id	sid	tid	token	lemma	pos
ejpam-3362	1	1	on	on	ADP
ejpam-3362	1	2	a	a	DET
ejpam-3362	1	3	graph	graph	NOUN
ejpam-3362	1	4	induced	induce	VERB
ejpam-3362	1	5	by	by	ADP
ejpam-3362	1	6	a	a	DET
ejpam-3362	1	7	hyper	hyper	ADJ
ejpam-3362	1	8	bci	bci	NOUN
ejpam-3362	1	9	-	-	ADJ
ejpam-3362	1	10	algebra	algebra	ADJ
ejpam-3362	1	11	european	european	ADJ
ejpam-3362	1	12	journal	journal	PROPN
ejpam-3362	1	13	of	of	ADP
ejpam-3362	1	14	pure	pure	ADJ
ejpam-3362	1	15	and	and	CCONJ
ejpam-3362	1	16	applied	apply	VERB
ejpam-3362	1	17	mathematics	mathematic	NOUN
ejpam-3362	1	18	vol	vol	NOUN
ejpam-3362	1	19	.	.	PROPN
ejpam-3362	2	1	12	12	NUM
ejpam-3362	2	2	,	,	PUNCT
ejpam-3362	2	3	no	no	INTJ
ejpam-3362	2	4	.	.	NOUN
ejpam-3362	2	5	1	1	NUM
ejpam-3362	2	6	,	,	PUNCT
ejpam-3362	2	7	2019	2019	NUM
ejpam-3362	2	8	,	,	PUNCT
ejpam-3362	2	9	146	146	NUM
ejpam-3362	2	10	-	-	SYM
ejpam-3362	2	11	158	158	NUM
ejpam-3362	2	12	issn	issn	PROPN
ejpam-3362	2	13	1307	1307	NUM
ejpam-3362	2	14	-	-	SYM
ejpam-3362	2	15	5543	5543	NUM
ejpam-3362	2	16	–	–	PUNCT
ejpam-3362	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3362	2	18	published	publish	VERB
ejpam-3362	2	19	by	by	ADP
ejpam-3362	2	20	new	new	PROPN
ejpam-3362	2	21	york	york	PROPN
ejpam-3362	2	22	business	business	PROPN
ejpam-3362	2	23	global	global	PROPN
ejpam-3362	2	24	on	on	ADP
ejpam-3362	2	25	a	a	DET
ejpam-3362	2	26	graph	graph	NOUN
ejpam-3362	2	27	induced	induce	VERB
ejpam-3362	2	28	by	by	ADP
ejpam-3362	2	29	a	a	DET
ejpam-3362	2	30	hyper	hyper	ADJ
ejpam-3362	2	31	bci	bci	NOUN
ejpam-3362	2	32	-	-	ADJ
ejpam-3362	2	33	algebra	algebra	NOUN
ejpam-3362	2	34	michelle	michelle	NOUN
ejpam-3362	2	35	t.	t.	PROPN
ejpam-3362	2	36	panganduyon1	panganduyon1	PROPN
ejpam-3362	2	37	,	,	PUNCT
ejpam-3362	2	38	sergio	sergio	PROPN
ejpam-3362	2	39	r.	r.	PROPN
ejpam-3362	2	40	canoy	canoy	PROPN
ejpam-3362	2	41	,	,	PUNCT
ejpam-3362	2	42	jr.1,∗	jr.1,∗	PROPN
ejpam-3362	2	43	department	department	PROPN
ejpam-3362	2	44	of	of	ADP
ejpam-3362	2	45	mathematics	mathematics	PROPN
ejpam-3362	2	46	and	and	CCONJ
ejpam-3362	2	47	statistics	statistic	NOUN
ejpam-3362	2	48	,	,	PUNCT
ejpam-3362	2	49	college	college	NOUN
ejpam-3362	2	50	of	of	ADP
ejpam-3362	2	51	science	science	NOUN
ejpam-3362	2	52	and	and	CCONJ
ejpam-3362	2	53	mathematics	mathematic	NOUN
ejpam-3362	2	54	,	,	PUNCT
ejpam-3362	2	55	center	center	NOUN
ejpam-3362	2	56	for	for	ADP
ejpam-3362	2	57	graph	graph	NOUN
ejpam-3362	2	58	theory	theory	NOUN
ejpam-3362	2	59	,	,	PUNCT
ejpam-3362	2	60	algebra	algebra	NOUN
ejpam-3362	2	61	,	,	PUNCT
ejpam-3362	2	62	and	and	CCONJ
ejpam-3362	2	63	analysis	analysis	NOUN
ejpam-3362	2	64	-	-	PUNCT
ejpam-3362	2	65	prism	prism	NOUN
ejpam-3362	2	66	,	,	PUNCT
ejpam-3362	2	67	mindanao	mindanao	PROPN
ejpam-3362	2	68	state	state	PROPN
ejpam-3362	2	69	university	university	PROPN
ejpam-3362	2	70	-	-	PUNCT
ejpam-3362	2	71	iligan	iligan	PROPN
ejpam-3362	2	72	institute	institute	PROPN
ejpam-3362	2	73	of	of	ADP
ejpam-3362	2	74	technology	technology	PROPN
ejpam-3362	2	75	,	,	PUNCT
ejpam-3362	2	76	9200	9200	NUM
ejpam-3362	2	77	iligan	iligan	ADJ
ejpam-3362	2	78	city	city	NOUN
ejpam-3362	2	79	,	,	PUNCT
ejpam-3362	2	80	philippines	philippine	NOUN
ejpam-3362	2	81	abstract	abstract	ADJ
ejpam-3362	2	82	.	.	PUNCT
ejpam-3362	3	1	this	this	DET
ejpam-3362	3	2	paper	paper	NOUN
ejpam-3362	3	3	introduces	introduce	VERB
ejpam-3362	3	4	the	the	DET
ejpam-3362	3	5	notion	notion	NOUN
ejpam-3362	3	6	of	of	ADP
ejpam-3362	3	7	the	the	DET
ejpam-3362	3	8	zero	zero	NUM
ejpam-3362	3	9	divisor	divisor	NOUN
ejpam-3362	3	10	graph	graph	NOUN
ejpam-3362	3	11	of	of	ADP
ejpam-3362	3	12	a	a	DET
ejpam-3362	3	13	hyper	hyper	ADJ
ejpam-3362	3	14	bci	bci	NOUN
ejpam-3362	3	15	-	-	NOUN
ejpam-3362	3	16	algebra	algebra	NOUN
ejpam-3362	3	17	and	and	CCONJ
ejpam-3362	3	18	investigates	investigate	VERB
ejpam-3362	3	19	some	some	PRON
ejpam-3362	3	20	of	of	ADP
ejpam-3362	3	21	its	its	PRON
ejpam-3362	3	22	properties	property	NOUN
ejpam-3362	3	23	.	.	PUNCT
ejpam-3362	4	1	2010	2010	NUM
ejpam-3362	4	2	mathematics	mathematic	NOUN
ejpam-3362	4	3	subject	subject	NOUN
ejpam-3362	4	4	classifications	classification	NOUN
ejpam-3362	4	5	:	:	PUNCT
ejpam-3362	4	6	20m14	20m14	NUM
ejpam-3362	4	7	,	,	PUNCT
ejpam-3362	4	8	05c25	05c25	NOUN
ejpam-3362	4	9	key	key	ADJ
ejpam-3362	4	10	words	word	NOUN
ejpam-3362	4	11	and	and	CCONJ
ejpam-3362	4	12	phrases	phrase	NOUN
ejpam-3362	4	13	:	:	PUNCT
ejpam-3362	4	14	zero	zero	NUM
ejpam-3362	4	15	divisor	divisor	NOUN
ejpam-3362	4	16	graph	graph	NOUN
ejpam-3362	4	17	,	,	PUNCT
ejpam-3362	4	18	hyper	hyper	ADJ
ejpam-3362	4	19	bci	bci	NOUN
ejpam-3362	4	20	-	-	NOUN
ejpam-3362	4	21	algebra	algebra	NOUN
ejpam-3362	4	22	,	,	PUNCT
ejpam-3362	4	23	hyperatom	hyperatom	NOUN
ejpam-3362	4	24	,	,	PUNCT
ejpam-3362	4	25	complete	complete	ADJ
ejpam-3362	4	26	,	,	PUNCT
ejpam-3362	4	27	star	star	NOUN
ejpam-3362	4	28	1	1	NUM
ejpam-3362	4	29	.	.	PUNCT
ejpam-3362	5	1	introduction	introduction	NOUN
ejpam-3362	5	2	graph	graph	NOUN
ejpam-3362	5	3	theory	theory	NOUN
ejpam-3362	5	4	and	and	CCONJ
ejpam-3362	5	5	abstract	abstract	ADJ
ejpam-3362	5	6	algebra	algebra	NOUN
ejpam-3362	5	7	have	have	AUX
ejpam-3362	5	8	been	be	AUX
ejpam-3362	5	9	profoundly	profoundly	ADV
ejpam-3362	5	10	studied	study	VERB
ejpam-3362	5	11	by	by	ADP
ejpam-3362	5	12	mathematicians	mathematician	NOUN
ejpam-3362	5	13	because	because	SCONJ
ejpam-3362	5	14	of	of	ADP
ejpam-3362	5	15	the	the	DET
ejpam-3362	5	16	interesting	interesting	ADJ
ejpam-3362	5	17	topics	topic	NOUN
ejpam-3362	5	18	laid	lay	VERB
ejpam-3362	5	19	upon	upon	SCONJ
ejpam-3362	5	20	these	these	DET
ejpam-3362	5	21	branches	branch	NOUN
ejpam-3362	5	22	of	of	ADP
ejpam-3362	5	23	mathematics	mathematic	NOUN
ejpam-3362	5	24	.	.	PUNCT
ejpam-3362	6	1	indeed	indeed	ADV
ejpam-3362	6	2	,	,	PUNCT
ejpam-3362	6	3	some	some	DET
ejpam-3362	6	4	authors	author	NOUN
ejpam-3362	6	5	studied	study	VERB
ejpam-3362	6	6	graph	graph	NOUN
ejpam-3362	6	7	theory	theory	NOUN
ejpam-3362	6	8	to	to	PART
ejpam-3362	6	9	build	build	VERB
ejpam-3362	6	10	connections	connection	NOUN
ejpam-3362	6	11	with	with	ADP
ejpam-3362	6	12	certain	certain	ADJ
ejpam-3362	6	13	algebraic	algebraic	ADJ
ejpam-3362	6	14	structures	structure	NOUN
ejpam-3362	6	15	such	such	ADJ
ejpam-3362	6	16	as	as	ADP
ejpam-3362	6	17	commutative	commutative	ADJ
ejpam-3362	6	18	semigroups	semigroup	NOUN
ejpam-3362	6	19	,	,	PUNCT
ejpam-3362	6	20	commutative	commutative	ADJ
ejpam-3362	6	21	rings	ring	NOUN
ejpam-3362	6	22	,	,	PUNCT
ejpam-3362	6	23	and	and	CCONJ
ejpam-3362	6	24	non	non	ADJ
ejpam-3362	6	25	-	-	ADJ
ejpam-3362	6	26	commutative	commutative	ADJ
ejpam-3362	6	27	rings	ring	NOUN
ejpam-3362	6	28	.	.	PUNCT
ejpam-3362	7	1	beck	beck	PROPN
ejpam-3362	7	2	,	,	PUNCT
ejpam-3362	7	3	in	in	ADP
ejpam-3362	7	4	his	his	PRON
ejpam-3362	7	5	work	work	NOUN
ejpam-3362	7	6	in	in	ADP
ejpam-3362	7	7	[	[	X
ejpam-3362	7	8	1	1	NUM
ejpam-3362	7	9	]	]	PUNCT
ejpam-3362	7	10	,	,	PUNCT
ejpam-3362	7	11	associated	associate	VERB
ejpam-3362	7	12	to	to	ADP
ejpam-3362	7	13	any	any	DET
ejpam-3362	7	14	commutative	commutative	ADJ
ejpam-3362	7	15	ring	ring	NOUN
ejpam-3362	7	16	r	r	NOUN
ejpam-3362	7	17	its	its	PRON
ejpam-3362	7	18	zero	zero	NUM
ejpam-3362	7	19	divisor	divisor	NOUN
ejpam-3362	7	20	graph	graph	NOUN
ejpam-3362	7	21	g(r	g(r	PROPN
ejpam-3362	7	22	)	)	PUNCT
ejpam-3362	7	23	whose	whose	DET
ejpam-3362	7	24	vertices	vertex	NOUN
ejpam-3362	7	25	are	be	AUX
ejpam-3362	7	26	the	the	DET
ejpam-3362	7	27	zero	zero	NUM
ejpam-3362	7	28	divisors	divisor	NOUN
ejpam-3362	7	29	of	of	ADP
ejpam-3362	7	30	r	r	NOUN
ejpam-3362	7	31	(	(	PUNCT
ejpam-3362	7	32	including	include	VERB
ejpam-3362	7	33	an	an	DET
ejpam-3362	7	34	element	element	NOUN
ejpam-3362	7	35	0	0	NUM
ejpam-3362	7	36	of	of	ADP
ejpam-3362	7	37	r	r	NOUN
ejpam-3362	7	38	)	)	PUNCT
ejpam-3362	7	39	and	and	CCONJ
ejpam-3362	7	40	where	where	SCONJ
ejpam-3362	7	41	adjacency	adjacency	NOUN
ejpam-3362	7	42	between	between	ADP
ejpam-3362	7	43	two	two	NUM
ejpam-3362	7	44	distinct	distinct	ADJ
ejpam-3362	7	45	elements	element	NOUN
ejpam-3362	7	46	of	of	ADP
ejpam-3362	7	47	r	r	NOUN
ejpam-3362	7	48	is	be	AUX
ejpam-3362	7	49	defined	define	VERB
ejpam-3362	7	50	as	as	SCONJ
ejpam-3362	7	51	follows	follow	VERB
ejpam-3362	7	52	:	:	PUNCT
ejpam-3362	7	53	two	two	NUM
ejpam-3362	7	54	vertices	vertex	NOUN
ejpam-3362	7	55	x	x	X
ejpam-3362	7	56	,	,	PUNCT
ejpam-3362	7	57	y	y	PROPN
ejpam-3362	7	58	are	be	AUX
ejpam-3362	7	59	adjacent	adjacent	ADJ
ejpam-3362	7	60	if	if	SCONJ
ejpam-3362	7	61	and	and	CCONJ
ejpam-3362	7	62	only	only	ADV
ejpam-3362	7	63	if	if	SCONJ
ejpam-3362	7	64	xy	xy	PROPN
ejpam-3362	7	65	=	=	NOUN
ejpam-3362	7	66	0	0	PROPN
ejpam-3362	7	67	.	.	PUNCT
ejpam-3362	8	1	in	in	ADP
ejpam-3362	8	2	2002	2002	NUM
ejpam-3362	8	3	,	,	PUNCT
ejpam-3362	8	4	demeyer	demeyer	NOUN
ejpam-3362	8	5	et	et	PROPN
ejpam-3362	8	6	al	al	PROPN
ejpam-3362	8	7	.	.	PUNCT
ejpam-3362	9	1	[	[	X
ejpam-3362	9	2	2	2	X
ejpam-3362	9	3	]	]	PUNCT
ejpam-3362	9	4	also	also	ADV
ejpam-3362	9	5	pioneered	pioneer	VERB
ejpam-3362	9	6	the	the	DET
ejpam-3362	9	7	notion	notion	NOUN
ejpam-3362	9	8	of	of	ADP
ejpam-3362	9	9	zero	zero	NUM
ejpam-3362	9	10	-	-	PUNCT
ejpam-3362	9	11	divisor	divisor	NOUN
ejpam-3362	9	12	graph	graph	NOUN
ejpam-3362	9	13	of	of	ADP
ejpam-3362	9	14	commutative	commutative	ADJ
ejpam-3362	9	15	semigroup	semigroup	NOUN
ejpam-3362	9	16	s	s	PROPN
ejpam-3362	9	17	with	with	ADP
ejpam-3362	9	18	0	0	NUM
ejpam-3362	9	19	.	.	PUNCT
ejpam-3362	10	1	they	they	PRON
ejpam-3362	10	2	associated	associate	VERB
ejpam-3362	10	3	an	an	DET
ejpam-3362	10	4	undirected	undirected	ADJ
ejpam-3362	10	5	graph	graph	NOUN
ejpam-3362	10	6	γ(s	γ(	NOUN
ejpam-3362	10	7	)	)	PUNCT
ejpam-3362	10	8	to	to	ADP
ejpam-3362	10	9	any	any	DET
ejpam-3362	10	10	commutative	commutative	ADJ
ejpam-3362	10	11	semigroup	semigroup	NOUN
ejpam-3362	10	12	s	s	X
ejpam-3362	10	13	with	with	ADP
ejpam-3362	10	14	0	0	NUM
ejpam-3362	10	15	whose	whose	DET
ejpam-3362	10	16	vertices	vertex	NOUN
ejpam-3362	10	17	are	be	AUX
ejpam-3362	10	18	the	the	DET
ejpam-3362	10	19	nonzero	nonzero	ADJ
ejpam-3362	10	20	zero	zero	NUM
ejpam-3362	10	21	divisors	divisor	NOUN
ejpam-3362	10	22	of	of	ADP
ejpam-3362	10	23	s	s	PROPN
ejpam-3362	10	24	,	,	PUNCT
ejpam-3362	10	25	such	such	ADJ
ejpam-3362	10	26	that	that	SCONJ
ejpam-3362	10	27	two	two	NUM
ejpam-3362	10	28	vertices	vertex	NOUN
ejpam-3362	10	29	x	x	X
ejpam-3362	10	30	,	,	PUNCT
ejpam-3362	10	31	y	y	PROPN
ejpam-3362	10	32	are	be	AUX
ejpam-3362	10	33	adjacent	adjacent	ADJ
ejpam-3362	10	34	if	if	SCONJ
ejpam-3362	10	35	and	and	CCONJ
ejpam-3362	10	36	only	only	ADV
ejpam-3362	10	37	if	if	SCONJ
ejpam-3362	10	38	xy	xy	PROPN
ejpam-3362	10	39	=	=	NOUN
ejpam-3362	10	40	0	0	X
ejpam-3362	10	41	.	.	PUNCT
ejpam-3362	11	1	more	more	ADV
ejpam-3362	11	2	recently	recently	ADV
ejpam-3362	11	3	,	,	PUNCT
ejpam-3362	11	4	y.	y.	PROPN
ejpam-3362	11	5	b.	b.	PROPN
ejpam-3362	11	6	jun	jun	PROPN
ejpam-3362	11	7	and	and	CCONJ
ejpam-3362	11	8	k.	k.	PROPN
ejpam-3362	11	9	j.	j.	PROPN
ejpam-3362	11	10	lee	lee	PROPN
ejpam-3362	12	1	[	[	X
ejpam-3362	12	2	5	5	NUM
ejpam-3362	12	3	]	]	PUNCT
ejpam-3362	12	4	introduced	introduce	VERB
ejpam-3362	12	5	the	the	DET
ejpam-3362	12	6	concept	concept	NOUN
ejpam-3362	12	7	of	of	ADP
ejpam-3362	12	8	associated	associated	ADJ
ejpam-3362	12	9	graph	graph	NOUN
ejpam-3362	12	10	of	of	ADP
ejpam-3362	12	11	bci	bci	NOUN
ejpam-3362	12	12	-	-	NOUN
ejpam-3362	12	13	algebra	algebra	NOUN
ejpam-3362	12	14	and	and	CCONJ
ejpam-3362	12	15	verified	verify	VERB
ejpam-3362	12	16	some	some	DET
ejpam-3362	12	17	properties	property	NOUN
ejpam-3362	12	18	of	of	ADP
ejpam-3362	12	19	the	the	DET
ejpam-3362	12	20	graph	graph	NOUN
ejpam-3362	12	21	.	.	PUNCT
ejpam-3362	13	1	motivated	motivate	VERB
ejpam-3362	13	2	by	by	ADP
ejpam-3362	13	3	these	these	DET
ejpam-3362	13	4	works	work	NOUN
ejpam-3362	13	5	,	,	PUNCT
ejpam-3362	13	6	in	in	ADP
ejpam-3362	13	7	this	this	DET
ejpam-3362	13	8	paper	paper	NOUN
ejpam-3362	13	9	,	,	PUNCT
ejpam-3362	13	10	we	we	PRON
ejpam-3362	13	11	shall	shall	AUX
ejpam-3362	13	12	introduce	introduce	VERB
ejpam-3362	13	13	the	the	DET
ejpam-3362	13	14	notion	notion	NOUN
ejpam-3362	13	15	of	of	ADP
ejpam-3362	13	16	the	the	DET
ejpam-3362	13	17	zero	zero	NUM
ejpam-3362	13	18	divisor	divisor	NOUN
ejpam-3362	13	19	graph	graph	NOUN
ejpam-3362	13	20	of	of	ADP
ejpam-3362	13	21	a	a	DET
ejpam-3362	13	22	hyper	hyper	ADJ
ejpam-3362	13	23	bci	bci	NOUN
ejpam-3362	13	24	-	-	NOUN
ejpam-3362	13	25	algebra	algebra	NOUN
ejpam-3362	13	26	and	and	CCONJ
ejpam-3362	13	27	investigate	investigate	VERB
ejpam-3362	13	28	some	some	PRON
ejpam-3362	13	29	of	of	ADP
ejpam-3362	13	30	its	its	PRON
ejpam-3362	13	31	properties	property	NOUN
ejpam-3362	13	32	.	.	PUNCT
ejpam-3362	14	1	∗corresponding	∗corresponde	VERB
ejpam-3362	14	2	author	author	NOUN
ejpam-3362	14	3	.	.	PUNCT
ejpam-3362	15	1	doi	doi	NOUN
ejpam-3362	15	2	:	:	PUNCT
ejpam-3362	15	3	https://doi.org/10.29020/nybg.ejpam.v12i1.3362	https://doi.org/10.29020/nybg.ejpam.v12i1.3362	VERB
ejpam-3362	15	4	email	email	NOUN
ejpam-3362	15	5	addresses	address	NOUN
ejpam-3362	15	6	:	:	PUNCT
ejpam-3362	15	7	michelle.panganduyon@g.msuiit.edu.ph	michelle.panganduyon@g.msuiit.edu.ph	NOUN
ejpam-3362	15	8	(	(	PUNCT
ejpam-3362	15	9	m.	m.	NOUN
ejpam-3362	15	10	panganduyon	panganduyon	NOUN
ejpam-3362	15	11	)	)	PUNCT
ejpam-3362	15	12	,	,	PUNCT
ejpam-3362	15	13	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-3362	15	14	(	(	PUNCT
ejpam-3362	15	15	s.	s.	PROPN
ejpam-3362	15	16	canoy	canoy	PROPN
ejpam-3362	15	17	)	)	PUNCT
ejpam-3362	15	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3362	16	1	146	146	NUM
ejpam-3362	16	2	c	c	X
ejpam-3362	16	3	©	©	PROPN
ejpam-3362	16	4	2019	2019	NUM
ejpam-3362	16	5	ejpam	ejpam	NOUN
ejpam-3362	16	6	all	all	DET
ejpam-3362	16	7	rights	right	NOUN
ejpam-3362	16	8	reserved	reserve	VERB
ejpam-3362	16	9	.	.	PUNCT
ejpam-3362	17	1	m.	m.	NOUN
ejpam-3362	17	2	panganduyon	panganduyon	NOUN
ejpam-3362	17	3	,	,	PUNCT
ejpam-3362	17	4	s.	s.	PROPN
ejpam-3362	17	5	canoy	canoy	PROPN
ejpam-3362	17	6	/	/	SYM
ejpam-3362	17	7	eur	eur	PROPN
ejpam-3362	17	8	.	.	PUNCT
ejpam-3362	18	1	j.	j.	PROPN
ejpam-3362	18	2	pure	pure	PROPN
ejpam-3362	18	3	appl	appl	PROPN
ejpam-3362	18	4	.	.	PROPN
ejpam-3362	18	5	math	math	PROPN
ejpam-3362	18	6	,	,	PUNCT
ejpam-3362	18	7	12	12	NUM
ejpam-3362	18	8	(	(	PUNCT
ejpam-3362	18	9	1	1	NUM
ejpam-3362	18	10	)	)	PUNCT
ejpam-3362	18	11	(	(	PUNCT
ejpam-3362	18	12	2019	2019	NUM
ejpam-3362	18	13	)	)	PUNCT
ejpam-3362	18	14	,	,	PUNCT
ejpam-3362	18	15	146	146	NUM
ejpam-3362	18	16	-	-	SYM
ejpam-3362	18	17	158	158	NUM
ejpam-3362	18	18	147	147	NUM
ejpam-3362	18	19	2	2	NUM
ejpam-3362	18	20	.	.	PUNCT
ejpam-3362	18	21	preliminaries	preliminary	NOUN
ejpam-3362	18	22	the	the	DET
ejpam-3362	18	23	concepts	concept	NOUN
ejpam-3362	18	24	on	on	ADP
ejpam-3362	18	25	graph	graph	NOUN
ejpam-3362	18	26	theory	theory	NOUN
ejpam-3362	18	27	are	be	AUX
ejpam-3362	18	28	taken	take	VERB
ejpam-3362	18	29	from	from	ADP
ejpam-3362	18	30	[	[	X
ejpam-3362	18	31	4	4	NUM
ejpam-3362	18	32	]	]	PUNCT
ejpam-3362	18	33	:	:	PUNCT
ejpam-3362	18	34	a	a	DET
ejpam-3362	18	35	graph	graph	NOUN
ejpam-3362	18	36	g	g	NOUN
ejpam-3362	18	37	is	be	AUX
ejpam-3362	18	38	an	an	DET
ejpam-3362	18	39	ordered	order	VERB
ejpam-3362	18	40	pair	pair	NOUN
ejpam-3362	18	41	(	(	PUNCT
ejpam-3362	18	42	v	v	NOUN
ejpam-3362	18	43	(	(	PUNCT
ejpam-3362	18	44	g	g	NOUN
ejpam-3362	18	45	)	)	PUNCT
ejpam-3362	18	46	,	,	PUNCT
ejpam-3362	18	47	e(g	e(g	PROPN
ejpam-3362	18	48	)	)	PUNCT
ejpam-3362	18	49	)	)	PUNCT
ejpam-3362	18	50	,	,	PUNCT
ejpam-3362	18	51	where	where	SCONJ
ejpam-3362	18	52	v	v	X
ejpam-3362	18	53	(	(	PUNCT
ejpam-3362	18	54	g	g	NOUN
ejpam-3362	18	55	)	)	PUNCT
ejpam-3362	18	56	is	be	AUX
ejpam-3362	18	57	a	a	DET
ejpam-3362	18	58	finite	finite	NOUN
ejpam-3362	18	59	nonempty	nonempty	ADV
ejpam-3362	18	60	set	set	NOUN
ejpam-3362	18	61	called	call	VERB
ejpam-3362	18	62	the	the	DET
ejpam-3362	18	63	vertex	vertex	NOUN
ejpam-3362	18	64	set	set	NOUN
ejpam-3362	18	65	of	of	ADP
ejpam-3362	18	66	g	g	PROPN
ejpam-3362	18	67	and	and	CCONJ
ejpam-3362	18	68	e(g	e(g	PROPN
ejpam-3362	18	69	)	)	PUNCT
ejpam-3362	18	70	is	be	AUX
ejpam-3362	18	71	a	a	DET
ejpam-3362	18	72	set	set	NOUN
ejpam-3362	18	73	of	of	ADP
ejpam-3362	18	74	unordered	unordered	ADJ
ejpam-3362	18	75	pairs	pair	NOUN
ejpam-3362	18	76	{	{	PUNCT
ejpam-3362	18	77	u	u	NOUN
ejpam-3362	18	78	,	,	PUNCT
ejpam-3362	18	79	v	v	NOUN
ejpam-3362	18	80	}	}	PUNCT
ejpam-3362	18	81	(	(	PUNCT
ejpam-3362	18	82	or	or	CCONJ
ejpam-3362	18	83	simply	simply	ADV
ejpam-3362	18	84	uv	uv	NOUN
ejpam-3362	18	85	)	)	PUNCT
ejpam-3362	18	86	of	of	ADP
ejpam-3362	18	87	distinct	distinct	ADJ
ejpam-3362	18	88	elements	element	NOUN
ejpam-3362	18	89	from	from	ADP
ejpam-3362	18	90	v	v	PRON
ejpam-3362	18	91	(	(	PUNCT
ejpam-3362	18	92	g	g	NOUN
ejpam-3362	18	93	)	)	PUNCT
ejpam-3362	18	94	called	call	VERB
ejpam-3362	18	95	the	the	DET
ejpam-3362	18	96	edge	edge	NOUN
ejpam-3362	18	97	set	set	NOUN
ejpam-3362	18	98	of	of	ADP
ejpam-3362	18	99	g.	g.	PROPN
ejpam-3362	18	100	the	the	DET
ejpam-3362	18	101	elements	element	NOUN
ejpam-3362	18	102	of	of	ADP
ejpam-3362	18	103	v	v	NOUN
ejpam-3362	18	104	(	(	PUNCT
ejpam-3362	18	105	g	g	NOUN
ejpam-3362	18	106	)	)	PUNCT
ejpam-3362	18	107	are	be	AUX
ejpam-3362	18	108	called	call	VERB
ejpam-3362	18	109	vertices	vertex	NOUN
ejpam-3362	18	110	and	and	CCONJ
ejpam-3362	18	111	the	the	DET
ejpam-3362	18	112	cardinality	cardinality	NOUN
ejpam-3362	18	113	|v	|v	PROPN
ejpam-3362	18	114	(	(	PUNCT
ejpam-3362	18	115	g)|	g)|	NOUN
ejpam-3362	18	116	of	of	ADP
ejpam-3362	18	117	v	v	NOUN
ejpam-3362	18	118	(	(	PUNCT
ejpam-3362	18	119	g	g	NOUN
ejpam-3362	18	120	)	)	PUNCT
ejpam-3362	18	121	is	be	AUX
ejpam-3362	18	122	the	the	DET
ejpam-3362	18	123	order	order	NOUN
ejpam-3362	18	124	of	of	ADP
ejpam-3362	18	125	g.	g.	PROPN
ejpam-3362	18	126	the	the	DET
ejpam-3362	18	127	elements	element	NOUN
ejpam-3362	18	128	of	of	ADP
ejpam-3362	18	129	e(g	e(g	PROPN
ejpam-3362	18	130	)	)	PUNCT
ejpam-3362	18	131	are	be	AUX
ejpam-3362	18	132	called	call	VERB
ejpam-3362	18	133	edges	edge	NOUN
ejpam-3362	18	134	and	and	CCONJ
ejpam-3362	18	135	the	the	DET
ejpam-3362	18	136	cardinality	cardinality	NOUN
ejpam-3362	18	137	|e(g)|	|e(g)|	PROPN
ejpam-3362	18	138	of	of	ADP
ejpam-3362	18	139	e(g	e(g	PROPN
ejpam-3362	18	140	)	)	PUNCT
ejpam-3362	18	141	is	be	AUX
ejpam-3362	18	142	the	the	DET
ejpam-3362	18	143	size	size	NOUN
ejpam-3362	18	144	of	of	ADP
ejpam-3362	18	145	g.	g.	PROPN
ejpam-3362	18	146	a	a	DET
ejpam-3362	18	147	graph	graph	NOUN
ejpam-3362	18	148	k	k	NOUN
ejpam-3362	18	149	=	=	SYM
ejpam-3362	18	150	(	(	PUNCT
ejpam-3362	18	151	v	v	NOUN
ejpam-3362	18	152	(	(	PUNCT
ejpam-3362	18	153	k	k	NOUN
ejpam-3362	18	154	)	)	PUNCT
ejpam-3362	18	155	,	,	PUNCT
ejpam-3362	18	156	e(k	e(k	NOUN
ejpam-3362	18	157	)	)	PUNCT
ejpam-3362	18	158	)	)	PUNCT
ejpam-3362	18	159	is	be	AUX
ejpam-3362	18	160	a	a	DET
ejpam-3362	18	161	subgraph	subgraph	NOUN
ejpam-3362	18	162	of	of	ADP
ejpam-3362	18	163	a	a	DET
ejpam-3362	18	164	graph	graph	NOUN
ejpam-3362	18	165	g	g	NOUN
ejpam-3362	18	166	=	=	PUNCT
ejpam-3362	18	167	(	(	PUNCT
ejpam-3362	18	168	v	v	NOUN
ejpam-3362	18	169	(	(	PUNCT
ejpam-3362	18	170	g	g	NOUN
ejpam-3362	18	171	)	)	PUNCT
ejpam-3362	18	172	,	,	PUNCT
ejpam-3362	18	173	e(g	e(g	PROPN
ejpam-3362	18	174	)	)	PUNCT
ejpam-3362	18	175	)	)	PUNCT
ejpam-3362	19	1	if	if	SCONJ
ejpam-3362	19	2	v	v	X
ejpam-3362	19	3	(	(	PUNCT
ejpam-3362	19	4	k	k	NOUN
ejpam-3362	19	5	)	)	PUNCT
ejpam-3362	19	6	⊆	⊆	NUM
ejpam-3362	19	7	v	v	NOUN
ejpam-3362	19	8	(	(	PUNCT
ejpam-3362	19	9	g	g	NOUN
ejpam-3362	19	10	)	)	PUNCT
ejpam-3362	19	11	and	and	CCONJ
ejpam-3362	19	12	e(k	e(k	NOUN
ejpam-3362	19	13	)	)	PUNCT
ejpam-3362	19	14	⊆	⊆	NUM
ejpam-3362	19	15	e(g	e(g	PROPN
ejpam-3362	19	16	)	)	PUNCT
ejpam-3362	19	17	.	.	PUNCT
ejpam-3362	20	1	two	two	NUM
ejpam-3362	20	2	vertices	vertice	VERB
ejpam-3362	20	3	u	u	NOUN
ejpam-3362	20	4	,	,	PUNCT
ejpam-3362	20	5	v	v	NOUN
ejpam-3362	20	6	of	of	ADP
ejpam-3362	20	7	a	a	DET
ejpam-3362	20	8	graph	graph	NOUN
ejpam-3362	20	9	g	g	NOUN
ejpam-3362	20	10	are	be	AUX
ejpam-3362	20	11	adjacent	adjacent	ADJ
ejpam-3362	20	12	,	,	PUNCT
ejpam-3362	20	13	or	or	CCONJ
ejpam-3362	20	14	neighbors	neighbor	NOUN
ejpam-3362	20	15	,	,	PUNCT
ejpam-3362	20	16	if	if	SCONJ
ejpam-3362	20	17	uv	uv	NOUN
ejpam-3362	20	18	is	be	AUX
ejpam-3362	20	19	an	an	DET
ejpam-3362	20	20	edge	edge	NOUN
ejpam-3362	20	21	of	of	ADP
ejpam-3362	20	22	g.	g.	PROPN
ejpam-3362	20	23	the	the	DET
ejpam-3362	20	24	set	set	NOUN
ejpam-3362	20	25	of	of	ADP
ejpam-3362	20	26	neighbors	neighbor	NOUN
ejpam-3362	20	27	of	of	ADP
ejpam-3362	20	28	a	a	DET
ejpam-3362	20	29	vertex	vertex	NOUN
ejpam-3362	20	30	v	v	NOUN
ejpam-3362	20	31	of	of	ADP
ejpam-3362	20	32	g	g	PROPN
ejpam-3362	20	33	is	be	AUX
ejpam-3362	20	34	denoted	denote	VERB
ejpam-3362	20	35	by	by	ADP
ejpam-3362	20	36	ng(v	ng(v	NOUN
ejpam-3362	20	37	)	)	PUNCT
ejpam-3362	20	38	and	and	CCONJ
ejpam-3362	20	39	the	the	DET
ejpam-3362	20	40	degree	degree	NOUN
ejpam-3362	20	41	of	of	ADP
ejpam-3362	20	42	v	v	NOUN
ejpam-3362	20	43	in	in	ADP
ejpam-3362	20	44	g	g	NOUN
ejpam-3362	20	45	,	,	PUNCT
ejpam-3362	20	46	denoted	denote	VERB
ejpam-3362	20	47	deg	deg	PROPN
ejpam-3362	20	48	v	v	NOUN
ejpam-3362	20	49	,	,	PUNCT
ejpam-3362	20	50	is	be	AUX
ejpam-3362	20	51	equal	equal	ADJ
ejpam-3362	20	52	to	to	ADP
ejpam-3362	20	53	|ng(v)|	|ng(v)|	NOUN
ejpam-3362	20	54	.	.	PUNCT
ejpam-3362	21	1	the	the	DET
ejpam-3362	21	2	degree	degree	NOUN
ejpam-3362	21	3	of	of	ADP
ejpam-3362	21	4	g	g	NOUN
ejpam-3362	21	5	,	,	PUNCT
ejpam-3362	21	6	denoted	denote	VERB
ejpam-3362	21	7	by	by	ADP
ejpam-3362	21	8	∆(g	∆(g	PROPN
ejpam-3362	21	9	)	)	PUNCT
ejpam-3362	21	10	,	,	PUNCT
ejpam-3362	21	11	is	be	AUX
ejpam-3362	21	12	equal	equal	ADJ
ejpam-3362	21	13	to	to	ADP
ejpam-3362	21	14	the	the	DET
ejpam-3362	21	15	largest	large	ADJ
ejpam-3362	21	16	degree	degree	NOUN
ejpam-3362	21	17	of	of	ADP
ejpam-3362	21	18	a	a	DET
ejpam-3362	21	19	vertex	vertex	NOUN
ejpam-3362	21	20	of	of	ADP
ejpam-3362	21	21	g.	g.	PROPN
ejpam-3362	21	22	a	a	DET
ejpam-3362	21	23	vertex	vertex	NOUN
ejpam-3362	21	24	w	w	NOUN
ejpam-3362	21	25	of	of	ADP
ejpam-3362	21	26	g	g	PROPN
ejpam-3362	21	27	is	be	AUX
ejpam-3362	21	28	called	call	VERB
ejpam-3362	21	29	an	an	DET
ejpam-3362	21	30	isolated	isolated	ADJ
ejpam-3362	21	31	vertex	vertex	NOUN
ejpam-3362	21	32	if	if	SCONJ
ejpam-3362	21	33	degg(w	degg(w	PROPN
ejpam-3362	21	34	)	)	PUNCT
ejpam-3362	21	35	=	=	SYM
ejpam-3362	21	36	|ng(w)|	|ng(w)|	X
ejpam-3362	21	37	=	=	NOUN
ejpam-3362	21	38	0	0	NUM
ejpam-3362	21	39	.	.	PUNCT
ejpam-3362	22	1	the	the	DET
ejpam-3362	22	2	set	set	NOUN
ejpam-3362	22	3	of	of	ADP
ejpam-3362	22	4	all	all	DET
ejpam-3362	22	5	isolated	isolated	ADJ
ejpam-3362	22	6	vertices	vertex	NOUN
ejpam-3362	22	7	of	of	ADP
ejpam-3362	22	8	g	g	NOUN
ejpam-3362	22	9	will	will	AUX
ejpam-3362	22	10	be	be	AUX
ejpam-3362	22	11	denoted	denote	VERB
ejpam-3362	22	12	by	by	ADP
ejpam-3362	22	13	i(g	i(g	NOUN
ejpam-3362	22	14	)	)	PUNCT
ejpam-3362	22	15	.	.	PUNCT
ejpam-3362	23	1	a	a	DET
ejpam-3362	23	2	graph	graph	NOUN
ejpam-3362	23	3	g	g	NOUN
ejpam-3362	23	4	is	be	AUX
ejpam-3362	23	5	called	call	VERB
ejpam-3362	23	6	an	an	DET
ejpam-3362	23	7	empty	empty	ADJ
ejpam-3362	23	8	graph	graph	NOUN
ejpam-3362	23	9	,	,	PUNCT
ejpam-3362	23	10	denoted	denote	VERB
ejpam-3362	23	11	by	by	ADP
ejpam-3362	23	12	k	k	PROPN
ejpam-3362	23	13	|v	|v	PROPN
ejpam-3362	23	14	(	(	PUNCT
ejpam-3362	23	15	g)|	g)|	INTJ
ejpam-3362	23	16	,	,	PUNCT
ejpam-3362	23	17	if	if	SCONJ
ejpam-3362	23	18	e(g	e(g	NOUN
ejpam-3362	23	19	)	)	PUNCT
ejpam-3362	24	1	=	=	PUNCT
ejpam-3362	24	2	∅	∅	NOUN
ejpam-3362	24	3	,	,	PUNCT
ejpam-3362	24	4	that	that	ADV
ejpam-3362	24	5	is	is	ADV
ejpam-3362	24	6	,	,	PUNCT
ejpam-3362	24	7	i(g	i(g	ADV
ejpam-3362	24	8	)	)	PUNCT
ejpam-3362	25	1	=	=	SYM
ejpam-3362	25	2	v	v	X
ejpam-3362	25	3	(	(	PUNCT
ejpam-3362	25	4	g	g	NOUN
ejpam-3362	25	5	)	)	PUNCT
ejpam-3362	25	6	.	.	PUNCT
ejpam-3362	26	1	a	a	DET
ejpam-3362	26	2	walk	walk	NOUN
ejpam-3362	26	3	of	of	ADP
ejpam-3362	26	4	a	a	DET
ejpam-3362	26	5	graph	graph	NOUN
ejpam-3362	26	6	g	g	NOUN
ejpam-3362	26	7	is	be	AUX
ejpam-3362	26	8	an	an	DET
ejpam-3362	26	9	alternating	alternate	VERB
ejpam-3362	26	10	sequence	sequence	NOUN
ejpam-3362	26	11	of	of	ADP
ejpam-3362	26	12	vertices	vertex	NOUN
ejpam-3362	26	13	and	and	CCONJ
ejpam-3362	26	14	edges	edge	NOUN
ejpam-3362	26	15	,	,	PUNCT
ejpam-3362	26	16	beginning	begin	VERB
ejpam-3362	26	17	and	and	CCONJ
ejpam-3362	26	18	ending	end	VERB
ejpam-3362	26	19	with	with	ADP
ejpam-3362	26	20	vertices	vertex	NOUN
ejpam-3362	26	21	,	,	PUNCT
ejpam-3362	26	22	v0	v0	NOUN
ejpam-3362	26	23	,	,	PUNCT
ejpam-3362	26	24	e1	e1	PROPN
ejpam-3362	26	25	,	,	PUNCT
ejpam-3362	26	26	v1	v1	NOUN
ejpam-3362	26	27	,	,	PUNCT
ejpam-3362	26	28	.	.	PUNCT
ejpam-3362	26	29	.	.	PUNCT
ejpam-3362	27	1	.	.	PUNCT
ejpam-3362	28	1	,	,	PUNCT
ejpam-3362	28	2	vn−1	vn−1	ADJ
ejpam-3362	28	3	,	,	PUNCT
ejpam-3362	28	4	en	en	X
ejpam-3362	28	5	,	,	PUNCT
ejpam-3362	28	6	vn	vn	NOUN
ejpam-3362	28	7	,	,	PUNCT
ejpam-3362	28	8	in	in	ADP
ejpam-3362	28	9	which	which	PRON
ejpam-3362	28	10	each	each	DET
ejpam-3362	28	11	edge	edge	NOUN
ejpam-3362	28	12	is	be	AUX
ejpam-3362	28	13	incident	incident	NOUN
ejpam-3362	28	14	with	with	ADP
ejpam-3362	28	15	the	the	DET
ejpam-3362	28	16	two	two	NUM
ejpam-3362	28	17	vertices	vertex	NOUN
ejpam-3362	28	18	immediately	immediately	ADV
ejpam-3362	28	19	preceding	precede	VERB
ejpam-3362	28	20	and	and	CCONJ
ejpam-3362	28	21	following	follow	VERB
ejpam-3362	28	22	it	it	PRON
ejpam-3362	28	23	.	.	PUNCT
ejpam-3362	29	1	this	this	DET
ejpam-3362	29	2	walk	walk	NOUN
ejpam-3362	29	3	joins	join	VERB
ejpam-3362	29	4	v0	v0	PROPN
ejpam-3362	29	5	and	and	CCONJ
ejpam-3362	29	6	vn	vn	NOUN
ejpam-3362	29	7	;	;	PUNCT
ejpam-3362	29	8	and	and	CCONJ
ejpam-3362	29	9	is	be	AUX
ejpam-3362	29	10	sometimes	sometimes	ADV
ejpam-3362	29	11	called	call	VERB
ejpam-3362	29	12	a	a	DET
ejpam-3362	29	13	v0	v0	NOUN
ejpam-3362	29	14	-	-	PUNCT
ejpam-3362	29	15	vn	vn	NOUN
ejpam-3362	29	16	walk	walk	NOUN
ejpam-3362	29	17	.	.	PUNCT
ejpam-3362	30	1	it	it	PRON
ejpam-3362	30	2	is	be	AUX
ejpam-3362	30	3	closed	close	VERB
ejpam-3362	30	4	if	if	SCONJ
ejpam-3362	30	5	v0	v0	NOUN
ejpam-3362	30	6	=	=	SYM
ejpam-3362	30	7	vn	vn	PROPN
ejpam-3362	30	8	and	and	CCONJ
ejpam-3362	30	9	is	be	AUX
ejpam-3362	30	10	open	open	ADJ
ejpam-3362	30	11	otherwise	otherwise	ADV
ejpam-3362	30	12	.	.	PUNCT
ejpam-3362	31	1	it	it	PRON
ejpam-3362	31	2	is	be	AUX
ejpam-3362	31	3	a	a	DET
ejpam-3362	31	4	path	path	NOUN
ejpam-3362	31	5	if	if	SCONJ
ejpam-3362	31	6	all	all	DET
ejpam-3362	31	7	the	the	DET
ejpam-3362	31	8	vertices	vertex	NOUN
ejpam-3362	31	9	(	(	PUNCT
ejpam-3362	31	10	and	and	CCONJ
ejpam-3362	31	11	thus	thus	ADV
ejpam-3362	31	12	necessarily	necessarily	ADV
ejpam-3362	31	13	all	all	DET
ejpam-3362	31	14	the	the	DET
ejpam-3362	31	15	edges	edge	NOUN
ejpam-3362	31	16	)	)	PUNCT
ejpam-3362	31	17	are	be	AUX
ejpam-3362	31	18	distinct	distinct	ADJ
ejpam-3362	31	19	.	.	PUNCT
ejpam-3362	32	1	if	if	SCONJ
ejpam-3362	32	2	the	the	DET
ejpam-3362	32	3	walk	walk	NOUN
ejpam-3362	32	4	is	be	AUX
ejpam-3362	32	5	closed	closed	ADJ
ejpam-3362	32	6	,	,	PUNCT
ejpam-3362	32	7	then	then	ADV
ejpam-3362	32	8	it	it	PRON
ejpam-3362	32	9	is	be	AUX
ejpam-3362	32	10	a	a	DET
ejpam-3362	32	11	cycle	cycle	NOUN
ejpam-3362	32	12	provided	provide	VERB
ejpam-3362	32	13	its	its	PRON
ejpam-3362	32	14	n	n	PRON
ejpam-3362	32	15	vertices	vertex	NOUN
ejpam-3362	32	16	are	be	AUX
ejpam-3362	32	17	distinct	distinct	ADJ
ejpam-3362	32	18	and	and	CCONJ
ejpam-3362	32	19	n	n	PRON
ejpam-3362	32	20	≥	≥	NOUN
ejpam-3362	32	21	3	3	X
ejpam-3362	32	22	.	.	PUNCT
ejpam-3362	33	1	we	we	PRON
ejpam-3362	33	2	denote	denote	VERB
ejpam-3362	33	3	by	by	ADP
ejpam-3362	33	4	cn	cn	PROPN
ejpam-3362	33	5	the	the	DET
ejpam-3362	33	6	graph	graph	NOUN
ejpam-3362	33	7	consisting	consist	VERB
ejpam-3362	33	8	of	of	ADP
ejpam-3362	33	9	a	a	DET
ejpam-3362	33	10	cycle	cycle	NOUN
ejpam-3362	33	11	with	with	ADP
ejpam-3362	33	12	n	n	CCONJ
ejpam-3362	33	13	vertices	vertex	NOUN
ejpam-3362	33	14	and	and	CCONJ
ejpam-3362	33	15	by	by	ADP
ejpam-3362	33	16	pn	pn	PROPN
ejpam-3362	33	17	a	a	DET
ejpam-3362	33	18	path	path	NOUN
ejpam-3362	33	19	with	with	ADP
ejpam-3362	33	20	n	n	SYM
ejpam-3362	33	21	vertices	vertex	NOUN
ejpam-3362	33	22	.	.	PUNCT
ejpam-3362	34	1	a	a	DET
ejpam-3362	34	2	graph	graph	NOUN
ejpam-3362	34	3	is	be	AUX
ejpam-3362	34	4	connected	connect	VERB
ejpam-3362	34	5	if	if	SCONJ
ejpam-3362	34	6	every	every	DET
ejpam-3362	34	7	pair	pair	NOUN
ejpam-3362	34	8	of	of	ADP
ejpam-3362	34	9	vertices	vertex	NOUN
ejpam-3362	34	10	are	be	AUX
ejpam-3362	34	11	joined	join	VERB
ejpam-3362	34	12	by	by	ADP
ejpam-3362	34	13	a	a	DET
ejpam-3362	34	14	path	path	NOUN
ejpam-3362	34	15	.	.	PUNCT
ejpam-3362	35	1	a	a	DET
ejpam-3362	35	2	maximal	maximal	ADJ
ejpam-3362	35	3	connected	connected	ADJ
ejpam-3362	35	4	subgraph	subgraph	NOUN
ejpam-3362	35	5	of	of	ADP
ejpam-3362	35	6	g	g	PROPN
ejpam-3362	35	7	is	be	AUX
ejpam-3362	35	8	called	call	VERB
ejpam-3362	35	9	a	a	DET
ejpam-3362	35	10	component	component	NOUN
ejpam-3362	35	11	of	of	ADP
ejpam-3362	35	12	g.	g.	PROPN
ejpam-3362	35	13	the	the	DET
ejpam-3362	35	14	complete	complete	ADJ
ejpam-3362	35	15	graph	graph	NOUN
ejpam-3362	35	16	kp	kp	PROPN
ejpam-3362	35	17	has	have	VERB
ejpam-3362	35	18	every	every	DET
ejpam-3362	35	19	pair	pair	NOUN
ejpam-3362	35	20	of	of	ADP
ejpam-3362	35	21	its	its	PRON
ejpam-3362	35	22	p	p	NOUN
ejpam-3362	35	23	vertices	vertex	NOUN
ejpam-3362	35	24	adjacent	adjacent	ADJ
ejpam-3362	35	25	.	.	PUNCT
ejpam-3362	36	1	a	a	DET
ejpam-3362	36	2	bipartite	bipartite	PROPN
ejpam-3362	36	3	graph	graph	NOUN
ejpam-3362	36	4	g	g	PROPN
ejpam-3362	36	5	is	be	AUX
ejpam-3362	36	6	a	a	DET
ejpam-3362	36	7	graph	graph	NOUN
ejpam-3362	36	8	whose	whose	DET
ejpam-3362	36	9	vertex	vertex	NOUN
ejpam-3362	36	10	set	set	NOUN
ejpam-3362	36	11	v	v	NOUN
ejpam-3362	36	12	can	can	AUX
ejpam-3362	36	13	be	be	AUX
ejpam-3362	36	14	partitioned	partition	VERB
ejpam-3362	36	15	into	into	ADP
ejpam-3362	36	16	two	two	NUM
ejpam-3362	36	17	subsets	subset	NOUN
ejpam-3362	36	18	v1	v1	NOUN
ejpam-3362	36	19	and	and	CCONJ
ejpam-3362	36	20	v2	v2	VERB
ejpam-3362	36	21	such	such	ADJ
ejpam-3362	36	22	that	that	SCONJ
ejpam-3362	36	23	every	every	DET
ejpam-3362	36	24	edge	edge	NOUN
ejpam-3362	36	25	of	of	ADP
ejpam-3362	36	26	g	g	PROPN
ejpam-3362	36	27	joins	join	VERB
ejpam-3362	36	28	v1	v1	NOUN
ejpam-3362	36	29	with	with	ADP
ejpam-3362	36	30	v2	v2	NOUN
ejpam-3362	36	31	.	.	PUNCT
ejpam-3362	37	1	if	if	SCONJ
ejpam-3362	37	2	g	g	PROPN
ejpam-3362	37	3	contains	contain	VERB
ejpam-3362	37	4	every	every	DET
ejpam-3362	37	5	edge	edge	NOUN
ejpam-3362	37	6	joining	join	VERB
ejpam-3362	37	7	v1	v1	NOUN
ejpam-3362	37	8	and	and	CCONJ
ejpam-3362	37	9	v2	v2	NOUN
ejpam-3362	37	10	,	,	PUNCT
ejpam-3362	37	11	then	then	ADV
ejpam-3362	37	12	g	g	PROPN
ejpam-3362	37	13	is	be	AUX
ejpam-3362	37	14	a	a	DET
ejpam-3362	37	15	complete	complete	ADJ
ejpam-3362	37	16	bipartite	bipartite	NOUN
ejpam-3362	37	17	.	.	PUNCT
ejpam-3362	38	1	if	if	SCONJ
ejpam-3362	38	2	v1	v1	NOUN
ejpam-3362	38	3	and	and	CCONJ
ejpam-3362	38	4	v2	v2	PROPN
ejpam-3362	38	5	have	have	VERB
ejpam-3362	38	6	m	m	PRON
ejpam-3362	38	7	and	and	CCONJ
ejpam-3362	38	8	n	n	ADV
ejpam-3362	38	9	vertices	vertex	NOUN
ejpam-3362	38	10	,	,	PUNCT
ejpam-3362	38	11	respectively	respectively	ADV
ejpam-3362	38	12	,	,	PUNCT
ejpam-3362	38	13	then	then	ADV
ejpam-3362	38	14	we	we	PRON
ejpam-3362	38	15	write	write	VERB
ejpam-3362	38	16	g	g	PROPN
ejpam-3362	38	17	=	=	SYM
ejpam-3362	38	18	km	km	PROPN
ejpam-3362	38	19	,	,	PUNCT
ejpam-3362	38	20	n.	n.	NOUN
ejpam-3362	38	21	a	a	DET
ejpam-3362	38	22	star	star	NOUN
ejpam-3362	38	23	is	be	AUX
ejpam-3362	38	24	a	a	DET
ejpam-3362	38	25	complete	complete	ADJ
ejpam-3362	38	26	bipartite	bipartite	PROPN
ejpam-3362	38	27	k1,n	k1,n	PROPN
ejpam-3362	38	28	.	.	PUNCT
ejpam-3362	39	1	the	the	DET
ejpam-3362	39	2	kronecker	kronecker	NOUN
ejpam-3362	39	3	product	product	NOUN
ejpam-3362	39	4	g	g	PROPN
ejpam-3362	39	5	⊗	⊗	PROPN
ejpam-3362	39	6	k	k	PROPN
ejpam-3362	39	7	of	of	ADP
ejpam-3362	39	8	two	two	NUM
ejpam-3362	39	9	graphs	graph	NOUN
ejpam-3362	39	10	g	g	NOUN
ejpam-3362	39	11	and	and	CCONJ
ejpam-3362	39	12	k	k	PROPN
ejpam-3362	39	13	is	be	AUX
ejpam-3362	39	14	the	the	DET
ejpam-3362	39	15	graph	graph	NOUN
ejpam-3362	39	16	with	with	ADP
ejpam-3362	39	17	vertex	vertex	NOUN
ejpam-3362	39	18	set	set	VERB
ejpam-3362	39	19	v	v	NOUN
ejpam-3362	39	20	(	(	PUNCT
ejpam-3362	39	21	g	g	PROPN
ejpam-3362	39	22	⊗	⊗	PROPN
ejpam-3362	39	23	k	k	PROPN
ejpam-3362	39	24	)	)	PUNCT
ejpam-3362	39	25	=	=	SYM
ejpam-3362	39	26	v	v	X
ejpam-3362	39	27	(	(	PUNCT
ejpam-3362	39	28	g	g	NOUN
ejpam-3362	39	29	)	)	PUNCT
ejpam-3362	39	30	×	×	NOUN
ejpam-3362	39	31	v	v	NOUN
ejpam-3362	39	32	(	(	PUNCT
ejpam-3362	39	33	k	k	NOUN
ejpam-3362	39	34	)	)	PUNCT
ejpam-3362	39	35	and	and	CCONJ
ejpam-3362	39	36	edge	edge	NOUN
ejpam-3362	39	37	set	set	VERB
ejpam-3362	39	38	e(g	e(g	PROPN
ejpam-3362	39	39	⊗	⊗	PROPN
ejpam-3362	39	40	k	k	NOUN
ejpam-3362	39	41	)	)	PUNCT
ejpam-3362	39	42	satisfying	satisfy	VERB
ejpam-3362	39	43	the	the	DET
ejpam-3362	39	44	following	follow	VERB
ejpam-3362	39	45	conditions	condition	NOUN
ejpam-3362	39	46	:	:	PUNCT
ejpam-3362	39	47	(	(	PUNCT
ejpam-3362	39	48	x	x	X
ejpam-3362	39	49	,	,	PUNCT
ejpam-3362	39	50	u)(y	u)(y	PROPN
ejpam-3362	39	51	,	,	PUNCT
ejpam-3362	39	52	v	v	NOUN
ejpam-3362	39	53	)	)	PUNCT
ejpam-3362	39	54	∈	∈	PROPN
ejpam-3362	39	55	e(g⊗k	e(g⊗k	VERB
ejpam-3362	39	56	)	)	PUNCT
ejpam-3362	40	1	if	if	SCONJ
ejpam-3362	40	2	and	and	CCONJ
ejpam-3362	40	3	only	only	ADV
ejpam-3362	40	4	if	if	SCONJ
ejpam-3362	40	5	xy	xy	PROPN
ejpam-3362	40	6	∈	∈	PROPN
ejpam-3362	40	7	e(g	e(g	PROPN
ejpam-3362	40	8	)	)	PUNCT
ejpam-3362	40	9	and	and	CCONJ
ejpam-3362	40	10	uv	uv	NOUN
ejpam-3362	40	11	∈	∈	PROPN
ejpam-3362	40	12	e(k	e(k	NOUN
ejpam-3362	40	13	)	)	PUNCT
ejpam-3362	40	14	.	.	PUNCT
ejpam-3362	41	1	let	let	VERB
ejpam-3362	41	2	g	g	PROPN
ejpam-3362	41	3	and	and	CCONJ
ejpam-3362	41	4	k	k	PROPN
ejpam-3362	41	5	be	be	AUX
ejpam-3362	41	6	graphs	graph	NOUN
ejpam-3362	41	7	and	and	CCONJ
ejpam-3362	41	8	let	let	VERB
ejpam-3362	41	9	f	f	NOUN
ejpam-3362	41	10	:	:	PUNCT
ejpam-3362	41	11	v	v	X
ejpam-3362	41	12	(	(	PUNCT
ejpam-3362	41	13	g	g	NOUN
ejpam-3362	41	14	)	)	PUNCT
ejpam-3362	41	15	→	→	SYM
ejpam-3362	41	16	v	v	X
ejpam-3362	41	17	(	(	PUNCT
ejpam-3362	41	18	k	k	NOUN
ejpam-3362	41	19	)	)	PUNCT
ejpam-3362	41	20	be	be	AUX
ejpam-3362	41	21	a	a	DET
ejpam-3362	41	22	function	function	NOUN
ejpam-3362	41	23	.	.	PUNCT
ejpam-3362	42	1	then	then	ADV
ejpam-3362	42	2	f	f	PROPN
ejpam-3362	42	3	is	be	AUX
ejpam-3362	42	4	a	a	DET
ejpam-3362	42	5	graph	graph	NOUN
ejpam-3362	42	6	homomorphism	homomorphism	NOUN
ejpam-3362	42	7	if	if	SCONJ
ejpam-3362	42	8	f(x)f(y	f(x)f(y	NOUN
ejpam-3362	42	9	)	)	PUNCT
ejpam-3362	42	10	∈	∈	PROPN
ejpam-3362	42	11	e(k	e(k	NOUN
ejpam-3362	42	12	)	)	PUNCT
ejpam-3362	42	13	whenever	whenever	SCONJ
ejpam-3362	42	14	xy	xy	PROPN
ejpam-3362	42	15	∈	∈	PROPN
ejpam-3362	42	16	e(g	e(g	PROPN
ejpam-3362	42	17	)	)	PUNCT
ejpam-3362	42	18	.	.	PUNCT
ejpam-3362	43	1	two	two	NUM
ejpam-3362	43	2	graphs	graph	NOUN
ejpam-3362	43	3	g	g	PROPN
ejpam-3362	43	4	and	and	CCONJ
ejpam-3362	43	5	k	k	PROPN
ejpam-3362	43	6	are	be	AUX
ejpam-3362	43	7	isomorphic	isomorphic	ADJ
ejpam-3362	43	8	(	(	PUNCT
ejpam-3362	43	9	written	write	VERB
ejpam-3362	43	10	as	as	ADP
ejpam-3362	43	11	g	g	PROPN
ejpam-3362	43	12	∼=	∼=	PROPN
ejpam-3362	43	13	k	k	NOUN
ejpam-3362	43	14	)	)	PUNCT
ejpam-3362	43	15	if	if	SCONJ
ejpam-3362	43	16	there	there	PRON
ejpam-3362	43	17	exists	exist	VERB
ejpam-3362	43	18	a	a	DET
ejpam-3362	43	19	one	one	NUM
ejpam-3362	43	20	-	-	PUNCT
ejpam-3362	43	21	to	to	ADP
ejpam-3362	43	22	-	-	PUNCT
ejpam-3362	43	23	one	one	NUM
ejpam-3362	43	24	correspondence	correspondence	NOUN
ejpam-3362	43	25	between	between	ADP
ejpam-3362	43	26	the	the	DET
ejpam-3362	43	27	vertex	vertex	NOUN
ejpam-3362	43	28	sets	set	NOUN
ejpam-3362	43	29	which	which	PRON
ejpam-3362	43	30	preserves	preserve	VERB
ejpam-3362	43	31	adjacency	adjacency	NOUN
ejpam-3362	43	32	.	.	PUNCT
ejpam-3362	44	1	a	a	DET
ejpam-3362	44	2	hyperoperation	hyperoperation	NOUN
ejpam-3362	44	3	on	on	ADP
ejpam-3362	44	4	a	a	DET
ejpam-3362	44	5	nonempty	nonempty	ADV
ejpam-3362	44	6	set	set	VERB
ejpam-3362	44	7	h	h	NOUN
ejpam-3362	44	8	is	be	AUX
ejpam-3362	44	9	a	a	DET
ejpam-3362	44	10	map	map	NOUN
ejpam-3362	44	11	from	from	ADP
ejpam-3362	44	12	h×h	h×h	PROPN
ejpam-3362	44	13	into	into	ADP
ejpam-3362	44	14	p	p	PROPN
ejpam-3362	44	15	∗(h	∗(h	PROPN
ejpam-3362	44	16	)	)	PUNCT
ejpam-3362	45	1	=	=	SYM
ejpam-3362	45	2	p	p	X
ejpam-3362	45	3	(	(	PUNCT
ejpam-3362	45	4	h)\{∅	h)\{∅	PROPN
ejpam-3362	45	5	}	}	PUNCT
ejpam-3362	45	6	.	.	PUNCT
ejpam-3362	46	1	let	let	VERB
ejpam-3362	46	2	~	~	PUNCT
ejpam-3362	46	3	be	be	AUX
ejpam-3362	46	4	a	a	DET
ejpam-3362	46	5	hyperoperation	hyperoperation	NOUN
ejpam-3362	46	6	on	on	ADP
ejpam-3362	46	7	h	h	NOUN
ejpam-3362	46	8	and	and	CCONJ
ejpam-3362	46	9	(	(	PUNCT
ejpam-3362	46	10	x	x	NOUN
ejpam-3362	46	11	,	,	PUNCT
ejpam-3362	46	12	y	y	NOUN
ejpam-3362	46	13	)	)	PUNCT
ejpam-3362	46	14	∈	∈	PROPN
ejpam-3362	46	15	h×h	h×h	PROPN
ejpam-3362	46	16	.	.	PUNCT
ejpam-3362	47	1	then	then	ADV
ejpam-3362	47	2	its	its	PRON
ejpam-3362	47	3	image	image	NOUN
ejpam-3362	47	4	under	under	ADP
ejpam-3362	47	5	~	~	PROPN
ejpam-3362	47	6	,	,	PUNCT
ejpam-3362	47	7	denoted	denote	VERB
ejpam-3362	47	8	by	by	ADP
ejpam-3362	47	9	x~	x~	PROPN
ejpam-3362	47	10	y	y	PROPN
ejpam-3362	47	11	,	,	PUNCT
ejpam-3362	47	12	is	be	AUX
ejpam-3362	47	13	called	call	VERB
ejpam-3362	47	14	the	the	DET
ejpam-3362	47	15	hyperproduct	hyperproduct	NOUN
ejpam-3362	47	16	of	of	ADP
ejpam-3362	47	17	x	x	PUNCT
ejpam-3362	47	18	and	and	CCONJ
ejpam-3362	47	19	y.	y.	NOUN
ejpam-3362	47	20	if	if	SCONJ
ejpam-3362	47	21	a	a	PRON
ejpam-3362	47	22	and	and	CCONJ
ejpam-3362	47	23	b	b	NOUN
ejpam-3362	47	24	are	be	AUX
ejpam-3362	47	25	nonempty	nonempty	ADJ
ejpam-3362	47	26	subsets	subset	NOUN
ejpam-3362	47	27	of	of	ADP
ejpam-3362	47	28	h	h	NOUN
ejpam-3362	47	29	,	,	PUNCT
ejpam-3362	47	30	then	then	ADV
ejpam-3362	47	31	a~	a~	PROPN
ejpam-3362	47	32	b	b	PROPN
ejpam-3362	47	33	is	be	AUX
ejpam-3362	47	34	given	give	VERB
ejpam-3362	47	35	by	by	ADP
ejpam-3362	47	36	a~	a~	PROPN
ejpam-3362	47	37	b	b	PROPN
ejpam-3362	47	38	=	=	PUNCT
ejpam-3362	47	39	⋃	⋃	PROPN
ejpam-3362	47	40	a∈a	a∈a	ADJ
ejpam-3362	47	41	,	,	PUNCT
ejpam-3362	47	42	b∈b	b∈b	NOUN
ejpam-3362	47	43	a~	a~	PROPN
ejpam-3362	47	44	b.	b.	PROPN
ejpam-3362	47	45	we	we	PRON
ejpam-3362	47	46	shall	shall	AUX
ejpam-3362	47	47	use	use	VERB
ejpam-3362	47	48	x~	x~	PROPN
ejpam-3362	47	49	y	y	PROPN
ejpam-3362	47	50	instead	instead	ADV
ejpam-3362	47	51	of	of	ADP
ejpam-3362	47	52	x~	x~	PROPN
ejpam-3362	47	53	{	{	PUNCT
ejpam-3362	47	54	y	y	NOUN
ejpam-3362	47	55	}	}	PUNCT
ejpam-3362	47	56	,	,	PUNCT
ejpam-3362	47	57	{	{	PUNCT
ejpam-3362	47	58	x}~	x}~	PROPN
ejpam-3362	47	59	y	y	PROPN
ejpam-3362	47	60	,	,	PUNCT
ejpam-3362	47	61	or	or	CCONJ
ejpam-3362	47	62	{	{	PUNCT
ejpam-3362	47	63	x	x	NOUN
ejpam-3362	47	64	}	}	PUNCT
ejpam-3362	47	65	~	~	PUNCT
ejpam-3362	47	66	{	{	PUNCT
ejpam-3362	47	67	y	y	NOUN
ejpam-3362	47	68	}	}	PUNCT
ejpam-3362	47	69	.	.	PUNCT
ejpam-3362	48	1	when	when	SCONJ
ejpam-3362	48	2	a	a	DET
ejpam-3362	48	3	⊆	⊆	NUM
ejpam-3362	48	4	h	h	NOUN
ejpam-3362	48	5	and	and	CCONJ
ejpam-3362	48	6	x	x	PUNCT
ejpam-3362	48	7	∈	∈	PROPN
ejpam-3362	48	8	h	h	NOUN
ejpam-3362	48	9	,	,	PUNCT
ejpam-3362	48	10	we	we	PRON
ejpam-3362	48	11	agree	agree	VERB
ejpam-3362	48	12	to	to	PART
ejpam-3362	48	13	write	write	VERB
ejpam-3362	48	14	a	a	DET
ejpam-3362	48	15	~	~	PUNCT
ejpam-3362	48	16	x	x	SYM
ejpam-3362	48	17	instead	instead	ADV
ejpam-3362	48	18	of	of	ADP
ejpam-3362	48	19	a	a	PRON
ejpam-3362	48	20	~	~	PUNCT
ejpam-3362	48	21	{	{	PUNCT
ejpam-3362	48	22	x	x	NOUN
ejpam-3362	48	23	}	}	PUNCT
ejpam-3362	48	24	.	.	PUNCT
ejpam-3362	49	1	similarly	similarly	ADV
ejpam-3362	49	2	,	,	PUNCT
ejpam-3362	49	3	we	we	PRON
ejpam-3362	49	4	write	write	VERB
ejpam-3362	49	5	x	x	PUNCT
ejpam-3362	49	6	~	~	NOUN
ejpam-3362	49	7	a	a	PRON
ejpam-3362	49	8	for	for	ADP
ejpam-3362	49	9	{	{	PUNCT
ejpam-3362	49	10	x}~a	x}~a	NOUN
ejpam-3362	49	11	.	.	PUNCT
ejpam-3362	50	1	in	in	ADP
ejpam-3362	50	2	effect	effect	NOUN
ejpam-3362	50	3	,	,	PUNCT
ejpam-3362	50	4	a~	a~	PROPN
ejpam-3362	50	5	x	x	PUNCT
ejpam-3362	50	6	=	=	PUNCT
ejpam-3362	50	7	⋃	⋃	VERB
ejpam-3362	50	8	a∈a	a∈a	ADJ
ejpam-3362	50	9	a~	a~	PROPN
ejpam-3362	50	10	x	x	X
ejpam-3362	50	11	and	and	CCONJ
ejpam-3362	50	12	x	x	X
ejpam-3362	50	13	~	~	PUNCT
ejpam-3362	50	14	a	a	DET
ejpam-3362	50	15	=	=	X
ejpam-3362	50	16	⋃	⋃	NOUN
ejpam-3362	50	17	a∈a	a∈a	ADJ
ejpam-3362	50	18	x~	x~	PROPN
ejpam-3362	50	19	a.	a.	NOUN
ejpam-3362	50	20	m.	m.	NOUN
ejpam-3362	50	21	panganduyon	panganduyon	NOUN
ejpam-3362	50	22	,	,	PUNCT
ejpam-3362	50	23	s.	s.	PROPN
ejpam-3362	50	24	canoy	canoy	PROPN
ejpam-3362	50	25	/	/	SYM
ejpam-3362	50	26	eur	eur	PROPN
ejpam-3362	50	27	.	.	PUNCT
ejpam-3362	51	1	j.	j.	PROPN
ejpam-3362	51	2	pure	pure	PROPN
ejpam-3362	51	3	appl	appl	PROPN
ejpam-3362	51	4	.	.	PROPN
ejpam-3362	51	5	math	math	PROPN
ejpam-3362	51	6	,	,	PUNCT
ejpam-3362	51	7	12	12	NUM
ejpam-3362	51	8	(	(	PUNCT
ejpam-3362	51	9	1	1	NUM
ejpam-3362	51	10	)	)	PUNCT
ejpam-3362	51	11	(	(	PUNCT
ejpam-3362	51	12	2019	2019	NUM
ejpam-3362	51	13	)	)	PUNCT
ejpam-3362	51	14	,	,	PUNCT
ejpam-3362	51	15	146	146	NUM
ejpam-3362	51	16	-	-	SYM
ejpam-3362	51	17	158	158	NUM
ejpam-3362	51	18	148	148	NUM
ejpam-3362	51	19	a	a	DET
ejpam-3362	51	20	hyper	hyper	ADJ
ejpam-3362	51	21	bci	bci	NOUN
ejpam-3362	51	22	-	-	NOUN
ejpam-3362	51	23	algebra	algebra	NOUN
ejpam-3362	51	24	(	(	PUNCT
ejpam-3362	51	25	h,~	h,~	NOUN
ejpam-3362	51	26	,	,	PUNCT
ejpam-3362	51	27	0	0	NUM
ejpam-3362	51	28	)	)	PUNCT
ejpam-3362	51	29	is	be	AUX
ejpam-3362	51	30	a	a	DET
ejpam-3362	51	31	nonempty	nonempty	ADV
ejpam-3362	51	32	set	set	VERB
ejpam-3362	51	33	h	h	NOUN
ejpam-3362	51	34	endowed	endow	VERB
ejpam-3362	51	35	with	with	ADP
ejpam-3362	51	36	a	a	DET
ejpam-3362	51	37	hyperoperation	hyperoperation	NOUN
ejpam-3362	51	38	“	"	PUNCT
ejpam-3362	51	39	~	~	PUNCT
ejpam-3362	51	40	”	"	PUNCT
ejpam-3362	51	41	and	and	CCONJ
ejpam-3362	51	42	a	a	DET
ejpam-3362	51	43	constant	constant	ADJ
ejpam-3362	51	44	0	0	NUM
ejpam-3362	51	45	satisfying	satisfy	VERB
ejpam-3362	51	46	the	the	DET
ejpam-3362	51	47	following	follow	VERB
ejpam-3362	51	48	axioms	axiom	NOUN
ejpam-3362	51	49	:	:	PUNCT
ejpam-3362	51	50	for	for	ADP
ejpam-3362	51	51	all	all	DET
ejpam-3362	51	52	x	x	NOUN
ejpam-3362	51	53	,	,	PUNCT
ejpam-3362	51	54	y	y	PROPN
ejpam-3362	51	55	,	,	PUNCT
ejpam-3362	51	56	z	z	PROPN
ejpam-3362	51	57	∈	∈	PROPN
ejpam-3362	51	58	h	h	NOUN
ejpam-3362	51	59	,	,	PUNCT
ejpam-3362	51	60	(	(	PUNCT
ejpam-3362	51	61	b1	b1	NOUN
ejpam-3362	51	62	)	)	PUNCT
ejpam-3362	51	63	(	(	PUNCT
ejpam-3362	51	64	(	(	PUNCT
ejpam-3362	51	65	x~	x~	PROPN
ejpam-3362	51	66	z)~	z)~	PROPN
ejpam-3362	51	67	(	(	PUNCT
ejpam-3362	51	68	y	y	PROPN
ejpam-3362	51	69	~	~	PUNCT
ejpam-3362	51	70	z	z	NOUN
ejpam-3362	51	71	)	)	PUNCT
ejpam-3362	51	72	)	)	PUNCT
ejpam-3362	51	73	�	�	PROPN
ejpam-3362	51	74	x~	x~	NUM
ejpam-3362	51	75	y	y	PROPN
ejpam-3362	51	76	,	,	PUNCT
ejpam-3362	51	77	(	(	PUNCT
ejpam-3362	51	78	b2	b2	NOUN
ejpam-3362	51	79	)	)	PUNCT
ejpam-3362	51	80	(	(	PUNCT
ejpam-3362	51	81	x~	x~	PROPN
ejpam-3362	51	82	y)~	y)~	PROPN
ejpam-3362	51	83	z	z	NOUN
ejpam-3362	51	84	=	=	SYM
ejpam-3362	51	85	(	(	PUNCT
ejpam-3362	51	86	x~	x~	PROPN
ejpam-3362	51	87	z)~	z)~	PROPN
ejpam-3362	51	88	y	y	PROPN
ejpam-3362	51	89	,	,	PUNCT
ejpam-3362	51	90	(	(	PUNCT
ejpam-3362	51	91	b3	b3	PROPN
ejpam-3362	51	92	)	)	PUNCT
ejpam-3362	51	93	x	x	NOUN
ejpam-3362	51	94	�	�	PROPN
ejpam-3362	51	95	x	x	SYM
ejpam-3362	51	96	,	,	PUNCT
ejpam-3362	51	97	(	(	PUNCT
ejpam-3362	51	98	b4	b4	NOUN
ejpam-3362	51	99	)	)	PUNCT
ejpam-3362	51	100	x	x	NOUN
ejpam-3362	51	101	�	�	PROPN
ejpam-3362	51	102	y	y	PROPN
ejpam-3362	51	103	and	and	CCONJ
ejpam-3362	51	104	y	y	PROPN
ejpam-3362	51	105	�	�	PROPN
ejpam-3362	51	106	x	x	PUNCT
ejpam-3362	51	107	imply	imply	VERB
ejpam-3362	51	108	x	x	X
ejpam-3362	51	109	=	=	SYM
ejpam-3362	51	110	y	y	PROPN
ejpam-3362	51	111	,	,	PUNCT
ejpam-3362	51	112	(	(	PUNCT
ejpam-3362	51	113	b5	b5	PROPN
ejpam-3362	51	114	)	)	PUNCT
ejpam-3362	51	115	0~	0~	NOUN
ejpam-3362	51	116	(	(	PUNCT
ejpam-3362	51	117	0~	0~	NOUN
ejpam-3362	51	118	x	x	SYM
ejpam-3362	51	119	)	)	PUNCT
ejpam-3362	51	120	�	�	PROPN
ejpam-3362	51	121	x	x	SYM
ejpam-3362	51	122	,	,	PUNCT
ejpam-3362	51	123	x	x	PROPN
ejpam-3362	51	124	6=	6=	ADP
ejpam-3362	51	125	0	0	NUM
ejpam-3362	51	126	,	,	PUNCT
ejpam-3362	51	127	where	where	SCONJ
ejpam-3362	51	128	for	for	ADP
ejpam-3362	51	129	every	every	DET
ejpam-3362	51	130	a	a	PROPN
ejpam-3362	51	131	,	,	PUNCT
ejpam-3362	51	132	b	b	PROPN
ejpam-3362	51	133	⊆	⊆	NUM
ejpam-3362	51	134	h	h	NOUN
ejpam-3362	51	135	,	,	PUNCT
ejpam-3362	51	136	a	a	DET
ejpam-3362	51	137	�	�	PROPN
ejpam-3362	51	138	b	b	PROPN
ejpam-3362	51	139	if	if	SCONJ
ejpam-3362	52	1	and	and	CCONJ
ejpam-3362	52	2	only	only	ADV
ejpam-3362	52	3	if	if	SCONJ
ejpam-3362	52	4	for	for	ADP
ejpam-3362	52	5	each	each	DET
ejpam-3362	52	6	a	a	DET
ejpam-3362	52	7	∈	∈	PROPN
ejpam-3362	52	8	a	a	PRON
ejpam-3362	52	9	,	,	PUNCT
ejpam-3362	52	10	there	there	PRON
ejpam-3362	52	11	exists	exist	VERB
ejpam-3362	52	12	b	b	PROPN
ejpam-3362	52	13	∈	∈	PROPN
ejpam-3362	52	14	b	b	NOUN
ejpam-3362	52	15	such	such	ADJ
ejpam-3362	52	16	that	that	DET
ejpam-3362	52	17	0	0	NUM
ejpam-3362	52	18	∈	∈	PROPN
ejpam-3362	52	19	a	a	DET
ejpam-3362	52	20	~	~	PUNCT
ejpam-3362	52	21	b.	b.	PROPN
ejpam-3362	52	22	in	in	ADP
ejpam-3362	52	23	particular	particular	ADJ
ejpam-3362	52	24	,	,	PUNCT
ejpam-3362	52	25	for	for	ADP
ejpam-3362	52	26	every	every	DET
ejpam-3362	52	27	x	x	NOUN
ejpam-3362	52	28	,	,	PUNCT
ejpam-3362	52	29	y	y	PROPN
ejpam-3362	52	30	∈	∈	PROPN
ejpam-3362	52	31	h	h	NOUN
ejpam-3362	52	32	,	,	PUNCT
ejpam-3362	52	33	x	x	PROPN
ejpam-3362	52	34	�	�	PROPN
ejpam-3362	52	35	y	y	PROPN
ejpam-3362	52	36	if	if	SCONJ
ejpam-3362	52	37	and	and	CCONJ
ejpam-3362	52	38	only	only	ADV
ejpam-3362	52	39	if	if	SCONJ
ejpam-3362	52	40	0	0	NUM
ejpam-3362	52	41	∈	∈	NOUN
ejpam-3362	52	42	x	x	X
ejpam-3362	52	43	~	~	PUNCT
ejpam-3362	52	44	y.	y.	NOUN
ejpam-3362	52	45	in	in	ADP
ejpam-3362	52	46	such	such	ADJ
ejpam-3362	52	47	case	case	NOUN
ejpam-3362	52	48	,	,	PUNCT
ejpam-3362	52	49	we	we	PRON
ejpam-3362	52	50	call	call	VERB
ejpam-3362	52	51	“	"	PUNCT
ejpam-3362	52	52	�	�	PROPN
ejpam-3362	52	53	”	"	PUNCT
ejpam-3362	52	54	the	the	DET
ejpam-3362	52	55	hyper	hyper	ADJ
ejpam-3362	52	56	order	order	NOUN
ejpam-3362	52	57	in	in	ADP
ejpam-3362	52	58	h	h	PROPN
ejpam-3362	52	59	(	(	PUNCT
ejpam-3362	52	60	see	see	VERB
ejpam-3362	52	61	[	[	X
ejpam-3362	52	62	7	7	NUM
ejpam-3362	52	63	]	]	NUM
ejpam-3362	52	64	)	)	PUNCT
ejpam-3362	52	65	.	.	PUNCT
ejpam-3362	53	1	a	a	DET
ejpam-3362	53	2	hyper	hyper	ADJ
ejpam-3362	53	3	bci	bci	NOUN
ejpam-3362	53	4	-	-	NOUN
ejpam-3362	53	5	algebra	algebra	NOUN
ejpam-3362	53	6	(	(	PUNCT
ejpam-3362	53	7	h,~	h,~	NOUN
ejpam-3362	53	8	,	,	PUNCT
ejpam-3362	53	9	0	0	NUM
ejpam-3362	53	10	)	)	PUNCT
ejpam-3362	53	11	is	be	AUX
ejpam-3362	53	12	said	say	VERB
ejpam-3362	53	13	to	to	PART
ejpam-3362	53	14	be	be	AUX
ejpam-3362	53	15	ordered	order	VERB
ejpam-3362	53	16	if	if	SCONJ
ejpam-3362	53	17	for	for	SCONJ
ejpam-3362	53	18	each	each	DET
ejpam-3362	53	19	x	x	NOUN
ejpam-3362	53	20	,	,	PUNCT
ejpam-3362	53	21	y	y	PROPN
ejpam-3362	53	22	,	,	PUNCT
ejpam-3362	53	23	z	z	PROPN
ejpam-3362	53	24	∈	∈	PROPN
ejpam-3362	53	25	h	h	NOUN
ejpam-3362	53	26	,	,	PUNCT
ejpam-3362	53	27	x	x	NOUN
ejpam-3362	53	28	�	�	PROPN
ejpam-3362	53	29	y	y	PROPN
ejpam-3362	53	30	and	and	CCONJ
ejpam-3362	53	31	y	y	PROPN
ejpam-3362	53	32	�	�	PROPN
ejpam-3362	53	33	z	z	PROPN
ejpam-3362	53	34	imply	imply	VERB
ejpam-3362	53	35	x	x	X
ejpam-3362	53	36	�	�	PROPN
ejpam-3362	53	37	z.	z.	PROPN
ejpam-3362	53	38	example	example	NOUN
ejpam-3362	54	1	1	1	NUM
ejpam-3362	54	2	.	.	PUNCT
ejpam-3362	55	1	[	[	X
ejpam-3362	55	2	7	7	X
ejpam-3362	55	3	]	]	X
ejpam-3362	55	4	let	let	NOUN
ejpam-3362	55	5	h	h	NOUN
ejpam-3362	55	6	=	=	PRON
ejpam-3362	55	7	{	{	PUNCT
ejpam-3362	55	8	0	0	NUM
ejpam-3362	55	9	,	,	PUNCT
ejpam-3362	55	10	1	1	NUM
ejpam-3362	55	11	,	,	PUNCT
ejpam-3362	55	12	2	2	NUM
ejpam-3362	55	13	}	}	PUNCT
ejpam-3362	55	14	.	.	PUNCT
ejpam-3362	56	1	define	define	VERB
ejpam-3362	56	2	the	the	DET
ejpam-3362	56	3	hyperoperation	hyperoperation	NOUN
ejpam-3362	56	4	“	"	PUNCT
ejpam-3362	56	5	~	~	PUNCT
ejpam-3362	56	6	”	"	PUNCT
ejpam-3362	56	7	by	by	ADP
ejpam-3362	56	8	the	the	DET
ejpam-3362	56	9	cayley	cayley	ADJ
ejpam-3362	56	10	table	table	NOUN
ejpam-3362	56	11	shown	show	VERB
ejpam-3362	56	12	below	below	ADV
ejpam-3362	56	13	.	.	PUNCT
ejpam-3362	57	1	~	~	PUNCT
ejpam-3362	57	2	0	0	NUM
ejpam-3362	58	1	1	1	NUM
ejpam-3362	58	2	2	2	NUM
ejpam-3362	58	3	0	0	NUM
ejpam-3362	58	4	{	{	PUNCT
ejpam-3362	58	5	0	0	NUM
ejpam-3362	58	6	,	,	PUNCT
ejpam-3362	58	7	1	1	NUM
ejpam-3362	58	8	}	}	PUNCT
ejpam-3362	58	9	{	{	PUNCT
ejpam-3362	58	10	0	0	NUM
ejpam-3362	58	11	,	,	PUNCT
ejpam-3362	58	12	1	1	NUM
ejpam-3362	58	13	}	}	PUNCT
ejpam-3362	58	14	{	{	PUNCT
ejpam-3362	58	15	0	0	NUM
ejpam-3362	58	16	,	,	PUNCT
ejpam-3362	58	17	1	1	NUM
ejpam-3362	58	18	}	}	SYM
ejpam-3362	58	19	1	1	NUM
ejpam-3362	58	20	{	{	PUNCT
ejpam-3362	58	21	1	1	NUM
ejpam-3362	58	22	}	}	PUNCT
ejpam-3362	58	23	{	{	PUNCT
ejpam-3362	58	24	0	0	NUM
ejpam-3362	58	25	,	,	PUNCT
ejpam-3362	58	26	1	1	NUM
ejpam-3362	58	27	}	}	PUNCT
ejpam-3362	58	28	{	{	PUNCT
ejpam-3362	58	29	0	0	NUM
ejpam-3362	58	30	,	,	PUNCT
ejpam-3362	58	31	1	1	NUM
ejpam-3362	58	32	}	}	SYM
ejpam-3362	58	33	2	2	NUM
ejpam-3362	58	34	{	{	PUNCT
ejpam-3362	58	35	2	2	NUM
ejpam-3362	58	36	}	}	PUNCT
ejpam-3362	58	37	{	{	PUNCT
ejpam-3362	58	38	1	1	NUM
ejpam-3362	58	39	,	,	PUNCT
ejpam-3362	58	40	2	2	NUM
ejpam-3362	58	41	}	}	PUNCT
ejpam-3362	58	42	{	{	PUNCT
ejpam-3362	58	43	0	0	NUM
ejpam-3362	58	44	,	,	PUNCT
ejpam-3362	58	45	1	1	NUM
ejpam-3362	58	46	,	,	PUNCT
ejpam-3362	58	47	2	2	NUM
ejpam-3362	58	48	}	}	PUNCT
ejpam-3362	58	49	then	then	ADV
ejpam-3362	58	50	by	by	ADP
ejpam-3362	58	51	routine	routine	ADJ
ejpam-3362	58	52	calculations	calculation	NOUN
ejpam-3362	58	53	,	,	PUNCT
ejpam-3362	58	54	(	(	PUNCT
ejpam-3362	58	55	h,~	h,~	NOUN
ejpam-3362	58	56	,	,	PUNCT
ejpam-3362	58	57	0	0	NUM
ejpam-3362	58	58	)	)	PUNCT
ejpam-3362	58	59	is	be	AUX
ejpam-3362	58	60	a	a	DET
ejpam-3362	58	61	hyper	hyper	ADJ
ejpam-3362	58	62	bci	bci	NOUN
ejpam-3362	58	63	-	-	NOUN
ejpam-3362	58	64	algebra	algebra	NOUN
ejpam-3362	58	65	.	.	PUNCT
ejpam-3362	59	1	further	far	ADV
ejpam-3362	59	2	,	,	PUNCT
ejpam-3362	59	3	h	h	PROPN
ejpam-3362	59	4	is	be	AUX
ejpam-3362	59	5	ordered	order	VERB
ejpam-3362	59	6	.	.	PUNCT
ejpam-3362	60	1	let	let	VERB
ejpam-3362	60	2	(	(	PUNCT
ejpam-3362	60	3	h1,~1	h1,~1	PROPN
ejpam-3362	60	4	,	,	PUNCT
ejpam-3362	60	5	01	01	NUM
ejpam-3362	60	6	)	)	PUNCT
ejpam-3362	60	7	and	and	CCONJ
ejpam-3362	60	8	(	(	PUNCT
ejpam-3362	60	9	h2,~2	h2,~2	NOUN
ejpam-3362	60	10	,	,	PUNCT
ejpam-3362	60	11	02	02	NUM
ejpam-3362	60	12	)	)	PUNCT
ejpam-3362	60	13	be	be	VERB
ejpam-3362	60	14	two	two	NUM
ejpam-3362	60	15	hyper	hyper	ADJ
ejpam-3362	60	16	bci	bci	NOUN
ejpam-3362	60	17	-	-	PUNCT
ejpam-3362	60	18	algebras	algebra	NOUN
ejpam-3362	60	19	.	.	PUNCT
ejpam-3362	61	1	consider	consider	VERB
ejpam-3362	61	2	a	a	DET
ejpam-3362	61	3	mapping	mapping	NOUN
ejpam-3362	61	4	f	f	NOUN
ejpam-3362	61	5	:	:	PUNCT
ejpam-3362	61	6	h1	h1	PROPN
ejpam-3362	61	7	→	→	SYM
ejpam-3362	61	8	h2	h2	PROPN
ejpam-3362	61	9	.	.	PUNCT
ejpam-3362	62	1	then	then	ADV
ejpam-3362	62	2	f	f	PROPN
ejpam-3362	62	3	is	be	AUX
ejpam-3362	62	4	said	say	VERB
ejpam-3362	62	5	to	to	PART
ejpam-3362	62	6	be	be	AUX
ejpam-3362	62	7	a	a	DET
ejpam-3362	62	8	homomorphism	homomorphism	NOUN
ejpam-3362	62	9	if	if	SCONJ
ejpam-3362	62	10	f(x	f(x	PROPN
ejpam-3362	62	11	~1	~1	VERB
ejpam-3362	62	12	y	y	PRON
ejpam-3362	62	13	)	)	PUNCT
ejpam-3362	62	14	=	=	SYM
ejpam-3362	62	15	f(x	f(x	PROPN
ejpam-3362	62	16	)	)	PUNCT
ejpam-3362	62	17	~2	~2	NOUN
ejpam-3362	62	18	f(y	f(y	NOUN
ejpam-3362	62	19	)	)	PUNCT
ejpam-3362	62	20	,	,	PUNCT
ejpam-3362	62	21	for	for	ADP
ejpam-3362	62	22	all	all	DET
ejpam-3362	62	23	x	x	NOUN
ejpam-3362	62	24	,	,	PUNCT
ejpam-3362	62	25	y	y	PROPN
ejpam-3362	62	26	∈	∈	PROPN
ejpam-3362	62	27	h1	h1	PROPN
ejpam-3362	62	28	.	.	PUNCT
ejpam-3362	63	1	if	if	SCONJ
ejpam-3362	63	2	f	f	PROPN
ejpam-3362	63	3	is	be	AUX
ejpam-3362	63	4	a	a	DET
ejpam-3362	63	5	homomorphism	homomorphism	NOUN
ejpam-3362	63	6	and	and	CCONJ
ejpam-3362	63	7	f(01	f(01	NOUN
ejpam-3362	63	8	)	)	PUNCT
ejpam-3362	63	9	=	=	SYM
ejpam-3362	63	10	02	02	NUM
ejpam-3362	63	11	,	,	PUNCT
ejpam-3362	63	12	then	then	ADV
ejpam-3362	63	13	we	we	PRON
ejpam-3362	63	14	call	call	VERB
ejpam-3362	63	15	f	f	PROPN
ejpam-3362	63	16	a	a	DET
ejpam-3362	63	17	hyper	hyper	ADJ
ejpam-3362	63	18	homomorphism	homomorphism	NOUN
ejpam-3362	63	19	.	.	PUNCT
ejpam-3362	64	1	if	if	SCONJ
ejpam-3362	64	2	f	f	PROPN
ejpam-3362	64	3	is	be	AUX
ejpam-3362	64	4	a	a	DET
ejpam-3362	64	5	homomorphism	homomorphism	NOUN
ejpam-3362	64	6	,	,	PUNCT
ejpam-3362	64	7	one	one	NUM
ejpam-3362	64	8	-	-	PUNCT
ejpam-3362	64	9	to	to	ADP
ejpam-3362	64	10	-	-	PUNCT
ejpam-3362	64	11	one	one	NUM
ejpam-3362	64	12	,	,	PUNCT
ejpam-3362	64	13	and	and	CCONJ
ejpam-3362	64	14	onto	onto	ADP
ejpam-3362	64	15	,	,	PUNCT
ejpam-3362	64	16	we	we	PRON
ejpam-3362	64	17	say	say	VERB
ejpam-3362	64	18	that	that	SCONJ
ejpam-3362	64	19	f	f	PROPN
ejpam-3362	64	20	is	be	AUX
ejpam-3362	64	21	an	an	DET
ejpam-3362	64	22	isomorphism	isomorphism	NOUN
ejpam-3362	64	23	and	and	CCONJ
ejpam-3362	64	24	(	(	PUNCT
ejpam-3362	64	25	h1,~1	h1,~1	PROPN
ejpam-3362	64	26	,	,	PUNCT
ejpam-3362	64	27	01	01	NUM
ejpam-3362	64	28	)	)	PUNCT
ejpam-3362	64	29	and	and	CCONJ
ejpam-3362	64	30	(	(	PUNCT
ejpam-3362	64	31	h2,~2	h2,~2	NOUN
ejpam-3362	64	32	,	,	PUNCT
ejpam-3362	64	33	02	02	NUM
ejpam-3362	64	34	)	)	PUNCT
ejpam-3362	64	35	are	be	AUX
ejpam-3362	64	36	isomorphic	isomorphic	ADJ
ejpam-3362	64	37	,	,	PUNCT
ejpam-3362	64	38	denoted	denote	VERB
ejpam-3362	64	39	by	by	ADP
ejpam-3362	64	40	h1	h1	PROPN
ejpam-3362	64	41	∼=	∼=	PROPN
ejpam-3362	64	42	h2	h2	NOUN
ejpam-3362	64	43	(	(	PUNCT
ejpam-3362	64	44	see	see	VERB
ejpam-3362	64	45	[	[	X
ejpam-3362	64	46	6	6	NUM
ejpam-3362	64	47	]	]	NUM
ejpam-3362	64	48	)	)	PUNCT
ejpam-3362	64	49	.	.	PUNCT
ejpam-3362	65	1	let	let	VERB
ejpam-3362	65	2	f	f	NOUN
ejpam-3362	65	3	:	:	PUNCT
ejpam-3362	65	4	h1	h1	PROPN
ejpam-3362	65	5	→	→	SYM
ejpam-3362	65	6	h2	h2	PROPN
ejpam-3362	65	7	be	be	AUX
ejpam-3362	65	8	a	a	DET
ejpam-3362	65	9	hyper	hyper	ADJ
ejpam-3362	65	10	homomorphism	homomorphism	NOUN
ejpam-3362	65	11	of	of	ADP
ejpam-3362	65	12	hyper	hyper	ADJ
ejpam-3362	65	13	bci	bci	NOUN
ejpam-3362	65	14	-	-	PUNCT
ejpam-3362	65	15	algebras	algebra	NOUN
ejpam-3362	65	16	.	.	PUNCT
ejpam-3362	66	1	if	if	SCONJ
ejpam-3362	66	2	f	f	PROPN
ejpam-3362	66	3	is	be	AUX
ejpam-3362	66	4	one	one	NUM
ejpam-3362	66	5	to	to	ADP
ejpam-3362	66	6	one	one	NUM
ejpam-3362	66	7	(	(	PUNCT
ejpam-3362	66	8	resp	resp	NOUN
ejpam-3362	66	9	.	.	PUNCT
ejpam-3362	67	1	onto	onto	ADP
ejpam-3362	67	2	)	)	PUNCT
ejpam-3362	68	1	we	we	PRON
ejpam-3362	68	2	say	say	VERB
ejpam-3362	68	3	f	f	PROPN
ejpam-3362	68	4	is	be	AUX
ejpam-3362	68	5	a	a	DET
ejpam-3362	68	6	hyper	hyper	ADJ
ejpam-3362	68	7	monomorphism	monomorphism	NOUN
ejpam-3362	68	8	(	(	PUNCT
ejpam-3362	68	9	resp	resp	NOUN
ejpam-3362	68	10	.	.	PUNCT
ejpam-3362	68	11	hyper	hyper	PROPN
ejpam-3362	68	12	epimorphism	epimorphism	NOUN
ejpam-3362	68	13	)	)	PUNCT
ejpam-3362	68	14	.	.	PUNCT
ejpam-3362	69	1	if	if	SCONJ
ejpam-3362	69	2	f	f	PROPN
ejpam-3362	69	3	is	be	AUX
ejpam-3362	69	4	a	a	DET
ejpam-3362	69	5	hyper	hyper	ADJ
ejpam-3362	69	6	homomorphism	homomorphism	NOUN
ejpam-3362	69	7	and	and	CCONJ
ejpam-3362	69	8	a	a	DET
ejpam-3362	69	9	bijection	bijection	NOUN
ejpam-3362	69	10	,	,	PUNCT
ejpam-3362	69	11	f	f	PROPN
ejpam-3362	69	12	is	be	AUX
ejpam-3362	69	13	said	say	VERB
ejpam-3362	69	14	to	to	PART
ejpam-3362	69	15	be	be	AUX
ejpam-3362	69	16	a	a	DET
ejpam-3362	69	17	hyper	hyper	ADJ
ejpam-3362	69	18	isomorphism	isomorphism	NOUN
ejpam-3362	69	19	,	,	PUNCT
ejpam-3362	69	20	denoted	denote	VERB
ejpam-3362	69	21	by	by	ADP
ejpam-3362	69	22	h1	h1	PROPN
ejpam-3362	69	23	∼=h	∼=h	ADJ
ejpam-3362	69	24	h2	h2	NOUN
ejpam-3362	69	25	(	(	PUNCT
ejpam-3362	69	26	see	see	VERB
ejpam-3362	69	27	[	[	X
ejpam-3362	69	28	3	3	NUM
ejpam-3362	69	29	]	]	NUM
ejpam-3362	69	30	)	)	PUNCT
ejpam-3362	69	31	.	.	PUNCT
ejpam-3362	70	1	throughout	throughout	ADP
ejpam-3362	70	2	this	this	DET
ejpam-3362	70	3	study	study	NOUN
ejpam-3362	70	4	,	,	PUNCT
ejpam-3362	70	5	we	we	PRON
ejpam-3362	70	6	denote	denote	VERB
ejpam-3362	70	7	a	a	DET
ejpam-3362	70	8	hyper	hyper	ADJ
ejpam-3362	70	9	bci	bci	NOUN
ejpam-3362	70	10	-	-	NOUN
ejpam-3362	70	11	algebra	algebra	NOUN
ejpam-3362	70	12	(	(	PUNCT
ejpam-3362	70	13	h,~	h,~	NOUN
ejpam-3362	70	14	,	,	PUNCT
ejpam-3362	70	15	0	0	NUM
ejpam-3362	70	16	)	)	PUNCT
ejpam-3362	70	17	by	by	ADP
ejpam-3362	70	18	h	h	NOUN
ejpam-3362	70	19	,	,	PUNCT
ejpam-3362	70	20	unless	unless	SCONJ
ejpam-3362	70	21	otherwise	otherwise	ADV
ejpam-3362	70	22	specified	specify	VERB
ejpam-3362	70	23	.	.	PUNCT
ejpam-3362	71	1	the	the	DET
ejpam-3362	71	2	following	follow	VERB
ejpam-3362	71	3	results	result	NOUN
ejpam-3362	71	4	generated	generated	AUX
ejpam-3362	71	5	previously	previously	ADV
ejpam-3362	71	6	give	give	VERB
ejpam-3362	71	7	some	some	PRON
ejpam-3362	71	8	of	of	ADP
ejpam-3362	71	9	the	the	DET
ejpam-3362	71	10	properties	property	NOUN
ejpam-3362	71	11	of	of	ADP
ejpam-3362	71	12	a	a	DET
ejpam-3362	71	13	hyper	hyper	ADJ
ejpam-3362	71	14	bcialgebra	bcialgebra	NOUN
ejpam-3362	71	15	.	.	PUNCT
ejpam-3362	72	1	proposition	proposition	NOUN
ejpam-3362	72	2	1	1	NUM
ejpam-3362	72	3	.	.	PUNCT
ejpam-3362	73	1	[	[	X
ejpam-3362	73	2	7	7	X
ejpam-3362	73	3	]	]	PUNCT
ejpam-3362	73	4	in	in	ADP
ejpam-3362	73	5	any	any	DET
ejpam-3362	73	6	hyper	hyper	ADJ
ejpam-3362	73	7	bci	bci	NOUN
ejpam-3362	73	8	-	-	ADJ
ejpam-3362	73	9	algebra	algebra	ADJ
ejpam-3362	73	10	h	h	NOUN
ejpam-3362	73	11	,	,	PUNCT
ejpam-3362	73	12	the	the	DET
ejpam-3362	73	13	following	follow	VERB
ejpam-3362	73	14	hold	hold	NOUN
ejpam-3362	73	15	:	:	PUNCT
ejpam-3362	73	16	(	(	PUNCT
ejpam-3362	73	17	i	i	NOUN
ejpam-3362	73	18	)	)	PUNCT
ejpam-3362	73	19	x	x	SYM
ejpam-3362	73	20	�	�	PROPN
ejpam-3362	73	21	0	0	NUM
ejpam-3362	73	22	implies	imply	VERB
ejpam-3362	73	23	x=0	x=0	PROPN
ejpam-3362	73	24	,	,	PUNCT
ejpam-3362	73	25	(	(	PUNCT
ejpam-3362	73	26	ii	ii	NOUN
ejpam-3362	73	27	)	)	PUNCT
ejpam-3362	73	28	0	0	PUNCT
ejpam-3362	74	1	∈	∈	PROPN
ejpam-3362	74	2	x~	x~	NUM
ejpam-3362	74	3	(	(	PUNCT
ejpam-3362	74	4	x~	x~	PROPN
ejpam-3362	74	5	0	0	NUM
ejpam-3362	74	6	)	)	PUNCT
ejpam-3362	74	7	,	,	PUNCT
ejpam-3362	74	8	m.	m.	NOUN
ejpam-3362	74	9	panganduyon	panganduyon	NOUN
ejpam-3362	74	10	,	,	PUNCT
ejpam-3362	74	11	s.	s.	PROPN
ejpam-3362	74	12	canoy	canoy	PROPN
ejpam-3362	74	13	/	/	SYM
ejpam-3362	74	14	eur	eur	PROPN
ejpam-3362	74	15	.	.	PUNCT
ejpam-3362	75	1	j.	j.	PROPN
ejpam-3362	75	2	pure	pure	PROPN
ejpam-3362	75	3	appl	appl	PROPN
ejpam-3362	75	4	.	.	PROPN
ejpam-3362	75	5	math	math	PROPN
ejpam-3362	75	6	,	,	PUNCT
ejpam-3362	75	7	12	12	NUM
ejpam-3362	75	8	(	(	PUNCT
ejpam-3362	75	9	1	1	NUM
ejpam-3362	75	10	)	)	PUNCT
ejpam-3362	75	11	(	(	PUNCT
ejpam-3362	75	12	2019	2019	NUM
ejpam-3362	75	13	)	)	PUNCT
ejpam-3362	75	14	,	,	PUNCT
ejpam-3362	75	15	146	146	NUM
ejpam-3362	75	16	-	-	SYM
ejpam-3362	75	17	158	158	NUM
ejpam-3362	75	18	149	149	NUM
ejpam-3362	75	19	(	(	PUNCT
ejpam-3362	75	20	iii	iii	NOUN
ejpam-3362	75	21	)	)	PUNCT
ejpam-3362	75	22	x	x	NOUN
ejpam-3362	75	23	�	�	PROPN
ejpam-3362	75	24	x~	x~	NUM
ejpam-3362	75	25	0	0	NUM
ejpam-3362	75	26	,	,	PUNCT
ejpam-3362	75	27	(	(	PUNCT
ejpam-3362	75	28	iv	iv	X
ejpam-3362	75	29	)	)	PUNCT
ejpam-3362	75	30	0~	0~	NOUN
ejpam-3362	75	31	(	(	PUNCT
ejpam-3362	75	32	x~	x~	PROPN
ejpam-3362	75	33	y	y	X
ejpam-3362	75	34	)	)	PUNCT
ejpam-3362	75	35	�	�	PROPN
ejpam-3362	75	36	y	y	PROPN
ejpam-3362	75	37	~	~	PUNCT
ejpam-3362	75	38	x	x	X
ejpam-3362	75	39	,	,	PUNCT
ejpam-3362	75	40	(	(	PUNCT
ejpam-3362	75	41	v	v	NOUN
ejpam-3362	75	42	)	)	PUNCT
ejpam-3362	75	43	a	a	DET
ejpam-3362	75	44	�	�	PROPN
ejpam-3362	75	45	a	a	PRON
ejpam-3362	75	46	,	,	PUNCT
ejpam-3362	75	47	(	(	PUNCT
ejpam-3362	75	48	vi	vi	NOUN
ejpam-3362	75	49	)	)	PUNCT
ejpam-3362	75	50	a	a	DET
ejpam-3362	75	51	⊆	⊆	NUM
ejpam-3362	75	52	b	b	NOUN
ejpam-3362	75	53	implies	imply	VERB
ejpam-3362	75	54	a	a	DET
ejpam-3362	75	55	�	�	PROPN
ejpam-3362	75	56	b	b	PROPN
ejpam-3362	75	57	,	,	PUNCT
ejpam-3362	75	58	(	(	PUNCT
ejpam-3362	75	59	vii	vii	PROPN
ejpam-3362	75	60	)	)	PUNCT
ejpam-3362	75	61	a	a	DET
ejpam-3362	75	62	�	�	PROPN
ejpam-3362	75	63	{	{	PUNCT
ejpam-3362	75	64	0	0	NUM
ejpam-3362	75	65	}	}	PUNCT
ejpam-3362	75	66	implies	imply	VERB
ejpam-3362	75	67	a	a	PRON
ejpam-3362	75	68	=	=	SYM
ejpam-3362	75	69	{	{	PUNCT
ejpam-3362	75	70	0	0	NUM
ejpam-3362	75	71	}	}	PUNCT
ejpam-3362	75	72	,	,	PUNCT
ejpam-3362	75	73	(	(	PUNCT
ejpam-3362	75	74	viii	viii	NOUN
ejpam-3362	75	75	)	)	PUNCT
ejpam-3362	75	76	x~	x~	PROPN
ejpam-3362	75	77	0	0	NUM
ejpam-3362	75	78	�	�	PROPN
ejpam-3362	75	79	{	{	PUNCT
ejpam-3362	75	80	y	y	NOUN
ejpam-3362	75	81	}	}	PUNCT
ejpam-3362	75	82	implies	imply	VERB
ejpam-3362	75	83	x	x	X
ejpam-3362	75	84	�	�	PROPN
ejpam-3362	75	85	y	y	PROPN
ejpam-3362	75	86	,	,	PUNCT
ejpam-3362	75	87	(	(	PUNCT
ejpam-3362	75	88	ix	ix	PROPN
ejpam-3362	75	89	)	)	PUNCT
ejpam-3362	75	90	y	y	PROPN
ejpam-3362	75	91	�	�	PROPN
ejpam-3362	75	92	z	z	PROPN
ejpam-3362	75	93	implies	imply	VERB
ejpam-3362	75	94	x~	x~	PROPN
ejpam-3362	75	95	z	z	PROPN
ejpam-3362	75	96	�	�	PROPN
ejpam-3362	75	97	x~	x~	NUM
ejpam-3362	75	98	y	y	PROPN
ejpam-3362	75	99	,	,	PUNCT
ejpam-3362	75	100	(	(	PUNCT
ejpam-3362	75	101	x	x	X
ejpam-3362	75	102	)	)	PUNCT
ejpam-3362	76	1	x~	x~	PROPN
ejpam-3362	76	2	y	y	SYM
ejpam-3362	76	3	=	=	PUNCT
ejpam-3362	76	4	{	{	PUNCT
ejpam-3362	76	5	0	0	NUM
ejpam-3362	76	6	}	}	PUNCT
ejpam-3362	76	7	implies	imply	VERB
ejpam-3362	76	8	(	(	PUNCT
ejpam-3362	76	9	x~	x~	PROPN
ejpam-3362	76	10	z)~	z)~	PROPN
ejpam-3362	76	11	(	(	PUNCT
ejpam-3362	76	12	y	y	PROPN
ejpam-3362	76	13	~	~	PUNCT
ejpam-3362	76	14	z	z	X
ejpam-3362	76	15	)	)	PUNCT
ejpam-3362	76	16	=	=	SYM
ejpam-3362	76	17	{	{	PUNCT
ejpam-3362	76	18	0	0	NUM
ejpam-3362	76	19	}	}	PUNCT
ejpam-3362	76	20	and	and	CCONJ
ejpam-3362	76	21	x~	x~	PROPN
ejpam-3362	76	22	z	z	PROPN
ejpam-3362	76	23	�	�	PROPN
ejpam-3362	76	24	y	y	PROPN
ejpam-3362	76	25	~	~	PUNCT
ejpam-3362	76	26	z	z	X
ejpam-3362	76	27	,	,	PUNCT
ejpam-3362	76	28	(	(	PUNCT
ejpam-3362	76	29	xi	xi	PROPN
ejpam-3362	76	30	)	)	PUNCT
ejpam-3362	76	31	a	a	DET
ejpam-3362	76	32	~	~	NOUN
ejpam-3362	76	33	a	a	PRON
ejpam-3362	76	34	=	=	PUNCT
ejpam-3362	76	35	{	{	PUNCT
ejpam-3362	76	36	0	0	NUM
ejpam-3362	76	37	}	}	PUNCT
ejpam-3362	76	38	implies	imply	VERB
ejpam-3362	76	39	a	a	DET
ejpam-3362	76	40	is	be	AUX
ejpam-3362	76	41	a	a	DET
ejpam-3362	76	42	singleton	singleton	NOUN
ejpam-3362	76	43	,	,	PUNCT
ejpam-3362	76	44	(	(	PUNCT
ejpam-3362	76	45	xii	xii	NOUN
ejpam-3362	76	46	)	)	PUNCT
ejpam-3362	77	1	a~	a~	PROPN
ejpam-3362	77	2	{	{	PUNCT
ejpam-3362	77	3	0	0	NUM
ejpam-3362	77	4	}	}	PUNCT
ejpam-3362	77	5	=	=	PRON
ejpam-3362	77	6	{	{	PUNCT
ejpam-3362	77	7	0	0	NUM
ejpam-3362	77	8	}	}	PUNCT
ejpam-3362	77	9	implies	imply	VERB
ejpam-3362	77	10	a	a	DET
ejpam-3362	77	11	=	=	X
ejpam-3362	77	12	{	{	PUNCT
ejpam-3362	77	13	0	0	NUM
ejpam-3362	77	14	}	}	PUNCT
ejpam-3362	77	15	.	.	PUNCT
ejpam-3362	78	1	for	for	ADP
ejpam-3362	78	2	all	all	DET
ejpam-3362	78	3	x	x	PROPN
ejpam-3362	78	4	,	,	PUNCT
ejpam-3362	78	5	y	y	PROPN
ejpam-3362	78	6	,	,	PUNCT
ejpam-3362	78	7	z	z	PROPN
ejpam-3362	78	8	∈	∈	PROPN
ejpam-3362	78	9	h	h	NOUN
ejpam-3362	78	10	and	and	CCONJ
ejpam-3362	78	11	for	for	ADP
ejpam-3362	78	12	all	all	DET
ejpam-3362	78	13	non	non	ADJ
ejpam-3362	78	14	-	-	ADJ
ejpam-3362	78	15	empty	empty	ADJ
ejpam-3362	78	16	subsets	subset	NOUN
ejpam-3362	78	17	a	a	PRON
ejpam-3362	78	18	and	and	CCONJ
ejpam-3362	78	19	b	b	PROPN
ejpam-3362	78	20	of	of	ADP
ejpam-3362	78	21	h.	h.	PROPN
ejpam-3362	78	22	theorem	theorem	PROPN
ejpam-3362	78	23	1	1	NUM
ejpam-3362	78	24	.	.	PUNCT
ejpam-3362	79	1	[	[	X
ejpam-3362	79	2	3	3	X
ejpam-3362	79	3	]	]	PUNCT
ejpam-3362	79	4	let	let	VERB
ejpam-3362	79	5	f	f	PROPN
ejpam-3362	79	6	:	:	PUNCT
ejpam-3362	79	7	h1	h1	PROPN
ejpam-3362	79	8	→	→	SYM
ejpam-3362	79	9	h2	h2	PROPN
ejpam-3362	79	10	be	be	AUX
ejpam-3362	79	11	a	a	DET
ejpam-3362	79	12	hyper	hyper	ADJ
ejpam-3362	79	13	homomorphism	homomorphism	NOUN
ejpam-3362	79	14	.	.	PUNCT
ejpam-3362	80	1	then	then	ADV
ejpam-3362	80	2	the	the	DET
ejpam-3362	80	3	following	follow	VERB
ejpam-3362	80	4	hold	hold	NOUN
ejpam-3362	80	5	:	:	PUNCT
ejpam-3362	80	6	(	(	PUNCT
ejpam-3362	80	7	i	i	NOUN
ejpam-3362	80	8	)	)	PUNCT
ejpam-3362	80	9	if	if	SCONJ
ejpam-3362	80	10	x	x	X
ejpam-3362	80	11	�	�	PROPN
ejpam-3362	80	12	y	y	PROPN
ejpam-3362	80	13	,	,	PUNCT
ejpam-3362	80	14	where	where	SCONJ
ejpam-3362	80	15	x	x	X
ejpam-3362	80	16	,	,	PUNCT
ejpam-3362	80	17	y	y	PROPN
ejpam-3362	80	18	∈	∈	PROPN
ejpam-3362	80	19	h1	h1	PROPN
ejpam-3362	80	20	,	,	PUNCT
ejpam-3362	80	21	then	then	ADV
ejpam-3362	80	22	f(x	f(x	PROPN
ejpam-3362	80	23	)	)	PUNCT
ejpam-3362	80	24	�	�	PROPN
ejpam-3362	80	25	f(y	f(y	PROPN
ejpam-3362	80	26	)	)	PUNCT
ejpam-3362	80	27	.	.	PUNCT
ejpam-3362	81	1	(	(	PUNCT
ejpam-3362	81	2	ii	ii	NOUN
ejpam-3362	81	3	)	)	PUNCT
ejpam-3362	81	4	if	if	SCONJ
ejpam-3362	81	5	a	a	PRON
ejpam-3362	81	6	,	,	PUNCT
ejpam-3362	81	7	b	b	NOUN
ejpam-3362	81	8	⊆	⊆	NUM
ejpam-3362	81	9	h1	h1	VERB
ejpam-3362	81	10	such	such	ADJ
ejpam-3362	81	11	that	that	SCONJ
ejpam-3362	81	12	a	a	DET
ejpam-3362	81	13	�	�	PROPN
ejpam-3362	81	14	b	b	PROPN
ejpam-3362	81	15	,	,	PUNCT
ejpam-3362	81	16	then	then	ADV
ejpam-3362	81	17	f(a	f(a	PROPN
ejpam-3362	81	18	)	)	PUNCT
ejpam-3362	81	19	�	�	PROPN
ejpam-3362	81	20	f(b	f(b	PROPN
ejpam-3362	81	21	)	)	PUNCT
ejpam-3362	81	22	.	.	PUNCT
ejpam-3362	82	1	3	3	X
ejpam-3362	82	2	.	.	NUM
ejpam-3362	82	3	zero	zero	NUM
ejpam-3362	82	4	divisor	divisor	NOUN
ejpam-3362	82	5	graph	graph	NOUN
ejpam-3362	82	6	of	of	ADP
ejpam-3362	82	7	a	a	DET
ejpam-3362	82	8	hyper	hyper	ADJ
ejpam-3362	82	9	bci	bci	NOUN
ejpam-3362	82	10	-	-	NOUN
ejpam-3362	82	11	algebra	algebra	NOUN
ejpam-3362	82	12	let	let	VERB
ejpam-3362	82	13	h	h	NOUN
ejpam-3362	82	14	be	be	AUX
ejpam-3362	82	15	a	a	DET
ejpam-3362	82	16	hyper	hyper	ADJ
ejpam-3362	82	17	bci	bci	NOUN
ejpam-3362	82	18	-	-	NOUN
ejpam-3362	82	19	algebra	algebra	NOUN
ejpam-3362	82	20	and	and	CCONJ
ejpam-3362	82	21	a	a	DET
ejpam-3362	82	22	⊆	⊆	NUM
ejpam-3362	82	23	h.	h.	NOUN
ejpam-3362	82	24	we	we	PRON
ejpam-3362	82	25	will	will	AUX
ejpam-3362	82	26	use	use	VERB
ejpam-3362	82	27	the	the	DET
ejpam-3362	82	28	notation	notation	NOUN
ejpam-3362	82	29	lh(a	lh(a	NOUN
ejpam-3362	82	30	)	)	PUNCT
ejpam-3362	82	31	to	to	PART
ejpam-3362	82	32	denote	denote	VERB
ejpam-3362	82	33	the	the	DET
ejpam-3362	82	34	set	set	NOUN
ejpam-3362	82	35	lh(a	lh(a	NOUN
ejpam-3362	82	36	)	)	PUNCT
ejpam-3362	82	37	:	:	PUNCT
ejpam-3362	83	1	=	=	SYM
ejpam-3362	83	2	{	{	PUNCT
ejpam-3362	83	3	x	x	PUNCT
ejpam-3362	83	4	∈	∈	PROPN
ejpam-3362	83	5	h|x	h|x	NOUN
ejpam-3362	83	6	�	�	PROPN
ejpam-3362	83	7	a,∀	a,∀	PROPN
ejpam-3362	83	8	a	a	DET
ejpam-3362	83	9	∈	∈	PROPN
ejpam-3362	83	10	a	a	DET
ejpam-3362	83	11	}	}	PUNCT
ejpam-3362	83	12	=	=	SYM
ejpam-3362	83	13	{	{	PUNCT
ejpam-3362	83	14	x	x	PUNCT
ejpam-3362	83	15	∈	∈	PROPN
ejpam-3362	83	16	h|0	h|0	PROPN
ejpam-3362	83	17	∈	∈	NOUN
ejpam-3362	83	18	x~	x~	PROPN
ejpam-3362	83	19	a,∀	a,∀	PROPN
ejpam-3362	83	20	a	a	DET
ejpam-3362	83	21	∈	∈	PROPN
ejpam-3362	83	22	a	a	PRON
ejpam-3362	83	23	}	}	PUNCT
ejpam-3362	83	24	.	.	PUNCT
ejpam-3362	84	1	if	if	SCONJ
ejpam-3362	84	2	a	a	PRON
ejpam-3362	84	3	=	=	X
ejpam-3362	84	4	{	{	PUNCT
ejpam-3362	84	5	a	a	NOUN
ejpam-3362	84	6	}	}	PUNCT
ejpam-3362	84	7	,	,	PUNCT
ejpam-3362	84	8	we	we	PRON
ejpam-3362	84	9	write	write	VERB
ejpam-3362	84	10	lh({a	lh({a	PROPN
ejpam-3362	84	11	}	}	PUNCT
ejpam-3362	84	12	)	)	PUNCT
ejpam-3362	85	1	=	=	SYM
ejpam-3362	85	2	lh(a	lh(a	NOUN
ejpam-3362	85	3	)	)	PUNCT
ejpam-3362	85	4	.	.	PUNCT
ejpam-3362	86	1	for	for	ADP
ejpam-3362	86	2	any	any	DET
ejpam-3362	86	3	x	x	SYM
ejpam-3362	86	4	∈	∈	PROPN
ejpam-3362	86	5	h	h	NOUN
ejpam-3362	86	6	,	,	PUNCT
ejpam-3362	86	7	the	the	DET
ejpam-3362	86	8	set	set	NOUN
ejpam-3362	86	9	of	of	ADP
ejpam-3362	86	10	zero	zero	NUM
ejpam-3362	86	11	divisors	divisor	NOUN
ejpam-3362	86	12	of	of	ADP
ejpam-3362	86	13	x	x	SYM
ejpam-3362	86	14	is	be	AUX
ejpam-3362	86	15	zx	zx	PROPN
ejpam-3362	86	16	=	=	PUNCT
ejpam-3362	86	17	{	{	PUNCT
ejpam-3362	86	18	y	y	PROPN
ejpam-3362	86	19	∈	∈	PROPN
ejpam-3362	86	20	h|lh({x	h|lh({x	PROPN
ejpam-3362	86	21	,	,	PUNCT
ejpam-3362	86	22	y	y	NOUN
ejpam-3362	86	23	}	}	PUNCT
ejpam-3362	86	24	)	)	PUNCT
ejpam-3362	86	25	=	=	PUNCT
ejpam-3362	86	26	{	{	PUNCT
ejpam-3362	86	27	0	0	NUM
ejpam-3362	86	28	}	}	PUNCT
ejpam-3362	86	29	}	}	PUNCT
ejpam-3362	86	30	.	.	PUNCT
ejpam-3362	87	1	let	let	VERB
ejpam-3362	87	2	h	h	PRON
ejpam-3362	87	3	be	be	AUX
ejpam-3362	87	4	a	a	DET
ejpam-3362	87	5	finite	finite	ADJ
ejpam-3362	87	6	hyper	hyper	ADJ
ejpam-3362	87	7	bci	bci	NOUN
ejpam-3362	87	8	-	-	NOUN
ejpam-3362	87	9	algebra	algebra	NOUN
ejpam-3362	87	10	.	.	PUNCT
ejpam-3362	88	1	the	the	DET
ejpam-3362	88	2	zero	zero	NUM
ejpam-3362	88	3	divisor	divisor	NOUN
ejpam-3362	88	4	graph	graph	NOUN
ejpam-3362	88	5	γ(h	γ(h	NOUN
ejpam-3362	88	6	)	)	PUNCT
ejpam-3362	88	7	of	of	ADP
ejpam-3362	88	8	h	h	NOUN
ejpam-3362	88	9	is	be	AUX
ejpam-3362	88	10	the	the	DET
ejpam-3362	88	11	graph	graph	NOUN
ejpam-3362	88	12	whose	whose	DET
ejpam-3362	88	13	vertex	vertex	NOUN
ejpam-3362	88	14	set	set	NOUN
ejpam-3362	88	15	v	v	NOUN
ejpam-3362	88	16	(	(	PUNCT
ejpam-3362	88	17	γ(h	γ(h	NOUN
ejpam-3362	88	18	)	)	PUNCT
ejpam-3362	88	19	)	)	PUNCT
ejpam-3362	89	1	=	=	SYM
ejpam-3362	89	2	h	h	NOUN
ejpam-3362	89	3	and	and	CCONJ
ejpam-3362	89	4	edge	edge	VERB
ejpam-3362	89	5	set	set	ADJ
ejpam-3362	89	6	e(γ(h	e(γ(h	NOUN
ejpam-3362	89	7	)	)	PUNCT
ejpam-3362	89	8	)	)	PUNCT
ejpam-3362	90	1	satisfying	satisfy	VERB
ejpam-3362	90	2	the	the	DET
ejpam-3362	90	3	following	follow	VERB
ejpam-3362	90	4	condition	condition	NOUN
ejpam-3362	90	5	:	:	PUNCT
ejpam-3362	90	6	for	for	ADP
ejpam-3362	90	7	every	every	DET
ejpam-3362	90	8	distinct	distinct	ADJ
ejpam-3362	90	9	x	x	NOUN
ejpam-3362	90	10	,	,	PUNCT
ejpam-3362	90	11	y	y	PROPN
ejpam-3362	90	12	∈	∈	PROPN
ejpam-3362	90	13	h	h	NOUN
ejpam-3362	90	14	,	,	PUNCT
ejpam-3362	90	15	xy	xy	PROPN
ejpam-3362	90	16	∈	∈	PROPN
ejpam-3362	90	17	e(γ(h	e(γ(h	PROPN
ejpam-3362	90	18	)	)	PUNCT
ejpam-3362	90	19	)	)	PUNCT
ejpam-3362	91	1	if	if	SCONJ
ejpam-3362	91	2	and	and	CCONJ
ejpam-3362	91	3	only	only	ADV
ejpam-3362	91	4	if	if	SCONJ
ejpam-3362	91	5	lh({x	lh({x	NOUN
ejpam-3362	91	6	,	,	PUNCT
ejpam-3362	91	7	y	y	NOUN
ejpam-3362	91	8	}	}	PUNCT
ejpam-3362	91	9	)	)	PUNCT
ejpam-3362	92	1	=	=	PUNCT
ejpam-3362	92	2	{	{	PUNCT
ejpam-3362	92	3	0	0	NUM
ejpam-3362	92	4	}	}	PUNCT
ejpam-3362	92	5	(	(	PUNCT
ejpam-3362	92	6	equivalently	equivalently	ADV
ejpam-3362	92	7	,	,	PUNCT
ejpam-3362	92	8	x	x	PROPN
ejpam-3362	92	9	∈	∈	PROPN
ejpam-3362	92	10	zy	zy	NOUN
ejpam-3362	92	11	or	or	CCONJ
ejpam-3362	92	12	y	y	PROPN
ejpam-3362	92	13	∈	∈	PROPN
ejpam-3362	92	14	zx	zx	NUM
ejpam-3362	92	15	)	)	PUNCT
ejpam-3362	92	16	.	.	PUNCT
ejpam-3362	93	1	although	although	SCONJ
ejpam-3362	93	2	there	there	PRON
ejpam-3362	93	3	are	be	VERB
ejpam-3362	93	4	infinite	infinite	ADJ
ejpam-3362	93	5	hyper	hyper	ADJ
ejpam-3362	93	6	bci	bci	NOUN
ejpam-3362	93	7	-	-	PUNCT
ejpam-3362	93	8	algebras	algebra	NOUN
ejpam-3362	93	9	,	,	PUNCT
ejpam-3362	93	10	this	this	DET
ejpam-3362	93	11	paper	paper	NOUN
ejpam-3362	93	12	only	only	ADV
ejpam-3362	93	13	considers	consider	VERB
ejpam-3362	93	14	zero	zero	NUM
ejpam-3362	93	15	divisor	divisor	NOUN
ejpam-3362	93	16	graphs	graph	NOUN
ejpam-3362	93	17	of	of	ADP
ejpam-3362	93	18	finite	finite	PROPN
ejpam-3362	93	19	hyper	hyper	ADJ
ejpam-3362	93	20	bci	bci	NOUN
ejpam-3362	93	21	-	-	PUNCT
ejpam-3362	93	22	algebras	algebra	NOUN
ejpam-3362	93	23	.	.	PUNCT
ejpam-3362	93	24	example	example	NOUN
ejpam-3362	93	25	2	2	NUM
ejpam-3362	93	26	.	.	X
ejpam-3362	93	27	consider	consider	VERB
ejpam-3362	93	28	the	the	DET
ejpam-3362	93	29	hyper	hyper	ADJ
ejpam-3362	93	30	bci	bci	NOUN
ejpam-3362	93	31	-	-	ADJ
ejpam-3362	93	32	algebra	algebra	NOUN
ejpam-3362	93	33	h	h	NOUN
ejpam-3362	93	34	defined	define	VERB
ejpam-3362	93	35	in	in	ADP
ejpam-3362	93	36	example	example	NOUN
ejpam-3362	94	1	1	1	X
ejpam-3362	94	2	.	.	PUNCT
ejpam-3362	95	1	then	then	ADV
ejpam-3362	95	2	lh({0	lh({0	X
ejpam-3362	95	3	,	,	PUNCT
ejpam-3362	95	4	1	1	NUM
ejpam-3362	95	5	}	}	PUNCT
ejpam-3362	95	6	)	)	PUNCT
ejpam-3362	95	7	=	=	SYM
ejpam-3362	95	8	lh({0	lh({0	PROPN
ejpam-3362	95	9	,	,	PUNCT
ejpam-3362	95	10	2	2	NUM
ejpam-3362	95	11	}	}	PUNCT
ejpam-3362	95	12	)	)	PUNCT
ejpam-3362	96	1	=	=	SYM
ejpam-3362	96	2	{	{	PUNCT
ejpam-3362	96	3	0	0	NUM
ejpam-3362	96	4	}	}	PUNCT
ejpam-3362	96	5	and	and	CCONJ
ejpam-3362	96	6	lh({1	lh({1	NUM
ejpam-3362	96	7	,	,	PUNCT
ejpam-3362	96	8	2	2	NUM
ejpam-3362	96	9	}	}	PUNCT
ejpam-3362	96	10	)	)	PUNCT
ejpam-3362	97	1	=	=	SYM
ejpam-3362	97	2	{	{	PUNCT
ejpam-3362	97	3	0	0	NUM
ejpam-3362	97	4	,	,	PUNCT
ejpam-3362	97	5	1	1	NUM
ejpam-3362	97	6	}	}	PUNCT
ejpam-3362	97	7	.	.	PUNCT
ejpam-3362	98	1	the	the	DET
ejpam-3362	98	2	zero	zero	NUM
ejpam-3362	98	3	divisors	divisor	NOUN
ejpam-3362	98	4	of	of	ADP
ejpam-3362	98	5	x	x	PART
ejpam-3362	98	6	∈	∈	PROPN
ejpam-3362	98	7	h	h	NOUN
ejpam-3362	98	8	are	be	AUX
ejpam-3362	98	9	z0	z0	PROPN
ejpam-3362	98	10	=	=	PUNCT
ejpam-3362	98	11	{	{	PUNCT
ejpam-3362	98	12	y	y	PROPN
ejpam-3362	98	13	∈	∈	PROPN
ejpam-3362	98	14	h|lh({0	h|lh({0	PROPN
ejpam-3362	98	15	,	,	PUNCT
ejpam-3362	98	16	y	y	NOUN
ejpam-3362	98	17	}	}	PUNCT
ejpam-3362	98	18	)	)	PUNCT
ejpam-3362	98	19	=	=	PUNCT
ejpam-3362	98	20	{	{	PUNCT
ejpam-3362	98	21	0	0	NUM
ejpam-3362	98	22	}	}	PUNCT
ejpam-3362	98	23	}	}	PUNCT
ejpam-3362	98	24	=	=	SYM
ejpam-3362	98	25	{	{	PUNCT
ejpam-3362	98	26	1	1	NUM
ejpam-3362	98	27	,	,	PUNCT
ejpam-3362	98	28	2	2	NUM
ejpam-3362	98	29	}	}	PUNCT
ejpam-3362	98	30	and	and	CCONJ
ejpam-3362	98	31	z1	z1	PROPN
ejpam-3362	98	32	=	=	SYM
ejpam-3362	98	33	{	{	PUNCT
ejpam-3362	98	34	0	0	NUM
ejpam-3362	98	35	}	}	PUNCT
ejpam-3362	98	36	=	=	SYM
ejpam-3362	98	37	z2	z2	PROPN
ejpam-3362	98	38	.	.	PUNCT
ejpam-3362	99	1	thus	thus	ADV
ejpam-3362	99	2	,	,	PUNCT
ejpam-3362	99	3	the	the	DET
ejpam-3362	99	4	zero	zero	NUM
ejpam-3362	99	5	divisor	divisor	NOUN
ejpam-3362	99	6	graph	graph	NOUN
ejpam-3362	99	7	γ(h	γ(h	NOUN
ejpam-3362	99	8	)	)	PUNCT
ejpam-3362	99	9	of	of	ADP
ejpam-3362	99	10	h	h	NOUN
ejpam-3362	99	11	is	be	AUX
ejpam-3362	99	12	given	give	VERB
ejpam-3362	99	13	by	by	ADP
ejpam-3362	99	14	the	the	DET
ejpam-3362	99	15	following	follow	VERB
ejpam-3362	99	16	figure	figure	NOUN
ejpam-3362	99	17	:	:	PUNCT
ejpam-3362	99	18	m.	m.	NOUN
ejpam-3362	99	19	panganduyon	panganduyon	NOUN
ejpam-3362	99	20	,	,	PUNCT
ejpam-3362	99	21	s.	s.	PROPN
ejpam-3362	99	22	canoy	canoy	PROPN
ejpam-3362	99	23	/	/	SYM
ejpam-3362	99	24	eur	eur	PROPN
ejpam-3362	99	25	.	.	PUNCT
ejpam-3362	100	1	j.	j.	PROPN
ejpam-3362	100	2	pure	pure	PROPN
ejpam-3362	100	3	appl	appl	PROPN
ejpam-3362	100	4	.	.	PROPN
ejpam-3362	100	5	math	math	PROPN
ejpam-3362	100	6	,	,	PUNCT
ejpam-3362	100	7	12	12	NUM
ejpam-3362	100	8	(	(	PUNCT
ejpam-3362	100	9	1	1	NUM
ejpam-3362	100	10	)	)	PUNCT
ejpam-3362	100	11	(	(	PUNCT
ejpam-3362	100	12	2019	2019	NUM
ejpam-3362	100	13	)	)	PUNCT
ejpam-3362	100	14	,	,	PUNCT
ejpam-3362	100	15	146	146	NUM
ejpam-3362	100	16	-	-	SYM
ejpam-3362	100	17	158	158	NUM
ejpam-3362	100	18	150	150	NUM
ejpam-3362	100	19	1	1	NUM
ejpam-3362	100	20	2	2	NUM
ejpam-3362	100	21	0	0	NUM
ejpam-3362	100	22	the	the	DET
ejpam-3362	100	23	next	next	ADJ
ejpam-3362	100	24	result	result	NOUN
ejpam-3362	100	25	gives	give	VERB
ejpam-3362	100	26	some	some	DET
ejpam-3362	100	27	properties	property	NOUN
ejpam-3362	100	28	of	of	ADP
ejpam-3362	100	29	the	the	DET
ejpam-3362	100	30	operator	operator	NOUN
ejpam-3362	100	31	lh	lh	PROPN
ejpam-3362	100	32	.	.	PUNCT
ejpam-3362	101	1	proposition	proposition	NOUN
ejpam-3362	101	2	2	2	NUM
ejpam-3362	101	3	.	.	PUNCT
ejpam-3362	102	1	let	let	VERB
ejpam-3362	102	2	a	a	PRON
ejpam-3362	102	3	and	and	CCONJ
ejpam-3362	102	4	b	b	NOUN
ejpam-3362	102	5	be	be	AUX
ejpam-3362	102	6	subsets	subset	NOUN
ejpam-3362	102	7	of	of	ADP
ejpam-3362	102	8	h.	h.	PROPN
ejpam-3362	102	9	then	then	ADV
ejpam-3362	102	10	the	the	DET
ejpam-3362	102	11	following	follow	VERB
ejpam-3362	102	12	hold	hold	NOUN
ejpam-3362	102	13	:	:	PUNCT
ejpam-3362	102	14	(	(	PUNCT
ejpam-3362	102	15	i	i	NOUN
ejpam-3362	102	16	)	)	PUNCT
ejpam-3362	102	17	lh(∅	lh(∅	PROPN
ejpam-3362	102	18	)	)	PUNCT
ejpam-3362	103	1	=	=	SYM
ejpam-3362	103	2	h	h	PROPN
ejpam-3362	103	3	(	(	PUNCT
ejpam-3362	103	4	ii	ii	PROPN
ejpam-3362	103	5	)	)	PUNCT
ejpam-3362	103	6	lh({0	lh({0	NOUN
ejpam-3362	103	7	}	}	PUNCT
ejpam-3362	103	8	)	)	PUNCT
ejpam-3362	104	1	=	=	PUNCT
ejpam-3362	104	2	{	{	PUNCT
ejpam-3362	104	3	0	0	NUM
ejpam-3362	104	4	}	}	PUNCT
ejpam-3362	104	5	(	(	PUNCT
ejpam-3362	104	6	iii	iii	X
ejpam-3362	104	7	)	)	PUNCT
ejpam-3362	104	8	if	if	SCONJ
ejpam-3362	104	9	a	a	DET
ejpam-3362	104	10	⊆	⊆	NUM
ejpam-3362	104	11	b	b	NOUN
ejpam-3362	104	12	,	,	PUNCT
ejpam-3362	104	13	then	then	ADV
ejpam-3362	104	14	lh(b	lh(b	NOUN
ejpam-3362	104	15	)	)	PUNCT
ejpam-3362	104	16	⊆	⊆	NUM
ejpam-3362	104	17	lh(a	lh(a	NUM
ejpam-3362	104	18	)	)	PUNCT
ejpam-3362	104	19	.	.	PUNCT
ejpam-3362	105	1	(	(	PUNCT
ejpam-3362	105	2	iv	iv	X
ejpam-3362	105	3	)	)	PUNCT
ejpam-3362	105	4	lh(a	lh(a	NOUN
ejpam-3362	105	5	)	)	PUNCT
ejpam-3362	106	1	=	=	SYM
ejpam-3362	107	1	⋂	⋂	PROPN
ejpam-3362	107	2	a∈a	a∈a	ADJ
ejpam-3362	107	3	lh({a	lh({a	NOUN
ejpam-3362	107	4	}	}	PUNCT
ejpam-3362	107	5	)	)	PUNCT
ejpam-3362	107	6	(	(	PUNCT
ejpam-3362	107	7	v	v	NOUN
ejpam-3362	107	8	)	)	PUNCT
ejpam-3362	107	9	if	if	SCONJ
ejpam-3362	107	10	x	x	SYM
ejpam-3362	107	11	∈	∈	PROPN
ejpam-3362	107	12	h	h	NOUN
ejpam-3362	107	13	,	,	PUNCT
ejpam-3362	107	14	then	then	ADV
ejpam-3362	107	15	x	x	X
ejpam-3362	107	16	∈	∈	PROPN
ejpam-3362	107	17	lh({x	lh({x	NOUN
ejpam-3362	107	18	}	}	PUNCT
ejpam-3362	107	19	)	)	PUNCT
ejpam-3362	107	20	.	.	PUNCT
ejpam-3362	108	1	furthermore	furthermore	ADV
ejpam-3362	108	2	,	,	PUNCT
ejpam-3362	108	3	lh({x	lh({x	NOUN
ejpam-3362	108	4	}	}	PUNCT
ejpam-3362	108	5	)	)	PUNCT
ejpam-3362	109	1	=	=	PUNCT
ejpam-3362	109	2	{	{	PUNCT
ejpam-3362	109	3	0	0	NUM
ejpam-3362	109	4	}	}	PUNCT
ejpam-3362	109	5	if	if	SCONJ
ejpam-3362	109	6	and	and	CCONJ
ejpam-3362	109	7	only	only	ADV
ejpam-3362	109	8	if	if	SCONJ
ejpam-3362	109	9	x	x	SYM
ejpam-3362	109	10	=	=	NOUN
ejpam-3362	109	11	0	0	X
ejpam-3362	109	12	.	.	PUNCT
ejpam-3362	110	1	proof	proof	NOUN
ejpam-3362	110	2	.	.	PUNCT
ejpam-3362	111	1	(	(	PUNCT
ejpam-3362	111	2	i	i	NOUN
ejpam-3362	111	3	)	)	PUNCT
ejpam-3362	111	4	suppose	suppose	VERB
ejpam-3362	111	5	lh(∅	lh(∅	PROPN
ejpam-3362	111	6	)	)	PUNCT
ejpam-3362	111	7	6=	6=	PUNCT
ejpam-3362	112	1	h.	h.	PROPN
ejpam-3362	112	2	then	then	ADV
ejpam-3362	112	3	∃h	∃h	VERB
ejpam-3362	112	4	∈	∈	PROPN
ejpam-3362	112	5	h	h	NOUN
ejpam-3362	112	6	such	such	ADJ
ejpam-3362	112	7	that	that	SCONJ
ejpam-3362	112	8	h	h	PROPN
ejpam-3362	112	9	/∈	/∈	PUNCT
ejpam-3362	112	10	lh(∅	lh(∅	PROPN
ejpam-3362	112	11	)	)	PUNCT
ejpam-3362	112	12	;	;	PUNCT
ejpam-3362	112	13	i.e.	i.e.	X
ejpam-3362	112	14	,	,	PUNCT
ejpam-3362	112	15	∃	∃	PROPN
ejpam-3362	112	16	a	a	DET
ejpam-3362	112	17	∈	∈	PROPN
ejpam-3362	112	18	∅	∅	NOUN
ejpam-3362	112	19	such	such	ADJ
ejpam-3362	112	20	that	that	SCONJ
ejpam-3362	112	21	a	a	DET
ejpam-3362	112	22	6	6	NUM
ejpam-3362	112	23	�	�	PROPN
ejpam-3362	112	24	h	h	NOUN
ejpam-3362	112	25	,	,	PUNCT
ejpam-3362	112	26	a	a	DET
ejpam-3362	112	27	contradiction	contradiction	NOUN
ejpam-3362	112	28	.	.	PUNCT
ejpam-3362	113	1	therefore	therefore	ADV
ejpam-3362	113	2	,	,	PUNCT
ejpam-3362	113	3	lh(∅	lh(∅	PROPN
ejpam-3362	113	4	)	)	PUNCT
ejpam-3362	114	1	=	=	SYM
ejpam-3362	114	2	h.	h.	PROPN
ejpam-3362	114	3	(	(	PUNCT
ejpam-3362	114	4	ii	ii	PROPN
ejpam-3362	114	5	)	)	PUNCT
ejpam-3362	114	6	by	by	ADP
ejpam-3362	114	7	definition	definition	NOUN
ejpam-3362	114	8	,	,	PUNCT
ejpam-3362	114	9	lh({0	lh({0	NOUN
ejpam-3362	114	10	}	}	PUNCT
ejpam-3362	114	11	)	)	PUNCT
ejpam-3362	114	12	=	=	PRON
ejpam-3362	115	1	{	{	PUNCT
ejpam-3362	115	2	x	x	PUNCT
ejpam-3362	115	3	∈	∈	PROPN
ejpam-3362	115	4	h|x	h|x	NOUN
ejpam-3362	115	5	�	�	PROPN
ejpam-3362	115	6	0	0	NUM
ejpam-3362	115	7	}	}	PUNCT
ejpam-3362	115	8	=	=	PRON
ejpam-3362	115	9	{	{	PUNCT
ejpam-3362	115	10	0	0	NUM
ejpam-3362	115	11	}	}	PUNCT
ejpam-3362	115	12	,	,	PUNCT
ejpam-3362	115	13	by	by	ADP
ejpam-3362	115	14	proposition	proposition	NOUN
ejpam-3362	115	15	1	1	NUM
ejpam-3362	115	16	.	.	PUNCT
ejpam-3362	115	17	(	(	PUNCT
ejpam-3362	115	18	iii	iii	X
ejpam-3362	115	19	)	)	PUNCT
ejpam-3362	115	20	let	let	VERB
ejpam-3362	115	21	x	x	X
ejpam-3362	115	22	∈	∈	NOUN
ejpam-3362	115	23	lh(b	lh(b	NOUN
ejpam-3362	115	24	)	)	PUNCT
ejpam-3362	115	25	.	.	PUNCT
ejpam-3362	116	1	then	then	ADV
ejpam-3362	116	2	x	x	SYM
ejpam-3362	116	3	�	�	PROPN
ejpam-3362	116	4	b	b	PROPN
ejpam-3362	116	5	,	,	PUNCT
ejpam-3362	116	6	∀	∀	X
ejpam-3362	116	7	b	b	PROPN
ejpam-3362	116	8	∈	∈	PROPN
ejpam-3362	116	9	b.	b.	PROPN
ejpam-3362	116	10	since	since	SCONJ
ejpam-3362	116	11	a	a	DET
ejpam-3362	116	12	⊆	⊆	NUM
ejpam-3362	116	13	b	b	NOUN
ejpam-3362	116	14	,	,	PUNCT
ejpam-3362	116	15	x	x	PROPN
ejpam-3362	116	16	�	�	PROPN
ejpam-3362	116	17	a	a	NOUN
ejpam-3362	116	18	,	,	PUNCT
ejpam-3362	116	19	∀	∀	VERB
ejpam-3362	116	20	a	a	DET
ejpam-3362	116	21	∈	∈	PROPN
ejpam-3362	116	22	a.	a.	NOUN
ejpam-3362	116	23	thus	thus	ADV
ejpam-3362	116	24	,	,	PUNCT
ejpam-3362	116	25	x	x	PROPN
ejpam-3362	116	26	∈	∈	PROPN
ejpam-3362	116	27	lh(a	lh(a	NOUN
ejpam-3362	116	28	)	)	PUNCT
ejpam-3362	116	29	.	.	PUNCT
ejpam-3362	117	1	hence	hence	ADV
ejpam-3362	117	2	,	,	PUNCT
ejpam-3362	117	3	lh(b	lh(b	NOUN
ejpam-3362	117	4	)	)	PUNCT
ejpam-3362	117	5	⊆	⊆	NUM
ejpam-3362	117	6	lh(a	lh(a	NUM
ejpam-3362	117	7	)	)	PUNCT
ejpam-3362	117	8	.	.	PUNCT
ejpam-3362	118	1	(	(	PUNCT
ejpam-3362	118	2	iv	iv	X
ejpam-3362	118	3	)	)	PUNCT
ejpam-3362	118	4	follows	follow	VERB
ejpam-3362	118	5	from	from	ADP
ejpam-3362	118	6	the	the	DET
ejpam-3362	118	7	definition	definition	NOUN
ejpam-3362	118	8	of	of	ADP
ejpam-3362	118	9	lh(a	lh(a	NOUN
ejpam-3362	118	10	):	):	PUNCT
ejpam-3362	118	11	lh(a	lh(a	NUM
ejpam-3362	118	12	)	)	PUNCT
ejpam-3362	119	1	=	=	PRON
ejpam-3362	119	2	{	{	PUNCT
ejpam-3362	119	3	x	x	PUNCT
ejpam-3362	119	4	∈	∈	PROPN
ejpam-3362	119	5	h|x	h|x	NOUN
ejpam-3362	119	6	�	�	PROPN
ejpam-3362	119	7	a,∀	a,∀	PROPN
ejpam-3362	119	8	a	a	DET
ejpam-3362	119	9	∈	∈	PROPN
ejpam-3362	119	10	a	a	DET
ejpam-3362	119	11	}	}	PUNCT
ejpam-3362	119	12	=	=	SYM
ejpam-3362	119	13	{	{	PUNCT
ejpam-3362	119	14	x	x	SYM
ejpam-3362	119	15	∈	∈	PROPN
ejpam-3362	119	16	h|x	h|x	ADJ
ejpam-3362	119	17	∈	∈	PROPN
ejpam-3362	119	18	lh({a}),∀	lh({a}),∀	VERB
ejpam-3362	119	19	a	a	DET
ejpam-3362	119	20	∈	∈	PROPN
ejpam-3362	119	21	a	a	PRON
ejpam-3362	119	22	}	}	PUNCT
ejpam-3362	119	23	=	=	SYM
ejpam-3362	119	24	⋂	⋂	PROPN
ejpam-3362	119	25	a∈a	a∈a	ADJ
ejpam-3362	119	26	lh({a	lh({a	NOUN
ejpam-3362	119	27	}	}	PUNCT
ejpam-3362	119	28	)	)	PUNCT
ejpam-3362	119	29	.	.	PUNCT
ejpam-3362	120	1	(	(	PUNCT
ejpam-3362	120	2	v	v	X
ejpam-3362	120	3	)	)	PUNCT
ejpam-3362	120	4	let	let	VERB
ejpam-3362	121	1	x	x	SYM
ejpam-3362	121	2	∈	∈	PROPN
ejpam-3362	121	3	h.	h.	PROPN
ejpam-3362	121	4	by	by	ADP
ejpam-3362	121	5	(	(	PUNCT
ejpam-3362	121	6	b3	b3	PROPN
ejpam-3362	121	7	)	)	PUNCT
ejpam-3362	121	8	,	,	PUNCT
ejpam-3362	121	9	x	x	X
ejpam-3362	121	10	�	�	PROPN
ejpam-3362	121	11	x.	x.	PROPN
ejpam-3362	121	12	hence	hence	ADV
ejpam-3362	121	13	,	,	PUNCT
ejpam-3362	121	14	x	x	PUNCT
ejpam-3362	121	15	∈	∈	PROPN
ejpam-3362	121	16	lh({x	lh({x	NOUN
ejpam-3362	121	17	}	}	PUNCT
ejpam-3362	121	18	)	)	PUNCT
ejpam-3362	121	19	.	.	PUNCT
ejpam-3362	122	1	furthermore	furthermore	ADV
ejpam-3362	122	2	,	,	PUNCT
ejpam-3362	122	3	x	x	PUNCT
ejpam-3362	122	4	∈	∈	PROPN
ejpam-3362	122	5	lh({x	lh({x	NOUN
ejpam-3362	122	6	}	}	PUNCT
ejpam-3362	122	7	)	)	PUNCT
ejpam-3362	123	1	=	=	SYM
ejpam-3362	123	2	{	{	PUNCT
ejpam-3362	123	3	0	0	NUM
ejpam-3362	123	4	}	}	PUNCT
ejpam-3362	123	5	implies	imply	VERB
ejpam-3362	123	6	x	x	PUNCT
ejpam-3362	123	7	=	=	SYM
ejpam-3362	123	8	0	0	PUNCT
ejpam-3362	123	9	and	and	CCONJ
ejpam-3362	123	10	if	if	SCONJ
ejpam-3362	123	11	x	x	X
ejpam-3362	123	12	=	=	SYM
ejpam-3362	123	13	0	0	NUM
ejpam-3362	123	14	,	,	PUNCT
ejpam-3362	123	15	then	then	ADV
ejpam-3362	123	16	lh({x	lh({x	NOUN
ejpam-3362	123	17	}	}	PUNCT
ejpam-3362	123	18	)	)	PUNCT
ejpam-3362	124	1	=	=	SYM
ejpam-3362	124	2	lh({0	lh({0	X
ejpam-3362	124	3	}	}	PUNCT
ejpam-3362	124	4	)	)	PUNCT
ejpam-3362	125	1	=	=	PRON
ejpam-3362	125	2	{	{	PUNCT
ejpam-3362	125	3	0	0	NUM
ejpam-3362	125	4	}	}	PUNCT
ejpam-3362	125	5	by	by	ADP
ejpam-3362	125	6	(	(	PUNCT
ejpam-3362	125	7	ii	ii	NOUN
ejpam-3362	125	8	)	)	PUNCT
ejpam-3362	125	9	.	.	PUNCT
ejpam-3362	126	1	�	�	PROPN
ejpam-3362	126	2	the	the	DET
ejpam-3362	126	3	zero	zero	NUM
ejpam-3362	126	4	divisor	divisor	NOUN
ejpam-3362	126	5	graph	graph	NOUN
ejpam-3362	126	6	of	of	ADP
ejpam-3362	126	7	a	a	DET
ejpam-3362	126	8	hyper	hyper	ADJ
ejpam-3362	126	9	bci	bci	NOUN
ejpam-3362	126	10	-	-	NOUN
ejpam-3362	126	11	algebra	algebra	NOUN
ejpam-3362	126	12	is	be	AUX
ejpam-3362	126	13	not	not	PART
ejpam-3362	126	14	always	always	ADV
ejpam-3362	126	15	connected	connect	VERB
ejpam-3362	126	16	:	:	PUNCT
ejpam-3362	126	17	m.	m.	NOUN
ejpam-3362	126	18	panganduyon	panganduyon	NOUN
ejpam-3362	126	19	,	,	PUNCT
ejpam-3362	126	20	s.	s.	PROPN
ejpam-3362	126	21	canoy	canoy	PROPN
ejpam-3362	126	22	/	/	SYM
ejpam-3362	126	23	eur	eur	PROPN
ejpam-3362	126	24	.	.	PUNCT
ejpam-3362	127	1	j.	j.	PROPN
ejpam-3362	127	2	pure	pure	PROPN
ejpam-3362	127	3	appl	appl	PROPN
ejpam-3362	127	4	.	.	PROPN
ejpam-3362	127	5	math	math	PROPN
ejpam-3362	127	6	,	,	PUNCT
ejpam-3362	127	7	12	12	NUM
ejpam-3362	127	8	(	(	PUNCT
ejpam-3362	127	9	1	1	NUM
ejpam-3362	127	10	)	)	PUNCT
ejpam-3362	127	11	(	(	PUNCT
ejpam-3362	127	12	2019	2019	NUM
ejpam-3362	127	13	)	)	PUNCT
ejpam-3362	127	14	,	,	PUNCT
ejpam-3362	127	15	146	146	NUM
ejpam-3362	127	16	-	-	SYM
ejpam-3362	127	17	158	158	NUM
ejpam-3362	127	18	151	151	NUM
ejpam-3362	127	19	example	example	NOUN
ejpam-3362	127	20	3	3	NUM
ejpam-3362	127	21	.	.	X
ejpam-3362	127	22	consider	consider	VERB
ejpam-3362	127	23	the	the	DET
ejpam-3362	127	24	hyper	hyper	ADJ
ejpam-3362	127	25	bci	bci	NOUN
ejpam-3362	127	26	-	-	ADJ
ejpam-3362	127	27	algebra	algebra	ADJ
ejpam-3362	127	28	h	h	NOUN
ejpam-3362	127	29	with	with	ADP
ejpam-3362	127	30	‘	'	PUNCT
ejpam-3362	127	31	~	~	NOUN
ejpam-3362	127	32	’	'	PUNCT
ejpam-3362	127	33	defined	define	VERB
ejpam-3362	127	34	by	by	ADP
ejpam-3362	127	35	the	the	DET
ejpam-3362	127	36	following	following	ADJ
ejpam-3362	127	37	cayley	cayley	ADJ
ejpam-3362	127	38	table	table	NOUN
ejpam-3362	127	39	:	:	PUNCT
ejpam-3362	127	40	~	~	PUNCT
ejpam-3362	127	41	0	0	NUM
ejpam-3362	128	1	1	1	NUM
ejpam-3362	128	2	2	2	NUM
ejpam-3362	128	3	0	0	NUM
ejpam-3362	128	4	{	{	PUNCT
ejpam-3362	128	5	0	0	NUM
ejpam-3362	128	6	,	,	PUNCT
ejpam-3362	128	7	1	1	NUM
ejpam-3362	128	8	}	}	PUNCT
ejpam-3362	128	9	{	{	PUNCT
ejpam-3362	128	10	0	0	NUM
ejpam-3362	128	11	,	,	PUNCT
ejpam-3362	128	12	1	1	NUM
ejpam-3362	128	13	}	}	PUNCT
ejpam-3362	128	14	{	{	PUNCT
ejpam-3362	128	15	2	2	NUM
ejpam-3362	128	16	}	}	SYM
ejpam-3362	128	17	1	1	NUM
ejpam-3362	128	18	{	{	PUNCT
ejpam-3362	128	19	1	1	NUM
ejpam-3362	128	20	}	}	PUNCT
ejpam-3362	128	21	{	{	PUNCT
ejpam-3362	128	22	0	0	NUM
ejpam-3362	128	23	,	,	PUNCT
ejpam-3362	128	24	1	1	NUM
ejpam-3362	128	25	}	}	PUNCT
ejpam-3362	128	26	{	{	PUNCT
ejpam-3362	128	27	2	2	NUM
ejpam-3362	128	28	}	}	SYM
ejpam-3362	128	29	2	2	NUM
ejpam-3362	128	30	{	{	PUNCT
ejpam-3362	128	31	2	2	NUM
ejpam-3362	128	32	}	}	PUNCT
ejpam-3362	128	33	{	{	PUNCT
ejpam-3362	128	34	2	2	NUM
ejpam-3362	128	35	}	}	PUNCT
ejpam-3362	128	36	{	{	PUNCT
ejpam-3362	128	37	0	0	NUM
ejpam-3362	128	38	,	,	PUNCT
ejpam-3362	128	39	1	1	NUM
ejpam-3362	128	40	}	}	PUNCT
ejpam-3362	128	41	then	then	ADV
ejpam-3362	128	42	lh({0	lh({0	X
ejpam-3362	128	43	,	,	PUNCT
ejpam-3362	128	44	1	1	NUM
ejpam-3362	128	45	}	}	PUNCT
ejpam-3362	128	46	)	)	PUNCT
ejpam-3362	128	47	=	=	PUNCT
ejpam-3362	128	48	{	{	PUNCT
ejpam-3362	128	49	0	0	NUM
ejpam-3362	128	50	}	}	PUNCT
ejpam-3362	128	51	;	;	PUNCT
ejpam-3362	128	52	lh({0	lh({0	PROPN
ejpam-3362	128	53	,	,	PUNCT
ejpam-3362	128	54	2	2	NUM
ejpam-3362	128	55	}	}	PUNCT
ejpam-3362	128	56	)	)	PUNCT
ejpam-3362	129	1	=	=	NOUN
ejpam-3362	129	2	∅	∅	NOUN
ejpam-3362	129	3	=	=	SYM
ejpam-3362	129	4	lh({1	lh({1	NOUN
ejpam-3362	129	5	,	,	PUNCT
ejpam-3362	129	6	2	2	NUM
ejpam-3362	129	7	}	}	PUNCT
ejpam-3362	129	8	)	)	PUNCT
ejpam-3362	129	9	.	.	PUNCT
ejpam-3362	130	1	thus	thus	ADV
ejpam-3362	130	2	,	,	PUNCT
ejpam-3362	130	3	the	the	DET
ejpam-3362	130	4	zero	zero	NUM
ejpam-3362	130	5	divisor	divisor	NOUN
ejpam-3362	130	6	graph	graph	NOUN
ejpam-3362	130	7	γ(h	γ(h	NOUN
ejpam-3362	130	8	)	)	PUNCT
ejpam-3362	130	9	of	of	ADP
ejpam-3362	130	10	h	h	NOUN
ejpam-3362	130	11	is	be	AUX
ejpam-3362	130	12	given	give	VERB
ejpam-3362	130	13	below	below	ADP
ejpam-3362	130	14	:	:	PUNCT
ejpam-3362	130	15	1	1	NUM
ejpam-3362	130	16	2	2	NUM
ejpam-3362	130	17	0	0	NUM
ejpam-3362	130	18	example	example	NOUN
ejpam-3362	130	19	4	4	NUM
ejpam-3362	130	20	.	.	X
ejpam-3362	131	1	consider	consider	VERB
ejpam-3362	131	2	h	h	NOUN
ejpam-3362	131	3	defined	define	VERB
ejpam-3362	131	4	by	by	ADP
ejpam-3362	131	5	the	the	DET
ejpam-3362	131	6	following	following	ADJ
ejpam-3362	131	7	cayley	cayley	ADJ
ejpam-3362	131	8	table	table	NOUN
ejpam-3362	131	9	:	:	PUNCT
ejpam-3362	131	10	~	~	PUNCT
ejpam-3362	131	11	0	0	NUM
ejpam-3362	132	1	1	1	NUM
ejpam-3362	132	2	2	2	NUM
ejpam-3362	132	3	3	3	NUM
ejpam-3362	132	4	0	0	NUM
ejpam-3362	132	5	{	{	PUNCT
ejpam-3362	132	6	0	0	NUM
ejpam-3362	132	7	}	}	PUNCT
ejpam-3362	132	8	{	{	PUNCT
ejpam-3362	132	9	0	0	NUM
ejpam-3362	132	10	}	}	PUNCT
ejpam-3362	132	11	{	{	PUNCT
ejpam-3362	132	12	2	2	NUM
ejpam-3362	132	13	}	}	PUNCT
ejpam-3362	132	14	{	{	PUNCT
ejpam-3362	132	15	2	2	NUM
ejpam-3362	132	16	}	}	SYM
ejpam-3362	132	17	1	1	NUM
ejpam-3362	132	18	{	{	PUNCT
ejpam-3362	132	19	1	1	NUM
ejpam-3362	132	20	}	}	PUNCT
ejpam-3362	132	21	{	{	PUNCT
ejpam-3362	132	22	0	0	NUM
ejpam-3362	132	23	}	}	PUNCT
ejpam-3362	132	24	{	{	PUNCT
ejpam-3362	132	25	2	2	NUM
ejpam-3362	132	26	}	}	PUNCT
ejpam-3362	132	27	{	{	PUNCT
ejpam-3362	132	28	2	2	NUM
ejpam-3362	132	29	}	}	SYM
ejpam-3362	132	30	2	2	NUM
ejpam-3362	132	31	{	{	PUNCT
ejpam-3362	132	32	2	2	NUM
ejpam-3362	132	33	}	}	PUNCT
ejpam-3362	132	34	{	{	PUNCT
ejpam-3362	132	35	2	2	NUM
ejpam-3362	132	36	}	}	PUNCT
ejpam-3362	132	37	{	{	PUNCT
ejpam-3362	132	38	0	0	NUM
ejpam-3362	132	39	}	}	PUNCT
ejpam-3362	132	40	{	{	PUNCT
ejpam-3362	132	41	0	0	NUM
ejpam-3362	132	42	}	}	SYM
ejpam-3362	132	43	3	3	NUM
ejpam-3362	132	44	{	{	PUNCT
ejpam-3362	132	45	3	3	NUM
ejpam-3362	132	46	}	}	PUNCT
ejpam-3362	132	47	{	{	PUNCT
ejpam-3362	132	48	2	2	NUM
ejpam-3362	132	49	}	}	PUNCT
ejpam-3362	132	50	{	{	PUNCT
ejpam-3362	132	51	1	1	NUM
ejpam-3362	132	52	}	}	PUNCT
ejpam-3362	132	53	{	{	PUNCT
ejpam-3362	132	54	0	0	NUM
ejpam-3362	132	55	,	,	PUNCT
ejpam-3362	132	56	1	1	NUM
ejpam-3362	132	57	}	}	PUNCT
ejpam-3362	132	58	then	then	ADV
ejpam-3362	132	59	lh({0	lh({0	X
ejpam-3362	132	60	,	,	PUNCT
ejpam-3362	132	61	1	1	NUM
ejpam-3362	132	62	}	}	PUNCT
ejpam-3362	132	63	)	)	PUNCT
ejpam-3362	133	1	=	=	PUNCT
ejpam-3362	133	2	{	{	PUNCT
ejpam-3362	133	3	0	0	NUM
ejpam-3362	133	4	}	}	PUNCT
ejpam-3362	133	5	,	,	PUNCT
ejpam-3362	133	6	lh({0	lh({0	NOUN
ejpam-3362	133	7	,	,	PUNCT
ejpam-3362	133	8	2	2	NUM
ejpam-3362	133	9	}	}	PUNCT
ejpam-3362	133	10	)	)	PUNCT
ejpam-3362	134	1	=	=	SYM
ejpam-3362	134	2	lh({0	lh({0	PROPN
ejpam-3362	134	3	,	,	PUNCT
ejpam-3362	134	4	3	3	NUM
ejpam-3362	134	5	}	}	PUNCT
ejpam-3362	134	6	)	)	PUNCT
ejpam-3362	135	1	=	=	SYM
ejpam-3362	135	2	lh({1	lh({1	NOUN
ejpam-3362	135	3	,	,	PUNCT
ejpam-3362	135	4	2	2	NUM
ejpam-3362	135	5	}	}	PUNCT
ejpam-3362	135	6	)	)	PUNCT
ejpam-3362	136	1	=	=	SYM
ejpam-3362	136	2	lh({1	lh({1	NOUN
ejpam-3362	136	3	,	,	PUNCT
ejpam-3362	136	4	3	3	NUM
ejpam-3362	136	5	}	}	PUNCT
ejpam-3362	136	6	)	)	PUNCT
ejpam-3362	137	1	=	=	NOUN
ejpam-3362	137	2	∅	∅	NOUN
ejpam-3362	137	3	,	,	PUNCT
ejpam-3362	137	4	and	and	CCONJ
ejpam-3362	137	5	lh({2	lh({2	NOUN
ejpam-3362	137	6	,	,	PUNCT
ejpam-3362	137	7	3	3	NUM
ejpam-3362	137	8	}	}	PUNCT
ejpam-3362	137	9	)	)	PUNCT
ejpam-3362	137	10	=	=	PUNCT
ejpam-3362	137	11	{	{	PUNCT
ejpam-3362	137	12	2	2	NUM
ejpam-3362	137	13	}	}	PUNCT
ejpam-3362	137	14	.	.	PUNCT
ejpam-3362	138	1	the	the	DET
ejpam-3362	138	2	zero	zero	NUM
ejpam-3362	138	3	divisor	divisor	NOUN
ejpam-3362	138	4	graph	graph	NOUN
ejpam-3362	138	5	γ(h	γ(h	NOUN
ejpam-3362	138	6	)	)	PUNCT
ejpam-3362	138	7	of	of	ADP
ejpam-3362	138	8	h	h	NOUN
ejpam-3362	138	9	is	be	AUX
ejpam-3362	138	10	given	give	VERB
ejpam-3362	138	11	below	below	ADP
ejpam-3362	138	12	1	1	NUM
ejpam-3362	138	13	3	3	NUM
ejpam-3362	138	14	0	0	NUM
ejpam-3362	138	15	2	2	NUM
ejpam-3362	138	16	proposition	proposition	NOUN
ejpam-3362	138	17	3	3	NUM
ejpam-3362	138	18	.	.	PUNCT
ejpam-3362	139	1	let	let	VERB
ejpam-3362	139	2	h	h	PRON
ejpam-3362	139	3	be	be	AUX
ejpam-3362	139	4	a	a	DET
ejpam-3362	139	5	hyper	hyper	ADJ
ejpam-3362	139	6	bci	bci	NOUN
ejpam-3362	139	7	-	-	NOUN
ejpam-3362	139	8	algebra	algebra	NOUN
ejpam-3362	139	9	with	with	ADP
ejpam-3362	139	10	|h|	|h|	PROPN
ejpam-3362	139	11	≥	≥	NUM
ejpam-3362	139	12	2	2	NUM
ejpam-3362	139	13	.	.	PUNCT
ejpam-3362	140	1	then	then	ADV
ejpam-3362	140	2	(	(	PUNCT
ejpam-3362	140	3	i	i	NOUN
ejpam-3362	140	4	)	)	PUNCT
ejpam-3362	140	5	degγ(h)(0	degγ(h)(0	ADJ
ejpam-3362	140	6	)	)	PUNCT
ejpam-3362	140	7	=	=	SYM
ejpam-3362	141	1	|{x	|{x	PUNCT
ejpam-3362	141	2	∈	∈	PROPN
ejpam-3362	141	3	h	h	NOUN
ejpam-3362	141	4	\	\	PUNCT
ejpam-3362	141	5	{	{	PUNCT
ejpam-3362	141	6	0	0	NUM
ejpam-3362	141	7	}	}	PUNCT
ejpam-3362	141	8	:	:	PUNCT
ejpam-3362	141	9	0	0	NUM
ejpam-3362	141	10	∈	∈	NOUN
ejpam-3362	141	11	lh(x)}|	lh(x)}|	NOUN
ejpam-3362	141	12	=	=	SYM
ejpam-3362	141	13	∆(γ(h	∆(γ(h	NOUN
ejpam-3362	141	14	)	)	PUNCT
ejpam-3362	141	15	)	)	PUNCT
ejpam-3362	141	16	;	;	PUNCT
ejpam-3362	141	17	(	(	PUNCT
ejpam-3362	141	18	ii	ii	NOUN
ejpam-3362	141	19	)	)	PUNCT
ejpam-3362	141	20	γ(h	γ(h	NOUN
ejpam-3362	141	21	)	)	PUNCT
ejpam-3362	141	22	=	=	PUNCT
ejpam-3362	142	1	k	k	PROPN
ejpam-3362	142	2	|h|	|h|	PROPN
ejpam-3362	142	3	if	if	SCONJ
ejpam-3362	143	1	and	and	CCONJ
ejpam-3362	143	2	only	only	ADV
ejpam-3362	143	3	if	if	SCONJ
ejpam-3362	143	4	0	0	NUM
ejpam-3362	143	5	/∈	/∈	INTJ
ejpam-3362	143	6	lh(x	lh(x	NOUN
ejpam-3362	143	7	)	)	PUNCT
ejpam-3362	143	8	for	for	ADP
ejpam-3362	143	9	all	all	DET
ejpam-3362	143	10	x	x	SYM
ejpam-3362	143	11	∈	∈	PROPN
ejpam-3362	143	12	h	h	NOUN
ejpam-3362	143	13	\	\	PUNCT
ejpam-3362	143	14	{	{	PUNCT
ejpam-3362	143	15	0	0	NUM
ejpam-3362	143	16	}	}	PUNCT
ejpam-3362	143	17	;	;	PUNCT
ejpam-3362	143	18	and	and	CCONJ
ejpam-3362	143	19	(	(	PUNCT
ejpam-3362	143	20	iii	iii	X
ejpam-3362	143	21	)	)	PUNCT
ejpam-3362	143	22	if	if	SCONJ
ejpam-3362	143	23	γ(h	γ(h	NOUN
ejpam-3362	143	24	)	)	PUNCT
ejpam-3362	143	25	6=	6=	PUNCT
ejpam-3362	144	1	k	k	PROPN
ejpam-3362	144	2	|h|	|h|	PROPN
ejpam-3362	144	3	,	,	PUNCT
ejpam-3362	144	4	then	then	ADV
ejpam-3362	144	5	i(γ(h	i(γ(h	NUM
ejpam-3362	144	6	)	)	PUNCT
ejpam-3362	144	7	)	)	PUNCT
ejpam-3362	145	1	=	=	PRON
ejpam-3362	145	2	{	{	PUNCT
ejpam-3362	145	3	x	x	PUNCT
ejpam-3362	145	4	∈	∈	PROPN
ejpam-3362	145	5	h	h	NOUN
ejpam-3362	145	6	\	\	PUNCT
ejpam-3362	145	7	{	{	PUNCT
ejpam-3362	145	8	0	0	NUM
ejpam-3362	145	9	}	}	PUNCT
ejpam-3362	145	10	:	:	PUNCT
ejpam-3362	145	11	0	0	NUM
ejpam-3362	145	12	/∈	/∈	INTJ
ejpam-3362	145	13	lh(x	lh(x	NOUN
ejpam-3362	145	14	)	)	PUNCT
ejpam-3362	145	15	}	}	PUNCT
ejpam-3362	145	16	.	.	PUNCT
ejpam-3362	146	1	proof	proof	NOUN
ejpam-3362	146	2	.	.	PUNCT
ejpam-3362	147	1	m.	m.	NOUN
ejpam-3362	147	2	panganduyon	panganduyon	NOUN
ejpam-3362	147	3	,	,	PUNCT
ejpam-3362	147	4	s.	s.	PROPN
ejpam-3362	147	5	canoy	canoy	PROPN
ejpam-3362	147	6	/	/	SYM
ejpam-3362	147	7	eur	eur	PROPN
ejpam-3362	147	8	.	.	PUNCT
ejpam-3362	148	1	j.	j.	PROPN
ejpam-3362	148	2	pure	pure	PROPN
ejpam-3362	148	3	appl	appl	PROPN
ejpam-3362	148	4	.	.	PROPN
ejpam-3362	148	5	math	math	PROPN
ejpam-3362	148	6	,	,	PUNCT
ejpam-3362	148	7	12	12	NUM
ejpam-3362	148	8	(	(	PUNCT
ejpam-3362	148	9	1	1	NUM
ejpam-3362	148	10	)	)	PUNCT
ejpam-3362	148	11	(	(	PUNCT
ejpam-3362	148	12	2019	2019	NUM
ejpam-3362	148	13	)	)	PUNCT
ejpam-3362	148	14	,	,	PUNCT
ejpam-3362	148	15	146	146	NUM
ejpam-3362	148	16	-	-	SYM
ejpam-3362	148	17	158	158	NUM
ejpam-3362	148	18	152	152	NUM
ejpam-3362	148	19	(	(	PUNCT
ejpam-3362	148	20	i	i	NOUN
ejpam-3362	148	21	)	)	PUNCT
ejpam-3362	148	22	note	note	VERB
ejpam-3362	148	23	that	that	SCONJ
ejpam-3362	148	24	for	for	ADP
ejpam-3362	148	25	any	any	DET
ejpam-3362	148	26	x	x	SYM
ejpam-3362	148	27	∈	∈	PROPN
ejpam-3362	148	28	h	h	NOUN
ejpam-3362	148	29	\{0	\{0	NOUN
ejpam-3362	148	30	}	}	PUNCT
ejpam-3362	148	31	,	,	PUNCT
ejpam-3362	148	32	0x	0x	PROPN
ejpam-3362	148	33	∈	∈	PROPN
ejpam-3362	148	34	e(γ(h	e(γ(h	PROPN
ejpam-3362	148	35	)	)	PUNCT
ejpam-3362	148	36	)	)	PUNCT
ejpam-3362	149	1	if	if	SCONJ
ejpam-3362	149	2	and	and	CCONJ
ejpam-3362	149	3	only	only	ADV
ejpam-3362	149	4	if	if	SCONJ
ejpam-3362	149	5	lh({0	lh({0	PROPN
ejpam-3362	149	6	,	,	PUNCT
ejpam-3362	149	7	x	x	NOUN
ejpam-3362	149	8	}	}	PUNCT
ejpam-3362	149	9	)	)	PUNCT
ejpam-3362	149	10	=	=	PUNCT
ejpam-3362	149	11	{	{	PUNCT
ejpam-3362	149	12	0	0	NUM
ejpam-3362	149	13	}	}	PUNCT
ejpam-3362	149	14	.	.	PUNCT
ejpam-3362	150	1	hence	hence	ADV
ejpam-3362	150	2	,	,	PUNCT
ejpam-3362	150	3	by	by	ADP
ejpam-3362	150	4	proposition	proposition	NOUN
ejpam-3362	150	5	2(ii	2(ii	NUM
ejpam-3362	150	6	)	)	PUNCT
ejpam-3362	150	7	,	,	PUNCT
ejpam-3362	150	8	0x	0x	PROPN
ejpam-3362	150	9	∈	∈	PROPN
ejpam-3362	150	10	e(γ(h	e(γ(h	PROPN
ejpam-3362	150	11	)	)	PUNCT
ejpam-3362	150	12	)	)	PUNCT
ejpam-3362	151	1	if	if	SCONJ
ejpam-3362	151	2	and	and	CCONJ
ejpam-3362	151	3	only	only	ADV
ejpam-3362	151	4	if	if	SCONJ
ejpam-3362	151	5	0	0	NUM
ejpam-3362	151	6	∈	∈	PROPN
ejpam-3362	151	7	lh(x	lh(x	NOUN
ejpam-3362	151	8	)	)	PUNCT
ejpam-3362	151	9	.	.	PUNCT
ejpam-3362	152	1	thus	thus	ADV
ejpam-3362	152	2	,	,	PUNCT
ejpam-3362	152	3	degγ(h	degγ(h	NOUN
ejpam-3362	152	4	)	)	PUNCT
ejpam-3362	152	5	0	0	NUM
ejpam-3362	153	1	=	=	SYM
ejpam-3362	153	2	|{x	|{x	PUNCT
ejpam-3362	153	3	∈	∈	PROPN
ejpam-3362	153	4	h	h	NOUN
ejpam-3362	153	5	\	\	PUNCT
ejpam-3362	153	6	{	{	PUNCT
ejpam-3362	153	7	0	0	NUM
ejpam-3362	153	8	}	}	PUNCT
ejpam-3362	153	9	:	:	PUNCT
ejpam-3362	153	10	0x	0x	NOUN
ejpam-3362	153	11	∈	∈	PROPN
ejpam-3362	153	12	e(γ(h))}|	e(γ(h))}|	PROPN
ejpam-3362	153	13	=	=	SYM
ejpam-3362	153	14	|{x	|{x	PUNCT
ejpam-3362	153	15	∈	∈	PROPN
ejpam-3362	153	16	h	h	NOUN
ejpam-3362	153	17	\	\	PUNCT
ejpam-3362	153	18	{	{	PUNCT
ejpam-3362	153	19	0	0	NUM
ejpam-3362	153	20	}	}	PUNCT
ejpam-3362	153	21	:	:	PUNCT
ejpam-3362	153	22	0	0	NUM
ejpam-3362	153	23	∈	∈	NOUN
ejpam-3362	153	24	lh(x)}|	lh(x)}|	NOUN
ejpam-3362	153	25	.	.	PUNCT
ejpam-3362	154	1	let	let	VERB
ejpam-3362	154	2	x	x	SYM
ejpam-3362	154	3	∈	∈	PROPN
ejpam-3362	154	4	h	h	NOUN
ejpam-3362	154	5	\	\	PUNCT
ejpam-3362	154	6	{	{	PUNCT
ejpam-3362	154	7	0	0	NUM
ejpam-3362	154	8	}	}	PUNCT
ejpam-3362	154	9	and	and	CCONJ
ejpam-3362	154	10	let	let	VERB
ejpam-3362	154	11	y	y	PROPN
ejpam-3362	154	12	∈	∈	PROPN
ejpam-3362	154	13	nγ(h)(x	nγ(h)(x	NUM
ejpam-3362	154	14	)	)	PUNCT
ejpam-3362	154	15	.	.	PUNCT
ejpam-3362	155	1	then	then	ADV
ejpam-3362	155	2	lh({x	lh({x	NOUN
ejpam-3362	155	3	,	,	PUNCT
ejpam-3362	155	4	y	y	NOUN
ejpam-3362	155	5	}	}	PUNCT
ejpam-3362	155	6	)	)	PUNCT
ejpam-3362	156	1	=	=	PUNCT
ejpam-3362	156	2	{	{	PUNCT
ejpam-3362	156	3	0	0	NUM
ejpam-3362	156	4	}	}	PUNCT
ejpam-3362	156	5	.	.	PUNCT
ejpam-3362	157	1	by	by	ADP
ejpam-3362	157	2	proposition	proposition	NOUN
ejpam-3362	157	3	2(ii	2(ii	NUM
ejpam-3362	157	4	)	)	PUNCT
ejpam-3362	157	5	and	and	CCONJ
ejpam-3362	157	6	2(iv	2(iv	NUM
ejpam-3362	157	7	)	)	PUNCT
ejpam-3362	157	8	,	,	PUNCT
ejpam-3362	157	9	it	it	PRON
ejpam-3362	157	10	follows	follow	VERB
ejpam-3362	157	11	that	that	SCONJ
ejpam-3362	157	12	lh(0	lh(0	NOUN
ejpam-3362	157	13	,	,	PUNCT
ejpam-3362	157	14	y	y	NOUN
ejpam-3362	157	15	)	)	PUNCT
ejpam-3362	157	16	=	=	PUNCT
ejpam-3362	157	17	{	{	PUNCT
ejpam-3362	157	18	0	0	NUM
ejpam-3362	157	19	}	}	PUNCT
ejpam-3362	157	20	,	,	PUNCT
ejpam-3362	157	21	that	that	ADV
ejpam-3362	157	22	is	is	ADV
ejpam-3362	157	23	,	,	PUNCT
ejpam-3362	157	24	y	y	PROPN
ejpam-3362	157	25	∈	∈	PROPN
ejpam-3362	157	26	nγ(h)(0	nγ(h)(0	PROPN
ejpam-3362	157	27	)	)	PUNCT
ejpam-3362	157	28	.	.	PUNCT
ejpam-3362	158	1	thus	thus	ADV
ejpam-3362	158	2	,	,	PUNCT
ejpam-3362	158	3	degγ(h)(x	degγ(h)(x	NOUN
ejpam-3362	158	4	)	)	PUNCT
ejpam-3362	158	5	=	=	NOUN
ejpam-3362	158	6	|nγ(h)(x)|	|nγ(h)(x)|	ADP
ejpam-3362	158	7	≤	≤	NUM
ejpam-3362	158	8	|nγ(h)(0)|	|nγ(h)(0)|	NOUN
ejpam-3362	158	9	=	=	SYM
ejpam-3362	158	10	degγ(h)(0	degγ(h)(0	PROPN
ejpam-3362	158	11	)	)	PUNCT
ejpam-3362	158	12	.	.	PUNCT
ejpam-3362	159	1	since	since	SCONJ
ejpam-3362	159	2	x	x	PRON
ejpam-3362	159	3	was	be	AUX
ejpam-3362	159	4	arbitrarily	arbitrarily	ADV
ejpam-3362	159	5	chosen	choose	VERB
ejpam-3362	159	6	,	,	PUNCT
ejpam-3362	159	7	it	it	PRON
ejpam-3362	159	8	follows	follow	VERB
ejpam-3362	159	9	that	that	SCONJ
ejpam-3362	159	10	∆(γ(h))|	∆(γ(h))|	NOUN
ejpam-3362	159	11	=	=	SYM
ejpam-3362	159	12	degγ(h)(0	degγ(h)(0	NOUN
ejpam-3362	159	13	)	)	PUNCT
ejpam-3362	159	14	.	.	PUNCT
ejpam-3362	160	1	(	(	PUNCT
ejpam-3362	160	2	ii	ii	NOUN
ejpam-3362	160	3	)	)	PUNCT
ejpam-3362	160	4	suppose	suppose	VERB
ejpam-3362	160	5	that	that	SCONJ
ejpam-3362	160	6	γ(h	γ(h	NOUN
ejpam-3362	160	7	)	)	PUNCT
ejpam-3362	160	8	=	=	PUNCT
ejpam-3362	161	1	k	k	PROPN
ejpam-3362	161	2	|h|	|h|	PROPN
ejpam-3362	161	3	.	.	PUNCT
ejpam-3362	162	1	that	that	PRON
ejpam-3362	162	2	is	is	ADV
ejpam-3362	162	3	,	,	PUNCT
ejpam-3362	162	4	i(γ(h	i(γ(h	NUM
ejpam-3362	162	5	)	)	PUNCT
ejpam-3362	162	6	)	)	PUNCT
ejpam-3362	163	1	=	=	SYM
ejpam-3362	163	2	v	v	X
ejpam-3362	163	3	(	(	PUNCT
ejpam-3362	163	4	γ(h	γ(h	NOUN
ejpam-3362	163	5	)	)	PUNCT
ejpam-3362	163	6	)	)	PUNCT
ejpam-3362	163	7	.	.	PUNCT
ejpam-3362	164	1	this	this	PRON
ejpam-3362	164	2	implies	imply	VERB
ejpam-3362	164	3	that	that	SCONJ
ejpam-3362	164	4	degγ(h	degγ(h	NOUN
ejpam-3362	164	5	)	)	PUNCT
ejpam-3362	164	6	0	0	NUM
ejpam-3362	165	1	=	=	SYM
ejpam-3362	165	2	0	0	X
ejpam-3362	165	3	.	.	PUNCT
ejpam-3362	166	1	hence	hence	ADV
ejpam-3362	166	2	,	,	PUNCT
ejpam-3362	166	3	0x	0x	PROPN
ejpam-3362	166	4	/∈	/∈	PUNCT
ejpam-3362	166	5	e(γ(h	e(γ(h	NOUN
ejpam-3362	166	6	)	)	PUNCT
ejpam-3362	166	7	)	)	PUNCT
ejpam-3362	166	8	for	for	ADP
ejpam-3362	166	9	all	all	DET
ejpam-3362	166	10	x	x	SYM
ejpam-3362	166	11	∈	∈	PROPN
ejpam-3362	166	12	h.	h.	PROPN
ejpam-3362	166	13	thus	thus	ADV
ejpam-3362	166	14	,	,	PUNCT
ejpam-3362	166	15	0	0	NUM
ejpam-3362	166	16	/∈	/∈	INTJ
ejpam-3362	166	17	lh(x	lh(x	NOUN
ejpam-3362	166	18	)	)	PUNCT
ejpam-3362	166	19	for	for	ADP
ejpam-3362	166	20	all	all	DET
ejpam-3362	166	21	x	x	SYM
ejpam-3362	166	22	∈	∈	PROPN
ejpam-3362	166	23	h	h	NOUN
ejpam-3362	166	24	\	\	PUNCT
ejpam-3362	166	25	{	{	PUNCT
ejpam-3362	166	26	0	0	NUM
ejpam-3362	166	27	}	}	PUNCT
ejpam-3362	166	28	.	.	PUNCT
ejpam-3362	167	1	for	for	ADP
ejpam-3362	167	2	the	the	DET
ejpam-3362	167	3	converse	converse	NOUN
ejpam-3362	167	4	,	,	PUNCT
ejpam-3362	167	5	suppose	suppose	VERB
ejpam-3362	167	6	that	that	SCONJ
ejpam-3362	167	7	0	0	NUM
ejpam-3362	167	8	/∈	/∈	INTJ
ejpam-3362	167	9	lh(x	lh(x	NOUN
ejpam-3362	167	10	)	)	PUNCT
ejpam-3362	167	11	for	for	ADP
ejpam-3362	167	12	all	all	DET
ejpam-3362	167	13	x	x	SYM
ejpam-3362	167	14	∈	∈	PROPN
ejpam-3362	167	15	h	h	NOUN
ejpam-3362	167	16	\	\	PUNCT
ejpam-3362	167	17	{	{	PUNCT
ejpam-3362	167	18	0	0	NUM
ejpam-3362	167	19	}	}	PUNCT
ejpam-3362	167	20	.	.	PUNCT
ejpam-3362	168	1	by	by	ADP
ejpam-3362	168	2	(	(	PUNCT
ejpam-3362	168	3	i	i	NOUN
ejpam-3362	168	4	)	)	PUNCT
ejpam-3362	168	5	,	,	PUNCT
ejpam-3362	168	6	it	it	PRON
ejpam-3362	168	7	follows	follow	VERB
ejpam-3362	168	8	that	that	SCONJ
ejpam-3362	168	9	degγ(h	degγ(h	NOUN
ejpam-3362	168	10	)	)	PUNCT
ejpam-3362	168	11	0	0	NUM
ejpam-3362	169	1	=	=	SYM
ejpam-3362	169	2	∆(γ(h	∆(γ(h	NOUN
ejpam-3362	169	3	)	)	PUNCT
ejpam-3362	169	4	)	)	PUNCT
ejpam-3362	170	1	=	=	SYM
ejpam-3362	170	2	0	0	X
ejpam-3362	170	3	.	.	PUNCT
ejpam-3362	171	1	therefore	therefore	ADV
ejpam-3362	171	2	,	,	PUNCT
ejpam-3362	171	3	γ(h	γ(h	NOUN
ejpam-3362	171	4	)	)	PUNCT
ejpam-3362	171	5	=	=	PUNCT
ejpam-3362	172	1	k	k	PROPN
ejpam-3362	172	2	|h|	|h|	PROPN
ejpam-3362	172	3	.	.	PUNCT
ejpam-3362	173	1	(	(	PUNCT
ejpam-3362	173	2	iii	iii	X
ejpam-3362	173	3	)	)	PUNCT
ejpam-3362	173	4	suppose	suppose	VERB
ejpam-3362	173	5	that	that	SCONJ
ejpam-3362	173	6	γ(h	γ(h	NOUN
ejpam-3362	173	7	)	)	PUNCT
ejpam-3362	173	8	6=	6=	PUNCT
ejpam-3362	174	1	k	k	PROPN
ejpam-3362	174	2	|h|	|h|	PROPN
ejpam-3362	174	3	.	.	PUNCT
ejpam-3362	175	1	then	then	ADV
ejpam-3362	175	2	degγ(h	degγ(h	NOUN
ejpam-3362	175	3	)	)	PUNCT
ejpam-3362	175	4	0	0	NUM
ejpam-3362	176	1	=	=	SYM
ejpam-3362	176	2	∆(γ(h	∆(γ(h	NOUN
ejpam-3362	176	3	)	)	PUNCT
ejpam-3362	176	4	)	)	PUNCT
ejpam-3362	177	1	6=	6=	ADP
ejpam-3362	177	2	0	0	NUM
ejpam-3362	177	3	,	,	PUNCT
ejpam-3362	177	4	i.e.	i.e.	X
ejpam-3362	177	5	,	,	PUNCT
ejpam-3362	177	6	0	0	NUM
ejpam-3362	177	7	/∈	/∈	PUNCT
ejpam-3362	177	8	i(γ(h	i(γ(h	NUM
ejpam-3362	177	9	)	)	PUNCT
ejpam-3362	177	10	)	)	PUNCT
ejpam-3362	177	11	.	.	PUNCT
ejpam-3362	178	1	let	let	VERB
ejpam-3362	178	2	x	x	SYM
ejpam-3362	178	3	∈	∈	PROPN
ejpam-3362	178	4	h	h	NOUN
ejpam-3362	178	5	\	\	PUNCT
ejpam-3362	178	6	{	{	PUNCT
ejpam-3362	178	7	0	0	NUM
ejpam-3362	178	8	}	}	PUNCT
ejpam-3362	178	9	.	.	PUNCT
ejpam-3362	179	1	if	if	SCONJ
ejpam-3362	179	2	0	0	NUM
ejpam-3362	179	3	/∈	/∈	INTJ
ejpam-3362	179	4	lh(x	lh(x	NOUN
ejpam-3362	179	5	)	)	PUNCT
ejpam-3362	179	6	,	,	PUNCT
ejpam-3362	179	7	then	then	ADV
ejpam-3362	179	8	lh(x	lh(x	PROPN
ejpam-3362	179	9	,	,	PUNCT
ejpam-3362	179	10	y	y	PROPN
ejpam-3362	179	11	)	)	PUNCT
ejpam-3362	179	12	6=	6=	ADP
ejpam-3362	179	13	{	{	PUNCT
ejpam-3362	179	14	0	0	NUM
ejpam-3362	179	15	}	}	PUNCT
ejpam-3362	179	16	for	for	ADP
ejpam-3362	179	17	all	all	DET
ejpam-3362	179	18	y	y	PROPN
ejpam-3362	179	19	∈	∈	PROPN
ejpam-3362	179	20	h	h	NOUN
ejpam-3362	179	21	\	\	PUNCT
ejpam-3362	179	22	{	{	PUNCT
ejpam-3362	179	23	x	x	NOUN
ejpam-3362	179	24	}	}	PUNCT
ejpam-3362	179	25	.	.	PUNCT
ejpam-3362	180	1	thus	thus	ADV
ejpam-3362	180	2	,	,	PUNCT
ejpam-3362	180	3	degγ(h)(x	degγ(h)(x	NOUN
ejpam-3362	180	4	)	)	PUNCT
ejpam-3362	180	5	=	=	SYM
ejpam-3362	180	6	0	0	NUM
ejpam-3362	180	7	,	,	PUNCT
ejpam-3362	180	8	i.e.	i.e.	X
ejpam-3362	180	9	,	,	PUNCT
ejpam-3362	180	10	x	x	PROPN
ejpam-3362	180	11	∈	∈	PROPN
ejpam-3362	180	12	i(γ(h	i(γ(h	NUM
ejpam-3362	180	13	)	)	PUNCT
ejpam-3362	180	14	)	)	PUNCT
ejpam-3362	180	15	.	.	PUNCT
ejpam-3362	181	1	conversely	conversely	ADV
ejpam-3362	181	2	,	,	PUNCT
ejpam-3362	181	3	if	if	SCONJ
ejpam-3362	181	4	x	x	PROPN
ejpam-3362	181	5	∈	∈	PROPN
ejpam-3362	181	6	i(γ(h	i(γ(h	NUM
ejpam-3362	181	7	)	)	PUNCT
ejpam-3362	181	8	)	)	PUNCT
ejpam-3362	181	9	,	,	PUNCT
ejpam-3362	181	10	then	then	ADV
ejpam-3362	181	11	0x	0x	NUM
ejpam-3362	181	12	/∈	/∈	PUNCT
ejpam-3362	181	13	e(γ(h	e(γ(h	NOUN
ejpam-3362	181	14	)	)	PUNCT
ejpam-3362	181	15	)	)	PUNCT
ejpam-3362	181	16	,	,	PUNCT
ejpam-3362	181	17	i.e.	i.e.	X
ejpam-3362	181	18	,	,	PUNCT
ejpam-3362	181	19	lh(0	lh(0	NOUN
ejpam-3362	181	20	,	,	PUNCT
ejpam-3362	181	21	x	x	X
ejpam-3362	181	22	)	)	PUNCT
ejpam-3362	181	23	6=	6=	PUNCT
ejpam-3362	181	24	{	{	PUNCT
ejpam-3362	181	25	0	0	NUM
ejpam-3362	181	26	}	}	PUNCT
ejpam-3362	181	27	.	.	PUNCT
ejpam-3362	182	1	by	by	ADP
ejpam-3362	182	2	proposition	proposition	NOUN
ejpam-3362	182	3	2(ii	2(ii	NUM
ejpam-3362	182	4	)	)	PUNCT
ejpam-3362	182	5	and	and	CCONJ
ejpam-3362	182	6	2(iv	2(iv	NUM
ejpam-3362	182	7	)	)	PUNCT
ejpam-3362	182	8	,	,	PUNCT
ejpam-3362	182	9	0	0	NUM
ejpam-3362	182	10	/∈	/∈	INTJ
ejpam-3362	182	11	lh(x	lh(x	NOUN
ejpam-3362	182	12	)	)	PUNCT
ejpam-3362	182	13	.	.	PUNCT
ejpam-3362	183	1	therefore	therefore	ADV
ejpam-3362	183	2	,	,	PUNCT
ejpam-3362	183	3	i(γ(h	i(γ(h	NUM
ejpam-3362	183	4	)	)	PUNCT
ejpam-3362	183	5	)	)	PUNCT
ejpam-3362	184	1	=	=	PRON
ejpam-3362	184	2	{	{	PUNCT
ejpam-3362	184	3	x	x	PUNCT
ejpam-3362	184	4	∈	∈	PROPN
ejpam-3362	184	5	h	h	NOUN
ejpam-3362	184	6	\	\	PUNCT
ejpam-3362	184	7	{	{	PUNCT
ejpam-3362	184	8	0	0	NUM
ejpam-3362	184	9	}	}	PUNCT
ejpam-3362	184	10	:	:	PUNCT
ejpam-3362	184	11	0	0	NUM
ejpam-3362	184	12	/∈	/∈	INTJ
ejpam-3362	184	13	lh(x	lh(x	NOUN
ejpam-3362	184	14	)	)	PUNCT
ejpam-3362	184	15	}	}	PUNCT
ejpam-3362	184	16	.	.	PUNCT
ejpam-3362	185	1	�	�	PROPN
ejpam-3362	185	2	next	next	ADV
ejpam-3362	185	3	,	,	PUNCT
ejpam-3362	185	4	we	we	PRON
ejpam-3362	185	5	give	give	VERB
ejpam-3362	185	6	equivalent	equivalent	ADJ
ejpam-3362	185	7	statements	statement	NOUN
ejpam-3362	185	8	for	for	ADP
ejpam-3362	185	9	connectedness	connectedness	NOUN
ejpam-3362	185	10	of	of	ADP
ejpam-3362	185	11	the	the	DET
ejpam-3362	185	12	zero	zero	NUM
ejpam-3362	185	13	divisor	divisor	NOUN
ejpam-3362	185	14	graph	graph	NOUN
ejpam-3362	185	15	.	.	PUNCT
ejpam-3362	186	1	proposition	proposition	NOUN
ejpam-3362	186	2	4	4	NUM
ejpam-3362	186	3	.	.	PUNCT
ejpam-3362	187	1	let	let	VERB
ejpam-3362	187	2	h	h	PRON
ejpam-3362	187	3	be	be	AUX
ejpam-3362	187	4	a	a	DET
ejpam-3362	187	5	hyper	hyper	ADJ
ejpam-3362	187	6	bci	bci	NOUN
ejpam-3362	187	7	-	-	NOUN
ejpam-3362	187	8	algebra	algebra	NOUN
ejpam-3362	187	9	with	with	ADP
ejpam-3362	187	10	|h|	|h|	PROPN
ejpam-3362	187	11	≥	≥	NUM
ejpam-3362	187	12	2	2	NUM
ejpam-3362	187	13	.	.	PUNCT
ejpam-3362	188	1	then	then	ADV
ejpam-3362	188	2	the	the	DET
ejpam-3362	188	3	following	following	NOUN
ejpam-3362	188	4	are	be	AUX
ejpam-3362	188	5	equivalent	equivalent	ADJ
ejpam-3362	188	6	:	:	PUNCT
ejpam-3362	188	7	(	(	PUNCT
ejpam-3362	188	8	i	i	NOUN
ejpam-3362	188	9	)	)	PUNCT
ejpam-3362	188	10	γ(h	γ(h	NOUN
ejpam-3362	188	11	)	)	PUNCT
ejpam-3362	188	12	is	be	AUX
ejpam-3362	188	13	connected	connect	VERB
ejpam-3362	188	14	.	.	PUNCT
ejpam-3362	189	1	(	(	PUNCT
ejpam-3362	189	2	ii	ii	NOUN
ejpam-3362	189	3	)	)	PUNCT
ejpam-3362	189	4	lh({x	lh({x	NOUN
ejpam-3362	189	5	,	,	PUNCT
ejpam-3362	189	6	0	0	NUM
ejpam-3362	189	7	}	}	PUNCT
ejpam-3362	189	8	)	)	PUNCT
ejpam-3362	190	1	=	=	PRON
ejpam-3362	190	2	{	{	PUNCT
ejpam-3362	190	3	0	0	NUM
ejpam-3362	190	4	}	}	PUNCT
ejpam-3362	190	5	for	for	ADP
ejpam-3362	190	6	all	all	DET
ejpam-3362	190	7	x	x	SYM
ejpam-3362	190	8	∈	∈	PROPN
ejpam-3362	190	9	h	h	NOUN
ejpam-3362	190	10	\	\	PUNCT
ejpam-3362	190	11	{	{	PUNCT
ejpam-3362	190	12	0	0	NUM
ejpam-3362	190	13	}	}	PUNCT
ejpam-3362	190	14	.	.	PUNCT
ejpam-3362	191	1	(	(	PUNCT
ejpam-3362	191	2	iii	iii	NOUN
ejpam-3362	191	3	)	)	PUNCT
ejpam-3362	191	4	0	0	NUM
ejpam-3362	191	5	∈	∈	PROPN
ejpam-3362	191	6	lh(x	lh(x	NOUN
ejpam-3362	191	7	)	)	PUNCT
ejpam-3362	191	8	for	for	ADP
ejpam-3362	191	9	all	all	DET
ejpam-3362	191	10	x	x	SYM
ejpam-3362	191	11	∈	∈	PROPN
ejpam-3362	191	12	h	h	NOUN
ejpam-3362	191	13	\	\	PUNCT
ejpam-3362	191	14	{	{	PUNCT
ejpam-3362	191	15	0	0	NUM
ejpam-3362	191	16	}	}	PUNCT
ejpam-3362	191	17	.	.	PUNCT
ejpam-3362	192	1	(	(	PUNCT
ejpam-3362	192	2	iv	iv	X
ejpam-3362	192	3	)	)	PUNCT
ejpam-3362	192	4	∆(γ(h	∆(γ(h	NOUN
ejpam-3362	192	5	)	)	PUNCT
ejpam-3362	192	6	)	)	PUNCT
ejpam-3362	193	1	=	=	SYM
ejpam-3362	193	2	|h|	|h|	PROPN
ejpam-3362	193	3	−	−	NUM
ejpam-3362	193	4	1	1	NUM
ejpam-3362	193	5	(	(	PUNCT
ejpam-3362	193	6	v	v	NOUN
ejpam-3362	193	7	)	)	PUNCT
ejpam-3362	193	8	i(γ(h	i(γ(h	NUM
ejpam-3362	193	9	)	)	PUNCT
ejpam-3362	193	10	)	)	PUNCT
ejpam-3362	194	1	=	=	NOUN
ejpam-3362	194	2	∅	∅	NOUN
ejpam-3362	194	3	proof	proof	NOUN
ejpam-3362	194	4	.	.	PUNCT
ejpam-3362	195	1	(	(	PUNCT
ejpam-3362	195	2	i)⇔(ii	i)⇔(ii	NOUN
ejpam-3362	195	3	)	)	PUNCT
ejpam-3362	195	4	suppose	suppose	VERB
ejpam-3362	195	5	lh({x	lh({x	NOUN
ejpam-3362	195	6	,	,	PUNCT
ejpam-3362	195	7	0	0	NUM
ejpam-3362	195	8	}	}	PUNCT
ejpam-3362	195	9	)	)	PUNCT
ejpam-3362	195	10	6=	6=	ADP
ejpam-3362	195	11	{	{	PUNCT
ejpam-3362	195	12	0	0	NUM
ejpam-3362	195	13	}	}	PUNCT
ejpam-3362	195	14	for	for	ADP
ejpam-3362	195	15	some	some	DET
ejpam-3362	195	16	x	x	SYM
ejpam-3362	195	17	∈	∈	PROPN
ejpam-3362	195	18	h.	h.	NOUN
ejpam-3362	195	19	then	then	ADV
ejpam-3362	195	20	0	0	NUM
ejpam-3362	195	21	/∈	/∈	INTJ
ejpam-3362	195	22	lh(x	lh(x	PROPN
ejpam-3362	195	23	)	)	PUNCT
ejpam-3362	195	24	,	,	PUNCT
ejpam-3362	195	25	by	by	ADP
ejpam-3362	195	26	proposition	proposition	NOUN
ejpam-3362	195	27	2(ii	2(ii	NUM
ejpam-3362	195	28	)	)	PUNCT
ejpam-3362	195	29	and	and	CCONJ
ejpam-3362	195	30	2(iv	2(iv	NUM
ejpam-3362	195	31	)	)	PUNCT
ejpam-3362	195	32	.	.	PUNCT
ejpam-3362	196	1	thus	thus	ADV
ejpam-3362	196	2	,	,	PUNCT
ejpam-3362	196	3	0	0	NUM
ejpam-3362	196	4	/∈	/∈	SYM
ejpam-3362	197	1	lh({x	lh({x	NOUN
ejpam-3362	197	2	,	,	PUNCT
ejpam-3362	197	3	y	y	NOUN
ejpam-3362	197	4	}	}	PUNCT
ejpam-3362	197	5	)	)	PUNCT
ejpam-3362	198	1	=	=	SYM
ejpam-3362	198	2	lh({x	lh({x	NOUN
ejpam-3362	198	3	}	}	PUNCT
ejpam-3362	198	4	)	)	PUNCT
ejpam-3362	198	5	∩	∩	NOUN
ejpam-3362	198	6	lh({y	lh({y	NOUN
ejpam-3362	198	7	}	}	PUNCT
ejpam-3362	198	8	)	)	PUNCT
ejpam-3362	198	9	for	for	ADP
ejpam-3362	198	10	all	all	DET
ejpam-3362	198	11	y	y	PROPN
ejpam-3362	198	12	∈	∈	PROPN
ejpam-3362	198	13	h.	h.	NOUN
ejpam-3362	198	14	that	that	PRON
ejpam-3362	198	15	is	be	AUX
ejpam-3362	198	16	,	,	PUNCT
ejpam-3362	198	17	for	for	ADP
ejpam-3362	198	18	all	all	DET
ejpam-3362	198	19	y	y	PROPN
ejpam-3362	198	20	∈	∈	PROPN
ejpam-3362	198	21	h	h	NOUN
ejpam-3362	198	22	,	,	PUNCT
ejpam-3362	198	23	xy	xy	PROPN
ejpam-3362	198	24	/∈	/∈	PUNCT
ejpam-3362	198	25	e(γ(h	e(γ(h	PROPN
ejpam-3362	198	26	)	)	PUNCT
ejpam-3362	198	27	)	)	PUNCT
ejpam-3362	198	28	.	.	PUNCT
ejpam-3362	199	1	this	this	PRON
ejpam-3362	199	2	implies	imply	VERB
ejpam-3362	199	3	that	that	SCONJ
ejpam-3362	199	4	γ(h	γ(h	NOUN
ejpam-3362	199	5	)	)	PUNCT
ejpam-3362	199	6	is	be	AUX
ejpam-3362	199	7	disconnected	disconnect	VERB
ejpam-3362	199	8	.	.	PUNCT
ejpam-3362	200	1	for	for	ADP
ejpam-3362	200	2	the	the	DET
ejpam-3362	200	3	converse	converse	NOUN
ejpam-3362	200	4	,	,	PUNCT
ejpam-3362	200	5	suppose	suppose	VERB
ejpam-3362	200	6	that	that	SCONJ
ejpam-3362	200	7	lh({x	lh({x	NOUN
ejpam-3362	200	8	,	,	PUNCT
ejpam-3362	200	9	0	0	NUM
ejpam-3362	200	10	}	}	PUNCT
ejpam-3362	200	11	)	)	PUNCT
ejpam-3362	201	1	=	=	PRON
ejpam-3362	201	2	{	{	PUNCT
ejpam-3362	201	3	0	0	NUM
ejpam-3362	201	4	}	}	PUNCT
ejpam-3362	201	5	for	for	ADP
ejpam-3362	201	6	all	all	DET
ejpam-3362	201	7	x	x	SYM
ejpam-3362	201	8	∈	∈	PROPN
ejpam-3362	201	9	h	h	NOUN
ejpam-3362	201	10	\	\	PUNCT
ejpam-3362	201	11	{	{	PUNCT
ejpam-3362	201	12	0	0	NUM
ejpam-3362	201	13	}	}	PUNCT
ejpam-3362	201	14	.	.	PUNCT
ejpam-3362	202	1	then	then	ADV
ejpam-3362	202	2	degγ(h)(0	degγ(h)(0	ADJ
ejpam-3362	202	3	)	)	PUNCT
ejpam-3362	202	4	=	=	SYM
ejpam-3362	203	1	|h|	|h|	PROPN
ejpam-3362	203	2	−	−	NOUN
ejpam-3362	204	1	1	1	NUM
ejpam-3362	204	2	.	.	PUNCT
ejpam-3362	204	3	therefore	therefore	ADV
ejpam-3362	204	4	,	,	PUNCT
ejpam-3362	204	5	γ(h	γ(h	NOUN
ejpam-3362	204	6	)	)	PUNCT
ejpam-3362	204	7	is	be	AUX
ejpam-3362	204	8	connected	connect	VERB
ejpam-3362	204	9	.	.	PUNCT
ejpam-3362	205	1	m.	m.	NOUN
ejpam-3362	205	2	panganduyon	panganduyon	NOUN
ejpam-3362	205	3	,	,	PUNCT
ejpam-3362	205	4	s.	s.	PROPN
ejpam-3362	205	5	canoy	canoy	PROPN
ejpam-3362	205	6	/	/	SYM
ejpam-3362	205	7	eur	eur	PROPN
ejpam-3362	205	8	.	.	PUNCT
ejpam-3362	206	1	j.	j.	PROPN
ejpam-3362	206	2	pure	pure	PROPN
ejpam-3362	206	3	appl	appl	PROPN
ejpam-3362	206	4	.	.	PROPN
ejpam-3362	206	5	math	math	PROPN
ejpam-3362	206	6	,	,	PUNCT
ejpam-3362	206	7	12	12	NUM
ejpam-3362	206	8	(	(	PUNCT
ejpam-3362	206	9	1	1	NUM
ejpam-3362	206	10	)	)	PUNCT
ejpam-3362	206	11	(	(	PUNCT
ejpam-3362	206	12	2019	2019	NUM
ejpam-3362	206	13	)	)	PUNCT
ejpam-3362	206	14	,	,	PUNCT
ejpam-3362	206	15	146	146	NUM
ejpam-3362	206	16	-	-	SYM
ejpam-3362	206	17	158	158	NUM
ejpam-3362	206	18	153	153	NUM
ejpam-3362	206	19	(	(	PUNCT
ejpam-3362	206	20	ii)⇔(iii	ii)⇔(iii	X
ejpam-3362	206	21	)	)	PUNCT
ejpam-3362	206	22	this	this	PRON
ejpam-3362	206	23	follows	follow	VERB
ejpam-3362	206	24	from	from	ADP
ejpam-3362	206	25	proposition	proposition	NOUN
ejpam-3362	206	26	2(ii	2(ii	NUM
ejpam-3362	206	27	)	)	PUNCT
ejpam-3362	206	28	and	and	CCONJ
ejpam-3362	206	29	2(iv	2(iv	NUM
ejpam-3362	206	30	)	)	PUNCT
ejpam-3362	206	31	.	.	PUNCT
ejpam-3362	207	1	(	(	PUNCT
ejpam-3362	207	2	iii)⇔(iv	iii)⇔(iv	ADP
ejpam-3362	207	3	)	)	PUNCT
ejpam-3362	207	4	this	this	PRON
ejpam-3362	207	5	follows	follow	VERB
ejpam-3362	207	6	from	from	ADP
ejpam-3362	207	7	proposition	proposition	NOUN
ejpam-3362	207	8	3(i	3(i	NUM
ejpam-3362	207	9	)	)	PUNCT
ejpam-3362	207	10	.	.	PUNCT
ejpam-3362	208	1	(	(	PUNCT
ejpam-3362	208	2	iv)⇔(v	iv)⇔(v	X
ejpam-3362	208	3	)	)	PUNCT
ejpam-3362	208	4	by	by	ADP
ejpam-3362	208	5	proposition	proposition	NOUN
ejpam-3362	208	6	3(i	3(i	NUM
ejpam-3362	208	7	)	)	PUNCT
ejpam-3362	208	8	,	,	PUNCT
ejpam-3362	208	9	degγ(h)(0	degγ(h)(0	ADJ
ejpam-3362	208	10	)	)	PUNCT
ejpam-3362	208	11	=	=	SYM
ejpam-3362	209	1	|h|	|h|	PROPN
ejpam-3362	209	2	−	−	NOUN
ejpam-3362	209	3	1	1	NUM
ejpam-3362	209	4	.	.	PUNCT
ejpam-3362	210	1	this	this	PRON
ejpam-3362	210	2	implies	imply	VERB
ejpam-3362	210	3	that	that	SCONJ
ejpam-3362	210	4	0x	0x	PROPN
ejpam-3362	210	5	∈	∈	PROPN
ejpam-3362	210	6	e(γ(h	e(γ(h	NOUN
ejpam-3362	210	7	)	)	PUNCT
ejpam-3362	210	8	)	)	PUNCT
ejpam-3362	210	9	for	for	ADP
ejpam-3362	210	10	each	each	DET
ejpam-3362	210	11	x	x	SYM
ejpam-3362	210	12	∈	∈	PROPN
ejpam-3362	210	13	h	h	NOUN
ejpam-3362	210	14	\	\	PUNCT
ejpam-3362	210	15	{	{	PUNCT
ejpam-3362	210	16	0	0	NUM
ejpam-3362	210	17	}	}	PUNCT
ejpam-3362	210	18	.	.	PUNCT
ejpam-3362	211	1	hence	hence	ADV
ejpam-3362	211	2	,	,	PUNCT
ejpam-3362	211	3	i(γ(h	i(γ(h	NUM
ejpam-3362	211	4	)	)	PUNCT
ejpam-3362	211	5	)	)	PUNCT
ejpam-3362	212	1	=	=	NOUN
ejpam-3362	212	2	∅.	∅.	VERB
ejpam-3362	212	3	conversely	conversely	ADV
ejpam-3362	212	4	,	,	PUNCT
ejpam-3362	212	5	suppose	suppose	VERB
ejpam-3362	212	6	that	that	SCONJ
ejpam-3362	212	7	i(γ(h	i(γ(h	NUM
ejpam-3362	212	8	)	)	PUNCT
ejpam-3362	212	9	)	)	PUNCT
ejpam-3362	213	1	=	=	NOUN
ejpam-3362	213	2	∅	∅	NOUN
ejpam-3362	213	3	and	and	CCONJ
ejpam-3362	213	4	let	let	VERB
ejpam-3362	213	5	x	x	PUNCT
ejpam-3362	213	6	∈	∈	PROPN
ejpam-3362	213	7	h	h	NOUN
ejpam-3362	213	8	\	\	PUNCT
ejpam-3362	213	9	{	{	PUNCT
ejpam-3362	213	10	0	0	NUM
ejpam-3362	213	11	}	}	PUNCT
ejpam-3362	213	12	.	.	PUNCT
ejpam-3362	214	1	since	since	SCONJ
ejpam-3362	214	2	x	x	PROPN
ejpam-3362	214	3	/∈	/∈	PROPN
ejpam-3362	214	4	i(γ(h	i(γ(h	NUM
ejpam-3362	214	5	)	)	PUNCT
ejpam-3362	214	6	)	)	PUNCT
ejpam-3362	214	7	,	,	PUNCT
ejpam-3362	214	8	there	there	PRON
ejpam-3362	214	9	exists	exist	VERB
ejpam-3362	214	10	y	y	PROPN
ejpam-3362	214	11	∈	∈	PROPN
ejpam-3362	214	12	h	h	NOUN
ejpam-3362	214	13	\	\	PUNCT
ejpam-3362	214	14	{	{	PUNCT
ejpam-3362	214	15	x	x	X
ejpam-3362	214	16	}	}	PUNCT
ejpam-3362	214	17	such	such	ADJ
ejpam-3362	214	18	that	that	SCONJ
ejpam-3362	214	19	lh(x	lh(x	PROPN
ejpam-3362	214	20	,	,	PUNCT
ejpam-3362	214	21	y	y	PROPN
ejpam-3362	214	22	)	)	PUNCT
ejpam-3362	214	23	=	=	PRON
ejpam-3362	214	24	{	{	PUNCT
ejpam-3362	214	25	0	0	NUM
ejpam-3362	214	26	}	}	PUNCT
ejpam-3362	214	27	.	.	PUNCT
ejpam-3362	215	1	hence	hence	ADV
ejpam-3362	215	2	,	,	PUNCT
ejpam-3362	215	3	0	0	NUM
ejpam-3362	215	4	∈	∈	PROPN
ejpam-3362	215	5	lh(x	lh(x	PUNCT
ejpam-3362	215	6	)	)	PUNCT
ejpam-3362	215	7	by	by	ADP
ejpam-3362	215	8	proposition	proposition	NOUN
ejpam-3362	215	9	2(iv	2(iv	NUM
ejpam-3362	215	10	)	)	PUNCT
ejpam-3362	215	11	.	.	PUNCT
ejpam-3362	216	1	by	by	ADP
ejpam-3362	216	2	proposition	proposition	NOUN
ejpam-3362	216	3	3(i	3(i	NUM
ejpam-3362	216	4	)	)	PUNCT
ejpam-3362	216	5	,	,	PUNCT
ejpam-3362	216	6	it	it	PRON
ejpam-3362	216	7	follows	follow	VERB
ejpam-3362	216	8	that	that	SCONJ
ejpam-3362	216	9	degγ(h)(0	degγ(h)(0	ADJ
ejpam-3362	216	10	)	)	PUNCT
ejpam-3362	216	11	=	=	SYM
ejpam-3362	216	12	∆(γ(h	∆(γ(h	NOUN
ejpam-3362	216	13	)	)	PUNCT
ejpam-3362	216	14	)	)	PUNCT
ejpam-3362	217	1	=	=	SYM
ejpam-3362	217	2	|h|	|h|	PROPN
ejpam-3362	217	3	−	−	NOUN
ejpam-3362	217	4	1	1	X
ejpam-3362	217	5	.	.	PUNCT
ejpam-3362	217	6	�	�	PROPN
ejpam-3362	217	7	remark	remark	VERB
ejpam-3362	217	8	1	1	NUM
ejpam-3362	217	9	.	.	PUNCT
ejpam-3362	218	1	let	let	VERB
ejpam-3362	218	2	h	h	PRON
ejpam-3362	218	3	be	be	AUX
ejpam-3362	218	4	a	a	DET
ejpam-3362	218	5	hyper	hyper	ADJ
ejpam-3362	218	6	bci	bci	NOUN
ejpam-3362	218	7	-	-	NOUN
ejpam-3362	218	8	algebra	algebra	NOUN
ejpam-3362	218	9	with	with	ADP
ejpam-3362	218	10	|h|	|h|	PROPN
ejpam-3362	218	11	≥	≥	NOUN
ejpam-3362	218	12	2	2	NUM
ejpam-3362	218	13	.	.	PUNCT
ejpam-3362	219	1	if	if	SCONJ
ejpam-3362	219	2	γ(h	γ(h	NOUN
ejpam-3362	219	3	)	)	PUNCT
ejpam-3362	219	4	is	be	AUX
ejpam-3362	219	5	connected	connect	VERB
ejpam-3362	219	6	,	,	PUNCT
ejpam-3362	219	7	then	then	ADV
ejpam-3362	219	8	(	(	PUNCT
ejpam-3362	219	9	i	i	NOUN
ejpam-3362	219	10	)	)	PUNCT
ejpam-3362	219	11	diam(γ(h	diam(γ(h	PROPN
ejpam-3362	219	12	)	)	PUNCT
ejpam-3362	219	13	)	)	PUNCT
ejpam-3362	220	1	=	=	SYM
ejpam-3362	220	2	2	2	NUM
ejpam-3362	220	3	;	;	PUNCT
ejpam-3362	220	4	(	(	PUNCT
ejpam-3362	220	5	ii	ii	NOUN
ejpam-3362	220	6	)	)	PUNCT
ejpam-3362	220	7	degγ(h	degγ(h	NOUN
ejpam-3362	220	8	)	)	PUNCT
ejpam-3362	220	9	0	0	NUM
ejpam-3362	221	1	=	=	SYM
ejpam-3362	221	2	|h|	|h|	PROPN
ejpam-3362	221	3	−	−	PROPN
ejpam-3362	221	4	1	1	NUM
ejpam-3362	221	5	=	=	SYM
ejpam-3362	221	6	∆(γ(h	∆(γ(h	NOUN
ejpam-3362	221	7	)	)	PUNCT
ejpam-3362	221	8	)	)	PUNCT
ejpam-3362	221	9	.	.	PUNCT
ejpam-3362	222	1	proposition	proposition	NOUN
ejpam-3362	222	2	5	5	NUM
ejpam-3362	222	3	.	.	PUNCT
ejpam-3362	223	1	let	let	VERB
ejpam-3362	223	2	h	h	PRON
ejpam-3362	223	3	be	be	AUX
ejpam-3362	223	4	a	a	DET
ejpam-3362	223	5	hyper	hyper	ADJ
ejpam-3362	223	6	bci	bci	NOUN
ejpam-3362	223	7	-	-	NOUN
ejpam-3362	223	8	algebra	algebra	NOUN
ejpam-3362	223	9	such	such	ADJ
ejpam-3362	223	10	that	that	DET
ejpam-3362	223	11	lh{x	lh{x	PROPN
ejpam-3362	223	12	,	,	PUNCT
ejpam-3362	223	13	0	0	NUM
ejpam-3362	223	14	}	}	PUNCT
ejpam-3362	223	15	6=	6=	NOUN
ejpam-3362	223	16	∅	∅	NOUN
ejpam-3362	223	17	for	for	ADP
ejpam-3362	223	18	all	all	DET
ejpam-3362	223	19	x	x	SYM
ejpam-3362	223	20	∈	∈	PROPN
ejpam-3362	223	21	h.	h.	PROPN
ejpam-3362	223	22	then	then	ADV
ejpam-3362	223	23	lh{x	lh{x	PROPN
ejpam-3362	223	24	,	,	PUNCT
ejpam-3362	223	25	0	0	NUM
ejpam-3362	223	26	}	}	PUNCT
ejpam-3362	223	27	=	=	SYM
ejpam-3362	223	28	{	{	PUNCT
ejpam-3362	223	29	0	0	NUM
ejpam-3362	223	30	}	}	PUNCT
ejpam-3362	223	31	.	.	PUNCT
ejpam-3362	224	1	proof	proof	NOUN
ejpam-3362	224	2	.	.	PUNCT
ejpam-3362	225	1	suppose	suppose	VERB
ejpam-3362	225	2	that	that	SCONJ
ejpam-3362	225	3	lh{x	lh{x	PROPN
ejpam-3362	225	4	,	,	PUNCT
ejpam-3362	225	5	0	0	NUM
ejpam-3362	225	6	}	}	PUNCT
ejpam-3362	225	7	6=	6=	NOUN
ejpam-3362	225	8	∅	∅	NOUN
ejpam-3362	225	9	for	for	ADP
ejpam-3362	225	10	all	all	DET
ejpam-3362	225	11	x	x	SYM
ejpam-3362	225	12	∈	∈	PROPN
ejpam-3362	225	13	h.	h.	NOUN
ejpam-3362	225	14	then	then	ADV
ejpam-3362	225	15	there	there	PRON
ejpam-3362	225	16	exists	exist	VERB
ejpam-3362	225	17	y	y	PROPN
ejpam-3362	225	18	∈	∈	PROPN
ejpam-3362	225	19	lh{x	lh{x	PROPN
ejpam-3362	225	20	,	,	PUNCT
ejpam-3362	225	21	0	0	NUM
ejpam-3362	225	22	}	}	PUNCT
ejpam-3362	225	23	.	.	PUNCT
ejpam-3362	226	1	note	note	VERB
ejpam-3362	226	2	that	that	SCONJ
ejpam-3362	226	3	y	y	PROPN
ejpam-3362	226	4	∈	∈	PROPN
ejpam-3362	226	5	lh{0	lh{0	PROPN
ejpam-3362	226	6	}	}	PUNCT
ejpam-3362	226	7	=	=	SYM
ejpam-3362	226	8	{	{	PUNCT
ejpam-3362	226	9	0	0	NUM
ejpam-3362	226	10	}	}	PUNCT
ejpam-3362	226	11	means	mean	VERB
ejpam-3362	226	12	that	that	SCONJ
ejpam-3362	226	13	y	y	PROPN
ejpam-3362	226	14	=	=	NOUN
ejpam-3362	226	15	0	0	PROPN
ejpam-3362	226	16	.	.	PUNCT
ejpam-3362	227	1	it	it	PRON
ejpam-3362	227	2	follows	follow	VERB
ejpam-3362	227	3	from	from	ADP
ejpam-3362	227	4	proposition	proposition	NOUN
ejpam-3362	227	5	2(ii	2(ii	NUM
ejpam-3362	227	6	)	)	PUNCT
ejpam-3362	227	7	and	and	CCONJ
ejpam-3362	227	8	2(iv	2(iv	NUM
ejpam-3362	227	9	)	)	PUNCT
ejpam-3362	227	10	that	that	PRON
ejpam-3362	227	11	lh{x	lh{x	PROPN
ejpam-3362	227	12	,	,	PUNCT
ejpam-3362	227	13	0	0	NUM
ejpam-3362	227	14	}	}	PUNCT
ejpam-3362	227	15	=	=	SYM
ejpam-3362	227	16	{	{	PUNCT
ejpam-3362	227	17	0	0	NUM
ejpam-3362	227	18	}	}	PUNCT
ejpam-3362	227	19	.	.	PUNCT
ejpam-3362	228	1	�	�	PROPN
ejpam-3362	228	2	remark	remark	VERB
ejpam-3362	228	3	2	2	NUM
ejpam-3362	228	4	.	.	PUNCT
ejpam-3362	229	1	let	let	VERB
ejpam-3362	229	2	h	h	PRON
ejpam-3362	229	3	be	be	AUX
ejpam-3362	229	4	a	a	DET
ejpam-3362	229	5	hyper	hyper	ADJ
ejpam-3362	229	6	bci	bci	NOUN
ejpam-3362	229	7	-	-	NOUN
ejpam-3362	229	8	algebra	algebra	NOUN
ejpam-3362	229	9	such	such	ADJ
ejpam-3362	229	10	that	that	DET
ejpam-3362	229	11	lh{x	lh{x	PROPN
ejpam-3362	229	12	,	,	PUNCT
ejpam-3362	229	13	0	0	NUM
ejpam-3362	229	14	}	}	PUNCT
ejpam-3362	229	15	6=	6=	NOUN
ejpam-3362	229	16	∅	∅	NOUN
ejpam-3362	229	17	for	for	ADP
ejpam-3362	229	18	all	all	DET
ejpam-3362	229	19	x	x	SYM
ejpam-3362	229	20	∈	∈	PROPN
ejpam-3362	229	21	h.	h.	NOUN
ejpam-3362	229	22	then	then	ADV
ejpam-3362	229	23	0x	0x	PROPN
ejpam-3362	229	24	∈	∈	PROPN
ejpam-3362	229	25	e(γ(h	e(γ(h	NOUN
ejpam-3362	229	26	)	)	PUNCT
ejpam-3362	229	27	)	)	PUNCT
ejpam-3362	229	28	∀	∀	X
ejpam-3362	230	1	x	x	SYM
ejpam-3362	230	2	∈	∈	NOUN
ejpam-3362	230	3	h	h	NOUN
ejpam-3362	230	4	\	\	PUNCT
ejpam-3362	230	5	{	{	PUNCT
ejpam-3362	230	6	0	0	NUM
ejpam-3362	230	7	}	}	PUNCT
ejpam-3362	230	8	.	.	PUNCT
ejpam-3362	231	1	proposition	proposition	NOUN
ejpam-3362	231	2	6	6	NUM
ejpam-3362	231	3	.	.	PUNCT
ejpam-3362	232	1	if	if	SCONJ
ejpam-3362	232	2	|h|	|h|	PROPN
ejpam-3362	232	3	>	>	X
ejpam-3362	232	4	3	3	NUM
ejpam-3362	232	5	,	,	PUNCT
ejpam-3362	232	6	then	then	ADV
ejpam-3362	232	7	γ(h	γ(h	NOUN
ejpam-3362	232	8	)	)	PUNCT
ejpam-3362	232	9	is	be	AUX
ejpam-3362	232	10	neither	neither	CCONJ
ejpam-3362	232	11	a	a	DET
ejpam-3362	232	12	cycle	cycle	NOUN
ejpam-3362	232	13	nor	nor	CCONJ
ejpam-3362	232	14	a	a	DET
ejpam-3362	232	15	path	path	NOUN
ejpam-3362	232	16	.	.	PUNCT
ejpam-3362	233	1	proof	proof	NOUN
ejpam-3362	233	2	.	.	PUNCT
ejpam-3362	234	1	case	case	NOUN
ejpam-3362	234	2	1	1	NUM
ejpam-3362	234	3	.	.	PUNCT
ejpam-3362	235	1	∃	∃	PROPN
ejpam-3362	235	2	x	x	SYM
ejpam-3362	235	3	∈	∈	PROPN
ejpam-3362	235	4	h	h	NOUN
ejpam-3362	235	5	\	\	PUNCT
ejpam-3362	235	6	{	{	PUNCT
ejpam-3362	235	7	0	0	NUM
ejpam-3362	235	8	}	}	PUNCT
ejpam-3362	235	9	such	such	ADJ
ejpam-3362	235	10	that	that	PRON
ejpam-3362	235	11	0	0	NUM
ejpam-3362	235	12	/∈	/∈	INTJ
ejpam-3362	235	13	lh(x	lh(x	NOUN
ejpam-3362	235	14	)	)	PUNCT
ejpam-3362	235	15	.	.	PUNCT
ejpam-3362	236	1	then	then	ADV
ejpam-3362	236	2	γ(h	γ(h	PROPN
ejpam-3362	236	3	)	)	PUNCT
ejpam-3362	236	4	is	be	AUX
ejpam-3362	236	5	disconnected	disconnect	VERB
ejpam-3362	236	6	,	,	PUNCT
ejpam-3362	236	7	and	and	CCONJ
ejpam-3362	236	8	the	the	DET
ejpam-3362	236	9	result	result	NOUN
ejpam-3362	236	10	follows	follow	VERB
ejpam-3362	236	11	.	.	PUNCT
ejpam-3362	237	1	case	case	NOUN
ejpam-3362	237	2	2	2	NUM
ejpam-3362	237	3	.	.	NOUN
ejpam-3362	237	4	0	0	NUM
ejpam-3362	237	5	∈	∈	PROPN
ejpam-3362	237	6	lh(x	lh(x	NOUN
ejpam-3362	237	7	)	)	PUNCT
ejpam-3362	237	8	∀	∀	X
ejpam-3362	238	1	x	x	SYM
ejpam-3362	238	2	∈	∈	PROPN
ejpam-3362	238	3	h.	h.	NOUN
ejpam-3362	238	4	then	then	ADV
ejpam-3362	238	5	0x	0x	PROPN
ejpam-3362	238	6	∈	∈	PROPN
ejpam-3362	238	7	e(γ(h	e(γ(h	NOUN
ejpam-3362	238	8	)	)	PUNCT
ejpam-3362	238	9	)	)	PUNCT
ejpam-3362	238	10	∀	∀	X
ejpam-3362	239	1	x	x	SYM
ejpam-3362	239	2	∈	∈	NOUN
ejpam-3362	239	3	h	h	NOUN
ejpam-3362	239	4	\	\	PUNCT
ejpam-3362	239	5	{	{	PUNCT
ejpam-3362	239	6	0	0	NUM
ejpam-3362	239	7	}	}	PUNCT
ejpam-3362	239	8	.	.	PUNCT
ejpam-3362	240	1	evidently	evidently	ADV
ejpam-3362	240	2	,	,	PUNCT
ejpam-3362	240	3	γ(h	γ(h	PROPN
ejpam-3362	240	4	)	)	PUNCT
ejpam-3362	240	5	is	be	AUX
ejpam-3362	240	6	neither	neither	CCONJ
ejpam-3362	240	7	a	a	DET
ejpam-3362	240	8	cycle	cycle	NOUN
ejpam-3362	240	9	nor	nor	CCONJ
ejpam-3362	240	10	a	a	DET
ejpam-3362	240	11	path	path	NOUN
ejpam-3362	240	12	.	.	PUNCT
ejpam-3362	241	1	�	�	PROPN
ejpam-3362	241	2	corollary	corollary	NOUN
ejpam-3362	241	3	1	1	NUM
ejpam-3362	241	4	.	.	PUNCT
ejpam-3362	242	1	if	if	SCONJ
ejpam-3362	242	2	a	a	DET
ejpam-3362	242	3	graph	graph	NOUN
ejpam-3362	242	4	g	g	NOUN
ejpam-3362	242	5	is	be	AUX
ejpam-3362	242	6	a	a	DET
ejpam-3362	242	7	cycle	cycle	NOUN
ejpam-3362	242	8	or	or	CCONJ
ejpam-3362	242	9	a	a	DET
ejpam-3362	242	10	path	path	NOUN
ejpam-3362	242	11	of	of	ADP
ejpam-3362	242	12	order	order	NOUN
ejpam-3362	242	13	n	n	PRON
ejpam-3362	242	14	≥	≥	NOUN
ejpam-3362	242	15	4	4	NUM
ejpam-3362	242	16	,	,	PUNCT
ejpam-3362	242	17	then	then	ADV
ejpam-3362	242	18	there	there	PRON
ejpam-3362	242	19	is	be	VERB
ejpam-3362	242	20	no	no	DET
ejpam-3362	242	21	hyper	hyper	ADJ
ejpam-3362	242	22	bci	bci	NOUN
ejpam-3362	242	23	-	-	ADJ
ejpam-3362	242	24	algebra	algebra	NOUN
ejpam-3362	242	25	h	h	NOUN
ejpam-3362	242	26	such	such	ADJ
ejpam-3362	242	27	that	that	DET
ejpam-3362	242	28	γ(h	γ(h	NOUN
ejpam-3362	242	29	)	)	PUNCT
ejpam-3362	242	30	∼=	∼=	PROPN
ejpam-3362	242	31	g.	g.	NOUN
ejpam-3362	242	32	proof	proof	NOUN
ejpam-3362	242	33	.	.	PUNCT
ejpam-3362	243	1	immediate	immediate	ADJ
ejpam-3362	243	2	from	from	ADP
ejpam-3362	243	3	proposition	proposition	NOUN
ejpam-3362	243	4	6	6	NUM
ejpam-3362	243	5	.	.	PUNCT
ejpam-3362	243	6	�	�	PROPN
ejpam-3362	243	7	theorem	theorem	AUX
ejpam-3362	243	8	2	2	NUM
ejpam-3362	243	9	.	.	PUNCT
ejpam-3362	244	1	let	let	VERB
ejpam-3362	244	2	h	h	PRON
ejpam-3362	244	3	be	be	AUX
ejpam-3362	244	4	a	a	DET
ejpam-3362	244	5	hyper	hyper	ADJ
ejpam-3362	244	6	bci	bci	NOUN
ejpam-3362	244	7	-	-	NOUN
ejpam-3362	244	8	algebra	algebra	NOUN
ejpam-3362	244	9	with	with	ADP
ejpam-3362	244	10	|h|	|h|	PROPN
ejpam-3362	244	11	≥	≥	NUM
ejpam-3362	244	12	2	2	NUM
ejpam-3362	244	13	.	.	PUNCT
ejpam-3362	245	1	then	then	ADV
ejpam-3362	245	2	g	g	PROPN
ejpam-3362	245	3	=	=	SYM
ejpam-3362	245	4	γ(h	γ(h	NOUN
ejpam-3362	245	5	)	)	PUNCT
ejpam-3362	245	6	can	can	AUX
ejpam-3362	245	7	not	not	PART
ejpam-3362	245	8	have	have	VERB
ejpam-3362	245	9	two	two	NUM
ejpam-3362	245	10	nontrivial	nontrivial	ADJ
ejpam-3362	245	11	components	component	NOUN
ejpam-3362	245	12	;	;	PUNCT
ejpam-3362	245	13	that	that	PRON
ejpam-3362	245	14	is	is	ADV
ejpam-3362	245	15	,	,	PUNCT
ejpam-3362	245	16	g	g	PROPN
ejpam-3362	245	17	can	can	AUX
ejpam-3362	245	18	only	only	ADV
ejpam-3362	245	19	have	have	VERB
ejpam-3362	245	20	at	at	ADP
ejpam-3362	245	21	most	most	ADJ
ejpam-3362	245	22	one	one	NUM
ejpam-3362	245	23	non	non	ADJ
ejpam-3362	245	24	-	-	ADJ
ejpam-3362	245	25	trivial	trivial	ADJ
ejpam-3362	245	26	component	component	NOUN
ejpam-3362	245	27	.	.	PUNCT
ejpam-3362	246	1	proof	proof	NOUN
ejpam-3362	246	2	.	.	PUNCT
ejpam-3362	247	1	if	if	SCONJ
ejpam-3362	247	2	g	g	PROPN
ejpam-3362	247	3	is	be	AUX
ejpam-3362	247	4	connected	connect	VERB
ejpam-3362	247	5	,	,	PUNCT
ejpam-3362	247	6	then	then	ADV
ejpam-3362	247	7	we	we	PRON
ejpam-3362	247	8	are	be	AUX
ejpam-3362	247	9	done	do	VERB
ejpam-3362	247	10	.	.	PUNCT
ejpam-3362	248	1	suppose	suppose	VERB
ejpam-3362	248	2	that	that	SCONJ
ejpam-3362	248	3	g	g	PROPN
ejpam-3362	248	4	is	be	AUX
ejpam-3362	248	5	disconnected	disconnect	VERB
ejpam-3362	248	6	.	.	PUNCT
ejpam-3362	249	1	suppose	suppose	VERB
ejpam-3362	249	2	further	far	ADV
ejpam-3362	249	3	that	that	SCONJ
ejpam-3362	249	4	g	g	PROPN
ejpam-3362	249	5	has	have	VERB
ejpam-3362	249	6	two	two	NUM
ejpam-3362	249	7	distinct	distinct	ADJ
ejpam-3362	249	8	non	non	ADJ
ejpam-3362	249	9	-	-	ADJ
ejpam-3362	249	10	trivial	trivial	ADJ
ejpam-3362	249	11	components	component	NOUN
ejpam-3362	249	12	,	,	PUNCT
ejpam-3362	249	13	say	say	VERB
ejpam-3362	249	14	g1	g1	PROPN
ejpam-3362	249	15	and	and	CCONJ
ejpam-3362	249	16	g2	g2	PROPN
ejpam-3362	249	17	.	.	PUNCT
ejpam-3362	250	1	let	let	VERB
ejpam-3362	250	2	g3	g3	PROPN
ejpam-3362	250	3	be	be	AUX
ejpam-3362	250	4	a	a	DET
ejpam-3362	250	5	component	component	NOUN
ejpam-3362	250	6	of	of	ADP
ejpam-3362	250	7	g	g	NOUN
ejpam-3362	250	8	with	with	ADP
ejpam-3362	250	9	0	0	NUM
ejpam-3362	250	10	∈	∈	PROPN
ejpam-3362	250	11	v	v	ADP
ejpam-3362	250	12	(	(	PUNCT
ejpam-3362	250	13	g3	g3	PROPN
ejpam-3362	250	14	)	)	PUNCT
ejpam-3362	250	15	(	(	PUNCT
ejpam-3362	250	16	g3	g3	PROPN
ejpam-3362	250	17	may	may	AUX
ejpam-3362	250	18	be	be	AUX
ejpam-3362	250	19	g1	g1	PROPN
ejpam-3362	250	20	or	or	CCONJ
ejpam-3362	250	21	g2	g2	PROPN
ejpam-3362	250	22	)	)	PUNCT
ejpam-3362	250	23	.	.	PUNCT
ejpam-3362	251	1	if	if	SCONJ
ejpam-3362	251	2	g3	g3	PROPN
ejpam-3362	251	3	is	be	AUX
ejpam-3362	251	4	different	different	ADJ
ejpam-3362	251	5	from	from	ADP
ejpam-3362	251	6	g1	g1	PROPN
ejpam-3362	251	7	,	,	PUNCT
ejpam-3362	251	8	then	then	ADV
ejpam-3362	251	9	0	0	NUM
ejpam-3362	251	10	/∈	/∈	INTJ
ejpam-3362	251	11	lh(x	lh(x	NOUN
ejpam-3362	251	12	)	)	PUNCT
ejpam-3362	251	13	for	for	ADP
ejpam-3362	251	14	all	all	PRON
ejpam-3362	251	15	x	x	SYM
ejpam-3362	251	16	∈	∈	PROPN
ejpam-3362	251	17	v	v	NOUN
ejpam-3362	251	18	(	(	PUNCT
ejpam-3362	251	19	g1	g1	PROPN
ejpam-3362	251	20	)	)	PUNCT
ejpam-3362	251	21	.	.	PUNCT
ejpam-3362	252	1	similarly	similarly	ADV
ejpam-3362	252	2	,	,	PUNCT
ejpam-3362	252	3	if	if	SCONJ
ejpam-3362	252	4	g3	g3	PROPN
ejpam-3362	252	5	is	be	AUX
ejpam-3362	252	6	not	not	PART
ejpam-3362	252	7	g2	g2	PROPN
ejpam-3362	252	8	,	,	PUNCT
ejpam-3362	252	9	then	then	ADV
ejpam-3362	252	10	0	0	NUM
ejpam-3362	252	11	/∈	/∈	PUNCT
ejpam-3362	252	12	lh(y	lh(y	X
ejpam-3362	252	13	)	)	PUNCT
ejpam-3362	252	14	for	for	ADP
ejpam-3362	252	15	all	all	DET
ejpam-3362	252	16	y	y	PROPN
ejpam-3362	252	17	∈	∈	PROPN
ejpam-3362	252	18	v	v	PROPN
ejpam-3362	252	19	(	(	PUNCT
ejpam-3362	252	20	g2	g2	PROPN
ejpam-3362	252	21	)	)	PUNCT
ejpam-3362	252	22	.	.	PUNCT
ejpam-3362	253	1	hence	hence	ADV
ejpam-3362	253	2	,	,	PUNCT
ejpam-3362	253	3	by	by	ADP
ejpam-3362	253	4	proposition	proposition	NOUN
ejpam-3362	253	5	4	4	NUM
ejpam-3362	253	6	,	,	PUNCT
ejpam-3362	253	7	g1	g1	PROPN
ejpam-3362	253	8	or	or	CCONJ
ejpam-3362	253	9	g2	g2	PROPN
ejpam-3362	253	10	is	be	AUX
ejpam-3362	253	11	the	the	DET
ejpam-3362	253	12	trivial	trivial	ADJ
ejpam-3362	253	13	graph	graph	NOUN
ejpam-3362	253	14	,	,	PUNCT
ejpam-3362	253	15	a	a	DET
ejpam-3362	253	16	contradiction	contradiction	NOUN
ejpam-3362	253	17	.	.	PUNCT
ejpam-3362	254	1	�	�	PROPN
ejpam-3362	254	2	m.	m.	NOUN
ejpam-3362	254	3	panganduyon	panganduyon	NOUN
ejpam-3362	254	4	,	,	PUNCT
ejpam-3362	254	5	s.	s.	PROPN
ejpam-3362	254	6	canoy	canoy	PROPN
ejpam-3362	254	7	/	/	SYM
ejpam-3362	254	8	eur	eur	PROPN
ejpam-3362	254	9	.	.	PUNCT
ejpam-3362	255	1	j.	j.	PROPN
ejpam-3362	255	2	pure	pure	PROPN
ejpam-3362	255	3	appl	appl	PROPN
ejpam-3362	255	4	.	.	PROPN
ejpam-3362	255	5	math	math	PROPN
ejpam-3362	255	6	,	,	PUNCT
ejpam-3362	255	7	12	12	NUM
ejpam-3362	255	8	(	(	PUNCT
ejpam-3362	255	9	1	1	NUM
ejpam-3362	255	10	)	)	PUNCT
ejpam-3362	255	11	(	(	PUNCT
ejpam-3362	255	12	2019	2019	NUM
ejpam-3362	255	13	)	)	PUNCT
ejpam-3362	255	14	,	,	PUNCT
ejpam-3362	255	15	146	146	NUM
ejpam-3362	255	16	-	-	SYM
ejpam-3362	255	17	158	158	NUM
ejpam-3362	255	18	154	154	NUM
ejpam-3362	255	19	proposition	proposition	NOUN
ejpam-3362	255	20	7	7	NUM
ejpam-3362	255	21	.	.	PUNCT
ejpam-3362	256	1	let	let	VERB
ejpam-3362	256	2	h	h	PRON
ejpam-3362	256	3	be	be	AUX
ejpam-3362	256	4	an	an	DET
ejpam-3362	256	5	ordered	order	VERB
ejpam-3362	256	6	hyper	hyper	ADJ
ejpam-3362	256	7	bci	bci	NOUN
ejpam-3362	256	8	-	-	NOUN
ejpam-3362	256	9	algebra	algebra	NOUN
ejpam-3362	256	10	.	.	PUNCT
ejpam-3362	257	1	then	then	ADV
ejpam-3362	257	2	the	the	DET
ejpam-3362	257	3	following	follow	VERB
ejpam-3362	257	4	hold	hold	NOUN
ejpam-3362	257	5	:	:	PUNCT
ejpam-3362	257	6	(	(	PUNCT
ejpam-3362	257	7	i	i	NOUN
ejpam-3362	257	8	)	)	PUNCT
ejpam-3362	257	9	for	for	ADP
ejpam-3362	257	10	any	any	DET
ejpam-3362	257	11	subset	subset	NOUN
ejpam-3362	257	12	a	a	PRON
ejpam-3362	257	13	of	of	ADP
ejpam-3362	257	14	h	h	NOUN
ejpam-3362	257	15	,	,	PUNCT
ejpam-3362	257	16	lh(lh(a	lh(lh(a	NOUN
ejpam-3362	257	17	)	)	PUNCT
ejpam-3362	257	18	)	)	PUNCT
ejpam-3362	258	1	⊆	⊆	NUM
ejpam-3362	258	2	lh(a	lh(a	NUM
ejpam-3362	258	3	)	)	PUNCT
ejpam-3362	258	4	.	.	PUNCT
ejpam-3362	259	1	(	(	PUNCT
ejpam-3362	259	2	ii	ii	NOUN
ejpam-3362	259	3	)	)	PUNCT
ejpam-3362	259	4	for	for	ADP
ejpam-3362	259	5	any	any	DET
ejpam-3362	259	6	a	a	PRON
ejpam-3362	259	7	,	,	PUNCT
ejpam-3362	259	8	b	b	X
ejpam-3362	259	9	∈	∈	PROPN
ejpam-3362	259	10	h	h	NOUN
ejpam-3362	259	11	,	,	PUNCT
ejpam-3362	259	12	if	if	SCONJ
ejpam-3362	259	13	a	a	DET
ejpam-3362	259	14	�	�	PROPN
ejpam-3362	259	15	b	b	PROPN
ejpam-3362	259	16	,	,	PUNCT
ejpam-3362	259	17	then	then	ADV
ejpam-3362	259	18	lh({a	lh({a	PROPN
ejpam-3362	259	19	}	}	PUNCT
ejpam-3362	259	20	)	)	PUNCT
ejpam-3362	260	1	⊆	⊆	NUM
ejpam-3362	260	2	lh({b	lh({b	NOUN
ejpam-3362	260	3	}	}	PUNCT
ejpam-3362	260	4	)	)	PUNCT
ejpam-3362	260	5	and	and	CCONJ
ejpam-3362	260	6	zb	zb	VERB
ejpam-3362	260	7	⊆	⊆	NUM
ejpam-3362	260	8	za	za	PROPN
ejpam-3362	260	9	.	.	PUNCT
ejpam-3362	261	1	proof	proof	NOUN
ejpam-3362	261	2	.	.	PUNCT
ejpam-3362	262	1	(	(	PUNCT
ejpam-3362	262	2	i	i	NOUN
ejpam-3362	262	3	)	)	PUNCT
ejpam-3362	262	4	let	let	VERB
ejpam-3362	262	5	x	x	PUNCT
ejpam-3362	262	6	∈	∈	PROPN
ejpam-3362	262	7	lh(lh(a	lh(lh(a	PROPN
ejpam-3362	262	8	)	)	PUNCT
ejpam-3362	262	9	)	)	PUNCT
ejpam-3362	262	10	.	.	PUNCT
ejpam-3362	263	1	then	then	ADV
ejpam-3362	263	2	x	x	SYM
ejpam-3362	263	3	�	�	PROPN
ejpam-3362	263	4	b	b	PROPN
ejpam-3362	263	5	for	for	ADP
ejpam-3362	263	6	all	all	DET
ejpam-3362	263	7	b	b	PROPN
ejpam-3362	263	8	∈	∈	PROPN
ejpam-3362	263	9	lh(a	lh(a	NOUN
ejpam-3362	263	10	)	)	PUNCT
ejpam-3362	263	11	.	.	PUNCT
ejpam-3362	264	1	since	since	SCONJ
ejpam-3362	264	2	b	b	PROPN
ejpam-3362	264	3	�	�	PROPN
ejpam-3362	264	4	a	a	PROPN
ejpam-3362	264	5	for	for	ADP
ejpam-3362	264	6	all	all	DET
ejpam-3362	264	7	a	a	DET
ejpam-3362	264	8	∈	∈	PROPN
ejpam-3362	264	9	a	a	PRON
ejpam-3362	264	10	and	and	CCONJ
ejpam-3362	264	11	h	h	NOUN
ejpam-3362	264	12	is	be	AUX
ejpam-3362	264	13	ordered	order	VERB
ejpam-3362	264	14	,	,	PUNCT
ejpam-3362	264	15	it	it	PRON
ejpam-3362	264	16	follows	follow	VERB
ejpam-3362	264	17	that	that	SCONJ
ejpam-3362	264	18	x	x	PROPN
ejpam-3362	264	19	�	�	PROPN
ejpam-3362	264	20	a	a	X
ejpam-3362	264	21	for	for	ADP
ejpam-3362	264	22	all	all	DET
ejpam-3362	264	23	a	a	DET
ejpam-3362	264	24	∈	∈	PROPN
ejpam-3362	264	25	a.	a.	NOUN
ejpam-3362	264	26	thus	thus	ADV
ejpam-3362	264	27	,	,	PUNCT
ejpam-3362	264	28	x	x	PROPN
ejpam-3362	264	29	∈	∈	PROPN
ejpam-3362	264	30	lh(a	lh(a	NOUN
ejpam-3362	264	31	)	)	PUNCT
ejpam-3362	264	32	and	and	CCONJ
ejpam-3362	264	33	the	the	DET
ejpam-3362	264	34	result	result	NOUN
ejpam-3362	264	35	follows	follow	VERB
ejpam-3362	264	36	.	.	PUNCT
ejpam-3362	265	1	(	(	PUNCT
ejpam-3362	265	2	ii	ii	NOUN
ejpam-3362	265	3	)	)	PUNCT
ejpam-3362	265	4	suppose	suppose	VERB
ejpam-3362	265	5	x	x	X
ejpam-3362	265	6	∈	∈	PROPN
ejpam-3362	265	7	lh({a	lh({a	PROPN
ejpam-3362	265	8	}	}	PUNCT
ejpam-3362	265	9	)	)	PUNCT
ejpam-3362	265	10	.	.	PUNCT
ejpam-3362	266	1	then	then	ADV
ejpam-3362	266	2	x	x	X
ejpam-3362	266	3	�	�	PROPN
ejpam-3362	266	4	a.	a.	NOUN
ejpam-3362	266	5	since	since	SCONJ
ejpam-3362	266	6	h	h	PROPN
ejpam-3362	266	7	is	be	AUX
ejpam-3362	266	8	ordered	order	VERB
ejpam-3362	266	9	and	and	CCONJ
ejpam-3362	266	10	a	a	DET
ejpam-3362	266	11	�	�	PROPN
ejpam-3362	266	12	b	b	PROPN
ejpam-3362	266	13	,	,	PUNCT
ejpam-3362	266	14	x	x	PROPN
ejpam-3362	266	15	�	�	PROPN
ejpam-3362	266	16	b.	b.	PROPN
ejpam-3362	266	17	that	that	PRON
ejpam-3362	266	18	is	be	AUX
ejpam-3362	266	19	,	,	PUNCT
ejpam-3362	266	20	x	x	SYM
ejpam-3362	266	21	∈	∈	NOUN
ejpam-3362	266	22	lh({b	lh({b	NOUN
ejpam-3362	266	23	}	}	PUNCT
ejpam-3362	266	24	)	)	PUNCT
ejpam-3362	266	25	.	.	PUNCT
ejpam-3362	267	1	hence	hence	ADV
ejpam-3362	267	2	,	,	PUNCT
ejpam-3362	267	3	lh({a	lh({a	PROPN
ejpam-3362	267	4	}	}	PUNCT
ejpam-3362	267	5	)	)	PUNCT
ejpam-3362	267	6	⊆	⊆	NUM
ejpam-3362	267	7	lh({b	lh({b	NOUN
ejpam-3362	267	8	}	}	PUNCT
ejpam-3362	267	9	)	)	PUNCT
ejpam-3362	267	10	.	.	PUNCT
ejpam-3362	268	1	now	now	ADV
ejpam-3362	268	2	,	,	PUNCT
ejpam-3362	268	3	suppose	suppose	VERB
ejpam-3362	268	4	x	x	X
ejpam-3362	268	5	∈	∈	PROPN
ejpam-3362	268	6	zb	zb	X
ejpam-3362	268	7	.	.	PUNCT
ejpam-3362	268	8	then	then	ADV
ejpam-3362	268	9	lh({b	lh({b	ADV
ejpam-3362	268	10	,	,	PUNCT
ejpam-3362	268	11	x	x	NOUN
ejpam-3362	268	12	}	}	PUNCT
ejpam-3362	268	13	)	)	PUNCT
ejpam-3362	268	14	=	=	PUNCT
ejpam-3362	268	15	{	{	PUNCT
ejpam-3362	268	16	0	0	NUM
ejpam-3362	268	17	}	}	PUNCT
ejpam-3362	268	18	.	.	PUNCT
ejpam-3362	269	1	since	since	SCONJ
ejpam-3362	269	2	lh({a	lh({a	PROPN
ejpam-3362	269	3	,	,	PUNCT
ejpam-3362	269	4	x	x	NOUN
ejpam-3362	269	5	}	}	PUNCT
ejpam-3362	269	6	)	)	PUNCT
ejpam-3362	269	7	⊆	⊆	NUM
ejpam-3362	269	8	lh({b	lh({b	ADJ
ejpam-3362	269	9	,	,	PUNCT
ejpam-3362	269	10	x	x	NOUN
ejpam-3362	269	11	}	}	PUNCT
ejpam-3362	269	12	)	)	PUNCT
ejpam-3362	269	13	,	,	PUNCT
ejpam-3362	269	14	we	we	PRON
ejpam-3362	269	15	have	have	VERB
ejpam-3362	269	16	lh({a	lh({a	PROPN
ejpam-3362	269	17	,	,	PUNCT
ejpam-3362	269	18	x	x	NOUN
ejpam-3362	269	19	}	}	PUNCT
ejpam-3362	269	20	)	)	PUNCT
ejpam-3362	269	21	=	=	PUNCT
ejpam-3362	269	22	{	{	PUNCT
ejpam-3362	269	23	0	0	NUM
ejpam-3362	269	24	}	}	PUNCT
ejpam-3362	269	25	.	.	PUNCT
ejpam-3362	270	1	this	this	PRON
ejpam-3362	270	2	means	mean	VERB
ejpam-3362	270	3	that	that	SCONJ
ejpam-3362	270	4	x	x	PROPN
ejpam-3362	270	5	∈	∈	PROPN
ejpam-3362	270	6	za	za	PROPN
ejpam-3362	270	7	.	.	PUNCT
ejpam-3362	271	1	thus	thus	ADV
ejpam-3362	271	2	,	,	PUNCT
ejpam-3362	271	3	zb	zb	PROPN
ejpam-3362	271	4	⊆	⊆	NUM
ejpam-3362	271	5	za	za	PROPN
ejpam-3362	271	6	.	.	PUNCT
ejpam-3362	271	7	�	�	PROPN
ejpam-3362	271	8	proposition	proposition	PROPN
ejpam-3362	271	9	8	8	NUM
ejpam-3362	271	10	.	.	PUNCT
ejpam-3362	272	1	let	let	VERB
ejpam-3362	272	2	h	h	PRON
ejpam-3362	272	3	be	be	AUX
ejpam-3362	272	4	a	a	DET
ejpam-3362	272	5	hyper	hyper	ADJ
ejpam-3362	272	6	bci	bci	NOUN
ejpam-3362	272	7	-	-	NOUN
ejpam-3362	272	8	algebra	algebra	NOUN
ejpam-3362	272	9	.	.	PUNCT
ejpam-3362	273	1	then	then	ADV
ejpam-3362	273	2	(	(	PUNCT
ejpam-3362	273	3	i	i	NOUN
ejpam-3362	273	4	)	)	PUNCT
ejpam-3362	273	5	degγ(h	degγ(h	NOUN
ejpam-3362	273	6	)	)	PUNCT
ejpam-3362	273	7	x	x	X
ejpam-3362	274	1	=	=	PUNCT
ejpam-3362	274	2	|zx|	|zx|	NOUN
ejpam-3362	274	3	for	for	ADP
ejpam-3362	274	4	all	all	DET
ejpam-3362	274	5	nonzero	nonzero	NOUN
ejpam-3362	274	6	x	x	SYM
ejpam-3362	274	7	∈	∈	PROPN
ejpam-3362	274	8	h.	h.	PROPN
ejpam-3362	274	9	(	(	PUNCT
ejpam-3362	274	10	ii	ii	PROPN
ejpam-3362	274	11	)	)	PUNCT
ejpam-3362	274	12	y	y	PROPN
ejpam-3362	274	13	∈	∈	PROPN
ejpam-3362	274	14	zx	zx	INTJ
ejpam-3362	274	15	if	if	SCONJ
ejpam-3362	274	16	and	and	CCONJ
ejpam-3362	274	17	only	only	ADV
ejpam-3362	274	18	if	if	SCONJ
ejpam-3362	274	19	x	x	PROPN
ejpam-3362	274	20	∈	∈	PROPN
ejpam-3362	274	21	zy	zy	PROPN
ejpam-3362	274	22	for	for	ADP
ejpam-3362	274	23	all	all	DET
ejpam-3362	274	24	x	x	NOUN
ejpam-3362	274	25	,	,	PUNCT
ejpam-3362	274	26	y	y	PROPN
ejpam-3362	274	27	∈	∈	PROPN
ejpam-3362	274	28	h.	h.	NOUN
ejpam-3362	274	29	proof	proof	NOUN
ejpam-3362	274	30	.	.	PUNCT
ejpam-3362	275	1	let	let	VERB
ejpam-3362	275	2	x	x	PRON
ejpam-3362	275	3	,	,	PUNCT
ejpam-3362	275	4	y	y	PROPN
ejpam-3362	275	5	∈	∈	PROPN
ejpam-3362	275	6	h.	h.	PROPN
ejpam-3362	275	7	(	(	PUNCT
ejpam-3362	275	8	i	i	NOUN
ejpam-3362	275	9	)	)	PUNCT
ejpam-3362	275	10	if	if	SCONJ
ejpam-3362	275	11	x	x	PROPN
ejpam-3362	275	12	6=	6=	ADP
ejpam-3362	275	13	0	0	NUM
ejpam-3362	275	14	,	,	PUNCT
ejpam-3362	275	15	then	then	ADV
ejpam-3362	275	16	|zx|	|zx|	PRON
ejpam-3362	275	17	=	=	PUNCT
ejpam-3362	275	18	|{y	|{y	PUNCT
ejpam-3362	275	19	∈	∈	PROPN
ejpam-3362	275	20	h	h	NOUN
ejpam-3362	275	21	\	\	PUNCT
ejpam-3362	275	22	{	{	PUNCT
ejpam-3362	275	23	x	x	NOUN
ejpam-3362	275	24	}	}	PUNCT
ejpam-3362	275	25	:	:	PUNCT
ejpam-3362	275	26	lh({x	lh({x	NUM
ejpam-3362	275	27	,	,	PUNCT
ejpam-3362	275	28	y	y	NOUN
ejpam-3362	275	29	}	}	PUNCT
ejpam-3362	275	30	)	)	PUNCT
ejpam-3362	276	1	=	=	SYM
ejpam-3362	276	2	{	{	PUNCT
ejpam-3362	276	3	0}}|	0}}|	X
ejpam-3362	276	4	=	=	PUNCT
ejpam-3362	276	5	|{y	|{y	PUNCT
ejpam-3362	276	6	∈	∈	PROPN
ejpam-3362	276	7	h	h	NOUN
ejpam-3362	276	8	:	:	PUNCT
ejpam-3362	276	9	xy	xy	PROPN
ejpam-3362	276	10	∈	∈	PROPN
ejpam-3362	276	11	e(γ(h))}|	e(γ(h))}|	PROPN
ejpam-3362	276	12	=	=	SYM
ejpam-3362	276	13	degγ(h	degγ(h	NOUN
ejpam-3362	276	14	)	)	PUNCT
ejpam-3362	276	15	x.	x.	NOUN
ejpam-3362	276	16	(	(	PUNCT
ejpam-3362	276	17	ii	ii	PROPN
ejpam-3362	276	18	)	)	PUNCT
ejpam-3362	276	19	y	y	PROPN
ejpam-3362	276	20	∈	∈	PROPN
ejpam-3362	276	21	zx	zx	NOUN
ejpam-3362	276	22	means	mean	VERB
ejpam-3362	276	23	that	that	SCONJ
ejpam-3362	276	24	lh({x	lh({x	NOUN
ejpam-3362	276	25	,	,	PUNCT
ejpam-3362	276	26	y	y	NOUN
ejpam-3362	276	27	}	}	PUNCT
ejpam-3362	276	28	)	)	PUNCT
ejpam-3362	276	29	=	=	PUNCT
ejpam-3362	276	30	{	{	PUNCT
ejpam-3362	276	31	0	0	NUM
ejpam-3362	276	32	}	}	PUNCT
ejpam-3362	276	33	,	,	PUNCT
ejpam-3362	276	34	which	which	PRON
ejpam-3362	276	35	further	far	ADV
ejpam-3362	276	36	means	mean	VERB
ejpam-3362	276	37	that	that	SCONJ
ejpam-3362	276	38	x	x	PROPN
ejpam-3362	276	39	∈	∈	PROPN
ejpam-3362	276	40	zy	zy	PROPN
ejpam-3362	276	41	.	.	PUNCT
ejpam-3362	276	42	�	�	PROPN
ejpam-3362	276	43	lemma	lemma	PROPN
ejpam-3362	276	44	1	1	X
ejpam-3362	276	45	.	.	PUNCT
ejpam-3362	277	1	let	let	VERB
ejpam-3362	277	2	f	f	NOUN
ejpam-3362	277	3	:	:	PUNCT
ejpam-3362	277	4	h1	h1	PROPN
ejpam-3362	277	5	→	→	SYM
ejpam-3362	277	6	h2	h2	PROPN
ejpam-3362	277	7	be	be	AUX
ejpam-3362	277	8	a	a	DET
ejpam-3362	277	9	hyper	hyper	ADJ
ejpam-3362	277	10	monomorphism	monomorphism	NOUN
ejpam-3362	277	11	of	of	ADP
ejpam-3362	277	12	hyper	hyper	ADJ
ejpam-3362	277	13	bci	bci	NOUN
ejpam-3362	277	14	-	-	PUNCT
ejpam-3362	277	15	algebras	algebras	X
ejpam-3362	277	16	.	.	PUNCT
ejpam-3362	278	1	then	then	ADV
ejpam-3362	278	2	for	for	ADP
ejpam-3362	278	3	any	any	DET
ejpam-3362	278	4	x	x	NOUN
ejpam-3362	278	5	,	,	PUNCT
ejpam-3362	278	6	y	y	PROPN
ejpam-3362	278	7	∈	∈	PROPN
ejpam-3362	278	8	h1	h1	PROPN
ejpam-3362	278	9	,	,	PUNCT
ejpam-3362	278	10	x	x	X
ejpam-3362	278	11	�	�	PROPN
ejpam-3362	278	12	y	y	PROPN
ejpam-3362	278	13	if	if	SCONJ
ejpam-3362	278	14	and	and	CCONJ
ejpam-3362	278	15	only	only	ADV
ejpam-3362	278	16	if	if	SCONJ
ejpam-3362	278	17	f(x	f(x	PROPN
ejpam-3362	278	18	)	)	PUNCT
ejpam-3362	278	19	�	�	PROPN
ejpam-3362	278	20	f(y	f(y	PROPN
ejpam-3362	278	21	)	)	PUNCT
ejpam-3362	278	22	.	.	PUNCT
ejpam-3362	279	1	proof	proof	NOUN
ejpam-3362	279	2	.	.	PUNCT
ejpam-3362	280	1	the	the	DET
ejpam-3362	280	2	sufficiency	sufficiency	NOUN
ejpam-3362	280	3	part	part	NOUN
ejpam-3362	280	4	is	be	AUX
ejpam-3362	280	5	done	do	VERB
ejpam-3362	280	6	by	by	ADP
ejpam-3362	280	7	theorem	theorem	NOUN
ejpam-3362	280	8	1(i	1(i	NUM
ejpam-3362	280	9	)	)	PUNCT
ejpam-3362	280	10	.	.	PUNCT
ejpam-3362	281	1	now	now	ADV
ejpam-3362	281	2	,	,	PUNCT
ejpam-3362	281	3	suppose	suppose	VERB
ejpam-3362	281	4	f(x	f(x	PROPN
ejpam-3362	281	5	)	)	PUNCT
ejpam-3362	281	6	�	�	PROPN
ejpam-3362	281	7	f(y	f(y	PROPN
ejpam-3362	281	8	)	)	PUNCT
ejpam-3362	281	9	.	.	PUNCT
ejpam-3362	282	1	then	then	ADV
ejpam-3362	282	2	02	02	NUM
ejpam-3362	282	3	∈	∈	PROPN
ejpam-3362	282	4	f(x	f(x	PROPN
ejpam-3362	282	5	)	)	PUNCT
ejpam-3362	282	6	~2	~2	NOUN
ejpam-3362	282	7	f(y	f(y	NOUN
ejpam-3362	282	8	)	)	PUNCT
ejpam-3362	283	1	=	=	SYM
ejpam-3362	283	2	f(x	f(x	PROPN
ejpam-3362	283	3	~1	~1	VERB
ejpam-3362	283	4	y	y	NOUN
ejpam-3362	283	5	)	)	PUNCT
ejpam-3362	283	6	.	.	PUNCT
ejpam-3362	284	1	thus	thus	ADV
ejpam-3362	284	2	,	,	PUNCT
ejpam-3362	284	3	01	01	NUM
ejpam-3362	284	4	=	=	PUNCT
ejpam-3362	284	5	f−1(02	f−1(02	NOUN
ejpam-3362	284	6	)	)	PUNCT
ejpam-3362	284	7	∈	∈	PROPN
ejpam-3362	284	8	f−1f(x	f−1f(x	PROPN
ejpam-3362	284	9	~1	~1	X
ejpam-3362	284	10	y	y	NOUN
ejpam-3362	284	11	)	)	PUNCT
ejpam-3362	284	12	=	=	PUNCT
ejpam-3362	284	13	x	x	NOUN
ejpam-3362	284	14	~1	~1	VERB
ejpam-3362	284	15	y.	y.	PROPN
ejpam-3362	284	16	hence	hence	ADV
ejpam-3362	284	17	,	,	PUNCT
ejpam-3362	284	18	x	x	X
ejpam-3362	284	19	�	�	PROPN
ejpam-3362	284	20	y.	y.	PROPN
ejpam-3362	284	21	�	�	PROPN
ejpam-3362	284	22	proposition	proposition	NOUN
ejpam-3362	284	23	9	9	NUM
ejpam-3362	284	24	.	.	PUNCT
ejpam-3362	285	1	let	let	VERB
ejpam-3362	285	2	f	f	NOUN
ejpam-3362	285	3	:	:	PUNCT
ejpam-3362	285	4	h1	h1	PROPN
ejpam-3362	285	5	→	→	SYM
ejpam-3362	285	6	h2	h2	PROPN
ejpam-3362	285	7	be	be	AUX
ejpam-3362	285	8	a	a	DET
ejpam-3362	285	9	hyper	hyper	ADJ
ejpam-3362	285	10	monomorphism	monomorphism	NOUN
ejpam-3362	285	11	of	of	ADP
ejpam-3362	285	12	hyper	hyper	ADJ
ejpam-3362	285	13	bci	bci	NOUN
ejpam-3362	285	14	-	-	PUNCT
ejpam-3362	285	15	algebras	algebra	NOUN
ejpam-3362	285	16	.	.	PUNCT
ejpam-3362	286	1	then	then	ADV
ejpam-3362	286	2	lh2(f(a	lh2(f(a	PROPN
ejpam-3362	286	3	)	)	PUNCT
ejpam-3362	286	4	)	)	PUNCT
ejpam-3362	287	1	=	=	PUNCT
ejpam-3362	287	2	f(lh1(a	f(lh1(a	NOUN
ejpam-3362	287	3	)	)	PUNCT
ejpam-3362	287	4	)	)	PUNCT
ejpam-3362	288	1	where	where	SCONJ
ejpam-3362	288	2	a	a	DET
ejpam-3362	288	3	⊆	⊆	NUM
ejpam-3362	288	4	h1	h1	NOUN
ejpam-3362	288	5	.	.	PUNCT
ejpam-3362	288	6	m.	m.	NOUN
ejpam-3362	288	7	panganduyon	panganduyon	NOUN
ejpam-3362	288	8	,	,	PUNCT
ejpam-3362	288	9	s.	s.	PROPN
ejpam-3362	288	10	canoy	canoy	PROPN
ejpam-3362	288	11	/	/	SYM
ejpam-3362	288	12	eur	eur	PROPN
ejpam-3362	288	13	.	.	PUNCT
ejpam-3362	289	1	j.	j.	PROPN
ejpam-3362	289	2	pure	pure	PROPN
ejpam-3362	289	3	appl	appl	PROPN
ejpam-3362	289	4	.	.	PROPN
ejpam-3362	289	5	math	math	PROPN
ejpam-3362	289	6	,	,	PUNCT
ejpam-3362	289	7	12	12	NUM
ejpam-3362	289	8	(	(	PUNCT
ejpam-3362	289	9	1	1	NUM
ejpam-3362	289	10	)	)	PUNCT
ejpam-3362	289	11	(	(	PUNCT
ejpam-3362	289	12	2019	2019	NUM
ejpam-3362	289	13	)	)	PUNCT
ejpam-3362	289	14	,	,	PUNCT
ejpam-3362	289	15	146	146	NUM
ejpam-3362	289	16	-	-	SYM
ejpam-3362	289	17	158	158	NUM
ejpam-3362	289	18	155	155	NUM
ejpam-3362	289	19	proof	proof	NOUN
ejpam-3362	289	20	.	.	PUNCT
ejpam-3362	290	1	let	let	VERB
ejpam-3362	290	2	f	f	NOUN
ejpam-3362	290	3	:	:	PUNCT
ejpam-3362	290	4	h1	h1	PROPN
ejpam-3362	290	5	→	→	SYM
ejpam-3362	290	6	h2	h2	PROPN
ejpam-3362	290	7	be	be	AUX
ejpam-3362	290	8	a	a	DET
ejpam-3362	290	9	hyper	hyper	ADJ
ejpam-3362	290	10	monomorphism	monomorphism	NOUN
ejpam-3362	290	11	.	.	PUNCT
ejpam-3362	291	1	let	let	VERB
ejpam-3362	291	2	a	a	DET
ejpam-3362	291	3	⊆	⊆	NUM
ejpam-3362	291	4	h1	h1	NOUN
ejpam-3362	291	5	.	.	PUNCT
ejpam-3362	292	1	y	y	PROPN
ejpam-3362	292	2	∈	∈	PROPN
ejpam-3362	292	3	f(lh1(a	f(lh1(a	PROPN
ejpam-3362	292	4	)	)	PUNCT
ejpam-3362	292	5	)	)	PUNCT
ejpam-3362	293	1	⇐	⇐	ADJ
ejpam-3362	293	2	⇒	⇒	PROPN
ejpam-3362	293	3	f−1(y	f−1(y	PROPN
ejpam-3362	293	4	)	)	PUNCT
ejpam-3362	293	5	∈	∈	PROPN
ejpam-3362	293	6	lh1(a	lh1(a	PROPN
ejpam-3362	293	7	)	)	PUNCT
ejpam-3362	293	8	⇐	⇐	ADJ
ejpam-3362	293	9	⇒	⇒	PROPN
ejpam-3362	293	10	f−1(y	f−1(y	PROPN
ejpam-3362	293	11	)	)	PUNCT
ejpam-3362	293	12	�	�	PROPN
ejpam-3362	293	13	a	a	PRON
ejpam-3362	293	14	for	for	ADP
ejpam-3362	293	15	all	all	DET
ejpam-3362	293	16	a	a	DET
ejpam-3362	293	17	∈	∈	NOUN
ejpam-3362	293	18	a	a	DET
ejpam-3362	293	19	⇐	⇐	ADJ
ejpam-3362	293	20	⇒	⇒	PROPN
ejpam-3362	293	21	y	y	PROPN
ejpam-3362	293	22	�	�	PROPN
ejpam-3362	293	23	f(a	f(a	PROPN
ejpam-3362	293	24	)	)	PUNCT
ejpam-3362	293	25	for	for	ADP
ejpam-3362	293	26	all	all	DET
ejpam-3362	293	27	a	a	DET
ejpam-3362	293	28	∈	∈	PROPN
ejpam-3362	293	29	a	a	PRON
ejpam-3362	293	30	,	,	PUNCT
ejpam-3362	293	31	by	by	ADP
ejpam-3362	293	32	lemma	lemma	PROPN
ejpam-3362	293	33	1	1	NUM
ejpam-3362	293	34	⇐	⇐	PROPN
ejpam-3362	293	35	⇒	⇒	PROPN
ejpam-3362	293	36	y	y	PROPN
ejpam-3362	293	37	∈	∈	PROPN
ejpam-3362	293	38	lh2(f(a	lh2(f(a	NOUN
ejpam-3362	293	39	)	)	PUNCT
ejpam-3362	293	40	)	)	PUNCT
ejpam-3362	293	41	therefore	therefore	ADV
ejpam-3362	293	42	,	,	PUNCT
ejpam-3362	293	43	lh2(f(a	lh2(f(a	NOUN
ejpam-3362	293	44	)	)	PUNCT
ejpam-3362	293	45	)	)	PUNCT
ejpam-3362	293	46	=	=	PUNCT
ejpam-3362	293	47	f(lh1(a	f(lh1(a	NOUN
ejpam-3362	293	48	)	)	PUNCT
ejpam-3362	293	49	)	)	PUNCT
ejpam-3362	293	50	.	.	PUNCT
ejpam-3362	294	1	�	�	PROPN
ejpam-3362	294	2	theorem	theorem	VERB
ejpam-3362	294	3	3	3	X
ejpam-3362	294	4	.	.	PUNCT
ejpam-3362	295	1	let	let	VERB
ejpam-3362	295	2	h1	h1	VERB
ejpam-3362	295	3	and	and	CCONJ
ejpam-3362	295	4	h2	h2	NOUN
ejpam-3362	295	5	be	be	AUX
ejpam-3362	295	6	hyper	hyper	ADJ
ejpam-3362	295	7	bci	bci	NOUN
ejpam-3362	295	8	-	-	PUNCT
ejpam-3362	295	9	algebras	algebra	NOUN
ejpam-3362	295	10	.	.	PUNCT
ejpam-3362	296	1	if	if	SCONJ
ejpam-3362	296	2	h1	h1	PROPN
ejpam-3362	296	3	∼=h	∼=h	ADJ
ejpam-3362	296	4	h2	h2	PROPN
ejpam-3362	296	5	,	,	PUNCT
ejpam-3362	296	6	then	then	ADV
ejpam-3362	296	7	γ(h1	γ(h1	NOUN
ejpam-3362	296	8	)	)	PUNCT
ejpam-3362	296	9	∼=	∼=	PART
ejpam-3362	296	10	γ(h2	γ(h2	NOUN
ejpam-3362	296	11	)	)	PUNCT
ejpam-3362	296	12	.	.	PUNCT
ejpam-3362	297	1	proof	proof	NOUN
ejpam-3362	297	2	.	.	PUNCT
ejpam-3362	298	1	suppose	suppose	VERB
ejpam-3362	298	2	h1	h1	PROPN
ejpam-3362	298	3	∼=h	∼=h	ADJ
ejpam-3362	298	4	h2	h2	PROPN
ejpam-3362	298	5	,	,	PUNCT
ejpam-3362	298	6	say	say	VERB
ejpam-3362	298	7	f	f	X
ejpam-3362	298	8	:	:	PUNCT
ejpam-3362	298	9	h1	h1	PROPN
ejpam-3362	298	10	→	→	SYM
ejpam-3362	298	11	h2	h2	PROPN
ejpam-3362	298	12	is	be	AUX
ejpam-3362	298	13	a	a	DET
ejpam-3362	298	14	hyper	hyper	ADJ
ejpam-3362	298	15	isomorphism	isomorphism	NOUN
ejpam-3362	298	16	.	.	PUNCT
ejpam-3362	299	1	since	since	SCONJ
ejpam-3362	299	2	v	v	NOUN
ejpam-3362	299	3	(	(	PUNCT
ejpam-3362	299	4	γ(h1	γ(h1	NOUN
ejpam-3362	299	5	)	)	PUNCT
ejpam-3362	299	6	)	)	PUNCT
ejpam-3362	300	1	=	=	PRON
ejpam-3362	300	2	h1	h1	NOUN
ejpam-3362	300	3	and	and	CCONJ
ejpam-3362	300	4	v	v	NOUN
ejpam-3362	300	5	(	(	PUNCT
ejpam-3362	300	6	γ(h2	γ(h2	NOUN
ejpam-3362	300	7	)	)	PUNCT
ejpam-3362	300	8	)	)	PUNCT
ejpam-3362	301	1	=	=	SYM
ejpam-3362	301	2	h2	h2	NOUN
ejpam-3362	301	3	,	,	PUNCT
ejpam-3362	301	4	there	there	PRON
ejpam-3362	301	5	exists	exist	VERB
ejpam-3362	301	6	a	a	DET
ejpam-3362	301	7	one	one	NUM
ejpam-3362	301	8	-	-	PUNCT
ejpam-3362	301	9	to	to	ADP
ejpam-3362	301	10	-	-	PUNCT
ejpam-3362	301	11	one	one	NUM
ejpam-3362	301	12	correspondence	correspondence	NOUN
ejpam-3362	301	13	between	between	ADP
ejpam-3362	301	14	the	the	DET
ejpam-3362	301	15	vertex	vertex	NOUN
ejpam-3362	301	16	sets	set	NOUN
ejpam-3362	301	17	.	.	PUNCT
ejpam-3362	302	1	note	note	VERB
ejpam-3362	302	2	that	that	SCONJ
ejpam-3362	302	3	for	for	ADP
ejpam-3362	302	4	any	any	DET
ejpam-3362	302	5	distinct	distinct	ADJ
ejpam-3362	302	6	elements	element	NOUN
ejpam-3362	302	7	x	x	X
ejpam-3362	302	8	,	,	PUNCT
ejpam-3362	302	9	y	y	PROPN
ejpam-3362	302	10	∈	∈	PROPN
ejpam-3362	302	11	h1	h1	PROPN
ejpam-3362	302	12	,	,	PUNCT
ejpam-3362	302	13	xy	xy	PROPN
ejpam-3362	302	14	∈	∈	PROPN
ejpam-3362	302	15	e(γ(h1	e(γ(h1	PROPN
ejpam-3362	302	16	)	)	PUNCT
ejpam-3362	302	17	)	)	PUNCT
ejpam-3362	303	1	if	if	SCONJ
ejpam-3362	303	2	and	and	CCONJ
ejpam-3362	303	3	only	only	ADV
ejpam-3362	303	4	if	if	SCONJ
ejpam-3362	303	5	lh1({x	lh1({x	PROPN
ejpam-3362	303	6	,	,	PUNCT
ejpam-3362	303	7	y	y	NOUN
ejpam-3362	303	8	}	}	PUNCT
ejpam-3362	303	9	)	)	PUNCT
ejpam-3362	304	1	=	=	PUNCT
ejpam-3362	304	2	{	{	PUNCT
ejpam-3362	304	3	0	0	NUM
ejpam-3362	304	4	}	}	PUNCT
ejpam-3362	304	5	.	.	PUNCT
ejpam-3362	305	1	by	by	ADP
ejpam-3362	305	2	proposition	proposition	NOUN
ejpam-3362	305	3	9	9	NUM
ejpam-3362	305	4	,	,	PUNCT
ejpam-3362	305	5	xy	xy	PROPN
ejpam-3362	305	6	∈	∈	PROPN
ejpam-3362	305	7	e(γ(h1	e(γ(h1	PROPN
ejpam-3362	305	8	)	)	PUNCT
ejpam-3362	305	9	)	)	PUNCT
ejpam-3362	306	1	if	if	SCONJ
ejpam-3362	306	2	and	and	CCONJ
ejpam-3362	306	3	only	only	ADV
ejpam-3362	306	4	if	if	SCONJ
ejpam-3362	306	5	lh2({f(x	lh2({f(x	PROPN
ejpam-3362	306	6	)	)	PUNCT
ejpam-3362	306	7	,	,	PUNCT
ejpam-3362	306	8	f(y	f(y	NOUN
ejpam-3362	306	9	)	)	PUNCT
ejpam-3362	306	10	}	}	PUNCT
ejpam-3362	306	11	)	)	PUNCT
ejpam-3362	307	1	=	=	PRON
ejpam-3362	307	2	{	{	PUNCT
ejpam-3362	307	3	0	0	NUM
ejpam-3362	307	4	}	}	PUNCT
ejpam-3362	307	5	.	.	PUNCT
ejpam-3362	308	1	thus	thus	ADV
ejpam-3362	308	2	,	,	PUNCT
ejpam-3362	308	3	xy	xy	PROPN
ejpam-3362	308	4	∈	∈	PROPN
ejpam-3362	308	5	e(γ(h1	e(γ(h1	PROPN
ejpam-3362	308	6	)	)	PUNCT
ejpam-3362	308	7	)	)	PUNCT
ejpam-3362	309	1	if	if	SCONJ
ejpam-3362	309	2	and	and	CCONJ
ejpam-3362	309	3	only	only	ADV
ejpam-3362	309	4	if	if	SCONJ
ejpam-3362	309	5	f(x)f(y	f(x)f(y	NOUN
ejpam-3362	309	6	)	)	PUNCT
ejpam-3362	309	7	∈	∈	PROPN
ejpam-3362	309	8	e(γ(h2	e(γ(h2	NOUN
ejpam-3362	309	9	)	)	PUNCT
ejpam-3362	309	10	)	)	PUNCT
ejpam-3362	309	11	.	.	PUNCT
ejpam-3362	310	1	consequently	consequently	ADV
ejpam-3362	310	2	,	,	PUNCT
ejpam-3362	310	3	γ(h1	γ(h1	NOUN
ejpam-3362	310	4	)	)	PUNCT
ejpam-3362	310	5	∼=	∼=	NOUN
ejpam-3362	310	6	γ(h2	γ(h2	NOUN
ejpam-3362	310	7	)	)	PUNCT
ejpam-3362	310	8	.	.	PUNCT
ejpam-3362	311	1	�	�	PROPN
ejpam-3362	311	2	3.1	3.1	NUM
ejpam-3362	311	3	.	.	PUNCT
ejpam-3362	312	1	on	on	ADP
ejpam-3362	312	2	zero	zero	NUM
ejpam-3362	312	3	divisor	divisor	NOUN
ejpam-3362	312	4	graphs	graph	NOUN
ejpam-3362	312	5	involving	involve	VERB
ejpam-3362	312	6	hyperatoms	hyperatom	NOUN
ejpam-3362	312	7	definition	definition	NOUN
ejpam-3362	312	8	1	1	NUM
ejpam-3362	312	9	.	.	PUNCT
ejpam-3362	313	1	an	an	DET
ejpam-3362	313	2	element	element	NOUN
ejpam-3362	313	3	a	a	PRON
ejpam-3362	313	4	of	of	ADP
ejpam-3362	313	5	a	a	DET
ejpam-3362	313	6	hyper	hyper	ADJ
ejpam-3362	313	7	bci	bci	NOUN
ejpam-3362	313	8	-	-	ADJ
ejpam-3362	313	9	algebra	algebra	NOUN
ejpam-3362	313	10	h	h	NOUN
ejpam-3362	313	11	is	be	AUX
ejpam-3362	313	12	called	call	VERB
ejpam-3362	313	13	a	a	DET
ejpam-3362	313	14	hyperatom	hyperatom	NOUN
ejpam-3362	313	15	if	if	SCONJ
ejpam-3362	313	16	for	for	ADP
ejpam-3362	313	17	each	each	DET
ejpam-3362	313	18	x	x	SYM
ejpam-3362	313	19	∈	∈	PROPN
ejpam-3362	313	20	h	h	NOUN
ejpam-3362	313	21	,	,	PUNCT
ejpam-3362	313	22	x	x	PRON
ejpam-3362	313	23	�	�	PROPN
ejpam-3362	314	1	a	a	PRON
ejpam-3362	314	2	implies	imply	VERB
ejpam-3362	314	3	x	x	PUNCT
ejpam-3362	314	4	=	=	SYM
ejpam-3362	314	5	0	0	NUM
ejpam-3362	314	6	or	or	CCONJ
ejpam-3362	314	7	x	x	X
ejpam-3362	314	8	=	=	NOUN
ejpam-3362	314	9	a.	a.	NOUN
ejpam-3362	314	10	denote	denote	NOUN
ejpam-3362	314	11	by	by	ADP
ejpam-3362	314	12	a(h	a(h	PROPN
ejpam-3362	314	13	)	)	PUNCT
ejpam-3362	314	14	the	the	DET
ejpam-3362	314	15	set	set	NOUN
ejpam-3362	314	16	of	of	ADP
ejpam-3362	314	17	all	all	DET
ejpam-3362	314	18	hyperatoms	hyperatom	NOUN
ejpam-3362	314	19	of	of	ADP
ejpam-3362	314	20	h	h	NOUN
ejpam-3362	314	21	,	,	PUNCT
ejpam-3362	314	22	and	and	CCONJ
ejpam-3362	314	23	by	by	ADP
ejpam-3362	314	24	a∗(h	a∗(h	PROPN
ejpam-3362	314	25	)	)	PUNCT
ejpam-3362	314	26	the	the	DET
ejpam-3362	314	27	set	set	NOUN
ejpam-3362	314	28	of	of	ADP
ejpam-3362	314	29	all	all	DET
ejpam-3362	314	30	nonzero	nonzero	PROPN
ejpam-3362	314	31	hyperatoms	hyperatom	NOUN
ejpam-3362	314	32	of	of	ADP
ejpam-3362	314	33	h	h	NOUN
ejpam-3362	314	34	;	;	PUNCT
ejpam-3362	314	35	i.e.	i.e.	X
ejpam-3362	314	36	,	,	PUNCT
ejpam-3362	314	37	a∗(h	a∗(h	PROPN
ejpam-3362	314	38	)	)	PUNCT
ejpam-3362	314	39	=	=	SYM
ejpam-3362	314	40	a(h	a(h	PROPN
ejpam-3362	314	41	)	)	PUNCT
ejpam-3362	314	42	\	\	NOUN
ejpam-3362	314	43	{	{	PUNCT
ejpam-3362	314	44	0	0	NUM
ejpam-3362	314	45	}	}	PUNCT
ejpam-3362	314	46	.	.	PUNCT
ejpam-3362	315	1	obviously	obviously	ADV
ejpam-3362	315	2	,	,	PUNCT
ejpam-3362	315	3	0	0	NUM
ejpam-3362	315	4	∈	∈	PROPN
ejpam-3362	315	5	a(h	a(h	PROPN
ejpam-3362	315	6	)	)	PUNCT
ejpam-3362	315	7	.	.	PUNCT
ejpam-3362	316	1	definition	definition	NOUN
ejpam-3362	316	2	2	2	NUM
ejpam-3362	316	3	.	.	PUNCT
ejpam-3362	317	1	a	a	DET
ejpam-3362	317	2	hyper	hyper	ADJ
ejpam-3362	317	3	bci	bci	NOUN
ejpam-3362	317	4	-	-	ADJ
ejpam-3362	317	5	algebra	algebra	NOUN
ejpam-3362	317	6	h	h	NOUN
ejpam-3362	317	7	is	be	AUX
ejpam-3362	317	8	said	say	VERB
ejpam-3362	317	9	to	to	PART
ejpam-3362	317	10	be	be	AUX
ejpam-3362	317	11	hyperatomic	hyperatomic	ADJ
ejpam-3362	317	12	if	if	SCONJ
ejpam-3362	317	13	each	each	DET
ejpam-3362	317	14	element	element	NOUN
ejpam-3362	317	15	of	of	ADP
ejpam-3362	317	16	h	h	NOUN
ejpam-3362	317	17	is	be	AUX
ejpam-3362	317	18	a	a	DET
ejpam-3362	317	19	hyperatom	hyperatom	NOUN
ejpam-3362	317	20	,	,	PUNCT
ejpam-3362	317	21	that	that	ADV
ejpam-3362	317	22	is	is	ADV
ejpam-3362	317	23	,	,	PUNCT
ejpam-3362	317	24	a(h	a(h	PROPN
ejpam-3362	317	25	)	)	PUNCT
ejpam-3362	317	26	=	=	SYM
ejpam-3362	317	27	h.	h.	PROPN
ejpam-3362	317	28	remark	remark	NOUN
ejpam-3362	317	29	3	3	NUM
ejpam-3362	317	30	.	.	PUNCT
ejpam-3362	318	1	a	a	DET
ejpam-3362	318	2	hyper	hyper	ADJ
ejpam-3362	318	3	bci	bci	NOUN
ejpam-3362	318	4	-	-	ADJ
ejpam-3362	318	5	algebra	algebra	NOUN
ejpam-3362	318	6	h	h	NOUN
ejpam-3362	318	7	is	be	AUX
ejpam-3362	318	8	hyperatomic	hyperatomic	ADJ
ejpam-3362	318	9	if	if	SCONJ
ejpam-3362	318	10	and	and	CCONJ
ejpam-3362	318	11	only	only	ADV
ejpam-3362	318	12	if	if	SCONJ
ejpam-3362	318	13	lh(x	lh(x	PUNCT
ejpam-3362	318	14	)	)	PUNCT
ejpam-3362	318	15	=	=	SYM
ejpam-3362	319	1	{	{	PUNCT
ejpam-3362	319	2	x	x	NOUN
ejpam-3362	319	3	}	}	PUNCT
ejpam-3362	319	4	or	or	CCONJ
ejpam-3362	319	5	lh(x	lh(x	PUNCT
ejpam-3362	319	6	)	)	PUNCT
ejpam-3362	320	1	=	=	SYM
ejpam-3362	320	2	{	{	PUNCT
ejpam-3362	320	3	0	0	NUM
ejpam-3362	320	4	,	,	PUNCT
ejpam-3362	320	5	x	x	NOUN
ejpam-3362	320	6	}	}	PUNCT
ejpam-3362	320	7	for	for	ADP
ejpam-3362	320	8	each	each	DET
ejpam-3362	320	9	x	x	SYM
ejpam-3362	320	10	∈	∈	PROPN
ejpam-3362	320	11	h.	h.	PROPN
ejpam-3362	320	12	remark	remark	PROPN
ejpam-3362	320	13	4	4	NUM
ejpam-3362	320	14	.	.	PUNCT
ejpam-3362	321	1	a	a	DET
ejpam-3362	321	2	hyperatomic	hyperatomic	ADJ
ejpam-3362	321	3	hyper	hyper	ADJ
ejpam-3362	321	4	bci	bci	NOUN
ejpam-3362	321	5	-	-	NOUN
ejpam-3362	321	6	algebra	algebra	NOUN
ejpam-3362	321	7	is	be	AUX
ejpam-3362	321	8	ordered	order	VERB
ejpam-3362	321	9	.	.	PUNCT
ejpam-3362	322	1	proof	proof	NOUN
ejpam-3362	322	2	.	.	PUNCT
ejpam-3362	323	1	suppose	suppose	VERB
ejpam-3362	323	2	h	h	NOUN
ejpam-3362	323	3	is	be	AUX
ejpam-3362	323	4	a	a	DET
ejpam-3362	323	5	hyperatomic	hyperatomic	ADJ
ejpam-3362	323	6	hyper	hyper	ADJ
ejpam-3362	323	7	bci	bci	NOUN
ejpam-3362	323	8	-	-	NOUN
ejpam-3362	323	9	algebra	algebra	NOUN
ejpam-3362	323	10	.	.	PUNCT
ejpam-3362	324	1	let	let	VERB
ejpam-3362	324	2	x	x	PRON
ejpam-3362	324	3	,	,	PUNCT
ejpam-3362	324	4	y	y	PROPN
ejpam-3362	324	5	,	,	PUNCT
ejpam-3362	324	6	z	z	PROPN
ejpam-3362	324	7	∈	∈	PROPN
ejpam-3362	324	8	h	h	NOUN
ejpam-3362	324	9	such	such	ADJ
ejpam-3362	324	10	that	that	SCONJ
ejpam-3362	324	11	x	x	SYM
ejpam-3362	324	12	�	�	PROPN
ejpam-3362	324	13	y	y	PROPN
ejpam-3362	324	14	and	and	CCONJ
ejpam-3362	324	15	y	y	PROPN
ejpam-3362	324	16	�	�	PROPN
ejpam-3362	324	17	z.	z.	PROPN
ejpam-3362	324	18	then	then	ADV
ejpam-3362	324	19	by	by	ADP
ejpam-3362	324	20	remark	remark	NOUN
ejpam-3362	324	21	3	3	NUM
ejpam-3362	324	22	,	,	PUNCT
ejpam-3362	324	23	lh(z	lh(z	PUNCT
ejpam-3362	324	24	)	)	PUNCT
ejpam-3362	324	25	=	=	SYM
ejpam-3362	325	1	{	{	PUNCT
ejpam-3362	325	2	z	z	NOUN
ejpam-3362	325	3	}	}	PUNCT
ejpam-3362	325	4	or	or	CCONJ
ejpam-3362	325	5	lh(z	lh(z	NOUN
ejpam-3362	325	6	)	)	PUNCT
ejpam-3362	325	7	=	=	SYM
ejpam-3362	325	8	{	{	PUNCT
ejpam-3362	325	9	0	0	NUM
ejpam-3362	325	10	,	,	PUNCT
ejpam-3362	325	11	z	z	NOUN
ejpam-3362	325	12	}	}	PUNCT
ejpam-3362	325	13	.	.	PUNCT
ejpam-3362	326	1	thus	thus	ADV
ejpam-3362	326	2	,	,	PUNCT
ejpam-3362	326	3	y	y	PROPN
ejpam-3362	326	4	�	�	PROPN
ejpam-3362	326	5	z	z	PROPN
ejpam-3362	326	6	implies	imply	VERB
ejpam-3362	326	7	that	that	SCONJ
ejpam-3362	326	8	y	y	PROPN
ejpam-3362	326	9	=	=	SYM
ejpam-3362	326	10	0	0	PROPN
ejpam-3362	326	11	or	or	CCONJ
ejpam-3362	326	12	y	y	PROPN
ejpam-3362	326	13	=	=	PUNCT
ejpam-3362	326	14	z.	z.	PROPN
ejpam-3362	327	1	if	if	SCONJ
ejpam-3362	327	2	y	y	PROPN
ejpam-3362	327	3	=	=	SYM
ejpam-3362	327	4	0	0	PROPN
ejpam-3362	327	5	,	,	PUNCT
ejpam-3362	327	6	then	then	ADV
ejpam-3362	327	7	x	x	PART
ejpam-3362	327	8	�	�	PROPN
ejpam-3362	327	9	0	0	PUNCT
ejpam-3362	327	10	since	since	SCONJ
ejpam-3362	327	11	x	x	PROPN
ejpam-3362	327	12	�	�	PROPN
ejpam-3362	327	13	y.	y.	PROPN
ejpam-3362	327	14	by	by	ADP
ejpam-3362	327	15	proposition	proposition	NOUN
ejpam-3362	327	16	1	1	NUM
ejpam-3362	327	17	,	,	PUNCT
ejpam-3362	327	18	x	x	PUNCT
ejpam-3362	327	19	=	=	PUNCT
ejpam-3362	327	20	0	0	X
ejpam-3362	327	21	.	.	PUNCT
ejpam-3362	328	1	since	since	SCONJ
ejpam-3362	328	2	0	0	NUM
ejpam-3362	328	3	�	�	PROPN
ejpam-3362	328	4	z	z	PROPN
ejpam-3362	328	5	and	and	CCONJ
ejpam-3362	328	6	x	x	SYM
ejpam-3362	328	7	=	=	SYM
ejpam-3362	328	8	0	0	NUM
ejpam-3362	328	9	,	,	PUNCT
ejpam-3362	328	10	we	we	PRON
ejpam-3362	328	11	have	have	VERB
ejpam-3362	328	12	x	x	X
ejpam-3362	328	13	�	�	PROPN
ejpam-3362	328	14	z.	z.	PROPN
ejpam-3362	329	1	if	if	SCONJ
ejpam-3362	329	2	y	y	PROPN
ejpam-3362	329	3	=	=	SYM
ejpam-3362	329	4	z	z	PROPN
ejpam-3362	329	5	,	,	PUNCT
ejpam-3362	329	6	then	then	ADV
ejpam-3362	329	7	the	the	DET
ejpam-3362	329	8	assumption	assumption	NOUN
ejpam-3362	329	9	x	x	PRON
ejpam-3362	329	10	�	�	PROPN
ejpam-3362	329	11	y	y	PROPN
ejpam-3362	329	12	implies	imply	VERB
ejpam-3362	329	13	that	that	SCONJ
ejpam-3362	329	14	x	x	X
ejpam-3362	329	15	�	�	PROPN
ejpam-3362	329	16	z.	z.	PROPN
ejpam-3362	329	17	hence	hence	ADV
ejpam-3362	329	18	,	,	PUNCT
ejpam-3362	329	19	h	h	PROPN
ejpam-3362	329	20	is	be	AUX
ejpam-3362	329	21	ordered	order	VERB
ejpam-3362	329	22	.	.	PUNCT
ejpam-3362	330	1	�	�	PROPN
ejpam-3362	330	2	example	example	NOUN
ejpam-3362	330	3	5	5	NUM
ejpam-3362	330	4	.	.	PUNCT
ejpam-3362	330	5	consider	consider	VERB
ejpam-3362	330	6	the	the	DET
ejpam-3362	330	7	hyper	hyper	ADJ
ejpam-3362	330	8	bci	bci	NOUN
ejpam-3362	330	9	-	-	ADJ
ejpam-3362	330	10	algebra	algebra	NOUN
ejpam-3362	330	11	defined	define	VERB
ejpam-3362	330	12	by	by	ADP
ejpam-3362	330	13	the	the	DET
ejpam-3362	330	14	cayley	cayley	ADJ
ejpam-3362	330	15	table	table	NOUN
ejpam-3362	330	16	:	:	PUNCT
ejpam-3362	330	17	~	~	PUNCT
ejpam-3362	330	18	0	0	NUM
ejpam-3362	331	1	1	1	NUM
ejpam-3362	331	2	2	2	NUM
ejpam-3362	331	3	0	0	NUM
ejpam-3362	331	4	{	{	PUNCT
ejpam-3362	331	5	0	0	NUM
ejpam-3362	331	6	}	}	PUNCT
ejpam-3362	331	7	{	{	PUNCT
ejpam-3362	331	8	0	0	NUM
ejpam-3362	331	9	,	,	PUNCT
ejpam-3362	331	10	1	1	NUM
ejpam-3362	331	11	}	}	PUNCT
ejpam-3362	331	12	{	{	PUNCT
ejpam-3362	331	13	0	0	NUM
ejpam-3362	331	14	,	,	PUNCT
ejpam-3362	331	15	1	1	NUM
ejpam-3362	331	16	}	}	SYM
ejpam-3362	331	17	1	1	NUM
ejpam-3362	331	18	{	{	PUNCT
ejpam-3362	331	19	1	1	NUM
ejpam-3362	331	20	}	}	PUNCT
ejpam-3362	331	21	{	{	PUNCT
ejpam-3362	331	22	0	0	NUM
ejpam-3362	331	23	,	,	PUNCT
ejpam-3362	331	24	1	1	NUM
ejpam-3362	331	25	}	}	PUNCT
ejpam-3362	331	26	{	{	PUNCT
ejpam-3362	331	27	1	1	NUM
ejpam-3362	331	28	}	}	SYM
ejpam-3362	331	29	2	2	NUM
ejpam-3362	331	30	{	{	PUNCT
ejpam-3362	331	31	2	2	NUM
ejpam-3362	331	32	}	}	PUNCT
ejpam-3362	331	33	{	{	PUNCT
ejpam-3362	331	34	2	2	NUM
ejpam-3362	331	35	}	}	PUNCT
ejpam-3362	331	36	{	{	PUNCT
ejpam-3362	331	37	0	0	NUM
ejpam-3362	331	38	,	,	PUNCT
ejpam-3362	331	39	1	1	NUM
ejpam-3362	331	40	,	,	PUNCT
ejpam-3362	331	41	2	2	NUM
ejpam-3362	331	42	}	}	PUNCT
ejpam-3362	331	43	m.	m.	NOUN
ejpam-3362	331	44	panganduyon	panganduyon	NOUN
ejpam-3362	331	45	,	,	PUNCT
ejpam-3362	331	46	s.	s.	PROPN
ejpam-3362	331	47	canoy	canoy	PROPN
ejpam-3362	331	48	/	/	SYM
ejpam-3362	331	49	eur	eur	PROPN
ejpam-3362	331	50	.	.	PUNCT
ejpam-3362	332	1	j.	j.	PROPN
ejpam-3362	332	2	pure	pure	PROPN
ejpam-3362	332	3	appl	appl	PROPN
ejpam-3362	332	4	.	.	PROPN
ejpam-3362	332	5	math	math	PROPN
ejpam-3362	332	6	,	,	PUNCT
ejpam-3362	332	7	12	12	NUM
ejpam-3362	332	8	(	(	PUNCT
ejpam-3362	332	9	1	1	NUM
ejpam-3362	332	10	)	)	PUNCT
ejpam-3362	332	11	(	(	PUNCT
ejpam-3362	332	12	2019	2019	NUM
ejpam-3362	332	13	)	)	PUNCT
ejpam-3362	332	14	,	,	PUNCT
ejpam-3362	332	15	146	146	NUM
ejpam-3362	332	16	-	-	SYM
ejpam-3362	332	17	158	158	NUM
ejpam-3362	332	18	156	156	NUM
ejpam-3362	332	19	h	h	NOUN
ejpam-3362	332	20	is	be	AUX
ejpam-3362	332	21	hyperatomic	hyperatomic	ADJ
ejpam-3362	332	22	since	since	SCONJ
ejpam-3362	332	23	all	all	DET
ejpam-3362	332	24	its	its	PRON
ejpam-3362	332	25	elements	element	NOUN
ejpam-3362	332	26	are	be	AUX
ejpam-3362	332	27	hyperatoms	hyperatom	NOUN
ejpam-3362	332	28	.	.	PUNCT
ejpam-3362	333	1	example	example	NOUN
ejpam-3362	333	2	6	6	NUM
ejpam-3362	333	3	.	.	PUNCT
ejpam-3362	334	1	the	the	DET
ejpam-3362	334	2	hyper	hyper	ADJ
ejpam-3362	334	3	bci	bci	NOUN
ejpam-3362	334	4	-	-	ADJ
ejpam-3362	334	5	algebra	algebra	ADJ
ejpam-3362	334	6	h	h	NOUN
ejpam-3362	334	7	in	in	ADP
ejpam-3362	334	8	example	example	NOUN
ejpam-3362	334	9	1	1	NUM
ejpam-3362	334	10	is	be	AUX
ejpam-3362	334	11	not	not	PART
ejpam-3362	334	12	hyperatomic	hyperatomic	ADJ
ejpam-3362	334	13	since	since	SCONJ
ejpam-3362	334	14	2	2	NUM
ejpam-3362	334	15	is	be	AUX
ejpam-3362	334	16	not	not	PART
ejpam-3362	334	17	a	a	DET
ejpam-3362	334	18	hyperatom	hyperatom	NOUN
ejpam-3362	334	19	of	of	ADP
ejpam-3362	334	20	h	h	NOUN
ejpam-3362	334	21	:	:	PUNCT
ejpam-3362	334	22	∃x	∃x	ADJ
ejpam-3362	334	23	=	=	SYM
ejpam-3362	334	24	1	1	NUM
ejpam-3362	334	25	∈	∈	NOUN
ejpam-3362	334	26	h	h	NOUN
ejpam-3362	334	27	with	with	ADP
ejpam-3362	334	28	1	1	NUM
ejpam-3362	334	29	�	�	SYM
ejpam-3362	334	30	2	2	NUM
ejpam-3362	334	31	but	but	CCONJ
ejpam-3362	334	32	x	x	X
ejpam-3362	335	1	=	=	SYM
ejpam-3362	335	2	1	1	NUM
ejpam-3362	335	3	6=	6=	NUM
ejpam-3362	335	4	0	0	NUM
ejpam-3362	335	5	and	and	CCONJ
ejpam-3362	335	6	x	x	SYM
ejpam-3362	335	7	=	=	SYM
ejpam-3362	335	8	1	1	NUM
ejpam-3362	335	9	6=	6=	NUM
ejpam-3362	335	10	2	2	NUM
ejpam-3362	335	11	.	.	PUNCT
ejpam-3362	335	12	however	however	ADV
ejpam-3362	335	13	,	,	PUNCT
ejpam-3362	335	14	the	the	DET
ejpam-3362	335	15	hyper	hyper	ADJ
ejpam-3362	335	16	bci	bci	NOUN
ejpam-3362	335	17	-	-	ADJ
ejpam-3362	335	18	algebra	algebra	ADJ
ejpam-3362	335	19	h	h	NOUN
ejpam-3362	335	20	in	in	ADP
ejpam-3362	335	21	example	example	NOUN
ejpam-3362	335	22	3	3	NUM
ejpam-3362	335	23	is	be	AUX
ejpam-3362	335	24	hyperatomic	hyperatomic	ADJ
ejpam-3362	335	25	.	.	PUNCT
ejpam-3362	336	1	proposition	proposition	NOUN
ejpam-3362	336	2	10	10	NUM
ejpam-3362	336	3	.	.	PUNCT
ejpam-3362	337	1	let	let	VERB
ejpam-3362	337	2	h	h	PRON
ejpam-3362	337	3	be	be	AUX
ejpam-3362	337	4	a	a	DET
ejpam-3362	337	5	hyper	hyper	ADJ
ejpam-3362	337	6	bci	bci	NOUN
ejpam-3362	337	7	-	-	NOUN
ejpam-3362	337	8	algebra	algebra	NOUN
ejpam-3362	337	9	such	such	ADJ
ejpam-3362	337	10	that	that	SCONJ
ejpam-3362	337	11	|h|	|h|	PROPN
ejpam-3362	337	12	≥	≥	NOUN
ejpam-3362	337	13	2	2	NUM
ejpam-3362	337	14	.	.	PUNCT
ejpam-3362	338	1	if	if	SCONJ
ejpam-3362	338	2	x	x	PRON
ejpam-3362	338	3	and	and	CCONJ
ejpam-3362	338	4	y	y	PROPN
ejpam-3362	338	5	are	be	AUX
ejpam-3362	338	6	distinct	distinct	ADJ
ejpam-3362	338	7	nonzero	nonzero	ADJ
ejpam-3362	338	8	hyperatoms	hyperatom	NOUN
ejpam-3362	338	9	of	of	ADP
ejpam-3362	338	10	h	h	NOUN
ejpam-3362	338	11	,	,	PUNCT
ejpam-3362	338	12	then	then	ADV
ejpam-3362	338	13	lh({x	lh({x	NOUN
ejpam-3362	338	14	,	,	PUNCT
ejpam-3362	338	15	y	y	NOUN
ejpam-3362	338	16	}	}	PUNCT
ejpam-3362	338	17	)	)	PUNCT
ejpam-3362	339	1	=	=	PUNCT
ejpam-3362	339	2	{	{	PUNCT
ejpam-3362	339	3	0	0	NUM
ejpam-3362	339	4	}	}	PUNCT
ejpam-3362	339	5	or	or	CCONJ
ejpam-3362	339	6	∅.	∅.	PRON
ejpam-3362	339	7	proof	proof	NOUN
ejpam-3362	339	8	.	.	PUNCT
ejpam-3362	340	1	the	the	DET
ejpam-3362	340	2	result	result	NOUN
ejpam-3362	340	3	depends	depend	VERB
ejpam-3362	340	4	on	on	ADP
ejpam-3362	340	5	whether	whether	SCONJ
ejpam-3362	340	6	or	or	CCONJ
ejpam-3362	340	7	not	not	PART
ejpam-3362	340	8	0	0	NUM
ejpam-3362	340	9	∈	∈	NOUN
ejpam-3362	340	10	lh(x	lh(x	NOUN
ejpam-3362	340	11	)	)	PUNCT
ejpam-3362	340	12	for	for	ADP
ejpam-3362	340	13	all	all	DET
ejpam-3362	340	14	x	x	SYM
ejpam-3362	340	15	∈	∈	PROPN
ejpam-3362	340	16	h.	h.	NOUN
ejpam-3362	341	1	if	if	SCONJ
ejpam-3362	341	2	0	0	NUM
ejpam-3362	341	3	/∈	/∈	INTJ
ejpam-3362	341	4	lh(x	lh(x	NOUN
ejpam-3362	341	5	)	)	PUNCT
ejpam-3362	341	6	,	,	PUNCT
ejpam-3362	341	7	then	then	ADV
ejpam-3362	341	8	lh(x	lh(x	PUNCT
ejpam-3362	341	9	)	)	PUNCT
ejpam-3362	342	1	=	=	PRON
ejpam-3362	342	2	{	{	PUNCT
ejpam-3362	342	3	x	x	NOUN
ejpam-3362	342	4	}	}	PUNCT
ejpam-3362	342	5	.	.	PUNCT
ejpam-3362	343	1	hence	hence	ADV
ejpam-3362	343	2	,	,	PUNCT
ejpam-3362	343	3	lh({x	lh({x	PRON
ejpam-3362	343	4	,	,	PUNCT
ejpam-3362	343	5	y	y	NOUN
ejpam-3362	343	6	}	}	PUNCT
ejpam-3362	343	7	)	)	PUNCT
ejpam-3362	344	1	=	=	PUNCT
ejpam-3362	344	2	∅.	∅.	VERB
ejpam-3362	344	3	if	if	SCONJ
ejpam-3362	344	4	0	0	NUM
ejpam-3362	344	5	∈	∈	PROPN
ejpam-3362	344	6	lh({x	lh({x	NOUN
ejpam-3362	344	7	}	}	PUNCT
ejpam-3362	344	8	)	)	PUNCT
ejpam-3362	344	9	,	,	PUNCT
ejpam-3362	344	10	then	then	ADV
ejpam-3362	344	11	lh({x	lh({x	NOUN
ejpam-3362	344	12	}	}	PUNCT
ejpam-3362	344	13	)	)	PUNCT
ejpam-3362	344	14	=	=	PUNCT
ejpam-3362	344	15	{	{	PUNCT
ejpam-3362	344	16	0	0	NUM
ejpam-3362	344	17	,	,	PUNCT
ejpam-3362	344	18	x	x	NOUN
ejpam-3362	344	19	}	}	PUNCT
ejpam-3362	344	20	.	.	PUNCT
ejpam-3362	345	1	since	since	SCONJ
ejpam-3362	345	2	lh({y	lh({y	NOUN
ejpam-3362	345	3	}	}	PUNCT
ejpam-3362	345	4	)	)	PUNCT
ejpam-3362	345	5	=	=	PUNCT
ejpam-3362	345	6	{	{	PUNCT
ejpam-3362	345	7	0	0	NUM
ejpam-3362	345	8	}	}	PUNCT
ejpam-3362	345	9	or	or	CCONJ
ejpam-3362	345	10	{	{	PUNCT
ejpam-3362	345	11	0	0	NUM
ejpam-3362	345	12	,	,	PUNCT
ejpam-3362	345	13	y	y	NOUN
ejpam-3362	345	14	}	}	PUNCT
ejpam-3362	345	15	by	by	ADP
ejpam-3362	345	16	remark	remark	NOUN
ejpam-3362	345	17	3	3	NUM
ejpam-3362	345	18	,	,	PUNCT
ejpam-3362	345	19	we	we	PRON
ejpam-3362	345	20	have	have	VERB
ejpam-3362	345	21	lh({x	lh({x	NOUN
ejpam-3362	345	22	,	,	PUNCT
ejpam-3362	345	23	y	y	NOUN
ejpam-3362	345	24	}	}	PUNCT
ejpam-3362	345	25	)	)	PUNCT
ejpam-3362	346	1	=	=	PUNCT
ejpam-3362	346	2	{	{	PUNCT
ejpam-3362	346	3	0	0	NUM
ejpam-3362	346	4	}	}	PUNCT
ejpam-3362	346	5	or	or	CCONJ
ejpam-3362	346	6	∅.	∅.	PRON
ejpam-3362	346	7	�	�	PROPN
ejpam-3362	346	8	we	we	PRON
ejpam-3362	346	9	have	have	VERB
ejpam-3362	346	10	the	the	DET
ejpam-3362	346	11	following	follow	VERB
ejpam-3362	346	12	characterization	characterization	NOUN
ejpam-3362	346	13	for	for	ADP
ejpam-3362	346	14	a	a	DET
ejpam-3362	346	15	complete	complete	ADJ
ejpam-3362	346	16	graph	graph	NOUN
ejpam-3362	346	17	:	:	PUNCT
ejpam-3362	346	18	proposition	proposition	NOUN
ejpam-3362	346	19	11	11	NUM
ejpam-3362	346	20	.	.	PUNCT
ejpam-3362	347	1	let	let	VERB
ejpam-3362	347	2	h	h	PRON
ejpam-3362	347	3	be	be	AUX
ejpam-3362	347	4	a	a	DET
ejpam-3362	347	5	hyper	hyper	ADJ
ejpam-3362	347	6	bci	bci	NOUN
ejpam-3362	347	7	-	-	NOUN
ejpam-3362	347	8	algebra	algebra	NOUN
ejpam-3362	347	9	such	such	ADJ
ejpam-3362	347	10	that	that	SCONJ
ejpam-3362	347	11	|h|	|h|	PROPN
ejpam-3362	347	12	≥	≥	NUM
ejpam-3362	347	13	2	2	NUM
ejpam-3362	347	14	.	.	PUNCT
ejpam-3362	347	15	then	then	ADV
ejpam-3362	347	16	γ(h	γ(h	PROPN
ejpam-3362	347	17	)	)	PUNCT
ejpam-3362	347	18	is	be	AUX
ejpam-3362	347	19	a	a	DET
ejpam-3362	347	20	complete	complete	ADJ
ejpam-3362	347	21	graph	graph	NOUN
ejpam-3362	347	22	if	if	SCONJ
ejpam-3362	347	23	and	and	CCONJ
ejpam-3362	347	24	only	only	ADV
ejpam-3362	347	25	if	if	SCONJ
ejpam-3362	347	26	γ(h	γ(h	NOUN
ejpam-3362	347	27	)	)	PUNCT
ejpam-3362	347	28	is	be	AUX
ejpam-3362	347	29	connected	connect	VERB
ejpam-3362	347	30	and	and	CCONJ
ejpam-3362	347	31	h	h	NOUN
ejpam-3362	347	32	is	be	AUX
ejpam-3362	347	33	hyperatomic	hyperatomic	ADJ
ejpam-3362	347	34	.	.	PUNCT
ejpam-3362	348	1	proof	proof	NOUN
ejpam-3362	348	2	.	.	PUNCT
ejpam-3362	349	1	if	if	SCONJ
ejpam-3362	349	2	γ(h	γ(h	NOUN
ejpam-3362	349	3	)	)	PUNCT
ejpam-3362	349	4	is	be	AUX
ejpam-3362	349	5	disconnected	disconnect	VERB
ejpam-3362	349	6	,	,	PUNCT
ejpam-3362	349	7	then	then	ADV
ejpam-3362	349	8	γ(h	γ(h	NOUN
ejpam-3362	349	9	)	)	PUNCT
ejpam-3362	349	10	is	be	AUX
ejpam-3362	349	11	not	not	PART
ejpam-3362	349	12	a	a	DET
ejpam-3362	349	13	complete	complete	ADJ
ejpam-3362	349	14	graph	graph	NOUN
ejpam-3362	349	15	,	,	PUNCT
ejpam-3362	349	16	and	and	CCONJ
ejpam-3362	349	17	we	we	PRON
ejpam-3362	349	18	are	be	AUX
ejpam-3362	349	19	done	do	VERB
ejpam-3362	349	20	.	.	PUNCT
ejpam-3362	350	1	assume	assume	VERB
ejpam-3362	350	2	that	that	SCONJ
ejpam-3362	350	3	γ(h	γ(h	NOUN
ejpam-3362	350	4	)	)	PUNCT
ejpam-3362	350	5	is	be	AUX
ejpam-3362	350	6	connected	connect	VERB
ejpam-3362	350	7	.	.	PUNCT
ejpam-3362	351	1	by	by	ADP
ejpam-3362	351	2	proposition	proposition	NOUN
ejpam-3362	351	3	4	4	NUM
ejpam-3362	351	4	,	,	PUNCT
ejpam-3362	351	5	0	0	NUM
ejpam-3362	351	6	∈	∈	PROPN
ejpam-3362	351	7	lh(x	lh(x	PUNCT
ejpam-3362	351	8	)	)	PUNCT
ejpam-3362	351	9	for	for	ADP
ejpam-3362	351	10	all	all	DET
ejpam-3362	351	11	x	x	SYM
ejpam-3362	351	12	∈	∈	PROPN
ejpam-3362	351	13	h.	h.	NOUN
ejpam-3362	351	14	since	since	SCONJ
ejpam-3362	351	15	x	x	PROPN
ejpam-3362	351	16	∈	∈	PROPN
ejpam-3362	351	17	lh{x	lh{x	PROPN
ejpam-3362	351	18	}	}	PUNCT
ejpam-3362	351	19	,	,	PUNCT
ejpam-3362	351	20	we	we	PRON
ejpam-3362	351	21	now	now	ADV
ejpam-3362	351	22	have	have	VERB
ejpam-3362	351	23	0	0	NUM
ejpam-3362	351	24	,	,	PUNCT
ejpam-3362	351	25	x	x	X
ejpam-3362	351	26	∈	∈	NOUN
ejpam-3362	351	27	lh(x	lh(x	NOUN
ejpam-3362	351	28	)	)	PUNCT
ejpam-3362	351	29	.	.	PUNCT
ejpam-3362	352	1	if	if	SCONJ
ejpam-3362	352	2	h	h	NOUN
ejpam-3362	352	3	is	be	AUX
ejpam-3362	352	4	not	not	PART
ejpam-3362	352	5	hyperatomic	hyperatomic	ADJ
ejpam-3362	352	6	,	,	PUNCT
ejpam-3362	352	7	then	then	ADV
ejpam-3362	352	8	there	there	PRON
ejpam-3362	352	9	exists	exist	VERB
ejpam-3362	352	10	z	z	PROPN
ejpam-3362	352	11	∈	∈	PROPN
ejpam-3362	352	12	h	h	NOUN
ejpam-3362	352	13	\	\	PUNCT
ejpam-3362	352	14	{	{	PUNCT
ejpam-3362	352	15	0	0	NUM
ejpam-3362	352	16	}	}	PUNCT
ejpam-3362	352	17	such	such	ADJ
ejpam-3362	352	18	that	that	SCONJ
ejpam-3362	352	19	y	y	PROPN
ejpam-3362	352	20	�	�	PROPN
ejpam-3362	352	21	z	z	PROPN
ejpam-3362	352	22	with	with	ADP
ejpam-3362	352	23	y	y	PROPN
ejpam-3362	352	24	/∈	/∈	PUNCT
ejpam-3362	352	25	{	{	PUNCT
ejpam-3362	352	26	0	0	NUM
ejpam-3362	352	27	,	,	PUNCT
ejpam-3362	352	28	z	z	NOUN
ejpam-3362	352	29	}	}	PUNCT
ejpam-3362	352	30	.	.	PUNCT
ejpam-3362	353	1	since	since	SCONJ
ejpam-3362	353	2	y	y	PROPN
ejpam-3362	353	3	∈	∈	PROPN
ejpam-3362	353	4	lh{y	lh{y	PROPN
ejpam-3362	353	5	}	}	PUNCT
ejpam-3362	353	6	,	,	PUNCT
ejpam-3362	353	7	y	y	PROPN
ejpam-3362	353	8	∈	∈	PROPN
ejpam-3362	353	9	lh{y	lh{y	PROPN
ejpam-3362	353	10	,	,	PUNCT
ejpam-3362	353	11	z	z	NOUN
ejpam-3362	353	12	}	}	PUNCT
ejpam-3362	353	13	.	.	PUNCT
ejpam-3362	354	1	this	this	PRON
ejpam-3362	354	2	means	mean	VERB
ejpam-3362	354	3	that	that	SCONJ
ejpam-3362	354	4	lh{y	lh{y	ADJ
ejpam-3362	354	5	,	,	PUNCT
ejpam-3362	354	6	z	z	NOUN
ejpam-3362	354	7	}	}	PUNCT
ejpam-3362	354	8	6=	6=	NUM
ejpam-3362	354	9	{	{	PUNCT
ejpam-3362	354	10	0	0	NUM
ejpam-3362	354	11	}	}	PUNCT
ejpam-3362	354	12	,	,	PUNCT
ejpam-3362	354	13	implying	imply	VERB
ejpam-3362	354	14	that	that	SCONJ
ejpam-3362	354	15	yz	yz	PROPN
ejpam-3362	354	16	/∈	/∈	PUNCT
ejpam-3362	354	17	e(γ(h	e(γ(h	PROPN
ejpam-3362	354	18	)	)	PUNCT
ejpam-3362	354	19	)	)	PUNCT
ejpam-3362	354	20	.	.	PUNCT
ejpam-3362	355	1	therefore	therefore	ADV
ejpam-3362	355	2	,	,	PUNCT
ejpam-3362	355	3	γ(h	γ(h	NOUN
ejpam-3362	355	4	)	)	PUNCT
ejpam-3362	355	5	is	be	AUX
ejpam-3362	355	6	not	not	PART
ejpam-3362	355	7	complete	complete	ADJ
ejpam-3362	355	8	.	.	PUNCT
ejpam-3362	356	1	conversely	conversely	ADV
ejpam-3362	356	2	,	,	PUNCT
ejpam-3362	356	3	suppose	suppose	VERB
ejpam-3362	356	4	γ(h	γ(h	NOUN
ejpam-3362	356	5	)	)	PUNCT
ejpam-3362	356	6	is	be	AUX
ejpam-3362	356	7	connected	connect	VERB
ejpam-3362	356	8	and	and	CCONJ
ejpam-3362	356	9	h	h	NOUN
ejpam-3362	356	10	is	be	AUX
ejpam-3362	356	11	hyperatomic	hyperatomic	ADJ
ejpam-3362	356	12	.	.	PUNCT
ejpam-3362	357	1	then	then	ADV
ejpam-3362	357	2	by	by	ADP
ejpam-3362	357	3	remark	remark	NOUN
ejpam-3362	357	4	3	3	NUM
ejpam-3362	357	5	,	,	PUNCT
ejpam-3362	357	6	lh{x	lh{x	PROPN
ejpam-3362	357	7	}	}	PUNCT
ejpam-3362	357	8	=	=	SYM
ejpam-3362	357	9	{	{	PUNCT
ejpam-3362	357	10	0	0	NUM
ejpam-3362	357	11	,	,	PUNCT
ejpam-3362	357	12	x	x	NOUN
ejpam-3362	357	13	}	}	PUNCT
ejpam-3362	357	14	for	for	ADP
ejpam-3362	357	15	all	all	DET
ejpam-3362	357	16	x	x	SYM
ejpam-3362	357	17	∈	∈	PROPN
ejpam-3362	357	18	h	h	NOUN
ejpam-3362	357	19	\	\	PUNCT
ejpam-3362	357	20	{	{	PUNCT
ejpam-3362	357	21	0	0	NUM
ejpam-3362	357	22	}	}	PUNCT
ejpam-3362	357	23	.	.	PUNCT
ejpam-3362	358	1	thus	thus	ADV
ejpam-3362	358	2	,	,	PUNCT
ejpam-3362	358	3	for	for	ADP
ejpam-3362	358	4	any	any	DET
ejpam-3362	358	5	distinct	distinct	ADJ
ejpam-3362	358	6	nonzero	nonzero	NOUN
ejpam-3362	358	7	elements	element	NOUN
ejpam-3362	358	8	x	x	X
ejpam-3362	358	9	,	,	PUNCT
ejpam-3362	358	10	y	y	PROPN
ejpam-3362	358	11	of	of	ADP
ejpam-3362	358	12	h	h	NOUN
ejpam-3362	358	13	=	=	SYM
ejpam-3362	358	14	v	v	PROPN
ejpam-3362	358	15	(	(	PUNCT
ejpam-3362	358	16	γ(h	γ(h	NOUN
ejpam-3362	358	17	)	)	PUNCT
ejpam-3362	358	18	)	)	PUNCT
ejpam-3362	358	19	,	,	PUNCT
ejpam-3362	358	20	lh{x	lh{x	PROPN
ejpam-3362	358	21	}	}	PUNCT
ejpam-3362	358	22	∩	∩	ADJ
ejpam-3362	358	23	lh{y	lh{y	ADJ
ejpam-3362	358	24	}	}	PUNCT
ejpam-3362	358	25	=	=	PUNCT
ejpam-3362	358	26	{	{	PUNCT
ejpam-3362	358	27	0	0	NUM
ejpam-3362	358	28	}	}	PUNCT
ejpam-3362	358	29	,	,	PUNCT
ejpam-3362	358	30	that	that	ADV
ejpam-3362	358	31	is	is	ADV
ejpam-3362	358	32	,	,	PUNCT
ejpam-3362	358	33	xy	xy	PROPN
ejpam-3362	358	34	∈	∈	PROPN
ejpam-3362	358	35	e(γ(h	e(γ(h	PROPN
ejpam-3362	358	36	)	)	PUNCT
ejpam-3362	358	37	)	)	PUNCT
ejpam-3362	358	38	.	.	PUNCT
ejpam-3362	359	1	consequently	consequently	ADV
ejpam-3362	359	2	,	,	PUNCT
ejpam-3362	359	3	γ(h	γ(h	PROPN
ejpam-3362	359	4	)	)	PUNCT
ejpam-3362	359	5	is	be	AUX
ejpam-3362	359	6	a	a	DET
ejpam-3362	359	7	complete	complete	ADJ
ejpam-3362	359	8	graph	graph	NOUN
ejpam-3362	359	9	.	.	PUNCT
ejpam-3362	360	1	�	�	PROPN
ejpam-3362	360	2	example	example	NOUN
ejpam-3362	360	3	7	7	NUM
ejpam-3362	360	4	.	.	PUNCT
ejpam-3362	361	1	the	the	DET
ejpam-3362	361	2	hyper	hyper	ADJ
ejpam-3362	361	3	bci	bci	NOUN
ejpam-3362	361	4	-	-	NOUN
ejpam-3362	361	5	algebra	algebra	NOUN
ejpam-3362	361	6	in	in	ADP
ejpam-3362	361	7	example	example	NOUN
ejpam-3362	361	8	5	5	NUM
ejpam-3362	361	9	has	have	VERB
ejpam-3362	361	10	a	a	DET
ejpam-3362	361	11	complete	complete	ADJ
ejpam-3362	361	12	zero	zero	NUM
ejpam-3362	361	13	divisor	divisor	NOUN
ejpam-3362	361	14	graph	graph	NOUN
ejpam-3362	361	15	:	:	PUNCT
ejpam-3362	361	16	1	1	NUM
ejpam-3362	361	17	2	2	NUM
ejpam-3362	361	18	0	0	NUM
ejpam-3362	361	19	remark	remark	NOUN
ejpam-3362	361	20	5	5	NUM
ejpam-3362	361	21	.	.	PUNCT
ejpam-3362	362	1	given	give	VERB
ejpam-3362	362	2	an	an	DET
ejpam-3362	362	3	ordered	order	VERB
ejpam-3362	362	4	hyper	hyper	ADJ
ejpam-3362	362	5	bci	bci	NOUN
ejpam-3362	362	6	-	-	ADJ
ejpam-3362	362	7	algebra	algebra	ADJ
ejpam-3362	362	8	h	h	NOUN
ejpam-3362	362	9	,	,	PUNCT
ejpam-3362	362	10	it	it	PRON
ejpam-3362	362	11	is	be	AUX
ejpam-3362	362	12	not	not	PART
ejpam-3362	362	13	always	always	ADV
ejpam-3362	362	14	true	true	ADJ
ejpam-3362	362	15	that	that	SCONJ
ejpam-3362	362	16	there	there	PRON
ejpam-3362	362	17	exists	exist	VERB
ejpam-3362	362	18	a	a	DET
ejpam-3362	362	19	∈	∈	PROPN
ejpam-3362	362	20	a∗(h	a∗(h	PROPN
ejpam-3362	362	21	)	)	PUNCT
ejpam-3362	362	22	=	=	SYM
ejpam-3362	362	23	a(h	a(h	PROPN
ejpam-3362	362	24	)	)	PUNCT
ejpam-3362	362	25	\	\	NOUN
ejpam-3362	362	26	{	{	PUNCT
ejpam-3362	362	27	0	0	NUM
ejpam-3362	362	28	}	}	PUNCT
ejpam-3362	362	29	such	such	ADJ
ejpam-3362	362	30	that	that	SCONJ
ejpam-3362	362	31	a	a	DET
ejpam-3362	362	32	�	�	PROPN
ejpam-3362	362	33	x	x	PUNCT
ejpam-3362	362	34	for	for	ADP
ejpam-3362	362	35	all	all	PRON
ejpam-3362	362	36	x	x	SYM
ejpam-3362	362	37	∈	∈	PROPN
ejpam-3362	362	38	h	h	NOUN
ejpam-3362	362	39	\	\	PUNCT
ejpam-3362	362	40	{	{	PUNCT
ejpam-3362	362	41	0	0	NUM
ejpam-3362	362	42	}	}	PUNCT
ejpam-3362	362	43	.	.	PUNCT
ejpam-3362	363	1	example	example	NOUN
ejpam-3362	363	2	8	8	NUM
ejpam-3362	363	3	.	.	PUNCT
ejpam-3362	364	1	consider	consider	VERB
ejpam-3362	364	2	the	the	DET
ejpam-3362	364	3	hyper	hyper	ADJ
ejpam-3362	364	4	bci	bci	NOUN
ejpam-3362	364	5	-	-	ADJ
ejpam-3362	364	6	algebra	algebra	NOUN
ejpam-3362	364	7	h	h	NOUN
ejpam-3362	364	8	defined	define	VERB
ejpam-3362	364	9	in	in	ADP
ejpam-3362	364	10	example	example	NOUN
ejpam-3362	364	11	3	3	X
ejpam-3362	364	12	.	.	PUNCT
ejpam-3362	364	13	h	h	PROPN
ejpam-3362	364	14	is	be	AUX
ejpam-3362	364	15	hyperatomic	hyperatomic	ADJ
ejpam-3362	364	16	and	and	CCONJ
ejpam-3362	364	17	hence	hence	ADV
ejpam-3362	364	18	,	,	PUNCT
ejpam-3362	364	19	ordered	order	VERB
ejpam-3362	364	20	and	and	CCONJ
ejpam-3362	364	21	a∗(h	a∗(h	PROPN
ejpam-3362	364	22	)	)	PUNCT
ejpam-3362	364	23	=	=	PRON
ejpam-3362	365	1	{	{	PUNCT
ejpam-3362	365	2	1	1	NUM
ejpam-3362	365	3	,	,	PUNCT
ejpam-3362	365	4	2	2	NUM
ejpam-3362	365	5	}	}	PUNCT
ejpam-3362	365	6	.	.	PUNCT
ejpam-3362	366	1	notice	notice	VERB
ejpam-3362	366	2	that	that	SCONJ
ejpam-3362	366	3	neither	neither	CCONJ
ejpam-3362	366	4	1	1	NUM
ejpam-3362	366	5	�	�	NOUN
ejpam-3362	366	6	x	x	SYM
ejpam-3362	366	7	nor	nor	CCONJ
ejpam-3362	366	8	2	2	NUM
ejpam-3362	366	9	�	�	NOUN
ejpam-3362	366	10	x	x	PUNCT
ejpam-3362	366	11	for	for	ADP
ejpam-3362	366	12	all	all	PRON
ejpam-3362	366	13	x	x	SYM
ejpam-3362	366	14	∈	∈	PROPN
ejpam-3362	366	15	h	h	NOUN
ejpam-3362	366	16	\	\	PUNCT
ejpam-3362	366	17	{	{	PUNCT
ejpam-3362	366	18	0	0	NUM
ejpam-3362	366	19	}	}	PUNCT
ejpam-3362	366	20	.	.	PUNCT
ejpam-3362	367	1	but	but	CCONJ
ejpam-3362	367	2	for	for	ADP
ejpam-3362	367	3	each	each	DET
ejpam-3362	367	4	x	x	SYM
ejpam-3362	367	5	∈	∈	PROPN
ejpam-3362	367	6	h	h	NOUN
ejpam-3362	367	7	\	\	PUNCT
ejpam-3362	367	8	{	{	PUNCT
ejpam-3362	367	9	0	0	NUM
ejpam-3362	367	10	}	}	PUNCT
ejpam-3362	367	11	,	,	PUNCT
ejpam-3362	367	12	there	there	PRON
ejpam-3362	367	13	exists	exist	VERB
ejpam-3362	367	14	a	a	DET
ejpam-3362	367	15	∈	∈	PROPN
ejpam-3362	367	16	a∗(h	a∗(h	PROPN
ejpam-3362	367	17	)	)	PUNCT
ejpam-3362	367	18	such	such	ADJ
ejpam-3362	367	19	that	that	SCONJ
ejpam-3362	367	20	a	a	DET
ejpam-3362	367	21	�	�	PROPN
ejpam-3362	367	22	x.	x.	NOUN
ejpam-3362	367	23	theorem	theorem	VERB
ejpam-3362	367	24	4	4	NUM
ejpam-3362	367	25	.	.	PUNCT
ejpam-3362	368	1	let	let	VERB
ejpam-3362	368	2	h	h	PRON
ejpam-3362	368	3	be	be	AUX
ejpam-3362	368	4	an	an	DET
ejpam-3362	368	5	ordered	order	VERB
ejpam-3362	368	6	hyper	hyper	ADJ
ejpam-3362	368	7	bci	bci	NOUN
ejpam-3362	368	8	-	-	NOUN
ejpam-3362	368	9	algebra	algebra	NOUN
ejpam-3362	368	10	with	with	ADP
ejpam-3362	368	11	|h|	|h|	PROPN
ejpam-3362	368	12	≥	≥	NUM
ejpam-3362	368	13	2	2	NUM
ejpam-3362	368	14	.	.	PUNCT
ejpam-3362	369	1	then	then	ADV
ejpam-3362	369	2	the	the	DET
ejpam-3362	369	3	following	follow	VERB
ejpam-3362	369	4	hold	hold	NOUN
ejpam-3362	369	5	:	:	PUNCT
ejpam-3362	369	6	m.	m.	NOUN
ejpam-3362	369	7	panganduyon	panganduyon	NOUN
ejpam-3362	369	8	,	,	PUNCT
ejpam-3362	369	9	s.	s.	PROPN
ejpam-3362	369	10	canoy	canoy	PROPN
ejpam-3362	369	11	/	/	SYM
ejpam-3362	369	12	eur	eur	PROPN
ejpam-3362	369	13	.	.	PUNCT
ejpam-3362	370	1	j.	j.	PROPN
ejpam-3362	370	2	pure	pure	PROPN
ejpam-3362	370	3	appl	appl	PROPN
ejpam-3362	370	4	.	.	PROPN
ejpam-3362	370	5	math	math	PROPN
ejpam-3362	370	6	,	,	PUNCT
ejpam-3362	370	7	12	12	NUM
ejpam-3362	370	8	(	(	PUNCT
ejpam-3362	370	9	1	1	NUM
ejpam-3362	370	10	)	)	PUNCT
ejpam-3362	370	11	(	(	PUNCT
ejpam-3362	370	12	2019	2019	NUM
ejpam-3362	370	13	)	)	PUNCT
ejpam-3362	371	1	,	,	PUNCT
ejpam-3362	371	2	146	146	NUM
ejpam-3362	371	3	-	-	SYM
ejpam-3362	371	4	158	158	NUM
ejpam-3362	371	5	157	157	NUM
ejpam-3362	371	6	(	(	PUNCT
ejpam-3362	371	7	i	i	NOUN
ejpam-3362	371	8	)	)	PUNCT
ejpam-3362	371	9	for	for	ADP
ejpam-3362	371	10	each	each	DET
ejpam-3362	371	11	x	x	SYM
ejpam-3362	371	12	∈	∈	PROPN
ejpam-3362	371	13	h	h	NOUN
ejpam-3362	371	14	,	,	PUNCT
ejpam-3362	371	15	there	there	PRON
ejpam-3362	371	16	is	be	VERB
ejpam-3362	371	17	ax	ax	NOUN
ejpam-3362	371	18	∈	∈	PROPN
ejpam-3362	371	19	a∗(h	a∗(h	PROPN
ejpam-3362	371	20	)	)	PUNCT
ejpam-3362	371	21	such	such	ADJ
ejpam-3362	371	22	that	that	DET
ejpam-3362	371	23	ax	ax	NOUN
ejpam-3362	371	24	�	�	PROPN
ejpam-3362	371	25	x.	x.	PROPN
ejpam-3362	371	26	in	in	ADP
ejpam-3362	371	27	particular	particular	ADJ
ejpam-3362	371	28	,	,	PUNCT
ejpam-3362	371	29	a∗(h	a∗(h	PROPN
ejpam-3362	371	30	)	)	PUNCT
ejpam-3362	371	31	6=	6=	ADP
ejpam-3362	371	32	∅.	∅.	PROPN
ejpam-3362	371	33	(	(	PUNCT
ejpam-3362	371	34	ii	ii	NOUN
ejpam-3362	371	35	)	)	PUNCT
ejpam-3362	371	36	there	there	PRON
ejpam-3362	371	37	exists	exist	VERB
ejpam-3362	371	38	a	a	DET
ejpam-3362	371	39	∈	∈	PROPN
ejpam-3362	371	40	h\{0	h\{0	NOUN
ejpam-3362	371	41	}	}	PUNCT
ejpam-3362	371	42	such	such	ADJ
ejpam-3362	371	43	that	that	SCONJ
ejpam-3362	371	44	a	a	DET
ejpam-3362	371	45	�	�	PROPN
ejpam-3362	371	46	x	x	PUNCT
ejpam-3362	371	47	for	for	ADP
ejpam-3362	371	48	all	all	DET
ejpam-3362	371	49	x	x	SYM
ejpam-3362	371	50	∈	∈	PROPN
ejpam-3362	371	51	h\{0	h\{0	NOUN
ejpam-3362	371	52	}	}	PUNCT
ejpam-3362	371	53	if	if	SCONJ
ejpam-3362	372	1	and	and	CCONJ
ejpam-3362	372	2	only	only	ADV
ejpam-3362	372	3	if	if	SCONJ
ejpam-3362	372	4	|a∗(h)|	|a∗(h)|	PROPN
ejpam-3362	372	5	=	=	SYM
ejpam-3362	372	6	1	1	NUM
ejpam-3362	372	7	(	(	PUNCT
ejpam-3362	372	8	that	that	PRON
ejpam-3362	372	9	is	is	ADV
ejpam-3362	372	10	,	,	PUNCT
ejpam-3362	372	11	a∗(h	a∗(h	PROPN
ejpam-3362	372	12	)	)	PUNCT
ejpam-3362	372	13	=	=	PRON
ejpam-3362	372	14	{	{	PUNCT
ejpam-3362	372	15	a	a	NOUN
ejpam-3362	372	16	}	}	PUNCT
ejpam-3362	372	17	)	)	PUNCT
ejpam-3362	372	18	.	.	PUNCT
ejpam-3362	373	1	proof	proof	NOUN
ejpam-3362	373	2	.	.	PUNCT
ejpam-3362	374	1	(	(	PUNCT
ejpam-3362	374	2	i	i	NOUN
ejpam-3362	374	3	)	)	PUNCT
ejpam-3362	374	4	let	let	VERB
ejpam-3362	374	5	x	x	PUNCT
ejpam-3362	374	6	∈	∈	PROPN
ejpam-3362	374	7	h	h	NOUN
ejpam-3362	374	8	\	\	PUNCT
ejpam-3362	374	9	{	{	PUNCT
ejpam-3362	374	10	0	0	NUM
ejpam-3362	374	11	}	}	PUNCT
ejpam-3362	374	12	.	.	PUNCT
ejpam-3362	375	1	if	if	SCONJ
ejpam-3362	375	2	x	x	PRON
ejpam-3362	375	3	is	be	AUX
ejpam-3362	375	4	a	a	DET
ejpam-3362	375	5	hyperatom	hyperatom	NOUN
ejpam-3362	375	6	,	,	PUNCT
ejpam-3362	375	7	then	then	ADV
ejpam-3362	375	8	take	take	VERB
ejpam-3362	375	9	ax	ax	NOUN
ejpam-3362	375	10	=	=	PUNCT
ejpam-3362	375	11	x.	x.	NOUN
ejpam-3362	375	12	if	if	SCONJ
ejpam-3362	375	13	x	x	PRON
ejpam-3362	375	14	is	be	AUX
ejpam-3362	375	15	not	not	PART
ejpam-3362	375	16	a	a	DET
ejpam-3362	375	17	hyperatom	hyperatom	NOUN
ejpam-3362	375	18	,	,	PUNCT
ejpam-3362	375	19	there	there	PRON
ejpam-3362	375	20	exists	exist	VERB
ejpam-3362	375	21	x1	x1	PROPN
ejpam-3362	375	22	∈	∈	PROPN
ejpam-3362	375	23	h	h	NOUN
ejpam-3362	375	24	\{0	\{0	NOUN
ejpam-3362	375	25	,	,	PUNCT
ejpam-3362	375	26	x	x	NOUN
ejpam-3362	375	27	}	}	PUNCT
ejpam-3362	375	28	such	such	ADJ
ejpam-3362	375	29	that	that	SCONJ
ejpam-3362	375	30	x1	x1	PROPN
ejpam-3362	375	31	�	�	PROPN
ejpam-3362	375	32	x.	x.	VERB
ejpam-3362	375	33	again	again	ADV
ejpam-3362	375	34	,	,	PUNCT
ejpam-3362	375	35	if	if	SCONJ
ejpam-3362	375	36	x1	x1	PROPN
ejpam-3362	375	37	is	be	AUX
ejpam-3362	375	38	a	a	DET
ejpam-3362	375	39	hyperatom	hyperatom	NOUN
ejpam-3362	375	40	,	,	PUNCT
ejpam-3362	375	41	then	then	ADV
ejpam-3362	375	42	take	take	VERB
ejpam-3362	375	43	ax	ax	NOUN
ejpam-3362	375	44	=	=	PUNCT
ejpam-3362	375	45	x1	x1	PROPN
ejpam-3362	375	46	.	.	PUNCT
ejpam-3362	376	1	otherwise	otherwise	ADV
ejpam-3362	376	2	,	,	PUNCT
ejpam-3362	376	3	there	there	PRON
ejpam-3362	376	4	exists	exist	VERB
ejpam-3362	376	5	x2	x2	PROPN
ejpam-3362	376	6	∈	∈	PROPN
ejpam-3362	376	7	h	h	NOUN
ejpam-3362	376	8	\{0	\{0	NOUN
ejpam-3362	376	9	,	,	PUNCT
ejpam-3362	376	10	x	x	PRON
ejpam-3362	376	11	,	,	PUNCT
ejpam-3362	376	12	x1	x1	NUM
ejpam-3362	376	13	}	}	PUNCT
ejpam-3362	376	14	such	such	ADJ
ejpam-3362	376	15	that	that	SCONJ
ejpam-3362	376	16	x2	x2	PROPN
ejpam-3362	376	17	�	�	PROPN
ejpam-3362	376	18	x1	x1	PROPN
ejpam-3362	376	19	�	�	PROPN
ejpam-3362	376	20	x.	x.	NOUN
ejpam-3362	376	21	since	since	SCONJ
ejpam-3362	376	22	h	h	PROPN
ejpam-3362	376	23	is	be	AUX
ejpam-3362	376	24	finite	finite	ADJ
ejpam-3362	376	25	,	,	PUNCT
ejpam-3362	376	26	continuing	continue	VERB
ejpam-3362	376	27	in	in	ADP
ejpam-3362	376	28	this	this	DET
ejpam-3362	376	29	fashion	fashion	NOUN
ejpam-3362	376	30	yields	yield	NOUN
ejpam-3362	376	31	a	a	DET
ejpam-3362	376	32	terminal	terminal	ADJ
ejpam-3362	376	33	point	point	NOUN
ejpam-3362	376	34	xn	xn	X
ejpam-3362	376	35	∈	∈	PROPN
ejpam-3362	376	36	h\{0	h\{0	NOUN
ejpam-3362	376	37	,	,	PUNCT
ejpam-3362	376	38	x	x	X
ejpam-3362	376	39	,	,	PUNCT
ejpam-3362	376	40	x1	x1	PROPN
ejpam-3362	376	41	,	,	PUNCT
ejpam-3362	376	42	.	.	PUNCT
ejpam-3362	376	43	.	.	PUNCT
ejpam-3362	377	1	.	.	PUNCT
ejpam-3362	378	1	,	,	PUNCT
ejpam-3362	378	2	xn−1	xn−1	PROPN
ejpam-3362	378	3	}	}	PUNCT
ejpam-3362	378	4	with	with	ADP
ejpam-3362	378	5	xn	xn	PROPN
ejpam-3362	378	6	�	�	PROPN
ejpam-3362	378	7	xn−1	xn−1	PROPN
ejpam-3362	378	8	�	�	PROPN
ejpam-3362	378	9	·	·	PUNCT
ejpam-3362	378	10	·	·	PUNCT
ejpam-3362	378	11	·	·	PUNCT
ejpam-3362	379	1	�	�	PROPN
ejpam-3362	379	2	x2	x2	PROPN
ejpam-3362	379	3	�	�	PROPN
ejpam-3362	379	4	x1	x1	PROPN
ejpam-3362	379	5	�	�	PROPN
ejpam-3362	379	6	x	x	PUNCT
ejpam-3362	379	7	such	such	ADJ
ejpam-3362	379	8	that	that	SCONJ
ejpam-3362	379	9	only	only	ADV
ejpam-3362	379	10	z	z	NOUN
ejpam-3362	379	11	=	=	SYM
ejpam-3362	379	12	0	0	PUNCT
ejpam-3362	379	13	(	(	PUNCT
ejpam-3362	379	14	provided	provide	VERB
ejpam-3362	379	15	0	0	NUM
ejpam-3362	379	16	∈	∈	PROPN
ejpam-3362	379	17	lh{x	lh{x	PROPN
ejpam-3362	379	18	}	}	PUNCT
ejpam-3362	379	19	)	)	PUNCT
ejpam-3362	379	20	or	or	CCONJ
ejpam-3362	379	21	z	z	NOUN
ejpam-3362	379	22	=	=	SYM
ejpam-3362	379	23	xn	xn	PROPN
ejpam-3362	379	24	satisfies	satisfie	NOUN
ejpam-3362	379	25	z	z	PROPN
ejpam-3362	379	26	�	�	PROPN
ejpam-3362	379	27	x.	x.	NOUN
ejpam-3362	380	1	this	this	PRON
ejpam-3362	380	2	implies	imply	VERB
ejpam-3362	380	3	that	that	DET
ejpam-3362	380	4	ax	ax	NOUN
ejpam-3362	380	5	=	=	PUNCT
ejpam-3362	380	6	xn	xn	PROPN
ejpam-3362	380	7	∈	∈	PROPN
ejpam-3362	380	8	a∗(h	a∗(h	PROPN
ejpam-3362	380	9	)	)	PUNCT
ejpam-3362	380	10	and	and	CCONJ
ejpam-3362	380	11	ax	ax	PROPN
ejpam-3362	380	12	�	�	PROPN
ejpam-3362	380	13	x.	x.	PROPN
ejpam-3362	380	14	(	(	PUNCT
ejpam-3362	380	15	ii	ii	NOUN
ejpam-3362	380	16	)	)	PUNCT
ejpam-3362	380	17	suppose	suppose	VERB
ejpam-3362	380	18	that	that	SCONJ
ejpam-3362	380	19	there	there	PRON
ejpam-3362	380	20	exists	exist	VERB
ejpam-3362	380	21	a	a	DET
ejpam-3362	380	22	∈	∈	PROPN
ejpam-3362	380	23	h	h	NOUN
ejpam-3362	380	24	\	\	PUNCT
ejpam-3362	380	25	{	{	PUNCT
ejpam-3362	380	26	0	0	NUM
ejpam-3362	380	27	}	}	PUNCT
ejpam-3362	380	28	such	such	ADJ
ejpam-3362	380	29	that	that	SCONJ
ejpam-3362	380	30	a	a	DET
ejpam-3362	380	31	�	�	PROPN
ejpam-3362	380	32	x	x	PUNCT
ejpam-3362	380	33	for	for	ADP
ejpam-3362	380	34	all	all	PRON
ejpam-3362	380	35	x	x	SYM
ejpam-3362	380	36	∈	∈	PROPN
ejpam-3362	380	37	h	h	NOUN
ejpam-3362	380	38	\	\	PUNCT
ejpam-3362	380	39	{	{	PUNCT
ejpam-3362	380	40	0	0	NUM
ejpam-3362	380	41	}	}	PUNCT
ejpam-3362	380	42	.	.	PUNCT
ejpam-3362	381	1	choose	choose	VERB
ejpam-3362	381	2	any	any	DET
ejpam-3362	381	3	b	b	PROPN
ejpam-3362	381	4	∈	∈	PROPN
ejpam-3362	381	5	a∗(h	a∗(h	PROPN
ejpam-3362	381	6	)	)	PUNCT
ejpam-3362	381	7	.	.	PUNCT
ejpam-3362	382	1	then	then	ADV
ejpam-3362	382	2	a	a	DET
ejpam-3362	382	3	�	�	PROPN
ejpam-3362	382	4	b.	b.	PROPN
ejpam-3362	382	5	since	since	SCONJ
ejpam-3362	382	6	b	b	PROPN
ejpam-3362	382	7	∈	∈	PROPN
ejpam-3362	382	8	a(h	a(h	PROPN
ejpam-3362	382	9	)	)	PUNCT
ejpam-3362	382	10	and	and	CCONJ
ejpam-3362	382	11	a	a	DET
ejpam-3362	382	12	6=	6=	NUM
ejpam-3362	382	13	0	0	NUM
ejpam-3362	382	14	,	,	PUNCT
ejpam-3362	382	15	it	it	PRON
ejpam-3362	382	16	follows	follow	VERB
ejpam-3362	382	17	that	that	SCONJ
ejpam-3362	382	18	a	a	DET
ejpam-3362	382	19	=	=	X
ejpam-3362	382	20	b.	b.	PROPN
ejpam-3362	382	21	thus	thus	ADV
ejpam-3362	382	22	a	a	DET
ejpam-3362	382	23	∈	∈	PROPN
ejpam-3362	382	24	a∗(h	a∗(h	PROPN
ejpam-3362	382	25	)	)	PUNCT
ejpam-3362	382	26	.	.	PUNCT
ejpam-3362	383	1	since	since	SCONJ
ejpam-3362	383	2	b	b	PROPN
ejpam-3362	383	3	was	be	AUX
ejpam-3362	383	4	arbitrarily	arbitrarily	ADV
ejpam-3362	383	5	chosen	choose	VERB
ejpam-3362	383	6	,	,	PUNCT
ejpam-3362	383	7	we	we	PRON
ejpam-3362	383	8	have	have	VERB
ejpam-3362	383	9	a∗(h	a∗(h	PROPN
ejpam-3362	383	10	)	)	PUNCT
ejpam-3362	383	11	=	=	PRON
ejpam-3362	383	12	{	{	PUNCT
ejpam-3362	383	13	a	a	X
ejpam-3362	383	14	}	}	PUNCT
ejpam-3362	383	15	.	.	PUNCT
ejpam-3362	384	1	conversely	conversely	ADV
ejpam-3362	384	2	,	,	PUNCT
ejpam-3362	384	3	suppose	suppose	VERB
ejpam-3362	384	4	that	that	SCONJ
ejpam-3362	384	5	|a∗(h)|	|a∗(h)|	PRON
ejpam-3362	384	6	=	=	SYM
ejpam-3362	384	7	1	1	NUM
ejpam-3362	384	8	,	,	PUNCT
ejpam-3362	384	9	say	say	VERB
ejpam-3362	384	10	a∗(h	a∗(h	PROPN
ejpam-3362	384	11	)	)	PUNCT
ejpam-3362	384	12	=	=	PRON
ejpam-3362	384	13	{	{	PUNCT
ejpam-3362	384	14	a	a	X
ejpam-3362	384	15	}	}	PUNCT
ejpam-3362	384	16	.	.	PUNCT
ejpam-3362	385	1	let	let	VERB
ejpam-3362	385	2	x	x	SYM
ejpam-3362	385	3	∈	∈	PROPN
ejpam-3362	385	4	h	h	NOUN
ejpam-3362	385	5	\	\	PUNCT
ejpam-3362	385	6	{	{	PUNCT
ejpam-3362	385	7	0	0	NUM
ejpam-3362	385	8	}	}	PUNCT
ejpam-3362	385	9	.	.	PUNCT
ejpam-3362	386	1	then	then	ADV
ejpam-3362	386	2	by	by	ADP
ejpam-3362	386	3	(	(	PUNCT
ejpam-3362	386	4	i	i	NOUN
ejpam-3362	386	5	)	)	PUNCT
ejpam-3362	386	6	,	,	PUNCT
ejpam-3362	386	7	a	a	DET
ejpam-3362	386	8	�	�	PROPN
ejpam-3362	386	9	x.	x.	NOUN
ejpam-3362	386	10	�	�	PROPN
ejpam-3362	386	11	example	example	NOUN
ejpam-3362	386	12	9	9	NUM
ejpam-3362	386	13	.	.	PUNCT
ejpam-3362	386	14	consider	consider	VERB
ejpam-3362	386	15	the	the	DET
ejpam-3362	386	16	ordered	order	VERB
ejpam-3362	386	17	hyper	hyper	ADJ
ejpam-3362	386	18	bci	bci	NOUN
ejpam-3362	386	19	-	-	ADJ
ejpam-3362	386	20	algebra	algebra	NOUN
ejpam-3362	386	21	h	h	NOUN
ejpam-3362	386	22	defined	define	VERB
ejpam-3362	386	23	in	in	ADP
ejpam-3362	386	24	example	example	NOUN
ejpam-3362	386	25	1	1	NUM
ejpam-3362	386	26	.	.	X
ejpam-3362	387	1	note	note	VERB
ejpam-3362	387	2	that	that	SCONJ
ejpam-3362	387	3	1	1	NUM
ejpam-3362	387	4	is	be	AUX
ejpam-3362	387	5	the	the	DET
ejpam-3362	387	6	only	only	ADJ
ejpam-3362	387	7	nonzero	nonzero	ADJ
ejpam-3362	387	8	hyperatom	hyperatom	NOUN
ejpam-3362	387	9	of	of	ADP
ejpam-3362	387	10	h	h	NOUN
ejpam-3362	387	11	and	and	CCONJ
ejpam-3362	387	12	the	the	DET
ejpam-3362	387	13	zero	zero	NUM
ejpam-3362	387	14	divisor	divisor	NOUN
ejpam-3362	387	15	graph	graph	NOUN
ejpam-3362	387	16	γ(h	γ(h	NOUN
ejpam-3362	387	17	)	)	PUNCT
ejpam-3362	387	18	of	of	ADP
ejpam-3362	387	19	h	h	NOUN
ejpam-3362	387	20	is	be	AUX
ejpam-3362	387	21	a	a	DET
ejpam-3362	387	22	star	star	NOUN
ejpam-3362	387	23	.	.	PUNCT
ejpam-3362	388	1	as	as	ADP
ejpam-3362	388	2	a	a	DET
ejpam-3362	388	3	generalization	generalization	NOUN
ejpam-3362	388	4	of	of	ADP
ejpam-3362	388	5	example	example	NOUN
ejpam-3362	388	6	9	9	NUM
ejpam-3362	388	7	,	,	PUNCT
ejpam-3362	388	8	we	we	PRON
ejpam-3362	388	9	have	have	VERB
ejpam-3362	388	10	the	the	DET
ejpam-3362	388	11	following	follow	VERB
ejpam-3362	388	12	theorem	theorem	VERB
ejpam-3362	388	13	.	.	PUNCT
ejpam-3362	388	14	theorem	theorem	NOUN
ejpam-3362	388	15	5	5	NUM
ejpam-3362	388	16	.	.	PUNCT
ejpam-3362	389	1	let	let	VERB
ejpam-3362	389	2	h	h	NOUN
ejpam-3362	389	3	be	be	AUX
ejpam-3362	389	4	an	an	DET
ejpam-3362	389	5	ordered	order	VERB
ejpam-3362	389	6	hyper	hyper	ADJ
ejpam-3362	389	7	bci	bci	NOUN
ejpam-3362	389	8	-	-	NOUN
ejpam-3362	389	9	algebra	algebra	NOUN
ejpam-3362	389	10	with	with	ADP
ejpam-3362	389	11	|h|	|h|	PROPN
ejpam-3362	389	12	≥	≥	NUM
ejpam-3362	389	13	2	2	NUM
ejpam-3362	389	14	.	.	PUNCT
ejpam-3362	389	15	then	then	ADV
ejpam-3362	389	16	γ(h	γ(h	PROPN
ejpam-3362	389	17	)	)	PUNCT
ejpam-3362	389	18	is	be	AUX
ejpam-3362	389	19	a	a	DET
ejpam-3362	389	20	star	star	NOUN
ejpam-3362	389	21	if	if	SCONJ
ejpam-3362	390	1	and	and	CCONJ
ejpam-3362	390	2	only	only	ADV
ejpam-3362	390	3	if	if	SCONJ
ejpam-3362	390	4	γ(h	γ(h	NOUN
ejpam-3362	390	5	)	)	PUNCT
ejpam-3362	390	6	is	be	AUX
ejpam-3362	390	7	connected	connect	VERB
ejpam-3362	390	8	and	and	CCONJ
ejpam-3362	390	9	|a∗(h)|	|a∗(h)|	PROPN
ejpam-3362	390	10	=	=	SYM
ejpam-3362	390	11	1	1	X
ejpam-3362	390	12	.	.	PUNCT
ejpam-3362	391	1	proof	proof	NOUN
ejpam-3362	391	2	.	.	PUNCT
ejpam-3362	392	1	suppose	suppose	VERB
ejpam-3362	392	2	that	that	SCONJ
ejpam-3362	392	3	γ(h	γ(h	NOUN
ejpam-3362	392	4	)	)	PUNCT
ejpam-3362	392	5	is	be	AUX
ejpam-3362	392	6	a	a	DET
ejpam-3362	392	7	star	star	NOUN
ejpam-3362	392	8	.	.	PUNCT
ejpam-3362	393	1	then	then	ADV
ejpam-3362	393	2	γ(h	γ(h	PROPN
ejpam-3362	393	3	)	)	PUNCT
ejpam-3362	393	4	is	be	AUX
ejpam-3362	393	5	connected	connect	VERB
ejpam-3362	393	6	.	.	PUNCT
ejpam-3362	394	1	if	if	SCONJ
ejpam-3362	394	2	|h|	|h|	PRON
ejpam-3362	394	3	=	=	SYM
ejpam-3362	394	4	2	2	NUM
ejpam-3362	394	5	,	,	PUNCT
ejpam-3362	394	6	then	then	ADV
ejpam-3362	394	7	clearly	clearly	ADV
ejpam-3362	394	8	,	,	PUNCT
ejpam-3362	394	9	|a∗(h)|	|a∗(h)|	PROPN
ejpam-3362	394	10	=	=	SYM
ejpam-3362	394	11	1	1	X
ejpam-3362	394	12	.	.	PUNCT
ejpam-3362	394	13	suppose	suppose	VERB
ejpam-3362	394	14	that	that	SCONJ
ejpam-3362	394	15	|h|	|h|	PROPN
ejpam-3362	394	16	≥	≥	NUM
ejpam-3362	394	17	3	3	NUM
ejpam-3362	394	18	.	.	PUNCT
ejpam-3362	394	19	by	by	ADP
ejpam-3362	394	20	proposition	proposition	NOUN
ejpam-3362	394	21	3(i	3(i	NUM
ejpam-3362	394	22	)	)	PUNCT
ejpam-3362	394	23	,	,	PUNCT
ejpam-3362	394	24	0	0	NUM
ejpam-3362	394	25	is	be	AUX
ejpam-3362	394	26	the	the	DET
ejpam-3362	394	27	central	central	ADJ
ejpam-3362	394	28	vertex	vertex	NOUN
ejpam-3362	394	29	of	of	ADP
ejpam-3362	394	30	γ(h	γ(h	NOUN
ejpam-3362	394	31	)	)	PUNCT
ejpam-3362	394	32	.	.	PUNCT
ejpam-3362	395	1	suppose	suppose	VERB
ejpam-3362	395	2	further	far	ADV
ejpam-3362	395	3	that	that	SCONJ
ejpam-3362	395	4	|a∗(h)|	|a∗(h)|	PROPN
ejpam-3362	395	5	≥	≥	NUM
ejpam-3362	395	6	2	2	NUM
ejpam-3362	395	7	,	,	PUNCT
ejpam-3362	395	8	say	say	VERB
ejpam-3362	395	9	a	a	PRON
ejpam-3362	395	10	,	,	PUNCT
ejpam-3362	395	11	b	b	PROPN
ejpam-3362	395	12	∈	∈	PROPN
ejpam-3362	395	13	a∗(h	a∗(h	PROPN
ejpam-3362	395	14	)	)	PUNCT
ejpam-3362	395	15	with	with	ADP
ejpam-3362	395	16	a	a	DET
ejpam-3362	395	17	6=	6=	ADP
ejpam-3362	395	18	b.	b.	PROPN
ejpam-3362	395	19	since	since	SCONJ
ejpam-3362	395	20	0a	0a	PROPN
ejpam-3362	395	21	,	,	PUNCT
ejpam-3362	395	22	0b	0b	PROPN
ejpam-3362	395	23	∈	∈	PROPN
ejpam-3362	395	24	e(γ(h	e(γ(h	PROPN
ejpam-3362	395	25	)	)	PUNCT
ejpam-3362	395	26	)	)	PUNCT
ejpam-3362	395	27	,	,	PUNCT
ejpam-3362	395	28	0	0	NUM
ejpam-3362	395	29	∈	∈	PROPN
ejpam-3362	395	30	lh(a	lh(a	NOUN
ejpam-3362	395	31	)	)	PUNCT
ejpam-3362	395	32	∩	∩	NOUN
ejpam-3362	395	33	lh(b	lh(b	NUM
ejpam-3362	395	34	)	)	PUNCT
ejpam-3362	395	35	.	.	PUNCT
ejpam-3362	396	1	by	by	ADP
ejpam-3362	396	2	proposition	proposition	NOUN
ejpam-3362	396	3	10	10	NUM
ejpam-3362	396	4	,	,	PUNCT
ejpam-3362	396	5	ab	ab	PROPN
ejpam-3362	396	6	∈	∈	PROPN
ejpam-3362	396	7	e(γ(h	e(γ(h	PROPN
ejpam-3362	396	8	)	)	PUNCT
ejpam-3362	396	9	)	)	PUNCT
ejpam-3362	396	10	.	.	PUNCT
ejpam-3362	397	1	this	this	PRON
ejpam-3362	397	2	implies	imply	VERB
ejpam-3362	397	3	that	that	SCONJ
ejpam-3362	397	4	γ(h	γ(h	NOUN
ejpam-3362	397	5	)	)	PUNCT
ejpam-3362	397	6	is	be	AUX
ejpam-3362	397	7	not	not	PART
ejpam-3362	397	8	a	a	DET
ejpam-3362	397	9	star	star	NOUN
ejpam-3362	397	10	,	,	PUNCT
ejpam-3362	397	11	a	a	DET
ejpam-3362	397	12	contradiction	contradiction	NOUN
ejpam-3362	397	13	.	.	PUNCT
ejpam-3362	398	1	therefore	therefore	ADV
ejpam-3362	398	2	,	,	PUNCT
ejpam-3362	398	3	|a∗(h)|	|a∗(h)|	PROPN
ejpam-3362	398	4	=	=	SYM
ejpam-3362	398	5	1	1	X
ejpam-3362	398	6	.	.	PUNCT
ejpam-3362	398	7	conversely	conversely	ADV
ejpam-3362	398	8	,	,	PUNCT
ejpam-3362	398	9	suppose	suppose	VERB
ejpam-3362	398	10	that	that	SCONJ
ejpam-3362	398	11	γ(h	γ(h	NOUN
ejpam-3362	398	12	)	)	PUNCT
ejpam-3362	398	13	is	be	AUX
ejpam-3362	398	14	connected	connect	VERB
ejpam-3362	398	15	and	and	CCONJ
ejpam-3362	398	16	|a∗(h)|	|a∗(h)|	PROPN
ejpam-3362	398	17	=	=	SYM
ejpam-3362	398	18	1	1	NUM
ejpam-3362	398	19	,	,	PUNCT
ejpam-3362	398	20	say	say	VERB
ejpam-3362	398	21	a∗(h	a∗(h	PROPN
ejpam-3362	398	22	)	)	PUNCT
ejpam-3362	398	23	=	=	PRON
ejpam-3362	398	24	{	{	PUNCT
ejpam-3362	398	25	a	a	X
ejpam-3362	398	26	}	}	PUNCT
ejpam-3362	398	27	.	.	PUNCT
ejpam-3362	399	1	if	if	SCONJ
ejpam-3362	399	2	|h|	|h|	PRON
ejpam-3362	399	3	=	=	SYM
ejpam-3362	399	4	2	2	NUM
ejpam-3362	399	5	,	,	PUNCT
ejpam-3362	399	6	then	then	ADV
ejpam-3362	399	7	γ(h	γ(h	NOUN
ejpam-3362	399	8	)	)	PUNCT
ejpam-3362	399	9	=	=	SYM
ejpam-3362	399	10	p2	p2	PROPN
ejpam-3362	399	11	,	,	PUNCT
ejpam-3362	399	12	a	a	DET
ejpam-3362	399	13	star	star	NOUN
ejpam-3362	399	14	.	.	PUNCT
ejpam-3362	399	15	suppose	suppose	VERB
ejpam-3362	399	16	that	that	SCONJ
ejpam-3362	399	17	|h|	|h|	PROPN
ejpam-3362	399	18	≥	≥	NUM
ejpam-3362	399	19	3	3	NUM
ejpam-3362	399	20	and	and	CCONJ
ejpam-3362	399	21	let	let	VERB
ejpam-3362	399	22	y	y	PRON
ejpam-3362	399	23	,	,	PUNCT
ejpam-3362	399	24	z	z	PROPN
ejpam-3362	399	25	∈	∈	PROPN
ejpam-3362	399	26	h\{0	h\{0	NOUN
ejpam-3362	399	27	}	}	PUNCT
ejpam-3362	399	28	.	.	PUNCT
ejpam-3362	400	1	by	by	ADP
ejpam-3362	400	2	theorem	theorem	NOUN
ejpam-3362	400	3	4(ii	4(ii	NUM
ejpam-3362	400	4	)	)	PUNCT
ejpam-3362	400	5	,	,	PUNCT
ejpam-3362	400	6	a	a	DET
ejpam-3362	400	7	�	�	PROPN
ejpam-3362	400	8	y	y	PROPN
ejpam-3362	400	9	and	and	CCONJ
ejpam-3362	400	10	a	a	DET
ejpam-3362	400	11	�	�	PROPN
ejpam-3362	400	12	z.	z.	PROPN
ejpam-3362	400	13	that	that	PRON
ejpam-3362	400	14	is	be	AUX
ejpam-3362	400	15	,	,	PUNCT
ejpam-3362	400	16	a	a	DET
ejpam-3362	400	17	∈	∈	NOUN
ejpam-3362	400	18	lh({y	lh({y	NOUN
ejpam-3362	400	19	,	,	PUNCT
ejpam-3362	400	20	z	z	NOUN
ejpam-3362	400	21	}	}	PUNCT
ejpam-3362	400	22	)	)	PUNCT
ejpam-3362	400	23	.	.	PUNCT
ejpam-3362	401	1	this	this	PRON
ejpam-3362	401	2	implies	imply	VERB
ejpam-3362	401	3	that	that	SCONJ
ejpam-3362	401	4	yz	yz	PROPN
ejpam-3362	401	5	/∈	/∈	PUNCT
ejpam-3362	401	6	e(γ(h	e(γ(h	PROPN
ejpam-3362	401	7	)	)	PUNCT
ejpam-3362	401	8	)	)	PUNCT
ejpam-3362	401	9	.	.	PUNCT
ejpam-3362	402	1	since	since	SCONJ
ejpam-3362	402	2	γ(h	γ(h	PROPN
ejpam-3362	402	3	)	)	PUNCT
ejpam-3362	402	4	is	be	AUX
ejpam-3362	402	5	connected	connect	VERB
ejpam-3362	402	6	,	,	PUNCT
ejpam-3362	402	7	by	by	ADP
ejpam-3362	402	8	proposition	proposition	NOUN
ejpam-3362	402	9	4	4	NUM
ejpam-3362	402	10	,	,	PUNCT
ejpam-3362	402	11	0x	0x	PROPN
ejpam-3362	402	12	∈	∈	PROPN
ejpam-3362	402	13	e(γ(h	e(γ(h	NOUN
ejpam-3362	402	14	)	)	PUNCT
ejpam-3362	402	15	)	)	PUNCT
ejpam-3362	402	16	for	for	ADP
ejpam-3362	402	17	all	all	DET
ejpam-3362	402	18	x	x	SYM
ejpam-3362	402	19	∈	∈	PROPN
ejpam-3362	402	20	h	h	NOUN
ejpam-3362	402	21	\	\	PUNCT
ejpam-3362	402	22	{	{	PUNCT
ejpam-3362	402	23	0	0	NUM
ejpam-3362	402	24	}	}	PUNCT
ejpam-3362	402	25	.	.	PUNCT
ejpam-3362	403	1	consequently	consequently	ADV
ejpam-3362	403	2	,	,	PUNCT
ejpam-3362	403	3	γ(h	γ(h	PROPN
ejpam-3362	403	4	)	)	PUNCT
ejpam-3362	403	5	is	be	AUX
ejpam-3362	403	6	a	a	DET
ejpam-3362	403	7	star	star	NOUN
ejpam-3362	403	8	.	.	PUNCT
ejpam-3362	404	1	�	�	PROPN
ejpam-3362	404	2	acknowledgements	acknowledgement	NOUN
ejpam-3362	404	3	this	this	DET
ejpam-3362	404	4	research	research	NOUN
ejpam-3362	404	5	is	be	AUX
ejpam-3362	404	6	funded	fund	VERB
ejpam-3362	404	7	by	by	ADP
ejpam-3362	404	8	the	the	DET
ejpam-3362	404	9	philippine	philippine	PROPN
ejpam-3362	404	10	department	department	PROPN
ejpam-3362	404	11	of	of	ADP
ejpam-3362	404	12	science	science	NOUN
ejpam-3362	404	13	and	and	CCONJ
ejpam-3362	404	14	technologyaccelerated	technologyaccelerated	ADJ
ejpam-3362	404	15	science	science	NOUN
ejpam-3362	404	16	and	and	CCONJ
ejpam-3362	404	17	technology	technology	NOUN
ejpam-3362	404	18	human	human	ADJ
ejpam-3362	404	19	resource	resource	NOUN
ejpam-3362	404	20	development	development	NOUN
ejpam-3362	404	21	program	program	NOUN
ejpam-3362	404	22	(	(	PUNCT
ejpam-3362	404	23	dostasthrdp	dostasthrdp	PROPN
ejpam-3362	404	24	)	)	PUNCT
ejpam-3362	404	25	and	and	CCONJ
ejpam-3362	404	26	mindanao	mindanao	PROPN
ejpam-3362	404	27	state	state	PROPN
ejpam-3362	404	28	university	university	PROPN
ejpam-3362	404	29	-	-	PUNCT
ejpam-3362	404	30	iligan	iligan	PROPN
ejpam-3362	404	31	institute	institute	PROPN
ejpam-3362	404	32	of	of	ADP
ejpam-3362	404	33	technology	technology	PROPN
ejpam-3362	404	34	.	.	PUNCT
ejpam-3362	405	1	references	reference	NOUN
ejpam-3362	405	2	158	158	NUM
ejpam-3362	405	3	references	reference	NOUN
ejpam-3362	405	4	[	[	X
ejpam-3362	405	5	1	1	NUM
ejpam-3362	405	6	]	]	X
ejpam-3362	405	7	beck	beck	PROPN
ejpam-3362	405	8	,	,	PUNCT
ejpam-3362	405	9	i.	i.	PROPN
ejpam-3362	405	10	,	,	PUNCT
ejpam-3362	405	11	coloring	coloring	NOUN
ejpam-3362	405	12	of	of	ADP
ejpam-3362	405	13	commutative	commutative	ADJ
ejpam-3362	405	14	rings	ring	NOUN
ejpam-3362	405	15	,	,	PUNCT
ejpam-3362	405	16	journal	journal	NOUN
ejpam-3362	405	17	of	of	ADP
ejpam-3362	405	18	algebra	algebra	PROPN
ejpam-3362	405	19	,	,	PUNCT
ejpam-3362	405	20	116	116	NUM
ejpam-3362	405	21	(	(	PUNCT
ejpam-3362	405	22	1988	1988	NUM
ejpam-3362	405	23	)	)	PUNCT
ejpam-3362	405	24	,	,	PUNCT
ejpam-3362	405	25	208	208	NUM
ejpam-3362	405	26	-	-	SYM
ejpam-3362	405	27	226	226	NUM
ejpam-3362	405	28	.	.	PUNCT
ejpam-3362	406	1	[	[	X
ejpam-3362	406	2	2	2	NUM
ejpam-3362	406	3	]	]	X
ejpam-3362	406	4	demeyer	demeyer	NOUN
ejpam-3362	406	5	,	,	PUNCT
ejpam-3362	406	6	f.r	f.r	PROPN
ejpam-3362	406	7	.	.	PROPN
ejpam-3362	406	8	,	,	PUNCT
ejpam-3362	406	9	mckenzie	mckenzie	NOUN
ejpam-3362	406	10	,	,	PUNCT
ejpam-3362	406	11	t.	t.	PROPN
ejpam-3362	406	12	and	and	CCONJ
ejpam-3362	406	13	schneider	schneider	PROPN
ejpam-3362	406	14	,	,	PUNCT
ejpam-3362	406	15	k.	k.	PROPN
ejpam-3362	406	16	,	,	PUNCT
ejpam-3362	406	17	the	the	DET
ejpam-3362	406	18	zero	zero	NUM
ejpam-3362	406	19	-	-	PUNCT
ejpam-3362	406	20	divisor	divisor	NOUN
ejpam-3362	406	21	graph	graph	NOUN
ejpam-3362	406	22	of	of	ADP
ejpam-3362	406	23	a	a	DET
ejpam-3362	406	24	commutative	commutative	ADJ
ejpam-3362	406	25	semigroup	semigroup	NOUN
ejpam-3362	406	26	,	,	PUNCT
ejpam-3362	406	27	semigroup	semigroup	PROPN
ejpam-3362	406	28	forum	forum	PROPN
ejpam-3362	406	29	,	,	PUNCT
ejpam-3362	406	30	65	65	NUM
ejpam-3362	406	31	(	(	PUNCT
ejpam-3362	406	32	2002	2002	NUM
ejpam-3362	406	33	)	)	PUNCT
ejpam-3362	406	34	,	,	PUNCT
ejpam-3362	406	35	206	206	NUM
ejpam-3362	406	36	-	-	SYM
ejpam-3362	406	37	214	214	NUM
ejpam-3362	406	38	.	.	PUNCT
ejpam-3362	407	1	[	[	X
ejpam-3362	407	2	3	3	NUM
ejpam-3362	407	3	]	]	PUNCT
ejpam-3362	407	4	flores	flore	NOUN
ejpam-3362	407	5	,	,	PUNCT
ejpam-3362	407	6	g.b.c	g.b.c	NOUN
ejpam-3362	407	7	.	.	PUNCT
ejpam-3362	408	1	and	and	CCONJ
ejpam-3362	408	2	petalcorin	petalcorin	NOUN
ejpam-3362	408	3	,	,	PUNCT
ejpam-3362	408	4	g.c	g.c	PROPN
ejpam-3362	408	5	.	.	PROPN
ejpam-3362	408	6	,	,	PUNCT
ejpam-3362	408	7	some	some	DET
ejpam-3362	408	8	hyper	hyper	ADJ
ejpam-3362	408	9	isomorphism	isomorphism	NOUN
ejpam-3362	408	10	theorems	theorem	NOUN
ejpam-3362	408	11	of	of	ADP
ejpam-3362	408	12	hyper	hyper	ADJ
ejpam-3362	408	13	bci	bci	NOUN
ejpam-3362	408	14	-	-	PUNCT
ejpam-3362	408	15	algebras	algebra	NOUN
ejpam-3362	408	16	,	,	PUNCT
ejpam-3362	408	17	journal	journal	NOUN
ejpam-3362	408	18	of	of	ADP
ejpam-3362	408	19	algebra	algebra	PROPN
ejpam-3362	408	20	and	and	CCONJ
ejpam-3362	408	21	applied	apply	VERB
ejpam-3362	408	22	mathematics	mathematic	NOUN
ejpam-3362	408	23	,	,	PUNCT
ejpam-3362	408	24	13	13	NUM
ejpam-3362	408	25	(	(	PUNCT
ejpam-3362	408	26	2015	2015	NUM
ejpam-3362	408	27	)	)	PUNCT
ejpam-3362	408	28	,	,	PUNCT
ejpam-3362	408	29	15	15	NUM
ejpam-3362	408	30	-	-	SYM
ejpam-3362	408	31	31	31	NUM
ejpam-3362	408	32	.	.	PUNCT
ejpam-3362	409	1	[	[	X
ejpam-3362	409	2	4	4	NUM
ejpam-3362	409	3	]	]	X
ejpam-3362	409	4	harary	harary	NOUN
ejpam-3362	409	5	,	,	PUNCT
ejpam-3362	409	6	f.	f.	PROPN
ejpam-3362	409	7	,	,	PUNCT
ejpam-3362	409	8	graph	graph	NOUN
ejpam-3362	409	9	theory	theory	NOUN
ejpam-3362	409	10	,	,	PUNCT
ejpam-3362	409	11	addison	addison	PROPN
ejpam-3362	409	12	-	-	PUNCT
ejpam-3362	409	13	wesley	wesley	PROPN
ejpam-3362	409	14	publishing	publishing	PROPN
ejpam-3362	409	15	company	company	PROPN
ejpam-3362	409	16	,	,	PUNCT
ejpam-3362	409	17	inc	inc	PROPN
ejpam-3362	409	18	.	.	PROPN
ejpam-3362	409	19	,usa	,usa	PUNCT
ejpam-3362	409	20	,	,	PUNCT
ejpam-3362	409	21	1969	1969	NUM
ejpam-3362	409	22	.	.	PUNCT
ejpam-3362	410	1	[	[	X
ejpam-3362	410	2	5	5	NUM
ejpam-3362	410	3	]	]	X
ejpam-3362	410	4	jun	jun	PROPN
ejpam-3362	410	5	,	,	PUNCT
ejpam-3362	410	6	y.b	y.b	PROPN
ejpam-3362	410	7	.	.	PROPN
ejpam-3362	410	8	and	and	CCONJ
ejpam-3362	410	9	lee	lee	PROPN
ejpam-3362	410	10	,	,	PUNCT
ejpam-3362	410	11	k.j	k.j	PROPN
ejpam-3362	410	12	.	.	PROPN
ejpam-3362	410	13	,	,	PUNCT
ejpam-3362	410	14	graphs	graph	NOUN
ejpam-3362	410	15	based	base	VERB
ejpam-3362	410	16	on	on	ADP
ejpam-3362	410	17	bck	bck	PROPN
ejpam-3362	410	18	/	/	SYM
ejpam-3362	410	19	bci	bci	NOUN
ejpam-3362	410	20	-	-	PUNCT
ejpam-3362	410	21	algebras	algebra	NOUN
ejpam-3362	410	22	,	,	PUNCT
ejpam-3362	410	23	international	international	ADJ
ejpam-3362	410	24	journal	journal	NOUN
ejpam-3362	410	25	of	of	ADP
ejpam-3362	410	26	mathematics	mathematics	PROPN
ejpam-3362	410	27	and	and	CCONJ
ejpam-3362	410	28	mathematical	mathematical	ADJ
ejpam-3362	410	29	sciences	science	NOUN
ejpam-3362	410	30	,	,	PUNCT
ejpam-3362	410	31	2011	2011	NUM
ejpam-3362	410	32	(	(	PUNCT
ejpam-3362	410	33	2011	2011	NUM
ejpam-3362	410	34	)	)	PUNCT
ejpam-3362	410	35	,	,	PUNCT
ejpam-3362	410	36	1	1	NUM
ejpam-3362	410	37	-	-	SYM
ejpam-3362	410	38	8	8	NUM
ejpam-3362	410	39	.	.	PUNCT
ejpam-3362	411	1	[	[	X
ejpam-3362	411	2	6	6	NUM
ejpam-3362	411	3	]	]	X
ejpam-3362	411	4	nisar	nisar	PROPN
ejpam-3362	411	5	,	,	PUNCT
ejpam-3362	411	6	f.	f.	PROPN
ejpam-3362	411	7	,	,	PUNCT
ejpam-3362	411	8	tariq	tariq	PROPN
ejpam-3362	411	9	,	,	PUNCT
ejpam-3362	411	10	r.s	r.s	PROPN
ejpam-3362	411	11	.	.	PROPN
ejpam-3362	411	12	and	and	CCONJ
ejpam-3362	411	13	bhatti	bhatti	PROPN
ejpam-3362	411	14	,	,	PUNCT
ejpam-3362	411	15	s.a	s.a	PROPN
ejpam-3362	411	16	.	.	PROPN
ejpam-3362	411	17	,	,	PUNCT
ejpam-3362	411	18	fuzzy	fuzzy	ADJ
ejpam-3362	411	19	ideals	ideal	NOUN
ejpam-3362	411	20	in	in	ADP
ejpam-3362	411	21	hyper	hyper	ADJ
ejpam-3362	411	22	bci	bci	NOUN
ejpam-3362	411	23	-	-	PUNCT
ejpam-3362	411	24	algebras	algebra	NOUN
ejpam-3362	411	25	,	,	PUNCT
ejpam-3362	411	26	world	world	NOUN
ejpam-3362	411	27	applied	apply	VERB
ejpam-3362	411	28	science	science	NOUN
ejpam-3362	411	29	journal	journal	NOUN
ejpam-3362	411	30	,	,	PUNCT
ejpam-3362	411	31	12(2012	12(2012	NUM
ejpam-3362	411	32	)	)	PUNCT
ejpam-3362	411	33	,	,	PUNCT
ejpam-3362	411	34	1771	1771	NUM
ejpam-3362	411	35	-	-	SYM
ejpam-3362	411	36	1777	1777	NUM
ejpam-3362	411	37	.	.	PUNCT
ejpam-3362	412	1	[	[	X
ejpam-3362	412	2	7	7	X
ejpam-3362	412	3	]	]	X
ejpam-3362	412	4	xin	xin	PROPN
ejpam-3362	412	5	,	,	PUNCT
ejpam-3362	412	6	x.l	x.l	PROPN
ejpam-3362	412	7	.	.	PROPN
ejpam-3362	412	8	,	,	PUNCT
ejpam-3362	412	9	hyper	hyper	ADJ
ejpam-3362	412	10	bci	bci	NOUN
ejpam-3362	412	11	-	-	PUNCT
ejpam-3362	412	12	algebras	algebras	X
ejpam-3362	412	13	,	,	PUNCT
ejpam-3362	412	14	discuss	discuss	VERB
ejpam-3362	412	15	math	math	NOUN
ejpam-3362	412	16	.	.	PUNCT
ejpam-3362	413	1	soc	soc	PROPN
ejpam-3362	413	2	.	.	PUNCT
ejpam-3362	413	3	,	,	PUNCT
ejpam-3362	413	4	26(2006	26(2006	NUM
ejpam-3362	413	5	)	)	PUNCT
ejpam-3362	413	6	,	,	PUNCT
ejpam-3362	413	7	5	5	NUM
ejpam-3362	413	8	-	-	SYM
ejpam-3362	413	9	19	19	NUM
ejpam-3362	413	10	.	.	PUNCT