id	sid	tid	token	lemma	pos
ejpam-6264	1	1	european	european	PROPN
ejpam-6264	1	2	journal	journal	PROPN
ejpam-6264	1	3	of	of	ADP
ejpam-6264	1	4	pure	pure	ADJ
ejpam-6264	1	5	and	and	CCONJ
ejpam-6264	1	6	applied	applied	ADJ
ejpam-6264	1	7	mathematics	mathematic	NOUN
ejpam-6264	1	8	2025	2025	NUM
ejpam-6264	1	9	,	,	PUNCT
ejpam-6264	1	10	vol	vol	NOUN
ejpam-6264	1	11	.	.	PROPN
ejpam-6264	1	12	18	18	NUM
ejpam-6264	1	13	,	,	PUNCT
ejpam-6264	1	14	issue	issue	NOUN
ejpam-6264	1	15	4	4	NUM
ejpam-6264	1	16	,	,	PUNCT
ejpam-6264	1	17	article	article	NOUN
ejpam-6264	1	18	number	number	NOUN
ejpam-6264	1	19	6264	6264	NUM
ejpam-6264	1	20	issn	issn	VERB
ejpam-6264	1	21	1307	1307	NUM
ejpam-6264	1	22	-	-	SYM
ejpam-6264	1	23	5543	5543	NUM
ejpam-6264	1	24	–	–	PUNCT
ejpam-6264	1	25	ejpam.com	ejpam.com	X
ejpam-6264	1	26	published	publish	VERB
ejpam-6264	1	27	by	by	ADP
ejpam-6264	1	28	new	new	PROPN
ejpam-6264	1	29	york	york	PROPN
ejpam-6264	1	30	business	business	PROPN
ejpam-6264	1	31	global	global	ADJ
ejpam-6264	1	32	total	total	ADJ
ejpam-6264	1	33	modern	modern	ADJ
ejpam-6264	1	34	roman	roman	ADJ
ejpam-6264	1	35	dominating	dominating	NOUN
ejpam-6264	1	36	functions	function	NOUN
ejpam-6264	1	37	in	in	ADP
ejpam-6264	1	38	graphs	graph	NOUN
ejpam-6264	1	39	sherihatha	sherihatha	PROPN
ejpam-6264	1	40	r.	r.	PROPN
ejpam-6264	1	41	ahamad1,2	ahamad1,2	PROPN
ejpam-6264	1	42	,	,	PUNCT
ejpam-6264	1	43	jerry	jerry	NOUN
ejpam-6264	1	44	boy	boy	NOUN
ejpam-6264	1	45	g.	g.	PROPN
ejpam-6264	1	46	cariaga1,2	cariaga1,2	PROPN
ejpam-6264	1	47	,	,	PUNCT
ejpam-6264	1	48	sheila	sheila	PROPN
ejpam-6264	1	49	m.	m.	PROPN
ejpam-6264	1	50	menchavez1,2	menchavez1,2	PROPN
ejpam-6264	1	51	,	,	PUNCT
ejpam-6264	1	52	ferdinand	ferdinand	PROPN
ejpam-6264	1	53	p.	p.	PROPN
ejpam-6264	1	54	jamil1,2,∗	jamil1,2,∗	PROPN
ejpam-6264	2	1	1	1	NUM
ejpam-6264	2	2	department	department	NOUN
ejpam-6264	2	3	of	of	ADP
ejpam-6264	2	4	mathematics	mathematic	NOUN
ejpam-6264	2	5	and	and	CCONJ
ejpam-6264	2	6	statistics	statistic	NOUN
ejpam-6264	2	7	,	,	PUNCT
ejpam-6264	2	8	college	college	NOUN
ejpam-6264	2	9	of	of	ADP
ejpam-6264	2	10	science	science	NOUN
ejpam-6264	2	11	and	and	CCONJ
ejpam-6264	2	12	mathematics	mathematic	NOUN
ejpam-6264	2	13	,	,	PUNCT
ejpam-6264	2	14	msu	msu	PROPN
ejpam-6264	2	15	-	-	PUNCT
ejpam-6264	2	16	iligan	iligan	PROPN
ejpam-6264	2	17	institute	institute	PROPN
ejpam-6264	2	18	of	of	ADP
ejpam-6264	2	19	technology	technology	PROPN
ejpam-6264	2	20	,	,	PUNCT
ejpam-6264	2	21	9200	9200	NUM
ejpam-6264	2	22	iligan	iligan	ADJ
ejpam-6264	2	23	city	city	NOUN
ejpam-6264	2	24	,	,	PUNCT
ejpam-6264	2	25	philippines	philippine	NOUN
ejpam-6264	2	26	2	2	NUM
ejpam-6264	2	27	cmtps	cmtps	NOUN
ejpam-6264	2	28	,	,	PUNCT
ejpam-6264	2	29	premier	premier	PROPN
ejpam-6264	2	30	research	research	PROPN
ejpam-6264	2	31	institute	institute	PROPN
ejpam-6264	2	32	of	of	ADP
ejpam-6264	2	33	science	science	NOUN
ejpam-6264	2	34	and	and	CCONJ
ejpam-6264	2	35	mathematics	mathematic	NOUN
ejpam-6264	2	36	,	,	PUNCT
ejpam-6264	2	37	msu	msu	PROPN
ejpam-6264	2	38	-	-	PUNCT
ejpam-6264	2	39	iligan	iligan	PROPN
ejpam-6264	2	40	institute	institute	PROPN
ejpam-6264	2	41	of	of	ADP
ejpam-6264	2	42	technology	technology	PROPN
ejpam-6264	2	43	,	,	PUNCT
ejpam-6264	2	44	9200	9200	NUM
ejpam-6264	2	45	iligan	iligan	ADJ
ejpam-6264	2	46	city	city	NOUN
ejpam-6264	2	47	,	,	PUNCT
ejpam-6264	2	48	philippines	philippine	NOUN
ejpam-6264	2	49	abstract	abstract	ADJ
ejpam-6264	2	50	.	.	PUNCT
ejpam-6264	3	1	let	let	VERB
ejpam-6264	3	2	g	g	PROPN
ejpam-6264	3	3	=	=	SYM
ejpam-6264	3	4	(	(	PUNCT
ejpam-6264	3	5	v	v	NOUN
ejpam-6264	3	6	(	(	PUNCT
ejpam-6264	3	7	g	g	NOUN
ejpam-6264	3	8	)	)	PUNCT
ejpam-6264	3	9	,	,	PUNCT
ejpam-6264	3	10	e(g	e(g	PROPN
ejpam-6264	3	11	)	)	PUNCT
ejpam-6264	3	12	)	)	PUNCT
ejpam-6264	3	13	be	be	AUX
ejpam-6264	3	14	any	any	DET
ejpam-6264	3	15	connected	connected	ADJ
ejpam-6264	3	16	graph	graph	NOUN
ejpam-6264	3	17	.	.	PUNCT
ejpam-6264	4	1	a	a	DET
ejpam-6264	4	2	function	function	NOUN
ejpam-6264	4	3	f	f	NOUN
ejpam-6264	4	4	:	:	PUNCT
ejpam-6264	4	5	v	v	X
ejpam-6264	4	6	(	(	PUNCT
ejpam-6264	4	7	g	g	NOUN
ejpam-6264	4	8	)	)	PUNCT
ejpam-6264	4	9	→	→	SYM
ejpam-6264	4	10	{	{	PUNCT
ejpam-6264	4	11	0	0	NUM
ejpam-6264	4	12	,	,	PUNCT
ejpam-6264	4	13	1	1	NUM
ejpam-6264	4	14	,	,	PUNCT
ejpam-6264	4	15	2	2	NUM
ejpam-6264	4	16	,	,	PUNCT
ejpam-6264	4	17	3	3	NUM
ejpam-6264	4	18	}	}	PUNCT
ejpam-6264	4	19	is	be	AUX
ejpam-6264	4	20	a	a	DET
ejpam-6264	4	21	modern	modern	ADJ
ejpam-6264	4	22	roman	roman	ADJ
ejpam-6264	4	23	dominating	dominating	NOUN
ejpam-6264	4	24	function	function	NOUN
ejpam-6264	4	25	of	of	ADP
ejpam-6264	4	26	g	g	PROPN
ejpam-6264	4	27	if	if	SCONJ
ejpam-6264	4	28	for	for	ADP
ejpam-6264	4	29	each	each	PRON
ejpam-6264	4	30	v	v	NUM
ejpam-6264	4	31	∈	∈	PROPN
ejpam-6264	4	32	v	v	NOUN
ejpam-6264	4	33	(	(	PUNCT
ejpam-6264	4	34	g	g	NOUN
ejpam-6264	4	35	)	)	PUNCT
ejpam-6264	4	36	with	with	ADP
ejpam-6264	4	37	f(v	f(v	NOUN
ejpam-6264	4	38	)	)	PUNCT
ejpam-6264	4	39	=	=	SYM
ejpam-6264	4	40	0	0	NUM
ejpam-6264	4	41	,	,	PUNCT
ejpam-6264	4	42	there	there	PRON
ejpam-6264	4	43	exist	exist	VERB
ejpam-6264	4	44	u	u	NOUN
ejpam-6264	4	45	,	,	PUNCT
ejpam-6264	4	46	w	w	PROPN
ejpam-6264	4	47	∈	∈	PROPN
ejpam-6264	4	48	ng(v	ng(v	PUNCT
ejpam-6264	4	49	)	)	PUNCT
ejpam-6264	4	50	such	such	ADJ
ejpam-6264	4	51	that	that	DET
ejpam-6264	4	52	f(u	f(u	PROPN
ejpam-6264	4	53	)	)	PUNCT
ejpam-6264	4	54	=	=	SYM
ejpam-6264	4	55	2	2	NUM
ejpam-6264	4	56	and	and	CCONJ
ejpam-6264	4	57	f(w	f(w	NUM
ejpam-6264	4	58	)	)	PUNCT
ejpam-6264	4	59	=	=	SYM
ejpam-6264	4	60	3	3	NUM
ejpam-6264	4	61	;	;	PUNCT
ejpam-6264	4	62	and	and	CCONJ
ejpam-6264	4	63	for	for	ADP
ejpam-6264	4	64	each	each	PRON
ejpam-6264	4	65	v	v	NUM
ejpam-6264	4	66	∈	∈	PROPN
ejpam-6264	4	67	v	v	NOUN
ejpam-6264	4	68	(	(	PUNCT
ejpam-6264	4	69	g	g	NOUN
ejpam-6264	4	70	)	)	PUNCT
ejpam-6264	4	71	with	with	ADP
ejpam-6264	4	72	f(v	f(v	NOUN
ejpam-6264	4	73	)	)	PUNCT
ejpam-6264	4	74	=	=	SYM
ejpam-6264	4	75	1	1	NUM
ejpam-6264	4	76	,	,	PUNCT
ejpam-6264	4	77	there	there	PRON
ejpam-6264	4	78	exists	exist	VERB
ejpam-6264	4	79	u	u	PROPN
ejpam-6264	4	80	∈	∈	PROPN
ejpam-6264	4	81	ng(v	ng(v	PUNCT
ejpam-6264	4	82	)	)	PUNCT
ejpam-6264	4	83	such	such	ADJ
ejpam-6264	4	84	that	that	DET
ejpam-6264	4	85	f(u	f(u	PROPN
ejpam-6264	4	86	)	)	PUNCT
ejpam-6264	5	1	=	=	SYM
ejpam-6264	5	2	2	2	NUM
ejpam-6264	5	3	or	or	CCONJ
ejpam-6264	5	4	f(u	f(u	PROPN
ejpam-6264	5	5	)	)	PUNCT
ejpam-6264	5	6	=	=	SYM
ejpam-6264	6	1	3	3	X
ejpam-6264	6	2	.	.	X
ejpam-6264	7	1	in	in	ADP
ejpam-6264	7	2	addition	addition	NOUN
ejpam-6264	7	3	,	,	PUNCT
ejpam-6264	7	4	if	if	SCONJ
ejpam-6264	7	5	every	every	DET
ejpam-6264	7	6	subgraph	subgraph	NOUN
ejpam-6264	7	7	induced	induce	VERB
ejpam-6264	7	8	by	by	ADP
ejpam-6264	7	9	the	the	DET
ejpam-6264	7	10	set	set	NOUN
ejpam-6264	7	11	{	{	PUNCT
ejpam-6264	7	12	v	v	NOUN
ejpam-6264	7	13	∈	∈	PROPN
ejpam-6264	7	14	v	v	NOUN
ejpam-6264	7	15	(	(	PUNCT
ejpam-6264	7	16	g	g	NOUN
ejpam-6264	7	17	)	)	PUNCT
ejpam-6264	7	18	:	:	PUNCT
ejpam-6264	7	19	f(v	f(v	NOUN
ejpam-6264	7	20	)	)	PUNCT
ejpam-6264	7	21	>	>	X
ejpam-6264	7	22	0	0	NUM
ejpam-6264	7	23	}	}	PUNCT
ejpam-6264	7	24	is	be	AUX
ejpam-6264	7	25	isolated	isolate	VERB
ejpam-6264	7	26	-	-	PUNCT
ejpam-6264	7	27	free	free	ADJ
ejpam-6264	7	28	,	,	PUNCT
ejpam-6264	7	29	then	then	ADV
ejpam-6264	7	30	we	we	PRON
ejpam-6264	7	31	say	say	VERB
ejpam-6264	7	32	that	that	SCONJ
ejpam-6264	7	33	f	f	PROPN
ejpam-6264	7	34	is	be	AUX
ejpam-6264	7	35	a	a	DET
ejpam-6264	7	36	total	total	ADJ
ejpam-6264	7	37	modern	modern	ADJ
ejpam-6264	7	38	roman	roman	ADJ
ejpam-6264	7	39	dominating	dominating	NOUN
ejpam-6264	7	40	function	function	NOUN
ejpam-6264	7	41	of	of	ADP
ejpam-6264	7	42	g.	g.	PROPN
ejpam-6264	7	43	the	the	DET
ejpam-6264	7	44	minimum	minimum	ADJ
ejpam-6264	7	45	weight	weight	NOUN
ejpam-6264	7	46	ωtmr	ωtmr	PROPN
ejpam-6264	7	47	g	g	PROPN
ejpam-6264	7	48	(	(	PUNCT
ejpam-6264	7	49	f	f	X
ejpam-6264	7	50	)	)	PUNCT
ejpam-6264	7	51	=	=	SYM
ejpam-6264	7	52	∑	∑	PUNCT
ejpam-6264	7	53	v∈v	v∈v	PROPN
ejpam-6264	7	54	(	(	PUNCT
ejpam-6264	7	55	g	g	NOUN
ejpam-6264	7	56	)	)	PUNCT
ejpam-6264	7	57	f(v	f(v	NOUN
ejpam-6264	7	58	)	)	PUNCT
ejpam-6264	7	59	of	of	ADP
ejpam-6264	7	60	a	a	DET
ejpam-6264	7	61	total	total	ADJ
ejpam-6264	7	62	modern	modern	ADJ
ejpam-6264	7	63	roman	roman	ADJ
ejpam-6264	7	64	dominating	dominating	NOUN
ejpam-6264	7	65	function	function	NOUN
ejpam-6264	7	66	f	f	PROPN
ejpam-6264	7	67	of	of	ADP
ejpam-6264	7	68	g	g	PROPN
ejpam-6264	7	69	is	be	AUX
ejpam-6264	7	70	called	call	VERB
ejpam-6264	7	71	the	the	DET
ejpam-6264	7	72	total	total	ADJ
ejpam-6264	7	73	modern	modern	ADJ
ejpam-6264	7	74	roman	roman	ADJ
ejpam-6264	7	75	domination	domination	NOUN
ejpam-6264	7	76	number	number	NOUN
ejpam-6264	7	77	,	,	PUNCT
ejpam-6264	7	78	γtmr(g	γtmr(g	NOUN
ejpam-6264	7	79	)	)	PUNCT
ejpam-6264	7	80	,	,	PUNCT
ejpam-6264	7	81	of	of	ADP
ejpam-6264	7	82	g.	g.	PROPN
ejpam-6264	7	83	in	in	ADP
ejpam-6264	7	84	this	this	DET
ejpam-6264	7	85	paper	paper	NOUN
ejpam-6264	7	86	,	,	PUNCT
ejpam-6264	7	87	we	we	PRON
ejpam-6264	7	88	initiate	initiate	VERB
ejpam-6264	7	89	the	the	DET
ejpam-6264	7	90	study	study	NOUN
ejpam-6264	7	91	of	of	ADP
ejpam-6264	7	92	total	total	ADJ
ejpam-6264	7	93	modern	modern	ADJ
ejpam-6264	7	94	roman	roman	ADJ
ejpam-6264	7	95	domination	domination	NOUN
ejpam-6264	7	96	.	.	PUNCT
ejpam-6264	8	1	we	we	PRON
ejpam-6264	8	2	characterize	characterize	VERB
ejpam-6264	8	3	graphs	graph	NOUN
ejpam-6264	8	4	with	with	ADP
ejpam-6264	8	5	smaller	small	ADJ
ejpam-6264	8	6	total	total	ADJ
ejpam-6264	8	7	modern	modern	ADJ
ejpam-6264	8	8	roman	roman	ADJ
ejpam-6264	8	9	domination	domination	NOUN
ejpam-6264	8	10	number	number	NOUN
ejpam-6264	8	11	and	and	CCONJ
ejpam-6264	8	12	obtain	obtain	VERB
ejpam-6264	8	13	the	the	DET
ejpam-6264	8	14	γtmr(g	γtmr(g	NOUN
ejpam-6264	8	15	)	)	PUNCT
ejpam-6264	8	16	of	of	ADP
ejpam-6264	8	17	some	some	DET
ejpam-6264	8	18	special	special	ADJ
ejpam-6264	8	19	graphs	graph	NOUN
ejpam-6264	8	20	.	.	PUNCT
ejpam-6264	9	1	moreover	moreover	ADV
ejpam-6264	9	2	,	,	PUNCT
ejpam-6264	9	3	we	we	PRON
ejpam-6264	9	4	investigate	investigate	VERB
ejpam-6264	9	5	and	and	CCONJ
ejpam-6264	9	6	characterize	characterize	VERB
ejpam-6264	9	7	the	the	DET
ejpam-6264	9	8	total	total	ADJ
ejpam-6264	9	9	modern	modern	ADJ
ejpam-6264	9	10	roman	roman	ADJ
ejpam-6264	9	11	domination	domination	NOUN
ejpam-6264	9	12	in	in	ADP
ejpam-6264	9	13	the	the	DET
ejpam-6264	9	14	join	join	NOUN
ejpam-6264	9	15	and	and	CCONJ
ejpam-6264	9	16	corona	corona	NOUN
ejpam-6264	9	17	of	of	ADP
ejpam-6264	9	18	graphs	graph	NOUN
ejpam-6264	9	19	.	.	PUNCT
ejpam-6264	10	1	2020	2020	NUM
ejpam-6264	10	2	mathematics	mathematic	NOUN
ejpam-6264	10	3	subject	subject	NOUN
ejpam-6264	10	4	classifications	classification	NOUN
ejpam-6264	10	5	:	:	PUNCT
ejpam-6264	10	6	05c69	05c69	X
ejpam-6264	10	7	key	key	ADJ
ejpam-6264	10	8	words	word	NOUN
ejpam-6264	10	9	and	and	CCONJ
ejpam-6264	10	10	phrases	phrase	NOUN
ejpam-6264	10	11	:	:	PUNCT
ejpam-6264	10	12	dominating	dominate	VERB
ejpam-6264	10	13	set	set	NOUN
ejpam-6264	10	14	,	,	PUNCT
ejpam-6264	10	15	domination	domination	NOUN
ejpam-6264	10	16	number	number	NOUN
ejpam-6264	10	17	,	,	PUNCT
ejpam-6264	10	18	modern	modern	ADJ
ejpam-6264	10	19	roman	roman	ADJ
ejpam-6264	10	20	dominating	dominating	NOUN
ejpam-6264	10	21	function	function	NOUN
ejpam-6264	10	22	,	,	PUNCT
ejpam-6264	10	23	modern	modern	ADJ
ejpam-6264	10	24	roman	roman	ADJ
ejpam-6264	10	25	domination	domination	NOUN
ejpam-6264	10	26	number	number	NOUN
ejpam-6264	10	27	,	,	PUNCT
ejpam-6264	10	28	total	total	ADJ
ejpam-6264	10	29	modern	modern	ADJ
ejpam-6264	10	30	roman	roman	ADJ
ejpam-6264	10	31	dominating	dominating	NOUN
ejpam-6264	10	32	function	function	NOUN
ejpam-6264	10	33	,	,	PUNCT
ejpam-6264	10	34	total	total	ADJ
ejpam-6264	10	35	modern	modern	ADJ
ejpam-6264	10	36	roman	roman	ADJ
ejpam-6264	10	37	domination	domination	NOUN
ejpam-6264	10	38	number	number	NOUN
ejpam-6264	10	39	1	1	NUM
ejpam-6264	10	40	.	.	PUNCT
ejpam-6264	10	41	introduction	introduction	NOUN
ejpam-6264	10	42	the	the	DET
ejpam-6264	10	43	concept	concept	NOUN
ejpam-6264	10	44	of	of	ADP
ejpam-6264	10	45	roman	roman	ADJ
ejpam-6264	10	46	domination	domination	NOUN
ejpam-6264	10	47	was	be	AUX
ejpam-6264	10	48	introduced	introduce	VERB
ejpam-6264	10	49	by	by	ADP
ejpam-6264	10	50	cockayne	cockayne	PROPN
ejpam-6264	10	51	et	et	PROPN
ejpam-6264	10	52	al	al	PROPN
ejpam-6264	10	53	.	.	PUNCT
ejpam-6264	11	1	[	[	X
ejpam-6264	11	2	1	1	X
ejpam-6264	11	3	]	]	PUNCT
ejpam-6264	11	4	in	in	ADP
ejpam-6264	11	5	2004	2004	NUM
ejpam-6264	11	6	,	,	PUNCT
ejpam-6264	11	7	inspired	inspire	VERB
ejpam-6264	11	8	by	by	ADP
ejpam-6264	11	9	the	the	DET
ejpam-6264	11	10	strategies	strategy	NOUN
ejpam-6264	11	11	for	for	ADP
ejpam-6264	11	12	defending	defend	VERB
ejpam-6264	11	13	the	the	DET
ejpam-6264	11	14	roman	roman	ADJ
ejpam-6264	11	15	empire	empire	NOUN
ejpam-6264	11	16	presented	present	VERB
ejpam-6264	11	17	in	in	ADP
ejpam-6264	11	18	the	the	DET
ejpam-6264	11	19	work	work	NOUN
ejpam-6264	11	20	of	of	ADP
ejpam-6264	11	21	revelle	revelle	NOUN
ejpam-6264	11	22	and	and	CCONJ
ejpam-6264	11	23	rosing[2	rosing[2	PRON
ejpam-6264	11	24	]	]	PUNCT
ejpam-6264	11	25	and	and	CCONJ
ejpam-6264	11	26	stewart	stewart	PROPN
ejpam-6264	12	1	[	[	X
ejpam-6264	12	2	3	3	NUM
ejpam-6264	12	3	]	]	PUNCT
ejpam-6264	12	4	.	.	PUNCT
ejpam-6264	13	1	since	since	SCONJ
ejpam-6264	13	2	then	then	ADV
ejpam-6264	13	3	,	,	PUNCT
ejpam-6264	13	4	it	it	PRON
ejpam-6264	13	5	has	have	AUX
ejpam-6264	13	6	become	become	VERB
ejpam-6264	13	7	an	an	DET
ejpam-6264	13	8	active	active	ADJ
ejpam-6264	13	9	research	research	NOUN
ejpam-6264	13	10	field	field	NOUN
ejpam-6264	13	11	in	in	ADP
ejpam-6264	13	12	graph	graph	NOUN
ejpam-6264	13	13	theory	theory	NOUN
ejpam-6264	13	14	,	,	PUNCT
ejpam-6264	13	15	with	with	ADP
ejpam-6264	13	16	numerous	numerous	ADJ
ejpam-6264	13	17	studies	study	NOUN
ejpam-6264	13	18	exploring	explore	VERB
ejpam-6264	13	19	this	this	DET
ejpam-6264	13	20	concept	concept	NOUN
ejpam-6264	13	21	(	(	PUNCT
ejpam-6264	13	22	see	see	VERB
ejpam-6264	13	23	[	[	X
ejpam-6264	13	24	4],[5],[6],[7],[8],[9],[10	4],[5],[6],[7],[8],[9],[10	NOUN
ejpam-6264	13	25	]	]	PUNCT
ejpam-6264	13	26	,	,	PUNCT
ejpam-6264	13	27	∗corresponding	∗corresponde	VERB
ejpam-6264	13	28	author	author	NOUN
ejpam-6264	13	29	.	.	PUNCT
ejpam-6264	14	1	doi	doi	NOUN
ejpam-6264	14	2	:	:	PUNCT
ejpam-6264	14	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6264	https://doi.org/10.29020/nybg.ejpam.v18i4.6264	PROPN
ejpam-6264	14	4	email	email	NOUN
ejpam-6264	14	5	addresses	address	NOUN
ejpam-6264	14	6	:	:	PUNCT
ejpam-6264	14	7	sherihatha.ahamad@g.msuiit.edu.ph	sherihatha.ahamad@g.msuiit.edu.ph	PROPN
ejpam-6264	14	8	(	(	PUNCT
ejpam-6264	14	9	s.	s.	PROPN
ejpam-6264	14	10	r.	r.	PROPN
ejpam-6264	14	11	ahamad	ahamad	PROPN
ejpam-6264	14	12	)	)	PUNCT
ejpam-6264	14	13	,	,	PUNCT
ejpam-6264	14	14	jerryboy.cariaga@g.msuiit.edu.ph	jerryboy.cariaga@g.msuiit.edu.ph	PROPN
ejpam-6264	14	15	(	(	PUNCT
ejpam-6264	14	16	j.	j.	PROPN
ejpam-6264	14	17	b.	b.	PROPN
ejpam-6264	14	18	g.	g.	PROPN
ejpam-6264	14	19	cariaga	cariaga	PROPN
ejpam-6264	14	20	)	)	PUNCT
ejpam-6264	14	21	,	,	PUNCT
ejpam-6264	14	22	sheila.menchavez@g.msuiit.edu.ph	sheila.menchavez@g.msuiit.edu.ph	PROPN
ejpam-6264	14	23	(	(	PUNCT
ejpam-6264	14	24	s.	s.	PROPN
ejpam-6264	14	25	m.	m.	PROPN
ejpam-6264	14	26	menchavez	menchavez	PROPN
ejpam-6264	14	27	)	)	PUNCT
ejpam-6264	14	28	,	,	PUNCT
ejpam-6264	14	29	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-6264	14	30	(	(	PUNCT
ejpam-6264	14	31	f.	f.	PROPN
ejpam-6264	14	32	p.	p.	PROPN
ejpam-6264	14	33	jamil	jamil	PROPN
ejpam-6264	14	34	)	)	PUNCT
ejpam-6264	14	35	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6264	15	1	1	1	NUM
ejpam-6264	15	2	copyright	copyright	NOUN
ejpam-6264	15	3	:	:	PUNCT
ejpam-6264	15	4	©	©	PROPN
ejpam-6264	15	5	2025	2025	NUM
ejpam-6264	15	6	the	the	DET
ejpam-6264	15	7	author(s	author(s	NOUN
ejpam-6264	15	8	)	)	PUNCT
ejpam-6264	15	9	.	.	PUNCT
ejpam-6264	16	1	(	(	PUNCT
ejpam-6264	16	2	cc	cc	NOUN
ejpam-6264	16	3	by	by	ADP
ejpam-6264	16	4	-	-	PUNCT
ejpam-6264	16	5	nc	nc	PROPN
ejpam-6264	16	6	4.0	4.0	NUM
ejpam-6264	16	7	)	)	PUNCT
ejpam-6264	16	8	s.	s.	PROPN
ejpam-6264	16	9	ahamad	ahamad	VERB
ejpam-6264	16	10	et	et	PROPN
ejpam-6264	16	11	al	al	PROPN
ejpam-6264	16	12	.	.	PUNCT
ejpam-6264	16	13	/	/	SYM
ejpam-6264	16	14	eur	eur	PROPN
ejpam-6264	16	15	.	.	PUNCT
ejpam-6264	17	1	j.	j.	PROPN
ejpam-6264	17	2	pure	pure	PROPN
ejpam-6264	17	3	appl	appl	PROPN
ejpam-6264	17	4	.	.	PROPN
ejpam-6264	17	5	math	math	PROPN
ejpam-6264	17	6	,	,	PUNCT
ejpam-6264	17	7	18	18	NUM
ejpam-6264	17	8	(	(	PUNCT
ejpam-6264	17	9	4	4	NUM
ejpam-6264	17	10	)	)	PUNCT
ejpam-6264	17	11	(	(	PUNCT
ejpam-6264	17	12	2025	2025	NUM
ejpam-6264	17	13	)	)	PUNCT
ejpam-6264	17	14	,	,	PUNCT
ejpam-6264	17	15	6264	6264	NUM
ejpam-6264	17	16	2	2	NUM
ejpam-6264	17	17	of	of	ADP
ejpam-6264	17	18	20	20	NUM
ejpam-6264	17	19	[	[	X
ejpam-6264	17	20	11],[12],[13],[14	11],[12],[13],[14	NUM
ejpam-6264	17	21	]	]	NUM
ejpam-6264	17	22	)	)	PUNCT
ejpam-6264	17	23	.	.	PUNCT
ejpam-6264	18	1	a	a	DET
ejpam-6264	18	2	new	new	ADJ
ejpam-6264	18	3	model	model	NOUN
ejpam-6264	18	4	of	of	ADP
ejpam-6264	18	5	graph	graph	NOUN
ejpam-6264	18	6	domination	domination	NOUN
ejpam-6264	18	7	is	be	AUX
ejpam-6264	18	8	introduced	introduce	VERB
ejpam-6264	18	9	in	in	ADP
ejpam-6264	18	10	[	[	X
ejpam-6264	18	11	5	5	NUM
ejpam-6264	18	12	]	]	PUNCT
ejpam-6264	18	13	based	base	VERB
ejpam-6264	18	14	on	on	ADP
ejpam-6264	18	15	the	the	DET
ejpam-6264	18	16	roman	roman	ADJ
ejpam-6264	18	17	domination	domination	NOUN
ejpam-6264	18	18	and	and	CCONJ
ejpam-6264	18	19	is	be	AUX
ejpam-6264	18	20	called	call	VERB
ejpam-6264	18	21	modern	modern	ADJ
ejpam-6264	18	22	roman	roman	ADJ
ejpam-6264	18	23	domination	domination	NOUN
ejpam-6264	18	24	.	.	PUNCT
ejpam-6264	19	1	in	in	ADP
ejpam-6264	19	2	this	this	DET
ejpam-6264	19	3	paper	paper	NOUN
ejpam-6264	19	4	,	,	PUNCT
ejpam-6264	19	5	we	we	PRON
ejpam-6264	19	6	introduce	introduce	VERB
ejpam-6264	19	7	the	the	DET
ejpam-6264	19	8	concept	concept	NOUN
ejpam-6264	19	9	of	of	ADP
ejpam-6264	19	10	total	total	ADJ
ejpam-6264	19	11	modern	modern	ADJ
ejpam-6264	19	12	roman	roman	ADJ
ejpam-6264	19	13	domination	domination	NOUN
ejpam-6264	19	14	domination	domination	NOUN
ejpam-6264	19	15	in	in	ADP
ejpam-6264	19	16	graphs	graph	NOUN
ejpam-6264	19	17	.	.	PUNCT
ejpam-6264	20	1	it	it	PRON
ejpam-6264	20	2	focuses	focus	VERB
ejpam-6264	20	3	on	on	ADP
ejpam-6264	20	4	providing	provide	VERB
ejpam-6264	20	5	the	the	DET
ejpam-6264	20	6	total	total	ADJ
ejpam-6264	20	7	modern	modern	ADJ
ejpam-6264	20	8	roman	roman	ADJ
ejpam-6264	20	9	domination	domination	NOUN
ejpam-6264	20	10	number	number	NOUN
ejpam-6264	20	11	of	of	ADP
ejpam-6264	20	12	some	some	DET
ejpam-6264	20	13	special	special	ADJ
ejpam-6264	20	14	graphs	graph	NOUN
ejpam-6264	20	15	and	and	CCONJ
ejpam-6264	20	16	some	some	DET
ejpam-6264	20	17	characterizations	characterization	NOUN
ejpam-6264	20	18	for	for	ADP
ejpam-6264	20	19	the	the	DET
ejpam-6264	20	20	total	total	ADJ
ejpam-6264	20	21	modern	modern	ADJ
ejpam-6264	20	22	roman	roman	ADJ
ejpam-6264	20	23	domination	domination	NOUN
ejpam-6264	20	24	of	of	ADP
ejpam-6264	20	25	the	the	DET
ejpam-6264	20	26	join	join	NOUN
ejpam-6264	20	27	and	and	CCONJ
ejpam-6264	20	28	corona	corona	NOUN
ejpam-6264	20	29	of	of	ADP
ejpam-6264	20	30	graphs	graph	NOUN
ejpam-6264	20	31	.	.	PUNCT
ejpam-6264	21	1	2	2	X
ejpam-6264	21	2	.	.	X
ejpam-6264	21	3	terminology	terminology	NOUN
ejpam-6264	21	4	and	and	CCONJ
ejpam-6264	21	5	notation	notation	NOUN
ejpam-6264	21	6	the	the	DET
ejpam-6264	21	7	symbols	symbol	NOUN
ejpam-6264	21	8	v	v	ADP
ejpam-6264	21	9	(	(	PUNCT
ejpam-6264	21	10	g	g	NOUN
ejpam-6264	21	11	)	)	PUNCT
ejpam-6264	21	12	and	and	CCONJ
ejpam-6264	21	13	e(g	e(g	PROPN
ejpam-6264	21	14	)	)	PUNCT
ejpam-6264	21	15	denote	denote	VERB
ejpam-6264	21	16	the	the	DET
ejpam-6264	21	17	vertex	vertex	NOUN
ejpam-6264	21	18	set	set	NOUN
ejpam-6264	21	19	and	and	CCONJ
ejpam-6264	21	20	edge	edge	NOUN
ejpam-6264	21	21	set	set	NOUN
ejpam-6264	21	22	,	,	PUNCT
ejpam-6264	21	23	respectively	respectively	ADV
ejpam-6264	21	24	,	,	PUNCT
ejpam-6264	21	25	of	of	ADP
ejpam-6264	21	26	a	a	DET
ejpam-6264	21	27	graph	graph	NOUN
ejpam-6264	21	28	g.	g.	NOUN
ejpam-6264	21	29	for	for	ADP
ejpam-6264	21	30	s	s	PROPN
ejpam-6264	21	31	⊆	⊆	NUM
ejpam-6264	21	32	v	v	NOUN
ejpam-6264	21	33	(	(	PUNCT
ejpam-6264	21	34	g	g	NOUN
ejpam-6264	21	35	)	)	PUNCT
ejpam-6264	21	36	,	,	PUNCT
ejpam-6264	21	37	|s|	|s|	PROPN
ejpam-6264	21	38	is	be	AUX
ejpam-6264	21	39	the	the	DET
ejpam-6264	21	40	cardinality	cardinality	NOUN
ejpam-6264	21	41	of	of	ADP
ejpam-6264	21	42	s.	s.	PROPN
ejpam-6264	21	43	in	in	ADP
ejpam-6264	21	44	particular	particular	ADJ
ejpam-6264	21	45	,	,	PUNCT
ejpam-6264	21	46	|v	|v	PROPN
ejpam-6264	21	47	(	(	PUNCT
ejpam-6264	21	48	g)|	g)|	NOUN
ejpam-6264	21	49	and	and	CCONJ
ejpam-6264	21	50	|e(g)|	|e(g)|	PROPN
ejpam-6264	21	51	are	be	AUX
ejpam-6264	21	52	the	the	DET
ejpam-6264	21	53	order	order	NOUN
ejpam-6264	21	54	and	and	CCONJ
ejpam-6264	21	55	size	size	NOUN
ejpam-6264	21	56	,	,	PUNCT
ejpam-6264	21	57	respectively	respectively	ADV
ejpam-6264	21	58	,	,	PUNCT
ejpam-6264	21	59	of	of	ADP
ejpam-6264	21	60	g.	g.	PROPN
ejpam-6264	21	61	all	all	DET
ejpam-6264	21	62	graph	graph	NOUN
ejpam-6264	21	63	terminologies	terminology	NOUN
ejpam-6264	21	64	that	that	PRON
ejpam-6264	21	65	are	be	AUX
ejpam-6264	21	66	not	not	PART
ejpam-6264	21	67	introduced	introduce	VERB
ejpam-6264	21	68	but	but	CCONJ
ejpam-6264	21	69	are	be	AUX
ejpam-6264	21	70	being	be	AUX
ejpam-6264	21	71	used	use	VERB
ejpam-6264	21	72	here	here	ADV
ejpam-6264	21	73	are	be	AUX
ejpam-6264	21	74	adapted	adapt	VERB
ejpam-6264	21	75	from	from	ADP
ejpam-6264	21	76	[	[	X
ejpam-6264	21	77	15	15	NUM
ejpam-6264	21	78	]	]	PUNCT
ejpam-6264	21	79	.	.	PUNCT
ejpam-6264	22	1	the	the	DET
ejpam-6264	22	2	set	set	NOUN
ejpam-6264	22	3	of	of	ADP
ejpam-6264	22	4	neighbors	neighbor	NOUN
ejpam-6264	22	5	of	of	ADP
ejpam-6264	22	6	a	a	DET
ejpam-6264	22	7	vertex	vertex	NOUN
ejpam-6264	22	8	u	u	NOUN
ejpam-6264	22	9	in	in	ADP
ejpam-6264	22	10	g	g	NOUN
ejpam-6264	22	11	,	,	PUNCT
ejpam-6264	22	12	denoted	denote	VERB
ejpam-6264	22	13	by	by	ADP
ejpam-6264	22	14	ng(u	ng(u	NOUN
ejpam-6264	22	15	)	)	PUNCT
ejpam-6264	22	16	,	,	PUNCT
ejpam-6264	22	17	is	be	AUX
ejpam-6264	22	18	called	call	VERB
ejpam-6264	22	19	the	the	DET
ejpam-6264	22	20	open	open	ADJ
ejpam-6264	22	21	neighborhood	neighborhood	NOUN
ejpam-6264	22	22	of	of	ADP
ejpam-6264	22	23	u	u	PROPN
ejpam-6264	22	24	in	in	ADP
ejpam-6264	22	25	g.	g.	PROPN
ejpam-6264	22	26	the	the	DET
ejpam-6264	22	27	closed	close	VERB
ejpam-6264	22	28	neighborhood	neighborhood	NOUN
ejpam-6264	22	29	of	of	ADP
ejpam-6264	22	30	u	u	NOUN
ejpam-6264	22	31	in	in	ADP
ejpam-6264	22	32	g	g	PROPN
ejpam-6264	22	33	is	be	AUX
ejpam-6264	22	34	the	the	DET
ejpam-6264	22	35	set	set	NOUN
ejpam-6264	22	36	ng[u	ng[u	PROPN
ejpam-6264	22	37	]	]	X
ejpam-6264	22	38	=	=	SYM
ejpam-6264	22	39	ng(u	ng(u	PROPN
ejpam-6264	22	40	)	)	PUNCT
ejpam-6264	22	41	∪	∪	NOUN
ejpam-6264	22	42	{	{	PUNCT
ejpam-6264	22	43	u	u	NOUN
ejpam-6264	22	44	}	}	PUNCT
ejpam-6264	22	45	.	.	PUNCT
ejpam-6264	23	1	if	if	SCONJ
ejpam-6264	23	2	s	s	VERB
ejpam-6264	23	3	⊆	⊆	NUM
ejpam-6264	23	4	v	v	NOUN
ejpam-6264	23	5	(	(	PUNCT
ejpam-6264	23	6	g	g	NOUN
ejpam-6264	23	7	)	)	PUNCT
ejpam-6264	23	8	,	,	PUNCT
ejpam-6264	23	9	the	the	DET
ejpam-6264	23	10	open	open	ADJ
ejpam-6264	23	11	neighborhood	neighborhood	NOUN
ejpam-6264	23	12	of	of	ADP
ejpam-6264	23	13	s	s	NOUN
ejpam-6264	23	14	in	in	ADP
ejpam-6264	23	15	g	g	PROPN
ejpam-6264	23	16	is	be	AUX
ejpam-6264	23	17	the	the	DET
ejpam-6264	23	18	set	set	NOUN
ejpam-6264	23	19	ng(s	ng(s	NOUN
ejpam-6264	23	20	)	)	PUNCT
ejpam-6264	23	21	=	=	SYM
ejpam-6264	23	22	∪	∪	ADP
ejpam-6264	23	23	u∈s	u∈	NOUN
ejpam-6264	23	24	ng(u	ng(u	NOUN
ejpam-6264	23	25	)	)	PUNCT
ejpam-6264	23	26	.	.	PUNCT
ejpam-6264	24	1	the	the	DET
ejpam-6264	24	2	closed	closed	ADJ
ejpam-6264	24	3	neighborhood	neighborhood	NOUN
ejpam-6264	24	4	of	of	ADP
ejpam-6264	24	5	s	s	NOUN
ejpam-6264	24	6	in	in	ADP
ejpam-6264	24	7	g	g	PROPN
ejpam-6264	24	8	is	be	AUX
ejpam-6264	24	9	the	the	DET
ejpam-6264	24	10	set	set	VERB
ejpam-6264	24	11	ng[s	ng[	NOUN
ejpam-6264	24	12	]	]	PUNCT
ejpam-6264	24	13	=	=	PUNCT
ejpam-6264	24	14	ng(s)∪s	ng(s)∪s	PROPN
ejpam-6264	24	15	.	.	PUNCT
ejpam-6264	25	1	for	for	ADP
ejpam-6264	25	2	s	s	PROPN
ejpam-6264	25	3	⊆	⊆	NUM
ejpam-6264	25	4	v	v	NOUN
ejpam-6264	25	5	(	(	PUNCT
ejpam-6264	25	6	g	g	NOUN
ejpam-6264	25	7	)	)	PUNCT
ejpam-6264	25	8	of	of	ADP
ejpam-6264	25	9	a	a	DET
ejpam-6264	25	10	connected	connected	ADJ
ejpam-6264	25	11	graph	graph	NOUN
ejpam-6264	25	12	g	g	NOUN
ejpam-6264	25	13	,	,	PUNCT
ejpam-6264	25	14	ng(s	ng(s	NUM
ejpam-6264	25	15	)	)	PUNCT
ejpam-6264	25	16	=	=	PUNCT
ejpam-6264	25	17	∪	∪	ADP
ejpam-6264	25	18	v∈s	v∈s	NOUN
ejpam-6264	25	19	ng(v	ng(v	NOUN
ejpam-6264	25	20	)	)	PUNCT
ejpam-6264	25	21	and	and	CCONJ
ejpam-6264	25	22	ng[s	ng[	NOUN
ejpam-6264	25	23	]	]	PUNCT
ejpam-6264	25	24	=	=	SYM
ejpam-6264	25	25	s	s	NOUN
ejpam-6264	25	26	∪ng(s	∪ng(s	NOUN
ejpam-6264	25	27	)	)	PUNCT
ejpam-6264	25	28	.	.	PUNCT
ejpam-6264	26	1	a	a	DET
ejpam-6264	26	2	set	set	NOUN
ejpam-6264	26	3	s	s	NOUN
ejpam-6264	26	4	⊆	⊆	NUM
ejpam-6264	26	5	v	v	NOUN
ejpam-6264	26	6	(	(	PUNCT
ejpam-6264	26	7	g	g	NOUN
ejpam-6264	26	8	)	)	PUNCT
ejpam-6264	26	9	is	be	AUX
ejpam-6264	26	10	a	a	DET
ejpam-6264	26	11	dominating	dominating	NOUN
ejpam-6264	26	12	set	set	VERB
ejpam-6264	26	13	in	in	ADP
ejpam-6264	26	14	g	g	PROPN
ejpam-6264	26	15	if	if	SCONJ
ejpam-6264	26	16	ng[s	ng[	NOUN
ejpam-6264	26	17	]	]	PUNCT
ejpam-6264	26	18	=	=	SYM
ejpam-6264	26	19	v	v	NOUN
ejpam-6264	26	20	(	(	PUNCT
ejpam-6264	26	21	g	g	NOUN
ejpam-6264	26	22	)	)	PUNCT
ejpam-6264	26	23	.	.	PUNCT
ejpam-6264	27	1	thus	thus	ADV
ejpam-6264	27	2	,	,	PUNCT
ejpam-6264	27	3	s	s	VERB
ejpam-6264	27	4	is	be	AUX
ejpam-6264	27	5	a	a	DET
ejpam-6264	27	6	dominating	dominating	NOUN
ejpam-6264	27	7	set	set	VERB
ejpam-6264	27	8	in	in	ADP
ejpam-6264	27	9	g	g	PROPN
ejpam-6264	27	10	if	if	SCONJ
ejpam-6264	27	11	and	and	CCONJ
ejpam-6264	27	12	only	only	ADV
ejpam-6264	27	13	if	if	SCONJ
ejpam-6264	27	14	for	for	ADP
ejpam-6264	27	15	each	each	DET
ejpam-6264	27	16	v	v	NUM
ejpam-6264	27	17	∈	∈	PROPN
ejpam-6264	27	18	v	v	NOUN
ejpam-6264	27	19	(	(	PUNCT
ejpam-6264	27	20	g	g	NOUN
ejpam-6264	27	21	)	)	PUNCT
ejpam-6264	27	22	\s	\	NOUN
ejpam-6264	27	23	,	,	PUNCT
ejpam-6264	27	24	there	there	PRON
ejpam-6264	27	25	exists	exist	VERB
ejpam-6264	27	26	u	u	PROPN
ejpam-6264	27	27	∈	∈	PROPN
ejpam-6264	27	28	s	s	PROPN
ejpam-6264	27	29	,	,	PUNCT
ejpam-6264	27	30	such	such	ADJ
ejpam-6264	27	31	that	that	SCONJ
ejpam-6264	27	32	uv	uv	PROPN
ejpam-6264	27	33	∈	∈	PROPN
ejpam-6264	27	34	e(g	e(g	PROPN
ejpam-6264	27	35	)	)	PUNCT
ejpam-6264	27	36	.	.	PUNCT
ejpam-6264	28	1	the	the	DET
ejpam-6264	28	2	minimum	minimum	ADJ
ejpam-6264	28	3	cardinality	cardinality	NOUN
ejpam-6264	28	4	of	of	ADP
ejpam-6264	28	5	a	a	DET
ejpam-6264	28	6	dominating	dominating	NOUN
ejpam-6264	28	7	set	set	NOUN
ejpam-6264	28	8	in	in	ADP
ejpam-6264	28	9	g	g	NOUN
ejpam-6264	28	10	,	,	PUNCT
ejpam-6264	28	11	denoted	denote	VERB
ejpam-6264	28	12	by	by	ADP
ejpam-6264	28	13	γ(g	γ(g	PROPN
ejpam-6264	28	14	)	)	PUNCT
ejpam-6264	28	15	,	,	PUNCT
ejpam-6264	28	16	is	be	AUX
ejpam-6264	28	17	the	the	DET
ejpam-6264	28	18	domination	domination	NOUN
ejpam-6264	28	19	number	number	NOUN
ejpam-6264	28	20	of	of	ADP
ejpam-6264	28	21	g.	g.	PROPN
ejpam-6264	28	22	a	a	DET
ejpam-6264	28	23	dominating	dominating	NOUN
ejpam-6264	28	24	set	set	NOUN
ejpam-6264	28	25	s	s	NOUN
ejpam-6264	28	26	of	of	ADP
ejpam-6264	28	27	g	g	NOUN
ejpam-6264	28	28	with	with	ADP
ejpam-6264	28	29	|s|	|s|	PROPN
ejpam-6264	28	30	=	=	SYM
ejpam-6264	28	31	γ(g	γ(g	PROPN
ejpam-6264	28	32	)	)	PUNCT
ejpam-6264	28	33	is	be	AUX
ejpam-6264	28	34	called	call	VERB
ejpam-6264	28	35	a	a	DET
ejpam-6264	28	36	γ	γ	NOUN
ejpam-6264	28	37	set	set	NOUN
ejpam-6264	28	38	of	of	ADP
ejpam-6264	28	39	g.	g.	PROPN
ejpam-6264	28	40	the	the	DET
ejpam-6264	28	41	authors	author	NOUN
ejpam-6264	28	42	always	always	ADV
ejpam-6264	28	43	refer	refer	VERB
ejpam-6264	28	44	to	to	ADP
ejpam-6264	28	45	[	[	X
ejpam-6264	28	46	16	16	NUM
ejpam-6264	28	47	]	]	PUNCT
ejpam-6264	28	48	for	for	ADP
ejpam-6264	28	49	the	the	DET
ejpam-6264	28	50	introduction	introduction	NOUN
ejpam-6264	28	51	and	and	CCONJ
ejpam-6264	28	52	more	more	ADV
ejpam-6264	28	53	comprehensive	comprehensive	ADJ
ejpam-6264	28	54	discussion	discussion	NOUN
ejpam-6264	28	55	of	of	ADP
ejpam-6264	28	56	the	the	DET
ejpam-6264	28	57	development	development	NOUN
ejpam-6264	28	58	of	of	ADP
ejpam-6264	28	59	the	the	DET
ejpam-6264	28	60	concept	concept	NOUN
ejpam-6264	28	61	of	of	ADP
ejpam-6264	28	62	domination	domination	NOUN
ejpam-6264	28	63	in	in	ADP
ejpam-6264	28	64	graphs	graph	NOUN
ejpam-6264	28	65	.	.	PUNCT
ejpam-6264	29	1	for	for	ADP
ejpam-6264	29	2	a	a	DET
ejpam-6264	29	3	positive	positive	ADJ
ejpam-6264	29	4	integer	integer	NOUN
ejpam-6264	29	5	k	k	PROPN
ejpam-6264	29	6	,	,	PUNCT
ejpam-6264	29	7	a	a	DET
ejpam-6264	29	8	set	set	NOUN
ejpam-6264	29	9	d	d	NOUN
ejpam-6264	29	10	⊆	⊆	NUM
ejpam-6264	29	11	v	v	ADP
ejpam-6264	29	12	(	(	PUNCT
ejpam-6264	29	13	g	g	NOUN
ejpam-6264	29	14	)	)	PUNCT
ejpam-6264	29	15	is	be	AUX
ejpam-6264	29	16	called	call	VERB
ejpam-6264	29	17	a	a	DET
ejpam-6264	29	18	k	k	ADJ
ejpam-6264	29	19	-	-	PUNCT
ejpam-6264	29	20	dominating	dominating	NOUN
ejpam-6264	29	21	set	set	NOUN
ejpam-6264	29	22	if	if	SCONJ
ejpam-6264	29	23	each	each	DET
ejpam-6264	29	24	x	x	SYM
ejpam-6264	29	25	∈	∈	PROPN
ejpam-6264	29	26	v	v	ADP
ejpam-6264	29	27	(	(	PUNCT
ejpam-6264	29	28	g	g	NOUN
ejpam-6264	29	29	)	)	PUNCT
ejpam-6264	29	30	\d	\d	NOUN
ejpam-6264	29	31	is	be	AUX
ejpam-6264	29	32	adjacent	adjacent	ADJ
ejpam-6264	29	33	to	to	ADP
ejpam-6264	29	34	at	at	ADP
ejpam-6264	29	35	least	least	ADJ
ejpam-6264	29	36	k	k	X
ejpam-6264	29	37	vertices	vertice	VERB
ejpam-6264	29	38	in	in	ADP
ejpam-6264	29	39	d.	d.	PROPN
ejpam-6264	29	40	the	the	DET
ejpam-6264	29	41	k	k	ADJ
ejpam-6264	29	42	-	-	PUNCT
ejpam-6264	29	43	domination	domination	NOUN
ejpam-6264	29	44	number	number	NOUN
ejpam-6264	29	45	γk(g	γk(g	PUNCT
ejpam-6264	29	46	)	)	PUNCT
ejpam-6264	29	47	is	be	AUX
ejpam-6264	29	48	then	then	ADV
ejpam-6264	29	49	defined	define	VERB
ejpam-6264	29	50	to	to	PART
ejpam-6264	29	51	be	be	AUX
ejpam-6264	29	52	the	the	DET
ejpam-6264	29	53	smallest	small	ADJ
ejpam-6264	29	54	cardinality	cardinality	NOUN
ejpam-6264	29	55	of	of	ADP
ejpam-6264	29	56	a	a	DET
ejpam-6264	29	57	k	k	ADV
ejpam-6264	29	58	-	-	PUNCT
ejpam-6264	29	59	dominating	dominating	ADJ
ejpam-6264	29	60	set	set	NOUN
ejpam-6264	29	61	of	of	ADP
ejpam-6264	29	62	g.	g.	PROPN
ejpam-6264	29	63	for	for	ADP
ejpam-6264	29	64	k	k	PROPN
ejpam-6264	29	65	=	=	SYM
ejpam-6264	29	66	2	2	NUM
ejpam-6264	29	67	,	,	PUNCT
ejpam-6264	29	68	we	we	PRON
ejpam-6264	29	69	have	have	VERB
ejpam-6264	29	70	d	d	NOUN
ejpam-6264	29	71	as	as	ADP
ejpam-6264	29	72	2	2	NUM
ejpam-6264	29	73	-	-	PUNCT
ejpam-6264	29	74	dominating	dominating	NOUN
ejpam-6264	29	75	set	set	NOUN
ejpam-6264	29	76	with	with	ADP
ejpam-6264	29	77	2	2	NUM
ejpam-6264	29	78	-	-	PUNCT
ejpam-6264	29	79	domination	domination	NOUN
ejpam-6264	29	80	number	number	NOUN
ejpam-6264	29	81	denoted	denote	VERB
ejpam-6264	29	82	by	by	ADP
ejpam-6264	29	83	γ2(g	γ2(g	NOUN
ejpam-6264	29	84	)	)	PUNCT
ejpam-6264	30	1	[	[	X
ejpam-6264	30	2	8	8	NUM
ejpam-6264	30	3	]	]	PUNCT
ejpam-6264	30	4	.	.	PUNCT
ejpam-6264	31	1	a	a	DET
ejpam-6264	31	2	roman	roman	ADJ
ejpam-6264	31	3	dominating	dominating	NOUN
ejpam-6264	31	4	function	function	NOUN
ejpam-6264	31	5	(	(	PUNCT
ejpam-6264	31	6	rdf	rdf	NOUN
ejpam-6264	31	7	)	)	PUNCT
ejpam-6264	31	8	on	on	ADP
ejpam-6264	31	9	g	g	PROPN
ejpam-6264	31	10	is	be	AUX
ejpam-6264	31	11	a	a	DET
ejpam-6264	31	12	function	function	NOUN
ejpam-6264	31	13	f	f	NOUN
ejpam-6264	31	14	:	:	PUNCT
ejpam-6264	31	15	v	v	X
ejpam-6264	31	16	(	(	PUNCT
ejpam-6264	31	17	g	g	NOUN
ejpam-6264	31	18	)	)	PUNCT
ejpam-6264	31	19	→	→	SYM
ejpam-6264	31	20	{	{	PUNCT
ejpam-6264	31	21	0	0	NUM
ejpam-6264	31	22	,	,	PUNCT
ejpam-6264	31	23	1	1	NUM
ejpam-6264	31	24	,	,	PUNCT
ejpam-6264	31	25	2	2	NUM
ejpam-6264	31	26	}	}	PUNCT
ejpam-6264	31	27	such	such	ADJ
ejpam-6264	31	28	that	that	SCONJ
ejpam-6264	31	29	every	every	DET
ejpam-6264	31	30	vertex	vertex	NOUN
ejpam-6264	31	31	u	u	NOUN
ejpam-6264	31	32	∈	∈	PROPN
ejpam-6264	31	33	v	v	ADP
ejpam-6264	31	34	(	(	PUNCT
ejpam-6264	31	35	g	g	NOUN
ejpam-6264	31	36	)	)	PUNCT
ejpam-6264	31	37	with	with	ADP
ejpam-6264	31	38	f(u	f(u	PROPN
ejpam-6264	31	39	)	)	PUNCT
ejpam-6264	32	1	=	=	SYM
ejpam-6264	32	2	0	0	NUM
ejpam-6264	32	3	is	be	AUX
ejpam-6264	32	4	adjacent	adjacent	ADJ
ejpam-6264	32	5	to	to	ADP
ejpam-6264	32	6	at	at	ADV
ejpam-6264	32	7	least	least	ADV
ejpam-6264	32	8	one	one	NUM
ejpam-6264	32	9	vertex	vertex	NOUN
ejpam-6264	32	10	v	v	NOUN
ejpam-6264	32	11	with	with	ADP
ejpam-6264	32	12	f(v	f(v	NOUN
ejpam-6264	32	13	)	)	PUNCT
ejpam-6264	32	14	=	=	SYM
ejpam-6264	33	1	2	2	X
ejpam-6264	33	2	.	.	PUNCT
ejpam-6264	33	3	the	the	DET
ejpam-6264	33	4	weight	weight	NOUN
ejpam-6264	33	5	of	of	ADP
ejpam-6264	33	6	an	an	DET
ejpam-6264	33	7	rdf	rdf	NOUN
ejpam-6264	33	8	is	be	AUX
ejpam-6264	33	9	the	the	DET
ejpam-6264	33	10	value	value	NOUN
ejpam-6264	33	11	ωg(f	ωg(f	PRON
ejpam-6264	33	12	)	)	PUNCT
ejpam-6264	33	13	=	=	SYM
ejpam-6264	33	14	∑	∑	PUNCT
ejpam-6264	33	15	u∈v	u∈v	NOUN
ejpam-6264	33	16	(	(	PUNCT
ejpam-6264	33	17	g	g	NOUN
ejpam-6264	33	18	)	)	PUNCT
ejpam-6264	33	19	f(u	f(u	PROPN
ejpam-6264	33	20	)	)	PUNCT
ejpam-6264	33	21	.	.	PUNCT
ejpam-6264	34	1	the	the	DET
ejpam-6264	34	2	roman	roman	ADJ
ejpam-6264	34	3	domination	domination	NOUN
ejpam-6264	34	4	number	number	NOUN
ejpam-6264	34	5	γr(g	γr(g	PROPN
ejpam-6264	34	6	)	)	PUNCT
ejpam-6264	34	7	is	be	AUX
ejpam-6264	34	8	the	the	DET
ejpam-6264	34	9	minimum	minimum	ADJ
ejpam-6264	34	10	weight	weight	NOUN
ejpam-6264	34	11	of	of	ADP
ejpam-6264	34	12	an	an	DET
ejpam-6264	34	13	rdf	rdf	NOUN
ejpam-6264	34	14	on	on	ADP
ejpam-6264	34	15	g.	g.	PROPN
ejpam-6264	34	16	an	an	DET
ejpam-6264	34	17	rdf	rdf	NOUN
ejpam-6264	34	18	with	with	ADP
ejpam-6264	34	19	ωg(f	ωg(f	NOUN
ejpam-6264	34	20	)	)	PUNCT
ejpam-6264	34	21	=	=	SYM
ejpam-6264	34	22	γr(g	γr(g	NOUN
ejpam-6264	34	23	)	)	PUNCT
ejpam-6264	34	24	is	be	AUX
ejpam-6264	34	25	referred	refer	VERB
ejpam-6264	34	26	to	to	ADP
ejpam-6264	34	27	as	as	ADP
ejpam-6264	34	28	a	a	DET
ejpam-6264	34	29	γr	γr	NOUN
ejpam-6264	34	30	-	-	NOUN
ejpam-6264	34	31	function	function	NOUN
ejpam-6264	34	32	[	[	X
ejpam-6264	34	33	8	8	NUM
ejpam-6264	34	34	]	]	PUNCT
ejpam-6264	34	35	.	.	PUNCT
ejpam-6264	35	1	a	a	DET
ejpam-6264	35	2	modern	modern	ADJ
ejpam-6264	35	3	roman	roman	ADJ
ejpam-6264	35	4	dominating	dominating	NOUN
ejpam-6264	35	5	function	function	NOUN
ejpam-6264	35	6	(	(	PUNCT
ejpam-6264	35	7	mrdf	mrdf	NOUN
ejpam-6264	35	8	)	)	PUNCT
ejpam-6264	35	9	on	on	ADP
ejpam-6264	35	10	g	g	PROPN
ejpam-6264	35	11	is	be	AUX
ejpam-6264	35	12	a	a	DET
ejpam-6264	35	13	function	function	NOUN
ejpam-6264	35	14	f	f	NOUN
ejpam-6264	35	15	:	:	PUNCT
ejpam-6264	35	16	v	v	X
ejpam-6264	35	17	(	(	PUNCT
ejpam-6264	35	18	g	g	NOUN
ejpam-6264	35	19	)	)	PUNCT
ejpam-6264	35	20	→	→	SYM
ejpam-6264	35	21	{	{	PUNCT
ejpam-6264	35	22	0	0	NUM
ejpam-6264	35	23	,	,	PUNCT
ejpam-6264	35	24	1	1	NUM
ejpam-6264	35	25	,	,	PUNCT
ejpam-6264	35	26	2	2	NUM
ejpam-6264	35	27	,	,	PUNCT
ejpam-6264	35	28	3	3	NUM
ejpam-6264	35	29	}	}	PUNCT
ejpam-6264	35	30	if	if	SCONJ
ejpam-6264	35	31	(	(	PUNCT
ejpam-6264	35	32	p1	p1	NOUN
ejpam-6264	35	33	)	)	PUNCT
ejpam-6264	35	34	for	for	ADP
ejpam-6264	35	35	each	each	PRON
ejpam-6264	35	36	v	v	NUM
ejpam-6264	35	37	∈	∈	PROPN
ejpam-6264	35	38	v	v	NOUN
ejpam-6264	35	39	(	(	PUNCT
ejpam-6264	35	40	g	g	NOUN
ejpam-6264	35	41	)	)	PUNCT
ejpam-6264	35	42	with	with	ADP
ejpam-6264	35	43	f(v	f(v	NOUN
ejpam-6264	35	44	)	)	PUNCT
ejpam-6264	35	45	=	=	SYM
ejpam-6264	35	46	0	0	NUM
ejpam-6264	35	47	,	,	PUNCT
ejpam-6264	35	48	there	there	PRON
ejpam-6264	35	49	exist	exist	VERB
ejpam-6264	35	50	u	u	NOUN
ejpam-6264	35	51	,	,	PUNCT
ejpam-6264	35	52	w	w	PROPN
ejpam-6264	35	53	∈	∈	PROPN
ejpam-6264	35	54	ng(v	ng(v	PUNCT
ejpam-6264	35	55	)	)	PUNCT
ejpam-6264	35	56	such	such	ADJ
ejpam-6264	35	57	that	that	DET
ejpam-6264	35	58	f(u	f(u	PROPN
ejpam-6264	35	59	)	)	PUNCT
ejpam-6264	35	60	=	=	SYM
ejpam-6264	35	61	2	2	NUM
ejpam-6264	35	62	and	and	CCONJ
ejpam-6264	35	63	f(w	f(w	NUM
ejpam-6264	35	64	)	)	PUNCT
ejpam-6264	35	65	=	=	SYM
ejpam-6264	35	66	3	3	NUM
ejpam-6264	35	67	;	;	PUNCT
ejpam-6264	35	68	and	and	CCONJ
ejpam-6264	35	69	s.	s.	PROPN
ejpam-6264	35	70	ahamad	ahamad	VERB
ejpam-6264	35	71	et	et	PROPN
ejpam-6264	35	72	al	al	PROPN
ejpam-6264	35	73	.	.	PUNCT
ejpam-6264	35	74	/	/	SYM
ejpam-6264	35	75	eur	eur	PROPN
ejpam-6264	35	76	.	.	PUNCT
ejpam-6264	36	1	j.	j.	PROPN
ejpam-6264	36	2	pure	pure	PROPN
ejpam-6264	36	3	appl	appl	PROPN
ejpam-6264	36	4	.	.	PROPN
ejpam-6264	36	5	math	math	PROPN
ejpam-6264	36	6	,	,	PUNCT
ejpam-6264	36	7	18	18	NUM
ejpam-6264	36	8	(	(	PUNCT
ejpam-6264	36	9	4	4	NUM
ejpam-6264	36	10	)	)	PUNCT
ejpam-6264	36	11	(	(	PUNCT
ejpam-6264	36	12	2025	2025	NUM
ejpam-6264	36	13	)	)	PUNCT
ejpam-6264	36	14	,	,	PUNCT
ejpam-6264	36	15	6264	6264	NUM
ejpam-6264	36	16	3	3	NUM
ejpam-6264	36	17	of	of	ADP
ejpam-6264	36	18	20	20	NUM
ejpam-6264	36	19	(	(	PUNCT
ejpam-6264	36	20	p2	p2	PROPN
ejpam-6264	36	21	)	)	PUNCT
ejpam-6264	36	22	for	for	ADP
ejpam-6264	36	23	each	each	PRON
ejpam-6264	36	24	v	v	NUM
ejpam-6264	36	25	∈	∈	PROPN
ejpam-6264	36	26	v	v	NOUN
ejpam-6264	36	27	(	(	PUNCT
ejpam-6264	36	28	g	g	NOUN
ejpam-6264	36	29	)	)	PUNCT
ejpam-6264	36	30	with	with	ADP
ejpam-6264	36	31	f(v	f(v	NOUN
ejpam-6264	36	32	)	)	PUNCT
ejpam-6264	36	33	=	=	SYM
ejpam-6264	37	1	1	1	NUM
ejpam-6264	37	2	,	,	PUNCT
ejpam-6264	37	3	there	there	PRON
ejpam-6264	37	4	exists	exist	VERB
ejpam-6264	37	5	u	u	PROPN
ejpam-6264	37	6	∈	∈	PROPN
ejpam-6264	37	7	ng(v	ng(v	PUNCT
ejpam-6264	37	8	)	)	PUNCT
ejpam-6264	37	9	such	such	ADJ
ejpam-6264	37	10	that	that	DET
ejpam-6264	37	11	f(u	f(u	PROPN
ejpam-6264	37	12	)	)	PUNCT
ejpam-6264	37	13	=	=	SYM
ejpam-6264	37	14	2	2	NUM
ejpam-6264	37	15	or	or	CCONJ
ejpam-6264	37	16	f(u	f(u	PROPN
ejpam-6264	37	17	)	)	PUNCT
ejpam-6264	37	18	=	=	SYM
ejpam-6264	38	1	3	3	X
ejpam-6264	38	2	.	.	PUNCT
ejpam-6264	38	3	the	the	DET
ejpam-6264	38	4	weight	weight	NOUN
ejpam-6264	38	5	of	of	ADP
ejpam-6264	38	6	a	a	DET
ejpam-6264	38	7	modern	modern	ADJ
ejpam-6264	38	8	roman	roman	ADJ
ejpam-6264	38	9	dominating	dominating	NOUN
ejpam-6264	38	10	function	function	NOUN
ejpam-6264	38	11	f	f	PROPN
ejpam-6264	38	12	of	of	ADP
ejpam-6264	38	13	g	g	PROPN
ejpam-6264	38	14	is	be	AUX
ejpam-6264	38	15	the	the	DET
ejpam-6264	38	16	sum	sum	NOUN
ejpam-6264	38	17	ωmr	ωmr	NOUN
ejpam-6264	38	18	g	g	PROPN
ejpam-6264	38	19	(	(	PUNCT
ejpam-6264	38	20	f	f	X
ejpam-6264	38	21	)	)	PUNCT
ejpam-6264	38	22	=	=	SYM
ejpam-6264	38	23	∑	∑	PUNCT
ejpam-6264	38	24	v∈v	v∈v	PROPN
ejpam-6264	38	25	(	(	PUNCT
ejpam-6264	38	26	g	g	NOUN
ejpam-6264	38	27	)	)	PUNCT
ejpam-6264	38	28	f(v	f(v	NOUN
ejpam-6264	38	29	)	)	PUNCT
ejpam-6264	38	30	and	and	CCONJ
ejpam-6264	38	31	its	its	PRON
ejpam-6264	38	32	minimum	minimum	ADJ
ejpam-6264	38	33	weight	weight	NOUN
ejpam-6264	38	34	is	be	AUX
ejpam-6264	38	35	called	call	VERB
ejpam-6264	38	36	the	the	DET
ejpam-6264	38	37	modern	modern	ADJ
ejpam-6264	38	38	roman	roman	ADJ
ejpam-6264	38	39	domination	domination	NOUN
ejpam-6264	38	40	number	number	NOUN
ejpam-6264	38	41	γmr(g	γmr(g	PROPN
ejpam-6264	38	42	)	)	PUNCT
ejpam-6264	38	43	of	of	ADP
ejpam-6264	38	44	g	g	PROPN
ejpam-6264	38	45	[	[	X
ejpam-6264	38	46	5	5	NUM
ejpam-6264	38	47	]	]	PUNCT
ejpam-6264	38	48	.	.	PUNCT
ejpam-6264	39	1	for	for	ADP
ejpam-6264	39	2	a	a	DET
ejpam-6264	39	3	function	function	NOUN
ejpam-6264	39	4	f	f	NOUN
ejpam-6264	39	5	:	:	PUNCT
ejpam-6264	39	6	v	v	X
ejpam-6264	39	7	(	(	PUNCT
ejpam-6264	39	8	g	g	NOUN
ejpam-6264	39	9	)	)	PUNCT
ejpam-6264	39	10	→	→	SYM
ejpam-6264	39	11	{	{	PUNCT
ejpam-6264	39	12	0	0	NUM
ejpam-6264	39	13	,	,	PUNCT
ejpam-6264	39	14	1	1	NUM
ejpam-6264	39	15	,	,	PUNCT
ejpam-6264	39	16	2	2	NUM
ejpam-6264	39	17	,	,	PUNCT
ejpam-6264	39	18	3	3	NUM
ejpam-6264	39	19	}	}	PUNCT
ejpam-6264	39	20	on	on	ADP
ejpam-6264	39	21	a	a	DET
ejpam-6264	39	22	graph	graph	NOUN
ejpam-6264	39	23	g	g	NOUN
ejpam-6264	39	24	,	,	PUNCT
ejpam-6264	39	25	let	let	VERB
ejpam-6264	39	26	(	(	PUNCT
ejpam-6264	39	27	v0	v0	NOUN
ejpam-6264	39	28	,	,	PUNCT
ejpam-6264	39	29	v1	v1	NOUN
ejpam-6264	39	30	,	,	PUNCT
ejpam-6264	39	31	v2	v2	PROPN
ejpam-6264	39	32	,	,	PUNCT
ejpam-6264	39	33	v3	v3	PROPN
ejpam-6264	39	34	)	)	PUNCT
ejpam-6264	39	35	be	be	VERB
ejpam-6264	39	36	the	the	DET
ejpam-6264	39	37	ordered	order	VERB
ejpam-6264	39	38	partition	partition	NOUN
ejpam-6264	39	39	induced	induce	VERB
ejpam-6264	39	40	by	by	ADP
ejpam-6264	39	41	f	f	PROPN
ejpam-6264	39	42	,	,	PUNCT
ejpam-6264	39	43	where	where	SCONJ
ejpam-6264	39	44	vi	vi	VERB
ejpam-6264	39	45	=	=	PRON
ejpam-6264	39	46	{	{	PUNCT
ejpam-6264	39	47	v	v	NUM
ejpam-6264	39	48	∈	∈	NOUN
ejpam-6264	39	49	v	v	NOUN
ejpam-6264	39	50	(	(	PUNCT
ejpam-6264	39	51	g	g	NOUN
ejpam-6264	39	52	)	)	PUNCT
ejpam-6264	39	53	:	:	PUNCT
ejpam-6264	39	54	f(v	f(v	NOUN
ejpam-6264	39	55	)	)	PUNCT
ejpam-6264	40	1	=	=	PUNCT
ejpam-6264	40	2	i	i	PROPN
ejpam-6264	40	3	}	}	PUNCT
ejpam-6264	40	4	for	for	ADP
ejpam-6264	40	5	i	i	PROPN
ejpam-6264	40	6	∈	∈	PROPN
ejpam-6264	40	7	{	{	PUNCT
ejpam-6264	40	8	0	0	NUM
ejpam-6264	40	9	,	,	PUNCT
ejpam-6264	40	10	1	1	NUM
ejpam-6264	40	11	,	,	PUNCT
ejpam-6264	40	12	2	2	NUM
ejpam-6264	40	13	,	,	PUNCT
ejpam-6264	40	14	3	3	NUM
ejpam-6264	40	15	}	}	PUNCT
ejpam-6264	40	16	.	.	PUNCT
ejpam-6264	41	1	then	then	ADV
ejpam-6264	41	2	we	we	PRON
ejpam-6264	41	3	can	can	AUX
ejpam-6264	41	4	write	write	VERB
ejpam-6264	41	5	f	f	PROPN
ejpam-6264	41	6	=	=	SYM
ejpam-6264	41	7	(	(	PUNCT
ejpam-6264	41	8	v0	v0	PROPN
ejpam-6264	41	9	,	,	PUNCT
ejpam-6264	41	10	v1	v1	NOUN
ejpam-6264	41	11	,	,	PUNCT
ejpam-6264	41	12	v2	v2	PROPN
ejpam-6264	41	13	,	,	PUNCT
ejpam-6264	41	14	v3	v3	PROPN
ejpam-6264	41	15	)	)	PUNCT
ejpam-6264	41	16	.	.	PUNCT
ejpam-6264	42	1	the	the	DET
ejpam-6264	42	2	weight	weight	NOUN
ejpam-6264	42	3	of	of	ADP
ejpam-6264	42	4	f	f	PROPN
ejpam-6264	42	5	is	be	AUX
ejpam-6264	42	6	defined	define	VERB
ejpam-6264	42	7	by	by	ADP
ejpam-6264	42	8	ωg(f	ωg(f	NOUN
ejpam-6264	42	9	)	)	PUNCT
ejpam-6264	42	10	=	=	PUNCT
ejpam-6264	42	11	|v1|+	|v1|+	ADP
ejpam-6264	42	12	2|v2|+	2|v2|+	NUM
ejpam-6264	42	13	3|v3|	3|v3|	NUM
ejpam-6264	42	14	.	.	PUNCT
ejpam-6264	43	1	3	3	X
ejpam-6264	43	2	.	.	X
ejpam-6264	43	3	known	know	VERB
ejpam-6264	43	4	results	result	NOUN
ejpam-6264	43	5	we	we	PRON
ejpam-6264	43	6	make	make	VERB
ejpam-6264	43	7	use	use	NOUN
ejpam-6264	43	8	of	of	ADP
ejpam-6264	43	9	the	the	DET
ejpam-6264	43	10	following	follow	VERB
ejpam-6264	43	11	known	know	VERB
ejpam-6264	43	12	results	result	NOUN
ejpam-6264	43	13	from	from	ADP
ejpam-6264	43	14	[	[	X
ejpam-6264	43	15	7	7	NUM
ejpam-6264	43	16	]	]	PUNCT
ejpam-6264	43	17	.	.	PUNCT
ejpam-6264	44	1	proposition	proposition	NOUN
ejpam-6264	44	2	1	1	NUM
ejpam-6264	44	3	.	.	PUNCT
ejpam-6264	45	1	let	let	VERB
ejpam-6264	45	2	g	g	NOUN
ejpam-6264	45	3	be	be	AUX
ejpam-6264	45	4	any	any	DET
ejpam-6264	45	5	graph	graph	NOUN
ejpam-6264	45	6	with	with	ADP
ejpam-6264	45	7	no	no	DET
ejpam-6264	45	8	isolated	isolated	ADJ
ejpam-6264	45	9	vertex	vertex	NOUN
ejpam-6264	45	10	.	.	PUNCT
ejpam-6264	46	1	if	if	SCONJ
ejpam-6264	46	2	f	f	PROPN
ejpam-6264	46	3	=	=	SYM
ejpam-6264	46	4	(	(	PUNCT
ejpam-6264	46	5	v0	v0	PROPN
ejpam-6264	46	6	,	,	PUNCT
ejpam-6264	46	7	v1	v1	NOUN
ejpam-6264	46	8	,	,	PUNCT
ejpam-6264	46	9	v2	v2	PROPN
ejpam-6264	46	10	,	,	PUNCT
ejpam-6264	46	11	v3	v3	PROPN
ejpam-6264	46	12	)	)	PUNCT
ejpam-6264	46	13	a	a	DET
ejpam-6264	46	14	γmr	γmr	ADJ
ejpam-6264	46	15	-	-	PUNCT
ejpam-6264	46	16	function	function	NOUN
ejpam-6264	46	17	of	of	ADP
ejpam-6264	46	18	g	g	NOUN
ejpam-6264	46	19	,	,	PUNCT
ejpam-6264	46	20	then	then	ADV
ejpam-6264	46	21	the	the	DET
ejpam-6264	46	22	following	follow	VERB
ejpam-6264	46	23	holds	hold	VERB
ejpam-6264	46	24	:	:	PUNCT
ejpam-6264	46	25	(	(	PUNCT
ejpam-6264	46	26	i	i	NOUN
ejpam-6264	46	27	)	)	PUNCT
ejpam-6264	46	28	v0	v0	NOUN
ejpam-6264	46	29	=	=	SYM
ejpam-6264	46	30	∅	∅	NOUN
ejpam-6264	46	31	if	if	SCONJ
ejpam-6264	46	32	and	and	CCONJ
ejpam-6264	46	33	only	only	ADV
ejpam-6264	46	34	if	if	SCONJ
ejpam-6264	46	35	v3	v3	PROPN
ejpam-6264	46	36	=	=	SYM
ejpam-6264	46	37	∅	∅	NOUN
ejpam-6264	46	38	and	and	CCONJ
ejpam-6264	46	39	v2	v2	PROPN
ejpam-6264	46	40	is	be	AUX
ejpam-6264	46	41	a	a	DET
ejpam-6264	46	42	γ	γ	NOUN
ejpam-6264	46	43	-	-	PUNCT
ejpam-6264	46	44	set	set	NOUN
ejpam-6264	46	45	of	of	ADP
ejpam-6264	46	46	g.	g.	PROPN
ejpam-6264	46	47	moreover	moreover	ADV
ejpam-6264	46	48	,	,	PUNCT
ejpam-6264	46	49	γmr(g	γmr(g	PROPN
ejpam-6264	46	50	)	)	PUNCT
ejpam-6264	47	1	=	=	SYM
ejpam-6264	47	2	|v	|v	PROPN
ejpam-6264	47	3	(	(	PUNCT
ejpam-6264	47	4	g)|+	g)|+	PROPN
ejpam-6264	47	5	γ(g	γ(g	PROPN
ejpam-6264	47	6	)	)	PUNCT
ejpam-6264	47	7	.	.	PUNCT
ejpam-6264	48	1	(	(	PUNCT
ejpam-6264	48	2	ii	ii	NOUN
ejpam-6264	48	3	)	)	PUNCT
ejpam-6264	48	4	v1	v1	NOUN
ejpam-6264	48	5	=	=	SYM
ejpam-6264	48	6	∅	∅	NOUN
ejpam-6264	48	7	if	if	SCONJ
ejpam-6264	48	8	and	and	CCONJ
ejpam-6264	48	9	only	only	ADV
ejpam-6264	48	10	if	if	SCONJ
ejpam-6264	48	11	v2	v2	PROPN
ejpam-6264	48	12	∪	∪	X
ejpam-6264	48	13	v3	v3	PROPN
ejpam-6264	48	14	is	be	AUX
ejpam-6264	48	15	a	a	DET
ejpam-6264	48	16	2	2	NUM
ejpam-6264	48	17	-	-	PUNCT
ejpam-6264	48	18	dominating	dominating	NOUN
ejpam-6264	48	19	set	set	NOUN
ejpam-6264	48	20	of	of	ADP
ejpam-6264	48	21	g.	g.	PROPN
ejpam-6264	48	22	moreover	moreover	ADV
ejpam-6264	48	23	,	,	PUNCT
ejpam-6264	48	24	if	if	SCONJ
ejpam-6264	48	25	v1	v1	NOUN
ejpam-6264	48	26	=	=	SYM
ejpam-6264	48	27	∅	∅	NOUN
ejpam-6264	48	28	,	,	PUNCT
ejpam-6264	48	29	⟨v2	⟨v2	ADJ
ejpam-6264	48	30	∪	∪	ADJ
ejpam-6264	48	31	v3⟩	v3⟩	PRON
ejpam-6264	48	32	is	be	AUX
ejpam-6264	48	33	connected	connect	VERB
ejpam-6264	48	34	and	and	CCONJ
ejpam-6264	48	35	v3	v3	PROPN
ejpam-6264	48	36	is	be	AUX
ejpam-6264	48	37	a	a	DET
ejpam-6264	48	38	γ	γ	NOUN
ejpam-6264	48	39	-	-	PUNCT
ejpam-6264	48	40	set	set	NOUN
ejpam-6264	48	41	of	of	ADP
ejpam-6264	48	42	g	g	NOUN
ejpam-6264	48	43	,	,	PUNCT
ejpam-6264	48	44	then	then	ADV
ejpam-6264	48	45	γmr(g	γmr(g	NUM
ejpam-6264	48	46	)	)	PUNCT
ejpam-6264	48	47	≥	≥	PROPN
ejpam-6264	48	48	γ(g	γ(g	PROPN
ejpam-6264	48	49	)	)	PUNCT
ejpam-6264	49	1	+	+	CCONJ
ejpam-6264	49	2	2γ2(g	2γ2(g	NUM
ejpam-6264	49	3	)	)	PUNCT
ejpam-6264	49	4	.	.	PUNCT
ejpam-6264	50	1	proposition	proposition	NOUN
ejpam-6264	50	2	2	2	NUM
ejpam-6264	50	3	.	.	PUNCT
ejpam-6264	51	1	let	let	VERB
ejpam-6264	51	2	g	g	NOUN
ejpam-6264	51	3	and	and	CCONJ
ejpam-6264	51	4	h	h	NOUN
ejpam-6264	51	5	be	be	VERB
ejpam-6264	51	6	any	any	DET
ejpam-6264	51	7	graphs	graph	NOUN
ejpam-6264	51	8	and	and	CCONJ
ejpam-6264	51	9	let	let	VERB
ejpam-6264	51	10	f	f	PROPN
ejpam-6264	51	11	∈	∈	PROPN
ejpam-6264	51	12	(	(	PUNCT
ejpam-6264	51	13	v0	v0	NOUN
ejpam-6264	51	14	,	,	PUNCT
ejpam-6264	51	15	v1	v1	NOUN
ejpam-6264	51	16	,	,	PUNCT
ejpam-6264	51	17	v2	v2	PROPN
ejpam-6264	51	18	,	,	PUNCT
ejpam-6264	51	19	v3	v3	PROPN
ejpam-6264	51	20	)	)	PUNCT
ejpam-6264	51	21	be	be	VERB
ejpam-6264	51	22	a	a	DET
ejpam-6264	51	23	function	function	NOUN
ejpam-6264	51	24	on	on	ADP
ejpam-6264	51	25	v	v	NOUN
ejpam-6264	51	26	(	(	PUNCT
ejpam-6264	51	27	g+h	g+h	PROPN
ejpam-6264	51	28	)	)	PUNCT
ejpam-6264	51	29	with	with	ADP
ejpam-6264	51	30	v2	v2	PROPN
ejpam-6264	51	31	̸=	̸=	PROPN
ejpam-6264	51	32	∅	∅	NOUN
ejpam-6264	51	33	and	and	CCONJ
ejpam-6264	51	34	v3	v3	PROPN
ejpam-6264	51	35	̸=	̸=	PROPN
ejpam-6264	51	36	∅.	∅.	ADV
ejpam-6264	51	37	then	then	ADV
ejpam-6264	51	38	f	f	PROPN
ejpam-6264	51	39	∈	∈	PROPN
ejpam-6264	51	40	mrdf	mrdf	NOUN
ejpam-6264	51	41	(	(	PUNCT
ejpam-6264	51	42	g+h	g+h	NOUN
ejpam-6264	51	43	)	)	PUNCT
ejpam-6264	52	1	if	if	SCONJ
ejpam-6264	52	2	and	and	CCONJ
ejpam-6264	52	3	only	only	ADV
ejpam-6264	52	4	if	if	SCONJ
ejpam-6264	52	5	one	one	NUM
ejpam-6264	52	6	of	of	ADP
ejpam-6264	52	7	the	the	DET
ejpam-6264	52	8	following	follow	VERB
ejpam-6264	52	9	holds	hold	VERB
ejpam-6264	52	10	:	:	PUNCT
ejpam-6264	52	11	(	(	PUNCT
ejpam-6264	52	12	i	i	NOUN
ejpam-6264	52	13	)	)	PUNCT
ejpam-6264	52	14	f	f	PROPN
ejpam-6264	52	15	|g	|g	PROPN
ejpam-6264	52	16	∈	∈	PROPN
ejpam-6264	52	17	mrdf	mrdf	NOUN
ejpam-6264	52	18	(	(	PUNCT
ejpam-6264	52	19	g	g	NOUN
ejpam-6264	52	20	)	)	PUNCT
ejpam-6264	52	21	and	and	CCONJ
ejpam-6264	52	22	one	one	NUM
ejpam-6264	52	23	of	of	ADP
ejpam-6264	52	24	the	the	DET
ejpam-6264	52	25	following	following	NOUN
ejpam-6264	52	26	holds	hold	VERB
ejpam-6264	52	27	:	:	PUNCT
ejpam-6264	52	28	(	(	PUNCT
ejpam-6264	52	29	a	a	X
ejpam-6264	52	30	)	)	PUNCT
ejpam-6264	52	31	|v2	|v2	NOUN
ejpam-6264	52	32	∩	∩	ADJ
ejpam-6264	52	33	v	v	X
ejpam-6264	52	34	(	(	PUNCT
ejpam-6264	52	35	g)|	g)|	VERB
ejpam-6264	52	36	≥	≥	NOUN
ejpam-6264	52	37	1	1	NUM
ejpam-6264	52	38	and	and	CCONJ
ejpam-6264	52	39	|v3	|v3	NOUN
ejpam-6264	52	40	∩	∩	ADJ
ejpam-6264	52	41	v	v	X
ejpam-6264	52	42	(	(	PUNCT
ejpam-6264	52	43	g)|	g)|	X
ejpam-6264	52	44	≥	≥	NOUN
ejpam-6264	52	45	1	1	NUM
ejpam-6264	52	46	(	(	PUNCT
ejpam-6264	52	47	b	b	NOUN
ejpam-6264	52	48	)	)	PUNCT
ejpam-6264	52	49	v2	v2	NOUN
ejpam-6264	52	50	∩	∩	ADJ
ejpam-6264	52	51	v	v	NOUN
ejpam-6264	52	52	(	(	PUNCT
ejpam-6264	52	53	g	g	NOUN
ejpam-6264	52	54	)	)	PUNCT
ejpam-6264	52	55	=	=	NOUN
ejpam-6264	52	56	∅	∅	NOUN
ejpam-6264	52	57	and	and	CCONJ
ejpam-6264	52	58	each	each	PRON
ejpam-6264	52	59	of	of	ADP
ejpam-6264	52	60	the	the	DET
ejpam-6264	52	61	following	follow	VERB
ejpam-6264	52	62	holds	hold	VERB
ejpam-6264	52	63	:	:	PUNCT
ejpam-6264	52	64	(	(	PUNCT
ejpam-6264	52	65	b1	b1	NOUN
ejpam-6264	52	66	)	)	PUNCT
ejpam-6264	52	67	v3	v3	PROPN
ejpam-6264	52	68	is	be	AUX
ejpam-6264	52	69	a	a	DET
ejpam-6264	52	70	dominating	dominating	NOUN
ejpam-6264	52	71	set	set	NOUN
ejpam-6264	52	72	of	of	ADP
ejpam-6264	52	73	g.	g.	PROPN
ejpam-6264	52	74	(	(	PUNCT
ejpam-6264	52	75	b2	b2	NOUN
ejpam-6264	52	76	)	)	PUNCT
ejpam-6264	52	77	v2	v2	NOUN
ejpam-6264	52	78	∩	∩	ADJ
ejpam-6264	52	79	v	v	NOUN
ejpam-6264	52	80	(	(	PUNCT
ejpam-6264	52	81	h	h	NOUN
ejpam-6264	52	82	)	)	PUNCT
ejpam-6264	52	83	is	be	AUX
ejpam-6264	52	84	a	a	DET
ejpam-6264	52	85	dominating	dominating	NOUN
ejpam-6264	52	86	set	set	NOUN
ejpam-6264	52	87	of	of	ADP
ejpam-6264	52	88	v0	v0	NOUN
ejpam-6264	52	89	∩	∩	X
ejpam-6264	52	90	v	v	X
ejpam-6264	52	91	(	(	PUNCT
ejpam-6264	52	92	h	h	NOUN
ejpam-6264	52	93	)	)	PUNCT
ejpam-6264	52	94	.	.	PUNCT
ejpam-6264	53	1	(	(	PUNCT
ejpam-6264	53	2	c	c	X
ejpam-6264	53	3	)	)	PUNCT
ejpam-6264	53	4	v3	v3	PROPN
ejpam-6264	53	5	∩	∩	ADJ
ejpam-6264	53	6	v	v	X
ejpam-6264	53	7	(	(	PUNCT
ejpam-6264	53	8	g	g	NOUN
ejpam-6264	53	9	)	)	PUNCT
ejpam-6264	53	10	=	=	NOUN
ejpam-6264	53	11	∅	∅	NOUN
ejpam-6264	53	12	and	and	CCONJ
ejpam-6264	53	13	each	each	PRON
ejpam-6264	53	14	of	of	ADP
ejpam-6264	53	15	the	the	DET
ejpam-6264	53	16	following	follow	VERB
ejpam-6264	53	17	holds	hold	VERB
ejpam-6264	53	18	:	:	PUNCT
ejpam-6264	53	19	(	(	PUNCT
ejpam-6264	53	20	c1	c1	NOUN
ejpam-6264	53	21	)	)	PUNCT
ejpam-6264	53	22	v2	v2	PROPN
ejpam-6264	53	23	is	be	AUX
ejpam-6264	53	24	a	a	DET
ejpam-6264	53	25	dominating	dominating	NOUN
ejpam-6264	53	26	set	set	NOUN
ejpam-6264	53	27	of	of	ADP
ejpam-6264	53	28	g.	g.	PROPN
ejpam-6264	53	29	(	(	PUNCT
ejpam-6264	53	30	c2	c2	PROPN
ejpam-6264	53	31	)	)	PUNCT
ejpam-6264	53	32	v3	v3	PROPN
ejpam-6264	53	33	∩	∩	ADJ
ejpam-6264	53	34	v	v	X
ejpam-6264	53	35	(	(	PUNCT
ejpam-6264	53	36	h	h	NOUN
ejpam-6264	53	37	)	)	PUNCT
ejpam-6264	53	38	is	be	AUX
ejpam-6264	53	39	a	a	DET
ejpam-6264	53	40	dominating	dominating	NOUN
ejpam-6264	53	41	set	set	NOUN
ejpam-6264	53	42	of	of	ADP
ejpam-6264	53	43	v0	v0	NOUN
ejpam-6264	53	44	∩	∩	X
ejpam-6264	53	45	v	v	X
ejpam-6264	53	46	(	(	PUNCT
ejpam-6264	53	47	h	h	NOUN
ejpam-6264	53	48	)	)	PUNCT
ejpam-6264	53	49	.	.	PUNCT
ejpam-6264	54	1	(	(	PUNCT
ejpam-6264	54	2	ii	ii	X
ejpam-6264	54	3	)	)	PUNCT
ejpam-6264	54	4	f	f	PROPN
ejpam-6264	54	5	|h	|h	X
ejpam-6264	54	6	∈	∈	PROPN
ejpam-6264	54	7	mrdf	mrdf	NOUN
ejpam-6264	54	8	(	(	PUNCT
ejpam-6264	54	9	h	h	NOUN
ejpam-6264	54	10	)	)	PUNCT
ejpam-6264	54	11	and	and	CCONJ
ejpam-6264	54	12	one	one	NUM
ejpam-6264	54	13	of	of	ADP
ejpam-6264	54	14	the	the	DET
ejpam-6264	54	15	following	following	NOUN
ejpam-6264	54	16	holds	hold	VERB
ejpam-6264	54	17	:	:	PUNCT
ejpam-6264	54	18	(	(	PUNCT
ejpam-6264	54	19	a	a	X
ejpam-6264	54	20	)	)	PUNCT
ejpam-6264	54	21	|v2	|v2	NOUN
ejpam-6264	54	22	∩	∩	ADJ
ejpam-6264	54	23	v	v	X
ejpam-6264	54	24	(	(	PUNCT
ejpam-6264	54	25	h)|	h)|	PROPN
ejpam-6264	54	26	≥	≥	NUM
ejpam-6264	54	27	1	1	NUM
ejpam-6264	54	28	and	and	CCONJ
ejpam-6264	54	29	|v3	|v3	NOUN
ejpam-6264	54	30	∩	∩	ADJ
ejpam-6264	54	31	v	v	X
ejpam-6264	54	32	(	(	PUNCT
ejpam-6264	54	33	h)|	h)|	PROPN
ejpam-6264	54	34	≥	≥	NUM
ejpam-6264	54	35	1	1	NUM
ejpam-6264	54	36	(	(	PUNCT
ejpam-6264	54	37	b	b	NOUN
ejpam-6264	54	38	)	)	PUNCT
ejpam-6264	54	39	v2	v2	NOUN
ejpam-6264	54	40	∩	∩	ADJ
ejpam-6264	54	41	v	v	NOUN
ejpam-6264	54	42	(	(	PUNCT
ejpam-6264	54	43	h	h	NOUN
ejpam-6264	54	44	)	)	PUNCT
ejpam-6264	54	45	=	=	NOUN
ejpam-6264	54	46	∅	∅	NOUN
ejpam-6264	54	47	and	and	CCONJ
ejpam-6264	54	48	each	each	PRON
ejpam-6264	54	49	of	of	ADP
ejpam-6264	54	50	the	the	DET
ejpam-6264	54	51	following	follow	VERB
ejpam-6264	54	52	holds	hold	VERB
ejpam-6264	54	53	:	:	PUNCT
ejpam-6264	54	54	(	(	PUNCT
ejpam-6264	54	55	b1	b1	NOUN
ejpam-6264	54	56	)	)	PUNCT
ejpam-6264	54	57	v3	v3	PROPN
ejpam-6264	54	58	is	be	AUX
ejpam-6264	54	59	a	a	DET
ejpam-6264	54	60	dominating	dominating	NOUN
ejpam-6264	54	61	set	set	NOUN
ejpam-6264	54	62	of	of	ADP
ejpam-6264	54	63	h.	h.	PROPN
ejpam-6264	54	64	s.	s.	PROPN
ejpam-6264	54	65	ahamad	ahamad	VERB
ejpam-6264	54	66	et	et	PROPN
ejpam-6264	54	67	al	al	PROPN
ejpam-6264	54	68	.	.	PUNCT
ejpam-6264	54	69	/	/	SYM
ejpam-6264	54	70	eur	eur	PROPN
ejpam-6264	54	71	.	.	PUNCT
ejpam-6264	55	1	j.	j.	PROPN
ejpam-6264	55	2	pure	pure	PROPN
ejpam-6264	55	3	appl	appl	PROPN
ejpam-6264	55	4	.	.	PROPN
ejpam-6264	55	5	math	math	PROPN
ejpam-6264	55	6	,	,	PUNCT
ejpam-6264	55	7	18	18	NUM
ejpam-6264	55	8	(	(	PUNCT
ejpam-6264	55	9	4	4	NUM
ejpam-6264	55	10	)	)	PUNCT
ejpam-6264	55	11	(	(	PUNCT
ejpam-6264	55	12	2025	2025	NUM
ejpam-6264	55	13	)	)	PUNCT
ejpam-6264	55	14	,	,	PUNCT
ejpam-6264	55	15	6264	6264	NUM
ejpam-6264	55	16	4	4	NUM
ejpam-6264	55	17	of	of	ADP
ejpam-6264	55	18	20	20	NUM
ejpam-6264	55	19	(	(	PUNCT
ejpam-6264	55	20	b2	b2	NOUN
ejpam-6264	55	21	)	)	PUNCT
ejpam-6264	55	22	v2	v2	NOUN
ejpam-6264	55	23	∩	∩	ADJ
ejpam-6264	55	24	v	v	NOUN
ejpam-6264	55	25	(	(	PUNCT
ejpam-6264	55	26	g	g	NOUN
ejpam-6264	55	27	)	)	PUNCT
ejpam-6264	55	28	is	be	AUX
ejpam-6264	55	29	a	a	DET
ejpam-6264	55	30	dominating	dominating	NOUN
ejpam-6264	55	31	set	set	NOUN
ejpam-6264	55	32	of	of	ADP
ejpam-6264	55	33	v0	v0	NOUN
ejpam-6264	55	34	∩	∩	X
ejpam-6264	55	35	v	v	X
ejpam-6264	55	36	(	(	PUNCT
ejpam-6264	55	37	g	g	NOUN
ejpam-6264	55	38	)	)	PUNCT
ejpam-6264	55	39	.	.	PUNCT
ejpam-6264	56	1	(	(	PUNCT
ejpam-6264	56	2	c	c	X
ejpam-6264	56	3	)	)	PUNCT
ejpam-6264	56	4	v3	v3	PROPN
ejpam-6264	56	5	∩	∩	ADJ
ejpam-6264	56	6	v	v	X
ejpam-6264	56	7	(	(	PUNCT
ejpam-6264	56	8	h	h	NOUN
ejpam-6264	56	9	)	)	PUNCT
ejpam-6264	56	10	=	=	NOUN
ejpam-6264	56	11	∅	∅	NOUN
ejpam-6264	56	12	and	and	CCONJ
ejpam-6264	56	13	each	each	PRON
ejpam-6264	56	14	of	of	ADP
ejpam-6264	56	15	the	the	DET
ejpam-6264	56	16	following	follow	VERB
ejpam-6264	56	17	holds	hold	VERB
ejpam-6264	56	18	:	:	PUNCT
ejpam-6264	56	19	(	(	PUNCT
ejpam-6264	56	20	c1	c1	NOUN
ejpam-6264	56	21	)	)	PUNCT
ejpam-6264	56	22	v2	v2	PROPN
ejpam-6264	56	23	is	be	AUX
ejpam-6264	56	24	a	a	DET
ejpam-6264	56	25	dominating	dominating	NOUN
ejpam-6264	56	26	set	set	NOUN
ejpam-6264	56	27	of	of	ADP
ejpam-6264	56	28	h.	h.	PROPN
ejpam-6264	56	29	(	(	PUNCT
ejpam-6264	56	30	c2	c2	PROPN
ejpam-6264	56	31	)	)	PUNCT
ejpam-6264	56	32	v3	v3	PROPN
ejpam-6264	56	33	∩	∩	ADJ
ejpam-6264	56	34	v	v	X
ejpam-6264	56	35	(	(	PUNCT
ejpam-6264	56	36	g	g	NOUN
ejpam-6264	56	37	)	)	PUNCT
ejpam-6264	56	38	is	be	AUX
ejpam-6264	56	39	a	a	DET
ejpam-6264	56	40	dominating	dominating	NOUN
ejpam-6264	56	41	set	set	NOUN
ejpam-6264	56	42	of	of	ADP
ejpam-6264	56	43	v0	v0	NOUN
ejpam-6264	56	44	∩	∩	X
ejpam-6264	56	45	v	v	X
ejpam-6264	56	46	(	(	PUNCT
ejpam-6264	56	47	g	g	NOUN
ejpam-6264	56	48	)	)	PUNCT
ejpam-6264	56	49	.	.	PUNCT
ejpam-6264	57	1	(	(	PUNCT
ejpam-6264	57	2	iii	iii	X
ejpam-6264	57	3	)	)	PUNCT
ejpam-6264	57	4	f	f	PROPN
ejpam-6264	57	5	|g	|g	VERB
ejpam-6264	57	6	̸∈	̸∈	PROPN
ejpam-6264	57	7	mrdf	mrdf	PROPN
ejpam-6264	57	8	(	(	PUNCT
ejpam-6264	57	9	g	g	NOUN
ejpam-6264	57	10	)	)	PUNCT
ejpam-6264	57	11	,	,	PUNCT
ejpam-6264	57	12	f	f	PROPN
ejpam-6264	57	13	|h	|h	X
ejpam-6264	57	14	̸∈	̸∈	PROPN
ejpam-6264	57	15	mrdf	mrdf	PROPN
ejpam-6264	57	16	(	(	PUNCT
ejpam-6264	57	17	h	h	NOUN
ejpam-6264	57	18	)	)	PUNCT
ejpam-6264	57	19	and	and	CCONJ
ejpam-6264	57	20	each	each	PRON
ejpam-6264	57	21	of	of	ADP
ejpam-6264	57	22	the	the	DET
ejpam-6264	57	23	following	following	NOUN
ejpam-6264	57	24	holds	hold	VERB
ejpam-6264	57	25	:	:	PUNCT
ejpam-6264	57	26	(	(	PUNCT
ejpam-6264	57	27	a	a	X
ejpam-6264	57	28	)	)	PUNCT
ejpam-6264	57	29	v2	v2	PROPN
ejpam-6264	57	30	∩	∩	ADJ
ejpam-6264	57	31	v	v	NOUN
ejpam-6264	57	32	(	(	PUNCT
ejpam-6264	57	33	h	h	NOUN
ejpam-6264	57	34	)	)	PUNCT
ejpam-6264	57	35	̸=	̸=	PROPN
ejpam-6264	57	36	∅	∅	NOUN
ejpam-6264	57	37	whenever	whenever	SCONJ
ejpam-6264	57	38	ng(x	ng(x	NUM
ejpam-6264	57	39	)	)	PUNCT
ejpam-6264	57	40	∩	∩	NOUN
ejpam-6264	57	41	v2	v2	NOUN
ejpam-6264	57	42	=	=	PUNCT
ejpam-6264	57	43	∅	∅	NOUN
ejpam-6264	57	44	for	for	ADP
ejpam-6264	57	45	some	some	DET
ejpam-6264	57	46	x	x	SYM
ejpam-6264	57	47	∈	∈	PROPN
ejpam-6264	57	48	v0	v0	NOUN
ejpam-6264	57	49	∩	∩	X
ejpam-6264	57	50	v	v	X
ejpam-6264	57	51	(	(	PUNCT
ejpam-6264	57	52	g	g	NOUN
ejpam-6264	57	53	)	)	PUNCT
ejpam-6264	57	54	.	.	PUNCT
ejpam-6264	58	1	(	(	PUNCT
ejpam-6264	58	2	b	b	X
ejpam-6264	58	3	)	)	PUNCT
ejpam-6264	58	4	v3	v3	PROPN
ejpam-6264	58	5	∩	∩	ADJ
ejpam-6264	58	6	v	v	X
ejpam-6264	58	7	(	(	PUNCT
ejpam-6264	58	8	h	h	NOUN
ejpam-6264	58	9	)	)	PUNCT
ejpam-6264	58	10	̸=	̸=	PROPN
ejpam-6264	58	11	∅	∅	NOUN
ejpam-6264	58	12	whenever	whenever	SCONJ
ejpam-6264	58	13	ng(x	ng(x	NUM
ejpam-6264	58	14	)	)	PUNCT
ejpam-6264	58	15	∩	∩	PROPN
ejpam-6264	58	16	v3	v3	NOUN
ejpam-6264	58	17	=	=	PUNCT
ejpam-6264	58	18	∅	∅	NOUN
ejpam-6264	58	19	for	for	ADP
ejpam-6264	58	20	some	some	DET
ejpam-6264	58	21	x	x	SYM
ejpam-6264	58	22	∈	∈	PROPN
ejpam-6264	58	23	v0	v0	NOUN
ejpam-6264	58	24	∩	∩	X
ejpam-6264	58	25	v	v	X
ejpam-6264	58	26	(	(	PUNCT
ejpam-6264	58	27	g	g	NOUN
ejpam-6264	58	28	)	)	PUNCT
ejpam-6264	58	29	.	.	PUNCT
ejpam-6264	59	1	(	(	PUNCT
ejpam-6264	59	2	c	c	X
ejpam-6264	59	3	)	)	PUNCT
ejpam-6264	59	4	v2	v2	NOUN
ejpam-6264	59	5	∩	∩	ADJ
ejpam-6264	59	6	v	v	NOUN
ejpam-6264	59	7	(	(	PUNCT
ejpam-6264	59	8	h	h	NOUN
ejpam-6264	59	9	)	)	PUNCT
ejpam-6264	59	10	̸=	̸=	PROPN
ejpam-6264	59	11	∅	∅	NOUN
ejpam-6264	59	12	or	or	CCONJ
ejpam-6264	59	13	v3	v3	PROPN
ejpam-6264	59	14	∩	∩	ADJ
ejpam-6264	59	15	v	v	X
ejpam-6264	59	16	(	(	PUNCT
ejpam-6264	59	17	h	h	NOUN
ejpam-6264	59	18	)	)	PUNCT
ejpam-6264	59	19	̸=	̸=	NOUN
ejpam-6264	59	20	∅	∅	NOUN
ejpam-6264	59	21	whenever	whenever	SCONJ
ejpam-6264	59	22	∃x	∃x	PROPN
ejpam-6264	59	23	∈	∈	PROPN
ejpam-6264	59	24	v1	v1	NOUN
ejpam-6264	59	25	with	with	ADP
ejpam-6264	59	26	ng(x)∩	ng(x)∩	PUNCT
ejpam-6264	59	27	v2	v2	NOUN
ejpam-6264	59	28	=	=	NOUN
ejpam-6264	59	29	∅	∅	NOUN
ejpam-6264	59	30	and	and	CCONJ
ejpam-6264	59	31	ng(x	ng(x	NUM
ejpam-6264	59	32	)	)	PUNCT
ejpam-6264	59	33	∩	∩	NOUN
ejpam-6264	59	34	v3	v3	PROPN
ejpam-6264	59	35	=	=	SYM
ejpam-6264	59	36	∅	∅	NOUN
ejpam-6264	59	37	(	(	PUNCT
ejpam-6264	59	38	d	d	X
ejpam-6264	59	39	)	)	PUNCT
ejpam-6264	59	40	v2	v2	NOUN
ejpam-6264	59	41	∩	∩	ADJ
ejpam-6264	59	42	v	v	NOUN
ejpam-6264	59	43	(	(	PUNCT
ejpam-6264	59	44	g	g	NOUN
ejpam-6264	59	45	)	)	PUNCT
ejpam-6264	59	46	̸=	̸=	PROPN
ejpam-6264	59	47	∅	∅	NOUN
ejpam-6264	59	48	whenever	whenever	SCONJ
ejpam-6264	59	49	nh(x	nh(x	NUM
ejpam-6264	59	50	)	)	PUNCT
ejpam-6264	59	51	∩	∩	ADJ
ejpam-6264	59	52	v2	v2	NOUN
ejpam-6264	59	53	=	=	PUNCT
ejpam-6264	59	54	∅	∅	NOUN
ejpam-6264	59	55	for	for	ADP
ejpam-6264	59	56	some	some	DET
ejpam-6264	59	57	x	x	SYM
ejpam-6264	59	58	∈	∈	PROPN
ejpam-6264	59	59	v0	v0	NOUN
ejpam-6264	59	60	∩	∩	X
ejpam-6264	59	61	v	v	X
ejpam-6264	59	62	(	(	PUNCT
ejpam-6264	59	63	h	h	NOUN
ejpam-6264	59	64	)	)	PUNCT
ejpam-6264	59	65	.	.	PUNCT
ejpam-6264	60	1	(	(	PUNCT
ejpam-6264	60	2	e	e	X
ejpam-6264	60	3	)	)	PUNCT
ejpam-6264	60	4	v3	v3	PROPN
ejpam-6264	60	5	∩	∩	ADJ
ejpam-6264	60	6	v	v	X
ejpam-6264	60	7	(	(	PUNCT
ejpam-6264	60	8	g	g	NOUN
ejpam-6264	60	9	)	)	PUNCT
ejpam-6264	60	10	̸=	̸=	PROPN
ejpam-6264	60	11	∅	∅	NOUN
ejpam-6264	60	12	whenever	whenever	SCONJ
ejpam-6264	60	13	nh(x	nh(x	NUM
ejpam-6264	60	14	)	)	PUNCT
ejpam-6264	60	15	∩	∩	ADJ
ejpam-6264	60	16	v3	v3	NOUN
ejpam-6264	60	17	=	=	PUNCT
ejpam-6264	60	18	∅	∅	NOUN
ejpam-6264	60	19	for	for	ADP
ejpam-6264	60	20	some	some	DET
ejpam-6264	60	21	x	x	SYM
ejpam-6264	60	22	∈	∈	PROPN
ejpam-6264	60	23	v0	v0	NOUN
ejpam-6264	60	24	∩	∩	X
ejpam-6264	60	25	v	v	X
ejpam-6264	60	26	(	(	PUNCT
ejpam-6264	60	27	h	h	NOUN
ejpam-6264	60	28	)	)	PUNCT
ejpam-6264	60	29	.	.	PUNCT
ejpam-6264	61	1	(	(	PUNCT
ejpam-6264	61	2	f	f	X
ejpam-6264	61	3	)	)	PUNCT
ejpam-6264	61	4	v2	v2	PROPN
ejpam-6264	61	5	∩	∩	ADJ
ejpam-6264	61	6	v	v	NOUN
ejpam-6264	61	7	(	(	PUNCT
ejpam-6264	61	8	g	g	NOUN
ejpam-6264	61	9	)	)	PUNCT
ejpam-6264	61	10	̸=	̸=	PROPN
ejpam-6264	61	11	∅	∅	NOUN
ejpam-6264	61	12	or	or	CCONJ
ejpam-6264	61	13	v3	v3	PROPN
ejpam-6264	61	14	∩	∩	ADJ
ejpam-6264	61	15	v	v	X
ejpam-6264	61	16	(	(	PUNCT
ejpam-6264	61	17	g	g	NOUN
ejpam-6264	61	18	)	)	PUNCT
ejpam-6264	61	19	̸=	̸=	PROPN
ejpam-6264	61	20	∅	∅	NOUN
ejpam-6264	61	21	whenever	whenever	SCONJ
ejpam-6264	61	22	∃x	∃x	PROPN
ejpam-6264	61	23	∈	∈	PROPN
ejpam-6264	61	24	v1	v1	NOUN
ejpam-6264	61	25	with	with	ADP
ejpam-6264	61	26	nh(x)∩	nh(x)∩	NOUN
ejpam-6264	61	27	v2	v2	NOUN
ejpam-6264	61	28	=	=	NOUN
ejpam-6264	61	29	∅	∅	NOUN
ejpam-6264	61	30	and	and	CCONJ
ejpam-6264	61	31	nh(x	nh(x	NUM
ejpam-6264	61	32	)	)	PUNCT
ejpam-6264	61	33	∩	∩	ADJ
ejpam-6264	61	34	v3	v3	PROPN
ejpam-6264	61	35	=	=	PUNCT
ejpam-6264	61	36	∅	∅	NOUN
ejpam-6264	61	37	4	4	NUM
ejpam-6264	61	38	.	.	PUNCT
ejpam-6264	61	39	results	result	NOUN
ejpam-6264	61	40	definition	definition	NOUN
ejpam-6264	61	41	1	1	NUM
ejpam-6264	61	42	.	.	PUNCT
ejpam-6264	62	1	if	if	SCONJ
ejpam-6264	62	2	f	f	PROPN
ejpam-6264	62	3	=	=	SYM
ejpam-6264	62	4	(	(	PUNCT
ejpam-6264	62	5	v0	v0	PROPN
ejpam-6264	62	6	,	,	PUNCT
ejpam-6264	62	7	v1	v1	NOUN
ejpam-6264	62	8	,	,	PUNCT
ejpam-6264	62	9	v2	v2	PROPN
ejpam-6264	62	10	,	,	PUNCT
ejpam-6264	62	11	v3	v3	PROPN
ejpam-6264	62	12	)	)	PUNCT
ejpam-6264	62	13	is	be	AUX
ejpam-6264	62	14	a	a	DET
ejpam-6264	62	15	modern	modern	ADJ
ejpam-6264	62	16	roman	roman	ADJ
ejpam-6264	62	17	dominating	dominating	NOUN
ejpam-6264	62	18	function	function	NOUN
ejpam-6264	62	19	of	of	ADP
ejpam-6264	62	20	a	a	DET
ejpam-6264	62	21	non	non	ADJ
ejpam-6264	62	22	-	-	ADJ
ejpam-6264	62	23	isolated	isolated	ADJ
ejpam-6264	62	24	graph	graph	NOUN
ejpam-6264	62	25	g	g	NOUN
ejpam-6264	62	26	,	,	PUNCT
ejpam-6264	62	27	then	then	ADV
ejpam-6264	62	28	it	it	PRON
ejpam-6264	62	29	is	be	AUX
ejpam-6264	62	30	said	say	VERB
ejpam-6264	62	31	to	to	PART
ejpam-6264	62	32	be	be	AUX
ejpam-6264	62	33	a	a	DET
ejpam-6264	62	34	total	total	ADJ
ejpam-6264	62	35	modern	modern	ADJ
ejpam-6264	62	36	roman	roman	ADJ
ejpam-6264	62	37	dominating	dominating	NOUN
ejpam-6264	62	38	function	function	NOUN
ejpam-6264	62	39	(	(	PUNCT
ejpam-6264	62	40	tmrdf	tmrdf	NOUN
ejpam-6264	62	41	(	(	PUNCT
ejpam-6264	62	42	g	g	NOUN
ejpam-6264	62	43	)	)	PUNCT
ejpam-6264	62	44	)	)	PUNCT
ejpam-6264	62	45	of	of	ADP
ejpam-6264	62	46	g	g	NOUN
ejpam-6264	62	47	provided	provide	VERB
ejpam-6264	62	48	it	it	PRON
ejpam-6264	62	49	satisfies	satisfy	VERB
ejpam-6264	62	50	the	the	DET
ejpam-6264	62	51	following	follow	VERB
ejpam-6264	62	52	additional	additional	ADJ
ejpam-6264	62	53	property	property	NOUN
ejpam-6264	62	54	:	:	PUNCT
ejpam-6264	62	55	(	(	PUNCT
ejpam-6264	62	56	p3	p3	PROPN
ejpam-6264	62	57	)	)	PUNCT
ejpam-6264	62	58	the	the	DET
ejpam-6264	62	59	set	set	NOUN
ejpam-6264	62	60	{	{	PUNCT
ejpam-6264	62	61	v	v	NOUN
ejpam-6264	62	62	∈	∈	PROPN
ejpam-6264	62	63	v	v	NOUN
ejpam-6264	62	64	(	(	PUNCT
ejpam-6264	62	65	g	g	NOUN
ejpam-6264	62	66	)	)	PUNCT
ejpam-6264	62	67	:	:	PUNCT
ejpam-6264	62	68	f(v	f(v	NOUN
ejpam-6264	62	69	)	)	PUNCT
ejpam-6264	62	70	>	>	X
ejpam-6264	62	71	0	0	NUM
ejpam-6264	62	72	}	}	PUNCT
ejpam-6264	62	73	induces	induce	VERB
ejpam-6264	62	74	an	an	DET
ejpam-6264	62	75	isolated	isolate	VERB
ejpam-6264	62	76	-	-	PUNCT
ejpam-6264	62	77	free	free	ADJ
ejpam-6264	62	78	subgraph	subgraph	NOUN
ejpam-6264	62	79	.	.	PUNCT
ejpam-6264	63	1	the	the	DET
ejpam-6264	63	2	minimum	minimum	ADJ
ejpam-6264	63	3	weight	weight	NOUN
ejpam-6264	63	4	ωtmr	ωtmr	PROPN
ejpam-6264	63	5	g	g	PROPN
ejpam-6264	63	6	(	(	PUNCT
ejpam-6264	63	7	f	f	X
ejpam-6264	63	8	)	)	PUNCT
ejpam-6264	63	9	=	=	SYM
ejpam-6264	63	10	∑	∑	PUNCT
ejpam-6264	63	11	v∈v	v∈v	PROPN
ejpam-6264	63	12	(	(	PUNCT
ejpam-6264	63	13	g	g	NOUN
ejpam-6264	63	14	)	)	PUNCT
ejpam-6264	63	15	f(v	f(v	NOUN
ejpam-6264	63	16	)	)	PUNCT
ejpam-6264	63	17	of	of	ADP
ejpam-6264	63	18	a	a	DET
ejpam-6264	63	19	total	total	ADJ
ejpam-6264	63	20	modern	modern	ADJ
ejpam-6264	63	21	roman	roman	ADJ
ejpam-6264	63	22	dominating	dominating	NOUN
ejpam-6264	63	23	function	function	NOUN
ejpam-6264	63	24	f	f	PROPN
ejpam-6264	63	25	of	of	ADP
ejpam-6264	63	26	g	g	PROPN
ejpam-6264	63	27	is	be	AUX
ejpam-6264	63	28	called	call	VERB
ejpam-6264	63	29	the	the	DET
ejpam-6264	63	30	total	total	ADJ
ejpam-6264	63	31	modern	modern	ADJ
ejpam-6264	63	32	roman	roman	ADJ
ejpam-6264	63	33	domination	domination	NOUN
ejpam-6264	63	34	number	number	NOUN
ejpam-6264	63	35	γtmr(g	γtmr(g	PROPN
ejpam-6264	63	36	)	)	PUNCT
ejpam-6264	63	37	of	of	ADP
ejpam-6264	63	38	g.	g.	PROPN
ejpam-6264	63	39	a	a	DET
ejpam-6264	63	40	total	total	ADJ
ejpam-6264	63	41	modern	modern	ADJ
ejpam-6264	63	42	roman	roman	ADJ
ejpam-6264	63	43	dominating	dominating	NOUN
ejpam-6264	63	44	function	function	NOUN
ejpam-6264	63	45	of	of	ADP
ejpam-6264	63	46	g	g	NOUN
ejpam-6264	63	47	with	with	ADP
ejpam-6264	63	48	weight	weight	NOUN
ejpam-6264	63	49	ωg(f	ωg(f	PRON
ejpam-6264	63	50	)	)	PUNCT
ejpam-6264	63	51	=	=	SYM
ejpam-6264	63	52	γtmr(g	γtmr(g	NOUN
ejpam-6264	63	53	)	)	PUNCT
ejpam-6264	63	54	is	be	AUX
ejpam-6264	63	55	called	call	VERB
ejpam-6264	63	56	a	a	DET
ejpam-6264	63	57	γtmr	γtmr	NOUN
ejpam-6264	63	58	-	-	PUNCT
ejpam-6264	63	59	function	function	NOUN
ejpam-6264	63	60	of	of	ADP
ejpam-6264	63	61	g.	g.	PROPN
ejpam-6264	63	62	example	example	NOUN
ejpam-6264	63	63	1	1	X
ejpam-6264	63	64	.	.	X
ejpam-6264	63	65	consider	consider	VERB
ejpam-6264	63	66	the	the	DET
ejpam-6264	63	67	graph	graph	NOUN
ejpam-6264	63	68	g	g	NOUN
ejpam-6264	63	69	in	in	ADP
ejpam-6264	63	70	figure	figure	NOUN
ejpam-6264	63	71	1	1	NUM
ejpam-6264	63	72	.	.	PUNCT
ejpam-6264	64	1	the	the	DET
ejpam-6264	64	2	function	function	NOUN
ejpam-6264	64	3	f	f	X
ejpam-6264	64	4	:	:	PUNCT
ejpam-6264	64	5	v	v	X
ejpam-6264	64	6	(	(	PUNCT
ejpam-6264	64	7	g	g	NOUN
ejpam-6264	64	8	)	)	PUNCT
ejpam-6264	64	9	→	→	SYM
ejpam-6264	64	10	{	{	PUNCT
ejpam-6264	64	11	0	0	NUM
ejpam-6264	64	12	,	,	PUNCT
ejpam-6264	64	13	1	1	NUM
ejpam-6264	64	14	,	,	PUNCT
ejpam-6264	64	15	2	2	NUM
ejpam-6264	64	16	,	,	PUNCT
ejpam-6264	64	17	3	3	NUM
ejpam-6264	64	18	}	}	PUNCT
ejpam-6264	64	19	given	give	VERB
ejpam-6264	64	20	by	by	ADP
ejpam-6264	64	21	f(a	f(a	PROPN
ejpam-6264	64	22	)	)	PUNCT
ejpam-6264	64	23	=	=	SYM
ejpam-6264	64	24	3	3	NUM
ejpam-6264	64	25	,	,	PUNCT
ejpam-6264	64	26	f(g	f(g	NOUN
ejpam-6264	64	27	)	)	PUNCT
ejpam-6264	64	28	=	=	SYM
ejpam-6264	64	29	2	2	NUM
ejpam-6264	64	30	,	,	PUNCT
ejpam-6264	64	31	f(b	f(b	PROPN
ejpam-6264	64	32	)	)	PUNCT
ejpam-6264	64	33	=	=	SYM
ejpam-6264	64	34	1	1	NUM
ejpam-6264	64	35	and	and	CCONJ
ejpam-6264	64	36	f(c	f(c	PROPN
ejpam-6264	64	37	)	)	PUNCT
ejpam-6264	64	38	=	=	SYM
ejpam-6264	64	39	f(d	f(d	PROPN
ejpam-6264	64	40	)	)	PUNCT
ejpam-6264	64	41	=	=	SYM
ejpam-6264	64	42	f(e	f(e	NOUN
ejpam-6264	64	43	)	)	PUNCT
ejpam-6264	64	44	=	=	SYM
ejpam-6264	64	45	f(h	f(h	NOUN
ejpam-6264	64	46	)	)	PUNCT
ejpam-6264	65	1	=	=	SYM
ejpam-6264	65	2	0	0	NUM
ejpam-6264	65	3	is	be	AUX
ejpam-6264	65	4	a	a	DET
ejpam-6264	65	5	total	total	ADJ
ejpam-6264	65	6	modern	modern	ADJ
ejpam-6264	65	7	roman	roman	ADJ
ejpam-6264	65	8	dominating	dominating	NOUN
ejpam-6264	65	9	function	function	NOUN
ejpam-6264	65	10	of	of	ADP
ejpam-6264	65	11	g.	g.	PROPN
ejpam-6264	65	12	it	it	PRON
ejpam-6264	65	13	can	can	AUX
ejpam-6264	65	14	be	be	AUX
ejpam-6264	65	15	verified	verify	VERB
ejpam-6264	65	16	that	that	SCONJ
ejpam-6264	65	17	,	,	PUNCT
ejpam-6264	65	18	γtmr(g	γtmr(g	NOUN
ejpam-6264	65	19	)	)	PUNCT
ejpam-6264	65	20	=	=	PUNCT
ejpam-6264	65	21	6	6	NUM
ejpam-6264	65	22	.	.	NOUN
ejpam-6264	65	23	0	0	NUM
ejpam-6264	66	1	d	d	NOUN
ejpam-6264	66	2	0e	0e	PROPN
ejpam-6264	66	3	0c	0c	NOUN
ejpam-6264	66	4	0h	0h	X
ejpam-6264	66	5	3a	3a	NUM
ejpam-6264	66	6	2	2	NUM
ejpam-6264	66	7	g	g	NOUN
ejpam-6264	66	8	g	g	PROPN
ejpam-6264	66	9	:	:	PUNCT
ejpam-6264	66	10	1b	1b	PROPN
ejpam-6264	66	11	s.	s.	PROPN
ejpam-6264	66	12	ahamad	ahamad	VERB
ejpam-6264	66	13	et	et	PROPN
ejpam-6264	66	14	al	al	PROPN
ejpam-6264	66	15	.	.	PUNCT
ejpam-6264	66	16	/	/	SYM
ejpam-6264	66	17	eur	eur	PROPN
ejpam-6264	66	18	.	.	PUNCT
ejpam-6264	67	1	j.	j.	PROPN
ejpam-6264	67	2	pure	pure	PROPN
ejpam-6264	67	3	appl	appl	PROPN
ejpam-6264	67	4	.	.	PROPN
ejpam-6264	67	5	math	math	PROPN
ejpam-6264	67	6	,	,	PUNCT
ejpam-6264	67	7	18	18	NUM
ejpam-6264	67	8	(	(	PUNCT
ejpam-6264	67	9	4	4	NUM
ejpam-6264	67	10	)	)	PUNCT
ejpam-6264	67	11	(	(	PUNCT
ejpam-6264	67	12	2025	2025	NUM
ejpam-6264	67	13	)	)	PUNCT
ejpam-6264	67	14	,	,	PUNCT
ejpam-6264	67	15	6264	6264	NUM
ejpam-6264	67	16	5	5	NUM
ejpam-6264	67	17	of	of	ADP
ejpam-6264	67	18	20	20	NUM
ejpam-6264	67	19	figure	figure	NOUN
ejpam-6264	67	20	1	1	NUM
ejpam-6264	67	21	:	:	PUNCT
ejpam-6264	67	22	graph	graph	VERB
ejpam-6264	67	23	g	g	NOUN
ejpam-6264	67	24	of	of	ADP
ejpam-6264	67	25	order	order	NOUN
ejpam-6264	67	26	7	7	NUM
ejpam-6264	67	27	with	with	ADP
ejpam-6264	67	28	γtmr(g	γtmr(g	NOUN
ejpam-6264	67	29	)	)	PUNCT
ejpam-6264	67	30	=	=	SYM
ejpam-6264	67	31	6	6	NUM
ejpam-6264	67	32	proposition	proposition	NOUN
ejpam-6264	67	33	3	3	NUM
ejpam-6264	67	34	.	.	PUNCT
ejpam-6264	68	1	let	let	VERB
ejpam-6264	68	2	g	g	NOUN
ejpam-6264	68	3	be	be	AUX
ejpam-6264	68	4	any	any	DET
ejpam-6264	68	5	isolated	isolate	VERB
ejpam-6264	68	6	-	-	PUNCT
ejpam-6264	68	7	free	free	ADJ
ejpam-6264	68	8	graph	graph	NOUN
ejpam-6264	68	9	.	.	PUNCT
ejpam-6264	69	1	then	then	ADV
ejpam-6264	69	2	γ(g	γ(g	PROPN
ejpam-6264	69	3	)	)	PUNCT
ejpam-6264	69	4	+	+	NUM
ejpam-6264	69	5	γt(g	γt(g	NOUN
ejpam-6264	70	1	)	)	PUNCT
ejpam-6264	70	2	≤	≤	NUM
ejpam-6264	70	3	γtmr(g	γtmr(g	NUM
ejpam-6264	70	4	)	)	PUNCT
ejpam-6264	70	5	.	.	PUNCT
ejpam-6264	71	1	moreover	moreover	ADV
ejpam-6264	71	2	,	,	PUNCT
ejpam-6264	71	3	this	this	DET
ejpam-6264	71	4	bound	bind	VERB
ejpam-6264	71	5	is	be	AUX
ejpam-6264	71	6	sharp	sharp	ADJ
ejpam-6264	71	7	whenever	whenever	SCONJ
ejpam-6264	71	8	,	,	PUNCT
ejpam-6264	71	9	g	g	PROPN
ejpam-6264	71	10	=	=	PUNCT
ejpam-6264	71	11	•∪n	•∪n	ADV
ejpam-6264	71	12	i=1p2i	i=1p2i	ADV
ejpam-6264	71	13	,	,	PUNCT
ejpam-6264	71	14	where	where	SCONJ
ejpam-6264	71	15	i	i	PRON
ejpam-6264	71	16	=	=	NOUN
ejpam-6264	71	17	1	1	NUM
ejpam-6264	71	18	,	,	PUNCT
ejpam-6264	71	19	2	2	NUM
ejpam-6264	71	20	,	,	PUNCT
ejpam-6264	71	21	·	·	PUNCT
ejpam-6264	71	22	·	·	PUNCT
ejpam-6264	71	23	·	·	PUNCT
ejpam-6264	71	24	n.	n.	NOUN
ejpam-6264	71	25	proof	proof	NOUN
ejpam-6264	71	26	.	.	PUNCT
ejpam-6264	72	1	let	let	VERB
ejpam-6264	72	2	g	g	PRON
ejpam-6264	72	3	be	be	AUX
ejpam-6264	72	4	a	a	DET
ejpam-6264	72	5	graph	graph	NOUN
ejpam-6264	72	6	with	with	ADP
ejpam-6264	72	7	no	no	DET
ejpam-6264	72	8	isolated	isolated	ADJ
ejpam-6264	72	9	vertex	vertex	NOUN
ejpam-6264	72	10	and	and	CCONJ
ejpam-6264	72	11	f	f	NOUN
ejpam-6264	72	12	=	=	SYM
ejpam-6264	72	13	(	(	PUNCT
ejpam-6264	72	14	v0	v0	PROPN
ejpam-6264	72	15	,	,	PUNCT
ejpam-6264	72	16	v1	v1	NOUN
ejpam-6264	72	17	,	,	PUNCT
ejpam-6264	72	18	v2	v2	PROPN
ejpam-6264	72	19	,	,	PUNCT
ejpam-6264	72	20	v3	v3	PROPN
ejpam-6264	72	21	)	)	PUNCT
ejpam-6264	72	22	be	be	VERB
ejpam-6264	72	23	a	a	DET
ejpam-6264	72	24	γtmrfunction	γtmrfunction	NOUN
ejpam-6264	72	25	on	on	ADP
ejpam-6264	72	26	g.	g.	PROPN
ejpam-6264	72	27	then	then	ADV
ejpam-6264	72	28	v2	v2	PROPN
ejpam-6264	72	29	∪	∪	X
ejpam-6264	72	30	v3	v3	PROPN
ejpam-6264	72	31	is	be	AUX
ejpam-6264	72	32	a	a	DET
ejpam-6264	72	33	dominating	dominating	NOUN
ejpam-6264	72	34	set	set	NOUN
ejpam-6264	72	35	of	of	ADP
ejpam-6264	72	36	g.	g.	PROPN
ejpam-6264	72	37	moreover	moreover	ADV
ejpam-6264	72	38	,	,	PUNCT
ejpam-6264	72	39	v1	v1	VERB
ejpam-6264	72	40	∪	∪	ADJ
ejpam-6264	72	41	v2	v2	PROPN
ejpam-6264	72	42	∪	∪	X
ejpam-6264	72	43	v3	v3	PROPN
ejpam-6264	72	44	is	be	AUX
ejpam-6264	72	45	a	a	DET
ejpam-6264	72	46	total	total	ADJ
ejpam-6264	72	47	dominating	dominating	NOUN
ejpam-6264	72	48	set	set	NOUN
ejpam-6264	72	49	of	of	ADP
ejpam-6264	72	50	g.	g.	PROPN
ejpam-6264	72	51	thus	thus	ADV
ejpam-6264	72	52	,	,	PUNCT
ejpam-6264	72	53	γtmr(g	γtmr(g	NOUN
ejpam-6264	72	54	)	)	PUNCT
ejpam-6264	73	1	=	=	VERB
ejpam-6264	73	2	ωtmr	ωtmr	ADJ
ejpam-6264	73	3	g	g	PROPN
ejpam-6264	73	4	(	(	PUNCT
ejpam-6264	73	5	f	f	X
ejpam-6264	73	6	)	)	PUNCT
ejpam-6264	74	1	=	=	NOUN
ejpam-6264	74	2	|v1|+	|v1|+	ADP
ejpam-6264	74	3	2|v2|+	2|v2|+	NUM
ejpam-6264	74	4	3|v3|	3|v3|	NUM
ejpam-6264	74	5	=(	=(	NOUN
ejpam-6264	74	6	|v1|+	|v1|+	SYM
ejpam-6264	74	7	|v2|+	|v2|+	NOUN
ejpam-6264	74	8	|v3|	|v3|	NOUN
ejpam-6264	74	9	)	)	PUNCT
ejpam-6264	75	1	+	+	CCONJ
ejpam-6264	75	2	(	(	PUNCT
ejpam-6264	75	3	v2|+	v2|+	NOUN
ejpam-6264	75	4	|v3|	|v3|	NOUN
ejpam-6264	75	5	)	)	PUNCT
ejpam-6264	76	1	+	+	NUM
ejpam-6264	76	2	|v3|	|v3|	NOUN
ejpam-6264	76	3	≥γt(g	≥γt(g	NUM
ejpam-6264	76	4	)	)	PUNCT
ejpam-6264	76	5	+	+	NUM
ejpam-6264	76	6	γ(g	γ(g	PROPN
ejpam-6264	76	7	)	)	PUNCT
ejpam-6264	76	8	.	.	PUNCT
ejpam-6264	77	1	hence	hence	ADV
ejpam-6264	77	2	,	,	PUNCT
ejpam-6264	77	3	we	we	PRON
ejpam-6264	77	4	obtained	obtain	VERB
ejpam-6264	77	5	the	the	DET
ejpam-6264	77	6	desired	desire	VERB
ejpam-6264	77	7	lower	lower	ADV
ejpam-6264	77	8	bound	bind	VERB
ejpam-6264	77	9	.	.	PUNCT
ejpam-6264	78	1	moreover	moreover	ADV
ejpam-6264	78	2	,	,	PUNCT
ejpam-6264	78	3	the	the	DET
ejpam-6264	78	4	bound	bind	VERB
ejpam-6264	78	5	is	be	AUX
ejpam-6264	78	6	sharp	sharp	ADJ
ejpam-6264	78	7	by	by	ADP
ejpam-6264	78	8	considering	consider	VERB
ejpam-6264	78	9	the	the	DET
ejpam-6264	78	10	disjoint	disjoint	PROPN
ejpam-6264	78	11	union	union	NOUN
ejpam-6264	78	12	of	of	ADP
ejpam-6264	78	13	copies	copy	NOUN
ejpam-6264	78	14	of	of	ADP
ejpam-6264	78	15	k2	k2	PROPN
ejpam-6264	78	16	.	.	PUNCT
ejpam-6264	79	1	proposition	proposition	NOUN
ejpam-6264	79	2	4	4	NUM
ejpam-6264	79	3	.	.	PUNCT
ejpam-6264	80	1	let	let	VERB
ejpam-6264	80	2	g	g	NOUN
ejpam-6264	80	3	be	be	AUX
ejpam-6264	80	4	any	any	DET
ejpam-6264	80	5	graph	graph	NOUN
ejpam-6264	80	6	with	with	ADP
ejpam-6264	80	7	no	no	DET
ejpam-6264	80	8	isolated	isolated	ADJ
ejpam-6264	80	9	vertex	vertex	NOUN
ejpam-6264	80	10	and	and	CCONJ
ejpam-6264	80	11	f	f	NOUN
ejpam-6264	80	12	=	=	SYM
ejpam-6264	80	13	(	(	PUNCT
ejpam-6264	80	14	v0	v0	PROPN
ejpam-6264	80	15	,	,	PUNCT
ejpam-6264	80	16	v1	v1	NOUN
ejpam-6264	80	17	,	,	PUNCT
ejpam-6264	80	18	v2	v2	PROPN
ejpam-6264	80	19	,	,	PUNCT
ejpam-6264	80	20	v3	v3	PROPN
ejpam-6264	80	21	)	)	PUNCT
ejpam-6264	80	22	a	a	DET
ejpam-6264	80	23	γtmr	γtmr	NOUN
ejpam-6264	80	24	-	-	PUNCT
ejpam-6264	80	25	function	function	NOUN
ejpam-6264	80	26	of	of	ADP
ejpam-6264	80	27	g.	g.	PROPN
ejpam-6264	80	28	then	then	ADV
ejpam-6264	80	29	v0	v0	PROPN
ejpam-6264	80	30	=	=	SYM
ejpam-6264	80	31	∅	∅	NOUN
ejpam-6264	80	32	if	if	SCONJ
ejpam-6264	80	33	and	and	CCONJ
ejpam-6264	80	34	only	only	ADV
ejpam-6264	80	35	if	if	SCONJ
ejpam-6264	80	36	v3	v3	PROPN
ejpam-6264	80	37	=	=	SYM
ejpam-6264	80	38	∅	∅	NOUN
ejpam-6264	80	39	and	and	CCONJ
ejpam-6264	80	40	v2	v2	PROPN
ejpam-6264	80	41	is	be	AUX
ejpam-6264	80	42	a	a	DET
ejpam-6264	80	43	γ	γ	NOUN
ejpam-6264	80	44	-	-	PUNCT
ejpam-6264	80	45	set	set	NOUN
ejpam-6264	80	46	of	of	ADP
ejpam-6264	80	47	g.	g.	PROPN
ejpam-6264	80	48	proof	proof	PROPN
ejpam-6264	80	49	.	.	PUNCT
ejpam-6264	81	1	the	the	DET
ejpam-6264	81	2	result	result	NOUN
ejpam-6264	81	3	follows	follow	VERB
ejpam-6264	81	4	immediately	immediately	ADV
ejpam-6264	81	5	from	from	ADP
ejpam-6264	81	6	proposition	proposition	NOUN
ejpam-6264	81	7	1	1	NUM
ejpam-6264	81	8	.	.	PUNCT
ejpam-6264	81	9	proposition	proposition	NOUN
ejpam-6264	81	10	5	5	NUM
ejpam-6264	81	11	.	.	PUNCT
ejpam-6264	82	1	let	let	VERB
ejpam-6264	82	2	g	g	NOUN
ejpam-6264	82	3	be	be	AUX
ejpam-6264	82	4	any	any	DET
ejpam-6264	82	5	graph	graph	NOUN
ejpam-6264	82	6	with	with	ADP
ejpam-6264	82	7	no	no	DET
ejpam-6264	82	8	isolated	isolated	ADJ
ejpam-6264	82	9	vertex	vertex	NOUN
ejpam-6264	82	10	and	and	CCONJ
ejpam-6264	82	11	f	f	NOUN
ejpam-6264	82	12	=	=	SYM
ejpam-6264	82	13	(	(	PUNCT
ejpam-6264	82	14	v0	v0	PROPN
ejpam-6264	82	15	,	,	PUNCT
ejpam-6264	82	16	v1	v1	NOUN
ejpam-6264	82	17	,	,	PUNCT
ejpam-6264	82	18	v2	v2	PROPN
ejpam-6264	82	19	,	,	PUNCT
ejpam-6264	82	20	v3	v3	PROPN
ejpam-6264	82	21	)	)	PUNCT
ejpam-6264	82	22	a	a	DET
ejpam-6264	82	23	γtmr	γtmr	NOUN
ejpam-6264	82	24	-	-	PUNCT
ejpam-6264	82	25	function	function	NOUN
ejpam-6264	82	26	of	of	ADP
ejpam-6264	82	27	g.	g.	PROPN
ejpam-6264	83	1	then	then	ADV
ejpam-6264	83	2	one	one	NUM
ejpam-6264	83	3	of	of	ADP
ejpam-6264	83	4	the	the	DET
ejpam-6264	83	5	following	follow	VERB
ejpam-6264	83	6	holds	hold	VERB
ejpam-6264	83	7	:	:	PUNCT
ejpam-6264	83	8	(	(	PUNCT
ejpam-6264	83	9	i	i	NOUN
ejpam-6264	83	10	)	)	PUNCT
ejpam-6264	83	11	if	if	SCONJ
ejpam-6264	83	12	|v0|	|v0|	NOUN
ejpam-6264	83	13	=	=	SYM
ejpam-6264	83	14	0	0	NUM
ejpam-6264	83	15	,	,	PUNCT
ejpam-6264	83	16	then	then	ADV
ejpam-6264	83	17	|v1|	|v1|	NOUN
ejpam-6264	83	18	̸=	̸=	PROPN
ejpam-6264	83	19	0	0	NUM
ejpam-6264	83	20	;	;	PUNCT
ejpam-6264	83	21	(	(	PUNCT
ejpam-6264	83	22	ii	ii	NOUN
ejpam-6264	83	23	)	)	PUNCT
ejpam-6264	83	24	if	if	SCONJ
ejpam-6264	83	25	|v1|	|v1|	NUM
ejpam-6264	83	26	=	=	SYM
ejpam-6264	83	27	0	0	NUM
ejpam-6264	83	28	,	,	PUNCT
ejpam-6264	83	29	then	then	ADV
ejpam-6264	83	30	|v0|	|v0|	VERB
ejpam-6264	83	31	̸=	̸=	PROPN
ejpam-6264	83	32	0	0	NUM
ejpam-6264	83	33	.	.	PUNCT
ejpam-6264	84	1	proof	proof	NOUN
ejpam-6264	84	2	.	.	PUNCT
ejpam-6264	85	1	(	(	PUNCT
ejpam-6264	85	2	i	i	NOUN
ejpam-6264	85	3	)	)	PUNCT
ejpam-6264	85	4	let	let	VERB
ejpam-6264	85	5	|v0|	|v0|	NOUN
ejpam-6264	85	6	=	=	SYM
ejpam-6264	85	7	0	0	PUNCT
ejpam-6264	85	8	and	and	CCONJ
ejpam-6264	85	9	suppose	suppose	VERB
ejpam-6264	85	10	that	that	SCONJ
ejpam-6264	85	11	|v1|	|v1|	NOUN
ejpam-6264	85	12	=	=	SYM
ejpam-6264	85	13	0	0	X
ejpam-6264	85	14	.	.	PUNCT
ejpam-6264	86	1	then	then	ADV
ejpam-6264	86	2	γtmr(g	γtmr(g	NUM
ejpam-6264	86	3	)	)	PUNCT
ejpam-6264	86	4	=	=	SYM
ejpam-6264	86	5	2|v2|	2|v2|	NUM
ejpam-6264	86	6	+	+	CCONJ
ejpam-6264	86	7	3|v3|	3|v3|	NUM
ejpam-6264	86	8	and	and	CCONJ
ejpam-6264	86	9	⟨v2	⟨v2	ADJ
ejpam-6264	86	10	∪	∪	ADJ
ejpam-6264	86	11	v3⟩	v3⟩	NOUN
ejpam-6264	86	12	is	be	AUX
ejpam-6264	86	13	a	a	DET
ejpam-6264	86	14	total	total	ADJ
ejpam-6264	86	15	dominating	dominating	NOUN
ejpam-6264	86	16	set	set	NOUN
ejpam-6264	86	17	of	of	ADP
ejpam-6264	86	18	g.	g.	PROPN
ejpam-6264	86	19	let	let	VERB
ejpam-6264	86	20	d	d	NOUN
ejpam-6264	86	21	⊆	⊆	NUM
ejpam-6264	86	22	v2	v2	PROPN
ejpam-6264	86	23	∪	∪	X
ejpam-6264	86	24	v3	v3	PROPN
ejpam-6264	86	25	be	be	VERB
ejpam-6264	86	26	a	a	DET
ejpam-6264	86	27	dominating	dominating	NOUN
ejpam-6264	86	28	set	set	NOUN
ejpam-6264	86	29	of	of	ADP
ejpam-6264	86	30	the	the	DET
ejpam-6264	86	31	induced	induced	ADJ
ejpam-6264	86	32	subgraph	subgraph	NOUN
ejpam-6264	86	33	⟨v2	⟨v2	ADJ
ejpam-6264	86	34	∪	∪	ADJ
ejpam-6264	86	35	v3⟩.	v3⟩.	NOUN
ejpam-6264	86	36	define	define	VERB
ejpam-6264	86	37	a	a	DET
ejpam-6264	86	38	function	function	NOUN
ejpam-6264	86	39	h	h	NOUN
ejpam-6264	86	40	=	=	PUNCT
ejpam-6264	86	41	(	(	PUNCT
ejpam-6264	86	42	v	v	NUM
ejpam-6264	86	43	′	′	NUM
ejpam-6264	86	44	0	0	NUM
ejpam-6264	86	45	,	,	PUNCT
ejpam-6264	86	46	v	v	NOUN
ejpam-6264	86	47	′	′	NUM
ejpam-6264	86	48	1	1	NUM
ejpam-6264	86	49	,	,	PUNCT
ejpam-6264	86	50	v	v	NOUN
ejpam-6264	86	51	′	′	NUM
ejpam-6264	86	52	2	2	NUM
ejpam-6264	86	53	,	,	PUNCT
ejpam-6264	86	54	v	v	NOUN
ejpam-6264	86	55	′	′	NUM
ejpam-6264	86	56	3	3	NUM
ejpam-6264	86	57	)	)	PUNCT
ejpam-6264	86	58	,	,	PUNCT
ejpam-6264	86	59	where	where	SCONJ
ejpam-6264	86	60	v	v	X
ejpam-6264	86	61	′	′	NOUN
ejpam-6264	86	62	0	0	NUM
ejpam-6264	87	1	=	=	NOUN
ejpam-6264	87	2	∅	∅	NOUN
ejpam-6264	87	3	,	,	PUNCT
ejpam-6264	87	4	v	v	NOUN
ejpam-6264	87	5	′	′	NOUN
ejpam-6264	87	6	1	1	NUM
ejpam-6264	87	7	=	=	SYM
ejpam-6264	87	8	(	(	PUNCT
ejpam-6264	87	9	v2	v2	PROPN
ejpam-6264	87	10	∪	∪	X
ejpam-6264	87	11	v3	v3	PROPN
ejpam-6264	87	12	)	)	PUNCT
ejpam-6264	87	13	\d	\d	NOUN
ejpam-6264	87	14	,	,	PUNCT
ejpam-6264	87	15	v	v	NOUN
ejpam-6264	87	16	′	′	NUM
ejpam-6264	87	17	2	2	NUM
ejpam-6264	87	18	=	=	SYM
ejpam-6264	87	19	d	d	NOUN
ejpam-6264	87	20	and	and	CCONJ
ejpam-6264	87	21	v	v	X
ejpam-6264	87	22	′	′	NUM
ejpam-6264	87	23	3	3	NUM
ejpam-6264	87	24	=	=	NOUN
ejpam-6264	87	25	∅.	∅.	NOUN
ejpam-6264	87	26	then	then	ADV
ejpam-6264	87	27	h	h	PROPN
ejpam-6264	87	28	∈	∈	PROPN
ejpam-6264	87	29	tmrdf	tmrdf	NOUN
ejpam-6264	87	30	(	(	PUNCT
ejpam-6264	87	31	g	g	NOUN
ejpam-6264	87	32	)	)	PUNCT
ejpam-6264	87	33	and	and	CCONJ
ejpam-6264	87	34	thus	thus	ADV
ejpam-6264	87	35	,	,	PUNCT
ejpam-6264	87	36	ωtmr	ωtmr	PROPN
ejpam-6264	87	37	g	g	PROPN
ejpam-6264	87	38	(	(	PUNCT
ejpam-6264	87	39	h	h	NOUN
ejpam-6264	87	40	)	)	PUNCT
ejpam-6264	87	41	=	=	SYM
ejpam-6264	87	42	|v	|v	PROPN
ejpam-6264	87	43	′	′	NUM
ejpam-6264	87	44	1	1	NUM
ejpam-6264	87	45	|+	|+	NOUN
ejpam-6264	87	46	2|v	2|v	NOUN
ejpam-6264	88	1	′	′	NUM
ejpam-6264	88	2	2	2	NUM
ejpam-6264	89	1	|	|	ADV
ejpam-6264	89	2	≤	≤	NUM
ejpam-6264	89	3	2|v2|+	2|v2|+	NUM
ejpam-6264	89	4	3|v3|	3|v3|	NUM
ejpam-6264	89	5	=	=	PUNCT
ejpam-6264	89	6	ωtmr	ωtmr	ADJ
ejpam-6264	89	7	g	g	PROPN
ejpam-6264	89	8	(	(	PUNCT
ejpam-6264	89	9	f	f	PROPN
ejpam-6264	89	10	)	)	PUNCT
ejpam-6264	89	11	,	,	PUNCT
ejpam-6264	89	12	a	a	DET
ejpam-6264	89	13	contradiction	contradiction	NOUN
ejpam-6264	89	14	.	.	PUNCT
ejpam-6264	90	1	hence	hence	ADV
ejpam-6264	90	2	,	,	PUNCT
ejpam-6264	90	3	|v1|	|v1|	NOUN
ejpam-6264	90	4	̸=	̸=	PROPN
ejpam-6264	90	5	0	0	NUM
ejpam-6264	90	6	.	.	PUNCT
ejpam-6264	91	1	(	(	PUNCT
ejpam-6264	91	2	ii	ii	NOUN
ejpam-6264	91	3	)	)	PUNCT
ejpam-6264	91	4	let	let	VERB
ejpam-6264	91	5	|v1|	|v1|	NOUN
ejpam-6264	91	6	=	=	SYM
ejpam-6264	91	7	0	0	NUM
ejpam-6264	91	8	with	with	ADP
ejpam-6264	91	9	|v3|	|v3|	NOUN
ejpam-6264	91	10	̸=	̸=	PROPN
ejpam-6264	91	11	0	0	PUNCT
ejpam-6264	91	12	and	and	CCONJ
ejpam-6264	91	13	suppose	suppose	VERB
ejpam-6264	91	14	that	that	SCONJ
ejpam-6264	91	15	|v0|	|v0|	NOUN
ejpam-6264	91	16	=	=	SYM
ejpam-6264	91	17	0	0	X
ejpam-6264	91	18	.	.	PUNCT
ejpam-6264	92	1	then	then	ADV
ejpam-6264	92	2	γtmr(g	γtmr(g	NUM
ejpam-6264	92	3	)	)	PUNCT
ejpam-6264	92	4	=	=	PUNCT
ejpam-6264	93	1	ωtmr	ωtmr	ADJ
ejpam-6264	93	2	g	g	PROPN
ejpam-6264	93	3	(	(	PUNCT
ejpam-6264	93	4	f	f	X
ejpam-6264	93	5	)	)	PUNCT
ejpam-6264	93	6	=	=	SYM
ejpam-6264	93	7	2|v2|	2|v2|	NUM
ejpam-6264	93	8	+	+	CCONJ
ejpam-6264	93	9	3|v3|	3|v3|	NUM
ejpam-6264	93	10	and	and	CCONJ
ejpam-6264	93	11	since	since	SCONJ
ejpam-6264	93	12	f	f	PROPN
ejpam-6264	93	13	is	be	AUX
ejpam-6264	93	14	a	a	DET
ejpam-6264	93	15	γtmr	γtmr	ADJ
ejpam-6264	93	16	-	-	PUNCT
ejpam-6264	93	17	function	function	NOUN
ejpam-6264	93	18	,	,	PUNCT
ejpam-6264	93	19	⟨v2	⟨v2	ADJ
ejpam-6264	93	20	∪	∪	ADJ
ejpam-6264	93	21	v3⟩	v3⟩	NOUN
ejpam-6264	93	22	is	be	AUX
ejpam-6264	93	23	a	a	DET
ejpam-6264	93	24	total	total	ADJ
ejpam-6264	93	25	dominating	dominating	NOUN
ejpam-6264	93	26	set	set	VERB
ejpam-6264	93	27	in	in	ADP
ejpam-6264	93	28	g.	g.	PROPN
ejpam-6264	93	29	consider	consider	VERB
ejpam-6264	93	30	the	the	DET
ejpam-6264	93	31	vertices	vertex	NOUN
ejpam-6264	93	32	x	x	X
ejpam-6264	93	33	∈	∈	NOUN
ejpam-6264	93	34	v	v	NOUN
ejpam-6264	93	35	(	(	PUNCT
ejpam-6264	93	36	g	g	NOUN
ejpam-6264	93	37	)	)	PUNCT
ejpam-6264	93	38	such	such	ADJ
ejpam-6264	93	39	that	that	SCONJ
ejpam-6264	93	40	x	x	SYM
ejpam-6264	93	41	∈	∈	PROPN
ejpam-6264	93	42	ng(v2	ng(v2	NOUN
ejpam-6264	93	43	)	)	PUNCT
ejpam-6264	93	44	∩	∩	NOUN
ejpam-6264	93	45	ng(v3	ng(v3	NOUN
ejpam-6264	93	46	)	)	PUNCT
ejpam-6264	93	47	.	.	PUNCT
ejpam-6264	94	1	let	let	VERB
ejpam-6264	94	2	v	v	VERB
ejpam-6264	94	3	′′	′′	PROPN
ejpam-6264	94	4	1	1	NUM
ejpam-6264	94	5	=	=	NOUN
ejpam-6264	94	6	∅	∅	NOUN
ejpam-6264	94	7	,	,	PUNCT
ejpam-6264	94	8	v	v	ADP
ejpam-6264	94	9	′′	′′	PROPN
ejpam-6264	94	10	0	0	NUM
ejpam-6264	94	11	=	=	SYM
ejpam-6264	94	12	ng(v2	ng(v2	NOUN
ejpam-6264	94	13	)	)	PUNCT
ejpam-6264	94	14	∩	∩	NOUN
ejpam-6264	94	15	ng(v3	ng(v3	NOUN
ejpam-6264	94	16	)	)	PUNCT
ejpam-6264	94	17	,	,	PUNCT
ejpam-6264	94	18	v	v	ADP
ejpam-6264	94	19	′′	′′	PROPN
ejpam-6264	94	20	2	2	NUM
ejpam-6264	94	21	=	=	SYM
ejpam-6264	94	22	v2	v2	PROPN
ejpam-6264	94	23	\	\	PROPN
ejpam-6264	94	24	(	(	PUNCT
ejpam-6264	94	25	ng(v2	ng(v2	NOUN
ejpam-6264	94	26	)	)	PUNCT
ejpam-6264	94	27	∩	∩	ADJ
ejpam-6264	94	28	ng(v3	ng(v3	NOUN
ejpam-6264	94	29	)	)	PUNCT
ejpam-6264	94	30	)	)	PUNCT
ejpam-6264	94	31	.	.	PUNCT
ejpam-6264	95	1	then	then	ADV
ejpam-6264	95	2	the	the	DET
ejpam-6264	95	3	function	function	NOUN
ejpam-6264	95	4	defined	define	VERB
ejpam-6264	95	5	by	by	ADP
ejpam-6264	95	6	h	h	NOUN
ejpam-6264	95	7	=	=	SYM
ejpam-6264	95	8	(	(	PUNCT
ejpam-6264	95	9	v	v	NUM
ejpam-6264	95	10	′′	′′	PROPN
ejpam-6264	95	11	0	0	NUM
ejpam-6264	95	12	,	,	PUNCT
ejpam-6264	95	13	v	v	ADP
ejpam-6264	95	14	′′	′′	PROPN
ejpam-6264	95	15	1	1	NUM
ejpam-6264	95	16	,	,	PUNCT
ejpam-6264	95	17	v	v	ADP
ejpam-6264	95	18	′′	′′	PROPN
ejpam-6264	95	19	2	2	NUM
ejpam-6264	95	20	,	,	PUNCT
ejpam-6264	95	21	v	v	ADP
ejpam-6264	95	22	′′	′′	PROPN
ejpam-6264	95	23	3	3	NUM
ejpam-6264	95	24	)	)	PUNCT
ejpam-6264	95	25	∈	∈	NOUN
ejpam-6264	95	26	tmrdf	tmrdf	NOUN
ejpam-6264	95	27	(	(	PUNCT
ejpam-6264	95	28	g	g	NOUN
ejpam-6264	95	29	)	)	PUNCT
ejpam-6264	95	30	.	.	PUNCT
ejpam-6264	96	1	thus	thus	ADV
ejpam-6264	96	2	,	,	PUNCT
ejpam-6264	96	3	ωtmr	ωtmr	PROPN
ejpam-6264	96	4	g	g	PROPN
ejpam-6264	96	5	(	(	PUNCT
ejpam-6264	96	6	h	h	NOUN
ejpam-6264	96	7	)	)	PUNCT
ejpam-6264	96	8	=	=	SYM
ejpam-6264	96	9	2|v	2|v	X
ejpam-6264	97	1	′′	′′	NOUN
ejpam-6264	97	2	2	2	NUM
ejpam-6264	98	1	|	|	ADV
ejpam-6264	98	2	+	+	SYM
ejpam-6264	98	3	3|v	3|v	NUM
ejpam-6264	98	4	′′	′′	NOUN
ejpam-6264	98	5	3	3	NUM
ejpam-6264	98	6	|	|	ADV
ejpam-6264	98	7	≤	≤	NUM
ejpam-6264	98	8	2|v2|	2|v2|	NUM
ejpam-6264	98	9	+	+	CCONJ
ejpam-6264	98	10	3|v3|	3|v3|	NUM
ejpam-6264	98	11	=	=	SYM
ejpam-6264	98	12	ωtmr	ωtmr	ADJ
ejpam-6264	98	13	g	g	PROPN
ejpam-6264	98	14	(	(	PUNCT
ejpam-6264	98	15	f	f	X
ejpam-6264	98	16	)	)	PUNCT
ejpam-6264	98	17	=	=	SYM
ejpam-6264	98	18	γtmr(g	γtmr(g	PROPN
ejpam-6264	98	19	)	)	PUNCT
ejpam-6264	98	20	,	,	PUNCT
ejpam-6264	98	21	a	a	DET
ejpam-6264	98	22	contradiction	contradiction	NOUN
ejpam-6264	98	23	.	.	PUNCT
ejpam-6264	99	1	hence	hence	ADV
ejpam-6264	99	2	,	,	PUNCT
ejpam-6264	99	3	|v0|	|v0|	NOUN
ejpam-6264	99	4	̸=	̸=	PROPN
ejpam-6264	99	5	0	0	NUM
ejpam-6264	99	6	.	.	PUNCT
ejpam-6264	100	1	s.	s.	PROPN
ejpam-6264	100	2	ahamad	ahamad	VERB
ejpam-6264	100	3	et	et	PROPN
ejpam-6264	100	4	al	al	PROPN
ejpam-6264	100	5	.	.	PUNCT
ejpam-6264	100	6	/	/	SYM
ejpam-6264	100	7	eur	eur	PROPN
ejpam-6264	100	8	.	.	PUNCT
ejpam-6264	101	1	j.	j.	PROPN
ejpam-6264	101	2	pure	pure	PROPN
ejpam-6264	101	3	appl	appl	PROPN
ejpam-6264	101	4	.	.	PROPN
ejpam-6264	101	5	math	math	PROPN
ejpam-6264	101	6	,	,	PUNCT
ejpam-6264	101	7	18	18	NUM
ejpam-6264	101	8	(	(	PUNCT
ejpam-6264	101	9	4	4	NUM
ejpam-6264	101	10	)	)	PUNCT
ejpam-6264	101	11	(	(	PUNCT
ejpam-6264	101	12	2025	2025	NUM
ejpam-6264	101	13	)	)	PUNCT
ejpam-6264	101	14	,	,	PUNCT
ejpam-6264	101	15	6264	6264	NUM
ejpam-6264	101	16	6	6	NUM
ejpam-6264	101	17	of	of	ADP
ejpam-6264	101	18	20	20	NUM
ejpam-6264	101	19	remark	remark	NOUN
ejpam-6264	101	20	1	1	NUM
ejpam-6264	101	21	.	.	PUNCT
ejpam-6264	102	1	the	the	DET
ejpam-6264	102	2	converse	converse	NOUN
ejpam-6264	102	3	of	of	ADP
ejpam-6264	102	4	(	(	PUNCT
ejpam-6264	102	5	ii	ii	PROPN
ejpam-6264	102	6	)	)	PUNCT
ejpam-6264	102	7	and	and	CCONJ
ejpam-6264	102	8	(	(	PUNCT
ejpam-6264	102	9	iii	iii	NOUN
ejpam-6264	102	10	)	)	PUNCT
ejpam-6264	102	11	need	need	AUX
ejpam-6264	102	12	not	not	PART
ejpam-6264	102	13	be	be	AUX
ejpam-6264	102	14	true	true	ADJ
ejpam-6264	102	15	.	.	PUNCT
ejpam-6264	103	1	proposition	proposition	NOUN
ejpam-6264	103	2	6	6	NUM
ejpam-6264	103	3	.	.	PUNCT
ejpam-6264	104	1	let	let	VERB
ejpam-6264	104	2	g	g	PRON
ejpam-6264	104	3	be	be	AUX
ejpam-6264	104	4	a	a	DET
ejpam-6264	104	5	nontrivial	nontrivial	ADJ
ejpam-6264	104	6	connected	connect	VERB
ejpam-6264	104	7	graph	graph	NOUN
ejpam-6264	104	8	and	and	CCONJ
ejpam-6264	104	9	f	f	NOUN
ejpam-6264	104	10	=	=	SYM
ejpam-6264	104	11	(	(	PUNCT
ejpam-6264	104	12	v0	v0	PROPN
ejpam-6264	104	13	,	,	PUNCT
ejpam-6264	104	14	v1	v1	NOUN
ejpam-6264	104	15	,	,	PUNCT
ejpam-6264	104	16	v2	v2	PROPN
ejpam-6264	104	17	,	,	PUNCT
ejpam-6264	104	18	v3	v3	PROPN
ejpam-6264	104	19	)	)	PUNCT
ejpam-6264	104	20	a	a	DET
ejpam-6264	104	21	γtmrfunction	γtmrfunction	NOUN
ejpam-6264	104	22	of	of	ADP
ejpam-6264	104	23	g.	g.	PROPN
ejpam-6264	105	1	then	then	ADV
ejpam-6264	105	2	(	(	PUNCT
ejpam-6264	105	3	i	i	NOUN
ejpam-6264	105	4	)	)	PUNCT
ejpam-6264	105	5	|v0|	|v0|	NOUN
ejpam-6264	105	6	=	=	SYM
ejpam-6264	105	7	0	0	PUNCT
ejpam-6264	106	1	if	if	SCONJ
ejpam-6264	106	2	and	and	CCONJ
ejpam-6264	106	3	only	only	ADV
ejpam-6264	106	4	if	if	SCONJ
ejpam-6264	106	5	v2	v2	PROPN
ejpam-6264	106	6	is	be	AUX
ejpam-6264	106	7	a	a	DET
ejpam-6264	106	8	γ	γ	NOUN
ejpam-6264	106	9	-	-	PUNCT
ejpam-6264	106	10	set	set	NOUN
ejpam-6264	106	11	of	of	ADP
ejpam-6264	106	12	g	g	NOUN
ejpam-6264	106	13	and	and	CCONJ
ejpam-6264	106	14	v	v	NOUN
ejpam-6264	106	15	(	(	PUNCT
ejpam-6264	106	16	g	g	NOUN
ejpam-6264	106	17	)	)	PUNCT
ejpam-6264	106	18	is	be	AUX
ejpam-6264	106	19	a	a	DET
ejpam-6264	106	20	total	total	ADJ
ejpam-6264	106	21	dominating	dominating	NOUN
ejpam-6264	106	22	set	set	NOUN
ejpam-6264	106	23	of	of	ADP
ejpam-6264	106	24	g.	g.	PROPN
ejpam-6264	106	25	(	(	PUNCT
ejpam-6264	106	26	ii	ii	PROPN
ejpam-6264	106	27	)	)	PUNCT
ejpam-6264	106	28	|v1|	|v1|	NOUN
ejpam-6264	107	1	=	=	SYM
ejpam-6264	107	2	0	0	PUNCT
ejpam-6264	107	3	if	if	SCONJ
ejpam-6264	107	4	and	and	CCONJ
ejpam-6264	107	5	only	only	ADV
ejpam-6264	107	6	if	if	SCONJ
ejpam-6264	107	7	v2	v2	PROPN
ejpam-6264	107	8	∪	∪	X
ejpam-6264	107	9	v3	v3	PROPN
ejpam-6264	107	10	is	be	AUX
ejpam-6264	107	11	both	both	CCONJ
ejpam-6264	107	12	a	a	DET
ejpam-6264	107	13	γ2	γ2	NOUN
ejpam-6264	107	14	-	-	PUNCT
ejpam-6264	107	15	set	set	VERB
ejpam-6264	107	16	and	and	CCONJ
ejpam-6264	107	17	γt	γt	NOUN
ejpam-6264	107	18	-	-	VERB
ejpam-6264	107	19	set	set	NOUN
ejpam-6264	107	20	of	of	ADP
ejpam-6264	107	21	g.	g.	PROPN
ejpam-6264	107	22	proof	proof	NOUN
ejpam-6264	107	23	.	.	PUNCT
ejpam-6264	108	1	(	(	PUNCT
ejpam-6264	108	2	i	i	NOUN
ejpam-6264	108	3	)	)	PUNCT
ejpam-6264	108	4	suppose	suppose	VERB
ejpam-6264	108	5	|v0|	|v0|	NOUN
ejpam-6264	108	6	=	=	SYM
ejpam-6264	108	7	0	0	NUM
ejpam-6264	108	8	,	,	PUNCT
ejpam-6264	108	9	then	then	ADV
ejpam-6264	108	10	|v3|	|v3|	NOUN
ejpam-6264	108	11	=	=	NOUN
ejpam-6264	108	12	0	0	NUM
ejpam-6264	108	13	by	by	ADP
ejpam-6264	108	14	proposition	proposition	NOUN
ejpam-6264	108	15	4	4	NUM
ejpam-6264	108	16	,	,	PUNCT
ejpam-6264	108	17	v2	v2	PROPN
ejpam-6264	108	18	is	be	AUX
ejpam-6264	108	19	a	a	DET
ejpam-6264	108	20	γ	γ	NOUN
ejpam-6264	108	21	-	-	PUNCT
ejpam-6264	108	22	set	set	NOUN
ejpam-6264	108	23	of	of	ADP
ejpam-6264	108	24	g.	g.	PROPN
ejpam-6264	108	25	it	it	PRON
ejpam-6264	108	26	remains	remain	VERB
ejpam-6264	108	27	to	to	PART
ejpam-6264	108	28	show	show	VERB
ejpam-6264	108	29	that	that	SCONJ
ejpam-6264	108	30	v	v	NOUN
ejpam-6264	108	31	(	(	PUNCT
ejpam-6264	108	32	g	g	NOUN
ejpam-6264	108	33	)	)	PUNCT
ejpam-6264	108	34	is	be	AUX
ejpam-6264	108	35	a	a	DET
ejpam-6264	108	36	γt	γt	NOUN
ejpam-6264	108	37	-	-	NOUN
ejpam-6264	108	38	set	set	NOUN
ejpam-6264	108	39	of	of	ADP
ejpam-6264	108	40	g.	g.	PROPN
ejpam-6264	108	41	note	note	VERB
ejpam-6264	108	42	that	that	SCONJ
ejpam-6264	108	43	v	v	X
ejpam-6264	108	44	(	(	PUNCT
ejpam-6264	108	45	g	g	NOUN
ejpam-6264	108	46	)	)	PUNCT
ejpam-6264	108	47	=	=	SYM
ejpam-6264	108	48	v1	v1	VERB
ejpam-6264	108	49	∪	∪	NOUN
ejpam-6264	108	50	v2	v2	NOUN
ejpam-6264	108	51	and	and	CCONJ
ejpam-6264	108	52	⟨v1	⟨v1	PROPN
ejpam-6264	108	53	∪	∪	NOUN
ejpam-6264	108	54	v2⟩	v2⟩	PROPN
ejpam-6264	108	55	is	be	AUX
ejpam-6264	108	56	isolated	isolate	VERB
ejpam-6264	108	57	-	-	PUNCT
ejpam-6264	108	58	free	free	ADJ
ejpam-6264	108	59	.	.	PUNCT
ejpam-6264	109	1	it	it	PRON
ejpam-6264	109	2	follows	follow	VERB
ejpam-6264	109	3	that	that	SCONJ
ejpam-6264	109	4	v	v	X
ejpam-6264	109	5	(	(	PUNCT
ejpam-6264	109	6	g	g	NOUN
ejpam-6264	109	7	)	)	PUNCT
ejpam-6264	109	8	is	be	AUX
ejpam-6264	109	9	a	a	DET
ejpam-6264	109	10	total	total	ADJ
ejpam-6264	109	11	dominating	dominating	NOUN
ejpam-6264	109	12	set	set	NOUN
ejpam-6264	109	13	of	of	ADP
ejpam-6264	109	14	g.	g.	PROPN
ejpam-6264	109	15	conversely	conversely	ADV
ejpam-6264	109	16	,	,	PUNCT
ejpam-6264	109	17	since	since	SCONJ
ejpam-6264	109	18	v	v	NOUN
ejpam-6264	109	19	(	(	PUNCT
ejpam-6264	109	20	g	g	NOUN
ejpam-6264	109	21	)	)	PUNCT
ejpam-6264	109	22	is	be	AUX
ejpam-6264	109	23	a	a	DET
ejpam-6264	109	24	total	total	ADJ
ejpam-6264	109	25	dominating	dominating	NOUN
ejpam-6264	109	26	set	set	NOUN
ejpam-6264	109	27	of	of	ADP
ejpam-6264	109	28	g	g	NOUN
ejpam-6264	109	29	,	,	PUNCT
ejpam-6264	109	30	f(v	f(v	PROPN
ejpam-6264	109	31	)	)	PUNCT
ejpam-6264	109	32	̸=	̸=	NOUN
ejpam-6264	109	33	0	0	NUM
ejpam-6264	109	34	for	for	ADP
ejpam-6264	109	35	all	all	DET
ejpam-6264	109	36	v	v	ADP
ejpam-6264	109	37	∈	∈	NUM
ejpam-6264	109	38	v	v	NOUN
ejpam-6264	109	39	(	(	PUNCT
ejpam-6264	109	40	g	g	NOUN
ejpam-6264	109	41	)	)	PUNCT
ejpam-6264	109	42	by	by	ADP
ejpam-6264	109	43	definition	definition	NOUN
ejpam-6264	109	44	.	.	PUNCT
ejpam-6264	110	1	hence	hence	ADV
ejpam-6264	110	2	,	,	PUNCT
ejpam-6264	110	3	|v0|	|v0|	NOUN
ejpam-6264	110	4	=	=	SYM
ejpam-6264	110	5	0	0	X
ejpam-6264	110	6	.	.	PUNCT
ejpam-6264	110	7	(	(	PUNCT
ejpam-6264	110	8	ii	ii	NOUN
ejpam-6264	110	9	)	)	PUNCT
ejpam-6264	110	10	suppose	suppose	VERB
ejpam-6264	110	11	|v1|	|v1|	NOUN
ejpam-6264	110	12	=	=	SYM
ejpam-6264	110	13	0	0	X
ejpam-6264	110	14	.	.	PUNCT
ejpam-6264	111	1	then	then	ADV
ejpam-6264	111	2	|v0|	|v0|	VERB
ejpam-6264	111	3	̸=	̸=	PROPN
ejpam-6264	111	4	0	0	NUM
ejpam-6264	111	5	by	by	ADP
ejpam-6264	111	6	proposition	proposition	NOUN
ejpam-6264	111	7	5	5	NUM
ejpam-6264	111	8	(	(	PUNCT
ejpam-6264	111	9	ii	ii	NOUN
ejpam-6264	111	10	)	)	PUNCT
ejpam-6264	111	11	.	.	PUNCT
ejpam-6264	112	1	by	by	ADP
ejpam-6264	112	2	(	(	PUNCT
ejpam-6264	112	3	p1	p1	PROPN
ejpam-6264	112	4	)	)	PUNCT
ejpam-6264	112	5	,	,	PUNCT
ejpam-6264	112	6	for	for	ADP
ejpam-6264	112	7	every	every	DET
ejpam-6264	112	8	v	v	PROPN
ejpam-6264	112	9	∈	∈	PROPN
ejpam-6264	112	10	v0	v0	NOUN
ejpam-6264	112	11	,	,	PUNCT
ejpam-6264	112	12	|v2∩ng(v)|	|v2∩ng(v)|	VERB
ejpam-6264	112	13	≥	≥	NOUN
ejpam-6264	112	14	1	1	NUM
ejpam-6264	112	15	and	and	CCONJ
ejpam-6264	112	16	|v3∩ng(v)|	|v3∩ng(v)|	ADP
ejpam-6264	112	17	≥	≥	X
ejpam-6264	112	18	1	1	NUM
ejpam-6264	112	19	.	.	PUNCT
ejpam-6264	113	1	this	this	PRON
ejpam-6264	113	2	implies	imply	VERB
ejpam-6264	113	3	that	that	SCONJ
ejpam-6264	113	4	v2∪v3	v2∪v3	PROPN
ejpam-6264	113	5	is	be	AUX
ejpam-6264	113	6	a	a	DET
ejpam-6264	113	7	2	2	NUM
ejpam-6264	113	8	-	-	PUNCT
ejpam-6264	113	9	dominating	dominating	NOUN
ejpam-6264	113	10	set	set	NOUN
ejpam-6264	113	11	of	of	ADP
ejpam-6264	113	12	g.	g.	PROPN
ejpam-6264	113	13	suppose	suppose	VERB
ejpam-6264	113	14	v2	v2	PROPN
ejpam-6264	113	15	∪	∪	X
ejpam-6264	113	16	v3	v3	PROPN
ejpam-6264	113	17	is	be	AUX
ejpam-6264	113	18	not	not	PART
ejpam-6264	113	19	a	a	DET
ejpam-6264	113	20	γ2	γ2	NOUN
ejpam-6264	113	21	-	-	PUNCT
ejpam-6264	113	22	set	set	NOUN
ejpam-6264	113	23	of	of	ADP
ejpam-6264	113	24	g.	g.	PROPN
ejpam-6264	113	25	then	then	ADV
ejpam-6264	113	26	there	there	PRON
ejpam-6264	113	27	exists	exist	VERB
ejpam-6264	113	28	d	d	PROPN
ejpam-6264	113	29	⊆	⊆	NUM
ejpam-6264	113	30	v2	v2	PROPN
ejpam-6264	113	31	∪	∪	X
ejpam-6264	113	32	v3	v3	PROPN
ejpam-6264	113	33	such	such	ADJ
ejpam-6264	113	34	that	that	SCONJ
ejpam-6264	113	35	d	d	NOUN
ejpam-6264	113	36	is	be	AUX
ejpam-6264	113	37	a	a	DET
ejpam-6264	113	38	γ2	γ2	NOUN
ejpam-6264	113	39	-	-	PUNCT
ejpam-6264	113	40	set	set	NOUN
ejpam-6264	113	41	of	of	ADP
ejpam-6264	113	42	g.	g.	PROPN
ejpam-6264	113	43	define	define	VERB
ejpam-6264	113	44	a	a	DET
ejpam-6264	113	45	function	function	NOUN
ejpam-6264	113	46	g	g	NOUN
ejpam-6264	113	47	=	=	SYM
ejpam-6264	113	48	(	(	PUNCT
ejpam-6264	113	49	v	v	NOUN
ejpam-6264	113	50	∗	∗	NOUN
ejpam-6264	113	51	0	0	NUM
ejpam-6264	113	52	,	,	PUNCT
ejpam-6264	113	53	v	v	NOUN
ejpam-6264	113	54	∗	∗	NOUN
ejpam-6264	113	55	1	1	NUM
ejpam-6264	113	56	,	,	PUNCT
ejpam-6264	113	57	v	v	NOUN
ejpam-6264	113	58	∗	∗	NOUN
ejpam-6264	113	59	2	2	NUM
ejpam-6264	113	60	,	,	PUNCT
ejpam-6264	113	61	v	v	NOUN
ejpam-6264	113	62	∗	∗	NOUN
ejpam-6264	113	63	3	3	NUM
ejpam-6264	113	64	)	)	PUNCT
ejpam-6264	113	65	,	,	PUNCT
ejpam-6264	113	66	such	such	ADJ
ejpam-6264	113	67	that	that	DET
ejpam-6264	113	68	v	v	ADP
ejpam-6264	113	69	∗	∗	NOUN
ejpam-6264	113	70	0	0	NUM
ejpam-6264	113	71	=	=	NOUN
ejpam-6264	113	72	∅	∅	NOUN
ejpam-6264	113	73	,	,	PUNCT
ejpam-6264	113	74	v	v	NOUN
ejpam-6264	113	75	∗	∗	NOUN
ejpam-6264	113	76	1	1	NUM
ejpam-6264	113	77	=	=	SYM
ejpam-6264	113	78	(	(	PUNCT
ejpam-6264	113	79	v2	v2	PROPN
ejpam-6264	113	80	∪	∪	X
ejpam-6264	113	81	v3	v3	PROPN
ejpam-6264	113	82	)	)	PUNCT
ejpam-6264	113	83	\d	\d	NOUN
ejpam-6264	113	84	,	,	PUNCT
ejpam-6264	113	85	v	v	NOUN
ejpam-6264	113	86	∗	∗	NOUN
ejpam-6264	113	87	2	2	NUM
ejpam-6264	113	88	=	=	SYM
ejpam-6264	113	89	d	d	NOUN
ejpam-6264	113	90	∩	∩	X
ejpam-6264	113	91	v2	v2	PROPN
ejpam-6264	113	92	and	and	CCONJ
ejpam-6264	113	93	v	v	NOUN
ejpam-6264	113	94	∗	∗	NOUN
ejpam-6264	113	95	3	3	NUM
ejpam-6264	113	96	=	=	SYM
ejpam-6264	113	97	d	d	PROPN
ejpam-6264	113	98	∩	∩	PROPN
ejpam-6264	113	99	v3	v3	PROPN
ejpam-6264	113	100	.	.	PUNCT
ejpam-6264	114	1	then	then	ADV
ejpam-6264	114	2	g	g	PROPN
ejpam-6264	114	3	∈	∈	PROPN
ejpam-6264	114	4	tmrdf	tmrdf	NOUN
ejpam-6264	114	5	(	(	PUNCT
ejpam-6264	114	6	g	g	NOUN
ejpam-6264	114	7	)	)	PUNCT
ejpam-6264	114	8	and	and	CCONJ
ejpam-6264	114	9	so	so	ADV
ejpam-6264	114	10	,	,	PUNCT
ejpam-6264	114	11	ωtmr	ωtmr	PROPN
ejpam-6264	114	12	g	g	PROPN
ejpam-6264	114	13	(	(	PUNCT
ejpam-6264	114	14	g	g	NOUN
ejpam-6264	114	15	)	)	PUNCT
ejpam-6264	114	16	=	=	SYM
ejpam-6264	114	17	|v	|v	PROPN
ejpam-6264	114	18	∗	∗	NOUN
ejpam-6264	114	19	1	1	NUM
ejpam-6264	114	20	|+2|v	|+2|v	NOUN
ejpam-6264	114	21	∗	∗	NOUN
ejpam-6264	114	22	2	2	NUM
ejpam-6264	114	23	|+3|v	|+3|v	NOUN
ejpam-6264	114	24	∗	∗	NOUN
ejpam-6264	114	25	3	3	NUM
ejpam-6264	114	26	|	|	NOUN
ejpam-6264	114	27	=	=	NOUN
ejpam-6264	114	28	|(v2∪v3)\d|+2|d∩v2|+3|d∩v3|	|(v2∪v3)\d|+2|d∩v2|+3|d∩v3|	NOUN
ejpam-6264	114	29	≤	≤	ADV
ejpam-6264	114	30	2|v2|+3|v3|−|(v2∪v3)\d|	2|v2|+3|v3|−|(v2∪v3)\d|	NUM
ejpam-6264	114	31	=	=	SYM
ejpam-6264	114	32	ωtmr	ωtmr	ADJ
ejpam-6264	114	33	g	g	NOUN
ejpam-6264	114	34	(	(	PUNCT
ejpam-6264	114	35	f)−|(v2∪v3)∩d|	f)−|(v2∪v3)∩d|	PROPN
ejpam-6264	114	36	≤	≤	NUM
ejpam-6264	114	37	ωtmr	ωtmr	ADJ
ejpam-6264	114	38	g	g	PROPN
ejpam-6264	114	39	(	(	PUNCT
ejpam-6264	114	40	f	f	PROPN
ejpam-6264	114	41	)	)	PUNCT
ejpam-6264	114	42	.	.	PUNCT
ejpam-6264	115	1	this	this	PRON
ejpam-6264	115	2	is	be	AUX
ejpam-6264	115	3	a	a	DET
ejpam-6264	115	4	contradiction	contradiction	NOUN
ejpam-6264	115	5	.	.	PUNCT
ejpam-6264	116	1	thus	thus	ADV
ejpam-6264	116	2	,	,	PUNCT
ejpam-6264	116	3	v2∪v3	v2∪v3	X
ejpam-6264	116	4	is	be	AUX
ejpam-6264	116	5	a	a	DET
ejpam-6264	116	6	γ2	γ2	NOUN
ejpam-6264	116	7	-	-	PUNCT
ejpam-6264	116	8	set	set	NOUN
ejpam-6264	116	9	of	of	ADP
ejpam-6264	116	10	g.	g.	PROPN
ejpam-6264	116	11	now	now	ADV
ejpam-6264	116	12	,	,	PUNCT
ejpam-6264	116	13	by	by	ADP
ejpam-6264	116	14	(	(	PUNCT
ejpam-6264	116	15	p3	p3	PROPN
ejpam-6264	116	16	)	)	PUNCT
ejpam-6264	116	17	v2	v2	PROPN
ejpam-6264	116	18	∪	∪	X
ejpam-6264	116	19	v3	v3	PROPN
ejpam-6264	116	20	is	be	AUX
ejpam-6264	116	21	a	a	DET
ejpam-6264	116	22	total	total	ADJ
ejpam-6264	116	23	dominating	dominating	NOUN
ejpam-6264	116	24	set	set	NOUN
ejpam-6264	116	25	of	of	ADP
ejpam-6264	116	26	g.	g.	PROPN
ejpam-6264	116	27	suppose	suppose	VERB
ejpam-6264	116	28	v2	v2	PROPN
ejpam-6264	116	29	∪	∪	X
ejpam-6264	116	30	v3	v3	PROPN
ejpam-6264	116	31	is	be	AUX
ejpam-6264	116	32	not	not	PART
ejpam-6264	116	33	a	a	DET
ejpam-6264	116	34	γt	γt	NOUN
ejpam-6264	116	35	-	-	NOUN
ejpam-6264	116	36	set	set	NOUN
ejpam-6264	116	37	of	of	ADP
ejpam-6264	116	38	g.	g.	PROPN
ejpam-6264	116	39	then	then	ADV
ejpam-6264	116	40	there	there	PRON
ejpam-6264	116	41	exists	exist	VERB
ejpam-6264	116	42	d	d	PROPN
ejpam-6264	116	43	⊆	⊆	X
ejpam-6264	116	44	v2∪v3	v2∪v3	X
ejpam-6264	116	45	such	such	ADJ
ejpam-6264	116	46	that	that	SCONJ
ejpam-6264	116	47	d	d	NOUN
ejpam-6264	116	48	is	be	AUX
ejpam-6264	116	49	a	a	DET
ejpam-6264	116	50	γt−set	γt−set	NOUN
ejpam-6264	116	51	of	of	ADP
ejpam-6264	116	52	g.	g.	PROPN
ejpam-6264	116	53	let	let	VERB
ejpam-6264	116	54	v	v	X
ejpam-6264	116	55	”	"	PUNCT
ejpam-6264	116	56	0	0	NUM
ejpam-6264	117	1	=	=	SYM
ejpam-6264	117	2	(	(	PUNCT
ejpam-6264	117	3	v2∪v3)\d	v2∪v3)\d	NOUN
ejpam-6264	117	4	,	,	PUNCT
ejpam-6264	117	5	v	v	NOUN
ejpam-6264	117	6	”	"	PUNCT
ejpam-6264	117	7	1	1	NUM
ejpam-6264	117	8	=	=	NOUN
ejpam-6264	117	9	∅	∅	NOUN
ejpam-6264	117	10	,	,	PUNCT
ejpam-6264	117	11	v	v	NOUN
ejpam-6264	117	12	”	"	PUNCT
ejpam-6264	117	13	2	2	NUM
ejpam-6264	117	14	=	=	SYM
ejpam-6264	117	15	d	d	NOUN
ejpam-6264	117	16	∩	∩	X
ejpam-6264	117	17	v2	v2	PROPN
ejpam-6264	117	18	and	and	CCONJ
ejpam-6264	117	19	v	v	NOUN
ejpam-6264	117	20	”	"	PUNCT
ejpam-6264	117	21	3	3	NUM
ejpam-6264	117	22	=	=	SYM
ejpam-6264	117	23	d	d	PROPN
ejpam-6264	117	24	∩	∩	PROPN
ejpam-6264	117	25	v3	v3	PROPN
ejpam-6264	117	26	.	.	PUNCT
ejpam-6264	118	1	then	then	ADV
ejpam-6264	118	2	g	g	PROPN
ejpam-6264	118	3	=	=	SYM
ejpam-6264	118	4	(	(	PUNCT
ejpam-6264	118	5	v	v	NOUN
ejpam-6264	118	6	”	"	PUNCT
ejpam-6264	118	7	0	0	NUM
ejpam-6264	118	8	,	,	PUNCT
ejpam-6264	118	9	∅	∅	NOUN
ejpam-6264	118	10	,	,	PUNCT
ejpam-6264	118	11	v	v	NOUN
ejpam-6264	118	12	”	"	PUNCT
ejpam-6264	118	13	2	2	NUM
ejpam-6264	118	14	,	,	PUNCT
ejpam-6264	118	15	v	v	NOUN
ejpam-6264	118	16	”	"	PUNCT
ejpam-6264	118	17	3	3	NUM
ejpam-6264	118	18	)	)	PUNCT
ejpam-6264	118	19	∈	∈	NOUN
ejpam-6264	118	20	tmrdf	tmrdf	NOUN
ejpam-6264	118	21	(	(	PUNCT
ejpam-6264	118	22	g	g	NOUN
ejpam-6264	118	23	)	)	PUNCT
ejpam-6264	118	24	and	and	CCONJ
ejpam-6264	118	25	ωtmr	ωtmr	PROPN
ejpam-6264	118	26	g	g	PROPN
ejpam-6264	118	27	(	(	PUNCT
ejpam-6264	118	28	g	g	NOUN
ejpam-6264	118	29	)	)	PUNCT
ejpam-6264	118	30	=	=	SYM
ejpam-6264	118	31	2|v	2|v	NUM
ejpam-6264	118	32	”	"	PUNCT
ejpam-6264	118	33	2	2	NUM
ejpam-6264	119	1	|	|	ADV
ejpam-6264	119	2	+	+	NUM
ejpam-6264	119	3	3|v	3|v	NUM
ejpam-6264	119	4	”	"	PUNCT
ejpam-6264	119	5	3	3	NUM
ejpam-6264	119	6	|	|	ADV
ejpam-6264	119	7	≤	≤	NUM
ejpam-6264	119	8	2|v2|	2|v2|	NUM
ejpam-6264	119	9	+	+	CCONJ
ejpam-6264	119	10	3|v3|	3|v3|	NUM
ejpam-6264	119	11	=	=	SYM
ejpam-6264	119	12	ωtmr	ωtmr	ADJ
ejpam-6264	119	13	g	g	PROPN
ejpam-6264	119	14	(	(	PUNCT
ejpam-6264	119	15	f	f	PROPN
ejpam-6264	119	16	)	)	PUNCT
ejpam-6264	119	17	,	,	PUNCT
ejpam-6264	119	18	a	a	DET
ejpam-6264	119	19	contradiction	contradiction	NOUN
ejpam-6264	119	20	.	.	PUNCT
ejpam-6264	120	1	hence	hence	ADV
ejpam-6264	120	2	,	,	PUNCT
ejpam-6264	120	3	v2	v2	PROPN
ejpam-6264	120	4	∪	∪	X
ejpam-6264	120	5	v3	v3	PROPN
ejpam-6264	120	6	is	be	AUX
ejpam-6264	120	7	a	a	DET
ejpam-6264	120	8	γt	γt	NOUN
ejpam-6264	120	9	-	-	NOUN
ejpam-6264	120	10	set	set	NOUN
ejpam-6264	120	11	of	of	ADP
ejpam-6264	120	12	g.	g.	NOUN
ejpam-6264	120	13	conversely	conversely	ADV
ejpam-6264	120	14	,	,	PUNCT
ejpam-6264	120	15	let	let	VERB
ejpam-6264	120	16	v2	v2	PROPN
ejpam-6264	120	17	∪	∪	X
ejpam-6264	120	18	v3	v3	PROPN
ejpam-6264	120	19	be	be	AUX
ejpam-6264	120	20	a	a	DET
ejpam-6264	120	21	γ2	γ2	NOUN
ejpam-6264	120	22	-	-	PUNCT
ejpam-6264	120	23	set	set	VERB
ejpam-6264	120	24	and	and	CCONJ
ejpam-6264	120	25	γt	γt	NOUN
ejpam-6264	120	26	-	-	VERB
ejpam-6264	120	27	set	set	NOUN
ejpam-6264	120	28	of	of	ADP
ejpam-6264	120	29	g.	g.	PROPN
ejpam-6264	120	30	suppose	suppose	VERB
ejpam-6264	120	31	|v1|	|v1|	NOUN
ejpam-6264	120	32	̸=	̸=	PROPN
ejpam-6264	120	33	0	0	NUM
ejpam-6264	120	34	.	.	PUNCT
ejpam-6264	121	1	then	then	ADV
ejpam-6264	121	2	there	there	PRON
ejpam-6264	121	3	exists	exist	VERB
ejpam-6264	121	4	y	y	PROPN
ejpam-6264	121	5	∈	∈	PROPN
ejpam-6264	121	6	v1	v1	NOUN
ejpam-6264	121	7	such	such	ADJ
ejpam-6264	121	8	that	that	SCONJ
ejpam-6264	121	9	y	y	PROPN
ejpam-6264	121	10	∈	∈	PROPN
ejpam-6264	121	11	ng(x	ng(x	NUM
ejpam-6264	121	12	)	)	PUNCT
ejpam-6264	121	13	∩	∩	NOUN
ejpam-6264	121	14	ng(z	ng(z	PROPN
ejpam-6264	121	15	)	)	PUNCT
ejpam-6264	121	16	where	where	SCONJ
ejpam-6264	121	17	x	x	PUNCT
ejpam-6264	121	18	∈	∈	PROPN
ejpam-6264	121	19	v2	v2	PROPN
ejpam-6264	121	20	and	and	CCONJ
ejpam-6264	121	21	z	z	NOUN
ejpam-6264	121	22	∈	∈	PROPN
ejpam-6264	121	23	v3	v3	PROPN
ejpam-6264	121	24	.	.	PUNCT
ejpam-6264	122	1	define	define	VERB
ejpam-6264	122	2	a	a	DET
ejpam-6264	122	3	function	function	NOUN
ejpam-6264	122	4	g	g	NOUN
ejpam-6264	122	5	=	=	SYM
ejpam-6264	122	6	(	(	PUNCT
ejpam-6264	122	7	v	v	NOUN
ejpam-6264	122	8	∗	∗	NOUN
ejpam-6264	122	9	0	0	NUM
ejpam-6264	122	10	,	,	PUNCT
ejpam-6264	122	11	v	v	NOUN
ejpam-6264	122	12	∗	∗	NOUN
ejpam-6264	122	13	1	1	NUM
ejpam-6264	122	14	,	,	PUNCT
ejpam-6264	122	15	v	v	NOUN
ejpam-6264	122	16	∗	∗	NOUN
ejpam-6264	122	17	2	2	NUM
ejpam-6264	122	18	,	,	PUNCT
ejpam-6264	122	19	v	v	NOUN
ejpam-6264	122	20	∗	∗	X
ejpam-6264	122	21	3	3	NUM
ejpam-6264	122	22	)	)	PUNCT
ejpam-6264	122	23	for	for	ADP
ejpam-6264	122	24	which	which	PRON
ejpam-6264	122	25	v0	v0	NOUN
ejpam-6264	122	26	=	=	SYM
ejpam-6264	122	27	v	v	ADP
ejpam-6264	122	28	∗	∗	NOUN
ejpam-6264	122	29	0	0	NUM
ejpam-6264	122	30	,	,	PUNCT
ejpam-6264	122	31	v1	v1	NOUN
ejpam-6264	122	32	=	=	SYM
ejpam-6264	122	33	v	v	NOUN
ejpam-6264	122	34	∗	∗	NOUN
ejpam-6264	122	35	1	1	NUM
ejpam-6264	122	36	̸=	̸=	PROPN
ejpam-6264	122	37	∅	∅	NOUN
ejpam-6264	122	38	,	,	PUNCT
ejpam-6264	122	39	v2	v2	PROPN
ejpam-6264	122	40	=	=	SYM
ejpam-6264	122	41	v	v	NOUN
ejpam-6264	122	42	∗	∗	NOUN
ejpam-6264	122	43	2	2	NUM
ejpam-6264	122	44	and	and	CCONJ
ejpam-6264	122	45	v3	v3	PROPN
ejpam-6264	122	46	=	=	PROPN
ejpam-6264	122	47	v	v	PROPN
ejpam-6264	122	48	∗	∗	NOUN
ejpam-6264	122	49	3	3	NUM
ejpam-6264	122	50	.	.	PUNCT
ejpam-6264	123	1	then	then	ADV
ejpam-6264	123	2	g	g	PROPN
ejpam-6264	123	3	∈	∈	PROPN
ejpam-6264	123	4	tmrdf	tmrdf	NOUN
ejpam-6264	123	5	(	(	PUNCT
ejpam-6264	123	6	g	g	NOUN
ejpam-6264	123	7	)	)	PUNCT
ejpam-6264	123	8	.	.	PUNCT
ejpam-6264	124	1	thus	thus	ADV
ejpam-6264	124	2	,	,	PUNCT
ejpam-6264	124	3	ωtmr	ωtmr	PROPN
ejpam-6264	124	4	g	g	PROPN
ejpam-6264	124	5	(	(	PUNCT
ejpam-6264	124	6	g	g	NOUN
ejpam-6264	124	7	)	)	PUNCT
ejpam-6264	124	8	=	=	SYM
ejpam-6264	124	9	3|v	3|v	NUM
ejpam-6264	124	10	∗	∗	NOUN
ejpam-6264	124	11	3	3	NUM
ejpam-6264	124	12	|+2|v	|+2|v	NOUN
ejpam-6264	124	13	∗	∗	NOUN
ejpam-6264	124	14	2	2	NUM
ejpam-6264	124	15	|+	|+	NOUN
ejpam-6264	124	16	|v	|v	PROPN
ejpam-6264	124	17	∗	∗	NOUN
ejpam-6264	124	18	1	1	NUM
ejpam-6264	124	19	|	|	ADV
ejpam-6264	124	20	≤	≤	PUNCT
ejpam-6264	124	21	3|v3|+2|v2|	3|v3|+2|v2|	NUM
ejpam-6264	124	22	=	=	SYM
ejpam-6264	124	23	ωtmr	ωtmr	PROPN
ejpam-6264	124	24	g	g	PROPN
ejpam-6264	124	25	(	(	PUNCT
ejpam-6264	124	26	f	f	PROPN
ejpam-6264	124	27	)	)	PUNCT
ejpam-6264	124	28	.	.	PUNCT
ejpam-6264	125	1	this	this	PRON
ejpam-6264	125	2	contradicts	contradict	VERB
ejpam-6264	125	3	the	the	DET
ejpam-6264	125	4	fact	fact	NOUN
ejpam-6264	125	5	that	that	SCONJ
ejpam-6264	125	6	f	f	PROPN
ejpam-6264	125	7	is	be	AUX
ejpam-6264	125	8	a	a	DET
ejpam-6264	125	9	γtmr	γtmr	ADJ
ejpam-6264	125	10	-	-	PUNCT
ejpam-6264	125	11	function	function	NOUN
ejpam-6264	125	12	of	of	ADP
ejpam-6264	125	13	g.	g.	PROPN
ejpam-6264	125	14	hence	hence	ADV
ejpam-6264	125	15	,	,	PUNCT
ejpam-6264	125	16	|v1|	|v1|	NOUN
ejpam-6264	125	17	=	=	SYM
ejpam-6264	125	18	0	0	X
ejpam-6264	125	19	.	.	PUNCT
ejpam-6264	126	1	proposition	proposition	NOUN
ejpam-6264	126	2	7	7	NUM
ejpam-6264	126	3	.	.	PUNCT
ejpam-6264	127	1	let	let	VERB
ejpam-6264	127	2	g	g	PRON
ejpam-6264	127	3	be	be	AUX
ejpam-6264	127	4	a	a	DET
ejpam-6264	127	5	connected	connected	ADJ
ejpam-6264	127	6	graph	graph	NOUN
ejpam-6264	127	7	of	of	ADP
ejpam-6264	127	8	order	order	NOUN
ejpam-6264	127	9	n	n	PRON
ejpam-6264	127	10	≥	≥	NOUN
ejpam-6264	127	11	2	2	NUM
ejpam-6264	127	12	.	.	PUNCT
ejpam-6264	128	1	then	then	ADV
ejpam-6264	128	2	(	(	PUNCT
ejpam-6264	128	3	i	i	NOUN
ejpam-6264	128	4	)	)	PUNCT
ejpam-6264	128	5	γtmr(g	γtmr(g	PROPN
ejpam-6264	128	6	)	)	PUNCT
ejpam-6264	128	7	=	=	SYM
ejpam-6264	128	8	3	3	NUM
ejpam-6264	128	9	if	if	SCONJ
ejpam-6264	128	10	and	and	CCONJ
ejpam-6264	128	11	only	only	ADV
ejpam-6264	128	12	if	if	SCONJ
ejpam-6264	128	13	g	g	PROPN
ejpam-6264	128	14	∈	∈	PROPN
ejpam-6264	128	15	{	{	PUNCT
ejpam-6264	128	16	p2,k2	p2,k2	PROPN
ejpam-6264	128	17	}	}	PUNCT
ejpam-6264	128	18	.	.	PUNCT
ejpam-6264	129	1	(	(	PUNCT
ejpam-6264	129	2	ii	ii	NOUN
ejpam-6264	129	3	)	)	PUNCT
ejpam-6264	129	4	γtmr(g	γtmr(g	NOUN
ejpam-6264	129	5	)	)	PUNCT
ejpam-6264	130	1	=	=	SYM
ejpam-6264	130	2	4	4	NUM
ejpam-6264	130	3	if	if	SCONJ
ejpam-6264	130	4	and	and	CCONJ
ejpam-6264	130	5	only	only	ADV
ejpam-6264	130	6	if	if	SCONJ
ejpam-6264	130	7	g	g	PROPN
ejpam-6264	130	8	∈	∈	PROPN
ejpam-6264	130	9	{	{	PUNCT
ejpam-6264	130	10	p3,k3	p3,k3	PROPN
ejpam-6264	130	11	}	}	PUNCT
ejpam-6264	130	12	.	.	PUNCT
ejpam-6264	131	1	proof	proof	NOUN
ejpam-6264	131	2	.	.	PUNCT
ejpam-6264	132	1	(	(	PUNCT
ejpam-6264	132	2	i	i	NOUN
ejpam-6264	132	3	)	)	PUNCT
ejpam-6264	132	4	wlog	wlog	NOUN
ejpam-6264	132	5	,	,	PUNCT
ejpam-6264	132	6	suppose	suppose	VERB
ejpam-6264	132	7	g	g	PROPN
ejpam-6264	132	8	=	=	SYM
ejpam-6264	132	9	k2	k2	PROPN
ejpam-6264	132	10	.	.	PUNCT
ejpam-6264	133	1	let	let	VERB
ejpam-6264	133	2	v	v	X
ejpam-6264	133	3	(	(	PUNCT
ejpam-6264	133	4	g	g	NOUN
ejpam-6264	133	5	)	)	PUNCT
ejpam-6264	133	6	=	=	NOUN
ejpam-6264	133	7	{	{	PUNCT
ejpam-6264	133	8	a	a	DET
ejpam-6264	133	9	,	,	PUNCT
ejpam-6264	133	10	b	b	NOUN
ejpam-6264	133	11	}	}	PUNCT
ejpam-6264	133	12	,	,	PUNCT
ejpam-6264	133	13	then	then	ADV
ejpam-6264	133	14	f	f	PROPN
ejpam-6264	133	15	=	=	SYM
ejpam-6264	133	16	(	(	PUNCT
ejpam-6264	133	17	∅	∅	NOUN
ejpam-6264	133	18	,	,	PUNCT
ejpam-6264	133	19	{	{	PUNCT
ejpam-6264	133	20	a	a	X
ejpam-6264	133	21	}	}	PUNCT
ejpam-6264	133	22	,	,	PUNCT
ejpam-6264	133	23	{	{	PUNCT
ejpam-6264	133	24	b},∅	b},∅	NOUN
ejpam-6264	133	25	)	)	PUNCT
ejpam-6264	133	26	∈	∈	PROPN
ejpam-6264	133	27	tmrdf	tmrdf	NOUN
ejpam-6264	133	28	(	(	PUNCT
ejpam-6264	133	29	g+h	g+h	PROPN
ejpam-6264	133	30	)	)	PUNCT
ejpam-6264	133	31	.	.	PUNCT
ejpam-6264	134	1	thus	thus	ADV
ejpam-6264	134	2	,	,	PUNCT
ejpam-6264	134	3	γtmr(g	γtmr(g	NOUN
ejpam-6264	134	4	)	)	PUNCT
ejpam-6264	134	5	≤	≤	NOUN
ejpam-6264	134	6	ωtmr	ωtmr	ADV
ejpam-6264	134	7	g	g	PROPN
ejpam-6264	134	8	=	=	SYM
ejpam-6264	134	9	3	3	X
ejpam-6264	134	10	.	.	PUNCT
ejpam-6264	135	1	since	since	SCONJ
ejpam-6264	135	2	g	g	PROPN
ejpam-6264	135	3	can	can	AUX
ejpam-6264	135	4	not	not	PART
ejpam-6264	135	5	be	be	AUX
ejpam-6264	135	6	trivial	trivial	ADJ
ejpam-6264	135	7	,	,	PUNCT
ejpam-6264	135	8	γtmr(g	γtmr(g	NUM
ejpam-6264	135	9	)	)	PUNCT
ejpam-6264	135	10	≥	≥	NOUN
ejpam-6264	135	11	3	3	NUM
ejpam-6264	135	12	.	.	PUNCT
ejpam-6264	136	1	hence	hence	ADV
ejpam-6264	136	2	,	,	PUNCT
ejpam-6264	136	3	γtmr(g	γtmr(g	PROPN
ejpam-6264	136	4	+	+	CCONJ
ejpam-6264	136	5	h	h	NOUN
ejpam-6264	136	6	)	)	PUNCT
ejpam-6264	136	7	=	=	SYM
ejpam-6264	136	8	3	3	X
ejpam-6264	136	9	.	.	PUNCT
ejpam-6264	136	10	conversely	conversely	ADV
ejpam-6264	136	11	,	,	PUNCT
ejpam-6264	136	12	suppose	suppose	VERB
ejpam-6264	136	13	γtmr(g	γtmr(g	NUM
ejpam-6264	136	14	)	)	PUNCT
ejpam-6264	136	15	=	=	SYM
ejpam-6264	136	16	3	3	NUM
ejpam-6264	136	17	and	and	CCONJ
ejpam-6264	136	18	f	f	NOUN
ejpam-6264	136	19	=	=	SYM
ejpam-6264	136	20	(	(	PUNCT
ejpam-6264	136	21	v0	v0	PROPN
ejpam-6264	136	22	,	,	PUNCT
ejpam-6264	136	23	v1	v1	NOUN
ejpam-6264	136	24	,	,	PUNCT
ejpam-6264	136	25	v2	v2	PROPN
ejpam-6264	136	26	,	,	PUNCT
ejpam-6264	136	27	v3	v3	PROPN
ejpam-6264	136	28	)	)	PUNCT
ejpam-6264	136	29	a	a	DET
ejpam-6264	136	30	γtmr	γtmr	NOUN
ejpam-6264	136	31	-	-	PUNCT
ejpam-6264	136	32	function	function	NOUN
ejpam-6264	136	33	of	of	ADP
ejpam-6264	136	34	g.	g.	PROPN
ejpam-6264	136	35	then	then	ADV
ejpam-6264	136	36	v	v	X
ejpam-6264	136	37	(	(	PUNCT
ejpam-6264	136	38	g	g	NOUN
ejpam-6264	136	39	)	)	PUNCT
ejpam-6264	136	40	=	=	SYM
ejpam-6264	136	41	v1	v1	VERB
ejpam-6264	136	42	∪	∪	NOUN
ejpam-6264	136	43	v2	v2	NOUN
ejpam-6264	136	44	with	with	ADP
ejpam-6264	136	45	|v1|	|v1|	NOUN
ejpam-6264	136	46	=	=	SYM
ejpam-6264	136	47	|v2|	|v2|	NOUN
ejpam-6264	136	48	=	=	SYM
ejpam-6264	136	49	1	1	NUM
ejpam-6264	136	50	and	and	CCONJ
ejpam-6264	136	51	so	so	ADV
ejpam-6264	136	52	,	,	PUNCT
ejpam-6264	136	53	|v	|v	PROPN
ejpam-6264	136	54	(	(	PUNCT
ejpam-6264	136	55	g	g	PROPN
ejpam-6264	136	56	+	+	PROPN
ejpam-6264	136	57	h)|	h)|	NOUN
ejpam-6264	136	58	=	=	ADJ
ejpam-6264	136	59	2	2	X
ejpam-6264	136	60	.	.	PUNCT
ejpam-6264	137	1	moreover	moreover	ADV
ejpam-6264	137	2	,	,	PUNCT
ejpam-6264	137	3	⟨v1	⟨v1	PROPN
ejpam-6264	137	4	∪	∪	ADP
ejpam-6264	137	5	v2⟩	v2⟩	PROPN
ejpam-6264	137	6	is	be	AUX
ejpam-6264	137	7	connected	connect	VERB
ejpam-6264	137	8	.	.	PUNCT
ejpam-6264	138	1	thus	thus	ADV
ejpam-6264	138	2	,	,	PUNCT
ejpam-6264	138	3	g	g	PROPN
ejpam-6264	138	4	=	=	SYM
ejpam-6264	138	5	k2	k2	PROPN
ejpam-6264	138	6	.	.	PUNCT
ejpam-6264	139	1	(	(	PUNCT
ejpam-6264	139	2	ii	ii	NOUN
ejpam-6264	139	3	)	)	PUNCT
ejpam-6264	139	4	wlog	wlog	NOUN
ejpam-6264	139	5	,	,	PUNCT
ejpam-6264	139	6	we	we	PRON
ejpam-6264	139	7	assume	assume	VERB
ejpam-6264	139	8	that	that	SCONJ
ejpam-6264	139	9	g	g	NOUN
ejpam-6264	139	10	=	=	SYM
ejpam-6264	139	11	k3	k3	PROPN
ejpam-6264	139	12	.	.	PUNCT
ejpam-6264	140	1	let	let	VERB
ejpam-6264	140	2	v	v	X
ejpam-6264	140	3	(	(	PUNCT
ejpam-6264	140	4	g	g	NOUN
ejpam-6264	140	5	)	)	PUNCT
ejpam-6264	140	6	=	=	SYM
ejpam-6264	140	7	{	{	PUNCT
ejpam-6264	140	8	x	x	NOUN
ejpam-6264	140	9	,	,	PUNCT
ejpam-6264	140	10	y	y	PROPN
ejpam-6264	140	11	,	,	PUNCT
ejpam-6264	140	12	z	z	NOUN
ejpam-6264	140	13	}	}	PUNCT
ejpam-6264	140	14	.	.	PUNCT
ejpam-6264	141	1	define	define	VERB
ejpam-6264	141	2	a	a	DET
ejpam-6264	141	3	function	function	NOUN
ejpam-6264	141	4	f	f	NOUN
ejpam-6264	141	5	=	=	SYM
ejpam-6264	141	6	(	(	PUNCT
ejpam-6264	141	7	v0	v0	PROPN
ejpam-6264	141	8	,	,	PUNCT
ejpam-6264	141	9	v1	v1	NOUN
ejpam-6264	141	10	,	,	PUNCT
ejpam-6264	141	11	v2	v2	PROPN
ejpam-6264	141	12	,	,	PUNCT
ejpam-6264	141	13	v3	v3	PROPN
ejpam-6264	141	14	)	)	PUNCT
ejpam-6264	142	1	where	where	SCONJ
ejpam-6264	142	2	v0	v0	NOUN
ejpam-6264	142	3	=	=	SYM
ejpam-6264	142	4	∅	∅	NOUN
ejpam-6264	142	5	=	=	SYM
ejpam-6264	142	6	v3	v3	PROPN
ejpam-6264	142	7	,	,	PUNCT
ejpam-6264	142	8	v1	v1	NOUN
ejpam-6264	142	9	=	=	SYM
ejpam-6264	142	10	{	{	PUNCT
ejpam-6264	142	11	x	x	NOUN
ejpam-6264	142	12	,	,	PUNCT
ejpam-6264	142	13	z	z	NOUN
ejpam-6264	142	14	}	}	PUNCT
ejpam-6264	142	15	and	and	CCONJ
ejpam-6264	142	16	v2	v2	NOUN
ejpam-6264	142	17	=	=	SYM
ejpam-6264	142	18	{	{	PUNCT
ejpam-6264	142	19	y	y	NOUN
ejpam-6264	142	20	}	}	PUNCT
ejpam-6264	142	21	.	.	PUNCT
ejpam-6264	143	1	then	then	ADV
ejpam-6264	143	2	f	f	PROPN
ejpam-6264	143	3	∈	∈	PROPN
ejpam-6264	143	4	tmrdf	tmrdf	NOUN
ejpam-6264	143	5	(	(	PUNCT
ejpam-6264	143	6	g	g	NOUN
ejpam-6264	143	7	)	)	PUNCT
ejpam-6264	143	8	and	and	CCONJ
ejpam-6264	143	9	thus	thus	ADV
ejpam-6264	143	10	,	,	PUNCT
ejpam-6264	143	11	γtmr(g	γtmr(g	NOUN
ejpam-6264	143	12	)	)	PUNCT
ejpam-6264	143	13	≤	≤	NOUN
ejpam-6264	143	14	ωtmr	ωtmr	ADJ
ejpam-6264	143	15	g+h(f	g+h(f	NOUN
ejpam-6264	143	16	)	)	PUNCT
ejpam-6264	143	17	=	=	NOUN
ejpam-6264	143	18	|v1|	|v1|	NOUN
ejpam-6264	143	19	+	+	CCONJ
ejpam-6264	143	20	2|v2|	2|v2|	NUM
ejpam-6264	143	21	=	=	SYM
ejpam-6264	143	22	4	4	X
ejpam-6264	143	23	.	.	PUNCT
ejpam-6264	143	24	since	since	ADV
ejpam-6264	143	25	,	,	PUNCT
ejpam-6264	143	26	g	g	PROPN
ejpam-6264	143	27	̸=	̸=	PROPN
ejpam-6264	143	28	k2	k2	PROPN
ejpam-6264	143	29	,	,	PUNCT
ejpam-6264	143	30	γtmr(g	γtmr(g	NOUN
ejpam-6264	143	31	)	)	PUNCT
ejpam-6264	143	32	≥	≥	NOUN
ejpam-6264	143	33	4	4	NUM
ejpam-6264	143	34	by	by	ADP
ejpam-6264	143	35	(	(	PUNCT
ejpam-6264	143	36	i	i	NOUN
ejpam-6264	143	37	)	)	PUNCT
ejpam-6264	143	38	.	.	PUNCT
ejpam-6264	144	1	hence	hence	ADV
ejpam-6264	144	2	,	,	PUNCT
ejpam-6264	144	3	γtmr(g	γtmr(g	PROPN
ejpam-6264	144	4	)	)	PUNCT
ejpam-6264	144	5	=	=	SYM
ejpam-6264	144	6	4	4	X
ejpam-6264	144	7	.	.	PUNCT
ejpam-6264	144	8	conversely	conversely	ADV
ejpam-6264	144	9	,	,	PUNCT
ejpam-6264	144	10	suppose	suppose	VERB
ejpam-6264	144	11	that	that	SCONJ
ejpam-6264	144	12	γtmr(g	γtmr(g	NOUN
ejpam-6264	144	13	)	)	PUNCT
ejpam-6264	144	14	=	=	SYM
ejpam-6264	144	15	4	4	NUM
ejpam-6264	144	16	and	and	CCONJ
ejpam-6264	144	17	f	f	NOUN
ejpam-6264	144	18	=	=	SYM
ejpam-6264	144	19	(	(	PUNCT
ejpam-6264	144	20	v0	v0	PROPN
ejpam-6264	144	21	,	,	PUNCT
ejpam-6264	144	22	v1	v1	NOUN
ejpam-6264	144	23	,	,	PUNCT
ejpam-6264	144	24	v2	v2	PROPN
ejpam-6264	144	25	,	,	PUNCT
ejpam-6264	144	26	v3	v3	PROPN
ejpam-6264	144	27	)	)	PUNCT
ejpam-6264	144	28	is	be	AUX
ejpam-6264	144	29	a	a	DET
ejpam-6264	144	30	s.	s.	PROPN
ejpam-6264	144	31	ahamad	ahamad	PROPN
ejpam-6264	144	32	et	et	PROPN
ejpam-6264	144	33	al	al	PROPN
ejpam-6264	144	34	.	.	PUNCT
ejpam-6264	144	35	/	/	SYM
ejpam-6264	144	36	eur	eur	PROPN
ejpam-6264	144	37	.	.	PUNCT
ejpam-6264	145	1	j.	j.	PROPN
ejpam-6264	145	2	pure	pure	PROPN
ejpam-6264	145	3	appl	appl	PROPN
ejpam-6264	145	4	.	.	PROPN
ejpam-6264	145	5	math	math	PROPN
ejpam-6264	145	6	,	,	PUNCT
ejpam-6264	145	7	18	18	NUM
ejpam-6264	145	8	(	(	PUNCT
ejpam-6264	145	9	4	4	NUM
ejpam-6264	145	10	)	)	PUNCT
ejpam-6264	145	11	(	(	PUNCT
ejpam-6264	145	12	2025	2025	NUM
ejpam-6264	145	13	)	)	PUNCT
ejpam-6264	145	14	,	,	PUNCT
ejpam-6264	145	15	6264	6264	NUM
ejpam-6264	145	16	7	7	NUM
ejpam-6264	145	17	of	of	ADP
ejpam-6264	145	18	20	20	NUM
ejpam-6264	145	19	γtmr	γtmr	ADJ
ejpam-6264	145	20	-	-	PUNCT
ejpam-6264	145	21	function	function	NOUN
ejpam-6264	145	22	of	of	ADP
ejpam-6264	145	23	g.	g.	PROPN
ejpam-6264	145	24	then	then	ADV
ejpam-6264	145	25	γtmr(g	γtmr(g	NUM
ejpam-6264	145	26	)	)	PUNCT
ejpam-6264	146	1	=	=	NOUN
ejpam-6264	146	2	|v1|	|v1|	NOUN
ejpam-6264	146	3	+	+	CCONJ
ejpam-6264	146	4	|v2|	|v2|	NOUN
ejpam-6264	146	5	+	+	CCONJ
ejpam-6264	146	6	|v3|	|v3|	NOUN
ejpam-6264	146	7	=	=	SYM
ejpam-6264	146	8	4	4	X
ejpam-6264	146	9	.	.	PUNCT
ejpam-6264	147	1	if	if	SCONJ
ejpam-6264	147	2	|v3|	|v3|	NOUN
ejpam-6264	147	3	=	=	SYM
ejpam-6264	147	4	1	1	NUM
ejpam-6264	147	5	,	,	PUNCT
ejpam-6264	147	6	then	then	ADV
ejpam-6264	147	7	|v1|	|v1|	NOUN
ejpam-6264	147	8	=	=	SYM
ejpam-6264	147	9	1	1	X
ejpam-6264	147	10	.	.	PUNCT
ejpam-6264	148	1	this	this	PRON
ejpam-6264	148	2	implies	imply	VERB
ejpam-6264	148	3	that	that	SCONJ
ejpam-6264	148	4	|v	|v	PROPN
ejpam-6264	148	5	(	(	PUNCT
ejpam-6264	148	6	g)|	g)|	NOUN
ejpam-6264	148	7	=	=	SYM
ejpam-6264	148	8	2	2	NUM
ejpam-6264	148	9	and	and	CCONJ
ejpam-6264	148	10	so	so	ADV
ejpam-6264	148	11	,	,	PUNCT
ejpam-6264	148	12	g	g	PROPN
ejpam-6264	148	13	=	=	SYM
ejpam-6264	148	14	k2	k2	PROPN
ejpam-6264	148	15	since	since	SCONJ
ejpam-6264	148	16	⟨v1	⟨v1	PROPN
ejpam-6264	148	17	∪	∪	ADP
ejpam-6264	148	18	v3⟩	v3⟩	PRON
ejpam-6264	148	19	must	must	AUX
ejpam-6264	148	20	be	be	AUX
ejpam-6264	148	21	connected	connect	VERB
ejpam-6264	148	22	.	.	PUNCT
ejpam-6264	149	1	but	but	CCONJ
ejpam-6264	149	2	γtmr(k2	γtmr(k2	NOUN
ejpam-6264	149	3	)	)	PUNCT
ejpam-6264	150	1	=	=	SYM
ejpam-6264	150	2	3	3	X
ejpam-6264	150	3	.	.	PUNCT
ejpam-6264	150	4	thus	thus	ADV
ejpam-6264	150	5	,	,	PUNCT
ejpam-6264	150	6	|v3|	|v3|	NOUN
ejpam-6264	150	7	=	=	SYM
ejpam-6264	150	8	0	0	X
ejpam-6264	150	9	.	.	PUNCT
ejpam-6264	151	1	it	it	PRON
ejpam-6264	151	2	follows	follow	VERB
ejpam-6264	151	3	that	that	SCONJ
ejpam-6264	151	4	|v0|	|v0|	NOUN
ejpam-6264	151	5	=	=	SYM
ejpam-6264	151	6	0	0	X
ejpam-6264	151	7	.	.	PUNCT
ejpam-6264	152	1	similarly	similarly	ADV
ejpam-6264	152	2	,	,	PUNCT
ejpam-6264	152	3	|v2|	|v2|	ADV
ejpam-6264	152	4	̸=	̸=	PROPN
ejpam-6264	152	5	2	2	NUM
ejpam-6264	152	6	and	and	CCONJ
ejpam-6264	152	7	so	so	ADV
ejpam-6264	152	8	,	,	PUNCT
ejpam-6264	152	9	|v2|	|v2|	ADV
ejpam-6264	152	10	≤	≤	NOUN
ejpam-6264	152	11	1	1	NUM
ejpam-6264	152	12	.	.	PUNCT
ejpam-6264	153	1	moreover	moreover	ADV
ejpam-6264	153	2	,	,	PUNCT
ejpam-6264	153	3	if	if	SCONJ
ejpam-6264	153	4	v2	v2	NOUN
ejpam-6264	153	5	=	=	NOUN
ejpam-6264	153	6	∅	∅	NOUN
ejpam-6264	153	7	,	,	PUNCT
ejpam-6264	153	8	that	that	PRON
ejpam-6264	153	9	is	be	AUX
ejpam-6264	153	10	v	v	NOUN
ejpam-6264	153	11	(	(	PUNCT
ejpam-6264	153	12	g	g	NOUN
ejpam-6264	153	13	)	)	PUNCT
ejpam-6264	153	14	=	=	SYM
ejpam-6264	153	15	v1	v1	NOUN
ejpam-6264	153	16	,	,	PUNCT
ejpam-6264	153	17	then	then	ADV
ejpam-6264	153	18	(	(	PUNCT
ejpam-6264	153	19	p2	p2	PROPN
ejpam-6264	153	20	)	)	PUNCT
ejpam-6264	153	21	is	be	AUX
ejpam-6264	153	22	not	not	PART
ejpam-6264	153	23	satisfied	satisfied	ADJ
ejpam-6264	153	24	.	.	PUNCT
ejpam-6264	154	1	thus	thus	ADV
ejpam-6264	154	2	,	,	PUNCT
ejpam-6264	154	3	|v2|	|v2|	NOUN
ejpam-6264	154	4	=	=	SYM
ejpam-6264	154	5	1	1	NUM
ejpam-6264	154	6	and	and	CCONJ
ejpam-6264	154	7	hence	hence	ADV
ejpam-6264	154	8	,	,	PUNCT
ejpam-6264	154	9	|v1|	|v1|	NOUN
ejpam-6264	154	10	=	=	SYM
ejpam-6264	154	11	2	2	X
ejpam-6264	154	12	.	.	PUNCT
ejpam-6264	155	1	moreover	moreover	ADV
ejpam-6264	155	2	,	,	PUNCT
ejpam-6264	155	3	the	the	DET
ejpam-6264	155	4	induced	induced	ADJ
ejpam-6264	155	5	subgraph	subgraph	NOUN
ejpam-6264	155	6	⟨v1	⟨v1	PROPN
ejpam-6264	155	7	∪	∪	ADP
ejpam-6264	155	8	v2⟩	v2⟩	PROPN
ejpam-6264	155	9	is	be	AUX
ejpam-6264	155	10	isolated	isolate	VERB
ejpam-6264	155	11	-	-	PUNCT
ejpam-6264	155	12	free	free	ADJ
ejpam-6264	155	13	.	.	PUNCT
ejpam-6264	156	1	this	this	PRON
ejpam-6264	156	2	means	mean	VERB
ejpam-6264	156	3	that	that	SCONJ
ejpam-6264	156	4	since	since	SCONJ
ejpam-6264	156	5	g	g	PROPN
ejpam-6264	156	6	is	be	AUX
ejpam-6264	156	7	connected	connect	VERB
ejpam-6264	156	8	,	,	PUNCT
ejpam-6264	156	9	|v	|v	PROPN
ejpam-6264	156	10	(	(	PUNCT
ejpam-6264	156	11	g)|	g)|	NOUN
ejpam-6264	156	12	=	=	PUNCT
ejpam-6264	156	13	|v1	|v1	NOUN
ejpam-6264	156	14	∪	∪	X
ejpam-6264	156	15	v2|	v2|	X
ejpam-6264	157	1	=	=	SYM
ejpam-6264	157	2	3	3	X
ejpam-6264	157	3	.	.	X
ejpam-6264	158	1	therefore	therefore	ADV
ejpam-6264	158	2	,	,	PUNCT
ejpam-6264	158	3	g	g	PROPN
ejpam-6264	158	4	=	=	SYM
ejpam-6264	158	5	k3	k3	PROPN
ejpam-6264	158	6	.	.	PUNCT
ejpam-6264	159	1	proposition	proposition	NOUN
ejpam-6264	159	2	8	8	NUM
ejpam-6264	159	3	.	.	PUNCT
ejpam-6264	160	1	for	for	ADP
ejpam-6264	160	2	a	a	DET
ejpam-6264	160	3	connected	connected	ADJ
ejpam-6264	160	4	graph	graph	NOUN
ejpam-6264	160	5	g	g	PROPN
ejpam-6264	160	6	,	,	PUNCT
ejpam-6264	160	7	γtmr(g	γtmr(g	NOUN
ejpam-6264	160	8	)	)	PUNCT
ejpam-6264	160	9	=	=	SYM
ejpam-6264	160	10	5	5	NUM
ejpam-6264	160	11	if	if	SCONJ
ejpam-6264	160	12	and	and	CCONJ
ejpam-6264	160	13	only	only	ADV
ejpam-6264	160	14	if	if	SCONJ
ejpam-6264	160	15	|v	|v	PROPN
ejpam-6264	160	16	(	(	PUNCT
ejpam-6264	160	17	g)|	g)|	NOUN
ejpam-6264	160	18	=	=	SYM
ejpam-6264	160	19	4	4	NUM
ejpam-6264	160	20	and	and	CCONJ
ejpam-6264	160	21	γ(g	γ(g	PROPN
ejpam-6264	160	22	)	)	PUNCT
ejpam-6264	160	23	=	=	SYM
ejpam-6264	160	24	1	1	NUM
ejpam-6264	160	25	or	or	CCONJ
ejpam-6264	160	26	γt2(g	γt2(g	NUM
ejpam-6264	160	27	)	)	PUNCT
ejpam-6264	160	28	=	=	SYM
ejpam-6264	160	29	2	2	NUM
ejpam-6264	160	30	and	and	CCONJ
ejpam-6264	160	31	|v	|v	PROPN
ejpam-6264	160	32	(	(	PUNCT
ejpam-6264	160	33	g)|	g)|	X
ejpam-6264	160	34	≥	≥	NOUN
ejpam-6264	160	35	4	4	NUM
ejpam-6264	160	36	.	.	PUNCT
ejpam-6264	161	1	proof	proof	NOUN
ejpam-6264	161	2	.	.	PUNCT
ejpam-6264	162	1	if	if	SCONJ
ejpam-6264	162	2	γtmr(g	γtmr(g	NUM
ejpam-6264	162	3	)	)	PUNCT
ejpam-6264	162	4	=	=	SYM
ejpam-6264	162	5	5	5	NUM
ejpam-6264	162	6	,	,	PUNCT
ejpam-6264	162	7	then	then	ADV
ejpam-6264	162	8	|v3|	|v3|	VERB
ejpam-6264	162	9	≤	≤	NUM
ejpam-6264	162	10	1	1	NUM
ejpam-6264	162	11	and	and	CCONJ
ejpam-6264	162	12	1	1	NUM
ejpam-6264	162	13	≤	≤	NOUN
ejpam-6264	162	14	|v2|	|v2|	NOUN
ejpam-6264	162	15	≤	≤	NOUN
ejpam-6264	162	16	2	2	NUM
ejpam-6264	162	17	.	.	PUNCT
ejpam-6264	163	1	also	also	ADV
ejpam-6264	163	2	,	,	PUNCT
ejpam-6264	163	3	by	by	ADP
ejpam-6264	163	4	proposition	proposition	NOUN
ejpam-6264	163	5	7	7	NUM
ejpam-6264	163	6	(	(	PUNCT
ejpam-6264	163	7	ii	ii	NOUN
ejpam-6264	163	8	)	)	PUNCT
ejpam-6264	163	9	,	,	PUNCT
ejpam-6264	163	10	|v	|v	PROPN
ejpam-6264	163	11	(	(	PUNCT
ejpam-6264	163	12	g)|	g)|	X
ejpam-6264	163	13	≥	≥	NOUN
ejpam-6264	163	14	4	4	NUM
ejpam-6264	163	15	.	.	PUNCT
ejpam-6264	164	1	now	now	ADV
ejpam-6264	164	2	,	,	PUNCT
ejpam-6264	164	3	if	if	SCONJ
ejpam-6264	164	4	|v3|	|v3|	NOUN
ejpam-6264	164	5	=	=	SYM
ejpam-6264	164	6	0	0	PROPN
ejpam-6264	164	7	,	,	PUNCT
ejpam-6264	164	8	then	then	ADV
ejpam-6264	164	9	|v0|	|v0|	NOUN
ejpam-6264	164	10	=	=	SYM
ejpam-6264	164	11	0	0	X
ejpam-6264	164	12	.	.	PUNCT
ejpam-6264	165	1	hence	hence	ADV
ejpam-6264	165	2	,	,	PUNCT
ejpam-6264	165	3	there	there	PRON
ejpam-6264	165	4	are	be	VERB
ejpam-6264	165	5	only	only	ADV
ejpam-6264	165	6	two	two	NUM
ejpam-6264	165	7	cases	case	NOUN
ejpam-6264	165	8	to	to	PART
ejpam-6264	165	9	consider	consider	VERB
ejpam-6264	165	10	,	,	PUNCT
ejpam-6264	165	11	namely	namely	ADV
ejpam-6264	165	12	,	,	PUNCT
ejpam-6264	165	13	|v2|	|v2|	NOUN
ejpam-6264	165	14	=	=	SYM
ejpam-6264	165	15	1	1	NUM
ejpam-6264	165	16	and	and	CCONJ
ejpam-6264	165	17	|v2|	|v2|	ADV
ejpam-6264	165	18	≤	≤	NOUN
ejpam-6264	165	19	2	2	NUM
ejpam-6264	165	20	.	.	PUNCT
ejpam-6264	166	1	if	if	SCONJ
ejpam-6264	166	2	|v2|	|v2|	NOUN
ejpam-6264	166	3	=	=	SYM
ejpam-6264	166	4	2	2	NUM
ejpam-6264	166	5	,	,	PUNCT
ejpam-6264	166	6	then	then	ADV
ejpam-6264	166	7	|v1|	|v1|	NOUN
ejpam-6264	166	8	=	=	SYM
ejpam-6264	166	9	1	1	X
ejpam-6264	166	10	.	.	PUNCT
ejpam-6264	166	11	therefore	therefore	ADV
ejpam-6264	166	12	,	,	PUNCT
ejpam-6264	166	13	|v	|v	PROPN
ejpam-6264	166	14	(	(	PUNCT
ejpam-6264	166	15	g)|	g)|	NOUN
ejpam-6264	166	16	=	=	SYM
ejpam-6264	166	17	3	3	NUM
ejpam-6264	166	18	which	which	PRON
ejpam-6264	166	19	is	be	AUX
ejpam-6264	166	20	not	not	PART
ejpam-6264	166	21	possible	possible	ADJ
ejpam-6264	166	22	by	by	ADP
ejpam-6264	166	23	proposition	proposition	NOUN
ejpam-6264	166	24	7	7	NUM
ejpam-6264	166	25	(	(	PUNCT
ejpam-6264	166	26	ii	ii	NOUN
ejpam-6264	166	27	)	)	PUNCT
ejpam-6264	166	28	.	.	PUNCT
ejpam-6264	167	1	if	if	SCONJ
ejpam-6264	167	2	|v2|	|v2|	NOUN
ejpam-6264	167	3	=	=	SYM
ejpam-6264	167	4	1	1	NUM
ejpam-6264	167	5	,	,	PUNCT
ejpam-6264	167	6	then	then	ADV
ejpam-6264	167	7	|v1|	|v1|	NOUN
ejpam-6264	167	8	=	=	SYM
ejpam-6264	167	9	3	3	X
ejpam-6264	167	10	.	.	PUNCT
ejpam-6264	167	11	by	by	ADP
ejpam-6264	167	12	(	(	PUNCT
ejpam-6264	167	13	p2	p2	PROPN
ejpam-6264	167	14	)	)	PUNCT
ejpam-6264	167	15	,	,	PUNCT
ejpam-6264	167	16	⟨v1	⟨v1	PROPN
ejpam-6264	167	17	∪	∪	ADP
ejpam-6264	167	18	v2⟩	v2⟩	PROPN
ejpam-6264	167	19	must	must	AUX
ejpam-6264	167	20	be	be	AUX
ejpam-6264	167	21	connected	connect	VERB
ejpam-6264	167	22	and	and	CCONJ
ejpam-6264	167	23	v2	v2	NOUN
ejpam-6264	167	24	is	be	AUX
ejpam-6264	167	25	a	a	DET
ejpam-6264	167	26	dominating	dominating	NOUN
ejpam-6264	167	27	set	set	NOUN
ejpam-6264	167	28	in	in	ADP
ejpam-6264	167	29	g	g	PROPN
ejpam-6264	167	30	,	,	PUNCT
ejpam-6264	167	31	it	it	PRON
ejpam-6264	167	32	follows	follow	VERB
ejpam-6264	167	33	that	that	SCONJ
ejpam-6264	167	34	v2	v2	PROPN
ejpam-6264	167	35	is	be	AUX
ejpam-6264	167	36	a	a	DET
ejpam-6264	167	37	γ	γ	NOUN
ejpam-6264	167	38	-	-	PUNCT
ejpam-6264	167	39	set	set	VERB
ejpam-6264	167	40	in	in	ADP
ejpam-6264	167	41	g.	g.	PROPN
ejpam-6264	167	42	therefore	therefore	ADV
ejpam-6264	167	43	,	,	PUNCT
ejpam-6264	167	44	|v	|v	PROPN
ejpam-6264	167	45	(	(	PUNCT
ejpam-6264	167	46	g)|	g)|	NOUN
ejpam-6264	167	47	=	=	SYM
ejpam-6264	167	48	4	4	NUM
ejpam-6264	167	49	and	and	CCONJ
ejpam-6264	167	50	γ(g	γ(g	PROPN
ejpam-6264	167	51	)	)	PUNCT
ejpam-6264	168	1	=	=	PUNCT
ejpam-6264	168	2	1	1	X
ejpam-6264	168	3	.	.	PUNCT
ejpam-6264	168	4	now	now	ADV
ejpam-6264	168	5	,	,	PUNCT
ejpam-6264	168	6	suppose	suppose	VERB
ejpam-6264	168	7	that	that	SCONJ
ejpam-6264	168	8	|v3|	|v3|	NOUN
ejpam-6264	168	9	=	=	NOUN
ejpam-6264	168	10	1	1	X
ejpam-6264	168	11	.	.	PUNCT
ejpam-6264	169	1	if	if	SCONJ
ejpam-6264	169	2	|v2|	|v2|	NOUN
ejpam-6264	169	3	=	=	SYM
ejpam-6264	169	4	0	0	NUM
ejpam-6264	169	5	,	,	PUNCT
ejpam-6264	169	6	then	then	ADV
ejpam-6264	169	7	|v1|	|v1|	NOUN
ejpam-6264	169	8	=	=	SYM
ejpam-6264	169	9	2	2	X
ejpam-6264	169	10	.	.	PUNCT
ejpam-6264	169	11	consequently	consequently	ADV
ejpam-6264	169	12	,	,	PUNCT
ejpam-6264	169	13	|v	|v	PROPN
ejpam-6264	169	14	(	(	PUNCT
ejpam-6264	169	15	g)|	g)|	NOUN
ejpam-6264	169	16	=	=	SYM
ejpam-6264	169	17	3	3	NUM
ejpam-6264	169	18	.	.	PUNCT
ejpam-6264	170	1	thus	thus	ADV
ejpam-6264	170	2	,	,	PUNCT
ejpam-6264	170	3	g	g	PROPN
ejpam-6264	170	4	∈	∈	PROPN
ejpam-6264	170	5	{	{	PUNCT
ejpam-6264	170	6	k3	k3	PROPN
ejpam-6264	170	7	,	,	PUNCT
ejpam-6264	170	8	p3	p3	PROPN
ejpam-6264	170	9	}	}	PUNCT
ejpam-6264	170	10	,	,	PUNCT
ejpam-6264	170	11	a	a	DET
ejpam-6264	170	12	contradiction	contradiction	NOUN
ejpam-6264	170	13	by	by	ADP
ejpam-6264	170	14	proposition	proposition	NOUN
ejpam-6264	170	15	7	7	NUM
ejpam-6264	170	16	(	(	PUNCT
ejpam-6264	170	17	ii	ii	NOUN
ejpam-6264	170	18	)	)	PUNCT
ejpam-6264	170	19	.	.	PUNCT
ejpam-6264	171	1	if	if	SCONJ
ejpam-6264	171	2	|v2|	|v2|	NOUN
ejpam-6264	171	3	=	=	SYM
ejpam-6264	171	4	1	1	NUM
ejpam-6264	171	5	,	,	PUNCT
ejpam-6264	171	6	then	then	ADV
ejpam-6264	171	7	|v1|	|v1|	NOUN
ejpam-6264	171	8	=	=	SYM
ejpam-6264	171	9	0	0	X
ejpam-6264	171	10	.	.	PUNCT
ejpam-6264	172	1	it	it	PRON
ejpam-6264	172	2	follows	follow	VERB
ejpam-6264	172	3	that	that	SCONJ
ejpam-6264	172	4	|v2	|v2	NOUN
ejpam-6264	172	5	∪	∪	ADP
ejpam-6264	172	6	v3|	v3|	NOUN
ejpam-6264	172	7	=	=	SYM
ejpam-6264	172	8	2	2	X
ejpam-6264	172	9	.	.	PUNCT
ejpam-6264	172	10	by	by	ADP
ejpam-6264	172	11	proposition	proposition	NOUN
ejpam-6264	172	12	6	6	NUM
ejpam-6264	172	13	,	,	PUNCT
ejpam-6264	172	14	v2	v2	PROPN
ejpam-6264	172	15	∪	∪	X
ejpam-6264	172	16	v3	v3	PROPN
ejpam-6264	172	17	is	be	AUX
ejpam-6264	172	18	a	a	DET
ejpam-6264	172	19	γt2	γt2	NOUN
ejpam-6264	172	20	-	-	PUNCT
ejpam-6264	172	21	set	set	NOUN
ejpam-6264	172	22	in	in	ADP
ejpam-6264	172	23	g.	g.	PROPN
ejpam-6264	172	24	hence	hence	ADV
ejpam-6264	172	25	,	,	PUNCT
ejpam-6264	172	26	|v	|v	PROPN
ejpam-6264	172	27	(	(	PUNCT
ejpam-6264	172	28	g)|	g)|	X
ejpam-6264	172	29	≥	≥	NUM
ejpam-6264	172	30	4	4	NUM
ejpam-6264	172	31	and	and	CCONJ
ejpam-6264	172	32	γt2(g	γt2(g	NUM
ejpam-6264	172	33	)	)	PUNCT
ejpam-6264	172	34	=	=	SYM
ejpam-6264	172	35	2	2	X
ejpam-6264	172	36	.	.	PUNCT
ejpam-6264	172	37	conversely	conversely	ADV
ejpam-6264	172	38	,	,	PUNCT
ejpam-6264	172	39	suppose	suppose	VERB
ejpam-6264	172	40	|v	|v	PROPN
ejpam-6264	172	41	(	(	PUNCT
ejpam-6264	172	42	g)|	g)|	NOUN
ejpam-6264	172	43	=	=	SYM
ejpam-6264	172	44	4	4	NUM
ejpam-6264	172	45	and	and	CCONJ
ejpam-6264	172	46	γ(g	γ(g	PROPN
ejpam-6264	172	47	)	)	PUNCT
ejpam-6264	173	1	=	=	SYM
ejpam-6264	173	2	1	1	X
ejpam-6264	173	3	.	.	PUNCT
ejpam-6264	173	4	by	by	ADP
ejpam-6264	173	5	proposition	proposition	NOUN
ejpam-6264	173	6	7	7	NUM
ejpam-6264	173	7	(	(	PUNCT
ejpam-6264	173	8	ii	ii	NOUN
ejpam-6264	173	9	)	)	PUNCT
ejpam-6264	173	10	,	,	PUNCT
ejpam-6264	173	11	γ(g	γ(g	PROPN
ejpam-6264	173	12	)	)	PUNCT
ejpam-6264	173	13	≥	≥	NOUN
ejpam-6264	173	14	5	5	NUM
ejpam-6264	173	15	.	.	PUNCT
ejpam-6264	174	1	let	let	VERB
ejpam-6264	174	2	v	v	PART
ejpam-6264	174	3	be	be	AUX
ejpam-6264	174	4	a	a	DET
ejpam-6264	174	5	dominating	dominating	NOUN
ejpam-6264	174	6	vertex	vertex	NOUN
ejpam-6264	174	7	of	of	ADP
ejpam-6264	174	8	g	g	NOUN
ejpam-6264	174	9	and	and	CCONJ
ejpam-6264	174	10	define	define	VERB
ejpam-6264	174	11	a	a	DET
ejpam-6264	174	12	function	function	NOUN
ejpam-6264	174	13	f	f	NOUN
ejpam-6264	174	14	=	=	SYM
ejpam-6264	174	15	(	(	PUNCT
ejpam-6264	174	16	v0	v0	PROPN
ejpam-6264	174	17	,	,	PUNCT
ejpam-6264	174	18	v1	v1	NOUN
ejpam-6264	174	19	,	,	PUNCT
ejpam-6264	174	20	v2	v2	PROPN
ejpam-6264	174	21	,	,	PUNCT
ejpam-6264	174	22	v3	v3	PROPN
ejpam-6264	174	23	)	)	PUNCT
ejpam-6264	174	24	on	on	ADP
ejpam-6264	174	25	v	v	ADP
ejpam-6264	174	26	(	(	PUNCT
ejpam-6264	174	27	g	g	NOUN
ejpam-6264	174	28	)	)	PUNCT
ejpam-6264	174	29	such	such	ADJ
ejpam-6264	174	30	that	that	DET
ejpam-6264	174	31	v0	v0	NOUN
ejpam-6264	174	32	=	=	SYM
ejpam-6264	174	33	∅	∅	NOUN
ejpam-6264	174	34	=	=	SYM
ejpam-6264	174	35	v3	v3	PROPN
ejpam-6264	174	36	,	,	PUNCT
ejpam-6264	174	37	v2	v2	PROPN
ejpam-6264	174	38	=	=	SYM
ejpam-6264	174	39	{	{	PUNCT
ejpam-6264	174	40	v	v	NOUN
ejpam-6264	174	41	}	}	PUNCT
ejpam-6264	174	42	,	,	PUNCT
ejpam-6264	174	43	v1	v1	NOUN
ejpam-6264	174	44	=	=	SYM
ejpam-6264	174	45	v	v	NOUN
ejpam-6264	174	46	(	(	PUNCT
ejpam-6264	174	47	g	g	NOUN
ejpam-6264	174	48	)	)	PUNCT
ejpam-6264	174	49	\	\	NOUN
ejpam-6264	174	50	{	{	PUNCT
ejpam-6264	174	51	v	v	NOUN
ejpam-6264	174	52	}	}	PUNCT
ejpam-6264	174	53	.	.	PUNCT
ejpam-6264	175	1	then	then	ADV
ejpam-6264	175	2	f	f	PROPN
ejpam-6264	175	3	∈	∈	PROPN
ejpam-6264	175	4	tmrdf	tmrdf	NOUN
ejpam-6264	175	5	(	(	PUNCT
ejpam-6264	175	6	g	g	NOUN
ejpam-6264	175	7	)	)	PUNCT
ejpam-6264	175	8	and	and	CCONJ
ejpam-6264	175	9	ωtmr	ωtmr	PROPN
ejpam-6264	175	10	g	g	PROPN
ejpam-6264	175	11	(	(	PUNCT
ejpam-6264	175	12	f	f	X
ejpam-6264	175	13	)	)	PUNCT
ejpam-6264	175	14	=	=	SYM
ejpam-6264	175	15	5	5	X
ejpam-6264	175	16	.	.	PUNCT
ejpam-6264	176	1	this	this	PRON
ejpam-6264	176	2	implies	imply	VERB
ejpam-6264	176	3	that	that	SCONJ
ejpam-6264	176	4	γtmr(g	γtmr(g	NUM
ejpam-6264	176	5	)	)	PUNCT
ejpam-6264	176	6	=	=	SYM
ejpam-6264	177	1	5	5	X
ejpam-6264	177	2	.	.	PUNCT
ejpam-6264	178	1	next	next	ADV
ejpam-6264	178	2	,	,	PUNCT
ejpam-6264	178	3	suppose	suppose	VERB
ejpam-6264	178	4	that	that	SCONJ
ejpam-6264	178	5	γt2(g	γt2(g	VERB
ejpam-6264	178	6	)	)	PUNCT
ejpam-6264	178	7	=	=	SYM
ejpam-6264	178	8	2	2	NUM
ejpam-6264	178	9	and	and	CCONJ
ejpam-6264	178	10	|v	|v	PROPN
ejpam-6264	178	11	(	(	PUNCT
ejpam-6264	178	12	g)|	g)|	X
ejpam-6264	178	13	≥	≥	NOUN
ejpam-6264	178	14	4	4	NUM
ejpam-6264	178	15	.	.	PUNCT
ejpam-6264	179	1	let	let	VERB
ejpam-6264	179	2	d	d	NOUN
ejpam-6264	179	3	=	=	PUNCT
ejpam-6264	179	4	{	{	PUNCT
ejpam-6264	179	5	u	u	NOUN
ejpam-6264	179	6	,	,	PUNCT
ejpam-6264	179	7	v	v	NOUN
ejpam-6264	179	8	}	}	PUNCT
ejpam-6264	179	9	be	be	AUX
ejpam-6264	179	10	the	the	DET
ejpam-6264	179	11	γt2	γt2	NOUN
ejpam-6264	179	12	-	-	PUNCT
ejpam-6264	179	13	set	set	NOUN
ejpam-6264	179	14	of	of	ADP
ejpam-6264	179	15	g.	g.	PROPN
ejpam-6264	179	16	define	define	VERB
ejpam-6264	179	17	a	a	DET
ejpam-6264	179	18	function	function	NOUN
ejpam-6264	179	19	g	g	NOUN
ejpam-6264	179	20	=	=	SYM
ejpam-6264	179	21	(	(	PUNCT
ejpam-6264	179	22	v0	v0	PROPN
ejpam-6264	179	23	,	,	PUNCT
ejpam-6264	179	24	v1	v1	NOUN
ejpam-6264	179	25	,	,	PUNCT
ejpam-6264	179	26	v2	v2	PROPN
ejpam-6264	179	27	,	,	PUNCT
ejpam-6264	179	28	v3	v3	PROPN
ejpam-6264	179	29	)	)	PUNCT
ejpam-6264	179	30	such	such	ADJ
ejpam-6264	179	31	that	that	DET
ejpam-6264	179	32	v1	v1	NOUN
ejpam-6264	179	33	=	=	SYM
ejpam-6264	179	34	∅	∅	NOUN
ejpam-6264	179	35	and	and	CCONJ
ejpam-6264	179	36	g(x	g(x	NOUN
ejpam-6264	179	37	)	)	PUNCT
ejpam-6264	180	1	=	=	SYM
ejpam-6264	180	2			NOUN
ejpam-6264	180	3	3	3	NUM
ejpam-6264	180	4	,	,	PUNCT
ejpam-6264	180	5	if	if	SCONJ
ejpam-6264	180	6	x	x	ADP
ejpam-6264	180	7	=	=	PUNCT
ejpam-6264	180	8	u.	u.	NOUN
ejpam-6264	180	9	2	2	NUM
ejpam-6264	180	10	,	,	PUNCT
ejpam-6264	180	11	if	if	SCONJ
ejpam-6264	180	12	x	x	ADP
ejpam-6264	180	13	=	=	SYM
ejpam-6264	180	14	v	v	ADP
ejpam-6264	180	15	0	0	NUM
ejpam-6264	180	16	,	,	PUNCT
ejpam-6264	180	17	if	if	SCONJ
ejpam-6264	180	18	x	x	PROPN
ejpam-6264	180	19	∈	∈	PROPN
ejpam-6264	180	20	v	v	ADP
ejpam-6264	180	21	(	(	PUNCT
ejpam-6264	180	22	g	g	NOUN
ejpam-6264	180	23	)	)	PUNCT
ejpam-6264	180	24	\d	\d	NOUN
ejpam-6264	180	25	.	.	PUNCT
ejpam-6264	181	1	then	then	ADV
ejpam-6264	181	2	g	g	PROPN
ejpam-6264	181	3	∈	∈	PROPN
ejpam-6264	181	4	tmrdf	tmrdf	NOUN
ejpam-6264	181	5	(	(	PUNCT
ejpam-6264	181	6	g	g	NOUN
ejpam-6264	181	7	)	)	PUNCT
ejpam-6264	181	8	and	and	CCONJ
ejpam-6264	181	9	ωtmr	ωtmr	PROPN
ejpam-6264	181	10	g	g	PROPN
ejpam-6264	181	11	(	(	PUNCT
ejpam-6264	181	12	g	g	NOUN
ejpam-6264	181	13	)	)	PUNCT
ejpam-6264	181	14	=	=	SYM
ejpam-6264	181	15	5	5	X
ejpam-6264	181	16	.	.	PUNCT
ejpam-6264	182	1	since	since	SCONJ
ejpam-6264	182	2	g	g	PROPN
ejpam-6264	182	3	̸∈	̸∈	PROPN
ejpam-6264	182	4	{	{	PUNCT
ejpam-6264	182	5	k3	k3	PROPN
ejpam-6264	182	6	,	,	PUNCT
ejpam-6264	182	7	p3	p3	PROPN
ejpam-6264	182	8	}	}	PUNCT
ejpam-6264	182	9	,	,	PUNCT
ejpam-6264	182	10	we	we	PRON
ejpam-6264	182	11	must	must	AUX
ejpam-6264	182	12	have	have	VERB
ejpam-6264	182	13	ωtmr	ωtmr	ADJ
ejpam-6264	182	14	g	g	PROPN
ejpam-6264	182	15	(	(	PUNCT
ejpam-6264	182	16	g	g	NOUN
ejpam-6264	182	17	)	)	PUNCT
ejpam-6264	182	18	=	=	SYM
ejpam-6264	182	19	5	5	X
ejpam-6264	182	20	.	.	X
ejpam-6264	183	1	hence	hence	ADV
ejpam-6264	183	2	,	,	PUNCT
ejpam-6264	183	3	γtmr(g	γtmr(g	PROPN
ejpam-6264	183	4	)	)	PUNCT
ejpam-6264	183	5	=	=	SYM
ejpam-6264	183	6	5	5	X
ejpam-6264	183	7	.	.	PUNCT
ejpam-6264	183	8	corollary	corollary	ADJ
ejpam-6264	183	9	1	1	NUM
ejpam-6264	183	10	.	.	PUNCT
ejpam-6264	184	1	for	for	ADP
ejpam-6264	184	2	a	a	DET
ejpam-6264	184	3	connected	connected	ADJ
ejpam-6264	184	4	graph	graph	NOUN
ejpam-6264	184	5	g	g	NOUN
ejpam-6264	184	6	of	of	ADP
ejpam-6264	184	7	order	order	NOUN
ejpam-6264	184	8	4	4	NUM
ejpam-6264	184	9	,	,	PUNCT
ejpam-6264	184	10	γtmr(g	γtmr(g	NOUN
ejpam-6264	184	11	)	)	PUNCT
ejpam-6264	184	12	=	=	SYM
ejpam-6264	184	13	5	5	NUM
ejpam-6264	184	14	if	if	SCONJ
ejpam-6264	184	15	and	and	CCONJ
ejpam-6264	184	16	only	only	ADV
ejpam-6264	184	17	if	if	SCONJ
ejpam-6264	184	18	g	g	PROPN
ejpam-6264	184	19	∈	∈	PROPN
ejpam-6264	184	20	{	{	PUNCT
ejpam-6264	184	21	k1	k1	NOUN
ejpam-6264	184	22	+	+	CCONJ
ejpam-6264	184	23	(	(	PUNCT
ejpam-6264	184	24	k1	k1	NOUN
ejpam-6264	184	25	∪k2),k1	∪k2),k1	NOUN
ejpam-6264	184	26	+	+	PROPN
ejpam-6264	184	27	k3,k1	k3,k1	PROPN
ejpam-6264	184	28	+	+	PROPN
ejpam-6264	184	29	k3,k1	k3,k1	PROPN
ejpam-6264	184	30	+	+	NUM
ejpam-6264	184	31	p3	p3	PROPN
ejpam-6264	184	32	}	}	PUNCT
ejpam-6264	184	33	.	.	PUNCT
ejpam-6264	185	1	proof	proof	NOUN
ejpam-6264	185	2	.	.	PUNCT
ejpam-6264	186	1	the	the	DET
ejpam-6264	186	2	proof	proof	NOUN
ejpam-6264	186	3	follows	follow	VERB
ejpam-6264	186	4	directly	directly	ADV
ejpam-6264	186	5	from	from	ADP
ejpam-6264	186	6	proposition	proposition	NOUN
ejpam-6264	186	7	8	8	NUM
ejpam-6264	186	8	.	.	PUNCT
ejpam-6264	187	1	proposition	proposition	NOUN
ejpam-6264	187	2	9	9	NUM
ejpam-6264	187	3	.	.	PUNCT
ejpam-6264	188	1	let	let	VERB
ejpam-6264	188	2	g	g	PRON
ejpam-6264	188	3	be	be	AUX
ejpam-6264	188	4	a	a	DET
ejpam-6264	188	5	disconnected	disconnected	ADJ
ejpam-6264	188	6	graph	graph	NOUN
ejpam-6264	188	7	with	with	ADP
ejpam-6264	188	8	nontrivial	nontrivial	ADJ
ejpam-6264	188	9	components	component	NOUN
ejpam-6264	188	10	g1	g1	PROPN
ejpam-6264	188	11	,	,	PUNCT
ejpam-6264	188	12	g2	g2	PROPN
ejpam-6264	188	13	,	,	PUNCT
ejpam-6264	188	14	·	·	PUNCT
ejpam-6264	188	15	·	·	PUNCT
ejpam-6264	188	16	·	·	PUNCT
ejpam-6264	188	17	,	,	PUNCT
ejpam-6264	188	18	gn	gn	PROPN
ejpam-6264	188	19	.	.	PROPN
ejpam-6264	188	20	then	then	ADV
ejpam-6264	188	21	γtmr(g	γtmr(g	NUM
ejpam-6264	188	22	)	)	PUNCT
ejpam-6264	189	1	=	=	SYM
ejpam-6264	190	1	∑n	∑n	PROPN
ejpam-6264	190	2	i=1	i=1	PROPN
ejpam-6264	190	3	γtmr(gi	γtmr(gi	NOUN
ejpam-6264	190	4	)	)	PUNCT
ejpam-6264	190	5	.	.	PUNCT
ejpam-6264	191	1	proof	proof	NOUN
ejpam-6264	191	2	.	.	PUNCT
ejpam-6264	192	1	let	let	VERB
ejpam-6264	192	2	g1	g1	PROPN
ejpam-6264	192	3	,	,	PUNCT
ejpam-6264	192	4	g2	g2	PROPN
ejpam-6264	192	5	,	,	PUNCT
ejpam-6264	192	6	·	·	PUNCT
ejpam-6264	192	7	·	·	PUNCT
ejpam-6264	192	8	·	·	PUNCT
ejpam-6264	192	9	,	,	PUNCT
ejpam-6264	192	10	gn	gn	X
ejpam-6264	192	11	be	be	AUX
ejpam-6264	192	12	the	the	DET
ejpam-6264	192	13	components	component	NOUN
ejpam-6264	192	14	of	of	ADP
ejpam-6264	192	15	g.	g.	PROPN
ejpam-6264	192	16	let	let	VERB
ejpam-6264	192	17	f1	f1	NOUN
ejpam-6264	192	18	,	,	PUNCT
ejpam-6264	192	19	f2	f2	PROPN
ejpam-6264	192	20	,	,	PUNCT
ejpam-6264	192	21	·	·	PUNCT
ejpam-6264	192	22	·	·	PUNCT
ejpam-6264	192	23	·	·	PUNCT
ejpam-6264	192	24	,	,	PUNCT
ejpam-6264	192	25	fn	fn	PROPN
ejpam-6264	192	26	be	be	AUX
ejpam-6264	192	27	γtmrfunctions	γtmrfunction	NOUN
ejpam-6264	192	28	of	of	ADP
ejpam-6264	192	29	g1	g1	NOUN
ejpam-6264	192	30	,	,	PUNCT
ejpam-6264	192	31	g2	g2	PROPN
ejpam-6264	192	32	,	,	PUNCT
ejpam-6264	192	33	·	·	PUNCT
ejpam-6264	192	34	·	·	PUNCT
ejpam-6264	192	35	·	·	PUNCT
ejpam-6264	192	36	,	,	PUNCT
ejpam-6264	192	37	gn	gn	PROPN
ejpam-6264	192	38	respectively	respectively	ADV
ejpam-6264	192	39	.	.	PUNCT
ejpam-6264	193	1	define	define	VERB
ejpam-6264	193	2	a	a	DET
ejpam-6264	193	3	function	function	NOUN
ejpam-6264	193	4	f	f	NOUN
ejpam-6264	193	5	:	:	PUNCT
ejpam-6264	193	6	v	v	X
ejpam-6264	193	7	(	(	PUNCT
ejpam-6264	193	8	g	g	NOUN
ejpam-6264	193	9	)	)	PUNCT
ejpam-6264	193	10	−→	−→	NOUN
ejpam-6264	193	11	{	{	PUNCT
ejpam-6264	193	12	0	0	NUM
ejpam-6264	193	13	,	,	PUNCT
ejpam-6264	193	14	1	1	NUM
ejpam-6264	193	15	,	,	PUNCT
ejpam-6264	193	16	2	2	NUM
ejpam-6264	193	17	,	,	PUNCT
ejpam-6264	193	18	3	3	NUM
ejpam-6264	193	19	}	}	PUNCT
ejpam-6264	193	20	given	give	VERB
ejpam-6264	193	21	by	by	ADP
ejpam-6264	193	22	s.	s.	PROPN
ejpam-6264	193	23	ahamad	ahamad	PROPN
ejpam-6264	193	24	et	et	PROPN
ejpam-6264	193	25	al	al	PROPN
ejpam-6264	193	26	.	.	PUNCT
ejpam-6264	193	27	/	/	SYM
ejpam-6264	193	28	eur	eur	PROPN
ejpam-6264	193	29	.	.	PUNCT
ejpam-6264	194	1	j.	j.	PROPN
ejpam-6264	194	2	pure	pure	PROPN
ejpam-6264	194	3	appl	appl	PROPN
ejpam-6264	194	4	.	.	PROPN
ejpam-6264	194	5	math	math	PROPN
ejpam-6264	194	6	,	,	PUNCT
ejpam-6264	194	7	18	18	NUM
ejpam-6264	194	8	(	(	PUNCT
ejpam-6264	194	9	4	4	NUM
ejpam-6264	194	10	)	)	PUNCT
ejpam-6264	194	11	(	(	PUNCT
ejpam-6264	194	12	2025	2025	NUM
ejpam-6264	194	13	)	)	PUNCT
ejpam-6264	194	14	,	,	PUNCT
ejpam-6264	194	15	6264	6264	NUM
ejpam-6264	194	16	8	8	NUM
ejpam-6264	194	17	of	of	ADP
ejpam-6264	194	18	20	20	NUM
ejpam-6264	194	19	f(x	f(x	PROPN
ejpam-6264	194	20	)	)	PUNCT
ejpam-6264	194	21	=	=	PUNCT
ejpam-6264	194	22			NOUN
ejpam-6264	194	23	f1(x	f1(x	NUM
ejpam-6264	194	24	)	)	PUNCT
ejpam-6264	194	25	,	,	PUNCT
ejpam-6264	194	26	if	if	SCONJ
ejpam-6264	194	27	x	x	SYM
ejpam-6264	194	28	∈	∈	PROPN
ejpam-6264	194	29	v	v	NOUN
ejpam-6264	194	30	(	(	PUNCT
ejpam-6264	194	31	g1	g1	PROPN
ejpam-6264	194	32	)	)	PUNCT
ejpam-6264	194	33	.	.	PUNCT
ejpam-6264	195	1	f2(x	f2(x	X
ejpam-6264	195	2	)	)	PUNCT
ejpam-6264	195	3	,	,	PUNCT
ejpam-6264	195	4	if	if	SCONJ
ejpam-6264	195	5	x	x	SYM
ejpam-6264	195	6	∈	∈	PROPN
ejpam-6264	195	7	v	v	X
ejpam-6264	195	8	(	(	PUNCT
ejpam-6264	195	9	g2	g2	PROPN
ejpam-6264	195	10	)	)	PUNCT
ejpam-6264	195	11	.	.	PUNCT
ejpam-6264	195	12	...	...	PUNCT
ejpam-6264	196	1	fn(x	fn(x	X
ejpam-6264	196	2	)	)	PUNCT
ejpam-6264	196	3	,	,	PUNCT
ejpam-6264	196	4	if	if	SCONJ
ejpam-6264	196	5	x	x	SYM
ejpam-6264	196	6	∈	∈	PROPN
ejpam-6264	196	7	v	v	X
ejpam-6264	196	8	(	(	PUNCT
ejpam-6264	196	9	gn	gn	PROPN
ejpam-6264	196	10	)	)	PUNCT
ejpam-6264	196	11	.	.	PUNCT
ejpam-6264	197	1	then	then	ADV
ejpam-6264	197	2	f	f	PROPN
ejpam-6264	197	3	is	be	AUX
ejpam-6264	197	4	a	a	DET
ejpam-6264	197	5	γtmr	γtmr	ADJ
ejpam-6264	197	6	-	-	PUNCT
ejpam-6264	197	7	function	function	NOUN
ejpam-6264	197	8	of	of	ADP
ejpam-6264	197	9	g.	g.	PROPN
ejpam-6264	197	10	thus	thus	ADV
ejpam-6264	197	11	γtmr(g	γtmr(g	NUM
ejpam-6264	197	12	)	)	PUNCT
ejpam-6264	197	13	≤	≤	NOUN
ejpam-6264	198	1	∑n	∑n	PROPN
ejpam-6264	198	2	i=1	i=1	PROPN
ejpam-6264	198	3	γtmr(gi	γtmr(gi	PROPN
ejpam-6264	198	4	)	)	PUNCT
ejpam-6264	198	5	.	.	PUNCT
ejpam-6264	199	1	conversely	conversely	ADV
ejpam-6264	199	2	,	,	PUNCT
ejpam-6264	199	3	let	let	VERB
ejpam-6264	199	4	f	f	PRON
ejpam-6264	199	5	be	be	AUX
ejpam-6264	199	6	a	a	DET
ejpam-6264	199	7	γtmr	γtmr	NOUN
ejpam-6264	199	8	-	-	PUNCT
ejpam-6264	199	9	function	function	NOUN
ejpam-6264	199	10	of	of	ADP
ejpam-6264	199	11	g.	g.	PROPN
ejpam-6264	199	12	then	then	ADV
ejpam-6264	199	13	the	the	DET
ejpam-6264	199	14	restriction	restriction	NOUN
ejpam-6264	199	15	f	f	PROPN
ejpam-6264	199	16	|gi	|gi	NOUN
ejpam-6264	199	17	of	of	ADP
ejpam-6264	199	18	f	f	PROPN
ejpam-6264	199	19	to	to	PART
ejpam-6264	199	20	gi	gi	INTJ
ejpam-6264	199	21	,	,	PUNCT
ejpam-6264	199	22	where	where	SCONJ
ejpam-6264	199	23	i	i	PRON
ejpam-6264	199	24	=	=	NOUN
ejpam-6264	199	25	1	1	NUM
ejpam-6264	199	26	,	,	PUNCT
ejpam-6264	199	27	2	2	NUM
ejpam-6264	199	28	,	,	PUNCT
ejpam-6264	199	29	·	·	PUNCT
ejpam-6264	199	30	·	·	PUNCT
ejpam-6264	199	31	·	·	PUNCT
ejpam-6264	199	32	,	,	PUNCT
ejpam-6264	199	33	n	n	X
ejpam-6264	199	34	is	be	AUX
ejpam-6264	199	35	a	a	DET
ejpam-6264	199	36	γtmr	γtmr	NOUN
ejpam-6264	199	37	-	-	PUNCT
ejpam-6264	199	38	function	function	NOUN
ejpam-6264	199	39	of	of	ADP
ejpam-6264	199	40	gi	gi	NOUN
ejpam-6264	199	41	.	.	PUNCT
ejpam-6264	200	1	thus	thus	ADV
ejpam-6264	200	2	,	,	PUNCT
ejpam-6264	200	3	γtmr(gi	γtmr(gi	NOUN
ejpam-6264	200	4	)	)	PUNCT
ejpam-6264	200	5	≤	≤	PUNCT
ejpam-6264	200	6	ωtmr	ωtmr	ADJ
ejpam-6264	200	7	g	g	PROPN
ejpam-6264	200	8	(	(	PUNCT
ejpam-6264	200	9	f	f	PROPN
ejpam-6264	200	10	|gi	|gi	NOUN
ejpam-6264	200	11	)	)	PUNCT
ejpam-6264	200	12	for	for	ADP
ejpam-6264	200	13	all	all	DET
ejpam-6264	200	14	i	i	PRON
ejpam-6264	200	15	=	=	NOUN
ejpam-6264	200	16	1	1	NUM
ejpam-6264	200	17	,	,	PUNCT
ejpam-6264	200	18	2	2	NUM
ejpam-6264	200	19	,	,	PUNCT
ejpam-6264	200	20	·	·	PUNCT
ejpam-6264	200	21	·	·	PUNCT
ejpam-6264	200	22	·	·	PUNCT
ejpam-6264	200	23	,	,	PUNCT
ejpam-6264	200	24	n.	n.	PROPN
ejpam-6264	200	25	hence,∑n	hence,∑n	NOUN
ejpam-6264	200	26	i=1	i=1	PROPN
ejpam-6264	200	27	γtmr(gi	γtmr(gi	PROPN
ejpam-6264	200	28	)	)	PUNCT
ejpam-6264	200	29	≤	≤	NOUN
ejpam-6264	200	30	γtmr(g	γtmr(g	NUM
ejpam-6264	200	31	)	)	PUNCT
ejpam-6264	200	32	.	.	PUNCT
ejpam-6264	201	1	hence	hence	ADV
ejpam-6264	201	2	,	,	PUNCT
ejpam-6264	201	3	combining	combine	VERB
ejpam-6264	201	4	the	the	DET
ejpam-6264	201	5	results	result	NOUN
ejpam-6264	201	6	,	,	PUNCT
ejpam-6264	201	7	∑n	∑n	PROPN
ejpam-6264	201	8	i=1	i=1	PROPN
ejpam-6264	201	9	γtmr(gi	γtmr(gi	PROPN
ejpam-6264	201	10	)	)	PUNCT
ejpam-6264	201	11	≤	≤	NOUN
ejpam-6264	201	12	γtmr(g	γtmr(g	NOUN
ejpam-6264	201	13	)	)	PUNCT
ejpam-6264	202	1	≤∑n	≤∑n	PROPN
ejpam-6264	202	2	i=1	i=1	PROPN
ejpam-6264	202	3	γtmr(gi	γtmr(gi	NOUN
ejpam-6264	202	4	)	)	PUNCT
ejpam-6264	202	5	.	.	PUNCT
ejpam-6264	203	1	therefore	therefore	ADV
ejpam-6264	203	2	,	,	PUNCT
ejpam-6264	203	3	γtmr(g	γtmr(g	NOUN
ejpam-6264	203	4	)	)	PUNCT
ejpam-6264	203	5	=	=	SYM
ejpam-6264	204	1	∑n	∑n	PROPN
ejpam-6264	204	2	i=1	i=1	PROPN
ejpam-6264	204	3	γtmr(gi	γtmr(gi	PROPN
ejpam-6264	204	4	)	)	PUNCT
ejpam-6264	204	5	.	.	PUNCT
ejpam-6264	205	1	proposition	proposition	NOUN
ejpam-6264	205	2	10	10	NUM
ejpam-6264	205	3	.	.	PUNCT
ejpam-6264	206	1	if	if	SCONJ
ejpam-6264	206	2	g	g	PROPN
ejpam-6264	206	3	∈	∈	PROPN
ejpam-6264	206	4	{	{	PUNCT
ejpam-6264	206	5	pn	pn	PROPN
ejpam-6264	206	6	,	,	PUNCT
ejpam-6264	206	7	cn	cn	PROPN
ejpam-6264	206	8	}	}	PUNCT
ejpam-6264	206	9	,	,	PUNCT
ejpam-6264	206	10	then	then	ADV
ejpam-6264	206	11	γtmr(g	γtmr(g	NUM
ejpam-6264	206	12	)	)	PUNCT
ejpam-6264	206	13	=	=	SYM
ejpam-6264	206	14	n+	n+	X
ejpam-6264	206	15	⌈n	⌈n	NOUN
ejpam-6264	206	16	3	3	NUM
ejpam-6264	206	17	⌉	⌉	X
ejpam-6264	206	18	.	.	PUNCT
ejpam-6264	207	1	proof	proof	NOUN
ejpam-6264	207	2	.	.	PUNCT
ejpam-6264	208	1	let	let	VERB
ejpam-6264	208	2	g	g	PROPN
ejpam-6264	208	3	∈	∈	PROPN
ejpam-6264	208	4	{	{	PUNCT
ejpam-6264	208	5	pn	pn	PROPN
ejpam-6264	208	6	,	,	PUNCT
ejpam-6264	208	7	cn	cn	PROPN
ejpam-6264	208	8	}	}	PUNCT
ejpam-6264	208	9	.	.	PUNCT
ejpam-6264	209	1	suppose	suppose	VERB
ejpam-6264	210	1	g	g	PROPN
ejpam-6264	210	2	=	=	PUNCT
ejpam-6264	210	3	[	[	X
ejpam-6264	210	4	v1	v1	NOUN
ejpam-6264	210	5	,	,	PUNCT
ejpam-6264	210	6	v2	v2	PROPN
ejpam-6264	210	7	,	,	PUNCT
ejpam-6264	210	8	·	·	PUNCT
ejpam-6264	210	9	·	·	PUNCT
ejpam-6264	210	10	·	·	PUNCT
ejpam-6264	210	11	,	,	PUNCT
ejpam-6264	210	12	vn	vn	ADP
ejpam-6264	210	13	]	]	PUNCT
ejpam-6264	210	14	.	.	PUNCT
ejpam-6264	211	1	if	if	SCONJ
ejpam-6264	211	2	n	n	PRON
ejpam-6264	211	3	≡	≡	PROPN
ejpam-6264	211	4	0(mod	0(mod	NOUN
ejpam-6264	211	5	3	3	NUM
ejpam-6264	211	6	)	)	PUNCT
ejpam-6264	211	7	.	.	PUNCT
ejpam-6264	212	1	put	put	VERB
ejpam-6264	212	2	v2	v2	NOUN
ejpam-6264	212	3	=	=	PUNCT
ejpam-6264	212	4	{	{	PUNCT
ejpam-6264	212	5	v2	v2	PROPN
ejpam-6264	212	6	,	,	PUNCT
ejpam-6264	212	7	v5	v5	PROPN
ejpam-6264	212	8	,	,	PUNCT
ejpam-6264	212	9	·	·	PUNCT
ejpam-6264	212	10	·	·	PUNCT
ejpam-6264	212	11	·	·	PUNCT
ejpam-6264	212	12	,	,	PUNCT
ejpam-6264	212	13	vn−7	vn−7	PROPN
ejpam-6264	212	14	,	,	PUNCT
ejpam-6264	212	15	vn−4	vn−4	NOUN
ejpam-6264	212	16	,	,	PUNCT
ejpam-6264	212	17	vn−1	vn−1	ADJ
ejpam-6264	212	18	}	}	PUNCT
ejpam-6264	212	19	,	,	PUNCT
ejpam-6264	212	20	v1	v1	NOUN
ejpam-6264	212	21	=	=	SYM
ejpam-6264	212	22	v	v	NOUN
ejpam-6264	212	23	(	(	PUNCT
ejpam-6264	212	24	g	g	NOUN
ejpam-6264	212	25	)	)	PUNCT
ejpam-6264	212	26	\	\	PROPN
ejpam-6264	212	27	v2	v2	PROPN
ejpam-6264	212	28	,	,	PUNCT
ejpam-6264	212	29	|v0|	|v0|	NOUN
ejpam-6264	212	30	=	=	SYM
ejpam-6264	212	31	0	0	NUM
ejpam-6264	212	32	=	=	SYM
ejpam-6264	212	33	|v3|	|v3|	NOUN
ejpam-6264	212	34	.	.	PUNCT
ejpam-6264	213	1	then	then	ADV
ejpam-6264	213	2	f	f	PROPN
ejpam-6264	213	3	=	=	SYM
ejpam-6264	213	4	(	(	PUNCT
ejpam-6264	213	5	v0	v0	PROPN
ejpam-6264	213	6	,	,	PUNCT
ejpam-6264	213	7	v1	v1	NOUN
ejpam-6264	213	8	,	,	PUNCT
ejpam-6264	213	9	v2	v2	PROPN
ejpam-6264	213	10	,	,	PUNCT
ejpam-6264	213	11	v3	v3	PROPN
ejpam-6264	213	12	)	)	PUNCT
ejpam-6264	213	13	is	be	AUX
ejpam-6264	213	14	a	a	DET
ejpam-6264	213	15	tmrdf	tmrdf	NOUN
ejpam-6264	213	16	on	on	ADP
ejpam-6264	213	17	g.	g.	PROPN
ejpam-6264	213	18	if	if	SCONJ
ejpam-6264	213	19	n	n	PRON
ejpam-6264	213	20	≡	≡	PROPN
ejpam-6264	213	21	1(mod	1(mod	NUM
ejpam-6264	213	22	3	3	NUM
ejpam-6264	213	23	)	)	PUNCT
ejpam-6264	213	24	.	.	PUNCT
ejpam-6264	214	1	put	put	VERB
ejpam-6264	214	2	v2	v2	NOUN
ejpam-6264	214	3	=	=	PUNCT
ejpam-6264	214	4	{	{	PUNCT
ejpam-6264	214	5	v2	v2	PROPN
ejpam-6264	214	6	,	,	PUNCT
ejpam-6264	214	7	·	·	PUNCT
ejpam-6264	214	8	·	·	PUNCT
ejpam-6264	214	9	·	·	PUNCT
ejpam-6264	214	10	,	,	PUNCT
ejpam-6264	214	11	vn−8	vn−8	PROPN
ejpam-6264	214	12	,	,	PUNCT
ejpam-6264	214	13	vn−5	vn−5	PROPN
ejpam-6264	214	14	,	,	PUNCT
ejpam-6264	214	15	vn−2	vn−2	PROPN
ejpam-6264	214	16	,	,	PUNCT
ejpam-6264	214	17	vn	vn	NOUN
ejpam-6264	214	18	}	}	PUNCT
ejpam-6264	214	19	,	,	PUNCT
ejpam-6264	214	20	v1	v1	PROPN
ejpam-6264	214	21	=	=	SYM
ejpam-6264	214	22	v	v	NOUN
ejpam-6264	214	23	(	(	PUNCT
ejpam-6264	214	24	g	g	NOUN
ejpam-6264	214	25	)	)	PUNCT
ejpam-6264	214	26	\	\	PROPN
ejpam-6264	214	27	v2	v2	PROPN
ejpam-6264	214	28	,	,	PUNCT
ejpam-6264	214	29	|v0|	|v0|	NOUN
ejpam-6264	214	30	=	=	SYM
ejpam-6264	214	31	0	0	NUM
ejpam-6264	214	32	=	=	SYM
ejpam-6264	214	33	|v3|	|v3|	NOUN
ejpam-6264	214	34	.	.	PUNCT
ejpam-6264	215	1	then	then	ADV
ejpam-6264	215	2	f	f	PROPN
ejpam-6264	215	3	=	=	SYM
ejpam-6264	215	4	(	(	PUNCT
ejpam-6264	215	5	v0	v0	PROPN
ejpam-6264	215	6	,	,	PUNCT
ejpam-6264	215	7	v1	v1	NOUN
ejpam-6264	215	8	,	,	PUNCT
ejpam-6264	215	9	v2	v2	PROPN
ejpam-6264	215	10	,	,	PUNCT
ejpam-6264	215	11	v3	v3	PROPN
ejpam-6264	215	12	)	)	PUNCT
ejpam-6264	215	13	is	be	AUX
ejpam-6264	215	14	a	a	DET
ejpam-6264	215	15	tmrdf	tmrdf	NOUN
ejpam-6264	215	16	on	on	ADP
ejpam-6264	215	17	g.	g.	PROPN
ejpam-6264	215	18	if	if	SCONJ
ejpam-6264	215	19	n	n	PRON
ejpam-6264	215	20	≡	≡	PROPN
ejpam-6264	215	21	2(mod	2(mod	NUM
ejpam-6264	215	22	3	3	X
ejpam-6264	215	23	)	)	PUNCT
ejpam-6264	215	24	.	.	PUNCT
ejpam-6264	216	1	put	put	VERB
ejpam-6264	216	2	v2	v2	NOUN
ejpam-6264	216	3	=	=	PUNCT
ejpam-6264	216	4	{	{	PUNCT
ejpam-6264	216	5	v2	v2	PROPN
ejpam-6264	216	6	,	,	PUNCT
ejpam-6264	216	7	v5	v5	PROPN
ejpam-6264	216	8	,	,	PUNCT
ejpam-6264	216	9	·	·	PUNCT
ejpam-6264	216	10	·	·	PUNCT
ejpam-6264	216	11	·	·	PUNCT
ejpam-6264	216	12	,	,	PUNCT
ejpam-6264	216	13	vn−9	vn−9	NOUN
ejpam-6264	216	14	,	,	PUNCT
ejpam-6264	216	15	vn−6	vn−6	PROPN
ejpam-6264	216	16	,	,	PUNCT
ejpam-6264	216	17	vn−3	vn−3	PROPN
ejpam-6264	216	18	,	,	PUNCT
ejpam-6264	216	19	vn	vn	NOUN
ejpam-6264	216	20	}	}	PUNCT
ejpam-6264	216	21	,	,	PUNCT
ejpam-6264	216	22	v1	v1	PROPN
ejpam-6264	216	23	=	=	SYM
ejpam-6264	216	24	v	v	NOUN
ejpam-6264	216	25	(	(	PUNCT
ejpam-6264	216	26	g	g	NOUN
ejpam-6264	216	27	)	)	PUNCT
ejpam-6264	216	28	\	\	PROPN
ejpam-6264	216	29	v2	v2	PROPN
ejpam-6264	216	30	,	,	PUNCT
ejpam-6264	216	31	|v0|	|v0|	NOUN
ejpam-6264	216	32	=	=	SYM
ejpam-6264	216	33	0	0	NUM
ejpam-6264	216	34	=	=	SYM
ejpam-6264	216	35	|v3|	|v3|	NOUN
ejpam-6264	216	36	.	.	PUNCT
ejpam-6264	217	1	then	then	ADV
ejpam-6264	217	2	f	f	PROPN
ejpam-6264	217	3	=	=	SYM
ejpam-6264	217	4	(	(	PUNCT
ejpam-6264	217	5	v0	v0	PROPN
ejpam-6264	217	6	,	,	PUNCT
ejpam-6264	217	7	v1	v1	NOUN
ejpam-6264	217	8	,	,	PUNCT
ejpam-6264	217	9	v2	v2	PROPN
ejpam-6264	217	10	,	,	PUNCT
ejpam-6264	217	11	v3	v3	PROPN
ejpam-6264	217	12	)	)	PUNCT
ejpam-6264	217	13	is	be	AUX
ejpam-6264	217	14	a	a	DET
ejpam-6264	217	15	tmrdf	tmrdf	NOUN
ejpam-6264	217	16	on	on	ADP
ejpam-6264	217	17	g.	g.	PROPN
ejpam-6264	217	18	in	in	ADP
ejpam-6264	217	19	any	any	DET
ejpam-6264	217	20	case	case	NOUN
ejpam-6264	217	21	,	,	PUNCT
ejpam-6264	217	22	γtmr(g	γtmr(g	NOUN
ejpam-6264	217	23	)	)	PUNCT
ejpam-6264	217	24	≤	≤	NOUN
ejpam-6264	217	25	ωtmr	ωtmr	ADJ
ejpam-6264	217	26	g	g	PROPN
ejpam-6264	217	27	(	(	PUNCT
ejpam-6264	217	28	f	f	X
ejpam-6264	217	29	)	)	PUNCT
ejpam-6264	217	30	=	=	SYM
ejpam-6264	217	31	|v1|+	|v1|+	ADV
ejpam-6264	217	32	|v2|	|v2|	NOUN
ejpam-6264	217	33	=	=	SYM
ejpam-6264	217	34	n	n	NOUN
ejpam-6264	217	35	+	+	CCONJ
ejpam-6264	217	36	⌈n	⌈n	VERB
ejpam-6264	217	37	3	3	NUM
ejpam-6264	217	38	⌉	⌉	NOUN
ejpam-6264	217	39	.	.	PUNCT
ejpam-6264	218	1	since	since	SCONJ
ejpam-6264	218	2	|v0|	|v0|	NOUN
ejpam-6264	218	3	=	=	SYM
ejpam-6264	218	4	0	0	NUM
ejpam-6264	218	5	,	,	PUNCT
ejpam-6264	218	6	by	by	ADP
ejpam-6264	218	7	proposition	proposition	NOUN
ejpam-6264	218	8	6	6	NUM
ejpam-6264	218	9	,	,	PUNCT
ejpam-6264	218	10	v2	v2	PROPN
ejpam-6264	218	11	is	be	AUX
ejpam-6264	218	12	a	a	DET
ejpam-6264	218	13	γ	γ	NOUN
ejpam-6264	218	14	-	-	PUNCT
ejpam-6264	218	15	set	set	NOUN
ejpam-6264	218	16	of	of	ADP
ejpam-6264	218	17	g	g	NOUN
ejpam-6264	218	18	and	and	CCONJ
ejpam-6264	218	19	v	v	NOUN
ejpam-6264	218	20	(	(	PUNCT
ejpam-6264	218	21	g	g	NOUN
ejpam-6264	218	22	)	)	PUNCT
ejpam-6264	218	23	is	be	AUX
ejpam-6264	218	24	a	a	DET
ejpam-6264	218	25	γt	γt	NOUN
ejpam-6264	218	26	-	-	NOUN
ejpam-6264	218	27	set	set	NOUN
ejpam-6264	218	28	of	of	ADP
ejpam-6264	218	29	g.	g.	NOUN
ejpam-6264	218	30	by	by	ADP
ejpam-6264	218	31	proposition	proposition	NOUN
ejpam-6264	218	32	3	3	NUM
ejpam-6264	218	33	,	,	PUNCT
ejpam-6264	218	34	γ(g	γ(g	PROPN
ejpam-6264	218	35	)	)	PUNCT
ejpam-6264	218	36	+	+	NUM
ejpam-6264	218	37	γt(g	γt(g	NOUN
ejpam-6264	218	38	)	)	PUNCT
ejpam-6264	219	1	=	=	VERB
ejpam-6264	219	2	|v2|	|v2|	NOUN
ejpam-6264	219	3	+	+	CCONJ
ejpam-6264	219	4	|v	|v	X
ejpam-6264	219	5	(	(	PUNCT
ejpam-6264	219	6	g)|	g)|	NOUN
ejpam-6264	219	7	=	=	PUNCT
ejpam-6264	219	8	n	n	NOUN
ejpam-6264	219	9	+	+	CCONJ
ejpam-6264	219	10	⌈n	⌈n	ADJ
ejpam-6264	219	11	3	3	NUM
ejpam-6264	219	12	⌉	⌉	X
ejpam-6264	219	13	≤	≤	NUM
ejpam-6264	219	14	γtmr(g	γtmr(g	NUM
ejpam-6264	219	15	)	)	PUNCT
ejpam-6264	219	16	.	.	PUNCT
ejpam-6264	220	1	thus	thus	ADV
ejpam-6264	220	2	,	,	PUNCT
ejpam-6264	220	3	γtmr(g	γtmr(g	NOUN
ejpam-6264	220	4	)	)	PUNCT
ejpam-6264	220	5	=	=	SYM
ejpam-6264	221	1	n+	n+	X
ejpam-6264	221	2	⌈n	⌈n	NOUN
ejpam-6264	221	3	3	3	NUM
ejpam-6264	221	4	⌉	⌉	X
ejpam-6264	221	5	.	.	PUNCT
ejpam-6264	222	1	the	the	DET
ejpam-6264	222	2	n	n	CCONJ
ejpam-6264	222	3	-	-	PUNCT
ejpam-6264	222	4	barbell	barbell	NOUN
ejpam-6264	222	5	graph	graph	NOUN
ejpam-6264	222	6	is	be	AUX
ejpam-6264	222	7	a	a	DET
ejpam-6264	222	8	simple	simple	ADJ
ejpam-6264	222	9	graph	graph	NOUN
ejpam-6264	222	10	obtained	obtain	VERB
ejpam-6264	222	11	by	by	ADP
ejpam-6264	222	12	joining	join	VERB
ejpam-6264	222	13	two	two	NUM
ejpam-6264	222	14	copies	copy	NOUN
ejpam-6264	222	15	of	of	ADP
ejpam-6264	222	16	complete	complete	ADJ
ejpam-6264	222	17	graph	graph	NOUN
ejpam-6264	222	18	kn≥3	kn≥3	NOUN
ejpam-6264	222	19	by	by	ADP
ejpam-6264	222	20	a	a	DET
ejpam-6264	222	21	bridge	bridge	NOUN
ejpam-6264	222	22	and	and	CCONJ
ejpam-6264	222	23	is	be	AUX
ejpam-6264	222	24	denoted	denote	VERB
ejpam-6264	222	25	by	by	ADP
ejpam-6264	222	26	bn	bn	PROPN
ejpam-6264	222	27	.	.	PUNCT
ejpam-6264	222	28	figure	figure	NOUN
ejpam-6264	222	29	2	2	NUM
ejpam-6264	222	30	shows	show	VERB
ejpam-6264	222	31	the	the	DET
ejpam-6264	222	32	n	n	CCONJ
ejpam-6264	222	33	-	-	PUNCT
ejpam-6264	222	34	barbell	barbell	NOUN
ejpam-6264	222	35	graphs	graph	NOUN
ejpam-6264	222	36	b3	b3	PROPN
ejpam-6264	222	37	and	and	CCONJ
ejpam-6264	222	38	b5	b5	PROPN
ejpam-6264	222	39	,	,	PUNCT
ejpam-6264	222	40	respectively	respectively	ADV
ejpam-6264	222	41	.	.	PUNCT
ejpam-6264	223	1	1	1	NUM
ejpam-6264	223	2	1	1	NUM
ejpam-6264	223	3	1	1	NUM
ejpam-6264	223	4	1	1	NUM
ejpam-6264	223	5	0	0	NUM
ejpam-6264	223	6	0	0	NUM
ejpam-6264	223	7	0	0	NUM
ejpam-6264	223	8	0	0	NUM
ejpam-6264	223	9	0	0	NUM
ejpam-6264	223	10	0	0	NUM
ejpam-6264	223	11	b3	b3	PROPN
ejpam-6264	223	12	:	:	PUNCT
ejpam-6264	223	13	b5	b5	NOUN
ejpam-6264	223	14	:	:	PUNCT
ejpam-6264	223	15	2	2	NUM
ejpam-6264	223	16	2	2	NUM
ejpam-6264	223	17	2	2	NUM
ejpam-6264	223	18	3	3	NUM
ejpam-6264	223	19	3	3	NUM
ejpam-6264	223	20	2	2	NUM
ejpam-6264	223	21	figure	figure	NOUN
ejpam-6264	223	22	2	2	NUM
ejpam-6264	223	23	:	:	PUNCT
ejpam-6264	223	24	the	the	DET
ejpam-6264	223	25	graphs	graph	NOUN
ejpam-6264	223	26	b3	b3	PROPN
ejpam-6264	223	27	and	and	CCONJ
ejpam-6264	223	28	b5	b5	PROPN
ejpam-6264	223	29	with	with	ADP
ejpam-6264	223	30	γtmr(b3	γtmr(b3	NOUN
ejpam-6264	223	31	)	)	PUNCT
ejpam-6264	223	32	=	=	SYM
ejpam-6264	223	33	8	8	NUM
ejpam-6264	223	34	and	and	CCONJ
ejpam-6264	223	35	γtmr(b5	γtmr(b5	NOUN
ejpam-6264	223	36	)	)	PUNCT
ejpam-6264	224	1	=	=	SYM
ejpam-6264	224	2	10	10	NUM
ejpam-6264	224	3	,	,	PUNCT
ejpam-6264	224	4	respectively	respectively	ADV
ejpam-6264	224	5	.	.	PUNCT
ejpam-6264	225	1	proposition	proposition	NOUN
ejpam-6264	225	2	11	11	NUM
ejpam-6264	225	3	.	.	PUNCT
ejpam-6264	226	1	for	for	ADP
ejpam-6264	226	2	any	any	DET
ejpam-6264	226	3	n	n	CCONJ
ejpam-6264	226	4	-	-	PUNCT
ejpam-6264	226	5	barbell	barbell	NOUN
ejpam-6264	226	6	graph	graph	NOUN
ejpam-6264	226	7	bn	bn	ADP
ejpam-6264	226	8	where	where	SCONJ
ejpam-6264	226	9	n	n	PRON
ejpam-6264	226	10	≥	≥	X
ejpam-6264	226	11	3	3	NUM
ejpam-6264	226	12	,	,	PUNCT
ejpam-6264	226	13	γtmr(bn	γtmr(bn	NUM
ejpam-6264	226	14	)	)	PUNCT
ejpam-6264	226	15	=	=	NOUN
ejpam-6264	226	16	{	{	PUNCT
ejpam-6264	226	17	8	8	NUM
ejpam-6264	226	18	,	,	PUNCT
ejpam-6264	226	19	if	if	SCONJ
ejpam-6264	226	20	n	n	NOUN
ejpam-6264	226	21	=	=	SYM
ejpam-6264	226	22	3	3	NUM
ejpam-6264	226	23	.	.	NOUN
ejpam-6264	226	24	10	10	NUM
ejpam-6264	226	25	,	,	PUNCT
ejpam-6264	226	26	if	if	SCONJ
ejpam-6264	226	27	n	n	PRON
ejpam-6264	226	28	≥	≥	NOUN
ejpam-6264	226	29	4	4	NUM
ejpam-6264	226	30	.	.	PUNCT
ejpam-6264	227	1	s.	s.	PROPN
ejpam-6264	227	2	ahamad	ahamad	VERB
ejpam-6264	227	3	et	et	PROPN
ejpam-6264	227	4	al	al	PROPN
ejpam-6264	227	5	.	.	PUNCT
ejpam-6264	227	6	/	/	SYM
ejpam-6264	227	7	eur	eur	PROPN
ejpam-6264	227	8	.	.	PUNCT
ejpam-6264	228	1	j.	j.	PROPN
ejpam-6264	228	2	pure	pure	PROPN
ejpam-6264	228	3	appl	appl	PROPN
ejpam-6264	228	4	.	.	PROPN
ejpam-6264	228	5	math	math	PROPN
ejpam-6264	228	6	,	,	PUNCT
ejpam-6264	228	7	18	18	NUM
ejpam-6264	228	8	(	(	PUNCT
ejpam-6264	228	9	4	4	NUM
ejpam-6264	228	10	)	)	PUNCT
ejpam-6264	228	11	(	(	PUNCT
ejpam-6264	228	12	2025	2025	NUM
ejpam-6264	228	13	)	)	PUNCT
ejpam-6264	228	14	,	,	PUNCT
ejpam-6264	228	15	6264	6264	NUM
ejpam-6264	228	16	9	9	NUM
ejpam-6264	228	17	of	of	ADP
ejpam-6264	228	18	20	20	NUM
ejpam-6264	228	19	proof	proof	NOUN
ejpam-6264	228	20	.	.	PUNCT
ejpam-6264	229	1	let	let	VERB
ejpam-6264	229	2	bn	bn	PART
ejpam-6264	229	3	be	be	AUX
ejpam-6264	229	4	any	any	DET
ejpam-6264	229	5	n	n	CCONJ
ejpam-6264	229	6	-	-	PUNCT
ejpam-6264	229	7	barbell	barbell	NOUN
ejpam-6264	229	8	graph	graph	NOUN
ejpam-6264	229	9	and	and	CCONJ
ejpam-6264	229	10	uv	uv	NOUN
ejpam-6264	229	11	∈	∈	PROPN
ejpam-6264	229	12	e(bn	e(bn	PROPN
ejpam-6264	229	13	)	)	PUNCT
ejpam-6264	229	14	be	be	VERB
ejpam-6264	229	15	the	the	DET
ejpam-6264	229	16	bridge	bridge	NOUN
ejpam-6264	229	17	that	that	PRON
ejpam-6264	229	18	joins	join	VERB
ejpam-6264	229	19	the	the	DET
ejpam-6264	229	20	two	two	NUM
ejpam-6264	229	21	copies	copy	NOUN
ejpam-6264	229	22	of	of	ADP
ejpam-6264	229	23	kn	kn	PROPN
ejpam-6264	229	24	.	.	PUNCT
ejpam-6264	230	1	if	if	SCONJ
ejpam-6264	230	2	n	n	NUM
ejpam-6264	230	3	=	=	SYM
ejpam-6264	230	4	3	3	NUM
ejpam-6264	230	5	,	,	PUNCT
ejpam-6264	230	6	define	define	VERB
ejpam-6264	230	7	a	a	DET
ejpam-6264	230	8	function	function	NOUN
ejpam-6264	230	9	f	f	NOUN
ejpam-6264	230	10	=	=	SYM
ejpam-6264	230	11	(	(	PUNCT
ejpam-6264	230	12	v0	v0	PROPN
ejpam-6264	230	13	,	,	PUNCT
ejpam-6264	230	14	v1	v1	NOUN
ejpam-6264	230	15	,	,	PUNCT
ejpam-6264	230	16	v2	v2	PROPN
ejpam-6264	230	17	,	,	PUNCT
ejpam-6264	230	18	v3	v3	PROPN
ejpam-6264	230	19	)	)	PUNCT
ejpam-6264	230	20	given	give	VERB
ejpam-6264	230	21	by	by	ADP
ejpam-6264	230	22	f(x	f(x	PROPN
ejpam-6264	230	23	)	)	PUNCT
ejpam-6264	231	1	=	=	PRON
ejpam-6264	231	2	{	{	PUNCT
ejpam-6264	231	3	2	2	NUM
ejpam-6264	231	4	,	,	PUNCT
ejpam-6264	231	5	x	x	SYM
ejpam-6264	231	6	∈	∈	NOUN
ejpam-6264	231	7	{	{	PUNCT
ejpam-6264	231	8	u	u	NOUN
ejpam-6264	231	9	,	,	PUNCT
ejpam-6264	231	10	v	v	NOUN
ejpam-6264	231	11	}	}	PUNCT
ejpam-6264	231	12	.	.	PUNCT
ejpam-6264	232	1	1	1	NUM
ejpam-6264	232	2	,	,	PUNCT
ejpam-6264	232	3	otherwise	otherwise	ADV
ejpam-6264	232	4	.	.	PUNCT
ejpam-6264	233	1	then	then	ADV
ejpam-6264	233	2	f	f	PROPN
ejpam-6264	233	3	is	be	AUX
ejpam-6264	233	4	a	a	DET
ejpam-6264	233	5	tmrdf	tmrdf	NOUN
ejpam-6264	233	6	of	of	ADP
ejpam-6264	233	7	b3	b3	PROPN
ejpam-6264	233	8	.	.	PUNCT
ejpam-6264	234	1	thus	thus	ADV
ejpam-6264	234	2	,	,	PUNCT
ejpam-6264	234	3	γtmr(b3	γtmr(b3	ADV
ejpam-6264	234	4	)	)	PUNCT
ejpam-6264	235	1	≤	≤	NUM
ejpam-6264	235	2	ωtmr	ωtmr	PROPN
ejpam-6264	235	3	b3	b3	PROPN
ejpam-6264	235	4	(	(	PUNCT
ejpam-6264	235	5	f	f	X
ejpam-6264	235	6	)	)	PUNCT
ejpam-6264	235	7	=	=	SYM
ejpam-6264	235	8	8	8	X
ejpam-6264	235	9	.	.	PUNCT
ejpam-6264	235	10	clearly	clearly	ADV
ejpam-6264	235	11	γ(b3	γ(b3	VERB
ejpam-6264	235	12	)	)	PUNCT
ejpam-6264	235	13	=	=	SYM
ejpam-6264	235	14	2	2	NUM
ejpam-6264	235	15	=	=	SYM
ejpam-6264	235	16	γt(b3	γt(b3	NOUN
ejpam-6264	235	17	)	)	PUNCT
ejpam-6264	235	18	.	.	PUNCT
ejpam-6264	236	1	thus	thus	ADV
ejpam-6264	236	2	,	,	PUNCT
ejpam-6264	236	3	by	by	ADP
ejpam-6264	236	4	proposition	proposition	NOUN
ejpam-6264	236	5	3	3	NUM
ejpam-6264	236	6	,	,	PUNCT
ejpam-6264	236	7	γtmr(b3	γtmr(b3	NOUN
ejpam-6264	236	8	)	)	PUNCT
ejpam-6264	236	9	≥	≥	NOUN
ejpam-6264	236	10	8	8	NUM
ejpam-6264	236	11	.	.	PUNCT
ejpam-6264	237	1	therefore	therefore	ADV
ejpam-6264	237	2	,	,	PUNCT
ejpam-6264	237	3	γtmr(b3	γtmr(b3	ADV
ejpam-6264	237	4	)	)	PUNCT
ejpam-6264	237	5	=	=	SYM
ejpam-6264	238	1	8	8	X
ejpam-6264	238	2	.	.	PUNCT
ejpam-6264	239	1	if	if	SCONJ
ejpam-6264	239	2	n	n	NUM
ejpam-6264	239	3	≥	≥	NOUN
ejpam-6264	239	4	4	4	NUM
ejpam-6264	239	5	.	.	PUNCT
ejpam-6264	239	6	pick	pick	VERB
ejpam-6264	239	7	any	any	DET
ejpam-6264	239	8	v′	v′	NOUN
ejpam-6264	239	9	,	,	PUNCT
ejpam-6264	239	10	u′	u′	PROPN
ejpam-6264	239	11	∈	∈	PROPN
ejpam-6264	239	12	v	v	NOUN
ejpam-6264	239	13	(	(	PUNCT
ejpam-6264	239	14	bn	bn	NOUN
ejpam-6264	239	15	)	)	PUNCT
ejpam-6264	239	16	such	such	ADJ
ejpam-6264	239	17	that	that	DET
ejpam-6264	239	18	v′	v′	PROPN
ejpam-6264	239	19	̸=	̸=	PROPN
ejpam-6264	239	20	u	u	NOUN
ejpam-6264	239	21	,	,	PUNCT
ejpam-6264	239	22	u′	u′	PROPN
ejpam-6264	239	23	̸=	̸=	PROPN
ejpam-6264	239	24	v	v	NOUN
ejpam-6264	239	25	,	,	PUNCT
ejpam-6264	239	26	and	and	CCONJ
ejpam-6264	239	27	v′v	v′v	NUM
ejpam-6264	239	28	,	,	PUNCT
ejpam-6264	239	29	u′u	u′u	ADV
ejpam-6264	239	30	∈	∈	PROPN
ejpam-6264	239	31	e(bn	e(bn	PROPN
ejpam-6264	239	32	)	)	PUNCT
ejpam-6264	239	33	.	.	PUNCT
ejpam-6264	240	1	now	now	ADV
ejpam-6264	240	2	,	,	PUNCT
ejpam-6264	240	3	define	define	VERB
ejpam-6264	240	4	a	a	DET
ejpam-6264	240	5	function	function	NOUN
ejpam-6264	240	6	f	f	NOUN
ejpam-6264	240	7	=	=	SYM
ejpam-6264	240	8	(	(	PUNCT
ejpam-6264	240	9	v0	v0	PROPN
ejpam-6264	240	10	,	,	PUNCT
ejpam-6264	240	11	v1	v1	NOUN
ejpam-6264	240	12	,	,	PUNCT
ejpam-6264	240	13	v2	v2	PROPN
ejpam-6264	240	14	,	,	PUNCT
ejpam-6264	240	15	v3	v3	PROPN
ejpam-6264	240	16	)	)	PUNCT
ejpam-6264	240	17	given	give	VERB
ejpam-6264	240	18	by	by	ADP
ejpam-6264	240	19	f(x	f(x	PROPN
ejpam-6264	240	20	)	)	PUNCT
ejpam-6264	241	1	=	=	PUNCT
ejpam-6264	242	1			NOUN
ejpam-6264	242	2	0	0	NUM
ejpam-6264	242	3	,	,	PUNCT
ejpam-6264	242	4	x	x	SYM
ejpam-6264	242	5	∈	∈	NOUN
ejpam-6264	242	6	v	v	ADP
ejpam-6264	242	7	(	(	PUNCT
ejpam-6264	242	8	bn	bn	NOUN
ejpam-6264	242	9	)	)	PUNCT
ejpam-6264	242	10	\	\	NOUN
ejpam-6264	242	11	{	{	PUNCT
ejpam-6264	242	12	u	u	NOUN
ejpam-6264	242	13	,	,	PUNCT
ejpam-6264	242	14	v	v	NOUN
ejpam-6264	242	15	,	,	PUNCT
ejpam-6264	242	16	u′	u′	PROPN
ejpam-6264	242	17	,	,	PUNCT
ejpam-6264	242	18	v′	v′	PROPN
ejpam-6264	242	19	}	}	PUNCT
ejpam-6264	242	20	.	.	PUNCT
ejpam-6264	243	1	3	3	NUM
ejpam-6264	243	2	,	,	PUNCT
ejpam-6264	243	3	x	x	X
ejpam-6264	243	4	∈	∈	PROPN
ejpam-6264	243	5	{	{	PUNCT
ejpam-6264	243	6	u	u	NOUN
ejpam-6264	243	7	,	,	PUNCT
ejpam-6264	243	8	v	v	NOUN
ejpam-6264	243	9	}	}	PUNCT
ejpam-6264	243	10	.	.	PUNCT
ejpam-6264	244	1	2	2	NUM
ejpam-6264	244	2	,	,	PUNCT
ejpam-6264	244	3	x	x	X
ejpam-6264	244	4	∈	∈	NOUN
ejpam-6264	244	5	{	{	PUNCT
ejpam-6264	244	6	u′	u′	PROPN
ejpam-6264	244	7	,	,	PUNCT
ejpam-6264	244	8	v′	v′	PROPN
ejpam-6264	244	9	}	}	PUNCT
ejpam-6264	244	10	.	.	PUNCT
ejpam-6264	245	1	then	then	ADV
ejpam-6264	245	2	f	f	PROPN
ejpam-6264	245	3	is	be	AUX
ejpam-6264	245	4	a	a	DET
ejpam-6264	245	5	tmrdf	tmrdf	NOUN
ejpam-6264	245	6	of	of	ADP
ejpam-6264	245	7	bn	bn	NOUN
ejpam-6264	245	8	.	.	PUNCT
ejpam-6264	246	1	thus	thus	ADV
ejpam-6264	246	2	,	,	PUNCT
ejpam-6264	246	3	γtmr(bn	γtmr(bn	X
ejpam-6264	246	4	)	)	PUNCT
ejpam-6264	246	5	≤	≤	NOUN
ejpam-6264	246	6	ωtmr	ωtmr	PROPN
ejpam-6264	246	7	bn	bn	PROPN
ejpam-6264	246	8	(	(	PUNCT
ejpam-6264	246	9	f	f	X
ejpam-6264	246	10	)	)	PUNCT
ejpam-6264	246	11	=	=	SYM
ejpam-6264	246	12	10	10	NUM
ejpam-6264	246	13	.	.	PUNCT
ejpam-6264	246	14	clearly	clearly	ADV
ejpam-6264	246	15	γ(bn	γ(bn	NUM
ejpam-6264	246	16	)	)	PUNCT
ejpam-6264	246	17	=	=	SYM
ejpam-6264	246	18	2	2	NUM
ejpam-6264	246	19	=	=	SYM
ejpam-6264	246	20	γt(bn	γt(bn	PROPN
ejpam-6264	246	21	)	)	PUNCT
ejpam-6264	246	22	.	.	PUNCT
ejpam-6264	247	1	thus	thus	ADV
ejpam-6264	247	2	,	,	PUNCT
ejpam-6264	247	3	by	by	ADP
ejpam-6264	247	4	proposition	proposition	NOUN
ejpam-6264	247	5	3	3	NUM
ejpam-6264	247	6	,	,	PUNCT
ejpam-6264	247	7	γtmr(bn	γtmr(bn	NUM
ejpam-6264	247	8	)	)	PUNCT
ejpam-6264	247	9	≥	≥	NOUN
ejpam-6264	247	10	10	10	NUM
ejpam-6264	247	11	.	.	PUNCT
ejpam-6264	248	1	therefore	therefore	ADV
ejpam-6264	248	2	,	,	PUNCT
ejpam-6264	248	3	for	for	ADP
ejpam-6264	248	4	all	all	DET
ejpam-6264	248	5	n	n	PRON
ejpam-6264	248	6	≥	≥	NUM
ejpam-6264	248	7	4	4	NUM
ejpam-6264	248	8	,	,	PUNCT
ejpam-6264	248	9	γtmr(bn	γtmr(bn	NUM
ejpam-6264	248	10	)	)	PUNCT
ejpam-6264	248	11	=	=	SYM
ejpam-6264	248	12	10	10	NUM
ejpam-6264	248	13	.	.	PUNCT
ejpam-6264	249	1	the	the	DET
ejpam-6264	249	2	windmill	windmill	NOUN
ejpam-6264	249	3	graph	graph	NOUN
ejpam-6264	249	4	wd(k	wd(k	PROPN
ejpam-6264	249	5	,	,	PUNCT
ejpam-6264	249	6	n)=	n)=	NOUN
ejpam-6264	249	7	g	g	NOUN
ejpam-6264	249	8	=	=	SYM
ejpam-6264	249	9	k1	k1	PROPN
ejpam-6264	249	10	+	+	CCONJ
ejpam-6264	249	11	nkk−1	nkk−1	PROPN
ejpam-6264	249	12	is	be	AUX
ejpam-6264	249	13	constructed	construct	VERB
ejpam-6264	249	14	for	for	ADP
ejpam-6264	249	15	k	k	PROPN
ejpam-6264	249	16	≥	≥	NUM
ejpam-6264	249	17	2	2	NUM
ejpam-6264	249	18	and	and	CCONJ
ejpam-6264	249	19	n	n	PRON
ejpam-6264	249	20	≥	≥	NOUN
ejpam-6264	249	21	2	2	NUM
ejpam-6264	249	22	by	by	ADP
ejpam-6264	249	23	joining	join	VERB
ejpam-6264	249	24	n	n	PRON
ejpam-6264	249	25	copies	copy	NOUN
ejpam-6264	249	26	of	of	ADP
ejpam-6264	249	27	the	the	DET
ejpam-6264	249	28	complete	complete	ADJ
ejpam-6264	249	29	graph	graph	NOUN
ejpam-6264	249	30	kk	kk	X
ejpam-6264	249	31	at	at	ADP
ejpam-6264	249	32	a	a	DET
ejpam-6264	249	33	shared	share	VERB
ejpam-6264	249	34	vertex	vertex	NOUN
ejpam-6264	249	35	.	.	PUNCT
ejpam-6264	250	1	it	it	PRON
ejpam-6264	250	2	has	have	VERB
ejpam-6264	250	3	n(k	n(k	PROPN
ejpam-6264	250	4	−	−	PROPN
ejpam-6264	250	5	1	1	NUM
ejpam-6264	250	6	)	)	PUNCT
ejpam-6264	250	7	+	+	CCONJ
ejpam-6264	250	8	1	1	NUM
ejpam-6264	250	9	vertices	vertex	NOUN
ejpam-6264	250	10	and	and	CCONJ
ejpam-6264	250	11	1	1	NUM
ejpam-6264	250	12	2nk(k	2nk(k	NUM
ejpam-6264	250	13	−	−	NUM
ejpam-6264	250	14	1	1	NUM
ejpam-6264	250	15	)	)	PUNCT
ejpam-6264	250	16	edges	edge	NOUN
ejpam-6264	250	17	.	.	PUNCT
ejpam-6264	251	1	the	the	DET
ejpam-6264	251	2	case	case	NOUN
ejpam-6264	251	3	k	k	NOUN
ejpam-6264	251	4	=	=	SYM
ejpam-6264	251	5	3	3	NUM
ejpam-6264	251	6	corresponds	correspond	VERB
ejpam-6264	251	7	to	to	ADP
ejpam-6264	251	8	the	the	DET
ejpam-6264	251	9	dutch	dutch	ADJ
ejpam-6264	251	10	windmill	windmill	NOUN
ejpam-6264	251	11	graph	graph	NOUN
ejpam-6264	251	12	(	(	PUNCT
ejpam-6264	251	13	also	also	ADV
ejpam-6264	251	14	called	call	VERB
ejpam-6264	251	15	friendship	friendship	NOUN
ejpam-6264	251	16	graph	graph	NOUN
ejpam-6264	251	17	)	)	PUNCT
ejpam-6264	251	18	gn	gn	PROPN
ejpam-6264	251	19	3	3	NUM
ejpam-6264	251	20	=	=	SYM
ejpam-6264	251	21	k1	k1	NOUN
ejpam-6264	251	22	+	+	CCONJ
ejpam-6264	251	23	nk2	nk2	NOUN
ejpam-6264	251	24	and	and	CCONJ
ejpam-6264	251	25	the	the	DET
ejpam-6264	251	26	case	case	NOUN
ejpam-6264	251	27	n	n	NOUN
ejpam-6264	251	28	=	=	SYM
ejpam-6264	251	29	2	2	NUM
ejpam-6264	251	30	corresponds	correspond	NOUN
ejpam-6264	251	31	to	to	ADP
ejpam-6264	251	32	the	the	DET
ejpam-6264	251	33	butterfly	butterfly	NOUN
ejpam-6264	251	34	graph	graph	NOUN
ejpam-6264	251	35	g2	g2	PROPN
ejpam-6264	251	36	3	3	NUM
ejpam-6264	251	37	=	=	SYM
ejpam-6264	251	38	k1	k1	NOUN
ejpam-6264	251	39	+	+	NOUN
ejpam-6264	251	40	2k2	2k2	NUM
ejpam-6264	251	41	.	.	PUNCT
ejpam-6264	252	1	the	the	DET
ejpam-6264	252	2	graphs	graph	NOUN
ejpam-6264	252	3	in	in	ADP
ejpam-6264	252	4	figures	figure	NOUN
ejpam-6264	252	5	3	3	NUM
ejpam-6264	252	6	,	,	PUNCT
ejpam-6264	252	7	4	4	NUM
ejpam-6264	252	8	,	,	PUNCT
ejpam-6264	252	9	and	and	CCONJ
ejpam-6264	252	10	5	5	NUM
ejpam-6264	252	11	are	be	AUX
ejpam-6264	252	12	the	the	DET
ejpam-6264	252	13	windmill	windmill	NOUN
ejpam-6264	252	14	graph	graph	NOUN
ejpam-6264	252	15	wd(4	wd(4	PROPN
ejpam-6264	252	16	,	,	PUNCT
ejpam-6264	252	17	2	2	NUM
ejpam-6264	252	18	)	)	PUNCT
ejpam-6264	252	19	,	,	PUNCT
ejpam-6264	252	20	friendship	friendship	NOUN
ejpam-6264	252	21	graph	graph	NOUN
ejpam-6264	252	22	g4	g4	NOUN
ejpam-6264	252	23	3	3	NUM
ejpam-6264	252	24	and	and	CCONJ
ejpam-6264	252	25	butterfly	butterfly	NOUN
ejpam-6264	252	26	graphs	graph	NOUN
ejpam-6264	252	27	g2	g2	PROPN
ejpam-6264	252	28	3	3	NUM
ejpam-6264	252	29	,	,	PUNCT
ejpam-6264	252	30	respectively	respectively	ADV
ejpam-6264	252	31	.	.	PUNCT
ejpam-6264	253	1	3	3	NUM
ejpam-6264	253	2	22	22	NUM
ejpam-6264	253	3	0	0	NUM
ejpam-6264	253	4	00	00	NUM
ejpam-6264	253	5	0	0	NUM
ejpam-6264	253	6	figure	figure	NOUN
ejpam-6264	253	7	3	3	NUM
ejpam-6264	253	8	:	:	PUNCT
ejpam-6264	253	9	a	a	DET
ejpam-6264	253	10	windmill	windmill	NOUN
ejpam-6264	253	11	graph	graph	NOUN
ejpam-6264	253	12	wd(4	wd(4	PROPN
ejpam-6264	253	13	,	,	PUNCT
ejpam-6264	253	14	2	2	NUM
ejpam-6264	253	15	)	)	PUNCT
ejpam-6264	253	16	with	with	ADP
ejpam-6264	253	17	γtmr(wd(4	γtmr(wd(4	NOUN
ejpam-6264	253	18	,	,	PUNCT
ejpam-6264	253	19	2	2	NUM
ejpam-6264	253	20	)	)	PUNCT
ejpam-6264	253	21	)	)	PUNCT
ejpam-6264	254	1	=	=	PUNCT
ejpam-6264	254	2	7	7	NUM
ejpam-6264	254	3	2	2	NUM
ejpam-6264	254	4	1	1	NUM
ejpam-6264	254	5	1	1	NUM
ejpam-6264	254	6	1	1	NUM
ejpam-6264	254	7	1	1	NUM
ejpam-6264	254	8	11	11	NUM
ejpam-6264	254	9	1	1	NUM
ejpam-6264	254	10	1	1	NUM
ejpam-6264	254	11	figure	figure	NOUN
ejpam-6264	254	12	4	4	NUM
ejpam-6264	254	13	:	:	PUNCT
ejpam-6264	254	14	a	a	DET
ejpam-6264	254	15	friendship	friendship	NOUN
ejpam-6264	254	16	graph	graph	NOUN
ejpam-6264	254	17	g4	g4	NOUN
ejpam-6264	254	18	3	3	NUM
ejpam-6264	254	19	with	with	ADP
ejpam-6264	254	20	γtmr(g	γtmr(g	PROPN
ejpam-6264	254	21	4	4	NUM
ejpam-6264	254	22	3	3	NUM
ejpam-6264	254	23	)	)	PUNCT
ejpam-6264	254	24	=	=	SYM
ejpam-6264	255	1	10	10	NUM
ejpam-6264	255	2	s.	s.	PROPN
ejpam-6264	255	3	ahamad	ahamad	VERB
ejpam-6264	255	4	et	et	PROPN
ejpam-6264	255	5	al	al	PROPN
ejpam-6264	255	6	.	.	PUNCT
ejpam-6264	255	7	/	/	SYM
ejpam-6264	255	8	eur	eur	PROPN
ejpam-6264	255	9	.	.	PUNCT
ejpam-6264	256	1	j.	j.	PROPN
ejpam-6264	256	2	pure	pure	PROPN
ejpam-6264	256	3	appl	appl	PROPN
ejpam-6264	256	4	.	.	PROPN
ejpam-6264	256	5	math	math	PROPN
ejpam-6264	256	6	,	,	PUNCT
ejpam-6264	256	7	18	18	NUM
ejpam-6264	256	8	(	(	PUNCT
ejpam-6264	256	9	4	4	NUM
ejpam-6264	256	10	)	)	PUNCT
ejpam-6264	256	11	(	(	PUNCT
ejpam-6264	256	12	2025	2025	NUM
ejpam-6264	256	13	)	)	PUNCT
ejpam-6264	256	14	,	,	PUNCT
ejpam-6264	256	15	6264	6264	NUM
ejpam-6264	256	16	10	10	NUM
ejpam-6264	256	17	of	of	ADP
ejpam-6264	256	18	20	20	NUM
ejpam-6264	256	19	2	2	NUM
ejpam-6264	256	20	1	1	NUM
ejpam-6264	256	21	11	11	NUM
ejpam-6264	256	22	1	1	NUM
ejpam-6264	256	23	figure	figure	NOUN
ejpam-6264	256	24	5	5	NUM
ejpam-6264	256	25	:	:	PUNCT
ejpam-6264	256	26	a	a	DET
ejpam-6264	256	27	butterfly	butterfly	NOUN
ejpam-6264	256	28	graph	graph	NOUN
ejpam-6264	256	29	g2	g2	PROPN
ejpam-6264	256	30	3	3	NUM
ejpam-6264	256	31	with	with	ADP
ejpam-6264	256	32	γtmr(g	γtmr(g	PROPN
ejpam-6264	256	33	2	2	NUM
ejpam-6264	256	34	3	3	NUM
ejpam-6264	256	35	)	)	PUNCT
ejpam-6264	256	36	=	=	SYM
ejpam-6264	256	37	6	6	NUM
ejpam-6264	256	38	proposition	proposition	NOUN
ejpam-6264	256	39	12	12	NUM
ejpam-6264	256	40	.	.	PUNCT
ejpam-6264	257	1	for	for	ADP
ejpam-6264	257	2	any	any	DET
ejpam-6264	257	3	windmill	windmill	NOUN
ejpam-6264	257	4	graph	graph	NOUN
ejpam-6264	257	5	g	g	PROPN
ejpam-6264	257	6	=	=	PROPN
ejpam-6264	257	7	k1	k1	PROPN
ejpam-6264	257	8	+	+	CCONJ
ejpam-6264	257	9	nkk−1	nkk−1	PROPN
ejpam-6264	257	10	,	,	PUNCT
ejpam-6264	257	11	where	where	SCONJ
ejpam-6264	257	12	k	k	PROPN
ejpam-6264	257	13	≥	≥	VERB
ejpam-6264	257	14	4	4	NUM
ejpam-6264	257	15	and	and	CCONJ
ejpam-6264	257	16	n	n	PRON
ejpam-6264	257	17	≥	≥	NOUN
ejpam-6264	257	18	2	2	NUM
ejpam-6264	257	19	,	,	PUNCT
ejpam-6264	257	20	γtmr(g	γtmr(g	NOUN
ejpam-6264	257	21	)	)	PUNCT
ejpam-6264	257	22	=	=	SYM
ejpam-6264	257	23	2n+	2n+	NUM
ejpam-6264	257	24	3	3	NUM
ejpam-6264	257	25	.	.	PUNCT
ejpam-6264	257	26	proof	proof	NOUN
ejpam-6264	257	27	.	.	PUNCT
ejpam-6264	258	1	let	let	VERB
ejpam-6264	258	2	g	g	NOUN
ejpam-6264	258	3	=	=	VERB
ejpam-6264	258	4	k1	k1	PROPN
ejpam-6264	258	5	+	+	CCONJ
ejpam-6264	258	6	nkk−1	nkk−1	PROPN
ejpam-6264	258	7	,	,	PUNCT
ejpam-6264	258	8	where	where	SCONJ
ejpam-6264	258	9	k	k	PROPN
ejpam-6264	258	10	≥	≥	VERB
ejpam-6264	258	11	4	4	NUM
ejpam-6264	258	12	and	and	CCONJ
ejpam-6264	258	13	n	n	PRON
ejpam-6264	258	14	≥	≥	NOUN
ejpam-6264	258	15	2	2	NUM
ejpam-6264	258	16	.	.	PUNCT
ejpam-6264	258	17	suppose	suppose	VERB
ejpam-6264	258	18	v	v	X
ejpam-6264	258	19	(	(	PUNCT
ejpam-6264	258	20	k1	k1	NOUN
ejpam-6264	258	21	)	)	PUNCT
ejpam-6264	258	22	=	=	SYM
ejpam-6264	258	23	{	{	PUNCT
ejpam-6264	258	24	u	u	NOUN
ejpam-6264	258	25	}	}	PUNCT
ejpam-6264	258	26	be	be	AUX
ejpam-6264	258	27	the	the	DET
ejpam-6264	258	28	central	central	ADJ
ejpam-6264	258	29	vertex	vertex	NOUN
ejpam-6264	258	30	in	in	ADP
ejpam-6264	258	31	g	g	NOUN
ejpam-6264	258	32	,	,	PUNCT
ejpam-6264	258	33	then	then	ADV
ejpam-6264	258	34	pick	pick	VERB
ejpam-6264	258	35	a	a	DET
ejpam-6264	258	36	vertex	vertex	NOUN
ejpam-6264	258	37	v	v	NOUN
ejpam-6264	258	38	in	in	ADP
ejpam-6264	258	39	each	each	DET
ejpam-6264	258	40	copies	copy	NOUN
ejpam-6264	258	41	of	of	ADP
ejpam-6264	258	42	the	the	DET
ejpam-6264	258	43	complete	complete	ADJ
ejpam-6264	258	44	graph	graph	NOUN
ejpam-6264	258	45	kk−1	kk−1	PROPN
ejpam-6264	258	46	and	and	CCONJ
ejpam-6264	258	47	define	define	VERB
ejpam-6264	258	48	a	a	DET
ejpam-6264	258	49	function	function	NOUN
ejpam-6264	258	50	f	f	NOUN
ejpam-6264	258	51	=	=	SYM
ejpam-6264	258	52	(	(	PUNCT
ejpam-6264	258	53	v0	v0	PROPN
ejpam-6264	258	54	,	,	PUNCT
ejpam-6264	258	55	v1	v1	NOUN
ejpam-6264	258	56	,	,	PUNCT
ejpam-6264	258	57	v2	v2	PROPN
ejpam-6264	258	58	,	,	PUNCT
ejpam-6264	258	59	v3	v3	PROPN
ejpam-6264	258	60	)	)	PUNCT
ejpam-6264	258	61	given	give	VERB
ejpam-6264	258	62	by	by	ADP
ejpam-6264	258	63	f(x	f(x	PROPN
ejpam-6264	258	64	)	)	PUNCT
ejpam-6264	259	1	=	=	PUNCT
ejpam-6264	260	1			NOUN
ejpam-6264	260	2	3	3	NUM
ejpam-6264	260	3	,	,	PUNCT
ejpam-6264	260	4	x	x	PUNCT
ejpam-6264	260	5	=	=	PUNCT
ejpam-6264	260	6	u.	u.	NOUN
ejpam-6264	260	7	2	2	NUM
ejpam-6264	260	8	,	,	PUNCT
ejpam-6264	260	9	x	x	PUNCT
ejpam-6264	260	10	=	=	PUNCT
ejpam-6264	261	1	v.	v.	ADP
ejpam-6264	261	2	0	0	NUM
ejpam-6264	261	3	,	,	PUNCT
ejpam-6264	261	4	otherwise	otherwise	ADV
ejpam-6264	261	5	.	.	PUNCT
ejpam-6264	262	1	then	then	ADV
ejpam-6264	262	2	f	f	PROPN
ejpam-6264	262	3	∈	∈	PROPN
ejpam-6264	262	4	tmrdf	tmrdf	NOUN
ejpam-6264	262	5	(	(	PUNCT
ejpam-6264	262	6	g	g	NOUN
ejpam-6264	262	7	)	)	PUNCT
ejpam-6264	262	8	.	.	PUNCT
ejpam-6264	263	1	thus	thus	ADV
ejpam-6264	263	2	,	,	PUNCT
ejpam-6264	263	3	γtmr(g	γtmr(g	NOUN
ejpam-6264	263	4	)	)	PUNCT
ejpam-6264	263	5	≤	≤	NOUN
ejpam-6264	263	6	ωtmr	ωtmr	ADJ
ejpam-6264	263	7	g	g	PROPN
ejpam-6264	263	8	(	(	PUNCT
ejpam-6264	263	9	f	f	X
ejpam-6264	263	10	)	)	PUNCT
ejpam-6264	263	11	=	=	SYM
ejpam-6264	263	12	2n	2n	NUM
ejpam-6264	264	1	+	+	CCONJ
ejpam-6264	264	2	3	3	X
ejpam-6264	264	3	.	.	PUNCT
ejpam-6264	264	4	now	now	ADV
ejpam-6264	264	5	,	,	PUNCT
ejpam-6264	264	6	since	since	SCONJ
ejpam-6264	264	7	γ(g	γ(g	PROPN
ejpam-6264	264	8	)	)	PUNCT
ejpam-6264	264	9	=	=	SYM
ejpam-6264	264	10	1	1	NUM
ejpam-6264	264	11	and	and	CCONJ
ejpam-6264	264	12	γt(g	γt(g	PUNCT
ejpam-6264	264	13	)	)	PUNCT
ejpam-6264	264	14	=	=	SYM
ejpam-6264	264	15	2	2	NUM
ejpam-6264	264	16	,	,	PUNCT
ejpam-6264	264	17	by	by	ADP
ejpam-6264	264	18	proposition	proposition	NOUN
ejpam-6264	264	19	3	3	NUM
ejpam-6264	264	20	,	,	PUNCT
ejpam-6264	264	21	γtmr(g	γtmr(g	NUM
ejpam-6264	264	22	)	)	PUNCT
ejpam-6264	264	23	≥	≥	NOUN
ejpam-6264	264	24	2n+	2n+	NUM
ejpam-6264	264	25	3	3	NUM
ejpam-6264	264	26	.	.	PUNCT
ejpam-6264	265	1	hence	hence	ADV
ejpam-6264	265	2	,	,	PUNCT
ejpam-6264	265	3	γtmr(g	γtmr(g	PROPN
ejpam-6264	265	4	)	)	PUNCT
ejpam-6264	266	1	=	=	SYM
ejpam-6264	267	1	2n+	2n+	NUM
ejpam-6264	267	2	3	3	X
ejpam-6264	267	3	.	.	PUNCT
ejpam-6264	268	1	proposition	proposition	NOUN
ejpam-6264	268	2	13	13	NUM
ejpam-6264	268	3	.	.	PUNCT
ejpam-6264	269	1	for	for	ADP
ejpam-6264	269	2	any	any	DET
ejpam-6264	269	3	friendship	friendship	NOUN
ejpam-6264	269	4	graph	graph	NOUN
ejpam-6264	269	5	g	g	PROPN
ejpam-6264	269	6	,	,	PUNCT
ejpam-6264	269	7	γtmr(g	γtmr(g	NOUN
ejpam-6264	269	8	)	)	PUNCT
ejpam-6264	269	9	=	=	SYM
ejpam-6264	269	10	2n+	2n+	NUM
ejpam-6264	269	11	2	2	NUM
ejpam-6264	269	12	.	.	PUNCT
ejpam-6264	269	13	proof	proof	NOUN
ejpam-6264	269	14	.	.	PUNCT
ejpam-6264	270	1	let	let	VERB
ejpam-6264	270	2	g	g	NOUN
ejpam-6264	270	3	=	=	PUNCT
ejpam-6264	270	4	k1+nk2	k1+nk2	NOUN
ejpam-6264	270	5	,	,	PUNCT
ejpam-6264	270	6	n	n	PRON
ejpam-6264	270	7	≥	≥	NOUN
ejpam-6264	270	8	2	2	NUM
ejpam-6264	270	9	.	.	PUNCT
ejpam-6264	271	1	let	let	VERB
ejpam-6264	271	2	v	v	NOUN
ejpam-6264	271	3	(	(	PUNCT
ejpam-6264	271	4	k1	k1	NOUN
ejpam-6264	271	5	)	)	PUNCT
ejpam-6264	271	6	=	=	SYM
ejpam-6264	271	7	{	{	PUNCT
ejpam-6264	271	8	u	u	NOUN
ejpam-6264	271	9	}	}	PUNCT
ejpam-6264	271	10	be	be	AUX
ejpam-6264	271	11	the	the	DET
ejpam-6264	271	12	central	central	ADJ
ejpam-6264	271	13	vertex	vertex	NOUN
ejpam-6264	271	14	in	in	ADP
ejpam-6264	271	15	g.	g.	PROPN
ejpam-6264	271	16	define	define	VERB
ejpam-6264	271	17	a	a	DET
ejpam-6264	271	18	function	function	NOUN
ejpam-6264	271	19	f	f	NOUN
ejpam-6264	271	20	=	=	SYM
ejpam-6264	271	21	(	(	PUNCT
ejpam-6264	271	22	∅	∅	NOUN
ejpam-6264	271	23	,	,	PUNCT
ejpam-6264	271	24	v	v	NOUN
ejpam-6264	271	25	(	(	PUNCT
ejpam-6264	271	26	g)\{u	g)\{u	PROPN
ejpam-6264	271	27	}	}	PUNCT
ejpam-6264	271	28	,	,	PUNCT
ejpam-6264	271	29	{	{	PUNCT
ejpam-6264	271	30	u},∅	u},∅	PROPN
ejpam-6264	271	31	)	)	PUNCT
ejpam-6264	271	32	.	.	PUNCT
ejpam-6264	272	1	then	then	ADV
ejpam-6264	272	2	for	for	ADP
ejpam-6264	272	3	all	all	DET
ejpam-6264	272	4	vi	vi	PROPN
ejpam-6264	272	5	∈	∈	PROPN
ejpam-6264	272	6	v1	v1	NOUN
ejpam-6264	272	7	,	,	PUNCT
ejpam-6264	272	8	1	1	NUM
ejpam-6264	272	9	≤	≤	NUM
ejpam-6264	272	10	i	i	PRON
ejpam-6264	272	11	≤	≤	PROPN
ejpam-6264	272	12	n	n	CCONJ
ejpam-6264	272	13	,	,	PUNCT
ejpam-6264	272	14	f(ng[vi	f(ng[vi	PROPN
ejpam-6264	272	15	]	]	X
ejpam-6264	272	16	)	)	PUNCT
ejpam-6264	272	17	=	=	SYM
ejpam-6264	273	1	2n+2	2n+2	PROPN
ejpam-6264	273	2	.	.	PUNCT
ejpam-6264	274	1	thus	thus	ADV
ejpam-6264	274	2	,	,	PUNCT
ejpam-6264	274	3	f	f	PROPN
ejpam-6264	274	4	∈	∈	PROPN
ejpam-6264	274	5	tmrdf	tmrdf	NOUN
ejpam-6264	274	6	(	(	PUNCT
ejpam-6264	274	7	g	g	NOUN
ejpam-6264	274	8	)	)	PUNCT
ejpam-6264	274	9	and	and	CCONJ
ejpam-6264	274	10	γtmr(g	γtmr(g	NUM
ejpam-6264	274	11	)	)	PUNCT
ejpam-6264	274	12	≤	≤	NOUN
ejpam-6264	274	13	ωtmr	ωtmr	ADJ
ejpam-6264	274	14	g	g	PROPN
ejpam-6264	274	15	(	(	PUNCT
ejpam-6264	274	16	f	f	X
ejpam-6264	274	17	)	)	PUNCT
ejpam-6264	274	18	=	=	SYM
ejpam-6264	274	19	2n	2n	NUM
ejpam-6264	275	1	+	+	CCONJ
ejpam-6264	275	2	2	2	X
ejpam-6264	275	3	.	.	X
ejpam-6264	275	4	clearly	clearly	ADV
ejpam-6264	275	5	,	,	PUNCT
ejpam-6264	275	6	{	{	PUNCT
ejpam-6264	275	7	u	u	NOUN
ejpam-6264	275	8	}	}	PUNCT
ejpam-6264	275	9	is	be	AUX
ejpam-6264	275	10	a	a	DET
ejpam-6264	275	11	γ	γ	NOUN
ejpam-6264	275	12	-	-	PUNCT
ejpam-6264	275	13	set	set	NOUN
ejpam-6264	275	14	of	of	ADP
ejpam-6264	275	15	g	g	NOUN
ejpam-6264	275	16	,	,	PUNCT
ejpam-6264	275	17	and	and	CCONJ
ejpam-6264	275	18	so	so	ADV
ejpam-6264	275	19	γ(g	γ(g	PROPN
ejpam-6264	275	20	)	)	PUNCT
ejpam-6264	275	21	=	=	PUNCT
ejpam-6264	276	1	1	1	X
ejpam-6264	276	2	.	.	PUNCT
ejpam-6264	276	3	moreover	moreover	ADV
ejpam-6264	276	4	,	,	PUNCT
ejpam-6264	276	5	γt(g	γt(g	PUNCT
ejpam-6264	276	6	)	)	PUNCT
ejpam-6264	276	7	=	=	SYM
ejpam-6264	276	8	2	2	NUM
ejpam-6264	276	9	and	and	CCONJ
ejpam-6264	276	10	so	so	ADV
ejpam-6264	276	11	,	,	PUNCT
ejpam-6264	276	12	by	by	ADP
ejpam-6264	276	13	proposition	proposition	NOUN
ejpam-6264	276	14	3	3	NUM
ejpam-6264	276	15	,	,	PUNCT
ejpam-6264	276	16	γtmr(g	γtmr(g	NUM
ejpam-6264	276	17	)	)	PUNCT
ejpam-6264	276	18	≥	≥	NOUN
ejpam-6264	276	19	2n	2n	NUM
ejpam-6264	277	1	+	+	CCONJ
ejpam-6264	277	2	2	2	X
ejpam-6264	277	3	.	.	X
ejpam-6264	277	4	hence	hence	ADV
ejpam-6264	277	5	,	,	PUNCT
ejpam-6264	277	6	γtmr(g	γtmr(g	PROPN
ejpam-6264	277	7	)	)	PUNCT
ejpam-6264	278	1	=	=	SYM
ejpam-6264	279	1	2n+	2n+	NUM
ejpam-6264	279	2	2	2	NUM
ejpam-6264	279	3	.	.	PUNCT
ejpam-6264	279	4	corollary	corollary	ADJ
ejpam-6264	279	5	2	2	NUM
ejpam-6264	279	6	.	.	PUNCT
ejpam-6264	280	1	for	for	ADP
ejpam-6264	280	2	a	a	DET
ejpam-6264	280	3	butterfly	butterfly	NOUN
ejpam-6264	280	4	graph	graph	NOUN
ejpam-6264	280	5	g	g	PROPN
ejpam-6264	280	6	,	,	PUNCT
ejpam-6264	280	7	γtmr(g	γtmr(g	NOUN
ejpam-6264	280	8	)	)	PUNCT
ejpam-6264	280	9	=	=	SYM
ejpam-6264	280	10	6	6	X
ejpam-6264	280	11	.	.	PUNCT
ejpam-6264	280	12	proof	proof	NOUN
ejpam-6264	280	13	.	.	PUNCT
ejpam-6264	281	1	the	the	DET
ejpam-6264	281	2	result	result	NOUN
ejpam-6264	281	3	follows	follow	VERB
ejpam-6264	281	4	from	from	ADP
ejpam-6264	281	5	proposition	proposition	NOUN
ejpam-6264	281	6	13	13	NUM
ejpam-6264	281	7	.	.	PUNCT
ejpam-6264	282	1	a	a	DET
ejpam-6264	282	2	graph	graph	NOUN
ejpam-6264	282	3	g	g	NOUN
ejpam-6264	282	4	is	be	AUX
ejpam-6264	282	5	called	call	VERB
ejpam-6264	282	6	bipartite	bipartite	ADJ
ejpam-6264	282	7	if	if	SCONJ
ejpam-6264	282	8	the	the	DET
ejpam-6264	282	9	vertex	vertex	NOUN
ejpam-6264	282	10	set	set	VERB
ejpam-6264	282	11	v	v	NOUN
ejpam-6264	282	12	(	(	PUNCT
ejpam-6264	282	13	g	g	NOUN
ejpam-6264	282	14	)	)	PUNCT
ejpam-6264	282	15	of	of	ADP
ejpam-6264	282	16	g	g	NOUN
ejpam-6264	282	17	can	can	AUX
ejpam-6264	282	18	be	be	AUX
ejpam-6264	282	19	partitioned	partition	VERB
ejpam-6264	282	20	into	into	ADP
ejpam-6264	282	21	two	two	NUM
ejpam-6264	282	22	subsets	subset	NOUN
ejpam-6264	282	23	v1	v1	NOUN
ejpam-6264	282	24	and	and	CCONJ
ejpam-6264	282	25	v2	v2	VERB
ejpam-6264	282	26	such	such	ADJ
ejpam-6264	282	27	that	that	SCONJ
ejpam-6264	282	28	every	every	DET
ejpam-6264	282	29	edge	edge	NOUN
ejpam-6264	282	30	in	in	ADP
ejpam-6264	282	31	g	g	PROPN
ejpam-6264	282	32	joins	join	VERB
ejpam-6264	282	33	a	a	DET
ejpam-6264	282	34	vertex	vertex	NOUN
ejpam-6264	282	35	in	in	ADP
ejpam-6264	282	36	v1	v1	NOUN
ejpam-6264	282	37	with	with	ADP
ejpam-6264	282	38	a	a	DET
ejpam-6264	282	39	vertex	vertex	NOUN
ejpam-6264	282	40	in	in	ADP
ejpam-6264	282	41	v2	v2	NOUN
ejpam-6264	282	42	.	.	PUNCT
ejpam-6264	283	1	if	if	SCONJ
ejpam-6264	283	2	g	g	PROPN
ejpam-6264	283	3	is	be	AUX
ejpam-6264	283	4	bipartite	bipartite	ADJ
ejpam-6264	283	5	such	such	ADJ
ejpam-6264	283	6	that	that	SCONJ
ejpam-6264	283	7	g	g	PROPN
ejpam-6264	283	8	contains	contain	VERB
ejpam-6264	283	9	every	every	DET
ejpam-6264	283	10	edge	edge	NOUN
ejpam-6264	283	11	incident	incident	NOUN
ejpam-6264	283	12	with	with	ADP
ejpam-6264	283	13	any	any	DET
ejpam-6264	283	14	pair	pair	NOUN
ejpam-6264	283	15	of	of	ADP
ejpam-6264	283	16	vertices	vertex	NOUN
ejpam-6264	283	17	in	in	ADP
ejpam-6264	283	18	v1	v1	NOUN
ejpam-6264	283	19	and	and	CCONJ
ejpam-6264	283	20	v2	v2	NOUN
ejpam-6264	283	21	,	,	PUNCT
ejpam-6264	283	22	then	then	ADV
ejpam-6264	283	23	g	g	PROPN
ejpam-6264	283	24	is	be	AUX
ejpam-6264	283	25	a	a	DET
ejpam-6264	283	26	complete	complete	ADJ
ejpam-6264	283	27	bipartite	bipartite	NOUN
ejpam-6264	283	28	graph	graph	NOUN
ejpam-6264	283	29	;	;	PUNCT
ejpam-6264	283	30	in	in	ADP
ejpam-6264	283	31	this	this	DET
ejpam-6264	283	32	case	case	NOUN
ejpam-6264	283	33	,	,	PUNCT
ejpam-6264	283	34	g	g	PROPN
ejpam-6264	283	35	=	=	SYM
ejpam-6264	283	36	km	km	PROPN
ejpam-6264	283	37	,	,	PUNCT
ejpam-6264	283	38	n	n	CCONJ
ejpam-6264	283	39	if	if	SCONJ
ejpam-6264	283	40	|v1|	|v1|	NUM
ejpam-6264	283	41	=	=	SYM
ejpam-6264	283	42	m	m	NOUN
ejpam-6264	283	43	and	and	CCONJ
ejpam-6264	283	44	|v2|	|v2|	ADV
ejpam-6264	283	45	=	=	PUNCT
ejpam-6264	283	46	n.	n.	NOUN
ejpam-6264	283	47	figure	figure	NOUN
ejpam-6264	283	48	6	6	NUM
ejpam-6264	283	49	shows	show	VERB
ejpam-6264	283	50	the	the	DET
ejpam-6264	283	51	complete	complete	ADJ
ejpam-6264	283	52	bipartite	bipartite	PROPN
ejpam-6264	283	53	graph	graph	NOUN
ejpam-6264	283	54	k7,5	k7,5	PROPN
ejpam-6264	283	55	.	.	PUNCT
ejpam-6264	283	56	proposition	proposition	NOUN
ejpam-6264	283	57	14	14	NUM
ejpam-6264	283	58	.	.	PUNCT
ejpam-6264	284	1	for	for	ADP
ejpam-6264	284	2	a	a	DET
ejpam-6264	284	3	complete	complete	ADJ
ejpam-6264	284	4	bipartite	bipartite	NOUN
ejpam-6264	284	5	graph	graph	NOUN
ejpam-6264	284	6	km	km	PROPN
ejpam-6264	284	7	,	,	PUNCT
ejpam-6264	284	8	n	n	CCONJ
ejpam-6264	284	9	,	,	PUNCT
ejpam-6264	284	10	let	let	VERB
ejpam-6264	284	11	p	p	NOUN
ejpam-6264	284	12	=	=	NOUN
ejpam-6264	284	13	min{m	min{m	PROPN
ejpam-6264	284	14	,	,	PUNCT
ejpam-6264	284	15	n},m	n},m	PROPN
ejpam-6264	284	16	,	,	PUNCT
ejpam-6264	284	17	n	n	PRON
ejpam-6264	284	18	≥	≥	NOUN
ejpam-6264	284	19	2	2	NUM
ejpam-6264	284	20	.	.	PUNCT
ejpam-6264	285	1	then	then	ADV
ejpam-6264	285	2	γtmr(km	γtmr(km	PROPN
ejpam-6264	285	3	,	,	PUNCT
ejpam-6264	285	4	n	n	CCONJ
ejpam-6264	285	5	)	)	PUNCT
ejpam-6264	285	6	=	=	PUNCT
ejpam-6264	285	7			NOUN
ejpam-6264	285	8	6	6	NUM
ejpam-6264	285	9	,	,	PUNCT
ejpam-6264	285	10	if	if	SCONJ
ejpam-6264	285	11	p	p	NOUN
ejpam-6264	285	12	=	=	NOUN
ejpam-6264	285	13	2	2	NUM
ejpam-6264	285	14	.	.	NOUN
ejpam-6264	285	15	8	8	NUM
ejpam-6264	285	16	,	,	PUNCT
ejpam-6264	285	17	if	if	SCONJ
ejpam-6264	285	18	p	p	NOUN
ejpam-6264	285	19	=	=	NOUN
ejpam-6264	285	20	3	3	NUM
ejpam-6264	285	21	9	9	NUM
ejpam-6264	285	22	,	,	PUNCT
ejpam-6264	285	23	if	if	SCONJ
ejpam-6264	285	24	p	p	NOUN
ejpam-6264	285	25	=	=	NOUN
ejpam-6264	285	26	4	4	NUM
ejpam-6264	285	27	10	10	NUM
ejpam-6264	285	28	,	,	PUNCT
ejpam-6264	285	29	if	if	SCONJ
ejpam-6264	285	30	p	p	PRON
ejpam-6264	285	31	≥	≥	NOUN
ejpam-6264	285	32	5	5	NUM
ejpam-6264	285	33	.	.	PUNCT
ejpam-6264	286	1	s.	s.	PROPN
ejpam-6264	286	2	ahamad	ahamad	VERB
ejpam-6264	286	3	et	et	PROPN
ejpam-6264	286	4	al	al	PROPN
ejpam-6264	286	5	.	.	PUNCT
ejpam-6264	286	6	/	/	SYM
ejpam-6264	286	7	eur	eur	PROPN
ejpam-6264	286	8	.	.	PUNCT
ejpam-6264	287	1	j.	j.	PROPN
ejpam-6264	287	2	pure	pure	PROPN
ejpam-6264	287	3	appl	appl	PROPN
ejpam-6264	287	4	.	.	PROPN
ejpam-6264	287	5	math	math	PROPN
ejpam-6264	287	6	,	,	PUNCT
ejpam-6264	287	7	18	18	NUM
ejpam-6264	287	8	(	(	PUNCT
ejpam-6264	287	9	4	4	NUM
ejpam-6264	287	10	)	)	PUNCT
ejpam-6264	287	11	(	(	PUNCT
ejpam-6264	287	12	2025	2025	NUM
ejpam-6264	287	13	)	)	PUNCT
ejpam-6264	287	14	,	,	PUNCT
ejpam-6264	287	15	6264	6264	NUM
ejpam-6264	287	16	11	11	NUM
ejpam-6264	287	17	of	of	ADP
ejpam-6264	287	18	20	20	NUM
ejpam-6264	287	19	....................................	....................................	PUNCT
ejpam-6264	287	20	....................................	....................................	PUNCT
ejpam-6264	288	1	....................................	....................................	PUNCT
ejpam-6264	288	2	....................................	....................................	PUNCT
ejpam-6264	289	1	....................................	....................................	PUNCT
ejpam-6264	289	2	....................................	....................................	PUNCT
ejpam-6264	290	1	....................................	....................................	PUNCT
ejpam-6264	290	2	....................................	....................................	PUNCT
ejpam-6264	291	1	....................................	....................................	PUNCT
ejpam-6264	291	2	....................................	....................................	PUNCT
ejpam-6264	292	1	....................................	....................................	PUNCT
ejpam-6264	292	2	....................................	....................................	PUNCT
ejpam-6264	293	1	.........................................................................................................................................................................................................................	.........................................................................................................................................................................................................................	PUNCT
ejpam-6264	293	2	...............................................................................................................................................................................................................................................	...............................................................................................................................................................................................................................................	PUNCT
ejpam-6264	293	3	..............................................................................................................................................................................................................................................................................	..............................................................................................................................................................................................................................................................................	PUNCT
ejpam-6264	293	4	....................................................................................................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6264	294	1	...........................................................................................................................................................................................................................................................................................................................................................................	...........................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6264	294	2	........	........	PUNCT
ejpam-6264	294	3	........	........	PUNCT
ejpam-6264	294	4	........	........	PUNCT
ejpam-6264	294	5	........	........	PUNCT
ejpam-6264	294	6	........	........	PUNCT
ejpam-6264	294	7	........	........	PUNCT
ejpam-6264	294	8	........	........	PUNCT
ejpam-6264	294	9	........	........	PUNCT
ejpam-6264	294	10	........	........	PUNCT
ejpam-6264	294	11	........	........	PUNCT
ejpam-6264	294	12	........	........	PUNCT
ejpam-6264	294	13	........	........	PUNCT
ejpam-6264	294	14	........	........	PUNCT
ejpam-6264	294	15	........	........	PUNCT
ejpam-6264	294	16	........	........	PUNCT
ejpam-6264	294	17	........	........	PUNCT
ejpam-6264	294	18	........	........	PUNCT
ejpam-6264	294	19	........	........	PUNCT
ejpam-6264	294	20	........	........	PUNCT
ejpam-6264	294	21	........	........	PUNCT
ejpam-6264	294	22	........	........	PUNCT
ejpam-6264	294	23	........	........	PUNCT
ejpam-6264	294	24	........	........	PUNCT
ejpam-6264	294	25	........	........	PUNCT
ejpam-6264	295	1	........	........	PUNCT
ejpam-6264	295	2	..........................................................................................................................................................................................................................	..........................................................................................................................................................................................................................	PUNCT
ejpam-6264	296	1	...............................................................................................................................................................................................................................................	...............................................................................................................................................................................................................................................	PUNCT
ejpam-6264	296	2	..............................................................................................................................................................................................................................................................................	..............................................................................................................................................................................................................................................................................	PUNCT
ejpam-6264	297	1	.............................................................................................................................................................................................................................................................................................................................	.............................................................................................................................................................................................................................................................................................................................	PROPN
ejpam-6264	297	2	........	........	PUNCT
ejpam-6264	297	3	........	........	PUNCT
ejpam-6264	297	4	........	........	PUNCT
ejpam-6264	297	5	........	........	PUNCT
ejpam-6264	297	6	........	........	PUNCT
ejpam-6264	297	7	........	........	PUNCT
ejpam-6264	297	8	........	........	PUNCT
ejpam-6264	297	9	........	........	PUNCT
ejpam-6264	297	10	........	........	PUNCT
ejpam-6264	297	11	........	........	PUNCT
ejpam-6264	297	12	........	........	PUNCT
ejpam-6264	297	13	........	........	PUNCT
ejpam-6264	297	14	........	........	PUNCT
ejpam-6264	297	15	........	........	PUNCT
ejpam-6264	297	16	........	........	PUNCT
ejpam-6264	297	17	........	........	PUNCT
ejpam-6264	297	18	........	........	PUNCT
ejpam-6264	297	19	........	........	PUNCT
ejpam-6264	297	20	........	........	PUNCT
ejpam-6264	297	21	........	........	PUNCT
ejpam-6264	297	22	........	........	PUNCT
ejpam-6264	297	23	........	........	PUNCT
ejpam-6264	297	24	........	........	PUNCT
ejpam-6264	297	25	........	........	PUNCT
ejpam-6264	297	26	........	........	PUNCT
ejpam-6264	297	27	........	........	PUNCT
ejpam-6264	297	28	.........	.........	PUNCT
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ejpam-6264	298	2	........	........	PUNCT
ejpam-6264	298	3	........	........	PUNCT
ejpam-6264	298	4	........	........	PUNCT
ejpam-6264	298	5	........	........	PUNCT
ejpam-6264	298	6	........	........	PUNCT
ejpam-6264	298	7	........	........	PUNCT
ejpam-6264	298	8	........	........	PUNCT
ejpam-6264	298	9	........	........	PUNCT
ejpam-6264	298	10	........	........	PUNCT
ejpam-6264	298	11	........	........	PUNCT
ejpam-6264	298	12	........	........	PUNCT
ejpam-6264	298	13	........	........	PUNCT
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ejpam-6264	298	15	........	........	PUNCT
ejpam-6264	298	16	........	........	PUNCT
ejpam-6264	298	17	........	........	PUNCT
ejpam-6264	298	18	........	........	PUNCT
ejpam-6264	298	19	........	........	PUNCT
ejpam-6264	298	20	........	........	PUNCT
ejpam-6264	298	21	........	........	PUNCT
ejpam-6264	298	22	........	........	PUNCT
ejpam-6264	298	23	........	........	PUNCT
ejpam-6264	298	24	........	........	PUNCT
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ejpam-6264	299	2	..........................................................................................................................................................................................................................	..........................................................................................................................................................................................................................	PUNCT
ejpam-6264	300	1	...............................................................................................................................................................................................................................................	...............................................................................................................................................................................................................................................	PUNCT
ejpam-6264	300	2	........................................................................................................................................................................................................................................................................................	........................................................................................................................................................................................................................................................................................	PUNCT
ejpam-6264	301	1	.........	.........	PUNCT
ejpam-6264	302	1	.........	.........	PUNCT
ejpam-6264	302	2	.........	.........	PUNCT
ejpam-6264	303	1	.........	.........	PUNCT
ejpam-6264	303	2	.........	.........	PUNCT
ejpam-6264	304	1	.........	.........	PUNCT
ejpam-6264	304	2	.........	.........	PUNCT
ejpam-6264	305	1	.........	.........	PUNCT
ejpam-6264	305	2	.........	.........	PUNCT
ejpam-6264	306	1	.........	.........	PUNCT
ejpam-6264	306	2	.........	.........	PUNCT
ejpam-6264	307	1	.........	.........	PUNCT
ejpam-6264	307	2	.........	.........	PUNCT
ejpam-6264	308	1	.........	.........	PUNCT
ejpam-6264	308	2	.........	.........	PUNCT
ejpam-6264	309	1	.........	.........	PUNCT
ejpam-6264	309	2	.........	.........	PUNCT
ejpam-6264	310	1	.........	.........	PUNCT
ejpam-6264	310	2	.........	.........	PUNCT
ejpam-6264	311	1	.........	.........	PUNCT
ejpam-6264	311	2	.........	.........	PUNCT
ejpam-6264	312	1	.........	.........	PUNCT
ejpam-6264	312	2	.........	.........	PUNCT
ejpam-6264	313	1	.........	.........	PUNCT
ejpam-6264	313	2	.........	.........	PUNCT
ejpam-6264	314	1	....	....	PUNCT
ejpam-6264	314	2	.........	.........	PUNCT
ejpam-6264	314	3	........	........	PUNCT
ejpam-6264	314	4	........	........	PUNCT
ejpam-6264	314	5	........	........	PUNCT
ejpam-6264	314	6	........	........	PUNCT
ejpam-6264	314	7	........	........	PUNCT
ejpam-6264	314	8	........	........	PUNCT
ejpam-6264	314	9	........	........	PUNCT
ejpam-6264	314	10	........	........	PUNCT
ejpam-6264	314	11	........	........	PUNCT
ejpam-6264	314	12	........	........	PUNCT
ejpam-6264	314	13	........	........	PUNCT
ejpam-6264	314	14	........	........	PUNCT
ejpam-6264	314	15	........	........	PUNCT
ejpam-6264	314	16	........	........	PUNCT
ejpam-6264	314	17	........	........	PUNCT
ejpam-6264	314	18	........	........	PUNCT
ejpam-6264	314	19	........	........	PUNCT
ejpam-6264	314	20	........	........	PUNCT
ejpam-6264	314	21	........	........	PUNCT
ejpam-6264	314	22	........	........	PUNCT
ejpam-6264	314	23	........	........	PUNCT
ejpam-6264	314	24	........	........	PUNCT
ejpam-6264	314	25	........	........	PUNCT
ejpam-6264	314	26	........	........	PUNCT
ejpam-6264	314	27	........	........	PUNCT
ejpam-6264	314	28	........	........	PUNCT
ejpam-6264	314	29	.........	.........	PUNCT
ejpam-6264	314	30	........	........	PUNCT
ejpam-6264	314	31	........	........	PUNCT
ejpam-6264	314	32	........	........	PUNCT
ejpam-6264	314	33	........	........	PUNCT
ejpam-6264	314	34	........	........	PUNCT
ejpam-6264	314	35	........	........	PUNCT
ejpam-6264	314	36	........	........	PUNCT
ejpam-6264	314	37	........	........	PUNCT
ejpam-6264	314	38	........	........	PUNCT
ejpam-6264	314	39	........	........	PUNCT
ejpam-6264	314	40	........	........	PUNCT
ejpam-6264	314	41	........	........	PUNCT
ejpam-6264	314	42	........	........	PUNCT
ejpam-6264	314	43	........	........	PUNCT
ejpam-6264	314	44	........	........	PUNCT
ejpam-6264	314	45	........	........	PUNCT
ejpam-6264	314	46	........	........	PUNCT
ejpam-6264	314	47	........	........	PUNCT
ejpam-6264	314	48	........	........	PUNCT
ejpam-6264	314	49	........	........	PUNCT
ejpam-6264	314	50	........	........	PUNCT
ejpam-6264	314	51	........	........	PUNCT
ejpam-6264	314	52	........	........	PUNCT
ejpam-6264	314	53	........	........	PUNCT
ejpam-6264	314	54	........	........	PUNCT
ejpam-6264	315	1	..........................................................................................................................................................................................................................	..........................................................................................................................................................................................................................	PUNCT
ejpam-6264	315	2	..........................................................................................................................................................................................................................................................	..........................................................................................................................................................................................................................................................	PUNCT
ejpam-6264	316	1	..........	..........	PUNCT
ejpam-6264	316	2	..........	..........	PUNCT
ejpam-6264	317	1	..........	..........	PUNCT
ejpam-6264	317	2	..........	..........	PUNCT
ejpam-6264	318	1	..........	..........	PUNCT
ejpam-6264	318	2	..........	..........	PUNCT
ejpam-6264	319	1	..........	..........	PUNCT
ejpam-6264	319	2	..........	..........	PUNCT
ejpam-6264	320	1	..........	..........	PUNCT
ejpam-6264	320	2	..........	..........	PUNCT
ejpam-6264	321	1	..........	..........	PUNCT
ejpam-6264	321	2	..........	..........	PUNCT
ejpam-6264	322	1	..........	..........	PUNCT
ejpam-6264	322	2	..........	..........	PUNCT
ejpam-6264	323	1	..........	..........	PUNCT
ejpam-6264	323	2	..........	..........	PUNCT
ejpam-6264	324	1	..........	..........	PUNCT
ejpam-6264	324	2	..........	..........	PUNCT
ejpam-6264	325	1	..........	..........	PUNCT
ejpam-6264	325	2	..........	..........	PUNCT
ejpam-6264	326	1	..........	..........	PUNCT
ejpam-6264	326	2	..........	..........	PUNCT
ejpam-6264	327	1	..........	..........	PUNCT
ejpam-6264	327	2	..........	..........	PUNCT
ejpam-6264	328	1	..........	..........	PUNCT
ejpam-6264	328	2	.........	.........	PUNCT
ejpam-6264	329	1	..........	..........	PUNCT
ejpam-6264	329	2	.........	.........	PUNCT
ejpam-6264	330	1	.........	.........	PUNCT
ejpam-6264	330	2	.........	.........	PUNCT
ejpam-6264	331	1	.........	.........	PUNCT
ejpam-6264	331	2	.........	.........	PUNCT
ejpam-6264	332	1	.........	.........	PUNCT
ejpam-6264	332	2	.........	.........	PUNCT
ejpam-6264	333	1	.........	.........	PUNCT
ejpam-6264	333	2	.........	.........	PUNCT
ejpam-6264	334	1	.........	.........	PUNCT
ejpam-6264	334	2	.........	.........	PUNCT
ejpam-6264	335	1	.........	.........	PUNCT
ejpam-6264	335	2	.........	.........	PUNCT
ejpam-6264	336	1	.........	.........	PUNCT
ejpam-6264	336	2	.........	.........	PUNCT
ejpam-6264	337	1	.........	.........	PUNCT
ejpam-6264	337	2	.........	.........	PUNCT
ejpam-6264	338	1	.........	.........	PUNCT
ejpam-6264	338	2	.........	.........	PUNCT
ejpam-6264	339	1	.........	.........	PUNCT
ejpam-6264	339	2	.........	.........	PUNCT
ejpam-6264	340	1	.........	.........	PUNCT
ejpam-6264	340	2	.........	.........	PUNCT
ejpam-6264	341	1	.........	.........	PUNCT
ejpam-6264	341	2	.........	.........	PUNCT
ejpam-6264	342	1	....	....	PUNCT
ejpam-6264	342	2	.........	.........	PUNCT
ejpam-6264	342	3	........	........	PUNCT
ejpam-6264	342	4	........	........	PUNCT
ejpam-6264	342	5	........	........	PUNCT
ejpam-6264	342	6	........	........	PUNCT
ejpam-6264	342	7	........	........	PUNCT
ejpam-6264	342	8	........	........	PUNCT
ejpam-6264	342	9	........	........	PUNCT
ejpam-6264	342	10	........	........	PUNCT
ejpam-6264	342	11	........	........	PUNCT
ejpam-6264	342	12	........	........	PUNCT
ejpam-6264	342	13	........	........	PUNCT
ejpam-6264	342	14	........	........	PUNCT
ejpam-6264	342	15	........	........	PUNCT
ejpam-6264	342	16	........	........	PUNCT
ejpam-6264	342	17	........	........	PUNCT
ejpam-6264	342	18	........	........	PUNCT
ejpam-6264	342	19	........	........	PUNCT
ejpam-6264	342	20	........	........	PUNCT
ejpam-6264	342	21	........	........	PUNCT
ejpam-6264	342	22	........	........	PUNCT
ejpam-6264	342	23	........	........	PUNCT
ejpam-6264	342	24	........	........	PUNCT
ejpam-6264	342	25	........	........	PUNCT
ejpam-6264	342	26	........	........	PUNCT
ejpam-6264	342	27	........	........	PUNCT
ejpam-6264	342	28	........	........	PUNCT
ejpam-6264	342	29	.........	.........	PUNCT
ejpam-6264	342	30	........	........	PUNCT
ejpam-6264	342	31	........	........	PUNCT
ejpam-6264	342	32	........	........	PUNCT
ejpam-6264	342	33	........	........	PUNCT
ejpam-6264	342	34	........	........	PUNCT
ejpam-6264	342	35	........	........	PUNCT
ejpam-6264	342	36	........	........	PUNCT
ejpam-6264	342	37	........	........	PUNCT
ejpam-6264	342	38	........	........	PUNCT
ejpam-6264	342	39	........	........	PUNCT
ejpam-6264	342	40	........	........	PUNCT
ejpam-6264	342	41	........	........	PUNCT
ejpam-6264	342	42	........	........	PUNCT
ejpam-6264	342	43	........	........	PUNCT
ejpam-6264	342	44	........	........	PUNCT
ejpam-6264	342	45	........	........	PUNCT
ejpam-6264	342	46	........	........	PUNCT
ejpam-6264	342	47	........	........	PUNCT
ejpam-6264	342	48	........	........	PUNCT
ejpam-6264	342	49	........	........	PUNCT
ejpam-6264	342	50	........	........	PUNCT
ejpam-6264	342	51	........	........	PUNCT
ejpam-6264	342	52	........	........	PUNCT
ejpam-6264	342	53	........	........	PUNCT
ejpam-6264	342	54	........	........	PUNCT
ejpam-6264	343	1	.......................................................................................................................................................................................................................................	.......................................................................................................................................................................................................................................	PUNCT
ejpam-6264	343	2	............	............	PUNCT
ejpam-6264	343	3	............	............	PUNCT
ejpam-6264	343	4	............	............	PUNCT
ejpam-6264	343	5	............	............	PUNCT
ejpam-6264	343	6	............	............	PUNCT
ejpam-6264	343	7	............	............	PUNCT
ejpam-6264	343	8	............	............	PUNCT
ejpam-6264	343	9	............	............	PUNCT
ejpam-6264	343	10	............	............	PUNCT
ejpam-6264	343	11	............	............	PUNCT
ejpam-6264	343	12	............	............	PUNCT
ejpam-6264	343	13	............	............	PUNCT
ejpam-6264	343	14	............	............	PUNCT
ejpam-6264	343	15	............	............	PUNCT
ejpam-6264	343	16	............	............	PUNCT
ejpam-6264	343	17	............	............	PUNCT
ejpam-6264	343	18	............	............	PUNCT
ejpam-6264	343	19	............	............	PUNCT
ejpam-6264	343	20	............	............	PUNCT
ejpam-6264	343	21	............	............	PUNCT
ejpam-6264	343	22	............	............	PUNCT
ejpam-6264	343	23	............	............	PUNCT
ejpam-6264	343	24	............	............	PUNCT
ejpam-6264	343	25	............	............	PUNCT
ejpam-6264	343	26	.......	.......	PUNCT
ejpam-6264	343	27	...........	...........	PUNCT
ejpam-6264	344	1	..........	..........	PUNCT
ejpam-6264	344	2	..........	..........	PUNCT
ejpam-6264	345	1	..........	..........	PUNCT
ejpam-6264	345	2	..........	..........	PUNCT
ejpam-6264	346	1	..........	..........	PUNCT
ejpam-6264	346	2	..........	..........	PUNCT
ejpam-6264	347	1	..........	..........	PUNCT
ejpam-6264	347	2	..........	..........	PUNCT
ejpam-6264	348	1	..........	..........	PUNCT
ejpam-6264	348	2	..........	..........	PUNCT
ejpam-6264	349	1	..........	..........	PUNCT
ejpam-6264	349	2	..........	..........	PUNCT
ejpam-6264	350	1	..........	..........	PUNCT
ejpam-6264	350	2	..........	..........	PUNCT
ejpam-6264	351	1	..........	..........	PUNCT
ejpam-6264	351	2	..........	..........	PUNCT
ejpam-6264	352	1	..........	..........	PUNCT
ejpam-6264	352	2	..........	..........	PUNCT
ejpam-6264	353	1	..........	..........	PUNCT
ejpam-6264	353	2	..........	..........	PUNCT
ejpam-6264	354	1	..........	..........	PUNCT
ejpam-6264	354	2	..........	..........	PUNCT
ejpam-6264	355	1	..........	..........	PUNCT
ejpam-6264	355	2	..........	..........	PUNCT
ejpam-6264	356	1	..........	..........	PUNCT
ejpam-6264	356	2	.........	.........	PUNCT
ejpam-6264	357	1	..........	..........	PUNCT
ejpam-6264	357	2	.........	.........	PUNCT
ejpam-6264	358	1	.........	.........	PUNCT
ejpam-6264	358	2	.........	.........	PUNCT
ejpam-6264	359	1	.........	.........	PUNCT
ejpam-6264	359	2	.........	.........	PUNCT
ejpam-6264	360	1	.........	.........	PUNCT
ejpam-6264	360	2	.........	.........	PUNCT
ejpam-6264	361	1	.........	.........	PUNCT
ejpam-6264	361	2	.........	.........	PUNCT
ejpam-6264	362	1	.........	.........	PUNCT
ejpam-6264	362	2	.........	.........	PUNCT
ejpam-6264	363	1	.........	.........	PUNCT
ejpam-6264	363	2	.........	.........	PUNCT
ejpam-6264	364	1	.........	.........	PUNCT
ejpam-6264	364	2	.........	.........	PUNCT
ejpam-6264	365	1	.........	.........	PUNCT
ejpam-6264	365	2	.........	.........	PUNCT
ejpam-6264	366	1	.........	.........	PUNCT
ejpam-6264	366	2	.........	.........	PUNCT
ejpam-6264	367	1	.........	.........	PUNCT
ejpam-6264	367	2	.........	.........	PUNCT
ejpam-6264	368	1	.........	.........	PUNCT
ejpam-6264	368	2	.........	.........	PUNCT
ejpam-6264	369	1	.........	.........	PUNCT
ejpam-6264	369	2	.........	.........	PUNCT
ejpam-6264	370	1	....	....	PUNCT
ejpam-6264	370	2	.........	.........	PUNCT
ejpam-6264	370	3	........	........	PUNCT
ejpam-6264	370	4	........	........	PUNCT
ejpam-6264	370	5	........	........	PUNCT
ejpam-6264	370	6	........	........	PUNCT
ejpam-6264	370	7	........	........	PUNCT
ejpam-6264	370	8	........	........	PUNCT
ejpam-6264	370	9	........	........	PUNCT
ejpam-6264	370	10	........	........	PUNCT
ejpam-6264	370	11	........	........	PUNCT
ejpam-6264	370	12	........	........	PUNCT
ejpam-6264	370	13	........	........	PUNCT
ejpam-6264	370	14	........	........	PUNCT
ejpam-6264	370	15	........	........	PUNCT
ejpam-6264	370	16	........	........	PUNCT
ejpam-6264	370	17	........	........	PUNCT
ejpam-6264	370	18	........	........	PUNCT
ejpam-6264	370	19	........	........	PUNCT
ejpam-6264	370	20	........	........	PUNCT
ejpam-6264	370	21	........	........	PUNCT
ejpam-6264	370	22	........	........	PUNCT
ejpam-6264	370	23	........	........	PUNCT
ejpam-6264	370	24	........	........	PUNCT
ejpam-6264	370	25	........	........	PUNCT
ejpam-6264	370	26	........	........	PUNCT
ejpam-6264	370	27	........	........	PUNCT
ejpam-6264	370	28	........	........	PUNCT
ejpam-6264	370	29	.........	.........	PUNCT
ejpam-6264	370	30	........	........	PUNCT
ejpam-6264	370	31	........	........	PUNCT
ejpam-6264	370	32	........	........	PUNCT
ejpam-6264	370	33	........	........	PUNCT
ejpam-6264	370	34	........	........	PUNCT
ejpam-6264	370	35	........	........	PUNCT
ejpam-6264	370	36	........	........	PUNCT
ejpam-6264	370	37	........	........	PUNCT
ejpam-6264	370	38	........	........	PUNCT
ejpam-6264	370	39	........	........	PUNCT
ejpam-6264	370	40	........	........	PUNCT
ejpam-6264	370	41	........	........	PUNCT
ejpam-6264	370	42	........	........	PUNCT
ejpam-6264	370	43	........	........	PUNCT
ejpam-6264	370	44	........	........	PUNCT
ejpam-6264	370	45	........	........	PUNCT
ejpam-6264	370	46	........	........	PUNCT
ejpam-6264	370	47	........	........	PUNCT
ejpam-6264	370	48	........	........	PUNCT
ejpam-6264	370	49	........	........	PUNCT
ejpam-6264	370	50	........	........	PUNCT
ejpam-6264	370	51	........	........	PUNCT
ejpam-6264	370	52	........	........	PUNCT
ejpam-6264	370	53	........	........	PUNCT
ejpam-6264	370	54	........	........	PUNCT
ejpam-6264	370	55	.	.	PUNCT
ejpam-6264	371	1	..............	..............	PUNCT
ejpam-6264	371	2	.............	.............	PUNCT
ejpam-6264	371	3	.............	.............	PUNCT
ejpam-6264	371	4	.............	.............	PUNCT
ejpam-6264	371	5	.............	.............	PUNCT
ejpam-6264	371	6	.............	.............	PUNCT
ejpam-6264	371	7	.............	.............	PUNCT
ejpam-6264	371	8	.............	.............	PUNCT
ejpam-6264	371	9	.............	.............	PUNCT
ejpam-6264	371	10	.............	.............	PUNCT
ejpam-6264	371	11	.............	.............	PUNCT
ejpam-6264	371	12	.............	.............	PUNCT
ejpam-6264	371	13	.............	.............	PUNCT
ejpam-6264	371	14	.............	.............	PUNCT
ejpam-6264	371	15	.............	.............	PUNCT
ejpam-6264	371	16	.............	.............	PUNCT
ejpam-6264	371	17	.............	.............	PUNCT
ejpam-6264	371	18	.............	.............	PUNCT
ejpam-6264	371	19	.............	.............	PUNCT
ejpam-6264	371	20	.............	.............	PUNCT
ejpam-6264	371	21	.............	.............	PUNCT
ejpam-6264	371	22	.............	.............	PUNCT
ejpam-6264	371	23	.............	.............	PUNCT
ejpam-6264	371	24	.............	.............	PUNCT
ejpam-6264	371	25	.............	.............	PUNCT
ejpam-6264	371	26	.............	.............	PUNCT
ejpam-6264	371	27	.............	.............	PUNCT
ejpam-6264	372	1	..	..	PUNCT
ejpam-6264	372	2	.............	.............	PUNCT
ejpam-6264	372	3	............	............	PUNCT
ejpam-6264	372	4	............	............	PUNCT
ejpam-6264	372	5	............	............	PUNCT
ejpam-6264	372	6	............	............	PUNCT
ejpam-6264	372	7	............	............	PUNCT
ejpam-6264	372	8	............	............	PUNCT
ejpam-6264	372	9	............	............	PUNCT
ejpam-6264	372	10	............	............	PUNCT
ejpam-6264	372	11	............	............	PUNCT
ejpam-6264	372	12	............	............	PUNCT
ejpam-6264	372	13	............	............	PUNCT
ejpam-6264	372	14	............	............	PUNCT
ejpam-6264	372	15	............	............	PUNCT
ejpam-6264	372	16	............	............	PUNCT
ejpam-6264	372	17	............	............	PUNCT
ejpam-6264	372	18	............	............	PUNCT
ejpam-6264	372	19	............	............	PUNCT
ejpam-6264	372	20	............	............	PUNCT
ejpam-6264	372	21	............	............	PUNCT
ejpam-6264	372	22	............	............	PUNCT
ejpam-6264	372	23	............	............	PUNCT
ejpam-6264	372	24	............	............	PUNCT
ejpam-6264	372	25	............	............	PUNCT
ejpam-6264	372	26	............	............	PUNCT
ejpam-6264	372	27	.......	.......	PUNCT
ejpam-6264	372	28	...........	...........	PUNCT
ejpam-6264	372	29	..........	..........	PUNCT
ejpam-6264	373	1	..........	..........	PUNCT
ejpam-6264	373	2	..........	..........	PUNCT
ejpam-6264	374	1	..........	..........	PUNCT
ejpam-6264	374	2	..........	..........	PUNCT
ejpam-6264	375	1	..........	..........	PUNCT
ejpam-6264	375	2	..........	..........	PUNCT
ejpam-6264	376	1	..........	..........	PUNCT
ejpam-6264	376	2	..........	..........	PUNCT
ejpam-6264	377	1	..........	..........	PUNCT
ejpam-6264	377	2	..........	..........	PUNCT
ejpam-6264	378	1	..........	..........	PUNCT
ejpam-6264	378	2	..........	..........	PUNCT
ejpam-6264	379	1	..........	..........	PUNCT
ejpam-6264	379	2	..........	..........	PUNCT
ejpam-6264	380	1	..........	..........	PUNCT
ejpam-6264	380	2	..........	..........	PUNCT
ejpam-6264	381	1	..........	..........	PUNCT
ejpam-6264	381	2	..........	..........	PUNCT
ejpam-6264	382	1	..........	..........	PUNCT
ejpam-6264	382	2	..........	..........	PUNCT
ejpam-6264	383	1	..........	..........	PUNCT
ejpam-6264	383	2	..........	..........	PUNCT
ejpam-6264	384	1	..........	..........	PUNCT
ejpam-6264	384	2	..........	..........	PUNCT
ejpam-6264	385	1	.........	.........	PUNCT
ejpam-6264	385	2	..........	..........	PUNCT
ejpam-6264	386	1	.........	.........	PUNCT
ejpam-6264	386	2	.........	.........	PUNCT
ejpam-6264	387	1	.........	.........	PUNCT
ejpam-6264	387	2	.........	.........	PUNCT
ejpam-6264	388	1	.........	.........	PUNCT
ejpam-6264	388	2	.........	.........	PUNCT
ejpam-6264	389	1	.........	.........	PUNCT
ejpam-6264	389	2	.........	.........	PUNCT
ejpam-6264	390	1	.........	.........	PUNCT
ejpam-6264	390	2	.........	.........	PUNCT
ejpam-6264	391	1	.........	.........	PUNCT
ejpam-6264	391	2	.........	.........	PUNCT
ejpam-6264	392	1	.........	.........	PUNCT
ejpam-6264	392	2	.........	.........	PUNCT
ejpam-6264	393	1	.........	.........	PUNCT
ejpam-6264	393	2	.........	.........	PUNCT
ejpam-6264	394	1	.........	.........	PUNCT
ejpam-6264	394	2	.........	.........	PUNCT
ejpam-6264	395	1	.........	.........	PUNCT
ejpam-6264	395	2	.........	.........	PUNCT
ejpam-6264	396	1	.........	.........	PUNCT
ejpam-6264	396	2	.........	.........	PUNCT
ejpam-6264	397	1	.........	.........	PUNCT
ejpam-6264	397	2	.........	.........	PUNCT
ejpam-6264	398	1	.........	.........	PUNCT
ejpam-6264	398	2	....	....	PUNCT
ejpam-6264	398	3	.........	.........	PUNCT
ejpam-6264	398	4	........	........	PUNCT
ejpam-6264	398	5	........	........	PUNCT
ejpam-6264	398	6	........	........	PUNCT
ejpam-6264	398	7	........	........	PUNCT
ejpam-6264	398	8	........	........	PUNCT
ejpam-6264	398	9	........	........	PUNCT
ejpam-6264	398	10	........	........	PUNCT
ejpam-6264	398	11	........	........	PUNCT
ejpam-6264	398	12	........	........	PUNCT
ejpam-6264	398	13	........	........	PUNCT
ejpam-6264	398	14	........	........	PUNCT
ejpam-6264	398	15	........	........	PUNCT
ejpam-6264	398	16	........	........	PUNCT
ejpam-6264	398	17	........	........	PUNCT
ejpam-6264	398	18	........	........	PUNCT
ejpam-6264	398	19	........	........	PUNCT
ejpam-6264	398	20	........	........	PUNCT
ejpam-6264	398	21	........	........	PUNCT
ejpam-6264	398	22	........	........	PUNCT
ejpam-6264	398	23	........	........	PUNCT
ejpam-6264	398	24	........	........	PUNCT
ejpam-6264	398	25	........	........	PUNCT
ejpam-6264	398	26	........	........	PUNCT
ejpam-6264	398	27	........	........	PUNCT
ejpam-6264	398	28	........	........	PUNCT
ejpam-6264	398	29	........	........	PUNCT
ejpam-6264	399	1	k7,5	k7,5	PROPN
ejpam-6264	399	2	:	:	PUNCT
ejpam-6264	399	3	figure	figure	NOUN
ejpam-6264	399	4	6	6	NUM
ejpam-6264	399	5	:	:	PUNCT
ejpam-6264	399	6	a	a	DET
ejpam-6264	399	7	complete	complete	ADJ
ejpam-6264	399	8	bipartite	bipartite	PROPN
ejpam-6264	399	9	g	g	PROPN
ejpam-6264	399	10	=	=	SYM
ejpam-6264	399	11	k7,5	k7,5	PROPN
ejpam-6264	399	12	proof	proof	NOUN
ejpam-6264	399	13	.	.	PUNCT
ejpam-6264	400	1	let	let	VERB
ejpam-6264	400	2	g	g	PRON
ejpam-6264	400	3	be	be	AUX
ejpam-6264	400	4	a	a	DET
ejpam-6264	400	5	complete	complete	ADJ
ejpam-6264	400	6	bipartite	bipartite	NOUN
ejpam-6264	400	7	graph	graph	NOUN
ejpam-6264	400	8	km	km	PROPN
ejpam-6264	400	9	,	,	PUNCT
ejpam-6264	400	10	n	n	PROPN
ejpam-6264	400	11	and	and	CCONJ
ejpam-6264	400	12	x	x	SYM
ejpam-6264	400	13	and	and	CCONJ
ejpam-6264	400	14	y	y	PROPN
ejpam-6264	400	15	be	be	AUX
ejpam-6264	400	16	partite	partite	ADJ
ejpam-6264	400	17	sets	set	NOUN
ejpam-6264	400	18	of	of	ADP
ejpam-6264	400	19	km	km	PROPN
ejpam-6264	400	20	,	,	PUNCT
ejpam-6264	400	21	n	n	CCONJ
ejpam-6264	400	22	,	,	PUNCT
ejpam-6264	400	23	where	where	SCONJ
ejpam-6264	400	24	|x|	|x|	PROPN
ejpam-6264	400	25	=	=	SYM
ejpam-6264	400	26	m	m	PROPN
ejpam-6264	400	27	and	and	CCONJ
ejpam-6264	400	28	|y	|y	X
ejpam-6264	400	29	|	|	NOUN
ejpam-6264	400	30	=	=	SYM
ejpam-6264	400	31	n	n	CCONJ
ejpam-6264	400	32	,	,	PUNCT
ejpam-6264	400	33	m	m	PROPN
ejpam-6264	400	34	,	,	PUNCT
ejpam-6264	400	35	n	n	PRON
ejpam-6264	400	36	≥	≥	NOUN
ejpam-6264	400	37	2	2	NUM
ejpam-6264	400	38	.	.	PUNCT
ejpam-6264	401	1	let	let	VERB
ejpam-6264	401	2	p	p	NOUN
ejpam-6264	401	3	=	=	NOUN
ejpam-6264	401	4	min{m	min{m	PROPN
ejpam-6264	401	5	,	,	PUNCT
ejpam-6264	401	6	n	n	CCONJ
ejpam-6264	401	7	}	}	PUNCT
ejpam-6264	401	8	.	.	PUNCT
ejpam-6264	402	1	if	if	SCONJ
ejpam-6264	402	2	p	p	NOUN
ejpam-6264	402	3	=	=	SYM
ejpam-6264	402	4	2	2	NUM
ejpam-6264	402	5	and	and	CCONJ
ejpam-6264	402	6	wlog	wlog	NOUN
ejpam-6264	402	7	,	,	PUNCT
ejpam-6264	402	8	we	we	PRON
ejpam-6264	402	9	let	let	VERB
ejpam-6264	402	10	x	x	PUNCT
ejpam-6264	402	11	=	=	PRON
ejpam-6264	402	12	{	{	PUNCT
ejpam-6264	402	13	x1	x1	PROPN
ejpam-6264	402	14	,	,	PUNCT
ejpam-6264	402	15	x2	x2	PROPN
ejpam-6264	402	16	}	}	PUNCT
ejpam-6264	402	17	and	and	CCONJ
ejpam-6264	402	18	pick	pick	VERB
ejpam-6264	402	19	a	a	DET
ejpam-6264	402	20	vertex	vertex	NOUN
ejpam-6264	402	21	y1	y1	NOUN
ejpam-6264	402	22	∈	∈	PROPN
ejpam-6264	402	23	y	y	PROPN
ejpam-6264	402	24	and	and	CCONJ
ejpam-6264	402	25	define	define	VERB
ejpam-6264	402	26	a	a	DET
ejpam-6264	402	27	function	function	NOUN
ejpam-6264	402	28	f	f	NOUN
ejpam-6264	402	29	=	=	SYM
ejpam-6264	402	30	(	(	PUNCT
ejpam-6264	402	31	v0	v0	PROPN
ejpam-6264	402	32	,	,	PUNCT
ejpam-6264	402	33	v1	v1	NOUN
ejpam-6264	402	34	,	,	PUNCT
ejpam-6264	402	35	v2	v2	PROPN
ejpam-6264	402	36	,	,	PUNCT
ejpam-6264	402	37	v3	v3	PROPN
ejpam-6264	402	38	)	)	PUNCT
ejpam-6264	402	39	given	give	VERB
ejpam-6264	402	40	by	by	ADP
ejpam-6264	402	41	f(z	f(z	PROPN
ejpam-6264	402	42	)	)	PUNCT
ejpam-6264	402	43	=	=	PUNCT
ejpam-6264	402	44			NOUN
ejpam-6264	402	45	3	3	NUM
ejpam-6264	402	46	,	,	PUNCT
ejpam-6264	402	47	z	z	NOUN
ejpam-6264	402	48	=	=	SYM
ejpam-6264	402	49	{	{	PUNCT
ejpam-6264	402	50	x1	x1	PROPN
ejpam-6264	402	51	}	}	PUNCT
ejpam-6264	402	52	.	.	PUNCT
ejpam-6264	403	1	2	2	NUM
ejpam-6264	403	2	,	,	PUNCT
ejpam-6264	403	3	z	z	NOUN
ejpam-6264	403	4	=	=	SYM
ejpam-6264	403	5	{	{	PUNCT
ejpam-6264	403	6	x2	x2	PROPN
ejpam-6264	403	7	}	}	PUNCT
ejpam-6264	403	8	.	.	PUNCT
ejpam-6264	404	1	1	1	NUM
ejpam-6264	404	2	,	,	PUNCT
ejpam-6264	404	3	z	z	NOUN
ejpam-6264	404	4	=	=	SYM
ejpam-6264	404	5	{	{	PUNCT
ejpam-6264	404	6	y1	y1	NOUN
ejpam-6264	404	7	}	}	PUNCT
ejpam-6264	404	8	.	.	PUNCT
ejpam-6264	405	1	0	0	NUM
ejpam-6264	405	2	,	,	PUNCT
ejpam-6264	405	3	otherwise	otherwise	ADV
ejpam-6264	405	4	.	.	PUNCT
ejpam-6264	406	1	then	then	ADV
ejpam-6264	406	2	f	f	PROPN
ejpam-6264	406	3	is	be	AUX
ejpam-6264	406	4	a	a	DET
ejpam-6264	406	5	tmrdf	tmrdf	NOUN
ejpam-6264	406	6	of	of	ADP
ejpam-6264	406	7	g.	g.	PROPN
ejpam-6264	406	8	thus	thus	ADV
ejpam-6264	406	9	,	,	PUNCT
ejpam-6264	406	10	γtmr(g	γtmr(g	NOUN
ejpam-6264	406	11	)	)	PUNCT
ejpam-6264	406	12	≤	≤	NOUN
ejpam-6264	406	13	ωtmr	ωtmr	ADJ
ejpam-6264	406	14	g	g	PROPN
ejpam-6264	406	15	(	(	PUNCT
ejpam-6264	406	16	f	f	X
ejpam-6264	406	17	)	)	PUNCT
ejpam-6264	406	18	=	=	SYM
ejpam-6264	406	19	6	6	X
ejpam-6264	406	20	.	.	PUNCT
ejpam-6264	406	21	by	by	ADP
ejpam-6264	406	22	proposition	proposition	NOUN
ejpam-6264	406	23	3	3	NUM
ejpam-6264	406	24	,	,	PUNCT
ejpam-6264	406	25	γtmr(g	γtmr(g	NOUN
ejpam-6264	406	26	)	)	PUNCT
ejpam-6264	406	27	≥	≥	NOUN
ejpam-6264	406	28	6	6	NUM
ejpam-6264	406	29	.	.	PUNCT
ejpam-6264	407	1	thus	thus	ADV
ejpam-6264	407	2	,	,	PUNCT
ejpam-6264	407	3	γtmr(g	γtmr(g	NOUN
ejpam-6264	407	4	)	)	PUNCT
ejpam-6264	407	5	=	=	SYM
ejpam-6264	408	1	6	6	X
ejpam-6264	408	2	.	.	PUNCT
ejpam-6264	409	1	if	if	SCONJ
ejpam-6264	409	2	p	p	NOUN
ejpam-6264	409	3	=	=	SYM
ejpam-6264	409	4	3	3	NUM
ejpam-6264	409	5	and	and	CCONJ
ejpam-6264	409	6	wlog	wlog	NOUN
ejpam-6264	409	7	,	,	PUNCT
ejpam-6264	409	8	we	we	PRON
ejpam-6264	409	9	let	let	VERB
ejpam-6264	409	10	x	x	PUNCT
ejpam-6264	409	11	=	=	PRON
ejpam-6264	409	12	{	{	PUNCT
ejpam-6264	409	13	x1	x1	PROPN
ejpam-6264	409	14	,	,	PUNCT
ejpam-6264	409	15	x2	x2	PROPN
ejpam-6264	409	16	,	,	PUNCT
ejpam-6264	409	17	x3	x3	ADJ
ejpam-6264	409	18	}	}	PUNCT
ejpam-6264	409	19	and	and	CCONJ
ejpam-6264	409	20	pick	pick	VERB
ejpam-6264	409	21	a	a	DET
ejpam-6264	409	22	vertex	vertex	NOUN
ejpam-6264	409	23	y1	y1	NOUN
ejpam-6264	409	24	∈	∈	PROPN
ejpam-6264	409	25	y	y	PROPN
ejpam-6264	409	26	and	and	CCONJ
ejpam-6264	409	27	define	define	VERB
ejpam-6264	409	28	a	a	DET
ejpam-6264	409	29	function	function	NOUN
ejpam-6264	409	30	f	f	NOUN
ejpam-6264	409	31	=	=	SYM
ejpam-6264	409	32	(	(	PUNCT
ejpam-6264	409	33	v0	v0	PROPN
ejpam-6264	409	34	,	,	PUNCT
ejpam-6264	409	35	v1	v1	NOUN
ejpam-6264	409	36	,	,	PUNCT
ejpam-6264	409	37	v2	v2	PROPN
ejpam-6264	409	38	,	,	PUNCT
ejpam-6264	409	39	v3	v3	PROPN
ejpam-6264	409	40	)	)	PUNCT
ejpam-6264	409	41	given	give	VERB
ejpam-6264	409	42	by	by	ADP
ejpam-6264	409	43	f(z	f(z	PROPN
ejpam-6264	409	44	)	)	PUNCT
ejpam-6264	409	45	=	=	PUNCT
ejpam-6264	409	46			NOUN
ejpam-6264	409	47	3	3	NUM
ejpam-6264	409	48	,	,	PUNCT
ejpam-6264	409	49	z	z	NOUN
ejpam-6264	409	50	=	=	SYM
ejpam-6264	409	51	{	{	PUNCT
ejpam-6264	409	52	x1	x1	PROPN
ejpam-6264	409	53	}	}	PUNCT
ejpam-6264	409	54	.	.	PUNCT
ejpam-6264	410	1	2	2	NUM
ejpam-6264	410	2	,	,	PUNCT
ejpam-6264	410	3	z	z	NOUN
ejpam-6264	410	4	∈	∈	PROPN
ejpam-6264	410	5	{	{	PUNCT
ejpam-6264	410	6	x2	x2	PROPN
ejpam-6264	410	7	,	,	PUNCT
ejpam-6264	410	8	x3	x3	ADJ
ejpam-6264	410	9	}	}	PUNCT
ejpam-6264	410	10	.	.	PUNCT
ejpam-6264	411	1	1	1	NUM
ejpam-6264	411	2	,	,	PUNCT
ejpam-6264	411	3	z	z	NOUN
ejpam-6264	411	4	=	=	SYM
ejpam-6264	411	5	{	{	PUNCT
ejpam-6264	411	6	y1	y1	NOUN
ejpam-6264	411	7	}	}	PUNCT
ejpam-6264	411	8	.	.	PUNCT
ejpam-6264	412	1	0	0	NUM
ejpam-6264	412	2	,	,	PUNCT
ejpam-6264	412	3	otherwise	otherwise	ADV
ejpam-6264	412	4	.	.	PUNCT
ejpam-6264	413	1	then	then	ADV
ejpam-6264	413	2	f	f	PROPN
ejpam-6264	413	3	is	be	AUX
ejpam-6264	413	4	a	a	DET
ejpam-6264	413	5	tmrdf	tmrdf	NOUN
ejpam-6264	413	6	of	of	ADP
ejpam-6264	413	7	g.	g.	PROPN
ejpam-6264	413	8	thus	thus	ADV
ejpam-6264	413	9	,	,	PUNCT
ejpam-6264	413	10	γtmr(g	γtmr(g	NOUN
ejpam-6264	413	11	)	)	PUNCT
ejpam-6264	413	12	≤	≤	NOUN
ejpam-6264	413	13	ωtmr	ωtmr	ADJ
ejpam-6264	413	14	g	g	PROPN
ejpam-6264	413	15	(	(	PUNCT
ejpam-6264	413	16	f	f	X
ejpam-6264	413	17	)	)	PUNCT
ejpam-6264	413	18	=	=	SYM
ejpam-6264	413	19	8	8	X
ejpam-6264	413	20	.	.	PUNCT
ejpam-6264	413	21	by	by	ADP
ejpam-6264	413	22	proposition	proposition	NOUN
ejpam-6264	413	23	3	3	NUM
ejpam-6264	413	24	,	,	PUNCT
ejpam-6264	413	25	γtmr(g	γtmr(g	NOUN
ejpam-6264	413	26	)	)	PUNCT
ejpam-6264	413	27	≥	≥	NOUN
ejpam-6264	413	28	8	8	NUM
ejpam-6264	413	29	.	.	PUNCT
ejpam-6264	414	1	thus	thus	ADV
ejpam-6264	414	2	,	,	PUNCT
ejpam-6264	414	3	γtmr(g	γtmr(g	NOUN
ejpam-6264	414	4	)	)	PUNCT
ejpam-6264	414	5	=	=	SYM
ejpam-6264	415	1	8	8	X
ejpam-6264	415	2	.	.	PUNCT
ejpam-6264	416	1	if	if	SCONJ
ejpam-6264	416	2	p	p	NOUN
ejpam-6264	416	3	=	=	NOUN
ejpam-6264	416	4	4	4	NUM
ejpam-6264	416	5	and	and	CCONJ
ejpam-6264	416	6	wlog	wlog	NOUN
ejpam-6264	416	7	,	,	PUNCT
ejpam-6264	416	8	we	we	PRON
ejpam-6264	416	9	let	let	VERB
ejpam-6264	416	10	x	x	PUNCT
ejpam-6264	416	11	=	=	PRON
ejpam-6264	416	12	{	{	PUNCT
ejpam-6264	416	13	x1	x1	PROPN
ejpam-6264	416	14	,	,	PUNCT
ejpam-6264	416	15	x2	x2	PROPN
ejpam-6264	416	16	,	,	PUNCT
ejpam-6264	416	17	x3	x3	ADJ
ejpam-6264	416	18	,	,	PUNCT
ejpam-6264	416	19	x4	x4	ADJ
ejpam-6264	416	20	}	}	PUNCT
ejpam-6264	416	21	and	and	CCONJ
ejpam-6264	416	22	pick	pick	VERB
ejpam-6264	416	23	a	a	DET
ejpam-6264	416	24	vertex	vertex	NOUN
ejpam-6264	416	25	y1	y1	NOUN
ejpam-6264	416	26	∈	∈	PROPN
ejpam-6264	416	27	y	y	PROPN
ejpam-6264	416	28	and	and	CCONJ
ejpam-6264	416	29	define	define	VERB
ejpam-6264	416	30	a	a	DET
ejpam-6264	416	31	function	function	NOUN
ejpam-6264	416	32	f	f	NOUN
ejpam-6264	416	33	=	=	SYM
ejpam-6264	416	34	(	(	PUNCT
ejpam-6264	416	35	v0	v0	PROPN
ejpam-6264	416	36	,	,	PUNCT
ejpam-6264	416	37	v1	v1	NOUN
ejpam-6264	416	38	,	,	PUNCT
ejpam-6264	416	39	v2	v2	PROPN
ejpam-6264	416	40	,	,	PUNCT
ejpam-6264	416	41	v3	v3	PROPN
ejpam-6264	416	42	)	)	PUNCT
ejpam-6264	416	43	given	give	VERB
ejpam-6264	416	44	by	by	ADP
ejpam-6264	416	45	f(z	f(z	PROPN
ejpam-6264	416	46	)	)	PUNCT
ejpam-6264	416	47	=	=	PUNCT
ejpam-6264	416	48			NOUN
ejpam-6264	416	49	3	3	NUM
ejpam-6264	416	50	,	,	PUNCT
ejpam-6264	416	51	z	z	NOUN
ejpam-6264	416	52	=	=	SYM
ejpam-6264	416	53	{	{	PUNCT
ejpam-6264	416	54	x1	x1	PROPN
ejpam-6264	416	55	}	}	PUNCT
ejpam-6264	416	56	.	.	PUNCT
ejpam-6264	417	1	2	2	NUM
ejpam-6264	417	2	,	,	PUNCT
ejpam-6264	417	3	z	z	NOUN
ejpam-6264	417	4	∈	∈	PROPN
ejpam-6264	417	5	{	{	PUNCT
ejpam-6264	417	6	x2	x2	PROPN
ejpam-6264	417	7	,	,	PUNCT
ejpam-6264	417	8	y1	y1	NOUN
ejpam-6264	417	9	,	,	PUNCT
ejpam-6264	417	10	}	}	PUNCT
ejpam-6264	417	11	.	.	PUNCT
ejpam-6264	418	1	1	1	NUM
ejpam-6264	418	2	,	,	PUNCT
ejpam-6264	418	3	z	z	NOUN
ejpam-6264	418	4	∈	∈	PROPN
ejpam-6264	418	5	{	{	PUNCT
ejpam-6264	418	6	x3	x3	PROPN
ejpam-6264	418	7	,	,	PUNCT
ejpam-6264	418	8	x4	x4	PROPN
ejpam-6264	418	9	}	}	PUNCT
ejpam-6264	418	10	.	.	PUNCT
ejpam-6264	419	1	0	0	NUM
ejpam-6264	419	2	,	,	PUNCT
ejpam-6264	419	3	otherwise	otherwise	ADV
ejpam-6264	419	4	.	.	PUNCT
ejpam-6264	420	1	then	then	ADV
ejpam-6264	420	2	f	f	PROPN
ejpam-6264	420	3	is	be	AUX
ejpam-6264	420	4	a	a	DET
ejpam-6264	420	5	tmrdf	tmrdf	NOUN
ejpam-6264	420	6	of	of	ADP
ejpam-6264	420	7	g.	g.	PROPN
ejpam-6264	420	8	thus	thus	ADV
ejpam-6264	420	9	,	,	PUNCT
ejpam-6264	420	10	γtmr(g	γtmr(g	NOUN
ejpam-6264	420	11	)	)	PUNCT
ejpam-6264	420	12	≤	≤	NOUN
ejpam-6264	420	13	ωtmr	ωtmr	ADJ
ejpam-6264	420	14	g	g	PROPN
ejpam-6264	420	15	(	(	PUNCT
ejpam-6264	420	16	f	f	X
ejpam-6264	420	17	)	)	PUNCT
ejpam-6264	420	18	=	=	SYM
ejpam-6264	420	19	9	9	X
ejpam-6264	420	20	.	.	PUNCT
ejpam-6264	421	1	by	by	ADP
ejpam-6264	421	2	proposition	proposition	NOUN
ejpam-6264	421	3	3	3	NUM
ejpam-6264	421	4	,	,	PUNCT
ejpam-6264	421	5	γtmr(g	γtmr(g	NOUN
ejpam-6264	421	6	)	)	PUNCT
ejpam-6264	421	7	≥	≥	NOUN
ejpam-6264	421	8	9	9	NUM
ejpam-6264	421	9	.	.	PUNCT
ejpam-6264	422	1	thus	thus	ADV
ejpam-6264	422	2	,	,	PUNCT
ejpam-6264	422	3	γtmr(g	γtmr(g	NOUN
ejpam-6264	422	4	)	)	PUNCT
ejpam-6264	422	5	=	=	SYM
ejpam-6264	423	1	9	9	X
ejpam-6264	423	2	.	.	X
ejpam-6264	424	1	if	if	SCONJ
ejpam-6264	424	2	p	p	PROPN
ejpam-6264	424	3	≥	≥	NOUN
ejpam-6264	424	4	5	5	NUM
ejpam-6264	424	5	,	,	PUNCT
ejpam-6264	424	6	let	let	VERB
ejpam-6264	424	7	x	x	SYM
ejpam-6264	424	8	=	=	SYM
ejpam-6264	424	9	km	km	NOUN
ejpam-6264	424	10	and	and	CCONJ
ejpam-6264	424	11	y	y	PROPN
ejpam-6264	424	12	=	=	SYM
ejpam-6264	424	13	kn	kn	PROPN
ejpam-6264	424	14	.	.	PROPN
ejpam-6264	424	15	wlog	wlog	PROPN
ejpam-6264	424	16	,	,	PUNCT
ejpam-6264	424	17	let	let	VERB
ejpam-6264	424	18	s.	s.	PROPN
ejpam-6264	424	19	ahamad	ahamad	VERB
ejpam-6264	424	20	et	et	PROPN
ejpam-6264	424	21	al	al	PROPN
ejpam-6264	424	22	.	.	PUNCT
ejpam-6264	424	23	/	/	SYM
ejpam-6264	424	24	eur	eur	PROPN
ejpam-6264	424	25	.	.	PUNCT
ejpam-6264	425	1	j.	j.	PROPN
ejpam-6264	425	2	pure	pure	PROPN
ejpam-6264	425	3	appl	appl	PROPN
ejpam-6264	425	4	.	.	PROPN
ejpam-6264	425	5	math	math	PROPN
ejpam-6264	425	6	,	,	PUNCT
ejpam-6264	425	7	18	18	NUM
ejpam-6264	425	8	(	(	PUNCT
ejpam-6264	425	9	4	4	NUM
ejpam-6264	425	10	)	)	PUNCT
ejpam-6264	425	11	(	(	PUNCT
ejpam-6264	425	12	2025	2025	NUM
ejpam-6264	425	13	)	)	PUNCT
ejpam-6264	425	14	,	,	PUNCT
ejpam-6264	425	15	6264	6264	NUM
ejpam-6264	425	16	12	12	NUM
ejpam-6264	425	17	of	of	ADP
ejpam-6264	425	18	20	20	NUM
ejpam-6264	425	19	{	{	PUNCT
ejpam-6264	425	20	x1	x1	PROPN
ejpam-6264	425	21	,	,	PUNCT
ejpam-6264	425	22	x2	x2	PROPN
ejpam-6264	425	23	}	}	PUNCT
ejpam-6264	425	24	∈	∈	PROPN
ejpam-6264	425	25	v	v	NOUN
ejpam-6264	425	26	(	(	PUNCT
ejpam-6264	425	27	km	km	PROPN
ejpam-6264	425	28	)	)	PUNCT
ejpam-6264	425	29	,	,	PUNCT
ejpam-6264	425	30	{	{	PUNCT
ejpam-6264	425	31	y1	y1	NOUN
ejpam-6264	425	32	,	,	PUNCT
ejpam-6264	425	33	y2	y2	NOUN
ejpam-6264	425	34	}	}	PUNCT
ejpam-6264	425	35	∈	∈	PROPN
ejpam-6264	425	36	v	v	NOUN
ejpam-6264	425	37	(	(	PUNCT
ejpam-6264	425	38	kn	kn	PROPN
ejpam-6264	425	39	)	)	PUNCT
ejpam-6264	425	40	and	and	CCONJ
ejpam-6264	425	41	define	define	VERB
ejpam-6264	425	42	a	a	DET
ejpam-6264	425	43	function	function	NOUN
ejpam-6264	425	44	f	f	NOUN
ejpam-6264	425	45	=	=	SYM
ejpam-6264	425	46	(	(	PUNCT
ejpam-6264	425	47	v0	v0	PROPN
ejpam-6264	425	48	,	,	PUNCT
ejpam-6264	425	49	v1	v1	NOUN
ejpam-6264	425	50	,	,	PUNCT
ejpam-6264	425	51	v2	v2	PROPN
ejpam-6264	425	52	,	,	PUNCT
ejpam-6264	425	53	v3	v3	PROPN
ejpam-6264	425	54	)	)	PUNCT
ejpam-6264	425	55	given	give	VERB
ejpam-6264	425	56	by	by	ADP
ejpam-6264	425	57	f(z	f(z	PROPN
ejpam-6264	425	58	)	)	PUNCT
ejpam-6264	425	59	=	=	PUNCT
ejpam-6264	426	1			NOUN
ejpam-6264	426	2	3	3	NUM
ejpam-6264	426	3	,	,	PUNCT
ejpam-6264	426	4	z	z	PROPN
ejpam-6264	426	5	∈	∈	PROPN
ejpam-6264	426	6	{	{	PUNCT
ejpam-6264	426	7	x1	x1	PROPN
ejpam-6264	426	8	,	,	PUNCT
ejpam-6264	426	9	y1	y1	PROPN
ejpam-6264	426	10	}	}	PUNCT
ejpam-6264	426	11	.	.	PUNCT
ejpam-6264	427	1	2	2	NUM
ejpam-6264	427	2	,	,	PUNCT
ejpam-6264	427	3	z	z	NOUN
ejpam-6264	427	4	∈	∈	PROPN
ejpam-6264	427	5	{	{	PUNCT
ejpam-6264	427	6	x2	x2	PROPN
ejpam-6264	427	7	,	,	PUNCT
ejpam-6264	427	8	y2	y2	PROPN
ejpam-6264	427	9	}	}	PUNCT
ejpam-6264	427	10	.	.	PUNCT
ejpam-6264	428	1	0	0	NUM
ejpam-6264	428	2	,	,	PUNCT
ejpam-6264	428	3	otherwise	otherwise	ADV
ejpam-6264	428	4	.	.	PUNCT
ejpam-6264	429	1	then	then	ADV
ejpam-6264	429	2	f	f	PROPN
ejpam-6264	429	3	is	be	AUX
ejpam-6264	429	4	a	a	DET
ejpam-6264	429	5	tmrdf	tmrdf	NOUN
ejpam-6264	429	6	of	of	ADP
ejpam-6264	429	7	g.	g.	PROPN
ejpam-6264	429	8	thus	thus	ADV
ejpam-6264	429	9	,	,	PUNCT
ejpam-6264	429	10	γtmr(g	γtmr(g	NOUN
ejpam-6264	429	11	)	)	PUNCT
ejpam-6264	429	12	≤	≤	NOUN
ejpam-6264	429	13	ωtmr	ωtmr	ADJ
ejpam-6264	429	14	g	g	PROPN
ejpam-6264	429	15	(	(	PUNCT
ejpam-6264	429	16	f	f	X
ejpam-6264	429	17	)	)	PUNCT
ejpam-6264	429	18	=	=	SYM
ejpam-6264	429	19	10	10	NUM
ejpam-6264	429	20	.	.	PUNCT
ejpam-6264	430	1	by	by	ADP
ejpam-6264	430	2	proposition	proposition	NOUN
ejpam-6264	430	3	3	3	NUM
ejpam-6264	430	4	,	,	PUNCT
ejpam-6264	430	5	γtmr(g	γtmr(g	NOUN
ejpam-6264	430	6	)	)	PUNCT
ejpam-6264	430	7	≥	≥	NOUN
ejpam-6264	430	8	10	10	NUM
ejpam-6264	430	9	.	.	PUNCT
ejpam-6264	431	1	thus	thus	ADV
ejpam-6264	431	2	,	,	PUNCT
ejpam-6264	431	3	γtmr(g	γtmr(g	NOUN
ejpam-6264	431	4	)	)	PUNCT
ejpam-6264	431	5	=	=	SYM
ejpam-6264	432	1	10	10	NUM
ejpam-6264	432	2	.	.	PUNCT
ejpam-6264	433	1	the	the	DET
ejpam-6264	433	2	star	star	PROPN
ejpam-6264	433	3	sn	sn	PROPN
ejpam-6264	433	4	of	of	ADP
ejpam-6264	433	5	order	order	NOUN
ejpam-6264	433	6	n+	n+	ADP
ejpam-6264	433	7	1	1	NUM
ejpam-6264	433	8	is	be	AUX
ejpam-6264	433	9	the	the	DET
ejpam-6264	433	10	graph	graph	NOUN
ejpam-6264	433	11	kn	kn	PROPN
ejpam-6264	433	12	+	+	NOUN
ejpam-6264	433	13	k1	k1	PROPN
ejpam-6264	433	14	.	.	PUNCT
ejpam-6264	434	1	the	the	DET
ejpam-6264	434	2	graph	graph	NOUN
ejpam-6264	434	3	in	in	ADP
ejpam-6264	434	4	figures	figure	NOUN
ejpam-6264	434	5	7	7	NUM
ejpam-6264	434	6	is	be	AUX
ejpam-6264	434	7	the	the	DET
ejpam-6264	434	8	star	star	NOUN
ejpam-6264	434	9	graph	graph	NOUN
ejpam-6264	434	10	s6	s6	PROPN
ejpam-6264	434	11	.	.	PUNCT
ejpam-6264	435	1	2	2	NUM
ejpam-6264	435	2	1	1	NUM
ejpam-6264	435	3	1	1	NUM
ejpam-6264	435	4	1	1	NUM
ejpam-6264	435	5	1	1	NUM
ejpam-6264	435	6	1	1	NUM
ejpam-6264	435	7	2	2	NUM
ejpam-6264	435	8	figure	figure	NOUN
ejpam-6264	435	9	7	7	NUM
ejpam-6264	435	10	:	:	PUNCT
ejpam-6264	435	11	a	a	DET
ejpam-6264	435	12	star	star	NOUN
ejpam-6264	435	13	graph	graph	NOUN
ejpam-6264	435	14	s6	s6	PROPN
ejpam-6264	435	15	with	with	ADP
ejpam-6264	435	16	γtmr(s6	γtmr(s6	NOUN
ejpam-6264	435	17	)	)	PUNCT
ejpam-6264	435	18	=	=	SYM
ejpam-6264	435	19	7	7	NUM
ejpam-6264	435	20	proposition	proposition	NOUN
ejpam-6264	435	21	15	15	NUM
ejpam-6264	435	22	.	.	PUNCT
ejpam-6264	436	1	if	if	SCONJ
ejpam-6264	436	2	g	g	PROPN
ejpam-6264	436	3	=	=	SYM
ejpam-6264	436	4	sn	sn	PROPN
ejpam-6264	436	5	,	,	PUNCT
ejpam-6264	436	6	n	n	PRON
ejpam-6264	436	7	≥	≥	NUM
ejpam-6264	436	8	1	1	NUM
ejpam-6264	436	9	,	,	PUNCT
ejpam-6264	436	10	then	then	ADV
ejpam-6264	436	11	γtmr(g	γtmr(g	NUM
ejpam-6264	436	12	)	)	PUNCT
ejpam-6264	436	13	=	=	PUNCT
ejpam-6264	436	14	n+	n+	PUNCT
ejpam-6264	436	15	2	2	X
ejpam-6264	436	16	.	.	X
ejpam-6264	436	17	proof	proof	NOUN
ejpam-6264	436	18	.	.	PUNCT
ejpam-6264	437	1	let	let	VERB
ejpam-6264	437	2	g	g	PROPN
ejpam-6264	437	3	=	=	PUNCT
ejpam-6264	437	4	sn	sn	PROPN
ejpam-6264	437	5	where	where	SCONJ
ejpam-6264	437	6	v	v	X
ejpam-6264	437	7	(	(	PUNCT
ejpam-6264	437	8	g	g	NOUN
ejpam-6264	437	9	)	)	PUNCT
ejpam-6264	437	10	=	=	SYM
ejpam-6264	437	11	v	v	X
ejpam-6264	437	12	(	(	PUNCT
ejpam-6264	437	13	k1	k1	NOUN
ejpam-6264	437	14	+	+	PROPN
ejpam-6264	437	15	kn	kn	PROPN
ejpam-6264	437	16	)	)	PUNCT
ejpam-6264	437	17	and	and	CCONJ
ejpam-6264	437	18	v	v	NOUN
ejpam-6264	437	19	(	(	PUNCT
ejpam-6264	437	20	k1	k1	NOUN
ejpam-6264	437	21	)	)	PUNCT
ejpam-6264	437	22	=	=	SYM
ejpam-6264	437	23	{	{	PUNCT
ejpam-6264	437	24	u	u	NOUN
ejpam-6264	437	25	}	}	PUNCT
ejpam-6264	437	26	is	be	AUX
ejpam-6264	437	27	a	a	DET
ejpam-6264	437	28	central	central	ADJ
ejpam-6264	437	29	vertex	vertex	NOUN
ejpam-6264	437	30	of	of	ADP
ejpam-6264	437	31	g.	g.	PROPN
ejpam-6264	437	32	now	now	ADV
ejpam-6264	437	33	,	,	PUNCT
ejpam-6264	437	34	define	define	VERB
ejpam-6264	437	35	a	a	DET
ejpam-6264	437	36	function	function	NOUN
ejpam-6264	437	37	f	f	NOUN
ejpam-6264	437	38	=	=	SYM
ejpam-6264	437	39	(	(	PUNCT
ejpam-6264	437	40	v0	v0	PROPN
ejpam-6264	437	41	,	,	PUNCT
ejpam-6264	437	42	v1	v1	NOUN
ejpam-6264	437	43	,	,	PUNCT
ejpam-6264	437	44	v2	v2	PROPN
ejpam-6264	437	45	,	,	PUNCT
ejpam-6264	437	46	v3	v3	PROPN
ejpam-6264	437	47	)	)	PUNCT
ejpam-6264	437	48	given	give	VERB
ejpam-6264	437	49	by	by	ADP
ejpam-6264	437	50	f(x	f(x	PROPN
ejpam-6264	437	51	)	)	PUNCT
ejpam-6264	438	1	=	=	PRON
ejpam-6264	438	2	{	{	PUNCT
ejpam-6264	438	3	2	2	NUM
ejpam-6264	438	4	,	,	PUNCT
ejpam-6264	438	5	x	x	PUNCT
ejpam-6264	438	6	=	=	PRON
ejpam-6264	438	7	{	{	PUNCT
ejpam-6264	438	8	u	u	NOUN
ejpam-6264	438	9	}	}	PUNCT
ejpam-6264	438	10	.	.	PUNCT
ejpam-6264	439	1	1	1	NUM
ejpam-6264	439	2	,	,	PUNCT
ejpam-6264	439	3	otherwise	otherwise	ADV
ejpam-6264	439	4	.	.	PUNCT
ejpam-6264	440	1	then	then	ADV
ejpam-6264	440	2	f	f	PROPN
ejpam-6264	440	3	∈	∈	PROPN
ejpam-6264	440	4	tmrdf	tmrdf	NOUN
ejpam-6264	440	5	(	(	PUNCT
ejpam-6264	440	6	g	g	NOUN
ejpam-6264	440	7	)	)	PUNCT
ejpam-6264	440	8	.	.	PUNCT
ejpam-6264	441	1	it	it	PRON
ejpam-6264	441	2	follows	follow	VERB
ejpam-6264	441	3	that	that	SCONJ
ejpam-6264	441	4	γtmr(g	γtmr(g	NOUN
ejpam-6264	441	5	)	)	PUNCT
ejpam-6264	441	6	≤	≤	NOUN
ejpam-6264	441	7	n	n	PRON
ejpam-6264	441	8	+	+	NOUN
ejpam-6264	441	9	2	2	X
ejpam-6264	441	10	.	.	PUNCT
ejpam-6264	441	11	now	now	ADV
ejpam-6264	441	12	,	,	PUNCT
ejpam-6264	441	13	suppose	suppose	VERB
ejpam-6264	441	14	that	that	SCONJ
ejpam-6264	441	15	g	g	PROPN
ejpam-6264	441	16	=	=	SYM
ejpam-6264	441	17	(	(	PUNCT
ejpam-6264	441	18	w0,w1,w2,w3	w0,w1,w2,w3	PROPN
ejpam-6264	441	19	)	)	PUNCT
ejpam-6264	441	20	is	be	AUX
ejpam-6264	441	21	a	a	DET
ejpam-6264	441	22	γtmr	γtmr	NOUN
ejpam-6264	441	23	-	-	PUNCT
ejpam-6264	441	24	function	function	NOUN
ejpam-6264	441	25	of	of	ADP
ejpam-6264	441	26	g.	g.	PROPN
ejpam-6264	441	27	if	if	SCONJ
ejpam-6264	441	28	w0	w0	PROPN
ejpam-6264	441	29	=	=	SYM
ejpam-6264	441	30	∅	∅	NOUN
ejpam-6264	441	31	,	,	PUNCT
ejpam-6264	441	32	then	then	ADV
ejpam-6264	441	33	w3	w3	PROPN
ejpam-6264	441	34	=	=	PUNCT
ejpam-6264	441	35	∅.	∅.	NOUN
ejpam-6264	441	36	since	since	SCONJ
ejpam-6264	441	37	g	g	PROPN
ejpam-6264	441	38	is	be	AUX
ejpam-6264	441	39	a	a	DET
ejpam-6264	441	40	γtmr	γtmr	ADJ
ejpam-6264	441	41	-	-	PUNCT
ejpam-6264	441	42	function	function	NOUN
ejpam-6264	441	43	of	of	ADP
ejpam-6264	441	44	g	g	NOUN
ejpam-6264	441	45	,	,	PUNCT
ejpam-6264	441	46	|w2|	|w2|	NOUN
ejpam-6264	441	47	=	=	SYM
ejpam-6264	441	48	|v	|v	PROPN
ejpam-6264	441	49	(	(	PUNCT
ejpam-6264	441	50	k1)|	k1)|	NOUN
ejpam-6264	441	51	=	=	SYM
ejpam-6264	441	52	1	1	NUM
ejpam-6264	441	53	and	and	CCONJ
ejpam-6264	441	54	|w1|	|w1|	NOUN
ejpam-6264	441	55	=	=	SYM
ejpam-6264	441	56	|v	|v	X
ejpam-6264	441	57	(	(	PUNCT
ejpam-6264	441	58	kn)|	kn)|	PROPN
ejpam-6264	441	59	=	=	PUNCT
ejpam-6264	441	60	n.	n.	PROPN
ejpam-6264	441	61	hence	hence	ADV
ejpam-6264	441	62	,	,	PUNCT
ejpam-6264	441	63	γtmr(g	γtmr(g	PROPN
ejpam-6264	441	64	)	)	PUNCT
ejpam-6264	441	65	=	=	PUNCT
ejpam-6264	441	66	ωtmr	ωtmr	ADJ
ejpam-6264	441	67	g	g	PROPN
ejpam-6264	441	68	(	(	PUNCT
ejpam-6264	441	69	g	g	NOUN
ejpam-6264	441	70	)	)	PUNCT
ejpam-6264	441	71	≥	≥	NOUN
ejpam-6264	441	72	n	n	NOUN
ejpam-6264	441	73	+	+	NUM
ejpam-6264	441	74	2	2	NUM
ejpam-6264	441	75	.	.	X
ejpam-6264	441	76	if	if	SCONJ
ejpam-6264	441	77	|w0|	|w0|	VERB
ejpam-6264	441	78	̸=	̸=	PROPN
ejpam-6264	441	79	0	0	NUM
ejpam-6264	441	80	,	,	PUNCT
ejpam-6264	441	81	then	then	ADV
ejpam-6264	441	82	|w2|	|w2|	NOUN
ejpam-6264	441	83	≥	≥	NOUN
ejpam-6264	441	84	1	1	NUM
ejpam-6264	441	85	and	and	CCONJ
ejpam-6264	441	86	|w3|	|w3|	PRON
ejpam-6264	441	87	≥	≥	NOUN
ejpam-6264	441	88	1	1	NUM
ejpam-6264	441	89	.	.	PUNCT
ejpam-6264	442	1	it	it	PRON
ejpam-6264	442	2	follows	follow	VERB
ejpam-6264	442	3	that	that	SCONJ
ejpam-6264	442	4	γtmr(g	γtmr(g	NOUN
ejpam-6264	442	5	)	)	PUNCT
ejpam-6264	442	6	=	=	PUNCT
ejpam-6264	442	7	ωtmr	ωtmr	ADJ
ejpam-6264	442	8	g	g	PROPN
ejpam-6264	442	9	(	(	PUNCT
ejpam-6264	442	10	g	g	NOUN
ejpam-6264	442	11	)	)	PUNCT
ejpam-6264	442	12	=	=	SYM
ejpam-6264	443	1	2|w2|+	2|w2|+	NUM
ejpam-6264	443	2	3|w3|	3|w3|	NUM
ejpam-6264	443	3	≥	≥	NOUN
ejpam-6264	443	4	n+	n+	PUNCT
ejpam-6264	443	5	2	2	X
ejpam-6264	443	6	.	.	X
ejpam-6264	443	7	therefore	therefore	ADV
ejpam-6264	443	8	,	,	PUNCT
ejpam-6264	443	9	γtmr(g	γtmr(g	NOUN
ejpam-6264	443	10	)	)	PUNCT
ejpam-6264	443	11	=	=	PUNCT
ejpam-6264	443	12	n+	n+	PUNCT
ejpam-6264	443	13	2	2	X
ejpam-6264	443	14	.	.	X
ejpam-6264	443	15	proposition	proposition	NOUN
ejpam-6264	443	16	16	16	NUM
ejpam-6264	443	17	.	.	PUNCT
ejpam-6264	444	1	for	for	ADP
ejpam-6264	444	2	a	a	DET
ejpam-6264	444	3	complete	complete	ADJ
ejpam-6264	444	4	graph	graph	NOUN
ejpam-6264	444	5	kn	kn	PROPN
ejpam-6264	444	6	,	,	PUNCT
ejpam-6264	444	7	γtmr(kn	γtmr(kn	NOUN
ejpam-6264	444	8	)	)	PUNCT
ejpam-6264	444	9	=	=	SYM
ejpam-6264	444	10	5	5	NUM
ejpam-6264	444	11	for	for	ADP
ejpam-6264	444	12	all	all	DET
ejpam-6264	444	13	n	n	PRON
ejpam-6264	444	14	≥	≥	NOUN
ejpam-6264	444	15	4	4	NUM
ejpam-6264	444	16	.	.	PUNCT
ejpam-6264	445	1	proof	proof	NOUN
ejpam-6264	445	2	.	.	PUNCT
ejpam-6264	446	1	pick	pick	VERB
ejpam-6264	446	2	any	any	DET
ejpam-6264	446	3	x	x	NOUN
ejpam-6264	446	4	,	,	PUNCT
ejpam-6264	446	5	y	y	PROPN
ejpam-6264	446	6	∈	∈	PROPN
ejpam-6264	446	7	v	v	PROPN
ejpam-6264	446	8	(	(	PUNCT
ejpam-6264	446	9	kn	kn	PROPN
ejpam-6264	446	10	)	)	PUNCT
ejpam-6264	446	11	with	with	ADP
ejpam-6264	446	12	x	x	PUNCT
ejpam-6264	446	13	̸=	̸=	PROPN
ejpam-6264	446	14	y.	y.	PROPN
ejpam-6264	446	15	clearly	clearly	ADV
ejpam-6264	446	16	,	,	PUNCT
ejpam-6264	446	17	g	g	PROPN
ejpam-6264	446	18	=	=	SYM
ejpam-6264	446	19	(	(	PUNCT
ejpam-6264	446	20	v	v	NOUN
ejpam-6264	446	21	(	(	PUNCT
ejpam-6264	446	22	kn	kn	PROPN
ejpam-6264	446	23	)	)	PUNCT
ejpam-6264	446	24	\	\	NOUN
ejpam-6264	447	1	{	{	PUNCT
ejpam-6264	447	2	x	x	NOUN
ejpam-6264	447	3	,	,	PUNCT
ejpam-6264	447	4	y},∅	y},∅	PROPN
ejpam-6264	447	5	,	,	PUNCT
ejpam-6264	447	6	{	{	PUNCT
ejpam-6264	447	7	x	x	X
ejpam-6264	447	8	}	}	PUNCT
ejpam-6264	447	9	,	,	PUNCT
ejpam-6264	447	10	{	{	PUNCT
ejpam-6264	447	11	y	y	NOUN
ejpam-6264	447	12	}	}	PUNCT
ejpam-6264	447	13	)	)	PUNCT
ejpam-6264	447	14	∈	∈	PROPN
ejpam-6264	447	15	tmrdf	tmrdf	NOUN
ejpam-6264	447	16	(	(	PUNCT
ejpam-6264	447	17	kn	kn	PROPN
ejpam-6264	447	18	)	)	PUNCT
ejpam-6264	447	19	.	.	PUNCT
ejpam-6264	448	1	it	it	PRON
ejpam-6264	448	2	follows	follow	VERB
ejpam-6264	448	3	that	that	SCONJ
ejpam-6264	448	4	γtmr(kn	γtmr(kn	NOUN
ejpam-6264	448	5	)	)	PUNCT
ejpam-6264	448	6	≤	≤	NOUN
ejpam-6264	448	7	5	5	NUM
ejpam-6264	448	8	.	.	PUNCT
ejpam-6264	449	1	on	on	ADP
ejpam-6264	449	2	the	the	DET
ejpam-6264	449	3	other	other	ADJ
ejpam-6264	449	4	hand	hand	NOUN
ejpam-6264	449	5	,	,	PUNCT
ejpam-6264	449	6	suppose	suppose	VERB
ejpam-6264	449	7	that	that	SCONJ
ejpam-6264	449	8	f	f	PROPN
ejpam-6264	449	9	=	=	SYM
ejpam-6264	449	10	(	(	PUNCT
ejpam-6264	449	11	v0	v0	PROPN
ejpam-6264	449	12	,	,	PUNCT
ejpam-6264	449	13	v1	v1	NOUN
ejpam-6264	449	14	,	,	PUNCT
ejpam-6264	449	15	v2	v2	PROPN
ejpam-6264	449	16	,	,	PUNCT
ejpam-6264	449	17	v3	v3	PROPN
ejpam-6264	449	18	)	)	PUNCT
ejpam-6264	449	19	is	be	AUX
ejpam-6264	449	20	a	a	DET
ejpam-6264	449	21	γtmr	γtmr	ADJ
ejpam-6264	449	22	-	-	PUNCT
ejpam-6264	449	23	function	function	NOUN
ejpam-6264	449	24	of	of	ADP
ejpam-6264	449	25	kn	kn	PROPN
ejpam-6264	449	26	.	.	PUNCT
ejpam-6264	450	1	if	if	SCONJ
ejpam-6264	450	2	v0	v0	NOUN
ejpam-6264	450	3	=	=	SYM
ejpam-6264	450	4	∅	∅	NOUN
ejpam-6264	450	5	,	,	PUNCT
ejpam-6264	450	6	then	then	ADV
ejpam-6264	450	7	v3	v3	PROPN
ejpam-6264	450	8	=	=	PUNCT
ejpam-6264	450	9	∅.	∅.	NOUN
ejpam-6264	450	10	since	since	SCONJ
ejpam-6264	450	11	f	f	PROPN
ejpam-6264	450	12	is	be	AUX
ejpam-6264	450	13	a	a	DET
ejpam-6264	450	14	γtmr	γtmr	ADJ
ejpam-6264	450	15	-	-	PUNCT
ejpam-6264	450	16	function	function	NOUN
ejpam-6264	450	17	of	of	ADP
ejpam-6264	450	18	kn	kn	PROPN
ejpam-6264	450	19	,	,	PUNCT
ejpam-6264	450	20	|v2|	|v2|	NOUN
ejpam-6264	450	21	=	=	SYM
ejpam-6264	450	22	1	1	NUM
ejpam-6264	450	23	and	and	CCONJ
ejpam-6264	450	24	|v1|	|v1|	NOUN
ejpam-6264	450	25	=	=	SYM
ejpam-6264	450	26	n	n	CCONJ
ejpam-6264	450	27	−	−	PROPN
ejpam-6264	450	28	1	1	NUM
ejpam-6264	450	29	.	.	PUNCT
ejpam-6264	451	1	hence	hence	ADV
ejpam-6264	451	2	,	,	PUNCT
ejpam-6264	451	3	γtmr(kn	γtmr(kn	NOUN
ejpam-6264	451	4	)	)	PUNCT
ejpam-6264	451	5	=	=	PUNCT
ejpam-6264	452	1	ωtmr	ωtmr	PROPN
ejpam-6264	452	2	kn	kn	PROPN
ejpam-6264	452	3	(	(	PUNCT
ejpam-6264	452	4	f	f	X
ejpam-6264	452	5	)	)	PUNCT
ejpam-6264	452	6	=	=	SYM
ejpam-6264	452	7	n	n	PROPN
ejpam-6264	452	8	+	+	NOUN
ejpam-6264	452	9	1	1	NUM
ejpam-6264	452	10	≥	≥	NOUN
ejpam-6264	452	11	5	5	NUM
ejpam-6264	452	12	.	.	PUNCT
ejpam-6264	453	1	if	if	SCONJ
ejpam-6264	453	2	v0	v0	NOUN
ejpam-6264	453	3	̸=	̸=	PROPN
ejpam-6264	453	4	∅	∅	NOUN
ejpam-6264	453	5	,	,	PUNCT
ejpam-6264	453	6	then	then	ADV
ejpam-6264	453	7	|v2|	|v2|	VERB
ejpam-6264	453	8	≥	≥	NOUN
ejpam-6264	453	9	1	1	NUM
ejpam-6264	453	10	and	and	CCONJ
ejpam-6264	453	11	|v3|	|v3|	PROPN
ejpam-6264	453	12	≥	≥	NUM
ejpam-6264	453	13	1	1	NUM
ejpam-6264	453	14	.	.	PUNCT
ejpam-6264	454	1	it	it	PRON
ejpam-6264	454	2	follows	follow	VERB
ejpam-6264	454	3	that	that	SCONJ
ejpam-6264	454	4	γtmr(kn	γtmr(kn	NOUN
ejpam-6264	454	5	)	)	PUNCT
ejpam-6264	454	6	=	=	PUNCT
ejpam-6264	455	1	ωtmr	ωtmr	PROPN
ejpam-6264	455	2	kn	kn	PROPN
ejpam-6264	455	3	(	(	PUNCT
ejpam-6264	455	4	f	f	X
ejpam-6264	455	5	)	)	PUNCT
ejpam-6264	455	6	=	=	SYM
ejpam-6264	455	7	2|v2|	2|v2|	NUM
ejpam-6264	455	8	+	+	CCONJ
ejpam-6264	455	9	3|v3|	3|v3|	NUM
ejpam-6264	455	10	≥	≥	NOUN
ejpam-6264	455	11	5	5	NUM
ejpam-6264	455	12	.	.	PUNCT
ejpam-6264	456	1	therefore	therefore	ADV
ejpam-6264	456	2	,	,	PUNCT
ejpam-6264	456	3	γtmr(kn	γtmr(kn	NOUN
ejpam-6264	456	4	)	)	PUNCT
ejpam-6264	456	5	=	=	SYM
ejpam-6264	457	1	5	5	X
ejpam-6264	457	2	.	.	PUNCT
ejpam-6264	458	1	s.	s.	PROPN
ejpam-6264	458	2	ahamad	ahamad	VERB
ejpam-6264	458	3	et	et	PROPN
ejpam-6264	458	4	al	al	PROPN
ejpam-6264	458	5	.	.	PUNCT
ejpam-6264	458	6	/	/	SYM
ejpam-6264	458	7	eur	eur	PROPN
ejpam-6264	458	8	.	.	PUNCT
ejpam-6264	459	1	j.	j.	PROPN
ejpam-6264	459	2	pure	pure	PROPN
ejpam-6264	459	3	appl	appl	PROPN
ejpam-6264	459	4	.	.	PROPN
ejpam-6264	459	5	math	math	PROPN
ejpam-6264	459	6	,	,	PUNCT
ejpam-6264	459	7	18	18	NUM
ejpam-6264	459	8	(	(	PUNCT
ejpam-6264	459	9	4	4	NUM
ejpam-6264	459	10	)	)	PUNCT
ejpam-6264	459	11	(	(	PUNCT
ejpam-6264	459	12	2025	2025	NUM
ejpam-6264	459	13	)	)	PUNCT
ejpam-6264	459	14	,	,	PUNCT
ejpam-6264	459	15	6264	6264	NUM
ejpam-6264	459	16	13	13	NUM
ejpam-6264	459	17	of	of	ADP
ejpam-6264	459	18	20	20	NUM
ejpam-6264	459	19	5	5	NUM
ejpam-6264	459	20	.	.	PUNCT
ejpam-6264	460	1	on	on	ADP
ejpam-6264	460	2	the	the	DET
ejpam-6264	460	3	join	join	NOUN
ejpam-6264	460	4	of	of	ADP
ejpam-6264	460	5	graphs	graph	NOUN
ejpam-6264	460	6	given	give	VERB
ejpam-6264	460	7	two	two	NUM
ejpam-6264	460	8	graphs	graph	NOUN
ejpam-6264	460	9	g	g	NOUN
ejpam-6264	460	10	and	and	CCONJ
ejpam-6264	460	11	h	h	NOUN
ejpam-6264	460	12	with	with	ADP
ejpam-6264	460	13	disjoint	disjoint	ADJ
ejpam-6264	460	14	vertex	vertex	NOUN
ejpam-6264	460	15	sets	set	NOUN
ejpam-6264	460	16	,	,	PUNCT
ejpam-6264	460	17	the	the	DET
ejpam-6264	460	18	join	join	NOUN
ejpam-6264	460	19	g+h	g+h	PROPN
ejpam-6264	460	20	of	of	ADP
ejpam-6264	460	21	graphs	graph	NOUN
ejpam-6264	460	22	g	g	PROPN
ejpam-6264	460	23	and	and	CCONJ
ejpam-6264	460	24	h	h	NOUN
ejpam-6264	460	25	,	,	PUNCT
ejpam-6264	460	26	is	be	AUX
ejpam-6264	460	27	the	the	DET
ejpam-6264	460	28	graph	graph	NOUN
ejpam-6264	460	29	with	with	ADP
ejpam-6264	460	30	vertex	vertex	NOUN
ejpam-6264	460	31	-	-	PUNCT
ejpam-6264	460	32	set	set	VERB
ejpam-6264	460	33	v	v	NOUN
ejpam-6264	460	34	(	(	PUNCT
ejpam-6264	460	35	g+h	g+h	NOUN
ejpam-6264	460	36	)	)	PUNCT
ejpam-6264	460	37	=	=	SYM
ejpam-6264	460	38	v	v	X
ejpam-6264	460	39	(	(	PUNCT
ejpam-6264	460	40	g)∪v	g)∪v	NOUN
ejpam-6264	460	41	(	(	PUNCT
ejpam-6264	460	42	h	h	NOUN
ejpam-6264	460	43	)	)	PUNCT
ejpam-6264	460	44	and	and	CCONJ
ejpam-6264	460	45	edge	edge	NOUN
ejpam-6264	460	46	-	-	PUNCT
ejpam-6264	460	47	set	set	VERB
ejpam-6264	460	48	e(g	e(g	NOUN
ejpam-6264	460	49	+	+	CCONJ
ejpam-6264	460	50	h	h	NOUN
ejpam-6264	460	51	)	)	PUNCT
ejpam-6264	460	52	=	=	SYM
ejpam-6264	460	53	e(g	e(g	PROPN
ejpam-6264	460	54	)	)	PUNCT
ejpam-6264	460	55	∪	∪	ADP
ejpam-6264	460	56	e(h	e(h	PROPN
ejpam-6264	460	57	)	)	PUNCT
ejpam-6264	460	58	∪	∪	NOUN
ejpam-6264	460	59	{	{	PUNCT
ejpam-6264	460	60	uv	uv	NOUN
ejpam-6264	460	61	:	:	PUNCT
ejpam-6264	460	62	u	u	PROPN
ejpam-6264	460	63	∈	∈	PROPN
ejpam-6264	460	64	v	v	ADP
ejpam-6264	460	65	(	(	PUNCT
ejpam-6264	460	66	g	g	NOUN
ejpam-6264	460	67	)	)	PUNCT
ejpam-6264	460	68	and	and	CCONJ
ejpam-6264	460	69	v	v	ADP
ejpam-6264	460	70	∈	∈	PROPN
ejpam-6264	460	71	v	v	NOUN
ejpam-6264	460	72	(	(	PUNCT
ejpam-6264	460	73	h	h	NOUN
ejpam-6264	460	74	)	)	PUNCT
ejpam-6264	460	75	}	}	PUNCT
ejpam-6264	461	1	[	[	X
ejpam-6264	461	2	8	8	NUM
ejpam-6264	461	3	]	]	PUNCT
ejpam-6264	461	4	.	.	PUNCT
ejpam-6264	462	1	in	in	ADP
ejpam-6264	462	2	this	this	DET
ejpam-6264	462	3	section	section	NOUN
ejpam-6264	462	4	,	,	PUNCT
ejpam-6264	462	5	the	the	DET
ejpam-6264	462	6	following	follow	VERB
ejpam-6264	462	7	proposition	proposition	NOUN
ejpam-6264	462	8	characterizes	characterize	VERB
ejpam-6264	462	9	all	all	DET
ejpam-6264	462	10	tmrdf	tmrdf	NOUN
ejpam-6264	462	11	on	on	ADP
ejpam-6264	462	12	the	the	DET
ejpam-6264	462	13	join	join	NOUN
ejpam-6264	462	14	of	of	ADP
ejpam-6264	462	15	graphs	graph	NOUN
ejpam-6264	462	16	.	.	PUNCT
ejpam-6264	463	1	proposition	proposition	NOUN
ejpam-6264	463	2	17	17	NUM
ejpam-6264	463	3	.	.	PUNCT
ejpam-6264	464	1	let	let	VERB
ejpam-6264	464	2	g	g	NOUN
ejpam-6264	465	1	and	and	CCONJ
ejpam-6264	465	2	h	h	NOUN
ejpam-6264	465	3	be	be	VERB
ejpam-6264	465	4	any	any	DET
ejpam-6264	465	5	graphs	graph	NOUN
ejpam-6264	465	6	and	and	CCONJ
ejpam-6264	465	7	let	let	VERB
ejpam-6264	465	8	f	f	PROPN
ejpam-6264	465	9	∈	∈	PROPN
ejpam-6264	465	10	(	(	PUNCT
ejpam-6264	465	11	v0	v0	NOUN
ejpam-6264	465	12	,	,	PUNCT
ejpam-6264	465	13	v1	v1	NOUN
ejpam-6264	465	14	,	,	PUNCT
ejpam-6264	465	15	v2	v2	PROPN
ejpam-6264	465	16	,	,	PUNCT
ejpam-6264	465	17	v3	v3	PROPN
ejpam-6264	465	18	)	)	PUNCT
ejpam-6264	465	19	be	be	VERB
ejpam-6264	465	20	a	a	DET
ejpam-6264	465	21	function	function	NOUN
ejpam-6264	465	22	on	on	ADP
ejpam-6264	465	23	v	v	NOUN
ejpam-6264	465	24	(	(	PUNCT
ejpam-6264	465	25	g+h	g+h	PROPN
ejpam-6264	465	26	)	)	PUNCT
ejpam-6264	465	27	with	with	ADP
ejpam-6264	465	28	v2	v2	PROPN
ejpam-6264	465	29	̸=	̸=	PROPN
ejpam-6264	465	30	∅	∅	NOUN
ejpam-6264	465	31	and	and	CCONJ
ejpam-6264	465	32	v3	v3	PROPN
ejpam-6264	465	33	̸=	̸=	PROPN
ejpam-6264	465	34	∅.	∅.	ADV
ejpam-6264	465	35	then	then	ADV
ejpam-6264	465	36	f	f	PROPN
ejpam-6264	465	37	∈	∈	PROPN
ejpam-6264	465	38	tmrdf	tmrdf	NOUN
ejpam-6264	465	39	(	(	PUNCT
ejpam-6264	465	40	g+h	g+h	NOUN
ejpam-6264	465	41	)	)	PUNCT
ejpam-6264	466	1	if	if	SCONJ
ejpam-6264	466	2	and	and	CCONJ
ejpam-6264	466	3	only	only	ADV
ejpam-6264	466	4	if	if	SCONJ
ejpam-6264	466	5	one	one	NUM
ejpam-6264	466	6	of	of	ADP
ejpam-6264	466	7	the	the	DET
ejpam-6264	466	8	following	follow	VERB
ejpam-6264	466	9	holds	hold	VERB
ejpam-6264	466	10	:	:	PUNCT
ejpam-6264	466	11	(	(	PUNCT
ejpam-6264	466	12	i	i	NOUN
ejpam-6264	466	13	)	)	PUNCT
ejpam-6264	466	14	f	f	PROPN
ejpam-6264	466	15	|g	|g	PROPN
ejpam-6264	466	16	∈	∈	PROPN
ejpam-6264	466	17	tmrdf	tmrdf	NOUN
ejpam-6264	466	18	(	(	PUNCT
ejpam-6264	466	19	g	g	NOUN
ejpam-6264	466	20	)	)	PUNCT
ejpam-6264	466	21	and	and	CCONJ
ejpam-6264	466	22	one	one	NUM
ejpam-6264	466	23	of	of	ADP
ejpam-6264	466	24	the	the	DET
ejpam-6264	466	25	following	following	NOUN
ejpam-6264	466	26	holds	hold	VERB
ejpam-6264	466	27	:	:	PUNCT
ejpam-6264	466	28	(	(	PUNCT
ejpam-6264	466	29	a	a	X
ejpam-6264	466	30	)	)	PUNCT
ejpam-6264	466	31	|v2	|v2	NOUN
ejpam-6264	466	32	∩	∩	ADJ
ejpam-6264	466	33	v	v	X
ejpam-6264	466	34	(	(	PUNCT
ejpam-6264	466	35	g)|	g)|	VERB
ejpam-6264	466	36	≥	≥	NOUN
ejpam-6264	466	37	1	1	NUM
ejpam-6264	466	38	and	and	CCONJ
ejpam-6264	466	39	|v3	|v3	NOUN
ejpam-6264	466	40	∩	∩	ADJ
ejpam-6264	466	41	v	v	X
ejpam-6264	466	42	(	(	PUNCT
ejpam-6264	466	43	g)|	g)|	X
ejpam-6264	466	44	≥	≥	NOUN
ejpam-6264	466	45	1	1	NUM
ejpam-6264	466	46	(	(	PUNCT
ejpam-6264	466	47	b	b	NOUN
ejpam-6264	466	48	)	)	PUNCT
ejpam-6264	466	49	v2	v2	NOUN
ejpam-6264	466	50	∩	∩	ADJ
ejpam-6264	466	51	v	v	NOUN
ejpam-6264	466	52	(	(	PUNCT
ejpam-6264	466	53	g	g	NOUN
ejpam-6264	466	54	)	)	PUNCT
ejpam-6264	466	55	=	=	NOUN
ejpam-6264	466	56	∅	∅	NOUN
ejpam-6264	466	57	and	and	CCONJ
ejpam-6264	466	58	each	each	PRON
ejpam-6264	466	59	of	of	ADP
ejpam-6264	466	60	the	the	DET
ejpam-6264	466	61	following	follow	VERB
ejpam-6264	466	62	holds	hold	VERB
ejpam-6264	466	63	:	:	PUNCT
ejpam-6264	466	64	(	(	PUNCT
ejpam-6264	466	65	b1	b1	NOUN
ejpam-6264	466	66	)	)	PUNCT
ejpam-6264	466	67	v3	v3	PROPN
ejpam-6264	466	68	is	be	AUX
ejpam-6264	466	69	a	a	DET
ejpam-6264	466	70	dominating	dominating	NOUN
ejpam-6264	466	71	set	set	NOUN
ejpam-6264	466	72	of	of	ADP
ejpam-6264	466	73	g.	g.	PROPN
ejpam-6264	466	74	(	(	PUNCT
ejpam-6264	466	75	b2	b2	NOUN
ejpam-6264	466	76	)	)	PUNCT
ejpam-6264	466	77	v2	v2	NOUN
ejpam-6264	466	78	∩	∩	ADJ
ejpam-6264	466	79	v	v	NOUN
ejpam-6264	466	80	(	(	PUNCT
ejpam-6264	466	81	h	h	NOUN
ejpam-6264	466	82	)	)	PUNCT
ejpam-6264	466	83	is	be	AUX
ejpam-6264	466	84	a	a	DET
ejpam-6264	466	85	dominating	dominating	NOUN
ejpam-6264	466	86	set	set	NOUN
ejpam-6264	466	87	of	of	ADP
ejpam-6264	466	88	v0	v0	NOUN
ejpam-6264	466	89	∩	∩	X
ejpam-6264	466	90	v	v	X
ejpam-6264	466	91	(	(	PUNCT
ejpam-6264	466	92	h	h	NOUN
ejpam-6264	466	93	)	)	PUNCT
ejpam-6264	466	94	.	.	PUNCT
ejpam-6264	467	1	(	(	PUNCT
ejpam-6264	467	2	c	c	X
ejpam-6264	467	3	)	)	PUNCT
ejpam-6264	467	4	v3	v3	PROPN
ejpam-6264	467	5	∩	∩	ADJ
ejpam-6264	467	6	v	v	X
ejpam-6264	467	7	(	(	PUNCT
ejpam-6264	467	8	g	g	NOUN
ejpam-6264	467	9	)	)	PUNCT
ejpam-6264	467	10	=	=	NOUN
ejpam-6264	467	11	∅	∅	NOUN
ejpam-6264	467	12	and	and	CCONJ
ejpam-6264	467	13	each	each	PRON
ejpam-6264	467	14	of	of	ADP
ejpam-6264	467	15	the	the	DET
ejpam-6264	467	16	following	follow	VERB
ejpam-6264	467	17	holds	hold	VERB
ejpam-6264	467	18	:	:	PUNCT
ejpam-6264	467	19	(	(	PUNCT
ejpam-6264	467	20	c1	c1	NOUN
ejpam-6264	467	21	)	)	PUNCT
ejpam-6264	467	22	v2	v2	PROPN
ejpam-6264	467	23	is	be	AUX
ejpam-6264	467	24	a	a	DET
ejpam-6264	467	25	dominating	dominating	NOUN
ejpam-6264	467	26	set	set	NOUN
ejpam-6264	467	27	of	of	ADP
ejpam-6264	467	28	g.	g.	PROPN
ejpam-6264	467	29	(	(	PUNCT
ejpam-6264	467	30	c2	c2	PROPN
ejpam-6264	467	31	)	)	PUNCT
ejpam-6264	467	32	v3	v3	PROPN
ejpam-6264	467	33	∩	∩	ADJ
ejpam-6264	467	34	v	v	X
ejpam-6264	467	35	(	(	PUNCT
ejpam-6264	467	36	h	h	NOUN
ejpam-6264	467	37	)	)	PUNCT
ejpam-6264	467	38	is	be	AUX
ejpam-6264	467	39	a	a	DET
ejpam-6264	467	40	dominating	dominating	NOUN
ejpam-6264	467	41	set	set	NOUN
ejpam-6264	467	42	of	of	ADP
ejpam-6264	467	43	v0	v0	NOUN
ejpam-6264	467	44	∩	∩	X
ejpam-6264	467	45	v	v	X
ejpam-6264	467	46	(	(	PUNCT
ejpam-6264	467	47	h	h	NOUN
ejpam-6264	467	48	)	)	PUNCT
ejpam-6264	467	49	.	.	PUNCT
ejpam-6264	468	1	(	(	PUNCT
ejpam-6264	468	2	ii	ii	X
ejpam-6264	468	3	)	)	PUNCT
ejpam-6264	468	4	f	f	PROPN
ejpam-6264	468	5	|h	|h	PROPN
ejpam-6264	468	6	∈	∈	PROPN
ejpam-6264	468	7	tmrdf	tmrdf	NOUN
ejpam-6264	468	8	(	(	PUNCT
ejpam-6264	468	9	h	h	NOUN
ejpam-6264	468	10	)	)	PUNCT
ejpam-6264	468	11	and	and	CCONJ
ejpam-6264	468	12	one	one	NUM
ejpam-6264	468	13	of	of	ADP
ejpam-6264	468	14	the	the	DET
ejpam-6264	468	15	following	following	NOUN
ejpam-6264	468	16	holds	hold	VERB
ejpam-6264	468	17	:	:	PUNCT
ejpam-6264	468	18	(	(	PUNCT
ejpam-6264	468	19	a	a	X
ejpam-6264	468	20	)	)	PUNCT
ejpam-6264	468	21	|v2	|v2	NOUN
ejpam-6264	468	22	∩	∩	ADJ
ejpam-6264	468	23	v	v	X
ejpam-6264	468	24	(	(	PUNCT
ejpam-6264	468	25	h)|	h)|	PROPN
ejpam-6264	468	26	≥	≥	NUM
ejpam-6264	468	27	1	1	NUM
ejpam-6264	468	28	and	and	CCONJ
ejpam-6264	468	29	|v3	|v3	NOUN
ejpam-6264	468	30	∩	∩	ADJ
ejpam-6264	468	31	v	v	X
ejpam-6264	468	32	(	(	PUNCT
ejpam-6264	468	33	h)|	h)|	PROPN
ejpam-6264	468	34	≥	≥	NUM
ejpam-6264	468	35	1	1	NUM
ejpam-6264	468	36	(	(	PUNCT
ejpam-6264	468	37	b	b	NOUN
ejpam-6264	468	38	)	)	PUNCT
ejpam-6264	468	39	v2	v2	NOUN
ejpam-6264	468	40	∩	∩	ADJ
ejpam-6264	468	41	v	v	NOUN
ejpam-6264	468	42	(	(	PUNCT
ejpam-6264	468	43	h	h	NOUN
ejpam-6264	468	44	)	)	PUNCT
ejpam-6264	468	45	=	=	NOUN
ejpam-6264	468	46	∅	∅	NOUN
ejpam-6264	468	47	and	and	CCONJ
ejpam-6264	468	48	each	each	PRON
ejpam-6264	468	49	of	of	ADP
ejpam-6264	468	50	the	the	DET
ejpam-6264	468	51	following	follow	VERB
ejpam-6264	468	52	holds	hold	VERB
ejpam-6264	468	53	:	:	PUNCT
ejpam-6264	468	54	(	(	PUNCT
ejpam-6264	468	55	b1	b1	NOUN
ejpam-6264	468	56	)	)	PUNCT
ejpam-6264	468	57	v3	v3	PROPN
ejpam-6264	468	58	is	be	AUX
ejpam-6264	468	59	a	a	DET
ejpam-6264	468	60	dominating	dominating	NOUN
ejpam-6264	468	61	set	set	NOUN
ejpam-6264	468	62	of	of	ADP
ejpam-6264	468	63	h.	h.	PROPN
ejpam-6264	468	64	(	(	PUNCT
ejpam-6264	468	65	b2	b2	NOUN
ejpam-6264	468	66	)	)	PUNCT
ejpam-6264	468	67	v2	v2	PROPN
ejpam-6264	468	68	∩	∩	ADJ
ejpam-6264	468	69	v	v	NOUN
ejpam-6264	468	70	(	(	PUNCT
ejpam-6264	468	71	g	g	NOUN
ejpam-6264	468	72	)	)	PUNCT
ejpam-6264	468	73	is	be	AUX
ejpam-6264	468	74	a	a	DET
ejpam-6264	468	75	dominating	dominating	NOUN
ejpam-6264	468	76	set	set	NOUN
ejpam-6264	468	77	of	of	ADP
ejpam-6264	468	78	v0	v0	NOUN
ejpam-6264	468	79	∩	∩	X
ejpam-6264	468	80	v	v	X
ejpam-6264	468	81	(	(	PUNCT
ejpam-6264	468	82	g	g	NOUN
ejpam-6264	468	83	)	)	PUNCT
ejpam-6264	468	84	.	.	PUNCT
ejpam-6264	469	1	(	(	PUNCT
ejpam-6264	469	2	c	c	X
ejpam-6264	469	3	)	)	PUNCT
ejpam-6264	469	4	v3	v3	PROPN
ejpam-6264	469	5	∩	∩	ADJ
ejpam-6264	469	6	v	v	X
ejpam-6264	469	7	(	(	PUNCT
ejpam-6264	469	8	h	h	NOUN
ejpam-6264	469	9	)	)	PUNCT
ejpam-6264	469	10	=	=	NOUN
ejpam-6264	469	11	∅	∅	NOUN
ejpam-6264	469	12	and	and	CCONJ
ejpam-6264	469	13	each	each	PRON
ejpam-6264	469	14	of	of	ADP
ejpam-6264	469	15	the	the	DET
ejpam-6264	469	16	following	follow	VERB
ejpam-6264	469	17	holds	hold	VERB
ejpam-6264	469	18	:	:	PUNCT
ejpam-6264	469	19	(	(	PUNCT
ejpam-6264	469	20	c1	c1	NOUN
ejpam-6264	469	21	)	)	PUNCT
ejpam-6264	469	22	v2	v2	PROPN
ejpam-6264	469	23	is	be	AUX
ejpam-6264	469	24	a	a	DET
ejpam-6264	469	25	dominating	dominating	NOUN
ejpam-6264	469	26	set	set	NOUN
ejpam-6264	469	27	of	of	ADP
ejpam-6264	469	28	h.	h.	PROPN
ejpam-6264	469	29	(	(	PUNCT
ejpam-6264	469	30	c2	c2	PROPN
ejpam-6264	469	31	)	)	PUNCT
ejpam-6264	469	32	v3	v3	PROPN
ejpam-6264	469	33	∩	∩	ADJ
ejpam-6264	469	34	v	v	X
ejpam-6264	469	35	(	(	PUNCT
ejpam-6264	469	36	g	g	NOUN
ejpam-6264	469	37	)	)	PUNCT
ejpam-6264	469	38	is	be	AUX
ejpam-6264	469	39	a	a	DET
ejpam-6264	469	40	dominating	dominating	NOUN
ejpam-6264	469	41	set	set	NOUN
ejpam-6264	469	42	of	of	ADP
ejpam-6264	469	43	v0	v0	NOUN
ejpam-6264	469	44	∩	∩	X
ejpam-6264	469	45	v	v	X
ejpam-6264	469	46	(	(	PUNCT
ejpam-6264	469	47	g	g	NOUN
ejpam-6264	469	48	)	)	PUNCT
ejpam-6264	469	49	.	.	PUNCT
ejpam-6264	470	1	(	(	PUNCT
ejpam-6264	470	2	iii	iii	X
ejpam-6264	470	3	)	)	PUNCT
ejpam-6264	470	4	f	f	PROPN
ejpam-6264	470	5	|g	|g	VERB
ejpam-6264	470	6	̸∈	̸∈	PROPN
ejpam-6264	470	7	tmrdf	tmrdf	PROPN
ejpam-6264	470	8	(	(	PUNCT
ejpam-6264	470	9	g	g	NOUN
ejpam-6264	470	10	)	)	PUNCT
ejpam-6264	470	11	,	,	PUNCT
ejpam-6264	471	1	f	f	PROPN
ejpam-6264	471	2	|h	|h	X
ejpam-6264	471	3	̸∈	̸∈	PROPN
ejpam-6264	471	4	tmrdf	tmrdf	PROPN
ejpam-6264	471	5	(	(	PUNCT
ejpam-6264	471	6	h	h	NOUN
ejpam-6264	471	7	)	)	PUNCT
ejpam-6264	471	8	and	and	CCONJ
ejpam-6264	471	9	each	each	PRON
ejpam-6264	471	10	of	of	ADP
ejpam-6264	471	11	the	the	DET
ejpam-6264	471	12	following	following	NOUN
ejpam-6264	471	13	holds	hold	VERB
ejpam-6264	471	14	:	:	PUNCT
ejpam-6264	471	15	(	(	PUNCT
ejpam-6264	471	16	a	a	X
ejpam-6264	471	17	)	)	PUNCT
ejpam-6264	471	18	v2	v2	PROPN
ejpam-6264	471	19	∩	∩	ADJ
ejpam-6264	471	20	v	v	NOUN
ejpam-6264	471	21	(	(	PUNCT
ejpam-6264	471	22	h	h	NOUN
ejpam-6264	471	23	)	)	PUNCT
ejpam-6264	471	24	̸=	̸=	PROPN
ejpam-6264	471	25	∅	∅	NOUN
ejpam-6264	471	26	whenever	whenever	SCONJ
ejpam-6264	471	27	ng(x	ng(x	NUM
ejpam-6264	471	28	)	)	PUNCT
ejpam-6264	471	29	∩	∩	NOUN
ejpam-6264	471	30	v2	v2	NOUN
ejpam-6264	471	31	=	=	PUNCT
ejpam-6264	471	32	∅	∅	NOUN
ejpam-6264	471	33	for	for	ADP
ejpam-6264	471	34	some	some	DET
ejpam-6264	471	35	x	x	SYM
ejpam-6264	471	36	∈	∈	PROPN
ejpam-6264	471	37	v0	v0	NOUN
ejpam-6264	471	38	∩	∩	X
ejpam-6264	471	39	v	v	X
ejpam-6264	471	40	(	(	PUNCT
ejpam-6264	471	41	g	g	NOUN
ejpam-6264	471	42	)	)	PUNCT
ejpam-6264	471	43	.	.	PUNCT
ejpam-6264	472	1	(	(	PUNCT
ejpam-6264	472	2	b	b	X
ejpam-6264	472	3	)	)	PUNCT
ejpam-6264	472	4	v3	v3	PROPN
ejpam-6264	472	5	∩	∩	ADJ
ejpam-6264	472	6	v	v	X
ejpam-6264	472	7	(	(	PUNCT
ejpam-6264	472	8	h	h	NOUN
ejpam-6264	472	9	)	)	PUNCT
ejpam-6264	472	10	̸=	̸=	PROPN
ejpam-6264	472	11	∅	∅	NOUN
ejpam-6264	472	12	whenever	whenever	SCONJ
ejpam-6264	472	13	ng(x	ng(x	NUM
ejpam-6264	472	14	)	)	PUNCT
ejpam-6264	472	15	∩	∩	PROPN
ejpam-6264	472	16	v3	v3	NOUN
ejpam-6264	472	17	=	=	PUNCT
ejpam-6264	472	18	∅	∅	NOUN
ejpam-6264	472	19	for	for	ADP
ejpam-6264	472	20	some	some	DET
ejpam-6264	472	21	x	x	SYM
ejpam-6264	472	22	∈	∈	PROPN
ejpam-6264	472	23	v0	v0	NOUN
ejpam-6264	472	24	∩	∩	X
ejpam-6264	472	25	v	v	X
ejpam-6264	472	26	(	(	PUNCT
ejpam-6264	472	27	g	g	NOUN
ejpam-6264	472	28	)	)	PUNCT
ejpam-6264	472	29	.	.	PUNCT
ejpam-6264	473	1	(	(	PUNCT
ejpam-6264	473	2	c	c	X
ejpam-6264	473	3	)	)	PUNCT
ejpam-6264	473	4	v2	v2	NOUN
ejpam-6264	473	5	∩	∩	ADJ
ejpam-6264	473	6	v	v	NOUN
ejpam-6264	473	7	(	(	PUNCT
ejpam-6264	473	8	h	h	NOUN
ejpam-6264	473	9	)	)	PUNCT
ejpam-6264	473	10	̸=	̸=	PROPN
ejpam-6264	473	11	∅	∅	NOUN
ejpam-6264	473	12	or	or	CCONJ
ejpam-6264	473	13	v3	v3	PROPN
ejpam-6264	473	14	∩	∩	ADJ
ejpam-6264	473	15	v	v	X
ejpam-6264	473	16	(	(	PUNCT
ejpam-6264	473	17	h	h	NOUN
ejpam-6264	473	18	)	)	PUNCT
ejpam-6264	473	19	̸=	̸=	NOUN
ejpam-6264	473	20	∅	∅	NOUN
ejpam-6264	473	21	whenever	whenever	SCONJ
ejpam-6264	473	22	∃x	∃x	PROPN
ejpam-6264	473	23	∈	∈	PROPN
ejpam-6264	473	24	v1	v1	NOUN
ejpam-6264	473	25	with	with	ADP
ejpam-6264	473	26	ng(x)∩	ng(x)∩	PUNCT
ejpam-6264	473	27	v2	v2	NOUN
ejpam-6264	473	28	=	=	NOUN
ejpam-6264	473	29	∅	∅	NOUN
ejpam-6264	473	30	and	and	CCONJ
ejpam-6264	473	31	ng(x	ng(x	NUM
ejpam-6264	473	32	)	)	PUNCT
ejpam-6264	473	33	∩	∩	NOUN
ejpam-6264	473	34	v3	v3	PROPN
ejpam-6264	473	35	=	=	SYM
ejpam-6264	473	36	∅	∅	NOUN
ejpam-6264	473	37	(	(	PUNCT
ejpam-6264	473	38	d	d	X
ejpam-6264	473	39	)	)	PUNCT
ejpam-6264	473	40	v2	v2	NOUN
ejpam-6264	473	41	∩	∩	ADJ
ejpam-6264	473	42	v	v	NOUN
ejpam-6264	473	43	(	(	PUNCT
ejpam-6264	473	44	g	g	NOUN
ejpam-6264	473	45	)	)	PUNCT
ejpam-6264	473	46	̸=	̸=	PROPN
ejpam-6264	473	47	∅	∅	NOUN
ejpam-6264	473	48	whenever	whenever	SCONJ
ejpam-6264	473	49	nh(x	nh(x	NUM
ejpam-6264	473	50	)	)	PUNCT
ejpam-6264	473	51	∩	∩	ADJ
ejpam-6264	473	52	v2	v2	NOUN
ejpam-6264	473	53	=	=	PUNCT
ejpam-6264	473	54	∅	∅	NOUN
ejpam-6264	473	55	for	for	ADP
ejpam-6264	473	56	some	some	DET
ejpam-6264	473	57	x	x	SYM
ejpam-6264	473	58	∈	∈	PROPN
ejpam-6264	473	59	v0	v0	NOUN
ejpam-6264	473	60	∩	∩	X
ejpam-6264	473	61	v	v	X
ejpam-6264	473	62	(	(	PUNCT
ejpam-6264	473	63	h	h	NOUN
ejpam-6264	473	64	)	)	PUNCT
ejpam-6264	473	65	.	.	PUNCT
ejpam-6264	474	1	(	(	PUNCT
ejpam-6264	474	2	e	e	X
ejpam-6264	474	3	)	)	PUNCT
ejpam-6264	474	4	v3	v3	PROPN
ejpam-6264	474	5	∩	∩	ADJ
ejpam-6264	474	6	v	v	X
ejpam-6264	474	7	(	(	PUNCT
ejpam-6264	474	8	g	g	NOUN
ejpam-6264	474	9	)	)	PUNCT
ejpam-6264	474	10	̸=	̸=	PROPN
ejpam-6264	474	11	∅	∅	NOUN
ejpam-6264	474	12	whenever	whenever	SCONJ
ejpam-6264	474	13	nh(x	nh(x	NUM
ejpam-6264	474	14	)	)	PUNCT
ejpam-6264	474	15	∩	∩	ADJ
ejpam-6264	474	16	v3	v3	NOUN
ejpam-6264	474	17	=	=	PUNCT
ejpam-6264	474	18	∅	∅	NOUN
ejpam-6264	474	19	for	for	ADP
ejpam-6264	474	20	some	some	DET
ejpam-6264	474	21	x	x	SYM
ejpam-6264	474	22	∈	∈	PROPN
ejpam-6264	474	23	v0	v0	NOUN
ejpam-6264	474	24	∩	∩	X
ejpam-6264	474	25	v	v	X
ejpam-6264	474	26	(	(	PUNCT
ejpam-6264	474	27	h	h	NOUN
ejpam-6264	474	28	)	)	PUNCT
ejpam-6264	474	29	.	.	PUNCT
ejpam-6264	475	1	s.	s.	PROPN
ejpam-6264	475	2	ahamad	ahamad	VERB
ejpam-6264	475	3	et	et	PROPN
ejpam-6264	475	4	al	al	PROPN
ejpam-6264	475	5	.	.	PUNCT
ejpam-6264	475	6	/	/	SYM
ejpam-6264	475	7	eur	eur	PROPN
ejpam-6264	475	8	.	.	PUNCT
ejpam-6264	476	1	j.	j.	PROPN
ejpam-6264	476	2	pure	pure	PROPN
ejpam-6264	476	3	appl	appl	PROPN
ejpam-6264	476	4	.	.	PROPN
ejpam-6264	476	5	math	math	PROPN
ejpam-6264	476	6	,	,	PUNCT
ejpam-6264	476	7	18	18	NUM
ejpam-6264	476	8	(	(	PUNCT
ejpam-6264	476	9	4	4	NUM
ejpam-6264	476	10	)	)	PUNCT
ejpam-6264	476	11	(	(	PUNCT
ejpam-6264	476	12	2025	2025	NUM
ejpam-6264	476	13	)	)	PUNCT
ejpam-6264	476	14	,	,	PUNCT
ejpam-6264	476	15	6264	6264	NUM
ejpam-6264	476	16	14	14	NUM
ejpam-6264	476	17	of	of	ADP
ejpam-6264	476	18	20	20	NUM
ejpam-6264	476	19	(	(	PUNCT
ejpam-6264	476	20	f	f	X
ejpam-6264	476	21	)	)	PUNCT
ejpam-6264	476	22	v2	v2	PROPN
ejpam-6264	476	23	∩	∩	ADJ
ejpam-6264	476	24	v	v	NOUN
ejpam-6264	476	25	(	(	PUNCT
ejpam-6264	476	26	g	g	NOUN
ejpam-6264	476	27	)	)	PUNCT
ejpam-6264	476	28	̸=	̸=	PROPN
ejpam-6264	476	29	∅	∅	NOUN
ejpam-6264	476	30	or	or	CCONJ
ejpam-6264	476	31	v3	v3	PROPN
ejpam-6264	476	32	∩	∩	ADJ
ejpam-6264	476	33	v	v	X
ejpam-6264	476	34	(	(	PUNCT
ejpam-6264	476	35	g	g	NOUN
ejpam-6264	476	36	)	)	PUNCT
ejpam-6264	476	37	̸=	̸=	PROPN
ejpam-6264	476	38	∅	∅	NOUN
ejpam-6264	476	39	whenever	whenever	SCONJ
ejpam-6264	476	40	∃x	∃x	PROPN
ejpam-6264	476	41	∈	∈	PROPN
ejpam-6264	476	42	v1	v1	NOUN
ejpam-6264	476	43	with	with	ADP
ejpam-6264	476	44	nh(x)∩	nh(x)∩	NOUN
ejpam-6264	476	45	v2	v2	NOUN
ejpam-6264	476	46	=	=	NOUN
ejpam-6264	476	47	∅	∅	NOUN
ejpam-6264	476	48	and	and	CCONJ
ejpam-6264	476	49	nh(x	nh(x	NUM
ejpam-6264	476	50	)	)	PUNCT
ejpam-6264	476	51	∩	∩	ADJ
ejpam-6264	476	52	v3	v3	PROPN
ejpam-6264	476	53	=	=	SYM
ejpam-6264	476	54	∅	∅	NOUN
ejpam-6264	476	55	(	(	PUNCT
ejpam-6264	476	56	g	g	NOUN
ejpam-6264	476	57	)	)	PUNCT
ejpam-6264	476	58	for	for	ADP
ejpam-6264	476	59	every	every	DET
ejpam-6264	476	60	x	x	SYM
ejpam-6264	476	61	∈	∈	PROPN
ejpam-6264	476	62	v1	v1	NOUN
ejpam-6264	476	63	∪	∪	NOUN
ejpam-6264	476	64	v2	v2	PROPN
ejpam-6264	476	65	∪	∪	X
ejpam-6264	476	66	v3	v3	PROPN
ejpam-6264	476	67	,	,	PUNCT
ejpam-6264	476	68	(	(	PUNCT
ejpam-6264	476	69	v1	v1	VERB
ejpam-6264	476	70	∪	∪	VERB
ejpam-6264	476	71	v2	v2	NOUN
ejpam-6264	476	72	∪	∪	ADJ
ejpam-6264	476	73	v3)∩	v3)∩	NOUN
ejpam-6264	476	74	v	v	NOUN
ejpam-6264	476	75	(	(	PUNCT
ejpam-6264	476	76	h	h	NOUN
ejpam-6264	476	77	)	)	PUNCT
ejpam-6264	476	78	̸=	̸=	NOUN
ejpam-6264	476	79	∅	∅	NOUN
ejpam-6264	476	80	whenever	whenever	SCONJ
ejpam-6264	476	81	x	x	SYM
ejpam-6264	476	82	∈	∈	PROPN
ejpam-6264	476	83	v	v	X
ejpam-6264	476	84	(	(	PUNCT
ejpam-6264	476	85	g	g	NOUN
ejpam-6264	476	86	)	)	PUNCT
ejpam-6264	476	87	and	and	CCONJ
ejpam-6264	476	88	ng(x	ng(x	NUM
ejpam-6264	476	89	)	)	PUNCT
ejpam-6264	476	90	⊆	⊆	NUM
ejpam-6264	476	91	v0	v0	NOUN
ejpam-6264	476	92	.	.	PUNCT
ejpam-6264	477	1	(	(	PUNCT
ejpam-6264	477	2	h	h	NOUN
ejpam-6264	477	3	)	)	PUNCT
ejpam-6264	477	4	for	for	ADP
ejpam-6264	477	5	every	every	DET
ejpam-6264	477	6	x	x	SYM
ejpam-6264	477	7	∈	∈	PROPN
ejpam-6264	477	8	v1	v1	NOUN
ejpam-6264	477	9	∪	∪	NOUN
ejpam-6264	477	10	v2	v2	PROPN
ejpam-6264	477	11	∪	∪	X
ejpam-6264	477	12	v3	v3	PROPN
ejpam-6264	477	13	,	,	PUNCT
ejpam-6264	477	14	(	(	PUNCT
ejpam-6264	477	15	v1	v1	VERB
ejpam-6264	477	16	∪	∪	VERB
ejpam-6264	477	17	v2	v2	NOUN
ejpam-6264	477	18	∪	∪	ADJ
ejpam-6264	477	19	v3)∩	v3)∩	NOUN
ejpam-6264	477	20	v	v	NOUN
ejpam-6264	477	21	(	(	PUNCT
ejpam-6264	477	22	g	g	NOUN
ejpam-6264	477	23	)	)	PUNCT
ejpam-6264	477	24	=	=	NOUN
ejpam-6264	477	25	̸	̸	ADJ
ejpam-6264	477	26	∅	∅	NOUN
ejpam-6264	477	27	whenever	whenever	SCONJ
ejpam-6264	477	28	x	x	SYM
ejpam-6264	477	29	∈	∈	PROPN
ejpam-6264	477	30	v	v	ADP
ejpam-6264	477	31	(	(	PUNCT
ejpam-6264	477	32	h	h	NOUN
ejpam-6264	477	33	)	)	PUNCT
ejpam-6264	477	34	and	and	CCONJ
ejpam-6264	477	35	nh(x	nh(x	NUM
ejpam-6264	477	36	)	)	PUNCT
ejpam-6264	477	37	⊆	⊆	NUM
ejpam-6264	477	38	v0	v0	NOUN
ejpam-6264	477	39	.	.	PUNCT
ejpam-6264	478	1	proof	proof	NOUN
ejpam-6264	478	2	.	.	PUNCT
ejpam-6264	479	1	suppose	suppose	VERB
ejpam-6264	479	2	f	f	PROPN
ejpam-6264	479	3	|g	|g	PROPN
ejpam-6264	479	4	∈	∈	PROPN
ejpam-6264	479	5	tmrdf	tmrdf	NOUN
ejpam-6264	479	6	(	(	PUNCT
ejpam-6264	479	7	g	g	NOUN
ejpam-6264	479	8	)	)	PUNCT
ejpam-6264	479	9	.	.	PUNCT
ejpam-6264	480	1	assume	assume	VERB
ejpam-6264	480	2	that	that	SCONJ
ejpam-6264	480	3	(	(	PUNCT
ejpam-6264	480	4	i)(a	i)(a	NOUN
ejpam-6264	480	5	)	)	PUNCT
ejpam-6264	480	6	holds	hold	VERB
ejpam-6264	480	7	.	.	PUNCT
ejpam-6264	481	1	let	let	VERB
ejpam-6264	481	2	v	v	NUM
ejpam-6264	481	3	∈	∈	PROPN
ejpam-6264	481	4	v0	v0	NOUN
ejpam-6264	481	5	∩	∩	X
ejpam-6264	481	6	v	v	X
ejpam-6264	481	7	(	(	PUNCT
ejpam-6264	481	8	g	g	NOUN
ejpam-6264	481	9	)	)	PUNCT
ejpam-6264	481	10	.	.	PUNCT
ejpam-6264	482	1	by	by	ADP
ejpam-6264	482	2	assumption	assumption	NOUN
ejpam-6264	482	3	,	,	PUNCT
ejpam-6264	482	4	there	there	PRON
ejpam-6264	482	5	exist	exist	VERB
ejpam-6264	482	6	u	u	PROPN
ejpam-6264	482	7	∈	∈	PROPN
ejpam-6264	482	8	v2	v2	PROPN
ejpam-6264	482	9	∩	∩	ADJ
ejpam-6264	482	10	v	v	NOUN
ejpam-6264	482	11	(	(	PUNCT
ejpam-6264	482	12	g	g	NOUN
ejpam-6264	482	13	)	)	PUNCT
ejpam-6264	482	14	and	and	CCONJ
ejpam-6264	482	15	w	w	PROPN
ejpam-6264	482	16	∈	∈	PROPN
ejpam-6264	482	17	v3	v3	PROPN
ejpam-6264	482	18	∩	∩	PROPN
ejpam-6264	482	19	v	v	X
ejpam-6264	482	20	(	(	PUNCT
ejpam-6264	482	21	g	g	NOUN
ejpam-6264	482	22	)	)	PUNCT
ejpam-6264	482	23	such	such	ADJ
ejpam-6264	482	24	that	that	SCONJ
ejpam-6264	482	25	uv	uv	NOUN
ejpam-6264	482	26	,	,	PUNCT
ejpam-6264	482	27	wv	wv	PROPN
ejpam-6264	482	28	∈	∈	PROPN
ejpam-6264	482	29	e(g	e(g	PROPN
ejpam-6264	482	30	)	)	PUNCT
ejpam-6264	483	1	⊆	⊆	NUM
ejpam-6264	483	2	e(g+h	e(g+h	NUM
ejpam-6264	483	3	)	)	PUNCT
ejpam-6264	483	4	.	.	PUNCT
ejpam-6264	484	1	let	let	VERB
ejpam-6264	484	2	v	v	NUM
ejpam-6264	484	3	∈	∈	PROPN
ejpam-6264	484	4	v0	v0	NOUN
ejpam-6264	484	5	∩	∩	X
ejpam-6264	484	6	v	v	X
ejpam-6264	484	7	(	(	PUNCT
ejpam-6264	484	8	h	h	NOUN
ejpam-6264	484	9	)	)	PUNCT
ejpam-6264	484	10	.	.	PUNCT
ejpam-6264	485	1	note	note	VERB
ejpam-6264	485	2	that	that	SCONJ
ejpam-6264	485	3	|v2	|v2	NOUN
ejpam-6264	485	4	∩	∩	PROPN
ejpam-6264	485	5	v	v	X
ejpam-6264	485	6	(	(	PUNCT
ejpam-6264	485	7	g)|	g)|	VERB
ejpam-6264	485	8	≥	≥	NOUN
ejpam-6264	485	9	1	1	NUM
ejpam-6264	485	10	and	and	CCONJ
ejpam-6264	485	11	|v3	|v3	NOUN
ejpam-6264	485	12	∩	∩	ADJ
ejpam-6264	485	13	v	v	X
ejpam-6264	485	14	(	(	PUNCT
ejpam-6264	485	15	g)|	g)|	VERB
ejpam-6264	485	16	≥	≥	NOUN
ejpam-6264	485	17	1	1	NUM
ejpam-6264	485	18	.	.	PUNCT
ejpam-6264	485	19	take	take	VERB
ejpam-6264	485	20	u	u	PRON
ejpam-6264	485	21	∈	∈	NOUN
ejpam-6264	485	22	v2∩v	v2∩v	NOUN
ejpam-6264	485	23	(	(	PUNCT
ejpam-6264	485	24	g	g	NOUN
ejpam-6264	485	25	)	)	PUNCT
ejpam-6264	485	26	and	and	CCONJ
ejpam-6264	485	27	w	w	PROPN
ejpam-6264	485	28	∈	∈	PROPN
ejpam-6264	486	1	v3∩v	v3∩v	X
ejpam-6264	486	2	(	(	PUNCT
ejpam-6264	486	3	g	g	NOUN
ejpam-6264	486	4	)	)	PUNCT
ejpam-6264	486	5	.	.	PUNCT
ejpam-6264	487	1	then	then	ADV
ejpam-6264	487	2	vu	vu	X
ejpam-6264	487	3	,	,	PUNCT
ejpam-6264	487	4	vw	vw	PROPN
ejpam-6264	487	5	∈	∈	PROPN
ejpam-6264	487	6	e(g+h	e(g+h	NUM
ejpam-6264	487	7	)	)	PUNCT
ejpam-6264	487	8	.	.	PUNCT
ejpam-6264	488	1	also	also	ADV
ejpam-6264	488	2	,	,	PUNCT
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ejpam-6264	488	4	f	f	PROPN
ejpam-6264	488	5	|g	|g	PROPN
ejpam-6264	488	6	∈	∈	PROPN
ejpam-6264	488	7	tmrdf	tmrdf	NOUN
ejpam-6264	488	8	(	(	PUNCT
ejpam-6264	488	9	g	g	NOUN
ejpam-6264	488	10	)	)	PUNCT
ejpam-6264	488	11	,	,	PUNCT
ejpam-6264	488	12	uw	uw	PROPN
ejpam-6264	488	13	∈	∈	PROPN
ejpam-6264	488	14	e(g	e(g	PROPN
ejpam-6264	488	15	)	)	PUNCT
ejpam-6264	488	16	⊆	⊆	NUM
ejpam-6264	488	17	e(g	e(g	NOUN
ejpam-6264	488	18	+	+	CCONJ
ejpam-6264	488	19	h	h	NOUN
ejpam-6264	488	20	)	)	PUNCT
ejpam-6264	488	21	.	.	PUNCT
ejpam-6264	489	1	let	let	VERB
ejpam-6264	489	2	v	v	NUM
ejpam-6264	489	3	∈	∈	NOUN
ejpam-6264	489	4	v1	v1	NOUN
ejpam-6264	489	5	∩	∩	ADJ
ejpam-6264	489	6	v	v	NOUN
ejpam-6264	489	7	(	(	PUNCT
ejpam-6264	489	8	g	g	NOUN
ejpam-6264	489	9	)	)	PUNCT
ejpam-6264	489	10	.	.	PUNCT
ejpam-6264	490	1	since	since	SCONJ
ejpam-6264	490	2	f	f	PROPN
ejpam-6264	490	3	|g	|g	PROPN
ejpam-6264	490	4	∈	∈	PROPN
ejpam-6264	490	5	tmrdf	tmrdf	NOUN
ejpam-6264	490	6	(	(	PUNCT
ejpam-6264	490	7	g	g	NOUN
ejpam-6264	490	8	)	)	PUNCT
ejpam-6264	490	9	,	,	PUNCT
ejpam-6264	490	10	there	there	PRON
ejpam-6264	490	11	exists	exist	VERB
ejpam-6264	490	12	u	u	PROPN
ejpam-6264	490	13	∈	∈	PROPN
ejpam-6264	490	14	(	(	PUNCT
ejpam-6264	490	15	v2∪v3)∩v	v2∪v3)∩v	PROPN
ejpam-6264	490	16	(	(	PUNCT
ejpam-6264	490	17	g	g	NOUN
ejpam-6264	490	18	)	)	PUNCT
ejpam-6264	490	19	such	such	ADJ
ejpam-6264	490	20	that	that	SCONJ
ejpam-6264	490	21	uv	uv	PROPN
ejpam-6264	490	22	∈	∈	PROPN
ejpam-6264	490	23	e(g	e(g	PROPN
ejpam-6264	490	24	)	)	PUNCT
ejpam-6264	490	25	⊆	⊆	NUM
ejpam-6264	490	26	e(g+h	e(g+h	NUM
ejpam-6264	490	27	)	)	PUNCT
ejpam-6264	490	28	.	.	PUNCT
ejpam-6264	491	1	now	now	ADV
ejpam-6264	491	2	,	,	PUNCT
ejpam-6264	491	3	assume	assume	VERB
ejpam-6264	491	4	v	v	ADP
ejpam-6264	491	5	∈	∈	PROPN
ejpam-6264	491	6	v1∩v	v1∩v	NOUN
ejpam-6264	491	7	(	(	PUNCT
ejpam-6264	491	8	h	h	NOUN
ejpam-6264	491	9	)	)	PUNCT
ejpam-6264	491	10	.	.	PUNCT
ejpam-6264	492	1	since	since	SCONJ
ejpam-6264	492	2	|v2	|v2	NOUN
ejpam-6264	492	3	∩	∩	PROPN
ejpam-6264	492	4	v	v	X
ejpam-6264	492	5	(	(	PUNCT
ejpam-6264	492	6	g)|	g)|	VERB
ejpam-6264	492	7	≥	≥	NOUN
ejpam-6264	492	8	1	1	NUM
ejpam-6264	492	9	and	and	CCONJ
ejpam-6264	492	10	|v3	|v3	NOUN
ejpam-6264	492	11	∩	∩	ADJ
ejpam-6264	492	12	v	v	X
ejpam-6264	492	13	(	(	PUNCT
ejpam-6264	492	14	g)|	g)|	VERB
ejpam-6264	492	15	≥	≥	NOUN
ejpam-6264	492	16	1	1	NUM
ejpam-6264	492	17	,	,	PUNCT
ejpam-6264	492	18	there	there	PRON
ejpam-6264	492	19	exists	exist	VERB
ejpam-6264	492	20	z	z	NOUN
ejpam-6264	492	21	∈	∈	PROPN
ejpam-6264	492	22	v2	v2	PROPN
ejpam-6264	492	23	∩	∩	ADJ
ejpam-6264	492	24	v	v	NOUN
ejpam-6264	492	25	(	(	PUNCT
ejpam-6264	492	26	g	g	NOUN
ejpam-6264	492	27	)	)	PUNCT
ejpam-6264	492	28	or	or	CCONJ
ejpam-6264	492	29	z	z	NOUN
ejpam-6264	492	30	∈	∈	PROPN
ejpam-6264	492	31	v3	v3	PROPN
ejpam-6264	492	32	∩	∩	PROPN
ejpam-6264	492	33	v	v	X
ejpam-6264	492	34	(	(	PUNCT
ejpam-6264	492	35	g	g	NOUN
ejpam-6264	492	36	)	)	PUNCT
ejpam-6264	492	37	such	such	ADJ
ejpam-6264	492	38	that	that	SCONJ
ejpam-6264	492	39	z	z	PROPN
ejpam-6264	492	40	∈	∈	PROPN
ejpam-6264	492	41	ng+h(v	ng+h(v	NOUN
ejpam-6264	492	42	)	)	PUNCT
ejpam-6264	492	43	.	.	PUNCT
ejpam-6264	493	1	thus	thus	ADV
ejpam-6264	493	2	,	,	PUNCT
ejpam-6264	493	3	f	f	PROPN
ejpam-6264	493	4	∈	∈	PROPN
ejpam-6264	493	5	tmrdf	tmrdf	NOUN
ejpam-6264	493	6	(	(	PUNCT
ejpam-6264	493	7	g	g	PROPN
ejpam-6264	493	8	+	+	PROPN
ejpam-6264	493	9	h	h	NOUN
ejpam-6264	493	10	)	)	PUNCT
ejpam-6264	493	11	.	.	PUNCT
ejpam-6264	494	1	similarly	similarly	ADV
ejpam-6264	494	2	,	,	PUNCT
ejpam-6264	494	3	if	if	SCONJ
ejpam-6264	494	4	f	f	PROPN
ejpam-6264	494	5	|h	|h	X
ejpam-6264	494	6	∈	∈	PROPN
ejpam-6264	494	7	tmrdf	tmrdf	NOUN
ejpam-6264	494	8	(	(	PUNCT
ejpam-6264	494	9	h	h	NOUN
ejpam-6264	494	10	)	)	PUNCT
ejpam-6264	494	11	with	with	ADP
ejpam-6264	494	12	|v2	|v2	NOUN
ejpam-6264	494	13	∩	∩	ADJ
ejpam-6264	494	14	v	v	X
ejpam-6264	494	15	(	(	PUNCT
ejpam-6264	494	16	h)|	h)|	PROPN
ejpam-6264	494	17	≥	≥	NUM
ejpam-6264	494	18	1	1	NUM
ejpam-6264	494	19	and	and	CCONJ
ejpam-6264	494	20	|v3	|v3	NOUN
ejpam-6264	494	21	∩	∩	ADJ
ejpam-6264	494	22	v	v	X
ejpam-6264	494	23	(	(	PUNCT
ejpam-6264	494	24	h)|	h)|	PROPN
ejpam-6264	494	25	≥	≥	NUM
ejpam-6264	494	26	1	1	NUM
ejpam-6264	494	27	,	,	PUNCT
ejpam-6264	494	28	then	then	ADV
ejpam-6264	494	29	f	f	PROPN
ejpam-6264	494	30	∈	∈	PROPN
ejpam-6264	494	31	tmrdf	tmrdf	NOUN
ejpam-6264	494	32	(	(	PUNCT
ejpam-6264	494	33	g+h	g+h	PROPN
ejpam-6264	494	34	)	)	PUNCT
ejpam-6264	494	35	.	.	PUNCT
ejpam-6264	495	1	assume	assume	VERB
ejpam-6264	495	2	(	(	PUNCT
ejpam-6264	495	3	i)(b	i)(b	NUM
ejpam-6264	495	4	)	)	PUNCT
ejpam-6264	495	5	holds	hold	NOUN
ejpam-6264	495	6	.	.	PUNCT
ejpam-6264	496	1	since	since	SCONJ
ejpam-6264	496	2	f	f	PROPN
ejpam-6264	496	3	|g	|g	PROPN
ejpam-6264	496	4	∈	∈	PROPN
ejpam-6264	496	5	tmrdf	tmrdf	NOUN
ejpam-6264	496	6	(	(	PUNCT
ejpam-6264	496	7	g	g	NOUN
ejpam-6264	496	8	)	)	PUNCT
ejpam-6264	496	9	,	,	PUNCT
ejpam-6264	496	10	v0	v0	PROPN
ejpam-6264	496	11	∩	∩	ADJ
ejpam-6264	496	12	v	v	X
ejpam-6264	496	13	(	(	PUNCT
ejpam-6264	496	14	g	g	NOUN
ejpam-6264	496	15	)	)	PUNCT
ejpam-6264	496	16	=	=	NOUN
ejpam-6264	496	17	∅.	∅.	ADP
ejpam-6264	496	18	thus	thus	ADV
ejpam-6264	496	19	,	,	PUNCT
ejpam-6264	496	20	v0	v0	NOUN
ejpam-6264	496	21	⊆	⊆	NUM
ejpam-6264	496	22	v	v	NOUN
ejpam-6264	496	23	(	(	PUNCT
ejpam-6264	496	24	h	h	NOUN
ejpam-6264	496	25	)	)	PUNCT
ejpam-6264	496	26	.	.	PUNCT
ejpam-6264	497	1	let	let	VERB
ejpam-6264	497	2	v	v	NUM
ejpam-6264	497	3	∈	∈	PROPN
ejpam-6264	497	4	v0	v0	NOUN
ejpam-6264	497	5	.	.	PUNCT
ejpam-6264	498	1	by	by	ADP
ejpam-6264	498	2	(	(	PUNCT
ejpam-6264	498	3	b2	b2	NOUN
ejpam-6264	498	4	)	)	PUNCT
ejpam-6264	498	5	,	,	PUNCT
ejpam-6264	498	6	there	there	PRON
ejpam-6264	498	7	exists	exist	VERB
ejpam-6264	498	8	u	u	PROPN
ejpam-6264	498	9	∈	∈	PROPN
ejpam-6264	498	10	v2	v2	PROPN
ejpam-6264	498	11	∩	∩	ADJ
ejpam-6264	498	12	v	v	NOUN
ejpam-6264	498	13	(	(	PUNCT
ejpam-6264	498	14	h	h	NOUN
ejpam-6264	498	15	)	)	PUNCT
ejpam-6264	498	16	such	such	ADJ
ejpam-6264	498	17	that	that	SCONJ
ejpam-6264	498	18	uv	uv	PROPN
ejpam-6264	498	19	∈	∈	PROPN
ejpam-6264	498	20	e(h	e(h	PROPN
ejpam-6264	498	21	)	)	PUNCT
ejpam-6264	498	22	⊆	⊆	NUM
ejpam-6264	498	23	e(g	e(g	NOUN
ejpam-6264	498	24	+	+	PROPN
ejpam-6264	498	25	h	h	NOUN
ejpam-6264	498	26	)	)	PUNCT
ejpam-6264	498	27	.	.	PUNCT
ejpam-6264	499	1	also	also	ADV
ejpam-6264	499	2	,	,	PUNCT
ejpam-6264	499	3	since	since	SCONJ
ejpam-6264	499	4	v3	v3	PROPN
ejpam-6264	499	5	is	be	AUX
ejpam-6264	499	6	a	a	DET
ejpam-6264	499	7	dominating	dominating	NOUN
ejpam-6264	499	8	set	set	NOUN
ejpam-6264	499	9	of	of	ADP
ejpam-6264	499	10	g	g	PROPN
ejpam-6264	499	11	,	,	PUNCT
ejpam-6264	499	12	v3	v3	PROPN
ejpam-6264	499	13	∩	∩	PROPN
ejpam-6264	499	14	v	v	X
ejpam-6264	499	15	(	(	PUNCT
ejpam-6264	499	16	g	g	NOUN
ejpam-6264	499	17	)	)	PUNCT
ejpam-6264	499	18	̸=	̸=	PROPN
ejpam-6264	499	19	∅.	∅.	AUX
ejpam-6264	499	20	pick	pick	VERB
ejpam-6264	499	21	w	w	PROPN
ejpam-6264	499	22	∈	∈	PROPN
ejpam-6264	499	23	v3	v3	PROPN
ejpam-6264	499	24	∩	∩	PROPN
ejpam-6264	499	25	v	v	X
ejpam-6264	499	26	(	(	PUNCT
ejpam-6264	499	27	g	g	NOUN
ejpam-6264	499	28	)	)	PUNCT
ejpam-6264	499	29	.	.	PUNCT
ejpam-6264	500	1	then	then	ADV
ejpam-6264	500	2	vw	vw	PROPN
ejpam-6264	500	3	∈	∈	PROPN
ejpam-6264	500	4	e(g	e(g	PROPN
ejpam-6264	501	1	+	+	CCONJ
ejpam-6264	501	2	h	h	NOUN
ejpam-6264	501	3	)	)	PUNCT
ejpam-6264	501	4	.	.	PUNCT
ejpam-6264	502	1	moreover	moreover	ADV
ejpam-6264	502	2	,	,	PUNCT
ejpam-6264	502	3	uw	uw	PROPN
ejpam-6264	502	4	∈	∈	PROPN
ejpam-6264	502	5	e(g+h	e(g+h	NUM
ejpam-6264	502	6	)	)	PUNCT
ejpam-6264	502	7	.	.	PUNCT
ejpam-6264	503	1	let	let	VERB
ejpam-6264	503	2	v	v	NUM
ejpam-6264	503	3	∈	∈	PROPN
ejpam-6264	503	4	v1∩v	v1∩v	NOUN
ejpam-6264	503	5	(	(	PUNCT
ejpam-6264	503	6	g	g	NOUN
ejpam-6264	503	7	)	)	PUNCT
ejpam-6264	503	8	.	.	PUNCT
ejpam-6264	504	1	by	by	ADP
ejpam-6264	504	2	assumption	assumption	NOUN
ejpam-6264	504	3	,	,	PUNCT
ejpam-6264	504	4	there	there	PRON
ejpam-6264	504	5	exists	exist	VERB
ejpam-6264	504	6	u	u	PROPN
ejpam-6264	504	7	∈	∈	PROPN
ejpam-6264	504	8	v3∩v	v3∩v	X
ejpam-6264	504	9	(	(	PUNCT
ejpam-6264	504	10	g	g	NOUN
ejpam-6264	504	11	)	)	PUNCT
ejpam-6264	504	12	such	such	ADJ
ejpam-6264	504	13	that	that	SCONJ
ejpam-6264	504	14	uv	uv	PROPN
ejpam-6264	504	15	∈	∈	PROPN
ejpam-6264	504	16	e(g	e(g	PROPN
ejpam-6264	504	17	)	)	PUNCT
ejpam-6264	505	1	⊆	⊆	NUM
ejpam-6264	505	2	e(g	e(g	NOUN
ejpam-6264	505	3	+	+	PROPN
ejpam-6264	505	4	h	h	NOUN
ejpam-6264	505	5	)	)	PUNCT
ejpam-6264	505	6	.	.	PUNCT
ejpam-6264	506	1	now	now	ADV
ejpam-6264	506	2	,	,	PUNCT
ejpam-6264	506	3	let	let	VERB
ejpam-6264	506	4	v	v	NUM
ejpam-6264	506	5	∈	∈	NOUN
ejpam-6264	506	6	v1	v1	NOUN
ejpam-6264	506	7	∩	∩	ADJ
ejpam-6264	506	8	v	v	NOUN
ejpam-6264	506	9	(	(	PUNCT
ejpam-6264	506	10	h	h	NOUN
ejpam-6264	506	11	)	)	PUNCT
ejpam-6264	506	12	.	.	PUNCT
ejpam-6264	507	1	by	by	ADP
ejpam-6264	507	2	(	(	PUNCT
ejpam-6264	507	3	b1	b1	NOUN
ejpam-6264	507	4	)	)	PUNCT
ejpam-6264	507	5	,	,	PUNCT
ejpam-6264	507	6	there	there	PRON
ejpam-6264	507	7	exists	exist	VERB
ejpam-6264	507	8	u	u	PROPN
ejpam-6264	507	9	∈	∈	PROPN
ejpam-6264	507	10	v3	v3	PROPN
ejpam-6264	507	11	∩	∩	PROPN
ejpam-6264	507	12	v	v	X
ejpam-6264	507	13	(	(	PUNCT
ejpam-6264	507	14	g	g	NOUN
ejpam-6264	507	15	)	)	PUNCT
ejpam-6264	507	16	.	.	PUNCT
ejpam-6264	508	1	then	then	ADV
ejpam-6264	508	2	uv	uv	PROPN
ejpam-6264	508	3	∈	∈	PROPN
ejpam-6264	508	4	e(g	e(g	NOUN
ejpam-6264	509	1	+	+	CCONJ
ejpam-6264	509	2	h	h	NOUN
ejpam-6264	509	3	)	)	PUNCT
ejpam-6264	509	4	.	.	PUNCT
ejpam-6264	510	1	therefore	therefore	ADV
ejpam-6264	510	2	,	,	PUNCT
ejpam-6264	510	3	f	f	PROPN
ejpam-6264	510	4	∈	∈	PROPN
ejpam-6264	510	5	tmdrf	tmdrf	NOUN
ejpam-6264	510	6	(	(	PUNCT
ejpam-6264	510	7	g	g	PROPN
ejpam-6264	510	8	+	+	NOUN
ejpam-6264	510	9	h	h	NOUN
ejpam-6264	510	10	)	)	PUNCT
ejpam-6264	510	11	.	.	PUNCT
ejpam-6264	511	1	assume	assume	VERB
ejpam-6264	511	2	(	(	PUNCT
ejpam-6264	511	3	i)(c	i)(c	NOUN
ejpam-6264	511	4	)	)	PUNCT
ejpam-6264	511	5	holds	hold	VERB
ejpam-6264	511	6	.	.	PUNCT
ejpam-6264	512	1	since	since	SCONJ
ejpam-6264	512	2	f	f	PROPN
ejpam-6264	512	3	|g	|g	PROPN
ejpam-6264	512	4	∈	∈	PROPN
ejpam-6264	512	5	tmrdf	tmrdf	NOUN
ejpam-6264	512	6	(	(	PUNCT
ejpam-6264	512	7	g	g	NOUN
ejpam-6264	512	8	)	)	PUNCT
ejpam-6264	512	9	,	,	PUNCT
ejpam-6264	512	10	v0	v0	PROPN
ejpam-6264	512	11	∩	∩	ADJ
ejpam-6264	512	12	v	v	X
ejpam-6264	512	13	(	(	PUNCT
ejpam-6264	512	14	g	g	NOUN
ejpam-6264	512	15	)	)	PUNCT
ejpam-6264	512	16	=	=	NOUN
ejpam-6264	512	17	∅.	∅.	ADP
ejpam-6264	512	18	thus	thus	ADV
ejpam-6264	512	19	,	,	PUNCT
ejpam-6264	512	20	v0	v0	NOUN
ejpam-6264	512	21	⊆	⊆	NUM
ejpam-6264	512	22	v	v	NOUN
ejpam-6264	512	23	(	(	PUNCT
ejpam-6264	512	24	h	h	NOUN
ejpam-6264	512	25	)	)	PUNCT
ejpam-6264	512	26	.	.	PUNCT
ejpam-6264	513	1	let	let	VERB
ejpam-6264	513	2	v	v	NUM
ejpam-6264	513	3	∈	∈	PROPN
ejpam-6264	513	4	v0	v0	NOUN
ejpam-6264	513	5	.	.	PUNCT
ejpam-6264	514	1	by	by	ADP
ejpam-6264	514	2	(	(	PUNCT
ejpam-6264	514	3	c2	c2	PROPN
ejpam-6264	514	4	)	)	PUNCT
ejpam-6264	514	5	,	,	PUNCT
ejpam-6264	514	6	there	there	PRON
ejpam-6264	514	7	exists	exist	VERB
ejpam-6264	514	8	u	u	PROPN
ejpam-6264	514	9	∈	∈	PROPN
ejpam-6264	514	10	v3∩v	v3∩v	X
ejpam-6264	514	11	(	(	PUNCT
ejpam-6264	514	12	h	h	NOUN
ejpam-6264	514	13	)	)	PUNCT
ejpam-6264	514	14	such	such	ADJ
ejpam-6264	514	15	that	that	SCONJ
ejpam-6264	514	16	uv	uv	PROPN
ejpam-6264	514	17	∈	∈	PROPN
ejpam-6264	514	18	e(h	e(h	PROPN
ejpam-6264	514	19	)	)	PUNCT
ejpam-6264	514	20	⊆	⊆	NUM
ejpam-6264	514	21	e(g+h	e(g+h	NUM
ejpam-6264	514	22	)	)	PUNCT
ejpam-6264	514	23	.	.	PUNCT
ejpam-6264	515	1	also	also	ADV
ejpam-6264	515	2	,	,	PUNCT
ejpam-6264	515	3	since	since	SCONJ
ejpam-6264	515	4	v2	v2	PROPN
ejpam-6264	515	5	is	be	AUX
ejpam-6264	515	6	a	a	DET
ejpam-6264	515	7	dominating	dominating	NOUN
ejpam-6264	515	8	set	set	NOUN
ejpam-6264	515	9	of	of	ADP
ejpam-6264	515	10	g	g	PROPN
ejpam-6264	515	11	,	,	PUNCT
ejpam-6264	515	12	v2∩v	v2∩v	PROPN
ejpam-6264	515	13	(	(	PUNCT
ejpam-6264	515	14	g	g	NOUN
ejpam-6264	515	15	)	)	PUNCT
ejpam-6264	515	16	̸=	̸=	PROPN
ejpam-6264	515	17	∅.	∅.	AUX
ejpam-6264	515	18	pick	pick	VERB
ejpam-6264	515	19	w	w	PROPN
ejpam-6264	515	20	∈	∈	PROPN
ejpam-6264	515	21	v2∩v	v2∩v	NOUN
ejpam-6264	515	22	(	(	PUNCT
ejpam-6264	515	23	g	g	NOUN
ejpam-6264	515	24	)	)	PUNCT
ejpam-6264	515	25	.	.	PUNCT
ejpam-6264	516	1	then	then	ADV
ejpam-6264	516	2	wv	wv	PROPN
ejpam-6264	516	3	∈	∈	PROPN
ejpam-6264	516	4	e(g+h	e(g+h	NUM
ejpam-6264	516	5	)	)	PUNCT
ejpam-6264	516	6	.	.	PUNCT
ejpam-6264	517	1	moreover	moreover	ADV
ejpam-6264	517	2	,	,	PUNCT
ejpam-6264	517	3	uw	uw	PROPN
ejpam-6264	517	4	∈	∈	PROPN
ejpam-6264	517	5	e(g+h	e(g+h	NUM
ejpam-6264	517	6	)	)	PUNCT
ejpam-6264	517	7	.	.	PUNCT
ejpam-6264	518	1	let	let	VERB
ejpam-6264	518	2	v	v	NUM
ejpam-6264	518	3	∈	∈	PROPN
ejpam-6264	518	4	v1∩v	v1∩v	NOUN
ejpam-6264	518	5	(	(	PUNCT
ejpam-6264	518	6	g	g	NOUN
ejpam-6264	518	7	)	)	PUNCT
ejpam-6264	518	8	.	.	PUNCT
ejpam-6264	519	1	by	by	ADP
ejpam-6264	519	2	(	(	PUNCT
ejpam-6264	519	3	c1	c1	PROPN
ejpam-6264	519	4	)	)	PUNCT
ejpam-6264	519	5	,	,	PUNCT
ejpam-6264	519	6	there	there	PRON
ejpam-6264	519	7	exists	exist	VERB
ejpam-6264	519	8	u	u	PROPN
ejpam-6264	519	9	∈	∈	PROPN
ejpam-6264	519	10	v2∩v	v2∩v	NOUN
ejpam-6264	519	11	(	(	PUNCT
ejpam-6264	519	12	g	g	NOUN
ejpam-6264	519	13	)	)	PUNCT
ejpam-6264	519	14	such	such	ADJ
ejpam-6264	519	15	that	that	SCONJ
ejpam-6264	519	16	uv	uv	PROPN
ejpam-6264	519	17	∈	∈	PROPN
ejpam-6264	519	18	e(g	e(g	PROPN
ejpam-6264	519	19	)	)	PUNCT
ejpam-6264	520	1	⊆	⊆	NUM
ejpam-6264	520	2	e(g+h	e(g+h	NUM
ejpam-6264	520	3	)	)	PUNCT
ejpam-6264	520	4	.	.	PUNCT
ejpam-6264	521	1	now	now	ADV
ejpam-6264	521	2	,	,	PUNCT
ejpam-6264	521	3	let	let	VERB
ejpam-6264	521	4	v	v	NUM
ejpam-6264	521	5	∈	∈	NOUN
ejpam-6264	521	6	v1	v1	NOUN
ejpam-6264	521	7	∩	∩	ADJ
ejpam-6264	521	8	v	v	NOUN
ejpam-6264	521	9	(	(	PUNCT
ejpam-6264	521	10	h	h	NOUN
ejpam-6264	521	11	)	)	PUNCT
ejpam-6264	521	12	.	.	PUNCT
ejpam-6264	522	1	by	by	ADP
ejpam-6264	522	2	(	(	PUNCT
ejpam-6264	522	3	c1	c1	PROPN
ejpam-6264	522	4	)	)	PUNCT
ejpam-6264	522	5	,	,	PUNCT
ejpam-6264	522	6	there	there	PRON
ejpam-6264	522	7	exists	exist	VERB
ejpam-6264	522	8	u	u	PROPN
ejpam-6264	522	9	∈	∈	PROPN
ejpam-6264	522	10	v2	v2	PROPN
ejpam-6264	522	11	∩	∩	ADJ
ejpam-6264	522	12	v	v	NOUN
ejpam-6264	522	13	(	(	PUNCT
ejpam-6264	522	14	g	g	NOUN
ejpam-6264	522	15	)	)	PUNCT
ejpam-6264	522	16	.	.	PUNCT
ejpam-6264	523	1	then	then	ADV
ejpam-6264	523	2	uv	uv	PROPN
ejpam-6264	523	3	∈	∈	PROPN
ejpam-6264	523	4	e(g+h	e(g+h	NUM
ejpam-6264	523	5	)	)	PUNCT
ejpam-6264	523	6	.	.	PUNCT
ejpam-6264	524	1	therefore	therefore	ADV
ejpam-6264	524	2	,	,	PUNCT
ejpam-6264	524	3	f	f	PROPN
ejpam-6264	524	4	∈	∈	PROPN
ejpam-6264	524	5	tmdrf	tmdrf	NOUN
ejpam-6264	524	6	(	(	PUNCT
ejpam-6264	524	7	g	g	PROPN
ejpam-6264	524	8	+	+	NOUN
ejpam-6264	524	9	h	h	NOUN
ejpam-6264	524	10	)	)	PUNCT
ejpam-6264	524	11	.	.	PUNCT
ejpam-6264	525	1	similarly	similarly	ADV
ejpam-6264	525	2	,	,	PUNCT
ejpam-6264	525	3	if	if	SCONJ
ejpam-6264	525	4	(	(	PUNCT
ejpam-6264	525	5	ii	ii	NOUN
ejpam-6264	525	6	)	)	PUNCT
ejpam-6264	525	7	holds	hold	VERB
ejpam-6264	525	8	,	,	PUNCT
ejpam-6264	525	9	then	then	ADV
ejpam-6264	525	10	f	f	PROPN
ejpam-6264	525	11	∈	∈	PROPN
ejpam-6264	525	12	tmrdf	tmrdf	NOUN
ejpam-6264	525	13	(	(	PUNCT
ejpam-6264	525	14	g	g	NOUN
ejpam-6264	525	15	+	+	NOUN
ejpam-6264	525	16	h	h	NOUN
ejpam-6264	525	17	)	)	PUNCT
ejpam-6264	525	18	.	.	PUNCT
ejpam-6264	526	1	suppose	suppose	VERB
ejpam-6264	526	2	(	(	PUNCT
ejpam-6264	526	3	iii	iii	NOUN
ejpam-6264	526	4	)	)	PUNCT
ejpam-6264	526	5	holds	hold	VERB
ejpam-6264	526	6	,	,	PUNCT
ejpam-6264	526	7	that	that	PRON
ejpam-6264	526	8	is	be	AUX
ejpam-6264	526	9	f	f	PROPN
ejpam-6264	526	10	|g	|g	PART
ejpam-6264	526	11	̸∈	̸∈	PROPN
ejpam-6264	526	12	tmrdf	tmrdf	PROPN
ejpam-6264	526	13	(	(	PUNCT
ejpam-6264	526	14	g	g	NOUN
ejpam-6264	526	15	)	)	PUNCT
ejpam-6264	526	16	and	and	CCONJ
ejpam-6264	526	17	f	f	PROPN
ejpam-6264	526	18	|h	|h	X
ejpam-6264	526	19	̸∈	̸∈	PROPN
ejpam-6264	526	20	tmrdf	tmrdf	PROPN
ejpam-6264	526	21	(	(	PUNCT
ejpam-6264	526	22	g	g	NOUN
ejpam-6264	526	23	)	)	PUNCT
ejpam-6264	526	24	.	.	PUNCT
ejpam-6264	527	1	let	let	VERB
ejpam-6264	527	2	v	v	NUM
ejpam-6264	527	3	∈	∈	PROPN
ejpam-6264	527	4	v0	v0	NOUN
ejpam-6264	527	5	∩	∩	X
ejpam-6264	527	6	v	v	X
ejpam-6264	527	7	(	(	PUNCT
ejpam-6264	527	8	g	g	NOUN
ejpam-6264	527	9	)	)	PUNCT
ejpam-6264	527	10	.	.	PUNCT
ejpam-6264	528	1	if	if	SCONJ
ejpam-6264	528	2	ng(v)∩v2	ng(v)∩v2	NOUN
ejpam-6264	528	3	=	=	SYM
ejpam-6264	528	4	∅	∅	NOUN
ejpam-6264	528	5	and	and	CCONJ
ejpam-6264	528	6	ng(v)∩v3	ng(v)∩v3	VERB
ejpam-6264	528	7	̸=	̸=	PROPN
ejpam-6264	528	8	∅.	∅.	ADV
ejpam-6264	528	9	take	take	VERB
ejpam-6264	528	10	u	u	PRON
ejpam-6264	528	11	∈	∈	NOUN
ejpam-6264	528	12	v3∩v	v3∩v	X
ejpam-6264	528	13	(	(	PUNCT
ejpam-6264	528	14	g	g	NOUN
ejpam-6264	528	15	)	)	PUNCT
ejpam-6264	528	16	such	such	ADJ
ejpam-6264	528	17	that	that	SCONJ
ejpam-6264	528	18	uv	uv	PROPN
ejpam-6264	528	19	∈	∈	PROPN
ejpam-6264	528	20	e(g	e(g	PROPN
ejpam-6264	528	21	)	)	PUNCT
ejpam-6264	529	1	⊆	⊆	NUM
ejpam-6264	529	2	e(g+h	e(g+h	NUM
ejpam-6264	529	3	)	)	PUNCT
ejpam-6264	529	4	.	.	PUNCT
ejpam-6264	530	1	since	since	SCONJ
ejpam-6264	530	2	ng(v)∩v2	ng(v)∩v2	NOUN
ejpam-6264	530	3	=	=	SYM
ejpam-6264	530	4	∅	∅	NOUN
ejpam-6264	530	5	,	,	PUNCT
ejpam-6264	530	6	by	by	ADP
ejpam-6264	530	7	assumption	assumption	NOUN
ejpam-6264	530	8	,	,	PUNCT
ejpam-6264	530	9	there	there	PRON
ejpam-6264	530	10	exists	exist	VERB
ejpam-6264	530	11	w	w	PROPN
ejpam-6264	530	12	∈	∈	PROPN
ejpam-6264	530	13	v2∩v	v2∩v	NOUN
ejpam-6264	530	14	(	(	PUNCT
ejpam-6264	530	15	h	h	NOUN
ejpam-6264	530	16	)	)	PUNCT
ejpam-6264	530	17	such	such	ADJ
ejpam-6264	530	18	that	that	SCONJ
ejpam-6264	530	19	vw	vw	PROPN
ejpam-6264	530	20	∈	∈	PROPN
ejpam-6264	530	21	e(g+h	e(g+h	NUM
ejpam-6264	530	22	)	)	PUNCT
ejpam-6264	530	23	.	.	PUNCT
ejpam-6264	531	1	moreover	moreover	ADV
ejpam-6264	531	2	,	,	PUNCT
ejpam-6264	531	3	uw	uw	PROPN
ejpam-6264	531	4	∈	∈	PROPN
ejpam-6264	531	5	e(g+h	e(g+h	NUM
ejpam-6264	531	6	)	)	PUNCT
ejpam-6264	531	7	.	.	PUNCT
ejpam-6264	532	1	if	if	SCONJ
ejpam-6264	532	2	ng(v	ng(v	NOUN
ejpam-6264	532	3	)	)	PUNCT
ejpam-6264	532	4	∩	∩	NOUN
ejpam-6264	532	5	v2	v2	PROPN
ejpam-6264	532	6	̸=	̸=	PROPN
ejpam-6264	532	7	∅	∅	NOUN
ejpam-6264	532	8	and	and	CCONJ
ejpam-6264	532	9	ng(v	ng(v	NUM
ejpam-6264	532	10	)	)	PUNCT
ejpam-6264	532	11	∩	∩	NOUN
ejpam-6264	532	12	v3	v3	NOUN
ejpam-6264	532	13	=	=	PUNCT
ejpam-6264	532	14	∅.	∅.	PART
ejpam-6264	532	15	pick	pick	VERB
ejpam-6264	532	16	u	u	PRON
ejpam-6264	532	17	∈	∈	PROPN
ejpam-6264	532	18	v2	v2	PROPN
ejpam-6264	532	19	∩	∩	ADJ
ejpam-6264	532	20	v	v	NOUN
ejpam-6264	532	21	(	(	PUNCT
ejpam-6264	532	22	g	g	NOUN
ejpam-6264	532	23	)	)	PUNCT
ejpam-6264	532	24	such	such	ADJ
ejpam-6264	532	25	that	that	SCONJ
ejpam-6264	532	26	uv	uv	PROPN
ejpam-6264	532	27	∈	∈	PROPN
ejpam-6264	532	28	e(g	e(g	PROPN
ejpam-6264	532	29	)	)	PUNCT
ejpam-6264	532	30	⊆	⊆	NUM
ejpam-6264	532	31	e(g	e(g	NOUN
ejpam-6264	532	32	+	+	CCONJ
ejpam-6264	532	33	h	h	NOUN
ejpam-6264	532	34	)	)	PUNCT
ejpam-6264	532	35	.	.	PUNCT
ejpam-6264	533	1	since	since	SCONJ
ejpam-6264	533	2	ng(v	ng(v	NOUN
ejpam-6264	533	3	)	)	PUNCT
ejpam-6264	533	4	∩	∩	ADJ
ejpam-6264	533	5	v3	v3	NOUN
ejpam-6264	533	6	=	=	SYM
ejpam-6264	533	7	∅	∅	NOUN
ejpam-6264	533	8	,	,	PUNCT
ejpam-6264	533	9	by	by	ADP
ejpam-6264	533	10	assumption	assumption	NOUN
ejpam-6264	533	11	,	,	PUNCT
ejpam-6264	533	12	there	there	PRON
ejpam-6264	533	13	exists	exist	VERB
ejpam-6264	533	14	w	w	PROPN
ejpam-6264	533	15	∈	∈	PROPN
ejpam-6264	533	16	v3	v3	PROPN
ejpam-6264	533	17	∩	∩	PROPN
ejpam-6264	533	18	v	v	X
ejpam-6264	533	19	(	(	PUNCT
ejpam-6264	533	20	h	h	NOUN
ejpam-6264	533	21	)	)	PUNCT
ejpam-6264	533	22	such	such	ADJ
ejpam-6264	533	23	that	that	SCONJ
ejpam-6264	533	24	vw	vw	PROPN
ejpam-6264	533	25	∈	∈	PROPN
ejpam-6264	533	26	e(g+h	e(g+h	NUM
ejpam-6264	533	27	)	)	PUNCT
ejpam-6264	533	28	.	.	PUNCT
ejpam-6264	534	1	moreover	moreover	ADV
ejpam-6264	534	2	,	,	PUNCT
ejpam-6264	534	3	uw	uw	PROPN
ejpam-6264	534	4	∈	∈	PROPN
ejpam-6264	534	5	e(g+h	e(g+h	NUM
ejpam-6264	534	6	)	)	PUNCT
ejpam-6264	534	7	.	.	PUNCT
ejpam-6264	535	1	if	if	SCONJ
ejpam-6264	535	2	ng(v)∩	ng(v)∩	PRON
ejpam-6264	535	3	v2	v2	VERB
ejpam-6264	535	4	=	=	SYM
ejpam-6264	535	5	∅	∅	NOUN
ejpam-6264	535	6	and	and	CCONJ
ejpam-6264	535	7	ng(v	ng(v	NUM
ejpam-6264	535	8	)	)	PUNCT
ejpam-6264	535	9	∩	∩	NOUN
ejpam-6264	535	10	v3	v3	NOUN
ejpam-6264	535	11	=	=	PUNCT
ejpam-6264	535	12	∅.	∅.	NOUN
ejpam-6264	535	13	then	then	ADV
ejpam-6264	535	14	by	by	ADP
ejpam-6264	535	15	assumption	assumption	NOUN
ejpam-6264	535	16	,	,	PUNCT
ejpam-6264	535	17	v2	v2	PROPN
ejpam-6264	535	18	∩	∩	ADJ
ejpam-6264	535	19	v	v	NOUN
ejpam-6264	535	20	(	(	PUNCT
ejpam-6264	535	21	h	h	NOUN
ejpam-6264	535	22	)	)	PUNCT
ejpam-6264	535	23	̸=	̸=	PROPN
ejpam-6264	535	24	∅	∅	NOUN
ejpam-6264	535	25	and	and	CCONJ
ejpam-6264	535	26	v3	v3	PROPN
ejpam-6264	535	27	∩	∩	PROPN
ejpam-6264	535	28	v	v	X
ejpam-6264	535	29	(	(	PUNCT
ejpam-6264	535	30	h	h	NOUN
ejpam-6264	535	31	)	)	PUNCT
ejpam-6264	535	32	̸=	̸=	PROPN
ejpam-6264	535	33	∅	∅	NOUN
ejpam-6264	535	34	and	and	CCONJ
ejpam-6264	535	35	so	so	ADV
ejpam-6264	535	36	,	,	PUNCT
ejpam-6264	535	37	there	there	PRON
ejpam-6264	535	38	exist	exist	VERB
ejpam-6264	535	39	u	u	PROPN
ejpam-6264	535	40	∈	∈	PROPN
ejpam-6264	535	41	v2	v2	PROPN
ejpam-6264	535	42	∩	∩	ADJ
ejpam-6264	535	43	v	v	NOUN
ejpam-6264	535	44	(	(	PUNCT
ejpam-6264	535	45	h	h	NOUN
ejpam-6264	535	46	)	)	PUNCT
ejpam-6264	535	47	and	and	CCONJ
ejpam-6264	535	48	w	w	PROPN
ejpam-6264	535	49	∈	∈	PROPN
ejpam-6264	535	50	v3	v3	PROPN
ejpam-6264	535	51	∩	∩	PROPN
ejpam-6264	535	52	v	v	X
ejpam-6264	535	53	(	(	PUNCT
ejpam-6264	535	54	h	h	NOUN
ejpam-6264	535	55	)	)	PUNCT
ejpam-6264	535	56	such	such	ADJ
ejpam-6264	535	57	that	that	SCONJ
ejpam-6264	535	58	vu	vu	PROPN
ejpam-6264	535	59	,	,	PUNCT
ejpam-6264	535	60	vw	vw	PROPN
ejpam-6264	535	61	∈	∈	PROPN
ejpam-6264	535	62	e(g	e(g	PROPN
ejpam-6264	535	63	+	+	CCONJ
ejpam-6264	535	64	h	h	NOUN
ejpam-6264	535	65	)	)	PUNCT
ejpam-6264	535	66	.	.	PUNCT
ejpam-6264	536	1	also	also	ADV
ejpam-6264	536	2	,	,	PUNCT
ejpam-6264	536	3	by	by	ADP
ejpam-6264	536	4	assumption	assumption	NOUN
ejpam-6264	536	5	,	,	PUNCT
ejpam-6264	536	6	there	there	PRON
ejpam-6264	536	7	exists	exist	VERB
ejpam-6264	536	8	x	x	X
ejpam-6264	536	9	∈	∈	PROPN
ejpam-6264	536	10	v	v	X
ejpam-6264	536	11	(	(	PUNCT
ejpam-6264	536	12	g	g	NOUN
ejpam-6264	536	13	)	)	PUNCT
ejpam-6264	536	14	\	\	NOUN
ejpam-6264	536	15	v0	v0	NOUN
ejpam-6264	536	16	such	such	ADJ
ejpam-6264	536	17	that	that	SCONJ
ejpam-6264	536	18	ux	ux	PROPN
ejpam-6264	536	19	,	,	PUNCT
ejpam-6264	536	20	wx	wx	PROPN
ejpam-6264	536	21	∈	∈	PROPN
ejpam-6264	536	22	e(g	e(g	PROPN
ejpam-6264	536	23	+	+	CCONJ
ejpam-6264	536	24	h	h	NOUN
ejpam-6264	536	25	)	)	PUNCT
ejpam-6264	536	26	.	.	PUNCT
ejpam-6264	537	1	now	now	ADV
ejpam-6264	537	2	,	,	PUNCT
ejpam-6264	537	3	suppose	suppose	VERB
ejpam-6264	537	4	f(v	f(v	NOUN
ejpam-6264	537	5	)	)	PUNCT
ejpam-6264	537	6	=	=	SYM
ejpam-6264	538	1	1	1	X
ejpam-6264	538	2	.	.	X
ejpam-6264	539	1	if	if	SCONJ
ejpam-6264	539	2	ng(v	ng(v	NOUN
ejpam-6264	539	3	)	)	PUNCT
ejpam-6264	539	4	∩	∩	ADJ
ejpam-6264	539	5	v2	v2	NOUN
ejpam-6264	539	6	=	=	SYM
ejpam-6264	539	7	∅	∅	NOUN
ejpam-6264	539	8	and	and	CCONJ
ejpam-6264	539	9	ng(v	ng(v	NUM
ejpam-6264	539	10	)	)	PUNCT
ejpam-6264	539	11	∩	∩	NOUN
ejpam-6264	539	12	v3	v3	NOUN
ejpam-6264	539	13	=	=	PUNCT
ejpam-6264	539	14	∅.	∅.	NOUN
ejpam-6264	539	15	then	then	ADV
ejpam-6264	539	16	by	by	ADP
ejpam-6264	539	17	assumption	assumption	NOUN
ejpam-6264	539	18	,	,	PUNCT
ejpam-6264	539	19	there	there	PRON
ejpam-6264	539	20	exist	exist	VERB
ejpam-6264	539	21	z	z	NOUN
ejpam-6264	539	22	∈	∈	PROPN
ejpam-6264	539	23	v2	v2	PROPN
ejpam-6264	539	24	∩	∩	ADJ
ejpam-6264	539	25	v	v	NOUN
ejpam-6264	539	26	(	(	PUNCT
ejpam-6264	539	27	h	h	NOUN
ejpam-6264	539	28	)	)	PUNCT
ejpam-6264	539	29	or	or	CCONJ
ejpam-6264	539	30	z	z	NOUN
ejpam-6264	539	31	∈	∈	PROPN
ejpam-6264	539	32	v3	v3	PROPN
ejpam-6264	539	33	∩	∩	PROPN
ejpam-6264	539	34	v	v	X
ejpam-6264	539	35	(	(	PUNCT
ejpam-6264	539	36	h	h	NOUN
ejpam-6264	539	37	)	)	PUNCT
ejpam-6264	539	38	such	such	ADJ
ejpam-6264	539	39	that	that	SCONJ
ejpam-6264	539	40	vz	vz	PROPN
ejpam-6264	539	41	∈	∈	PROPN
ejpam-6264	539	42	e(g	e(g	PROPN
ejpam-6264	540	1	+	+	CCONJ
ejpam-6264	540	2	h	h	NOUN
ejpam-6264	540	3	)	)	PUNCT
ejpam-6264	540	4	satisfying	satisfying	NOUN
ejpam-6264	540	5	(	(	PUNCT
ejpam-6264	540	6	p2	p2	PROPN
ejpam-6264	540	7	)	)	PUNCT
ejpam-6264	540	8	.	.	PUNCT
ejpam-6264	541	1	therefore	therefore	ADV
ejpam-6264	541	2	,	,	PUNCT
ejpam-6264	541	3	f	f	PROPN
ejpam-6264	541	4	∈	∈	PROPN
ejpam-6264	541	5	tmrdf	tmrdf	NOUN
ejpam-6264	541	6	(	(	PUNCT
ejpam-6264	541	7	g	g	NOUN
ejpam-6264	541	8	+	+	NOUN
ejpam-6264	541	9	h	h	NOUN
ejpam-6264	541	10	)	)	PUNCT
ejpam-6264	541	11	.	.	PUNCT
ejpam-6264	542	1	similarly	similarly	ADV
ejpam-6264	542	2	,	,	PUNCT
ejpam-6264	542	3	for	for	ADP
ejpam-6264	542	4	v	v	ADP
ejpam-6264	542	5	∈	∈	PROPN
ejpam-6264	542	6	v	v	NOUN
ejpam-6264	542	7	(	(	PUNCT
ejpam-6264	542	8	h	h	NOUN
ejpam-6264	542	9	)	)	PUNCT
ejpam-6264	542	10	such	such	ADJ
ejpam-6264	542	11	that	that	SCONJ
ejpam-6264	542	12	f(v	f(v	NOUN
ejpam-6264	542	13	)	)	PUNCT
ejpam-6264	542	14	∈	∈	PROPN
ejpam-6264	542	15	{	{	PUNCT
ejpam-6264	542	16	0	0	NUM
ejpam-6264	542	17	,	,	PUNCT
ejpam-6264	542	18	1	1	NUM
ejpam-6264	542	19	}	}	PUNCT
ejpam-6264	542	20	,	,	PUNCT
ejpam-6264	542	21	f	f	PROPN
ejpam-6264	542	22	∈	∈	PROPN
ejpam-6264	542	23	tmrdf	tmrdf	NOUN
ejpam-6264	542	24	(	(	PUNCT
ejpam-6264	542	25	g	g	NOUN
ejpam-6264	542	26	+	+	NOUN
ejpam-6264	542	27	h	h	NOUN
ejpam-6264	542	28	)	)	PUNCT
ejpam-6264	542	29	.	.	PUNCT
ejpam-6264	543	1	now	now	ADV
ejpam-6264	543	2	,	,	PUNCT
ejpam-6264	543	3	let	let	VERB
ejpam-6264	543	4	v	v	NUM
ejpam-6264	543	5	∈	∈	NOUN
ejpam-6264	543	6	v1	v1	NOUN
ejpam-6264	543	7	∪	∪	NOUN
ejpam-6264	543	8	v2	v2	PROPN
ejpam-6264	543	9	∪	∪	X
ejpam-6264	543	10	v3	v3	PROPN
ejpam-6264	543	11	.	.	PUNCT
ejpam-6264	544	1	if	if	SCONJ
ejpam-6264	544	2	v	v	NUM
ejpam-6264	544	3	∈	∈	PROPN
ejpam-6264	544	4	v	v	NOUN
ejpam-6264	544	5	(	(	PUNCT
ejpam-6264	544	6	g	g	NOUN
ejpam-6264	544	7	)	)	PUNCT
ejpam-6264	544	8	with	with	ADP
ejpam-6264	544	9	ng(v	ng(v	NOUN
ejpam-6264	544	10	)	)	PUNCT
ejpam-6264	544	11	⊆	⊆	NUM
ejpam-6264	544	12	v0	v0	NOUN
ejpam-6264	544	13	,	,	PUNCT
ejpam-6264	544	14	then	then	ADV
ejpam-6264	544	15	by	by	ADP
ejpam-6264	544	16	(	(	PUNCT
ejpam-6264	544	17	iii)(g	iii)(g	NOUN
ejpam-6264	544	18	)	)	PUNCT
ejpam-6264	544	19	,	,	PUNCT
ejpam-6264	544	20	(	(	PUNCT
ejpam-6264	544	21	v1	v1	VERB
ejpam-6264	544	22	∪	∪	ADP
ejpam-6264	544	23	v2	v2	PROPN
ejpam-6264	544	24	∪	∪	X
ejpam-6264	544	25	v3	v3	PROPN
ejpam-6264	544	26	)	)	PUNCT
ejpam-6264	544	27	∩	∩	PROPN
ejpam-6264	544	28	v	v	ADP
ejpam-6264	544	29	(	(	PUNCT
ejpam-6264	544	30	h	h	NOUN
ejpam-6264	544	31	)	)	PUNCT
ejpam-6264	544	32	̸=	̸=	PROPN
ejpam-6264	544	33	∅.	∅.	ADP
ejpam-6264	544	34	this	this	PRON
ejpam-6264	544	35	means	mean	VERB
ejpam-6264	544	36	that	that	SCONJ
ejpam-6264	544	37	ng+h(v	ng+h(v	NOUN
ejpam-6264	544	38	)	)	PUNCT
ejpam-6264	544	39	∩	∩	NOUN
ejpam-6264	544	40	(	(	PUNCT
ejpam-6264	544	41	v1	v1	VERB
ejpam-6264	544	42	∪	∪	ADP
ejpam-6264	544	43	v2	v2	PROPN
ejpam-6264	544	44	∪	∪	X
ejpam-6264	544	45	v3	v3	NOUN
ejpam-6264	544	46	)	)	PUNCT
ejpam-6264	544	47	̸=	̸=	PROPN
ejpam-6264	544	48	∅.	∅.	PRON
ejpam-6264	544	49	similarly	similarly	ADV
ejpam-6264	544	50	,	,	PUNCT
ejpam-6264	544	51	ng+h(v	ng+h(v	NOUN
ejpam-6264	544	52	)	)	PUNCT
ejpam-6264	544	53	∩	∩	NOUN
ejpam-6264	544	54	(	(	PUNCT
ejpam-6264	544	55	v1	v1	VERB
ejpam-6264	544	56	∪	∪	ADP
ejpam-6264	544	57	v2	v2	PROPN
ejpam-6264	544	58	∪	∪	X
ejpam-6264	544	59	v3	v3	PROPN
ejpam-6264	544	60	)	)	PUNCT
ejpam-6264	544	61	̸=	̸=	PROPN
ejpam-6264	544	62	∅	∅	NOUN
ejpam-6264	544	63	,	,	PUNCT
ejpam-6264	544	64	for	for	ADP
ejpam-6264	544	65	each	each	DET
ejpam-6264	544	66	v	v	NUM
ejpam-6264	544	67	∈	∈	PROPN
ejpam-6264	544	68	v	v	NOUN
ejpam-6264	544	69	(	(	PUNCT
ejpam-6264	544	70	h	h	NOUN
ejpam-6264	544	71	)	)	PUNCT
ejpam-6264	544	72	with	with	ADP
ejpam-6264	544	73	nh(v	nh(v	NOUN
ejpam-6264	544	74	)	)	PUNCT
ejpam-6264	544	75	⊆	⊆	NUM
ejpam-6264	544	76	v0	v0	NOUN
ejpam-6264	544	77	.	.	PUNCT
ejpam-6264	545	1	thus	thus	ADV
ejpam-6264	545	2	,	,	PUNCT
ejpam-6264	545	3	s.	s.	PROPN
ejpam-6264	545	4	ahamad	ahamad	VERB
ejpam-6264	545	5	et	et	PROPN
ejpam-6264	545	6	al	al	PROPN
ejpam-6264	545	7	.	.	PUNCT
ejpam-6264	545	8	/	/	SYM
ejpam-6264	545	9	eur	eur	PROPN
ejpam-6264	545	10	.	.	PUNCT
ejpam-6264	546	1	j.	j.	PROPN
ejpam-6264	546	2	pure	pure	PROPN
ejpam-6264	546	3	appl	appl	PROPN
ejpam-6264	546	4	.	.	PROPN
ejpam-6264	546	5	math	math	PROPN
ejpam-6264	546	6	,	,	PUNCT
ejpam-6264	546	7	18	18	NUM
ejpam-6264	546	8	(	(	PUNCT
ejpam-6264	546	9	4	4	NUM
ejpam-6264	546	10	)	)	PUNCT
ejpam-6264	546	11	(	(	PUNCT
ejpam-6264	546	12	2025	2025	NUM
ejpam-6264	546	13	)	)	PUNCT
ejpam-6264	546	14	,	,	PUNCT
ejpam-6264	546	15	6264	6264	NUM
ejpam-6264	546	16	15	15	NUM
ejpam-6264	546	17	of	of	ADP
ejpam-6264	546	18	20	20	NUM
ejpam-6264	546	19	⟨v1	⟨v1	PROPN
ejpam-6264	546	20	∪	∪	ADP
ejpam-6264	546	21	v2	v2	PROPN
ejpam-6264	546	22	∪	∪	NOUN
ejpam-6264	546	23	v3⟩	v3⟩	PRON
ejpam-6264	546	24	has	have	VERB
ejpam-6264	546	25	no	no	DET
ejpam-6264	546	26	isolated	isolated	ADJ
ejpam-6264	546	27	vertex	vertex	NOUN
ejpam-6264	546	28	.	.	PUNCT
ejpam-6264	547	1	therefore	therefore	ADV
ejpam-6264	547	2	,	,	PUNCT
ejpam-6264	547	3	f	f	PROPN
ejpam-6264	547	4	∈	∈	PROPN
ejpam-6264	547	5	tmrdf	tmrdf	NOUN
ejpam-6264	547	6	(	(	PUNCT
ejpam-6264	547	7	g+h	g+h	PROPN
ejpam-6264	547	8	)	)	PUNCT
ejpam-6264	547	9	.	.	PUNCT
ejpam-6264	548	1	conversely	conversely	ADV
ejpam-6264	548	2	,	,	PUNCT
ejpam-6264	548	3	suppose	suppose	VERB
ejpam-6264	548	4	f	f	PROPN
ejpam-6264	548	5	∈	∈	PROPN
ejpam-6264	548	6	tmrdf	tmrdf	NOUN
ejpam-6264	548	7	(	(	PUNCT
ejpam-6264	548	8	g+h	g+h	PROPN
ejpam-6264	548	9	)	)	PUNCT
ejpam-6264	548	10	.	.	PUNCT
ejpam-6264	549	1	consider	consider	VERB
ejpam-6264	549	2	the	the	DET
ejpam-6264	549	3	following	follow	VERB
ejpam-6264	549	4	cases	case	NOUN
ejpam-6264	549	5	:	:	PUNCT
ejpam-6264	549	6	case	case	NOUN
ejpam-6264	549	7	1	1	NUM
ejpam-6264	549	8	:	:	PUNCT
ejpam-6264	549	9	suppose	suppose	VERB
ejpam-6264	549	10	f	f	PROPN
ejpam-6264	549	11	|g	|g	PROPN
ejpam-6264	549	12	∈	∈	PROPN
ejpam-6264	549	13	tmrdf	tmrdf	NOUN
ejpam-6264	549	14	(	(	PUNCT
ejpam-6264	549	15	g	g	NOUN
ejpam-6264	549	16	)	)	PUNCT
ejpam-6264	549	17	.	.	PUNCT
ejpam-6264	550	1	if	if	SCONJ
ejpam-6264	550	2	(	(	PUNCT
ejpam-6264	550	3	i)(a	i)(a	NOUN
ejpam-6264	550	4	)	)	PUNCT
ejpam-6264	550	5	holds	hold	VERB
ejpam-6264	550	6	,	,	PUNCT
ejpam-6264	550	7	we	we	PRON
ejpam-6264	550	8	are	be	AUX
ejpam-6264	550	9	done	do	VERB
ejpam-6264	550	10	.	.	PUNCT
ejpam-6264	551	1	suppose	suppose	VERB
ejpam-6264	551	2	(	(	PUNCT
ejpam-6264	551	3	i)(a	i)(a	NOUN
ejpam-6264	551	4	)	)	PUNCT
ejpam-6264	551	5	does	do	AUX
ejpam-6264	551	6	not	not	PART
ejpam-6264	551	7	hold	hold	VERB
ejpam-6264	551	8	.	.	PUNCT
ejpam-6264	552	1	thus	thus	ADV
ejpam-6264	552	2	,	,	PUNCT
ejpam-6264	552	3	either	either	CCONJ
ejpam-6264	552	4	v2	v2	PROPN
ejpam-6264	552	5	∩	∩	ADJ
ejpam-6264	552	6	v	v	NOUN
ejpam-6264	552	7	(	(	PUNCT
ejpam-6264	552	8	g	g	NOUN
ejpam-6264	552	9	)	)	PUNCT
ejpam-6264	552	10	=	=	NOUN
ejpam-6264	552	11	∅	∅	NOUN
ejpam-6264	552	12	or	or	CCONJ
ejpam-6264	552	13	v3	v3	PROPN
ejpam-6264	552	14	∩	∩	ADJ
ejpam-6264	552	15	v	v	X
ejpam-6264	552	16	(	(	PUNCT
ejpam-6264	552	17	g	g	NOUN
ejpam-6264	552	18	)	)	PUNCT
ejpam-6264	552	19	=	=	VERB
ejpam-6264	552	20	∅.	∅.	AUX
ejpam-6264	552	21	suppose	suppose	VERB
ejpam-6264	552	22	v2	v2	PROPN
ejpam-6264	552	23	∩	∩	NOUN
ejpam-6264	552	24	v	v	NOUN
ejpam-6264	552	25	(	(	PUNCT
ejpam-6264	552	26	g	g	NOUN
ejpam-6264	552	27	)	)	PUNCT
ejpam-6264	552	28	=	=	PUNCT
ejpam-6264	552	29	∅.	∅.	ADP
ejpam-6264	552	30	necessarily	necessarily	ADV
ejpam-6264	552	31	,	,	PUNCT
ejpam-6264	552	32	v0	v0	PROPN
ejpam-6264	552	33	∩	∩	ADJ
ejpam-6264	552	34	v	v	X
ejpam-6264	552	35	(	(	PUNCT
ejpam-6264	552	36	g	g	NOUN
ejpam-6264	552	37	)	)	PUNCT
ejpam-6264	552	38	=	=	VERB
ejpam-6264	552	39	∅.	∅.	AUX
ejpam-6264	552	40	let	let	VERB
ejpam-6264	552	41	v	v	NUM
ejpam-6264	552	42	∈	∈	PROPN
ejpam-6264	552	43	v1	v1	NOUN
ejpam-6264	552	44	∩	∩	ADJ
ejpam-6264	552	45	v	v	NOUN
ejpam-6264	552	46	(	(	PUNCT
ejpam-6264	552	47	g	g	NOUN
ejpam-6264	552	48	)	)	PUNCT
ejpam-6264	552	49	.	.	PUNCT
ejpam-6264	553	1	since	since	SCONJ
ejpam-6264	553	2	f	f	PROPN
ejpam-6264	553	3	|g	|g	PROPN
ejpam-6264	553	4	∈	∈	PROPN
ejpam-6264	553	5	tmrdf	tmrdf	NOUN
ejpam-6264	553	6	(	(	PUNCT
ejpam-6264	553	7	g	g	NOUN
ejpam-6264	553	8	)	)	PUNCT
ejpam-6264	553	9	,	,	PUNCT
ejpam-6264	553	10	there	there	PRON
ejpam-6264	553	11	exists	exist	VERB
ejpam-6264	553	12	u	u	PROPN
ejpam-6264	553	13	∈	∈	PROPN
ejpam-6264	553	14	v3	v3	PROPN
ejpam-6264	553	15	such	such	ADJ
ejpam-6264	553	16	that	that	SCONJ
ejpam-6264	553	17	uv	uv	PROPN
ejpam-6264	553	18	∈	∈	PROPN
ejpam-6264	553	19	e(g	e(g	PROPN
ejpam-6264	553	20	)	)	PUNCT
ejpam-6264	553	21	.	.	PUNCT
ejpam-6264	554	1	thus	thus	ADV
ejpam-6264	554	2	,	,	PUNCT
ejpam-6264	554	3	v3	v3	PROPN
ejpam-6264	554	4	is	be	AUX
ejpam-6264	554	5	a	a	DET
ejpam-6264	554	6	dominating	dominating	NOUN
ejpam-6264	554	7	set	set	NOUN
ejpam-6264	554	8	of	of	ADP
ejpam-6264	554	9	g	g	NOUN
ejpam-6264	554	10	,	,	PUNCT
ejpam-6264	554	11	and	and	CCONJ
ejpam-6264	554	12	so	so	ADV
ejpam-6264	554	13	,	,	PUNCT
ejpam-6264	554	14	(	(	PUNCT
ejpam-6264	554	15	b1	b1	NOUN
ejpam-6264	554	16	)	)	PUNCT
ejpam-6264	554	17	holds	hold	VERB
ejpam-6264	554	18	.	.	PUNCT
ejpam-6264	555	1	also	also	ADV
ejpam-6264	555	2	,	,	PUNCT
ejpam-6264	555	3	since	since	SCONJ
ejpam-6264	555	4	v2	v2	PROPN
ejpam-6264	555	5	∩	∩	NOUN
ejpam-6264	555	6	v	v	NOUN
ejpam-6264	555	7	(	(	PUNCT
ejpam-6264	555	8	g	g	NOUN
ejpam-6264	555	9	)	)	PUNCT
ejpam-6264	555	10	=	=	NOUN
ejpam-6264	555	11	∅	∅	NOUN
ejpam-6264	555	12	,	,	PUNCT
ejpam-6264	555	13	then	then	ADV
ejpam-6264	555	14	v2	v2	VERB
ejpam-6264	555	15	⊆	⊆	NUM
ejpam-6264	555	16	v	v	NOUN
ejpam-6264	555	17	(	(	PUNCT
ejpam-6264	555	18	h	h	NOUN
ejpam-6264	555	19	)	)	PUNCT
ejpam-6264	555	20	.	.	PUNCT
ejpam-6264	556	1	hence	hence	ADV
ejpam-6264	556	2	,	,	PUNCT
ejpam-6264	556	3	v2	v2	PROPN
ejpam-6264	556	4	∩	∩	ADJ
ejpam-6264	556	5	v	v	NOUN
ejpam-6264	556	6	(	(	PUNCT
ejpam-6264	556	7	h	h	NOUN
ejpam-6264	556	8	)	)	PUNCT
ejpam-6264	556	9	̸=	̸=	PROPN
ejpam-6264	556	10	∅.	∅.	AUX
ejpam-6264	556	11	pick	pick	VERB
ejpam-6264	556	12	w	w	PROPN
ejpam-6264	556	13	∈	∈	PROPN
ejpam-6264	556	14	v2	v2	NOUN
ejpam-6264	556	15	and	and	CCONJ
ejpam-6264	556	16	let	let	VERB
ejpam-6264	556	17	v	v	NUM
ejpam-6264	556	18	∈	∈	PROPN
ejpam-6264	556	19	v0	v0	NOUN
ejpam-6264	556	20	∩	∩	X
ejpam-6264	556	21	v	v	X
ejpam-6264	556	22	(	(	PUNCT
ejpam-6264	556	23	h	h	NOUN
ejpam-6264	556	24	)	)	PUNCT
ejpam-6264	556	25	.	.	PUNCT
ejpam-6264	557	1	since	since	SCONJ
ejpam-6264	557	2	f	f	PROPN
ejpam-6264	557	3	∈	∈	PROPN
ejpam-6264	557	4	tmrdf	tmrdf	NOUN
ejpam-6264	557	5	(	(	PUNCT
ejpam-6264	557	6	g+h	g+h	PROPN
ejpam-6264	557	7	)	)	PUNCT
ejpam-6264	557	8	,	,	PUNCT
ejpam-6264	557	9	vw	vw	PROPN
ejpam-6264	557	10	∈	∈	PROPN
ejpam-6264	557	11	e(h	e(h	PROPN
ejpam-6264	557	12	)	)	PUNCT
ejpam-6264	557	13	⊆	⊆	NUM
ejpam-6264	557	14	e(g+h	e(g+h	NUM
ejpam-6264	557	15	)	)	PUNCT
ejpam-6264	557	16	.	.	PUNCT
ejpam-6264	558	1	thus	thus	ADV
ejpam-6264	558	2	,	,	PUNCT
ejpam-6264	558	3	(	(	PUNCT
ejpam-6264	558	4	b2	b2	NOUN
ejpam-6264	558	5	)	)	PUNCT
ejpam-6264	558	6	holds	hold	VERB
ejpam-6264	558	7	.	.	PUNCT
ejpam-6264	559	1	also	also	ADV
ejpam-6264	559	2	,	,	PUNCT
ejpam-6264	559	3	since	since	SCONJ
ejpam-6264	559	4	v3	v3	PROPN
ejpam-6264	559	5	is	be	AUX
ejpam-6264	559	6	a	a	DET
ejpam-6264	559	7	dominating	dominating	NOUN
ejpam-6264	559	8	set	set	NOUN
ejpam-6264	559	9	of	of	ADP
ejpam-6264	559	10	g	g	NOUN
ejpam-6264	559	11	,	,	PUNCT
ejpam-6264	559	12	there	there	PRON
ejpam-6264	559	13	exists	exist	VERB
ejpam-6264	559	14	u	u	PROPN
ejpam-6264	559	15	∈	∈	PROPN
ejpam-6264	559	16	v3	v3	PROPN
ejpam-6264	559	17	∩	∩	PROPN
ejpam-6264	559	18	v	v	X
ejpam-6264	559	19	(	(	PUNCT
ejpam-6264	559	20	g	g	NOUN
ejpam-6264	559	21	)	)	PUNCT
ejpam-6264	559	22	where	where	SCONJ
ejpam-6264	559	23	uv	uv	NOUN
ejpam-6264	559	24	∈	∈	PROPN
ejpam-6264	559	25	e(g+h	e(g+h	NUM
ejpam-6264	559	26	)	)	PUNCT
ejpam-6264	559	27	.	.	PUNCT
ejpam-6264	560	1	suppose	suppose	VERB
ejpam-6264	560	2	v3	v3	PROPN
ejpam-6264	560	3	∩	∩	PROPN
ejpam-6264	560	4	v	v	X
ejpam-6264	560	5	(	(	PUNCT
ejpam-6264	560	6	g	g	NOUN
ejpam-6264	560	7	)	)	PUNCT
ejpam-6264	560	8	=	=	NOUN
ejpam-6264	560	9	∅	∅	NOUN
ejpam-6264	560	10	,	,	PUNCT
ejpam-6264	560	11	then	then	ADV
ejpam-6264	560	12	similarly	similarly	ADV
ejpam-6264	560	13	,	,	PUNCT
ejpam-6264	560	14	(	(	PUNCT
ejpam-6264	560	15	i)(c1	i)(c1	NOUN
ejpam-6264	560	16	)	)	PUNCT
ejpam-6264	560	17	and	and	CCONJ
ejpam-6264	560	18	(	(	PUNCT
ejpam-6264	560	19	i)(c2	i)(c2	NOUN
ejpam-6264	560	20	)	)	PUNCT
ejpam-6264	560	21	hold	hold	NOUN
ejpam-6264	560	22	.	.	PUNCT
ejpam-6264	561	1	furthermore	furthermore	ADV
ejpam-6264	561	2	,	,	PUNCT
ejpam-6264	561	3	the	the	DET
ejpam-6264	561	4	case	case	NOUN
ejpam-6264	561	5	where	where	SCONJ
ejpam-6264	561	6	f	f	PROPN
ejpam-6264	561	7	|h	|h	X
ejpam-6264	561	8	∈	∈	PROPN
ejpam-6264	561	9	tmrdf	tmrdf	NOUN
ejpam-6264	561	10	(	(	PUNCT
ejpam-6264	561	11	h	h	NOUN
ejpam-6264	561	12	)	)	PUNCT
ejpam-6264	561	13	is	be	AUX
ejpam-6264	561	14	similar	similar	ADJ
ejpam-6264	561	15	.	.	PUNCT
ejpam-6264	562	1	case	case	NOUN
ejpam-6264	562	2	2	2	NUM
ejpam-6264	562	3	:	:	PUNCT
ejpam-6264	562	4	suppose	suppose	VERB
ejpam-6264	562	5	f	f	PROPN
ejpam-6264	562	6	|h	|h	PROPN
ejpam-6264	562	7	∈	∈	PROPN
ejpam-6264	562	8	tmrdf	tmrdf	NOUN
ejpam-6264	562	9	(	(	PUNCT
ejpam-6264	562	10	h	h	NOUN
ejpam-6264	562	11	)	)	PUNCT
ejpam-6264	562	12	.	.	PUNCT
ejpam-6264	563	1	this	this	PRON
ejpam-6264	563	2	can	can	AUX
ejpam-6264	563	3	be	be	AUX
ejpam-6264	563	4	proven	prove	VERB
ejpam-6264	563	5	similarly	similarly	ADV
ejpam-6264	563	6	with	with	ADP
ejpam-6264	563	7	case	case	NOUN
ejpam-6264	563	8	1	1	NUM
ejpam-6264	563	9	.	.	PUNCT
ejpam-6264	563	10	case	case	NOUN
ejpam-6264	563	11	3	3	X
ejpam-6264	563	12	:	:	PUNCT
ejpam-6264	563	13	assume	assume	VERB
ejpam-6264	563	14	f	f	PROPN
ejpam-6264	563	15	|g	|g	PROPN
ejpam-6264	563	16	/∈	/∈	PUNCT
ejpam-6264	564	1	tmrdf	tmrdf	NOUN
ejpam-6264	564	2	(	(	PUNCT
ejpam-6264	564	3	g	g	NOUN
ejpam-6264	564	4	)	)	PUNCT
ejpam-6264	564	5	and	and	CCONJ
ejpam-6264	564	6	f	f	PROPN
ejpam-6264	564	7	|h	|h	PROPN
ejpam-6264	564	8	/∈	/∈	PUNCT
ejpam-6264	565	1	tmrdf	tmrdf	PROPN
ejpam-6264	565	2	(	(	PUNCT
ejpam-6264	565	3	h	h	NOUN
ejpam-6264	565	4	)	)	PUNCT
ejpam-6264	565	5	.	.	PUNCT
ejpam-6264	566	1	suppose	suppose	VERB
ejpam-6264	566	2	ng(x	ng(x	NOUN
ejpam-6264	566	3	)	)	PUNCT
ejpam-6264	566	4	∩	∩	NOUN
ejpam-6264	566	5	v2	v2	NOUN
ejpam-6264	566	6	=	=	PUNCT
ejpam-6264	566	7	∅	∅	NOUN
ejpam-6264	566	8	for	for	ADP
ejpam-6264	566	9	some	some	DET
ejpam-6264	566	10	x	x	SYM
ejpam-6264	566	11	∈	∈	PROPN
ejpam-6264	566	12	v0	v0	NOUN
ejpam-6264	566	13	.	.	PUNCT
ejpam-6264	567	1	since	since	SCONJ
ejpam-6264	567	2	f	f	PROPN
ejpam-6264	567	3	∈	∈	PROPN
ejpam-6264	567	4	tmrdf	tmrdf	NOUN
ejpam-6264	567	5	(	(	PUNCT
ejpam-6264	567	6	g	g	NOUN
ejpam-6264	567	7	+	+	NOUN
ejpam-6264	567	8	h	h	NOUN
ejpam-6264	567	9	)	)	PUNCT
ejpam-6264	567	10	,	,	PUNCT
ejpam-6264	567	11	there	there	PRON
ejpam-6264	567	12	exists	exist	VERB
ejpam-6264	567	13	y	y	PROPN
ejpam-6264	567	14	∈	∈	PROPN
ejpam-6264	567	15	v2	v2	PROPN
ejpam-6264	567	16	∩	∩	NOUN
ejpam-6264	567	17	ng+h(x	ng+h(x	PROPN
ejpam-6264	567	18	)	)	PUNCT
ejpam-6264	567	19	.	.	PUNCT
ejpam-6264	568	1	since	since	SCONJ
ejpam-6264	568	2	y	y	PROPN
ejpam-6264	568	3	/∈	/∈	PUNCT
ejpam-6264	568	4	v	v	INTJ
ejpam-6264	568	5	(	(	PUNCT
ejpam-6264	568	6	g	g	NOUN
ejpam-6264	568	7	)	)	PUNCT
ejpam-6264	568	8	,	,	PUNCT
ejpam-6264	568	9	y	y	PROPN
ejpam-6264	568	10	∈	∈	PROPN
ejpam-6264	568	11	v	v	ADP
ejpam-6264	568	12	(	(	PUNCT
ejpam-6264	568	13	h	h	NOUN
ejpam-6264	568	14	)	)	PUNCT
ejpam-6264	568	15	.	.	PUNCT
ejpam-6264	569	1	hence	hence	ADV
ejpam-6264	569	2	,	,	PUNCT
ejpam-6264	569	3	y	y	PROPN
ejpam-6264	569	4	∈	∈	PROPN
ejpam-6264	569	5	v2	v2	PROPN
ejpam-6264	569	6	∩	∩	ADJ
ejpam-6264	569	7	v	v	NOUN
ejpam-6264	569	8	(	(	PUNCT
ejpam-6264	569	9	h	h	NOUN
ejpam-6264	569	10	)	)	PUNCT
ejpam-6264	569	11	.	.	PUNCT
ejpam-6264	570	1	thus	thus	ADV
ejpam-6264	570	2	,	,	PUNCT
ejpam-6264	570	3	v2	v2	PROPN
ejpam-6264	570	4	∩	∩	ADJ
ejpam-6264	570	5	v	v	NOUN
ejpam-6264	570	6	(	(	PUNCT
ejpam-6264	570	7	h	h	NOUN
ejpam-6264	570	8	)	)	PUNCT
ejpam-6264	570	9	̸=	̸=	PROPN
ejpam-6264	570	10	∅	∅	NOUN
ejpam-6264	570	11	satisfying	satisfy	VERB
ejpam-6264	570	12	(	(	PUNCT
ejpam-6264	570	13	iii)(a	iii)(a	PROPN
ejpam-6264	570	14	)	)	PUNCT
ejpam-6264	570	15	.	.	PUNCT
ejpam-6264	571	1	following	follow	VERB
ejpam-6264	571	2	similar	similar	ADJ
ejpam-6264	571	3	argument	argument	NOUN
ejpam-6264	571	4	,	,	PUNCT
ejpam-6264	571	5	if	if	SCONJ
ejpam-6264	571	6	ng(x	ng(x	NUM
ejpam-6264	571	7	)	)	PUNCT
ejpam-6264	571	8	∩	∩	PROPN
ejpam-6264	571	9	v3	v3	NOUN
ejpam-6264	571	10	=	=	PUNCT
ejpam-6264	571	11	∅	∅	NOUN
ejpam-6264	571	12	for	for	ADP
ejpam-6264	571	13	some	some	DET
ejpam-6264	571	14	x	x	SYM
ejpam-6264	571	15	∈	∈	PROPN
ejpam-6264	571	16	v0	v0	NOUN
ejpam-6264	571	17	,	,	PUNCT
ejpam-6264	571	18	v3	v3	PROPN
ejpam-6264	571	19	∩	∩	PROPN
ejpam-6264	571	20	v	v	X
ejpam-6264	571	21	(	(	PUNCT
ejpam-6264	571	22	h	h	NOUN
ejpam-6264	571	23	)	)	PUNCT
ejpam-6264	571	24	̸=	̸=	PROPN
ejpam-6264	571	25	∅.	∅.	ADV
ejpam-6264	571	26	thus	thus	ADV
ejpam-6264	571	27	,	,	PUNCT
ejpam-6264	571	28	(	(	PUNCT
ejpam-6264	571	29	iii)(b	iii)(b	ADJ
ejpam-6264	571	30	)	)	PUNCT
ejpam-6264	571	31	holds	hold	VERB
ejpam-6264	571	32	.	.	PUNCT
ejpam-6264	572	1	suppose	suppose	VERB
ejpam-6264	572	2	ng(x	ng(x	NOUN
ejpam-6264	572	3	)	)	PUNCT
ejpam-6264	572	4	∩	∩	NOUN
ejpam-6264	572	5	v2	v2	NOUN
ejpam-6264	572	6	=	=	SYM
ejpam-6264	572	7	∅	∅	NOUN
ejpam-6264	572	8	and	and	CCONJ
ejpam-6264	572	9	ng(x	ng(x	NUM
ejpam-6264	572	10	)	)	PUNCT
ejpam-6264	572	11	∩	∩	NOUN
ejpam-6264	572	12	v3	v3	PROPN
ejpam-6264	572	13	=	=	PUNCT
ejpam-6264	572	14	∅	∅	NOUN
ejpam-6264	572	15	for	for	ADP
ejpam-6264	572	16	some	some	DET
ejpam-6264	572	17	x	x	SYM
ejpam-6264	572	18	∈	∈	PROPN
ejpam-6264	572	19	v1	v1	NOUN
ejpam-6264	572	20	.	.	PUNCT
ejpam-6264	573	1	since	since	SCONJ
ejpam-6264	573	2	f	f	PROPN
ejpam-6264	573	3	∈	∈	PROPN
ejpam-6264	573	4	tmrdf	tmrdf	NOUN
ejpam-6264	573	5	(	(	PUNCT
ejpam-6264	573	6	g	g	NOUN
ejpam-6264	573	7	+	+	NOUN
ejpam-6264	573	8	h	h	NOUN
ejpam-6264	573	9	)	)	PUNCT
ejpam-6264	573	10	,	,	PUNCT
ejpam-6264	573	11	there	there	PRON
ejpam-6264	573	12	exists	exist	VERB
ejpam-6264	573	13	y	y	PROPN
ejpam-6264	573	14	∈	∈	PROPN
ejpam-6264	573	15	v2	v2	PROPN
ejpam-6264	573	16	or	or	CCONJ
ejpam-6264	573	17	y	y	PROPN
ejpam-6264	573	18	∈	∈	PROPN
ejpam-6264	573	19	v3	v3	PROPN
ejpam-6264	573	20	such	such	ADJ
ejpam-6264	573	21	that	that	SCONJ
ejpam-6264	573	22	xy	xy	PROPN
ejpam-6264	573	23	∈	∈	PROPN
ejpam-6264	573	24	e(g	e(g	PROPN
ejpam-6264	574	1	+	+	CCONJ
ejpam-6264	574	2	h	h	NOUN
ejpam-6264	574	3	)	)	PUNCT
ejpam-6264	574	4	.	.	PUNCT
ejpam-6264	575	1	since	since	SCONJ
ejpam-6264	575	2	y	y	PROPN
ejpam-6264	575	3	/∈	/∈	PUNCT
ejpam-6264	575	4	v	v	INTJ
ejpam-6264	575	5	(	(	PUNCT
ejpam-6264	575	6	g	g	NOUN
ejpam-6264	575	7	)	)	PUNCT
ejpam-6264	575	8	,	,	PUNCT
ejpam-6264	575	9	y	y	PROPN
ejpam-6264	575	10	∈	∈	PROPN
ejpam-6264	575	11	v	v	ADP
ejpam-6264	575	12	(	(	PUNCT
ejpam-6264	575	13	h	h	NOUN
ejpam-6264	575	14	)	)	PUNCT
ejpam-6264	575	15	.	.	PUNCT
ejpam-6264	576	1	necessarily	necessarily	ADV
ejpam-6264	576	2	y	y	PROPN
ejpam-6264	576	3	∈	∈	PROPN
ejpam-6264	576	4	v2	v2	PROPN
ejpam-6264	576	5	∩	∩	ADJ
ejpam-6264	576	6	v	v	NOUN
ejpam-6264	576	7	(	(	PUNCT
ejpam-6264	576	8	h	h	NOUN
ejpam-6264	576	9	)	)	PUNCT
ejpam-6264	576	10	or	or	CCONJ
ejpam-6264	576	11	y	y	PROPN
ejpam-6264	576	12	∈	∈	PROPN
ejpam-6264	576	13	v3	v3	PROPN
ejpam-6264	576	14	∩	∩	PROPN
ejpam-6264	576	15	v	v	X
ejpam-6264	576	16	(	(	PUNCT
ejpam-6264	576	17	h	h	NOUN
ejpam-6264	576	18	)	)	PUNCT
ejpam-6264	576	19	.	.	PUNCT
ejpam-6264	577	1	thus	thus	ADV
ejpam-6264	577	2	,	,	PUNCT
ejpam-6264	577	3	v2	v2	PROPN
ejpam-6264	577	4	∩	∩	ADJ
ejpam-6264	577	5	v	v	NOUN
ejpam-6264	577	6	(	(	PUNCT
ejpam-6264	577	7	h	h	NOUN
ejpam-6264	577	8	)	)	PUNCT
ejpam-6264	577	9	̸=	̸=	PROPN
ejpam-6264	577	10	∅	∅	NOUN
ejpam-6264	577	11	or	or	CCONJ
ejpam-6264	577	12	v3	v3	PROPN
ejpam-6264	577	13	∩	∩	ADJ
ejpam-6264	577	14	v	v	X
ejpam-6264	577	15	(	(	PUNCT
ejpam-6264	577	16	h	h	NOUN
ejpam-6264	577	17	)	)	PUNCT
ejpam-6264	577	18	̸=	̸=	PROPN
ejpam-6264	577	19	∅	∅	NOUN
ejpam-6264	577	20	satisfying	satisfy	VERB
ejpam-6264	577	21	(	(	PUNCT
ejpam-6264	577	22	iii)(c	iii)(c	PROPN
ejpam-6264	577	23	)	)	PUNCT
ejpam-6264	577	24	.	.	PUNCT
ejpam-6264	578	1	moreover	moreover	ADV
ejpam-6264	578	2	,	,	PUNCT
ejpam-6264	578	3	assume	assume	VERB
ejpam-6264	578	4	that	that	SCONJ
ejpam-6264	578	5	⟨(v1	⟨(v1	VERB
ejpam-6264	578	6	∪	∪	ADP
ejpam-6264	578	7	v2	v2	PROPN
ejpam-6264	578	8	∪	∪	X
ejpam-6264	578	9	v3	v3	PROPN
ejpam-6264	578	10	)	)	PUNCT
ejpam-6264	578	11	∩	∩	ADJ
ejpam-6264	578	12	v	v	X
ejpam-6264	578	13	(	(	PUNCT
ejpam-6264	578	14	g)⟩	g)⟩	PROPN
ejpam-6264	578	15	has	have	VERB
ejpam-6264	578	16	an	an	DET
ejpam-6264	578	17	isolated	isolated	ADJ
ejpam-6264	578	18	vertex	vertex	NOUN
ejpam-6264	578	19	.	.	PUNCT
ejpam-6264	579	1	let	let	VERB
ejpam-6264	579	2	v	v	X
ejpam-6264	579	3	∈	∈	PROPN
ejpam-6264	580	1	[	[	X
ejpam-6264	580	2	(	(	PUNCT
ejpam-6264	580	3	v1	v1	VERB
ejpam-6264	580	4	∪	∪	NOUN
ejpam-6264	580	5	v2	v2	PROPN
ejpam-6264	580	6	∪	∪	X
ejpam-6264	580	7	v3	v3	PROPN
ejpam-6264	580	8	)	)	PUNCT
ejpam-6264	580	9	∩	∩	PROPN
ejpam-6264	580	10	v	v	X
ejpam-6264	580	11	(	(	PUNCT
ejpam-6264	580	12	g	g	NOUN
ejpam-6264	580	13	)	)	PUNCT
ejpam-6264	580	14	]	]	PUNCT
ejpam-6264	580	15	such	such	ADJ
ejpam-6264	580	16	that	that	SCONJ
ejpam-6264	580	17	ng(v	ng(v	NUM
ejpam-6264	580	18	)	)	PUNCT
ejpam-6264	580	19	⊆	⊆	NUM
ejpam-6264	580	20	v0	v0	NOUN
ejpam-6264	580	21	.	.	PUNCT
ejpam-6264	581	1	since	since	SCONJ
ejpam-6264	581	2	f	f	PROPN
ejpam-6264	581	3	∈	∈	PROPN
ejpam-6264	581	4	tmrdf	tmrdf	NOUN
ejpam-6264	581	5	(	(	PUNCT
ejpam-6264	581	6	g+h	g+h	PROPN
ejpam-6264	581	7	)	)	PUNCT
ejpam-6264	581	8	,	,	PUNCT
ejpam-6264	581	9	⟨v1∪v2∪v3⟩	⟨v1∪v2∪v3⟩	NOUN
ejpam-6264	581	10	is	be	AUX
ejpam-6264	581	11	isolated	isolate	VERB
ejpam-6264	581	12	-	-	PUNCT
ejpam-6264	581	13	free	free	ADJ
ejpam-6264	581	14	vertex	vertex	NOUN
ejpam-6264	581	15	.	.	PUNCT
ejpam-6264	582	1	thus	thus	ADV
ejpam-6264	582	2	,	,	PUNCT
ejpam-6264	582	3	(	(	PUNCT
ejpam-6264	582	4	v1∪v2∪v3)∩v	v1∪v2∪v3)∩v	PROPN
ejpam-6264	582	5	(	(	PUNCT
ejpam-6264	582	6	h	h	NOUN
ejpam-6264	582	7	)	)	PUNCT
ejpam-6264	582	8	̸=	̸=	PROPN
ejpam-6264	582	9	∅.	∅.	PRON
ejpam-6264	582	10	hence	hence	ADV
ejpam-6264	582	11	,	,	PUNCT
ejpam-6264	582	12	(	(	PUNCT
ejpam-6264	582	13	iii)(g	iii)(g	NOUN
ejpam-6264	582	14	)	)	PUNCT
ejpam-6264	582	15	holds	hold	VERB
ejpam-6264	582	16	.	.	PUNCT
ejpam-6264	583	1	similarly	similarly	ADV
ejpam-6264	583	2	,	,	PUNCT
ejpam-6264	583	3	(	(	PUNCT
ejpam-6264	583	4	iii)(d	iii)(d	ADV
ejpam-6264	583	5	)	)	PUNCT
ejpam-6264	583	6	,	,	PUNCT
ejpam-6264	583	7	(	(	PUNCT
ejpam-6264	583	8	iii)(e	iii)(e	NOUN
ejpam-6264	583	9	)	)	PUNCT
ejpam-6264	583	10	,	,	PUNCT
ejpam-6264	583	11	(	(	PUNCT
ejpam-6264	583	12	iii)(f	iii)(f	ADV
ejpam-6264	583	13	)	)	PUNCT
ejpam-6264	583	14	,	,	PUNCT
ejpam-6264	583	15	and	and	CCONJ
ejpam-6264	583	16	(	(	PUNCT
ejpam-6264	583	17	iii)(h	iii)(h	NOUN
ejpam-6264	583	18	)	)	PUNCT
ejpam-6264	583	19	follows	follow	VERB
ejpam-6264	583	20	.	.	PUNCT
ejpam-6264	584	1	corollary	corollary	ADJ
ejpam-6264	584	2	3	3	X
ejpam-6264	584	3	.	.	PUNCT
ejpam-6264	585	1	let	let	VERB
ejpam-6264	585	2	g	g	NOUN
ejpam-6264	586	1	and	and	CCONJ
ejpam-6264	586	2	h	h	NOUN
ejpam-6264	586	3	be	be	VERB
ejpam-6264	586	4	any	any	DET
ejpam-6264	586	5	nontrivial	nontrivial	ADJ
ejpam-6264	586	6	graphs	graph	NOUN
ejpam-6264	586	7	.	.	PUNCT
ejpam-6264	587	1	then	then	ADV
ejpam-6264	587	2	3	3	NUM
ejpam-6264	587	3	≤	≤	NUM
ejpam-6264	587	4	γtmr(g+h	γtmr(g+h	NOUN
ejpam-6264	587	5	)	)	PUNCT
ejpam-6264	587	6	≤	≤	NUM
ejpam-6264	587	7	10	10	NUM
ejpam-6264	587	8	.	.	PUNCT
ejpam-6264	588	1	proof	proof	NOUN
ejpam-6264	588	2	.	.	PUNCT
ejpam-6264	589	1	since	since	SCONJ
ejpam-6264	589	2	g+h	g+h	PROPN
ejpam-6264	589	3	is	be	AUX
ejpam-6264	589	4	not	not	PART
ejpam-6264	589	5	a	a	DET
ejpam-6264	589	6	trivial	trivial	ADJ
ejpam-6264	589	7	graphs	graph	NOUN
ejpam-6264	589	8	,	,	PUNCT
ejpam-6264	589	9	γtmr(g+h	γtmr(g+h	NOUN
ejpam-6264	589	10	)	)	PUNCT
ejpam-6264	589	11	>	>	X
ejpam-6264	590	1	2	2	X
ejpam-6264	590	2	.	.	X
ejpam-6264	590	3	that	that	PRON
ejpam-6264	590	4	is	be	AUX
ejpam-6264	590	5	,	,	PUNCT
ejpam-6264	590	6	γtmr(g+h	γtmr(g+h	PROPN
ejpam-6264	590	7	)	)	PUNCT
ejpam-6264	590	8	≥	≥	NOUN
ejpam-6264	590	9	3	3	NUM
ejpam-6264	590	10	.	.	PUNCT
ejpam-6264	591	1	on	on	ADP
ejpam-6264	591	2	the	the	DET
ejpam-6264	591	3	other	other	ADJ
ejpam-6264	591	4	hand	hand	NOUN
ejpam-6264	591	5	,	,	PUNCT
ejpam-6264	591	6	let	let	VERB
ejpam-6264	591	7	v	v	NOUN
ejpam-6264	591	8	(	(	PUNCT
ejpam-6264	591	9	g	g	NOUN
ejpam-6264	591	10	)	)	PUNCT
ejpam-6264	591	11	=	=	SYM
ejpam-6264	591	12	{	{	PUNCT
ejpam-6264	591	13	v1	v1	PROPN
ejpam-6264	591	14	,	,	PUNCT
ejpam-6264	591	15	v2	v2	PROPN
ejpam-6264	591	16	,	,	PUNCT
ejpam-6264	591	17	·	·	PUNCT
ejpam-6264	591	18	·	·	PUNCT
ejpam-6264	591	19	·	·	PUNCT
ejpam-6264	591	20	,	,	PUNCT
ejpam-6264	591	21	vn	vn	INTJ
ejpam-6264	591	22	}	}	PUNCT
ejpam-6264	591	23	and	and	CCONJ
ejpam-6264	591	24	v	v	NOUN
ejpam-6264	591	25	(	(	PUNCT
ejpam-6264	591	26	h	h	NOUN
ejpam-6264	591	27	)	)	PUNCT
ejpam-6264	591	28	=	=	PRON
ejpam-6264	591	29	{	{	PUNCT
ejpam-6264	591	30	u1	u1	NOUN
ejpam-6264	591	31	,	,	PUNCT
ejpam-6264	591	32	u2	u2	PROPN
ejpam-6264	591	33	,	,	PUNCT
ejpam-6264	591	34	·	·	PUNCT
ejpam-6264	591	35	·	·	PUNCT
ejpam-6264	591	36	·	·	PUNCT
ejpam-6264	591	37	,	,	PUNCT
ejpam-6264	591	38	un	un	PROPN
ejpam-6264	591	39	}	}	PUNCT
ejpam-6264	591	40	.	.	PUNCT
ejpam-6264	592	1	now	now	ADV
ejpam-6264	592	2	,	,	PUNCT
ejpam-6264	592	3	define	define	VERB
ejpam-6264	592	4	a	a	DET
ejpam-6264	592	5	function	function	NOUN
ejpam-6264	592	6	f	f	NOUN
ejpam-6264	592	7	=	=	SYM
ejpam-6264	592	8	(	(	PUNCT
ejpam-6264	592	9	v0	v0	PROPN
ejpam-6264	592	10	,	,	PUNCT
ejpam-6264	592	11	v1	v1	NOUN
ejpam-6264	592	12	,	,	PUNCT
ejpam-6264	592	13	v2	v2	PROPN
ejpam-6264	592	14	,	,	PUNCT
ejpam-6264	592	15	v3	v3	PROPN
ejpam-6264	592	16	)	)	PUNCT
ejpam-6264	592	17	on	on	ADP
ejpam-6264	592	18	v	v	ADP
ejpam-6264	592	19	(	(	PUNCT
ejpam-6264	592	20	g+h	g+h	NOUN
ejpam-6264	592	21	)	)	PUNCT
ejpam-6264	592	22	given	give	VERB
ejpam-6264	592	23	by	by	ADP
ejpam-6264	592	24	f(x	f(x	PROPN
ejpam-6264	592	25	)	)	PUNCT
ejpam-6264	593	1	=	=	PUNCT
ejpam-6264	594	1			NOUN
ejpam-6264	594	2	2	2	NUM
ejpam-6264	594	3	,	,	PUNCT
ejpam-6264	594	4	if	if	SCONJ
ejpam-6264	594	5	x	x	SYM
ejpam-6264	594	6	∈	∈	PROPN
ejpam-6264	594	7	{	{	PUNCT
ejpam-6264	594	8	v1	v1	NOUN
ejpam-6264	594	9	,	,	PUNCT
ejpam-6264	594	10	u1	u1	NOUN
ejpam-6264	594	11	}	}	PUNCT
ejpam-6264	594	12	.	.	PUNCT
ejpam-6264	595	1	3	3	NUM
ejpam-6264	595	2	,	,	PUNCT
ejpam-6264	595	3	if	if	SCONJ
ejpam-6264	595	4	x	x	SYM
ejpam-6264	595	5	∈	∈	PROPN
ejpam-6264	595	6	{	{	PUNCT
ejpam-6264	595	7	v2	v2	NOUN
ejpam-6264	595	8	,	,	PUNCT
ejpam-6264	595	9	u2	u2	PROPN
ejpam-6264	595	10	}	}	PUNCT
ejpam-6264	595	11	.	.	PUNCT
ejpam-6264	596	1	0	0	NUM
ejpam-6264	596	2	,	,	PUNCT
ejpam-6264	596	3	if	if	SCONJ
ejpam-6264	596	4	x	x	PROPN
ejpam-6264	596	5	∈	∈	PROPN
ejpam-6264	596	6	v	v	NOUN
ejpam-6264	596	7	(	(	PUNCT
ejpam-6264	596	8	g+h	g+h	NOUN
ejpam-6264	596	9	)	)	PUNCT
ejpam-6264	596	10	\	\	NOUN
ejpam-6264	596	11	{	{	PUNCT
ejpam-6264	596	12	v1	v1	NOUN
ejpam-6264	596	13	,	,	PUNCT
ejpam-6264	596	14	v2	v2	PROPN
ejpam-6264	596	15	,	,	PUNCT
ejpam-6264	596	16	u1	u1	NOUN
ejpam-6264	596	17	,	,	PUNCT
ejpam-6264	596	18	u2	u2	PROPN
ejpam-6264	596	19	}	}	PUNCT
ejpam-6264	596	20	.	.	PUNCT
ejpam-6264	597	1	for	for	ADP
ejpam-6264	597	2	every	every	DET
ejpam-6264	597	3	x	x	SYM
ejpam-6264	597	4	∈	∈	PROPN
ejpam-6264	597	5	v	v	NOUN
ejpam-6264	597	6	(	(	PUNCT
ejpam-6264	597	7	g+h	g+h	PROPN
ejpam-6264	597	8	)	)	PUNCT
ejpam-6264	597	9	.	.	PUNCT
ejpam-6264	598	1	then	then	ADV
ejpam-6264	598	2	f	f	PROPN
ejpam-6264	598	3	∈	∈	PROPN
ejpam-6264	598	4	tmrdf	tmrdf	NOUN
ejpam-6264	598	5	(	(	PUNCT
ejpam-6264	598	6	g+h	g+h	PROPN
ejpam-6264	598	7	)	)	PUNCT
ejpam-6264	598	8	.	.	PUNCT
ejpam-6264	599	1	thus	thus	ADV
ejpam-6264	599	2	,	,	PUNCT
ejpam-6264	599	3	γtmr(g+h	γtmr(g+h	NOUN
ejpam-6264	599	4	)	)	PUNCT
ejpam-6264	599	5	≤	≤	NUM
ejpam-6264	599	6	ωtmr	ωtmr	ADJ
ejpam-6264	599	7	g+h(f	g+h(f	NOUN
ejpam-6264	599	8	)	)	PUNCT
ejpam-6264	599	9	=	=	SYM
ejpam-6264	600	1	10	10	NUM
ejpam-6264	600	2	.	.	PUNCT
ejpam-6264	601	1	hence	hence	ADV
ejpam-6264	601	2	,	,	PUNCT
ejpam-6264	601	3	3	3	NUM
ejpam-6264	601	4	≤	≤	NUM
ejpam-6264	601	5	γtmr(g+h	γtmr(g+h	NOUN
ejpam-6264	601	6	)	)	PUNCT
ejpam-6264	601	7	≤	≤	NUM
ejpam-6264	601	8	10	10	NUM
ejpam-6264	601	9	.	.	PUNCT
ejpam-6264	602	1	corollary	corollary	ADJ
ejpam-6264	602	2	4	4	NUM
ejpam-6264	602	3	.	.	PUNCT
ejpam-6264	603	1	let	let	VERB
ejpam-6264	603	2	g	g	NOUN
ejpam-6264	603	3	be	be	AUX
ejpam-6264	603	4	any	any	DET
ejpam-6264	603	5	graph	graph	NOUN
ejpam-6264	603	6	of	of	ADP
ejpam-6264	603	7	order	order	NOUN
ejpam-6264	603	8	n	n	CCONJ
ejpam-6264	603	9	,	,	PUNCT
ejpam-6264	603	10	then	then	ADV
ejpam-6264	603	11	γtmr(k1+g	γtmr(k1+g	PROPN
ejpam-6264	603	12	)	)	PUNCT
ejpam-6264	603	13	≤	≤	NOUN
ejpam-6264	603	14	min{2+n	min{2+n	NOUN
ejpam-6264	603	15	,	,	PUNCT
ejpam-6264	603	16	3	3	NUM
ejpam-6264	603	17	+	+	NOUN
ejpam-6264	603	18	2γ(g	2γ(g	NUM
ejpam-6264	603	19	)	)	PUNCT
ejpam-6264	603	20	}	}	PUNCT
ejpam-6264	603	21	,	,	PUNCT
ejpam-6264	603	22	and	and	CCONJ
ejpam-6264	603	23	this	this	DET
ejpam-6264	603	24	upper	upper	ADJ
ejpam-6264	603	25	bound	bind	VERB
ejpam-6264	603	26	is	be	AUX
ejpam-6264	603	27	sharp	sharp	ADJ
ejpam-6264	603	28	.	.	PUNCT
ejpam-6264	604	1	proof	proof	NOUN
ejpam-6264	604	2	.	.	PUNCT
ejpam-6264	605	1	define	define	VERB
ejpam-6264	605	2	a	a	DET
ejpam-6264	605	3	function	function	NOUN
ejpam-6264	605	4	g	g	NOUN
ejpam-6264	605	5	=	=	SYM
ejpam-6264	605	6	(	(	PUNCT
ejpam-6264	605	7	v0	v0	PROPN
ejpam-6264	605	8	,	,	PUNCT
ejpam-6264	605	9	v1	v1	NOUN
ejpam-6264	605	10	,	,	PUNCT
ejpam-6264	605	11	v2	v2	PROPN
ejpam-6264	605	12	,	,	PUNCT
ejpam-6264	605	13	v3	v3	PROPN
ejpam-6264	605	14	)	)	PUNCT
ejpam-6264	605	15	for	for	ADP
ejpam-6264	605	16	which	which	PRON
ejpam-6264	605	17	v1	v1	NOUN
ejpam-6264	605	18	=	=	SYM
ejpam-6264	605	19	v	v	NOUN
ejpam-6264	605	20	(	(	PUNCT
ejpam-6264	605	21	g	g	NOUN
ejpam-6264	605	22	)	)	PUNCT
ejpam-6264	605	23	,	,	PUNCT
ejpam-6264	605	24	v2	v2	PROPN
ejpam-6264	605	25	=	=	SYM
ejpam-6264	605	26	v	v	PROPN
ejpam-6264	605	27	(	(	PUNCT
ejpam-6264	605	28	k1	k1	NOUN
ejpam-6264	605	29	)	)	PUNCT
ejpam-6264	605	30	and	and	CCONJ
ejpam-6264	605	31	s.	s.	PROPN
ejpam-6264	605	32	ahamad	ahamad	VERB
ejpam-6264	605	33	et	et	PROPN
ejpam-6264	605	34	al	al	PROPN
ejpam-6264	605	35	.	.	PUNCT
ejpam-6264	605	36	/	/	SYM
ejpam-6264	605	37	eur	eur	PROPN
ejpam-6264	605	38	.	.	PUNCT
ejpam-6264	606	1	j.	j.	PROPN
ejpam-6264	606	2	pure	pure	PROPN
ejpam-6264	606	3	appl	appl	PROPN
ejpam-6264	606	4	.	.	PROPN
ejpam-6264	606	5	math	math	PROPN
ejpam-6264	606	6	,	,	PUNCT
ejpam-6264	606	7	18	18	NUM
ejpam-6264	606	8	(	(	PUNCT
ejpam-6264	606	9	4	4	NUM
ejpam-6264	606	10	)	)	PUNCT
ejpam-6264	606	11	(	(	PUNCT
ejpam-6264	606	12	2025	2025	NUM
ejpam-6264	606	13	)	)	PUNCT
ejpam-6264	606	14	,	,	PUNCT
ejpam-6264	606	15	6264	6264	NUM
ejpam-6264	606	16	16	16	NUM
ejpam-6264	606	17	of	of	ADP
ejpam-6264	606	18	20	20	NUM
ejpam-6264	606	19	v0	v0	NOUN
ejpam-6264	606	20	=	=	SYM
ejpam-6264	606	21	v3	v3	PROPN
ejpam-6264	606	22	=	=	PUNCT
ejpam-6264	606	23	∅.	∅.	NOUN
ejpam-6264	606	24	then	then	ADV
ejpam-6264	606	25	,	,	PUNCT
ejpam-6264	606	26	g	g	PROPN
ejpam-6264	606	27	∈	∈	PROPN
ejpam-6264	606	28	tmrdf	tmrdf	NOUN
ejpam-6264	606	29	(	(	PUNCT
ejpam-6264	606	30	k1	k1	NOUN
ejpam-6264	606	31	+	+	PROPN
ejpam-6264	606	32	g	g	NOUN
ejpam-6264	606	33	)	)	PUNCT
ejpam-6264	606	34	.	.	PUNCT
ejpam-6264	607	1	thus	thus	ADV
ejpam-6264	607	2	,	,	PUNCT
ejpam-6264	607	3	γtmr(k1	γtmr(k1	NOUN
ejpam-6264	607	4	+	+	PROPN
ejpam-6264	607	5	g	g	NOUN
ejpam-6264	607	6	)	)	PUNCT
ejpam-6264	607	7	≤	≤	NOUN
ejpam-6264	607	8	ωtmr	ωtmr	ADJ
ejpam-6264	607	9	g	g	PROPN
ejpam-6264	607	10	(	(	PUNCT
ejpam-6264	607	11	g	g	NOUN
ejpam-6264	607	12	)	)	PUNCT
ejpam-6264	607	13	=	=	SYM
ejpam-6264	607	14	2|v2|+	2|v2|+	NUM
ejpam-6264	607	15	|v1|	|v1|	NOUN
ejpam-6264	607	16	=	=	SYM
ejpam-6264	607	17	2(1	2(1	NUM
ejpam-6264	607	18	)	)	PUNCT
ejpam-6264	607	19	+	+	CCONJ
ejpam-6264	607	20	n	n	CCONJ
ejpam-6264	607	21	=	=	SYM
ejpam-6264	607	22	2	2	NUM
ejpam-6264	607	23	+	+	CCONJ
ejpam-6264	607	24	n.	n.	NOUN
ejpam-6264	607	25	now	now	ADV
ejpam-6264	607	26	,	,	PUNCT
ejpam-6264	607	27	let	let	VERB
ejpam-6264	607	28	v	v	NOUN
ejpam-6264	607	29	(	(	PUNCT
ejpam-6264	607	30	k1	k1	NOUN
ejpam-6264	607	31	)	)	PUNCT
ejpam-6264	607	32	=	=	SYM
ejpam-6264	607	33	{	{	PUNCT
ejpam-6264	607	34	x	x	NOUN
ejpam-6264	607	35	}	}	PUNCT
ejpam-6264	607	36	and	and	CCONJ
ejpam-6264	607	37	d	d	X
ejpam-6264	607	38	a	a	DET
ejpam-6264	607	39	γ	γ	X
ejpam-6264	607	40	-	-	PUNCT
ejpam-6264	607	41	set	set	NOUN
ejpam-6264	607	42	of	of	ADP
ejpam-6264	607	43	g.	g.	PROPN
ejpam-6264	607	44	define	define	VERB
ejpam-6264	607	45	a	a	DET
ejpam-6264	607	46	function	function	NOUN
ejpam-6264	607	47	h	h	NOUN
ejpam-6264	607	48	=	=	PUNCT
ejpam-6264	607	49	(	(	PUNCT
ejpam-6264	607	50	v	v	NUM
ejpam-6264	607	51	′	′	NUM
ejpam-6264	607	52	0	0	NUM
ejpam-6264	607	53	,	,	PUNCT
ejpam-6264	607	54	v	v	NOUN
ejpam-6264	607	55	′	′	NUM
ejpam-6264	607	56	1	1	NUM
ejpam-6264	607	57	,	,	PUNCT
ejpam-6264	607	58	v	v	NOUN
ejpam-6264	607	59	′	′	NUM
ejpam-6264	607	60	2	2	NUM
ejpam-6264	607	61	,	,	PUNCT
ejpam-6264	607	62	v	v	ADJ
ejpam-6264	607	63	′	′	NUM
ejpam-6264	607	64	3	3	NUM
ejpam-6264	607	65	)	)	PUNCT
ejpam-6264	607	66	for	for	ADP
ejpam-6264	607	67	which	which	PRON
ejpam-6264	607	68	v	v	ADP
ejpam-6264	607	69	′	′	NUM
ejpam-6264	607	70	0	0	NUM
ejpam-6264	608	1	=	=	SYM
ejpam-6264	608	2	v	v	ADJ
ejpam-6264	608	3	(	(	PUNCT
ejpam-6264	608	4	g	g	NOUN
ejpam-6264	608	5	)	)	PUNCT
ejpam-6264	608	6	\d	\d	NOUN
ejpam-6264	608	7	,	,	PUNCT
ejpam-6264	608	8	v	v	NOUN
ejpam-6264	608	9	′	′	NUM
ejpam-6264	608	10	1	1	NUM
ejpam-6264	608	11	=	=	NOUN
ejpam-6264	608	12	∅	∅	NOUN
ejpam-6264	608	13	,	,	PUNCT
ejpam-6264	608	14	v	v	NOUN
ejpam-6264	608	15	′	′	NOUN
ejpam-6264	608	16	2	2	NUM
ejpam-6264	608	17	=	=	SYM
ejpam-6264	608	18	d	d	NOUN
ejpam-6264	608	19	and	and	CCONJ
ejpam-6264	608	20	v	v	X
ejpam-6264	608	21	′	′	NUM
ejpam-6264	608	22	3	3	NUM
ejpam-6264	608	23	=	=	SYM
ejpam-6264	608	24	{	{	PUNCT
ejpam-6264	608	25	x	x	NOUN
ejpam-6264	608	26	}	}	PUNCT
ejpam-6264	608	27	.	.	PUNCT
ejpam-6264	609	1	then	then	ADV
ejpam-6264	609	2	,	,	PUNCT
ejpam-6264	609	3	h	h	PROPN
ejpam-6264	609	4	∈	∈	PROPN
ejpam-6264	609	5	tmrdf	tmrdf	NOUN
ejpam-6264	609	6	(	(	PUNCT
ejpam-6264	609	7	k1	k1	NOUN
ejpam-6264	609	8	+	+	PROPN
ejpam-6264	609	9	g	g	NOUN
ejpam-6264	609	10	)	)	PUNCT
ejpam-6264	609	11	.	.	PUNCT
ejpam-6264	610	1	thus	thus	ADV
ejpam-6264	610	2	,	,	PUNCT
ejpam-6264	610	3	γtmr(k1	γtmr(k1	NOUN
ejpam-6264	610	4	+	+	PROPN
ejpam-6264	610	5	g	g	NOUN
ejpam-6264	610	6	)	)	PUNCT
ejpam-6264	610	7	≤	≤	NOUN
ejpam-6264	610	8	ωtmr	ωtmr	ADJ
ejpam-6264	610	9	g	g	PROPN
ejpam-6264	610	10	(	(	PUNCT
ejpam-6264	610	11	h	h	NOUN
ejpam-6264	610	12	)	)	PUNCT
ejpam-6264	610	13	=	=	SYM
ejpam-6264	611	1	3|v	3|v	NUM
ejpam-6264	611	2	′	′	NUM
ejpam-6264	611	3	3	3	NUM
ejpam-6264	611	4	|+	|+	NOUN
ejpam-6264	611	5	2|v	2|v	NOUN
ejpam-6264	612	1	′	′	NOUN
ejpam-6264	612	2	2	2	NUM
ejpam-6264	612	3	|	|	ADV
ejpam-6264	612	4	=	=	SYM
ejpam-6264	612	5	3(1	3(1	NUM
ejpam-6264	612	6	)	)	PUNCT
ejpam-6264	613	1	+	+	CCONJ
ejpam-6264	613	2	2|d|	2|d|	NUM
ejpam-6264	613	3	=	=	SYM
ejpam-6264	613	4	3	3	NUM
ejpam-6264	613	5	+	+	NUM
ejpam-6264	613	6	2γ(g	2γ(g	NUM
ejpam-6264	613	7	)	)	PUNCT
ejpam-6264	613	8	.	.	PUNCT
ejpam-6264	614	1	moreover	moreover	ADV
ejpam-6264	614	2	,	,	PUNCT
ejpam-6264	614	3	for	for	ADP
ejpam-6264	614	4	the	the	DET
ejpam-6264	614	5	sharpness	sharpness	NOUN
ejpam-6264	614	6	,	,	PUNCT
ejpam-6264	614	7	consider	consider	VERB
ejpam-6264	614	8	the	the	DET
ejpam-6264	614	9	graphs	graph	NOUN
ejpam-6264	614	10	k1+g	k1+g	VERB
ejpam-6264	614	11	,	,	PUNCT
ejpam-6264	614	12	g	g	PROPN
ejpam-6264	614	13	∈	∈	PROPN
ejpam-6264	614	14	{	{	PUNCT
ejpam-6264	614	15	kn	kn	PROPN
ejpam-6264	614	16	,	,	PUNCT
ejpam-6264	614	17	kn	kn	PROPN
ejpam-6264	614	18	}	}	PUNCT
ejpam-6264	614	19	.	.	PUNCT
ejpam-6264	615	1	strict	strict	ADJ
ejpam-6264	615	2	inequality	inequality	NOUN
ejpam-6264	615	3	may	may	AUX
ejpam-6264	615	4	also	also	ADV
ejpam-6264	615	5	be	be	AUX
ejpam-6264	615	6	attained	attain	VERB
ejpam-6264	615	7	such	such	ADJ
ejpam-6264	615	8	as	as	ADP
ejpam-6264	615	9	the	the	DET
ejpam-6264	615	10	graph	graph	NOUN
ejpam-6264	615	11	k1	k1	NOUN
ejpam-6264	615	12	+	+	CCONJ
ejpam-6264	615	13	p7	p7	PROPN
ejpam-6264	615	14	.	.	PUNCT
ejpam-6264	615	15	example	example	NOUN
ejpam-6264	616	1	2	2	NUM
ejpam-6264	616	2	.	.	X
ejpam-6264	616	3	consider	consider	VERB
ejpam-6264	616	4	the	the	DET
ejpam-6264	616	5	graphs	graph	NOUN
ejpam-6264	616	6	k1	k1	NOUN
ejpam-6264	616	7	+	+	CCONJ
ejpam-6264	616	8	p7	p7	ADJ
ejpam-6264	616	9	and	and	CCONJ
ejpam-6264	616	10	k1	k1	NOUN
ejpam-6264	616	11	+	+	CCONJ
ejpam-6264	616	12	k5	k5	PROPN
ejpam-6264	616	13	in	in	ADP
ejpam-6264	616	14	figure	figure	NOUN
ejpam-6264	616	15	8	8	NUM
ejpam-6264	616	16	and	and	CCONJ
ejpam-6264	616	17	figure	figure	VERB
ejpam-6264	616	18	9	9	NUM
ejpam-6264	616	19	,	,	PUNCT
ejpam-6264	616	20	respectively	respectively	ADV
ejpam-6264	616	21	.	.	PUNCT
ejpam-6264	617	1	2b	2b	NUM
ejpam-6264	617	2	0c	0c	NOUN
ejpam-6264	617	3	1	1	NUM
ejpam-6264	617	4	d	d	NOUN
ejpam-6264	617	5	0	0	NUM
ejpam-6264	617	6	e	e	NOUN
ejpam-6264	617	7	2	2	NUM
ejpam-6264	617	8	f	f	X
ejpam-6264	617	9	0a	0a	NOUN
ejpam-6264	617	10	0	0	PUNCT
ejpam-6264	617	11	g	g	PROPN
ejpam-6264	617	12	3	3	NUM
ejpam-6264	617	13	u	u	NOUN
ejpam-6264	617	14	k1	k1	NOUN
ejpam-6264	617	15	+	+	CCONJ
ejpam-6264	617	16	p7	p7	ADJ
ejpam-6264	617	17	:	:	PUNCT
ejpam-6264	617	18	figure	figure	NOUN
ejpam-6264	617	19	8	8	NUM
ejpam-6264	617	20	:	:	PUNCT
ejpam-6264	617	21	the	the	DET
ejpam-6264	617	22	graph	graph	NOUN
ejpam-6264	617	23	k1	k1	NOUN
ejpam-6264	617	24	+	+	CCONJ
ejpam-6264	617	25	p7	p7	PROPN
ejpam-6264	617	26	with	with	ADP
ejpam-6264	617	27	γtmr(k1	γtmr(k1	NOUN
ejpam-6264	617	28	+	+	CCONJ
ejpam-6264	617	29	p7	p7	ADJ
ejpam-6264	617	30	)	)	PUNCT
ejpam-6264	617	31	=	=	SYM
ejpam-6264	617	32	8	8	NUM
ejpam-6264	617	33	in	in	ADP
ejpam-6264	617	34	figure	figure	NOUN
ejpam-6264	617	35	8	8	NUM
ejpam-6264	617	36	,	,	PUNCT
ejpam-6264	617	37	the	the	DET
ejpam-6264	617	38	function	function	NOUN
ejpam-6264	617	39	f	f	X
ejpam-6264	617	40	:	:	PUNCT
ejpam-6264	617	41	v	v	NOUN
ejpam-6264	617	42	(	(	PUNCT
ejpam-6264	617	43	k1	k1	NOUN
ejpam-6264	617	44	+	+	CCONJ
ejpam-6264	617	45	p7	p7	ADJ
ejpam-6264	617	46	)	)	PUNCT
ejpam-6264	617	47	→	→	SYM
ejpam-6264	617	48	{	{	PUNCT
ejpam-6264	617	49	0	0	NUM
ejpam-6264	617	50	,	,	PUNCT
ejpam-6264	617	51	1	1	NUM
ejpam-6264	617	52	,	,	PUNCT
ejpam-6264	617	53	2	2	NUM
ejpam-6264	617	54	,	,	PUNCT
ejpam-6264	617	55	3	3	NUM
ejpam-6264	617	56	}	}	PUNCT
ejpam-6264	617	57	given	give	VERB
ejpam-6264	617	58	by	by	ADP
ejpam-6264	617	59	f(u	f(u	PROPN
ejpam-6264	617	60	)	)	PUNCT
ejpam-6264	617	61	=	=	SYM
ejpam-6264	617	62	3	3	NUM
ejpam-6264	617	63	,	,	PUNCT
ejpam-6264	617	64	f(b	f(b	PROPN
ejpam-6264	617	65	)	)	PUNCT
ejpam-6264	617	66	=	=	SYM
ejpam-6264	617	67	f(f	f(f	X
ejpam-6264	617	68	)	)	PUNCT
ejpam-6264	617	69	=	=	SYM
ejpam-6264	617	70	2	2	NUM
ejpam-6264	617	71	,	,	PUNCT
ejpam-6264	617	72	f(a	f(a	NOUN
ejpam-6264	617	73	)	)	PUNCT
ejpam-6264	617	74	=	=	SYM
ejpam-6264	617	75	f(c	f(c	PROPN
ejpam-6264	617	76	)	)	PUNCT
ejpam-6264	617	77	=	=	SYM
ejpam-6264	617	78	f(g	f(g	NOUN
ejpam-6264	617	79	)	)	PUNCT
ejpam-6264	617	80	=	=	SYM
ejpam-6264	617	81	f(e	f(e	NOUN
ejpam-6264	617	82	)	)	PUNCT
ejpam-6264	617	83	=	=	SYM
ejpam-6264	617	84	0	0	NUM
ejpam-6264	617	85	,	,	PUNCT
ejpam-6264	617	86	and	and	CCONJ
ejpam-6264	617	87	f(d	f(d	PROPN
ejpam-6264	617	88	)	)	PUNCT
ejpam-6264	617	89	=	=	SYM
ejpam-6264	617	90	1	1	X
ejpam-6264	617	91	.	.	X
ejpam-6264	617	92	observe	observe	VERB
ejpam-6264	617	93	that	that	SCONJ
ejpam-6264	617	94	{	{	PUNCT
ejpam-6264	617	95	b	b	X
ejpam-6264	617	96	,	,	PUNCT
ejpam-6264	617	97	d	d	PROPN
ejpam-6264	617	98	,	,	PUNCT
ejpam-6264	617	99	f	f	X
ejpam-6264	617	100	}	}	PUNCT
ejpam-6264	617	101	is	be	AUX
ejpam-6264	617	102	a	a	DET
ejpam-6264	617	103	dominating	dominating	NOUN
ejpam-6264	617	104	set	set	NOUN
ejpam-6264	617	105	of	of	ADP
ejpam-6264	617	106	p7	p7	PROPN
ejpam-6264	617	107	.	.	PUNCT
ejpam-6264	618	1	thus	thus	ADV
ejpam-6264	618	2	,	,	PUNCT
ejpam-6264	618	3	the	the	DET
ejpam-6264	618	4	γ(p7	γ(p7	NOUN
ejpam-6264	618	5	)	)	PUNCT
ejpam-6264	618	6	=	=	SYM
ejpam-6264	618	7	3	3	NUM
ejpam-6264	618	8	and	and	CCONJ
ejpam-6264	618	9	observe	observe	VERB
ejpam-6264	618	10	further	far	ADV
ejpam-6264	618	11	that	that	SCONJ
ejpam-6264	618	12	f	f	PROPN
ejpam-6264	618	13	is	be	AUX
ejpam-6264	618	14	a	a	DET
ejpam-6264	618	15	total	total	ADJ
ejpam-6264	618	16	modern	modern	ADJ
ejpam-6264	618	17	roman	roman	ADJ
ejpam-6264	618	18	dominating	dominating	NOUN
ejpam-6264	618	19	function	function	NOUN
ejpam-6264	618	20	of	of	ADP
ejpam-6264	618	21	g	g	NOUN
ejpam-6264	618	22	with	with	ADP
ejpam-6264	618	23	weight	weight	NOUN
ejpam-6264	618	24	8	8	NUM
ejpam-6264	618	25	.	.	PUNCT
ejpam-6264	619	1	it	it	PRON
ejpam-6264	619	2	can	can	AUX
ejpam-6264	619	3	be	be	AUX
ejpam-6264	619	4	verified	verify	VERB
ejpam-6264	619	5	that	that	SCONJ
ejpam-6264	619	6	8	8	NUM
ejpam-6264	619	7	=	=	SYM
ejpam-6264	619	8	γtmr(k1	γtmr(k1	NOUN
ejpam-6264	619	9	+	+	CCONJ
ejpam-6264	619	10	p7	p7	ADJ
ejpam-6264	619	11	)	)	PUNCT
ejpam-6264	619	12	<	<	X
ejpam-6264	619	13	min{2	min{2	NOUN
ejpam-6264	619	14	+	+	CCONJ
ejpam-6264	619	15	n	n	CCONJ
ejpam-6264	619	16	,	,	PUNCT
ejpam-6264	619	17	3	3	NUM
ejpam-6264	619	18	+	+	NUM
ejpam-6264	619	19	2(γ(p7	2(γ(p7	NUM
ejpam-6264	619	20	)	)	PUNCT
ejpam-6264	619	21	)	)	PUNCT
ejpam-6264	619	22	}	}	PUNCT
ejpam-6264	619	23	=	=	PUNCT
ejpam-6264	620	1	9	9	NUM
ejpam-6264	620	2	.	.	NOUN
ejpam-6264	621	1	3	3	NUM
ejpam-6264	621	2	0	0	NUM
ejpam-6264	621	3	0	0	NUM
ejpam-6264	621	4	2	2	NUM
ejpam-6264	621	5	0	0	NUM
ejpam-6264	621	6	0k1	0k1	NOUN
ejpam-6264	622	1	+	+	ADV
ejpam-6264	622	2	k5	k5	PROPN
ejpam-6264	622	3	:	:	PUNCT
ejpam-6264	622	4	figure	figure	NOUN
ejpam-6264	622	5	9	9	NUM
ejpam-6264	622	6	:	:	PUNCT
ejpam-6264	622	7	the	the	DET
ejpam-6264	622	8	graph	graph	NOUN
ejpam-6264	622	9	k1	k1	PROPN
ejpam-6264	622	10	+	+	NOUN
ejpam-6264	622	11	k5	k5	PROPN
ejpam-6264	622	12	with	with	ADP
ejpam-6264	622	13	γtmr(k1	γtmr(k1	PROPN
ejpam-6264	622	14	+	+	SYM
ejpam-6264	622	15	k5	k5	PROPN
ejpam-6264	622	16	)	)	PUNCT
ejpam-6264	622	17	=	=	SYM
ejpam-6264	623	1	5	5	X
ejpam-6264	623	2	.	.	PUNCT
ejpam-6264	624	1	s.	s.	PROPN
ejpam-6264	624	2	ahamad	ahamad	VERB
ejpam-6264	624	3	et	et	PROPN
ejpam-6264	624	4	al	al	PROPN
ejpam-6264	624	5	.	.	PUNCT
ejpam-6264	624	6	/	/	SYM
ejpam-6264	624	7	eur	eur	PROPN
ejpam-6264	624	8	.	.	PUNCT
ejpam-6264	625	1	j.	j.	PROPN
ejpam-6264	625	2	pure	pure	PROPN
ejpam-6264	625	3	appl	appl	PROPN
ejpam-6264	625	4	.	.	PROPN
ejpam-6264	625	5	math	math	PROPN
ejpam-6264	625	6	,	,	PUNCT
ejpam-6264	625	7	18	18	NUM
ejpam-6264	625	8	(	(	PUNCT
ejpam-6264	625	9	4	4	NUM
ejpam-6264	625	10	)	)	PUNCT
ejpam-6264	625	11	(	(	PUNCT
ejpam-6264	625	12	2025	2025	NUM
ejpam-6264	625	13	)	)	PUNCT
ejpam-6264	625	14	,	,	PUNCT
ejpam-6264	625	15	6264	6264	NUM
ejpam-6264	625	16	17	17	NUM
ejpam-6264	625	17	of	of	ADP
ejpam-6264	625	18	20	20	NUM
ejpam-6264	625	19	in	in	ADP
ejpam-6264	625	20	figure	figure	NOUN
ejpam-6264	625	21	9	9	NUM
ejpam-6264	625	22	,	,	PUNCT
ejpam-6264	625	23	observe	observe	VERB
ejpam-6264	625	24	that	that	SCONJ
ejpam-6264	625	25	f	f	PROPN
ejpam-6264	625	26	is	be	AUX
ejpam-6264	625	27	a	a	DET
ejpam-6264	625	28	total	total	ADJ
ejpam-6264	625	29	modern	modern	ADJ
ejpam-6264	625	30	roman	roman	ADJ
ejpam-6264	625	31	dominating	dominating	NOUN
ejpam-6264	625	32	function	function	NOUN
ejpam-6264	625	33	of	of	ADP
ejpam-6264	625	34	k1+k5	k1+k5	PROPN
ejpam-6264	625	35	with	with	ADP
ejpam-6264	625	36	weight	weight	NOUN
ejpam-6264	625	37	5	5	NUM
ejpam-6264	625	38	.	.	PUNCT
ejpam-6264	626	1	it	it	PRON
ejpam-6264	626	2	can	can	AUX
ejpam-6264	626	3	be	be	AUX
ejpam-6264	626	4	verified	verify	VERB
ejpam-6264	626	5	that	that	SCONJ
ejpam-6264	626	6	γtmr(k1	γtmr(k1	PROPN
ejpam-6264	626	7	+	+	SYM
ejpam-6264	626	8	k5	k5	PROPN
ejpam-6264	626	9	)	)	PUNCT
ejpam-6264	626	10	=	=	SYM
ejpam-6264	626	11	min{2	min{2	NOUN
ejpam-6264	626	12	+	+	CCONJ
ejpam-6264	626	13	n	n	CCONJ
ejpam-6264	626	14	,	,	PUNCT
ejpam-6264	626	15	3	3	NUM
ejpam-6264	626	16	+	+	SYM
ejpam-6264	626	17	2(γ(k1	2(γ(k1	NUM
ejpam-6264	626	18	+	+	ADJ
ejpam-6264	626	19	k5	k5	PROPN
ejpam-6264	626	20	)	)	PUNCT
ejpam-6264	626	21	)	)	PUNCT
ejpam-6264	626	22	}	}	PUNCT
ejpam-6264	626	23	=	=	SYM
ejpam-6264	626	24	5	5	X
ejpam-6264	626	25	.	.	PUNCT
ejpam-6264	626	26	corollary	corollary	ADJ
ejpam-6264	626	27	5	5	NUM
ejpam-6264	626	28	.	.	PUNCT
ejpam-6264	627	1	let	let	VERB
ejpam-6264	627	2	g	g	NOUN
ejpam-6264	627	3	and	and	CCONJ
ejpam-6264	627	4	h	h	NOUN
ejpam-6264	627	5	be	be	VERB
ejpam-6264	627	6	any	any	DET
ejpam-6264	627	7	graphs	graph	NOUN
ejpam-6264	627	8	.	.	PUNCT
ejpam-6264	628	1	then	then	ADV
ejpam-6264	628	2	(	(	PUNCT
ejpam-6264	628	3	i	i	NOUN
ejpam-6264	628	4	)	)	PUNCT
ejpam-6264	628	5	γtmr(g+h	γtmr(g+h	PROPN
ejpam-6264	628	6	)	)	PUNCT
ejpam-6264	629	1	=	=	SYM
ejpam-6264	629	2	3	3	NUM
ejpam-6264	629	3	if	if	SCONJ
ejpam-6264	629	4	and	and	CCONJ
ejpam-6264	629	5	only	only	ADV
ejpam-6264	629	6	if	if	SCONJ
ejpam-6264	629	7	g	g	PROPN
ejpam-6264	629	8	=	=	SYM
ejpam-6264	629	9	k1	k1	PROPN
ejpam-6264	629	10	and	and	CCONJ
ejpam-6264	629	11	h	h	NOUN
ejpam-6264	629	12	=	=	PROPN
ejpam-6264	629	13	k1	k1	PROPN
ejpam-6264	629	14	.	.	PUNCT
ejpam-6264	630	1	(	(	PUNCT
ejpam-6264	630	2	ii	ii	NOUN
ejpam-6264	630	3	)	)	PUNCT
ejpam-6264	630	4	γtmr(g+h	γtmr(g+h	PROPN
ejpam-6264	630	5	)	)	PUNCT
ejpam-6264	631	1	=	=	SYM
ejpam-6264	631	2	4	4	NUM
ejpam-6264	631	3	if	if	SCONJ
ejpam-6264	631	4	and	and	CCONJ
ejpam-6264	631	5	only	only	ADV
ejpam-6264	631	6	if	if	SCONJ
ejpam-6264	631	7	g	g	PROPN
ejpam-6264	631	8	=	=	SYM
ejpam-6264	631	9	k1	k1	PROPN
ejpam-6264	631	10	and	and	CCONJ
ejpam-6264	631	11	h	h	NOUN
ejpam-6264	631	12	∈	∈	PROPN
ejpam-6264	631	13	{	{	PUNCT
ejpam-6264	631	14	k2,k2	k2,k2	PROPN
ejpam-6264	631	15	}	}	PUNCT
ejpam-6264	631	16	or	or	CCONJ
ejpam-6264	631	17	vise	vise	VERB
ejpam-6264	631	18	versa	versa	ADV
ejpam-6264	631	19	.	.	PUNCT
ejpam-6264	632	1	(	(	PUNCT
ejpam-6264	632	2	iii	iii	NOUN
ejpam-6264	632	3	)	)	PUNCT
ejpam-6264	632	4	γtmr(g+h	γtmr(g+h	NOUN
ejpam-6264	632	5	)	)	PUNCT
ejpam-6264	633	1	=	=	SYM
ejpam-6264	633	2	5	5	NUM
ejpam-6264	633	3	if	if	SCONJ
ejpam-6264	633	4	and	and	CCONJ
ejpam-6264	633	5	only	only	ADV
ejpam-6264	633	6	if	if	SCONJ
ejpam-6264	633	7	one	one	NUM
ejpam-6264	633	8	of	of	ADP
ejpam-6264	633	9	the	the	DET
ejpam-6264	633	10	following	following	NOUN
ejpam-6264	633	11	holds	hold	VERB
ejpam-6264	633	12	:	:	PUNCT
ejpam-6264	633	13	(	(	PUNCT
ejpam-6264	633	14	a	a	X
ejpam-6264	633	15	)	)	PUNCT
ejpam-6264	633	16	g	g	NOUN
ejpam-6264	633	17	=	=	SYM
ejpam-6264	633	18	k1	k1	PROPN
ejpam-6264	633	19	and	and	CCONJ
ejpam-6264	633	20	h	h	NOUN
ejpam-6264	633	21	∈	∈	PROPN
ejpam-6264	633	22	{	{	PUNCT
ejpam-6264	633	23	p3,k3,k3,k1	p3,k3,k3,k1	NOUN
ejpam-6264	633	24	∪k2	∪k2	X
ejpam-6264	633	25	}	}	PUNCT
ejpam-6264	633	26	and	and	CCONJ
ejpam-6264	633	27	vise	vise	VERB
ejpam-6264	633	28	versa	versa	ADV
ejpam-6264	633	29	.	.	PUNCT
ejpam-6264	634	1	(	(	PUNCT
ejpam-6264	634	2	b	b	X
ejpam-6264	634	3	)	)	PUNCT
ejpam-6264	634	4	γ(g	γ(g	PROPN
ejpam-6264	634	5	)	)	PUNCT
ejpam-6264	635	1	=	=	SYM
ejpam-6264	635	2	1	1	NUM
ejpam-6264	635	3	and	and	CCONJ
ejpam-6264	635	4	γ(h	γ(h	NOUN
ejpam-6264	635	5	)	)	PUNCT
ejpam-6264	635	6	=	=	SYM
ejpam-6264	636	1	1	1	X
ejpam-6264	636	2	.	.	PUNCT
ejpam-6264	636	3	(	(	PUNCT
ejpam-6264	636	4	c	c	X
ejpam-6264	636	5	)	)	PUNCT
ejpam-6264	636	6	γ2(g	γ2(g	NOUN
ejpam-6264	636	7	)	)	PUNCT
ejpam-6264	636	8	=	=	SYM
ejpam-6264	636	9	2	2	NUM
ejpam-6264	636	10	or	or	CCONJ
ejpam-6264	636	11	γ2(h	γ2(h	NUM
ejpam-6264	636	12	)	)	PUNCT
ejpam-6264	636	13	=	=	SYM
ejpam-6264	637	1	2	2	X
ejpam-6264	637	2	.	.	PUNCT
ejpam-6264	637	3	proof	proof	NOUN
ejpam-6264	637	4	.	.	PUNCT
ejpam-6264	638	1	the	the	DET
ejpam-6264	638	2	proof	proof	NOUN
ejpam-6264	638	3	follows	follow	VERB
ejpam-6264	638	4	immediately	immediately	ADV
ejpam-6264	638	5	from	from	ADP
ejpam-6264	638	6	proposition	proposition	NOUN
ejpam-6264	638	7	17	17	NUM
ejpam-6264	638	8	.	.	NOUN
ejpam-6264	639	1	6	6	NUM
ejpam-6264	639	2	.	.	X
ejpam-6264	640	1	on	on	ADP
ejpam-6264	640	2	the	the	DET
ejpam-6264	640	3	corona	corona	NOUN
ejpam-6264	640	4	of	of	ADP
ejpam-6264	640	5	graphs	graph	NOUN
ejpam-6264	640	6	let	let	VERB
ejpam-6264	640	7	g	g	NOUN
ejpam-6264	640	8	and	and	CCONJ
ejpam-6264	640	9	h	h	NOUN
ejpam-6264	640	10	be	be	AUX
ejpam-6264	640	11	graphs	graph	NOUN
ejpam-6264	640	12	with	with	ADP
ejpam-6264	640	13	disjoint	disjoint	ADJ
ejpam-6264	640	14	vertex	vertex	NOUN
ejpam-6264	640	15	sets	set	NOUN
ejpam-6264	640	16	.	.	PUNCT
ejpam-6264	641	1	the	the	DET
ejpam-6264	641	2	corona	corona	NOUN
ejpam-6264	641	3	of	of	ADP
ejpam-6264	641	4	g	g	PROPN
ejpam-6264	641	5	and	and	CCONJ
ejpam-6264	641	6	h	h	NOUN
ejpam-6264	641	7	is	be	AUX
ejpam-6264	641	8	the	the	DET
ejpam-6264	641	9	graph	graph	NOUN
ejpam-6264	641	10	g	g	PROPN
ejpam-6264	641	11	◦	◦	NOUN
ejpam-6264	641	12	h	h	NOUN
ejpam-6264	641	13	obtained	obtain	VERB
ejpam-6264	641	14	by	by	ADP
ejpam-6264	641	15	taking	take	VERB
ejpam-6264	641	16	one	one	NUM
ejpam-6264	641	17	copy	copy	NOUN
ejpam-6264	641	18	of	of	ADP
ejpam-6264	641	19	g	g	PROPN
ejpam-6264	641	20	and	and	CCONJ
ejpam-6264	641	21	|v	|v	PROPN
ejpam-6264	641	22	(	(	PUNCT
ejpam-6264	641	23	g)|	g)|	NOUN
ejpam-6264	641	24	copies	copy	NOUN
ejpam-6264	641	25	of	of	ADP
ejpam-6264	641	26	h	h	NOUN
ejpam-6264	641	27	,	,	PUNCT
ejpam-6264	641	28	and	and	CCONJ
ejpam-6264	641	29	then	then	ADV
ejpam-6264	641	30	joining	join	VERB
ejpam-6264	641	31	the	the	DET
ejpam-6264	641	32	ith	ith	PROPN
ejpam-6264	641	33	vertex	vertex	NOUN
ejpam-6264	641	34	of	of	ADP
ejpam-6264	641	35	g	g	NOUN
ejpam-6264	641	36	to	to	ADP
ejpam-6264	641	37	every	every	DET
ejpam-6264	641	38	vertex	vertex	NOUN
ejpam-6264	641	39	of	of	ADP
ejpam-6264	641	40	the	the	DET
ejpam-6264	641	41	ith	ith	PROPN
ejpam-6264	641	42	copy	copy	NOUN
ejpam-6264	641	43	of	of	ADP
ejpam-6264	641	44	h.	h.	PROPN
ejpam-6264	641	45	for	for	ADP
ejpam-6264	641	46	convenience	convenience	NOUN
ejpam-6264	641	47	,	,	PUNCT
ejpam-6264	641	48	we	we	PRON
ejpam-6264	641	49	adapt	adapt	VERB
ejpam-6264	641	50	the	the	DET
ejpam-6264	641	51	notation	notation	NOUN
ejpam-6264	641	52	hv	hv	PROPN
ejpam-6264	641	53	+	+	PROPN
ejpam-6264	641	54	v	v	NOUN
ejpam-6264	641	55	used	use	VERB
ejpam-6264	641	56	in	in	ADP
ejpam-6264	641	57	[	[	X
ejpam-6264	641	58	8	8	NUM
ejpam-6264	641	59	]	]	PUNCT
ejpam-6264	641	60	to	to	PART
ejpam-6264	641	61	denote	denote	VERB
ejpam-6264	641	62	the	the	DET
ejpam-6264	641	63	subgraph	subgraph	NOUN
ejpam-6264	641	64	of	of	ADP
ejpam-6264	641	65	g	g	PROPN
ejpam-6264	641	66	◦	◦	NOUN
ejpam-6264	641	67	h	h	NOUN
ejpam-6264	641	68	corresponding	correspond	VERB
ejpam-6264	641	69	to	to	ADP
ejpam-6264	641	70	the	the	DET
ejpam-6264	641	71	join	join	NOUN
ejpam-6264	641	72	hv	hv	PROPN
ejpam-6264	641	73	+	+	CCONJ
ejpam-6264	641	74	⟨{v}⟩	⟨{v}⟩	NOUN
ejpam-6264	641	75	,	,	PUNCT
ejpam-6264	641	76	v	v	ADP
ejpam-6264	641	77	∈	∈	NOUN
ejpam-6264	641	78	v	v	NOUN
ejpam-6264	641	79	(	(	PUNCT
ejpam-6264	641	80	g	g	NOUN
ejpam-6264	641	81	)	)	PUNCT
ejpam-6264	641	82	.	.	PUNCT
ejpam-6264	642	1	proposition	proposition	NOUN
ejpam-6264	642	2	18	18	NUM
ejpam-6264	642	3	.	.	PUNCT
ejpam-6264	643	1	let	let	VERB
ejpam-6264	643	2	g	g	NOUN
ejpam-6264	643	3	and	and	CCONJ
ejpam-6264	643	4	h	h	NOUN
ejpam-6264	643	5	be	be	AUX
ejpam-6264	643	6	nontrivial	nontrivial	ADJ
ejpam-6264	643	7	graphs	graph	NOUN
ejpam-6264	643	8	.	.	PUNCT
ejpam-6264	644	1	let	let	VERB
ejpam-6264	644	2	f	f	PROPN
ejpam-6264	644	3	=	=	SYM
ejpam-6264	644	4	(	(	PUNCT
ejpam-6264	644	5	v0	v0	PROPN
ejpam-6264	644	6	,	,	PUNCT
ejpam-6264	644	7	v1	v1	NOUN
ejpam-6264	644	8	,	,	PUNCT
ejpam-6264	644	9	v2	v2	PROPN
ejpam-6264	644	10	,	,	PUNCT
ejpam-6264	644	11	v3	v3	PROPN
ejpam-6264	644	12	)	)	PUNCT
ejpam-6264	644	13	be	be	VERB
ejpam-6264	644	14	any	any	DET
ejpam-6264	644	15	function	function	NOUN
ejpam-6264	644	16	on	on	ADP
ejpam-6264	644	17	v	v	NOUN
ejpam-6264	644	18	(	(	PUNCT
ejpam-6264	644	19	g	g	PROPN
ejpam-6264	644	20	◦	◦	NOUN
ejpam-6264	644	21	h	h	NOUN
ejpam-6264	644	22	)	)	PUNCT
ejpam-6264	644	23	.	.	PUNCT
ejpam-6264	645	1	then	then	ADV
ejpam-6264	645	2	f	f	PROPN
ejpam-6264	645	3	∈	∈	PROPN
ejpam-6264	645	4	tmrdf	tmrdf	NOUN
ejpam-6264	645	5	(	(	PUNCT
ejpam-6264	645	6	g	g	PROPN
ejpam-6264	645	7	◦	◦	NOUN
ejpam-6264	645	8	h	h	NOUN
ejpam-6264	645	9	)	)	PUNCT
ejpam-6264	645	10	if	if	SCONJ
ejpam-6264	646	1	and	and	CCONJ
ejpam-6264	646	2	only	only	ADV
ejpam-6264	646	3	if	if	SCONJ
ejpam-6264	646	4	each	each	PRON
ejpam-6264	646	5	of	of	ADP
ejpam-6264	646	6	the	the	DET
ejpam-6264	646	7	following	follow	VERB
ejpam-6264	646	8	holds	hold	VERB
ejpam-6264	646	9	:	:	PUNCT
ejpam-6264	646	10	(	(	PUNCT
ejpam-6264	646	11	i	i	NOUN
ejpam-6264	646	12	)	)	PUNCT
ejpam-6264	646	13	for	for	ADP
ejpam-6264	646	14	every	every	PRON
ejpam-6264	646	15	v	v	NOUN
ejpam-6264	646	16	∈	∈	NOUN
ejpam-6264	646	17	(	(	PUNCT
ejpam-6264	646	18	v0	v0	NOUN
ejpam-6264	646	19	∪	∪	X
ejpam-6264	646	20	v1)∩	v1)∩	NOUN
ejpam-6264	646	21	v	v	NOUN
ejpam-6264	646	22	(	(	PUNCT
ejpam-6264	646	23	g	g	NOUN
ejpam-6264	646	24	)	)	PUNCT
ejpam-6264	646	25	,	,	PUNCT
ejpam-6264	646	26	f	f	PROPN
ejpam-6264	646	27	|hv	|hv	PROPN
ejpam-6264	646	28	∈	∈	PROPN
ejpam-6264	646	29	tmrdf	tmrdf	NOUN
ejpam-6264	646	30	(	(	PUNCT
ejpam-6264	646	31	hv	hv	NOUN
ejpam-6264	646	32	)	)	PUNCT
ejpam-6264	646	33	.	.	PUNCT
ejpam-6264	647	1	moreover	moreover	ADV
ejpam-6264	647	2	,	,	PUNCT
ejpam-6264	647	3	if	if	SCONJ
ejpam-6264	647	4	v	v	NUM
ejpam-6264	647	5	∈	∈	PROPN
ejpam-6264	647	6	v0	v0	NOUN
ejpam-6264	647	7	∩	∩	X
ejpam-6264	647	8	v	v	X
ejpam-6264	647	9	(	(	PUNCT
ejpam-6264	647	10	g	g	NOUN
ejpam-6264	647	11	)	)	PUNCT
ejpam-6264	647	12	,	,	PUNCT
ejpam-6264	647	13	then	then	ADV
ejpam-6264	647	14	the	the	DET
ejpam-6264	647	15	following	follow	VERB
ejpam-6264	647	16	holds	hold	VERB
ejpam-6264	647	17	:	:	PUNCT
ejpam-6264	647	18	(	(	PUNCT
ejpam-6264	647	19	a	a	X
ejpam-6264	647	20	)	)	PUNCT
ejpam-6264	647	21	if	if	SCONJ
ejpam-6264	647	22	|v	|v	PROPN
ejpam-6264	647	23	v	v	ADP
ejpam-6264	647	24	2	2	NUM
ejpam-6264	647	25	|	|	ADV
ejpam-6264	647	26	̸=	̸=	PROPN
ejpam-6264	647	27	0	0	NUM
ejpam-6264	647	28	and	and	CCONJ
ejpam-6264	647	29	|v	|v	X
ejpam-6264	647	30	v	v	ADP
ejpam-6264	647	31	3	3	NUM
ejpam-6264	648	1	|	|	ADV
ejpam-6264	648	2	=	=	SYM
ejpam-6264	648	3	0	0	NUM
ejpam-6264	648	4	,	,	PUNCT
ejpam-6264	648	5	then	then	ADV
ejpam-6264	648	6	|ng(v	|ng(v	NOUN
ejpam-6264	648	7	)	)	PUNCT
ejpam-6264	648	8	∩	∩	NOUN
ejpam-6264	648	9	v3|	v3|	NOUN
ejpam-6264	648	10	≥	≥	NUM
ejpam-6264	648	11	1	1	NUM
ejpam-6264	648	12	;	;	PUNCT
ejpam-6264	648	13	and	and	CCONJ
ejpam-6264	648	14	(	(	PUNCT
ejpam-6264	648	15	b	b	X
ejpam-6264	648	16	)	)	PUNCT
ejpam-6264	648	17	if	if	SCONJ
ejpam-6264	648	18	|v	|v	PROPN
ejpam-6264	648	19	v	v	ADP
ejpam-6264	648	20	2	2	NUM
ejpam-6264	648	21	|	|	NOUN
ejpam-6264	648	22	=	=	SYM
ejpam-6264	648	23	0	0	NUM
ejpam-6264	648	24	and	and	CCONJ
ejpam-6264	648	25	|v	|v	X
ejpam-6264	648	26	v	v	ADP
ejpam-6264	648	27	3	3	NUM
ejpam-6264	648	28	|	|	ADV
ejpam-6264	648	29	̸=	̸=	PROPN
ejpam-6264	648	30	0	0	NUM
ejpam-6264	648	31	,	,	PUNCT
ejpam-6264	648	32	then	then	ADV
ejpam-6264	648	33	|ng(v	|ng(v	PROPN
ejpam-6264	648	34	)	)	PUNCT
ejpam-6264	648	35	∩	∩	ADJ
ejpam-6264	648	36	v2|	v2|	X
ejpam-6264	648	37	≥	≥	NUM
ejpam-6264	648	38	1	1	NUM
ejpam-6264	648	39	.	.	PUNCT
ejpam-6264	648	40	(	(	PUNCT
ejpam-6264	648	41	ii	ii	NOUN
ejpam-6264	648	42	)	)	PUNCT
ejpam-6264	648	43	for	for	ADP
ejpam-6264	648	44	every	every	DET
ejpam-6264	648	45	v	v	PROPN
ejpam-6264	648	46	∈	∈	PROPN
ejpam-6264	648	47	v2	v2	NOUN
ejpam-6264	648	48	∩	∩	ADJ
ejpam-6264	648	49	v	v	NOUN
ejpam-6264	648	50	(	(	PUNCT
ejpam-6264	648	51	g	g	NOUN
ejpam-6264	648	52	)	)	PUNCT
ejpam-6264	648	53	,	,	PUNCT
ejpam-6264	648	54	v3	v3	PROPN
ejpam-6264	648	55	∩	∩	PROPN
ejpam-6264	648	56	v	v	PROPN
ejpam-6264	648	57	(	(	PUNCT
ejpam-6264	648	58	hv	hv	X
ejpam-6264	648	59	)	)	PUNCT
ejpam-6264	648	60	is	be	AUX
ejpam-6264	648	61	a	a	DET
ejpam-6264	648	62	dominating	dominating	NOUN
ejpam-6264	648	63	set	set	NOUN
ejpam-6264	648	64	of	of	ADP
ejpam-6264	648	65	⟨v0	⟨v0	PROPN
ejpam-6264	648	66	∩	∩	ADJ
ejpam-6264	648	67	v	v	NOUN
ejpam-6264	648	68	(	(	PUNCT
ejpam-6264	648	69	hv)⟩.	hv)⟩.	NOUN
ejpam-6264	648	70	(	(	PUNCT
ejpam-6264	648	71	iii	iii	NOUN
ejpam-6264	648	72	)	)	PUNCT
ejpam-6264	648	73	for	for	ADP
ejpam-6264	648	74	every	every	DET
ejpam-6264	648	75	v	v	PROPN
ejpam-6264	648	76	∈	∈	PROPN
ejpam-6264	648	77	v3	v3	PROPN
ejpam-6264	648	78	∩	∩	PROPN
ejpam-6264	648	79	v	v	X
ejpam-6264	648	80	(	(	PUNCT
ejpam-6264	648	81	g	g	NOUN
ejpam-6264	648	82	)	)	PUNCT
ejpam-6264	648	83	,	,	PUNCT
ejpam-6264	648	84	v2	v2	PROPN
ejpam-6264	648	85	∩	∩	ADJ
ejpam-6264	648	86	v	v	NOUN
ejpam-6264	648	87	(	(	PUNCT
ejpam-6264	648	88	hv	hv	X
ejpam-6264	648	89	)	)	PUNCT
ejpam-6264	648	90	is	be	AUX
ejpam-6264	648	91	a	a	DET
ejpam-6264	648	92	dominating	dominating	NOUN
ejpam-6264	648	93	set	set	NOUN
ejpam-6264	648	94	of	of	ADP
ejpam-6264	648	95	⟨v0	⟨v0	PROPN
ejpam-6264	648	96	∩	∩	ADJ
ejpam-6264	648	97	v	v	NOUN
ejpam-6264	648	98	(	(	PUNCT
ejpam-6264	648	99	hv)⟩.	hv)⟩.	NOUN
ejpam-6264	648	100	proof	proof	NOUN
ejpam-6264	648	101	.	.	PUNCT
ejpam-6264	649	1	(	(	PUNCT
ejpam-6264	649	2	i	i	NOUN
ejpam-6264	649	3	)	)	PUNCT
ejpam-6264	649	4	suppose	suppose	VERB
ejpam-6264	649	5	f	f	PROPN
ejpam-6264	649	6	∈	∈	PROPN
ejpam-6264	649	7	tmrdf	tmrdf	NOUN
ejpam-6264	649	8	(	(	PUNCT
ejpam-6264	649	9	g	g	PROPN
ejpam-6264	649	10	◦	◦	NOUN
ejpam-6264	649	11	h	h	NOUN
ejpam-6264	649	12	)	)	PUNCT
ejpam-6264	649	13	and	and	CCONJ
ejpam-6264	649	14	let	let	VERB
ejpam-6264	649	15	v	v	X
ejpam-6264	649	16	∈	∈	PROPN
ejpam-6264	649	17	(	(	PUNCT
ejpam-6264	649	18	v0	v0	NOUN
ejpam-6264	649	19	∪	∪	X
ejpam-6264	649	20	v1	v1	NOUN
ejpam-6264	649	21	)	)	PUNCT
ejpam-6264	649	22	∩	∩	ADJ
ejpam-6264	649	23	v	v	X
ejpam-6264	649	24	(	(	PUNCT
ejpam-6264	649	25	g	g	NOUN
ejpam-6264	649	26	)	)	PUNCT
ejpam-6264	649	27	.	.	PUNCT
ejpam-6264	650	1	let	let	VERB
ejpam-6264	650	2	u	u	PRON
ejpam-6264	650	3	∈	∈	PROPN
ejpam-6264	650	4	v	v	ADP
ejpam-6264	650	5	v	v	NOUN
ejpam-6264	650	6	0	0	NUM
ejpam-6264	650	7	.	.	PUNCT
ejpam-6264	651	1	then	then	ADV
ejpam-6264	651	2	u	u	PROPN
ejpam-6264	651	3	∈	∈	PROPN
ejpam-6264	651	4	v0	v0	NOUN
ejpam-6264	651	5	and	and	CCONJ
ejpam-6264	651	6	there	there	PRON
ejpam-6264	651	7	exist	exist	VERB
ejpam-6264	651	8	w	w	PROPN
ejpam-6264	651	9	,	,	PUNCT
ejpam-6264	651	10	z	z	PROPN
ejpam-6264	651	11	∈	∈	PROPN
ejpam-6264	651	12	ng	ng	PROPN
ejpam-6264	651	13	◦	◦	PROPN
ejpam-6264	651	14	h(u	h(u	PROPN
ejpam-6264	651	15	)	)	PUNCT
ejpam-6264	651	16	such	such	ADJ
ejpam-6264	651	17	that	that	SCONJ
ejpam-6264	651	18	w	w	PROPN
ejpam-6264	651	19	∈	∈	PROPN
ejpam-6264	651	20	v2	v2	PROPN
ejpam-6264	651	21	and	and	CCONJ
ejpam-6264	651	22	z	z	NOUN
ejpam-6264	651	23	∈	∈	PROPN
ejpam-6264	651	24	v3	v3	PROPN
ejpam-6264	651	25	.	.	PUNCT
ejpam-6264	652	1	but	but	CCONJ
ejpam-6264	652	2	ng	ng	PROPN
ejpam-6264	652	3	◦	◦	PROPN
ejpam-6264	652	4	h(u	h(u	PROPN
ejpam-6264	652	5	)	)	PUNCT
ejpam-6264	653	1	=	=	PRON
ejpam-6264	653	2	{	{	PUNCT
ejpam-6264	653	3	v	v	NOUN
ejpam-6264	653	4	}	}	PUNCT
ejpam-6264	653	5	∪	∪	ADJ
ejpam-6264	653	6	nhv(u	nhv(u	PROPN
ejpam-6264	653	7	)	)	PUNCT
ejpam-6264	653	8	and	and	CCONJ
ejpam-6264	653	9	v	v	ADP
ejpam-6264	653	10	∈	∈	PROPN
ejpam-6264	653	11	v0	v0	NOUN
ejpam-6264	653	12	∪	∪	X
ejpam-6264	653	13	v1	v1	NOUN
ejpam-6264	653	14	.	.	PUNCT
ejpam-6264	654	1	thus	thus	ADV
ejpam-6264	654	2	,	,	PUNCT
ejpam-6264	654	3	w	w	PROPN
ejpam-6264	654	4	,	,	PUNCT
ejpam-6264	654	5	z	z	PROPN
ejpam-6264	654	6	∈	∈	PROPN
ejpam-6264	654	7	nhv(u	nhv(u	PROPN
ejpam-6264	654	8	)	)	PUNCT
ejpam-6264	654	9	.	.	PUNCT
ejpam-6264	655	1	moreover	moreover	ADV
ejpam-6264	655	2	,	,	PUNCT
ejpam-6264	655	3	let	let	VERB
ejpam-6264	655	4	u	u	PRON
ejpam-6264	655	5	∈	∈	PROPN
ejpam-6264	655	6	v	v	ADP
ejpam-6264	655	7	v	v	ADP
ejpam-6264	655	8	1	1	NUM
ejpam-6264	655	9	.	.	PUNCT
ejpam-6264	656	1	then	then	ADV
ejpam-6264	656	2	u	u	PROPN
ejpam-6264	656	3	∈	∈	PROPN
ejpam-6264	656	4	v1	v1	NOUN
ejpam-6264	656	5	and	and	CCONJ
ejpam-6264	656	6	there	there	PRON
ejpam-6264	656	7	exists	exist	VERB
ejpam-6264	656	8	x	x	X
ejpam-6264	656	9	∈	∈	PROPN
ejpam-6264	656	10	v2	v2	PROPN
ejpam-6264	656	11	∪	∪	X
ejpam-6264	656	12	v3	v3	PROPN
ejpam-6264	656	13	such	such	ADJ
ejpam-6264	656	14	that	that	SCONJ
ejpam-6264	656	15	x	x	SYM
ejpam-6264	656	16	∈	∈	PROPN
ejpam-6264	656	17	ng	ng	PROPN
ejpam-6264	656	18	◦	◦	NOUN
ejpam-6264	656	19	h(u	h(u	PROPN
ejpam-6264	656	20	)	)	PUNCT
ejpam-6264	656	21	,	,	PUNCT
ejpam-6264	656	22	x	x	PUNCT
ejpam-6264	656	23	∈	∈	PROPN
ejpam-6264	656	24	(	(	PUNCT
ejpam-6264	656	25	v	v	NOUN
ejpam-6264	656	26	v	v	ADP
ejpam-6264	656	27	2	2	NUM
ejpam-6264	656	28	∪	∪	NOUN
ejpam-6264	656	29	v	v	NUM
ejpam-6264	656	30	v	v	ADP
ejpam-6264	656	31	3	3	NUM
ejpam-6264	656	32	)	)	PUNCT
ejpam-6264	656	33	and	and	CCONJ
ejpam-6264	656	34	so	so	ADV
ejpam-6264	656	35	x	x	SYM
ejpam-6264	656	36	∈	∈	PROPN
ejpam-6264	656	37	nhv(u	nhv(u	PROPN
ejpam-6264	656	38	)	)	PUNCT
ejpam-6264	656	39	.	.	PUNCT
ejpam-6264	657	1	now	now	ADV
ejpam-6264	657	2	,	,	PUNCT
ejpam-6264	657	3	let	let	VERB
ejpam-6264	657	4	u	u	PRON
ejpam-6264	657	5	∈	∈	PROPN
ejpam-6264	657	6	v	v	ADP
ejpam-6264	657	7	v	v	ADP
ejpam-6264	657	8	2	2	NUM
ejpam-6264	657	9	∪	∪	NOUN
ejpam-6264	657	10	v	v	NUM
ejpam-6264	657	11	v	v	ADP
ejpam-6264	657	12	3	3	NUM
ejpam-6264	657	13	.	.	PUNCT
ejpam-6264	658	1	by	by	ADP
ejpam-6264	658	2	(	(	PUNCT
ejpam-6264	658	3	p3	p3	PROPN
ejpam-6264	658	4	)	)	PUNCT
ejpam-6264	658	5	,	,	PUNCT
ejpam-6264	658	6	there	there	PRON
ejpam-6264	658	7	exists	exist	VERB
ejpam-6264	658	8	z′	z′	NUM
ejpam-6264	658	9	∈	∈	PROPN
ejpam-6264	658	10	v	v	ADP
ejpam-6264	658	11	(	(	PUNCT
ejpam-6264	658	12	hv	hv	PROPN
ejpam-6264	658	13	)	)	PUNCT
ejpam-6264	658	14	\	\	PROPN
ejpam-6264	659	1	v	v	ADP
ejpam-6264	659	2	v	v	NOUN
ejpam-6264	659	3	0	0	NUM
ejpam-6264	659	4	such	such	ADJ
ejpam-6264	659	5	that	that	SCONJ
ejpam-6264	659	6	z	z	PROPN
ejpam-6264	659	7	∈	∈	PROPN
ejpam-6264	659	8	ng	ng	PROPN
ejpam-6264	659	9	◦	◦	NOUN
ejpam-6264	659	10	h(u	h(u	PROPN
ejpam-6264	659	11	)	)	PUNCT
ejpam-6264	659	12	.	.	PUNCT
ejpam-6264	660	1	thus	thus	ADV
ejpam-6264	660	2	,	,	PUNCT
ejpam-6264	660	3	f	f	PROPN
ejpam-6264	660	4	|hv	|hv	PROPN
ejpam-6264	660	5	∈	∈	PROPN
ejpam-6264	660	6	tmrdf	tmrdf	NOUN
ejpam-6264	660	7	(	(	PUNCT
ejpam-6264	660	8	hv	hv	NOUN
ejpam-6264	660	9	)	)	PUNCT
ejpam-6264	660	10	.	.	PUNCT
ejpam-6264	661	1	now	now	ADV
ejpam-6264	661	2	,	,	PUNCT
ejpam-6264	661	3	let	let	VERB
ejpam-6264	661	4	v	v	PRON
ejpam-6264	661	5	∈	∈	PROPN
ejpam-6264	661	6	v0	v0	NOUN
ejpam-6264	661	7	∩	∩	X
ejpam-6264	661	8	v	v	X
ejpam-6264	661	9	(	(	PUNCT
ejpam-6264	661	10	g	g	NOUN
ejpam-6264	661	11	)	)	PUNCT
ejpam-6264	661	12	.	.	PUNCT
ejpam-6264	662	1	suppose	suppose	VERB
ejpam-6264	662	2	that	that	SCONJ
ejpam-6264	662	3	s.	s.	PROPN
ejpam-6264	662	4	ahamad	ahamad	VERB
ejpam-6264	662	5	et	et	PROPN
ejpam-6264	662	6	al	al	PROPN
ejpam-6264	662	7	.	.	PUNCT
ejpam-6264	662	8	/	/	SYM
ejpam-6264	662	9	eur	eur	PROPN
ejpam-6264	662	10	.	.	PUNCT
ejpam-6264	663	1	j.	j.	PROPN
ejpam-6264	663	2	pure	pure	PROPN
ejpam-6264	663	3	appl	appl	PROPN
ejpam-6264	663	4	.	.	PROPN
ejpam-6264	663	5	math	math	PROPN
ejpam-6264	663	6	,	,	PUNCT
ejpam-6264	663	7	18	18	NUM
ejpam-6264	663	8	(	(	PUNCT
ejpam-6264	663	9	4	4	NUM
ejpam-6264	663	10	)	)	PUNCT
ejpam-6264	663	11	(	(	PUNCT
ejpam-6264	663	12	2025	2025	NUM
ejpam-6264	663	13	)	)	PUNCT
ejpam-6264	663	14	,	,	PUNCT
ejpam-6264	663	15	6264	6264	NUM
ejpam-6264	663	16	18	18	NUM
ejpam-6264	663	17	of	of	ADP
ejpam-6264	663	18	20	20	NUM
ejpam-6264	663	19	|v	|v	NOUN
ejpam-6264	663	20	v	v	ADP
ejpam-6264	663	21	2	2	NUM
ejpam-6264	663	22	|	|	ADV
ejpam-6264	663	23	̸=	̸=	PROPN
ejpam-6264	663	24	0	0	NUM
ejpam-6264	663	25	and	and	CCONJ
ejpam-6264	663	26	|v	|v	X
ejpam-6264	663	27	v	v	ADP
ejpam-6264	663	28	3	3	NUM
ejpam-6264	663	29	|	|	ADV
ejpam-6264	663	30	=	=	NOUN
ejpam-6264	663	31	0	0	X
ejpam-6264	663	32	.	.	PUNCT
ejpam-6264	664	1	then	then	ADV
ejpam-6264	664	2	u	u	PROPN
ejpam-6264	664	3	∈	∈	PROPN
ejpam-6264	664	4	ng	ng	PROPN
ejpam-6264	664	5	◦	◦	NOUN
ejpam-6264	664	6	h(v	h(v	NOUN
ejpam-6264	664	7	)	)	PUNCT
ejpam-6264	664	8	and	and	CCONJ
ejpam-6264	664	9	u	u	PROPN
ejpam-6264	664	10	∈	∈	PROPN
ejpam-6264	664	11	v3	v3	PROPN
ejpam-6264	664	12	.	.	PUNCT
ejpam-6264	665	1	hence	hence	ADV
ejpam-6264	665	2	,	,	PUNCT
ejpam-6264	665	3	u	u	PROPN
ejpam-6264	665	4	∈	∈	PROPN
ejpam-6264	665	5	ng(v	ng(v	PUNCT
ejpam-6264	665	6	)	)	PUNCT
ejpam-6264	665	7	∩	∩	PROPN
ejpam-6264	665	8	v3	v3	PROPN
ejpam-6264	665	9	.	.	PUNCT
ejpam-6264	666	1	thus	thus	ADV
ejpam-6264	666	2	,	,	PUNCT
ejpam-6264	666	3	|ng(v)∩	|ng(v)∩	PROPN
ejpam-6264	666	4	v3|	v3|	NOUN
ejpam-6264	666	5	≥	≥	NUM
ejpam-6264	666	6	1	1	NUM
ejpam-6264	666	7	.	.	PUNCT
ejpam-6264	666	8	following	follow	VERB
ejpam-6264	666	9	similar	similar	ADJ
ejpam-6264	666	10	argument	argument	NOUN
ejpam-6264	666	11	,	,	PUNCT
ejpam-6264	666	12	if	if	SCONJ
ejpam-6264	666	13	|v	|v	PROPN
ejpam-6264	666	14	v	v	ADP
ejpam-6264	666	15	3	3	NUM
ejpam-6264	666	16	|	|	ADV
ejpam-6264	666	17	̸=	̸=	PROPN
ejpam-6264	666	18	0	0	NUM
ejpam-6264	666	19	and	and	CCONJ
ejpam-6264	666	20	|v	|v	X
ejpam-6264	666	21	v	v	ADP
ejpam-6264	666	22	2	2	NUM
ejpam-6264	667	1	|	|	NOUN
ejpam-6264	667	2	=	=	SYM
ejpam-6264	667	3	0	0	NUM
ejpam-6264	667	4	,	,	PUNCT
ejpam-6264	667	5	|ng(v)∩	|ng(v)∩	PROPN
ejpam-6264	667	6	v2|	v2|	X
ejpam-6264	667	7	≥	≥	NUM
ejpam-6264	667	8	1	1	NUM
ejpam-6264	667	9	.	.	PUNCT
ejpam-6264	668	1	this	this	PRON
ejpam-6264	668	2	proves	prove	VERB
ejpam-6264	668	3	(	(	PUNCT
ejpam-6264	668	4	i	i	NOUN
ejpam-6264	668	5	)	)	PUNCT
ejpam-6264	668	6	.	.	PUNCT
ejpam-6264	669	1	suppose	suppose	VERB
ejpam-6264	669	2	that	that	SCONJ
ejpam-6264	669	3	v	v	NUM
ejpam-6264	669	4	∈	∈	PROPN
ejpam-6264	669	5	v2	v2	PROPN
ejpam-6264	669	6	∩	∩	ADJ
ejpam-6264	669	7	v	v	NOUN
ejpam-6264	669	8	(	(	PUNCT
ejpam-6264	669	9	g	g	NOUN
ejpam-6264	669	10	)	)	PUNCT
ejpam-6264	669	11	and	and	CCONJ
ejpam-6264	669	12	let	let	VERB
ejpam-6264	669	13	u	u	PRON
ejpam-6264	669	14	∈	∈	PROPN
ejpam-6264	669	15	v	v	ADP
ejpam-6264	669	16	v	v	NOUN
ejpam-6264	669	17	0	0	NUM
ejpam-6264	669	18	.	.	PUNCT
ejpam-6264	670	1	by	by	ADP
ejpam-6264	670	2	definition	definition	NOUN
ejpam-6264	670	3	,	,	PUNCT
ejpam-6264	670	4	there	there	PRON
ejpam-6264	670	5	exists	exist	VERB
ejpam-6264	670	6	{	{	PUNCT
ejpam-6264	670	7	x	x	NOUN
ejpam-6264	670	8	,	,	PUNCT
ejpam-6264	670	9	y	y	PROPN
ejpam-6264	670	10	}	}	PUNCT
ejpam-6264	670	11	⊆	⊆	NUM
ejpam-6264	670	12	ng	ng	PROPN
ejpam-6264	670	13	◦	◦	NOUN
ejpam-6264	670	14	h(u	h(u	PROPN
ejpam-6264	670	15	)	)	PUNCT
ejpam-6264	671	1	=	=	PRON
ejpam-6264	671	2	{	{	PUNCT
ejpam-6264	671	3	v	v	NOUN
ejpam-6264	671	4	}	}	PUNCT
ejpam-6264	671	5	+	+	CCONJ
ejpam-6264	671	6	nhv(u	nhv(u	ADJ
ejpam-6264	671	7	)	)	PUNCT
ejpam-6264	671	8	such	such	ADJ
ejpam-6264	671	9	that	that	SCONJ
ejpam-6264	671	10	x	x	SYM
ejpam-6264	671	11	∈	∈	PROPN
ejpam-6264	671	12	v2	v2	PROPN
ejpam-6264	671	13	and	and	CCONJ
ejpam-6264	671	14	y	y	PROPN
ejpam-6264	671	15	∈	∈	PROPN
ejpam-6264	671	16	v3	v3	PROPN
ejpam-6264	671	17	.	.	PUNCT
ejpam-6264	672	1	if	if	SCONJ
ejpam-6264	672	2	v	v	NUM
ejpam-6264	672	3	∈	∈	PROPN
ejpam-6264	672	4	v2	v2	NOUN
ejpam-6264	672	5	and	and	CCONJ
ejpam-6264	672	6	take	take	VERB
ejpam-6264	672	7	x	x	NOUN
ejpam-6264	672	8	=	=	SYM
ejpam-6264	672	9	v	v	NOUN
ejpam-6264	672	10	,	,	PUNCT
ejpam-6264	672	11	then	then	ADV
ejpam-6264	672	12	y	y	PROPN
ejpam-6264	672	13	∈	∈	PROPN
ejpam-6264	672	14	v	v	ADP
ejpam-6264	672	15	v	v	NOUN
ejpam-6264	672	16	3	3	NUM
ejpam-6264	672	17	and	and	CCONJ
ejpam-6264	672	18	y	y	PROPN
ejpam-6264	672	19	∈	∈	PROPN
ejpam-6264	672	20	nhv(u	nhv(u	PROPN
ejpam-6264	672	21	)	)	PUNCT
ejpam-6264	672	22	.	.	PUNCT
ejpam-6264	673	1	thus	thus	ADV
ejpam-6264	673	2	,	,	PUNCT
ejpam-6264	673	3	v	v	X
ejpam-6264	673	4	v	v	NOUN
ejpam-6264	673	5	3	3	NUM
ejpam-6264	673	6	dominates	dominate	VERB
ejpam-6264	673	7	v	v	ADP
ejpam-6264	673	8	v	v	NOUN
ejpam-6264	673	9	0	0	NUM
ejpam-6264	673	10	.	.	PUNCT
ejpam-6264	674	1	hence	hence	ADV
ejpam-6264	674	2	,	,	PUNCT
ejpam-6264	674	3	v3	v3	PROPN
ejpam-6264	674	4	∩	∩	PROPN
ejpam-6264	674	5	v	v	PROPN
ejpam-6264	674	6	(	(	PUNCT
ejpam-6264	674	7	hv	hv	X
ejpam-6264	674	8	)	)	PUNCT
ejpam-6264	674	9	is	be	AUX
ejpam-6264	674	10	a	a	DET
ejpam-6264	674	11	dominating	dominating	NOUN
ejpam-6264	674	12	set	set	NOUN
ejpam-6264	674	13	of	of	ADP
ejpam-6264	674	14	⟨v0	⟨v0	PROPN
ejpam-6264	674	15	∩	∩	ADJ
ejpam-6264	674	16	v	v	NOUN
ejpam-6264	674	17	(	(	PUNCT
ejpam-6264	674	18	hv)⟩.	hv)⟩.	NOUN
ejpam-6264	674	19	this	this	PRON
ejpam-6264	674	20	proves	prove	VERB
ejpam-6264	674	21	(	(	PUNCT
ejpam-6264	674	22	ii	ii	NOUN
ejpam-6264	674	23	)	)	PUNCT
ejpam-6264	674	24	.	.	PUNCT
ejpam-6264	675	1	similarly	similarly	ADV
ejpam-6264	675	2	,	,	PUNCT
ejpam-6264	675	3	(	(	PUNCT
ejpam-6264	675	4	iii	iii	NOUN
ejpam-6264	675	5	)	)	PUNCT
ejpam-6264	675	6	follows	follow	VERB
ejpam-6264	675	7	.	.	PUNCT
ejpam-6264	676	1	conversely	conversely	ADV
ejpam-6264	676	2	,	,	PUNCT
ejpam-6264	676	3	suppose	suppose	VERB
ejpam-6264	676	4	(	(	PUNCT
ejpam-6264	676	5	i	i	NOUN
ejpam-6264	676	6	)	)	PUNCT
ejpam-6264	676	7	,	,	PUNCT
ejpam-6264	676	8	(	(	PUNCT
ejpam-6264	676	9	ii	ii	NOUN
ejpam-6264	676	10	)	)	PUNCT
ejpam-6264	676	11	and	and	CCONJ
ejpam-6264	676	12	(	(	PUNCT
ejpam-6264	676	13	iii	iii	X
ejpam-6264	676	14	)	)	PUNCT
ejpam-6264	676	15	hold	hold	VERB
ejpam-6264	676	16	for	for	ADP
ejpam-6264	676	17	f	f	PROPN
ejpam-6264	676	18	.	.	PUNCT
ejpam-6264	677	1	let	let	VERB
ejpam-6264	677	2	u	u	PRON
ejpam-6264	677	3	∈	∈	PROPN
ejpam-6264	677	4	v0	v0	NOUN
ejpam-6264	677	5	and	and	CCONJ
ejpam-6264	677	6	v	v	ADP
ejpam-6264	677	7	∈	∈	PROPN
ejpam-6264	677	8	v	v	NOUN
ejpam-6264	677	9	(	(	PUNCT
ejpam-6264	677	10	g	g	NOUN
ejpam-6264	677	11	)	)	PUNCT
ejpam-6264	677	12	for	for	ADP
ejpam-6264	677	13	which	which	PRON
ejpam-6264	677	14	u	u	PROPN
ejpam-6264	677	15	∈	∈	PROPN
ejpam-6264	677	16	v	v	NOUN
ejpam-6264	677	17	(	(	PUNCT
ejpam-6264	677	18	hv	hv	PROPN
ejpam-6264	677	19	+	+	PROPN
ejpam-6264	677	20	v	v	NOUN
ejpam-6264	677	21	)	)	PUNCT
ejpam-6264	677	22	.	.	PUNCT
ejpam-6264	678	1	consider	consider	VERB
ejpam-6264	678	2	the	the	DET
ejpam-6264	678	3	following	follow	VERB
ejpam-6264	678	4	cases	case	NOUN
ejpam-6264	678	5	:	:	PUNCT
ejpam-6264	678	6	case	case	NOUN
ejpam-6264	678	7	1	1	NUM
ejpam-6264	678	8	:	:	PUNCT
ejpam-6264	678	9	suppose	suppose	VERB
ejpam-6264	678	10	u	u	PROPN
ejpam-6264	678	11	=	=	NOUN
ejpam-6264	678	12	v.	v.	PROPN
ejpam-6264	678	13	by	by	ADP
ejpam-6264	678	14	(	(	PUNCT
ejpam-6264	678	15	i	i	PROPN
ejpam-6264	678	16	)	)	PUNCT
ejpam-6264	678	17	,	,	PUNCT
ejpam-6264	678	18	f	f	PROPN
ejpam-6264	678	19	|hv	|hv	PROPN
ejpam-6264	678	20	∈	∈	PROPN
ejpam-6264	678	21	tmrdf	tmrdf	NOUN
ejpam-6264	678	22	(	(	PUNCT
ejpam-6264	678	23	hv	hv	NOUN
ejpam-6264	678	24	)	)	PUNCT
ejpam-6264	678	25	.	.	PUNCT
ejpam-6264	679	1	thus	thus	ADV
ejpam-6264	679	2	,	,	PUNCT
ejpam-6264	679	3	there	there	PRON
ejpam-6264	679	4	exist	exist	VERB
ejpam-6264	679	5	w	w	NOUN
ejpam-6264	679	6	,	,	PUNCT
ejpam-6264	679	7	z	z	PROPN
ejpam-6264	679	8	∈	∈	PROPN
ejpam-6264	679	9	nhv(u	nhv(u	PROPN
ejpam-6264	679	10	)	)	PUNCT
ejpam-6264	679	11	such	such	ADJ
ejpam-6264	679	12	that	that	SCONJ
ejpam-6264	679	13	w	w	PROPN
ejpam-6264	679	14	∈	∈	PROPN
ejpam-6264	679	15	v	v	ADP
ejpam-6264	679	16	v	v	NOUN
ejpam-6264	679	17	2	2	NUM
ejpam-6264	679	18	and	and	CCONJ
ejpam-6264	679	19	z	z	NOUN
ejpam-6264	679	20	∈	∈	PROPN
ejpam-6264	679	21	v	v	ADP
ejpam-6264	679	22	v	v	NOUN
ejpam-6264	679	23	3	3	NUM
ejpam-6264	679	24	.	.	PUNCT
ejpam-6264	680	1	hence	hence	ADV
ejpam-6264	680	2	,	,	PUNCT
ejpam-6264	680	3	w	w	PROPN
ejpam-6264	680	4	∈	∈	PROPN
ejpam-6264	680	5	v2	v2	PROPN
ejpam-6264	680	6	and	and	CCONJ
ejpam-6264	680	7	z	z	NOUN
ejpam-6264	680	8	∈	∈	PROPN
ejpam-6264	680	9	v3	v3	PROPN
ejpam-6264	680	10	and	and	CCONJ
ejpam-6264	680	11	w	w	PROPN
ejpam-6264	680	12	,	,	PUNCT
ejpam-6264	680	13	z	z	PROPN
ejpam-6264	680	14	∈	∈	PROPN
ejpam-6264	680	15	ng	ng	PROPN
ejpam-6264	680	16	◦	◦	NOUN
ejpam-6264	680	17	h(u	h(u	PROPN
ejpam-6264	680	18	)	)	PUNCT
ejpam-6264	680	19	.	.	PUNCT
ejpam-6264	681	1	now	now	ADV
ejpam-6264	681	2	,	,	PUNCT
ejpam-6264	681	3	if	if	SCONJ
ejpam-6264	681	4	|v	|v	PROPN
ejpam-6264	681	5	v	v	ADP
ejpam-6264	681	6	3	3	NUM
ejpam-6264	681	7	|	|	ADV
ejpam-6264	681	8	̸=	̸=	PROPN
ejpam-6264	681	9	0	0	NUM
ejpam-6264	681	10	and	and	CCONJ
ejpam-6264	681	11	|v	|v	X
ejpam-6264	681	12	v	v	ADP
ejpam-6264	681	13	2	2	NUM
ejpam-6264	682	1	|	|	NOUN
ejpam-6264	682	2	=	=	SYM
ejpam-6264	682	3	0	0	NUM
ejpam-6264	682	4	,	,	PUNCT
ejpam-6264	682	5	then	then	ADV
ejpam-6264	682	6	by	by	ADP
ejpam-6264	682	7	(	(	PUNCT
ejpam-6264	682	8	i)(a	i)(a	NOUN
ejpam-6264	682	9	)	)	PUNCT
ejpam-6264	682	10	,	,	PUNCT
ejpam-6264	682	11	|ng(u	|ng(u	X
ejpam-6264	682	12	)	)	PUNCT
ejpam-6264	682	13	∩	∩	ADJ
ejpam-6264	682	14	v2|	v2|	X
ejpam-6264	682	15	≥	≥	NUM
ejpam-6264	682	16	1	1	NUM
ejpam-6264	682	17	.	.	PUNCT
ejpam-6264	683	1	hence	hence	ADV
ejpam-6264	683	2	,	,	PUNCT
ejpam-6264	683	3	there	there	PRON
ejpam-6264	683	4	exist	exist	VERB
ejpam-6264	683	5	z	z	NOUN
ejpam-6264	683	6	∈	∈	PROPN
ejpam-6264	683	7	v	v	ADP
ejpam-6264	683	8	v	v	NOUN
ejpam-6264	683	9	3	3	NUM
ejpam-6264	683	10	and	and	CCONJ
ejpam-6264	683	11	w	w	PROPN
ejpam-6264	683	12	∈	∈	PROPN
ejpam-6264	683	13	ng(u	ng(u	NOUN
ejpam-6264	683	14	)	)	PUNCT
ejpam-6264	683	15	∩	∩	ADJ
ejpam-6264	683	16	v2	v2	PROPN
ejpam-6264	683	17	and	and	CCONJ
ejpam-6264	683	18	w	w	NOUN
ejpam-6264	683	19	,	,	PUNCT
ejpam-6264	683	20	z	z	PROPN
ejpam-6264	683	21	∈	∈	PROPN
ejpam-6264	683	22	ng	ng	PROPN
ejpam-6264	683	23	◦	◦	NOUN
ejpam-6264	683	24	h(u	h(u	PROPN
ejpam-6264	683	25	)	)	PUNCT
ejpam-6264	683	26	.	.	PUNCT
ejpam-6264	684	1	similarly	similarly	ADV
ejpam-6264	684	2	,	,	PUNCT
ejpam-6264	684	3	if	if	SCONJ
ejpam-6264	684	4	|v	|v	PROPN
ejpam-6264	684	5	v	v	ADP
ejpam-6264	684	6	2	2	NUM
ejpam-6264	684	7	|	|	ADV
ejpam-6264	684	8	̸=	̸=	PROPN
ejpam-6264	684	9	0	0	NUM
ejpam-6264	684	10	and	and	CCONJ
ejpam-6264	684	11	|v	|v	X
ejpam-6264	684	12	v	v	ADP
ejpam-6264	684	13	3	3	NUM
ejpam-6264	685	1	|	|	ADV
ejpam-6264	685	2	=	=	SYM
ejpam-6264	685	3	0	0	NUM
ejpam-6264	685	4	,	,	PUNCT
ejpam-6264	685	5	then	then	ADV
ejpam-6264	685	6	by	by	ADP
ejpam-6264	685	7	(	(	PUNCT
ejpam-6264	685	8	i)(b	i)(b	NUM
ejpam-6264	685	9	)	)	PUNCT
ejpam-6264	685	10	,	,	PUNCT
ejpam-6264	685	11	|ng(u	|ng(u	X
ejpam-6264	685	12	)	)	PUNCT
ejpam-6264	685	13	∩	∩	NOUN
ejpam-6264	685	14	v3|	v3|	X
ejpam-6264	685	15	≥	≥	NUM
ejpam-6264	685	16	1	1	NUM
ejpam-6264	685	17	.	.	PUNCT
ejpam-6264	686	1	so	so	ADV
ejpam-6264	686	2	,	,	PUNCT
ejpam-6264	686	3	there	there	PRON
ejpam-6264	686	4	exist	exist	VERB
ejpam-6264	686	5	w	w	PRON
ejpam-6264	686	6	∈	∈	PROPN
ejpam-6264	686	7	v	v	ADP
ejpam-6264	686	8	v	v	NOUN
ejpam-6264	686	9	2	2	NUM
ejpam-6264	686	10	and	and	CCONJ
ejpam-6264	686	11	z	z	NOUN
ejpam-6264	686	12	∈	∈	PROPN
ejpam-6264	686	13	ng(v	ng(v	PUNCT
ejpam-6264	686	14	)	)	PUNCT
ejpam-6264	686	15	∩	∩	PROPN
ejpam-6264	686	16	v3	v3	VERB
ejpam-6264	686	17	such	such	ADJ
ejpam-6264	686	18	that	that	SCONJ
ejpam-6264	686	19	w	w	NOUN
ejpam-6264	686	20	,	,	PUNCT
ejpam-6264	686	21	z	z	PROPN
ejpam-6264	686	22	∈	∈	PROPN
ejpam-6264	686	23	ng	ng	PROPN
ejpam-6264	686	24	◦	◦	NOUN
ejpam-6264	686	25	h(u	h(u	PROPN
ejpam-6264	686	26	)	)	PUNCT
ejpam-6264	686	27	.	.	PUNCT
ejpam-6264	687	1	case	case	NOUN
ejpam-6264	687	2	2	2	NUM
ejpam-6264	687	3	:	:	PUNCT
ejpam-6264	687	4	suppose	suppose	VERB
ejpam-6264	687	5	u	u	PRON
ejpam-6264	687	6	̸=	̸=	PROPN
ejpam-6264	687	7	v.	v.	CCONJ
ejpam-6264	687	8	then	then	ADV
ejpam-6264	687	9	u	u	PROPN
ejpam-6264	687	10	∈	∈	PROPN
ejpam-6264	687	11	v	v	ADP
ejpam-6264	687	12	v	v	NOUN
ejpam-6264	687	13	0	0	NUM
ejpam-6264	687	14	.	.	PUNCT
ejpam-6264	688	1	let	let	VERB
ejpam-6264	688	2	v	v	NUM
ejpam-6264	688	3	∈	∈	PROPN
ejpam-6264	688	4	v1∩v	v1∩v	NOUN
ejpam-6264	688	5	(	(	PUNCT
ejpam-6264	688	6	g	g	NOUN
ejpam-6264	688	7	)	)	PUNCT
ejpam-6264	688	8	.	.	PUNCT
ejpam-6264	689	1	by	by	ADP
ejpam-6264	689	2	(	(	PUNCT
ejpam-6264	689	3	i	i	NOUN
ejpam-6264	689	4	)	)	PUNCT
ejpam-6264	689	5	,	,	PUNCT
ejpam-6264	689	6	f	f	PROPN
ejpam-6264	689	7	|hv	|hv	PROPN
ejpam-6264	689	8	∈	∈	PROPN
ejpam-6264	689	9	tmrdf	tmrdf	NOUN
ejpam-6264	689	10	(	(	PUNCT
ejpam-6264	689	11	g	g	NOUN
ejpam-6264	689	12	◦	◦	NOUN
ejpam-6264	689	13	h	h	NOUN
ejpam-6264	689	14	)	)	PUNCT
ejpam-6264	689	15	.	.	PUNCT
ejpam-6264	690	1	thus	thus	ADV
ejpam-6264	690	2	,	,	PUNCT
ejpam-6264	690	3	there	there	PRON
ejpam-6264	690	4	exist	exist	VERB
ejpam-6264	690	5	w	w	NOUN
ejpam-6264	690	6	,	,	PUNCT
ejpam-6264	690	7	z	z	PROPN
ejpam-6264	690	8	∈	∈	PROPN
ejpam-6264	690	9	nhv(u	nhv(u	PROPN
ejpam-6264	690	10	)	)	PUNCT
ejpam-6264	690	11	such	such	ADJ
ejpam-6264	690	12	that	that	SCONJ
ejpam-6264	690	13	w	w	PROPN
ejpam-6264	690	14	∈	∈	PROPN
ejpam-6264	690	15	v	v	ADP
ejpam-6264	690	16	v	v	NOUN
ejpam-6264	690	17	2	2	NUM
ejpam-6264	690	18	and	and	CCONJ
ejpam-6264	690	19	z	z	NOUN
ejpam-6264	690	20	∈	∈	PROPN
ejpam-6264	690	21	v	v	ADP
ejpam-6264	690	22	v	v	NOUN
ejpam-6264	690	23	3	3	NUM
ejpam-6264	690	24	.	.	PUNCT
ejpam-6264	691	1	if	if	SCONJ
ejpam-6264	691	2	v	v	NUM
ejpam-6264	691	3	∈	∈	PROPN
ejpam-6264	691	4	v2	v2	PROPN
ejpam-6264	691	5	∩	∩	ADJ
ejpam-6264	691	6	v	v	NOUN
ejpam-6264	691	7	(	(	PUNCT
ejpam-6264	691	8	g	g	NOUN
ejpam-6264	691	9	)	)	PUNCT
ejpam-6264	691	10	.	.	PUNCT
ejpam-6264	692	1	by	by	ADP
ejpam-6264	692	2	(	(	PUNCT
ejpam-6264	692	3	ii	ii	NOUN
ejpam-6264	692	4	)	)	PUNCT
ejpam-6264	692	5	,	,	PUNCT
ejpam-6264	692	6	v	v	X
ejpam-6264	692	7	v	v	NOUN
ejpam-6264	692	8	3	3	NUM
ejpam-6264	692	9	dominates	dominate	VERB
ejpam-6264	692	10	v	v	ADP
ejpam-6264	692	11	v	v	NOUN
ejpam-6264	692	12	0	0	NUM
ejpam-6264	692	13	.	.	PUNCT
ejpam-6264	693	1	hence	hence	ADV
ejpam-6264	693	2	,	,	PUNCT
ejpam-6264	693	3	there	there	PRON
ejpam-6264	693	4	exist	exist	VERB
ejpam-6264	693	5	w	w	PROPN
ejpam-6264	693	6	,	,	PUNCT
ejpam-6264	693	7	v	v	NOUN
ejpam-6264	693	8	∈	∈	PROPN
ejpam-6264	693	9	nhv(u	nhv(u	PROPN
ejpam-6264	693	10	)	)	PUNCT
ejpam-6264	693	11	such	such	ADJ
ejpam-6264	693	12	that	that	SCONJ
ejpam-6264	693	13	w	w	PROPN
ejpam-6264	693	14	∈	∈	PROPN
ejpam-6264	693	15	v	v	ADP
ejpam-6264	693	16	v	v	NOUN
ejpam-6264	693	17	3	3	NUM
ejpam-6264	693	18	.	.	PUNCT
ejpam-6264	694	1	also	also	ADV
ejpam-6264	694	2	,	,	PUNCT
ejpam-6264	694	3	if	if	SCONJ
ejpam-6264	694	4	v	v	PROPN
ejpam-6264	694	5	∈	∈	PROPN
ejpam-6264	694	6	v3	v3	PROPN
ejpam-6264	694	7	∩	∩	PROPN
ejpam-6264	694	8	v	v	X
ejpam-6264	694	9	(	(	PUNCT
ejpam-6264	694	10	g	g	NOUN
ejpam-6264	694	11	)	)	PUNCT
ejpam-6264	694	12	.	.	PUNCT
ejpam-6264	695	1	by	by	ADP
ejpam-6264	695	2	(	(	PUNCT
ejpam-6264	695	3	iii	iii	NOUN
ejpam-6264	695	4	)	)	PUNCT
ejpam-6264	695	5	,	,	PUNCT
ejpam-6264	695	6	v	v	NOUN
ejpam-6264	695	7	v	v	PRON
ejpam-6264	695	8	2	2	NUM
ejpam-6264	695	9	dominates	dominate	VERB
ejpam-6264	695	10	v	v	ADP
ejpam-6264	695	11	v	v	NOUN
ejpam-6264	695	12	0	0	NUM
ejpam-6264	695	13	.	.	PUNCT
ejpam-6264	696	1	thus	thus	ADV
ejpam-6264	696	2	,	,	PUNCT
ejpam-6264	696	3	there	there	PRON
ejpam-6264	696	4	exist	exist	VERB
ejpam-6264	696	5	w	w	PROPN
ejpam-6264	696	6	,	,	PUNCT
ejpam-6264	696	7	v	v	NOUN
ejpam-6264	696	8	∈	∈	PROPN
ejpam-6264	696	9	nhv(u	nhv(u	PROPN
ejpam-6264	696	10	)	)	PUNCT
ejpam-6264	696	11	such	such	ADJ
ejpam-6264	696	12	that	that	SCONJ
ejpam-6264	696	13	w	w	PROPN
ejpam-6264	696	14	∈	∈	PROPN
ejpam-6264	696	15	v	v	ADP
ejpam-6264	696	16	v	v	ADP
ejpam-6264	696	17	2	2	NUM
ejpam-6264	696	18	.	.	PUNCT
ejpam-6264	697	1	case	case	NOUN
ejpam-6264	697	2	1	1	NUM
ejpam-6264	697	3	and	and	CCONJ
ejpam-6264	697	4	case	case	NOUN
ejpam-6264	697	5	2	2	NUM
ejpam-6264	697	6	shows	show	VERB
ejpam-6264	697	7	that	that	SCONJ
ejpam-6264	697	8	there	there	PRON
ejpam-6264	697	9	exist	exist	VERB
ejpam-6264	697	10	w	w	PROPN
ejpam-6264	697	11	∈	∈	PROPN
ejpam-6264	697	12	v2	v2	PROPN
ejpam-6264	697	13	and	and	CCONJ
ejpam-6264	697	14	z	z	PROPN
ejpam-6264	697	15	∈	∈	PROPN
ejpam-6264	697	16	v3	v3	PROPN
ejpam-6264	697	17	such	such	ADJ
ejpam-6264	697	18	that	that	PRON
ejpam-6264	697	19	w	w	NOUN
ejpam-6264	697	20	,	,	PUNCT
ejpam-6264	697	21	z	z	PROPN
ejpam-6264	697	22	∈	∈	PROPN
ejpam-6264	697	23	ng	ng	PROPN
ejpam-6264	697	24	◦	◦	NOUN
ejpam-6264	697	25	h(u	h(u	PROPN
ejpam-6264	697	26	)	)	PUNCT
ejpam-6264	697	27	.	.	PUNCT
ejpam-6264	698	1	now	now	ADV
ejpam-6264	698	2	,	,	PUNCT
ejpam-6264	698	3	let	let	VERB
ejpam-6264	698	4	u	u	PRON
ejpam-6264	698	5	∈	∈	PROPN
ejpam-6264	698	6	v1	v1	NOUN
ejpam-6264	698	7	.	.	PUNCT
ejpam-6264	699	1	if	if	SCONJ
ejpam-6264	699	2	u	u	PROPN
ejpam-6264	699	3	∈	∈	PROPN
ejpam-6264	699	4	v	v	X
ejpam-6264	699	5	(	(	PUNCT
ejpam-6264	699	6	g	g	NOUN
ejpam-6264	699	7	)	)	PUNCT
ejpam-6264	699	8	,	,	PUNCT
ejpam-6264	699	9	then	then	ADV
ejpam-6264	699	10	there	there	PRON
ejpam-6264	699	11	exist	exist	VERB
ejpam-6264	699	12	x	x	PUNCT
ejpam-6264	699	13	∈	∈	PROPN
ejpam-6264	699	14	v	v	NUM
ejpam-6264	699	15	u	u	NOUN
ejpam-6264	699	16	2	2	NUM
ejpam-6264	699	17	∪	∪	X
ejpam-6264	699	18	v	v	NUM
ejpam-6264	699	19	u	u	NOUN
ejpam-6264	699	20	3	3	NUM
ejpam-6264	699	21	such	such	ADJ
ejpam-6264	699	22	that	that	SCONJ
ejpam-6264	699	23	x	x	SYM
ejpam-6264	699	24	∈	∈	PROPN
ejpam-6264	699	25	nhu(u	nhu(u	NOUN
ejpam-6264	699	26	)	)	PUNCT
ejpam-6264	699	27	since	since	SCONJ
ejpam-6264	699	28	f	f	PROPN
ejpam-6264	699	29	|hu	|hu	NUM
ejpam-6264	699	30	∈	∈	PROPN
ejpam-6264	699	31	tmrdf	tmrdf	NOUN
ejpam-6264	699	32	(	(	PUNCT
ejpam-6264	699	33	hu	hu	PROPN
ejpam-6264	699	34	)	)	PUNCT
ejpam-6264	699	35	.	.	PUNCT
ejpam-6264	700	1	this	this	PRON
ejpam-6264	700	2	implies	imply	VERB
ejpam-6264	700	3	that	that	SCONJ
ejpam-6264	700	4	x	x	PUNCT
ejpam-6264	700	5	∈	∈	PROPN
ejpam-6264	700	6	v2	v2	NOUN
ejpam-6264	700	7	∪	∪	X
ejpam-6264	700	8	v3	v3	PROPN
ejpam-6264	700	9	and	and	CCONJ
ejpam-6264	700	10	x	x	PUNCT
ejpam-6264	700	11	∈	∈	PROPN
ejpam-6264	700	12	ng	ng	PROPN
ejpam-6264	700	13	◦	◦	NOUN
ejpam-6264	700	14	h(u	h(u	PROPN
ejpam-6264	700	15	)	)	PUNCT
ejpam-6264	700	16	.	.	PUNCT
ejpam-6264	701	1	suppose	suppose	VERB
ejpam-6264	701	2	u	u	PRON
ejpam-6264	701	3	∈	∈	PROPN
ejpam-6264	701	4	v	v	ADP
ejpam-6264	701	5	(	(	PUNCT
ejpam-6264	701	6	hv	hv	PROPN
ejpam-6264	701	7	)	)	PUNCT
ejpam-6264	701	8	for	for	ADP
ejpam-6264	701	9	some	some	DET
ejpam-6264	701	10	v	v	ADP
ejpam-6264	701	11	∈	∈	PROPN
ejpam-6264	701	12	v	v	NOUN
ejpam-6264	701	13	(	(	PUNCT
ejpam-6264	701	14	g	g	NOUN
ejpam-6264	701	15	)	)	PUNCT
ejpam-6264	701	16	.	.	PUNCT
ejpam-6264	702	1	if	if	SCONJ
ejpam-6264	702	2	v	v	NUM
ejpam-6264	702	3	∈	∈	PROPN
ejpam-6264	702	4	(	(	PUNCT
ejpam-6264	702	5	v2	v2	PROPN
ejpam-6264	702	6	∪	∪	X
ejpam-6264	702	7	v3	v3	PROPN
ejpam-6264	702	8	)	)	PUNCT
ejpam-6264	702	9	∩	∩	PROPN
ejpam-6264	702	10	v	v	X
ejpam-6264	702	11	(	(	PUNCT
ejpam-6264	702	12	g	g	NOUN
ejpam-6264	702	13	)	)	PUNCT
ejpam-6264	702	14	,	,	PUNCT
ejpam-6264	702	15	then	then	ADV
ejpam-6264	702	16	v	v	X
ejpam-6264	702	17	∈	∈	PROPN
ejpam-6264	702	18	(	(	PUNCT
ejpam-6264	702	19	v2	v2	PROPN
ejpam-6264	702	20	∪	∪	X
ejpam-6264	702	21	v3	v3	PROPN
ejpam-6264	702	22	)	)	PUNCT
ejpam-6264	702	23	∩ng	∩ng	VERB
ejpam-6264	702	24	◦	◦	NOUN
ejpam-6264	702	25	h(u	h(u	PROPN
ejpam-6264	702	26	)	)	PUNCT
ejpam-6264	702	27	.	.	PUNCT
ejpam-6264	703	1	if	if	SCONJ
ejpam-6264	703	2	v	v	NUM
ejpam-6264	703	3	∈	∈	PROPN
ejpam-6264	703	4	v0∪v1	v0∪v1	NOUN
ejpam-6264	703	5	,	,	PUNCT
ejpam-6264	703	6	then	then	ADV
ejpam-6264	703	7	there	there	PRON
ejpam-6264	703	8	exist	exist	VERB
ejpam-6264	703	9	w	w	PRON
ejpam-6264	703	10	∈	∈	PROPN
ejpam-6264	703	11	v	v	ADP
ejpam-6264	703	12	v	v	ADP
ejpam-6264	703	13	2	2	NUM
ejpam-6264	703	14	∪v	∪v	NOUN
ejpam-6264	703	15	v	v	NOUN
ejpam-6264	703	16	3	3	NUM
ejpam-6264	703	17	such	such	ADJ
ejpam-6264	703	18	that	that	DET
ejpam-6264	703	19	w	w	PROPN
ejpam-6264	703	20	∈	∈	PROPN
ejpam-6264	703	21	nhv(u	nhv(u	PROPN
ejpam-6264	703	22	)	)	PUNCT
ejpam-6264	703	23	since	since	SCONJ
ejpam-6264	703	24	f	f	PROPN
ejpam-6264	703	25	|hv	|hv	PROPN
ejpam-6264	703	26	∈	∈	PROPN
ejpam-6264	703	27	tmrdf	tmrdf	NOUN
ejpam-6264	703	28	(	(	PUNCT
ejpam-6264	703	29	hv	hv	NOUN
ejpam-6264	703	30	)	)	PUNCT
ejpam-6264	703	31	by	by	ADP
ejpam-6264	703	32	(	(	PUNCT
ejpam-6264	703	33	i	i	NOUN
ejpam-6264	703	34	)	)	PUNCT
ejpam-6264	703	35	.	.	PUNCT
ejpam-6264	704	1	it	it	PRON
ejpam-6264	704	2	implies	imply	VERB
ejpam-6264	704	3	that	that	SCONJ
ejpam-6264	704	4	w	w	PROPN
ejpam-6264	704	5	∈	∈	PROPN
ejpam-6264	704	6	v2∪v3	v2∪v3	PROPN
ejpam-6264	704	7	and	and	CCONJ
ejpam-6264	704	8	w	w	PROPN
ejpam-6264	704	9	∈	∈	PROPN
ejpam-6264	704	10	ng	ng	PROPN
ejpam-6264	704	11	◦	◦	NOUN
ejpam-6264	704	12	h(u	h(u	PROPN
ejpam-6264	704	13	)	)	PUNCT
ejpam-6264	704	14	.	.	PUNCT
ejpam-6264	705	1	therefore	therefore	ADV
ejpam-6264	705	2	,	,	PUNCT
ejpam-6264	705	3	f	f	PROPN
ejpam-6264	705	4	∈	∈	PROPN
ejpam-6264	705	5	tmrdf	tmrdf	NOUN
ejpam-6264	705	6	(	(	PUNCT
ejpam-6264	705	7	g	g	NOUN
ejpam-6264	705	8	◦	◦	NOUN
ejpam-6264	705	9	h	h	NOUN
ejpam-6264	705	10	)	)	PUNCT
ejpam-6264	705	11	.	.	PUNCT
ejpam-6264	706	1	corollary	corollary	ADJ
ejpam-6264	706	2	6	6	NUM
ejpam-6264	706	3	.	.	PUNCT
ejpam-6264	707	1	let	let	VERB
ejpam-6264	707	2	g	g	NOUN
ejpam-6264	708	1	and	and	CCONJ
ejpam-6264	708	2	h	h	NOUN
ejpam-6264	708	3	be	be	VERB
ejpam-6264	708	4	any	any	DET
ejpam-6264	708	5	graph	graph	NOUN
ejpam-6264	708	6	with	with	ADP
ejpam-6264	708	7	|v	|v	PROPN
ejpam-6264	708	8	(	(	PUNCT
ejpam-6264	708	9	g)|	g)|	NOUN
ejpam-6264	708	10	=	=	PUNCT
ejpam-6264	708	11	n	n	NOUN
ejpam-6264	708	12	and	and	CCONJ
ejpam-6264	708	13	|v	|v	PROPN
ejpam-6264	708	14	(	(	PUNCT
ejpam-6264	708	15	h)|	h)|	NOUN
ejpam-6264	708	16	=	=	PUNCT
ejpam-6264	708	17	m	m	NOUN
ejpam-6264	708	18	and	and	CCONJ
ejpam-6264	708	19	let	let	VERB
ejpam-6264	708	20	f	f	PROPN
ejpam-6264	708	21	=	=	SYM
ejpam-6264	708	22	(	(	PUNCT
ejpam-6264	708	23	v0	v0	PROPN
ejpam-6264	708	24	,	,	PUNCT
ejpam-6264	708	25	v1	v1	NOUN
ejpam-6264	708	26	,	,	PUNCT
ejpam-6264	708	27	v2	v2	PROPN
ejpam-6264	708	28	,	,	PUNCT
ejpam-6264	708	29	v3	v3	PROPN
ejpam-6264	708	30	)	)	PUNCT
ejpam-6264	708	31	be	be	VERB
ejpam-6264	708	32	a	a	DET
ejpam-6264	708	33	γtmr	γtmr	NOUN
ejpam-6264	708	34	-	-	PUNCT
ejpam-6264	708	35	function	function	NOUN
ejpam-6264	708	36	of	of	ADP
ejpam-6264	708	37	g	g	PROPN
ejpam-6264	708	38	◦	◦	NOUN
ejpam-6264	708	39	h.	h.	NOUN
ejpam-6264	708	40	then	then	ADV
ejpam-6264	708	41	3n	3n	NUM
ejpam-6264	708	42	≤	≤	NUM
ejpam-6264	708	43	∑	∑	PUNCT
ejpam-6264	708	44	a∈v	a∈v	PROPN
ejpam-6264	708	45	(	(	PUNCT
ejpam-6264	708	46	v+hv	v+hv	NOUN
ejpam-6264	708	47	)	)	PUNCT
ejpam-6264	708	48	f(a	f(a	NOUN
ejpam-6264	708	49	)	)	PUNCT
ejpam-6264	708	50	≤	≤	NOUN
ejpam-6264	708	51	2n+nm	2n+nm	NUM
ejpam-6264	708	52	,	,	PUNCT
ejpam-6264	708	53	for	for	ADP
ejpam-6264	708	54	each	each	DET
ejpam-6264	708	55	v	v	NUM
ejpam-6264	708	56	∈	∈	PROPN
ejpam-6264	708	57	v	v	NOUN
ejpam-6264	708	58	(	(	PUNCT
ejpam-6264	708	59	g	g	NOUN
ejpam-6264	708	60	)	)	PUNCT
ejpam-6264	708	61	.	.	PUNCT
ejpam-6264	709	1	proof	proof	NOUN
ejpam-6264	709	2	.	.	PUNCT
ejpam-6264	710	1	let	let	VERB
ejpam-6264	710	2	v	v	NUM
ejpam-6264	710	3	∈	∈	PROPN
ejpam-6264	710	4	v	v	NOUN
ejpam-6264	710	5	(	(	PUNCT
ejpam-6264	710	6	g	g	NOUN
ejpam-6264	710	7	)	)	PUNCT
ejpam-6264	710	8	.	.	PUNCT
ejpam-6264	711	1	if	if	SCONJ
ejpam-6264	711	2	v	v	NUM
ejpam-6264	711	3	∈	∈	PROPN
ejpam-6264	711	4	v2	v2	PROPN
ejpam-6264	711	5	∪	∪	X
ejpam-6264	711	6	v3	v3	PROPN
ejpam-6264	711	7	,	,	PUNCT
ejpam-6264	711	8	then	then	ADV
ejpam-6264	711	9	3n	3n	NUM
ejpam-6264	711	10	≤	≤	NUM
ejpam-6264	711	11	∑	∑	PUNCT
ejpam-6264	711	12	p∈v	p∈v	NOUN
ejpam-6264	711	13	(	(	PUNCT
ejpam-6264	711	14	hv	hv	NOUN
ejpam-6264	711	15	)	)	PUNCT
ejpam-6264	711	16	f(p	f(p	PROPN
ejpam-6264	711	17	)	)	PUNCT
ejpam-6264	711	18	≤	≤	NUM
ejpam-6264	711	19	∑	∑	PUNCT
ejpam-6264	711	20	a∈v	a∈v	PROPN
ejpam-6264	711	21	(	(	PUNCT
ejpam-6264	711	22	v+hv	v+hv	NOUN
ejpam-6264	711	23	)	)	PUNCT
ejpam-6264	711	24	f(a	f(a	NOUN
ejpam-6264	711	25	)	)	PUNCT
ejpam-6264	711	26	≤	≤	NUM
ejpam-6264	711	27	2n	2n	NUM
ejpam-6264	711	28	+	+	CCONJ
ejpam-6264	711	29	nm	nm	X
ejpam-6264	711	30	.	.	PUNCT
ejpam-6264	711	31	suppose	suppose	VERB
ejpam-6264	711	32	that	that	SCONJ
ejpam-6264	711	33	v	v	PROPN
ejpam-6264	711	34	∈	∈	PROPN
ejpam-6264	711	35	v0	v0	NOUN
ejpam-6264	711	36	.	.	PUNCT
ejpam-6264	712	1	by	by	ADP
ejpam-6264	712	2	proposition	proposition	NOUN
ejpam-6264	712	3	18	18	NUM
ejpam-6264	712	4	,	,	PUNCT
ejpam-6264	712	5	f	f	PROPN
ejpam-6264	712	6	|hv	|hv	PROPN
ejpam-6264	712	7	∈	∈	PROPN
ejpam-6264	712	8	tmrdf	tmrdf	NOUN
ejpam-6264	712	9	(	(	PUNCT
ejpam-6264	712	10	hv	hv	NOUN
ejpam-6264	712	11	)	)	PUNCT
ejpam-6264	712	12	.	.	PUNCT
ejpam-6264	713	1	thus	thus	ADV
ejpam-6264	713	2	,	,	PUNCT
ejpam-6264	713	3	3n	3n	NUM
ejpam-6264	713	4	≤∑	≤∑	PROPN
ejpam-6264	713	5	a∈v	a∈v	PROPN
ejpam-6264	713	6	(	(	PUNCT
ejpam-6264	713	7	v+hv	v+hv	NOUN
ejpam-6264	713	8	)	)	PUNCT
ejpam-6264	713	9	f(a	f(a	NOUN
ejpam-6264	713	10	)	)	PUNCT
ejpam-6264	713	11	≤	≤	NUM
ejpam-6264	713	12	2n	2n	NUM
ejpam-6264	713	13	+	+	CCONJ
ejpam-6264	713	14	nm	nm	NOUN
ejpam-6264	713	15	.	.	PUNCT
ejpam-6264	714	1	if	if	SCONJ
ejpam-6264	714	2	v	v	NUM
ejpam-6264	714	3	∈	∈	PROPN
ejpam-6264	714	4	v1	v1	NOUN
ejpam-6264	714	5	,	,	PUNCT
ejpam-6264	714	6	then	then	ADV
ejpam-6264	714	7	by	by	ADP
ejpam-6264	714	8	proposition	proposition	NOUN
ejpam-6264	714	9	18	18	NUM
ejpam-6264	714	10	,	,	PUNCT
ejpam-6264	714	11	f	f	PROPN
ejpam-6264	714	12	|hv	|hv	PROPN
ejpam-6264	714	13	∈	∈	PROPN
ejpam-6264	714	14	tmrdf	tmrdf	NOUN
ejpam-6264	714	15	(	(	PUNCT
ejpam-6264	714	16	hv	hv	NOUN
ejpam-6264	714	17	)	)	PUNCT
ejpam-6264	714	18	.	.	PUNCT
ejpam-6264	715	1	thus	thus	ADV
ejpam-6264	715	2	,	,	PUNCT
ejpam-6264	715	3	3n	3n	NUM
ejpam-6264	715	4	≤	≤	NUM
ejpam-6264	715	5	∑	∑	PUNCT
ejpam-6264	715	6	p∈v	p∈v	NOUN
ejpam-6264	715	7	(	(	PUNCT
ejpam-6264	715	8	hv	hv	NOUN
ejpam-6264	715	9	)	)	PUNCT
ejpam-6264	715	10	f(p	f(p	PROPN
ejpam-6264	715	11	)	)	PUNCT
ejpam-6264	715	12	≤	≤	NUM
ejpam-6264	715	13	∑	∑	PUNCT
ejpam-6264	715	14	a∈v	a∈v	PROPN
ejpam-6264	715	15	(	(	PUNCT
ejpam-6264	715	16	v+hv	v+hv	NOUN
ejpam-6264	715	17	)	)	PUNCT
ejpam-6264	715	18	f(a	f(a	NOUN
ejpam-6264	715	19	)	)	PUNCT
ejpam-6264	715	20	≤	≤	NUM
ejpam-6264	715	21	2n	2n	NUM
ejpam-6264	715	22	+	+	CCONJ
ejpam-6264	715	23	nm	nm	X
ejpam-6264	715	24	.	.	PUNCT
ejpam-6264	716	1	moreover	moreover	ADV
ejpam-6264	716	2	,	,	PUNCT
ejpam-6264	716	3	the	the	DET
ejpam-6264	716	4	bounds	bound	NOUN
ejpam-6264	716	5	are	be	AUX
ejpam-6264	716	6	sharp	sharp	ADJ
ejpam-6264	716	7	if	if	SCONJ
ejpam-6264	716	8	h	h	NOUN
ejpam-6264	716	9	=	=	SYM
ejpam-6264	716	10	k1	k1	PROPN
ejpam-6264	716	11	and	and	CCONJ
ejpam-6264	716	12	g	g	PROPN
ejpam-6264	716	13	∈	∈	PROPN
ejpam-6264	716	14	{	{	PUNCT
ejpam-6264	716	15	pn	pn	PROPN
ejpam-6264	716	16	,	,	PUNCT
ejpam-6264	716	17	cn	cn	PROPN
ejpam-6264	716	18	,	,	PUNCT
ejpam-6264	716	19	kn	kn	PROPN
ejpam-6264	716	20	}	}	PUNCT
ejpam-6264	716	21	.	.	PUNCT
ejpam-6264	717	1	corollary	corollary	ADJ
ejpam-6264	717	2	7	7	NUM
ejpam-6264	717	3	.	.	PUNCT
ejpam-6264	718	1	let	let	VERB
ejpam-6264	718	2	g	g	PRON
ejpam-6264	718	3	be	be	AUX
ejpam-6264	718	4	a	a	DET
ejpam-6264	718	5	connected	connected	ADJ
ejpam-6264	718	6	graph	graph	NOUN
ejpam-6264	718	7	of	of	ADP
ejpam-6264	718	8	order	order	NOUN
ejpam-6264	718	9	n	n	PRON
ejpam-6264	718	10	≥	≥	NOUN
ejpam-6264	718	11	1	1	NUM
ejpam-6264	718	12	and	and	CCONJ
ejpam-6264	718	13	km	km	PROPN
ejpam-6264	718	14	be	be	AUX
ejpam-6264	718	15	the	the	DET
ejpam-6264	718	16	complete	complete	ADJ
ejpam-6264	718	17	graph	graph	NOUN
ejpam-6264	718	18	,	,	PUNCT
ejpam-6264	718	19	then	then	ADV
ejpam-6264	718	20	γtmr(g	γtmr(g	PROPN
ejpam-6264	718	21	◦	◦	NOUN
ejpam-6264	718	22	km	km	NOUN
ejpam-6264	718	23	)	)	PUNCT
ejpam-6264	719	1	=	=	PRON
ejpam-6264	719	2	{	{	PUNCT
ejpam-6264	719	3	4n	4n	NOUN
ejpam-6264	719	4	,	,	PUNCT
ejpam-6264	719	5	if	if	SCONJ
ejpam-6264	719	6	m	m	VERB
ejpam-6264	719	7	=	=	NOUN
ejpam-6264	719	8	2	2	NUM
ejpam-6264	719	9	.	.	NOUN
ejpam-6264	719	10	5n	5n	NUM
ejpam-6264	719	11	,	,	PUNCT
ejpam-6264	719	12	if	if	SCONJ
ejpam-6264	719	13	m	m	PROPN
ejpam-6264	719	14	≥	≥	NOUN
ejpam-6264	719	15	3	3	NUM
ejpam-6264	719	16	.	.	PUNCT
ejpam-6264	720	1	proof	proof	NOUN
ejpam-6264	720	2	.	.	PUNCT
ejpam-6264	721	1	if	if	SCONJ
ejpam-6264	721	2	n	n	NOUN
ejpam-6264	721	3	=	=	SYM
ejpam-6264	721	4	1	1	NUM
ejpam-6264	721	5	,	,	PUNCT
ejpam-6264	721	6	then	then	ADV
ejpam-6264	721	7	g	g	ADP
ejpam-6264	721	8	◦	◦	NOUN
ejpam-6264	721	9	km	km	NOUN
ejpam-6264	721	10	=	=	SYM
ejpam-6264	721	11	km+1	km+1	PROPN
ejpam-6264	721	12	.	.	NOUN
ejpam-6264	722	1	hence	hence	ADV
ejpam-6264	722	2	,	,	PUNCT
ejpam-6264	722	3	if	if	SCONJ
ejpam-6264	722	4	m	m	ADV
ejpam-6264	722	5	=	=	SYM
ejpam-6264	722	6	2	2	NUM
ejpam-6264	722	7	,	,	PUNCT
ejpam-6264	722	8	γtmr(g	γtmr(g	PROPN
ejpam-6264	722	9	◦	◦	NOUN
ejpam-6264	722	10	k2	k2	NOUN
ejpam-6264	722	11	)	)	PUNCT
ejpam-6264	722	12	=	=	SYM
ejpam-6264	722	13	γtmr(k3	γtmr(k3	NOUN
ejpam-6264	722	14	)	)	PUNCT
ejpam-6264	722	15	=	=	SYM
ejpam-6264	722	16	4	4	NUM
ejpam-6264	722	17	by	by	ADP
ejpam-6264	722	18	proposition	proposition	NOUN
ejpam-6264	722	19	7	7	NUM
ejpam-6264	722	20	(	(	PUNCT
ejpam-6264	722	21	ii	ii	NOUN
ejpam-6264	722	22	)	)	PUNCT
ejpam-6264	722	23	.	.	PUNCT
ejpam-6264	723	1	if	if	SCONJ
ejpam-6264	723	2	m	m	PROPN
ejpam-6264	723	3	≥	≥	VERB
ejpam-6264	723	4	4	4	NUM
ejpam-6264	723	5	,	,	PUNCT
ejpam-6264	723	6	then	then	ADV
ejpam-6264	723	7	γtmr(km+1	γtmr(km+1	NUM
ejpam-6264	723	8	)	)	PUNCT
ejpam-6264	723	9	=	=	SYM
ejpam-6264	723	10	5	5	NUM
ejpam-6264	723	11	by	by	ADP
ejpam-6264	723	12	proposition	proposition	NOUN
ejpam-6264	723	13	8	8	NUM
ejpam-6264	723	14	.	.	PUNCT
ejpam-6264	724	1	now	now	ADV
ejpam-6264	724	2	,	,	PUNCT
ejpam-6264	724	3	if	if	SCONJ
ejpam-6264	724	4	n	n	PROPN
ejpam-6264	724	5	>	>	X
ejpam-6264	724	6	1	1	NUM
ejpam-6264	724	7	,	,	PUNCT
ejpam-6264	724	8	s.	s.	PROPN
ejpam-6264	724	9	ahamad	ahamad	VERB
ejpam-6264	724	10	et	et	PROPN
ejpam-6264	724	11	al	al	PROPN
ejpam-6264	724	12	.	.	PUNCT
ejpam-6264	724	13	/	/	SYM
ejpam-6264	724	14	eur	eur	PROPN
ejpam-6264	724	15	.	.	PUNCT
ejpam-6264	725	1	j.	j.	PROPN
ejpam-6264	725	2	pure	pure	PROPN
ejpam-6264	725	3	appl	appl	PROPN
ejpam-6264	725	4	.	.	PROPN
ejpam-6264	725	5	math	math	PROPN
ejpam-6264	725	6	,	,	PUNCT
ejpam-6264	725	7	18	18	NUM
ejpam-6264	725	8	(	(	PUNCT
ejpam-6264	725	9	4	4	NUM
ejpam-6264	725	10	)	)	PUNCT
ejpam-6264	725	11	(	(	PUNCT
ejpam-6264	725	12	2025	2025	NUM
ejpam-6264	725	13	)	)	PUNCT
ejpam-6264	725	14	,	,	PUNCT
ejpam-6264	725	15	6264	6264	NUM
ejpam-6264	725	16	19	19	NUM
ejpam-6264	725	17	of	of	ADP
ejpam-6264	725	18	20	20	NUM
ejpam-6264	725	19	then	then	ADV
ejpam-6264	725	20	for	for	ADP
ejpam-6264	725	21	m	m	PROPN
ejpam-6264	725	22	=	=	SYM
ejpam-6264	725	23	2	2	NUM
ejpam-6264	725	24	,	,	PUNCT
ejpam-6264	725	25	let	let	VERB
ejpam-6264	725	26	v	v	NOUN
ejpam-6264	725	27	(	(	PUNCT
ejpam-6264	725	28	k2	k2	NOUN
ejpam-6264	725	29	)	)	PUNCT
ejpam-6264	725	30	=	=	SYM
ejpam-6264	725	31	{	{	PUNCT
ejpam-6264	725	32	x	x	NOUN
ejpam-6264	725	33	,	,	PUNCT
ejpam-6264	725	34	y	y	NOUN
ejpam-6264	725	35	}	}	PUNCT
ejpam-6264	725	36	and	and	CCONJ
ejpam-6264	725	37	v	v	X
ejpam-6264	725	38	(	(	PUNCT
ejpam-6264	725	39	g	g	NOUN
ejpam-6264	725	40	)	)	PUNCT
ejpam-6264	725	41	=	=	SYM
ejpam-6264	725	42	{	{	PUNCT
ejpam-6264	725	43	v1	v1	PROPN
ejpam-6264	725	44	,	,	PUNCT
ejpam-6264	725	45	v2	v2	PROPN
ejpam-6264	725	46	,	,	PUNCT
ejpam-6264	725	47	·	·	PUNCT
ejpam-6264	725	48	·	·	PUNCT
ejpam-6264	725	49	·	·	PUNCT
ejpam-6264	725	50	,	,	PUNCT
ejpam-6264	725	51	vn	vn	PROPN
ejpam-6264	725	52	}	}	PUNCT
ejpam-6264	725	53	.	.	PUNCT
ejpam-6264	726	1	define	define	VERB
ejpam-6264	726	2	a	a	DET
ejpam-6264	726	3	function	function	NOUN
ejpam-6264	726	4	f	f	NOUN
ejpam-6264	726	5	=	=	SYM
ejpam-6264	726	6	(	(	PUNCT
ejpam-6264	726	7	v0	v0	PROPN
ejpam-6264	726	8	,	,	PUNCT
ejpam-6264	726	9	v1	v1	NOUN
ejpam-6264	726	10	,	,	PUNCT
ejpam-6264	726	11	v2	v2	PROPN
ejpam-6264	726	12	,	,	PUNCT
ejpam-6264	726	13	v3	v3	PROPN
ejpam-6264	726	14	)	)	PUNCT
ejpam-6264	726	15	on	on	ADP
ejpam-6264	726	16	v	v	NUM
ejpam-6264	726	17	(	(	PUNCT
ejpam-6264	726	18	g	g	PROPN
ejpam-6264	726	19	◦	◦	NOUN
ejpam-6264	726	20	k2	k2	NOUN
ejpam-6264	726	21	)	)	PUNCT
ejpam-6264	726	22	where	where	SCONJ
ejpam-6264	726	23	v0	v0	NOUN
ejpam-6264	726	24	=	=	SYM
ejpam-6264	726	25	∅	∅	NOUN
ejpam-6264	726	26	=	=	SYM
ejpam-6264	726	27	v3	v3	PROPN
ejpam-6264	726	28	,	,	PUNCT
ejpam-6264	726	29	v1	v1	NOUN
ejpam-6264	726	30	=	=	SYM
ejpam-6264	726	31	∪	∪	ADJ
ejpam-6264	726	32	v∈v	v∈v	NOUN
ejpam-6264	726	33	(	(	PUNCT
ejpam-6264	726	34	g	g	NOUN
ejpam-6264	726	35	)	)	PUNCT
ejpam-6264	726	36	v	v	NOUN
ejpam-6264	726	37	(	(	PUNCT
ejpam-6264	726	38	hv	hv	PROPN
ejpam-6264	726	39	)	)	PUNCT
ejpam-6264	726	40	,	,	PUNCT
ejpam-6264	726	41	v2	v2	PROPN
ejpam-6264	726	42	=	=	SYM
ejpam-6264	726	43	v	v	NOUN
ejpam-6264	726	44	(	(	PUNCT
ejpam-6264	726	45	g	g	NOUN
ejpam-6264	726	46	)	)	PUNCT
ejpam-6264	726	47	.	.	PUNCT
ejpam-6264	727	1	then	then	ADV
ejpam-6264	727	2	f	f	PROPN
ejpam-6264	727	3	∈	∈	PROPN
ejpam-6264	727	4	tmrdf	tmrdf	NOUN
ejpam-6264	727	5	(	(	PUNCT
ejpam-6264	727	6	g	g	NOUN
ejpam-6264	727	7	◦	◦	NOUN
ejpam-6264	727	8	k2	k2	NOUN
ejpam-6264	727	9	)	)	PUNCT
ejpam-6264	727	10	.	.	PUNCT
ejpam-6264	728	1	it	it	PRON
ejpam-6264	728	2	follows	follow	VERB
ejpam-6264	728	3	that	that	SCONJ
ejpam-6264	728	4	γtmr(g	γtmr(g	PROPN
ejpam-6264	728	5	◦	◦	NOUN
ejpam-6264	728	6	k2	k2	ADJ
ejpam-6264	728	7	)	)	PUNCT
ejpam-6264	728	8	≤	≤	NOUN
ejpam-6264	728	9	4n	4n	NOUN
ejpam-6264	728	10	.	.	PUNCT
ejpam-6264	729	1	now	now	ADV
ejpam-6264	729	2	,	,	PUNCT
ejpam-6264	729	3	suppose	suppose	VERB
ejpam-6264	729	4	that	that	SCONJ
ejpam-6264	729	5	g	g	PROPN
ejpam-6264	729	6	=	=	SYM
ejpam-6264	729	7	(	(	PUNCT
ejpam-6264	729	8	w0,w1,w2,w3	w0,w1,w2,w3	PROPN
ejpam-6264	729	9	)	)	PUNCT
ejpam-6264	729	10	is	be	AUX
ejpam-6264	729	11	a	a	DET
ejpam-6264	729	12	γtmr	γtmr	NOUN
ejpam-6264	729	13	-	-	PUNCT
ejpam-6264	729	14	function	function	NOUN
ejpam-6264	729	15	of	of	ADP
ejpam-6264	729	16	g	g	NOUN
ejpam-6264	729	17	◦	◦	NOUN
ejpam-6264	729	18	k2	k2	ADJ
ejpam-6264	729	19	.	.	PUNCT
ejpam-6264	730	1	if	if	SCONJ
ejpam-6264	730	2	w0	w0	PROPN
ejpam-6264	730	3	=	=	SYM
ejpam-6264	730	4	∅	∅	NOUN
ejpam-6264	730	5	,	,	PUNCT
ejpam-6264	730	6	then	then	ADV
ejpam-6264	730	7	w3	w3	PROPN
ejpam-6264	730	8	=	=	PUNCT
ejpam-6264	730	9	∅.	∅.	NOUN
ejpam-6264	730	10	since	since	SCONJ
ejpam-6264	730	11	g	g	PROPN
ejpam-6264	730	12	is	be	AUX
ejpam-6264	730	13	a	a	DET
ejpam-6264	730	14	γtmr	γtmr	ADJ
ejpam-6264	730	15	-	-	PUNCT
ejpam-6264	730	16	function	function	NOUN
ejpam-6264	730	17	of	of	ADP
ejpam-6264	730	18	g	g	PROPN
ejpam-6264	730	19	◦	◦	NOUN
ejpam-6264	730	20	k2	k2	PROPN
ejpam-6264	730	21	,	,	PUNCT
ejpam-6264	730	22	γtmr(g	γtmr(g	PROPN
ejpam-6264	730	23	◦	◦	NOUN
ejpam-6264	730	24	k2	k2	NOUN
ejpam-6264	730	25	)	)	PUNCT
ejpam-6264	730	26	=	=	PUNCT
ejpam-6264	730	27	ωtmr	ωtmr	ADJ
ejpam-6264	730	28	g	g	PROPN
ejpam-6264	730	29	◦	◦	NOUN
ejpam-6264	730	30	k2	k2	X
ejpam-6264	730	31	(	(	PUNCT
ejpam-6264	730	32	g	g	NOUN
ejpam-6264	730	33	)	)	PUNCT
ejpam-6264	730	34	≥	≥	NOUN
ejpam-6264	730	35	4n	4n	X
ejpam-6264	730	36	.	.	PUNCT
ejpam-6264	731	1	if	if	SCONJ
ejpam-6264	731	2	|w0|	|w0|	VERB
ejpam-6264	731	3	̸=	̸=	PROPN
ejpam-6264	731	4	0	0	NUM
ejpam-6264	731	5	,	,	PUNCT
ejpam-6264	731	6	then	then	ADV
ejpam-6264	731	7	|w2|	|w2|	NOUN
ejpam-6264	731	8	≥	≥	NOUN
ejpam-6264	731	9	1	1	NUM
ejpam-6264	731	10	and	and	CCONJ
ejpam-6264	731	11	|w3|	|w3|	PRON
ejpam-6264	731	12	≥	≥	NOUN
ejpam-6264	731	13	1	1	NUM
ejpam-6264	731	14	.	.	PUNCT
ejpam-6264	732	1	it	it	PRON
ejpam-6264	732	2	follows	follow	VERB
ejpam-6264	732	3	that	that	SCONJ
ejpam-6264	732	4	γtmr(g	γtmr(g	PROPN
ejpam-6264	732	5	◦	◦	NOUN
ejpam-6264	732	6	k2	k2	NOUN
ejpam-6264	732	7	)	)	PUNCT
ejpam-6264	732	8	=	=	PUNCT
ejpam-6264	732	9	ωtmr	ωtmr	ADJ
ejpam-6264	732	10	g	g	PROPN
ejpam-6264	732	11	◦	◦	NOUN
ejpam-6264	732	12	k2	k2	X
ejpam-6264	732	13	(	(	PUNCT
ejpam-6264	732	14	g	g	NOUN
ejpam-6264	732	15	)	)	PUNCT
ejpam-6264	732	16	=	=	SYM
ejpam-6264	732	17	2|w2|+3|w3|	2|w2|+3|w3|	NUM
ejpam-6264	732	18	≥	≥	NOUN
ejpam-6264	732	19	4n	4n	X
ejpam-6264	732	20	.	.	PUNCT
ejpam-6264	733	1	therefore	therefore	ADV
ejpam-6264	733	2	,	,	PUNCT
ejpam-6264	733	3	γtmr(g	γtmr(g	PROPN
ejpam-6264	733	4	◦	◦	NOUN
ejpam-6264	733	5	k2	k2	NOUN
ejpam-6264	733	6	)	)	PUNCT
ejpam-6264	733	7	=	=	SYM
ejpam-6264	734	1	4n	4n	X
ejpam-6264	734	2	.	.	PUNCT
ejpam-6264	735	1	for	for	ADP
ejpam-6264	735	2	m	m	PROPN
ejpam-6264	735	3	≥	≥	NOUN
ejpam-6264	735	4	3	3	NUM
ejpam-6264	735	5	,	,	PUNCT
ejpam-6264	735	6	let	let	VERB
ejpam-6264	735	7	v	v	X
ejpam-6264	735	8	(	(	PUNCT
ejpam-6264	735	9	g	g	NOUN
ejpam-6264	735	10	)	)	PUNCT
ejpam-6264	735	11	=	=	SYM
ejpam-6264	735	12	{	{	PUNCT
ejpam-6264	735	13	v1	v1	PROPN
ejpam-6264	735	14	,	,	PUNCT
ejpam-6264	735	15	v2	v2	PROPN
ejpam-6264	735	16	,	,	PUNCT
ejpam-6264	735	17	·	·	PUNCT
ejpam-6264	735	18	·	·	PUNCT
ejpam-6264	735	19	·	·	PUNCT
ejpam-6264	735	20	,	,	PUNCT
ejpam-6264	735	21	vn	vn	INTJ
ejpam-6264	735	22	}	}	PUNCT
ejpam-6264	735	23	and	and	CCONJ
ejpam-6264	735	24	wlog	wlog	NOUN
ejpam-6264	735	25	,	,	PUNCT
ejpam-6264	735	26	pick	pick	VERB
ejpam-6264	735	27	a	a	DET
ejpam-6264	735	28	vertex	vertex	NOUN
ejpam-6264	735	29	u	u	NOUN
ejpam-6264	735	30	∈	∈	PROPN
ejpam-6264	735	31	v	v	NOUN
ejpam-6264	735	32	(	(	PUNCT
ejpam-6264	735	33	km	km	PROPN
ejpam-6264	735	34	)	)	PUNCT
ejpam-6264	735	35	.	.	PUNCT
ejpam-6264	736	1	define	define	VERB
ejpam-6264	736	2	a	a	DET
ejpam-6264	736	3	function	function	NOUN
ejpam-6264	736	4	f	f	NOUN
ejpam-6264	736	5	=	=	SYM
ejpam-6264	736	6	(	(	PUNCT
ejpam-6264	736	7	v0	v0	PROPN
ejpam-6264	736	8	,	,	PUNCT
ejpam-6264	736	9	v1	v1	NOUN
ejpam-6264	736	10	,	,	PUNCT
ejpam-6264	736	11	v2	v2	PROPN
ejpam-6264	736	12	,	,	PUNCT
ejpam-6264	736	13	v3	v3	PROPN
ejpam-6264	736	14	)	)	PUNCT
ejpam-6264	736	15	on	on	ADP
ejpam-6264	736	16	v	v	NUM
ejpam-6264	736	17	(	(	PUNCT
ejpam-6264	736	18	g	g	PROPN
ejpam-6264	736	19	◦	◦	NOUN
ejpam-6264	736	20	km	km	NOUN
ejpam-6264	736	21	)	)	PUNCT
ejpam-6264	736	22	by	by	ADP
ejpam-6264	736	23	f(x	f(x	PROPN
ejpam-6264	736	24	)	)	PUNCT
ejpam-6264	737	1	=	=	PUNCT
ejpam-6264	738	1			NOUN
ejpam-6264	738	2	3	3	NUM
ejpam-6264	738	3	,	,	PUNCT
ejpam-6264	738	4	if	if	SCONJ
ejpam-6264	738	5	x	x	PROPN
ejpam-6264	738	6	∈	∈	PROPN
ejpam-6264	738	7	v	v	X
ejpam-6264	738	8	(	(	PUNCT
ejpam-6264	738	9	g	g	NOUN
ejpam-6264	738	10	)	)	PUNCT
ejpam-6264	738	11	.	.	PUNCT
ejpam-6264	739	1	2	2	NUM
ejpam-6264	739	2	,	,	PUNCT
ejpam-6264	739	3	if	if	SCONJ
ejpam-6264	739	4	x	x	PROPN
ejpam-6264	739	5	∈	∈	PROPN
ejpam-6264	739	6	∪	∪	VERB
ejpam-6264	739	7	v∈v	v∈v	NOUN
ejpam-6264	739	8	(	(	PUNCT
ejpam-6264	739	9	g	g	NOUN
ejpam-6264	739	10	)	)	PUNCT
ejpam-6264	739	11	v	v	NOUN
ejpam-6264	739	12	(	(	PUNCT
ejpam-6264	739	13	uv	uv	NOUN
ejpam-6264	739	14	)	)	PUNCT
ejpam-6264	739	15	.	.	PUNCT
ejpam-6264	740	1	0	0	PUNCT
ejpam-6264	740	2	,	,	PUNCT
ejpam-6264	740	3	if	if	SCONJ
ejpam-6264	740	4	x	x	PROPN
ejpam-6264	740	5	∈	∈	PROPN
ejpam-6264	740	6	∪	∪	VERB
ejpam-6264	740	7	v∈v	v∈v	NOUN
ejpam-6264	740	8	(	(	PUNCT
ejpam-6264	740	9	g	g	NOUN
ejpam-6264	740	10	)	)	PUNCT
ejpam-6264	740	11	v	v	NOUN
ejpam-6264	740	12	(	(	PUNCT
ejpam-6264	740	13	(	(	PUNCT
ejpam-6264	740	14	h	h	NOUN
ejpam-6264	740	15	\	\	NOUN
ejpam-6264	740	16	u)v	u)v	PUNCT
ejpam-6264	740	17	)	)	PUNCT
ejpam-6264	740	18	.	.	PUNCT
ejpam-6264	741	1	then	then	ADV
ejpam-6264	741	2	f	f	PROPN
ejpam-6264	741	3	∈	∈	PROPN
ejpam-6264	741	4	tmrdf	tmrdf	NOUN
ejpam-6264	741	5	(	(	PUNCT
ejpam-6264	741	6	g	g	PROPN
ejpam-6264	741	7	◦	◦	NOUN
ejpam-6264	741	8	km	km	PROPN
ejpam-6264	741	9	)	)	PUNCT
ejpam-6264	741	10	.	.	PUNCT
ejpam-6264	742	1	it	it	PRON
ejpam-6264	742	2	follows	follow	VERB
ejpam-6264	742	3	that	that	SCONJ
ejpam-6264	742	4	γtmr(g	γtmr(g	PROPN
ejpam-6264	742	5	◦	◦	PROPN
ejpam-6264	742	6	km	km	NOUN
ejpam-6264	742	7	)	)	PUNCT
ejpam-6264	742	8	≤	≤	NUM
ejpam-6264	742	9	5n	5n	NOUN
ejpam-6264	742	10	.	.	PUNCT
ejpam-6264	743	1	now	now	ADV
ejpam-6264	743	2	,	,	PUNCT
ejpam-6264	743	3	suppose	suppose	VERB
ejpam-6264	743	4	that	that	SCONJ
ejpam-6264	743	5	g	g	PROPN
ejpam-6264	743	6	=	=	SYM
ejpam-6264	743	7	(	(	PUNCT
ejpam-6264	743	8	w0,w1,w2,w3	w0,w1,w2,w3	PROPN
ejpam-6264	743	9	)	)	PUNCT
ejpam-6264	743	10	is	be	AUX
ejpam-6264	743	11	a	a	DET
ejpam-6264	743	12	γtmr	γtmr	NOUN
ejpam-6264	743	13	-	-	PUNCT
ejpam-6264	743	14	function	function	NOUN
ejpam-6264	743	15	of	of	ADP
ejpam-6264	743	16	g	g	NOUN
ejpam-6264	743	17	◦	◦	NOUN
ejpam-6264	743	18	km	km	NOUN
ejpam-6264	743	19	.	.	PUNCT
ejpam-6264	744	1	if	if	SCONJ
ejpam-6264	744	2	w0	w0	PROPN
ejpam-6264	744	3	=	=	SYM
ejpam-6264	744	4	∅	∅	NOUN
ejpam-6264	744	5	,	,	PUNCT
ejpam-6264	744	6	then	then	ADV
ejpam-6264	744	7	w3	w3	PROPN
ejpam-6264	744	8	=	=	PUNCT
ejpam-6264	744	9	∅.	∅.	NOUN
ejpam-6264	744	10	since	since	SCONJ
ejpam-6264	744	11	g	g	PROPN
ejpam-6264	744	12	is	be	AUX
ejpam-6264	744	13	a	a	DET
ejpam-6264	744	14	γtmr	γtmr	ADJ
ejpam-6264	744	15	-	-	PUNCT
ejpam-6264	744	16	function	function	NOUN
ejpam-6264	744	17	of	of	ADP
ejpam-6264	744	18	g	g	NOUN
ejpam-6264	744	19	◦	◦	NOUN
ejpam-6264	744	20	km	km	NOUN
ejpam-6264	744	21	,	,	PUNCT
ejpam-6264	744	22	γtmr(g	γtmr(g	PROPN
ejpam-6264	744	23	◦	◦	NOUN
ejpam-6264	744	24	km	km	NOUN
ejpam-6264	744	25	)	)	PUNCT
ejpam-6264	744	26	=	=	PUNCT
ejpam-6264	744	27	ωtmr	ωtmr	ADV
ejpam-6264	744	28	g	g	ADP
ejpam-6264	744	29	◦	◦	NOUN
ejpam-6264	744	30	km	km	NOUN
ejpam-6264	744	31	(	(	PUNCT
ejpam-6264	744	32	g	g	NOUN
ejpam-6264	744	33	)	)	PUNCT
ejpam-6264	744	34	≥	≥	NUM
ejpam-6264	744	35	5n	5n	NOUN
ejpam-6264	744	36	.	.	PUNCT
ejpam-6264	745	1	if	if	SCONJ
ejpam-6264	745	2	|w0|	|w0|	VERB
ejpam-6264	745	3	̸=	̸=	PROPN
ejpam-6264	745	4	0	0	NUM
ejpam-6264	745	5	,	,	PUNCT
ejpam-6264	745	6	then	then	ADV
ejpam-6264	745	7	|w2|	|w2|	NOUN
ejpam-6264	745	8	≥	≥	NOUN
ejpam-6264	745	9	1	1	NUM
ejpam-6264	745	10	and	and	CCONJ
ejpam-6264	745	11	|w3|	|w3|	PRON
ejpam-6264	745	12	≥	≥	NOUN
ejpam-6264	745	13	1	1	NUM
ejpam-6264	745	14	.	.	PUNCT
ejpam-6264	746	1	it	it	PRON
ejpam-6264	746	2	follows	follow	VERB
ejpam-6264	746	3	that	that	SCONJ
ejpam-6264	746	4	γtmr(g	γtmr(g	PROPN
ejpam-6264	746	5	◦	◦	PROPN
ejpam-6264	746	6	km	km	NOUN
ejpam-6264	746	7	)	)	PUNCT
ejpam-6264	746	8	=	=	PUNCT
ejpam-6264	747	1	ωtmr	ωtmr	ADV
ejpam-6264	747	2	g	g	ADP
ejpam-6264	747	3	◦	◦	NOUN
ejpam-6264	747	4	km	km	NOUN
ejpam-6264	747	5	(	(	PUNCT
ejpam-6264	747	6	g	g	NOUN
ejpam-6264	747	7	)	)	PUNCT
ejpam-6264	747	8	=	=	SYM
ejpam-6264	747	9	2|w2|	2|w2|	NUM
ejpam-6264	747	10	+	+	SYM
ejpam-6264	747	11	3|w3|	3|w3|	NUM
ejpam-6264	747	12	≥	≥	NUM
ejpam-6264	747	13	5n	5n	NUM
ejpam-6264	747	14	.	.	PUNCT
ejpam-6264	748	1	therefore	therefore	ADV
ejpam-6264	748	2	,	,	PUNCT
ejpam-6264	748	3	γtmr(g	γtmr(g	PROPN
ejpam-6264	748	4	◦	◦	NOUN
ejpam-6264	748	5	km	km	NOUN
ejpam-6264	748	6	)	)	PUNCT
ejpam-6264	748	7	=	=	SYM
ejpam-6264	748	8	5n	5n	X
ejpam-6264	748	9	.	.	PUNCT
ejpam-6264	749	1	corollary	corollary	ADJ
ejpam-6264	749	2	8	8	NUM
ejpam-6264	749	3	.	.	PUNCT
ejpam-6264	750	1	if	if	SCONJ
ejpam-6264	750	2	kn	kn	PROPN
ejpam-6264	750	3	is	be	AUX
ejpam-6264	750	4	a	a	DET
ejpam-6264	750	5	complete	complete	ADJ
ejpam-6264	750	6	graph	graph	NOUN
ejpam-6264	750	7	of	of	ADP
ejpam-6264	750	8	order	order	NOUN
ejpam-6264	750	9	n	n	PRON
ejpam-6264	750	10	≥	≥	NOUN
ejpam-6264	750	11	1	1	NUM
ejpam-6264	750	12	,	,	PUNCT
ejpam-6264	750	13	then	then	ADV
ejpam-6264	750	14	(	(	PUNCT
ejpam-6264	750	15	i	i	NOUN
ejpam-6264	750	16	)	)	PUNCT
ejpam-6264	750	17	γtmr(k1	γtmr(k1	PROPN
ejpam-6264	750	18	◦	◦	PROPN
ejpam-6264	750	19	kn	kn	PROPN
ejpam-6264	750	20	)	)	PUNCT
ejpam-6264	750	21	=	=	PUNCT
ejpam-6264	751	1	n+	n+	PUNCT
ejpam-6264	751	2	2	2	X
ejpam-6264	751	3	.	.	PUNCT
ejpam-6264	751	4	(	(	PUNCT
ejpam-6264	751	5	ii	ii	NOUN
ejpam-6264	751	6	)	)	PUNCT
ejpam-6264	751	7	γtmr(kn	γtmr(kn	PROPN
ejpam-6264	751	8	◦	◦	NOUN
ejpam-6264	751	9	k1	k1	PROPN
ejpam-6264	751	10	)	)	PUNCT
ejpam-6264	751	11	=	=	SYM
ejpam-6264	752	1	3n	3n	NOUN
ejpam-6264	752	2	.	.	PUNCT
ejpam-6264	753	1	proof	proof	NOUN
ejpam-6264	753	2	.	.	PUNCT
ejpam-6264	754	1	statement	statement	NOUN
ejpam-6264	754	2	(	(	PUNCT
ejpam-6264	754	3	i	i	NOUN
ejpam-6264	754	4	)	)	PUNCT
ejpam-6264	754	5	follows	follow	VERB
ejpam-6264	754	6	from	from	ADP
ejpam-6264	754	7	the	the	DET
ejpam-6264	754	8	fact	fact	NOUN
ejpam-6264	754	9	that	that	SCONJ
ejpam-6264	754	10	k1	k1	PROPN
ejpam-6264	754	11	◦	◦	NOUN
ejpam-6264	754	12	kn	kn	NOUN
ejpam-6264	754	13	=	=	PUNCT
ejpam-6264	754	14	sn	sn	PROPN
ejpam-6264	754	15	and	and	CCONJ
ejpam-6264	754	16	by	by	ADP
ejpam-6264	754	17	proposition	proposition	NOUN
ejpam-6264	754	18	15	15	NUM
ejpam-6264	754	19	,	,	PUNCT
ejpam-6264	754	20	γtmr(k1	γtmr(k1	PROPN
ejpam-6264	754	21	◦	◦	PROPN
ejpam-6264	754	22	kn	kn	PROPN
ejpam-6264	754	23	)	)	PUNCT
ejpam-6264	754	24	=	=	SYM
ejpam-6264	754	25	γtmr(sn	γtmr(sn	ADJ
ejpam-6264	754	26	)	)	PUNCT
ejpam-6264	754	27	=	=	SYM
ejpam-6264	754	28	n	n	PROPN
ejpam-6264	754	29	+	+	NOUN
ejpam-6264	754	30	2	2	NUM
ejpam-6264	754	31	.	.	X
ejpam-6264	754	32	for	for	ADP
ejpam-6264	754	33	(	(	PUNCT
ejpam-6264	754	34	ii	ii	NOUN
ejpam-6264	754	35	)	)	PUNCT
ejpam-6264	754	36	,	,	PUNCT
ejpam-6264	754	37	note	note	VERB
ejpam-6264	754	38	that	that	SCONJ
ejpam-6264	754	39	kn	kn	PROPN
ejpam-6264	754	40	◦	◦	PROPN
ejpam-6264	754	41	k1	k1	PROPN
ejpam-6264	754	42	is	be	AUX
ejpam-6264	754	43	the	the	DET
ejpam-6264	754	44	disjoint	disjoint	PROPN
ejpam-6264	754	45	union	union	NOUN
ejpam-6264	754	46	n	n	PROPN
ejpam-6264	754	47	copies	copy	NOUN
ejpam-6264	754	48	of	of	ADP
ejpam-6264	754	49	k2	k2	NOUN
ejpam-6264	754	50	.	.	PUNCT
ejpam-6264	755	1	using	use	VERB
ejpam-6264	755	2	proposition	proposition	NOUN
ejpam-6264	755	3	7	7	NUM
ejpam-6264	755	4	(	(	PUNCT
ejpam-6264	755	5	i	i	NOUN
ejpam-6264	755	6	)	)	PUNCT
ejpam-6264	755	7	and	and	CCONJ
ejpam-6264	755	8	proposition	proposition	NOUN
ejpam-6264	755	9	9	9	NUM
ejpam-6264	755	10	,	,	PUNCT
ejpam-6264	755	11	we	we	PRON
ejpam-6264	755	12	have	have	VERB
ejpam-6264	755	13	γtmr(kn	γtmr(kn	PROPN
ejpam-6264	755	14	◦	◦	NOUN
ejpam-6264	755	15	k1	k1	NOUN
ejpam-6264	755	16	)	)	PUNCT
ejpam-6264	756	1	=	=	SYM
ejpam-6264	756	2	3n	3n	NOUN
ejpam-6264	756	3	.	.	PUNCT
ejpam-6264	757	1	acknowledgements	acknowledgement	NOUN
ejpam-6264	757	2	s.	s.	PROPN
ejpam-6264	757	3	ahamad	ahamad	PROPN
ejpam-6264	757	4	would	would	AUX
ejpam-6264	757	5	like	like	VERB
ejpam-6264	757	6	to	to	PART
ejpam-6264	757	7	thank	thank	VERB
ejpam-6264	757	8	the	the	DET
ejpam-6264	757	9	department	department	NOUN
ejpam-6264	757	10	of	of	ADP
ejpam-6264	757	11	science	science	NOUN
ejpam-6264	757	12	and	and	CCONJ
ejpam-6264	757	13	technology	technology	NOUN
ejpam-6264	757	14	accelerated	accelerate	VERB
ejpam-6264	757	15	science	science	NOUN
ejpam-6264	757	16	and	and	CCONJ
ejpam-6264	757	17	technology	technology	NOUN
ejpam-6264	757	18	human	human	ADJ
ejpam-6264	757	19	resource	resource	NOUN
ejpam-6264	757	20	development	development	NOUN
ejpam-6264	757	21	program	program	NOUN
ejpam-6264	757	22	(	(	PUNCT
ejpam-6264	757	23	dost	dost	NOUN
ejpam-6264	757	24	-	-	PUNCT
ejpam-6264	757	25	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-6264	757	26	for	for	ADP
ejpam-6264	757	27	the	the	DET
ejpam-6264	757	28	funding	funding	NOUN
ejpam-6264	757	29	support	support	NOUN
ejpam-6264	757	30	.	.	PUNCT
ejpam-6264	758	1	references	reference	NOUN
ejpam-6264	758	2	[	[	X
ejpam-6264	758	3	1	1	X
ejpam-6264	758	4	]	]	PUNCT
ejpam-6264	758	5	e.	e.	PROPN
ejpam-6264	758	6	j.	j.	PROPN
ejpam-6264	758	7	cockayne	cockayne	PROPN
ejpam-6264	758	8	,	,	PUNCT
ejpam-6264	758	9	p.	p.	PROPN
ejpam-6264	758	10	m.	m.	NOUN
ejpam-6264	758	11	dreyer	dreyer	PROPN
ejpam-6264	758	12	sr	sr	PROPN
ejpam-6264	758	13	.	.	PROPN
ejpam-6264	758	14	,	,	PUNCT
ejpam-6264	758	15	s.	s.	PROPN
ejpam-6264	758	16	m.	m.	PROPN
ejpam-6264	758	17	hedetniemi	hedetniemi	ADV
ejpam-6264	758	18	,	,	PUNCT
ejpam-6264	758	19	and	and	CCONJ
ejpam-6264	758	20	s.	s.	PROPN
ejpam-6264	758	21	t.	t.	PROPN
ejpam-6264	758	22	hedetniemi	hedetniemi	PROPN
ejpam-6264	758	23	.	.	PUNCT
ejpam-6264	759	1	roman	roman	ADJ
ejpam-6264	759	2	domination	domination	NOUN
ejpam-6264	759	3	in	in	ADP
ejpam-6264	759	4	graphs	graph	NOUN
ejpam-6264	759	5	.	.	PUNCT
ejpam-6264	760	1	discrete	discrete	ADJ
ejpam-6264	760	2	mathematics	mathematic	NOUN
ejpam-6264	760	3	,	,	PUNCT
ejpam-6264	760	4	278(1	278(1	NUM
ejpam-6264	760	5	-	-	SYM
ejpam-6264	760	6	3	3	NUM
ejpam-6264	760	7	)	)	PUNCT
ejpam-6264	760	8	,	,	PUNCT
ejpam-6264	760	9	2004	2004	NUM
ejpam-6264	760	10	.	.	PUNCT
ejpam-6264	761	1	[	[	X
ejpam-6264	761	2	2	2	NUM
ejpam-6264	761	3	]	]	PUNCT
ejpam-6264	761	4	c.	c.	PROPN
ejpam-6264	761	5	s.	s.	PROPN
ejpam-6264	761	6	revelle	revelle	PROPN
ejpam-6264	761	7	and	and	CCONJ
ejpam-6264	761	8	k.	k.	PROPN
ejpam-6264	761	9	e.	e.	PROPN
ejpam-6264	761	10	rosing	rosing	PROPN
ejpam-6264	761	11	.	.	PUNCT
ejpam-6264	762	1	defendens	defenden	VERB
ejpam-6264	762	2	imperium	imperium	NOUN
ejpam-6264	762	3	romanum	romanum	NOUN
ejpam-6264	762	4	:	:	PUNCT
ejpam-6264	762	5	a	a	DET
ejpam-6264	762	6	classical	classical	ADJ
ejpam-6264	762	7	problem	problem	NOUN
ejpam-6264	762	8	in	in	ADP
ejpam-6264	762	9	military	military	ADJ
ejpam-6264	762	10	strategy	strategy	NOUN
ejpam-6264	762	11	.	.	PUNCT
ejpam-6264	763	1	american	american	PROPN
ejpam-6264	763	2	mathematical	mathematical	PROPN
ejpam-6264	763	3	monthly	monthly	PROPN
ejpam-6264	763	4	,	,	PUNCT
ejpam-6264	763	5	107(7):585–594	107(7):585–594	PROPN
ejpam-6264	763	6	,	,	PUNCT
ejpam-6264	763	7	2000	2000	NUM
ejpam-6264	763	8	.	.	PUNCT
ejpam-6264	764	1	[	[	X
ejpam-6264	764	2	3	3	NUM
ejpam-6264	764	3	]	]	X
ejpam-6264	764	4	i.	i.	PROPN
ejpam-6264	764	5	stewart	stewart	PROPN
ejpam-6264	764	6	.	.	PUNCT
ejpam-6264	765	1	defend	defend	VERB
ejpam-6264	765	2	the	the	DET
ejpam-6264	765	3	roman	roman	ADJ
ejpam-6264	765	4	empire	empire	NOUN
ejpam-6264	765	5	!	!	PUNCT
ejpam-6264	766	1	scientific	scientific	ADJ
ejpam-6264	766	2	american	american	PROPN
ejpam-6264	766	3	,	,	PUNCT
ejpam-6264	766	4	281(6):136–139	281(6):136–139	PROPN
ejpam-6264	766	5	,	,	PUNCT
ejpam-6264	766	6	1999	1999	NUM
ejpam-6264	766	7	.	.	PUNCT
ejpam-6264	767	1	[	[	X
ejpam-6264	767	2	4	4	NUM
ejpam-6264	767	3	]	]	PUNCT
ejpam-6264	767	4	a.	a.	NOUN
ejpam-6264	767	5	a.	a.	PROPN
ejpam-6264	767	6	hossein	hossein	PROPN
ejpam-6264	767	7	,	,	PUNCT
ejpam-6264	767	8	a.	a.	PROPN
ejpam-6264	767	9	h.	h.	PROPN
ejpam-6264	767	10	michael	michael	PROPN
ejpam-6264	767	11	,	,	PUNCT
ejpam-6264	767	12	s.	s.	PROPN
ejpam-6264	767	13	vladimir	vladimir	PROPN
ejpam-6264	767	14	,	,	PUNCT
ejpam-6264	767	15	and	and	CCONJ
ejpam-6264	767	16	g.	g.	PROPN
ejpam-6264	767	17	y.	y.	PROPN
ejpam-6264	767	18	ismael	ismael	PROPN
ejpam-6264	767	19	.	.	PUNCT
ejpam-6264	768	1	total	total	ADJ
ejpam-6264	768	2	roman	roman	ADJ
ejpam-6264	768	3	domination	domination	NOUN
ejpam-6264	768	4	in	in	ADP
ejpam-6264	768	5	graphs	graph	NOUN
ejpam-6264	768	6	.	.	PUNCT
ejpam-6264	769	1	applicable	applicable	ADJ
ejpam-6264	769	2	analysis	analysis	NOUN
ejpam-6264	769	3	and	and	CCONJ
ejpam-6264	769	4	discrete	discrete	ADJ
ejpam-6264	769	5	mathematics	mathematic	NOUN
ejpam-6264	769	6	,	,	PUNCT
ejpam-6264	769	7	10(2):501–517	10(2):501–517	PROPN
ejpam-6264	769	8	,	,	PUNCT
ejpam-6264	769	9	2016	2016	NUM
ejpam-6264	769	10	.	.	PUNCT
ejpam-6264	770	1	s.	s.	PROPN
ejpam-6264	770	2	ahamad	ahamad	VERB
ejpam-6264	770	3	et	et	PROPN
ejpam-6264	770	4	al	al	PROPN
ejpam-6264	770	5	.	.	PUNCT
ejpam-6264	770	6	/	/	SYM
ejpam-6264	770	7	eur	eur	PROPN
ejpam-6264	770	8	.	.	PUNCT
ejpam-6264	771	1	j.	j.	PROPN
ejpam-6264	771	2	pure	pure	PROPN
ejpam-6264	771	3	appl	appl	PROPN
ejpam-6264	771	4	.	.	PROPN
ejpam-6264	771	5	math	math	PROPN
ejpam-6264	771	6	,	,	PUNCT
ejpam-6264	771	7	18	18	NUM
ejpam-6264	771	8	(	(	PUNCT
ejpam-6264	771	9	4	4	NUM
ejpam-6264	771	10	)	)	PUNCT
ejpam-6264	771	11	(	(	PUNCT
ejpam-6264	771	12	2025	2025	NUM
ejpam-6264	771	13	)	)	PUNCT
ejpam-6264	771	14	,	,	PUNCT
ejpam-6264	771	15	6264	6264	NUM
ejpam-6264	771	16	20	20	NUM
ejpam-6264	771	17	of	of	ADP
ejpam-6264	771	18	20	20	NUM
ejpam-6264	772	1	[	[	SYM
ejpam-6264	772	2	5	5	NUM
ejpam-6264	772	3	]	]	PUNCT
ejpam-6264	772	4	a.	a.	NOUN
ejpam-6264	772	5	h.	h.	PROPN
ejpam-6264	772	6	hassan	hassan	PROPN
ejpam-6264	772	7	and	and	CCONJ
ejpam-6264	772	8	a.	a.	PROPN
ejpam-6264	772	9	o.	o.	PROPN
ejpam-6264	772	10	ahmed	ahmed	PROPN
ejpam-6264	772	11	.	.	PUNCT
ejpam-6264	773	1	modern	modern	ADJ
ejpam-6264	773	2	roman	roman	ADJ
ejpam-6264	773	3	domination	domination	NOUN
ejpam-6264	773	4	in	in	ADP
ejpam-6264	773	5	graphs	graph	NOUN
ejpam-6264	773	6	.	.	PUNCT
ejpam-6264	774	1	basrah	basrah	PROPN
ejpam-6264	774	2	journal	journal	PROPN
ejpam-6264	774	3	of	of	ADP
ejpam-6264	774	4	agricultural	agricultural	ADJ
ejpam-6264	774	5	sciences	science	NOUN
ejpam-6264	774	6	,	,	PUNCT
ejpam-6264	774	7	august	august	PROPN
ejpam-6264	774	8	2018	2018	NUM
ejpam-6264	774	9	.	.	PUNCT
ejpam-6264	775	1	[	[	X
ejpam-6264	775	2	6	6	NUM
ejpam-6264	775	3	]	]	PUNCT
ejpam-6264	775	4	a.	a.	NOUN
ejpam-6264	775	5	o.	o.	PROPN
ejpam-6264	775	6	ahmed	ahmed	PROPN
ejpam-6264	775	7	and	and	CCONJ
ejpam-6264	775	8	n.	n.	PROPN
ejpam-6264	775	9	a.	a.	PROPN
ejpam-6264	775	10	manal	manal	PROPN
ejpam-6264	775	11	.	.	PUNCT
ejpam-6264	776	1	calculating	calculate	VERB
ejpam-6264	776	2	modern	modern	ADJ
ejpam-6264	776	3	roman	roman	ADJ
ejpam-6264	776	4	domination	domination	NOUN
ejpam-6264	776	5	of	of	ADP
ejpam-6264	776	6	fan	fan	NOUN
ejpam-6264	776	7	graph	graph	NOUN
ejpam-6264	776	8	and	and	CCONJ
ejpam-6264	776	9	double	double	ADJ
ejpam-6264	776	10	fan	fan	NOUN
ejpam-6264	776	11	graph	graph	NOUN
ejpam-6264	776	12	.	.	PUNCT
ejpam-6264	777	1	journal	journal	PROPN
ejpam-6264	777	2	of	of	ADP
ejpam-6264	777	3	applied	apply	VERB
ejpam-6264	777	4	sciences	science	NOUN
ejpam-6264	777	5	and	and	CCONJ
ejpam-6264	777	6	nanotechnology	nanotechnology	PROPN
ejpam-6264	777	7	,	,	PUNCT
ejpam-6264	777	8	june	june	PROPN
ejpam-6264	777	9	2022	2022	NUM
ejpam-6264	777	10	.	.	PUNCT
ejpam-6264	778	1	[	[	X
ejpam-6264	778	2	7	7	X
ejpam-6264	778	3	]	]	X
ejpam-6264	778	4	e.	e.	PROPN
ejpam-6264	778	5	w.	w.	PROPN
ejpam-6264	778	6	chambers	chambers	PROPN
ejpam-6264	778	7	et	et	PROPN
ejpam-6264	778	8	al	al	PROPN
ejpam-6264	778	9	.	.	PROPN
ejpam-6264	778	10	extremal	extremal	ADJ
ejpam-6264	778	11	problems	problem	NOUN
ejpam-6264	778	12	for	for	ADP
ejpam-6264	778	13	roman	roman	ADJ
ejpam-6264	778	14	domination	domination	NOUN
ejpam-6264	778	15	.	.	PUNCT
ejpam-6264	779	1	siam	siam	PROPN
ejpam-6264	779	2	journal	journal	PROPN
ejpam-6264	779	3	on	on	ADP
ejpam-6264	779	4	discrete	discrete	ADJ
ejpam-6264	779	5	mathematics	mathematic	NOUN
ejpam-6264	779	6	,	,	PUNCT
ejpam-6264	779	7	2004	2004	NUM
ejpam-6264	779	8	.	.	PUNCT
ejpam-6264	780	1	[	[	X
ejpam-6264	780	2	8	8	X
ejpam-6264	780	3	]	]	PUNCT
ejpam-6264	780	4	j.	j.	PROPN
ejpam-6264	780	5	b.	b.	PROPN
ejpam-6264	780	6	cariaga	cariaga	PROPN
ejpam-6264	780	7	and	and	CCONJ
ejpam-6264	780	8	f.	f.	PROPN
ejpam-6264	780	9	p.	p.	PROPN
ejpam-6264	780	10	jamil	jamil	PROPN
ejpam-6264	780	11	.	.	PUNCT
ejpam-6264	781	1	on	on	ADP
ejpam-6264	781	2	double	double	ADJ
ejpam-6264	781	3	roman	roman	ADJ
ejpam-6264	781	4	dominating	dominating	NOUN
ejpam-6264	781	5	functions	function	NOUN
ejpam-6264	781	6	in	in	ADP
ejpam-6264	781	7	graphs	graph	NOUN
ejpam-6264	781	8	.	.	PUNCT
ejpam-6264	782	1	european	european	ADJ
ejpam-6264	782	2	journal	journal	PROPN
ejpam-6264	782	3	of	of	ADP
ejpam-6264	782	4	pure	pure	ADJ
ejpam-6264	782	5	and	and	CCONJ
ejpam-6264	782	6	applied	applied	ADJ
ejpam-6264	782	7	mathematics	mathematic	NOUN
ejpam-6264	782	8	,	,	PUNCT
ejpam-6264	782	9	16(2):847–863	16(2):847–863	NOUN
ejpam-6264	782	10	,	,	PUNCT
ejpam-6264	782	11	2023	2023	NUM
ejpam-6264	782	12	.	.	PUNCT
ejpam-6264	783	1	[	[	X
ejpam-6264	783	2	9	9	NUM
ejpam-6264	783	3	]	]	X
ejpam-6264	783	4	l.	l.	PROPN
ejpam-6264	783	5	m.	m.	PROPN
ejpam-6264	783	6	paleta	paleta	PROPN
ejpam-6264	783	7	and	and	CCONJ
ejpam-6264	783	8	f.	f.	PROPN
ejpam-6264	783	9	p.	p.	PROPN
ejpam-6264	783	10	jamil	jamil	PROPN
ejpam-6264	783	11	.	.	PUNCT
ejpam-6264	784	1	more	more	ADJ
ejpam-6264	784	2	on	on	ADP
ejpam-6264	784	3	perfect	perfect	ADJ
ejpam-6264	784	4	roman	roman	ADJ
ejpam-6264	784	5	domination	domination	NOUN
ejpam-6264	784	6	in	in	ADP
ejpam-6264	784	7	graphs	graph	NOUN
ejpam-6264	784	8	.	.	PUNCT
ejpam-6264	785	1	european	european	ADJ
ejpam-6264	785	2	journal	journal	PROPN
ejpam-6264	785	3	of	of	ADP
ejpam-6264	785	4	pure	pure	ADJ
ejpam-6264	785	5	and	and	CCONJ
ejpam-6264	785	6	applied	applied	ADJ
ejpam-6264	785	7	mathematics	mathematic	NOUN
ejpam-6264	785	8	,	,	PUNCT
ejpam-6264	785	9	13(3):529–548	13(3):529–548	NOUN
ejpam-6264	785	10	,	,	PUNCT
ejpam-6264	785	11	2020	2020	NUM
ejpam-6264	785	12	.	.	PUNCT
ejpam-6264	786	1	[	[	X
ejpam-6264	786	2	10	10	NUM
ejpam-6264	786	3	]	]	PUNCT
ejpam-6264	786	4	m.	m.	NOUN
ejpam-6264	786	5	a.	a.	PROPN
ejpam-6264	786	6	henning	henning	PROPN
ejpam-6264	786	7	and	and	CCONJ
ejpam-6264	786	8	s.	s.	PROPN
ejpam-6264	786	9	t.	t.	PROPN
ejpam-6264	786	10	hedetniemi	hedetniemi	PROPN
ejpam-6264	786	11	.	.	PUNCT
ejpam-6264	787	1	defending	defend	VERB
ejpam-6264	787	2	the	the	DET
ejpam-6264	787	3	roman	roman	ADJ
ejpam-6264	787	4	empire	empire	NOUN
ejpam-6264	787	5	—	—	PUNCT
ejpam-6264	787	6	a	a	DET
ejpam-6264	787	7	new	new	ADJ
ejpam-6264	787	8	strategy	strategy	NOUN
ejpam-6264	787	9	.	.	PUNCT
ejpam-6264	788	1	discrete	discrete	ADJ
ejpam-6264	788	2	mathematics	mathematic	NOUN
ejpam-6264	788	3	,	,	PUNCT
ejpam-6264	788	4	266(1	266(1	NUM
ejpam-6264	788	5	-	-	SYM
ejpam-6264	788	6	3	3	NUM
ejpam-6264	788	7	)	)	PUNCT
ejpam-6264	788	8	,	,	PUNCT
ejpam-6264	788	9	2003	2003	NUM
ejpam-6264	788	10	.	.	PUNCT
ejpam-6264	789	1	[	[	X
ejpam-6264	789	2	11	11	NUM
ejpam-6264	789	3	]	]	PUNCT
ejpam-6264	789	4	r.	r.	PROPN
ejpam-6264	789	5	j.	j.	PROPN
ejpam-6264	789	6	fortosa	fortosa	PROPN
ejpam-6264	789	7	,	,	PUNCT
ejpam-6264	789	8	f.	f.	PROPN
ejpam-6264	789	9	p.	p.	PROPN
ejpam-6264	789	10	jamil	jamil	PROPN
ejpam-6264	789	11	,	,	PUNCT
ejpam-6264	789	12	and	and	CCONJ
ejpam-6264	789	13	s.	s.	PROPN
ejpam-6264	789	14	r.	r.	PROPN
ejpam-6264	789	15	canoy	canoy	PROPN
ejpam-6264	789	16	.	.	PUNCT
ejpam-6264	790	1	convex	convex	VERB
ejpam-6264	790	2	roman	roman	ADJ
ejpam-6264	790	3	dominating	dominating	NOUN
ejpam-6264	790	4	functions	function	NOUN
ejpam-6264	790	5	on	on	ADP
ejpam-6264	790	6	graphs	graph	NOUN
ejpam-6264	790	7	under	under	ADP
ejpam-6264	790	8	some	some	DET
ejpam-6264	790	9	binary	binary	ADJ
ejpam-6264	790	10	operations	operation	NOUN
ejpam-6264	790	11	.	.	PUNCT
ejpam-6264	791	1	european	european	ADJ
ejpam-6264	791	2	journal	journal	PROPN
ejpam-6264	791	3	of	of	ADP
ejpam-6264	791	4	pure	pure	ADJ
ejpam-6264	791	5	and	and	CCONJ
ejpam-6264	791	6	applied	applied	ADJ
ejpam-6264	791	7	mathematics	mathematic	NOUN
ejpam-6264	791	8	,	,	PUNCT
ejpam-6264	791	9	17(2):1335–1351	17(2):1335–1351	NUM
ejpam-6264	791	10	,	,	PUNCT
ejpam-6264	791	11	2024	2024	NUM
ejpam-6264	791	12	.	.	PUNCT
ejpam-6264	792	1	[	[	X
ejpam-6264	792	2	12	12	NUM
ejpam-6264	792	3	]	]	X
ejpam-6264	792	4	s.	s.	PROPN
ejpam-6264	792	5	r.	r.	PROPN
ejpam-6264	792	6	canoy	canoy	PROPN
ejpam-6264	792	7	jr	jr	PROPN
ejpam-6264	792	8	,	,	PUNCT
ejpam-6264	792	9	f.	f.	PROPN
ejpam-6264	792	10	p.	p.	PROPN
ejpam-6264	792	11	jamil	jamil	PROPN
ejpam-6264	792	12	,	,	PUNCT
ejpam-6264	792	13	and	and	CCONJ
ejpam-6264	792	14	s.	s.	PROPN
ejpam-6264	792	15	m.	m.	PROPN
ejpam-6264	792	16	menchavez	menchavez	PROPN
ejpam-6264	792	17	.	.	PUNCT
ejpam-6264	793	1	hop	hop	PROPN
ejpam-6264	793	2	italian	italian	ADJ
ejpam-6264	793	3	domination	domination	NOUN
ejpam-6264	793	4	in	in	ADP
ejpam-6264	793	5	graphs	graph	NOUN
ejpam-6264	793	6	.	.	PUNCT
ejpam-6264	794	1	european	european	ADJ
ejpam-6264	794	2	journal	journal	PROPN
ejpam-6264	794	3	of	of	ADP
ejpam-6264	794	4	pure	pure	ADJ
ejpam-6264	794	5	and	and	CCONJ
ejpam-6264	794	6	applied	applied	ADJ
ejpam-6264	794	7	mathematics	mathematic	NOUN
ejpam-6264	794	8	,	,	PUNCT
ejpam-6264	794	9	16(4):2431–2449	16(4):2431–2449	NUM
ejpam-6264	794	10	,	,	PUNCT
ejpam-6264	794	11	2023	2023	NUM
ejpam-6264	794	12	.	.	PUNCT
ejpam-6264	795	1	[	[	X
ejpam-6264	795	2	13	13	NUM
ejpam-6264	795	3	]	]	X
ejpam-6264	795	4	s.	s.	PROPN
ejpam-6264	795	5	salah	salah	PROPN
ejpam-6264	795	6	,	,	PUNCT
ejpam-6264	795	7	a.	a.	NOUN
ejpam-6264	795	8	a.	a.	NOUN
ejpam-6264	795	9	omran	omran	PROPN
ejpam-6264	795	10	,	,	PUNCT
ejpam-6264	795	11	and	and	CCONJ
ejpam-6264	795	12	m.	m.	PROPN
ejpam-6264	795	13	n.	n.	PROPN
ejpam-6264	795	14	al	al	PROPN
ejpam-6264	795	15	-	-	PUNCT
ejpam-6264	795	16	harere	harere	PROPN
ejpam-6264	795	17	.	.	PUNCT
ejpam-6264	796	1	modern	modern	ADJ
ejpam-6264	796	2	roman	roman	ADJ
ejpam-6264	796	3	domination	domination	NOUN
ejpam-6264	796	4	on	on	ADP
ejpam-6264	796	5	two	two	NUM
ejpam-6264	796	6	operations	operation	NOUN
ejpam-6264	796	7	in	in	ADP
ejpam-6264	796	8	certain	certain	ADJ
ejpam-6264	796	9	graphs	graph	NOUN
ejpam-6264	796	10	.	.	PUNCT
ejpam-6264	797	1	in	in	ADP
ejpam-6264	797	2	aip	aip	PROPN
ejpam-6264	797	3	conference	conference	NOUN
ejpam-6264	797	4	proceedings	proceeding	NOUN
ejpam-6264	797	5	,	,	PUNCT
ejpam-6264	797	6	volume	volume	NOUN
ejpam-6264	797	7	2386	2386	NUM
ejpam-6264	797	8	,	,	PUNCT
ejpam-6264	797	9	page	page	NOUN
ejpam-6264	797	10	060014	060014	NUM
ejpam-6264	797	11	,	,	PUNCT
ejpam-6264	797	12	2022	2022	NUM
ejpam-6264	797	13	.	.	PUNCT
ejpam-6264	798	1	[	[	X
ejpam-6264	798	2	14	14	NUM
ejpam-6264	798	3	]	]	PUNCT
ejpam-6264	798	4	s.	s.	PROPN
ejpam-6264	798	5	s.	s.	PROPN
ejpam-6264	798	6	majeed	majeed	PROPN
ejpam-6264	798	7	,	,	PUNCT
ejpam-6264	798	8	a.	a.	NOUN
ejpam-6264	798	9	a.	a.	NOUN
ejpam-6264	798	10	omran	omran	PROPN
ejpam-6264	798	11	,	,	PUNCT
ejpam-6264	798	12	and	and	CCONJ
ejpam-6264	798	13	m.	m.	NOUN
ejpam-6264	798	14	n.	n.	PROPN
ejpam-6264	798	15	yaqoob	yaqoob	PROPN
ejpam-6264	798	16	.	.	PUNCT
ejpam-6264	799	1	modern	modern	ADJ
ejpam-6264	799	2	roman	roman	ADJ
ejpam-6264	799	3	domination	domination	NOUN
ejpam-6264	799	4	of	of	ADP
ejpam-6264	799	5	corona	corona	NOUN
ejpam-6264	799	6	of	of	ADP
ejpam-6264	799	7	cycle	cycle	NOUN
ejpam-6264	799	8	graph	graph	NOUN
ejpam-6264	799	9	with	with	ADP
ejpam-6264	799	10	some	some	DET
ejpam-6264	799	11	certain	certain	ADJ
ejpam-6264	799	12	graphs	graph	NOUN
ejpam-6264	799	13	.	.	PUNCT
ejpam-6264	800	1	international	international	ADJ
ejpam-6264	800	2	journal	journal	NOUN
ejpam-6264	800	3	of	of	ADP
ejpam-6264	800	4	mathematics	mathematic	NOUN
ejpam-6264	800	5	and	and	CCONJ
ejpam-6264	800	6	computer	computer	NOUN
ejpam-6264	800	7	science	science	NOUN
ejpam-6264	800	8	,	,	PUNCT
ejpam-6264	800	9	january	january	PROPN
ejpam-6264	800	10	2022	2022	NUM
ejpam-6264	800	11	.	.	PUNCT
ejpam-6264	801	1	[	[	X
ejpam-6264	801	2	15	15	NUM
ejpam-6264	801	3	]	]	X
ejpam-6264	801	4	f.	f.	PROPN
ejpam-6264	801	5	buckley	buckley	PROPN
ejpam-6264	801	6	and	and	CCONJ
ejpam-6264	801	7	f.	f.	PROPN
ejpam-6264	801	8	harary	harary	PROPN
ejpam-6264	801	9	.	.	PUNCT
ejpam-6264	802	1	distance	distance	NOUN
ejpam-6264	802	2	in	in	ADP
ejpam-6264	802	3	graphs	graph	NOUN
ejpam-6264	802	4	.	.	PUNCT
ejpam-6264	803	1	addison	addison	PROPN
ejpam-6264	803	2	-	-	PUNCT
ejpam-6264	803	3	wesley	wesley	PROPN
ejpam-6264	803	4	,	,	PUNCT
ejpam-6264	803	5	redwood	redwood	NOUN
ejpam-6264	803	6	city	city	NOUN
ejpam-6264	803	7	,	,	PUNCT
ejpam-6264	803	8	ca	ca	NOUN
ejpam-6264	803	9	,	,	PUNCT
ejpam-6264	803	10	1990	1990	NUM
ejpam-6264	803	11	.	.	PUNCT
ejpam-6264	804	1	[	[	X
ejpam-6264	804	2	16	16	NUM
ejpam-6264	804	3	]	]	X
ejpam-6264	804	4	e.	e.	PROPN
ejpam-6264	804	5	j.	j.	PROPN
ejpam-6264	804	6	cockayne	cockayne	PROPN
ejpam-6264	804	7	and	and	CCONJ
ejpam-6264	804	8	s.	s.	PROPN
ejpam-6264	804	9	t.	t.	PROPN
ejpam-6264	804	10	hedetniemi	hedetniemi	PROPN
ejpam-6264	804	11	.	.	PUNCT
ejpam-6264	805	1	towards	towards	ADP
ejpam-6264	805	2	a	a	DET
ejpam-6264	805	3	theory	theory	NOUN
ejpam-6264	805	4	of	of	ADP
ejpam-6264	805	5	domination	domination	NOUN
ejpam-6264	805	6	in	in	ADP
ejpam-6264	805	7	graphs	graph	NOUN
ejpam-6264	805	8	.	.	PUNCT
ejpam-6264	806	1	networks	network	NOUN
ejpam-6264	806	2	:	:	PUNCT
ejpam-6264	806	3	an	an	DET
ejpam-6264	806	4	international	international	ADJ
ejpam-6264	806	5	journal	journal	NOUN
ejpam-6264	806	6	,	,	PUNCT
ejpam-6264	806	7	1977	1977	NUM
ejpam-6264	806	8	.	.	PUNCT