id	sid	tid	token	lemma	pos
ejpam-7078	1	1	european	european	PROPN
ejpam-7078	1	2	journal	journal	PROPN
ejpam-7078	1	3	of	of	ADP
ejpam-7078	1	4	pure	pure	ADJ
ejpam-7078	1	5	and	and	CCONJ
ejpam-7078	1	6	applied	applied	ADJ
ejpam-7078	1	7	mathematics	mathematic	NOUN
ejpam-7078	1	8	2025	2025	NUM
ejpam-7078	1	9	,	,	PUNCT
ejpam-7078	1	10	vol	vol	NOUN
ejpam-7078	1	11	.	.	PROPN
ejpam-7078	1	12	18	18	NUM
ejpam-7078	1	13	,	,	PUNCT
ejpam-7078	1	14	issue	issue	NOUN
ejpam-7078	1	15	4	4	NUM
ejpam-7078	1	16	,	,	PUNCT
ejpam-7078	1	17	article	article	NOUN
ejpam-7078	1	18	number	number	NOUN
ejpam-7078	1	19	7078	7078	NUM
ejpam-7078	1	20	issn	issn	PROPN
ejpam-7078	1	21	1307	1307	NUM
ejpam-7078	1	22	-	-	SYM
ejpam-7078	1	23	5543	5543	NUM
ejpam-7078	1	24	–	–	PUNCT
ejpam-7078	1	25	ejpam.com	ejpam.com	X
ejpam-7078	1	26	published	publish	VERB
ejpam-7078	1	27	by	by	ADP
ejpam-7078	1	28	new	new	PROPN
ejpam-7078	1	29	york	york	PROPN
ejpam-7078	1	30	business	business	PROPN
ejpam-7078	1	31	global	global	PROPN
ejpam-7078	1	32	super	super	PROPN
ejpam-7078	1	33	hop	hop	PROPN
ejpam-7078	1	34	roman	roman	ADJ
ejpam-7078	1	35	domination	domination	NOUN
ejpam-7078	1	36	in	in	ADP
ejpam-7078	1	37	graphs	graph	NOUN
ejpam-7078	1	38	leomarich	leomarich	PROPN
ejpam-7078	1	39	f.	f.	PROPN
ejpam-7078	1	40	casinillo1	casinillo1	PROPN
ejpam-7078	1	41	,	,	PUNCT
ejpam-7078	1	42	sergio	sergio	PROPN
ejpam-7078	1	43	r.	r.	PROPN
ejpam-7078	1	44	canoy	canoy	PROPN
ejpam-7078	1	45	,	,	PUNCT
ejpam-7078	1	46	jr.1,2,∗	jr.1,2,∗	PROPN
ejpam-7078	1	47	1	1	NUM
ejpam-7078	1	48	department	department	NOUN
ejpam-7078	1	49	of	of	ADP
ejpam-7078	1	50	mathematics	mathematic	NOUN
ejpam-7078	1	51	and	and	CCONJ
ejpam-7078	1	52	statistics	statistic	NOUN
ejpam-7078	1	53	,	,	PUNCT
ejpam-7078	1	54	college	college	NOUN
ejpam-7078	1	55	of	of	ADP
ejpam-7078	1	56	science	science	NOUN
ejpam-7078	1	57	and	and	CCONJ
ejpam-7078	1	58	mathematics	mathematic	NOUN
ejpam-7078	1	59	,	,	PUNCT
ejpam-7078	1	60	msu	msu	PROPN
ejpam-7078	1	61	-	-	PUNCT
ejpam-7078	1	62	iligan	iligan	PROPN
ejpam-7078	1	63	institute	institute	PROPN
ejpam-7078	1	64	of	of	ADP
ejpam-7078	1	65	technology	technology	PROPN
ejpam-7078	1	66	,	,	PUNCT
ejpam-7078	1	67	9200	9200	NUM
ejpam-7078	1	68	iligan	iligan	ADJ
ejpam-7078	1	69	city	city	NOUN
ejpam-7078	1	70	,	,	PUNCT
ejpam-7078	1	71	philippines	philippine	NOUN
ejpam-7078	1	72	2	2	NUM
ejpam-7078	1	73	center	center	NOUN
ejpam-7078	1	74	for	for	ADP
ejpam-7078	1	75	mathematical	mathematical	ADJ
ejpam-7078	1	76	and	and	CCONJ
ejpam-7078	1	77	theoretical	theoretical	ADJ
ejpam-7078	1	78	physical	physical	ADJ
ejpam-7078	1	79	sciences	science	NOUN
ejpam-7078	1	80	,	,	PUNCT
ejpam-7078	1	81	premier	premier	PROPN
ejpam-7078	1	82	research	research	PROPN
ejpam-7078	1	83	institute	institute	PROPN
ejpam-7078	1	84	of	of	ADP
ejpam-7078	1	85	science	science	NOUN
ejpam-7078	1	86	and	and	CCONJ
ejpam-7078	1	87	mathematics	mathematic	NOUN
ejpam-7078	1	88	,	,	PUNCT
ejpam-7078	1	89	msu	msu	PROPN
ejpam-7078	1	90	-	-	PUNCT
ejpam-7078	1	91	iligan	iligan	PROPN
ejpam-7078	1	92	institute	institute	PROPN
ejpam-7078	1	93	of	of	ADP
ejpam-7078	1	94	technology	technology	PROPN
ejpam-7078	1	95	,	,	PUNCT
ejpam-7078	1	96	9200	9200	NUM
ejpam-7078	1	97	iligan	iligan	ADJ
ejpam-7078	1	98	city	city	NOUN
ejpam-7078	1	99	,	,	PUNCT
ejpam-7078	1	100	philippines	philippine	NOUN
ejpam-7078	1	101	abstract	abstract	ADJ
ejpam-7078	1	102	.	.	PUNCT
ejpam-7078	2	1	letg	letg	NOUN
ejpam-7078	2	2	=	=	PUNCT
ejpam-7078	2	3	(	(	PUNCT
ejpam-7078	2	4	v	v	NOUN
ejpam-7078	2	5	(	(	PUNCT
ejpam-7078	2	6	g	g	NOUN
ejpam-7078	2	7	)	)	PUNCT
ejpam-7078	2	8	,	,	PUNCT
ejpam-7078	2	9	e(g	e(g	PROPN
ejpam-7078	2	10	)	)	PUNCT
ejpam-7078	2	11	)	)	PUNCT
ejpam-7078	2	12	be	be	AUX
ejpam-7078	2	13	a	a	DET
ejpam-7078	2	14	simple	simple	ADJ
ejpam-7078	2	15	undirected	undirected	ADJ
ejpam-7078	2	16	graph	graph	NOUN
ejpam-7078	2	17	.	.	PUNCT
ejpam-7078	3	1	a	a	DET
ejpam-7078	3	2	function	function	NOUN
ejpam-7078	3	3	f	f	NOUN
ejpam-7078	3	4	:	:	PUNCT
ejpam-7078	3	5	v	v	X
ejpam-7078	3	6	(	(	PUNCT
ejpam-7078	3	7	g	g	NOUN
ejpam-7078	3	8	)	)	PUNCT
ejpam-7078	3	9	→	→	SYM
ejpam-7078	3	10	{	{	PUNCT
ejpam-7078	3	11	0	0	NUM
ejpam-7078	3	12	,	,	PUNCT
ejpam-7078	3	13	1	1	NUM
ejpam-7078	3	14	,	,	PUNCT
ejpam-7078	3	15	2	2	NUM
ejpam-7078	3	16	}	}	PUNCT
ejpam-7078	3	17	is	be	AUX
ejpam-7078	3	18	a	a	DET
ejpam-7078	3	19	super	super	ADV
ejpam-7078	3	20	hop	hop	NOUN
ejpam-7078	3	21	roman	roman	ADJ
ejpam-7078	3	22	dominating	dominating	NOUN
ejpam-7078	3	23	function	function	NOUN
ejpam-7078	3	24	(	(	PUNCT
ejpam-7078	3	25	shrdf	shrdf	NOUN
ejpam-7078	3	26	)	)	PUNCT
ejpam-7078	3	27	on	on	ADP
ejpam-7078	3	28	g	g	PROPN
ejpam-7078	3	29	if	if	SCONJ
ejpam-7078	3	30	for	for	ADP
ejpam-7078	3	31	every	every	PRON
ejpam-7078	3	32	v	v	NUM
ejpam-7078	3	33	∈	∈	NOUN
ejpam-7078	3	34	v	v	NOUN
ejpam-7078	3	35	(	(	PUNCT
ejpam-7078	3	36	g	g	NOUN
ejpam-7078	3	37	)	)	PUNCT
ejpam-7078	3	38	with	with	ADP
ejpam-7078	3	39	f(v	f(v	NOUN
ejpam-7078	3	40	)	)	PUNCT
ejpam-7078	3	41	=	=	SYM
ejpam-7078	3	42	0	0	NUM
ejpam-7078	3	43	,	,	PUNCT
ejpam-7078	3	44	there	there	PRON
ejpam-7078	3	45	exist	exist	VERB
ejpam-7078	3	46	w	w	PROPN
ejpam-7078	3	47	,	,	PUNCT
ejpam-7078	3	48	u	u	PROPN
ejpam-7078	3	49	∈	∈	PROPN
ejpam-7078	3	50	v	v	NOUN
ejpam-7078	3	51	(	(	PUNCT
ejpam-7078	3	52	g	g	NOUN
ejpam-7078	3	53	)	)	PUNCT
ejpam-7078	3	54	with	with	ADP
ejpam-7078	3	55	f(w	f(w	NOUN
ejpam-7078	3	56	)	)	PUNCT
ejpam-7078	3	57	=	=	SYM
ejpam-7078	3	58	2	2	NUM
ejpam-7078	3	59	and	and	CCONJ
ejpam-7078	3	60	f(u	f(u	PROPN
ejpam-7078	3	61	)	)	PUNCT
ejpam-7078	3	62	̸=	̸=	PROPN
ejpam-7078	3	63	0	0	NUM
ejpam-7078	3	64	such	such	ADJ
ejpam-7078	3	65	that	that	PRON
ejpam-7078	3	66	dg(v	dg(v	NOUN
ejpam-7078	3	67	,	,	PUNCT
ejpam-7078	3	68	w	w	NOUN
ejpam-7078	3	69	)	)	PUNCT
ejpam-7078	3	70	=	=	SYM
ejpam-7078	3	71	2	2	NUM
ejpam-7078	3	72	,	,	PUNCT
ejpam-7078	3	73	and	and	CCONJ
ejpam-7078	3	74	n2	n2	ADJ
ejpam-7078	3	75	g(u	g(u	PROPN
ejpam-7078	3	76	)	)	PUNCT
ejpam-7078	3	77	∩	∩	NOUN
ejpam-7078	3	78	{	{	PUNCT
ejpam-7078	3	79	x	x	SYM
ejpam-7078	3	80	∈	∈	PROPN
ejpam-7078	3	81	v	v	NOUN
ejpam-7078	3	82	(	(	PUNCT
ejpam-7078	3	83	g	g	NOUN
ejpam-7078	3	84	)	)	PUNCT
ejpam-7078	3	85	:	:	PUNCT
ejpam-7078	3	86	f(x	f(x	PROPN
ejpam-7078	3	87	)	)	PUNCT
ejpam-7078	3	88	=	=	PUNCT
ejpam-7078	4	1	0	0	X
ejpam-7078	4	2	}	}	PUNCT
ejpam-7078	4	3	=	=	SYM
ejpam-7078	4	4	{	{	PUNCT
ejpam-7078	4	5	v	v	NOUN
ejpam-7078	4	6	}	}	PUNCT
ejpam-7078	4	7	.	.	PUNCT
ejpam-7078	5	1	the	the	DET
ejpam-7078	5	2	weight	weight	NOUN
ejpam-7078	5	3	of	of	ADP
ejpam-7078	5	4	shrdf	shrdf	PROPN
ejpam-7078	5	5	f	f	PROPN
ejpam-7078	5	6	,	,	PUNCT
ejpam-7078	5	7	denoted	denote	VERB
ejpam-7078	5	8	ωshr	ωshr	NOUN
ejpam-7078	5	9	g	g	PROPN
ejpam-7078	5	10	(	(	PUNCT
ejpam-7078	5	11	f	f	PROPN
ejpam-7078	5	12	)	)	PUNCT
ejpam-7078	5	13	,	,	PUNCT
ejpam-7078	5	14	is	be	AUX
ejpam-7078	5	15	given	give	VERB
ejpam-7078	5	16	by	by	ADP
ejpam-7078	5	17	ωshr	ωshr	NOUN
ejpam-7078	5	18	g	g	PROPN
ejpam-7078	5	19	(	(	PUNCT
ejpam-7078	5	20	f	f	X
ejpam-7078	5	21	)	)	PUNCT
ejpam-7078	6	1	=	=	SYM
ejpam-7078	6	2	∑	∑	PUNCT
ejpam-7078	6	3	y∈v	y∈v	NOUN
ejpam-7078	6	4	(	(	PUNCT
ejpam-7078	6	5	g	g	NOUN
ejpam-7078	6	6	)	)	PUNCT
ejpam-7078	6	7	f(y	f(y	NOUN
ejpam-7078	6	8	)	)	PUNCT
ejpam-7078	6	9	.	.	PUNCT
ejpam-7078	7	1	the	the	DET
ejpam-7078	7	2	super	super	PROPN
ejpam-7078	7	3	hop	hop	PROPN
ejpam-7078	7	4	roman	roman	ADJ
ejpam-7078	7	5	domination	domination	NOUN
ejpam-7078	7	6	number	number	NOUN
ejpam-7078	7	7	of	of	ADP
ejpam-7078	7	8	a	a	DET
ejpam-7078	7	9	graph	graph	NOUN
ejpam-7078	7	10	g	g	NOUN
ejpam-7078	7	11	,	,	PUNCT
ejpam-7078	7	12	denoted	denote	VERB
ejpam-7078	7	13	γshr(g	γshr(g	NOUN
ejpam-7078	7	14	)	)	PUNCT
ejpam-7078	7	15	,	,	PUNCT
ejpam-7078	7	16	is	be	AUX
ejpam-7078	7	17	the	the	DET
ejpam-7078	7	18	minimum	minimum	ADJ
ejpam-7078	7	19	weight	weight	NOUN
ejpam-7078	7	20	of	of	ADP
ejpam-7078	7	21	an	an	DET
ejpam-7078	7	22	shrdf	shrdf	NOUN
ejpam-7078	7	23	on	on	ADP
ejpam-7078	7	24	g	g	NOUN
ejpam-7078	7	25	,	,	PUNCT
ejpam-7078	7	26	that	that	ADV
ejpam-7078	7	27	is	is	ADV
ejpam-7078	7	28	,	,	PUNCT
ejpam-7078	7	29	γshr(g	γshr(g	NOUN
ejpam-7078	7	30	)	)	PUNCT
ejpam-7078	7	31	=	=	SYM
ejpam-7078	7	32	min{ωshr	min{ωshr	NOUN
ejpam-7078	7	33	g	g	NOUN
ejpam-7078	7	34	(	(	PUNCT
ejpam-7078	7	35	f	f	PROPN
ejpam-7078	7	36	)	)	PUNCT
ejpam-7078	7	37	:	:	PUNCT
ejpam-7078	8	1	f	f	PROPN
ejpam-7078	8	2	is	be	AUX
ejpam-7078	8	3	an	an	DET
ejpam-7078	8	4	shrdf	shrdf	NOUN
ejpam-7078	8	5	on	on	ADP
ejpam-7078	8	6	g	g	NOUN
ejpam-7078	8	7	}	}	PUNCT
ejpam-7078	8	8	.	.	PUNCT
ejpam-7078	9	1	in	in	ADP
ejpam-7078	9	2	this	this	DET
ejpam-7078	9	3	paper	paper	NOUN
ejpam-7078	9	4	,	,	PUNCT
ejpam-7078	9	5	we	we	PRON
ejpam-7078	9	6	make	make	VERB
ejpam-7078	9	7	an	an	DET
ejpam-7078	9	8	initial	initial	ADJ
ejpam-7078	9	9	investigation	investigation	NOUN
ejpam-7078	9	10	of	of	ADP
ejpam-7078	9	11	this	this	DET
ejpam-7078	9	12	newly	newly	ADV
ejpam-7078	9	13	defined	define	VERB
ejpam-7078	9	14	variation	variation	NOUN
ejpam-7078	9	15	of	of	ADP
ejpam-7078	9	16	hop	hop	NOUN
ejpam-7078	9	17	roman	roman	ADJ
ejpam-7078	9	18	domination	domination	NOUN
ejpam-7078	9	19	in	in	ADP
ejpam-7078	9	20	graphs	graph	NOUN
ejpam-7078	9	21	.	.	PUNCT
ejpam-7078	10	1	some	some	DET
ejpam-7078	10	2	bounds	bound	NOUN
ejpam-7078	10	3	and	and	CCONJ
ejpam-7078	10	4	exact	exact	ADJ
ejpam-7078	10	5	values	value	NOUN
ejpam-7078	10	6	of	of	ADP
ejpam-7078	10	7	the	the	DET
ejpam-7078	10	8	parameter	parameter	NOUN
ejpam-7078	10	9	are	be	AUX
ejpam-7078	10	10	obtained	obtain	VERB
ejpam-7078	10	11	and	and	CCONJ
ejpam-7078	10	12	some	some	DET
ejpam-7078	10	13	characterizations	characterization	NOUN
ejpam-7078	10	14	on	on	ADP
ejpam-7078	10	15	some	some	DET
ejpam-7078	10	16	classes	class	NOUN
ejpam-7078	10	17	of	of	ADP
ejpam-7078	10	18	graphs	graph	NOUN
ejpam-7078	10	19	are	be	AUX
ejpam-7078	10	20	given	give	VERB
ejpam-7078	10	21	.	.	PUNCT
ejpam-7078	11	1	2020	2020	NUM
ejpam-7078	11	2	mathematics	mathematic	NOUN
ejpam-7078	11	3	subject	subject	NOUN
ejpam-7078	11	4	classifications	classification	NOUN
ejpam-7078	11	5	:	:	PUNCT
ejpam-7078	11	6	05c69	05c69	X
ejpam-7078	11	7	key	key	ADJ
ejpam-7078	11	8	words	word	NOUN
ejpam-7078	11	9	and	and	CCONJ
ejpam-7078	11	10	phrases	phrase	NOUN
ejpam-7078	11	11	:	:	PUNCT
ejpam-7078	11	12	super	super	ADJ
ejpam-7078	11	13	domination	domination	NOUN
ejpam-7078	11	14	,	,	PUNCT
ejpam-7078	11	15	hop	hop	NOUN
ejpam-7078	11	16	roman	roman	ADJ
ejpam-7078	11	17	domination	domination	NOUN
ejpam-7078	11	18	,	,	PUNCT
ejpam-7078	11	19	super	super	ADP
ejpam-7078	11	20	hop	hop	PROPN
ejpam-7078	11	21	roman	roman	ADJ
ejpam-7078	11	22	domination	domination	NOUN
ejpam-7078	11	23	1	1	NUM
ejpam-7078	11	24	.	.	PUNCT
ejpam-7078	12	1	introduction	introduction	NOUN
ejpam-7078	12	2	domination	domination	NOUN
ejpam-7078	12	3	is	be	AUX
ejpam-7078	12	4	one	one	NUM
ejpam-7078	12	5	of	of	ADP
ejpam-7078	12	6	the	the	DET
ejpam-7078	12	7	major	major	ADJ
ejpam-7078	12	8	concepts	concept	NOUN
ejpam-7078	12	9	in	in	ADP
ejpam-7078	12	10	graph	graph	NOUN
ejpam-7078	12	11	theory	theory	NOUN
ejpam-7078	12	12	that	that	PRON
ejpam-7078	12	13	is	be	AUX
ejpam-7078	12	14	rigorously	rigorously	ADV
ejpam-7078	12	15	studied	study	VERB
ejpam-7078	12	16	by	by	ADP
ejpam-7078	12	17	several	several	ADJ
ejpam-7078	12	18	discrete	discrete	ADJ
ejpam-7078	12	19	mathematicians	mathematician	NOUN
ejpam-7078	12	20	due	due	ADJ
ejpam-7078	12	21	to	to	ADP
ejpam-7078	12	22	its	its	PRON
ejpam-7078	12	23	interesting	interesting	ADJ
ejpam-7078	12	24	theoretic	theoretic	ADJ
ejpam-7078	12	25	structures	structure	NOUN
ejpam-7078	12	26	[	[	X
ejpam-7078	12	27	1	1	NUM
ejpam-7078	12	28	]	]	PUNCT
ejpam-7078	12	29	,	,	PUNCT
ejpam-7078	12	30	[	[	X
ejpam-7078	12	31	2	2	NUM
ejpam-7078	12	32	]	]	PUNCT
ejpam-7078	12	33	,	,	PUNCT
ejpam-7078	12	34	[	[	X
ejpam-7078	12	35	3	3	NUM
ejpam-7078	12	36	]	]	PUNCT
ejpam-7078	12	37	,	,	PUNCT
ejpam-7078	12	38	[	[	X
ejpam-7078	12	39	4	4	NUM
ejpam-7078	12	40	]	]	PUNCT
ejpam-7078	12	41	,	,	PUNCT
ejpam-7078	12	42	[	[	X
ejpam-7078	12	43	5	5	NUM
ejpam-7078	12	44	]	]	PUNCT
ejpam-7078	12	45	,	,	PUNCT
ejpam-7078	12	46	[	[	X
ejpam-7078	12	47	6	6	NUM
ejpam-7078	12	48	]	]	PUNCT
ejpam-7078	12	49	,	,	PUNCT
ejpam-7078	12	50	[	[	X
ejpam-7078	12	51	7	7	NUM
ejpam-7078	12	52	]	]	PUNCT
ejpam-7078	12	53	,	,	PUNCT
ejpam-7078	12	54	[	[	X
ejpam-7078	12	55	8	8	NUM
ejpam-7078	12	56	]	]	PUNCT
ejpam-7078	12	57	,	,	PUNCT
ejpam-7078	12	58	[	[	X
ejpam-7078	12	59	9	9	NUM
ejpam-7078	12	60	]	]	PUNCT
ejpam-7078	12	61	.	.	PUNCT
ejpam-7078	13	1	roman	roman	ADJ
ejpam-7078	13	2	dominating	dominating	NOUN
ejpam-7078	13	3	function	function	NOUN
ejpam-7078	13	4	is	be	AUX
ejpam-7078	13	5	one	one	NUM
ejpam-7078	13	6	of	of	ADP
ejpam-7078	13	7	the	the	DET
ejpam-7078	13	8	topics	topic	NOUN
ejpam-7078	13	9	in	in	ADP
ejpam-7078	13	10	the	the	DET
ejpam-7078	13	11	theory	theory	NOUN
ejpam-7078	13	12	of	of	ADP
ejpam-7078	13	13	domination	domination	NOUN
ejpam-7078	13	14	that	that	PRON
ejpam-7078	13	15	remains	remain	VERB
ejpam-7078	13	16	intriguing	intriguing	ADJ
ejpam-7078	13	17	and	and	CCONJ
ejpam-7078	13	18	have	have	AUX
ejpam-7078	13	19	been	be	AUX
ejpam-7078	13	20	a	a	DET
ejpam-7078	13	21	center	center	NOUN
ejpam-7078	13	22	of	of	ADP
ejpam-7078	13	23	mathematics	mathematic	NOUN
ejpam-7078	13	24	research	research	NOUN
ejpam-7078	13	25	.	.	PUNCT
ejpam-7078	14	1	roman	roman	ADJ
ejpam-7078	14	2	domination	domination	NOUN
ejpam-7078	14	3	was	be	AUX
ejpam-7078	14	4	pioneered	pioneer	VERB
ejpam-7078	14	5	by	by	ADP
ejpam-7078	14	6	cockayne	cockayne	PROPN
ejpam-7078	14	7	et	et	PROPN
ejpam-7078	14	8	al	al	PROPN
ejpam-7078	14	9	.	.	PUNCT
ejpam-7078	15	1	[	[	X
ejpam-7078	15	2	5	5	NUM
ejpam-7078	15	3	]	]	PUNCT
ejpam-7078	15	4	in	in	ADP
ejpam-7078	15	5	2004	2004	NUM
ejpam-7078	15	6	which	which	PRON
ejpam-7078	15	7	is	be	AUX
ejpam-7078	15	8	based	base	VERB
ejpam-7078	15	9	on	on	ADP
ejpam-7078	15	10	the	the	DET
ejpam-7078	15	11	defence	defence	NOUN
ejpam-7078	15	12	strategy	strategy	NOUN
ejpam-7078	15	13	of	of	ADP
ejpam-7078	15	14	roman	roman	ADJ
ejpam-7078	15	15	emperor	emperor	NOUN
ejpam-7078	15	16	constantine	constantine	VERB
ejpam-7078	15	17	the	the	DET
ejpam-7078	15	18	great	great	ADJ
ejpam-7078	15	19	around	around	ADP
ejpam-7078	15	20	the	the	DET
ejpam-7078	15	21	fourth	fourth	ADJ
ejpam-7078	15	22	century	century	NOUN
ejpam-7078	15	23	a.d	a.d	PROPN
ejpam-7078	15	24	.	.	PROPN
ejpam-7078	16	1	currently	currently	ADV
ejpam-7078	16	2	,	,	PUNCT
ejpam-7078	16	3	there	there	PRON
ejpam-7078	16	4	are	be	VERB
ejpam-7078	16	5	now	now	ADV
ejpam-7078	16	6	several	several	ADJ
ejpam-7078	16	7	variations	variation	NOUN
ejpam-7078	16	8	of	of	ADP
ejpam-7078	16	9	roman	roman	ADJ
ejpam-7078	16	10	domination	domination	NOUN
ejpam-7078	16	11	that	that	PRON
ejpam-7078	16	12	has	have	AUX
ejpam-7078	16	13	been	be	AUX
ejpam-7078	16	14	published	publish	VERB
ejpam-7078	16	15	in	in	ADP
ejpam-7078	16	16	the	the	DET
ejpam-7078	16	17	literature	literature	NOUN
ejpam-7078	16	18	of	of	ADP
ejpam-7078	16	19	graph	graph	NOUN
ejpam-7078	16	20	theory	theory	NOUN
ejpam-7078	16	21	and	and	CCONJ
ejpam-7078	16	22	can	can	AUX
ejpam-7078	16	23	be	be	AUX
ejpam-7078	16	24	found	find	VERB
ejpam-7078	16	25	in	in	ADP
ejpam-7078	16	26	[	[	X
ejpam-7078	16	27	10	10	NUM
ejpam-7078	16	28	]	]	PUNCT
ejpam-7078	16	29	,	,	PUNCT
ejpam-7078	16	30	[	[	X
ejpam-7078	16	31	11	11	NUM
ejpam-7078	16	32	]	]	PUNCT
ejpam-7078	16	33	,	,	PUNCT
ejpam-7078	16	34	[	[	X
ejpam-7078	16	35	12	12	NUM
ejpam-7078	16	36	]	]	PUNCT
ejpam-7078	16	37	.	.	PUNCT
ejpam-7078	17	1	in	in	ADP
ejpam-7078	17	2	the	the	DET
ejpam-7078	17	3	year	year	NOUN
ejpam-7078	17	4	2017	2017	NUM
ejpam-7078	17	5	,	,	PUNCT
ejpam-7078	17	6	shabani	shabani	PROPN
ejpam-7078	17	7	et	et	PROPN
ejpam-7078	17	8	al	al	PROPN
ejpam-7078	17	9	.	.	PUNCT
ejpam-7078	18	1	[	[	X
ejpam-7078	18	2	13	13	NUM
ejpam-7078	18	3	]	]	PUNCT
ejpam-7078	18	4	formally	formally	ADV
ejpam-7078	18	5	introduced	introduce	VERB
ejpam-7078	18	6	the	the	DET
ejpam-7078	18	7	hop	hop	NOUN
ejpam-7078	18	8	roman	roman	ADJ
ejpam-7078	18	9	domination	domination	NOUN
ejpam-7078	18	10	in	in	ADP
ejpam-7078	18	11	graphs	graph	NOUN
ejpam-7078	18	12	which	which	PRON
ejpam-7078	18	13	is	be	AUX
ejpam-7078	18	14	extensively	extensively	ADV
ejpam-7078	18	15	studied	study	VERB
ejpam-7078	18	16	recently	recently	ADV
ejpam-7078	18	17	.	.	PUNCT
ejpam-7078	19	1	in	in	ADP
ejpam-7078	19	2	addition	addition	NOUN
ejpam-7078	19	3	,	,	PUNCT
ejpam-7078	19	4	super	super	ADJ
ejpam-7078	19	5	dominating	dominating	NOUN
ejpam-7078	19	6	sets	set	NOUN
ejpam-7078	19	7	in	in	ADP
ejpam-7078	19	8	graphs	graph	NOUN
ejpam-7078	19	9	initiated	initiate	VERB
ejpam-7078	19	10	by	by	ADP
ejpam-7078	19	11	∗corresponding	∗corresponde	VERB
ejpam-7078	19	12	author	author	NOUN
ejpam-7078	19	13	.	.	PUNCT
ejpam-7078	20	1	doi	doi	PROPN
ejpam-7078	20	2	:	:	PUNCT
ejpam-7078	20	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7078	https://doi.org/10.29020/nybg.ejpam.v18i4.7078	PROPN
ejpam-7078	20	4	email	email	NOUN
ejpam-7078	20	5	addresses	address	NOUN
ejpam-7078	20	6	:	:	PUNCT
ejpam-7078	20	7	leomarich.casinillo@g.msuiit.edu.ph	leomarich.casinillo@g.msuiit.edu.ph	PROPN
ejpam-7078	20	8	(	(	PUNCT
ejpam-7078	20	9	l.	l.	PROPN
ejpam-7078	20	10	f.	f.	PROPN
ejpam-7078	20	11	casinillo	casinillo	PROPN
ejpam-7078	20	12	)	)	PUNCT
ejpam-7078	20	13	,	,	PUNCT
ejpam-7078	20	14	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-7078	20	15	(	(	PUNCT
ejpam-7078	20	16	s.	s.	PROPN
ejpam-7078	20	17	r.	r.	PROPN
ejpam-7078	20	18	canoy	canoy	PROPN
ejpam-7078	20	19	jr	jr	PROPN
ejpam-7078	20	20	.	.	PUNCT
ejpam-7078	20	21	)	)	PUNCT
ejpam-7078	20	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7078	21	1	1	1	NUM
ejpam-7078	21	2	copyright	copyright	NOUN
ejpam-7078	21	3	:	:	PUNCT
ejpam-7078	21	4	©	©	PROPN
ejpam-7078	21	5	2025	2025	NUM
ejpam-7078	21	6	the	the	DET
ejpam-7078	21	7	author(s	author(s	NOUN
ejpam-7078	21	8	)	)	PUNCT
ejpam-7078	21	9	.	.	PUNCT
ejpam-7078	22	1	(	(	PUNCT
ejpam-7078	22	2	cc	cc	NOUN
ejpam-7078	22	3	by	by	ADP
ejpam-7078	22	4	-	-	PUNCT
ejpam-7078	22	5	nc	nc	PROPN
ejpam-7078	22	6	4.0	4.0	NUM
ejpam-7078	22	7	)	)	PUNCT
ejpam-7078	22	8	l.	l.	PROPN
ejpam-7078	22	9	f.	f.	PROPN
ejpam-7078	22	10	casinillo	casinillo	PROPN
ejpam-7078	22	11	,	,	PUNCT
ejpam-7078	22	12	s.	s.	PROPN
ejpam-7078	22	13	r.	r.	PROPN
ejpam-7078	22	14	canoy	canoy	PROPN
ejpam-7078	22	15	jr	jr	PROPN
ejpam-7078	22	16	.	.	PROPN
ejpam-7078	22	17	/	/	SYM
ejpam-7078	22	18	eur	eur	PROPN
ejpam-7078	22	19	.	.	PUNCT
ejpam-7078	23	1	j.	j.	PROPN
ejpam-7078	23	2	pure	pure	PROPN
ejpam-7078	23	3	appl	appl	PROPN
ejpam-7078	23	4	.	.	PROPN
ejpam-7078	23	5	math	math	PROPN
ejpam-7078	23	6	,	,	PUNCT
ejpam-7078	23	7	18	18	NUM
ejpam-7078	23	8	(	(	PUNCT
ejpam-7078	23	9	4	4	NUM
ejpam-7078	23	10	)	)	PUNCT
ejpam-7078	23	11	(	(	PUNCT
ejpam-7078	23	12	2025	2025	NUM
ejpam-7078	23	13	)	)	PUNCT
ejpam-7078	23	14	,	,	PUNCT
ejpam-7078	23	15	7078	7078	NUM
ejpam-7078	23	16	2	2	NUM
ejpam-7078	23	17	of	of	ADP
ejpam-7078	23	18	15	15	NUM
ejpam-7078	23	19	lemańska	lemańska	NOUN
ejpam-7078	23	20	et	et	PROPN
ejpam-7078	23	21	al	al	PROPN
ejpam-7078	23	22	.	.	PUNCT
ejpam-7078	24	1	[	[	X
ejpam-7078	24	2	14	14	NUM
ejpam-7078	24	3	]	]	PUNCT
ejpam-7078	24	4	also	also	ADV
ejpam-7078	24	5	captures	capture	VERB
ejpam-7078	24	6	the	the	DET
ejpam-7078	24	7	attention	attention	NOUN
ejpam-7078	24	8	of	of	ADP
ejpam-7078	24	9	many	many	ADJ
ejpam-7078	24	10	graph	graph	NOUN
ejpam-7078	24	11	theorists	theorist	NOUN
ejpam-7078	24	12	.	.	PUNCT
ejpam-7078	25	1	motivated	motivate	VERB
ejpam-7078	25	2	by	by	ADP
ejpam-7078	25	3	hop	hop	PROPN
ejpam-7078	25	4	roman	roman	ADJ
ejpam-7078	25	5	domination	domination	NOUN
ejpam-7078	25	6	and	and	CCONJ
ejpam-7078	25	7	super	super	ADJ
ejpam-7078	25	8	domination	domination	NOUN
ejpam-7078	25	9	,	,	PUNCT
ejpam-7078	25	10	the	the	DET
ejpam-7078	25	11	author	author	NOUN
ejpam-7078	25	12	introduced	introduce	VERB
ejpam-7078	25	13	a	a	DET
ejpam-7078	25	14	new	new	ADJ
ejpam-7078	25	15	parameter	parameter	NOUN
ejpam-7078	25	16	called	call	VERB
ejpam-7078	25	17	super	sup	ADJ
ejpam-7078	25	18	hop	hop	PROPN
ejpam-7078	25	19	roman	roman	ADJ
ejpam-7078	25	20	domination	domination	NOUN
ejpam-7078	25	21	and	and	CCONJ
ejpam-7078	25	22	investigated	investigate	VERB
ejpam-7078	25	23	its	its	PRON
ejpam-7078	25	24	mathematical	mathematical	ADJ
ejpam-7078	25	25	properties	property	NOUN
ejpam-7078	25	26	.	.	PUNCT
ejpam-7078	26	1	let	let	VERB
ejpam-7078	26	2	g	g	PROPN
ejpam-7078	26	3	=	=	SYM
ejpam-7078	26	4	(	(	PUNCT
ejpam-7078	26	5	v	v	NOUN
ejpam-7078	26	6	(	(	PUNCT
ejpam-7078	26	7	g	g	NOUN
ejpam-7078	26	8	)	)	PUNCT
ejpam-7078	26	9	,	,	PUNCT
ejpam-7078	26	10	e(g	e(g	PROPN
ejpam-7078	26	11	)	)	PUNCT
ejpam-7078	26	12	)	)	PUNCT
ejpam-7078	27	1	be	be	AUX
ejpam-7078	27	2	a	a	DET
ejpam-7078	27	3	simple	simple	ADJ
ejpam-7078	27	4	,	,	PUNCT
ejpam-7078	27	5	undirected	undirected	ADJ
ejpam-7078	27	6	and	and	CCONJ
ejpam-7078	27	7	finite	finite	ADJ
ejpam-7078	27	8	graph	graph	NOUN
ejpam-7078	27	9	where	where	SCONJ
ejpam-7078	27	10	v	v	NOUN
ejpam-7078	27	11	(	(	PUNCT
ejpam-7078	27	12	g	g	NOUN
ejpam-7078	27	13	)	)	PUNCT
ejpam-7078	27	14	is	be	AUX
ejpam-7078	27	15	the	the	DET
ejpam-7078	27	16	vertex	vertex	NOUN
ejpam-7078	27	17	set	set	NOUN
ejpam-7078	27	18	and	and	CCONJ
ejpam-7078	27	19	e(g	e(g	PROPN
ejpam-7078	27	20	)	)	PUNCT
ejpam-7078	27	21	is	be	AUX
ejpam-7078	27	22	the	the	DET
ejpam-7078	27	23	edge	edge	NOUN
ejpam-7078	27	24	set	set	NOUN
ejpam-7078	27	25	of	of	ADP
ejpam-7078	27	26	g.	g.	PROPN
ejpam-7078	27	27	the	the	DET
ejpam-7078	27	28	cardinality	cardinality	NOUN
ejpam-7078	27	29	of	of	ADP
ejpam-7078	27	30	v	v	NOUN
ejpam-7078	27	31	(	(	PUNCT
ejpam-7078	27	32	g	g	NOUN
ejpam-7078	27	33	)	)	PUNCT
ejpam-7078	27	34	denoted	denote	VERB
ejpam-7078	27	35	by	by	ADP
ejpam-7078	27	36	|v	|v	PROPN
ejpam-7078	27	37	(	(	PUNCT
ejpam-7078	27	38	g)|	g)|	PROPN
ejpam-7078	27	39	is	be	AUX
ejpam-7078	27	40	called	call	VERB
ejpam-7078	27	41	the	the	DET
ejpam-7078	27	42	order	order	NOUN
ejpam-7078	27	43	of	of	ADP
ejpam-7078	27	44	g	g	PROPN
ejpam-7078	27	45	and	and	CCONJ
ejpam-7078	27	46	the	the	DET
ejpam-7078	27	47	cardinality	cardinality	NOUN
ejpam-7078	27	48	of	of	ADP
ejpam-7078	27	49	e(g	e(g	PROPN
ejpam-7078	27	50	)	)	PUNCT
ejpam-7078	27	51	denoted	denote	VERB
ejpam-7078	27	52	by	by	ADP
ejpam-7078	27	53	|e(g)|	|e(g)|	PROPN
ejpam-7078	27	54	is	be	AUX
ejpam-7078	27	55	called	call	VERB
ejpam-7078	27	56	the	the	DET
ejpam-7078	27	57	size	size	NOUN
ejpam-7078	27	58	of	of	ADP
ejpam-7078	27	59	g.	g.	PROPN
ejpam-7078	27	60	the	the	DET
ejpam-7078	27	61	complement	complement	NOUN
ejpam-7078	27	62	of	of	ADP
ejpam-7078	27	63	a	a	DET
ejpam-7078	27	64	graph	graph	NOUN
ejpam-7078	27	65	g	g	NOUN
ejpam-7078	27	66	denoted	denote	VERB
ejpam-7078	27	67	by	by	ADP
ejpam-7078	27	68	g	g	PROPN
ejpam-7078	27	69	is	be	AUX
ejpam-7078	27	70	the	the	DET
ejpam-7078	27	71	graph	graph	NOUN
ejpam-7078	27	72	that	that	PRON
ejpam-7078	27	73	satisfies	satisfy	VERB
ejpam-7078	27	74	the	the	DET
ejpam-7078	27	75	following	follow	VERB
ejpam-7078	27	76	conditions	condition	NOUN
ejpam-7078	27	77	:	:	PUNCT
ejpam-7078	27	78	(	(	PUNCT
ejpam-7078	27	79	i	i	NOUN
ejpam-7078	27	80	)	)	PUNCT
ejpam-7078	27	81	v	v	NOUN
ejpam-7078	27	82	(	(	PUNCT
ejpam-7078	27	83	g	g	NOUN
ejpam-7078	27	84	)	)	PUNCT
ejpam-7078	28	1	=	=	NOUN
ejpam-7078	28	2	v	v	X
ejpam-7078	28	3	(	(	PUNCT
ejpam-7078	28	4	g	g	NOUN
ejpam-7078	28	5	)	)	PUNCT
ejpam-7078	28	6	;	;	PUNCT
ejpam-7078	28	7	and	and	CCONJ
ejpam-7078	28	8	(	(	PUNCT
ejpam-7078	28	9	ii	ii	NOUN
ejpam-7078	28	10	)	)	PUNCT
ejpam-7078	28	11	uv	uv	PROPN
ejpam-7078	28	12	∈	∈	PROPN
ejpam-7078	28	13	e(g	e(g	PROPN
ejpam-7078	28	14	)	)	PUNCT
ejpam-7078	29	1	if	if	SCONJ
ejpam-7078	29	2	and	and	CCONJ
ejpam-7078	29	3	only	only	ADV
ejpam-7078	29	4	if	if	SCONJ
ejpam-7078	29	5	uv	uv	PROPN
ejpam-7078	29	6	/∈	/∈	PUNCT
ejpam-7078	29	7	e(g	e(g	PROPN
ejpam-7078	29	8	)	)	PUNCT
ejpam-7078	29	9	.	.	PUNCT
ejpam-7078	30	1	all	all	PRON
ejpam-7078	30	2	needed	need	VERB
ejpam-7078	30	3	basic	basic	ADJ
ejpam-7078	30	4	concepts	concept	NOUN
ejpam-7078	30	5	and	and	CCONJ
ejpam-7078	30	6	terminologies	terminology	NOUN
ejpam-7078	30	7	used	use	VERB
ejpam-7078	30	8	in	in	ADP
ejpam-7078	30	9	this	this	DET
ejpam-7078	30	10	study	study	NOUN
ejpam-7078	30	11	which	which	PRON
ejpam-7078	30	12	are	be	AUX
ejpam-7078	30	13	not	not	PART
ejpam-7078	30	14	define	define	NOUN
ejpam-7078	30	15	are	be	AUX
ejpam-7078	30	16	found	find	VERB
ejpam-7078	30	17	in	in	ADP
ejpam-7078	30	18	[	[	X
ejpam-7078	30	19	15	15	NUM
ejpam-7078	30	20	]	]	PUNCT
ejpam-7078	30	21	,	,	PUNCT
ejpam-7078	31	1	[	[	X
ejpam-7078	31	2	16	16	NUM
ejpam-7078	31	3	]	]	PUNCT
ejpam-7078	31	4	,	,	PUNCT
ejpam-7078	32	1	[	[	X
ejpam-7078	32	2	6	6	NUM
ejpam-7078	32	3	]	]	PUNCT
ejpam-7078	32	4	.	.	PUNCT
ejpam-7078	33	1	let	let	VERB
ejpam-7078	33	2	x	x	SYM
ejpam-7078	33	3	∈	∈	PROPN
ejpam-7078	33	4	v	v	X
ejpam-7078	33	5	(	(	PUNCT
ejpam-7078	33	6	g	g	NOUN
ejpam-7078	33	7	)	)	PUNCT
ejpam-7078	33	8	.	.	PUNCT
ejpam-7078	34	1	then	then	ADV
ejpam-7078	34	2	the	the	DET
ejpam-7078	34	3	open	open	ADJ
ejpam-7078	34	4	neighborhood	neighborhood	NOUN
ejpam-7078	34	5	of	of	ADP
ejpam-7078	34	6	x	x	PUNCT
ejpam-7078	34	7	in	in	ADP
ejpam-7078	34	8	g	g	PROPN
ejpam-7078	34	9	is	be	AUX
ejpam-7078	34	10	the	the	DET
ejpam-7078	34	11	set	set	NOUN
ejpam-7078	34	12	ng(x	ng(x	NUM
ejpam-7078	34	13	)	)	PUNCT
ejpam-7078	34	14	=	=	PRON
ejpam-7078	34	15	{	{	PUNCT
ejpam-7078	34	16	y	y	PROPN
ejpam-7078	34	17	∈	∈	PROPN
ejpam-7078	34	18	v	v	NOUN
ejpam-7078	34	19	(	(	PUNCT
ejpam-7078	34	20	g	g	NOUN
ejpam-7078	34	21	)	)	PUNCT
ejpam-7078	34	22	:	:	PUNCT
ejpam-7078	34	23	xy	xy	PROPN
ejpam-7078	34	24	∈	∈	PROPN
ejpam-7078	34	25	e(g	e(g	PROPN
ejpam-7078	34	26	)	)	PUNCT
ejpam-7078	34	27	}	}	PUNCT
ejpam-7078	34	28	and	and	CCONJ
ejpam-7078	34	29	the	the	DET
ejpam-7078	34	30	closed	closed	ADJ
ejpam-7078	34	31	neighborhood	neighborhood	NOUN
ejpam-7078	34	32	of	of	ADP
ejpam-7078	34	33	a	a	DET
ejpam-7078	34	34	vertex	vertex	NOUN
ejpam-7078	34	35	x	x	SYM
ejpam-7078	34	36	∈	∈	NOUN
ejpam-7078	34	37	v	v	ADP
ejpam-7078	34	38	(	(	PUNCT
ejpam-7078	34	39	g	g	NOUN
ejpam-7078	34	40	)	)	PUNCT
ejpam-7078	34	41	is	be	AUX
ejpam-7078	34	42	the	the	DET
ejpam-7078	34	43	set	set	NOUN
ejpam-7078	34	44	ng[x	ng[x	PROPN
ejpam-7078	34	45	]	]	PUNCT
ejpam-7078	34	46	=	=	SYM
ejpam-7078	34	47	ng(x)∪	ng(x)∪	NOUN
ejpam-7078	34	48	{	{	PUNCT
ejpam-7078	34	49	x	x	NOUN
ejpam-7078	34	50	}	}	PUNCT
ejpam-7078	34	51	.	.	PUNCT
ejpam-7078	35	1	let	let	VERB
ejpam-7078	35	2	o	o	NOUN
ejpam-7078	35	3	⊆	⊆	NUM
ejpam-7078	35	4	v	v	NOUN
ejpam-7078	35	5	(	(	PUNCT
ejpam-7078	35	6	g	g	NOUN
ejpam-7078	35	7	)	)	PUNCT
ejpam-7078	35	8	.	.	PUNCT
ejpam-7078	36	1	then	then	ADV
ejpam-7078	36	2	,	,	PUNCT
ejpam-7078	36	3	the	the	DET
ejpam-7078	36	4	set	set	NOUN
ejpam-7078	36	5	ng(o	ng(o	NOUN
ejpam-7078	36	6	)	)	PUNCT
ejpam-7078	36	7	=	=	PUNCT
ejpam-7078	36	8	n(o	n(o	X
ejpam-7078	36	9	)	)	PUNCT
ejpam-7078	36	10	=	=	SYM
ejpam-7078	36	11	⋃	⋃	NOUN
ejpam-7078	36	12	v∈o	v∈o	NOUN
ejpam-7078	36	13	ng(v	ng(v	PUNCT
ejpam-7078	36	14	)	)	PUNCT
ejpam-7078	36	15	is	be	AUX
ejpam-7078	36	16	called	call	VERB
ejpam-7078	36	17	the	the	DET
ejpam-7078	36	18	open	open	ADJ
ejpam-7078	36	19	neighborhood	neighborhood	NOUN
ejpam-7078	36	20	of	of	ADP
ejpam-7078	36	21	o	o	PROPN
ejpam-7078	36	22	and	and	CCONJ
ejpam-7078	36	23	the	the	DET
ejpam-7078	36	24	set	set	NOUN
ejpam-7078	36	25	ng[o	ng[o	PROPN
ejpam-7078	36	26	]	]	X
ejpam-7078	36	27	=	=	SYM
ejpam-7078	36	28	n	n	PRON
ejpam-7078	37	1	[	[	X
ejpam-7078	37	2	o	o	X
ejpam-7078	37	3	]	]	X
ejpam-7078	37	4	=	=	SYM
ejpam-7078	37	5	n(x	n(x	X
ejpam-7078	37	6	)	)	PUNCT
ejpam-7078	37	7	∪	∪	NOUN
ejpam-7078	37	8	x	x	VERB
ejpam-7078	37	9	is	be	AUX
ejpam-7078	37	10	called	call	VERB
ejpam-7078	37	11	the	the	DET
ejpam-7078	37	12	closed	closed	ADJ
ejpam-7078	37	13	neighborhood	neighborhood	NOUN
ejpam-7078	37	14	of	of	ADP
ejpam-7078	37	15	o.	o.	NOUN
ejpam-7078	37	16	let	let	VERB
ejpam-7078	37	17	u	u	PRON
ejpam-7078	37	18	and	and	CCONJ
ejpam-7078	37	19	v	v	NOUN
ejpam-7078	37	20	be	be	AUX
ejpam-7078	37	21	two	two	NUM
ejpam-7078	37	22	distinct	distinct	ADJ
ejpam-7078	37	23	vertices	vertex	NOUN
ejpam-7078	37	24	in	in	ADP
ejpam-7078	37	25	graph	graph	NOUN
ejpam-7078	37	26	g.	g.	PROPN
ejpam-7078	37	27	then	then	ADV
ejpam-7078	37	28	,	,	PUNCT
ejpam-7078	37	29	the	the	DET
ejpam-7078	37	30	distance	distance	NOUN
ejpam-7078	37	31	between	between	ADP
ejpam-7078	37	32	u	u	NOUN
ejpam-7078	37	33	and	and	CCONJ
ejpam-7078	37	34	v	v	NOUN
ejpam-7078	37	35	denoted	denote	VERB
ejpam-7078	37	36	by	by	ADP
ejpam-7078	37	37	dg(u	dg(u	PROPN
ejpam-7078	37	38	,	,	PUNCT
ejpam-7078	37	39	v	v	NOUN
ejpam-7078	37	40	)	)	PUNCT
ejpam-7078	37	41	is	be	AUX
ejpam-7078	37	42	the	the	DET
ejpam-7078	37	43	length	length	NOUN
ejpam-7078	37	44	of	of	ADP
ejpam-7078	37	45	the	the	DET
ejpam-7078	37	46	shortest	short	ADJ
ejpam-7078	37	47	walk	walk	NOUN
ejpam-7078	37	48	between	between	ADP
ejpam-7078	37	49	u	u	NOUN
ejpam-7078	37	50	and	and	CCONJ
ejpam-7078	37	51	v	v	NOUN
ejpam-7078	37	52	in	in	ADP
ejpam-7078	37	53	g.	g.	PROPN
ejpam-7078	37	54	if	if	SCONJ
ejpam-7078	37	55	there	there	PRON
ejpam-7078	37	56	is	be	VERB
ejpam-7078	37	57	no	no	DET
ejpam-7078	37	58	such	such	ADJ
ejpam-7078	37	59	walk	walk	NOUN
ejpam-7078	37	60	between	between	ADP
ejpam-7078	37	61	u	u	NOUN
ejpam-7078	37	62	and	and	CCONJ
ejpam-7078	37	63	v	v	NOUN
ejpam-7078	37	64	in	in	ADP
ejpam-7078	37	65	g	g	PROPN
ejpam-7078	37	66	,	,	PUNCT
ejpam-7078	37	67	then	then	ADV
ejpam-7078	37	68	we	we	PRON
ejpam-7078	37	69	define	define	VERB
ejpam-7078	37	70	the	the	DET
ejpam-7078	37	71	distance	distance	NOUN
ejpam-7078	37	72	as	as	ADP
ejpam-7078	37	73	dg(u	dg(u	X
ejpam-7078	37	74	,	,	PUNCT
ejpam-7078	37	75	v	v	NOUN
ejpam-7078	37	76	)	)	PUNCT
ejpam-7078	37	77	=	=	SYM
ejpam-7078	37	78	∞.	∞.	PROPN
ejpam-7078	37	79	now	now	ADV
ejpam-7078	37	80	,	,	PUNCT
ejpam-7078	37	81	let	let	VERB
ejpam-7078	37	82	v	v	NUM
ejpam-7078	37	83	∈	∈	PROPN
ejpam-7078	37	84	v	v	NOUN
ejpam-7078	37	85	(	(	PUNCT
ejpam-7078	37	86	g	g	NOUN
ejpam-7078	37	87	)	)	PUNCT
ejpam-7078	37	88	.	.	PUNCT
ejpam-7078	38	1	then	then	ADV
ejpam-7078	38	2	,	,	PUNCT
ejpam-7078	38	3	the	the	DET
ejpam-7078	38	4	set	set	ADJ
ejpam-7078	38	5	n2	n2	ADJ
ejpam-7078	38	6	g(v	g(v	PROPN
ejpam-7078	38	7	)	)	PUNCT
ejpam-7078	38	8	=	=	PRON
ejpam-7078	38	9	{	{	PUNCT
ejpam-7078	38	10	u	u	NOUN
ejpam-7078	38	11	∈	∈	PROPN
ejpam-7078	38	12	v	v	NOUN
ejpam-7078	38	13	(	(	PUNCT
ejpam-7078	38	14	g	g	NOUN
ejpam-7078	38	15	)	)	PUNCT
ejpam-7078	38	16	:	:	PUNCT
ejpam-7078	39	1	degg(u	degg(u	NUM
ejpam-7078	39	2	,	,	PUNCT
ejpam-7078	39	3	v	v	NOUN
ejpam-7078	39	4	)	)	PUNCT
ejpam-7078	39	5	=	=	SYM
ejpam-7078	40	1	2	2	X
ejpam-7078	40	2	}	}	PUNCT
ejpam-7078	40	3	is	be	AUX
ejpam-7078	40	4	called	call	VERB
ejpam-7078	40	5	the	the	DET
ejpam-7078	40	6	open	open	ADJ
ejpam-7078	40	7	hop	hop	NOUN
ejpam-7078	40	8	-	-	PUNCT
ejpam-7078	40	9	neighborhood	neighborhood	NOUN
ejpam-7078	40	10	and	and	CCONJ
ejpam-7078	40	11	each	each	DET
ejpam-7078	40	12	element	element	NOUN
ejpam-7078	40	13	of	of	ADP
ejpam-7078	40	14	n2	n2	ADJ
ejpam-7078	40	15	g(v	g(v	PROPN
ejpam-7078	40	16	)	)	PUNCT
ejpam-7078	40	17	is	be	AUX
ejpam-7078	40	18	called	call	VERB
ejpam-7078	40	19	hop	hop	PROPN
ejpam-7078	40	20	-	-	PUNCT
ejpam-7078	40	21	neigbor	neigbor	PROPN
ejpam-7078	40	22	of	of	ADP
ejpam-7078	40	23	vertex	vertex	PROPN
ejpam-7078	40	24	v.	v.	ADP
ejpam-7078	40	25	moreover	moreover	ADV
ejpam-7078	40	26	,	,	PUNCT
ejpam-7078	40	27	for	for	ADP
ejpam-7078	40	28	h	h	PROPN
ejpam-7078	40	29	⊆	⊆	NUM
ejpam-7078	40	30	v	v	NOUN
ejpam-7078	40	31	(	(	PUNCT
ejpam-7078	40	32	g	g	NOUN
ejpam-7078	40	33	)	)	PUNCT
ejpam-7078	40	34	,	,	PUNCT
ejpam-7078	40	35	n2	n2	NOUN
ejpam-7078	40	36	g(h	g(h	PROPN
ejpam-7078	40	37	)	)	PUNCT
ejpam-7078	41	1	=	=	SYM
ejpam-7078	41	2	⋃	⋃	NOUN
ejpam-7078	41	3	v∈h	v∈h	NOUN
ejpam-7078	41	4	n2	n2	ADJ
ejpam-7078	41	5	g(v	g(v	PROPN
ejpam-7078	41	6	)	)	PUNCT
ejpam-7078	41	7	and	and	CCONJ
ejpam-7078	41	8	n2	n2	PROPN
ejpam-7078	41	9	g[h	g[h	PROPN
ejpam-7078	41	10	]	]	PUNCT
ejpam-7078	41	11	=	=	SYM
ejpam-7078	41	12	n2	n2	PROPN
ejpam-7078	41	13	g(h	g(h	PROPN
ejpam-7078	41	14	)	)	PUNCT
ejpam-7078	41	15	∪h	∪h	NUM
ejpam-7078	41	16	.	.	PUNCT
ejpam-7078	42	1	a	a	DET
ejpam-7078	42	2	subset	subset	NOUN
ejpam-7078	42	3	d	d	NOUN
ejpam-7078	42	4	of	of	ADP
ejpam-7078	42	5	vertex	vertex	NOUN
ejpam-7078	42	6	set	set	VERB
ejpam-7078	42	7	v	v	NOUN
ejpam-7078	42	8	(	(	PUNCT
ejpam-7078	42	9	g	g	NOUN
ejpam-7078	42	10	)	)	PUNCT
ejpam-7078	42	11	is	be	AUX
ejpam-7078	42	12	a	a	DET
ejpam-7078	42	13	dominating	dominating	NOUN
ejpam-7078	42	14	set	set	NOUN
ejpam-7078	42	15	of	of	ADP
ejpam-7078	42	16	g	g	PROPN
ejpam-7078	42	17	if	if	SCONJ
ejpam-7078	42	18	for	for	ADP
ejpam-7078	42	19	every	every	PRON
ejpam-7078	42	20	v	v	NUM
ejpam-7078	42	21	∈	∈	NOUN
ejpam-7078	42	22	v	v	NOUN
ejpam-7078	42	23	(	(	PUNCT
ejpam-7078	42	24	g	g	NOUN
ejpam-7078	42	25	)	)	PUNCT
ejpam-7078	42	26	\	\	PUNCT
ejpam-7078	43	1	d	d	X
ejpam-7078	43	2	,	,	PUNCT
ejpam-7078	43	3	there	there	PRON
ejpam-7078	43	4	exists	exist	VERB
ejpam-7078	43	5	u	u	NOUN
ejpam-7078	43	6	∈	∈	PROPN
ejpam-7078	43	7	d	d	ADP
ejpam-7078	43	8	such	such	ADJ
ejpam-7078	43	9	that	that	SCONJ
ejpam-7078	43	10	uv	uv	NOUN
ejpam-7078	43	11	is	be	AUX
ejpam-7078	43	12	an	an	DET
ejpam-7078	43	13	edge	edge	NOUN
ejpam-7078	43	14	of	of	ADP
ejpam-7078	43	15	g	g	NOUN
ejpam-7078	43	16	[	[	X
ejpam-7078	43	17	6	6	NUM
ejpam-7078	43	18	]	]	PUNCT
ejpam-7078	43	19	.	.	PUNCT
ejpam-7078	44	1	in	in	ADP
ejpam-7078	44	2	that	that	DET
ejpam-7078	44	3	case	case	NOUN
ejpam-7078	44	4	,	,	PUNCT
ejpam-7078	44	5	n	n	X
ejpam-7078	45	1	[	[	X
ejpam-7078	45	2	d	d	X
ejpam-7078	45	3	]	]	X
ejpam-7078	45	4	=	=	SYM
ejpam-7078	45	5	v	v	NOUN
ejpam-7078	45	6	(	(	PUNCT
ejpam-7078	45	7	g	g	NOUN
ejpam-7078	45	8	)	)	PUNCT
ejpam-7078	45	9	.	.	PUNCT
ejpam-7078	46	1	the	the	DET
ejpam-7078	46	2	domination	domination	NOUN
ejpam-7078	46	3	number	number	NOUN
ejpam-7078	46	4	denoted	denote	VERB
ejpam-7078	46	5	by	by	ADP
ejpam-7078	46	6	γ(g	γ(g	PROPN
ejpam-7078	46	7	)	)	PUNCT
ejpam-7078	46	8	is	be	AUX
ejpam-7078	46	9	the	the	DET
ejpam-7078	46	10	minimum	minimum	ADJ
ejpam-7078	46	11	cardinality	cardinality	NOUN
ejpam-7078	46	12	of	of	ADP
ejpam-7078	46	13	a	a	DET
ejpam-7078	46	14	dominating	dominating	NOUN
ejpam-7078	46	15	set	set	NOUN
ejpam-7078	46	16	d	d	PROPN
ejpam-7078	46	17	in	in	ADP
ejpam-7078	46	18	g.	g.	PROPN
ejpam-7078	46	19	if	if	SCONJ
ejpam-7078	46	20	d	d	PROPN
ejpam-7078	46	21	is	be	AUX
ejpam-7078	46	22	a	a	DET
ejpam-7078	46	23	dominating	dominating	NOUN
ejpam-7078	46	24	set	set	VERB
ejpam-7078	46	25	with	with	ADP
ejpam-7078	46	26	|d|	|d|	PROPN
ejpam-7078	46	27	=	=	SYM
ejpam-7078	46	28	γ(g	γ(g	PROPN
ejpam-7078	46	29	)	)	PUNCT
ejpam-7078	46	30	,	,	PUNCT
ejpam-7078	46	31	then	then	ADV
ejpam-7078	46	32	we	we	PRON
ejpam-7078	46	33	call	call	VERB
ejpam-7078	46	34	d	d	ADP
ejpam-7078	46	35	a	a	DET
ejpam-7078	46	36	minimum	minimum	ADJ
ejpam-7078	46	37	dominating	dominating	NOUN
ejpam-7078	46	38	set	set	NOUN
ejpam-7078	46	39	of	of	ADP
ejpam-7078	46	40	g	g	NOUN
ejpam-7078	46	41	or	or	CCONJ
ejpam-7078	46	42	a	a	DET
ejpam-7078	46	43	γ	γ	NOUN
ejpam-7078	46	44	-	-	PUNCT
ejpam-7078	46	45	set	set	NOUN
ejpam-7078	46	46	in	in	ADP
ejpam-7078	46	47	g.	g.	PROPN
ejpam-7078	46	48	a	a	DET
ejpam-7078	46	49	dominating	dominating	NOUN
ejpam-7078	46	50	set	set	NOUN
ejpam-7078	46	51	s	s	PROPN
ejpam-7078	46	52	⊆	⊆	NUM
ejpam-7078	46	53	v	v	NOUN
ejpam-7078	46	54	(	(	PUNCT
ejpam-7078	46	55	g	g	NOUN
ejpam-7078	46	56	)	)	PUNCT
ejpam-7078	46	57	is	be	AUX
ejpam-7078	46	58	called	call	VERB
ejpam-7078	46	59	a	a	DET
ejpam-7078	46	60	super	super	ADJ
ejpam-7078	46	61	dominating	dominating	NOUN
ejpam-7078	46	62	set	set	NOUN
ejpam-7078	46	63	of	of	ADP
ejpam-7078	46	64	g	g	PROPN
ejpam-7078	46	65	if	if	SCONJ
ejpam-7078	46	66	for	for	ADP
ejpam-7078	46	67	every	every	DET
ejpam-7078	46	68	vertex	vertex	NOUN
ejpam-7078	46	69	u	u	NOUN
ejpam-7078	46	70	∈	∈	PROPN
ejpam-7078	46	71	v	v	NOUN
ejpam-7078	46	72	(	(	PUNCT
ejpam-7078	46	73	g)\s	g)\s	NOUN
ejpam-7078	46	74	,	,	PUNCT
ejpam-7078	46	75	there	there	PRON
ejpam-7078	46	76	exists	exist	VERB
ejpam-7078	46	77	v	v	ADP
ejpam-7078	46	78	∈	∈	PROPN
ejpam-7078	46	79	s	s	VERB
ejpam-7078	46	80	such	such	ADJ
ejpam-7078	46	81	that	that	PRON
ejpam-7078	46	82	n(v)∩	n(v)∩	PROPN
ejpam-7078	46	83	(	(	PUNCT
ejpam-7078	46	84	v	v	NOUN
ejpam-7078	46	85	(	(	PUNCT
ejpam-7078	46	86	g)\s	g)\s	NOUN
ejpam-7078	46	87	)	)	PUNCT
ejpam-7078	46	88	=	=	PUNCT
ejpam-7078	46	89	{	{	PUNCT
ejpam-7078	46	90	u	u	NOUN
ejpam-7078	46	91	}	}	PUNCT
ejpam-7078	47	1	[	[	X
ejpam-7078	47	2	8	8	NUM
ejpam-7078	47	3	]	]	PUNCT
ejpam-7078	47	4	.	.	PUNCT
ejpam-7078	48	1	in	in	ADP
ejpam-7078	48	2	that	that	DET
ejpam-7078	48	3	case	case	NOUN
ejpam-7078	48	4	,	,	PUNCT
ejpam-7078	48	5	v	v	NOUN
ejpam-7078	48	6	is	be	AUX
ejpam-7078	48	7	a	a	DET
ejpam-7078	48	8	private	private	ADJ
ejpam-7078	48	9	neighbor	neighbor	NOUN
ejpam-7078	48	10	of	of	ADP
ejpam-7078	48	11	u	u	NOUN
ejpam-7078	48	12	with	with	ADP
ejpam-7078	48	13	respect	respect	NOUN
ejpam-7078	48	14	to	to	ADP
ejpam-7078	48	15	v	v	NOUN
ejpam-7078	48	16	(	(	PUNCT
ejpam-7078	48	17	g	g	NOUN
ejpam-7078	48	18	)	)	PUNCT
ejpam-7078	48	19	\	\	PUNCT
ejpam-7078	49	1	s.	s.	PROPN
ejpam-7078	49	2	the	the	DET
ejpam-7078	49	3	smallest	small	ADJ
ejpam-7078	49	4	cardinality	cardinality	NOUN
ejpam-7078	49	5	of	of	ADP
ejpam-7078	49	6	a	a	DET
ejpam-7078	49	7	super	super	ADJ
ejpam-7078	49	8	dominating	dominating	NOUN
ejpam-7078	49	9	set	set	NOUN
ejpam-7078	49	10	of	of	ADP
ejpam-7078	49	11	g	g	PROPN
ejpam-7078	49	12	is	be	AUX
ejpam-7078	49	13	called	call	VERB
ejpam-7078	49	14	the	the	DET
ejpam-7078	49	15	super	super	ADJ
ejpam-7078	49	16	domination	domination	NOUN
ejpam-7078	49	17	number	number	NOUN
ejpam-7078	49	18	denoted	denote	VERB
ejpam-7078	49	19	by	by	ADP
ejpam-7078	49	20	γsp(g	γsp(g	NOUN
ejpam-7078	49	21	)	)	PUNCT
ejpam-7078	49	22	.	.	PUNCT
ejpam-7078	50	1	a	a	DET
ejpam-7078	50	2	super	super	ADJ
ejpam-7078	50	3	dominating	dominating	NOUN
ejpam-7078	50	4	set	set	NOUN
ejpam-7078	50	5	of	of	ADP
ejpam-7078	50	6	cardinality	cardinality	PROPN
ejpam-7078	50	7	γsp(g	γsp(g	NOUN
ejpam-7078	50	8	)	)	PUNCT
ejpam-7078	50	9	is	be	AUX
ejpam-7078	50	10	called	call	VERB
ejpam-7078	50	11	γsp	γsp	NOUN
ejpam-7078	50	12	-	-	PUNCT
ejpam-7078	50	13	set	set	NOUN
ejpam-7078	50	14	in	in	ADP
ejpam-7078	50	15	g.	g.	PROPN
ejpam-7078	50	16	a	a	DET
ejpam-7078	50	17	set	set	NOUN
ejpam-7078	50	18	s	s	PROPN
ejpam-7078	50	19	⊆	⊆	NUM
ejpam-7078	50	20	v	v	NOUN
ejpam-7078	50	21	(	(	PUNCT
ejpam-7078	50	22	g	g	NOUN
ejpam-7078	50	23	)	)	PUNCT
ejpam-7078	50	24	is	be	AUX
ejpam-7078	50	25	called	call	VERB
ejpam-7078	50	26	a	a	DET
ejpam-7078	50	27	hop	hop	NOUN
ejpam-7078	50	28	dominating	dominating	NOUN
ejpam-7078	50	29	set	set	NOUN
ejpam-7078	50	30	of	of	ADP
ejpam-7078	50	31	g	g	PROPN
ejpam-7078	50	32	if	if	SCONJ
ejpam-7078	50	33	for	for	ADP
ejpam-7078	50	34	every	every	DET
ejpam-7078	50	35	vertex	vertex	NOUN
ejpam-7078	50	36	in	in	ADP
ejpam-7078	50	37	v	v	NUM
ejpam-7078	50	38	∈	∈	NOUN
ejpam-7078	50	39	v	v	NOUN
ejpam-7078	50	40	(	(	PUNCT
ejpam-7078	50	41	g)\s	g)\s	NOUN
ejpam-7078	50	42	,	,	PUNCT
ejpam-7078	50	43	there	there	PRON
ejpam-7078	50	44	exists	exist	VERB
ejpam-7078	50	45	u	u	PROPN
ejpam-7078	50	46	∈	∈	PROPN
ejpam-7078	50	47	s	s	VERB
ejpam-7078	50	48	such	such	ADJ
ejpam-7078	50	49	that	that	DET
ejpam-7078	50	50	dg(u	dg(u	ADJ
ejpam-7078	50	51	,	,	PUNCT
ejpam-7078	50	52	v	v	NOUN
ejpam-7078	50	53	)	)	PUNCT
ejpam-7078	50	54	=	=	SYM
ejpam-7078	50	55	2	2	NUM
ejpam-7078	51	1	[	[	X
ejpam-7078	51	2	17	17	NUM
ejpam-7078	51	3	]	]	PUNCT
ejpam-7078	51	4	.	.	PUNCT
ejpam-7078	52	1	the	the	DET
ejpam-7078	52	2	smallest	small	ADJ
ejpam-7078	52	3	cardinality	cardinality	NOUN
ejpam-7078	52	4	of	of	ADP
ejpam-7078	52	5	a	a	DET
ejpam-7078	52	6	hop	hop	NOUN
ejpam-7078	52	7	dominating	dominating	NOUN
ejpam-7078	52	8	set	set	NOUN
ejpam-7078	52	9	in	in	ADP
ejpam-7078	52	10	g	g	NOUN
ejpam-7078	52	11	,	,	PUNCT
ejpam-7078	52	12	denoted	denote	VERB
ejpam-7078	52	13	γh(g	γh(g	NOUN
ejpam-7078	52	14	)	)	PUNCT
ejpam-7078	52	15	,	,	PUNCT
ejpam-7078	52	16	is	be	AUX
ejpam-7078	52	17	called	call	VERB
ejpam-7078	52	18	the	the	DET
ejpam-7078	52	19	hop	hop	NOUN
ejpam-7078	52	20	domination	domination	NOUN
ejpam-7078	52	21	number	number	NOUN
ejpam-7078	52	22	of	of	ADP
ejpam-7078	52	23	g.	g.	PROPN
ejpam-7078	52	24	a	a	DET
ejpam-7078	52	25	hop	hop	NOUN
ejpam-7078	52	26	dominating	dominating	NOUN
ejpam-7078	52	27	set	set	NOUN
ejpam-7078	52	28	of	of	ADP
ejpam-7078	52	29	cardinality	cardinality	NOUN
ejpam-7078	52	30	γh(g	γh(g	PUNCT
ejpam-7078	52	31	)	)	PUNCT
ejpam-7078	52	32	is	be	AUX
ejpam-7078	52	33	called	call	VERB
ejpam-7078	52	34	a	a	DET
ejpam-7078	52	35	γh	γh	ADV
ejpam-7078	52	36	-	-	PUNCT
ejpam-7078	52	37	set	set	NOUN
ejpam-7078	52	38	in	in	ADP
ejpam-7078	52	39	g.	g.	PROPN
ejpam-7078	52	40	a	a	DET
ejpam-7078	52	41	hop	hop	NOUN
ejpam-7078	52	42	dominating	dominating	NOUN
ejpam-7078	52	43	set	set	NOUN
ejpam-7078	52	44	s	s	PROPN
ejpam-7078	52	45	⊆	⊆	NUM
ejpam-7078	52	46	v	v	NOUN
ejpam-7078	52	47	(	(	PUNCT
ejpam-7078	52	48	g	g	NOUN
ejpam-7078	52	49	)	)	PUNCT
ejpam-7078	52	50	is	be	AUX
ejpam-7078	52	51	called	call	VERB
ejpam-7078	52	52	super	super	ADV
ejpam-7078	52	53	hop	hop	NOUN
ejpam-7078	52	54	dominating	dominate	VERB
ejpam-7078	52	55	if	if	SCONJ
ejpam-7078	52	56	for	for	ADP
ejpam-7078	52	57	every	every	DET
ejpam-7078	52	58	vertex	vertex	NOUN
ejpam-7078	52	59	v	v	ADP
ejpam-7078	52	60	∈	∈	NOUN
ejpam-7078	52	61	v	v	NOUN
ejpam-7078	52	62	(	(	PUNCT
ejpam-7078	52	63	g	g	NOUN
ejpam-7078	52	64	)	)	PUNCT
ejpam-7078	52	65	\	\	PROPN
ejpam-7078	53	1	s	s	X
ejpam-7078	53	2	,	,	PUNCT
ejpam-7078	53	3	there	there	PRON
ejpam-7078	53	4	exists	exist	VERB
ejpam-7078	53	5	u	u	NOUN
ejpam-7078	53	6	∈	∈	PROPN
ejpam-7078	53	7	d	d	ADP
ejpam-7078	53	8	such	such	ADJ
ejpam-7078	53	9	that	that	DET
ejpam-7078	53	10	n2	n2	ADJ
ejpam-7078	53	11	g(u	g(u	PROPN
ejpam-7078	53	12	)	)	PUNCT
ejpam-7078	53	13	∩	∩	NOUN
ejpam-7078	53	14	(	(	PUNCT
ejpam-7078	53	15	v	v	NOUN
ejpam-7078	53	16	(	(	PUNCT
ejpam-7078	53	17	g	g	NOUN
ejpam-7078	53	18	)	)	PUNCT
ejpam-7078	53	19	\	\	PROPN
ejpam-7078	54	1	s	s	X
ejpam-7078	54	2	)	)	PUNCT
ejpam-7078	54	3	=	=	SYM
ejpam-7078	54	4	{	{	PUNCT
ejpam-7078	54	5	v	v	NOUN
ejpam-7078	54	6	}	}	PUNCT
ejpam-7078	54	7	[	[	X
ejpam-7078	54	8	18	18	NUM
ejpam-7078	54	9	]	]	PUNCT
ejpam-7078	54	10	.	.	PUNCT
ejpam-7078	55	1	the	the	DET
ejpam-7078	55	2	smallest	small	ADJ
ejpam-7078	55	3	cardinality	cardinality	NOUN
ejpam-7078	55	4	of	of	ADP
ejpam-7078	55	5	a	a	DET
ejpam-7078	55	6	super	super	ADV
ejpam-7078	55	7	hop	hop	NOUN
ejpam-7078	55	8	dominating	dominating	NOUN
ejpam-7078	55	9	set	set	VERB
ejpam-7078	55	10	in	in	ADP
ejpam-7078	55	11	g	g	NOUN
ejpam-7078	55	12	,	,	PUNCT
ejpam-7078	55	13	denoted	denote	VERB
ejpam-7078	55	14	γsh(g	γsh(g	NOUN
ejpam-7078	55	15	)	)	PUNCT
ejpam-7078	55	16	,	,	PUNCT
ejpam-7078	55	17	is	be	AUX
ejpam-7078	55	18	called	call	VERB
ejpam-7078	55	19	the	the	DET
ejpam-7078	55	20	super	super	PROPN
ejpam-7078	55	21	hop	hop	NOUN
ejpam-7078	55	22	domination	domination	NOUN
ejpam-7078	55	23	number	number	NOUN
ejpam-7078	55	24	of	of	ADP
ejpam-7078	55	25	g.	g.	PROPN
ejpam-7078	55	26	a	a	DET
ejpam-7078	55	27	super	super	ADV
ejpam-7078	55	28	hop	hop	NOUN
ejpam-7078	55	29	dominating	dominating	NOUN
ejpam-7078	55	30	set	set	NOUN
ejpam-7078	55	31	of	of	ADP
ejpam-7078	55	32	cardinality	cardinality	PROPN
ejpam-7078	55	33	γsh(g	γsh(g	NOUN
ejpam-7078	55	34	)	)	PUNCT
ejpam-7078	55	35	is	be	AUX
ejpam-7078	55	36	called	call	VERB
ejpam-7078	55	37	a	a	DET
ejpam-7078	55	38	γsh	γsh	NOUN
ejpam-7078	55	39	-	-	PUNCT
ejpam-7078	55	40	set	set	VERB
ejpam-7078	55	41	in	in	ADP
ejpam-7078	55	42	g.	g.	PROPN
ejpam-7078	55	43	hop	hop	PROPN
ejpam-7078	55	44	domination	domination	PROPN
ejpam-7078	55	45	and	and	CCONJ
ejpam-7078	55	46	some	some	PRON
ejpam-7078	55	47	of	of	ADP
ejpam-7078	55	48	its	its	PRON
ejpam-7078	55	49	variants	variant	NOUN
ejpam-7078	55	50	have	have	AUX
ejpam-7078	55	51	beed	be	VERB
ejpam-7078	55	52	studied	study	VERB
ejpam-7078	55	53	previously	previously	ADV
ejpam-7078	55	54	in	in	ADP
ejpam-7078	55	55	[	[	X
ejpam-7078	55	56	18	18	NUM
ejpam-7078	55	57	]	]	PUNCT
ejpam-7078	55	58	,	,	PUNCT
ejpam-7078	55	59	[	[	X
ejpam-7078	55	60	19	19	NUM
ejpam-7078	55	61	]	]	PUNCT
ejpam-7078	55	62	,	,	PUNCT
ejpam-7078	56	1	[	[	X
ejpam-7078	56	2	20	20	NUM
ejpam-7078	56	3	]	]	PUNCT
ejpam-7078	56	4	,	,	PUNCT
ejpam-7078	57	1	[	[	X
ejpam-7078	57	2	21	21	NUM
ejpam-7078	57	3	]	]	PUNCT
ejpam-7078	57	4	,	,	PUNCT
ejpam-7078	58	1	[	[	X
ejpam-7078	58	2	22	22	NUM
ejpam-7078	58	3	]	]	PUNCT
ejpam-7078	58	4	,	,	PUNCT
ejpam-7078	58	5	and	and	CCONJ
ejpam-7078	58	6	[	[	X
ejpam-7078	58	7	23	23	NUM
ejpam-7078	58	8	]	]	PUNCT
ejpam-7078	58	9	.	.	PUNCT
ejpam-7078	59	1	let	let	VERB
ejpam-7078	59	2	f	f	NOUN
ejpam-7078	59	3	:	:	PUNCT
ejpam-7078	59	4	v	v	X
ejpam-7078	59	5	(	(	PUNCT
ejpam-7078	59	6	g	g	NOUN
ejpam-7078	59	7	)	)	PUNCT
ejpam-7078	59	8	→	→	SYM
ejpam-7078	59	9	{	{	PUNCT
ejpam-7078	59	10	0	0	NUM
ejpam-7078	59	11	,	,	PUNCT
ejpam-7078	59	12	1	1	NUM
ejpam-7078	59	13	,	,	PUNCT
ejpam-7078	59	14	2	2	NUM
ejpam-7078	59	15	}	}	PUNCT
ejpam-7078	59	16	be	be	AUX
ejpam-7078	59	17	a	a	DET
ejpam-7078	59	18	function	function	NOUN
ejpam-7078	59	19	on	on	ADP
ejpam-7078	59	20	g.	g.	PROPN
ejpam-7078	59	21	let	let	VERB
ejpam-7078	59	22	the	the	DET
ejpam-7078	59	23	sets	set	NOUN
ejpam-7078	59	24	v0	v0	PROPN
ejpam-7078	59	25	,	,	PUNCT
ejpam-7078	59	26	v1	v1	PROPN
ejpam-7078	59	27	,	,	PUNCT
ejpam-7078	59	28	v2	v2	PROPN
ejpam-7078	59	29	be	be	AUX
ejpam-7078	59	30	given	give	VERB
ejpam-7078	59	31	as	as	SCONJ
ejpam-7078	59	32	follows	follow	VERB
ejpam-7078	59	33	:	:	PUNCT
ejpam-7078	59	34	v0	v0	NOUN
ejpam-7078	59	35	=	=	SYM
ejpam-7078	59	36	{	{	PUNCT
ejpam-7078	59	37	v	v	NUM
ejpam-7078	59	38	∈	∈	NOUN
ejpam-7078	59	39	v	v	NOUN
ejpam-7078	59	40	(	(	PUNCT
ejpam-7078	59	41	g	g	NOUN
ejpam-7078	59	42	)	)	PUNCT
ejpam-7078	59	43	:	:	PUNCT
ejpam-7078	59	44	f(v	f(v	NOUN
ejpam-7078	59	45	)	)	PUNCT
ejpam-7078	59	46	=	=	SYM
ejpam-7078	59	47	0	0	NUM
ejpam-7078	59	48	}	}	PUNCT
ejpam-7078	59	49	;	;	PUNCT
ejpam-7078	59	50	v1	v1	NOUN
ejpam-7078	59	51	=	=	SYM
ejpam-7078	59	52	{	{	PUNCT
ejpam-7078	59	53	v	v	NUM
ejpam-7078	59	54	∈	∈	NOUN
ejpam-7078	59	55	v	v	NOUN
ejpam-7078	59	56	(	(	PUNCT
ejpam-7078	59	57	g	g	NOUN
ejpam-7078	59	58	)	)	PUNCT
ejpam-7078	59	59	:	:	PUNCT
ejpam-7078	59	60	f(v	f(v	NOUN
ejpam-7078	59	61	)	)	PUNCT
ejpam-7078	59	62	=	=	PUNCT
ejpam-7078	60	1	1	1	NUM
ejpam-7078	60	2	}	}	PUNCT
ejpam-7078	60	3	;	;	PUNCT
ejpam-7078	60	4	and	and	CCONJ
ejpam-7078	60	5	l.	l.	PROPN
ejpam-7078	60	6	f.	f.	PROPN
ejpam-7078	60	7	casinillo	casinillo	PROPN
ejpam-7078	60	8	,	,	PUNCT
ejpam-7078	60	9	s.	s.	PROPN
ejpam-7078	60	10	r.	r.	PROPN
ejpam-7078	60	11	canoy	canoy	PROPN
ejpam-7078	60	12	jr	jr	PROPN
ejpam-7078	60	13	.	.	PROPN
ejpam-7078	60	14	/	/	SYM
ejpam-7078	60	15	eur	eur	PROPN
ejpam-7078	60	16	.	.	PUNCT
ejpam-7078	61	1	j.	j.	PROPN
ejpam-7078	61	2	pure	pure	PROPN
ejpam-7078	61	3	appl	appl	PROPN
ejpam-7078	61	4	.	.	PROPN
ejpam-7078	61	5	math	math	PROPN
ejpam-7078	61	6	,	,	PUNCT
ejpam-7078	61	7	18	18	NUM
ejpam-7078	61	8	(	(	PUNCT
ejpam-7078	61	9	4	4	NUM
ejpam-7078	61	10	)	)	PUNCT
ejpam-7078	61	11	(	(	PUNCT
ejpam-7078	61	12	2025	2025	NUM
ejpam-7078	61	13	)	)	PUNCT
ejpam-7078	61	14	,	,	PUNCT
ejpam-7078	61	15	7078	7078	NUM
ejpam-7078	61	16	3	3	NUM
ejpam-7078	61	17	of	of	ADP
ejpam-7078	61	18	15	15	NUM
ejpam-7078	61	19	v2	v2	NOUN
ejpam-7078	61	20	=	=	SYM
ejpam-7078	61	21	{	{	PUNCT
ejpam-7078	61	22	v	v	NUM
ejpam-7078	61	23	∈	∈	NOUN
ejpam-7078	61	24	v	v	NOUN
ejpam-7078	61	25	(	(	PUNCT
ejpam-7078	61	26	g	g	NOUN
ejpam-7078	61	27	)	)	PUNCT
ejpam-7078	61	28	:	:	PUNCT
ejpam-7078	61	29	f(v	f(v	NOUN
ejpam-7078	61	30	)	)	PUNCT
ejpam-7078	61	31	=	=	PUNCT
ejpam-7078	61	32	2	2	NUM
ejpam-7078	61	33	}	}	PUNCT
ejpam-7078	61	34	.	.	PUNCT
ejpam-7078	62	1	in	in	ADP
ejpam-7078	62	2	this	this	DET
ejpam-7078	62	3	case	case	NOUN
ejpam-7078	62	4	,	,	PUNCT
ejpam-7078	62	5	we	we	PRON
ejpam-7078	62	6	may	may	AUX
ejpam-7078	62	7	denote	denote	VERB
ejpam-7078	62	8	f	f	PROPN
ejpam-7078	62	9	by	by	ADP
ejpam-7078	62	10	f	f	PROPN
ejpam-7078	62	11	=	=	SYM
ejpam-7078	62	12	(	(	PUNCT
ejpam-7078	62	13	v0	v0	PROPN
ejpam-7078	62	14	,	,	PUNCT
ejpam-7078	62	15	v1	v1	NOUN
ejpam-7078	62	16	,	,	PUNCT
ejpam-7078	62	17	v2	v2	PROPN
ejpam-7078	62	18	)	)	PUNCT
ejpam-7078	62	19	.	.	PUNCT
ejpam-7078	63	1	a	a	DET
ejpam-7078	63	2	function	function	NOUN
ejpam-7078	63	3	f	f	X
ejpam-7078	63	4	=	=	SYM
ejpam-7078	63	5	(	(	PUNCT
ejpam-7078	63	6	v0	v0	PROPN
ejpam-7078	63	7	,	,	PUNCT
ejpam-7078	63	8	v1	v1	NOUN
ejpam-7078	63	9	,	,	PUNCT
ejpam-7078	63	10	v2	v2	PROPN
ejpam-7078	63	11	)	)	PUNCT
ejpam-7078	63	12	is	be	AUX
ejpam-7078	63	13	a	a	DET
ejpam-7078	63	14	hop	hop	NOUN
ejpam-7078	63	15	roman	roman	ADJ
ejpam-7078	63	16	dominating	dominating	NOUN
ejpam-7078	63	17	function	function	NOUN
ejpam-7078	63	18	(	(	PUNCT
ejpam-7078	63	19	hrdf	hrdf	NOUN
ejpam-7078	63	20	)	)	PUNCT
ejpam-7078	63	21	on	on	ADP
ejpam-7078	63	22	g	g	PROPN
ejpam-7078	63	23	if	if	SCONJ
ejpam-7078	63	24	for	for	ADP
ejpam-7078	63	25	every	every	DET
ejpam-7078	63	26	v	v	PROPN
ejpam-7078	63	27	∈	∈	PROPN
ejpam-7078	63	28	v0	v0	NOUN
ejpam-7078	63	29	,	,	PUNCT
ejpam-7078	63	30	there	there	PRON
ejpam-7078	63	31	exists	exist	VERB
ejpam-7078	63	32	u	u	PROPN
ejpam-7078	63	33	∈	∈	PROPN
ejpam-7078	63	34	v2	v2	NOUN
ejpam-7078	63	35	such	such	ADJ
ejpam-7078	63	36	that	that	DET
ejpam-7078	63	37	dg(u	dg(u	ADJ
ejpam-7078	63	38	,	,	PUNCT
ejpam-7078	63	39	v	v	NOUN
ejpam-7078	63	40	)	)	PUNCT
ejpam-7078	64	1	=	=	SYM
ejpam-7078	64	2	2	2	X
ejpam-7078	64	3	.	.	PUNCT
ejpam-7078	65	1	the	the	DET
ejpam-7078	65	2	weight	weight	NOUN
ejpam-7078	65	3	of	of	ADP
ejpam-7078	65	4	f	f	PROPN
ejpam-7078	65	5	is	be	AUX
ejpam-7078	65	6	given	give	VERB
ejpam-7078	65	7	by	by	ADP
ejpam-7078	65	8	ωhr	ωhr	ADJ
ejpam-7078	65	9	g	g	PROPN
ejpam-7078	65	10	(	(	PUNCT
ejpam-7078	65	11	f	f	X
ejpam-7078	65	12	)	)	PUNCT
ejpam-7078	65	13	=	=	SYM
ejpam-7078	65	14	∑	∑	PUNCT
ejpam-7078	65	15	v∈v	v∈v	PROPN
ejpam-7078	65	16	(	(	PUNCT
ejpam-7078	65	17	g	g	NOUN
ejpam-7078	65	18	)	)	PUNCT
ejpam-7078	65	19	f(v	f(v	NOUN
ejpam-7078	65	20	)	)	PUNCT
ejpam-7078	65	21	.	.	PUNCT
ejpam-7078	66	1	the	the	DET
ejpam-7078	66	2	hop	hop	PROPN
ejpam-7078	66	3	roman	roman	ADJ
ejpam-7078	66	4	domination	domination	NOUN
ejpam-7078	66	5	number	number	NOUN
ejpam-7078	66	6	of	of	ADP
ejpam-7078	66	7	g	g	NOUN
ejpam-7078	66	8	,	,	PUNCT
ejpam-7078	66	9	denoted	denote	VERB
ejpam-7078	66	10	γhr(g	γhr(g	PROPN
ejpam-7078	66	11	)	)	PUNCT
ejpam-7078	66	12	,	,	PUNCT
ejpam-7078	66	13	is	be	AUX
ejpam-7078	66	14	the	the	DET
ejpam-7078	66	15	minimum	minimum	ADJ
ejpam-7078	66	16	weight	weight	NOUN
ejpam-7078	66	17	of	of	ADP
ejpam-7078	66	18	an	an	DET
ejpam-7078	66	19	hrdf	hrdf	NOUN
ejpam-7078	66	20	on	on	ADP
ejpam-7078	66	21	g	g	PROPN
ejpam-7078	66	22	,	,	PUNCT
ejpam-7078	66	23	that	that	ADV
ejpam-7078	66	24	is	is	ADV
ejpam-7078	66	25	,	,	PUNCT
ejpam-7078	66	26	γhr(g	γhr(g	PROPN
ejpam-7078	66	27	)	)	PUNCT
ejpam-7078	66	28	=	=	PRON
ejpam-7078	66	29	min{ωhr	min{ωhr	NOUN
ejpam-7078	66	30	g	g	PROPN
ejpam-7078	66	31	(	(	PUNCT
ejpam-7078	66	32	f	f	PROPN
ejpam-7078	66	33	)	)	PUNCT
ejpam-7078	66	34	:	:	PUNCT
ejpam-7078	67	1	f	f	PROPN
ejpam-7078	67	2	is	be	AUX
ejpam-7078	67	3	an	an	DET
ejpam-7078	67	4	hrdf	hrdf	NOUN
ejpam-7078	67	5	on	on	ADP
ejpam-7078	67	6	g	g	NOUN
ejpam-7078	67	7	}	}	PUNCT
ejpam-7078	67	8	.	.	PUNCT
ejpam-7078	68	1	any	any	DET
ejpam-7078	68	2	hrdf	hrdf	NOUN
ejpam-7078	68	3	f	f	X
ejpam-7078	68	4	on	on	ADP
ejpam-7078	68	5	g	g	PROPN
ejpam-7078	68	6	with	with	ADP
ejpam-7078	68	7	ωhr	ωhr	ADJ
ejpam-7078	68	8	g	g	PROPN
ejpam-7078	68	9	(	(	PUNCT
ejpam-7078	68	10	f	f	X
ejpam-7078	68	11	)	)	PUNCT
ejpam-7078	68	12	=	=	SYM
ejpam-7078	68	13	γhr(g	γhr(g	PROPN
ejpam-7078	68	14	)	)	PUNCT
ejpam-7078	68	15	is	be	AUX
ejpam-7078	68	16	called	call	VERB
ejpam-7078	68	17	a	a	DET
ejpam-7078	68	18	γhr	γhr	NOUN
ejpam-7078	68	19	-	-	NOUN
ejpam-7078	68	20	function	function	NOUN
ejpam-7078	68	21	on	on	ADP
ejpam-7078	68	22	g.	g.	PROPN
ejpam-7078	68	23	a	a	DET
ejpam-7078	68	24	function	function	NOUN
ejpam-7078	68	25	f	f	PROPN
ejpam-7078	68	26	=	=	SYM
ejpam-7078	68	27	(	(	PUNCT
ejpam-7078	68	28	v0	v0	PROPN
ejpam-7078	68	29	,	,	PUNCT
ejpam-7078	68	30	v1	v1	NOUN
ejpam-7078	68	31	,	,	PUNCT
ejpam-7078	68	32	v2	v2	PROPN
ejpam-7078	68	33	)	)	PUNCT
ejpam-7078	68	34	is	be	AUX
ejpam-7078	68	35	a	a	DET
ejpam-7078	68	36	super	super	ADV
ejpam-7078	68	37	hop	hop	NOUN
ejpam-7078	68	38	roman	roman	ADJ
ejpam-7078	68	39	dominating	dominating	NOUN
ejpam-7078	68	40	function	function	NOUN
ejpam-7078	68	41	(	(	PUNCT
ejpam-7078	68	42	shrdf	shrdf	NOUN
ejpam-7078	68	43	)	)	PUNCT
ejpam-7078	68	44	on	on	ADP
ejpam-7078	68	45	g	g	PROPN
ejpam-7078	68	46	if	if	SCONJ
ejpam-7078	68	47	it	it	PRON
ejpam-7078	68	48	satisfies	satisfy	VERB
ejpam-7078	68	49	the	the	DET
ejpam-7078	68	50	following	follow	VERB
ejpam-7078	68	51	conditions	condition	NOUN
ejpam-7078	68	52	:	:	PUNCT
ejpam-7078	68	53	(	(	PUNCT
ejpam-7078	68	54	shr1	shr1	PROPN
ejpam-7078	68	55	)	)	PUNCT
ejpam-7078	68	56	f	f	PROPN
ejpam-7078	68	57	is	be	AUX
ejpam-7078	68	58	a	a	DET
ejpam-7078	68	59	hop	hop	NOUN
ejpam-7078	68	60	roman	roman	ADJ
ejpam-7078	68	61	dominating	dominating	NOUN
ejpam-7078	68	62	function	function	NOUN
ejpam-7078	68	63	on	on	ADP
ejpam-7078	68	64	g	g	PROPN
ejpam-7078	68	65	;	;	PUNCT
ejpam-7078	68	66	and	and	CCONJ
ejpam-7078	68	67	(	(	PUNCT
ejpam-7078	68	68	shr2	shr2	NOUN
ejpam-7078	68	69	)	)	PUNCT
ejpam-7078	68	70	for	for	ADP
ejpam-7078	68	71	each	each	DET
ejpam-7078	68	72	v	v	ADP
ejpam-7078	68	73	∈	∈	PROPN
ejpam-7078	68	74	v0	v0	NOUN
ejpam-7078	68	75	,	,	PUNCT
ejpam-7078	68	76	there	there	PRON
ejpam-7078	68	77	exists	exist	VERB
ejpam-7078	68	78	w	w	PROPN
ejpam-7078	68	79	∈	∈	NOUN
ejpam-7078	68	80	v1	v1	NOUN
ejpam-7078	68	81	∪	∪	X
ejpam-7078	68	82	v2	v2	NOUN
ejpam-7078	68	83	such	such	ADJ
ejpam-7078	68	84	that	that	DET
ejpam-7078	68	85	n2	n2	PROPN
ejpam-7078	68	86	g(w	g(w	PROPN
ejpam-7078	68	87	)	)	PUNCT
ejpam-7078	68	88	∩	∩	ADJ
ejpam-7078	68	89	v0	v0	NOUN
ejpam-7078	68	90	=	=	SYM
ejpam-7078	68	91	{	{	PUNCT
ejpam-7078	68	92	v	v	NOUN
ejpam-7078	68	93	}	}	PUNCT
ejpam-7078	68	94	.	.	PUNCT
ejpam-7078	69	1	the	the	DET
ejpam-7078	69	2	weight	weight	NOUN
ejpam-7078	69	3	ωshr	ωshr	NOUN
ejpam-7078	69	4	g	g	PROPN
ejpam-7078	69	5	(	(	PUNCT
ejpam-7078	69	6	f	f	NOUN
ejpam-7078	69	7	)	)	PUNCT
ejpam-7078	69	8	of	of	ADP
ejpam-7078	69	9	an	an	DET
ejpam-7078	69	10	shrdf	shrdf	NOUN
ejpam-7078	69	11	f	f	PROPN
ejpam-7078	69	12	is	be	AUX
ejpam-7078	69	13	given	give	VERB
ejpam-7078	69	14	by	by	ADP
ejpam-7078	69	15	ωshr	ωshr	NOUN
ejpam-7078	69	16	g	g	PROPN
ejpam-7078	69	17	(	(	PUNCT
ejpam-7078	69	18	f	f	X
ejpam-7078	69	19	)	)	PUNCT
ejpam-7078	69	20	=	=	SYM
ejpam-7078	70	1	∑	∑	PUNCT
ejpam-7078	70	2	u∈v	u∈v	NOUN
ejpam-7078	70	3	(	(	PUNCT
ejpam-7078	70	4	g	g	NOUN
ejpam-7078	70	5	)	)	PUNCT
ejpam-7078	70	6	f(u	f(u	PROPN
ejpam-7078	70	7	)	)	PUNCT
ejpam-7078	70	8	,	,	PUNCT
ejpam-7078	70	9	that	that	ADV
ejpam-7078	70	10	is	is	ADV
ejpam-7078	70	11	,	,	PUNCT
ejpam-7078	70	12	ωshr	ωshr	NOUN
ejpam-7078	70	13	g	g	PROPN
ejpam-7078	70	14	(	(	PUNCT
ejpam-7078	70	15	f	f	X
ejpam-7078	70	16	)	)	PUNCT
ejpam-7078	70	17	=	=	PUNCT
ejpam-7078	70	18	|v1|+2|v2|	|v1|+2|v2|	NOUN
ejpam-7078	70	19	.	.	PUNCT
ejpam-7078	71	1	the	the	DET
ejpam-7078	71	2	super	super	PROPN
ejpam-7078	71	3	hop	hop	PROPN
ejpam-7078	71	4	roman	roman	ADJ
ejpam-7078	71	5	domination	domination	NOUN
ejpam-7078	71	6	number	number	NOUN
ejpam-7078	71	7	ofg	ofg	PROPN
ejpam-7078	71	8	,	,	PUNCT
ejpam-7078	71	9	denoted	denote	VERB
ejpam-7078	71	10	γshr(g	γshr(g	PROPN
ejpam-7078	71	11	)	)	PUNCT
ejpam-7078	71	12	,	,	PUNCT
ejpam-7078	71	13	is	be	AUX
ejpam-7078	71	14	the	the	DET
ejpam-7078	71	15	minimum	minimum	ADJ
ejpam-7078	71	16	weight	weight	NOUN
ejpam-7078	71	17	of	of	ADP
ejpam-7078	71	18	an	an	DET
ejpam-7078	71	19	shrdf	shrdf	NOUN
ejpam-7078	71	20	ong	ong	PROPN
ejpam-7078	71	21	,	,	PUNCT
ejpam-7078	71	22	that	that	ADV
ejpam-7078	71	23	is	is	ADV
ejpam-7078	71	24	,	,	PUNCT
ejpam-7078	71	25	γshr(g	γshr(g	NOUN
ejpam-7078	71	26	)	)	PUNCT
ejpam-7078	72	1	=	=	SYM
ejpam-7078	72	2	min{ωshr	min{ωshr	NOUN
ejpam-7078	72	3	g	g	NOUN
ejpam-7078	72	4	(	(	PUNCT
ejpam-7078	72	5	f	f	PROPN
ejpam-7078	72	6	)	)	PUNCT
ejpam-7078	72	7	:	:	PUNCT
ejpam-7078	73	1	f	f	PROPN
ejpam-7078	73	2	is	be	AUX
ejpam-7078	73	3	an	an	DET
ejpam-7078	73	4	shrdf	shrdf	NOUN
ejpam-7078	73	5	on	on	ADP
ejpam-7078	73	6	g	g	NOUN
ejpam-7078	73	7	}	}	PUNCT
ejpam-7078	73	8	.	.	PUNCT
ejpam-7078	74	1	any	any	DET
ejpam-7078	74	2	shrdf	shrdf	NOUN
ejpam-7078	74	3	f	f	X
ejpam-7078	74	4	on	on	ADP
ejpam-7078	74	5	g	g	PROPN
ejpam-7078	74	6	with	with	ADP
ejpam-7078	74	7	ωshr	ωshr	NOUN
ejpam-7078	74	8	g	g	PROPN
ejpam-7078	74	9	(	(	PUNCT
ejpam-7078	74	10	f	f	X
ejpam-7078	74	11	)	)	PUNCT
ejpam-7078	74	12	=	=	SYM
ejpam-7078	74	13	γshr(g	γshr(g	NOUN
ejpam-7078	74	14	)	)	PUNCT
ejpam-7078	74	15	is	be	AUX
ejpam-7078	74	16	called	call	VERB
ejpam-7078	74	17	a	a	DET
ejpam-7078	74	18	γshr	γshr	NOUN
ejpam-7078	74	19	-	-	PUNCT
ejpam-7078	74	20	function	function	NOUN
ejpam-7078	74	21	on	on	ADP
ejpam-7078	74	22	g.	g.	PROPN
ejpam-7078	74	23	consider	consider	VERB
ejpam-7078	74	24	the	the	DET
ejpam-7078	74	25	graph	graph	NOUN
ejpam-7078	74	26	g	g	NOUN
ejpam-7078	74	27	with	with	ADP
ejpam-7078	74	28	|v	|v	PROPN
ejpam-7078	74	29	(	(	PUNCT
ejpam-7078	74	30	g)|	g)|	NOUN
ejpam-7078	74	31	=	=	NOUN
ejpam-7078	74	32	10	10	NUM
ejpam-7078	74	33	in	in	ADP
ejpam-7078	74	34	figure	figure	NOUN
ejpam-7078	74	35	1	1	NUM
ejpam-7078	74	36	below	below	ADV
ejpam-7078	74	37	.	.	PUNCT
ejpam-7078	75	1	let	let	VERB
ejpam-7078	75	2	f	f	PROPN
ejpam-7078	75	3	=	=	SYM
ejpam-7078	75	4	(	(	PUNCT
ejpam-7078	75	5	v0	v0	PROPN
ejpam-7078	75	6	,	,	PUNCT
ejpam-7078	75	7	v1	v1	NOUN
ejpam-7078	75	8	,	,	PUNCT
ejpam-7078	75	9	v2	v2	PROPN
ejpam-7078	75	10	)	)	PUNCT
ejpam-7078	75	11	be	be	AUX
ejpam-7078	75	12	a	a	DET
ejpam-7078	75	13	function	function	NOUN
ejpam-7078	75	14	on	on	ADP
ejpam-7078	75	15	g	g	PROPN
ejpam-7078	75	16	such	such	ADJ
ejpam-7078	75	17	that	that	DET
ejpam-7078	75	18	v0	v0	NOUN
ejpam-7078	75	19	=	=	SYM
ejpam-7078	75	20	{	{	PUNCT
ejpam-7078	75	21	v5	v5	PROPN
ejpam-7078	75	22	,	,	PUNCT
ejpam-7078	75	23	v6	v6	NOUN
ejpam-7078	75	24	,	,	PUNCT
ejpam-7078	75	25	v8	v8	PROPN
ejpam-7078	75	26	}	}	PUNCT
ejpam-7078	75	27	,	,	PUNCT
ejpam-7078	75	28	v1	v1	NOUN
ejpam-7078	75	29	=	=	SYM
ejpam-7078	75	30	{	{	PUNCT
ejpam-7078	75	31	v1	v1	PROPN
ejpam-7078	75	32	,	,	PUNCT
ejpam-7078	75	33	v2	v2	PROPN
ejpam-7078	75	34	,	,	PUNCT
ejpam-7078	75	35	v4	v4	NOUN
ejpam-7078	75	36	,	,	PUNCT
ejpam-7078	75	37	v7	v7	NUM
ejpam-7078	75	38	,	,	PUNCT
ejpam-7078	75	39	v9	v9	NOUN
ejpam-7078	75	40	,	,	PUNCT
ejpam-7078	75	41	v10	v10	NOUN
ejpam-7078	75	42	}	}	PUNCT
ejpam-7078	75	43	,	,	PUNCT
ejpam-7078	75	44	and	and	CCONJ
ejpam-7078	75	45	v2	v2	NOUN
ejpam-7078	75	46	=	=	SYM
ejpam-7078	75	47	{	{	PUNCT
ejpam-7078	75	48	v3	v3	PROPN
ejpam-7078	75	49	}	}	PUNCT
ejpam-7078	75	50	.	.	PUNCT
ejpam-7078	76	1	observe	observe	VERB
ejpam-7078	76	2	that	that	SCONJ
ejpam-7078	76	3	f	f	PROPN
ejpam-7078	76	4	is	be	AUX
ejpam-7078	76	5	a	a	DET
ejpam-7078	76	6	γshr	γshr	NOUN
ejpam-7078	76	7	-	-	PUNCT
ejpam-7078	76	8	function	function	NOUN
ejpam-7078	76	9	on	on	ADP
ejpam-7078	76	10	g.	g.	PROPN
ejpam-7078	76	11	hence	hence	ADV
ejpam-7078	76	12	,	,	PUNCT
ejpam-7078	76	13	γshr(g	γshr(g	NOUN
ejpam-7078	76	14	)	)	PUNCT
ejpam-7078	76	15	=	=	SYM
ejpam-7078	76	16	8	8	NUM
ejpam-7078	76	17	.	.	NOUN
ejpam-7078	76	18	1	1	NUM
ejpam-7078	76	19	v1	v1	PROPN
ejpam-7078	76	20	1v2	1v2	NUM
ejpam-7078	76	21	2	2	NUM
ejpam-7078	76	22	v3	v3	PROPN
ejpam-7078	76	23	1	1	NUM
ejpam-7078	76	24	v4	v4	NOUN
ejpam-7078	76	25	0	0	NUM
ejpam-7078	76	26	v5	v5	PROPN
ejpam-7078	76	27	0	0	NUM
ejpam-7078	76	28	v6	v6	NOUN
ejpam-7078	76	29	1	1	NUM
ejpam-7078	76	30	v7	v7	NOUN
ejpam-7078	76	31	0	0	NUM
ejpam-7078	77	1	v8	v8	PROPN
ejpam-7078	77	2	1	1	NUM
ejpam-7078	77	3	v9	v9	PROPN
ejpam-7078	77	4	1	1	NUM
ejpam-7078	77	5	v10	v10	NOUN
ejpam-7078	77	6	figure	figure	NOUN
ejpam-7078	77	7	1	1	NUM
ejpam-7078	77	8	:	:	PUNCT
ejpam-7078	77	9	a	a	DET
ejpam-7078	77	10	graph	graph	NOUN
ejpam-7078	77	11	g	g	NOUN
ejpam-7078	77	12	with	with	ADP
ejpam-7078	77	13	γshr(g	γshr(g	NOUN
ejpam-7078	77	14	)	)	PUNCT
ejpam-7078	77	15	=	=	SYM
ejpam-7078	77	16	8	8	X
ejpam-7078	77	17	.	.	PUNCT
ejpam-7078	78	1	l.	l.	PROPN
ejpam-7078	78	2	f.	f.	PROPN
ejpam-7078	78	3	casinillo	casinillo	PROPN
ejpam-7078	78	4	,	,	PUNCT
ejpam-7078	78	5	s.	s.	PROPN
ejpam-7078	78	6	r.	r.	PROPN
ejpam-7078	78	7	canoy	canoy	PROPN
ejpam-7078	78	8	jr	jr	PROPN
ejpam-7078	78	9	.	.	PROPN
ejpam-7078	78	10	/	/	SYM
ejpam-7078	78	11	eur	eur	PROPN
ejpam-7078	78	12	.	.	PUNCT
ejpam-7078	79	1	j.	j.	PROPN
ejpam-7078	79	2	pure	pure	PROPN
ejpam-7078	79	3	appl	appl	PROPN
ejpam-7078	79	4	.	.	PROPN
ejpam-7078	79	5	math	math	PROPN
ejpam-7078	79	6	,	,	PUNCT
ejpam-7078	79	7	18	18	NUM
ejpam-7078	79	8	(	(	PUNCT
ejpam-7078	79	9	4	4	NUM
ejpam-7078	79	10	)	)	PUNCT
ejpam-7078	79	11	(	(	PUNCT
ejpam-7078	79	12	2025	2025	NUM
ejpam-7078	79	13	)	)	PUNCT
ejpam-7078	79	14	,	,	PUNCT
ejpam-7078	79	15	7078	7078	NUM
ejpam-7078	79	16	4	4	NUM
ejpam-7078	79	17	of	of	ADP
ejpam-7078	79	18	15	15	NUM
ejpam-7078	79	19	in	in	ADP
ejpam-7078	79	20	this	this	DET
ejpam-7078	79	21	paper	paper	NOUN
ejpam-7078	79	22	,	,	PUNCT
ejpam-7078	79	23	we	we	PRON
ejpam-7078	79	24	do	do	VERB
ejpam-7078	79	25	an	an	DET
ejpam-7078	79	26	initial	initial	ADJ
ejpam-7078	79	27	investigation	investigation	NOUN
ejpam-7078	79	28	of	of	ADP
ejpam-7078	79	29	super	super	ADJ
ejpam-7078	79	30	hop	hop	PROPN
ejpam-7078	79	31	roman	roman	ADJ
ejpam-7078	79	32	domination	domination	NOUN
ejpam-7078	79	33	in	in	ADP
ejpam-7078	79	34	graphs	graph	NOUN
ejpam-7078	79	35	.	.	PUNCT
ejpam-7078	80	1	2	2	X
ejpam-7078	80	2	.	.	X
ejpam-7078	80	3	known	know	VERB
ejpam-7078	80	4	results	result	NOUN
ejpam-7078	80	5	we	we	PRON
ejpam-7078	80	6	shall	shall	AUX
ejpam-7078	80	7	need	need	VERB
ejpam-7078	80	8	the	the	DET
ejpam-7078	80	9	results	result	NOUN
ejpam-7078	80	10	obtained	obtain	VERB
ejpam-7078	80	11	by	by	ADP
ejpam-7078	80	12	canoy	canoy	PROPN
ejpam-7078	80	13	et	et	PROPN
ejpam-7078	80	14	al	al	PROPN
ejpam-7078	80	15	.	.	PUNCT
ejpam-7078	81	1	in	in	ADP
ejpam-7078	81	2	[	[	X
ejpam-7078	81	3	18	18	NUM
ejpam-7078	81	4	]	]	PUNCT
ejpam-7078	81	5	.	.	PUNCT
ejpam-7078	82	1	theorem	theorem	NOUN
ejpam-7078	82	2	1	1	X
ejpam-7078	82	3	.	.	PUNCT
ejpam-7078	83	1	let	let	VERB
ejpam-7078	83	2	g	g	PRON
ejpam-7078	83	3	be	be	AUX
ejpam-7078	83	4	a	a	DET
ejpam-7078	83	5	graph	graph	NOUN
ejpam-7078	83	6	of	of	ADP
ejpam-7078	83	7	order	order	NOUN
ejpam-7078	83	8	n	n	PRON
ejpam-7078	83	9	≥	≥	NOUN
ejpam-7078	83	10	1	1	NUM
ejpam-7078	83	11	.	.	PUNCT
ejpam-7078	83	12	then	then	ADV
ejpam-7078	83	13	⌈n2	⌈n2	VERB
ejpam-7078	83	14	⌉	⌉	ADP
ejpam-7078	83	15	≤	≤	ADV
ejpam-7078	83	16	γsh(g	γsh(g	NOUN
ejpam-7078	83	17	)	)	PUNCT
ejpam-7078	83	18	.	.	PUNCT
ejpam-7078	84	1	in	in	ADP
ejpam-7078	84	2	particular	particular	ADJ
ejpam-7078	84	3	,	,	PUNCT
ejpam-7078	84	4	n	n	DET
ejpam-7078	84	5	≤	≤	NOUN
ejpam-7078	84	6	2γsh(g	2γsh(g	NOUN
ejpam-7078	84	7	)	)	PUNCT
ejpam-7078	84	8	.	.	PUNCT
ejpam-7078	85	1	theorem	theorem	NOUN
ejpam-7078	85	2	2	2	NUM
ejpam-7078	85	3	.	.	PUNCT
ejpam-7078	86	1	let	let	VERB
ejpam-7078	86	2	g	g	PRON
ejpam-7078	86	3	be	be	AUX
ejpam-7078	86	4	a	a	DET
ejpam-7078	86	5	graph	graph	NOUN
ejpam-7078	86	6	of	of	ADP
ejpam-7078	86	7	order	order	NOUN
ejpam-7078	86	8	n	n	PRON
ejpam-7078	86	9	≥	≥	NOUN
ejpam-7078	86	10	1	1	NUM
ejpam-7078	86	11	.	.	PUNCT
ejpam-7078	87	1	then	then	ADV
ejpam-7078	87	2	γsh(g	γsh(g	NOUN
ejpam-7078	87	3	)	)	PUNCT
ejpam-7078	87	4	=	=	SYM
ejpam-7078	88	1	n	n	NOUN
ejpam-7078	88	2	if	if	SCONJ
ejpam-7078	88	3	and	and	CCONJ
ejpam-7078	88	4	only	only	ADV
ejpam-7078	88	5	if	if	SCONJ
ejpam-7078	88	6	each	each	DET
ejpam-7078	88	7	component	component	NOUN
ejpam-7078	88	8	g′	g′	NOUN
ejpam-7078	88	9	of	of	ADP
ejpam-7078	88	10	g	g	PROPN
ejpam-7078	88	11	is	be	AUX
ejpam-7078	88	12	a	a	DET
ejpam-7078	88	13	complete	complete	ADJ
ejpam-7078	88	14	graph	graph	NOUN
ejpam-7078	88	15	.	.	PUNCT
ejpam-7078	89	1	corollary	corollary	ADJ
ejpam-7078	89	2	1	1	NUM
ejpam-7078	89	3	.	.	PUNCT
ejpam-7078	90	1	let	let	VERB
ejpam-7078	90	2	g	g	PRON
ejpam-7078	90	3	be	be	AUX
ejpam-7078	90	4	a	a	DET
ejpam-7078	90	5	connected	connected	ADJ
ejpam-7078	90	6	graph	graph	NOUN
ejpam-7078	90	7	of	of	ADP
ejpam-7078	90	8	order	order	NOUN
ejpam-7078	90	9	n.	n.	NOUN
ejpam-7078	90	10	then	then	ADV
ejpam-7078	90	11	γsh(g	γsh(g	NOUN
ejpam-7078	90	12	)	)	PUNCT
ejpam-7078	90	13	=	=	SYM
ejpam-7078	91	1	n	n	NOUN
ejpam-7078	91	2	if	if	SCONJ
ejpam-7078	91	3	and	and	CCONJ
ejpam-7078	91	4	only	only	ADV
ejpam-7078	91	5	if	if	SCONJ
ejpam-7078	91	6	g	g	PROPN
ejpam-7078	91	7	=	=	PROPN
ejpam-7078	91	8	kn	kn	PROPN
ejpam-7078	91	9	.	.	PROPN
ejpam-7078	91	10	3	3	X
ejpam-7078	91	11	.	.	X
ejpam-7078	91	12	results	result	VERB
ejpam-7078	91	13	this	this	DET
ejpam-7078	91	14	section	section	NOUN
ejpam-7078	91	15	explores	explore	VERB
ejpam-7078	91	16	the	the	DET
ejpam-7078	91	17	properties	property	NOUN
ejpam-7078	91	18	of	of	ADP
ejpam-7078	91	19	the	the	DET
ejpam-7078	91	20	super	super	PROPN
ejpam-7078	91	21	hop	hop	PROPN
ejpam-7078	91	22	roman	roman	ADJ
ejpam-7078	91	23	dominating	dominating	NOUN
ejpam-7078	91	24	function	function	NOUN
ejpam-7078	91	25	in	in	ADP
ejpam-7078	91	26	graphs	graph	NOUN
ejpam-7078	91	27	.	.	PUNCT
ejpam-7078	92	1	proposition	proposition	NOUN
ejpam-7078	92	2	1	1	NUM
ejpam-7078	92	3	.	.	PUNCT
ejpam-7078	93	1	let	let	VERB
ejpam-7078	93	2	g	g	PRON
ejpam-7078	93	3	be	be	AUX
ejpam-7078	93	4	a	a	DET
ejpam-7078	93	5	graph	graph	NOUN
ejpam-7078	93	6	of	of	ADP
ejpam-7078	93	7	order	order	NOUN
ejpam-7078	93	8	n	n	PRON
ejpam-7078	93	9	≥	≥	NOUN
ejpam-7078	93	10	1	1	NUM
ejpam-7078	93	11	and	and	CCONJ
ejpam-7078	93	12	f	f	NOUN
ejpam-7078	93	13	=	=	SYM
ejpam-7078	93	14	(	(	PUNCT
ejpam-7078	93	15	v0	v0	PROPN
ejpam-7078	93	16	,	,	PUNCT
ejpam-7078	93	17	v1	v1	NOUN
ejpam-7078	93	18	,	,	PUNCT
ejpam-7078	93	19	v2	v2	PROPN
ejpam-7078	93	20	)	)	PUNCT
ejpam-7078	93	21	be	be	AUX
ejpam-7078	93	22	an	an	DET
ejpam-7078	93	23	shrdf	shrdf	NOUN
ejpam-7078	93	24	on	on	ADP
ejpam-7078	93	25	g.	g.	PROPN
ejpam-7078	93	26	then	then	ADV
ejpam-7078	93	27	v1	v1	VERB
ejpam-7078	93	28	∪	∪	ADJ
ejpam-7078	93	29	v2	v2	NOUN
ejpam-7078	93	30	is	be	AUX
ejpam-7078	93	31	a	a	DET
ejpam-7078	93	32	super	super	ADV
ejpam-7078	93	33	hop	hop	NOUN
ejpam-7078	93	34	dominating	dominating	NOUN
ejpam-7078	93	35	set	set	VERB
ejpam-7078	93	36	on	on	ADP
ejpam-7078	93	37	g.	g.	PROPN
ejpam-7078	93	38	moreover	moreover	ADV
ejpam-7078	93	39	,	,	PUNCT
ejpam-7078	93	40	if	if	SCONJ
ejpam-7078	93	41	f	f	PROPN
ejpam-7078	93	42	is	be	AUX
ejpam-7078	93	43	a	a	DET
ejpam-7078	93	44	γshr	γshr	NOUN
ejpam-7078	93	45	-	-	PUNCT
ejpam-7078	93	46	function	function	NOUN
ejpam-7078	93	47	on	on	ADP
ejpam-7078	93	48	g	g	NOUN
ejpam-7078	93	49	,	,	PUNCT
ejpam-7078	93	50	then	then	ADV
ejpam-7078	93	51	the	the	DET
ejpam-7078	93	52	following	following	ADJ
ejpam-7078	93	53	statements	statement	NOUN
ejpam-7078	93	54	hold	hold	VERB
ejpam-7078	93	55	:	:	PUNCT
ejpam-7078	93	56	(	(	PUNCT
ejpam-7078	93	57	i	i	NOUN
ejpam-7078	93	58	)	)	PUNCT
ejpam-7078	93	59	v0	v0	NOUN
ejpam-7078	93	60	=	=	SYM
ejpam-7078	93	61	∅	∅	NOUN
ejpam-7078	94	1	if	if	SCONJ
ejpam-7078	94	2	and	and	CCONJ
ejpam-7078	94	3	only	only	ADV
ejpam-7078	94	4	if	if	SCONJ
ejpam-7078	94	5	v2	v2	PROPN
ejpam-7078	94	6	=	=	PUNCT
ejpam-7078	94	7	∅.	∅.	NOUN
ejpam-7078	94	8	in	in	ADP
ejpam-7078	94	9	this	this	DET
ejpam-7078	94	10	case	case	NOUN
ejpam-7078	94	11	,	,	PUNCT
ejpam-7078	94	12	γshr(g	γshr(g	NOUN
ejpam-7078	94	13	)	)	PUNCT
ejpam-7078	95	1	=	=	SYM
ejpam-7078	95	2	|v	|v	PROPN
ejpam-7078	95	3	(	(	PUNCT
ejpam-7078	95	4	g)|	g)|	NOUN
ejpam-7078	95	5	=	=	PUNCT
ejpam-7078	95	6	n	n	CCONJ
ejpam-7078	95	7	;	;	PUNCT
ejpam-7078	95	8	and	and	CCONJ
ejpam-7078	95	9	(	(	PUNCT
ejpam-7078	95	10	ii	ii	NOUN
ejpam-7078	95	11	)	)	PUNCT
ejpam-7078	95	12	if	if	SCONJ
ejpam-7078	95	13	v1	v1	NOUN
ejpam-7078	95	14	=	=	SYM
ejpam-7078	95	15	∅	∅	NOUN
ejpam-7078	95	16	,	,	PUNCT
ejpam-7078	95	17	then	then	ADV
ejpam-7078	95	18	v2	v2	PROPN
ejpam-7078	95	19	is	be	AUX
ejpam-7078	95	20	a	a	DET
ejpam-7078	95	21	γsh	γsh	NOUN
ejpam-7078	95	22	-	-	PUNCT
ejpam-7078	95	23	set	set	VERB
ejpam-7078	95	24	and	and	CCONJ
ejpam-7078	95	25	γshr(g	γshr(g	NOUN
ejpam-7078	95	26	)	)	PUNCT
ejpam-7078	96	1	=	=	PUNCT
ejpam-7078	96	2	2γsh(g	2γsh(g	X
ejpam-7078	96	3	)	)	PUNCT
ejpam-7078	96	4	=	=	SYM
ejpam-7078	96	5	n.	n.	NOUN
ejpam-7078	96	6	proof	proof	NOUN
ejpam-7078	96	7	.	.	PUNCT
ejpam-7078	97	1	assume	assume	VERB
ejpam-7078	97	2	that	that	SCONJ
ejpam-7078	97	3	f	f	PROPN
ejpam-7078	97	4	=	=	SYM
ejpam-7078	97	5	(	(	PUNCT
ejpam-7078	97	6	v0	v0	PROPN
ejpam-7078	97	7	,	,	PUNCT
ejpam-7078	97	8	v1	v1	NOUN
ejpam-7078	97	9	,	,	PUNCT
ejpam-7078	97	10	v2	v2	PROPN
ejpam-7078	97	11	)	)	PUNCT
ejpam-7078	97	12	is	be	AUX
ejpam-7078	97	13	an	an	DET
ejpam-7078	97	14	shrdf	shrdf	NOUN
ejpam-7078	97	15	on	on	ADP
ejpam-7078	97	16	g	g	NOUN
ejpam-7078	97	17	and	and	CCONJ
ejpam-7078	97	18	let	let	VERB
ejpam-7078	97	19	v	v	NUM
ejpam-7078	97	20	∈	∈	PROPN
ejpam-7078	97	21	v	v	NOUN
ejpam-7078	97	22	(	(	PUNCT
ejpam-7078	97	23	g	g	NOUN
ejpam-7078	97	24	)	)	PUNCT
ejpam-7078	97	25	\	\	PUNCT
ejpam-7078	98	1	(	(	PUNCT
ejpam-7078	98	2	v1	v1	VERB
ejpam-7078	98	3	∪	∪	NOUN
ejpam-7078	98	4	v2	v2	NOUN
ejpam-7078	98	5	)	)	PUNCT
ejpam-7078	98	6	.	.	PUNCT
ejpam-7078	99	1	then	then	ADV
ejpam-7078	99	2	v	v	ADP
ejpam-7078	99	3	∈	∈	PROPN
ejpam-7078	99	4	v0	v0	NOUN
ejpam-7078	99	5	.	.	PUNCT
ejpam-7078	100	1	since	since	SCONJ
ejpam-7078	100	2	f	f	PROPN
ejpam-7078	100	3	satisfies	satisfie	NOUN
ejpam-7078	100	4	(	(	PUNCT
ejpam-7078	100	5	shr2	shr2	NOUN
ejpam-7078	100	6	)	)	PUNCT
ejpam-7078	100	7	,	,	PUNCT
ejpam-7078	100	8	there	there	PRON
ejpam-7078	100	9	exists	exist	VERB
ejpam-7078	100	10	w	w	PROPN
ejpam-7078	100	11	∈	∈	PROPN
ejpam-7078	100	12	v1∪v2	v1∪v2	ADP
ejpam-7078	100	13	such	such	ADJ
ejpam-7078	100	14	that	that	DET
ejpam-7078	100	15	n2	n2	PROPN
ejpam-7078	100	16	g(w)∩v0	g(w)∩v0	PROPN
ejpam-7078	100	17	=	=	SYM
ejpam-7078	100	18	{	{	PUNCT
ejpam-7078	100	19	v	v	NOUN
ejpam-7078	100	20	}	}	PUNCT
ejpam-7078	100	21	.	.	PUNCT
ejpam-7078	101	1	this	this	PRON
ejpam-7078	101	2	implies	imply	VERB
ejpam-7078	101	3	that	that	SCONJ
ejpam-7078	101	4	v1	v1	NOUN
ejpam-7078	101	5	∪	∪	NOUN
ejpam-7078	101	6	v2	v2	NOUN
ejpam-7078	101	7	is	be	AUX
ejpam-7078	101	8	a	a	DET
ejpam-7078	101	9	super	super	ADV
ejpam-7078	101	10	hop	hop	NOUN
ejpam-7078	101	11	dominating	dominating	NOUN
ejpam-7078	101	12	set	set	VERB
ejpam-7078	101	13	on	on	ADP
ejpam-7078	101	14	g.	g.	PROPN
ejpam-7078	101	15	now	now	ADV
ejpam-7078	101	16	,	,	PUNCT
ejpam-7078	101	17	suppose	suppose	VERB
ejpam-7078	101	18	f	f	PROPN
ejpam-7078	101	19	is	be	AUX
ejpam-7078	101	20	a	a	DET
ejpam-7078	101	21	γshr	γshr	NOUN
ejpam-7078	101	22	-	-	PUNCT
ejpam-7078	101	23	function	function	NOUN
ejpam-7078	101	24	on	on	ADP
ejpam-7078	101	25	g.	g.	PROPN
ejpam-7078	101	26	let	let	VERB
ejpam-7078	101	27	v0	v0	PROPN
ejpam-7078	101	28	=	=	PUNCT
ejpam-7078	101	29	∅.	∅.	NOUN
ejpam-7078	101	30	assume	assume	VERB
ejpam-7078	101	31	for	for	ADP
ejpam-7078	101	32	a	a	DET
ejpam-7078	101	33	moment	moment	NOUN
ejpam-7078	101	34	that	that	PRON
ejpam-7078	101	35	v2	v2	VERB
ejpam-7078	101	36	̸=	̸=	PROPN
ejpam-7078	101	37	∅	∅	NOUN
ejpam-7078	101	38	,	,	PUNCT
ejpam-7078	101	39	say	say	VERB
ejpam-7078	101	40	w	w	PROPN
ejpam-7078	101	41	∈	∈	PROPN
ejpam-7078	101	42	v2	v2	PROPN
ejpam-7078	101	43	.	.	PUNCT
ejpam-7078	102	1	let	let	VERB
ejpam-7078	102	2	w0	w0	PROPN
ejpam-7078	102	3	=	=	PROPN
ejpam-7078	102	4	v0	v0	PROPN
ejpam-7078	102	5	,	,	PUNCT
ejpam-7078	102	6	w1	w1	NOUN
ejpam-7078	102	7	=	=	SYM
ejpam-7078	102	8	v1	v1	NOUN
ejpam-7078	102	9	∪	∪	X
ejpam-7078	102	10	{	{	PUNCT
ejpam-7078	102	11	w	w	NOUN
ejpam-7078	102	12	}	}	PUNCT
ejpam-7078	102	13	,	,	PUNCT
ejpam-7078	102	14	and	and	CCONJ
ejpam-7078	102	15	w2	w2	NOUN
ejpam-7078	102	16	=	=	SYM
ejpam-7078	102	17	v2	v2	PROPN
ejpam-7078	102	18	\	\	PROPN
ejpam-7078	102	19	{	{	PUNCT
ejpam-7078	102	20	w	w	NOUN
ejpam-7078	102	21	}	}	PUNCT
ejpam-7078	102	22	.	.	PUNCT
ejpam-7078	103	1	then	then	ADV
ejpam-7078	103	2	g	g	PROPN
ejpam-7078	103	3	=	=	SYM
ejpam-7078	103	4	(	(	PUNCT
ejpam-7078	103	5	w0,w1,w2	w0,w1,w2	PROPN
ejpam-7078	103	6	)	)	PUNCT
ejpam-7078	103	7	is	be	AUX
ejpam-7078	103	8	a	a	DET
ejpam-7078	103	9	super	super	ADV
ejpam-7078	103	10	hop	hop	NOUN
ejpam-7078	103	11	roman	roman	ADJ
ejpam-7078	103	12	dominating	dominating	NOUN
ejpam-7078	103	13	function	function	NOUN
ejpam-7078	103	14	on	on	ADP
ejpam-7078	103	15	g.	g.	PROPN
ejpam-7078	103	16	it	it	PRON
ejpam-7078	103	17	follows	follow	VERB
ejpam-7078	103	18	that	that	DET
ejpam-7078	103	19	ωshr	ωshr	NOUN
ejpam-7078	103	20	g	g	PROPN
ejpam-7078	103	21	(	(	PUNCT
ejpam-7078	103	22	g	g	NOUN
ejpam-7078	103	23	)	)	PUNCT
ejpam-7078	103	24	=	=	SYM
ejpam-7078	103	25	|w1|+	|w1|+	PROPN
ejpam-7078	103	26	2|w2|	2|w2|	NUM
ejpam-7078	103	27	=	=	SYM
ejpam-7078	103	28	(	(	PUNCT
ejpam-7078	103	29	|v1|+	|v1|+	ADP
ejpam-7078	103	30	1	1	NUM
ejpam-7078	103	31	)	)	PUNCT
ejpam-7078	103	32	+	+	CCONJ
ejpam-7078	104	1	2(|v2|	2(|v2|	NUM
ejpam-7078	104	2	−	−	NUM
ejpam-7078	104	3	1	1	NUM
ejpam-7078	104	4	)	)	PUNCT
ejpam-7078	104	5	=	=	PUNCT
ejpam-7078	104	6	|v1|+	|v1|+	PRON
ejpam-7078	104	7	2|v2|	2|v2|	NUM
ejpam-7078	104	8	−	−	NOUN
ejpam-7078	104	9	1	1	NUM
ejpam-7078	104	10	<	<	X
ejpam-7078	104	11	ωshr	ωshr	PROPN
ejpam-7078	104	12	g	g	PROPN
ejpam-7078	104	13	(	(	PUNCT
ejpam-7078	104	14	f	f	X
ejpam-7078	104	15	)	)	PUNCT
ejpam-7078	104	16	=	=	SYM
ejpam-7078	104	17	γshr(g	γshr(g	NOUN
ejpam-7078	104	18	)	)	PUNCT
ejpam-7078	104	19	,	,	PUNCT
ejpam-7078	104	20	a	a	DET
ejpam-7078	104	21	contradiction	contradiction	NOUN
ejpam-7078	104	22	to	to	ADP
ejpam-7078	104	23	the	the	DET
ejpam-7078	104	24	assumption	assumption	NOUN
ejpam-7078	104	25	that	that	SCONJ
ejpam-7078	104	26	f	f	PROPN
ejpam-7078	104	27	is	be	AUX
ejpam-7078	104	28	a	a	DET
ejpam-7078	104	29	γshr	γshr	NOUN
ejpam-7078	104	30	-	-	PUNCT
ejpam-7078	104	31	function	function	NOUN
ejpam-7078	104	32	on	on	ADP
ejpam-7078	104	33	g.	g.	PROPN
ejpam-7078	104	34	thus	thus	ADV
ejpam-7078	104	35	,	,	PUNCT
ejpam-7078	104	36	v2	v2	PROPN
ejpam-7078	104	37	=	=	PUNCT
ejpam-7078	104	38	∅.	∅.	VERB
ejpam-7078	104	39	conversely	conversely	ADV
ejpam-7078	104	40	,	,	PUNCT
ejpam-7078	104	41	suppose	suppose	VERB
ejpam-7078	104	42	that	that	SCONJ
ejpam-7078	104	43	|v2|	|v2|	NOUN
ejpam-7078	104	44	=	=	SYM
ejpam-7078	104	45	0	0	X
ejpam-7078	104	46	.	.	PUNCT
ejpam-7078	105	1	since	since	SCONJ
ejpam-7078	105	2	f	f	PROPN
ejpam-7078	105	3	satisfies	satisfie	NOUN
ejpam-7078	105	4	(	(	PUNCT
ejpam-7078	105	5	shr1	shr1	PROPN
ejpam-7078	105	6	)	)	PUNCT
ejpam-7078	105	7	,	,	PUNCT
ejpam-7078	105	8	the	the	DET
ejpam-7078	105	9	assumption	assumption	NOUN
ejpam-7078	105	10	that	that	SCONJ
ejpam-7078	105	11	|v2|	|v2|	ADV
ejpam-7078	105	12	=	=	SYM
ejpam-7078	105	13	0	0	NUM
ejpam-7078	105	14	forces	force	NOUN
ejpam-7078	105	15	|v0|	|v0|	NOUN
ejpam-7078	105	16	=	=	SYM
ejpam-7078	105	17	0	0	X
ejpam-7078	105	18	.	.	PUNCT
ejpam-7078	106	1	this	this	PRON
ejpam-7078	106	2	,	,	PUNCT
ejpam-7078	106	3	in	in	ADP
ejpam-7078	106	4	turn	turn	NOUN
ejpam-7078	106	5	,	,	PUNCT
ejpam-7078	106	6	implies	imply	VERB
ejpam-7078	106	7	that	that	SCONJ
ejpam-7078	106	8	|v1|	|v1|	NOUN
ejpam-7078	106	9	=	=	PUNCT
ejpam-7078	106	10	n.	n.	PROPN
ejpam-7078	106	11	thus	thus	ADV
ejpam-7078	106	12	,	,	PUNCT
ejpam-7078	106	13	γshr(g	γshr(g	NOUN
ejpam-7078	106	14	)	)	PUNCT
ejpam-7078	106	15	=	=	SYM
ejpam-7078	106	16	|v1|+2|v2|	|v1|+2|v2|	NUM
ejpam-7078	106	17	=	=	SYM
ejpam-7078	106	18	|v1|	|v1|	NOUN
ejpam-7078	106	19	=	=	PUNCT
ejpam-7078	106	20	|v	|v	PROPN
ejpam-7078	106	21	(	(	PUNCT
ejpam-7078	106	22	g)|	g)|	NOUN
ejpam-7078	106	23	=	=	PUNCT
ejpam-7078	106	24	n	n	CCONJ
ejpam-7078	106	25	,	,	PUNCT
ejpam-7078	106	26	showing	show	VERB
ejpam-7078	106	27	that	that	SCONJ
ejpam-7078	106	28	(	(	PUNCT
ejpam-7078	106	29	i	i	NOUN
ejpam-7078	106	30	)	)	PUNCT
ejpam-7078	106	31	holds	hold	VERB
ejpam-7078	106	32	.	.	PUNCT
ejpam-7078	107	1	l.	l.	PROPN
ejpam-7078	107	2	f.	f.	PROPN
ejpam-7078	107	3	casinillo	casinillo	PROPN
ejpam-7078	107	4	,	,	PUNCT
ejpam-7078	107	5	s.	s.	PROPN
ejpam-7078	107	6	r.	r.	PROPN
ejpam-7078	107	7	canoy	canoy	PROPN
ejpam-7078	107	8	jr	jr	PROPN
ejpam-7078	107	9	.	.	PROPN
ejpam-7078	107	10	/	/	SYM
ejpam-7078	107	11	eur	eur	PROPN
ejpam-7078	107	12	.	.	PUNCT
ejpam-7078	108	1	j.	j.	PROPN
ejpam-7078	108	2	pure	pure	PROPN
ejpam-7078	108	3	appl	appl	PROPN
ejpam-7078	108	4	.	.	PROPN
ejpam-7078	108	5	math	math	PROPN
ejpam-7078	108	6	,	,	PUNCT
ejpam-7078	108	7	18	18	NUM
ejpam-7078	108	8	(	(	PUNCT
ejpam-7078	108	9	4	4	NUM
ejpam-7078	108	10	)	)	PUNCT
ejpam-7078	108	11	(	(	PUNCT
ejpam-7078	108	12	2025	2025	NUM
ejpam-7078	108	13	)	)	PUNCT
ejpam-7078	108	14	,	,	PUNCT
ejpam-7078	108	15	7078	7078	NUM
ejpam-7078	108	16	5	5	NUM
ejpam-7078	108	17	of	of	ADP
ejpam-7078	108	18	15	15	NUM
ejpam-7078	108	19	next	next	ADJ
ejpam-7078	108	20	,	,	PUNCT
ejpam-7078	108	21	suppose	suppose	VERB
ejpam-7078	108	22	v1	v1	NOUN
ejpam-7078	108	23	=	=	SYM
ejpam-7078	108	24	∅.	∅.	NOUN
ejpam-7078	108	25	then	then	ADV
ejpam-7078	108	26	v1	v1	VERB
ejpam-7078	108	27	∪	∪	ADJ
ejpam-7078	108	28	v2	v2	NOUN
ejpam-7078	108	29	=	=	SYM
ejpam-7078	108	30	v2	v2	PROPN
ejpam-7078	108	31	is	be	AUX
ejpam-7078	108	32	a	a	DET
ejpam-7078	108	33	super	super	ADV
ejpam-7078	108	34	hop	hop	NOUN
ejpam-7078	108	35	dominating	dominating	NOUN
ejpam-7078	108	36	set	set	NOUN
ejpam-7078	108	37	.	.	PUNCT
ejpam-7078	109	1	suppose	suppose	VERB
ejpam-7078	109	2	v2	v2	NOUN
ejpam-7078	109	3	is	be	AUX
ejpam-7078	109	4	not	not	PART
ejpam-7078	109	5	a	a	DET
ejpam-7078	109	6	γsh	γsh	NOUN
ejpam-7078	109	7	-	-	PUNCT
ejpam-7078	109	8	set	set	VERB
ejpam-7078	109	9	in	in	ADP
ejpam-7078	109	10	g.	g.	PROPN
ejpam-7078	109	11	let	let	VERB
ejpam-7078	109	12	v	v	X
ejpam-7078	109	13	′	′	NUM
ejpam-7078	109	14	2	2	NUM
ejpam-7078	109	15	be	be	AUX
ejpam-7078	109	16	a	a	DET
ejpam-7078	109	17	γsh	γsh	NOUN
ejpam-7078	109	18	-	-	PUNCT
ejpam-7078	109	19	set	set	VERB
ejpam-7078	109	20	in	in	ADP
ejpam-7078	109	21	g.	g.	PROPN
ejpam-7078	109	22	then	then	ADV
ejpam-7078	109	23	,	,	PUNCT
ejpam-7078	109	24	we	we	PRON
ejpam-7078	109	25	obtain	obtain	VERB
ejpam-7078	109	26	|v	|v	PROPN
ejpam-7078	109	27	′	′	NUM
ejpam-7078	109	28	2	2	NUM
ejpam-7078	110	1	|	|	ADV
ejpam-7078	110	2	<	<	X
ejpam-7078	110	3	|v2|	|v2|	NOUN
ejpam-7078	110	4	.	.	PUNCT
ejpam-7078	111	1	define	define	VERB
ejpam-7078	111	2	a	a	DET
ejpam-7078	111	3	function	function	NOUN
ejpam-7078	111	4	g	g	NOUN
ejpam-7078	111	5	=	=	SYM
ejpam-7078	111	6	(	(	PUNCT
ejpam-7078	111	7	w0,w1,w2	w0,w1,w2	ADP
ejpam-7078	111	8	)	)	PUNCT
ejpam-7078	111	9	on	on	ADP
ejpam-7078	111	10	g	g	PROPN
ejpam-7078	112	1	where	where	SCONJ
ejpam-7078	112	2	w0	w0	PROPN
ejpam-7078	112	3	=	=	PROPN
ejpam-7078	112	4	v	v	PROPN
ejpam-7078	112	5	(	(	PUNCT
ejpam-7078	112	6	g	g	NOUN
ejpam-7078	112	7	)	)	PUNCT
ejpam-7078	112	8	\	\	PROPN
ejpam-7078	112	9	v	v	ADP
ejpam-7078	112	10	′	′	NUM
ejpam-7078	112	11	2	2	NUM
ejpam-7078	112	12	,	,	PUNCT
ejpam-7078	112	13	w1	w1	NOUN
ejpam-7078	112	14	=	=	SYM
ejpam-7078	112	15	∅	∅	NOUN
ejpam-7078	112	16	and	and	CCONJ
ejpam-7078	112	17	w2	w2	NOUN
ejpam-7078	112	18	=	=	PROPN
ejpam-7078	112	19	v	v	NOUN
ejpam-7078	112	20	′	′	NUM
ejpam-7078	112	21	2	2	NUM
ejpam-7078	112	22	.	.	PUNCT
ejpam-7078	113	1	then	then	ADV
ejpam-7078	113	2	g	g	PROPN
ejpam-7078	113	3	is	be	AUX
ejpam-7078	113	4	an	an	DET
ejpam-7078	113	5	shrdf	shrdf	NOUN
ejpam-7078	113	6	on	on	ADP
ejpam-7078	113	7	g	g	PROPN
ejpam-7078	113	8	and	and	CCONJ
ejpam-7078	113	9	ωshr	ωshr	PROPN
ejpam-7078	113	10	g	g	PROPN
ejpam-7078	113	11	(	(	PUNCT
ejpam-7078	113	12	g	g	NOUN
ejpam-7078	113	13	)	)	PUNCT
ejpam-7078	113	14	=	=	SYM
ejpam-7078	113	15	2|w2|	2|w2|	X
ejpam-7078	113	16	<	<	X
ejpam-7078	113	17	2|v2|	2|v2|	NUM
ejpam-7078	113	18	=	=	SYM
ejpam-7078	113	19	γshr(g	γshr(g	NOUN
ejpam-7078	113	20	)	)	PUNCT
ejpam-7078	113	21	,	,	PUNCT
ejpam-7078	113	22	a	a	DET
ejpam-7078	113	23	contradiction	contradiction	NOUN
ejpam-7078	113	24	.	.	PUNCT
ejpam-7078	114	1	therefore	therefore	ADV
ejpam-7078	114	2	v2	v2	PROPN
ejpam-7078	114	3	is	be	AUX
ejpam-7078	114	4	a	a	DET
ejpam-7078	114	5	γsh	γsh	NOUN
ejpam-7078	114	6	-	-	PUNCT
ejpam-7078	114	7	set	set	NOUN
ejpam-7078	114	8	on	on	ADP
ejpam-7078	114	9	g	g	PROPN
ejpam-7078	114	10	and	and	CCONJ
ejpam-7078	114	11	γshr(g	γshr(g	NOUN
ejpam-7078	114	12	)	)	PUNCT
ejpam-7078	115	1	=	=	SYM
ejpam-7078	115	2	2|v2|	2|v2|	NUM
ejpam-7078	115	3	=	=	SYM
ejpam-7078	115	4	2γsh(g	2γsh(g	NOUN
ejpam-7078	115	5	)	)	PUNCT
ejpam-7078	115	6	.	.	PUNCT
ejpam-7078	116	1	by	by	ADP
ejpam-7078	116	2	theorem	theorem	NOUN
ejpam-7078	116	3	1	1	NUM
ejpam-7078	116	4	,	,	PUNCT
ejpam-7078	116	5	γshr(g	γshr(g	NOUN
ejpam-7078	116	6	)	)	PUNCT
ejpam-7078	116	7	=	=	VERB
ejpam-7078	116	8	n.	n.	NOUN
ejpam-7078	116	9	this	this	PRON
ejpam-7078	116	10	shows	show	VERB
ejpam-7078	116	11	that	that	SCONJ
ejpam-7078	116	12	(	(	PUNCT
ejpam-7078	116	13	ii	ii	NOUN
ejpam-7078	116	14	)	)	PUNCT
ejpam-7078	116	15	holds	hold	VERB
ejpam-7078	116	16	.	.	PUNCT
ejpam-7078	117	1	lemma	lemma	PROPN
ejpam-7078	117	2	1	1	X
ejpam-7078	117	3	.	.	PUNCT
ejpam-7078	118	1	let	let	VERB
ejpam-7078	118	2	g	g	PRON
ejpam-7078	118	3	be	be	AUX
ejpam-7078	118	4	a	a	DET
ejpam-7078	118	5	graph	graph	NOUN
ejpam-7078	118	6	of	of	ADP
ejpam-7078	118	7	order	order	NOUN
ejpam-7078	118	8	n	n	NOUN
ejpam-7078	118	9	and	and	CCONJ
ejpam-7078	118	10	let	let	VERB
ejpam-7078	118	11	f	f	PROPN
ejpam-7078	118	12	=	=	SYM
ejpam-7078	118	13	(	(	PUNCT
ejpam-7078	118	14	v0	v0	PROPN
ejpam-7078	118	15	,	,	PUNCT
ejpam-7078	118	16	v1	v1	NOUN
ejpam-7078	118	17	,	,	PUNCT
ejpam-7078	118	18	v2	v2	PROPN
ejpam-7078	118	19	)	)	PUNCT
ejpam-7078	118	20	be	be	AUX
ejpam-7078	118	21	a	a	DET
ejpam-7078	118	22	γshr	γshr	NOUN
ejpam-7078	118	23	-	-	PUNCT
ejpam-7078	118	24	function	function	NOUN
ejpam-7078	118	25	on	on	ADP
ejpam-7078	118	26	g.	g.	PROPN
ejpam-7078	118	27	then	then	ADV
ejpam-7078	118	28	|v2|	|v2|	VERB
ejpam-7078	118	29	≤	≤	NOUN
ejpam-7078	118	30	|v0|	|v0|	NOUN
ejpam-7078	118	31	and	and	CCONJ
ejpam-7078	118	32	|v0|	|v0|	NOUN
ejpam-7078	118	33	≤	≤	NOUN
ejpam-7078	118	34	|v1|+	|v1|+	CCONJ
ejpam-7078	118	35	|v2|	|v2|	NOUN
ejpam-7078	118	36	.	.	PUNCT
ejpam-7078	119	1	moreover	moreover	ADV
ejpam-7078	119	2	,	,	PUNCT
ejpam-7078	119	3	each	each	PRON
ejpam-7078	119	4	of	of	ADP
ejpam-7078	119	5	the	the	DET
ejpam-7078	119	6	following	following	ADJ
ejpam-7078	119	7	statements	statement	NOUN
ejpam-7078	119	8	hold	hold	VERB
ejpam-7078	119	9	:	:	PUNCT
ejpam-7078	119	10	(	(	PUNCT
ejpam-7078	119	11	i	i	NOUN
ejpam-7078	119	12	)	)	PUNCT
ejpam-7078	119	13	if	if	SCONJ
ejpam-7078	119	14	|v0|	|v0|	NOUN
ejpam-7078	119	15	=	=	SYM
ejpam-7078	119	16	|v2|	|v2|	NOUN
ejpam-7078	119	17	,	,	PUNCT
ejpam-7078	119	18	then	then	ADV
ejpam-7078	119	19	γshr(g	γshr(g	NOUN
ejpam-7078	119	20	)	)	PUNCT
ejpam-7078	119	21	=	=	SYM
ejpam-7078	120	1	n.	n.	NOUN
ejpam-7078	120	2	(	(	PUNCT
ejpam-7078	120	3	ii	ii	PROPN
ejpam-7078	120	4	)	)	PUNCT
ejpam-7078	120	5	if	if	SCONJ
ejpam-7078	120	6	γshr(g	γshr(g	PROPN
ejpam-7078	120	7	)	)	PUNCT
ejpam-7078	120	8	<	<	X
ejpam-7078	120	9	n	n	CCONJ
ejpam-7078	120	10	,	,	PUNCT
ejpam-7078	120	11	then	then	ADV
ejpam-7078	120	12	1	1	NUM
ejpam-7078	120	13	≤	≤	NUM
ejpam-7078	120	14	|v1|	|v1|	NOUN
ejpam-7078	120	15	<	<	X
ejpam-7078	120	16	n.	n.	NOUN
ejpam-7078	120	17	proof	proof	NOUN
ejpam-7078	120	18	.	.	PUNCT
ejpam-7078	121	1	if	if	SCONJ
ejpam-7078	121	2	|v0|	|v0|	NOUN
ejpam-7078	121	3	=	=	SYM
ejpam-7078	121	4	0	0	NUM
ejpam-7078	121	5	,	,	PUNCT
ejpam-7078	121	6	then	then	ADV
ejpam-7078	121	7	|v2|	|v2|	ADV
ejpam-7078	121	8	=	=	SYM
ejpam-7078	121	9	0	0	NUM
ejpam-7078	121	10	by	by	ADP
ejpam-7078	121	11	proposition	proposition	NOUN
ejpam-7078	121	12	1	1	NUM
ejpam-7078	121	13	.	.	PUNCT
ejpam-7078	122	1	hence	hence	ADV
ejpam-7078	122	2	,	,	PUNCT
ejpam-7078	122	3	|v0|	|v0|	NOUN
ejpam-7078	122	4	=	=	SYM
ejpam-7078	122	5	|v2|	|v2|	NOUN
ejpam-7078	122	6	.	.	PUNCT
ejpam-7078	123	1	so	so	ADV
ejpam-7078	123	2	suppose	suppose	VERB
ejpam-7078	123	3	|v0|	|v0|	NOUN
ejpam-7078	123	4	̸=	̸=	PROPN
ejpam-7078	123	5	0	0	NUM
ejpam-7078	123	6	.	.	PUNCT
ejpam-7078	124	1	since	since	SCONJ
ejpam-7078	124	2	f	f	PROPN
ejpam-7078	124	3	satisfies	satisfie	NOUN
ejpam-7078	124	4	(	(	PUNCT
ejpam-7078	124	5	shr1	shr1	PROPN
ejpam-7078	124	6	)	)	PUNCT
ejpam-7078	124	7	,	,	PUNCT
ejpam-7078	124	8	it	it	PRON
ejpam-7078	124	9	follows	follow	VERB
ejpam-7078	124	10	that	that	SCONJ
ejpam-7078	124	11	for	for	ADP
ejpam-7078	124	12	each	each	DET
ejpam-7078	124	13	v	v	ADP
ejpam-7078	124	14	∈	∈	PROPN
ejpam-7078	124	15	v0	v0	NOUN
ejpam-7078	124	16	,	,	PUNCT
ejpam-7078	124	17	there	there	PRON
ejpam-7078	124	18	exists	exist	VERB
ejpam-7078	124	19	zv	zv	PROPN
ejpam-7078	124	20	∈	∈	PROPN
ejpam-7078	124	21	v2	v2	PROPN
ejpam-7078	124	22	∩	∩	ADJ
ejpam-7078	124	23	n2	n2	ADJ
ejpam-7078	124	24	g(v	g(v	PROPN
ejpam-7078	124	25	)	)	PUNCT
ejpam-7078	124	26	.	.	PUNCT
ejpam-7078	125	1	hence	hence	ADV
ejpam-7078	125	2	,	,	PUNCT
ejpam-7078	125	3	the	the	DET
ejpam-7078	125	4	assignment	assignment	NOUN
ejpam-7078	125	5	v	v	NOUN
ejpam-7078	125	6	→	→	SYM
ejpam-7078	125	7	zv	zv	PROPN
ejpam-7078	125	8	defines	define	VERB
ejpam-7078	125	9	a	a	DET
ejpam-7078	125	10	function	function	NOUN
ejpam-7078	125	11	ψ	ψ	NOUN
ejpam-7078	125	12	from	from	ADP
ejpam-7078	125	13	v0	v0	NOUN
ejpam-7078	125	14	into	into	ADP
ejpam-7078	125	15	v2	v2	PROPN
ejpam-7078	125	16	.	.	PUNCT
ejpam-7078	126	1	since	since	SCONJ
ejpam-7078	126	2	f	f	PROPN
ejpam-7078	126	3	is	be	AUX
ejpam-7078	126	4	a	a	DET
ejpam-7078	126	5	γshr	γshr	NOUN
ejpam-7078	126	6	-	-	PUNCT
ejpam-7078	126	7	function	function	NOUN
ejpam-7078	126	8	on	on	ADP
ejpam-7078	126	9	g	g	PROPN
ejpam-7078	126	10	,	,	PUNCT
ejpam-7078	126	11	ψ	ψ	NOUN
ejpam-7078	126	12	must	must	AUX
ejpam-7078	126	13	be	be	AUX
ejpam-7078	126	14	onto	onto	ADP
ejpam-7078	126	15	.	.	PUNCT
ejpam-7078	127	1	thus	thus	ADV
ejpam-7078	127	2	,	,	PUNCT
ejpam-7078	127	3	|v2|	|v2|	ADV
ejpam-7078	127	4	≤	≤	NUM
ejpam-7078	127	5	|v0|	|v0|	NOUN
ejpam-7078	127	6	.	.	PUNCT
ejpam-7078	128	1	now	now	ADV
ejpam-7078	128	2	,	,	PUNCT
ejpam-7078	128	3	by	by	ADP
ejpam-7078	128	4	proposition	proposition	NOUN
ejpam-7078	128	5	1(i	1(i	NUM
ejpam-7078	128	6	)	)	PUNCT
ejpam-7078	128	7	,	,	PUNCT
ejpam-7078	128	8	v1	v1	VERB
ejpam-7078	128	9	∪	∪	NOUN
ejpam-7078	128	10	v2	v2	NOUN
ejpam-7078	128	11	is	be	AUX
ejpam-7078	128	12	a	a	DET
ejpam-7078	128	13	super	super	ADV
ejpam-7078	128	14	hop	hop	NOUN
ejpam-7078	128	15	dominating	dominating	NOUN
ejpam-7078	128	16	set	set	NOUN
ejpam-7078	128	17	.	.	PUNCT
ejpam-7078	129	1	hence	hence	ADV
ejpam-7078	129	2	,	,	PUNCT
ejpam-7078	129	3	for	for	ADP
ejpam-7078	129	4	every	every	DET
ejpam-7078	129	5	v	v	PROPN
ejpam-7078	129	6	∈	∈	PROPN
ejpam-7078	129	7	v0	v0	NOUN
ejpam-7078	129	8	,	,	PUNCT
ejpam-7078	129	9	there	there	PRON
ejpam-7078	129	10	exists	exist	VERB
ejpam-7078	129	11	wv	wv	PROPN
ejpam-7078	129	12	∈	∈	PROPN
ejpam-7078	129	13	v1	v1	PROPN
ejpam-7078	129	14	∪	∪	VERB
ejpam-7078	129	15	v2	v2	NOUN
ejpam-7078	129	16	such	such	ADJ
ejpam-7078	129	17	that	that	DET
ejpam-7078	129	18	n2	n2	ADJ
ejpam-7078	129	19	g(wv	g(wv	NOUN
ejpam-7078	129	20	)	)	PUNCT
ejpam-7078	129	21	∩	∩	ADJ
ejpam-7078	129	22	v0	v0	NOUN
ejpam-7078	129	23	=	=	SYM
ejpam-7078	129	24	{	{	PUNCT
ejpam-7078	129	25	v	v	NOUN
ejpam-7078	129	26	}	}	PUNCT
ejpam-7078	129	27	.	.	PUNCT
ejpam-7078	130	1	define	define	VERB
ejpam-7078	130	2	the	the	DET
ejpam-7078	130	3	function	function	NOUN
ejpam-7078	130	4	h	h	NOUN
ejpam-7078	130	5	:	:	PUNCT
ejpam-7078	130	6	v0	v0	PROPN
ejpam-7078	130	7	→	→	SYM
ejpam-7078	130	8	{	{	PUNCT
ejpam-7078	130	9	wv	wv	PROPN
ejpam-7078	130	10	:	:	PUNCT
ejpam-7078	130	11	v	v	PROPN
ejpam-7078	130	12	∈	∈	PROPN
ejpam-7078	130	13	v0	v0	NOUN
ejpam-7078	130	14	}	}	PUNCT
ejpam-7078	130	15	by	by	ADP
ejpam-7078	130	16	h(v	h(v	PROPN
ejpam-7078	130	17	)	)	PUNCT
ejpam-7078	131	1	=	=	SYM
ejpam-7078	131	2	wv	wv	PROPN
ejpam-7078	131	3	for	for	ADP
ejpam-7078	131	4	each	each	DET
ejpam-7078	131	5	v	v	ADP
ejpam-7078	131	6	∈	∈	PROPN
ejpam-7078	131	7	v0	v0	NOUN
ejpam-7078	131	8	.	.	PUNCT
ejpam-7078	132	1	then	then	ADV
ejpam-7078	132	2	h	h	PROPN
ejpam-7078	132	3	is	be	AUX
ejpam-7078	132	4	a	a	DET
ejpam-7078	132	5	one	one	NUM
ejpam-7078	132	6	-	-	PUNCT
ejpam-7078	132	7	one	one	NOUN
ejpam-7078	132	8	and	and	CCONJ
ejpam-7078	132	9	onto	onto	ADP
ejpam-7078	132	10	function	function	NOUN
ejpam-7078	132	11	.	.	PUNCT
ejpam-7078	133	1	thus	thus	ADV
ejpam-7078	133	2	,	,	PUNCT
ejpam-7078	133	3	|v0|	|v0|	NOUN
ejpam-7078	133	4	=	=	PUNCT
ejpam-7078	133	5	|{wv	|{wv	NOUN
ejpam-7078	133	6	:	:	PUNCT
ejpam-7078	133	7	v	v	NUM
ejpam-7078	133	8	∈	∈	PROPN
ejpam-7078	133	9	v0}|	v0}|	NOUN
ejpam-7078	133	10	.	.	PUNCT
ejpam-7078	134	1	since	since	SCONJ
ejpam-7078	134	2	{	{	PUNCT
ejpam-7078	134	3	wv	wv	PROPN
ejpam-7078	134	4	:	:	PUNCT
ejpam-7078	134	5	v	v	PROPN
ejpam-7078	134	6	∈	∈	PROPN
ejpam-7078	134	7	v0	v0	NOUN
ejpam-7078	134	8	}	}	PUNCT
ejpam-7078	134	9	⊆	⊆	NUM
ejpam-7078	134	10	v1	v1	NOUN
ejpam-7078	134	11	∪	∪	NOUN
ejpam-7078	134	12	v2	v2	NOUN
ejpam-7078	134	13	,	,	PUNCT
ejpam-7078	134	14	it	it	PRON
ejpam-7078	134	15	follows	follow	VERB
ejpam-7078	134	16	that	that	SCONJ
ejpam-7078	134	17	|v0|	|v0|	VERB
ejpam-7078	134	18	≤	≤	NOUN
ejpam-7078	134	19	|v1	|v1	X
ejpam-7078	134	20	∪	∪	ADP
ejpam-7078	134	21	v2|	v2|	PROPN
ejpam-7078	134	22	.	.	PUNCT
ejpam-7078	135	1	next	next	ADJ
ejpam-7078	135	2	,	,	PUNCT
ejpam-7078	135	3	if	if	SCONJ
ejpam-7078	135	4	|v0|	|v0|	NOUN
ejpam-7078	135	5	=	=	SYM
ejpam-7078	135	6	|v2|	|v2|	NOUN
ejpam-7078	135	7	,	,	PUNCT
ejpam-7078	135	8	then	then	ADV
ejpam-7078	135	9	we	we	PRON
ejpam-7078	135	10	have	have	VERB
ejpam-7078	135	11	γshr(g	γshr(g	NOUN
ejpam-7078	135	12	)	)	PUNCT
ejpam-7078	135	13	=	=	SYM
ejpam-7078	136	1	|v1|+2|v2|	|v1|+2|v2|	NUM
ejpam-7078	136	2	=	=	SYM
ejpam-7078	136	3	|v1|+	|v1|+	X
ejpam-7078	136	4	|v2|+	|v2|+	NOUN
ejpam-7078	136	5	|v0|	|v0|	NOUN
ejpam-7078	136	6	=	=	SYM
ejpam-7078	136	7	|v	|v	X
ejpam-7078	136	8	(	(	PUNCT
ejpam-7078	136	9	g)|	g)|	NOUN
ejpam-7078	136	10	=	=	PUNCT
ejpam-7078	136	11	n.	n.	NOUN
ejpam-7078	136	12	this	this	PRON
ejpam-7078	136	13	shows	show	VERB
ejpam-7078	136	14	that	that	SCONJ
ejpam-7078	136	15	(	(	PUNCT
ejpam-7078	136	16	i	i	NOUN
ejpam-7078	136	17	)	)	PUNCT
ejpam-7078	136	18	holds	hold	VERB
ejpam-7078	136	19	.	.	PUNCT
ejpam-7078	137	1	finally	finally	ADV
ejpam-7078	137	2	,	,	PUNCT
ejpam-7078	137	3	suppose	suppose	VERB
ejpam-7078	137	4	that	that	SCONJ
ejpam-7078	137	5	γshr(g	γshr(g	NOUN
ejpam-7078	137	6	)	)	PUNCT
ejpam-7078	137	7	<	<	X
ejpam-7078	138	1	n.	n.	PROPN
ejpam-7078	138	2	then	then	ADV
ejpam-7078	138	3	|v0|	|v0|	VERB
ejpam-7078	138	4	̸=	̸=	PROPN
ejpam-7078	138	5	|v2|	|v2|	ADV
ejpam-7078	138	6	by	by	ADP
ejpam-7078	138	7	(	(	PUNCT
ejpam-7078	138	8	the	the	DET
ejpam-7078	138	9	contrapostive	contrapostive	NOUN
ejpam-7078	138	10	of	of	ADP
ejpam-7078	138	11	)	)	PUNCT
ejpam-7078	138	12	(	(	PUNCT
ejpam-7078	138	13	i	i	NOUN
ejpam-7078	138	14	)	)	PUNCT
ejpam-7078	138	15	.	.	PUNCT
ejpam-7078	138	16	assume	assume	VERB
ejpam-7078	138	17	that	that	SCONJ
ejpam-7078	138	18	|v1|	|v1|	NOUN
ejpam-7078	138	19	=	=	SYM
ejpam-7078	138	20	0	0	X
ejpam-7078	138	21	.	.	PUNCT
ejpam-7078	139	1	then	then	ADV
ejpam-7078	139	2	v2	v2	PROPN
ejpam-7078	139	3	is	be	AUX
ejpam-7078	139	4	a	a	DET
ejpam-7078	139	5	γsh	γsh	NOUN
ejpam-7078	139	6	-	-	PUNCT
ejpam-7078	139	7	set	set	NOUN
ejpam-7078	139	8	on	on	ADP
ejpam-7078	139	9	g	g	PROPN
ejpam-7078	139	10	and	and	CCONJ
ejpam-7078	139	11	γshr(g	γshr(g	NOUN
ejpam-7078	139	12	)	)	PUNCT
ejpam-7078	140	1	=	=	PUNCT
ejpam-7078	140	2	2γsh(g	2γsh(g	X
ejpam-7078	140	3	)	)	PUNCT
ejpam-7078	140	4	=	=	SYM
ejpam-7078	140	5	n	n	X
ejpam-7078	140	6	by	by	ADP
ejpam-7078	140	7	proposition	proposition	NOUN
ejpam-7078	140	8	1	1	NUM
ejpam-7078	140	9	.	.	PUNCT
ejpam-7078	141	1	this	this	PRON
ejpam-7078	141	2	contradicts	contradict	VERB
ejpam-7078	141	3	the	the	DET
ejpam-7078	141	4	assumption	assumption	NOUN
ejpam-7078	141	5	that	that	SCONJ
ejpam-7078	141	6	γshr(g	γshr(g	NOUN
ejpam-7078	141	7	)	)	PUNCT
ejpam-7078	141	8	<	<	X
ejpam-7078	141	9	n.	n.	PROPN
ejpam-7078	141	10	therefore	therefore	ADV
ejpam-7078	141	11	|v1|	|v1|	VERB
ejpam-7078	141	12	≥	≥	PROPN
ejpam-7078	141	13	1	1	NUM
ejpam-7078	141	14	,	,	PUNCT
ejpam-7078	141	15	showing	show	VERB
ejpam-7078	141	16	that	that	SCONJ
ejpam-7078	141	17	(	(	PUNCT
ejpam-7078	141	18	ii	ii	NOUN
ejpam-7078	141	19	)	)	PUNCT
ejpam-7078	141	20	holds	hold	VERB
ejpam-7078	141	21	.	.	PUNCT
ejpam-7078	142	1	this	this	PRON
ejpam-7078	142	2	proves	prove	VERB
ejpam-7078	142	3	the	the	DET
ejpam-7078	142	4	assertion	assertion	NOUN
ejpam-7078	142	5	.	.	PUNCT
ejpam-7078	143	1	proposition	proposition	NOUN
ejpam-7078	143	2	2	2	NUM
ejpam-7078	143	3	.	.	PUNCT
ejpam-7078	144	1	let	let	VERB
ejpam-7078	144	2	g	g	PRON
ejpam-7078	144	3	be	be	AUX
ejpam-7078	144	4	a	a	DET
ejpam-7078	144	5	graph	graph	NOUN
ejpam-7078	144	6	of	of	ADP
ejpam-7078	144	7	order	order	NOUN
ejpam-7078	144	8	n	n	NOUN
ejpam-7078	144	9	and	and	CCONJ
ejpam-7078	144	10	let	let	VERB
ejpam-7078	144	11	f	f	PROPN
ejpam-7078	144	12	=	=	SYM
ejpam-7078	144	13	(	(	PUNCT
ejpam-7078	144	14	v0	v0	PROPN
ejpam-7078	144	15	,	,	PUNCT
ejpam-7078	144	16	v1	v1	NOUN
ejpam-7078	144	17	,	,	PUNCT
ejpam-7078	144	18	v2	v2	PROPN
ejpam-7078	144	19	)	)	PUNCT
ejpam-7078	144	20	be	be	AUX
ejpam-7078	144	21	a	a	DET
ejpam-7078	144	22	γshr	γshr	NOUN
ejpam-7078	144	23	-	-	PUNCT
ejpam-7078	144	24	function	function	NOUN
ejpam-7078	144	25	on	on	ADP
ejpam-7078	144	26	g.	g.	PROPN
ejpam-7078	144	27	then	then	ADV
ejpam-7078	144	28	each	each	PRON
ejpam-7078	144	29	of	of	ADP
ejpam-7078	144	30	the	the	DET
ejpam-7078	144	31	following	following	ADJ
ejpam-7078	144	32	statements	statement	NOUN
ejpam-7078	144	33	holds	hold	VERB
ejpam-7078	144	34	:	:	PUNCT
ejpam-7078	144	35	(	(	PUNCT
ejpam-7078	144	36	i	i	NOUN
ejpam-7078	144	37	)	)	PUNCT
ejpam-7078	144	38	γshr(g	γshr(g	NOUN
ejpam-7078	144	39	)	)	PUNCT
ejpam-7078	144	40	<	<	X
ejpam-7078	144	41	n	n	X
ejpam-7078	144	42	if	if	SCONJ
ejpam-7078	145	1	and	and	CCONJ
ejpam-7078	145	2	only	only	ADV
ejpam-7078	145	3	if	if	SCONJ
ejpam-7078	145	4	1	1	NUM
ejpam-7078	145	5	≤	≤	NUM
ejpam-7078	145	6	|v2|	|v2|	NOUN
ejpam-7078	145	7	<	<	X
ejpam-7078	145	8	|v0|	|v0|	NOUN
ejpam-7078	145	9	.	.	PUNCT
ejpam-7078	145	10	(	(	PUNCT
ejpam-7078	145	11	ii	ii	NOUN
ejpam-7078	145	12	)	)	PUNCT
ejpam-7078	145	13	γshr(g	γshr(g	NOUN
ejpam-7078	145	14	)	)	PUNCT
ejpam-7078	145	15	=	=	SYM
ejpam-7078	146	1	n	n	NOUN
ejpam-7078	146	2	if	if	SCONJ
ejpam-7078	146	3	and	and	CCONJ
ejpam-7078	146	4	only	only	ADV
ejpam-7078	146	5	if	if	SCONJ
ejpam-7078	146	6	|v0|	|v0|	NOUN
ejpam-7078	146	7	=	=	SYM
ejpam-7078	146	8	|v2|	|v2|	NOUN
ejpam-7078	146	9	.	.	PUNCT
ejpam-7078	147	1	proof	proof	NOUN
ejpam-7078	147	2	.	.	PUNCT
ejpam-7078	148	1	(	(	PUNCT
ejpam-7078	148	2	i	i	NOUN
ejpam-7078	148	3	)	)	PUNCT
ejpam-7078	148	4	suppose	suppose	VERB
ejpam-7078	148	5	γshr(g	γshr(g	NOUN
ejpam-7078	148	6	)	)	PUNCT
ejpam-7078	148	7	<	<	X
ejpam-7078	148	8	n.	n.	NOUN
ejpam-7078	148	9	by	by	ADP
ejpam-7078	148	10	lemma	lemma	PROPN
ejpam-7078	148	11	1	1	NUM
ejpam-7078	148	12	,	,	PUNCT
ejpam-7078	148	13	and	and	CCONJ
ejpam-7078	148	14	property	property	NOUN
ejpam-7078	148	15	(	(	PUNCT
ejpam-7078	148	16	shr1	shr1	PROPN
ejpam-7078	148	17	)	)	PUNCT
ejpam-7078	148	18	,	,	PUNCT
ejpam-7078	148	19	we	we	PRON
ejpam-7078	148	20	have	have	VERB
ejpam-7078	148	21	1	1	NUM
ejpam-7078	148	22	≤	≤	NUM
ejpam-7078	148	23	|v2|	|v2|	NOUN
ejpam-7078	148	24	<	<	X
ejpam-7078	148	25	|v0|	|v0|	NOUN
ejpam-7078	148	26	.	.	PUNCT
ejpam-7078	149	1	for	for	ADP
ejpam-7078	149	2	the	the	DET
ejpam-7078	149	3	converse	converse	NOUN
ejpam-7078	149	4	,	,	PUNCT
ejpam-7078	149	5	suppose	suppose	VERB
ejpam-7078	149	6	that	that	SCONJ
ejpam-7078	149	7	1	1	NUM
ejpam-7078	149	8	≤	≤	NUM
ejpam-7078	149	9	|v2|	|v2|	NOUN
ejpam-7078	149	10	<	<	X
ejpam-7078	149	11	|v0|	|v0|	NOUN
ejpam-7078	149	12	.	.	PUNCT
ejpam-7078	150	1	then	then	ADV
ejpam-7078	150	2	γshr(g	γshr(g	NUM
ejpam-7078	150	3	)	)	PUNCT
ejpam-7078	150	4	=	=	PUNCT
ejpam-7078	151	1	ωshr	ωshr	NOUN
ejpam-7078	151	2	g	g	PROPN
ejpam-7078	151	3	(	(	PUNCT
ejpam-7078	151	4	f	f	X
ejpam-7078	151	5	)	)	PUNCT
ejpam-7078	151	6	=	=	PUNCT
ejpam-7078	152	1	|v1|+	|v1|+	PRON
ejpam-7078	152	2	2|v2|	2|v2|	NUM
ejpam-7078	152	3	<	<	X
ejpam-7078	152	4	|v1|+	|v1|+	PRON
ejpam-7078	152	5	|v2|+	|v2|+	ADJ
ejpam-7078	152	6	|v0|	|v0|	NOUN
ejpam-7078	152	7	=	=	SYM
ejpam-7078	152	8	n.	n.	PROPN
ejpam-7078	152	9	l.	l.	PROPN
ejpam-7078	152	10	f.	f.	PROPN
ejpam-7078	152	11	casinillo	casinillo	PROPN
ejpam-7078	152	12	,	,	PUNCT
ejpam-7078	152	13	s.	s.	PROPN
ejpam-7078	152	14	r.	r.	PROPN
ejpam-7078	152	15	canoy	canoy	PROPN
ejpam-7078	152	16	jr	jr	PROPN
ejpam-7078	152	17	.	.	PROPN
ejpam-7078	152	18	/	/	SYM
ejpam-7078	152	19	eur	eur	PROPN
ejpam-7078	152	20	.	.	PUNCT
ejpam-7078	153	1	j.	j.	PROPN
ejpam-7078	153	2	pure	pure	PROPN
ejpam-7078	153	3	appl	appl	PROPN
ejpam-7078	153	4	.	.	PROPN
ejpam-7078	153	5	math	math	PROPN
ejpam-7078	153	6	,	,	PUNCT
ejpam-7078	153	7	18	18	NUM
ejpam-7078	153	8	(	(	PUNCT
ejpam-7078	153	9	4	4	NUM
ejpam-7078	153	10	)	)	PUNCT
ejpam-7078	153	11	(	(	PUNCT
ejpam-7078	153	12	2025	2025	NUM
ejpam-7078	153	13	)	)	PUNCT
ejpam-7078	153	14	,	,	PUNCT
ejpam-7078	153	15	7078	7078	NUM
ejpam-7078	153	16	6	6	NUM
ejpam-7078	153	17	of	of	ADP
ejpam-7078	153	18	15	15	NUM
ejpam-7078	153	19	(	(	PUNCT
ejpam-7078	153	20	ii	ii	NOUN
ejpam-7078	153	21	)	)	PUNCT
ejpam-7078	153	22	suppose	suppose	VERB
ejpam-7078	153	23	γshr(g	γshr(g	NOUN
ejpam-7078	153	24	)	)	PUNCT
ejpam-7078	153	25	=	=	SYM
ejpam-7078	153	26	n.	n.	NOUN
ejpam-7078	153	27	assume	assume	VERB
ejpam-7078	153	28	for	for	ADP
ejpam-7078	153	29	a	a	DET
ejpam-7078	153	30	moment	moment	NOUN
ejpam-7078	153	31	that	that	PRON
ejpam-7078	153	32	|v0|	|v0|	VERB
ejpam-7078	153	33	̸=	̸=	PROPN
ejpam-7078	153	34	|v2|	|v2|	ADV
ejpam-7078	153	35	.	.	PUNCT
ejpam-7078	154	1	by	by	ADP
ejpam-7078	154	2	proposition	proposition	NOUN
ejpam-7078	154	3	1(i	1(i	NUM
ejpam-7078	154	4	)	)	PUNCT
ejpam-7078	154	5	,	,	PUNCT
ejpam-7078	154	6	|v0|	|v0|	VERB
ejpam-7078	154	7	̸=	̸=	PROPN
ejpam-7078	154	8	0	0	NUM
ejpam-7078	154	9	and	and	CCONJ
ejpam-7078	154	10	|v2|	|v2|	ADV
ejpam-7078	154	11	̸=	̸=	PROPN
ejpam-7078	154	12	0	0	NUM
ejpam-7078	154	13	.	.	PUNCT
ejpam-7078	155	1	lemma	lemma	PROPN
ejpam-7078	155	2	1	1	NUM
ejpam-7078	155	3	would	would	AUX
ejpam-7078	155	4	now	now	ADV
ejpam-7078	155	5	imply	imply	VERB
ejpam-7078	155	6	that	that	SCONJ
ejpam-7078	155	7	1	1	NUM
ejpam-7078	155	8	≤	≤	NUM
ejpam-7078	155	9	|v2|	|v2|	NOUN
ejpam-7078	155	10	<	<	X
ejpam-7078	155	11	|v0|	|v0|	NOUN
ejpam-7078	155	12	.	.	PUNCT
ejpam-7078	156	1	this	this	PRON
ejpam-7078	156	2	implies	imply	VERB
ejpam-7078	156	3	that	that	SCONJ
ejpam-7078	156	4	γshr(g	γshr(g	NOUN
ejpam-7078	156	5	)	)	PUNCT
ejpam-7078	156	6	<	<	X
ejpam-7078	156	7	n	n	X
ejpam-7078	156	8	by	by	ADP
ejpam-7078	156	9	(	(	PUNCT
ejpam-7078	156	10	i	i	NOUN
ejpam-7078	156	11	)	)	PUNCT
ejpam-7078	156	12	,	,	PUNCT
ejpam-7078	156	13	a	a	DET
ejpam-7078	156	14	contradiction	contradiction	NOUN
ejpam-7078	156	15	to	to	ADP
ejpam-7078	156	16	our	our	PRON
ejpam-7078	156	17	assumption	assumption	NOUN
ejpam-7078	156	18	.	.	PUNCT
ejpam-7078	157	1	therefore	therefore	ADV
ejpam-7078	157	2	,	,	PUNCT
ejpam-7078	157	3	|v0|	|v0|	NOUN
ejpam-7078	157	4	=	=	SYM
ejpam-7078	157	5	|v2|	|v2|	NOUN
ejpam-7078	157	6	.	.	PUNCT
ejpam-7078	158	1	the	the	DET
ejpam-7078	158	2	converse	converse	NOUN
ejpam-7078	158	3	follows	follow	VERB
ejpam-7078	158	4	from	from	ADP
ejpam-7078	158	5	lemma	lemma	PROPN
ejpam-7078	158	6	1(i	1(i	NUM
ejpam-7078	158	7	)	)	PUNCT
ejpam-7078	158	8	.	.	PUNCT
ejpam-7078	159	1	theorem	theorem	NOUN
ejpam-7078	159	2	3	3	X
ejpam-7078	159	3	.	.	PUNCT
ejpam-7078	160	1	let	let	VERB
ejpam-7078	160	2	g	g	PRON
ejpam-7078	160	3	be	be	AUX
ejpam-7078	160	4	a	a	DET
ejpam-7078	160	5	graph	graph	NOUN
ejpam-7078	160	6	of	of	ADP
ejpam-7078	160	7	order	order	NOUN
ejpam-7078	160	8	n	n	NOUN
ejpam-7078	160	9	and	and	CCONJ
ejpam-7078	160	10	let	let	VERB
ejpam-7078	160	11	f	f	PROPN
ejpam-7078	160	12	=	=	SYM
ejpam-7078	160	13	(	(	PUNCT
ejpam-7078	160	14	v0	v0	PROPN
ejpam-7078	160	15	,	,	PUNCT
ejpam-7078	160	16	v1	v1	NOUN
ejpam-7078	160	17	,	,	PUNCT
ejpam-7078	160	18	v2	v2	PROPN
ejpam-7078	160	19	)	)	PUNCT
ejpam-7078	160	20	be	be	AUX
ejpam-7078	160	21	an	an	DET
ejpam-7078	160	22	shrdf	shrdf	NOUN
ejpam-7078	160	23	on	on	ADP
ejpam-7078	160	24	g.	g.	PROPN
ejpam-7078	160	25	then	then	ADV
ejpam-7078	160	26	,	,	PUNCT
ejpam-7078	160	27	v1∪v2	v1∪v2	ADV
ejpam-7078	160	28	is	be	AUX
ejpam-7078	160	29	a	a	DET
ejpam-7078	160	30	minimal	minimal	ADJ
ejpam-7078	160	31	super	super	ADJ
ejpam-7078	160	32	hop	hop	NOUN
ejpam-7078	160	33	dominating	dominating	NOUN
ejpam-7078	160	34	set	set	NOUN
ejpam-7078	160	35	of	of	ADP
ejpam-7078	160	36	g	g	PROPN
ejpam-7078	161	1	if	if	SCONJ
ejpam-7078	161	2	and	and	CCONJ
ejpam-7078	161	3	only	only	ADV
ejpam-7078	161	4	if	if	SCONJ
ejpam-7078	161	5	each	each	DET
ejpam-7078	161	6	u	u	PROPN
ejpam-7078	161	7	∈	∈	PROPN
ejpam-7078	161	8	v2	v2	PROPN
ejpam-7078	161	9	,	,	PUNCT
ejpam-7078	161	10	there	there	PRON
ejpam-7078	161	11	exists	exist	VERB
ejpam-7078	161	12	a	a	DET
ejpam-7078	161	13	vertex	vertex	NOUN
ejpam-7078	161	14	v	v	ADP
ejpam-7078	161	15	∈	∈	PROPN
ejpam-7078	161	16	v0	v0	NOUN
ejpam-7078	161	17	such	such	ADJ
ejpam-7078	161	18	that	that	DET
ejpam-7078	161	19	n2	n2	ADJ
ejpam-7078	161	20	g(v)∩v2	g(v)∩v2	PROPN
ejpam-7078	161	21	=	=	SYM
ejpam-7078	161	22	{	{	PUNCT
ejpam-7078	161	23	u	u	NOUN
ejpam-7078	161	24	}	}	PUNCT
ejpam-7078	161	25	or	or	CCONJ
ejpam-7078	161	26	dg(v	dg(v	PUNCT
ejpam-7078	161	27	,	,	PUNCT
ejpam-7078	161	28	w	w	NOUN
ejpam-7078	161	29	)	)	PUNCT
ejpam-7078	161	30	̸=	̸=	PROPN
ejpam-7078	161	31	2	2	NUM
ejpam-7078	161	32	for	for	ADP
ejpam-7078	161	33	all	all	DET
ejpam-7078	161	34	w	w	PROPN
ejpam-7078	161	35	∈	∈	NOUN
ejpam-7078	161	36	(	(	PUNCT
ejpam-7078	161	37	v1∪v2)\{u	v1∪v2)\{u	NOUN
ejpam-7078	161	38	}	}	PUNCT
ejpam-7078	161	39	.	.	PUNCT
ejpam-7078	162	1	proof	proof	NOUN
ejpam-7078	162	2	.	.	PUNCT
ejpam-7078	163	1	let	let	VERB
ejpam-7078	163	2	f	f	PROPN
ejpam-7078	163	3	=	=	SYM
ejpam-7078	163	4	(	(	PUNCT
ejpam-7078	163	5	v0	v0	PROPN
ejpam-7078	163	6	,	,	PUNCT
ejpam-7078	163	7	v1	v1	NOUN
ejpam-7078	163	8	,	,	PUNCT
ejpam-7078	163	9	v2	v2	PROPN
ejpam-7078	163	10	)	)	PUNCT
ejpam-7078	163	11	be	be	AUX
ejpam-7078	163	12	an	an	DET
ejpam-7078	163	13	shrdf	shrdf	NOUN
ejpam-7078	163	14	on	on	ADP
ejpam-7078	163	15	g	g	NOUN
ejpam-7078	163	16	of	of	ADP
ejpam-7078	163	17	order	order	NOUN
ejpam-7078	163	18	n.	n.	NOUN
ejpam-7078	163	19	then	then	ADV
ejpam-7078	163	20	by	by	ADP
ejpam-7078	163	21	proposition	proposition	NOUN
ejpam-7078	163	22	1	1	NUM
ejpam-7078	163	23	,	,	PUNCT
ejpam-7078	163	24	v1	v1	NOUN
ejpam-7078	163	25	∪	∪	NOUN
ejpam-7078	163	26	v2	v2	NOUN
ejpam-7078	163	27	is	be	AUX
ejpam-7078	163	28	a	a	DET
ejpam-7078	163	29	super	super	ADV
ejpam-7078	163	30	hop	hop	NOUN
ejpam-7078	163	31	dominating	dominating	NOUN
ejpam-7078	163	32	set	set	VERB
ejpam-7078	163	33	on	on	ADP
ejpam-7078	163	34	g.	g.	PROPN
ejpam-7078	163	35	(	(	PUNCT
ejpam-7078	163	36	⇒	⇒	PROPN
ejpam-7078	163	37	)	)	PUNCT
ejpam-7078	163	38	assume	assume	VERB
ejpam-7078	163	39	that	that	SCONJ
ejpam-7078	163	40	v1	v1	NOUN
ejpam-7078	163	41	∪	∪	NOUN
ejpam-7078	163	42	v2	v2	NOUN
ejpam-7078	163	43	is	be	AUX
ejpam-7078	163	44	a	a	DET
ejpam-7078	163	45	minimal	minimal	ADJ
ejpam-7078	163	46	super	super	ADJ
ejpam-7078	163	47	hop	hop	NOUN
ejpam-7078	163	48	dominating	dominating	NOUN
ejpam-7078	163	49	set	set	VERB
ejpam-7078	163	50	on	on	ADP
ejpam-7078	163	51	g.	g.	PROPN
ejpam-7078	163	52	then	then	ADV
ejpam-7078	163	53	for	for	ADP
ejpam-7078	163	54	every	every	DET
ejpam-7078	163	55	u	u	PROPN
ejpam-7078	163	56	∈	∈	PROPN
ejpam-7078	163	57	v1	v1	NOUN
ejpam-7078	163	58	∪v2	∪v2	NOUN
ejpam-7078	163	59	,	,	PUNCT
ejpam-7078	163	60	(	(	PUNCT
ejpam-7078	163	61	v1	v1	NOUN
ejpam-7078	163	62	∪v2	∪v2	NOUN
ejpam-7078	163	63	)	)	PUNCT
ejpam-7078	163	64	\	\	NOUN
ejpam-7078	163	65	{	{	PUNCT
ejpam-7078	163	66	u	u	NOUN
ejpam-7078	163	67	}	}	PUNCT
ejpam-7078	163	68	is	be	AUX
ejpam-7078	163	69	not	not	PART
ejpam-7078	163	70	a	a	DET
ejpam-7078	163	71	super	super	ADV
ejpam-7078	163	72	hop	hop	NOUN
ejpam-7078	163	73	dominating	dominating	NOUN
ejpam-7078	163	74	set	set	NOUN
ejpam-7078	163	75	of	of	ADP
ejpam-7078	163	76	g.	g.	PROPN
ejpam-7078	164	1	this	this	PRON
ejpam-7078	164	2	means	mean	VERB
ejpam-7078	164	3	that	that	SCONJ
ejpam-7078	164	4	there	there	PRON
ejpam-7078	164	5	exists	exist	VERB
ejpam-7078	164	6	v	v	ADP
ejpam-7078	164	7	∈	∈	PROPN
ejpam-7078	164	8	v	v	NOUN
ejpam-7078	164	9	(	(	PUNCT
ejpam-7078	164	10	g	g	NOUN
ejpam-7078	164	11	)	)	PUNCT
ejpam-7078	164	12	\	\	PUNCT
ejpam-7078	165	1	(	(	PUNCT
ejpam-7078	165	2	(	(	PUNCT
ejpam-7078	165	3	v1	v1	VERB
ejpam-7078	165	4	∪	∪	NOUN
ejpam-7078	165	5	v2	v2	NOUN
ejpam-7078	165	6	)	)	PUNCT
ejpam-7078	165	7	\	\	NOUN
ejpam-7078	165	8	{	{	PUNCT
ejpam-7078	165	9	u	u	NOUN
ejpam-7078	165	10	}	}	PUNCT
ejpam-7078	165	11	)	)	PUNCT
ejpam-7078	165	12	such	such	ADJ
ejpam-7078	165	13	that	that	PRON
ejpam-7078	165	14	dg(v	dg(v	ADJ
ejpam-7078	165	15	,	,	PUNCT
ejpam-7078	165	16	w	w	NOUN
ejpam-7078	165	17	)	)	PUNCT
ejpam-7078	165	18	̸=	̸=	PROPN
ejpam-7078	165	19	2	2	NUM
ejpam-7078	165	20	for	for	ADP
ejpam-7078	165	21	all	all	DET
ejpam-7078	165	22	w	w	PROPN
ejpam-7078	165	23	∈	∈	NOUN
ejpam-7078	165	24	(	(	PUNCT
ejpam-7078	165	25	v1	v1	NOUN
ejpam-7078	165	26	∪	∪	NOUN
ejpam-7078	165	27	v2	v2	NOUN
ejpam-7078	165	28	)	)	PUNCT
ejpam-7078	165	29	\	\	NOUN
ejpam-7078	165	30	{	{	PUNCT
ejpam-7078	165	31	u	u	NOUN
ejpam-7078	165	32	}	}	PUNCT
ejpam-7078	165	33	.	.	PUNCT
ejpam-7078	166	1	suppose	suppose	VERB
ejpam-7078	166	2	that	that	SCONJ
ejpam-7078	166	3	v	v	AUX
ejpam-7078	166	4	̸=	̸=	PROPN
ejpam-7078	166	5	u.	u.	VERB
ejpam-7078	166	6	it	it	PRON
ejpam-7078	166	7	is	be	AUX
ejpam-7078	166	8	worth	worth	ADJ
ejpam-7078	166	9	noting	note	VERB
ejpam-7078	166	10	that	that	SCONJ
ejpam-7078	166	11	v1	v1	NOUN
ejpam-7078	166	12	∪	∪	NOUN
ejpam-7078	166	13	v2	v2	NOUN
ejpam-7078	166	14	is	be	AUX
ejpam-7078	166	15	a	a	DET
ejpam-7078	166	16	super	super	ADV
ejpam-7078	166	17	hop	hop	NOUN
ejpam-7078	166	18	dominating	dominating	NOUN
ejpam-7078	166	19	set	set	NOUN
ejpam-7078	166	20	,	,	PUNCT
ejpam-7078	166	21	hence	hence	ADV
ejpam-7078	166	22	,	,	PUNCT
ejpam-7078	166	23	v	v	X
ejpam-7078	166	24	must	must	AUX
ejpam-7078	166	25	be	be	AUX
ejpam-7078	166	26	super	super	ADV
ejpam-7078	166	27	hop	hop	NOUN
ejpam-7078	166	28	dominated	dominate	VERB
ejpam-7078	166	29	by	by	ADP
ejpam-7078	166	30	v1	v1	PROPN
ejpam-7078	166	31	∪	∪	NOUN
ejpam-7078	166	32	v2	v2	NOUN
ejpam-7078	166	33	.	.	PUNCT
ejpam-7078	167	1	so	so	ADV
ejpam-7078	167	2	,	,	PUNCT
ejpam-7078	167	3	it	it	PRON
ejpam-7078	167	4	follows	follow	VERB
ejpam-7078	167	5	that	that	SCONJ
ejpam-7078	167	6	dg(u	dg(u	ADJ
ejpam-7078	167	7	,	,	PUNCT
ejpam-7078	167	8	v	v	NOUN
ejpam-7078	167	9	)	)	PUNCT
ejpam-7078	167	10	=	=	SYM
ejpam-7078	167	11	2	2	NUM
ejpam-7078	167	12	which	which	PRON
ejpam-7078	167	13	implies	imply	VERB
ejpam-7078	167	14	that	that	SCONJ
ejpam-7078	167	15	n2	n2	ADJ
ejpam-7078	167	16	g(v)∩v2	g(v)∩v2	PROPN
ejpam-7078	167	17	=	=	SYM
ejpam-7078	167	18	{	{	PUNCT
ejpam-7078	167	19	u	u	NOUN
ejpam-7078	167	20	}	}	PUNCT
ejpam-7078	167	21	.	.	PUNCT
ejpam-7078	168	1	now	now	ADV
ejpam-7078	168	2	,	,	PUNCT
ejpam-7078	168	3	suppose	suppose	VERB
ejpam-7078	168	4	that	that	SCONJ
ejpam-7078	168	5	v	v	NOUN
ejpam-7078	168	6	=	=	X
ejpam-7078	168	7	u.	u.	NOUN
ejpam-7078	168	8	then	then	ADV
ejpam-7078	168	9	it	it	PRON
ejpam-7078	168	10	simply	simply	ADV
ejpam-7078	168	11	follows	follow	VERB
ejpam-7078	168	12	that	that	PRON
ejpam-7078	168	13	dg(v	dg(v	NOUN
ejpam-7078	168	14	,	,	PUNCT
ejpam-7078	168	15	w	w	NOUN
ejpam-7078	168	16	)	)	PUNCT
ejpam-7078	168	17	=	=	NOUN
ejpam-7078	168	18	̸	̸	ADV
ejpam-7078	168	19	2	2	NUM
ejpam-7078	168	20	for	for	ADP
ejpam-7078	168	21	every	every	DET
ejpam-7078	168	22	w	w	PROPN
ejpam-7078	168	23	∈	∈	PROPN
ejpam-7078	168	24	(	(	PUNCT
ejpam-7078	168	25	v1	v1	NOUN
ejpam-7078	168	26	∪	∪	NOUN
ejpam-7078	168	27	v2	v2	NOUN
ejpam-7078	168	28	)	)	PUNCT
ejpam-7078	168	29	\	\	NOUN
ejpam-7078	168	30	{	{	PUNCT
ejpam-7078	168	31	u	u	NOUN
ejpam-7078	168	32	}	}	PUNCT
ejpam-7078	168	33	.	.	PUNCT
ejpam-7078	169	1	(	(	PUNCT
ejpam-7078	169	2	⇐	⇐	NOUN
ejpam-7078	169	3	)	)	PUNCT
ejpam-7078	169	4	as	as	ADP
ejpam-7078	169	5	for	for	ADP
ejpam-7078	169	6	the	the	DET
ejpam-7078	169	7	converse	converse	NOUN
ejpam-7078	169	8	,	,	PUNCT
ejpam-7078	169	9	we	we	PRON
ejpam-7078	169	10	assume	assume	VERB
ejpam-7078	169	11	that	that	SCONJ
ejpam-7078	169	12	for	for	ADP
ejpam-7078	169	13	every	every	DET
ejpam-7078	169	14	u	u	PROPN
ejpam-7078	169	15	∈	∈	PROPN
ejpam-7078	169	16	v2	v2	NOUN
ejpam-7078	169	17	,	,	PUNCT
ejpam-7078	169	18	there	there	PRON
ejpam-7078	169	19	exists	exist	VERB
ejpam-7078	169	20	v	v	ADP
ejpam-7078	169	21	∈	∈	PROPN
ejpam-7078	169	22	v0	v0	NOUN
ejpam-7078	169	23	such	such	ADJ
ejpam-7078	169	24	that	that	DET
ejpam-7078	169	25	n2	n2	ADJ
ejpam-7078	169	26	g(v	g(v	X
ejpam-7078	169	27	)	)	PUNCT
ejpam-7078	170	1	∩	∩	ADJ
ejpam-7078	170	2	v2	v2	NOUN
ejpam-7078	170	3	=	=	SYM
ejpam-7078	170	4	{	{	PUNCT
ejpam-7078	170	5	u	u	NOUN
ejpam-7078	170	6	}	}	PUNCT
ejpam-7078	170	7	.	.	PUNCT
ejpam-7078	171	1	then	then	ADV
ejpam-7078	171	2	it	it	PRON
ejpam-7078	171	3	follows	follow	VERB
ejpam-7078	171	4	that	that	SCONJ
ejpam-7078	171	5	for	for	SCONJ
ejpam-7078	171	6	every	every	DET
ejpam-7078	171	7	v	v	PROPN
ejpam-7078	171	8	∈	∈	PROPN
ejpam-7078	171	9	v0	v0	NOUN
ejpam-7078	171	10	is	be	AUX
ejpam-7078	171	11	not	not	PART
ejpam-7078	171	12	hop	hop	ADV
ejpam-7078	171	13	dominated	dominate	VERB
ejpam-7078	171	14	by	by	ADP
ejpam-7078	171	15	the	the	DET
ejpam-7078	171	16	set	set	NOUN
ejpam-7078	171	17	(	(	PUNCT
ejpam-7078	171	18	v1	v1	NOUN
ejpam-7078	171	19	∪	∪	NOUN
ejpam-7078	171	20	v2	v2	NOUN
ejpam-7078	171	21	)	)	PUNCT
ejpam-7078	171	22	\	\	NOUN
ejpam-7078	171	23	{	{	PUNCT
ejpam-7078	171	24	u	u	NOUN
ejpam-7078	171	25	}	}	PUNCT
ejpam-7078	171	26	.	.	PUNCT
ejpam-7078	172	1	on	on	ADP
ejpam-7078	172	2	the	the	DET
ejpam-7078	172	3	other	other	ADJ
ejpam-7078	172	4	hand	hand	NOUN
ejpam-7078	172	5	,	,	PUNCT
ejpam-7078	172	6	assume	assume	VERB
ejpam-7078	172	7	that	that	SCONJ
ejpam-7078	172	8	for	for	ADP
ejpam-7078	172	9	every	every	DET
ejpam-7078	172	10	u	u	PROPN
ejpam-7078	172	11	∈	∈	PROPN
ejpam-7078	172	12	v2	v2	PROPN
ejpam-7078	172	13	,	,	PUNCT
ejpam-7078	172	14	we	we	PRON
ejpam-7078	172	15	have	have	VERB
ejpam-7078	172	16	dg(u	dg(u	ADJ
ejpam-7078	172	17	,	,	PUNCT
ejpam-7078	172	18	w	w	NOUN
ejpam-7078	172	19	)	)	PUNCT
ejpam-7078	172	20	̸=	̸=	PROPN
ejpam-7078	172	21	2	2	NUM
ejpam-7078	172	22	for	for	ADP
ejpam-7078	172	23	all	all	DET
ejpam-7078	172	24	w	w	PROPN
ejpam-7078	172	25	∈	∈	NOUN
ejpam-7078	172	26	(	(	PUNCT
ejpam-7078	172	27	v1	v1	NOUN
ejpam-7078	172	28	∪	∪	NOUN
ejpam-7078	172	29	v2	v2	NOUN
ejpam-7078	172	30	)	)	PUNCT
ejpam-7078	172	31	\	\	NOUN
ejpam-7078	172	32	{	{	PUNCT
ejpam-7078	172	33	u	u	NOUN
ejpam-7078	172	34	}	}	PUNCT
ejpam-7078	172	35	.	.	PUNCT
ejpam-7078	173	1	this	this	PRON
ejpam-7078	173	2	implies	imply	VERB
ejpam-7078	173	3	that	that	SCONJ
ejpam-7078	173	4	u	u	PRON
ejpam-7078	173	5	can	can	AUX
ejpam-7078	173	6	not	not	PART
ejpam-7078	173	7	be	be	AUX
ejpam-7078	173	8	super	super	ADV
ejpam-7078	173	9	hop	hop	NOUN
ejpam-7078	173	10	dominated	dominate	VERB
ejpam-7078	173	11	by	by	ADP
ejpam-7078	173	12	any	any	DET
ejpam-7078	173	13	vertex	vertex	NOUN
ejpam-7078	174	1	x	x	X
ejpam-7078	174	2	∈	∈	NOUN
ejpam-7078	174	3	(	(	PUNCT
ejpam-7078	174	4	v1	v1	NOUN
ejpam-7078	174	5	∪	∪	NOUN
ejpam-7078	174	6	v2	v2	NOUN
ejpam-7078	174	7	)	)	PUNCT
ejpam-7078	174	8	\	\	NOUN
ejpam-7078	174	9	{	{	PUNCT
ejpam-7078	174	10	u	u	NOUN
ejpam-7078	174	11	}	}	PUNCT
ejpam-7078	174	12	and	and	CCONJ
ejpam-7078	174	13	hence	hence	ADV
ejpam-7078	174	14	,	,	PUNCT
ejpam-7078	174	15	(	(	PUNCT
ejpam-7078	174	16	v1	v1	VERB
ejpam-7078	174	17	∪	∪	NOUN
ejpam-7078	174	18	v2	v2	NOUN
ejpam-7078	174	19	)	)	PUNCT
ejpam-7078	174	20	\	\	NOUN
ejpam-7078	174	21	{	{	PUNCT
ejpam-7078	174	22	u	u	NOUN
ejpam-7078	174	23	}	}	PUNCT
ejpam-7078	174	24	is	be	AUX
ejpam-7078	174	25	not	not	PART
ejpam-7078	174	26	a	a	DET
ejpam-7078	174	27	super	super	ADV
ejpam-7078	174	28	hop	hop	NOUN
ejpam-7078	174	29	dominating	dominating	NOUN
ejpam-7078	174	30	set	set	NOUN
ejpam-7078	174	31	of	of	ADP
ejpam-7078	174	32	g.	g.	PROPN
ejpam-7078	174	33	therefore	therefore	ADV
ejpam-7078	174	34	,	,	PUNCT
ejpam-7078	174	35	it	it	PRON
ejpam-7078	174	36	is	be	AUX
ejpam-7078	174	37	concluded	conclude	VERB
ejpam-7078	174	38	that	that	SCONJ
ejpam-7078	174	39	v1∪v2	v1∪v2	PROPN
ejpam-7078	174	40	is	be	AUX
ejpam-7078	174	41	a	a	DET
ejpam-7078	174	42	minimal	minimal	ADJ
ejpam-7078	174	43	super	super	ADJ
ejpam-7078	174	44	hop	hop	NOUN
ejpam-7078	174	45	dominating	dominating	NOUN
ejpam-7078	174	46	set	set	NOUN
ejpam-7078	174	47	of	of	ADP
ejpam-7078	174	48	g.	g.	PROPN
ejpam-7078	174	49	the	the	DET
ejpam-7078	174	50	next	next	ADJ
ejpam-7078	174	51	result	result	NOUN
ejpam-7078	174	52	gives	give	VERB
ejpam-7078	174	53	some	some	DET
ejpam-7078	174	54	bounds	bound	NOUN
ejpam-7078	174	55	on	on	ADP
ejpam-7078	174	56	the	the	DET
ejpam-7078	174	57	super	super	PROPN
ejpam-7078	174	58	hop	hop	PROPN
ejpam-7078	174	59	roman	roman	ADJ
ejpam-7078	174	60	domination	domination	NOUN
ejpam-7078	174	61	number	number	NOUN
ejpam-7078	174	62	of	of	ADP
ejpam-7078	174	63	a	a	DET
ejpam-7078	174	64	graph	graph	NOUN
ejpam-7078	174	65	.	.	PUNCT
ejpam-7078	175	1	theorem	theorem	NOUN
ejpam-7078	175	2	4	4	NUM
ejpam-7078	175	3	.	.	PUNCT
ejpam-7078	176	1	let	let	VERB
ejpam-7078	176	2	g	g	PRON
ejpam-7078	176	3	be	be	AUX
ejpam-7078	176	4	a	a	DET
ejpam-7078	176	5	connected	connected	ADJ
ejpam-7078	176	6	graph	graph	NOUN
ejpam-7078	176	7	of	of	ADP
ejpam-7078	176	8	order	order	NOUN
ejpam-7078	176	9	n	n	PRON
ejpam-7078	176	10	≥	≥	NOUN
ejpam-7078	176	11	1	1	NUM
ejpam-7078	176	12	.	.	PUNCT
ejpam-7078	177	1	then	then	ADV
ejpam-7078	177	2	,	,	PUNCT
ejpam-7078	177	3	max{γsh(g	max{γsh(g	PROPN
ejpam-7078	177	4	)	)	PUNCT
ejpam-7078	177	5	,	,	PUNCT
ejpam-7078	177	6	γr(g	γr(g	PROPN
ejpam-7078	177	7	)	)	PUNCT
ejpam-7078	177	8	}	}	PUNCT
ejpam-7078	177	9	≤	≤	NUM
ejpam-7078	177	10	γshr(g	γshr(g	NOUN
ejpam-7078	177	11	)	)	PUNCT
ejpam-7078	177	12	≤	≤	ADJ
ejpam-7078	177	13	n.	n.	NOUN
ejpam-7078	177	14	proof	proof	NOUN
ejpam-7078	177	15	.	.	PUNCT
ejpam-7078	178	1	since	since	SCONJ
ejpam-7078	178	2	every	every	DET
ejpam-7078	178	3	super	super	ADJ
ejpam-7078	178	4	hop	hop	PROPN
ejpam-7078	178	5	roman	roman	ADJ
ejpam-7078	178	6	dominating	dominating	NOUN
ejpam-7078	178	7	function	function	NOUN
ejpam-7078	178	8	is	be	AUX
ejpam-7078	178	9	roman	roman	ADJ
ejpam-7078	178	10	dominating	dominating	NOUN
ejpam-7078	178	11	,	,	PUNCT
ejpam-7078	178	12	it	it	PRON
ejpam-7078	178	13	follows	follow	VERB
ejpam-7078	178	14	that	that	PRON
ejpam-7078	178	15	γr(g	γr(g	NOUN
ejpam-7078	178	16	)	)	PUNCT
ejpam-7078	178	17	≤	≤	PUNCT
ejpam-7078	179	1	γshr(g	γshr(g	NOUN
ejpam-7078	179	2	)	)	PUNCT
ejpam-7078	179	3	.	.	PUNCT
ejpam-7078	180	1	let	let	VERB
ejpam-7078	180	2	f	f	PROPN
ejpam-7078	180	3	=	=	SYM
ejpam-7078	180	4	(	(	PUNCT
ejpam-7078	180	5	v0	v0	PROPN
ejpam-7078	180	6	,	,	PUNCT
ejpam-7078	180	7	v1	v1	NOUN
ejpam-7078	180	8	,	,	PUNCT
ejpam-7078	180	9	v2	v2	PROPN
ejpam-7078	180	10	)	)	PUNCT
ejpam-7078	180	11	be	be	AUX
ejpam-7078	180	12	a	a	DET
ejpam-7078	180	13	γshr	γshr	NOUN
ejpam-7078	180	14	-	-	PUNCT
ejpam-7078	180	15	function	function	NOUN
ejpam-7078	180	16	on	on	ADP
ejpam-7078	180	17	g.	g.	PROPN
ejpam-7078	180	18	by	by	ADP
ejpam-7078	180	19	proposition	proposition	NOUN
ejpam-7078	180	20	1	1	NUM
ejpam-7078	180	21	,	,	PUNCT
ejpam-7078	180	22	v1	v1	NOUN
ejpam-7078	180	23	∪	∪	NOUN
ejpam-7078	180	24	v2	v2	NOUN
ejpam-7078	180	25	is	be	AUX
ejpam-7078	180	26	a	a	DET
ejpam-7078	180	27	super	super	ADV
ejpam-7078	180	28	hop	hop	NOUN
ejpam-7078	180	29	dominating	dominating	NOUN
ejpam-7078	180	30	set	set	NOUN
ejpam-7078	180	31	.	.	PUNCT
ejpam-7078	181	1	this	this	PRON
ejpam-7078	181	2	implies	imply	VERB
ejpam-7078	181	3	that	that	SCONJ
ejpam-7078	181	4	γsh(g	γsh(g	NOUN
ejpam-7078	181	5	)	)	PUNCT
ejpam-7078	181	6	≤	≤	NOUN
ejpam-7078	181	7	|v1|	|v1|	NOUN
ejpam-7078	181	8	+	+	CCONJ
ejpam-7078	181	9	|v2|	|v2|	NOUN
ejpam-7078	181	10	≤	≤	NOUN
ejpam-7078	181	11	|v1|	|v1|	NOUN
ejpam-7078	181	12	+	+	CCONJ
ejpam-7078	181	13	2|v2|	2|v2|	NUM
ejpam-7078	181	14	=	=	SYM
ejpam-7078	181	15	γshr(g	γshr(g	NOUN
ejpam-7078	181	16	)	)	PUNCT
ejpam-7078	181	17	.	.	PUNCT
ejpam-7078	182	1	therefore	therefore	ADV
ejpam-7078	182	2	,	,	PUNCT
ejpam-7078	182	3	max{γsh(g	max{γsh(g	PROPN
ejpam-7078	182	4	)	)	PUNCT
ejpam-7078	182	5	,	,	PUNCT
ejpam-7078	182	6	γr(g	γr(g	PROPN
ejpam-7078	182	7	)	)	PUNCT
ejpam-7078	182	8	}	}	PUNCT
ejpam-7078	182	9	≤	≤	NUM
ejpam-7078	182	10	γshr(g	γshr(g	NOUN
ejpam-7078	182	11	)	)	PUNCT
ejpam-7078	182	12	.	.	PUNCT
ejpam-7078	183	1	since	since	SCONJ
ejpam-7078	183	2	h	h	NOUN
ejpam-7078	183	3	=	=	SYM
ejpam-7078	183	4	(	(	PUNCT
ejpam-7078	183	5	∅	∅	NOUN
ejpam-7078	183	6	,	,	PUNCT
ejpam-7078	183	7	v	v	NOUN
ejpam-7078	183	8	(	(	PUNCT
ejpam-7078	183	9	g),∅	g),∅	NOUN
ejpam-7078	183	10	)	)	PUNCT
ejpam-7078	183	11	is	be	AUX
ejpam-7078	183	12	an	an	DET
ejpam-7078	183	13	shrdf	shrdf	NOUN
ejpam-7078	183	14	on	on	ADP
ejpam-7078	183	15	g	g	NOUN
ejpam-7078	183	16	,	,	PUNCT
ejpam-7078	183	17	we	we	PRON
ejpam-7078	183	18	have	have	VERB
ejpam-7078	183	19	γshr(g	γshr(g	NOUN
ejpam-7078	183	20	)	)	PUNCT
ejpam-7078	183	21	≤	≤	NOUN
ejpam-7078	183	22	ωshr	ωshr	NOUN
ejpam-7078	183	23	g	g	PROPN
ejpam-7078	183	24	(	(	PUNCT
ejpam-7078	183	25	h	h	NOUN
ejpam-7078	183	26	)	)	PUNCT
ejpam-7078	183	27	=	=	SYM
ejpam-7078	183	28	|v	|v	PROPN
ejpam-7078	183	29	(	(	PUNCT
ejpam-7078	183	30	g)|	g)|	NOUN
ejpam-7078	183	31	=	=	NOUN
ejpam-7078	183	32	n.	n.	NOUN
ejpam-7078	183	33	we	we	PRON
ejpam-7078	183	34	note	note	VERB
ejpam-7078	183	35	that	that	SCONJ
ejpam-7078	183	36	for	for	ADP
ejpam-7078	183	37	any	any	DET
ejpam-7078	183	38	graph	graph	NOUN
ejpam-7078	183	39	g	g	NOUN
ejpam-7078	183	40	,	,	PUNCT
ejpam-7078	183	41	it	it	PRON
ejpam-7078	183	42	is	be	AUX
ejpam-7078	183	43	easy	easy	ADJ
ejpam-7078	183	44	to	to	PART
ejpam-7078	183	45	show	show	VERB
ejpam-7078	183	46	that	that	SCONJ
ejpam-7078	183	47	γshr(g	γshr(g	NOUN
ejpam-7078	183	48	)	)	PUNCT
ejpam-7078	183	49	≤	≤	NOUN
ejpam-7078	183	50	2γsh(g	2γsh(g	NOUN
ejpam-7078	183	51	)	)	PUNCT
ejpam-7078	183	52	.	.	PUNCT
ejpam-7078	184	1	indeed	indeed	ADV
ejpam-7078	184	2	,	,	PUNCT
ejpam-7078	184	3	if	if	SCONJ
ejpam-7078	184	4	s	s	AUX
ejpam-7078	184	5	be	be	AUX
ejpam-7078	184	6	a	a	DET
ejpam-7078	184	7	γsh	γsh	NOUN
ejpam-7078	184	8	-	-	PUNCT
ejpam-7078	184	9	set	set	NOUN
ejpam-7078	184	10	on	on	ADP
ejpam-7078	184	11	g	g	NOUN
ejpam-7078	184	12	,	,	PUNCT
ejpam-7078	184	13	then	then	ADV
ejpam-7078	184	14	g	g	PROPN
ejpam-7078	184	15	=	=	PUNCT
ejpam-7078	184	16	(	(	PUNCT
ejpam-7078	184	17	v	v	NUM
ejpam-7078	184	18	′	′	NUM
ejpam-7078	184	19	0	0	NUM
ejpam-7078	184	20	,	,	PUNCT
ejpam-7078	184	21	v	v	NOUN
ejpam-7078	184	22	′	′	NUM
ejpam-7078	184	23	1	1	NUM
ejpam-7078	184	24	,	,	PUNCT
ejpam-7078	184	25	v	v	NOUN
ejpam-7078	184	26	′	′	NUM
ejpam-7078	184	27	2	2	NUM
ejpam-7078	184	28	)	)	PUNCT
ejpam-7078	184	29	,	,	PUNCT
ejpam-7078	184	30	where	where	SCONJ
ejpam-7078	184	31	v	v	X
ejpam-7078	184	32	′	′	NOUN
ejpam-7078	184	33	0	0	NUM
ejpam-7078	185	1	=	=	SYM
ejpam-7078	185	2	v	v	ADJ
ejpam-7078	185	3	(	(	PUNCT
ejpam-7078	185	4	g	g	NOUN
ejpam-7078	185	5	)	)	PUNCT
ejpam-7078	185	6	\	\	PROPN
ejpam-7078	186	1	s	s	X
ejpam-7078	186	2	,	,	PUNCT
ejpam-7078	186	3	v	v	ADJ
ejpam-7078	186	4	′	′	NOUN
ejpam-7078	186	5	1	1	NUM
ejpam-7078	186	6	=	=	NOUN
ejpam-7078	186	7	∅	∅	NOUN
ejpam-7078	186	8	,	,	PUNCT
ejpam-7078	186	9	and	and	CCONJ
ejpam-7078	186	10	v	v	X
ejpam-7078	186	11	′	′	NUM
ejpam-7078	186	12	2	2	NUM
ejpam-7078	186	13	=	=	SYM
ejpam-7078	186	14	s	s	NOUN
ejpam-7078	186	15	,	,	PUNCT
ejpam-7078	186	16	is	be	AUX
ejpam-7078	186	17	a	a	DET
ejpam-7078	186	18	shrdf	shrdf	NOUN
ejpam-7078	186	19	on	on	ADP
ejpam-7078	186	20	g.	g.	PROPN
ejpam-7078	186	21	thus	thus	ADV
ejpam-7078	186	22	,	,	PUNCT
ejpam-7078	186	23	we	we	PRON
ejpam-7078	186	24	obtain	obtain	VERB
ejpam-7078	186	25	γshr(g	γshr(g	NOUN
ejpam-7078	186	26	)	)	PUNCT
ejpam-7078	186	27	≤	≤	NOUN
ejpam-7078	186	28	ωshr	ωshr	NOUN
ejpam-7078	186	29	g	g	PROPN
ejpam-7078	186	30	(	(	PUNCT
ejpam-7078	186	31	g	g	NOUN
ejpam-7078	186	32	)	)	PUNCT
ejpam-7078	186	33	=	=	PUNCT
ejpam-7078	187	1	|v	|v	PROPN
ejpam-7078	187	2	′	′	NOUN
ejpam-7078	187	3	1	1	NUM
ejpam-7078	188	1	|	|	ADV
ejpam-7078	189	1	+	+	CCONJ
ejpam-7078	189	2	2|v	2|v	NUM
ejpam-7078	190	1	′	′	NUM
ejpam-7078	190	2	2	2	NUM
ejpam-7078	190	3	|	|	NOUN
ejpam-7078	190	4	=	=	SYM
ejpam-7078	190	5	2|s|	2|s|	NUM
ejpam-7078	190	6	=	=	SYM
ejpam-7078	190	7	2γsh(g	2γsh(g	NOUN
ejpam-7078	190	8	)	)	PUNCT
ejpam-7078	190	9	.	.	PUNCT
ejpam-7078	191	1	however	however	ADV
ejpam-7078	191	2	,	,	PUNCT
ejpam-7078	191	3	2γsh(g	2γsh(g	X
ejpam-7078	191	4	)	)	PUNCT
ejpam-7078	191	5	is	be	AUX
ejpam-7078	191	6	not	not	PART
ejpam-7078	191	7	always	always	ADV
ejpam-7078	191	8	the	the	DET
ejpam-7078	191	9	best	well	ADV
ejpam-7078	191	10	upper	upper	ADJ
ejpam-7078	191	11	bound	bind	VERB
ejpam-7078	191	12	because	because	SCONJ
ejpam-7078	191	13	n	n	PRON
ejpam-7078	191	14	≤	≤	NOUN
ejpam-7078	191	15	2γsh(g	2γsh(g	NOUN
ejpam-7078	191	16	)	)	PUNCT
ejpam-7078	191	17	by	by	ADP
ejpam-7078	191	18	theorem	theorem	NOUN
ejpam-7078	191	19	1	1	NUM
ejpam-7078	191	20	.	.	PUNCT
ejpam-7078	192	1	the	the	DET
ejpam-7078	192	2	next	next	ADJ
ejpam-7078	192	3	result	result	NOUN
ejpam-7078	192	4	simply	simply	ADV
ejpam-7078	192	5	says	say	VERB
ejpam-7078	192	6	that	that	SCONJ
ejpam-7078	192	7	the	the	DET
ejpam-7078	192	8	super	super	PROPN
ejpam-7078	192	9	hop	hop	PROPN
ejpam-7078	192	10	roman	roman	ADJ
ejpam-7078	192	11	domination	domination	NOUN
ejpam-7078	192	12	number	number	NOUN
ejpam-7078	192	13	of	of	ADP
ejpam-7078	192	14	a	a	DET
ejpam-7078	192	15	graph	graph	NOUN
ejpam-7078	192	16	is	be	AUX
ejpam-7078	192	17	the	the	DET
ejpam-7078	192	18	sum	sum	NOUN
ejpam-7078	192	19	of	of	ADP
ejpam-7078	192	20	the	the	DET
ejpam-7078	192	21	super	super	ADV
ejpam-7078	192	22	roman	roman	ADJ
ejpam-7078	192	23	domination	domination	NOUN
ejpam-7078	192	24	numbers	number	NOUN
ejpam-7078	192	25	of	of	ADP
ejpam-7078	192	26	its	its	PRON
ejpam-7078	192	27	components	component	NOUN
ejpam-7078	192	28	.	.	PUNCT
ejpam-7078	193	1	for	for	ADP
ejpam-7078	193	2	completeness	completeness	NOUN
ejpam-7078	193	3	,	,	PUNCT
ejpam-7078	193	4	we	we	PRON
ejpam-7078	193	5	show	show	VERB
ejpam-7078	193	6	its	its	PRON
ejpam-7078	193	7	proof	proof	NOUN
ejpam-7078	193	8	here	here	ADV
ejpam-7078	193	9	.	.	PUNCT
ejpam-7078	194	1	l.	l.	PROPN
ejpam-7078	194	2	f.	f.	PROPN
ejpam-7078	194	3	casinillo	casinillo	PROPN
ejpam-7078	194	4	,	,	PUNCT
ejpam-7078	194	5	s.	s.	PROPN
ejpam-7078	194	6	r.	r.	PROPN
ejpam-7078	194	7	canoy	canoy	PROPN
ejpam-7078	194	8	jr	jr	PROPN
ejpam-7078	194	9	.	.	PROPN
ejpam-7078	194	10	/	/	SYM
ejpam-7078	194	11	eur	eur	PROPN
ejpam-7078	194	12	.	.	PUNCT
ejpam-7078	195	1	j.	j.	PROPN
ejpam-7078	195	2	pure	pure	PROPN
ejpam-7078	195	3	appl	appl	PROPN
ejpam-7078	195	4	.	.	PROPN
ejpam-7078	195	5	math	math	PROPN
ejpam-7078	195	6	,	,	PUNCT
ejpam-7078	195	7	18	18	NUM
ejpam-7078	195	8	(	(	PUNCT
ejpam-7078	195	9	4	4	NUM
ejpam-7078	195	10	)	)	PUNCT
ejpam-7078	195	11	(	(	PUNCT
ejpam-7078	195	12	2025	2025	NUM
ejpam-7078	195	13	)	)	PUNCT
ejpam-7078	195	14	,	,	PUNCT
ejpam-7078	195	15	7078	7078	NUM
ejpam-7078	195	16	7	7	NUM
ejpam-7078	195	17	of	of	ADP
ejpam-7078	195	18	15	15	NUM
ejpam-7078	195	19	theorem	theorem	NOUN
ejpam-7078	195	20	5	5	NUM
ejpam-7078	195	21	.	.	PUNCT
ejpam-7078	196	1	let	let	VERB
ejpam-7078	196	2	g1	g1	PROPN
ejpam-7078	196	3	,	,	PUNCT
ejpam-7078	196	4	g2	g2	PROPN
ejpam-7078	196	5	,	,	PUNCT
ejpam-7078	196	6	.	.	PUNCT
ejpam-7078	196	7	.	.	PUNCT
ejpam-7078	197	1	.	.	PUNCT
ejpam-7078	198	1	,	,	PUNCT
ejpam-7078	198	2	gk	gk	PROPN
ejpam-7078	198	3	be	be	AUX
ejpam-7078	198	4	the	the	DET
ejpam-7078	198	5	components	component	NOUN
ejpam-7078	198	6	of	of	ADP
ejpam-7078	198	7	graph	graph	NOUN
ejpam-7078	198	8	g	g	NOUN
ejpam-7078	198	9	of	of	ADP
ejpam-7078	198	10	order	order	NOUN
ejpam-7078	198	11	n.	n.	NOUN
ejpam-7078	199	1	then	then	ADV
ejpam-7078	199	2	f	f	PROPN
ejpam-7078	199	3	is	be	AUX
ejpam-7078	199	4	an	an	DET
ejpam-7078	199	5	shrdf	shrdf	NOUN
ejpam-7078	199	6	on	on	ADP
ejpam-7078	199	7	g	g	PROPN
ejpam-7078	199	8	if	if	SCONJ
ejpam-7078	200	1	and	and	CCONJ
ejpam-7078	200	2	only	only	ADV
ejpam-7078	200	3	if	if	SCONJ
ejpam-7078	200	4	the	the	DET
ejpam-7078	200	5	restriction	restriction	NOUN
ejpam-7078	200	6	function	function	VERB
ejpam-7078	200	7	f	f	PROPN
ejpam-7078	201	1	|gj	|gj	PROPN
ejpam-7078	201	2	is	be	AUX
ejpam-7078	201	3	an	an	DET
ejpam-7078	201	4	shrdf	shrdf	NOUN
ejpam-7078	201	5	on	on	ADP
ejpam-7078	201	6	gj	gj	NOUN
ejpam-7078	201	7	for	for	ADP
ejpam-7078	201	8	each	each	DET
ejpam-7078	201	9	j	j	PROPN
ejpam-7078	201	10	∈	∈	PROPN
ejpam-7078	201	11	{	{	PUNCT
ejpam-7078	201	12	1	1	NUM
ejpam-7078	201	13	,	,	PUNCT
ejpam-7078	201	14	2	2	NUM
ejpam-7078	201	15	,	,	PUNCT
ejpam-7078	201	16	...	...	PUNCT
ejpam-7078	201	17	k	k	X
ejpam-7078	201	18	}	}	PUNCT
ejpam-7078	201	19	.	.	PUNCT
ejpam-7078	202	1	moreover	moreover	ADV
ejpam-7078	202	2	,	,	PUNCT
ejpam-7078	202	3	γshr(g	γshr(g	NOUN
ejpam-7078	202	4	)	)	PUNCT
ejpam-7078	202	5	=	=	PUNCT
ejpam-7078	203	1	∑k	∑k	PROPN
ejpam-7078	203	2	j=1	j=1	PROPN
ejpam-7078	203	3	γshr(gj	γshr(gj	PROPN
ejpam-7078	203	4	)	)	PUNCT
ejpam-7078	203	5	.	.	PUNCT
ejpam-7078	204	1	proof	proof	NOUN
ejpam-7078	204	2	.	.	PUNCT
ejpam-7078	205	1	suppose	suppose	VERB
ejpam-7078	205	2	f	f	X
ejpam-7078	205	3	=	=	SYM
ejpam-7078	205	4	(	(	PUNCT
ejpam-7078	205	5	v0	v0	PROPN
ejpam-7078	205	6	,	,	PUNCT
ejpam-7078	205	7	v1	v1	NOUN
ejpam-7078	205	8	,	,	PUNCT
ejpam-7078	205	9	v2	v2	PROPN
ejpam-7078	205	10	)	)	PUNCT
ejpam-7078	205	11	is	be	AUX
ejpam-7078	205	12	an	an	DET
ejpam-7078	205	13	shrdf	shrdf	NOUN
ejpam-7078	205	14	on	on	ADP
ejpam-7078	205	15	g.	g.	PROPN
ejpam-7078	205	16	for	for	ADP
ejpam-7078	205	17	each	each	DET
ejpam-7078	205	18	j	j	PROPN
ejpam-7078	205	19	∈	∈	PROPN
ejpam-7078	205	20	{	{	PUNCT
ejpam-7078	205	21	1	1	NUM
ejpam-7078	205	22	,	,	PUNCT
ejpam-7078	205	23	2	2	NUM
ejpam-7078	205	24	,	,	PUNCT
ejpam-7078	205	25	...	...	PUNCT
ejpam-7078	205	26	,	,	PUNCT
ejpam-7078	205	27	k	k	X
ejpam-7078	205	28	}	}	PUNCT
ejpam-7078	205	29	,	,	PUNCT
ejpam-7078	205	30	let	let	VERB
ejpam-7078	205	31	v	v	ADP
ejpam-7078	205	32	j	j	PROPN
ejpam-7078	205	33	0	0	PUNCT
ejpam-7078	205	34	=	=	SYM
ejpam-7078	205	35	v0∩v	v0∩v	PROPN
ejpam-7078	205	36	(	(	PUNCT
ejpam-7078	205	37	gj	gj	PROPN
ejpam-7078	205	38	)	)	PUNCT
ejpam-7078	205	39	,	,	PUNCT
ejpam-7078	205	40	v	v	X
ejpam-7078	205	41	j	j	PROPN
ejpam-7078	205	42	1	1	NUM
ejpam-7078	205	43	=	=	SYM
ejpam-7078	205	44	v1∩v	v1∩v	NOUN
ejpam-7078	205	45	(	(	PUNCT
ejpam-7078	205	46	gj	gj	NOUN
ejpam-7078	205	47	)	)	PUNCT
ejpam-7078	205	48	and	and	CCONJ
ejpam-7078	205	49	v	v	X
ejpam-7078	205	50	j	j	PROPN
ejpam-7078	205	51	2	2	NUM
ejpam-7078	205	52	=	=	SYM
ejpam-7078	205	53	v2∩v	v2∩v	NOUN
ejpam-7078	205	54	(	(	PUNCT
ejpam-7078	205	55	gj	gj	NOUN
ejpam-7078	205	56	)	)	PUNCT
ejpam-7078	205	57	.	.	PUNCT
ejpam-7078	206	1	then	then	ADV
ejpam-7078	206	2	f	f	PROPN
ejpam-7078	206	3	|gj	|gj	PROPN
ejpam-7078	206	4	=	=	SYM
ejpam-7078	206	5	(	(	PUNCT
ejpam-7078	206	6	v	v	NUM
ejpam-7078	206	7	j	j	PROPN
ejpam-7078	206	8	0	0	NUM
ejpam-7078	206	9	,	,	PUNCT
ejpam-7078	206	10	v	v	PART
ejpam-7078	206	11	j	j	PROPN
ejpam-7078	206	12	1	1	NUM
ejpam-7078	206	13	,	,	PUNCT
ejpam-7078	206	14	v	v	PART
ejpam-7078	206	15	j	j	PROPN
ejpam-7078	206	16	2	2	NUM
ejpam-7078	206	17	)	)	PUNCT
ejpam-7078	206	18	for	for	ADP
ejpam-7078	206	19	all	all	DET
ejpam-7078	206	20	j	j	PROPN
ejpam-7078	206	21	∈	∈	PROPN
ejpam-7078	206	22	{	{	PUNCT
ejpam-7078	206	23	1	1	NUM
ejpam-7078	206	24	,	,	PUNCT
ejpam-7078	206	25	2	2	NUM
ejpam-7078	206	26	,	,	PUNCT
ejpam-7078	206	27	...	...	PUNCT
ejpam-7078	206	28	,	,	PUNCT
ejpam-7078	206	29	k	k	NOUN
ejpam-7078	206	30	}	}	PUNCT
ejpam-7078	206	31	.	.	PUNCT
ejpam-7078	207	1	let	let	VERB
ejpam-7078	207	2	j	j	PROPN
ejpam-7078	207	3	∈	∈	PROPN
ejpam-7078	207	4	{	{	PUNCT
ejpam-7078	207	5	1	1	NUM
ejpam-7078	207	6	,	,	PUNCT
ejpam-7078	207	7	2	2	NUM
ejpam-7078	207	8	,	,	PUNCT
ejpam-7078	207	9	...	...	PUNCT
ejpam-7078	207	10	,	,	PUNCT
ejpam-7078	207	11	k	k	NOUN
ejpam-7078	207	12	}	}	PUNCT
ejpam-7078	207	13	and	and	CCONJ
ejpam-7078	207	14	let	let	VERB
ejpam-7078	207	15	v	v	NUM
ejpam-7078	207	16	∈	∈	PROPN
ejpam-7078	207	17	v	v	PROPN
ejpam-7078	207	18	j	j	PROPN
ejpam-7078	207	19	0	0	NUM
ejpam-7078	207	20	.	.	PUNCT
ejpam-7078	208	1	then	then	ADV
ejpam-7078	208	2	v	v	ADP
ejpam-7078	208	3	∈	∈	PROPN
ejpam-7078	208	4	v0	v0	NOUN
ejpam-7078	208	5	.	.	PUNCT
ejpam-7078	209	1	since	since	SCONJ
ejpam-7078	209	2	f	f	PROPN
ejpam-7078	209	3	is	be	AUX
ejpam-7078	209	4	a	a	DET
ejpam-7078	209	5	hop	hop	NOUN
ejpam-7078	209	6	roman	roman	ADJ
ejpam-7078	209	7	dominating	dominating	NOUN
ejpam-7078	209	8	function	function	NOUN
ejpam-7078	209	9	on	on	ADP
ejpam-7078	209	10	g	g	PROPN
ejpam-7078	209	11	,	,	PUNCT
ejpam-7078	209	12	it	it	PRON
ejpam-7078	209	13	follows	follow	VERB
ejpam-7078	209	14	that	that	SCONJ
ejpam-7078	209	15	there	there	PRON
ejpam-7078	209	16	exists	exist	VERB
ejpam-7078	209	17	w	w	PROPN
ejpam-7078	209	18	∈	∈	NOUN
ejpam-7078	209	19	v2	v2	NOUN
ejpam-7078	210	1	such	such	ADJ
ejpam-7078	210	2	that	that	SCONJ
ejpam-7078	210	3	dg(w	dg(w	NUM
ejpam-7078	210	4	,	,	PUNCT
ejpam-7078	210	5	v	v	NOUN
ejpam-7078	210	6	)	)	PUNCT
ejpam-7078	210	7	=	=	SYM
ejpam-7078	210	8	2	2	X
ejpam-7078	210	9	.	.	PUNCT
ejpam-7078	211	1	this	this	PRON
ejpam-7078	211	2	implies	imply	VERB
ejpam-7078	211	3	that	that	SCONJ
ejpam-7078	211	4	w	w	PROPN
ejpam-7078	211	5	∈	∈	PROPN
ejpam-7078	211	6	v	v	PROPN
ejpam-7078	211	7	j	j	PROPN
ejpam-7078	211	8	2	2	NUM
ejpam-7078	211	9	and	and	CCONJ
ejpam-7078	211	10	dgj	dgj	ADJ
ejpam-7078	211	11	(	(	PUNCT
ejpam-7078	211	12	w	w	NOUN
ejpam-7078	211	13	,	,	PUNCT
ejpam-7078	211	14	v	v	NOUN
ejpam-7078	211	15	)	)	PUNCT
ejpam-7078	211	16	=	=	SYM
ejpam-7078	211	17	2	2	NUM
ejpam-7078	211	18	,	,	PUNCT
ejpam-7078	211	19	showing	show	VERB
ejpam-7078	211	20	that	that	SCONJ
ejpam-7078	211	21	f	f	PROPN
ejpam-7078	211	22	|gj	|gj	NOUN
ejpam-7078	211	23	is	be	AUX
ejpam-7078	211	24	a	a	DET
ejpam-7078	211	25	hop	hop	NOUN
ejpam-7078	211	26	roman	roman	ADJ
ejpam-7078	211	27	dominating	dominating	NOUN
ejpam-7078	211	28	function	function	NOUN
ejpam-7078	211	29	on	on	ADP
ejpam-7078	211	30	gj	gj	NOUN
ejpam-7078	211	31	.	.	PUNCT
ejpam-7078	212	1	moreover	moreover	ADV
ejpam-7078	212	2	,	,	PUNCT
ejpam-7078	212	3	since	since	SCONJ
ejpam-7078	212	4	f	f	PROPN
ejpam-7078	212	5	satisfies	satisfie	NOUN
ejpam-7078	212	6	(	(	PUNCT
ejpam-7078	212	7	shr2	shr2	NOUN
ejpam-7078	212	8	)	)	PUNCT
ejpam-7078	212	9	,	,	PUNCT
ejpam-7078	212	10	there	there	PRON
ejpam-7078	212	11	exists	exist	VERB
ejpam-7078	212	12	z	z	NOUN
ejpam-7078	212	13	∈	∈	PROPN
ejpam-7078	212	14	v1	v1	NOUN
ejpam-7078	212	15	∪	∪	VERB
ejpam-7078	212	16	v2	v2	NOUN
ejpam-7078	212	17	such	such	ADJ
ejpam-7078	212	18	that	that	DET
ejpam-7078	212	19	n2	n2	ADJ
ejpam-7078	212	20	g(z	g(z	PROPN
ejpam-7078	212	21	)	)	PUNCT
ejpam-7078	212	22	∩	∩	NOUN
ejpam-7078	212	23	v0	v0	NOUN
ejpam-7078	212	24	=	=	SYM
ejpam-7078	212	25	{	{	PUNCT
ejpam-7078	212	26	v	v	NOUN
ejpam-7078	212	27	}	}	PUNCT
ejpam-7078	212	28	.	.	PUNCT
ejpam-7078	213	1	this	this	PRON
ejpam-7078	213	2	means	mean	VERB
ejpam-7078	213	3	that	that	SCONJ
ejpam-7078	213	4	z	z	PROPN
ejpam-7078	213	5	∈	∈	PROPN
ejpam-7078	213	6	v	v	PROPN
ejpam-7078	213	7	j	j	PROPN
ejpam-7078	213	8	1	1	NUM
ejpam-7078	213	9	∪	∪	PROPN
ejpam-7078	213	10	v	v	NUM
ejpam-7078	213	11	j	j	PROPN
ejpam-7078	213	12	2	2	NUM
ejpam-7078	213	13	and	and	CCONJ
ejpam-7078	213	14	n2	n2	ADJ
ejpam-7078	213	15	gj	gj	PROPN
ejpam-7078	213	16	(	(	PUNCT
ejpam-7078	213	17	z	z	NOUN
ejpam-7078	213	18	)	)	PUNCT
ejpam-7078	213	19	∩	∩	ADJ
ejpam-7078	213	20	v0	v0	NOUN
ejpam-7078	213	21	=	=	SYM
ejpam-7078	213	22	{	{	PUNCT
ejpam-7078	213	23	v	v	NOUN
ejpam-7078	213	24	}	}	PUNCT
ejpam-7078	213	25	.	.	PUNCT
ejpam-7078	214	1	therefore	therefore	ADV
ejpam-7078	214	2	,	,	PUNCT
ejpam-7078	214	3	f	f	PROPN
ejpam-7078	214	4	|gj	|gj	PROPN
ejpam-7078	214	5	is	be	AUX
ejpam-7078	214	6	an	an	DET
ejpam-7078	214	7	shrdf	shrdf	NOUN
ejpam-7078	214	8	on	on	ADP
ejpam-7078	214	9	gj	gj	NOUN
ejpam-7078	214	10	.	.	PUNCT
ejpam-7078	215	1	if	if	SCONJ
ejpam-7078	215	2	,	,	PUNCT
ejpam-7078	215	3	in	in	ADP
ejpam-7078	215	4	particular	particular	ADJ
ejpam-7078	215	5	,	,	PUNCT
ejpam-7078	215	6	f	f	PROPN
ejpam-7078	215	7	is	be	AUX
ejpam-7078	215	8	a	a	DET
ejpam-7078	215	9	γshr	γshr	NOUN
ejpam-7078	215	10	-	-	PUNCT
ejpam-7078	215	11	function	function	NOUN
ejpam-7078	215	12	on	on	ADP
ejpam-7078	215	13	g	g	PROPN
ejpam-7078	215	14	,	,	PUNCT
ejpam-7078	215	15	then	then	ADV
ejpam-7078	215	16	γshr(g	γshr(g	NOUN
ejpam-7078	215	17	)	)	PUNCT
ejpam-7078	215	18	=	=	PUNCT
ejpam-7078	215	19	ωshr	ωshr	NOUN
ejpam-7078	215	20	g	g	PROPN
ejpam-7078	215	21	(	(	PUNCT
ejpam-7078	215	22	f	f	X
ejpam-7078	215	23	)	)	PUNCT
ejpam-7078	215	24	=	=	PUNCT
ejpam-7078	215	25	|v1|+	|v1|+	PRON
ejpam-7078	215	26	2|v2|	2|v2|	NUM
ejpam-7078	215	27	=	=	SYM
ejpam-7078	215	28	k∑	k∑	NOUN
ejpam-7078	216	1	j=1	j=1	PROPN
ejpam-7078	216	2	∣∣v	∣∣v	PROPN
ejpam-7078	216	3	j	j	PROPN
ejpam-7078	216	4	1	1	NUM
ejpam-7078	216	5	|+	|+	NOUN
ejpam-7078	216	6	2	2	NUM
ejpam-7078	216	7	k∑	k∑	NOUN
ejpam-7078	216	8	j=1	j=1	PROPN
ejpam-7078	216	9	∣∣v	∣∣v	PROPN
ejpam-7078	216	10	j	j	PROPN
ejpam-7078	216	11	2	2	NUM
ejpam-7078	216	12	|	|	NOUN
ejpam-7078	216	13	=	=	SYM
ejpam-7078	216	14	k∑	k∑	NOUN
ejpam-7078	217	1	j=1	j=1	NOUN
ejpam-7078	217	2	(	(	PUNCT
ejpam-7078	217	3	∣∣v	∣∣v	NOUN
ejpam-7078	217	4	j	j	NOUN
ejpam-7078	217	5	1	1	NUM
ejpam-7078	217	6	|+	|+	NOUN
ejpam-7078	217	7	2	2	NUM
ejpam-7078	217	8	∣∣v	∣∣v	NOUN
ejpam-7078	217	9	j	j	NOUN
ejpam-7078	217	10	2	2	NUM
ejpam-7078	217	11	|	|	CCONJ
ejpam-7078	217	12	)	)	PUNCT
ejpam-7078	217	13	≥	≥	NOUN
ejpam-7078	217	14	k∑	k∑	VERB
ejpam-7078	217	15	j=1	j=1	PROPN
ejpam-7078	217	16	γshr(gj	γshr(gj	PROPN
ejpam-7078	217	17	)	)	PUNCT
ejpam-7078	217	18	.	.	PUNCT
ejpam-7078	218	1	next	next	ADV
ejpam-7078	218	2	,	,	PUNCT
ejpam-7078	218	3	suppose	suppose	VERB
ejpam-7078	218	4	that	that	SCONJ
ejpam-7078	218	5	f	f	PROPN
ejpam-7078	218	6	|gj	|gj	PROPN
ejpam-7078	218	7	=	=	SYM
ejpam-7078	218	8	(	(	PUNCT
ejpam-7078	218	9	w	w	PROPN
ejpam-7078	218	10	j	j	PROPN
ejpam-7078	218	11	0	0	NUM
ejpam-7078	218	12	,	,	PUNCT
ejpam-7078	218	13	w	w	PROPN
ejpam-7078	218	14	j	j	PROPN
ejpam-7078	218	15	1	1	NUM
ejpam-7078	218	16	,	,	PUNCT
ejpam-7078	218	17	w	w	PROPN
ejpam-7078	218	18	j	j	NOUN
ejpam-7078	218	19	2	2	NUM
ejpam-7078	218	20	)	)	PUNCT
ejpam-7078	218	21	is	be	AUX
ejpam-7078	218	22	an	an	DET
ejpam-7078	218	23	shrdf	shrdf	NOUN
ejpam-7078	218	24	on	on	ADP
ejpam-7078	218	25	gj	gj	NOUN
ejpam-7078	218	26	for	for	ADP
ejpam-7078	218	27	each	each	DET
ejpam-7078	218	28	j	j	PROPN
ejpam-7078	218	29	∈	∈	PROPN
ejpam-7078	218	30	{	{	PUNCT
ejpam-7078	218	31	1	1	NUM
ejpam-7078	218	32	,	,	PUNCT
ejpam-7078	218	33	2	2	NUM
ejpam-7078	218	34	,	,	PUNCT
ejpam-7078	218	35	...	...	PUNCT
ejpam-7078	218	36	k	k	X
ejpam-7078	218	37	}	}	PUNCT
ejpam-7078	218	38	.	.	PUNCT
ejpam-7078	219	1	then	then	ADV
ejpam-7078	219	2	v0	v0	PROPN
ejpam-7078	219	3	=	=	SYM
ejpam-7078	219	4	⋃k	⋃k	NUM
ejpam-7078	219	5	j=1w	j=1w	PROPN
ejpam-7078	219	6	j	j	PROPN
ejpam-7078	219	7	0	0	NUM
ejpam-7078	219	8	,	,	PUNCT
ejpam-7078	219	9	v1	v1	NOUN
ejpam-7078	219	10	=	=	SYM
ejpam-7078	219	11	⋃k	⋃k	NUM
ejpam-7078	219	12	j=1w	j=1w	PROPN
ejpam-7078	219	13	j	j	PROPN
ejpam-7078	219	14	1	1	NUM
ejpam-7078	219	15	and	and	CCONJ
ejpam-7078	219	16	v2	v2	PROPN
ejpam-7078	219	17	=	=	SYM
ejpam-7078	219	18	⋃k	⋃k	NUM
ejpam-7078	219	19	j=1w	j=1w	PROPN
ejpam-7078	219	20	j	j	PROPN
ejpam-7078	219	21	2	2	NUM
ejpam-7078	219	22	.	.	PUNCT
ejpam-7078	220	1	let	let	VERB
ejpam-7078	220	2	v	v	NUM
ejpam-7078	220	3	∈	∈	PROPN
ejpam-7078	220	4	v0	v0	NOUN
ejpam-7078	220	5	.	.	PUNCT
ejpam-7078	221	1	then	then	ADV
ejpam-7078	221	2	v	v	X
ejpam-7078	221	3	∈	∈	PROPN
ejpam-7078	221	4	v	v	ADP
ejpam-7078	221	5	j	j	PROPN
ejpam-7078	221	6	0	0	NUM
ejpam-7078	221	7	for	for	ADP
ejpam-7078	221	8	some	some	DET
ejpam-7078	221	9	j	j	PROPN
ejpam-7078	221	10	∈	∈	PROPN
ejpam-7078	221	11	{	{	PUNCT
ejpam-7078	221	12	1	1	NUM
ejpam-7078	221	13	,	,	PUNCT
ejpam-7078	221	14	2	2	NUM
ejpam-7078	221	15	,	,	PUNCT
ejpam-7078	221	16	...	...	PUNCT
ejpam-7078	221	17	k	k	X
ejpam-7078	221	18	}	}	PUNCT
ejpam-7078	221	19	.	.	PUNCT
ejpam-7078	222	1	since	since	SCONJ
ejpam-7078	222	2	f	f	PROPN
ejpam-7078	222	3	|gj	|gj	PROPN
ejpam-7078	222	4	is	be	AUX
ejpam-7078	222	5	a	a	DET
ejpam-7078	222	6	hop	hop	NOUN
ejpam-7078	222	7	roman	roman	ADJ
ejpam-7078	222	8	dominating	dominating	NOUN
ejpam-7078	222	9	function	function	NOUN
ejpam-7078	222	10	on	on	ADP
ejpam-7078	222	11	g	g	PROPN
ejpam-7078	222	12	,	,	PUNCT
ejpam-7078	222	13	it	it	PRON
ejpam-7078	222	14	follows	follow	VERB
ejpam-7078	222	15	that	that	SCONJ
ejpam-7078	222	16	there	there	PRON
ejpam-7078	222	17	exists	exist	VERB
ejpam-7078	222	18	w	w	PROPN
ejpam-7078	222	19	∈	∈	PROPN
ejpam-7078	222	20	v	v	PROPN
ejpam-7078	222	21	j	j	PROPN
ejpam-7078	222	22	2	2	NUM
ejpam-7078	222	23	such	such	ADJ
ejpam-7078	222	24	that	that	DET
ejpam-7078	222	25	dgj	dgj	NOUN
ejpam-7078	222	26	(	(	PUNCT
ejpam-7078	222	27	w	w	NOUN
ejpam-7078	222	28	,	,	PUNCT
ejpam-7078	222	29	v	v	NOUN
ejpam-7078	222	30	)	)	PUNCT
ejpam-7078	222	31	=	=	SYM
ejpam-7078	223	1	2	2	X
ejpam-7078	223	2	.	.	PUNCT
ejpam-7078	223	3	it	it	PRON
ejpam-7078	223	4	follows	follow	VERB
ejpam-7078	223	5	that	that	SCONJ
ejpam-7078	223	6	w	w	PROPN
ejpam-7078	223	7	∈	∈	PROPN
ejpam-7078	223	8	v2	v2	PROPN
ejpam-7078	223	9	.	.	PUNCT
ejpam-7078	224	1	also	also	ADV
ejpam-7078	224	2	,	,	PUNCT
ejpam-7078	224	3	since	since	SCONJ
ejpam-7078	224	4	f	f	PROPN
ejpam-7078	224	5	|gj	|gj	ADP
ejpam-7078	224	6	satisfies	satisfie	NOUN
ejpam-7078	224	7	(	(	PUNCT
ejpam-7078	224	8	shr2	shr2	NOUN
ejpam-7078	224	9	)	)	PUNCT
ejpam-7078	224	10	,	,	PUNCT
ejpam-7078	224	11	there	there	PRON
ejpam-7078	224	12	exists	exist	VERB
ejpam-7078	224	13	z	z	PROPN
ejpam-7078	224	14	∈	∈	PROPN
ejpam-7078	224	15	v	v	PROPN
ejpam-7078	224	16	j	j	PROPN
ejpam-7078	224	17	1	1	NUM
ejpam-7078	224	18	∪	∪	PROPN
ejpam-7078	224	19	v	v	NUM
ejpam-7078	224	20	j	j	PROPN
ejpam-7078	224	21	2	2	NUM
ejpam-7078	224	22	such	such	ADJ
ejpam-7078	224	23	that	that	DET
ejpam-7078	224	24	n2	n2	ADJ
ejpam-7078	224	25	g(z	g(z	PROPN
ejpam-7078	224	26	)	)	PUNCT
ejpam-7078	224	27	∩	∩	PROPN
ejpam-7078	224	28	v	v	ADP
ejpam-7078	224	29	j	j	PROPN
ejpam-7078	224	30	0	0	PUNCT
ejpam-7078	225	1	=	=	SYM
ejpam-7078	225	2	{	{	PUNCT
ejpam-7078	225	3	v	v	NOUN
ejpam-7078	225	4	}	}	PUNCT
ejpam-7078	225	5	.	.	PUNCT
ejpam-7078	226	1	this	this	PRON
ejpam-7078	226	2	implies	imply	VERB
ejpam-7078	226	3	that	that	SCONJ
ejpam-7078	226	4	z	z	PROPN
ejpam-7078	226	5	∈	∈	PROPN
ejpam-7078	226	6	v1	v1	NOUN
ejpam-7078	226	7	∪	∪	NOUN
ejpam-7078	226	8	v2	v2	PROPN
ejpam-7078	226	9	and	and	CCONJ
ejpam-7078	226	10	n2	n2	ADJ
ejpam-7078	226	11	g(z	g(z	PROPN
ejpam-7078	226	12	)	)	PUNCT
ejpam-7078	226	13	∩	∩	NOUN
ejpam-7078	226	14	v0	v0	NOUN
ejpam-7078	226	15	=	=	SYM
ejpam-7078	226	16	{	{	PUNCT
ejpam-7078	226	17	v	v	NOUN
ejpam-7078	226	18	}	}	PUNCT
ejpam-7078	226	19	.	.	PUNCT
ejpam-7078	227	1	accordingly	accordingly	ADV
ejpam-7078	227	2	,	,	PUNCT
ejpam-7078	227	3	f	f	PROPN
ejpam-7078	227	4	is	be	AUX
ejpam-7078	227	5	an	an	DET
ejpam-7078	227	6	shrdf	shrdf	NOUN
ejpam-7078	227	7	on	on	ADP
ejpam-7078	227	8	g.	g.	PROPN
ejpam-7078	227	9	if	if	SCONJ
ejpam-7078	227	10	,	,	PUNCT
ejpam-7078	227	11	in	in	ADP
ejpam-7078	227	12	particular	particular	ADJ
ejpam-7078	227	13	,	,	PUNCT
ejpam-7078	227	14	f	f	PROPN
ejpam-7078	227	15	|gj	|gj	PROPN
ejpam-7078	227	16	is	be	AUX
ejpam-7078	227	17	a	a	DET
ejpam-7078	227	18	γshr	γshr	NOUN
ejpam-7078	227	19	-	-	PUNCT
ejpam-7078	227	20	function	function	NOUN
ejpam-7078	227	21	on	on	ADP
ejpam-7078	227	22	gj	gj	NOUN
ejpam-7078	227	23	for	for	ADP
ejpam-7078	227	24	all	all	DET
ejpam-7078	227	25	j	j	PROPN
ejpam-7078	227	26	∈	∈	PROPN
ejpam-7078	227	27	{	{	PUNCT
ejpam-7078	227	28	1	1	NUM
ejpam-7078	227	29	,	,	PUNCT
ejpam-7078	227	30	2	2	NUM
ejpam-7078	227	31	,	,	PUNCT
ejpam-7078	227	32	...	...	PUNCT
ejpam-7078	227	33	k	k	X
ejpam-7078	227	34	}	}	PUNCT
ejpam-7078	227	35	,	,	PUNCT
ejpam-7078	227	36	then	then	ADV
ejpam-7078	227	37	k∑	k∑	PROPN
ejpam-7078	227	38	j=1	j=1	PROPN
ejpam-7078	227	39	γshr(gj	γshr(gj	PROPN
ejpam-7078	227	40	)	)	PUNCT
ejpam-7078	227	41	=	=	SYM
ejpam-7078	227	42	k∑	k∑	PROPN
ejpam-7078	228	1	j=1	j=1	PROPN
ejpam-7078	228	2	ωshr	ωshr	PROPN
ejpam-7078	228	3	g	g	PROPN
ejpam-7078	228	4	(	(	PUNCT
ejpam-7078	228	5	f	f	PROPN
ejpam-7078	228	6	|gj	|gj	ADP
ejpam-7078	228	7	)	)	PUNCT
ejpam-7078	228	8	=	=	SYM
ejpam-7078	228	9	k∑	k∑	NOUN
ejpam-7078	229	1	j=1	j=1	NOUN
ejpam-7078	229	2	(	(	PUNCT
ejpam-7078	229	3	∣∣w	∣∣w	ADV
ejpam-7078	229	4	j	j	PROPN
ejpam-7078	229	5	1	1	NUM
ejpam-7078	229	6	|+	|+	NOUN
ejpam-7078	229	7	2	2	NUM
ejpam-7078	229	8	∣∣w	∣∣w	NOUN
ejpam-7078	229	9	j	j	NOUN
ejpam-7078	229	10	2	2	NUM
ejpam-7078	229	11	|	|	ADV
ejpam-7078	229	12	)	)	PUNCT
ejpam-7078	229	13	=	=	PUNCT
ejpam-7078	230	1	k∑	k∑	PROPN
ejpam-7078	231	1	j=1	j=1	PROPN
ejpam-7078	231	2	∣∣w	∣∣w	PROPN
ejpam-7078	231	3	j	j	PROPN
ejpam-7078	231	4	1	1	NUM
ejpam-7078	231	5	|+	|+	NOUN
ejpam-7078	231	6	2	2	NUM
ejpam-7078	231	7	k∑	k∑	NOUN
ejpam-7078	231	8	i=1	i=1	PROPN
ejpam-7078	232	1	∣∣w	∣∣w	ADV
ejpam-7078	232	2	j	j	PROPN
ejpam-7078	232	3	2	2	NUM
ejpam-7078	232	4	|	|	NOUN
ejpam-7078	232	5	=	=	SYM
ejpam-7078	232	6	|v1|+	|v1|+	ADP
ejpam-7078	232	7	2|v2|	2|v2|	NUM
ejpam-7078	232	8	≥	≥	NOUN
ejpam-7078	232	9	γshr(g	γshr(g	NOUN
ejpam-7078	232	10	)	)	PUNCT
ejpam-7078	232	11	.	.	PUNCT
ejpam-7078	233	1	this	this	PRON
ejpam-7078	233	2	proves	prove	VERB
ejpam-7078	233	3	the	the	DET
ejpam-7078	233	4	assertion	assertion	NOUN
ejpam-7078	233	5	.	.	PUNCT
ejpam-7078	234	1	l.	l.	PROPN
ejpam-7078	234	2	f.	f.	PROPN
ejpam-7078	234	3	casinillo	casinillo	PROPN
ejpam-7078	234	4	,	,	PUNCT
ejpam-7078	234	5	s.	s.	PROPN
ejpam-7078	234	6	r.	r.	PROPN
ejpam-7078	234	7	canoy	canoy	PROPN
ejpam-7078	234	8	jr	jr	PROPN
ejpam-7078	234	9	.	.	PROPN
ejpam-7078	234	10	/	/	SYM
ejpam-7078	234	11	eur	eur	PROPN
ejpam-7078	234	12	.	.	PUNCT
ejpam-7078	235	1	j.	j.	PROPN
ejpam-7078	235	2	pure	pure	PROPN
ejpam-7078	235	3	appl	appl	PROPN
ejpam-7078	235	4	.	.	PROPN
ejpam-7078	235	5	math	math	PROPN
ejpam-7078	235	6	,	,	PUNCT
ejpam-7078	235	7	18	18	NUM
ejpam-7078	235	8	(	(	PUNCT
ejpam-7078	235	9	4	4	NUM
ejpam-7078	235	10	)	)	PUNCT
ejpam-7078	235	11	(	(	PUNCT
ejpam-7078	235	12	2025	2025	NUM
ejpam-7078	235	13	)	)	PUNCT
ejpam-7078	235	14	,	,	PUNCT
ejpam-7078	235	15	7078	7078	NUM
ejpam-7078	235	16	8	8	NUM
ejpam-7078	235	17	of	of	ADP
ejpam-7078	235	18	15	15	NUM
ejpam-7078	235	19	corollary	corollary	ADJ
ejpam-7078	235	20	2	2	NUM
ejpam-7078	235	21	.	.	PUNCT
ejpam-7078	236	1	let	let	VERB
ejpam-7078	236	2	g1	g1	PROPN
ejpam-7078	236	3	,	,	PUNCT
ejpam-7078	236	4	g2	g2	PROPN
ejpam-7078	236	5	,	,	PUNCT
ejpam-7078	236	6	.	.	PUNCT
ejpam-7078	236	7	.	.	PUNCT
ejpam-7078	237	1	.	.	PUNCT
ejpam-7078	238	1	,	,	PUNCT
ejpam-7078	238	2	gk	gk	PROPN
ejpam-7078	238	3	be	be	AUX
ejpam-7078	238	4	the	the	DET
ejpam-7078	238	5	components	component	NOUN
ejpam-7078	238	6	of	of	ADP
ejpam-7078	238	7	a	a	DET
ejpam-7078	238	8	graph	graph	NOUN
ejpam-7078	238	9	g	g	NOUN
ejpam-7078	238	10	of	of	ADP
ejpam-7078	238	11	order	order	NOUN
ejpam-7078	238	12	n.	n.	NOUN
ejpam-7078	238	13	if	if	SCONJ
ejpam-7078	238	14	gj	gj	NOUN
ejpam-7078	238	15	is	be	AUX
ejpam-7078	238	16	complete	complete	ADJ
ejpam-7078	238	17	for	for	ADP
ejpam-7078	238	18	every	every	DET
ejpam-7078	238	19	j	j	PROPN
ejpam-7078	238	20	∈	∈	PROPN
ejpam-7078	238	21	{	{	PUNCT
ejpam-7078	238	22	1	1	NUM
ejpam-7078	238	23	,	,	PUNCT
ejpam-7078	238	24	2	2	NUM
ejpam-7078	238	25	,	,	PUNCT
ejpam-7078	238	26	·	·	PUNCT
ejpam-7078	238	27	·	·	PUNCT
ejpam-7078	238	28	·	·	PUNCT
ejpam-7078	238	29	,	,	PUNCT
ejpam-7078	238	30	k	k	X
ejpam-7078	238	31	}	}	PUNCT
ejpam-7078	238	32	,	,	PUNCT
ejpam-7078	238	33	then	then	ADV
ejpam-7078	238	34	γshr(g	γshr(g	NOUN
ejpam-7078	238	35	)	)	PUNCT
ejpam-7078	238	36	=	=	VERB
ejpam-7078	239	1	n.	n.	NOUN
ejpam-7078	239	2	in	in	ADP
ejpam-7078	239	3	particular	particular	ADJ
ejpam-7078	239	4	,	,	PUNCT
ejpam-7078	239	5	γshr(kn	γshr(kn	NOUN
ejpam-7078	239	6	)	)	PUNCT
ejpam-7078	239	7	=	=	SYM
ejpam-7078	239	8	γshr(kn	γshr(kn	NOUN
ejpam-7078	239	9	)	)	PUNCT
ejpam-7078	239	10	=	=	SYM
ejpam-7078	239	11	n.	n.	NOUN
ejpam-7078	239	12	proof	proof	NOUN
ejpam-7078	239	13	.	.	PUNCT
ejpam-7078	240	1	this	this	PRON
ejpam-7078	240	2	follows	follow	VERB
ejpam-7078	240	3	from	from	ADP
ejpam-7078	240	4	theorem	theorem	ADJ
ejpam-7078	240	5	2	2	NUM
ejpam-7078	240	6	,	,	PUNCT
ejpam-7078	240	7	theorem	theorem	VERB
ejpam-7078	240	8	4	4	NUM
ejpam-7078	240	9	,	,	PUNCT
ejpam-7078	240	10	and	and	CCONJ
ejpam-7078	240	11	theorem	theorem	VERB
ejpam-7078	240	12	5	5	NUM
ejpam-7078	240	13	.	.	PUNCT
ejpam-7078	240	14	proposition	proposition	NOUN
ejpam-7078	240	15	3	3	X
ejpam-7078	240	16	.	.	PUNCT
ejpam-7078	241	1	let	let	VERB
ejpam-7078	241	2	g	g	PRON
ejpam-7078	241	3	be	be	AUX
ejpam-7078	241	4	a	a	DET
ejpam-7078	241	5	graph	graph	NOUN
ejpam-7078	241	6	of	of	ADP
ejpam-7078	241	7	order	order	NOUN
ejpam-7078	241	8	n	n	PRON
ejpam-7078	241	9	≥	≥	NOUN
ejpam-7078	241	10	1	1	NUM
ejpam-7078	241	11	.	.	PUNCT
ejpam-7078	242	1	then	then	ADV
ejpam-7078	242	2	(	(	PUNCT
ejpam-7078	242	3	i	i	NOUN
ejpam-7078	242	4	)	)	PUNCT
ejpam-7078	242	5	γshr(g	γshr(g	NOUN
ejpam-7078	242	6	)	)	PUNCT
ejpam-7078	242	7	=	=	SYM
ejpam-7078	242	8	1	1	NUM
ejpam-7078	242	9	if	if	SCONJ
ejpam-7078	242	10	and	and	CCONJ
ejpam-7078	242	11	only	only	ADV
ejpam-7078	242	12	if	if	SCONJ
ejpam-7078	242	13	g	g	PROPN
ejpam-7078	242	14	=	=	SYM
ejpam-7078	242	15	k1	k1	PROPN
ejpam-7078	242	16	;	;	PUNCT
ejpam-7078	242	17	(	(	PUNCT
ejpam-7078	242	18	ii	ii	NOUN
ejpam-7078	242	19	)	)	PUNCT
ejpam-7078	242	20	γshr(g	γshr(g	NOUN
ejpam-7078	242	21	)	)	PUNCT
ejpam-7078	242	22	=	=	SYM
ejpam-7078	242	23	2	2	NUM
ejpam-7078	243	1	if	if	SCONJ
ejpam-7078	243	2	and	and	CCONJ
ejpam-7078	243	3	only	only	ADV
ejpam-7078	243	4	if	if	SCONJ
ejpam-7078	243	5	g	g	PROPN
ejpam-7078	243	6	∈	∈	PROPN
ejpam-7078	243	7	{	{	PUNCT
ejpam-7078	243	8	k2,k2	k2,k2	PROPN
ejpam-7078	243	9	}	}	PUNCT
ejpam-7078	243	10	;	;	PUNCT
ejpam-7078	243	11	and	and	CCONJ
ejpam-7078	243	12	(	(	PUNCT
ejpam-7078	243	13	iii	iii	X
ejpam-7078	243	14	)	)	PUNCT
ejpam-7078	243	15	γshr(g	γshr(g	NOUN
ejpam-7078	243	16	)	)	PUNCT
ejpam-7078	243	17	=	=	SYM
ejpam-7078	243	18	3	3	NUM
ejpam-7078	243	19	if	if	SCONJ
ejpam-7078	243	20	and	and	CCONJ
ejpam-7078	243	21	only	only	ADV
ejpam-7078	243	22	if	if	SCONJ
ejpam-7078	243	23	g	g	PROPN
ejpam-7078	243	24	∈	∈	PROPN
ejpam-7078	243	25	{	{	PUNCT
ejpam-7078	243	26	p3,k3,k3,k2	p3,k3,k3,k2	NOUN
ejpam-7078	243	27	∪k1	∪k1	ADJ
ejpam-7078	243	28	}	}	PUNCT
ejpam-7078	243	29	.	.	PUNCT
ejpam-7078	244	1	proof	proof	NOUN
ejpam-7078	244	2	.	.	PUNCT
ejpam-7078	245	1	let	let	VERB
ejpam-7078	245	2	f	f	PROPN
ejpam-7078	245	3	=	=	SYM
ejpam-7078	245	4	(	(	PUNCT
ejpam-7078	245	5	v0	v0	PROPN
ejpam-7078	245	6	,	,	PUNCT
ejpam-7078	245	7	v1	v1	NOUN
ejpam-7078	245	8	,	,	PUNCT
ejpam-7078	245	9	v2	v2	PROPN
ejpam-7078	245	10	)	)	PUNCT
ejpam-7078	245	11	be	be	AUX
ejpam-7078	245	12	a	a	DET
ejpam-7078	245	13	γshr	γshr	NOUN
ejpam-7078	245	14	-	-	PUNCT
ejpam-7078	245	15	function	function	NOUN
ejpam-7078	245	16	on	on	ADP
ejpam-7078	245	17	g.	g.	PROPN
ejpam-7078	245	18	(	(	PUNCT
ejpam-7078	245	19	i	i	NOUN
ejpam-7078	245	20	)	)	PUNCT
ejpam-7078	245	21	suppose	suppose	VERB
ejpam-7078	245	22	γshr(g	γshr(g	NOUN
ejpam-7078	245	23	)	)	PUNCT
ejpam-7078	245	24	=	=	SYM
ejpam-7078	246	1	1	1	X
ejpam-7078	246	2	.	.	PUNCT
ejpam-7078	246	3	then	then	ADV
ejpam-7078	246	4	|v1|	|v1|	NOUN
ejpam-7078	246	5	+	+	CCONJ
ejpam-7078	246	6	2|v2|	2|v2|	NUM
ejpam-7078	246	7	=	=	SYM
ejpam-7078	246	8	1	1	X
ejpam-7078	246	9	.	.	PUNCT
ejpam-7078	247	1	this	this	PRON
ejpam-7078	247	2	implies	imply	VERB
ejpam-7078	247	3	that	that	DET
ejpam-7078	247	4	|v2|	|v2|	NOUN
ejpam-7078	247	5	=	=	SYM
ejpam-7078	247	6	0	0	X
ejpam-7078	247	7	.	.	PUNCT
ejpam-7078	247	8	by	by	ADP
ejpam-7078	247	9	proposition	proposition	NOUN
ejpam-7078	247	10	1(i	1(i	NUM
ejpam-7078	247	11	)	)	PUNCT
ejpam-7078	247	12	,	,	PUNCT
ejpam-7078	247	13	|v0|	|v0|	NOUN
ejpam-7078	247	14	=	=	SYM
ejpam-7078	247	15	0	0	X
ejpam-7078	247	16	.	.	PUNCT
ejpam-7078	248	1	hence	hence	ADV
ejpam-7078	248	2	,	,	PUNCT
ejpam-7078	248	3	|v1|	|v1|	NOUN
ejpam-7078	248	4	=	=	SYM
ejpam-7078	248	5	|v	|v	PROPN
ejpam-7078	248	6	(	(	PUNCT
ejpam-7078	248	7	g)|	g)|	NOUN
ejpam-7078	248	8	=	=	SYM
ejpam-7078	248	9	1	1	NUM
ejpam-7078	248	10	,	,	PUNCT
ejpam-7078	248	11	i.e.	i.e.	X
ejpam-7078	248	12	,	,	PUNCT
ejpam-7078	248	13	g	g	PROPN
ejpam-7078	248	14	=	=	SYM
ejpam-7078	248	15	k1	k1	PROPN
ejpam-7078	248	16	.	.	PUNCT
ejpam-7078	249	1	the	the	DET
ejpam-7078	249	2	converse	converse	NOUN
ejpam-7078	249	3	is	be	AUX
ejpam-7078	249	4	clear	clear	ADJ
ejpam-7078	249	5	.	.	PUNCT
ejpam-7078	250	1	(	(	PUNCT
ejpam-7078	250	2	ii	ii	NOUN
ejpam-7078	250	3	)	)	PUNCT
ejpam-7078	250	4	suppose	suppose	VERB
ejpam-7078	250	5	γshr(g	γshr(g	NOUN
ejpam-7078	250	6	)	)	PUNCT
ejpam-7078	250	7	=	=	SYM
ejpam-7078	250	8	|v1|	|v1|	NOUN
ejpam-7078	250	9	+	+	CCONJ
ejpam-7078	250	10	2|v2|	2|v2|	NUM
ejpam-7078	250	11	=	=	SYM
ejpam-7078	250	12	2	2	X
ejpam-7078	250	13	.	.	PUNCT
ejpam-7078	250	14	then	then	ADV
ejpam-7078	250	15	|v2|	|v2|	ADV
ejpam-7078	250	16	≤	≤	NOUN
ejpam-7078	250	17	1	1	NUM
ejpam-7078	250	18	.	.	PUNCT
ejpam-7078	250	19	suppose	suppose	VERB
ejpam-7078	250	20	|v2|	|v2|	NOUN
ejpam-7078	250	21	=	=	SYM
ejpam-7078	250	22	1	1	X
ejpam-7078	250	23	.	.	PUNCT
ejpam-7078	250	24	then	then	ADV
ejpam-7078	250	25	|v1|	|v1|	VERB
ejpam-7078	250	26	=	=	SYM
ejpam-7078	250	27	0	0	NUM
ejpam-7078	250	28	and	and	CCONJ
ejpam-7078	250	29	|v0|	|v0|	NOUN
ejpam-7078	250	30	̸=	̸=	PROPN
ejpam-7078	250	31	0	0	NUM
ejpam-7078	250	32	.	.	PUNCT
ejpam-7078	251	1	let	let	VERB
ejpam-7078	251	2	v2	v2	VERB
ejpam-7078	251	3	=	=	PUNCT
ejpam-7078	251	4	{	{	PUNCT
ejpam-7078	251	5	v	v	NOUN
ejpam-7078	251	6	}	}	PUNCT
ejpam-7078	251	7	and	and	CCONJ
ejpam-7078	251	8	let	let	VERB
ejpam-7078	251	9	w	w	PROPN
ejpam-7078	251	10	∈	∈	PROPN
ejpam-7078	251	11	v0	v0	NOUN
ejpam-7078	251	12	.	.	PUNCT
ejpam-7078	252	1	then	then	ADV
ejpam-7078	252	2	dg(v	dg(v	PUNCT
ejpam-7078	252	3	,	,	PUNCT
ejpam-7078	252	4	w	w	NOUN
ejpam-7078	252	5	)	)	PUNCT
ejpam-7078	252	6	=	=	SYM
ejpam-7078	252	7	2	2	X
ejpam-7078	252	8	.	.	X
ejpam-7078	252	9	let	let	VERB
ejpam-7078	252	10	x	x	SYM
ejpam-7078	252	11	∈	∈	PROPN
ejpam-7078	252	12	ng(w	ng(w	NOUN
ejpam-7078	252	13	)	)	PUNCT
ejpam-7078	252	14	∩	∩	NOUN
ejpam-7078	252	15	ng(v	ng(v	NUM
ejpam-7078	252	16	)	)	PUNCT
ejpam-7078	252	17	.	.	PUNCT
ejpam-7078	253	1	since	since	SCONJ
ejpam-7078	253	2	|v1|	|v1|	NUM
ejpam-7078	253	3	=	=	SYM
ejpam-7078	253	4	0	0	NUM
ejpam-7078	253	5	,	,	PUNCT
ejpam-7078	253	6	this	this	PRON
ejpam-7078	253	7	implies	imply	VERB
ejpam-7078	253	8	that	that	SCONJ
ejpam-7078	253	9	v2	v2	PROPN
ejpam-7078	253	10	is	be	AUX
ejpam-7078	253	11	not	not	PART
ejpam-7078	253	12	a	a	DET
ejpam-7078	253	13	hop	hop	NOUN
ejpam-7078	253	14	dominating	dominating	NOUN
ejpam-7078	253	15	set	set	NOUN
ejpam-7078	253	16	in	in	ADP
ejpam-7078	253	17	g	g	PROPN
ejpam-7078	253	18	,	,	PUNCT
ejpam-7078	253	19	a	a	DET
ejpam-7078	253	20	contradiction	contradiction	NOUN
ejpam-7078	253	21	.	.	PUNCT
ejpam-7078	254	1	thus	thus	ADV
ejpam-7078	254	2	,	,	PUNCT
ejpam-7078	254	3	|v2|	|v2|	NOUN
ejpam-7078	254	4	=	=	SYM
ejpam-7078	254	5	0	0	X
ejpam-7078	254	6	.	.	PUNCT
ejpam-7078	255	1	this	this	PRON
ejpam-7078	255	2	implies	imply	VERB
ejpam-7078	255	3	that	that	SCONJ
ejpam-7078	255	4	|v0|	|v0|	NOUN
ejpam-7078	255	5	=	=	SYM
ejpam-7078	255	6	0	0	NUM
ejpam-7078	255	7	and	and	CCONJ
ejpam-7078	255	8	γshr(g	γshr(g	NUM
ejpam-7078	255	9	)	)	PUNCT
ejpam-7078	255	10	=	=	SYM
ejpam-7078	255	11	|v1|	|v1|	NOUN
ejpam-7078	255	12	=	=	SYM
ejpam-7078	255	13	|v	|v	PROPN
ejpam-7078	255	14	(	(	PUNCT
ejpam-7078	255	15	g)|	g)|	NOUN
ejpam-7078	255	16	=	=	SYM
ejpam-7078	255	17	2	2	NUM
ejpam-7078	255	18	.	.	PUNCT
ejpam-7078	256	1	therefore	therefore	ADV
ejpam-7078	256	2	,	,	PUNCT
ejpam-7078	256	3	g	g	PROPN
ejpam-7078	256	4	∈	∈	PROPN
ejpam-7078	256	5	{	{	PUNCT
ejpam-7078	256	6	k2,k2	k2,k2	PROPN
ejpam-7078	256	7	}	}	PUNCT
ejpam-7078	256	8	.	.	PUNCT
ejpam-7078	257	1	conversely	conversely	ADV
ejpam-7078	257	2	,	,	PUNCT
ejpam-7078	257	3	suppose	suppose	VERB
ejpam-7078	257	4	that	that	SCONJ
ejpam-7078	257	5	g	g	PROPN
ejpam-7078	257	6	∈	∈	PROPN
ejpam-7078	257	7	{	{	PUNCT
ejpam-7078	257	8	k2,k2	k2,k2	PROPN
ejpam-7078	257	9	}	}	PUNCT
ejpam-7078	257	10	.	.	PUNCT
ejpam-7078	258	1	then	then	ADV
ejpam-7078	258	2	clearly	clearly	ADV
ejpam-7078	258	3	,	,	PUNCT
ejpam-7078	258	4	γshr(g	γshr(g	NOUN
ejpam-7078	258	5	)	)	PUNCT
ejpam-7078	258	6	=	=	SYM
ejpam-7078	259	1	2	2	X
ejpam-7078	259	2	.	.	PUNCT
ejpam-7078	259	3	(	(	PUNCT
ejpam-7078	259	4	iii	iii	NOUN
ejpam-7078	259	5	)	)	PUNCT
ejpam-7078	259	6	suppose	suppose	VERB
ejpam-7078	259	7	γshr(g	γshr(g	NOUN
ejpam-7078	259	8	)	)	PUNCT
ejpam-7078	259	9	=	=	SYM
ejpam-7078	259	10	|v1|	|v1|	NOUN
ejpam-7078	259	11	+	+	CCONJ
ejpam-7078	259	12	2|v2|	2|v2|	NUM
ejpam-7078	259	13	=	=	SYM
ejpam-7078	259	14	3	3	X
ejpam-7078	259	15	.	.	PUNCT
ejpam-7078	259	16	then	then	ADV
ejpam-7078	259	17	|v2|	|v2|	ADV
ejpam-7078	259	18	≤	≤	NUM
ejpam-7078	259	19	1	1	NUM
ejpam-7078	259	20	.	.	PUNCT
ejpam-7078	260	1	if	if	SCONJ
ejpam-7078	260	2	|v2|	|v2|	NOUN
ejpam-7078	260	3	=	=	SYM
ejpam-7078	260	4	0	0	NUM
ejpam-7078	260	5	,	,	PUNCT
ejpam-7078	260	6	then	then	ADV
ejpam-7078	260	7	|v0|	|v0|	NOUN
ejpam-7078	260	8	=	=	SYM
ejpam-7078	260	9	0	0	NUM
ejpam-7078	260	10	and	and	CCONJ
ejpam-7078	260	11	|v1|	|v1|	NOUN
ejpam-7078	260	12	=	=	SYM
ejpam-7078	260	13	|v	|v	PROPN
ejpam-7078	260	14	(	(	PUNCT
ejpam-7078	260	15	g)|	g)|	NOUN
ejpam-7078	260	16	=	=	SYM
ejpam-7078	260	17	3	3	NUM
ejpam-7078	260	18	.	.	PUNCT
ejpam-7078	260	19	hence	hence	ADV
ejpam-7078	260	20	,	,	PUNCT
ejpam-7078	260	21	g	g	PROPN
ejpam-7078	260	22	∈	∈	PROPN
ejpam-7078	260	23	{	{	PUNCT
ejpam-7078	260	24	p3,k3,k3	p3,k3,k3	NOUN
ejpam-7078	260	25	,	,	PUNCT
ejpam-7078	260	26	p2	p2	NOUN
ejpam-7078	260	27	∪k1	∪k1	ADV
ejpam-7078	260	28	}	}	PUNCT
ejpam-7078	260	29	.	.	PUNCT
ejpam-7078	261	1	next	next	ADV
ejpam-7078	261	2	,	,	PUNCT
ejpam-7078	261	3	suppose	suppose	VERB
ejpam-7078	261	4	that	that	SCONJ
ejpam-7078	261	5	|v2|	|v2|	NOUN
ejpam-7078	261	6	=	=	SYM
ejpam-7078	261	7	1	1	X
ejpam-7078	261	8	.	.	PUNCT
ejpam-7078	261	9	then	then	ADV
ejpam-7078	261	10	|v1|	|v1|	NOUN
ejpam-7078	261	11	=	=	SYM
ejpam-7078	261	12	1	1	NUM
ejpam-7078	261	13	and	and	CCONJ
ejpam-7078	261	14	|v0|	|v0|	NOUN
ejpam-7078	261	15	≥	≥	NOUN
ejpam-7078	261	16	1	1	NUM
ejpam-7078	261	17	.	.	PUNCT
ejpam-7078	262	1	let	let	VERB
ejpam-7078	262	2	v	v	NUM
ejpam-7078	262	3	∈	∈	PROPN
ejpam-7078	262	4	v2	v2	PROPN
ejpam-7078	262	5	and	and	CCONJ
ejpam-7078	262	6	u	u	NOUN
ejpam-7078	262	7	∈	∈	PROPN
ejpam-7078	262	8	v0	v0	NOUN
ejpam-7078	262	9	.	.	PUNCT
ejpam-7078	263	1	then	then	ADV
ejpam-7078	263	2	dg(u	dg(u	X
ejpam-7078	263	3	,	,	PUNCT
ejpam-7078	263	4	v	v	NOUN
ejpam-7078	263	5	)	)	PUNCT
ejpam-7078	263	6	=	=	SYM
ejpam-7078	263	7	2	2	X
ejpam-7078	263	8	.	.	PUNCT
ejpam-7078	263	9	now	now	ADV
ejpam-7078	263	10	,	,	PUNCT
ejpam-7078	263	11	let	let	VERB
ejpam-7078	263	12	x	x	X
ejpam-7078	263	13	∈	∈	PROPN
ejpam-7078	263	14	ng(v)∩ng(u	ng(v)∩ng(u	PROPN
ejpam-7078	263	15	)	)	PUNCT
ejpam-7078	263	16	.	.	PUNCT
ejpam-7078	264	1	since	since	SCONJ
ejpam-7078	264	2	f	f	PROPN
ejpam-7078	264	3	satisfies	satisfie	NOUN
ejpam-7078	264	4	(	(	PUNCT
ejpam-7078	264	5	shr1	shr1	PROPN
ejpam-7078	264	6	)	)	PUNCT
ejpam-7078	264	7	and	and	CCONJ
ejpam-7078	264	8	x	x	PUNCT
ejpam-7078	264	9	∈	∈	NOUN
ejpam-7078	264	10	ng(v	ng(v	NOUN
ejpam-7078	264	11	)	)	PUNCT
ejpam-7078	264	12	,	,	PUNCT
ejpam-7078	264	13	it	it	PRON
ejpam-7078	264	14	follows	follow	VERB
ejpam-7078	264	15	that	that	SCONJ
ejpam-7078	264	16	x	x	PUNCT
ejpam-7078	264	17	∈	∈	PROPN
ejpam-7078	264	18	v1	v1	NOUN
ejpam-7078	264	19	.	.	PUNCT
ejpam-7078	265	1	suppose	suppose	VERB
ejpam-7078	265	2	now	now	ADV
ejpam-7078	266	1	that	that	SCONJ
ejpam-7078	266	2	|v	|v	PROPN
ejpam-7078	266	3	(	(	PUNCT
ejpam-7078	266	4	g)|	g)|	X
ejpam-7078	266	5	≥	≥	NOUN
ejpam-7078	266	6	4	4	NUM
ejpam-7078	266	7	.	.	PUNCT
ejpam-7078	266	8	let	let	VERB
ejpam-7078	266	9	w	w	NOUN
ejpam-7078	266	10	∈	∈	PROPN
ejpam-7078	266	11	v	v	ADP
ejpam-7078	266	12	(	(	PUNCT
ejpam-7078	266	13	g	g	NOUN
ejpam-7078	266	14	)	)	PUNCT
ejpam-7078	266	15	\	\	NOUN
ejpam-7078	267	1	{	{	PUNCT
ejpam-7078	267	2	u	u	NOUN
ejpam-7078	267	3	,	,	PUNCT
ejpam-7078	267	4	v	v	NOUN
ejpam-7078	267	5	,	,	PUNCT
ejpam-7078	267	6	x	x	NOUN
ejpam-7078	267	7	}	}	PUNCT
ejpam-7078	267	8	.	.	PUNCT
ejpam-7078	268	1	since	since	SCONJ
ejpam-7078	268	2	|v1|	|v1|	NOUN
ejpam-7078	268	3	=	=	SYM
ejpam-7078	268	4	|v2|	|v2|	NOUN
ejpam-7078	268	5	=	=	SYM
ejpam-7078	268	6	1	1	X
ejpam-7078	268	7	,	,	PUNCT
ejpam-7078	268	8	it	it	PRON
ejpam-7078	268	9	follows	follow	VERB
ejpam-7078	268	10	that	that	SCONJ
ejpam-7078	268	11	w	w	PROPN
ejpam-7078	268	12	∈	∈	PROPN
ejpam-7078	268	13	v0	v0	NOUN
ejpam-7078	268	14	and	and	CCONJ
ejpam-7078	268	15	dg(w	dg(w	NOUN
ejpam-7078	268	16	,	,	PUNCT
ejpam-7078	268	17	v	v	NOUN
ejpam-7078	268	18	)	)	PUNCT
ejpam-7078	268	19	=	=	SYM
ejpam-7078	268	20	2	2	X
ejpam-7078	268	21	.	.	X
ejpam-7078	268	22	let	let	VERB
ejpam-7078	268	23	y	y	PROPN
ejpam-7078	268	24	∈	∈	PROPN
ejpam-7078	268	25	ng(v	ng(v	NOUN
ejpam-7078	268	26	)	)	PUNCT
ejpam-7078	268	27	∩	∩	NOUN
ejpam-7078	268	28	ng(w	ng(w	NOUN
ejpam-7078	268	29	)	)	PUNCT
ejpam-7078	268	30	.	.	PUNCT
ejpam-7078	269	1	again	again	ADV
ejpam-7078	269	2	,	,	PUNCT
ejpam-7078	269	3	this	this	PRON
ejpam-7078	269	4	will	will	AUX
ejpam-7078	269	5	imply	imply	VERB
ejpam-7078	269	6	that	that	SCONJ
ejpam-7078	269	7	y	y	PROPN
ejpam-7078	269	8	∈	∈	PROPN
ejpam-7078	269	9	v1	v1	NOUN
ejpam-7078	269	10	.	.	PUNCT
ejpam-7078	270	1	hence	hence	ADV
ejpam-7078	270	2	,	,	PUNCT
ejpam-7078	270	3	x	x	PUNCT
ejpam-7078	270	4	=	=	PUNCT
ejpam-7078	270	5	y.	y.	PROPN
ejpam-7078	270	6	however	however	ADV
ejpam-7078	270	7	,	,	PUNCT
ejpam-7078	270	8	since	since	SCONJ
ejpam-7078	270	9	u	u	PRON
ejpam-7078	270	10	̸=	̸=	PROPN
ejpam-7078	270	11	w	w	PROPN
ejpam-7078	270	12	,	,	PUNCT
ejpam-7078	270	13	it	it	PRON
ejpam-7078	270	14	follows	follow	VERB
ejpam-7078	270	15	that	that	SCONJ
ejpam-7078	270	16	f	f	PROPN
ejpam-7078	270	17	does	do	AUX
ejpam-7078	270	18	not	not	PART
ejpam-7078	270	19	satisfy	satisfy	VERB
ejpam-7078	270	20	(	(	PUNCT
ejpam-7078	270	21	shr2	shr2	PROPN
ejpam-7078	270	22	)	)	PUNCT
ejpam-7078	270	23	,	,	PUNCT
ejpam-7078	270	24	a	a	DET
ejpam-7078	270	25	contradiction	contradiction	NOUN
ejpam-7078	270	26	.	.	PUNCT
ejpam-7078	271	1	thus	thus	ADV
ejpam-7078	271	2	,	,	PUNCT
ejpam-7078	271	3	|v	|v	PROPN
ejpam-7078	271	4	(	(	PUNCT
ejpam-7078	271	5	g)|	g)|	NOUN
ejpam-7078	271	6	=	=	SYM
ejpam-7078	271	7	3	3	NUM
ejpam-7078	271	8	and	and	CCONJ
ejpam-7078	271	9	g	g	PROPN
ejpam-7078	271	10	=	=	PROPN
ejpam-7078	271	11	p3	p3	PROPN
ejpam-7078	271	12	.	.	PUNCT
ejpam-7078	272	1	the	the	DET
ejpam-7078	272	2	converse	converse	NOUN
ejpam-7078	272	3	is	be	AUX
ejpam-7078	272	4	clear	clear	ADJ
ejpam-7078	272	5	.	.	PUNCT
ejpam-7078	273	1	theorem	theorem	ADJ
ejpam-7078	273	2	6	6	NUM
ejpam-7078	273	3	.	.	PUNCT
ejpam-7078	274	1	let	let	VERB
ejpam-7078	274	2	g	g	PRON
ejpam-7078	274	3	be	be	AUX
ejpam-7078	274	4	a	a	DET
ejpam-7078	274	5	graph	graph	NOUN
ejpam-7078	274	6	.	.	PUNCT
ejpam-7078	275	1	then	then	ADV
ejpam-7078	275	2	γshr(g	γshr(g	NUM
ejpam-7078	275	3	)	)	PUNCT
ejpam-7078	275	4	=	=	PUNCT
ejpam-7078	275	5	4	4	NUM
ejpam-7078	275	6	if	if	SCONJ
ejpam-7078	275	7	and	and	CCONJ
ejpam-7078	275	8	only	only	ADV
ejpam-7078	275	9	if	if	SCONJ
ejpam-7078	275	10	it	it	PRON
ejpam-7078	275	11	satisfies	satisfy	VERB
ejpam-7078	275	12	one	one	NUM
ejpam-7078	275	13	of	of	ADP
ejpam-7078	275	14	the	the	DET
ejpam-7078	275	15	following	following	NOUN
ejpam-7078	275	16	:	:	PUNCT
ejpam-7078	275	17	(	(	PUNCT
ejpam-7078	275	18	i	i	NOUN
ejpam-7078	275	19	)	)	PUNCT
ejpam-7078	275	20	|v	|v	PROPN
ejpam-7078	275	21	(	(	PUNCT
ejpam-7078	275	22	g)|	g)|	NOUN
ejpam-7078	275	23	=	=	NOUN
ejpam-7078	275	24	4	4	NUM
ejpam-7078	275	25	;	;	PUNCT
ejpam-7078	275	26	or	or	CCONJ
ejpam-7078	275	27	(	(	PUNCT
ejpam-7078	275	28	ii	ii	NOUN
ejpam-7078	275	29	)	)	PUNCT
ejpam-7078	275	30	v	v	NOUN
ejpam-7078	275	31	(	(	PUNCT
ejpam-7078	275	32	g	g	NOUN
ejpam-7078	275	33	)	)	PUNCT
ejpam-7078	275	34	=	=	SYM
ejpam-7078	275	35	{	{	PUNCT
ejpam-7078	275	36	x	x	NOUN
ejpam-7078	275	37	,	,	PUNCT
ejpam-7078	275	38	y	y	PROPN
ejpam-7078	275	39	,	,	PUNCT
ejpam-7078	275	40	p	p	X
ejpam-7078	275	41	,	,	PUNCT
ejpam-7078	275	42	q	q	ADJ
ejpam-7078	275	43	,	,	PUNCT
ejpam-7078	275	44	v	v	NOUN
ejpam-7078	275	45	}	}	PUNCT
ejpam-7078	275	46	such	such	ADJ
ejpam-7078	275	47	that	that	SCONJ
ejpam-7078	275	48	ng(v	ng(v	PUNCT
ejpam-7078	275	49	)	)	PUNCT
ejpam-7078	275	50	=	=	PRON
ejpam-7078	275	51	{	{	PUNCT
ejpam-7078	275	52	p	p	X
ejpam-7078	275	53	,	,	PUNCT
ejpam-7078	275	54	q	q	ADJ
ejpam-7078	275	55	}	}	PUNCT
ejpam-7078	275	56	,	,	PUNCT
ejpam-7078	275	57	n2	n2	ADJ
ejpam-7078	275	58	g(v	g(v	X
ejpam-7078	275	59	)	)	PUNCT
ejpam-7078	275	60	=	=	PRON
ejpam-7078	275	61	{	{	PUNCT
ejpam-7078	275	62	x	x	NOUN
ejpam-7078	275	63	,	,	PUNCT
ejpam-7078	275	64	y	y	PROPN
ejpam-7078	275	65	}	}	PUNCT
ejpam-7078	275	66	,	,	PUNCT
ejpam-7078	275	67	x	x	SYM
ejpam-7078	275	68	∈	∈	PROPN
ejpam-7078	275	69	n2	n2	NOUN
ejpam-7078	275	70	g(p	g(p	PROPN
ejpam-7078	275	71	)	)	PUNCT
ejpam-7078	275	72	\n2	\n2	VERB
ejpam-7078	275	73	g(q	g(q	NOUN
ejpam-7078	275	74	)	)	PUNCT
ejpam-7078	275	75	and	and	CCONJ
ejpam-7078	275	76	y	y	PROPN
ejpam-7078	275	77	∈	∈	PROPN
ejpam-7078	275	78	n2	n2	NOUN
ejpam-7078	275	79	g(q	g(q	X
ejpam-7078	275	80	)	)	PUNCT
ejpam-7078	275	81	\n2	\n2	ADJ
ejpam-7078	275	82	g(p	g(p	NOUN
ejpam-7078	275	83	)	)	PUNCT
ejpam-7078	275	84	.	.	PUNCT
ejpam-7078	276	1	l.	l.	PROPN
ejpam-7078	276	2	f.	f.	PROPN
ejpam-7078	276	3	casinillo	casinillo	PROPN
ejpam-7078	276	4	,	,	PUNCT
ejpam-7078	276	5	s.	s.	PROPN
ejpam-7078	276	6	r.	r.	PROPN
ejpam-7078	276	7	canoy	canoy	PROPN
ejpam-7078	276	8	jr	jr	PROPN
ejpam-7078	276	9	.	.	PROPN
ejpam-7078	276	10	/	/	SYM
ejpam-7078	276	11	eur	eur	PROPN
ejpam-7078	276	12	.	.	PUNCT
ejpam-7078	277	1	j.	j.	PROPN
ejpam-7078	277	2	pure	pure	PROPN
ejpam-7078	277	3	appl	appl	PROPN
ejpam-7078	277	4	.	.	PROPN
ejpam-7078	277	5	math	math	PROPN
ejpam-7078	277	6	,	,	PUNCT
ejpam-7078	277	7	18	18	NUM
ejpam-7078	277	8	(	(	PUNCT
ejpam-7078	277	9	4	4	NUM
ejpam-7078	277	10	)	)	PUNCT
ejpam-7078	277	11	(	(	PUNCT
ejpam-7078	277	12	2025	2025	NUM
ejpam-7078	277	13	)	)	PUNCT
ejpam-7078	277	14	,	,	PUNCT
ejpam-7078	277	15	7078	7078	NUM
ejpam-7078	277	16	9	9	NUM
ejpam-7078	277	17	of	of	ADP
ejpam-7078	277	18	15	15	NUM
ejpam-7078	277	19	proof	proof	NOUN
ejpam-7078	277	20	.	.	PUNCT
ejpam-7078	278	1	let	let	VERB
ejpam-7078	278	2	f	f	PROPN
ejpam-7078	278	3	=	=	SYM
ejpam-7078	278	4	(	(	PUNCT
ejpam-7078	278	5	v0	v0	PROPN
ejpam-7078	278	6	,	,	PUNCT
ejpam-7078	278	7	v1	v1	NOUN
ejpam-7078	278	8	,	,	PUNCT
ejpam-7078	278	9	v2	v2	PROPN
ejpam-7078	278	10	)	)	PUNCT
ejpam-7078	278	11	be	be	AUX
ejpam-7078	278	12	a	a	DET
ejpam-7078	278	13	γshr	γshr	NOUN
ejpam-7078	278	14	-	-	PUNCT
ejpam-7078	278	15	function	function	NOUN
ejpam-7078	278	16	on	on	ADP
ejpam-7078	278	17	g.	g.	PROPN
ejpam-7078	278	18	assume	assume	VERB
ejpam-7078	278	19	that	that	SCONJ
ejpam-7078	278	20	γshr(g	γshr(g	NOUN
ejpam-7078	278	21	)	)	PUNCT
ejpam-7078	278	22	=	=	PUNCT
ejpam-7078	279	1	4	4	X
ejpam-7078	279	2	.	.	PUNCT
ejpam-7078	279	3	then	then	ADV
ejpam-7078	279	4	|v1|	|v1|	NOUN
ejpam-7078	279	5	+	+	CCONJ
ejpam-7078	279	6	2|v2|	2|v2|	NUM
ejpam-7078	279	7	=	=	SYM
ejpam-7078	279	8	4	4	NUM
ejpam-7078	279	9	and	and	CCONJ
ejpam-7078	279	10	so	so	ADV
ejpam-7078	279	11	,	,	PUNCT
ejpam-7078	279	12	|v2|	|v2|	ADV
ejpam-7078	279	13	≤	≤	NOUN
ejpam-7078	279	14	2	2	NUM
ejpam-7078	279	15	.	.	PUNCT
ejpam-7078	280	1	first	first	ADV
ejpam-7078	280	2	,	,	PUNCT
ejpam-7078	280	3	suppose	suppose	VERB
ejpam-7078	280	4	that	that	SCONJ
ejpam-7078	280	5	|v2|	|v2|	NOUN
ejpam-7078	280	6	=	=	SYM
ejpam-7078	280	7	0	0	X
ejpam-7078	280	8	.	.	PUNCT
ejpam-7078	281	1	then	then	ADV
ejpam-7078	281	2	|v0|	|v0|	NOUN
ejpam-7078	281	3	=	=	SYM
ejpam-7078	281	4	0	0	NUM
ejpam-7078	281	5	and	and	CCONJ
ejpam-7078	281	6	|v1|	|v1|	NOUN
ejpam-7078	281	7	=	=	SYM
ejpam-7078	281	8	|v	|v	PROPN
ejpam-7078	281	9	(	(	PUNCT
ejpam-7078	281	10	g)|	g)|	NOUN
ejpam-7078	281	11	=	=	NOUN
ejpam-7078	281	12	4	4	NUM
ejpam-7078	281	13	.	.	PUNCT
ejpam-7078	282	1	next	next	ADV
ejpam-7078	282	2	,	,	PUNCT
ejpam-7078	282	3	suppose	suppose	VERB
ejpam-7078	282	4	|v2|	|v2|	NOUN
ejpam-7078	282	5	=	=	SYM
ejpam-7078	282	6	1	1	X
ejpam-7078	282	7	.	.	PUNCT
ejpam-7078	282	8	then	then	ADV
ejpam-7078	282	9	|v1|	|v1|	NOUN
ejpam-7078	282	10	=	=	SYM
ejpam-7078	282	11	1	1	NUM
ejpam-7078	282	12	and	and	CCONJ
ejpam-7078	282	13	|v0|	|v0|	NOUN
ejpam-7078	282	14	≥	≥	NUM
ejpam-7078	282	15	1	1	NUM
ejpam-7078	282	16	.	.	PUNCT
ejpam-7078	282	17	suppose	suppose	VERB
ejpam-7078	282	18	|v0|	|v0|	NOUN
ejpam-7078	282	19	≥	≥	NUM
ejpam-7078	282	20	3	3	NUM
ejpam-7078	282	21	.	.	PUNCT
ejpam-7078	283	1	let	let	VERB
ejpam-7078	283	2	a	a	DET
ejpam-7078	283	3	,	,	PUNCT
ejpam-7078	283	4	b	b	NOUN
ejpam-7078	283	5	,	,	PUNCT
ejpam-7078	283	6	c	c	PROPN
ejpam-7078	283	7	∈	∈	PROPN
ejpam-7078	283	8	v0	v0	NOUN
ejpam-7078	283	9	.	.	PUNCT
ejpam-7078	284	1	since	since	SCONJ
ejpam-7078	284	2	f	f	PROPN
ejpam-7078	284	3	satisfies	satisfie	NOUN
ejpam-7078	284	4	(	(	PUNCT
ejpam-7078	284	5	shr1	shr1	PROPN
ejpam-7078	284	6	)	)	PUNCT
ejpam-7078	284	7	,	,	PUNCT
ejpam-7078	284	8	we	we	PRON
ejpam-7078	284	9	have	have	VERB
ejpam-7078	284	10	n2	n2	ADJ
ejpam-7078	284	11	g(v	g(v	X
ejpam-7078	284	12	)	)	PUNCT
ejpam-7078	284	13	∩	∩	ADJ
ejpam-7078	284	14	v0	v0	NOUN
ejpam-7078	284	15	=	=	SYM
ejpam-7078	284	16	{	{	PUNCT
ejpam-7078	284	17	a	a	PRON
ejpam-7078	284	18	,	,	PUNCT
ejpam-7078	284	19	b	b	NOUN
ejpam-7078	284	20	,	,	PUNCT
ejpam-7078	284	21	c	c	NOUN
ejpam-7078	284	22	}	}	PUNCT
ejpam-7078	284	23	.	.	PUNCT
ejpam-7078	285	1	this	this	DET
ejpam-7078	285	2	forces	force	NOUN
ejpam-7078	285	3	|ng(p)∩v0|	|ng(p)∩v0|	PROPN
ejpam-7078	285	4	=	=	SYM
ejpam-7078	285	5	1	1	NUM
ejpam-7078	285	6	for	for	ADP
ejpam-7078	285	7	every	every	DET
ejpam-7078	285	8	p	p	PROPN
ejpam-7078	285	9	∈	∈	PROPN
ejpam-7078	285	10	v1	v1	NOUN
ejpam-7078	285	11	because	because	SCONJ
ejpam-7078	285	12	f	f	PROPN
ejpam-7078	285	13	satisfies	satisfie	NOUN
ejpam-7078	285	14	(	(	PUNCT
ejpam-7078	285	15	shr2	shr2	NOUN
ejpam-7078	285	16	)	)	PUNCT
ejpam-7078	285	17	.	.	PUNCT
ejpam-7078	286	1	however	however	ADV
ejpam-7078	286	2	,	,	PUNCT
ejpam-7078	286	3	this	this	PRON
ejpam-7078	286	4	is	be	AUX
ejpam-7078	286	5	not	not	PART
ejpam-7078	286	6	possible	possible	ADJ
ejpam-7078	286	7	because	because	SCONJ
ejpam-7078	286	8	|v1|	|v1|	NOUN
ejpam-7078	286	9	=	=	SYM
ejpam-7078	286	10	2	2	NUM
ejpam-7078	286	11	and	and	CCONJ
ejpam-7078	286	12	|v0|	|v0|	NOUN
ejpam-7078	286	13	≥	≥	PROPN
ejpam-7078	286	14	3	3	NUM
ejpam-7078	286	15	.	.	PUNCT
ejpam-7078	287	1	therefore	therefore	ADV
ejpam-7078	287	2	,	,	PUNCT
ejpam-7078	287	3	|v0|	|v0|	NOUN
ejpam-7078	287	4	≤	≤	NUM
ejpam-7078	287	5	2	2	NUM
ejpam-7078	287	6	.	.	PUNCT
ejpam-7078	288	1	consequently	consequently	ADV
ejpam-7078	288	2	,	,	PUNCT
ejpam-7078	288	3	4	4	NUM
ejpam-7078	288	4	≤	≤	NUM
ejpam-7078	288	5	|v	|v	X
ejpam-7078	288	6	(	(	PUNCT
ejpam-7078	288	7	g)|	g)|	VERB
ejpam-7078	288	8	≤	≤	NOUN
ejpam-7078	288	9	5	5	NUM
ejpam-7078	288	10	.	.	PUNCT
ejpam-7078	289	1	if	if	SCONJ
ejpam-7078	289	2	|v0|	|v0|	NOUN
ejpam-7078	289	3	=	=	SYM
ejpam-7078	289	4	1	1	NUM
ejpam-7078	289	5	,	,	PUNCT
ejpam-7078	289	6	then	then	ADV
ejpam-7078	289	7	|v	|v	PROPN
ejpam-7078	289	8	(	(	PUNCT
ejpam-7078	289	9	g)|	g)|	NOUN
ejpam-7078	289	10	=	=	SYM
ejpam-7078	289	11	4	4	X
ejpam-7078	289	12	.	.	PUNCT
ejpam-7078	289	13	suppose	suppose	VERB
ejpam-7078	289	14	|v0|	|v0|	NOUN
ejpam-7078	289	15	=	=	SYM
ejpam-7078	289	16	2	2	X
ejpam-7078	289	17	.	.	PUNCT
ejpam-7078	289	18	then	then	ADV
ejpam-7078	289	19	|v	|v	PROPN
ejpam-7078	289	20	(	(	PUNCT
ejpam-7078	289	21	g)|	g)|	NOUN
ejpam-7078	289	22	=	=	SYM
ejpam-7078	289	23	5	5	X
ejpam-7078	289	24	.	.	PUNCT
ejpam-7078	289	25	let	let	VERB
ejpam-7078	289	26	v0	v0	NOUN
ejpam-7078	289	27	=	=	SYM
ejpam-7078	289	28	{	{	PUNCT
ejpam-7078	289	29	x	x	PROPN
ejpam-7078	289	30	,	,	PUNCT
ejpam-7078	289	31	y	y	NOUN
ejpam-7078	289	32	}	}	PUNCT
ejpam-7078	289	33	,	,	PUNCT
ejpam-7078	289	34	v1	v1	NOUN
ejpam-7078	289	35	=	=	SYM
ejpam-7078	289	36	{	{	PUNCT
ejpam-7078	289	37	p	p	X
ejpam-7078	289	38	,	,	PUNCT
ejpam-7078	289	39	q	q	NOUN
ejpam-7078	289	40	}	}	PUNCT
ejpam-7078	289	41	and	and	CCONJ
ejpam-7078	289	42	v2	v2	NOUN
ejpam-7078	289	43	=	=	SYM
ejpam-7078	289	44	{	{	PUNCT
ejpam-7078	289	45	v	v	NOUN
ejpam-7078	289	46	}	}	PUNCT
ejpam-7078	289	47	.	.	PUNCT
ejpam-7078	290	1	then	then	ADV
ejpam-7078	290	2	ng(v	ng(v	PUNCT
ejpam-7078	290	3	)	)	PUNCT
ejpam-7078	290	4	∩	∩	ADJ
ejpam-7078	290	5	v0	v0	NOUN
ejpam-7078	290	6	=	=	SYM
ejpam-7078	290	7	v0	v0	NOUN
ejpam-7078	290	8	=	=	SYM
ejpam-7078	290	9	{	{	PUNCT
ejpam-7078	290	10	x	x	PROPN
ejpam-7078	290	11	,	,	PUNCT
ejpam-7078	290	12	y	y	PROPN
ejpam-7078	290	13	}	}	PUNCT
ejpam-7078	290	14	.	.	PUNCT
ejpam-7078	291	1	since	since	SCONJ
ejpam-7078	291	2	f	f	PROPN
ejpam-7078	291	3	satisfies	satisfie	NOUN
ejpam-7078	291	4	(	(	PUNCT
ejpam-7078	291	5	shr2	shr2	PROPN
ejpam-7078	291	6	)	)	PUNCT
ejpam-7078	291	7	,	,	PUNCT
ejpam-7078	291	8	we	we	PRON
ejpam-7078	291	9	may	may	AUX
ejpam-7078	291	10	assume	assume	VERB
ejpam-7078	291	11	that	that	SCONJ
ejpam-7078	291	12	n2	n2	ADJ
ejpam-7078	291	13	g(p)∩v0	g(p)∩v0	PROPN
ejpam-7078	291	14	=	=	SYM
ejpam-7078	291	15	{	{	PUNCT
ejpam-7078	291	16	x	x	NOUN
ejpam-7078	291	17	}	}	PUNCT
ejpam-7078	291	18	and	and	CCONJ
ejpam-7078	291	19	n2	n2	ADJ
ejpam-7078	291	20	g(q)∩v0	g(q)∩v0	PROPN
ejpam-7078	291	21	=	=	SYM
ejpam-7078	291	22	{	{	PUNCT
ejpam-7078	291	23	y	y	NOUN
ejpam-7078	291	24	}	}	PUNCT
ejpam-7078	291	25	.	.	PUNCT
ejpam-7078	292	1	let	let	VERB
ejpam-7078	292	2	z	z	NOUN
ejpam-7078	292	3	∈	∈	PROPN
ejpam-7078	292	4	ng(x)∩ng(v	ng(x)∩ng(v	PROPN
ejpam-7078	292	5	)	)	PUNCT
ejpam-7078	292	6	.	.	PUNCT
ejpam-7078	293	1	since	since	SCONJ
ejpam-7078	293	2	p	p	PROPN
ejpam-7078	293	3	∈	∈	PROPN
ejpam-7078	293	4	n2	n2	NOUN
ejpam-7078	293	5	g(x	g(x	PROPN
ejpam-7078	293	6	)	)	PUNCT
ejpam-7078	293	7	and	and	CCONJ
ejpam-7078	293	8	y	y	PROPN
ejpam-7078	293	9	∈	∈	PROPN
ejpam-7078	293	10	n2	n2	ADJ
ejpam-7078	293	11	g(v	g(v	PROPN
ejpam-7078	293	12	)	)	PUNCT
ejpam-7078	293	13	,	,	PUNCT
ejpam-7078	293	14	it	it	PRON
ejpam-7078	293	15	follows	follow	VERB
ejpam-7078	293	16	that	that	PRON
ejpam-7078	293	17	z	z	NOUN
ejpam-7078	293	18	/∈	/∈	PUNCT
ejpam-7078	294	1	{	{	PUNCT
ejpam-7078	294	2	p	p	X
ejpam-7078	294	3	,	,	PUNCT
ejpam-7078	294	4	y	y	PROPN
ejpam-7078	294	5	}	}	PUNCT
ejpam-7078	294	6	.	.	PUNCT
ejpam-7078	295	1	this	this	DET
ejpam-7078	295	2	forces	force	NOUN
ejpam-7078	295	3	z	z	NOUN
ejpam-7078	295	4	=	=	SYM
ejpam-7078	295	5	q.	q.	NOUN
ejpam-7078	295	6	hence	hence	ADV
ejpam-7078	295	7	,	,	PUNCT
ejpam-7078	295	8	q	q	PROPN
ejpam-7078	295	9	∈	∈	PROPN
ejpam-7078	295	10	ng(v	ng(v	PRON
ejpam-7078	295	11	)	)	PUNCT
ejpam-7078	295	12	.	.	PUNCT
ejpam-7078	296	1	similarly	similarly	ADV
ejpam-7078	296	2	,	,	PUNCT
ejpam-7078	296	3	p	p	PROPN
ejpam-7078	296	4	∈	∈	PROPN
ejpam-7078	296	5	ng(v	ng(v	PRON
ejpam-7078	296	6	)	)	PUNCT
ejpam-7078	296	7	.	.	PUNCT
ejpam-7078	297	1	this	this	PRON
ejpam-7078	297	2	shows	show	VERB
ejpam-7078	297	3	that	that	SCONJ
ejpam-7078	297	4	(	(	PUNCT
ejpam-7078	297	5	ii	ii	NOUN
ejpam-7078	297	6	)	)	PUNCT
ejpam-7078	297	7	holds	hold	VERB
ejpam-7078	297	8	.	.	PUNCT
ejpam-7078	298	1	finally	finally	ADV
ejpam-7078	298	2	,	,	PUNCT
ejpam-7078	298	3	suppose	suppose	VERB
ejpam-7078	298	4	|v2|	|v2|	NOUN
ejpam-7078	298	5	=	=	SYM
ejpam-7078	298	6	2	2	X
ejpam-7078	298	7	.	.	PUNCT
ejpam-7078	298	8	then	then	ADV
ejpam-7078	298	9	|v1|	|v1|	VERB
ejpam-7078	298	10	=	=	SYM
ejpam-7078	298	11	0	0	PUNCT
ejpam-7078	298	12	and	and	CCONJ
ejpam-7078	298	13	,	,	PUNCT
ejpam-7078	298	14	by	by	ADP
ejpam-7078	298	15	lemma	lemma	PROPN
ejpam-7078	298	16	1	1	NUM
ejpam-7078	298	17	,	,	PUNCT
ejpam-7078	298	18	|v0|	|v0|	NOUN
ejpam-7078	298	19	=	=	SYM
ejpam-7078	298	20	2	2	X
ejpam-7078	298	21	.	.	PUNCT
ejpam-7078	299	1	it	it	PRON
ejpam-7078	299	2	follows	follow	VERB
ejpam-7078	299	3	that	that	SCONJ
ejpam-7078	299	4	|v	|v	PROPN
ejpam-7078	299	5	(	(	PUNCT
ejpam-7078	299	6	g)|	g)|	NOUN
ejpam-7078	299	7	=	=	NOUN
ejpam-7078	299	8	4	4	NUM
ejpam-7078	299	9	.	.	X
ejpam-7078	299	10	for	for	ADP
ejpam-7078	299	11	the	the	DET
ejpam-7078	299	12	converse	converse	NOUN
ejpam-7078	299	13	,	,	PUNCT
ejpam-7078	299	14	suppose	suppose	VERB
ejpam-7078	299	15	first	first	ADV
ejpam-7078	299	16	that	that	SCONJ
ejpam-7078	299	17	|v	|v	PROPN
ejpam-7078	299	18	(	(	PUNCT
ejpam-7078	299	19	g)|	g)|	NOUN
ejpam-7078	299	20	=	=	NOUN
ejpam-7078	299	21	4	4	NUM
ejpam-7078	299	22	.	.	PUNCT
ejpam-7078	299	23	by	by	ADP
ejpam-7078	299	24	theorem	theorem	NOUN
ejpam-7078	299	25	4	4	NUM
ejpam-7078	299	26	and	and	CCONJ
ejpam-7078	299	27	proposition	proposition	NOUN
ejpam-7078	299	28	3	3	NUM
ejpam-7078	299	29	,	,	PUNCT
ejpam-7078	299	30	we	we	PRON
ejpam-7078	299	31	have	have	VERB
ejpam-7078	299	32	γshr(g	γshr(g	NOUN
ejpam-7078	299	33	)	)	PUNCT
ejpam-7078	299	34	=	=	PUNCT
ejpam-7078	300	1	4	4	X
ejpam-7078	300	2	.	.	PUNCT
ejpam-7078	301	1	next	next	ADV
ejpam-7078	301	2	,	,	PUNCT
ejpam-7078	301	3	suppose	suppose	VERB
ejpam-7078	301	4	that	that	SCONJ
ejpam-7078	301	5	(	(	PUNCT
ejpam-7078	301	6	ii	ii	NOUN
ejpam-7078	301	7	)	)	PUNCT
ejpam-7078	301	8	holds	hold	VERB
ejpam-7078	301	9	.	.	PUNCT
ejpam-7078	302	1	let	let	VERB
ejpam-7078	302	2	v0	v0	NOUN
ejpam-7078	302	3	=	=	SYM
ejpam-7078	302	4	{	{	PUNCT
ejpam-7078	302	5	x	x	PROPN
ejpam-7078	302	6	,	,	PUNCT
ejpam-7078	302	7	y	y	NOUN
ejpam-7078	302	8	}	}	PUNCT
ejpam-7078	302	9	,	,	PUNCT
ejpam-7078	302	10	v1	v1	NOUN
ejpam-7078	302	11	=	=	SYM
ejpam-7078	302	12	{	{	PUNCT
ejpam-7078	302	13	p	p	X
ejpam-7078	302	14	,	,	PUNCT
ejpam-7078	302	15	q	q	NOUN
ejpam-7078	302	16	}	}	PUNCT
ejpam-7078	302	17	,	,	PUNCT
ejpam-7078	302	18	and	and	CCONJ
ejpam-7078	302	19	v2	v2	NOUN
ejpam-7078	302	20	=	=	SYM
ejpam-7078	302	21	{	{	PUNCT
ejpam-7078	302	22	v	v	NOUN
ejpam-7078	302	23	}	}	PUNCT
ejpam-7078	302	24	.	.	PUNCT
ejpam-7078	303	1	by	by	ADP
ejpam-7078	303	2	assumption	assumption	NOUN
ejpam-7078	303	3	,	,	PUNCT
ejpam-7078	303	4	h	h	NOUN
ejpam-7078	303	5	=	=	SYM
ejpam-7078	303	6	(	(	PUNCT
ejpam-7078	303	7	v0	v0	PROPN
ejpam-7078	303	8	,	,	PUNCT
ejpam-7078	303	9	v1	v1	NOUN
ejpam-7078	303	10	,	,	PUNCT
ejpam-7078	303	11	v2	v2	PROPN
ejpam-7078	303	12	)	)	PUNCT
ejpam-7078	303	13	is	be	AUX
ejpam-7078	303	14	an	an	DET
ejpam-7078	303	15	shrdf	shrdf	NOUN
ejpam-7078	303	16	on	on	ADP
ejpam-7078	303	17	g.	g.	PROPN
ejpam-7078	303	18	hence	hence	ADV
ejpam-7078	303	19	,	,	PUNCT
ejpam-7078	303	20	proposition	proposition	NOUN
ejpam-7078	303	21	3	3	NUM
ejpam-7078	303	22	would	would	AUX
ejpam-7078	303	23	imply	imply	VERB
ejpam-7078	303	24	that	that	DET
ejpam-7078	303	25	γshr(g	γshr(g	NOUN
ejpam-7078	303	26	)	)	PUNCT
ejpam-7078	303	27	=	=	PUNCT
ejpam-7078	303	28	ωshr	ωshr	NOUN
ejpam-7078	303	29	g	g	PROPN
ejpam-7078	303	30	(	(	PUNCT
ejpam-7078	303	31	h	h	NOUN
ejpam-7078	303	32	)	)	PUNCT
ejpam-7078	303	33	=	=	SYM
ejpam-7078	303	34	4	4	X
ejpam-7078	303	35	.	.	X
ejpam-7078	303	36	proposition	proposition	NOUN
ejpam-7078	303	37	4	4	NUM
ejpam-7078	303	38	.	.	PUNCT
ejpam-7078	304	1	let	let	VERB
ejpam-7078	304	2	g	g	PROPN
ejpam-7078	304	3	=	=	VERB
ejpam-7078	304	4	pn	pn	PROPN
ejpam-7078	304	5	with	with	ADP
ejpam-7078	304	6	n	n	PRON
ejpam-7078	304	7	≥	≥	NUM
ejpam-7078	304	8	1	1	NUM
ejpam-7078	304	9	.	.	PUNCT
ejpam-7078	305	1	then	then	ADV
ejpam-7078	305	2	γshr(g	γshr(g	NUM
ejpam-7078	305	3	)	)	PUNCT
ejpam-7078	305	4	=	=	SYM
ejpam-7078	305	5	{	{	PUNCT
ejpam-7078	305	6	n	n	CCONJ
ejpam-7078	305	7	,	,	PUNCT
ejpam-7078	305	8	if	if	SCONJ
ejpam-7078	305	9	n	n	PRON
ejpam-7078	305	10	≤	≤	NUM
ejpam-7078	305	11	8	8	NUM
ejpam-7078	305	12	,	,	PUNCT
ejpam-7078	305	13	n−	n−	NOUN
ejpam-7078	305	14	k	k	NOUN
ejpam-7078	305	15	,	,	PUNCT
ejpam-7078	305	16	if	if	SCONJ
ejpam-7078	305	17	n	n	PRON
ejpam-7078	305	18	≥	≥	NOUN
ejpam-7078	305	19	9	9	NUM
ejpam-7078	305	20	,	,	PUNCT
ejpam-7078	305	21	where	where	SCONJ
ejpam-7078	305	22	k	k	PROPN
ejpam-7078	305	23	=	=	PUNCT
ejpam-7078	305	24	⌊n+1	⌊n+1	NOUN
ejpam-7078	305	25	10	10	NUM
ejpam-7078	305	26	⌋.	⌋.	ADV
ejpam-7078	305	27	proof	proof	NOUN
ejpam-7078	305	28	.	.	PUNCT
ejpam-7078	306	1	assume	assume	VERB
ejpam-7078	306	2	that	that	SCONJ
ejpam-7078	306	3	g	g	PROPN
ejpam-7078	306	4	=	=	PUNCT
ejpam-7078	306	5	pn	pn	PROPN
ejpam-7078	306	6	=	=	PUNCT
ejpam-7078	307	1	[	[	X
ejpam-7078	307	2	v1	v1	NOUN
ejpam-7078	307	3	,	,	PUNCT
ejpam-7078	307	4	v2	v2	PROPN
ejpam-7078	307	5	,	,	PUNCT
ejpam-7078	307	6	...	...	PUNCT
ejpam-7078	307	7	,	,	PUNCT
ejpam-7078	307	8	vn	vn	X
ejpam-7078	307	9	]	]	X
ejpam-7078	307	10	with	with	ADP
ejpam-7078	307	11	n	n	PRON
ejpam-7078	307	12	≥	≥	NUM
ejpam-7078	307	13	1	1	NUM
ejpam-7078	307	14	.	.	PUNCT
ejpam-7078	308	1	let	let	VERB
ejpam-7078	308	2	f	f	PROPN
ejpam-7078	308	3	=	=	SYM
ejpam-7078	308	4	(	(	PUNCT
ejpam-7078	308	5	v0	v0	PROPN
ejpam-7078	308	6	,	,	PUNCT
ejpam-7078	308	7	v1	v1	NOUN
ejpam-7078	308	8	,	,	PUNCT
ejpam-7078	308	9	v2	v2	PROPN
ejpam-7078	308	10	)	)	PUNCT
ejpam-7078	308	11	be	be	AUX
ejpam-7078	308	12	a	a	DET
ejpam-7078	308	13	γshr	γshr	NOUN
ejpam-7078	308	14	-	-	PUNCT
ejpam-7078	308	15	function	function	NOUN
ejpam-7078	308	16	on	on	ADP
ejpam-7078	308	17	g	g	PROPN
ejpam-7078	308	18	and	and	CCONJ
ejpam-7078	308	19	let	let	VERB
ejpam-7078	308	20	n	n	PRON
ejpam-7078	308	21	≤	≤	ADV
ejpam-7078	308	22	8	8	NUM
ejpam-7078	308	23	.	.	PUNCT
ejpam-7078	309	1	if	if	SCONJ
ejpam-7078	309	2	v1	v1	PROPN
ejpam-7078	309	3	=	=	SYM
ejpam-7078	309	4	v	v	NOUN
ejpam-7078	309	5	(	(	PUNCT
ejpam-7078	309	6	g	g	NOUN
ejpam-7078	309	7	)	)	PUNCT
ejpam-7078	309	8	,	,	PUNCT
ejpam-7078	309	9	then	then	ADV
ejpam-7078	309	10	we	we	PRON
ejpam-7078	309	11	are	be	AUX
ejpam-7078	309	12	done	do	VERB
ejpam-7078	309	13	.	.	PUNCT
ejpam-7078	310	1	assume	assume	VERB
ejpam-7078	310	2	for	for	ADP
ejpam-7078	310	3	a	a	DET
ejpam-7078	310	4	moment	moment	NOUN
ejpam-7078	310	5	that	that	SCONJ
ejpam-7078	310	6	γshr(g	γshr(g	NOUN
ejpam-7078	310	7	)	)	PUNCT
ejpam-7078	310	8	<	<	X
ejpam-7078	310	9	n.	n.	PROPN
ejpam-7078	310	10	then	then	ADV
ejpam-7078	310	11	v1	v1	VERB
ejpam-7078	310	12	̸=	̸=	PROPN
ejpam-7078	310	13	v	v	NOUN
ejpam-7078	310	14	(	(	PUNCT
ejpam-7078	310	15	g	g	NOUN
ejpam-7078	310	16	)	)	PUNCT
ejpam-7078	310	17	and	and	CCONJ
ejpam-7078	310	18	by	by	ADP
ejpam-7078	310	19	proposition	proposition	NOUN
ejpam-7078	310	20	2	2	NUM
ejpam-7078	310	21	,	,	PUNCT
ejpam-7078	310	22	it	it	PRON
ejpam-7078	310	23	follows	follow	VERB
ejpam-7078	310	24	that	that	SCONJ
ejpam-7078	310	25	|v0|	|v0|	NOUN
ejpam-7078	310	26	>	>	X
ejpam-7078	310	27	|v2|	|v2|	NOUN
ejpam-7078	310	28	.	.	PUNCT
ejpam-7078	311	1	this	this	PRON
ejpam-7078	311	2	implies	imply	VERB
ejpam-7078	311	3	that	that	SCONJ
ejpam-7078	311	4	there	there	PRON
ejpam-7078	311	5	exists	exist	VERB
ejpam-7078	311	6	u	u	PROPN
ejpam-7078	311	7	∈	∈	PROPN
ejpam-7078	311	8	v2	v2	NOUN
ejpam-7078	311	9	such	such	ADJ
ejpam-7078	311	10	that	that	SCONJ
ejpam-7078	311	11	|n2	|n2	PROPN
ejpam-7078	311	12	g(u)∩v0|	g(u)∩v0|	NOUN
ejpam-7078	311	13	=	=	SYM
ejpam-7078	311	14	2	2	X
ejpam-7078	311	15	.	.	PUNCT
ejpam-7078	312	1	let	let	VERB
ejpam-7078	312	2	x	x	PRON
ejpam-7078	312	3	,	,	PUNCT
ejpam-7078	312	4	y	y	PROPN
ejpam-7078	312	5	∈	∈	PROPN
ejpam-7078	312	6	n2	n2	PROPN
ejpam-7078	312	7	g(u)∩v0	g(u)∩v0	PROPN
ejpam-7078	312	8	.	.	PUNCT
ejpam-7078	313	1	then	then	ADV
ejpam-7078	313	2	by	by	ADP
ejpam-7078	313	3	definition	definition	NOUN
ejpam-7078	313	4	of	of	ADP
ejpam-7078	313	5	super	super	ADJ
ejpam-7078	313	6	dominating	dominating	NOUN
ejpam-7078	313	7	set	set	NOUN
ejpam-7078	313	8	,	,	PUNCT
ejpam-7078	313	9	there	there	PRON
ejpam-7078	313	10	exists	exist	VERB
ejpam-7078	313	11	a	a	DET
ejpam-7078	313	12	,	,	PUNCT
ejpam-7078	313	13	b	b	PROPN
ejpam-7078	313	14	∈	∈	PROPN
ejpam-7078	313	15	v1	v1	NOUN
ejpam-7078	313	16	∪	∪	VERB
ejpam-7078	313	17	v2	v2	NOUN
ejpam-7078	313	18	such	such	ADJ
ejpam-7078	313	19	that	that	DET
ejpam-7078	313	20	n2	n2	PROPN
ejpam-7078	313	21	g(a	g(a	PROPN
ejpam-7078	313	22	)	)	PUNCT
ejpam-7078	313	23	∩	∩	ADJ
ejpam-7078	313	24	v0	v0	NOUN
ejpam-7078	313	25	=	=	SYM
ejpam-7078	313	26	{	{	PUNCT
ejpam-7078	313	27	x	x	NOUN
ejpam-7078	313	28	}	}	PUNCT
ejpam-7078	313	29	and	and	CCONJ
ejpam-7078	313	30	n2	n2	ADJ
ejpam-7078	313	31	g(b	g(b	PROPN
ejpam-7078	313	32	)	)	PUNCT
ejpam-7078	313	33	∩	∩	ADJ
ejpam-7078	313	34	v0	v0	NOUN
ejpam-7078	313	35	=	=	SYM
ejpam-7078	313	36	{	{	PUNCT
ejpam-7078	313	37	y	y	NOUN
ejpam-7078	313	38	}	}	PUNCT
ejpam-7078	313	39	.	.	PUNCT
ejpam-7078	314	1	clearly	clearly	ADV
ejpam-7078	314	2	,	,	PUNCT
ejpam-7078	314	3	u	u	NOUN
ejpam-7078	314	4	/∈	/∈	PUNCT
ejpam-7078	314	5	{	{	PUNCT
ejpam-7078	314	6	a	a	PRON
ejpam-7078	314	7	,	,	PUNCT
ejpam-7078	314	8	b	b	NOUN
ejpam-7078	314	9	}	}	PUNCT
ejpam-7078	314	10	.	.	PUNCT
ejpam-7078	315	1	hence	hence	ADV
ejpam-7078	315	2	,	,	PUNCT
ejpam-7078	315	3	n	n	PRON
ejpam-7078	315	4	≥	≥	NOUN
ejpam-7078	315	5	9	9	NUM
ejpam-7078	315	6	,	,	PUNCT
ejpam-7078	315	7	a	a	DET
ejpam-7078	315	8	contradiction	contradiction	NOUN
ejpam-7078	315	9	since	since	SCONJ
ejpam-7078	315	10	n	n	ADV
ejpam-7078	315	11	≤	≤	NUM
ejpam-7078	315	12	8	8	NUM
ejpam-7078	315	13	.	.	PUNCT
ejpam-7078	316	1	thus	thus	ADV
ejpam-7078	316	2	,	,	PUNCT
ejpam-7078	316	3	γshr(g	γshr(g	NOUN
ejpam-7078	316	4	)	)	PUNCT
ejpam-7078	316	5	=	=	SYM
ejpam-7078	317	1	n	n	ADV
ejpam-7078	317	2	whenever	whenever	SCONJ
ejpam-7078	317	3	n	n	PRON
ejpam-7078	317	4	≤	≤	NUM
ejpam-7078	317	5	8	8	NUM
ejpam-7078	317	6	.	.	PUNCT
ejpam-7078	318	1	now	now	ADV
ejpam-7078	318	2	,	,	PUNCT
ejpam-7078	318	3	let	let	VERB
ejpam-7078	318	4	n	n	PRON
ejpam-7078	318	5	≥	≥	NOUN
ejpam-7078	318	6	9	9	NUM
ejpam-7078	318	7	.	.	PUNCT
ejpam-7078	319	1	then	then	ADV
ejpam-7078	319	2	,	,	PUNCT
ejpam-7078	319	3	consider	consider	VERB
ejpam-7078	319	4	the	the	DET
ejpam-7078	319	5	following	follow	VERB
ejpam-7078	319	6	cases	case	NOUN
ejpam-7078	319	7	:	:	PUNCT
ejpam-7078	319	8	case	case	NOUN
ejpam-7078	319	9	1	1	NUM
ejpam-7078	319	10	:	:	PUNCT
ejpam-7078	319	11	n	n	NUM
ejpam-7078	319	12	≡	≡	PROPN
ejpam-7078	319	13	0	0	PUNCT
ejpam-7078	320	1	(	(	PUNCT
ejpam-7078	320	2	mod	mod	PROPN
ejpam-7078	320	3	10	10	NUM
ejpam-7078	320	4	)	)	PUNCT
ejpam-7078	320	5	let	let	VERB
ejpam-7078	320	6	n	n	NOUN
ejpam-7078	320	7	=	=	NOUN
ejpam-7078	320	8	10k	10k	NOUN
ejpam-7078	321	1	where	where	SCONJ
ejpam-7078	321	2	k	k	PROPN
ejpam-7078	321	3	∈	∈	PROPN
ejpam-7078	321	4	n.	n.	NOUN
ejpam-7078	321	5	then	then	ADV
ejpam-7078	321	6	k	k	PROPN
ejpam-7078	321	7	=	=	PUNCT
ejpam-7078	321	8	⌊n+1	⌊n+1	NOUN
ejpam-7078	322	1	10	10	NUM
ejpam-7078	322	2	⌋	⌋	NOUN
ejpam-7078	322	3	=	=	PUNCT
ejpam-7078	322	4	n	n	PRON
ejpam-7078	322	5	10	10	NUM
ejpam-7078	322	6	.	.	PUNCT
ejpam-7078	323	1	now	now	ADV
ejpam-7078	323	2	,	,	PUNCT
ejpam-7078	323	3	let	let	VERB
ejpam-7078	323	4	si	si	X
ejpam-7078	323	5	=	=	VERB
ejpam-7078	323	6	{	{	PUNCT
ejpam-7078	323	7	v10i−9	v10i−9	NOUN
ejpam-7078	323	8	,	,	PUNCT
ejpam-7078	323	9	v10i−1	v10i−1	NOUN
ejpam-7078	323	10	,	,	PUNCT
ejpam-7078	323	11	v10i	v10i	PUNCT
ejpam-7078	323	12	}	}	PUNCT
ejpam-7078	323	13	and	and	CCONJ
ejpam-7078	323	14	di	di	X
ejpam-7078	323	15	=	=	PUNCT
ejpam-7078	323	16	{	{	PUNCT
ejpam-7078	323	17	v10i−6	v10i−6	NOUN
ejpam-7078	323	18	,	,	PUNCT
ejpam-7078	323	19	v10i−5	v10i−5	NOUN
ejpam-7078	323	20	,	,	PUNCT
ejpam-7078	323	21	v10i−4	v10i−4	ADP
ejpam-7078	323	22	}	}	PUNCT
ejpam-7078	323	23	for	for	ADP
ejpam-7078	323	24	each	each	DET
ejpam-7078	323	25	i	i	PRON
ejpam-7078	323	26	∈	∈	PROPN
ejpam-7078	323	27	{	{	PUNCT
ejpam-7078	323	28	1	1	NUM
ejpam-7078	323	29	,	,	PUNCT
ejpam-7078	323	30	2	2	NUM
ejpam-7078	323	31	,	,	PUNCT
ejpam-7078	323	32	...	...	PUNCT
ejpam-7078	323	33	,	,	PUNCT
ejpam-7078	323	34	k	k	NOUN
ejpam-7078	323	35	}	}	PUNCT
ejpam-7078	323	36	.	.	PUNCT
ejpam-7078	324	1	set	set	VERB
ejpam-7078	324	2	w1	w1	NOUN
ejpam-7078	324	3	=	=	SYM
ejpam-7078	324	4	k⋃	k⋃	X
ejpam-7078	324	5	i=1	i=1	X
ejpam-7078	324	6	si	si	PROPN
ejpam-7078	324	7	,	,	PUNCT
ejpam-7078	324	8	w2	w2	NOUN
ejpam-7078	324	9	=	=	PUNCT
ejpam-7078	324	10	k⋃	k⋃	PROPN
ejpam-7078	324	11	i=1	i=1	PROPN
ejpam-7078	324	12	di	di	PROPN
ejpam-7078	324	13	and	and	CCONJ
ejpam-7078	324	14	w0	w0	PROPN
ejpam-7078	324	15	=	=	PROPN
ejpam-7078	324	16	v	v	PROPN
ejpam-7078	324	17	(	(	PUNCT
ejpam-7078	324	18	g	g	NOUN
ejpam-7078	324	19	)	)	PUNCT
ejpam-7078	324	20	\	\	PUNCT
ejpam-7078	324	21	(	(	PUNCT
ejpam-7078	324	22	w1	w1	NOUN
ejpam-7078	324	23	∪w2	∪w2	NOUN
ejpam-7078	324	24	)	)	PUNCT
ejpam-7078	324	25	.	.	PUNCT
ejpam-7078	325	1	then	then	ADV
ejpam-7078	325	2	,	,	PUNCT
ejpam-7078	325	3	g	g	PROPN
ejpam-7078	325	4	=	=	PUNCT
ejpam-7078	325	5	(	(	PUNCT
ejpam-7078	325	6	w0,w1,w2	w0,w1,w2	PROPN
ejpam-7078	325	7	)	)	PUNCT
ejpam-7078	325	8	is	be	AUX
ejpam-7078	325	9	an	an	DET
ejpam-7078	325	10	hrdf	hrdf	NOUN
ejpam-7078	325	11	on	on	ADP
ejpam-7078	325	12	g.	g.	PROPN
ejpam-7078	325	13	then	then	ADV
ejpam-7078	325	14	,	,	PUNCT
ejpam-7078	325	15	it	it	PRON
ejpam-7078	325	16	is	be	AUX
ejpam-7078	325	17	easy	easy	ADJ
ejpam-7078	325	18	to	to	PART
ejpam-7078	325	19	see	see	VERB
ejpam-7078	325	20	that	that	PRON
ejpam-7078	325	21	for	for	ADP
ejpam-7078	325	22	every	every	DET
ejpam-7078	325	23	v	v	NOUN
ejpam-7078	325	24	=	=	SYM
ejpam-7078	325	25	vj	vj	PROPN
ejpam-7078	325	26	∈	∈	PROPN
ejpam-7078	325	27	w0	w0	PROPN
ejpam-7078	325	28	,	,	PUNCT
ejpam-7078	325	29	there	there	PRON
ejpam-7078	325	30	exists	exist	VERB
ejpam-7078	325	31	u	u	NOUN
ejpam-7078	325	32	=	=	PROPN
ejpam-7078	325	33	vt	vt	PROPN
ejpam-7078	325	34	∈	∈	PROPN
ejpam-7078	325	35	w2	w2	NOUN
ejpam-7078	325	36	such	such	ADJ
ejpam-7078	325	37	that	that	DET
ejpam-7078	325	38	dg(u	dg(u	ADJ
ejpam-7078	325	39	,	,	PUNCT
ejpam-7078	325	40	v	v	NOUN
ejpam-7078	325	41	)	)	PUNCT
ejpam-7078	325	42	=	=	SYM
ejpam-7078	325	43	2	2	NUM
ejpam-7078	325	44	and	and	CCONJ
ejpam-7078	325	45	there	there	PRON
ejpam-7078	325	46	exists	exist	VERB
ejpam-7078	325	47	w	w	NOUN
ejpam-7078	325	48	=	=	VERB
ejpam-7078	325	49	vl	vl	PROPN
ejpam-7078	325	50	∈	∈	PROPN
ejpam-7078	325	51	(	(	PUNCT
ejpam-7078	325	52	w1	w1	NOUN
ejpam-7078	325	53	∪w2	∪w2	NOUN
ejpam-7078	325	54	)	)	PUNCT
ejpam-7078	325	55	such	such	ADJ
ejpam-7078	325	56	that	that	DET
ejpam-7078	325	57	n2	n2	PROPN
ejpam-7078	325	58	g(w)∩w0	g(w)∩w0	PROPN
ejpam-7078	325	59	=	=	PUNCT
ejpam-7078	325	60	{	{	PUNCT
ejpam-7078	325	61	v	v	NOUN
ejpam-7078	325	62	}	}	PUNCT
ejpam-7078	325	63	.	.	PUNCT
ejpam-7078	326	1	by	by	ADP
ejpam-7078	326	2	construction	construction	NOUN
ejpam-7078	326	3	,	,	PUNCT
ejpam-7078	326	4	it	it	PRON
ejpam-7078	326	5	follows	follow	VERB
ejpam-7078	326	6	that	that	SCONJ
ejpam-7078	326	7	g	g	PROPN
ejpam-7078	326	8	is	be	AUX
ejpam-7078	326	9	a	a	DET
ejpam-7078	326	10	γshr	γshr	NOUN
ejpam-7078	326	11	-	-	PUNCT
ejpam-7078	326	12	function	function	NOUN
ejpam-7078	326	13	on	on	ADP
ejpam-7078	326	14	g.	g.	PROPN
ejpam-7078	326	15	thus	thus	ADV
ejpam-7078	326	16	,	,	PUNCT
ejpam-7078	326	17	we	we	PRON
ejpam-7078	326	18	get	get	VERB
ejpam-7078	326	19	γshr(g	γshr(g	NOUN
ejpam-7078	326	20	)	)	PUNCT
ejpam-7078	326	21	=	=	PUNCT
ejpam-7078	326	22	ωshr	ωshr	NOUN
ejpam-7078	326	23	g	g	PROPN
ejpam-7078	326	24	(	(	PUNCT
ejpam-7078	326	25	g	g	NOUN
ejpam-7078	326	26	)	)	PUNCT
ejpam-7078	326	27	=	=	SYM
ejpam-7078	326	28	|w1|+	|w1|+	PROPN
ejpam-7078	326	29	2|w2|	2|w2|	NUM
ejpam-7078	327	1	=	=	SYM
ejpam-7078	327	2	k∑	k∑	PROPN
ejpam-7078	328	1	i=1	i=1	PROPN
ejpam-7078	328	2	|si|+	|si|+	PROPN
ejpam-7078	328	3	2	2	NUM
ejpam-7078	328	4	k∑	k∑	NOUN
ejpam-7078	328	5	i=1	i=1	PROPN
ejpam-7078	329	1	|di|	|di|	PROPN
ejpam-7078	329	2	l.	l.	PROPN
ejpam-7078	329	3	f.	f.	PROPN
ejpam-7078	329	4	casinillo	casinillo	PROPN
ejpam-7078	329	5	,	,	PUNCT
ejpam-7078	329	6	s.	s.	PROPN
ejpam-7078	329	7	r.	r.	PROPN
ejpam-7078	329	8	canoy	canoy	PROPN
ejpam-7078	329	9	jr	jr	PROPN
ejpam-7078	329	10	.	.	PROPN
ejpam-7078	329	11	/	/	SYM
ejpam-7078	329	12	eur	eur	PROPN
ejpam-7078	329	13	.	.	PUNCT
ejpam-7078	330	1	j.	j.	PROPN
ejpam-7078	330	2	pure	pure	PROPN
ejpam-7078	330	3	appl	appl	PROPN
ejpam-7078	330	4	.	.	PROPN
ejpam-7078	330	5	math	math	PROPN
ejpam-7078	330	6	,	,	PUNCT
ejpam-7078	330	7	18	18	NUM
ejpam-7078	330	8	(	(	PUNCT
ejpam-7078	330	9	4	4	NUM
ejpam-7078	330	10	)	)	PUNCT
ejpam-7078	330	11	(	(	PUNCT
ejpam-7078	330	12	2025	2025	NUM
ejpam-7078	330	13	)	)	PUNCT
ejpam-7078	330	14	,	,	PUNCT
ejpam-7078	330	15	7078	7078	NUM
ejpam-7078	330	16	10	10	NUM
ejpam-7078	330	17	of	of	ADP
ejpam-7078	330	18	15	15	NUM
ejpam-7078	330	19	=	=	SYM
ejpam-7078	330	20	3k	3k	NOUN
ejpam-7078	330	21	+	+	CCONJ
ejpam-7078	330	22	2(3k	2(3k	X
ejpam-7078	330	23	)	)	PUNCT
ejpam-7078	330	24	=	=	SYM
ejpam-7078	331	1	9k	9k	NUM
ejpam-7078	331	2	=	=	NOUN
ejpam-7078	331	3	10k	10k	NOUN
ejpam-7078	331	4	−	−	PROPN
ejpam-7078	331	5	k	k	NOUN
ejpam-7078	332	1	=	=	PUNCT
ejpam-7078	332	2	n−	n−	PROPN
ejpam-7078	332	3	k	k	NOUN
ejpam-7078	332	4	where	where	SCONJ
ejpam-7078	332	5	k	k	NOUN
ejpam-7078	332	6	=	=	PUNCT
ejpam-7078	332	7	n	n	PROPN
ejpam-7078	332	8	10	10	NUM
ejpam-7078	332	9	.	.	PUNCT
ejpam-7078	333	1	case	case	NOUN
ejpam-7078	333	2	2	2	NUM
ejpam-7078	333	3	:	:	PUNCT
ejpam-7078	333	4	n	n	NUM
ejpam-7078	333	5	≡	≡	PROPN
ejpam-7078	333	6	r	r	NOUN
ejpam-7078	333	7	(	(	PUNCT
ejpam-7078	333	8	mod	mod	PROPN
ejpam-7078	333	9	10	10	NUM
ejpam-7078	333	10	)	)	PUNCT
ejpam-7078	333	11	where	where	SCONJ
ejpam-7078	333	12	1	1	NUM
ejpam-7078	333	13	≤	≤	NOUN
ejpam-7078	333	14	r	r	NOUN
ejpam-7078	333	15	≤	≤	NUM
ejpam-7078	333	16	8	8	NUM
ejpam-7078	333	17	let	let	VERB
ejpam-7078	333	18	n	n	NOUN
ejpam-7078	333	19	=	=	NOUN
ejpam-7078	333	20	10k	10k	NOUN
ejpam-7078	333	21	+	+	CCONJ
ejpam-7078	333	22	r	r	NOUN
ejpam-7078	333	23	where	where	SCONJ
ejpam-7078	333	24	k	k	PROPN
ejpam-7078	333	25	∈	∈	PROPN
ejpam-7078	333	26	n	n	PRON
ejpam-7078	333	27	and	and	CCONJ
ejpam-7078	333	28	1	1	NUM
ejpam-7078	333	29	≤	≤	NOUN
ejpam-7078	333	30	r	r	NOUN
ejpam-7078	333	31	≤	≤	NUM
ejpam-7078	333	32	8	8	NUM
ejpam-7078	333	33	.	.	PUNCT
ejpam-7078	334	1	then	then	ADV
ejpam-7078	334	2	k	k	PROPN
ejpam-7078	334	3	=	=	PUNCT
ejpam-7078	334	4	⌊n+1	⌊n+1	NUM
ejpam-7078	334	5	10	10	NUM
ejpam-7078	334	6	⌋	⌋	NOUN
ejpam-7078	334	7	=	=	PUNCT
ejpam-7078	334	8	n−r	n−r	NOUN
ejpam-7078	334	9	10	10	NUM
ejpam-7078	334	10	where	where	SCONJ
ejpam-7078	334	11	r	r	NOUN
ejpam-7078	334	12	∈	∈	PROPN
ejpam-7078	334	13	{	{	PUNCT
ejpam-7078	334	14	1	1	NUM
ejpam-7078	334	15	,	,	PUNCT
ejpam-7078	334	16	2	2	NUM
ejpam-7078	334	17	,	,	PUNCT
ejpam-7078	334	18	...	...	PUNCT
ejpam-7078	334	19	,	,	PUNCT
ejpam-7078	334	20	8	8	NUM
ejpam-7078	334	21	}	}	PUNCT
ejpam-7078	334	22	.	.	PUNCT
ejpam-7078	335	1	in	in	ADP
ejpam-7078	335	2	view	view	NOUN
ejpam-7078	335	3	of	of	ADP
ejpam-7078	335	4	case	case	NOUN
ejpam-7078	335	5	1	1	NUM
ejpam-7078	335	6	,	,	PUNCT
ejpam-7078	335	7	we	we	PRON
ejpam-7078	335	8	let	let	VERB
ejpam-7078	335	9	s′	s′	ADJ
ejpam-7078	335	10	i	i	PRON
ejpam-7078	335	11	=	=	SYM
ejpam-7078	335	12	{	{	PUNCT
ejpam-7078	335	13	v10i−9	v10i−9	NOUN
ejpam-7078	335	14	,	,	PUNCT
ejpam-7078	335	15	v10i−1	v10i−1	NOUN
ejpam-7078	335	16	,	,	PUNCT
ejpam-7078	335	17	v10i	v10i	PUNCT
ejpam-7078	335	18	}	}	PUNCT
ejpam-7078	335	19	andd′	andd′	PROPN
ejpam-7078	336	1	i	i	PRON
ejpam-7078	336	2	=	=	X
ejpam-7078	336	3	{	{	PUNCT
ejpam-7078	336	4	v10i−6	v10i−6	NOUN
ejpam-7078	336	5	,	,	PUNCT
ejpam-7078	336	6	v10i−5	v10i−5	NOUN
ejpam-7078	336	7	,	,	PUNCT
ejpam-7078	336	8	v10i−4	v10i−4	ADP
ejpam-7078	336	9	}	}	PUNCT
ejpam-7078	336	10	for	for	ADP
ejpam-7078	336	11	each	each	DET
ejpam-7078	336	12	i	i	PRON
ejpam-7078	336	13	∈	∈	PROPN
ejpam-7078	336	14	{	{	PUNCT
ejpam-7078	336	15	1	1	NUM
ejpam-7078	336	16	,	,	PUNCT
ejpam-7078	336	17	2	2	NUM
ejpam-7078	336	18	,	,	PUNCT
ejpam-7078	336	19	...	...	PUNCT
ejpam-7078	336	20	,	,	PUNCT
ejpam-7078	336	21	k	k	NOUN
ejpam-7078	336	22	}	}	PUNCT
ejpam-7078	336	23	.	.	PUNCT
ejpam-7078	337	1	again	again	ADV
ejpam-7078	337	2	,	,	PUNCT
ejpam-7078	337	3	set	set	VERB
ejpam-7078	337	4	w	w	NOUN
ejpam-7078	337	5	′	′	NOUN
ejpam-7078	337	6	1	1	NUM
ejpam-7078	337	7	=	=	SYM
ejpam-7078	337	8	(	(	PUNCT
ejpam-7078	337	9	k⋃	k⋃	X
ejpam-7078	337	10	i=1	i=1	PROPN
ejpam-7078	337	11	s′	s′	PROPN
ejpam-7078	337	12	i	i	X
ejpam-7078	337	13	)	)	PUNCT
ejpam-7078	337	14	∪	∪	ADP
ejpam-7078	337	15	{	{	PUNCT
ejpam-7078	337	16	vn−r+1	vn−r+1	NOUN
ejpam-7078	337	17	,	,	PUNCT
ejpam-7078	337	18	...	...	PUNCT
ejpam-7078	337	19	,	,	PUNCT
ejpam-7078	337	20	vn	vn	PROPN
ejpam-7078	337	21	}	}	PUNCT
ejpam-7078	337	22	where	where	SCONJ
ejpam-7078	337	23	1	1	NUM
ejpam-7078	337	24	≤	≤	NOUN
ejpam-7078	337	25	r	r	NOUN
ejpam-7078	337	26	≤	≤	NUM
ejpam-7078	337	27	8	8	NUM
ejpam-7078	337	28	,	,	PUNCT
ejpam-7078	337	29	w	w	NOUN
ejpam-7078	337	30	′	′	NOUN
ejpam-7078	337	31	2	2	NUM
ejpam-7078	337	32	=	=	SYM
ejpam-7078	337	33	k⋃	k⋃	X
ejpam-7078	337	34	i=1	i=1	PRON
ejpam-7078	337	35	d′	d′	PROPN
ejpam-7078	338	1	i	i	PRON
ejpam-7078	338	2	and	and	CCONJ
ejpam-7078	338	3	w	w	NOUN
ejpam-7078	338	4	′	′	NUM
ejpam-7078	338	5	0	0	NUM
ejpam-7078	339	1	=	=	SYM
ejpam-7078	339	2	v	v	ADJ
ejpam-7078	339	3	(	(	PUNCT
ejpam-7078	339	4	g	g	NOUN
ejpam-7078	339	5	)	)	PUNCT
ejpam-7078	339	6	\	\	PUNCT
ejpam-7078	340	1	(	(	PUNCT
ejpam-7078	340	2	w	w	NOUN
ejpam-7078	340	3	′	′	NOUN
ejpam-7078	340	4	1	1	NUM
ejpam-7078	340	5	∪w	∪w	NUM
ejpam-7078	340	6	′	′	NUM
ejpam-7078	340	7	2	2	NUM
ejpam-7078	340	8	)	)	PUNCT
ejpam-7078	340	9	.	.	PUNCT
ejpam-7078	341	1	so	so	ADV
ejpam-7078	341	2	,	,	PUNCT
ejpam-7078	341	3	g′	g′	NOUN
ejpam-7078	341	4	=	=	SYM
ejpam-7078	341	5	(	(	PUNCT
ejpam-7078	341	6	w	w	NOUN
ejpam-7078	341	7	′	′	NUM
ejpam-7078	341	8	0,w	0,w	NUM
ejpam-7078	342	1	′	′	NUM
ejpam-7078	342	2	1,w	1,w	NUM
ejpam-7078	342	3	′	′	NUM
ejpam-7078	342	4	2	2	NUM
ejpam-7078	342	5	)	)	PUNCT
ejpam-7078	342	6	is	be	AUX
ejpam-7078	342	7	an	an	DET
ejpam-7078	342	8	hrdf	hrdf	NOUN
ejpam-7078	342	9	on	on	ADP
ejpam-7078	342	10	g.	g.	PROPN
ejpam-7078	342	11	note	note	VERB
ejpam-7078	342	12	that	that	SCONJ
ejpam-7078	342	13	for	for	ADP
ejpam-7078	342	14	every	every	DET
ejpam-7078	342	15	v′	v′	NOUN
ejpam-7078	342	16	=	=	PUNCT
ejpam-7078	343	1	vj	vj	INTJ
ejpam-7078	343	2	∈	∈	PROPN
ejpam-7078	343	3	w	w	ADP
ejpam-7078	343	4	′	′	NOUN
ejpam-7078	343	5	0	0	NUM
ejpam-7078	343	6	,	,	PUNCT
ejpam-7078	343	7	there	there	PRON
ejpam-7078	343	8	exists	exist	VERB
ejpam-7078	343	9	u′	u′	PROPN
ejpam-7078	343	10	=	=	SYM
ejpam-7078	343	11	vt	vt	PROPN
ejpam-7078	343	12	∈	∈	PROPN
ejpam-7078	344	1	w	w	NOUN
ejpam-7078	344	2	′	′	NOUN
ejpam-7078	344	3	2	2	NUM
ejpam-7078	344	4	such	such	ADJ
ejpam-7078	344	5	that	that	SCONJ
ejpam-7078	344	6	dg(u′	dg(u′	PROPN
ejpam-7078	344	7	,	,	PUNCT
ejpam-7078	344	8	v′	v′	NUM
ejpam-7078	344	9	)	)	PUNCT
ejpam-7078	344	10	=	=	SYM
ejpam-7078	344	11	2	2	NUM
ejpam-7078	344	12	and	and	CCONJ
ejpam-7078	344	13	there	there	PRON
ejpam-7078	344	14	exists	exist	VERB
ejpam-7078	344	15	w′	w′	NOUN
ejpam-7078	344	16	=	=	PUNCT
ejpam-7078	344	17	vl	vl	PROPN
ejpam-7078	344	18	∈	∈	PROPN
ejpam-7078	344	19	(	(	PUNCT
ejpam-7078	344	20	w	w	NOUN
ejpam-7078	344	21	′	′	NUM
ejpam-7078	344	22	1	1	NUM
ejpam-7078	344	23	∪w	∪w	NUM
ejpam-7078	344	24	′	′	NUM
ejpam-7078	344	25	2	2	X
ejpam-7078	344	26	)	)	PUNCT
ejpam-7078	344	27	such	such	ADJ
ejpam-7078	344	28	that	that	DET
ejpam-7078	344	29	n2	n2	PROPN
ejpam-7078	344	30	g(w	g(w	PROPN
ejpam-7078	344	31	′	′	NOUN
ejpam-7078	344	32	)	)	PUNCT
ejpam-7078	344	33	∩w	∩w	NOUN
ejpam-7078	345	1	′	′	NUM
ejpam-7078	345	2	0	0	NUM
ejpam-7078	346	1	=	=	NOUN
ejpam-7078	346	2	{	{	PUNCT
ejpam-7078	346	3	v′	v′	NOUN
ejpam-7078	346	4	}	}	PUNCT
ejpam-7078	346	5	.	.	PUNCT
ejpam-7078	347	1	by	by	ADP
ejpam-7078	347	2	construction	construction	NOUN
ejpam-7078	347	3	,	,	PUNCT
ejpam-7078	347	4	it	it	PRON
ejpam-7078	347	5	implies	imply	VERB
ejpam-7078	347	6	that	that	SCONJ
ejpam-7078	347	7	g′	g′	NOUN
ejpam-7078	347	8	is	be	AUX
ejpam-7078	347	9	a	a	DET
ejpam-7078	347	10	γshr	γshr	NOUN
ejpam-7078	347	11	-	-	PUNCT
ejpam-7078	347	12	function	function	NOUN
ejpam-7078	347	13	on	on	ADP
ejpam-7078	347	14	g.	g.	PROPN
ejpam-7078	347	15	hence	hence	ADV
ejpam-7078	347	16	,	,	PUNCT
ejpam-7078	347	17	we	we	PRON
ejpam-7078	347	18	have	have	VERB
ejpam-7078	347	19	ωshr(g	ωshr(g	NOUN
ejpam-7078	347	20	′	′	NUM
ejpam-7078	347	21	)	)	PUNCT
ejpam-7078	348	1	=	=	NOUN
ejpam-7078	349	1	|w	|w	NOUN
ejpam-7078	349	2	′	′	NUM
ejpam-7078	350	1	1|+	1|+	NUM
ejpam-7078	350	2	2|w	2|w	NUM
ejpam-7078	350	3	′	′	NUM
ejpam-7078	350	4	2|	2|	NUM
ejpam-7078	351	1	=	=	PUNCT
ejpam-7078	351	2	(	(	PUNCT
ejpam-7078	351	3	k∑	k∑	VERB
ejpam-7078	351	4	i=1	i=1	PROPN
ejpam-7078	351	5	|si|+	|si|+	PROPN
ejpam-7078	351	6	r	r	NOUN
ejpam-7078	351	7	)	)	PUNCT
ejpam-7078	352	1	+	+	CCONJ
ejpam-7078	352	2	2	2	NUM
ejpam-7078	352	3	k∑	k∑	NOUN
ejpam-7078	352	4	i=1	i=1	PROPN
ejpam-7078	352	5	|di|	|di|	NOUN
ejpam-7078	352	6	=	=	PUNCT
ejpam-7078	353	1	3k	3k	NOUN
ejpam-7078	354	1	+	+	CCONJ
ejpam-7078	354	2	r	r	NOUN
ejpam-7078	354	3	+	+	NOUN
ejpam-7078	354	4	2(3k	2(3k	NUM
ejpam-7078	354	5	)	)	PUNCT
ejpam-7078	354	6	=	=	SYM
ejpam-7078	355	1	9k	9k	NUM
ejpam-7078	355	2	+	+	CCONJ
ejpam-7078	355	3	r	r	NOUN
ejpam-7078	355	4	=	=	SYM
ejpam-7078	355	5	(	(	PUNCT
ejpam-7078	355	6	10k	10k	NOUN
ejpam-7078	355	7	+	+	CCONJ
ejpam-7078	355	8	r)−	r)−	PROPN
ejpam-7078	355	9	k	k	NOUN
ejpam-7078	356	1	=	=	PUNCT
ejpam-7078	356	2	n−	n−	NOUN
ejpam-7078	356	3	k	k	NOUN
ejpam-7078	357	1	where	where	SCONJ
ejpam-7078	357	2	k	k	NOUN
ejpam-7078	357	3	=	=	PUNCT
ejpam-7078	357	4	n−r	n−r	NOUN
ejpam-7078	357	5	10	10	NUM
ejpam-7078	357	6	for	for	ADP
ejpam-7078	357	7	all	all	DET
ejpam-7078	357	8	r	r	NOUN
ejpam-7078	357	9	∈	∈	NOUN
ejpam-7078	357	10	{	{	PUNCT
ejpam-7078	357	11	1	1	NUM
ejpam-7078	357	12	,	,	PUNCT
ejpam-7078	357	13	2	2	NUM
ejpam-7078	357	14	,	,	PUNCT
ejpam-7078	357	15	...	...	PUNCT
ejpam-7078	357	16	,	,	PUNCT
ejpam-7078	357	17	8	8	NUM
ejpam-7078	357	18	}	}	PUNCT
ejpam-7078	357	19	.	.	PUNCT
ejpam-7078	358	1	case	case	NOUN
ejpam-7078	358	2	3	3	NUM
ejpam-7078	358	3	:	:	PUNCT
ejpam-7078	358	4	n	n	NUM
ejpam-7078	358	5	≡	≡	PROPN
ejpam-7078	358	6	9	9	NUM
ejpam-7078	358	7	(	(	PUNCT
ejpam-7078	358	8	mod	mod	PROPN
ejpam-7078	358	9	10	10	NUM
ejpam-7078	358	10	)	)	PUNCT
ejpam-7078	358	11	let	let	VERB
ejpam-7078	358	12	n	n	NOUN
ejpam-7078	358	13	=	=	NOUN
ejpam-7078	358	14	10p+9	10p+9	NUM
ejpam-7078	358	15	where	where	SCONJ
ejpam-7078	358	16	p	p	PROPN
ejpam-7078	358	17	∈	∈	PROPN
ejpam-7078	358	18	n∪{0	n∪{0	NOUN
ejpam-7078	358	19	}	}	PUNCT
ejpam-7078	358	20	.	.	PUNCT
ejpam-7078	359	1	then	then	ADV
ejpam-7078	359	2	k	k	PROPN
ejpam-7078	359	3	=	=	PUNCT
ejpam-7078	359	4	⌊n+1	⌊n+1	NOUN
ejpam-7078	359	5	10	10	NUM
ejpam-7078	359	6	⌋	⌋	NOUN
ejpam-7078	360	1	=	=	PUNCT
ejpam-7078	360	2	p+1	p+1	NOUN
ejpam-7078	361	1	=	=	SYM
ejpam-7078	362	1	n+1	n+1	PROPN
ejpam-7078	362	2	10	10	NUM
ejpam-7078	362	3	where	where	SCONJ
ejpam-7078	362	4	p	p	PROPN
ejpam-7078	362	5	∈	∈	PROPN
ejpam-7078	362	6	n∪{0	n∪{0	NOUN
ejpam-7078	362	7	}	}	PUNCT
ejpam-7078	362	8	.	.	PUNCT
ejpam-7078	363	1	again	again	ADV
ejpam-7078	363	2	,	,	PUNCT
ejpam-7078	363	3	by	by	ADP
ejpam-7078	363	4	case	case	NOUN
ejpam-7078	363	5	1	1	NUM
ejpam-7078	363	6	,	,	PUNCT
ejpam-7078	363	7	we	we	PRON
ejpam-7078	363	8	let	let	VERB
ejpam-7078	363	9	s′′	s′′	PROPN
ejpam-7078	363	10	i	i	PRON
ejpam-7078	363	11	=	=	PUNCT
ejpam-7078	363	12	{	{	PUNCT
ejpam-7078	363	13	v10i−9	v10i−9	NOUN
ejpam-7078	363	14	,	,	PUNCT
ejpam-7078	363	15	v10i−1	v10i−1	NOUN
ejpam-7078	363	16	,	,	PUNCT
ejpam-7078	363	17	v10i	v10i	PUNCT
ejpam-7078	363	18	}	}	PUNCT
ejpam-7078	363	19	and	and	CCONJ
ejpam-7078	363	20	d′′	d′′	NOUN
ejpam-7078	364	1	i	i	PRON
ejpam-7078	364	2	=	=	PUNCT
ejpam-7078	364	3	{	{	PUNCT
ejpam-7078	364	4	v10i−6	v10i−6	NOUN
ejpam-7078	364	5	,	,	PUNCT
ejpam-7078	364	6	v10i−5	v10i−5	NOUN
ejpam-7078	364	7	,	,	PUNCT
ejpam-7078	364	8	v10i−4	v10i−4	ADP
ejpam-7078	364	9	}	}	PUNCT
ejpam-7078	364	10	for	for	ADP
ejpam-7078	364	11	each	each	DET
ejpam-7078	364	12	i	i	PRON
ejpam-7078	364	13	∈	∈	PROPN
ejpam-7078	364	14	{	{	PUNCT
ejpam-7078	364	15	1	1	NUM
ejpam-7078	364	16	,	,	PUNCT
ejpam-7078	364	17	2	2	NUM
ejpam-7078	364	18	,	,	PUNCT
ejpam-7078	364	19	...	...	PUNCT
ejpam-7078	364	20	,	,	PUNCT
ejpam-7078	364	21	k	k	NOUN
ejpam-7078	364	22	}	}	PUNCT
ejpam-7078	364	23	.	.	PUNCT
ejpam-7078	365	1	now	now	ADV
ejpam-7078	365	2	,	,	PUNCT
ejpam-7078	365	3	set	set	VERB
ejpam-7078	365	4	w	w	PRON
ejpam-7078	365	5	′′	′′	PROPN
ejpam-7078	365	6	1	1	NUM
ejpam-7078	365	7	=	=	SYM
ejpam-7078	365	8	(	(	PUNCT
ejpam-7078	365	9	k⋃	k⋃	X
ejpam-7078	365	10	i=1	i=1	PROPN
ejpam-7078	365	11	s′	s′	PROPN
ejpam-7078	365	12	i	i	X
ejpam-7078	365	13	)	)	PUNCT
ejpam-7078	365	14	∪	∪	ADP
ejpam-7078	365	15	{	{	PUNCT
ejpam-7078	365	16	vn−8	vn−8	PROPN
ejpam-7078	365	17	,	,	PUNCT
ejpam-7078	365	18	vn	vn	NOUN
ejpam-7078	365	19	}	}	PUNCT
ejpam-7078	365	20	,	,	PUNCT
ejpam-7078	365	21	w	w	PROPN
ejpam-7078	365	22	′′	′′	PROPN
ejpam-7078	365	23	2	2	NUM
ejpam-7078	365	24	=	=	SYM
ejpam-7078	365	25	(	(	PUNCT
ejpam-7078	365	26	k⋃	k⋃	X
ejpam-7078	365	27	i=1	i=1	PROPN
ejpam-7078	365	28	d′′	d′′	PROPN
ejpam-7078	365	29	i	i	PROPN
ejpam-7078	365	30	)	)	PUNCT
ejpam-7078	365	31	∪	∪	ADP
ejpam-7078	365	32	{	{	PUNCT
ejpam-7078	365	33	vn−5	vn−5	NOUN
ejpam-7078	365	34	,	,	PUNCT
ejpam-7078	365	35	vn−4	vn−4	NOUN
ejpam-7078	365	36	,	,	PUNCT
ejpam-7078	365	37	vn−3	vn−3	PROPN
ejpam-7078	365	38	}	}	PUNCT
ejpam-7078	365	39	and	and	CCONJ
ejpam-7078	365	40	w	w	ADP
ejpam-7078	365	41	′′	′′	NOUN
ejpam-7078	365	42	0	0	NUM
ejpam-7078	366	1	=	=	SYM
ejpam-7078	366	2	v	v	NOUN
ejpam-7078	366	3	(	(	PUNCT
ejpam-7078	366	4	g	g	NOUN
ejpam-7078	366	5	)	)	PUNCT
ejpam-7078	366	6	\	\	PUNCT
ejpam-7078	367	1	(	(	PUNCT
ejpam-7078	367	2	w	w	NOUN
ejpam-7078	367	3	′′	′′	PROPN
ejpam-7078	367	4	1	1	NUM
ejpam-7078	367	5	∪w	∪w	PUNCT
ejpam-7078	367	6	′′	′′	PROPN
ejpam-7078	367	7	2	2	NUM
ejpam-7078	367	8	)	)	PUNCT
ejpam-7078	367	9	.	.	PUNCT
ejpam-7078	368	1	thus	thus	ADV
ejpam-7078	368	2	,	,	PUNCT
ejpam-7078	368	3	g′′	g′′	PROPN
ejpam-7078	368	4	=	=	PRON
ejpam-7078	368	5	(	(	PUNCT
ejpam-7078	368	6	w	w	PROPN
ejpam-7078	368	7	′′	′′	NOUN
ejpam-7078	368	8	0	0	NUM
ejpam-7078	368	9	,	,	PUNCT
ejpam-7078	368	10	w	w	PROPN
ejpam-7078	368	11	′′	′′	PROPN
ejpam-7078	368	12	1	1	NUM
ejpam-7078	368	13	,	,	PUNCT
ejpam-7078	368	14	w	w	NOUN
ejpam-7078	368	15	′′	′′	NOUN
ejpam-7078	368	16	2	2	NUM
ejpam-7078	368	17	)	)	PUNCT
ejpam-7078	368	18	is	be	AUX
ejpam-7078	368	19	an	an	DET
ejpam-7078	368	20	hrdf	hrdf	NOUN
ejpam-7078	368	21	on	on	ADP
ejpam-7078	368	22	g.	g.	PROPN
ejpam-7078	368	23	now	now	ADV
ejpam-7078	368	24	,	,	PUNCT
ejpam-7078	368	25	for	for	ADP
ejpam-7078	368	26	every	every	DET
ejpam-7078	368	27	v′′	v′′	NOUN
ejpam-7078	368	28	=	=	SYM
ejpam-7078	368	29	vj	vj	ADP
ejpam-7078	368	30	∈	∈	PROPN
ejpam-7078	368	31	w	w	PROPN
ejpam-7078	368	32	′′	′′	PROPN
ejpam-7078	368	33	0	0	NUM
ejpam-7078	368	34	,	,	PUNCT
ejpam-7078	368	35	there	there	PRON
ejpam-7078	368	36	exists	exist	VERB
ejpam-7078	368	37	u′′	u′′	PROPN
ejpam-7078	368	38	=	=	PROPN
ejpam-7078	368	39	vt	vt	PROPN
ejpam-7078	368	40	∈	∈	PROPN
ejpam-7078	368	41	w	w	PROPN
ejpam-7078	368	42	′′	′′	PROPN
ejpam-7078	368	43	2	2	NUM
ejpam-7078	368	44	such	such	ADJ
ejpam-7078	368	45	that	that	DET
ejpam-7078	368	46	dg(u′′	dg(u′′	PROPN
ejpam-7078	368	47	,	,	PUNCT
ejpam-7078	368	48	v′′	v′′	NOUN
ejpam-7078	368	49	)	)	PUNCT
ejpam-7078	368	50	=	=	SYM
ejpam-7078	368	51	2	2	NUM
ejpam-7078	368	52	and	and	CCONJ
ejpam-7078	368	53	there	there	PRON
ejpam-7078	368	54	exists	exist	VERB
ejpam-7078	368	55	w′′	w′′	NOUN
ejpam-7078	368	56	=	=	SYM
ejpam-7078	368	57	vl	vl	PROPN
ejpam-7078	368	58	∈	∈	PROPN
ejpam-7078	368	59	(	(	PUNCT
ejpam-7078	368	60	w	w	NOUN
ejpam-7078	368	61	′′	′′	PROPN
ejpam-7078	368	62	1	1	NUM
ejpam-7078	368	63	∪w	∪w	PUNCT
ejpam-7078	368	64	′′	′′	PROPN
ejpam-7078	368	65	2	2	NUM
ejpam-7078	368	66	)	)	PUNCT
ejpam-7078	368	67	such	such	ADJ
ejpam-7078	368	68	that	that	DET
ejpam-7078	368	69	n2	n2	PROPN
ejpam-7078	368	70	g(w	g(w	PROPN
ejpam-7078	368	71	′′	′′	PROPN
ejpam-7078	368	72	)	)	PUNCT
ejpam-7078	368	73	∩w	∩w	PUNCT
ejpam-7078	369	1	′′	′′	NOUN
ejpam-7078	369	2	0	0	NUM
ejpam-7078	369	3	=	=	NOUN
ejpam-7078	369	4	{	{	PUNCT
ejpam-7078	369	5	v′′	v′′	NOUN
ejpam-7078	369	6	}	}	PUNCT
ejpam-7078	369	7	.	.	PUNCT
ejpam-7078	370	1	by	by	ADP
ejpam-7078	370	2	construction	construction	NOUN
ejpam-7078	370	3	,	,	PUNCT
ejpam-7078	370	4	it	it	PRON
ejpam-7078	370	5	follows	follow	VERB
ejpam-7078	370	6	that	that	SCONJ
ejpam-7078	370	7	g′′	g′′	PROPN
ejpam-7078	370	8	is	be	AUX
ejpam-7078	370	9	a	a	DET
ejpam-7078	370	10	γshr	γshr	NOUN
ejpam-7078	370	11	-	-	PUNCT
ejpam-7078	370	12	function	function	NOUN
ejpam-7078	370	13	on	on	ADP
ejpam-7078	370	14	g.	g.	PROPN
ejpam-7078	370	15	hence	hence	ADV
ejpam-7078	370	16	,	,	PUNCT
ejpam-7078	370	17	we	we	PRON
ejpam-7078	370	18	have	have	VERB
ejpam-7078	370	19	γshr(g	γshr(g	NOUN
ejpam-7078	370	20	)	)	PUNCT
ejpam-7078	371	1	=	=	PUNCT
ejpam-7078	371	2	ωshr	ωshr	NOUN
ejpam-7078	371	3	g	g	PROPN
ejpam-7078	371	4	(	(	PUNCT
ejpam-7078	371	5	g′′	g′′	PROPN
ejpam-7078	371	6	)	)	PUNCT
ejpam-7078	371	7	=	=	NOUN
ejpam-7078	372	1	|w	|w	NOUN
ejpam-7078	372	2	′′	′′	PROPN
ejpam-7078	372	3	1	1	NUM
ejpam-7078	372	4	|+	|+	NOUN
ejpam-7078	372	5	2|w	2|w	NUM
ejpam-7078	372	6	′′	′′	NOUN
ejpam-7078	372	7	2	2	NUM
ejpam-7078	373	1	|	|	ADV
ejpam-7078	373	2	=	=	SYM
ejpam-7078	373	3	(	(	PUNCT
ejpam-7078	373	4	p∑	p∑	NOUN
ejpam-7078	373	5	i=1	i=1	PRON
ejpam-7078	374	1	|s′′	|s′′	ADV
ejpam-7078	375	1	i	i	PRON
ejpam-7078	375	2	|+	|+	VERB
ejpam-7078	375	3	2	2	NUM
ejpam-7078	375	4	)	)	PUNCT
ejpam-7078	376	1	+	+	CCONJ
ejpam-7078	376	2	2	2	NUM
ejpam-7078	376	3	(	(	PUNCT
ejpam-7078	376	4	p∑	p∑	NOUN
ejpam-7078	376	5	i=1	i=1	PROPN
ejpam-7078	376	6	|d′′	|d′′	VERB
ejpam-7078	376	7	i	i	PRON
ejpam-7078	376	8	|+	|+	VERB
ejpam-7078	376	9	3	3	X
ejpam-7078	376	10	)	)	PUNCT
ejpam-7078	376	11	l.	l.	PROPN
ejpam-7078	376	12	f.	f.	PROPN
ejpam-7078	376	13	casinillo	casinillo	PROPN
ejpam-7078	376	14	,	,	PUNCT
ejpam-7078	376	15	s.	s.	PROPN
ejpam-7078	376	16	r.	r.	PROPN
ejpam-7078	376	17	canoy	canoy	PROPN
ejpam-7078	376	18	jr	jr	PROPN
ejpam-7078	376	19	.	.	PROPN
ejpam-7078	376	20	/	/	SYM
ejpam-7078	376	21	eur	eur	PROPN
ejpam-7078	376	22	.	.	PUNCT
ejpam-7078	377	1	j.	j.	PROPN
ejpam-7078	377	2	pure	pure	PROPN
ejpam-7078	377	3	appl	appl	PROPN
ejpam-7078	377	4	.	.	PROPN
ejpam-7078	377	5	math	math	PROPN
ejpam-7078	377	6	,	,	PUNCT
ejpam-7078	377	7	18	18	NUM
ejpam-7078	377	8	(	(	PUNCT
ejpam-7078	377	9	4	4	NUM
ejpam-7078	377	10	)	)	PUNCT
ejpam-7078	377	11	(	(	PUNCT
ejpam-7078	377	12	2025	2025	NUM
ejpam-7078	377	13	)	)	PUNCT
ejpam-7078	377	14	,	,	PUNCT
ejpam-7078	377	15	7078	7078	NUM
ejpam-7078	377	16	11	11	NUM
ejpam-7078	377	17	of	of	ADP
ejpam-7078	377	18	15	15	NUM
ejpam-7078	377	19	=	=	SYM
ejpam-7078	377	20	3p+	3p+	NUM
ejpam-7078	377	21	2	2	NUM
ejpam-7078	377	22	+	+	NUM
ejpam-7078	377	23	2(3p+	2(3p+	NUM
ejpam-7078	377	24	3	3	NUM
ejpam-7078	377	25	)	)	PUNCT
ejpam-7078	377	26	=	=	SYM
ejpam-7078	377	27	9p+	9p+	NUM
ejpam-7078	377	28	8	8	NUM
ejpam-7078	377	29	=	=	SYM
ejpam-7078	377	30	(	(	PUNCT
ejpam-7078	377	31	10p+	10p+	NUM
ejpam-7078	377	32	9)−	9)−	NUM
ejpam-7078	377	33	(	(	PUNCT
ejpam-7078	377	34	p+	p+	NOUN
ejpam-7078	377	35	1	1	NUM
ejpam-7078	377	36	)	)	PUNCT
ejpam-7078	377	37	=	=	SYM
ejpam-7078	378	1	n−	n−	NOUN
ejpam-7078	378	2	k	k	X
ejpam-7078	378	3	where	where	SCONJ
ejpam-7078	378	4	k	k	PROPN
ejpam-7078	378	5	=	=	SYM
ejpam-7078	378	6	n+1	n+1	PROPN
ejpam-7078	378	7	10	10	NUM
ejpam-7078	378	8	.	.	PUNCT
ejpam-7078	379	1	this	this	PRON
ejpam-7078	379	2	proves	prove	VERB
ejpam-7078	379	3	the	the	DET
ejpam-7078	379	4	assertion	assertion	NOUN
ejpam-7078	379	5	.	.	PUNCT
ejpam-7078	380	1	the	the	DET
ejpam-7078	380	2	proof	proof	NOUN
ejpam-7078	380	3	of	of	ADP
ejpam-7078	380	4	the	the	DET
ejpam-7078	380	5	next	next	ADJ
ejpam-7078	380	6	result	result	NOUN
ejpam-7078	380	7	is	be	AUX
ejpam-7078	380	8	similar	similar	ADJ
ejpam-7078	380	9	to	to	ADP
ejpam-7078	380	10	that	that	PRON
ejpam-7078	380	11	of	of	ADP
ejpam-7078	380	12	proposition	proposition	NOUN
ejpam-7078	380	13	4	4	NUM
ejpam-7078	380	14	.	.	PUNCT
ejpam-7078	380	15	proposition	proposition	NOUN
ejpam-7078	380	16	5	5	NUM
ejpam-7078	380	17	.	.	PUNCT
ejpam-7078	381	1	let	let	VERB
ejpam-7078	381	2	g	g	PROPN
ejpam-7078	381	3	=	=	SYM
ejpam-7078	381	4	cn	cn	PROPN
ejpam-7078	381	5	with	with	ADP
ejpam-7078	381	6	n	n	PRON
ejpam-7078	381	7	≥	≥	NUM
ejpam-7078	381	8	3	3	NUM
ejpam-7078	381	9	.	.	PUNCT
ejpam-7078	382	1	then	then	ADV
ejpam-7078	382	2	,	,	PUNCT
ejpam-7078	382	3	γshr(g	γshr(g	NOUN
ejpam-7078	382	4	)	)	PUNCT
ejpam-7078	382	5	=	=	SYM
ejpam-7078	383	1			PROPN
ejpam-7078	383	2	n	n	CCONJ
ejpam-7078	383	3	,	,	PUNCT
ejpam-7078	383	4	if	if	SCONJ
ejpam-7078	383	5	n	n	ADV
ejpam-7078	383	6	∈	∈	PROPN
ejpam-7078	383	7	{	{	PUNCT
ejpam-7078	383	8	3	3	NUM
ejpam-7078	383	9	,	,	PUNCT
ejpam-7078	383	10	4	4	NUM
ejpam-7078	383	11	,	,	PUNCT
ejpam-7078	383	12	6	6	NUM
ejpam-7078	383	13	,	,	PUNCT
ejpam-7078	383	14	7	7	NUM
ejpam-7078	383	15	,	,	PUNCT
ejpam-7078	383	16	8	8	NUM
ejpam-7078	383	17	,	,	PUNCT
ejpam-7078	383	18	9	9	NUM
ejpam-7078	383	19	}	}	SYM
ejpam-7078	383	20	4	4	NUM
ejpam-7078	383	21	,	,	PUNCT
ejpam-7078	383	22	if	if	SCONJ
ejpam-7078	383	23	n	n	NOUN
ejpam-7078	383	24	=	=	SYM
ejpam-7078	383	25	5	5	NUM
ejpam-7078	383	26	n−	n−	NOUN
ejpam-7078	383	27	k	k	NOUN
ejpam-7078	383	28	,	,	PUNCT
ejpam-7078	383	29	if	if	SCONJ
ejpam-7078	383	30	n	n	PRON
ejpam-7078	383	31	≥	≥	NOUN
ejpam-7078	383	32	10	10	NUM
ejpam-7078	383	33	,	,	PUNCT
ejpam-7078	383	34	where	where	SCONJ
ejpam-7078	383	35	k	k	NOUN
ejpam-7078	383	36	=	=	SYM
ejpam-7078	383	37	⌊	⌊	PROPN
ejpam-7078	383	38	n	n	PART
ejpam-7078	383	39	10⌋.	10⌋.	NUM
ejpam-7078	383	40	theorem	theorem	NOUN
ejpam-7078	383	41	7	7	NUM
ejpam-7078	383	42	.	.	PUNCT
ejpam-7078	384	1	let	let	VERB
ejpam-7078	384	2	g	g	PRON
ejpam-7078	384	3	be	be	AUX
ejpam-7078	384	4	a	a	DET
ejpam-7078	384	5	graph	graph	NOUN
ejpam-7078	384	6	of	of	ADP
ejpam-7078	384	7	order	order	NOUN
ejpam-7078	384	8	n.	n.	NOUN
ejpam-7078	384	9	then	then	ADV
ejpam-7078	384	10	γsh(g	γsh(g	NOUN
ejpam-7078	384	11	)	)	PUNCT
ejpam-7078	385	1	=	=	SYM
ejpam-7078	385	2	γshr(g	γshr(g	NOUN
ejpam-7078	385	3	)	)	PUNCT
ejpam-7078	385	4	if	if	SCONJ
ejpam-7078	385	5	and	and	CCONJ
ejpam-7078	385	6	only	only	ADV
ejpam-7078	385	7	if	if	SCONJ
ejpam-7078	385	8	each	each	DET
ejpam-7078	385	9	component	component	NOUN
ejpam-7078	385	10	of	of	ADP
ejpam-7078	385	11	g	g	PROPN
ejpam-7078	385	12	is	be	AUX
ejpam-7078	385	13	complete	complete	ADJ
ejpam-7078	385	14	.	.	PUNCT
ejpam-7078	386	1	in	in	ADP
ejpam-7078	386	2	this	this	DET
ejpam-7078	386	3	case	case	NOUN
ejpam-7078	386	4	,	,	PUNCT
ejpam-7078	386	5	γsh(g	γsh(g	NOUN
ejpam-7078	386	6	)	)	PUNCT
ejpam-7078	386	7	=	=	SYM
ejpam-7078	386	8	γshr(g	γshr(g	NOUN
ejpam-7078	386	9	)	)	PUNCT
ejpam-7078	386	10	=	=	SYM
ejpam-7078	386	11	n.	n.	NOUN
ejpam-7078	386	12	proof	proof	NOUN
ejpam-7078	386	13	.	.	PUNCT
ejpam-7078	387	1	suppose	suppose	VERB
ejpam-7078	387	2	γsh(g	γsh(g	NOUN
ejpam-7078	387	3	)	)	PUNCT
ejpam-7078	387	4	=	=	SYM
ejpam-7078	387	5	γshr(g	γshr(g	NOUN
ejpam-7078	387	6	)	)	PUNCT
ejpam-7078	387	7	and	and	CCONJ
ejpam-7078	387	8	let	let	VERB
ejpam-7078	387	9	f	f	PROPN
ejpam-7078	387	10	=	=	SYM
ejpam-7078	387	11	(	(	PUNCT
ejpam-7078	387	12	v0	v0	PROPN
ejpam-7078	387	13	,	,	PUNCT
ejpam-7078	387	14	v1	v1	NOUN
ejpam-7078	387	15	,	,	PUNCT
ejpam-7078	387	16	v2	v2	PROPN
ejpam-7078	387	17	)	)	PUNCT
ejpam-7078	387	18	be	be	AUX
ejpam-7078	387	19	a	a	DET
ejpam-7078	387	20	γshr	γshr	NOUN
ejpam-7078	387	21	-	-	PUNCT
ejpam-7078	387	22	function	function	NOUN
ejpam-7078	387	23	on	on	ADP
ejpam-7078	387	24	g.	g.	PROPN
ejpam-7078	387	25	by	by	ADP
ejpam-7078	387	26	proposition	proposition	NOUN
ejpam-7078	387	27	1	1	NUM
ejpam-7078	387	28	,	,	PUNCT
ejpam-7078	387	29	v1	v1	NOUN
ejpam-7078	387	30	∪	∪	NOUN
ejpam-7078	387	31	v2	v2	NOUN
ejpam-7078	387	32	is	be	AUX
ejpam-7078	387	33	a	a	DET
ejpam-7078	387	34	super	super	ADV
ejpam-7078	387	35	hop	hop	NOUN
ejpam-7078	387	36	dominating	dominating	NOUN
ejpam-7078	387	37	set	set	VERB
ejpam-7078	387	38	on	on	ADP
ejpam-7078	387	39	g.	g.	PROPN
ejpam-7078	387	40	hence	hence	ADV
ejpam-7078	387	41	,	,	PUNCT
ejpam-7078	387	42	γsh(g	γsh(g	SYM
ejpam-7078	387	43	)	)	PUNCT
ejpam-7078	387	44	≤	≤	NOUN
ejpam-7078	387	45	|v1|+	|v1|+	PUNCT
ejpam-7078	387	46	|v2|	|v2|	ADV
ejpam-7078	387	47	≤	≤	NUM
ejpam-7078	387	48	|v1|+	|v1|+	PRON
ejpam-7078	387	49	2|v2|	2|v2|	NUM
ejpam-7078	387	50	=	=	SYM
ejpam-7078	387	51	γshr(g	γshr(g	NOUN
ejpam-7078	387	52	)	)	PUNCT
ejpam-7078	387	53	.	.	PUNCT
ejpam-7078	388	1	since	since	SCONJ
ejpam-7078	388	2	γsh(g	γsh(g	NOUN
ejpam-7078	388	3	)	)	PUNCT
ejpam-7078	388	4	=	=	SYM
ejpam-7078	388	5	γshr(g	γshr(g	NOUN
ejpam-7078	388	6	)	)	PUNCT
ejpam-7078	388	7	,	,	PUNCT
ejpam-7078	388	8	it	it	PRON
ejpam-7078	388	9	follows	follow	VERB
ejpam-7078	388	10	that	that	DET
ejpam-7078	388	11	|v2|	|v2|	NOUN
ejpam-7078	388	12	=	=	SYM
ejpam-7078	388	13	0	0	X
ejpam-7078	388	14	.	.	PUNCT
ejpam-7078	389	1	by	by	ADP
ejpam-7078	389	2	proposition	proposition	NOUN
ejpam-7078	389	3	1(i	1(i	NUM
ejpam-7078	389	4	)	)	PUNCT
ejpam-7078	389	5	,	,	PUNCT
ejpam-7078	389	6	we	we	PRON
ejpam-7078	389	7	have	have	VERB
ejpam-7078	389	8	|v0|	|v0|	NOUN
ejpam-7078	389	9	=	=	SYM
ejpam-7078	389	10	0	0	X
ejpam-7078	389	11	.	.	PUNCT
ejpam-7078	390	1	this	this	PRON
ejpam-7078	390	2	implies	imply	VERB
ejpam-7078	390	3	that	that	SCONJ
ejpam-7078	390	4	|v1|	|v1|	NOUN
ejpam-7078	390	5	=	=	SYM
ejpam-7078	390	6	n	n	PROPN
ejpam-7078	390	7	=	=	SYM
ejpam-7078	390	8	|v	|v	X
ejpam-7078	390	9	(	(	PUNCT
ejpam-7078	390	10	g)|	g)|	NOUN
ejpam-7078	390	11	.	.	PUNCT
ejpam-7078	391	1	thus	thus	ADV
ejpam-7078	391	2	,	,	PUNCT
ejpam-7078	391	3	γsh(g	γsh(g	NOUN
ejpam-7078	391	4	)	)	PUNCT
ejpam-7078	391	5	=	=	SYM
ejpam-7078	391	6	γshr(g	γshr(g	NOUN
ejpam-7078	391	7	)	)	PUNCT
ejpam-7078	391	8	=	=	VERB
ejpam-7078	392	1	n.	n.	NOUN
ejpam-7078	392	2	by	by	ADP
ejpam-7078	392	3	theorem	theorem	NOUN
ejpam-7078	392	4	2	2	NUM
ejpam-7078	392	5	,	,	PUNCT
ejpam-7078	392	6	we	we	PRON
ejpam-7078	392	7	find	find	VERB
ejpam-7078	392	8	that	that	SCONJ
ejpam-7078	392	9	each	each	DET
ejpam-7078	392	10	component	component	NOUN
ejpam-7078	392	11	of	of	ADP
ejpam-7078	392	12	g	g	PROPN
ejpam-7078	392	13	is	be	AUX
ejpam-7078	392	14	complete	complete	ADJ
ejpam-7078	392	15	.	.	PUNCT
ejpam-7078	393	1	for	for	ADP
ejpam-7078	393	2	the	the	DET
ejpam-7078	393	3	converse	converse	NOUN
ejpam-7078	393	4	,	,	PUNCT
ejpam-7078	393	5	suppose	suppose	VERB
ejpam-7078	393	6	that	that	SCONJ
ejpam-7078	393	7	every	every	DET
ejpam-7078	393	8	component	component	NOUN
ejpam-7078	393	9	of	of	ADP
ejpam-7078	393	10	g	g	PROPN
ejpam-7078	393	11	is	be	AUX
ejpam-7078	393	12	complete	complete	ADJ
ejpam-7078	393	13	.	.	PUNCT
ejpam-7078	394	1	by	by	ADP
ejpam-7078	394	2	theorem	theorem	NOUN
ejpam-7078	394	3	2	2	NUM
ejpam-7078	394	4	and	and	CCONJ
ejpam-7078	394	5	corollary	corollary	ADJ
ejpam-7078	394	6	2	2	NUM
ejpam-7078	394	7	,	,	PUNCT
ejpam-7078	394	8	we	we	PRON
ejpam-7078	394	9	have	have	VERB
ejpam-7078	394	10	γsh(g	γsh(g	NOUN
ejpam-7078	394	11	)	)	PUNCT
ejpam-7078	394	12	=	=	SYM
ejpam-7078	394	13	γshr(g	γshr(g	NOUN
ejpam-7078	394	14	)	)	PUNCT
ejpam-7078	394	15	=	=	SYM
ejpam-7078	394	16	n.	n.	NOUN
ejpam-7078	394	17	theorem	theorem	VERB
ejpam-7078	394	18	8	8	NUM
ejpam-7078	394	19	.	.	PUNCT
ejpam-7078	395	1	let	let	VERB
ejpam-7078	395	2	g	g	PRON
ejpam-7078	395	3	be	be	AUX
ejpam-7078	395	4	a	a	DET
ejpam-7078	395	5	graph	graph	NOUN
ejpam-7078	395	6	of	of	ADP
ejpam-7078	395	7	order	order	NOUN
ejpam-7078	395	8	n	n	PRON
ejpam-7078	395	9	such	such	ADJ
ejpam-7078	395	10	that	that	SCONJ
ejpam-7078	395	11	γsh(g	γsh(g	NOUN
ejpam-7078	395	12	)	)	PUNCT
ejpam-7078	395	13	<	<	X
ejpam-7078	395	14	γshr(g	γshr(g	PROPN
ejpam-7078	395	15	)	)	PUNCT
ejpam-7078	395	16	.	.	PUNCT
ejpam-7078	396	1	then	then	ADV
ejpam-7078	396	2	γshr(g	γshr(g	NOUN
ejpam-7078	396	3	)	)	PUNCT
ejpam-7078	396	4	=	=	SYM
ejpam-7078	396	5	γsh(g	γsh(g	NOUN
ejpam-7078	396	6	)	)	PUNCT
ejpam-7078	396	7	+	+	CCONJ
ejpam-7078	396	8	1	1	NUM
ejpam-7078	396	9	if	if	SCONJ
ejpam-7078	396	10	and	and	CCONJ
ejpam-7078	396	11	only	only	ADV
ejpam-7078	396	12	if	if	SCONJ
ejpam-7078	396	13	there	there	PRON
ejpam-7078	396	14	exist	exist	VERB
ejpam-7078	396	15	a	a	DET
ejpam-7078	396	16	set	set	NOUN
ejpam-7078	396	17	s	s	NOUN
ejpam-7078	396	18	⊆	⊆	NUM
ejpam-7078	396	19	v	v	NOUN
ejpam-7078	396	20	(	(	PUNCT
ejpam-7078	396	21	g	g	NOUN
ejpam-7078	396	22	)	)	PUNCT
ejpam-7078	396	23	and	and	CCONJ
ejpam-7078	396	24	vertex	vertex	NOUN
ejpam-7078	396	25	v	v	ADP
ejpam-7078	396	26	such	such	DET
ejpam-7078	396	27	that	that	SCONJ
ejpam-7078	396	28	s	s	VERB
ejpam-7078	396	29	∪	∪	X
ejpam-7078	396	30	{	{	PUNCT
ejpam-7078	396	31	v	v	NOUN
ejpam-7078	396	32	}	}	PUNCT
ejpam-7078	396	33	is	be	AUX
ejpam-7078	396	34	a	a	DET
ejpam-7078	396	35	γsh	γsh	NOUN
ejpam-7078	396	36	-	-	PUNCT
ejpam-7078	396	37	set	set	NOUN
ejpam-7078	396	38	of	of	ADP
ejpam-7078	396	39	g	g	NOUN
ejpam-7078	396	40	and	and	CCONJ
ejpam-7078	396	41	v	v	NOUN
ejpam-7078	396	42	(	(	PUNCT
ejpam-7078	396	43	g	g	NOUN
ejpam-7078	396	44	)	)	PUNCT
ejpam-7078	396	45	\	\	PUNCT
ejpam-7078	397	1	(	(	PUNCT
ejpam-7078	397	2	s	s	NOUN
ejpam-7078	397	3	∪	∪	X
ejpam-7078	397	4	{	{	PUNCT
ejpam-7078	397	5	v	v	NOUN
ejpam-7078	397	6	}	}	PUNCT
ejpam-7078	397	7	)	)	PUNCT
ejpam-7078	397	8	⊆	⊆	NUM
ejpam-7078	397	9	n2	n2	ADJ
ejpam-7078	397	10	g(v	g(v	PROPN
ejpam-7078	397	11	)	)	PUNCT
ejpam-7078	397	12	.	.	PUNCT
ejpam-7078	398	1	proof	proof	NOUN
ejpam-7078	398	2	.	.	PUNCT
ejpam-7078	399	1	suppose	suppose	VERB
ejpam-7078	399	2	γshr(g	γshr(g	NOUN
ejpam-7078	399	3	)	)	PUNCT
ejpam-7078	399	4	=	=	PUNCT
ejpam-7078	399	5	γsh(g	γsh(g	NOUN
ejpam-7078	399	6	)	)	PUNCT
ejpam-7078	399	7	+	+	SYM
ejpam-7078	399	8	1	1	NUM
ejpam-7078	399	9	and	and	CCONJ
ejpam-7078	399	10	let	let	VERB
ejpam-7078	399	11	f	f	PROPN
ejpam-7078	399	12	=	=	SYM
ejpam-7078	399	13	(	(	PUNCT
ejpam-7078	399	14	v0	v0	PROPN
ejpam-7078	399	15	,	,	PUNCT
ejpam-7078	399	16	v1	v1	NOUN
ejpam-7078	399	17	,	,	PUNCT
ejpam-7078	399	18	v2	v2	PROPN
ejpam-7078	399	19	)	)	PUNCT
ejpam-7078	399	20	be	be	AUX
ejpam-7078	399	21	a	a	DET
ejpam-7078	399	22	γshr	γshr	NOUN
ejpam-7078	399	23	-	-	PUNCT
ejpam-7078	399	24	function	function	NOUN
ejpam-7078	399	25	on	on	ADP
ejpam-7078	399	26	g.	g.	PROPN
ejpam-7078	399	27	if	if	SCONJ
ejpam-7078	399	28	γsh(g	γsh(g	NOUN
ejpam-7078	399	29	)	)	PUNCT
ejpam-7078	399	30	=	=	SYM
ejpam-7078	400	1	|v1|+	|v1|+	DET
ejpam-7078	400	2	|v2|	|v2|	NOUN
ejpam-7078	400	3	,	,	PUNCT
ejpam-7078	400	4	then	then	ADV
ejpam-7078	400	5	the	the	DET
ejpam-7078	400	6	assumption	assumption	NOUN
ejpam-7078	400	7	implies	imply	VERB
ejpam-7078	400	8	that	that	SCONJ
ejpam-7078	400	9	|v1|+	|v1|+	ADP
ejpam-7078	400	10	|v2|+	|v2|+	PROPN
ejpam-7078	400	11	1	1	NUM
ejpam-7078	400	12	=	=	SYM
ejpam-7078	400	13	|v1|+	|v1|+	PRON
ejpam-7078	400	14	2|v2|	2|v2|	NUM
ejpam-7078	400	15	.	.	PUNCT
ejpam-7078	401	1	hence	hence	ADV
ejpam-7078	401	2	,	,	PUNCT
ejpam-7078	401	3	|v2|	|v2|	NOUN
ejpam-7078	401	4	=	=	SYM
ejpam-7078	401	5	1	1	NUM
ejpam-7078	401	6	and	and	CCONJ
ejpam-7078	401	7	|v1|	|v1|	NOUN
ejpam-7078	401	8	=	=	SYM
ejpam-7078	401	9	γsh(g	γsh(g	NOUN
ejpam-7078	401	10	)	)	PUNCT
ejpam-7078	401	11	−	−	PROPN
ejpam-7078	402	1	1	1	X
ejpam-7078	402	2	.	.	PUNCT
ejpam-7078	403	1	this	this	PRON
ejpam-7078	403	2	implies	imply	VERB
ejpam-7078	403	3	that	that	SCONJ
ejpam-7078	403	4	v1	v1	NOUN
ejpam-7078	403	5	∪	∪	NOUN
ejpam-7078	403	6	v2	v2	NOUN
ejpam-7078	403	7	is	be	AUX
ejpam-7078	403	8	a	a	DET
ejpam-7078	403	9	γsh	γsh	NOUN
ejpam-7078	403	10	-	-	PUNCT
ejpam-7078	403	11	set	set	VERB
ejpam-7078	403	12	in	in	ADP
ejpam-7078	403	13	g.	g.	PROPN
ejpam-7078	403	14	let	let	VERB
ejpam-7078	403	15	v2	v2	VERB
ejpam-7078	403	16	=	=	PUNCT
ejpam-7078	403	17	{	{	PUNCT
ejpam-7078	403	18	v	v	NOUN
ejpam-7078	403	19	}	}	PUNCT
ejpam-7078	403	20	and	and	CCONJ
ejpam-7078	403	21	s	s	NOUN
ejpam-7078	403	22	=	=	NOUN
ejpam-7078	403	23	v1	v1	PROPN
ejpam-7078	403	24	.	.	PUNCT
ejpam-7078	404	1	then	then	ADV
ejpam-7078	404	2	v0	v0	PROPN
ejpam-7078	404	3	=	=	SYM
ejpam-7078	404	4	v	v	PROPN
ejpam-7078	404	5	(	(	PUNCT
ejpam-7078	404	6	g	g	NOUN
ejpam-7078	404	7	)	)	PUNCT
ejpam-7078	404	8	\	\	PUNCT
ejpam-7078	405	1	(	(	PUNCT
ejpam-7078	405	2	s	s	NOUN
ejpam-7078	405	3	∪	∪	X
ejpam-7078	405	4	{	{	PUNCT
ejpam-7078	405	5	v	v	NOUN
ejpam-7078	405	6	}	}	PUNCT
ejpam-7078	405	7	)	)	PUNCT
ejpam-7078	405	8	.	.	PUNCT
ejpam-7078	406	1	since	since	SCONJ
ejpam-7078	406	2	f	f	PROPN
ejpam-7078	406	3	satisfies	satisfie	NOUN
ejpam-7078	406	4	(	(	PUNCT
ejpam-7078	406	5	shr1	shr1	PROPN
ejpam-7078	406	6	)	)	PUNCT
ejpam-7078	406	7	,	,	PUNCT
ejpam-7078	406	8	we	we	PRON
ejpam-7078	406	9	have	have	VERB
ejpam-7078	406	10	v	v	NUM
ejpam-7078	406	11	(	(	PUNCT
ejpam-7078	406	12	g	g	NOUN
ejpam-7078	406	13	)	)	PUNCT
ejpam-7078	406	14	\	\	PUNCT
ejpam-7078	407	1	(	(	PUNCT
ejpam-7078	407	2	s	s	NOUN
ejpam-7078	407	3	∪	∪	X
ejpam-7078	407	4	{	{	PUNCT
ejpam-7078	407	5	v	v	NOUN
ejpam-7078	407	6	}	}	PUNCT
ejpam-7078	407	7	)	)	PUNCT
ejpam-7078	407	8	⊆	⊆	NUM
ejpam-7078	407	9	n2	n2	ADJ
ejpam-7078	407	10	g(v	g(v	PROPN
ejpam-7078	407	11	)	)	PUNCT
ejpam-7078	407	12	.	.	PUNCT
ejpam-7078	408	1	next	next	ADV
ejpam-7078	408	2	,	,	PUNCT
ejpam-7078	408	3	suppose	suppose	VERB
ejpam-7078	408	4	that	that	SCONJ
ejpam-7078	408	5	γsh(g	γsh(g	NOUN
ejpam-7078	408	6	)	)	PUNCT
ejpam-7078	408	7	<	<	X
ejpam-7078	408	8	|v1|	|v1|	NOUN
ejpam-7078	408	9	+	+	X
ejpam-7078	408	10	|v2|	|v2|	NOUN
ejpam-7078	408	11	.	.	PUNCT
ejpam-7078	409	1	then	then	ADV
ejpam-7078	409	2	γsh(g	γsh(g	NOUN
ejpam-7078	409	3	)	)	PUNCT
ejpam-7078	409	4	+	+	CCONJ
ejpam-7078	409	5	1	1	NUM
ejpam-7078	409	6	≤	≤	NOUN
ejpam-7078	409	7	|v1|	|v1|	NOUN
ejpam-7078	409	8	+	+	X
ejpam-7078	409	9	|v2|	|v2|	NOUN
ejpam-7078	409	10	.	.	PUNCT
ejpam-7078	410	1	since	since	SCONJ
ejpam-7078	410	2	γshr(g	γshr(g	NUM
ejpam-7078	410	3	)	)	PUNCT
ejpam-7078	410	4	=	=	SYM
ejpam-7078	410	5	γsh(g	γsh(g	NOUN
ejpam-7078	410	6	)	)	PUNCT
ejpam-7078	410	7	+	+	SYM
ejpam-7078	410	8	1	1	NUM
ejpam-7078	410	9	,	,	PUNCT
ejpam-7078	410	10	we	we	PRON
ejpam-7078	410	11	have	have	VERB
ejpam-7078	410	12	|v1|	|v1|	NOUN
ejpam-7078	410	13	+	+	CCONJ
ejpam-7078	410	14	2|v2|	2|v2|	NUM
ejpam-7078	410	15	≤	≤	NUM
ejpam-7078	410	16	|v1|	|v1|	NOUN
ejpam-7078	410	17	+	+	X
ejpam-7078	410	18	|v2|	|v2|	NOUN
ejpam-7078	410	19	.	.	PUNCT
ejpam-7078	411	1	hence	hence	ADV
ejpam-7078	411	2	,	,	PUNCT
ejpam-7078	411	3	it	it	PRON
ejpam-7078	411	4	implies	imply	VERB
ejpam-7078	411	5	that	that	DET
ejpam-7078	411	6	|v2|	|v2|	NOUN
ejpam-7078	411	7	=	=	SYM
ejpam-7078	411	8	0	0	PUNCT
ejpam-7078	412	1	and	and	CCONJ
ejpam-7078	412	2	so	so	ADV
ejpam-7078	412	3	,	,	PUNCT
ejpam-7078	412	4	|v0|	|v0|	NOUN
ejpam-7078	412	5	=	=	SYM
ejpam-7078	412	6	0	0	NUM
ejpam-7078	412	7	and	and	CCONJ
ejpam-7078	412	8	|v1|	|v1|	NOUN
ejpam-7078	412	9	=	=	SYM
ejpam-7078	412	10	n.	n.	PROPN
ejpam-7078	412	11	consequently	consequently	ADV
ejpam-7078	412	12	,	,	PUNCT
ejpam-7078	412	13	γsh(g	γsh(g	NOUN
ejpam-7078	412	14	)	)	PUNCT
ejpam-7078	412	15	=	=	SYM
ejpam-7078	413	1	n−1	n−1	PROPN
ejpam-7078	413	2	.	.	PUNCT
ejpam-7078	413	3	let	let	VERB
ejpam-7078	413	4	q	q	NOUN
ejpam-7078	413	5	=	=	SYM
ejpam-7078	413	6	v	v	X
ejpam-7078	413	7	(	(	PUNCT
ejpam-7078	413	8	g	g	NOUN
ejpam-7078	413	9	)	)	PUNCT
ejpam-7078	413	10	\	\	NOUN
ejpam-7078	413	11	{	{	PUNCT
ejpam-7078	413	12	x	x	NOUN
ejpam-7078	413	13	}	}	PUNCT
ejpam-7078	413	14	be	be	AUX
ejpam-7078	413	15	a	a	DET
ejpam-7078	413	16	γsh	γsh	NOUN
ejpam-7078	413	17	-	-	PUNCT
ejpam-7078	413	18	set	set	NOUN
ejpam-7078	413	19	on	on	ADP
ejpam-7078	413	20	g.	g.	PROPN
ejpam-7078	413	21	then	then	ADV
ejpam-7078	413	22	there	there	PRON
ejpam-7078	413	23	exists	exist	VERB
ejpam-7078	413	24	v	v	ADP
ejpam-7078	413	25	∈	∈	PROPN
ejpam-7078	413	26	q	q	NOUN
ejpam-7078	413	27	such	such	ADJ
ejpam-7078	413	28	that	that	SCONJ
ejpam-7078	413	29	x	x	SYM
ejpam-7078	413	30	∈	∈	PROPN
ejpam-7078	413	31	n2	n2	NOUN
ejpam-7078	413	32	g(v	g(v	PROPN
ejpam-7078	413	33	)	)	PUNCT
ejpam-7078	413	34	.	.	PUNCT
ejpam-7078	414	1	let	let	VERB
ejpam-7078	414	2	s	s	PRON
ejpam-7078	414	3	=	=	VERB
ejpam-7078	414	4	q	q	X
ejpam-7078	414	5	\	\	PROPN
ejpam-7078	414	6	{	{	PUNCT
ejpam-7078	414	7	v	v	NOUN
ejpam-7078	414	8	}	}	PUNCT
ejpam-7078	414	9	.	.	PUNCT
ejpam-7078	415	1	then	then	ADV
ejpam-7078	415	2	s	s	VERB
ejpam-7078	415	3	∪	∪	ADJ
ejpam-7078	415	4	{	{	PUNCT
ejpam-7078	415	5	v	v	NOUN
ejpam-7078	415	6	}	}	PUNCT
ejpam-7078	415	7	=	=	PUNCT
ejpam-7078	415	8	q	q	NOUN
ejpam-7078	415	9	is	be	AUX
ejpam-7078	415	10	γsh	γsh	NOUN
ejpam-7078	415	11	-	-	PUNCT
ejpam-7078	415	12	set	set	VERB
ejpam-7078	415	13	in	in	ADP
ejpam-7078	415	14	g	g	PROPN
ejpam-7078	415	15	and	and	CCONJ
ejpam-7078	415	16	v	v	NOUN
ejpam-7078	415	17	(	(	PUNCT
ejpam-7078	415	18	g	g	NOUN
ejpam-7078	415	19	)	)	PUNCT
ejpam-7078	415	20	\	\	PUNCT
ejpam-7078	416	1	(	(	PUNCT
ejpam-7078	416	2	s	s	NOUN
ejpam-7078	416	3	∪	∪	X
ejpam-7078	416	4	{	{	PUNCT
ejpam-7078	416	5	v	v	NOUN
ejpam-7078	416	6	}	}	PUNCT
ejpam-7078	416	7	)	)	PUNCT
ejpam-7078	416	8	=	=	SYM
ejpam-7078	416	9	{	{	PUNCT
ejpam-7078	416	10	x	x	NOUN
ejpam-7078	416	11	}	}	PUNCT
ejpam-7078	416	12	⊆	⊆	NUM
ejpam-7078	416	13	n2	n2	ADJ
ejpam-7078	416	14	g(v	g(v	PROPN
ejpam-7078	416	15	)	)	PUNCT
ejpam-7078	416	16	.	.	PUNCT
ejpam-7078	417	1	for	for	ADP
ejpam-7078	417	2	the	the	DET
ejpam-7078	417	3	converse	converse	NOUN
ejpam-7078	417	4	,	,	PUNCT
ejpam-7078	417	5	suppose	suppose	VERB
ejpam-7078	417	6	there	there	PRON
ejpam-7078	417	7	exist	exist	VERB
ejpam-7078	417	8	a	a	DET
ejpam-7078	417	9	set	set	NOUN
ejpam-7078	417	10	s	s	NOUN
ejpam-7078	417	11	⊆	⊆	NUM
ejpam-7078	417	12	v	v	NOUN
ejpam-7078	417	13	(	(	PUNCT
ejpam-7078	417	14	g	g	NOUN
ejpam-7078	417	15	)	)	PUNCT
ejpam-7078	417	16	and	and	CCONJ
ejpam-7078	417	17	vertex	vertex	NOUN
ejpam-7078	417	18	v	v	ADP
ejpam-7078	417	19	such	such	DET
ejpam-7078	417	20	that	that	SCONJ
ejpam-7078	417	21	s	s	VERB
ejpam-7078	417	22	∪	∪	X
ejpam-7078	417	23	{	{	PUNCT
ejpam-7078	417	24	v	v	NOUN
ejpam-7078	417	25	}	}	PUNCT
ejpam-7078	417	26	is	be	AUX
ejpam-7078	417	27	a	a	DET
ejpam-7078	417	28	γsh	γsh	NOUN
ejpam-7078	417	29	-	-	PUNCT
ejpam-7078	417	30	set	set	NOUN
ejpam-7078	417	31	of	of	ADP
ejpam-7078	417	32	g	g	NOUN
ejpam-7078	417	33	and	and	CCONJ
ejpam-7078	417	34	v	v	NOUN
ejpam-7078	417	35	(	(	PUNCT
ejpam-7078	417	36	g	g	NOUN
ejpam-7078	417	37	)	)	PUNCT
ejpam-7078	417	38	\	\	PUNCT
ejpam-7078	418	1	(	(	PUNCT
ejpam-7078	418	2	s	s	NOUN
ejpam-7078	418	3	∪	∪	X
ejpam-7078	418	4	{	{	PUNCT
ejpam-7078	418	5	v	v	NOUN
ejpam-7078	418	6	}	}	PUNCT
ejpam-7078	418	7	)	)	PUNCT
ejpam-7078	418	8	⊆	⊆	NUM
ejpam-7078	418	9	n2	n2	ADJ
ejpam-7078	418	10	g(v	g(v	PROPN
ejpam-7078	418	11	)	)	PUNCT
ejpam-7078	418	12	.	.	PUNCT
ejpam-7078	419	1	let	let	VERB
ejpam-7078	419	2	v0	v0	NOUN
ejpam-7078	419	3	=	=	SYM
ejpam-7078	419	4	v	v	PROPN
ejpam-7078	419	5	(	(	PUNCT
ejpam-7078	419	6	g	g	NOUN
ejpam-7078	419	7	)	)	PUNCT
ejpam-7078	419	8	\	\	PUNCT
ejpam-7078	420	1	(	(	PUNCT
ejpam-7078	420	2	s	s	NOUN
ejpam-7078	420	3	∪	∪	X
ejpam-7078	420	4	{	{	PUNCT
ejpam-7078	420	5	v	v	NOUN
ejpam-7078	420	6	}	}	PUNCT
ejpam-7078	420	7	)	)	PUNCT
ejpam-7078	420	8	,	,	PUNCT
ejpam-7078	420	9	v1	v1	NOUN
ejpam-7078	420	10	=	=	SYM
ejpam-7078	420	11	s	s	NOUN
ejpam-7078	420	12	,	,	PUNCT
ejpam-7078	420	13	and	and	CCONJ
ejpam-7078	420	14	l.	l.	PROPN
ejpam-7078	420	15	f.	f.	PROPN
ejpam-7078	420	16	casinillo	casinillo	PROPN
ejpam-7078	420	17	,	,	PUNCT
ejpam-7078	420	18	s.	s.	PROPN
ejpam-7078	420	19	r.	r.	PROPN
ejpam-7078	420	20	canoy	canoy	PROPN
ejpam-7078	420	21	jr	jr	PROPN
ejpam-7078	420	22	.	.	PROPN
ejpam-7078	420	23	/	/	SYM
ejpam-7078	420	24	eur	eur	PROPN
ejpam-7078	420	25	.	.	PUNCT
ejpam-7078	421	1	j.	j.	PROPN
ejpam-7078	421	2	pure	pure	PROPN
ejpam-7078	421	3	appl	appl	PROPN
ejpam-7078	421	4	.	.	PROPN
ejpam-7078	421	5	math	math	PROPN
ejpam-7078	421	6	,	,	PUNCT
ejpam-7078	421	7	18	18	NUM
ejpam-7078	421	8	(	(	PUNCT
ejpam-7078	421	9	4	4	NUM
ejpam-7078	421	10	)	)	PUNCT
ejpam-7078	421	11	(	(	PUNCT
ejpam-7078	421	12	2025	2025	NUM
ejpam-7078	421	13	)	)	PUNCT
ejpam-7078	421	14	,	,	PUNCT
ejpam-7078	421	15	7078	7078	NUM
ejpam-7078	421	16	12	12	NUM
ejpam-7078	421	17	of	of	ADP
ejpam-7078	421	18	15	15	NUM
ejpam-7078	421	19	v2	v2	NOUN
ejpam-7078	421	20	=	=	SYM
ejpam-7078	421	21	{	{	PUNCT
ejpam-7078	421	22	v	v	NOUN
ejpam-7078	421	23	}	}	PUNCT
ejpam-7078	421	24	.	.	PUNCT
ejpam-7078	422	1	then	then	ADV
ejpam-7078	422	2	g	g	PROPN
ejpam-7078	422	3	=	=	SYM
ejpam-7078	422	4	(	(	PUNCT
ejpam-7078	422	5	v0	v0	PROPN
ejpam-7078	422	6	,	,	PUNCT
ejpam-7078	422	7	v1	v1	NOUN
ejpam-7078	422	8	,	,	PUNCT
ejpam-7078	422	9	v2	v2	PROPN
ejpam-7078	422	10	)	)	PUNCT
ejpam-7078	422	11	is	be	AUX
ejpam-7078	422	12	an	an	DET
ejpam-7078	422	13	shrdf	shrdf	NOUN
ejpam-7078	422	14	on	on	ADP
ejpam-7078	422	15	g.	g.	PROPN
ejpam-7078	422	16	hence	hence	ADV
ejpam-7078	422	17	,	,	PUNCT
ejpam-7078	422	18	γshr(g	γshr(g	NOUN
ejpam-7078	422	19	)	)	PUNCT
ejpam-7078	422	20	≤	≤	NOUN
ejpam-7078	422	21	ωshr	ωshr	NOUN
ejpam-7078	422	22	g	g	PROPN
ejpam-7078	422	23	(	(	PUNCT
ejpam-7078	422	24	g	g	NOUN
ejpam-7078	422	25	)	)	PUNCT
ejpam-7078	422	26	=	=	PUNCT
ejpam-7078	422	27	|v1|+	|v1|+	PRON
ejpam-7078	422	28	2|v2|	2|v2|	NUM
ejpam-7078	422	29	=	=	SYM
ejpam-7078	422	30	|s|+	|s|+	NOUN
ejpam-7078	422	31	2	2	NUM
ejpam-7078	422	32	=	=	SYM
ejpam-7078	422	33	(	(	PUNCT
ejpam-7078	422	34	γsh(g)−	γsh(g)−	PROPN
ejpam-7078	422	35	1	1	NUM
ejpam-7078	422	36	)	)	PUNCT
ejpam-7078	422	37	+	+	CCONJ
ejpam-7078	422	38	2	2	NUM
ejpam-7078	422	39	=	=	SYM
ejpam-7078	422	40	γsh(g	γsh(g	NOUN
ejpam-7078	422	41	)	)	PUNCT
ejpam-7078	422	42	+	+	NUM
ejpam-7078	422	43	1	1	X
ejpam-7078	422	44	.	.	PUNCT
ejpam-7078	422	45	since	since	SCONJ
ejpam-7078	422	46	γsh(g	γsh(g	NOUN
ejpam-7078	422	47	)	)	PUNCT
ejpam-7078	422	48	<	<	X
ejpam-7078	422	49	γshr(g	γshr(g	PROPN
ejpam-7078	422	50	)	)	PUNCT
ejpam-7078	422	51	,	,	PUNCT
ejpam-7078	422	52	it	it	PRON
ejpam-7078	422	53	follows	follow	VERB
ejpam-7078	422	54	that	that	SCONJ
ejpam-7078	422	55	γshr(g	γshr(g	NOUN
ejpam-7078	422	56	)	)	PUNCT
ejpam-7078	422	57	=	=	PUNCT
ejpam-7078	422	58	γsh(g	γsh(g	NOUN
ejpam-7078	422	59	)	)	PUNCT
ejpam-7078	422	60	+	+	NOUN
ejpam-7078	423	1	1	1	X
ejpam-7078	423	2	.	.	X
ejpam-7078	423	3	the	the	DET
ejpam-7078	423	4	join	join	NOUN
ejpam-7078	423	5	of	of	ADP
ejpam-7078	423	6	graphsg	graphsg	NOUN
ejpam-7078	423	7	andh	andh	NOUN
ejpam-7078	423	8	is	be	AUX
ejpam-7078	423	9	the	the	DET
ejpam-7078	423	10	graphg+h	graphg+h	NOUN
ejpam-7078	423	11	with	with	ADP
ejpam-7078	423	12	vertex	vertex	NOUN
ejpam-7078	423	13	set	set	VERB
ejpam-7078	423	14	v	v	NOUN
ejpam-7078	423	15	(	(	PUNCT
ejpam-7078	423	16	g+h	g+h	NOUN
ejpam-7078	423	17	)	)	PUNCT
ejpam-7078	423	18	=	=	SYM
ejpam-7078	423	19	v	v	X
ejpam-7078	423	20	(	(	PUNCT
ejpam-7078	423	21	g)∪v	g)∪v	NOUN
ejpam-7078	423	22	(	(	PUNCT
ejpam-7078	423	23	h	h	NOUN
ejpam-7078	423	24	)	)	PUNCT
ejpam-7078	423	25	and	and	CCONJ
ejpam-7078	423	26	edge	edge	NOUN
ejpam-7078	423	27	set	set	VERB
ejpam-7078	423	28	e(g+h	e(g+h	NUM
ejpam-7078	423	29	)	)	PUNCT
ejpam-7078	423	30	=	=	SYM
ejpam-7078	423	31	e(g	e(g	NOUN
ejpam-7078	423	32	)	)	PUNCT
ejpam-7078	423	33	∪	∪	ADP
ejpam-7078	423	34	e(h	e(h	PROPN
ejpam-7078	423	35	)	)	PUNCT
ejpam-7078	423	36	∈	∈	PROPN
ejpam-7078	423	37	{	{	PUNCT
ejpam-7078	423	38	uv	uv	NOUN
ejpam-7078	423	39	:	:	PUNCT
ejpam-7078	423	40	u	u	PROPN
ejpam-7078	423	41	∈	∈	PROPN
ejpam-7078	423	42	v	v	ADP
ejpam-7078	423	43	(	(	PUNCT
ejpam-7078	423	44	g	g	NOUN
ejpam-7078	423	45	)	)	PUNCT
ejpam-7078	423	46	and	and	CCONJ
ejpam-7078	423	47	v	v	ADP
ejpam-7078	423	48	∈	∈	PROPN
ejpam-7078	423	49	v	v	NOUN
ejpam-7078	423	50	(	(	PUNCT
ejpam-7078	423	51	h	h	NOUN
ejpam-7078	423	52	)	)	PUNCT
ejpam-7078	423	53	}	}	PUNCT
ejpam-7078	423	54	.	.	PUNCT
ejpam-7078	424	1	theorem	theorem	VERB
ejpam-7078	424	2	9	9	NUM
ejpam-7078	424	3	.	.	PUNCT
ejpam-7078	425	1	let	let	VERB
ejpam-7078	425	2	h	h	PRON
ejpam-7078	425	3	be	be	AUX
ejpam-7078	425	4	a	a	DET
ejpam-7078	425	5	non	non	ADJ
ejpam-7078	425	6	-	-	ADJ
ejpam-7078	425	7	complete	complete	ADJ
ejpam-7078	425	8	graph	graph	NOUN
ejpam-7078	425	9	.	.	PUNCT
ejpam-7078	426	1	then	then	ADV
ejpam-7078	426	2	f	f	PROPN
ejpam-7078	426	3	=	=	SYM
ejpam-7078	426	4	(	(	PUNCT
ejpam-7078	426	5	v0	v0	PROPN
ejpam-7078	426	6	,	,	PUNCT
ejpam-7078	426	7	v1	v1	NOUN
ejpam-7078	426	8	,	,	PUNCT
ejpam-7078	426	9	v2	v2	PROPN
ejpam-7078	426	10	)	)	PUNCT
ejpam-7078	426	11	is	be	AUX
ejpam-7078	426	12	an	an	DET
ejpam-7078	426	13	shrdf	shrdf	NOUN
ejpam-7078	426	14	on	on	ADP
ejpam-7078	426	15	a	a	DET
ejpam-7078	426	16	graph	graph	NOUN
ejpam-7078	426	17	g	g	PROPN
ejpam-7078	426	18	=	=	PROPN
ejpam-7078	426	19	kn	kn	PROPN
ejpam-7078	427	1	+	+	PROPN
ejpam-7078	427	2	h	h	NOUN
ejpam-7078	427	3	if	if	SCONJ
ejpam-7078	427	4	and	and	CCONJ
ejpam-7078	427	5	only	only	ADV
ejpam-7078	427	6	if	if	SCONJ
ejpam-7078	427	7	the	the	DET
ejpam-7078	427	8	following	follow	VERB
ejpam-7078	427	9	conditions	condition	NOUN
ejpam-7078	427	10	are	be	AUX
ejpam-7078	427	11	satisfied	satisfied	ADJ
ejpam-7078	427	12	:	:	PUNCT
ejpam-7078	427	13	(	(	PUNCT
ejpam-7078	427	14	i	i	NOUN
ejpam-7078	427	15	)	)	PUNCT
ejpam-7078	427	16	v	v	PROPN
ejpam-7078	427	17	(	(	PUNCT
ejpam-7078	427	18	kn	kn	PROPN
ejpam-7078	427	19	)	)	PUNCT
ejpam-7078	427	20	⊆	⊆	NUM
ejpam-7078	427	21	v1	v1	NOUN
ejpam-7078	427	22	∪	∪	NOUN
ejpam-7078	427	23	v2	v2	NOUN
ejpam-7078	427	24	;	;	PUNCT
ejpam-7078	427	25	and	and	CCONJ
ejpam-7078	427	26	(	(	PUNCT
ejpam-7078	427	27	ii	ii	NOUN
ejpam-7078	427	28	)	)	PUNCT
ejpam-7078	427	29	f	f	PROPN
ejpam-7078	427	30	|h	|h	PROPN
ejpam-7078	427	31	is	be	AUX
ejpam-7078	427	32	an	an	DET
ejpam-7078	427	33	shrdf	shrdf	NOUN
ejpam-7078	427	34	on	on	ADP
ejpam-7078	427	35	h.	h.	NOUN
ejpam-7078	427	36	proof	proof	NOUN
ejpam-7078	427	37	.	.	PUNCT
ejpam-7078	428	1	suppose	suppose	VERB
ejpam-7078	428	2	that	that	SCONJ
ejpam-7078	428	3	f	f	PROPN
ejpam-7078	428	4	=	=	SYM
ejpam-7078	428	5	(	(	PUNCT
ejpam-7078	428	6	v0	v0	PROPN
ejpam-7078	428	7	,	,	PUNCT
ejpam-7078	428	8	v1	v1	NOUN
ejpam-7078	428	9	,	,	PUNCT
ejpam-7078	428	10	v2	v2	PROPN
ejpam-7078	428	11	)	)	PUNCT
ejpam-7078	428	12	is	be	AUX
ejpam-7078	428	13	an	an	DET
ejpam-7078	428	14	shrdf	shrdf	NOUN
ejpam-7078	428	15	on	on	ADP
ejpam-7078	428	16	g.	g.	PROPN
ejpam-7078	428	17	let	let	VERB
ejpam-7078	428	18	x	x	SYM
ejpam-7078	428	19	∈	∈	PROPN
ejpam-7078	428	20	v	v	X
ejpam-7078	428	21	(	(	PUNCT
ejpam-7078	428	22	kn	kn	PROPN
ejpam-7078	428	23	)	)	PUNCT
ejpam-7078	428	24	.	.	PUNCT
ejpam-7078	429	1	since	since	SCONJ
ejpam-7078	429	2	xy	xy	PROPN
ejpam-7078	429	3	∈	∈	PROPN
ejpam-7078	429	4	e(g	e(g	PROPN
ejpam-7078	429	5	)	)	PUNCT
ejpam-7078	429	6	for	for	ADP
ejpam-7078	429	7	all	all	DET
ejpam-7078	429	8	y	y	PROPN
ejpam-7078	429	9	∈	∈	PROPN
ejpam-7078	429	10	v	v	ADP
ejpam-7078	429	11	(	(	PUNCT
ejpam-7078	429	12	g	g	NOUN
ejpam-7078	429	13	)	)	PUNCT
ejpam-7078	429	14	\	\	NOUN
ejpam-7078	429	15	{	{	PUNCT
ejpam-7078	429	16	x	x	NOUN
ejpam-7078	429	17	}	}	PUNCT
ejpam-7078	429	18	and	and	CCONJ
ejpam-7078	429	19	f	f	PROPN
ejpam-7078	429	20	is	be	AUX
ejpam-7078	429	21	an	an	DET
ejpam-7078	429	22	hrdf	hrdf	NOUN
ejpam-7078	429	23	on	on	ADP
ejpam-7078	429	24	g	g	PROPN
ejpam-7078	429	25	,	,	PUNCT
ejpam-7078	429	26	it	it	PRON
ejpam-7078	429	27	follows	follow	VERB
ejpam-7078	429	28	that	that	SCONJ
ejpam-7078	429	29	x	x	PROPN
ejpam-7078	429	30	/∈	/∈	PUNCT
ejpam-7078	429	31	v0	v0	PROPN
ejpam-7078	429	32	.	.	PUNCT
ejpam-7078	430	1	hence	hence	ADV
ejpam-7078	430	2	,	,	PUNCT
ejpam-7078	430	3	x	x	PUNCT
ejpam-7078	430	4	∈	∈	NOUN
ejpam-7078	430	5	v1	v1	NOUN
ejpam-7078	430	6	∪	∪	X
ejpam-7078	430	7	v2	v2	NOUN
ejpam-7078	430	8	.	.	PUNCT
ejpam-7078	431	1	this	this	PRON
ejpam-7078	431	2	shows	show	VERB
ejpam-7078	431	3	that	that	SCONJ
ejpam-7078	431	4	(	(	PUNCT
ejpam-7078	431	5	i	i	NOUN
ejpam-7078	431	6	)	)	PUNCT
ejpam-7078	431	7	holds	hold	VERB
ejpam-7078	431	8	.	.	PUNCT
ejpam-7078	432	1	this	this	PRON
ejpam-7078	432	2	implies	imply	VERB
ejpam-7078	432	3	that	that	SCONJ
ejpam-7078	432	4	v0	v0	NOUN
ejpam-7078	432	5	⊆	⊆	NUM
ejpam-7078	432	6	v	v	NOUN
ejpam-7078	432	7	(	(	PUNCT
ejpam-7078	432	8	h	h	NOUN
ejpam-7078	432	9	)	)	PUNCT
ejpam-7078	432	10	.	.	PUNCT
ejpam-7078	433	1	note	note	VERB
ejpam-7078	433	2	that	that	SCONJ
ejpam-7078	433	3	f	f	PROPN
ejpam-7078	433	4	|h	|h	X
ejpam-7078	433	5	=	=	SYM
ejpam-7078	433	6	(	(	PUNCT
ejpam-7078	433	7	v	v	NUM
ejpam-7078	433	8	h	h	NOUN
ejpam-7078	433	9	0	0	NUM
ejpam-7078	433	10	,	,	PUNCT
ejpam-7078	433	11	v	v	NOUN
ejpam-7078	433	12	h	h	NOUN
ejpam-7078	433	13	1	1	NUM
ejpam-7078	433	14	,	,	PUNCT
ejpam-7078	433	15	v	v	NOUN
ejpam-7078	433	16	h	h	NOUN
ejpam-7078	433	17	2	2	NUM
ejpam-7078	433	18	)	)	PUNCT
ejpam-7078	433	19	,	,	PUNCT
ejpam-7078	433	20	where	where	SCONJ
ejpam-7078	433	21	v	v	NOUN
ejpam-7078	433	22	h	h	NOUN
ejpam-7078	433	23	0	0	NUM
ejpam-7078	433	24	=	=	SYM
ejpam-7078	433	25	v0	v0	PROPN
ejpam-7078	433	26	,	,	PUNCT
ejpam-7078	433	27	v	v	NOUN
ejpam-7078	433	28	h	h	NOUN
ejpam-7078	433	29	1	1	NUM
ejpam-7078	433	30	=	=	SYM
ejpam-7078	433	31	v1	v1	NOUN
ejpam-7078	433	32	∩	∩	ADJ
ejpam-7078	433	33	v	v	NOUN
ejpam-7078	433	34	(	(	PUNCT
ejpam-7078	433	35	h	h	NOUN
ejpam-7078	433	36	)	)	PUNCT
ejpam-7078	433	37	,	,	PUNCT
ejpam-7078	433	38	and	and	CCONJ
ejpam-7078	433	39	v	v	ADP
ejpam-7078	433	40	h	h	NOUN
ejpam-7078	433	41	2	2	NUM
ejpam-7078	433	42	=	=	SYM
ejpam-7078	433	43	v2	v2	PROPN
ejpam-7078	433	44	∩	∩	ADJ
ejpam-7078	433	45	v	v	NOUN
ejpam-7078	433	46	(	(	PUNCT
ejpam-7078	433	47	h	h	NOUN
ejpam-7078	433	48	)	)	PUNCT
ejpam-7078	433	49	.	.	PUNCT
ejpam-7078	434	1	let	let	VERB
ejpam-7078	434	2	v	v	NUM
ejpam-7078	434	3	∈	∈	PROPN
ejpam-7078	434	4	v	v	ADP
ejpam-7078	434	5	h	h	NOUN
ejpam-7078	434	6	0	0	PUNCT
ejpam-7078	434	7	.	.	PUNCT
ejpam-7078	435	1	since	since	SCONJ
ejpam-7078	435	2	f	f	PROPN
ejpam-7078	435	3	is	be	AUX
ejpam-7078	435	4	an	an	DET
ejpam-7078	435	5	hrdf	hrdf	NOUN
ejpam-7078	435	6	on	on	ADP
ejpam-7078	435	7	g	g	NOUN
ejpam-7078	435	8	,	,	PUNCT
ejpam-7078	435	9	there	there	PRON
ejpam-7078	435	10	exists	exist	VERB
ejpam-7078	435	11	w	w	PROPN
ejpam-7078	435	12	∈	∈	PROPN
ejpam-7078	435	13	v2∩n2	v2∩n2	ADP
ejpam-7078	435	14	g(v	g(v	NOUN
ejpam-7078	435	15	)	)	PUNCT
ejpam-7078	435	16	.	.	PUNCT
ejpam-7078	436	1	hence	hence	ADV
ejpam-7078	436	2	,	,	PUNCT
ejpam-7078	436	3	w	w	PROPN
ejpam-7078	436	4	∈	∈	PROPN
ejpam-7078	436	5	v	v	ADP
ejpam-7078	436	6	h	h	NOUN
ejpam-7078	436	7	2	2	NUM
ejpam-7078	436	8	,	,	PUNCT
ejpam-7078	436	9	showing	show	VERB
ejpam-7078	436	10	that	that	SCONJ
ejpam-7078	436	11	f	f	PROPN
ejpam-7078	436	12	|h	|h	PROPN
ejpam-7078	436	13	is	be	AUX
ejpam-7078	436	14	an	an	DET
ejpam-7078	436	15	hrdf	hrdf	NOUN
ejpam-7078	436	16	on	on	ADP
ejpam-7078	436	17	h.	h.	PROPN
ejpam-7078	436	18	since	since	SCONJ
ejpam-7078	436	19	v1	v1	PROPN
ejpam-7078	436	20	∪	∪	NOUN
ejpam-7078	436	21	v2	v2	NOUN
ejpam-7078	436	22	is	be	AUX
ejpam-7078	436	23	a	a	DET
ejpam-7078	436	24	super	super	ADJ
ejpam-7078	436	25	dominating	dominating	NOUN
ejpam-7078	436	26	set	set	NOUN
ejpam-7078	436	27	in	in	ADP
ejpam-7078	436	28	g	g	NOUN
ejpam-7078	436	29	,	,	PUNCT
ejpam-7078	436	30	there	there	PRON
ejpam-7078	436	31	exists	exist	VERB
ejpam-7078	436	32	z	z	NOUN
ejpam-7078	436	33	∈	∈	PROPN
ejpam-7078	436	34	v1	v1	NOUN
ejpam-7078	436	35	∪	∪	VERB
ejpam-7078	436	36	v2	v2	NOUN
ejpam-7078	436	37	such	such	ADJ
ejpam-7078	436	38	that	that	DET
ejpam-7078	436	39	n2	n2	ADJ
ejpam-7078	436	40	g(z	g(z	PROPN
ejpam-7078	436	41	)	)	PUNCT
ejpam-7078	436	42	∩	∩	NOUN
ejpam-7078	436	43	v0	v0	NOUN
ejpam-7078	436	44	=	=	SYM
ejpam-7078	436	45	{	{	PUNCT
ejpam-7078	436	46	v	v	NOUN
ejpam-7078	436	47	}	}	PUNCT
ejpam-7078	436	48	.	.	PUNCT
ejpam-7078	437	1	this	this	PRON
ejpam-7078	437	2	implies	imply	VERB
ejpam-7078	437	3	that	that	SCONJ
ejpam-7078	437	4	z	z	PROPN
ejpam-7078	437	5	∈	∈	PROPN
ejpam-7078	437	6	v	v	ADP
ejpam-7078	437	7	h	h	NOUN
ejpam-7078	437	8	1	1	NUM
ejpam-7078	437	9	∪	∪	ADP
ejpam-7078	437	10	v	v	NUM
ejpam-7078	437	11	h	h	NOUN
ejpam-7078	437	12	2	2	NUM
ejpam-7078	437	13	.	.	PUNCT
ejpam-7078	438	1	thus	thus	ADV
ejpam-7078	438	2	,	,	PUNCT
ejpam-7078	438	3	f	f	PROPN
ejpam-7078	438	4	|h	|h	PROPN
ejpam-7078	438	5	is	be	AUX
ejpam-7078	438	6	a	a	DET
ejpam-7078	438	7	shrdf	shrdf	NOUN
ejpam-7078	438	8	on	on	ADP
ejpam-7078	438	9	h.	h.	PROPN
ejpam-7078	438	10	this	this	PRON
ejpam-7078	438	11	shows	show	VERB
ejpam-7078	438	12	that	that	SCONJ
ejpam-7078	438	13	(	(	PUNCT
ejpam-7078	438	14	ii	ii	NOUN
ejpam-7078	438	15	)	)	PUNCT
ejpam-7078	438	16	also	also	ADV
ejpam-7078	438	17	holds	hold	VERB
ejpam-7078	438	18	.	.	PUNCT
ejpam-7078	439	1	for	for	ADP
ejpam-7078	439	2	the	the	DET
ejpam-7078	439	3	converse	converse	NOUN
ejpam-7078	439	4	,	,	PUNCT
ejpam-7078	439	5	suppose	suppose	VERB
ejpam-7078	439	6	(	(	PUNCT
ejpam-7078	439	7	i	i	NOUN
ejpam-7078	439	8	)	)	PUNCT
ejpam-7078	439	9	and	and	CCONJ
ejpam-7078	439	10	(	(	PUNCT
ejpam-7078	439	11	ii	ii	NOUN
ejpam-7078	439	12	)	)	PUNCT
ejpam-7078	439	13	hold	hold	VERB
ejpam-7078	439	14	.	.	PUNCT
ejpam-7078	440	1	let	let	VERB
ejpam-7078	440	2	v	v	NUM
ejpam-7078	440	3	h	h	NOUN
ejpam-7078	440	4	1	1	NUM
ejpam-7078	440	5	=	=	SYM
ejpam-7078	440	6	v1	v1	NOUN
ejpam-7078	440	7	∩	∩	ADJ
ejpam-7078	440	8	v	v	NOUN
ejpam-7078	440	9	(	(	PUNCT
ejpam-7078	440	10	h	h	NOUN
ejpam-7078	440	11	)	)	PUNCT
ejpam-7078	440	12	,	,	PUNCT
ejpam-7078	440	13	v	v	NOUN
ejpam-7078	440	14	h	h	NOUN
ejpam-7078	440	15	2	2	NUM
ejpam-7078	440	16	=	=	SYM
ejpam-7078	440	17	v2	v2	PROPN
ejpam-7078	440	18	∩	∩	ADJ
ejpam-7078	440	19	v	v	NOUN
ejpam-7078	440	20	(	(	PUNCT
ejpam-7078	440	21	h	h	NOUN
ejpam-7078	440	22	)	)	PUNCT
ejpam-7078	440	23	,	,	PUNCT
ejpam-7078	440	24	v	v	NOUN
ejpam-7078	440	25	n	n	PRON
ejpam-7078	440	26	1	1	NUM
ejpam-7078	440	27	=	=	SYM
ejpam-7078	440	28	v1	v1	NOUN
ejpam-7078	440	29	∩	∩	ADJ
ejpam-7078	440	30	v	v	X
ejpam-7078	440	31	(	(	PUNCT
ejpam-7078	440	32	kn	kn	PROPN
ejpam-7078	440	33	)	)	PUNCT
ejpam-7078	440	34	,	,	PUNCT
ejpam-7078	440	35	and	and	CCONJ
ejpam-7078	440	36	v	v	ADP
ejpam-7078	440	37	n	n	PRON
ejpam-7078	440	38	2	2	NUM
ejpam-7078	440	39	=	=	SYM
ejpam-7078	440	40	v2	v2	PROPN
ejpam-7078	440	41	∩	∩	ADJ
ejpam-7078	440	42	v	v	NOUN
ejpam-7078	440	43	(	(	PUNCT
ejpam-7078	440	44	kn	kn	PROPN
ejpam-7078	440	45	)	)	PUNCT
ejpam-7078	440	46	.	.	PUNCT
ejpam-7078	441	1	from	from	ADP
ejpam-7078	441	2	(	(	PUNCT
ejpam-7078	441	3	i	i	NOUN
ejpam-7078	441	4	)	)	PUNCT
ejpam-7078	441	5	,	,	PUNCT
ejpam-7078	441	6	it	it	PRON
ejpam-7078	441	7	follows	follow	VERB
ejpam-7078	441	8	that	that	DET
ejpam-7078	441	9	v0	v0	NOUN
ejpam-7078	441	10	=	=	SYM
ejpam-7078	442	1	v	v	NUM
ejpam-7078	442	2	h	h	NOUN
ejpam-7078	442	3	0	0	NUM
ejpam-7078	442	4	⊆	⊆	NUM
ejpam-7078	442	5	v	v	ADP
ejpam-7078	442	6	(	(	PUNCT
ejpam-7078	442	7	h	h	NOUN
ejpam-7078	442	8	)	)	PUNCT
ejpam-7078	442	9	.	.	PUNCT
ejpam-7078	443	1	if	if	SCONJ
ejpam-7078	443	2	v0	v0	NOUN
ejpam-7078	443	3	=	=	SYM
ejpam-7078	443	4	∅	∅	NOUN
ejpam-7078	443	5	,	,	PUNCT
ejpam-7078	443	6	then	then	ADV
ejpam-7078	443	7	f	f	PROPN
ejpam-7078	443	8	=	=	SYM
ejpam-7078	443	9	(	(	PUNCT
ejpam-7078	443	10	∅	∅	NOUN
ejpam-7078	443	11	,	,	PUNCT
ejpam-7078	443	12	v	v	NOUN
ejpam-7078	443	13	h	h	NOUN
ejpam-7078	443	14	1	1	NUM
ejpam-7078	443	15	∪	∪	ADP
ejpam-7078	443	16	v	v	NUM
ejpam-7078	443	17	n	n	ADP
ejpam-7078	443	18	1	1	NUM
ejpam-7078	443	19	,	,	PUNCT
ejpam-7078	443	20	v	v	NOUN
ejpam-7078	443	21	h	h	NOUN
ejpam-7078	443	22	2	2	NUM
ejpam-7078	443	23	∪	∪	X
ejpam-7078	443	24	v	v	ADP
ejpam-7078	443	25	n	n	PRON
ejpam-7078	443	26	2	2	NUM
ejpam-7078	443	27	)	)	PUNCT
ejpam-7078	443	28	is	be	AUX
ejpam-7078	443	29	an	an	DET
ejpam-7078	443	30	shrdf	shrdf	NOUN
ejpam-7078	443	31	on	on	ADP
ejpam-7078	443	32	g.	g.	PROPN
ejpam-7078	443	33	suppose	suppose	VERB
ejpam-7078	443	34	v0	v0	PROPN
ejpam-7078	443	35	̸=	̸=	PROPN
ejpam-7078	443	36	∅.	∅.	ADV
ejpam-7078	443	37	let	let	VERB
ejpam-7078	443	38	x	x	SYM
ejpam-7078	443	39	∈	∈	PROPN
ejpam-7078	443	40	v0	v0	NOUN
ejpam-7078	443	41	.	.	PUNCT
ejpam-7078	444	1	since	since	SCONJ
ejpam-7078	444	2	f	f	PROPN
ejpam-7078	444	3	|h	|h	X
ejpam-7078	444	4	=	=	SYM
ejpam-7078	444	5	(	(	PUNCT
ejpam-7078	444	6	v0	v0	PROPN
ejpam-7078	444	7	,	,	PUNCT
ejpam-7078	444	8	v	v	PART
ejpam-7078	444	9	h	h	NOUN
ejpam-7078	444	10	1	1	NUM
ejpam-7078	444	11	,	,	PUNCT
ejpam-7078	444	12	v	v	NOUN
ejpam-7078	444	13	h	h	NOUN
ejpam-7078	444	14	2	2	NUM
ejpam-7078	444	15	)	)	PUNCT
ejpam-7078	444	16	is	be	AUX
ejpam-7078	444	17	an	an	DET
ejpam-7078	444	18	hrdf	hrdf	NOUN
ejpam-7078	444	19	on	on	ADP
ejpam-7078	444	20	h	h	NOUN
ejpam-7078	444	21	,	,	PUNCT
ejpam-7078	444	22	there	there	PRON
ejpam-7078	444	23	exists	exist	VERB
ejpam-7078	444	24	y	y	PROPN
ejpam-7078	444	25	∈	∈	PROPN
ejpam-7078	444	26	v	v	ADP
ejpam-7078	444	27	h	h	NOUN
ejpam-7078	444	28	2	2	NUM
ejpam-7078	444	29	∩n2	∩n2	PROPN
ejpam-7078	444	30	h(x	h(x	PROPN
ejpam-7078	444	31	)	)	PUNCT
ejpam-7078	444	32	.	.	PUNCT
ejpam-7078	445	1	hence	hence	ADV
ejpam-7078	445	2	,	,	PUNCT
ejpam-7078	445	3	y	y	PROPN
ejpam-7078	445	4	∈	∈	PROPN
ejpam-7078	445	5	v2	v2	PROPN
ejpam-7078	445	6	∩n2	∩n2	PROPN
ejpam-7078	445	7	g(x	g(x	PROPN
ejpam-7078	445	8	)	)	PUNCT
ejpam-7078	445	9	,	,	PUNCT
ejpam-7078	445	10	showing	show	VERB
ejpam-7078	445	11	that	that	SCONJ
ejpam-7078	445	12	f	f	PROPN
ejpam-7078	445	13	=	=	SYM
ejpam-7078	445	14	(	(	PUNCT
ejpam-7078	445	15	v0	v0	PROPN
ejpam-7078	445	16	,	,	PUNCT
ejpam-7078	445	17	v1	v1	NOUN
ejpam-7078	445	18	,	,	PUNCT
ejpam-7078	445	19	v2	v2	PROPN
ejpam-7078	445	20	)	)	PUNCT
ejpam-7078	445	21	is	be	AUX
ejpam-7078	445	22	an	an	DET
ejpam-7078	445	23	hrdf	hrdf	NOUN
ejpam-7078	445	24	on	on	ADP
ejpam-7078	445	25	g.	g.	PROPN
ejpam-7078	445	26	also	also	ADV
ejpam-7078	445	27	,	,	PUNCT
ejpam-7078	445	28	since	since	SCONJ
ejpam-7078	445	29	f	f	PROPN
ejpam-7078	445	30	|h	|h	X
ejpam-7078	445	31	satisfies	satisfie	NOUN
ejpam-7078	445	32	(	(	PUNCT
ejpam-7078	445	33	shr2	shr2	NOUN
ejpam-7078	445	34	)	)	PUNCT
ejpam-7078	445	35	on	on	ADP
ejpam-7078	445	36	h	h	NOUN
ejpam-7078	445	37	,	,	PUNCT
ejpam-7078	445	38	it	it	PRON
ejpam-7078	445	39	follows	follow	VERB
ejpam-7078	445	40	that	that	SCONJ
ejpam-7078	445	41	there	there	PRON
ejpam-7078	445	42	exists	exist	VERB
ejpam-7078	445	43	z	z	NOUN
ejpam-7078	445	44	∈	∈	PROPN
ejpam-7078	445	45	v	v	ADP
ejpam-7078	445	46	h	h	NOUN
ejpam-7078	445	47	1	1	NUM
ejpam-7078	445	48	∪v	∪v	NOUN
ejpam-7078	445	49	h	h	NOUN
ejpam-7078	445	50	2	2	NUM
ejpam-7078	445	51	such	such	ADJ
ejpam-7078	445	52	that	that	DET
ejpam-7078	445	53	n2	n2	PROPN
ejpam-7078	445	54	h(z)∩v0	h(z)∩v0	PROPN
ejpam-7078	445	55	=	=	SYM
ejpam-7078	445	56	{	{	PUNCT
ejpam-7078	445	57	x	x	NOUN
ejpam-7078	445	58	}	}	PUNCT
ejpam-7078	445	59	.	.	PUNCT
ejpam-7078	446	1	since	since	SCONJ
ejpam-7078	446	2	v	v	NUM
ejpam-7078	446	3	h	h	NOUN
ejpam-7078	446	4	1	1	NUM
ejpam-7078	446	5	∪v	∪v	NOUN
ejpam-7078	446	6	h	h	NOUN
ejpam-7078	446	7	2	2	NUM
ejpam-7078	446	8	⊆	⊆	NUM
ejpam-7078	446	9	v1∪v2	v1∪v2	PROPN
ejpam-7078	446	10	,	,	PUNCT
ejpam-7078	446	11	we	we	PRON
ejpam-7078	446	12	find	find	VERB
ejpam-7078	446	13	that	that	SCONJ
ejpam-7078	446	14	z	z	PROPN
ejpam-7078	446	15	∈	∈	PROPN
ejpam-7078	446	16	v1∪v2	v1∪v2	PROPN
ejpam-7078	446	17	.	.	PUNCT
ejpam-7078	447	1	consequently	consequently	ADV
ejpam-7078	447	2	,	,	PUNCT
ejpam-7078	447	3	f	f	PROPN
ejpam-7078	447	4	=	=	SYM
ejpam-7078	447	5	(	(	PUNCT
ejpam-7078	447	6	v0	v0	PROPN
ejpam-7078	447	7	,	,	PUNCT
ejpam-7078	447	8	v1	v1	NOUN
ejpam-7078	447	9	,	,	PUNCT
ejpam-7078	447	10	v2	v2	PROPN
ejpam-7078	447	11	)	)	PUNCT
ejpam-7078	447	12	is	be	AUX
ejpam-7078	447	13	an	an	DET
ejpam-7078	447	14	shrdf	shrdf	NOUN
ejpam-7078	447	15	on	on	ADP
ejpam-7078	447	16	a	a	DET
ejpam-7078	447	17	graph	graph	NOUN
ejpam-7078	447	18	g.	g.	NOUN
ejpam-7078	447	19	the	the	DET
ejpam-7078	447	20	following	follow	VERB
ejpam-7078	447	21	corollaries	corollary	NOUN
ejpam-7078	447	22	below	below	ADV
ejpam-7078	447	23	are	be	AUX
ejpam-7078	447	24	direct	direct	ADJ
ejpam-7078	447	25	consequence	consequence	NOUN
ejpam-7078	447	26	of	of	ADP
ejpam-7078	447	27	theorem	theorem	ADJ
ejpam-7078	447	28	9	9	NUM
ejpam-7078	448	1	.	.	PUNCT
ejpam-7078	448	2	corollary	corollary	ADJ
ejpam-7078	448	3	3	3	X
ejpam-7078	448	4	.	.	PUNCT
ejpam-7078	449	1	let	let	VERB
ejpam-7078	449	2	g	g	NOUN
ejpam-7078	449	3	be	be	AUX
ejpam-7078	449	4	any	any	DET
ejpam-7078	449	5	graph	graph	NOUN
ejpam-7078	449	6	.	.	PUNCT
ejpam-7078	450	1	then	then	ADV
ejpam-7078	450	2	γshr(kn	γshr(kn	VERB
ejpam-7078	450	3	+	+	NOUN
ejpam-7078	450	4	g	g	NOUN
ejpam-7078	450	5	)	)	PUNCT
ejpam-7078	450	6	=	=	SYM
ejpam-7078	450	7	n+	n+	PUNCT
ejpam-7078	450	8	γshr(g	γshr(g	NOUN
ejpam-7078	450	9	)	)	PUNCT
ejpam-7078	450	10	.	.	PUNCT
ejpam-7078	451	1	proof	proof	NOUN
ejpam-7078	451	2	.	.	PUNCT
ejpam-7078	452	1	let	let	VERB
ejpam-7078	452	2	d	d	NOUN
ejpam-7078	452	3	=	=	SYM
ejpam-7078	452	4	v	v	PROPN
ejpam-7078	452	5	(	(	PUNCT
ejpam-7078	452	6	kn	kn	PROPN
ejpam-7078	452	7	)	)	PUNCT
ejpam-7078	452	8	and	and	CCONJ
ejpam-7078	452	9	let	let	VERB
ejpam-7078	452	10	g	g	PROPN
ejpam-7078	452	11	=	=	SYM
ejpam-7078	452	12	(	(	PUNCT
ejpam-7078	452	13	v0	v0	PROPN
ejpam-7078	452	14	,	,	PUNCT
ejpam-7078	452	15	v1	v1	NOUN
ejpam-7078	452	16	,	,	PUNCT
ejpam-7078	452	17	v2	v2	PROPN
ejpam-7078	452	18	)	)	PUNCT
ejpam-7078	452	19	be	be	AUX
ejpam-7078	452	20	a	a	DET
ejpam-7078	452	21	γshr	γshr	NOUN
ejpam-7078	452	22	-	-	PUNCT
ejpam-7078	452	23	function	function	NOUN
ejpam-7078	452	24	on	on	ADP
ejpam-7078	452	25	g.	g.	PROPN
ejpam-7078	452	26	let	let	VERB
ejpam-7078	452	27	v	v	NOUN
ejpam-7078	452	28	′	′	NOUN
ejpam-7078	452	29	0	0	NUM
ejpam-7078	453	1	=	=	SYM
ejpam-7078	453	2	v0	v0	PROPN
ejpam-7078	453	3	,	,	PUNCT
ejpam-7078	453	4	v	v	NOUN
ejpam-7078	453	5	′	′	NOUN
ejpam-7078	453	6	1	1	NUM
ejpam-7078	453	7	=	=	SYM
ejpam-7078	453	8	d	d	X
ejpam-7078	453	9	∪	∪	X
ejpam-7078	453	10	v1	v1	NOUN
ejpam-7078	453	11	,	,	PUNCT
ejpam-7078	453	12	and	and	CCONJ
ejpam-7078	453	13	v	v	X
ejpam-7078	453	14	′	′	NUM
ejpam-7078	453	15	2	2	NUM
ejpam-7078	453	16	=	=	SYM
ejpam-7078	453	17	v2	v2	PROPN
ejpam-7078	453	18	.	.	PUNCT
ejpam-7078	454	1	then	then	ADV
ejpam-7078	454	2	f	f	PROPN
ejpam-7078	454	3	=	=	PRON
ejpam-7078	454	4	(	(	PUNCT
ejpam-7078	454	5	v	v	NUM
ejpam-7078	454	6	′	′	NUM
ejpam-7078	454	7	0	0	NUM
ejpam-7078	454	8	,	,	PUNCT
ejpam-7078	454	9	v	v	NOUN
ejpam-7078	454	10	′	′	NUM
ejpam-7078	454	11	1	1	NUM
ejpam-7078	454	12	,	,	PUNCT
ejpam-7078	454	13	v	v	NOUN
ejpam-7078	454	14	′	′	NUM
ejpam-7078	454	15	2	2	NUM
ejpam-7078	454	16	)	)	PUNCT
ejpam-7078	454	17	is	be	AUX
ejpam-7078	454	18	an	an	DET
ejpam-7078	454	19	shrdf	shrdf	NOUN
ejpam-7078	454	20	on	on	ADP
ejpam-7078	454	21	kn	kn	PROPN
ejpam-7078	454	22	+	+	CCONJ
ejpam-7078	454	23	g	g	NOUN
ejpam-7078	454	24	by	by	ADP
ejpam-7078	454	25	theorem	theorem	NOUN
ejpam-7078	454	26	9	9	NUM
ejpam-7078	454	27	.	.	PUNCT
ejpam-7078	455	1	hence	hence	ADV
ejpam-7078	455	2	,	,	PUNCT
ejpam-7078	455	3	we	we	PRON
ejpam-7078	455	4	have	have	VERB
ejpam-7078	455	5	γshr(kn	γshr(kn	NOUN
ejpam-7078	455	6	+	+	NOUN
ejpam-7078	455	7	g	g	NOUN
ejpam-7078	455	8	)	)	PUNCT
ejpam-7078	455	9	≤	≤	NOUN
ejpam-7078	455	10	ωshr	ωshr	NOUN
ejpam-7078	455	11	kn+g(f	kn+g(f	PROPN
ejpam-7078	455	12	)	)	PUNCT
ejpam-7078	456	1	=	=	SYM
ejpam-7078	456	2	|v	|v	PROPN
ejpam-7078	456	3	′	′	NUM
ejpam-7078	456	4	1	1	NUM
ejpam-7078	456	5	|+	|+	NOUN
ejpam-7078	457	1	2|v	2|v	NOUN
ejpam-7078	458	1	′	′	NOUN
ejpam-7078	458	2	2	2	NUM
ejpam-7078	459	1	|	|	ADV
ejpam-7078	459	2	=	=	SYM
ejpam-7078	459	3	(	(	PUNCT
ejpam-7078	459	4	|d	|d	NOUN
ejpam-7078	459	5	∪	∪	ADJ
ejpam-7078	459	6	v1|	v1|	NOUN
ejpam-7078	459	7	)	)	PUNCT
ejpam-7078	459	8	+	+	NUM
ejpam-7078	459	9	2|v2|	2|v2|	NUM
ejpam-7078	459	10	=	=	SYM
ejpam-7078	459	11	(	(	PUNCT
ejpam-7078	459	12	|d|+	|d|+	NOUN
ejpam-7078	459	13	|v1|	|v1|	NOUN
ejpam-7078	459	14	)	)	PUNCT
ejpam-7078	460	1	+	+	NUM
ejpam-7078	460	2	2|v2|	2|v2|	NUM
ejpam-7078	460	3	=	=	SYM
ejpam-7078	460	4	|d|+	|d|+	NOUN
ejpam-7078	460	5	(	(	PUNCT
ejpam-7078	460	6	|v1|+	|v1|+	ADV
ejpam-7078	460	7	2|v2|	2|v2|	NUM
ejpam-7078	460	8	)	)	PUNCT
ejpam-7078	460	9	=	=	SYM
ejpam-7078	460	10	n+	n+	PUNCT
ejpam-7078	460	11	γshr(g	γshr(g	NOUN
ejpam-7078	460	12	)	)	PUNCT
ejpam-7078	460	13	.	.	PUNCT
ejpam-7078	461	1	l.	l.	PROPN
ejpam-7078	461	2	f.	f.	PROPN
ejpam-7078	461	3	casinillo	casinillo	PROPN
ejpam-7078	461	4	,	,	PUNCT
ejpam-7078	461	5	s.	s.	PROPN
ejpam-7078	461	6	r.	r.	PROPN
ejpam-7078	461	7	canoy	canoy	PROPN
ejpam-7078	461	8	jr	jr	PROPN
ejpam-7078	461	9	.	.	PROPN
ejpam-7078	461	10	/	/	SYM
ejpam-7078	461	11	eur	eur	PROPN
ejpam-7078	461	12	.	.	PUNCT
ejpam-7078	462	1	j.	j.	PROPN
ejpam-7078	462	2	pure	pure	PROPN
ejpam-7078	462	3	appl	appl	PROPN
ejpam-7078	462	4	.	.	PROPN
ejpam-7078	462	5	math	math	PROPN
ejpam-7078	462	6	,	,	PUNCT
ejpam-7078	462	7	18	18	NUM
ejpam-7078	462	8	(	(	PUNCT
ejpam-7078	462	9	4	4	NUM
ejpam-7078	462	10	)	)	PUNCT
ejpam-7078	462	11	(	(	PUNCT
ejpam-7078	462	12	2025	2025	NUM
ejpam-7078	462	13	)	)	PUNCT
ejpam-7078	462	14	,	,	PUNCT
ejpam-7078	462	15	7078	7078	NUM
ejpam-7078	462	16	13	13	NUM
ejpam-7078	462	17	of	of	ADP
ejpam-7078	462	18	15	15	NUM
ejpam-7078	462	19	on	on	ADP
ejpam-7078	462	20	the	the	DET
ejpam-7078	462	21	other	other	ADJ
ejpam-7078	462	22	hand	hand	NOUN
ejpam-7078	462	23	,	,	PUNCT
ejpam-7078	462	24	let	let	VERB
ejpam-7078	462	25	h	h	NOUN
ejpam-7078	462	26	=	=	PRON
ejpam-7078	462	27	(	(	PUNCT
ejpam-7078	462	28	w0,w1,w2	w0,w1,w2	ADV
ejpam-7078	462	29	)	)	PUNCT
ejpam-7078	462	30	be	be	AUX
ejpam-7078	462	31	a	a	DET
ejpam-7078	462	32	γshr	γshr	NOUN
ejpam-7078	462	33	-	-	PUNCT
ejpam-7078	462	34	function	function	NOUN
ejpam-7078	462	35	on	on	ADP
ejpam-7078	462	36	kn	kn	PROPN
ejpam-7078	462	37	+	+	CCONJ
ejpam-7078	462	38	g.	g.	PROPN
ejpam-7078	462	39	by	by	ADP
ejpam-7078	462	40	theorem	theorem	NOUN
ejpam-7078	462	41	9	9	NUM
ejpam-7078	462	42	,	,	PUNCT
ejpam-7078	462	43	we	we	PRON
ejpam-7078	462	44	have	have	VERB
ejpam-7078	462	45	v	v	NUM
ejpam-7078	462	46	(	(	PUNCT
ejpam-7078	462	47	kn	kn	PROPN
ejpam-7078	462	48	)	)	PUNCT
ejpam-7078	462	49	⊆	⊆	NUM
ejpam-7078	462	50	w1	w1	NOUN
ejpam-7078	462	51	∪w2	∪w2	NOUN
ejpam-7078	462	52	and	and	CCONJ
ejpam-7078	462	53	h|g	h|g	NOUN
ejpam-7078	462	54	is	be	AUX
ejpam-7078	462	55	an	an	DET
ejpam-7078	462	56	shrdf	shrdf	NOUN
ejpam-7078	462	57	on	on	ADP
ejpam-7078	462	58	g.	g.	PROPN
ejpam-7078	462	59	since	since	SCONJ
ejpam-7078	462	60	h	h	PROPN
ejpam-7078	462	61	is	be	AUX
ejpam-7078	462	62	a	a	DET
ejpam-7078	462	63	γshr	γshr	NOUN
ejpam-7078	462	64	-	-	PUNCT
ejpam-7078	462	65	function	function	NOUN
ejpam-7078	462	66	,	,	PUNCT
ejpam-7078	462	67	we	we	PRON
ejpam-7078	462	68	have	have	VERB
ejpam-7078	462	69	v	v	NUM
ejpam-7078	462	70	(	(	PUNCT
ejpam-7078	462	71	kn	kn	PROPN
ejpam-7078	462	72	)	)	PUNCT
ejpam-7078	462	73	⊆	⊆	NUM
ejpam-7078	462	74	w1	w1	NOUN
ejpam-7078	462	75	,	,	PUNCT
ejpam-7078	462	76	i.e.	i.e.	X
ejpam-7078	462	77	,	,	PUNCT
ejpam-7078	462	78	w1	w1	NOUN
ejpam-7078	462	79	=	=	SYM
ejpam-7078	462	80	v	v	PROPN
ejpam-7078	462	81	(	(	PUNCT
ejpam-7078	462	82	kn	kn	PROPN
ejpam-7078	462	83	)	)	PUNCT
ejpam-7078	462	84	∪	∪	NOUN
ejpam-7078	462	85	(	(	PUNCT
ejpam-7078	462	86	w1	w1	NOUN
ejpam-7078	462	87	∩	∩	ADJ
ejpam-7078	462	88	v	v	X
ejpam-7078	462	89	(	(	PUNCT
ejpam-7078	462	90	g	g	NOUN
ejpam-7078	462	91	)	)	PUNCT
ejpam-7078	462	92	)	)	PUNCT
ejpam-7078	462	93	and	and	CCONJ
ejpam-7078	462	94	h|g	h|g	NOUN
ejpam-7078	463	1	=	=	SYM
ejpam-7078	463	2	(	(	PUNCT
ejpam-7078	463	3	w0,w1	w0,w1	PROPN
ejpam-7078	463	4	∩	∩	NOUN
ejpam-7078	463	5	v	v	X
ejpam-7078	463	6	(	(	PUNCT
ejpam-7078	463	7	g),w2	g),w2	NOUN
ejpam-7078	463	8	)	)	PUNCT
ejpam-7078	463	9	thus	thus	ADV
ejpam-7078	463	10	,	,	PUNCT
ejpam-7078	463	11	γshr(kn	γshr(kn	NOUN
ejpam-7078	463	12	+	+	NOUN
ejpam-7078	463	13	g	g	NOUN
ejpam-7078	463	14	)	)	PUNCT
ejpam-7078	463	15	=	=	SYM
ejpam-7078	463	16	ωshr	ωshr	PROPN
ejpam-7078	463	17	kn+g(h	kn+g(h	PROPN
ejpam-7078	463	18	)	)	PUNCT
ejpam-7078	463	19	=	=	SYM
ejpam-7078	463	20	|w1|+	|w1|+	PROPN
ejpam-7078	463	21	2|w2|	2|w2|	NUM
ejpam-7078	463	22	=	=	SYM
ejpam-7078	463	23	(	(	PUNCT
ejpam-7078	463	24	|v	|v	X
ejpam-7078	463	25	(	(	PUNCT
ejpam-7078	463	26	kn)|+	kn)|+	ADJ
ejpam-7078	463	27	|w1	|w1	PROPN
ejpam-7078	463	28	∩	∩	ADJ
ejpam-7078	463	29	v	v	X
ejpam-7078	463	30	(	(	PUNCT
ejpam-7078	463	31	g)|	g)|	PROPN
ejpam-7078	463	32	)	)	PUNCT
ejpam-7078	463	33	+	+	NUM
ejpam-7078	463	34	2|w2|	2|w2|	NUM
ejpam-7078	463	35	=	=	SYM
ejpam-7078	463	36	n+	n+	ADP
ejpam-7078	463	37	|w1	|w1	PROPN
ejpam-7078	463	38	∩	∩	ADJ
ejpam-7078	463	39	v	v	X
ejpam-7078	463	40	(	(	PUNCT
ejpam-7078	463	41	g)|+	g)|+	NOUN
ejpam-7078	463	42	2|w2|	2|w2|	NUM
ejpam-7078	463	43	=	=	SYM
ejpam-7078	463	44	n+	n+	PART
ejpam-7078	463	45	ωshr	ωshr	PROPN
ejpam-7078	463	46	g	g	PROPN
ejpam-7078	463	47	(	(	PUNCT
ejpam-7078	463	48	h|g	h|g	PROPN
ejpam-7078	463	49	)	)	PUNCT
ejpam-7078	463	50	≥	≥	NUM
ejpam-7078	463	51	n+	n+	NUM
ejpam-7078	463	52	γshr(g	γshr(g	NOUN
ejpam-7078	463	53	)	)	PUNCT
ejpam-7078	463	54	.	.	PUNCT
ejpam-7078	464	1	therefore	therefore	ADV
ejpam-7078	464	2	,	,	PUNCT
ejpam-7078	464	3	γshr(kn	γshr(kn	NOUN
ejpam-7078	464	4	+	+	NOUN
ejpam-7078	464	5	g	g	NOUN
ejpam-7078	464	6	)	)	PUNCT
ejpam-7078	464	7	=	=	SYM
ejpam-7078	464	8	n+	n+	PUNCT
ejpam-7078	464	9	γshr(g	γshr(g	NOUN
ejpam-7078	464	10	)	)	PUNCT
ejpam-7078	464	11	.	.	PUNCT
ejpam-7078	465	1	this	this	PRON
ejpam-7078	465	2	establishes	establish	VERB
ejpam-7078	465	3	the	the	DET
ejpam-7078	465	4	desired	desire	VERB
ejpam-7078	465	5	equality	equality	NOUN
ejpam-7078	465	6	.	.	PUNCT
ejpam-7078	466	1	corollary	corollary	ADJ
ejpam-7078	466	2	4	4	NUM
ejpam-7078	466	3	.	.	PUNCT
ejpam-7078	467	1	let	let	VERB
ejpam-7078	467	2	n	n	PRON
ejpam-7078	467	3	be	be	AUX
ejpam-7078	467	4	a	a	DET
ejpam-7078	467	5	positive	positive	ADJ
ejpam-7078	467	6	integer	integer	NOUN
ejpam-7078	467	7	greater	great	ADJ
ejpam-7078	467	8	than	than	ADP
ejpam-7078	467	9	or	or	CCONJ
ejpam-7078	467	10	equal	equal	ADJ
ejpam-7078	467	11	to	to	ADP
ejpam-7078	467	12	3	3	NUM
ejpam-7078	467	13	.	.	PUNCT
ejpam-7078	468	1	then	then	ADV
ejpam-7078	468	2	each	each	DET
ejpam-7078	468	3	the	the	DET
ejpam-7078	468	4	following	follow	VERB
ejpam-7078	468	5	holds	hold	NOUN
ejpam-7078	468	6	:	:	PUNCT
ejpam-7078	468	7	(	(	PUNCT
ejpam-7078	468	8	i	i	NOUN
ejpam-7078	468	9	)	)	PUNCT
ejpam-7078	468	10	γshr(sn	γshr(sn	ADJ
ejpam-7078	468	11	)	)	PUNCT
ejpam-7078	468	12	=	=	SYM
ejpam-7078	468	13	γshr(k1,n	γshr(k1,n	X
ejpam-7078	468	14	)	)	PUNCT
ejpam-7078	468	15	=	=	SYM
ejpam-7078	468	16	n+	n+	PUNCT
ejpam-7078	469	1	1	1	NUM
ejpam-7078	469	2	;	;	PUNCT
ejpam-7078	469	3	(	(	PUNCT
ejpam-7078	469	4	ii	ii	NOUN
ejpam-7078	469	5	)	)	PUNCT
ejpam-7078	469	6	γshr(fn	γshr(fn	NOUN
ejpam-7078	469	7	)	)	PUNCT
ejpam-7078	469	8	=	=	SYM
ejpam-7078	469	9	γshr(k1	γshr(k1	NOUN
ejpam-7078	469	10	+	+	CCONJ
ejpam-7078	469	11	pn	pn	NOUN
ejpam-7078	469	12	)	)	PUNCT
ejpam-7078	469	13	=	=	PRON
ejpam-7078	469	14	{	{	PUNCT
ejpam-7078	469	15	n+	n+	NOUN
ejpam-7078	469	16	1	1	NUM
ejpam-7078	469	17	,	,	PUNCT
ejpam-7078	469	18	if	if	SCONJ
ejpam-7078	469	19	n	n	PRON
ejpam-7078	469	20	≤	≤	NUM
ejpam-7078	469	21	8	8	NUM
ejpam-7078	469	22	n−	n−	NOUN
ejpam-7078	469	23	k	k	NOUN
ejpam-7078	470	1	+	+	NOUN
ejpam-7078	470	2	1	1	NUM
ejpam-7078	470	3	,	,	PUNCT
ejpam-7078	470	4	if	if	SCONJ
ejpam-7078	470	5	n	n	PRON
ejpam-7078	470	6	≥	≥	NOUN
ejpam-7078	470	7	9	9	NUM
ejpam-7078	470	8	,	,	PUNCT
ejpam-7078	470	9	where	where	SCONJ
ejpam-7078	470	10	k	k	PROPN
ejpam-7078	470	11	=	=	PUNCT
ejpam-7078	470	12	⌊n+1	⌊n+1	NOUN
ejpam-7078	470	13	10	10	NUM
ejpam-7078	470	14	⌋.	⌋.	ADJ
ejpam-7078	470	15	(	(	PUNCT
ejpam-7078	470	16	iii	iii	X
ejpam-7078	470	17	)	)	PUNCT
ejpam-7078	470	18	γshr(wn	γshr(wn	NOUN
ejpam-7078	470	19	)	)	PUNCT
ejpam-7078	470	20	=	=	SYM
ejpam-7078	470	21	γshr(k1	γshr(k1	NOUN
ejpam-7078	470	22	+	+	X
ejpam-7078	470	23	cn	cn	NOUN
ejpam-7078	470	24	)	)	PUNCT
ejpam-7078	470	25	=	=	SYM
ejpam-7078	470	26	{	{	PUNCT
ejpam-7078	470	27	n+	n+	NOUN
ejpam-7078	470	28	1	1	NUM
ejpam-7078	470	29	,	,	PUNCT
ejpam-7078	470	30	if	if	SCONJ
ejpam-7078	470	31	3	3	NUM
ejpam-7078	470	32	≤	≤	NUM
ejpam-7078	470	33	n	n	PRON
ejpam-7078	470	34	≤	≤	NOUN
ejpam-7078	470	35	9	9	NUM
ejpam-7078	470	36	n−	n−	NOUN
ejpam-7078	470	37	k	k	PROPN
ejpam-7078	471	1	+	+	CCONJ
ejpam-7078	471	2	1	1	NUM
ejpam-7078	471	3	,	,	PUNCT
ejpam-7078	471	4	if	if	SCONJ
ejpam-7078	471	5	n	n	PRON
ejpam-7078	471	6	≥	≥	NOUN
ejpam-7078	471	7	10	10	NUM
ejpam-7078	471	8	,	,	PUNCT
ejpam-7078	471	9	where	where	SCONJ
ejpam-7078	471	10	k	k	NOUN
ejpam-7078	471	11	=	=	SYM
ejpam-7078	471	12	⌊	⌊	PROPN
ejpam-7078	471	13	n	n	PART
ejpam-7078	471	14	10⌋.	10⌋.	NUM
ejpam-7078	471	15	theorem	theorem	ADJ
ejpam-7078	471	16	10	10	NUM
ejpam-7078	471	17	.	.	PUNCT
ejpam-7078	472	1	let	let	VERB
ejpam-7078	472	2	g	g	NOUN
ejpam-7078	472	3	and	and	CCONJ
ejpam-7078	472	4	h	h	NOUN
ejpam-7078	472	5	be	be	VERB
ejpam-7078	472	6	any	any	DET
ejpam-7078	472	7	non	non	ADJ
ejpam-7078	472	8	-	-	ADJ
ejpam-7078	472	9	complete	complete	ADJ
ejpam-7078	472	10	graphs	graph	NOUN
ejpam-7078	472	11	.	.	PUNCT
ejpam-7078	473	1	then	then	ADV
ejpam-7078	473	2	,	,	PUNCT
ejpam-7078	473	3	f	f	PROPN
ejpam-7078	473	4	=	=	SYM
ejpam-7078	473	5	(	(	PUNCT
ejpam-7078	473	6	v0	v0	PROPN
ejpam-7078	473	7	,	,	PUNCT
ejpam-7078	473	8	v1	v1	NOUN
ejpam-7078	473	9	,	,	PUNCT
ejpam-7078	473	10	v2	v2	PROPN
ejpam-7078	473	11	)	)	PUNCT
ejpam-7078	473	12	is	be	AUX
ejpam-7078	473	13	a	a	DET
ejpam-7078	473	14	shrdf	shrdf	NOUN
ejpam-7078	473	15	on	on	ADP
ejpam-7078	473	16	g+h	g+h	PROPN
ejpam-7078	474	1	if	if	SCONJ
ejpam-7078	474	2	and	and	CCONJ
ejpam-7078	474	3	only	only	ADV
ejpam-7078	474	4	if	if	SCONJ
ejpam-7078	474	5	f	f	PROPN
ejpam-7078	474	6	|g	|g	VERB
ejpam-7078	474	7	and	and	CCONJ
ejpam-7078	474	8	f	f	PROPN
ejpam-7078	474	9	|h	|h	NOUN
ejpam-7078	474	10	are	be	AUX
ejpam-7078	474	11	shrdf	shrdf	NOUN
ejpam-7078	474	12	on	on	ADP
ejpam-7078	474	13	g	g	PROPN
ejpam-7078	474	14	and	and	CCONJ
ejpam-7078	474	15	h	h	NOUN
ejpam-7078	474	16	,	,	PUNCT
ejpam-7078	474	17	respectively	respectively	ADV
ejpam-7078	474	18	.	.	PUNCT
ejpam-7078	475	1	proof	proof	NOUN
ejpam-7078	475	2	.	.	PUNCT
ejpam-7078	476	1	let	let	VERB
ejpam-7078	476	2	f	f	PROPN
ejpam-7078	476	3	=	=	SYM
ejpam-7078	476	4	(	(	PUNCT
ejpam-7078	476	5	v0	v0	PROPN
ejpam-7078	476	6	,	,	PUNCT
ejpam-7078	476	7	v1	v1	NOUN
ejpam-7078	476	8	,	,	PUNCT
ejpam-7078	476	9	v2	v2	PROPN
ejpam-7078	476	10	)	)	PUNCT
ejpam-7078	476	11	be	be	AUX
ejpam-7078	476	12	an	an	DET
ejpam-7078	476	13	rdf	rdf	NOUN
ejpam-7078	476	14	on	on	ADP
ejpam-7078	476	15	g	g	PROPN
ejpam-7078	476	16	+	+	NOUN
ejpam-7078	476	17	h	h	NOUN
ejpam-7078	476	18	,	,	PUNCT
ejpam-7078	476	19	and	and	CCONJ
ejpam-7078	476	20	let	let	VERB
ejpam-7078	476	21	v	v	PRON
ejpam-7078	476	22	g	g	NOUN
ejpam-7078	477	1	i	i	PRON
ejpam-7078	477	2	=	=	SYM
ejpam-7078	477	3	vi	vi	PROPN
ejpam-7078	477	4	∩	∩	ADJ
ejpam-7078	477	5	v	v	NOUN
ejpam-7078	477	6	(	(	PUNCT
ejpam-7078	477	7	g	g	NOUN
ejpam-7078	477	8	)	)	PUNCT
ejpam-7078	477	9	and	and	CCONJ
ejpam-7078	477	10	v	v	NUM
ejpam-7078	477	11	h	h	NOUN
ejpam-7078	478	1	i	i	NOUN
ejpam-7078	478	2	=	=	SYM
ejpam-7078	478	3	vi	vi	PROPN
ejpam-7078	478	4	∩	∩	ADJ
ejpam-7078	478	5	v	v	NOUN
ejpam-7078	478	6	(	(	PUNCT
ejpam-7078	478	7	h	h	NOUN
ejpam-7078	478	8	)	)	PUNCT
ejpam-7078	478	9	for	for	ADP
ejpam-7078	478	10	i	i	PROPN
ejpam-7078	478	11	∈	∈	PROPN
ejpam-7078	478	12	{	{	PUNCT
ejpam-7078	478	13	0	0	NUM
ejpam-7078	478	14	,	,	PUNCT
ejpam-7078	478	15	1	1	NUM
ejpam-7078	478	16	,	,	PUNCT
ejpam-7078	478	17	2	2	NUM
ejpam-7078	478	18	}	}	PUNCT
ejpam-7078	478	19	.	.	PUNCT
ejpam-7078	479	1	then	then	ADV
ejpam-7078	479	2	f	f	PROPN
ejpam-7078	479	3	|g	|g	PROPN
ejpam-7078	479	4	=	=	X
ejpam-7078	479	5	(	(	PUNCT
ejpam-7078	479	6	v	v	NOUN
ejpam-7078	479	7	g	g	NOUN
ejpam-7078	479	8	0	0	NUM
ejpam-7078	479	9	,	,	PUNCT
ejpam-7078	479	10	v	v	ADP
ejpam-7078	479	11	g	g	PROPN
ejpam-7078	479	12	1	1	NUM
ejpam-7078	479	13	,	,	PUNCT
ejpam-7078	479	14	v	v	ADP
ejpam-7078	479	15	g	g	PROPN
ejpam-7078	479	16	2	2	NUM
ejpam-7078	479	17	)	)	PUNCT
ejpam-7078	479	18	and	and	CCONJ
ejpam-7078	479	19	f	f	PROPN
ejpam-7078	479	20	|h	|h	X
ejpam-7078	479	21	=	=	SYM
ejpam-7078	479	22	(	(	PUNCT
ejpam-7078	479	23	v	v	NUM
ejpam-7078	479	24	h	h	NOUN
ejpam-7078	479	25	0	0	NUM
ejpam-7078	479	26	,	,	PUNCT
ejpam-7078	479	27	v	v	NOUN
ejpam-7078	479	28	h	h	NOUN
ejpam-7078	479	29	1	1	NUM
ejpam-7078	479	30	,	,	PUNCT
ejpam-7078	479	31	v	v	NOUN
ejpam-7078	479	32	h	h	NOUN
ejpam-7078	479	33	2	2	NUM
ejpam-7078	479	34	)	)	PUNCT
ejpam-7078	479	35	.	.	PUNCT
ejpam-7078	479	36	suppose	suppose	VERB
ejpam-7078	479	37	that	that	SCONJ
ejpam-7078	479	38	f	f	PROPN
ejpam-7078	479	39	is	be	AUX
ejpam-7078	479	40	an	an	DET
ejpam-7078	479	41	shrdf	shrdf	NOUN
ejpam-7078	479	42	on	on	ADP
ejpam-7078	479	43	g	g	PROPN
ejpam-7078	479	44	+	+	CCONJ
ejpam-7078	479	45	h.	h.	PROPN
ejpam-7078	479	46	let	let	VERB
ejpam-7078	479	47	v	v	ADP
ejpam-7078	479	48	∈	∈	PROPN
ejpam-7078	479	49	v	v	ADP
ejpam-7078	479	50	g	g	PROPN
ejpam-7078	479	51	0	0	NUM
ejpam-7078	479	52	.	.	PUNCT
ejpam-7078	480	1	since	since	SCONJ
ejpam-7078	480	2	f	f	PROPN
ejpam-7078	480	3	satisfies	satisfie	NOUN
ejpam-7078	480	4	(	(	PUNCT
ejpam-7078	480	5	shr1	shr1	PROPN
ejpam-7078	480	6	)	)	PUNCT
ejpam-7078	480	7	and	and	CCONJ
ejpam-7078	480	8	(	(	PUNCT
ejpam-7078	480	9	shr2	shr2	NOUN
ejpam-7078	480	10	)	)	PUNCT
ejpam-7078	480	11	on	on	ADP
ejpam-7078	480	12	g+h	g+h	PROPN
ejpam-7078	480	13	,	,	PUNCT
ejpam-7078	480	14	there	there	PRON
ejpam-7078	480	15	exists	exist	VERB
ejpam-7078	480	16	u	u	PROPN
ejpam-7078	480	17	∈	∈	PROPN
ejpam-7078	480	18	v2	v2	NOUN
ejpam-7078	480	19	such	such	ADJ
ejpam-7078	480	20	that	that	DET
ejpam-7078	480	21	dg+h(u	dg+h(u	PROPN
ejpam-7078	480	22	,	,	PUNCT
ejpam-7078	480	23	v	v	NOUN
ejpam-7078	480	24	)	)	PUNCT
ejpam-7078	480	25	=	=	SYM
ejpam-7078	480	26	2	2	NUM
ejpam-7078	480	27	and	and	CCONJ
ejpam-7078	480	28	there	there	PRON
ejpam-7078	480	29	exists	exist	VERB
ejpam-7078	480	30	w	w	PROPN
ejpam-7078	480	31	∈	∈	PROPN
ejpam-7078	480	32	v1∪v2	v1∪v2	ADP
ejpam-7078	480	33	such	such	ADJ
ejpam-7078	480	34	that	that	DET
ejpam-7078	480	35	n2	n2	ADJ
ejpam-7078	480	36	g+h(w	g+h(w	NOUN
ejpam-7078	480	37	)	)	PUNCT
ejpam-7078	480	38	∩	∩	ADJ
ejpam-7078	480	39	v0	v0	NOUN
ejpam-7078	480	40	=	=	SYM
ejpam-7078	480	41	{	{	PUNCT
ejpam-7078	480	42	v	v	NOUN
ejpam-7078	480	43	}	}	PUNCT
ejpam-7078	480	44	.	.	PUNCT
ejpam-7078	481	1	since	since	SCONJ
ejpam-7078	481	2	vx	vx	PROPN
ejpam-7078	481	3	∈	∈	PROPN
ejpam-7078	481	4	e(g	e(g	PROPN
ejpam-7078	481	5	+	+	PROPN
ejpam-7078	481	6	h	h	NOUN
ejpam-7078	481	7	)	)	PUNCT
ejpam-7078	481	8	for	for	ADP
ejpam-7078	481	9	all	all	PRON
ejpam-7078	481	10	x	x	SYM
ejpam-7078	481	11	∈	∈	PROPN
ejpam-7078	481	12	v	v	NOUN
ejpam-7078	481	13	(	(	PUNCT
ejpam-7078	481	14	h	h	NOUN
ejpam-7078	481	15	)	)	PUNCT
ejpam-7078	481	16	,	,	PUNCT
ejpam-7078	481	17	it	it	PRON
ejpam-7078	481	18	follows	follow	VERB
ejpam-7078	481	19	that	that	SCONJ
ejpam-7078	481	20	u	u	PROPN
ejpam-7078	481	21	∈	∈	PROPN
ejpam-7078	481	22	v	v	ADP
ejpam-7078	481	23	g	g	PROPN
ejpam-7078	481	24	2	2	NUM
ejpam-7078	481	25	,	,	PUNCT
ejpam-7078	481	26	w	w	PROPN
ejpam-7078	481	27	∈	∈	PROPN
ejpam-7078	481	28	v	v	ADP
ejpam-7078	481	29	g	g	PROPN
ejpam-7078	481	30	1	1	NUM
ejpam-7078	481	31	∪	∪	ADP
ejpam-7078	481	32	v	v	ADP
ejpam-7078	481	33	g	g	PROPN
ejpam-7078	481	34	2	2	NUM
ejpam-7078	481	35	,	,	PUNCT
ejpam-7078	481	36	dg(u	dg(u	X
ejpam-7078	481	37	,	,	PUNCT
ejpam-7078	481	38	v	v	NOUN
ejpam-7078	481	39	)	)	PUNCT
ejpam-7078	481	40	=	=	SYM
ejpam-7078	481	41	2	2	NUM
ejpam-7078	481	42	,	,	PUNCT
ejpam-7078	481	43	and	and	CCONJ
ejpam-7078	481	44	n2	n2	ADJ
ejpam-7078	481	45	g(w)∩	g(w)∩	X
ejpam-7078	482	1	v	v	ADP
ejpam-7078	482	2	g	g	NOUN
ejpam-7078	482	3	0	0	NUM
ejpam-7078	482	4	=	=	SYM
ejpam-7078	482	5	{	{	PUNCT
ejpam-7078	482	6	v	v	NOUN
ejpam-7078	482	7	}	}	PUNCT
ejpam-7078	482	8	.	.	PUNCT
ejpam-7078	483	1	thus	thus	ADV
ejpam-7078	483	2	,	,	PUNCT
ejpam-7078	483	3	f	f	PROPN
ejpam-7078	483	4	|g	|g	PROPN
ejpam-7078	483	5	is	be	AUX
ejpam-7078	483	6	an	an	DET
ejpam-7078	483	7	shrdf	shrdf	NOUN
ejpam-7078	483	8	on	on	ADP
ejpam-7078	483	9	g.	g.	NOUN
ejpam-7078	483	10	using	use	VERB
ejpam-7078	483	11	similar	similar	ADJ
ejpam-7078	483	12	argument	argument	NOUN
ejpam-7078	483	13	,	,	PUNCT
ejpam-7078	483	14	f	f	PROPN
ejpam-7078	483	15	|h	|h	PROPN
ejpam-7078	483	16	is	be	AUX
ejpam-7078	483	17	also	also	ADV
ejpam-7078	483	18	an	an	DET
ejpam-7078	483	19	shrdf	shrdf	NOUN
ejpam-7078	483	20	on	on	ADP
ejpam-7078	483	21	h.	h.	NOUN
ejpam-7078	483	22	conversely	conversely	ADV
ejpam-7078	483	23	,	,	PUNCT
ejpam-7078	483	24	suppose	suppose	VERB
ejpam-7078	483	25	that	that	SCONJ
ejpam-7078	483	26	f	f	PROPN
ejpam-7078	483	27	|g	|g	PROPN
ejpam-7078	483	28	and	and	CCONJ
ejpam-7078	483	29	f	f	PROPN
ejpam-7078	483	30	|h	|h	NOUN
ejpam-7078	483	31	are	be	AUX
ejpam-7078	483	32	shrdf	shrdf	NOUN
ejpam-7078	483	33	on	on	ADP
ejpam-7078	483	34	g	g	PROPN
ejpam-7078	483	35	and	and	CCONJ
ejpam-7078	483	36	h	h	NOUN
ejpam-7078	483	37	,	,	PUNCT
ejpam-7078	483	38	respectively	respectively	ADV
ejpam-7078	483	39	.	.	PUNCT
ejpam-7078	484	1	let	let	VERB
ejpam-7078	484	2	v′	v′	NOUN
ejpam-7078	484	3	∈	∈	PROPN
ejpam-7078	484	4	v0	v0	NOUN
ejpam-7078	484	5	.	.	PUNCT
ejpam-7078	485	1	then	then	ADV
ejpam-7078	485	2	,	,	PUNCT
ejpam-7078	485	3	either	either	CCONJ
ejpam-7078	485	4	v′	v′	PROPN
ejpam-7078	485	5	∈	∈	PROPN
ejpam-7078	485	6	v	v	ADP
ejpam-7078	485	7	g	g	NOUN
ejpam-7078	485	8	0	0	NUM
ejpam-7078	485	9	or	or	CCONJ
ejpam-7078	485	10	v′	v′	PROPN
ejpam-7078	485	11	∈	∈	PROPN
ejpam-7078	485	12	v	v	ADP
ejpam-7078	485	13	h	h	NOUN
ejpam-7078	485	14	0	0	PUNCT
ejpam-7078	485	15	.	.	PUNCT
ejpam-7078	486	1	without	without	ADP
ejpam-7078	486	2	loss	loss	NOUN
ejpam-7078	486	3	of	of	ADP
ejpam-7078	486	4	generality	generality	NOUN
ejpam-7078	486	5	,	,	PUNCT
ejpam-7078	486	6	suppose	suppose	VERB
ejpam-7078	486	7	that	that	SCONJ
ejpam-7078	486	8	v′	v′	PROPN
ejpam-7078	486	9	∈	∈	PROPN
ejpam-7078	486	10	v	v	ADP
ejpam-7078	486	11	g	g	PROPN
ejpam-7078	486	12	0	0	NUM
ejpam-7078	486	13	.	.	PUNCT
ejpam-7078	487	1	since	since	SCONJ
ejpam-7078	487	2	f	f	PROPN
ejpam-7078	487	3	|g	|g	PROPN
ejpam-7078	487	4	is	be	AUX
ejpam-7078	487	5	an	an	DET
ejpam-7078	487	6	shrdf	shrdf	NOUN
ejpam-7078	487	7	on	on	ADP
ejpam-7078	487	8	g	g	NOUN
ejpam-7078	487	9	,	,	PUNCT
ejpam-7078	487	10	there	there	PRON
ejpam-7078	487	11	exists	exist	VERB
ejpam-7078	487	12	u′	u′	PROPN
ejpam-7078	487	13	∈	∈	PROPN
ejpam-7078	487	14	v	v	ADP
ejpam-7078	487	15	g	g	PROPN
ejpam-7078	487	16	2	2	NUM
ejpam-7078	487	17	such	such	ADJ
ejpam-7078	487	18	that	that	SCONJ
ejpam-7078	487	19	dg(u′	dg(u′	PROPN
ejpam-7078	487	20	,	,	PUNCT
ejpam-7078	487	21	v′	v′	NUM
ejpam-7078	487	22	)	)	PUNCT
ejpam-7078	488	1	=	=	SYM
ejpam-7078	488	2	2	2	NUM
ejpam-7078	488	3	and	and	CCONJ
ejpam-7078	488	4	there	there	PRON
ejpam-7078	488	5	exists	exist	VERB
ejpam-7078	488	6	w′	w′	PROPN
ejpam-7078	488	7	∈	∈	PROPN
ejpam-7078	488	8	v	v	ADP
ejpam-7078	488	9	g	g	PROPN
ejpam-7078	488	10	1	1	NUM
ejpam-7078	488	11	∪	∪	ADP
ejpam-7078	488	12	v	v	ADP
ejpam-7078	488	13	g	g	PROPN
ejpam-7078	488	14	2	2	NUM
ejpam-7078	488	15	such	such	ADJ
ejpam-7078	488	16	that	that	DET
ejpam-7078	488	17	n2	n2	PROPN
ejpam-7078	488	18	g(w	g(w	PROPN
ejpam-7078	488	19	′	′	NOUN
ejpam-7078	488	20	)	)	PUNCT
ejpam-7078	488	21	∩	∩	NOUN
ejpam-7078	488	22	v	v	ADP
ejpam-7078	488	23	g	g	NOUN
ejpam-7078	488	24	0	0	NUM
ejpam-7078	488	25	=	=	SYM
ejpam-7078	488	26	{	{	PUNCT
ejpam-7078	488	27	v′	v′	NOUN
ejpam-7078	488	28	}	}	PUNCT
ejpam-7078	488	29	.	.	PUNCT
ejpam-7078	489	1	since	since	SCONJ
ejpam-7078	489	2	v	v	NUM
ejpam-7078	489	3	g	g	PROPN
ejpam-7078	489	4	2	2	NUM
ejpam-7078	489	5	⊂	⊂	NOUN
ejpam-7078	489	6	v2	v2	PROPN
ejpam-7078	489	7	and	and	CCONJ
ejpam-7078	489	8	v	v	ADP
ejpam-7078	489	9	g	g	NOUN
ejpam-7078	489	10	1	1	NUM
ejpam-7078	489	11	∪	∪	ADP
ejpam-7078	489	12	v	v	ADP
ejpam-7078	489	13	g	g	PROPN
ejpam-7078	489	14	2	2	NUM
ejpam-7078	489	15	⊆	⊆	NUM
ejpam-7078	489	16	v1	v1	NOUN
ejpam-7078	489	17	∪	∪	NOUN
ejpam-7078	489	18	v2	v2	NOUN
ejpam-7078	489	19	,	,	PUNCT
ejpam-7078	489	20	it	it	PRON
ejpam-7078	489	21	implies	imply	VERB
ejpam-7078	489	22	that	that	SCONJ
ejpam-7078	489	23	u′	u′	PROPN
ejpam-7078	489	24	∈	∈	PROPN
ejpam-7078	489	25	v2	v2	PROPN
ejpam-7078	489	26	and	and	CCONJ
ejpam-7078	489	27	w′	w′	PROPN
ejpam-7078	489	28	∈	∈	NOUN
ejpam-7078	489	29	v1	v1	NOUN
ejpam-7078	489	30	∪	∪	NOUN
ejpam-7078	489	31	v2	v2	NOUN
ejpam-7078	489	32	for	for	ADP
ejpam-7078	489	33	which	which	PRON
ejpam-7078	489	34	dg+h(u′	dg+h(u′	NOUN
ejpam-7078	489	35	,	,	PUNCT
ejpam-7078	489	36	v′	v′	NUM
ejpam-7078	489	37	)	)	PUNCT
ejpam-7078	490	1	=	=	SYM
ejpam-7078	490	2	2	2	NUM
ejpam-7078	490	3	and	and	CCONJ
ejpam-7078	490	4	n2	n2	PROPN
ejpam-7078	490	5	g+h(w′	g+h(w′	PROPN
ejpam-7078	490	6	)	)	PUNCT
ejpam-7078	490	7	∩	∩	PROPN
ejpam-7078	490	8	v	v	ADP
ejpam-7078	490	9	g	g	NOUN
ejpam-7078	490	10	0	0	NUM
ejpam-7078	490	11	=	=	SYM
ejpam-7078	490	12	{	{	PUNCT
ejpam-7078	490	13	v′	v′	NOUN
ejpam-7078	490	14	}	}	PUNCT
ejpam-7078	490	15	.	.	PUNCT
ejpam-7078	491	1	thus	thus	ADV
ejpam-7078	491	2	,	,	PUNCT
ejpam-7078	491	3	f	f	PROPN
ejpam-7078	491	4	is	be	AUX
ejpam-7078	491	5	an	an	DET
ejpam-7078	491	6	shrdf	shrdf	NOUN
ejpam-7078	491	7	on	on	ADP
ejpam-7078	491	8	g+h	g+h	PROPN
ejpam-7078	491	9	.	.	PUNCT
ejpam-7078	492	1	l.	l.	PROPN
ejpam-7078	492	2	f.	f.	PROPN
ejpam-7078	492	3	casinillo	casinillo	PROPN
ejpam-7078	492	4	,	,	PUNCT
ejpam-7078	492	5	s.	s.	PROPN
ejpam-7078	492	6	r.	r.	PROPN
ejpam-7078	492	7	canoy	canoy	PROPN
ejpam-7078	492	8	jr	jr	PROPN
ejpam-7078	492	9	.	.	PROPN
ejpam-7078	492	10	/	/	SYM
ejpam-7078	492	11	eur	eur	PROPN
ejpam-7078	492	12	.	.	PUNCT
ejpam-7078	493	1	j.	j.	PROPN
ejpam-7078	493	2	pure	pure	PROPN
ejpam-7078	493	3	appl	appl	PROPN
ejpam-7078	493	4	.	.	PROPN
ejpam-7078	493	5	math	math	PROPN
ejpam-7078	493	6	,	,	PUNCT
ejpam-7078	493	7	18	18	NUM
ejpam-7078	493	8	(	(	PUNCT
ejpam-7078	493	9	4	4	NUM
ejpam-7078	493	10	)	)	PUNCT
ejpam-7078	493	11	(	(	PUNCT
ejpam-7078	493	12	2025	2025	NUM
ejpam-7078	493	13	)	)	PUNCT
ejpam-7078	493	14	,	,	PUNCT
ejpam-7078	493	15	7078	7078	NUM
ejpam-7078	493	16	14	14	NUM
ejpam-7078	493	17	of	of	ADP
ejpam-7078	493	18	15	15	NUM
ejpam-7078	493	19	the	the	DET
ejpam-7078	493	20	next	next	ADJ
ejpam-7078	493	21	result	result	NOUN
ejpam-7078	493	22	follows	follow	VERB
ejpam-7078	493	23	from	from	ADP
ejpam-7078	493	24	theorem	theorem	ADJ
ejpam-7078	493	25	10	10	NUM
ejpam-7078	493	26	.	.	PUNCT
ejpam-7078	494	1	corollary	corollary	ADJ
ejpam-7078	494	2	5	5	NUM
ejpam-7078	494	3	.	.	PUNCT
ejpam-7078	495	1	let	let	VERB
ejpam-7078	495	2	g	g	NOUN
ejpam-7078	495	3	and	and	CCONJ
ejpam-7078	495	4	h	h	NOUN
ejpam-7078	495	5	be	be	VERB
ejpam-7078	495	6	any	any	DET
ejpam-7078	495	7	two	two	NUM
ejpam-7078	495	8	graphs	graph	NOUN
ejpam-7078	495	9	.	.	PUNCT
ejpam-7078	496	1	then	then	ADV
ejpam-7078	496	2	,	,	PUNCT
ejpam-7078	496	3	γshr(g+h	γshr(g+h	NOUN
ejpam-7078	496	4	)	)	PUNCT
ejpam-7078	497	1	=	=	PUNCT
ejpam-7078	497	2	γshr(g)+γshr(h	γshr(g)+γshr(h	PROPN
ejpam-7078	497	3	)	)	PUNCT
ejpam-7078	497	4	.	.	PUNCT
ejpam-7078	498	1	proof	proof	NOUN
ejpam-7078	498	2	.	.	PUNCT
ejpam-7078	499	1	let	let	VERB
ejpam-7078	499	2	g	g	PROPN
ejpam-7078	499	3	=	=	PUNCT
ejpam-7078	499	4	(	(	PUNCT
ejpam-7078	499	5	v	v	NOUN
ejpam-7078	499	6	g	g	NOUN
ejpam-7078	499	7	0	0	NUM
ejpam-7078	499	8	,	,	PUNCT
ejpam-7078	499	9	v	v	ADP
ejpam-7078	499	10	g	g	PROPN
ejpam-7078	499	11	1	1	NUM
ejpam-7078	499	12	,	,	PUNCT
ejpam-7078	499	13	v	v	ADP
ejpam-7078	499	14	g	g	PROPN
ejpam-7078	499	15	2	2	NUM
ejpam-7078	499	16	)	)	PUNCT
ejpam-7078	499	17	and	and	CCONJ
ejpam-7078	499	18	h	h	NOUN
ejpam-7078	499	19	=	=	SYM
ejpam-7078	499	20	(	(	PUNCT
ejpam-7078	499	21	v	v	NUM
ejpam-7078	499	22	h	h	NOUN
ejpam-7078	499	23	0	0	NUM
ejpam-7078	499	24	,	,	PUNCT
ejpam-7078	500	1	v	v	NOUN
ejpam-7078	500	2	h	h	NOUN
ejpam-7078	500	3	1	1	NUM
ejpam-7078	500	4	,	,	PUNCT
ejpam-7078	500	5	v	v	NOUN
ejpam-7078	500	6	h	h	NOUN
ejpam-7078	500	7	2	2	NUM
ejpam-7078	500	8	)	)	PUNCT
ejpam-7078	500	9	be	be	AUX
ejpam-7078	500	10	γshr	γshr	NOUN
ejpam-7078	500	11	-	-	PUNCT
ejpam-7078	500	12	functions	function	NOUN
ejpam-7078	500	13	on	on	ADP
ejpam-7078	500	14	g	g	PROPN
ejpam-7078	500	15	and	and	CCONJ
ejpam-7078	500	16	h	h	NOUN
ejpam-7078	500	17	,	,	PUNCT
ejpam-7078	500	18	respectively	respectively	ADV
ejpam-7078	500	19	.	.	PUNCT
ejpam-7078	501	1	let	let	VERB
ejpam-7078	501	2	vi	vi	NOUN
ejpam-7078	501	3	=	=	NOUN
ejpam-7078	502	1	v	v	NOUN
ejpam-7078	502	2	g	g	NOUN
ejpam-7078	503	1	i	i	PRON
ejpam-7078	503	2	∪	∪	VERB
ejpam-7078	503	3	v	v	NUM
ejpam-7078	503	4	h	h	NOUN
ejpam-7078	504	1	i	i	PRON
ejpam-7078	504	2	for	for	ADP
ejpam-7078	504	3	each	each	DET
ejpam-7078	504	4	i	i	PRON
ejpam-7078	504	5	∈	∈	PROPN
ejpam-7078	504	6	{	{	PUNCT
ejpam-7078	504	7	0	0	NUM
ejpam-7078	504	8	,	,	PUNCT
ejpam-7078	504	9	1	1	NUM
ejpam-7078	504	10	,	,	PUNCT
ejpam-7078	504	11	2	2	NUM
ejpam-7078	504	12	}	}	PUNCT
ejpam-7078	504	13	.	.	PUNCT
ejpam-7078	505	1	then	then	ADV
ejpam-7078	505	2	g	g	PROPN
ejpam-7078	505	3	=	=	SYM
ejpam-7078	505	4	f	f	PROPN
ejpam-7078	505	5	|g	|g	NOUN
ejpam-7078	505	6	and	and	CCONJ
ejpam-7078	505	7	g	g	NOUN
ejpam-7078	505	8	=	=	SYM
ejpam-7078	505	9	f	f	PROPN
ejpam-7078	505	10	|h	|h	X
ejpam-7078	505	11	where	where	SCONJ
ejpam-7078	505	12	f	f	PROPN
ejpam-7078	505	13	=	=	SYM
ejpam-7078	505	14	(	(	PUNCT
ejpam-7078	505	15	v0	v0	PROPN
ejpam-7078	505	16	,	,	PUNCT
ejpam-7078	505	17	v1	v1	NOUN
ejpam-7078	505	18	,	,	PUNCT
ejpam-7078	505	19	v2	v2	PROPN
ejpam-7078	505	20	)	)	PUNCT
ejpam-7078	505	21	.	.	PUNCT
ejpam-7078	506	1	by	by	ADP
ejpam-7078	506	2	theorem	theorem	NOUN
ejpam-7078	506	3	10	10	NUM
ejpam-7078	506	4	,	,	PUNCT
ejpam-7078	506	5	f	f	PROPN
ejpam-7078	506	6	is	be	AUX
ejpam-7078	506	7	an	an	DET
ejpam-7078	506	8	shrdf	shrdf	NOUN
ejpam-7078	506	9	on	on	ADP
ejpam-7078	506	10	g+h	g+h	PROPN
ejpam-7078	506	11	.	.	PUNCT
ejpam-7078	507	1	hence	hence	ADV
ejpam-7078	507	2	,	,	PUNCT
ejpam-7078	507	3	we	we	PRON
ejpam-7078	507	4	have	have	VERB
ejpam-7078	507	5	γshr(g+h	γshr(g+h	NOUN
ejpam-7078	507	6	)	)	PUNCT
ejpam-7078	507	7	≤	≤	NUM
ejpam-7078	507	8	ωshr	ωshr	PROPN
ejpam-7078	507	9	g+h(f	g+h(f	NOUN
ejpam-7078	507	10	)	)	PUNCT
ejpam-7078	507	11	=	=	PUNCT
ejpam-7078	507	12	|v1|+	|v1|+	PRON
ejpam-7078	507	13	2|v2|	2|v2|	NUM
ejpam-7078	507	14	=	=	SYM
ejpam-7078	507	15	|v	|v	PROPN
ejpam-7078	507	16	g	g	PROPN
ejpam-7078	507	17	1	1	NUM
ejpam-7078	507	18	∪	∪	ADP
ejpam-7078	507	19	v	v	NUM
ejpam-7078	507	20	h	h	NOUN
ejpam-7078	507	21	1	1	NUM
ejpam-7078	507	22	|+	|+	NOUN
ejpam-7078	508	1	2|v	2|v	NOUN
ejpam-7078	509	1	g	g	ADP
ejpam-7078	509	2	2	2	NUM
ejpam-7078	509	3	∪	∪	NOUN
ejpam-7078	509	4	v	v	NUM
ejpam-7078	509	5	h	h	NOUN
ejpam-7078	509	6	2	2	NUM
ejpam-7078	509	7	|	|	NOUN
ejpam-7078	509	8	=	=	PUNCT
ejpam-7078	509	9	(	(	PUNCT
ejpam-7078	509	10	|v	|v	PROPN
ejpam-7078	509	11	g	g	PROPN
ejpam-7078	509	12	1	1	NUM
ejpam-7078	509	13	|+	|+	NOUN
ejpam-7078	509	14	2|v	2|v	NOUN
ejpam-7078	510	1	g	g	NOUN
ejpam-7078	510	2	2	2	NUM
ejpam-7078	510	3	|	|	NOUN
ejpam-7078	510	4	)	)	PUNCT
ejpam-7078	511	1	+	+	CCONJ
ejpam-7078	511	2	(	(	PUNCT
ejpam-7078	511	3	|v	|v	PROPN
ejpam-7078	511	4	h	h	NOUN
ejpam-7078	511	5	1	1	NUM
ejpam-7078	511	6	|+	|+	NOUN
ejpam-7078	511	7	2|v	2|v	NUM
ejpam-7078	511	8	h	h	NOUN
ejpam-7078	511	9	2	2	NUM
ejpam-7078	511	10	|	|	NOUN
ejpam-7078	511	11	)	)	PUNCT
ejpam-7078	511	12	=	=	SYM
ejpam-7078	511	13	γshr(g	γshr(g	NOUN
ejpam-7078	511	14	)	)	PUNCT
ejpam-7078	512	1	+	+	NUM
ejpam-7078	512	2	γshr(h	γshr(h	NOUN
ejpam-7078	512	3	)	)	PUNCT
ejpam-7078	512	4	.	.	PUNCT
ejpam-7078	513	1	now	now	ADV
ejpam-7078	513	2	,	,	PUNCT
ejpam-7078	513	3	let	let	VERB
ejpam-7078	513	4	f	f	PRON
ejpam-7078	513	5	′	′	NUM
ejpam-7078	514	1	=	=	PUNCT
ejpam-7078	514	2	(	(	PUNCT
ejpam-7078	514	3	v	v	NUM
ejpam-7078	514	4	′	′	NUM
ejpam-7078	514	5	0	0	NUM
ejpam-7078	514	6	,	,	PUNCT
ejpam-7078	514	7	v	v	NOUN
ejpam-7078	514	8	′	′	NUM
ejpam-7078	514	9	1	1	NUM
ejpam-7078	514	10	,	,	PUNCT
ejpam-7078	514	11	v	v	NOUN
ejpam-7078	514	12	′	′	NUM
ejpam-7078	514	13	2	2	NUM
ejpam-7078	514	14	)	)	PUNCT
ejpam-7078	514	15	be	be	AUX
ejpam-7078	514	16	a	a	DET
ejpam-7078	514	17	γshr	γshr	NOUN
ejpam-7078	514	18	-	-	PUNCT
ejpam-7078	514	19	function	function	NOUN
ejpam-7078	514	20	on	on	ADP
ejpam-7078	514	21	g	g	PROPN
ejpam-7078	514	22	+	+	CCONJ
ejpam-7078	514	23	h.	h.	PROPN
ejpam-7078	514	24	then	then	ADV
ejpam-7078	514	25	it	it	PRON
ejpam-7078	514	26	follows	follow	VERB
ejpam-7078	514	27	that	that	SCONJ
ejpam-7078	514	28	f	f	PROPN
ejpam-7078	514	29	′|g	′|g	PROPN
ejpam-7078	515	1	=	=	PRON
ejpam-7078	516	1	(	(	PUNCT
ejpam-7078	516	2	v	v	NUM
ejpam-7078	516	3	′	′	NUM
ejpam-7078	516	4	0	0	NUM
ejpam-7078	517	1	∩	∩	ADJ
ejpam-7078	517	2	v	v	ADJ
ejpam-7078	517	3	(	(	PUNCT
ejpam-7078	517	4	g	g	NOUN
ejpam-7078	517	5	)	)	PUNCT
ejpam-7078	517	6	,	,	PUNCT
ejpam-7078	517	7	v	v	X
ejpam-7078	517	8	′	′	NUM
ejpam-7078	517	9	1	1	NUM
ejpam-7078	517	10	∩	∩	NOUN
ejpam-7078	517	11	v	v	NOUN
ejpam-7078	517	12	(	(	PUNCT
ejpam-7078	517	13	g	g	NOUN
ejpam-7078	517	14	)	)	PUNCT
ejpam-7078	517	15	,	,	PUNCT
ejpam-7078	517	16	v	v	NOUN
ejpam-7078	517	17	′	′	NUM
ejpam-7078	517	18	2	2	NUM
ejpam-7078	517	19	∩	∩	X
ejpam-7078	517	20	v	v	NOUN
ejpam-7078	517	21	(	(	PUNCT
ejpam-7078	517	22	g	g	NOUN
ejpam-7078	517	23	)	)	PUNCT
ejpam-7078	517	24	)	)	PUNCT
ejpam-7078	517	25	and	and	CCONJ
ejpam-7078	517	26	f	f	PROPN
ejpam-7078	517	27	′|h	′|h	PROPN
ejpam-7078	517	28	=	=	SYM
ejpam-7078	517	29	(	(	PUNCT
ejpam-7078	517	30	v	v	NUM
ejpam-7078	517	31	′	′	NUM
ejpam-7078	517	32	0	0	NUM
ejpam-7078	517	33	∩	∩	PROPN
ejpam-7078	517	34	v	v	ADJ
ejpam-7078	517	35	(	(	PUNCT
ejpam-7078	517	36	h	h	NOUN
ejpam-7078	517	37	)	)	PUNCT
ejpam-7078	517	38	,	,	PUNCT
ejpam-7078	517	39	v	v	X
ejpam-7078	517	40	′	′	NUM
ejpam-7078	517	41	1	1	NUM
ejpam-7078	517	42	∩	∩	X
ejpam-7078	517	43	v	v	NOUN
ejpam-7078	517	44	(	(	PUNCT
ejpam-7078	517	45	h	h	NOUN
ejpam-7078	517	46	)	)	PUNCT
ejpam-7078	517	47	,	,	PUNCT
ejpam-7078	517	48	v	v	X
ejpam-7078	517	49	′	′	NUM
ejpam-7078	517	50	2	2	NUM
ejpam-7078	517	51	∩	∩	X
ejpam-7078	517	52	v	v	NOUN
ejpam-7078	517	53	(	(	PUNCT
ejpam-7078	517	54	h	h	NOUN
ejpam-7078	517	55	)	)	PUNCT
ejpam-7078	517	56	)	)	PUNCT
ejpam-7078	517	57	are	be	AUX
ejpam-7078	517	58	shrdf	shrdf	NOUN
ejpam-7078	517	59	on	on	ADP
ejpam-7078	517	60	g	g	PROPN
ejpam-7078	517	61	and	and	CCONJ
ejpam-7078	517	62	h	h	NOUN
ejpam-7078	517	63	,	,	PUNCT
ejpam-7078	517	64	respectively	respectively	ADV
ejpam-7078	517	65	,	,	PUNCT
ejpam-7078	517	66	by	by	ADP
ejpam-7078	517	67	theorem	theorem	NOUN
ejpam-7078	517	68	10	10	NUM
ejpam-7078	517	69	.	.	PUNCT
ejpam-7078	518	1	thus	thus	ADV
ejpam-7078	518	2	,	,	PUNCT
ejpam-7078	518	3	we	we	PRON
ejpam-7078	518	4	get	get	VERB
ejpam-7078	518	5	γshr(g+h	γshr(g+h	NOUN
ejpam-7078	518	6	)	)	PUNCT
ejpam-7078	519	1	=	=	PUNCT
ejpam-7078	519	2	ωshr	ωshr	NOUN
ejpam-7078	519	3	g+h(f	g+h(f	NOUN
ejpam-7078	519	4	′	′	NUM
ejpam-7078	519	5	)	)	PUNCT
ejpam-7078	519	6	=	=	PUNCT
ejpam-7078	519	7	|v	|v	PROPN
ejpam-7078	519	8	′	′	NUM
ejpam-7078	519	9	1	1	NUM
ejpam-7078	519	10	|+	|+	NOUN
ejpam-7078	520	1	2|v	2|v	NOUN
ejpam-7078	521	1	′	′	NOUN
ejpam-7078	521	2	2	2	NUM
ejpam-7078	521	3	|	|	ADV
ejpam-7078	521	4	=	=	SYM
ejpam-7078	521	5	|(v	|(v	NUM
ejpam-7078	521	6	′	′	NUM
ejpam-7078	521	7	1	1	NUM
ejpam-7078	521	8	∩	∩	NOUN
ejpam-7078	521	9	v	v	NOUN
ejpam-7078	521	10	(	(	PUNCT
ejpam-7078	521	11	g	g	NOUN
ejpam-7078	521	12	)	)	PUNCT
ejpam-7078	521	13	)	)	PUNCT
ejpam-7078	521	14	∪	∪	NOUN
ejpam-7078	521	15	(	(	PUNCT
ejpam-7078	521	16	v	v	NOUN
ejpam-7078	521	17	′	′	NUM
ejpam-7078	521	18	1	1	NUM
ejpam-7078	521	19	∩	∩	X
ejpam-7078	521	20	v	v	NOUN
ejpam-7078	521	21	(	(	PUNCT
ejpam-7078	521	22	h))|+	h))|+	NUM
ejpam-7078	521	23	2|(v	2|(v	NUM
ejpam-7078	521	24	′	′	NUM
ejpam-7078	521	25	2	2	NUM
ejpam-7078	521	26	∩	∩	X
ejpam-7078	521	27	v	v	NOUN
ejpam-7078	521	28	(	(	PUNCT
ejpam-7078	521	29	g	g	NOUN
ejpam-7078	521	30	)	)	PUNCT
ejpam-7078	521	31	)	)	PUNCT
ejpam-7078	521	32	∪	∪	NOUN
ejpam-7078	521	33	(	(	PUNCT
ejpam-7078	521	34	v	v	NOUN
ejpam-7078	521	35	′	′	NUM
ejpam-7078	521	36	2	2	NUM
ejpam-7078	521	37	∩	∩	X
ejpam-7078	521	38	v	v	NOUN
ejpam-7078	521	39	(	(	PUNCT
ejpam-7078	521	40	h))|	h))|	PROPN
ejpam-7078	521	41	=	=	PUNCT
ejpam-7078	521	42	(	(	PUNCT
ejpam-7078	521	43	|v	|v	PROPN
ejpam-7078	521	44	′	′	NUM
ejpam-7078	521	45	1	1	NUM
ejpam-7078	521	46	∩	∩	X
ejpam-7078	521	47	v	v	NOUN
ejpam-7078	521	48	(	(	PUNCT
ejpam-7078	521	49	g)|+	g)|+	NOUN
ejpam-7078	521	50	2|v	2|v	PROPN
ejpam-7078	521	51	′	′	NUM
ejpam-7078	521	52	2	2	NUM
ejpam-7078	521	53	∩	∩	X
ejpam-7078	521	54	v	v	X
ejpam-7078	521	55	(	(	PUNCT
ejpam-7078	521	56	g)|	g)|	PROPN
ejpam-7078	521	57	)	)	PUNCT
ejpam-7078	521	58	+	+	CCONJ
ejpam-7078	521	59	(	(	PUNCT
ejpam-7078	521	60	|v	|v	ADJ
ejpam-7078	521	61	′	′	NUM
ejpam-7078	521	62	1	1	NUM
ejpam-7078	521	63	∩	∩	X
ejpam-7078	521	64	v	v	NOUN
ejpam-7078	521	65	(	(	PUNCT
ejpam-7078	521	66	g)|+	g)|+	NOUN
ejpam-7078	521	67	2|v	2|v	PROPN
ejpam-7078	521	68	′	′	NUM
ejpam-7078	521	69	2	2	NUM
ejpam-7078	521	70	∩	∩	X
ejpam-7078	521	71	v	v	X
ejpam-7078	521	72	(	(	PUNCT
ejpam-7078	521	73	g)|	g)|	NOUN
ejpam-7078	521	74	)	)	PUNCT
ejpam-7078	521	75	=	=	NOUN
ejpam-7078	521	76	ωshr	ωshr	NOUN
ejpam-7078	521	77	g	g	PROPN
ejpam-7078	521	78	(	(	PUNCT
ejpam-7078	521	79	f	f	PROPN
ejpam-7078	521	80	′|g	′|g	PROPN
ejpam-7078	521	81	)	)	PUNCT
ejpam-7078	522	1	+	+	CCONJ
ejpam-7078	522	2	ωshr	ωshr	NOUN
ejpam-7078	522	3	h	h	NOUN
ejpam-7078	522	4	(	(	PUNCT
ejpam-7078	522	5	f	f	PROPN
ejpam-7078	522	6	′|h	′|h	PROPN
ejpam-7078	522	7	)	)	PUNCT
ejpam-7078	522	8	≥	≥	NOUN
ejpam-7078	522	9	γshr(g	γshr(g	NOUN
ejpam-7078	522	10	)	)	PUNCT
ejpam-7078	523	1	+	+	NUM
ejpam-7078	523	2	γshr(h	γshr(h	NOUN
ejpam-7078	523	3	)	)	PUNCT
ejpam-7078	523	4	.	.	PUNCT
ejpam-7078	524	1	therefore	therefore	ADV
ejpam-7078	524	2	,	,	PUNCT
ejpam-7078	524	3	γshr(g+h	γshr(g+h	NOUN
ejpam-7078	524	4	)	)	PUNCT
ejpam-7078	525	1	=	=	PUNCT
ejpam-7078	525	2	γshr(g	γshr(g	NOUN
ejpam-7078	525	3	)	)	PUNCT
ejpam-7078	526	1	+	+	NUM
ejpam-7078	526	2	γshr(h	γshr(h	NOUN
ejpam-7078	526	3	)	)	PUNCT
ejpam-7078	526	4	.	.	PUNCT
ejpam-7078	527	1	this	this	PRON
ejpam-7078	527	2	establishes	establish	VERB
ejpam-7078	527	3	the	the	DET
ejpam-7078	527	4	desired	desire	VERB
ejpam-7078	527	5	equality	equality	NOUN
ejpam-7078	527	6	.	.	PUNCT
ejpam-7078	528	1	the	the	DET
ejpam-7078	528	2	next	next	ADJ
ejpam-7078	528	3	result	result	NOUN
ejpam-7078	528	4	is	be	AUX
ejpam-7078	528	5	a	a	DET
ejpam-7078	528	6	direct	direct	ADJ
ejpam-7078	528	7	consequence	consequence	NOUN
ejpam-7078	528	8	of	of	ADP
ejpam-7078	528	9	corollary	corollary	ADJ
ejpam-7078	528	10	2	2	NUM
ejpam-7078	528	11	and	and	CCONJ
ejpam-7078	528	12	corollary	corollary	ADJ
ejpam-7078	528	13	5	5	NUM
ejpam-7078	528	14	.	.	PUNCT
ejpam-7078	528	15	corollary	corollary	ADJ
ejpam-7078	528	16	6	6	NUM
ejpam-7078	528	17	.	.	PUNCT
ejpam-7078	529	1	if	if	SCONJ
ejpam-7078	529	2	g	g	PROPN
ejpam-7078	529	3	=	=	SYM
ejpam-7078	529	4	km	km	PROPN
ejpam-7078	529	5	,	,	PUNCT
ejpam-7078	529	6	n	n	CCONJ
ejpam-7078	529	7	where	where	SCONJ
ejpam-7078	529	8	m	m	VERB
ejpam-7078	529	9	,	,	PUNCT
ejpam-7078	529	10	n	n	PRON
ejpam-7078	529	11	≥	≥	NOUN
ejpam-7078	529	12	1	1	NUM
ejpam-7078	529	13	,	,	PUNCT
ejpam-7078	529	14	then	then	ADV
ejpam-7078	529	15	γshr(g	γshr(g	NOUN
ejpam-7078	529	16	)	)	PUNCT
ejpam-7078	529	17	=	=	SYM
ejpam-7078	529	18	m+	m+	NUM
ejpam-7078	529	19	n.	n.	NOUN
ejpam-7078	529	20	4	4	NUM
ejpam-7078	529	21	.	.	PUNCT
ejpam-7078	529	22	conclusion	conclusion	NOUN
ejpam-7078	529	23	this	this	DET
ejpam-7078	529	24	study	study	NOUN
ejpam-7078	529	25	introduced	introduce	VERB
ejpam-7078	529	26	a	a	DET
ejpam-7078	529	27	new	new	ADJ
ejpam-7078	529	28	variation	variation	NOUN
ejpam-7078	529	29	of	of	ADP
ejpam-7078	529	30	hop	hop	PROPN
ejpam-7078	529	31	roman	roman	ADJ
ejpam-7078	529	32	domination	domination	NOUN
ejpam-7078	529	33	called	call	VERB
ejpam-7078	529	34	super	super	ADV
ejpam-7078	529	35	hop	hop	PROPN
ejpam-7078	529	36	roman	roman	ADJ
ejpam-7078	529	37	domination	domination	NOUN
ejpam-7078	529	38	.	.	PUNCT
ejpam-7078	530	1	some	some	DET
ejpam-7078	530	2	bounds	bound	NOUN
ejpam-7078	530	3	and	and	CCONJ
ejpam-7078	530	4	exact	exact	ADJ
ejpam-7078	530	5	values	value	NOUN
ejpam-7078	530	6	of	of	ADP
ejpam-7078	530	7	the	the	DET
ejpam-7078	530	8	super	super	PROPN
ejpam-7078	530	9	hop	hop	PROPN
ejpam-7078	530	10	roman	roman	ADJ
ejpam-7078	530	11	domination	domination	NOUN
ejpam-7078	530	12	number	number	NOUN
ejpam-7078	530	13	of	of	ADP
ejpam-7078	530	14	some	some	DET
ejpam-7078	530	15	classes	class	NOUN
ejpam-7078	530	16	of	of	ADP
ejpam-7078	530	17	graphs	graph	NOUN
ejpam-7078	530	18	were	be	AUX
ejpam-7078	530	19	determined	determine	VERB
ejpam-7078	530	20	.	.	PUNCT
ejpam-7078	531	1	necessary	necessary	ADJ
ejpam-7078	531	2	and	and	CCONJ
ejpam-7078	531	3	sufficient	sufficient	ADJ
ejpam-7078	531	4	conditions	condition	NOUN
ejpam-7078	531	5	for	for	SCONJ
ejpam-7078	531	6	functions	function	NOUN
ejpam-7078	531	7	to	to	PART
ejpam-7078	531	8	be	be	AUX
ejpam-7078	531	9	super	super	ADV
ejpam-7078	531	10	hop	hop	ADV
ejpam-7078	531	11	roman	roman	ADJ
ejpam-7078	531	12	dominating	dominating	NOUN
ejpam-7078	531	13	in	in	ADP
ejpam-7078	531	14	the	the	DET
ejpam-7078	531	15	join	join	NOUN
ejpam-7078	531	16	of	of	ADP
ejpam-7078	531	17	some	some	DET
ejpam-7078	531	18	graphs	graph	NOUN
ejpam-7078	531	19	were	be	AUX
ejpam-7078	531	20	obtained	obtain	VERB
ejpam-7078	531	21	.	.	PUNCT
ejpam-7078	532	1	the	the	DET
ejpam-7078	532	2	newly	newly	ADV
ejpam-7078	532	3	defined	define	VERB
ejpam-7078	532	4	parameter	parameter	NOUN
ejpam-7078	532	5	can	can	AUX
ejpam-7078	532	6	be	be	AUX
ejpam-7078	532	7	studied	study	VERB
ejpam-7078	532	8	for	for	ADP
ejpam-7078	532	9	other	other	ADJ
ejpam-7078	532	10	classes	class	NOUN
ejpam-7078	532	11	of	of	ADP
ejpam-7078	532	12	graphs	graph	NOUN
ejpam-7078	532	13	and	and	CCONJ
ejpam-7078	532	14	sharp	sharp	ADJ
ejpam-7078	532	15	and	and	CCONJ
ejpam-7078	532	16	tight	tight	ADJ
ejpam-7078	532	17	bounds	bound	NOUN
ejpam-7078	532	18	on	on	ADP
ejpam-7078	532	19	the	the	DET
ejpam-7078	532	20	parameter	parameter	NOUN
ejpam-7078	532	21	may	may	AUX
ejpam-7078	532	22	be	be	AUX
ejpam-7078	532	23	obtained	obtain	VERB
ejpam-7078	532	24	.	.	PUNCT
ejpam-7078	533	1	references	reference	NOUN
ejpam-7078	533	2	[	[	X
ejpam-7078	533	3	1	1	NUM
ejpam-7078	533	4	]	]	PUNCT
ejpam-7078	533	5	b.	b.	PROPN
ejpam-7078	533	6	s.	s.	PROPN
ejpam-7078	533	7	anand	anand	PROPN
ejpam-7078	533	8	,	,	PUNCT
ejpam-7078	533	9	j.	j.	PROPN
ejpam-7078	533	10	a.	a.	PROPN
ejpam-7078	533	11	dayap	dayap	PROPN
ejpam-7078	533	12	,	,	PUNCT
ejpam-7078	533	13	l.	l.	PROPN
ejpam-7078	533	14	f.	f.	PROPN
ejpam-7078	533	15	casinillo	casinillo	PROPN
ejpam-7078	533	16	,	,	PUNCT
ejpam-7078	533	17	r.	r.	PROPN
ejpam-7078	533	18	pepper	pepper	NOUN
ejpam-7078	533	19	,	,	PUNCT
ejpam-7078	533	20	and	and	CCONJ
ejpam-7078	533	21	r.	r.	PROPN
ejpam-7078	533	22	s.	s.	PROPN
ejpam-7078	533	23	nair	nair	PROPN
ejpam-7078	533	24	.	.	PUNCT
ejpam-7078	534	1	on	on	ADP
ejpam-7078	534	2	distance	distance	NOUN
ejpam-7078	534	3	kdomination	kdomination	NOUN
ejpam-7078	534	4	number	number	NOUN
ejpam-7078	534	5	of	of	ADP
ejpam-7078	534	6	graphs	graph	NOUN
ejpam-7078	534	7	under	under	ADP
ejpam-7078	534	8	product	product	NOUN
ejpam-7078	534	9	operations	operation	NOUN
ejpam-7078	534	10	.	.	PUNCT
ejpam-7078	535	1	gulf	gulf	PROPN
ejpam-7078	535	2	journal	journal	PROPN
ejpam-7078	535	3	of	of	ADP
ejpam-7078	535	4	mathematics	mathematic	NOUN
ejpam-7078	535	5	,	,	PUNCT
ejpam-7078	535	6	19(1):117–124	19(1):117–124	NUM
ejpam-7078	535	7	,	,	PUNCT
ejpam-7078	535	8	2025	2025	NUM
ejpam-7078	535	9	.	.	PUNCT
ejpam-7078	536	1	l.	l.	PROPN
ejpam-7078	536	2	f.	f.	PROPN
ejpam-7078	536	3	casinillo	casinillo	PROPN
ejpam-7078	536	4	,	,	PUNCT
ejpam-7078	536	5	s.	s.	PROPN
ejpam-7078	536	6	r.	r.	PROPN
ejpam-7078	536	7	canoy	canoy	PROPN
ejpam-7078	536	8	jr	jr	PROPN
ejpam-7078	536	9	.	.	PROPN
ejpam-7078	536	10	/	/	SYM
ejpam-7078	536	11	eur	eur	PROPN
ejpam-7078	536	12	.	.	PUNCT
ejpam-7078	537	1	j.	j.	PROPN
ejpam-7078	537	2	pure	pure	PROPN
ejpam-7078	537	3	appl	appl	PROPN
ejpam-7078	537	4	.	.	PROPN
ejpam-7078	537	5	math	math	PROPN
ejpam-7078	537	6	,	,	PUNCT
ejpam-7078	537	7	18	18	NUM
ejpam-7078	537	8	(	(	PUNCT
ejpam-7078	537	9	4	4	NUM
ejpam-7078	537	10	)	)	PUNCT
ejpam-7078	537	11	(	(	PUNCT
ejpam-7078	537	12	2025	2025	NUM
ejpam-7078	537	13	)	)	PUNCT
ejpam-7078	537	14	,	,	PUNCT
ejpam-7078	537	15	7078	7078	NUM
ejpam-7078	537	16	15	15	NUM
ejpam-7078	537	17	of	of	ADP
ejpam-7078	537	18	15	15	NUM
ejpam-7078	537	19	[	[	SYM
ejpam-7078	537	20	2	2	NUM
ejpam-7078	537	21	]	]	PUNCT
ejpam-7078	537	22	l.	l.	PROPN
ejpam-7078	537	23	f.	f.	PROPN
ejpam-7078	537	24	casinillo	casinillo	PROPN
ejpam-7078	537	25	.	.	PUNCT
ejpam-7078	538	1	new	new	ADJ
ejpam-7078	538	2	counting	counting	NOUN
ejpam-7078	538	3	formula	formula	NOUN
ejpam-7078	538	4	for	for	ADP
ejpam-7078	538	5	dominating	dominating	NOUN
ejpam-7078	538	6	sets	set	NOUN
ejpam-7078	538	7	in	in	ADP
ejpam-7078	538	8	path	path	NOUN
ejpam-7078	538	9	and	and	CCONJ
ejpam-7078	538	10	cycle	cycle	NOUN
ejpam-7078	538	11	graphs	graph	NOUN
ejpam-7078	538	12	.	.	PUNCT
ejpam-7078	539	1	journal	journal	NOUN
ejpam-7078	539	2	of	of	ADP
ejpam-7078	539	3	fundamental	fundamental	ADJ
ejpam-7078	539	4	mathematics	mathematic	NOUN
ejpam-7078	539	5	and	and	CCONJ
ejpam-7078	539	6	applications	application	NOUN
ejpam-7078	539	7	,	,	PUNCT
ejpam-7078	539	8	3(2):170–177	3(2):170–177	NUM
ejpam-7078	539	9	,	,	PUNCT
ejpam-7078	539	10	2020	2020	NUM
ejpam-7078	539	11	.	.	PUNCT
ejpam-7078	540	1	[	[	X
ejpam-7078	540	2	3	3	X
ejpam-7078	540	3	]	]	X
ejpam-7078	540	4	l.	l.	PROPN
ejpam-7078	540	5	f.	f.	PROPN
ejpam-7078	540	6	casinillo	casinillo	PROPN
ejpam-7078	540	7	.	.	PUNCT
ejpam-7078	541	1	odd	odd	ADJ
ejpam-7078	541	2	and	and	CCONJ
ejpam-7078	541	3	even	even	ADV
ejpam-7078	541	4	repetition	repetition	VERB
ejpam-7078	541	5	sequences	sequence	NOUN
ejpam-7078	541	6	of	of	ADP
ejpam-7078	541	7	independent	independent	ADJ
ejpam-7078	541	8	domination	domination	NOUN
ejpam-7078	541	9	number	number	NOUN
ejpam-7078	541	10	.	.	PUNCT
ejpam-7078	542	1	notes	note	NOUN
ejpam-7078	542	2	on	on	ADP
ejpam-7078	542	3	number	number	NOUN
ejpam-7078	542	4	theory	theory	NOUN
ejpam-7078	542	5	and	and	CCONJ
ejpam-7078	542	6	discrete	discrete	ADJ
ejpam-7078	542	7	mathematics	mathematic	NOUN
ejpam-7078	542	8	,	,	PUNCT
ejpam-7078	542	9	26(1):8–20	26(1):8–20	NUM
ejpam-7078	542	10	,	,	PUNCT
ejpam-7078	542	11	2020	2020	NUM
ejpam-7078	542	12	.	.	PUNCT
ejpam-7078	543	1	[	[	X
ejpam-7078	543	2	4	4	NUM
ejpam-7078	543	3	]	]	PUNCT
ejpam-7078	543	4	l.	l.	PROPN
ejpam-7078	543	5	f.	f.	PROPN
ejpam-7078	543	6	casinillo	casinillo	PROPN
ejpam-7078	543	7	.	.	PUNCT
ejpam-7078	544	1	a	a	DET
ejpam-7078	544	2	closer	close	ADJ
ejpam-7078	544	3	look	look	NOUN
ejpam-7078	544	4	at	at	ADP
ejpam-7078	544	5	a	a	DET
ejpam-7078	544	6	path	path	NOUN
ejpam-7078	544	7	domination	domination	NOUN
ejpam-7078	544	8	number	number	NOUN
ejpam-7078	544	9	in	in	ADP
ejpam-7078	544	10	grid	grid	NOUN
ejpam-7078	544	11	graphs	graph	NOUN
ejpam-7078	544	12	.	.	PUNCT
ejpam-7078	545	1	journal	journal	NOUN
ejpam-7078	545	2	of	of	ADP
ejpam-7078	545	3	fundamental	fundamental	ADJ
ejpam-7078	545	4	mathematics	mathematic	NOUN
ejpam-7078	545	5	and	and	CCONJ
ejpam-7078	545	6	applications	application	NOUN
ejpam-7078	545	7	,	,	PUNCT
ejpam-7078	545	8	6(1):18–26	6(1):18–26	NUM
ejpam-7078	545	9	,	,	PUNCT
ejpam-7078	545	10	2023	2023	NUM
ejpam-7078	545	11	.	.	PUNCT
ejpam-7078	546	1	[	[	X
ejpam-7078	546	2	5	5	X
ejpam-7078	546	3	]	]	PUNCT
ejpam-7078	546	4	e.	e.	PROPN
ejpam-7078	546	5	j.	j.	PROPN
ejpam-7078	546	6	cockayne	cockayne	PROPN
ejpam-7078	546	7	,	,	PUNCT
ejpam-7078	546	8	p.	p.	NOUN
ejpam-7078	546	9	a.	a.	NOUN
ejpam-7078	546	10	dreyer	dreyer	PROPN
ejpam-7078	546	11	jr	jr	PROPN
ejpam-7078	546	12	,	,	PUNCT
ejpam-7078	546	13	s.	s.	PROPN
ejpam-7078	546	14	m.	m.	PROPN
ejpam-7078	546	15	hedetniemi	hedetniemi	ADV
ejpam-7078	546	16	,	,	PUNCT
ejpam-7078	546	17	and	and	CCONJ
ejpam-7078	546	18	s.	s.	PROPN
ejpam-7078	546	19	t.	t.	PROPN
ejpam-7078	546	20	hedetniemi	hedetniemi	PROPN
ejpam-7078	546	21	.	.	PUNCT
ejpam-7078	547	1	roman	roman	ADJ
ejpam-7078	547	2	domination	domination	NOUN
ejpam-7078	547	3	in	in	ADP
ejpam-7078	547	4	graphs	graph	NOUN
ejpam-7078	547	5	.	.	PUNCT
ejpam-7078	548	1	discrete	discrete	ADJ
ejpam-7078	548	2	mathematics	mathematic	NOUN
ejpam-7078	548	3	,	,	PUNCT
ejpam-7078	548	4	278(1	278(1	NUM
ejpam-7078	548	5	-	-	SYM
ejpam-7078	548	6	3):11–22	3):11–22	NUM
ejpam-7078	548	7	,	,	PUNCT
ejpam-7078	548	8	2004	2004	NUM
ejpam-7078	548	9	.	.	PUNCT
ejpam-7078	549	1	[	[	X
ejpam-7078	549	2	6	6	NUM
ejpam-7078	549	3	]	]	PUNCT
ejpam-7078	549	4	t.	t.	PROPN
ejpam-7078	549	5	w.	w.	PROPN
ejpam-7078	549	6	haynes	haynes	PROPN
ejpam-7078	549	7	,	,	PUNCT
ejpam-7078	549	8	s.	s.	PROPN
ejpam-7078	549	9	hedetniemi	hedetniemi	PROPN
ejpam-7078	549	10	,	,	PUNCT
ejpam-7078	549	11	and	and	CCONJ
ejpam-7078	549	12	p.	p.	PROPN
ejpam-7078	549	13	slater	slater	PROPN
ejpam-7078	549	14	.	.	PUNCT
ejpam-7078	550	1	fundamentals	fundamental	NOUN
ejpam-7078	550	2	of	of	ADP
ejpam-7078	550	3	domination	domination	NOUN
ejpam-7078	550	4	in	in	ADP
ejpam-7078	550	5	graphs	graph	NOUN
ejpam-7078	550	6	.	.	PUNCT
ejpam-7078	551	1	crc	crc	PROPN
ejpam-7078	551	2	press	press	PROPN
ejpam-7078	551	3	,	,	PUNCT
ejpam-7078	551	4	2013	2013	NUM
ejpam-7078	551	5	.	.	PUNCT
ejpam-7078	552	1	[	[	X
ejpam-7078	552	2	7	7	X
ejpam-7078	552	3	]	]	X
ejpam-7078	552	4	m.	m.	NOUN
ejpam-7078	552	5	a.	a.	PROPN
ejpam-7078	552	6	henning	henning	PROPN
ejpam-7078	552	7	.	.	PUNCT
ejpam-7078	553	1	distance	distance	NOUN
ejpam-7078	553	2	domination	domination	NOUN
ejpam-7078	553	3	in	in	ADP
ejpam-7078	553	4	graphs	graph	NOUN
ejpam-7078	553	5	.	.	PUNCT
ejpam-7078	554	1	in	in	ADP
ejpam-7078	554	2	domination	domination	NOUN
ejpam-7078	554	3	in	in	ADP
ejpam-7078	554	4	graphs	graph	NOUN
ejpam-7078	554	5	:	:	PUNCT
ejpam-7078	554	6	advanced	advanced	ADJ
ejpam-7078	554	7	topics	topic	NOUN
ejpam-7078	554	8	,	,	PUNCT
ejpam-7078	554	9	pages	page	NOUN
ejpam-7078	554	10	321–350	321–350	NUM
ejpam-7078	554	11	.	.	PUNCT
ejpam-7078	555	1	routledge	routledge	PROPN
ejpam-7078	555	2	,	,	PUNCT
ejpam-7078	555	3	2017	2017	NUM
ejpam-7078	555	4	.	.	PUNCT
ejpam-7078	556	1	[	[	X
ejpam-7078	556	2	8	8	X
ejpam-7078	556	3	]	]	PUNCT
ejpam-7078	556	4	s.	s.	PROPN
ejpam-7078	556	5	m.	m.	PROPN
ejpam-7078	556	6	paraico	paraico	PROPN
ejpam-7078	556	7	and	and	CCONJ
ejpam-7078	556	8	s.	s.	PROPN
ejpam-7078	556	9	r.	r.	PROPN
ejpam-7078	556	10	canoy	canoy	PROPN
ejpam-7078	556	11	jr	jr	PROPN
ejpam-7078	556	12	.	.	PUNCT
ejpam-7078	556	13	super	super	PROPN
ejpam-7078	556	14	domination	domination	NOUN
ejpam-7078	556	15	in	in	ADP
ejpam-7078	556	16	graphs	graph	NOUN
ejpam-7078	556	17	.	.	PUNCT
ejpam-7078	557	1	journal	journal	NOUN
ejpam-7078	557	2	of	of	ADP
ejpam-7078	557	3	analysis	analysis	NOUN
ejpam-7078	557	4	and	and	CCONJ
ejpam-7078	557	5	applications	application	NOUN
ejpam-7078	557	6	,	,	PUNCT
ejpam-7078	557	7	15(2	15(2	NUM
ejpam-7078	557	8	)	)	PUNCT
ejpam-7078	557	9	,	,	PUNCT
ejpam-7078	557	10	2017	2017	NUM
ejpam-7078	557	11	.	.	PUNCT
ejpam-7078	558	1	[	[	X
ejpam-7078	558	2	9	9	X
ejpam-7078	558	3	]	]	PUNCT
ejpam-7078	558	4	p.	p.	PROPN
ejpam-7078	558	5	j.	j.	PROPN
ejpam-7078	558	6	slater	slater	PROPN
ejpam-7078	558	7	.	.	PUNCT
ejpam-7078	559	1	r	r	X
ejpam-7078	559	2	-	-	PUNCT
ejpam-7078	559	3	domination	domination	NOUN
ejpam-7078	559	4	in	in	ADP
ejpam-7078	559	5	graphs	graph	NOUN
ejpam-7078	559	6	.	.	PUNCT
ejpam-7078	560	1	journal	journal	NOUN
ejpam-7078	560	2	of	of	ADP
ejpam-7078	560	3	the	the	DET
ejpam-7078	560	4	acm	acm	PROPN
ejpam-7078	560	5	,	,	PUNCT
ejpam-7078	560	6	23(3):446–450	23(3):446–450	PROPN
ejpam-7078	560	7	,	,	PUNCT
ejpam-7078	560	8	1976	1976	NUM
ejpam-7078	560	9	.	.	PUNCT
ejpam-7078	561	1	[	[	X
ejpam-7078	561	2	10	10	NUM
ejpam-7078	561	3	]	]	X
ejpam-7078	561	4	h.	h.	PROPN
ejpam-7078	561	5	a.	a.	NOUN
ejpam-7078	561	6	ahangar	ahangar	PROPN
ejpam-7078	561	7	,	,	PUNCT
ejpam-7078	561	8	m.	m.	NOUN
ejpam-7078	561	9	chellali	chellali	PROPN
ejpam-7078	561	10	,	,	PUNCT
ejpam-7078	561	11	and	and	CCONJ
ejpam-7078	561	12	s.	s.	PROPN
ejpam-7078	561	13	m.	m.	PROPN
ejpam-7078	561	14	sheikholeslami	sheikholeslami	PROPN
ejpam-7078	561	15	.	.	PUNCT
ejpam-7078	562	1	restrained	restrained	ADJ
ejpam-7078	562	2	roman	roman	ADJ
ejpam-7078	562	3	domination	domination	NOUN
ejpam-7078	562	4	in	in	ADP
ejpam-7078	562	5	graphs	graph	NOUN
ejpam-7078	562	6	.	.	PUNCT
ejpam-7078	563	1	discrete	discrete	ADJ
ejpam-7078	563	2	applied	apply	VERB
ejpam-7078	563	3	mathematics	mathematic	NOUN
ejpam-7078	563	4	,	,	PUNCT
ejpam-7078	563	5	232:1–7	232:1–7	NUM
ejpam-7078	563	6	,	,	PUNCT
ejpam-7078	563	7	2017	2017	NUM
ejpam-7078	563	8	.	.	PUNCT
ejpam-7078	564	1	[	[	X
ejpam-7078	564	2	11	11	NUM
ejpam-7078	564	3	]	]	PUNCT
ejpam-7078	564	4	m.	m.	NOUN
ejpam-7078	564	5	chellali	chellali	PROPN
ejpam-7078	564	6	,	,	PUNCT
ejpam-7078	564	7	t.	t.	PROPN
ejpam-7078	564	8	w.	w.	PROPN
ejpam-7078	564	9	haynes	haynes	PROPN
ejpam-7078	564	10	,	,	PUNCT
ejpam-7078	564	11	and	and	CCONJ
ejpam-7078	564	12	s.	s.	PROPN
ejpam-7078	564	13	t.	t.	PROPN
ejpam-7078	564	14	hedetniemi	hedetniemi	PROPN
ejpam-7078	564	15	.	.	PUNCT
ejpam-7078	565	1	roman	roman	ADJ
ejpam-7078	565	2	and	and	CCONJ
ejpam-7078	565	3	total	total	ADJ
ejpam-7078	565	4	domination	domination	NOUN
ejpam-7078	565	5	.	.	PUNCT
ejpam-7078	566	1	quaestiones	quaestione	NOUN
ejpam-7078	566	2	mathematicae	mathematicae	PROPN
ejpam-7078	566	3	,	,	PUNCT
ejpam-7078	566	4	38:749–757	38:749–757	PROPN
ejpam-7078	566	5	,	,	PUNCT
ejpam-7078	566	6	2015	2015	NUM
ejpam-7078	566	7	.	.	PUNCT
ejpam-7078	567	1	[	[	X
ejpam-7078	567	2	12	12	NUM
ejpam-7078	567	3	]	]	PUNCT
ejpam-7078	567	4	r.	r.	PROPN
ejpam-7078	567	5	l.	l.	PROPN
ejpam-7078	567	6	pushpam	pushpam	PROPN
ejpam-7078	567	7	and	and	CCONJ
ejpam-7078	567	8	s.	s.	PROPN
ejpam-7078	567	9	padmapriea	padmapriea	PROPN
ejpam-7078	567	10	.	.	PUNCT
ejpam-7078	568	1	restrained	restrained	ADJ
ejpam-7078	568	2	roman	roman	ADJ
ejpam-7078	568	3	domination	domination	NOUN
ejpam-7078	568	4	in	in	ADP
ejpam-7078	568	5	graphs	graph	NOUN
ejpam-7078	568	6	.	.	PUNCT
ejpam-7078	569	1	transactions	transaction	NOUN
ejpam-7078	569	2	on	on	ADP
ejpam-7078	569	3	combinatorics	combinatoric	NOUN
ejpam-7078	569	4	,	,	PUNCT
ejpam-7078	569	5	4(1):1–17	4(1):1–17	NUM
ejpam-7078	569	6	,	,	PUNCT
ejpam-7078	569	7	2015	2015	NUM
ejpam-7078	569	8	.	.	PUNCT
ejpam-7078	570	1	[	[	X
ejpam-7078	570	2	13	13	NUM
ejpam-7078	570	3	]	]	X
ejpam-7078	570	4	e.	e.	PROPN
ejpam-7078	570	5	shabani	shabani	PROPN
ejpam-7078	570	6	.	.	PUNCT
ejpam-7078	571	1	hop	hop	PROPN
ejpam-7078	571	2	roman	roman	ADJ
ejpam-7078	571	3	domination	domination	NOUN
ejpam-7078	571	4	in	in	ADP
ejpam-7078	571	5	graphs	graph	NOUN
ejpam-7078	571	6	,	,	PUNCT
ejpam-7078	571	7	2017	2017	NUM
ejpam-7078	571	8	.	.	PUNCT
ejpam-7078	572	1	manuscript	manuscript	NOUN
ejpam-7078	572	2	.	.	PUNCT
ejpam-7078	573	1	[	[	X
ejpam-7078	573	2	14	14	NUM
ejpam-7078	573	3	]	]	X
ejpam-7078	573	4	m.	m.	NOUN
ejpam-7078	573	5	lemanska	lemanska	PROPN
ejpam-7078	573	6	,	,	PUNCT
ejpam-7078	573	7	v.	v.	ADP
ejpam-7078	573	8	swaminathan	swaminathan	ADV
ejpam-7078	573	9	,	,	PUNCT
ejpam-7078	573	10	y.	y.	PROPN
ejpam-7078	573	11	b.	b.	PROPN
ejpam-7078	573	12	venkatakrishnan	venkatakrishnan	PROPN
ejpam-7078	573	13	,	,	PUNCT
ejpam-7078	573	14	and	and	CCONJ
ejpam-7078	573	15	r.	r.	PROPN
ejpam-7078	573	16	zuazua	zuazua	PROPN
ejpam-7078	573	17	.	.	PUNCT
ejpam-7078	574	1	super	super	ADJ
ejpam-7078	574	2	dominating	dominating	NOUN
ejpam-7078	574	3	sets	set	NOUN
ejpam-7078	574	4	in	in	ADP
ejpam-7078	574	5	graphs	graph	NOUN
ejpam-7078	574	6	.	.	PUNCT
ejpam-7078	575	1	proceedings	proceeding	NOUN
ejpam-7078	575	2	of	of	ADP
ejpam-7078	575	3	the	the	DET
ejpam-7078	575	4	national	national	PROPN
ejpam-7078	575	5	academy	academy	PROPN
ejpam-7078	575	6	of	of	ADP
ejpam-7078	575	7	sciences	sciences	PROPN
ejpam-7078	575	8	,	,	PUNCT
ejpam-7078	575	9	india	india	PROPN
ejpam-7078	575	10	section	section	PROPN
ejpam-7078	575	11	a	a	PRON
ejpam-7078	575	12	:	:	PUNCT
ejpam-7078	575	13	physical	physical	ADJ
ejpam-7078	575	14	sciences	science	NOUN
ejpam-7078	575	15	,	,	PUNCT
ejpam-7078	575	16	85(3):353–357	85(3):353–357	NOUN
ejpam-7078	575	17	,	,	PUNCT
ejpam-7078	575	18	2015	2015	NUM
ejpam-7078	575	19	.	.	PUNCT
ejpam-7078	576	1	[	[	X
ejpam-7078	576	2	15	15	NUM
ejpam-7078	576	3	]	]	X
ejpam-7078	576	4	l.	l.	PROPN
ejpam-7078	576	5	f.	f.	PROPN
ejpam-7078	576	6	casinillo	casinillo	PROPN
ejpam-7078	576	7	.	.	PUNCT
ejpam-7078	577	1	a	a	DET
ejpam-7078	577	2	note	note	NOUN
ejpam-7078	577	3	on	on	ADP
ejpam-7078	577	4	fibonacci	fibonacci	NOUN
ejpam-7078	577	5	and	and	CCONJ
ejpam-7078	577	6	lucas	lucas	PROPN
ejpam-7078	577	7	number	number	NOUN
ejpam-7078	577	8	of	of	ADP
ejpam-7078	577	9	domination	domination	NOUN
ejpam-7078	577	10	in	in	ADP
ejpam-7078	577	11	path	path	NOUN
ejpam-7078	577	12	.	.	PUNCT
ejpam-7078	578	1	electronic	electronic	ADJ
ejpam-7078	578	2	journal	journal	NOUN
ejpam-7078	578	3	of	of	ADP
ejpam-7078	578	4	graph	graph	NOUN
ejpam-7078	578	5	theory	theory	NOUN
ejpam-7078	578	6	and	and	CCONJ
ejpam-7078	578	7	applications	application	NOUN
ejpam-7078	578	8	,	,	PUNCT
ejpam-7078	578	9	6(2):317–325	6(2):317–325	NUM
ejpam-7078	578	10	,	,	PUNCT
ejpam-7078	578	11	2018	2018	NUM
ejpam-7078	578	12	.	.	PUNCT
ejpam-7078	579	1	[	[	X
ejpam-7078	579	2	16	16	NUM
ejpam-7078	579	3	]	]	X
ejpam-7078	579	4	g.	g.	PROPN
ejpam-7078	579	5	chartrand	chartrand	PROPN
ejpam-7078	579	6	,	,	PUNCT
ejpam-7078	579	7	l.	l.	PROPN
ejpam-7078	579	8	lesniak	lesniak	PROPN
ejpam-7078	579	9	,	,	PUNCT
ejpam-7078	579	10	and	and	CCONJ
ejpam-7078	579	11	p.	p.	PROPN
ejpam-7078	579	12	zhang	zhang	PROPN
ejpam-7078	579	13	.	.	PUNCT
ejpam-7078	579	14	graphs	graph	NOUN
ejpam-7078	579	15	and	and	CCONJ
ejpam-7078	579	16	digraphs	digraph	NOUN
ejpam-7078	579	17	.	.	PUNCT
ejpam-7078	580	1	crc	crc	PROPN
ejpam-7078	580	2	press	press	PROPN
ejpam-7078	580	3	,	,	PUNCT
ejpam-7078	580	4	2016	2016	NUM
ejpam-7078	580	5	.	.	PUNCT
ejpam-7078	581	1	[	[	X
ejpam-7078	581	2	17	17	NUM
ejpam-7078	581	3	]	]	X
ejpam-7078	581	4	c.	c.	PROPN
ejpam-7078	581	5	natarajan	natarajan	PROPN
ejpam-7078	581	6	and	and	CCONJ
ejpam-7078	581	7	s.	s.	PROPN
ejpam-7078	581	8	ayyaswamy	ayyaswamy	PROPN
ejpam-7078	581	9	.	.	PUNCT
ejpam-7078	582	1	hop	hop	PROPN
ejpam-7078	582	2	domination	domination	NOUN
ejpam-7078	582	3	in	in	ADP
ejpam-7078	582	4	graphs	graphs	PROPN
ejpam-7078	582	5	ii	ii	PROPN
ejpam-7078	582	6	.	.	PUNCT
ejpam-7078	582	7	electronic	electronic	ADJ
ejpam-7078	582	8	journal	journal	NOUN
ejpam-7078	582	9	of	of	ADP
ejpam-7078	582	10	graph	graph	NOUN
ejpam-7078	582	11	theory	theory	NOUN
ejpam-7078	582	12	and	and	CCONJ
ejpam-7078	582	13	applications	application	NOUN
ejpam-7078	582	14	,	,	PUNCT
ejpam-7078	582	15	23(2):187–199	23(2):187–199	NUM
ejpam-7078	582	16	,	,	PUNCT
ejpam-7078	582	17	2015	2015	NUM
ejpam-7078	582	18	.	.	PUNCT
ejpam-7078	583	1	[	[	X
ejpam-7078	583	2	18	18	NUM
ejpam-7078	583	3	]	]	X
ejpam-7078	583	4	s.	s.	PROPN
ejpam-7078	583	5	canoy	canoy	PROPN
ejpam-7078	583	6	jr	jr	PROPN
ejpam-7078	583	7	and	and	CCONJ
ejpam-7078	583	8	g.	g.	PROPN
ejpam-7078	583	9	p.	p.	NOUN
ejpam-7078	583	10	salasalan	salasalan	NOUN
ejpam-7078	583	11	.	.	PUNCT
ejpam-7078	584	1	a	a	DET
ejpam-7078	584	2	variant	variant	NOUN
ejpam-7078	584	3	of	of	ADP
ejpam-7078	584	4	hop	hop	NOUN
ejpam-7078	584	5	domination	domination	NOUN
ejpam-7078	584	6	in	in	ADP
ejpam-7078	584	7	graphs	graph	NOUN
ejpam-7078	584	8	.	.	PUNCT
ejpam-7078	585	1	european	european	ADJ
ejpam-7078	585	2	journal	journal	PROPN
ejpam-7078	585	3	of	of	ADP
ejpam-7078	585	4	pure	pure	ADJ
ejpam-7078	585	5	and	and	CCONJ
ejpam-7078	585	6	applied	applied	ADJ
ejpam-7078	585	7	mathematics	mathematic	NOUN
ejpam-7078	585	8	,	,	PUNCT
ejpam-7078	585	9	16(4):2431–2449	16(4):2431–2449	NUM
ejpam-7078	585	10	,	,	PUNCT
ejpam-7078	585	11	2022	2022	NUM
ejpam-7078	585	12	.	.	PUNCT
ejpam-7078	586	1	[	[	X
ejpam-7078	586	2	19	19	NUM
ejpam-7078	586	3	]	]	X
ejpam-7078	586	4	j.	j.	PROPN
ejpam-7078	586	5	hassan	hassan	PROPN
ejpam-7078	586	6	and	and	CCONJ
ejpam-7078	586	7	s.	s.	PROPN
ejpam-7078	586	8	canoy	canoy	PROPN
ejpam-7078	586	9	jr	jr	PROPN
ejpam-7078	586	10	.	.	PROPN
ejpam-7078	586	11	hop	hop	PROPN
ejpam-7078	586	12	independent	independent	ADJ
ejpam-7078	586	13	hop	hop	NOUN
ejpam-7078	586	14	domination	domination	NOUN
ejpam-7078	586	15	in	in	ADP
ejpam-7078	586	16	graphs	graph	NOUN
ejpam-7078	586	17	.	.	PUNCT
ejpam-7078	587	1	european	european	ADJ
ejpam-7078	587	2	journal	journal	PROPN
ejpam-7078	587	3	of	of	ADP
ejpam-7078	587	4	pure	pure	ADJ
ejpam-7078	587	5	and	and	CCONJ
ejpam-7078	587	6	applied	applied	ADJ
ejpam-7078	587	7	mathematics	mathematic	NOUN
ejpam-7078	587	8	,	,	PUNCT
ejpam-7078	587	9	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-7078	587	10	,	,	PUNCT
ejpam-7078	587	11	2022	2022	NUM
ejpam-7078	587	12	.	.	PUNCT
ejpam-7078	588	1	[	[	X
ejpam-7078	588	2	20	20	NUM
ejpam-7078	588	3	]	]	PUNCT
ejpam-7078	588	4	j.	j.	PROPN
ejpam-7078	588	5	hassan	hassan	PROPN
ejpam-7078	588	6	,	,	PUNCT
ejpam-7078	588	7	s.	s.	PROPN
ejpam-7078	588	8	canoy	canoy	PROPN
ejpam-7078	588	9	jr	jr	PROPN
ejpam-7078	588	10	,	,	PUNCT
ejpam-7078	588	11	and	and	CCONJ
ejpam-7078	588	12	a.	a.	PROPN
ejpam-7078	588	13	aradais	aradais	PROPN
ejpam-7078	588	14	.	.	PUNCT
ejpam-7078	589	1	hop	hop	PROPN
ejpam-7078	589	2	independent	independent	ADJ
ejpam-7078	589	3	sets	set	NOUN
ejpam-7078	589	4	in	in	ADP
ejpam-7078	589	5	graphs	graph	NOUN
ejpam-7078	589	6	.	.	PUNCT
ejpam-7078	590	1	european	european	ADJ
ejpam-7078	590	2	journal	journal	PROPN
ejpam-7078	590	3	of	of	ADP
ejpam-7078	590	4	pure	pure	ADJ
ejpam-7078	590	5	and	and	CCONJ
ejpam-7078	590	6	applied	applied	ADJ
ejpam-7078	590	7	mathematics	mathematic	NOUN
ejpam-7078	590	8	,	,	PUNCT
ejpam-7078	590	9	15(2):467–477	15(2):467–477	PROPN
ejpam-7078	590	10	,	,	PUNCT
ejpam-7078	590	11	2022	2022	NUM
ejpam-7078	590	12	.	.	PUNCT
ejpam-7078	591	1	[	[	X
ejpam-7078	591	2	21	21	NUM
ejpam-7078	591	3	]	]	PUNCT
ejpam-7078	591	4	j.	j.	PROPN
ejpam-7078	591	5	hassan	hassan	PROPN
ejpam-7078	591	6	,	,	PUNCT
ejpam-7078	591	7	s.	s.	PROPN
ejpam-7078	591	8	canoy	canoy	PROPN
ejpam-7078	591	9	jr	jr	PROPN
ejpam-7078	591	10	,	,	PUNCT
ejpam-7078	591	11	and	and	CCONJ
ejpam-7078	591	12	c.	c.	PROPN
ejpam-7078	591	13	j.	j.	PROPN
ejpam-7078	591	14	saromines	saromines	PROPN
ejpam-7078	591	15	.	.	PUNCT
ejpam-7078	592	1	convex	convex	VERB
ejpam-7078	592	2	hop	hop	NOUN
ejpam-7078	592	3	domination	domination	NOUN
ejpam-7078	592	4	in	in	ADP
ejpam-7078	592	5	graphs	graph	NOUN
ejpam-7078	592	6	.	.	PUNCT
ejpam-7078	593	1	european	european	ADJ
ejpam-7078	593	2	journal	journal	PROPN
ejpam-7078	593	3	of	of	ADP
ejpam-7078	593	4	pure	pure	ADJ
ejpam-7078	593	5	and	and	CCONJ
ejpam-7078	593	6	applied	applied	ADJ
ejpam-7078	593	7	mathematics	mathematic	NOUN
ejpam-7078	593	8	,	,	PUNCT
ejpam-7078	593	9	16(1):319–335	16(1):319–335	NUM
ejpam-7078	593	10	,	,	PUNCT
ejpam-7078	593	11	2023	2023	NUM
ejpam-7078	593	12	.	.	PUNCT
ejpam-7078	594	1	[	[	X
ejpam-7078	594	2	22	22	NUM
ejpam-7078	594	3	]	]	X
ejpam-7078	594	4	s.	s.	PROPN
ejpam-7078	594	5	canoy	canoy	PROPN
ejpam-7078	594	6	jr	jr	PROPN
ejpam-7078	594	7	and	and	CCONJ
ejpam-7078	594	8	g.	g.	PROPN
ejpam-7078	594	9	salasalan	salasalan	NOUN
ejpam-7078	594	10	.	.	PUNCT
ejpam-7078	595	1	locating	locate	VERB
ejpam-7078	595	2	-	-	PUNCT
ejpam-7078	595	3	hop	hop	NOUN
ejpam-7078	595	4	domination	domination	NOUN
ejpam-7078	595	5	in	in	ADP
ejpam-7078	595	6	graphs	graph	NOUN
ejpam-7078	595	7	.	.	PUNCT
ejpam-7078	596	1	kyungpook	kyungpook	PROPN
ejpam-7078	596	2	mathematical	mathematical	PROPN
ejpam-7078	596	3	journal	journal	PROPN
ejpam-7078	596	4	,	,	PUNCT
ejpam-7078	596	5	62(1):193–204	62(1):193–204	PROPN
ejpam-7078	596	6	,	,	PUNCT
ejpam-7078	596	7	2022	2022	NUM
ejpam-7078	596	8	.	.	PUNCT
ejpam-7078	597	1	[	[	X
ejpam-7078	597	2	23	23	NUM
ejpam-7078	597	3	]	]	X
ejpam-7078	597	4	g.	g.	NOUN
ejpam-7078	597	5	salasalan	salasalan	PROPN
ejpam-7078	597	6	and	and	CCONJ
ejpam-7078	597	7	s.	s.	PROPN
ejpam-7078	597	8	canoy	canoy	PROPN
ejpam-7078	597	9	jr	jr	PROPN
ejpam-7078	597	10	.	.	PUNCT
ejpam-7078	597	11	revisiting	revisit	VERB
ejpam-7078	597	12	domination	domination	NOUN
ejpam-7078	597	13	,	,	PUNCT
ejpam-7078	597	14	hop	hop	NOUN
ejpam-7078	597	15	domination	domination	NOUN
ejpam-7078	597	16	,	,	PUNCT
ejpam-7078	597	17	and	and	CCONJ
ejpam-7078	597	18	global	global	ADJ
ejpam-7078	597	19	hop	hop	NOUN
ejpam-7078	597	20	domination	domination	NOUN
ejpam-7078	597	21	in	in	ADP
ejpam-7078	597	22	graphs	graph	NOUN
ejpam-7078	597	23	.	.	PUNCT
ejpam-7078	598	1	european	european	ADJ
ejpam-7078	598	2	journal	journal	PROPN
ejpam-7078	598	3	of	of	ADP
ejpam-7078	598	4	pure	pure	ADJ
ejpam-7078	598	5	and	and	CCONJ
ejpam-7078	598	6	applied	applied	ADJ
ejpam-7078	598	7	mathematics	mathematic	NOUN
ejpam-7078	598	8	,	,	PUNCT
ejpam-7078	598	9	14(4):1415–1428	14(4):1415–1428	NUM
ejpam-7078	598	10	,	,	PUNCT
ejpam-7078	598	11	2021	2021	NUM
ejpam-7078	598	12	.	.	PUNCT