id	sid	tid	token	lemma	pos
ejpam-5205	1	1	european	european	PROPN
ejpam-5205	1	2	journal	journal	PROPN
ejpam-5205	1	3	of	of	ADP
ejpam-5205	1	4	pure	pure	ADJ
ejpam-5205	1	5	and	and	CCONJ
ejpam-5205	1	6	applied	apply	VERB
ejpam-5205	1	7	mathematics	mathematic	NOUN
ejpam-5205	1	8	vol	vol	NOUN
ejpam-5205	1	9	.	.	PROPN
ejpam-5205	2	1	17	17	NUM
ejpam-5205	2	2	,	,	PUNCT
ejpam-5205	2	3	no	no	INTJ
ejpam-5205	2	4	.	.	NOUN
ejpam-5205	2	5	2	2	NUM
ejpam-5205	2	6	,	,	PUNCT
ejpam-5205	2	7	2024	2024	NUM
ejpam-5205	2	8	,	,	PUNCT
ejpam-5205	2	9	1335	1335	NUM
ejpam-5205	2	10	-	-	SYM
ejpam-5205	2	11	1351	1351	NUM
ejpam-5205	2	12	issn	issn	PROPN
ejpam-5205	2	13	1307	1307	NUM
ejpam-5205	2	14	-	-	SYM
ejpam-5205	2	15	5543	5543	NUM
ejpam-5205	2	16	–	–	PUNCT
ejpam-5205	3	1	ejpam.com	ejpam.com	X
ejpam-5205	3	2	published	publish	VERB
ejpam-5205	3	3	by	by	ADP
ejpam-5205	3	4	new	new	PROPN
ejpam-5205	3	5	york	york	PROPN
ejpam-5205	3	6	business	business	PROPN
ejpam-5205	3	7	global	global	ADJ
ejpam-5205	3	8	convex	convex	PROPN
ejpam-5205	3	9	roman	roman	ADJ
ejpam-5205	3	10	dominating	dominating	NOUN
ejpam-5205	3	11	functions	function	NOUN
ejpam-5205	3	12	on	on	ADP
ejpam-5205	3	13	graphs	graph	NOUN
ejpam-5205	3	14	under	under	ADP
ejpam-5205	3	15	some	some	DET
ejpam-5205	3	16	binary	binary	ADJ
ejpam-5205	3	17	operations	operation	NOUN
ejpam-5205	3	18	rona	rona	PROPN
ejpam-5205	3	19	jane	jane	PROPN
ejpam-5205	3	20	g.	g.	PROPN
ejpam-5205	3	21	fortosa1,∗	fortosa1,∗	PROPN
ejpam-5205	3	22	,	,	PUNCT
ejpam-5205	3	23	ferdinand	ferdinand	PROPN
ejpam-5205	4	1	p.	p.	PROPN
ejpam-5205	4	2	jamil1,2	jamil1,2	PROPN
ejpam-5205	4	3	,	,	PUNCT
ejpam-5205	4	4	sergio	sergio	PROPN
ejpam-5205	4	5	r.	r.	PROPN
ejpam-5205	4	6	canoy	canoy	PROPN
ejpam-5205	4	7	,	,	PUNCT
ejpam-5205	4	8	jr.1,2	jr.1,2	ADJ
ejpam-5205	4	9	1	1	NUM
ejpam-5205	4	10	department	department	NOUN
ejpam-5205	4	11	of	of	ADP
ejpam-5205	4	12	mathematics	mathematic	NOUN
ejpam-5205	4	13	and	and	CCONJ
ejpam-5205	4	14	statistics	statistic	NOUN
ejpam-5205	4	15	,	,	PUNCT
ejpam-5205	4	16	college	college	NOUN
ejpam-5205	4	17	of	of	ADP
ejpam-5205	4	18	science	science	NOUN
ejpam-5205	4	19	and	and	CCONJ
ejpam-5205	4	20	mathematics	mathematic	NOUN
ejpam-5205	4	21	,	,	PUNCT
ejpam-5205	4	22	msu	msu	PROPN
ejpam-5205	4	23	-	-	PUNCT
ejpam-5205	4	24	iligan	iligan	PROPN
ejpam-5205	4	25	institute	institute	PROPN
ejpam-5205	4	26	of	of	ADP
ejpam-5205	4	27	technology	technology	PROPN
ejpam-5205	4	28	,	,	PUNCT
ejpam-5205	4	29	9200	9200	NUM
ejpam-5205	4	30	iligan	iligan	ADJ
ejpam-5205	4	31	city	city	NOUN
ejpam-5205	4	32	,	,	PUNCT
ejpam-5205	4	33	philippines	philippine	NOUN
ejpam-5205	4	34	2	2	NUM
ejpam-5205	4	35	center	center	NOUN
ejpam-5205	4	36	of	of	ADP
ejpam-5205	4	37	mathematical	mathematical	ADJ
ejpam-5205	4	38	and	and	CCONJ
ejpam-5205	4	39	theoretical	theoretical	ADJ
ejpam-5205	4	40	physical	physical	ADJ
ejpam-5205	4	41	sciencesprism	sciencesprism	NOUN
ejpam-5205	4	42	,	,	PUNCT
ejpam-5205	4	43	msu	msu	PROPN
ejpam-5205	4	44	-	-	PUNCT
ejpam-5205	4	45	iligan	iligan	PROPN
ejpam-5205	4	46	institute	institute	PROPN
ejpam-5205	4	47	of	of	ADP
ejpam-5205	4	48	technology	technology	PROPN
ejpam-5205	4	49	,	,	PUNCT
ejpam-5205	4	50	9200	9200	NUM
ejpam-5205	4	51	iligan	iligan	ADJ
ejpam-5205	4	52	city	city	NOUN
ejpam-5205	4	53	,	,	PUNCT
ejpam-5205	4	54	philippines	philippine	NOUN
ejpam-5205	4	55	abstract	abstract	ADJ
ejpam-5205	4	56	.	.	PUNCT
ejpam-5205	5	1	let	let	VERB
ejpam-5205	5	2	g	g	PRON
ejpam-5205	5	3	be	be	AUX
ejpam-5205	5	4	a	a	DET
ejpam-5205	5	5	connected	connected	ADJ
ejpam-5205	5	6	graph	graph	NOUN
ejpam-5205	5	7	.	.	PUNCT
ejpam-5205	6	1	a	a	DET
ejpam-5205	6	2	function	function	NOUN
ejpam-5205	6	3	f	f	NOUN
ejpam-5205	6	4	:	:	PUNCT
ejpam-5205	6	5	v	v	X
ejpam-5205	6	6	(	(	PUNCT
ejpam-5205	6	7	g	g	NOUN
ejpam-5205	6	8	)	)	PUNCT
ejpam-5205	6	9	→	→	SYM
ejpam-5205	6	10	{	{	PUNCT
ejpam-5205	6	11	0	0	NUM
ejpam-5205	6	12	,	,	PUNCT
ejpam-5205	6	13	1	1	NUM
ejpam-5205	6	14	,	,	PUNCT
ejpam-5205	6	15	2	2	NUM
ejpam-5205	6	16	}	}	PUNCT
ejpam-5205	6	17	is	be	AUX
ejpam-5205	6	18	a	a	DET
ejpam-5205	6	19	convex	convex	ADJ
ejpam-5205	6	20	roman	roman	ADJ
ejpam-5205	6	21	dominating	dominating	NOUN
ejpam-5205	6	22	function	function	NOUN
ejpam-5205	6	23	(	(	PUNCT
ejpam-5205	6	24	or	or	CCONJ
ejpam-5205	6	25	cvrdf	cvrdf	NOUN
ejpam-5205	6	26	)	)	PUNCT
ejpam-5205	6	27	if	if	SCONJ
ejpam-5205	6	28	every	every	DET
ejpam-5205	6	29	vertex	vertex	NOUN
ejpam-5205	6	30	u	u	NOUN
ejpam-5205	6	31	for	for	ADP
ejpam-5205	6	32	which	which	PRON
ejpam-5205	6	33	f(u	f(u	PROPN
ejpam-5205	6	34	)	)	PUNCT
ejpam-5205	7	1	=	=	SYM
ejpam-5205	7	2	0	0	NUM
ejpam-5205	7	3	is	be	AUX
ejpam-5205	7	4	adjacent	adjacent	ADJ
ejpam-5205	7	5	to	to	ADP
ejpam-5205	7	6	at	at	ADV
ejpam-5205	7	7	least	least	ADV
ejpam-5205	7	8	one	one	NUM
ejpam-5205	7	9	vertex	vertex	NOUN
ejpam-5205	7	10	v	v	NOUN
ejpam-5205	7	11	for	for	ADP
ejpam-5205	7	12	which	which	PRON
ejpam-5205	7	13	f(v	f(v	NOUN
ejpam-5205	7	14	)	)	PUNCT
ejpam-5205	7	15	=	=	SYM
ejpam-5205	7	16	2	2	NUM
ejpam-5205	7	17	and	and	CCONJ
ejpam-5205	7	18	v1	v1	VERB
ejpam-5205	7	19	∪	∪	NOUN
ejpam-5205	7	20	v2	v2	NOUN
ejpam-5205	7	21	is	be	AUX
ejpam-5205	7	22	convex	convex	NOUN
ejpam-5205	7	23	.	.	PUNCT
ejpam-5205	8	1	the	the	DET
ejpam-5205	8	2	weight	weight	NOUN
ejpam-5205	8	3	of	of	ADP
ejpam-5205	8	4	a	a	DET
ejpam-5205	8	5	convex	convex	ADJ
ejpam-5205	8	6	roman	roman	ADJ
ejpam-5205	8	7	dominating	dominating	NOUN
ejpam-5205	8	8	function	function	NOUN
ejpam-5205	8	9	f	f	PROPN
ejpam-5205	8	10	,	,	PUNCT
ejpam-5205	8	11	denoted	denote	VERB
ejpam-5205	8	12	by	by	ADP
ejpam-5205	8	13	ωcvr	ωcvr	PROPN
ejpam-5205	8	14	g	g	PROPN
ejpam-5205	8	15	(	(	PUNCT
ejpam-5205	8	16	f	f	PROPN
ejpam-5205	8	17	)	)	PUNCT
ejpam-5205	8	18	,	,	PUNCT
ejpam-5205	8	19	is	be	AUX
ejpam-5205	8	20	given	give	VERB
ejpam-5205	8	21	by	by	ADP
ejpam-5205	8	22	ωcvr	ωcvr	PROPN
ejpam-5205	8	23	g	g	PROPN
ejpam-5205	8	24	(	(	PUNCT
ejpam-5205	8	25	f	f	X
ejpam-5205	8	26	)	)	PUNCT
ejpam-5205	8	27	=	=	SYM
ejpam-5205	8	28	∑	∑	PUNCT
ejpam-5205	8	29	v∈v	v∈v	PROPN
ejpam-5205	8	30	(	(	PUNCT
ejpam-5205	8	31	g	g	NOUN
ejpam-5205	8	32	)	)	PUNCT
ejpam-5205	8	33	f(v	f(v	NOUN
ejpam-5205	8	34	)	)	PUNCT
ejpam-5205	8	35	.	.	PUNCT
ejpam-5205	9	1	the	the	DET
ejpam-5205	9	2	minimum	minimum	ADJ
ejpam-5205	9	3	weight	weight	NOUN
ejpam-5205	9	4	of	of	ADP
ejpam-5205	9	5	a	a	DET
ejpam-5205	9	6	cvrdf	cvrdf	NOUN
ejpam-5205	9	7	on	on	ADP
ejpam-5205	9	8	g	g	NOUN
ejpam-5205	9	9	,	,	PUNCT
ejpam-5205	9	10	denoted	denote	VERB
ejpam-5205	9	11	by	by	ADP
ejpam-5205	9	12	γcvr(g	γcvr(g	PROPN
ejpam-5205	9	13	)	)	PUNCT
ejpam-5205	9	14	,	,	PUNCT
ejpam-5205	9	15	is	be	AUX
ejpam-5205	9	16	called	call	VERB
ejpam-5205	9	17	the	the	DET
ejpam-5205	9	18	convex	convex	ADJ
ejpam-5205	9	19	roman	roman	ADJ
ejpam-5205	9	20	domination	domination	NOUN
ejpam-5205	9	21	number	number	NOUN
ejpam-5205	9	22	of	of	ADP
ejpam-5205	9	23	g.	g.	PROPN
ejpam-5205	9	24	in	in	ADP
ejpam-5205	9	25	this	this	DET
ejpam-5205	9	26	paper	paper	NOUN
ejpam-5205	9	27	,	,	PUNCT
ejpam-5205	9	28	we	we	PRON
ejpam-5205	9	29	specifically	specifically	ADV
ejpam-5205	9	30	study	study	VERB
ejpam-5205	9	31	the	the	DET
ejpam-5205	9	32	concept	concept	NOUN
ejpam-5205	9	33	of	of	ADP
ejpam-5205	9	34	convex	convex	ADJ
ejpam-5205	9	35	roman	roman	ADJ
ejpam-5205	9	36	domination	domination	NOUN
ejpam-5205	9	37	in	in	ADP
ejpam-5205	9	38	the	the	DET
ejpam-5205	9	39	corona	corona	NOUN
ejpam-5205	9	40	and	and	CCONJ
ejpam-5205	9	41	edge	edge	NOUN
ejpam-5205	9	42	corona	corona	NOUN
ejpam-5205	9	43	of	of	ADP
ejpam-5205	9	44	graphs	graph	NOUN
ejpam-5205	9	45	,	,	PUNCT
ejpam-5205	9	46	complementary	complementary	ADJ
ejpam-5205	9	47	prism	prism	NOUN
ejpam-5205	9	48	,	,	PUNCT
ejpam-5205	9	49	lexicographic	lexicographic	ADJ
ejpam-5205	9	50	product	product	NOUN
ejpam-5205	9	51	,	,	PUNCT
ejpam-5205	9	52	and	and	CCONJ
ejpam-5205	9	53	cartesian	cartesian	ADJ
ejpam-5205	9	54	product	product	NOUN
ejpam-5205	9	55	of	of	ADP
ejpam-5205	9	56	graphs	graph	NOUN
ejpam-5205	9	57	.	.	PUNCT
ejpam-5205	10	1	2020	2020	NUM
ejpam-5205	10	2	mathematics	mathematic	NOUN
ejpam-5205	10	3	subject	subject	NOUN
ejpam-5205	10	4	classifications	classification	NOUN
ejpam-5205	10	5	:	:	PUNCT
ejpam-5205	10	6	05c69	05c69	X
ejpam-5205	10	7	key	key	ADJ
ejpam-5205	10	8	words	word	NOUN
ejpam-5205	10	9	and	and	CCONJ
ejpam-5205	10	10	phrases	phrase	NOUN
ejpam-5205	10	11	:	:	PUNCT
ejpam-5205	10	12	convex	convex	PROPN
ejpam-5205	10	13	set	set	NOUN
ejpam-5205	10	14	,	,	PUNCT
ejpam-5205	10	15	roman	roman	ADJ
ejpam-5205	10	16	dominating	dominating	NOUN
ejpam-5205	10	17	function	function	NOUN
ejpam-5205	10	18	,	,	PUNCT
ejpam-5205	10	19	roman	roman	ADJ
ejpam-5205	10	20	domination	domination	NOUN
ejpam-5205	10	21	number	number	NOUN
ejpam-5205	10	22	,	,	PUNCT
ejpam-5205	10	23	convex	convex	ADJ
ejpam-5205	10	24	roman	roman	ADJ
ejpam-5205	10	25	dominating	dominating	NOUN
ejpam-5205	10	26	function	function	NOUN
ejpam-5205	10	27	,	,	PUNCT
ejpam-5205	10	28	convex	convex	VERB
ejpam-5205	10	29	roman	roman	ADJ
ejpam-5205	10	30	domination	domination	NOUN
ejpam-5205	10	31	number	number	NOUN
ejpam-5205	10	32	,	,	PUNCT
ejpam-5205	10	33	corona	corona	NOUN
ejpam-5205	10	34	,	,	PUNCT
ejpam-5205	10	35	edge	edge	NOUN
ejpam-5205	10	36	corona	corona	NOUN
ejpam-5205	10	37	,	,	PUNCT
ejpam-5205	10	38	complementary	complementary	ADJ
ejpam-5205	10	39	prism	prism	NOUN
ejpam-5205	10	40	,	,	PUNCT
ejpam-5205	10	41	lexicographic	lexicographic	ADJ
ejpam-5205	10	42	product	product	NOUN
ejpam-5205	10	43	,	,	PUNCT
ejpam-5205	10	44	cartesian	cartesian	ADJ
ejpam-5205	10	45	product	product	NOUN
ejpam-5205	10	46	1	1	NUM
ejpam-5205	10	47	.	.	PUNCT
ejpam-5205	11	1	introduction	introduction	NOUN
ejpam-5205	11	2	roman	roman	ADJ
ejpam-5205	11	3	domination	domination	NOUN
ejpam-5205	11	4	was	be	AUX
ejpam-5205	11	5	first	first	ADV
ejpam-5205	11	6	introduced	introduce	VERB
ejpam-5205	11	7	by	by	ADP
ejpam-5205	11	8	cockayne	cockayne	NOUN
ejpam-5205	11	9	,	,	PUNCT
ejpam-5205	11	10	dreyer	dreyer	PROPN
ejpam-5205	11	11	and	and	CCONJ
ejpam-5205	11	12	hedetnieme	hedetnieme	NOUN
ejpam-5205	11	13	in	in	ADP
ejpam-5205	11	14	[	[	X
ejpam-5205	11	15	8	8	NUM
ejpam-5205	11	16	]	]	PUNCT
ejpam-5205	11	17	which	which	PRON
ejpam-5205	11	18	was	be	AUX
ejpam-5205	11	19	inspired	inspire	VERB
ejpam-5205	11	20	by	by	ADP
ejpam-5205	11	21	the	the	DET
ejpam-5205	11	22	defense	defense	NOUN
ejpam-5205	11	23	strategy	strategy	NOUN
ejpam-5205	11	24	of	of	ADP
ejpam-5205	11	25	the	the	DET
ejpam-5205	11	26	roman	roman	ADJ
ejpam-5205	11	27	emperor	emperor	NOUN
ejpam-5205	11	28	constantine	constantine	VERB
ejpam-5205	11	29	the	the	DET
ejpam-5205	11	30	great	great	ADJ
ejpam-5205	11	31	during	during	ADP
ejpam-5205	11	32	the	the	DET
ejpam-5205	11	33	4th	4th	ADJ
ejpam-5205	11	34	century	century	NOUN
ejpam-5205	11	35	ad	ad	NOUN
ejpam-5205	11	36	(	(	PUNCT
ejpam-5205	11	37	see	see	VERB
ejpam-5205	11	38	[	[	X
ejpam-5205	11	39	23	23	NUM
ejpam-5205	11	40	]	]	PUNCT
ejpam-5205	11	41	and	and	CCONJ
ejpam-5205	11	42	[	[	X
ejpam-5205	11	43	24	24	NUM
ejpam-5205	11	44	]	]	PUNCT
ejpam-5205	11	45	)	)	PUNCT
ejpam-5205	11	46	.	.	PUNCT
ejpam-5205	12	1	after	after	ADP
ejpam-5205	12	2	several	several	ADJ
ejpam-5205	12	3	years	year	NOUN
ejpam-5205	12	4	,	,	PUNCT
ejpam-5205	12	5	lots	lot	NOUN
ejpam-5205	12	6	of	of	ADP
ejpam-5205	12	7	variations	variation	NOUN
ejpam-5205	12	8	on	on	ADP
ejpam-5205	12	9	this	this	DET
ejpam-5205	12	10	concept	concept	NOUN
ejpam-5205	12	11	have	have	AUX
ejpam-5205	12	12	been	be	AUX
ejpam-5205	12	13	introduced	introduce	VERB
ejpam-5205	12	14	and	and	CCONJ
ejpam-5205	12	15	studied	study	VERB
ejpam-5205	12	16	(	(	PUNCT
ejpam-5205	12	17	see	see	VERB
ejpam-5205	12	18	[	[	X
ejpam-5205	12	19	1	1	NUM
ejpam-5205	12	20	]	]	PUNCT
ejpam-5205	12	21	,	,	PUNCT
ejpam-5205	12	22	[	[	X
ejpam-5205	12	23	2	2	NUM
ejpam-5205	12	24	]	]	PUNCT
ejpam-5205	12	25	,	,	PUNCT
ejpam-5205	12	26	[	[	X
ejpam-5205	12	27	3	3	NUM
ejpam-5205	12	28	]	]	PUNCT
ejpam-5205	12	29	,	,	PUNCT
ejpam-5205	12	30	[	[	X
ejpam-5205	12	31	4	4	NUM
ejpam-5205	12	32	]	]	PUNCT
ejpam-5205	12	33	,	,	PUNCT
ejpam-5205	12	34	[	[	X
ejpam-5205	12	35	5	5	NUM
ejpam-5205	12	36	]	]	PUNCT
ejpam-5205	12	37	,	,	PUNCT
ejpam-5205	12	38	[	[	X
ejpam-5205	12	39	7	7	NUM
ejpam-5205	12	40	]	]	PUNCT
ejpam-5205	12	41	,	,	PUNCT
ejpam-5205	12	42	[	[	X
ejpam-5205	12	43	13	13	NUM
ejpam-5205	12	44	]	]	PUNCT
ejpam-5205	12	45	,	,	PUNCT
ejpam-5205	12	46	[	[	X
ejpam-5205	12	47	16	16	NUM
ejpam-5205	12	48	]	]	PUNCT
ejpam-5205	12	49	,	,	PUNCT
ejpam-5205	12	50	[	[	X
ejpam-5205	12	51	19	19	NUM
ejpam-5205	12	52	]	]	PUNCT
ejpam-5205	12	53	,	,	PUNCT
ejpam-5205	12	54	[	[	X
ejpam-5205	12	55	20	20	NUM
ejpam-5205	12	56	]	]	PUNCT
ejpam-5205	12	57	,	,	PUNCT
ejpam-5205	12	58	and	and	CCONJ
ejpam-5205	12	59	[	[	X
ejpam-5205	12	60	22	22	NUM
ejpam-5205	12	61	]	]	PUNCT
ejpam-5205	12	62	)	)	PUNCT
ejpam-5205	12	63	.	.	PUNCT
ejpam-5205	13	1	the	the	DET
ejpam-5205	13	2	concept	concept	NOUN
ejpam-5205	13	3	of	of	ADP
ejpam-5205	13	4	convex	convex	ADJ
ejpam-5205	13	5	domination	domination	NOUN
ejpam-5205	13	6	in	in	ADP
ejpam-5205	13	7	graphs	graph	NOUN
ejpam-5205	13	8	was	be	AUX
ejpam-5205	13	9	first	first	ADV
ejpam-5205	13	10	introduced	introduce	VERB
ejpam-5205	13	11	by	by	ADP
ejpam-5205	13	12	lemanska	lemanska	NOUN
ejpam-5205	13	13	in	in	ADP
ejpam-5205	13	14	2004	2004	NUM
ejpam-5205	13	15	[	[	X
ejpam-5205	13	16	18	18	NUM
ejpam-5205	13	17	]	]	PUNCT
ejpam-5205	13	18	.	.	PUNCT
ejpam-5205	14	1	convex	convex	PROPN
ejpam-5205	14	2	domination	domination	NOUN
ejpam-5205	14	3	is	be	AUX
ejpam-5205	14	4	a	a	DET
ejpam-5205	14	5	concept	concept	NOUN
ejpam-5205	14	6	in	in	ADP
ejpam-5205	14	7	graph	graph	NOUN
ejpam-5205	14	8	theory	theory	NOUN
ejpam-5205	14	9	that	that	PRON
ejpam-5205	14	10	combines	combine	VERB
ejpam-5205	14	11	the	the	DET
ejpam-5205	14	12	notions	notion	NOUN
ejpam-5205	14	13	of	of	ADP
ejpam-5205	14	14	convexity	convexity	NOUN
ejpam-5205	14	15	and	and	CCONJ
ejpam-5205	14	16	domination	domination	NOUN
ejpam-5205	14	17	.	.	PUNCT
ejpam-5205	15	1	studies	study	NOUN
ejpam-5205	15	2	related	relate	VERB
ejpam-5205	15	3	on	on	ADP
ejpam-5205	15	4	convexity	convexity	NOUN
ejpam-5205	15	5	and	and	CCONJ
ejpam-5205	15	6	dominaton	dominaton	NOUN
ejpam-5205	15	7	in	in	ADP
ejpam-5205	15	8	graphs	graph	NOUN
ejpam-5205	15	9	can	can	AUX
ejpam-5205	15	10	be	be	AUX
ejpam-5205	15	11	found	find	VERB
ejpam-5205	15	12	in	in	ADP
ejpam-5205	15	13	[	[	X
ejpam-5205	15	14	14	14	NUM
ejpam-5205	15	15	]	]	PUNCT
ejpam-5205	15	16	,	,	PUNCT
ejpam-5205	15	17	[	[	X
ejpam-5205	15	18	15	15	NUM
ejpam-5205	15	19	]	]	PUNCT
ejpam-5205	15	20	,	,	PUNCT
ejpam-5205	15	21	[	[	X
ejpam-5205	15	22	6	6	NUM
ejpam-5205	15	23	]	]	PUNCT
ejpam-5205	15	24	,	,	PUNCT
ejpam-5205	16	1	[	[	X
ejpam-5205	16	2	9	9	NUM
ejpam-5205	16	3	]	]	PUNCT
ejpam-5205	16	4	,	,	PUNCT
ejpam-5205	16	5	[	[	X
ejpam-5205	16	6	11	11	NUM
ejpam-5205	16	7	]	]	PUNCT
ejpam-5205	16	8	,	,	PUNCT
ejpam-5205	16	9	[	[	X
ejpam-5205	16	10	12	12	NUM
ejpam-5205	16	11	]	]	PUNCT
ejpam-5205	16	12	,	,	PUNCT
ejpam-5205	16	13	and	and	CCONJ
ejpam-5205	16	14	[	[	X
ejpam-5205	16	15	21	21	NUM
ejpam-5205	16	16	]	]	PUNCT
ejpam-5205	16	17	.	.	PUNCT
ejpam-5205	17	1	a	a	DET
ejpam-5205	17	2	subset	subset	NOUN
ejpam-5205	17	3	of	of	ADP
ejpam-5205	17	4	vertices	vertex	NOUN
ejpam-5205	17	5	in	in	ADP
ejpam-5205	17	6	a	a	DET
ejpam-5205	17	7	graph	graph	NOUN
ejpam-5205	17	8	is	be	AUX
ejpam-5205	17	9	said	say	VERB
ejpam-5205	17	10	to	to	PART
ejpam-5205	17	11	be	be	AUX
ejpam-5205	17	12	a	a	DET
ejpam-5205	17	13	convex	convex	NOUN
ejpam-5205	17	14	dominating	dominating	NOUN
ejpam-5205	17	15	set	set	NOUN
ejpam-5205	17	16	if	if	SCONJ
ejpam-5205	17	17	it	it	PRON
ejpam-5205	17	18	is	be	AUX
ejpam-5205	17	19	both	both	CCONJ
ejpam-5205	17	20	a	a	DET
ejpam-5205	17	21	convex	convex	NOUN
ejpam-5205	17	22	set	set	VERB
ejpam-5205	17	23	and	and	CCONJ
ejpam-5205	17	24	a	a	DET
ejpam-5205	17	25	dominating	dominating	NOUN
ejpam-5205	17	26	set	set	NOUN
ejpam-5205	17	27	,	,	PUNCT
ejpam-5205	17	28	which	which	PRON
ejpam-5205	17	29	means	mean	VERB
ejpam-5205	17	30	∗corresponding	∗corresponde	VERB
ejpam-5205	17	31	author	author	NOUN
ejpam-5205	17	32	.	.	PUNCT
ejpam-5205	18	1	doi	doi	NOUN
ejpam-5205	18	2	:	:	PUNCT
ejpam-5205	18	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5205	https://doi.org/10.29020/nybg.ejpam.v17i2.5205	NOUN
ejpam-5205	18	4	email	email	NOUN
ejpam-5205	18	5	addresses	address	NOUN
ejpam-5205	18	6	:	:	PUNCT
ejpam-5205	19	1	ronajane.fortosa@g.msuiit.edu.ph	ronajane.fortosa@g.msuiit.edu.ph	PROPN
ejpam-5205	19	2	(	(	PUNCT
ejpam-5205	19	3	r.j	r.j	PROPN
ejpam-5205	19	4	.	.	PROPN
ejpam-5205	19	5	fortosa	fortosa	PROPN
ejpam-5205	19	6	)	)	PUNCT
ejpam-5205	19	7	,	,	PUNCT
ejpam-5205	19	8	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-5205	19	9	(	(	PUNCT
ejpam-5205	19	10	s.	s.	PROPN
ejpam-5205	19	11	canoy	canoy	PROPN
ejpam-5205	19	12	)	)	PUNCT
ejpam-5205	19	13	,	,	PUNCT
ejpam-5205	19	14	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-5205	19	15	(	(	PUNCT
ejpam-5205	19	16	f.	f.	PROPN
ejpam-5205	19	17	jamil	jamil	PROPN
ejpam-5205	19	18	)	)	PUNCT
ejpam-5205	19	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5205	19	20	1335	1335	NUM
ejpam-5205	20	1	©	©	ADP
ejpam-5205	20	2	2024	2024	NUM
ejpam-5205	20	3	ejpam	ejpam	NOUN
ejpam-5205	20	4	all	all	DET
ejpam-5205	20	5	rights	right	NOUN
ejpam-5205	20	6	reserved	reserve	VERB
ejpam-5205	20	7	.	.	PUNCT
ejpam-5205	21	1	r.	r.	PROPN
ejpam-5205	21	2	fortosa	fortosa	PROPN
ejpam-5205	21	3	,	,	PUNCT
ejpam-5205	21	4	s.	s.	PROPN
ejpam-5205	21	5	canoy	canoy	PROPN
ejpam-5205	21	6	jr	jr	PROPN
ejpam-5205	21	7	.	.	PROPN
ejpam-5205	21	8	/	/	SYM
ejpam-5205	21	9	eur	eur	PROPN
ejpam-5205	21	10	.	.	PUNCT
ejpam-5205	22	1	j.	j.	PROPN
ejpam-5205	22	2	pure	pure	PROPN
ejpam-5205	22	3	appl	appl	PROPN
ejpam-5205	22	4	.	.	PROPN
ejpam-5205	22	5	math	math	PROPN
ejpam-5205	22	6	,	,	PUNCT
ejpam-5205	22	7	17	17	NUM
ejpam-5205	22	8	(	(	PUNCT
ejpam-5205	22	9	2	2	NUM
ejpam-5205	22	10	)	)	PUNCT
ejpam-5205	22	11	(	(	PUNCT
ejpam-5205	22	12	2024	2024	NUM
ejpam-5205	22	13	)	)	PUNCT
ejpam-5205	22	14	,	,	PUNCT
ejpam-5205	22	15	1335	1335	NUM
ejpam-5205	22	16	-	-	SYM
ejpam-5205	22	17	1351	1351	NUM
ejpam-5205	22	18	1336	1336	NUM
ejpam-5205	22	19	that	that	PRON
ejpam-5205	22	20	every	every	DET
ejpam-5205	22	21	vertex	vertex	NOUN
ejpam-5205	22	22	on	on	ADP
ejpam-5205	22	23	the	the	DET
ejpam-5205	22	24	shortest	short	ADJ
ejpam-5205	22	25	path	path	NOUN
ejpam-5205	22	26	between	between	ADP
ejpam-5205	22	27	any	any	DET
ejpam-5205	22	28	two	two	NUM
ejpam-5205	22	29	vertices	vertex	NOUN
ejpam-5205	22	30	in	in	ADP
ejpam-5205	22	31	the	the	DET
ejpam-5205	22	32	set	set	NOUN
ejpam-5205	22	33	is	be	AUX
ejpam-5205	22	34	also	also	ADV
ejpam-5205	22	35	in	in	ADP
ejpam-5205	22	36	the	the	DET
ejpam-5205	22	37	set	set	NOUN
ejpam-5205	22	38	and	and	CCONJ
ejpam-5205	22	39	every	every	DET
ejpam-5205	22	40	vertex	vertex	NOUN
ejpam-5205	22	41	in	in	ADP
ejpam-5205	22	42	the	the	DET
ejpam-5205	22	43	graph	graph	NOUN
ejpam-5205	22	44	is	be	AUX
ejpam-5205	22	45	either	either	CCONJ
ejpam-5205	22	46	in	in	ADP
ejpam-5205	22	47	the	the	DET
ejpam-5205	22	48	set	set	NOUN
ejpam-5205	22	49	or	or	CCONJ
ejpam-5205	22	50	adjacent	adjacent	ADJ
ejpam-5205	22	51	to	to	ADP
ejpam-5205	22	52	a	a	DET
ejpam-5205	22	53	vertex	vertex	NOUN
ejpam-5205	22	54	in	in	ADP
ejpam-5205	22	55	the	the	DET
ejpam-5205	22	56	set	set	NOUN
ejpam-5205	22	57	.	.	PUNCT
ejpam-5205	23	1	the	the	DET
ejpam-5205	23	2	convex	convex	ADJ
ejpam-5205	23	3	roman	roman	ADJ
ejpam-5205	23	4	domination	domination	NOUN
ejpam-5205	23	5	was	be	AUX
ejpam-5205	23	6	introduced	introduce	VERB
ejpam-5205	23	7	and	and	CCONJ
ejpam-5205	23	8	initially	initially	ADV
ejpam-5205	23	9	investigated	investigate	VERB
ejpam-5205	23	10	in	in	ADP
ejpam-5205	23	11	[	[	X
ejpam-5205	23	12	10	10	NUM
ejpam-5205	23	13	]	]	PUNCT
ejpam-5205	23	14	where	where	SCONJ
ejpam-5205	23	15	properties	property	NOUN
ejpam-5205	23	16	of	of	ADP
ejpam-5205	23	17	convex	convex	ADJ
ejpam-5205	23	18	roman	roman	ADJ
ejpam-5205	23	19	dominating	dominating	NOUN
ejpam-5205	23	20	functions	function	NOUN
ejpam-5205	23	21	and	and	CCONJ
ejpam-5205	23	22	convex	convex	VERB
ejpam-5205	23	23	roman	roman	ADJ
ejpam-5205	23	24	domination	domination	NOUN
ejpam-5205	23	25	number	number	NOUN
ejpam-5205	23	26	of	of	ADP
ejpam-5205	23	27	some	some	DET
ejpam-5205	23	28	graphs	graph	NOUN
ejpam-5205	23	29	and	and	CCONJ
ejpam-5205	23	30	the	the	DET
ejpam-5205	23	31	join	join	NOUN
ejpam-5205	23	32	of	of	ADP
ejpam-5205	23	33	two	two	NUM
ejpam-5205	23	34	graphs	graph	NOUN
ejpam-5205	23	35	have	have	AUX
ejpam-5205	23	36	been	be	AUX
ejpam-5205	23	37	obtained	obtain	VERB
ejpam-5205	23	38	.	.	PUNCT
ejpam-5205	24	1	in	in	ADP
ejpam-5205	24	2	this	this	DET
ejpam-5205	24	3	present	present	ADJ
ejpam-5205	24	4	paper	paper	NOUN
ejpam-5205	24	5	,	,	PUNCT
ejpam-5205	24	6	authors	author	NOUN
ejpam-5205	24	7	continued	continue	VERB
ejpam-5205	24	8	the	the	DET
ejpam-5205	24	9	study	study	NOUN
ejpam-5205	24	10	of	of	ADP
ejpam-5205	24	11	convex	convex	ADJ
ejpam-5205	24	12	roman	roman	ADJ
ejpam-5205	24	13	domination	domination	NOUN
ejpam-5205	24	14	,	,	PUNCT
ejpam-5205	24	15	specifically	specifically	ADV
ejpam-5205	24	16	on	on	ADP
ejpam-5205	24	17	the	the	DET
ejpam-5205	24	18	corona	corona	NOUN
ejpam-5205	24	19	,	,	PUNCT
ejpam-5205	24	20	edge	edge	NOUN
ejpam-5205	24	21	corona	corona	NOUN
ejpam-5205	24	22	,	,	PUNCT
ejpam-5205	24	23	complementary	complementary	ADJ
ejpam-5205	24	24	prism	prism	NOUN
ejpam-5205	24	25	,	,	PUNCT
ejpam-5205	24	26	lexicographic	lexicographic	ADJ
ejpam-5205	24	27	product	product	NOUN
ejpam-5205	24	28	,	,	PUNCT
ejpam-5205	24	29	and	and	CCONJ
ejpam-5205	24	30	cartesian	cartesian	ADJ
ejpam-5205	24	31	product	product	NOUN
ejpam-5205	24	32	of	of	ADP
ejpam-5205	24	33	graphs	graph	NOUN
ejpam-5205	24	34	.	.	PUNCT
ejpam-5205	25	1	let	let	VERB
ejpam-5205	25	2	g	g	PRON
ejpam-5205	25	3	be	be	AUX
ejpam-5205	25	4	a	a	DET
ejpam-5205	25	5	connected	connected	ADJ
ejpam-5205	25	6	graph	graph	NOUN
ejpam-5205	25	7	.	.	PUNCT
ejpam-5205	26	1	for	for	ADP
ejpam-5205	26	2	vertices	vertex	NOUN
ejpam-5205	26	3	u	u	NOUN
ejpam-5205	26	4	and	and	CCONJ
ejpam-5205	26	5	v	v	NOUN
ejpam-5205	26	6	in	in	ADP
ejpam-5205	26	7	g	g	PROPN
ejpam-5205	26	8	,	,	PUNCT
ejpam-5205	26	9	a	a	DET
ejpam-5205	26	10	u	u	NOUN
ejpam-5205	26	11	-	-	NOUN
ejpam-5205	26	12	v	v	ADJ
ejpam-5205	26	13	geodesic	geodesic	NOUN
ejpam-5205	26	14	is	be	AUX
ejpam-5205	26	15	any	any	DET
ejpam-5205	26	16	shortest	short	ADJ
ejpam-5205	26	17	path	path	NOUN
ejpam-5205	26	18	in	in	ADP
ejpam-5205	26	19	g	g	NOUN
ejpam-5205	26	20	joining	join	VERB
ejpam-5205	26	21	u	u	NOUN
ejpam-5205	26	22	and	and	CCONJ
ejpam-5205	26	23	v.	v.	ADP
ejpam-5205	26	24	the	the	DET
ejpam-5205	26	25	length	length	NOUN
ejpam-5205	26	26	of	of	ADP
ejpam-5205	26	27	a	a	DET
ejpam-5205	26	28	u	u	NOUN
ejpam-5205	26	29	-	-	NOUN
ejpam-5205	26	30	v	v	ADJ
ejpam-5205	26	31	geodesic	geodesic	NOUN
ejpam-5205	26	32	is	be	AUX
ejpam-5205	26	33	called	call	VERB
ejpam-5205	26	34	the	the	DET
ejpam-5205	26	35	distance	distance	NOUN
ejpam-5205	26	36	dg(u	dg(u	X
ejpam-5205	26	37	,	,	PUNCT
ejpam-5205	26	38	v	v	NOUN
ejpam-5205	26	39	)	)	PUNCT
ejpam-5205	26	40	between	between	ADP
ejpam-5205	26	41	u	u	PROPN
ejpam-5205	26	42	and	and	CCONJ
ejpam-5205	26	43	v.	v.	NOUN
ejpam-5205	26	44	for	for	ADP
ejpam-5205	26	45	every	every	DET
ejpam-5205	26	46	two	two	NUM
ejpam-5205	26	47	vertices	vertex	NOUN
ejpam-5205	26	48	u	u	NOUN
ejpam-5205	26	49	and	and	CCONJ
ejpam-5205	26	50	v	v	NOUN
ejpam-5205	26	51	of	of	ADP
ejpam-5205	26	52	g	g	NOUN
ejpam-5205	26	53	,	,	PUNCT
ejpam-5205	26	54	the	the	DET
ejpam-5205	26	55	symbol	symbol	NOUN
ejpam-5205	26	56	ig[u	ig[u	PROPN
ejpam-5205	26	57	,	,	PUNCT
ejpam-5205	26	58	v	v	NOUN
ejpam-5205	26	59	]	]	PUNCT
ejpam-5205	26	60	is	be	AUX
ejpam-5205	26	61	used	use	VERB
ejpam-5205	26	62	to	to	PART
ejpam-5205	26	63	denote	denote	VERB
ejpam-5205	26	64	the	the	DET
ejpam-5205	26	65	set	set	NOUN
ejpam-5205	26	66	of	of	ADP
ejpam-5205	26	67	vertices	vertex	NOUN
ejpam-5205	26	68	lying	lie	VERB
ejpam-5205	26	69	on	on	ADP
ejpam-5205	26	70	any	any	PRON
ejpam-5205	26	71	of	of	ADP
ejpam-5205	26	72	the	the	DET
ejpam-5205	26	73	u	u	NOUN
ejpam-5205	26	74	-	-	NOUN
ejpam-5205	26	75	v	v	ADJ
ejpam-5205	26	76	geodesics	geodesic	NOUN
ejpam-5205	26	77	.	.	PUNCT
ejpam-5205	27	1	the	the	DET
ejpam-5205	27	2	set	set	NOUN
ejpam-5205	27	3	of	of	ADP
ejpam-5205	27	4	neighbors	neighbor	NOUN
ejpam-5205	27	5	of	of	ADP
ejpam-5205	27	6	a	a	DET
ejpam-5205	27	7	vertex	vertex	NOUN
ejpam-5205	27	8	u	u	NOUN
ejpam-5205	27	9	∈	∈	PROPN
ejpam-5205	27	10	g	g	NOUN
ejpam-5205	27	11	,	,	PUNCT
ejpam-5205	27	12	denoted	denote	VERB
ejpam-5205	27	13	by	by	ADP
ejpam-5205	27	14	ng(u	ng(u	NOUN
ejpam-5205	27	15	)	)	PUNCT
ejpam-5205	27	16	,	,	PUNCT
ejpam-5205	27	17	is	be	AUX
ejpam-5205	27	18	called	call	VERB
ejpam-5205	27	19	the	the	DET
ejpam-5205	27	20	open	open	ADJ
ejpam-5205	27	21	neighborhood	neighborhood	NOUN
ejpam-5205	27	22	of	of	ADP
ejpam-5205	27	23	u.	u.	VERB
ejpam-5205	27	24	the	the	DET
ejpam-5205	27	25	closed	closed	ADJ
ejpam-5205	27	26	neighborhood	neighborhood	NOUN
ejpam-5205	27	27	of	of	ADP
ejpam-5205	27	28	u	u	NOUN
ejpam-5205	27	29	is	be	AUX
ejpam-5205	27	30	the	the	DET
ejpam-5205	27	31	set	set	NOUN
ejpam-5205	27	32	ng[u	ng[u	PROPN
ejpam-5205	27	33	]	]	X
ejpam-5205	27	34	=	=	SYM
ejpam-5205	27	35	ng(u	ng(u	PROPN
ejpam-5205	27	36	)	)	PUNCT
ejpam-5205	27	37	∪	∪	NOUN
ejpam-5205	27	38	{	{	PUNCT
ejpam-5205	27	39	u	u	NOUN
ejpam-5205	27	40	}	}	PUNCT
ejpam-5205	27	41	.	.	PUNCT
ejpam-5205	28	1	the	the	DET
ejpam-5205	28	2	degree	degree	NOUN
ejpam-5205	28	3	of	of	ADP
ejpam-5205	28	4	a	a	DET
ejpam-5205	28	5	vertex	vertex	NOUN
ejpam-5205	28	6	v	v	ADP
ejpam-5205	28	7	denoted	denote	VERB
ejpam-5205	28	8	degg(v	degg(v	PROPN
ejpam-5205	28	9	)	)	PUNCT
ejpam-5205	28	10	in	in	ADP
ejpam-5205	28	11	a	a	DET
ejpam-5205	28	12	graph	graph	NOUN
ejpam-5205	28	13	g	g	NOUN
ejpam-5205	28	14	is	be	AUX
ejpam-5205	28	15	the	the	DET
ejpam-5205	28	16	number	number	NOUN
ejpam-5205	28	17	of	of	ADP
ejpam-5205	28	18	vertices	vertex	NOUN
ejpam-5205	28	19	in	in	ADP
ejpam-5205	28	20	g	g	PROPN
ejpam-5205	28	21	that	that	PRON
ejpam-5205	28	22	are	be	AUX
ejpam-5205	28	23	adjacent	adjacent	ADJ
ejpam-5205	28	24	to	to	ADP
ejpam-5205	28	25	v.	v.	ADP
ejpam-5205	28	26	hence	hence	ADV
ejpam-5205	28	27	,	,	PUNCT
ejpam-5205	28	28	degg(v	degg(v	PROPN
ejpam-5205	28	29	)	)	PUNCT
ejpam-5205	28	30	=	=	SYM
ejpam-5205	28	31	|n(v)|	|n(v)|	PROPN
ejpam-5205	28	32	.	.	PUNCT
ejpam-5205	29	1	the	the	DET
ejpam-5205	29	2	largest	large	ADJ
ejpam-5205	29	3	degree	degree	NOUN
ejpam-5205	29	4	among	among	ADP
ejpam-5205	29	5	the	the	DET
ejpam-5205	29	6	vertices	vertex	NOUN
ejpam-5205	29	7	of	of	ADP
ejpam-5205	29	8	g	g	PROPN
ejpam-5205	29	9	is	be	AUX
ejpam-5205	29	10	called	call	VERB
ejpam-5205	29	11	the	the	DET
ejpam-5205	29	12	maximum	maximum	ADJ
ejpam-5205	29	13	degree	degree	NOUN
ejpam-5205	29	14	of	of	ADP
ejpam-5205	29	15	g	g	NOUN
ejpam-5205	29	16	and	and	CCONJ
ejpam-5205	29	17	is	be	AUX
ejpam-5205	29	18	denoted	denote	VERB
ejpam-5205	29	19	by	by	ADP
ejpam-5205	29	20	△	△	PROPN
ejpam-5205	29	21	(	(	PUNCT
ejpam-5205	29	22	g	g	NOUN
ejpam-5205	29	23	)	)	PUNCT
ejpam-5205	29	24	.	.	PUNCT
ejpam-5205	30	1	the	the	DET
ejpam-5205	30	2	minimum	minimum	NOUN
ejpam-5205	30	3	degree	degree	NOUN
ejpam-5205	30	4	of	of	ADP
ejpam-5205	30	5	g	g	PROPN
ejpam-5205	30	6	is	be	AUX
ejpam-5205	30	7	denoted	denote	VERB
ejpam-5205	30	8	by	by	ADP
ejpam-5205	30	9	δ(g	δ(g	NOUN
ejpam-5205	30	10	)	)	PUNCT
ejpam-5205	30	11	.	.	PUNCT
ejpam-5205	31	1	a	a	DET
ejpam-5205	31	2	graph	graph	NOUN
ejpam-5205	31	3	g	g	NOUN
ejpam-5205	31	4	is	be	AUX
ejpam-5205	31	5	connected	connect	VERB
ejpam-5205	31	6	if	if	SCONJ
ejpam-5205	31	7	every	every	DET
ejpam-5205	31	8	pair	pair	NOUN
ejpam-5205	31	9	of	of	ADP
ejpam-5205	31	10	its	its	PRON
ejpam-5205	31	11	vertices	vertex	NOUN
ejpam-5205	31	12	can	can	AUX
ejpam-5205	31	13	be	be	AUX
ejpam-5205	31	14	joined	join	VERB
ejpam-5205	31	15	by	by	ADP
ejpam-5205	31	16	a	a	DET
ejpam-5205	31	17	path	path	NOUN
ejpam-5205	31	18	.	.	PUNCT
ejpam-5205	32	1	a	a	DET
ejpam-5205	32	2	set	set	NOUN
ejpam-5205	32	3	s	s	NOUN
ejpam-5205	32	4	⊆	⊆	NUM
ejpam-5205	32	5	v	v	NOUN
ejpam-5205	32	6	(	(	PUNCT
ejpam-5205	32	7	g	g	NOUN
ejpam-5205	32	8	)	)	PUNCT
ejpam-5205	32	9	is	be	AUX
ejpam-5205	32	10	said	say	VERB
ejpam-5205	32	11	to	to	PART
ejpam-5205	32	12	be	be	AUX
ejpam-5205	32	13	a	a	DET
ejpam-5205	32	14	dominating	dominating	NOUN
ejpam-5205	32	15	set	set	NOUN
ejpam-5205	32	16	of	of	ADP
ejpam-5205	32	17	a	a	DET
ejpam-5205	32	18	graph	graph	NOUN
ejpam-5205	32	19	g	g	NOUN
ejpam-5205	32	20	if	if	SCONJ
ejpam-5205	32	21	every	every	DET
ejpam-5205	32	22	vertex	vertex	NOUN
ejpam-5205	32	23	v	v	ADP
ejpam-5205	32	24	∈	∈	PROPN
ejpam-5205	32	25	v	v	NOUN
ejpam-5205	32	26	(	(	PUNCT
ejpam-5205	32	27	g	g	NOUN
ejpam-5205	32	28	)	)	PUNCT
ejpam-5205	32	29	is	be	AUX
ejpam-5205	32	30	either	either	CCONJ
ejpam-5205	32	31	an	an	DET
ejpam-5205	32	32	element	element	NOUN
ejpam-5205	32	33	of	of	ADP
ejpam-5205	32	34	s	s	PRON
ejpam-5205	32	35	or	or	CCONJ
ejpam-5205	32	36	is	be	AUX
ejpam-5205	32	37	adjacent	adjacent	ADJ
ejpam-5205	32	38	to	to	ADP
ejpam-5205	32	39	an	an	DET
ejpam-5205	32	40	element	element	NOUN
ejpam-5205	32	41	of	of	ADP
ejpam-5205	32	42	s.	s.	PROPN
ejpam-5205	32	43	thus	thus	ADV
ejpam-5205	32	44	,	,	PUNCT
ejpam-5205	32	45	n	n	X
ejpam-5205	32	46	[	[	X
ejpam-5205	32	47	s	s	X
ejpam-5205	32	48	]	]	X
ejpam-5205	32	49	=	=	SYM
ejpam-5205	32	50	v	v	NOUN
ejpam-5205	32	51	(	(	PUNCT
ejpam-5205	32	52	g	g	NOUN
ejpam-5205	32	53	)	)	PUNCT
ejpam-5205	32	54	.	.	PUNCT
ejpam-5205	33	1	the	the	DET
ejpam-5205	33	2	smallest	small	ADJ
ejpam-5205	33	3	cardinality	cardinality	NOUN
ejpam-5205	33	4	of	of	ADP
ejpam-5205	33	5	a	a	DET
ejpam-5205	33	6	dominating	dominating	NOUN
ejpam-5205	33	7	set	set	NOUN
ejpam-5205	33	8	s	s	PART
ejpam-5205	33	9	is	be	AUX
ejpam-5205	33	10	called	call	VERB
ejpam-5205	33	11	the	the	DET
ejpam-5205	33	12	domination	domination	NOUN
ejpam-5205	33	13	number	number	NOUN
ejpam-5205	33	14	of	of	ADP
ejpam-5205	33	15	g	g	NOUN
ejpam-5205	33	16	and	and	CCONJ
ejpam-5205	33	17	is	be	AUX
ejpam-5205	33	18	denoted	denote	VERB
ejpam-5205	33	19	by	by	ADP
ejpam-5205	33	20	γ(g	γ(g	PROPN
ejpam-5205	33	21	)	)	PUNCT
ejpam-5205	33	22	.	.	PUNCT
ejpam-5205	34	1	that	that	PRON
ejpam-5205	34	2	is	be	AUX
ejpam-5205	34	3	γ(g	γ(g	PROPN
ejpam-5205	34	4	)	)	PUNCT
ejpam-5205	35	1	=	=	NOUN
ejpam-5205	35	2	min{|s|	min{|s|	NOUN
ejpam-5205	35	3	:	:	PUNCT
ejpam-5205	35	4	s	s	VERB
ejpam-5205	35	5	is	be	AUX
ejpam-5205	35	6	a	a	DET
ejpam-5205	35	7	dominating	dominating	NOUN
ejpam-5205	35	8	set	set	NOUN
ejpam-5205	35	9	of	of	ADP
ejpam-5205	35	10	g	g	NOUN
ejpam-5205	35	11	}	}	PUNCT
ejpam-5205	35	12	.	.	PUNCT
ejpam-5205	36	1	any	any	DET
ejpam-5205	36	2	dominating	dominating	NOUN
ejpam-5205	36	3	set	set	NOUN
ejpam-5205	36	4	s	s	NOUN
ejpam-5205	36	5	of	of	ADP
ejpam-5205	36	6	g	g	NOUN
ejpam-5205	36	7	with	with	ADP
ejpam-5205	36	8	|s|	|s|	PROPN
ejpam-5205	36	9	=	=	SYM
ejpam-5205	36	10	γ(g	γ(g	PROPN
ejpam-5205	36	11	)	)	PUNCT
ejpam-5205	36	12	is	be	AUX
ejpam-5205	36	13	called	call	VERB
ejpam-5205	36	14	a	a	DET
ejpam-5205	36	15	γ	γ	NOUN
ejpam-5205	36	16	-	-	PUNCT
ejpam-5205	36	17	set	set	NOUN
ejpam-5205	36	18	of	of	ADP
ejpam-5205	36	19	g.	g.	PROPN
ejpam-5205	36	20	if	if	SCONJ
ejpam-5205	36	21	s	s	X
ejpam-5205	36	22	is	be	AUX
ejpam-5205	36	23	a	a	DET
ejpam-5205	36	24	clique	clique	NOUN
ejpam-5205	36	25	(	(	PUNCT
ejpam-5205	36	26	the	the	DET
ejpam-5205	36	27	induced	induced	ADJ
ejpam-5205	36	28	graph	graph	NOUN
ejpam-5205	36	29	⟨s⟩	⟨s⟩	PROPN
ejpam-5205	36	30	is	be	AUX
ejpam-5205	36	31	complete	complete	ADJ
ejpam-5205	36	32	)	)	PUNCT
ejpam-5205	36	33	and	and	CCONJ
ejpam-5205	36	34	a	a	DET
ejpam-5205	36	35	dominating	dominating	NOUN
ejpam-5205	36	36	set	set	NOUN
ejpam-5205	36	37	,	,	PUNCT
ejpam-5205	36	38	then	then	ADV
ejpam-5205	36	39	s	s	VERB
ejpam-5205	36	40	is	be	AUX
ejpam-5205	36	41	called	call	VERB
ejpam-5205	36	42	a	a	DET
ejpam-5205	36	43	clique	clique	NOUN
ejpam-5205	36	44	dominating	dominating	NOUN
ejpam-5205	36	45	set	set	VERB
ejpam-5205	36	46	in	in	ADP
ejpam-5205	36	47	g.	g.	PROPN
ejpam-5205	36	48	a	a	DET
ejpam-5205	36	49	clique	clique	ADJ
ejpam-5205	36	50	domination	domination	NOUN
ejpam-5205	36	51	number	number	NOUN
ejpam-5205	36	52	γcl(g	γcl(g	PROPN
ejpam-5205	36	53	)	)	PUNCT
ejpam-5205	36	54	of	of	ADP
ejpam-5205	36	55	g	g	PROPN
ejpam-5205	36	56	is	be	AUX
ejpam-5205	36	57	the	the	DET
ejpam-5205	36	58	smallest	small	ADJ
ejpam-5205	36	59	cardinality	cardinality	NOUN
ejpam-5205	36	60	of	of	ADP
ejpam-5205	36	61	a	a	DET
ejpam-5205	36	62	clique	clique	NOUN
ejpam-5205	36	63	dominating	dominating	NOUN
ejpam-5205	36	64	set	set	VERB
ejpam-5205	36	65	in	in	ADP
ejpam-5205	36	66	g.	g.	PROPN
ejpam-5205	36	67	a	a	DET
ejpam-5205	36	68	set	set	NOUN
ejpam-5205	36	69	s	s	PROPN
ejpam-5205	36	70	⊆	⊆	NUM
ejpam-5205	36	71	v	v	NOUN
ejpam-5205	36	72	(	(	PUNCT
ejpam-5205	36	73	g	g	NOUN
ejpam-5205	36	74	)	)	PUNCT
ejpam-5205	36	75	is	be	AUX
ejpam-5205	36	76	convex	convex	ADJ
ejpam-5205	36	77	if	if	SCONJ
ejpam-5205	36	78	for	for	ADP
ejpam-5205	36	79	every	every	DET
ejpam-5205	36	80	two	two	NUM
ejpam-5205	36	81	vertices	vertex	NOUN
ejpam-5205	36	82	x	x	X
ejpam-5205	36	83	,	,	PUNCT
ejpam-5205	36	84	y	y	PROPN
ejpam-5205	36	85	∈	∈	PROPN
ejpam-5205	36	86	s	s	PROPN
ejpam-5205	36	87	,	,	PUNCT
ejpam-5205	36	88	ig[x	ig[x	PROPN
ejpam-5205	36	89	,	,	PUNCT
ejpam-5205	36	90	y	y	PROPN
ejpam-5205	36	91	]	]	X
ejpam-5205	36	92	⊆	⊆	NUM
ejpam-5205	36	93	s.	s.	PROPN
ejpam-5205	36	94	the	the	DET
ejpam-5205	36	95	largest	large	ADJ
ejpam-5205	36	96	cardinality	cardinality	NOUN
ejpam-5205	36	97	of	of	ADP
ejpam-5205	36	98	a	a	DET
ejpam-5205	36	99	proper	proper	ADJ
ejpam-5205	36	100	convex	convex	NOUN
ejpam-5205	36	101	set	set	VERB
ejpam-5205	36	102	in	in	ADP
ejpam-5205	36	103	g	g	NOUN
ejpam-5205	36	104	,	,	PUNCT
ejpam-5205	36	105	denoted	denote	VERB
ejpam-5205	36	106	by	by	ADP
ejpam-5205	36	107	con(g	con(g	NOUN
ejpam-5205	36	108	)	)	PUNCT
ejpam-5205	36	109	,	,	PUNCT
ejpam-5205	36	110	is	be	AUX
ejpam-5205	36	111	called	call	VERB
ejpam-5205	36	112	the	the	DET
ejpam-5205	36	113	convexity	convexity	NOUN
ejpam-5205	36	114	number	number	NOUN
ejpam-5205	36	115	of	of	ADP
ejpam-5205	36	116	g.	g.	PROPN
ejpam-5205	36	117	a	a	DET
ejpam-5205	36	118	set	set	NOUN
ejpam-5205	36	119	s	s	PROPN
ejpam-5205	36	120	⊆	⊆	NUM
ejpam-5205	36	121	v	v	NOUN
ejpam-5205	36	122	(	(	PUNCT
ejpam-5205	36	123	g	g	NOUN
ejpam-5205	36	124	)	)	PUNCT
ejpam-5205	36	125	is	be	AUX
ejpam-5205	36	126	convex	convex	VERB
ejpam-5205	36	127	dominating	dominate	VERB
ejpam-5205	36	128	if	if	SCONJ
ejpam-5205	36	129	s	s	VERB
ejpam-5205	36	130	is	be	AUX
ejpam-5205	36	131	both	both	PRON
ejpam-5205	36	132	convex	convex	ADJ
ejpam-5205	36	133	and	and	CCONJ
ejpam-5205	36	134	dominating	dominating	NOUN
ejpam-5205	36	135	.	.	PUNCT
ejpam-5205	37	1	the	the	DET
ejpam-5205	37	2	minimum	minimum	ADJ
ejpam-5205	37	3	cardinality	cardinality	NOUN
ejpam-5205	37	4	among	among	ADP
ejpam-5205	37	5	all	all	DET
ejpam-5205	37	6	convex	convex	ADJ
ejpam-5205	37	7	dominating	dominating	NOUN
ejpam-5205	37	8	sets	set	NOUN
ejpam-5205	37	9	in	in	ADP
ejpam-5205	37	10	g	g	NOUN
ejpam-5205	37	11	,	,	PUNCT
ejpam-5205	37	12	denoted	denote	VERB
ejpam-5205	37	13	by	by	ADP
ejpam-5205	37	14	γcon(g	γcon(g	NOUN
ejpam-5205	37	15	)	)	PUNCT
ejpam-5205	37	16	is	be	AUX
ejpam-5205	37	17	called	call	VERB
ejpam-5205	37	18	the	the	DET
ejpam-5205	37	19	convex	convex	ADJ
ejpam-5205	37	20	domination	domination	NOUN
ejpam-5205	37	21	number	number	NOUN
ejpam-5205	37	22	of	of	ADP
ejpam-5205	37	23	g.	g.	PROPN
ejpam-5205	37	24	any	any	DET
ejpam-5205	37	25	convex	convex	NOUN
ejpam-5205	37	26	dominating	dominating	NOUN
ejpam-5205	37	27	set	set	NOUN
ejpam-5205	37	28	s	s	NOUN
ejpam-5205	37	29	of	of	ADP
ejpam-5205	37	30	g	g	NOUN
ejpam-5205	37	31	with	with	ADP
ejpam-5205	37	32	|s|	|s|	NOUN
ejpam-5205	37	33	=	=	SYM
ejpam-5205	37	34	γcon(g	γcon(g	NOUN
ejpam-5205	37	35	)	)	PUNCT
ejpam-5205	37	36	is	be	AUX
ejpam-5205	37	37	called	call	VERB
ejpam-5205	37	38	a	a	DET
ejpam-5205	37	39	γcon	γcon	NOUN
ejpam-5205	37	40	-	-	PUNCT
ejpam-5205	37	41	set	set	NOUN
ejpam-5205	37	42	of	of	ADP
ejpam-5205	37	43	g.	g.	PROPN
ejpam-5205	37	44	a	a	DET
ejpam-5205	37	45	function	function	NOUN
ejpam-5205	38	1	f	f	NOUN
ejpam-5205	38	2	:	:	PUNCT
ejpam-5205	38	3	v	v	X
ejpam-5205	38	4	(	(	PUNCT
ejpam-5205	38	5	g	g	NOUN
ejpam-5205	38	6	)	)	PUNCT
ejpam-5205	38	7	→	→	SYM
ejpam-5205	38	8	{	{	PUNCT
ejpam-5205	38	9	0	0	NUM
ejpam-5205	38	10	,	,	PUNCT
ejpam-5205	38	11	1	1	NUM
ejpam-5205	38	12	,	,	PUNCT
ejpam-5205	38	13	2	2	NUM
ejpam-5205	38	14	}	}	PUNCT
ejpam-5205	38	15	is	be	AUX
ejpam-5205	38	16	a	a	DET
ejpam-5205	38	17	roman	roman	ADJ
ejpam-5205	38	18	dominating	dominating	NOUN
ejpam-5205	38	19	function	function	NOUN
ejpam-5205	38	20	(	(	PUNCT
ejpam-5205	38	21	or	or	CCONJ
ejpam-5205	38	22	just	just	ADV
ejpam-5205	38	23	rdf	rdf	VERB
ejpam-5205	38	24	)	)	PUNCT
ejpam-5205	38	25	if	if	SCONJ
ejpam-5205	38	26	every	every	DET
ejpam-5205	38	27	vertex	vertex	NOUN
ejpam-5205	38	28	u	u	NOUN
ejpam-5205	38	29	for	for	ADP
ejpam-5205	38	30	which	which	PRON
ejpam-5205	38	31	f(u	f(u	PROPN
ejpam-5205	38	32	)	)	PUNCT
ejpam-5205	39	1	=	=	SYM
ejpam-5205	39	2	0	0	NUM
ejpam-5205	39	3	is	be	AUX
ejpam-5205	39	4	adjacent	adjacent	ADJ
ejpam-5205	39	5	to	to	ADP
ejpam-5205	39	6	at	at	ADV
ejpam-5205	39	7	least	least	ADV
ejpam-5205	39	8	one	one	NUM
ejpam-5205	39	9	vertex	vertex	NOUN
ejpam-5205	39	10	v	v	NOUN
ejpam-5205	39	11	for	for	ADP
ejpam-5205	39	12	which	which	PRON
ejpam-5205	39	13	f(v	f(v	NOUN
ejpam-5205	39	14	)	)	PUNCT
ejpam-5205	39	15	=	=	SYM
ejpam-5205	40	1	2	2	X
ejpam-5205	40	2	.	.	PUNCT
ejpam-5205	40	3	the	the	DET
ejpam-5205	40	4	weight	weight	NOUN
ejpam-5205	40	5	of	of	ADP
ejpam-5205	40	6	an	an	DET
ejpam-5205	40	7	rdf	rdf	NOUN
ejpam-5205	40	8	f	f	NOUN
ejpam-5205	40	9	is	be	AUX
ejpam-5205	40	10	given	give	VERB
ejpam-5205	40	11	by	by	ADP
ejpam-5205	40	12	ωg(f	ωg(f	NOUN
ejpam-5205	40	13	)	)	PUNCT
ejpam-5205	40	14	=	=	SYM
ejpam-5205	40	15	∑	∑	PUNCT
ejpam-5205	40	16	v∈v	v∈v	PROPN
ejpam-5205	40	17	(	(	PUNCT
ejpam-5205	40	18	g	g	NOUN
ejpam-5205	40	19	)	)	PUNCT
ejpam-5205	40	20	f(v	f(v	NOUN
ejpam-5205	40	21	)	)	PUNCT
ejpam-5205	40	22	.	.	PUNCT
ejpam-5205	41	1	the	the	DET
ejpam-5205	41	2	roman	roman	ADJ
ejpam-5205	41	3	domination	domination	NOUN
ejpam-5205	41	4	number	number	NOUN
ejpam-5205	41	5	of	of	ADP
ejpam-5205	41	6	a	a	DET
ejpam-5205	41	7	graph	graph	NOUN
ejpam-5205	41	8	g	g	NOUN
ejpam-5205	41	9	,	,	PUNCT
ejpam-5205	41	10	denoted	denote	VERB
ejpam-5205	41	11	by	by	ADP
ejpam-5205	41	12	γr(g	γr(g	PROPN
ejpam-5205	41	13	)	)	PUNCT
ejpam-5205	41	14	,	,	PUNCT
ejpam-5205	41	15	is	be	AUX
ejpam-5205	41	16	the	the	DET
ejpam-5205	41	17	minimum	minimum	ADJ
ejpam-5205	41	18	weight	weight	NOUN
ejpam-5205	41	19	of	of	ADP
ejpam-5205	41	20	an	an	DET
ejpam-5205	41	21	rdf	rdf	NOUN
ejpam-5205	41	22	on	on	ADP
ejpam-5205	41	23	g.	g.	PROPN
ejpam-5205	41	24	any	any	DET
ejpam-5205	41	25	rdf	rdf	VERB
ejpam-5205	41	26	f	f	NOUN
ejpam-5205	41	27	on	on	ADP
ejpam-5205	41	28	g	g	NOUN
ejpam-5205	41	29	with	with	ADP
ejpam-5205	41	30	ωg(f	ωg(f	NOUN
ejpam-5205	41	31	)	)	PUNCT
ejpam-5205	41	32	=	=	SYM
ejpam-5205	41	33	γr(g	γr(g	NOUN
ejpam-5205	41	34	)	)	PUNCT
ejpam-5205	41	35	is	be	AUX
ejpam-5205	41	36	called	call	VERB
ejpam-5205	41	37	a	a	DET
ejpam-5205	41	38	γr	γr	PROPN
ejpam-5205	41	39	-	-	NOUN
ejpam-5205	41	40	function	function	NOUN
ejpam-5205	41	41	.	.	PUNCT
ejpam-5205	42	1	if	if	SCONJ
ejpam-5205	42	2	f	f	PROPN
ejpam-5205	42	3	is	be	AUX
ejpam-5205	42	4	an	an	DET
ejpam-5205	42	5	rdf	rdf	NOUN
ejpam-5205	42	6	on	on	ADP
ejpam-5205	42	7	g	g	PROPN
ejpam-5205	42	8	and	and	CCONJ
ejpam-5205	42	9	vi	vi	NOUN
ejpam-5205	42	10	=	=	NOUN
ejpam-5205	42	11	{	{	PUNCT
ejpam-5205	42	12	v	v	NUM
ejpam-5205	42	13	∈	∈	NOUN
ejpam-5205	42	14	v	v	NOUN
ejpam-5205	42	15	(	(	PUNCT
ejpam-5205	42	16	g	g	NOUN
ejpam-5205	42	17	)	)	PUNCT
ejpam-5205	42	18	:	:	PUNCT
ejpam-5205	42	19	f(v	f(v	NOUN
ejpam-5205	42	20	)	)	PUNCT
ejpam-5205	43	1	=	=	PUNCT
ejpam-5205	43	2	i	i	PROPN
ejpam-5205	43	3	}	}	PUNCT
ejpam-5205	43	4	for	for	ADP
ejpam-5205	43	5	i	i	PROPN
ejpam-5205	43	6	∈	∈	PROPN
ejpam-5205	43	7	{	{	PUNCT
ejpam-5205	43	8	0	0	NUM
ejpam-5205	43	9	,	,	PUNCT
ejpam-5205	43	10	1	1	NUM
ejpam-5205	43	11	,	,	PUNCT
ejpam-5205	43	12	2	2	NUM
ejpam-5205	43	13	}	}	PUNCT
ejpam-5205	43	14	,	,	PUNCT
ejpam-5205	43	15	then	then	ADV
ejpam-5205	43	16	we	we	PRON
ejpam-5205	43	17	denote	denote	VERB
ejpam-5205	43	18	f	f	PROPN
ejpam-5205	43	19	by	by	ADP
ejpam-5205	43	20	f	f	PROPN
ejpam-5205	43	21	=	=	SYM
ejpam-5205	43	22	(	(	PUNCT
ejpam-5205	43	23	v0	v0	PROPN
ejpam-5205	43	24	,	,	PUNCT
ejpam-5205	43	25	v1	v1	NOUN
ejpam-5205	43	26	,	,	PUNCT
ejpam-5205	43	27	v2	v2	PROPN
ejpam-5205	43	28	)	)	PUNCT
ejpam-5205	43	29	.	.	PUNCT
ejpam-5205	44	1	in	in	ADP
ejpam-5205	44	2	this	this	DET
ejpam-5205	44	3	case	case	NOUN
ejpam-5205	44	4	,	,	PUNCT
ejpam-5205	44	5	ωg(f	ωg(f	NUM
ejpam-5205	44	6	)	)	PUNCT
ejpam-5205	44	7	=	=	PUNCT
ejpam-5205	44	8	|v1|+	|v1|+	DET
ejpam-5205	44	9	2|v2|	2|v2|	NUM
ejpam-5205	44	10	.	.	PUNCT
ejpam-5205	45	1	a	a	DET
ejpam-5205	45	2	roman	roman	ADJ
ejpam-5205	45	3	dominating	dominating	NOUN
ejpam-5205	45	4	function	function	NOUN
ejpam-5205	45	5	f	f	PROPN
ejpam-5205	45	6	=	=	SYM
ejpam-5205	45	7	(	(	PUNCT
ejpam-5205	45	8	v0	v0	PROPN
ejpam-5205	45	9	,	,	PUNCT
ejpam-5205	45	10	v1	v1	NOUN
ejpam-5205	45	11	,	,	PUNCT
ejpam-5205	45	12	v2	v2	PROPN
ejpam-5205	45	13	)	)	PUNCT
ejpam-5205	45	14	on	on	ADP
ejpam-5205	45	15	g	g	PROPN
ejpam-5205	45	16	is	be	AUX
ejpam-5205	45	17	a	a	DET
ejpam-5205	45	18	convex	convex	ADJ
ejpam-5205	45	19	roman	roman	ADJ
ejpam-5205	45	20	dominating	dominating	NOUN
ejpam-5205	45	21	function	function	NOUN
ejpam-5205	45	22	(	(	PUNCT
ejpam-5205	45	23	or	or	CCONJ
ejpam-5205	45	24	cvrdf	cvrdf	NOUN
ejpam-5205	45	25	)	)	PUNCT
ejpam-5205	45	26	if	if	SCONJ
ejpam-5205	45	27	v1	v1	NOUN
ejpam-5205	45	28	∪	∪	VERB
ejpam-5205	45	29	v2	v2	PROPN
ejpam-5205	45	30	is	be	AUX
ejpam-5205	45	31	convex	convex	NOUN
ejpam-5205	45	32	.	.	PUNCT
ejpam-5205	46	1	the	the	DET
ejpam-5205	46	2	weight	weight	NOUN
ejpam-5205	46	3	of	of	ADP
ejpam-5205	46	4	a	a	DET
ejpam-5205	46	5	convex	convex	ADJ
ejpam-5205	46	6	roman	roman	ADJ
ejpam-5205	46	7	dominating	dominating	NOUN
ejpam-5205	46	8	function	function	NOUN
ejpam-5205	46	9	f	f	PROPN
ejpam-5205	46	10	=	=	SYM
ejpam-5205	46	11	(	(	PUNCT
ejpam-5205	46	12	v0	v0	PROPN
ejpam-5205	46	13	,	,	PUNCT
ejpam-5205	46	14	v1	v1	NOUN
ejpam-5205	46	15	,	,	PUNCT
ejpam-5205	46	16	v2	v2	PROPN
ejpam-5205	46	17	)	)	PUNCT
ejpam-5205	46	18	on	on	ADP
ejpam-5205	46	19	g	g	PROPN
ejpam-5205	46	20	is	be	AUX
ejpam-5205	46	21	given	give	VERB
ejpam-5205	46	22	by	by	ADP
ejpam-5205	46	23	ωcvr	ωcvr	PROPN
ejpam-5205	46	24	g	g	PROPN
ejpam-5205	46	25	(	(	PUNCT
ejpam-5205	46	26	f	f	X
ejpam-5205	46	27	)	)	PUNCT
ejpam-5205	46	28	=	=	NOUN
ejpam-5205	46	29	|v1|	|v1|	NOUN
ejpam-5205	46	30	+	+	CCONJ
ejpam-5205	46	31	2|v2|	2|v2|	NUM
ejpam-5205	46	32	.	.	PUNCT
ejpam-5205	47	1	the	the	DET
ejpam-5205	47	2	minimum	minimum	PROPN
ejpam-5205	47	3	weight	weight	NOUN
ejpam-5205	47	4	r.	r.	PROPN
ejpam-5205	47	5	fortosa	fortosa	PROPN
ejpam-5205	47	6	,	,	PUNCT
ejpam-5205	47	7	s.	s.	PROPN
ejpam-5205	47	8	canoy	canoy	PROPN
ejpam-5205	47	9	jr	jr	PROPN
ejpam-5205	47	10	.	.	PROPN
ejpam-5205	47	11	/	/	SYM
ejpam-5205	47	12	eur	eur	PROPN
ejpam-5205	47	13	.	.	PUNCT
ejpam-5205	48	1	j.	j.	PROPN
ejpam-5205	48	2	pure	pure	PROPN
ejpam-5205	48	3	appl	appl	PROPN
ejpam-5205	48	4	.	.	PROPN
ejpam-5205	48	5	math	math	PROPN
ejpam-5205	48	6	,	,	PUNCT
ejpam-5205	48	7	17	17	NUM
ejpam-5205	48	8	(	(	PUNCT
ejpam-5205	48	9	2	2	NUM
ejpam-5205	48	10	)	)	PUNCT
ejpam-5205	48	11	(	(	PUNCT
ejpam-5205	48	12	2024	2024	NUM
ejpam-5205	48	13	)	)	PUNCT
ejpam-5205	48	14	,	,	PUNCT
ejpam-5205	48	15	1335	1335	NUM
ejpam-5205	48	16	-	-	SYM
ejpam-5205	48	17	1351	1351	NUM
ejpam-5205	48	18	1337	1337	NUM
ejpam-5205	48	19	of	of	ADP
ejpam-5205	48	20	a	a	DET
ejpam-5205	48	21	cvrdf	cvrdf	NOUN
ejpam-5205	48	22	on	on	ADP
ejpam-5205	48	23	g	g	NOUN
ejpam-5205	48	24	,	,	PUNCT
ejpam-5205	48	25	denoted	denote	VERB
ejpam-5205	48	26	by	by	ADP
ejpam-5205	48	27	γcvr(g	γcvr(g	PROPN
ejpam-5205	48	28	)	)	PUNCT
ejpam-5205	48	29	,	,	PUNCT
ejpam-5205	48	30	is	be	AUX
ejpam-5205	48	31	called	call	VERB
ejpam-5205	48	32	the	the	DET
ejpam-5205	48	33	convex	convex	ADJ
ejpam-5205	48	34	roman	roman	ADJ
ejpam-5205	48	35	domination	domination	NOUN
ejpam-5205	48	36	number	number	NOUN
ejpam-5205	48	37	of	of	ADP
ejpam-5205	48	38	g.	g.	PROPN
ejpam-5205	48	39	any	any	DET
ejpam-5205	48	40	cvrdf	cvrdf	NOUN
ejpam-5205	48	41	f	f	PROPN
ejpam-5205	48	42	on	on	ADP
ejpam-5205	48	43	g	g	PROPN
ejpam-5205	48	44	with	with	ADP
ejpam-5205	48	45	ωcvr	ωcvr	PROPN
ejpam-5205	48	46	g	g	PROPN
ejpam-5205	48	47	(	(	PUNCT
ejpam-5205	48	48	f	f	X
ejpam-5205	48	49	)	)	PUNCT
ejpam-5205	48	50	=	=	SYM
ejpam-5205	48	51	γcvr(g	γcvr(g	NOUN
ejpam-5205	48	52	)	)	PUNCT
ejpam-5205	48	53	is	be	AUX
ejpam-5205	48	54	called	call	VERB
ejpam-5205	48	55	a	a	DET
ejpam-5205	48	56	γcvr	γcvr	NOUN
ejpam-5205	48	57	-	-	PUNCT
ejpam-5205	48	58	function	function	NOUN
ejpam-5205	48	59	.	.	PUNCT
ejpam-5205	49	1	2	2	X
ejpam-5205	49	2	.	.	X
ejpam-5205	49	3	known	know	VERB
ejpam-5205	49	4	results	result	VERB
ejpam-5205	49	5	the	the	DET
ejpam-5205	49	6	following	follow	VERB
ejpam-5205	49	7	results	result	NOUN
ejpam-5205	49	8	are	be	AUX
ejpam-5205	49	9	useful	useful	ADJ
ejpam-5205	49	10	in	in	ADP
ejpam-5205	49	11	this	this	DET
ejpam-5205	49	12	study	study	NOUN
ejpam-5205	49	13	.	.	PUNCT
ejpam-5205	50	1	proposition	proposition	NOUN
ejpam-5205	50	2	1	1	NUM
ejpam-5205	50	3	.	.	PUNCT
ejpam-5205	51	1	[	[	X
ejpam-5205	51	2	10	10	NUM
ejpam-5205	51	3	]	]	PUNCT
ejpam-5205	51	4	let	let	VERB
ejpam-5205	51	5	n	n	PRON
ejpam-5205	51	6	be	be	AUX
ejpam-5205	51	7	a	a	DET
ejpam-5205	51	8	positive	positive	ADJ
ejpam-5205	51	9	integer	integer	NOUN
ejpam-5205	51	10	.	.	PUNCT
ejpam-5205	52	1	then	then	ADV
ejpam-5205	52	2	γcvr(pn	γcvr(pn	ADJ
ejpam-5205	52	3	)	)	PUNCT
ejpam-5205	52	4	=	=	PUNCT
ejpam-5205	53	1			NOUN
ejpam-5205	53	2	1	1	NUM
ejpam-5205	53	3	,	,	PUNCT
ejpam-5205	53	4	n	n	NOUN
ejpam-5205	53	5	=	=	SYM
ejpam-5205	53	6	1	1	NUM
ejpam-5205	53	7	2	2	NUM
ejpam-5205	53	8	,	,	PUNCT
ejpam-5205	53	9	n	n	NOUN
ejpam-5205	53	10	=	=	SYM
ejpam-5205	53	11	2	2	NUM
ejpam-5205	53	12	,	,	PUNCT
ejpam-5205	53	13	3	3	NUM
ejpam-5205	53	14	n	n	CCONJ
ejpam-5205	53	15	,	,	PUNCT
ejpam-5205	53	16	n	n	PRON
ejpam-5205	53	17	≥	≥	NOUN
ejpam-5205	53	18	4	4	NUM
ejpam-5205	53	19	.	.	PUNCT
ejpam-5205	53	20	proposition	proposition	NOUN
ejpam-5205	53	21	2	2	NUM
ejpam-5205	53	22	.	.	PUNCT
ejpam-5205	54	1	[	[	X
ejpam-5205	54	2	10	10	NUM
ejpam-5205	54	3	]	]	PUNCT
ejpam-5205	54	4	let	let	VERB
ejpam-5205	54	5	g	g	PRON
ejpam-5205	54	6	be	be	AUX
ejpam-5205	54	7	a	a	DET
ejpam-5205	54	8	non	non	ADJ
ejpam-5205	54	9	-	-	ADJ
ejpam-5205	54	10	trivial	trivial	ADJ
ejpam-5205	54	11	connected	connected	ADJ
ejpam-5205	54	12	graph	graph	NOUN
ejpam-5205	54	13	and	and	CCONJ
ejpam-5205	54	14	let	let	VERB
ejpam-5205	54	15	f	f	PROPN
ejpam-5205	54	16	=	=	SYM
ejpam-5205	54	17	(	(	PUNCT
ejpam-5205	54	18	v0	v0	PROPN
ejpam-5205	54	19	,	,	PUNCT
ejpam-5205	54	20	v1	v1	NOUN
ejpam-5205	54	21	,	,	PUNCT
ejpam-5205	54	22	v2	v2	PROPN
ejpam-5205	54	23	)	)	PUNCT
ejpam-5205	54	24	be	be	AUX
ejpam-5205	54	25	a	a	DET
ejpam-5205	54	26	γcvr	γcvr	NOUN
ejpam-5205	54	27	-	-	PUNCT
ejpam-5205	54	28	function	function	NOUN
ejpam-5205	54	29	on	on	ADP
ejpam-5205	54	30	g.	g.	PROPN
ejpam-5205	54	31	then	then	ADV
ejpam-5205	54	32	the	the	DET
ejpam-5205	54	33	following	follow	VERB
ejpam-5205	54	34	hold	hold	NOUN
ejpam-5205	54	35	:	:	PUNCT
ejpam-5205	54	36	(	(	PUNCT
ejpam-5205	54	37	i	i	NOUN
ejpam-5205	54	38	)	)	PUNCT
ejpam-5205	55	1	if	if	SCONJ
ejpam-5205	55	2	|v0|	|v0|	NOUN
ejpam-5205	55	3	=	=	SYM
ejpam-5205	55	4	0	0	NUM
ejpam-5205	55	5	,	,	PUNCT
ejpam-5205	55	6	then	then	ADV
ejpam-5205	55	7	|v2|	|v2|	ADV
ejpam-5205	55	8	=	=	SYM
ejpam-5205	55	9	0	0	X
ejpam-5205	55	10	.	.	PUNCT
ejpam-5205	55	11	(	(	PUNCT
ejpam-5205	55	12	ii	ii	NOUN
ejpam-5205	55	13	)	)	PUNCT
ejpam-5205	55	14	if	if	SCONJ
ejpam-5205	55	15	|v0|	|v0|	NOUN
ejpam-5205	55	16	=	=	SYM
ejpam-5205	55	17	1	1	NUM
ejpam-5205	55	18	,	,	PUNCT
ejpam-5205	55	19	then	then	ADV
ejpam-5205	55	20	|v2|	|v2|	ADV
ejpam-5205	55	21	=	=	SYM
ejpam-5205	56	1	1	1	X
ejpam-5205	56	2	.	.	PUNCT
ejpam-5205	56	3	(	(	PUNCT
ejpam-5205	56	4	iii	iii	NOUN
ejpam-5205	56	5	)	)	PUNCT
ejpam-5205	56	6	|v1|	|v1|	NOUN
ejpam-5205	56	7	=	=	SYM
ejpam-5205	56	8	0	0	PUNCT
ejpam-5205	57	1	if	if	SCONJ
ejpam-5205	57	2	and	and	CCONJ
ejpam-5205	57	3	only	only	ADV
ejpam-5205	57	4	if	if	SCONJ
ejpam-5205	57	5	v2	v2	PROPN
ejpam-5205	57	6	is	be	AUX
ejpam-5205	57	7	a	a	DET
ejpam-5205	57	8	γcon	γcon	NOUN
ejpam-5205	57	9	-	-	PUNCT
ejpam-5205	57	10	set	set	VERB
ejpam-5205	57	11	in	in	ADP
ejpam-5205	57	12	g	g	NOUN
ejpam-5205	57	13	theorem	theorem	NOUN
ejpam-5205	57	14	1	1	NUM
ejpam-5205	57	15	.	.	PUNCT
ejpam-5205	58	1	[	[	X
ejpam-5205	58	2	15	15	NUM
ejpam-5205	58	3	]	]	PUNCT
ejpam-5205	58	4	let	let	VERB
ejpam-5205	58	5	g	g	PRON
ejpam-5205	58	6	be	be	AUX
ejpam-5205	58	7	a	a	DET
ejpam-5205	58	8	connected	connected	ADJ
ejpam-5205	58	9	graph	graph	NOUN
ejpam-5205	58	10	and	and	CCONJ
ejpam-5205	58	11	km	km	VERB
ejpam-5205	58	12	the	the	DET
ejpam-5205	58	13	complete	complete	ADJ
ejpam-5205	58	14	graph	graph	NOUN
ejpam-5205	58	15	of	of	ADP
ejpam-5205	58	16	order	order	NOUN
ejpam-5205	58	17	m.	m.	NOUN
ejpam-5205	58	18	then	then	ADV
ejpam-5205	58	19	a	a	DET
ejpam-5205	58	20	proper	proper	ADJ
ejpam-5205	58	21	subset	subset	NOUN
ejpam-5205	58	22	c	c	NOUN
ejpam-5205	58	23	=	=	SYM
ejpam-5205	58	24	s1	s1	PROPN
ejpam-5205	58	25	∪	∪	X
ejpam-5205	58	26	s2	s2	NOUN
ejpam-5205	58	27	of	of	ADP
ejpam-5205	58	28	v	v	NOUN
ejpam-5205	58	29	(	(	PUNCT
ejpam-5205	58	30	g+km	g+km	PROPN
ejpam-5205	58	31	)	)	PUNCT
ejpam-5205	58	32	,	,	PUNCT
ejpam-5205	58	33	where	where	SCONJ
ejpam-5205	58	34	s1	s1	PROPN
ejpam-5205	58	35	⊆	⊆	NUM
ejpam-5205	58	36	v	v	NOUN
ejpam-5205	58	37	(	(	PUNCT
ejpam-5205	58	38	g	g	NOUN
ejpam-5205	58	39	)	)	PUNCT
ejpam-5205	58	40	and	and	CCONJ
ejpam-5205	58	41	s2	s2	VERB
ejpam-5205	58	42	⊆	⊆	NUM
ejpam-5205	58	43	v	v	NOUN
ejpam-5205	58	44	(	(	PUNCT
ejpam-5205	58	45	km	km	PROPN
ejpam-5205	58	46	)	)	PUNCT
ejpam-5205	58	47	,	,	PUNCT
ejpam-5205	58	48	is	be	AUX
ejpam-5205	58	49	convex	convex	ADJ
ejpam-5205	58	50	in	in	ADP
ejpam-5205	58	51	g+km	g+km	PROPN
ejpam-5205	58	52	if	if	SCONJ
ejpam-5205	59	1	and	and	CCONJ
ejpam-5205	59	2	only	only	ADV
ejpam-5205	59	3	if	if	SCONJ
ejpam-5205	59	4	either	either	CCONJ
ejpam-5205	59	5	(	(	PUNCT
ejpam-5205	59	6	i	i	NOUN
ejpam-5205	59	7	)	)	PUNCT
ejpam-5205	59	8	s1	s1	NOUN
ejpam-5205	59	9	induces	induce	VERB
ejpam-5205	59	10	a	a	DET
ejpam-5205	59	11	complete	complete	ADJ
ejpam-5205	59	12	subgraph	subgraph	NOUN
ejpam-5205	59	13	of	of	ADP
ejpam-5205	59	14	g	g	NOUN
ejpam-5205	59	15	,	,	PUNCT
ejpam-5205	59	16	or	or	CCONJ
ejpam-5205	59	17	(	(	PUNCT
ejpam-5205	59	18	ii	ii	NOUN
ejpam-5205	59	19	)	)	PUNCT
ejpam-5205	59	20	s1	s1	NOUN
ejpam-5205	59	21	=	=	SYM
ejpam-5205	59	22	v	v	PROPN
ejpam-5205	59	23	(	(	PUNCT
ejpam-5205	59	24	g	g	NOUN
ejpam-5205	59	25	)	)	PUNCT
ejpam-5205	59	26	\	\	PROPN
ejpam-5205	59	27	s	s	PART
ejpam-5205	59	28	and	and	CCONJ
ejpam-5205	59	29	s2	s2	PROPN
ejpam-5205	59	30	=	=	SYM
ejpam-5205	59	31	v	v	PROPN
ejpam-5205	59	32	(	(	PUNCT
ejpam-5205	59	33	km	km	PROPN
ejpam-5205	59	34	)	)	PUNCT
ejpam-5205	59	35	for	for	ADP
ejpam-5205	59	36	some	some	DET
ejpam-5205	59	37	non	non	ADJ
ejpam-5205	59	38	-	-	ADJ
ejpam-5205	59	39	connecting	connecting	ADJ
ejpam-5205	59	40	set	set	NOUN
ejpam-5205	59	41	s	s	PROPN
ejpam-5205	59	42	in	in	ADP
ejpam-5205	59	43	g.	g.	PROPN
ejpam-5205	59	44	theorem	theorem	PROPN
ejpam-5205	59	45	2	2	NUM
ejpam-5205	59	46	.	.	PUNCT
ejpam-5205	60	1	[	[	X
ejpam-5205	60	2	14	14	NUM
ejpam-5205	60	3	]	]	PUNCT
ejpam-5205	60	4	let	let	VERB
ejpam-5205	60	5	g	g	PRON
ejpam-5205	60	6	be	be	AUX
ejpam-5205	60	7	a	a	DET
ejpam-5205	60	8	connected	connected	ADJ
ejpam-5205	60	9	graph	graph	NOUN
ejpam-5205	60	10	and	and	CCONJ
ejpam-5205	60	11	km	km	VERB
ejpam-5205	60	12	the	the	DET
ejpam-5205	60	13	complete	complete	ADJ
ejpam-5205	60	14	graph	graph	NOUN
ejpam-5205	60	15	of	of	ADP
ejpam-5205	60	16	order	order	NOUN
ejpam-5205	60	17	n	n	PRON
ejpam-5205	60	18	≥	≥	NOUN
ejpam-5205	60	19	2	2	NUM
ejpam-5205	60	20	.	.	PUNCT
ejpam-5205	60	21	a	a	DET
ejpam-5205	60	22	subset	subset	NOUN
ejpam-5205	60	23	c	c	NOUN
ejpam-5205	61	1	=	=	SYM
ejpam-5205	61	2	⋃	⋃	PROPN
ejpam-5205	61	3	x∈s({x}×tx	x∈s({x}×tx	PROPN
ejpam-5205	61	4	)	)	PUNCT
ejpam-5205	61	5	,	,	PUNCT
ejpam-5205	61	6	where	where	SCONJ
ejpam-5205	61	7	s	s	VERB
ejpam-5205	61	8	⊆	⊆	NUM
ejpam-5205	61	9	v	v	NOUN
ejpam-5205	61	10	(	(	PUNCT
ejpam-5205	61	11	g	g	NOUN
ejpam-5205	61	12	)	)	PUNCT
ejpam-5205	61	13	and	and	CCONJ
ejpam-5205	61	14	tx	tx	VERB
ejpam-5205	61	15	⊆	⊆	NUM
ejpam-5205	61	16	v	v	NOUN
ejpam-5205	61	17	(	(	PUNCT
ejpam-5205	61	18	h	h	NOUN
ejpam-5205	61	19	)	)	PUNCT
ejpam-5205	61	20	,	,	PUNCT
ejpam-5205	61	21	is	be	AUX
ejpam-5205	61	22	a	a	DET
ejpam-5205	61	23	convex	convex	NOUN
ejpam-5205	61	24	set	set	VERB
ejpam-5205	61	25	in	in	ADP
ejpam-5205	61	26	g[km	g[km	PROPN
ejpam-5205	61	27	]	]	X
ejpam-5205	61	28	if	if	SCONJ
ejpam-5205	61	29	and	and	CCONJ
ejpam-5205	61	30	only	only	ADV
ejpam-5205	61	31	if	if	SCONJ
ejpam-5205	61	32	s	s	NOUN
ejpam-5205	61	33	is	be	AUX
ejpam-5205	61	34	a	a	DET
ejpam-5205	61	35	convex	convex	NOUN
ejpam-5205	61	36	set	set	VERB
ejpam-5205	61	37	in	in	ADP
ejpam-5205	61	38	g	g	PROPN
ejpam-5205	61	39	and	and	CCONJ
ejpam-5205	61	40	tx	tx	PROPN
ejpam-5205	61	41	=	=	SYM
ejpam-5205	61	42	v	v	PROPN
ejpam-5205	61	43	(	(	PUNCT
ejpam-5205	61	44	km	km	PROPN
ejpam-5205	61	45	)	)	PUNCT
ejpam-5205	61	46	for	for	ADP
ejpam-5205	61	47	each	each	DET
ejpam-5205	61	48	x	x	SYM
ejpam-5205	61	49	∈	∈	PROPN
ejpam-5205	61	50	s0	s0	NOUN
ejpam-5205	61	51	=	=	PUNCT
ejpam-5205	61	52	i(s	i(s	NOUN
ejpam-5205	61	53	)	)	PUNCT
ejpam-5205	61	54	∩	∩	PROPN
ejpam-5205	61	55	s.	s.	PROPN
ejpam-5205	61	56	theorem	theorem	VERB
ejpam-5205	61	57	3	3	NUM
ejpam-5205	61	58	.	.	PUNCT
ejpam-5205	62	1	[	[	X
ejpam-5205	62	2	15	15	NUM
ejpam-5205	62	3	]	]	PUNCT
ejpam-5205	62	4	let	let	VERB
ejpam-5205	62	5	g	g	NOUN
ejpam-5205	62	6	and	and	CCONJ
ejpam-5205	62	7	h	h	NOUN
ejpam-5205	62	8	be	be	AUX
ejpam-5205	62	9	connected	connect	VERB
ejpam-5205	62	10	non	non	ADJ
ejpam-5205	62	11	-	-	ADJ
ejpam-5205	62	12	complete	complete	ADJ
ejpam-5205	62	13	graphs	graph	NOUN
ejpam-5205	62	14	.	.	PUNCT
ejpam-5205	63	1	a	a	DET
ejpam-5205	63	2	subset	subset	NOUN
ejpam-5205	63	3	c	c	NOUN
ejpam-5205	64	1	=	=	NOUN
ejpam-5205	64	2	⋃	⋃	NOUN
ejpam-5205	64	3	x∈s({x	x∈s({x	NOUN
ejpam-5205	64	4	}	}	SYM
ejpam-5205	64	5	×	×	PROPN
ejpam-5205	64	6	tx	tx	PROPN
ejpam-5205	64	7	)	)	PUNCT
ejpam-5205	64	8	of	of	ADP
ejpam-5205	64	9	v	v	NOUN
ejpam-5205	64	10	(	(	PUNCT
ejpam-5205	64	11	g[h	g[h	PROPN
ejpam-5205	64	12	]	]	PUNCT
ejpam-5205	64	13	)	)	PUNCT
ejpam-5205	64	14	is	be	AUX
ejpam-5205	64	15	a	a	DET
ejpam-5205	64	16	convex	convex	NOUN
ejpam-5205	64	17	set	set	VERB
ejpam-5205	64	18	in	in	ADP
ejpam-5205	64	19	g[h	g[h	PROPN
ejpam-5205	64	20	]	]	PUNCT
ejpam-5205	64	21	if	if	SCONJ
ejpam-5205	64	22	and	and	CCONJ
ejpam-5205	64	23	only	only	ADV
ejpam-5205	64	24	if	if	SCONJ
ejpam-5205	64	25	s	s	NOUN
ejpam-5205	64	26	is	be	AUX
ejpam-5205	64	27	a	a	DET
ejpam-5205	64	28	clique	clique	NOUN
ejpam-5205	64	29	set	set	VERB
ejpam-5205	64	30	in	in	ADP
ejpam-5205	64	31	g	g	PROPN
ejpam-5205	64	32	and	and	CCONJ
ejpam-5205	64	33	tx	tx	PROPN
ejpam-5205	64	34	is	be	AUX
ejpam-5205	64	35	a	a	DET
ejpam-5205	64	36	clique	clique	NOUN
ejpam-5205	64	37	in	in	ADP
ejpam-5205	64	38	h	h	NOUN
ejpam-5205	64	39	for	for	ADP
ejpam-5205	64	40	each	each	PRON
ejpam-5205	64	41	x	x	SYM
ejpam-5205	64	42	∈	∈	PROPN
ejpam-5205	64	43	s.	s.	PROPN
ejpam-5205	64	44	theorem	theorem	VERB
ejpam-5205	64	45	4	4	NUM
ejpam-5205	64	46	.	.	PUNCT
ejpam-5205	65	1	[	[	X
ejpam-5205	65	2	17	17	NUM
ejpam-5205	65	3	]	]	PUNCT
ejpam-5205	65	4	let	let	VERB
ejpam-5205	65	5	g	g	PROPN
ejpam-5205	65	6	and	and	CCONJ
ejpam-5205	65	7	h	h	NOUN
ejpam-5205	65	8	be	be	AUX
ejpam-5205	65	9	connected	connect	VERB
ejpam-5205	65	10	non	non	ADJ
ejpam-5205	65	11	-	-	ADJ
ejpam-5205	65	12	complete	complete	ADJ
ejpam-5205	65	13	graphs	graph	NOUN
ejpam-5205	65	14	.	.	PUNCT
ejpam-5205	66	1	a	a	DET
ejpam-5205	66	2	subset	subset	NOUN
ejpam-5205	66	3	c	c	NOUN
ejpam-5205	66	4	=	=	PUNCT
ejpam-5205	66	5	⋃	⋃	PROPN
ejpam-5205	66	6	x∈s({x}×	x∈s({x}×	PROPN
ejpam-5205	66	7	tx	tx	PROPN
ejpam-5205	66	8	)	)	PUNCT
ejpam-5205	66	9	of	of	ADP
ejpam-5205	66	10	v	v	NOUN
ejpam-5205	66	11	(	(	PUNCT
ejpam-5205	66	12	g[h	g[h	PROPN
ejpam-5205	66	13	]	]	PUNCT
ejpam-5205	66	14	)	)	PUNCT
ejpam-5205	66	15	is	be	AUX
ejpam-5205	66	16	a	a	DET
ejpam-5205	66	17	convex	convex	NOUN
ejpam-5205	66	18	dominating	dominating	NOUN
ejpam-5205	66	19	set	set	VERB
ejpam-5205	66	20	in	in	ADP
ejpam-5205	66	21	g[h	g[h	PROPN
ejpam-5205	66	22	]	]	PUNCT
ejpam-5205	66	23	if	if	SCONJ
ejpam-5205	66	24	and	and	CCONJ
ejpam-5205	66	25	only	only	ADV
ejpam-5205	66	26	if	if	SCONJ
ejpam-5205	66	27	s	s	NOUN
ejpam-5205	66	28	is	be	AUX
ejpam-5205	66	29	a	a	DET
ejpam-5205	66	30	clique	clique	NOUN
ejpam-5205	66	31	dominating	dominating	NOUN
ejpam-5205	66	32	set	set	VERB
ejpam-5205	66	33	in	in	ADP
ejpam-5205	66	34	g	g	PROPN
ejpam-5205	66	35	and	and	CCONJ
ejpam-5205	66	36	tx	tx	PROPN
ejpam-5205	66	37	is	be	AUX
ejpam-5205	66	38	a	a	DET
ejpam-5205	66	39	clique	clique	NOUN
ejpam-5205	66	40	in	in	ADP
ejpam-5205	66	41	h	h	NOUN
ejpam-5205	66	42	for	for	ADP
ejpam-5205	66	43	each	each	PRON
ejpam-5205	66	44	x	x	SYM
ejpam-5205	66	45	∈	∈	PROPN
ejpam-5205	66	46	s.	s.	PROPN
ejpam-5205	66	47	theorem	theorem	VERB
ejpam-5205	66	48	5	5	NUM
ejpam-5205	66	49	.	.	PUNCT
ejpam-5205	67	1	[	[	X
ejpam-5205	67	2	15	15	NUM
ejpam-5205	67	3	]	]	PUNCT
ejpam-5205	67	4	let	let	VERB
ejpam-5205	67	5	g	g	NOUN
ejpam-5205	67	6	and	and	CCONJ
ejpam-5205	67	7	h	h	NOUN
ejpam-5205	67	8	be	be	VERB
ejpam-5205	67	9	two	two	NUM
ejpam-5205	67	10	connected	connected	ADJ
ejpam-5205	67	11	graphs	graph	NOUN
ejpam-5205	67	12	.	.	PUNCT
ejpam-5205	68	1	a	a	DET
ejpam-5205	68	2	set	set	NOUN
ejpam-5205	68	3	c	c	PROPN
ejpam-5205	68	4	∈	∈	PROPN
ejpam-5205	68	5	v	v	NOUN
ejpam-5205	68	6	(	(	PUNCT
ejpam-5205	68	7	g	g	NOUN
ejpam-5205	68	8	□	□	NOUN
ejpam-5205	68	9	h	h	NOUN
ejpam-5205	68	10	)	)	PUNCT
ejpam-5205	68	11	is	be	AUX
ejpam-5205	68	12	a	a	DET
ejpam-5205	68	13	convex	convex	NOUN
ejpam-5205	68	14	set	set	VERB
ejpam-5205	68	15	in	in	ADP
ejpam-5205	68	16	g	g	PROPN
ejpam-5205	68	17	□	□	PROPN
ejpam-5205	68	18	h	h	NOUN
ejpam-5205	68	19	if	if	SCONJ
ejpam-5205	69	1	and	and	CCONJ
ejpam-5205	69	2	only	only	ADV
ejpam-5205	69	3	if	if	SCONJ
ejpam-5205	69	4	c	c	NOUN
ejpam-5205	69	5	=	=	VERB
ejpam-5205	70	1	cg	cg	NOUN
ejpam-5205	70	2	×	×	NOUN
ejpam-5205	70	3	ch	ch	NOUN
ejpam-5205	70	4	,	,	PUNCT
ejpam-5205	70	5	where	where	SCONJ
ejpam-5205	70	6	cg	cg	NOUN
ejpam-5205	70	7	and	and	CCONJ
ejpam-5205	70	8	ch	ch	PROPN
ejpam-5205	70	9	are	be	AUX
ejpam-5205	70	10	convex	convex	NOUN
ejpam-5205	70	11	sets	set	NOUN
ejpam-5205	70	12	in	in	ADP
ejpam-5205	70	13	g	g	PROPN
ejpam-5205	70	14	and	and	CCONJ
ejpam-5205	70	15	h	h	NOUN
ejpam-5205	70	16	respectively	respectively	ADV
ejpam-5205	70	17	.	.	PUNCT
ejpam-5205	71	1	theorem	theorem	VERB
ejpam-5205	71	2	6	6	NUM
ejpam-5205	71	3	.	.	PUNCT
ejpam-5205	72	1	[	[	X
ejpam-5205	72	2	17	17	NUM
ejpam-5205	72	3	]	]	PUNCT
ejpam-5205	72	4	let	let	VERB
ejpam-5205	72	5	g	g	PROPN
ejpam-5205	72	6	and	and	CCONJ
ejpam-5205	72	7	h	h	NOUN
ejpam-5205	72	8	be	be	AUX
ejpam-5205	72	9	connected	connect	VERB
ejpam-5205	72	10	graphs	graph	NOUN
ejpam-5205	72	11	.	.	PUNCT
ejpam-5205	73	1	a	a	DET
ejpam-5205	73	2	subset	subset	NOUN
ejpam-5205	73	3	c	c	NOUN
ejpam-5205	73	4	of	of	ADP
ejpam-5205	73	5	v	v	NOUN
ejpam-5205	73	6	(	(	PUNCT
ejpam-5205	73	7	g	g	NOUN
ejpam-5205	73	8	□	□	NOUN
ejpam-5205	73	9	h	h	NOUN
ejpam-5205	73	10	)	)	PUNCT
ejpam-5205	73	11	is	be	AUX
ejpam-5205	73	12	a	a	DET
ejpam-5205	73	13	convex	convex	NOUN
ejpam-5205	73	14	dominating	dominating	NOUN
ejpam-5205	73	15	set	set	VERB
ejpam-5205	73	16	in	in	ADP
ejpam-5205	73	17	g	g	PROPN
ejpam-5205	73	18	□	□	PROPN
ejpam-5205	73	19	h	h	NOUN
ejpam-5205	73	20	if	if	SCONJ
ejpam-5205	74	1	and	and	CCONJ
ejpam-5205	74	2	only	only	ADV
ejpam-5205	74	3	if	if	SCONJ
ejpam-5205	74	4	c	c	NOUN
ejpam-5205	74	5	=	=	SYM
ejpam-5205	74	6	c1	c1	PROPN
ejpam-5205	74	7	×	×	PROPN
ejpam-5205	74	8	c2	c2	PROPN
ejpam-5205	74	9	and	and	CCONJ
ejpam-5205	74	10	one	one	NUM
ejpam-5205	74	11	of	of	ADP
ejpam-5205	74	12	the	the	DET
ejpam-5205	74	13	following	follow	VERB
ejpam-5205	74	14	conditions	condition	NOUN
ejpam-5205	74	15	holds	hold	VERB
ejpam-5205	74	16	:	:	PUNCT
ejpam-5205	74	17	r.	r.	PROPN
ejpam-5205	74	18	fortosa	fortosa	PROPN
ejpam-5205	74	19	,	,	PUNCT
ejpam-5205	74	20	s.	s.	PROPN
ejpam-5205	74	21	canoy	canoy	PROPN
ejpam-5205	74	22	jr	jr	PROPN
ejpam-5205	74	23	.	.	PROPN
ejpam-5205	74	24	/	/	SYM
ejpam-5205	74	25	eur	eur	PROPN
ejpam-5205	74	26	.	.	PUNCT
ejpam-5205	75	1	j.	j.	PROPN
ejpam-5205	75	2	pure	pure	PROPN
ejpam-5205	75	3	appl	appl	PROPN
ejpam-5205	75	4	.	.	PROPN
ejpam-5205	75	5	math	math	PROPN
ejpam-5205	75	6	,	,	PUNCT
ejpam-5205	75	7	17	17	NUM
ejpam-5205	75	8	(	(	PUNCT
ejpam-5205	75	9	2	2	NUM
ejpam-5205	75	10	)	)	PUNCT
ejpam-5205	75	11	(	(	PUNCT
ejpam-5205	75	12	2024	2024	NUM
ejpam-5205	75	13	)	)	PUNCT
ejpam-5205	75	14	,	,	PUNCT
ejpam-5205	75	15	1335	1335	NUM
ejpam-5205	75	16	-	-	SYM
ejpam-5205	75	17	1351	1351	NUM
ejpam-5205	75	18	1338	1338	NUM
ejpam-5205	75	19	(	(	PUNCT
ejpam-5205	75	20	i	i	NOUN
ejpam-5205	75	21	)	)	PUNCT
ejpam-5205	75	22	c1	c1	PROPN
ejpam-5205	75	23	is	be	AUX
ejpam-5205	75	24	a	a	DET
ejpam-5205	75	25	convex	convex	NOUN
ejpam-5205	75	26	dominating	dominating	NOUN
ejpam-5205	75	27	set	set	VERB
ejpam-5205	75	28	in	in	ADP
ejpam-5205	75	29	g	g	PROPN
ejpam-5205	75	30	and	and	CCONJ
ejpam-5205	75	31	c2	c2	PROPN
ejpam-5205	75	32	=	=	SYM
ejpam-5205	75	33	v	v	PROPN
ejpam-5205	75	34	(	(	PUNCT
ejpam-5205	75	35	h	h	NOUN
ejpam-5205	75	36	)	)	PUNCT
ejpam-5205	75	37	,	,	PUNCT
ejpam-5205	75	38	or	or	CCONJ
ejpam-5205	75	39	(	(	PUNCT
ejpam-5205	75	40	ii	ii	NOUN
ejpam-5205	75	41	)	)	PUNCT
ejpam-5205	75	42	c2	c2	PROPN
ejpam-5205	75	43	is	be	AUX
ejpam-5205	75	44	a	a	DET
ejpam-5205	75	45	convex	convex	NOUN
ejpam-5205	75	46	dominating	dominating	NOUN
ejpam-5205	75	47	set	set	VERB
ejpam-5205	75	48	in	in	ADP
ejpam-5205	75	49	h	h	NOUN
ejpam-5205	75	50	and	and	CCONJ
ejpam-5205	75	51	c1	c1	PROPN
ejpam-5205	75	52	=	=	PROPN
ejpam-5205	75	53	v	v	PROPN
ejpam-5205	75	54	(	(	PUNCT
ejpam-5205	75	55	g	g	NOUN
ejpam-5205	75	56	)	)	PUNCT
ejpam-5205	75	57	.	.	PUNCT
ejpam-5205	76	1	theorem	theorem	VERB
ejpam-5205	76	2	7	7	NUM
ejpam-5205	76	3	.	.	PUNCT
ejpam-5205	77	1	[	[	X
ejpam-5205	77	2	10	10	NUM
ejpam-5205	77	3	]	]	PUNCT
ejpam-5205	77	4	let	let	VERB
ejpam-5205	77	5	g	g	PRON
ejpam-5205	77	6	be	be	AUX
ejpam-5205	77	7	a	a	DET
ejpam-5205	77	8	connected	connected	ADJ
ejpam-5205	77	9	graph	graph	NOUN
ejpam-5205	77	10	on	on	ADP
ejpam-5205	77	11	n	n	DET
ejpam-5205	77	12	vertices	vertex	NOUN
ejpam-5205	77	13	.	.	PUNCT
ejpam-5205	78	1	then	then	ADV
ejpam-5205	78	2	each	each	PRON
ejpam-5205	78	3	of	of	ADP
ejpam-5205	78	4	the	the	DET
ejpam-5205	78	5	the	the	DET
ejpam-5205	78	6	following	following	ADJ
ejpam-5205	78	7	statements	statement	NOUN
ejpam-5205	78	8	holds	hold	VERB
ejpam-5205	78	9	.	.	PUNCT
ejpam-5205	79	1	(	(	PUNCT
ejpam-5205	79	2	i	i	NOUN
ejpam-5205	79	3	)	)	PUNCT
ejpam-5205	79	4	γcvr(g	γcvr(g	PROPN
ejpam-5205	79	5	)	)	PUNCT
ejpam-5205	79	6	=	=	SYM
ejpam-5205	79	7	1	1	NUM
ejpam-5205	79	8	if	if	SCONJ
ejpam-5205	79	9	and	and	CCONJ
ejpam-5205	79	10	only	only	ADV
ejpam-5205	79	11	if	if	SCONJ
ejpam-5205	79	12	g	g	PROPN
ejpam-5205	79	13	=	=	SYM
ejpam-5205	79	14	k1	k1	PROPN
ejpam-5205	79	15	(	(	PUNCT
ejpam-5205	79	16	ii	ii	NOUN
ejpam-5205	79	17	)	)	PUNCT
ejpam-5205	79	18	γcvr(g	γcvr(g	NOUN
ejpam-5205	79	19	)	)	PUNCT
ejpam-5205	79	20	=	=	SYM
ejpam-5205	79	21	2	2	NUM
ejpam-5205	79	22	if	if	SCONJ
ejpam-5205	79	23	and	and	CCONJ
ejpam-5205	79	24	only	only	ADV
ejpam-5205	79	25	if	if	SCONJ
ejpam-5205	79	26	g	g	PROPN
ejpam-5205	79	27	=	=	SYM
ejpam-5205	79	28	k2	k2	PROPN
ejpam-5205	79	29	or	or	CCONJ
ejpam-5205	79	30	g	g	NOUN
ejpam-5205	79	31	=	=	PROPN
ejpam-5205	79	32	k1	k1	PROPN
ejpam-5205	80	1	+	+	NOUN
ejpam-5205	80	2	h	h	NOUN
ejpam-5205	80	3	for	for	ADP
ejpam-5205	80	4	some	some	DET
ejpam-5205	80	5	graph	graph	NOUN
ejpam-5205	80	6	h	h	NOUN
ejpam-5205	80	7	corollary	corollary	ADJ
ejpam-5205	81	1	1	1	NUM
ejpam-5205	81	2	.	.	PUNCT
ejpam-5205	82	1	[	[	X
ejpam-5205	82	2	10	10	NUM
ejpam-5205	82	3	]	]	PUNCT
ejpam-5205	82	4	for	for	ADP
ejpam-5205	82	5	any	any	DET
ejpam-5205	82	6	connected	connected	ADJ
ejpam-5205	82	7	graph	graph	NOUN
ejpam-5205	82	8	g	g	NOUN
ejpam-5205	82	9	of	of	ADP
ejpam-5205	82	10	order	order	NOUN
ejpam-5205	82	11	n	n	CCONJ
ejpam-5205	82	12	,	,	PUNCT
ejpam-5205	82	13	γcvr(g	γcvr(g	PROPN
ejpam-5205	82	14	)	)	PUNCT
ejpam-5205	82	15	=	=	SYM
ejpam-5205	82	16	2	2	NUM
ejpam-5205	83	1	if	if	SCONJ
ejpam-5205	83	2	and	and	CCONJ
ejpam-5205	83	3	only	only	ADV
ejpam-5205	83	4	if	if	SCONJ
ejpam-5205	83	5	g	g	PROPN
ejpam-5205	83	6	̸=	̸=	PROPN
ejpam-5205	83	7	k1	k1	PROPN
ejpam-5205	83	8	and	and	CCONJ
ejpam-5205	83	9	γ(g	γ(g	PROPN
ejpam-5205	83	10	)	)	PUNCT
ejpam-5205	83	11	=	=	SYM
ejpam-5205	83	12	1	1	X
ejpam-5205	83	13	.	.	X
ejpam-5205	83	14	proposition	proposition	NOUN
ejpam-5205	83	15	3	3	NUM
ejpam-5205	83	16	.	.	PUNCT
ejpam-5205	84	1	[	[	X
ejpam-5205	84	2	10	10	NUM
ejpam-5205	84	3	]	]	PUNCT
ejpam-5205	84	4	there	there	PRON
ejpam-5205	84	5	exists	exist	VERB
ejpam-5205	84	6	no	no	DET
ejpam-5205	84	7	connected	connected	ADJ
ejpam-5205	84	8	graph	graph	NOUN
ejpam-5205	84	9	g	g	NOUN
ejpam-5205	84	10	with	with	ADP
ejpam-5205	84	11	γcvr(g	γcvr(g	NOUN
ejpam-5205	84	12	)	)	PUNCT
ejpam-5205	84	13	=	=	SYM
ejpam-5205	84	14	3	3	X
ejpam-5205	84	15	.	.	X
ejpam-5205	84	16	proposition	proposition	NOUN
ejpam-5205	84	17	4	4	NUM
ejpam-5205	84	18	.	.	PUNCT
ejpam-5205	85	1	[	[	X
ejpam-5205	85	2	10	10	NUM
ejpam-5205	85	3	]	]	PUNCT
ejpam-5205	85	4	for	for	ADP
ejpam-5205	85	5	any	any	DET
ejpam-5205	85	6	connected	connected	ADJ
ejpam-5205	85	7	graph	graph	NOUN
ejpam-5205	85	8	g	g	NOUN
ejpam-5205	85	9	of	of	ADP
ejpam-5205	85	10	order	order	NOUN
ejpam-5205	85	11	n	n	CCONJ
ejpam-5205	85	12	,	,	PUNCT
ejpam-5205	85	13	1	1	NUM
ejpam-5205	85	14	≤	≤	NUM
ejpam-5205	85	15	γcon(g	γcon(g	PROPN
ejpam-5205	85	16	)	)	PUNCT
ejpam-5205	85	17	≤	≤	NOUN
ejpam-5205	85	18	γcvr(g	γcvr(g	PROPN
ejpam-5205	85	19	)	)	PUNCT
ejpam-5205	85	20	≤	≤	NUM
ejpam-5205	85	21	min{n	min{n	NOUN
ejpam-5205	85	22	,	,	PUNCT
ejpam-5205	85	23	2γcon(g	2γcon(g	NUM
ejpam-5205	85	24	)	)	PUNCT
ejpam-5205	85	25	}	}	PUNCT
ejpam-5205	85	26	.	.	PUNCT
ejpam-5205	86	1	3	3	X
ejpam-5205	86	2	.	.	X
ejpam-5205	86	3	results	result	NOUN
ejpam-5205	86	4	let	let	VERB
ejpam-5205	86	5	g	g	NOUN
ejpam-5205	86	6	and	and	CCONJ
ejpam-5205	86	7	h	h	NOUN
ejpam-5205	86	8	be	be	AUX
ejpam-5205	86	9	connected	connect	VERB
ejpam-5205	86	10	graphs	graph	NOUN
ejpam-5205	86	11	.	.	PUNCT
ejpam-5205	87	1	the	the	DET
ejpam-5205	87	2	corona	corona	NOUN
ejpam-5205	87	3	of	of	ADP
ejpam-5205	87	4	g	g	PROPN
ejpam-5205	87	5	and	and	CCONJ
ejpam-5205	87	6	h	h	NOUN
ejpam-5205	87	7	is	be	AUX
ejpam-5205	87	8	the	the	DET
ejpam-5205	87	9	graph	graph	NOUN
ejpam-5205	87	10	g	g	PROPN
ejpam-5205	87	11	◦	◦	NOUN
ejpam-5205	87	12	h	h	NOUN
ejpam-5205	87	13	obtained	obtain	VERB
ejpam-5205	87	14	by	by	ADP
ejpam-5205	87	15	taking	take	VERB
ejpam-5205	87	16	one	one	NUM
ejpam-5205	87	17	copy	copy	NOUN
ejpam-5205	87	18	of	of	ADP
ejpam-5205	87	19	g	g	PROPN
ejpam-5205	87	20	and	and	CCONJ
ejpam-5205	87	21	|v	|v	PROPN
ejpam-5205	87	22	(	(	PUNCT
ejpam-5205	87	23	g)|	g)|	NOUN
ejpam-5205	87	24	copies	copy	NOUN
ejpam-5205	87	25	of	of	ADP
ejpam-5205	87	26	h	h	NOUN
ejpam-5205	87	27	,	,	PUNCT
ejpam-5205	87	28	and	and	CCONJ
ejpam-5205	87	29	then	then	ADV
ejpam-5205	87	30	joining	join	VERB
ejpam-5205	87	31	the	the	DET
ejpam-5205	87	32	ith	ith	PROPN
ejpam-5205	87	33	vertex	vertex	NOUN
ejpam-5205	87	34	of	of	ADP
ejpam-5205	87	35	g	g	NOUN
ejpam-5205	87	36	to	to	ADP
ejpam-5205	87	37	every	every	DET
ejpam-5205	87	38	vertices	vertex	NOUN
ejpam-5205	87	39	of	of	ADP
ejpam-5205	87	40	the	the	DET
ejpam-5205	87	41	ith	ith	PROPN
ejpam-5205	87	42	copy	copy	NOUN
ejpam-5205	87	43	of	of	ADP
ejpam-5205	87	44	h.	h.	PROPN
ejpam-5205	87	45	for	for	ADP
ejpam-5205	87	46	convenience	convenience	NOUN
ejpam-5205	87	47	,	,	PUNCT
ejpam-5205	87	48	we	we	PRON
ejpam-5205	87	49	write	write	VERB
ejpam-5205	87	50	hv	hv	PROPN
ejpam-5205	87	51	to	to	PART
ejpam-5205	87	52	denote	denote	VERB
ejpam-5205	87	53	the	the	DET
ejpam-5205	87	54	copy	copy	NOUN
ejpam-5205	87	55	of	of	ADP
ejpam-5205	87	56	h	h	NOUN
ejpam-5205	87	57	joined	join	VERB
ejpam-5205	87	58	to	to	ADP
ejpam-5205	87	59	v	v	VERB
ejpam-5205	87	60	and	and	CCONJ
ejpam-5205	87	61	write	write	VERB
ejpam-5205	87	62	hv	hv	PROPN
ejpam-5205	88	1	+	+	PROPN
ejpam-5205	88	2	v	v	NOUN
ejpam-5205	88	3	=	=	SYM
ejpam-5205	88	4	hv	hv	PROPN
ejpam-5205	88	5	+	+	PROPN
ejpam-5205	88	6	⟨v⟩.	⟨v⟩.	PROPN
ejpam-5205	88	7	let	let	VERB
ejpam-5205	88	8	g	g	PRON
ejpam-5205	88	9	be	be	AUX
ejpam-5205	88	10	a	a	DET
ejpam-5205	88	11	graph	graph	NOUN
ejpam-5205	88	12	.	.	PUNCT
ejpam-5205	89	1	a	a	DET
ejpam-5205	89	2	non	non	ADJ
ejpam-5205	89	3	-	-	ADJ
ejpam-5205	89	4	empty	empty	ADJ
ejpam-5205	89	5	subset	subset	NOUN
ejpam-5205	89	6	s	s	NOUN
ejpam-5205	89	7	of	of	ADP
ejpam-5205	89	8	v	v	NOUN
ejpam-5205	89	9	(	(	PUNCT
ejpam-5205	89	10	g	g	NOUN
ejpam-5205	89	11	)	)	PUNCT
ejpam-5205	89	12	is	be	AUX
ejpam-5205	89	13	a	a	DET
ejpam-5205	89	14	non	non	ADJ
ejpam-5205	89	15	-	-	ADJ
ejpam-5205	89	16	connecting	connecting	ADJ
ejpam-5205	89	17	set	set	NOUN
ejpam-5205	89	18	in	in	ADP
ejpam-5205	89	19	g	g	PROPN
ejpam-5205	89	20	if	if	SCONJ
ejpam-5205	89	21	it	it	PRON
ejpam-5205	89	22	satisfies	satisfy	VERB
ejpam-5205	89	23	the	the	DET
ejpam-5205	89	24	following	follow	VERB
ejpam-5205	89	25	condition	condition	NOUN
ejpam-5205	89	26	:	:	PUNCT
ejpam-5205	89	27	for	for	SCONJ
ejpam-5205	89	28	every	every	DET
ejpam-5205	89	29	pair	pair	NOUN
ejpam-5205	89	30	of	of	ADP
ejpam-5205	89	31	vertices	vertex	NOUN
ejpam-5205	89	32	u	u	NOUN
ejpam-5205	89	33	,	,	PUNCT
ejpam-5205	89	34	v	v	NOUN
ejpam-5205	89	35	∈	∈	PROPN
ejpam-5205	89	36	v	v	NOUN
ejpam-5205	89	37	(	(	PUNCT
ejpam-5205	89	38	g	g	NOUN
ejpam-5205	89	39	)	)	PUNCT
ejpam-5205	89	40	\	\	PROPN
ejpam-5205	90	1	s	s	PART
ejpam-5205	90	2	with	with	ADP
ejpam-5205	90	3	dg(u	dg(u	ADJ
ejpam-5205	90	4	,	,	PUNCT
ejpam-5205	90	5	v	v	NOUN
ejpam-5205	90	6	)	)	PUNCT
ejpam-5205	90	7	=	=	SYM
ejpam-5205	91	1	2	2	NUM
ejpam-5205	91	2	,	,	PUNCT
ejpam-5205	91	3	we	we	PRON
ejpam-5205	91	4	have	have	VERB
ejpam-5205	91	5	ng(u	ng(u	NOUN
ejpam-5205	91	6	)	)	PUNCT
ejpam-5205	91	7	∩	∩	NOUN
ejpam-5205	91	8	ng(v	ng(v	NUM
ejpam-5205	91	9	)	)	PUNCT
ejpam-5205	91	10	∩	∩	NOUN
ejpam-5205	91	11	s	s	PART
ejpam-5205	91	12	=	=	PUNCT
ejpam-5205	91	13	∅.	∅.	VERB
ejpam-5205	91	14	a	a	DET
ejpam-5205	91	15	non	non	ADJ
ejpam-5205	91	16	-	-	ADJ
ejpam-5205	91	17	connecting	connecting	ADJ
ejpam-5205	91	18	set	set	NOUN
ejpam-5205	91	19	with	with	ADP
ejpam-5205	91	20	minimum	minimum	ADJ
ejpam-5205	91	21	cardinality	cardinality	NOUN
ejpam-5205	91	22	is	be	AUX
ejpam-5205	91	23	called	call	VERB
ejpam-5205	91	24	a	a	DET
ejpam-5205	91	25	minimum	minimum	ADJ
ejpam-5205	91	26	non	non	ADJ
ejpam-5205	91	27	-	-	ADJ
ejpam-5205	91	28	connecting	connecting	ADJ
ejpam-5205	91	29	set	set	NOUN
ejpam-5205	91	30	.	.	PUNCT
ejpam-5205	92	1	let	let	VERB
ejpam-5205	92	2	f	f	PROPN
ejpam-5205	92	3	=	=	SYM
ejpam-5205	92	4	(	(	PUNCT
ejpam-5205	92	5	v0	v0	PROPN
ejpam-5205	92	6	,	,	PUNCT
ejpam-5205	92	7	v1	v1	NOUN
ejpam-5205	92	8	,	,	PUNCT
ejpam-5205	92	9	v2	v2	PROPN
ejpam-5205	92	10	)	)	PUNCT
ejpam-5205	92	11	be	be	AUX
ejpam-5205	92	12	a	a	DET
ejpam-5205	92	13	cvrdf	cvrdf	NOUN
ejpam-5205	92	14	on	on	ADP
ejpam-5205	92	15	g	g	PROPN
ejpam-5205	92	16	◦	◦	NOUN
ejpam-5205	92	17	h.	h.	NOUN
ejpam-5205	92	18	for	for	ADP
ejpam-5205	92	19	each	each	DET
ejpam-5205	92	20	v	v	NUM
ejpam-5205	92	21	∈	∈	PROPN
ejpam-5205	92	22	v	v	NOUN
ejpam-5205	92	23	(	(	PUNCT
ejpam-5205	92	24	g	g	NOUN
ejpam-5205	92	25	)	)	PUNCT
ejpam-5205	92	26	,	,	PUNCT
ejpam-5205	92	27	let	let	VERB
ejpam-5205	92	28	sv	sv	INTJ
ejpam-5205	92	29	k	k	NOUN
ejpam-5205	92	30	=	=	PUNCT
ejpam-5205	92	31	vk	vk	PROPN
ejpam-5205	92	32	∩	∩	X
ejpam-5205	92	33	v	v	X
ejpam-5205	92	34	(	(	PUNCT
ejpam-5205	92	35	hv	hv	PROPN
ejpam-5205	92	36	)	)	PUNCT
ejpam-5205	92	37	where	where	SCONJ
ejpam-5205	92	38	k	k	PROPN
ejpam-5205	92	39	=	=	SYM
ejpam-5205	92	40	0	0	NUM
ejpam-5205	92	41	,	,	PUNCT
ejpam-5205	92	42	1	1	NUM
ejpam-5205	92	43	,	,	PUNCT
ejpam-5205	92	44	2	2	NUM
ejpam-5205	92	45	.	.	X
ejpam-5205	92	46	theorem	theorem	NOUN
ejpam-5205	92	47	8	8	NUM
ejpam-5205	92	48	.	.	PUNCT
ejpam-5205	93	1	let	let	VERB
ejpam-5205	93	2	g	g	PRON
ejpam-5205	93	3	be	be	AUX
ejpam-5205	93	4	a	a	DET
ejpam-5205	93	5	non	non	ADJ
ejpam-5205	93	6	-	-	ADJ
ejpam-5205	93	7	trivial	trivial	ADJ
ejpam-5205	93	8	connected	connected	ADJ
ejpam-5205	93	9	graph	graph	NOUN
ejpam-5205	93	10	and	and	CCONJ
ejpam-5205	93	11	let	let	VERB
ejpam-5205	93	12	h	h	NOUN
ejpam-5205	93	13	be	be	AUX
ejpam-5205	93	14	any	any	DET
ejpam-5205	93	15	graphs	graph	NOUN
ejpam-5205	93	16	.	.	PUNCT
ejpam-5205	94	1	then	then	ADV
ejpam-5205	94	2	f	f	X
ejpam-5205	94	3	=	=	SYM
ejpam-5205	94	4	(	(	PUNCT
ejpam-5205	94	5	v0	v0	PROPN
ejpam-5205	94	6	,	,	PUNCT
ejpam-5205	94	7	v1	v1	NOUN
ejpam-5205	94	8	,	,	PUNCT
ejpam-5205	94	9	v2	v2	PROPN
ejpam-5205	94	10	)	)	PUNCT
ejpam-5205	94	11	is	be	AUX
ejpam-5205	94	12	a	a	DET
ejpam-5205	94	13	cvrdf	cvrdf	NOUN
ejpam-5205	94	14	on	on	ADP
ejpam-5205	94	15	g	g	PROPN
ejpam-5205	94	16	◦	◦	NOUN
ejpam-5205	94	17	h	h	NOUN
ejpam-5205	94	18	if	if	SCONJ
ejpam-5205	95	1	and	and	CCONJ
ejpam-5205	95	2	only	only	ADV
ejpam-5205	95	3	if	if	SCONJ
ejpam-5205	95	4	each	each	PRON
ejpam-5205	95	5	of	of	ADP
ejpam-5205	95	6	the	the	DET
ejpam-5205	95	7	following	follow	VERB
ejpam-5205	95	8	conditions	condition	NOUN
ejpam-5205	95	9	hold	hold	VERB
ejpam-5205	95	10	:	:	PUNCT
ejpam-5205	95	11	(	(	PUNCT
ejpam-5205	95	12	i	i	NOUN
ejpam-5205	95	13	)	)	PUNCT
ejpam-5205	95	14	v0	v0	PROPN
ejpam-5205	95	15	∩	∩	ADJ
ejpam-5205	95	16	v	v	X
ejpam-5205	95	17	(	(	PUNCT
ejpam-5205	95	18	g	g	NOUN
ejpam-5205	95	19	)	)	PUNCT
ejpam-5205	95	20	=	=	NOUN
ejpam-5205	95	21	∅	∅	NOUN
ejpam-5205	95	22	(	(	PUNCT
ejpam-5205	95	23	ii	ii	NOUN
ejpam-5205	95	24	)	)	PUNCT
ejpam-5205	95	25	for	for	ADP
ejpam-5205	95	26	each	each	DET
ejpam-5205	95	27	v	v	NUM
ejpam-5205	95	28	∈	∈	PROPN
ejpam-5205	95	29	v2	v2	NOUN
ejpam-5205	95	30	∩	∩	ADJ
ejpam-5205	95	31	v	v	NOUN
ejpam-5205	95	32	(	(	PUNCT
ejpam-5205	95	33	g	g	NOUN
ejpam-5205	95	34	)	)	PUNCT
ejpam-5205	95	35	,	,	PUNCT
ejpam-5205	95	36	sv	sv	PROPN
ejpam-5205	95	37	1	1	NUM
ejpam-5205	95	38	∪	∪	X
ejpam-5205	95	39	sv	sv	NOUN
ejpam-5205	95	40	2	2	NUM
ejpam-5205	95	41	induces	induce	VERB
ejpam-5205	95	42	a	a	DET
ejpam-5205	95	43	complete	complete	ADJ
ejpam-5205	95	44	subgraph	subgraph	NOUN
ejpam-5205	95	45	of	of	ADP
ejpam-5205	95	46	hv	hv	PROPN
ejpam-5205	95	47	or	or	CCONJ
ejpam-5205	95	48	v	v	PROPN
ejpam-5205	95	49	(	(	PUNCT
ejpam-5205	95	50	hv	hv	PROPN
ejpam-5205	95	51	)	)	PUNCT
ejpam-5205	95	52	\	\	PUNCT
ejpam-5205	96	1	(	(	PUNCT
ejpam-5205	96	2	sv	sv	NOUN
ejpam-5205	96	3	1	1	NUM
ejpam-5205	96	4	∪	∪	NOUN
ejpam-5205	96	5	sv	sv	NOUN
ejpam-5205	96	6	2	2	NUM
ejpam-5205	96	7	)	)	PUNCT
ejpam-5205	96	8	is	be	AUX
ejpam-5205	96	9	a	a	DET
ejpam-5205	96	10	non	non	ADJ
ejpam-5205	96	11	-	-	ADJ
ejpam-5205	96	12	connecting	connecting	ADJ
ejpam-5205	96	13	set	set	NOUN
ejpam-5205	96	14	in	in	ADP
ejpam-5205	96	15	hv	hv	PROPN
ejpam-5205	96	16	.	.	PUNCT
ejpam-5205	97	1	(	(	PUNCT
ejpam-5205	97	2	iii	iii	NOUN
ejpam-5205	97	3	)	)	PUNCT
ejpam-5205	97	4	for	for	ADP
ejpam-5205	97	5	each	each	DET
ejpam-5205	97	6	v	v	X
ejpam-5205	97	7	∈	∈	PROPN
ejpam-5205	97	8	v1∩v	v1∩v	NOUN
ejpam-5205	97	9	(	(	PUNCT
ejpam-5205	97	10	g	g	NOUN
ejpam-5205	97	11	)	)	PUNCT
ejpam-5205	97	12	such	such	ADJ
ejpam-5205	97	13	that	that	SCONJ
ejpam-5205	97	14	sv	sv	PROPN
ejpam-5205	97	15	1	1	NUM
ejpam-5205	97	16	̸=	̸=	PROPN
ejpam-5205	97	17	v	v	PROPN
ejpam-5205	97	18	(	(	PUNCT
ejpam-5205	97	19	hv	hv	PROPN
ejpam-5205	97	20	)	)	PUNCT
ejpam-5205	97	21	,	,	PUNCT
ejpam-5205	97	22	sv	sv	PROPN
ejpam-5205	97	23	2	2	NUM
ejpam-5205	97	24	̸=	̸=	PROPN
ejpam-5205	97	25	∅	∅	NOUN
ejpam-5205	97	26	,	,	PUNCT
ejpam-5205	97	27	sv	sv	PROPN
ejpam-5205	97	28	0	0	NUM
ejpam-5205	97	29	⊆	⊆	NUM
ejpam-5205	97	30	nhv(sv	nhv(sv	NOUN
ejpam-5205	97	31	2	2	NUM
ejpam-5205	97	32	)	)	PUNCT
ejpam-5205	97	33	,	,	PUNCT
ejpam-5205	97	34	and	and	CCONJ
ejpam-5205	97	35	sv	sv	PROPN
ejpam-5205	97	36	1	1	NUM
ejpam-5205	97	37	∪sv	∪sv	NOUN
ejpam-5205	97	38	2	2	NUM
ejpam-5205	97	39	induces	induce	VERB
ejpam-5205	97	40	a	a	DET
ejpam-5205	97	41	complete	complete	ADJ
ejpam-5205	97	42	subgraph	subgraph	NOUN
ejpam-5205	97	43	of	of	ADP
ejpam-5205	97	44	hv	hv	PROPN
ejpam-5205	97	45	or	or	CCONJ
ejpam-5205	97	46	v	v	PROPN
ejpam-5205	97	47	(	(	PUNCT
ejpam-5205	97	48	hv	hv	PROPN
ejpam-5205	97	49	)	)	PUNCT
ejpam-5205	97	50	\	\	PUNCT
ejpam-5205	98	1	(	(	PUNCT
ejpam-5205	98	2	sv	sv	NOUN
ejpam-5205	98	3	1	1	NUM
ejpam-5205	98	4	∪	∪	NOUN
ejpam-5205	98	5	sv	sv	NOUN
ejpam-5205	98	6	2	2	NUM
ejpam-5205	98	7	)	)	PUNCT
ejpam-5205	98	8	is	be	AUX
ejpam-5205	98	9	a	a	DET
ejpam-5205	98	10	non	non	ADJ
ejpam-5205	98	11	-	-	ADJ
ejpam-5205	98	12	connecting	connecting	ADJ
ejpam-5205	98	13	set	set	NOUN
ejpam-5205	98	14	in	in	ADP
ejpam-5205	98	15	hv	hv	NOUN
ejpam-5205	98	16	and	and	CCONJ
ejpam-5205	98	17	proof	proof	NOUN
ejpam-5205	98	18	.	.	PUNCT
ejpam-5205	99	1	let	let	VERB
ejpam-5205	99	2	f	f	PROPN
ejpam-5205	99	3	=	=	SYM
ejpam-5205	99	4	(	(	PUNCT
ejpam-5205	99	5	v0	v0	PROPN
ejpam-5205	99	6	,	,	PUNCT
ejpam-5205	99	7	v1	v1	NOUN
ejpam-5205	99	8	,	,	PUNCT
ejpam-5205	99	9	v2	v2	PROPN
ejpam-5205	99	10	)	)	PUNCT
ejpam-5205	99	11	be	be	AUX
ejpam-5205	99	12	a	a	DET
ejpam-5205	99	13	cvrdf	cvrdf	NOUN
ejpam-5205	99	14	of	of	ADP
ejpam-5205	99	15	g	g	PROPN
ejpam-5205	99	16	◦	◦	PROPN
ejpam-5205	99	17	h.	h.	PROPN
ejpam-5205	99	18	since	since	SCONJ
ejpam-5205	99	19	v1	v1	PROPN
ejpam-5205	99	20	∪	∪	NOUN
ejpam-5205	99	21	v2	v2	NOUN
ejpam-5205	99	22	is	be	AUX
ejpam-5205	99	23	a	a	DET
ejpam-5205	99	24	dominating	dominating	NOUN
ejpam-5205	99	25	set	set	NOUN
ejpam-5205	99	26	of	of	ADP
ejpam-5205	99	27	g	g	PROPN
ejpam-5205	99	28	◦	◦	NOUN
ejpam-5205	99	29	h	h	NOUN
ejpam-5205	99	30	,	,	PUNCT
ejpam-5205	99	31	v	v	X
ejpam-5205	99	32	(	(	PUNCT
ejpam-5205	99	33	v	v	PROPN
ejpam-5205	99	34	+	+	NOUN
ejpam-5205	99	35	hv	hv	NOUN
ejpam-5205	99	36	)	)	PUNCT
ejpam-5205	99	37	∩	∩	NOUN
ejpam-5205	99	38	(	(	PUNCT
ejpam-5205	99	39	v1	v1	NOUN
ejpam-5205	99	40	∪	∪	NOUN
ejpam-5205	99	41	v2	v2	NOUN
ejpam-5205	99	42	)	)	PUNCT
ejpam-5205	99	43	̸=	̸=	PROPN
ejpam-5205	99	44	∅	∅	NOUN
ejpam-5205	99	45	(	(	PUNCT
ejpam-5205	99	46	1	1	X
ejpam-5205	99	47	)	)	PUNCT
ejpam-5205	99	48	r.	r.	PROPN
ejpam-5205	99	49	fortosa	fortosa	PROPN
ejpam-5205	99	50	,	,	PUNCT
ejpam-5205	100	1	s.	s.	PROPN
ejpam-5205	100	2	canoy	canoy	PROPN
ejpam-5205	100	3	jr	jr	PROPN
ejpam-5205	100	4	.	.	PROPN
ejpam-5205	100	5	/	/	SYM
ejpam-5205	100	6	eur	eur	PROPN
ejpam-5205	100	7	.	.	PUNCT
ejpam-5205	101	1	j.	j.	PROPN
ejpam-5205	101	2	pure	pure	PROPN
ejpam-5205	101	3	appl	appl	PROPN
ejpam-5205	101	4	.	.	PROPN
ejpam-5205	101	5	math	math	PROPN
ejpam-5205	101	6	,	,	PUNCT
ejpam-5205	101	7	17	17	NUM
ejpam-5205	101	8	(	(	PUNCT
ejpam-5205	101	9	2	2	NUM
ejpam-5205	101	10	)	)	PUNCT
ejpam-5205	101	11	(	(	PUNCT
ejpam-5205	101	12	2024	2024	NUM
ejpam-5205	101	13	)	)	PUNCT
ejpam-5205	101	14	,	,	PUNCT
ejpam-5205	101	15	1335	1335	NUM
ejpam-5205	101	16	-	-	SYM
ejpam-5205	101	17	1351	1351	NUM
ejpam-5205	101	18	1339	1339	NUM
ejpam-5205	101	19	for	for	ADP
ejpam-5205	101	20	each	each	DET
ejpam-5205	101	21	v	v	NUM
ejpam-5205	101	22	∈	∈	PROPN
ejpam-5205	101	23	v	v	NOUN
ejpam-5205	101	24	(	(	PUNCT
ejpam-5205	101	25	g	g	NOUN
ejpam-5205	101	26	)	)	PUNCT
ejpam-5205	101	27	.	.	PUNCT
ejpam-5205	102	1	suppose	suppose	VERB
ejpam-5205	102	2	that	that	SCONJ
ejpam-5205	102	3	there	there	PRON
ejpam-5205	102	4	exists	exist	VERB
ejpam-5205	102	5	v	v	ADP
ejpam-5205	102	6	∈	∈	PROPN
ejpam-5205	102	7	v0	v0	NOUN
ejpam-5205	102	8	∩	∩	X
ejpam-5205	102	9	v	v	X
ejpam-5205	102	10	(	(	PUNCT
ejpam-5205	102	11	g	g	NOUN
ejpam-5205	102	12	)	)	PUNCT
ejpam-5205	102	13	.	.	PUNCT
ejpam-5205	103	1	then	then	ADV
ejpam-5205	103	2	(	(	PUNCT
ejpam-5205	103	3	1	1	X
ejpam-5205	103	4	)	)	PUNCT
ejpam-5205	103	5	implies	imply	VERB
ejpam-5205	103	6	that	that	SCONJ
ejpam-5205	103	7	sv	sv	PROPN
ejpam-5205	103	8	1	1	NUM
ejpam-5205	103	9	∪	∪	X
ejpam-5205	103	10	sv	sv	NOUN
ejpam-5205	103	11	2	2	NUM
ejpam-5205	103	12	̸=	̸=	PROPN
ejpam-5205	103	13	∅.	∅.	AUX
ejpam-5205	103	14	pick	pick	VERB
ejpam-5205	103	15	w	w	PROPN
ejpam-5205	103	16	∈	∈	PROPN
ejpam-5205	103	17	v	v	ADP
ejpam-5205	103	18	(	(	PUNCT
ejpam-5205	103	19	g	g	NOUN
ejpam-5205	103	20	)	)	PUNCT
ejpam-5205	103	21	\	\	NOUN
ejpam-5205	103	22	{	{	PUNCT
ejpam-5205	103	23	v	v	NOUN
ejpam-5205	103	24	}	}	PUNCT
ejpam-5205	103	25	.	.	PUNCT
ejpam-5205	104	1	if	if	SCONJ
ejpam-5205	104	2	w	w	PROPN
ejpam-5205	104	3	∈	∈	PROPN
ejpam-5205	104	4	v1	v1	NOUN
ejpam-5205	104	5	∪	∪	NOUN
ejpam-5205	104	6	v2	v2	NOUN
ejpam-5205	104	7	,	,	PUNCT
ejpam-5205	104	8	then	then	ADV
ejpam-5205	104	9	the	the	DET
ejpam-5205	104	10	convexity	convexity	NOUN
ejpam-5205	104	11	of	of	ADP
ejpam-5205	104	12	v1	v1	PROPN
ejpam-5205	104	13	∪	∪	NOUN
ejpam-5205	104	14	v2	v2	PROPN
ejpam-5205	104	15	implies	imply	VERB
ejpam-5205	104	16	that	that	SCONJ
ejpam-5205	104	17	v	v	NUM
ejpam-5205	104	18	∈	∈	PROPN
ejpam-5205	104	19	ig	ig	PROPN
ejpam-5205	104	20	◦	◦	NOUN
ejpam-5205	104	21	h	h	NOUN
ejpam-5205	105	1	[	[	X
ejpam-5205	105	2	z	z	X
ejpam-5205	105	3	,	,	PUNCT
ejpam-5205	105	4	w	w	PROPN
ejpam-5205	105	5	]	]	PUNCT
ejpam-5205	105	6	⊆	⊆	NUM
ejpam-5205	105	7	v1	v1	NOUN
ejpam-5205	105	8	∪	∪	NOUN
ejpam-5205	105	9	v2	v2	NOUN
ejpam-5205	105	10	for	for	ADP
ejpam-5205	105	11	all	all	DET
ejpam-5205	105	12	z	z	NOUN
ejpam-5205	105	13	∈	∈	NOUN
ejpam-5205	105	14	sv	sv	NOUN
ejpam-5205	105	15	1	1	NUM
ejpam-5205	105	16	∪	∪	ADP
ejpam-5205	105	17	sv	sv	PROPN
ejpam-5205	105	18	2	2	NUM
ejpam-5205	105	19	.	.	PUNCT
ejpam-5205	105	20	suppose	suppose	VERB
ejpam-5205	105	21	that	that	SCONJ
ejpam-5205	105	22	w	w	PROPN
ejpam-5205	105	23	∈	∈	PROPN
ejpam-5205	105	24	v0	v0	NOUN
ejpam-5205	105	25	.	.	PUNCT
ejpam-5205	106	1	then	then	ADV
ejpam-5205	106	2	by	by	ADP
ejpam-5205	106	3	(	(	PUNCT
ejpam-5205	106	4	1	1	NUM
ejpam-5205	106	5	)	)	PUNCT
ejpam-5205	106	6	,	,	PUNCT
ejpam-5205	106	7	sw	sw	PROPN
ejpam-5205	106	8	1	1	NUM
ejpam-5205	106	9	∪	∪	X
ejpam-5205	106	10	sw	sw	PROPN
ejpam-5205	106	11	2	2	NUM
ejpam-5205	106	12	̸=	̸=	PROPN
ejpam-5205	106	13	∅	∅	NOUN
ejpam-5205	106	14	,	,	PUNCT
ejpam-5205	106	15	and	and	CCONJ
ejpam-5205	106	16	w	w	NOUN
ejpam-5205	106	17	,	,	PUNCT
ejpam-5205	106	18	v	v	NOUN
ejpam-5205	106	19	∈	∈	PROPN
ejpam-5205	106	20	ig	ig	PROPN
ejpam-5205	106	21	◦	◦	NOUN
ejpam-5205	106	22	h	h	NOUN
ejpam-5205	107	1	[	[	X
ejpam-5205	107	2	a	a	X
ejpam-5205	107	3	,	,	PUNCT
ejpam-5205	107	4	b	b	NOUN
ejpam-5205	107	5	]	]	PUNCT
ejpam-5205	107	6	⊆	⊆	NUM
ejpam-5205	107	7	v1	v1	NOUN
ejpam-5205	107	8	∪	∪	NOUN
ejpam-5205	107	9	v2	v2	NOUN
ejpam-5205	107	10	,	,	PUNCT
ejpam-5205	107	11	for	for	ADP
ejpam-5205	107	12	all	all	DET
ejpam-5205	107	13	a	a	DET
ejpam-5205	107	14	∈	∈	NOUN
ejpam-5205	107	15	sv	sv	NOUN
ejpam-5205	107	16	1	1	NUM
ejpam-5205	107	17	∪	∪	NOUN
ejpam-5205	107	18	sv	sv	NOUN
ejpam-5205	107	19	2	2	NUM
ejpam-5205	107	20	and	and	CCONJ
ejpam-5205	107	21	b	b	PROPN
ejpam-5205	107	22	∈	∈	PROPN
ejpam-5205	107	23	sw	sw	PROPN
ejpam-5205	107	24	1	1	NUM
ejpam-5205	107	25	∪	∪	X
ejpam-5205	107	26	sw	sw	PROPN
ejpam-5205	107	27	2	2	NUM
ejpam-5205	107	28	.	.	PUNCT
ejpam-5205	108	1	in	in	ADP
ejpam-5205	108	2	any	any	DET
ejpam-5205	108	3	case	case	NOUN
ejpam-5205	108	4	,	,	PUNCT
ejpam-5205	108	5	we	we	PRON
ejpam-5205	108	6	get	get	VERB
ejpam-5205	108	7	a	a	DET
ejpam-5205	108	8	contradiction	contradiction	NOUN
ejpam-5205	108	9	.	.	PUNCT
ejpam-5205	109	1	thus	thus	ADV
ejpam-5205	109	2	,	,	PUNCT
ejpam-5205	109	3	v0	v0	PROPN
ejpam-5205	109	4	∩	∩	ADJ
ejpam-5205	109	5	v	v	X
ejpam-5205	109	6	(	(	PUNCT
ejpam-5205	109	7	g	g	NOUN
ejpam-5205	109	8	)	)	PUNCT
ejpam-5205	109	9	=	=	NOUN
ejpam-5205	109	10	∅	∅	NOUN
ejpam-5205	109	11	,	,	PUNCT
ejpam-5205	109	12	showing	show	VERB
ejpam-5205	109	13	that	that	SCONJ
ejpam-5205	109	14	(	(	PUNCT
ejpam-5205	109	15	i	i	NOUN
ejpam-5205	109	16	)	)	PUNCT
ejpam-5205	109	17	holds	hold	VERB
ejpam-5205	109	18	.	.	PUNCT
ejpam-5205	110	1	next	next	ADV
ejpam-5205	110	2	,	,	PUNCT
ejpam-5205	110	3	let	let	VERB
ejpam-5205	110	4	v	v	NUM
ejpam-5205	110	5	∈	∈	PROPN
ejpam-5205	110	6	v2	v2	PROPN
ejpam-5205	110	7	∩	∩	ADJ
ejpam-5205	110	8	v	v	NOUN
ejpam-5205	110	9	(	(	PUNCT
ejpam-5205	110	10	g	g	NOUN
ejpam-5205	110	11	)	)	PUNCT
ejpam-5205	110	12	.	.	PUNCT
ejpam-5205	111	1	by	by	ADP
ejpam-5205	111	2	theorem	theorem	NOUN
ejpam-5205	111	3	1	1	NUM
ejpam-5205	111	4	,	,	PUNCT
ejpam-5205	111	5	convexity	convexity	NOUN
ejpam-5205	111	6	of	of	ADP
ejpam-5205	111	7	v1	v1	PROPN
ejpam-5205	111	8	∪	∪	NOUN
ejpam-5205	111	9	v2	v2	PROPN
ejpam-5205	111	10	implies	imply	VERB
ejpam-5205	111	11	that	that	SCONJ
ejpam-5205	111	12	sv	sv	PROPN
ejpam-5205	111	13	1	1	NUM
ejpam-5205	111	14	∪	∪	X
ejpam-5205	111	15	sv	sv	NOUN
ejpam-5205	111	16	2	2	NUM
ejpam-5205	111	17	induces	induce	VERB
ejpam-5205	111	18	a	a	DET
ejpam-5205	111	19	complete	complete	ADJ
ejpam-5205	111	20	subgraph	subgraph	NOUN
ejpam-5205	111	21	of	of	ADP
ejpam-5205	111	22	hv	hv	PROPN
ejpam-5205	111	23	or	or	CCONJ
ejpam-5205	111	24	v	v	PROPN
ejpam-5205	111	25	(	(	PUNCT
ejpam-5205	111	26	hv	hv	PROPN
ejpam-5205	111	27	)	)	PUNCT
ejpam-5205	111	28	\	\	PUNCT
ejpam-5205	112	1	(	(	PUNCT
ejpam-5205	112	2	sv	sv	NOUN
ejpam-5205	112	3	1	1	NUM
ejpam-5205	112	4	∪	∪	NOUN
ejpam-5205	112	5	sv	sv	NOUN
ejpam-5205	112	6	2	2	NUM
ejpam-5205	112	7	)	)	PUNCT
ejpam-5205	112	8	is	be	AUX
ejpam-5205	112	9	a	a	DET
ejpam-5205	112	10	non	non	ADJ
ejpam-5205	112	11	-	-	ADJ
ejpam-5205	112	12	connecting	connecting	ADJ
ejpam-5205	112	13	set	set	NOUN
ejpam-5205	112	14	in	in	ADP
ejpam-5205	112	15	hv	hv	PROPN
ejpam-5205	112	16	.	.	PUNCT
ejpam-5205	113	1	hence	hence	ADV
ejpam-5205	113	2	,	,	PUNCT
ejpam-5205	113	3	(	(	PUNCT
ejpam-5205	113	4	ii	ii	NOUN
ejpam-5205	113	5	)	)	PUNCT
ejpam-5205	113	6	holds	hold	VERB
ejpam-5205	113	7	.	.	PUNCT
ejpam-5205	114	1	suppose	suppose	VERB
ejpam-5205	114	2	v	v	NUM
ejpam-5205	114	3	∈	∈	PROPN
ejpam-5205	114	4	v1	v1	NOUN
ejpam-5205	114	5	∩	∩	ADJ
ejpam-5205	114	6	v	v	X
ejpam-5205	114	7	(	(	PUNCT
ejpam-5205	114	8	g	g	NOUN
ejpam-5205	114	9	)	)	PUNCT
ejpam-5205	114	10	such	such	ADJ
ejpam-5205	114	11	that	that	SCONJ
ejpam-5205	114	12	sv	sv	PROPN
ejpam-5205	114	13	1	1	NUM
ejpam-5205	114	14	̸=	̸=	PROPN
ejpam-5205	114	15	v	v	PROPN
ejpam-5205	114	16	(	(	PUNCT
ejpam-5205	114	17	hv	hv	PROPN
ejpam-5205	114	18	)	)	PUNCT
ejpam-5205	114	19	.	.	PUNCT
ejpam-5205	115	1	then	then	ADV
ejpam-5205	115	2	sv	sv	PROPN
ejpam-5205	115	3	2	2	NUM
ejpam-5205	115	4	̸=	̸=	PROPN
ejpam-5205	115	5	∅	∅	NOUN
ejpam-5205	115	6	and	and	CCONJ
ejpam-5205	115	7	sv	sv	INTJ
ejpam-5205	115	8	0	0	NUM
ejpam-5205	115	9	⊆	⊆	NUM
ejpam-5205	115	10	nhv(sv	nhv(sv	NOUN
ejpam-5205	115	11	2	2	NUM
ejpam-5205	115	12	)	)	PUNCT
ejpam-5205	115	13	because	because	SCONJ
ejpam-5205	115	14	f	f	PROPN
ejpam-5205	115	15	is	be	AUX
ejpam-5205	115	16	an	an	DET
ejpam-5205	115	17	rdf	rdf	NOUN
ejpam-5205	115	18	on	on	ADP
ejpam-5205	115	19	g	g	PROPN
ejpam-5205	115	20	◦	◦	NOUN
ejpam-5205	115	21	h.	h.	NOUN
ejpam-5205	115	22	again	again	ADV
ejpam-5205	115	23	,	,	PUNCT
ejpam-5205	115	24	by	by	ADP
ejpam-5205	115	25	theorem	theorem	NOUN
ejpam-5205	115	26	1	1	NUM
ejpam-5205	115	27	,	,	PUNCT
ejpam-5205	115	28	sv	sv	PROPN
ejpam-5205	115	29	1	1	NUM
ejpam-5205	115	30	∪	∪	X
ejpam-5205	115	31	sv	sv	NOUN
ejpam-5205	115	32	2	2	NUM
ejpam-5205	115	33	induces	induce	VERB
ejpam-5205	115	34	a	a	DET
ejpam-5205	115	35	complete	complete	ADJ
ejpam-5205	115	36	subgraph	subgraph	NOUN
ejpam-5205	115	37	of	of	ADP
ejpam-5205	115	38	hv	hv	PROPN
ejpam-5205	115	39	or	or	CCONJ
ejpam-5205	115	40	v	v	PROPN
ejpam-5205	115	41	(	(	PUNCT
ejpam-5205	115	42	hv	hv	PROPN
ejpam-5205	115	43	)	)	PUNCT
ejpam-5205	115	44	\	\	PUNCT
ejpam-5205	116	1	(	(	PUNCT
ejpam-5205	116	2	sv	sv	NOUN
ejpam-5205	116	3	1	1	NUM
ejpam-5205	116	4	∪	∪	NOUN
ejpam-5205	116	5	sv	sv	NOUN
ejpam-5205	116	6	2	2	NUM
ejpam-5205	116	7	)	)	PUNCT
ejpam-5205	116	8	is	be	AUX
ejpam-5205	116	9	a	a	DET
ejpam-5205	116	10	non	non	ADJ
ejpam-5205	116	11	-	-	ADJ
ejpam-5205	116	12	connecting	connecting	ADJ
ejpam-5205	116	13	set	set	NOUN
ejpam-5205	116	14	in	in	ADP
ejpam-5205	116	15	hv	hv	PROPN
ejpam-5205	116	16	,	,	PUNCT
ejpam-5205	116	17	showing	show	VERB
ejpam-5205	116	18	that	that	SCONJ
ejpam-5205	116	19	(	(	PUNCT
ejpam-5205	116	20	iii	iii	NOUN
ejpam-5205	116	21	)	)	PUNCT
ejpam-5205	116	22	holds	hold	VERB
ejpam-5205	116	23	.	.	PUNCT
ejpam-5205	117	1	conversely	conversely	ADV
ejpam-5205	117	2	,	,	PUNCT
ejpam-5205	117	3	suppose	suppose	VERB
ejpam-5205	117	4	that	that	SCONJ
ejpam-5205	117	5	(	(	PUNCT
ejpam-5205	117	6	i	i	NOUN
ejpam-5205	117	7	)	)	PUNCT
ejpam-5205	117	8	,	,	PUNCT
ejpam-5205	117	9	(	(	PUNCT
ejpam-5205	117	10	ii	ii	NOUN
ejpam-5205	117	11	)	)	PUNCT
ejpam-5205	117	12	and	and	CCONJ
ejpam-5205	117	13	(	(	PUNCT
ejpam-5205	117	14	iii	iii	NOUN
ejpam-5205	117	15	)	)	PUNCT
ejpam-5205	117	16	hold	hold	NOUN
ejpam-5205	117	17	.	.	PUNCT
ejpam-5205	118	1	let	let	VERB
ejpam-5205	118	2	x	x	SYM
ejpam-5205	118	3	∈	∈	PROPN
ejpam-5205	118	4	v0	v0	NOUN
ejpam-5205	118	5	.	.	PUNCT
ejpam-5205	119	1	by	by	ADP
ejpam-5205	119	2	(	(	PUNCT
ejpam-5205	119	3	i	i	NOUN
ejpam-5205	119	4	)	)	PUNCT
ejpam-5205	119	5	,	,	PUNCT
ejpam-5205	119	6	x	x	PUNCT
ejpam-5205	119	7	∈	∈	NOUN
ejpam-5205	119	8	sv	sv	NOUN
ejpam-5205	119	9	0	0	NUM
ejpam-5205	120	1	for	for	ADP
ejpam-5205	120	2	some	some	DET
ejpam-5205	120	3	v	v	ADP
ejpam-5205	120	4	∈	∈	NOUN
ejpam-5205	120	5	v	v	NOUN
ejpam-5205	120	6	(	(	PUNCT
ejpam-5205	120	7	g	g	NOUN
ejpam-5205	120	8	)	)	PUNCT
ejpam-5205	120	9	.	.	PUNCT
ejpam-5205	121	1	if	if	SCONJ
ejpam-5205	121	2	v	v	NUM
ejpam-5205	121	3	∈	∈	PROPN
ejpam-5205	121	4	v2	v2	NOUN
ejpam-5205	121	5	,	,	PUNCT
ejpam-5205	121	6	then	then	ADV
ejpam-5205	121	7	x	x	PART
ejpam-5205	121	8	∈	∈	PROPN
ejpam-5205	121	9	ng	ng	PROPN
ejpam-5205	121	10	◦	◦	NOUN
ejpam-5205	121	11	h(v	h(v	PROPN
ejpam-5205	121	12	)	)	PUNCT
ejpam-5205	121	13	.	.	PUNCT
ejpam-5205	122	1	suppose	suppose	VERB
ejpam-5205	122	2	v	v	ADP
ejpam-5205	122	3	∈	∈	PROPN
ejpam-5205	122	4	v1	v1	NOUN
ejpam-5205	122	5	.	.	PUNCT
ejpam-5205	123	1	by	by	ADP
ejpam-5205	123	2	(	(	PUNCT
ejpam-5205	123	3	iii	iii	NOUN
ejpam-5205	123	4	)	)	PUNCT
ejpam-5205	123	5	,	,	PUNCT
ejpam-5205	123	6	sv	sv	PROPN
ejpam-5205	123	7	2	2	NUM
ejpam-5205	123	8	̸=	̸=	PROPN
ejpam-5205	123	9	∅	∅	NOUN
ejpam-5205	123	10	and	and	CCONJ
ejpam-5205	123	11	x	x	PUNCT
ejpam-5205	123	12	∈	∈	PROPN
ejpam-5205	123	13	ng	ng	PROPN
ejpam-5205	123	14	◦	◦	NOUN
ejpam-5205	123	15	h(sv	h(sv	PROPN
ejpam-5205	123	16	2	2	NUM
ejpam-5205	123	17	)	)	PUNCT
ejpam-5205	123	18	.	.	PUNCT
ejpam-5205	124	1	thus	thus	ADV
ejpam-5205	124	2	f	f	X
ejpam-5205	124	3	=	=	SYM
ejpam-5205	124	4	(	(	PUNCT
ejpam-5205	124	5	v0	v0	PROPN
ejpam-5205	124	6	,	,	PUNCT
ejpam-5205	124	7	v1	v1	NOUN
ejpam-5205	124	8	,	,	PUNCT
ejpam-5205	124	9	v2	v2	PROPN
ejpam-5205	124	10	)	)	PUNCT
ejpam-5205	124	11	is	be	AUX
ejpam-5205	124	12	an	an	DET
ejpam-5205	124	13	rdf	rdf	NOUN
ejpam-5205	124	14	on	on	ADP
ejpam-5205	124	15	g	g	PROPN
ejpam-5205	124	16	◦	◦	NOUN
ejpam-5205	124	17	h.	h.	NOUN
ejpam-5205	124	18	now	now	ADV
ejpam-5205	124	19	,	,	PUNCT
ejpam-5205	124	20	let	let	VERB
ejpam-5205	124	21	p	p	PRON
ejpam-5205	124	22	,	,	PUNCT
ejpam-5205	124	23	q	q	PROPN
ejpam-5205	124	24	∈	∈	NOUN
ejpam-5205	124	25	v1	v1	NOUN
ejpam-5205	124	26	∪	∪	NOUN
ejpam-5205	124	27	v2	v2	NOUN
ejpam-5205	124	28	and	and	CCONJ
ejpam-5205	124	29	let	let	VERB
ejpam-5205	124	30	v	v	NOUN
ejpam-5205	124	31	,	,	PUNCT
ejpam-5205	124	32	w	w	PROPN
ejpam-5205	124	33	∈	∈	PROPN
ejpam-5205	124	34	v	v	ADP
ejpam-5205	124	35	(	(	PUNCT
ejpam-5205	124	36	g	g	NOUN
ejpam-5205	124	37	)	)	PUNCT
ejpam-5205	124	38	such	such	ADJ
ejpam-5205	124	39	that	that	SCONJ
ejpam-5205	124	40	p	p	PROPN
ejpam-5205	124	41	∈	∈	PROPN
ejpam-5205	124	42	v	v	NOUN
ejpam-5205	124	43	(	(	PUNCT
ejpam-5205	124	44	v	v	PROPN
ejpam-5205	124	45	+	+	NOUN
ejpam-5205	124	46	hv	hv	NOUN
ejpam-5205	124	47	)	)	PUNCT
ejpam-5205	124	48	and	and	CCONJ
ejpam-5205	124	49	q	q	PROPN
ejpam-5205	124	50	∈	∈	PROPN
ejpam-5205	124	51	v	v	NOUN
ejpam-5205	124	52	(	(	PUNCT
ejpam-5205	124	53	w	w	NOUN
ejpam-5205	124	54	+	+	NOUN
ejpam-5205	124	55	hw	hw	NOUN
ejpam-5205	124	56	)	)	PUNCT
ejpam-5205	124	57	.	.	PUNCT
ejpam-5205	125	1	consider	consider	VERB
ejpam-5205	125	2	the	the	DET
ejpam-5205	125	3	following	follow	VERB
ejpam-5205	125	4	cases	case	NOUN
ejpam-5205	125	5	.	.	PUNCT
ejpam-5205	126	1	case	case	NOUN
ejpam-5205	126	2	1	1	NUM
ejpam-5205	126	3	.	.	PUNCT
ejpam-5205	127	1	v	v	X
ejpam-5205	127	2	=	=	PUNCT
ejpam-5205	127	3	w.	w.	NOUN
ejpam-5205	127	4	if	if	SCONJ
ejpam-5205	127	5	p	p	PROPN
ejpam-5205	127	6	=	=	X
ejpam-5205	127	7	v	v	NOUN
ejpam-5205	127	8	or	or	CCONJ
ejpam-5205	127	9	q	q	NOUN
ejpam-5205	127	10	=	=	ADJ
ejpam-5205	127	11	v	v	NOUN
ejpam-5205	127	12	,	,	PUNCT
ejpam-5205	127	13	then	then	ADV
ejpam-5205	127	14	ig	ig	PROPN
ejpam-5205	127	15	◦	◦	NOUN
ejpam-5205	127	16	h	h	NOUN
ejpam-5205	128	1	[	[	X
ejpam-5205	128	2	p	p	X
ejpam-5205	128	3	,	,	PUNCT
ejpam-5205	128	4	q	q	X
ejpam-5205	128	5	]	]	X
ejpam-5205	128	6	=	=	X
ejpam-5205	128	7	{	{	PUNCT
ejpam-5205	128	8	p	p	X
ejpam-5205	128	9	,	,	PUNCT
ejpam-5205	128	10	q	q	ADJ
ejpam-5205	128	11	}	}	PUNCT
ejpam-5205	128	12	⊆	⊆	NUM
ejpam-5205	128	13	v1	v1	NOUN
ejpam-5205	128	14	∪	∪	NOUN
ejpam-5205	128	15	v2	v2	NOUN
ejpam-5205	128	16	.	.	PUNCT
ejpam-5205	129	1	suppose	suppose	VERB
ejpam-5205	129	2	p	p	X
ejpam-5205	129	3	,	,	PUNCT
ejpam-5205	129	4	q	q	PROPN
ejpam-5205	129	5	∈	∈	PROPN
ejpam-5205	129	6	v	v	ADP
ejpam-5205	129	7	(	(	PUNCT
ejpam-5205	129	8	hv	hv	PROPN
ejpam-5205	129	9	)	)	PUNCT
ejpam-5205	129	10	.	.	PUNCT
ejpam-5205	130	1	if	if	SCONJ
ejpam-5205	130	2	dhv(p	dhv(p	PROPN
ejpam-5205	130	3	,	,	PUNCT
ejpam-5205	130	4	q	q	NOUN
ejpam-5205	130	5	)	)	PUNCT
ejpam-5205	130	6	=	=	SYM
ejpam-5205	130	7	1	1	NUM
ejpam-5205	130	8	,	,	PUNCT
ejpam-5205	130	9	then	then	ADV
ejpam-5205	130	10	ig	ig	PROPN
ejpam-5205	130	11	◦	◦	NOUN
ejpam-5205	130	12	h	h	NOUN
ejpam-5205	131	1	[	[	X
ejpam-5205	131	2	p	p	X
ejpam-5205	131	3	,	,	PUNCT
ejpam-5205	131	4	q	q	X
ejpam-5205	131	5	]	]	X
ejpam-5205	131	6	=	=	X
ejpam-5205	131	7	{	{	PUNCT
ejpam-5205	131	8	p	p	X
ejpam-5205	131	9	,	,	PUNCT
ejpam-5205	131	10	q	q	ADJ
ejpam-5205	131	11	}	}	PUNCT
ejpam-5205	131	12	⊆	⊆	NUM
ejpam-5205	131	13	v1	v1	NOUN
ejpam-5205	131	14	∪	∪	NOUN
ejpam-5205	131	15	v2	v2	NOUN
ejpam-5205	131	16	.	.	PUNCT
ejpam-5205	132	1	if	if	SCONJ
ejpam-5205	132	2	dhv(p	dhv(p	PROPN
ejpam-5205	132	3	,	,	PUNCT
ejpam-5205	132	4	q	q	NOUN
ejpam-5205	132	5	)	)	PUNCT
ejpam-5205	132	6	=	=	SYM
ejpam-5205	132	7	2	2	NUM
ejpam-5205	132	8	,	,	PUNCT
ejpam-5205	132	9	then	then	ADV
ejpam-5205	132	10	ig	ig	PROPN
ejpam-5205	132	11	◦	◦	NOUN
ejpam-5205	132	12	h	h	NOUN
ejpam-5205	133	1	[	[	X
ejpam-5205	133	2	p	p	X
ejpam-5205	133	3	,	,	PUNCT
ejpam-5205	133	4	q	q	X
ejpam-5205	133	5	]	]	X
ejpam-5205	133	6	=	=	X
ejpam-5205	133	7	{	{	PUNCT
ejpam-5205	133	8	p	p	X
ejpam-5205	133	9	,	,	PUNCT
ejpam-5205	133	10	q	q	ADJ
ejpam-5205	133	11	,	,	PUNCT
ejpam-5205	133	12	v	v	NOUN
ejpam-5205	133	13	}	}	PUNCT
ejpam-5205	133	14	∪	∪	X
ejpam-5205	133	15	(	(	PUNCT
ejpam-5205	133	16	nhv(p	nhv(p	PROPN
ejpam-5205	133	17	)	)	PUNCT
ejpam-5205	133	18	∩nhv(q	∩nhv(q	NUM
ejpam-5205	133	19	)	)	PUNCT
ejpam-5205	133	20	)	)	PUNCT
ejpam-5205	134	1	⊆	⊆	NUM
ejpam-5205	134	2	sv	sv	NOUN
ejpam-5205	134	3	1	1	NUM
ejpam-5205	134	4	∪	∪	NOUN
ejpam-5205	134	5	sv	sv	NOUN
ejpam-5205	134	6	2	2	NUM
ejpam-5205	134	7	∪	∪	X
ejpam-5205	134	8	{	{	PUNCT
ejpam-5205	134	9	v	v	NOUN
ejpam-5205	134	10	}	}	PUNCT
ejpam-5205	134	11	⊆	⊆	NUM
ejpam-5205	134	12	v1	v1	NOUN
ejpam-5205	134	13	∪	∪	NOUN
ejpam-5205	134	14	v2	v2	NOUN
ejpam-5205	134	15	since	since	SCONJ
ejpam-5205	134	16	v	v	PROPN
ejpam-5205	134	17	(	(	PUNCT
ejpam-5205	134	18	hv	hv	PROPN
ejpam-5205	134	19	)	)	PUNCT
ejpam-5205	134	20	\	\	PUNCT
ejpam-5205	134	21	(	(	PUNCT
ejpam-5205	134	22	sv	sv	NOUN
ejpam-5205	134	23	1	1	NUM
ejpam-5205	134	24	∪sv	∪sv	NOUN
ejpam-5205	134	25	2	2	NUM
ejpam-5205	134	26	)	)	PUNCT
ejpam-5205	134	27	is	be	AUX
ejpam-5205	134	28	a	a	DET
ejpam-5205	134	29	non	non	ADJ
ejpam-5205	134	30	-	-	ADJ
ejpam-5205	134	31	connecting	connecting	ADJ
ejpam-5205	134	32	set	set	NOUN
ejpam-5205	134	33	in	in	ADP
ejpam-5205	134	34	hv	hv	PROPN
ejpam-5205	134	35	(	(	PUNCT
ejpam-5205	134	36	by	by	ADP
ejpam-5205	134	37	(	(	PUNCT
ejpam-5205	134	38	ii	ii	NOUN
ejpam-5205	134	39	)	)	PUNCT
ejpam-5205	134	40	and	and	CCONJ
ejpam-5205	134	41	(	(	PUNCT
ejpam-5205	134	42	iii	iii	NOUN
ejpam-5205	134	43	)	)	PUNCT
ejpam-5205	134	44	)	)	PUNCT
ejpam-5205	134	45	.	.	PUNCT
ejpam-5205	135	1	if	if	SCONJ
ejpam-5205	135	2	dhv(p	dhv(p	PROPN
ejpam-5205	135	3	,	,	PUNCT
ejpam-5205	135	4	q	q	NOUN
ejpam-5205	135	5	)	)	PUNCT
ejpam-5205	135	6	>	>	X
ejpam-5205	135	7	2	2	NUM
ejpam-5205	135	8	,	,	PUNCT
ejpam-5205	135	9	then	then	ADV
ejpam-5205	135	10	ig	ig	PROPN
ejpam-5205	135	11	◦	◦	NOUN
ejpam-5205	135	12	h	h	NOUN
ejpam-5205	136	1	[	[	X
ejpam-5205	136	2	p	p	X
ejpam-5205	136	3	,	,	PUNCT
ejpam-5205	136	4	q	q	X
ejpam-5205	136	5	]	]	X
ejpam-5205	136	6	=	=	X
ejpam-5205	136	7	{	{	PUNCT
ejpam-5205	136	8	p	p	X
ejpam-5205	136	9	,	,	PUNCT
ejpam-5205	136	10	q	q	ADJ
ejpam-5205	136	11	,	,	PUNCT
ejpam-5205	136	12	v	v	NOUN
ejpam-5205	136	13	}	}	PUNCT
ejpam-5205	136	14	⊆	⊆	NUM
ejpam-5205	136	15	v1	v1	NOUN
ejpam-5205	136	16	∪	∪	NOUN
ejpam-5205	136	17	v2	v2	NOUN
ejpam-5205	136	18	.	.	PUNCT
ejpam-5205	136	19	case	case	NOUN
ejpam-5205	136	20	2	2	NUM
ejpam-5205	136	21	.	.	NOUN
ejpam-5205	136	22	v	v	ADP
ejpam-5205	136	23	̸=	̸=	PROPN
ejpam-5205	136	24	w.	w.	NOUN
ejpam-5205	136	25	consider	consider	VERB
ejpam-5205	136	26	the	the	DET
ejpam-5205	136	27	following	follow	VERB
ejpam-5205	136	28	subcases	subcase	NOUN
ejpam-5205	136	29	.	.	PUNCT
ejpam-5205	137	1	subcase	subcase	PROPN
ejpam-5205	137	2	1	1	NUM
ejpam-5205	137	3	.	.	PUNCT
ejpam-5205	138	1	p	p	NOUN
ejpam-5205	138	2	=	=	X
ejpam-5205	138	3	v	v	PROPN
ejpam-5205	138	4	and	and	CCONJ
ejpam-5205	138	5	q	q	NOUN
ejpam-5205	138	6	=	=	SYM
ejpam-5205	138	7	w.	w.	PROPN
ejpam-5205	138	8	then	then	ADV
ejpam-5205	138	9	v	v	X
ejpam-5205	138	10	(	(	PUNCT
ejpam-5205	138	11	g	g	NOUN
ejpam-5205	138	12	)	)	PUNCT
ejpam-5205	138	13	⊆	⊆	NUM
ejpam-5205	138	14	v1	v1	NOUN
ejpam-5205	138	15	∪	∪	NOUN
ejpam-5205	138	16	v2	v2	NOUN
ejpam-5205	138	17	by	by	ADP
ejpam-5205	138	18	(	(	PUNCT
ejpam-5205	138	19	i	i	NOUN
ejpam-5205	138	20	)	)	PUNCT
ejpam-5205	138	21	.	.	PUNCT
ejpam-5205	139	1	since	since	SCONJ
ejpam-5205	139	2	every	every	DET
ejpam-5205	139	3	p	p	NOUN
ejpam-5205	139	4	-	-	PUNCT
ejpam-5205	139	5	q	q	NOUN
ejpam-5205	139	6	geodesic	geodesic	NOUN
ejpam-5205	139	7	in	in	ADP
ejpam-5205	139	8	g	g	PROPN
ejpam-5205	139	9	◦	◦	NOUN
ejpam-5205	139	10	h	h	NOUN
ejpam-5205	139	11	is	be	AUX
ejpam-5205	139	12	a	a	DET
ejpam-5205	139	13	p	p	NOUN
ejpam-5205	139	14	-	-	PUNCT
ejpam-5205	139	15	q	q	NOUN
ejpam-5205	139	16	geodesic	geodesic	NOUN
ejpam-5205	139	17	in	in	ADP
ejpam-5205	139	18	g	g	PROPN
ejpam-5205	139	19	,	,	PUNCT
ejpam-5205	139	20	it	it	PRON
ejpam-5205	139	21	follows	follow	VERB
ejpam-5205	139	22	that	that	SCONJ
ejpam-5205	139	23	ig	ig	PROPN
ejpam-5205	139	24	◦	◦	NOUN
ejpam-5205	139	25	h	h	NOUN
ejpam-5205	140	1	[	[	X
ejpam-5205	140	2	p	p	X
ejpam-5205	140	3	,	,	PUNCT
ejpam-5205	140	4	q	q	X
ejpam-5205	140	5	]	]	X
ejpam-5205	140	6	=	=	PUNCT
ejpam-5205	140	7	ig[p	ig[p	PROPN
ejpam-5205	140	8	,	,	PUNCT
ejpam-5205	140	9	q	q	X
ejpam-5205	140	10	]	]	X
ejpam-5205	140	11	⊆	⊆	NUM
ejpam-5205	140	12	(	(	PUNCT
ejpam-5205	140	13	v1	v1	VERB
ejpam-5205	140	14	∪	∪	NOUN
ejpam-5205	140	15	v2	v2	NOUN
ejpam-5205	140	16	)	)	PUNCT
ejpam-5205	140	17	.	.	PUNCT
ejpam-5205	141	1	subcase	subcase	PROPN
ejpam-5205	141	2	2	2	NUM
ejpam-5205	141	3	.	.	PUNCT
ejpam-5205	142	1	p	p	NOUN
ejpam-5205	142	2	=	=	X
ejpam-5205	142	3	v	v	PROPN
ejpam-5205	142	4	and	and	CCONJ
ejpam-5205	142	5	q	q	NOUN
ejpam-5205	142	6	∈	∈	PROPN
ejpam-5205	142	7	v	v	ADP
ejpam-5205	142	8	(	(	PUNCT
ejpam-5205	142	9	hw	hw	NOUN
ejpam-5205	142	10	)	)	PUNCT
ejpam-5205	142	11	(	(	PUNCT
ejpam-5205	142	12	or	or	CCONJ
ejpam-5205	142	13	q	q	ADJ
ejpam-5205	142	14	=	=	SYM
ejpam-5205	142	15	w	w	PROPN
ejpam-5205	142	16	and	and	CCONJ
ejpam-5205	142	17	p	p	NOUN
ejpam-5205	142	18	∈	∈	PROPN
ejpam-5205	142	19	v	v	ADP
ejpam-5205	142	20	(	(	PUNCT
ejpam-5205	142	21	hv	hv	NOUN
ejpam-5205	142	22	)	)	PUNCT
ejpam-5205	142	23	)	)	PUNCT
ejpam-5205	142	24	.	.	PUNCT
ejpam-5205	143	1	then	then	ADV
ejpam-5205	143	2	ig	ig	PROPN
ejpam-5205	143	3	◦	◦	NOUN
ejpam-5205	143	4	h	h	NOUN
ejpam-5205	144	1	[	[	X
ejpam-5205	144	2	p	p	X
ejpam-5205	144	3	,	,	PUNCT
ejpam-5205	144	4	q	q	X
ejpam-5205	144	5	]	]	X
ejpam-5205	144	6	=	=	SYM
ejpam-5205	144	7	ig[v	ig[v	PROPN
ejpam-5205	144	8	,	,	PUNCT
ejpam-5205	144	9	w	w	PROPN
ejpam-5205	144	10	]	]	X
ejpam-5205	144	11	∪	∪	X
ejpam-5205	144	12	{	{	PUNCT
ejpam-5205	144	13	q	q	NOUN
ejpam-5205	144	14	}	}	PUNCT
ejpam-5205	144	15	⊆	⊆	NUM
ejpam-5205	144	16	(	(	PUNCT
ejpam-5205	144	17	v1	v1	VERB
ejpam-5205	144	18	∪	∪	NOUN
ejpam-5205	144	19	v2	v2	NOUN
ejpam-5205	144	20	)	)	PUNCT
ejpam-5205	144	21	.	.	PUNCT
ejpam-5205	145	1	subcase	subcase	PROPN
ejpam-5205	145	2	3	3	NUM
ejpam-5205	145	3	.	.	PUNCT
ejpam-5205	146	1	p	p	PROPN
ejpam-5205	146	2	∈	∈	PROPN
ejpam-5205	146	3	v	v	ADP
ejpam-5205	146	4	(	(	PUNCT
ejpam-5205	146	5	hv	hv	PROPN
ejpam-5205	146	6	)	)	PUNCT
ejpam-5205	146	7	and	and	CCONJ
ejpam-5205	146	8	q	q	PROPN
ejpam-5205	146	9	∈	∈	PROPN
ejpam-5205	146	10	v	v	ADP
ejpam-5205	146	11	(	(	PUNCT
ejpam-5205	146	12	hw	hw	NOUN
ejpam-5205	146	13	)	)	PUNCT
ejpam-5205	146	14	.	.	PUNCT
ejpam-5205	147	1	then	then	ADV
ejpam-5205	147	2	ig	ig	PROPN
ejpam-5205	147	3	◦	◦	NOUN
ejpam-5205	147	4	h	h	NOUN
ejpam-5205	148	1	[	[	X
ejpam-5205	148	2	p	p	X
ejpam-5205	148	3	,	,	PUNCT
ejpam-5205	148	4	q	q	X
ejpam-5205	148	5	]	]	X
ejpam-5205	148	6	=	=	SYM
ejpam-5205	148	7	ig[v	ig[v	PROPN
ejpam-5205	148	8	,	,	PUNCT
ejpam-5205	148	9	w	w	PROPN
ejpam-5205	148	10	]	]	X
ejpam-5205	148	11	∪	∪	X
ejpam-5205	148	12	{	{	PUNCT
ejpam-5205	148	13	p	p	X
ejpam-5205	148	14	,	,	PUNCT
ejpam-5205	148	15	q	q	ADJ
ejpam-5205	148	16	}	}	PUNCT
ejpam-5205	148	17	⊆	⊆	NUM
ejpam-5205	148	18	v1	v1	NOUN
ejpam-5205	148	19	∪	∪	NOUN
ejpam-5205	148	20	v2	v2	NOUN
ejpam-5205	148	21	.	.	PUNCT
ejpam-5205	149	1	therefore	therefore	ADV
ejpam-5205	149	2	,	,	PUNCT
ejpam-5205	149	3	v1	v1	VERB
ejpam-5205	149	4	∪	∪	NOUN
ejpam-5205	149	5	v2	v2	NOUN
ejpam-5205	149	6	is	be	AUX
ejpam-5205	149	7	a	a	DET
ejpam-5205	149	8	convex	convex	NOUN
ejpam-5205	149	9	set	set	VERB
ejpam-5205	149	10	in	in	ADP
ejpam-5205	149	11	g	g	PROPN
ejpam-5205	149	12	◦	◦	NOUN
ejpam-5205	149	13	h.	h.	NOUN
ejpam-5205	149	14	accordingly	accordingly	ADV
ejpam-5205	149	15	,	,	PUNCT
ejpam-5205	149	16	f	f	PROPN
ejpam-5205	149	17	is	be	AUX
ejpam-5205	149	18	a	a	DET
ejpam-5205	149	19	cvrdf	cvrdf	NOUN
ejpam-5205	149	20	on	on	ADP
ejpam-5205	149	21	g	g	PROPN
ejpam-5205	149	22	◦	◦	NOUN
ejpam-5205	149	23	h.	h.	NOUN
ejpam-5205	149	24	corollary	corollary	ADJ
ejpam-5205	149	25	2	2	PROPN
ejpam-5205	149	26	.	.	PUNCT
ejpam-5205	150	1	let	let	VERB
ejpam-5205	150	2	g	g	PRON
ejpam-5205	150	3	be	be	AUX
ejpam-5205	150	4	a	a	DET
ejpam-5205	150	5	non	non	ADJ
ejpam-5205	150	6	-	-	ADJ
ejpam-5205	150	7	trivial	trivial	ADJ
ejpam-5205	150	8	connected	connected	ADJ
ejpam-5205	150	9	graph	graph	NOUN
ejpam-5205	150	10	of	of	ADP
ejpam-5205	150	11	order	order	NOUN
ejpam-5205	150	12	n	n	NOUN
ejpam-5205	150	13	and	and	CCONJ
ejpam-5205	150	14	let	let	VERB
ejpam-5205	150	15	h	h	NOUN
ejpam-5205	150	16	be	be	AUX
ejpam-5205	150	17	any	any	DET
ejpam-5205	150	18	graph	graph	NOUN
ejpam-5205	150	19	.	.	PUNCT
ejpam-5205	151	1	then	then	ADV
ejpam-5205	151	2	γcvr(g	γcvr(g	VERB
ejpam-5205	151	3	◦	◦	NOUN
ejpam-5205	151	4	h	h	NOUN
ejpam-5205	151	5	)	)	PUNCT
ejpam-5205	151	6	=	=	SYM
ejpam-5205	151	7	2n	2n	NUM
ejpam-5205	151	8	.	.	PUNCT
ejpam-5205	152	1	proof	proof	NOUN
ejpam-5205	152	2	.	.	PUNCT
ejpam-5205	153	1	let	let	VERB
ejpam-5205	153	2	v	v	NOUN
ejpam-5205	153	3	′	′	NOUN
ejpam-5205	153	4	2	2	NUM
ejpam-5205	153	5	=	=	SYM
ejpam-5205	153	6	v	v	NOUN
ejpam-5205	153	7	(	(	PUNCT
ejpam-5205	153	8	g	g	NOUN
ejpam-5205	153	9	)	)	PUNCT
ejpam-5205	153	10	,	,	PUNCT
ejpam-5205	153	11	v	v	X
ejpam-5205	153	12	′	′	NOUN
ejpam-5205	153	13	0	0	NUM
ejpam-5205	154	1	=	=	PUNCT
ejpam-5205	154	2	⋃	⋃	NOUN
ejpam-5205	154	3	v∈v	v∈v	NOUN
ejpam-5205	154	4	(	(	PUNCT
ejpam-5205	154	5	g	g	NOUN
ejpam-5205	154	6	)	)	PUNCT
ejpam-5205	154	7	v	v	NOUN
ejpam-5205	154	8	(	(	PUNCT
ejpam-5205	154	9	hv	hv	NOUN
ejpam-5205	154	10	)	)	PUNCT
ejpam-5205	154	11	,	,	PUNCT
ejpam-5205	154	12	and	and	CCONJ
ejpam-5205	154	13	v	v	X
ejpam-5205	154	14	′	′	NUM
ejpam-5205	154	15	1	1	NUM
ejpam-5205	154	16	=	=	VERB
ejpam-5205	154	17	∅.	∅.	X
ejpam-5205	154	18	by	by	ADP
ejpam-5205	154	19	theorem	theorem	NOUN
ejpam-5205	154	20	8	8	NUM
ejpam-5205	154	21	,	,	PUNCT
ejpam-5205	154	22	g	g	NOUN
ejpam-5205	154	23	=	=	PUNCT
ejpam-5205	154	24	(	(	PUNCT
ejpam-5205	154	25	v	v	NUM
ejpam-5205	154	26	′	′	NUM
ejpam-5205	154	27	0	0	NUM
ejpam-5205	154	28	,	,	PUNCT
ejpam-5205	154	29	v	v	NOUN
ejpam-5205	154	30	′	′	NUM
ejpam-5205	154	31	1	1	NUM
ejpam-5205	154	32	,	,	PUNCT
ejpam-5205	154	33	v	v	NOUN
ejpam-5205	154	34	′	′	NUM
ejpam-5205	154	35	2	2	NUM
ejpam-5205	154	36	)	)	PUNCT
ejpam-5205	154	37	is	be	AUX
ejpam-5205	154	38	a	a	DET
ejpam-5205	154	39	cvrdf	cvrdf	NOUN
ejpam-5205	154	40	on	on	ADP
ejpam-5205	154	41	g	g	PROPN
ejpam-5205	154	42	◦	◦	NOUN
ejpam-5205	154	43	h.	h.	NOUN
ejpam-5205	154	44	thus	thus	ADV
ejpam-5205	154	45	,	,	PUNCT
ejpam-5205	154	46	γcvr(g	γcvr(g	PROPN
ejpam-5205	154	47	◦	◦	NOUN
ejpam-5205	154	48	h	h	NOUN
ejpam-5205	154	49	)	)	PUNCT
ejpam-5205	154	50	≤	≤	NUM
ejpam-5205	154	51	ωcvr	ωcvr	ADP
ejpam-5205	154	52	g	g	PROPN
ejpam-5205	154	53	◦	◦	NOUN
ejpam-5205	154	54	h(g	h(g	NOUN
ejpam-5205	154	55	)	)	PUNCT
ejpam-5205	154	56	=	=	SYM
ejpam-5205	155	1	|v	|v	PROPN
ejpam-5205	155	2	′	′	NOUN
ejpam-5205	155	3	1	1	NUM
ejpam-5205	155	4	|+2|v	|+2|v	NOUN
ejpam-5205	156	1	′	′	NOUN
ejpam-5205	156	2	2	2	NUM
ejpam-5205	156	3	|	|	ADV
ejpam-5205	156	4	=	=	SYM
ejpam-5205	156	5	2n	2n	NUM
ejpam-5205	156	6	.	.	PUNCT
ejpam-5205	157	1	next	next	ADV
ejpam-5205	157	2	,	,	PUNCT
ejpam-5205	157	3	let	let	VERB
ejpam-5205	157	4	f	f	PROPN
ejpam-5205	157	5	=	=	SYM
ejpam-5205	157	6	(	(	PUNCT
ejpam-5205	157	7	v0	v0	PROPN
ejpam-5205	157	8	,	,	PUNCT
ejpam-5205	157	9	v1	v1	NOUN
ejpam-5205	157	10	,	,	PUNCT
ejpam-5205	157	11	v2	v2	PROPN
ejpam-5205	157	12	)	)	PUNCT
ejpam-5205	157	13	be	be	AUX
ejpam-5205	157	14	a	a	DET
ejpam-5205	157	15	γcvr	γcvr	NOUN
ejpam-5205	157	16	-	-	PUNCT
ejpam-5205	157	17	function	function	NOUN
ejpam-5205	157	18	on	on	ADP
ejpam-5205	157	19	g	g	PROPN
ejpam-5205	157	20	◦	◦	PROPN
ejpam-5205	157	21	h.	h.	PROPN
ejpam-5205	157	22	let	let	VERB
ejpam-5205	157	23	v	v	NUM
ejpam-5205	157	24	∗	∗	NOUN
ejpam-5205	157	25	1	1	NUM
ejpam-5205	157	26	=	=	SYM
ejpam-5205	157	27	v1	v1	NOUN
ejpam-5205	157	28	∩	∩	ADJ
ejpam-5205	157	29	v	v	NOUN
ejpam-5205	157	30	(	(	PUNCT
ejpam-5205	157	31	g	g	NOUN
ejpam-5205	157	32	)	)	PUNCT
ejpam-5205	157	33	and	and	CCONJ
ejpam-5205	157	34	v	v	ADP
ejpam-5205	157	35	∗	∗	NOUN
ejpam-5205	157	36	2	2	NUM
ejpam-5205	157	37	=	=	SYM
ejpam-5205	157	38	v2	v2	NOUN
ejpam-5205	157	39	∩	∩	NOUN
ejpam-5205	157	40	v	v	NOUN
ejpam-5205	157	41	(	(	PUNCT
ejpam-5205	157	42	g	g	NOUN
ejpam-5205	157	43	)	)	PUNCT
ejpam-5205	157	44	and	and	CCONJ
ejpam-5205	157	45	let	let	VERB
ejpam-5205	157	46	|v	|v	PROPN
ejpam-5205	157	47	∗	∗	NOUN
ejpam-5205	157	48	1	1	NUM
ejpam-5205	158	1	|	|	ADV
ejpam-5205	158	2	=	=	SYM
ejpam-5205	158	3	k.	k.	PROPN
ejpam-5205	159	1	then	then	ADV
ejpam-5205	159	2	|v	|v	PROPN
ejpam-5205	159	3	∗	∗	NOUN
ejpam-5205	159	4	2	2	NUM
ejpam-5205	159	5	|	|	NOUN
ejpam-5205	159	6	=	=	SYM
ejpam-5205	159	7	n−	n−	PROPN
ejpam-5205	159	8	k.	k.	ADV
ejpam-5205	159	9	let	let	VERB
ejpam-5205	159	10	d	d	NOUN
ejpam-5205	159	11	=	=	PRON
ejpam-5205	159	12	{	{	PUNCT
ejpam-5205	159	13	v	v	NUM
ejpam-5205	159	14	∈	∈	NOUN
ejpam-5205	159	15	v	v	ADP
ejpam-5205	159	16	∗	∗	NOUN
ejpam-5205	159	17	1	1	NUM
ejpam-5205	159	18	:	:	PUNCT
ejpam-5205	159	19	sv	sv	PROPN
ejpam-5205	159	20	1	1	NUM
ejpam-5205	159	21	̸=	̸=	PROPN
ejpam-5205	159	22	∅	∅	NOUN
ejpam-5205	159	23	}	}	PUNCT
ejpam-5205	159	24	.	.	PUNCT
ejpam-5205	160	1	then	then	ADV
ejpam-5205	160	2	sv	sv	PROPN
ejpam-5205	160	3	2	2	NUM
ejpam-5205	160	4	̸=	̸=	PROPN
ejpam-5205	160	5	∅	∅	NOUN
ejpam-5205	160	6	for	for	ADP
ejpam-5205	160	7	all	all	DET
ejpam-5205	160	8	v	v	PRON
ejpam-5205	160	9	∈	∈	PROPN
ejpam-5205	160	10	v1	v1	NOUN
ejpam-5205	160	11	\d	\d	NOUN
ejpam-5205	160	12	by	by	ADP
ejpam-5205	160	13	(	(	PUNCT
ejpam-5205	160	14	iii	iii	NOUN
ejpam-5205	160	15	)	)	PUNCT
ejpam-5205	160	16	.	.	PUNCT
ejpam-5205	161	1	hence	hence	ADV
ejpam-5205	161	2	,	,	PUNCT
ejpam-5205	161	3	γcvr(g	γcvr(g	ADV
ejpam-5205	161	4	◦	◦	NOUN
ejpam-5205	161	5	h	h	NOUN
ejpam-5205	161	6	)	)	PUNCT
ejpam-5205	162	1	=	=	PUNCT
ejpam-5205	162	2	ωcvr	ωcvr	ADP
ejpam-5205	162	3	g	g	PROPN
ejpam-5205	162	4	◦	◦	NOUN
ejpam-5205	162	5	h(f	h(f	NUM
ejpam-5205	162	6	)	)	PUNCT
ejpam-5205	162	7	r.	r.	PROPN
ejpam-5205	162	8	fortosa	fortosa	PROPN
ejpam-5205	162	9	,	,	PUNCT
ejpam-5205	162	10	s.	s.	PROPN
ejpam-5205	162	11	canoy	canoy	PROPN
ejpam-5205	162	12	jr	jr	PROPN
ejpam-5205	162	13	.	.	PROPN
ejpam-5205	162	14	/	/	SYM
ejpam-5205	162	15	eur	eur	PROPN
ejpam-5205	162	16	.	.	PUNCT
ejpam-5205	163	1	j.	j.	PROPN
ejpam-5205	163	2	pure	pure	PROPN
ejpam-5205	163	3	appl	appl	PROPN
ejpam-5205	163	4	.	.	PROPN
ejpam-5205	163	5	math	math	PROPN
ejpam-5205	163	6	,	,	PUNCT
ejpam-5205	163	7	17	17	NUM
ejpam-5205	163	8	(	(	PUNCT
ejpam-5205	163	9	2	2	NUM
ejpam-5205	163	10	)	)	PUNCT
ejpam-5205	163	11	(	(	PUNCT
ejpam-5205	163	12	2024	2024	NUM
ejpam-5205	163	13	)	)	PUNCT
ejpam-5205	163	14	,	,	PUNCT
ejpam-5205	163	15	1335	1335	NUM
ejpam-5205	163	16	-	-	SYM
ejpam-5205	163	17	1351	1351	NUM
ejpam-5205	163	18	1340	1340	NUM
ejpam-5205	163	19	=	=	SYM
ejpam-5205	163	20	|v1|+	|v1|+	PRON
ejpam-5205	163	21	2|v2|	2|v2|	NUM
ejpam-5205	163	22	=	=	SYM
ejpam-5205	164	1	k	k	PROPN
ejpam-5205	164	2	+	+	CCONJ
ejpam-5205	164	3	∑	∑	PUNCT
ejpam-5205	164	4	v∈v	v∈v	NOUN
ejpam-5205	164	5	(	(	PUNCT
ejpam-5205	164	6	g	g	NOUN
ejpam-5205	164	7	)	)	PUNCT
ejpam-5205	164	8	|sv	|sv	NUM
ejpam-5205	164	9	1	1	NUM
ejpam-5205	164	10	|+	|+	NOUN
ejpam-5205	164	11	2	2	NUM
ejpam-5205	164	12	(n−	(n−	PROPN
ejpam-5205	164	13	k	k	NOUN
ejpam-5205	164	14	)	)	PUNCT
ejpam-5205	165	1	+	+	CCONJ
ejpam-5205	165	2	∑	∑	PUNCT
ejpam-5205	165	3	v∈v	v∈v	NOUN
ejpam-5205	165	4	(	(	PUNCT
ejpam-5205	165	5	g	g	NOUN
ejpam-5205	165	6	)	)	PUNCT
ejpam-5205	165	7	|sv	|sv	NUM
ejpam-5205	165	8	2	2	NUM
ejpam-5205	165	9	|	|	ADV
ejpam-5205	165	10			VERB
ejpam-5205	165	11	=	=	PUNCT
ejpam-5205	166	1	2n−	2n−	NUM
ejpam-5205	166	2	k	k	X
ejpam-5205	166	3	+	+	CCONJ
ejpam-5205	166	4	∑	∑	PUNCT
ejpam-5205	166	5	v∈v	v∈v	NOUN
ejpam-5205	166	6	(	(	PUNCT
ejpam-5205	166	7	g	g	NOUN
ejpam-5205	166	8	)	)	PUNCT
ejpam-5205	166	9	|sv	|sv	NUM
ejpam-5205	166	10	1	1	NUM
ejpam-5205	166	11	|+	|+	ADP
ejpam-5205	166	12	2	2	NUM
ejpam-5205	166	13	∑	∑	NOUN
ejpam-5205	166	14	v∈v	v∈v	NOUN
ejpam-5205	166	15	(	(	PUNCT
ejpam-5205	166	16	g	g	NOUN
ejpam-5205	166	17	)	)	PUNCT
ejpam-5205	166	18	|sv	|sv	NUM
ejpam-5205	166	19	2	2	NUM
ejpam-5205	167	1	|	|	ADV
ejpam-5205	167	2	≥	≥	NOUN
ejpam-5205	167	3	2n−	2n−	NUM
ejpam-5205	167	4	k	k	X
ejpam-5205	168	1	+	+	CCONJ
ejpam-5205	168	2	∑	∑	PUNCT
ejpam-5205	168	3	v∈d	v∈d	ADJ
ejpam-5205	168	4	|sv	|sv	NUM
ejpam-5205	168	5	1	1	NUM
ejpam-5205	168	6	|+	|+	ADP
ejpam-5205	168	7	2	2	NUM
ejpam-5205	168	8	∑	∑	PUNCT
ejpam-5205	168	9	v∈v1\d	v∈v1\d	ADJ
ejpam-5205	168	10	|sv	|sv	NUM
ejpam-5205	168	11	2	2	NUM
ejpam-5205	168	12	|	|	ADV
ejpam-5205	168	13	≥	≥	NOUN
ejpam-5205	168	14	2n−	2n−	NUM
ejpam-5205	168	15	k	k	NOUN
ejpam-5205	168	16	+	+	CCONJ
ejpam-5205	168	17	|d|+	|d|+	NOUN
ejpam-5205	168	18	2|v1|	2|v1|	NUM
ejpam-5205	168	19	−	−	NOUN
ejpam-5205	168	20	2|d|	2|d|	NUM
ejpam-5205	168	21	=	=	SYM
ejpam-5205	168	22	2n+	2n+	NUM
ejpam-5205	169	1	k	k	NOUN
ejpam-5205	169	2	−	−	PROPN
ejpam-5205	170	1	|d|	|d|	PROPN
ejpam-5205	170	2	≥	≥	NOUN
ejpam-5205	170	3	2n	2n	NUM
ejpam-5205	170	4	.	.	PUNCT
ejpam-5205	171	1	this	this	PRON
ejpam-5205	171	2	proves	prove	VERB
ejpam-5205	171	3	the	the	DET
ejpam-5205	171	4	desired	desire	VERB
ejpam-5205	171	5	equality	equality	NOUN
ejpam-5205	171	6	.	.	PUNCT
ejpam-5205	172	1	given	give	VERB
ejpam-5205	172	2	graphs	graph	NOUN
ejpam-5205	172	3	g	g	NOUN
ejpam-5205	173	1	and	and	CCONJ
ejpam-5205	173	2	h	h	NOUN
ejpam-5205	173	3	we	we	PRON
ejpam-5205	173	4	write	write	VERB
ejpam-5205	173	5	huv	huv	PROPN
ejpam-5205	173	6	to	to	PART
ejpam-5205	173	7	denote	denote	VERB
ejpam-5205	173	8	that	that	DET
ejpam-5205	173	9	copy	copy	NOUN
ejpam-5205	173	10	of	of	ADP
ejpam-5205	173	11	h	h	NOUN
ejpam-5205	173	12	that	that	PRON
ejpam-5205	173	13	is	be	AUX
ejpam-5205	173	14	being	be	AUX
ejpam-5205	173	15	joined	join	VERB
ejpam-5205	173	16	with	with	ADP
ejpam-5205	173	17	the	the	DET
ejpam-5205	173	18	end	end	NOUN
ejpam-5205	173	19	vertices	vertex	NOUN
ejpam-5205	173	20	of	of	ADP
ejpam-5205	173	21	the	the	DET
ejpam-5205	173	22	edge	edge	NOUN
ejpam-5205	173	23	uv	uv	PROPN
ejpam-5205	173	24	∈	∈	PROPN
ejpam-5205	173	25	e(g	e(g	PROPN
ejpam-5205	173	26	)	)	PUNCT
ejpam-5205	173	27	in	in	ADP
ejpam-5205	173	28	the	the	DET
ejpam-5205	173	29	edge	edge	NOUN
ejpam-5205	173	30	corona	corona	NOUN
ejpam-5205	173	31	g	g	PROPN
ejpam-5205	173	32	⋄h	⋄h	PROPN
ejpam-5205	173	33	.	.	PUNCT
ejpam-5205	174	1	if	if	SCONJ
ejpam-5205	174	2	h	h	NOUN
ejpam-5205	174	3	=	=	PRON
ejpam-5205	174	4	{	{	PUNCT
ejpam-5205	174	5	x	x	NOUN
ejpam-5205	174	6	}	}	PUNCT
ejpam-5205	174	7	,	,	PUNCT
ejpam-5205	174	8	then	then	ADV
ejpam-5205	174	9	we	we	PRON
ejpam-5205	174	10	write	write	VERB
ejpam-5205	174	11	v	v	NOUN
ejpam-5205	174	12	(	(	PUNCT
ejpam-5205	174	13	huv	huv	PROPN
ejpam-5205	174	14	)	)	PUNCT
ejpam-5205	174	15	=	=	PRON
ejpam-5205	174	16	{	{	PUNCT
ejpam-5205	174	17	xuv	xuv	NOUN
ejpam-5205	174	18	}	}	PUNCT
ejpam-5205	174	19	.	.	PUNCT
ejpam-5205	175	1	recall	recall	VERB
ejpam-5205	175	2	that	that	PRON
ejpam-5205	175	3	for	for	ADP
ejpam-5205	175	4	subsets	subset	NOUN
ejpam-5205	175	5	a	a	DET
ejpam-5205	175	6	and	and	CCONJ
ejpam-5205	175	7	b	b	PROPN
ejpam-5205	175	8	of	of	ADP
ejpam-5205	175	9	v	v	NOUN
ejpam-5205	175	10	(	(	PUNCT
ejpam-5205	175	11	g	g	NOUN
ejpam-5205	175	12	)	)	PUNCT
ejpam-5205	175	13	,	,	PUNCT
ejpam-5205	175	14	we	we	PRON
ejpam-5205	175	15	have	have	VERB
ejpam-5205	175	16	dg(a	dg(a	NOUN
ejpam-5205	175	17	,	,	PUNCT
ejpam-5205	175	18	b	b	NOUN
ejpam-5205	175	19	)	)	PUNCT
ejpam-5205	175	20	=	=	SYM
ejpam-5205	175	21	min{dg(a	min{dg(a	PROPN
ejpam-5205	175	22	,	,	PUNCT
ejpam-5205	175	23	b	b	NOUN
ejpam-5205	175	24	)	)	PUNCT
ejpam-5205	175	25	:	:	PUNCT
ejpam-5205	175	26	a	a	DET
ejpam-5205	175	27	∈	∈	PROPN
ejpam-5205	175	28	a	a	PRON
ejpam-5205	175	29	and	and	CCONJ
ejpam-5205	175	30	b	b	NOUN
ejpam-5205	175	31	∈	∈	PROPN
ejpam-5205	175	32	b	b	NOUN
ejpam-5205	175	33	}	}	PUNCT
ejpam-5205	175	34	.	.	PUNCT
ejpam-5205	176	1	let	let	VERB
ejpam-5205	176	2	f	f	PROPN
ejpam-5205	176	3	=	=	SYM
ejpam-5205	176	4	(	(	PUNCT
ejpam-5205	176	5	v0	v0	PROPN
ejpam-5205	176	6	,	,	PUNCT
ejpam-5205	176	7	v1	v1	NOUN
ejpam-5205	176	8	,	,	PUNCT
ejpam-5205	176	9	v2	v2	PROPN
ejpam-5205	176	10	)	)	PUNCT
ejpam-5205	176	11	be	be	AUX
ejpam-5205	176	12	a	a	DET
ejpam-5205	176	13	cvrdf	cvrdf	NOUN
ejpam-5205	176	14	on	on	ADP
ejpam-5205	176	15	g⋄h	g⋄h	PROPN
ejpam-5205	176	16	.	.	PUNCT
ejpam-5205	177	1	for	for	ADP
ejpam-5205	177	2	each	each	DET
ejpam-5205	177	3	v	v	NUM
ejpam-5205	177	4	∈	∈	PROPN
ejpam-5205	177	5	v	v	NOUN
ejpam-5205	177	6	(	(	PUNCT
ejpam-5205	177	7	g	g	NOUN
ejpam-5205	177	8	)	)	PUNCT
ejpam-5205	177	9	,	,	PUNCT
ejpam-5205	177	10	let	let	VERB
ejpam-5205	177	11	suv	suv	PROPN
ejpam-5205	177	12	1	1	NUM
ejpam-5205	177	13	=	=	SYM
ejpam-5205	177	14	v1∩v	v1∩v	NOUN
ejpam-5205	177	15	(	(	PUNCT
ejpam-5205	177	16	huv	huv	PROPN
ejpam-5205	177	17	)	)	PUNCT
ejpam-5205	177	18	and	and	CCONJ
ejpam-5205	177	19	suv	suv	PROPN
ejpam-5205	177	20	2	2	NUM
ejpam-5205	177	21	=	=	SYM
ejpam-5205	177	22	v2	v2	PROPN
ejpam-5205	177	23	∩	∩	ADJ
ejpam-5205	177	24	v	v	NOUN
ejpam-5205	177	25	(	(	PUNCT
ejpam-5205	177	26	huv	huv	PROPN
ejpam-5205	177	27	)	)	PUNCT
ejpam-5205	177	28	.	.	PUNCT
ejpam-5205	178	1	denote	denote	VERB
ejpam-5205	178	2	v	v	ADP
ejpam-5205	178	3	0	0	NUM
ejpam-5205	178	4	g	g	NOUN
ejpam-5205	178	5	=	=	SYM
ejpam-5205	178	6	v	v	PROPN
ejpam-5205	178	7	(	(	PUNCT
ejpam-5205	178	8	g	g	NOUN
ejpam-5205	178	9	)	)	PUNCT
ejpam-5205	178	10	∩	∩	PROPN
ejpam-5205	178	11	v0	v0	NOUN
ejpam-5205	178	12	,	,	PUNCT
ejpam-5205	178	13	v	v	NOUN
ejpam-5205	178	14	1	1	NUM
ejpam-5205	178	15	g	g	NOUN
ejpam-5205	178	16	=	=	SYM
ejpam-5205	178	17	v	v	PROPN
ejpam-5205	178	18	(	(	PUNCT
ejpam-5205	178	19	g	g	NOUN
ejpam-5205	178	20	)	)	PUNCT
ejpam-5205	178	21	∩	∩	NOUN
ejpam-5205	178	22	v1	v1	NOUN
ejpam-5205	178	23	,	,	PUNCT
ejpam-5205	178	24	and	and	CCONJ
ejpam-5205	178	25	v	v	ADP
ejpam-5205	178	26	2	2	NUM
ejpam-5205	178	27	g	g	NOUN
ejpam-5205	178	28	=	=	SYM
ejpam-5205	178	29	v	v	PROPN
ejpam-5205	178	30	(	(	PUNCT
ejpam-5205	178	31	g	g	NOUN
ejpam-5205	178	32	)	)	PUNCT
ejpam-5205	178	33	∩	∩	ADJ
ejpam-5205	178	34	v2	v2	PROPN
ejpam-5205	178	35	.	.	PUNCT
ejpam-5205	179	1	note	note	VERB
ejpam-5205	179	2	that	that	SCONJ
ejpam-5205	179	3	since	since	SCONJ
ejpam-5205	179	4	γ(k2	γ(k2	NOUN
ejpam-5205	179	5	⋄	⋄	PROPN
ejpam-5205	179	6	h	h	NOUN
ejpam-5205	179	7	)	)	PUNCT
ejpam-5205	179	8	=	=	SYM
ejpam-5205	179	9	1	1	NUM
ejpam-5205	179	10	for	for	ADP
ejpam-5205	179	11	any	any	DET
ejpam-5205	179	12	graph	graph	NOUN
ejpam-5205	179	13	h	h	NOUN
ejpam-5205	179	14	,	,	PUNCT
ejpam-5205	179	15	it	it	PRON
ejpam-5205	179	16	follows	follow	VERB
ejpam-5205	179	17	from	from	ADP
ejpam-5205	179	18	corollary	corollary	ADJ
ejpam-5205	179	19	1	1	NUM
ejpam-5205	179	20	that	that	PRON
ejpam-5205	179	21	γcvr(k2	γcvr(k2	VERB
ejpam-5205	179	22	⋄h	⋄h	NOUN
ejpam-5205	179	23	)	)	PUNCT
ejpam-5205	180	1	=	=	SYM
ejpam-5205	180	2	2	2	X
ejpam-5205	180	3	.	.	X
ejpam-5205	180	4	theorem	theorem	NOUN
ejpam-5205	180	5	9	9	NUM
ejpam-5205	180	6	.	.	PUNCT
ejpam-5205	181	1	let	let	VERB
ejpam-5205	181	2	g	g	PRON
ejpam-5205	181	3	be	be	AUX
ejpam-5205	181	4	a	a	DET
ejpam-5205	181	5	non	non	ADJ
ejpam-5205	181	6	-	-	ADJ
ejpam-5205	181	7	trivial	trivial	ADJ
ejpam-5205	181	8	connected	connected	ADJ
ejpam-5205	181	9	graph	graph	NOUN
ejpam-5205	181	10	such	such	ADJ
ejpam-5205	181	11	that	that	SCONJ
ejpam-5205	181	12	g	g	PROPN
ejpam-5205	181	13	̸=	̸=	PROPN
ejpam-5205	181	14	k2	k2	NOUN
ejpam-5205	181	15	and	and	CCONJ
ejpam-5205	181	16	let	let	VERB
ejpam-5205	181	17	h	h	NOUN
ejpam-5205	181	18	be	be	AUX
ejpam-5205	181	19	any	any	DET
ejpam-5205	181	20	graph	graph	NOUN
ejpam-5205	181	21	.	.	PUNCT
ejpam-5205	182	1	then	then	ADV
ejpam-5205	182	2	f	f	PROPN
ejpam-5205	182	3	=	=	SYM
ejpam-5205	182	4	(	(	PUNCT
ejpam-5205	182	5	v0	v0	PROPN
ejpam-5205	182	6	,	,	PUNCT
ejpam-5205	182	7	v1	v1	NOUN
ejpam-5205	182	8	,	,	PUNCT
ejpam-5205	182	9	v2	v2	PROPN
ejpam-5205	182	10	)	)	PUNCT
ejpam-5205	182	11	is	be	AUX
ejpam-5205	182	12	a	a	DET
ejpam-5205	182	13	cvrdf	cvrdf	NOUN
ejpam-5205	182	14	on	on	ADP
ejpam-5205	182	15	g	g	PROPN
ejpam-5205	182	16	⋄	⋄	PROPN
ejpam-5205	182	17	h	h	NOUN
ejpam-5205	183	1	if	if	SCONJ
ejpam-5205	183	2	and	and	CCONJ
ejpam-5205	183	3	only	only	ADV
ejpam-5205	183	4	if	if	SCONJ
ejpam-5205	183	5	each	each	PRON
ejpam-5205	183	6	of	of	ADP
ejpam-5205	183	7	the	the	DET
ejpam-5205	183	8	following	follow	VERB
ejpam-5205	183	9	conditions	condition	NOUN
ejpam-5205	183	10	holds	hold	VERB
ejpam-5205	183	11	.	.	PUNCT
ejpam-5205	184	1	(	(	PUNCT
ejpam-5205	184	2	i	i	NOUN
ejpam-5205	184	3	)	)	PUNCT
ejpam-5205	184	4	|{u	|{u	PROPN
ejpam-5205	184	5	,	,	PUNCT
ejpam-5205	184	6	v	v	NOUN
ejpam-5205	184	7	}	}	PUNCT
ejpam-5205	184	8	∩	∩	NOUN
ejpam-5205	184	9	(	(	PUNCT
ejpam-5205	184	10	v	v	NOUN
ejpam-5205	184	11	1	1	NUM
ejpam-5205	184	12	g	g	NOUN
ejpam-5205	184	13	∪	∪	NOUN
ejpam-5205	184	14	v	v	ADP
ejpam-5205	184	15	2	2	NUM
ejpam-5205	184	16	g)|	g)|	NOUN
ejpam-5205	184	17	=	=	NOUN
ejpam-5205	184	18	̸	̸	NUM
ejpam-5205	184	19	0	0	NUM
ejpam-5205	184	20	for	for	ADP
ejpam-5205	184	21	each	each	DET
ejpam-5205	184	22	uv	uv	PROPN
ejpam-5205	184	23	∈	∈	PROPN
ejpam-5205	184	24	e(g	e(g	PROPN
ejpam-5205	184	25	)	)	PUNCT
ejpam-5205	184	26	.	.	PUNCT
ejpam-5205	185	1	(	(	PUNCT
ejpam-5205	185	2	ii	ii	NOUN
ejpam-5205	185	3	)	)	PUNCT
ejpam-5205	185	4	for	for	ADP
ejpam-5205	185	5	each	each	DET
ejpam-5205	185	6	pair	pair	NOUN
ejpam-5205	185	7	of	of	ADP
ejpam-5205	185	8	distinct	distinct	ADJ
ejpam-5205	185	9	edges	edge	NOUN
ejpam-5205	185	10	uv	uv	NOUN
ejpam-5205	185	11	and	and	CCONJ
ejpam-5205	185	12	zw	zw	PROPN
ejpam-5205	185	13	of	of	ADP
ejpam-5205	185	14	g	g	PROPN
ejpam-5205	185	15	,	,	PUNCT
ejpam-5205	185	16	ig(x	ig(x	X
ejpam-5205	185	17	,	,	PUNCT
ejpam-5205	185	18	y	y	PROPN
ejpam-5205	185	19	)	)	PUNCT
ejpam-5205	186	1	⊆	⊆	NUM
ejpam-5205	186	2	v	v	ADP
ejpam-5205	186	3	1	1	NUM
ejpam-5205	186	4	g	g	NOUN
ejpam-5205	186	5	∪	∪	NOUN
ejpam-5205	186	6	v	v	ADP
ejpam-5205	186	7	2	2	NUM
ejpam-5205	186	8	g	g	NOUN
ejpam-5205	186	9	whenever	whenever	SCONJ
ejpam-5205	186	10	x	x	SYM
ejpam-5205	186	11	∈	∈	PROPN
ejpam-5205	186	12	{	{	PUNCT
ejpam-5205	186	13	u	u	NOUN
ejpam-5205	186	14	,	,	PUNCT
ejpam-5205	186	15	v	v	NOUN
ejpam-5205	186	16	}	}	PUNCT
ejpam-5205	186	17	∩	∩	NOUN
ejpam-5205	186	18	(	(	PUNCT
ejpam-5205	186	19	v	v	NOUN
ejpam-5205	186	20	1	1	NUM
ejpam-5205	186	21	g	g	NOUN
ejpam-5205	186	22	∪	∪	NOUN
ejpam-5205	186	23	v	v	ADP
ejpam-5205	186	24	2	2	NUM
ejpam-5205	186	25	g	g	NOUN
ejpam-5205	186	26	)	)	PUNCT
ejpam-5205	186	27	and	and	CCONJ
ejpam-5205	186	28	y	y	PROPN
ejpam-5205	186	29	∈	∈	PROPN
ejpam-5205	186	30	{	{	PUNCT
ejpam-5205	186	31	z	z	NOUN
ejpam-5205	186	32	,	,	PUNCT
ejpam-5205	186	33	w	w	NOUN
ejpam-5205	186	34	}	}	PUNCT
ejpam-5205	186	35	∩	∩	NOUN
ejpam-5205	186	36	(	(	PUNCT
ejpam-5205	186	37	v	v	NOUN
ejpam-5205	186	38	1	1	NUM
ejpam-5205	186	39	g	g	NOUN
ejpam-5205	186	40	∪	∪	NOUN
ejpam-5205	186	41	v	v	ADP
ejpam-5205	186	42	2	2	NUM
ejpam-5205	186	43	g	g	NOUN
ejpam-5205	186	44	)	)	PUNCT
ejpam-5205	186	45	.	.	PUNCT
ejpam-5205	187	1	(	(	PUNCT
ejpam-5205	187	2	iii	iii	X
ejpam-5205	187	3	)	)	PUNCT
ejpam-5205	187	4	for	for	ADP
ejpam-5205	187	5	every	every	DET
ejpam-5205	187	6	pair	pair	NOUN
ejpam-5205	187	7	of	of	ADP
ejpam-5205	187	8	distinct	distinct	ADJ
ejpam-5205	187	9	edges	edge	NOUN
ejpam-5205	187	10	e	e	NOUN
ejpam-5205	187	11	and	and	CCONJ
ejpam-5205	187	12	e′	e′	PROPN
ejpam-5205	187	13	of	of	ADP
ejpam-5205	187	14	g	g	PROPN
ejpam-5205	187	15	with	with	ADP
ejpam-5205	187	16	se	se	PROPN
ejpam-5205	187	17	1	1	NUM
ejpam-5205	187	18	∪	∪	X
ejpam-5205	187	19	se	se	X
ejpam-5205	187	20	2	2	NUM
ejpam-5205	187	21	̸=	̸=	PROPN
ejpam-5205	187	22	∅	∅	NOUN
ejpam-5205	187	23	and	and	CCONJ
ejpam-5205	187	24	se′	se′	NOUN
ejpam-5205	187	25	1	1	NUM
ejpam-5205	187	26	∪	∪	VERB
ejpam-5205	187	27	se′	se′	NOUN
ejpam-5205	187	28	2	2	NUM
ejpam-5205	187	29	̸=	̸=	PROPN
ejpam-5205	187	30	∅	∅	NOUN
ejpam-5205	187	31	,	,	PUNCT
ejpam-5205	187	32	v	v	NOUN
ejpam-5205	187	33	,	,	PUNCT
ejpam-5205	187	34	z	z	PROPN
ejpam-5205	187	35	∈	∈	PROPN
ejpam-5205	187	36	v	v	ADP
ejpam-5205	187	37	1	1	NUM
ejpam-5205	187	38	g	g	NOUN
ejpam-5205	187	39	∪	∪	NOUN
ejpam-5205	187	40	v	v	ADP
ejpam-5205	187	41	2	2	NUM
ejpam-5205	187	42	g	g	NOUN
ejpam-5205	187	43	whenever	whenever	SCONJ
ejpam-5205	187	44	v	v	NOUN
ejpam-5205	187	45	and	and	CCONJ
ejpam-5205	187	46	z	z	NOUN
ejpam-5205	187	47	are	be	AUX
ejpam-5205	187	48	incident	incident	NOUN
ejpam-5205	187	49	with	with	ADP
ejpam-5205	187	50	e	e	NOUN
ejpam-5205	187	51	and	and	CCONJ
ejpam-5205	187	52	e′	e′	PROPN
ejpam-5205	187	53	,	,	PUNCT
ejpam-5205	187	54	respectively	respectively	ADV
ejpam-5205	187	55	,	,	PUNCT
ejpam-5205	187	56	with	with	ADP
ejpam-5205	187	57	dg(v	dg(v	NOUN
ejpam-5205	187	58	,	,	PUNCT
ejpam-5205	187	59	z	z	NOUN
ejpam-5205	187	60	)	)	PUNCT
ejpam-5205	187	61	=	=	SYM
ejpam-5205	187	62	dg({u	dg({u	PROPN
ejpam-5205	187	63	,	,	PUNCT
ejpam-5205	187	64	v	v	NOUN
ejpam-5205	187	65	}	}	PUNCT
ejpam-5205	187	66	,	,	PUNCT
ejpam-5205	187	67	{	{	PUNCT
ejpam-5205	187	68	z	z	NOUN
ejpam-5205	187	69	,	,	PUNCT
ejpam-5205	187	70	w	w	NOUN
ejpam-5205	187	71	}	}	PUNCT
ejpam-5205	187	72	)	)	PUNCT
ejpam-5205	187	73	.	.	PUNCT
ejpam-5205	188	1	(	(	PUNCT
ejpam-5205	188	2	iv	iv	X
ejpam-5205	188	3	)	)	PUNCT
ejpam-5205	188	4	for	for	ADP
ejpam-5205	188	5	each	each	DET
ejpam-5205	188	6	uv	uv	PROPN
ejpam-5205	188	7	∈	∈	PROPN
ejpam-5205	188	8	e(g	e(g	PROPN
ejpam-5205	188	9	)	)	PUNCT
ejpam-5205	188	10	such	such	ADJ
ejpam-5205	188	11	that	that	SCONJ
ejpam-5205	188	12	{	{	PUNCT
ejpam-5205	188	13	u	u	NOUN
ejpam-5205	188	14	,	,	PUNCT
ejpam-5205	188	15	v	v	NOUN
ejpam-5205	188	16	}	}	PUNCT
ejpam-5205	188	17	∩	∩	NOUN
ejpam-5205	188	18	(	(	PUNCT
ejpam-5205	188	19	v1	v1	NOUN
ejpam-5205	188	20	∪	∪	X
ejpam-5205	188	21	v2	v2	NOUN
ejpam-5205	188	22	)	)	PUNCT
ejpam-5205	188	23	=	=	PRON
ejpam-5205	188	24	{	{	PUNCT
ejpam-5205	188	25	v	v	NOUN
ejpam-5205	188	26	}	}	PUNCT
ejpam-5205	188	27	,	,	PUNCT
ejpam-5205	188	28	it	it	PRON
ejpam-5205	188	29	holds	hold	VERB
ejpam-5205	188	30	that	that	SCONJ
ejpam-5205	188	31	(	(	PUNCT
ejpam-5205	188	32	a	a	X
ejpam-5205	188	33	)	)	PUNCT
ejpam-5205	188	34	suv	suv	NOUN
ejpam-5205	188	35	1	1	NUM
ejpam-5205	188	36	∪	∪	PROPN
ejpam-5205	188	37	suv	suv	NOUN
ejpam-5205	188	38	2	2	NUM
ejpam-5205	188	39	a	a	DET
ejpam-5205	188	40	clique	clique	NOUN
ejpam-5205	188	41	in	in	ADP
ejpam-5205	188	42	huv	huv	PROPN
ejpam-5205	188	43	whenever	whenever	SCONJ
ejpam-5205	188	44	suv	suv	PROPN
ejpam-5205	188	45	1	1	NUM
ejpam-5205	188	46	∪	∪	PROPN
ejpam-5205	188	47	suv	suv	X
ejpam-5205	188	48	2	2	NUM
ejpam-5205	188	49	̸=	̸=	PROPN
ejpam-5205	188	50	∅	∅	NOUN
ejpam-5205	188	51	and	and	CCONJ
ejpam-5205	188	52	(	(	PUNCT
ejpam-5205	188	53	b	b	NOUN
ejpam-5205	188	54	)	)	PUNCT
ejpam-5205	188	55	v	v	NOUN
ejpam-5205	188	56	∈	∈	PROPN
ejpam-5205	188	57	v	v	ADP
ejpam-5205	188	58	2	2	NUM
ejpam-5205	188	59	g	g	NOUN
ejpam-5205	188	60	or	or	CCONJ
ejpam-5205	188	61	suv	suv	PROPN
ejpam-5205	188	62	2	2	NUM
ejpam-5205	188	63	̸=	̸=	PROPN
ejpam-5205	188	64	∅	∅	NOUN
ejpam-5205	188	65	and	and	CCONJ
ejpam-5205	188	66	suv	suv	PROPN
ejpam-5205	188	67	0	0	NUM
ejpam-5205	188	68	⊆	⊆	NUM
ejpam-5205	188	69	nhuv(suv	nhuv(suv	NOUN
ejpam-5205	188	70	2	2	NUM
ejpam-5205	188	71	)	)	PUNCT
ejpam-5205	188	72	.	.	PUNCT
ejpam-5205	189	1	(	(	PUNCT
ejpam-5205	189	2	v	v	NOUN
ejpam-5205	189	3	)	)	PUNCT
ejpam-5205	189	4	for	for	ADP
ejpam-5205	189	5	each	each	DET
ejpam-5205	189	6	uv	uv	PROPN
ejpam-5205	189	7	∈	∈	PROPN
ejpam-5205	189	8	e(g	e(g	PROPN
ejpam-5205	189	9	)	)	PUNCT
ejpam-5205	189	10	such	such	ADJ
ejpam-5205	189	11	that	that	SCONJ
ejpam-5205	189	12	{	{	PUNCT
ejpam-5205	189	13	u	u	NOUN
ejpam-5205	189	14	,	,	PUNCT
ejpam-5205	189	15	v	v	NOUN
ejpam-5205	189	16	}	}	PUNCT
ejpam-5205	189	17	⊆	⊆	NUM
ejpam-5205	189	18	(	(	PUNCT
ejpam-5205	189	19	v1	v1	VERB
ejpam-5205	189	20	∪	∪	NOUN
ejpam-5205	189	21	v2	v2	NOUN
ejpam-5205	189	22	)	)	PUNCT
ejpam-5205	189	23	and	and	CCONJ
ejpam-5205	189	24	suv	suv	PROPN
ejpam-5205	189	25	1	1	NUM
ejpam-5205	189	26	∪	∪	PROPN
ejpam-5205	189	27	suv	suv	NOUN
ejpam-5205	189	28	2	2	NUM
ejpam-5205	189	29	̸=	̸=	PROPN
ejpam-5205	189	30	v	v	NOUN
ejpam-5205	189	31	(	(	PUNCT
ejpam-5205	189	32	huv	huv	PROPN
ejpam-5205	189	33	)	)	PUNCT
ejpam-5205	189	34	,	,	PUNCT
ejpam-5205	189	35	it	it	PRON
ejpam-5205	189	36	holds	hold	VERB
ejpam-5205	189	37	that	that	SCONJ
ejpam-5205	189	38	r.	r.	PROPN
ejpam-5205	189	39	fortosa	fortosa	PROPN
ejpam-5205	189	40	,	,	PUNCT
ejpam-5205	189	41	s.	s.	PROPN
ejpam-5205	189	42	canoy	canoy	PROPN
ejpam-5205	189	43	jr	jr	PROPN
ejpam-5205	189	44	.	.	PROPN
ejpam-5205	189	45	/	/	SYM
ejpam-5205	189	46	eur	eur	PROPN
ejpam-5205	189	47	.	.	PUNCT
ejpam-5205	190	1	j.	j.	PROPN
ejpam-5205	190	2	pure	pure	PROPN
ejpam-5205	190	3	appl	appl	PROPN
ejpam-5205	190	4	.	.	PROPN
ejpam-5205	190	5	math	math	PROPN
ejpam-5205	190	6	,	,	PUNCT
ejpam-5205	190	7	17	17	NUM
ejpam-5205	190	8	(	(	PUNCT
ejpam-5205	190	9	2	2	NUM
ejpam-5205	190	10	)	)	PUNCT
ejpam-5205	190	11	(	(	PUNCT
ejpam-5205	190	12	2024	2024	NUM
ejpam-5205	190	13	)	)	PUNCT
ejpam-5205	190	14	,	,	PUNCT
ejpam-5205	190	15	1335	1335	NUM
ejpam-5205	190	16	-	-	SYM
ejpam-5205	190	17	1351	1351	NUM
ejpam-5205	190	18	1341	1341	NUM
ejpam-5205	190	19	(	(	PUNCT
ejpam-5205	190	20	c	c	NOUN
ejpam-5205	190	21	)	)	PUNCT
ejpam-5205	190	22	v	v	NOUN
ejpam-5205	190	23	(	(	PUNCT
ejpam-5205	190	24	huv	huv	PROPN
ejpam-5205	190	25	)	)	PUNCT
ejpam-5205	190	26	\	\	PROPN
ejpam-5205	191	1	(	(	PUNCT
ejpam-5205	191	2	suv	suv	NOUN
ejpam-5205	191	3	1	1	NUM
ejpam-5205	191	4	∪	∪	PROPN
ejpam-5205	191	5	suv	suv	X
ejpam-5205	191	6	2	2	NUM
ejpam-5205	191	7	)	)	PUNCT
ejpam-5205	191	8	is	be	AUX
ejpam-5205	191	9	a	a	DET
ejpam-5205	191	10	non	non	ADJ
ejpam-5205	191	11	-	-	ADJ
ejpam-5205	191	12	connecting	connecting	ADJ
ejpam-5205	191	13	set	set	NOUN
ejpam-5205	191	14	in	in	ADP
ejpam-5205	191	15	huv	huv	PROPN
ejpam-5205	191	16	and	and	CCONJ
ejpam-5205	191	17	(	(	PUNCT
ejpam-5205	191	18	d	d	NOUN
ejpam-5205	191	19	)	)	PUNCT
ejpam-5205	191	20	{	{	PUNCT
ejpam-5205	191	21	u	u	NOUN
ejpam-5205	191	22	,	,	PUNCT
ejpam-5205	191	23	v	v	NOUN
ejpam-5205	191	24	}	}	PUNCT
ejpam-5205	191	25	∩	∩	NOUN
ejpam-5205	191	26	v	v	ADP
ejpam-5205	191	27	2	2	NUM
ejpam-5205	191	28	g	g	NOUN
ejpam-5205	191	29	̸=	̸=	PROPN
ejpam-5205	191	30	∅	∅	NOUN
ejpam-5205	191	31	or	or	CCONJ
ejpam-5205	191	32	suv	suv	PROPN
ejpam-5205	191	33	2	2	NUM
ejpam-5205	191	34	̸=	̸=	PROPN
ejpam-5205	191	35	∅	∅	NOUN
ejpam-5205	191	36	and	and	CCONJ
ejpam-5205	191	37	suv	suv	PROPN
ejpam-5205	191	38	0	0	NUM
ejpam-5205	192	1	⊆	⊆	NUM
ejpam-5205	192	2	nhuv(suv	nhuv(suv	NOUN
ejpam-5205	192	3	2	2	NUM
ejpam-5205	192	4	)	)	PUNCT
ejpam-5205	192	5	.	.	PUNCT
ejpam-5205	193	1	proof	proof	NOUN
ejpam-5205	193	2	.	.	PUNCT
ejpam-5205	194	1	let	let	VERB
ejpam-5205	194	2	u	u	NOUN
ejpam-5205	194	3	,	,	PUNCT
ejpam-5205	194	4	v	v	PROPN
ejpam-5205	194	5	∈	∈	PROPN
ejpam-5205	194	6	v	v	NOUN
ejpam-5205	194	7	(	(	PUNCT
ejpam-5205	194	8	g	g	NOUN
ejpam-5205	194	9	)	)	PUNCT
ejpam-5205	194	10	such	such	ADJ
ejpam-5205	194	11	that	that	SCONJ
ejpam-5205	194	12	uv	uv	PROPN
ejpam-5205	194	13	∈	∈	PROPN
ejpam-5205	194	14	e(g	e(g	PROPN
ejpam-5205	194	15	)	)	PUNCT
ejpam-5205	194	16	.	.	PUNCT
ejpam-5205	195	1	then	then	ADV
ejpam-5205	195	2	|{u	|{u	VERB
ejpam-5205	195	3	,	,	PUNCT
ejpam-5205	195	4	v}∩(v	v}∩(v	PROPN
ejpam-5205	195	5	1	1	NUM
ejpam-5205	195	6	g∪v	g∪v	NOUN
ejpam-5205	195	7	2	2	NUM
ejpam-5205	195	8	g)|	g)|	NOUN
ejpam-5205	195	9	=	=	NOUN
ejpam-5205	195	10	̸	̸	NUM
ejpam-5205	195	11	0	0	PUNCT
ejpam-5205	196	1	because	because	SCONJ
ejpam-5205	196	2	v1∪v2	v1∪v2	ADV
ejpam-5205	196	3	is	be	AUX
ejpam-5205	196	4	convex	convex	ADJ
ejpam-5205	196	5	in	in	ADP
ejpam-5205	196	6	g	g	PROPN
ejpam-5205	196	7	⋄h	⋄h	PROPN
ejpam-5205	196	8	and	and	CCONJ
ejpam-5205	196	9	g	g	PROPN
ejpam-5205	196	10	̸=	̸=	PROPN
ejpam-5205	196	11	k2	k2	NOUN
ejpam-5205	196	12	.	.	PUNCT
ejpam-5205	197	1	thus	thus	ADV
ejpam-5205	197	2	,	,	PUNCT
ejpam-5205	197	3	(	(	PUNCT
ejpam-5205	197	4	i	i	NOUN
ejpam-5205	197	5	)	)	PUNCT
ejpam-5205	197	6	holds	hold	VERB
ejpam-5205	197	7	.	.	PUNCT
ejpam-5205	198	1	let	let	VERB
ejpam-5205	199	1	uv	uv	INTJ
ejpam-5205	199	2	and	and	CCONJ
ejpam-5205	199	3	zw	zw	AUX
ejpam-5205	199	4	be	be	AUX
ejpam-5205	199	5	distinct	distinct	ADJ
ejpam-5205	199	6	edges	edge	NOUN
ejpam-5205	199	7	of	of	ADP
ejpam-5205	199	8	g	g	NOUN
ejpam-5205	199	9	and	and	CCONJ
ejpam-5205	199	10	let	let	VERB
ejpam-5205	199	11	x	x	X
ejpam-5205	199	12	∈	∈	PROPN
ejpam-5205	199	13	{	{	PUNCT
ejpam-5205	199	14	u	u	NOUN
ejpam-5205	199	15	,	,	PUNCT
ejpam-5205	199	16	v	v	NOUN
ejpam-5205	199	17	}	}	PUNCT
ejpam-5205	199	18	∩	∩	NOUN
ejpam-5205	199	19	(	(	PUNCT
ejpam-5205	199	20	v	v	NOUN
ejpam-5205	199	21	1	1	NUM
ejpam-5205	199	22	g	g	NOUN
ejpam-5205	199	23	∪	∪	NOUN
ejpam-5205	199	24	v	v	ADP
ejpam-5205	199	25	2	2	NUM
ejpam-5205	199	26	g	g	NOUN
ejpam-5205	199	27	)	)	PUNCT
ejpam-5205	199	28	and	and	CCONJ
ejpam-5205	199	29	y	y	PROPN
ejpam-5205	199	30	∈	∈	PROPN
ejpam-5205	199	31	{	{	PUNCT
ejpam-5205	199	32	z	z	NOUN
ejpam-5205	199	33	,	,	PUNCT
ejpam-5205	199	34	w	w	NOUN
ejpam-5205	199	35	}	}	PUNCT
ejpam-5205	199	36	∩	∩	NOUN
ejpam-5205	199	37	(	(	PUNCT
ejpam-5205	199	38	v	v	NOUN
ejpam-5205	199	39	1	1	NUM
ejpam-5205	199	40	g	g	NOUN
ejpam-5205	199	41	∪	∪	NOUN
ejpam-5205	199	42	v	v	ADP
ejpam-5205	199	43	2	2	NUM
ejpam-5205	199	44	g	g	NOUN
ejpam-5205	199	45	)	)	PUNCT
ejpam-5205	199	46	.	.	PUNCT
ejpam-5205	200	1	since	since	SCONJ
ejpam-5205	200	2	v1	v1	NOUN
ejpam-5205	200	3	∪	∪	NOUN
ejpam-5205	200	4	v2	v2	NOUN
ejpam-5205	200	5	is	be	AUX
ejpam-5205	200	6	convex	convex	NOUN
ejpam-5205	200	7	in	in	ADP
ejpam-5205	200	8	g	g	PROPN
ejpam-5205	200	9	⋄	⋄	PROPN
ejpam-5205	200	10	h	h	NOUN
ejpam-5205	200	11	,	,	PUNCT
ejpam-5205	200	12	it	it	PRON
ejpam-5205	200	13	follows	follow	VERB
ejpam-5205	200	14	that	that	SCONJ
ejpam-5205	200	15	ig(x	ig(x	ADV
ejpam-5205	200	16	,	,	PUNCT
ejpam-5205	200	17	y	y	NOUN
ejpam-5205	200	18	)	)	PUNCT
ejpam-5205	200	19	=	=	SYM
ejpam-5205	200	20	ig⋄h(x	ig⋄h(x	PROPN
ejpam-5205	200	21	,	,	PUNCT
ejpam-5205	200	22	y	y	PROPN
ejpam-5205	200	23	)	)	PUNCT
ejpam-5205	200	24	⊆	⊆	NUM
ejpam-5205	200	25	v1	v1	NOUN
ejpam-5205	200	26	∪	∪	NOUN
ejpam-5205	200	27	v2	v2	NOUN
ejpam-5205	200	28	.	.	PUNCT
ejpam-5205	201	1	therefore	therefore	ADV
ejpam-5205	201	2	,	,	PUNCT
ejpam-5205	201	3	ig(x	ig(x	X
ejpam-5205	201	4	,	,	PUNCT
ejpam-5205	201	5	y	y	PROPN
ejpam-5205	201	6	)	)	PUNCT
ejpam-5205	201	7	⊆	⊆	NUM
ejpam-5205	201	8	v	v	ADP
ejpam-5205	201	9	1	1	NUM
ejpam-5205	201	10	g	g	NOUN
ejpam-5205	201	11	∪	∪	NOUN
ejpam-5205	201	12	v	v	ADP
ejpam-5205	201	13	2	2	NUM
ejpam-5205	201	14	g	g	NOUN
ejpam-5205	201	15	,	,	PUNCT
ejpam-5205	201	16	showing	show	VERB
ejpam-5205	201	17	that	that	SCONJ
ejpam-5205	201	18	(	(	PUNCT
ejpam-5205	201	19	ii	ii	NOUN
ejpam-5205	201	20	)	)	PUNCT
ejpam-5205	201	21	holds	hold	VERB
ejpam-5205	201	22	.	.	PUNCT
ejpam-5205	202	1	let	let	VERB
ejpam-5205	202	2	e	e	NOUN
ejpam-5205	202	3	and	and	CCONJ
ejpam-5205	202	4	e′	e′	VERB
ejpam-5205	202	5	be	be	AUX
ejpam-5205	202	6	distinct	distinct	ADJ
ejpam-5205	202	7	edges	edge	NOUN
ejpam-5205	202	8	of	of	ADP
ejpam-5205	202	9	g	g	NOUN
ejpam-5205	202	10	with	with	ADP
ejpam-5205	202	11	se	se	X
ejpam-5205	202	12	1	1	NUM
ejpam-5205	202	13	∪	∪	X
ejpam-5205	202	14	se	se	X
ejpam-5205	202	15	2	2	NUM
ejpam-5205	202	16	̸=	̸=	PROPN
ejpam-5205	202	17	∅	∅	NOUN
ejpam-5205	202	18	and	and	CCONJ
ejpam-5205	202	19	se′	se′	NOUN
ejpam-5205	202	20	1	1	NUM
ejpam-5205	202	21	∪	∪	VERB
ejpam-5205	202	22	se′	se′	NOUN
ejpam-5205	202	23	2	2	NUM
ejpam-5205	202	24	̸=	̸=	PROPN
ejpam-5205	202	25	∅	∅	NOUN
ejpam-5205	202	26	and	and	CCONJ
ejpam-5205	202	27	suppose	suppose	VERB
ejpam-5205	202	28	that	that	SCONJ
ejpam-5205	202	29	v	v	NOUN
ejpam-5205	202	30	and	and	CCONJ
ejpam-5205	202	31	z	z	NOUN
ejpam-5205	202	32	are	be	AUX
ejpam-5205	202	33	incident	incident	NOUN
ejpam-5205	202	34	with	with	ADP
ejpam-5205	202	35	e	e	NOUN
ejpam-5205	202	36	and	and	CCONJ
ejpam-5205	202	37	e′	e′	PROPN
ejpam-5205	202	38	,	,	PUNCT
ejpam-5205	202	39	respectively	respectively	ADV
ejpam-5205	202	40	,	,	PUNCT
ejpam-5205	202	41	with	with	ADP
ejpam-5205	202	42	dg(v	dg(v	NOUN
ejpam-5205	202	43	,	,	PUNCT
ejpam-5205	202	44	z	z	NOUN
ejpam-5205	202	45	)	)	PUNCT
ejpam-5205	202	46	=	=	SYM
ejpam-5205	202	47	dg({u	dg({u	PROPN
ejpam-5205	202	48	,	,	PUNCT
ejpam-5205	202	49	v	v	NOUN
ejpam-5205	202	50	}	}	PUNCT
ejpam-5205	202	51	,	,	PUNCT
ejpam-5205	202	52	{	{	PUNCT
ejpam-5205	202	53	z	z	NOUN
ejpam-5205	202	54	,	,	PUNCT
ejpam-5205	202	55	w	w	NOUN
ejpam-5205	202	56	}	}	PUNCT
ejpam-5205	202	57	)	)	PUNCT
ejpam-5205	202	58	.	.	PUNCT
ejpam-5205	203	1	let	let	VERB
ejpam-5205	203	2	x	x	SYM
ejpam-5205	203	3	∈	∈	PROPN
ejpam-5205	203	4	se	se	X
ejpam-5205	203	5	1	1	NUM
ejpam-5205	203	6	∪	∪	X
ejpam-5205	203	7	se	se	X
ejpam-5205	203	8	2	2	NUM
ejpam-5205	203	9	and	and	CCONJ
ejpam-5205	203	10	y	y	PROPN
ejpam-5205	203	11	∈	∈	PROPN
ejpam-5205	203	12	se′	se′	NOUN
ejpam-5205	203	13	1	1	NUM
ejpam-5205	203	14	∪	∪	VERB
ejpam-5205	203	15	se′	se′	NOUN
ejpam-5205	203	16	2	2	NUM
ejpam-5205	203	17	.	.	PUNCT
ejpam-5205	204	1	then	then	ADV
ejpam-5205	204	2	ig[v	ig[v	PROPN
ejpam-5205	204	3	,	,	PUNCT
ejpam-5205	204	4	z	z	X
ejpam-5205	204	5	]	]	X
ejpam-5205	204	6	⊆	⊆	NUM
ejpam-5205	204	7	ig⋄h	ig⋄h	PROPN
ejpam-5205	205	1	[	[	X
ejpam-5205	205	2	x	x	X
ejpam-5205	205	3	,	,	PUNCT
ejpam-5205	205	4	y	y	PROPN
ejpam-5205	205	5	]	]	X
ejpam-5205	205	6	.	.	PUNCT
ejpam-5205	206	1	since	since	SCONJ
ejpam-5205	206	2	v1	v1	NOUN
ejpam-5205	206	3	∪	∪	NOUN
ejpam-5205	206	4	v2	v2	NOUN
ejpam-5205	206	5	is	be	AUX
ejpam-5205	206	6	convex	convex	NOUN
ejpam-5205	206	7	,	,	PUNCT
ejpam-5205	206	8	ig⋄h	ig⋄h	PROPN
ejpam-5205	207	1	[	[	X
ejpam-5205	207	2	x	x	X
ejpam-5205	207	3	,	,	PUNCT
ejpam-5205	207	4	y	y	PROPN
ejpam-5205	207	5	]	]	X
ejpam-5205	207	6	⊆	⊆	NUM
ejpam-5205	207	7	v1	v1	NOUN
ejpam-5205	207	8	∪	∪	NOUN
ejpam-5205	207	9	v2	v2	NOUN
ejpam-5205	207	10	.	.	PUNCT
ejpam-5205	208	1	hence	hence	ADV
ejpam-5205	208	2	,	,	PUNCT
ejpam-5205	208	3	v	v	NOUN
ejpam-5205	208	4	,	,	PUNCT
ejpam-5205	208	5	z	z	PROPN
ejpam-5205	208	6	∈	∈	PROPN
ejpam-5205	208	7	v	v	ADP
ejpam-5205	208	8	1	1	NUM
ejpam-5205	208	9	g	g	NOUN
ejpam-5205	208	10	∪	∪	NOUN
ejpam-5205	208	11	v	v	ADP
ejpam-5205	208	12	2	2	NUM
ejpam-5205	208	13	g.	g.	NOUN
ejpam-5205	208	14	this	this	PRON
ejpam-5205	208	15	shows	show	VERB
ejpam-5205	208	16	that	that	SCONJ
ejpam-5205	208	17	(	(	PUNCT
ejpam-5205	208	18	iii	iii	NOUN
ejpam-5205	208	19	)	)	PUNCT
ejpam-5205	208	20	holds	hold	VERB
ejpam-5205	208	21	.	.	PUNCT
ejpam-5205	209	1	now	now	ADV
ejpam-5205	209	2	,	,	PUNCT
ejpam-5205	209	3	let	let	VERB
ejpam-5205	209	4	uv	uv	PRON
ejpam-5205	209	5	∈	∈	PROPN
ejpam-5205	209	6	e(g	e(g	PROPN
ejpam-5205	209	7	)	)	PUNCT
ejpam-5205	209	8	such	such	ADJ
ejpam-5205	209	9	that	that	SCONJ
ejpam-5205	209	10	{	{	PUNCT
ejpam-5205	209	11	u	u	NOUN
ejpam-5205	209	12	,	,	PUNCT
ejpam-5205	209	13	v	v	NOUN
ejpam-5205	209	14	}	}	PUNCT
ejpam-5205	209	15	∩	∩	NOUN
ejpam-5205	209	16	(	(	PUNCT
ejpam-5205	209	17	v1	v1	NOUN
ejpam-5205	209	18	∪	∪	X
ejpam-5205	209	19	v2	v2	NOUN
ejpam-5205	209	20	)	)	PUNCT
ejpam-5205	209	21	=	=	PRON
ejpam-5205	209	22	{	{	PUNCT
ejpam-5205	209	23	v	v	NOUN
ejpam-5205	209	24	}	}	PUNCT
ejpam-5205	209	25	.	.	PUNCT
ejpam-5205	210	1	since	since	SCONJ
ejpam-5205	210	2	v1	v1	NOUN
ejpam-5205	210	3	∪	∪	NOUN
ejpam-5205	210	4	v2	v2	NOUN
ejpam-5205	210	5	is	be	AUX
ejpam-5205	210	6	convex	convex	NOUN
ejpam-5205	210	7	,	,	PUNCT
ejpam-5205	210	8	(	(	PUNCT
ejpam-5205	210	9	a	a	PRON
ejpam-5205	210	10	)	)	PUNCT
ejpam-5205	210	11	holds	hold	NOUN
ejpam-5205	210	12	.	.	PUNCT
ejpam-5205	211	1	also	also	ADV
ejpam-5205	211	2	,	,	PUNCT
ejpam-5205	211	3	(	(	PUNCT
ejpam-5205	211	4	b	b	X
ejpam-5205	211	5	)	)	PUNCT
ejpam-5205	211	6	holds	hold	VERB
ejpam-5205	211	7	since	since	SCONJ
ejpam-5205	211	8	f	f	PROPN
ejpam-5205	211	9	is	be	AUX
ejpam-5205	211	10	a	a	DET
ejpam-5205	211	11	cvrdf	cvrdf	NOUN
ejpam-5205	211	12	on	on	ADP
ejpam-5205	211	13	g	g	PROPN
ejpam-5205	211	14	⋄h	⋄h	PROPN
ejpam-5205	211	15	.	.	PUNCT
ejpam-5205	212	1	thus	thus	ADV
ejpam-5205	212	2	,	,	PUNCT
ejpam-5205	212	3	(	(	PUNCT
ejpam-5205	212	4	iv	iv	X
ejpam-5205	212	5	)	)	PUNCT
ejpam-5205	212	6	holds	hold	NOUN
ejpam-5205	212	7	.	.	PUNCT
ejpam-5205	213	1	next	next	ADV
ejpam-5205	213	2	,	,	PUNCT
ejpam-5205	213	3	let	let	VERB
ejpam-5205	213	4	uv	uv	PRON
ejpam-5205	213	5	∈	∈	PROPN
ejpam-5205	213	6	e(g	e(g	PROPN
ejpam-5205	213	7	)	)	PUNCT
ejpam-5205	213	8	such	such	ADJ
ejpam-5205	213	9	that	that	SCONJ
ejpam-5205	213	10	{	{	PUNCT
ejpam-5205	213	11	u	u	NOUN
ejpam-5205	213	12	,	,	PUNCT
ejpam-5205	213	13	v	v	NOUN
ejpam-5205	213	14	}	}	PUNCT
ejpam-5205	213	15	⊆	⊆	NUM
ejpam-5205	213	16	(	(	PUNCT
ejpam-5205	213	17	v1	v1	VERB
ejpam-5205	213	18	∪	∪	NOUN
ejpam-5205	213	19	v2	v2	NOUN
ejpam-5205	213	20	)	)	PUNCT
ejpam-5205	213	21	and	and	CCONJ
ejpam-5205	213	22	suv	suv	PROPN
ejpam-5205	213	23	1	1	NUM
ejpam-5205	213	24	∪	∪	PROPN
ejpam-5205	213	25	suv	suv	NOUN
ejpam-5205	213	26	2	2	NUM
ejpam-5205	213	27	̸=	̸=	PROPN
ejpam-5205	213	28	v	v	NOUN
ejpam-5205	213	29	(	(	PUNCT
ejpam-5205	213	30	huv	huv	PROPN
ejpam-5205	213	31	)	)	PUNCT
ejpam-5205	213	32	.	.	PUNCT
ejpam-5205	214	1	by	by	ADP
ejpam-5205	214	2	theorem	theorem	NOUN
ejpam-5205	214	3	1	1	NUM
ejpam-5205	214	4	,	,	PUNCT
ejpam-5205	214	5	(	(	PUNCT
ejpam-5205	214	6	c	c	X
ejpam-5205	214	7	)	)	PUNCT
ejpam-5205	214	8	holds	hold	NOUN
ejpam-5205	214	9	.	.	PUNCT
ejpam-5205	215	1	since	since	SCONJ
ejpam-5205	215	2	f	f	PROPN
ejpam-5205	215	3	is	be	AUX
ejpam-5205	215	4	cvrdf	cvrdf	NOUN
ejpam-5205	215	5	on	on	ADP
ejpam-5205	215	6	g	g	PROPN
ejpam-5205	215	7	⋄h	⋄h	PROPN
ejpam-5205	215	8	,	,	PUNCT
ejpam-5205	215	9	(	(	PUNCT
ejpam-5205	215	10	d	d	X
ejpam-5205	215	11	)	)	PUNCT
ejpam-5205	215	12	also	also	ADV
ejpam-5205	215	13	holds	hold	VERB
ejpam-5205	215	14	.	.	PUNCT
ejpam-5205	216	1	hence	hence	ADV
ejpam-5205	216	2	,	,	PUNCT
ejpam-5205	216	3	(	(	PUNCT
ejpam-5205	216	4	v	v	NOUN
ejpam-5205	216	5	)	)	PUNCT
ejpam-5205	216	6	holds	hold	VERB
ejpam-5205	216	7	.	.	PUNCT
ejpam-5205	217	1	conversely	conversely	ADV
ejpam-5205	217	2	,	,	PUNCT
ejpam-5205	217	3	assume	assume	VERB
ejpam-5205	217	4	that	that	SCONJ
ejpam-5205	217	5	(	(	PUNCT
ejpam-5205	217	6	i	i	NOUN
ejpam-5205	217	7	)	)	PUNCT
ejpam-5205	217	8	,	,	PUNCT
ejpam-5205	217	9	(	(	PUNCT
ejpam-5205	217	10	ii	ii	NOUN
ejpam-5205	217	11	)	)	PUNCT
ejpam-5205	217	12	,	,	PUNCT
ejpam-5205	217	13	(	(	PUNCT
ejpam-5205	217	14	iii	iii	NOUN
ejpam-5205	217	15	)	)	PUNCT
ejpam-5205	217	16	,	,	PUNCT
ejpam-5205	217	17	and	and	CCONJ
ejpam-5205	217	18	(	(	PUNCT
ejpam-5205	217	19	iv	iv	X
ejpam-5205	217	20	)	)	PUNCT
ejpam-5205	217	21	hold	hold	NOUN
ejpam-5205	217	22	.	.	PUNCT
ejpam-5205	218	1	let	let	VERB
ejpam-5205	218	2	x	x	PUNCT
ejpam-5205	218	3	∈	∈	PROPN
ejpam-5205	218	4	v0	v0	NOUN
ejpam-5205	218	5	and	and	CCONJ
ejpam-5205	218	6	let	let	VERB
ejpam-5205	218	7	uv	uv	PRON
ejpam-5205	218	8	∈	∈	PROPN
ejpam-5205	218	9	e(g	e(g	PROPN
ejpam-5205	218	10	)	)	PUNCT
ejpam-5205	218	11	such	such	ADJ
ejpam-5205	218	12	that	that	SCONJ
ejpam-5205	218	13	x	x	SYM
ejpam-5205	218	14	∈	∈	NOUN
ejpam-5205	218	15	v	v	NOUN
ejpam-5205	218	16	(	(	PUNCT
ejpam-5205	218	17	{	{	PUNCT
ejpam-5205	218	18	u	u	NOUN
ejpam-5205	218	19	,	,	PUNCT
ejpam-5205	218	20	v}+huv	v}+huv	PROPN
ejpam-5205	218	21	)	)	PUNCT
ejpam-5205	218	22	.	.	PUNCT
ejpam-5205	219	1	consider	consider	VERB
ejpam-5205	219	2	the	the	DET
ejpam-5205	219	3	following	follow	VERB
ejpam-5205	219	4	cases	case	NOUN
ejpam-5205	219	5	:	:	PUNCT
ejpam-5205	219	6	case	case	NOUN
ejpam-5205	219	7	1	1	NUM
ejpam-5205	219	8	.	.	PUNCT
ejpam-5205	219	9	suppose	suppose	VERB
ejpam-5205	219	10	that	that	SCONJ
ejpam-5205	219	11	x	x	PUNCT
ejpam-5205	219	12	∈	∈	PROPN
ejpam-5205	219	13	v	v	ADP
ejpam-5205	219	14	0	0	NUM
ejpam-5205	219	15	g	g	NOUN
ejpam-5205	219	16	,	,	PUNCT
ejpam-5205	219	17	say	say	VERB
ejpam-5205	219	18	x	x	X
ejpam-5205	219	19	=	=	PUNCT
ejpam-5205	219	20	u.	u.	NOUN
ejpam-5205	219	21	suppose	suppose	VERB
ejpam-5205	219	22	v	v	X
ejpam-5205	219	23	/∈	/∈	PROPN
ejpam-5205	219	24	v	v	NOUN
ejpam-5205	219	25	2	2	NUM
ejpam-5205	219	26	g.	g.	NOUN
ejpam-5205	219	27	then	then	ADV
ejpam-5205	219	28	suv	suv	PROPN
ejpam-5205	220	1	2	2	NUM
ejpam-5205	220	2	̸=	̸=	PROPN
ejpam-5205	220	3	∅	∅	NOUN
ejpam-5205	220	4	by	by	ADP
ejpam-5205	220	5	(	(	PUNCT
ejpam-5205	220	6	iv)(b	iv)(b	ADJ
ejpam-5205	220	7	)	)	PUNCT
ejpam-5205	220	8	.	.	PUNCT
ejpam-5205	221	1	let	let	VERB
ejpam-5205	221	2	p	p	PROPN
ejpam-5205	221	3	∈	∈	PROPN
ejpam-5205	221	4	suv	suv	PROPN
ejpam-5205	221	5	2	2	NUM
ejpam-5205	221	6	.	.	PUNCT
ejpam-5205	222	1	then	then	ADV
ejpam-5205	222	2	p	p	PROPN
ejpam-5205	222	3	∈	∈	PROPN
ejpam-5205	222	4	v2	v2	NOUN
ejpam-5205	222	5	∩ng⋄h(u	∩ng⋄h(u	PROPN
ejpam-5205	222	6	)	)	PUNCT
ejpam-5205	222	7	.	.	PUNCT
ejpam-5205	223	1	case	case	NOUN
ejpam-5205	223	2	2	2	X
ejpam-5205	223	3	.	.	PUNCT
ejpam-5205	223	4	suppose	suppose	VERB
ejpam-5205	223	5	that	that	SCONJ
ejpam-5205	223	6	x	x	PROPN
ejpam-5205	223	7	∈	∈	PROPN
ejpam-5205	223	8	suv	suv	NOUN
ejpam-5205	223	9	0	0	NUM
ejpam-5205	223	10	.	.	PUNCT
ejpam-5205	224	1	if	if	SCONJ
ejpam-5205	224	2	u	u	PROPN
ejpam-5205	224	3	∈	∈	PROPN
ejpam-5205	224	4	v2	v2	NOUN
ejpam-5205	224	5	or	or	CCONJ
ejpam-5205	224	6	v	v	ADP
ejpam-5205	224	7	∈	∈	PROPN
ejpam-5205	224	8	v2	v2	NOUN
ejpam-5205	224	9	,	,	PUNCT
ejpam-5205	224	10	then	then	ADV
ejpam-5205	224	11	xu	xu	PROPN
ejpam-5205	225	1	∈	∈	PROPN
ejpam-5205	225	2	e(g	e(g	PROPN
ejpam-5205	225	3	⋄h	⋄h	PROPN
ejpam-5205	225	4	)	)	PUNCT
ejpam-5205	225	5	or	or	CCONJ
ejpam-5205	225	6	xv	xv	PROPN
ejpam-5205	225	7	∈	∈	PROPN
ejpam-5205	225	8	e(g	e(g	PROPN
ejpam-5205	225	9	⋄h	⋄h	PROPN
ejpam-5205	225	10	)	)	PUNCT
ejpam-5205	225	11	.	.	PUNCT
ejpam-5205	226	1	suppose	suppose	VERB
ejpam-5205	226	2	u	u	NOUN
ejpam-5205	226	3	,	,	PUNCT
ejpam-5205	226	4	v	v	NOUN
ejpam-5205	226	5	/∈	/∈	PUNCT
ejpam-5205	227	1	v2	v2	INTJ
ejpam-5205	227	2	.	.	PUNCT
ejpam-5205	228	1	then	then	ADV
ejpam-5205	228	2	,	,	PUNCT
ejpam-5205	228	3	by	by	ADP
ejpam-5205	228	4	(	(	PUNCT
ejpam-5205	228	5	iv)(b	iv)(b	ADJ
ejpam-5205	228	6	)	)	PUNCT
ejpam-5205	228	7	,	,	PUNCT
ejpam-5205	228	8	there	there	PRON
ejpam-5205	228	9	exists	exist	VERB
ejpam-5205	228	10	q	q	PROPN
ejpam-5205	228	11	∈	∈	PROPN
ejpam-5205	228	12	suv	suv	NOUN
ejpam-5205	228	13	2	2	NUM
ejpam-5205	228	14	∩nhuv(x	∩nhuv(x	NOUN
ejpam-5205	228	15	)	)	PUNCT
ejpam-5205	228	16	.	.	PUNCT
ejpam-5205	229	1	hence	hence	ADV
ejpam-5205	229	2	,	,	PUNCT
ejpam-5205	229	3	q	q	PROPN
ejpam-5205	229	4	∈	∈	PROPN
ejpam-5205	229	5	v2	v2	PROPN
ejpam-5205	229	6	∩ng⋄h(x	∩ng⋄h(x	NOUN
ejpam-5205	229	7	)	)	PUNCT
ejpam-5205	229	8	.	.	PUNCT
ejpam-5205	230	1	thus	thus	ADV
ejpam-5205	230	2	,	,	PUNCT
ejpam-5205	230	3	by	by	ADP
ejpam-5205	230	4	case	case	NOUN
ejpam-5205	230	5	1	1	NUM
ejpam-5205	230	6	and	and	CCONJ
ejpam-5205	230	7	case	case	NOUN
ejpam-5205	230	8	2	2	NUM
ejpam-5205	230	9	,	,	PUNCT
ejpam-5205	230	10	f	f	X
ejpam-5205	230	11	=	=	SYM
ejpam-5205	230	12	(	(	PUNCT
ejpam-5205	230	13	v0	v0	PROPN
ejpam-5205	230	14	,	,	PUNCT
ejpam-5205	230	15	v1	v1	NOUN
ejpam-5205	230	16	,	,	PUNCT
ejpam-5205	230	17	v2	v2	PROPN
ejpam-5205	230	18	)	)	PUNCT
ejpam-5205	230	19	is	be	AUX
ejpam-5205	230	20	an	an	DET
ejpam-5205	230	21	rdf	rdf	NOUN
ejpam-5205	230	22	on	on	ADP
ejpam-5205	230	23	g	g	PROPN
ejpam-5205	230	24	⋄h	⋄h	PROPN
ejpam-5205	230	25	.	.	PUNCT
ejpam-5205	231	1	next	next	ADV
ejpam-5205	231	2	,	,	PUNCT
ejpam-5205	231	3	let	let	VERB
ejpam-5205	231	4	x	x	PRON
ejpam-5205	231	5	,	,	PUNCT
ejpam-5205	231	6	y	y	PROPN
ejpam-5205	231	7	∈	∈	PROPN
ejpam-5205	231	8	v1	v1	NOUN
ejpam-5205	231	9	∪v2	∪v2	NOUN
ejpam-5205	231	10	(	(	PUNCT
ejpam-5205	231	11	x	x	PROPN
ejpam-5205	231	12	̸=	̸=	PROPN
ejpam-5205	231	13	y	y	PROPN
ejpam-5205	231	14	)	)	PUNCT
ejpam-5205	231	15	and	and	CCONJ
ejpam-5205	231	16	uv	uv	INTJ
ejpam-5205	231	17	,	,	PUNCT
ejpam-5205	231	18	zw	zw	PROPN
ejpam-5205	231	19	∈	∈	PROPN
ejpam-5205	231	20	e(g	e(g	PROPN
ejpam-5205	231	21	)	)	PUNCT
ejpam-5205	231	22	such	such	ADJ
ejpam-5205	231	23	that	that	SCONJ
ejpam-5205	231	24	x	x	SYM
ejpam-5205	231	25	∈	∈	NOUN
ejpam-5205	231	26	v	v	NOUN
ejpam-5205	231	27	(	(	PUNCT
ejpam-5205	231	28	{	{	PUNCT
ejpam-5205	231	29	u	u	NOUN
ejpam-5205	231	30	,	,	PUNCT
ejpam-5205	231	31	v}+huv	v}+huv	PROPN
ejpam-5205	231	32	)	)	PUNCT
ejpam-5205	231	33	and	and	CCONJ
ejpam-5205	231	34	y	y	PROPN
ejpam-5205	231	35	∈	∈	PROPN
ejpam-5205	231	36	v	v	X
ejpam-5205	231	37	(	(	PUNCT
ejpam-5205	231	38	{	{	PUNCT
ejpam-5205	231	39	z	z	NOUN
ejpam-5205	231	40	,	,	PUNCT
ejpam-5205	231	41	w}+hzw	w}+hzw	PROPN
ejpam-5205	231	42	)	)	PUNCT
ejpam-5205	231	43	.	.	PUNCT
ejpam-5205	232	1	consider	consider	VERB
ejpam-5205	232	2	the	the	DET
ejpam-5205	232	3	following	follow	VERB
ejpam-5205	232	4	cases	case	NOUN
ejpam-5205	232	5	:	:	PUNCT
ejpam-5205	232	6	case	case	NOUN
ejpam-5205	232	7	1	1	NUM
ejpam-5205	232	8	.	.	PUNCT
ejpam-5205	232	9	uv	uv	NOUN
ejpam-5205	232	10	=	=	NOUN
ejpam-5205	232	11	zw	zw	PROPN
ejpam-5205	232	12	.	.	PUNCT
ejpam-5205	233	1	if	if	SCONJ
ejpam-5205	233	2	x	x	NOUN
ejpam-5205	233	3	=	=	SYM
ejpam-5205	233	4	u	u	PROPN
ejpam-5205	233	5	and	and	CCONJ
ejpam-5205	233	6	y	y	PROPN
ejpam-5205	233	7	=	=	PUNCT
ejpam-5205	233	8	v	v	PROPN
ejpam-5205	233	9	,	,	PUNCT
ejpam-5205	233	10	then	then	ADV
ejpam-5205	233	11	ig⋄h	ig⋄h	PROPN
ejpam-5205	234	1	[	[	X
ejpam-5205	234	2	x	x	X
ejpam-5205	234	3	,	,	PUNCT
ejpam-5205	234	4	y	y	PROPN
ejpam-5205	234	5	]	]	X
ejpam-5205	234	6	=	=	PUNCT
ejpam-5205	234	7	{	{	PUNCT
ejpam-5205	234	8	x	x	PROPN
ejpam-5205	234	9	,	,	PUNCT
ejpam-5205	234	10	y	y	PROPN
ejpam-5205	234	11	}	}	PUNCT
ejpam-5205	234	12	⊆	⊆	NUM
ejpam-5205	234	13	v1	v1	NOUN
ejpam-5205	234	14	∪	∪	NOUN
ejpam-5205	234	15	v2	v2	NOUN
ejpam-5205	234	16	.	.	PUNCT
ejpam-5205	234	17	suppose	suppose	VERB
ejpam-5205	234	18	that	that	SCONJ
ejpam-5205	234	19	x	x	NOUN
ejpam-5205	234	20	,	,	PUNCT
ejpam-5205	234	21	y	y	PROPN
ejpam-5205	234	22	∈	∈	PROPN
ejpam-5205	234	23	suv	suv	PROPN
ejpam-5205	234	24	1	1	NUM
ejpam-5205	234	25	∪	∪	PROPN
ejpam-5205	234	26	suv	suv	NOUN
ejpam-5205	234	27	2	2	NUM
ejpam-5205	234	28	.	.	PUNCT
ejpam-5205	235	1	if	if	SCONJ
ejpam-5205	235	2	|{u	|{u	PROPN
ejpam-5205	235	3	,	,	PUNCT
ejpam-5205	235	4	v	v	NOUN
ejpam-5205	235	5	}	}	PUNCT
ejpam-5205	235	6	∩	∩	NOUN
ejpam-5205	235	7	(	(	PUNCT
ejpam-5205	235	8	v1	v1	NOUN
ejpam-5205	235	9	∪	∪	ADJ
ejpam-5205	235	10	v2)|	v2)|	PROPN
ejpam-5205	235	11	=	=	SYM
ejpam-5205	235	12	1	1	NUM
ejpam-5205	235	13	,	,	PUNCT
ejpam-5205	235	14	then	then	ADV
ejpam-5205	235	15	suv	suv	PROPN
ejpam-5205	235	16	1	1	NUM
ejpam-5205	235	17	∪	∪	X
ejpam-5205	235	18	suv	suv	X
ejpam-5205	235	19	2	2	NUM
ejpam-5205	235	20	induces	induce	VERB
ejpam-5205	235	21	a	a	DET
ejpam-5205	235	22	complete	complete	ADJ
ejpam-5205	235	23	subgraph	subgraph	NOUN
ejpam-5205	235	24	of	of	ADP
ejpam-5205	235	25	huv	huv	PROPN
ejpam-5205	235	26	by	by	ADP
ejpam-5205	235	27	(	(	PUNCT
ejpam-5205	235	28	iv)(a	iv)(a	PROPN
ejpam-5205	235	29	)	)	PUNCT
ejpam-5205	235	30	.	.	PUNCT
ejpam-5205	236	1	therefore	therefore	ADV
ejpam-5205	236	2	,	,	PUNCT
ejpam-5205	236	3	ig⋄h	ig⋄h	PROPN
ejpam-5205	237	1	[	[	X
ejpam-5205	237	2	x	x	X
ejpam-5205	237	3	,	,	PUNCT
ejpam-5205	237	4	y	y	PROPN
ejpam-5205	237	5	]	]	X
ejpam-5205	237	6	=	=	PUNCT
ejpam-5205	237	7	{	{	PUNCT
ejpam-5205	237	8	x	x	PROPN
ejpam-5205	237	9	,	,	PUNCT
ejpam-5205	237	10	y	y	PROPN
ejpam-5205	237	11	}	}	PUNCT
ejpam-5205	237	12	⊆	⊆	NUM
ejpam-5205	237	13	v1	v1	NOUN
ejpam-5205	237	14	∪	∪	NOUN
ejpam-5205	237	15	v2	v2	NOUN
ejpam-5205	237	16	.	.	PUNCT
ejpam-5205	237	17	suppose	suppose	VERB
ejpam-5205	237	18	that	that	SCONJ
ejpam-5205	237	19	|{u	|{u	PROPN
ejpam-5205	237	20	,	,	PUNCT
ejpam-5205	237	21	v	v	NOUN
ejpam-5205	237	22	}	}	PUNCT
ejpam-5205	237	23	∩	∩	NOUN
ejpam-5205	237	24	(	(	PUNCT
ejpam-5205	237	25	v1	v1	NOUN
ejpam-5205	237	26	∪	∪	ADJ
ejpam-5205	237	27	v2)|	v2)|	NOUN
ejpam-5205	237	28	=	=	SYM
ejpam-5205	237	29	2	2	X
ejpam-5205	237	30	.	.	PUNCT
ejpam-5205	237	31	clearly	clearly	ADV
ejpam-5205	237	32	,	,	PUNCT
ejpam-5205	237	33	ig⋄h	ig⋄h	PROPN
ejpam-5205	238	1	[	[	X
ejpam-5205	238	2	x	x	X
ejpam-5205	238	3	,	,	PUNCT
ejpam-5205	238	4	y	y	PROPN
ejpam-5205	238	5	]	]	X
ejpam-5205	238	6	⊆	⊆	NUM
ejpam-5205	238	7	v1	v1	NOUN
ejpam-5205	238	8	∪	∪	NOUN
ejpam-5205	238	9	v2	v2	PROPN
ejpam-5205	238	10	if	if	SCONJ
ejpam-5205	238	11	suv	suv	PROPN
ejpam-5205	238	12	1	1	NUM
ejpam-5205	238	13	∪	∪	PROPN
ejpam-5205	238	14	suv	suv	X
ejpam-5205	238	15	2	2	NUM
ejpam-5205	238	16	=	=	SYM
ejpam-5205	238	17	v	v	PROPN
ejpam-5205	238	18	(	(	PUNCT
ejpam-5205	238	19	huv	huv	PROPN
ejpam-5205	238	20	)	)	PUNCT
ejpam-5205	238	21	.	.	PUNCT
ejpam-5205	239	1	suppose	suppose	VERB
ejpam-5205	239	2	suv	suv	PROPN
ejpam-5205	239	3	1	1	NUM
ejpam-5205	239	4	∪	∪	PROPN
ejpam-5205	239	5	suv	suv	NOUN
ejpam-5205	239	6	2	2	NUM
ejpam-5205	239	7	̸=	̸=	PROPN
ejpam-5205	239	8	v	v	NOUN
ejpam-5205	239	9	(	(	PUNCT
ejpam-5205	239	10	huv	huv	PROPN
ejpam-5205	239	11	)	)	PUNCT
ejpam-5205	239	12	.	.	PUNCT
ejpam-5205	240	1	then	then	ADV
ejpam-5205	240	2	v	v	X
ejpam-5205	240	3	(	(	PUNCT
ejpam-5205	240	4	huv	huv	PROPN
ejpam-5205	240	5	)	)	PUNCT
ejpam-5205	240	6	\	\	PROPN
ejpam-5205	240	7	suv	suv	PROPN
ejpam-5205	240	8	1	1	NUM
ejpam-5205	240	9	∪	∪	X
ejpam-5205	240	10	suv	suv	X
ejpam-5205	240	11	2	2	NUM
ejpam-5205	240	12	is	be	AUX
ejpam-5205	240	13	a	a	DET
ejpam-5205	240	14	non	non	ADJ
ejpam-5205	240	15	-	-	ADJ
ejpam-5205	240	16	connecting	connecting	ADJ
ejpam-5205	240	17	set	set	NOUN
ejpam-5205	240	18	in	in	ADP
ejpam-5205	240	19	huv	huv	PROPN
ejpam-5205	240	20	by	by	ADP
ejpam-5205	240	21	(	(	PUNCT
ejpam-5205	240	22	v)(c	v)(c	PROPN
ejpam-5205	240	23	)	)	PUNCT
ejpam-5205	240	24	.	.	PUNCT
ejpam-5205	241	1	hence	hence	ADV
ejpam-5205	241	2	,	,	PUNCT
ejpam-5205	241	3	nhuv(x	nhuv(x	NOUN
ejpam-5205	241	4	)	)	PUNCT
ejpam-5205	241	5	∩nhuv(y	∩nhuv(y	PROPN
ejpam-5205	241	6	)	)	PUNCT
ejpam-5205	241	7	⊆	⊆	NUM
ejpam-5205	241	8	suv	suv	NOUN
ejpam-5205	241	9	1	1	NUM
ejpam-5205	241	10	∪	∪	PROPN
ejpam-5205	241	11	suv	suv	X
ejpam-5205	241	12	2	2	NUM
ejpam-5205	241	13	.	.	PUNCT
ejpam-5205	242	1	therefore	therefore	ADV
ejpam-5205	242	2	,	,	PUNCT
ejpam-5205	242	3	ig⋄h	ig⋄h	PROPN
ejpam-5205	243	1	[	[	X
ejpam-5205	243	2	x	x	X
ejpam-5205	243	3	,	,	PUNCT
ejpam-5205	243	4	y	y	PROPN
ejpam-5205	243	5	]	]	X
ejpam-5205	243	6	⊆	⊆	NUM
ejpam-5205	243	7	v1	v1	NOUN
ejpam-5205	243	8	∪	∪	NOUN
ejpam-5205	243	9	v2	v2	NOUN
ejpam-5205	243	10	.	.	PUNCT
ejpam-5205	243	11	case	case	NOUN
ejpam-5205	243	12	2	2	NUM
ejpam-5205	243	13	.	.	PUNCT
ejpam-5205	244	1	uv	uv	NOUN
ejpam-5205	244	2	̸=	̸=	PROPN
ejpam-5205	244	3	zw	zw	PROPN
ejpam-5205	244	4	.	.	PUNCT
ejpam-5205	244	5	suppose	suppose	VERB
ejpam-5205	245	1	that	that	SCONJ
ejpam-5205	245	2	x	x	PUNCT
ejpam-5205	245	3	∈	∈	PROPN
ejpam-5205	245	4	{	{	PUNCT
ejpam-5205	245	5	u	u	NOUN
ejpam-5205	245	6	,	,	PUNCT
ejpam-5205	245	7	v	v	NOUN
ejpam-5205	245	8	}	}	PUNCT
ejpam-5205	245	9	and	and	CCONJ
ejpam-5205	245	10	y	y	PROPN
ejpam-5205	245	11	∈	∈	PROPN
ejpam-5205	245	12	{	{	PUNCT
ejpam-5205	245	13	z	z	NOUN
ejpam-5205	245	14	,	,	PUNCT
ejpam-5205	245	15	w	w	NOUN
ejpam-5205	245	16	}	}	PUNCT
ejpam-5205	245	17	.	.	PUNCT
ejpam-5205	246	1	by	by	ADP
ejpam-5205	246	2	(	(	PUNCT
ejpam-5205	246	3	ii	ii	NOUN
ejpam-5205	246	4	)	)	PUNCT
ejpam-5205	246	5	,	,	PUNCT
ejpam-5205	246	6	ig⋄h	ig⋄h	PROPN
ejpam-5205	247	1	[	[	X
ejpam-5205	247	2	x	x	X
ejpam-5205	247	3	,	,	PUNCT
ejpam-5205	247	4	y	y	PROPN
ejpam-5205	247	5	]	]	X
ejpam-5205	247	6	=	=	SYM
ejpam-5205	247	7	ig[x	ig[x	PROPN
ejpam-5205	247	8	,	,	PUNCT
ejpam-5205	247	9	y	y	PROPN
ejpam-5205	247	10	]	]	X
ejpam-5205	247	11	⊆	⊆	NUM
ejpam-5205	247	12	v	v	SYM
ejpam-5205	247	13	1	1	NUM
ejpam-5205	247	14	g∪v	g∪v	NOUN
ejpam-5205	247	15	2	2	NUM
ejpam-5205	247	16	g.	g.	NOUN
ejpam-5205	247	17	suppose	suppose	VERB
ejpam-5205	247	18	that	that	SCONJ
ejpam-5205	247	19	x	x	PROPN
ejpam-5205	247	20	∈	∈	PROPN
ejpam-5205	247	21	suv	suv	NOUN
ejpam-5205	247	22	1	1	NUM
ejpam-5205	247	23	∪suv	∪suv	X
ejpam-5205	247	24	2	2	NUM
ejpam-5205	247	25	and	and	CCONJ
ejpam-5205	247	26	y	y	PROPN
ejpam-5205	247	27	∈	∈	PROPN
ejpam-5205	247	28	szw	szw	VERB
ejpam-5205	247	29	1	1	NUM
ejpam-5205	247	30	∪szw	∪szw	NOUN
ejpam-5205	247	31	2	2	NUM
ejpam-5205	247	32	.	.	PUNCT
ejpam-5205	248	1	suppose	suppose	VERB
ejpam-5205	248	2	uv	uv	NOUN
ejpam-5205	248	3	and	and	CCONJ
ejpam-5205	248	4	zw	zw	PROPN
ejpam-5205	248	5	are	be	AUX
ejpam-5205	248	6	adjacent	adjacent	ADJ
ejpam-5205	248	7	,	,	PUNCT
ejpam-5205	248	8	say	say	VERB
ejpam-5205	248	9	v	v	ADP
ejpam-5205	248	10	=	=	PUNCT
ejpam-5205	248	11	z.	z.	PROPN
ejpam-5205	248	12	then	then	ADV
ejpam-5205	248	13	v	v	X
ejpam-5205	248	14	∈	∈	PROPN
ejpam-5205	248	15	v	v	ADP
ejpam-5205	248	16	1	1	NUM
ejpam-5205	248	17	g	g	NOUN
ejpam-5205	248	18	∪	∪	NOUN
ejpam-5205	248	19	v	v	ADP
ejpam-5205	248	20	2	2	NUM
ejpam-5205	248	21	g	g	NOUN
ejpam-5205	248	22	by	by	ADP
ejpam-5205	248	23	(	(	PUNCT
ejpam-5205	248	24	iii	iii	NOUN
ejpam-5205	248	25	)	)	PUNCT
ejpam-5205	248	26	.	.	PUNCT
ejpam-5205	249	1	hence	hence	ADV
ejpam-5205	249	2	,	,	PUNCT
ejpam-5205	249	3	ig⋄h	ig⋄h	PROPN
ejpam-5205	250	1	[	[	X
ejpam-5205	250	2	x	x	X
ejpam-5205	250	3	,	,	PUNCT
ejpam-5205	250	4	y	y	PROPN
ejpam-5205	250	5	]	]	X
ejpam-5205	250	6	=	=	PUNCT
ejpam-5205	250	7	{	{	PUNCT
ejpam-5205	250	8	x	x	NOUN
ejpam-5205	250	9	,	,	PUNCT
ejpam-5205	250	10	v	v	NOUN
ejpam-5205	250	11	,	,	PUNCT
ejpam-5205	250	12	y	y	NOUN
ejpam-5205	250	13	}	}	PUNCT
ejpam-5205	250	14	⊆	⊆	NUM
ejpam-5205	250	15	v1	v1	NOUN
ejpam-5205	250	16	∪	∪	NOUN
ejpam-5205	250	17	v2	v2	NOUN
ejpam-5205	250	18	.	.	PUNCT
ejpam-5205	251	1	next	next	ADV
ejpam-5205	251	2	,	,	PUNCT
ejpam-5205	251	3	suppose	suppose	VERB
ejpam-5205	251	4	that	that	SCONJ
ejpam-5205	251	5	uv	uv	NOUN
ejpam-5205	251	6	and	and	CCONJ
ejpam-5205	251	7	zw	zw	PROPN
ejpam-5205	251	8	are	be	AUX
ejpam-5205	251	9	non	non	ADJ
ejpam-5205	251	10	-	-	ADJ
ejpam-5205	251	11	adjacent	adjacent	ADJ
ejpam-5205	251	12	.	.	PUNCT
ejpam-5205	252	1	let	let	VERB
ejpam-5205	252	2	a	a	PRON
ejpam-5205	252	3	and	and	CCONJ
ejpam-5205	252	4	b	b	NOUN
ejpam-5205	252	5	be	be	AUX
ejpam-5205	252	6	incident	incident	NOUN
ejpam-5205	252	7	with	with	ADP
ejpam-5205	252	8	e	e	NOUN
ejpam-5205	252	9	=	=	NOUN
ejpam-5205	252	10	uv	uv	NOUN
ejpam-5205	252	11	and	and	CCONJ
ejpam-5205	252	12	e′	e′	NOUN
ejpam-5205	252	13	=	=	PROPN
ejpam-5205	252	14	zw	zw	PROPN
ejpam-5205	252	15	,	,	PUNCT
ejpam-5205	252	16	respectively	respectively	ADV
ejpam-5205	252	17	,	,	PUNCT
ejpam-5205	252	18	with	with	ADP
ejpam-5205	252	19	dg(a	dg(a	PROPN
ejpam-5205	252	20	,	,	PUNCT
ejpam-5205	252	21	b	b	NOUN
ejpam-5205	252	22	)	)	PUNCT
ejpam-5205	252	23	=	=	SYM
ejpam-5205	252	24	dg({u	dg({u	PROPN
ejpam-5205	252	25	,	,	PUNCT
ejpam-5205	252	26	v	v	NOUN
ejpam-5205	252	27	}	}	PUNCT
ejpam-5205	252	28	,	,	PUNCT
ejpam-5205	252	29	{	{	PUNCT
ejpam-5205	252	30	z	z	NOUN
ejpam-5205	252	31	,	,	PUNCT
ejpam-5205	252	32	w	w	NOUN
ejpam-5205	252	33	}	}	PUNCT
ejpam-5205	252	34	)	)	PUNCT
ejpam-5205	252	35	.	.	PUNCT
ejpam-5205	253	1	then	then	ADV
ejpam-5205	253	2	a	a	DET
ejpam-5205	253	3	,	,	PUNCT
ejpam-5205	253	4	b	b	X
ejpam-5205	253	5	∈	∈	PROPN
ejpam-5205	253	6	v	v	ADP
ejpam-5205	253	7	1	1	NUM
ejpam-5205	253	8	g	g	NOUN
ejpam-5205	253	9	∪v	∪v	ADP
ejpam-5205	253	10	2	2	NUM
ejpam-5205	253	11	g	g	NOUN
ejpam-5205	253	12	,	,	PUNCT
ejpam-5205	253	13	by	by	ADP
ejpam-5205	253	14	(	(	PUNCT
ejpam-5205	253	15	iii	iii	NOUN
ejpam-5205	253	16	)	)	PUNCT
ejpam-5205	253	17	.	.	PUNCT
ejpam-5205	254	1	moreover	moreover	ADV
ejpam-5205	254	2	,	,	PUNCT
ejpam-5205	254	3	ig[a	ig[a	PROPN
ejpam-5205	254	4	,	,	PUNCT
ejpam-5205	254	5	b	b	X
ejpam-5205	254	6	]	]	X
ejpam-5205	254	7	⊆	⊆	NUM
ejpam-5205	254	8	v	v	ADP
ejpam-5205	254	9	1	1	NUM
ejpam-5205	254	10	g	g	NOUN
ejpam-5205	254	11	∪v	∪v	ADP
ejpam-5205	254	12	2	2	NUM
ejpam-5205	254	13	g	g	NOUN
ejpam-5205	254	14	,	,	PUNCT
ejpam-5205	254	15	by	by	ADP
ejpam-5205	254	16	(	(	PUNCT
ejpam-5205	254	17	ii	ii	NOUN
ejpam-5205	254	18	)	)	PUNCT
ejpam-5205	254	19	.	.	PUNCT
ejpam-5205	255	1	therefore	therefore	ADV
ejpam-5205	255	2	,	,	PUNCT
ejpam-5205	255	3	ig⋄h(x	ig⋄h(x	PROPN
ejpam-5205	255	4	,	,	PUNCT
ejpam-5205	255	5	y	y	NOUN
ejpam-5205	255	6	)	)	PUNCT
ejpam-5205	255	7	=	=	SYM
ejpam-5205	255	8	ig[a	ig[a	PROPN
ejpam-5205	255	9	,	,	PUNCT
ejpam-5205	255	10	b	b	NOUN
ejpam-5205	255	11	]	]	PUNCT
ejpam-5205	255	12	⊆	⊆	NUM
ejpam-5205	255	13	v1	v1	NOUN
ejpam-5205	255	14	∪	∪	NOUN
ejpam-5205	255	15	v2	v2	NOUN
ejpam-5205	255	16	.	.	PUNCT
ejpam-5205	256	1	finally	finally	ADV
ejpam-5205	256	2	,	,	PUNCT
ejpam-5205	256	3	suppose	suppose	VERB
ejpam-5205	256	4	that	that	SCONJ
ejpam-5205	256	5	x	x	PROPN
ejpam-5205	256	6	∈	∈	PROPN
ejpam-5205	256	7	suv	suv	NOUN
ejpam-5205	256	8	1	1	NUM
ejpam-5205	256	9	∪	∪	PROPN
ejpam-5205	256	10	suv	suv	X
ejpam-5205	256	11	2	2	NUM
ejpam-5205	256	12	and	and	CCONJ
ejpam-5205	256	13	y	y	PROPN
ejpam-5205	256	14	∈	∈	PROPN
ejpam-5205	256	15	{	{	PUNCT
ejpam-5205	256	16	z	z	NOUN
ejpam-5205	256	17	,	,	PUNCT
ejpam-5205	256	18	w	w	NOUN
ejpam-5205	256	19	}	}	PUNCT
ejpam-5205	256	20	.	.	PUNCT
ejpam-5205	257	1	suppose	suppose	VERB
ejpam-5205	257	2	that	that	SCONJ
ejpam-5205	257	3	a	a	PRON
ejpam-5205	257	4	and	and	CCONJ
ejpam-5205	257	5	b	b	NOUN
ejpam-5205	257	6	are	be	AUX
ejpam-5205	257	7	the	the	DET
ejpam-5205	257	8	vertices	vertex	NOUN
ejpam-5205	257	9	described	describe	VERB
ejpam-5205	257	10	earlier	early	ADV
ejpam-5205	257	11	.	.	PUNCT
ejpam-5205	258	1	if	if	SCONJ
ejpam-5205	258	2	b	b	PROPN
ejpam-5205	258	3	=	=	SYM
ejpam-5205	258	4	y	y	PROPN
ejpam-5205	258	5	,	,	PUNCT
ejpam-5205	258	6	then	then	ADV
ejpam-5205	258	7	r.	r.	PROPN
ejpam-5205	258	8	fortosa	fortosa	PROPN
ejpam-5205	258	9	,	,	PUNCT
ejpam-5205	258	10	s.	s.	PROPN
ejpam-5205	258	11	canoy	canoy	PROPN
ejpam-5205	258	12	jr	jr	PROPN
ejpam-5205	258	13	.	.	PROPN
ejpam-5205	258	14	/	/	SYM
ejpam-5205	258	15	eur	eur	PROPN
ejpam-5205	258	16	.	.	PUNCT
ejpam-5205	259	1	j.	j.	PROPN
ejpam-5205	259	2	pure	pure	PROPN
ejpam-5205	259	3	appl	appl	PROPN
ejpam-5205	259	4	.	.	PROPN
ejpam-5205	259	5	math	math	PROPN
ejpam-5205	259	6	,	,	PUNCT
ejpam-5205	259	7	17	17	NUM
ejpam-5205	259	8	(	(	PUNCT
ejpam-5205	259	9	2	2	NUM
ejpam-5205	259	10	)	)	PUNCT
ejpam-5205	259	11	(	(	PUNCT
ejpam-5205	259	12	2024	2024	NUM
ejpam-5205	259	13	)	)	PUNCT
ejpam-5205	259	14	,	,	PUNCT
ejpam-5205	259	15	1335	1335	NUM
ejpam-5205	259	16	-	-	SYM
ejpam-5205	259	17	1351	1351	NUM
ejpam-5205	259	18	1342	1342	NUM
ejpam-5205	259	19	ig⋄h(x	ig⋄h(x	NOUN
ejpam-5205	259	20	,	,	PUNCT
ejpam-5205	259	21	y	y	NOUN
ejpam-5205	259	22	)	)	PUNCT
ejpam-5205	259	23	=	=	SYM
ejpam-5205	259	24	ig(a	ig(a	NOUN
ejpam-5205	259	25	,	,	PUNCT
ejpam-5205	259	26	b)∪{a	b)∪{a	NOUN
ejpam-5205	259	27	}	}	PUNCT
ejpam-5205	259	28	⊆	⊆	NUM
ejpam-5205	259	29	v1∪v2	v1∪v2	PROPN
ejpam-5205	259	30	,	,	PUNCT
ejpam-5205	259	31	by	by	ADP
ejpam-5205	259	32	(	(	PUNCT
ejpam-5205	259	33	ii	ii	NOUN
ejpam-5205	259	34	)	)	PUNCT
ejpam-5205	259	35	.	.	PUNCT
ejpam-5205	260	1	again	again	ADV
ejpam-5205	260	2	,	,	PUNCT
ejpam-5205	260	3	by	by	ADP
ejpam-5205	260	4	(	(	PUNCT
ejpam-5205	260	5	ii	ii	NOUN
ejpam-5205	260	6	)	)	PUNCT
ejpam-5205	260	7	,	,	PUNCT
ejpam-5205	260	8	ig⋄h(x	ig⋄h(x	PROPN
ejpam-5205	260	9	,	,	PUNCT
ejpam-5205	260	10	y	y	NOUN
ejpam-5205	260	11	)	)	PUNCT
ejpam-5205	260	12	=	=	SYM
ejpam-5205	260	13	ig[a	ig[a	PROPN
ejpam-5205	260	14	,	,	PUNCT
ejpam-5205	260	15	b	b	X
ejpam-5205	260	16	]	]	PUNCT
ejpam-5205	260	17	⊆	⊆	NUM
ejpam-5205	260	18	v1∪v2	v1∪v2	ADV
ejpam-5205	260	19	if	if	SCONJ
ejpam-5205	260	20	b	b	PROPN
ejpam-5205	260	21	̸=	̸=	PROPN
ejpam-5205	260	22	y.	y.	PROPN
ejpam-5205	260	23	therefore	therefore	ADV
ejpam-5205	260	24	,	,	PUNCT
ejpam-5205	260	25	v1	v1	VERB
ejpam-5205	260	26	∪	∪	NOUN
ejpam-5205	260	27	v2	v2	NOUN
ejpam-5205	260	28	is	be	AUX
ejpam-5205	260	29	convex	convex	NOUN
ejpam-5205	260	30	in	in	ADP
ejpam-5205	260	31	g	g	PROPN
ejpam-5205	260	32	⋄h	⋄h	PROPN
ejpam-5205	260	33	.	.	PUNCT
ejpam-5205	260	34	accordingly	accordingly	ADV
ejpam-5205	260	35	,	,	PUNCT
ejpam-5205	260	36	f	f	PROPN
ejpam-5205	260	37	is	be	AUX
ejpam-5205	260	38	a	a	DET
ejpam-5205	260	39	cvrdf	cvrdf	NOUN
ejpam-5205	260	40	on	on	ADP
ejpam-5205	260	41	g	g	PROPN
ejpam-5205	260	42	⋄h	⋄h	PROPN
ejpam-5205	260	43	.	.	PUNCT
ejpam-5205	261	1	lemma	lemma	PROPN
ejpam-5205	261	2	1	1	X
ejpam-5205	261	3	.	.	PUNCT
ejpam-5205	262	1	let	let	VERB
ejpam-5205	262	2	g	g	PRON
ejpam-5205	262	3	be	be	AUX
ejpam-5205	262	4	a	a	DET
ejpam-5205	262	5	non	non	ADJ
ejpam-5205	262	6	-	-	ADJ
ejpam-5205	262	7	complete	complete	ADJ
ejpam-5205	262	8	connected	connected	ADJ
ejpam-5205	262	9	graph	graph	NOUN
ejpam-5205	262	10	and	and	CCONJ
ejpam-5205	262	11	h	h	NOUN
ejpam-5205	262	12	be	be	AUX
ejpam-5205	262	13	any	any	DET
ejpam-5205	262	14	graph	graph	NOUN
ejpam-5205	262	15	of	of	ADP
ejpam-5205	262	16	order	order	NOUN
ejpam-5205	262	17	n.	n.	NOUN
ejpam-5205	262	18	if	if	SCONJ
ejpam-5205	262	19	w0	w0	PROPN
ejpam-5205	262	20	=	=	SYM
ejpam-5205	262	21	ext(g	ext(g	PROPN
ejpam-5205	262	22	)	)	PUNCT
ejpam-5205	262	23	,	,	PUNCT
ejpam-5205	262	24	w1	w1	NOUN
ejpam-5205	262	25	∪w2	∪w2	NOUN
ejpam-5205	262	26	=	=	SYM
ejpam-5205	262	27	v	v	X
ejpam-5205	262	28	(	(	PUNCT
ejpam-5205	262	29	g	g	NOUN
ejpam-5205	262	30	)	)	PUNCT
ejpam-5205	262	31	\ext(g	\ext(g	NOUN
ejpam-5205	262	32	)	)	PUNCT
ejpam-5205	262	33	and	and	CCONJ
ejpam-5205	262	34	{	{	PUNCT
ejpam-5205	262	35	u	u	NOUN
ejpam-5205	262	36	,	,	PUNCT
ejpam-5205	262	37	v	v	NOUN
ejpam-5205	262	38	}	}	PUNCT
ejpam-5205	262	39	∩w2	∩w2	NOUN
ejpam-5205	262	40	̸=	̸=	NOUN
ejpam-5205	262	41	∅	∅	NOUN
ejpam-5205	262	42	for	for	ADP
ejpam-5205	262	43	each	each	DET
ejpam-5205	262	44	uv	uv	PROPN
ejpam-5205	262	45	∈	∈	PROPN
ejpam-5205	262	46	e(g	e(g	PROPN
ejpam-5205	262	47	)	)	PUNCT
ejpam-5205	262	48	such	such	ADJ
ejpam-5205	262	49	that	that	SCONJ
ejpam-5205	262	50	|{u	|{u	PROPN
ejpam-5205	262	51	,	,	PUNCT
ejpam-5205	262	52	v	v	NOUN
ejpam-5205	262	53	}	}	PUNCT
ejpam-5205	262	54	∩	∩	NOUN
ejpam-5205	262	55	ext(g)|	ext(g)|	NOUN
ejpam-5205	262	56	=	=	NOUN
ejpam-5205	262	57	̸	̸	NUM
ejpam-5205	262	58	2	2	NUM
ejpam-5205	262	59	,	,	PUNCT
ejpam-5205	262	60	then	then	ADV
ejpam-5205	262	61	f	f	PROPN
ejpam-5205	262	62	|g	|g	PROPN
ejpam-5205	262	63	=	=	X
ejpam-5205	262	64	(	(	PUNCT
ejpam-5205	262	65	w0,w1,w2	w0,w1,w2	PROPN
ejpam-5205	262	66	)	)	PUNCT
ejpam-5205	262	67	is	be	AUX
ejpam-5205	262	68	a	a	DET
ejpam-5205	262	69	cvrdf	cvrdf	NOUN
ejpam-5205	262	70	on	on	ADP
ejpam-5205	262	71	g.	g.	PROPN
ejpam-5205	262	72	proof	proof	NOUN
ejpam-5205	262	73	.	.	PUNCT
ejpam-5205	263	1	let	let	VERB
ejpam-5205	263	2	x	x	X
ejpam-5205	263	3	∈	∈	PROPN
ejpam-5205	263	4	w0	w0	PROPN
ejpam-5205	263	5	.	.	PUNCT
ejpam-5205	264	1	since	since	SCONJ
ejpam-5205	264	2	g	g	PROPN
ejpam-5205	264	3	is	be	AUX
ejpam-5205	264	4	non	non	ADJ
ejpam-5205	264	5	-	-	ADJ
ejpam-5205	264	6	complete	complete	ADJ
ejpam-5205	264	7	,	,	PUNCT
ejpam-5205	264	8	there	there	PRON
ejpam-5205	264	9	exists	exist	VERB
ejpam-5205	264	10	y	y	PROPN
ejpam-5205	264	11	∈	∈	PROPN
ejpam-5205	264	12	(	(	PUNCT
ejpam-5205	264	13	v	v	NOUN
ejpam-5205	264	14	(	(	PUNCT
ejpam-5205	264	15	g	g	NOUN
ejpam-5205	264	16	)	)	PUNCT
ejpam-5205	264	17	\	\	NOUN
ejpam-5205	264	18	ext(g	ext(g	NOUN
ejpam-5205	264	19	)	)	PUNCT
ejpam-5205	264	20	)	)	PUNCT
ejpam-5205	264	21	∩ng(x	∩ng(x	NOUN
ejpam-5205	264	22	)	)	PUNCT
ejpam-5205	264	23	.	.	PUNCT
ejpam-5205	265	1	by	by	ADP
ejpam-5205	265	2	assumption	assumption	NOUN
ejpam-5205	265	3	,	,	PUNCT
ejpam-5205	265	4	this	this	PRON
ejpam-5205	265	5	implies	imply	VERB
ejpam-5205	265	6	that	that	SCONJ
ejpam-5205	265	7	y	y	PROPN
ejpam-5205	265	8	∈	∈	PROPN
ejpam-5205	265	9	w2	w2	NOUN
ejpam-5205	265	10	,	,	PUNCT
ejpam-5205	265	11	showing	show	VERB
ejpam-5205	265	12	that	that	SCONJ
ejpam-5205	265	13	f	f	PROPN
ejpam-5205	265	14	is	be	AUX
ejpam-5205	265	15	an	an	DET
ejpam-5205	265	16	rdf	rdf	NOUN
ejpam-5205	265	17	on	on	ADP
ejpam-5205	265	18	g.	g.	PROPN
ejpam-5205	265	19	moreover	moreover	ADV
ejpam-5205	265	20	,	,	PUNCT
ejpam-5205	265	21	since	since	SCONJ
ejpam-5205	265	22	v	v	NOUN
ejpam-5205	265	23	(	(	PUNCT
ejpam-5205	265	24	g	g	NOUN
ejpam-5205	265	25	)	)	PUNCT
ejpam-5205	265	26	\	\	NOUN
ejpam-5205	265	27	ext(g	ext(g	PROPN
ejpam-5205	265	28	)	)	PUNCT
ejpam-5205	265	29	is	be	AUX
ejpam-5205	265	30	convex	convex	ADJ
ejpam-5205	265	31	in	in	ADP
ejpam-5205	265	32	g	g	PROPN
ejpam-5205	265	33	,	,	PUNCT
ejpam-5205	265	34	it	it	PRON
ejpam-5205	265	35	follows	follow	VERB
ejpam-5205	265	36	that	that	SCONJ
ejpam-5205	265	37	f	f	PROPN
ejpam-5205	265	38	is	be	AUX
ejpam-5205	265	39	a	a	DET
ejpam-5205	265	40	cvrdf	cvrdf	NOUN
ejpam-5205	265	41	on	on	ADP
ejpam-5205	265	42	g.	g.	PROPN
ejpam-5205	265	43	henceforth	henceforth	ADV
ejpam-5205	265	44	,	,	PUNCT
ejpam-5205	265	45	we	we	PRON
ejpam-5205	265	46	refer	refer	VERB
ejpam-5205	265	47	f	f	PROPN
ejpam-5205	265	48	in	in	ADP
ejpam-5205	265	49	lemma	lemma	PROPN
ejpam-5205	265	50	1	1	NUM
ejpam-5205	265	51	as	as	ADP
ejpam-5205	265	52	a	a	DET
ejpam-5205	265	53	cvrdf	cvrdf	NOUN
ejpam-5205	265	54	*	*	PUNCT
ejpam-5205	265	55	on	on	ADP
ejpam-5205	265	56	g.	g.	PROPN
ejpam-5205	265	57	corollary	corollary	NOUN
ejpam-5205	265	58	3	3	X
ejpam-5205	265	59	.	.	PUNCT
ejpam-5205	266	1	let	let	VERB
ejpam-5205	266	2	g	g	PRON
ejpam-5205	266	3	be	be	AUX
ejpam-5205	266	4	a	a	DET
ejpam-5205	266	5	non	non	ADJ
ejpam-5205	266	6	-	-	ADJ
ejpam-5205	266	7	complete	complete	ADJ
ejpam-5205	266	8	connected	connected	ADJ
ejpam-5205	266	9	graph	graph	NOUN
ejpam-5205	266	10	and	and	CCONJ
ejpam-5205	266	11	h	h	NOUN
ejpam-5205	266	12	any	any	DET
ejpam-5205	266	13	graph	graph	NOUN
ejpam-5205	266	14	of	of	ADP
ejpam-5205	266	15	order	order	NOUN
ejpam-5205	266	16	n.	n.	NOUN
ejpam-5205	266	17	then	then	ADV
ejpam-5205	266	18	γcvr(g	γcvr(g	PROPN
ejpam-5205	266	19	⋄h	⋄h	PROPN
ejpam-5205	266	20	)	)	PUNCT
ejpam-5205	266	21	≤	≤	NOUN
ejpam-5205	266	22	min{ωcvr	min{ωcvr	NOUN
ejpam-5205	266	23	g	g	PROPN
ejpam-5205	266	24	(	(	PUNCT
ejpam-5205	266	25	f	f	PROPN
ejpam-5205	266	26	)	)	PUNCT
ejpam-5205	266	27	:	:	PUNCT
ejpam-5205	267	1	f	f	X
ejpam-5205	267	2	=	=	PUNCT
ejpam-5205	267	3	(	(	PUNCT
ejpam-5205	267	4	w0,w1,w2	w0,w1,w2	PROPN
ejpam-5205	267	5	)	)	PUNCT
ejpam-5205	267	6	is	be	AUX
ejpam-5205	267	7	a	a	DET
ejpam-5205	267	8	cvrdf	cvrdf	NOUN
ejpam-5205	267	9	∗	∗	NOUN
ejpam-5205	267	10	on	on	ADP
ejpam-5205	267	11	g	g	NOUN
ejpam-5205	267	12	}	}	PUNCT
ejpam-5205	267	13	.	.	PUNCT
ejpam-5205	268	1	proof	proof	NOUN
ejpam-5205	268	2	.	.	PUNCT
ejpam-5205	269	1	let	let	VERB
ejpam-5205	269	2	k	k	NOUN
ejpam-5205	269	3	=	=	PUNCT
ejpam-5205	269	4	min{ωcvr	min{ωcvr	X
ejpam-5205	269	5	g	g	PROPN
ejpam-5205	269	6	(	(	PUNCT
ejpam-5205	269	7	f	f	PROPN
ejpam-5205	269	8	)	)	PUNCT
ejpam-5205	269	9	:	:	PUNCT
ejpam-5205	270	1	f	f	X
ejpam-5205	270	2	=	=	PUNCT
ejpam-5205	270	3	(	(	PUNCT
ejpam-5205	270	4	w0,w1,w2	w0,w1,w2	PROPN
ejpam-5205	270	5	)	)	PUNCT
ejpam-5205	270	6	is	be	AUX
ejpam-5205	270	7	a	a	DET
ejpam-5205	270	8	cvrdf	cvrdf	NOUN
ejpam-5205	270	9	∗	∗	NOUN
ejpam-5205	270	10	on	on	ADP
ejpam-5205	270	11	g	g	NOUN
ejpam-5205	270	12	}	}	PUNCT
ejpam-5205	270	13	.	.	PUNCT
ejpam-5205	271	1	let	let	VERB
ejpam-5205	271	2	g	g	PROPN
ejpam-5205	271	3	=	=	SYM
ejpam-5205	271	4	(	(	PUNCT
ejpam-5205	271	5	w0,w1,w2	w0,w1,w2	ADV
ejpam-5205	271	6	)	)	PUNCT
ejpam-5205	271	7	be	be	AUX
ejpam-5205	271	8	a	a	DET
ejpam-5205	271	9	cvrdf	cvrdf	NOUN
ejpam-5205	271	10	*	*	PUNCT
ejpam-5205	271	11	on	on	ADP
ejpam-5205	271	12	g	g	PRON
ejpam-5205	272	1	such	such	ADJ
ejpam-5205	272	2	that	that	PRON
ejpam-5205	272	3	ωcvr	ωcvr	PROPN
ejpam-5205	272	4	g	g	PROPN
ejpam-5205	272	5	(	(	PUNCT
ejpam-5205	272	6	g	g	NOUN
ejpam-5205	272	7	)	)	PUNCT
ejpam-5205	272	8	=	=	VERB
ejpam-5205	272	9	k.	k.	PROPN
ejpam-5205	272	10	let	let	VERB
ejpam-5205	272	11	v0	v0	NOUN
ejpam-5205	272	12	=	=	SYM
ejpam-5205	272	13	ext(g	ext(g	PROPN
ejpam-5205	272	14	)	)	PUNCT
ejpam-5205	272	15	∪	∪	NOUN
ejpam-5205	272	16	(	(	PUNCT
ejpam-5205	272	17	⋃	⋃	PROPN
ejpam-5205	272	18	e∈e(g	e∈e(g	NOUN
ejpam-5205	272	19	)	)	PUNCT
ejpam-5205	272	20	v	v	NOUN
ejpam-5205	272	21	(	(	PUNCT
ejpam-5205	272	22	he	he	PRON
ejpam-5205	272	23	)	)	PUNCT
ejpam-5205	272	24	)	)	PUNCT
ejpam-5205	272	25	,	,	PUNCT
ejpam-5205	272	26	v1	v1	NOUN
ejpam-5205	272	27	=	=	SYM
ejpam-5205	272	28	w1	w1	NOUN
ejpam-5205	272	29	,	,	PUNCT
ejpam-5205	272	30	v2	v2	NOUN
ejpam-5205	272	31	=	=	SYM
ejpam-5205	272	32	w2	w2	NOUN
ejpam-5205	272	33	,	,	PUNCT
ejpam-5205	272	34	and	and	CCONJ
ejpam-5205	272	35	let	let	VERB
ejpam-5205	272	36	h	h	NOUN
ejpam-5205	272	37	=	=	SYM
ejpam-5205	272	38	(	(	PUNCT
ejpam-5205	272	39	v0	v0	PROPN
ejpam-5205	272	40	,	,	PUNCT
ejpam-5205	272	41	v1	v1	NOUN
ejpam-5205	272	42	,	,	PUNCT
ejpam-5205	272	43	v2	v2	PROPN
ejpam-5205	272	44	)	)	PUNCT
ejpam-5205	272	45	.	.	PUNCT
ejpam-5205	273	1	clearly	clearly	ADV
ejpam-5205	273	2	,	,	PUNCT
ejpam-5205	273	3	h|g	h|g	NOUN
ejpam-5205	273	4	=	=	PUNCT
ejpam-5205	273	5	g.	g.	PROPN
ejpam-5205	273	6	hence	hence	ADV
ejpam-5205	273	7	,	,	PUNCT
ejpam-5205	273	8	h	h	NOUN
ejpam-5205	273	9	satisfies	satisfie	NOUN
ejpam-5205	273	10	(	(	PUNCT
ejpam-5205	273	11	i	i	NOUN
ejpam-5205	273	12	)	)	PUNCT
ejpam-5205	273	13	.	.	PUNCT
ejpam-5205	274	1	also	also	ADV
ejpam-5205	274	2	,	,	PUNCT
ejpam-5205	274	3	(	(	PUNCT
ejpam-5205	274	4	ii	ii	NOUN
ejpam-5205	274	5	)	)	PUNCT
ejpam-5205	274	6	,	,	PUNCT
ejpam-5205	274	7	(	(	PUNCT
ejpam-5205	274	8	iii	iii	NOUN
ejpam-5205	274	9	)	)	PUNCT
ejpam-5205	274	10	and	and	CCONJ
ejpam-5205	274	11	(	(	PUNCT
ejpam-5205	274	12	iv	iv	X
ejpam-5205	274	13	)	)	PUNCT
ejpam-5205	274	14	of	of	ADP
ejpam-5205	274	15	theorem	theorem	ADJ
ejpam-5205	274	16	9	9	NUM
ejpam-5205	274	17	hold	hold	NOUN
ejpam-5205	274	18	.	.	PUNCT
ejpam-5205	275	1	thus	thus	ADV
ejpam-5205	275	2	,	,	PUNCT
ejpam-5205	275	3	by	by	ADP
ejpam-5205	275	4	theorem	theorem	NOUN
ejpam-5205	275	5	9	9	NUM
ejpam-5205	275	6	,	,	PUNCT
ejpam-5205	275	7	h	h	NOUN
ejpam-5205	275	8	is	be	AUX
ejpam-5205	275	9	a	a	DET
ejpam-5205	275	10	cvrdf	cvrdf	NOUN
ejpam-5205	275	11	on	on	ADP
ejpam-5205	275	12	g	g	PROPN
ejpam-5205	275	13	⋄h	⋄h	PROPN
ejpam-5205	275	14	.	.	PUNCT
ejpam-5205	276	1	moreover	moreover	ADV
ejpam-5205	276	2	,	,	PUNCT
ejpam-5205	276	3	γcvr(g	γcvr(g	ADV
ejpam-5205	276	4	⋄h	⋄h	PROPN
ejpam-5205	276	5	)	)	PUNCT
ejpam-5205	276	6	≤	≤	NOUN
ejpam-5205	276	7	ωg⋄h(h	ωg⋄h(h	NUM
ejpam-5205	276	8	)	)	PUNCT
ejpam-5205	276	9	=	=	PUNCT
ejpam-5205	276	10	|v1|+	|v1|+	PRON
ejpam-5205	276	11	2|v2|	2|v2|	NUM
ejpam-5205	276	12	=	=	SYM
ejpam-5205	276	13	|w1|+	|w1|+	PROPN
ejpam-5205	276	14	2|w2|	2|w2|	NUM
ejpam-5205	276	15	=	=	SYM
ejpam-5205	276	16	γ∗cvr(g	γ∗cvr(g	PROPN
ejpam-5205	276	17	)	)	PUNCT
ejpam-5205	276	18	.	.	PUNCT
ejpam-5205	277	1	remark	remark	PROPN
ejpam-5205	277	2	1	1	NUM
ejpam-5205	277	3	.	.	PUNCT
ejpam-5205	278	1	the	the	DET
ejpam-5205	278	2	bound	bind	VERB
ejpam-5205	278	3	given	give	VERB
ejpam-5205	278	4	in	in	ADP
ejpam-5205	278	5	corollary	corollary	ADJ
ejpam-5205	278	6	3	3	NUM
ejpam-5205	278	7	is	be	AUX
ejpam-5205	278	8	sharp	sharp	ADJ
ejpam-5205	278	9	.	.	PUNCT
ejpam-5205	279	1	it	it	PRON
ejpam-5205	279	2	can	can	AUX
ejpam-5205	279	3	be	be	AUX
ejpam-5205	279	4	verified	verify	VERB
ejpam-5205	279	5	that	that	SCONJ
ejpam-5205	279	6	for	for	ADP
ejpam-5205	279	7	any	any	DET
ejpam-5205	279	8	graph	graph	NOUN
ejpam-5205	279	9	h	h	NOUN
ejpam-5205	279	10	and	and	CCONJ
ejpam-5205	279	11	positive	positive	ADJ
ejpam-5205	279	12	integer	integer	NOUN
ejpam-5205	279	13	n	n	PRON
ejpam-5205	279	14	≥	≥	NOUN
ejpam-5205	279	15	3	3	NUM
ejpam-5205	279	16	,	,	PUNCT
ejpam-5205	279	17	the	the	DET
ejpam-5205	279	18	following	follow	VERB
ejpam-5205	279	19	holds	hold	VERB
ejpam-5205	279	20	:	:	PUNCT
ejpam-5205	279	21	γcvr(pn	γcvr(pn	ADJ
ejpam-5205	279	22	⋄h	⋄h	PROPN
ejpam-5205	279	23	)	)	PUNCT
ejpam-5205	279	24	=	=	PUNCT
ejpam-5205	279	25	min{ωcvr	min{ωcvr	X
ejpam-5205	279	26	pn	pn	PROPN
ejpam-5205	279	27	(	(	PUNCT
ejpam-5205	279	28	f	f	PROPN
ejpam-5205	279	29	)	)	PUNCT
ejpam-5205	279	30	:	:	PUNCT
ejpam-5205	280	1	f	f	PROPN
ejpam-5205	280	2	is	be	AUX
ejpam-5205	280	3	a	a	DET
ejpam-5205	280	4	cvrdf	cvrdf	NOUN
ejpam-5205	280	5	∗	∗	NOUN
ejpam-5205	280	6	on	on	ADP
ejpam-5205	280	7	pn	pn	PROPN
ejpam-5205	280	8	}	}	PUNCT
ejpam-5205	280	9	=	=	SYM
ejpam-5205	280	10	{	{	PUNCT
ejpam-5205	280	11	3n−4	3n−4	NUM
ejpam-5205	280	12	2	2	NUM
ejpam-5205	280	13	,	,	PUNCT
ejpam-5205	280	14	if	if	SCONJ
ejpam-5205	280	15	n	n	PRON
ejpam-5205	280	16	is	be	AUX
ejpam-5205	280	17	even	even	ADV
ejpam-5205	280	18	3n−5	3n−5	NUM
ejpam-5205	280	19	2	2	NUM
ejpam-5205	280	20	,	,	PUNCT
ejpam-5205	280	21	if	if	SCONJ
ejpam-5205	280	22	n	n	PRON
ejpam-5205	280	23	is	be	AUX
ejpam-5205	280	24	odd	odd	ADJ
ejpam-5205	280	25	.	.	PUNCT
ejpam-5205	281	1	for	for	ADP
ejpam-5205	281	2	a	a	DET
ejpam-5205	281	3	graph	graph	NOUN
ejpam-5205	281	4	g	g	NOUN
ejpam-5205	281	5	,	,	PUNCT
ejpam-5205	281	6	the	the	DET
ejpam-5205	281	7	complementary	complementary	ADJ
ejpam-5205	281	8	prism	prism	NOUN
ejpam-5205	281	9	,	,	PUNCT
ejpam-5205	281	10	denoted	denote	VERB
ejpam-5205	281	11	gg	gg	NOUN
ejpam-5205	281	12	,	,	PUNCT
ejpam-5205	281	13	is	be	AUX
ejpam-5205	281	14	formed	form	VERB
ejpam-5205	281	15	from	from	ADP
ejpam-5205	281	16	the	the	DET
ejpam-5205	281	17	disjoint	disjoint	PROPN
ejpam-5205	281	18	union	union	NOUN
ejpam-5205	281	19	of	of	ADP
ejpam-5205	281	20	g	g	PROPN
ejpam-5205	281	21	and	and	CCONJ
ejpam-5205	281	22	its	its	PRON
ejpam-5205	281	23	complement	complement	NOUN
ejpam-5205	281	24	g	g	NOUN
ejpam-5205	281	25	by	by	ADP
ejpam-5205	281	26	adding	add	VERB
ejpam-5205	281	27	a	a	DET
ejpam-5205	281	28	perfect	perfect	ADJ
ejpam-5205	281	29	matching	matching	NOUN
ejpam-5205	281	30	between	between	ADP
ejpam-5205	281	31	corresponding	corresponding	ADJ
ejpam-5205	281	32	vertices	vertex	NOUN
ejpam-5205	281	33	of	of	ADP
ejpam-5205	281	34	g	g	PROPN
ejpam-5205	281	35	and	and	CCONJ
ejpam-5205	281	36	g.	g.	NOUN
ejpam-5205	281	37	for	for	ADP
ejpam-5205	281	38	each	each	DET
ejpam-5205	281	39	v	v	NUM
ejpam-5205	281	40	∈	∈	PROPN
ejpam-5205	281	41	v	v	NOUN
ejpam-5205	281	42	(	(	PUNCT
ejpam-5205	281	43	g	g	NOUN
ejpam-5205	281	44	)	)	PUNCT
ejpam-5205	281	45	,	,	PUNCT
ejpam-5205	281	46	let	let	VERB
ejpam-5205	281	47	v	v	PART
ejpam-5205	281	48	denote	denote	VERB
ejpam-5205	281	49	the	the	DET
ejpam-5205	281	50	vertex	vertex	NOUN
ejpam-5205	281	51	corresponding	correspond	VERB
ejpam-5205	281	52	to	to	ADP
ejpam-5205	281	53	v	v	NOUN
ejpam-5205	281	54	in	in	ADP
ejpam-5205	281	55	g.	g.	PROPN
ejpam-5205	281	56	formally	formally	ADV
ejpam-5205	281	57	,	,	PUNCT
ejpam-5205	281	58	the	the	DET
ejpam-5205	281	59	graph	graph	NOUN
ejpam-5205	281	60	gg	gg	NOUN
ejpam-5205	281	61	is	be	AUX
ejpam-5205	281	62	formed	form	VERB
ejpam-5205	281	63	from	from	ADP
ejpam-5205	281	64	g∪g	g∪g	NOUN
ejpam-5205	281	65	by	by	ADP
ejpam-5205	281	66	adding	add	VERB
ejpam-5205	281	67	the	the	DET
ejpam-5205	281	68	edge	edge	NOUN
ejpam-5205	281	69	vv	vv	NOUN
ejpam-5205	281	70	for	for	ADP
ejpam-5205	281	71	every	every	DET
ejpam-5205	281	72	v	v	NUM
ejpam-5205	281	73	∈	∈	NOUN
ejpam-5205	281	74	v	v	NOUN
ejpam-5205	281	75	(	(	PUNCT
ejpam-5205	281	76	g	g	NOUN
ejpam-5205	281	77	)	)	PUNCT
ejpam-5205	281	78	.	.	PUNCT
ejpam-5205	282	1	proposition	proposition	NOUN
ejpam-5205	282	2	5	5	NUM
ejpam-5205	282	3	.	.	PUNCT
ejpam-5205	283	1	let	let	VERB
ejpam-5205	283	2	g	g	PRON
ejpam-5205	283	3	be	be	AUX
ejpam-5205	283	4	a	a	DET
ejpam-5205	283	5	graph	graph	NOUN
ejpam-5205	283	6	on	on	ADP
ejpam-5205	283	7	n	n	DET
ejpam-5205	283	8	vertices	vertex	NOUN
ejpam-5205	283	9	.	.	PUNCT
ejpam-5205	284	1	then	then	ADV
ejpam-5205	284	2	each	each	PRON
ejpam-5205	284	3	of	of	ADP
ejpam-5205	284	4	the	the	DET
ejpam-5205	284	5	following	follow	VERB
ejpam-5205	284	6	holds	hold	NOUN
ejpam-5205	284	7	.	.	PUNCT
ejpam-5205	285	1	(	(	PUNCT
ejpam-5205	285	2	i	i	NOUN
ejpam-5205	285	3	)	)	PUNCT
ejpam-5205	285	4	γcvr(gg	γcvr(gg	NOUN
ejpam-5205	285	5	)	)	PUNCT
ejpam-5205	285	6	=	=	SYM
ejpam-5205	285	7	2	2	NUM
ejpam-5205	285	8	if	if	SCONJ
ejpam-5205	285	9	and	and	CCONJ
ejpam-5205	285	10	only	only	ADV
ejpam-5205	285	11	if	if	SCONJ
ejpam-5205	285	12	g	g	PROPN
ejpam-5205	285	13	=	=	PROPN
ejpam-5205	285	14	k1	k1	PROPN
ejpam-5205	285	15	.	.	PUNCT
ejpam-5205	286	1	(	(	PUNCT
ejpam-5205	286	2	i	i	NOUN
ejpam-5205	286	3	)	)	PUNCT
ejpam-5205	286	4	γcvr(gg	γcvr(gg	NOUN
ejpam-5205	286	5	)	)	PUNCT
ejpam-5205	286	6	=	=	SYM
ejpam-5205	287	1	4	4	NUM
ejpam-5205	287	2	if	if	SCONJ
ejpam-5205	287	3	and	and	CCONJ
ejpam-5205	287	4	only	only	ADV
ejpam-5205	287	5	if	if	SCONJ
ejpam-5205	287	6	g	g	PROPN
ejpam-5205	287	7	=	=	SYM
ejpam-5205	287	8	k2	k2	PROPN
ejpam-5205	287	9	or	or	CCONJ
ejpam-5205	287	10	k2	k2	ADJ
ejpam-5205	287	11	.	.	PUNCT
ejpam-5205	288	1	proof	proof	NOUN
ejpam-5205	288	2	.	.	PUNCT
ejpam-5205	289	1	(	(	PUNCT
ejpam-5205	289	2	i	i	NOUN
ejpam-5205	289	3	)	)	PUNCT
ejpam-5205	289	4	suppose	suppose	VERB
ejpam-5205	289	5	that	that	SCONJ
ejpam-5205	289	6	g	g	PROPN
ejpam-5205	289	7	=	=	PROPN
ejpam-5205	289	8	k1	k1	PROPN
ejpam-5205	289	9	.	.	PUNCT
ejpam-5205	290	1	then	then	ADV
ejpam-5205	290	2	gg	gg	PROPN
ejpam-5205	290	3	=	=	SYM
ejpam-5205	290	4	k2	k2	PROPN
ejpam-5205	290	5	.	.	PUNCT
ejpam-5205	291	1	by	by	ADP
ejpam-5205	291	2	theorem	theorem	NOUN
ejpam-5205	291	3	7	7	NUM
ejpam-5205	291	4	,	,	PUNCT
ejpam-5205	291	5	we	we	PRON
ejpam-5205	291	6	are	be	AUX
ejpam-5205	291	7	done	do	VERB
ejpam-5205	291	8	.	.	PUNCT
ejpam-5205	292	1	(	(	PUNCT
ejpam-5205	292	2	ii	ii	NOUN
ejpam-5205	292	3	)	)	PUNCT
ejpam-5205	292	4	suppose	suppose	VERB
ejpam-5205	292	5	that	that	SCONJ
ejpam-5205	292	6	g	g	PROPN
ejpam-5205	292	7	=	=	SYM
ejpam-5205	292	8	k2	k2	PROPN
ejpam-5205	292	9	or	or	CCONJ
ejpam-5205	292	10	g	g	NOUN
ejpam-5205	292	11	=	=	SYM
ejpam-5205	292	12	k2	k2	PROPN
ejpam-5205	292	13	.	.	PUNCT
ejpam-5205	293	1	then	then	ADV
ejpam-5205	293	2	g	g	PROPN
ejpam-5205	293	3	=	=	SYM
ejpam-5205	293	4	p4	p4	ADJ
ejpam-5205	293	5	and	and	CCONJ
ejpam-5205	293	6	by	by	ADP
ejpam-5205	293	7	theorem	theorem	ADJ
ejpam-5205	293	8	1	1	NUM
ejpam-5205	293	9	,	,	PUNCT
ejpam-5205	293	10	γcvr(gg	γcvr(gg	NOUN
ejpam-5205	293	11	)	)	PUNCT
ejpam-5205	293	12	=	=	SYM
ejpam-5205	293	13	γcvr(p4	γcvr(p4	NOUN
ejpam-5205	293	14	)	)	PUNCT
ejpam-5205	293	15	=	=	SYM
ejpam-5205	293	16	4	4	X
ejpam-5205	293	17	.	.	X
ejpam-5205	294	1	conversely	conversely	ADV
ejpam-5205	294	2	,	,	PUNCT
ejpam-5205	294	3	suppose	suppose	VERB
ejpam-5205	294	4	that	that	SCONJ
ejpam-5205	294	5	γcvr(gg	γcvr(gg	NOUN
ejpam-5205	294	6	)	)	PUNCT
ejpam-5205	294	7	=	=	PUNCT
ejpam-5205	295	1	4	4	X
ejpam-5205	295	2	.	.	X
ejpam-5205	295	3	let	let	VERB
ejpam-5205	295	4	f	f	PROPN
ejpam-5205	295	5	=	=	SYM
ejpam-5205	295	6	(	(	PUNCT
ejpam-5205	295	7	v0	v0	PROPN
ejpam-5205	295	8	,	,	PUNCT
ejpam-5205	295	9	v1	v1	NOUN
ejpam-5205	295	10	,	,	PUNCT
ejpam-5205	295	11	v2	v2	PROPN
ejpam-5205	295	12	)	)	PUNCT
ejpam-5205	295	13	be	be	AUX
ejpam-5205	295	14	a	a	DET
ejpam-5205	295	15	γcvr	γcvr	NOUN
ejpam-5205	295	16	-	-	PUNCT
ejpam-5205	295	17	function	function	NOUN
ejpam-5205	295	18	.	.	PUNCT
ejpam-5205	296	1	then	then	ADV
ejpam-5205	296	2	ωcvr	ωcvr	PROPN
ejpam-5205	296	3	gg	gg	PROPN
ejpam-5205	296	4	(	(	PUNCT
ejpam-5205	296	5	f	f	X
ejpam-5205	296	6	)	)	PUNCT
ejpam-5205	296	7	=	=	NOUN
ejpam-5205	296	8	|v1|	|v1|	NOUN
ejpam-5205	296	9	+	+	CCONJ
ejpam-5205	296	10	2|v2|	2|v2|	NUM
ejpam-5205	296	11	=	=	SYM
ejpam-5205	296	12	4	4	X
ejpam-5205	296	13	.	.	PUNCT
ejpam-5205	296	14	then	then	ADV
ejpam-5205	296	15	|v2|	|v2|	ADV
ejpam-5205	296	16	≤	≤	NOUN
ejpam-5205	296	17	2	2	NUM
ejpam-5205	296	18	.	.	PUNCT
ejpam-5205	297	1	if	if	SCONJ
ejpam-5205	297	2	r.	r.	PROPN
ejpam-5205	297	3	fortosa	fortosa	PROPN
ejpam-5205	297	4	,	,	PUNCT
ejpam-5205	297	5	s.	s.	PROPN
ejpam-5205	297	6	canoy	canoy	PROPN
ejpam-5205	297	7	jr	jr	PROPN
ejpam-5205	297	8	.	.	PROPN
ejpam-5205	297	9	/	/	SYM
ejpam-5205	297	10	eur	eur	PROPN
ejpam-5205	297	11	.	.	PUNCT
ejpam-5205	298	1	j.	j.	PROPN
ejpam-5205	298	2	pure	pure	PROPN
ejpam-5205	298	3	appl	appl	PROPN
ejpam-5205	298	4	.	.	PROPN
ejpam-5205	298	5	math	math	PROPN
ejpam-5205	298	6	,	,	PUNCT
ejpam-5205	298	7	17	17	NUM
ejpam-5205	298	8	(	(	PUNCT
ejpam-5205	298	9	2	2	NUM
ejpam-5205	298	10	)	)	PUNCT
ejpam-5205	298	11	(	(	PUNCT
ejpam-5205	298	12	2024	2024	NUM
ejpam-5205	298	13	)	)	PUNCT
ejpam-5205	298	14	,	,	PUNCT
ejpam-5205	298	15	1335	1335	NUM
ejpam-5205	298	16	-	-	SYM
ejpam-5205	298	17	1351	1351	NUM
ejpam-5205	298	18	1343	1343	NUM
ejpam-5205	298	19	|v2|	|v2|	NOUN
ejpam-5205	298	20	=	=	SYM
ejpam-5205	298	21	0	0	NUM
ejpam-5205	298	22	,	,	PUNCT
ejpam-5205	298	23	then	then	ADV
ejpam-5205	298	24	v1	v1	VERB
ejpam-5205	298	25	=	=	SYM
ejpam-5205	298	26	v	v	PROPN
ejpam-5205	298	27	(	(	PUNCT
ejpam-5205	298	28	gg	gg	NOUN
ejpam-5205	298	29	)	)	PUNCT
ejpam-5205	298	30	.	.	PUNCT
ejpam-5205	299	1	hence	hence	ADV
ejpam-5205	299	2	,	,	PUNCT
ejpam-5205	299	3	gg	gg	NOUN
ejpam-5205	299	4	=	=	SYM
ejpam-5205	299	5	p4	p4	ADJ
ejpam-5205	299	6	.	.	PUNCT
ejpam-5205	300	1	this	this	PRON
ejpam-5205	300	2	implies	imply	VERB
ejpam-5205	300	3	that	that	SCONJ
ejpam-5205	300	4	g	g	PROPN
ejpam-5205	300	5	∈	∈	PROPN
ejpam-5205	300	6	{	{	PUNCT
ejpam-5205	300	7	k2,k2	k2,k2	PROPN
ejpam-5205	300	8	}	}	PUNCT
ejpam-5205	300	9	.	.	PUNCT
ejpam-5205	301	1	suppose	suppose	VERB
ejpam-5205	301	2	that	that	SCONJ
ejpam-5205	301	3	|v2|	|v2|	NOUN
ejpam-5205	301	4	=	=	SYM
ejpam-5205	301	5	1	1	X
ejpam-5205	301	6	,	,	PUNCT
ejpam-5205	301	7	say	say	VERB
ejpam-5205	301	8	v2	v2	NOUN
ejpam-5205	301	9	=	=	SYM
ejpam-5205	301	10	{	{	PUNCT
ejpam-5205	301	11	u	u	NOUN
ejpam-5205	301	12	}	}	PUNCT
ejpam-5205	301	13	.	.	PUNCT
ejpam-5205	302	1	then	then	ADV
ejpam-5205	302	2	|v1|	|v1|	NOUN
ejpam-5205	302	3	=	=	SYM
ejpam-5205	302	4	2	2	NUM
ejpam-5205	302	5	.	.	NOUN
ejpam-5205	302	6	wlog	wlog	NOUN
ejpam-5205	302	7	,	,	PUNCT
ejpam-5205	302	8	asssume	asssume	VERB
ejpam-5205	302	9	that	that	SCONJ
ejpam-5205	302	10	u	u	PROPN
ejpam-5205	302	11	∈	∈	PROPN
ejpam-5205	302	12	v	v	NOUN
ejpam-5205	302	13	(	(	PUNCT
ejpam-5205	302	14	g	g	NOUN
ejpam-5205	302	15	)	)	PUNCT
ejpam-5205	302	16	.	.	PUNCT
ejpam-5205	303	1	suppose	suppose	VERB
ejpam-5205	303	2	|v	|v	PROPN
ejpam-5205	303	3	(	(	PUNCT
ejpam-5205	303	4	g)|	g)|	X
ejpam-5205	303	5	≥	≥	NOUN
ejpam-5205	303	6	3	3	NUM
ejpam-5205	303	7	and	and	CCONJ
ejpam-5205	303	8	let	let	VERB
ejpam-5205	303	9	v	v	NOUN
ejpam-5205	303	10	,	,	PUNCT
ejpam-5205	303	11	w	w	PROPN
ejpam-5205	303	12	∈	∈	PROPN
ejpam-5205	303	13	v	v	ADP
ejpam-5205	303	14	(	(	PUNCT
ejpam-5205	303	15	g	g	NOUN
ejpam-5205	303	16	)	)	PUNCT
ejpam-5205	303	17	\	\	NOUN
ejpam-5205	303	18	{	{	PUNCT
ejpam-5205	303	19	u	u	NOUN
ejpam-5205	303	20	}	}	PUNCT
ejpam-5205	303	21	.	.	PUNCT
ejpam-5205	304	1	since	since	SCONJ
ejpam-5205	304	2	v	v	NOUN
ejpam-5205	304	3	,	,	PUNCT
ejpam-5205	304	4	w	w	PROPN
ejpam-5205	304	5	/∈	/∈	PROPN
ejpam-5205	304	6	ngg(u	ngg(u	PROPN
ejpam-5205	304	7	)	)	PUNCT
ejpam-5205	304	8	,	,	PUNCT
ejpam-5205	304	9	v1	v1	NOUN
ejpam-5205	304	10	=	=	SYM
ejpam-5205	304	11	{	{	PUNCT
ejpam-5205	304	12	v	v	NOUN
ejpam-5205	304	13	,	,	PUNCT
ejpam-5205	304	14	w	w	NOUN
ejpam-5205	304	15	}	}	PUNCT
ejpam-5205	304	16	.	.	PUNCT
ejpam-5205	305	1	because	because	SCONJ
ejpam-5205	305	2	v1	v1	PROPN
ejpam-5205	305	3	∪v2	∪v2	PROPN
ejpam-5205	305	4	is	be	AUX
ejpam-5205	305	5	convex	convex	PROPN
ejpam-5205	305	6	,	,	PUNCT
ejpam-5205	305	7	one	one	NUM
ejpam-5205	305	8	of	of	ADP
ejpam-5205	305	9	the	the	DET
ejpam-5205	305	10	following	follow	VERB
ejpam-5205	305	11	holds	hold	VERB
ejpam-5205	305	12	:	:	PUNCT
ejpam-5205	305	13	u	u	PROPN
ejpam-5205	305	14	∈	∈	PROPN
ejpam-5205	305	15	igg[u	igg[u	PROPN
ejpam-5205	305	16	,	,	PUNCT
ejpam-5205	305	17	z	z	X
ejpam-5205	305	18	]	]	X
ejpam-5205	305	19	⊆	⊆	NUM
ejpam-5205	305	20	v1	v1	NOUN
ejpam-5205	305	21	∪	∪	NOUN
ejpam-5205	305	22	v2	v2	NOUN
ejpam-5205	305	23	,	,	PUNCT
ejpam-5205	305	24	where	where	SCONJ
ejpam-5205	305	25	z	z	PROPN
ejpam-5205	305	26	∈	∈	PROPN
ejpam-5205	305	27	{	{	PUNCT
ejpam-5205	305	28	v	v	NOUN
ejpam-5205	305	29	,	,	PUNCT
ejpam-5205	305	30	w	w	NOUN
ejpam-5205	305	31	}	}	PUNCT
ejpam-5205	305	32	,	,	PUNCT
ejpam-5205	305	33	v	v	PROPN
ejpam-5205	305	34	∈	∈	PROPN
ejpam-5205	305	35	igg[u	igg[u	NOUN
ejpam-5205	305	36	,	,	PUNCT
ejpam-5205	305	37	z	z	X
ejpam-5205	305	38	]	]	X
ejpam-5205	305	39	⊆	⊆	NUM
ejpam-5205	305	40	v1	v1	NOUN
ejpam-5205	305	41	∪	∪	NOUN
ejpam-5205	305	42	v2	v2	NOUN
ejpam-5205	305	43	,	,	PUNCT
ejpam-5205	305	44	where	where	SCONJ
ejpam-5205	305	45	z	z	PROPN
ejpam-5205	305	46	∈	∈	PROPN
ejpam-5205	305	47	{	{	PUNCT
ejpam-5205	305	48	v	v	NOUN
ejpam-5205	305	49	,	,	PUNCT
ejpam-5205	305	50	w	w	NOUN
ejpam-5205	305	51	}	}	PUNCT
ejpam-5205	305	52	,	,	PUNCT
ejpam-5205	305	53	w	w	PROPN
ejpam-5205	305	54	∈	∈	PROPN
ejpam-5205	305	55	igg[u	igg[u	NOUN
ejpam-5205	305	56	,	,	PUNCT
ejpam-5205	305	57	z	z	X
ejpam-5205	305	58	]	]	X
ejpam-5205	305	59	⊆	⊆	NUM
ejpam-5205	305	60	v1	v1	NOUN
ejpam-5205	305	61	∪	∪	NOUN
ejpam-5205	305	62	v2	v2	NOUN
ejpam-5205	305	63	,	,	PUNCT
ejpam-5205	305	64	where	where	SCONJ
ejpam-5205	305	65	z	z	PROPN
ejpam-5205	305	66	∈	∈	PROPN
ejpam-5205	305	67	{	{	PUNCT
ejpam-5205	305	68	v	v	NOUN
ejpam-5205	305	69	,	,	PUNCT
ejpam-5205	305	70	w	w	NOUN
ejpam-5205	305	71	}	}	PUNCT
ejpam-5205	305	72	.	.	PUNCT
ejpam-5205	306	1	in	in	ADP
ejpam-5205	306	2	any	any	DET
ejpam-5205	306	3	case	case	NOUN
ejpam-5205	306	4	,	,	PUNCT
ejpam-5205	306	5	we	we	PRON
ejpam-5205	306	6	have	have	VERB
ejpam-5205	306	7	a	a	DET
ejpam-5205	306	8	contradiction	contradiction	NOUN
ejpam-5205	306	9	.	.	PUNCT
ejpam-5205	307	1	thus	thus	ADV
ejpam-5205	307	2	,	,	PUNCT
ejpam-5205	307	3	|v	|v	PROPN
ejpam-5205	307	4	(	(	PUNCT
ejpam-5205	307	5	g)|	g)|	VERB
ejpam-5205	307	6	≤	≤	ADJ
ejpam-5205	307	7	2	2	NUM
ejpam-5205	307	8	.	.	PUNCT
ejpam-5205	307	9	but	but	CCONJ
ejpam-5205	307	10	by	by	ADP
ejpam-5205	307	11	statement	statement	NOUN
ejpam-5205	307	12	(	(	PUNCT
ejpam-5205	307	13	i	i	NOUN
ejpam-5205	307	14	)	)	PUNCT
ejpam-5205	307	15	,	,	PUNCT
ejpam-5205	307	16	|v	|v	PROPN
ejpam-5205	307	17	(	(	PUNCT
ejpam-5205	307	18	g)|	g)|	NOUN
ejpam-5205	307	19	=	=	SYM
ejpam-5205	307	20	2	2	NUM
ejpam-5205	307	21	.	.	PUNCT
ejpam-5205	308	1	this	this	PRON
ejpam-5205	308	2	means	mean	VERB
ejpam-5205	308	3	that	that	SCONJ
ejpam-5205	308	4	g	g	PROPN
ejpam-5205	308	5	∈	∈	PROPN
ejpam-5205	308	6	{	{	PUNCT
ejpam-5205	308	7	k2,k2	k2,k2	PROPN
ejpam-5205	308	8	}	}	PUNCT
ejpam-5205	308	9	.	.	PUNCT
ejpam-5205	309	1	if	if	SCONJ
ejpam-5205	309	2	|v2|	|v2|	NOUN
ejpam-5205	309	3	=	=	SYM
ejpam-5205	309	4	2	2	NUM
ejpam-5205	309	5	,	,	PUNCT
ejpam-5205	309	6	then	then	ADV
ejpam-5205	309	7	|v1|	|v1|	VERB
ejpam-5205	309	8	=	=	SYM
ejpam-5205	309	9	0	0	X
ejpam-5205	309	10	.	.	PUNCT
ejpam-5205	309	11	by	by	ADP
ejpam-5205	309	12	proposition	proposition	NOUN
ejpam-5205	309	13	2	2	NUM
ejpam-5205	309	14	,	,	PUNCT
ejpam-5205	309	15	v2	v2	PROPN
ejpam-5205	309	16	is	be	AUX
ejpam-5205	309	17	a	a	DET
ejpam-5205	309	18	γcon	γcon	NOUN
ejpam-5205	309	19	-	-	PUNCT
ejpam-5205	309	20	set	set	NOUN
ejpam-5205	309	21	in	in	ADP
ejpam-5205	309	22	gg	gg	PROPN
ejpam-5205	309	23	.	.	PUNCT
ejpam-5205	310	1	let	let	VERB
ejpam-5205	310	2	v2	v2	VERB
ejpam-5205	310	3	=	=	SYM
ejpam-5205	310	4	{	{	PUNCT
ejpam-5205	310	5	x	x	PROPN
ejpam-5205	310	6	,	,	PUNCT
ejpam-5205	310	7	y	y	PROPN
ejpam-5205	310	8	}	}	PUNCT
ejpam-5205	310	9	.	.	PUNCT
ejpam-5205	311	1	wlog	wlog	PROPN
ejpam-5205	311	2	,	,	PUNCT
ejpam-5205	311	3	assume	assume	VERB
ejpam-5205	311	4	that	that	SCONJ
ejpam-5205	311	5	x	x	PUNCT
ejpam-5205	311	6	∈	∈	NOUN
ejpam-5205	311	7	v	v	X
ejpam-5205	311	8	(	(	PUNCT
ejpam-5205	311	9	g	g	NOUN
ejpam-5205	311	10	)	)	PUNCT
ejpam-5205	311	11	.	.	PUNCT
ejpam-5205	312	1	if	if	SCONJ
ejpam-5205	312	2	x	x	X
ejpam-5205	312	3	=	=	SYM
ejpam-5205	312	4	y	y	PROPN
ejpam-5205	312	5	,	,	PUNCT
ejpam-5205	312	6	then	then	ADV
ejpam-5205	312	7	ng[x	ng[x	PROPN
ejpam-5205	312	8	]	]	X
ejpam-5205	312	9	=	=	SYM
ejpam-5205	313	1	v	v	X
ejpam-5205	313	2	(	(	PUNCT
ejpam-5205	313	3	g	g	NOUN
ejpam-5205	313	4	)	)	PUNCT
ejpam-5205	313	5	and	and	CCONJ
ejpam-5205	313	6	ng[y	ng[y	PROPN
ejpam-5205	313	7	]	]	X
ejpam-5205	313	8	=	=	SYM
ejpam-5205	313	9	v	v	X
ejpam-5205	313	10	(	(	PUNCT
ejpam-5205	313	11	g	g	NOUN
ejpam-5205	313	12	)	)	PUNCT
ejpam-5205	313	13	.	.	PUNCT
ejpam-5205	314	1	this	this	PRON
ejpam-5205	314	2	is	be	AUX
ejpam-5205	314	3	possible	possible	ADJ
ejpam-5205	314	4	only	only	ADV
ejpam-5205	314	5	if	if	SCONJ
ejpam-5205	314	6	g	g	PROPN
ejpam-5205	314	7	=	=	SYM
ejpam-5205	314	8	k1	k1	PROPN
ejpam-5205	314	9	,	,	PUNCT
ejpam-5205	314	10	a	a	DET
ejpam-5205	314	11	contradiction	contradiction	NOUN
ejpam-5205	314	12	.	.	PUNCT
ejpam-5205	315	1	thus	thus	ADV
ejpam-5205	315	2	y	y	PROPN
ejpam-5205	315	3	∈	∈	PROPN
ejpam-5205	315	4	v	v	ADP
ejpam-5205	315	5	(	(	PUNCT
ejpam-5205	315	6	g	g	NOUN
ejpam-5205	315	7	)	)	PUNCT
ejpam-5205	315	8	and	and	CCONJ
ejpam-5205	315	9	xy	xy	PROPN
ejpam-5205	315	10	∈	∈	PROPN
ejpam-5205	315	11	e(g	e(g	PROPN
ejpam-5205	315	12	)	)	PUNCT
ejpam-5205	315	13	.	.	PUNCT
ejpam-5205	316	1	now	now	ADV
ejpam-5205	316	2	,	,	PUNCT
ejpam-5205	316	3	for	for	ADP
ejpam-5205	316	4	each	each	DET
ejpam-5205	316	5	z	z	NOUN
ejpam-5205	316	6	∈	∈	PROPN
ejpam-5205	316	7	v0	v0	NOUN
ejpam-5205	316	8	=	=	SYM
ejpam-5205	316	9	v	v	PROPN
ejpam-5205	316	10	(	(	PUNCT
ejpam-5205	316	11	g	g	NOUN
ejpam-5205	316	12	)	)	PUNCT
ejpam-5205	316	13	\	\	NOUN
ejpam-5205	316	14	{	{	PUNCT
ejpam-5205	316	15	x	x	NOUN
ejpam-5205	316	16	,	,	PUNCT
ejpam-5205	316	17	y	y	PROPN
ejpam-5205	316	18	}	}	PUNCT
ejpam-5205	316	19	,	,	PUNCT
ejpam-5205	316	20	xz	xz	PROPN
ejpam-5205	316	21	/∈	/∈	PUNCT
ejpam-5205	316	22	e(gg	e(gg	NUM
ejpam-5205	316	23	)	)	PUNCT
ejpam-5205	316	24	and	and	CCONJ
ejpam-5205	316	25	yz	yz	X
ejpam-5205	316	26	/∈	/∈	PUNCT
ejpam-5205	316	27	e(gg	e(gg	NUM
ejpam-5205	316	28	)	)	PUNCT
ejpam-5205	316	29	.	.	PUNCT
ejpam-5205	317	1	hence	hence	ADV
ejpam-5205	317	2	,	,	PUNCT
ejpam-5205	317	3	v	v	X
ejpam-5205	317	4	(	(	PUNCT
ejpam-5205	317	5	g	g	NOUN
ejpam-5205	317	6	)	)	PUNCT
ejpam-5205	317	7	\	\	NOUN
ejpam-5205	317	8	{	{	PUNCT
ejpam-5205	317	9	x	x	NOUN
ejpam-5205	317	10	,	,	PUNCT
ejpam-5205	317	11	y	y	PROPN
ejpam-5205	317	12	}	}	PUNCT
ejpam-5205	317	13	=	=	PUNCT
ejpam-5205	317	14	∅.	∅.	VERB
ejpam-5205	317	15	therefore	therefore	ADV
ejpam-5205	317	16	,	,	PUNCT
ejpam-5205	317	17	g	g	PROPN
ejpam-5205	317	18	∈	∈	PROPN
ejpam-5205	317	19	{	{	PUNCT
ejpam-5205	317	20	k2,k2	k2,k2	PROPN
ejpam-5205	317	21	}	}	PUNCT
ejpam-5205	317	22	.	.	PUNCT
ejpam-5205	318	1	proposition	proposition	NOUN
ejpam-5205	318	2	6	6	NUM
ejpam-5205	318	3	.	.	PUNCT
ejpam-5205	319	1	for	for	ADP
ejpam-5205	319	2	any	any	DET
ejpam-5205	319	3	connected	connected	ADJ
ejpam-5205	319	4	graph	graph	NOUN
ejpam-5205	319	5	g	g	NOUN
ejpam-5205	319	6	of	of	ADP
ejpam-5205	319	7	order	order	NOUN
ejpam-5205	319	8	n	n	CCONJ
ejpam-5205	319	9	,	,	PUNCT
ejpam-5205	319	10	2	2	NUM
ejpam-5205	319	11	≤	≤	NOUN
ejpam-5205	319	12	γcvr(gg	γcvr(gg	NOUN
ejpam-5205	319	13	)	)	PUNCT
ejpam-5205	319	14	≤	≤	NOUN
ejpam-5205	319	15	2min{γcon(gg	2min{γcon(gg	NUM
ejpam-5205	319	16	)	)	PUNCT
ejpam-5205	319	17	,	,	PUNCT
ejpam-5205	319	18	n	n	CCONJ
ejpam-5205	319	19	}	}	PUNCT
ejpam-5205	319	20	.	.	PUNCT
ejpam-5205	320	1	in	in	ADP
ejpam-5205	320	2	particular	particular	ADJ
ejpam-5205	320	3	,	,	PUNCT
ejpam-5205	320	4	(	(	PUNCT
ejpam-5205	320	5	i	i	NOUN
ejpam-5205	320	6	)	)	PUNCT
ejpam-5205	320	7	γcvr(gg	γcvr(gg	NOUN
ejpam-5205	320	8	)	)	PUNCT
ejpam-5205	320	9	=	=	SYM
ejpam-5205	321	1	2γcon(gg	2γcon(gg	NUM
ejpam-5205	321	2	)	)	PUNCT
ejpam-5205	321	3	if	if	SCONJ
ejpam-5205	321	4	there	there	PRON
ejpam-5205	321	5	exists	exist	VERB
ejpam-5205	321	6	a	a	DET
ejpam-5205	321	7	γcvr	γcvr	NOUN
ejpam-5205	321	8	-	-	PUNCT
ejpam-5205	321	9	function	function	NOUN
ejpam-5205	321	10	f	f	NOUN
ejpam-5205	321	11	=	=	SYM
ejpam-5205	321	12	(	(	PUNCT
ejpam-5205	321	13	v0	v0	PROPN
ejpam-5205	321	14	,	,	PUNCT
ejpam-5205	321	15	v1	v1	NOUN
ejpam-5205	321	16	,	,	PUNCT
ejpam-5205	321	17	v2	v2	PROPN
ejpam-5205	321	18	)	)	PUNCT
ejpam-5205	321	19	with	with	ADP
ejpam-5205	321	20	v1	v1	NOUN
ejpam-5205	321	21	=	=	SYM
ejpam-5205	321	22	∅.	∅.	X
ejpam-5205	321	23	(	(	PUNCT
ejpam-5205	321	24	ii	ii	NOUN
ejpam-5205	321	25	)	)	PUNCT
ejpam-5205	321	26	if	if	SCONJ
ejpam-5205	321	27	g	g	PROPN
ejpam-5205	321	28	=	=	SYM
ejpam-5205	321	29	kn	kn	PROPN
ejpam-5205	321	30	,	,	PUNCT
ejpam-5205	321	31	then	then	ADV
ejpam-5205	321	32	γcvr(gg	γcvr(gg	NOUN
ejpam-5205	321	33	)	)	PUNCT
ejpam-5205	321	34	=	=	PUNCT
ejpam-5205	321	35	2n	2n	X
ejpam-5205	321	36	.	.	PUNCT
ejpam-5205	322	1	proof	proof	NOUN
ejpam-5205	322	2	.	.	PUNCT
ejpam-5205	323	1	by	by	ADP
ejpam-5205	323	2	proposition	proposition	NOUN
ejpam-5205	323	3	4	4	NUM
ejpam-5205	323	4	,	,	PUNCT
ejpam-5205	323	5	γcvr(gg	γcvr(gg	NOUN
ejpam-5205	323	6	)	)	PUNCT
ejpam-5205	323	7	≤	≤	NOUN
ejpam-5205	323	8	2γcon(gg	2γcon(gg	NUM
ejpam-5205	323	9	)	)	PUNCT
ejpam-5205	323	10	.	.	PUNCT
ejpam-5205	324	1	define	define	VERB
ejpam-5205	324	2	f	f	PROPN
ejpam-5205	324	3	=	=	SYM
ejpam-5205	324	4	(	(	PUNCT
ejpam-5205	324	5	v0	v0	PROPN
ejpam-5205	324	6	,	,	PUNCT
ejpam-5205	324	7	v1	v1	NOUN
ejpam-5205	324	8	,	,	PUNCT
ejpam-5205	324	9	v2	v2	PROPN
ejpam-5205	324	10	)	)	PUNCT
ejpam-5205	324	11	,	,	PUNCT
ejpam-5205	324	12	where	where	SCONJ
ejpam-5205	324	13	v2	v2	PROPN
ejpam-5205	324	14	=	=	SYM
ejpam-5205	324	15	v	v	NOUN
ejpam-5205	324	16	(	(	PUNCT
ejpam-5205	324	17	g	g	NOUN
ejpam-5205	324	18	)	)	PUNCT
ejpam-5205	324	19	,	,	PUNCT
ejpam-5205	324	20	v1	v1	NOUN
ejpam-5205	324	21	=	=	SYM
ejpam-5205	324	22	∅	∅	NOUN
ejpam-5205	324	23	,	,	PUNCT
ejpam-5205	324	24	and	and	CCONJ
ejpam-5205	324	25	v0	v0	PROPN
ejpam-5205	324	26	=	=	SYM
ejpam-5205	324	27	v	v	PROPN
ejpam-5205	324	28	(	(	PUNCT
ejpam-5205	324	29	g	g	NOUN
ejpam-5205	324	30	)	)	PUNCT
ejpam-5205	324	31	.	.	PUNCT
ejpam-5205	325	1	then	then	ADV
ejpam-5205	325	2	f	f	PROPN
ejpam-5205	325	3	is	be	AUX
ejpam-5205	325	4	a	a	DET
ejpam-5205	325	5	cvrdf	cvrdf	NOUN
ejpam-5205	325	6	of	of	ADP
ejpam-5205	325	7	gg	gg	PROPN
ejpam-5205	325	8	.	.	PUNCT
ejpam-5205	326	1	thus	thus	ADV
ejpam-5205	326	2	γcvr(gg	γcvr(gg	ADJ
ejpam-5205	326	3	)	)	PUNCT
ejpam-5205	326	4	≤	≤	NOUN
ejpam-5205	326	5	2|v2|	2|v2|	NUM
ejpam-5205	326	6	=	=	SYM
ejpam-5205	326	7	2n	2n	NUM
ejpam-5205	326	8	.	.	PUNCT
ejpam-5205	327	1	it	it	PRON
ejpam-5205	327	2	is	be	AUX
ejpam-5205	327	3	worth	worth	ADJ
ejpam-5205	327	4	noting	note	VERB
ejpam-5205	327	5	that	that	SCONJ
ejpam-5205	327	6	if	if	SCONJ
ejpam-5205	327	7	g	g	PROPN
ejpam-5205	327	8	=	=	SYM
ejpam-5205	327	9	p4	p4	ADJ
ejpam-5205	327	10	,	,	PUNCT
ejpam-5205	327	11	γcon(gg	γcon(gg	NOUN
ejpam-5205	327	12	)	)	PUNCT
ejpam-5205	327	13	=	=	SYM
ejpam-5205	327	14	8	8	NUM
ejpam-5205	327	15	>	>	SYM
ejpam-5205	327	16	4	4	NUM
ejpam-5205	327	17	.	.	PUNCT
ejpam-5205	328	1	if	if	SCONJ
ejpam-5205	328	2	g	g	NOUN
ejpam-5205	328	3	=	=	SYM
ejpam-5205	328	4	p5	p5	PROPN
ejpam-5205	328	5	,	,	PUNCT
ejpam-5205	328	6	γcon(gg	γcon(gg	NOUN
ejpam-5205	328	7	)	)	PUNCT
ejpam-5205	328	8	=	=	SYM
ejpam-5205	328	9	4	4	NUM
ejpam-5205	328	10	<	<	SYM
ejpam-5205	328	11	5	5	NUM
ejpam-5205	328	12	.	.	PUNCT
ejpam-5205	329	1	the	the	DET
ejpam-5205	329	2	lexicographic	lexicographic	ADJ
ejpam-5205	329	3	product	product	NOUN
ejpam-5205	329	4	of	of	ADP
ejpam-5205	329	5	two	two	NUM
ejpam-5205	329	6	graphs	graph	NOUN
ejpam-5205	329	7	g	g	NOUN
ejpam-5205	329	8	and	and	CCONJ
ejpam-5205	329	9	h	h	NOUN
ejpam-5205	329	10	is	be	AUX
ejpam-5205	329	11	the	the	DET
ejpam-5205	329	12	graph	graph	NOUN
ejpam-5205	329	13	g[h	g[h	PROPN
ejpam-5205	329	14	]	]	PUNCT
ejpam-5205	329	15	with	with	ADP
ejpam-5205	329	16	v	v	NOUN
ejpam-5205	329	17	(	(	PUNCT
ejpam-5205	329	18	g[h	g[h	PROPN
ejpam-5205	329	19	]	]	PUNCT
ejpam-5205	329	20	)	)	PUNCT
ejpam-5205	329	21	=	=	SYM
ejpam-5205	329	22	v	v	X
ejpam-5205	329	23	(	(	PUNCT
ejpam-5205	329	24	g)×v	g)×v	PROPN
ejpam-5205	329	25	(	(	PUNCT
ejpam-5205	329	26	h	h	NOUN
ejpam-5205	329	27	)	)	PUNCT
ejpam-5205	329	28	and	and	CCONJ
ejpam-5205	329	29	(	(	PUNCT
ejpam-5205	329	30	u1	u1	NOUN
ejpam-5205	329	31	,	,	PUNCT
ejpam-5205	329	32	u2)(v1	u2)(v1	NOUN
ejpam-5205	329	33	,	,	PUNCT
ejpam-5205	329	34	v2	v2	NOUN
ejpam-5205	329	35	)	)	PUNCT
ejpam-5205	329	36	∈	∈	NOUN
ejpam-5205	329	37	e(g[h	e(g[h	NOUN
ejpam-5205	329	38	]	]	PUNCT
ejpam-5205	329	39	)	)	PUNCT
ejpam-5205	330	1	if	if	SCONJ
ejpam-5205	330	2	and	and	CCONJ
ejpam-5205	330	3	only	only	ADV
ejpam-5205	330	4	if	if	SCONJ
ejpam-5205	330	5	either	either	CCONJ
ejpam-5205	330	6	u1v1	u1v1	PROPN
ejpam-5205	330	7	∈	∈	PROPN
ejpam-5205	330	8	e(g	e(g	PROPN
ejpam-5205	330	9	)	)	PUNCT
ejpam-5205	330	10	or	or	CCONJ
ejpam-5205	330	11	u1	u1	NOUN
ejpam-5205	330	12	=	=	SYM
ejpam-5205	330	13	v1	v1	NOUN
ejpam-5205	330	14	and	and	CCONJ
ejpam-5205	330	15	u2v2	u2v2	ADJ
ejpam-5205	330	16	∈	∈	PROPN
ejpam-5205	330	17	e(h	e(h	PROPN
ejpam-5205	330	18	)	)	PUNCT
ejpam-5205	330	19	.	.	PUNCT
ejpam-5205	331	1	for	for	ADP
ejpam-5205	331	2	s	s	PROPN
ejpam-5205	331	3	⊆	⊆	NUM
ejpam-5205	331	4	v	v	NOUN
ejpam-5205	331	5	(	(	PUNCT
ejpam-5205	331	6	g[h	g[h	PROPN
ejpam-5205	331	7	]	]	PUNCT
ejpam-5205	331	8	)	)	PUNCT
ejpam-5205	331	9	,	,	PUNCT
ejpam-5205	331	10	we	we	PRON
ejpam-5205	331	11	write	write	VERB
ejpam-5205	331	12	sg	sg	X
ejpam-5205	331	13	=	=	PUNCT
ejpam-5205	331	14	{	{	PUNCT
ejpam-5205	331	15	x	x	PUNCT
ejpam-5205	331	16	∈	∈	PROPN
ejpam-5205	331	17	v	v	NOUN
ejpam-5205	331	18	(	(	PUNCT
ejpam-5205	331	19	g	g	NOUN
ejpam-5205	331	20	)	)	PUNCT
ejpam-5205	331	21	:	:	PUNCT
ejpam-5205	331	22	(	(	PUNCT
ejpam-5205	331	23	x	x	X
ejpam-5205	331	24	,	,	PUNCT
ejpam-5205	331	25	a	a	PRON
ejpam-5205	331	26	)	)	PUNCT
ejpam-5205	331	27	∈	∈	NOUN
ejpam-5205	331	28	s	s	NOUN
ejpam-5205	331	29	for	for	ADP
ejpam-5205	331	30	some	some	PRON
ejpam-5205	331	31	a	a	DET
ejpam-5205	331	32	∈	∈	PROPN
ejpam-5205	331	33	v	v	NOUN
ejpam-5205	331	34	(	(	PUNCT
ejpam-5205	331	35	h	h	NOUN
ejpam-5205	331	36	)	)	PUNCT
ejpam-5205	331	37	}	}	PUNCT
ejpam-5205	331	38	.	.	PUNCT
ejpam-5205	332	1	sg	sg	PROPN
ejpam-5205	332	2	is	be	AUX
ejpam-5205	332	3	referred	refer	VERB
ejpam-5205	332	4	to	to	ADP
ejpam-5205	332	5	as	as	ADP
ejpam-5205	332	6	the	the	DET
ejpam-5205	332	7	g	g	NOUN
ejpam-5205	332	8	-	-	PUNCT
ejpam-5205	332	9	projection	projection	NOUN
ejpam-5205	332	10	of	of	ADP
ejpam-5205	332	11	s	s	PRON
ejpam-5205	332	12	in	in	ADP
ejpam-5205	332	13	g[h	g[h	NOUN
ejpam-5205	332	14	]	]	PUNCT
ejpam-5205	332	15	.	.	PUNCT
ejpam-5205	333	1	let	let	VERB
ejpam-5205	333	2	f	f	PROPN
ejpam-5205	333	3	=	=	SYM
ejpam-5205	333	4	(	(	PUNCT
ejpam-5205	333	5	v0	v0	PROPN
ejpam-5205	333	6	,	,	PUNCT
ejpam-5205	333	7	v1	v1	NOUN
ejpam-5205	333	8	,	,	PUNCT
ejpam-5205	333	9	v2	v2	PROPN
ejpam-5205	333	10	)	)	PUNCT
ejpam-5205	333	11	be	be	AUX
ejpam-5205	333	12	a	a	DET
ejpam-5205	333	13	cvrdf	cvrdf	NOUN
ejpam-5205	333	14	on	on	ADP
ejpam-5205	333	15	g[h	g[h	NOUN
ejpam-5205	333	16	]	]	PUNCT
ejpam-5205	333	17	.	.	PUNCT
ejpam-5205	334	1	we	we	PRON
ejpam-5205	334	2	write	write	VERB
ejpam-5205	334	3	s0	s0	PROPN
ejpam-5205	334	4	g	g	PROPN
ejpam-5205	334	5	=	=	PRON
ejpam-5205	334	6	{	{	PUNCT
ejpam-5205	334	7	x	x	PROPN
ejpam-5205	334	8	∈	∈	PROPN
ejpam-5205	334	9	v	v	NOUN
ejpam-5205	334	10	(	(	PUNCT
ejpam-5205	334	11	g	g	NOUN
ejpam-5205	334	12	)	)	PUNCT
ejpam-5205	334	13	:	:	PUNCT
ejpam-5205	334	14	(	(	PUNCT
ejpam-5205	334	15	x	x	X
ejpam-5205	334	16	,	,	PUNCT
ejpam-5205	334	17	a	a	DET
ejpam-5205	334	18	)	)	PUNCT
ejpam-5205	334	19	∈	∈	NOUN
ejpam-5205	334	20	v0	v0	NOUN
ejpam-5205	334	21	for	for	ADP
ejpam-5205	334	22	some	some	DET
ejpam-5205	334	23	a	a	DET
ejpam-5205	334	24	∈	∈	PROPN
ejpam-5205	334	25	v	v	NOUN
ejpam-5205	334	26	(	(	PUNCT
ejpam-5205	334	27	h	h	NOUN
ejpam-5205	334	28	)	)	PUNCT
ejpam-5205	334	29	}	}	PUNCT
ejpam-5205	334	30	,	,	PUNCT
ejpam-5205	334	31	s1	s1	PROPN
ejpam-5205	334	32	g	g	PROPN
ejpam-5205	334	33	=	=	PUNCT
ejpam-5205	334	34	{	{	PUNCT
ejpam-5205	334	35	x	x	PROPN
ejpam-5205	334	36	∈	∈	PROPN
ejpam-5205	334	37	v	v	NOUN
ejpam-5205	334	38	(	(	PUNCT
ejpam-5205	334	39	g	g	NOUN
ejpam-5205	334	40	)	)	PUNCT
ejpam-5205	334	41	:	:	PUNCT
ejpam-5205	334	42	(	(	PUNCT
ejpam-5205	334	43	x	x	X
ejpam-5205	334	44	,	,	PUNCT
ejpam-5205	334	45	a	a	PRON
ejpam-5205	334	46	)	)	PUNCT
ejpam-5205	334	47	∈	∈	NOUN
ejpam-5205	334	48	v1	v1	NOUN
ejpam-5205	334	49	for	for	ADP
ejpam-5205	334	50	some	some	PRON
ejpam-5205	334	51	a	a	DET
ejpam-5205	334	52	∈	∈	PROPN
ejpam-5205	334	53	v	v	NOUN
ejpam-5205	334	54	(	(	PUNCT
ejpam-5205	334	55	h	h	NOUN
ejpam-5205	334	56	)	)	PUNCT
ejpam-5205	334	57	}	}	PUNCT
ejpam-5205	334	58	,	,	PUNCT
ejpam-5205	334	59	s2	s2	VERB
ejpam-5205	334	60	g	g	NOUN
ejpam-5205	334	61	=	=	SYM
ejpam-5205	334	62	{	{	PUNCT
ejpam-5205	334	63	x	x	PROPN
ejpam-5205	334	64	∈	∈	PROPN
ejpam-5205	334	65	v	v	NOUN
ejpam-5205	334	66	(	(	PUNCT
ejpam-5205	334	67	g	g	NOUN
ejpam-5205	334	68	)	)	PUNCT
ejpam-5205	334	69	:	:	PUNCT
ejpam-5205	334	70	(	(	PUNCT
ejpam-5205	334	71	x	x	X
ejpam-5205	334	72	,	,	PUNCT
ejpam-5205	334	73	a	a	PRON
ejpam-5205	334	74	)	)	PUNCT
ejpam-5205	334	75	∈	∈	NOUN
ejpam-5205	334	76	v2	v2	NOUN
ejpam-5205	334	77	for	for	ADP
ejpam-5205	334	78	some	some	PRON
ejpam-5205	334	79	a	a	DET
ejpam-5205	334	80	∈	∈	PROPN
ejpam-5205	334	81	v	v	NOUN
ejpam-5205	334	82	(	(	PUNCT
ejpam-5205	334	83	h	h	NOUN
ejpam-5205	334	84	)	)	PUNCT
ejpam-5205	334	85	}	}	PUNCT
ejpam-5205	334	86	,	,	PUNCT
ejpam-5205	334	87	v	v	NOUN
ejpam-5205	334	88	0	0	NUM
ejpam-5205	334	89	g	g	NOUN
ejpam-5205	334	90	=	=	SYM
ejpam-5205	334	91	s0	s0	PROPN
ejpam-5205	334	92	g	g	PROPN
ejpam-5205	334	93	\	\	PROPN
ejpam-5205	335	1	(	(	PUNCT
ejpam-5205	335	2	s1	s1	PROPN
ejpam-5205	335	3	g	g	PROPN
ejpam-5205	335	4	∪	∪	PROPN
ejpam-5205	335	5	s2	s2	PROPN
ejpam-5205	335	6	g	g	NOUN
ejpam-5205	335	7	)	)	PUNCT
ejpam-5205	335	8	,	,	PUNCT
ejpam-5205	335	9	r.	r.	PROPN
ejpam-5205	335	10	fortosa	fortosa	PROPN
ejpam-5205	335	11	,	,	PUNCT
ejpam-5205	335	12	s.	s.	PROPN
ejpam-5205	335	13	canoy	canoy	PROPN
ejpam-5205	335	14	jr	jr	PROPN
ejpam-5205	335	15	.	.	PROPN
ejpam-5205	335	16	/	/	SYM
ejpam-5205	335	17	eur	eur	PROPN
ejpam-5205	335	18	.	.	PUNCT
ejpam-5205	336	1	j.	j.	PROPN
ejpam-5205	336	2	pure	pure	PROPN
ejpam-5205	336	3	appl	appl	PROPN
ejpam-5205	336	4	.	.	PROPN
ejpam-5205	336	5	math	math	PROPN
ejpam-5205	336	6	,	,	PUNCT
ejpam-5205	336	7	17	17	NUM
ejpam-5205	336	8	(	(	PUNCT
ejpam-5205	336	9	2	2	NUM
ejpam-5205	336	10	)	)	PUNCT
ejpam-5205	336	11	(	(	PUNCT
ejpam-5205	336	12	2024	2024	NUM
ejpam-5205	336	13	)	)	PUNCT
ejpam-5205	336	14	,	,	PUNCT
ejpam-5205	336	15	1335	1335	NUM
ejpam-5205	336	16	-	-	SYM
ejpam-5205	336	17	1351	1351	NUM
ejpam-5205	336	18	1344	1344	NUM
ejpam-5205	336	19	v	v	ADP
ejpam-5205	336	20	1	1	NUM
ejpam-5205	336	21	g	g	NOUN
ejpam-5205	336	22	=	=	SYM
ejpam-5205	336	23	s1	s1	PROPN
ejpam-5205	336	24	g	g	PROPN
ejpam-5205	336	25	\	\	PROPN
ejpam-5205	336	26	(	(	PUNCT
ejpam-5205	336	27	s0	s0	PROPN
ejpam-5205	336	28	g	g	PROPN
ejpam-5205	336	29	∪	∪	PROPN
ejpam-5205	336	30	s2	s2	PROPN
ejpam-5205	336	31	g	g	NOUN
ejpam-5205	336	32	)	)	PUNCT
ejpam-5205	336	33	,	,	PUNCT
ejpam-5205	336	34	v	v	NOUN
ejpam-5205	336	35	2	2	NUM
ejpam-5205	336	36	g	g	NOUN
ejpam-5205	336	37	=	=	SYM
ejpam-5205	336	38	v	v	PROPN
ejpam-5205	336	39	(	(	PUNCT
ejpam-5205	336	40	g	g	NOUN
ejpam-5205	336	41	)	)	PUNCT
ejpam-5205	336	42	\	\	PUNCT
ejpam-5205	337	1	(	(	PUNCT
ejpam-5205	337	2	v	v	NOUN
ejpam-5205	337	3	0	0	NUM
ejpam-5205	337	4	g	g	NOUN
ejpam-5205	337	5	∪	∪	ADJ
ejpam-5205	337	6	v	v	ADP
ejpam-5205	337	7	1	1	NUM
ejpam-5205	337	8	g	g	NOUN
ejpam-5205	337	9	)	)	PUNCT
ejpam-5205	337	10	,	,	PUNCT
ejpam-5205	337	11	and	and	CCONJ
ejpam-5205	337	12	s0	s0	PROPN
ejpam-5205	337	13	f	f	PROPN
ejpam-5205	338	1	=	=	PRON
ejpam-5205	338	2	i(s1	i(s1	VERB
ejpam-5205	338	3	g	g	PROPN
ejpam-5205	338	4	∪	∪	PROPN
ejpam-5205	338	5	s2	s2	PROPN
ejpam-5205	338	6	g	g	NOUN
ejpam-5205	338	7	)	)	PUNCT
ejpam-5205	338	8	∩	∩	NOUN
ejpam-5205	338	9	(	(	PUNCT
ejpam-5205	338	10	s1	s1	PROPN
ejpam-5205	338	11	g	g	PROPN
ejpam-5205	338	12	∪	∪	PROPN
ejpam-5205	338	13	s2	s2	PROPN
ejpam-5205	338	14	g	g	NOUN
ejpam-5205	338	15	)	)	PUNCT
ejpam-5205	338	16	.	.	PUNCT
ejpam-5205	339	1	note	note	VERB
ejpam-5205	339	2	that	that	SCONJ
ejpam-5205	339	3	if	if	SCONJ
ejpam-5205	339	4	v	v	NOUN
ejpam-5205	339	5	1	1	NUM
ejpam-5205	339	6	g	g	ADP
ejpam-5205	339	7	̸=	̸=	PROPN
ejpam-5205	339	8	v	v	NOUN
ejpam-5205	339	9	(	(	PUNCT
ejpam-5205	339	10	g	g	NOUN
ejpam-5205	339	11	)	)	PUNCT
ejpam-5205	339	12	,	,	PUNCT
ejpam-5205	339	13	then	then	ADV
ejpam-5205	339	14	v	v	X
ejpam-5205	339	15	2	2	NUM
ejpam-5205	339	16	g	g	ADP
ejpam-5205	339	17	̸=	̸=	PROPN
ejpam-5205	339	18	∅	∅	NOUN
ejpam-5205	339	19	because	because	SCONJ
ejpam-5205	339	20	f	f	PROPN
ejpam-5205	339	21	is	be	AUX
ejpam-5205	339	22	a	a	DET
ejpam-5205	339	23	roman	roman	ADJ
ejpam-5205	339	24	dominating	dominating	NOUN
ejpam-5205	339	25	function	function	NOUN
ejpam-5205	339	26	on	on	ADP
ejpam-5205	339	27	g[h	g[h	PROPN
ejpam-5205	339	28	]	]	PUNCT
ejpam-5205	339	29	.	.	PUNCT
ejpam-5205	340	1	theorem	theorem	ADJ
ejpam-5205	340	2	10	10	NUM
ejpam-5205	340	3	.	.	PUNCT
ejpam-5205	341	1	let	let	VERB
ejpam-5205	341	2	g	g	PRON
ejpam-5205	341	3	be	be	AUX
ejpam-5205	341	4	a	a	DET
ejpam-5205	341	5	non	non	ADJ
ejpam-5205	341	6	-	-	ADJ
ejpam-5205	341	7	trivial	trivial	ADJ
ejpam-5205	341	8	connected	connected	ADJ
ejpam-5205	341	9	graph	graph	NOUN
ejpam-5205	341	10	and	and	CCONJ
ejpam-5205	341	11	km	km	VERB
ejpam-5205	341	12	a	a	DET
ejpam-5205	341	13	complete	complete	ADJ
ejpam-5205	341	14	graph	graph	NOUN
ejpam-5205	341	15	.	.	PUNCT
ejpam-5205	342	1	then	then	ADV
ejpam-5205	342	2	f	f	PROPN
ejpam-5205	342	3	=	=	SYM
ejpam-5205	342	4	(	(	PUNCT
ejpam-5205	342	5	v0	v0	PROPN
ejpam-5205	342	6	,	,	PUNCT
ejpam-5205	342	7	v1	v1	NOUN
ejpam-5205	342	8	,	,	PUNCT
ejpam-5205	342	9	v2	v2	PROPN
ejpam-5205	342	10	)	)	PUNCT
ejpam-5205	342	11	is	be	AUX
ejpam-5205	342	12	a	a	DET
ejpam-5205	342	13	cvrdf	cvrdf	NOUN
ejpam-5205	342	14	on	on	ADP
ejpam-5205	342	15	g[km	g[km	NOUN
ejpam-5205	342	16	]	]	X
ejpam-5205	342	17	if	if	SCONJ
ejpam-5205	342	18	and	and	CCONJ
ejpam-5205	342	19	only	only	ADV
ejpam-5205	342	20	if	if	SCONJ
ejpam-5205	342	21	each	each	PRON
ejpam-5205	342	22	of	of	ADP
ejpam-5205	342	23	the	the	DET
ejpam-5205	342	24	following	follow	VERB
ejpam-5205	342	25	conditions	condition	NOUN
ejpam-5205	342	26	hold	hold	VERB
ejpam-5205	342	27	:	:	PUNCT
ejpam-5205	342	28	(	(	PUNCT
ejpam-5205	342	29	i	i	NOUN
ejpam-5205	342	30	)	)	PUNCT
ejpam-5205	342	31	g|f	g|f	X
ejpam-5205	343	1	=	=	PUNCT
ejpam-5205	343	2	(	(	PUNCT
ejpam-5205	343	3	v	v	NOUN
ejpam-5205	343	4	0	0	NUM
ejpam-5205	343	5	g	g	NOUN
ejpam-5205	343	6	,	,	PUNCT
ejpam-5205	343	7	v	v	NOUN
ejpam-5205	343	8	1	1	NUM
ejpam-5205	343	9	g	g	NOUN
ejpam-5205	343	10	,	,	PUNCT
ejpam-5205	343	11	v	v	NOUN
ejpam-5205	343	12	2	2	NUM
ejpam-5205	343	13	g	g	NOUN
ejpam-5205	343	14	)	)	PUNCT
ejpam-5205	343	15	is	be	AUX
ejpam-5205	343	16	a	a	DET
ejpam-5205	343	17	cvrdf	cvrdf	NOUN
ejpam-5205	343	18	on	on	ADP
ejpam-5205	343	19	g.	g.	PROPN
ejpam-5205	343	20	(	(	PUNCT
ejpam-5205	343	21	ii	ii	PROPN
ejpam-5205	343	22	)	)	PUNCT
ejpam-5205	343	23	s1	s1	PROPN
ejpam-5205	343	24	g	g	PROPN
ejpam-5205	343	25	∪	∪	PROPN
ejpam-5205	343	26	s2	s2	PROPN
ejpam-5205	343	27	g	g	PROPN
ejpam-5205	343	28	is	be	AUX
ejpam-5205	343	29	convex	convex	ADJ
ejpam-5205	343	30	in	in	ADP
ejpam-5205	343	31	g.	g.	PROPN
ejpam-5205	343	32	(	(	PUNCT
ejpam-5205	343	33	iii	iii	NOUN
ejpam-5205	343	34	)	)	PUNCT
ejpam-5205	343	35	{	{	PUNCT
ejpam-5205	343	36	x	x	NOUN
ejpam-5205	343	37	}	}	PUNCT
ejpam-5205	343	38	×	×	NOUN
ejpam-5205	343	39	v	v	NOUN
ejpam-5205	343	40	(	(	PUNCT
ejpam-5205	343	41	km	km	PROPN
ejpam-5205	343	42	)	)	PUNCT
ejpam-5205	343	43	⊆	⊆	NUM
ejpam-5205	343	44	v1	v1	NOUN
ejpam-5205	343	45	∪	∪	NOUN
ejpam-5205	343	46	v2	v2	NOUN
ejpam-5205	343	47	for	for	ADP
ejpam-5205	343	48	x	x	PROPN
ejpam-5205	343	49	∈	∈	PROPN
ejpam-5205	343	50	s0	s0	PROPN
ejpam-5205	343	51	f	f	PROPN
ejpam-5205	343	52	.	.	PUNCT
ejpam-5205	344	1	(	(	PUNCT
ejpam-5205	344	2	iv	iv	X
ejpam-5205	344	3	)	)	PUNCT
ejpam-5205	344	4	for	for	ADP
ejpam-5205	344	5	each	each	DET
ejpam-5205	344	6	v	v	X
ejpam-5205	344	7	∈	∈	NOUN
ejpam-5205	344	8	(	(	PUNCT
ejpam-5205	344	9	s0	s0	PROPN
ejpam-5205	344	10	g	g	PROPN
ejpam-5205	344	11	\	\	PROPN
ejpam-5205	344	12	s2	s2	PROPN
ejpam-5205	344	13	g	g	NOUN
ejpam-5205	344	14	)	)	PUNCT
ejpam-5205	344	15	∩	∩	NOUN
ejpam-5205	344	16	s1	s1	PROPN
ejpam-5205	344	17	g	g	PROPN
ejpam-5205	344	18	,	,	PUNCT
ejpam-5205	344	19	there	there	PRON
ejpam-5205	344	20	exists	exist	VERB
ejpam-5205	344	21	w	w	PROPN
ejpam-5205	344	22	∈	∈	PROPN
ejpam-5205	344	23	s2	s2	NOUN
ejpam-5205	344	24	g	g	PROPN
ejpam-5205	344	25	∩ng(v	∩ng(v	PROPN
ejpam-5205	344	26	)	)	PUNCT
ejpam-5205	344	27	.	.	PUNCT
ejpam-5205	345	1	proof	proof	NOUN
ejpam-5205	345	2	.	.	PUNCT
ejpam-5205	346	1	let	let	VERB
ejpam-5205	346	2	f	f	PROPN
ejpam-5205	346	3	=	=	SYM
ejpam-5205	346	4	(	(	PUNCT
ejpam-5205	346	5	v0	v0	PROPN
ejpam-5205	346	6	,	,	PUNCT
ejpam-5205	346	7	v1	v1	NOUN
ejpam-5205	346	8	,	,	PUNCT
ejpam-5205	346	9	v2	v2	PROPN
ejpam-5205	346	10	)	)	PUNCT
ejpam-5205	346	11	be	be	AUX
ejpam-5205	346	12	a	a	DET
ejpam-5205	346	13	cvrdf	cvrdf	NOUN
ejpam-5205	346	14	on	on	ADP
ejpam-5205	346	15	g[km	g[km	PROPN
ejpam-5205	346	16	]	]	PUNCT
ejpam-5205	346	17	.	.	PUNCT
ejpam-5205	347	1	consider	consider	VERB
ejpam-5205	347	2	the	the	DET
ejpam-5205	347	3	function	function	NOUN
ejpam-5205	347	4	gf	gf	NOUN
ejpam-5205	347	5	=	=	PUNCT
ejpam-5205	348	1	(	(	PUNCT
ejpam-5205	348	2	v	v	NOUN
ejpam-5205	348	3	0	0	NUM
ejpam-5205	348	4	g	g	NOUN
ejpam-5205	348	5	,	,	PUNCT
ejpam-5205	348	6	v	v	NOUN
ejpam-5205	348	7	1	1	NUM
ejpam-5205	348	8	g	g	NOUN
ejpam-5205	348	9	,	,	PUNCT
ejpam-5205	348	10	v	v	NOUN
ejpam-5205	348	11	2	2	NUM
ejpam-5205	348	12	g	g	NOUN
ejpam-5205	348	13	)	)	PUNCT
ejpam-5205	348	14	on	on	ADP
ejpam-5205	348	15	g.	g.	PROPN
ejpam-5205	348	16	let	let	VERB
ejpam-5205	348	17	x	x	SYM
ejpam-5205	348	18	∈	∈	PROPN
ejpam-5205	348	19	v	v	ADP
ejpam-5205	348	20	0	0	NUM
ejpam-5205	348	21	g	g	NOUN
ejpam-5205	348	22	and	and	CCONJ
ejpam-5205	348	23	let	let	VERB
ejpam-5205	348	24	q	q	PROPN
ejpam-5205	348	25	∈	∈	PROPN
ejpam-5205	348	26	v	v	NOUN
ejpam-5205	348	27	(	(	PUNCT
ejpam-5205	348	28	km	km	PROPN
ejpam-5205	348	29	)	)	PUNCT
ejpam-5205	348	30	.	.	PUNCT
ejpam-5205	349	1	then	then	ADV
ejpam-5205	349	2	(	(	PUNCT
ejpam-5205	349	3	x	x	X
ejpam-5205	349	4	,	,	PUNCT
ejpam-5205	349	5	q	q	NOUN
ejpam-5205	349	6	)	)	PUNCT
ejpam-5205	349	7	∈	∈	PROPN
ejpam-5205	349	8	v0	v0	NOUN
ejpam-5205	349	9	.	.	PUNCT
ejpam-5205	350	1	since	since	SCONJ
ejpam-5205	350	2	f	f	PROPN
ejpam-5205	350	3	is	be	AUX
ejpam-5205	350	4	a	a	DET
ejpam-5205	350	5	cvrdf	cvrdf	NOUN
ejpam-5205	350	6	on	on	ADP
ejpam-5205	350	7	g[km	g[km	PROPN
ejpam-5205	350	8	]	]	PUNCT
ejpam-5205	350	9	,	,	PUNCT
ejpam-5205	350	10	there	there	PRON
ejpam-5205	350	11	exists	exist	VERB
ejpam-5205	350	12	(	(	PUNCT
ejpam-5205	350	13	y	y	PROPN
ejpam-5205	350	14	,	,	PUNCT
ejpam-5205	350	15	t	t	PROPN
ejpam-5205	350	16	)	)	PUNCT
ejpam-5205	350	17	∈	∈	PROPN
ejpam-5205	350	18	v2	v2	NOUN
ejpam-5205	350	19	such	such	ADJ
ejpam-5205	350	20	that	that	SCONJ
ejpam-5205	350	21	(	(	PUNCT
ejpam-5205	350	22	x	x	NOUN
ejpam-5205	350	23	,	,	PUNCT
ejpam-5205	350	24	q)(y	q)(y	PROPN
ejpam-5205	350	25	,	,	PUNCT
ejpam-5205	350	26	t	t	X
ejpam-5205	350	27	)	)	PUNCT
ejpam-5205	350	28	∈	∈	PROPN
ejpam-5205	350	29	e(g[km	e(g[km	PROPN
ejpam-5205	350	30	]	]	X
ejpam-5205	350	31	)	)	PUNCT
ejpam-5205	350	32	.	.	PUNCT
ejpam-5205	351	1	this	this	PRON
ejpam-5205	351	2	implies	imply	VERB
ejpam-5205	351	3	that	that	SCONJ
ejpam-5205	351	4	xy	xy	PROPN
ejpam-5205	351	5	∈	∈	PROPN
ejpam-5205	351	6	e(g	e(g	PROPN
ejpam-5205	351	7	)	)	PUNCT
ejpam-5205	351	8	and	and	CCONJ
ejpam-5205	351	9	y	y	PROPN
ejpam-5205	351	10	∈	∈	PROPN
ejpam-5205	351	11	v	v	ADP
ejpam-5205	351	12	2	2	NUM
ejpam-5205	351	13	g.	g.	NOUN
ejpam-5205	351	14	thus	thus	ADV
ejpam-5205	351	15	,	,	PUNCT
ejpam-5205	351	16	g|f	g|f	PROPN
ejpam-5205	351	17	is	be	AUX
ejpam-5205	351	18	an	an	DET
ejpam-5205	351	19	rdf	rdf	NOUN
ejpam-5205	351	20	on	on	ADP
ejpam-5205	351	21	g.	g.	PROPN
ejpam-5205	351	22	let	let	VERB
ejpam-5205	351	23	u	u	NOUN
ejpam-5205	351	24	,	,	PUNCT
ejpam-5205	351	25	v	v	PROPN
ejpam-5205	351	26	∈	∈	PROPN
ejpam-5205	351	27	v	v	ADP
ejpam-5205	351	28	1	1	NUM
ejpam-5205	351	29	g	g	NOUN
ejpam-5205	351	30	∪	∪	NOUN
ejpam-5205	351	31	v	v	ADP
ejpam-5205	351	32	2	2	NUM
ejpam-5205	351	33	g	g	NOUN
ejpam-5205	351	34	such	such	ADJ
ejpam-5205	351	35	that	that	SCONJ
ejpam-5205	351	36	u	u	NOUN
ejpam-5205	351	37	̸=	̸=	PROPN
ejpam-5205	351	38	v.	v.	CCONJ
ejpam-5205	351	39	let	let	VERB
ejpam-5205	351	40	x	x	X
ejpam-5205	351	41	∈	∈	PROPN
ejpam-5205	351	42	ig(u	ig(u	NOUN
ejpam-5205	351	43	,	,	PUNCT
ejpam-5205	351	44	v	v	NOUN
ejpam-5205	351	45	)	)	PUNCT
ejpam-5205	351	46	.	.	PUNCT
ejpam-5205	352	1	let	let	VERB
ejpam-5205	352	2	p	p	NOUN
ejpam-5205	352	3	(	(	PUNCT
ejpam-5205	352	4	u	u	NOUN
ejpam-5205	352	5	,	,	PUNCT
ejpam-5205	352	6	v	v	NOUN
ejpam-5205	352	7	)	)	PUNCT
ejpam-5205	352	8	=	=	PUNCT
ejpam-5205	353	1	[	[	X
ejpam-5205	353	2	u	u	NOUN
ejpam-5205	353	3	,	,	PUNCT
ejpam-5205	353	4	u1	u1	NOUN
ejpam-5205	353	5	,	,	PUNCT
ejpam-5205	353	6	u2	u2	NOUN
ejpam-5205	353	7	,	,	PUNCT
ejpam-5205	353	8	.	.	PUNCT
ejpam-5205	353	9	.	.	PUNCT
ejpam-5205	354	1	.	.	PUNCT
ejpam-5205	355	1	,	,	PUNCT
ejpam-5205	355	2	uk	uk	PROPN
ejpam-5205	355	3	,	,	PUNCT
ejpam-5205	355	4	v	v	NOUN
ejpam-5205	355	5	]	]	PUNCT
ejpam-5205	355	6	be	be	AUX
ejpam-5205	355	7	a	a	DET
ejpam-5205	355	8	u	u	NOUN
ejpam-5205	355	9	-	-	NOUN
ejpam-5205	355	10	v	v	ADJ
ejpam-5205	355	11	geodesic	geodesic	NOUN
ejpam-5205	355	12	in	in	ADP
ejpam-5205	355	13	g	g	NOUN
ejpam-5205	355	14	with	with	ADP
ejpam-5205	355	15	x	x	X
ejpam-5205	355	16	=	=	VERB
ejpam-5205	355	17	ur	ur	INTJ
ejpam-5205	355	18	for	for	ADP
ejpam-5205	355	19	some	some	DET
ejpam-5205	355	20	1	1	NUM
ejpam-5205	355	21	≤	≤	NOUN
ejpam-5205	355	22	r	r	NOUN
ejpam-5205	355	23	≤	≤	NOUN
ejpam-5205	355	24	k.	k.	NOUN
ejpam-5205	355	25	consider	consider	VERB
ejpam-5205	355	26	the	the	DET
ejpam-5205	355	27	following	follow	VERB
ejpam-5205	355	28	cases	case	NOUN
ejpam-5205	355	29	:	:	PUNCT
ejpam-5205	355	30	case	case	NOUN
ejpam-5205	355	31	1	1	NUM
ejpam-5205	355	32	.	.	X
ejpam-5205	355	33	u	u	NOUN
ejpam-5205	355	34	,	,	PUNCT
ejpam-5205	355	35	v	v	PROPN
ejpam-5205	355	36	∈	∈	PROPN
ejpam-5205	355	37	v	v	ADP
ejpam-5205	355	38	1	1	NUM
ejpam-5205	355	39	g	g	NOUN
ejpam-5205	355	40	(	(	PUNCT
ejpam-5205	355	41	or	or	CCONJ
ejpam-5205	355	42	u	u	NOUN
ejpam-5205	355	43	,	,	PUNCT
ejpam-5205	355	44	v	v	ADP
ejpam-5205	355	45	∈	∈	PROPN
ejpam-5205	355	46	v	v	ADP
ejpam-5205	355	47	2	2	NUM
ejpam-5205	355	48	g	g	NOUN
ejpam-5205	355	49	)	)	PUNCT
ejpam-5205	355	50	pick	pick	VERB
ejpam-5205	355	51	any	any	DET
ejpam-5205	355	52	t	t	NOUN
ejpam-5205	355	53	∈	∈	PROPN
ejpam-5205	355	54	v	v	PROPN
ejpam-5205	355	55	(	(	PUNCT
ejpam-5205	355	56	km	km	PROPN
ejpam-5205	355	57	)	)	PUNCT
ejpam-5205	355	58	.	.	PUNCT
ejpam-5205	356	1	then	then	ADV
ejpam-5205	356	2	(	(	PUNCT
ejpam-5205	356	3	u	u	NOUN
ejpam-5205	356	4	,	,	PUNCT
ejpam-5205	356	5	t	t	PROPN
ejpam-5205	356	6	)	)	PUNCT
ejpam-5205	356	7	∈	∈	PROPN
ejpam-5205	356	8	v1	v1	NOUN
ejpam-5205	356	9	.	.	PUNCT
ejpam-5205	357	1	then	then	ADV
ejpam-5205	357	2	p	p	X
ejpam-5205	357	3	(	(	PUNCT
ejpam-5205	357	4	(	(	PUNCT
ejpam-5205	357	5	u	u	NOUN
ejpam-5205	357	6	,	,	PUNCT
ejpam-5205	357	7	t	t	PROPN
ejpam-5205	357	8	)	)	PUNCT
ejpam-5205	357	9	,	,	PUNCT
ejpam-5205	357	10	(	(	PUNCT
ejpam-5205	357	11	v	v	NOUN
ejpam-5205	357	12	,	,	PUNCT
ejpam-5205	357	13	t	t	PROPN
ejpam-5205	357	14	)	)	PUNCT
ejpam-5205	357	15	=	=	PUNCT
ejpam-5205	358	1	[	[	X
ejpam-5205	358	2	(	(	PUNCT
ejpam-5205	358	3	u	u	NOUN
ejpam-5205	358	4	,	,	PUNCT
ejpam-5205	358	5	t	t	PROPN
ejpam-5205	358	6	)	)	PUNCT
ejpam-5205	358	7	,	,	PUNCT
ejpam-5205	358	8	(	(	PUNCT
ejpam-5205	358	9	u1	u1	PROPN
ejpam-5205	358	10	,	,	PUNCT
ejpam-5205	358	11	t	t	PROPN
ejpam-5205	358	12	)	)	PUNCT
ejpam-5205	358	13	,	,	PUNCT
ejpam-5205	358	14	.	.	PUNCT
ejpam-5205	358	15	.	.	PUNCT
ejpam-5205	358	16	.	.	PUNCT
ejpam-5205	359	1	,	,	PUNCT
ejpam-5205	359	2	(	(	PUNCT
ejpam-5205	359	3	ur−1	ur−1	PROPN
ejpam-5205	359	4	,	,	PUNCT
ejpam-5205	359	5	t	t	PROPN
ejpam-5205	359	6	)	)	PUNCT
ejpam-5205	359	7	,	,	PUNCT
ejpam-5205	359	8	(	(	PUNCT
ejpam-5205	359	9	ur	ur	INTJ
ejpam-5205	359	10	,	,	PUNCT
ejpam-5205	359	11	t	t	PROPN
ejpam-5205	359	12	)	)	PUNCT
ejpam-5205	359	13	,	,	PUNCT
ejpam-5205	359	14	.	.	PUNCT
ejpam-5205	359	15	.	.	PUNCT
ejpam-5205	359	16	.	.	PUNCT
ejpam-5205	360	1	,	,	PUNCT
ejpam-5205	360	2	(	(	PUNCT
ejpam-5205	360	3	uk	uk	PROPN
ejpam-5205	360	4	,	,	PUNCT
ejpam-5205	360	5	t	t	PROPN
ejpam-5205	360	6	)	)	PUNCT
ejpam-5205	360	7	,	,	PUNCT
ejpam-5205	360	8	(	(	PUNCT
ejpam-5205	360	9	v	v	NOUN
ejpam-5205	360	10	,	,	PUNCT
ejpam-5205	360	11	t	t	PROPN
ejpam-5205	360	12	)	)	PUNCT
ejpam-5205	360	13	]	]	PUNCT
ejpam-5205	360	14	is	be	AUX
ejpam-5205	360	15	a	a	DET
ejpam-5205	360	16	(	(	PUNCT
ejpam-5205	360	17	u	u	NOUN
ejpam-5205	360	18	,	,	PUNCT
ejpam-5205	360	19	t)-(v	t)-(v	PROPN
ejpam-5205	360	20	,	,	PUNCT
ejpam-5205	360	21	t	t	PROPN
ejpam-5205	360	22	)	)	PUNCT
ejpam-5205	360	23	geodesic	geodesic	NOUN
ejpam-5205	360	24	in	in	ADP
ejpam-5205	360	25	g[km	g[km	PROPN
ejpam-5205	360	26	]	]	PUNCT
ejpam-5205	360	27	.	.	PUNCT
ejpam-5205	361	1	since	since	SCONJ
ejpam-5205	361	2	v1	v1	NOUN
ejpam-5205	361	3	∪	∪	NOUN
ejpam-5205	361	4	v2	v2	NOUN
ejpam-5205	361	5	is	be	AUX
ejpam-5205	361	6	a	a	DET
ejpam-5205	361	7	convex	convex	NOUN
ejpam-5205	361	8	set	set	VERB
ejpam-5205	361	9	in	in	ADP
ejpam-5205	361	10	g[km	g[km	PROPN
ejpam-5205	361	11	]	]	PUNCT
ejpam-5205	361	12	,	,	PUNCT
ejpam-5205	361	13	it	it	PRON
ejpam-5205	361	14	follows	follow	VERB
ejpam-5205	361	15	that	that	SCONJ
ejpam-5205	361	16	(	(	PUNCT
ejpam-5205	361	17	ur	ur	INTJ
ejpam-5205	361	18	,	,	PUNCT
ejpam-5205	361	19	t	t	PROPN
ejpam-5205	361	20	)	)	PUNCT
ejpam-5205	361	21	∈	∈	PROPN
ejpam-5205	361	22	v1	v1	NOUN
ejpam-5205	361	23	∪	∪	X
ejpam-5205	361	24	v2	v2	NOUN
ejpam-5205	361	25	.	.	PUNCT
ejpam-5205	362	1	this	this	PRON
ejpam-5205	362	2	implies	imply	VERB
ejpam-5205	362	3	that	that	SCONJ
ejpam-5205	362	4	x	x	X
ejpam-5205	362	5	=	=	PRON
ejpam-5205	362	6	ur	ur	INTJ
ejpam-5205	362	7	∈	∈	PROPN
ejpam-5205	362	8	v	v	ADP
ejpam-5205	362	9	1	1	NUM
ejpam-5205	362	10	g	g	NOUN
ejpam-5205	362	11	∪	∪	NOUN
ejpam-5205	362	12	v	v	ADP
ejpam-5205	362	13	2	2	NUM
ejpam-5205	362	14	g.	g.	NOUN
ejpam-5205	362	15	a	a	DET
ejpam-5205	362	16	similar	similar	ADJ
ejpam-5205	362	17	argument	argument	NOUN
ejpam-5205	362	18	is	be	AUX
ejpam-5205	362	19	used	use	VERB
ejpam-5205	362	20	to	to	PART
ejpam-5205	362	21	show	show	VERB
ejpam-5205	362	22	that	that	SCONJ
ejpam-5205	362	23	x	x	SYM
ejpam-5205	363	1	∈	∈	NOUN
ejpam-5205	363	2	v	v	ADP
ejpam-5205	363	3	1	1	NUM
ejpam-5205	363	4	g	g	NOUN
ejpam-5205	363	5	∪	∪	NOUN
ejpam-5205	363	6	v	v	ADP
ejpam-5205	363	7	2	2	NUM
ejpam-5205	363	8	g	g	NOUN
ejpam-5205	363	9	whenever	whenever	SCONJ
ejpam-5205	363	10	u	u	NOUN
ejpam-5205	363	11	,	,	PUNCT
ejpam-5205	363	12	v	v	PROPN
ejpam-5205	363	13	∈	∈	PROPN
ejpam-5205	363	14	v	v	ADP
ejpam-5205	363	15	2	2	NUM
ejpam-5205	363	16	g.	g.	NOUN
ejpam-5205	363	17	case	case	NOUN
ejpam-5205	363	18	2	2	NUM
ejpam-5205	363	19	.	.	X
ejpam-5205	363	20	u	u	PROPN
ejpam-5205	363	21	∈	∈	PROPN
ejpam-5205	363	22	v	v	ADP
ejpam-5205	363	23	1	1	NUM
ejpam-5205	363	24	g	g	NOUN
ejpam-5205	363	25	and	and	CCONJ
ejpam-5205	363	26	v	v	ADP
ejpam-5205	363	27	∈	∈	PROPN
ejpam-5205	363	28	v	v	ADP
ejpam-5205	363	29	2	2	NUM
ejpam-5205	363	30	g	g	NOUN
ejpam-5205	363	31	pick	pick	VERB
ejpam-5205	363	32	any	any	DET
ejpam-5205	363	33	s	s	PROPN
ejpam-5205	363	34	∈	∈	PROPN
ejpam-5205	363	35	v	v	NOUN
ejpam-5205	363	36	(	(	PUNCT
ejpam-5205	363	37	km	km	PROPN
ejpam-5205	363	38	)	)	PUNCT
ejpam-5205	363	39	such	such	ADJ
ejpam-5205	363	40	that	that	SCONJ
ejpam-5205	363	41	(	(	PUNCT
ejpam-5205	363	42	v	v	NOUN
ejpam-5205	363	43	,	,	PUNCT
ejpam-5205	363	44	s	s	PART
ejpam-5205	363	45	)	)	PUNCT
ejpam-5205	363	46	∈	∈	NOUN
ejpam-5205	363	47	v2	v2	NOUN
ejpam-5205	363	48	.	.	PUNCT
ejpam-5205	364	1	then	then	ADV
ejpam-5205	364	2	(	(	PUNCT
ejpam-5205	364	3	u	u	NOUN
ejpam-5205	364	4	,	,	PUNCT
ejpam-5205	364	5	s	s	PART
ejpam-5205	364	6	)	)	PUNCT
ejpam-5205	364	7	∈	∈	NOUN
ejpam-5205	364	8	v1	v1	NOUN
ejpam-5205	364	9	and	and	CCONJ
ejpam-5205	364	10	p	p	X
ejpam-5205	364	11	(	(	PUNCT
ejpam-5205	364	12	(	(	PUNCT
ejpam-5205	364	13	u	u	NOUN
ejpam-5205	364	14	,	,	PUNCT
ejpam-5205	364	15	s	s	PART
ejpam-5205	364	16	)	)	PUNCT
ejpam-5205	364	17	,	,	PUNCT
ejpam-5205	364	18	(	(	PUNCT
ejpam-5205	364	19	v	v	NOUN
ejpam-5205	364	20	,	,	PUNCT
ejpam-5205	364	21	s	s	NOUN
ejpam-5205	364	22	)	)	PUNCT
ejpam-5205	364	23	)	)	PUNCT
ejpam-5205	365	1	=	=	PUNCT
ejpam-5205	366	1	[	[	X
ejpam-5205	366	2	(	(	PUNCT
ejpam-5205	366	3	u	u	NOUN
ejpam-5205	366	4	,	,	PUNCT
ejpam-5205	366	5	s	s	PART
ejpam-5205	366	6	)	)	PUNCT
ejpam-5205	366	7	,	,	PUNCT
ejpam-5205	366	8	(	(	PUNCT
ejpam-5205	366	9	u1	u1	PROPN
ejpam-5205	366	10	,	,	PUNCT
ejpam-5205	366	11	s	s	NOUN
ejpam-5205	366	12	)	)	PUNCT
ejpam-5205	366	13	,	,	PUNCT
ejpam-5205	366	14	.	.	PUNCT
ejpam-5205	366	15	.	.	PUNCT
ejpam-5205	366	16	.	.	PUNCT
ejpam-5205	367	1	,	,	PUNCT
ejpam-5205	367	2	(	(	PUNCT
ejpam-5205	367	3	ur−1	ur−1	PROPN
ejpam-5205	367	4	,	,	PUNCT
ejpam-5205	367	5	s	s	PART
ejpam-5205	367	6	)	)	PUNCT
ejpam-5205	367	7	,	,	PUNCT
ejpam-5205	367	8	(	(	PUNCT
ejpam-5205	367	9	ur	ur	INTJ
ejpam-5205	367	10	,	,	PUNCT
ejpam-5205	367	11	s	s	PART
ejpam-5205	367	12	)	)	PUNCT
ejpam-5205	367	13	,	,	PUNCT
ejpam-5205	367	14	.	.	PUNCT
ejpam-5205	367	15	.	.	PUNCT
ejpam-5205	367	16	.	.	PUNCT
ejpam-5205	368	1	,	,	PUNCT
ejpam-5205	368	2	(	(	PUNCT
ejpam-5205	368	3	uk	uk	PROPN
ejpam-5205	368	4	,	,	PUNCT
ejpam-5205	368	5	s	s	PART
ejpam-5205	368	6	)	)	PUNCT
ejpam-5205	368	7	,	,	PUNCT
ejpam-5205	368	8	(	(	PUNCT
ejpam-5205	368	9	v	v	NOUN
ejpam-5205	368	10	,	,	PUNCT
ejpam-5205	368	11	s	s	PART
ejpam-5205	368	12	)	)	PUNCT
ejpam-5205	368	13	]	]	PUNCT
ejpam-5205	368	14	is	be	AUX
ejpam-5205	368	15	a	a	DET
ejpam-5205	368	16	(	(	PUNCT
ejpam-5205	368	17	u	u	NOUN
ejpam-5205	368	18	,	,	PUNCT
ejpam-5205	368	19	s)-(v	s)-(v	PROPN
ejpam-5205	368	20	,	,	PUNCT
ejpam-5205	368	21	s	s	X
ejpam-5205	368	22	)	)	PUNCT
ejpam-5205	368	23	geodesic	geodesic	NOUN
ejpam-5205	368	24	in	in	ADP
ejpam-5205	368	25	g[km	g[km	PROPN
ejpam-5205	368	26	]	]	PUNCT
ejpam-5205	368	27	.	.	PUNCT
ejpam-5205	369	1	since	since	SCONJ
ejpam-5205	369	2	v1∪v2	v1∪v2	ADV
ejpam-5205	369	3	is	be	VERB
ejpam-5205	369	4	a	a	DET
ejpam-5205	369	5	convex	convex	NOUN
ejpam-5205	369	6	set	set	VERB
ejpam-5205	369	7	in	in	ADP
ejpam-5205	369	8	g[km	g[km	PROPN
ejpam-5205	369	9	]	]	PUNCT
ejpam-5205	369	10	,	,	PUNCT
ejpam-5205	369	11	it	it	PRON
ejpam-5205	369	12	follows	follow	VERB
ejpam-5205	369	13	that	that	SCONJ
ejpam-5205	369	14	(	(	PUNCT
ejpam-5205	369	15	ur	ur	INTJ
ejpam-5205	369	16	,	,	PUNCT
ejpam-5205	369	17	s	s	PART
ejpam-5205	369	18	)	)	PUNCT
ejpam-5205	369	19	∈	∈	PROPN
ejpam-5205	370	1	v1∪v2	v1∪v2	PROPN
ejpam-5205	370	2	.	.	PUNCT
ejpam-5205	371	1	this	this	PRON
ejpam-5205	371	2	implies	imply	VERB
ejpam-5205	371	3	that	that	SCONJ
ejpam-5205	371	4	x	x	X
ejpam-5205	371	5	=	=	PRON
ejpam-5205	371	6	ur	ur	INTJ
ejpam-5205	371	7	∈	∈	PROPN
ejpam-5205	371	8	v	v	ADP
ejpam-5205	371	9	1	1	NUM
ejpam-5205	371	10	g	g	NOUN
ejpam-5205	371	11	∪	∪	NOUN
ejpam-5205	371	12	v	v	ADP
ejpam-5205	371	13	2	2	NUM
ejpam-5205	371	14	g.	g.	NOUN
ejpam-5205	371	15	therefore	therefore	ADV
ejpam-5205	371	16	,	,	PUNCT
ejpam-5205	371	17	g	g	PROPN
ejpam-5205	371	18	is	be	AUX
ejpam-5205	371	19	a	a	DET
ejpam-5205	371	20	cvrdf	cvrdf	NOUN
ejpam-5205	371	21	on	on	ADP
ejpam-5205	371	22	g	g	NOUN
ejpam-5205	371	23	,	,	PUNCT
ejpam-5205	371	24	showing	show	VERB
ejpam-5205	371	25	that	that	SCONJ
ejpam-5205	371	26	(	(	PUNCT
ejpam-5205	371	27	i	i	NOUN
ejpam-5205	371	28	)	)	PUNCT
ejpam-5205	371	29	holds	hold	VERB
ejpam-5205	371	30	.	.	PUNCT
ejpam-5205	372	1	let	let	VERB
ejpam-5205	372	2	x	x	PRON
ejpam-5205	372	3	,	,	PUNCT
ejpam-5205	372	4	y	y	PROPN
ejpam-5205	372	5	∈	∈	PROPN
ejpam-5205	372	6	s1	s1	PROPN
ejpam-5205	372	7	g	g	PROPN
ejpam-5205	372	8	∪	∪	PROPN
ejpam-5205	372	9	s2	s2	VERB
ejpam-5205	372	10	g	g	NOUN
ejpam-5205	372	11	with	with	ADP
ejpam-5205	372	12	x	x	X
ejpam-5205	372	13	̸=	̸=	PROPN
ejpam-5205	372	14	y	y	PROPN
ejpam-5205	372	15	and	and	CCONJ
ejpam-5205	372	16	let	let	VERB
ejpam-5205	372	17	z	z	NOUN
ejpam-5205	372	18	∈	∈	PROPN
ejpam-5205	372	19	ig(x	ig(x	X
ejpam-5205	372	20	,	,	PUNCT
ejpam-5205	372	21	y	y	NOUN
ejpam-5205	372	22	)	)	PUNCT
ejpam-5205	372	23	.	.	PUNCT
ejpam-5205	373	1	let	let	VERB
ejpam-5205	373	2	p	p	NOUN
ejpam-5205	373	3	(	(	PUNCT
ejpam-5205	373	4	x	x	NOUN
ejpam-5205	373	5	,	,	PUNCT
ejpam-5205	373	6	y	y	NOUN
ejpam-5205	373	7	)	)	PUNCT
ejpam-5205	373	8	=	=	PUNCT
ejpam-5205	374	1	[	[	X
ejpam-5205	374	2	x	x	X
ejpam-5205	374	3	,	,	PUNCT
ejpam-5205	374	4	x1	x1	PROPN
ejpam-5205	374	5	,	,	PUNCT
ejpam-5205	374	6	x2	x2	PROPN
ejpam-5205	374	7	,	,	PUNCT
ejpam-5205	374	8	.	.	PUNCT
ejpam-5205	374	9	.	.	PUNCT
ejpam-5205	375	1	.	.	PUNCT
ejpam-5205	376	1	,	,	PUNCT
ejpam-5205	376	2	xk	xk	PROPN
ejpam-5205	376	3	,	,	PUNCT
ejpam-5205	376	4	y	y	PROPN
ejpam-5205	376	5	]	]	PUNCT
ejpam-5205	376	6	be	be	AUX
ejpam-5205	376	7	an	an	DET
ejpam-5205	376	8	x	x	NOUN
ejpam-5205	376	9	-	-	NOUN
ejpam-5205	376	10	y	y	ADJ
ejpam-5205	376	11	geodesic	geodesic	NOUN
ejpam-5205	376	12	in	in	ADP
ejpam-5205	376	13	g	g	PROPN
ejpam-5205	376	14	where	where	SCONJ
ejpam-5205	376	15	z	z	NOUN
ejpam-5205	376	16	=	=	SYM
ejpam-5205	376	17	xj	xj	PROPN
ejpam-5205	376	18	for	for	ADP
ejpam-5205	376	19	some	some	DET
ejpam-5205	376	20	1	1	NUM
ejpam-5205	376	21	≤	≤	NUM
ejpam-5205	376	22	j	j	PROPN
ejpam-5205	376	23	≤	≤	PROPN
ejpam-5205	376	24	k.	k.	PROPN
ejpam-5205	377	1	let	let	VERB
ejpam-5205	377	2	a	a	DET
ejpam-5205	377	3	,	,	PUNCT
ejpam-5205	377	4	b	b	PROPN
ejpam-5205	377	5	∈	∈	PROPN
ejpam-5205	377	6	v	v	NOUN
ejpam-5205	377	7	(	(	PUNCT
ejpam-5205	377	8	km	km	PROPN
ejpam-5205	377	9	)	)	PUNCT
ejpam-5205	377	10	such	such	ADJ
ejpam-5205	377	11	that	that	SCONJ
ejpam-5205	377	12	(	(	PUNCT
ejpam-5205	377	13	x	x	NOUN
ejpam-5205	377	14	,	,	PUNCT
ejpam-5205	377	15	a	a	PRON
ejpam-5205	377	16	)	)	PUNCT
ejpam-5205	377	17	,	,	PUNCT
ejpam-5205	377	18	(	(	PUNCT
ejpam-5205	377	19	y	y	PROPN
ejpam-5205	377	20	,	,	PUNCT
ejpam-5205	377	21	b	b	NOUN
ejpam-5205	377	22	)	)	PUNCT
ejpam-5205	377	23	∈	∈	NOUN
ejpam-5205	377	24	v1	v1	NOUN
ejpam-5205	377	25	∪	∪	X
ejpam-5205	377	26	v2	v2	NOUN
ejpam-5205	377	27	.	.	PUNCT
ejpam-5205	378	1	then	then	ADV
ejpam-5205	378	2	p	p	X
ejpam-5205	378	3	(	(	PUNCT
ejpam-5205	378	4	(	(	PUNCT
ejpam-5205	378	5	x	x	NOUN
ejpam-5205	378	6	,	,	PUNCT
ejpam-5205	378	7	a	a	PRON
ejpam-5205	378	8	)	)	PUNCT
ejpam-5205	378	9	,	,	PUNCT
ejpam-5205	378	10	(	(	PUNCT
ejpam-5205	378	11	y	y	PROPN
ejpam-5205	378	12	,	,	PUNCT
ejpam-5205	378	13	b	b	NOUN
ejpam-5205	378	14	)	)	PUNCT
ejpam-5205	378	15	)	)	PUNCT
ejpam-5205	379	1	=	=	PUNCT
ejpam-5205	380	1	[	[	X
ejpam-5205	380	2	(	(	PUNCT
ejpam-5205	380	3	x	x	NOUN
ejpam-5205	380	4	,	,	PUNCT
ejpam-5205	380	5	a	a	PRON
ejpam-5205	380	6	)	)	PUNCT
ejpam-5205	380	7	,	,	PUNCT
ejpam-5205	380	8	(	(	PUNCT
ejpam-5205	380	9	x1	x1	PROPN
ejpam-5205	380	10	,	,	PUNCT
ejpam-5205	380	11	a	a	NOUN
ejpam-5205	380	12	)	)	PUNCT
ejpam-5205	380	13	,	,	PUNCT
ejpam-5205	380	14	(	(	PUNCT
ejpam-5205	380	15	x2	x2	PROPN
ejpam-5205	380	16	,	,	PUNCT
ejpam-5205	380	17	a	a	PRON
ejpam-5205	380	18	)	)	PUNCT
ejpam-5205	380	19	,	,	PUNCT
ejpam-5205	380	20	.	.	PUNCT
ejpam-5205	380	21	.	.	PUNCT
ejpam-5205	380	22	.	.	PUNCT
ejpam-5205	381	1	,	,	PUNCT
ejpam-5205	381	2	(	(	PUNCT
ejpam-5205	381	3	xk	xk	PROPN
ejpam-5205	381	4	,	,	PUNCT
ejpam-5205	381	5	a	a	PRON
ejpam-5205	381	6	)	)	PUNCT
ejpam-5205	381	7	,	,	PUNCT
ejpam-5205	381	8	(	(	PUNCT
ejpam-5205	381	9	y	y	PROPN
ejpam-5205	381	10	,	,	PUNCT
ejpam-5205	381	11	b	b	NOUN
ejpam-5205	381	12	)	)	PUNCT
ejpam-5205	381	13	]	]	PUNCT
ejpam-5205	381	14	is	be	AUX
ejpam-5205	381	15	an	an	DET
ejpam-5205	381	16	(	(	PUNCT
ejpam-5205	381	17	x	x	NOUN
ejpam-5205	381	18	,	,	PUNCT
ejpam-5205	381	19	a)-(y	a)-(y	PROPN
ejpam-5205	381	20	,	,	PUNCT
ejpam-5205	381	21	b	b	NOUN
ejpam-5205	381	22	)	)	PUNCT
ejpam-5205	381	23	geodesic	geodesic	NOUN
ejpam-5205	381	24	in	in	ADP
ejpam-5205	381	25	g[km	g[km	PROPN
ejpam-5205	381	26	]	]	PUNCT
ejpam-5205	381	27	.	.	PUNCT
ejpam-5205	382	1	since	since	SCONJ
ejpam-5205	382	2	v1∪v2	v1∪v2	ADV
ejpam-5205	382	3	is	be	VERB
ejpam-5205	382	4	a	a	DET
ejpam-5205	382	5	convex	convex	NOUN
ejpam-5205	382	6	set	set	VERB
ejpam-5205	382	7	in	in	ADP
ejpam-5205	382	8	g[km	g[km	PROPN
ejpam-5205	382	9	]	]	X
ejpam-5205	382	10	,	,	PUNCT
ejpam-5205	382	11	(	(	PUNCT
ejpam-5205	382	12	xj	xj	PROPN
ejpam-5205	382	13	,	,	PUNCT
ejpam-5205	382	14	a	a	PRON
ejpam-5205	382	15	)	)	PUNCT
ejpam-5205	382	16	∈	∈	PROPN
ejpam-5205	382	17	v1∪v2	v1∪v2	PROPN
ejpam-5205	382	18	.	.	PUNCT
ejpam-5205	382	19	hence	hence	ADV
ejpam-5205	382	20	,	,	PUNCT
ejpam-5205	382	21	xj	xj	PROPN
ejpam-5205	382	22	∈	∈	PROPN
ejpam-5205	382	23	s1	s1	PROPN
ejpam-5205	382	24	g	g	PROPN
ejpam-5205	382	25	∪	∪	PROPN
ejpam-5205	382	26	s2	s2	PROPN
ejpam-5205	382	27	g.	g.	NOUN
ejpam-5205	382	28	this	this	PRON
ejpam-5205	382	29	shows	show	VERB
ejpam-5205	382	30	that	that	SCONJ
ejpam-5205	382	31	s	s	VERB
ejpam-5205	382	32	1	1	NUM
ejpam-5205	382	33	g	g	NOUN
ejpam-5205	382	34	∪	∪	ADJ
ejpam-5205	382	35	s2	s2	PROPN
ejpam-5205	382	36	g	g	PROPN
ejpam-5205	382	37	is	be	AUX
ejpam-5205	382	38	convex	convex	ADJ
ejpam-5205	382	39	in	in	ADP
ejpam-5205	382	40	g	g	NOUN
ejpam-5205	382	41	,	,	PUNCT
ejpam-5205	382	42	i.e.	i.e.	X
ejpam-5205	382	43	,	,	PUNCT
ejpam-5205	382	44	(	(	PUNCT
ejpam-5205	382	45	ii	ii	NOUN
ejpam-5205	382	46	)	)	PUNCT
ejpam-5205	382	47	holds	hold	VERB
ejpam-5205	382	48	.	.	PUNCT
ejpam-5205	383	1	next	next	ADV
ejpam-5205	383	2	,	,	PUNCT
ejpam-5205	383	3	let	let	VERB
ejpam-5205	383	4	x	x	PUNCT
ejpam-5205	383	5	∈	∈	PROPN
ejpam-5205	383	6	s0	s0	PROPN
ejpam-5205	383	7	f	f	PROPN
ejpam-5205	383	8	and	and	CCONJ
ejpam-5205	383	9	let	let	VERB
ejpam-5205	383	10	p	p	PRON
ejpam-5205	383	11	∈	∈	PROPN
ejpam-5205	383	12	v	v	NOUN
ejpam-5205	383	13	(	(	PUNCT
ejpam-5205	383	14	km	km	PROPN
ejpam-5205	383	15	)	)	PUNCT
ejpam-5205	383	16	.	.	PUNCT
ejpam-5205	384	1	then	then	ADV
ejpam-5205	384	2	x	x	SYM
ejpam-5205	384	3	∈	∈	PROPN
ejpam-5205	384	4	s1	s1	NOUN
ejpam-5205	384	5	g∪s2	g∪s2	VERB
ejpam-5205	384	6	g	g	NOUN
ejpam-5205	384	7	and	and	CCONJ
ejpam-5205	384	8	there	there	PRON
ejpam-5205	384	9	exists	exist	VERB
ejpam-5205	384	10	y	y	PROPN
ejpam-5205	384	11	,	,	PUNCT
ejpam-5205	384	12	z	z	NOUN
ejpam-5205	384	13	∈	∈	PROPN
ejpam-5205	384	14	s1	s1	NOUN
ejpam-5205	384	15	g∪s2	g∪s2	VERB
ejpam-5205	384	16	g	g	NOUN
ejpam-5205	384	17	such	such	ADJ
ejpam-5205	384	18	that	that	SCONJ
ejpam-5205	384	19	x	x	SYM
ejpam-5205	384	20	∈	∈	PROPN
ejpam-5205	384	21	ig(y	ig(y	NOUN
ejpam-5205	384	22	,	,	PUNCT
ejpam-5205	384	23	z	z	NOUN
ejpam-5205	384	24	)	)	PUNCT
ejpam-5205	384	25	.	.	PUNCT
ejpam-5205	385	1	again	again	ADV
ejpam-5205	385	2	,	,	PUNCT
ejpam-5205	385	3	by	by	ADP
ejpam-5205	385	4	convexity	convexity	NOUN
ejpam-5205	385	5	of	of	ADP
ejpam-5205	385	6	v1	v1	NOUN
ejpam-5205	385	7	∪	∪	NOUN
ejpam-5205	385	8	v2	v2	NOUN
ejpam-5205	385	9	,	,	PUNCT
ejpam-5205	385	10	(	(	PUNCT
ejpam-5205	385	11	x	x	X
ejpam-5205	385	12	,	,	PUNCT
ejpam-5205	385	13	p	p	NOUN
ejpam-5205	385	14	)	)	PUNCT
ejpam-5205	385	15	∈	∈	NOUN
ejpam-5205	385	16	v1	v1	NOUN
ejpam-5205	385	17	∪	∪	X
ejpam-5205	385	18	v2	v2	NOUN
ejpam-5205	385	19	.	.	PUNCT
ejpam-5205	386	1	this	this	PRON
ejpam-5205	386	2	shows	show	VERB
ejpam-5205	386	3	that	that	SCONJ
ejpam-5205	386	4	(	(	PUNCT
ejpam-5205	386	5	iii	iii	NOUN
ejpam-5205	386	6	)	)	PUNCT
ejpam-5205	386	7	holds	hold	VERB
ejpam-5205	386	8	.	.	PUNCT
ejpam-5205	387	1	r.	r.	PROPN
ejpam-5205	387	2	fortosa	fortosa	PROPN
ejpam-5205	387	3	,	,	PUNCT
ejpam-5205	387	4	s.	s.	PROPN
ejpam-5205	387	5	canoy	canoy	PROPN
ejpam-5205	387	6	jr	jr	PROPN
ejpam-5205	387	7	.	.	PROPN
ejpam-5205	387	8	/	/	SYM
ejpam-5205	387	9	eur	eur	PROPN
ejpam-5205	387	10	.	.	PUNCT
ejpam-5205	388	1	j.	j.	PROPN
ejpam-5205	388	2	pure	pure	PROPN
ejpam-5205	388	3	appl	appl	PROPN
ejpam-5205	388	4	.	.	PROPN
ejpam-5205	388	5	math	math	PROPN
ejpam-5205	388	6	,	,	PUNCT
ejpam-5205	388	7	17	17	NUM
ejpam-5205	388	8	(	(	PUNCT
ejpam-5205	388	9	2	2	NUM
ejpam-5205	388	10	)	)	PUNCT
ejpam-5205	388	11	(	(	PUNCT
ejpam-5205	388	12	2024	2024	NUM
ejpam-5205	388	13	)	)	PUNCT
ejpam-5205	388	14	,	,	PUNCT
ejpam-5205	388	15	1335	1335	NUM
ejpam-5205	388	16	-	-	SYM
ejpam-5205	388	17	1351	1351	NUM
ejpam-5205	388	18	1345	1345	NUM
ejpam-5205	388	19	finally	finally	ADV
ejpam-5205	388	20	,	,	PUNCT
ejpam-5205	388	21	let	let	VERB
ejpam-5205	388	22	v	v	X
ejpam-5205	388	23	∈	∈	NOUN
ejpam-5205	388	24	(	(	PUNCT
ejpam-5205	388	25	s0	s0	PROPN
ejpam-5205	388	26	g	g	PROPN
ejpam-5205	388	27	\	\	PROPN
ejpam-5205	388	28	s2	s2	PROPN
ejpam-5205	388	29	g	g	NOUN
ejpam-5205	388	30	)	)	PUNCT
ejpam-5205	388	31	∩	∩	NOUN
ejpam-5205	388	32	s1	s1	PROPN
ejpam-5205	388	33	g	g	NOUN
ejpam-5205	388	34	and	and	CCONJ
ejpam-5205	388	35	let	let	VERB
ejpam-5205	388	36	a	a	DET
ejpam-5205	388	37	∈	∈	PROPN
ejpam-5205	388	38	v	v	NOUN
ejpam-5205	388	39	(	(	PUNCT
ejpam-5205	388	40	km	km	PROPN
ejpam-5205	388	41	)	)	PUNCT
ejpam-5205	388	42	such	such	ADJ
ejpam-5205	388	43	that	that	SCONJ
ejpam-5205	388	44	(	(	PUNCT
ejpam-5205	388	45	v	v	NOUN
ejpam-5205	388	46	,	,	PUNCT
ejpam-5205	388	47	a	a	PRON
ejpam-5205	388	48	)	)	PUNCT
ejpam-5205	388	49	∈	∈	PROPN
ejpam-5205	388	50	v0	v0	NOUN
ejpam-5205	388	51	.	.	PUNCT
ejpam-5205	389	1	since	since	SCONJ
ejpam-5205	389	2	f	f	PROPN
ejpam-5205	389	3	is	be	AUX
ejpam-5205	389	4	a	a	DET
ejpam-5205	389	5	cvrdf	cvrdf	NOUN
ejpam-5205	389	6	on	on	ADP
ejpam-5205	389	7	g[km	g[km	PROPN
ejpam-5205	389	8	]	]	PUNCT
ejpam-5205	389	9	,	,	PUNCT
ejpam-5205	389	10	there	there	PRON
ejpam-5205	389	11	exists	exist	VERB
ejpam-5205	389	12	(	(	PUNCT
ejpam-5205	389	13	w	w	PROPN
ejpam-5205	389	14	,	,	PUNCT
ejpam-5205	389	15	b	b	NOUN
ejpam-5205	389	16	)	)	PUNCT
ejpam-5205	389	17	∈	∈	NOUN
ejpam-5205	389	18	v2	v2	NOUN
ejpam-5205	389	19	such	such	ADJ
ejpam-5205	389	20	that	that	SCONJ
ejpam-5205	389	21	(	(	PUNCT
ejpam-5205	389	22	v	v	NOUN
ejpam-5205	389	23	,	,	PUNCT
ejpam-5205	389	24	a)(w	a)(w	ADJ
ejpam-5205	389	25	,	,	PUNCT
ejpam-5205	389	26	b	b	X
ejpam-5205	389	27	)	)	PUNCT
ejpam-5205	389	28	∈	∈	PROPN
ejpam-5205	389	29	e(g[km	e(g[km	PROPN
ejpam-5205	389	30	]	]	NOUN
ejpam-5205	389	31	)	)	PUNCT
ejpam-5205	389	32	.	.	PUNCT
ejpam-5205	390	1	hence	hence	ADV
ejpam-5205	390	2	,	,	PUNCT
ejpam-5205	390	3	w	w	PROPN
ejpam-5205	390	4	∈	∈	PROPN
ejpam-5205	390	5	s2	s2	NOUN
ejpam-5205	390	6	g	g	NOUN
ejpam-5205	390	7	and	and	CCONJ
ejpam-5205	390	8	v	v	ADP
ejpam-5205	390	9	∈	∈	PROPN
ejpam-5205	390	10	ng(w	ng(w	NOUN
ejpam-5205	390	11	)	)	PUNCT
ejpam-5205	390	12	.	.	PUNCT
ejpam-5205	391	1	hence	hence	ADV
ejpam-5205	391	2	,	,	PUNCT
ejpam-5205	391	3	(	(	PUNCT
ejpam-5205	391	4	iv	iv	X
ejpam-5205	391	5	)	)	PUNCT
ejpam-5205	391	6	holds	hold	NOUN
ejpam-5205	391	7	.	.	PUNCT
ejpam-5205	392	1	conversely	conversely	ADV
ejpam-5205	392	2	,	,	PUNCT
ejpam-5205	392	3	assume	assume	VERB
ejpam-5205	392	4	that	that	SCONJ
ejpam-5205	392	5	(	(	PUNCT
ejpam-5205	392	6	i	i	NOUN
ejpam-5205	392	7	)	)	PUNCT
ejpam-5205	392	8	,	,	PUNCT
ejpam-5205	392	9	(	(	PUNCT
ejpam-5205	392	10	ii	ii	NOUN
ejpam-5205	392	11	)	)	PUNCT
ejpam-5205	392	12	,	,	PUNCT
ejpam-5205	392	13	(	(	PUNCT
ejpam-5205	392	14	iii	iii	NOUN
ejpam-5205	392	15	)	)	PUNCT
ejpam-5205	392	16	,	,	PUNCT
ejpam-5205	392	17	and	and	CCONJ
ejpam-5205	392	18	(	(	PUNCT
ejpam-5205	392	19	iv	iv	X
ejpam-5205	392	20	)	)	PUNCT
ejpam-5205	392	21	hold	hold	NOUN
ejpam-5205	392	22	.	.	PUNCT
ejpam-5205	393	1	let	let	VERB
ejpam-5205	393	2	(	(	PUNCT
ejpam-5205	393	3	v	v	NOUN
ejpam-5205	393	4	,	,	PUNCT
ejpam-5205	393	5	p	p	NOUN
ejpam-5205	393	6	)	)	PUNCT
ejpam-5205	393	7	∈	∈	PROPN
ejpam-5205	393	8	v0	v0	NOUN
ejpam-5205	393	9	.	.	PUNCT
ejpam-5205	394	1	then	then	ADV
ejpam-5205	394	2	v	v	X
ejpam-5205	394	3	∈	∈	PROPN
ejpam-5205	394	4	s0	s0	PROPN
ejpam-5205	394	5	g.	g.	PROPN
ejpam-5205	395	1	if	if	SCONJ
ejpam-5205	395	2	v	v	NUM
ejpam-5205	395	3	∈	∈	PROPN
ejpam-5205	395	4	s2	s2	NOUN
ejpam-5205	395	5	g	g	NOUN
ejpam-5205	395	6	,	,	PUNCT
ejpam-5205	395	7	then	then	ADV
ejpam-5205	395	8	(	(	PUNCT
ejpam-5205	395	9	v	v	NOUN
ejpam-5205	395	10	,	,	PUNCT
ejpam-5205	395	11	q	q	NOUN
ejpam-5205	395	12	)	)	PUNCT
ejpam-5205	395	13	∈	∈	NOUN
ejpam-5205	395	14	v2	v2	NOUN
ejpam-5205	395	15	for	for	ADP
ejpam-5205	395	16	some	some	DET
ejpam-5205	395	17	q	q	PROPN
ejpam-5205	395	18	∈	∈	PROPN
ejpam-5205	395	19	v	v	NOUN
ejpam-5205	395	20	(	(	PUNCT
ejpam-5205	395	21	km	km	PROPN
ejpam-5205	395	22	)	)	PUNCT
ejpam-5205	395	23	and	and	CCONJ
ejpam-5205	395	24	(	(	PUNCT
ejpam-5205	395	25	v	v	NOUN
ejpam-5205	395	26	,	,	PUNCT
ejpam-5205	395	27	p)(v	p)(v	PROPN
ejpam-5205	395	28	,	,	PUNCT
ejpam-5205	395	29	q	q	X
ejpam-5205	395	30	)	)	PUNCT
ejpam-5205	395	31	∈	∈	PROPN
ejpam-5205	395	32	e(g[km	e(g[km	PROPN
ejpam-5205	395	33	]	]	X
ejpam-5205	395	34	)	)	PUNCT
ejpam-5205	395	35	.	.	PUNCT
ejpam-5205	396	1	suppose	suppose	VERB
ejpam-5205	396	2	v	v	X
ejpam-5205	396	3	/∈	/∈	PUNCT
ejpam-5205	397	1	s2	s2	PROPN
ejpam-5205	397	2	g.	g.	PROPN
ejpam-5205	397	3	suppose	suppose	VERB
ejpam-5205	397	4	further	far	ADV
ejpam-5205	397	5	that	that	PRON
ejpam-5205	397	6	v	v	NUM
ejpam-5205	397	7	∈	∈	PROPN
ejpam-5205	397	8	s1	s1	PROPN
ejpam-5205	397	9	g.	g.	PROPN
ejpam-5205	397	10	then	then	ADV
ejpam-5205	397	11	by	by	ADP
ejpam-5205	397	12	(	(	PUNCT
ejpam-5205	397	13	iv	iv	X
ejpam-5205	397	14	)	)	PUNCT
ejpam-5205	397	15	,	,	PUNCT
ejpam-5205	397	16	there	there	PRON
ejpam-5205	397	17	exists	exist	VERB
ejpam-5205	397	18	w	w	PROPN
ejpam-5205	397	19	∈	∈	PROPN
ejpam-5205	397	20	s2	s2	NOUN
ejpam-5205	397	21	g	g	NOUN
ejpam-5205	397	22	such	such	DET
ejpam-5205	397	23	that	that	DET
ejpam-5205	397	24	v	v	PROPN
ejpam-5205	397	25	∈	∈	PROPN
ejpam-5205	397	26	ng(w	ng(w	NOUN
ejpam-5205	397	27	)	)	PUNCT
ejpam-5205	397	28	.	.	PUNCT
ejpam-5205	398	1	let	let	VERB
ejpam-5205	398	2	c	c	NOUN
ejpam-5205	398	3	∈	∈	PROPN
ejpam-5205	398	4	v	v	PROPN
ejpam-5205	398	5	(	(	PUNCT
ejpam-5205	398	6	km	km	PROPN
ejpam-5205	398	7	)	)	PUNCT
ejpam-5205	398	8	such	such	ADJ
ejpam-5205	398	9	that	that	SCONJ
ejpam-5205	398	10	(	(	PUNCT
ejpam-5205	398	11	w	w	PROPN
ejpam-5205	398	12	,	,	PUNCT
ejpam-5205	398	13	c	c	NOUN
ejpam-5205	398	14	)	)	PUNCT
ejpam-5205	398	15	∈	∈	NOUN
ejpam-5205	398	16	v2	v2	NOUN
ejpam-5205	398	17	.	.	PUNCT
ejpam-5205	399	1	then	then	ADV
ejpam-5205	399	2	(	(	PUNCT
ejpam-5205	399	3	v	v	NOUN
ejpam-5205	399	4	,	,	PUNCT
ejpam-5205	399	5	p)(w	p)(w	PROPN
ejpam-5205	399	6	,	,	PUNCT
ejpam-5205	399	7	c	c	NOUN
ejpam-5205	399	8	)	)	PUNCT
ejpam-5205	399	9	∈	∈	NOUN
ejpam-5205	399	10	e(g[h	e(g[h	NOUN
ejpam-5205	399	11	]	]	PUNCT
ejpam-5205	399	12	)	)	PUNCT
ejpam-5205	399	13	.	.	PUNCT
ejpam-5205	400	1	next	next	ADV
ejpam-5205	400	2	,	,	PUNCT
ejpam-5205	400	3	suppose	suppose	VERB
ejpam-5205	400	4	that	that	SCONJ
ejpam-5205	400	5	v	v	X
ejpam-5205	400	6	/∈	/∈	PUNCT
ejpam-5205	400	7	s1	s1	PROPN
ejpam-5205	400	8	g∪s2	g∪s2	VERB
ejpam-5205	400	9	g.	g.	NOUN
ejpam-5205	400	10	then	then	ADV
ejpam-5205	400	11	v	v	ADP
ejpam-5205	400	12	∈	∈	PROPN
ejpam-5205	400	13	v	v	ADP
ejpam-5205	400	14	0	0	NUM
ejpam-5205	400	15	g.	g.	NOUN
ejpam-5205	400	16	by	by	ADP
ejpam-5205	400	17	(	(	PUNCT
ejpam-5205	400	18	i	i	NOUN
ejpam-5205	400	19	)	)	PUNCT
ejpam-5205	400	20	,	,	PUNCT
ejpam-5205	400	21	there	there	PRON
ejpam-5205	400	22	exists	exist	VERB
ejpam-5205	400	23	z	z	PROPN
ejpam-5205	400	24	∈	∈	PROPN
ejpam-5205	400	25	v	v	ADP
ejpam-5205	400	26	2	2	NUM
ejpam-5205	400	27	g	g	NOUN
ejpam-5205	400	28	such	such	ADJ
ejpam-5205	400	29	that	that	SCONJ
ejpam-5205	400	30	vz	vz	PROPN
ejpam-5205	400	31	∈	∈	PROPN
ejpam-5205	400	32	e(g	e(g	PROPN
ejpam-5205	400	33	)	)	PUNCT
ejpam-5205	400	34	.	.	PUNCT
ejpam-5205	401	1	let	let	VERB
ejpam-5205	401	2	d	d	X
ejpam-5205	401	3	∈	∈	PROPN
ejpam-5205	401	4	v	v	PROPN
ejpam-5205	401	5	(	(	PUNCT
ejpam-5205	401	6	km	km	PROPN
ejpam-5205	401	7	)	)	PUNCT
ejpam-5205	401	8	such	such	ADJ
ejpam-5205	401	9	that	that	SCONJ
ejpam-5205	401	10	(	(	PUNCT
ejpam-5205	401	11	z	z	NOUN
ejpam-5205	401	12	,	,	PUNCT
ejpam-5205	401	13	d	d	NOUN
ejpam-5205	401	14	)	)	PUNCT
ejpam-5205	401	15	∈	∈	NOUN
ejpam-5205	401	16	v2	v2	NOUN
ejpam-5205	401	17	.	.	PUNCT
ejpam-5205	402	1	then	then	ADV
ejpam-5205	402	2	(	(	PUNCT
ejpam-5205	402	3	v	v	NOUN
ejpam-5205	402	4	,	,	PUNCT
ejpam-5205	402	5	p)(z	p)(z	PROPN
ejpam-5205	402	6	,	,	PUNCT
ejpam-5205	402	7	d	d	X
ejpam-5205	402	8	)	)	PUNCT
ejpam-5205	402	9	∈	∈	PROPN
ejpam-5205	402	10	e(g[km	e(g[km	PROPN
ejpam-5205	402	11	]	]	X
ejpam-5205	402	12	)	)	PUNCT
ejpam-5205	402	13	.	.	PUNCT
ejpam-5205	403	1	thus	thus	ADV
ejpam-5205	403	2	f	f	PROPN
ejpam-5205	403	3	is	be	AUX
ejpam-5205	403	4	an	an	DET
ejpam-5205	403	5	rdf	rdf	NOUN
ejpam-5205	403	6	on	on	ADP
ejpam-5205	403	7	g[km	g[km	NOUN
ejpam-5205	403	8	]	]	PUNCT
ejpam-5205	403	9	.	.	PUNCT
ejpam-5205	404	1	now	now	ADV
ejpam-5205	404	2	,	,	PUNCT
ejpam-5205	404	3	let	let	VERB
ejpam-5205	404	4	v1	v1	VERB
ejpam-5205	404	5	∪	∪	VERB
ejpam-5205	404	6	v2	v2	NOUN
ejpam-5205	404	7	=	=	SYM
ejpam-5205	404	8	⋃	⋃	PROPN
ejpam-5205	404	9	x∈s	x∈s	NOUN
ejpam-5205	405	1	[	[	X
ejpam-5205	405	2	{	{	PUNCT
ejpam-5205	405	3	x	x	NOUN
ejpam-5205	405	4	}	}	PUNCT
ejpam-5205	405	5	×	×	PROPN
ejpam-5205	405	6	tx	tx	PROPN
ejpam-5205	405	7	]	]	PUNCT
ejpam-5205	405	8	.	.	PUNCT
ejpam-5205	406	1	then	then	ADV
ejpam-5205	406	2	s	s	VERB
ejpam-5205	406	3	=	=	SYM
ejpam-5205	406	4	s1	s1	PROPN
ejpam-5205	406	5	g	g	PROPN
ejpam-5205	406	6	∪	∪	PROPN
ejpam-5205	406	7	s2	s2	NOUN
ejpam-5205	406	8	g	g	NOUN
ejpam-5205	406	9	and	and	CCONJ
ejpam-5205	406	10	tx	tx	VERB
ejpam-5205	406	11	⊆	⊆	NUM
ejpam-5205	406	12	v	v	NOUN
ejpam-5205	406	13	(	(	PUNCT
ejpam-5205	406	14	km	km	PROPN
ejpam-5205	406	15	)	)	PUNCT
ejpam-5205	406	16	for	for	ADP
ejpam-5205	406	17	each	each	DET
ejpam-5205	406	18	x	x	PROPN
ejpam-5205	406	19	∈	∈	PROPN
ejpam-5205	406	20	s.	s.	PROPN
ejpam-5205	406	21	morever	morever	PROPN
ejpam-5205	406	22	,	,	PUNCT
ejpam-5205	406	23	by	by	ADP
ejpam-5205	406	24	(	(	PUNCT
ejpam-5205	406	25	iii	iii	NOUN
ejpam-5205	406	26	)	)	PUNCT
ejpam-5205	406	27	,	,	PUNCT
ejpam-5205	406	28	tx	tx	PROPN
ejpam-5205	406	29	=	=	SYM
ejpam-5205	406	30	v	v	PROPN
ejpam-5205	406	31	(	(	PUNCT
ejpam-5205	406	32	km	km	PROPN
ejpam-5205	406	33	)	)	PUNCT
ejpam-5205	406	34	for	for	ADP
ejpam-5205	406	35	each	each	DET
ejpam-5205	406	36	x	x	SYM
ejpam-5205	406	37	∈	∈	PROPN
ejpam-5205	406	38	ig(s	ig(s	PRON
ejpam-5205	406	39	)	)	PUNCT
ejpam-5205	406	40	∩	∩	PROPN
ejpam-5205	406	41	s.	s.	PROPN
ejpam-5205	406	42	thus	thus	ADV
ejpam-5205	406	43	,	,	PUNCT
ejpam-5205	406	44	by	by	ADP
ejpam-5205	406	45	theorem	theorem	NOUN
ejpam-5205	406	46	2	2	NUM
ejpam-5205	406	47	,	,	PUNCT
ejpam-5205	406	48	v1	v1	NOUN
ejpam-5205	406	49	∪	∪	NOUN
ejpam-5205	406	50	v2	v2	NOUN
ejpam-5205	406	51	is	be	AUX
ejpam-5205	406	52	convex	convex	NOUN
ejpam-5205	406	53	in	in	ADP
ejpam-5205	406	54	g[km	g[km	PROPN
ejpam-5205	406	55	]	]	PUNCT
ejpam-5205	406	56	.	.	PUNCT
ejpam-5205	407	1	therefore	therefore	ADV
ejpam-5205	407	2	,	,	PUNCT
ejpam-5205	407	3	f	f	PROPN
ejpam-5205	407	4	is	be	AUX
ejpam-5205	407	5	a	a	DET
ejpam-5205	407	6	cvrdf	cvrdf	NOUN
ejpam-5205	407	7	on	on	ADP
ejpam-5205	407	8	g[km	g[km	PROPN
ejpam-5205	407	9	]	]	PUNCT
ejpam-5205	407	10	.	.	PUNCT
ejpam-5205	408	1	lemma	lemma	PROPN
ejpam-5205	408	2	2	2	X
ejpam-5205	408	3	.	.	PUNCT
ejpam-5205	409	1	let	let	VERB
ejpam-5205	409	2	g	g	PRON
ejpam-5205	409	3	be	be	AUX
ejpam-5205	409	4	a	a	DET
ejpam-5205	409	5	non	non	ADJ
ejpam-5205	409	6	-	-	ADJ
ejpam-5205	409	7	trivial	trivial	ADJ
ejpam-5205	409	8	connected	connected	ADJ
ejpam-5205	409	9	graph	graph	NOUN
ejpam-5205	409	10	with	with	ADP
ejpam-5205	409	11	g	g	PROPN
ejpam-5205	409	12	̸=	̸=	PROPN
ejpam-5205	409	13	k2	k2	NOUN
ejpam-5205	409	14	and	and	CCONJ
ejpam-5205	409	15	let	let	VERB
ejpam-5205	409	16	m	m	PRON
ejpam-5205	409	17	be	be	AUX
ejpam-5205	409	18	any	any	DET
ejpam-5205	409	19	positive	positive	ADJ
ejpam-5205	409	20	integer	integer	NOUN
ejpam-5205	409	21	.	.	PUNCT
ejpam-5205	410	1	if	if	SCONJ
ejpam-5205	410	2	h	h	PRON
ejpam-5205	410	3	=	=	SYM
ejpam-5205	410	4	(	(	PUNCT
ejpam-5205	410	5	w0,w1,w2	w0,w1,w2	PROPN
ejpam-5205	410	6	)	)	PUNCT
ejpam-5205	410	7	is	be	AUX
ejpam-5205	410	8	a	a	DET
ejpam-5205	410	9	cvrdf	cvrdf	NOUN
ejpam-5205	410	10	on	on	ADP
ejpam-5205	410	11	g	g	PROPN
ejpam-5205	410	12	such	such	ADJ
ejpam-5205	410	13	that	that	SCONJ
ejpam-5205	410	14	k	k	PROPN
ejpam-5205	410	15	=	=	SYM
ejpam-5205	410	16	ωcvr(h	ωcvr(h	PROPN
ejpam-5205	410	17	)	)	PUNCT
ejpam-5205	411	1	+	+	CCONJ
ejpam-5205	411	2	(	(	PUNCT
ejpam-5205	411	3	m−	m−	PROPN
ejpam-5205	411	4	1	1	NUM
ejpam-5205	411	5	)	)	PUNCT
ejpam-5205	411	6	∣∣s0	∣∣s0	NOUN
ejpam-5205	411	7	h	h	NOUN
ejpam-5205	411	8	∣∣	∣∣	X
ejpam-5205	411	9	=	=	SYM
ejpam-5205	411	10	min	min	X
ejpam-5205	411	11	{	{	PUNCT
ejpam-5205	411	12	ωcvr	ωcvr	PROPN
ejpam-5205	411	13	g	g	PROPN
ejpam-5205	411	14	(	(	PUNCT
ejpam-5205	411	15	h′	h′	PROPN
ejpam-5205	411	16	)	)	PUNCT
ejpam-5205	412	1	+	+	CCONJ
ejpam-5205	412	2	(	(	PUNCT
ejpam-5205	412	3	m−	m−	PROPN
ejpam-5205	412	4	1	1	NUM
ejpam-5205	412	5	)	)	PUNCT
ejpam-5205	412	6	∣∣s0	∣∣s0	NOUN
ejpam-5205	412	7	h′	h′	PROPN
ejpam-5205	412	8	∣∣	∣∣	X
ejpam-5205	412	9	}	}	PUNCT
ejpam-5205	412	10	,	,	PUNCT
ejpam-5205	412	11	then	then	ADV
ejpam-5205	412	12	w1	w1	PROPN
ejpam-5205	412	13	⊆	⊆	NUM
ejpam-5205	412	14	s0	s0	PROPN
ejpam-5205	412	15	h.	h.	PROPN
ejpam-5205	412	16	proof	proof	PROPN
ejpam-5205	412	17	.	.	PUNCT
ejpam-5205	412	18	suppose	suppose	VERB
ejpam-5205	412	19	there	there	PRON
ejpam-5205	412	20	exists	exist	VERB
ejpam-5205	412	21	x	x	X
ejpam-5205	412	22	∈	∈	PROPN
ejpam-5205	412	23	w1	w1	NOUN
ejpam-5205	412	24	\	\	PROPN
ejpam-5205	412	25	s0	s0	PROPN
ejpam-5205	412	26	h.	h.	PROPN
ejpam-5205	412	27	suppose	suppose	VERB
ejpam-5205	412	28	x	x	PUNCT
ejpam-5205	412	29	∈	∈	PROPN
ejpam-5205	412	30	ng(w0	ng(w0	NOUN
ejpam-5205	412	31	)	)	PUNCT
ejpam-5205	412	32	,	,	PUNCT
ejpam-5205	412	33	say	say	VERB
ejpam-5205	412	34	y	y	PROPN
ejpam-5205	412	35	∈	∈	PROPN
ejpam-5205	412	36	w0	w0	PROPN
ejpam-5205	412	37	∩	∩	NOUN
ejpam-5205	412	38	ng(x	ng(x	NUM
ejpam-5205	412	39	)	)	PUNCT
ejpam-5205	412	40	.	.	PUNCT
ejpam-5205	413	1	since	since	SCONJ
ejpam-5205	413	2	h	h	NOUN
ejpam-5205	413	3	is	be	AUX
ejpam-5205	413	4	an	an	DET
ejpam-5205	413	5	rdf	rdf	NOUN
ejpam-5205	413	6	on	on	ADP
ejpam-5205	413	7	g	g	NOUN
ejpam-5205	413	8	,	,	PUNCT
ejpam-5205	413	9	there	there	PRON
ejpam-5205	413	10	exists	exist	VERB
ejpam-5205	413	11	v	v	PROPN
ejpam-5205	413	12	∈	∈	PROPN
ejpam-5205	413	13	w2	w2	NOUN
ejpam-5205	413	14	such	such	ADJ
ejpam-5205	413	15	that	that	SCONJ
ejpam-5205	413	16	y	y	PROPN
ejpam-5205	413	17	∈	∈	PROPN
ejpam-5205	413	18	ng(v	ng(v	PRON
ejpam-5205	413	19	)	)	PUNCT
ejpam-5205	413	20	.	.	PUNCT
ejpam-5205	414	1	by	by	ADP
ejpam-5205	414	2	convexity	convexity	NOUN
ejpam-5205	414	3	of	of	ADP
ejpam-5205	414	4	w1	w1	PROPN
ejpam-5205	414	5	∪	∪	NOUN
ejpam-5205	414	6	w2	w2	NOUN
ejpam-5205	414	7	,	,	PUNCT
ejpam-5205	414	8	xv	xv	PROPN
ejpam-5205	414	9	∈	∈	PROPN
ejpam-5205	414	10	e(g	e(g	PROPN
ejpam-5205	414	11	)	)	PUNCT
ejpam-5205	414	12	.	.	PUNCT
ejpam-5205	415	1	let	let	VERB
ejpam-5205	416	1	w	w	NOUN
ejpam-5205	416	2	′	′	NOUN
ejpam-5205	416	3	0	0	NUM
ejpam-5205	417	1	=	=	SYM
ejpam-5205	417	2	w0	w0	PROPN
ejpam-5205	417	3	∪	∪	NOUN
ejpam-5205	417	4	{	{	PUNCT
ejpam-5205	417	5	x	x	NOUN
ejpam-5205	417	6	}	}	PUNCT
ejpam-5205	417	7	,	,	PUNCT
ejpam-5205	417	8	w	w	NOUN
ejpam-5205	417	9	′	′	NOUN
ejpam-5205	417	10	1	1	NUM
ejpam-5205	417	11	=	=	SYM
ejpam-5205	417	12	w1	w1	NOUN
ejpam-5205	417	13	\	\	NOUN
ejpam-5205	417	14	{	{	PUNCT
ejpam-5205	417	15	x	x	X
ejpam-5205	417	16	}	}	PUNCT
ejpam-5205	417	17	,	,	PUNCT
ejpam-5205	417	18	and	and	CCONJ
ejpam-5205	417	19	w	w	NOUN
ejpam-5205	417	20	′	′	NUM
ejpam-5205	417	21	2	2	NUM
ejpam-5205	417	22	=	=	NOUN
ejpam-5205	417	23	w2	w2	NOUN
ejpam-5205	417	24	.	.	PUNCT
ejpam-5205	418	1	then	then	ADV
ejpam-5205	418	2	h′	h′	PROPN
ejpam-5205	418	3	=	=	PUNCT
ejpam-5205	418	4	(	(	PUNCT
ejpam-5205	418	5	w	w	NOUN
ejpam-5205	418	6	′	′	NUM
ejpam-5205	418	7	0,w	0,w	NUM
ejpam-5205	419	1	′	′	NUM
ejpam-5205	419	2	1,w	1,w	NUM
ejpam-5205	419	3	′	′	NUM
ejpam-5205	419	4	2	2	NUM
ejpam-5205	419	5	)	)	PUNCT
ejpam-5205	419	6	is	be	AUX
ejpam-5205	419	7	an	an	DET
ejpam-5205	419	8	rdf	rdf	NOUN
ejpam-5205	419	9	on	on	ADP
ejpam-5205	419	10	g.	g.	PROPN
ejpam-5205	419	11	let	let	VERB
ejpam-5205	419	12	p	p	PRON
ejpam-5205	419	13	,	,	PUNCT
ejpam-5205	419	14	q	q	PROPN
ejpam-5205	419	15	∈	∈	PROPN
ejpam-5205	419	16	w	w	NOUN
ejpam-5205	419	17	′	′	NOUN
ejpam-5205	419	18	1	1	NUM
ejpam-5205	419	19	∪	∪	NOUN
ejpam-5205	419	20	w	w	PROPN
ejpam-5205	419	21	′	′	NUM
ejpam-5205	419	22	2	2	NUM
ejpam-5205	419	23	such	such	ADJ
ejpam-5205	419	24	that	that	SCONJ
ejpam-5205	419	25	p	p	PROPN
ejpam-5205	419	26	̸=	̸=	PROPN
ejpam-5205	419	27	q.	q.	NOUN
ejpam-5205	419	28	then	then	ADV
ejpam-5205	419	29	p	p	X
ejpam-5205	419	30	,	,	PUNCT
ejpam-5205	419	31	q	q	PROPN
ejpam-5205	419	32	∈	∈	PROPN
ejpam-5205	419	33	w1	w1	NOUN
ejpam-5205	419	34	∪	∪	NOUN
ejpam-5205	419	35	w2	w2	PROPN
ejpam-5205	419	36	and	and	CCONJ
ejpam-5205	419	37	ig(p	ig(p	ADJ
ejpam-5205	419	38	,	,	PUNCT
ejpam-5205	419	39	q	q	X
ejpam-5205	419	40	)	)	PUNCT
ejpam-5205	419	41	⊆	⊆	NUM
ejpam-5205	419	42	w1	w1	NOUN
ejpam-5205	419	43	∪	∪	NOUN
ejpam-5205	419	44	w2	w2	PROPN
ejpam-5205	419	45	since	since	SCONJ
ejpam-5205	419	46	w1	w1	PROPN
ejpam-5205	419	47	∪	∪	PROPN
ejpam-5205	419	48	w2	w2	PROPN
ejpam-5205	419	49	is	be	AUX
ejpam-5205	419	50	convex	convex	PROPN
ejpam-5205	419	51	.	.	PUNCT
ejpam-5205	420	1	let	let	VERB
ejpam-5205	420	2	z	z	NOUN
ejpam-5205	420	3	∈	∈	PROPN
ejpam-5205	420	4	ig(p	ig(p	NOUN
ejpam-5205	420	5	,	,	PUNCT
ejpam-5205	420	6	q	q	NOUN
ejpam-5205	420	7	)	)	PUNCT
ejpam-5205	420	8	.	.	PUNCT
ejpam-5205	421	1	since	since	SCONJ
ejpam-5205	421	2	x	x	PROPN
ejpam-5205	421	3	∈	∈	PROPN
ejpam-5205	421	4	w1	w1	NOUN
ejpam-5205	421	5	\	\	PROPN
ejpam-5205	421	6	s0	s0	PROPN
ejpam-5205	421	7	h	h	PROPN
ejpam-5205	421	8	,	,	PUNCT
ejpam-5205	421	9	x	x	PUNCT
ejpam-5205	421	10	/∈	/∈	X
ejpam-5205	421	11	ig(w1	ig(w1	NOUN
ejpam-5205	421	12	∪	∪	ADJ
ejpam-5205	421	13	w2	w2	NOUN
ejpam-5205	421	14	)	)	PUNCT
ejpam-5205	421	15	.	.	PUNCT
ejpam-5205	422	1	thus	thus	ADV
ejpam-5205	422	2	,	,	PUNCT
ejpam-5205	422	3	z	z	PROPN
ejpam-5205	422	4	̸=	̸=	PROPN
ejpam-5205	422	5	x.	x.	NOUN
ejpam-5205	422	6	hence	hence	ADV
ejpam-5205	422	7	,	,	PUNCT
ejpam-5205	422	8	z	z	PROPN
ejpam-5205	422	9	∈	∈	PROPN
ejpam-5205	422	10	w	w	NOUN
ejpam-5205	422	11	′	′	NOUN
ejpam-5205	422	12	1	1	NUM
ejpam-5205	422	13	∪	∪	NOUN
ejpam-5205	422	14	w	w	PROPN
ejpam-5205	422	15	′	′	NUM
ejpam-5205	422	16	2	2	NUM
ejpam-5205	422	17	,	,	PUNCT
ejpam-5205	422	18	i.e.	i.e.	X
ejpam-5205	422	19	,	,	PUNCT
ejpam-5205	422	20	ig(p	ig(p	ADJ
ejpam-5205	422	21	,	,	PUNCT
ejpam-5205	422	22	q	q	X
ejpam-5205	422	23	)	)	PUNCT
ejpam-5205	422	24	⊆	⊆	NUM
ejpam-5205	422	25	w	w	NOUN
ejpam-5205	422	26	′	′	NUM
ejpam-5205	422	27	1	1	NUM
ejpam-5205	422	28	∪	∪	NOUN
ejpam-5205	422	29	w	w	PROPN
ejpam-5205	422	30	′	′	NUM
ejpam-5205	422	31	2	2	NUM
ejpam-5205	422	32	,	,	PUNCT
ejpam-5205	422	33	showing	show	VERB
ejpam-5205	422	34	that	that	SCONJ
ejpam-5205	422	35	w	w	ADJ
ejpam-5205	422	36	′	′	NOUN
ejpam-5205	422	37	1	1	NUM
ejpam-5205	422	38	∪	∪	NOUN
ejpam-5205	422	39	w	w	NOUN
ejpam-5205	422	40	′	′	ADJ
ejpam-5205	422	41	2	2	NUM
ejpam-5205	422	42	is	be	AUX
ejpam-5205	422	43	convex	convex	ADJ
ejpam-5205	422	44	in	in	ADP
ejpam-5205	422	45	g.	g.	PROPN
ejpam-5205	422	46	therefore	therefore	ADV
ejpam-5205	422	47	,	,	PUNCT
ejpam-5205	422	48	h′	h′	PROPN
ejpam-5205	422	49	is	be	AUX
ejpam-5205	422	50	a	a	DET
ejpam-5205	422	51	cvrdf	cvrdf	NOUN
ejpam-5205	422	52	on	on	ADP
ejpam-5205	422	53	g	g	PROPN
ejpam-5205	422	54	and	and	CCONJ
ejpam-5205	422	55	ωcvr	ωcvr	PROPN
ejpam-5205	422	56	g	g	PROPN
ejpam-5205	422	57	(	(	PUNCT
ejpam-5205	422	58	h′	h′	PROPN
ejpam-5205	422	59	)	)	PUNCT
ejpam-5205	422	60	=	=	PUNCT
ejpam-5205	423	1	|w	|w	NOUN
ejpam-5205	423	2	′	′	NUM
ejpam-5205	423	3	1|	1|	NUM
ejpam-5205	424	1	+	+	CCONJ
ejpam-5205	425	1	2|w	2|w	NUM
ejpam-5205	426	1	′	′	NUM
ejpam-5205	426	2	2|	2|	NUM
ejpam-5205	427	1	=	=	PUNCT
ejpam-5205	428	1	|w1|	|w1|	NOUN
ejpam-5205	429	1	−	−	NOUN
ejpam-5205	429	2	1	1	NUM
ejpam-5205	429	3	+	+	NUM
ejpam-5205	429	4	2|w2|	2|w2|	NUM
ejpam-5205	429	5	<	<	X
ejpam-5205	429	6	ωcvr	ωcvr	PROPN
ejpam-5205	429	7	g	g	PROPN
ejpam-5205	429	8	(	(	PUNCT
ejpam-5205	429	9	h	h	NOUN
ejpam-5205	429	10	)	)	PUNCT
ejpam-5205	429	11	,	,	PUNCT
ejpam-5205	429	12	a	a	DET
ejpam-5205	429	13	contradiction	contradiction	NOUN
ejpam-5205	429	14	.	.	PUNCT
ejpam-5205	430	1	thus	thus	ADV
ejpam-5205	430	2	,	,	PUNCT
ejpam-5205	430	3	x	x	X
ejpam-5205	430	4	/∈	/∈	PUNCT
ejpam-5205	430	5	ng(w0	ng(w0	NOUN
ejpam-5205	430	6	)	)	PUNCT
ejpam-5205	430	7	.	.	PUNCT
ejpam-5205	431	1	next	next	ADV
ejpam-5205	431	2	,	,	PUNCT
ejpam-5205	431	3	suppose	suppose	VERB
ejpam-5205	431	4	x	x	X
ejpam-5205	431	5	∈	∈	PROPN
ejpam-5205	431	6	ng(w2	ng(w2	NOUN
ejpam-5205	431	7	)	)	PUNCT
ejpam-5205	431	8	,	,	PUNCT
ejpam-5205	431	9	say	say	VERB
ejpam-5205	431	10	{	{	PUNCT
ejpam-5205	431	11	z	z	NOUN
ejpam-5205	431	12	}	}	PUNCT
ejpam-5205	431	13	∈	∈	PROPN
ejpam-5205	431	14	w2	w2	NOUN
ejpam-5205	431	15	∩	∩	NOUN
ejpam-5205	431	16	ng(x	ng(x	NUM
ejpam-5205	431	17	)	)	PUNCT
ejpam-5205	431	18	.	.	PUNCT
ejpam-5205	432	1	following	follow	VERB
ejpam-5205	432	2	the	the	DET
ejpam-5205	432	3	argument	argument	NOUN
ejpam-5205	432	4	above	above	ADV
ejpam-5205	432	5	,	,	PUNCT
ejpam-5205	432	6	this	this	PRON
ejpam-5205	432	7	is	be	AUX
ejpam-5205	432	8	also	also	ADV
ejpam-5205	432	9	not	not	PART
ejpam-5205	432	10	possible	possible	ADJ
ejpam-5205	432	11	.	.	PUNCT
ejpam-5205	433	1	thus	thus	ADV
ejpam-5205	433	2	,	,	PUNCT
ejpam-5205	433	3	x	x	PROPN
ejpam-5205	433	4	/∈	/∈	PUNCT
ejpam-5205	433	5	ng(w2	ng(w2	NUM
ejpam-5205	433	6	)	)	PUNCT
ejpam-5205	433	7	.	.	PUNCT
ejpam-5205	434	1	therefore	therefore	ADV
ejpam-5205	434	2	,	,	PUNCT
ejpam-5205	434	3	ng(x	ng(x	NUM
ejpam-5205	434	4	)	)	PUNCT
ejpam-5205	434	5	⊆	⊆	NUM
ejpam-5205	434	6	w1	w1	NOUN
ejpam-5205	434	7	.	.	PUNCT
ejpam-5205	434	8	suppose	suppose	VERB
ejpam-5205	434	9	that	that	SCONJ
ejpam-5205	434	10	ng(x	ng(x	NUM
ejpam-5205	434	11	)	)	PUNCT
ejpam-5205	434	12	⊆	⊆	NUM
ejpam-5205	434	13	w1	w1	NOUN
ejpam-5205	434	14	\	\	NOUN
ejpam-5205	434	15	s0	s0	PROPN
ejpam-5205	434	16	h.	h.	PROPN
ejpam-5205	434	17	suppose	suppose	VERB
ejpam-5205	434	18	there	there	PRON
ejpam-5205	434	19	exists	exist	VERB
ejpam-5205	434	20	y	y	PROPN
ejpam-5205	434	21	∈	∈	PROPN
ejpam-5205	434	22	ng(x	ng(x	NUM
ejpam-5205	434	23	)	)	PUNCT
ejpam-5205	434	24	∩	∩	NOUN
ejpam-5205	434	25	(	(	PUNCT
ejpam-5205	434	26	w1	w1	NOUN
ejpam-5205	434	27	\	\	PROPN
ejpam-5205	434	28	s0	s0	PROPN
ejpam-5205	434	29	h	h	PROPN
ejpam-5205	434	30	)	)	PUNCT
ejpam-5205	434	31	.	.	PUNCT
ejpam-5205	435	1	since	since	SCONJ
ejpam-5205	435	2	|v	|v	PROPN
ejpam-5205	435	3	(	(	PUNCT
ejpam-5205	435	4	g)|	g)|	X
ejpam-5205	435	5	≥	≥	NOUN
ejpam-5205	435	6	3	3	NUM
ejpam-5205	435	7	,	,	PUNCT
ejpam-5205	435	8	there	there	PRON
ejpam-5205	435	9	exists	exist	VERB
ejpam-5205	435	10	z	z	PROPN
ejpam-5205	435	11	∈	∈	PROPN
ejpam-5205	435	12	ng(x	ng(x	NUM
ejpam-5205	435	13	)	)	PUNCT
ejpam-5205	435	14	∪	∪	ADP
ejpam-5205	435	15	ng(y	ng(y	NOUN
ejpam-5205	435	16	)	)	PUNCT
ejpam-5205	435	17	.	.	PUNCT
ejpam-5205	436	1	moreover	moreover	ADV
ejpam-5205	436	2	,	,	PUNCT
ejpam-5205	436	3	since	since	SCONJ
ejpam-5205	436	4	x	x	X
ejpam-5205	436	5	,	,	PUNCT
ejpam-5205	436	6	y	y	PROPN
ejpam-5205	436	7	/∈	/∈	PUNCT
ejpam-5205	436	8	s0	s0	PROPN
ejpam-5205	436	9	h	h	PROPN
ejpam-5205	436	10	,	,	PUNCT
ejpam-5205	436	11	z	z	PROPN
ejpam-5205	436	12	∈	∈	PROPN
ejpam-5205	436	13	ng(x	ng(x	NUM
ejpam-5205	436	14	)	)	PUNCT
ejpam-5205	436	15	∩	∩	NOUN
ejpam-5205	436	16	ng(y	ng(y	NOUN
ejpam-5205	436	17	)	)	PUNCT
ejpam-5205	436	18	.	.	PUNCT
ejpam-5205	437	1	it	it	PRON
ejpam-5205	437	2	follows	follow	VERB
ejpam-5205	437	3	that	that	SCONJ
ejpam-5205	437	4	y	y	PROPN
ejpam-5205	437	5	,	,	PUNCT
ejpam-5205	437	6	z	z	PROPN
ejpam-5205	437	7	∈	∈	PROPN
ejpam-5205	437	8	w1	w1	NOUN
ejpam-5205	437	9	\	\	PROPN
ejpam-5205	437	10	s0	s0	PROPN
ejpam-5205	437	11	h.	h.	PROPN
ejpam-5205	437	12	let	let	VERB
ejpam-5205	437	13	w	w	NOUN
ejpam-5205	437	14	∗	∗	X
ejpam-5205	437	15	0	0	NUM
ejpam-5205	437	16	=	=	SYM
ejpam-5205	437	17	w0	w0	PROPN
ejpam-5205	437	18	∪	∪	ADJ
ejpam-5205	437	19	{	{	PUNCT
ejpam-5205	437	20	x	x	NOUN
ejpam-5205	437	21	,	,	PUNCT
ejpam-5205	437	22	z	z	NOUN
ejpam-5205	437	23	}	}	PUNCT
ejpam-5205	437	24	,	,	PUNCT
ejpam-5205	437	25	w	w	PROPN
ejpam-5205	437	26	∗	∗	NOUN
ejpam-5205	437	27	1	1	NUM
ejpam-5205	438	1	=	=	SYM
ejpam-5205	438	2	w1	w1	NOUN
ejpam-5205	438	3	\	\	NOUN
ejpam-5205	438	4	{	{	PUNCT
ejpam-5205	438	5	x	x	X
ejpam-5205	438	6	,	,	PUNCT
ejpam-5205	438	7	z	z	PROPN
ejpam-5205	438	8	,	,	PUNCT
ejpam-5205	438	9	y	y	PROPN
ejpam-5205	438	10	}	}	PUNCT
ejpam-5205	438	11	,	,	PUNCT
ejpam-5205	438	12	and	and	CCONJ
ejpam-5205	438	13	w	w	NOUN
ejpam-5205	438	14	∗	∗	NOUN
ejpam-5205	438	15	2	2	NUM
ejpam-5205	438	16	=	=	NOUN
ejpam-5205	438	17	w2	w2	NOUN
ejpam-5205	438	18	∪	∪	NOUN
ejpam-5205	438	19	{	{	PUNCT
ejpam-5205	438	20	y	y	NOUN
ejpam-5205	438	21	}	}	PUNCT
ejpam-5205	438	22	.	.	PUNCT
ejpam-5205	439	1	then	then	ADV
ejpam-5205	439	2	h∗	h∗	PROPN
ejpam-5205	439	3	=	=	PUNCT
ejpam-5205	439	4	(	(	PUNCT
ejpam-5205	439	5	w	w	NOUN
ejpam-5205	439	6	∗	∗	NOUN
ejpam-5205	439	7	0	0	NUM
ejpam-5205	439	8	,	,	PUNCT
ejpam-5205	439	9	w	w	PROPN
ejpam-5205	439	10	∗	∗	NOUN
ejpam-5205	439	11	1	1	NUM
ejpam-5205	439	12	,	,	PUNCT
ejpam-5205	439	13	w	w	NOUN
ejpam-5205	439	14	∗	∗	NOUN
ejpam-5205	439	15	2	2	NUM
ejpam-5205	439	16	)	)	PUNCT
ejpam-5205	439	17	is	be	AUX
ejpam-5205	439	18	a	a	DET
ejpam-5205	439	19	cvrdf	cvrdf	NOUN
ejpam-5205	439	20	on	on	ADP
ejpam-5205	439	21	g	g	PROPN
ejpam-5205	439	22	and	and	CCONJ
ejpam-5205	439	23	ωcvr	ωcvr	PROPN
ejpam-5205	439	24	g	g	PROPN
ejpam-5205	439	25	(	(	PUNCT
ejpam-5205	439	26	h∗	h∗	PROPN
ejpam-5205	439	27	)	)	PUNCT
ejpam-5205	439	28	<	<	X
ejpam-5205	440	1	ωcvr	ωcvr	PROPN
ejpam-5205	440	2	g	g	PROPN
ejpam-5205	440	3	(	(	PUNCT
ejpam-5205	440	4	h	h	NOUN
ejpam-5205	440	5	)	)	PUNCT
ejpam-5205	440	6	.	.	PUNCT
ejpam-5205	441	1	since	since	SCONJ
ejpam-5205	441	2	s0	s0	PROPN
ejpam-5205	441	3	h∗	h∗	PROPN
ejpam-5205	441	4	⊆	⊆	NUM
ejpam-5205	441	5	s0	s0	PROPN
ejpam-5205	441	6	h	h	NOUN
ejpam-5205	441	7	,	,	PUNCT
ejpam-5205	441	8	it	it	PRON
ejpam-5205	441	9	follows	follow	VERB
ejpam-5205	441	10	that	that	SCONJ
ejpam-5205	441	11	ω	ω	PROPN
ejpam-5205	441	12	cvr	cvr	NOUN
ejpam-5205	441	13	g	g	PROPN
ejpam-5205	441	14	(	(	PUNCT
ejpam-5205	441	15	h∗)+	h∗)+	PROPN
ejpam-5205	441	16	(	(	PUNCT
ejpam-5205	441	17	m−	m−	PROPN
ejpam-5205	441	18	1	1	NUM
ejpam-5205	441	19	)	)	PUNCT
ejpam-5205	441	20	∣∣s0	∣∣s0	NOUN
ejpam-5205	441	21	h∗	h∗	NOUN
ejpam-5205	441	22	|	|	ADV
ejpam-5205	441	23	<	<	X
ejpam-5205	441	24	k	k	PROPN
ejpam-5205	441	25	,	,	PUNCT
ejpam-5205	441	26	a	a	DET
ejpam-5205	441	27	contradiction	contradiction	NOUN
ejpam-5205	441	28	.	.	PUNCT
ejpam-5205	442	1	therefore	therefore	ADV
ejpam-5205	442	2	,	,	PUNCT
ejpam-5205	442	3	ng(x	ng(x	NUM
ejpam-5205	442	4	)	)	PUNCT
ejpam-5205	442	5	∩	∩	NOUN
ejpam-5205	442	6	(	(	PUNCT
ejpam-5205	442	7	w1	w1	NOUN
ejpam-5205	442	8	∩	∩	ADJ
ejpam-5205	442	9	s0	s0	PROPN
ejpam-5205	442	10	h	h	NOUN
ejpam-5205	442	11	)	)	PUNCT
ejpam-5205	442	12	̸=	̸=	PROPN
ejpam-5205	442	13	∅.	∅.	ADV
ejpam-5205	442	14	let	let	VERB
ejpam-5205	442	15	vx	vx	PROPN
ejpam-5205	442	16	∈	∈	PROPN
ejpam-5205	442	17	ng(x	ng(x	NUM
ejpam-5205	442	18	)	)	PUNCT
ejpam-5205	442	19	∩	∩	NOUN
ejpam-5205	442	20	(	(	PUNCT
ejpam-5205	442	21	w1	w1	NOUN
ejpam-5205	442	22	∩	∩	ADJ
ejpam-5205	442	23	s0	s0	PROPN
ejpam-5205	442	24	h	h	NOUN
ejpam-5205	442	25	)	)	PUNCT
ejpam-5205	442	26	.	.	PUNCT
ejpam-5205	443	1	let	let	VERB
ejpam-5205	443	2	v0	v0	NOUN
ejpam-5205	443	3	=	=	PUNCT
ejpam-5205	443	4	w0∪{x	w0∪{x	NOUN
ejpam-5205	443	5	}	}	PUNCT
ejpam-5205	443	6	,	,	PUNCT
ejpam-5205	443	7	v1	v1	NOUN
ejpam-5205	443	8	=	=	SYM
ejpam-5205	443	9	w1\{x	w1\{x	PROPN
ejpam-5205	443	10	,	,	PUNCT
ejpam-5205	443	11	vx	vx	ADP
ejpam-5205	443	12	}	}	PUNCT
ejpam-5205	443	13	and	and	CCONJ
ejpam-5205	443	14	v2	v2	NOUN
ejpam-5205	443	15	=	=	PUNCT
ejpam-5205	443	16	w2∪{vx	w2∪{vx	NOUN
ejpam-5205	443	17	}	}	PUNCT
ejpam-5205	443	18	.	.	PUNCT
ejpam-5205	444	1	then	then	ADV
ejpam-5205	444	2	f	f	X
ejpam-5205	444	3	=	=	SYM
ejpam-5205	444	4	(	(	PUNCT
ejpam-5205	444	5	v0	v0	PROPN
ejpam-5205	444	6	,	,	PUNCT
ejpam-5205	444	7	v1	v1	NOUN
ejpam-5205	444	8	,	,	PUNCT
ejpam-5205	444	9	v2	v2	PROPN
ejpam-5205	444	10	)	)	PUNCT
ejpam-5205	444	11	is	be	AUX
ejpam-5205	444	12	a	a	DET
ejpam-5205	444	13	cvrdf	cvrdf	NOUN
ejpam-5205	444	14	on	on	ADP
ejpam-5205	444	15	g	g	PROPN
ejpam-5205	444	16	and	and	CCONJ
ejpam-5205	444	17	ωcvr	ωcvr	PROPN
ejpam-5205	444	18	g	g	PROPN
ejpam-5205	444	19	(	(	PUNCT
ejpam-5205	444	20	f	f	X
ejpam-5205	444	21	)	)	PUNCT
ejpam-5205	445	1	=	=	SYM
ejpam-5205	445	2	ωcvr	ωcvr	PROPN
ejpam-5205	445	3	g	g	PROPN
ejpam-5205	445	4	(	(	PUNCT
ejpam-5205	445	5	h	h	NOUN
ejpam-5205	445	6	)	)	PUNCT
ejpam-5205	445	7	.	.	PUNCT
ejpam-5205	446	1	since	since	SCONJ
ejpam-5205	446	2	x	x	PROPN
ejpam-5205	446	3	/∈	/∈	PUNCT
ejpam-5205	446	4	s0	s0	PROPN
ejpam-5205	446	5	f	f	PROPN
ejpam-5205	446	6	,	,	PUNCT
ejpam-5205	446	7	|s0	|s0	PROPN
ejpam-5205	447	1	f	f	PROPN
ejpam-5205	448	1	|	|	ADV
ejpam-5205	448	2	<	<	X
ejpam-5205	448	3	|s0	|s0	PROPN
ejpam-5205	448	4	h|	h|	PROPN
ejpam-5205	448	5	.	.	PUNCT
ejpam-5205	449	1	thus	thus	ADV
ejpam-5205	449	2	,	,	PUNCT
ejpam-5205	449	3	ωcvr	ωcvr	PROPN
ejpam-5205	449	4	g	g	PROPN
ejpam-5205	449	5	(	(	PUNCT
ejpam-5205	449	6	f	f	PROPN
ejpam-5205	449	7	)	)	PUNCT
ejpam-5205	450	1	+	+	CCONJ
ejpam-5205	450	2	(	(	PUNCT
ejpam-5205	450	3	m−	m−	PROPN
ejpam-5205	450	4	1	1	NUM
ejpam-5205	450	5	)	)	PUNCT
ejpam-5205	450	6	∣∣s0	∣∣s0	NOUN
ejpam-5205	450	7	f	f	NOUN
ejpam-5205	451	1	|	|	ADV
ejpam-5205	451	2	<	<	X
ejpam-5205	451	3	k	k	X
ejpam-5205	451	4	,	,	PUNCT
ejpam-5205	451	5	a	a	DET
ejpam-5205	451	6	contradiction	contradiction	NOUN
ejpam-5205	451	7	.	.	PUNCT
ejpam-5205	452	1	therefore	therefore	ADV
ejpam-5205	452	2	,	,	PUNCT
ejpam-5205	452	3	w1	w1	NOUN
ejpam-5205	452	4	\	\	PROPN
ejpam-5205	452	5	s0	s0	PROPN
ejpam-5205	452	6	h	h	NOUN
ejpam-5205	452	7	=	=	NOUN
ejpam-5205	452	8	∅	∅	NOUN
ejpam-5205	452	9	,	,	PUNCT
ejpam-5205	452	10	i.e	i.e	PROPN
ejpam-5205	452	11	,	,	PUNCT
ejpam-5205	452	12	w1	w1	NOUN
ejpam-5205	452	13	⊆	⊆	NUM
ejpam-5205	452	14	s0	s0	PROPN
ejpam-5205	452	15	h.	h.	PROPN
ejpam-5205	452	16	corollary	corollary	PROPN
ejpam-5205	452	17	4	4	X
ejpam-5205	452	18	.	.	PUNCT
ejpam-5205	453	1	let	let	VERB
ejpam-5205	453	2	g	g	PRON
ejpam-5205	453	3	be	be	AUX
ejpam-5205	453	4	a	a	DET
ejpam-5205	453	5	non	non	ADJ
ejpam-5205	453	6	-	-	ADJ
ejpam-5205	453	7	trivial	trivial	ADJ
ejpam-5205	453	8	connected	connected	ADJ
ejpam-5205	453	9	graph	graph	NOUN
ejpam-5205	453	10	and	and	CCONJ
ejpam-5205	453	11	km	km	PROPN
ejpam-5205	453	12	be	be	AUX
ejpam-5205	453	13	a	a	DET
ejpam-5205	453	14	complete	complete	ADJ
ejpam-5205	453	15	graph	graph	NOUN
ejpam-5205	453	16	of	of	ADP
ejpam-5205	453	17	order	order	NOUN
ejpam-5205	453	18	m	m	VERB
ejpam-5205	453	19	≥	≥	NOUN
ejpam-5205	453	20	1	1	NUM
ejpam-5205	453	21	.	.	PUNCT
ejpam-5205	454	1	then	then	ADV
ejpam-5205	454	2	γcvr(g[km	γcvr(g[km	PROPN
ejpam-5205	454	3	]	]	PUNCT
ejpam-5205	454	4	)	)	PUNCT
ejpam-5205	455	1	=	=	SYM
ejpam-5205	455	2	min	min	PROPN
ejpam-5205	455	3	{	{	PUNCT
ejpam-5205	455	4	ωcvr	ωcvr	PROPN
ejpam-5205	455	5	g	g	PROPN
ejpam-5205	455	6	(	(	PUNCT
ejpam-5205	455	7	g	g	PROPN
ejpam-5205	455	8	)	)	PUNCT
ejpam-5205	455	9	+	+	CCONJ
ejpam-5205	455	10	(	(	PUNCT
ejpam-5205	455	11	m−	m−	PROPN
ejpam-5205	455	12	1	1	NUM
ejpam-5205	455	13	)	)	PUNCT
ejpam-5205	455	14	∣∣s0	∣∣s0	NOUN
ejpam-5205	455	15	g	g	PROPN
ejpam-5205	456	1	|	|	NOUN
ejpam-5205	456	2	:	:	PUNCT
ejpam-5205	456	3	g	g	PROPN
ejpam-5205	456	4	is	be	AUX
ejpam-5205	456	5	a	a	DET
ejpam-5205	456	6	cvrdf	cvrdf	NOUN
ejpam-5205	456	7	on	on	ADP
ejpam-5205	456	8	g	g	PROPN
ejpam-5205	456	9	}	}	PUNCT
ejpam-5205	456	10	.	.	PUNCT
ejpam-5205	457	1	r.	r.	PROPN
ejpam-5205	457	2	fortosa	fortosa	PROPN
ejpam-5205	457	3	,	,	PUNCT
ejpam-5205	457	4	s.	s.	PROPN
ejpam-5205	457	5	canoy	canoy	PROPN
ejpam-5205	457	6	jr	jr	PROPN
ejpam-5205	457	7	.	.	PROPN
ejpam-5205	457	8	/	/	SYM
ejpam-5205	457	9	eur	eur	PROPN
ejpam-5205	457	10	.	.	PUNCT
ejpam-5205	458	1	j.	j.	PROPN
ejpam-5205	458	2	pure	pure	PROPN
ejpam-5205	458	3	appl	appl	PROPN
ejpam-5205	458	4	.	.	PROPN
ejpam-5205	458	5	math	math	PROPN
ejpam-5205	458	6	,	,	PUNCT
ejpam-5205	458	7	17	17	NUM
ejpam-5205	458	8	(	(	PUNCT
ejpam-5205	458	9	2	2	NUM
ejpam-5205	458	10	)	)	PUNCT
ejpam-5205	458	11	(	(	PUNCT
ejpam-5205	458	12	2024	2024	NUM
ejpam-5205	458	13	)	)	PUNCT
ejpam-5205	458	14	,	,	PUNCT
ejpam-5205	458	15	1335	1335	NUM
ejpam-5205	458	16	-	-	SYM
ejpam-5205	458	17	1351	1351	NUM
ejpam-5205	458	18	1346	1346	NUM
ejpam-5205	458	19	proof	proof	NOUN
ejpam-5205	458	20	.	.	PUNCT
ejpam-5205	459	1	let	let	VERB
ejpam-5205	459	2	k	k	NOUN
ejpam-5205	459	3	=	=	SYM
ejpam-5205	459	4	min	min	PROPN
ejpam-5205	459	5	{	{	PUNCT
ejpam-5205	459	6	ωcvr	ωcvr	PROPN
ejpam-5205	459	7	g	g	PROPN
ejpam-5205	459	8	(	(	PUNCT
ejpam-5205	459	9	g	g	PROPN
ejpam-5205	459	10	)	)	PUNCT
ejpam-5205	459	11	+	+	CCONJ
ejpam-5205	459	12	(	(	PUNCT
ejpam-5205	459	13	m−	m−	PROPN
ejpam-5205	459	14	1	1	NUM
ejpam-5205	459	15	)	)	PUNCT
ejpam-5205	459	16	∣∣s0	∣∣s0	NOUN
ejpam-5205	459	17	g	g	PROPN
ejpam-5205	460	1	|	|	NOUN
ejpam-5205	460	2	:	:	PUNCT
ejpam-5205	460	3	g	g	PROPN
ejpam-5205	460	4	is	be	AUX
ejpam-5205	460	5	a	a	DET
ejpam-5205	460	6	cvrdf	cvrdf	NOUN
ejpam-5205	460	7	on	on	ADP
ejpam-5205	460	8	g	g	PROPN
ejpam-5205	460	9	}	}	PUNCT
ejpam-5205	460	10	.	.	PUNCT
ejpam-5205	461	1	let	let	VERB
ejpam-5205	461	2	f	f	PROPN
ejpam-5205	461	3	=	=	SYM
ejpam-5205	461	4	(	(	PUNCT
ejpam-5205	461	5	v0	v0	PROPN
ejpam-5205	461	6	,	,	PUNCT
ejpam-5205	461	7	v1	v1	NOUN
ejpam-5205	461	8	,	,	PUNCT
ejpam-5205	461	9	v2	v2	PROPN
ejpam-5205	461	10	)	)	PUNCT
ejpam-5205	461	11	be	be	AUX
ejpam-5205	461	12	a	a	DET
ejpam-5205	461	13	γcvr	γcvr	NOUN
ejpam-5205	461	14	-	-	PUNCT
ejpam-5205	461	15	function	function	NOUN
ejpam-5205	461	16	on	on	ADP
ejpam-5205	461	17	g[km	g[km	PROPN
ejpam-5205	461	18	]	]	PUNCT
ejpam-5205	461	19	.	.	PUNCT
ejpam-5205	462	1	then	then	ADV
ejpam-5205	462	2	g	g	PROPN
ejpam-5205	462	3	=	=	PUNCT
ejpam-5205	462	4	(	(	PUNCT
ejpam-5205	462	5	v	v	NOUN
ejpam-5205	462	6	0	0	NUM
ejpam-5205	462	7	g	g	NOUN
ejpam-5205	462	8	,	,	PUNCT
ejpam-5205	462	9	v	v	NOUN
ejpam-5205	462	10	1	1	NUM
ejpam-5205	462	11	g	g	NOUN
ejpam-5205	462	12	,	,	PUNCT
ejpam-5205	462	13	v	v	NOUN
ejpam-5205	462	14	2	2	NUM
ejpam-5205	462	15	g	g	NOUN
ejpam-5205	462	16	)	)	PUNCT
ejpam-5205	462	17	is	be	AUX
ejpam-5205	462	18	a	a	DET
ejpam-5205	462	19	cvrdf	cvrdf	NOUN
ejpam-5205	462	20	on	on	ADP
ejpam-5205	462	21	g	g	NOUN
ejpam-5205	462	22	,	,	PUNCT
ejpam-5205	462	23	by	by	ADP
ejpam-5205	462	24	theorem	theorem	NOUN
ejpam-5205	462	25	10	10	NUM
ejpam-5205	462	26	(	(	PUNCT
ejpam-5205	462	27	i	i	NOUN
ejpam-5205	462	28	)	)	PUNCT
ejpam-5205	462	29	.	.	PUNCT
ejpam-5205	463	1	for	for	ADP
ejpam-5205	463	2	each	each	DET
ejpam-5205	463	3	x	x	SYM
ejpam-5205	463	4	∈	∈	PROPN
ejpam-5205	463	5	s1	s1	PROPN
ejpam-5205	463	6	g	g	NOUN
ejpam-5205	463	7	,	,	PUNCT
ejpam-5205	463	8	let	let	VERB
ejpam-5205	463	9	dx	dx	PROPN
ejpam-5205	463	10	=	=	PRON
ejpam-5205	463	11	{	{	PUNCT
ejpam-5205	463	12	(	(	PUNCT
ejpam-5205	463	13	x	x	NOUN
ejpam-5205	463	14	,	,	PUNCT
ejpam-5205	463	15	p	p	NOUN
ejpam-5205	463	16	)	)	PUNCT
ejpam-5205	463	17	∈	∈	NOUN
ejpam-5205	463	18	v1	v1	NOUN
ejpam-5205	463	19	:	:	PUNCT
ejpam-5205	463	20	p	p	X
ejpam-5205	463	21	∈	∈	PROPN
ejpam-5205	463	22	v	v	NOUN
ejpam-5205	463	23	(	(	PUNCT
ejpam-5205	463	24	km	km	NOUN
ejpam-5205	463	25	)	)	PUNCT
ejpam-5205	463	26	}	}	PUNCT
ejpam-5205	463	27	.	.	PUNCT
ejpam-5205	464	1	for	for	ADP
ejpam-5205	464	2	each	each	DET
ejpam-5205	464	3	y	y	PROPN
ejpam-5205	464	4	∈	∈	PROPN
ejpam-5205	464	5	s2	s2	PROPN
ejpam-5205	464	6	g	g	NOUN
ejpam-5205	464	7	,	,	PUNCT
ejpam-5205	464	8	let	let	VERB
ejpam-5205	464	9	ry	ry	VERB
ejpam-5205	464	10	=	=	PRON
ejpam-5205	464	11	{	{	PUNCT
ejpam-5205	464	12	(	(	PUNCT
ejpam-5205	464	13	y	y	NOUN
ejpam-5205	464	14	,	,	PUNCT
ejpam-5205	464	15	q	q	NOUN
ejpam-5205	464	16	)	)	PUNCT
ejpam-5205	464	17	∈	∈	NOUN
ejpam-5205	464	18	v2	v2	NOUN
ejpam-5205	464	19	:	:	PUNCT
ejpam-5205	464	20	q	q	PUNCT
ejpam-5205	464	21	∈	∈	PROPN
ejpam-5205	464	22	v	v	ADP
ejpam-5205	464	23	(	(	PUNCT
ejpam-5205	464	24	km	km	NOUN
ejpam-5205	464	25	)	)	PUNCT
ejpam-5205	464	26	}	}	PUNCT
ejpam-5205	464	27	.	.	PUNCT
ejpam-5205	465	1	since	since	SCONJ
ejpam-5205	465	2	f	f	PROPN
ejpam-5205	465	3	is	be	AUX
ejpam-5205	465	4	a	a	DET
ejpam-5205	465	5	γcvr	γcvr	NOUN
ejpam-5205	465	6	-	-	PUNCT
ejpam-5205	465	7	function	function	NOUN
ejpam-5205	465	8	,	,	PUNCT
ejpam-5205	465	9	s0	s0	PROPN
ejpam-5205	465	10	f	f	PROPN
ejpam-5205	466	1	⊆	⊆	NUM
ejpam-5205	466	2	v	v	ADP
ejpam-5205	466	3	1	1	NUM
ejpam-5205	466	4	g.	g.	NOUN
ejpam-5205	466	5	hence	hence	ADV
ejpam-5205	466	6	,	,	PUNCT
ejpam-5205	466	7	s0	s0	PROPN
ejpam-5205	466	8	f	f	PROPN
ejpam-5205	466	9	∩	∩	PROPN
ejpam-5205	466	10	s1	s1	PROPN
ejpam-5205	466	11	g	g	PROPN
ejpam-5205	466	12	=	=	PROPN
ejpam-5205	466	13	s0	s0	PROPN
ejpam-5205	466	14	f	f	PROPN
ejpam-5205	466	15	and	and	CCONJ
ejpam-5205	466	16	s0	s0	PROPN
ejpam-5205	466	17	f	f	PROPN
ejpam-5205	466	18	∩	∩	PROPN
ejpam-5205	466	19	s2	s2	VERB
ejpam-5205	466	20	g	g	NOUN
ejpam-5205	466	21	=	=	PUNCT
ejpam-5205	466	22	∅.	∅.	X
ejpam-5205	466	23	consequently	consequently	ADV
ejpam-5205	466	24	,	,	PUNCT
ejpam-5205	466	25	γcvr(g[km	γcvr(g[km	PROPN
ejpam-5205	466	26	]	]	X
ejpam-5205	466	27	)	)	PUNCT
ejpam-5205	466	28	=	=	PUNCT
ejpam-5205	466	29	ωg[km](f	ωg[km](f	NOUN
ejpam-5205	466	30	)	)	PUNCT
ejpam-5205	466	31	=	=	PUNCT
ejpam-5205	466	32	|v1|+	|v1|+	PRON
ejpam-5205	466	33	2|v2|	2|v2|	NUM
ejpam-5205	466	34	=	=	SYM
ejpam-5205	466	35	∑	∑	PUNCT
ejpam-5205	466	36	x∈s1	x∈s1	PROPN
ejpam-5205	466	37	g\s0	g\s0	PROPN
ejpam-5205	466	38	f	f	X
ejpam-5205	466	39	|dx|+	|dx|+	PROPN
ejpam-5205	466	40	∑	∑	PROPN
ejpam-5205	466	41	x∈s0	x∈s0	PROPN
ejpam-5205	466	42	f	f	PROPN
ejpam-5205	466	43	|dx|+	|dx|+	PROPN
ejpam-5205	466	44	2	2	NUM
ejpam-5205	466	45	∑	∑	NOUN
ejpam-5205	466	46	y∈s2	y∈s2	PROPN
ejpam-5205	466	47	g	g	PROPN
ejpam-5205	466	48	|ry|	|ry|	PROPN
ejpam-5205	466	49	≥	≥	PROPN
ejpam-5205	466	50	|s1	|s1	NOUN
ejpam-5205	466	51	g	g	PROPN
ejpam-5205	466	52	\	\	PROPN
ejpam-5205	466	53	s0	s0	PROPN
ejpam-5205	466	54	f	f	PROPN
ejpam-5205	466	55	|+m|s0	|+m|s0	PROPN
ejpam-5205	466	56	f	f	PROPN
ejpam-5205	466	57	|+	|+	X
ejpam-5205	466	58	2|s2	2|s2	PROPN
ejpam-5205	466	59	g|	g|	PROPN
ejpam-5205	466	60	=	=	NOUN
ejpam-5205	466	61	|s1	|s1	PROPN
ejpam-5205	466	62	g|+	g|+	PROPN
ejpam-5205	466	63	2|s2	2|s2	X
ejpam-5205	466	64	g|+	g|+	PROPN
ejpam-5205	466	65	(	(	PUNCT
ejpam-5205	466	66	m−	m−	PROPN
ejpam-5205	467	1	1)|s0	1)|s0	INTJ
ejpam-5205	467	2	f	f	PROPN
ejpam-5205	467	3	|	|	ADV
ejpam-5205	467	4	≥	≥	NOUN
ejpam-5205	467	5	|v	|v	X
ejpam-5205	467	6	1	1	NUM
ejpam-5205	468	1	g|+	g|+	PROPN
ejpam-5205	468	2	2|v	2|v	PROPN
ejpam-5205	468	3	2	2	NUM
ejpam-5205	468	4	g|+	g|+	PROPN
ejpam-5205	468	5	(	(	PUNCT
ejpam-5205	468	6	m−	m−	PROPN
ejpam-5205	468	7	1)|s0	1)|s0	NUM
ejpam-5205	468	8	g	g	NOUN
ejpam-5205	468	9	|	|	NOUN
ejpam-5205	468	10	=	=	SYM
ejpam-5205	468	11	ωcvr(g	ωcvr(g	NOUN
ejpam-5205	468	12	)	)	PUNCT
ejpam-5205	469	1	+	+	CCONJ
ejpam-5205	469	2	(	(	PUNCT
ejpam-5205	469	3	m−	m−	PROPN
ejpam-5205	469	4	1)|s0	1)|s0	NUM
ejpam-5205	469	5	g	g	PROPN
ejpam-5205	469	6	|	|	ADV
ejpam-5205	469	7	≥	≥	PROPN
ejpam-5205	469	8	k.	k.	PROPN
ejpam-5205	470	1	let	let	VERB
ejpam-5205	470	2	h	h	NOUN
ejpam-5205	470	3	=	=	PUNCT
ejpam-5205	470	4	(	(	PUNCT
ejpam-5205	470	5	w0,w1,w2	w0,w1,w2	ADV
ejpam-5205	470	6	)	)	PUNCT
ejpam-5205	470	7	be	be	AUX
ejpam-5205	470	8	a	a	DET
ejpam-5205	470	9	cvrdf	cvrdf	NOUN
ejpam-5205	470	10	on	on	ADP
ejpam-5205	470	11	g	g	PROPN
ejpam-5205	470	12	such	such	ADJ
ejpam-5205	470	13	that	that	SCONJ
ejpam-5205	470	14	k	k	PROPN
ejpam-5205	471	1	=	=	PUNCT
ejpam-5205	471	2	min{ωcvr	min{ωcvr	X
ejpam-5205	471	3	g	g	PROPN
ejpam-5205	471	4	(	(	PUNCT
ejpam-5205	471	5	g	g	NOUN
ejpam-5205	471	6	)	)	PUNCT
ejpam-5205	471	7	+	+	CCONJ
ejpam-5205	471	8	(	(	PUNCT
ejpam-5205	471	9	m	m	VERB
ejpam-5205	471	10	−	−	NOUN
ejpam-5205	471	11	1	1	NUM
ejpam-5205	471	12	)	)	PUNCT
ejpam-5205	471	13	∣∣s0	∣∣s0	NOUN
ejpam-5205	471	14	g	g	PROPN
ejpam-5205	471	15	∣∣	∣∣	NUM
ejpam-5205	471	16	:	:	PUNCT
ejpam-5205	471	17	g	g	NOUN
ejpam-5205	471	18	is	be	AUX
ejpam-5205	471	19	a	a	DET
ejpam-5205	471	20	cvrdf	cvrdf	NOUN
ejpam-5205	471	21	on	on	ADP
ejpam-5205	471	22	g	g	NOUN
ejpam-5205	471	23	}	}	PUNCT
ejpam-5205	471	24	.	.	PUNCT
ejpam-5205	472	1	by	by	ADP
ejpam-5205	472	2	lemma	lemma	PROPN
ejpam-5205	472	3	2	2	NUM
ejpam-5205	472	4	,	,	PUNCT
ejpam-5205	472	5	w1	w1	NOUN
ejpam-5205	472	6	⊆	⊆	NUM
ejpam-5205	472	7	s0	s0	PROPN
ejpam-5205	472	8	g	g	PROPN
ejpam-5205	472	9	.	.	PUNCT
ejpam-5205	473	1	let	let	VERB
ejpam-5205	473	2	p	p	PRON
ejpam-5205	473	3	∈	∈	PROPN
ejpam-5205	473	4	v	v	NOUN
ejpam-5205	473	5	(	(	PUNCT
ejpam-5205	473	6	km	km	PROPN
ejpam-5205	473	7	)	)	PUNCT
ejpam-5205	473	8	.	.	PUNCT
ejpam-5205	474	1	set	set	VERB
ejpam-5205	474	2	v1	v1	NOUN
ejpam-5205	474	3	=	=	SYM
ejpam-5205	474	4	(	(	PUNCT
ejpam-5205	474	5	w1	w1	NOUN
ejpam-5205	474	6	×	×	NOUN
ejpam-5205	474	7	{	{	PUNCT
ejpam-5205	474	8	p	p	NOUN
ejpam-5205	474	9	}	}	PUNCT
ejpam-5205	474	10	)	)	PUNCT
ejpam-5205	474	11	∪	∪	ADP
ejpam-5205	474	12	[	[	PUNCT
ejpam-5205	474	13	(	(	PUNCT
ejpam-5205	474	14	(	(	PUNCT
ejpam-5205	474	15	w1	w1	NOUN
ejpam-5205	474	16	∪w2	∪w2	NOUN
ejpam-5205	474	17	)	)	PUNCT
ejpam-5205	474	18	∩	∩	PROPN
ejpam-5205	474	19	s0	s0	PROPN
ejpam-5205	474	20	g	g	PROPN
ejpam-5205	474	21	)	)	PUNCT
ejpam-5205	474	22	×	×	NOUN
ejpam-5205	474	23	(	(	PUNCT
ejpam-5205	474	24	v	v	NOUN
ejpam-5205	474	25	(	(	PUNCT
ejpam-5205	474	26	km	km	NOUN
ejpam-5205	474	27	)	)	PUNCT
ejpam-5205	474	28	\	\	NOUN
ejpam-5205	474	29	{	{	PUNCT
ejpam-5205	474	30	p	p	X
ejpam-5205	474	31	}	}	PUNCT
ejpam-5205	474	32	)	)	PUNCT
ejpam-5205	474	33	]	]	PUNCT
ejpam-5205	474	34	,	,	PUNCT
ejpam-5205	474	35	v2	v2	PROPN
ejpam-5205	474	36	=	=	SYM
ejpam-5205	474	37	w2	w2	NOUN
ejpam-5205	474	38	×	×	NOUN
ejpam-5205	474	39	{	{	PUNCT
ejpam-5205	474	40	p	p	NOUN
ejpam-5205	474	41	}	}	PUNCT
ejpam-5205	474	42	,	,	PUNCT
ejpam-5205	474	43	and	and	CCONJ
ejpam-5205	474	44	v0	v0	NOUN
ejpam-5205	474	45	=	=	SYM
ejpam-5205	474	46	(	(	PUNCT
ejpam-5205	474	47	w0	w0	PROPN
ejpam-5205	474	48	×	×	PROPN
ejpam-5205	474	49	v	v	NOUN
ejpam-5205	474	50	(	(	PUNCT
ejpam-5205	474	51	km	km	NOUN
ejpam-5205	474	52	)	)	PUNCT
ejpam-5205	474	53	)	)	PUNCT
ejpam-5205	474	54	∪	∪	X
ejpam-5205	474	55	(	(	PUNCT
ejpam-5205	474	56	(	(	PUNCT
ejpam-5205	474	57	w1	w1	NOUN
ejpam-5205	474	58	\	\	NOUN
ejpam-5205	474	59	s0	s0	PROPN
ejpam-5205	474	60	g	g	PROPN
ejpam-5205	474	61	)	)	PUNCT
ejpam-5205	474	62	×	×	PROPN
ejpam-5205	474	63	v	v	NOUN
ejpam-5205	474	64	(	(	PUNCT
ejpam-5205	474	65	km	km	PROPN
ejpam-5205	474	66	)	)	PUNCT
ejpam-5205	474	67	)	)	PUNCT
ejpam-5205	474	68	.	.	PUNCT
ejpam-5205	475	1	let	let	VERB
ejpam-5205	475	2	f	f	PROPN
ejpam-5205	475	3	=	=	SYM
ejpam-5205	475	4	(	(	PUNCT
ejpam-5205	475	5	v0	v0	PROPN
ejpam-5205	475	6	,	,	PUNCT
ejpam-5205	475	7	v1	v1	NOUN
ejpam-5205	475	8	,	,	PUNCT
ejpam-5205	475	9	v2	v2	PROPN
ejpam-5205	475	10	)	)	PUNCT
ejpam-5205	475	11	.	.	PUNCT
ejpam-5205	476	1	then	then	ADV
ejpam-5205	476	2	v	v	X
ejpam-5205	476	3	0	0	NUM
ejpam-5205	476	4	g	g	NOUN
ejpam-5205	476	5	=	=	SYM
ejpam-5205	476	6	w0	w0	PROPN
ejpam-5205	476	7	,	,	PUNCT
ejpam-5205	476	8	v	v	NOUN
ejpam-5205	476	9	1	1	NUM
ejpam-5205	476	10	g	g	NOUN
ejpam-5205	476	11	=	=	PROPN
ejpam-5205	476	12	w1	w1	NOUN
ejpam-5205	476	13	,	,	PUNCT
ejpam-5205	476	14	and	and	CCONJ
ejpam-5205	476	15	v	v	ADP
ejpam-5205	476	16	2	2	NUM
ejpam-5205	476	17	g	g	NOUN
ejpam-5205	476	18	=	=	NOUN
ejpam-5205	476	19	w2	w2	NOUN
ejpam-5205	476	20	.	.	PUNCT
ejpam-5205	477	1	hence	hence	ADV
ejpam-5205	477	2	,	,	PUNCT
ejpam-5205	477	3	g	g	PROPN
ejpam-5205	477	4	=	=	PUNCT
ejpam-5205	477	5	h	h	NOUN
ejpam-5205	477	6	is	be	AUX
ejpam-5205	477	7	a	a	DET
ejpam-5205	477	8	cvrdf	cvrdf	NOUN
ejpam-5205	477	9	on	on	ADP
ejpam-5205	477	10	g.	g.	PROPN
ejpam-5205	477	11	also	also	ADV
ejpam-5205	477	12	,	,	PUNCT
ejpam-5205	477	13	s1	s1	PROPN
ejpam-5205	477	14	g	g	PROPN
ejpam-5205	477	15	∪	∪	PROPN
ejpam-5205	477	16	s2	s2	NOUN
ejpam-5205	477	17	g	g	NOUN
ejpam-5205	477	18	=	=	NOUN
ejpam-5205	477	19	w1	w1	NOUN
ejpam-5205	477	20	∪w2	∪w2	NOUN
ejpam-5205	477	21	is	be	AUX
ejpam-5205	477	22	convex	convex	ADJ
ejpam-5205	477	23	in	in	ADP
ejpam-5205	477	24	g	g	PROPN
ejpam-5205	477	25	since	since	SCONJ
ejpam-5205	477	26	h	h	NOUN
ejpam-5205	477	27	is	be	AUX
ejpam-5205	477	28	a	a	DET
ejpam-5205	477	29	cvrdf	cvrdf	NOUN
ejpam-5205	477	30	on	on	ADP
ejpam-5205	477	31	g.	g.	PROPN
ejpam-5205	477	32	clearly	clearly	ADV
ejpam-5205	477	33	,	,	PUNCT
ejpam-5205	477	34	(	(	PUNCT
ejpam-5205	477	35	iii	iii	NOUN
ejpam-5205	477	36	)	)	PUNCT
ejpam-5205	477	37	and	and	CCONJ
ejpam-5205	477	38	(	(	PUNCT
ejpam-5205	477	39	iv	iv	X
ejpam-5205	477	40	)	)	PUNCT
ejpam-5205	477	41	of	of	ADP
ejpam-5205	477	42	theorem	theorem	NOUN
ejpam-5205	477	43	10	10	NUM
ejpam-5205	477	44	is	be	AUX
ejpam-5205	477	45	satisfied	satisfied	ADJ
ejpam-5205	477	46	.	.	PUNCT
ejpam-5205	478	1	hence	hence	ADV
ejpam-5205	478	2	,	,	PUNCT
ejpam-5205	478	3	f	f	PROPN
ejpam-5205	478	4	is	be	AUX
ejpam-5205	478	5	a	a	DET
ejpam-5205	478	6	cvrdf	cvrdf	NOUN
ejpam-5205	478	7	on	on	ADP
ejpam-5205	478	8	g[km	g[km	PROPN
ejpam-5205	478	9	]	]	PUNCT
ejpam-5205	478	10	and	and	CCONJ
ejpam-5205	478	11	γcvr(g[km	γcvr(g[km	PROPN
ejpam-5205	478	12	]	]	PUNCT
ejpam-5205	478	13	)	)	PUNCT
ejpam-5205	478	14	≤	≤	NUM
ejpam-5205	478	15	ωg[km](f	ωg[km](f	NOUN
ejpam-5205	478	16	)	)	PUNCT
ejpam-5205	478	17	=	=	PUNCT
ejpam-5205	478	18	|v1|+	|v1|+	PRON
ejpam-5205	478	19	2|v2|	2|v2|	NUM
ejpam-5205	478	20	=	=	SYM
ejpam-5205	478	21	|w1|+	|w1|+	PROPN
ejpam-5205	478	22	(	(	PUNCT
ejpam-5205	478	23	m−	m−	PROPN
ejpam-5205	478	24	1)|(w1	1)|(w1	NUM
ejpam-5205	478	25	∪w2	∪w2	NOUN
ejpam-5205	478	26	)	)	PUNCT
ejpam-5205	478	27	∩	∩	PROPN
ejpam-5205	478	28	s0	s0	PROPN
ejpam-5205	478	29	g	g	PROPN
ejpam-5205	478	30	|+	|+	PROPN
ejpam-5205	478	31	2|w2|	2|w2|	PROPN
ejpam-5205	478	32	≤	≤	NUM
ejpam-5205	478	33	|w1|+	|w1|+	PROPN
ejpam-5205	478	34	2|w2|+	2|w2|+	PROPN
ejpam-5205	478	35	(	(	PUNCT
ejpam-5205	478	36	m−	m−	PROPN
ejpam-5205	478	37	1)|s0	1)|s0	NUM
ejpam-5205	478	38	g	g	NOUN
ejpam-5205	479	1	|	|	ADV
ejpam-5205	479	2	=	=	SYM
ejpam-5205	479	3	ωcvr	ωcvr	PROPN
ejpam-5205	479	4	g	g	PROPN
ejpam-5205	479	5	(	(	PUNCT
ejpam-5205	479	6	g	g	PROPN
ejpam-5205	479	7	)	)	PUNCT
ejpam-5205	479	8	+	+	CCONJ
ejpam-5205	479	9	(	(	PUNCT
ejpam-5205	479	10	m−	m−	PROPN
ejpam-5205	479	11	1)|s0	1)|s0	NUM
ejpam-5205	479	12	g	g	NOUN
ejpam-5205	479	13	|	|	ADV
ejpam-5205	479	14	=	=	PUNCT
ejpam-5205	479	15	k.	k.	PROPN
ejpam-5205	480	1	this	this	PRON
ejpam-5205	480	2	proves	prove	VERB
ejpam-5205	480	3	the	the	DET
ejpam-5205	480	4	desired	desire	VERB
ejpam-5205	480	5	equality	equality	NOUN
ejpam-5205	480	6	.	.	PUNCT
ejpam-5205	481	1	for	for	ADP
ejpam-5205	481	2	each	each	DET
ejpam-5205	481	3	x	x	SYM
ejpam-5205	481	4	∈	∈	PROPN
ejpam-5205	481	5	s1	s1	NOUN
ejpam-5205	481	6	g	g	PROPN
ejpam-5205	481	7	∪	∪	PROPN
ejpam-5205	481	8	s2	s2	PROPN
ejpam-5205	481	9	g	g	NOUN
ejpam-5205	481	10	,	,	PUNCT
ejpam-5205	481	11	we	we	PRON
ejpam-5205	481	12	write	write	VERB
ejpam-5205	481	13	t	t	PROPN
ejpam-5205	481	14	0	0	PUNCT
ejpam-5205	482	1	x	x	SYM
ejpam-5205	482	2	=	=	PRON
ejpam-5205	482	3	{	{	PUNCT
ejpam-5205	482	4	p	p	NOUN
ejpam-5205	482	5	∈	∈	PROPN
ejpam-5205	482	6	v	v	ADP
ejpam-5205	482	7	(	(	PUNCT
ejpam-5205	482	8	h	h	NOUN
ejpam-5205	482	9	)	)	PUNCT
ejpam-5205	482	10	:	:	PUNCT
ejpam-5205	482	11	(	(	PUNCT
ejpam-5205	482	12	x	x	X
ejpam-5205	482	13	,	,	PUNCT
ejpam-5205	482	14	p	p	NOUN
ejpam-5205	482	15	)	)	PUNCT
ejpam-5205	482	16	∈	∈	PROPN
ejpam-5205	482	17	v0	v0	NOUN
ejpam-5205	482	18	}	}	PUNCT
ejpam-5205	482	19	,	,	PUNCT
ejpam-5205	482	20	t	t	PROPN
ejpam-5205	482	21	1	1	NUM
ejpam-5205	482	22	x	x	X
ejpam-5205	482	23	=	=	PRON
ejpam-5205	482	24	{	{	PUNCT
ejpam-5205	482	25	p	p	NOUN
ejpam-5205	482	26	∈	∈	PROPN
ejpam-5205	482	27	v	v	ADP
ejpam-5205	482	28	(	(	PUNCT
ejpam-5205	482	29	h	h	NOUN
ejpam-5205	482	30	)	)	PUNCT
ejpam-5205	482	31	:	:	PUNCT
ejpam-5205	482	32	(	(	PUNCT
ejpam-5205	482	33	x	x	X
ejpam-5205	482	34	,	,	PUNCT
ejpam-5205	482	35	p	p	NOUN
ejpam-5205	482	36	)	)	PUNCT
ejpam-5205	482	37	∈	∈	PROPN
ejpam-5205	482	38	v1	v1	NOUN
ejpam-5205	482	39	}	}	PUNCT
ejpam-5205	482	40	,	,	PUNCT
ejpam-5205	482	41	and	and	CCONJ
ejpam-5205	482	42	t	t	X
ejpam-5205	482	43	2	2	NUM
ejpam-5205	482	44	x	x	X
ejpam-5205	482	45	=	=	PRON
ejpam-5205	482	46	{	{	PUNCT
ejpam-5205	482	47	p	p	NOUN
ejpam-5205	482	48	∈	∈	PROPN
ejpam-5205	482	49	v	v	ADP
ejpam-5205	482	50	(	(	PUNCT
ejpam-5205	482	51	h	h	NOUN
ejpam-5205	482	52	)	)	PUNCT
ejpam-5205	482	53	:	:	PUNCT
ejpam-5205	482	54	(	(	PUNCT
ejpam-5205	482	55	x	x	X
ejpam-5205	482	56	,	,	PUNCT
ejpam-5205	482	57	p	p	NOUN
ejpam-5205	482	58	)	)	PUNCT
ejpam-5205	482	59	∈	∈	PROPN
ejpam-5205	482	60	v2	v2	PROPN
ejpam-5205	482	61	}	}	PUNCT
ejpam-5205	482	62	.	.	PUNCT
ejpam-5205	483	1	theorem	theorem	NOUN
ejpam-5205	483	2	11	11	NUM
ejpam-5205	483	3	.	.	PUNCT
ejpam-5205	484	1	let	let	VERB
ejpam-5205	484	2	g	g	NOUN
ejpam-5205	484	3	and	and	CCONJ
ejpam-5205	484	4	h	h	NOUN
ejpam-5205	484	5	be	be	AUX
ejpam-5205	484	6	connected	connect	VERB
ejpam-5205	484	7	non	non	ADJ
ejpam-5205	484	8	-	-	ADJ
ejpam-5205	484	9	complete	complete	ADJ
ejpam-5205	484	10	graphs	graph	NOUN
ejpam-5205	484	11	with	with	ADP
ejpam-5205	484	12	γcl(g	γcl(g	NOUN
ejpam-5205	484	13	)	)	PUNCT
ejpam-5205	484	14	≥	≥	NOUN
ejpam-5205	485	1	2	2	NUM
ejpam-5205	485	2	.	.	PUNCT
ejpam-5205	485	3	then	then	ADV
ejpam-5205	485	4	f	f	PROPN
ejpam-5205	485	5	=	=	SYM
ejpam-5205	485	6	(	(	PUNCT
ejpam-5205	485	7	v0	v0	PROPN
ejpam-5205	485	8	,	,	PUNCT
ejpam-5205	485	9	v1	v1	NOUN
ejpam-5205	485	10	,	,	PUNCT
ejpam-5205	485	11	v2	v2	PROPN
ejpam-5205	485	12	)	)	PUNCT
ejpam-5205	485	13	is	be	AUX
ejpam-5205	485	14	cvrdf	cvrdf	NOUN
ejpam-5205	485	15	on	on	ADP
ejpam-5205	485	16	g[h	g[h	NOUN
ejpam-5205	485	17	]	]	PUNCT
ejpam-5205	485	18	if	if	SCONJ
ejpam-5205	486	1	and	and	CCONJ
ejpam-5205	486	2	only	only	ADV
ejpam-5205	486	3	if	if	SCONJ
ejpam-5205	486	4	each	each	PRON
ejpam-5205	486	5	of	of	ADP
ejpam-5205	486	6	the	the	DET
ejpam-5205	486	7	following	follow	VERB
ejpam-5205	486	8	conditions	condition	NOUN
ejpam-5205	486	9	hold	hold	VERB
ejpam-5205	486	10	:	:	PUNCT
ejpam-5205	486	11	(	(	PUNCT
ejpam-5205	486	12	i	i	NOUN
ejpam-5205	486	13	)	)	PUNCT
ejpam-5205	486	14	s1	s1	PROPN
ejpam-5205	486	15	g	g	PROPN
ejpam-5205	486	16	∪	∪	PROPN
ejpam-5205	486	17	s2	s2	PROPN
ejpam-5205	486	18	g	g	NOUN
ejpam-5205	486	19	is	be	AUX
ejpam-5205	486	20	a	a	DET
ejpam-5205	486	21	clique	clique	NOUN
ejpam-5205	486	22	dominating	dominating	NOUN
ejpam-5205	486	23	set	set	VERB
ejpam-5205	486	24	in	in	ADP
ejpam-5205	486	25	g.	g.	PROPN
ejpam-5205	486	26	(	(	PUNCT
ejpam-5205	486	27	ii	ii	PROPN
ejpam-5205	486	28	)	)	PUNCT
ejpam-5205	486	29	t	t	PROPN
ejpam-5205	486	30	1	1	NUM
ejpam-5205	486	31	x	x	SYM
ejpam-5205	486	32	∪	∪	ADP
ejpam-5205	486	33	t	t	PROPN
ejpam-5205	486	34	2	2	NUM
ejpam-5205	486	35	x	x	X
ejpam-5205	486	36	is	be	AUX
ejpam-5205	486	37	a	a	DET
ejpam-5205	486	38	clique	clique	NOUN
ejpam-5205	486	39	in	in	ADP
ejpam-5205	486	40	h	h	NOUN
ejpam-5205	486	41	for	for	ADP
ejpam-5205	486	42	each	each	DET
ejpam-5205	486	43	x	x	SYM
ejpam-5205	486	44	∈	∈	PROPN
ejpam-5205	486	45	s1	s1	NOUN
ejpam-5205	486	46	g	g	PROPN
ejpam-5205	486	47	∪	∪	PROPN
ejpam-5205	486	48	s2	s2	PROPN
ejpam-5205	486	49	g.	g.	PROPN
ejpam-5205	486	50	r.	r.	PROPN
ejpam-5205	486	51	fortosa	fortosa	PROPN
ejpam-5205	486	52	,	,	PUNCT
ejpam-5205	486	53	s.	s.	PROPN
ejpam-5205	486	54	canoy	canoy	PROPN
ejpam-5205	486	55	jr	jr	PROPN
ejpam-5205	486	56	.	.	PROPN
ejpam-5205	486	57	/	/	SYM
ejpam-5205	486	58	eur	eur	PROPN
ejpam-5205	486	59	.	.	PUNCT
ejpam-5205	487	1	j.	j.	PROPN
ejpam-5205	487	2	pure	pure	PROPN
ejpam-5205	487	3	appl	appl	PROPN
ejpam-5205	487	4	.	.	PROPN
ejpam-5205	487	5	math	math	PROPN
ejpam-5205	487	6	,	,	PUNCT
ejpam-5205	487	7	17	17	NUM
ejpam-5205	487	8	(	(	PUNCT
ejpam-5205	487	9	2	2	NUM
ejpam-5205	487	10	)	)	PUNCT
ejpam-5205	487	11	(	(	PUNCT
ejpam-5205	487	12	2024	2024	NUM
ejpam-5205	487	13	)	)	PUNCT
ejpam-5205	487	14	,	,	PUNCT
ejpam-5205	487	15	1335	1335	NUM
ejpam-5205	487	16	-	-	SYM
ejpam-5205	487	17	1351	1351	NUM
ejpam-5205	487	18	1347	1347	NUM
ejpam-5205	487	19	(	(	PUNCT
ejpam-5205	487	20	iii	iii	NOUN
ejpam-5205	487	21	)	)	PUNCT
ejpam-5205	487	22	t	t	NOUN
ejpam-5205	487	23	2	2	NUM
ejpam-5205	487	24	x	x	NOUN
ejpam-5205	487	25	is	be	AUX
ejpam-5205	487	26	a	a	DET
ejpam-5205	487	27	(	(	PUNCT
ejpam-5205	487	28	clique	clique	NOUN
ejpam-5205	487	29	)	)	PUNCT
ejpam-5205	487	30	dominating	dominating	NOUN
ejpam-5205	487	31	set	set	VERB
ejpam-5205	487	32	in	in	ADP
ejpam-5205	487	33	h	h	NOUN
ejpam-5205	487	34	for	for	ADP
ejpam-5205	487	35	each	each	DET
ejpam-5205	487	36	x	x	SYM
ejpam-5205	487	37	∈	∈	PROPN
ejpam-5205	487	38	s0	s0	NOUN
ejpam-5205	487	39	g	g	PROPN
ejpam-5205	487	40	\ng(s	\ng(s	NUM
ejpam-5205	487	41	2	2	NUM
ejpam-5205	487	42	g	g	NOUN
ejpam-5205	487	43	)	)	PUNCT
ejpam-5205	487	44	.	.	PUNCT
ejpam-5205	488	1	proof	proof	NOUN
ejpam-5205	488	2	.	.	PUNCT
ejpam-5205	489	1	let	let	VERB
ejpam-5205	489	2	f	f	PROPN
ejpam-5205	489	3	=	=	SYM
ejpam-5205	489	4	(	(	PUNCT
ejpam-5205	489	5	v0	v0	PROPN
ejpam-5205	489	6	,	,	PUNCT
ejpam-5205	489	7	v1	v1	NOUN
ejpam-5205	489	8	,	,	PUNCT
ejpam-5205	489	9	v2	v2	PROPN
ejpam-5205	489	10	)	)	PUNCT
ejpam-5205	489	11	be	be	AUX
ejpam-5205	489	12	a	a	DET
ejpam-5205	489	13	cvrdf	cvrdf	NOUN
ejpam-5205	489	14	on	on	ADP
ejpam-5205	489	15	g[h	g[h	NOUN
ejpam-5205	489	16	]	]	PUNCT
ejpam-5205	490	1	such	such	ADJ
ejpam-5205	490	2	that	that	SCONJ
ejpam-5205	490	3	γcl(g	γcl(g	NUM
ejpam-5205	490	4	)	)	PUNCT
ejpam-5205	490	5	≥	≥	NOUN
ejpam-5205	490	6	2	2	NUM
ejpam-5205	490	7	.	.	PUNCT
ejpam-5205	490	8	then	then	ADV
ejpam-5205	490	9	(	(	PUNCT
ejpam-5205	490	10	i	i	NOUN
ejpam-5205	490	11	)	)	PUNCT
ejpam-5205	490	12	and	and	CCONJ
ejpam-5205	490	13	(	(	PUNCT
ejpam-5205	490	14	ii	ii	NOUN
ejpam-5205	490	15	)	)	PUNCT
ejpam-5205	490	16	hold	hold	VERB
ejpam-5205	490	17	by	by	ADP
ejpam-5205	490	18	theorem	theorem	NOUN
ejpam-5205	490	19	4	4	NUM
ejpam-5205	490	20	.	.	PUNCT
ejpam-5205	491	1	now	now	ADV
ejpam-5205	491	2	,	,	PUNCT
ejpam-5205	491	3	let	let	VERB
ejpam-5205	491	4	x	x	PUNCT
ejpam-5205	491	5	∈	∈	NOUN
ejpam-5205	491	6	s0	s0	NOUN
ejpam-5205	491	7	g	g	PROPN
ejpam-5205	491	8	\ng(s	\ng(s	NUM
ejpam-5205	491	9	2	2	NUM
ejpam-5205	491	10	g	g	NOUN
ejpam-5205	491	11	)	)	PUNCT
ejpam-5205	491	12	and	and	CCONJ
ejpam-5205	491	13	let	let	VERB
ejpam-5205	491	14	p	p	PRON
ejpam-5205	491	15	∈	∈	PROPN
ejpam-5205	491	16	v	v	ADP
ejpam-5205	491	17	(	(	PUNCT
ejpam-5205	491	18	h	h	NOUN
ejpam-5205	491	19	)	)	PUNCT
ejpam-5205	491	20	\	\	PUNCT
ejpam-5205	492	1	(	(	PUNCT
ejpam-5205	492	2	t	t	NOUN
ejpam-5205	492	3	1	1	NUM
ejpam-5205	492	4	x	x	SYM
ejpam-5205	492	5	∪	∪	ADP
ejpam-5205	492	6	t	t	PROPN
ejpam-5205	492	7	2	2	NUM
ejpam-5205	492	8	x	x	X
ejpam-5205	492	9	)	)	PUNCT
ejpam-5205	492	10	.	.	PUNCT
ejpam-5205	493	1	since	since	SCONJ
ejpam-5205	493	2	f	f	PROPN
ejpam-5205	493	3	is	be	AUX
ejpam-5205	493	4	a	a	DET
ejpam-5205	493	5	cvrdf	cvrdf	NOUN
ejpam-5205	493	6	on	on	ADP
ejpam-5205	493	7	g[h	g[h	PROPN
ejpam-5205	493	8	]	]	PUNCT
ejpam-5205	493	9	,	,	PUNCT
ejpam-5205	493	10	there	there	PRON
ejpam-5205	493	11	exists	exist	VERB
ejpam-5205	493	12	(	(	PUNCT
ejpam-5205	493	13	x	x	X
ejpam-5205	493	14	,	,	PUNCT
ejpam-5205	493	15	q	q	NOUN
ejpam-5205	493	16	)	)	PUNCT
ejpam-5205	493	17	∈	∈	NOUN
ejpam-5205	493	18	v2	v2	NOUN
ejpam-5205	493	19	such	such	ADJ
ejpam-5205	493	20	that	that	SCONJ
ejpam-5205	493	21	(	(	PUNCT
ejpam-5205	493	22	x	x	NOUN
ejpam-5205	493	23	,	,	PUNCT
ejpam-5205	493	24	p)(x	p)(x	NOUN
ejpam-5205	493	25	,	,	PUNCT
ejpam-5205	493	26	q	q	X
ejpam-5205	493	27	)	)	PUNCT
ejpam-5205	493	28	∈	∈	NOUN
ejpam-5205	493	29	e(g[h	e(g[h	NOUN
ejpam-5205	493	30	]	]	PUNCT
ejpam-5205	493	31	)	)	PUNCT
ejpam-5205	493	32	.	.	PUNCT
ejpam-5205	494	1	hence	hence	ADV
ejpam-5205	494	2	,	,	PUNCT
ejpam-5205	494	3	x	x	PUNCT
ejpam-5205	494	4	∈	∈	PROPN
ejpam-5205	494	5	s2	s2	NOUN
ejpam-5205	494	6	g	g	NOUN
ejpam-5205	494	7	and	and	CCONJ
ejpam-5205	494	8	there	there	PRON
ejpam-5205	494	9	exists	exist	VERB
ejpam-5205	494	10	q	q	PROPN
ejpam-5205	494	11	∈	∈	PROPN
ejpam-5205	494	12	t	t	NOUN
ejpam-5205	494	13	2	2	NUM
ejpam-5205	494	14	x	x	NOUN
ejpam-5205	494	15	such	such	ADJ
ejpam-5205	494	16	that	that	DET
ejpam-5205	494	17	pq	pq	PROPN
ejpam-5205	494	18	∈	∈	PROPN
ejpam-5205	494	19	e(h	e(h	PROPN
ejpam-5205	494	20	)	)	PUNCT
ejpam-5205	494	21	.	.	PUNCT
ejpam-5205	495	1	it	it	PRON
ejpam-5205	495	2	follows	follow	VERB
ejpam-5205	495	3	that	that	SCONJ
ejpam-5205	495	4	t	t	PROPN
ejpam-5205	495	5	2	2	NUM
ejpam-5205	495	6	x	x	NOUN
ejpam-5205	495	7	is	be	AUX
ejpam-5205	495	8	a	a	DET
ejpam-5205	495	9	dominating	dominating	NOUN
ejpam-5205	495	10	set	set	NOUN
ejpam-5205	495	11	in	in	ADP
ejpam-5205	495	12	h	h	NOUN
ejpam-5205	495	13	,	,	PUNCT
ejpam-5205	495	14	showing	show	VERB
ejpam-5205	495	15	that	that	SCONJ
ejpam-5205	495	16	(	(	PUNCT
ejpam-5205	495	17	iii	iii	NOUN
ejpam-5205	495	18	)	)	PUNCT
ejpam-5205	495	19	holds	hold	VERB
ejpam-5205	495	20	.	.	PUNCT
ejpam-5205	496	1	for	for	ADP
ejpam-5205	496	2	the	the	DET
ejpam-5205	496	3	converse	converse	NOUN
ejpam-5205	496	4	,	,	PUNCT
ejpam-5205	496	5	suppose	suppose	VERB
ejpam-5205	496	6	that	that	SCONJ
ejpam-5205	496	7	(	(	PUNCT
ejpam-5205	496	8	i	i	NOUN
ejpam-5205	496	9	)	)	PUNCT
ejpam-5205	496	10	,	,	PUNCT
ejpam-5205	496	11	(	(	PUNCT
ejpam-5205	496	12	ii	ii	NOUN
ejpam-5205	496	13	)	)	PUNCT
ejpam-5205	496	14	,	,	PUNCT
ejpam-5205	496	15	and	and	CCONJ
ejpam-5205	496	16	(	(	PUNCT
ejpam-5205	496	17	iii	iii	NOUN
ejpam-5205	496	18	)	)	PUNCT
ejpam-5205	496	19	hold	hold	NOUN
ejpam-5205	496	20	.	.	PUNCT
ejpam-5205	497	1	let	let	VERB
ejpam-5205	497	2	(	(	PUNCT
ejpam-5205	497	3	x	x	X
ejpam-5205	497	4	,	,	PUNCT
ejpam-5205	497	5	p	p	NOUN
ejpam-5205	497	6	)	)	PUNCT
ejpam-5205	497	7	∈	∈	PROPN
ejpam-5205	497	8	v0	v0	NOUN
ejpam-5205	497	9	.	.	PUNCT
ejpam-5205	498	1	then	then	ADV
ejpam-5205	498	2	x	x	SYM
ejpam-5205	498	3	∈	∈	PROPN
ejpam-5205	498	4	s0	s0	PROPN
ejpam-5205	498	5	g.	g.	PROPN
ejpam-5205	498	6	if	if	SCONJ
ejpam-5205	498	7	x	x	SYM
ejpam-5205	498	8	∈	∈	PROPN
ejpam-5205	498	9	(	(	PUNCT
ejpam-5205	498	10	ng(s	ng(s	NOUN
ejpam-5205	498	11	2	2	NUM
ejpam-5205	498	12	g	g	NOUN
ejpam-5205	498	13	)	)	PUNCT
ejpam-5205	498	14	)	)	PUNCT
ejpam-5205	498	15	,	,	PUNCT
ejpam-5205	498	16	then	then	ADV
ejpam-5205	498	17	there	there	PRON
ejpam-5205	498	18	exists	exist	VERB
ejpam-5205	498	19	y	y	PROPN
ejpam-5205	498	20	∈	∈	PROPN
ejpam-5205	498	21	s2	s2	PROPN
ejpam-5205	498	22	g	g	NOUN
ejpam-5205	498	23	∩	∩	NOUN
ejpam-5205	498	24	ng(x	ng(x	NUM
ejpam-5205	498	25	)	)	PUNCT
ejpam-5205	498	26	.	.	PUNCT
ejpam-5205	499	1	let	let	VERB
ejpam-5205	499	2	r	r	NOUN
ejpam-5205	499	3	∈	∈	PROPN
ejpam-5205	499	4	t	t	NOUN
ejpam-5205	499	5	2	2	NUM
ejpam-5205	499	6	y	y	NOUN
ejpam-5205	499	7	.	.	PUNCT
ejpam-5205	500	1	then	then	ADV
ejpam-5205	500	2	(	(	PUNCT
ejpam-5205	500	3	y	y	NOUN
ejpam-5205	500	4	,	,	PUNCT
ejpam-5205	500	5	r	r	NOUN
ejpam-5205	500	6	)	)	PUNCT
ejpam-5205	500	7	∈	∈	NOUN
ejpam-5205	500	8	v2	v2	NOUN
ejpam-5205	500	9	∩	∩	NOUN
ejpam-5205	500	10	ng[h]((x	ng[h]((x	NOUN
ejpam-5205	500	11	,	,	PUNCT
ejpam-5205	500	12	p	p	NOUN
ejpam-5205	500	13	)	)	PUNCT
ejpam-5205	500	14	)	)	PUNCT
ejpam-5205	500	15	.	.	PUNCT
ejpam-5205	501	1	if	if	SCONJ
ejpam-5205	501	2	x	x	X
ejpam-5205	501	3	/∈	/∈	INTJ
ejpam-5205	501	4	(	(	PUNCT
ejpam-5205	501	5	ng(s	ng(s	NOUN
ejpam-5205	501	6	2	2	NUM
ejpam-5205	501	7	g	g	NOUN
ejpam-5205	501	8	)	)	PUNCT
ejpam-5205	501	9	)	)	PUNCT
ejpam-5205	501	10	,	,	PUNCT
ejpam-5205	501	11	then	then	ADV
ejpam-5205	501	12	there	there	PRON
ejpam-5205	501	13	exists	exist	VERB
ejpam-5205	501	14	q	q	PROPN
ejpam-5205	501	15	∈	∈	PROPN
ejpam-5205	501	16	t	t	NOUN
ejpam-5205	501	17	2	2	NUM
ejpam-5205	501	18	x	x	NOUN
ejpam-5205	501	19	∩	∩	X
ejpam-5205	501	20	nh(p	nh(p	NUM
ejpam-5205	501	21	)	)	PUNCT
ejpam-5205	501	22	by	by	ADP
ejpam-5205	501	23	(	(	PUNCT
ejpam-5205	501	24	iii	iii	NOUN
ejpam-5205	501	25	)	)	PUNCT
ejpam-5205	501	26	.	.	PUNCT
ejpam-5205	502	1	hence	hence	ADV
ejpam-5205	502	2	,	,	PUNCT
ejpam-5205	502	3	(	(	PUNCT
ejpam-5205	502	4	x	x	X
ejpam-5205	502	5	,	,	PUNCT
ejpam-5205	502	6	q	q	NOUN
ejpam-5205	502	7	)	)	PUNCT
ejpam-5205	502	8	∈	∈	PROPN
ejpam-5205	502	9	v2	v2	PROPN
ejpam-5205	502	10	∩ng[h	∩ng[h	NOUN
ejpam-5205	502	11	]	]	X
ejpam-5205	502	12	(	(	PUNCT
ejpam-5205	502	13	(	(	PUNCT
ejpam-5205	502	14	x	x	NOUN
ejpam-5205	502	15	,	,	PUNCT
ejpam-5205	502	16	p	p	NOUN
ejpam-5205	502	17	)	)	PUNCT
ejpam-5205	502	18	)	)	PUNCT
ejpam-5205	502	19	,	,	PUNCT
ejpam-5205	502	20	therefore	therefore	ADV
ejpam-5205	502	21	,	,	PUNCT
ejpam-5205	502	22	f	f	PROPN
ejpam-5205	502	23	is	be	AUX
ejpam-5205	502	24	an	an	DET
ejpam-5205	502	25	rdf	rdf	NOUN
ejpam-5205	502	26	on	on	ADP
ejpam-5205	502	27	g[h	g[h	NOUN
ejpam-5205	502	28	]	]	PUNCT
ejpam-5205	502	29	.	.	PUNCT
ejpam-5205	503	1	now	now	ADV
ejpam-5205	503	2	,	,	PUNCT
ejpam-5205	503	3	let	let	VERB
ejpam-5205	503	4	v1	v1	VERB
ejpam-5205	503	5	∪v2	∪v2	NOUN
ejpam-5205	504	1	=	=	PUNCT
ejpam-5205	504	2	⋃	⋃	PROPN
ejpam-5205	504	3	x∈s	x∈s	NOUN
ejpam-5205	505	1	[	[	X
ejpam-5205	505	2	{	{	PUNCT
ejpam-5205	505	3	x	x	NOUN
ejpam-5205	505	4	}	}	PUNCT
ejpam-5205	505	5	×	×	PROPN
ejpam-5205	505	6	tx	tx	PROPN
ejpam-5205	505	7	]	]	PUNCT
ejpam-5205	505	8	.	.	PUNCT
ejpam-5205	506	1	then	then	ADV
ejpam-5205	506	2	s	s	VERB
ejpam-5205	506	3	=	=	SYM
ejpam-5205	506	4	s1	s1	PROPN
ejpam-5205	506	5	g	g	PROPN
ejpam-5205	506	6	∪s2	∪s2	VERB
ejpam-5205	506	7	g	g	PROPN
ejpam-5205	506	8	and	and	CCONJ
ejpam-5205	506	9	tx	tx	PROPN
ejpam-5205	506	10	=	=	SYM
ejpam-5205	506	11	t	t	PROPN
ejpam-5205	506	12	1	1	NUM
ejpam-5205	506	13	x	x	SYM
ejpam-5205	506	14	∪t	∪t	NUM
ejpam-5205	506	15	2	2	NUM
ejpam-5205	506	16	x	x	X
ejpam-5205	506	17	.	.	PUNCT
ejpam-5205	507	1	by	by	ADP
ejpam-5205	507	2	(	(	PUNCT
ejpam-5205	507	3	i	i	NOUN
ejpam-5205	507	4	)	)	PUNCT
ejpam-5205	507	5	,	,	PUNCT
ejpam-5205	507	6	(	(	PUNCT
ejpam-5205	507	7	ii	ii	NOUN
ejpam-5205	507	8	)	)	PUNCT
ejpam-5205	507	9	and	and	CCONJ
ejpam-5205	507	10	theorem	theorem	VERB
ejpam-5205	507	11	3	3	NUM
ejpam-5205	507	12	,	,	PUNCT
ejpam-5205	507	13	v1	v1	NOUN
ejpam-5205	507	14	∪	∪	NOUN
ejpam-5205	507	15	v2	v2	NOUN
ejpam-5205	507	16	is	be	AUX
ejpam-5205	507	17	convex	convex	ADJ
ejpam-5205	507	18	in	in	ADP
ejpam-5205	507	19	g[h	g[h	PROPN
ejpam-5205	507	20	]	]	PUNCT
ejpam-5205	507	21	.	.	PUNCT
ejpam-5205	508	1	therefore	therefore	ADV
ejpam-5205	508	2	,	,	PUNCT
ejpam-5205	508	3	f	f	PROPN
ejpam-5205	508	4	is	be	AUX
ejpam-5205	508	5	a	a	DET
ejpam-5205	508	6	cvrdf	cvrdf	NOUN
ejpam-5205	508	7	on	on	ADP
ejpam-5205	508	8	g[h	g[h	NOUN
ejpam-5205	508	9	]	]	PUNCT
ejpam-5205	508	10	.	.	PUNCT
ejpam-5205	509	1	corollary	corollary	ADJ
ejpam-5205	509	2	5	5	NUM
ejpam-5205	509	3	.	.	PUNCT
ejpam-5205	510	1	let	let	VERB
ejpam-5205	510	2	g	g	NOUN
ejpam-5205	510	3	and	and	CCONJ
ejpam-5205	510	4	h	h	NOUN
ejpam-5205	510	5	be	be	AUX
ejpam-5205	510	6	connected	connect	VERB
ejpam-5205	510	7	non	non	ADJ
ejpam-5205	510	8	-	-	ADJ
ejpam-5205	510	9	complete	complete	ADJ
ejpam-5205	510	10	graphs	graph	NOUN
ejpam-5205	510	11	with	with	ADP
ejpam-5205	510	12	γcl(g	γcl(g	NOUN
ejpam-5205	510	13	)	)	PUNCT
ejpam-5205	510	14	≥	≥	NOUN
ejpam-5205	510	15	2	2	NUM
ejpam-5205	510	16	.	.	PUNCT
ejpam-5205	511	1	then	then	ADV
ejpam-5205	511	2	γcvr(g[h	γcvr(g[h	ADV
ejpam-5205	511	3	]	]	PUNCT
ejpam-5205	511	4	)	)	PUNCT
ejpam-5205	512	1	=	=	SYM
ejpam-5205	512	2	2γcl(g	2γcl(g	NUM
ejpam-5205	512	3	)	)	PUNCT
ejpam-5205	512	4	.	.	PUNCT
ejpam-5205	513	1	proof	proof	NOUN
ejpam-5205	513	2	.	.	PUNCT
ejpam-5205	514	1	let	let	VERB
ejpam-5205	514	2	d	d	PRON
ejpam-5205	514	3	be	be	AUX
ejpam-5205	514	4	a	a	DET
ejpam-5205	514	5	γcl	γcl	NOUN
ejpam-5205	514	6	-	-	PUNCT
ejpam-5205	514	7	set	set	VERB
ejpam-5205	514	8	in	in	ADP
ejpam-5205	514	9	g	g	NOUN
ejpam-5205	514	10	and	and	CCONJ
ejpam-5205	514	11	let	let	VERB
ejpam-5205	514	12	p	p	PRON
ejpam-5205	514	13	∈	∈	PROPN
ejpam-5205	514	14	v	v	ADP
ejpam-5205	514	15	(	(	PUNCT
ejpam-5205	514	16	h	h	NOUN
ejpam-5205	514	17	)	)	PUNCT
ejpam-5205	514	18	.	.	PUNCT
ejpam-5205	515	1	let	let	VERB
ejpam-5205	515	2	v1	v1	NOUN
ejpam-5205	515	3	=	=	NOUN
ejpam-5205	515	4	∅	∅	NOUN
ejpam-5205	515	5	,	,	PUNCT
ejpam-5205	515	6	v2	v2	PROPN
ejpam-5205	515	7	=	=	SYM
ejpam-5205	515	8	d	d	X
ejpam-5205	515	9	×	×	NOUN
ejpam-5205	515	10	{	{	PUNCT
ejpam-5205	515	11	p	p	NOUN
ejpam-5205	515	12	}	}	PUNCT
ejpam-5205	515	13	,	,	PUNCT
ejpam-5205	515	14	and	and	CCONJ
ejpam-5205	515	15	v0	v0	NOUN
ejpam-5205	515	16	=	=	PUNCT
ejpam-5205	516	1	[	[	X
ejpam-5205	516	2	(	(	PUNCT
ejpam-5205	516	3	v	v	NOUN
ejpam-5205	516	4	(	(	PUNCT
ejpam-5205	516	5	g	g	NOUN
ejpam-5205	516	6	)	)	PUNCT
ejpam-5205	516	7	\	\	PUNCT
ejpam-5205	517	1	d	d	X
ejpam-5205	517	2	)	)	PUNCT
ejpam-5205	517	3	×	×	NOUN
ejpam-5205	517	4	v	v	NOUN
ejpam-5205	517	5	(	(	PUNCT
ejpam-5205	517	6	h	h	NOUN
ejpam-5205	517	7	)	)	PUNCT
ejpam-5205	517	8	]	]	PUNCT
ejpam-5205	517	9	∪	∪	ADP
ejpam-5205	517	10	[	[	X
ejpam-5205	517	11	d	d	X
ejpam-5205	517	12	×	×	PROPN
ejpam-5205	517	13	(	(	PUNCT
ejpam-5205	517	14	v	v	NOUN
ejpam-5205	517	15	(	(	PUNCT
ejpam-5205	517	16	h	h	NOUN
ejpam-5205	517	17	)	)	PUNCT
ejpam-5205	517	18	\	\	NOUN
ejpam-5205	517	19	{	{	PUNCT
ejpam-5205	517	20	p	p	NOUN
ejpam-5205	517	21	}	}	PUNCT
ejpam-5205	517	22	)	)	PUNCT
ejpam-5205	517	23	]	]	PUNCT
ejpam-5205	517	24	.	.	PUNCT
ejpam-5205	518	1	then	then	ADV
ejpam-5205	518	2	s0	s0	PROPN
ejpam-5205	518	3	g	g	PROPN
ejpam-5205	518	4	=	=	SYM
ejpam-5205	518	5	v	v	PROPN
ejpam-5205	518	6	(	(	PUNCT
ejpam-5205	518	7	g	g	NOUN
ejpam-5205	518	8	)	)	PUNCT
ejpam-5205	518	9	\	\	PUNCT
ejpam-5205	519	1	d	d	X
ejpam-5205	519	2	,	,	PUNCT
ejpam-5205	519	3	s1	s1	PROPN
ejpam-5205	519	4	g	g	NOUN
ejpam-5205	519	5	=	=	NOUN
ejpam-5205	519	6	∅	∅	NOUN
ejpam-5205	519	7	,	,	PUNCT
ejpam-5205	519	8	and	and	CCONJ
ejpam-5205	519	9	s2	s2	VERB
ejpam-5205	519	10	g	g	PROPN
ejpam-5205	519	11	=	=	SYM
ejpam-5205	519	12	d.	d.	PROPN
ejpam-5205	519	13	by	by	ADP
ejpam-5205	519	14	assumption	assumption	NOUN
ejpam-5205	519	15	,	,	PUNCT
ejpam-5205	519	16	s1	s1	PROPN
ejpam-5205	519	17	g	g	PROPN
ejpam-5205	519	18	∪	∪	PROPN
ejpam-5205	519	19	s2	s2	NOUN
ejpam-5205	519	20	g	g	NOUN
ejpam-5205	519	21	=	=	PUNCT
ejpam-5205	520	1	d	d	NOUN
ejpam-5205	520	2	is	be	AUX
ejpam-5205	520	3	a	a	DET
ejpam-5205	520	4	clique	clique	NOUN
ejpam-5205	520	5	dominating	dominating	NOUN
ejpam-5205	520	6	set	set	VERB
ejpam-5205	520	7	in	in	ADP
ejpam-5205	520	8	g.	g.	PROPN
ejpam-5205	520	9	also	also	ADV
ejpam-5205	520	10	,	,	PUNCT
ejpam-5205	520	11	t	t	PROPN
ejpam-5205	520	12	2	2	NUM
ejpam-5205	520	13	x	x	X
ejpam-5205	520	14	=	=	PRON
ejpam-5205	520	15	{	{	PUNCT
ejpam-5205	520	16	p	p	X
ejpam-5205	520	17	}	}	PUNCT
ejpam-5205	520	18	is	be	AUX
ejpam-5205	520	19	a	a	DET
ejpam-5205	520	20	clique	clique	NOUN
ejpam-5205	520	21	set	set	VERB
ejpam-5205	520	22	in	in	ADP
ejpam-5205	520	23	h	h	NOUN
ejpam-5205	520	24	for	for	ADP
ejpam-5205	520	25	each	each	DET
ejpam-5205	520	26	x	x	SYM
ejpam-5205	520	27	∈	∈	PROPN
ejpam-5205	520	28	s2	s2	PROPN
ejpam-5205	520	29	g.	g.	PROPN
ejpam-5205	520	30	moreover	moreover	ADV
ejpam-5205	520	31	,	,	PUNCT
ejpam-5205	520	32	s0	s0	PROPN
ejpam-5205	520	33	g	g	PROPN
ejpam-5205	520	34	\ng(s	\ng(s	NUM
ejpam-5205	520	35	2	2	NUM
ejpam-5205	520	36	g	g	NOUN
ejpam-5205	520	37	)	)	PUNCT
ejpam-5205	520	38	=	=	PUNCT
ejpam-5205	520	39	∅.	∅.	VERB
ejpam-5205	520	40	hence	hence	ADV
ejpam-5205	520	41	,	,	PUNCT
ejpam-5205	520	42	(	(	PUNCT
ejpam-5205	520	43	i	i	NOUN
ejpam-5205	520	44	)	)	PUNCT
ejpam-5205	520	45	,	,	PUNCT
ejpam-5205	520	46	(	(	PUNCT
ejpam-5205	520	47	ii	ii	NOUN
ejpam-5205	520	48	)	)	PUNCT
ejpam-5205	520	49	,	,	PUNCT
ejpam-5205	520	50	and	and	CCONJ
ejpam-5205	520	51	(	(	PUNCT
ejpam-5205	520	52	iii	iii	NOUN
ejpam-5205	520	53	)	)	PUNCT
ejpam-5205	520	54	of	of	ADP
ejpam-5205	520	55	theorem	theorem	ADJ
ejpam-5205	520	56	11	11	NUM
ejpam-5205	520	57	hold	hold	NOUN
ejpam-5205	520	58	.	.	PUNCT
ejpam-5205	521	1	therefore	therefore	ADV
ejpam-5205	521	2	,	,	PUNCT
ejpam-5205	521	3	f	f	PROPN
ejpam-5205	521	4	=	=	SYM
ejpam-5205	521	5	(	(	PUNCT
ejpam-5205	521	6	v0	v0	PROPN
ejpam-5205	521	7	,	,	PUNCT
ejpam-5205	521	8	v1	v1	NOUN
ejpam-5205	521	9	,	,	PUNCT
ejpam-5205	521	10	v2	v2	PROPN
ejpam-5205	521	11	)	)	PUNCT
ejpam-5205	521	12	is	be	AUX
ejpam-5205	521	13	a	a	DET
ejpam-5205	521	14	cvrdf	cvrdf	NOUN
ejpam-5205	521	15	on	on	ADP
ejpam-5205	521	16	g[h	g[h	NOUN
ejpam-5205	521	17	]	]	PUNCT
ejpam-5205	521	18	and	and	CCONJ
ejpam-5205	521	19	γcvr(g[h	γcvr(g[h	NOUN
ejpam-5205	521	20	]	]	X
ejpam-5205	521	21	)	)	PUNCT
ejpam-5205	521	22	≤	≤	NUM
ejpam-5205	521	23	ωcvr	ωcvr	ADP
ejpam-5205	521	24	g[h](f	g[h](f	NOUN
ejpam-5205	521	25	)	)	PUNCT
ejpam-5205	521	26	=	=	SYM
ejpam-5205	521	27	2|v2|	2|v2|	NUM
ejpam-5205	521	28	=	=	SYM
ejpam-5205	521	29	2γcl(g	2γcl(g	NUM
ejpam-5205	521	30	)	)	PUNCT
ejpam-5205	521	31	.	.	PUNCT
ejpam-5205	522	1	now	now	ADV
ejpam-5205	522	2	,	,	PUNCT
ejpam-5205	522	3	let	let	VERB
ejpam-5205	522	4	f	f	PROPN
ejpam-5205	522	5	=	=	SYM
ejpam-5205	522	6	(	(	PUNCT
ejpam-5205	522	7	v0	v0	PROPN
ejpam-5205	522	8	,	,	PUNCT
ejpam-5205	522	9	v1	v1	NOUN
ejpam-5205	522	10	,	,	PUNCT
ejpam-5205	522	11	v2	v2	PROPN
ejpam-5205	522	12	)	)	PUNCT
ejpam-5205	522	13	be	be	AUX
ejpam-5205	522	14	a	a	DET
ejpam-5205	522	15	γcvr	γcvr	NOUN
ejpam-5205	522	16	-	-	PUNCT
ejpam-5205	522	17	function	function	NOUN
ejpam-5205	522	18	on	on	ADP
ejpam-5205	522	19	g[h	g[h	NOUN
ejpam-5205	522	20	]	]	PUNCT
ejpam-5205	522	21	.	.	PUNCT
ejpam-5205	523	1	by	by	ADP
ejpam-5205	523	2	theorem	theorem	NOUN
ejpam-5205	523	3	11	11	NUM
ejpam-5205	523	4	,	,	PUNCT
ejpam-5205	523	5	s1	s1	PROPN
ejpam-5205	523	6	g	g	PROPN
ejpam-5205	523	7	∪	∪	PROPN
ejpam-5205	523	8	s2	s2	PROPN
ejpam-5205	523	9	g	g	NOUN
ejpam-5205	523	10	is	be	AUX
ejpam-5205	523	11	a	a	DET
ejpam-5205	523	12	clique	clique	NOUN
ejpam-5205	523	13	dominating	dominating	NOUN
ejpam-5205	523	14	set	set	VERB
ejpam-5205	523	15	in	in	ADP
ejpam-5205	523	16	g.	g.	PROPN
ejpam-5205	523	17	since	since	SCONJ
ejpam-5205	523	18	g	g	PROPN
ejpam-5205	523	19	is	be	AUX
ejpam-5205	523	20	non	non	ADJ
ejpam-5205	523	21	-	-	ADJ
ejpam-5205	523	22	complete	complete	ADJ
ejpam-5205	523	23	and	and	CCONJ
ejpam-5205	523	24	γcl(g	γcl(g	NUM
ejpam-5205	523	25	)	)	PUNCT
ejpam-5205	523	26	≥	≥	NOUN
ejpam-5205	523	27	2	2	NUM
ejpam-5205	523	28	,	,	PUNCT
ejpam-5205	523	29	|s2	|s2	PROPN
ejpam-5205	523	30	g|	g|	PROPN
ejpam-5205	523	31	≥	≥	NUM
ejpam-5205	523	32	2	2	NUM
ejpam-5205	523	33	.	.	PUNCT
ejpam-5205	524	1	furthermore	furthermore	ADV
ejpam-5205	524	2	,	,	PUNCT
ejpam-5205	524	3	s2	s2	PROPN
ejpam-5205	524	4	g	g	PROPN
ejpam-5205	524	5	is	be	AUX
ejpam-5205	524	6	a	a	DET
ejpam-5205	524	7	clique	clique	NOUN
ejpam-5205	524	8	dominating	dominating	NOUN
ejpam-5205	524	9	set	set	VERB
ejpam-5205	524	10	in	in	ADP
ejpam-5205	524	11	g.	g.	PROPN
ejpam-5205	524	12	therefore	therefore	ADV
ejpam-5205	524	13	,	,	PUNCT
ejpam-5205	524	14	γcvr(g[h	γcvr(g[h	ADV
ejpam-5205	524	15	]	]	PUNCT
ejpam-5205	524	16	)	)	PUNCT
ejpam-5205	524	17	=	=	SYM
ejpam-5205	524	18	ωcvr	ωcvr	NOUN
ejpam-5205	524	19	g[h](f	g[h](f	NOUN
ejpam-5205	524	20	)	)	PUNCT
ejpam-5205	524	21	=	=	PUNCT
ejpam-5205	524	22	|v1|+	|v1|+	PRON
ejpam-5205	524	23	2|v2|	2|v2|	NUM
ejpam-5205	524	24	=	=	SYM
ejpam-5205	524	25	∑	∑	PUNCT
ejpam-5205	525	1	x∈s1	x∈s1	PROPN
ejpam-5205	525	2	g	g	PROPN
ejpam-5205	525	3	|t	|t	PROPN
ejpam-5205	525	4	1	1	NUM
ejpam-5205	525	5	x	x	NOUN
ejpam-5205	525	6	|+	|+	NOUN
ejpam-5205	525	7	2	2	NUM
ejpam-5205	525	8	∑	∑	PROPN
ejpam-5205	525	9	x∈s2	x∈s2	PROPN
ejpam-5205	525	10	g	g	PROPN
ejpam-5205	525	11	|t	|t	PROPN
ejpam-5205	525	12	2	2	NUM
ejpam-5205	525	13	x	x	NOUN
ejpam-5205	525	14	|	|	ADV
ejpam-5205	525	15	≥	≥	NOUN
ejpam-5205	525	16	|s1	|s1	NOUN
ejpam-5205	525	17	g|+	g|+	PROPN
ejpam-5205	525	18	2|s2	2|s2	PROPN
ejpam-5205	525	19	g|	g|	PROPN
ejpam-5205	525	20	≥	≥	PROPN
ejpam-5205	525	21	2γcl(g	2γcl(g	NUM
ejpam-5205	525	22	)	)	PUNCT
ejpam-5205	525	23	.	.	PUNCT
ejpam-5205	526	1	this	this	PRON
ejpam-5205	526	2	proves	prove	VERB
ejpam-5205	526	3	the	the	DET
ejpam-5205	526	4	desired	desire	VERB
ejpam-5205	526	5	equality	equality	NOUN
ejpam-5205	526	6	.	.	PUNCT
ejpam-5205	527	1	theorem	theorem	NOUN
ejpam-5205	527	2	12	12	NUM
ejpam-5205	527	3	.	.	PUNCT
ejpam-5205	528	1	let	let	VERB
ejpam-5205	528	2	g	g	NOUN
ejpam-5205	528	3	and	and	CCONJ
ejpam-5205	528	4	h	h	NOUN
ejpam-5205	528	5	be	be	AUX
ejpam-5205	528	6	non	non	ADJ
ejpam-5205	528	7	-	-	ADJ
ejpam-5205	528	8	complete	complete	ADJ
ejpam-5205	528	9	connected	connected	ADJ
ejpam-5205	528	10	graphs	graph	NOUN
ejpam-5205	528	11	with	with	ADP
ejpam-5205	528	12	γ(g	γ(g	PROPN
ejpam-5205	528	13	)	)	PUNCT
ejpam-5205	528	14	=	=	SYM
ejpam-5205	529	1	1	1	X
ejpam-5205	529	2	.	.	PUNCT
ejpam-5205	529	3	then	then	ADV
ejpam-5205	529	4	γcvr(g[h	γcvr(g[h	ADV
ejpam-5205	529	5	]	]	PUNCT
ejpam-5205	529	6	)	)	PUNCT
ejpam-5205	529	7	=	=	PRON
ejpam-5205	529	8	{	{	PUNCT
ejpam-5205	529	9	2	2	NUM
ejpam-5205	529	10	,	,	PUNCT
ejpam-5205	529	11	if	if	SCONJ
ejpam-5205	529	12	γ(h	γ(h	NOUN
ejpam-5205	529	13	)	)	PUNCT
ejpam-5205	529	14	=	=	SYM
ejpam-5205	529	15	1	1	NUM
ejpam-5205	529	16	4	4	NUM
ejpam-5205	529	17	,	,	PUNCT
ejpam-5205	529	18	if	if	SCONJ
ejpam-5205	529	19	γ(h	γ(h	NOUN
ejpam-5205	529	20	)	)	PUNCT
ejpam-5205	529	21	̸=	̸=	PROPN
ejpam-5205	529	22	1	1	NUM
ejpam-5205	529	23	r.	r.	PROPN
ejpam-5205	529	24	fortosa	fortosa	PROPN
ejpam-5205	529	25	,	,	PUNCT
ejpam-5205	529	26	s.	s.	PROPN
ejpam-5205	529	27	canoy	canoy	PROPN
ejpam-5205	529	28	jr	jr	PROPN
ejpam-5205	529	29	.	.	PROPN
ejpam-5205	529	30	/	/	SYM
ejpam-5205	529	31	eur	eur	PROPN
ejpam-5205	529	32	.	.	PUNCT
ejpam-5205	530	1	j.	j.	PROPN
ejpam-5205	530	2	pure	pure	PROPN
ejpam-5205	530	3	appl	appl	PROPN
ejpam-5205	530	4	.	.	PROPN
ejpam-5205	530	5	math	math	PROPN
ejpam-5205	530	6	,	,	PUNCT
ejpam-5205	530	7	17	17	NUM
ejpam-5205	530	8	(	(	PUNCT
ejpam-5205	530	9	2	2	NUM
ejpam-5205	530	10	)	)	PUNCT
ejpam-5205	530	11	(	(	PUNCT
ejpam-5205	530	12	2024	2024	NUM
ejpam-5205	530	13	)	)	PUNCT
ejpam-5205	530	14	,	,	PUNCT
ejpam-5205	530	15	1335	1335	NUM
ejpam-5205	530	16	-	-	SYM
ejpam-5205	530	17	1351	1351	NUM
ejpam-5205	530	18	1348	1348	NUM
ejpam-5205	530	19	proof	proof	NOUN
ejpam-5205	530	20	.	.	PUNCT
ejpam-5205	531	1	if	if	SCONJ
ejpam-5205	531	2	γ(h	γ(h	NOUN
ejpam-5205	531	3	)	)	PUNCT
ejpam-5205	531	4	=	=	SYM
ejpam-5205	531	5	1	1	NUM
ejpam-5205	531	6	,	,	PUNCT
ejpam-5205	531	7	then	then	ADV
ejpam-5205	531	8	γ(g[h	γ(g[h	NOUN
ejpam-5205	531	9	]	]	PUNCT
ejpam-5205	531	10	)	)	PUNCT
ejpam-5205	531	11	=	=	SYM
ejpam-5205	531	12	1	1	X
ejpam-5205	531	13	.	.	PUNCT
ejpam-5205	531	14	by	by	ADP
ejpam-5205	531	15	corollary	corollary	ADJ
ejpam-5205	531	16	1	1	NUM
ejpam-5205	531	17	,	,	PUNCT
ejpam-5205	531	18	γcvr(g[h	γcvr(g[h	ADV
ejpam-5205	531	19	]	]	PUNCT
ejpam-5205	531	20	)	)	PUNCT
ejpam-5205	531	21	=	=	SYM
ejpam-5205	532	1	2	2	X
ejpam-5205	532	2	.	.	PUNCT
ejpam-5205	533	1	next	next	ADV
ejpam-5205	533	2	,	,	PUNCT
ejpam-5205	533	3	let	let	VERB
ejpam-5205	533	4	γ(h	γ(h	NOUN
ejpam-5205	533	5	)	)	PUNCT
ejpam-5205	533	6	̸=	̸=	PROPN
ejpam-5205	533	7	2	2	NUM
ejpam-5205	533	8	.	.	PUNCT
ejpam-5205	534	1	let	let	VERB
ejpam-5205	534	2	v	v	PART
ejpam-5205	534	3	be	be	AUX
ejpam-5205	534	4	a	a	DET
ejpam-5205	534	5	dominating	dominating	NOUN
ejpam-5205	534	6	vertex	vertex	NOUN
ejpam-5205	534	7	ofg	ofg	PROPN
ejpam-5205	534	8	.	.	PUNCT
ejpam-5205	535	1	pick	pick	VERB
ejpam-5205	535	2	any	any	DET
ejpam-5205	535	3	w	w	NOUN
ejpam-5205	535	4	∈	∈	PROPN
ejpam-5205	535	5	ng(v	ng(v	PUNCT
ejpam-5205	535	6	)	)	PUNCT
ejpam-5205	535	7	and	and	CCONJ
ejpam-5205	535	8	p	p	PROPN
ejpam-5205	535	9	∈	∈	PROPN
ejpam-5205	535	10	v	v	ADP
ejpam-5205	535	11	(	(	PUNCT
ejpam-5205	535	12	h	h	NOUN
ejpam-5205	535	13	)	)	PUNCT
ejpam-5205	535	14	.	.	PUNCT
ejpam-5205	536	1	let	let	VERB
ejpam-5205	536	2	v0	v0	NOUN
ejpam-5205	536	3	=	=	PUNCT
ejpam-5205	537	1	[	[	X
ejpam-5205	537	2	v	v	X
ejpam-5205	537	3	(	(	PUNCT
ejpam-5205	537	4	g)\	g)\	PROPN
ejpam-5205	537	5	{	{	PUNCT
ejpam-5205	537	6	v	v	NOUN
ejpam-5205	537	7	,	,	PUNCT
ejpam-5205	537	8	w	w	NOUN
ejpam-5205	537	9	}	}	PUNCT
ejpam-5205	537	10	×	×	NOUN
ejpam-5205	537	11	v	v	NOUN
ejpam-5205	537	12	(	(	PUNCT
ejpam-5205	537	13	h	h	NOUN
ejpam-5205	537	14	)	)	PUNCT
ejpam-5205	537	15	]	]	PUNCT
ejpam-5205	537	16	∪	∪	ADP
ejpam-5205	537	17	[	[	X
ejpam-5205	537	18	{	{	PUNCT
ejpam-5205	537	19	v	v	NOUN
ejpam-5205	537	20	,	,	PUNCT
ejpam-5205	537	21	w	w	NOUN
ejpam-5205	537	22	}	}	PUNCT
ejpam-5205	537	23	×	×	NOUN
ejpam-5205	537	24	v	v	NOUN
ejpam-5205	537	25	(	(	PUNCT
ejpam-5205	537	26	h	h	NOUN
ejpam-5205	537	27	)	)	PUNCT
ejpam-5205	537	28	\	\	NOUN
ejpam-5205	537	29	{	{	PUNCT
ejpam-5205	537	30	p	p	NOUN
ejpam-5205	537	31	}	}	PUNCT
ejpam-5205	537	32	]	]	PUNCT
ejpam-5205	537	33	,	,	PUNCT
ejpam-5205	537	34	v1	v1	NOUN
ejpam-5205	537	35	=	=	SYM
ejpam-5205	537	36	∅	∅	NOUN
ejpam-5205	537	37	,	,	PUNCT
ejpam-5205	537	38	and	and	CCONJ
ejpam-5205	537	39	v2	v2	NOUN
ejpam-5205	537	40	=	=	SYM
ejpam-5205	537	41	{	{	PUNCT
ejpam-5205	537	42	v	v	NOUN
ejpam-5205	537	43	,	,	PUNCT
ejpam-5205	537	44	w	w	NOUN
ejpam-5205	537	45	}	}	PUNCT
ejpam-5205	537	46	×	×	NOUN
ejpam-5205	537	47	{	{	PUNCT
ejpam-5205	537	48	p	p	NOUN
ejpam-5205	537	49	}	}	PUNCT
ejpam-5205	537	50	.	.	PUNCT
ejpam-5205	538	1	let	let	VERB
ejpam-5205	538	2	(	(	PUNCT
ejpam-5205	538	3	x	x	NOUN
ejpam-5205	538	4	,	,	PUNCT
ejpam-5205	538	5	q	q	NOUN
ejpam-5205	538	6	)	)	PUNCT
ejpam-5205	538	7	∈	∈	PROPN
ejpam-5205	538	8	v0	v0	NOUN
ejpam-5205	538	9	.	.	PUNCT
ejpam-5205	539	1	if	if	SCONJ
ejpam-5205	539	2	x	x	SYM
ejpam-5205	539	3	∈	∈	PROPN
ejpam-5205	539	4	v	v	X
ejpam-5205	539	5	(	(	PUNCT
ejpam-5205	539	6	g	g	NOUN
ejpam-5205	539	7	)	)	PUNCT
ejpam-5205	539	8	\	\	NOUN
ejpam-5205	539	9	{	{	PUNCT
ejpam-5205	539	10	v	v	NOUN
ejpam-5205	539	11	,	,	PUNCT
ejpam-5205	539	12	w	w	NOUN
ejpam-5205	539	13	}	}	PUNCT
ejpam-5205	539	14	,	,	PUNCT
ejpam-5205	539	15	then	then	ADV
ejpam-5205	539	16	xv	xv	PROPN
ejpam-5205	539	17	∈	∈	PROPN
ejpam-5205	539	18	e(g	e(g	PROPN
ejpam-5205	539	19	)	)	PUNCT
ejpam-5205	539	20	.	.	PUNCT
ejpam-5205	540	1	hence	hence	ADV
ejpam-5205	540	2	,	,	PUNCT
ejpam-5205	540	3	(	(	PUNCT
ejpam-5205	540	4	v	v	NOUN
ejpam-5205	540	5	,	,	PUNCT
ejpam-5205	540	6	p	p	NOUN
ejpam-5205	540	7	)	)	PUNCT
ejpam-5205	540	8	∈	∈	PROPN
ejpam-5205	540	9	v2	v2	NOUN
ejpam-5205	540	10	and	and	CCONJ
ejpam-5205	540	11	(	(	PUNCT
ejpam-5205	540	12	x	x	X
ejpam-5205	540	13	,	,	PUNCT
ejpam-5205	540	14	q)(v	q)(v	NOUN
ejpam-5205	540	15	,	,	PUNCT
ejpam-5205	540	16	p	p	X
ejpam-5205	540	17	)	)	PUNCT
ejpam-5205	540	18	∈	∈	NOUN
ejpam-5205	540	19	e(g[h	e(g[h	NOUN
ejpam-5205	540	20	]	]	PUNCT
ejpam-5205	540	21	)	)	PUNCT
ejpam-5205	540	22	.	.	PUNCT
ejpam-5205	541	1	if	if	SCONJ
ejpam-5205	541	2	x	x	X
ejpam-5205	541	3	=	=	SYM
ejpam-5205	541	4	v	v	NOUN
ejpam-5205	541	5	,	,	PUNCT
ejpam-5205	541	6	then	then	ADV
ejpam-5205	541	7	(	(	PUNCT
ejpam-5205	541	8	w	w	PROPN
ejpam-5205	541	9	,	,	PUNCT
ejpam-5205	541	10	p	p	NOUN
ejpam-5205	541	11	)	)	PUNCT
ejpam-5205	541	12	∈	∈	PROPN
ejpam-5205	541	13	v2	v2	NOUN
ejpam-5205	541	14	∩	∩	NOUN
ejpam-5205	541	15	ng[h]((x	ng[h]((x	NOUN
ejpam-5205	541	16	,	,	PUNCT
ejpam-5205	541	17	q	q	NOUN
ejpam-5205	541	18	)	)	PUNCT
ejpam-5205	541	19	)	)	PUNCT
ejpam-5205	542	1	and	and	CCONJ
ejpam-5205	542	2	if	if	SCONJ
ejpam-5205	542	3	x	x	SYM
ejpam-5205	542	4	=	=	SYM
ejpam-5205	542	5	w	w	NOUN
ejpam-5205	542	6	,	,	PUNCT
ejpam-5205	542	7	then	then	ADV
ejpam-5205	542	8	(	(	PUNCT
ejpam-5205	542	9	v	v	NOUN
ejpam-5205	542	10	,	,	PUNCT
ejpam-5205	542	11	p	p	NOUN
ejpam-5205	542	12	)	)	PUNCT
ejpam-5205	542	13	∈	∈	PROPN
ejpam-5205	542	14	v2	v2	NOUN
ejpam-5205	542	15	∩	∩	NOUN
ejpam-5205	542	16	ng[h]((x	ng[h]((x	NOUN
ejpam-5205	542	17	,	,	PUNCT
ejpam-5205	542	18	q	q	NOUN
ejpam-5205	542	19	)	)	PUNCT
ejpam-5205	542	20	)	)	PUNCT
ejpam-5205	542	21	.	.	PUNCT
ejpam-5205	543	1	therefore	therefore	ADV
ejpam-5205	543	2	,	,	PUNCT
ejpam-5205	543	3	g	g	PROPN
ejpam-5205	543	4	=	=	SYM
ejpam-5205	543	5	(	(	PUNCT
ejpam-5205	543	6	v0	v0	PROPN
ejpam-5205	543	7	,	,	PUNCT
ejpam-5205	543	8	v1	v1	NOUN
ejpam-5205	543	9	,	,	PUNCT
ejpam-5205	543	10	v2	v2	PROPN
ejpam-5205	543	11	)	)	PUNCT
ejpam-5205	543	12	is	be	AUX
ejpam-5205	543	13	an	an	DET
ejpam-5205	543	14	rdf	rdf	NOUN
ejpam-5205	543	15	on	on	ADP
ejpam-5205	543	16	g[h	g[h	NOUN
ejpam-5205	543	17	]	]	PUNCT
ejpam-5205	543	18	.	.	PUNCT
ejpam-5205	544	1	now	now	ADV
ejpam-5205	544	2	,	,	PUNCT
ejpam-5205	544	3	v1	v1	VERB
ejpam-5205	544	4	∪	∪	NOUN
ejpam-5205	544	5	v2	v2	NOUN
ejpam-5205	544	6	=	=	SYM
ejpam-5205	544	7	v2	v2	PROPN
ejpam-5205	544	8	and	and	CCONJ
ejpam-5205	544	9	⟨v2⟩	⟨v2⟩	PRON
ejpam-5205	544	10	∼=	∼=	PROPN
ejpam-5205	544	11	k2	k2	NOUN
ejpam-5205	544	12	.	.	PUNCT
ejpam-5205	545	1	hence	hence	ADV
ejpam-5205	545	2	,	,	PUNCT
ejpam-5205	545	3	v1	v1	VERB
ejpam-5205	545	4	∪	∪	NOUN
ejpam-5205	545	5	v2	v2	NOUN
ejpam-5205	545	6	is	be	AUX
ejpam-5205	545	7	convex	convex	ADJ
ejpam-5205	545	8	in	in	ADP
ejpam-5205	545	9	g[h	g[h	PROPN
ejpam-5205	545	10	]	]	PUNCT
ejpam-5205	545	11	.	.	PUNCT
ejpam-5205	546	1	this	this	PRON
ejpam-5205	546	2	shows	show	VERB
ejpam-5205	546	3	that	that	SCONJ
ejpam-5205	546	4	g	g	PROPN
ejpam-5205	546	5	is	be	AUX
ejpam-5205	546	6	a	a	DET
ejpam-5205	546	7	cvrdf	cvrdf	NOUN
ejpam-5205	546	8	on	on	ADP
ejpam-5205	546	9	g[h	g[h	NOUN
ejpam-5205	546	10	]	]	PUNCT
ejpam-5205	546	11	.	.	PUNCT
ejpam-5205	547	1	since	since	SCONJ
ejpam-5205	547	2	ωcvr	ωcvr	PROPN
ejpam-5205	547	3	g[h](g	g[h](g	NOUN
ejpam-5205	547	4	)	)	PUNCT
ejpam-5205	547	5	=	=	SYM
ejpam-5205	547	6	2|v2|	2|v2|	NUM
ejpam-5205	547	7	=	=	SYM
ejpam-5205	547	8	4	4	NUM
ejpam-5205	547	9	,	,	PUNCT
ejpam-5205	547	10	γcvr(g[h	γcvr(g[h	ADV
ejpam-5205	547	11	]	]	PUNCT
ejpam-5205	547	12	)	)	PUNCT
ejpam-5205	547	13	=	=	SYM
ejpam-5205	547	14	4	4	NUM
ejpam-5205	547	15	by	by	ADP
ejpam-5205	547	16	proposition	proposition	NOUN
ejpam-5205	547	17	3	3	NUM
ejpam-5205	547	18	.	.	PUNCT
ejpam-5205	548	1	the	the	DET
ejpam-5205	548	2	cartesian	cartesian	ADJ
ejpam-5205	548	3	product	product	NOUN
ejpam-5205	548	4	g	g	ADP
ejpam-5205	548	5	×	×	NOUN
ejpam-5205	548	6	h	h	NOUN
ejpam-5205	548	7	of	of	ADP
ejpam-5205	548	8	two	two	NUM
ejpam-5205	548	9	graphs	graph	NOUN
ejpam-5205	548	10	g	g	NOUN
ejpam-5205	548	11	and	and	CCONJ
ejpam-5205	548	12	h	h	NOUN
ejpam-5205	548	13	is	be	AUX
ejpam-5205	548	14	the	the	DET
ejpam-5205	548	15	graph	graph	NOUN
ejpam-5205	548	16	with	with	ADP
ejpam-5205	548	17	v	v	NOUN
ejpam-5205	548	18	(	(	PUNCT
ejpam-5205	548	19	g×h	g×h	NOUN
ejpam-5205	548	20	)	)	PUNCT
ejpam-5205	548	21	=	=	SYM
ejpam-5205	548	22	v	v	NOUN
ejpam-5205	548	23	(	(	PUNCT
ejpam-5205	548	24	g)×	g)×	NOUN
ejpam-5205	548	25	v	v	NOUN
ejpam-5205	548	26	(	(	PUNCT
ejpam-5205	548	27	h	h	NOUN
ejpam-5205	548	28	)	)	PUNCT
ejpam-5205	548	29	and	and	CCONJ
ejpam-5205	548	30	(	(	PUNCT
ejpam-5205	548	31	u	u	NOUN
ejpam-5205	548	32	,	,	PUNCT
ejpam-5205	548	33	u′)(v	u′)(v	NOUN
ejpam-5205	548	34	,	,	PUNCT
ejpam-5205	548	35	v′	v′	NOUN
ejpam-5205	548	36	)	)	PUNCT
ejpam-5205	548	37	∈	∈	PROPN
ejpam-5205	548	38	e(g×h	e(g×h	NOUN
ejpam-5205	548	39	)	)	PUNCT
ejpam-5205	548	40	if	if	SCONJ
ejpam-5205	548	41	and	and	CCONJ
ejpam-5205	548	42	only	only	ADV
ejpam-5205	548	43	if	if	SCONJ
ejpam-5205	548	44	either	either	DET
ejpam-5205	548	45	uv	uv	PROPN
ejpam-5205	548	46	∈	∈	PROPN
ejpam-5205	548	47	e(g	e(g	PROPN
ejpam-5205	548	48	)	)	PUNCT
ejpam-5205	548	49	and	and	CCONJ
ejpam-5205	548	50	u′	u′	PROPN
ejpam-5205	548	51	=	=	SYM
ejpam-5205	548	52	v′	v′	NOUN
ejpam-5205	548	53	or	or	CCONJ
ejpam-5205	548	54	u	u	NOUN
ejpam-5205	548	55	=	=	PROPN
ejpam-5205	548	56	v	v	PROPN
ejpam-5205	548	57	and	and	CCONJ
ejpam-5205	548	58	u′v′	u′v′	PROPN
ejpam-5205	548	59	∈	∈	PROPN
ejpam-5205	548	60	e(h	e(h	PROPN
ejpam-5205	548	61	)	)	PUNCT
ejpam-5205	548	62	.	.	PUNCT
ejpam-5205	549	1	lemma	lemma	PROPN
ejpam-5205	549	2	3	3	X
ejpam-5205	549	3	.	.	PUNCT
ejpam-5205	550	1	let	let	VERB
ejpam-5205	550	2	g	g	NOUN
ejpam-5205	551	1	and	and	CCONJ
ejpam-5205	551	2	h	h	NOUN
ejpam-5205	551	3	be	be	VERB
ejpam-5205	551	4	a	a	DET
ejpam-5205	551	5	connected	connected	ADJ
ejpam-5205	551	6	graphs	graph	NOUN
ejpam-5205	551	7	.	.	PUNCT
ejpam-5205	552	1	if	if	SCONJ
ejpam-5205	552	2	f	f	PROPN
ejpam-5205	552	3	=	=	SYM
ejpam-5205	552	4	(	(	PUNCT
ejpam-5205	552	5	v0	v0	PROPN
ejpam-5205	552	6	,	,	PUNCT
ejpam-5205	552	7	v1	v1	NOUN
ejpam-5205	552	8	,	,	PUNCT
ejpam-5205	552	9	v2	v2	PROPN
ejpam-5205	552	10	)	)	PUNCT
ejpam-5205	552	11	is	be	AUX
ejpam-5205	552	12	a	a	DET
ejpam-5205	552	13	cvrdf	cvrdf	NOUN
ejpam-5205	552	14	on	on	ADP
ejpam-5205	552	15	g	g	NOUN
ejpam-5205	552	16	□	□	PROPN
ejpam-5205	552	17	h	h	NOUN
ejpam-5205	552	18	then	then	ADV
ejpam-5205	552	19	v1	v1	VERB
ejpam-5205	552	20	∪	∪	ADJ
ejpam-5205	552	21	v2	v2	NOUN
ejpam-5205	552	22	=	=	SYM
ejpam-5205	552	23	(	(	PUNCT
ejpam-5205	552	24	s1	s1	PROPN
ejpam-5205	552	25	g	g	PROPN
ejpam-5205	552	26	∪	∪	PROPN
ejpam-5205	552	27	s2	s2	NOUN
ejpam-5205	552	28	g)×	g)×	NOUN
ejpam-5205	552	29	(	(	PUNCT
ejpam-5205	552	30	s1	s1	PROPN
ejpam-5205	552	31	h	h	NOUN
ejpam-5205	552	32	∪	∪	PROPN
ejpam-5205	552	33	s2	s2	PROPN
ejpam-5205	552	34	h	h	NOUN
ejpam-5205	552	35	)	)	PUNCT
ejpam-5205	552	36	.	.	PUNCT
ejpam-5205	553	1	proof	proof	NOUN
ejpam-5205	553	2	.	.	PUNCT
ejpam-5205	554	1	if	if	SCONJ
ejpam-5205	554	2	(	(	PUNCT
ejpam-5205	554	3	x	x	X
ejpam-5205	554	4	,	,	PUNCT
ejpam-5205	554	5	p	p	NOUN
ejpam-5205	554	6	)	)	PUNCT
ejpam-5205	554	7	∈	∈	PROPN
ejpam-5205	554	8	v1	v1	NOUN
ejpam-5205	554	9	,	,	PUNCT
ejpam-5205	554	10	then	then	ADV
ejpam-5205	554	11	x	x	SYM
ejpam-5205	554	12	∈	∈	PROPN
ejpam-5205	554	13	s1	s1	PROPN
ejpam-5205	554	14	g	g	PROPN
ejpam-5205	554	15	and	and	CCONJ
ejpam-5205	554	16	p	p	NOUN
ejpam-5205	554	17	∈	∈	PROPN
ejpam-5205	554	18	s1	s1	NOUN
ejpam-5205	554	19	h	h	NOUN
ejpam-5205	554	20	.	.	PUNCT
ejpam-5205	555	1	thus	thus	ADV
ejpam-5205	555	2	(	(	PUNCT
ejpam-5205	555	3	x	x	X
ejpam-5205	555	4	,	,	PUNCT
ejpam-5205	555	5	p	p	NOUN
ejpam-5205	555	6	)	)	PUNCT
ejpam-5205	555	7	∈	∈	PROPN
ejpam-5205	555	8	s1	s1	NOUN
ejpam-5205	555	9	g	g	PROPN
ejpam-5205	555	10	×	×	PROPN
ejpam-5205	555	11	s1	s1	PROPN
ejpam-5205	555	12	h	h	NOUN
ejpam-5205	555	13	.	.	PUNCT
ejpam-5205	556	1	also	also	ADV
ejpam-5205	556	2	,	,	PUNCT
ejpam-5205	556	3	if	if	SCONJ
ejpam-5205	556	4	(	(	PUNCT
ejpam-5205	556	5	x	x	NOUN
ejpam-5205	556	6	,	,	PUNCT
ejpam-5205	556	7	p	p	NOUN
ejpam-5205	556	8	)	)	PUNCT
ejpam-5205	556	9	∈	∈	PROPN
ejpam-5205	556	10	v2	v2	NOUN
ejpam-5205	556	11	,	,	PUNCT
ejpam-5205	556	12	x	x	SYM
ejpam-5205	556	13	∈	∈	PROPN
ejpam-5205	556	14	s2	s2	NOUN
ejpam-5205	556	15	g	g	NOUN
ejpam-5205	556	16	and	and	CCONJ
ejpam-5205	556	17	p	p	NOUN
ejpam-5205	556	18	∈	∈	PROPN
ejpam-5205	556	19	s2	s2	NOUN
ejpam-5205	556	20	h	h	NOUN
ejpam-5205	556	21	.	.	PUNCT
ejpam-5205	557	1	thus	thus	ADV
ejpam-5205	557	2	(	(	PUNCT
ejpam-5205	557	3	x	x	X
ejpam-5205	557	4	,	,	PUNCT
ejpam-5205	557	5	p	p	NOUN
ejpam-5205	557	6	)	)	PUNCT
ejpam-5205	557	7	∈	∈	PROPN
ejpam-5205	557	8	s2	s2	NOUN
ejpam-5205	557	9	g	g	PROPN
ejpam-5205	557	10	×	×	PROPN
ejpam-5205	557	11	s2	s2	NOUN
ejpam-5205	557	12	h	h	NOUN
ejpam-5205	557	13	.	.	PUNCT
ejpam-5205	558	1	hence	hence	ADV
ejpam-5205	558	2	,	,	PUNCT
ejpam-5205	558	3	v1	v1	VERB
ejpam-5205	558	4	∪	∪	ADJ
ejpam-5205	558	5	v2	v2	PROPN
ejpam-5205	558	6	⊆	⊆	NUM
ejpam-5205	558	7	(	(	PUNCT
ejpam-5205	558	8	s1	s1	PROPN
ejpam-5205	558	9	g	g	PROPN
ejpam-5205	558	10	∪	∪	PROPN
ejpam-5205	558	11	s2	s2	NOUN
ejpam-5205	558	12	g)×	g)×	NOUN
ejpam-5205	558	13	(	(	PUNCT
ejpam-5205	558	14	s1	s1	PROPN
ejpam-5205	558	15	h	h	NOUN
ejpam-5205	558	16	∪	∪	PROPN
ejpam-5205	558	17	s2	s2	PROPN
ejpam-5205	558	18	h	h	NOUN
ejpam-5205	558	19	)	)	PUNCT
ejpam-5205	558	20	.	.	PUNCT
ejpam-5205	559	1	now	now	ADV
ejpam-5205	559	2	,	,	PUNCT
ejpam-5205	559	3	let	let	VERB
ejpam-5205	559	4	(	(	PUNCT
ejpam-5205	559	5	z	z	NOUN
ejpam-5205	559	6	,	,	PUNCT
ejpam-5205	559	7	q	q	ADJ
ejpam-5205	559	8	)	)	PUNCT
ejpam-5205	559	9	∈	∈	PROPN
ejpam-5205	559	10	(	(	PUNCT
ejpam-5205	559	11	s1	s1	NOUN
ejpam-5205	559	12	g∪s2	g∪s2	VERB
ejpam-5205	559	13	g)×(s1	g)×(s1	PROPN
ejpam-5205	559	14	h	h	NOUN
ejpam-5205	559	15	∪s2	∪s2	AUX
ejpam-5205	559	16	h	h	NOUN
ejpam-5205	559	17	)	)	PUNCT
ejpam-5205	559	18	.	.	PUNCT
ejpam-5205	560	1	suppose	suppose	VERB
ejpam-5205	560	2	that	that	SCONJ
ejpam-5205	560	3	(	(	PUNCT
ejpam-5205	560	4	z	z	NOUN
ejpam-5205	560	5	,	,	PUNCT
ejpam-5205	560	6	q	q	NOUN
ejpam-5205	560	7	)	)	PUNCT
ejpam-5205	560	8	∈	∈	PROPN
ejpam-5205	560	9	v0	v0	NOUN
ejpam-5205	560	10	.	.	PUNCT
ejpam-5205	561	1	suppose	suppose	VERB
ejpam-5205	561	2	z	z	NOUN
ejpam-5205	561	3	∈	∈	PROPN
ejpam-5205	561	4	s1	s1	PROPN
ejpam-5205	561	5	g	g	PROPN
ejpam-5205	561	6	and	and	CCONJ
ejpam-5205	561	7	q	q	NOUN
ejpam-5205	561	8	∈	∈	PROPN
ejpam-5205	561	9	s1	s1	NOUN
ejpam-5205	561	10	h	h	NOUN
ejpam-5205	561	11	.	.	PUNCT
ejpam-5205	562	1	since	since	SCONJ
ejpam-5205	562	2	f	f	PROPN
ejpam-5205	562	3	is	be	AUX
ejpam-5205	562	4	an	an	DET
ejpam-5205	562	5	rdf	rdf	NOUN
ejpam-5205	562	6	,	,	PUNCT
ejpam-5205	562	7	there	there	PRON
ejpam-5205	562	8	exists	exist	VERB
ejpam-5205	562	9	(	(	PUNCT
ejpam-5205	562	10	w	w	PROPN
ejpam-5205	562	11	,	,	PUNCT
ejpam-5205	562	12	t	t	PROPN
ejpam-5205	562	13	)	)	PUNCT
ejpam-5205	562	14	∈	∈	PROPN
ejpam-5205	562	15	v2	v2	PROPN
ejpam-5205	562	16	∩ng[h]((z	∩ng[h]((z	NOUN
ejpam-5205	562	17	,	,	PUNCT
ejpam-5205	562	18	q	q	NOUN
ejpam-5205	562	19	)	)	PUNCT
ejpam-5205	562	20	)	)	PUNCT
ejpam-5205	562	21	.	.	PUNCT
ejpam-5205	563	1	suppose	suppose	VERB
ejpam-5205	563	2	w	w	PROPN
ejpam-5205	563	3	=	=	PROPN
ejpam-5205	563	4	z.	z.	PROPN
ejpam-5205	563	5	then	then	ADV
ejpam-5205	563	6	tq	tq	INTJ
ejpam-5205	563	7	∈	∈	PROPN
ejpam-5205	563	8	e(h	e(h	PROPN
ejpam-5205	563	9	)	)	PUNCT
ejpam-5205	563	10	.	.	PUNCT
ejpam-5205	564	1	let	let	VERB
ejpam-5205	564	2	y	y	PROPN
ejpam-5205	564	3	∈	∈	PROPN
ejpam-5205	564	4	v	v	ADP
ejpam-5205	564	5	(	(	PUNCT
ejpam-5205	564	6	g	g	NOUN
ejpam-5205	564	7	)	)	PUNCT
ejpam-5205	564	8	such	such	ADJ
ejpam-5205	564	9	that	that	SCONJ
ejpam-5205	564	10	(	(	PUNCT
ejpam-5205	564	11	y	y	NOUN
ejpam-5205	564	12	,	,	PUNCT
ejpam-5205	564	13	q	q	NOUN
ejpam-5205	564	14	)	)	PUNCT
ejpam-5205	564	15	∈	∈	PROPN
ejpam-5205	564	16	v1	v1	NOUN
ejpam-5205	564	17	.	.	PUNCT
ejpam-5205	565	1	let	let	VERB
ejpam-5205	565	2	p	p	NOUN
ejpam-5205	565	3	(	(	PUNCT
ejpam-5205	565	4	y	y	PROPN
ejpam-5205	565	5	,	,	PUNCT
ejpam-5205	565	6	z	z	NOUN
ejpam-5205	565	7	)	)	PUNCT
ejpam-5205	565	8	=	=	PUNCT
ejpam-5205	566	1	[	[	X
ejpam-5205	566	2	y1	y1	INTJ
ejpam-5205	566	3	,	,	PUNCT
ejpam-5205	566	4	y2	y2	INTJ
ejpam-5205	566	5	,	,	PUNCT
ejpam-5205	566	6	.	.	PUNCT
ejpam-5205	566	7	.	.	PUNCT
ejpam-5205	566	8	.	.	PUNCT
ejpam-5205	567	1	,	,	PUNCT
ejpam-5205	567	2	yk	yk	PROPN
ejpam-5205	567	3	]	]	PUNCT
ejpam-5205	567	4	where	where	SCONJ
ejpam-5205	567	5	y1	y1	NOUN
ejpam-5205	567	6	=	=	SYM
ejpam-5205	567	7	y	y	PROPN
ejpam-5205	567	8	and	and	CCONJ
ejpam-5205	567	9	yk	yk	PROPN
ejpam-5205	568	1	=	=	PUNCT
ejpam-5205	568	2	z	z	AUX
ejpam-5205	568	3	be	be	AUX
ejpam-5205	568	4	a	a	DET
ejpam-5205	568	5	y	y	PROPN
ejpam-5205	568	6	-	-	PROPN
ejpam-5205	568	7	z	z	NOUN
ejpam-5205	568	8	geodesic	geodesic	NOUN
ejpam-5205	568	9	in	in	ADP
ejpam-5205	568	10	g	g	NOUN
ejpam-5205	568	11	for	for	ADP
ejpam-5205	568	12	some	some	DET
ejpam-5205	568	13	k	k	PROPN
ejpam-5205	568	14	≥	≥	NUM
ejpam-5205	568	15	1	1	NUM
ejpam-5205	568	16	.	.	PUNCT
ejpam-5205	569	1	then	then	ADV
ejpam-5205	569	2	,	,	PUNCT
ejpam-5205	569	3	p	p	X
ejpam-5205	569	4	(	(	PUNCT
ejpam-5205	569	5	(	(	PUNCT
ejpam-5205	569	6	y	y	PROPN
ejpam-5205	569	7	,	,	PUNCT
ejpam-5205	569	8	q	q	NOUN
ejpam-5205	569	9	)	)	PUNCT
ejpam-5205	569	10	,	,	PUNCT
ejpam-5205	569	11	(	(	PUNCT
ejpam-5205	569	12	z	z	X
ejpam-5205	569	13	,	,	PUNCT
ejpam-5205	569	14	t	t	PROPN
ejpam-5205	569	15	)	)	PUNCT
ejpam-5205	569	16	)	)	PUNCT
ejpam-5205	570	1	=	=	PUNCT
ejpam-5205	571	1	[	[	X
ejpam-5205	571	2	(	(	PUNCT
ejpam-5205	571	3	y1	y1	INTJ
ejpam-5205	571	4	,	,	PUNCT
ejpam-5205	571	5	q	q	NOUN
ejpam-5205	571	6	)	)	PUNCT
ejpam-5205	571	7	,	,	PUNCT
ejpam-5205	571	8	(	(	PUNCT
ejpam-5205	571	9	y2	y2	INTJ
ejpam-5205	571	10	,	,	PUNCT
ejpam-5205	571	11	q	q	NOUN
ejpam-5205	571	12	)	)	PUNCT
ejpam-5205	571	13	,	,	PUNCT
ejpam-5205	571	14	.	.	PUNCT
ejpam-5205	571	15	.	.	PUNCT
ejpam-5205	571	16	.	.	PUNCT
ejpam-5205	572	1	,	,	PUNCT
ejpam-5205	572	2	(	(	PUNCT
ejpam-5205	572	3	yk	yk	NOUN
ejpam-5205	572	4	,	,	PUNCT
ejpam-5205	572	5	q	q	NOUN
ejpam-5205	572	6	)	)	PUNCT
ejpam-5205	572	7	,	,	PUNCT
ejpam-5205	572	8	(	(	PUNCT
ejpam-5205	572	9	z	z	X
ejpam-5205	572	10	,	,	PUNCT
ejpam-5205	572	11	t	t	PROPN
ejpam-5205	572	12	)	)	PUNCT
ejpam-5205	572	13	]	]	PUNCT
ejpam-5205	572	14	is	be	AUX
ejpam-5205	572	15	also	also	ADV
ejpam-5205	572	16	(	(	PUNCT
ejpam-5205	572	17	y	y	NOUN
ejpam-5205	572	18	,	,	PUNCT
ejpam-5205	572	19	q)-(z	q)-(z	PROPN
ejpam-5205	572	20	,	,	PUNCT
ejpam-5205	572	21	t	t	PROPN
ejpam-5205	572	22	)	)	PUNCT
ejpam-5205	572	23	geodesic	geodesic	NOUN
ejpam-5205	572	24	in	in	ADP
ejpam-5205	572	25	g	g	PROPN
ejpam-5205	572	26	□	□	PROPN
ejpam-5205	572	27	h	h	NOUN
ejpam-5205	572	28	,	,	PUNCT
ejpam-5205	572	29	a	a	DET
ejpam-5205	572	30	contradiction	contradiction	NOUN
ejpam-5205	572	31	to	to	ADP
ejpam-5205	572	32	our	our	PRON
ejpam-5205	572	33	assumption	assumption	NOUN
ejpam-5205	572	34	that	that	SCONJ
ejpam-5205	572	35	v1	v1	NOUN
ejpam-5205	572	36	∪	∪	NOUN
ejpam-5205	572	37	v2	v2	PROPN
ejpam-5205	572	38	is	be	AUX
ejpam-5205	572	39	convex	convex	PROPN
ejpam-5205	572	40	.	.	PUNCT
ejpam-5205	573	1	suppose	suppose	VERB
ejpam-5205	573	2	w	w	ADP
ejpam-5205	573	3	̸=	̸=	PROPN
ejpam-5205	573	4	z.	z.	PROPN
ejpam-5205	573	5	then	then	ADV
ejpam-5205	573	6	wz	wz	PROPN
ejpam-5205	573	7	∈	∈	PROPN
ejpam-5205	573	8	e(g	e(g	PROPN
ejpam-5205	573	9	)	)	PUNCT
ejpam-5205	573	10	and	and	CCONJ
ejpam-5205	573	11	t	t	X
ejpam-5205	573	12	=	=	PUNCT
ejpam-5205	573	13	q.	q.	PROPN
ejpam-5205	573	14	since	since	SCONJ
ejpam-5205	573	15	z	z	PROPN
ejpam-5205	573	16	∈	∈	PROPN
ejpam-5205	573	17	s1	s1	PROPN
ejpam-5205	573	18	g	g	PROPN
ejpam-5205	573	19	,	,	PUNCT
ejpam-5205	573	20	there	there	PRON
ejpam-5205	573	21	exists	exist	VERB
ejpam-5205	573	22	r	r	NOUN
ejpam-5205	573	23	∈	∈	PROPN
ejpam-5205	573	24	v	v	NOUN
ejpam-5205	573	25	(	(	PUNCT
ejpam-5205	573	26	h	h	NOUN
ejpam-5205	573	27	)	)	PUNCT
ejpam-5205	573	28	such	such	ADJ
ejpam-5205	573	29	that	that	SCONJ
ejpam-5205	573	30	(	(	PUNCT
ejpam-5205	573	31	z	z	NOUN
ejpam-5205	573	32	,	,	PUNCT
ejpam-5205	573	33	r	r	NOUN
ejpam-5205	573	34	)	)	PUNCT
ejpam-5205	573	35	∈	∈	NOUN
ejpam-5205	573	36	v1	v1	NOUN
ejpam-5205	573	37	.	.	PUNCT
ejpam-5205	574	1	let	let	VERB
ejpam-5205	574	2	p	p	NOUN
ejpam-5205	574	3	(	(	PUNCT
ejpam-5205	574	4	q	q	NOUN
ejpam-5205	574	5	,	,	PUNCT
ejpam-5205	574	6	r	r	NOUN
ejpam-5205	574	7	)	)	PUNCT
ejpam-5205	574	8	=	=	PUNCT
ejpam-5205	575	1	[	[	X
ejpam-5205	575	2	q1	q1	PROPN
ejpam-5205	575	3	,	,	PUNCT
ejpam-5205	575	4	q2	q2	NOUN
ejpam-5205	575	5	,	,	PUNCT
ejpam-5205	575	6	.	.	PUNCT
ejpam-5205	575	7	.	.	PUNCT
ejpam-5205	576	1	.	.	PUNCT
ejpam-5205	577	1	,	,	PUNCT
ejpam-5205	577	2	qm	qm	PROPN
ejpam-5205	577	3	,	,	PUNCT
ejpam-5205	577	4	z	z	PROPN
ejpam-5205	577	5	]	]	X
ejpam-5205	577	6	where	where	SCONJ
ejpam-5205	577	7	q1	q1	NOUN
ejpam-5205	577	8	=	=	PROPN
ejpam-5205	577	9	q	q	PROPN
ejpam-5205	577	10	and	and	CCONJ
ejpam-5205	577	11	qm	qm	PROPN
ejpam-5205	577	12	=	=	NOUN
ejpam-5205	578	1	r	r	NOUN
ejpam-5205	578	2	be	be	AUX
ejpam-5205	578	3	a	a	DET
ejpam-5205	578	4	q	q	NOUN
ejpam-5205	578	5	−	−	NOUN
ejpam-5205	578	6	r	r	NOUN
ejpam-5205	578	7	geodesic	geodesic	NOUN
ejpam-5205	578	8	in	in	ADP
ejpam-5205	578	9	h.	h.	PROPN
ejpam-5205	579	1	then	then	ADV
ejpam-5205	579	2	p	p	X
ejpam-5205	579	3	(	(	PUNCT
ejpam-5205	579	4	(	(	PUNCT
ejpam-5205	579	5	w	w	NOUN
ejpam-5205	579	6	,	,	PUNCT
ejpam-5205	579	7	q)(z	q)(z	X
ejpam-5205	579	8	,	,	PUNCT
ejpam-5205	579	9	r	r	NOUN
ejpam-5205	579	10	)	)	PUNCT
ejpam-5205	579	11	)	)	PUNCT
ejpam-5205	580	1	=	=	PUNCT
ejpam-5205	581	1	[	[	X
ejpam-5205	581	2	(	(	PUNCT
ejpam-5205	581	3	w	w	PROPN
ejpam-5205	581	4	,	,	PUNCT
ejpam-5205	581	5	q	q	NOUN
ejpam-5205	581	6	)	)	PUNCT
ejpam-5205	581	7	,	,	PUNCT
ejpam-5205	581	8	(	(	PUNCT
ejpam-5205	581	9	z	z	NOUN
ejpam-5205	581	10	,	,	PUNCT
ejpam-5205	581	11	q1	q1	PROPN
ejpam-5205	581	12	)	)	PUNCT
ejpam-5205	581	13	,	,	PUNCT
ejpam-5205	581	14	(	(	PUNCT
ejpam-5205	581	15	z	z	NOUN
ejpam-5205	581	16	,	,	PUNCT
ejpam-5205	581	17	q2	q2	NOUN
ejpam-5205	581	18	)	)	PUNCT
ejpam-5205	581	19	,	,	PUNCT
ejpam-5205	581	20	.	.	PUNCT
ejpam-5205	581	21	.	.	PUNCT
ejpam-5205	582	1	.	.	PUNCT
ejpam-5205	583	1	,	,	PUNCT
ejpam-5205	583	2	(	(	PUNCT
ejpam-5205	583	3	z	z	X
ejpam-5205	583	4	,	,	PUNCT
ejpam-5205	583	5	qm	qm	PROPN
ejpam-5205	583	6	)	)	PUNCT
ejpam-5205	583	7	]	]	PUNCT
ejpam-5205	583	8	is	be	AUX
ejpam-5205	583	9	a	a	DET
ejpam-5205	583	10	(	(	PUNCT
ejpam-5205	583	11	w	w	NOUN
ejpam-5205	583	12	,	,	PUNCT
ejpam-5205	583	13	q)-(z	q)-(z	ADV
ejpam-5205	583	14	,	,	PUNCT
ejpam-5205	583	15	r	r	NOUN
ejpam-5205	583	16	)	)	PUNCT
ejpam-5205	583	17	geodesic	geodesic	NOUN
ejpam-5205	583	18	in	in	ADP
ejpam-5205	583	19	g	g	PROPN
ejpam-5205	583	20	□	□	PROPN
ejpam-5205	583	21	h	h	NOUN
ejpam-5205	583	22	,	,	PUNCT
ejpam-5205	583	23	a	a	DET
ejpam-5205	583	24	contradiction	contradiction	NOUN
ejpam-5205	583	25	to	to	ADP
ejpam-5205	583	26	our	our	PRON
ejpam-5205	583	27	assumption	assumption	NOUN
ejpam-5205	583	28	that	that	SCONJ
ejpam-5205	583	29	v1	v1	PROPN
ejpam-5205	583	30	∪v2	∪v2	PROPN
ejpam-5205	583	31	is	be	AUX
ejpam-5205	583	32	convex	convex	PROPN
ejpam-5205	583	33	.	.	PUNCT
ejpam-5205	584	1	similar	similar	ADJ
ejpam-5205	584	2	arguments	argument	NOUN
ejpam-5205	584	3	can	can	AUX
ejpam-5205	584	4	be	be	AUX
ejpam-5205	584	5	used	use	VERB
ejpam-5205	584	6	to	to	PART
ejpam-5205	584	7	show	show	VERB
ejpam-5205	584	8	that	that	SCONJ
ejpam-5205	584	9	a	a	DET
ejpam-5205	584	10	contradiction	contradiction	NOUN
ejpam-5205	584	11	is	be	AUX
ejpam-5205	584	12	obtained	obtain	VERB
ejpam-5205	584	13	when	when	SCONJ
ejpam-5205	584	14	z	z	PROPN
ejpam-5205	584	15	∈	∈	PROPN
ejpam-5205	584	16	s1	s1	PROPN
ejpam-5205	584	17	g	g	PROPN
ejpam-5205	584	18	,	,	PUNCT
ejpam-5205	584	19	q	q	NOUN
ejpam-5205	584	20	∈	∈	PROPN
ejpam-5205	584	21	s2	s2	NOUN
ejpam-5205	584	22	h	h	NOUN
ejpam-5205	584	23	or	or	CCONJ
ejpam-5205	584	24	z	z	NOUN
ejpam-5205	584	25	∈	∈	PROPN
ejpam-5205	584	26	s2	s2	NOUN
ejpam-5205	584	27	g	g	NOUN
ejpam-5205	584	28	,	,	PUNCT
ejpam-5205	584	29	q	q	NOUN
ejpam-5205	584	30	∈	∈	PROPN
ejpam-5205	584	31	s1	s1	NOUN
ejpam-5205	584	32	h	h	NOUN
ejpam-5205	584	33	or	or	CCONJ
ejpam-5205	584	34	z	z	NOUN
ejpam-5205	584	35	∈	∈	PROPN
ejpam-5205	584	36	s1	s1	PROPN
ejpam-5205	584	37	g	g	PROPN
ejpam-5205	584	38	,	,	PUNCT
ejpam-5205	584	39	q	q	NOUN
ejpam-5205	584	40	∈	∈	PROPN
ejpam-5205	584	41	s2	s2	NOUN
ejpam-5205	584	42	h	h	NOUN
ejpam-5205	584	43	.	.	PUNCT
ejpam-5205	585	1	therefore	therefore	ADV
ejpam-5205	585	2	(	(	PUNCT
ejpam-5205	585	3	z	z	NOUN
ejpam-5205	585	4	,	,	PUNCT
ejpam-5205	585	5	q	q	NOUN
ejpam-5205	585	6	)	)	PUNCT
ejpam-5205	585	7	∈	∈	NOUN
ejpam-5205	585	8	v1	v1	NOUN
ejpam-5205	585	9	∪	∪	NOUN
ejpam-5205	585	10	v2	v2	NOUN
ejpam-5205	585	11	showing	showing	NOUN
ejpam-5205	585	12	that	that	SCONJ
ejpam-5205	585	13	(	(	PUNCT
ejpam-5205	585	14	s1	s1	PROPN
ejpam-5205	585	15	g	g	PROPN
ejpam-5205	585	16	∪	∪	PROPN
ejpam-5205	585	17	s2	s2	NOUN
ejpam-5205	585	18	g)×	g)×	NOUN
ejpam-5205	585	19	(	(	PUNCT
ejpam-5205	585	20	s1	s1	PROPN
ejpam-5205	585	21	h	h	PROPN
ejpam-5205	585	22	∪	∪	PROPN
ejpam-5205	585	23	s2	s2	PROPN
ejpam-5205	585	24	h	h	NOUN
ejpam-5205	585	25	)	)	PUNCT
ejpam-5205	585	26	⊆	⊆	NUM
ejpam-5205	585	27	v1	v1	NOUN
ejpam-5205	585	28	∪	∪	NOUN
ejpam-5205	585	29	v2	v2	NOUN
ejpam-5205	585	30	.	.	PUNCT
ejpam-5205	586	1	this	this	PRON
ejpam-5205	586	2	proves	prove	VERB
ejpam-5205	586	3	the	the	DET
ejpam-5205	586	4	desired	desire	VERB
ejpam-5205	586	5	equality	equality	NOUN
ejpam-5205	586	6	.	.	PUNCT
ejpam-5205	587	1	theorem	theorem	VERB
ejpam-5205	587	2	13	13	NUM
ejpam-5205	587	3	.	.	PUNCT
ejpam-5205	588	1	let	let	VERB
ejpam-5205	588	2	g	g	NOUN
ejpam-5205	589	1	and	and	CCONJ
ejpam-5205	589	2	h	h	NOUN
ejpam-5205	589	3	be	be	VERB
ejpam-5205	589	4	a	a	DET
ejpam-5205	589	5	connected	connected	ADJ
ejpam-5205	589	6	graphs	graph	NOUN
ejpam-5205	589	7	.	.	PUNCT
ejpam-5205	590	1	then	then	ADV
ejpam-5205	590	2	f	f	X
ejpam-5205	590	3	=	=	SYM
ejpam-5205	590	4	(	(	PUNCT
ejpam-5205	590	5	v0	v0	PROPN
ejpam-5205	590	6	,	,	PUNCT
ejpam-5205	590	7	v1	v1	NOUN
ejpam-5205	590	8	,	,	PUNCT
ejpam-5205	590	9	v2	v2	PROPN
ejpam-5205	590	10	)	)	PUNCT
ejpam-5205	590	11	is	be	AUX
ejpam-5205	590	12	a	a	DET
ejpam-5205	590	13	cvrdf	cvrdf	NOUN
ejpam-5205	590	14	on	on	ADP
ejpam-5205	590	15	g	g	NOUN
ejpam-5205	590	16	□	□	PROPN
ejpam-5205	590	17	h	h	NOUN
ejpam-5205	590	18	if	if	SCONJ
ejpam-5205	591	1	and	and	CCONJ
ejpam-5205	591	2	only	only	ADV
ejpam-5205	591	3	if	if	SCONJ
ejpam-5205	591	4	the	the	DET
ejpam-5205	591	5	following	follow	VERB
ejpam-5205	591	6	conditions	condition	NOUN
ejpam-5205	591	7	hold	hold	VERB
ejpam-5205	591	8	:	:	PUNCT
ejpam-5205	591	9	(	(	PUNCT
ejpam-5205	591	10	i	i	NOUN
ejpam-5205	591	11	)	)	PUNCT
ejpam-5205	591	12	for	for	ADP
ejpam-5205	591	13	each	each	DET
ejpam-5205	591	14	x	x	SYM
ejpam-5205	591	15	∈	∈	PROPN
ejpam-5205	591	16	s0	s0	PROPN
ejpam-5205	591	17	g	g	PROPN
ejpam-5205	591	18	and	and	CCONJ
ejpam-5205	591	19	p	p	NOUN
ejpam-5205	591	20	∈	∈	PROPN
ejpam-5205	591	21	t	t	NOUN
ejpam-5205	591	22	0	0	NUM
ejpam-5205	591	23	x	x	SYM
ejpam-5205	591	24	,	,	PUNCT
ejpam-5205	591	25	there	there	PRON
ejpam-5205	591	26	exists	exist	VERB
ejpam-5205	591	27	q	q	PROPN
ejpam-5205	591	28	∈	∈	PROPN
ejpam-5205	591	29	t	t	NOUN
ejpam-5205	591	30	2	2	NUM
ejpam-5205	591	31	x	x	NOUN
ejpam-5205	591	32	∩	∩	X
ejpam-5205	591	33	nh(p	nh(p	NUM
ejpam-5205	591	34	)	)	PUNCT
ejpam-5205	591	35	or	or	CCONJ
ejpam-5205	591	36	y	y	PROPN
ejpam-5205	591	37	∈	∈	PROPN
ejpam-5205	591	38	s2	s2	PROPN
ejpam-5205	591	39	g	g	NOUN
ejpam-5205	591	40	∩	∩	NOUN
ejpam-5205	591	41	ng(x	ng(x	NUM
ejpam-5205	591	42	)	)	PUNCT
ejpam-5205	591	43	with	with	ADP
ejpam-5205	591	44	q	q	PROPN
ejpam-5205	591	45	=	=	PUNCT
ejpam-5205	591	46	p	p	X
ejpam-5205	591	47	∈	∈	PROPN
ejpam-5205	591	48	t	t	NOUN
ejpam-5205	591	49	2	2	NUM
ejpam-5205	591	50	y	y	PROPN
ejpam-5205	591	51	(	(	PUNCT
ejpam-5205	591	52	ii	ii	PROPN
ejpam-5205	591	53	)	)	PUNCT
ejpam-5205	591	54	v1	v1	PROPN
ejpam-5205	591	55	∪	∪	NOUN
ejpam-5205	591	56	v2	v2	NOUN
ejpam-5205	591	57	=	=	SYM
ejpam-5205	591	58	(	(	PUNCT
ejpam-5205	591	59	s1	s1	PROPN
ejpam-5205	591	60	g	g	PROPN
ejpam-5205	591	61	∪	∪	PROPN
ejpam-5205	591	62	s2	s2	NOUN
ejpam-5205	591	63	g)×	g)×	NOUN
ejpam-5205	591	64	(	(	PUNCT
ejpam-5205	591	65	s1	s1	PROPN
ejpam-5205	591	66	h	h	PROPN
ejpam-5205	591	67	∪	∪	PROPN
ejpam-5205	591	68	s2	s2	PROPN
ejpam-5205	591	69	h	h	NOUN
ejpam-5205	591	70	)	)	PUNCT
ejpam-5205	591	71	and	and	CCONJ
ejpam-5205	591	72	(	(	PUNCT
ejpam-5205	591	73	a	a	X
ejpam-5205	591	74	)	)	PUNCT
ejpam-5205	591	75	s1	s1	PROPN
ejpam-5205	591	76	g	g	PROPN
ejpam-5205	591	77	∪	∪	PROPN
ejpam-5205	591	78	s2	s2	PROPN
ejpam-5205	591	79	g	g	NOUN
ejpam-5205	591	80	is	be	AUX
ejpam-5205	591	81	a	a	DET
ejpam-5205	591	82	convex	convex	NOUN
ejpam-5205	591	83	dominating	dominating	NOUN
ejpam-5205	591	84	set	set	VERB
ejpam-5205	591	85	in	in	ADP
ejpam-5205	591	86	g	g	PROPN
ejpam-5205	591	87	and	and	CCONJ
ejpam-5205	591	88	s1	s1	PROPN
ejpam-5205	591	89	h	h	PROPN
ejpam-5205	591	90	∪	∪	PROPN
ejpam-5205	591	91	s2	s2	NOUN
ejpam-5205	591	92	h	h	NOUN
ejpam-5205	591	93	=	=	SYM
ejpam-5205	591	94	v	v	PROPN
ejpam-5205	591	95	(	(	PUNCT
ejpam-5205	591	96	h	h	NOUN
ejpam-5205	591	97	)	)	PUNCT
ejpam-5205	591	98	or	or	CCONJ
ejpam-5205	591	99	(	(	PUNCT
ejpam-5205	591	100	b	b	X
ejpam-5205	591	101	)	)	PUNCT
ejpam-5205	591	102	s1	s1	NOUN
ejpam-5205	591	103	h	h	PROPN
ejpam-5205	591	104	∪	∪	PROPN
ejpam-5205	591	105	s2	s2	PROPN
ejpam-5205	591	106	h	h	NOUN
ejpam-5205	591	107	is	be	AUX
ejpam-5205	591	108	a	a	DET
ejpam-5205	591	109	convex	convex	NOUN
ejpam-5205	591	110	dominating	dominating	NOUN
ejpam-5205	591	111	set	set	VERB
ejpam-5205	591	112	in	in	ADP
ejpam-5205	591	113	g	g	PROPN
ejpam-5205	591	114	and	and	CCONJ
ejpam-5205	591	115	s1	s1	PROPN
ejpam-5205	591	116	g	g	PROPN
ejpam-5205	591	117	∪	∪	PROPN
ejpam-5205	591	118	s2	s2	NOUN
ejpam-5205	591	119	g	g	NOUN
ejpam-5205	591	120	=	=	SYM
ejpam-5205	591	121	v	v	PROPN
ejpam-5205	591	122	(	(	PUNCT
ejpam-5205	591	123	g	g	NOUN
ejpam-5205	591	124	)	)	PUNCT
ejpam-5205	591	125	.	.	PUNCT
ejpam-5205	592	1	r.	r.	PROPN
ejpam-5205	592	2	fortosa	fortosa	PROPN
ejpam-5205	592	3	,	,	PUNCT
ejpam-5205	592	4	s.	s.	PROPN
ejpam-5205	592	5	canoy	canoy	PROPN
ejpam-5205	592	6	jr	jr	PROPN
ejpam-5205	592	7	.	.	PROPN
ejpam-5205	592	8	/	/	SYM
ejpam-5205	592	9	eur	eur	PROPN
ejpam-5205	592	10	.	.	PUNCT
ejpam-5205	593	1	j.	j.	PROPN
ejpam-5205	593	2	pure	pure	PROPN
ejpam-5205	593	3	appl	appl	PROPN
ejpam-5205	593	4	.	.	PROPN
ejpam-5205	593	5	math	math	PROPN
ejpam-5205	593	6	,	,	PUNCT
ejpam-5205	593	7	17	17	NUM
ejpam-5205	593	8	(	(	PUNCT
ejpam-5205	593	9	2	2	NUM
ejpam-5205	593	10	)	)	PUNCT
ejpam-5205	593	11	(	(	PUNCT
ejpam-5205	593	12	2024	2024	NUM
ejpam-5205	593	13	)	)	PUNCT
ejpam-5205	593	14	,	,	PUNCT
ejpam-5205	593	15	1335	1335	NUM
ejpam-5205	593	16	-	-	SYM
ejpam-5205	593	17	1351	1351	NUM
ejpam-5205	593	18	1349	1349	NUM
ejpam-5205	593	19	proof	proof	NOUN
ejpam-5205	593	20	.	.	PUNCT
ejpam-5205	594	1	let	let	VERB
ejpam-5205	594	2	f	f	PROPN
ejpam-5205	594	3	=	=	SYM
ejpam-5205	594	4	(	(	PUNCT
ejpam-5205	594	5	v0	v0	PROPN
ejpam-5205	594	6	,	,	PUNCT
ejpam-5205	594	7	v1	v1	NOUN
ejpam-5205	594	8	,	,	PUNCT
ejpam-5205	594	9	v2	v2	PROPN
ejpam-5205	594	10	)	)	PUNCT
ejpam-5205	594	11	be	be	AUX
ejpam-5205	594	12	a	a	DET
ejpam-5205	594	13	cvrdf	cvrdf	NOUN
ejpam-5205	594	14	on	on	ADP
ejpam-5205	594	15	g	g	NOUN
ejpam-5205	594	16	□	□	NOUN
ejpam-5205	594	17	h	h	NOUN
ejpam-5205	594	18	and	and	CCONJ
ejpam-5205	594	19	let	let	VERB
ejpam-5205	594	20	x	x	PUNCT
ejpam-5205	594	21	∈	∈	NOUN
ejpam-5205	594	22	s0	s0	PROPN
ejpam-5205	594	23	g	g	PROPN
ejpam-5205	594	24	and	and	CCONJ
ejpam-5205	594	25	p	p	NOUN
ejpam-5205	594	26	∈	∈	PROPN
ejpam-5205	594	27	t	t	NOUN
ejpam-5205	594	28	0	0	NUM
ejpam-5205	595	1	x	x	X
ejpam-5205	595	2	.	.	PUNCT
ejpam-5205	596	1	then	then	ADV
ejpam-5205	596	2	(	(	PUNCT
ejpam-5205	596	3	x	x	X
ejpam-5205	596	4	,	,	PUNCT
ejpam-5205	596	5	p	p	NOUN
ejpam-5205	596	6	)	)	PUNCT
ejpam-5205	596	7	∈	∈	PROPN
ejpam-5205	596	8	v0	v0	NOUN
ejpam-5205	596	9	.	.	PUNCT
ejpam-5205	597	1	this	this	PRON
ejpam-5205	597	2	shows	show	VERB
ejpam-5205	597	3	that	that	SCONJ
ejpam-5205	597	4	(	(	PUNCT
ejpam-5205	597	5	i	i	NOUN
ejpam-5205	597	6	)	)	PUNCT
ejpam-5205	597	7	holds	hold	VERB
ejpam-5205	597	8	.	.	PUNCT
ejpam-5205	598	1	by	by	ADP
ejpam-5205	598	2	lemma	lemma	PROPN
ejpam-5205	598	3	3	3	NUM
ejpam-5205	598	4	,	,	PUNCT
ejpam-5205	598	5	v1	v1	VERB
ejpam-5205	598	6	∪	∪	NOUN
ejpam-5205	598	7	v2	v2	NOUN
ejpam-5205	598	8	=	=	SYM
ejpam-5205	598	9	(	(	PUNCT
ejpam-5205	598	10	s1	s1	PROPN
ejpam-5205	598	11	g	g	PROPN
ejpam-5205	598	12	∪	∪	PROPN
ejpam-5205	598	13	s2	s2	PROPN
ejpam-5205	598	14	g	g	NOUN
ejpam-5205	598	15	)	)	PUNCT
ejpam-5205	598	16	×	×	NOUN
ejpam-5205	598	17	(	(	PUNCT
ejpam-5205	598	18	s1	s1	PROPN
ejpam-5205	598	19	h	h	PROPN
ejpam-5205	598	20	∪	∪	PROPN
ejpam-5205	598	21	s2	s2	PROPN
ejpam-5205	598	22	h	h	NOUN
ejpam-5205	598	23	)	)	PUNCT
ejpam-5205	598	24	.	.	PUNCT
ejpam-5205	599	1	hence	hence	ADV
ejpam-5205	599	2	,	,	PUNCT
ejpam-5205	599	3	by	by	ADP
ejpam-5205	599	4	theorem	theorem	NOUN
ejpam-5205	599	5	6	6	NUM
ejpam-5205	599	6	,	,	PUNCT
ejpam-5205	599	7	(	(	PUNCT
ejpam-5205	599	8	ii	ii	NOUN
ejpam-5205	599	9	)	)	PUNCT
ejpam-5205	599	10	holds	hold	VERB
ejpam-5205	599	11	.	.	PUNCT
ejpam-5205	600	1	conversely	conversely	ADV
ejpam-5205	600	2	,	,	PUNCT
ejpam-5205	600	3	suppose	suppose	VERB
ejpam-5205	600	4	that	that	SCONJ
ejpam-5205	600	5	(	(	PUNCT
ejpam-5205	600	6	i	i	NOUN
ejpam-5205	600	7	)	)	PUNCT
ejpam-5205	600	8	and	and	CCONJ
ejpam-5205	600	9	(	(	PUNCT
ejpam-5205	600	10	ii	ii	NOUN
ejpam-5205	600	11	)	)	PUNCT
ejpam-5205	600	12	hold	hold	VERB
ejpam-5205	600	13	.	.	PUNCT
ejpam-5205	601	1	by	by	ADP
ejpam-5205	601	2	(	(	PUNCT
ejpam-5205	601	3	i	i	NOUN
ejpam-5205	601	4	)	)	PUNCT
ejpam-5205	601	5	.	.	PUNCT
ejpam-5205	602	1	let	let	VERB
ejpam-5205	602	2	(	(	PUNCT
ejpam-5205	602	3	x	x	X
ejpam-5205	602	4	,	,	PUNCT
ejpam-5205	602	5	p	p	NOUN
ejpam-5205	602	6	)	)	PUNCT
ejpam-5205	602	7	∈	∈	PROPN
ejpam-5205	602	8	v0	v0	NOUN
ejpam-5205	602	9	.	.	PUNCT
ejpam-5205	603	1	then	then	ADV
ejpam-5205	603	2	x	x	SYM
ejpam-5205	603	3	∈	∈	PROPN
ejpam-5205	603	4	s0	s0	PROPN
ejpam-5205	603	5	g	g	PROPN
ejpam-5205	603	6	and	and	CCONJ
ejpam-5205	603	7	p	p	NOUN
ejpam-5205	603	8	∈	∈	PROPN
ejpam-5205	603	9	t	t	NOUN
ejpam-5205	603	10	0	0	NUM
ejpam-5205	603	11	x	x	X
ejpam-5205	603	12	.	.	PUNCT
ejpam-5205	604	1	by	by	ADP
ejpam-5205	604	2	(	(	PUNCT
ejpam-5205	604	3	i	i	NOUN
ejpam-5205	604	4	)	)	PUNCT
ejpam-5205	604	5	,	,	PUNCT
ejpam-5205	604	6	there	there	PRON
ejpam-5205	604	7	exists	exist	VERB
ejpam-5205	604	8	(	(	PUNCT
ejpam-5205	604	9	y	y	NOUN
ejpam-5205	604	10	,	,	PUNCT
ejpam-5205	604	11	q	q	X
ejpam-5205	604	12	)	)	PUNCT
ejpam-5205	604	13	∈	∈	PROPN
ejpam-5205	604	14	ng	ng	PROPN
ejpam-5205	604	15	□	□	PROPN
ejpam-5205	604	16	h	h	NOUN
ejpam-5205	604	17	(	(	PUNCT
ejpam-5205	604	18	(	(	PUNCT
ejpam-5205	604	19	x	x	NOUN
ejpam-5205	604	20	,	,	PUNCT
ejpam-5205	604	21	p	p	NOUN
ejpam-5205	604	22	)	)	PUNCT
ejpam-5205	604	23	)	)	PUNCT
ejpam-5205	604	24	.	.	PUNCT
ejpam-5205	605	1	this	this	PRON
ejpam-5205	605	2	implies	imply	VERB
ejpam-5205	605	3	that	that	SCONJ
ejpam-5205	605	4	f	f	PROPN
ejpam-5205	605	5	is	be	AUX
ejpam-5205	605	6	an	an	DET
ejpam-5205	605	7	rdf	rdf	NOUN
ejpam-5205	605	8	on	on	ADP
ejpam-5205	605	9	g	g	NOUN
ejpam-5205	605	10	□	□	PROPN
ejpam-5205	605	11	h.	h.	NOUN
ejpam-5205	605	12	by	by	ADP
ejpam-5205	605	13	(	(	PUNCT
ejpam-5205	605	14	a	a	X
ejpam-5205	605	15	)	)	PUNCT
ejpam-5205	605	16	and	and	CCONJ
ejpam-5205	605	17	(	(	PUNCT
ejpam-5205	605	18	b	b	NOUN
ejpam-5205	605	19	)	)	PUNCT
ejpam-5205	605	20	,	,	PUNCT
ejpam-5205	605	21	s1	s1	PROPN
ejpam-5205	605	22	g	g	PROPN
ejpam-5205	605	23	∪	∪	PROPN
ejpam-5205	605	24	s2	s2	PROPN
ejpam-5205	605	25	g	g	NOUN
ejpam-5205	605	26	and	and	CCONJ
ejpam-5205	605	27	s1	s1	PROPN
ejpam-5205	605	28	h	h	PROPN
ejpam-5205	605	29	∪	∪	PROPN
ejpam-5205	605	30	s2	s2	PROPN
ejpam-5205	605	31	h	h	NOUN
ejpam-5205	605	32	are	be	AUX
ejpam-5205	605	33	convex	convex	NOUN
ejpam-5205	605	34	sets	set	NOUN
ejpam-5205	605	35	in	in	ADP
ejpam-5205	605	36	g	g	PROPN
ejpam-5205	605	37	and	and	CCONJ
ejpam-5205	605	38	h	h	NOUN
ejpam-5205	605	39	,	,	PUNCT
ejpam-5205	605	40	respectively	respectively	ADV
ejpam-5205	605	41	.	.	PUNCT
ejpam-5205	606	1	hence	hence	ADV
ejpam-5205	606	2	,	,	PUNCT
ejpam-5205	606	3	by	by	ADP
ejpam-5205	606	4	theorem	theorem	NOUN
ejpam-5205	606	5	5	5	NUM
ejpam-5205	606	6	,	,	PUNCT
ejpam-5205	606	7	v1	v1	NOUN
ejpam-5205	606	8	∪	∪	NOUN
ejpam-5205	606	9	v2	v2	NOUN
ejpam-5205	606	10	is	be	AUX
ejpam-5205	606	11	convex	convex	ADJ
ejpam-5205	606	12	in	in	ADP
ejpam-5205	606	13	g	g	PROPN
ejpam-5205	606	14	□	□	PROPN
ejpam-5205	606	15	h.	h.	PROPN
ejpam-5205	606	16	therefore	therefore	ADV
ejpam-5205	606	17	,	,	PUNCT
ejpam-5205	606	18	f	f	PROPN
ejpam-5205	606	19	is	be	AUX
ejpam-5205	606	20	a	a	DET
ejpam-5205	606	21	cvrdf	cvrdf	NOUN
ejpam-5205	606	22	on	on	ADP
ejpam-5205	606	23	g	g	PROPN
ejpam-5205	606	24	□	□	PROPN
ejpam-5205	606	25	h.	h.	NOUN
ejpam-5205	606	26	corollary	corollary	NOUN
ejpam-5205	606	27	6	6	NUM
ejpam-5205	606	28	.	.	PUNCT
ejpam-5205	607	1	let	let	VERB
ejpam-5205	607	2	g	g	NOUN
ejpam-5205	607	3	and	and	CCONJ
ejpam-5205	607	4	h	h	NOUN
ejpam-5205	607	5	be	be	AUX
ejpam-5205	607	6	connected	connect	VERB
ejpam-5205	607	7	graphs	graph	NOUN
ejpam-5205	607	8	of	of	ADP
ejpam-5205	607	9	orders	order	NOUN
ejpam-5205	607	10	m	m	VERB
ejpam-5205	607	11	and	and	CCONJ
ejpam-5205	607	12	n	n	CCONJ
ejpam-5205	607	13	,	,	PUNCT
ejpam-5205	607	14	respectively	respectively	ADV
ejpam-5205	607	15	.	.	PUNCT
ejpam-5205	608	1	then	then	ADV
ejpam-5205	608	2	γcvr(g	γcvr(g	PROPN
ejpam-5205	608	3	□	□	SYM
ejpam-5205	608	4	h	h	NOUN
ejpam-5205	608	5	)	)	PUNCT
ejpam-5205	608	6	≤	≤	NOUN
ejpam-5205	608	7	min{n	min{n	NOUN
ejpam-5205	608	8	·	·	PUNCT
ejpam-5205	608	9	γcvr(g),m	γcvr(g),m	PUNCT
ejpam-5205	608	10	·	·	PUNCT
ejpam-5205	608	11	γcvr(h	γcvr(h	NOUN
ejpam-5205	608	12	)	)	PUNCT
ejpam-5205	608	13	}	}	PUNCT
ejpam-5205	608	14	.	.	PUNCT
ejpam-5205	609	1	proof	proof	NOUN
ejpam-5205	609	2	.	.	PUNCT
ejpam-5205	610	1	let	let	VERB
ejpam-5205	610	2	g	g	PROPN
ejpam-5205	610	3	=	=	SYM
ejpam-5205	610	4	(	(	PUNCT
ejpam-5205	610	5	w0,w1,w2	w0,w1,w2	ADV
ejpam-5205	610	6	)	)	PUNCT
ejpam-5205	610	7	be	be	AUX
ejpam-5205	610	8	a	a	DET
ejpam-5205	610	9	γcvr	γcvr	NOUN
ejpam-5205	610	10	-	-	PUNCT
ejpam-5205	610	11	function	function	NOUN
ejpam-5205	610	12	on	on	ADP
ejpam-5205	610	13	g.	g.	PROPN
ejpam-5205	610	14	set	set	PROPN
ejpam-5205	610	15	v0	v0	PROPN
ejpam-5205	610	16	=	=	SYM
ejpam-5205	610	17	w0	w0	PROPN
ejpam-5205	610	18	×	×	PROPN
ejpam-5205	610	19	v	v	NOUN
ejpam-5205	610	20	(	(	PUNCT
ejpam-5205	610	21	h	h	NOUN
ejpam-5205	610	22	)	)	PUNCT
ejpam-5205	610	23	,	,	PUNCT
ejpam-5205	610	24	v1	v1	NOUN
ejpam-5205	610	25	=	=	SYM
ejpam-5205	610	26	w1	w1	NOUN
ejpam-5205	610	27	×	×	NOUN
ejpam-5205	610	28	v	v	NOUN
ejpam-5205	610	29	(	(	PUNCT
ejpam-5205	610	30	h	h	NOUN
ejpam-5205	610	31	)	)	PUNCT
ejpam-5205	610	32	,	,	PUNCT
ejpam-5205	610	33	and	and	CCONJ
ejpam-5205	610	34	v2	v2	NOUN
ejpam-5205	610	35	=	=	SYM
ejpam-5205	610	36	w2	w2	NOUN
ejpam-5205	610	37	×	×	PROPN
ejpam-5205	610	38	v	v	PROPN
ejpam-5205	610	39	(	(	PUNCT
ejpam-5205	610	40	h	h	NOUN
ejpam-5205	610	41	)	)	PUNCT
ejpam-5205	610	42	.	.	PUNCT
ejpam-5205	611	1	let	let	VERB
ejpam-5205	611	2	f	f	PROPN
ejpam-5205	611	3	=	=	SYM
ejpam-5205	611	4	(	(	PUNCT
ejpam-5205	611	5	v0	v0	PROPN
ejpam-5205	611	6	,	,	PUNCT
ejpam-5205	611	7	v1	v1	NOUN
ejpam-5205	611	8	,	,	PUNCT
ejpam-5205	611	9	v2	v2	PROPN
ejpam-5205	611	10	)	)	PUNCT
ejpam-5205	611	11	.	.	PUNCT
ejpam-5205	612	1	then	then	ADV
ejpam-5205	612	2	s0	s0	PROPN
ejpam-5205	612	3	g	g	PROPN
ejpam-5205	612	4	=	=	PROPN
ejpam-5205	612	5	w0	w0	PROPN
ejpam-5205	612	6	,	,	PUNCT
ejpam-5205	612	7	s1	s1	NOUN
ejpam-5205	612	8	g	g	PROPN
ejpam-5205	612	9	=	=	PROPN
ejpam-5205	612	10	w1	w1	NOUN
ejpam-5205	612	11	,	,	PUNCT
ejpam-5205	612	12	and	and	CCONJ
ejpam-5205	612	13	s2	s2	VERB
ejpam-5205	612	14	g	g	NOUN
ejpam-5205	612	15	=	=	PROPN
ejpam-5205	612	16	w2	w2	NOUN
ejpam-5205	612	17	.	.	PUNCT
ejpam-5205	613	1	hence	hence	ADV
ejpam-5205	613	2	,	,	PUNCT
ejpam-5205	613	3	s1	s1	PROPN
ejpam-5205	613	4	g	g	PROPN
ejpam-5205	613	5	∪	∪	PROPN
ejpam-5205	613	6	s2	s2	NOUN
ejpam-5205	613	7	g	g	NOUN
ejpam-5205	613	8	=	=	NOUN
ejpam-5205	613	9	w1	w1	PROPN
ejpam-5205	613	10	∪	∪	NOUN
ejpam-5205	613	11	w2	w2	PROPN
ejpam-5205	613	12	is	be	AUX
ejpam-5205	613	13	a	a	DET
ejpam-5205	613	14	convex	convex	NOUN
ejpam-5205	613	15	dominating	dominating	NOUN
ejpam-5205	613	16	set	set	VERB
ejpam-5205	613	17	in	in	ADP
ejpam-5205	613	18	g	g	PROPN
ejpam-5205	613	19	and	and	CCONJ
ejpam-5205	613	20	s1	s1	PROPN
ejpam-5205	613	21	h	h	PROPN
ejpam-5205	613	22	∪	∪	PROPN
ejpam-5205	613	23	s2	s2	NOUN
ejpam-5205	613	24	h	h	NOUN
ejpam-5205	613	25	=	=	SYM
ejpam-5205	613	26	v	v	PROPN
ejpam-5205	613	27	(	(	PUNCT
ejpam-5205	613	28	h	h	NOUN
ejpam-5205	613	29	)	)	PUNCT
ejpam-5205	613	30	.	.	PUNCT
ejpam-5205	614	1	hence	hence	ADV
ejpam-5205	614	2	,	,	PUNCT
ejpam-5205	614	3	by	by	ADP
ejpam-5205	614	4	theorem	theorem	NOUN
ejpam-5205	614	5	13	13	NUM
ejpam-5205	614	6	,	,	PUNCT
ejpam-5205	614	7	f	f	X
ejpam-5205	614	8	=	=	SYM
ejpam-5205	614	9	(	(	PUNCT
ejpam-5205	614	10	v0	v0	PROPN
ejpam-5205	614	11	,	,	PUNCT
ejpam-5205	614	12	v1	v1	NOUN
ejpam-5205	614	13	,	,	PUNCT
ejpam-5205	614	14	v2	v2	PROPN
ejpam-5205	614	15	)	)	PUNCT
ejpam-5205	614	16	is	be	AUX
ejpam-5205	614	17	a	a	DET
ejpam-5205	614	18	cvrdf	cvrdf	NOUN
ejpam-5205	614	19	on	on	ADP
ejpam-5205	614	20	g	g	NOUN
ejpam-5205	614	21	□	□	PROPN
ejpam-5205	614	22	h	h	NOUN
ejpam-5205	614	23	and	and	CCONJ
ejpam-5205	614	24	γcvr(g	γcvr(g	NOUN
ejpam-5205	614	25	□	□	ADJ
ejpam-5205	614	26	h	h	NOUN
ejpam-5205	614	27	)	)	PUNCT
ejpam-5205	614	28	≤	≤	NOUN
ejpam-5205	614	29	ωcvr	ωcvr	ADP
ejpam-5205	614	30	g	g	PROPN
ejpam-5205	614	31	□	□	PROPN
ejpam-5205	614	32	h(f	h(f	X
ejpam-5205	614	33	)	)	PUNCT
ejpam-5205	614	34	=	=	PUNCT
ejpam-5205	614	35	|v1|+	|v1|+	PRON
ejpam-5205	614	36	2|v2|	2|v2|	NUM
ejpam-5205	614	37	=	=	SYM
ejpam-5205	614	38	|w1	|w1	NOUN
ejpam-5205	614	39	×	×	NOUN
ejpam-5205	614	40	v	v	NOUN
ejpam-5205	614	41	(	(	PUNCT
ejpam-5205	614	42	h)|+	h)|+	PROPN
ejpam-5205	614	43	2|w2	2|w2	NUM
ejpam-5205	614	44	×	×	NOUN
ejpam-5205	614	45	v	v	NOUN
ejpam-5205	614	46	(	(	PUNCT
ejpam-5205	614	47	h)|	h)|	NOUN
ejpam-5205	614	48	=	=	PUNCT
ejpam-5205	614	49	|v	|v	PROPN
ejpam-5205	614	50	(	(	PUNCT
ejpam-5205	614	51	h)|	h)|	PROPN
ejpam-5205	614	52	×	×	PROPN
ejpam-5205	614	53	(	(	PUNCT
ejpam-5205	614	54	|w1|+	|w1|+	PROPN
ejpam-5205	614	55	2|w2|	2|w2|	NUM
ejpam-5205	614	56	)	)	PUNCT
ejpam-5205	614	57	=	=	SYM
ejpam-5205	615	1	n(|w1|+	n(|w1|+	NUM
ejpam-5205	615	2	2|w2|	2|w2|	NUM
ejpam-5205	615	3	)	)	PUNCT
ejpam-5205	615	4	=	=	SYM
ejpam-5205	616	1	n	n	X
ejpam-5205	616	2	·	·	PUNCT
ejpam-5205	616	3	γcvr(g	γcvr(g	NOUN
ejpam-5205	616	4	)	)	PUNCT
ejpam-5205	616	5	.	.	PUNCT
ejpam-5205	617	1	a	a	DET
ejpam-5205	617	2	similar	similar	ADJ
ejpam-5205	617	3	argument	argument	NOUN
ejpam-5205	617	4	is	be	AUX
ejpam-5205	617	5	used	use	VERB
ejpam-5205	617	6	to	to	PART
ejpam-5205	617	7	show	show	VERB
ejpam-5205	617	8	that	that	SCONJ
ejpam-5205	617	9	γcvr(g	γcvr(g	PROPN
ejpam-5205	617	10	□	□	SYM
ejpam-5205	617	11	h	h	NOUN
ejpam-5205	617	12	)	)	PUNCT
ejpam-5205	617	13	≤	≤	NUM
ejpam-5205	617	14	m	m	VERB
ejpam-5205	617	15	·	·	PUNCT
ejpam-5205	617	16	γcvr(h	γcvr(h	NOUN
ejpam-5205	617	17	)	)	PUNCT
ejpam-5205	617	18	.	.	PUNCT
ejpam-5205	618	1	hence	hence	ADV
ejpam-5205	618	2	,	,	PUNCT
ejpam-5205	618	3	γcvr(g	γcvr(g	PROPN
ejpam-5205	618	4	□	□	SYM
ejpam-5205	618	5	h	h	NOUN
ejpam-5205	618	6	)	)	PUNCT
ejpam-5205	618	7	≤	≤	NOUN
ejpam-5205	618	8	min{n	min{n	NOUN
ejpam-5205	618	9	·	·	PUNCT
ejpam-5205	618	10	γcvr(g),m	γcvr(g),m	PUNCT
ejpam-5205	618	11	·	·	PUNCT
ejpam-5205	618	12	γcvr(h	γcvr(h	NOUN
ejpam-5205	618	13	)	)	PUNCT
ejpam-5205	618	14	}	}	PUNCT
ejpam-5205	618	15	.	.	PUNCT
ejpam-5205	619	1	remark	remark	NOUN
ejpam-5205	619	2	2	2	NUM
ejpam-5205	619	3	.	.	PUNCT
ejpam-5205	620	1	the	the	DET
ejpam-5205	620	2	bound	bind	VERB
ejpam-5205	620	3	given	give	VERB
ejpam-5205	620	4	in	in	ADP
ejpam-5205	620	5	corollary	corollary	ADJ
ejpam-5205	620	6	6	6	NUM
ejpam-5205	620	7	is	be	AUX
ejpam-5205	620	8	sharp	sharp	ADJ
ejpam-5205	620	9	.	.	PUNCT
ejpam-5205	621	1	it	it	PRON
ejpam-5205	621	2	can	can	AUX
ejpam-5205	621	3	be	be	AUX
ejpam-5205	621	4	verified	verify	VERB
ejpam-5205	621	5	that	that	SCONJ
ejpam-5205	621	6	for	for	ADP
ejpam-5205	621	7	any	any	DET
ejpam-5205	621	8	connected	connected	ADJ
ejpam-5205	621	9	graph	graph	NOUN
ejpam-5205	621	10	h	h	NOUN
ejpam-5205	621	11	of	of	ADP
ejpam-5205	621	12	order	order	NOUN
ejpam-5205	621	13	m	m	VERB
ejpam-5205	621	14	,	,	PUNCT
ejpam-5205	621	15	γcvr(kn	γcvr(kn	NOUN
ejpam-5205	621	16	□	□	NOUN
ejpam-5205	621	17	h	h	NOUN
ejpam-5205	621	18	)	)	PUNCT
ejpam-5205	621	19	=	=	SYM
ejpam-5205	621	20	2	2	NUM
ejpam-5205	621	21	m	m	NOUN
ejpam-5205	621	22	=	=	ADJ
ejpam-5205	621	23	γcvr(kn	γcvr(kn	PROPN
ejpam-5205	621	24	)	)	PUNCT
ejpam-5205	621	25	·	·	PUNCT
ejpam-5205	621	26	m.	m.	NOUN
ejpam-5205	621	27	4	4	NUM
ejpam-5205	621	28	.	.	PUNCT
ejpam-5205	621	29	conclusion	conclusion	VERB
ejpam-5205	621	30	the	the	DET
ejpam-5205	621	31	concept	concept	NOUN
ejpam-5205	621	32	of	of	ADP
ejpam-5205	621	33	convex	convex	ADJ
ejpam-5205	621	34	roman	roman	ADJ
ejpam-5205	621	35	domination	domination	NOUN
ejpam-5205	621	36	in	in	ADP
ejpam-5205	621	37	a	a	DET
ejpam-5205	621	38	graph	graph	NOUN
ejpam-5205	621	39	has	have	AUX
ejpam-5205	621	40	been	be	AUX
ejpam-5205	621	41	investigated	investigate	VERB
ejpam-5205	621	42	further	far	ADV
ejpam-5205	621	43	in	in	ADP
ejpam-5205	621	44	this	this	DET
ejpam-5205	621	45	study	study	NOUN
ejpam-5205	621	46	.	.	PUNCT
ejpam-5205	622	1	specifically	specifically	ADV
ejpam-5205	622	2	,	,	PUNCT
ejpam-5205	622	3	convex	convex	VERB
ejpam-5205	622	4	roman	roman	ADJ
ejpam-5205	622	5	dominating	dominating	NOUN
ejpam-5205	622	6	functions	function	NOUN
ejpam-5205	622	7	on	on	ADP
ejpam-5205	622	8	graphs	graph	NOUN
ejpam-5205	622	9	resulting	result	VERB
ejpam-5205	622	10	from	from	ADP
ejpam-5205	622	11	the	the	DET
ejpam-5205	622	12	corona	corona	NOUN
ejpam-5205	622	13	,	,	PUNCT
ejpam-5205	622	14	edge	edge	NOUN
ejpam-5205	622	15	corona	corona	NOUN
ejpam-5205	622	16	,	,	PUNCT
ejpam-5205	622	17	complementary	complementary	ADJ
ejpam-5205	622	18	prism	prism	NOUN
ejpam-5205	622	19	,	,	PUNCT
ejpam-5205	622	20	lexicographic	lexicographic	ADJ
ejpam-5205	622	21	,	,	PUNCT
ejpam-5205	622	22	and	and	CCONJ
ejpam-5205	622	23	cartesian	cartesian	ADJ
ejpam-5205	622	24	product	product	NOUN
ejpam-5205	622	25	of	of	ADP
ejpam-5205	622	26	graphs	graph	NOUN
ejpam-5205	622	27	have	have	AUX
ejpam-5205	622	28	been	be	AUX
ejpam-5205	622	29	characterized	characterize	VERB
ejpam-5205	622	30	.	.	PUNCT
ejpam-5205	623	1	these	these	DET
ejpam-5205	623	2	characterizations	characterization	NOUN
ejpam-5205	623	3	have	have	AUX
ejpam-5205	623	4	been	be	AUX
ejpam-5205	623	5	utilized	utilize	VERB
ejpam-5205	623	6	to	to	PART
ejpam-5205	623	7	derive	derive	VERB
ejpam-5205	623	8	bounds	bound	NOUN
ejpam-5205	623	9	or	or	CCONJ
ejpam-5205	623	10	exact	exact	ADJ
ejpam-5205	623	11	values	value	NOUN
ejpam-5205	623	12	for	for	ADP
ejpam-5205	623	13	the	the	DET
ejpam-5205	623	14	convex	convex	ADJ
ejpam-5205	623	15	roman	roman	ADJ
ejpam-5205	623	16	domination	domination	NOUN
ejpam-5205	623	17	number	number	NOUN
ejpam-5205	623	18	of	of	ADP
ejpam-5205	623	19	each	each	PRON
ejpam-5205	623	20	of	of	ADP
ejpam-5205	623	21	these	these	DET
ejpam-5205	623	22	graphs	graph	NOUN
ejpam-5205	623	23	.	.	PUNCT
ejpam-5205	624	1	interested	interested	ADJ
ejpam-5205	624	2	researchers	researcher	NOUN
ejpam-5205	624	3	may	may	AUX
ejpam-5205	624	4	investigate	investigate	VERB
ejpam-5205	624	5	this	this	DET
ejpam-5205	624	6	concept	concept	NOUN
ejpam-5205	624	7	for	for	ADP
ejpam-5205	624	8	other	other	ADJ
ejpam-5205	624	9	graphs	graph	NOUN
ejpam-5205	624	10	not	not	PART
ejpam-5205	624	11	considered	consider	VERB
ejpam-5205	624	12	in	in	ADP
ejpam-5205	624	13	this	this	DET
ejpam-5205	624	14	paper	paper	NOUN
ejpam-5205	624	15	.	.	PUNCT
ejpam-5205	625	1	moreover	moreover	ADV
ejpam-5205	625	2	,	,	PUNCT
ejpam-5205	625	3	it	it	PRON
ejpam-5205	625	4	may	may	AUX
ejpam-5205	625	5	be	be	AUX
ejpam-5205	625	6	interesting	interesting	ADJ
ejpam-5205	625	7	to	to	PART
ejpam-5205	625	8	investigate	investigate	VERB
ejpam-5205	625	9	the	the	DET
ejpam-5205	625	10	complexity	complexity	NOUN
ejpam-5205	625	11	of	of	ADP
ejpam-5205	625	12	the	the	DET
ejpam-5205	625	13	convex	convex	ADJ
ejpam-5205	625	14	roman	roman	ADJ
ejpam-5205	625	15	domination	domination	NOUN
ejpam-5205	625	16	problem	problem	NOUN
ejpam-5205	625	17	and	and	CCONJ
ejpam-5205	625	18	explore	explore	VERB
ejpam-5205	625	19	some	some	DET
ejpam-5205	625	20	relationships	relationship	NOUN
ejpam-5205	625	21	,	,	PUNCT
ejpam-5205	625	22	if	if	SCONJ
ejpam-5205	625	23	any	any	PRON
ejpam-5205	625	24	,	,	PUNCT
ejpam-5205	625	25	of	of	ADP
ejpam-5205	625	26	this	this	DET
ejpam-5205	625	27	newly	newly	ADV
ejpam-5205	625	28	defined	define	VERB
ejpam-5205	625	29	parameter	parameter	NOUN
ejpam-5205	625	30	with	with	ADP
ejpam-5205	625	31	other	other	ADJ
ejpam-5205	625	32	existing	exist	VERB
ejpam-5205	625	33	and	and	CCONJ
ejpam-5205	625	34	related	related	ADJ
ejpam-5205	625	35	parameters	parameter	NOUN
ejpam-5205	625	36	to	to	ADP
ejpam-5205	625	37	it	it	PRON
ejpam-5205	625	38	.	.	PUNCT
ejpam-5205	626	1	references	reference	NOUN
ejpam-5205	626	2	1350	1350	NUM
ejpam-5205	626	3	acknowledgements	acknowledgement	NOUN
ejpam-5205	626	4	the	the	DET
ejpam-5205	626	5	authors	author	NOUN
ejpam-5205	626	6	would	would	AUX
ejpam-5205	626	7	like	like	VERB
ejpam-5205	626	8	to	to	PART
ejpam-5205	626	9	thank	thank	VERB
ejpam-5205	626	10	the	the	DET
ejpam-5205	626	11	referees	referee	NOUN
ejpam-5205	626	12	for	for	ADP
ejpam-5205	626	13	the	the	DET
ejpam-5205	626	14	invaluable	invaluable	ADJ
ejpam-5205	626	15	comments	comment	NOUN
ejpam-5205	626	16	and	and	CCONJ
ejpam-5205	626	17	suggestions	suggestion	NOUN
ejpam-5205	626	18	they	they	PRON
ejpam-5205	626	19	gave	give	VERB
ejpam-5205	626	20	us	we	PRON
ejpam-5205	626	21	which	which	PRON
ejpam-5205	626	22	led	lead	VERB
ejpam-5205	626	23	to	to	ADP
ejpam-5205	626	24	the	the	DET
ejpam-5205	626	25	improvement	improvement	NOUN
ejpam-5205	626	26	of	of	ADP
ejpam-5205	626	27	the	the	DET
ejpam-5205	626	28	paper	paper	NOUN
ejpam-5205	626	29	.	.	PUNCT
ejpam-5205	627	1	the	the	DET
ejpam-5205	627	2	authors	author	NOUN
ejpam-5205	627	3	are	be	AUX
ejpam-5205	627	4	also	also	ADV
ejpam-5205	627	5	grateful	grateful	ADJ
ejpam-5205	627	6	to	to	ADP
ejpam-5205	627	7	the	the	DET
ejpam-5205	627	8	department	department	NOUN
ejpam-5205	627	9	of	of	ADP
ejpam-5205	627	10	science	science	NOUN
ejpam-5205	627	11	and	and	CCONJ
ejpam-5205	627	12	technology	technology	NOUN
ejpam-5205	627	13	accelerated	accelerate	VERB
ejpam-5205	627	14	science	science	NOUN
ejpam-5205	627	15	and	and	CCONJ
ejpam-5205	627	16	technology	technology	NOUN
ejpam-5205	627	17	human	human	ADJ
ejpam-5205	627	18	resource	resource	NOUN
ejpam-5205	627	19	development	development	NOUN
ejpam-5205	627	20	program	program	NOUN
ejpam-5205	627	21	(	(	PUNCT
ejpam-5205	627	22	dost	dost	NOUN
ejpam-5205	627	23	-	-	PUNCT
ejpam-5205	627	24	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-5205	627	25	and	and	CCONJ
ejpam-5205	627	26	msu	msu	PROPN
ejpam-5205	627	27	-	-	PUNCT
ejpam-5205	627	28	iligan	iligan	PROPN
ejpam-5205	627	29	institute	institute	PROPN
ejpam-5205	627	30	of	of	ADP
ejpam-5205	627	31	technology	technology	NOUN
ejpam-5205	627	32	for	for	ADP
ejpam-5205	627	33	funding	fund	VERB
ejpam-5205	627	34	this	this	DET
ejpam-5205	627	35	research	research	NOUN
ejpam-5205	627	36	.	.	PUNCT
ejpam-5205	628	1	references	reference	NOUN
ejpam-5205	628	2	[	[	X
ejpam-5205	628	3	1	1	NUM
ejpam-5205	628	4	]	]	PUNCT
ejpam-5205	628	5	m.	m.	NOUN
ejpam-5205	628	6	adabi	adabi	PROPN
ejpam-5205	628	7	,	,	PUNCT
ejpam-5205	628	8	e.	e.	PROPN
ejpam-5205	628	9	ebrahimi	ebrahimi	PROPN
ejpam-5205	628	10	targhi	targhi	PROPN
ejpam-5205	628	11	,	,	PUNCT
ejpam-5205	628	12	n.	n.	PROPN
ejpam-5205	628	13	jafari	jafari	PROPN
ejpam-5205	628	14	rad	rad	PROPN
ejpam-5205	628	15	,	,	PUNCT
ejpam-5205	628	16	and	and	CCONJ
ejpam-5205	628	17	m.	m.	NOUN
ejpam-5205	628	18	saied	saie	VERB
ejpam-5205	628	19	moradi	moradi	NOUN
ejpam-5205	628	20	.	.	PUNCT
ejpam-5205	629	1	properties	property	NOUN
ejpam-5205	629	2	of	of	ADP
ejpam-5205	629	3	independent	independent	ADJ
ejpam-5205	629	4	roman	roman	ADJ
ejpam-5205	629	5	domination	domination	NOUN
ejpam-5205	629	6	in	in	ADP
ejpam-5205	629	7	graphs	graph	NOUN
ejpam-5205	629	8	.	.	PUNCT
ejpam-5205	630	1	australasian	australasian	ADJ
ejpam-5205	630	2	journal	journal	NOUN
ejpam-5205	630	3	of	of	ADP
ejpam-5205	630	4	combinatorics	combinatoric	NOUN
ejpam-5205	630	5	,	,	PUNCT
ejpam-5205	630	6	52:11–18	52:11–18	NUM
ejpam-5205	630	7	,	,	PUNCT
ejpam-5205	630	8	2012	2012	NUM
ejpam-5205	630	9	.	.	PUNCT
ejpam-5205	631	1	[	[	X
ejpam-5205	631	2	2	2	NUM
ejpam-5205	631	3	]	]	X
ejpam-5205	631	4	h.a	h.a	PROPN
ejpam-5205	631	5	.	.	PROPN
ejpam-5205	631	6	ahangar	ahangar	PROPN
ejpam-5205	631	7	,	,	PUNCT
ejpam-5205	631	8	m.a	m.a	PROPN
ejpam-5205	631	9	.	.	PROPN
ejpam-5205	631	10	henning	henning	PROPN
ejpam-5205	631	11	,	,	PUNCT
ejpam-5205	631	12	v.	v.	ADP
ejpam-5205	631	13	samodivkin	samodivkin	NOUN
ejpam-5205	631	14	,	,	PUNCT
ejpam-5205	631	15	and	and	CCONJ
ejpam-5205	631	16	i.g	i.g	PROPN
ejpam-5205	631	17	.	.	PROPN
ejpam-5205	631	18	yero	yero	PROPN
ejpam-5205	631	19	.	.	PUNCT
ejpam-5205	631	20	total	total	ADJ
ejpam-5205	631	21	roman	roman	ADJ
ejpam-5205	631	22	domination	domination	NOUN
ejpam-5205	631	23	in	in	ADP
ejpam-5205	631	24	graphs	graph	NOUN
ejpam-5205	631	25	.	.	PUNCT
ejpam-5205	632	1	applicable	applicable	ADJ
ejpam-5205	632	2	analysis	analysis	NOUN
ejpam-5205	632	3	and	and	CCONJ
ejpam-5205	632	4	discrete	discrete	ADJ
ejpam-5205	632	5	mathematics	mathematic	NOUN
ejpam-5205	632	6	,	,	PUNCT
ejpam-5205	632	7	10(2):501–517	10(2):501–517	PROPN
ejpam-5205	632	8	,	,	PUNCT
ejpam-5205	632	9	2016	2016	NUM
ejpam-5205	632	10	.	.	PUNCT
ejpam-5205	633	1	[	[	X
ejpam-5205	633	2	3	3	X
ejpam-5205	633	3	]	]	X
ejpam-5205	633	4	m.p	m.p	PROPN
ejpam-5205	633	5	.	.	PROPN
ejpam-5205	633	6	alvarez	alvarez	PROPN
ejpam-5205	633	7	-	-	PUNCT
ejpam-5205	633	8	ruiz	ruiz	PROPN
ejpam-5205	633	9	,	,	PUNCT
ejpam-5205	633	10	t.	t.	PROPN
ejpam-5205	633	11	mediavilla	mediavilla	PROPN
ejpam-5205	633	12	-	-	PUNCT
ejpam-5205	633	13	gradolph	gradolph	NOUN
ejpam-5205	633	14	,	,	PUNCT
ejpam-5205	633	15	s.m	s.m	PROPN
ejpam-5205	633	16	.	.	PROPN
ejpam-5205	633	17	sheikholeslami	sheikholeslami	PROPN
ejpam-5205	633	18	,	,	PUNCT
ejpam-5205	633	19	j.c	j.c	PROPN
ejpam-5205	633	20	.	.	PROPN
ejpam-5205	633	21	valenzuelatripodoro	valenzuelatripodoro	PROPN
ejpam-5205	633	22	,	,	PUNCT
ejpam-5205	633	23	and	and	CCONJ
ejpam-5205	633	24	i.g	i.g	PROPN
ejpam-5205	633	25	.	.	PROPN
ejpam-5205	633	26	yero	yero	PROPN
ejpam-5205	633	27	.	.	PUNCT
ejpam-5205	634	1	on	on	ADP
ejpam-5205	634	2	the	the	DET
ejpam-5205	634	3	strong	strong	ADJ
ejpam-5205	634	4	roman	roman	ADJ
ejpam-5205	634	5	domination	domination	NOUN
ejpam-5205	634	6	number	number	NOUN
ejpam-5205	634	7	of	of	ADP
ejpam-5205	634	8	graphs	graph	NOUN
ejpam-5205	634	9	.	.	PUNCT
ejpam-5205	635	1	discrete	discrete	ADJ
ejpam-5205	635	2	applied	apply	VERB
ejpam-5205	635	3	mathematics	mathematic	NOUN
ejpam-5205	635	4	,	,	PUNCT
ejpam-5205	635	5	231:44–59	231:44–59	NUM
ejpam-5205	635	6	,	,	PUNCT
ejpam-5205	635	7	2017	2017	NUM
ejpam-5205	635	8	.	.	PUNCT
ejpam-5205	636	1	[	[	X
ejpam-5205	636	2	4	4	X
ejpam-5205	636	3	]	]	PUNCT
ejpam-5205	636	4	s.	s.	PROPN
ejpam-5205	636	5	banerjee	banerjee	PROPN
ejpam-5205	636	6	,	,	PUNCT
ejpam-5205	636	7	j.m	j.m	PROPN
ejpam-5205	636	8	.	.	PROPN
ejpam-5205	636	9	keil	keil	PROPN
ejpam-5205	636	10	,	,	PUNCT
ejpam-5205	636	11	and	and	CCONJ
ejpam-5205	636	12	d.	d.	PROPN
ejpam-5205	636	13	pradhan	pradhan	PROPN
ejpam-5205	636	14	.	.	PUNCT
ejpam-5205	637	1	perfect	perfect	ADJ
ejpam-5205	637	2	roman	roman	ADJ
ejpam-5205	637	3	domination	domination	NOUN
ejpam-5205	637	4	in	in	ADP
ejpam-5205	637	5	graphs	graph	NOUN
ejpam-5205	637	6	.	.	PUNCT
ejpam-5205	638	1	theoritical	theoritical	ADJ
ejpam-5205	638	2	computer	computer	NOUN
ejpam-5205	638	3	science	science	NOUN
ejpam-5205	638	4	,	,	PUNCT
ejpam-5205	638	5	796:1–21	796:1–21	NUM
ejpam-5205	638	6	,	,	PUNCT
ejpam-5205	638	7	2019	2019	NUM
ejpam-5205	638	8	.	.	PUNCT
ejpam-5205	639	1	[	[	X
ejpam-5205	639	2	5	5	NUM
ejpam-5205	639	3	]	]	X
ejpam-5205	639	4	r.a	r.a	PROPN
ejpam-5205	639	5	.	.	PROPN
ejpam-5205	639	6	beeler	beeler	PROPN
ejpam-5205	639	7	,	,	PUNCT
ejpam-5205	639	8	t.w	t.w	PROPN
ejpam-5205	639	9	.	.	PROPN
ejpam-5205	639	10	haynes	haynes	PROPN
ejpam-5205	639	11	,	,	PUNCT
ejpam-5205	639	12	and	and	CCONJ
ejpam-5205	639	13	s.t	s.t	PROPN
ejpam-5205	639	14	.	.	PROPN
ejpam-5205	639	15	hedetnieme	hedetnieme	PROPN
ejpam-5205	639	16	.	.	PUNCT
ejpam-5205	640	1	double	double	ADJ
ejpam-5205	640	2	roman	roman	ADJ
ejpam-5205	640	3	domination	domination	NOUN
ejpam-5205	640	4	.	.	PUNCT
ejpam-5205	641	1	discrete	discrete	ADJ
ejpam-5205	641	2	applied	apply	VERB
ejpam-5205	641	3	mathematics	mathematic	NOUN
ejpam-5205	641	4	,	,	PUNCT
ejpam-5205	641	5	211:23–29	211:23–29	NUM
ejpam-5205	641	6	,	,	PUNCT
ejpam-5205	641	7	2016	2016	NUM
ejpam-5205	641	8	.	.	PUNCT
ejpam-5205	642	1	[	[	X
ejpam-5205	642	2	6	6	NUM
ejpam-5205	642	3	]	]	PUNCT
ejpam-5205	642	4	g.	g.	PROPN
ejpam-5205	642	5	chartrand	chartrand	PROPN
ejpam-5205	642	6	,	,	PUNCT
ejpam-5205	642	7	j.	j.	PROPN
ejpam-5205	642	8	fink	fink	PROPN
ejpam-5205	642	9	,	,	PUNCT
ejpam-5205	642	10	and	and	CCONJ
ejpam-5205	642	11	p.	p.	PROPN
ejpam-5205	642	12	zhang	zhang	PROPN
ejpam-5205	642	13	.	.	PUNCT
ejpam-5205	643	1	convexity	convexity	NOUN
ejpam-5205	643	2	in	in	ADP
ejpam-5205	643	3	graphs	graph	NOUN
ejpam-5205	643	4	.	.	PUNCT
ejpam-5205	644	1	discrete	discrete	ADJ
ejpam-5205	644	2	applied	apply	VERB
ejpam-5205	644	3	mathematics	mathematic	NOUN
ejpam-5205	644	4	,	,	PUNCT
ejpam-5205	644	5	(	(	PUNCT
ejpam-5205	644	6	116):115–126	116):115–126	NOUN
ejpam-5205	644	7	,	,	PUNCT
ejpam-5205	644	8	2002	2002	NUM
ejpam-5205	644	9	.	.	PUNCT
ejpam-5205	645	1	[	[	X
ejpam-5205	645	2	7	7	X
ejpam-5205	645	3	]	]	X
ejpam-5205	645	4	m.	m.	NOUN
ejpam-5205	645	5	chellali	chellali	PROPN
ejpam-5205	645	6	,	,	PUNCT
ejpam-5205	645	7	t.w	t.w	PROPN
ejpam-5205	645	8	.	.	PROPN
ejpam-5205	645	9	haynes	haynes	PROPN
ejpam-5205	645	10	,	,	PUNCT
ejpam-5205	645	11	and	and	CCONJ
ejpam-5205	645	12	s.t	s.t	PROPN
ejpam-5205	645	13	.	.	PROPN
ejpam-5205	645	14	hedetnieme	hedetnieme	PROPN
ejpam-5205	645	15	.	.	PUNCT
ejpam-5205	646	1	roman	roman	NOUN
ejpam-5205	646	2	{	{	PUNCT
ejpam-5205	646	3	2	2	NUM
ejpam-5205	646	4	}	}	PUNCT
ejpam-5205	646	5	domination	domination	NOUN
ejpam-5205	646	6	.	.	PUNCT
ejpam-5205	647	1	discrete	discrete	ADJ
ejpam-5205	647	2	applied	apply	VERB
ejpam-5205	647	3	math	math	NOUN
ejpam-5205	647	4	,	,	PUNCT
ejpam-5205	647	5	204:22–28	204:22–28	NUM
ejpam-5205	647	6	,	,	PUNCT
ejpam-5205	647	7	2016	2016	NUM
ejpam-5205	647	8	.	.	PUNCT
ejpam-5205	648	1	[	[	X
ejpam-5205	648	2	8	8	NUM
ejpam-5205	648	3	]	]	SYM
ejpam-5205	648	4	e.j	e.j	PROPN
ejpam-5205	648	5	.	.	PROPN
ejpam-5205	648	6	cockayne	cockayne	PROPN
ejpam-5205	648	7	,	,	PUNCT
ejpam-5205	648	8	p.a	p.a	PROPN
ejpam-5205	648	9	.	.	PROPN
ejpam-5205	648	10	deryer	deryer	PROPN
ejpam-5205	648	11	,	,	PUNCT
ejpam-5205	648	12	s.m	s.m	PROPN
ejpam-5205	648	13	.	.	PROPN
ejpam-5205	648	14	hedetnieme	hedetnieme	PROPN
ejpam-5205	648	15	,	,	PUNCT
ejpam-5205	648	16	and	and	CCONJ
ejpam-5205	648	17	s.t	s.t	PROPN
ejpam-5205	648	18	.	.	PROPN
ejpam-5205	648	19	hedetnieme	hedetnieme	PROPN
ejpam-5205	648	20	.	.	PUNCT
ejpam-5205	649	1	roman	roman	ADJ
ejpam-5205	649	2	domination	domination	NOUN
ejpam-5205	649	3	in	in	ADP
ejpam-5205	649	4	graphs	graph	NOUN
ejpam-5205	649	5	.	.	PUNCT
ejpam-5205	650	1	discrete	discrete	ADJ
ejpam-5205	650	2	mathematics	mathematic	NOUN
ejpam-5205	650	3	,	,	PUNCT
ejpam-5205	650	4	278(13):11–22	278(13):11–22	NUM
ejpam-5205	650	5	,	,	PUNCT
ejpam-5205	650	6	2004	2004	NUM
ejpam-5205	650	7	.	.	PUNCT
ejpam-5205	651	1	[	[	X
ejpam-5205	651	2	9	9	NUM
ejpam-5205	651	3	]	]	X
ejpam-5205	651	4	e.l	e.l	PROPN
ejpam-5205	651	5	.	.	PROPN
ejpam-5205	651	6	enriquez	enriquez	PROPN
ejpam-5205	651	7	and	and	CCONJ
ejpam-5205	651	8	s.r	s.r	PROPN
ejpam-5205	651	9	.	.	PROPN
ejpam-5205	651	10	canoy	canoy	PROPN
ejpam-5205	651	11	jr	jr	PROPN
ejpam-5205	651	12	.	.	PROPN
ejpam-5205	651	13	on	on	ADP
ejpam-5205	651	14	a	a	DET
ejpam-5205	651	15	variant	variant	NOUN
ejpam-5205	651	16	of	of	ADP
ejpam-5205	651	17	convex	convex	ADJ
ejpam-5205	651	18	domination	domination	NOUN
ejpam-5205	651	19	in	in	ADP
ejpam-5205	651	20	a	a	DET
ejpam-5205	651	21	graph	graph	NOUN
ejpam-5205	651	22	.	.	PUNCT
ejpam-5205	652	1	international	international	ADJ
ejpam-5205	652	2	journal	journal	PROPN
ejpam-5205	652	3	of	of	ADP
ejpam-5205	652	4	mathematical	mathematical	ADJ
ejpam-5205	652	5	analysis	analysis	NOUN
ejpam-5205	652	6	,	,	PUNCT
ejpam-5205	652	7	9(32):1585–1592	9(32):1585–1592	NUM
ejpam-5205	652	8	,	,	PUNCT
ejpam-5205	652	9	2015	2015	NUM
ejpam-5205	652	10	.	.	PUNCT
ejpam-5205	653	1	[	[	X
ejpam-5205	653	2	10	10	NUM
ejpam-5205	653	3	]	]	X
ejpam-5205	653	4	r.j	r.j	PROPN
ejpam-5205	653	5	.	.	PROPN
ejpam-5205	653	6	fortosa	fortosa	PROPN
ejpam-5205	653	7	and	and	CCONJ
ejpam-5205	653	8	s.r	s.r	PROPN
ejpam-5205	653	9	.	.	PROPN
ejpam-5205	653	10	canoy	canoy	PROPN
ejpam-5205	653	11	jr	jr	PROPN
ejpam-5205	653	12	.	.	PROPN
ejpam-5205	653	13	convex	convex	PROPN
ejpam-5205	653	14	roman	roman	ADJ
ejpam-5205	653	15	dominating	dominating	NOUN
ejpam-5205	653	16	function	function	NOUN
ejpam-5205	653	17	in	in	ADP
ejpam-5205	653	18	graphs	graph	NOUN
ejpam-5205	653	19	.	.	PUNCT
ejpam-5205	654	1	european	european	ADJ
ejpam-5205	654	2	journal	journal	PROPN
ejpam-5205	654	3	of	of	ADP
ejpam-5205	654	4	pure	pure	ADJ
ejpam-5205	654	5	and	and	CCONJ
ejpam-5205	654	6	applied	applied	ADJ
ejpam-5205	654	7	mathematics	mathematic	NOUN
ejpam-5205	654	8	,	,	PUNCT
ejpam-5205	654	9	16(3):1705–1716	16(3):1705–1716	NUM
ejpam-5205	654	10	,	,	PUNCT
ejpam-5205	654	11	2023	2023	NUM
ejpam-5205	654	12	.	.	PUNCT
ejpam-5205	655	1	[	[	X
ejpam-5205	655	2	11	11	NUM
ejpam-5205	655	3	]	]	X
ejpam-5205	655	4	f.	f.	PROPN
ejpam-5205	655	5	harary	harary	PROPN
ejpam-5205	655	6	and	and	CCONJ
ejpam-5205	655	7	j.	j.	PROPN
ejpam-5205	655	8	nieminen	nieminen	PROPN
ejpam-5205	655	9	.	.	PUNCT
ejpam-5205	656	1	convexity	convexity	NOUN
ejpam-5205	656	2	in	in	ADP
ejpam-5205	656	3	graphs	graph	NOUN
ejpam-5205	656	4	.	.	PUNCT
ejpam-5205	657	1	journal	journal	PROPN
ejpam-5205	657	2	of	of	ADP
ejpam-5205	657	3	differential	differential	ADJ
ejpam-5205	657	4	geometry	geometry	NOUN
ejpam-5205	657	5	,	,	PUNCT
ejpam-5205	657	6	16(2):185–190	16(2):185–190	NUM
ejpam-5205	657	7	,	,	PUNCT
ejpam-5205	657	8	1981	1981	NUM
ejpam-5205	657	9	.	.	PUNCT
ejpam-5205	658	1	[	[	X
ejpam-5205	658	2	12	12	NUM
ejpam-5205	658	3	]	]	X
ejpam-5205	658	4	t.w	t.w	PROPN
ejpam-5205	658	5	.	.	PROPN
ejpam-5205	658	6	haynes	haynes	PROPN
ejpam-5205	658	7	,	,	PUNCT
ejpam-5205	658	8	s.t	s.t	PROPN
ejpam-5205	658	9	.	.	PROPN
ejpam-5205	658	10	hedetneme	hedetneme	PROPN
ejpam-5205	658	11	,	,	PUNCT
ejpam-5205	658	12	and	and	CCONJ
ejpam-5205	658	13	p.j	p.j	PROPN
ejpam-5205	658	14	.	.	PROPN
ejpam-5205	658	15	slater	slater	PROPN
ejpam-5205	658	16	.	.	PUNCT
ejpam-5205	659	1	distance	distance	NOUN
ejpam-5205	659	2	in	in	ADP
ejpam-5205	659	3	graphs	graph	NOUN
ejpam-5205	659	4	.	.	PUNCT
ejpam-5205	660	1	marcel	marcel	PROPN
ejpam-5205	660	2	dekker	dekker	PROPN
ejpam-5205	660	3	,	,	PUNCT
ejpam-5205	660	4	new	new	PROPN
ejpam-5205	660	5	york	york	PROPN
ejpam-5205	660	6	,	,	PUNCT
ejpam-5205	660	7	1980	1980	NUM
ejpam-5205	660	8	.	.	PUNCT
ejpam-5205	661	1	references	reference	NOUN
ejpam-5205	661	2	1351	1351	NUM
ejpam-5205	661	3	[	[	X
ejpam-5205	661	4	13	13	NUM
ejpam-5205	661	5	]	]	X
ejpam-5205	661	6	m.a	m.a	PROPN
ejpam-5205	661	7	.	.	PROPN
ejpam-5205	661	8	henning	henning	PROPN
ejpam-5205	661	9	,	,	PUNCT
ejpam-5205	661	10	w.f	w.f	PROPN
ejpam-5205	661	11	.	.	PROPN
ejpam-5205	661	12	klostermeyer	klostermeyer	PROPN
ejpam-5205	661	13	,	,	PUNCT
ejpam-5205	661	14	and	and	CCONJ
ejpam-5205	661	15	g.	g.	PROPN
ejpam-5205	661	16	macgillivray	macgillivray	PROPN
ejpam-5205	661	17	.	.	PUNCT
ejpam-5205	662	1	perfect	perfect	ADJ
ejpam-5205	662	2	roman	roman	ADJ
ejpam-5205	662	3	domination	domination	NOUN
ejpam-5205	662	4	in	in	ADP
ejpam-5205	662	5	trees	tree	NOUN
ejpam-5205	662	6	.	.	PUNCT
ejpam-5205	663	1	discrete	discrete	ADJ
ejpam-5205	663	2	applied	apply	VERB
ejpam-5205	663	3	mathematics	mathematic	NOUN
ejpam-5205	663	4	,	,	PUNCT
ejpam-5205	663	5	236:235–245	236:235–245	NUM
ejpam-5205	663	6	,	,	PUNCT
ejpam-5205	663	7	2018	2018	NUM
ejpam-5205	663	8	.	.	PUNCT
ejpam-5205	664	1	[	[	X
ejpam-5205	664	2	14	14	NUM
ejpam-5205	664	3	]	]	X
ejpam-5205	664	4	s.r	s.r	PROPN
ejpam-5205	664	5	.	.	PROPN
ejpam-5205	664	6	canoy	canoy	PROPN
ejpam-5205	664	7	jr	jr	PROPN
ejpam-5205	664	8	.	.	PUNCT
ejpam-5205	664	9	a	a	DET
ejpam-5205	664	10	short	short	ADJ
ejpam-5205	664	11	note	note	NOUN
ejpam-5205	664	12	on	on	ADP
ejpam-5205	664	13	convexity	convexity	NOUN
ejpam-5205	664	14	and	and	CCONJ
ejpam-5205	664	15	convex	convex	NOUN
ejpam-5205	664	16	domination	domination	NOUN
ejpam-5205	664	17	in	in	ADP
ejpam-5205	664	18	g[km	g[km	PROPN
ejpam-5205	664	19	]	]	PUNCT
ejpam-5205	664	20	.	.	PUNCT
ejpam-5205	665	1	applied	apply	VERB
ejpam-5205	665	2	mathematical	mathematical	ADJ
ejpam-5205	665	3	sciences	science	NOUN
ejpam-5205	665	4	,	,	PUNCT
ejpam-5205	665	5	8(115):5737–5741	8(115):5737–5741	NUM
ejpam-5205	665	6	,	,	PUNCT
ejpam-5205	665	7	2014	2014	NUM
ejpam-5205	665	8	.	.	PUNCT
ejpam-5205	666	1	[	[	X
ejpam-5205	666	2	15	15	NUM
ejpam-5205	666	3	]	]	X
ejpam-5205	666	4	s.r	s.r	PROPN
ejpam-5205	666	5	.	.	PROPN
ejpam-5205	666	6	canoy	canoy	PROPN
ejpam-5205	666	7	jr	jr	PROPN
ejpam-5205	666	8	and	and	CCONJ
ejpam-5205	666	9	i.j.l	i.j.l	PROPN
ejpam-5205	666	10	.	.	PROPN
ejpam-5205	666	11	garces	garces	PROPN
ejpam-5205	666	12	.	.	PUNCT
ejpam-5205	667	1	convex	convex	PROPN
ejpam-5205	667	2	sets	set	NOUN
ejpam-5205	667	3	under	under	ADP
ejpam-5205	667	4	some	some	DET
ejpam-5205	667	5	graph	graph	NOUN
ejpam-5205	667	6	operations	operation	NOUN
ejpam-5205	667	7	.	.	PUNCT
ejpam-5205	668	1	graphs	graph	NOUN
ejpam-5205	668	2	and	and	CCONJ
ejpam-5205	668	3	combinatorics	combinatoric	NOUN
ejpam-5205	668	4	,	,	PUNCT
ejpam-5205	668	5	18(4):787–793	18(4):787–793	NUM
ejpam-5205	668	6	,	,	PUNCT
ejpam-5205	668	7	2002	2002	NUM
ejpam-5205	668	8	.	.	PUNCT
ejpam-5205	669	1	[	[	X
ejpam-5205	669	2	16	16	NUM
ejpam-5205	669	3	]	]	PUNCT
ejpam-5205	669	4	k.	k.	PROPN
ejpam-5205	669	5	kammerling	kammerling	PROPN
ejpam-5205	669	6	and	and	CCONJ
ejpam-5205	669	7	l.	l.	PROPN
ejpam-5205	669	8	volkman	volkman	PROPN
ejpam-5205	669	9	.	.	PUNCT
ejpam-5205	670	1	roman	roman	ADJ
ejpam-5205	670	2	k	k	NOUN
ejpam-5205	670	3	-	-	PUNCT
ejpam-5205	670	4	domination	domination	NOUN
ejpam-5205	670	5	in	in	ADP
ejpam-5205	670	6	graphs	graph	NOUN
ejpam-5205	670	7	.	.	PUNCT
ejpam-5205	671	1	journal	journal	NOUN
ejpam-5205	671	2	of	of	ADP
ejpam-5205	671	3	the	the	DET
ejpam-5205	671	4	korean	korean	PROPN
ejpam-5205	671	5	mathematical	mathematical	ADJ
ejpam-5205	671	6	society	society	NOUN
ejpam-5205	671	7	,	,	PUNCT
ejpam-5205	671	8	46(6):1309–1318	46(6):1309–1318	PROPN
ejpam-5205	671	9	,	,	PUNCT
ejpam-5205	671	10	2009	2009	NUM
ejpam-5205	671	11	.	.	PUNCT
ejpam-5205	672	1	[	[	X
ejpam-5205	672	2	17	17	NUM
ejpam-5205	672	3	]	]	X
ejpam-5205	672	4	m.a	m.a	PROPN
ejpam-5205	672	5	.	.	PROPN
ejpam-5205	672	6	labendia	labendia	PROPN
ejpam-5205	672	7	and	and	CCONJ
ejpam-5205	672	8	s.r	s.r	PROPN
ejpam-5205	672	9	.	.	PROPN
ejpam-5205	672	10	canoy	canoy	PROPN
ejpam-5205	672	11	jr	jr	PROPN
ejpam-5205	672	12	.	.	PROPN
ejpam-5205	672	13	convex	convex	PROPN
ejpam-5205	672	14	dominatioin	dominatioin	VERB
ejpam-5205	672	15	in	in	ADP
ejpam-5205	672	16	the	the	DET
ejpam-5205	672	17	composition	composition	NOUN
ejpam-5205	672	18	and	and	CCONJ
ejpam-5205	672	19	cartesian	cartesian	ADJ
ejpam-5205	672	20	product	product	NOUN
ejpam-5205	672	21	of	of	ADP
ejpam-5205	672	22	graphs	graph	NOUN
ejpam-5205	672	23	.	.	PUNCT
ejpam-5205	673	1	czechoslovak	czechoslovak	ADJ
ejpam-5205	673	2	mathematical	mathematical	PROPN
ejpam-5205	673	3	journal	journal	PROPN
ejpam-5205	673	4	,	,	PUNCT
ejpam-5205	673	5	62:1003–1009	62:1003–1009	NUM
ejpam-5205	673	6	,	,	PUNCT
ejpam-5205	673	7	2012	2012	NUM
ejpam-5205	673	8	.	.	PUNCT
ejpam-5205	674	1	[	[	X
ejpam-5205	674	2	18	18	NUM
ejpam-5205	674	3	]	]	PUNCT
ejpam-5205	674	4	m.	m.	NOUN
ejpam-5205	674	5	lemanska	lemanska	PROPN
ejpam-5205	674	6	.	.	PUNCT
ejpam-5205	675	1	weakly	weakly	ADJ
ejpam-5205	675	2	convex	convex	NOUN
ejpam-5205	675	3	and	and	CCONJ
ejpam-5205	675	4	convex	convex	ADJ
ejpam-5205	675	5	domination	domination	NOUN
ejpam-5205	675	6	numbers	number	NOUN
ejpam-5205	675	7	.	.	PUNCT
ejpam-5205	676	1	opuscula	opuscula	PROPN
ejpam-5205	676	2	mathematica	mathematica	PROPN
ejpam-5205	676	3	,	,	PUNCT
ejpam-5205	676	4	24(2):181–188	24(2):181–188	PROPN
ejpam-5205	676	5	,	,	PUNCT
ejpam-5205	676	6	2004	2004	NUM
ejpam-5205	676	7	.	.	PUNCT
ejpam-5205	677	1	[	[	X
ejpam-5205	677	2	19	19	NUM
ejpam-5205	677	3	]	]	X
ejpam-5205	677	4	m.h	m.h	PROPN
ejpam-5205	677	5	.	.	PROPN
ejpam-5205	677	6	muddebiha	muddebiha	PROPN
ejpam-5205	677	7	and	and	CCONJ
ejpam-5205	677	8	sumangaladevi	sumangaladevi	ADJ
ejpam-5205	677	9	.	.	PUNCT
ejpam-5205	678	1	connected	connect	VERB
ejpam-5205	678	2	roman	roman	ADJ
ejpam-5205	678	3	domination	domination	NOUN
ejpam-5205	678	4	in	in	ADP
ejpam-5205	678	5	graphs	graph	NOUN
ejpam-5205	678	6	.	.	PUNCT
ejpam-5205	679	1	international	international	ADJ
ejpam-5205	679	2	journal	journal	PROPN
ejpam-5205	679	3	of	of	ADP
ejpam-5205	679	4	research	research	NOUN
ejpam-5205	679	5	and	and	CCONJ
ejpam-5205	679	6	engineering	engineering	NOUN
ejpam-5205	679	7	technology	technology	NOUN
ejpam-5205	679	8	,	,	PUNCT
ejpam-5205	679	9	2(10):333–340	2(10):333–340	NUM
ejpam-5205	679	10	,	,	PUNCT
ejpam-5205	679	11	2013	2013	NUM
ejpam-5205	679	12	.	.	PUNCT
ejpam-5205	680	1	[	[	X
ejpam-5205	680	2	20	20	NUM
ejpam-5205	680	3	]	]	X
ejpam-5205	680	4	l.m	l.m	PROPN
ejpam-5205	680	5	.	.	PROPN
ejpam-5205	680	6	paleta	paleta	PROPN
ejpam-5205	680	7	and	and	CCONJ
ejpam-5205	680	8	f.p	f.p	PROPN
ejpam-5205	680	9	.	.	PROPN
ejpam-5205	680	10	jamil	jamil	PROPN
ejpam-5205	680	11	.	.	PUNCT
ejpam-5205	681	1	on	on	ADP
ejpam-5205	681	2	perfect	perfect	ADJ
ejpam-5205	681	3	italian	italian	ADJ
ejpam-5205	681	4	domination	domination	NOUN
ejpam-5205	681	5	in	in	ADP
ejpam-5205	681	6	graphs	graph	NOUN
ejpam-5205	681	7	.	.	PUNCT
ejpam-5205	682	1	discrete	discrete	ADJ
ejpam-5205	682	2	mathematics	mathematic	NOUN
ejpam-5205	682	3	,	,	PUNCT
ejpam-5205	682	4	algorithms	algorithm	NOUN
ejpam-5205	682	5	and	and	CCONJ
ejpam-5205	682	6	applications	application	NOUN
ejpam-5205	682	7	,	,	PUNCT
ejpam-5205	682	8	page	page	NOUN
ejpam-5205	682	9	2350085	2350085	NUM
ejpam-5205	682	10	,	,	PUNCT
ejpam-5205	682	11	2023	2023	NUM
ejpam-5205	682	12	.	.	PUNCT
ejpam-5205	683	1	[	[	X
ejpam-5205	683	2	21	21	NUM
ejpam-5205	683	3	]	]	X
ejpam-5205	683	4	i.m	i.m	PROPN
ejpam-5205	683	5	.	.	PUNCT
ejpam-5205	684	1	pelayo	pelayo	PROPN
ejpam-5205	684	2	.	.	PUNCT
ejpam-5205	685	1	on	on	ADP
ejpam-5205	685	2	convexity	convexity	NOUN
ejpam-5205	685	3	in	in	ADP
ejpam-5205	685	4	graphs	graph	NOUN
ejpam-5205	685	5	.	.	PUNCT
ejpam-5205	686	1	technical	technical	ADJ
ejpam-5205	686	2	report	report	NOUN
ejpam-5205	686	3	,	,	PUNCT
ejpam-5205	686	4	online	online	ADV
ejpam-5205	686	5	:	:	PUNCT
ejpam-5205	687	1	http://www	http://www	PROPN
ejpam-5205	687	2	.	.	PUNCT
ejpam-5205	688	1	ma3	ma3	PROPN
ejpam-5205	688	2	.	.	PUNCT
ejpam-5205	689	1	upc	upc	PROPN
ejpam-5205	689	2	.	.	PUNCT
ejpam-5205	689	3	es	es	NOUN
ejpam-5205	689	4	/	/	SYM
ejpam-5205	689	5	users	user	NOUN
ejpam-5205	689	6	/	/	SYM
ejpam-5205	689	7	pelayo	pelayo	PROPN
ejpam-5205	689	8	/	/	SYM
ejpam-5205	689	9	research	research	NOUN
ejpam-5205	689	10	/	/	SYM
ejpam-5205	689	11	definitions	definition	NOUN
ejpam-5205	689	12	.	.	PUNCT
ejpam-5205	690	1	pdf	pdf	NOUN
ejpam-5205	690	2	.	.	PUNCT
ejpam-5205	690	3	,	,	PUNCT
ejpam-5205	690	4	pages	page	VERB
ejpam-5205	690	5	1–21	1–21	PROPN
ejpam-5205	690	6	,	,	PUNCT
ejpam-5205	690	7	2004	2004	NUM
ejpam-5205	690	8	.	.	PUNCT
ejpam-5205	691	1	[	[	X
ejpam-5205	691	2	22	22	NUM
ejpam-5205	691	3	]	]	PUNCT
ejpam-5205	691	4	p.r.l	p.r.l	NOUN
ejpam-5205	691	5	.	.	PUNCT
ejpam-5205	692	1	pushpam	pushpam	NOUN
ejpam-5205	692	2	and	and	CCONJ
ejpam-5205	692	3	t.n.m	t.n.m	NOUN
ejpam-5205	692	4	.	.	PUNCT
ejpam-5205	693	1	malini	malini	PROPN
ejpam-5205	693	2	mai	mai	PROPN
ejpam-5205	693	3	.	.	PROPN
ejpam-5205	693	4	edge	edge	PROPN
ejpam-5205	693	5	roman	roman	ADJ
ejpam-5205	693	6	domination	domination	NOUN
ejpam-5205	693	7	in	in	ADP
ejpam-5205	693	8	graphs	graph	NOUN
ejpam-5205	693	9	.	.	PUNCT
ejpam-5205	694	1	journal	journal	NOUN
ejpam-5205	694	2	of	of	ADP
ejpam-5205	694	3	combinatorial	combinatorial	ADJ
ejpam-5205	694	4	mathematics	mathematic	NOUN
ejpam-5205	694	5	and	and	CCONJ
ejpam-5205	694	6	combinatorial	combinatorial	ADJ
ejpam-5205	694	7	computing	computing	NOUN
ejpam-5205	694	8	,	,	PUNCT
ejpam-5205	694	9	69:175–182	69:175–182	NOUN
ejpam-5205	694	10	,	,	PUNCT
ejpam-5205	694	11	2009	2009	NUM
ejpam-5205	694	12	.	.	PUNCT
ejpam-5205	695	1	[	[	X
ejpam-5205	695	2	23	23	NUM
ejpam-5205	695	3	]	]	X
ejpam-5205	695	4	c.s	c.s	PROPN
ejpam-5205	695	5	.	.	PROPN
ejpam-5205	695	6	revelle	revelle	PROPN
ejpam-5205	695	7	and	and	CCONJ
ejpam-5205	695	8	k.e	k.e	PROPN
ejpam-5205	695	9	.	.	PUNCT
ejpam-5205	696	1	rosing	rosing	PROPN
ejpam-5205	696	2	.	.	PUNCT
ejpam-5205	697	1	defendens	defenden	VERB
ejpam-5205	697	2	imperium	imperium	NOUN
ejpam-5205	697	3	romanum	romanum	NOUN
ejpam-5205	697	4	:	:	PUNCT
ejpam-5205	697	5	a	a	DET
ejpam-5205	697	6	classical	classical	ADJ
ejpam-5205	697	7	problem	problem	NOUN
ejpam-5205	697	8	in	in	ADP
ejpam-5205	697	9	military	military	ADJ
ejpam-5205	697	10	strategy	strategy	NOUN
ejpam-5205	697	11	.	.	PUNCT
ejpam-5205	698	1	amerrican	amerrican	PROPN
ejpam-5205	698	2	mathematical	mathematical	PROPN
ejpam-5205	698	3	monthly	monthly	ADJ
ejpam-5205	698	4	,	,	PUNCT
ejpam-5205	698	5	107(7):585–594	107(7):585–594	PROPN
ejpam-5205	698	6	,	,	PUNCT
ejpam-5205	698	7	2000	2000	NUM
ejpam-5205	698	8	.	.	PUNCT
ejpam-5205	699	1	[	[	X
ejpam-5205	699	2	24	24	NUM
ejpam-5205	699	3	]	]	PUNCT
ejpam-5205	699	4	i.	i.	PROPN
ejpam-5205	699	5	stewart	stewart	PROPN
ejpam-5205	699	6	.	.	PUNCT
ejpam-5205	700	1	defend	defend	VERB
ejpam-5205	700	2	the	the	DET
ejpam-5205	700	3	roman	roman	ADJ
ejpam-5205	700	4	empire	empire	NOUN
ejpam-5205	700	5	!	!	PUNCT
ejpam-5205	701	1	scientific	scientific	ADJ
ejpam-5205	701	2	american	american	PROPN
ejpam-5205	701	3	,	,	PUNCT
ejpam-5205	701	4	281(6):136–138	281(6):136–138	PROPN
ejpam-5205	701	5	,	,	PUNCT
ejpam-5205	701	6	1999	1999	NUM
ejpam-5205	701	7	.	.	PUNCT