ejpam-3916	155	19	)	)	PUNCT
ejpam-3916	155	20	.	.	PUNCT
ejpam-3916	156	1	similarly	similarly	ADV
ejpam-3916	156	2	,	,	PUNCT
ejpam-3916	156	3	for	for	ADP
ejpam-3916	156	4	each	each	DET
ejpam-3916	156	5	w	w	PROPN
ejpam-3916	156	6	∈	∈	PROPN
ejpam-3916	156	7	ng(y	ng(y	NOUN
ejpam-3916	156	8	)	)	PUNCT
ejpam-3916	156	9	\	\	NOUN
ejpam-3916	156	10	{	{	PUNCT
ejpam-3916	156	11	x	x	X
ejpam-3916	156	12	}	}	PUNCT
ejpam-3916	156	13	,	,	PUNCT
ejpam-3916	156	14	there	there	PRON
ejpam-3916	156	15	exists	exist	VERB
ejpam-3916	156	16	q	q	PROPN
ejpam-3916	156	17	∈	∈	PROPN
ejpam-3916	156	18	ng(x	ng(x	NUM
ejpam-3916	156	19	)	)	PUNCT
ejpam-3916	156	20	\	\	NOUN
ejpam-3916	156	21	ng(w	ng(w	NOUN
ejpam-3916	156	22	)	)	PUNCT
ejpam-3916	156	23	,	,	PUNCT
ejpam-3916	156	24	showing	show	VERB
ejpam-3916	156	25	that	that	SCONJ
ejpam-3916	156	26	(	(	PUNCT
ejpam-3916	156	27	d	d	X
ejpam-3916	156	28	)	)	PUNCT
ejpam-3916	156	29	holds	hold	NOUN
ejpam-3916	156	30	.	.	PUNCT
ejpam-3916	157	1	for	for	ADP
ejpam-3916	157	2	the	the	DET
ejpam-3916	157	3	converse	converse	NOUN
ejpam-3916	157	4	,	,	PUNCT
ejpam-3916	157	5	suppose	suppose	VERB
ejpam-3916	157	6	first	first	ADV
ejpam-3916	157	7	that	that	SCONJ
ejpam-3916	157	8	g	g	PROPN
ejpam-3916	157	9	=	=	SYM
ejpam-3916	157	10	k2	k2	PROPN
ejpam-3916	157	11	or	or	CCONJ
ejpam-3916	157	12	g	g	NOUN
ejpam-3916	157	13	=	=	SYM
ejpam-3916	157	14	k2	k2	PROPN
ejpam-3916	157	15	.	.	PUNCT
ejpam-3916	158	1	then	then	ADV
ejpam-3916	158	2	,	,	PUNCT
ejpam-3916	158	3	clearly	clearly	ADV
ejpam-3916	158	4	,	,	PUNCT
ejpam-3916	158	5	γppnd(g	γppnd(g	ADJ
ejpam-3916	158	6	)	)	PUNCT
ejpam-3916	158	7	=	=	SYM
ejpam-3916	159	1	2	2	X
ejpam-3916	159	2	.	.	PUNCT
ejpam-3916	160	1	next	next	ADV
ejpam-3916	160	2	,	,	PUNCT
ejpam-3916	160	3	suppose	suppose	VERB
ejpam-3916	160	4	that	that	SCONJ
ejpam-3916	160	5	(	(	PUNCT
ejpam-3916	160	6	c	c	X
ejpam-3916	160	7	)	)	PUNCT
ejpam-3916	160	8	holds	hold	VERB
ejpam-3916	160	9	.	.	PUNCT
ejpam-3916	161	1	let	let	VERB
ejpam-3916	161	2	s	s	VERB
ejpam-3916	161	3	=	=	PUNCT
ejpam-3916	161	4	{	{	PUNCT
ejpam-3916	161	5	x	x	PROPN
ejpam-3916	161	6	,	,	PUNCT
ejpam-3916	161	7	y	y	NOUN
ejpam-3916	161	8	}	}	PUNCT
ejpam-3916	161	9	and	and	CCONJ
ejpam-3916	161	10	let	let	VERB
ejpam-3916	161	11	v	v	NUM
ejpam-3916	161	12	∈	∈	PROPN
ejpam-3916	161	13	v	v	NOUN
ejpam-3916	161	14	(	(	PUNCT
ejpam-3916	161	15	g)\s	g)\s	NOUN
ejpam-3916	161	16	.	.	PUNCT
ejpam-3916	162	1	by	by	ADP
ejpam-3916	162	2	assumption	assumption	NOUN
ejpam-3916	162	3	,	,	PUNCT
ejpam-3916	162	4	we	we	PRON
ejpam-3916	162	5	may	may	AUX
ejpam-3916	162	6	assume	assume	VERB
ejpam-3916	162	7	that	that	SCONJ
ejpam-3916	162	8	v	v	ADP
ejpam-3916	162	9	∈	∈	PROPN
ejpam-3916	162	10	ng(x	ng(x	NUM
ejpam-3916	162	11	)	)	PUNCT
ejpam-3916	162	12	\ng(y	\ng(y	NOUN
ejpam-3916	162	13	)	)	PUNCT
ejpam-3916	162	14	.	.	PUNCT
ejpam-3916	163	1	since	since	SCONJ
ejpam-3916	163	2	y	y	PROPN
ejpam-3916	163	3	∈	∈	PROPN
ejpam-3916	163	4	v	v	ADP
ejpam-3916	163	5	(	(	PUNCT
ejpam-3916	163	6	g	g	NOUN
ejpam-3916	163	7	)	)	PUNCT
ejpam-3916	163	8	\ng({x	\ng({x	NOUN
ejpam-3916	163	9	,	,	PUNCT
ejpam-3916	163	10	v	v	NOUN
ejpam-3916	163	11	}	}	PUNCT
ejpam-3916	163	12	)	)	PUNCT
ejpam-3916	163	13	,	,	PUNCT
ejpam-3916	163	14	ng({x	ng({x	PRON
ejpam-3916	163	15	,	,	PUNCT
ejpam-3916	163	16	v	v	NOUN
ejpam-3916	163	17	}	}	PUNCT
ejpam-3916	163	18	)	)	PUNCT
ejpam-3916	164	1	6=	6=	X
ejpam-3916	164	2	v	v	X
ejpam-3916	164	3	(	(	PUNCT
ejpam-3916	164	4	g	g	NOUN
ejpam-3916	164	5	)	)	PUNCT
ejpam-3916	164	6	.	.	PUNCT
ejpam-3916	165	1	thus	thus	ADV
ejpam-3916	165	2	,	,	PUNCT
ejpam-3916	165	3	s	s	VERB
ejpam-3916	165	4	is	be	AUX
ejpam-3916	165	5	a	a	DET
ejpam-3916	165	6	ppnd	ppnd	NOUN
ejpam-3916	165	7	set	set	NOUN
ejpam-3916	165	8	of	of	ADP
ejpam-3916	165	9	g.	g.	PROPN
ejpam-3916	165	10	since	since	SCONJ
ejpam-3916	165	11	g	g	PROPN
ejpam-3916	165	12	6=	6=	PROPN
ejpam-3916	165	13	k1	k1	NOUN
ejpam-3916	165	14	,	,	PUNCT
ejpam-3916	165	15	it	it	PRON
ejpam-3916	165	16	follows	follow	VERB
ejpam-3916	165	17	that	that	SCONJ
ejpam-3916	165	18	s	s	VERB
ejpam-3916	165	19	is	be	AUX
ejpam-3916	165	20	a	a	DET
ejpam-3916	165	21	γppnd	γppnd	NOUN
ejpam-3916	165	22	-	-	PUNCT
ejpam-3916	165	23	set	set	NOUN
ejpam-3916	165	24	,	,	PUNCT
ejpam-3916	165	25	i.e.	i.e.	X
ejpam-3916	165	26	,	,	PUNCT
ejpam-3916	165	27	γppnd(g	γppnd(g	ADJ
ejpam-3916	165	28	)	)	PUNCT
ejpam-3916	165	29	=	=	PUNCT
ejpam-3916	165	30	|s|	|s|	NOUN
ejpam-3916	165	31	=	=	SYM
ejpam-3916	165	32	2	2	NUM
ejpam-3916	165	33	.	.	PUNCT
ejpam-3916	165	34	finally	finally	ADV
ejpam-3916	165	35	,	,	PUNCT
ejpam-3916	165	36	suppose	suppose	VERB
ejpam-3916	165	37	that	that	SCONJ
ejpam-3916	165	38	(	(	PUNCT
ejpam-3916	165	39	d	d	X
ejpam-3916	165	40	)	)	PUNCT
ejpam-3916	165	41	holds	hold	VERB
ejpam-3916	165	42	.	.	PUNCT
ejpam-3916	166	1	let	let	VERB
ejpam-3916	166	2	s′	s′	ADJ
ejpam-3916	166	3	=	=	PUNCT
ejpam-3916	166	4	{	{	PUNCT
ejpam-3916	166	5	x	x	NOUN
ejpam-3916	166	6	,	,	PUNCT
ejpam-3916	166	7	y	y	NOUN
ejpam-3916	166	8	}	}	PUNCT
ejpam-3916	166	9	and	and	CCONJ
ejpam-3916	166	10	let	let	VERB
ejpam-3916	166	11	v	v	NUM
ejpam-3916	166	12	∈	∈	PROPN
ejpam-3916	166	13	v	v	NOUN
ejpam-3916	166	14	(	(	PUNCT
ejpam-3916	166	15	g	g	NOUN
ejpam-3916	166	16	)	)	PUNCT
ejpam-3916	166	17	\	\	PUNCT
ejpam-3916	167	1	s.	s.	PROPN
ejpam-3916	167	2	assume	assume	VERB
ejpam-3916	167	3	,	,	PUNCT
ejpam-3916	167	4	without	without	ADP
ejpam-3916	167	5	loss	loss	NOUN
ejpam-3916	167	6	of	of	ADP
ejpam-3916	167	7	generality	generality	NOUN
ejpam-3916	167	8	,	,	PUNCT
ejpam-3916	167	9	that	that	PRON
ejpam-3916	167	10	v	v	ADP
ejpam-3916	167	11	∈	∈	PROPN
ejpam-3916	167	12	ng(x	ng(x	NUM
ejpam-3916	167	13	)	)	PUNCT
ejpam-3916	167	14	.	.	PUNCT
ejpam-3916	168	1	by	by	ADP
ejpam-3916	168	2	assumption	assumption	NOUN
ejpam-3916	168	3	,	,	PUNCT
ejpam-3916	168	4	there	there	PRON
ejpam-3916	168	5	exists	exist	VERB
ejpam-3916	168	6	p	p	PROPN
ejpam-3916	168	7	∈	∈	PROPN
ejpam-3916	168	8	ng(y	ng(y	NOUN
ejpam-3916	168	9	)	)	PUNCT
ejpam-3916	168	10	\ng(v	\ng(v	NOUN
ejpam-3916	168	11	)	)	PUNCT
ejpam-3916	168	12	.	.	PUNCT
ejpam-3916	169	1	this	this	PRON
ejpam-3916	169	2	implies	imply	VERB
ejpam-3916	169	3	that	that	SCONJ
ejpam-3916	169	4	p	p	PROPN
ejpam-3916	169	5	/∈	/∈	PROPN
ejpam-3916	169	6	ng({x	ng({x	ADJ
ejpam-3916	169	7	,	,	PUNCT
ejpam-3916	169	8	v	v	NOUN
ejpam-3916	169	9	}	}	PUNCT
ejpam-3916	169	10	)	)	PUNCT
ejpam-3916	169	11	.	.	PUNCT
ejpam-3916	170	1	therefore	therefore	ADV
ejpam-3916	170	2	,	,	PUNCT
ejpam-3916	170	3	s	s	VERB
ejpam-3916	170	4	is	be	AUX
ejpam-3916	170	5	a	a	DET
ejpam-3916	170	6	γppnd	γppnd	NOUN
ejpam-3916	170	7	-	-	PUNCT
ejpam-3916	170	8	set	set	NOUN
ejpam-3916	170	9	of	of	ADP
ejpam-3916	170	10	g	g	NOUN
ejpam-3916	170	11	,	,	PUNCT
ejpam-3916	170	12	implying	imply	VERB
ejpam-3916	170	13	that	that	DET
ejpam-3916	170	14	γppnd(g	γppnd(g	NOUN
ejpam-3916	170	15	)	)	PUNCT
ejpam-3916	170	16	=	=	SYM
ejpam-3916	171	1	2	2	X
ejpam-3916	171	2	.	.	PUNCT
ejpam-3916	172	1	this	this	PRON
ejpam-3916	172	2	proves	prove	VERB
ejpam-3916	172	3	statement	statement	NOUN
ejpam-3916	172	4	(	(	PUNCT
ejpam-3916	172	5	ii	ii	NOUN
ejpam-3916	172	6	)	)	PUNCT
ejpam-3916	172	7	.	.	PUNCT
ejpam-3916	173	1	(	(	PUNCT
ejpam-3916	173	2	iii	iii	X
ejpam-3916	173	3	)	)	PUNCT
ejpam-3916	173	4	suppose	suppose	VERB
ejpam-3916	173	5	γppnd(g	γppnd(g	ADJ
ejpam-3916	173	6	)	)	PUNCT
ejpam-3916	173	7	=	=	VERB
ejpam-3916	173	8	n.	n.	NOUN
ejpam-3916	173	9	suppose	suppose	VERB
ejpam-3916	173	10	first	first	ADV
ejpam-3916	173	11	that	that	SCONJ
ejpam-3916	173	12	g	g	PROPN
ejpam-3916	173	13	is	be	AUX
ejpam-3916	173	14	disconnected	disconnect	VERB
ejpam-3916	173	15	.	.	PUNCT
ejpam-3916	174	1	suppose	suppose	VERB
ejpam-3916	174	2	further	far	ADV
ejpam-3916	174	3	that	that	PRON
ejpam-3916	174	4	g	g	PROPN
ejpam-3916	174	5	6=	6=	PROPN
ejpam-3916	175	1	kn	kn	PROPN
ejpam-3916	175	2	.	.	PUNCT
ejpam-3916	176	1	then	then	ADV
ejpam-3916	176	2	g	g	PROPN
ejpam-3916	176	3	has	have	VERB
ejpam-3916	176	4	a	a	DET
ejpam-3916	176	5	non	non	ADJ
ejpam-3916	176	6	-	-	ADJ
ejpam-3916	176	7	trivial	trivial	ADJ
ejpam-3916	176	8	component	component	NOUN
ejpam-3916	176	9	c.	c.	NOUN
ejpam-3916	176	10	hence	hence	ADV
ejpam-3916	176	11	,	,	PUNCT
ejpam-3916	176	12	there	there	PRON
ejpam-3916	176	13	exist	exist	VERB
ejpam-3916	176	14	distinct	distinct	ADJ
ejpam-3916	176	15	vertices	vertex	NOUN
ejpam-3916	176	16	x	x	X
ejpam-3916	176	17	,	,	PUNCT
ejpam-3916	176	18	y	y	PROPN
ejpam-3916	176	19	∈	∈	PROPN
ejpam-3916	176	20	v	v	NOUN
ejpam-3916	176	21	(	(	PUNCT
ejpam-3916	176	22	c	c	NOUN
ejpam-3916	176	23	)	)	PUNCT
ejpam-3916	176	24	such	such	ADJ
ejpam-3916	176	25	that	that	SCONJ
ejpam-3916	176	26	xy	xy	PROPN
ejpam-3916	176	27	∈	∈	PROPN
ejpam-3916	176	28	v	v	ADP
ejpam-3916	176	29	(	(	PUNCT
ejpam-3916	176	30	g	g	NOUN
ejpam-3916	176	31	)	)	PUNCT
ejpam-3916	176	32	.	.	PUNCT
ejpam-3916	177	1	let	let	VERB
ejpam-3916	177	2	sx	sx	PROPN
ejpam-3916	177	3	=	=	PUNCT
ejpam-3916	177	4	v	v	PROPN
ejpam-3916	177	5	(	(	PUNCT
ejpam-3916	177	6	g	g	NOUN
ejpam-3916	177	7	)	)	PUNCT
ejpam-3916	177	8	\	\	NOUN
ejpam-3916	177	9	{	{	PUNCT
ejpam-3916	177	10	x	x	NOUN
ejpam-3916	177	11	}	}	PUNCT
ejpam-3916	177	12	.	.	PUNCT
ejpam-3916	178	1	then	then	ADV
ejpam-3916	178	2	y	y	PROPN
ejpam-3916	178	3	∈	∈	PROPN
ejpam-3916	178	4	s	s	PART
ejpam-3916	178	5	∩ng(x	∩ng(x	NOUN
ejpam-3916	178	6	)	)	PUNCT
ejpam-3916	178	7	.	.	PUNCT
ejpam-3916	179	1	since	since	SCONJ
ejpam-3916	179	2	g	g	PROPN
ejpam-3916	179	3	is	be	AUX
ejpam-3916	179	4	disconnected	disconnect	VERB
ejpam-3916	179	5	,	,	PUNCT
ejpam-3916	179	6	ng(x	ng(x	NUM
ejpam-3916	179	7	,	,	PUNCT
ejpam-3916	179	8	y	y	NOUN
ejpam-3916	179	9	)	)	PUNCT
ejpam-3916	179	10	6=	6=	ADP
ejpam-3916	179	11	v	v	ADP
ejpam-3916	179	12	(	(	PUNCT
ejpam-3916	179	13	g	g	NOUN
ejpam-3916	179	14	)	)	PUNCT
ejpam-3916	179	15	and	and	CCONJ
ejpam-3916	179	16	there	there	PRON
ejpam-3916	179	17	exists	exist	VERB
ejpam-3916	179	18	w	w	PROPN
ejpam-3916	179	19	∈	∈	PROPN
ejpam-3916	179	20	s	s	PART
ejpam-3916	179	21	\ng(x	\ng(x	NOUN
ejpam-3916	179	22	)	)	PUNCT
ejpam-3916	179	23	.	.	PUNCT
ejpam-3916	180	1	hence	hence	ADV
ejpam-3916	180	2	,	,	PUNCT
ejpam-3916	180	3	s	s	VERB
ejpam-3916	180	4	is	be	AUX
ejpam-3916	180	5	a	a	DET
ejpam-3916	180	6	ppnd	ppnd	NOUN
ejpam-3916	180	7	set	set	NOUN
ejpam-3916	180	8	of	of	ADP
ejpam-3916	180	9	g	g	PROPN
ejpam-3916	180	10	and	and	CCONJ
ejpam-3916	180	11	γppnd(g	γppnd(g	ADJ
ejpam-3916	180	12	)	)	PUNCT
ejpam-3916	180	13	≤	≤	NUM
ejpam-3916	180	14	|s|	|s|	PROPN
ejpam-3916	180	15	=	=	SYM
ejpam-3916	180	16	n−	n−	NOUN
ejpam-3916	180	17	1	1	NUM
ejpam-3916	180	18	,	,	PUNCT
ejpam-3916	180	19	a	a	DET
ejpam-3916	180	20	contradiction	contradiction	NOUN
ejpam-3916	180	21	.	.	PUNCT
ejpam-3916	181	1	therefore	therefore	ADV
ejpam-3916	181	2	,	,	PUNCT
ejpam-3916	181	3	g	g	PROPN
ejpam-3916	181	4	=	=	PROPN
ejpam-3916	181	5	kn	kn	PROPN
ejpam-3916	181	6	.	.	PUNCT
ejpam-3916	182	1	next	next	ADV
ejpam-3916	182	2	,	,	PUNCT
ejpam-3916	182	3	suppose	suppose	VERB
ejpam-3916	182	4	that	that	SCONJ
ejpam-3916	182	5	g	g	PROPN
ejpam-3916	182	6	is	be	AUX
ejpam-3916	182	7	connected	connect	VERB
ejpam-3916	182	8	.	.	PUNCT
ejpam-3916	183	1	suppose	suppose	VERB
ejpam-3916	183	2	there	there	PRON
ejpam-3916	183	3	exist	exist	VERB
ejpam-3916	183	4	distinct	distinct	ADJ
ejpam-3916	183	5	adjacent	adjacent	ADJ
ejpam-3916	183	6	vertices	vertex	NOUN
ejpam-3916	183	7	u	u	NOUN
ejpam-3916	183	8	,	,	PUNCT
ejpam-3916	183	9	v	v	NOUN
ejpam-3916	183	10	∈	∈	PROPN
ejpam-3916	183	11	v	v	NOUN
ejpam-3916	183	12	(	(	PUNCT
ejpam-3916	183	13	g	g	NOUN
ejpam-3916	183	14	)	)	PUNCT
ejpam-3916	183	15	such	such	ADJ
ejpam-3916	183	16	that	that	PRON
ejpam-3916	183	17	ng({u	ng({u	NOUN
ejpam-3916	183	18	,	,	PUNCT
ejpam-3916	183	19	v	v	NOUN
ejpam-3916	183	20	}	}	PUNCT
ejpam-3916	183	21	)	)	PUNCT
ejpam-3916	184	1	6=	6=	X
ejpam-3916	184	2	v	v	X
ejpam-3916	184	3	(	(	PUNCT
ejpam-3916	184	4	g	g	NOUN
ejpam-3916	184	5	)	)	PUNCT
ejpam-3916	184	6	,	,	PUNCT
ejpam-3916	184	7	say	say	VERB
ejpam-3916	184	8	w	w	PROPN
ejpam-3916	184	9	∈	∈	PROPN
ejpam-3916	184	10	v	v	ADP
ejpam-3916	184	11	(	(	PUNCT
ejpam-3916	184	12	g	g	NOUN
ejpam-3916	184	13	)	)	PUNCT
ejpam-3916	184	14	\	\	NOUN
ejpam-3916	184	15	ng({u	ng({u	SYM
ejpam-3916	184	16	,	,	PUNCT
ejpam-3916	184	17	v	v	NOUN
ejpam-3916	184	18	}	}	PUNCT
ejpam-3916	184	19	)	)	PUNCT
ejpam-3916	184	20	.	.	PUNCT
ejpam-3916	185	1	let	let	VERB
ejpam-3916	185	2	su	su	PROPN
ejpam-3916	185	3	=	=	NOUN
ejpam-3916	185	4	v	v	PROPN
ejpam-3916	185	5	(	(	PUNCT
ejpam-3916	185	6	g	g	NOUN
ejpam-3916	185	7	)	)	PUNCT
ejpam-3916	185	8	\	\	NOUN
ejpam-3916	185	9	{	{	PUNCT
ejpam-3916	185	10	u	u	NOUN
ejpam-3916	185	11	}	}	PUNCT
ejpam-3916	185	12	.	.	PUNCT
ejpam-3916	186	1	then	then	ADV
ejpam-3916	186	2	v	v	X
ejpam-3916	186	3	,	,	PUNCT
ejpam-3916	186	4	w	w	PROPN
ejpam-3916	186	5	∈	∈	PROPN
ejpam-3916	186	6	s	s	PROPN
ejpam-3916	186	7	,	,	PUNCT
ejpam-3916	186	8	uw	uw	PROPN
ejpam-3916	186	9	/∈	/∈	PUNCT
ejpam-3916	186	10	e(g	e(g	PROPN
ejpam-3916	186	11	)	)	PUNCT
ejpam-3916	186	12	,	,	PUNCT
ejpam-3916	186	13	uv	uv	PROPN
ejpam-3916	186	14	∈	∈	PROPN
ejpam-3916	186	15	e(g	e(g	PROPN
ejpam-3916	186	16	)	)	PUNCT
ejpam-3916	186	17	,	,	PUNCT
ejpam-3916	186	18	and	and	CCONJ
ejpam-3916	186	19	ng({u	ng({u	CCONJ
ejpam-3916	186	20	,	,	PUNCT
ejpam-3916	186	21	v	v	NOUN
ejpam-3916	186	22	}	}	PUNCT
ejpam-3916	186	23	)	)	PUNCT
ejpam-3916	186	24	6=	6=	X
ejpam-3916	186	25	v	v	X
ejpam-3916	186	26	(	(	PUNCT
ejpam-3916	186	27	g	g	NOUN
ejpam-3916	186	28	)	)	PUNCT
ejpam-3916	186	29	.	.	PUNCT
ejpam-3916	187	1	this	this	PRON
ejpam-3916	187	2	implies	imply	VERB
ejpam-3916	187	3	that	that	SCONJ
ejpam-3916	187	4	s	s	VERB
ejpam-3916	187	5	is	be	AUX
ejpam-3916	187	6	a	a	DET
ejpam-3916	187	7	pairwise	pairwise	NOUN
ejpam-3916	187	8	and	and	CCONJ
ejpam-3916	187	9	pointwise	pointwise	VERB
ejpam-3916	187	10	non	non	ADJ
ejpam-3916	187	11	-	-	ADJ
ejpam-3916	187	12	dominating	dominating	ADJ
ejpam-3916	187	13	set	set	NOUN
ejpam-3916	187	14	of	of	ADP
ejpam-3916	187	15	g.	g.	PROPN
ejpam-3916	187	16	hence	hence	ADV
ejpam-3916	187	17	,	,	PUNCT
ejpam-3916	187	18	γppnd(g	γppnd(g	ADJ
ejpam-3916	187	19	)	)	PUNCT
ejpam-3916	187	20	≤	≤	NUM
ejpam-3916	187	21	|s|	|s|	PROPN
ejpam-3916	187	22	=	=	PUNCT
ejpam-3916	187	23	n	n	CCONJ
ejpam-3916	187	24	−	−	PROPN
ejpam-3916	187	25	1	1	NUM
ejpam-3916	187	26	,	,	PUNCT
ejpam-3916	187	27	a	a	DET
ejpam-3916	187	28	contradiction	contradiction	NOUN
ejpam-3916	187	29	.	.	PUNCT
ejpam-3916	188	1	therefore	therefore	ADV
ejpam-3916	188	2	,	,	PUNCT
ejpam-3916	188	3	ng({u	ng({u	X
ejpam-3916	188	4	,	,	PUNCT
ejpam-3916	188	5	v	v	NOUN
ejpam-3916	188	6	}	}	PUNCT
ejpam-3916	188	7	)	)	PUNCT
ejpam-3916	188	8	=	=	SYM
ejpam-3916	188	9	v	v	X
ejpam-3916	188	10	(	(	PUNCT
ejpam-3916	188	11	g	g	NOUN
ejpam-3916	188	12	)	)	PUNCT
ejpam-3916	188	13	for	for	ADP
ejpam-3916	188	14	each	each	DET
ejpam-3916	188	15	pair	pair	NOUN
ejpam-3916	188	16	of	of	ADP
ejpam-3916	188	17	adjacent	adjacent	ADJ
ejpam-3916	188	18	vertices	vertex	NOUN
ejpam-3916	188	19	u	u	NOUN
ejpam-3916	188	20	,	,	PUNCT
ejpam-3916	188	21	v	v	NOUN
ejpam-3916	188	22	∈	∈	PROPN
ejpam-3916	188	23	v	v	NOUN
ejpam-3916	188	24	(	(	PUNCT
ejpam-3916	188	25	g	g	NOUN
ejpam-3916	188	26	)	)	PUNCT
ejpam-3916	188	27	.	.	PUNCT
ejpam-3916	189	1	for	for	ADP
ejpam-3916	189	2	the	the	DET
ejpam-3916	189	3	converse	converse	NOUN
ejpam-3916	189	4	,	,	PUNCT
ejpam-3916	189	5	suppose	suppose	VERB
ejpam-3916	189	6	first	first	ADV
ejpam-3916	189	7	that	that	SCONJ
ejpam-3916	189	8	g	g	PROPN
ejpam-3916	189	9	=	=	PROPN
ejpam-3916	189	10	kn	kn	PROPN
ejpam-3916	189	11	.	.	PUNCT
ejpam-3916	190	1	then	then	ADV
ejpam-3916	190	2	,	,	PUNCT
ejpam-3916	190	3	clearly	clearly	ADV
ejpam-3916	190	4	,	,	PUNCT
ejpam-3916	190	5	s	s	NOUN
ejpam-3916	190	6	=	=	SYM
ejpam-3916	190	7	v	v	X
ejpam-3916	190	8	(	(	PUNCT
ejpam-3916	190	9	g	g	NOUN
ejpam-3916	190	10	)	)	PUNCT
ejpam-3916	190	11	is	be	AUX
ejpam-3916	190	12	the	the	DET
ejpam-3916	190	13	only	only	ADJ
ejpam-3916	190	14	pairwise	pairwise	NOUN
ejpam-3916	190	15	and	and	CCONJ
ejpam-3916	190	16	pointwise	pointwise	VERB
ejpam-3916	190	17	non	non	ADJ
ejpam-3916	190	18	-	-	ADJ
ejpam-3916	190	19	dominating	dominating	ADJ
ejpam-3916	190	20	set	set	NOUN
ejpam-3916	190	21	of	of	ADP
ejpam-3916	190	22	g.	g.	PROPN
ejpam-3916	190	23	thus	thus	ADV
ejpam-3916	190	24	,	,	PUNCT
ejpam-3916	190	25	γppnd(g	γppnd(g	ADJ
ejpam-3916	190	26	)	)	PUNCT
ejpam-3916	190	27	=	=	VERB
ejpam-3916	191	1	n.	n.	PROPN
ejpam-3916	191	2	next	next	ADV
ejpam-3916	191	3	,	,	PUNCT
ejpam-3916	191	4	suppose	suppose	VERB
ejpam-3916	191	5	that	that	SCONJ
ejpam-3916	191	6	g	g	PROPN
ejpam-3916	191	7	is	be	AUX
ejpam-3916	191	8	connected	connect	VERB
ejpam-3916	191	9	and	and	CCONJ
ejpam-3916	191	10	satisfies	satisfy	VERB
ejpam-3916	191	11	the	the	DET
ejpam-3916	191	12	condition	condition	NOUN
ejpam-3916	191	13	that	that	SCONJ
ejpam-3916	191	14	ng({u	ng({u	ADJ
ejpam-3916	191	15	,	,	PUNCT
ejpam-3916	191	16	v	v	NOUN
ejpam-3916	191	17	}	}	PUNCT
ejpam-3916	191	18	)	)	PUNCT
ejpam-3916	191	19	=	=	SYM
ejpam-3916	191	20	v	v	X
ejpam-3916	191	21	(	(	PUNCT
ejpam-3916	191	22	g	g	NOUN
ejpam-3916	191	23	)	)	PUNCT
ejpam-3916	191	24	for	for	ADP
ejpam-3916	191	25	each	each	DET
ejpam-3916	191	26	pair	pair	NOUN
ejpam-3916	191	27	of	of	ADP
ejpam-3916	191	28	adjacent	adjacent	ADJ
ejpam-3916	191	29	vertices	vertex	NOUN
ejpam-3916	191	30	u	u	NOUN
ejpam-3916	191	31	,	,	PUNCT
ejpam-3916	191	32	v	v	NOUN
ejpam-3916	191	33	∈	∈	PROPN
ejpam-3916	191	34	v	v	NOUN
ejpam-3916	191	35	(	(	PUNCT
ejpam-3916	191	36	g	g	NOUN
ejpam-3916	191	37	)	)	PUNCT
ejpam-3916	191	38	.	.	PUNCT
ejpam-3916	192	1	let	let	VERB
ejpam-3916	192	2	s	s	PRON
ejpam-3916	192	3	be	be	AUX
ejpam-3916	192	4	a	a	DET
ejpam-3916	192	5	γppnd	γppnd	NOUN
ejpam-3916	192	6	-	-	PUNCT
ejpam-3916	192	7	set	set	VERB
ejpam-3916	192	8	and	and	CCONJ
ejpam-3916	192	9	suppose	suppose	VERB
ejpam-3916	192	10	that	that	SCONJ
ejpam-3916	192	11	there	there	PRON
ejpam-3916	192	12	exists	exist	VERB
ejpam-3916	192	13	w	w	PROPN
ejpam-3916	192	14	∈	∈	PROPN
ejpam-3916	192	15	v	v	ADP
ejpam-3916	192	16	(	(	PUNCT
ejpam-3916	192	17	g	g	NOUN
ejpam-3916	192	18	)	)	PUNCT
ejpam-3916	192	19	\	\	PUNCT
ejpam-3916	193	1	s.	s.	PROPN
ejpam-3916	193	2	then	then	ADV
ejpam-3916	193	3	there	there	PRON
ejpam-3916	193	4	exists	exist	VERB
ejpam-3916	193	5	q	q	PROPN
ejpam-3916	193	6	∈	∈	PROPN
ejpam-3916	193	7	s	s	X
ejpam-3916	193	8	∩ng(w	∩ng(w	NOUN
ejpam-3916	193	9	)	)	PUNCT
ejpam-3916	193	10	such	such	ADJ
ejpam-3916	193	11	that	that	PRON
ejpam-3916	193	12	ng({q	ng({q	PROPN
ejpam-3916	193	13	,	,	PUNCT
ejpam-3916	193	14	w	w	NOUN
ejpam-3916	193	15	}	}	PUNCT
ejpam-3916	193	16	)	)	PUNCT
ejpam-3916	193	17	6=	6=	X
ejpam-3916	193	18	v	v	X
ejpam-3916	193	19	(	(	PUNCT
ejpam-3916	193	20	g	g	NOUN
ejpam-3916	193	21	)	)	PUNCT
ejpam-3916	193	22	,	,	PUNCT
ejpam-3916	193	23	contrary	contrary	ADV
ejpam-3916	193	24	to	to	ADP
ejpam-3916	193	25	our	our	PRON
ejpam-3916	193	26	assumption	assumption	NOUN
ejpam-3916	193	27	.	.	PUNCT
ejpam-3916	194	1	therefore	therefore	ADV
ejpam-3916	194	2	,	,	PUNCT
ejpam-3916	194	3	s	s	NOUN
ejpam-3916	194	4	=	=	SYM
ejpam-3916	194	5	v	v	X
ejpam-3916	194	6	(	(	PUNCT
ejpam-3916	194	7	g	g	NOUN
ejpam-3916	194	8	)	)	PUNCT
ejpam-3916	194	9	and	and	CCONJ
ejpam-3916	194	10	γppnd(g	γppnd(g	ADJ
ejpam-3916	194	11	)	)	PUNCT
ejpam-3916	194	12	=	=	VERB
ejpam-3916	194	13	n.	n.	NOUN
ejpam-3916	194	14	g.	g.	PROPN
ejpam-3916	194	15	salasalan	salasalan	NOUN
ejpam-3916	194	16	,	,	PUNCT
ejpam-3916	194	17	s.	s.	PROPN
ejpam-3916	194	18	canoy	canoy	PROPN
ejpam-3916	194	19	,	,	PUNCT
ejpam-3916	194	20	jr	jr	PROPN
ejpam-3916	194	21	.	.	PROPN
ejpam-3916	194	22	/	/	SYM
ejpam-3916	194	23	eur	eur	PROPN
ejpam-3916	194	24	.	.	PUNCT
ejpam-3916	195	1	j.	j.	PROPN
ejpam-3916	195	2	pure	pure	PROPN
ejpam-3916	195	3	appl	appl	PROPN
ejpam-3916	195	4	.	.	PROPN
ejpam-3916	195	5	math	math	PROPN
ejpam-3916	195	6	,	,	PUNCT
ejpam-3916	195	7	14	14	NUM
ejpam-3916	195	8	(	(	PUNCT
ejpam-3916	195	9	1	1	NUM
ejpam-3916	195	10	)	)	PUNCT
ejpam-3916	195	11	(	(	PUNCT
ejpam-3916	195	12	2021	2021	NUM
ejpam-3916	195	13	)	)	PUNCT
ejpam-3916	195	14	,	,	PUNCT
ejpam-3916	195	15	112	112	NUM
ejpam-3916	195	16	-	-	SYM
ejpam-3916	195	17	125	125	NUM
ejpam-3916	195	18	117	117	NUM
ejpam-3916	195	19	theorem	theorem	NOUN
ejpam-3916	195	20	4	4	NUM
ejpam-3916	195	21	.	.	PUNCT
ejpam-3916	196	1	let	let	VERB
ejpam-3916	196	2	g	g	NOUN
ejpam-3916	196	3	and	and	CCONJ
ejpam-3916	196	4	h	h	NOUN
ejpam-3916	196	5	be	be	VERB
ejpam-3916	196	6	any	any	DET
ejpam-3916	196	7	two	two	NUM
ejpam-3916	196	8	graphs	graph	NOUN
ejpam-3916	196	9	.	.	PUNCT
ejpam-3916	197	1	a	a	DET
ejpam-3916	197	2	set	set	NOUN
ejpam-3916	197	3	s	s	NOUN
ejpam-3916	197	4	⊆	⊆	NUM
ejpam-3916	197	5	v	v	NOUN
ejpam-3916	197	6	(	(	PUNCT
ejpam-3916	197	7	g	g	PROPN
ejpam-3916	197	8	+	+	NOUN
ejpam-3916	197	9	h	h	NOUN
ejpam-3916	197	10	)	)	PUNCT
ejpam-3916	197	11	is	be	AUX
ejpam-3916	197	12	a	a	DET
ejpam-3916	197	13	global	global	ADJ
ejpam-3916	197	14	hop	hop	NOUN
ejpam-3916	197	15	dominating	dominating	NOUN
ejpam-3916	197	16	set	set	NOUN
ejpam-3916	197	17	of	of	ADP
ejpam-3916	197	18	g	g	PROPN
ejpam-3916	198	1	+	+	CCONJ
ejpam-3916	198	2	h	h	NOUN
ejpam-3916	198	3	if	if	SCONJ
ejpam-3916	198	4	and	and	CCONJ
ejpam-3916	198	5	only	only	ADV
ejpam-3916	198	6	if	if	SCONJ
ejpam-3916	198	7	s	s	VERB
ejpam-3916	198	8	=	=	PUNCT
ejpam-3916	198	9	sg	sg	PART
ejpam-3916	198	10	∪	∪	NOUN
ejpam-3916	198	11	sh	sh	PROPN
ejpam-3916	199	1	and	and	CCONJ
ejpam-3916	199	2	sg	sg	PROPN
ejpam-3916	200	1	and	and	CCONJ
ejpam-3916	200	2	sh	sh	PROPN
ejpam-3916	200	3	are	be	AUX
ejpam-3916	200	4	pairwise	pairwise	NOUN
ejpam-3916	200	5	and	and	CCONJ
ejpam-3916	200	6	pointwise	pointwise	VERB
ejpam-3916	200	7	non	non	ADJ
ejpam-3916	200	8	-	-	ADJ
ejpam-3916	200	9	dominating	dominating	ADJ
ejpam-3916	200	10	sets	set	NOUN
ejpam-3916	200	11	of	of	ADP
ejpam-3916	200	12	g	g	PROPN
ejpam-3916	200	13	and	and	CCONJ
ejpam-3916	200	14	h	h	NOUN
ejpam-3916	200	15	,	,	PUNCT
ejpam-3916	200	16	respectively	respectively	ADV
ejpam-3916	200	17	.	.	PUNCT
ejpam-3916	201	1	proof	proof	NOUN
ejpam-3916	201	2	.	.	PUNCT
ejpam-3916	202	1	suppose	suppose	VERB
ejpam-3916	202	2	s	s	PRON
ejpam-3916	202	3	is	be	AUX
ejpam-3916	202	4	a	a	DET
ejpam-3916	202	5	global	global	ADJ
ejpam-3916	202	6	hop	hop	NOUN
ejpam-3916	202	7	dominating	dominating	NOUN
ejpam-3916	202	8	set	set	NOUN
ejpam-3916	202	9	of	of	ADP
ejpam-3916	202	10	g+h	g+h	PROPN
ejpam-3916	202	11	.	.	PUNCT
ejpam-3916	203	1	let	let	VERB
ejpam-3916	203	2	sg	sg	VERB
ejpam-3916	203	3	=	=	SYM
ejpam-3916	203	4	s	s	PART
ejpam-3916	203	5	∩	∩	ADJ
ejpam-3916	203	6	v	v	X
ejpam-3916	203	7	(	(	PUNCT
ejpam-3916	203	8	g	g	NOUN
ejpam-3916	203	9	)	)	PUNCT
ejpam-3916	203	10	and	and	CCONJ
ejpam-3916	203	11	sh	sh	INTJ
ejpam-3916	203	12	=	=	SYM
ejpam-3916	203	13	s	s	PROPN
ejpam-3916	203	14	∩	∩	ADJ
ejpam-3916	203	15	v	v	ADJ
ejpam-3916	203	16	(	(	PUNCT
ejpam-3916	203	17	h	h	NOUN
ejpam-3916	203	18	)	)	PUNCT
ejpam-3916	203	19	.	.	PUNCT
ejpam-3916	204	1	since	since	SCONJ
ejpam-3916	204	2	s	s	PROPN
ejpam-3916	204	3	is	be	AUX
ejpam-3916	204	4	a	a	DET
ejpam-3916	204	5	hop	hop	NOUN
ejpam-3916	204	6	dominating	dominating	NOUN
ejpam-3916	204	7	set	set	NOUN
ejpam-3916	204	8	of	of	ADP
ejpam-3916	204	9	g	g	PROPN
ejpam-3916	204	10	+	+	CCONJ
ejpam-3916	204	11	h	h	NOUN
ejpam-3916	204	12	,	,	PUNCT
ejpam-3916	204	13	sg	sg	ADP
ejpam-3916	204	14	6=	6=	NOUN
ejpam-3916	204	15	∅	∅	NOUN
ejpam-3916	204	16	and	and	CCONJ
ejpam-3916	204	17	sh	sh	PROPN
ejpam-3916	204	18	6=	6=	NOUN
ejpam-3916	204	19	∅.	∅.	ADV
ejpam-3916	204	20	let	let	VERB
ejpam-3916	204	21	v	v	ADP
ejpam-3916	204	22	∈	∈	PROPN
ejpam-3916	204	23	v	v	NOUN
ejpam-3916	204	24	(	(	PUNCT
ejpam-3916	204	25	g	g	NOUN
ejpam-3916	204	26	)	)	PUNCT
ejpam-3916	204	27	\	\	PROPN
ejpam-3916	204	28	sg	sg	PROPN
ejpam-3916	204	29	.	.	PUNCT
ejpam-3916	205	1	since	since	SCONJ
ejpam-3916	205	2	s	s	PROPN
ejpam-3916	205	3	is	be	AUX
ejpam-3916	205	4	a	a	DET
ejpam-3916	205	5	hop	hop	NOUN
ejpam-3916	205	6	dominating	dominating	NOUN
ejpam-3916	205	7	set	set	NOUN
ejpam-3916	205	8	of	of	ADP
ejpam-3916	205	9	g+h	g+h	PROPN
ejpam-3916	205	10	,	,	PUNCT
ejpam-3916	205	11	there	there	PRON
ejpam-3916	205	12	exists	exist	VERB
ejpam-3916	205	13	u	u	PROPN
ejpam-3916	205	14	∈	∈	PROPN
ejpam-3916	205	15	sg	sg	ADP
ejpam-3916	205	16	such	such	ADJ
ejpam-3916	206	1	that	that	PRON
ejpam-3916	206	2	dg+h(u	dg+h(u	PROPN
ejpam-3916	206	3	,	,	PUNCT
ejpam-3916	206	4	v	v	NOUN
ejpam-3916	206	5	)	)	PUNCT
ejpam-3916	206	6	=	=	SYM
ejpam-3916	206	7	2	2	X
ejpam-3916	206	8	.	.	PUNCT
ejpam-3916	206	9	this	this	PRON
ejpam-3916	206	10	implies	imply	VERB
ejpam-3916	206	11	that	that	SCONJ
ejpam-3916	206	12	uv	uv	PROPN
ejpam-3916	206	13	/∈	/∈	PUNCT
ejpam-3916	206	14	e(g	e(g	PROPN
ejpam-3916	206	15	)	)	PUNCT
ejpam-3916	206	16	.	.	PUNCT
ejpam-3916	207	1	now	now	ADV
ejpam-3916	207	2	,	,	PUNCT
ejpam-3916	207	3	since	since	SCONJ
ejpam-3916	207	4	s	s	NOUN
ejpam-3916	207	5	is	be	AUX
ejpam-3916	207	6	also	also	ADV
ejpam-3916	207	7	a	a	DET
ejpam-3916	207	8	hop	hop	NOUN
ejpam-3916	207	9	dominating	dominating	NOUN
ejpam-3916	207	10	set	set	NOUN
ejpam-3916	207	11	of	of	ADP
ejpam-3916	207	12	g+h	g+h	PROPN
ejpam-3916	207	13	=	=	PUNCT
ejpam-3916	208	1	g	g	PROPN
ejpam-3916	208	2	∪	∪	ADP
ejpam-3916	208	3	h	h	NOUN
ejpam-3916	208	4	,	,	PUNCT
ejpam-3916	208	5	there	there	PRON
ejpam-3916	208	6	exists	exist	VERB
ejpam-3916	208	7	w	w	PROPN
ejpam-3916	208	8	∈	∈	PROPN
ejpam-3916	208	9	sg	sg	ADP
ejpam-3916	208	10	such	such	ADJ
ejpam-3916	208	11	that	that	SCONJ
ejpam-3916	208	12	dg+h(v	dg+h(v	PROPN
ejpam-3916	208	13	,	,	PUNCT
ejpam-3916	208	14	w	w	NOUN
ejpam-3916	208	15	)	)	PUNCT
ejpam-3916	208	16	=	=	SYM
ejpam-3916	208	17	dg(v	dg(v	X
ejpam-3916	208	18	,	,	PUNCT
ejpam-3916	208	19	w	w	NOUN
ejpam-3916	208	20	)	)	PUNCT
ejpam-3916	209	1	=	=	SYM
ejpam-3916	209	2	2	2	X
ejpam-3916	209	3	.	.	PUNCT
ejpam-3916	210	1	this	this	PRON
ejpam-3916	210	2	implies	imply	VERB
ejpam-3916	210	3	that	that	SCONJ
ejpam-3916	210	4	vw	vw	PROPN
ejpam-3916	210	5	∈	∈	PROPN
ejpam-3916	210	6	e(g	e(g	PROPN
ejpam-3916	210	7	)	)	PUNCT
ejpam-3916	210	8	and	and	CCONJ
ejpam-3916	210	9	there	there	PRON
ejpam-3916	210	10	exists	exist	VERB
ejpam-3916	210	11	z	z	PROPN
ejpam-3916	210	12	∈	∈	PROPN
ejpam-3916	210	13	v	v	ADP
ejpam-3916	210	14	(	(	PUNCT
ejpam-3916	210	15	g	g	NOUN
ejpam-3916	210	16	)	)	PUNCT
ejpam-3916	210	17	such	such	ADJ
ejpam-3916	210	18	that	that	SCONJ
ejpam-3916	210	19	z	z	PROPN
ejpam-3916	210	20	∈	∈	PROPN
ejpam-3916	210	21	ng(v	ng(v	NOUN
ejpam-3916	210	22	)	)	PUNCT
ejpam-3916	210	23	∩	∩	NOUN
ejpam-3916	210	24	ng(w	ng(w	NOUN
ejpam-3916	210	25	)	)	PUNCT
ejpam-3916	210	26	.	.	PUNCT
ejpam-3916	211	1	thus	thus	ADV
ejpam-3916	211	2	,	,	PUNCT
ejpam-3916	211	3	z	z	NOUN
ejpam-3916	211	4	/∈	/∈	SYM
ejpam-3916	211	5	ng({v	ng({v	NOUN
ejpam-3916	211	6	,	,	PUNCT
ejpam-3916	211	7	w	w	NOUN
ejpam-3916	211	8	}	}	PUNCT
ejpam-3916	211	9	)	)	PUNCT
ejpam-3916	211	10	,	,	PUNCT
ejpam-3916	211	11	showing	show	VERB
ejpam-3916	211	12	that	that	SCONJ
ejpam-3916	211	13	ng({v	ng({v	NOUN
ejpam-3916	211	14	,	,	PUNCT
ejpam-3916	211	15	w	w	NOUN
ejpam-3916	211	16	}	}	PUNCT
ejpam-3916	211	17	)	)	PUNCT
ejpam-3916	211	18	6=	6=	X
ejpam-3916	211	19	v	v	X
ejpam-3916	211	20	(	(	PUNCT
ejpam-3916	211	21	g	g	NOUN
ejpam-3916	211	22	)	)	PUNCT
ejpam-3916	211	23	.	.	PUNCT
ejpam-3916	212	1	therefore	therefore	ADV
ejpam-3916	212	2	,	,	PUNCT
ejpam-3916	212	3	sg	sg	PROPN
ejpam-3916	212	4	is	be	AUX
ejpam-3916	212	5	a	a	DET
ejpam-3916	212	6	pairwise	pairwise	NOUN
ejpam-3916	212	7	and	and	CCONJ
ejpam-3916	212	8	pointwise	pointwise	VERB
ejpam-3916	212	9	non	non	ADJ
ejpam-3916	212	10	-	-	ADJ
ejpam-3916	212	11	dominating	dominating	ADJ
ejpam-3916	212	12	set	set	NOUN
ejpam-3916	212	13	of	of	ADP
ejpam-3916	212	14	g.	g.	PROPN
ejpam-3916	212	15	similarly	similarly	ADV
ejpam-3916	212	16	,	,	PUNCT
ejpam-3916	212	17	sh	sh	PROPN
ejpam-3916	212	18	is	be	AUX
ejpam-3916	212	19	a	a	DET
ejpam-3916	212	20	pairwise	pairwise	NOUN
ejpam-3916	212	21	and	and	CCONJ
ejpam-3916	212	22	pointwise	pointwise	VERB
ejpam-3916	212	23	nondominating	nondominate	VERB
ejpam-3916	212	24	set	set	NOUN
ejpam-3916	212	25	of	of	ADP
ejpam-3916	212	26	h.	h.	PROPN
ejpam-3916	212	27	for	for	ADP
ejpam-3916	212	28	the	the	DET
ejpam-3916	212	29	converse	converse	NOUN
ejpam-3916	212	30	,	,	PUNCT
ejpam-3916	212	31	suppose	suppose	VERB
ejpam-3916	212	32	that	that	SCONJ
ejpam-3916	212	33	s	s	VERB
ejpam-3916	212	34	=	=	PUNCT
ejpam-3916	212	35	sg∪sh	sg∪sh	PROPN
ejpam-3916	212	36	and	and	CCONJ
ejpam-3916	212	37	sg	sg	PROPN
ejpam-3916	212	38	and	and	CCONJ
ejpam-3916	212	39	sh	sh	PROPN
ejpam-3916	212	40	are	be	AUX
ejpam-3916	212	41	pairwise	pairwise	NOUN
ejpam-3916	212	42	and	and	CCONJ
ejpam-3916	212	43	pointwise	pointwise	VERB
ejpam-3916	212	44	non	non	ADJ
ejpam-3916	212	45	-	-	ADJ
ejpam-3916	212	46	dominating	dominating	ADJ
ejpam-3916	212	47	sets	set	NOUN
ejpam-3916	212	48	of	of	ADP
ejpam-3916	212	49	g	g	PROPN
ejpam-3916	212	50	and	and	CCONJ
ejpam-3916	212	51	h	h	NOUN
ejpam-3916	212	52	,	,	PUNCT
ejpam-3916	212	53	respectively	respectively	ADV
ejpam-3916	212	54	.	.	PUNCT
ejpam-3916	213	1	let	let	VERB
ejpam-3916	213	2	v	v	NUM
ejpam-3916	213	3	∈	∈	PROPN
ejpam-3916	213	4	v	v	NOUN
ejpam-3916	213	5	(	(	PUNCT
ejpam-3916	213	6	g	g	PROPN
ejpam-3916	213	7	+	+	NOUN
ejpam-3916	213	8	h	h	NOUN
ejpam-3916	213	9	)	)	PUNCT
ejpam-3916	213	10	\	\	PUNCT
ejpam-3916	214	1	s.	s.	PROPN
ejpam-3916	214	2	suppose	suppose	VERB
ejpam-3916	214	3	,	,	PUNCT
ejpam-3916	214	4	without	without	ADP
ejpam-3916	214	5	loss	loss	NOUN
ejpam-3916	214	6	of	of	ADP
ejpam-3916	214	7	generality	generality	NOUN
ejpam-3916	214	8	,	,	PUNCT
ejpam-3916	214	9	that	that	DET
ejpam-3916	214	10	v	v	NUM
ejpam-3916	214	11	∈	∈	PROPN
ejpam-3916	214	12	v	v	NOUN
ejpam-3916	214	13	(	(	PUNCT
ejpam-3916	214	14	g)\sg	g)\sg	PROPN
ejpam-3916	214	15	.	.	PROPN
ejpam-3916	214	16	since	since	SCONJ
ejpam-3916	214	17	sg	sg	PROPN
ejpam-3916	214	18	is	be	AUX
ejpam-3916	214	19	a	a	DET
ejpam-3916	214	20	pairwise	pairwise	NOUN
ejpam-3916	214	21	and	and	CCONJ
ejpam-3916	214	22	pointwise	pointwise	VERB
ejpam-3916	214	23	non	non	ADJ
ejpam-3916	214	24	-	-	ADJ
ejpam-3916	214	25	dominating	dominating	ADJ
ejpam-3916	214	26	set	set	NOUN
ejpam-3916	214	27	of	of	ADP
ejpam-3916	214	28	g	g	NOUN
ejpam-3916	214	29	,	,	PUNCT
ejpam-3916	214	30	there	there	PRON
ejpam-3916	214	31	exist	exist	VERB
ejpam-3916	214	32	u	u	NOUN
ejpam-3916	214	33	,	,	PUNCT
ejpam-3916	214	34	w	w	PROPN
ejpam-3916	214	35	∈	∈	PROPN
ejpam-3916	214	36	sg	sg	ADP
ejpam-3916	214	37	⊆	⊆	NUM
ejpam-3916	214	38	s	s	NOUN
ejpam-3916	214	39	such	such	ADJ
ejpam-3916	214	40	that	that	DET
ejpam-3916	214	41	uv	uv	NOUN
ejpam-3916	214	42	/∈	/∈	PUNCT
ejpam-3916	214	43	e(g	e(g	PROPN
ejpam-3916	214	44	)	)	PUNCT
ejpam-3916	214	45	,	,	PUNCT
ejpam-3916	214	46	wv	wv	PROPN
ejpam-3916	214	47	∈	∈	PROPN
ejpam-3916	214	48	e(g	e(g	PROPN
ejpam-3916	214	49	)	)	PUNCT
ejpam-3916	214	50	,	,	PUNCT
ejpam-3916	214	51	and	and	CCONJ
ejpam-3916	214	52	ng({w	ng({w	ADV
ejpam-3916	214	53	,	,	PUNCT
ejpam-3916	214	54	v	v	NOUN
ejpam-3916	214	55	}	}	PUNCT
ejpam-3916	214	56	)	)	PUNCT
ejpam-3916	214	57	6=	6=	X
ejpam-3916	214	58	v	v	X
ejpam-3916	214	59	(	(	PUNCT
ejpam-3916	214	60	g	g	NOUN
ejpam-3916	214	61	)	)	PUNCT
ejpam-3916	214	62	.	.	PUNCT
ejpam-3916	215	1	it	it	PRON
ejpam-3916	215	2	follows	follow	VERB
ejpam-3916	215	3	that	that	SCONJ
ejpam-3916	215	4	dg+h(u	dg+h(u	PROPN
ejpam-3916	215	5	,	,	PUNCT
ejpam-3916	215	6	v	v	NOUN
ejpam-3916	215	7	)	)	PUNCT
ejpam-3916	215	8	=	=	SYM
ejpam-3916	215	9	2	2	NUM
ejpam-3916	215	10	and	and	CCONJ
ejpam-3916	215	11	dg+h(w	dg+h(w	PROPN
ejpam-3916	215	12	,	,	PUNCT
ejpam-3916	215	13	v	v	NOUN
ejpam-3916	215	14	)	)	PUNCT
ejpam-3916	215	15	=	=	SYM
ejpam-3916	215	16	dg(w	dg(w	X
ejpam-3916	215	17	,	,	PUNCT
ejpam-3916	215	18	v	v	NOUN
ejpam-3916	215	19	)	)	PUNCT
ejpam-3916	215	20	=	=	SYM
ejpam-3916	215	21	2	2	X
ejpam-3916	215	22	.	.	PUNCT
ejpam-3916	215	23	thus	thus	ADV
ejpam-3916	215	24	,	,	PUNCT
ejpam-3916	215	25	s	s	VERB
ejpam-3916	215	26	is	be	AUX
ejpam-3916	215	27	a	a	DET
ejpam-3916	215	28	global	global	ADJ
ejpam-3916	215	29	dominating	dominating	NOUN
ejpam-3916	215	30	set	set	NOUN
ejpam-3916	215	31	of	of	ADP
ejpam-3916	215	32	g+h	g+h	PROPN
ejpam-3916	215	33	.	.	PUNCT
ejpam-3916	216	1	the	the	DET
ejpam-3916	216	2	next	next	ADJ
ejpam-3916	216	3	result	result	NOUN
ejpam-3916	216	4	is	be	AUX
ejpam-3916	216	5	immediate	immediate	ADJ
ejpam-3916	216	6	from	from	ADP
ejpam-3916	216	7	theorem	theorem	ADJ
ejpam-3916	216	8	4	4	NUM
ejpam-3916	216	9	and	and	CCONJ
ejpam-3916	216	10	theorem	theorem	VERB
ejpam-3916	216	11	3(iii	3(iii	NUM
ejpam-3916	216	12	)	)	PUNCT
ejpam-3916	216	13	.	.	PUNCT
ejpam-3916	217	1	corollary	corollary	ADJ
ejpam-3916	217	2	2	2	NUM
ejpam-3916	217	3	.	.	PUNCT
ejpam-3916	218	1	let	let	VERB
ejpam-3916	218	2	g	g	NOUN
ejpam-3916	218	3	and	and	CCONJ
ejpam-3916	218	4	h	h	NOUN
ejpam-3916	218	5	be	be	VERB
ejpam-3916	218	6	any	any	DET
ejpam-3916	218	7	two	two	NUM
ejpam-3916	218	8	graphs	graph	NOUN
ejpam-3916	218	9	.	.	PUNCT
ejpam-3916	219	1	then	then	ADV
ejpam-3916	219	2	γgh(g+h	γgh(g+h	NOUN
ejpam-3916	219	3	)	)	PUNCT
ejpam-3916	219	4	=	=	PUNCT
ejpam-3916	220	1	γppnd(g)+γppnd(h	γppnd(g)+γppnd(h	PROPN
ejpam-3916	220	2	)	)	PUNCT
ejpam-3916	220	3	.	.	PUNCT
ejpam-3916	221	1	in	in	ADP
ejpam-3916	221	2	particular	particular	ADJ
ejpam-3916	221	3	,	,	PUNCT
ejpam-3916	221	4	(	(	PUNCT
ejpam-3916	221	5	i	i	NOUN
ejpam-3916	221	6	)	)	PUNCT
ejpam-3916	221	7	γgh(kn	γgh(kn	NOUN
ejpam-3916	222	1	+	+	NOUN
ejpam-3916	222	2	h	h	NOUN
ejpam-3916	222	3	)	)	PUNCT
ejpam-3916	222	4	=	=	PUNCT
ejpam-3916	222	5	n+	n+	PUNCT
ejpam-3916	223	1	γppnd(h	γppnd(h	NOUN
ejpam-3916	223	2	)	)	PUNCT
ejpam-3916	223	3	for	for	ADP
ejpam-3916	223	4	all	all	DET
ejpam-3916	223	5	integer	integer	NOUN
ejpam-3916	223	6	n	n	PRON
ejpam-3916	223	7	≥	≥	NOUN
ejpam-3916	223	8	1	1	NUM
ejpam-3916	223	9	,	,	PUNCT
ejpam-3916	223	10	and	and	CCONJ
ejpam-3916	223	11	(	(	PUNCT
ejpam-3916	223	12	ii	ii	NOUN
ejpam-3916	223	13	)	)	PUNCT
ejpam-3916	223	14	γgh(km	γgh(km	NOUN
ejpam-3916	223	15	,	,	PUNCT
ejpam-3916	223	16	n	n	CCONJ
ejpam-3916	223	17	)	)	PUNCT
ejpam-3916	223	18	=	=	SYM
ejpam-3916	224	1	m+	m+	NUM
ejpam-3916	224	2	n	n	PROPN
ejpam-3916	224	3	for	for	ADP
ejpam-3916	224	4	all	all	DET
ejpam-3916	224	5	positive	positive	ADJ
ejpam-3916	224	6	integers	integer	NOUN
ejpam-3916	224	7	m	m	VERB
ejpam-3916	224	8	and	and	CCONJ
ejpam-3916	224	9	n.	n.	VERB
ejpam-3916	224	10	the	the	DET
ejpam-3916	224	11	corona	corona	NOUN
ejpam-3916	224	12	of	of	ADP
ejpam-3916	224	13	graphs	graph	NOUN
ejpam-3916	224	14	g	g	PROPN
ejpam-3916	224	15	and	and	CCONJ
ejpam-3916	224	16	h	h	NOUN
ejpam-3916	224	17	,	,	PUNCT
ejpam-3916	224	18	denoted	denote	VERB
ejpam-3916	224	19	by	by	ADP
ejpam-3916	224	20	g	g	PROPN
ejpam-3916	224	21	◦	◦	NOUN
ejpam-3916	224	22	h	h	NOUN
ejpam-3916	224	23	,	,	PUNCT
ejpam-3916	224	24	is	be	AUX
ejpam-3916	224	25	the	the	DET
ejpam-3916	224	26	graph	graph	NOUN
ejpam-3916	224	27	obtained	obtain	VERB
ejpam-3916	224	28	from	from	ADP
ejpam-3916	224	29	g	g	NOUN
ejpam-3916	224	30	by	by	ADP
ejpam-3916	224	31	taking	take	VERB
ejpam-3916	224	32	a	a	DET
ejpam-3916	224	33	copy	copy	NOUN
ejpam-3916	224	34	hv	hv	PROPN
ejpam-3916	224	35	of	of	ADP
ejpam-3916	224	36	h	h	PROPN
ejpam-3916	224	37	and	and	CCONJ
ejpam-3916	224	38	forming	form	VERB
ejpam-3916	224	39	the	the	DET
ejpam-3916	224	40	join	join	NOUN
ejpam-3916	224	41	〈	〈	PROPN
ejpam-3916	224	42	v〉+hv	v〉+hv	NOUN
ejpam-3916	224	43	=	=	SYM
ejpam-3916	224	44	v	v	ADP
ejpam-3916	224	45	+	+	NOUN
ejpam-3916	224	46	hv	hv	NOUN
ejpam-3916	224	47	for	for	ADP
ejpam-3916	224	48	each	each	DET
ejpam-3916	224	49	v	v	NUM
ejpam-3916	224	50	∈	∈	PROPN
ejpam-3916	224	51	v	v	NOUN
ejpam-3916	224	52	(	(	PUNCT
ejpam-3916	224	53	g	g	NOUN
ejpam-3916	224	54	)	)	PUNCT
ejpam-3916	224	55	.	.	PUNCT
ejpam-3916	225	1	theorem	theorem	NOUN
ejpam-3916	225	2	5	5	NUM
ejpam-3916	225	3	.	.	PUNCT
ejpam-3916	226	1	let	let	VERB
ejpam-3916	226	2	g	g	PRON
ejpam-3916	226	3	be	be	AUX
ejpam-3916	226	4	a	a	DET
ejpam-3916	226	5	connected	connected	ADJ
ejpam-3916	226	6	non	non	ADJ
ejpam-3916	226	7	-	-	ADJ
ejpam-3916	226	8	trivial	trivial	ADJ
ejpam-3916	226	9	graph	graph	NOUN
ejpam-3916	226	10	and	and	CCONJ
ejpam-3916	226	11	let	let	VERB
ejpam-3916	226	12	h	h	NOUN
ejpam-3916	226	13	be	be	AUX
ejpam-3916	226	14	any	any	DET
ejpam-3916	226	15	graph	graph	NOUN
ejpam-3916	226	16	.	.	PUNCT
ejpam-3916	227	1	a	a	DET
ejpam-3916	227	2	set	set	NOUN
ejpam-3916	227	3	c	c	NOUN
ejpam-3916	227	4	⊆	⊆	NUM
ejpam-3916	227	5	v	v	NOUN
ejpam-3916	227	6	(	(	PUNCT
ejpam-3916	227	7	g	g	PROPN
ejpam-3916	227	8	◦	◦	NOUN
ejpam-3916	227	9	h	h	NOUN
ejpam-3916	227	10	)	)	PUNCT
ejpam-3916	227	11	is	be	AUX
ejpam-3916	227	12	a	a	DET
ejpam-3916	227	13	global	global	ADJ
ejpam-3916	227	14	hop	hop	NOUN
ejpam-3916	227	15	dominating	dominating	NOUN
ejpam-3916	227	16	set	set	NOUN
ejpam-3916	227	17	of	of	ADP
ejpam-3916	227	18	g	g	PROPN
ejpam-3916	227	19	◦	◦	NOUN
ejpam-3916	227	20	h	h	NOUN
ejpam-3916	227	21	if	if	SCONJ
ejpam-3916	228	1	and	and	CCONJ
ejpam-3916	228	2	only	only	ADV
ejpam-3916	228	3	if	if	SCONJ
ejpam-3916	228	4	c	c	PROPN
ejpam-3916	228	5	=	=	SYM
ejpam-3916	228	6	a∪	a∪	PROPN
ejpam-3916	228	7	(	(	PUNCT
ejpam-3916	228	8	∪v∈v	∪v∈v	X
ejpam-3916	228	9	(	(	PUNCT
ejpam-3916	228	10	g)sv	g)sv	PROPN
ejpam-3916	228	11	)	)	PUNCT
ejpam-3916	228	12	,	,	PUNCT
ejpam-3916	228	13	where	where	SCONJ
ejpam-3916	228	14	a	a	DET
ejpam-3916	228	15	⊆	⊆	NUM
ejpam-3916	228	16	v	v	NOUN
ejpam-3916	228	17	(	(	PUNCT
ejpam-3916	228	18	g	g	NOUN
ejpam-3916	228	19	)	)	PUNCT
ejpam-3916	228	20	,	,	PUNCT
ejpam-3916	228	21	sv	sv	PROPN
ejpam-3916	228	22	⊆	⊆	NUM
ejpam-3916	228	23	v	v	X
ejpam-3916	228	24	(	(	PUNCT
ejpam-3916	228	25	hv	hv	PROPN
ejpam-3916	228	26	)	)	PUNCT
ejpam-3916	228	27	for	for	ADP
ejpam-3916	228	28	each	each	DET
ejpam-3916	228	29	v	v	NUM
ejpam-3916	228	30	∈	∈	PROPN
ejpam-3916	228	31	v	v	NOUN
ejpam-3916	228	32	(	(	PUNCT
ejpam-3916	228	33	g	g	NOUN
ejpam-3916	228	34	)	)	PUNCT
ejpam-3916	228	35	and	and	CCONJ
ejpam-3916	228	36	satisfy	satisfy	VERB
ejpam-3916	228	37	the	the	DET
ejpam-3916	228	38	following	follow	VERB
ejpam-3916	228	39	properties	property	NOUN
ejpam-3916	228	40	:	:	PUNCT
ejpam-3916	228	41	(	(	PUNCT
ejpam-3916	228	42	i	i	NOUN
ejpam-3916	228	43	)	)	PUNCT
ejpam-3916	228	44	for	for	ADP
ejpam-3916	228	45	each	each	DET
ejpam-3916	228	46	w	w	PROPN
ejpam-3916	228	47	∈	∈	PROPN
ejpam-3916	228	48	v	v	ADP
ejpam-3916	228	49	(	(	PUNCT
ejpam-3916	228	50	g	g	NOUN
ejpam-3916	228	51	)	)	PUNCT
ejpam-3916	228	52	\	\	PROPN
ejpam-3916	229	1	a	a	PRON
ejpam-3916	229	2	,	,	PUNCT
ejpam-3916	229	3	there	there	PRON
ejpam-3916	229	4	exists	exist	VERB
ejpam-3916	229	5	xw	xw	PROPN
ejpam-3916	229	6	∈	∈	PROPN
ejpam-3916	229	7	a	a	PRON
ejpam-3916	229	8	with	with	ADP
ejpam-3916	229	9	dg(w	dg(w	NOUN
ejpam-3916	229	10	,	,	PUNCT
ejpam-3916	229	11	xw	xw	PROPN
ejpam-3916	229	12	)	)	PUNCT
ejpam-3916	230	1	=	=	SYM
ejpam-3916	230	2	2	2	NUM
ejpam-3916	230	3	or	or	CCONJ
ejpam-3916	230	4	there	there	PRON
ejpam-3916	230	5	exists	exist	VERB
ejpam-3916	230	6	y	y	PROPN
ejpam-3916	230	7	∈	∈	PROPN
ejpam-3916	230	8	v	v	ADP
ejpam-3916	230	9	(	(	PUNCT
ejpam-3916	230	10	g	g	NOUN
ejpam-3916	230	11	)	)	PUNCT
ejpam-3916	230	12	∩ng(w	∩ng(w	PROPN
ejpam-3916	230	13	)	)	PUNCT
ejpam-3916	230	14	with	with	ADP
ejpam-3916	230	15	sy	sy	PROPN
ejpam-3916	230	16	6=	6=	ADP
ejpam-3916	230	17	∅.	∅.	PROPN
ejpam-3916	230	18	(	(	PUNCT
ejpam-3916	230	19	ii	ii	NOUN
ejpam-3916	230	20	)	)	PUNCT
ejpam-3916	230	21	sv	sv	PROPN
ejpam-3916	230	22	is	be	AUX
ejpam-3916	230	23	a	a	DET
ejpam-3916	230	24	dominating	dominating	NOUN
ejpam-3916	230	25	set	set	NOUN
ejpam-3916	230	26	of	of	ADP
ejpam-3916	230	27	hv	hv	PROPN
ejpam-3916	230	28	for	for	ADP
ejpam-3916	230	29	each	each	DET
ejpam-3916	230	30	v	v	ADP
ejpam-3916	230	31	∈	∈	PROPN
ejpam-3916	230	32	ng(a	ng(a	NOUN
ejpam-3916	230	33	)	)	PUNCT
ejpam-3916	230	34	\a	\a	ADJ
ejpam-3916	230	35	.	.	PUNCT
ejpam-3916	231	1	(	(	PUNCT
ejpam-3916	231	2	iii	iii	X
ejpam-3916	231	3	)	)	PUNCT
ejpam-3916	231	4	sv	sv	PROPN
ejpam-3916	231	5	is	be	AUX
ejpam-3916	231	6	a	a	DET
ejpam-3916	231	7	pointwise	pointwise	ADJ
ejpam-3916	231	8	non	non	ADJ
ejpam-3916	231	9	-	-	ADJ
ejpam-3916	231	10	dominating	dominating	ADJ
ejpam-3916	231	11	set	set	NOUN
ejpam-3916	231	12	of	of	ADP
ejpam-3916	231	13	hv	hv	PROPN
ejpam-3916	231	14	for	for	ADP
ejpam-3916	231	15	each	each	DET
ejpam-3916	231	16	v	v	ADP
ejpam-3916	231	17	∈	∈	PROPN
ejpam-3916	231	18	a	a	DET
ejpam-3916	231	19	\ng(a	\ng(a	NOUN
ejpam-3916	231	20	)	)	PUNCT
ejpam-3916	231	21	.	.	PUNCT
ejpam-3916	232	1	(	(	PUNCT
ejpam-3916	232	2	iv	iv	X
ejpam-3916	232	3	)	)	PUNCT
ejpam-3916	232	4	sv	sv	PROPN
ejpam-3916	232	5	is	be	AUX
ejpam-3916	232	6	a	a	DET
ejpam-3916	232	7	dominating	dominating	NOUN
ejpam-3916	232	8	pointwise	pointwise	ADV
ejpam-3916	232	9	non	non	ADJ
ejpam-3916	232	10	-	-	ADJ
ejpam-3916	232	11	dominating	dominating	ADJ
ejpam-3916	232	12	set	set	NOUN
ejpam-3916	232	13	of	of	ADP
ejpam-3916	232	14	hv	hv	PROPN
ejpam-3916	232	15	for	for	ADP
ejpam-3916	232	16	each	each	DET
ejpam-3916	232	17	v	v	NUM
ejpam-3916	232	18	∈	∈	PROPN
ejpam-3916	232	19	v	v	NOUN
ejpam-3916	232	20	(	(	PUNCT
ejpam-3916	232	21	g	g	NOUN
ejpam-3916	232	22	)	)	PUNCT
ejpam-3916	232	23	\ng[a	\ng[a	NOUN
ejpam-3916	232	24	]	]	PUNCT
ejpam-3916	232	25	.	.	PUNCT
ejpam-3916	233	1	g.	g.	PROPN
ejpam-3916	233	2	salasalan	salasalan	PROPN
ejpam-3916	233	3	,	,	PUNCT
ejpam-3916	233	4	s.	s.	PROPN
ejpam-3916	233	5	canoy	canoy	PROPN
ejpam-3916	233	6	,	,	PUNCT
ejpam-3916	233	7	jr	jr	PROPN
ejpam-3916	233	8	.	.	PROPN
ejpam-3916	233	9	/	/	SYM
ejpam-3916	233	10	eur	eur	PROPN
ejpam-3916	233	11	.	.	PUNCT
ejpam-3916	234	1	j.	j.	PROPN
ejpam-3916	234	2	pure	pure	PROPN
ejpam-3916	234	3	appl	appl	PROPN
ejpam-3916	234	4	.	.	PROPN
ejpam-3916	234	5	math	math	PROPN
ejpam-3916	234	6	,	,	PUNCT
ejpam-3916	234	7	14	14	NUM
ejpam-3916	234	8	(	(	PUNCT
ejpam-3916	234	9	1	1	NUM
ejpam-3916	234	10	)	)	PUNCT
ejpam-3916	234	11	(	(	PUNCT
ejpam-3916	234	12	2021	2021	NUM
ejpam-3916	234	13	)	)	PUNCT
ejpam-3916	234	14	,	,	PUNCT
ejpam-3916	234	15	112	112	NUM
ejpam-3916	234	16	-	-	SYM
ejpam-3916	234	17	125	125	NUM
ejpam-3916	234	18	118	118	NUM
ejpam-3916	234	19	proof	proof	NOUN
ejpam-3916	234	20	.	.	PUNCT
ejpam-3916	235	1	suppose	suppose	VERB
ejpam-3916	235	2	c	c	NOUN
ejpam-3916	235	3	is	be	AUX
ejpam-3916	235	4	a	a	DET
ejpam-3916	235	5	global	global	ADJ
ejpam-3916	235	6	hop	hop	NOUN
ejpam-3916	235	7	dominating	dominating	NOUN
ejpam-3916	235	8	set	set	NOUN
ejpam-3916	235	9	of	of	ADP
ejpam-3916	235	10	g	g	PROPN
ejpam-3916	235	11	◦	◦	NOUN
ejpam-3916	235	12	h	h	NOUN
ejpam-3916	235	13	and	and	CCONJ
ejpam-3916	235	14	let	let	VERB
ejpam-3916	235	15	a	a	PRON
ejpam-3916	235	16	=	=	SYM
ejpam-3916	235	17	c	c	NOUN
ejpam-3916	235	18	∩	∩	X
ejpam-3916	235	19	v	v	X
ejpam-3916	235	20	(	(	PUNCT
ejpam-3916	235	21	g	g	NOUN
ejpam-3916	235	22	)	)	PUNCT
ejpam-3916	235	23	.	.	PUNCT
ejpam-3916	236	1	let	let	VERB
ejpam-3916	236	2	sv	sv	VERB
ejpam-3916	236	3	=	=	SYM
ejpam-3916	236	4	c	c	PROPN
ejpam-3916	236	5	∩	∩	X
ejpam-3916	236	6	v	v	X
ejpam-3916	236	7	(	(	PUNCT
ejpam-3916	236	8	hv	hv	PROPN
ejpam-3916	236	9	)	)	PUNCT
ejpam-3916	236	10	for	for	ADP
ejpam-3916	236	11	each	each	DET
ejpam-3916	236	12	v	v	NUM
ejpam-3916	236	13	∈	∈	PROPN
ejpam-3916	236	14	v	v	NOUN
ejpam-3916	236	15	(	(	PUNCT
ejpam-3916	236	16	g	g	NOUN
ejpam-3916	236	17	)	)	PUNCT
ejpam-3916	236	18	.	.	PUNCT
ejpam-3916	237	1	then	then	ADV
ejpam-3916	237	2	a	a	DET
ejpam-3916	237	3	⊆	⊆	NUM
ejpam-3916	237	4	v	v	NOUN
ejpam-3916	237	5	(	(	PUNCT
ejpam-3916	237	6	g	g	NOUN
ejpam-3916	237	7	)	)	PUNCT
ejpam-3916	237	8	,	,	PUNCT
ejpam-3916	237	9	sv	sv	PROPN
ejpam-3916	237	10	⊆	⊆	NUM
ejpam-3916	237	11	v	v	X
ejpam-3916	237	12	(	(	PUNCT
ejpam-3916	237	13	hv	hv	PROPN
ejpam-3916	237	14	)	)	PUNCT
ejpam-3916	237	15	for	for	ADP
ejpam-3916	237	16	each	each	DET
ejpam-3916	237	17	v	v	NUM
ejpam-3916	237	18	∈	∈	PROPN
ejpam-3916	237	19	v	v	NOUN
ejpam-3916	237	20	(	(	PUNCT
ejpam-3916	237	21	g	g	NOUN
ejpam-3916	237	22	)	)	PUNCT
ejpam-3916	237	23	,	,	PUNCT
ejpam-3916	237	24	and	and	CCONJ
ejpam-3916	237	25	c	c	X
ejpam-3916	237	26	=	=	NOUN
ejpam-3916	237	27	a	a	DET
ejpam-3916	237	28	∪	∪	X
ejpam-3916	237	29	(	(	PUNCT
ejpam-3916	237	30	∪v∈v	∪v∈v	X
ejpam-3916	237	31	(	(	PUNCT
ejpam-3916	237	32	g)sv	g)sv	PROPN
ejpam-3916	237	33	)	)	PUNCT
ejpam-3916	237	34	.	.	PUNCT
ejpam-3916	238	1	now	now	ADV
ejpam-3916	238	2	,	,	PUNCT
ejpam-3916	238	3	since	since	SCONJ
ejpam-3916	238	4	c	c	PROPN
ejpam-3916	238	5	is	be	AUX
ejpam-3916	238	6	a	a	DET
ejpam-3916	238	7	hop	hop	NOUN
ejpam-3916	238	8	dominating	dominating	NOUN
ejpam-3916	238	9	set	set	NOUN
ejpam-3916	238	10	of	of	ADP
ejpam-3916	238	11	g	g	NOUN
ejpam-3916	238	12	,	,	PUNCT
ejpam-3916	238	13	(	(	PUNCT
ejpam-3916	238	14	i	i	NOUN
ejpam-3916	238	15	)	)	PUNCT
ejpam-3916	238	16	holds	hold	VERB
ejpam-3916	238	17	.	.	PUNCT
ejpam-3916	239	1	next	next	ADV
ejpam-3916	239	2	,	,	PUNCT
ejpam-3916	239	3	let	let	VERB
ejpam-3916	239	4	v	v	NUM
ejpam-3916	239	5	∈	∈	PROPN
ejpam-3916	239	6	v	v	NOUN
ejpam-3916	239	7	(	(	PUNCT
ejpam-3916	239	8	g	g	NOUN
ejpam-3916	239	9	)	)	PUNCT
ejpam-3916	239	10	and	and	CCONJ
ejpam-3916	239	11	consider	consider	VERB
ejpam-3916	239	12	the	the	DET
ejpam-3916	239	13	following	follow	VERB
ejpam-3916	239	14	cases	case	NOUN
ejpam-3916	239	15	:	:	PUNCT
ejpam-3916	239	16	case	case	NOUN
ejpam-3916	239	17	1	1	NUM
ejpam-3916	239	18	:	:	SYM
ejpam-3916	239	19	v	v	NUM
ejpam-3916	239	20	∈	∈	PROPN
ejpam-3916	239	21	ng(a	ng(a	NOUN
ejpam-3916	239	22	)	)	PUNCT
ejpam-3916	239	23	\a	\a	VERB
ejpam-3916	239	24	let	let	VERB
ejpam-3916	239	25	x	x	SYM
ejpam-3916	239	26	∈	∈	PROPN
ejpam-3916	239	27	v	v	ADP
ejpam-3916	239	28	(	(	PUNCT
ejpam-3916	239	29	hv	hv	PROPN
ejpam-3916	239	30	)	)	PUNCT
ejpam-3916	239	31	\	\	PROPN
ejpam-3916	240	1	sv	sv	PROPN
ejpam-3916	240	2	.	.	PUNCT
ejpam-3916	241	1	since	since	SCONJ
ejpam-3916	241	2	c	c	PROPN
ejpam-3916	241	3	is	be	AUX
ejpam-3916	241	4	hop	hop	NOUN
ejpam-3916	241	5	dominating	dominate	VERB
ejpam-3916	241	6	set	set	NOUN
ejpam-3916	241	7	of	of	ADP
ejpam-3916	241	8	g	g	PROPN
ejpam-3916	241	9	◦	◦	NOUN
ejpam-3916	241	10	h	h	NOUN
ejpam-3916	241	11	,	,	PUNCT
ejpam-3916	241	12	there	there	PRON
ejpam-3916	241	13	exists	exist	VERB
ejpam-3916	241	14	y	y	PROPN
ejpam-3916	241	15	∈	∈	PROPN
ejpam-3916	241	16	c	c	PROPN
ejpam-3916	241	17	such	such	ADJ
ejpam-3916	241	18	that	that	SCONJ
ejpam-3916	241	19	dg	dg	VERB
ejpam-3916	241	20	◦	◦	NOUN
ejpam-3916	241	21	h(x	h(x	PROPN
ejpam-3916	241	22	,	,	PUNCT
ejpam-3916	241	23	y	y	PROPN
ejpam-3916	241	24	)	)	PUNCT
ejpam-3916	241	25	=	=	SYM
ejpam-3916	242	1	2	2	X
ejpam-3916	242	2	.	.	PUNCT
ejpam-3916	242	3	since	since	SCONJ
ejpam-3916	242	4	v	v	NUM
ejpam-3916	242	5	/∈	/∈	PUNCT
ejpam-3916	242	6	a	a	PRON
ejpam-3916	242	7	and	and	CCONJ
ejpam-3916	242	8	v	v	NOUN
ejpam-3916	242	9	(	(	PUNCT
ejpam-3916	242	10	g	g	PROPN
ejpam-3916	242	11	◦	◦	NOUN
ejpam-3916	242	12	h	h	NOUN
ejpam-3916	242	13	)	)	PUNCT
ejpam-3916	243	1	\	\	PROPN
ejpam-3916	243	2	v	v	X
ejpam-3916	243	3	(	(	PUNCT
ejpam-3916	243	4	v	v	NOUN
ejpam-3916	243	5	+	+	CCONJ
ejpam-3916	243	6	hv	hv	PROPN
ejpam-3916	243	7	)	)	PUNCT
ejpam-3916	243	8	⊆	⊆	NUM
ejpam-3916	243	9	ng	ng	PROPN
ejpam-3916	243	10	◦	◦	NOUN
ejpam-3916	243	11	h(x	h(x	PROPN
ejpam-3916	243	12	)	)	PUNCT
ejpam-3916	244	1	,	,	PUNCT
ejpam-3916	244	2	it	it	PRON
ejpam-3916	244	3	follows	follow	VERB
ejpam-3916	244	4	that	that	SCONJ
ejpam-3916	244	5	y	y	PROPN
ejpam-3916	244	6	∈	∈	PROPN
ejpam-3916	244	7	sv	sv	PROPN
ejpam-3916	244	8	.	.	PUNCT
ejpam-3916	245	1	thus	thus	ADV
ejpam-3916	245	2	,	,	PUNCT
ejpam-3916	245	3	y	y	PROPN
ejpam-3916	245	4	∈	∈	PROPN
ejpam-3916	245	5	sv	sv	PROPN
ejpam-3916	245	6	∩	∩	PROPN
ejpam-3916	245	7	nhv(x	nhv(x	PROPN
ejpam-3916	245	8	)	)	PUNCT
ejpam-3916	245	9	,	,	PUNCT
ejpam-3916	245	10	showing	show	VERB
ejpam-3916	245	11	that	that	SCONJ
ejpam-3916	245	12	sv	sv	PROPN
ejpam-3916	245	13	is	be	AUX
ejpam-3916	245	14	a	a	DET
ejpam-3916	245	15	dominating	dominating	NOUN
ejpam-3916	245	16	set	set	NOUN
ejpam-3916	245	17	of	of	ADP
ejpam-3916	245	18	hv	hv	PROPN
ejpam-3916	245	19	.	.	PUNCT
ejpam-3916	246	1	therefore	therefore	ADV
ejpam-3916	246	2	,	,	PUNCT
ejpam-3916	246	3	(	(	PUNCT
ejpam-3916	246	4	ii	ii	NOUN
ejpam-3916	246	5	)	)	PUNCT
ejpam-3916	246	6	holds	hold	VERB
ejpam-3916	246	7	.	.	PUNCT
ejpam-3916	247	1	case	case	NOUN
ejpam-3916	247	2	2	2	NUM
ejpam-3916	247	3	:	:	SYM
ejpam-3916	247	4	v	v	NUM
ejpam-3916	247	5	∈	∈	PROPN
ejpam-3916	247	6	a	a	DET
ejpam-3916	247	7	\ng(a	\ng(a	NOUN
ejpam-3916	247	8	)	)	PUNCT
ejpam-3916	247	9	let	let	VERB
ejpam-3916	247	10	w	w	PROPN
ejpam-3916	247	11	∈	∈	VERB
ejpam-3916	247	12	a	a	DET
ejpam-3916	247	13	\ng(a	\ng(a	NOUN
ejpam-3916	247	14	)	)	PUNCT
ejpam-3916	247	15	and	and	CCONJ
ejpam-3916	247	16	let	let	VERB
ejpam-3916	247	17	q	q	PROPN
ejpam-3916	247	18	∈	∈	PROPN
ejpam-3916	247	19	v	v	ADP
ejpam-3916	247	20	(	(	PUNCT
ejpam-3916	247	21	hv	hv	NOUN
ejpam-3916	247	22	)	)	PUNCT
ejpam-3916	247	23	\sv	\sv	PROPN
ejpam-3916	247	24	.	.	PUNCT
ejpam-3916	248	1	since	since	SCONJ
ejpam-3916	248	2	c	c	PROPN
ejpam-3916	248	3	is	be	AUX
ejpam-3916	248	4	a	a	DET
ejpam-3916	248	5	hop	hop	NOUN
ejpam-3916	248	6	dominating	dominating	NOUN
ejpam-3916	248	7	set	set	NOUN
ejpam-3916	248	8	of	of	ADP
ejpam-3916	248	9	g	g	PROPN
ejpam-3916	248	10	◦	◦	NOUN
ejpam-3916	248	11	h	h	NOUN
ejpam-3916	248	12	,	,	PUNCT
ejpam-3916	248	13	there	there	PRON
ejpam-3916	248	14	exists	exist	VERB
ejpam-3916	248	15	u	u	PROPN
ejpam-3916	248	16	∈	∈	PROPN
ejpam-3916	248	17	c	c	NOUN
ejpam-3916	248	18	such	such	ADJ
ejpam-3916	248	19	that	that	SCONJ
ejpam-3916	248	20	dg	dg	VERB
ejpam-3916	248	21	◦	◦	NOUN
ejpam-3916	248	22	h(q	h(q	ADJ
ejpam-3916	248	23	,	,	PUNCT
ejpam-3916	248	24	u	u	NOUN
ejpam-3916	248	25	)	)	PUNCT
ejpam-3916	248	26	=	=	SYM
ejpam-3916	248	27	2	2	X
ejpam-3916	248	28	.	.	PUNCT
ejpam-3916	248	29	by	by	ADP
ejpam-3916	248	30	assumption	assumption	NOUN
ejpam-3916	248	31	,	,	PUNCT
ejpam-3916	248	32	u	u	NOUN
ejpam-3916	248	33	/∈	/∈	NOUN
ejpam-3916	248	34	a.	a.	PROPN
ejpam-3916	248	35	thus	thus	ADV
ejpam-3916	248	36	,	,	PUNCT
ejpam-3916	248	37	u	u	PROPN
ejpam-3916	248	38	∈	∈	PROPN
ejpam-3916	248	39	sv	sv	NOUN
ejpam-3916	248	40	and	and	CCONJ
ejpam-3916	248	41	qu	qu	PROPN
ejpam-3916	248	42	/∈	/∈	PUNCT
ejpam-3916	248	43	e(hv	e(hv	PROPN
ejpam-3916	248	44	)	)	PUNCT
ejpam-3916	248	45	.	.	PUNCT
ejpam-3916	249	1	therefore	therefore	ADV
ejpam-3916	249	2	sv	sv	PROPN
ejpam-3916	249	3	is	be	AUX
ejpam-3916	249	4	a	a	DET
ejpam-3916	249	5	pointwise	pointwise	ADJ
ejpam-3916	249	6	non	non	ADJ
ejpam-3916	249	7	-	-	ADJ
ejpam-3916	249	8	dominating	dominating	ADJ
ejpam-3916	249	9	set	set	NOUN
ejpam-3916	249	10	of	of	ADP
ejpam-3916	249	11	hv	hv	PROPN
ejpam-3916	249	12	,	,	PUNCT
ejpam-3916	249	13	showing	show	VERB
ejpam-3916	249	14	that	that	SCONJ
ejpam-3916	249	15	(	(	PUNCT
ejpam-3916	249	16	iii	iii	NOUN
ejpam-3916	249	17	)	)	PUNCT
ejpam-3916	249	18	holds	hold	VERB
ejpam-3916	249	19	.	.	PUNCT
ejpam-3916	250	1	case	case	NOUN
ejpam-3916	250	2	3	3	NUM
ejpam-3916	250	3	:	:	SYM
ejpam-3916	250	4	v	v	NUM
ejpam-3916	250	5	∈	∈	PROPN
ejpam-3916	250	6	v	v	NOUN
ejpam-3916	250	7	(	(	PUNCT
ejpam-3916	250	8	g	g	NOUN
ejpam-3916	250	9	)	)	PUNCT
ejpam-3916	250	10	\ng[a	\ng[a	NOUN
ejpam-3916	250	11	]	]	PUNCT
ejpam-3916	250	12	since	since	SCONJ
ejpam-3916	250	13	v	v	NUM
ejpam-3916	250	14	/∈	/∈	PUNCT
ejpam-3916	251	1	a	a	PRON
ejpam-3916	251	2	and	and	CCONJ
ejpam-3916	251	3	c	c	PROPN
ejpam-3916	251	4	is	be	AUX
ejpam-3916	251	5	a	a	DET
ejpam-3916	251	6	hop	hop	NOUN
ejpam-3916	251	7	dominating	dominating	NOUN
ejpam-3916	251	8	set	set	NOUN
ejpam-3916	251	9	of	of	ADP
ejpam-3916	251	10	g	g	NOUN
ejpam-3916	251	11	,	,	PUNCT
ejpam-3916	251	12	similar	similar	ADJ
ejpam-3916	251	13	arguments	argument	NOUN
ejpam-3916	251	14	in	in	ADP
ejpam-3916	251	15	case	case	NOUN
ejpam-3916	251	16	1	1	NUM
ejpam-3916	251	17	will	will	AUX
ejpam-3916	251	18	show	show	VERB
ejpam-3916	251	19	that	that	SCONJ
ejpam-3916	251	20	sv	sv	PROPN
ejpam-3916	251	21	is	be	AUX
ejpam-3916	251	22	a	a	DET
ejpam-3916	251	23	dominating	dominating	NOUN
ejpam-3916	251	24	set	set	NOUN
ejpam-3916	251	25	of	of	ADP
ejpam-3916	251	26	hv	hv	PROPN
ejpam-3916	251	27	.	.	PUNCT
ejpam-3916	252	1	further	far	ADV
ejpam-3916	252	2	,	,	PUNCT
ejpam-3916	252	3	since	since	SCONJ
ejpam-3916	252	4	v	v	NUM
ejpam-3916	252	5	/∈	/∈	PUNCT
ejpam-3916	252	6	ng(a	ng(a	NUM
ejpam-3916	252	7	)	)	PUNCT
ejpam-3916	252	8	,	,	PUNCT
ejpam-3916	252	9	the	the	DET
ejpam-3916	252	10	arguments	argument	NOUN
ejpam-3916	252	11	in	in	ADP
ejpam-3916	252	12	case	case	NOUN
ejpam-3916	252	13	2	2	NUM
ejpam-3916	252	14	can	can	AUX
ejpam-3916	252	15	be	be	AUX
ejpam-3916	252	16	used	use	VERB
ejpam-3916	252	17	to	to	PART
ejpam-3916	252	18	show	show	VERB
ejpam-3916	252	19	that	that	SCONJ
ejpam-3916	252	20	sv	sv	PROPN
ejpam-3916	252	21	is	be	AUX
ejpam-3916	252	22	a	a	DET
ejpam-3916	252	23	pointwise	pointwise	ADJ
ejpam-3916	252	24	non	non	ADJ
ejpam-3916	252	25	-	-	ADJ
ejpam-3916	252	26	dominating	dominating	ADJ
ejpam-3916	252	27	set	set	NOUN
ejpam-3916	252	28	of	of	ADP
ejpam-3916	252	29	hv	hv	PROPN
ejpam-3916	252	30	,	,	PUNCT
ejpam-3916	252	31	showing	show	VERB
ejpam-3916	252	32	that	that	SCONJ
ejpam-3916	252	33	(	(	PUNCT
ejpam-3916	252	34	iv	iv	X
ejpam-3916	252	35	)	)	PUNCT
ejpam-3916	252	36	holds	hold	NOUN
ejpam-3916	252	37	.	.	PUNCT
ejpam-3916	253	1	for	for	ADP
ejpam-3916	253	2	the	the	DET
ejpam-3916	253	3	converse	converse	NOUN
ejpam-3916	253	4	,	,	PUNCT
ejpam-3916	253	5	suppose	suppose	VERB
ejpam-3916	253	6	that	that	SCONJ
ejpam-3916	253	7	c	c	PROPN
ejpam-3916	253	8	has	have	VERB
ejpam-3916	253	9	the	the	DET
ejpam-3916	253	10	given	give	VERB
ejpam-3916	253	11	form	form	NOUN
ejpam-3916	253	12	and	and	CCONJ
ejpam-3916	253	13	satisfies	satisfie	NOUN
ejpam-3916	253	14	properties	property	NOUN
ejpam-3916	253	15	(	(	PUNCT
ejpam-3916	253	16	i	i	NOUN
ejpam-3916	253	17	)	)	PUNCT
ejpam-3916	253	18	,	,	PUNCT
ejpam-3916	253	19	(	(	PUNCT
ejpam-3916	253	20	ii	ii	NOUN
ejpam-3916	253	21	)	)	PUNCT
ejpam-3916	253	22	,	,	PUNCT
ejpam-3916	253	23	(	(	PUNCT
ejpam-3916	253	24	iii	iii	NOUN
ejpam-3916	253	25	)	)	PUNCT
ejpam-3916	253	26	,	,	PUNCT
ejpam-3916	253	27	and	and	CCONJ
ejpam-3916	253	28	(	(	PUNCT
ejpam-3916	253	29	iv	iv	X
ejpam-3916	253	30	)	)	PUNCT
ejpam-3916	253	31	.	.	PUNCT
ejpam-3916	254	1	next	next	ADV
ejpam-3916	254	2	,	,	PUNCT
ejpam-3916	254	3	let	let	VERB
ejpam-3916	254	4	z	z	NOUN
ejpam-3916	254	5	∈	∈	PROPN
ejpam-3916	254	6	v	v	NOUN
ejpam-3916	254	7	(	(	PUNCT
ejpam-3916	254	8	g	g	PROPN
ejpam-3916	254	9	◦	◦	NOUN
ejpam-3916	254	10	h	h	NOUN
ejpam-3916	254	11	)	)	PUNCT
ejpam-3916	254	12	\	\	NOUN
ejpam-3916	255	1	c	c	NOUN
ejpam-3916	255	2	=	=	SYM
ejpam-3916	255	3	v	v	PROPN
ejpam-3916	255	4	(	(	PUNCT
ejpam-3916	255	5	g	g	PROPN
ejpam-3916	255	6	◦	◦	NOUN
ejpam-3916	255	7	h	h	NOUN
ejpam-3916	255	8	)	)	PUNCT
ejpam-3916	255	9	\	\	NOUN
ejpam-3916	255	10	c	c	NOUN
ejpam-3916	255	11	and	and	CCONJ
ejpam-3916	255	12	let	let	VERB
ejpam-3916	255	13	v	v	NUM
ejpam-3916	255	14	∈	∈	PROPN
ejpam-3916	255	15	v	v	NOUN
ejpam-3916	255	16	(	(	PUNCT
ejpam-3916	255	17	g	g	NOUN
ejpam-3916	255	18	)	)	PUNCT
ejpam-3916	255	19	such	such	ADJ
ejpam-3916	255	20	that	that	SCONJ
ejpam-3916	255	21	z	z	PROPN
ejpam-3916	255	22	∈	∈	PROPN
ejpam-3916	255	23	v	v	NOUN
ejpam-3916	255	24	(	(	PUNCT
ejpam-3916	255	25	v	v	PROPN
ejpam-3916	255	26	+	+	PROPN
ejpam-3916	255	27	hv	hv	NOUN
ejpam-3916	255	28	)	)	PUNCT
ejpam-3916	255	29	.	.	PUNCT
ejpam-3916	256	1	consider	consider	VERB
ejpam-3916	256	2	the	the	DET
ejpam-3916	256	3	following	follow	VERB
ejpam-3916	256	4	cases	case	NOUN
ejpam-3916	256	5	:	:	PUNCT
ejpam-3916	256	6	case	case	NOUN
ejpam-3916	256	7	1	1	NUM
ejpam-3916	256	8	.	.	PUNCT
ejpam-3916	257	1	z	z	NOUN
ejpam-3916	257	2	=	=	NOUN
ejpam-3916	257	3	v	v	NOUN
ejpam-3916	257	4	then	then	ADV
ejpam-3916	257	5	there	there	PRON
ejpam-3916	257	6	exists	exist	VERB
ejpam-3916	257	7	h	h	NOUN
ejpam-3916	257	8	∈	∈	PROPN
ejpam-3916	257	9	c	c	PROPN
ejpam-3916	257	10	such	such	ADJ
ejpam-3916	257	11	that	that	SCONJ
ejpam-3916	257	12	dg	dg	AUX
ejpam-3916	257	13	◦	◦	NOUN
ejpam-3916	257	14	h(z	h(z	NOUN
ejpam-3916	257	15	,	,	PUNCT
ejpam-3916	257	16	h	h	NOUN
ejpam-3916	257	17	)	)	PUNCT
ejpam-3916	257	18	=	=	SYM
ejpam-3916	257	19	2	2	NUM
ejpam-3916	257	20	,	,	PUNCT
ejpam-3916	257	21	by	by	ADP
ejpam-3916	257	22	(	(	PUNCT
ejpam-3916	257	23	i	i	NOUN
ejpam-3916	257	24	)	)	PUNCT
ejpam-3916	257	25	.	.	PUNCT
ejpam-3916	258	1	now	now	ADV
ejpam-3916	258	2	,	,	PUNCT
ejpam-3916	258	3	from	from	ADP
ejpam-3916	258	4	the	the	DET
ejpam-3916	258	5	assumption	assumption	NOUN
ejpam-3916	258	6	that	that	SCONJ
ejpam-3916	258	7	(	(	PUNCT
ejpam-3916	258	8	ii	ii	NOUN
ejpam-3916	258	9	)	)	PUNCT
ejpam-3916	258	10	and	and	CCONJ
ejpam-3916	258	11	(	(	PUNCT
ejpam-3916	258	12	iv	iv	X
ejpam-3916	258	13	)	)	PUNCT
ejpam-3916	258	14	hold	hold	NOUN
ejpam-3916	258	15	,	,	PUNCT
ejpam-3916	258	16	it	it	PRON
ejpam-3916	258	17	follows	follow	VERB
ejpam-3916	258	18	that	that	SCONJ
ejpam-3916	258	19	sz	sz	PROPN
ejpam-3916	258	20	6=	6=	AUX
ejpam-3916	258	21	∅.	∅.	AUX
ejpam-3916	258	22	pick	pick	VERB
ejpam-3916	258	23	any	any	DET
ejpam-3916	258	24	p	p	PROPN
ejpam-3916	258	25	∈	∈	PROPN
ejpam-3916	258	26	sz	sz	PROPN
ejpam-3916	258	27	and	and	CCONJ
ejpam-3916	258	28	y	y	PROPN
ejpam-3916	258	29	∈	∈	PROPN
ejpam-3916	258	30	v	v	ADP
ejpam-3916	258	31	(	(	PUNCT
ejpam-3916	258	32	hw	hw	NOUN
ejpam-3916	258	33	)	)	PUNCT
ejpam-3916	258	34	,	,	PUNCT
ejpam-3916	258	35	where	where	SCONJ
ejpam-3916	258	36	w	w	PROPN
ejpam-3916	258	37	∈	∈	PROPN
ejpam-3916	258	38	v	v	ADP
ejpam-3916	258	39	(	(	PUNCT
ejpam-3916	258	40	g	g	NOUN
ejpam-3916	258	41	)	)	PUNCT
ejpam-3916	258	42	∩ng(z	∩ng(z	PROPN
ejpam-3916	258	43	)	)	PUNCT
ejpam-3916	258	44	.	.	PUNCT
ejpam-3916	259	1	then	then	ADV
ejpam-3916	259	2	zy	zy	PROPN
ejpam-3916	259	3	,	,	PUNCT
ejpam-3916	259	4	yp	yp	PROPN
ejpam-3916	259	5	∈	∈	PROPN
ejpam-3916	259	6	e(g	e(g	PROPN
ejpam-3916	259	7	◦	◦	PROPN
ejpam-3916	259	8	h	h	NOUN
ejpam-3916	259	9	)	)	PUNCT
ejpam-3916	259	10	;	;	PUNCT
ejpam-3916	259	11	hence	hence	ADV
ejpam-3916	259	12	,	,	PUNCT
ejpam-3916	259	13	dg	dg	X
ejpam-3916	259	14	◦	◦	NOUN
ejpam-3916	259	15	h(z	h(z	NOUN
ejpam-3916	259	16	,	,	PUNCT
ejpam-3916	259	17	p	p	NOUN
ejpam-3916	259	18	)	)	PUNCT
ejpam-3916	259	19	=	=	SYM
ejpam-3916	259	20	2	2	X
ejpam-3916	259	21	.	.	X
ejpam-3916	259	22	case	case	NOUN
ejpam-3916	259	23	2	2	NUM
ejpam-3916	259	24	.	.	PUNCT
ejpam-3916	259	25	z	z	NOUN
ejpam-3916	260	1	6=	6=	ADP
ejpam-3916	260	2	v	v	ADP
ejpam-3916	260	3	then	then	ADV
ejpam-3916	260	4	z	z	PROPN
ejpam-3916	260	5	∈	∈	PROPN
ejpam-3916	260	6	v	v	ADP
ejpam-3916	260	7	(	(	PUNCT
ejpam-3916	260	8	hv	hv	PROPN
ejpam-3916	260	9	)	)	PUNCT
ejpam-3916	260	10	\	\	PROPN
ejpam-3916	261	1	sv	sv	PROPN
ejpam-3916	261	2	.	.	PUNCT
ejpam-3916	262	1	if	if	SCONJ
ejpam-3916	262	2	v	v	NUM
ejpam-3916	262	3	∈	∈	PROPN
ejpam-3916	262	4	ng(a	ng(a	NOUN
ejpam-3916	262	5	)	)	PUNCT
ejpam-3916	262	6	,	,	PUNCT
ejpam-3916	262	7	then	then	ADV
ejpam-3916	262	8	dg	dg	VERB
ejpam-3916	262	9	◦	◦	NOUN
ejpam-3916	262	10	h(z	h(z	NOUN
ejpam-3916	262	11	,	,	PUNCT
ejpam-3916	262	12	a	a	PRON
ejpam-3916	262	13	)	)	PUNCT
ejpam-3916	262	14	=	=	SYM
ejpam-3916	262	15	2	2	NUM
ejpam-3916	262	16	for	for	ADP
ejpam-3916	262	17	a	a	DET
ejpam-3916	262	18	∈	∈	PROPN
ejpam-3916	262	19	a	a	DET
ejpam-3916	262	20	∩	∩	NOUN
ejpam-3916	262	21	ng(v	ng(v	NUM
ejpam-3916	262	22	)	)	PUNCT
ejpam-3916	262	23	.	.	PUNCT
ejpam-3916	263	1	if	if	SCONJ
ejpam-3916	263	2	v	v	NUM
ejpam-3916	263	3	/∈	/∈	PUNCT
ejpam-3916	263	4	ng(a	ng(a	NUM
ejpam-3916	263	5	)	)	PUNCT
ejpam-3916	263	6	,	,	PUNCT
ejpam-3916	263	7	then	then	ADV
ejpam-3916	263	8	there	there	PRON
ejpam-3916	263	9	exists	exist	VERB
ejpam-3916	263	10	b	b	PROPN
ejpam-3916	263	11	∈	∈	PROPN
ejpam-3916	263	12	sv	sv	X
ejpam-3916	264	1	⊂	⊂	PROPN
ejpam-3916	264	2	c	c	PROPN
ejpam-3916	265	1	such	such	ADJ
ejpam-3916	265	2	that	that	SCONJ
ejpam-3916	265	3	dg	dg	AUX
ejpam-3916	265	4	◦	◦	NOUN
ejpam-3916	265	5	h(z	h(z	NOUN
ejpam-3916	265	6	,	,	PUNCT
ejpam-3916	265	7	b	b	NOUN
ejpam-3916	265	8	)	)	PUNCT
ejpam-3916	265	9	=	=	SYM
ejpam-3916	265	10	2	2	NUM
ejpam-3916	265	11	by	by	ADP
ejpam-3916	265	12	(	(	PUNCT
ejpam-3916	265	13	iii	iii	NOUN
ejpam-3916	265	14	)	)	PUNCT
ejpam-3916	265	15	and	and	CCONJ
ejpam-3916	265	16	(	(	PUNCT
ejpam-3916	265	17	iv	iv	X
ejpam-3916	265	18	)	)	PUNCT
ejpam-3916	265	19	.	.	PUNCT
ejpam-3916	266	1	next	next	ADV
ejpam-3916	266	2	,	,	PUNCT
ejpam-3916	266	3	suppose	suppose	VERB
ejpam-3916	266	4	first	first	ADV
ejpam-3916	266	5	that	that	SCONJ
ejpam-3916	266	6	v	v	X
ejpam-3916	266	7	∈	∈	PROPN
ejpam-3916	266	8	a.	a.	NOUN
ejpam-3916	266	9	pick	pick	VERB
ejpam-3916	266	10	any	any	DET
ejpam-3916	266	11	w	w	PROPN
ejpam-3916	266	12	∈	∈	PROPN
ejpam-3916	266	13	v	v	ADP
ejpam-3916	266	14	(	(	PUNCT
ejpam-3916	266	15	g	g	NOUN
ejpam-3916	266	16	)	)	PUNCT
ejpam-3916	266	17	\	\	NOUN
ejpam-3916	266	18	{	{	PUNCT
ejpam-3916	266	19	v	v	NOUN
ejpam-3916	266	20	}	}	PUNCT
ejpam-3916	266	21	and	and	CCONJ
ejpam-3916	266	22	let	let	VERB
ejpam-3916	266	23	p	p	PRON
ejpam-3916	266	24	∈	∈	PROPN
ejpam-3916	266	25	v	v	NOUN
ejpam-3916	266	26	(	(	PUNCT
ejpam-3916	266	27	hw	hw	NOUN
ejpam-3916	266	28	)	)	PUNCT
ejpam-3916	266	29	.	.	PUNCT
ejpam-3916	267	1	then	then	ADV
ejpam-3916	267	2	p	p	PROPN
ejpam-3916	267	3	∈	∈	PROPN
ejpam-3916	267	4	ng	ng	PROPN
ejpam-3916	267	5	◦	◦	NOUN
ejpam-3916	267	6	h(z	h(z	NOUN
ejpam-3916	267	7	)	)	PUNCT
ejpam-3916	267	8	∩	∩	NOUN
ejpam-3916	267	9	ng	ng	PROPN
ejpam-3916	267	10	◦	◦	NOUN
ejpam-3916	267	11	h(v	h(v	PROPN
ejpam-3916	267	12	)	)	PUNCT
ejpam-3916	267	13	.	.	PUNCT
ejpam-3916	268	1	thus	thus	ADV
ejpam-3916	268	2	,	,	PUNCT
ejpam-3916	268	3	dg	dg	X
ejpam-3916	268	4	◦	◦	NOUN
ejpam-3916	268	5	h(z	h(z	NOUN
ejpam-3916	268	6	,	,	PUNCT
ejpam-3916	268	7	v	v	NOUN
ejpam-3916	268	8	)	)	PUNCT
ejpam-3916	268	9	=	=	SYM
ejpam-3916	268	10	2	2	X
ejpam-3916	268	11	.	.	PUNCT
ejpam-3916	268	12	suppose	suppose	VERB
ejpam-3916	268	13	now	now	ADV
ejpam-3916	268	14	that	that	SCONJ
ejpam-3916	268	15	v	v	X
ejpam-3916	268	16	/∈	/∈	INTJ
ejpam-3916	268	17	a.	a.	NOUN
ejpam-3916	268	18	by	by	ADP
ejpam-3916	268	19	(	(	PUNCT
ejpam-3916	268	20	ii	ii	NOUN
ejpam-3916	268	21	)	)	PUNCT
ejpam-3916	268	22	and	and	CCONJ
ejpam-3916	268	23	(	(	PUNCT
ejpam-3916	268	24	iv	iv	X
ejpam-3916	268	25	)	)	PUNCT
ejpam-3916	268	26	,	,	PUNCT
ejpam-3916	268	27	sv	sv	PROPN
ejpam-3916	268	28	is	be	AUX
ejpam-3916	268	29	a	a	DET
ejpam-3916	268	30	dominating	dominating	NOUN
ejpam-3916	268	31	set	set	NOUN
ejpam-3916	268	32	of	of	ADP
ejpam-3916	268	33	hv	hv	PROPN
ejpam-3916	268	34	.	.	PUNCT
ejpam-3916	269	1	it	it	PRON
ejpam-3916	269	2	follows	follow	VERB
ejpam-3916	269	3	that	that	SCONJ
ejpam-3916	269	4	there	there	PRON
ejpam-3916	269	5	exists	exist	VERB
ejpam-3916	269	6	q	q	PROPN
ejpam-3916	269	7	∈	∈	PROPN
ejpam-3916	269	8	sv	sv	NOUN
ejpam-3916	269	9	∩	∩	PROPN
ejpam-3916	269	10	nhv(z	nhv(z	PROPN
ejpam-3916	269	11	)	)	PUNCT
ejpam-3916	269	12	.	.	PUNCT
ejpam-3916	270	1	pick	pick	VERB
ejpam-3916	270	2	any	any	DET
ejpam-3916	270	3	u	u	PROPN
ejpam-3916	270	4	∈	∈	PROPN
ejpam-3916	270	5	v	v	NOUN
ejpam-3916	270	6	(	(	PUNCT
ejpam-3916	270	7	g	g	NOUN
ejpam-3916	270	8	)	)	PUNCT
ejpam-3916	270	9	\	\	NOUN
ejpam-3916	270	10	{	{	PUNCT
ejpam-3916	270	11	v	v	NOUN
ejpam-3916	270	12	}	}	PUNCT
ejpam-3916	270	13	.	.	PUNCT
ejpam-3916	271	1	then	then	ADV
ejpam-3916	271	2	u	u	PROPN
ejpam-3916	271	3	∈	∈	PROPN
ejpam-3916	271	4	ng	ng	PROPN
ejpam-3916	271	5	◦	◦	NOUN
ejpam-3916	271	6	h(z	h(z	NOUN
ejpam-3916	271	7	)	)	PUNCT
ejpam-3916	271	8	∩ng	∩ng	VERB
ejpam-3916	271	9	◦	◦	NOUN
ejpam-3916	271	10	h(q	h(q	ADV
ejpam-3916	271	11	)	)	PUNCT
ejpam-3916	271	12	.	.	PUNCT
ejpam-3916	272	1	hence	hence	ADV
ejpam-3916	272	2	,	,	PUNCT
ejpam-3916	272	3	there	there	PRON
ejpam-3916	272	4	exists	exist	VERB
ejpam-3916	272	5	q	q	PROPN
ejpam-3916	272	6	∈	∈	PROPN
ejpam-3916	272	7	c	c	NOUN
ejpam-3916	272	8	such	such	ADJ
ejpam-3916	272	9	that	that	SCONJ
ejpam-3916	272	10	dg	dg	AUX
ejpam-3916	272	11	◦	◦	NOUN
ejpam-3916	272	12	h(z	h(z	NOUN
ejpam-3916	272	13	,	,	PUNCT
ejpam-3916	272	14	q	q	NOUN
ejpam-3916	272	15	)	)	PUNCT
ejpam-3916	272	16	=	=	SYM
ejpam-3916	272	17	2	2	X
ejpam-3916	272	18	.	.	PUNCT
ejpam-3916	272	19	accordingly	accordingly	ADV
ejpam-3916	272	20	,	,	PUNCT
ejpam-3916	272	21	c	c	PROPN
ejpam-3916	272	22	is	be	AUX
ejpam-3916	272	23	a	a	DET
ejpam-3916	272	24	hop	hop	NOUN
ejpam-3916	272	25	dominating	dominating	NOUN
ejpam-3916	272	26	set	set	NOUN
ejpam-3916	272	27	of	of	ADP
ejpam-3916	272	28	g	g	NOUN
ejpam-3916	272	29	◦	◦	NOUN
ejpam-3916	272	30	h	h	NOUN
ejpam-3916	272	31	and	and	CCONJ
ejpam-3916	272	32	g	g	PROPN
ejpam-3916	272	33	◦	◦	NOUN
ejpam-3916	272	34	h	h	NOUN
ejpam-3916	272	35	,	,	PUNCT
ejpam-3916	272	36	showing	show	VERB
ejpam-3916	272	37	that	that	SCONJ
ejpam-3916	272	38	c	c	PROPN
ejpam-3916	272	39	is	be	AUX
ejpam-3916	272	40	a	a	DET
ejpam-3916	272	41	global	global	ADJ
ejpam-3916	272	42	hop	hop	NOUN
ejpam-3916	272	43	dominating	dominating	NOUN
ejpam-3916	272	44	set	set	NOUN
ejpam-3916	272	45	of	of	ADP
ejpam-3916	272	46	g	g	PROPN
ejpam-3916	272	47	◦	◦	NOUN
ejpam-3916	272	48	h.	h.	PROPN
ejpam-3916	272	49	corollary	corollary	ADJ
ejpam-3916	272	50	3	3	X
ejpam-3916	272	51	.	.	PUNCT
ejpam-3916	273	1	let	let	VERB
ejpam-3916	273	2	g	g	PRON
ejpam-3916	273	3	be	be	AUX
ejpam-3916	273	4	a	a	DET
ejpam-3916	273	5	connected	connected	ADJ
ejpam-3916	273	6	non	non	ADJ
ejpam-3916	273	7	-	-	ADJ
ejpam-3916	273	8	trivial	trivial	ADJ
ejpam-3916	273	9	graph	graph	NOUN
ejpam-3916	273	10	and	and	CCONJ
ejpam-3916	273	11	let	let	VERB
ejpam-3916	273	12	h	h	NOUN
ejpam-3916	273	13	be	be	AUX
ejpam-3916	273	14	any	any	DET
ejpam-3916	273	15	graph	graph	NOUN
ejpam-3916	273	16	.	.	PUNCT
ejpam-3916	274	1	then	then	ADV
ejpam-3916	274	2	γgh(g	γgh(g	PROPN
ejpam-3916	274	3	◦	◦	NOUN
ejpam-3916	274	4	h	h	NOUN
ejpam-3916	274	5	)	)	PUNCT
ejpam-3916	274	6	=	=	SYM
ejpam-3916	274	7	|v	|v	PROPN
ejpam-3916	274	8	(	(	PUNCT
ejpam-3916	274	9	g)|	g)|	NOUN
ejpam-3916	274	10	.	.	PUNCT
ejpam-3916	275	1	proof	proof	NOUN
ejpam-3916	275	2	.	.	PUNCT
ejpam-3916	276	1	let	let	VERB
ejpam-3916	276	2	a	a	DET
ejpam-3916	276	3	=	=	X
ejpam-3916	276	4	v	v	X
ejpam-3916	276	5	(	(	PUNCT
ejpam-3916	276	6	g	g	NOUN
ejpam-3916	276	7	)	)	PUNCT
ejpam-3916	276	8	and	and	CCONJ
ejpam-3916	276	9	set	set	VERB
ejpam-3916	276	10	sv	sv	X
ejpam-3916	277	1	=	=	NOUN
ejpam-3916	277	2	∅	∅	NOUN
ejpam-3916	277	3	for	for	ADP
ejpam-3916	277	4	each	each	PRON
ejpam-3916	277	5	v	v	NUM
ejpam-3916	277	6	∈	∈	PROPN
ejpam-3916	277	7	v	v	NOUN
ejpam-3916	277	8	(	(	PUNCT
ejpam-3916	277	9	g	g	NOUN
ejpam-3916	277	10	)	)	PUNCT
ejpam-3916	277	11	.	.	PUNCT
ejpam-3916	278	1	then	then	ADV
ejpam-3916	278	2	c	c	X
ejpam-3916	278	3	=	=	PUNCT
ejpam-3916	278	4	a	a	PRON
ejpam-3916	278	5	=	=	X
ejpam-3916	278	6	a	a	DET
ejpam-3916	278	7	∪	∪	X
ejpam-3916	278	8	(	(	PUNCT
ejpam-3916	278	9	∪v∈v	∪v∈v	X
ejpam-3916	278	10	(	(	PUNCT
ejpam-3916	278	11	g)sv	g)sv	PROPN
ejpam-3916	278	12	)	)	PUNCT
ejpam-3916	278	13	is	be	AUX
ejpam-3916	278	14	a	a	DET
ejpam-3916	278	15	global	global	ADJ
ejpam-3916	278	16	hop	hop	NOUN
ejpam-3916	278	17	dominating	dominating	NOUN
ejpam-3916	278	18	set	set	NOUN
ejpam-3916	278	19	of	of	ADP
ejpam-3916	278	20	g	g	NOUN
ejpam-3916	278	21	by	by	ADP
ejpam-3916	278	22	theorem	theorem	NOUN
ejpam-3916	278	23	5	5	NUM
ejpam-3916	278	24	.	.	PUNCT
ejpam-3916	279	1	hence	hence	ADV
ejpam-3916	279	2	,	,	PUNCT
ejpam-3916	279	3	γgh(g	γgh(g	PROPN
ejpam-3916	279	4	◦	◦	NOUN
ejpam-3916	279	5	h	h	NOUN
ejpam-3916	279	6	)	)	PUNCT
ejpam-3916	279	7	≤	≤	NOUN
ejpam-3916	279	8	|c|	|c|	PROPN
ejpam-3916	279	9	=	=	SYM
ejpam-3916	279	10	|v	|v	PROPN
ejpam-3916	279	11	(	(	PUNCT
ejpam-3916	279	12	g)|	g)|	PROPN
ejpam-3916	279	13	.	.	PUNCT
ejpam-3916	280	1	g.	g.	PROPN
ejpam-3916	280	2	salasalan	salasalan	PROPN
ejpam-3916	280	3	,	,	PUNCT
ejpam-3916	280	4	s.	s.	PROPN
ejpam-3916	280	5	canoy	canoy	PROPN
ejpam-3916	280	6	,	,	PUNCT
ejpam-3916	280	7	jr	jr	PROPN
ejpam-3916	280	8	.	.	PROPN
ejpam-3916	280	9	/	/	SYM
ejpam-3916	280	10	eur	eur	PROPN
ejpam-3916	280	11	.	.	PUNCT
ejpam-3916	281	1	j.	j.	PROPN
ejpam-3916	281	2	pure	pure	PROPN
ejpam-3916	281	3	appl	appl	PROPN
ejpam-3916	281	4	.	.	PROPN
ejpam-3916	281	5	math	math	PROPN
ejpam-3916	281	6	,	,	PUNCT
ejpam-3916	281	7	14	14	NUM
ejpam-3916	281	8	(	(	PUNCT
ejpam-3916	281	9	1	1	NUM
ejpam-3916	281	10	)	)	PUNCT
ejpam-3916	281	11	(	(	PUNCT
ejpam-3916	281	12	2021	2021	NUM
ejpam-3916	281	13	)	)	PUNCT
ejpam-3916	281	14	,	,	PUNCT
ejpam-3916	281	15	112	112	NUM
ejpam-3916	281	16	-	-	SYM
ejpam-3916	281	17	125	125	NUM
ejpam-3916	281	18	119	119	NUM
ejpam-3916	281	19	next	next	ADV
ejpam-3916	281	20	,	,	PUNCT
ejpam-3916	281	21	let	let	VERB
ejpam-3916	281	22	c0	c0	PROPN
ejpam-3916	281	23	be	be	AUX
ejpam-3916	281	24	a	a	DET
ejpam-3916	281	25	γgh	γgh	PROPN
ejpam-3916	281	26	-	-	PUNCT
ejpam-3916	281	27	set	set	NOUN
ejpam-3916	281	28	of	of	ADP
ejpam-3916	281	29	g	g	PROPN
ejpam-3916	281	30	◦	◦	NOUN
ejpam-3916	281	31	h.	h.	NOUN
ejpam-3916	281	32	then	then	ADV
ejpam-3916	281	33	c0	c0	PROPN
ejpam-3916	281	34	=	=	SYM
ejpam-3916	281	35	a0∪(∪v∈v	a0∪(∪v∈v	X
ejpam-3916	281	36	(	(	PUNCT
ejpam-3916	281	37	g)rv	g)rv	PROPN
ejpam-3916	281	38	)	)	PUNCT
ejpam-3916	281	39	,	,	PUNCT
ejpam-3916	281	40	where	where	SCONJ
ejpam-3916	281	41	a0	a0	PROPN
ejpam-3916	281	42	⊆	⊆	NUM
ejpam-3916	281	43	v	v	NOUN
ejpam-3916	281	44	(	(	PUNCT
ejpam-3916	281	45	g	g	NOUN
ejpam-3916	281	46	)	)	PUNCT
ejpam-3916	281	47	and	and	CCONJ
ejpam-3916	281	48	rv	rv	PROPN
ejpam-3916	281	49	⊆	⊆	NUM
ejpam-3916	281	50	v	v	ADP
ejpam-3916	281	51	(	(	PUNCT
ejpam-3916	281	52	hv	hv	PROPN
ejpam-3916	281	53	)	)	PUNCT
ejpam-3916	281	54	for	for	ADP
ejpam-3916	281	55	each	each	DET
ejpam-3916	281	56	v	v	NUM
ejpam-3916	281	57	∈	∈	PROPN
ejpam-3916	281	58	v	v	NOUN
ejpam-3916	281	59	(	(	PUNCT
ejpam-3916	281	60	g	g	NOUN
ejpam-3916	281	61	)	)	PUNCT
ejpam-3916	281	62	and	and	CCONJ
ejpam-3916	281	63	satisfy	satisfy	VERB
ejpam-3916	281	64	conditions	condition	NOUN
ejpam-3916	281	65	(	(	PUNCT
ejpam-3916	281	66	i	i	NOUN
ejpam-3916	281	67	)	)	PUNCT
ejpam-3916	281	68	,	,	PUNCT
ejpam-3916	281	69	(	(	PUNCT
ejpam-3916	281	70	ii	ii	NOUN
ejpam-3916	281	71	)	)	PUNCT
ejpam-3916	281	72	,	,	PUNCT
ejpam-3916	281	73	(	(	PUNCT
ejpam-3916	281	74	iii	iii	NOUN
ejpam-3916	281	75	)	)	PUNCT
ejpam-3916	281	76	,	,	PUNCT
ejpam-3916	281	77	and	and	CCONJ
ejpam-3916	281	78	(	(	PUNCT
ejpam-3916	281	79	iv	iv	X
ejpam-3916	281	80	)	)	PUNCT
ejpam-3916	281	81	of	of	ADP
ejpam-3916	281	82	theorem	theorem	NOUN
ejpam-3916	281	83	5	5	NUM
ejpam-3916	281	84	.	.	PUNCT
ejpam-3916	281	85	since	since	SCONJ
ejpam-3916	281	86	c0	c0	PROPN
ejpam-3916	281	87	is	be	AUX
ejpam-3916	281	88	a	a	DET
ejpam-3916	281	89	γgh	γgh	PROPN
ejpam-3916	281	90	-	-	PUNCT
ejpam-3916	281	91	set	set	NOUN
ejpam-3916	281	92	of	of	ADP
ejpam-3916	281	93	g	g	PROPN
ejpam-3916	281	94	◦	◦	NOUN
ejpam-3916	281	95	h	h	NOUN
ejpam-3916	281	96	,	,	PUNCT
ejpam-3916	281	97	it	it	PRON
ejpam-3916	281	98	follows	follow	VERB
ejpam-3916	281	99	that	that	PRON
ejpam-3916	281	100	rv	rv	NOUN
ejpam-3916	282	1	=	=	NOUN
ejpam-3916	282	2	∅	∅	NOUN
ejpam-3916	282	3	for	for	ADP
ejpam-3916	282	4	all	all	DET
ejpam-3916	282	5	v	v	ADP
ejpam-3916	282	6	∈	∈	NOUN
ejpam-3916	282	7	d1	d1	NOUN
ejpam-3916	282	8	=	=	SYM
ejpam-3916	282	9	a0∩ng(a0	a0∩ng(a0	X
ejpam-3916	282	10	)	)	PUNCT
ejpam-3916	282	11	.	.	PUNCT
ejpam-3916	283	1	from	from	ADP
ejpam-3916	283	2	conditions	condition	NOUN
ejpam-3916	283	3	(	(	PUNCT
ejpam-3916	283	4	ii	ii	NOUN
ejpam-3916	283	5	)	)	PUNCT
ejpam-3916	283	6	,	,	PUNCT
ejpam-3916	283	7	(	(	PUNCT
ejpam-3916	283	8	iii	iii	NOUN
ejpam-3916	283	9	)	)	PUNCT
ejpam-3916	283	10	,	,	PUNCT
ejpam-3916	283	11	and	and	CCONJ
ejpam-3916	283	12	(	(	PUNCT
ejpam-3916	283	13	iv	iv	X
ejpam-3916	283	14	)	)	PUNCT
ejpam-3916	283	15	,	,	PUNCT
ejpam-3916	283	16	we	we	PRON
ejpam-3916	283	17	find	find	VERB
ejpam-3916	283	18	that	that	SCONJ
ejpam-3916	283	19	|rv|	|rv|	PROPN
ejpam-3916	283	20	≥	≥	NOUN
ejpam-3916	283	21	1	1	NUM
ejpam-3916	283	22	for	for	ADP
ejpam-3916	283	23	each	each	DET
ejpam-3916	283	24	v	v	X
ejpam-3916	283	25	∈	∈	PROPN
ejpam-3916	283	26	d2	d2	PROPN
ejpam-3916	283	27	=	=	PUNCT
ejpam-3916	283	28	v	v	PROPN
ejpam-3916	283	29	(	(	PUNCT
ejpam-3916	283	30	g	g	NOUN
ejpam-3916	283	31	)	)	PUNCT
ejpam-3916	283	32	\d1	\d1	NOUN
ejpam-3916	283	33	.	.	PUNCT
ejpam-3916	284	1	thus	thus	ADV
ejpam-3916	284	2	,	,	PUNCT
ejpam-3916	284	3	γgh(g	γgh(g	PROPN
ejpam-3916	284	4	◦	◦	NOUN
ejpam-3916	284	5	h	h	NOUN
ejpam-3916	284	6	)	)	PUNCT
ejpam-3916	284	7	=	=	NOUN
ejpam-3916	284	8	|c0|	|c0|	NOUN
ejpam-3916	284	9	=	=	SYM
ejpam-3916	284	10	|a0|+	|a0|+	NOUN
ejpam-3916	284	11	∑	∑	PUNCT
ejpam-3916	284	12	v∈d2	v∈d2	NOUN
ejpam-3916	284	13	|rv|	|rv|	PROPN
ejpam-3916	284	14	≥	≥	PROPN
ejpam-3916	284	15	|a0|+	|a0|+	SYM
ejpam-3916	284	16	|d2|	|d2|	NOUN
ejpam-3916	284	17	=	=	SYM
ejpam-3916	284	18	|v	|v	PROPN
ejpam-3916	284	19	(	(	PUNCT
ejpam-3916	284	20	g)|+	g)|+	NOUN
ejpam-3916	284	21	(	(	PUNCT
ejpam-3916	284	22	|a0|	|a0|	NOUN
ejpam-3916	284	23	−	−	ADP
ejpam-3916	284	24	|d1|	|d1|	NOUN
ejpam-3916	284	25	)	)	PUNCT
ejpam-3916	284	26	≥	≥	PROPN
ejpam-3916	284	27	|v	|v	PROPN
ejpam-3916	284	28	(	(	PUNCT
ejpam-3916	284	29	g)|	g)|	PROPN
ejpam-3916	284	30	.	.	PUNCT
ejpam-3916	285	1	therefore	therefore	ADV
ejpam-3916	285	2	,	,	PUNCT
ejpam-3916	285	3	γgh(g	γgh(g	PROPN
ejpam-3916	285	4	◦	◦	NOUN
ejpam-3916	285	5	h	h	NOUN
ejpam-3916	285	6	)	)	PUNCT
ejpam-3916	285	7	=	=	SYM
ejpam-3916	285	8	|v	|v	PROPN
ejpam-3916	285	9	(	(	PUNCT
ejpam-3916	285	10	g)|	g)|	NOUN
ejpam-3916	285	11	.	.	PUNCT
ejpam-3916	286	1	the	the	DET
ejpam-3916	286	2	lexicographic	lexicographic	ADJ
ejpam-3916	286	3	product	product	NOUN
ejpam-3916	286	4	of	of	ADP
ejpam-3916	286	5	graphs	graph	NOUN
ejpam-3916	286	6	g	g	PROPN
ejpam-3916	286	7	and	and	CCONJ
ejpam-3916	286	8	h	h	NOUN
ejpam-3916	286	9	,	,	PUNCT
ejpam-3916	286	10	denoted	denote	VERB
ejpam-3916	286	11	by	by	ADP
ejpam-3916	286	12	g[h	g[h	NOUN
ejpam-3916	286	13	]	]	PUNCT
ejpam-3916	286	14	,	,	PUNCT
ejpam-3916	286	15	is	be	AUX
ejpam-3916	286	16	the	the	DET
ejpam-3916	286	17	graph	graph	NOUN
ejpam-3916	286	18	with	with	ADP
ejpam-3916	286	19	vertex	vertex	NOUN
ejpam-3916	286	20	set	set	VERB
ejpam-3916	286	21	v	v	NOUN
ejpam-3916	286	22	(	(	PUNCT
ejpam-3916	286	23	g[h	g[h	PROPN
ejpam-3916	286	24	]	]	PUNCT
ejpam-3916	286	25	)	)	PUNCT
ejpam-3916	286	26	=	=	SYM
ejpam-3916	286	27	v	v	X
ejpam-3916	286	28	(	(	PUNCT
ejpam-3916	286	29	g)×	g)×	NOUN
ejpam-3916	286	30	v	v	NOUN
ejpam-3916	286	31	(	(	PUNCT
ejpam-3916	286	32	h	h	NOUN
ejpam-3916	286	33	)	)	PUNCT
ejpam-3916	286	34	such	such	ADJ
ejpam-3916	286	35	that	that	SCONJ
ejpam-3916	286	36	(	(	PUNCT
ejpam-3916	286	37	v	v	NOUN
ejpam-3916	286	38	,	,	PUNCT
ejpam-3916	286	39	a)(u	a)(u	ADJ
ejpam-3916	286	40	,	,	PUNCT
ejpam-3916	286	41	b	b	X
ejpam-3916	286	42	)	)	PUNCT
ejpam-3916	286	43	∈	∈	NOUN
ejpam-3916	286	44	e(g[h	e(g[h	NOUN
ejpam-3916	286	45	]	]	PUNCT
ejpam-3916	286	46	)	)	PUNCT
ejpam-3916	286	47	if	if	SCONJ
ejpam-3916	286	48	and	and	CCONJ
ejpam-3916	286	49	only	only	ADV
ejpam-3916	286	50	if	if	SCONJ
ejpam-3916	286	51	either	either	DET
ejpam-3916	286	52	uv	uv	PROPN
ejpam-3916	286	53	∈	∈	PROPN
ejpam-3916	286	54	e(g	e(g	PROPN
ejpam-3916	286	55	)	)	PUNCT
ejpam-3916	286	56	or	or	CCONJ
ejpam-3916	286	57	u	u	X
ejpam-3916	286	58	=	=	PROPN
ejpam-3916	286	59	v	v	PROPN
ejpam-3916	286	60	and	and	CCONJ
ejpam-3916	286	61	ab	ab	PROPN
ejpam-3916	286	62	∈	∈	PROPN
ejpam-3916	286	63	e(h	e(h	PROPN
ejpam-3916	286	64	)	)	PUNCT
ejpam-3916	286	65	.	.	PUNCT
ejpam-3916	287	1	note	note	VERB
ejpam-3916	287	2	that	that	SCONJ
ejpam-3916	287	3	every	every	DET
ejpam-3916	287	4	non	non	ADJ
ejpam-3916	287	5	-	-	ADJ
ejpam-3916	287	6	empty	empty	ADJ
ejpam-3916	287	7	subset	subset	NOUN
ejpam-3916	287	8	c	c	NOUN
ejpam-3916	287	9	of	of	ADP
ejpam-3916	287	10	v	v	PROPN
ejpam-3916	287	11	(	(	PUNCT
ejpam-3916	287	12	g	g	NOUN
ejpam-3916	287	13	)	)	PUNCT
ejpam-3916	287	14	×	×	NOUN
ejpam-3916	287	15	v	v	NOUN
ejpam-3916	287	16	(	(	PUNCT
ejpam-3916	287	17	h	h	NOUN
ejpam-3916	287	18	)	)	PUNCT
ejpam-3916	287	19	can	can	AUX
ejpam-3916	287	20	be	be	AUX
ejpam-3916	287	21	expressed	express	VERB
ejpam-3916	287	22	as	as	ADP
ejpam-3916	287	23	c	c	X
ejpam-3916	287	24	=	=	SYM
ejpam-3916	287	25	∪x∈s	∪x∈s	PROPN
ejpam-3916	288	1	[	[	X
ejpam-3916	288	2	{	{	PUNCT
ejpam-3916	288	3	x	x	NOUN
ejpam-3916	288	4	}	}	PUNCT
ejpam-3916	288	5	×	×	PROPN
ejpam-3916	288	6	tx	tx	PROPN
ejpam-3916	288	7	]	]	X
ejpam-3916	288	8	,	,	PUNCT
ejpam-3916	288	9	where	where	SCONJ
ejpam-3916	288	10	s	s	VERB
ejpam-3916	288	11	⊆	⊆	NUM
ejpam-3916	288	12	v	v	NOUN
ejpam-3916	288	13	(	(	PUNCT
ejpam-3916	288	14	g	g	NOUN
ejpam-3916	288	15	)	)	PUNCT
ejpam-3916	288	16	and	and	CCONJ
ejpam-3916	288	17	tx	tx	VERB
ejpam-3916	288	18	⊆	⊆	NUM
ejpam-3916	288	19	v	v	NOUN
ejpam-3916	288	20	(	(	PUNCT
ejpam-3916	288	21	h	h	NOUN
ejpam-3916	288	22	)	)	PUNCT
ejpam-3916	288	23	for	for	ADP
ejpam-3916	288	24	each	each	DET
ejpam-3916	288	25	x	x	PROPN
ejpam-3916	288	26	∈	∈	PROPN
ejpam-3916	288	27	s.	s.	PROPN
ejpam-3916	288	28	theorem	theorem	VERB
ejpam-3916	288	29	6	6	NUM
ejpam-3916	288	30	.	.	PUNCT
ejpam-3916	289	1	let	let	VERB
ejpam-3916	289	2	g	g	NOUN
ejpam-3916	290	1	and	and	CCONJ
ejpam-3916	290	2	h	h	NOUN
ejpam-3916	290	3	be	be	AUX
ejpam-3916	290	4	connected	connect	VERB
ejpam-3916	290	5	non	non	ADJ
ejpam-3916	290	6	-	-	ADJ
ejpam-3916	290	7	trivial	trivial	ADJ
ejpam-3916	290	8	graphs	graph	NOUN
ejpam-3916	290	9	.	.	PUNCT
ejpam-3916	291	1	a	a	DET
ejpam-3916	291	2	subset	subset	NOUN
ejpam-3916	291	3	c	c	NOUN
ejpam-3916	291	4	=	=	SYM
ejpam-3916	291	5	∪x∈s	∪x∈s	PROPN
ejpam-3916	291	6	[	[	X
ejpam-3916	291	7	{	{	PUNCT
ejpam-3916	291	8	x	x	NOUN
ejpam-3916	291	9	}	}	PUNCT
ejpam-3916	291	10	×	×	PROPN
ejpam-3916	291	11	tx	tx	PROPN
ejpam-3916	291	12	]	]	PUNCT
ejpam-3916	291	13	of	of	ADP
ejpam-3916	291	14	v	v	NOUN
ejpam-3916	291	15	(	(	PUNCT
ejpam-3916	291	16	g[h	g[h	PROPN
ejpam-3916	291	17	]	]	PUNCT
ejpam-3916	291	18	)	)	PUNCT
ejpam-3916	291	19	is	be	AUX
ejpam-3916	291	20	a	a	DET
ejpam-3916	291	21	global	global	ADJ
ejpam-3916	291	22	hop	hop	NOUN
ejpam-3916	291	23	dominating	dominating	NOUN
ejpam-3916	291	24	set	set	NOUN
ejpam-3916	291	25	of	of	ADP
ejpam-3916	291	26	g[h	g[h	PROPN
ejpam-3916	291	27	]	]	PUNCT
ejpam-3916	292	1	if	if	SCONJ
ejpam-3916	292	2	and	and	CCONJ
ejpam-3916	292	3	only	only	ADV
ejpam-3916	292	4	if	if	SCONJ
ejpam-3916	292	5	the	the	DET
ejpam-3916	292	6	each	each	DET
ejpam-3916	292	7	following	follow	VERB
ejpam-3916	292	8	conditions	condition	NOUN
ejpam-3916	292	9	holds	hold	VERB
ejpam-3916	292	10	:	:	PUNCT
ejpam-3916	292	11	(	(	PUNCT
ejpam-3916	292	12	i	i	NOUN
ejpam-3916	292	13	)	)	PUNCT
ejpam-3916	292	14	s	s	VERB
ejpam-3916	292	15	is	be	AUX
ejpam-3916	292	16	both	both	PRON
ejpam-3916	292	17	a	a	DET
ejpam-3916	292	18	dominating	dominating	NOUN
ejpam-3916	292	19	and	and	CCONJ
ejpam-3916	292	20	a	a	DET
ejpam-3916	292	21	hop	hop	NOUN
ejpam-3916	292	22	dominating	dominating	NOUN
ejpam-3916	292	23	set	set	NOUN
ejpam-3916	292	24	of	of	ADP
ejpam-3916	292	25	g.	g.	PROPN
ejpam-3916	292	26	(	(	PUNCT
ejpam-3916	292	27	ii	ii	PROPN
ejpam-3916	292	28	)	)	PUNCT
ejpam-3916	292	29	tx	tx	PROPN
ejpam-3916	292	30	is	be	AUX
ejpam-3916	292	31	a	a	DET
ejpam-3916	292	32	pointwise	pointwise	ADJ
ejpam-3916	292	33	non	non	ADJ
ejpam-3916	292	34	-	-	ADJ
ejpam-3916	292	35	dominating	dominating	ADJ
ejpam-3916	292	36	set	set	NOUN
ejpam-3916	292	37	of	of	ADP
ejpam-3916	292	38	h	h	NOUN
ejpam-3916	292	39	for	for	ADP
ejpam-3916	292	40	each	each	DET
ejpam-3916	292	41	x	x	SYM
ejpam-3916	292	42	∈	∈	PROPN
ejpam-3916	292	43	s	s	VERB
ejpam-3916	292	44	with	with	ADP
ejpam-3916	292	45	|ng(x	|ng(x	ADP
ejpam-3916	292	46	,	,	PUNCT
ejpam-3916	292	47	2	2	X
ejpam-3916	292	48	)	)	PUNCT
ejpam-3916	292	49	∩	∩	NOUN
ejpam-3916	292	50	s|	s|	NOUN
ejpam-3916	292	51	=	=	SYM
ejpam-3916	293	1	0	0	X
ejpam-3916	293	2	.	.	PUNCT
ejpam-3916	293	3	(	(	PUNCT
ejpam-3916	293	4	iii	iii	X
ejpam-3916	293	5	)	)	PUNCT
ejpam-3916	293	6	tx	tx	PROPN
ejpam-3916	293	7	is	be	AUX
ejpam-3916	293	8	a	a	DET
ejpam-3916	293	9	dominating	dominating	NOUN
ejpam-3916	293	10	set	set	NOUN
ejpam-3916	293	11	of	of	ADP
ejpam-3916	293	12	h	h	NOUN
ejpam-3916	293	13	for	for	ADP
ejpam-3916	293	14	each	each	DET
ejpam-3916	293	15	x	x	SYM
ejpam-3916	293	16	∈	∈	NOUN
ejpam-3916	293	17	s	s	VERB
ejpam-3916	293	18	with	with	ADP
ejpam-3916	293	19	s∩ng(x	s∩ng(x	PROPN
ejpam-3916	293	20	)	)	PUNCT
ejpam-3916	293	21	=	=	NOUN
ejpam-3916	293	22	∅	∅	NOUN
ejpam-3916	293	23	or	or	CCONJ
ejpam-3916	293	24	[	[	X
ejpam-3916	293	25	v	v	X
ejpam-3916	293	26	(	(	PUNCT
ejpam-3916	293	27	g)\ng(x)]∩	g)\ng(x)]∩	NOUN
ejpam-3916	293	28	[	[	X
ejpam-3916	293	29	v	v	X
ejpam-3916	293	30	(	(	PUNCT
ejpam-3916	293	31	g	g	NOUN
ejpam-3916	293	32	)	)	PUNCT
ejpam-3916	293	33	\	\	NOUN
ejpam-3916	293	34	ng(y	ng(y	NOUN
ejpam-3916	293	35	)	)	PUNCT
ejpam-3916	293	36	]	]	PUNCT
ejpam-3916	294	1	=	=	PUNCT
ejpam-3916	294	2	∅	∅	NOUN
ejpam-3916	294	3	for	for	ADP
ejpam-3916	294	4	each	each	DET
ejpam-3916	294	5	y	y	PROPN
ejpam-3916	294	6	∈	∈	PROPN
ejpam-3916	294	7	s	s	PART
ejpam-3916	294	8	∩	∩	NOUN
ejpam-3916	294	9	ng(x	ng(x	NUM
ejpam-3916	294	10	)	)	PUNCT
ejpam-3916	294	11	.	.	PUNCT
ejpam-3916	295	1	if	if	SCONJ
ejpam-3916	295	2	,	,	PUNCT
ejpam-3916	295	3	in	in	ADP
ejpam-3916	295	4	addition	addition	NOUN
ejpam-3916	295	5	,	,	PUNCT
ejpam-3916	295	6	ng[x	ng[x	PROPN
ejpam-3916	295	7	]	]	X
ejpam-3916	295	8	=	=	SYM
ejpam-3916	295	9	v	v	X
ejpam-3916	295	10	(	(	PUNCT
ejpam-3916	295	11	g	g	NOUN
ejpam-3916	295	12	)	)	PUNCT
ejpam-3916	295	13	,	,	PUNCT
ejpam-3916	295	14	then	then	ADV
ejpam-3916	295	15	tx	tx	PROPN
ejpam-3916	295	16	is	be	AUX
ejpam-3916	295	17	a	a	DET
ejpam-3916	295	18	pairwise	pairwise	NOUN
ejpam-3916	295	19	non	non	ADJ
ejpam-3916	295	20	-	-	ADJ
ejpam-3916	295	21	dominating	dominating	ADJ
ejpam-3916	295	22	set	set	NOUN
ejpam-3916	295	23	of	of	ADP
ejpam-3916	295	24	h.	h.	PROPN
ejpam-3916	295	25	(	(	PUNCT
ejpam-3916	295	26	iv	iv	X
ejpam-3916	295	27	)	)	PUNCT
ejpam-3916	295	28	for	for	ADP
ejpam-3916	295	29	each	each	DET
ejpam-3916	295	30	z	z	PROPN
ejpam-3916	295	31	∈	∈	PROPN
ejpam-3916	295	32	v	v	NOUN
ejpam-3916	295	33	(	(	PUNCT
ejpam-3916	295	34	g)\s	g)\s	NOUN
ejpam-3916	295	35	,	,	PUNCT
ejpam-3916	295	36	there	there	PRON
ejpam-3916	295	37	exists	exist	VERB
ejpam-3916	295	38	y	y	PROPN
ejpam-3916	295	39	∈	∈	PROPN
ejpam-3916	295	40	s∩ng(z	s∩ng(z	PROPN
ejpam-3916	295	41	)	)	PUNCT
ejpam-3916	295	42	such	such	ADJ
ejpam-3916	295	43	that	that	SCONJ
ejpam-3916	295	44	[	[	X
ejpam-3916	295	45	v	v	X
ejpam-3916	295	46	(	(	PUNCT
ejpam-3916	295	47	g)\ng(z)]∩	g)\ng(z)]∩	NOUN
ejpam-3916	295	48	[	[	X
ejpam-3916	295	49	v	v	X
ejpam-3916	295	50	(	(	PUNCT
ejpam-3916	295	51	g)\	g)\	NOUN
ejpam-3916	295	52	ng(y	ng(y	NOUN
ejpam-3916	295	53	)	)	PUNCT
ejpam-3916	295	54	]	]	PUNCT
ejpam-3916	295	55	6=	6=	ADP
ejpam-3916	295	56	∅.	∅.	PRON
ejpam-3916	295	57	proof	proof	NOUN
ejpam-3916	295	58	.	.	PUNCT
ejpam-3916	296	1	suppose	suppose	VERB
ejpam-3916	296	2	c	c	NOUN
ejpam-3916	296	3	is	be	AUX
ejpam-3916	296	4	a	a	DET
ejpam-3916	296	5	global	global	ADJ
ejpam-3916	296	6	hop	hop	NOUN
ejpam-3916	296	7	dominating	dominating	NOUN
ejpam-3916	296	8	set	set	NOUN
ejpam-3916	296	9	of	of	ADP
ejpam-3916	296	10	g[h	g[h	PROPN
ejpam-3916	296	11	]	]	PUNCT
ejpam-3916	296	12	.	.	PUNCT
ejpam-3916	297	1	let	let	VERB
ejpam-3916	297	2	u	u	PRON
ejpam-3916	297	3	∈	∈	PROPN
ejpam-3916	297	4	v	v	ADP
ejpam-3916	297	5	(	(	PUNCT
ejpam-3916	297	6	g	g	NOUN
ejpam-3916	297	7	)	)	PUNCT
ejpam-3916	297	8	\	\	PROPN
ejpam-3916	297	9	s	s	PART
ejpam-3916	297	10	and	and	CCONJ
ejpam-3916	297	11	pick	pick	VERB
ejpam-3916	297	12	any	any	PRON
ejpam-3916	297	13	a	a	DET
ejpam-3916	297	14	∈	∈	PROPN
ejpam-3916	297	15	v	v	NOUN
ejpam-3916	297	16	(	(	PUNCT
ejpam-3916	297	17	h	h	NOUN
ejpam-3916	297	18	)	)	PUNCT
ejpam-3916	297	19	.	.	PUNCT
ejpam-3916	298	1	since	since	SCONJ
ejpam-3916	298	2	c	c	PROPN
ejpam-3916	298	3	is	be	AUX
ejpam-3916	298	4	a	a	DET
ejpam-3916	298	5	hop	hop	NOUN
ejpam-3916	298	6	dominating	dominating	NOUN
ejpam-3916	298	7	set	set	NOUN
ejpam-3916	298	8	of	of	ADP
ejpam-3916	298	9	g[h	g[h	PROPN
ejpam-3916	298	10	]	]	PUNCT
ejpam-3916	298	11	and	and	CCONJ
ejpam-3916	298	12	(	(	PUNCT
ejpam-3916	298	13	u	u	NOUN
ejpam-3916	298	14	,	,	PUNCT
ejpam-3916	298	15	a	a	PRON
ejpam-3916	298	16	)	)	PUNCT
ejpam-3916	298	17	/∈	/∈	PUNCT
ejpam-3916	299	1	c	c	X
ejpam-3916	299	2	,	,	PUNCT
ejpam-3916	299	3	there	there	PRON
ejpam-3916	299	4	exists	exist	VERB
ejpam-3916	299	5	(	(	PUNCT
ejpam-3916	299	6	y	y	PROPN
ejpam-3916	299	7	,	,	PUNCT
ejpam-3916	299	8	b	b	NOUN
ejpam-3916	299	9	)	)	PUNCT
ejpam-3916	299	10	∈	∈	PROPN
ejpam-3916	299	11	c	c	NOUN
ejpam-3916	299	12	such	such	ADJ
ejpam-3916	299	13	that	that	SCONJ
ejpam-3916	299	14	dg[h]((u	dg[h]((u	NOUN
ejpam-3916	299	15	,	,	PUNCT
ejpam-3916	299	16	a)(y	a)(y	PROPN
ejpam-3916	299	17	,	,	PUNCT
ejpam-3916	299	18	b	b	NOUN
ejpam-3916	299	19	)	)	PUNCT
ejpam-3916	299	20	)	)	PUNCT
ejpam-3916	300	1	=	=	SYM
ejpam-3916	300	2	2	2	X
ejpam-3916	300	3	.	.	PUNCT
ejpam-3916	301	1	this	this	PRON
ejpam-3916	301	2	implies	imply	VERB
ejpam-3916	301	3	that	that	SCONJ
ejpam-3916	301	4	y	y	PROPN
ejpam-3916	301	5	∈	∈	PROPN
ejpam-3916	301	6	s	s	X
ejpam-3916	301	7	and	and	CCONJ
ejpam-3916	301	8	dg(u	dg(u	X
ejpam-3916	301	9	,	,	PUNCT
ejpam-3916	301	10	y	y	NOUN
ejpam-3916	301	11	)	)	PUNCT
ejpam-3916	301	12	=	=	SYM
ejpam-3916	301	13	2	2	X
ejpam-3916	301	14	.	.	PUNCT
ejpam-3916	301	15	also	also	ADV
ejpam-3916	301	16	,	,	PUNCT
ejpam-3916	301	17	since	since	SCONJ
ejpam-3916	301	18	c	c	PROPN
ejpam-3916	301	19	is	be	AUX
ejpam-3916	301	20	a	a	DET
ejpam-3916	301	21	hop	hop	NOUN
ejpam-3916	301	22	dominating	dominating	NOUN
ejpam-3916	301	23	set	set	NOUN
ejpam-3916	301	24	of	of	ADP
ejpam-3916	301	25	g[h	g[h	PROPN
ejpam-3916	301	26	]	]	PUNCT
ejpam-3916	301	27	and	and	CCONJ
ejpam-3916	301	28	(	(	PUNCT
ejpam-3916	301	29	u	u	NOUN
ejpam-3916	301	30	,	,	PUNCT
ejpam-3916	301	31	a	a	PRON
ejpam-3916	301	32	)	)	PUNCT
ejpam-3916	301	33	/∈	/∈	PUNCT
ejpam-3916	302	1	c	c	X
ejpam-3916	302	2	,	,	PUNCT
ejpam-3916	302	3	there	there	PRON
ejpam-3916	302	4	exists	exist	VERB
ejpam-3916	302	5	(	(	PUNCT
ejpam-3916	302	6	z	z	NOUN
ejpam-3916	302	7	,	,	PUNCT
ejpam-3916	302	8	c	c	NOUN
ejpam-3916	302	9	)	)	PUNCT
ejpam-3916	302	10	∈	∈	PROPN
ejpam-3916	302	11	c	c	NOUN
ejpam-3916	303	1	such	such	ADJ
ejpam-3916	303	2	that	that	PRON
ejpam-3916	303	3	d	d	PROPN
ejpam-3916	303	4	g[h	g[h	PROPN
ejpam-3916	303	5	]	]	X
ejpam-3916	303	6	(	(	PUNCT
ejpam-3916	303	7	(	(	PUNCT
ejpam-3916	303	8	u	u	NOUN
ejpam-3916	303	9	,	,	PUNCT
ejpam-3916	303	10	a)(z	a)(z	NOUN
ejpam-3916	303	11	,	,	PUNCT
ejpam-3916	303	12	c	c	NOUN
ejpam-3916	303	13	)	)	PUNCT
ejpam-3916	303	14	)	)	PUNCT
ejpam-3916	304	1	=	=	SYM
ejpam-3916	304	2	2	2	X
ejpam-3916	304	3	.	.	PUNCT
ejpam-3916	304	4	it	it	PRON
ejpam-3916	304	5	follows	follow	VERB
ejpam-3916	304	6	that	that	SCONJ
ejpam-3916	304	7	z	z	PROPN
ejpam-3916	304	8	∈	∈	PROPN
ejpam-3916	304	9	s	s	X
ejpam-3916	304	10	and	and	CCONJ
ejpam-3916	304	11	dg(u	dg(u	X
ejpam-3916	304	12	,	,	PUNCT
ejpam-3916	304	13	z	z	NOUN
ejpam-3916	304	14	)	)	PUNCT
ejpam-3916	304	15	=	=	SYM
ejpam-3916	304	16	1	1	X
ejpam-3916	304	17	.	.	PUNCT
ejpam-3916	305	1	hence	hence	ADV
ejpam-3916	305	2	,	,	PUNCT
ejpam-3916	305	3	s	s	VERB
ejpam-3916	305	4	is	be	AUX
ejpam-3916	305	5	both	both	PRON
ejpam-3916	305	6	a	a	DET
ejpam-3916	305	7	dominating	dominating	NOUN
ejpam-3916	305	8	and	and	CCONJ
ejpam-3916	305	9	a	a	DET
ejpam-3916	305	10	hop	hop	NOUN
ejpam-3916	305	11	dominating	dominating	NOUN
ejpam-3916	305	12	set	set	NOUN
ejpam-3916	305	13	of	of	ADP
ejpam-3916	305	14	g	g	NOUN
ejpam-3916	305	15	,	,	PUNCT
ejpam-3916	305	16	showing	show	VERB
ejpam-3916	305	17	that	that	SCONJ
ejpam-3916	305	18	(	(	PUNCT
ejpam-3916	305	19	i	i	NOUN
ejpam-3916	305	20	)	)	PUNCT
ejpam-3916	305	21	holds	hold	VERB
ejpam-3916	305	22	.	.	PUNCT
ejpam-3916	306	1	let	let	VERB
ejpam-3916	306	2	x	x	SYM
ejpam-3916	306	3	∈	∈	PROPN
ejpam-3916	306	4	s.	s.	PROPN
ejpam-3916	306	5	suppose	suppose	VERB
ejpam-3916	306	6	that	that	SCONJ
ejpam-3916	306	7	|ng(x	|ng(x	PUNCT
ejpam-3916	306	8	,	,	PUNCT
ejpam-3916	306	9	2	2	X
ejpam-3916	306	10	)	)	PUNCT
ejpam-3916	306	11	∩	∩	NOUN
ejpam-3916	306	12	s|	s|	NOUN
ejpam-3916	306	13	=	=	SYM
ejpam-3916	307	1	0	0	X
ejpam-3916	307	2	.	.	PUNCT
ejpam-3916	308	1	then	then	ADV
ejpam-3916	308	2	tx	tx	PROPN
ejpam-3916	308	3	is	be	AUX
ejpam-3916	308	4	a	a	DET
ejpam-3916	308	5	pointwise	pointwise	ADJ
ejpam-3916	308	6	non	non	ADJ
ejpam-3916	308	7	-	-	ADJ
ejpam-3916	308	8	dominating	dominating	ADJ
ejpam-3916	308	9	set	set	NOUN
ejpam-3916	308	10	of	of	ADP
ejpam-3916	308	11	h.	h.	PROPN
ejpam-3916	308	12	hence	hence	PROPN
ejpam-3916	308	13	,	,	PUNCT
ejpam-3916	308	14	(	(	PUNCT
ejpam-3916	308	15	ii	ii	NOUN
ejpam-3916	308	16	)	)	PUNCT
ejpam-3916	308	17	holds	hold	VERB
ejpam-3916	308	18	.	.	PUNCT
ejpam-3916	309	1	suppose	suppose	VERB
ejpam-3916	309	2	now	now	ADV
ejpam-3916	309	3	that	that	SCONJ
ejpam-3916	309	4	s∩ng(x	s∩ng(x	ADP
ejpam-3916	309	5	)	)	PUNCT
ejpam-3916	309	6	=	=	NOUN
ejpam-3916	309	7	∅	∅	NOUN
ejpam-3916	309	8	or	or	CCONJ
ejpam-3916	309	9	[	[	X
ejpam-3916	309	10	v	v	X
ejpam-3916	309	11	(	(	PUNCT
ejpam-3916	309	12	g)\ng(x)]∩	g)\ng(x)]∩	NOUN
ejpam-3916	309	13	[	[	X
ejpam-3916	309	14	v	v	X
ejpam-3916	309	15	(	(	PUNCT
ejpam-3916	309	16	g)\	g)\	NOUN
ejpam-3916	309	17	ng(y	ng(y	NOUN
ejpam-3916	309	18	)	)	PUNCT
ejpam-3916	309	19	]	]	PUNCT
ejpam-3916	310	1	=	=	PUNCT
ejpam-3916	310	2	∅	∅	NOUN
ejpam-3916	310	3	for	for	ADP
ejpam-3916	310	4	each	each	DET
ejpam-3916	310	5	y	y	PROPN
ejpam-3916	310	6	∈	∈	PROPN
ejpam-3916	310	7	s	s	PART
ejpam-3916	310	8	∩ng(x	∩ng(x	NOUN
ejpam-3916	310	9	)	)	PUNCT
ejpam-3916	310	10	.	.	PUNCT
ejpam-3916	311	1	let	let	VERB
ejpam-3916	312	1	p	p	PRON
ejpam-3916	312	2	∈	∈	PROPN
ejpam-3916	312	3	v	v	ADP
ejpam-3916	312	4	(	(	PUNCT
ejpam-3916	312	5	h	h	NOUN
ejpam-3916	312	6	)	)	PUNCT
ejpam-3916	312	7	\	\	PROPN
ejpam-3916	312	8	tx	tx	PROPN
ejpam-3916	312	9	.	.	PUNCT
ejpam-3916	313	1	since	since	SCONJ
ejpam-3916	313	2	(	(	PUNCT
ejpam-3916	313	3	x	x	X
ejpam-3916	313	4	,	,	PUNCT
ejpam-3916	313	5	p	p	NOUN
ejpam-3916	313	6	)	)	PUNCT
ejpam-3916	313	7	∈	∈	PROPN
ejpam-3916	313	8	v	v	NOUN
ejpam-3916	313	9	(	(	PUNCT
ejpam-3916	313	10	g[h	g[h	PROPN
ejpam-3916	313	11	]	]	PUNCT
ejpam-3916	313	12	)	)	PUNCT
ejpam-3916	313	13	\c	\c	NOUN
ejpam-3916	313	14	an	an	DET
ejpam-3916	313	15	c	c	NOUN
ejpam-3916	313	16	is	be	AUX
ejpam-3916	313	17	a	a	DET
ejpam-3916	313	18	hop	hop	NOUN
ejpam-3916	313	19	dominating	dominating	NOUN
ejpam-3916	313	20	set	set	NOUN
ejpam-3916	313	21	of	of	ADP
ejpam-3916	313	22	g[h	g[h	PROPN
ejpam-3916	313	23	]	]	PUNCT
ejpam-3916	313	24	,	,	PUNCT
ejpam-3916	313	25	there	there	PRON
ejpam-3916	313	26	exists	exist	VERB
ejpam-3916	313	27	(	(	PUNCT
ejpam-3916	313	28	w	w	NOUN
ejpam-3916	313	29	,	,	PUNCT
ejpam-3916	313	30	q	q	NOUN
ejpam-3916	313	31	)	)	PUNCT
ejpam-3916	313	32	∈	∈	PROPN
ejpam-3916	313	33	c	c	NOUN
ejpam-3916	314	1	such	such	ADJ
ejpam-3916	314	2	that	that	PRON
ejpam-3916	314	3	d	d	PROPN
ejpam-3916	314	4	g[h	g[h	PROPN
ejpam-3916	314	5	]	]	X
ejpam-3916	314	6	(	(	PUNCT
ejpam-3916	314	7	(	(	PUNCT
ejpam-3916	314	8	x	x	NOUN
ejpam-3916	314	9	,	,	PUNCT
ejpam-3916	314	10	p)(w	p)(w	PROPN
ejpam-3916	314	11	,	,	PUNCT
ejpam-3916	314	12	q	q	NOUN
ejpam-3916	314	13	)	)	PUNCT
ejpam-3916	314	14	)	)	PUNCT
ejpam-3916	315	1	=	=	SYM
ejpam-3916	315	2	2	2	NUM
ejpam-3916	315	3	,	,	PUNCT
ejpam-3916	315	4	that	that	ADV
ejpam-3916	315	5	is	is	ADV
ejpam-3916	315	6	,	,	PUNCT
ejpam-3916	315	7	dg[h]((x	dg[h]((x	ADJ
ejpam-3916	315	8	,	,	PUNCT
ejpam-3916	315	9	p)(w	p)(w	PROPN
ejpam-3916	315	10	,	,	PUNCT
ejpam-3916	315	11	q	q	NOUN
ejpam-3916	315	12	)	)	PUNCT
ejpam-3916	315	13	)	)	PUNCT
ejpam-3916	316	1	=	=	PUNCT
ejpam-3916	316	2	1	1	X
ejpam-3916	316	3	.	.	X
ejpam-3916	317	1	if	if	SCONJ
ejpam-3916	317	2	s	s	ADP
ejpam-3916	317	3	∩	∩	NOUN
ejpam-3916	317	4	ng(x	ng(x	NUM
ejpam-3916	317	5	)	)	PUNCT
ejpam-3916	317	6	=	=	SYM
ejpam-3916	317	7	∅	∅	NOUN
ejpam-3916	317	8	,	,	PUNCT
ejpam-3916	317	9	then	then	ADV
ejpam-3916	317	10	w	w	NOUN
ejpam-3916	317	11	=	=	PUNCT
ejpam-3916	317	12	x	x	X
ejpam-3916	317	13	and	and	CCONJ
ejpam-3916	317	14	q	q	PROPN
ejpam-3916	317	15	∈	∈	PROPN
ejpam-3916	317	16	tx	tx	PROPN
ejpam-3916	317	17	∩	∩	NOUN
ejpam-3916	317	18	nh(p	nh(p	NUM
ejpam-3916	317	19	)	)	PUNCT
ejpam-3916	317	20	,	,	PUNCT
ejpam-3916	317	21	implying	imply	VERB
ejpam-3916	317	22	that	that	SCONJ
ejpam-3916	317	23	tx	tx	PROPN
ejpam-3916	317	24	is	be	AUX
ejpam-3916	317	25	a	a	DET
ejpam-3916	317	26	dominating	dominating	NOUN
ejpam-3916	317	27	set	set	NOUN
ejpam-3916	317	28	of	of	ADP
ejpam-3916	317	29	h.	h.	PROPN
ejpam-3916	317	30	suppose	suppose	VERB
ejpam-3916	317	31	s∩ng(x	s∩ng(x	PROPN
ejpam-3916	317	32	)	)	PUNCT
ejpam-3916	318	1	6=	6=	ADP
ejpam-3916	318	2	∅.	∅.	PROPN
ejpam-3916	318	3	suppose	suppose	VERB
ejpam-3916	318	4	further	far	ADV
ejpam-3916	318	5	that	that	PRON
ejpam-3916	318	6	w	w	ADP
ejpam-3916	318	7	6=	6=	PROPN
ejpam-3916	318	8	x.	x.	NOUN
ejpam-3916	318	9	then	then	ADV
ejpam-3916	318	10	w	w	PROPN
ejpam-3916	318	11	∈	∈	PROPN
ejpam-3916	318	12	s	s	PART
ejpam-3916	318	13	∩ng(x	∩ng(x	NOUN
ejpam-3916	318	14	)	)	PUNCT
ejpam-3916	318	15	.	.	PUNCT
ejpam-3916	319	1	by	by	ADP
ejpam-3916	319	2	assumption	assumption	NOUN
ejpam-3916	319	3	,	,	PUNCT
ejpam-3916	319	4	[	[	X
ejpam-3916	319	5	v	v	X
ejpam-3916	319	6	(	(	PUNCT
ejpam-3916	319	7	g	g	NOUN
ejpam-3916	319	8	)	)	PUNCT
ejpam-3916	319	9	\ng(x)]∩	\ng(x)]∩	NOUN
ejpam-3916	320	1	[	[	X
ejpam-3916	320	2	v	v	X
ejpam-3916	320	3	(	(	PUNCT
ejpam-3916	320	4	g	g	NOUN
ejpam-3916	320	5	)	)	PUNCT
ejpam-3916	320	6	\ng(w	\ng(w	PUNCT
ejpam-3916	320	7	)	)	PUNCT
ejpam-3916	320	8	]	]	PUNCT
ejpam-3916	321	1	=	=	PUNCT
ejpam-3916	321	2	∅.	∅.	AUX
ejpam-3916	321	3	let	let	VERB
ejpam-3916	321	4	[	[	X
ejpam-3916	321	5	(	(	PUNCT
ejpam-3916	321	6	x	x	X
ejpam-3916	321	7	,	,	PUNCT
ejpam-3916	321	8	p	p	NOUN
ejpam-3916	321	9	)	)	PUNCT
ejpam-3916	321	10	,	,	PUNCT
ejpam-3916	321	11	(	(	PUNCT
ejpam-3916	321	12	u	u	NOUN
ejpam-3916	321	13	,	,	PUNCT
ejpam-3916	321	14	t	t	PROPN
ejpam-3916	321	15	)	)	PUNCT
ejpam-3916	321	16	,	,	PUNCT
ejpam-3916	321	17	(	(	PUNCT
ejpam-3916	321	18	w	w	NOUN
ejpam-3916	321	19	,	,	PUNCT
ejpam-3916	321	20	q	q	NOUN
ejpam-3916	321	21	)	)	PUNCT
ejpam-3916	321	22	]	]	PUNCT
ejpam-3916	321	23	be	be	AUX
ejpam-3916	321	24	an	an	DET
ejpam-3916	321	25	(	(	PUNCT
ejpam-3916	321	26	x	x	NOUN
ejpam-3916	321	27	,	,	PUNCT
ejpam-3916	321	28	p)-(w	p)-(w	NUM
ejpam-3916	321	29	,	,	PUNCT
ejpam-3916	321	30	q	q	NOUN
ejpam-3916	321	31	)	)	PUNCT
ejpam-3916	321	32	geodesic	geodesic	NOUN
ejpam-3916	321	33	in	in	ADP
ejpam-3916	321	34	g[h	g[h	PROPN
ejpam-3916	321	35	]	]	PUNCT
ejpam-3916	321	36	.	.	PUNCT
ejpam-3916	322	1	suppose	suppose	VERB
ejpam-3916	322	2	u	u	PROPN
ejpam-3916	322	3	6=	6=	PROPN
ejpam-3916	322	4	x.	x.	PROPN
ejpam-3916	322	5	since	since	SCONJ
ejpam-3916	322	6	xu	xu	PROPN
ejpam-3916	322	7	∈	∈	PROPN
ejpam-3916	322	8	e(g	e(g	PROPN
ejpam-3916	322	9	)	)	PUNCT
ejpam-3916	322	10	,	,	PUNCT
ejpam-3916	323	1	u	u	PROPN
ejpam-3916	323	2	∈	∈	PROPN
ejpam-3916	323	3	v	v	ADP
ejpam-3916	323	4	(	(	PUNCT
ejpam-3916	323	5	g	g	NOUN
ejpam-3916	323	6	)	)	PUNCT
ejpam-3916	323	7	\	\	NOUN
ejpam-3916	323	8	ng(x	ng(x	NUM
ejpam-3916	323	9	)	)	PUNCT
ejpam-3916	323	10	.	.	PUNCT
ejpam-3916	324	1	the	the	DET
ejpam-3916	324	2	assumption	assumption	NOUN
ejpam-3916	324	3	would	would	AUX
ejpam-3916	324	4	now	now	ADV
ejpam-3916	324	5	imply	imply	VERB
ejpam-3916	324	6	that	that	SCONJ
ejpam-3916	324	7	u	u	PROPN
ejpam-3916	324	8	/∈	/∈	NOUN
ejpam-3916	324	9	v	v	INTJ
ejpam-3916	324	10	(	(	PUNCT
ejpam-3916	324	11	g	g	NOUN
ejpam-3916	324	12	)	)	PUNCT
ejpam-3916	324	13	\	\	NOUN
ejpam-3916	324	14	ng(w	ng(w	NOUN
ejpam-3916	324	15	)	)	PUNCT
ejpam-3916	324	16	.	.	PUNCT
ejpam-3916	325	1	thus	thus	ADV
ejpam-3916	325	2	,	,	PUNCT
ejpam-3916	325	3	u	u	PROPN
ejpam-3916	325	4	∈	∈	PROPN
ejpam-3916	325	5	ng(w	ng(w	NOUN
ejpam-3916	325	6	)	)	PUNCT
ejpam-3916	325	7	,	,	PUNCT
ejpam-3916	325	8	a	a	DET
ejpam-3916	325	9	contradiction	contradiction	NOUN
ejpam-3916	325	10	.	.	PUNCT
ejpam-3916	326	1	hence	hence	ADV
ejpam-3916	326	2	,	,	PUNCT
ejpam-3916	326	3	u	u	NOUN
ejpam-3916	326	4	=	=	NOUN
ejpam-3916	326	5	x.	x.	NOUN
ejpam-3916	327	1	this	this	PRON
ejpam-3916	327	2	,	,	PUNCT
ejpam-3916	327	3	however	however	ADV
ejpam-3916	327	4	,	,	PUNCT
ejpam-3916	327	5	is	be	AUX
ejpam-3916	327	6	not	not	PART
ejpam-3916	327	7	possible	possible	ADJ
ejpam-3916	327	8	because	because	SCONJ
ejpam-3916	327	9	xw	xw	PROPN
ejpam-3916	327	10	∈	∈	PROPN
ejpam-3916	327	11	e(g	e(g	PROPN
ejpam-3916	327	12	)	)	PUNCT
ejpam-3916	327	13	.	.	PUNCT
ejpam-3916	328	1	therefore	therefore	ADV
ejpam-3916	328	2	,	,	PUNCT
ejpam-3916	328	3	w	w	PROPN
ejpam-3916	328	4	=	=	SYM
ejpam-3916	328	5	x	x	NOUN
ejpam-3916	328	6	,	,	PUNCT
ejpam-3916	328	7	implying	imply	VERB
ejpam-3916	328	8	that	that	SCONJ
ejpam-3916	328	9	q	q	PUNCT
ejpam-3916	328	10	∈	∈	PROPN
ejpam-3916	328	11	tx	tx	PROPN
ejpam-3916	328	12	∩nh(p	∩nh(p	PROPN
ejpam-3916	328	13	)	)	PUNCT
ejpam-3916	328	14	.	.	PUNCT
ejpam-3916	329	1	hence	hence	ADV
ejpam-3916	329	2	,	,	PUNCT
ejpam-3916	329	3	tx	tx	PROPN
ejpam-3916	329	4	is	be	AUX
ejpam-3916	329	5	a	a	DET
ejpam-3916	329	6	dominating	dominating	NOUN
ejpam-3916	329	7	g.	g.	NOUN
ejpam-3916	329	8	salasalan	salasalan	NOUN
ejpam-3916	329	9	,	,	PUNCT
ejpam-3916	329	10	s.	s.	PROPN
ejpam-3916	329	11	canoy	canoy	PROPN
ejpam-3916	329	12	,	,	PUNCT
ejpam-3916	329	13	jr	jr	PROPN
ejpam-3916	329	14	.	.	PROPN
ejpam-3916	329	15	/	/	SYM
ejpam-3916	329	16	eur	eur	PROPN
ejpam-3916	329	17	.	.	PUNCT
ejpam-3916	330	1	j.	j.	PROPN
ejpam-3916	330	2	pure	pure	PROPN
ejpam-3916	330	3	appl	appl	PROPN
ejpam-3916	330	4	.	.	PROPN
ejpam-3916	330	5	math	math	PROPN
ejpam-3916	330	6	,	,	PUNCT
ejpam-3916	330	7	14	14	NUM
ejpam-3916	330	8	(	(	PUNCT
ejpam-3916	330	9	1	1	NUM
ejpam-3916	330	10	)	)	PUNCT
ejpam-3916	330	11	(	(	PUNCT
ejpam-3916	330	12	2021	2021	NUM
ejpam-3916	330	13	)	)	PUNCT
ejpam-3916	330	14	,	,	PUNCT
ejpam-3916	330	15	112	112	NUM
ejpam-3916	330	16	-	-	SYM
ejpam-3916	330	17	125	125	NUM
ejpam-3916	330	18	120	120	NUM
ejpam-3916	330	19	set	set	NOUN
ejpam-3916	330	20	of	of	ADP
ejpam-3916	330	21	h.	h.	PROPN
ejpam-3916	330	22	finally	finally	ADV
ejpam-3916	330	23	,	,	PUNCT
ejpam-3916	330	24	suppose	suppose	VERB
ejpam-3916	330	25	that	that	SCONJ
ejpam-3916	330	26	ng[x	ng[x	PROPN
ejpam-3916	330	27	]	]	X
ejpam-3916	330	28	=	=	SYM
ejpam-3916	330	29	v	v	X
ejpam-3916	330	30	(	(	PUNCT
ejpam-3916	330	31	g	g	NOUN
ejpam-3916	330	32	)	)	PUNCT
ejpam-3916	330	33	.	.	PUNCT
ejpam-3916	331	1	then	then	ADV
ejpam-3916	331	2	u	u	X
ejpam-3916	331	3	=	=	PUNCT
ejpam-3916	331	4	x	x	X
ejpam-3916	331	5	and	and	CCONJ
ejpam-3916	331	6	t	t	PROPN
ejpam-3916	331	7	∈	∈	PROPN
ejpam-3916	331	8	nh(p	nh(p	PROPN
ejpam-3916	331	9	)	)	PUNCT
ejpam-3916	331	10	∩	∩	NOUN
ejpam-3916	331	11	nh(q	nh(q	PRON
ejpam-3916	331	12	)	)	PUNCT
ejpam-3916	331	13	.	.	PUNCT
ejpam-3916	332	1	it	it	PRON
ejpam-3916	332	2	follows	follow	VERB
ejpam-3916	332	3	that	that	PRON
ejpam-3916	332	4	t	t	PROPN
ejpam-3916	332	5	/∈	/∈	PUNCT
ejpam-3916	332	6	nh	nh	PROPN
ejpam-3916	333	1	[	[	X
ejpam-3916	333	2	{	{	PUNCT
ejpam-3916	333	3	p	p	X
ejpam-3916	333	4	,	,	PUNCT
ejpam-3916	333	5	q	q	NOUN
ejpam-3916	333	6	}	}	PUNCT
ejpam-3916	333	7	]	]	PUNCT
ejpam-3916	333	8	.	.	PUNCT
ejpam-3916	334	1	thus	thus	ADV
ejpam-3916	334	2	,	,	PUNCT
ejpam-3916	334	3	tx	tx	PROPN
ejpam-3916	334	4	is	be	AUX
ejpam-3916	334	5	a	a	DET
ejpam-3916	334	6	pairwise	pairwise	NOUN
ejpam-3916	334	7	non	non	ADJ
ejpam-3916	334	8	-	-	ADJ
ejpam-3916	334	9	dominating	dominating	ADJ
ejpam-3916	334	10	set	set	NOUN
ejpam-3916	334	11	of	of	ADP
ejpam-3916	334	12	h.	h.	PROPN
ejpam-3916	334	13	therefore	therefore	ADV
ejpam-3916	334	14	,	,	PUNCT
ejpam-3916	334	15	(	(	PUNCT
ejpam-3916	334	16	iii	iii	X
ejpam-3916	334	17	)	)	PUNCT
ejpam-3916	334	18	holds	hold	VERB
ejpam-3916	334	19	.	.	PUNCT
ejpam-3916	335	1	now	now	ADV
ejpam-3916	335	2	let	let	VERB
ejpam-3916	335	3	z	z	NOUN
ejpam-3916	335	4	∈	∈	PROPN
ejpam-3916	335	5	v	v	NOUN
ejpam-3916	335	6	(	(	PUNCT
ejpam-3916	335	7	g)\s	g)\s	NOUN
ejpam-3916	335	8	.	.	PUNCT
ejpam-3916	336	1	choose	choose	VERB
ejpam-3916	336	2	any	any	DET
ejpam-3916	336	3	b	b	PROPN
ejpam-3916	336	4	∈	∈	PROPN
ejpam-3916	336	5	v	v	NOUN
ejpam-3916	336	6	(	(	PUNCT
ejpam-3916	336	7	h	h	NOUN
ejpam-3916	336	8	)	)	PUNCT
ejpam-3916	336	9	.	.	PUNCT
ejpam-3916	337	1	since	since	SCONJ
ejpam-3916	337	2	c	c	PROPN
ejpam-3916	337	3	is	be	AUX
ejpam-3916	337	4	a	a	DET
ejpam-3916	337	5	hop	hop	NOUN
ejpam-3916	337	6	dominating	dominating	NOUN
ejpam-3916	337	7	set	set	NOUN
ejpam-3916	337	8	of	of	ADP
ejpam-3916	337	9	g[h	g[h	PROPN
ejpam-3916	337	10	]	]	PUNCT
ejpam-3916	337	11	,	,	PUNCT
ejpam-3916	337	12	there	there	PRON
ejpam-3916	337	13	exists	exist	VERB
ejpam-3916	337	14	(	(	PUNCT
ejpam-3916	337	15	y	y	NOUN
ejpam-3916	337	16	,	,	PUNCT
ejpam-3916	337	17	c	c	NOUN
ejpam-3916	337	18	)	)	PUNCT
ejpam-3916	337	19	∈	∈	PROPN
ejpam-3916	337	20	c	c	NOUN
ejpam-3916	338	1	such	such	ADJ
ejpam-3916	338	2	that	that	PRON
ejpam-3916	338	3	d	d	PROPN
ejpam-3916	338	4	g[h	g[h	PROPN
ejpam-3916	338	5	]	]	X
ejpam-3916	338	6	(	(	PUNCT
ejpam-3916	338	7	(	(	PUNCT
ejpam-3916	338	8	z	z	NOUN
ejpam-3916	338	9	,	,	PUNCT
ejpam-3916	338	10	b)(y	b)(y	PROPN
ejpam-3916	338	11	,	,	PUNCT
ejpam-3916	338	12	c	c	NOUN
ejpam-3916	338	13	)	)	PUNCT
ejpam-3916	338	14	)	)	PUNCT
ejpam-3916	339	1	=	=	SYM
ejpam-3916	339	2	2	2	NUM
ejpam-3916	339	3	,	,	PUNCT
ejpam-3916	339	4	that	that	ADV
ejpam-3916	339	5	is	is	ADV
ejpam-3916	339	6	,	,	PUNCT
ejpam-3916	339	7	dg[h]((z	dg[h]((z	X
ejpam-3916	339	8	,	,	PUNCT
ejpam-3916	339	9	b)(y	b)(y	PROPN
ejpam-3916	339	10	,	,	PUNCT
ejpam-3916	339	11	c	c	NOUN
ejpam-3916	339	12	)	)	PUNCT
ejpam-3916	339	13	)	)	PUNCT
ejpam-3916	340	1	=	=	PUNCT
ejpam-3916	340	2	1	1	X
ejpam-3916	340	3	.	.	PUNCT
ejpam-3916	341	1	hence	hence	ADV
ejpam-3916	341	2	,	,	PUNCT
ejpam-3916	341	3	y	y	PROPN
ejpam-3916	341	4	∈	∈	PROPN
ejpam-3916	341	5	s	s	PART
ejpam-3916	341	6	∩	∩	NOUN
ejpam-3916	341	7	ng(z	ng(z	NUM
ejpam-3916	341	8	)	)	PUNCT
ejpam-3916	341	9	.	.	PUNCT
ejpam-3916	342	1	let	let	VERB
ejpam-3916	342	2	[	[	X
ejpam-3916	342	3	(	(	PUNCT
ejpam-3916	342	4	z	z	NOUN
ejpam-3916	342	5	,	,	PUNCT
ejpam-3916	342	6	b	b	NOUN
ejpam-3916	342	7	)	)	PUNCT
ejpam-3916	342	8	,	,	PUNCT
ejpam-3916	342	9	(	(	PUNCT
ejpam-3916	342	10	s	s	X
ejpam-3916	342	11	,	,	PUNCT
ejpam-3916	342	12	d	d	NOUN
ejpam-3916	342	13	)	)	PUNCT
ejpam-3916	342	14	,	,	PUNCT
ejpam-3916	342	15	(	(	PUNCT
ejpam-3916	342	16	y	y	NOUN
ejpam-3916	342	17	,	,	PUNCT
ejpam-3916	342	18	c	c	NOUN
ejpam-3916	342	19	)	)	PUNCT
ejpam-3916	342	20	]	]	PUNCT
ejpam-3916	342	21	be	be	AUX
ejpam-3916	342	22	a	a	DET
ejpam-3916	342	23	(	(	PUNCT
ejpam-3916	342	24	z	z	NOUN
ejpam-3916	342	25	,	,	PUNCT
ejpam-3916	342	26	b)-(y	b)-(y	PROPN
ejpam-3916	342	27	,	,	PUNCT
ejpam-3916	342	28	c	c	NOUN
ejpam-3916	342	29	)	)	PUNCT
ejpam-3916	342	30	geodesic	geodesic	NOUN
ejpam-3916	342	31	in	in	ADP
ejpam-3916	342	32	g[h	g[h	PROPN
ejpam-3916	342	33	]	]	PUNCT
ejpam-3916	342	34	.	.	PUNCT
ejpam-3916	343	1	then	then	ADV
ejpam-3916	343	2	s	s	VERB
ejpam-3916	343	3	∈	∈	PROPN
ejpam-3916	344	1	[	[	X
ejpam-3916	344	2	v	v	X
ejpam-3916	344	3	(	(	PUNCT
ejpam-3916	344	4	g	g	NOUN
ejpam-3916	344	5	)	)	PUNCT
ejpam-3916	344	6	\ng(z	\ng(z	NOUN
ejpam-3916	344	7	)	)	PUNCT
ejpam-3916	344	8	]	]	PUNCT
ejpam-3916	344	9	∩	∩	NOUN
ejpam-3916	344	10	[	[	X
ejpam-3916	344	11	v	v	X
ejpam-3916	344	12	(	(	PUNCT
ejpam-3916	344	13	g	g	NOUN
ejpam-3916	344	14	)	)	PUNCT
ejpam-3916	344	15	\ng(y	\ng(y	NOUN
ejpam-3916	344	16	)	)	PUNCT
ejpam-3916	344	17	]	]	PUNCT
ejpam-3916	344	18	,	,	PUNCT
ejpam-3916	344	19	showing	show	VERB
ejpam-3916	344	20	that	that	SCONJ
ejpam-3916	344	21	(	(	PUNCT
ejpam-3916	344	22	iv	iv	X
ejpam-3916	344	23	)	)	PUNCT
ejpam-3916	344	24	holds	hold	NOUN
ejpam-3916	344	25	.	.	PUNCT
ejpam-3916	345	1	for	for	ADP
ejpam-3916	345	2	the	the	DET
ejpam-3916	345	3	converse	converse	NOUN
ejpam-3916	345	4	,	,	PUNCT
ejpam-3916	345	5	suppose	suppose	VERB
ejpam-3916	345	6	that	that	SCONJ
ejpam-3916	345	7	c	c	PROPN
ejpam-3916	345	8	satisfies	satisfy	VERB
ejpam-3916	345	9	properties	property	NOUN
ejpam-3916	345	10	(	(	PUNCT
ejpam-3916	345	11	i	i	NOUN
ejpam-3916	345	12	)	)	PUNCT
ejpam-3916	345	13	,	,	PUNCT
ejpam-3916	345	14	(	(	PUNCT
ejpam-3916	345	15	ii	ii	NOUN
ejpam-3916	345	16	)	)	PUNCT
ejpam-3916	345	17	,	,	PUNCT
ejpam-3916	345	18	(	(	PUNCT
ejpam-3916	345	19	iii	iii	NOUN
ejpam-3916	345	20	)	)	PUNCT
ejpam-3916	345	21	,	,	PUNCT
ejpam-3916	345	22	and	and	CCONJ
ejpam-3916	345	23	(	(	PUNCT
ejpam-3916	345	24	iv	iv	X
ejpam-3916	345	25	)	)	PUNCT
ejpam-3916	345	26	.	.	PUNCT
ejpam-3916	346	1	by	by	ADP
ejpam-3916	346	2	(	(	PUNCT
ejpam-3916	346	3	i	i	NOUN
ejpam-3916	346	4	)	)	PUNCT
ejpam-3916	346	5	and	and	CCONJ
ejpam-3916	346	6	(	(	PUNCT
ejpam-3916	346	7	ii	ii	NOUN
ejpam-3916	346	8	)	)	PUNCT
ejpam-3916	346	9	,	,	PUNCT
ejpam-3916	346	10	c	c	PROPN
ejpam-3916	346	11	is	be	AUX
ejpam-3916	346	12	a	a	DET
ejpam-3916	346	13	hop	hop	NOUN
ejpam-3916	346	14	dominating	dominating	NOUN
ejpam-3916	346	15	set	set	NOUN
ejpam-3916	346	16	of	of	ADP
ejpam-3916	346	17	g[h	g[h	PROPN
ejpam-3916	346	18	]	]	PUNCT
ejpam-3916	346	19	.	.	PUNCT
ejpam-3916	347	1	let	let	VERB
ejpam-3916	347	2	(	(	PUNCT
ejpam-3916	347	3	v	v	NOUN
ejpam-3916	347	4	,	,	PUNCT
ejpam-3916	347	5	a	a	PRON
ejpam-3916	347	6	)	)	PUNCT
ejpam-3916	347	7	∈	∈	NOUN
ejpam-3916	347	8	v	v	NOUN
ejpam-3916	347	9	(	(	PUNCT
ejpam-3916	347	10	g[h	g[h	PROPN
ejpam-3916	347	11	]	]	PUNCT
ejpam-3916	347	12	)	)	PUNCT
ejpam-3916	347	13	\	\	PROPN
ejpam-3916	348	1	c	c	NOUN
ejpam-3916	349	1	and	and	CCONJ
ejpam-3916	349	2	consider	consider	VERB
ejpam-3916	349	3	the	the	DET
ejpam-3916	349	4	following	follow	VERB
ejpam-3916	349	5	cases	case	NOUN
ejpam-3916	349	6	:	:	PUNCT
ejpam-3916	349	7	case	case	NOUN
ejpam-3916	349	8	1	1	NUM
ejpam-3916	349	9	.	.	X
ejpam-3916	350	1	v	v	NUM
ejpam-3916	350	2	/∈	/∈	PUNCT
ejpam-3916	350	3	s	s	VERB
ejpam-3916	350	4	by	by	X
ejpam-3916	350	5	(	(	PUNCT
ejpam-3916	350	6	iv	iv	NOUN
ejpam-3916	350	7	)	)	PUNCT
ejpam-3916	350	8	,	,	PUNCT
ejpam-3916	350	9	let	let	VERB
ejpam-3916	350	10	y	y	PROPN
ejpam-3916	350	11	∈	∈	PROPN
ejpam-3916	350	12	s	s	PART
ejpam-3916	350	13	∩	∩	NOUN
ejpam-3916	350	14	ng(v	ng(v	X
ejpam-3916	350	15	)	)	PUNCT
ejpam-3916	350	16	and	and	CCONJ
ejpam-3916	350	17	let	let	VERB
ejpam-3916	350	18	u	u	PRON
ejpam-3916	350	19	∈	∈	PROPN
ejpam-3916	350	20	[	[	X
ejpam-3916	350	21	v	v	X
ejpam-3916	350	22	(	(	PUNCT
ejpam-3916	350	23	g	g	NOUN
ejpam-3916	350	24	)	)	PUNCT
ejpam-3916	350	25	\	\	NOUN
ejpam-3916	350	26	ng(v	ng(v	PUNCT
ejpam-3916	350	27	)	)	PUNCT
ejpam-3916	350	28	]	]	PUNCT
ejpam-3916	351	1	∩	∩	NOUN
ejpam-3916	351	2	[	[	X
ejpam-3916	351	3	v	v	X
ejpam-3916	351	4	(	(	PUNCT
ejpam-3916	351	5	g	g	NOUN
ejpam-3916	351	6	)	)	PUNCT
ejpam-3916	351	7	\	\	NOUN
ejpam-3916	351	8	ng(y	ng(y	NOUN
ejpam-3916	351	9	)	)	PUNCT
ejpam-3916	351	10	]	]	PUNCT
ejpam-3916	352	1	=	=	PUNCT
ejpam-3916	352	2	∅.	∅.	AUX
ejpam-3916	352	3	let	let	VERB
ejpam-3916	352	4	p	p	PROPN
ejpam-3916	352	5	∈	∈	PROPN
ejpam-3916	352	6	ty	ty	PRON
ejpam-3916	352	7	.	.	PUNCT
ejpam-3916	353	1	then	then	ADV
ejpam-3916	353	2	(	(	PUNCT
ejpam-3916	353	3	y	y	PROPN
ejpam-3916	353	4	,	,	PUNCT
ejpam-3916	353	5	p	p	NOUN
ejpam-3916	353	6	)	)	PUNCT
ejpam-3916	353	7	∈	∈	PROPN
ejpam-3916	353	8	c	c	NOUN
ejpam-3916	353	9	and	and	CCONJ
ejpam-3916	353	10	[	[	X
ejpam-3916	353	11	(	(	PUNCT
ejpam-3916	353	12	v	v	NOUN
ejpam-3916	353	13	,	,	PUNCT
ejpam-3916	353	14	a	a	PRON
ejpam-3916	353	15	)	)	PUNCT
ejpam-3916	353	16	,	,	PUNCT
ejpam-3916	353	17	(	(	PUNCT
ejpam-3916	353	18	u	u	NOUN
ejpam-3916	353	19	,	,	PUNCT
ejpam-3916	353	20	a	a	PRON
ejpam-3916	353	21	)	)	PUNCT
ejpam-3916	353	22	,	,	PUNCT
ejpam-3916	353	23	(	(	PUNCT
ejpam-3916	353	24	y	y	NOUN
ejpam-3916	353	25	,	,	PUNCT
ejpam-3916	353	26	p	p	NOUN
ejpam-3916	353	27	)	)	PUNCT
ejpam-3916	353	28	]	]	PUNCT
ejpam-3916	353	29	is	be	AUX
ejpam-3916	353	30	a	a	DET
ejpam-3916	353	31	(	(	PUNCT
ejpam-3916	353	32	v	v	NOUN
ejpam-3916	353	33	,	,	PUNCT
ejpam-3916	353	34	a)-(y	a)-(y	PROPN
ejpam-3916	353	35	,	,	PUNCT
ejpam-3916	353	36	p	p	NOUN
ejpam-3916	353	37	)	)	PUNCT
ejpam-3916	353	38	geodesic	geodesic	NOUN
ejpam-3916	353	39	in	in	ADP
ejpam-3916	353	40	g[h	g[h	PROPN
ejpam-3916	353	41	]	]	PUNCT
ejpam-3916	353	42	.	.	PUNCT
ejpam-3916	354	1	thus	thus	ADV
ejpam-3916	354	2	,	,	PUNCT
ejpam-3916	354	3	d	d	PROPN
ejpam-3916	354	4	g[h	g[h	PROPN
ejpam-3916	354	5	]	]	X
ejpam-3916	354	6	(	(	PUNCT
ejpam-3916	354	7	(	(	PUNCT
ejpam-3916	354	8	v	v	NOUN
ejpam-3916	354	9	,	,	PUNCT
ejpam-3916	354	10	a)(y	a)(y	PROPN
ejpam-3916	354	11	,	,	PUNCT
ejpam-3916	354	12	p	p	NOUN
ejpam-3916	354	13	)	)	PUNCT
ejpam-3916	354	14	)	)	PUNCT
ejpam-3916	355	1	=	=	SYM
ejpam-3916	355	2	2	2	X
ejpam-3916	355	3	.	.	X
ejpam-3916	355	4	case	case	NOUN
ejpam-3916	355	5	2	2	NUM
ejpam-3916	355	6	.	.	NOUN
ejpam-3916	355	7	v	v	NUM
ejpam-3916	355	8	∈	∈	PROPN
ejpam-3916	355	9	s	s	AUX
ejpam-3916	355	10	suppose	suppose	VERB
ejpam-3916	355	11	s∩ng(v	s∩ng(v	X
ejpam-3916	355	12	)	)	PUNCT
ejpam-3916	355	13	6=	6=	NOUN
ejpam-3916	355	14	∅	∅	NOUN
ejpam-3916	355	15	and	and	CCONJ
ejpam-3916	355	16	[	[	X
ejpam-3916	355	17	v	v	X
ejpam-3916	355	18	(	(	PUNCT
ejpam-3916	355	19	g)\ng(v)]∩[v	g)\ng(v)]∩[v	NOUN
ejpam-3916	355	20	(	(	PUNCT
ejpam-3916	355	21	g)\ng(y	g)\ng(y	PROPN
ejpam-3916	355	22	)	)	PUNCT
ejpam-3916	355	23	]	]	PUNCT
ejpam-3916	355	24	6=	6=	ADP
ejpam-3916	355	25	∅	∅	NOUN
ejpam-3916	355	26	for	for	ADP
ejpam-3916	355	27	some	some	DET
ejpam-3916	355	28	y	y	PROPN
ejpam-3916	355	29	∈	∈	PROPN
ejpam-3916	355	30	s∩ng(v	s∩ng(v	PROPN
ejpam-3916	355	31	)	)	PUNCT
ejpam-3916	355	32	.	.	PUNCT
ejpam-3916	356	1	choose	choose	VERB
ejpam-3916	356	2	any	any	DET
ejpam-3916	356	3	q	q	PUNCT
ejpam-3916	356	4	∈	∈	PROPN
ejpam-3916	356	5	ty	ty	INTJ
ejpam-3916	356	6	and	and	CCONJ
ejpam-3916	356	7	let	let	VERB
ejpam-3916	356	8	w	w	PROPN
ejpam-3916	356	9	∈	∈	PROPN
ejpam-3916	357	1	[	[	X
ejpam-3916	357	2	v	v	X
ejpam-3916	357	3	(	(	PUNCT
ejpam-3916	357	4	g	g	NOUN
ejpam-3916	357	5	)	)	PUNCT
ejpam-3916	357	6	\	\	NOUN
ejpam-3916	357	7	ng(v	ng(v	PUNCT
ejpam-3916	357	8	)	)	PUNCT
ejpam-3916	357	9	]	]	PUNCT
ejpam-3916	357	10	∩	∩	NOUN
ejpam-3916	357	11	[	[	X
ejpam-3916	357	12	v	v	X
ejpam-3916	357	13	(	(	PUNCT
ejpam-3916	357	14	g	g	NOUN
ejpam-3916	357	15	)	)	PUNCT
ejpam-3916	357	16	\	\	NOUN
ejpam-3916	357	17	ng(y	ng(y	NOUN
ejpam-3916	357	18	)	)	PUNCT
ejpam-3916	357	19	]	]	PUNCT
ejpam-3916	357	20	.	.	PUNCT
ejpam-3916	358	1	then	then	ADV
ejpam-3916	358	2	(	(	PUNCT
ejpam-3916	358	3	y	y	NOUN
ejpam-3916	358	4	,	,	PUNCT
ejpam-3916	358	5	q	q	X
ejpam-3916	358	6	)	)	PUNCT
ejpam-3916	358	7	∈	∈	PROPN
ejpam-3916	358	8	c	c	NOUN
ejpam-3916	358	9	and	and	CCONJ
ejpam-3916	358	10	[	[	X
ejpam-3916	358	11	(	(	PUNCT
ejpam-3916	358	12	v	v	NOUN
ejpam-3916	358	13	,	,	PUNCT
ejpam-3916	358	14	a	a	PRON
ejpam-3916	358	15	)	)	PUNCT
ejpam-3916	358	16	,	,	PUNCT
ejpam-3916	358	17	(	(	PUNCT
ejpam-3916	358	18	w	w	NOUN
ejpam-3916	358	19	,	,	PUNCT
ejpam-3916	358	20	a	a	NOUN
ejpam-3916	358	21	)	)	PUNCT
ejpam-3916	358	22	,	,	PUNCT
ejpam-3916	358	23	(	(	PUNCT
ejpam-3916	358	24	y	y	NOUN
ejpam-3916	358	25	,	,	PUNCT
ejpam-3916	358	26	q	q	NOUN
ejpam-3916	358	27	)	)	PUNCT
ejpam-3916	358	28	]	]	PUNCT
ejpam-3916	358	29	is	be	AUX
ejpam-3916	358	30	a	a	DET
ejpam-3916	358	31	(	(	PUNCT
ejpam-3916	358	32	v	v	NOUN
ejpam-3916	358	33	,	,	PUNCT
ejpam-3916	358	34	a)-(y	a)-(y	PROPN
ejpam-3916	358	35	,	,	PUNCT
ejpam-3916	358	36	q	q	NOUN
ejpam-3916	358	37	)	)	PUNCT
ejpam-3916	358	38	geodesic	geodesic	NOUN
ejpam-3916	358	39	in	in	ADP
ejpam-3916	358	40	g[h	g[h	PROPN
ejpam-3916	358	41	]	]	PUNCT
ejpam-3916	358	42	.	.	PUNCT
ejpam-3916	359	1	thus	thus	ADV
ejpam-3916	359	2	,	,	PUNCT
ejpam-3916	359	3	d	d	PROPN
ejpam-3916	359	4	g[h	g[h	PROPN
ejpam-3916	359	5	]	]	X
ejpam-3916	359	6	(	(	PUNCT
ejpam-3916	359	7	(	(	PUNCT
ejpam-3916	359	8	v	v	NOUN
ejpam-3916	359	9	,	,	PUNCT
ejpam-3916	359	10	a)(y	a)(y	PROPN
ejpam-3916	359	11	,	,	PUNCT
ejpam-3916	359	12	q	q	NOUN
ejpam-3916	359	13	)	)	PUNCT
ejpam-3916	359	14	)	)	PUNCT
ejpam-3916	360	1	=	=	SYM
ejpam-3916	360	2	2	2	X
ejpam-3916	360	3	.	.	PUNCT
ejpam-3916	361	1	next	next	ADV
ejpam-3916	361	2	,	,	PUNCT
ejpam-3916	361	3	suppose	suppose	VERB
ejpam-3916	361	4	that	that	SCONJ
ejpam-3916	361	5	s∩ng(v	s∩ng(v	ADJ
ejpam-3916	361	6	)	)	PUNCT
ejpam-3916	361	7	=	=	SYM
ejpam-3916	361	8	∅	∅	NOUN
ejpam-3916	361	9	or	or	CCONJ
ejpam-3916	361	10	[	[	X
ejpam-3916	361	11	v	v	X
ejpam-3916	361	12	(	(	PUNCT
ejpam-3916	361	13	g)\ng(v)]∩	g)\ng(v)]∩	NOUN
ejpam-3916	362	1	[	[	X
ejpam-3916	362	2	v	v	X
ejpam-3916	362	3	(	(	PUNCT
ejpam-3916	362	4	g)\ng(y	g)\ng(y	PROPN
ejpam-3916	362	5	)	)	PUNCT
ejpam-3916	362	6	]	]	PUNCT
ejpam-3916	363	1	=	=	PUNCT
ejpam-3916	363	2	∅	∅	NOUN
ejpam-3916	363	3	for	for	ADP
ejpam-3916	363	4	all	all	DET
ejpam-3916	363	5	y	y	PROPN
ejpam-3916	363	6	∈	∈	PROPN
ejpam-3916	363	7	s∩ng(v	s∩ng(v	PROPN
ejpam-3916	363	8	)	)	PUNCT
ejpam-3916	363	9	.	.	PUNCT
ejpam-3916	363	10	suppose	suppose	VERB
ejpam-3916	363	11	ng[v	ng[v	NOUN
ejpam-3916	363	12	]	]	X
ejpam-3916	363	13	=	=	SYM
ejpam-3916	363	14	v	v	X
ejpam-3916	363	15	(	(	PUNCT
ejpam-3916	363	16	g	g	NOUN
ejpam-3916	363	17	)	)	PUNCT
ejpam-3916	363	18	.	.	PUNCT
ejpam-3916	364	1	then	then	ADV
ejpam-3916	364	2	tv	tv	NOUN
ejpam-3916	364	3	is	be	AUX
ejpam-3916	364	4	a	a	DET
ejpam-3916	364	5	pairwise	pairwise	NOUN
ejpam-3916	364	6	non	non	ADJ
ejpam-3916	364	7	-	-	ADJ
ejpam-3916	364	8	dominating	dominating	ADJ
ejpam-3916	364	9	set	set	NOUN
ejpam-3916	364	10	of	of	ADP
ejpam-3916	364	11	h	h	NOUN
ejpam-3916	364	12	by	by	ADP
ejpam-3916	364	13	(	(	PUNCT
ejpam-3916	364	14	iii	iii	NOUN
ejpam-3916	364	15	)	)	PUNCT
ejpam-3916	364	16	.	.	PUNCT
ejpam-3916	365	1	hence	hence	ADV
ejpam-3916	365	2	,	,	PUNCT
ejpam-3916	365	3	there	there	PRON
ejpam-3916	365	4	exists	exist	VERB
ejpam-3916	365	5	d	d	PROPN
ejpam-3916	365	6	∈	∈	PROPN
ejpam-3916	365	7	tv∩nh(a	tv∩nh(a	PROPN
ejpam-3916	365	8	)	)	PUNCT
ejpam-3916	365	9	such	such	ADJ
ejpam-3916	365	10	that	that	DET
ejpam-3916	365	11	nh({a	nh({a	NOUN
ejpam-3916	365	12	,	,	PUNCT
ejpam-3916	365	13	d	d	NOUN
ejpam-3916	365	14	}	}	PUNCT
ejpam-3916	365	15	)	)	PUNCT
ejpam-3916	365	16	6=	6=	ADP
ejpam-3916	365	17	v	v	X
ejpam-3916	365	18	(	(	PUNCT
ejpam-3916	365	19	h	h	NOUN
ejpam-3916	365	20	)	)	PUNCT
ejpam-3916	365	21	.	.	PUNCT
ejpam-3916	366	1	this	this	PRON
ejpam-3916	366	2	implies	imply	VERB
ejpam-3916	366	3	that	that	SCONJ
ejpam-3916	366	4	(	(	PUNCT
ejpam-3916	366	5	v	v	NOUN
ejpam-3916	366	6	,	,	PUNCT
ejpam-3916	366	7	d	d	NOUN
ejpam-3916	366	8	)	)	PUNCT
ejpam-3916	366	9	∈	∈	PROPN
ejpam-3916	366	10	c	c	NOUN
ejpam-3916	366	11	and	and	CCONJ
ejpam-3916	366	12	there	there	PRON
ejpam-3916	366	13	exists	exist	VERB
ejpam-3916	366	14	t	t	PROPN
ejpam-3916	366	15	∈	∈	PROPN
ejpam-3916	366	16	v	v	ADP
ejpam-3916	366	17	(	(	PUNCT
ejpam-3916	366	18	h	h	NOUN
ejpam-3916	366	19	)	)	PUNCT
ejpam-3916	366	20	\nh({a	\nh({a	NOUN
ejpam-3916	366	21	,	,	PUNCT
ejpam-3916	366	22	d	d	NOUN
ejpam-3916	366	23	}	}	PUNCT
ejpam-3916	366	24	)	)	PUNCT
ejpam-3916	366	25	.	.	PUNCT
ejpam-3916	367	1	hence	hence	ADV
ejpam-3916	367	2	,	,	PUNCT
ejpam-3916	367	3	[	[	X
ejpam-3916	367	4	(	(	PUNCT
ejpam-3916	367	5	v	v	NOUN
ejpam-3916	367	6	,	,	PUNCT
ejpam-3916	367	7	a	a	PRON
ejpam-3916	367	8	)	)	PUNCT
ejpam-3916	367	9	,	,	PUNCT
ejpam-3916	367	10	(	(	PUNCT
ejpam-3916	367	11	v	v	NOUN
ejpam-3916	367	12	,	,	PUNCT
ejpam-3916	367	13	t	t	PROPN
ejpam-3916	367	14	)	)	PUNCT
ejpam-3916	367	15	,	,	PUNCT
ejpam-3916	367	16	(	(	PUNCT
ejpam-3916	367	17	v	v	NOUN
ejpam-3916	367	18	,	,	PUNCT
ejpam-3916	367	19	d	d	NOUN
ejpam-3916	367	20	)	)	PUNCT
ejpam-3916	367	21	]	]	PUNCT
ejpam-3916	367	22	is	be	AUX
ejpam-3916	367	23	a	a	DET
ejpam-3916	367	24	(	(	PUNCT
ejpam-3916	367	25	v	v	NOUN
ejpam-3916	367	26	,	,	PUNCT
ejpam-3916	367	27	a)-(v	a)-(v	PROPN
ejpam-3916	367	28	,	,	PUNCT
ejpam-3916	367	29	d	d	NOUN
ejpam-3916	367	30	)	)	PUNCT
ejpam-3916	367	31	geodesic	geodesic	NOUN
ejpam-3916	367	32	in	in	ADP
ejpam-3916	367	33	g[h	g[h	PROPN
ejpam-3916	367	34	]	]	PUNCT
ejpam-3916	367	35	,	,	PUNCT
ejpam-3916	367	36	that	that	ADV
ejpam-3916	367	37	is	is	ADV
ejpam-3916	367	38	,	,	PUNCT
ejpam-3916	367	39	d	d	PROPN
ejpam-3916	367	40	g[h	g[h	PROPN
ejpam-3916	367	41	]	]	X
ejpam-3916	367	42	(	(	PUNCT
ejpam-3916	367	43	(	(	PUNCT
ejpam-3916	367	44	v	v	NOUN
ejpam-3916	367	45	,	,	PUNCT
ejpam-3916	367	46	a	a	PRON
ejpam-3916	367	47	)	)	PUNCT
ejpam-3916	367	48	,	,	PUNCT
ejpam-3916	367	49	(	(	PUNCT
ejpam-3916	367	50	v	v	NOUN
ejpam-3916	367	51	,	,	PUNCT
ejpam-3916	367	52	d	d	NOUN
ejpam-3916	367	53	)	)	PUNCT
ejpam-3916	367	54	)	)	PUNCT
ejpam-3916	368	1	=	=	SYM
ejpam-3916	368	2	2	2	X
ejpam-3916	368	3	.	.	X
ejpam-3916	368	4	supposeng[v	supposeng[v	NOUN
ejpam-3916	368	5	]	]	PUNCT
ejpam-3916	368	6	6=	6=	NUM
ejpam-3916	368	7	v	v	ADP
ejpam-3916	368	8	(	(	PUNCT
ejpam-3916	368	9	g	g	NOUN
ejpam-3916	368	10	)	)	PUNCT
ejpam-3916	368	11	.	.	PUNCT
ejpam-3916	369	1	by	by	ADP
ejpam-3916	369	2	(	(	PUNCT
ejpam-3916	369	3	iii	iii	NOUN
ejpam-3916	369	4	)	)	PUNCT
ejpam-3916	369	5	,	,	PUNCT
ejpam-3916	369	6	tv	tv	NOUN
ejpam-3916	369	7	is	be	AUX
ejpam-3916	369	8	a	a	DET
ejpam-3916	369	9	dominating	dominating	NOUN
ejpam-3916	369	10	set	set	NOUN
ejpam-3916	369	11	of	of	ADP
ejpam-3916	369	12	h.	h.	PROPN
ejpam-3916	369	13	again	again	ADV
ejpam-3916	369	14	,	,	PUNCT
ejpam-3916	369	15	let	let	VERB
ejpam-3916	369	16	d	d	X
ejpam-3916	369	17	∈	∈	PROPN
ejpam-3916	369	18	tv	tv	NOUN
ejpam-3916	369	19	∩	∩	NOUN
ejpam-3916	369	20	nh(a	nh(a	NUM
ejpam-3916	369	21	)	)	PUNCT
ejpam-3916	369	22	and	and	CCONJ
ejpam-3916	369	23	pick	pick	VERB
ejpam-3916	369	24	w	w	PROPN
ejpam-3916	369	25	∈	∈	PROPN
ejpam-3916	369	26	v	v	ADP
ejpam-3916	369	27	(	(	PUNCT
ejpam-3916	369	28	h	h	NOUN
ejpam-3916	369	29	)	)	PUNCT
ejpam-3916	369	30	\	\	PUNCT
ejpam-3916	370	1	ng[v	ng[v	ADV
ejpam-3916	370	2	]	]	PUNCT
ejpam-3916	370	3	.	.	PUNCT
ejpam-3916	371	1	then	then	ADV
ejpam-3916	371	2	(	(	PUNCT
ejpam-3916	371	3	v	v	NOUN
ejpam-3916	371	4	,	,	PUNCT
ejpam-3916	371	5	d	d	NOUN
ejpam-3916	371	6	)	)	PUNCT
ejpam-3916	371	7	∈	∈	PROPN
ejpam-3916	371	8	c	c	NOUN
ejpam-3916	371	9	and	and	CCONJ
ejpam-3916	371	10	[	[	X
ejpam-3916	371	11	(	(	PUNCT
ejpam-3916	371	12	v	v	NOUN
ejpam-3916	371	13	,	,	PUNCT
ejpam-3916	371	14	a	a	PRON
ejpam-3916	371	15	)	)	PUNCT
ejpam-3916	371	16	,	,	PUNCT
ejpam-3916	371	17	(	(	PUNCT
ejpam-3916	371	18	w	w	NOUN
ejpam-3916	371	19	,	,	PUNCT
ejpam-3916	371	20	a	a	NOUN
ejpam-3916	371	21	)	)	PUNCT
ejpam-3916	371	22	,	,	PUNCT
ejpam-3916	371	23	(	(	PUNCT
ejpam-3916	371	24	v	v	NOUN
ejpam-3916	371	25	,	,	PUNCT
ejpam-3916	371	26	d	d	NOUN
ejpam-3916	371	27	)	)	PUNCT
ejpam-3916	371	28	]	]	PUNCT
ejpam-3916	371	29	is	be	AUX
ejpam-3916	371	30	a	a	DET
ejpam-3916	371	31	(	(	PUNCT
ejpam-3916	371	32	v	v	NOUN
ejpam-3916	371	33	,	,	PUNCT
ejpam-3916	371	34	a)-(v	a)-(v	PROPN
ejpam-3916	371	35	,	,	PUNCT
ejpam-3916	371	36	d	d	NOUN
ejpam-3916	371	37	)	)	PUNCT
ejpam-3916	371	38	geodesic	geodesic	NOUN
ejpam-3916	371	39	in	in	ADP
ejpam-3916	371	40	g[h	g[h	PROPN
ejpam-3916	371	41	]	]	PUNCT
ejpam-3916	371	42	.	.	PUNCT
ejpam-3916	372	1	thus	thus	ADV
ejpam-3916	372	2	,	,	PUNCT
ejpam-3916	372	3	d	d	PROPN
ejpam-3916	372	4	g[h	g[h	PROPN
ejpam-3916	372	5	]	]	X
ejpam-3916	372	6	(	(	PUNCT
ejpam-3916	372	7	(	(	PUNCT
ejpam-3916	372	8	v	v	NOUN
ejpam-3916	372	9	,	,	PUNCT
ejpam-3916	372	10	a	a	PRON
ejpam-3916	372	11	)	)	PUNCT
ejpam-3916	372	12	,	,	PUNCT
ejpam-3916	372	13	(	(	PUNCT
ejpam-3916	372	14	v	v	NOUN
ejpam-3916	372	15	,	,	PUNCT
ejpam-3916	372	16	d	d	NOUN
ejpam-3916	372	17	)	)	PUNCT
ejpam-3916	372	18	)	)	PUNCT
ejpam-3916	372	19	=	=	SYM
ejpam-3916	372	20	2	2	X
ejpam-3916	372	21	.	.	X
ejpam-3916	372	22	therefore	therefore	ADV
ejpam-3916	372	23	,	,	PUNCT
ejpam-3916	372	24	c	c	PROPN
ejpam-3916	372	25	is	be	AUX
ejpam-3916	372	26	a	a	DET
ejpam-3916	372	27	hop	hop	NOUN
ejpam-3916	372	28	dominating	dominating	NOUN
ejpam-3916	372	29	set	set	NOUN
ejpam-3916	372	30	of	of	ADP
ejpam-3916	372	31	g[h	g[h	PROPN
ejpam-3916	372	32	]	]	PUNCT
ejpam-3916	372	33	.	.	PUNCT
ejpam-3916	373	1	accordingly	accordingly	ADV
ejpam-3916	373	2	,	,	PUNCT
ejpam-3916	373	3	c	c	PROPN
ejpam-3916	373	4	is	be	AUX
ejpam-3916	373	5	a	a	DET
ejpam-3916	373	6	global	global	ADJ
ejpam-3916	373	7	hop	hop	NOUN
ejpam-3916	373	8	dominating	dominating	NOUN
ejpam-3916	373	9	set	set	NOUN
ejpam-3916	373	10	of	of	ADP
ejpam-3916	373	11	g[h	g[h	PROPN
ejpam-3916	373	12	]	]	PUNCT
ejpam-3916	373	13	.	.	PUNCT
ejpam-3916	374	1	a	a	DET
ejpam-3916	374	2	set	set	NOUN
ejpam-3916	374	3	s	s	NOUN
ejpam-3916	374	4	⊆	⊆	NUM
ejpam-3916	374	5	v	v	NOUN
ejpam-3916	374	6	(	(	PUNCT
ejpam-3916	374	7	g	g	NOUN
ejpam-3916	374	8	)	)	PUNCT
ejpam-3916	374	9	is	be	AUX
ejpam-3916	374	10	said	say	VERB
ejpam-3916	374	11	to	to	PART
ejpam-3916	374	12	be	be	AUX
ejpam-3916	374	13	dominating	dominate	VERB
ejpam-3916	374	14	complement	complement	NOUN
ejpam-3916	374	15	-	-	PUNCT
ejpam-3916	374	16	neighborhood	neighborhood	NOUN
ejpam-3916	374	17	intersecting	intersecting	NOUN
ejpam-3916	374	18	(	(	PUNCT
ejpam-3916	374	19	dcni	dcni	ADJ
ejpam-3916	374	20	)	)	PUNCT
ejpam-3916	374	21	(	(	PUNCT
ejpam-3916	374	22	resp	resp	NOUN
ejpam-3916	374	23	.	.	PUNCT
ejpam-3916	375	1	total	total	ADJ
ejpam-3916	375	2	dominating	dominating	NOUN
ejpam-3916	375	3	complement	complement	NOUN
ejpam-3916	375	4	-	-	PUNCT
ejpam-3916	375	5	neighborhood	neighborhood	NOUN
ejpam-3916	375	6	intersecting	intersecting	NOUN
ejpam-3916	375	7	(	(	PUNCT
ejpam-3916	375	8	tdcni	tdcni	NOUN
ejpam-3916	375	9	)	)	PUNCT
ejpam-3916	375	10	)	)	PUNCT
ejpam-3916	376	1	set	set	NOUN
ejpam-3916	376	2	of	of	ADP
ejpam-3916	376	3	a	a	DET
ejpam-3916	376	4	graph	graph	NOUN
ejpam-3916	376	5	g	g	NOUN
ejpam-3916	376	6	if	if	SCONJ
ejpam-3916	376	7	for	for	ADP
ejpam-3916	376	8	each	each	PRON
ejpam-3916	376	9	v	v	NUM
ejpam-3916	376	10	∈	∈	PROPN
ejpam-3916	376	11	v	v	NOUN
ejpam-3916	376	12	(	(	PUNCT
ejpam-3916	376	13	g	g	NOUN
ejpam-3916	376	14	)	)	PUNCT
ejpam-3916	376	15	\	\	PROPN
ejpam-3916	377	1	s	s	PART
ejpam-3916	377	2	(	(	PUNCT
ejpam-3916	377	3	resp	resp	NOUN
ejpam-3916	377	4	.	.	PUNCT
ejpam-3916	378	1	for	for	ADP
ejpam-3916	378	2	each	each	DET
ejpam-3916	378	3	v	v	NUM
ejpam-3916	378	4	∈	∈	PROPN
ejpam-3916	378	5	s	s	NOUN
ejpam-3916	378	6	)	)	PUNCT
ejpam-3916	378	7	,	,	PUNCT
ejpam-3916	378	8	there	there	PRON
ejpam-3916	378	9	exists	exist	VERB
ejpam-3916	378	10	w	w	PROPN
ejpam-3916	378	11	∈	∈	PROPN
ejpam-3916	378	12	s	s	PART
ejpam-3916	378	13	∩	∩	NOUN
ejpam-3916	378	14	ng(v	ng(v	NOUN
ejpam-3916	378	15	)	)	PUNCT
ejpam-3916	378	16	such	such	ADJ
ejpam-3916	378	17	that	that	SCONJ
ejpam-3916	378	18	(	(	PUNCT
ejpam-3916	378	19	v	v	NOUN
ejpam-3916	378	20	(	(	PUNCT
ejpam-3916	378	21	g	g	NOUN
ejpam-3916	378	22	)	)	PUNCT
ejpam-3916	378	23	\ng(v	\ng(v	NOUN
ejpam-3916	378	24	)	)	PUNCT
ejpam-3916	378	25	)	)	PUNCT
ejpam-3916	378	26	∩	∩	NOUN
ejpam-3916	378	27	(	(	PUNCT
ejpam-3916	378	28	v	v	NOUN
ejpam-3916	378	29	(	(	PUNCT
ejpam-3916	378	30	g	g	NOUN
ejpam-3916	378	31	)	)	PUNCT
ejpam-3916	378	32	\ng(w	\ng(w	PROPN
ejpam-3916	378	33	)	)	PUNCT
ejpam-3916	378	34	)	)	PUNCT
ejpam-3916	378	35	6=	6=	ADP
ejpam-3916	378	36	∅.	∅.	NOUN
ejpam-3916	378	37	let	let	VERB
ejpam-3916	378	38	γhcni(g	γhcni(g	NOUN
ejpam-3916	378	39	)	)	PUNCT
ejpam-3916	379	1	=	=	NOUN
ejpam-3916	379	2	min{|s|	min{|s|	NOUN
ejpam-3916	379	3	:	:	PUNCT
ejpam-3916	379	4	s	s	VERB
ejpam-3916	379	5	is	be	AUX
ejpam-3916	379	6	a	a	DET
ejpam-3916	379	7	dcni	dcni	ADJ
ejpam-3916	379	8	hop	hop	NOUN
ejpam-3916	379	9	dominating	dominating	NOUN
ejpam-3916	379	10	set	set	NOUN
ejpam-3916	379	11	of	of	ADP
ejpam-3916	379	12	g	g	NOUN
ejpam-3916	379	13	}	}	PUNCT
ejpam-3916	379	14	,	,	PUNCT
ejpam-3916	379	15	and	and	CCONJ
ejpam-3916	379	16	γtcni(g	γtcni(g	X
ejpam-3916	379	17	)	)	PUNCT
ejpam-3916	380	1	=	=	NOUN
ejpam-3916	380	2	min{|s|	min{|s|	NOUN
ejpam-3916	380	3	:	:	PUNCT
ejpam-3916	380	4	s	s	VERB
ejpam-3916	380	5	is	be	AUX
ejpam-3916	380	6	a	a	DET
ejpam-3916	380	7	tdcni	tdcni	NOUN
ejpam-3916	380	8	set	set	NOUN
ejpam-3916	380	9	of	of	ADP
ejpam-3916	380	10	g	g	NOUN
ejpam-3916	380	11	}	}	PUNCT
ejpam-3916	380	12	.	.	PUNCT
ejpam-3916	381	1	any	any	DET
ejpam-3916	381	2	dcni	dcni	ADJ
ejpam-3916	381	3	hop	hop	NOUN
ejpam-3916	381	4	dominating	dominating	NOUN
ejpam-3916	381	5	set	set	NOUN
ejpam-3916	381	6	of	of	ADP
ejpam-3916	381	7	g	g	PROPN
ejpam-3916	381	8	with	with	ADP
ejpam-3916	381	9	cardinality	cardinality	NOUN
ejpam-3916	381	10	γhcni(g	γhcni(g	PROPN
ejpam-3916	381	11	)	)	PUNCT
ejpam-3916	381	12	is	be	AUX
ejpam-3916	381	13	called	call	VERB
ejpam-3916	381	14	a	a	DET
ejpam-3916	381	15	γhcni	γhcni	NOUN
ejpam-3916	381	16	-	-	PUNCT
ejpam-3916	381	17	set	set	NOUN
ejpam-3916	381	18	of	of	ADP
ejpam-3916	381	19	g	g	PROPN
ejpam-3916	381	20	and	and	CCONJ
ejpam-3916	381	21	any	any	DET
ejpam-3916	381	22	tdcni	tdcni	NOUN
ejpam-3916	381	23	set	set	NOUN
ejpam-3916	381	24	of	of	ADP
ejpam-3916	381	25	g	g	NOUN
ejpam-3916	381	26	with	with	ADP
ejpam-3916	381	27	cardinality	cardinality	PROPN
ejpam-3916	381	28	γtcni(g	γtcni(g	PROPN
ejpam-3916	381	29	)	)	PUNCT
ejpam-3916	381	30	is	be	AUX
ejpam-3916	381	31	called	call	VERB
ejpam-3916	381	32	a	a	DET
ejpam-3916	381	33	γtcni	γtcni	NOUN
ejpam-3916	381	34	-	-	PUNCT
ejpam-3916	381	35	set	set	NOUN
ejpam-3916	381	36	of	of	ADP
ejpam-3916	381	37	g.	g.	PROPN
ejpam-3916	381	38	observe	observe	VERB
ejpam-3916	381	39	that	that	SCONJ
ejpam-3916	381	40	for	for	ADP
ejpam-3916	381	41	any	any	DET
ejpam-3916	381	42	graph	graph	NOUN
ejpam-3916	381	43	g	g	NOUN
ejpam-3916	381	44	,	,	PUNCT
ejpam-3916	381	45	the	the	DET
ejpam-3916	381	46	vertex	vertex	NOUN
ejpam-3916	381	47	set	set	VERB
ejpam-3916	381	48	v	v	NOUN
ejpam-3916	381	49	(	(	PUNCT
ejpam-3916	381	50	g	g	NOUN
ejpam-3916	381	51	)	)	PUNCT
ejpam-3916	381	52	is	be	AUX
ejpam-3916	381	53	a	a	DET
ejpam-3916	381	54	dominating	dominating	NOUN
ejpam-3916	381	55	complementneighborhood	complementneighborhood	NOUN
ejpam-3916	381	56	intersecting	intersecting	NOUN
ejpam-3916	381	57	and	and	CCONJ
ejpam-3916	381	58	hop	hop	NOUN
ejpam-3916	381	59	dominating	dominating	NOUN
ejpam-3916	381	60	set	set	NOUN
ejpam-3916	381	61	of	of	ADP
ejpam-3916	381	62	g.	g.	PROPN
ejpam-3916	381	63	also	also	ADV
ejpam-3916	381	64	,	,	PUNCT
ejpam-3916	381	65	if	if	SCONJ
ejpam-3916	381	66	g1	g1	PROPN
ejpam-3916	381	67	is	be	AUX
ejpam-3916	381	68	the	the	DET
ejpam-3916	381	69	graph	graph	NOUN
ejpam-3916	381	70	obtained	obtain	VERB
ejpam-3916	381	71	from	from	ADP
ejpam-3916	381	72	the	the	DET
ejpam-3916	381	73	cycle	cycle	NOUN
ejpam-3916	381	74	c4	c4	NOUN
ejpam-3916	381	75	=	=	PUNCT
ejpam-3916	382	1	[	[	X
ejpam-3916	382	2	a	a	PRON
ejpam-3916	382	3	,	,	PUNCT
ejpam-3916	382	4	b	b	NOUN
ejpam-3916	382	5	,	,	PUNCT
ejpam-3916	382	6	c	c	NOUN
ejpam-3916	382	7	,	,	PUNCT
ejpam-3916	382	8	d	d	NOUN
ejpam-3916	382	9	,	,	PUNCT
ejpam-3916	382	10	a	a	PRON
ejpam-3916	382	11	]	]	X
ejpam-3916	382	12	by	by	ADP
ejpam-3916	382	13	adding	add	VERB
ejpam-3916	382	14	the	the	DET
ejpam-3916	382	15	edges	edge	NOUN
ejpam-3916	382	16	av	av	PROPN
ejpam-3916	382	17	and	and	CCONJ
ejpam-3916	382	18	bw	bw	NOUN
ejpam-3916	382	19	,	,	PUNCT
ejpam-3916	382	20	then	then	ADV
ejpam-3916	382	21	s	s	VERB
ejpam-3916	382	22	=	=	PUNCT
ejpam-3916	382	23	{	{	PUNCT
ejpam-3916	382	24	a	a	DET
ejpam-3916	382	25	,	,	PUNCT
ejpam-3916	382	26	b	b	NOUN
ejpam-3916	382	27	}	}	PUNCT
ejpam-3916	382	28	is	be	AUX
ejpam-3916	382	29	a	a	DET
ejpam-3916	382	30	dcni	dcni	ADJ
ejpam-3916	382	31	g.	g.	PROPN
ejpam-3916	382	32	salasalan	salasalan	NOUN
ejpam-3916	382	33	,	,	PUNCT
ejpam-3916	382	34	s.	s.	PROPN
ejpam-3916	382	35	canoy	canoy	PROPN
ejpam-3916	382	36	,	,	PUNCT
ejpam-3916	382	37	jr	jr	PROPN
ejpam-3916	382	38	.	.	PROPN
ejpam-3916	382	39	/	/	SYM
ejpam-3916	382	40	eur	eur	PROPN
ejpam-3916	382	41	.	.	PUNCT
ejpam-3916	383	1	j.	j.	PROPN
ejpam-3916	383	2	pure	pure	PROPN
ejpam-3916	383	3	appl	appl	PROPN
ejpam-3916	383	4	.	.	PROPN
ejpam-3916	383	5	math	math	PROPN
ejpam-3916	383	6	,	,	PUNCT
ejpam-3916	383	7	14	14	NUM
ejpam-3916	383	8	(	(	PUNCT
ejpam-3916	383	9	1	1	NUM
ejpam-3916	383	10	)	)	PUNCT
ejpam-3916	383	11	(	(	PUNCT
ejpam-3916	383	12	2021	2021	NUM
ejpam-3916	383	13	)	)	PUNCT
ejpam-3916	383	14	,	,	PUNCT
ejpam-3916	383	15	112	112	NUM
ejpam-3916	383	16	-	-	SYM
ejpam-3916	383	17	125	125	NUM
ejpam-3916	383	18	121	121	NUM
ejpam-3916	383	19	hop	hop	NOUN
ejpam-3916	383	20	dominating	dominating	NOUN
ejpam-3916	383	21	set	set	NOUN
ejpam-3916	383	22	of	of	ADP
ejpam-3916	383	23	g1	g1	PROPN
ejpam-3916	383	24	.	.	PUNCT
ejpam-3916	384	1	proposition	proposition	NOUN
ejpam-3916	384	2	1	1	NUM
ejpam-3916	384	3	.	.	PUNCT
ejpam-3916	385	1	let	let	VERB
ejpam-3916	385	2	g	g	NOUN
ejpam-3916	385	3	be	be	AUX
ejpam-3916	385	4	graph	graph	NOUN
ejpam-3916	385	5	without	without	ADP
ejpam-3916	385	6	isolated	isolated	ADJ
ejpam-3916	385	7	vertices	vertex	NOUN
ejpam-3916	385	8	.	.	PUNCT
ejpam-3916	386	1	(	(	PUNCT
ejpam-3916	386	2	i	i	NOUN
ejpam-3916	386	3	)	)	PUNCT
ejpam-3916	386	4	if	if	SCONJ
ejpam-3916	386	5	g	g	PROPN
ejpam-3916	386	6	is	be	AUX
ejpam-3916	386	7	disconnected	disconnect	VERB
ejpam-3916	386	8	,	,	PUNCT
ejpam-3916	386	9	then	then	ADV
ejpam-3916	386	10	g	g	PROPN
ejpam-3916	386	11	admits	admit	VERB
ejpam-3916	386	12	a	a	DET
ejpam-3916	386	13	tdcni	tdcni	NOUN
ejpam-3916	386	14	set	set	NOUN
ejpam-3916	386	15	.	.	PUNCT
ejpam-3916	387	1	(	(	PUNCT
ejpam-3916	387	2	ii	ii	NOUN
ejpam-3916	387	3	)	)	PUNCT
ejpam-3916	387	4	if	if	SCONJ
ejpam-3916	387	5	g	g	PROPN
ejpam-3916	387	6	admits	admit	VERB
ejpam-3916	387	7	a	a	DET
ejpam-3916	387	8	tdcni	tdcni	PROPN
ejpam-3916	387	9	set	set	NOUN
ejpam-3916	387	10	,	,	PUNCT
ejpam-3916	387	11	then	then	ADV
ejpam-3916	387	12	3	3	NUM
ejpam-3916	387	13	≤	≤	NUM
ejpam-3916	387	14	γtcni(g	γtcni(g	PROPN
ejpam-3916	387	15	)	)	PUNCT
ejpam-3916	387	16	≤	≤	PROPN
ejpam-3916	387	17	|v	|v	X
ejpam-3916	387	18	(	(	PUNCT
ejpam-3916	387	19	g)|	g)|	NOUN
ejpam-3916	387	20	.	.	PUNCT
ejpam-3916	388	1	(	(	PUNCT
ejpam-3916	388	2	iii	iii	X
ejpam-3916	388	3	)	)	PUNCT
ejpam-3916	388	4	if	if	SCONJ
ejpam-3916	388	5	γt(g	γt(g	NOUN
ejpam-3916	388	6	)	)	PUNCT
ejpam-3916	388	7	6=	6=	ADP
ejpam-3916	388	8	2	2	NUM
ejpam-3916	388	9	,	,	PUNCT
ejpam-3916	388	10	then	then	ADV
ejpam-3916	388	11	g	g	PROPN
ejpam-3916	388	12	admits	admit	VERB
ejpam-3916	388	13	a	a	DET
ejpam-3916	388	14	tdcni	tdcni	NOUN
ejpam-3916	388	15	set	set	NOUN
ejpam-3916	388	16	.	.	PUNCT
ejpam-3916	389	1	if	if	SCONJ
ejpam-3916	389	2	,	,	PUNCT
ejpam-3916	389	3	in	in	ADP
ejpam-3916	389	4	addition	addition	NOUN
ejpam-3916	389	5	,	,	PUNCT
ejpam-3916	389	6	g	g	PROPN
ejpam-3916	389	7	has	have	VERB
ejpam-3916	389	8	at	at	ADP
ejpam-3916	389	9	most	most	ADV
ejpam-3916	389	10	one	one	NUM
ejpam-3916	389	11	vertex	vertex	NOUN
ejpam-3916	389	12	of	of	ADP
ejpam-3916	389	13	degree	degree	NOUN
ejpam-3916	389	14	one	one	NUM
ejpam-3916	389	15	,	,	PUNCT
ejpam-3916	389	16	then	then	ADV
ejpam-3916	389	17	γtcni(g	γtcni(g	PROPN
ejpam-3916	389	18	)	)	PUNCT
ejpam-3916	389	19	≤	≤	PROPN
ejpam-3916	389	20	|v	|v	X
ejpam-3916	389	21	(	(	PUNCT
ejpam-3916	389	22	g)|	g)|	INTJ
ejpam-3916	389	23	−	−	NOUN
ejpam-3916	389	24	1	1	NUM
ejpam-3916	389	25	.	.	PUNCT
ejpam-3916	390	1	proof	proof	NOUN
ejpam-3916	390	2	.	.	PUNCT
ejpam-3916	391	1	(	(	PUNCT
ejpam-3916	391	2	i	i	NOUN
ejpam-3916	391	3	)	)	PUNCT
ejpam-3916	391	4	suppose	suppose	VERB
ejpam-3916	391	5	g	g	PROPN
ejpam-3916	391	6	is	be	AUX
ejpam-3916	391	7	disconnected	disconnect	VERB
ejpam-3916	391	8	and	and	CCONJ
ejpam-3916	391	9	let	let	VERB
ejpam-3916	391	10	s	s	PRON
ejpam-3916	391	11	=	=	VERB
ejpam-3916	391	12	v	v	ADJ
ejpam-3916	391	13	(	(	PUNCT
ejpam-3916	391	14	g	g	NOUN
ejpam-3916	391	15	)	)	PUNCT
ejpam-3916	391	16	.	.	PUNCT
ejpam-3916	392	1	let	let	VERB
ejpam-3916	392	2	v	v	X
ejpam-3916	392	3	∈	∈	VERB
ejpam-3916	392	4	s.	s.	PROPN
ejpam-3916	392	5	since	since	SCONJ
ejpam-3916	392	6	g	g	PROPN
ejpam-3916	392	7	has	have	VERB
ejpam-3916	392	8	no	no	DET
ejpam-3916	392	9	isolated	isolated	ADJ
ejpam-3916	392	10	vertices	vertex	NOUN
ejpam-3916	392	11	,	,	PUNCT
ejpam-3916	392	12	there	there	PRON
ejpam-3916	392	13	exists	exist	VERB
ejpam-3916	392	14	w	w	PROPN
ejpam-3916	392	15	∈	∈	PROPN
ejpam-3916	392	16	s	s	PART
ejpam-3916	392	17	∩ng(v	∩ng(v	PROPN
ejpam-3916	392	18	)	)	PUNCT
ejpam-3916	392	19	.	.	PUNCT
ejpam-3916	393	1	let	let	VERB
ejpam-3916	393	2	c1	c1	PROPN
ejpam-3916	393	3	and	and	CCONJ
ejpam-3916	393	4	c2	c2	PROPN
ejpam-3916	393	5	be	be	AUX
ejpam-3916	393	6	distinct	distinct	ADJ
ejpam-3916	393	7	components	component	NOUN
ejpam-3916	393	8	of	of	ADP
ejpam-3916	393	9	g	g	PROPN
ejpam-3916	393	10	with	with	ADP
ejpam-3916	393	11	w	w	PROPN
ejpam-3916	393	12	,	,	PUNCT
ejpam-3916	393	13	v	v	PROPN
ejpam-3916	393	14	∈	∈	PROPN
ejpam-3916	393	15	c1	c1	NOUN
ejpam-3916	393	16	.	.	PUNCT
ejpam-3916	394	1	pick	pick	VERB
ejpam-3916	394	2	any	any	DET
ejpam-3916	394	3	z	z	PROPN
ejpam-3916	394	4	∈	∈	PROPN
ejpam-3916	394	5	c2	c2	PROPN
ejpam-3916	394	6	.	.	PUNCT
ejpam-3916	395	1	then	then	ADV
ejpam-3916	395	2	z	z	PROPN
ejpam-3916	395	3	∈	∈	PROPN
ejpam-3916	395	4	(	(	PUNCT
ejpam-3916	395	5	v	v	NOUN
ejpam-3916	395	6	(	(	PUNCT
ejpam-3916	395	7	g	g	NOUN
ejpam-3916	395	8	)	)	PUNCT
ejpam-3916	395	9	\	\	NOUN
ejpam-3916	395	10	ng(v	ng(v	NOUN
ejpam-3916	395	11	)	)	PUNCT
ejpam-3916	395	12	)	)	PUNCT
ejpam-3916	395	13	∩	∩	NOUN
ejpam-3916	395	14	(	(	PUNCT
ejpam-3916	395	15	v	v	NOUN
ejpam-3916	395	16	(	(	PUNCT
ejpam-3916	395	17	g	g	NOUN
ejpam-3916	395	18	)	)	PUNCT
ejpam-3916	395	19	\	\	NOUN
ejpam-3916	395	20	ng(w	ng(w	NOUN
ejpam-3916	395	21	)	)	PUNCT
ejpam-3916	395	22	)	)	PUNCT
ejpam-3916	395	23	.	.	PUNCT
ejpam-3916	396	1	hence	hence	ADV
ejpam-3916	396	2	,	,	PUNCT
ejpam-3916	396	3	s	s	NOUN
ejpam-3916	396	4	=	=	SYM
ejpam-3916	396	5	v	v	X
ejpam-3916	396	6	(	(	PUNCT
ejpam-3916	396	7	g	g	NOUN
ejpam-3916	396	8	)	)	PUNCT
ejpam-3916	396	9	is	be	AUX
ejpam-3916	396	10	a	a	DET
ejpam-3916	396	11	tdcni	tdcni	NOUN
ejpam-3916	396	12	set	set	NOUN
ejpam-3916	396	13	of	of	ADP
ejpam-3916	396	14	g.	g.	PROPN
ejpam-3916	396	15	(	(	PUNCT
ejpam-3916	396	16	ii	ii	PROPN
ejpam-3916	396	17	)	)	PUNCT
ejpam-3916	396	18	suppose	suppose	VERB
ejpam-3916	396	19	g	g	PROPN
ejpam-3916	396	20	admits	admit	VERB
ejpam-3916	396	21	a	a	DET
ejpam-3916	396	22	tcnid	tcnid	PROPN
ejpam-3916	396	23	set	set	NOUN
ejpam-3916	396	24	.	.	PUNCT
ejpam-3916	397	1	since	since	SCONJ
ejpam-3916	397	2	a	a	DET
ejpam-3916	397	3	tdcni	tdcni	NOUN
ejpam-3916	397	4	set	set	NOUN
ejpam-3916	397	5	is	be	AUX
ejpam-3916	397	6	a	a	DET
ejpam-3916	397	7	total	total	ADJ
ejpam-3916	397	8	dominating	dominating	NOUN
ejpam-3916	397	9	set	set	NOUN
ejpam-3916	397	10	,	,	PUNCT
ejpam-3916	397	11	it	it	PRON
ejpam-3916	397	12	follows	follow	VERB
ejpam-3916	397	13	that	that	SCONJ
ejpam-3916	397	14	2	2	NUM
ejpam-3916	397	15	≤	≤	NUM
ejpam-3916	397	16	γtcni(g	γtcni(g	PROPN
ejpam-3916	397	17	)	)	PUNCT
ejpam-3916	397	18	≤	≤	PROPN
ejpam-3916	397	19	n.	n.	NOUN
ejpam-3916	397	20	suppose	suppose	VERB
ejpam-3916	398	1	γtcni(g	γtcni(g	INTJ
ejpam-3916	398	2	)	)	PUNCT
ejpam-3916	398	3	=	=	SYM
ejpam-3916	398	4	2	2	NUM
ejpam-3916	398	5	,	,	PUNCT
ejpam-3916	398	6	say	say	VERB
ejpam-3916	398	7	s	s	X
ejpam-3916	398	8	=	=	PUNCT
ejpam-3916	398	9	{	{	PUNCT
ejpam-3916	398	10	x	x	PROPN
ejpam-3916	398	11	,	,	PUNCT
ejpam-3916	398	12	y	y	PRON
ejpam-3916	398	13	}	}	PUNCT
ejpam-3916	398	14	is	be	AUX
ejpam-3916	398	15	a	a	DET
ejpam-3916	398	16	γtcni	γtcni	NOUN
ejpam-3916	398	17	-	-	PUNCT
ejpam-3916	398	18	set	set	NOUN
ejpam-3916	398	19	of	of	ADP
ejpam-3916	398	20	g.	g.	PROPN
ejpam-3916	398	21	since	since	SCONJ
ejpam-3916	398	22	s	s	PROPN
ejpam-3916	398	23	is	be	AUX
ejpam-3916	398	24	a	a	DET
ejpam-3916	398	25	dominating	dominating	NOUN
ejpam-3916	398	26	set	set	NOUN
ejpam-3916	398	27	,	,	PUNCT
ejpam-3916	398	28	v	v	NOUN
ejpam-3916	398	29	(	(	PUNCT
ejpam-3916	398	30	g	g	NOUN
ejpam-3916	398	31	)	)	PUNCT
ejpam-3916	398	32	\	\	PUNCT
ejpam-3916	399	1	s	s	PART
ejpam-3916	399	2	⊆	⊆	NUM
ejpam-3916	399	3	ng({x	ng({x	ADJ
ejpam-3916	399	4	,	,	PUNCT
ejpam-3916	399	5	y	y	NOUN
ejpam-3916	399	6	}	}	PUNCT
ejpam-3916	399	7	)	)	PUNCT
ejpam-3916	399	8	.	.	PUNCT
ejpam-3916	400	1	hence	hence	ADV
ejpam-3916	400	2	,	,	PUNCT
ejpam-3916	400	3	(	(	PUNCT
ejpam-3916	400	4	v	v	NOUN
ejpam-3916	400	5	(	(	PUNCT
ejpam-3916	400	6	g	g	NOUN
ejpam-3916	400	7	)	)	PUNCT
ejpam-3916	400	8	\ng(x))∩	\ng(x))∩	NOUN
ejpam-3916	400	9	(	(	PUNCT
ejpam-3916	400	10	v	v	NOUN
ejpam-3916	400	11	(	(	PUNCT
ejpam-3916	400	12	g	g	NOUN
ejpam-3916	400	13	)	)	PUNCT
ejpam-3916	400	14	\ng(y	\ng(y	NOUN
ejpam-3916	400	15	)	)	PUNCT
ejpam-3916	400	16	)	)	PUNCT
ejpam-3916	400	17	=	=	NOUN
ejpam-3916	400	18	∅	∅	NOUN
ejpam-3916	400	19	,	,	PUNCT
ejpam-3916	400	20	contrary	contrary	ADJ
ejpam-3916	400	21	to	to	ADP
ejpam-3916	400	22	the	the	DET
ejpam-3916	400	23	assumption	assumption	NOUN
ejpam-3916	400	24	that	that	SCONJ
ejpam-3916	400	25	s	s	VERB
ejpam-3916	400	26	is	be	AUX
ejpam-3916	400	27	a	a	DET
ejpam-3916	400	28	tdcni	tdcni	NOUN
ejpam-3916	400	29	set	set	NOUN
ejpam-3916	400	30	.	.	PUNCT
ejpam-3916	401	1	thus	thus	ADV
ejpam-3916	401	2	,	,	PUNCT
ejpam-3916	401	3	3	3	NUM
ejpam-3916	401	4	≥	≥	NOUN
ejpam-3916	401	5	γtcni(g	γtcni(g	PROPN
ejpam-3916	401	6	)	)	PUNCT
ejpam-3916	401	7	.	.	PUNCT
ejpam-3916	402	1	(	(	PUNCT
ejpam-3916	402	2	iii	iii	X
ejpam-3916	402	3	)	)	PUNCT
ejpam-3916	402	4	suppose	suppose	VERB
ejpam-3916	402	5	γt(g	γt(g	NOUN
ejpam-3916	402	6	)	)	PUNCT
ejpam-3916	402	7	6=	6=	ADP
ejpam-3916	402	8	2	2	X
ejpam-3916	402	9	.	.	X
ejpam-3916	403	1	let	let	VERB
ejpam-3916	403	2	v	v	NUM
ejpam-3916	403	3	∈	∈	PROPN
ejpam-3916	403	4	v	v	NOUN
ejpam-3916	403	5	(	(	PUNCT
ejpam-3916	403	6	g	g	NOUN
ejpam-3916	403	7	)	)	PUNCT
ejpam-3916	403	8	and	and	CCONJ
ejpam-3916	403	9	let	let	VERB
ejpam-3916	403	10	w	w	PROPN
ejpam-3916	403	11	∈	∈	PROPN
ejpam-3916	403	12	v	v	ADP
ejpam-3916	403	13	(	(	PUNCT
ejpam-3916	403	14	g	g	NOUN
ejpam-3916	403	15	)	)	PUNCT
ejpam-3916	403	16	∩	∩	NOUN
ejpam-3916	403	17	ng(v	ng(v	NUM
ejpam-3916	403	18	)	)	PUNCT
ejpam-3916	403	19	.	.	PUNCT
ejpam-3916	404	1	by	by	ADP
ejpam-3916	404	2	assumption	assumption	NOUN
ejpam-3916	404	3	,	,	PUNCT
ejpam-3916	404	4	ng({v	ng({v	NUM
ejpam-3916	404	5	,	,	PUNCT
ejpam-3916	404	6	w	w	NOUN
ejpam-3916	404	7	}	}	PUNCT
ejpam-3916	404	8	6=	6=	ADP
ejpam-3916	404	9	v	v	ADP
ejpam-3916	404	10	(	(	PUNCT
ejpam-3916	404	11	g	g	NOUN
ejpam-3916	404	12	)	)	PUNCT
ejpam-3916	404	13	.	.	PUNCT
ejpam-3916	405	1	this	this	PRON
ejpam-3916	405	2	implies	imply	VERB
ejpam-3916	405	3	that	that	SCONJ
ejpam-3916	405	4	there	there	PRON
ejpam-3916	405	5	exists	exist	VERB
ejpam-3916	405	6	y	y	PROPN
ejpam-3916	405	7	∈	∈	PROPN
ejpam-3916	405	8	(	(	PUNCT
ejpam-3916	405	9	v	v	NOUN
ejpam-3916	405	10	(	(	PUNCT
ejpam-3916	405	11	g	g	NOUN
ejpam-3916	405	12	)	)	PUNCT
ejpam-3916	405	13	\ng(v))∩	\ng(v))∩	NOUN
ejpam-3916	405	14	(	(	PUNCT
ejpam-3916	405	15	v	v	NOUN
ejpam-3916	405	16	(	(	PUNCT
ejpam-3916	405	17	g	g	NOUN
ejpam-3916	405	18	)	)	PUNCT
ejpam-3916	405	19	\ng(w	\ng(w	PROPN
ejpam-3916	405	20	)	)	PUNCT
ejpam-3916	405	21	)	)	PUNCT
ejpam-3916	405	22	,	,	PUNCT
ejpam-3916	405	23	showing	show	VERB
ejpam-3916	405	24	that	that	PRON
ejpam-3916	405	25	v	v	NOUN
ejpam-3916	405	26	(	(	PUNCT
ejpam-3916	405	27	g	g	NOUN
ejpam-3916	405	28	)	)	PUNCT
ejpam-3916	405	29	is	be	AUX
ejpam-3916	405	30	a	a	DET
ejpam-3916	405	31	tdcni	tdcni	NOUN
ejpam-3916	405	32	set	set	NOUN
ejpam-3916	405	33	of	of	ADP
ejpam-3916	405	34	g.	g.	PROPN
ejpam-3916	405	35	suppose	suppose	VERB
ejpam-3916	405	36	further	far	ADV
ejpam-3916	405	37	that	that	SCONJ
ejpam-3916	405	38	g	g	PROPN
ejpam-3916	405	39	has	have	VERB
ejpam-3916	405	40	at	at	ADP
ejpam-3916	405	41	most	most	ADV
ejpam-3916	405	42	one	one	NUM
ejpam-3916	405	43	vertex	vertex	NOUN
ejpam-3916	405	44	of	of	ADP
ejpam-3916	405	45	degree	degree	NOUN
ejpam-3916	405	46	one	one	NUM
ejpam-3916	405	47	.	.	PUNCT
ejpam-3916	406	1	let	let	VERB
ejpam-3916	406	2	v	v	NUM
ejpam-3916	406	3	∈	∈	PROPN
ejpam-3916	406	4	v	v	NOUN
ejpam-3916	406	5	(	(	PUNCT
ejpam-3916	406	6	g	g	NOUN
ejpam-3916	406	7	)	)	PUNCT
ejpam-3916	406	8	such	such	ADJ
ejpam-3916	406	9	that	that	SCONJ
ejpam-3916	406	10	δ(g	δ(g	PROPN
ejpam-3916	406	11	)	)	PUNCT
ejpam-3916	406	12	=	=	SYM
ejpam-3916	406	13	degg(v	degg(v	PROPN
ejpam-3916	406	14	)	)	PUNCT
ejpam-3916	406	15	and	and	CCONJ
ejpam-3916	406	16	let	let	VERB
ejpam-3916	406	17	s	s	PRON
ejpam-3916	406	18	=	=	VERB
ejpam-3916	406	19	v	v	ADJ
ejpam-3916	406	20	(	(	PUNCT
ejpam-3916	406	21	g	g	NOUN
ejpam-3916	406	22	)	)	PUNCT
ejpam-3916	406	23	\	\	NOUN
ejpam-3916	406	24	{	{	PUNCT
ejpam-3916	406	25	v	v	NOUN
ejpam-3916	406	26	}	}	PUNCT
ejpam-3916	406	27	.	.	PUNCT
ejpam-3916	407	1	note	note	VERB
ejpam-3916	407	2	that	that	SCONJ
ejpam-3916	407	3	if	if	SCONJ
ejpam-3916	407	4	degg(v	degg(v	VERB
ejpam-3916	407	5	)	)	PUNCT
ejpam-3916	407	6	=	=	SYM
ejpam-3916	407	7	1	1	NUM
ejpam-3916	407	8	,	,	PUNCT
ejpam-3916	407	9	then	then	ADV
ejpam-3916	407	10	degg(w	degg(w	PROPN
ejpam-3916	407	11	)	)	PUNCT
ejpam-3916	407	12	≥	≥	NOUN
ejpam-3916	407	13	2	2	NUM
ejpam-3916	407	14	for	for	ADP
ejpam-3916	407	15	all	all	PRON
ejpam-3916	407	16	w	w	PROPN
ejpam-3916	407	17	∈	∈	PROPN
ejpam-3916	407	18	v	v	ADP
ejpam-3916	407	19	(	(	PUNCT
ejpam-3916	407	20	g	g	NOUN
ejpam-3916	407	21	)	)	PUNCT
ejpam-3916	407	22	\	\	NOUN
ejpam-3916	407	23	{	{	PUNCT
ejpam-3916	407	24	v	v	NOUN
ejpam-3916	407	25	}	}	PUNCT
ejpam-3916	407	26	.	.	PUNCT
ejpam-3916	408	1	let	let	VERB
ejpam-3916	408	2	u	u	PRON
ejpam-3916	408	3	∈	∈	PROPN
ejpam-3916	408	4	s	s	PART
ejpam-3916	408	5	∩ng(v	∩ng(v	PROPN
ejpam-3916	408	6	)	)	PUNCT
ejpam-3916	408	7	.	.	PUNCT
ejpam-3916	409	1	since	since	SCONJ
ejpam-3916	409	2	γ(g	γ(g	PROPN
ejpam-3916	409	3	)	)	PUNCT
ejpam-3916	409	4	6=	6=	ADP
ejpam-3916	409	5	2	2	NUM
ejpam-3916	409	6	,	,	PUNCT
ejpam-3916	409	7	(	(	PUNCT
ejpam-3916	409	8	v	v	NOUN
ejpam-3916	409	9	(	(	PUNCT
ejpam-3916	409	10	g	g	NOUN
ejpam-3916	409	11	)	)	PUNCT
ejpam-3916	409	12	\	\	NOUN
ejpam-3916	409	13	ng(v	ng(v	NOUN
ejpam-3916	409	14	)	)	PUNCT
ejpam-3916	409	15	)	)	PUNCT
ejpam-3916	409	16	∩	∩	NOUN
ejpam-3916	409	17	(	(	PUNCT
ejpam-3916	409	18	v	v	NOUN
ejpam-3916	409	19	(	(	PUNCT
ejpam-3916	409	20	g	g	NOUN
ejpam-3916	409	21	)	)	PUNCT
ejpam-3916	409	22	\	\	NOUN
ejpam-3916	409	23	ng(w	ng(w	NOUN
ejpam-3916	409	24	)	)	PUNCT
ejpam-3916	409	25	)	)	PUNCT
ejpam-3916	409	26	6=	6=	ADP
ejpam-3916	409	27	∅.	∅.	AUX
ejpam-3916	409	28	let	let	VERB
ejpam-3916	409	29	z	z	PROPN
ejpam-3916	409	30	∈	∈	PROPN
ejpam-3916	409	31	s.	s.	PROPN
ejpam-3916	409	32	since	since	SCONJ
ejpam-3916	409	33	degg(z	degg(z	PROPN
ejpam-3916	409	34	)	)	PUNCT
ejpam-3916	409	35	≥	≥	NOUN
ejpam-3916	409	36	2	2	NUM
ejpam-3916	409	37	,	,	PUNCT
ejpam-3916	409	38	there	there	PRON
ejpam-3916	409	39	exists	exist	VERB
ejpam-3916	409	40	y	y	PROPN
ejpam-3916	409	41	∈	∈	PROPN
ejpam-3916	409	42	s	s	VERB
ejpam-3916	409	43	∩ng(z	∩ng(z	PROPN
ejpam-3916	409	44	)	)	PUNCT
ejpam-3916	409	45	.	.	PUNCT
ejpam-3916	410	1	again	again	ADV
ejpam-3916	410	2	,	,	PUNCT
ejpam-3916	410	3	since	since	SCONJ
ejpam-3916	410	4	γ(g	γ(g	PROPN
ejpam-3916	410	5	)	)	PUNCT
ejpam-3916	410	6	6=	6=	ADP
ejpam-3916	410	7	2	2	NUM
ejpam-3916	410	8	,	,	PUNCT
ejpam-3916	410	9	(	(	PUNCT
ejpam-3916	410	10	v	v	NOUN
ejpam-3916	410	11	(	(	PUNCT
ejpam-3916	410	12	g	g	NOUN
ejpam-3916	410	13	)	)	PUNCT
ejpam-3916	410	14	\ng(z))∩	\ng(z))∩	NOUN
ejpam-3916	410	15	(	(	PUNCT
ejpam-3916	410	16	v	v	NOUN
ejpam-3916	410	17	(	(	PUNCT
ejpam-3916	410	18	g	g	NOUN
ejpam-3916	410	19	)	)	PUNCT
ejpam-3916	410	20	\ng(y	\ng(y	NOUN
ejpam-3916	410	21	)	)	PUNCT
ejpam-3916	410	22	)	)	PUNCT
ejpam-3916	410	23	6=	6=	ADP
ejpam-3916	410	24	∅.	∅.	VERB
ejpam-3916	410	25	this	this	PRON
ejpam-3916	410	26	implies	imply	VERB
ejpam-3916	410	27	that	that	SCONJ
ejpam-3916	410	28	s	s	VERB
ejpam-3916	410	29	is	be	AUX
ejpam-3916	410	30	a	a	DET
ejpam-3916	410	31	tdcni	tdcni	NOUN
ejpam-3916	410	32	set	set	NOUN
ejpam-3916	410	33	and	and	CCONJ
ejpam-3916	410	34	γtcni(g	γtcni(g	INTJ
ejpam-3916	410	35	)	)	PUNCT
ejpam-3916	410	36	≤	≤	NUM
ejpam-3916	410	37	|s|	|s|	PROPN
ejpam-3916	410	38	=	=	SYM
ejpam-3916	410	39	|v	|v	X
ejpam-3916	410	40	(	(	PUNCT
ejpam-3916	410	41	g)|	g)|	INTJ
ejpam-3916	410	42	−	−	NOUN
ejpam-3916	410	43	1	1	NUM
ejpam-3916	410	44	.	.	PUNCT
ejpam-3916	410	45	corollary	corollary	ADJ
ejpam-3916	410	46	4	4	NUM
ejpam-3916	410	47	.	.	PUNCT
ejpam-3916	411	1	let	let	VERB
ejpam-3916	411	2	g	g	NOUN
ejpam-3916	411	3	and	and	CCONJ
ejpam-3916	411	4	h	h	PROPN
ejpam-3916	411	5	be	be	VERB
ejpam-3916	411	6	non	non	ADJ
ejpam-3916	411	7	-	-	ADJ
ejpam-3916	411	8	trivial	trivial	ADJ
ejpam-3916	411	9	connected	connected	ADJ
ejpam-3916	411	10	graphs	graph	NOUN
ejpam-3916	411	11	.	.	PUNCT
ejpam-3916	412	1	(	(	PUNCT
ejpam-3916	412	2	i	i	NOUN
ejpam-3916	412	3	)	)	PUNCT
ejpam-3916	412	4	if	if	SCONJ
ejpam-3916	412	5	γ(g	γ(g	PROPN
ejpam-3916	412	6	)	)	PUNCT
ejpam-3916	412	7	=	=	SYM
ejpam-3916	413	1	1	1	NUM
ejpam-3916	413	2	,	,	PUNCT
ejpam-3916	413	3	then	then	ADV
ejpam-3916	413	4	γgh(g[h	γgh(g[h	NUM
ejpam-3916	413	5	]	]	PUNCT
ejpam-3916	413	6	)	)	PUNCT
ejpam-3916	413	7	≤	≤	NUM
ejpam-3916	414	1	γhcni(g).γppnd(h	γhcni(g).γppnd(h	PROPN
ejpam-3916	414	2	)	)	PUNCT
ejpam-3916	414	3	.	.	PUNCT
ejpam-3916	415	1	(	(	PUNCT
ejpam-3916	415	2	ii	ii	NOUN
ejpam-3916	415	3	)	)	PUNCT
ejpam-3916	415	4	if	if	SCONJ
ejpam-3916	415	5	γ(g	γ(g	PROPN
ejpam-3916	415	6	)	)	PUNCT
ejpam-3916	415	7	6=	6=	ADP
ejpam-3916	415	8	1	1	NUM
ejpam-3916	415	9	,	,	PUNCT
ejpam-3916	415	10	then	then	ADV
ejpam-3916	415	11	γgh(g[h	γgh(g[h	NUM
ejpam-3916	415	12	]	]	PUNCT
ejpam-3916	415	13	)	)	PUNCT
ejpam-3916	415	14	≤	≤	ADJ
ejpam-3916	415	15	γhcni(g).γpnd(h	γhcni(g).γpnd(h	NOUN
ejpam-3916	415	16	)	)	PUNCT
ejpam-3916	415	17	.	.	PUNCT
ejpam-3916	416	1	proof	proof	NOUN
ejpam-3916	416	2	.	.	PUNCT
ejpam-3916	417	1	let	let	VERB
ejpam-3916	417	2	s	s	PRON
ejpam-3916	417	3	be	be	AUX
ejpam-3916	417	4	a	a	DET
ejpam-3916	417	5	γhcni	γhcni	NOUN
ejpam-3916	417	6	-	-	PUNCT
ejpam-3916	417	7	set	set	NOUN
ejpam-3916	417	8	of	of	ADP
ejpam-3916	417	9	g.	g.	PROPN
ejpam-3916	417	10	let	let	VERB
ejpam-3916	417	11	d1	d1	PROPN
ejpam-3916	417	12	and	and	CCONJ
ejpam-3916	417	13	d2	d2	PROPN
ejpam-3916	417	14	be	be	AUX
ejpam-3916	417	15	,	,	PUNCT
ejpam-3916	417	16	respectively	respectively	ADV
ejpam-3916	417	17	,	,	PUNCT
ejpam-3916	417	18	a	a	DET
ejpam-3916	417	19	γppnd	γppnd	NOUN
ejpam-3916	417	20	-	-	PUNCT
ejpam-3916	417	21	set	set	VERB
ejpam-3916	417	22	and	and	CCONJ
ejpam-3916	417	23	γpnd	γpnd	NOUN
ejpam-3916	417	24	-	-	PUNCT
ejpam-3916	417	25	set	set	NOUN
ejpam-3916	417	26	of	of	ADP
ejpam-3916	417	27	h.	h.	PROPN
ejpam-3916	417	28	set	set	VERB
ejpam-3916	417	29	tx	tx	PROPN
ejpam-3916	418	1	=	=	SYM
ejpam-3916	419	1	d	d	PROPN
ejpam-3916	419	2	for	for	ADP
ejpam-3916	419	3	each	each	DET
ejpam-3916	419	4	x	x	SYM
ejpam-3916	419	5	∈	∈	PROPN
ejpam-3916	419	6	s	s	X
ejpam-3916	419	7	and	and	CCONJ
ejpam-3916	419	8	rx	rx	VERB
ejpam-3916	419	9	=	=	NOUN
ejpam-3916	419	10	d2	d2	PROPN
ejpam-3916	419	11	.	.	PUNCT
ejpam-3916	420	1	if	if	SCONJ
ejpam-3916	420	2	γ(g	γ(g	PROPN
ejpam-3916	420	3	)	)	PUNCT
ejpam-3916	420	4	=	=	SYM
ejpam-3916	420	5	1	1	NUM
ejpam-3916	420	6	,	,	PUNCT
ejpam-3916	420	7	then	then	ADV
ejpam-3916	420	8	c1	c1	PROPN
ejpam-3916	420	9	=	=	PUNCT
ejpam-3916	420	10	∪x∈s	∪x∈s	PROPN
ejpam-3916	420	11	[	[	X
ejpam-3916	420	12	{	{	PUNCT
ejpam-3916	420	13	x	x	NOUN
ejpam-3916	420	14	}	}	PUNCT
ejpam-3916	420	15	×	×	NOUN
ejpam-3916	420	16	tx	tx	NOUN
ejpam-3916	420	17	]	]	X
ejpam-3916	420	18	=	=	SYM
ejpam-3916	420	19	s	s	PART
ejpam-3916	420	20	×d1	×d1	PROPN
ejpam-3916	420	21	is	be	AUX
ejpam-3916	420	22	a	a	DET
ejpam-3916	420	23	global	global	ADJ
ejpam-3916	420	24	hop	hop	NOUN
ejpam-3916	420	25	dominating	dominating	NOUN
ejpam-3916	420	26	set	set	NOUN
ejpam-3916	420	27	of	of	ADP
ejpam-3916	420	28	g[h	g[h	PROPN
ejpam-3916	420	29	]	]	PUNCT
ejpam-3916	420	30	by	by	ADP
ejpam-3916	420	31	theorem	theorem	NOUN
ejpam-3916	420	32	6	6	NUM
ejpam-3916	420	33	.	.	PUNCT
ejpam-3916	421	1	hence	hence	ADV
ejpam-3916	421	2	,	,	PUNCT
ejpam-3916	421	3	γgh(g[h	γgh(g[h	NUM
ejpam-3916	421	4	]	]	PUNCT
ejpam-3916	421	5	)	)	PUNCT
ejpam-3916	421	6	≤	≤	NOUN
ejpam-3916	421	7	|c1|	|c1|	NOUN
ejpam-3916	421	8	=	=	SYM
ejpam-3916	421	9	|s||d1|	|s||d1|	PROPN
ejpam-3916	421	10	=	=	SYM
ejpam-3916	421	11	γhcni(g).γppnd(h	γhcni(g).γppnd(h	PROPN
ejpam-3916	421	12	)	)	PUNCT
ejpam-3916	421	13	,	,	PUNCT
ejpam-3916	421	14	proving	prove	VERB
ejpam-3916	421	15	that	that	SCONJ
ejpam-3916	421	16	(	(	PUNCT
ejpam-3916	421	17	i	i	NOUN
ejpam-3916	421	18	)	)	PUNCT
ejpam-3916	421	19	holds	hold	VERB
ejpam-3916	421	20	.	.	PUNCT
ejpam-3916	422	1	if	if	SCONJ
ejpam-3916	422	2	γ(g	γ(g	PROPN
ejpam-3916	422	3	)	)	PUNCT
ejpam-3916	422	4	6=	6=	ADP
ejpam-3916	422	5	1	1	NUM
ejpam-3916	422	6	,	,	PUNCT
ejpam-3916	422	7	then	then	ADV
ejpam-3916	422	8	c2	c2	PROPN
ejpam-3916	422	9	=	=	SYM
ejpam-3916	422	10	∪x∈s	∪x∈s	PROPN
ejpam-3916	422	11	[	[	X
ejpam-3916	422	12	{	{	PUNCT
ejpam-3916	422	13	x	x	NOUN
ejpam-3916	422	14	}	}	PUNCT
ejpam-3916	422	15	×	×	NOUN
ejpam-3916	422	16	rx	rx	NOUN
ejpam-3916	422	17	]	]	PUNCT
ejpam-3916	422	18	=	=	SYM
ejpam-3916	422	19	s	s	PART
ejpam-3916	422	20	×	×	PROPN
ejpam-3916	422	21	d2	d2	PROPN
ejpam-3916	422	22	is	be	AUX
ejpam-3916	422	23	a	a	DET
ejpam-3916	422	24	global	global	ADJ
ejpam-3916	422	25	hop	hop	NOUN
ejpam-3916	422	26	dominating	dominating	NOUN
ejpam-3916	422	27	set	set	NOUN
ejpam-3916	422	28	of	of	ADP
ejpam-3916	422	29	g[h	g[h	PROPN
ejpam-3916	422	30	]	]	PUNCT
ejpam-3916	422	31	by	by	ADP
ejpam-3916	422	32	theorem	theorem	NOUN
ejpam-3916	422	33	6	6	NUM
ejpam-3916	422	34	.	.	PUNCT
ejpam-3916	423	1	hence	hence	ADV
ejpam-3916	423	2	,	,	PUNCT
ejpam-3916	423	3	γgh(g[h	γgh(g[h	NUM
ejpam-3916	423	4	]	]	PUNCT
ejpam-3916	423	5	)	)	PUNCT
ejpam-3916	423	6	≤	≤	NUM
ejpam-3916	423	7	|c2|	|c2|	NOUN
ejpam-3916	423	8	=	=	SYM
ejpam-3916	423	9	|s||d2|	|s||d2|	PROPN
ejpam-3916	423	10	=	=	PUNCT
ejpam-3916	423	11	γhcni(g).γpnd(h	γhcni(g).γpnd(h	PROPN
ejpam-3916	423	12	)	)	PUNCT
ejpam-3916	423	13	,	,	PUNCT
ejpam-3916	423	14	showing	show	VERB
ejpam-3916	423	15	that	that	SCONJ
ejpam-3916	423	16	(	(	PUNCT
ejpam-3916	423	17	ii	ii	NOUN
ejpam-3916	423	18	)	)	PUNCT
ejpam-3916	423	19	holds	hold	VERB
ejpam-3916	423	20	.	.	PUNCT
ejpam-3916	424	1	remark	remark	PROPN
ejpam-3916	424	2	3	3	NUM
ejpam-3916	424	3	.	.	PUNCT
ejpam-3916	425	1	the	the	DET
ejpam-3916	425	2	bounds	bound	NOUN
ejpam-3916	425	3	in	in	ADP
ejpam-3916	425	4	corollary	corollary	ADJ
ejpam-3916	425	5	4	4	NUM
ejpam-3916	425	6	are	be	AUX
ejpam-3916	425	7	sharp	sharp	ADJ
ejpam-3916	425	8	.	.	PUNCT
ejpam-3916	426	1	g.	g.	PROPN
ejpam-3916	426	2	salasalan	salasalan	PROPN
ejpam-3916	426	3	,	,	PUNCT
ejpam-3916	426	4	s.	s.	PROPN
ejpam-3916	426	5	canoy	canoy	PROPN
ejpam-3916	426	6	,	,	PUNCT
ejpam-3916	426	7	jr	jr	PROPN
ejpam-3916	426	8	.	.	PROPN
ejpam-3916	426	9	/	/	SYM
ejpam-3916	426	10	eur	eur	PROPN
ejpam-3916	426	11	.	.	PUNCT
ejpam-3916	427	1	j.	j.	PROPN
ejpam-3916	427	2	pure	pure	PROPN
ejpam-3916	427	3	appl	appl	PROPN
ejpam-3916	427	4	.	.	PROPN
ejpam-3916	427	5	math	math	PROPN
ejpam-3916	427	6	,	,	PUNCT
ejpam-3916	427	7	14	14	NUM
ejpam-3916	427	8	(	(	PUNCT
ejpam-3916	427	9	1	1	NUM
ejpam-3916	427	10	)	)	PUNCT
ejpam-3916	427	11	(	(	PUNCT
ejpam-3916	427	12	2021	2021	NUM
ejpam-3916	427	13	)	)	PUNCT
ejpam-3916	427	14	,	,	PUNCT
ejpam-3916	427	15	112	112	NUM
ejpam-3916	427	16	-	-	SYM
ejpam-3916	427	17	125	125	NUM
ejpam-3916	427	18	122	122	NUM
ejpam-3916	427	19	to	to	PART
ejpam-3916	427	20	see	see	VERB
ejpam-3916	427	21	this	this	PRON
ejpam-3916	427	22	,	,	PUNCT
ejpam-3916	427	23	let	let	VERB
ejpam-3916	427	24	g1	g1	PROPN
ejpam-3916	427	25	be	be	AUX
ejpam-3916	427	26	the	the	DET
ejpam-3916	427	27	graph	graph	NOUN
ejpam-3916	427	28	obtained	obtain	VERB
ejpam-3916	427	29	from	from	ADP
ejpam-3916	427	30	the	the	DET
ejpam-3916	427	31	cycle	cycle	NOUN
ejpam-3916	427	32	c4	c4	NOUN
ejpam-3916	427	33	=	=	PUNCT
ejpam-3916	428	1	[	[	X
ejpam-3916	428	2	a	a	PRON
ejpam-3916	428	3	,	,	PUNCT
ejpam-3916	428	4	b	b	NOUN
ejpam-3916	428	5	,	,	PUNCT
ejpam-3916	428	6	c	c	NOUN
ejpam-3916	428	7	,	,	PUNCT
ejpam-3916	428	8	d	d	NOUN
ejpam-3916	428	9	,	,	PUNCT
ejpam-3916	428	10	a	a	PRON
ejpam-3916	428	11	]	]	X
ejpam-3916	428	12	by	by	ADP
ejpam-3916	428	13	adding	add	VERB
ejpam-3916	428	14	the	the	DET
ejpam-3916	428	15	edges	edge	NOUN
ejpam-3916	428	16	av	av	PROPN
ejpam-3916	428	17	and	and	CCONJ
ejpam-3916	428	18	bw	bw	NOUN
ejpam-3916	428	19	,	,	PUNCT
ejpam-3916	428	20	and	and	CCONJ
ejpam-3916	428	21	let	let	VERB
ejpam-3916	428	22	h	h	NOUN
ejpam-3916	428	23	=	=	PROPN
ejpam-3916	428	24	p3	p3	PROPN
ejpam-3916	428	25	.	.	PUNCT
ejpam-3916	429	1	as	as	SCONJ
ejpam-3916	429	2	pointed	point	VERB
ejpam-3916	429	3	out	out	ADP
ejpam-3916	429	4	earlier	early	ADV
ejpam-3916	429	5	,	,	PUNCT
ejpam-3916	429	6	s	s	VERB
ejpam-3916	429	7	=	=	PUNCT
ejpam-3916	429	8	{	{	PUNCT
ejpam-3916	429	9	a	a	DET
ejpam-3916	429	10	,	,	PUNCT
ejpam-3916	429	11	b	b	NOUN
ejpam-3916	429	12	}	}	PUNCT
ejpam-3916	429	13	is	be	AUX
ejpam-3916	429	14	a	a	DET
ejpam-3916	429	15	dcni	dcni	ADJ
ejpam-3916	429	16	hop	hop	NOUN
ejpam-3916	429	17	dominating	dominating	NOUN
ejpam-3916	429	18	set	set	NOUN
ejpam-3916	429	19	of	of	ADP
ejpam-3916	429	20	g1	g1	PROPN
ejpam-3916	429	21	.	.	PUNCT
ejpam-3916	430	1	in	in	ADP
ejpam-3916	430	2	fact	fact	NOUN
ejpam-3916	430	3	,	,	PUNCT
ejpam-3916	430	4	γhcni(g1	γhcni(g1	NOUN
ejpam-3916	430	5	)	)	PUNCT
ejpam-3916	430	6	=	=	SYM
ejpam-3916	430	7	|s|	|s|	NOUN
ejpam-3916	430	8	=	=	SYM
ejpam-3916	430	9	2	2	X
ejpam-3916	430	10	.	.	PUNCT
ejpam-3916	431	1	now	now	ADV
ejpam-3916	431	2	,	,	PUNCT
ejpam-3916	431	3	γpnd(h	γpnd(h	PROPN
ejpam-3916	431	4	)	)	PUNCT
ejpam-3916	431	5	=	=	SYM
ejpam-3916	431	6	2	2	NUM
ejpam-3916	431	7	by	by	ADP
ejpam-3916	431	8	theorem	theorem	NOUN
ejpam-3916	431	9	3(iii	3(iii	NUM
ejpam-3916	431	10	)	)	PUNCT
ejpam-3916	431	11	.	.	PUNCT
ejpam-3916	432	1	it	it	PRON
ejpam-3916	432	2	can	can	AUX
ejpam-3916	432	3	easily	easily	ADV
ejpam-3916	432	4	be	be	AUX
ejpam-3916	432	5	verified	verify	VERB
ejpam-3916	432	6	that	that	SCONJ
ejpam-3916	432	7	γgh(g[h	γgh(g[h	NUM
ejpam-3916	432	8	]	]	PUNCT
ejpam-3916	432	9	)	)	PUNCT
ejpam-3916	432	10	=	=	SYM
ejpam-3916	432	11	4	4	NUM
ejpam-3916	432	12	=	=	SYM
ejpam-3916	432	13	γhcni(g).γpnd(h	γhcni(g).γpnd(h	PROPN
ejpam-3916	432	14	)	)	PUNCT
ejpam-3916	432	15	.	.	PUNCT
ejpam-3916	433	1	also	also	ADV
ejpam-3916	433	2	,	,	PUNCT
ejpam-3916	433	3	γgh(p4[p2	γgh(p4[p2	NOUN
ejpam-3916	433	4	]	]	PUNCT
ejpam-3916	433	5	)	)	PUNCT
ejpam-3916	433	6	=	=	SYM
ejpam-3916	433	7	γhcni(p4).γpnd(p2	γhcni(p4).γpnd(p2	NUM
ejpam-3916	433	8	)	)	PUNCT
ejpam-3916	433	9	=	=	SYM
ejpam-3916	434	1	2(2	2(2	NUM
ejpam-3916	434	2	)	)	PUNCT
ejpam-3916	434	3	=	=	SYM
ejpam-3916	434	4	4	4	NUM
ejpam-3916	434	5	and	and	CCONJ
ejpam-3916	434	6	γgh(p2[p2	γgh(p2[p2	NOUN
ejpam-3916	434	7	]	]	X
ejpam-3916	434	8	)	)	PUNCT
ejpam-3916	434	9	=	=	SYM
ejpam-3916	434	10	γgh(k4	γgh(k4	PROPN
ejpam-3916	434	11	)	)	PUNCT
ejpam-3916	434	12	=	=	SYM
ejpam-3916	434	13	γhcni(p4).γppnd(p2	γhcni(p4).γppnd(p2	NOUN
ejpam-3916	434	14	)	)	PUNCT
ejpam-3916	434	15	=	=	SYM
ejpam-3916	435	1	2(2	2(2	NUM
ejpam-3916	435	2	)	)	PUNCT
ejpam-3916	435	3	=	=	SYM
ejpam-3916	436	1	4	4	X
ejpam-3916	436	2	.	.	PUNCT
ejpam-3916	436	3	the	the	DET
ejpam-3916	436	4	cartesian	cartesian	ADJ
ejpam-3916	436	5	product	product	NOUN
ejpam-3916	436	6	of	of	ADP
ejpam-3916	436	7	graphs	graph	NOUN
ejpam-3916	436	8	g	g	PROPN
ejpam-3916	436	9	and	and	CCONJ
ejpam-3916	436	10	h	h	NOUN
ejpam-3916	436	11	,	,	PUNCT
ejpam-3916	436	12	denoted	denote	VERB
ejpam-3916	436	13	by	by	ADP
ejpam-3916	436	14	g	g	PROPN
ejpam-3916	436	15	�	�	PROPN
ejpam-3916	436	16	h	h	NOUN
ejpam-3916	436	17	,	,	PUNCT
ejpam-3916	436	18	is	be	AUX
ejpam-3916	436	19	the	the	DET
ejpam-3916	436	20	graph	graph	NOUN
ejpam-3916	436	21	with	with	ADP
ejpam-3916	436	22	vertex	vertex	NOUN
ejpam-3916	436	23	set	set	VERB
ejpam-3916	436	24	v	v	NOUN
ejpam-3916	436	25	(	(	PUNCT
ejpam-3916	436	26	g	g	PROPN
ejpam-3916	436	27	�	�	NOUN
ejpam-3916	436	28	h	h	NOUN
ejpam-3916	436	29	)	)	PUNCT
ejpam-3916	436	30	=	=	NOUN
ejpam-3916	436	31	v	v	X
ejpam-3916	436	32	(	(	PUNCT
ejpam-3916	436	33	g	g	NOUN
ejpam-3916	436	34	)	)	PUNCT
ejpam-3916	436	35	×	×	NOUN
ejpam-3916	436	36	v	v	NOUN
ejpam-3916	436	37	(	(	PUNCT
ejpam-3916	436	38	h	h	NOUN
ejpam-3916	436	39	)	)	PUNCT
ejpam-3916	436	40	such	such	ADJ
ejpam-3916	436	41	that	that	SCONJ
ejpam-3916	436	42	(	(	PUNCT
ejpam-3916	436	43	v	v	NOUN
ejpam-3916	436	44	,	,	PUNCT
ejpam-3916	436	45	p)(u	p)(u	ADJ
ejpam-3916	436	46	,	,	PUNCT
ejpam-3916	436	47	q	q	ADJ
ejpam-3916	436	48	)	)	PUNCT
ejpam-3916	436	49	∈	∈	PROPN
ejpam-3916	436	50	e(g	e(g	PROPN
ejpam-3916	436	51	�	�	PROPN
ejpam-3916	436	52	h	h	PROPN
ejpam-3916	436	53	)	)	PUNCT
ejpam-3916	436	54	if	if	SCONJ
ejpam-3916	436	55	and	and	CCONJ
ejpam-3916	436	56	only	only	ADV
ejpam-3916	436	57	if	if	SCONJ
ejpam-3916	436	58	uv	uv	PROPN
ejpam-3916	436	59	∈	∈	PROPN
ejpam-3916	436	60	e(g	e(g	PROPN
ejpam-3916	436	61	)	)	PUNCT
ejpam-3916	436	62	and	and	CCONJ
ejpam-3916	436	63	p	p	NOUN
ejpam-3916	436	64	=	=	X
ejpam-3916	436	65	q	q	PUNCT
ejpam-3916	436	66	∈	∈	PROPN
ejpam-3916	436	67	e(h	e(h	PROPN
ejpam-3916	436	68	)	)	PUNCT
ejpam-3916	436	69	]	]	PUNCT
ejpam-3916	436	70	or	or	CCONJ
ejpam-3916	436	71	u	u	X
ejpam-3916	436	72	=	=	PROPN
ejpam-3916	436	73	v	v	PROPN
ejpam-3916	436	74	and	and	CCONJ
ejpam-3916	436	75	pq	pq	NOUN
ejpam-3916	436	76	∈	∈	PROPN
ejpam-3916	436	77	e(g	e(g	PROPN
ejpam-3916	436	78	)	)	PUNCT
ejpam-3916	436	79	.	.	PUNCT
ejpam-3916	437	1	theorem	theorem	VERB
ejpam-3916	437	2	7	7	NUM
ejpam-3916	437	3	.	.	PUNCT
ejpam-3916	438	1	let	let	VERB
ejpam-3916	438	2	g	g	NOUN
ejpam-3916	439	1	and	and	CCONJ
ejpam-3916	439	2	h	h	NOUN
ejpam-3916	439	3	be	be	AUX
ejpam-3916	439	4	connected	connect	VERB
ejpam-3916	439	5	non	non	ADJ
ejpam-3916	439	6	-	-	ADJ
ejpam-3916	439	7	trivial	trivial	ADJ
ejpam-3916	439	8	graphs	graph	NOUN
ejpam-3916	439	9	.	.	PUNCT
ejpam-3916	440	1	a	a	DET
ejpam-3916	440	2	subset	subset	NOUN
ejpam-3916	440	3	c	c	NOUN
ejpam-3916	440	4	=	=	SYM
ejpam-3916	440	5	∪x∈s	∪x∈s	PROPN
ejpam-3916	440	6	[	[	X
ejpam-3916	440	7	{	{	PUNCT
ejpam-3916	440	8	x}×tx	x}×tx	X
ejpam-3916	440	9	]	]	X
ejpam-3916	440	10	of	of	ADP
ejpam-3916	440	11	v	v	NOUN
ejpam-3916	440	12	(	(	PUNCT
ejpam-3916	440	13	g	g	PROPN
ejpam-3916	440	14	�	�	NOUN
ejpam-3916	440	15	h	h	NOUN
ejpam-3916	440	16	)	)	PUNCT
ejpam-3916	440	17	is	be	AUX
ejpam-3916	440	18	a	a	DET
ejpam-3916	440	19	global	global	ADJ
ejpam-3916	440	20	hop	hop	NOUN
ejpam-3916	440	21	dominating	dominating	NOUN
ejpam-3916	440	22	set	set	NOUN
ejpam-3916	440	23	of	of	ADP
ejpam-3916	440	24	g	g	PROPN
ejpam-3916	440	25	�	�	PROPN
ejpam-3916	440	26	h	h	NOUN
ejpam-3916	440	27	if	if	SCONJ
ejpam-3916	441	1	and	and	CCONJ
ejpam-3916	441	2	only	only	ADV
ejpam-3916	441	3	if	if	SCONJ
ejpam-3916	441	4	the	the	DET
ejpam-3916	441	5	following	follow	VERB
ejpam-3916	441	6	conditions	condition	NOUN
ejpam-3916	441	7	hold	hold	VERB
ejpam-3916	441	8	:	:	PUNCT
ejpam-3916	441	9	(	(	PUNCT
ejpam-3916	441	10	i	i	NOUN
ejpam-3916	441	11	)	)	PUNCT
ejpam-3916	441	12	for	for	ADP
ejpam-3916	441	13	each	each	DET
ejpam-3916	441	14	x	x	SYM
ejpam-3916	441	15	∈	∈	PROPN
ejpam-3916	441	16	v	v	ADP
ejpam-3916	441	17	(	(	PUNCT
ejpam-3916	441	18	g	g	NOUN
ejpam-3916	441	19	)	)	PUNCT
ejpam-3916	441	20	\	\	PROPN
ejpam-3916	441	21	s	s	PROPN
ejpam-3916	441	22	and	and	CCONJ
ejpam-3916	441	23	for	for	ADP
ejpam-3916	441	24	each	each	DET
ejpam-3916	441	25	p	p	PROPN
ejpam-3916	441	26	∈	∈	PROPN
ejpam-3916	441	27	v	v	ADP
ejpam-3916	441	28	(	(	PUNCT
ejpam-3916	441	29	h	h	NOUN
ejpam-3916	441	30	)	)	PUNCT
ejpam-3916	441	31	,	,	PUNCT
ejpam-3916	441	32	(	(	PUNCT
ejpam-3916	441	33	a	a	X
ejpam-3916	441	34	)	)	PUNCT
ejpam-3916	441	35	there	there	PRON
ejpam-3916	441	36	exists	exist	VERB
ejpam-3916	441	37	y	y	PROPN
ejpam-3916	441	38	∈	∈	PROPN
ejpam-3916	441	39	s	s	PART
ejpam-3916	441	40	∩	∩	NOUN
ejpam-3916	441	41	ng(x	ng(x	NUM
ejpam-3916	441	42	)	)	PUNCT
ejpam-3916	441	43	such	such	ADJ
ejpam-3916	441	44	that	that	SCONJ
ejpam-3916	441	45	ty	ty	NUM
ejpam-3916	441	46	∩	∩	NOUN
ejpam-3916	441	47	nh(p	nh(p	NUM
ejpam-3916	441	48	)	)	PUNCT
ejpam-3916	441	49	6=	6=	ADP
ejpam-3916	441	50	∅	∅	NOUN
ejpam-3916	441	51	or	or	CCONJ
ejpam-3916	441	52	there	there	PRON
ejpam-3916	441	53	exists	exist	VERB
ejpam-3916	441	54	z	z	PROPN
ejpam-3916	441	55	∈	∈	PROPN
ejpam-3916	441	56	s	s	PART
ejpam-3916	441	57	∩ng(x	∩ng(x	NOUN
ejpam-3916	441	58	,	,	PUNCT
ejpam-3916	441	59	2	2	NUM
ejpam-3916	441	60	)	)	PUNCT
ejpam-3916	441	61	such	such	ADJ
ejpam-3916	441	62	that	that	SCONJ
ejpam-3916	441	63	p	p	PROPN
ejpam-3916	441	64	∈	∈	PROPN
ejpam-3916	441	65	tz	tz	NOUN
ejpam-3916	441	66	,	,	PUNCT
ejpam-3916	441	67	and	and	CCONJ
ejpam-3916	441	68	(	(	PUNCT
ejpam-3916	441	69	b	b	X
ejpam-3916	441	70	)	)	PUNCT
ejpam-3916	441	71	there	there	PRON
ejpam-3916	441	72	exists	exist	VERB
ejpam-3916	441	73	w	w	PROPN
ejpam-3916	441	74	∈	∈	PROPN
ejpam-3916	441	75	s	s	PART
ejpam-3916	441	76	∩	∩	NOUN
ejpam-3916	441	77	ng(x	ng(x	NUM
ejpam-3916	441	78	)	)	PUNCT
ejpam-3916	441	79	such	such	ADJ
ejpam-3916	441	80	that	that	SCONJ
ejpam-3916	441	81	p	p	PROPN
ejpam-3916	441	82	∈	∈	PROPN
ejpam-3916	441	83	tw	tw	NOUN
ejpam-3916	441	84	and	and	CCONJ
ejpam-3916	441	85	[	[	X
ejpam-3916	441	86	nh	nh	X
ejpam-3916	442	1	[	[	X
ejpam-3916	442	2	p	p	X
ejpam-3916	442	3	]	]	X
ejpam-3916	442	4	6=	6=	ADP
ejpam-3916	442	5	v	v	ADP
ejpam-3916	442	6	(	(	PUNCT
ejpam-3916	442	7	h	h	NOUN
ejpam-3916	442	8	)	)	PUNCT
ejpam-3916	442	9	or	or	CCONJ
ejpam-3916	442	10	(	(	PUNCT
ejpam-3916	442	11	v	v	NOUN
ejpam-3916	442	12	(	(	PUNCT
ejpam-3916	442	13	g	g	NOUN
ejpam-3916	442	14	)	)	PUNCT
ejpam-3916	442	15	\	\	NOUN
ejpam-3916	442	16	ng(x	ng(x	NUM
ejpam-3916	442	17	)	)	PUNCT
ejpam-3916	442	18	)	)	PUNCT
ejpam-3916	443	1	∩	∩	NOUN
ejpam-3916	443	2	(	(	PUNCT
ejpam-3916	443	3	v	v	NOUN
ejpam-3916	443	4	(	(	PUNCT
ejpam-3916	443	5	g	g	NOUN
ejpam-3916	443	6	)	)	PUNCT
ejpam-3916	443	7	\ng(w	\ng(w	PROPN
ejpam-3916	443	8	)	)	PUNCT
ejpam-3916	443	9	)	)	PUNCT
ejpam-3916	443	10	6=	6=	ADP
ejpam-3916	443	11	∅	∅	NOUN
ejpam-3916	443	12	]	]	PUNCT
ejpam-3916	443	13	.	.	PUNCT
ejpam-3916	444	1	(	(	PUNCT
ejpam-3916	444	2	ii	ii	NOUN
ejpam-3916	444	3	)	)	PUNCT
ejpam-3916	444	4	for	for	ADP
ejpam-3916	444	5	each	each	DET
ejpam-3916	444	6	v	v	NOUN
ejpam-3916	444	7	∈	∈	PROPN
ejpam-3916	444	8	s	s	NOUN
ejpam-3916	444	9	and	and	CCONJ
ejpam-3916	444	10	for	for	ADP
ejpam-3916	444	11	each	each	DET
ejpam-3916	444	12	p	p	PROPN
ejpam-3916	444	13	∈	∈	PROPN
ejpam-3916	444	14	v	v	ADP
ejpam-3916	444	15	(	(	PUNCT
ejpam-3916	444	16	h	h	NOUN
ejpam-3916	444	17	)	)	PUNCT
ejpam-3916	444	18	\	\	NOUN
ejpam-3916	444	19	tv	tv	NOUN
ejpam-3916	444	20	,	,	PUNCT
ejpam-3916	444	21	the	the	DET
ejpam-3916	444	22	following	following	ADJ
ejpam-3916	444	23	statements	statement	NOUN
ejpam-3916	444	24	are	be	AUX
ejpam-3916	444	25	satisfied	satisfied	ADJ
ejpam-3916	444	26	:	:	PUNCT
ejpam-3916	444	27	(	(	PUNCT
ejpam-3916	444	28	c	c	X
ejpam-3916	444	29	)	)	PUNCT
ejpam-3916	444	30	nh(p	nh(p	NOUN
ejpam-3916	444	31	,	,	PUNCT
ejpam-3916	444	32	2)∩	2)∩	ADJ
ejpam-3916	444	33	tv	tv	NOUN
ejpam-3916	444	34	6=	6=	NOUN
ejpam-3916	444	35	∅	∅	NOUN
ejpam-3916	444	36	or	or	CCONJ
ejpam-3916	444	37	there	there	PRON
ejpam-3916	444	38	exists	exist	VERB
ejpam-3916	444	39	y	y	PROPN
ejpam-3916	444	40	∈	∈	PROPN
ejpam-3916	444	41	s	s	PART
ejpam-3916	444	42	∩ng(v	∩ng(v	PROPN
ejpam-3916	444	43	)	)	PUNCT
ejpam-3916	444	44	such	such	ADJ
ejpam-3916	444	45	that	that	SCONJ
ejpam-3916	444	46	ty	ty	NUM
ejpam-3916	444	47	∩nh(p	∩nh(p	NOUN
ejpam-3916	444	48	)	)	PUNCT
ejpam-3916	444	49	6=	6=	ADP
ejpam-3916	444	50	∅	∅	NOUN
ejpam-3916	444	51	,	,	PUNCT
ejpam-3916	444	52	or	or	CCONJ
ejpam-3916	444	53	there	there	PRON
ejpam-3916	444	54	exists	exist	VERB
ejpam-3916	444	55	z	z	PROPN
ejpam-3916	444	56	∈	∈	PROPN
ejpam-3916	444	57	s	s	PART
ejpam-3916	444	58	∩ng(v	∩ng(v	PROPN
ejpam-3916	444	59	,	,	PUNCT
ejpam-3916	444	60	2	2	NUM
ejpam-3916	444	61	)	)	PUNCT
ejpam-3916	444	62	such	such	ADJ
ejpam-3916	444	63	that	that	SCONJ
ejpam-3916	444	64	p	p	PROPN
ejpam-3916	444	65	∈	∈	PROPN
ejpam-3916	444	66	tz	tz	NOUN
ejpam-3916	444	67	.	.	PUNCT
ejpam-3916	445	1	(	(	PUNCT
ejpam-3916	445	2	d	d	X
ejpam-3916	445	3	)	)	PUNCT
ejpam-3916	445	4	nh(p	nh(p	NOUN
ejpam-3916	445	5	)	)	PUNCT
ejpam-3916	446	1	∩	∩	ADJ
ejpam-3916	446	2	tv	tv	NOUN
ejpam-3916	446	3	6=	6=	NOUN
ejpam-3916	446	4	∅	∅	NOUN
ejpam-3916	446	5	and	and	CCONJ
ejpam-3916	446	6	[	[	X
ejpam-3916	446	7	v	v	X
ejpam-3916	446	8	(	(	PUNCT
ejpam-3916	446	9	g	g	NOUN
ejpam-3916	446	10	)	)	PUNCT
ejpam-3916	446	11	\	\	PUNCT
ejpam-3916	447	1	ng[v	ng[v	X
ejpam-3916	447	2	]	]	PUNCT
ejpam-3916	447	3	6=	6=	ADP
ejpam-3916	447	4	∅	∅	NOUN
ejpam-3916	447	5	or	or	CCONJ
ejpam-3916	447	6	|v	|v	PROPN
ejpam-3916	447	7	(	(	PUNCT
ejpam-3916	447	8	h)|	h)|	PROPN
ejpam-3916	447	9	≥	≥	NOUN
ejpam-3916	447	10	3	3	NUM
ejpam-3916	447	11	]	]	PUNCT
ejpam-3916	447	12	or	or	CCONJ
ejpam-3916	447	13	there	there	PRON
ejpam-3916	447	14	exists	exist	VERB
ejpam-3916	447	15	u	u	PROPN
ejpam-3916	447	16	∈	∈	PROPN
ejpam-3916	447	17	s	s	PART
ejpam-3916	447	18	∩ng(v	∩ng(v	PROPN
ejpam-3916	447	19	)	)	PUNCT
ejpam-3916	447	20	such	such	ADJ
ejpam-3916	447	21	that	that	SCONJ
ejpam-3916	447	22	p	p	PROPN
ejpam-3916	447	23	∈	∈	PROPN
ejpam-3916	447	24	tu	tu	X
ejpam-3916	447	25	and	and	CCONJ
ejpam-3916	447	26	[	[	X
ejpam-3916	447	27	nh	nh	X
ejpam-3916	448	1	[	[	X
ejpam-3916	448	2	p	p	X
ejpam-3916	448	3	]	]	X
ejpam-3916	448	4	6=	6=	ADP
ejpam-3916	448	5	v	v	ADP
ejpam-3916	448	6	(	(	PUNCT
ejpam-3916	448	7	h	h	NOUN
ejpam-3916	448	8	)	)	PUNCT
ejpam-3916	448	9	or	or	CCONJ
ejpam-3916	448	10	(	(	PUNCT
ejpam-3916	448	11	v	v	NOUN
ejpam-3916	448	12	(	(	PUNCT
ejpam-3916	448	13	g	g	NOUN
ejpam-3916	448	14	)	)	PUNCT
ejpam-3916	448	15	\ng(v	\ng(v	NOUN
ejpam-3916	448	16	)	)	PUNCT
ejpam-3916	448	17	)	)	PUNCT
ejpam-3916	449	1	∩	∩	NOUN
ejpam-3916	449	2	(	(	PUNCT
ejpam-3916	449	3	v	v	NOUN
ejpam-3916	449	4	(	(	PUNCT
ejpam-3916	449	5	g	g	NOUN
ejpam-3916	449	6	)	)	PUNCT
ejpam-3916	449	7	\	\	NOUN
ejpam-3916	449	8	ng(u	ng(u	NOUN
ejpam-3916	449	9	)	)	PUNCT
ejpam-3916	449	10	)	)	PUNCT
ejpam-3916	450	1	6=	6=	ADP
ejpam-3916	450	2	∅	∅	NOUN
ejpam-3916	450	3	]	]	PUNCT
ejpam-3916	450	4	.	.	PUNCT
ejpam-3916	451	1	proof	proof	NOUN
ejpam-3916	451	2	.	.	PUNCT
ejpam-3916	452	1	suppose	suppose	VERB
ejpam-3916	452	2	c	c	NOUN
ejpam-3916	452	3	is	be	AUX
ejpam-3916	452	4	a	a	DET
ejpam-3916	452	5	global	global	ADJ
ejpam-3916	452	6	hop	hop	NOUN
ejpam-3916	452	7	dominating	dominating	NOUN
ejpam-3916	452	8	set	set	NOUN
ejpam-3916	452	9	of	of	ADP
ejpam-3916	452	10	g	g	PROPN
ejpam-3916	452	11	�	�	PROPN
ejpam-3916	452	12	h.	h.	PROPN
ejpam-3916	452	13	let	let	VERB
ejpam-3916	452	14	x	x	SYM
ejpam-3916	452	15	∈	∈	PROPN
ejpam-3916	452	16	v	v	X
ejpam-3916	452	17	(	(	PUNCT
ejpam-3916	452	18	g	g	NOUN
ejpam-3916	452	19	)	)	PUNCT
ejpam-3916	452	20	\	\	PROPN
ejpam-3916	452	21	s	s	PART
ejpam-3916	452	22	and	and	CCONJ
ejpam-3916	452	23	let	let	VERB
ejpam-3916	452	24	p	p	PRON
ejpam-3916	452	25	∈	∈	PROPN
ejpam-3916	452	26	v	v	ADP
ejpam-3916	452	27	(	(	PUNCT
ejpam-3916	452	28	h	h	NOUN
ejpam-3916	452	29	)	)	PUNCT
ejpam-3916	452	30	.	.	PUNCT
ejpam-3916	453	1	since	since	SCONJ
ejpam-3916	453	2	c	c	PROPN
ejpam-3916	453	3	is	be	AUX
ejpam-3916	453	4	a	a	DET
ejpam-3916	453	5	hop	hop	NOUN
ejpam-3916	453	6	dominating	dominating	NOUN
ejpam-3916	453	7	set	set	NOUN
ejpam-3916	453	8	of	of	ADP
ejpam-3916	453	9	g	g	PROPN
ejpam-3916	453	10	�	�	PROPN
ejpam-3916	453	11	h	h	PROPN
ejpam-3916	453	12	and	and	CCONJ
ejpam-3916	453	13	(	(	PUNCT
ejpam-3916	453	14	x	x	NOUN
ejpam-3916	453	15	,	,	PUNCT
ejpam-3916	453	16	p	p	NOUN
ejpam-3916	453	17	)	)	PUNCT
ejpam-3916	453	18	/∈	/∈	PUNCT
ejpam-3916	454	1	c	c	X
ejpam-3916	454	2	,	,	PUNCT
ejpam-3916	454	3	there	there	PRON
ejpam-3916	454	4	exists	exist	VERB
ejpam-3916	454	5	(	(	PUNCT
ejpam-3916	454	6	y	y	NOUN
ejpam-3916	454	7	,	,	PUNCT
ejpam-3916	454	8	q	q	X
ejpam-3916	454	9	)	)	PUNCT
ejpam-3916	454	10	∈	∈	PROPN
ejpam-3916	454	11	c	c	NOUN
ejpam-3916	454	12	such	such	ADJ
ejpam-3916	454	13	that	that	SCONJ
ejpam-3916	454	14	dg	dg	PROPN
ejpam-3916	454	15	�	�	PROPN
ejpam-3916	454	16	h((x	h((x	NOUN
ejpam-3916	454	17	,	,	PUNCT
ejpam-3916	454	18	p)(y	p)(y	PROPN
ejpam-3916	454	19	,	,	PUNCT
ejpam-3916	454	20	q	q	NOUN
ejpam-3916	454	21	)	)	PUNCT
ejpam-3916	454	22	)	)	PUNCT
ejpam-3916	455	1	=	=	SYM
ejpam-3916	455	2	2	2	X
ejpam-3916	455	3	.	.	PUNCT
ejpam-3916	455	4	since	since	SCONJ
ejpam-3916	455	5	y	y	PROPN
ejpam-3916	455	6	∈	∈	PROPN
ejpam-3916	455	7	s	s	PROPN
ejpam-3916	455	8	,	,	PUNCT
ejpam-3916	455	9	x	x	SYM
ejpam-3916	455	10	6=	6=	ADP
ejpam-3916	455	11	y.	y.	NOUN
ejpam-3916	455	12	if	if	SCONJ
ejpam-3916	455	13	xy	xy	PROPN
ejpam-3916	455	14	∈	∈	PROPN
ejpam-3916	455	15	e(g	e(g	PROPN
ejpam-3916	455	16	)	)	PUNCT
ejpam-3916	455	17	,	,	PUNCT
ejpam-3916	455	18	then	then	ADV
ejpam-3916	455	19	pq	pq	PROPN
ejpam-3916	455	20	∈	∈	PROPN
ejpam-3916	455	21	e(h	e(h	PROPN
ejpam-3916	455	22	)	)	PUNCT
ejpam-3916	455	23	.	.	PUNCT
ejpam-3916	456	1	hence	hence	ADV
ejpam-3916	456	2	,	,	PUNCT
ejpam-3916	456	3	q	q	PROPN
ejpam-3916	456	4	∈	∈	PROPN
ejpam-3916	456	5	ty∩nh(p	ty∩nh(p	PROPN
ejpam-3916	456	6	)	)	PUNCT
ejpam-3916	456	7	.	.	PUNCT
ejpam-3916	457	1	so	so	ADV
ejpam-3916	457	2	suppose	suppose	VERB
ejpam-3916	457	3	that	that	SCONJ
ejpam-3916	457	4	y	y	PROPN
ejpam-3916	457	5	/∈	/∈	PUNCT
ejpam-3916	457	6	ng(x	ng(x	NUM
ejpam-3916	457	7	)	)	PUNCT
ejpam-3916	457	8	.	.	PUNCT
ejpam-3916	458	1	since	since	SCONJ
ejpam-3916	458	2	dg	dg	PROPN
ejpam-3916	458	3	�	�	PROPN
ejpam-3916	458	4	h((x	h((x	NOUN
ejpam-3916	458	5	,	,	PUNCT
ejpam-3916	458	6	p)(y	p)(y	PROPN
ejpam-3916	458	7	,	,	PUNCT
ejpam-3916	458	8	q	q	NOUN
ejpam-3916	458	9	)	)	PUNCT
ejpam-3916	458	10	)	)	PUNCT
ejpam-3916	458	11	=	=	SYM
ejpam-3916	458	12	2	2	X
ejpam-3916	458	13	,	,	PUNCT
ejpam-3916	458	14	it	it	PRON
ejpam-3916	458	15	follows	follow	VERB
ejpam-3916	458	16	that	that	SCONJ
ejpam-3916	458	17	y	y	PROPN
ejpam-3916	458	18	∈	∈	PROPN
ejpam-3916	458	19	ng(x	ng(x	NUM
ejpam-3916	458	20	,	,	PUNCT
ejpam-3916	458	21	2	2	NUM
ejpam-3916	458	22	)	)	PUNCT
ejpam-3916	458	23	and	and	CCONJ
ejpam-3916	458	24	p	p	X
ejpam-3916	458	25	=	=	NOUN
ejpam-3916	458	26	q.	q.	NOUN
ejpam-3916	458	27	hence	hence	ADV
ejpam-3916	458	28	,	,	PUNCT
ejpam-3916	458	29	p	p	PROPN
ejpam-3916	458	30	∈	∈	PROPN
ejpam-3916	458	31	ty	ty	NOUN
ejpam-3916	458	32	,	,	PUNCT
ejpam-3916	458	33	showing	show	VERB
ejpam-3916	458	34	that	that	SCONJ
ejpam-3916	458	35	(	(	PUNCT
ejpam-3916	458	36	a	a	X
ejpam-3916	458	37	)	)	PUNCT
ejpam-3916	458	38	holds	hold	NOUN
ejpam-3916	458	39	.	.	PUNCT
ejpam-3916	459	1	now	now	ADV
ejpam-3916	459	2	,	,	PUNCT
ejpam-3916	459	3	since	since	SCONJ
ejpam-3916	459	4	c	c	PROPN
ejpam-3916	459	5	is	be	AUX
ejpam-3916	459	6	also	also	ADV
ejpam-3916	459	7	a	a	DET
ejpam-3916	459	8	hop	hop	NOUN
ejpam-3916	459	9	dominating	dominating	NOUN
ejpam-3916	459	10	set	set	NOUN
ejpam-3916	459	11	of	of	ADP
ejpam-3916	459	12	g	g	PROPN
ejpam-3916	459	13	�	�	PROPN
ejpam-3916	459	14	h	h	NOUN
ejpam-3916	459	15	,	,	PUNCT
ejpam-3916	459	16	there	there	PRON
ejpam-3916	459	17	exists	exist	VERB
ejpam-3916	459	18	(	(	PUNCT
ejpam-3916	459	19	w	w	PROPN
ejpam-3916	459	20	,	,	PUNCT
ejpam-3916	459	21	t	t	PROPN
ejpam-3916	459	22	)	)	PUNCT
ejpam-3916	459	23	∈	∈	PROPN
ejpam-3916	459	24	c	c	NOUN
ejpam-3916	459	25	such	such	ADJ
ejpam-3916	459	26	that	that	SCONJ
ejpam-3916	459	27	dg	dg	PROPN
ejpam-3916	459	28	�	�	PROPN
ejpam-3916	459	29	h((x	h((x	NOUN
ejpam-3916	459	30	,	,	PUNCT
ejpam-3916	459	31	p)(w	p)(w	PROPN
ejpam-3916	459	32	,	,	PUNCT
ejpam-3916	459	33	t	t	PROPN
ejpam-3916	459	34	)	)	PUNCT
ejpam-3916	459	35	)	)	PUNCT
ejpam-3916	460	1	=	=	SYM
ejpam-3916	460	2	2	2	X
ejpam-3916	460	3	.	.	PUNCT
ejpam-3916	460	4	it	it	PRON
ejpam-3916	460	5	follows	follow	VERB
ejpam-3916	460	6	that	that	SCONJ
ejpam-3916	460	7	dg	dg	PROPN
ejpam-3916	460	8	�	�	PROPN
ejpam-3916	460	9	h((x	h((x	NOUN
ejpam-3916	460	10	,	,	PUNCT
ejpam-3916	460	11	p)(w	p)(w	PROPN
ejpam-3916	460	12	,	,	PUNCT
ejpam-3916	460	13	t	t	PROPN
ejpam-3916	460	14	)	)	PUNCT
ejpam-3916	460	15	)	)	PUNCT
ejpam-3916	461	1	=	=	PUNCT
ejpam-3916	462	1	1	1	X
ejpam-3916	462	2	.	.	PUNCT
ejpam-3916	462	3	this	this	PRON
ejpam-3916	462	4	implies	imply	VERB
ejpam-3916	462	5	that	that	SCONJ
ejpam-3916	462	6	w	w	PROPN
ejpam-3916	462	7	∈	∈	PROPN
ejpam-3916	462	8	s	s	PART
ejpam-3916	462	9	∩	∩	NOUN
ejpam-3916	462	10	ng(x	ng(x	NUM
ejpam-3916	462	11	)	)	PUNCT
ejpam-3916	462	12	and	and	CCONJ
ejpam-3916	462	13	p	p	PROPN
ejpam-3916	462	14	∈	∈	PROPN
ejpam-3916	462	15	tw	tw	NOUN
ejpam-3916	462	16	.	.	PUNCT
ejpam-3916	463	1	now	now	ADV
ejpam-3916	463	2	,	,	PUNCT
ejpam-3916	463	3	if	if	SCONJ
ejpam-3916	463	4	[	[	X
ejpam-3916	463	5	(	(	PUNCT
ejpam-3916	463	6	x	x	NOUN
ejpam-3916	463	7	,	,	PUNCT
ejpam-3916	463	8	p	p	NOUN
ejpam-3916	463	9	)	)	PUNCT
ejpam-3916	463	10	,	,	PUNCT
ejpam-3916	463	11	(	(	PUNCT
ejpam-3916	463	12	z	z	X
ejpam-3916	463	13	,	,	PUNCT
ejpam-3916	463	14	s	s	PART
ejpam-3916	463	15	)	)	PUNCT
ejpam-3916	463	16	,	,	PUNCT
ejpam-3916	463	17	(	(	PUNCT
ejpam-3916	463	18	w	w	PROPN
ejpam-3916	463	19	,	,	PUNCT
ejpam-3916	463	20	t	t	PROPN
ejpam-3916	463	21	)	)	PUNCT
ejpam-3916	463	22	]	]	PUNCT
ejpam-3916	463	23	is	be	AUX
ejpam-3916	463	24	an	an	DET
ejpam-3916	463	25	(	(	PUNCT
ejpam-3916	463	26	x	x	NOUN
ejpam-3916	463	27	,	,	PUNCT
ejpam-3916	463	28	p)-(w	p)-(w	NUM
ejpam-3916	463	29	,	,	PUNCT
ejpam-3916	463	30	t	t	PROPN
ejpam-3916	463	31	)	)	PUNCT
ejpam-3916	463	32	geodesic	geodesic	NOUN
ejpam-3916	463	33	in	in	ADP
ejpam-3916	463	34	g	g	PROPN
ejpam-3916	463	35	�	�	PROPN
ejpam-3916	463	36	h	h	NOUN
ejpam-3916	463	37	,	,	PUNCT
ejpam-3916	463	38	then	then	ADV
ejpam-3916	463	39	s	s	VERB
ejpam-3916	463	40	∈	∈	PROPN
ejpam-3916	463	41	v	v	ADP
ejpam-3916	463	42	(	(	PUNCT
ejpam-3916	463	43	h	h	NOUN
ejpam-3916	463	44	)	)	PUNCT
ejpam-3916	463	45	\nh	\nh	PROPN
ejpam-3916	464	1	[	[	X
ejpam-3916	464	2	p	p	X
ejpam-3916	464	3	]	]	X
ejpam-3916	464	4	or	or	CCONJ
ejpam-3916	464	5	z	z	NOUN
ejpam-3916	464	6	∈	∈	PROPN
ejpam-3916	464	7	(	(	PUNCT
ejpam-3916	464	8	(	(	PUNCT
ejpam-3916	464	9	v	v	NOUN
ejpam-3916	464	10	(	(	PUNCT
ejpam-3916	464	11	g	g	NOUN
ejpam-3916	464	12	)	)	PUNCT
ejpam-3916	464	13	\ng(x	\ng(x	NOUN
ejpam-3916	464	14	)	)	PUNCT
ejpam-3916	464	15	∩	∩	NOUN
ejpam-3916	464	16	(	(	PUNCT
ejpam-3916	464	17	v	v	NOUN
ejpam-3916	464	18	(	(	PUNCT
ejpam-3916	464	19	g	g	NOUN
ejpam-3916	464	20	)	)	PUNCT
ejpam-3916	464	21	\ng(w	\ng(w	PROPN
ejpam-3916	464	22	)	)	PUNCT
ejpam-3916	464	23	)	)	PUNCT
ejpam-3916	464	24	.	.	PUNCT
ejpam-3916	465	1	this	this	PRON
ejpam-3916	465	2	shows	show	VERB
ejpam-3916	465	3	that	that	SCONJ
ejpam-3916	465	4	(	(	PUNCT
ejpam-3916	465	5	b	b	X
ejpam-3916	465	6	)	)	PUNCT
ejpam-3916	465	7	holds	hold	VERB
ejpam-3916	465	8	.	.	PUNCT
ejpam-3916	466	1	next	next	ADV
ejpam-3916	466	2	,	,	PUNCT
ejpam-3916	466	3	let	let	VERB
ejpam-3916	466	4	v	v	NUM
ejpam-3916	466	5	∈	∈	NOUN
ejpam-3916	466	6	s	s	PART
ejpam-3916	466	7	and	and	CCONJ
ejpam-3916	466	8	let	let	VERB
ejpam-3916	466	9	p	p	PRON
ejpam-3916	466	10	∈	∈	PROPN
ejpam-3916	466	11	v	v	ADP
ejpam-3916	466	12	(	(	PUNCT
ejpam-3916	466	13	h	h	NOUN
ejpam-3916	466	14	)	)	PUNCT
ejpam-3916	466	15	\	\	NOUN
ejpam-3916	466	16	tv	tv	NOUN
ejpam-3916	466	17	.	.	PUNCT
ejpam-3916	467	1	since	since	SCONJ
ejpam-3916	467	2	c	c	PROPN
ejpam-3916	467	3	is	be	AUX
ejpam-3916	467	4	a	a	DET
ejpam-3916	467	5	hop	hop	NOUN
ejpam-3916	467	6	dominating	dominating	NOUN
ejpam-3916	467	7	set	set	NOUN
ejpam-3916	467	8	of	of	ADP
ejpam-3916	467	9	g	g	PROPN
ejpam-3916	467	10	�	�	PROPN
ejpam-3916	467	11	h	h	PROPN
ejpam-3916	467	12	and	and	CCONJ
ejpam-3916	467	13	(	(	PUNCT
ejpam-3916	467	14	v	v	NOUN
ejpam-3916	467	15	,	,	PUNCT
ejpam-3916	467	16	p	p	NOUN
ejpam-3916	467	17	)	)	PUNCT
ejpam-3916	467	18	/∈	/∈	PUNCT
ejpam-3916	468	1	c	c	X
ejpam-3916	468	2	,	,	PUNCT
ejpam-3916	468	3	there	there	PRON
ejpam-3916	468	4	exists	exist	VERB
ejpam-3916	468	5	(	(	PUNCT
ejpam-3916	468	6	y	y	NOUN
ejpam-3916	468	7	,	,	PUNCT
ejpam-3916	468	8	q	q	X
ejpam-3916	468	9	)	)	PUNCT
ejpam-3916	468	10	∈	∈	PROPN
ejpam-3916	468	11	c	c	NOUN
ejpam-3916	468	12	such	such	ADJ
ejpam-3916	468	13	that	that	SCONJ
ejpam-3916	468	14	dg	dg	PROPN
ejpam-3916	468	15	�	�	PROPN
ejpam-3916	468	16	h((v	h((v	NOUN
ejpam-3916	468	17	,	,	PUNCT
ejpam-3916	468	18	p)(y	p)(y	PROPN
ejpam-3916	468	19	,	,	PUNCT
ejpam-3916	468	20	q	q	NOUN
ejpam-3916	468	21	)	)	PUNCT
ejpam-3916	468	22	)	)	PUNCT
ejpam-3916	469	1	=	=	SYM
ejpam-3916	469	2	2	2	X
ejpam-3916	469	3	.	.	X
ejpam-3916	469	4	suppose	suppose	VERB
ejpam-3916	469	5	y	y	PROPN
ejpam-3916	469	6	=	=	PROPN
ejpam-3916	469	7	v.	v.	PROPN
ejpam-3916	469	8	then	then	ADV
ejpam-3916	469	9	dh(p	dh(p	PROPN
ejpam-3916	469	10	,	,	PUNCT
ejpam-3916	469	11	q	q	X
ejpam-3916	469	12	)	)	PUNCT
ejpam-3916	469	13	=	=	SYM
ejpam-3916	469	14	2	2	NUM
ejpam-3916	469	15	and	and	CCONJ
ejpam-3916	469	16	so	so	ADV
ejpam-3916	469	17	q	q	X
ejpam-3916	469	18	∈	∈	PROPN
ejpam-3916	469	19	ng(p	ng(p	NOUN
ejpam-3916	469	20	,	,	PUNCT
ejpam-3916	469	21	2	2	X
ejpam-3916	469	22	)	)	PUNCT
ejpam-3916	469	23	∩	∩	ADJ
ejpam-3916	469	24	tv	tv	NOUN
ejpam-3916	469	25	.	.	PUNCT
ejpam-3916	470	1	suppose	suppose	VERB
ejpam-3916	470	2	y	y	PROPN
ejpam-3916	471	1	6=	6=	PROPN
ejpam-3916	471	2	v.	v.	ADP
ejpam-3916	471	3	if	if	SCONJ
ejpam-3916	471	4	dg(y	dg(y	ADJ
ejpam-3916	471	5	,	,	PUNCT
ejpam-3916	471	6	v	v	NOUN
ejpam-3916	471	7	)	)	PUNCT
ejpam-3916	471	8	=	=	SYM
ejpam-3916	471	9	1	1	NUM
ejpam-3916	471	10	,	,	PUNCT
ejpam-3916	471	11	then	then	ADV
ejpam-3916	471	12	y	y	PROPN
ejpam-3916	471	13	∈	∈	PROPN
ejpam-3916	471	14	s	s	PART
ejpam-3916	471	15	∩ng(v	∩ng(v	PROPN
ejpam-3916	471	16	)	)	PUNCT
ejpam-3916	471	17	and	and	CCONJ
ejpam-3916	471	18	dh(p	dh(p	PROPN
ejpam-3916	471	19	,	,	PUNCT
ejpam-3916	471	20	q	q	X
ejpam-3916	471	21	)	)	PUNCT
ejpam-3916	471	22	=	=	SYM
ejpam-3916	471	23	1	1	NUM
ejpam-3916	471	24	,	,	PUNCT
ejpam-3916	471	25	i.e.	i.e.	X
ejpam-3916	471	26	q	q	X
ejpam-3916	471	27	∈	∈	PROPN
ejpam-3916	471	28	ty	ty	NUM
ejpam-3916	471	29	∩nh(p	∩nh(p	NOUN
ejpam-3916	471	30	)	)	PUNCT
ejpam-3916	471	31	.	.	PUNCT
ejpam-3916	472	1	if	if	SCONJ
ejpam-3916	472	2	dg(y	dg(y	ADJ
ejpam-3916	472	3	,	,	PUNCT
ejpam-3916	472	4	v	v	NOUN
ejpam-3916	472	5	)	)	PUNCT
ejpam-3916	472	6	6=	6=	ADP
ejpam-3916	472	7	1	1	NUM
ejpam-3916	472	8	,	,	PUNCT
ejpam-3916	472	9	then	then	ADV
ejpam-3916	472	10	dg(y	dg(y	ADJ
ejpam-3916	472	11	,	,	PUNCT
ejpam-3916	472	12	v	v	NOUN
ejpam-3916	472	13	)	)	PUNCT
ejpam-3916	472	14	=	=	SYM
ejpam-3916	472	15	2	2	NUM
ejpam-3916	472	16	,	,	PUNCT
ejpam-3916	472	17	hence	hence	ADV
ejpam-3916	472	18	,	,	PUNCT
ejpam-3916	472	19	y	y	PROPN
ejpam-3916	472	20	∈	∈	PROPN
ejpam-3916	472	21	s	s	PART
ejpam-3916	472	22	∩ng(v	∩ng(v	PROPN
ejpam-3916	472	23	,	,	PUNCT
ejpam-3916	472	24	2	2	NUM
ejpam-3916	472	25	)	)	PUNCT
ejpam-3916	472	26	and	and	CCONJ
ejpam-3916	472	27	p	p	NOUN
ejpam-3916	472	28	=	=	ADJ
ejpam-3916	473	1	q	q	NOUN
ejpam-3916	473	2	,	,	PUNCT
ejpam-3916	473	3	that	that	ADV
ejpam-3916	473	4	is	is	ADV
ejpam-3916	473	5	,	,	PUNCT
ejpam-3916	473	6	p	p	PROPN
ejpam-3916	473	7	∈	∈	PROPN
ejpam-3916	473	8	ty	ty	PRON
ejpam-3916	473	9	.	.	PUNCT
ejpam-3916	474	1	thus	thus	ADV
ejpam-3916	474	2	,	,	PUNCT
ejpam-3916	474	3	(	(	PUNCT
ejpam-3916	474	4	b	b	X
ejpam-3916	474	5	)	)	PUNCT
ejpam-3916	474	6	holds	hold	VERB
ejpam-3916	474	7	.	.	PUNCT
ejpam-3916	475	1	on	on	ADP
ejpam-3916	475	2	the	the	DET
ejpam-3916	475	3	other	other	ADJ
ejpam-3916	475	4	hand	hand	NOUN
ejpam-3916	475	5	,	,	PUNCT
ejpam-3916	475	6	since	since	SCONJ
ejpam-3916	475	7	c	c	PROPN
ejpam-3916	475	8	is	be	AUX
ejpam-3916	475	9	also	also	ADV
ejpam-3916	475	10	a	a	DET
ejpam-3916	475	11	hop	hop	NOUN
ejpam-3916	475	12	dominating	dominating	NOUN
ejpam-3916	475	13	set	set	VERB
ejpam-3916	475	14	ofg	ofg	PROPN
ejpam-3916	475	15	�	�	PROPN
ejpam-3916	475	16	h	h	PROPN
ejpam-3916	475	17	and	and	CCONJ
ejpam-3916	475	18	(	(	PUNCT
ejpam-3916	475	19	v	v	NOUN
ejpam-3916	475	20	,	,	PUNCT
ejpam-3916	475	21	p	p	NOUN
ejpam-3916	475	22	)	)	PUNCT
ejpam-3916	475	23	/∈	/∈	PUNCT
ejpam-3916	476	1	v	v	INTJ
ejpam-3916	476	2	(	(	PUNCT
ejpam-3916	476	3	g	g	NOUN
ejpam-3916	476	4	�	�	PROPN
ejpam-3916	476	5	h)\	h)\	NOUN
ejpam-3916	476	6	c	c	NOUN
ejpam-3916	476	7	,	,	PUNCT
ejpam-3916	476	8	there	there	PRON
ejpam-3916	476	9	exists	exist	VERB
ejpam-3916	476	10	(	(	PUNCT
ejpam-3916	476	11	u	u	NOUN
ejpam-3916	476	12	,	,	PUNCT
ejpam-3916	476	13	t	t	PROPN
ejpam-3916	476	14	)	)	PUNCT
ejpam-3916	476	15	∈	∈	PROPN
ejpam-3916	476	16	c	c	NOUN
ejpam-3916	476	17	such	such	ADJ
ejpam-3916	476	18	that	that	SCONJ
ejpam-3916	476	19	dg	dg	PROPN
ejpam-3916	476	20	�	�	PROPN
ejpam-3916	476	21	h((v	h((v	NOUN
ejpam-3916	476	22	,	,	PUNCT
ejpam-3916	476	23	p)(u	p)(u	PROPN
ejpam-3916	476	24	,	,	PUNCT
ejpam-3916	476	25	t	t	PROPN
ejpam-3916	476	26	)	)	PUNCT
ejpam-3916	476	27	)	)	PUNCT
ejpam-3916	477	1	=	=	PUNCT
ejpam-3916	477	2	2	2	X
ejpam-3916	477	3	.	.	PUNCT
ejpam-3916	477	4	again	again	ADV
ejpam-3916	477	5	,	,	PUNCT
ejpam-3916	477	6	this	this	PRON
ejpam-3916	477	7	would	would	AUX
ejpam-3916	477	8	imply	imply	VERB
ejpam-3916	477	9	g.	g.	PROPN
ejpam-3916	477	10	salasalan	salasalan	NOUN
ejpam-3916	477	11	,	,	PUNCT
ejpam-3916	477	12	s.	s.	PROPN
ejpam-3916	477	13	canoy	canoy	PROPN
ejpam-3916	477	14	,	,	PUNCT
ejpam-3916	477	15	jr	jr	PROPN
ejpam-3916	477	16	.	.	PROPN
ejpam-3916	477	17	/	/	SYM
ejpam-3916	477	18	eur	eur	PROPN
ejpam-3916	477	19	.	.	PUNCT
ejpam-3916	478	1	j.	j.	PROPN
ejpam-3916	478	2	pure	pure	PROPN
ejpam-3916	478	3	appl	appl	PROPN
ejpam-3916	478	4	.	.	PROPN
ejpam-3916	478	5	math	math	PROPN
ejpam-3916	478	6	,	,	PUNCT
ejpam-3916	478	7	14	14	NUM
ejpam-3916	478	8	(	(	PUNCT
ejpam-3916	478	9	1	1	NUM
ejpam-3916	478	10	)	)	PUNCT
ejpam-3916	478	11	(	(	PUNCT
ejpam-3916	478	12	2021	2021	NUM
ejpam-3916	478	13	)	)	PUNCT
ejpam-3916	478	14	,	,	PUNCT
ejpam-3916	478	15	112	112	NUM
ejpam-3916	478	16	-	-	SYM
ejpam-3916	478	17	125	125	NUM
ejpam-3916	478	18	123	123	NUM
ejpam-3916	479	1	that	that	PRON
ejpam-3916	479	2	dg	dg	PROPN
ejpam-3916	479	3	�	�	PROPN
ejpam-3916	479	4	h((v	h((v	NOUN
ejpam-3916	479	5	,	,	PUNCT
ejpam-3916	479	6	p)(u	p)(u	PROPN
ejpam-3916	479	7	,	,	PUNCT
ejpam-3916	479	8	t	t	PROPN
ejpam-3916	479	9	)	)	PUNCT
ejpam-3916	479	10	)	)	PUNCT
ejpam-3916	480	1	=	=	PUNCT
ejpam-3916	480	2	1	1	X
ejpam-3916	480	3	.	.	X
ejpam-3916	481	1	if	if	SCONJ
ejpam-3916	481	2	u	u	PROPN
ejpam-3916	481	3	=	=	PROPN
ejpam-3916	481	4	v	v	NOUN
ejpam-3916	481	5	,	,	PUNCT
ejpam-3916	481	6	then	then	ADV
ejpam-3916	481	7	t	t	PROPN
ejpam-3916	481	8	∈	∈	PROPN
ejpam-3916	481	9	nh(p	nh(p	PROPN
ejpam-3916	481	10	)	)	PUNCT
ejpam-3916	481	11	∩	∩	ADJ
ejpam-3916	481	12	tv	tv	NOUN
ejpam-3916	481	13	.	.	PUNCT
ejpam-3916	482	1	since	since	SCONJ
ejpam-3916	482	2	dg	dg	PROPN
ejpam-3916	482	3	�	�	PROPN
ejpam-3916	482	4	h((v	h((v	NOUN
ejpam-3916	482	5	,	,	PUNCT
ejpam-3916	482	6	p)(u	p)(u	PROPN
ejpam-3916	482	7	,	,	PUNCT
ejpam-3916	482	8	t	t	PROPN
ejpam-3916	482	9	)	)	PUNCT
ejpam-3916	482	10	)	)	PUNCT
ejpam-3916	483	1	=	=	SYM
ejpam-3916	483	2	dg	dg	PROPN
ejpam-3916	483	3	�	�	PROPN
ejpam-3916	483	4	h((v	h((v	NOUN
ejpam-3916	483	5	,	,	PUNCT
ejpam-3916	483	6	p)(v	p)(v	PROPN
ejpam-3916	483	7	,	,	PUNCT
ejpam-3916	483	8	t	t	PROPN
ejpam-3916	483	9	)	)	PUNCT
ejpam-3916	483	10	)	)	PUNCT
ejpam-3916	484	1	=	=	SYM
ejpam-3916	484	2	2	2	NUM
ejpam-3916	484	3	,	,	PUNCT
ejpam-3916	484	4	v	v	NOUN
ejpam-3916	484	5	(	(	PUNCT
ejpam-3916	484	6	g	g	NOUN
ejpam-3916	484	7	)	)	PUNCT
ejpam-3916	484	8	\	\	PUNCT
ejpam-3916	485	1	ng[v	ng[v	X
ejpam-3916	485	2	]	]	PUNCT
ejpam-3916	485	3	6=	6=	ADP
ejpam-3916	485	4	∅	∅	NOUN
ejpam-3916	485	5	or	or	CCONJ
ejpam-3916	485	6	|v	|v	PROPN
ejpam-3916	485	7	(	(	PUNCT
ejpam-3916	485	8	h)|	h)|	PROPN
ejpam-3916	485	9	≥	≥	NUM
ejpam-3916	485	10	3	3	NUM
ejpam-3916	485	11	.	.	PUNCT
ejpam-3916	485	12	suppose	suppose	VERB
ejpam-3916	485	13	u	u	PROPN
ejpam-3916	485	14	6=	6=	PROPN
ejpam-3916	485	15	v.	v.	ADP
ejpam-3916	485	16	then	then	ADV
ejpam-3916	485	17	u	u	PROPN
ejpam-3916	485	18	∈	∈	PROPN
ejpam-3916	485	19	s	s	PART
ejpam-3916	485	20	∩	∩	NOUN
ejpam-3916	485	21	ng(v	ng(v	X
ejpam-3916	485	22	)	)	PUNCT
ejpam-3916	485	23	and	and	CCONJ
ejpam-3916	486	1	p	p	PROPN
ejpam-3916	486	2	∈	∈	PROPN
ejpam-3916	486	3	tu	tu	PROPN
ejpam-3916	486	4	.	.	PROPN
ejpam-3916	487	1	since	since	SCONJ
ejpam-3916	487	2	dg	dg	PROPN
ejpam-3916	487	3	�	�	PROPN
ejpam-3916	487	4	h((v	h((v	NOUN
ejpam-3916	487	5	,	,	PUNCT
ejpam-3916	487	6	p)(u	p)(u	PROPN
ejpam-3916	487	7	,	,	PUNCT
ejpam-3916	487	8	t	t	PROPN
ejpam-3916	487	9	)	)	PUNCT
ejpam-3916	487	10	)	)	PUNCT
ejpam-3916	488	1	=	=	SYM
ejpam-3916	488	2	2	2	NUM
ejpam-3916	488	3	,	,	PUNCT
ejpam-3916	488	4	v	v	NOUN
ejpam-3916	488	5	(	(	PUNCT
ejpam-3916	488	6	h	h	NOUN
ejpam-3916	488	7	)	)	PUNCT
ejpam-3916	488	8	\	\	NOUN
ejpam-3916	488	9	nh(p	nh(p	PROPN
ejpam-3916	488	10	)	)	PUNCT
ejpam-3916	488	11	6=	6=	ADP
ejpam-3916	488	12	∅	∅	NOUN
ejpam-3916	488	13	or	or	CCONJ
ejpam-3916	488	14	(	(	PUNCT
ejpam-3916	488	15	v	v	NOUN
ejpam-3916	488	16	(	(	PUNCT
ejpam-3916	488	17	g	g	NOUN
ejpam-3916	488	18	)	)	PUNCT
ejpam-3916	488	19	\	\	NOUN
ejpam-3916	488	20	ng(v	ng(v	NOUN
ejpam-3916	488	21	)	)	PUNCT
ejpam-3916	488	22	)	)	PUNCT
ejpam-3916	489	1	∩	∩	NOUN
ejpam-3916	489	2	(	(	PUNCT
ejpam-3916	489	3	v	v	NOUN
ejpam-3916	489	4	(	(	PUNCT
ejpam-3916	489	5	g	g	NOUN
ejpam-3916	489	6	)	)	PUNCT
ejpam-3916	489	7	\ng(u	\ng(u	NOUN
ejpam-3916	489	8	)	)	PUNCT
ejpam-3916	489	9	)	)	PUNCT
ejpam-3916	489	10	6=	6=	ADP
ejpam-3916	489	11	∅.	∅.	VERB
ejpam-3916	489	12	for	for	ADP
ejpam-3916	489	13	the	the	DET
ejpam-3916	489	14	converse	converse	NOUN
ejpam-3916	489	15	,	,	PUNCT
ejpam-3916	489	16	suppose	suppose	VERB
ejpam-3916	489	17	that	that	SCONJ
ejpam-3916	489	18	c	c	PROPN
ejpam-3916	489	19	satisfies	satisfy	VERB
ejpam-3916	489	20	properties	property	NOUN
ejpam-3916	489	21	(	(	PUNCT
ejpam-3916	489	22	i	i	NOUN
ejpam-3916	489	23	)	)	PUNCT
ejpam-3916	489	24	and	and	CCONJ
ejpam-3916	489	25	(	(	PUNCT
ejpam-3916	489	26	ii	ii	NOUN
ejpam-3916	489	27	)	)	PUNCT
ejpam-3916	489	28	.	.	PUNCT
ejpam-3916	490	1	let	let	VERB
ejpam-3916	490	2	(	(	PUNCT
ejpam-3916	490	3	v	v	NOUN
ejpam-3916	490	4	,	,	PUNCT
ejpam-3916	490	5	p	p	NOUN
ejpam-3916	490	6	)	)	PUNCT
ejpam-3916	490	7	∈	∈	PROPN
ejpam-3916	490	8	v	v	NOUN
ejpam-3916	490	9	(	(	PUNCT
ejpam-3916	490	10	g[h])\	g[h])\	NOUN
ejpam-3916	490	11	c	c	NOUN
ejpam-3916	490	12	and	and	CCONJ
ejpam-3916	490	13	consider	consider	VERB
ejpam-3916	490	14	the	the	DET
ejpam-3916	490	15	following	follow	VERB
ejpam-3916	490	16	cases	case	NOUN
ejpam-3916	490	17	:	:	PUNCT
ejpam-3916	490	18	case	case	NOUN
ejpam-3916	490	19	1	1	NUM
ejpam-3916	490	20	.	.	X
ejpam-3916	491	1	v	v	NUM
ejpam-3916	491	2	/∈	/∈	PUNCT
ejpam-3916	491	3	s	s	AUX
ejpam-3916	491	4	by	by	ADP
ejpam-3916	491	5	the	the	DET
ejpam-3916	491	6	assumption	assumption	NOUN
ejpam-3916	491	7	that	that	SCONJ
ejpam-3916	491	8	(	(	PUNCT
ejpam-3916	491	9	a	a	X
ejpam-3916	491	10	)	)	PUNCT
ejpam-3916	491	11	of	of	ADP
ejpam-3916	491	12	(	(	PUNCT
ejpam-3916	491	13	i	i	NOUN
ejpam-3916	491	14	)	)	PUNCT
ejpam-3916	491	15	holds	hold	VERB
ejpam-3916	491	16	,	,	PUNCT
ejpam-3916	491	17	suppose	suppose	VERB
ejpam-3916	491	18	first	first	ADV
ejpam-3916	491	19	that	that	SCONJ
ejpam-3916	491	20	there	there	PRON
ejpam-3916	491	21	exists	exist	VERB
ejpam-3916	491	22	y	y	PROPN
ejpam-3916	491	23	∈	∈	PROPN
ejpam-3916	491	24	s	s	PART
ejpam-3916	491	25	∩	∩	NOUN
ejpam-3916	491	26	ng(x	ng(x	NUM
ejpam-3916	491	27	)	)	PUNCT
ejpam-3916	491	28	such	such	ADJ
ejpam-3916	491	29	that	that	SCONJ
ejpam-3916	491	30	ty	ty	NUM
ejpam-3916	491	31	∩	∩	NOUN
ejpam-3916	491	32	nh(p	nh(p	X
ejpam-3916	491	33	)	)	PUNCT
ejpam-3916	491	34	6=	6=	ADP
ejpam-3916	491	35	∅.	∅.	AUX
ejpam-3916	491	36	let	let	VERB
ejpam-3916	491	37	q	q	NOUN
ejpam-3916	491	38	∈	∈	PROPN
ejpam-3916	491	39	ty	ty	ADP
ejpam-3916	491	40	∩	∩	NOUN
ejpam-3916	491	41	nh(p	nh(p	X
ejpam-3916	491	42	)	)	PUNCT
ejpam-3916	491	43	6=	6=	ADP
ejpam-3916	491	44	∅.	∅.	ADP
ejpam-3916	491	45	then	then	ADV
ejpam-3916	491	46	(	(	PUNCT
ejpam-3916	491	47	y	y	PROPN
ejpam-3916	491	48	,	,	PUNCT
ejpam-3916	491	49	q	q	X
ejpam-3916	491	50	)	)	PUNCT
ejpam-3916	491	51	∈	∈	PROPN
ejpam-3916	491	52	c	c	PROPN
ejpam-3916	491	53	and	and	CCONJ
ejpam-3916	491	54	dg	dg	PROPN
ejpam-3916	491	55	�	�	PROPN
ejpam-3916	491	56	h((v	h((v	NOUN
ejpam-3916	491	57	,	,	PUNCT
ejpam-3916	491	58	p)(y	p)(y	PROPN
ejpam-3916	491	59	,	,	PUNCT
ejpam-3916	491	60	q	q	NOUN
ejpam-3916	491	61	)	)	PUNCT
ejpam-3916	491	62	)	)	PUNCT
ejpam-3916	492	1	=	=	SYM
ejpam-3916	492	2	dg(v	dg(v	X
ejpam-3916	492	3	,	,	PUNCT
ejpam-3916	492	4	y	y	NOUN
ejpam-3916	492	5	)	)	PUNCT
ejpam-3916	492	6	+	+	NUM
ejpam-3916	492	7	dh(p	dh(p	NOUN
ejpam-3916	492	8	,	,	PUNCT
ejpam-3916	492	9	q	q	X
ejpam-3916	492	10	)	)	PUNCT
ejpam-3916	492	11	=	=	SYM
ejpam-3916	492	12	2	2	X
ejpam-3916	492	13	.	.	PUNCT
ejpam-3916	493	1	next	next	ADV
ejpam-3916	493	2	,	,	PUNCT
ejpam-3916	493	3	suppose	suppose	VERB
ejpam-3916	493	4	that	that	SCONJ
ejpam-3916	493	5	there	there	PRON
ejpam-3916	493	6	exists	exist	VERB
ejpam-3916	493	7	z	z	PROPN
ejpam-3916	493	8	∈	∈	PROPN
ejpam-3916	493	9	s	s	PART
ejpam-3916	493	10	∩ng(v	∩ng(v	PROPN
ejpam-3916	493	11	,	,	PUNCT
ejpam-3916	493	12	2	2	NUM
ejpam-3916	493	13	)	)	PUNCT
ejpam-3916	493	14	such	such	ADJ
ejpam-3916	493	15	that	that	SCONJ
ejpam-3916	493	16	p	p	PROPN
ejpam-3916	493	17	∈	∈	PROPN
ejpam-3916	493	18	tz	tz	NOUN
ejpam-3916	493	19	.	.	PUNCT
ejpam-3916	494	1	then	then	ADV
ejpam-3916	494	2	(	(	PUNCT
ejpam-3916	494	3	z	z	X
ejpam-3916	494	4	,	,	PUNCT
ejpam-3916	494	5	p	p	NOUN
ejpam-3916	494	6	)	)	PUNCT
ejpam-3916	494	7	∈	∈	PROPN
ejpam-3916	494	8	c	c	PROPN
ejpam-3916	494	9	and	and	CCONJ
ejpam-3916	494	10	dg	dg	PROPN
ejpam-3916	494	11	�	�	NOUN
ejpam-3916	494	12	h((v	h((v	NOUN
ejpam-3916	494	13	,	,	PUNCT
ejpam-3916	494	14	p)(z	p)(z	PROPN
ejpam-3916	494	15	,	,	PUNCT
ejpam-3916	494	16	p	p	NOUN
ejpam-3916	494	17	)	)	PUNCT
ejpam-3916	494	18	)	)	PUNCT
ejpam-3916	495	1	=	=	SYM
ejpam-3916	495	2	dg(v	dg(v	X
ejpam-3916	495	3	,	,	PUNCT
ejpam-3916	495	4	z	z	NOUN
ejpam-3916	495	5	)	)	PUNCT
ejpam-3916	495	6	=	=	SYM
ejpam-3916	495	7	2	2	X
ejpam-3916	495	8	.	.	PUNCT
ejpam-3916	495	9	since	since	SCONJ
ejpam-3916	495	10	(	(	PUNCT
ejpam-3916	495	11	b	b	NOUN
ejpam-3916	495	12	)	)	PUNCT
ejpam-3916	495	13	of	of	ADP
ejpam-3916	495	14	(	(	PUNCT
ejpam-3916	495	15	i	i	NOUN
ejpam-3916	495	16	)	)	PUNCT
ejpam-3916	495	17	also	also	ADV
ejpam-3916	495	18	holds	hold	VERB
ejpam-3916	495	19	,	,	PUNCT
ejpam-3916	495	20	suppose	suppose	VERB
ejpam-3916	495	21	that	that	SCONJ
ejpam-3916	495	22	there	there	PRON
ejpam-3916	495	23	exists	exist	VERB
ejpam-3916	495	24	w	w	PROPN
ejpam-3916	495	25	∈	∈	PROPN
ejpam-3916	495	26	s	s	PART
ejpam-3916	495	27	∩ng(v	∩ng(v	PROPN
ejpam-3916	495	28	)	)	PUNCT
ejpam-3916	495	29	such	such	ADJ
ejpam-3916	495	30	that	that	SCONJ
ejpam-3916	495	31	p	p	PROPN
ejpam-3916	495	32	∈	∈	PROPN
ejpam-3916	495	33	tw	tw	NOUN
ejpam-3916	495	34	.	.	PUNCT
ejpam-3916	496	1	then	then	ADV
ejpam-3916	496	2	(	(	PUNCT
ejpam-3916	496	3	w	w	PROPN
ejpam-3916	496	4	,	,	PUNCT
ejpam-3916	496	5	p	p	NOUN
ejpam-3916	496	6	)	)	PUNCT
ejpam-3916	496	7	∈	∈	PROPN
ejpam-3916	496	8	c	c	PROPN
ejpam-3916	496	9	∩ng	∩ng	PROPN
ejpam-3916	496	10	�	�	PROPN
ejpam-3916	496	11	h((v	h((v	NOUN
ejpam-3916	496	12	,	,	PUNCT
ejpam-3916	496	13	p	p	NOUN
ejpam-3916	496	14	)	)	PUNCT
ejpam-3916	496	15	)	)	PUNCT
ejpam-3916	496	16	.	.	PUNCT
ejpam-3916	497	1	if	if	SCONJ
ejpam-3916	497	2	nh	nh	PROPN
ejpam-3916	497	3	[	[	X
ejpam-3916	497	4	p	p	X
ejpam-3916	497	5	]	]	X
ejpam-3916	497	6	6=	6=	ADP
ejpam-3916	497	7	v	v	ADP
ejpam-3916	497	8	(	(	PUNCT
ejpam-3916	497	9	h	h	NOUN
ejpam-3916	497	10	)	)	PUNCT
ejpam-3916	497	11	,	,	PUNCT
ejpam-3916	497	12	we	we	PRON
ejpam-3916	497	13	may	may	AUX
ejpam-3916	497	14	pick	pick	VERB
ejpam-3916	497	15	any	any	DET
ejpam-3916	497	16	s	s	NOUN
ejpam-3916	497	17	∈	∈	PROPN
ejpam-3916	497	18	v	v	NOUN
ejpam-3916	497	19	(	(	PUNCT
ejpam-3916	497	20	h	h	NOUN
ejpam-3916	497	21	)	)	PUNCT
ejpam-3916	497	22	\nh	\nh	PROPN
ejpam-3916	498	1	[	[	X
ejpam-3916	498	2	p	p	X
ejpam-3916	498	3	]	]	X
ejpam-3916	498	4	.	.	PUNCT
ejpam-3916	499	1	then	then	ADV
ejpam-3916	499	2	(	(	PUNCT
ejpam-3916	499	3	w	w	PROPN
ejpam-3916	499	4	,	,	PUNCT
ejpam-3916	499	5	s	s	PART
ejpam-3916	499	6	)	)	PUNCT
ejpam-3916	499	7	/∈	/∈	PUNCT
ejpam-3916	499	8	ng	ng	PROPN
ejpam-3916	499	9	�	�	PROPN
ejpam-3916	499	10	h((v	h((v	NOUN
ejpam-3916	499	11	,	,	PUNCT
ejpam-3916	499	12	p))∪ng	p))∪ng	NOUN
ejpam-3916	499	13	�	�	NOUN
ejpam-3916	499	14	h((w	h((w	PROPN
ejpam-3916	499	15	,	,	PUNCT
ejpam-3916	499	16	p	p	NOUN
ejpam-3916	499	17	)	)	PUNCT
ejpam-3916	499	18	)	)	PUNCT
ejpam-3916	499	19	.	.	PUNCT
ejpam-3916	500	1	it	it	PRON
ejpam-3916	500	2	follows	follow	VERB
ejpam-3916	500	3	that	that	SCONJ
ejpam-3916	500	4	[	[	X
ejpam-3916	500	5	(	(	PUNCT
ejpam-3916	500	6	v	v	NOUN
ejpam-3916	500	7	,	,	PUNCT
ejpam-3916	500	8	p	p	NOUN
ejpam-3916	500	9	)	)	PUNCT
ejpam-3916	500	10	,	,	PUNCT
ejpam-3916	500	11	(	(	PUNCT
ejpam-3916	500	12	w	w	PROPN
ejpam-3916	500	13	,	,	PUNCT
ejpam-3916	500	14	s	s	PART
ejpam-3916	500	15	)	)	PUNCT
ejpam-3916	500	16	,	,	PUNCT
ejpam-3916	500	17	(	(	PUNCT
ejpam-3916	500	18	w	w	X
ejpam-3916	500	19	,	,	PUNCT
ejpam-3916	500	20	p	p	NOUN
ejpam-3916	500	21	)	)	PUNCT
ejpam-3916	500	22	]	]	PUNCT
ejpam-3916	500	23	is	be	AUX
ejpam-3916	500	24	a	a	DET
ejpam-3916	500	25	(	(	PUNCT
ejpam-3916	500	26	v	v	NOUN
ejpam-3916	500	27	,	,	PUNCT
ejpam-3916	500	28	p)(w	p)(w	PROPN
ejpam-3916	500	29	,	,	PUNCT
ejpam-3916	500	30	p	p	NOUN
ejpam-3916	500	31	)	)	PUNCT
ejpam-3916	500	32	geodesic	geodesic	NOUN
ejpam-3916	500	33	ing	ing	PROPN
ejpam-3916	500	34	�	�	PROPN
ejpam-3916	500	35	h.	h.	PROPN
ejpam-3916	500	36	thus	thus	ADV
ejpam-3916	500	37	,	,	PUNCT
ejpam-3916	500	38	dg	dg	PROPN
ejpam-3916	500	39	�	�	PROPN
ejpam-3916	500	40	h((v	h((v	NOUN
ejpam-3916	500	41	,	,	PUNCT
ejpam-3916	500	42	p)(w	p)(w	PROPN
ejpam-3916	500	43	,	,	PUNCT
ejpam-3916	500	44	p	p	NOUN
ejpam-3916	500	45	)	)	PUNCT
ejpam-3916	500	46	)	)	PUNCT
ejpam-3916	501	1	=	=	SYM
ejpam-3916	501	2	2	2	X
ejpam-3916	501	3	.	.	PUNCT
ejpam-3916	501	4	instead	instead	ADV
ejpam-3916	501	5	ofnh(p	ofnh(p	PROPN
ejpam-3916	501	6	)	)	PUNCT
ejpam-3916	501	7	6=	6=	SYM
ejpam-3916	501	8	v	v	ADP
ejpam-3916	501	9	(	(	PUNCT
ejpam-3916	501	10	h	h	NOUN
ejpam-3916	501	11	)	)	PUNCT
ejpam-3916	501	12	,	,	PUNCT
ejpam-3916	501	13	suppose	suppose	VERB
ejpam-3916	501	14	that	that	SCONJ
ejpam-3916	501	15	(	(	PUNCT
ejpam-3916	501	16	v	v	X
ejpam-3916	501	17	(	(	PUNCT
ejpam-3916	501	18	g)\ng(x))∩(v	g)\ng(x))∩(v	PROPN
ejpam-3916	501	19	(	(	PUNCT
ejpam-3916	501	20	g)\ng(w	g)\ng(w	PROPN
ejpam-3916	501	21	)	)	PUNCT
ejpam-3916	501	22	)	)	PUNCT
ejpam-3916	501	23	6=	6=	ADP
ejpam-3916	501	24	∅	∅	NOUN
ejpam-3916	501	25	]	]	PUNCT
ejpam-3916	501	26	,	,	PUNCT
ejpam-3916	501	27	say	say	VERB
ejpam-3916	501	28	u	u	PROPN
ejpam-3916	501	29	∈	∈	PROPN
ejpam-3916	501	30	(	(	PUNCT
ejpam-3916	501	31	v	v	NOUN
ejpam-3916	501	32	(	(	PUNCT
ejpam-3916	501	33	g)\ng(x))∩(v	g)\ng(x))∩(v	PROPN
ejpam-3916	501	34	(	(	PUNCT
ejpam-3916	501	35	g)\ng(w	g)\ng(w	PROPN
ejpam-3916	501	36	)	)	PUNCT
ejpam-3916	501	37	)	)	PUNCT
ejpam-3916	501	38	.	.	PUNCT
ejpam-3916	502	1	then	then	ADV
ejpam-3916	502	2	[	[	X
ejpam-3916	502	3	(	(	PUNCT
ejpam-3916	502	4	v	v	NOUN
ejpam-3916	502	5	,	,	PUNCT
ejpam-3916	502	6	p	p	NOUN
ejpam-3916	502	7	)	)	PUNCT
ejpam-3916	502	8	,	,	PUNCT
ejpam-3916	502	9	(	(	PUNCT
ejpam-3916	502	10	u	u	NOUN
ejpam-3916	502	11	,	,	PUNCT
ejpam-3916	502	12	p	p	NOUN
ejpam-3916	502	13	)	)	PUNCT
ejpam-3916	502	14	,	,	PUNCT
ejpam-3916	502	15	(	(	PUNCT
ejpam-3916	502	16	w	w	X
ejpam-3916	502	17	,	,	PUNCT
ejpam-3916	502	18	p	p	NOUN
ejpam-3916	502	19	)	)	PUNCT
ejpam-3916	502	20	]	]	PUNCT
ejpam-3916	502	21	is	be	AUX
ejpam-3916	502	22	a	a	DET
ejpam-3916	502	23	(	(	PUNCT
ejpam-3916	502	24	v	v	NOUN
ejpam-3916	502	25	,	,	PUNCT
ejpam-3916	502	26	p)-(w	p)-(w	NUM
ejpam-3916	502	27	,	,	PUNCT
ejpam-3916	502	28	p	p	NOUN
ejpam-3916	502	29	)	)	PUNCT
ejpam-3916	502	30	geodesic	geodesic	NOUN
ejpam-3916	502	31	in	in	ADP
ejpam-3916	502	32	g	g	PROPN
ejpam-3916	502	33	�	�	PROPN
ejpam-3916	502	34	h	h	NOUN
ejpam-3916	502	35	,	,	PUNCT
ejpam-3916	502	36	implying	imply	VERB
ejpam-3916	502	37	that	that	SCONJ
ejpam-3916	502	38	dg	dg	PROPN
ejpam-3916	502	39	�	�	PROPN
ejpam-3916	502	40	h((v	h((v	NOUN
ejpam-3916	502	41	,	,	PUNCT
ejpam-3916	502	42	p)(w	p)(w	PROPN
ejpam-3916	502	43	,	,	PUNCT
ejpam-3916	502	44	p	p	NOUN
ejpam-3916	502	45	)	)	PUNCT
ejpam-3916	502	46	)	)	PUNCT
ejpam-3916	503	1	=	=	SYM
ejpam-3916	503	2	2	2	X
ejpam-3916	503	3	.	.	X
ejpam-3916	503	4	case	case	NOUN
ejpam-3916	503	5	2	2	NUM
ejpam-3916	503	6	.	.	NOUN
ejpam-3916	504	1	v	v	NUM
ejpam-3916	504	2	∈	∈	NOUN
ejpam-3916	504	3	s	s	AUX
ejpam-3916	504	4	utilizing	utilize	VERB
ejpam-3916	504	5	(	(	PUNCT
ejpam-3916	504	6	c	c	NOUN
ejpam-3916	504	7	)	)	PUNCT
ejpam-3916	504	8	of	of	ADP
ejpam-3916	504	9	(	(	PUNCT
ejpam-3916	504	10	ii	ii	NOUN
ejpam-3916	504	11	)	)	PUNCT
ejpam-3916	504	12	,	,	PUNCT
ejpam-3916	504	13	suppose	suppose	VERB
ejpam-3916	504	14	first	first	ADV
ejpam-3916	504	15	that	that	SCONJ
ejpam-3916	504	16	nh(p	nh(p	PROPN
ejpam-3916	504	17	,	,	PUNCT
ejpam-3916	504	18	2)∩tv	2)∩tv	NUM
ejpam-3916	504	19	6=	6=	ADP
ejpam-3916	504	20	∅.	∅.	AUX
ejpam-3916	504	21	let	let	VERB
ejpam-3916	504	22	q	q	PROPN
ejpam-3916	504	23	∈	∈	PROPN
ejpam-3916	504	24	nh(p	nh(p	PROPN
ejpam-3916	504	25	,	,	PUNCT
ejpam-3916	504	26	2)∩tv	2)∩tv	NUM
ejpam-3916	504	27	.	.	PUNCT
ejpam-3916	505	1	then	then	ADV
ejpam-3916	505	2	(	(	PUNCT
ejpam-3916	505	3	v	v	NOUN
ejpam-3916	505	4	,	,	PUNCT
ejpam-3916	505	5	q	q	NOUN
ejpam-3916	505	6	)	)	PUNCT
ejpam-3916	505	7	∈	∈	PROPN
ejpam-3916	505	8	c	c	PROPN
ejpam-3916	505	9	and	and	CCONJ
ejpam-3916	505	10	dg	dg	PROPN
ejpam-3916	505	11	�	�	PROPN
ejpam-3916	505	12	h((v	h((v	NOUN
ejpam-3916	505	13	,	,	PUNCT
ejpam-3916	505	14	p)(v	p)(v	PROPN
ejpam-3916	505	15	,	,	PUNCT
ejpam-3916	505	16	q	q	NOUN
ejpam-3916	505	17	)	)	PUNCT
ejpam-3916	505	18	)	)	PUNCT
ejpam-3916	506	1	=	=	SYM
ejpam-3916	506	2	dh(p	dh(p	X
ejpam-3916	506	3	,	,	PUNCT
ejpam-3916	506	4	q	q	X
ejpam-3916	506	5	)	)	PUNCT
ejpam-3916	506	6	=	=	SYM
ejpam-3916	506	7	2	2	X
ejpam-3916	506	8	.	.	PUNCT
ejpam-3916	506	9	suppose	suppose	VERB
ejpam-3916	506	10	there	there	PRON
ejpam-3916	506	11	exists	exist	VERB
ejpam-3916	506	12	y	y	PROPN
ejpam-3916	506	13	∈	∈	PROPN
ejpam-3916	506	14	s	s	PART
ejpam-3916	506	15	∩ng(v	∩ng(v	PROPN
ejpam-3916	506	16	)	)	PUNCT
ejpam-3916	506	17	such	such	ADJ
ejpam-3916	506	18	that	that	SCONJ
ejpam-3916	506	19	ty∩nh(p	ty∩nh(p	PROPN
ejpam-3916	506	20	)	)	PUNCT
ejpam-3916	506	21	6=	6=	ADP
ejpam-3916	506	22	∅.	∅.	ADP
ejpam-3916	506	23	then	then	ADV
ejpam-3916	506	24	(	(	PUNCT
ejpam-3916	506	25	y	y	PROPN
ejpam-3916	506	26	,	,	PUNCT
ejpam-3916	506	27	t	t	PROPN
ejpam-3916	506	28	)	)	PUNCT
ejpam-3916	506	29	∈	∈	PROPN
ejpam-3916	506	30	c	c	PROPN
ejpam-3916	506	31	and	and	CCONJ
ejpam-3916	506	32	dg	dg	PROPN
ejpam-3916	506	33	�	�	PROPN
ejpam-3916	506	34	h((v	h((v	NOUN
ejpam-3916	506	35	,	,	PUNCT
ejpam-3916	506	36	p)(y	p)(y	PROPN
ejpam-3916	506	37	,	,	PUNCT
ejpam-3916	506	38	t	t	PROPN
ejpam-3916	506	39	)	)	PUNCT
ejpam-3916	506	40	)	)	PUNCT
ejpam-3916	507	1	=	=	SYM
ejpam-3916	507	2	2	2	NUM
ejpam-3916	507	3	,	,	PUNCT
ejpam-3916	507	4	where	where	SCONJ
ejpam-3916	507	5	t	t	PROPN
ejpam-3916	507	6	∈	∈	PROPN
ejpam-3916	507	7	ty∩nh(p	ty∩nh(p	PROPN
ejpam-3916	507	8	)	)	PUNCT
ejpam-3916	507	9	.	.	PUNCT
ejpam-3916	508	1	if	if	SCONJ
ejpam-3916	508	2	there	there	PRON
ejpam-3916	508	3	exists	exist	VERB
ejpam-3916	508	4	z	z	PROPN
ejpam-3916	508	5	∈	∈	PROPN
ejpam-3916	508	6	s	s	PART
ejpam-3916	508	7	∩ng(v	∩ng(v	PROPN
ejpam-3916	508	8	,	,	PUNCT
ejpam-3916	508	9	2	2	NUM
ejpam-3916	508	10	)	)	PUNCT
ejpam-3916	508	11	such	such	ADJ
ejpam-3916	508	12	that	that	SCONJ
ejpam-3916	508	13	p	p	PROPN
ejpam-3916	508	14	∈	∈	PROPN
ejpam-3916	508	15	tz	tz	NOUN
ejpam-3916	508	16	,	,	PUNCT
ejpam-3916	508	17	then	then	ADV
ejpam-3916	508	18	(	(	PUNCT
ejpam-3916	508	19	z	z	X
ejpam-3916	508	20	,	,	PUNCT
ejpam-3916	508	21	p	p	NOUN
ejpam-3916	508	22	)	)	PUNCT
ejpam-3916	508	23	∈	∈	PROPN
ejpam-3916	508	24	c	c	PROPN
ejpam-3916	508	25	and	and	CCONJ
ejpam-3916	508	26	dg	dg	PROPN
ejpam-3916	508	27	�	�	NOUN
ejpam-3916	508	28	h((v	h((v	NOUN
ejpam-3916	508	29	,	,	PUNCT
ejpam-3916	508	30	p)(z	p)(z	PROPN
ejpam-3916	508	31	,	,	PUNCT
ejpam-3916	508	32	p	p	NOUN
ejpam-3916	508	33	)	)	PUNCT
ejpam-3916	508	34	)	)	PUNCT
ejpam-3916	509	1	=	=	SYM
ejpam-3916	509	2	2	2	X
ejpam-3916	509	3	.	.	PUNCT
ejpam-3916	509	4	now	now	ADV
ejpam-3916	509	5	,	,	PUNCT
ejpam-3916	509	6	using	use	VERB
ejpam-3916	509	7	(	(	PUNCT
ejpam-3916	509	8	d	d	NOUN
ejpam-3916	509	9	)	)	PUNCT
ejpam-3916	509	10	of	of	ADP
ejpam-3916	509	11	(	(	PUNCT
ejpam-3916	509	12	ii	ii	NOUN
ejpam-3916	509	13	)	)	PUNCT
ejpam-3916	509	14	,	,	PUNCT
ejpam-3916	509	15	assume	assume	VERB
ejpam-3916	509	16	that	that	SCONJ
ejpam-3916	509	17	nh(p	nh(p	NOUN
ejpam-3916	509	18	)	)	PUNCT
ejpam-3916	509	19	∩	∩	ADJ
ejpam-3916	509	20	tv	tv	NOUN
ejpam-3916	509	21	6=	6=	PUNCT
ejpam-3916	509	22	∅	∅	NOUN
ejpam-3916	509	23	,	,	PUNCT
ejpam-3916	509	24	say	say	VERB
ejpam-3916	509	25	a	a	DET
ejpam-3916	509	26	∈	∈	PROPN
ejpam-3916	509	27	nh(p	nh(p	NUM
ejpam-3916	509	28	)	)	PUNCT
ejpam-3916	509	29	∩	∩	ADJ
ejpam-3916	509	30	tv	tv	NOUN
ejpam-3916	509	31	.	.	PUNCT
ejpam-3916	510	1	then	then	ADV
ejpam-3916	510	2	(	(	PUNCT
ejpam-3916	510	3	v	v	NOUN
ejpam-3916	510	4	,	,	PUNCT
ejpam-3916	510	5	a	a	DET
ejpam-3916	510	6	)	)	PUNCT
ejpam-3916	510	7	∈	∈	PROPN
ejpam-3916	510	8	c.	c.	NOUN
ejpam-3916	510	9	if	if	SCONJ
ejpam-3916	510	10	there	there	PRON
ejpam-3916	510	11	exists	exist	VERB
ejpam-3916	510	12	w	w	PROPN
ejpam-3916	510	13	∈	∈	PROPN
ejpam-3916	510	14	v	v	ADP
ejpam-3916	510	15	(	(	PUNCT
ejpam-3916	510	16	g	g	NOUN
ejpam-3916	510	17	)	)	PUNCT
ejpam-3916	510	18	\	\	PUNCT
ejpam-3916	511	1	ng[v	ng[v	ADV
ejpam-3916	511	2	]	]	PUNCT
ejpam-3916	511	3	,	,	PUNCT
ejpam-3916	511	4	then	then	ADV
ejpam-3916	511	5	[	[	X
ejpam-3916	511	6	(	(	PUNCT
ejpam-3916	511	7	v	v	NOUN
ejpam-3916	511	8	,	,	PUNCT
ejpam-3916	511	9	p	p	NOUN
ejpam-3916	511	10	)	)	PUNCT
ejpam-3916	511	11	,	,	PUNCT
ejpam-3916	511	12	(	(	PUNCT
ejpam-3916	511	13	w	w	X
ejpam-3916	511	14	,	,	PUNCT
ejpam-3916	511	15	p	p	NOUN
ejpam-3916	511	16	)	)	PUNCT
ejpam-3916	511	17	,	,	PUNCT
ejpam-3916	511	18	(	(	PUNCT
ejpam-3916	511	19	v	v	NOUN
ejpam-3916	511	20	,	,	PUNCT
ejpam-3916	511	21	a	a	PRON
ejpam-3916	511	22	)	)	PUNCT
ejpam-3916	511	23	]	]	PUNCT
ejpam-3916	511	24	is	be	AUX
ejpam-3916	511	25	a	a	DET
ejpam-3916	511	26	(	(	PUNCT
ejpam-3916	511	27	v	v	NOUN
ejpam-3916	511	28	,	,	PUNCT
ejpam-3916	511	29	p)-(v	p)-(v	PROPN
ejpam-3916	511	30	,	,	PUNCT
ejpam-3916	511	31	a	a	PRON
ejpam-3916	511	32	)	)	PUNCT
ejpam-3916	511	33	geodesic	geodesic	NOUN
ejpam-3916	511	34	in	in	ADP
ejpam-3916	511	35	g	g	PROPN
ejpam-3916	511	36	�	�	PROPN
ejpam-3916	511	37	h.	h.	PROPN
ejpam-3916	511	38	thus	thus	ADV
ejpam-3916	511	39	,	,	PUNCT
ejpam-3916	511	40	dg	dg	PROPN
ejpam-3916	511	41	�	�	PROPN
ejpam-3916	511	42	h((v	h((v	NOUN
ejpam-3916	511	43	,	,	PUNCT
ejpam-3916	511	44	p)(v	p)(v	PROPN
ejpam-3916	511	45	,	,	PUNCT
ejpam-3916	511	46	a	a	PRON
ejpam-3916	511	47	)	)	PUNCT
ejpam-3916	511	48	)	)	PUNCT
ejpam-3916	512	1	=	=	SYM
ejpam-3916	512	2	2	2	X
ejpam-3916	512	3	.	.	X
ejpam-3916	513	1	if	if	SCONJ
ejpam-3916	513	2	|v	|v	PROPN
ejpam-3916	513	3	(	(	PUNCT
ejpam-3916	513	4	h)|	h)|	PROPN
ejpam-3916	513	5	≥	≥	NUM
ejpam-3916	513	6	3	3	NUM
ejpam-3916	513	7	,	,	PUNCT
ejpam-3916	513	8	then	then	ADV
ejpam-3916	513	9	we	we	PRON
ejpam-3916	513	10	may	may	AUX
ejpam-3916	513	11	pick	pick	VERB
ejpam-3916	513	12	any	any	DET
ejpam-3916	513	13	b	b	PROPN
ejpam-3916	513	14	∈	∈	PROPN
ejpam-3916	513	15	v	v	NOUN
ejpam-3916	513	16	(	(	PUNCT
ejpam-3916	513	17	h	h	NOUN
ejpam-3916	513	18	)	)	PUNCT
ejpam-3916	513	19	\	\	NOUN
ejpam-3916	513	20	{	{	PUNCT
ejpam-3916	513	21	a	a	NOUN
ejpam-3916	513	22	,	,	PUNCT
ejpam-3916	513	23	p	p	NOUN
ejpam-3916	513	24	}	}	PUNCT
ejpam-3916	513	25	.	.	PUNCT
ejpam-3916	514	1	let	let	VERB
ejpam-3916	514	2	z	z	NOUN
ejpam-3916	514	3	∈	∈	PROPN
ejpam-3916	514	4	ng(v	ng(v	NOUN
ejpam-3916	514	5	)	)	PUNCT
ejpam-3916	514	6	.	.	PUNCT
ejpam-3916	515	1	then	then	ADV
ejpam-3916	515	2	[	[	X
ejpam-3916	515	3	(	(	PUNCT
ejpam-3916	515	4	v	v	NOUN
ejpam-3916	515	5	,	,	PUNCT
ejpam-3916	515	6	p	p	NOUN
ejpam-3916	515	7	)	)	PUNCT
ejpam-3916	515	8	,	,	PUNCT
ejpam-3916	515	9	(	(	PUNCT
ejpam-3916	515	10	z	z	X
ejpam-3916	515	11	,	,	PUNCT
ejpam-3916	515	12	b	b	NOUN
ejpam-3916	515	13	)	)	PUNCT
ejpam-3916	515	14	,	,	PUNCT
ejpam-3916	515	15	(	(	PUNCT
ejpam-3916	515	16	v	v	NOUN
ejpam-3916	515	17	,	,	PUNCT
ejpam-3916	515	18	a	a	PRON
ejpam-3916	515	19	)	)	PUNCT
ejpam-3916	515	20	]	]	PUNCT
ejpam-3916	515	21	is	be	AUX
ejpam-3916	515	22	a	a	DET
ejpam-3916	515	23	(	(	PUNCT
ejpam-3916	515	24	v	v	NOUN
ejpam-3916	515	25	,	,	PUNCT
ejpam-3916	515	26	p)-(v	p)-(v	PROPN
ejpam-3916	515	27	,	,	PUNCT
ejpam-3916	515	28	a	a	PRON
ejpam-3916	515	29	)	)	PUNCT
ejpam-3916	515	30	geodesic	geodesic	NOUN
ejpam-3916	515	31	in	in	ADP
ejpam-3916	515	32	g	g	PROPN
ejpam-3916	515	33	�	�	PROPN
ejpam-3916	515	34	h.	h.	PROPN
ejpam-3916	515	35	hence	hence	PROPN
ejpam-3916	515	36	,	,	PUNCT
ejpam-3916	515	37	dg	dg	PROPN
ejpam-3916	515	38	�	�	PROPN
ejpam-3916	515	39	h((v	h((v	NOUN
ejpam-3916	515	40	,	,	PUNCT
ejpam-3916	515	41	p)(v	p)(v	PROPN
ejpam-3916	515	42	,	,	PUNCT
ejpam-3916	515	43	a	a	PRON
ejpam-3916	515	44	)	)	PUNCT
ejpam-3916	515	45	)	)	PUNCT
ejpam-3916	516	1	=	=	SYM
ejpam-3916	516	2	2	2	X
ejpam-3916	516	3	.	.	PUNCT
ejpam-3916	517	1	next	next	ADV
ejpam-3916	517	2	,	,	PUNCT
ejpam-3916	517	3	assume	assume	VERB
ejpam-3916	517	4	that	that	SCONJ
ejpam-3916	517	5	there	there	PRON
ejpam-3916	517	6	exists	exist	VERB
ejpam-3916	517	7	u	u	PROPN
ejpam-3916	517	8	∈	∈	PROPN
ejpam-3916	517	9	s	s	PART
ejpam-3916	517	10	∩	∩	NOUN
ejpam-3916	517	11	ng(v	ng(v	NOUN
ejpam-3916	517	12	)	)	PUNCT
ejpam-3916	518	1	such	such	ADJ
ejpam-3916	518	2	that	that	AUX
ejpam-3916	518	3	p	p	PROPN
ejpam-3916	518	4	∈	∈	PROPN
ejpam-3916	518	5	tu	tu	PROPN
ejpam-3916	518	6	.	.	PUNCT
ejpam-3916	519	1	then	then	ADV
ejpam-3916	519	2	(	(	PUNCT
ejpam-3916	519	3	u	u	NOUN
ejpam-3916	519	4	,	,	PUNCT
ejpam-3916	519	5	p	p	NOUN
ejpam-3916	519	6	)	)	PUNCT
ejpam-3916	519	7	∈	∈	PROPN
ejpam-3916	519	8	c.	c.	NOUN
ejpam-3916	520	1	if	if	SCONJ
ejpam-3916	520	2	v	v	X
ejpam-3916	520	3	(	(	PUNCT
ejpam-3916	520	4	h	h	NOUN
ejpam-3916	520	5	)	)	PUNCT
ejpam-3916	520	6	\	\	NOUN
ejpam-3916	520	7	nh(p	nh(p	PROPN
ejpam-3916	520	8	)	)	PUNCT
ejpam-3916	520	9	,	,	PUNCT
ejpam-3916	520	10	then	then	ADV
ejpam-3916	520	11	[	[	X
ejpam-3916	520	12	(	(	PUNCT
ejpam-3916	520	13	v	v	NOUN
ejpam-3916	520	14	,	,	PUNCT
ejpam-3916	520	15	p	p	NOUN
ejpam-3916	520	16	)	)	PUNCT
ejpam-3916	520	17	,	,	PUNCT
ejpam-3916	520	18	(	(	PUNCT
ejpam-3916	520	19	u	u	NOUN
ejpam-3916	520	20	,	,	PUNCT
ejpam-3916	520	21	l	l	NOUN
ejpam-3916	520	22	)	)	PUNCT
ejpam-3916	520	23	,	,	PUNCT
ejpam-3916	520	24	(	(	PUNCT
ejpam-3916	520	25	u	u	NOUN
ejpam-3916	520	26	,	,	PUNCT
ejpam-3916	520	27	p	p	NOUN
ejpam-3916	520	28	)	)	PUNCT
ejpam-3916	520	29	]	]	PUNCT
ejpam-3916	520	30	is	be	AUX
ejpam-3916	520	31	a	a	DET
ejpam-3916	520	32	(	(	PUNCT
ejpam-3916	520	33	v	v	NOUN
ejpam-3916	520	34	,	,	PUNCT
ejpam-3916	520	35	p)-(u	p)-(u	NOUN
ejpam-3916	520	36	,	,	PUNCT
ejpam-3916	520	37	p	p	NOUN
ejpam-3916	520	38	)	)	PUNCT
ejpam-3916	520	39	geodesic	geodesic	NOUN
ejpam-3916	520	40	in	in	ADP
ejpam-3916	520	41	g	g	PROPN
ejpam-3916	520	42	�	�	PROPN
ejpam-3916	520	43	h.	h.	PROPN
ejpam-3916	520	44	this	this	PRON
ejpam-3916	520	45	implies	imply	VERB
ejpam-3916	520	46	that	that	SCONJ
ejpam-3916	520	47	dg	dg	PROPN
ejpam-3916	520	48	�	�	PROPN
ejpam-3916	520	49	h((v	h((v	NOUN
ejpam-3916	520	50	,	,	PUNCT
ejpam-3916	520	51	p)(u	p)(u	ADJ
ejpam-3916	520	52	,	,	PUNCT
ejpam-3916	520	53	p	p	NOUN
ejpam-3916	520	54	)	)	PUNCT
ejpam-3916	520	55	)	)	PUNCT
ejpam-3916	521	1	=	=	SYM
ejpam-3916	521	2	2	2	X
ejpam-3916	521	3	.	.	PUNCT
ejpam-3916	521	4	if	if	SCONJ
ejpam-3916	521	5	there	there	PRON
ejpam-3916	521	6	exists	exist	VERB
ejpam-3916	521	7	z	z	PROPN
ejpam-3916	521	8	∈	∈	PROPN
ejpam-3916	521	9	(	(	PUNCT
ejpam-3916	521	10	v	v	NOUN
ejpam-3916	521	11	(	(	PUNCT
ejpam-3916	521	12	g	g	NOUN
ejpam-3916	521	13	)	)	PUNCT
ejpam-3916	521	14	\ng(v	\ng(v	NOUN
ejpam-3916	521	15	)	)	PUNCT
ejpam-3916	521	16	)	)	PUNCT
ejpam-3916	521	17	∩	∩	NOUN
ejpam-3916	521	18	(	(	PUNCT
ejpam-3916	521	19	v	v	NOUN
ejpam-3916	521	20	(	(	PUNCT
ejpam-3916	521	21	g	g	NOUN
ejpam-3916	521	22	)	)	PUNCT
ejpam-3916	521	23	\ng(u	\ng(u	NOUN
ejpam-3916	521	24	)	)	PUNCT
ejpam-3916	521	25	)	)	PUNCT
ejpam-3916	521	26	,	,	PUNCT
ejpam-3916	521	27	then	then	ADV
ejpam-3916	521	28	[	[	X
ejpam-3916	521	29	(	(	PUNCT
ejpam-3916	521	30	v	v	NOUN
ejpam-3916	521	31	,	,	PUNCT
ejpam-3916	521	32	p	p	NOUN
ejpam-3916	521	33	)	)	PUNCT
ejpam-3916	521	34	,	,	PUNCT
ejpam-3916	521	35	(	(	PUNCT
ejpam-3916	521	36	z	z	X
ejpam-3916	521	37	,	,	PUNCT
ejpam-3916	521	38	p	p	NOUN
ejpam-3916	521	39	)	)	PUNCT
ejpam-3916	521	40	,	,	PUNCT
ejpam-3916	521	41	(	(	PUNCT
ejpam-3916	521	42	u	u	NOUN
ejpam-3916	521	43	,	,	PUNCT
ejpam-3916	521	44	p	p	NOUN
ejpam-3916	521	45	)	)	PUNCT
ejpam-3916	521	46	]	]	PUNCT
ejpam-3916	521	47	is	be	AUX
ejpam-3916	521	48	a	a	DET
ejpam-3916	521	49	(	(	PUNCT
ejpam-3916	521	50	v	v	NOUN
ejpam-3916	521	51	,	,	PUNCT
ejpam-3916	521	52	p)-(u	p)-(u	NOUN
ejpam-3916	521	53	,	,	PUNCT
ejpam-3916	521	54	p	p	NOUN
ejpam-3916	521	55	)	)	PUNCT
ejpam-3916	521	56	geodesic	geodesic	NOUN
ejpam-3916	521	57	in	in	ADP
ejpam-3916	521	58	g	g	PROPN
ejpam-3916	521	59	�	�	PROPN
ejpam-3916	521	60	h	h	NOUN
ejpam-3916	521	61	,	,	PUNCT
ejpam-3916	521	62	implying	imply	VERB
ejpam-3916	521	63	that	that	SCONJ
ejpam-3916	521	64	dg	dg	PROPN
ejpam-3916	521	65	�	�	PROPN
ejpam-3916	521	66	h((v	h((v	NOUN
ejpam-3916	521	67	,	,	PUNCT
ejpam-3916	521	68	p)(u	p)(u	ADJ
ejpam-3916	521	69	,	,	PUNCT
ejpam-3916	521	70	p	p	NOUN
ejpam-3916	521	71	)	)	PUNCT
ejpam-3916	521	72	)	)	PUNCT
ejpam-3916	522	1	=	=	SYM
ejpam-3916	522	2	2	2	X
ejpam-3916	522	3	.	.	X
ejpam-3916	522	4	therefore	therefore	ADV
ejpam-3916	522	5	,	,	PUNCT
ejpam-3916	522	6	c	c	PROPN
ejpam-3916	522	7	is	be	AUX
ejpam-3916	522	8	a	a	DET
ejpam-3916	522	9	hop	hop	NOUN
ejpam-3916	522	10	dominating	dominating	NOUN
ejpam-3916	522	11	set	set	NOUN
ejpam-3916	522	12	of	of	ADP
ejpam-3916	522	13	g	g	PROPN
ejpam-3916	522	14	�	�	PROPN
ejpam-3916	522	15	h	h	NOUN
ejpam-3916	522	16	and	and	CCONJ
ejpam-3916	522	17	g	g	PROPN
ejpam-3916	522	18	�	�	PROPN
ejpam-3916	522	19	h.	h.	PROPN
ejpam-3916	522	20	accordingly	accordingly	ADV
ejpam-3916	522	21	,	,	PUNCT
ejpam-3916	522	22	c	c	PROPN
ejpam-3916	522	23	is	be	AUX
ejpam-3916	522	24	a	a	DET
ejpam-3916	522	25	global	global	ADJ
ejpam-3916	522	26	hop	hop	NOUN
ejpam-3916	522	27	dominating	dominating	NOUN
ejpam-3916	522	28	set	set	NOUN
ejpam-3916	522	29	of	of	ADP
ejpam-3916	522	30	g	g	PROPN
ejpam-3916	522	31	�	�	PROPN
ejpam-3916	522	32	h.	h.	PROPN
ejpam-3916	522	33	corollary	corollary	NOUN
ejpam-3916	522	34	5	5	PROPN
ejpam-3916	522	35	.	.	PUNCT
ejpam-3916	523	1	let	let	VERB
ejpam-3916	523	2	g	g	NOUN
ejpam-3916	523	3	and	and	CCONJ
ejpam-3916	523	4	h	h	PROPN
ejpam-3916	523	5	be	be	VERB
ejpam-3916	523	6	non	non	ADJ
ejpam-3916	523	7	-	-	ADJ
ejpam-3916	523	8	trivial	trivial	ADJ
ejpam-3916	523	9	connected	connected	ADJ
ejpam-3916	523	10	graphs	graph	NOUN
ejpam-3916	523	11	.	.	PUNCT
ejpam-3916	524	1	(	(	PUNCT
ejpam-3916	524	2	i	i	NOUN
ejpam-3916	524	3	)	)	PUNCT
ejpam-3916	524	4	if	if	SCONJ
ejpam-3916	524	5	γ(h	γ(h	NOUN
ejpam-3916	524	6	)	)	PUNCT
ejpam-3916	524	7	=	=	SYM
ejpam-3916	524	8	1	1	NUM
ejpam-3916	524	9	,	,	PUNCT
ejpam-3916	524	10	then	then	ADV
ejpam-3916	524	11	γgh(g	γgh(g	NOUN
ejpam-3916	524	12	�	�	NOUN
ejpam-3916	524	13	h	h	NOUN
ejpam-3916	524	14	)	)	PUNCT
ejpam-3916	524	15	≤	≤	NOUN
ejpam-3916	524	16	|v	|v	X
ejpam-3916	524	17	(	(	PUNCT
ejpam-3916	524	18	h)|.γtcni(g	h)|.γtcni(g	INTJ
ejpam-3916	524	19	)	)	PUNCT
ejpam-3916	524	20	.	.	PUNCT
ejpam-3916	525	1	(	(	PUNCT
ejpam-3916	525	2	ii	ii	NOUN
ejpam-3916	525	3	)	)	PUNCT
ejpam-3916	525	4	if	if	SCONJ
ejpam-3916	525	5	γ(h	γ(h	NOUN
ejpam-3916	525	6	)	)	PUNCT
ejpam-3916	525	7	6=	6=	ADP
ejpam-3916	525	8	1	1	NUM
ejpam-3916	525	9	,	,	PUNCT
ejpam-3916	525	10	then	then	ADV
ejpam-3916	525	11	γgh(g	γgh(g	NOUN
ejpam-3916	525	12	�	�	NOUN
ejpam-3916	525	13	h	h	NOUN
ejpam-3916	525	14	)	)	PUNCT
ejpam-3916	525	15	≤	≤	NOUN
ejpam-3916	525	16	|v	|v	X
ejpam-3916	525	17	(	(	PUNCT
ejpam-3916	525	18	h)|.γt(g	h)|.γt(g	PROPN
ejpam-3916	525	19	)	)	PUNCT
ejpam-3916	525	20	.	.	PUNCT
ejpam-3916	526	1	proof	proof	NOUN
ejpam-3916	526	2	.	.	PUNCT
ejpam-3916	527	1	let	let	VERB
ejpam-3916	527	2	s	s	PRON
ejpam-3916	527	3	be	be	AUX
ejpam-3916	527	4	a	a	DET
ejpam-3916	527	5	γtcni	γtcni	NOUN
ejpam-3916	527	6	-	-	PUNCT
ejpam-3916	527	7	set	set	NOUN
ejpam-3916	527	8	of	of	ADP
ejpam-3916	527	9	g	g	NOUN
ejpam-3916	527	10	and	and	CCONJ
ejpam-3916	527	11	let	let	VERB
ejpam-3916	527	12	tx	tx	VERB
ejpam-3916	527	13	=	=	SYM
ejpam-3916	527	14	v	v	PROPN
ejpam-3916	527	15	(	(	PUNCT
ejpam-3916	527	16	h	h	NOUN
ejpam-3916	527	17	)	)	PUNCT
ejpam-3916	527	18	for	for	SCONJ
ejpam-3916	527	19	all	all	DET
ejpam-3916	527	20	x	x	SYM
ejpam-3916	527	21	∈	∈	PROPN
ejpam-3916	527	22	s.	s.	PROPN
ejpam-3916	527	23	let	let	VERB
ejpam-3916	527	24	c	c	NOUN
ejpam-3916	527	25	=	=	PUNCT
ejpam-3916	527	26	∪x∈s	∪x∈s	PROPN
ejpam-3916	527	27	[	[	X
ejpam-3916	527	28	{	{	PUNCT
ejpam-3916	527	29	x}×	x}×	PROPN
ejpam-3916	527	30	tx	tx	PROPN
ejpam-3916	527	31	]	]	X
ejpam-3916	527	32	=	=	SYM
ejpam-3916	527	33	s×v	s×v	PROPN
ejpam-3916	527	34	(	(	PUNCT
ejpam-3916	527	35	h	h	NOUN
ejpam-3916	527	36	)	)	PUNCT
ejpam-3916	527	37	.	.	PUNCT
ejpam-3916	528	1	if	if	SCONJ
ejpam-3916	528	2	γ(h	γ(h	NOUN
ejpam-3916	528	3	)	)	PUNCT
ejpam-3916	528	4	=	=	SYM
ejpam-3916	528	5	1	1	NUM
ejpam-3916	528	6	,	,	PUNCT
ejpam-3916	528	7	then	then	ADV
ejpam-3916	528	8	c	c	PROPN
ejpam-3916	528	9	is	be	AUX
ejpam-3916	528	10	a	a	DET
ejpam-3916	528	11	global	global	ADJ
ejpam-3916	528	12	hop	hop	NOUN
ejpam-3916	528	13	dominating	dominating	NOUN
ejpam-3916	528	14	set	set	NOUN
ejpam-3916	528	15	of	of	ADP
ejpam-3916	528	16	g	g	PROPN
ejpam-3916	528	17	�	�	PROPN
ejpam-3916	528	18	h	h	NOUN
ejpam-3916	528	19	by	by	ADP
ejpam-3916	528	20	theorem	theorem	NOUN
ejpam-3916	528	21	7	7	NUM
ejpam-3916	528	22	.	.	PUNCT
ejpam-3916	528	23	thus	thus	ADV
ejpam-3916	528	24	,	,	PUNCT
ejpam-3916	528	25	γgh(g	γgh(g	NOUN
ejpam-3916	528	26	�	�	NOUN
ejpam-3916	528	27	h	h	NOUN
ejpam-3916	528	28	)	)	PUNCT
ejpam-3916	528	29	≤	≤	NOUN
ejpam-3916	528	30	|c|	|c|	PROPN
ejpam-3916	528	31	=	=	SYM
ejpam-3916	528	32	|v	|v	PROPN
ejpam-3916	528	33	(	(	PUNCT
ejpam-3916	528	34	h)|.γtcni(g	h)|.γtcni(g	INTJ
ejpam-3916	528	35	)	)	PUNCT
ejpam-3916	528	36	.	.	PUNCT
ejpam-3916	529	1	references	reference	NOUN
ejpam-3916	529	2	124	124	NUM
ejpam-3916	529	3	next	next	ADV
ejpam-3916	529	4	,	,	PUNCT
ejpam-3916	529	5	let	let	VERB
ejpam-3916	529	6	s′	s′	NOUN
ejpam-3916	529	7	be	be	AUX
ejpam-3916	529	8	a	a	DET
ejpam-3916	529	9	γt	γt	NOUN
ejpam-3916	529	10	-	-	NOUN
ejpam-3916	529	11	set	set	NOUN
ejpam-3916	529	12	of	of	ADP
ejpam-3916	529	13	g	g	NOUN
ejpam-3916	529	14	and	and	CCONJ
ejpam-3916	529	15	let	let	VERB
ejpam-3916	529	16	rx	rx	VERB
ejpam-3916	529	17	=	=	NOUN
ejpam-3916	529	18	v	v	ADJ
ejpam-3916	529	19	(	(	PUNCT
ejpam-3916	529	20	h	h	NOUN
ejpam-3916	529	21	)	)	PUNCT
ejpam-3916	529	22	for	for	SCONJ
ejpam-3916	529	23	all	all	PRON
ejpam-3916	529	24	x	x	SYM
ejpam-3916	529	25	∈	∈	PROPN
ejpam-3916	529	26	s′.	s′.	PROPN
ejpam-3916	529	27	let	let	VERB
ejpam-3916	529	28	c	c	NOUN
ejpam-3916	529	29	′	′	VERB
ejpam-3916	529	30	=	=	PUNCT
ejpam-3916	530	1	∪x∈s	∪x∈s	PROPN
ejpam-3916	531	1	[	[	X
ejpam-3916	531	2	{	{	PUNCT
ejpam-3916	531	3	x	x	NOUN
ejpam-3916	531	4	}	}	PUNCT
ejpam-3916	531	5	×	×	NOUN
ejpam-3916	531	6	rx	rx	NOUN
ejpam-3916	531	7	]	]	X
ejpam-3916	531	8	=	=	SYM
ejpam-3916	531	9	s×v	s×v	PROPN
ejpam-3916	531	10	(	(	PUNCT
ejpam-3916	531	11	h	h	NOUN
ejpam-3916	531	12	)	)	PUNCT
ejpam-3916	531	13	.	.	PUNCT
ejpam-3916	532	1	if	if	SCONJ
ejpam-3916	532	2	γ(h	γ(h	PROPN
ejpam-3916	532	3	)	)	PUNCT
ejpam-3916	532	4	6=	6=	ADP
ejpam-3916	532	5	1	1	NUM
ejpam-3916	532	6	,	,	PUNCT
ejpam-3916	532	7	then	then	ADV
ejpam-3916	532	8	c	c	NOUN
ejpam-3916	532	9	′	′	PROPN
ejpam-3916	532	10	is	be	AUX
ejpam-3916	532	11	a	a	DET
ejpam-3916	532	12	global	global	ADJ
ejpam-3916	532	13	hop	hop	NOUN
ejpam-3916	532	14	dominating	dominating	NOUN
ejpam-3916	532	15	set	set	NOUN
ejpam-3916	532	16	of	of	ADP
ejpam-3916	532	17	g	g	PROPN
ejpam-3916	532	18	�	�	PROPN
ejpam-3916	532	19	h	h	NOUN
ejpam-3916	532	20	by	by	ADP
ejpam-3916	532	21	theorem	theorem	NOUN
ejpam-3916	532	22	7	7	NUM
ejpam-3916	532	23	.	.	PUNCT
ejpam-3916	533	1	this	this	PRON
ejpam-3916	533	2	implies	imply	VERB
ejpam-3916	533	3	that	that	SCONJ
ejpam-3916	533	4	γgh(g	γgh(g	NOUN
ejpam-3916	533	5	�	�	NOUN
ejpam-3916	533	6	h	h	NOUN
ejpam-3916	533	7	)	)	PUNCT
ejpam-3916	533	8	≤	≤	NOUN
ejpam-3916	533	9	|c	|c	VERB
ejpam-3916	533	10	′|	′|	NUM
ejpam-3916	533	11	=	=	SYM
ejpam-3916	533	12	|v	|v	X
ejpam-3916	533	13	(	(	PUNCT
ejpam-3916	533	14	h)|.γt(g	h)|.γt(g	PROPN
ejpam-3916	533	15	)	)	PUNCT
ejpam-3916	533	16	.	.	PUNCT
ejpam-3916	534	1	3	3	X
ejpam-3916	534	2	.	.	X
ejpam-3916	534	3	conclusion	conclusion	VERB
ejpam-3916	534	4	the	the	DET
ejpam-3916	534	5	global	global	ADJ
ejpam-3916	534	6	hop	hop	NOUN
ejpam-3916	534	7	dominating	dominating	NOUN
ejpam-3916	534	8	sets	set	NOUN
ejpam-3916	534	9	in	in	ADP
ejpam-3916	534	10	the	the	DET
ejpam-3916	534	11	join	join	NOUN
ejpam-3916	534	12	,	,	PUNCT
ejpam-3916	534	13	corona	corona	PROPN
ejpam-3916	534	14	,	,	PUNCT
ejpam-3916	534	15	lexicographic	lexicographic	ADJ
ejpam-3916	534	16	product	product	NOUN
ejpam-3916	534	17	,	,	PUNCT
ejpam-3916	534	18	and	and	CCONJ
ejpam-3916	534	19	the	the	DET
ejpam-3916	534	20	cartesian	cartesian	ADJ
ejpam-3916	534	21	product	product	NOUN
ejpam-3916	534	22	of	of	ADP
ejpam-3916	534	23	two	two	NUM
ejpam-3916	534	24	graphs	graph	NOUN
ejpam-3916	534	25	have	have	AUX
ejpam-3916	534	26	been	be	AUX
ejpam-3916	534	27	characterized	characterize	VERB
ejpam-3916	534	28	.	.	PUNCT
ejpam-3916	535	1	from	from	ADP
ejpam-3916	535	2	these	these	DET
ejpam-3916	535	3	characterizations	characterization	NOUN
ejpam-3916	535	4	,	,	PUNCT
ejpam-3916	535	5	we	we	PRON
ejpam-3916	535	6	determined	determine	VERB
ejpam-3916	535	7	either	either	CCONJ
ejpam-3916	535	8	the	the	DET
ejpam-3916	535	9	exact	exact	ADJ
ejpam-3916	535	10	values	value	NOUN
ejpam-3916	535	11	or	or	CCONJ
ejpam-3916	535	12	upper	upper	ADJ
ejpam-3916	535	13	bounds	bound	NOUN
ejpam-3916	535	14	of	of	ADP
ejpam-3916	535	15	the	the	DET
ejpam-3916	535	16	global	global	ADJ
ejpam-3916	535	17	hop	hop	PROPN
ejpam-3916	535	18	domination	domination	NOUN
ejpam-3916	535	19	numbers	number	NOUN
ejpam-3916	535	20	of	of	ADP
ejpam-3916	535	21	the	the	DET
ejpam-3916	535	22	corresponding	correspond	VERB
ejpam-3916	535	23	graphs	graph	NOUN
ejpam-3916	535	24	.	.	PUNCT
ejpam-3916	536	1	acknowledgements	acknowledgement	NOUN
ejpam-3916	536	2	the	the	DET
ejpam-3916	536	3	authors	author	NOUN
ejpam-3916	536	4	would	would	AUX
ejpam-3916	536	5	like	like	VERB
ejpam-3916	536	6	to	to	PART
ejpam-3916	536	7	thank	thank	VERB
ejpam-3916	536	8	the	the	DET
ejpam-3916	536	9	referees	referee	NOUN
ejpam-3916	536	10	for	for	ADP
ejpam-3916	536	11	reviewing	review	VERB
ejpam-3916	536	12	the	the	DET
ejpam-3916	536	13	paper	paper	NOUN
ejpam-3916	536	14	and	and	CCONJ
ejpam-3916	536	15	for	for	ADP
ejpam-3916	536	16	pointing	point	VERB
ejpam-3916	536	17	out	out	ADP
ejpam-3916	536	18	some	some	DET
ejpam-3916	536	19	(	(	PUNCT
ejpam-3916	536	20	minor	minor	ADJ
ejpam-3916	536	21	)	)	PUNCT
ejpam-3916	536	22	errors	error	NOUN
ejpam-3916	536	23	in	in	ADP
ejpam-3916	536	24	the	the	DET
ejpam-3916	536	25	original	original	ADJ
ejpam-3916	536	26	manuscript	manuscript	NOUN
ejpam-3916	536	27	.	.	PUNCT
ejpam-3916	537	1	also	also	ADV
ejpam-3916	537	2	,	,	PUNCT
ejpam-3916	537	3	we	we	PRON
ejpam-3916	537	4	would	would	AUX
ejpam-3916	537	5	like	like	VERB
ejpam-3916	537	6	to	to	PART
ejpam-3916	537	7	thank	thank	VERB
ejpam-3916	537	8	the	the	DET
ejpam-3916	537	9	department	department	NOUN
ejpam-3916	537	10	of	of	ADP
ejpam-3916	537	11	science	science	NOUN
ejpam-3916	537	12	and	and	CCONJ
ejpam-3916	537	13	technology	technology	NOUN
ejpam-3916	537	14	accelerated	accelerate	VERB
ejpam-3916	537	15	science	science	NOUN
ejpam-3916	537	16	and	and	CCONJ
ejpam-3916	537	17	technology	technology	NOUN
ejpam-3916	537	18	human	human	ADJ
ejpam-3916	537	19	resource	resource	NOUN
ejpam-3916	537	20	development	development	NOUN
ejpam-3916	537	21	program	program	NOUN
ejpam-3916	537	22	(	(	PUNCT
ejpam-3916	537	23	dost	dost	NOUN
ejpam-3916	537	24	-	-	PUNCT
ejpam-3916	537	25	asthrdp	asthrdp	NOUN
ejpam-3916	537	26	)	)	PUNCT
ejpam-3916	537	27	,	,	PUNCT
ejpam-3916	537	28	philippines	philippine	NOUN
ejpam-3916	537	29	for	for	ADP
ejpam-3916	537	30	funding	fund	VERB
ejpam-3916	537	31	this	this	DET
ejpam-3916	537	32	research	research	NOUN
ejpam-3916	537	33	.	.	PUNCT
ejpam-3916	538	1	references	reference	NOUN
ejpam-3916	538	2	[	[	X
ejpam-3916	538	3	1	1	NUM
ejpam-3916	538	4	]	]	PUNCT
ejpam-3916	538	5	s.	s.	PROPN
ejpam-3916	538	6	ayyaswamy	ayyaswamy	PROPN
ejpam-3916	538	7	,	,	PUNCT
ejpam-3916	538	8	b.	b.	PROPN
ejpam-3916	538	9	krishnakumari	krishnakumari	PROPN
ejpam-3916	538	10	,	,	PUNCT
ejpam-3916	538	11	b.	b.	PROPN
ejpam-3916	538	12	natarjan	natarjan	PROPN
ejpam-3916	538	13	,	,	PUNCT
ejpam-3916	538	14	and	and	CCONJ
ejpam-3916	538	15	y.	y.	PROPN
ejpam-3916	538	16	venkatakrishnan	venkatakrishnan	PROPN
ejpam-3916	538	17	.	.	PUNCT
ejpam-3916	539	1	bounds	bound	NOUN
ejpam-3916	539	2	on	on	ADP
ejpam-3916	539	3	the	the	DET
ejpam-3916	539	4	hop	hop	NOUN
ejpam-3916	539	5	domination	domination	NOUN
ejpam-3916	539	6	number	number	NOUN
ejpam-3916	539	7	of	of	ADP
ejpam-3916	539	8	a	a	DET
ejpam-3916	539	9	tree	tree	NOUN
ejpam-3916	539	10	.	.	PUNCT
ejpam-3916	540	1	proceedings	proceeding	NOUN
ejpam-3916	540	2	-	-	PUNCT
ejpam-3916	540	3	mathematical	mathematical	ADJ
ejpam-3916	540	4	sciences	science	NOUN
ejpam-3916	540	5	,	,	PUNCT
ejpam-3916	540	6	125(4):449	125(4):449	NUM
ejpam-3916	540	7	–	–	PUNCT
ejpam-3916	540	8	455	455	NUM
ejpam-3916	540	9	,	,	PUNCT
ejpam-3916	540	10	2015	2015	NUM
ejpam-3916	540	11	.	.	PUNCT
ejpam-3916	541	1	[	[	X
ejpam-3916	541	2	2	2	X
ejpam-3916	541	3	]	]	PUNCT
ejpam-3916	541	4	s.	s.	PROPN
ejpam-3916	541	5	jr	jr	PROPN
ejpam-3916	541	6	.	.	PROPN
ejpam-3916	541	7	canoy	canoy	PROPN
ejpam-3916	541	8	,	,	PUNCT
ejpam-3916	541	9	s.a	s.a	PROPN
ejpam-3916	541	10	.	.	PROPN
ejpam-3916	541	11	canoy	canoy	PROPN
ejpam-3916	541	12	,	,	PUNCT
ejpam-3916	541	13	and	and	CCONJ
ejpam-3916	541	14	m.	m.	NOUN
ejpam-3916	541	15	cruzate	cruzate	NOUN
ejpam-3916	541	16	.	.	PUNCT
ejpam-3916	542	1	global	global	ADJ
ejpam-3916	542	2	domination	domination	NOUN
ejpam-3916	542	3	in	in	ADP
ejpam-3916	542	4	a	a	DET
ejpam-3916	542	5	graph	graph	NOUN
ejpam-3916	542	6	.	.	PUNCT
ejpam-3916	543	1	advances	advance	NOUN
ejpam-3916	543	2	and	and	CCONJ
ejpam-3916	543	3	applications	application	NOUN
ejpam-3916	543	4	in	in	ADP
ejpam-3916	543	5	discrete	discrete	ADJ
ejpam-3916	543	6	mathematics	mathematic	NOUN
ejpam-3916	543	7	,	,	PUNCT
ejpam-3916	543	8	19(4):401–408	19(4):401–408	PROPN
ejpam-3916	543	9	,	,	PUNCT
ejpam-3916	543	10	2018	2018	NUM
ejpam-3916	543	11	.	.	PUNCT
ejpam-3916	544	1	[	[	X
ejpam-3916	544	2	3	3	X
ejpam-3916	544	3	]	]	PUNCT
ejpam-3916	544	4	s.	s.	PROPN
ejpam-3916	544	5	jr	jr	PROPN
ejpam-3916	544	6	.	.	PROPN
ejpam-3916	544	7	canoy	canoy	PROPN
ejpam-3916	544	8	,	,	PUNCT
ejpam-3916	544	9	r.	r.	NOUN
ejpam-3916	544	10	mollejon	mollejon	NOUN
ejpam-3916	544	11	,	,	PUNCT
ejpam-3916	544	12	and	and	CCONJ
ejpam-3916	544	13	j.g	j.g	PROPN
ejpam-3916	544	14	.	.	PROPN
ejpam-3916	544	15	canoy	canoy	PROPN
ejpam-3916	544	16	.	.	PUNCT
ejpam-3916	545	1	hop	hop	PROPN
ejpam-3916	545	2	dominating	dominating	NOUN
ejpam-3916	545	3	sets	set	NOUN
ejpam-3916	545	4	in	in	ADP
ejpam-3916	545	5	graphs	graph	NOUN
ejpam-3916	545	6	under	under	ADP
ejpam-3916	545	7	binary	binary	ADJ
ejpam-3916	545	8	operations	operation	NOUN
ejpam-3916	545	9	.	.	PUNCT
ejpam-3916	546	1	european	european	ADJ
ejpam-3916	546	2	journal	journal	PROPN
ejpam-3916	546	3	of	of	ADP
ejpam-3916	546	4	pure	pure	ADJ
ejpam-3916	546	5	and	and	CCONJ
ejpam-3916	546	6	applied	applied	ADJ
ejpam-3916	546	7	mathematics	mathematic	NOUN
ejpam-3916	546	8	,	,	PUNCT
ejpam-3916	546	9	12(4):1455	12(4):1455	NUM
ejpam-3916	546	10	–	–	PUNCT
ejpam-3916	546	11	1463	1463	NUM
ejpam-3916	546	12	,	,	PUNCT
ejpam-3916	546	13	2019	2019	NUM
ejpam-3916	546	14	.	.	PUNCT
ejpam-3916	547	1	[	[	X
ejpam-3916	547	2	4	4	X
ejpam-3916	547	3	]	]	X
ejpam-3916	547	4	w.	w.	PROPN
ejpam-3916	547	5	desormeaux	desormeaux	PROPN
ejpam-3916	547	6	,	,	PUNCT
ejpam-3916	547	7	p.	p.	PROPN
ejpam-3916	547	8	gibson	gibson	PROPN
ejpam-3916	547	9	,	,	PUNCT
ejpam-3916	547	10	and	and	CCONJ
ejpam-3916	547	11	t.	t.	PROPN
ejpam-3916	547	12	haynes	haynes	PROPN
ejpam-3916	547	13	.	.	PUNCT
ejpam-3916	548	1	bounds	bound	NOUN
ejpam-3916	548	2	on	on	ADP
ejpam-3916	548	3	the	the	DET
ejpam-3916	548	4	global	global	ADJ
ejpam-3916	548	5	domination	domination	NOUN
ejpam-3916	548	6	number	number	NOUN
ejpam-3916	548	7	.	.	PUNCT
ejpam-3916	549	1	quaestiones	quaestione	NOUN
ejpam-3916	549	2	mathematicae	mathematicae	PROPN
ejpam-3916	549	3	,	,	PUNCT
ejpam-3916	549	4	38(4):563–572	38(4):563–572	PROPN
ejpam-3916	549	5	,	,	PUNCT
ejpam-3916	549	6	2015	2015	NUM
ejpam-3916	549	7	.	.	PUNCT
ejpam-3916	550	1	[	[	X
ejpam-3916	550	2	5	5	X
ejpam-3916	550	3	]	]	PUNCT
ejpam-3916	550	4	t.	t.	PROPN
ejpam-3916	550	5	haynes	haynes	PROPN
ejpam-3916	550	6	,	,	PUNCT
ejpam-3916	550	7	s.	s.	PROPN
ejpam-3916	550	8	hedetniemi	hedetniemi	PROPN
ejpam-3916	550	9	,	,	PUNCT
ejpam-3916	550	10	and	and	CCONJ
ejpam-3916	550	11	p.	p.	PROPN
ejpam-3916	550	12	slater	slater	PROPN
ejpam-3916	550	13	.	.	PUNCT
ejpam-3916	551	1	domination	domination	NOUN
ejpam-3916	551	2	in	in	ADP
ejpam-3916	551	3	graphs	graph	NOUN
ejpam-3916	551	4	,	,	PUNCT
ejpam-3916	551	5	advanced	advanced	ADJ
ejpam-3916	551	6	topics	topic	NOUN
ejpam-3916	551	7	.	.	PUNCT
ejpam-3916	552	1	marcell	marcell	PROPN
ejpam-3916	552	2	dekker	dekker	PROPN
ejpam-3916	552	3	,	,	PUNCT
ejpam-3916	552	4	new	new	PROPN
ejpam-3916	552	5	york	york	PROPN
ejpam-3916	552	6	,	,	PUNCT
ejpam-3916	552	7	usa	usa	PROPN
ejpam-3916	552	8	,	,	PUNCT
ejpam-3916	552	9	1998	1998	NUM
ejpam-3916	552	10	.	.	PUNCT
ejpam-3916	553	1	[	[	X
ejpam-3916	553	2	6	6	NUM
ejpam-3916	553	3	]	]	PUNCT
ejpam-3916	553	4	t.	t.	PROPN
ejpam-3916	553	5	haynes	haynes	PROPN
ejpam-3916	553	6	,	,	PUNCT
ejpam-3916	553	7	s.	s.	PROPN
ejpam-3916	553	8	hedetniemi	hedetniemi	PROPN
ejpam-3916	553	9	,	,	PUNCT
ejpam-3916	553	10	and	and	CCONJ
ejpam-3916	553	11	p.	p.	PROPN
ejpam-3916	553	12	slater	slater	PROPN
ejpam-3916	553	13	.	.	PUNCT
ejpam-3916	554	1	fundamentals	fundamental	NOUN
ejpam-3916	554	2	of	of	ADP
ejpam-3916	554	3	domination	domination	NOUN
ejpam-3916	554	4	in	in	ADP
ejpam-3916	554	5	graphs	graph	NOUN
ejpam-3916	554	6	.	.	PUNCT
ejpam-3916	555	1	marcell	marcell	PROPN
ejpam-3916	555	2	dekker	dekker	PROPN
ejpam-3916	555	3	,	,	PUNCT
ejpam-3916	555	4	new	new	PROPN
ejpam-3916	555	5	york	york	PROPN
ejpam-3916	555	6	,	,	PUNCT
ejpam-3916	555	7	usa	usa	PROPN
ejpam-3916	555	8	,	,	PUNCT
ejpam-3916	555	9	1998	1998	NUM
ejpam-3916	555	10	.	.	PUNCT
ejpam-3916	556	1	[	[	X
ejpam-3916	556	2	7	7	X
ejpam-3916	556	3	]	]	X
ejpam-3916	556	4	m.	m.	NOUN
ejpam-3916	556	5	henning	henning	PROPN
ejpam-3916	556	6	and	and	CCONJ
ejpam-3916	556	7	n.	n.	PROPN
ejpam-3916	556	8	rad	rad	PROPN
ejpam-3916	556	9	.	.	PROPN
ejpam-3916	557	1	on	on	ADP
ejpam-3916	557	2	2	2	NUM
ejpam-3916	557	3	-	-	PUNCT
ejpam-3916	557	4	step	step	NOUN
ejpam-3916	557	5	and	and	CCONJ
ejpam-3916	557	6	hop	hop	NOUN
ejpam-3916	557	7	dominating	dominating	NOUN
ejpam-3916	557	8	sets	set	NOUN
ejpam-3916	557	9	in	in	ADP
ejpam-3916	557	10	graphs	graph	NOUN
ejpam-3916	557	11	.	.	PUNCT
ejpam-3916	558	1	graphs	graph	NOUN
ejpam-3916	558	2	and	and	CCONJ
ejpam-3916	558	3	combinatorics	combinatoric	NOUN
ejpam-3916	558	4	,	,	PUNCT
ejpam-3916	558	5	33(4):913–927	33(4):913–927	PROPN
ejpam-3916	558	6	,	,	PUNCT
ejpam-3916	558	7	2017	2017	NUM
ejpam-3916	558	8	.	.	PUNCT
ejpam-3916	559	1	[	[	X
ejpam-3916	559	2	8	8	NUM
ejpam-3916	559	3	]	]	X
ejpam-3916	559	4	g.	g.	PROPN
ejpam-3916	559	5	mahadevan	mahadevan	PROPN
ejpam-3916	559	6	and	and	CCONJ
ejpam-3916	559	7	v.	v.	ADP
ejpam-3916	559	8	vijayalakshmi	vijayalakshmi	NOUN
ejpam-3916	559	9	.	.	PUNCT
ejpam-3916	560	1	clone	clone	NOUN
ejpam-3916	560	2	hop	hop	NOUN
ejpam-3916	560	3	domination	domination	NOUN
ejpam-3916	560	4	number	number	NOUN
ejpam-3916	560	5	of	of	ADP
ejpam-3916	560	6	a	a	DET
ejpam-3916	560	7	graph	graph	NOUN
ejpam-3916	560	8	.	.	PUNCT
ejpam-3916	561	1	journal	journal	NOUN
ejpam-3916	561	2	of	of	ADP
ejpam-3916	561	3	discrete	discrete	ADJ
ejpam-3916	561	4	mathematical	mathematical	ADJ
ejpam-3916	561	5	sciences	science	NOUN
ejpam-3916	561	6	and	and	CCONJ
ejpam-3916	561	7	cryptography	cryptography	NOUN
ejpam-3916	561	8	,	,	PUNCT
ejpam-3916	561	9	22(5):719–729	22(5):719–729	PROPN
ejpam-3916	561	10	,	,	PUNCT
ejpam-3916	561	11	2019	2019	NUM
ejpam-3916	561	12	.	.	PUNCT
ejpam-3916	562	1	references	reference	NOUN
ejpam-3916	562	2	125	125	NUM
ejpam-3916	562	3	[	[	X
ejpam-3916	562	4	9	9	NUM
ejpam-3916	562	5	]	]	X
ejpam-3916	562	6	r.	r.	NOUN
ejpam-3916	562	7	mollejon	mollejon	NOUN
ejpam-3916	562	8	and	and	CCONJ
ejpam-3916	562	9	s.	s.	PROPN
ejpam-3916	562	10	jr	jr	PROPN
ejpam-3916	562	11	.	.	PROPN
ejpam-3916	562	12	canoy	canoy	PROPN
ejpam-3916	562	13	.	.	PUNCT
ejpam-3916	563	1	double	double	ADJ
ejpam-3916	563	2	hop	hop	NOUN
ejpam-3916	563	3	dominating	dominating	NOUN
ejpam-3916	563	4	sets	set	NOUN
ejpam-3916	563	5	in	in	ADP
ejpam-3916	563	6	graphs	graph	NOUN
ejpam-3916	563	7	.	.	PUNCT
ejpam-3916	564	1	discrete	discrete	ADJ
ejpam-3916	564	2	mathematics	mathematic	NOUN
ejpam-3916	564	3	,	,	PUNCT
ejpam-3916	564	4	algorithms	algorithm	NOUN
ejpam-3916	564	5	and	and	CCONJ
ejpam-3916	564	6	applications	application	NOUN
ejpam-3916	564	7	,	,	PUNCT
ejpam-3916	564	8	2020	2020	NUM
ejpam-3916	564	9	,	,	PUNCT
ejpam-3916	564	10	https://doi.org/10.1142/s1793830921500579	https://doi.org/10.1142/s1793830921500579	NUM
ejpam-3916	564	11	.	.	PUNCT
ejpam-3916	565	1	[	[	X
ejpam-3916	565	2	10	10	NUM
ejpam-3916	565	3	]	]	X
ejpam-3916	565	4	c.	c.	PROPN
ejpam-3916	565	5	natarajan	natarajan	PROPN
ejpam-3916	565	6	and	and	CCONJ
ejpam-3916	565	7	s.	s.	PROPN
ejpam-3916	565	8	ayyaswamy	ayyaswamy	PROPN
ejpam-3916	565	9	.	.	PUNCT
ejpam-3916	566	1	hop	hop	PROPN
ejpam-3916	566	2	domination	domination	NOUN
ejpam-3916	566	3	in	in	ADP
ejpam-3916	566	4	graphs	graphs	PROPN
ejpam-3916	566	5	ii	ii	PROPN
ejpam-3916	566	6	.	.	PUNCT
ejpam-3916	566	7	versita	versita	PROPN
ejpam-3916	566	8	,	,	PUNCT
ejpam-3916	566	9	23(2):187	23(2):187	NUM
ejpam-3916	566	10	–	–	PUNCT
ejpam-3916	566	11	199	199	NUM
ejpam-3916	566	12	,	,	PUNCT
ejpam-3916	566	13	2015	2015	NUM
ejpam-3916	566	14	.	.	PUNCT
ejpam-3916	567	1	[	[	X
ejpam-3916	567	2	11	11	NUM
ejpam-3916	567	3	]	]	X
ejpam-3916	567	4	y.	y.	NOUN
ejpam-3916	567	5	pabilona	pabilona	PROPN
ejpam-3916	567	6	and	and	CCONJ
ejpam-3916	567	7	h.	h.	PROPN
ejpam-3916	567	8	rara	rara	PROPN
ejpam-3916	567	9	.	.	PUNCT
ejpam-3916	568	1	connected	connect	VERB
ejpam-3916	568	2	hop	hop	NOUN
ejpam-3916	568	3	domination	domination	NOUN
ejpam-3916	568	4	in	in	ADP
ejpam-3916	568	5	graphs	graph	NOUN
ejpam-3916	568	6	under	under	ADP
ejpam-3916	568	7	some	some	DET
ejpam-3916	568	8	binary	binary	ADJ
ejpam-3916	568	9	operations	operation	NOUN
ejpam-3916	568	10	.	.	PUNCT
ejpam-3916	569	1	asian	asian	ADJ
ejpam-3916	569	2	-	-	PUNCT
ejpam-3916	569	3	european	european	ADJ
ejpam-3916	569	4	journal	journal	NOUN
ejpam-3916	569	5	of	of	ADP
ejpam-3916	569	6	mathematics	mathematic	NOUN
ejpam-3916	569	7	,	,	PUNCT
ejpam-3916	569	8	11(5):1850075–1–1850075–11	11(5):1850075–1–1850075–11	NUM
ejpam-3916	569	9	,	,	PUNCT
ejpam-3916	569	10	2018	2018	NUM
ejpam-3916	569	11	.	.	PUNCT