id	sid	tid	token	lemma	pos
ejpam-2473	1	1	compile	compile	NOUN
ejpam-2473	1	2	/	/	SYM
ejpam-2473	1	3	output.dvi	output.dvi	NOUN
ejpam-2473	1	4	european	european	ADJ
ejpam-2473	1	5	journal	journal	NOUN
ejpam-2473	1	6	of	of	ADP
ejpam-2473	1	7	pure	pure	ADJ
ejpam-2473	1	8	and	and	CCONJ
ejpam-2473	1	9	applied	apply	VERB
ejpam-2473	1	10	mathematics	mathematic	NOUN
ejpam-2473	1	11	vol	vol	NOUN
ejpam-2473	1	12	.	.	PROPN
ejpam-2473	2	1	9	9	NUM
ejpam-2473	2	2	,	,	PUNCT
ejpam-2473	2	3	no	no	INTJ
ejpam-2473	2	4	.	.	NOUN
ejpam-2473	2	5	1	1	NUM
ejpam-2473	2	6	,	,	PUNCT
ejpam-2473	2	7	2016	2016	NUM
ejpam-2473	2	8	,	,	PUNCT
ejpam-2473	2	9	34	34	NUM
ejpam-2473	2	10	-	-	SYM
ejpam-2473	2	11	38	38	NUM
ejpam-2473	2	12	issn	issn	PROPN
ejpam-2473	2	13	1307	1307	NUM
ejpam-2473	2	14	-	-	SYM
ejpam-2473	2	15	5543	5543	NUM
ejpam-2473	2	16	–	–	PUNCT
ejpam-2473	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2473	2	18	d	d	X
ejpam-2473	2	19	-	-	PUNCT
ejpam-2473	2	20	sets	set	NOUN
ejpam-2473	2	21	generated	generate	VERB
ejpam-2473	2	22	by	by	ADP
ejpam-2473	2	23	a	a	DET
ejpam-2473	2	24	subset	subset	NOUN
ejpam-2473	2	25	of	of	ADP
ejpam-2473	2	26	a	a	DET
ejpam-2473	2	27	group	group	NOUN
ejpam-2473	2	28	cristopher	cristopher	PROPN
ejpam-2473	2	29	john	john	PROPN
ejpam-2473	2	30	s.	s.	PROPN
ejpam-2473	2	31	rosero1	rosero1	PROPN
ejpam-2473	2	32	,	,	PUNCT
ejpam-2473	3	1	michael	michael	PROPN
ejpam-2473	3	2	p.	p.	PROPN
ejpam-2473	3	3	baldado	baldado	PROPN
ejpam-2473	4	1	jr	jr	PROPN
ejpam-2473	4	2	.	.	PROPN
ejpam-2473	4	3	2,∗	2,∗	NUM
ejpam-2473	4	4	1	1	NUM
ejpam-2473	4	5	mathematics	mathematic	NOUN
ejpam-2473	4	6	and	and	CCONJ
ejpam-2473	4	7	ict	ict	PROPN
ejpam-2473	4	8	department	department	PROPN
ejpam-2473	4	9	,	,	PUNCT
ejpam-2473	4	10	cebu	cebu	NOUN
ejpam-2473	4	11	normal	normal	ADJ
ejpam-2473	4	12	university	university	NOUN
ejpam-2473	4	13	,	,	PUNCT
ejpam-2473	4	14	cebu	cebu	NOUN
ejpam-2473	4	15	city	city	NOUN
ejpam-2473	4	16	,	,	PUNCT
ejpam-2473	4	17	philippines	philippine	NOUN
ejpam-2473	4	18	2	2	NUM
ejpam-2473	4	19	math	math	NOUN
ejpam-2473	4	20	department	department	NOUN
ejpam-2473	4	21	,	,	PUNCT
ejpam-2473	4	22	negros	negros	PROPN
ejpam-2473	4	23	oriental	oriental	ADJ
ejpam-2473	4	24	state	state	PROPN
ejpam-2473	4	25	university	university	PROPN
ejpam-2473	4	26	,	,	PUNCT
ejpam-2473	4	27	dumaguete	dumaguete	PROPN
ejpam-2473	4	28	city	city	PROPN
ejpam-2473	4	29	,	,	PUNCT
ejpam-2473	4	30	philippines	philippine	NOUN
ejpam-2473	4	31	abstract	abstract	ADJ
ejpam-2473	4	32	.	.	PUNCT
ejpam-2473	5	1	a	a	DET
ejpam-2473	5	2	subset	subset	NOUN
ejpam-2473	5	3	d	d	NOUN
ejpam-2473	5	4	of	of	ADP
ejpam-2473	5	5	a	a	DET
ejpam-2473	5	6	group	group	NOUN
ejpam-2473	5	7	g	g	NOUN
ejpam-2473	5	8	is	be	AUX
ejpam-2473	5	9	a	a	DET
ejpam-2473	5	10	d	d	X
ejpam-2473	5	11	-set	-set	NOUN
ejpam-2473	5	12	if	if	SCONJ
ejpam-2473	5	13	every	every	DET
ejpam-2473	5	14	element	element	NOUN
ejpam-2473	5	15	of	of	ADP
ejpam-2473	5	16	g	g	NOUN
ejpam-2473	5	17	,	,	PUNCT
ejpam-2473	5	18	not	not	PART
ejpam-2473	5	19	in	in	ADP
ejpam-2473	5	20	d	d	NOUN
ejpam-2473	5	21	,	,	PUNCT
ejpam-2473	5	22	has	have	VERB
ejpam-2473	5	23	its	its	PRON
ejpam-2473	5	24	inverse	inverse	NOUN
ejpam-2473	5	25	in	in	ADP
ejpam-2473	5	26	d.	d.	PROPN
ejpam-2473	5	27	let	let	VERB
ejpam-2473	5	28	a	a	PRON
ejpam-2473	5	29	be	be	AUX
ejpam-2473	5	30	a	a	DET
ejpam-2473	5	31	non	non	ADJ
ejpam-2473	5	32	-	-	ADJ
ejpam-2473	5	33	empty	empty	ADJ
ejpam-2473	5	34	subset	subset	NOUN
ejpam-2473	5	35	of	of	ADP
ejpam-2473	5	36	g.	g.	PROPN
ejpam-2473	5	37	a	a	DET
ejpam-2473	5	38	smallest	small	ADJ
ejpam-2473	5	39	d	d	NOUN
ejpam-2473	5	40	-set	-set	PUNCT
ejpam-2473	5	41	of	of	ADP
ejpam-2473	5	42	g	g	PROPN
ejpam-2473	5	43	that	that	PRON
ejpam-2473	5	44	contains	contain	VERB
ejpam-2473	5	45	a	a	PRON
ejpam-2473	5	46	is	be	AUX
ejpam-2473	5	47	called	call	VERB
ejpam-2473	5	48	a	a	DET
ejpam-2473	5	49	d	d	NOUN
ejpam-2473	5	50	-set	-set	ADV
ejpam-2473	5	51	generated	generate	VERB
ejpam-2473	5	52	by	by	ADP
ejpam-2473	5	53	a	a	PRON
ejpam-2473	5	54	,	,	PUNCT
ejpam-2473	5	55	denoted	denote	VERB
ejpam-2473	5	56	by	by	ADP
ejpam-2473	5	57	〈	〈	PROPN
ejpam-2473	5	58	a	a	DET
ejpam-2473	5	59	〉	〉	NOUN
ejpam-2473	5	60	.	.	PUNCT
ejpam-2473	6	1	note	note	VERB
ejpam-2473	6	2	that	that	SCONJ
ejpam-2473	6	3	〈	〈	PROPN
ejpam-2473	6	4	a	a	DET
ejpam-2473	6	5	〉	〉	NOUN
ejpam-2473	6	6	may	may	AUX
ejpam-2473	6	7	not	not	PART
ejpam-2473	6	8	be	be	AUX
ejpam-2473	6	9	unique	unique	ADJ
ejpam-2473	6	10	.	.	PUNCT
ejpam-2473	7	1	this	this	DET
ejpam-2473	7	2	paper	paper	NOUN
ejpam-2473	7	3	characterized	characterize	VERB
ejpam-2473	7	4	sets	set	VERB
ejpam-2473	7	5	a	a	PRON
ejpam-2473	7	6	with	with	ADP
ejpam-2473	7	7	unique	unique	ADJ
ejpam-2473	7	8	〈	〈	PROPN
ejpam-2473	7	9	a	a	DET
ejpam-2473	7	10	〉	〉	NOUN
ejpam-2473	7	11	and	and	CCONJ
ejpam-2473	7	12	sets	set	VERB
ejpam-2473	7	13	whose	whose	DET
ejpam-2473	7	14	number	number	NOUN
ejpam-2473	7	15	of	of	ADP
ejpam-2473	7	16	generated	generate	VERB
ejpam-2473	7	17	d	d	PROPN
ejpam-2473	7	18	-sets	-set	NOUN
ejpam-2473	7	19	is	be	AUX
ejpam-2473	7	20	equal	equal	ADJ
ejpam-2473	7	21	to	to	ADP
ejpam-2473	7	22	the	the	DET
ejpam-2473	7	23	index	index	NOUN
ejpam-2473	7	24	minimum	minimum	NOUN
ejpam-2473	7	25	.	.	PUNCT
ejpam-2473	8	1	2010	2010	NUM
ejpam-2473	8	2	mathematics	mathematic	NOUN
ejpam-2473	8	3	subject	subject	NOUN
ejpam-2473	8	4	classifications	classification	NOUN
ejpam-2473	8	5	:	:	PUNCT
ejpam-2473	8	6	20d99	20d99	NUM
ejpam-2473	8	7	key	key	ADJ
ejpam-2473	8	8	words	word	NOUN
ejpam-2473	8	9	and	and	CCONJ
ejpam-2473	8	10	phrases	phrase	NOUN
ejpam-2473	8	11	:	:	PUNCT
ejpam-2473	8	12	groups	group	NOUN
ejpam-2473	8	13	,	,	PUNCT
ejpam-2473	8	14	d	d	PROPN
ejpam-2473	8	15	-sets	-set	NOUN
ejpam-2473	8	16	,	,	PUNCT
ejpam-2473	8	17	index	index	NOUN
ejpam-2473	8	18	minimum	minimum	NOUN
ejpam-2473	8	19	1	1	NUM
ejpam-2473	8	20	.	.	PUNCT
ejpam-2473	9	1	introduction	introduction	NOUN
ejpam-2473	9	2	let	let	VERB
ejpam-2473	9	3	g	g	PRON
ejpam-2473	9	4	be	be	AUX
ejpam-2473	9	5	a	a	DET
ejpam-2473	9	6	group	group	NOUN
ejpam-2473	9	7	.	.	PUNCT
ejpam-2473	10	1	a	a	DET
ejpam-2473	10	2	subset	subset	NOUN
ejpam-2473	10	3	d	d	NOUN
ejpam-2473	10	4	of	of	ADP
ejpam-2473	10	5	g	g	PROPN
ejpam-2473	10	6	is	be	AUX
ejpam-2473	10	7	called	call	VERB
ejpam-2473	10	8	a	a	DET
ejpam-2473	10	9	d	d	NOUN
ejpam-2473	10	10	-set	-set	PUNCT
ejpam-2473	10	11	if	if	SCONJ
ejpam-2473	10	12	for	for	ADP
ejpam-2473	10	13	every	every	DET
ejpam-2473	10	14	x	x	PROPN
ejpam-2473	10	15	∈	∈	PROPN
ejpam-2473	10	16	g\d	g\d	X
ejpam-2473	10	17	,	,	PUNCT
ejpam-2473	10	18	x−1	x−1	PROPN
ejpam-2473	10	19	∈	∈	PROPN
ejpam-2473	10	20	d.	d.	PROPN
ejpam-2473	10	21	a	a	DET
ejpam-2473	10	22	smallest	small	ADJ
ejpam-2473	10	23	d	d	X
ejpam-2473	10	24	-set	-set	PUNCT
ejpam-2473	10	25	in	in	ADP
ejpam-2473	10	26	g	g	PROPN
ejpam-2473	10	27	is	be	AUX
ejpam-2473	10	28	called	call	VERB
ejpam-2473	10	29	a	a	DET
ejpam-2473	10	30	minimum	minimum	NOUN
ejpam-2473	10	31	d	d	NOUN
ejpam-2473	10	32	-set	-set	NUM
ejpam-2473	10	33	.	.	PUNCT
ejpam-2473	11	1	the	the	DET
ejpam-2473	11	2	number	number	NOUN
ejpam-2473	11	3	of	of	ADP
ejpam-2473	11	4	minimum	minimum	ADJ
ejpam-2473	11	5	d	d	NOUN
ejpam-2473	11	6	-sets	-set	NOUN
ejpam-2473	11	7	of	of	ADP
ejpam-2473	11	8	g	g	NOUN
ejpam-2473	11	9	is	be	AUX
ejpam-2473	11	10	called	call	VERB
ejpam-2473	11	11	the	the	DET
ejpam-2473	11	12	index	index	NOUN
ejpam-2473	11	13	minimum	minimum	NOUN
ejpam-2473	11	14	of	of	ADP
ejpam-2473	11	15	g.	g.	PROPN
ejpam-2473	11	16	please	please	INTJ
ejpam-2473	11	17	refer	refer	VERB
ejpam-2473	11	18	to	to	ADP
ejpam-2473	11	19	[	[	X
ejpam-2473	11	20	3	3	X
ejpam-2473	11	21	]	]	PUNCT
ejpam-2473	11	22	for	for	ADP
ejpam-2473	11	23	the	the	DET
ejpam-2473	11	24	concepts	concept	NOUN
ejpam-2473	11	25	that	that	PRON
ejpam-2473	11	26	are	be	AUX
ejpam-2473	11	27	not	not	PART
ejpam-2473	11	28	defined	define	VERB
ejpam-2473	11	29	in	in	ADP
ejpam-2473	11	30	this	this	DET
ejpam-2473	11	31	paper	paper	NOUN
ejpam-2473	11	32	.	.	PUNCT
ejpam-2473	12	1	in	in	ADP
ejpam-2473	12	2	[	[	X
ejpam-2473	12	3	1	1	NUM
ejpam-2473	12	4	]	]	PUNCT
ejpam-2473	12	5	,	,	PUNCT
ejpam-2473	12	6	we	we	PRON
ejpam-2473	12	7	proved	prove	VERB
ejpam-2473	12	8	that	that	SCONJ
ejpam-2473	12	9	if	if	SCONJ
ejpam-2473	12	10	x2	x2	PROPN
ejpam-2473	12	11	=	=	SYM
ejpam-2473	12	12	e	e	NOUN
ejpam-2473	12	13	,	,	PUNCT
ejpam-2473	12	14	then	then	ADV
ejpam-2473	12	15	x	x	PUNCT
ejpam-2473	12	16	is	be	AUX
ejpam-2473	12	17	an	an	DET
ejpam-2473	12	18	element	element	NOUN
ejpam-2473	12	19	of	of	ADP
ejpam-2473	12	20	any	any	DET
ejpam-2473	12	21	d	d	NOUN
ejpam-2473	12	22	-set	-set	NUM
ejpam-2473	12	23	.	.	PUNCT
ejpam-2473	13	1	thus	thus	ADV
ejpam-2473	13	2	,	,	PUNCT
ejpam-2473	13	3	if	if	SCONJ
ejpam-2473	13	4	s	s	PART
ejpam-2473	13	5	=	=	VERB
ejpam-2473	13	6	�	�	PROPN
ejpam-2473	13	7	s	s	PART
ejpam-2473	13	8	∈	∈	PROPN
ejpam-2473	13	9	g	g	NOUN
ejpam-2473	13	10	:	:	PUNCT
ejpam-2473	13	11	s2	s2	NOUN
ejpam-2473	13	12	=	=	PUNCT
ejpam-2473	13	13	e	e	PROPN
ejpam-2473	13	14	,	,	PUNCT
ejpam-2473	13	15	then	then	ADV
ejpam-2473	13	16	s	s	VERB
ejpam-2473	13	17	⊆	⊆	NUM
ejpam-2473	13	18	d	d	NOUN
ejpam-2473	13	19	for	for	ADP
ejpam-2473	13	20	all	all	DET
ejpam-2473	13	21	d	d	X
ejpam-2473	13	22	-set	-set	X
ejpam-2473	13	23	d.	d.	NOUN
ejpam-2473	14	1	it	it	PRON
ejpam-2473	14	2	is	be	AUX
ejpam-2473	14	3	mention	mention	NOUN
ejpam-2473	14	4	in	in	ADP
ejpam-2473	14	5	[	[	X
ejpam-2473	14	6	2	2	X
ejpam-2473	14	7	]	]	PUNCT
ejpam-2473	14	8	that	that	SCONJ
ejpam-2473	14	9	the	the	DET
ejpam-2473	14	10	relation	relation	NOUN
ejpam-2473	14	11	∼	∼	NOUN
ejpam-2473	14	12	defined	define	VERB
ejpam-2473	14	13	on	on	ADP
ejpam-2473	14	14	g\s	g\s	NOUN
ejpam-2473	14	15	given	give	VERB
ejpam-2473	14	16	by	by	ADP
ejpam-2473	14	17	x	x	PUNCT
ejpam-2473	14	18	∼	∼	NOUN
ejpam-2473	14	19	y	y	NOUN
ejpam-2473	14	20	if	if	SCONJ
ejpam-2473	14	21	and	and	CCONJ
ejpam-2473	14	22	only	only	ADV
ejpam-2473	14	23	if	if	SCONJ
ejpam-2473	14	24	x	x	NOUN
ejpam-2473	14	25	=	=	SYM
ejpam-2473	14	26	y	y	PROPN
ejpam-2473	14	27	or	or	CCONJ
ejpam-2473	14	28	x−1	x−1	PROPN
ejpam-2473	15	1	=	=	SYM
ejpam-2473	15	2	y	y	PROPN
ejpam-2473	15	3	is	be	AUX
ejpam-2473	15	4	an	an	DET
ejpam-2473	15	5	equivalence	equivalence	NOUN
ejpam-2473	15	6	relation	relation	NOUN
ejpam-2473	15	7	,	,	PUNCT
ejpam-2473	15	8	and	and	CCONJ
ejpam-2473	15	9	the	the	DET
ejpam-2473	15	10	equivalence	equivalence	NOUN
ejpam-2473	15	11	class	class	NOUN
ejpam-2473	15	12	containing	contain	VERB
ejpam-2473	15	13	x	x	SYM
ejpam-2473	15	14	is	be	AUX
ejpam-2473	15	15	{	{	PUNCT
ejpam-2473	15	16	x	x	INTJ
ejpam-2473	15	17	,	,	PUNCT
ejpam-2473	15	18	x−1	x−1	PROPN
ejpam-2473	15	19	}	}	PUNCT
ejpam-2473	15	20	.	.	PUNCT
ejpam-2473	16	1	thus	thus	ADV
ejpam-2473	16	2	,	,	PUNCT
ejpam-2473	16	3	g\s	g\s	ADP
ejpam-2473	16	4	=	=	SYM
ejpam-2473	16	5	{	{	PUNCT
ejpam-2473	16	6	a1	a1	PROPN
ejpam-2473	16	7	,	,	PUNCT
ejpam-2473	16	8	a−1	a−1	PROPN
ejpam-2473	16	9	1	1	NUM
ejpam-2473	16	10	}	}	PUNCT
ejpam-2473	16	11	∪{a2	∪{a2	PROPN
ejpam-2473	16	12	,	,	PUNCT
ejpam-2473	16	13	a−1	a−1	PROPN
ejpam-2473	16	14	2	2	NUM
ejpam-2473	16	15	}	}	PUNCT
ejpam-2473	16	16	∪	∪	X
ejpam-2473	16	17	·	·	PUNCT
ejpam-2473	16	18	·	·	PUNCT
ejpam-2473	16	19	·	·	PUNCT
ejpam-2473	16	20	∪{ac	∪{ac	X
ejpam-2473	16	21	,	,	PUNCT
ejpam-2473	16	22	a−1	a−1	PROPN
ejpam-2473	16	23	c	c	PROPN
ejpam-2473	16	24	}	}	PUNCT
ejpam-2473	16	25	.	.	PUNCT
ejpam-2473	17	1	if	if	SCONJ
ejpam-2473	17	2	ai	ai	VERB
ejpam-2473	17	3	6=	6=	ADP
ejpam-2473	17	4	a	a	DET
ejpam-2473	17	5	j	j	NOUN
ejpam-2473	17	6	for	for	ADP
ejpam-2473	17	7	i	i	PROPN
ejpam-2473	17	8	6=	6=	PROPN
ejpam-2473	17	9	j	j	PROPN
ejpam-2473	17	10	,	,	PUNCT
ejpam-2473	17	11	then	then	ADV
ejpam-2473	17	12	we	we	PRON
ejpam-2473	17	13	call	call	VERB
ejpam-2473	17	14	the	the	DET
ejpam-2473	17	15	given	give	VERB
ejpam-2473	17	16	partition	partition	NOUN
ejpam-2473	17	17	a	a	DET
ejpam-2473	17	18	canonical	canonical	ADJ
ejpam-2473	17	19	partition	partition	NOUN
ejpam-2473	17	20	of	of	ADP
ejpam-2473	17	21	g\s	g\s	NOUN
ejpam-2473	17	22	,	,	PUNCT
ejpam-2473	17	23	and	and	CCONJ
ejpam-2473	17	24	c	c	PROPN
ejpam-2473	17	25	is	be	AUX
ejpam-2473	17	26	called	call	VERB
ejpam-2473	17	27	the	the	DET
ejpam-2473	17	28	c	c	ADJ
ejpam-2473	17	29	-number	-number	PROPN
ejpam-2473	17	30	of	of	ADP
ejpam-2473	17	31	g.	g.	PROPN
ejpam-2473	17	32	clearly	clearly	ADV
ejpam-2473	17	33	,	,	PUNCT
ejpam-2473	17	34	c	c	NOUN
ejpam-2473	17	35	=	=	PUNCT
ejpam-2473	18	1	|g\s|/2	|g\s|/2	AUX
ejpam-2473	18	2	.	.	PROPN
ejpam-2473	18	3	remark	remark	PROPN
ejpam-2473	18	4	1	1	NUM
ejpam-2473	18	5	.	.	PUNCT
ejpam-2473	19	1	let	let	VERB
ejpam-2473	19	2	g	g	PRON
ejpam-2473	19	3	be	be	AUX
ejpam-2473	19	4	a	a	DET
ejpam-2473	19	5	finite	finite	ADJ
ejpam-2473	19	6	group	group	NOUN
ejpam-2473	19	7	and	and	CCONJ
ejpam-2473	19	8	d	d	NOUN
ejpam-2473	19	9	be	be	AUX
ejpam-2473	19	10	a	a	DET
ejpam-2473	19	11	d	d	NOUN
ejpam-2473	19	12	-set	-set	PUNCT
ejpam-2473	19	13	of	of	ADP
ejpam-2473	19	14	g.	g.	PROPN
ejpam-2473	20	1	then	then	ADV
ejpam-2473	20	2	d	d	PROPN
ejpam-2473	20	3	=	=	SYM
ejpam-2473	20	4	s	s	X
ejpam-2473	20	5	∪	∪	X
ejpam-2473	20	6	{	{	PUNCT
ejpam-2473	20	7	x1	x1	PROPN
ejpam-2473	20	8	,	,	PUNCT
ejpam-2473	20	9	x2	x2	PROPN
ejpam-2473	20	10	,	,	PUNCT
ejpam-2473	20	11	.	.	PUNCT
ejpam-2473	20	12	.	.	PUNCT
ejpam-2473	20	13	.	.	PUNCT
ejpam-2473	21	1	,	,	PUNCT
ejpam-2473	21	2	xc	xc	PROPN
ejpam-2473	21	3	}	}	PUNCT
ejpam-2473	21	4	,	,	PUNCT
ejpam-2473	21	5	where	where	SCONJ
ejpam-2473	21	6	x	x	X
ejpam-2473	21	7	i	i	PRON
ejpam-2473	21	8	∈	∈	PROPN
ejpam-2473	21	9	{	{	PUNCT
ejpam-2473	21	10	ai	ai	INTJ
ejpam-2473	21	11	,	,	PUNCT
ejpam-2473	21	12	a−1	a−1	PROPN
ejpam-2473	21	13	i	i	PROPN
ejpam-2473	21	14	}	}	PUNCT
ejpam-2473	21	15	for	for	ADP
ejpam-2473	21	16	i	i	PROPN
ejpam-2473	21	17	=	=	SYM
ejpam-2473	21	18	1,2	1,2	NUM
ejpam-2473	21	19	,	,	PUNCT
ejpam-2473	21	20	.	.	PUNCT
ejpam-2473	21	21	.	.	PUNCT
ejpam-2473	21	22	.	.	PUNCT
ejpam-2473	22	1	,	,	PUNCT
ejpam-2473	22	2	c	c	NOUN
ejpam-2473	22	3	and	and	CCONJ
ejpam-2473	22	4	g\s	g\s	ADP
ejpam-2473	22	5	=	=	SYM
ejpam-2473	22	6	{	{	PUNCT
ejpam-2473	22	7	a1	a1	PROPN
ejpam-2473	22	8	,	,	PUNCT
ejpam-2473	22	9	a−1	a−1	PROPN
ejpam-2473	22	10	1	1	NUM
ejpam-2473	22	11	}	}	PUNCT
ejpam-2473	22	12	∪	∪	ADJ
ejpam-2473	22	13	{	{	PUNCT
ejpam-2473	22	14	a2	a2	PROPN
ejpam-2473	22	15	,	,	PUNCT
ejpam-2473	22	16	a−1	a−1	PROPN
ejpam-2473	22	17	2	2	NUM
ejpam-2473	22	18	}	}	PUNCT
ejpam-2473	22	19	∪	∪	X
ejpam-2473	22	20	·	·	PUNCT
ejpam-2473	22	21	·	·	PUNCT
ejpam-2473	22	22	·	·	PUNCT
ejpam-2473	22	23	∪	∪	X
ejpam-2473	22	24	{	{	PUNCT
ejpam-2473	22	25	ac	ac	PROPN
ejpam-2473	22	26	,	,	PUNCT
ejpam-2473	22	27	a−1	a−1	PROPN
ejpam-2473	22	28	c	c	PROPN
ejpam-2473	22	29	}	}	PUNCT
ejpam-2473	22	30	is	be	AUX
ejpam-2473	22	31	a	a	DET
ejpam-2473	22	32	canonical	canonical	ADJ
ejpam-2473	22	33	partition	partition	NOUN
ejpam-2473	22	34	,	,	PUNCT
ejpam-2473	22	35	if	if	SCONJ
ejpam-2473	22	36	and	and	CCONJ
ejpam-2473	22	37	only	only	ADV
ejpam-2473	22	38	if	if	SCONJ
ejpam-2473	22	39	d	d	NOUN
ejpam-2473	22	40	is	be	AUX
ejpam-2473	22	41	a	a	DET
ejpam-2473	22	42	minimum	minimum	NOUN
ejpam-2473	22	43	d	d	NOUN
ejpam-2473	22	44	-set	-set	NOUN
ejpam-2473	22	45	.	.	PUNCT
ejpam-2473	23	1	to	to	PART
ejpam-2473	23	2	see	see	VERB
ejpam-2473	23	3	this	this	PRON
ejpam-2473	23	4	,	,	PUNCT
ejpam-2473	23	5	assume	assume	VERB
ejpam-2473	23	6	that	that	SCONJ
ejpam-2473	23	7	d	d	NOUN
ejpam-2473	23	8	=	=	PUNCT
ejpam-2473	23	9	s∪{x1	s∪{x1	NOUN
ejpam-2473	23	10	,	,	PUNCT
ejpam-2473	23	11	x2	x2	PROPN
ejpam-2473	23	12	,	,	PUNCT
ejpam-2473	23	13	.	.	PUNCT
ejpam-2473	23	14	.	.	PUNCT
ejpam-2473	24	1	.	.	PUNCT
ejpam-2473	25	1	,	,	PUNCT
ejpam-2473	25	2	xc	xc	PROPN
ejpam-2473	25	3	}	}	PUNCT
ejpam-2473	25	4	,	,	PUNCT
ejpam-2473	25	5	where	where	SCONJ
ejpam-2473	25	6	x	x	X
ejpam-2473	25	7	i	i	PRON
ejpam-2473	25	8	∈	∈	PROPN
ejpam-2473	25	9	{	{	PUNCT
ejpam-2473	25	10	ai	ai	INTJ
ejpam-2473	25	11	,	,	PUNCT
ejpam-2473	25	12	a−1	a−1	PROPN
ejpam-2473	25	13	i	i	PROPN
ejpam-2473	25	14	}	}	PUNCT
ejpam-2473	25	15	for	for	ADP
ejpam-2473	25	16	i	i	PROPN
ejpam-2473	25	17	=	=	SYM
ejpam-2473	25	18	1,2	1,2	NUM
ejpam-2473	25	19	,	,	PUNCT
ejpam-2473	25	20	.	.	PUNCT
ejpam-2473	25	21	.	.	PUNCT
ejpam-2473	25	22	.	.	PUNCT
ejpam-2473	26	1	,	,	PUNCT
ejpam-2473	26	2	c	c	NOUN
ejpam-2473	26	3	and	and	CCONJ
ejpam-2473	26	4	g\s	g\s	ADP
ejpam-2473	26	5	=	=	SYM
ejpam-2473	26	6	{	{	PUNCT
ejpam-2473	26	7	a1	a1	PROPN
ejpam-2473	26	8	,	,	PUNCT
ejpam-2473	26	9	a−1	a−1	PROPN
ejpam-2473	26	10	1	1	NUM
ejpam-2473	26	11	}	}	PUNCT
ejpam-2473	26	12	∪	∪	ADJ
ejpam-2473	26	13	{	{	PUNCT
ejpam-2473	26	14	a2	a2	PROPN
ejpam-2473	26	15	,	,	PUNCT
ejpam-2473	26	16	a−1	a−1	PROPN
ejpam-2473	26	17	2	2	NUM
ejpam-2473	26	18	}	}	PUNCT
ejpam-2473	26	19	∪	∪	X
ejpam-2473	26	20	·	·	PUNCT
ejpam-2473	26	21	·	·	PUNCT
ejpam-2473	26	22	·	·	PUNCT
ejpam-2473	26	23	∪	∪	X
ejpam-2473	26	24	{	{	PUNCT
ejpam-2473	26	25	ac	ac	PROPN
ejpam-2473	26	26	,	,	PUNCT
ejpam-2473	26	27	a−1	a−1	PROPN
ejpam-2473	26	28	c	c	PROPN
ejpam-2473	26	29	}	}	PUNCT
ejpam-2473	26	30	is	be	AUX
ejpam-2473	26	31	a	a	DET
ejpam-2473	26	32	canonical	canonical	ADJ
ejpam-2473	26	33	partition	partition	NOUN
ejpam-2473	26	34	,	,	PUNCT
ejpam-2473	26	35	and	and	CCONJ
ejpam-2473	26	36	d	d	NOUN
ejpam-2473	26	37	is	be	AUX
ejpam-2473	26	38	not	not	PART
ejpam-2473	26	39	a	a	DET
ejpam-2473	26	40	minimum	minimum	NOUN
ejpam-2473	26	41	d	d	NOUN
ejpam-2473	26	42	-set	-set	PUNCT
ejpam-2473	26	43	.	.	PUNCT
ejpam-2473	27	1	let	let	VERB
ejpam-2473	27	2	d′	d′	PRON
ejpam-2473	27	3	be	be	AUX
ejpam-2473	27	4	a	a	DET
ejpam-2473	27	5	minimum	minimum	NOUN
ejpam-2473	27	6	d	d	NOUN
ejpam-2473	27	7	-set	-set	NUM
ejpam-2473	27	8	.	.	PUNCT
ejpam-2473	28	1	then	then	ADV
ejpam-2473	28	2	�	�	PROPN
ejpam-2473	28	3	�	�	PROPN
ejpam-2473	28	4	d′	d′	PROPN
ejpam-2473	28	5	�	�	PROPN
ejpam-2473	28	6	�	�	PROPN
ejpam-2473	28	7	<	<	X
ejpam-2473	28	8	|d|	|d|	PROPN
ejpam-2473	28	9	.	.	PUNCT
ejpam-2473	29	1	let	let	VERB
ejpam-2473	29	2	x	x	SYM
ejpam-2473	29	3	∈	∈	PROPN
ejpam-2473	29	4	d\d′.	d\d′.	NOUN
ejpam-2473	29	5	since	since	SCONJ
ejpam-2473	29	6	the	the	DET
ejpam-2473	29	7	elements	element	NOUN
ejpam-2473	29	8	of	of	ADP
ejpam-2473	29	9	∗corresponding	∗corresponde	VERB
ejpam-2473	29	10	author	author	NOUN
ejpam-2473	29	11	.	.	PUNCT
ejpam-2473	30	1	email	email	NOUN
ejpam-2473	30	2	addresses	address	NOUN
ejpam-2473	30	3	:	:	PUNCT
ejpam-2473	30	4	crisrose_18@yahoo.com	crisrose_18@yahoo.com	X
ejpam-2473	30	5	(	(	PUNCT
ejpam-2473	30	6	c.	c.	PROPN
ejpam-2473	30	7	rosero	rosero	PROPN
ejpam-2473	30	8	)	)	PUNCT
ejpam-2473	30	9	,	,	PUNCT
ejpam-2473	30	10	mbaldadojr@yahoo.com	mbaldadojr@yahoo.com	X
ejpam-2473	30	11	(	(	PUNCT
ejpam-2473	30	12	m.	m.	NOUN
ejpam-2473	30	13	baldado	baldado	PROPN
ejpam-2473	30	14	)	)	PUNCT
ejpam-2473	30	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2473	31	1	34	34	NUM
ejpam-2473	31	2	c	c	X
ejpam-2473	31	3	©	©	PROPN
ejpam-2473	31	4	2016	2016	NUM
ejpam-2473	31	5	ejpam	ejpam	VERB
ejpam-2473	31	6	all	all	DET
ejpam-2473	31	7	rights	right	NOUN
ejpam-2473	31	8	reserved	reserve	VERB
ejpam-2473	31	9	.	.	PUNCT
ejpam-2473	32	1	c.	c.	PROPN
ejpam-2473	32	2	rosero	rosero	PROPN
ejpam-2473	32	3	,	,	PUNCT
ejpam-2473	32	4	m.	m.	NOUN
ejpam-2473	32	5	baldado	baldado	NOUN
ejpam-2473	32	6	/	/	SYM
ejpam-2473	32	7	eur	eur	PROPN
ejpam-2473	32	8	.	.	PUNCT
ejpam-2473	33	1	j.	j.	PROPN
ejpam-2473	33	2	pure	pure	PROPN
ejpam-2473	33	3	appl	appl	PROPN
ejpam-2473	33	4	.	.	PROPN
ejpam-2473	33	5	math	math	PROPN
ejpam-2473	33	6	,	,	PUNCT
ejpam-2473	33	7	9	9	NUM
ejpam-2473	33	8	(	(	PUNCT
ejpam-2473	33	9	2016	2016	NUM
ejpam-2473	33	10	)	)	PUNCT
ejpam-2473	33	11	,	,	PUNCT
ejpam-2473	33	12	34	34	NUM
ejpam-2473	33	13	-	-	SYM
ejpam-2473	33	14	38	38	NUM
ejpam-2473	33	15	35	35	NUM
ejpam-2473	33	16	s	s	NOUN
ejpam-2473	33	17	must	must	AUX
ejpam-2473	33	18	be	be	AUX
ejpam-2473	33	19	in	in	ADP
ejpam-2473	33	20	d′	d′	X
ejpam-2473	33	21	,	,	PUNCT
ejpam-2473	33	22	x	x	PUNCT
ejpam-2473	34	1	=	=	PUNCT
ejpam-2473	34	2	x	x	PUNCT
ejpam-2473	34	3	i	i	PRON
ejpam-2473	34	4	for	for	ADP
ejpam-2473	34	5	some	some	DET
ejpam-2473	34	6	i	i	PRON
ejpam-2473	34	7	∈	∈	PROPN
ejpam-2473	34	8	{	{	PUNCT
ejpam-2473	34	9	1,2	1,2	NUM
ejpam-2473	34	10	,	,	PUNCT
ejpam-2473	34	11	.	.	PUNCT
ejpam-2473	34	12	.	.	PUNCT
ejpam-2473	34	13	.	.	PUNCT
ejpam-2473	35	1	,	,	PUNCT
ejpam-2473	35	2	c	c	X
ejpam-2473	35	3	}	}	PUNCT
ejpam-2473	35	4	.	.	PUNCT
ejpam-2473	36	1	since	since	SCONJ
ejpam-2473	36	2	d′	d′	PRON
ejpam-2473	36	3	is	be	AUX
ejpam-2473	36	4	a	a	DET
ejpam-2473	36	5	d	d	NOUN
ejpam-2473	36	6	-set	-set	NOUN
ejpam-2473	36	7	,	,	PUNCT
ejpam-2473	36	8	x−1	x−1	PROPN
ejpam-2473	37	1	i	i	PRON
ejpam-2473	37	2	∈	∈	PROPN
ejpam-2473	37	3	d′.	d′.	VERB
ejpam-2473	37	4	hence	hence	ADV
ejpam-2473	37	5	,	,	PUNCT
ejpam-2473	37	6	x	x	PUNCT
ejpam-2473	37	7	i	i	NOUN
ejpam-2473	37	8	,	,	PUNCT
ejpam-2473	37	9	x−1	x−1	PROPN
ejpam-2473	38	1	i	i	PRON
ejpam-2473	38	2	∈	∈	PROPN
ejpam-2473	38	3	d.	d.	PROPN
ejpam-2473	38	4	this	this	PRON
ejpam-2473	38	5	is	be	AUX
ejpam-2473	38	6	a	a	DET
ejpam-2473	38	7	contradiction	contradiction	NOUN
ejpam-2473	38	8	.	.	PUNCT
ejpam-2473	39	1	conversely	conversely	ADV
ejpam-2473	39	2	,	,	PUNCT
ejpam-2473	39	3	assume	assume	VERB
ejpam-2473	39	4	that	that	SCONJ
ejpam-2473	39	5	d	d	NOUN
ejpam-2473	39	6	is	be	AUX
ejpam-2473	39	7	a	a	DET
ejpam-2473	39	8	minimum	minimum	NOUN
ejpam-2473	39	9	d	d	NOUN
ejpam-2473	39	10	-set	-set	PUNCT
ejpam-2473	39	11	and	and	CCONJ
ejpam-2473	39	12	d	d	X
ejpam-2473	40	1	6=	6=	SYM
ejpam-2473	40	2	s	s	NOUN
ejpam-2473	40	3	∪	∪	X
ejpam-2473	40	4	{	{	PUNCT
ejpam-2473	40	5	x1	x1	PROPN
ejpam-2473	40	6	,	,	PUNCT
ejpam-2473	40	7	x2	x2	PROPN
ejpam-2473	40	8	,	,	PUNCT
ejpam-2473	40	9	.	.	PUNCT
ejpam-2473	40	10	.	.	PUNCT
ejpam-2473	41	1	.	.	PUNCT
ejpam-2473	42	1	,	,	PUNCT
ejpam-2473	42	2	xc	xc	PROPN
ejpam-2473	42	3	}	}	PUNCT
ejpam-2473	42	4	,	,	PUNCT
ejpam-2473	42	5	where	where	SCONJ
ejpam-2473	42	6	x	x	X
ejpam-2473	42	7	i	i	PRON
ejpam-2473	42	8	∈	∈	PROPN
ejpam-2473	42	9	{	{	PUNCT
ejpam-2473	42	10	ai	ai	INTJ
ejpam-2473	42	11	,	,	PUNCT
ejpam-2473	42	12	a−1	a−1	PROPN
ejpam-2473	42	13	i	i	PROPN
ejpam-2473	42	14	}	}	PUNCT
ejpam-2473	42	15	for	for	ADP
ejpam-2473	42	16	i	i	PROPN
ejpam-2473	42	17	=	=	SYM
ejpam-2473	42	18	1,2	1,2	NUM
ejpam-2473	42	19	,	,	PUNCT
ejpam-2473	42	20	.	.	PUNCT
ejpam-2473	42	21	.	.	PUNCT
ejpam-2473	42	22	.	.	PUNCT
ejpam-2473	43	1	,	,	PUNCT
ejpam-2473	43	2	c	c	NOUN
ejpam-2473	43	3	and	and	CCONJ
ejpam-2473	43	4	g\s	g\s	ADP
ejpam-2473	43	5	=	=	SYM
ejpam-2473	43	6	{	{	PUNCT
ejpam-2473	43	7	a1	a1	PROPN
ejpam-2473	43	8	,	,	PUNCT
ejpam-2473	43	9	a−1	a−1	PROPN
ejpam-2473	43	10	1	1	NUM
ejpam-2473	43	11	}	}	PUNCT
ejpam-2473	43	12	∪	∪	ADJ
ejpam-2473	43	13	{	{	PUNCT
ejpam-2473	43	14	a2	a2	PROPN
ejpam-2473	43	15	,	,	PUNCT
ejpam-2473	43	16	a−1	a−1	PROPN
ejpam-2473	43	17	2	2	NUM
ejpam-2473	43	18	}	}	PUNCT
ejpam-2473	43	19	∪	∪	X
ejpam-2473	43	20	·	·	PUNCT
ejpam-2473	43	21	·	·	PUNCT
ejpam-2473	43	22	·	·	PUNCT
ejpam-2473	43	23	∪	∪	X
ejpam-2473	43	24	{	{	PUNCT
ejpam-2473	43	25	ac	ac	PROPN
ejpam-2473	43	26	,	,	PUNCT
ejpam-2473	43	27	a−1	a−1	PROPN
ejpam-2473	43	28	c	c	PROPN
ejpam-2473	43	29	}	}	PUNCT
ejpam-2473	43	30	is	be	AUX
ejpam-2473	43	31	a	a	DET
ejpam-2473	43	32	canonical	canonical	ADJ
ejpam-2473	43	33	partition	partition	NOUN
ejpam-2473	43	34	.	.	PUNCT
ejpam-2473	44	1	since	since	SCONJ
ejpam-2473	44	2	the	the	DET
ejpam-2473	44	3	elements	element	NOUN
ejpam-2473	44	4	of	of	ADP
ejpam-2473	44	5	s	s	PRON
ejpam-2473	44	6	must	must	AUX
ejpam-2473	44	7	be	be	AUX
ejpam-2473	44	8	in	in	ADP
ejpam-2473	44	9	d	d	PROPN
ejpam-2473	44	10	and	and	CCONJ
ejpam-2473	44	11	d	d	X
ejpam-2473	44	12	6=	6=	ADP
ejpam-2473	44	13	s	s	NOUN
ejpam-2473	44	14	∪	∪	X
ejpam-2473	44	15	{	{	PUNCT
ejpam-2473	44	16	x1	x1	PROPN
ejpam-2473	44	17	,	,	PUNCT
ejpam-2473	44	18	x2	x2	PROPN
ejpam-2473	44	19	,	,	PUNCT
ejpam-2473	44	20	.	.	PUNCT
ejpam-2473	44	21	.	.	PUNCT
ejpam-2473	45	1	.	.	PUNCT
ejpam-2473	46	1	,	,	PUNCT
ejpam-2473	46	2	xc	xc	PROPN
ejpam-2473	46	3	}	}	PUNCT
ejpam-2473	46	4	,	,	PUNCT
ejpam-2473	46	5	where	where	SCONJ
ejpam-2473	46	6	x	x	X
ejpam-2473	46	7	i	i	PRON
ejpam-2473	46	8	∈	∈	PROPN
ejpam-2473	46	9	{	{	PUNCT
ejpam-2473	46	10	ai	ai	INTJ
ejpam-2473	46	11	,	,	PUNCT
ejpam-2473	46	12	a−1	a−1	PROPN
ejpam-2473	46	13	i	i	PROPN
ejpam-2473	46	14	}	}	PUNCT
ejpam-2473	46	15	for	for	ADP
ejpam-2473	46	16	i	i	PROPN
ejpam-2473	46	17	=	=	SYM
ejpam-2473	46	18	1,2	1,2	NUM
ejpam-2473	46	19	,	,	PUNCT
ejpam-2473	46	20	.	.	PUNCT
ejpam-2473	46	21	.	.	PUNCT
ejpam-2473	46	22	.	.	PUNCT
ejpam-2473	47	1	,	,	PUNCT
ejpam-2473	47	2	c	c	NOUN
ejpam-2473	47	3	and	and	CCONJ
ejpam-2473	47	4	g\s	g\s	ADP
ejpam-2473	47	5	=	=	SYM
ejpam-2473	47	6	{	{	PUNCT
ejpam-2473	47	7	a1	a1	PROPN
ejpam-2473	47	8	,	,	PUNCT
ejpam-2473	47	9	a−1	a−1	PROPN
ejpam-2473	47	10	1	1	NUM
ejpam-2473	47	11	}	}	PUNCT
ejpam-2473	47	12	∪	∪	ADJ
ejpam-2473	47	13	{	{	PUNCT
ejpam-2473	47	14	a2	a2	PROPN
ejpam-2473	47	15	,	,	PUNCT
ejpam-2473	47	16	a−1	a−1	PROPN
ejpam-2473	47	17	2	2	NUM
ejpam-2473	47	18	}	}	PUNCT
ejpam-2473	47	19	∪	∪	X
ejpam-2473	47	20	·	·	PUNCT
ejpam-2473	47	21	·	·	PUNCT
ejpam-2473	47	22	·	·	PUNCT
ejpam-2473	47	23	∪	∪	X
ejpam-2473	47	24	{	{	PUNCT
ejpam-2473	47	25	ac	ac	PROPN
ejpam-2473	47	26	,	,	PUNCT
ejpam-2473	47	27	a−1	a−1	PROPN
ejpam-2473	47	28	c	c	PROPN
ejpam-2473	47	29	}	}	PUNCT
ejpam-2473	47	30	is	be	AUX
ejpam-2473	47	31	a	a	DET
ejpam-2473	47	32	canonical	canonical	ADJ
ejpam-2473	47	33	partition	partition	NOUN
ejpam-2473	47	34	,	,	PUNCT
ejpam-2473	47	35	there	there	PRON
ejpam-2473	47	36	exist	exist	VERB
ejpam-2473	47	37	x	x	SYM
ejpam-2473	47	38	∈	∈	NOUN
ejpam-2473	47	39	g\s	g\s	ADP
ejpam-2473	48	1	such	such	ADJ
ejpam-2473	48	2	that	that	SCONJ
ejpam-2473	48	3	{	{	PUNCT
ejpam-2473	48	4	x	x	X
ejpam-2473	48	5	,	,	PUNCT
ejpam-2473	48	6	x−1	x−1	PROPN
ejpam-2473	48	7	}	}	PUNCT
ejpam-2473	48	8	∈	∈	PROPN
ejpam-2473	48	9	d	d	NOUN
ejpam-2473	48	10	(	(	PUNCT
ejpam-2473	48	11	since	since	SCONJ
ejpam-2473	48	12	one	one	NUM
ejpam-2473	48	13	of	of	ADP
ejpam-2473	48	14	x	x	PUNCT
ejpam-2473	48	15	and	and	CCONJ
ejpam-2473	48	16	x−1	x−1	PROPN
ejpam-2473	48	17	must	must	AUX
ejpam-2473	48	18	be	be	AUX
ejpam-2473	48	19	in	in	ADP
ejpam-2473	48	20	d	d	PROPN
ejpam-2473	48	21	)	)	PUNCT
ejpam-2473	48	22	.	.	PUNCT
ejpam-2473	49	1	if	if	SCONJ
ejpam-2473	49	2	{	{	PUNCT
ejpam-2473	49	3	x	x	INTJ
ejpam-2473	49	4	,	,	PUNCT
ejpam-2473	49	5	x−1	x−1	PROPN
ejpam-2473	49	6	}	}	PUNCT
ejpam-2473	49	7	∈	∈	PROPN
ejpam-2473	49	8	d	d	NOUN
ejpam-2473	49	9	,	,	PUNCT
ejpam-2473	49	10	then	then	ADV
ejpam-2473	49	11	d\{x	d\{x	X
ejpam-2473	49	12	}	}	PUNCT
ejpam-2473	49	13	is	be	AUX
ejpam-2473	49	14	a	a	DET
ejpam-2473	49	15	d	d	NOUN
ejpam-2473	49	16	-set	-set	ADV
ejpam-2473	49	17	smaller	small	ADJ
ejpam-2473	49	18	than	than	ADP
ejpam-2473	49	19	d.	d.	PROPN
ejpam-2473	49	20	this	this	PRON
ejpam-2473	49	21	is	be	AUX
ejpam-2473	49	22	a	a	DET
ejpam-2473	49	23	contradiction	contradiction	NOUN
ejpam-2473	49	24	.	.	PUNCT
ejpam-2473	50	1	the	the	DET
ejpam-2473	50	2	following	follow	VERB
ejpam-2473	50	3	results	result	NOUN
ejpam-2473	50	4	are	be	AUX
ejpam-2473	50	5	found	find	VERB
ejpam-2473	50	6	in	in	ADP
ejpam-2473	50	7	[	[	X
ejpam-2473	50	8	2	2	NUM
ejpam-2473	50	9	]	]	PUNCT
ejpam-2473	50	10	.	.	PUNCT
ejpam-2473	51	1	they	they	PRON
ejpam-2473	51	2	will	will	AUX
ejpam-2473	51	3	be	be	AUX
ejpam-2473	51	4	used	use	VERB
ejpam-2473	51	5	in	in	ADP
ejpam-2473	51	6	the	the	DET
ejpam-2473	51	7	succeeding	succeed	VERB
ejpam-2473	51	8	sections	section	NOUN
ejpam-2473	51	9	.	.	PUNCT
ejpam-2473	52	1	theorem	theorem	NOUN
ejpam-2473	52	2	1	1	NUM
ejpam-2473	52	3	.	.	PUNCT
ejpam-2473	53	1	let	let	VERB
ejpam-2473	53	2	g	g	PRON
ejpam-2473	53	3	be	be	AUX
ejpam-2473	53	4	a	a	DET
ejpam-2473	53	5	finite	finite	ADJ
ejpam-2473	53	6	group	group	NOUN
ejpam-2473	53	7	.	.	PUNCT
ejpam-2473	54	1	if	if	SCONJ
ejpam-2473	54	2	c	c	PROPN
ejpam-2473	54	3	is	be	AUX
ejpam-2473	54	4	the	the	DET
ejpam-2473	54	5	c	c	ADJ
ejpam-2473	54	6	-number	-number	NOUN
ejpam-2473	54	7	of	of	ADP
ejpam-2473	54	8	g	g	NOUN
ejpam-2473	54	9	,	,	PUNCT
ejpam-2473	54	10	then	then	ADV
ejpam-2473	54	11	i	i	PRON
ejpam-2473	54	12	(	(	PUNCT
ejpam-2473	54	13	g	g	NOUN
ejpam-2473	54	14	)	)	PUNCT
ejpam-2473	54	15	=	=	SYM
ejpam-2473	54	16	2c	2c	NOUN
ejpam-2473	54	17	.	.	PUNCT
ejpam-2473	54	18	theorem	theorem	NOUN
ejpam-2473	54	19	2	2	NUM
ejpam-2473	54	20	.	.	PUNCT
ejpam-2473	55	1	let	let	VERB
ejpam-2473	55	2	g	g	PRON
ejpam-2473	55	3	be	be	AUX
ejpam-2473	55	4	a	a	DET
ejpam-2473	55	5	finite	finite	ADJ
ejpam-2473	55	6	group	group	NOUN
ejpam-2473	55	7	and	and	CCONJ
ejpam-2473	55	8	t	t	PROPN
ejpam-2473	55	9	be	be	VERB
ejpam-2473	55	10	the	the	DET
ejpam-2473	55	11	family	family	NOUN
ejpam-2473	55	12	of	of	ADP
ejpam-2473	55	13	all	all	PRON
ejpam-2473	55	14	of	of	ADP
ejpam-2473	55	15	its	its	PRON
ejpam-2473	55	16	d	d	PROPN
ejpam-2473	55	17	-sets	-set	NOUN
ejpam-2473	55	18	.	.	PUNCT
ejpam-2473	56	1	if	if	SCONJ
ejpam-2473	56	2	c	c	PROPN
ejpam-2473	56	3	is	be	AUX
ejpam-2473	56	4	the	the	DET
ejpam-2473	56	5	c	c	ADJ
ejpam-2473	56	6	-number	-number	NOUN
ejpam-2473	56	7	of	of	ADP
ejpam-2473	56	8	g	g	NOUN
ejpam-2473	56	9	,	,	PUNCT
ejpam-2473	56	10	then	then	ADV
ejpam-2473	56	11	|t	|t	VERB
ejpam-2473	56	12	|=	|=	X
ejpam-2473	56	13	3c	3c	NUM
ejpam-2473	56	14	.	.	PUNCT
ejpam-2473	57	1	theorem	theorem	ADJ
ejpam-2473	57	2	2	2	NUM
ejpam-2473	57	3	says	say	VERB
ejpam-2473	57	4	that	that	SCONJ
ejpam-2473	57	5	if	if	SCONJ
ejpam-2473	57	6	a⊆	a⊆	VERB
ejpam-2473	57	7	g	g	NOUN
ejpam-2473	57	8	,	,	PUNCT
ejpam-2473	57	9	then	then	ADV
ejpam-2473	57	10	i	i	PRON
ejpam-2473	57	11	(	(	PUNCT
ejpam-2473	57	12	a)≤	a)≤	PROPN
ejpam-2473	57	13	3c	3c	NUM
ejpam-2473	57	14	.	.	PUNCT
ejpam-2473	58	1	2	2	X
ejpam-2473	58	2	.	.	X
ejpam-2473	58	3	d	d	NOUN
ejpam-2473	58	4	-sets	-set	NOUN
ejpam-2473	58	5	generated	generate	VERB
ejpam-2473	58	6	by	by	ADP
ejpam-2473	58	7	a	a	DET
ejpam-2473	58	8	subset	subset	NOUN
ejpam-2473	58	9	all	all	DET
ejpam-2473	58	10	groups	group	NOUN
ejpam-2473	58	11	considered	consider	VERB
ejpam-2473	58	12	here	here	ADV
ejpam-2473	58	13	are	be	AUX
ejpam-2473	58	14	finite	finite	ADJ
ejpam-2473	58	15	groups	group	NOUN
ejpam-2473	58	16	.	.	PUNCT
ejpam-2473	59	1	let	let	VERB
ejpam-2473	59	2	g	g	PRON
ejpam-2473	59	3	be	be	AUX
ejpam-2473	59	4	a	a	DET
ejpam-2473	59	5	group	group	NOUN
ejpam-2473	59	6	and	and	CCONJ
ejpam-2473	59	7	a	a	DET
ejpam-2473	59	8	be	be	AUX
ejpam-2473	59	9	a	a	DET
ejpam-2473	59	10	non	non	ADJ
ejpam-2473	59	11	-	-	ADJ
ejpam-2473	59	12	empty	empty	ADJ
ejpam-2473	59	13	subset	subset	NOUN
ejpam-2473	59	14	of	of	ADP
ejpam-2473	59	15	g.	g.	PROPN
ejpam-2473	59	16	a	a	DET
ejpam-2473	59	17	smallest	small	ADJ
ejpam-2473	59	18	d	d	NOUN
ejpam-2473	59	19	-set	-set	PUNCT
ejpam-2473	59	20	of	of	ADP
ejpam-2473	59	21	g	g	PROPN
ejpam-2473	59	22	that	that	PRON
ejpam-2473	59	23	contains	contain	VERB
ejpam-2473	59	24	a	a	PRON
ejpam-2473	59	25	is	be	AUX
ejpam-2473	59	26	called	call	VERB
ejpam-2473	59	27	a	a	DET
ejpam-2473	59	28	d	d	NOUN
ejpam-2473	59	29	-set	-set	ADV
ejpam-2473	59	30	generated	generate	VERB
ejpam-2473	59	31	by	by	ADP
ejpam-2473	59	32	a	a	PRON
ejpam-2473	59	33	,	,	PUNCT
ejpam-2473	59	34	denoted	denote	VERB
ejpam-2473	59	35	by	by	ADP
ejpam-2473	59	36	〈	〈	PROPN
ejpam-2473	59	37	a	a	DET
ejpam-2473	59	38	〉	〉	NOUN
ejpam-2473	59	39	.	.	PUNCT
ejpam-2473	60	1	for	for	ADP
ejpam-2473	60	2	example	example	NOUN
ejpam-2473	60	3	,	,	PUNCT
ejpam-2473	60	4	consider	consider	VERB
ejpam-2473	60	5	the	the	DET
ejpam-2473	60	6	additive	additive	ADJ
ejpam-2473	60	7	group	group	NOUN
ejpam-2473	60	8	z6	z6	PROPN
ejpam-2473	60	9	=	=	PUNCT
ejpam-2473	60	10	{	{	PUNCT
ejpam-2473	60	11	0,1,2,3,4,5	0,1,2,3,4,5	NUM
ejpam-2473	60	12	}	}	PUNCT
ejpam-2473	60	13	.	.	PUNCT
ejpam-2473	61	1	note	note	VERB
ejpam-2473	61	2	that	that	SCONJ
ejpam-2473	61	3	sz6	sz6	NOUN
ejpam-2473	61	4	=	=	SYM
ejpam-2473	61	5	{	{	PUNCT
ejpam-2473	61	6	0,3	0,3	NUM
ejpam-2473	61	7	}	}	PUNCT
ejpam-2473	61	8	,	,	PUNCT
ejpam-2473	61	9	and	and	CCONJ
ejpam-2473	61	10	{	{	PUNCT
ejpam-2473	61	11	{	{	PUNCT
ejpam-2473	61	12	1,5	1,5	NUM
ejpam-2473	61	13	}	}	PUNCT
ejpam-2473	61	14	,	,	PUNCT
ejpam-2473	61	15	{	{	PUNCT
ejpam-2473	61	16	2,4	2,4	NUM
ejpam-2473	61	17	}	}	PUNCT
ejpam-2473	61	18	}	}	PUNCT
ejpam-2473	61	19	is	be	AUX
ejpam-2473	61	20	a	a	DET
ejpam-2473	61	21	canonical	canonical	ADJ
ejpam-2473	61	22	partition	partition	NOUN
ejpam-2473	61	23	of	of	ADP
ejpam-2473	61	24	z6	z6	PROPN
ejpam-2473	61	25	.	.	PUNCT
ejpam-2473	62	1	thus	thus	ADV
ejpam-2473	62	2	,	,	PUNCT
ejpam-2473	62	3	the	the	DET
ejpam-2473	62	4	c	c	PROPN
ejpam-2473	62	5	-number	-number	PROPN
ejpam-2473	62	6	of	of	ADP
ejpam-2473	62	7	z6	z6	PROPN
ejpam-2473	62	8	is	be	AUX
ejpam-2473	62	9	2	2	NUM
ejpam-2473	62	10	.	.	PUNCT
ejpam-2473	62	11	hence	hence	ADV
ejpam-2473	62	12	by	by	ADP
ejpam-2473	62	13	theorem	theorem	NOUN
ejpam-2473	62	14	2	2	NUM
ejpam-2473	62	15	,	,	PUNCT
ejpam-2473	62	16	|t	|t	PROPN
ejpam-2473	62	17	|=	|=	PUNCT
ejpam-2473	62	18	32	32	NUM
ejpam-2473	62	19	=	=	SYM
ejpam-2473	62	20	9	9	NUM
ejpam-2473	62	21	.	.	PUNCT
ejpam-2473	63	1	the	the	DET
ejpam-2473	63	2	elements	element	NOUN
ejpam-2473	63	3	of	of	ADP
ejpam-2473	63	4	t	t	PROPN
ejpam-2473	63	5	would	would	AUX
ejpam-2473	63	6	be	be	AUX
ejpam-2473	63	7	d1	d1	PROPN
ejpam-2473	63	8	=	=	PUNCT
ejpam-2473	63	9	{	{	PUNCT
ejpam-2473	63	10	0,3,1,5,2,4	0,3,1,5,2,4	NOUN
ejpam-2473	63	11	}	}	PUNCT
ejpam-2473	63	12	d2	d2	NOUN
ejpam-2473	63	13	=	=	SYM
ejpam-2473	63	14	{	{	PUNCT
ejpam-2473	63	15	0,3,1,2,5	0,3,1,2,5	NUM
ejpam-2473	63	16	}	}	PUNCT
ejpam-2473	63	17	d3	d3	PROPN
ejpam-2473	63	18	=	=	SYM
ejpam-2473	63	19	{	{	PUNCT
ejpam-2473	63	20	0,3,1,4,5	0,3,1,4,5	NUM
ejpam-2473	63	21	}	}	PUNCT
ejpam-2473	63	22	d4	d4	PROPN
ejpam-2473	63	23	=	=	SYM
ejpam-2473	63	24	{	{	PUNCT
ejpam-2473	63	25	0,3,1,2,4	0,3,1,2,4	NOUN
ejpam-2473	63	26	}	}	PUNCT
ejpam-2473	63	27	d5	d5	NOUN
ejpam-2473	63	28	=	=	SYM
ejpam-2473	63	29	{	{	PUNCT
ejpam-2473	63	30	0,3,2,4,5	0,3,2,4,5	NOUN
ejpam-2473	63	31	}	}	PUNCT
ejpam-2473	63	32	d6	d6	NOUN
ejpam-2473	63	33	=	=	SYM
ejpam-2473	63	34	{	{	PUNCT
ejpam-2473	63	35	0,3,1,2	0,3,1,2	NUM
ejpam-2473	63	36	}	}	PUNCT
ejpam-2473	63	37	d7	d7	PROPN
ejpam-2473	63	38	=	=	PUNCT
ejpam-2473	63	39	{	{	PUNCT
ejpam-2473	63	40	0,3,1,4	0,3,1,4	NOUN
ejpam-2473	63	41	}	}	PUNCT
ejpam-2473	63	42	d8	d8	NOUN
ejpam-2473	63	43	=	=	PUNCT
ejpam-2473	63	44	{	{	PUNCT
ejpam-2473	63	45	0,3,2,5	0,3,2,5	NOUN
ejpam-2473	63	46	}	}	PUNCT
ejpam-2473	63	47	d9	d9	PROPN
ejpam-2473	63	48	=	=	PUNCT
ejpam-2473	63	49	{	{	PUNCT
ejpam-2473	63	50	0,3,4,5	0,3,4,5	NUM
ejpam-2473	63	51	}	}	PUNCT
ejpam-2473	63	52	.	.	PUNCT
ejpam-2473	64	1	observe	observe	VERB
ejpam-2473	64	2	that	that	SCONJ
ejpam-2473	64	3	a=	a=	VERB
ejpam-2473	64	4	{	{	PUNCT
ejpam-2473	64	5	1,4	1,4	NUM
ejpam-2473	64	6	}	}	PUNCT
ejpam-2473	64	7	is	be	AUX
ejpam-2473	64	8	a	a	DET
ejpam-2473	64	9	subset	subset	NOUN
ejpam-2473	64	10	of	of	ADP
ejpam-2473	64	11	d1	d1	NOUN
ejpam-2473	64	12	,	,	PUNCT
ejpam-2473	64	13	d3	d3	PROPN
ejpam-2473	64	14	,	,	PUNCT
ejpam-2473	64	15	d4	d4	PROPN
ejpam-2473	64	16	,	,	PUNCT
ejpam-2473	64	17	and	and	CCONJ
ejpam-2473	64	18	d7	d7	PROPN
ejpam-2473	64	19	and	and	CCONJ
ejpam-2473	64	20	the	the	DET
ejpam-2473	64	21	smallest	small	ADJ
ejpam-2473	64	22	set	set	NOUN
ejpam-2473	64	23	among	among	ADP
ejpam-2473	64	24	these	these	PRON
ejpam-2473	64	25	is	be	AUX
ejpam-2473	64	26	d7	d7	PROPN
ejpam-2473	64	27	.	.	PUNCT
ejpam-2473	65	1	thus	thus	ADV
ejpam-2473	65	2	,	,	PUNCT
ejpam-2473	65	3	〈	〈	NOUN
ejpam-2473	65	4	1,4〉=	1,4〉=	NOUN
ejpam-2473	65	5	d7	d7	PROPN
ejpam-2473	65	6	=	=	PUNCT
ejpam-2473	65	7	{	{	PUNCT
ejpam-2473	65	8	0,3,1,4	0,3,1,4	NUM
ejpam-2473	65	9	}	}	PUNCT
ejpam-2473	65	10	.	.	PUNCT
ejpam-2473	66	1	note	note	VERB
ejpam-2473	66	2	that	that	SCONJ
ejpam-2473	66	3	〈	〈	PROPN
ejpam-2473	66	4	a	a	DET
ejpam-2473	66	5	〉	〉	NOUN
ejpam-2473	66	6	may	may	AUX
ejpam-2473	66	7	not	not	PART
ejpam-2473	66	8	be	be	AUX
ejpam-2473	66	9	unique	unique	ADJ
ejpam-2473	66	10	.	.	PUNCT
ejpam-2473	67	1	to	to	PART
ejpam-2473	67	2	see	see	VERB
ejpam-2473	67	3	this	this	PRON
ejpam-2473	67	4	,	,	PUNCT
ejpam-2473	67	5	let	let	VERB
ejpam-2473	67	6	b	b	NOUN
ejpam-2473	67	7	=	=	SYM
ejpam-2473	67	8	{	{	PUNCT
ejpam-2473	67	9	0,3	0,3	NOUN
ejpam-2473	67	10	}	}	PUNCT
ejpam-2473	67	11	.	.	PUNCT
ejpam-2473	68	1	then	then	ADV
ejpam-2473	68	2	d6	d6	VERB
ejpam-2473	68	3	and	and	CCONJ
ejpam-2473	68	4	d9	d9	PROPN
ejpam-2473	68	5	are	be	AUX
ejpam-2473	68	6	the	the	DET
ejpam-2473	68	7	smallest	small	ADJ
ejpam-2473	68	8	d	d	ADP
ejpam-2473	68	9	-sets	-set	NOUN
ejpam-2473	68	10	of	of	ADP
ejpam-2473	68	11	g	g	NOUN
ejpam-2473	68	12	containing	contain	VERB
ejpam-2473	68	13	{	{	PUNCT
ejpam-2473	68	14	0,3	0,3	NUM
ejpam-2473	68	15	}	}	PUNCT
ejpam-2473	68	16	.	.	PUNCT
ejpam-2473	69	1	hence	hence	ADV
ejpam-2473	69	2	,	,	PUNCT
ejpam-2473	69	3	〈	〈	PRON
ejpam-2473	69	4	0,3	0,3	NOUN
ejpam-2473	69	5	〉	〉	NOUN
ejpam-2473	69	6	=	=	SYM
ejpam-2473	69	7	d6	d6	NOUN
ejpam-2473	69	8	or	or	CCONJ
ejpam-2473	69	9	d9	d9	PROPN
ejpam-2473	69	10	.	.	PUNCT
ejpam-2473	70	1	we	we	PRON
ejpam-2473	70	2	denote	denote	VERB
ejpam-2473	70	3	by	by	ADP
ejpam-2473	70	4	i	i	PRON
ejpam-2473	70	5	(	(	PUNCT
ejpam-2473	70	6	a	a	X
ejpam-2473	70	7	)	)	PUNCT
ejpam-2473	70	8	the	the	DET
ejpam-2473	70	9	number	number	NOUN
ejpam-2473	70	10	of	of	ADP
ejpam-2473	70	11	distinct	distinct	ADJ
ejpam-2473	70	12	d	d	NOUN
ejpam-2473	70	13	-sets	-set	NOUN
ejpam-2473	70	14	of	of	ADP
ejpam-2473	70	15	g	g	NOUN
ejpam-2473	70	16	generated	generate	VERB
ejpam-2473	70	17	by	by	ADP
ejpam-2473	70	18	a.	a.	NOUN
ejpam-2473	70	19	remark	remark	PROPN
ejpam-2473	70	20	2	2	NUM
ejpam-2473	70	21	.	.	X
ejpam-2473	71	1	for	for	ADP
ejpam-2473	71	2	any	any	DET
ejpam-2473	71	3	nonempty	nonempty	NOUN
ejpam-2473	71	4	subset	subset	VERB
ejpam-2473	71	5	a	a	PRON
ejpam-2473	71	6	of	of	ADP
ejpam-2473	71	7	a	a	DET
ejpam-2473	71	8	finite	finite	ADJ
ejpam-2473	71	9	group	group	NOUN
ejpam-2473	71	10	g	g	PROPN
ejpam-2473	71	11	,	,	PUNCT
ejpam-2473	71	12	〈	〈	PROPN
ejpam-2473	71	13	a	a	DET
ejpam-2473	71	14	〉	〉	NOUN
ejpam-2473	71	15	always	always	ADV
ejpam-2473	71	16	exist	exist	VERB
ejpam-2473	71	17	since	since	SCONJ
ejpam-2473	71	18	g	g	PROPN
ejpam-2473	71	19	is	be	AUX
ejpam-2473	71	20	itself	itself	PRON
ejpam-2473	71	21	a	a	DET
ejpam-2473	71	22	d	d	NOUN
ejpam-2473	71	23	-set	-set	NOUN
ejpam-2473	71	24	.	.	PUNCT
ejpam-2473	72	1	hence	hence	ADV
ejpam-2473	72	2	,	,	PUNCT
ejpam-2473	72	3	i	i	PRON
ejpam-2473	72	4	(	(	PUNCT
ejpam-2473	72	5	a	a	NOUN
ejpam-2473	72	6	)	)	PUNCT
ejpam-2473	72	7	>	>	X
ejpam-2473	72	8	0	0	X
ejpam-2473	72	9	.	.	PUNCT
ejpam-2473	72	10	c.	c.	PROPN
ejpam-2473	72	11	rosero	rosero	PROPN
ejpam-2473	72	12	,	,	PUNCT
ejpam-2473	72	13	m.	m.	NOUN
ejpam-2473	72	14	baldado	baldado	NOUN
ejpam-2473	72	15	/	/	SYM
ejpam-2473	72	16	eur	eur	PROPN
ejpam-2473	72	17	.	.	PUNCT
ejpam-2473	73	1	j.	j.	PROPN
ejpam-2473	73	2	pure	pure	PROPN
ejpam-2473	73	3	appl	appl	PROPN
ejpam-2473	73	4	.	.	PROPN
ejpam-2473	73	5	math	math	PROPN
ejpam-2473	73	6	,	,	PUNCT
ejpam-2473	73	7	9	9	NUM
ejpam-2473	73	8	(	(	PUNCT
ejpam-2473	73	9	2016	2016	NUM
ejpam-2473	73	10	)	)	PUNCT
ejpam-2473	73	11	,	,	PUNCT
ejpam-2473	73	12	34	34	NUM
ejpam-2473	73	13	-	-	SYM
ejpam-2473	73	14	38	38	NUM
ejpam-2473	73	15	36	36	NUM
ejpam-2473	73	16	remark	remark	NOUN
ejpam-2473	73	17	3	3	NUM
ejpam-2473	73	18	.	.	PUNCT
ejpam-2473	74	1	let	let	VERB
ejpam-2473	74	2	g	g	PRON
ejpam-2473	74	3	be	be	AUX
ejpam-2473	74	4	a	a	DET
ejpam-2473	74	5	group	group	NOUN
ejpam-2473	74	6	and	and	CCONJ
ejpam-2473	74	7	d	d	NOUN
ejpam-2473	74	8	be	be	AUX
ejpam-2473	74	9	a	a	DET
ejpam-2473	74	10	minimum	minimum	NOUN
ejpam-2473	74	11	d	d	NOUN
ejpam-2473	74	12	-set	-set	PUNCT
ejpam-2473	74	13	of	of	ADP
ejpam-2473	74	14	g.	g.	PROPN
ejpam-2473	75	1	if	if	SCONJ
ejpam-2473	75	2	x	x	PROPN
ejpam-2473	75	3	∈	∈	PROPN
ejpam-2473	75	4	d\s	d\s	PROPN
ejpam-2473	75	5	,	,	PUNCT
ejpam-2473	75	6	then	then	ADV
ejpam-2473	75	7	x−1	x−1	PROPN
ejpam-2473	75	8	/∈	/∈	PROPN
ejpam-2473	75	9	d.	d.	PROPN
ejpam-2473	75	10	to	to	PART
ejpam-2473	75	11	see	see	VERB
ejpam-2473	75	12	this	this	PRON
ejpam-2473	75	13	,	,	PUNCT
ejpam-2473	75	14	suppose	suppose	VERB
ejpam-2473	75	15	that	that	SCONJ
ejpam-2473	75	16	x	x	SYM
ejpam-2473	75	17	∈	∈	PROPN
ejpam-2473	75	18	d\s	d\s	PROPN
ejpam-2473	75	19	and	and	CCONJ
ejpam-2473	75	20	x−1	x−1	PROPN
ejpam-2473	75	21	∈	∈	PROPN
ejpam-2473	75	22	d.	d.	PROPN
ejpam-2473	75	23	then	then	ADV
ejpam-2473	75	24	d\{x	d\{x	VERB
ejpam-2473	75	25	}	}	PUNCT
ejpam-2473	75	26	is	be	AUX
ejpam-2473	75	27	a	a	DET
ejpam-2473	75	28	d	d	NOUN
ejpam-2473	75	29	-set	-set	ADV
ejpam-2473	75	30	smaller	small	ADJ
ejpam-2473	75	31	than	than	ADP
ejpam-2473	75	32	d.	d.	PROPN
ejpam-2473	75	33	this	this	PRON
ejpam-2473	75	34	is	be	AUX
ejpam-2473	75	35	a	a	DET
ejpam-2473	75	36	contradiction	contradiction	NOUN
ejpam-2473	75	37	.	.	PUNCT
ejpam-2473	76	1	theorem	theorem	NOUN
ejpam-2473	76	2	3	3	X
ejpam-2473	76	3	.	.	PUNCT
ejpam-2473	77	1	let	let	VERB
ejpam-2473	77	2	g	g	PRON
ejpam-2473	77	3	be	be	AUX
ejpam-2473	77	4	a	a	DET
ejpam-2473	77	5	finite	finite	ADJ
ejpam-2473	77	6	group	group	NOUN
ejpam-2473	77	7	,	,	PUNCT
ejpam-2473	77	8	s	s	PART
ejpam-2473	77	9	=	=	PUNCT
ejpam-2473	77	10	�	�	PROPN
ejpam-2473	77	11	s	s	PART
ejpam-2473	77	12	∈	∈	PROPN
ejpam-2473	77	13	g	g	NOUN
ejpam-2473	77	14	:	:	PUNCT
ejpam-2473	77	15	s2	s2	NOUN
ejpam-2473	77	16	=	=	PUNCT
ejpam-2473	77	17	e	e	PROPN
ejpam-2473	77	18	and	and	CCONJ
ejpam-2473	77	19	a⊆	a⊆	PROPN
ejpam-2473	77	20	g.	g.	PROPN
ejpam-2473	77	21	then	then	ADV
ejpam-2473	77	22	a⊆	a⊆	VERB
ejpam-2473	77	23	s	s	PRON
ejpam-2473	78	1	if	if	SCONJ
ejpam-2473	79	1	and	and	CCONJ
ejpam-2473	79	2	only	only	ADV
ejpam-2473	79	3	if	if	SCONJ
ejpam-2473	79	4	a⊆	a⊆	ADP
ejpam-2473	79	5	d	d	NOUN
ejpam-2473	79	6	for	for	ADP
ejpam-2473	79	7	all	all	DET
ejpam-2473	79	8	minimum	minimum	NOUN
ejpam-2473	79	9	d	d	NOUN
ejpam-2473	79	10	-set	-set	PUNCT
ejpam-2473	79	11	d	d	NOUN
ejpam-2473	79	12	of	of	ADP
ejpam-2473	79	13	g.	g.	PROPN
ejpam-2473	79	14	proof	proof	NOUN
ejpam-2473	79	15	.	.	PUNCT
ejpam-2473	80	1	let	let	VERB
ejpam-2473	80	2	g	g	PRON
ejpam-2473	80	3	be	be	AUX
ejpam-2473	80	4	a	a	DET
ejpam-2473	80	5	finite	finite	ADJ
ejpam-2473	80	6	group	group	NOUN
ejpam-2473	80	7	,	,	PUNCT
ejpam-2473	80	8	s	s	PART
ejpam-2473	80	9	=	=	PUNCT
ejpam-2473	80	10	�	�	PROPN
ejpam-2473	80	11	s	s	PART
ejpam-2473	80	12	∈	∈	PROPN
ejpam-2473	80	13	g	g	NOUN
ejpam-2473	80	14	:	:	PUNCT
ejpam-2473	80	15	s2	s2	NOUN
ejpam-2473	80	16	=	=	PUNCT
ejpam-2473	80	17	e	e	PROPN
ejpam-2473	80	18	and	and	CCONJ
ejpam-2473	80	19	a⊆	a⊆	PROPN
ejpam-2473	80	20	g.	g.	NOUN
ejpam-2473	80	21	in	in	ADP
ejpam-2473	80	22	[	[	X
ejpam-2473	80	23	2	2	NUM
ejpam-2473	80	24	]	]	PUNCT
ejpam-2473	80	25	,	,	PUNCT
ejpam-2473	80	26	s	s	VERB
ejpam-2473	80	27	⊆	⊆	NUM
ejpam-2473	80	28	d	d	NOUN
ejpam-2473	80	29	for	for	ADP
ejpam-2473	80	30	all	all	DET
ejpam-2473	80	31	d	d	NOUN
ejpam-2473	80	32	-set	-set	X
ejpam-2473	80	33	d	d	NOUN
ejpam-2473	80	34	of	of	ADP
ejpam-2473	80	35	g.	g.	PROPN
ejpam-2473	81	1	so	so	ADV
ejpam-2473	81	2	,	,	PUNCT
ejpam-2473	81	3	if	if	SCONJ
ejpam-2473	81	4	a⊆	a⊆	NOUN
ejpam-2473	81	5	s	s	PART
ejpam-2473	81	6	,	,	PUNCT
ejpam-2473	81	7	then	then	ADV
ejpam-2473	81	8	a⊆	a⊆	VERB
ejpam-2473	81	9	d	d	NOUN
ejpam-2473	81	10	for	for	ADP
ejpam-2473	81	11	all	all	DET
ejpam-2473	81	12	d	d	NOUN
ejpam-2473	81	13	-set	-set	X
ejpam-2473	81	14	d	d	NOUN
ejpam-2473	81	15	of	of	ADP
ejpam-2473	81	16	g.	g.	PROPN
ejpam-2473	81	17	in	in	ADP
ejpam-2473	81	18	particular	particular	ADJ
ejpam-2473	81	19	,	,	PUNCT
ejpam-2473	81	20	a⊆	a⊆	VERB
ejpam-2473	81	21	d	d	NOUN
ejpam-2473	81	22	for	for	ADP
ejpam-2473	81	23	all	all	DET
ejpam-2473	81	24	minimum	minimum	NOUN
ejpam-2473	81	25	d	d	NOUN
ejpam-2473	81	26	-set	-set	PUNCT
ejpam-2473	81	27	d	d	NOUN
ejpam-2473	81	28	of	of	ADP
ejpam-2473	81	29	g.	g.	NOUN
ejpam-2473	81	30	conversely	conversely	ADV
ejpam-2473	81	31	,	,	PUNCT
ejpam-2473	81	32	assume	assume	VERB
ejpam-2473	81	33	that	that	SCONJ
ejpam-2473	81	34	a⊆	a⊆	VERB
ejpam-2473	81	35	d	d	X
ejpam-2473	81	36	for	for	ADP
ejpam-2473	81	37	all	all	DET
ejpam-2473	81	38	minimum	minimum	NOUN
ejpam-2473	81	39	d	d	NOUN
ejpam-2473	81	40	-set	-set	PUNCT
ejpam-2473	81	41	d	d	NOUN
ejpam-2473	81	42	of	of	ADP
ejpam-2473	81	43	g	g	PROPN
ejpam-2473	81	44	and	and	CCONJ
ejpam-2473	81	45	a	a	DET
ejpam-2473	81	46	6⊆	6⊆	NUM
ejpam-2473	81	47	s.	s.	PROPN
ejpam-2473	81	48	let	let	VERB
ejpam-2473	81	49	x	x	X
ejpam-2473	81	50	∈	∈	PROPN
ejpam-2473	81	51	a\s	a\s	PROPN
ejpam-2473	81	52	and	and	CCONJ
ejpam-2473	81	53	d	d	X
ejpam-2473	81	54	be	be	AUX
ejpam-2473	81	55	a	a	DET
ejpam-2473	81	56	minimum	minimum	NOUN
ejpam-2473	81	57	d	d	NOUN
ejpam-2473	81	58	-set	-set	X
ejpam-2473	81	59	containing	contain	VERB
ejpam-2473	81	60	a.	a.	NOUN
ejpam-2473	81	61	since	since	SCONJ
ejpam-2473	81	62	a⊆	a⊆	PROPN
ejpam-2473	82	1	d	d	NOUN
ejpam-2473	82	2	and	and	CCONJ
ejpam-2473	82	3	x	x	SYM
ejpam-2473	82	4	∈	∈	PROPN
ejpam-2473	82	5	a\s	a\s	PROPN
ejpam-2473	82	6	,	,	PUNCT
ejpam-2473	82	7	x	x	PROPN
ejpam-2473	82	8	∈	∈	PROPN
ejpam-2473	82	9	d\s	d\s	PROPN
ejpam-2473	82	10	.	.	PUNCT
ejpam-2473	83	1	hence	hence	ADV
ejpam-2473	83	2	by	by	ADP
ejpam-2473	83	3	remark	remark	NOUN
ejpam-2473	83	4	3	3	NUM
ejpam-2473	83	5	,	,	PUNCT
ejpam-2473	83	6	x−1	x−1	PROPN
ejpam-2473	83	7	/∈	/∈	PROPN
ejpam-2473	83	8	d.	d.	PROPN
ejpam-2473	83	9	note	note	VERB
ejpam-2473	83	10	that	that	SCONJ
ejpam-2473	83	11	d1	d1	PROPN
ejpam-2473	83	12	=	=	SYM
ejpam-2473	83	13	d\{x	d\{x	X
ejpam-2473	83	14	}	}	PUNCT
ejpam-2473	83	15	∪	∪	X
ejpam-2473	83	16	{	{	PUNCT
ejpam-2473	83	17	x−1	x−1	NOUN
ejpam-2473	83	18	}	}	PUNCT
ejpam-2473	83	19	is	be	AUX
ejpam-2473	83	20	a	a	DET
ejpam-2473	83	21	minimum	minimum	NOUN
ejpam-2473	83	22	d	d	NOUN
ejpam-2473	83	23	-set	-set	PUNCT
ejpam-2473	83	24	that	that	PRON
ejpam-2473	83	25	do	do	AUX
ejpam-2473	83	26	not	not	PART
ejpam-2473	83	27	contain	contain	VERB
ejpam-2473	83	28	a.	a.	NOUN
ejpam-2473	83	29	this	this	PRON
ejpam-2473	83	30	is	be	AUX
ejpam-2473	83	31	a	a	DET
ejpam-2473	83	32	contradiction	contradiction	NOUN
ejpam-2473	83	33	.	.	PUNCT
ejpam-2473	84	1	corollary	corollary	ADJ
ejpam-2473	84	2	1	1	NUM
ejpam-2473	84	3	.	.	PUNCT
ejpam-2473	85	1	let	let	VERB
ejpam-2473	85	2	g	g	PRON
ejpam-2473	85	3	be	be	AUX
ejpam-2473	85	4	a	a	DET
ejpam-2473	85	5	finite	finite	ADJ
ejpam-2473	85	6	group	group	NOUN
ejpam-2473	85	7	,	,	PUNCT
ejpam-2473	85	8	s	s	PART
ejpam-2473	85	9	=	=	PUNCT
ejpam-2473	85	10	�	�	PROPN
ejpam-2473	85	11	s	s	PART
ejpam-2473	85	12	∈	∈	PROPN
ejpam-2473	85	13	g	g	NOUN
ejpam-2473	85	14	:	:	PUNCT
ejpam-2473	85	15	s2	s2	NOUN
ejpam-2473	85	16	=	=	PUNCT
ejpam-2473	85	17	e	e	X
ejpam-2473	85	18	.	.	PUNCT
ejpam-2473	86	1	if	if	SCONJ
ejpam-2473	86	2	a⊆	a⊆	NOUN
ejpam-2473	86	3	s	s	VERB
ejpam-2473	86	4	,	,	PUNCT
ejpam-2473	86	5	then	then	ADV
ejpam-2473	86	6	i	i	PRON
ejpam-2473	86	7	(	(	PUNCT
ejpam-2473	86	8	a	a	X
ejpam-2473	86	9	)	)	PUNCT
ejpam-2473	86	10	=	=	SYM
ejpam-2473	86	11	2c	2c	NOUN
ejpam-2473	86	12	.	.	PUNCT
ejpam-2473	87	1	proof	proof	NOUN
ejpam-2473	87	2	.	.	PUNCT
ejpam-2473	88	1	this	this	PRON
ejpam-2473	88	2	follows	follow	VERB
ejpam-2473	88	3	from	from	ADP
ejpam-2473	88	4	theorem	theorem	ADJ
ejpam-2473	88	5	3	3	NUM
ejpam-2473	88	6	and	and	CCONJ
ejpam-2473	88	7	theorem	theorem	VERB
ejpam-2473	88	8	1	1	NUM
ejpam-2473	88	9	.	.	PUNCT
ejpam-2473	89	1	the	the	DET
ejpam-2473	89	2	next	next	ADJ
ejpam-2473	89	3	result	result	NOUN
ejpam-2473	89	4	characterizes	characterize	VERB
ejpam-2473	89	5	sets	set	NOUN
ejpam-2473	89	6	a	a	PRON
ejpam-2473	89	7	with	with	ADP
ejpam-2473	89	8	unique	unique	ADJ
ejpam-2473	89	9	generated	generated	ADJ
ejpam-2473	89	10	d	d	PROPN
ejpam-2473	89	11	-set	-set	ADV
ejpam-2473	89	12	.	.	PUNCT
ejpam-2473	90	1	theorem	theorem	NOUN
ejpam-2473	90	2	4	4	NUM
ejpam-2473	90	3	.	.	PUNCT
ejpam-2473	91	1	let	let	VERB
ejpam-2473	91	2	g	g	PRON
ejpam-2473	91	3	be	be	AUX
ejpam-2473	91	4	a	a	DET
ejpam-2473	91	5	finite	finite	ADJ
ejpam-2473	91	6	group	group	NOUN
ejpam-2473	91	7	and	and	CCONJ
ejpam-2473	91	8	a⊆	a⊆	PROPN
ejpam-2473	91	9	g.	g.	PROPN
ejpam-2473	92	1	then	then	ADV
ejpam-2473	92	2	,	,	PUNCT
ejpam-2473	92	3	i	i	PRON
ejpam-2473	92	4	(	(	PUNCT
ejpam-2473	92	5	a	a	X
ejpam-2473	92	6	)	)	PUNCT
ejpam-2473	92	7	=	=	SYM
ejpam-2473	92	8	1	1	NUM
ejpam-2473	92	9	if	if	SCONJ
ejpam-2473	92	10	and	and	CCONJ
ejpam-2473	92	11	only	only	ADV
ejpam-2473	92	12	if	if	SCONJ
ejpam-2473	92	13	a⊆	a⊆	ADP
ejpam-2473	92	14	d	d	NOUN
ejpam-2473	92	15	and	and	CCONJ
ejpam-2473	92	16	a⊇	a⊇	PROPN
ejpam-2473	92	17	(	(	PUNCT
ejpam-2473	92	18	d\s	d\s	PROPN
ejpam-2473	92	19	)	)	PUNCT
ejpam-2473	92	20	for	for	ADP
ejpam-2473	92	21	some	some	DET
ejpam-2473	92	22	d	d	NOUN
ejpam-2473	92	23	-set	-set	X
ejpam-2473	92	24	d	d	NOUN
ejpam-2473	92	25	of	of	ADP
ejpam-2473	92	26	g.	g.	PROPN
ejpam-2473	92	27	proof	proof	NOUN
ejpam-2473	92	28	.	.	PUNCT
ejpam-2473	93	1	let	let	VERB
ejpam-2473	93	2	g	g	PRON
ejpam-2473	93	3	be	be	AUX
ejpam-2473	93	4	a	a	DET
ejpam-2473	93	5	finite	finite	ADJ
ejpam-2473	93	6	group	group	NOUN
ejpam-2473	93	7	and	and	CCONJ
ejpam-2473	93	8	a	a	DET
ejpam-2473	93	9	⊆	⊆	NUM
ejpam-2473	93	10	g.	g.	NOUN
ejpam-2473	93	11	suppose	suppose	VERB
ejpam-2473	93	12	that	that	SCONJ
ejpam-2473	93	13	i	i	PRON
ejpam-2473	93	14	(	(	PUNCT
ejpam-2473	93	15	a	a	X
ejpam-2473	93	16	)	)	PUNCT
ejpam-2473	93	17	=	=	SYM
ejpam-2473	93	18	1	1	NUM
ejpam-2473	93	19	,	,	PUNCT
ejpam-2473	93	20	and	and	CCONJ
ejpam-2473	93	21	,	,	PUNCT
ejpam-2473	93	22	a	a	DET
ejpam-2473	93	23	6⊆	6⊆	NUM
ejpam-2473	93	24	d	d	NOUN
ejpam-2473	93	25	or	or	CCONJ
ejpam-2473	93	26	a	a	DET
ejpam-2473	93	27	(	(	PUNCT
ejpam-2473	93	28	d\s	d\s	PROPN
ejpam-2473	93	29	)	)	PUNCT
ejpam-2473	93	30	for	for	ADP
ejpam-2473	93	31	all	all	DET
ejpam-2473	93	32	d	d	NOUN
ejpam-2473	93	33	-set	-set	X
ejpam-2473	93	34	d	d	NOUN
ejpam-2473	93	35	of	of	ADP
ejpam-2473	93	36	g.	g.	PROPN
ejpam-2473	93	37	if	if	SCONJ
ejpam-2473	93	38	a	a	DET
ejpam-2473	93	39	6⊆	6⊆	PROPN
ejpam-2473	93	40	d	d	NOUN
ejpam-2473	93	41	for	for	ADP
ejpam-2473	93	42	all	all	DET
ejpam-2473	93	43	d	d	NOUN
ejpam-2473	93	44	-set	-set	X
ejpam-2473	93	45	d	d	NOUN
ejpam-2473	93	46	of	of	ADP
ejpam-2473	93	47	g	g	NOUN
ejpam-2473	93	48	,	,	PUNCT
ejpam-2473	93	49	then	then	ADV
ejpam-2473	93	50	i	i	PRON
ejpam-2473	93	51	(	(	PUNCT
ejpam-2473	93	52	a	a	X
ejpam-2473	93	53	)	)	PUNCT
ejpam-2473	93	54	=	=	SYM
ejpam-2473	94	1	0	0	X
ejpam-2473	94	2	.	.	PUNCT
ejpam-2473	95	1	this	this	PRON
ejpam-2473	95	2	is	be	AUX
ejpam-2473	95	3	a	a	DET
ejpam-2473	95	4	contradiction	contradiction	NOUN
ejpam-2473	95	5	(	(	PUNCT
ejpam-2473	95	6	by	by	ADP
ejpam-2473	95	7	remark	remark	NOUN
ejpam-2473	95	8	2	2	NUM
ejpam-2473	95	9	)	)	PUNCT
ejpam-2473	95	10	.	.	PUNCT
ejpam-2473	96	1	so	so	ADV
ejpam-2473	96	2	we	we	PRON
ejpam-2473	96	3	assume	assume	VERB
ejpam-2473	96	4	that	that	SCONJ
ejpam-2473	96	5	a	a	DET
ejpam-2473	96	6	⊆	⊆	NUM
ejpam-2473	96	7	d.	d.	NOUN
ejpam-2473	96	8	let	let	VERB
ejpam-2473	96	9	d1	d1	PROPN
ejpam-2473	96	10	be	be	AUX
ejpam-2473	96	11	a	a	DET
ejpam-2473	96	12	smallest	small	ADJ
ejpam-2473	96	13	d	d	NOUN
ejpam-2473	96	14	-set	-set	X
ejpam-2473	96	15	containing	contain	VERB
ejpam-2473	96	16	a.	a.	NOUN
ejpam-2473	96	17	if	if	SCONJ
ejpam-2473	96	18	a	a	DET
ejpam-2473	96	19	(	(	PUNCT
ejpam-2473	96	20	d\s	d\s	PROPN
ejpam-2473	96	21	)	)	PUNCT
ejpam-2473	96	22	for	for	ADP
ejpam-2473	96	23	all	all	DET
ejpam-2473	96	24	d	d	NOUN
ejpam-2473	96	25	-set	-set	X
ejpam-2473	97	1	d	d	NOUN
ejpam-2473	97	2	of	of	ADP
ejpam-2473	97	3	g	g	NOUN
ejpam-2473	97	4	,	,	PUNCT
ejpam-2473	97	5	then	then	ADV
ejpam-2473	97	6	a∪	a∪	PROPN
ejpam-2473	97	7	s	s	NOUN
ejpam-2473	97	8	is	be	AUX
ejpam-2473	97	9	not	not	PART
ejpam-2473	97	10	a	a	DET
ejpam-2473	97	11	d	d	NOUN
ejpam-2473	97	12	-set	-set	NOUN
ejpam-2473	97	13	,	,	PUNCT
ejpam-2473	97	14	that	that	SCONJ
ejpam-2473	98	1	a∪	a∪	PROPN
ejpam-2473	98	2	s	s	NOUN
ejpam-2473	98	3	is	be	AUX
ejpam-2473	98	4	properly	properly	ADV
ejpam-2473	98	5	contained	contain	VERB
ejpam-2473	98	6	in	in	ADP
ejpam-2473	98	7	d1	d1	NOUN
ejpam-2473	98	8	.	.	PUNCT
ejpam-2473	99	1	let	let	VERB
ejpam-2473	99	2	x	x	PUNCT
ejpam-2473	99	3	∈	∈	PROPN
ejpam-2473	99	4	d1\(a	d1\(a	PROPN
ejpam-2473	99	5	∪	∪	ADP
ejpam-2473	99	6	s	s	NOUN
ejpam-2473	99	7	)	)	PUNCT
ejpam-2473	99	8	.	.	PUNCT
ejpam-2473	100	1	then	then	ADV
ejpam-2473	100	2	d1\{x	d1\{x	PROPN
ejpam-2473	100	3	}	}	PUNCT
ejpam-2473	100	4	∪	∪	VERB
ejpam-2473	100	5	{	{	PUNCT
ejpam-2473	100	6	x	x	SYM
ejpam-2473	100	7	−1	−1	NOUN
ejpam-2473	100	8	}	}	PUNCT
ejpam-2473	100	9	is	be	AUX
ejpam-2473	100	10	a	a	DET
ejpam-2473	100	11	d	d	NOUN
ejpam-2473	100	12	-set	-set	VERB
ejpam-2473	100	13	containing	contain	VERB
ejpam-2473	100	14	a	a	PRON
ejpam-2473	100	15	with	with	ADP
ejpam-2473	100	16	�	�	PROPN
ejpam-2473	100	17	�	�	PROPN
ejpam-2473	100	18	d1	d1	PROPN
ejpam-2473	100	19	�	�	PROPN
ejpam-2473	100	20	�	�	PROPN
ejpam-2473	100	21	≤	≤	PROPN
ejpam-2473	100	22	|d|	|d|	PROPN
ejpam-2473	100	23	.	.	PUNCT
ejpam-2473	101	1	this	this	PRON
ejpam-2473	101	2	is	be	AUX
ejpam-2473	101	3	a	a	DET
ejpam-2473	101	4	contradiction	contradiction	NOUN
ejpam-2473	101	5	.	.	PUNCT
ejpam-2473	102	1	conversely	conversely	ADV
ejpam-2473	102	2	,	,	PUNCT
ejpam-2473	102	3	assume	assume	VERB
ejpam-2473	102	4	that	that	SCONJ
ejpam-2473	102	5	a	a	DET
ejpam-2473	102	6	⊆	⊆	NUM
ejpam-2473	102	7	d	d	PROPN
ejpam-2473	102	8	,	,	PUNCT
ejpam-2473	102	9	a	a	DET
ejpam-2473	102	10	⊇	⊇	X
ejpam-2473	102	11	(	(	PUNCT
ejpam-2473	102	12	d\s	d\s	PROPN
ejpam-2473	102	13	)	)	PUNCT
ejpam-2473	102	14	for	for	ADP
ejpam-2473	102	15	some	some	PRON
ejpam-2473	102	16	d	d	NOUN
ejpam-2473	102	17	-set	-set	X
ejpam-2473	103	1	d	d	NOUN
ejpam-2473	103	2	of	of	ADP
ejpam-2473	103	3	g	g	NOUN
ejpam-2473	103	4	,	,	PUNCT
ejpam-2473	103	5	and	and	CCONJ
ejpam-2473	103	6	i	i	PRON
ejpam-2473	103	7	(	(	PUNCT
ejpam-2473	103	8	a	a	X
ejpam-2473	103	9	)	)	PUNCT
ejpam-2473	103	10	>	>	X
ejpam-2473	104	1	1	1	X
ejpam-2473	104	2	.	.	PUNCT
ejpam-2473	105	1	if	if	SCONJ
ejpam-2473	105	2	a	a	DET
ejpam-2473	105	3	⊆	⊆	NUM
ejpam-2473	105	4	d	d	NOUN
ejpam-2473	105	5	and	and	CCONJ
ejpam-2473	105	6	a	a	DET
ejpam-2473	105	7	⊇	⊇	NOUN
ejpam-2473	105	8	(	(	PUNCT
ejpam-2473	105	9	d\s	d\s	PROPN
ejpam-2473	105	10	)	)	PUNCT
ejpam-2473	105	11	for	for	ADP
ejpam-2473	105	12	some	some	PRON
ejpam-2473	105	13	d	d	NOUN
ejpam-2473	105	14	-set	-set	X
ejpam-2473	106	1	d	d	NOUN
ejpam-2473	106	2	of	of	ADP
ejpam-2473	106	3	g	g	NOUN
ejpam-2473	106	4	,	,	PUNCT
ejpam-2473	106	5	then	then	ADV
ejpam-2473	106	6	d	d	X
ejpam-2473	106	7	=	=	PUNCT
ejpam-2473	106	8	a	a	DET
ejpam-2473	106	9	∪	∪	NOUN
ejpam-2473	106	10	s	s	NOUN
ejpam-2473	106	11	is	be	AUX
ejpam-2473	106	12	a	a	DET
ejpam-2473	106	13	smallest	small	ADJ
ejpam-2473	106	14	d	d	NOUN
ejpam-2473	106	15	-set	-set	X
ejpam-2473	106	16	containing	contain	VERB
ejpam-2473	106	17	a.	a.	NOUN
ejpam-2473	106	18	since	since	SCONJ
ejpam-2473	106	19	i	i	PRON
ejpam-2473	106	20	(	(	PUNCT
ejpam-2473	106	21	a	a	NOUN
ejpam-2473	106	22	)	)	PUNCT
ejpam-2473	106	23	>	>	X
ejpam-2473	106	24	1	1	NUM
ejpam-2473	106	25	,	,	PUNCT
ejpam-2473	106	26	let	let	VERB
ejpam-2473	106	27	d1	d1	PROPN
ejpam-2473	106	28	be	be	AUX
ejpam-2473	106	29	another	another	DET
ejpam-2473	106	30	smallest	small	ADJ
ejpam-2473	106	31	d	d	X
ejpam-2473	106	32	-set	-set	ADV
ejpam-2473	106	33	containing	contain	VERB
ejpam-2473	106	34	a.	a.	NOUN
ejpam-2473	106	35	since	since	SCONJ
ejpam-2473	106	36	a	a	DET
ejpam-2473	106	37	⊇	⊇	X
ejpam-2473	106	38	(	(	PUNCT
ejpam-2473	106	39	d\s	d\s	PROPN
ejpam-2473	106	40	)	)	PUNCT
ejpam-2473	106	41	,	,	PUNCT
ejpam-2473	106	42	d1	d1	PROPN
ejpam-2473	106	43	⊇	⊇	NOUN
ejpam-2473	106	44	(	(	PUNCT
ejpam-2473	106	45	d\s	d\s	PROPN
ejpam-2473	106	46	)	)	PUNCT
ejpam-2473	106	47	.	.	PUNCT
ejpam-2473	107	1	if	if	SCONJ
ejpam-2473	107	2	d	d	PROPN
ejpam-2473	107	3	6=	6=	ADP
ejpam-2473	107	4	d1	d1	PROPN
ejpam-2473	107	5	and	and	CCONJ
ejpam-2473	107	6	d1	d1	PROPN
ejpam-2473	107	7	⊇	⊇	NOUN
ejpam-2473	107	8	(	(	PUNCT
ejpam-2473	107	9	d\s	d\s	PROPN
ejpam-2473	107	10	)	)	PUNCT
ejpam-2473	107	11	,	,	PUNCT
ejpam-2473	107	12	d	d	X
ejpam-2473	107	13	is	be	AUX
ejpam-2473	107	14	a	a	DET
ejpam-2473	107	15	proper	proper	ADJ
ejpam-2473	107	16	subset	subset	NOUN
ejpam-2473	107	17	of	of	ADP
ejpam-2473	107	18	d1	d1	PROPN
ejpam-2473	107	19	(	(	PUNCT
ejpam-2473	107	20	since	since	SCONJ
ejpam-2473	107	21	d1	d1	PROPN
ejpam-2473	107	22	must	must	AUX
ejpam-2473	107	23	contain	contain	VERB
ejpam-2473	107	24	s	s	NOUN
ejpam-2473	107	25	)	)	PUNCT
ejpam-2473	107	26	.	.	PUNCT
ejpam-2473	108	1	hence	hence	ADV
ejpam-2473	108	2	|d|	|d|	PROPN
ejpam-2473	108	3	6=	6=	PROPN
ejpam-2473	108	4	�	�	PROPN
ejpam-2473	108	5	�	�	PROPN
ejpam-2473	108	6	d1	d1	PROPN
ejpam-2473	108	7	�	�	PROPN
ejpam-2473	108	8	�	�	PROPN
ejpam-2473	108	9	.	.	PUNCT
ejpam-2473	109	1	this	this	PRON
ejpam-2473	109	2	is	be	AUX
ejpam-2473	109	3	a	a	DET
ejpam-2473	109	4	contradiction	contradiction	NOUN
ejpam-2473	109	5	.	.	PUNCT
ejpam-2473	110	1	theorem	theorem	NOUN
ejpam-2473	110	2	5	5	NUM
ejpam-2473	110	3	.	.	PUNCT
ejpam-2473	111	1	let	let	VERB
ejpam-2473	111	2	g	g	PRON
ejpam-2473	111	3	be	be	AUX
ejpam-2473	111	4	a	a	DET
ejpam-2473	111	5	finite	finite	ADJ
ejpam-2473	111	6	group	group	NOUN
ejpam-2473	111	7	,	,	PUNCT
ejpam-2473	111	8	s	s	PART
ejpam-2473	111	9	=	=	PUNCT
ejpam-2473	111	10	�	�	PROPN
ejpam-2473	111	11	s	s	PART
ejpam-2473	111	12	∈	∈	PROPN
ejpam-2473	111	13	g	g	NOUN
ejpam-2473	111	14	:	:	PUNCT
ejpam-2473	111	15	s2	s2	NOUN
ejpam-2473	111	16	=	=	PUNCT
ejpam-2473	111	17	e	e	NOUN
ejpam-2473	111	18	,	,	PUNCT
ejpam-2473	111	19	and	and	CCONJ
ejpam-2473	111	20	a	a	DET
ejpam-2473	111	21	⊆	⊆	NUM
ejpam-2473	111	22	g.	g.	NOUN
ejpam-2473	111	23	if	if	SCONJ
ejpam-2473	111	24	x	x	PROPN
ejpam-2473	111	25	i	i	PROPN
ejpam-2473	111	26	6=	6=	PROPN
ejpam-2473	111	27	x−1	x−1	PROPN
ejpam-2473	111	28	j	j	PROPN
ejpam-2473	111	29	for	for	ADP
ejpam-2473	111	30	all	all	PRON
ejpam-2473	111	31	x	x	ADJ
ejpam-2473	111	32	i	i	PRON
ejpam-2473	111	33	,	,	PUNCT
ejpam-2473	111	34	x	x	PUNCT
ejpam-2473	111	35	j	j	PROPN
ejpam-2473	111	36	∈	∈	PROPN
ejpam-2473	111	37	a\s	a\s	PROPN
ejpam-2473	111	38	,	,	PUNCT
ejpam-2473	111	39	then	then	ADV
ejpam-2473	111	40	a	a	PRON
ejpam-2473	111	41	is	be	AUX
ejpam-2473	111	42	a	a	DET
ejpam-2473	111	43	subset	subset	NOUN
ejpam-2473	111	44	of	of	ADP
ejpam-2473	111	45	a	a	DET
ejpam-2473	111	46	minimum	minimum	NOUN
ejpam-2473	111	47	d	d	NOUN
ejpam-2473	111	48	-set	-set	NOUN
ejpam-2473	111	49	.	.	PUNCT
ejpam-2473	112	1	hence	hence	ADV
ejpam-2473	112	2	,	,	PUNCT
ejpam-2473	112	3	i	i	PRON
ejpam-2473	112	4	(	(	PUNCT
ejpam-2473	112	5	a)≤	a)≤	PROPN
ejpam-2473	112	6	2c	2c	NOUN
ejpam-2473	112	7	.	.	PUNCT
ejpam-2473	113	1	proof	proof	NOUN
ejpam-2473	113	2	.	.	PUNCT
ejpam-2473	114	1	let	let	VERB
ejpam-2473	114	2	g	g	PRON
ejpam-2473	114	3	be	be	AUX
ejpam-2473	114	4	a	a	DET
ejpam-2473	114	5	finite	finite	ADJ
ejpam-2473	114	6	group	group	NOUN
ejpam-2473	114	7	,	,	PUNCT
ejpam-2473	114	8	s	s	PART
ejpam-2473	114	9	=	=	PUNCT
ejpam-2473	114	10	�	�	PROPN
ejpam-2473	114	11	s	s	PART
ejpam-2473	114	12	∈	∈	PROPN
ejpam-2473	114	13	g	g	NOUN
ejpam-2473	114	14	:	:	PUNCT
ejpam-2473	114	15	s2	s2	NOUN
ejpam-2473	114	16	=	=	PUNCT
ejpam-2473	114	17	e	e	NOUN
ejpam-2473	114	18	,	,	PUNCT
ejpam-2473	114	19	and	and	CCONJ
ejpam-2473	114	20	a	a	DET
ejpam-2473	114	21	⊆	⊆	NUM
ejpam-2473	114	22	g.	g.	NOUN
ejpam-2473	114	23	from	from	ADP
ejpam-2473	114	24	remark	remark	NOUN
ejpam-2473	114	25	1	1	NUM
ejpam-2473	114	26	,	,	PUNCT
ejpam-2473	114	27	if	if	SCONJ
ejpam-2473	114	28	d	d	NOUN
ejpam-2473	114	29	is	be	AUX
ejpam-2473	114	30	a	a	DET
ejpam-2473	114	31	minimum	minimum	NOUN
ejpam-2473	114	32	d	d	NOUN
ejpam-2473	114	33	-set	-set	NOUN
ejpam-2473	114	34	,	,	PUNCT
ejpam-2473	114	35	then	then	ADV
ejpam-2473	114	36	d	d	X
ejpam-2473	114	37	=	=	SYM
ejpam-2473	114	38	s	s	PART
ejpam-2473	114	39	∪	∪	X
ejpam-2473	114	40	�	�	PROPN
ejpam-2473	114	41	a1	a1	PROPN
ejpam-2473	114	42	,	,	PUNCT
ejpam-2473	114	43	a2	a2	PROPN
ejpam-2473	114	44	,	,	PUNCT
ejpam-2473	114	45	.	.	PUNCT
ejpam-2473	114	46	.	.	PUNCT
ejpam-2473	115	1	.	.	PUNCT
ejpam-2473	116	1	,	,	PUNCT
ejpam-2473	116	2	ac	ac	PROPN
ejpam-2473	116	3	where	where	SCONJ
ejpam-2473	116	4	ai	ai	VERB
ejpam-2473	116	5	∈	∈	PROPN
ejpam-2473	116	6	�	�	PROPN
ejpam-2473	117	1	x	x	INTJ
ejpam-2473	117	2	i	i	PROPN
ejpam-2473	117	3	,	,	PUNCT
ejpam-2473	117	4	x−1	x−1	PROPN
ejpam-2473	117	5	i	i	PRON
ejpam-2473	117	6	for	for	ADP
ejpam-2473	117	7	i	i	X
ejpam-2473	117	8	=	=	SYM
ejpam-2473	117	9	1,2	1,2	NUM
ejpam-2473	117	10	,	,	PUNCT
ejpam-2473	117	11	.	.	PUNCT
ejpam-2473	117	12	.	.	PUNCT
ejpam-2473	117	13	.	.	PUNCT
ejpam-2473	118	1	,	,	PUNCT
ejpam-2473	119	1	c	c	X
ejpam-2473	119	2	where	where	SCONJ
ejpam-2473	119	3	�	�	PROPN
ejpam-2473	119	4	{	{	PUNCT
ejpam-2473	119	5	x	x	PROPN
ejpam-2473	119	6	i	i	PROPN
ejpam-2473	119	7	,	,	PUNCT
ejpam-2473	119	8	x−1	x−1	PROPN
ejpam-2473	120	1	i	i	PRON
ejpam-2473	120	2	}	}	PUNCT
ejpam-2473	120	3	:	:	PUNCT
ejpam-2473	121	1	i	i	NOUN
ejpam-2473	121	2	=	=	SYM
ejpam-2473	121	3	1,2	1,2	NUM
ejpam-2473	121	4	,	,	PUNCT
ejpam-2473	121	5	.	.	PUNCT
ejpam-2473	121	6	.	.	PUNCT
ejpam-2473	121	7	.	.	PUNCT
ejpam-2473	122	1	,	,	PUNCT
ejpam-2473	122	2	c	c	NOUN
ejpam-2473	122	3	is	be	AUX
ejpam-2473	122	4	a	a	DET
ejpam-2473	122	5	partition	partition	NOUN
ejpam-2473	122	6	of	of	ADP
ejpam-2473	122	7	g\s	g\s	NOUN
ejpam-2473	122	8	in	in	ADP
ejpam-2473	122	9	the	the	DET
ejpam-2473	122	10	sense	sense	NOUN
ejpam-2473	122	11	of	of	ADP
ejpam-2473	122	12	remark	remark	NOUN
ejpam-2473	122	13	1	1	NUM
ejpam-2473	122	14	.	.	PUNCT
ejpam-2473	123	1	thus	thus	ADV
ejpam-2473	123	2	,	,	PUNCT
ejpam-2473	123	3	if	if	SCONJ
ejpam-2473	123	4	x	x	PROPN
ejpam-2473	123	5	i	i	PROPN
ejpam-2473	123	6	6=	6=	PROPN
ejpam-2473	123	7	x−1	x−1	PROPN
ejpam-2473	123	8	j	j	PROPN
ejpam-2473	123	9	for	for	ADP
ejpam-2473	123	10	all	all	PRON
ejpam-2473	123	11	x	x	ADJ
ejpam-2473	123	12	i	i	PRON
ejpam-2473	123	13	,	,	PUNCT
ejpam-2473	123	14	x	x	PUNCT
ejpam-2473	123	15	j	j	PROPN
ejpam-2473	123	16	∈	∈	PROPN
ejpam-2473	123	17	a\s	a\s	PROPN
ejpam-2473	123	18	,	,	PUNCT
ejpam-2473	123	19	then	then	ADV
ejpam-2473	123	20	a	a	PRON
ejpam-2473	123	21	is	be	AUX
ejpam-2473	123	22	a	a	DET
ejpam-2473	123	23	subset	subset	NOUN
ejpam-2473	123	24	of	of	ADP
ejpam-2473	123	25	a	a	DET
ejpam-2473	123	26	minimum	minimum	NOUN
ejpam-2473	123	27	d	d	NOUN
ejpam-2473	123	28	-set	-set	NUM
ejpam-2473	123	29	.	.	PUNCT
ejpam-2473	124	1	we	we	PRON
ejpam-2473	124	2	recall	recall	VERB
ejpam-2473	124	3	the	the	DET
ejpam-2473	124	4	disjoint	disjoint	PROPN
ejpam-2473	124	5	union	union	NOUN
ejpam-2473	124	6	of	of	ADP
ejpam-2473	124	7	sets	set	NOUN
ejpam-2473	124	8	.	.	PUNCT
ejpam-2473	125	1	let	let	VERB
ejpam-2473	125	2	x	x	PRON
ejpam-2473	125	3	and	and	CCONJ
ejpam-2473	125	4	y	y	PROPN
ejpam-2473	125	5	be	be	AUX
ejpam-2473	125	6	sets	set	NOUN
ejpam-2473	125	7	.	.	PUNCT
ejpam-2473	126	1	the	the	DET
ejpam-2473	126	2	disjoint	disjoint	PROPN
ejpam-2473	126	3	union	union	NOUN
ejpam-2473	126	4	of	of	ADP
ejpam-2473	126	5	x	x	PROPN
ejpam-2473	126	6	and	and	CCONJ
ejpam-2473	126	7	y	y	PROPN
ejpam-2473	126	8	,	,	PUNCT
ejpam-2473	126	9	denoted	denote	VERB
ejpam-2473	126	10	by	by	ADP
ejpam-2473	126	11	x	x	X
ejpam-2473	126	12	∪̇	∪̇	PROPN
ejpam-2473	126	13	y	y	PROPN
ejpam-2473	126	14	,	,	PUNCT
ejpam-2473	126	15	is	be	AUX
ejpam-2473	126	16	found	find	VERB
ejpam-2473	126	17	by	by	ADP
ejpam-2473	126	18	combining	combine	VERB
ejpam-2473	126	19	the	the	DET
ejpam-2473	126	20	elements	element	NOUN
ejpam-2473	126	21	of	of	ADP
ejpam-2473	126	22	x	x	X
ejpam-2473	126	23	and	and	CCONJ
ejpam-2473	126	24	y	y	PROPN
ejpam-2473	126	25	,	,	PUNCT
ejpam-2473	126	26	treating	treat	VERB
ejpam-2473	126	27	all	all	DET
ejpam-2473	126	28	elements	element	NOUN
ejpam-2473	126	29	to	to	PART
ejpam-2473	126	30	be	be	AUX
ejpam-2473	126	31	distinct	distinct	ADJ
ejpam-2473	126	32	.	.	PUNCT
ejpam-2473	127	1	thus	thus	ADV
ejpam-2473	127	2	,	,	PUNCT
ejpam-2473	127	3	�	�	PROPN
ejpam-2473	127	4	�	�	PROPN
ejpam-2473	127	5	x	x	PROPN
ejpam-2473	127	6	∪̇	∪̇	PROPN
ejpam-2473	127	7	y	y	PROPN
ejpam-2473	127	8	�	�	PROPN
ejpam-2473	127	9	�	�	PROPN
ejpam-2473	127	10	=	=	PUNCT
ejpam-2473	127	11	|x	|x	NOUN
ejpam-2473	127	12	|+	|+	NOUN
ejpam-2473	127	13	|y	|y	NOUN
ejpam-2473	127	14	|	|	NOUN
ejpam-2473	127	15	.	.	PUNCT
ejpam-2473	128	1	c.	c.	PROPN
ejpam-2473	128	2	rosero	rosero	PROPN
ejpam-2473	128	3	,	,	PUNCT
ejpam-2473	128	4	m.	m.	NOUN
ejpam-2473	128	5	baldado	baldado	NOUN
ejpam-2473	128	6	/	/	SYM
ejpam-2473	128	7	eur	eur	PROPN
ejpam-2473	128	8	.	.	PUNCT
ejpam-2473	129	1	j.	j.	PROPN
ejpam-2473	129	2	pure	pure	PROPN
ejpam-2473	129	3	appl	appl	PROPN
ejpam-2473	129	4	.	.	PROPN
ejpam-2473	129	5	math	math	PROPN
ejpam-2473	129	6	,	,	PUNCT
ejpam-2473	129	7	9	9	NUM
ejpam-2473	129	8	(	(	PUNCT
ejpam-2473	129	9	2016	2016	NUM
ejpam-2473	129	10	)	)	PUNCT
ejpam-2473	129	11	,	,	PUNCT
ejpam-2473	129	12	34	34	NUM
ejpam-2473	129	13	-	-	SYM
ejpam-2473	129	14	38	38	NUM
ejpam-2473	129	15	37	37	NUM
ejpam-2473	129	16	theorem	theorem	NOUN
ejpam-2473	129	17	6	6	NUM
ejpam-2473	129	18	.	.	PUNCT
ejpam-2473	130	1	let	let	VERB
ejpam-2473	130	2	g	g	PRON
ejpam-2473	130	3	be	be	AUX
ejpam-2473	130	4	a	a	DET
ejpam-2473	130	5	finite	finite	ADJ
ejpam-2473	130	6	group	group	NOUN
ejpam-2473	130	7	,	,	PUNCT
ejpam-2473	130	8	s	s	PART
ejpam-2473	130	9	=	=	PUNCT
ejpam-2473	130	10	�	�	PROPN
ejpam-2473	130	11	s	s	PART
ejpam-2473	130	12	∈	∈	PROPN
ejpam-2473	130	13	g	g	NOUN
ejpam-2473	130	14	:	:	PUNCT
ejpam-2473	130	15	s2	s2	NOUN
ejpam-2473	130	16	=	=	PUNCT
ejpam-2473	130	17	e	e	X
ejpam-2473	130	18	,	,	PUNCT
ejpam-2473	130	19	q	q	NOUN
ejpam-2473	130	20	=	=	SYM
ejpam-2473	130	21	�	�	PROPN
ejpam-2473	130	22	x	x	SYM
ejpam-2473	130	23	∈	∈	PROPN
ejpam-2473	130	24	a\s	a\s	NOUN
ejpam-2473	130	25	:	:	PUNCT
ejpam-2473	131	1	x−1	x−1	PROPN
ejpam-2473	131	2	∈	∈	PROPN
ejpam-2473	131	3	a	a	PRON
ejpam-2473	131	4	,	,	PUNCT
ejpam-2473	131	5	and	and	CCONJ
ejpam-2473	131	6	a⊆	a⊆	PROPN
ejpam-2473	131	7	g.	g.	NOUN
ejpam-2473	132	1	then	then	ADV
ejpam-2473	132	2	i	i	PRON
ejpam-2473	132	3	(	(	PUNCT
ejpam-2473	132	4	a	a	X
ejpam-2473	132	5	)	)	PUNCT
ejpam-2473	132	6	=	=	SYM
ejpam-2473	132	7	2c−n	2c−n	NOUN
ejpam-2473	132	8	,	,	PUNCT
ejpam-2473	132	9	where	where	SCONJ
ejpam-2473	132	10	n=	n=	ADJ
ejpam-2473	132	11	|a|	|a|	PROPN
ejpam-2473	132	12	−	−	PROPN
ejpam-2473	132	13	|a∩	|a∩	NOUN
ejpam-2473	132	14	s|	s|	VERB
ejpam-2473	132	15	−	−	NOUN
ejpam-2473	132	16	|q|2	|q|2	PROPN
ejpam-2473	132	17	.	.	PUNCT
ejpam-2473	133	1	proof	proof	NOUN
ejpam-2473	133	2	.	.	PUNCT
ejpam-2473	134	1	let	let	VERB
ejpam-2473	134	2	g	g	PRON
ejpam-2473	134	3	be	be	AUX
ejpam-2473	134	4	a	a	DET
ejpam-2473	134	5	finite	finite	ADJ
ejpam-2473	134	6	group	group	NOUN
ejpam-2473	134	7	,	,	PUNCT
ejpam-2473	134	8	s	s	PART
ejpam-2473	134	9	=	=	PUNCT
ejpam-2473	134	10	�	�	PROPN
ejpam-2473	134	11	s	s	PART
ejpam-2473	134	12	∈	∈	PROPN
ejpam-2473	134	13	g	g	NOUN
ejpam-2473	134	14	:	:	PUNCT
ejpam-2473	134	15	s2	s2	NOUN
ejpam-2473	134	16	=	=	PUNCT
ejpam-2473	134	17	e	e	X
ejpam-2473	134	18	,	,	PUNCT
ejpam-2473	134	19	q	q	X
ejpam-2473	134	20	=	=	PUNCT
ejpam-2473	134	21	{	{	PUNCT
ejpam-2473	134	22	x	x	PUNCT
ejpam-2473	134	23	∈	∈	PROPN
ejpam-2473	134	24	a\s	a\s	NOUN
ejpam-2473	134	25	:	:	PUNCT
ejpam-2473	135	1	x−1	x−1	PROPN
ejpam-2473	135	2	∈	∈	PROPN
ejpam-2473	135	3	a	a	PRON
ejpam-2473	135	4	}	}	PUNCT
ejpam-2473	135	5	and	and	CCONJ
ejpam-2473	135	6	a	a	DET
ejpam-2473	135	7	⊆	⊆	NUM
ejpam-2473	135	8	g.	g.	NOUN
ejpam-2473	135	9	consider	consider	VERB
ejpam-2473	135	10	p	p	NOUN
ejpam-2473	135	11	=	=	PUNCT
ejpam-2473	135	12	a\	a\	NOUN
ejpam-2473	135	13	(	(	PUNCT
ejpam-2473	135	14	s	s	X
ejpam-2473	135	15	∪q	∪q	NUM
ejpam-2473	135	16	)	)	PUNCT
ejpam-2473	135	17	.	.	PUNCT
ejpam-2473	136	1	note	note	VERB
ejpam-2473	136	2	that	that	SCONJ
ejpam-2473	136	3	if	if	SCONJ
ejpam-2473	136	4	x	x	PROPN
ejpam-2473	136	5	∈	∈	PROPN
ejpam-2473	136	6	p	p	X
ejpam-2473	136	7	,	,	PUNCT
ejpam-2473	136	8	then	then	ADV
ejpam-2473	136	9	x−1	x−1	PROPN
ejpam-2473	136	10	∈	∈	PROPN
ejpam-2473	136	11	g\a	g\a	NOUN
ejpam-2473	136	12	.	.	PUNCT
ejpam-2473	137	1	thus	thus	ADV
ejpam-2473	137	2	,	,	PUNCT
ejpam-2473	137	3	a=(a∩	a=(a∩	PROPN
ejpam-2473	137	4	s	s	PART
ejpam-2473	137	5	)	)	PUNCT
ejpam-2473	137	6	∪̇q	∪̇q	VERB
ejpam-2473	137	7	∪̇	∪̇	PROPN
ejpam-2473	138	1	p	p	PROPN
ejpam-2473	138	2	=(	=(	PROPN
ejpam-2473	138	3	a∩	a∩	PROPN
ejpam-2473	138	4	s	s	PART
ejpam-2473	138	5	)	)	PUNCT
ejpam-2473	138	6	∪̇	∪̇	PROPN
ejpam-2473	138	7	�	�	PROPN
ejpam-2473	139	1	x1	x1	PROPN
ejpam-2473	139	2	,	,	PUNCT
ejpam-2473	139	3	x−1	x−1	PROPN
ejpam-2473	139	4	1	1	NUM
ejpam-2473	139	5	,	,	PUNCT
ejpam-2473	139	6	x2	x2	PROPN
ejpam-2473	139	7	,	,	PUNCT
ejpam-2473	139	8	x−1	x−1	PROPN
ejpam-2473	139	9	2	2	NUM
ejpam-2473	139	10	,	,	PUNCT
ejpam-2473	139	11	.	.	PUNCT
ejpam-2473	139	12	.	.	PUNCT
ejpam-2473	139	13	.	.	PUNCT
ejpam-2473	140	1	,	,	PUNCT
ejpam-2473	140	2	xk	xk	PROPN
ejpam-2473	140	3	,	,	PUNCT
ejpam-2473	140	4	x−1	x−1	PROPN
ejpam-2473	140	5	k	k	PROPN
ejpam-2473	140	6	∪̇	∪̇	PROPN
ejpam-2473	140	7	�	�	PROPN
ejpam-2473	140	8	xk+1	xk+1	PROPN
ejpam-2473	140	9	,	,	PUNCT
ejpam-2473	140	10	xk+2	xk+2	NUM
ejpam-2473	140	11	,	,	PUNCT
ejpam-2473	140	12	.	.	PUNCT
ejpam-2473	140	13	.	.	PUNCT
ejpam-2473	140	14	.	.	PUNCT
ejpam-2473	141	1	,	,	PUNCT
ejpam-2473	141	2	xn	xn	PROPN
ejpam-2473	141	3	.	.	PUNCT
ejpam-2473	142	1	(	(	PUNCT
ejpam-2473	142	2	1	1	X
ejpam-2473	142	3	)	)	PUNCT
ejpam-2473	142	4	it	it	PRON
ejpam-2473	142	5	can	can	AUX
ejpam-2473	142	6	be	be	AUX
ejpam-2473	142	7	shown	show	VERB
ejpam-2473	142	8	that	that	SCONJ
ejpam-2473	142	9	if	if	SCONJ
ejpam-2473	142	10	d	d	NOUN
ejpam-2473	142	11	is	be	AUX
ejpam-2473	142	12	a	a	DET
ejpam-2473	142	13	smallest	small	ADJ
ejpam-2473	142	14	d	d	NOUN
ejpam-2473	142	15	-set	-set	VERB
ejpam-2473	142	16	containing	contain	VERB
ejpam-2473	142	17	a	a	PRON
ejpam-2473	142	18	,	,	PUNCT
ejpam-2473	142	19	then	then	ADV
ejpam-2473	142	20	d	d	PROPN
ejpam-2473	142	21	is	be	AUX
ejpam-2473	142	22	of	of	ADP
ejpam-2473	142	23	the	the	DET
ejpam-2473	142	24	form	form	NOUN
ejpam-2473	143	1	d	d	NOUN
ejpam-2473	143	2	=	=	SYM
ejpam-2473	143	3	s	s	X
ejpam-2473	143	4	∪̇q	∪̇q	NUM
ejpam-2473	143	5	∪̇	∪̇	PROPN
ejpam-2473	143	6	p	p	PROPN
ejpam-2473	143	7	∪̇	∪̇	PROPN
ejpam-2473	143	8	�	�	PROPN
ejpam-2473	143	9	xn+1	xn+1	PROPN
ejpam-2473	143	10	,	,	PUNCT
ejpam-2473	143	11	xn+2	xn+2	PRON
ejpam-2473	143	12	,	,	PUNCT
ejpam-2473	143	13	.	.	PUNCT
ejpam-2473	143	14	.	.	PUNCT
ejpam-2473	143	15	.	.	PUNCT
ejpam-2473	144	1	,	,	PUNCT
ejpam-2473	144	2	xc	xc	PROPN
ejpam-2473	145	1	=	=	PROPN
ejpam-2473	145	2	s	s	PART
ejpam-2473	145	3	∪̇	∪̇	X
ejpam-2473	145	4	�	�	PROPN
ejpam-2473	145	5	x1	x1	PROPN
ejpam-2473	145	6	,	,	PUNCT
ejpam-2473	145	7	x−1	x−1	PROPN
ejpam-2473	145	8	1	1	NUM
ejpam-2473	145	9	,	,	PUNCT
ejpam-2473	145	10	x2	x2	PROPN
ejpam-2473	145	11	,	,	PUNCT
ejpam-2473	145	12	x−1	x−1	PROPN
ejpam-2473	145	13	2	2	NUM
ejpam-2473	145	14	,	,	PUNCT
ejpam-2473	145	15	.	.	PUNCT
ejpam-2473	145	16	.	.	PUNCT
ejpam-2473	145	17	.	.	PUNCT
ejpam-2473	146	1	,	,	PUNCT
ejpam-2473	146	2	xk	xk	PROPN
ejpam-2473	146	3	,	,	PUNCT
ejpam-2473	146	4	x−1	x−1	PROPN
ejpam-2473	146	5	k	k	PROPN
ejpam-2473	146	6	,	,	PUNCT
ejpam-2473	146	7	xk+1	xk+1	PROPN
ejpam-2473	146	8	,	,	PUNCT
ejpam-2473	146	9	xk+2	xk+2	NUM
ejpam-2473	146	10	,	,	PUNCT
ejpam-2473	146	11	.	.	PUNCT
ejpam-2473	146	12	.	.	PUNCT
ejpam-2473	146	13	.	.	PUNCT
ejpam-2473	147	1	,	,	PUNCT
ejpam-2473	147	2	xn	xn	PROPN
ejpam-2473	147	3	∪̇	∪̇	PROPN
ejpam-2473	147	4	�	�	PROPN
ejpam-2473	147	5	xn+1	xn+1	PROPN
ejpam-2473	147	6	,	,	PUNCT
ejpam-2473	147	7	xn+2	xn+2	PRON
ejpam-2473	147	8	,	,	PUNCT
ejpam-2473	147	9	.	.	PUNCT
ejpam-2473	147	10	.	.	PUNCT
ejpam-2473	148	1	.	.	PUNCT
ejpam-2473	149	1	,	,	PUNCT
ejpam-2473	149	2	xc	xc	PROPN
ejpam-2473	149	3	.	.	PUNCT
ejpam-2473	150	1	(	(	PUNCT
ejpam-2473	150	2	2	2	X
ejpam-2473	150	3	)	)	PUNCT
ejpam-2473	150	4	by	by	ADP
ejpam-2473	150	5	this	this	PRON
ejpam-2473	150	6	,	,	PUNCT
ejpam-2473	150	7	the	the	DET
ejpam-2473	150	8	number	number	NOUN
ejpam-2473	150	9	of	of	ADP
ejpam-2473	150	10	ways	way	NOUN
ejpam-2473	150	11	to	to	PART
ejpam-2473	150	12	choose	choose	VERB
ejpam-2473	150	13	a	a	DET
ejpam-2473	150	14	smallest	small	ADJ
ejpam-2473	150	15	d	d	NOUN
ejpam-2473	150	16	-set	-set	VERB
ejpam-2473	150	17	containing	contain	VERB
ejpam-2473	150	18	a	a	PRON
ejpam-2473	150	19	is	be	AUX
ejpam-2473	150	20	2	2	NUM
ejpam-2473	150	21	·	·	SYM
ejpam-2473	150	22	2	2	NUM
ejpam-2473	150	23	·	·	PUNCT
ejpam-2473	150	24	·	·	PUNCT
ejpam-2473	150	25	·	·	PUNCT
ejpam-2473	150	26	·	·	PUNCT
ejpam-2473	150	27	·	·	PUNCT
ejpam-2473	150	28	·	·	PUNCT
ejpam-2473	151	1	2	2	NUM
ejpam-2473	151	2	=	=	SYM
ejpam-2473	151	3	2c−n	2c−n	NOUN
ejpam-2473	151	4	,	,	PUNCT
ejpam-2473	151	5	where	where	SCONJ
ejpam-2473	151	6	n=	n=	ADJ
ejpam-2473	151	7	|q|	|q|	NUM
ejpam-2473	151	8	2	2	NUM
ejpam-2473	151	9	+	+	CCONJ
ejpam-2473	151	10	(	(	PUNCT
ejpam-2473	151	11	n−	n−	NOUN
ejpam-2473	151	12	k	k	NOUN
ejpam-2473	151	13	)	)	PUNCT
ejpam-2473	151	14	.	.	PUNCT
ejpam-2473	152	1	since	since	SCONJ
ejpam-2473	152	2	|a|=	|a|=	ADJ
ejpam-2473	152	3	|a∩	|a∩	NOUN
ejpam-2473	152	4	s|+	s|+	NOUN
ejpam-2473	152	5	|q|+	|q|+	NOUN
ejpam-2473	152	6	(	(	PUNCT
ejpam-2473	152	7	n−	n−	NOUN
ejpam-2473	152	8	k	k	NOUN
ejpam-2473	152	9	)	)	PUNCT
ejpam-2473	152	10	,	,	PUNCT
ejpam-2473	152	11	n=	n=	ADJ
ejpam-2473	152	12	|a|	|a|	PROPN
ejpam-2473	152	13	−	−	PROPN
ejpam-2473	152	14	|a∩	|a∩	NOUN
ejpam-2473	152	15	s|	s|	VERB
ejpam-2473	152	16	−	−	NOUN
ejpam-2473	152	17	|q|2	|q|2	PROPN
ejpam-2473	152	18	.	.	PUNCT
ejpam-2473	153	1	3	3	X
ejpam-2473	153	2	.	.	X
ejpam-2473	153	3	d	d	NOUN
ejpam-2473	153	4	-sets	-set	NOUN
ejpam-2473	153	5	generated	generate	VERB
ejpam-2473	153	6	by	by	ADP
ejpam-2473	153	7	a	a	DET
ejpam-2473	153	8	subgroup	subgroup	NOUN
ejpam-2473	153	9	the	the	DET
ejpam-2473	153	10	following	follow	VERB
ejpam-2473	153	11	are	be	AUX
ejpam-2473	153	12	consequences	consequence	NOUN
ejpam-2473	153	13	of	of	ADP
ejpam-2473	153	14	theorem	theorem	ADJ
ejpam-2473	153	15	6	6	NUM
ejpam-2473	153	16	.	.	PUNCT
ejpam-2473	153	17	corollary	corollary	ADJ
ejpam-2473	153	18	2	2	NUM
ejpam-2473	153	19	.	.	PUNCT
ejpam-2473	154	1	let	let	VERB
ejpam-2473	154	2	g	g	PRON
ejpam-2473	154	3	be	be	AUX
ejpam-2473	154	4	a	a	DET
ejpam-2473	154	5	finite	finite	ADJ
ejpam-2473	154	6	group	group	NOUN
ejpam-2473	154	7	,	,	PUNCT
ejpam-2473	154	8	s	s	PART
ejpam-2473	154	9	=	=	PUNCT
ejpam-2473	154	10	�	�	PROPN
ejpam-2473	154	11	s	s	PART
ejpam-2473	154	12	∈	∈	PROPN
ejpam-2473	154	13	g	g	NOUN
ejpam-2473	154	14	:	:	PUNCT
ejpam-2473	154	15	s2	s2	NOUN
ejpam-2473	154	16	=	=	PUNCT
ejpam-2473	154	17	e	e	NOUN
ejpam-2473	154	18	,	,	PUNCT
ejpam-2473	154	19	and	and	CCONJ
ejpam-2473	154	20	h	h	PROPN
ejpam-2473	154	21	≤	≤	PROPN
ejpam-2473	155	1	g.	g.	NOUN
ejpam-2473	155	2	then	then	ADV
ejpam-2473	155	3	i	i	PRON
ejpam-2473	155	4	(	(	PUNCT
ejpam-2473	155	5	a	a	X
ejpam-2473	155	6	)	)	PUNCT
ejpam-2473	156	1	=	=	SYM
ejpam-2473	156	2	2c−n	2c−n	NOUN
ejpam-2473	156	3	,	,	PUNCT
ejpam-2473	156	4	where	where	SCONJ
ejpam-2473	156	5	n=	n=	ADJ
ejpam-2473	156	6	|h\s|/2	|h\s|/2	NOUN
ejpam-2473	156	7	.	.	PUNCT
ejpam-2473	156	8	proof	proof	NOUN
ejpam-2473	156	9	.	.	PUNCT
ejpam-2473	157	1	let	let	VERB
ejpam-2473	157	2	g	g	PRON
ejpam-2473	157	3	be	be	AUX
ejpam-2473	157	4	a	a	DET
ejpam-2473	157	5	finite	finite	ADJ
ejpam-2473	157	6	group	group	NOUN
ejpam-2473	157	7	,	,	PUNCT
ejpam-2473	157	8	s	s	PART
ejpam-2473	157	9	=	=	PUNCT
ejpam-2473	157	10	�	�	PROPN
ejpam-2473	157	11	s	s	PART
ejpam-2473	157	12	∈	∈	PROPN
ejpam-2473	157	13	g	g	NOUN
ejpam-2473	157	14	:	:	PUNCT
ejpam-2473	157	15	s2	s2	NOUN
ejpam-2473	157	16	=	=	PUNCT
ejpam-2473	157	17	e	e	NOUN
ejpam-2473	157	18	,	,	PUNCT
ejpam-2473	157	19	and	and	CCONJ
ejpam-2473	157	20	h	h	PROPN
ejpam-2473	157	21	≤	≤	PROPN
ejpam-2473	157	22	g.	g.	NOUN
ejpam-2473	158	1	if	if	SCONJ
ejpam-2473	158	2	h	h	NOUN
ejpam-2473	158	3	≤	≤	X
ejpam-2473	158	4	g	g	NOUN
ejpam-2473	158	5	,	,	PUNCT
ejpam-2473	158	6	then	then	ADV
ejpam-2473	158	7	x	x	X
ejpam-2473	158	8	,	,	PUNCT
ejpam-2473	158	9	x−1	x−1	PROPN
ejpam-2473	158	10	∈	∈	PROPN
ejpam-2473	158	11	h	h	NOUN
ejpam-2473	158	12	for	for	ADP
ejpam-2473	158	13	all	all	PRON
ejpam-2473	158	14	x	x	SYM
ejpam-2473	158	15	∈	∈	PROPN
ejpam-2473	158	16	h.	h.	NOUN
ejpam-2473	158	17	let	let	VERB
ejpam-2473	158	18	q	q	NOUN
ejpam-2473	158	19	=	=	PUNCT
ejpam-2473	158	20	{	{	PUNCT
ejpam-2473	158	21	x	x	PUNCT
ejpam-2473	158	22	∈	∈	PROPN
ejpam-2473	158	23	a\s	a\s	NOUN
ejpam-2473	158	24	:	:	PUNCT
ejpam-2473	159	1	x−1	x−1	PROPN
ejpam-2473	159	2	∈	∈	PROPN
ejpam-2473	159	3	a	a	PRON
ejpam-2473	159	4	}	}	PUNCT
ejpam-2473	159	5	.	.	PUNCT
ejpam-2473	160	1	then	then	ADV
ejpam-2473	160	2	q	q	X
ejpam-2473	160	3	=	=	PUNCT
ejpam-2473	160	4	h\s	h\	NOUN
ejpam-2473	160	5	,	,	PUNCT
ejpam-2473	160	6	that	that	ADV
ejpam-2473	160	7	is	is	ADV
ejpam-2473	160	8	,	,	PUNCT
ejpam-2473	160	9	|q|	|q|	X
ejpam-2473	160	10	=	=	SYM
ejpam-2473	160	11	|h\s|	|h\s|	NUM
ejpam-2473	160	12	.	.	PUNCT
ejpam-2473	161	1	thus	thus	ADV
ejpam-2473	161	2	,	,	PUNCT
ejpam-2473	161	3	by	by	ADP
ejpam-2473	161	4	theorem	theorem	NOUN
ejpam-2473	161	5	6	6	NUM
ejpam-2473	161	6	,	,	PUNCT
ejpam-2473	161	7	i	i	PRON
ejpam-2473	161	8	(	(	PUNCT
ejpam-2473	161	9	h	h	NOUN
ejpam-2473	161	10	)	)	PUNCT
ejpam-2473	161	11	=	=	SYM
ejpam-2473	161	12	2	2	NUM
ejpam-2473	161	13	c−	c−	X
ejpam-2473	161	14	�	�	PROPN
ejpam-2473	161	15	|h|−|h∩s|−	|h|−|h∩s|−	NUM
ejpam-2473	161	16	|h\s|2	|h\s|2	PROPN
ejpam-2473	161	17	�	�	PROPN
ejpam-2473	161	18	=	=	SYM
ejpam-2473	161	19	2	2	NUM
ejpam-2473	161	20	c−	c−	X
ejpam-2473	161	21	�	�	PROPN
ejpam-2473	161	22	|h\s|−	|h\s|−	X
ejpam-2473	161	23	|h\s|2	|h\s|2	NOUN
ejpam-2473	161	24	�	�	PROPN
ejpam-2473	161	25	=	=	SYM
ejpam-2473	161	26	2	2	NUM
ejpam-2473	161	27	c−	c−	X
ejpam-2473	161	28	�	�	PROPN
ejpam-2473	161	29	|h\s|	|h\s|	NUM
ejpam-2473	161	30	2	2	NUM
ejpam-2473	161	31	�	�	PROPN
ejpam-2473	161	32	.	.	PUNCT
ejpam-2473	162	1	corollary	corollary	ADJ
ejpam-2473	162	2	3	3	NUM
ejpam-2473	162	3	.	.	PUNCT
ejpam-2473	163	1	let	let	VERB
ejpam-2473	163	2	g	g	PRON
ejpam-2473	163	3	be	be	AUX
ejpam-2473	163	4	a	a	DET
ejpam-2473	163	5	finite	finite	ADJ
ejpam-2473	163	6	group	group	NOUN
ejpam-2473	163	7	,	,	PUNCT
ejpam-2473	163	8	s	s	PART
ejpam-2473	163	9	=	=	PUNCT
ejpam-2473	163	10	�	�	PROPN
ejpam-2473	163	11	s	s	PART
ejpam-2473	163	12	∈	∈	PROPN
ejpam-2473	163	13	g	g	NOUN
ejpam-2473	163	14	:	:	PUNCT
ejpam-2473	163	15	s2	s2	NOUN
ejpam-2473	163	16	=	=	PUNCT
ejpam-2473	163	17	e	e	NOUN
ejpam-2473	163	18	,	,	PUNCT
ejpam-2473	163	19	and	and	CCONJ
ejpam-2473	163	20	h	h	PROPN
ejpam-2473	163	21	≤	≤	NOUN
ejpam-2473	164	1	g.	g.	NOUN
ejpam-2473	165	1	if	if	SCONJ
ejpam-2473	165	2	s	s	VERB
ejpam-2473	165	3	⊆	⊆	NUM
ejpam-2473	165	4	h	h	NOUN
ejpam-2473	165	5	,	,	PUNCT
ejpam-2473	165	6	then	then	ADV
ejpam-2473	165	7	i	i	PRON
ejpam-2473	165	8	(	(	PUNCT
ejpam-2473	165	9	h	h	NOUN
ejpam-2473	165	10	)	)	PUNCT
ejpam-2473	165	11	=	=	SYM
ejpam-2473	166	1	2	2	NUM
ejpam-2473	166	2	c−	c−	X
ejpam-2473	166	3	�	�	PROPN
ejpam-2473	166	4	|h|−|s|	|h|−|s|	VERB
ejpam-2473	166	5	2	2	NUM
ejpam-2473	166	6	�	�	PROPN
ejpam-2473	166	7	.	.	PUNCT
ejpam-2473	167	1	proof	proof	NOUN
ejpam-2473	167	2	.	.	PUNCT
ejpam-2473	168	1	let	let	VERB
ejpam-2473	168	2	g	g	PRON
ejpam-2473	168	3	be	be	AUX
ejpam-2473	168	4	a	a	DET
ejpam-2473	168	5	finite	finite	ADJ
ejpam-2473	168	6	group	group	NOUN
ejpam-2473	168	7	,	,	PUNCT
ejpam-2473	168	8	s	s	PART
ejpam-2473	168	9	=	=	PUNCT
ejpam-2473	168	10	�	�	PROPN
ejpam-2473	168	11	s	s	PART
ejpam-2473	168	12	∈	∈	PROPN
ejpam-2473	168	13	g	g	NOUN
ejpam-2473	168	14	:	:	PUNCT
ejpam-2473	168	15	s2	s2	NOUN
ejpam-2473	168	16	=	=	PUNCT
ejpam-2473	168	17	e	e	NOUN
ejpam-2473	168	18	,	,	PUNCT
ejpam-2473	168	19	and	and	CCONJ
ejpam-2473	168	20	h	h	PROPN
ejpam-2473	168	21	≤	≤	NOUN
ejpam-2473	168	22	g.	g.	NOUN
ejpam-2473	169	1	if	if	SCONJ
ejpam-2473	169	2	s	s	VERB
ejpam-2473	169	3	⊆	⊆	NUM
ejpam-2473	169	4	h	h	NOUN
ejpam-2473	169	5	,	,	PUNCT
ejpam-2473	169	6	then	then	ADV
ejpam-2473	169	7	|h\s|=	|h\s|=	CCONJ
ejpam-2473	169	8	|h|	|h|	NOUN
ejpam-2473	169	9	−	−	PROPN
ejpam-2473	169	10	|s|	|s|	PROPN
ejpam-2473	169	11	.	.	PUNCT
ejpam-2473	170	1	thus	thus	ADV
ejpam-2473	170	2	,	,	PUNCT
ejpam-2473	170	3	by	by	ADP
ejpam-2473	170	4	corollary	corollary	ADJ
ejpam-2473	170	5	2	2	NUM
ejpam-2473	170	6	,	,	PUNCT
ejpam-2473	170	7	i	i	PRON
ejpam-2473	170	8	(	(	PUNCT
ejpam-2473	170	9	h	h	NOUN
ejpam-2473	170	10	)	)	PUNCT
ejpam-2473	170	11	=	=	SYM
ejpam-2473	170	12	2	2	NUM
ejpam-2473	170	13	c−	c−	X
ejpam-2473	170	14	�	�	PROPN
ejpam-2473	170	15	|h|−|s|	|h|−|s|	VERB
ejpam-2473	170	16	2	2	NUM
ejpam-2473	170	17	�	�	PROPN
ejpam-2473	170	18	.	.	PUNCT
ejpam-2473	171	1	corollary	corollary	ADJ
ejpam-2473	171	2	4	4	NUM
ejpam-2473	171	3	.	.	PUNCT
ejpam-2473	172	1	let	let	VERB
ejpam-2473	172	2	g	g	PRON
ejpam-2473	172	3	be	be	AUX
ejpam-2473	172	4	a	a	DET
ejpam-2473	172	5	finite	finite	ADJ
ejpam-2473	172	6	group	group	NOUN
ejpam-2473	172	7	,	,	PUNCT
ejpam-2473	172	8	s	s	PART
ejpam-2473	172	9	=	=	PUNCT
ejpam-2473	172	10	�	�	PROPN
ejpam-2473	172	11	s	s	PART
ejpam-2473	172	12	∈	∈	PROPN
ejpam-2473	172	13	g	g	NOUN
ejpam-2473	172	14	:	:	PUNCT
ejpam-2473	172	15	s2	s2	NOUN
ejpam-2473	172	16	=	=	PUNCT
ejpam-2473	172	17	e	e	NOUN
ejpam-2473	172	18	,	,	PUNCT
ejpam-2473	172	19	and	and	CCONJ
ejpam-2473	172	20	h	h	PROPN
ejpam-2473	172	21	≤	≤	PROPN
ejpam-2473	172	22	g.	g.	NOUN
ejpam-2473	173	1	if	if	SCONJ
ejpam-2473	173	2	h	h	NOUN
ejpam-2473	173	3	∼=	∼=	PROPN
ejpam-2473	173	4	zp	zp	NOUN
ejpam-2473	173	5	where	where	SCONJ
ejpam-2473	173	6	p	p	NOUN
ejpam-2473	173	7	is	be	AUX
ejpam-2473	173	8	an	an	DET
ejpam-2473	173	9	odd	odd	ADJ
ejpam-2473	173	10	number	number	NOUN
ejpam-2473	173	11	,	,	PUNCT
ejpam-2473	173	12	then	then	ADV
ejpam-2473	173	13	i	i	PRON
ejpam-2473	173	14	(	(	PUNCT
ejpam-2473	173	15	h	h	NOUN
ejpam-2473	173	16	)	)	PUNCT
ejpam-2473	173	17	=	=	SYM
ejpam-2473	173	18	2	2	NUM
ejpam-2473	173	19	c−	c−	X
ejpam-2473	173	20	�	�	PROPN
ejpam-2473	173	21	|h|−1	|h|−1	NUM
ejpam-2473	173	22	2	2	NUM
ejpam-2473	173	23	�	�	NOUN
ejpam-2473	173	24	.	.	PUNCT
ejpam-2473	174	1	proof	proof	NOUN
ejpam-2473	174	2	.	.	PUNCT
ejpam-2473	175	1	let	let	VERB
ejpam-2473	175	2	g	g	PRON
ejpam-2473	175	3	be	be	AUX
ejpam-2473	175	4	a	a	DET
ejpam-2473	175	5	finite	finite	ADJ
ejpam-2473	175	6	group	group	NOUN
ejpam-2473	175	7	,	,	PUNCT
ejpam-2473	175	8	s	s	PART
ejpam-2473	175	9	=	=	PUNCT
ejpam-2473	175	10	�	�	PROPN
ejpam-2473	175	11	s	s	PART
ejpam-2473	175	12	∈	∈	PROPN
ejpam-2473	175	13	g	g	NOUN
ejpam-2473	175	14	:	:	PUNCT
ejpam-2473	175	15	s2	s2	NOUN
ejpam-2473	175	16	=	=	PUNCT
ejpam-2473	175	17	e	e	NOUN
ejpam-2473	175	18	,	,	PUNCT
ejpam-2473	175	19	and	and	CCONJ
ejpam-2473	175	20	h	h	PROPN
ejpam-2473	175	21	≤	≤	PROPN
ejpam-2473	175	22	g.	g.	NOUN
ejpam-2473	176	1	if	if	SCONJ
ejpam-2473	176	2	h	h	NOUN
ejpam-2473	176	3	∼=	∼=	PROPN
ejpam-2473	176	4	zp	zp	NOUN
ejpam-2473	176	5	where	where	SCONJ
ejpam-2473	176	6	p	p	NOUN
ejpam-2473	176	7	is	be	AUX
ejpam-2473	176	8	an	an	DET
ejpam-2473	176	9	odd	odd	ADJ
ejpam-2473	176	10	number	number	NOUN
ejpam-2473	176	11	,	,	PUNCT
ejpam-2473	176	12	then	then	ADV
ejpam-2473	176	13	s	s	AUX
ejpam-2473	176	14	=	=	SYM
ejpam-2473	176	15	{	{	PUNCT
ejpam-2473	176	16	e	e	NOUN
ejpam-2473	176	17	}	}	PUNCT
ejpam-2473	176	18	.	.	PUNCT
ejpam-2473	177	1	thus	thus	ADV
ejpam-2473	177	2	,	,	PUNCT
ejpam-2473	177	3	by	by	ADP
ejpam-2473	177	4	corollary	corollary	ADJ
ejpam-2473	177	5	3	3	NUM
ejpam-2473	177	6	,	,	PUNCT
ejpam-2473	177	7	i	i	PRON
ejpam-2473	177	8	(	(	PUNCT
ejpam-2473	177	9	h	h	NOUN
ejpam-2473	177	10	)	)	PUNCT
ejpam-2473	177	11	=	=	SYM
ejpam-2473	177	12	2	2	NUM
ejpam-2473	177	13	c−	c−	X
ejpam-2473	177	14	�	�	PROPN
ejpam-2473	177	15	|h|−1	|h|−1	NUM
ejpam-2473	177	16	2	2	NUM
ejpam-2473	177	17	�	�	PROPN
ejpam-2473	177	18	.	.	PUNCT
ejpam-2473	178	1	acknowledgements	acknowledgement	VERB
ejpam-2473	178	2	the	the	DET
ejpam-2473	178	3	authors	author	NOUN
ejpam-2473	178	4	would	would	AUX
ejpam-2473	178	5	like	like	VERB
ejpam-2473	178	6	to	to	PART
ejpam-2473	178	7	thank	thank	VERB
ejpam-2473	178	8	cebu	cebu	NOUN
ejpam-2473	178	9	normal	normal	ADJ
ejpam-2473	178	10	university	university	NOUN
ejpam-2473	178	11	,	,	PUNCT
ejpam-2473	178	12	cebu	cebu	NOUN
ejpam-2473	178	13	city	city	NOUN
ejpam-2473	178	14	and	and	CCONJ
ejpam-2473	178	15	negros	negros	PROPN
ejpam-2473	178	16	oriental	oriental	ADJ
ejpam-2473	178	17	state	state	PROPN
ejpam-2473	178	18	university	university	PROPN
ejpam-2473	178	19	,	,	PUNCT
ejpam-2473	178	20	dumaguete	dumaguete	NOUN
ejpam-2473	178	21	city	city	NOUN
ejpam-2473	178	22	for	for	ADP
ejpam-2473	178	23	allowing	allow	VERB
ejpam-2473	178	24	the	the	DET
ejpam-2473	178	25	authors	author	NOUN
ejpam-2473	178	26	to	to	PART
ejpam-2473	178	27	use	use	VERB
ejpam-2473	178	28	some	some	PRON
ejpam-2473	178	29	of	of	ADP
ejpam-2473	178	30	their	their	PRON
ejpam-2473	178	31	facilities	facility	NOUN
ejpam-2473	178	32	and	and	CCONJ
ejpam-2473	178	33	resources	resource	NOUN
ejpam-2473	178	34	in	in	ADP
ejpam-2473	178	35	the	the	DET
ejpam-2473	178	36	conduct	conduct	NOUN
ejpam-2473	178	37	of	of	ADP
ejpam-2473	178	38	this	this	DET
ejpam-2473	178	39	research	research	NOUN
ejpam-2473	178	40	.	.	PUNCT
ejpam-2473	179	1	references	reference	NOUN
ejpam-2473	179	2	38	38	NUM
ejpam-2473	179	3	references	reference	NOUN
ejpam-2473	179	4	[	[	X
ejpam-2473	179	5	1	1	NUM
ejpam-2473	179	6	]	]	PUNCT
ejpam-2473	179	7	j.	j.	PROPN
ejpam-2473	179	8	n.	n.	PROPN
ejpam-2473	179	9	buloron	buloron	PROPN
ejpam-2473	179	10	,	,	PUNCT
ejpam-2473	179	11	c.	c.	PROPN
ejpam-2473	179	12	s.	s.	PROPN
ejpam-2473	179	13	rocero	rocero	PROPN
ejpam-2473	179	14	,	,	PUNCT
ejpam-2473	179	15	j.	j.	PROPN
ejpam-2473	179	16	m.	m.	PROPN
ejpam-2473	179	17	ontolan	ontolan	PROPN
ejpam-2473	179	18	and	and	CCONJ
ejpam-2473	179	19	m.	m.	NOUN
ejpam-2473	179	20	p.	p.	PROPN
ejpam-2473	179	21	baldado	baldado	NOUN
ejpam-2473	180	1	jr	jr	PROPN
ejpam-2473	180	2	.	.	PUNCT
ejpam-2473	181	1	some	some	DET
ejpam-2473	181	2	properties	property	NOUN
ejpam-2473	181	3	of	of	ADP
ejpam-2473	181	4	d	d	NOUN
ejpam-2473	181	5	-sets	-set	NOUN
ejpam-2473	181	6	of	of	ADP
ejpam-2473	181	7	a	a	DET
ejpam-2473	181	8	group	group	NOUN
ejpam-2473	181	9	,	,	PUNCT
ejpam-2473	181	10	international	international	PROPN
ejpam-2473	181	11	mathematical	mathematical	ADJ
ejpam-2473	181	12	forum	forum	PROPN
ejpam-2473	181	13	,	,	PUNCT
ejpam-2473	181	14	9	9	NUM
ejpam-2473	181	15	,	,	PUNCT
ejpam-2473	181	16	1035	1035	NUM
ejpam-2473	181	17	-	-	SYM
ejpam-2473	181	18	1040	1040	NUM
ejpam-2473	181	19	,	,	PUNCT
ejpam-2473	181	20	2014	2014	NUM
ejpam-2473	181	21	.	.	PUNCT
ejpam-2473	182	1	[	[	X
ejpam-2473	182	2	2	2	X
ejpam-2473	182	3	]	]	PUNCT
ejpam-2473	182	4	j.	j.	PROPN
ejpam-2473	182	5	n.	n.	PROPN
ejpam-2473	182	6	buloron	buloron	PROPN
ejpam-2473	182	7	,	,	PUNCT
ejpam-2473	182	8	c.	c.	PROPN
ejpam-2473	182	9	s.	s.	PROPN
ejpam-2473	182	10	rocero	rocero	PROPN
ejpam-2473	182	11	,	,	PUNCT
ejpam-2473	182	12	j.	j.	PROPN
ejpam-2473	182	13	m.	m.	PROPN
ejpam-2473	182	14	ontolan	ontolan	PROPN
ejpam-2473	182	15	and	and	CCONJ
ejpam-2473	182	16	m.	m.	NOUN
ejpam-2473	182	17	p.	p.	PROPN
ejpam-2473	182	18	baldado	baldado	NOUN
ejpam-2473	182	19	jr	jr	PROPN
ejpam-2473	182	20	.	.	PUNCT
ejpam-2473	183	1	d	d	PROPN
ejpam-2473	183	2	-sets	-set	NOUN
ejpam-2473	183	3	of	of	ADP
ejpam-2473	183	4	finite	finite	ADJ
ejpam-2473	183	5	group	group	NOUN
ejpam-2473	183	6	,	,	PUNCT
ejpam-2473	183	7	international	international	ADJ
ejpam-2473	183	8	journal	journal	NOUN
ejpam-2473	183	9	of	of	ADP
ejpam-2473	183	10	algebra	algebra	PROPN
ejpam-2473	183	11	,	,	PUNCT
ejpam-2473	183	12	8	8	NUM
ejpam-2473	183	13	,	,	PUNCT
ejpam-2473	183	14	623	623	NUM
ejpam-2473	183	15	-	-	SYM
ejpam-2473	183	16	628	628	NUM
ejpam-2473	183	17	,	,	PUNCT
ejpam-2473	183	18	2014	2014	NUM
ejpam-2473	183	19	.	.	PUNCT
ejpam-2473	184	1	[	[	X
ejpam-2473	184	2	3	3	X
ejpam-2473	184	3	]	]	PUNCT
ejpam-2473	184	4	t.	t.	PROPN
ejpam-2473	184	5	w.	w.	PROPN
ejpam-2473	184	6	hungerford	hungerford	PROPN
ejpam-2473	184	7	.	.	PUNCT
ejpam-2473	185	1	algebra	algebra	PROPN
ejpam-2473	185	2	,	,	PUNCT
ejpam-2473	185	3	springer	springer	NOUN
ejpam-2473	185	4	-	-	PUNCT
ejpam-2473	185	5	verlag	verlag	PROPN
ejpam-2473	185	6	new	new	PROPN
ejpam-2473	185	7	york	york	PROPN
ejpam-2473	185	8	,	,	PUNCT
ejpam-2473	185	9	inc	inc	PROPN
ejpam-2473	185	10	,	,	PUNCT
ejpam-2473	185	11	1976	1976	NUM
ejpam-2473	185	12	.	.	PUNCT